[
  {
    "path": ".editorconfig",
    "content": "root = true\n\n[*]\nend_of_line = lf\ninsert_final_newline = true\n\n# Matches multiple files with brace expansion notation\n[*.{cc,hh}]\ncharset = utf-8\nindent_style = tab\nindent_size = 3\ntrim_trailing_whitespace = true\n\n"
  },
  {
    "path": ".gitattributes",
    "content": "*.hh    linguist-language=C++\n*.cc    linguist-language=C++\nlibs/** linguist-vendored"
  },
  {
    "path": ".github/workflows/appimage-modern.yml",
    "content": "# Modern AppImage build using AppImageBuilder\n# Supports both x86_64 and arm64 architectures on current GitHub runners\n# Uses Ubuntu 22.04 base for maximum compatibility\n\nname: AppImage (Modern)\n\non:\n  release:\n    types: [created]\n  # Uncomment for testing\n  #push:\n  #  branches: [devel]\n\njobs:\n  build:\n    name: AppImage ${{ matrix.arch }}\n\n    strategy:\n      fail-fast: false\n      matrix:\n        include:\n          - arch: x86_64\n            os: ubuntu-24.04\n            ubuntu_arch: amd64\n            appimage_arch: x86_64\n            repo: http://archive.ubuntu.com/ubuntu/\n          - arch: arm64\n            os: ubuntu-24.04-arm\n            ubuntu_arch: arm64\n            appimage_arch: aarch64\n            repo: http://ports.ubuntu.com/ubuntu-ports/\n\n    runs-on: ${{ matrix.os }}\n\n    steps:\n      - name: Checkout repository\n        uses: actions/checkout@v4\n\n      - name: Install AppImageBuilder\n        run: |\n          sudo apt update\n          sudo apt install -y python3-pip\n\n      - name: Clean up any existing AppDir\n        run: |\n          sudo rm -rf AppDir || true\n\n      - name: Create AppImageBuilder recipe\n        run: |\n          cat > AppImageBuilder.yml << 'EOF'\n          version: 1\n\n          script:\n            - mkdir -p AppDir\n\n          AppDir:\n            path: ./AppDir\n            app_info:\n              id: science.cadabra.cadabra2-gtk\n              name: Cadabra2\n              icon: cadabra2-gtk\n              version: latest\n              exec: usr/bin/cadabra2-gtk\n              exec_args: $@\n\n            apt:\n              arch: ${{ matrix.ubuntu_arch }}\n              sources:\n                - sourceline: deb ${{ matrix.repo }} jammy main universe\n                  key_url: 'http://keyserver.ubuntu.com/pks/lookup?op=get&search=0x871920D1991BC93C'\n                - sourceline: deb ${{ matrix.repo }} jammy-updates main universe\n                  key_url: 'http://keyserver.ubuntu.com/pks/lookup?op=get&search=0x871920D1991BC93C'\n\n              include:\n                # Core system libraries\n                - libc6\n                - libstdc++6\n                - libgcc-s1\n\n                # Shell interpreters\n                - bash\n                - dash\n                - perl-base\n                \n                # Cadabra dependencies\n                - libgmp10\n                - libgmpxx4ldbl\n                - libboost-system1.74.0\n                - libboost-filesystem1.74.0\n                - libboost-program-options1.74.0\n                - libboost-date-time1.74.0\n                - libsqlite3-0\n                - uuid-runtime\n                - libssl3\n                - libtbb12\n\n                # GTK and GUI dependencies\n                - libgtkmm-3.0-1v5\n                - libgtk-3-0\n                - libgdk-pixbuf2.0-0\n                - libcairo2\n                - libpango-1.0-0\n                - libpangocairo-1.0-0\n                - libatk1.0-0\n                - libglib2.0-0\n                - librsvg2-common\n                - adwaita-icon-theme\n                - hicolor-icon-theme\n                - libwayland-client0\n                - libwayland-cursor0\n                - libwayland-egl1-mesa\n \n                # Python dependencies (Ubuntu 22.04 uses Python 3.10)\n                - python3.10\n                - libpython3.10\n                - python3-pip\n                - python3-gmpy2\n\n              exclude:\n                - adwaita-icon-theme-full\n                - humanity-icon-theme\n                - ubuntu-mono\n\n            files:\n              exclude:\n                - usr/lib/python*/site-packages/pip*\n                - usr/lib/python*/site-packages/setuptools*\n                - usr/share/doc\n                - usr/share/man\n                - usr/share/locale\n                - var/cache\n                - var/lib/apt\n                - etc/apt\n\n            runtime:\n              env:\n                PATH: '${APPDIR}/usr/bin:${PATH}'\n                PYTHONHOME: '${APPDIR}/usr'\n                PYTHONPATH: '${APPDIR}/usr/lib/python3.10/site-packages:${APPDIR}/usr/lib/python3.10:${APPDIR}/usr/lib/python3.10/dist-packages'\n                LD_LIBRARY_PATH: '${APPDIR}/usr/lib:${APPDIR}/usr/lib/${{ matrix.arch }}-linux-gnu:${LD_LIBRARY_PATH}'\n                LC_ALL: C.UTF-8\n                LANG: C.UTF-8\n\n          AppImage:\n            update-information: gh-releases-zsync|kpeeters|cadabra2|latest|Cadabra*${{ matrix.arch }}.AppImage.zsync\n            sign-key: None\n            arch: ${{ matrix.appimage_arch }}\n            comp: gzip\n          EOF\n\n      - name: Build Cadabra2 in container\n        run: |\n          # Use Docker to build for the target architecture with Ubuntu 22.04\n          docker run --rm --privileged \\\n            --platform linux/${{ matrix.arch }} \\\n            -v $PWD:/workspace \\\n            -w /workspace \\\n            ubuntu:22.04 /bin/bash -c \"\n            # Stop on error inside the Docker container\n            set -e\n            \n            # Install dependencies\n            apt update\n            DEBIAN_FRONTEND=noninteractive apt install -y \\\n              build-essential cmake git \\\n              python3-dev python3-pip g++ \\\n              libgmp3-dev libgtkmm-3.0-dev \\\n              libboost-all-dev libssl-dev \\\n              libsqlite3-dev uuid-dev \\\n              python3-matplotlib python3-sympy \\\n              python3-gmpy2 python3-numpy \\\n              squashfs-tools file desktop-file-utils fakeroot strace patchelf zsync\n\n            # Install directly from the main branch of the appimage-builder repository,\n            # to deal with the issue reported in\n            # https://github.com/AppImageCrafters/appimage-builder/pull/281\n            pip3 install git+https://github.com/AppImageCrafters/appimage-builder.git@main\n\n            # Patch mpmath (bug fixed only in ubuntu-22.04)\n            # sed -i \\\"s/if other is 0:/if other == 0:/g\\\" /usr/lib/python3/dist-packages/mpmath/ctx_mp_python.py\n            # cat /usr/lib/python3/dist-packages/mpmath/ctx_mp_python.py\n            \n            # Build Cadabra2\n            git config --global --add safe.directory /workspace\n            mkdir -p build\n            cd build\n            cmake -DCMAKE_INSTALL_PREFIX=/usr \\\n                  -DCMAKE_BUILD_TYPE=Release \\\n                  -DENABLE_MATHEMATICA=OFF \\\n                  -DAPPIMAGE_MODE=ON \\\n                  ..\n\n            VERSION=\\$(cat /workspace/build/VERSION)\n            echo \\\"Building version \\${VERSION}\\\"\n\n            make -j\\$(nproc)\n            make install DESTDIR=/workspace/build/AppDir\n            make test\n                  \n            # Install Python packages directly into the AppDir after 'make install'\n            # Ensure the target path is correct for your AppDir's Python installation\n            pip3 install --target=/workspace/build/AppDir/usr/lib/python3.10/site-packages --upgrade mpmath>=1.2.0\n            pip3 install --target=/workspace/build/AppDir/usr/lib/python3.10/site-packages astunparse\n            pip3 install --target=/workspace/build/AppDir/usr/lib/python3.10/site-packages pillow sympy matplotlib numpy\n\n            # Update version in AppImageBuilder.yml\n            sed -i \\\"s/version: latest/version: \\${VERSION}/\\\" /workspace/AppImageBuilder.yml\n\n            # Build the AppImage\n            echo \\\"Now going to run appimage-builder, using:\\\"\n            echo \\\"---------\\\"\n            cat /workspace/AppImageBuilder.yml\n            echo \\\"---------\\\"\n            echo \\\"Here we go...\\\"\n            appimage-builder --recipe /workspace/AppImageBuilder.yml --skip-test\n            echo \\\"This is /workspace/build/AppDir/usr/bin/ :\\\"\n            echo \\\"---------\\\"\n            ls -la /workspace/build/AppDir/usr/bin/\n            echo \\\"---------\\\"\n          \"\n\n      - name: Rename AppImage\n        run: |\n          VERSION=`cat build/VERSION`\n          sudo chown runner:docker build -R\n\n          # Find and rename the AppImage\n          ls -la .\n          APPIMAGE_FILE=$(find . -name \"*.AppImage\" -type f | head -n 1)\n          if [ -n \"$APPIMAGE_FILE\" ]; then\n            mv \"$APPIMAGE_FILE\" \"Cadabra_${VERSION}_${{ matrix.arch }}.AppImage\"\n            chmod +x \"Cadabra_${VERSION}_${{ matrix.arch }}.AppImage\"\n          fi\n\n      - name: Upload artifacts\n        uses: actions/upload-artifact@v4\n        with:\n          name: cadabra2-appimage-${{ matrix.arch }}\n          path: Cadabra_*_${{ matrix.arch }}.AppImage\n          retention-days: 7\n\n      - name: Upload to release\n        if: github.event_name == 'release'\n        run: |\n          gh release upload \"${{ github.ref_name }}\" Cadabra_*_${{ matrix.arch }}.AppImage --clobber\n        env:\n          GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }}\n\n#       - name: Generate zsync file\n#         if: github.event_name == 'release'\n#         run: |\n#           # Install zsync\n#           sudo apt install -y zsync\n# \n#           # Generate zsync file for the AppImage\n#           APPIMAGE_FILE=$(find . -name \"Cadabra_*_${{ matrix.arch }}.AppImage\" -type f | head -n 1)\n#           if [ -n \\\"$APPIMAGE_FILE\\\" ]; then\n#             zsyncmake \\\"$APPIMAGE_FILE\\\"\n# \n#             # Upload zsync file to release\n#             gh release upload ${{ github.ref_name }} *.zsync --clobber || true\n#           fi\n#         env:\n#           GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }}\n"
  },
  {
    "path": ".github/workflows/c++lib.yml",
    "content": "# This is a build which gets triggered on every commit push, to\n# ensure that Cadabra builds as c++lib. Does not yet contain any\n# tests, it just checks for build issues.\n\nname: c++lib\n\non: [push]\n\njobs:\n  build:\n\n    runs-on: ubuntu-latest\n    \n    steps:\n    - uses: actions/checkout@v3\n\n    - name: get dependencies\n      run:  sudo apt-get update && sudo DEBIAN_FRONTEND=noninteractive apt-get install git cmake python3-dev g++ libpcre3 libpcre3-dev libgmp3-dev libboost-all-dev libgmp-dev libsqlite3-dev uuid-dev libmpfr-dev libmpc-dev \n\n    - name: configure\n      run:  mkdir build-lib && cd build-lib && cmake -DBUILD_AS_CPP_LIBRARY=ON ..\n      \n    - name: make\n      run:  cd build-lib && make\n      \n"
  },
  {
    "path": ".github/workflows/docker.yml",
    "content": "\n# Build docker images with a Jupyter server with Cadabra\n# kernel whenever a commit is pushed to github.\n#\n# Lint this thing with\n#\n#   yq eval docker.yml\n\nname: Docker\n\n# on: [push]\n\non:\n  release:\n    types: [released]\n\njobs:\n  build:\n    runs-on: ubuntu-latest\n\n#     strategy:\n#       fail-fast: false\n#       matrix:\n#         arch:\n#           - amd64\n#           - arm64\n\n    steps:\n    - name: Prepare\n      run: |\n        platform=${{ matrix.platform }}\n        echo \"PLATFORM_PAIR=${platform//\\//-}\" >> $GITHUB_ENV          \n\n    - name: Set up QEMU\n      uses: docker/setup-qemu-action@master\n\n    - uses: actions/checkout@v3\n\n#     - name: Exit if not on master branch\n#       if: github.ref != 'refs/heads/master'\n#       run: exit 1\n      \n    - name: Log in to Docker Hub\n      uses: docker/login-action@master\n      with:\n        username: ${{ secrets.DOCKER_USERNAME }}\n        password: ${{ secrets.DOCKER_PASSWORD }}\n\n    - name: Extract metadata (tags, labels) for Docker\n      id: meta\n      uses: docker/metadata-action@master\n      with:\n        images: kpeeters/cadabra2-jupyter\n\n    - name: Set up Docker Buildx\n      uses: docker/setup-buildx-action@master\n\n    - name: Build Docker image\n      uses: docker/build-push-action@master\n      with:\n        platforms: linux/amd64, linux/arm64\n        context: .\n        file: docker/Dockerfile\n        push: true\n#${{ github.ref == 'master' }}\n        labels: ${{ steps.meta.outputs.labels }}\n        tags:   kpeeters/cadabra2-jupyter:latest\n#        outputs: type=docker\n\n#     - name: Upload artifact to github assets\n#       uses: actions/upload-artifact@main\n#       with:\n#         name: cadabra2-jupyter-${{ matrix.arch }}\n#         path: cadabra2-jupyter-${{ matrix.arch }}.tar\n"
  },
  {
    "path": ".github/workflows/fedora-40-package.yml",
    "content": "# Create a Fedora 40 package on a github release event.\n# This assumes that the cadabra version is the same as the\n# release name, and it will attempt to add the .rpm file\n# to the release assets.\n\nname: Fedora-40 package\n\n# on: [push]\n\non:\n  release:\n    types: [created]\n\njobs:\n  build:\n\n    strategy:\n      matrix:\n        include:\n          - os: ubuntu-24.04\n            name: x86_64\n            display-name: \"Fedora 40 x86_64\"\n          - os: ubuntu-24.04-arm\n            name: arm64\n            display-name: \"Fedora 40 arm64\"\n    runs-on: ${{ matrix.os }}\n    \n    steps:\n    - uses: actions/checkout@v3\n\n    - name: Set up Docker Buildx\n      uses: docker/setup-buildx-action@master\n\n    - name: Pull Fedora image\n      run: docker pull fedora:40\n\n    - name: Set up GitHub CLI\n      run: |\n        sudo apt-get update\n        sudo apt-get install -y gh\n\n    - name: Authenticate GitHub CLI\n      run: gh auth setup-git\n      env:\n        GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }}\n          \n    - name: Build RPM in Fedora container\n      run: |\n        docker run --rm \\\n           -v ${{ github.workspace }}:/workspace \\\n           -w /workspace \\\n           fedora:40 \\\n           bash -c \" \n             git config --global --add safe.directory /workspace\n             dnf install -y rpm-build make gcc-c++ git python3-devel cmake gmp-devel libuuid-devel sqlite-devel openssl-devel gtkmm30-devel boost-devel python3-matplotlib python3-pip \n             pip3 install sympy \n             mkdir build \n             cd build \n             cmake -DPACKAGING_MODE=ON -DENABLE_MATHEMATICA=OFF -DCMAKE_INSTALL_PREFIX=/usr .. \n             make \n             cpack \n           \"\n\n    - name: Set version variables from output of cmake\n      run: |\n        VER=$(cat ${{ github.workspace }}/build/VERSION)\n        echo \"VERSION=$VER\" >> $GITHUB_ENV\n\n    - name: Upload Release Assets\n      run: |\n        gh release upload \"${{ env.VERSION }}\" build/cadabra2-${{ env.VERSION }}-fedora40-${{ matrix.name }}.rpm --clobber\n      env:\n        GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }}\n\n  test:\n    needs: build\n    runs-on: ubuntu-24.04\n    \n    steps:\n    - name: Set up Docker Buildx\n      uses: docker/setup-buildx-action@master\n\n    - name: Pull Fedora image\n      run: docker pull fedora:40\n\n    - name: Download package and run inside Fedora container\n      run: |\n        docker run --rm \\\n           -v ${{ github.workspace }}:/workspace \\\n           -w /workspace \\\n           fedora:40 \\\n           bash -c \" \n             dnf install -y xorg-x11-server-Xvfb wget curl jq\n             export VERSION=\\$(curl -s https://api.github.com/repos/kpeeters/cadabra2/releases|& jq .[0].tag_name -r)\n             export RPMNAME=cadabra2-\\${VERSION}-fedora40-x86_64.rpm\n             wget https://github.com/kpeeters/cadabra2/releases/download/\\${VERSION}/\\${RPMNAME}\n             dnf install -y \\${RPMNAME}\n             printf 'import sys\\nprint(sys.path)\\nimport cdb.main\\nex:=(A+B) (C+D);\\ndistribute(ex);\\nquit()\\n' > tst.cdb\n             cadabra2 tst.cdb\n             \n             xvfb-run -a cadabra2-gtk &\n             APP_PID=\\$!\n             sleep 10\n             if kill -0 \\$APP_PID 2>/dev/null; then\n                echo 'cadabra2-gtk started successfully'\n                kill \\$APP_PID\n                exit 0\n             else\n                echo 'cadabra2-gtk failed to start'\n                exit 1\n             fi\n           \"\n"
  },
  {
    "path": ".github/workflows/fedora-41-package.yml",
    "content": "# Create a Fedora 41 package on a github release event.\n# This assumes that the cadabra version is the same as the\n# release name, and it will attempt to add the .rpm file\n# to the release assets.\n\nname: Fedora-41 package\n\n# on: [push]\n\non:\n  release:\n    types: [created]\n\njobs:\n  build:\n\n    strategy:\n      matrix:\n        include:\n          - os: ubuntu-24.04\n            name: x86_64\n            display-name: \"Fedora 41 x86_64\"\n          - os: ubuntu-24.04-arm\n            name: arm64\n            display-name: \"Fedora 41 arm64\"\n    runs-on: ${{ matrix.os }}\n    \n    steps:\n    - uses: actions/checkout@v3\n\n    - name: Set up Docker Buildx\n      uses: docker/setup-buildx-action@master\n\n    - name: Pull Fedora image\n      run: docker pull fedora:41\n\n    - name: Set up GitHub CLI\n      run: |\n        sudo apt-get update\n        sudo apt-get install -y gh\n\n    - name: Authenticate GitHub CLI\n      run: gh auth setup-git\n      env:\n        GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }}\n          \n    - name: Build RPM in Fedora container\n      run: |\n        docker run --rm \\\n           -v ${{ github.workspace }}:/workspace \\\n           -w /workspace \\\n           fedora:41 \\\n           bash -c \" \n             git config --global --add safe.directory /workspace\n             dnf install -y rpm-build make gcc-c++ git python3-devel cmake gmp-devel libuuid-devel sqlite-devel openssl-devel gtkmm30-devel boost-devel python3-matplotlib python3-pip \n             pip3 install sympy \n             mkdir build \n             cd build \n             cmake -DPACKAGING_MODE=ON -DENABLE_MATHEMATICA=OFF -DCMAKE_INSTALL_PREFIX=/usr .. \n             make \n             cpack \n           \"\n\n    - name: Set version variables from output of cmake\n      run: |\n        VER=$(cat ${{ github.workspace }}/build/VERSION)\n        echo \"VERSION=$VER\" >> $GITHUB_ENV\n\n    - name: Upload Release Assets\n      run: |\n        gh release upload \"${{ env.VERSION }}\" build/cadabra2-${{ env.VERSION }}-fedora41-${{ matrix.name }}.rpm --clobber\n      env:\n        GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }}\n\n  test:\n    needs: build\n    runs-on: ubuntu-24.04\n    \n    steps:\n    - name: Set up Docker Buildx\n      uses: docker/setup-buildx-action@master\n\n    - name: Pull Fedora image\n      run: docker pull fedora:41\n\n    - name: Download package and run inside Fedora container\n      run: |\n        docker run --rm \\\n           -v ${{ github.workspace }}:/workspace \\\n           -w /workspace \\\n           fedora:41 \\\n           bash -c \" \n             dnf install -y xorg-x11-server-Xvfb wget curl jq\n             export VERSION=\\$(curl -s https://api.github.com/repos/kpeeters/cadabra2/releases|& jq .[0].tag_name -r)\n             export RPMNAME=cadabra2-\\${VERSION}-fedora41-x86_64.rpm\n             wget https://github.com/kpeeters/cadabra2/releases/download/\\${VERSION}/\\${RPMNAME}\n             dnf install -y \\${RPMNAME}\n             printf 'import sys\\nprint(sys.path)\\nimport cdb.main\\nex:=(A+B) (C+D);\\ndistribute(ex);\\nquit()\\n' > tst.cdb\n             cadabra2 tst.cdb\n             \n             xvfb-run -a cadabra2-gtk &\n             APP_PID=\\$!\n             sleep 10\n             if kill -0 \\$APP_PID 2>/dev/null; then\n                echo 'cadabra2-gtk started successfully'\n                kill \\$APP_PID\n                exit 0\n             else\n                echo 'cadabra2-gtk failed to start'\n                exit 1\n             fi\n           \"\n"
  },
  {
    "path": ".github/workflows/fedora-42-package.yml",
    "content": "# Create a Fedora 41 package on a github release event.\n# This assumes that the cadabra version is the same as the\n# release name, and it will attempt to add the .rpm file\n# to the release assets.\n\nname: Fedora-42 package\n\n# on: [push]\n\non:\n  release:\n    types: [created]\n\njobs:\n  build:\n\n    strategy:\n      matrix:\n        include:\n          - os: ubuntu-24.04\n            name: x86_64\n            display-name: \"Fedora 42 x86_64\"\n          - os: ubuntu-24.04-arm\n            name: arm64\n            display-name: \"Fedora 42 arm64\"\n    runs-on: ${{ matrix.os }}\n    \n    steps:\n    - uses: actions/checkout@v3\n\n    - name: Set up Docker Buildx\n      uses: docker/setup-buildx-action@master\n\n    - name: Pull Fedora image\n      run: docker pull fedora:42\n\n    - name: Set up GitHub CLI\n      run: |\n        sudo apt-get update\n        sudo apt-get install -y gh\n\n    - name: Authenticate GitHub CLI\n      run: gh auth setup-git\n      env:\n        GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }}\n          \n    - name: Build RPM in Fedora container\n      run: |\n        docker run --rm \\\n           -v ${{ github.workspace }}:/workspace \\\n           -w /workspace \\\n           fedora:42 \\\n           bash -c \" \n             git config --global --add safe.directory /workspace\n             dnf install -y rpm-build make gcc-c++ git python3-devel cmake gmp-devel libuuid-devel sqlite-devel openssl-devel gtkmm30-devel boost-devel python3-matplotlib python3-pip \n             pip3 install sympy \n             mkdir build \n             cd build \n             cmake -DPACKAGING_MODE=ON -DENABLE_MATHEMATICA=OFF -DCMAKE_INSTALL_PREFIX=/usr .. \n             make \n             cpack \n           \"\n\n    - name: Set version variables from output of cmake\n      run: |\n        VER=$(cat ${{ github.workspace }}/build/VERSION)\n        echo \"VERSION=$VER\" >> $GITHUB_ENV\n\n    - name: Upload Release Assets\n      if:   github.event_name == 'release'\n      run: |\n        gh release upload \"${{ env.VERSION }}\" build/cadabra2-${{ env.VERSION }}-fedora42-${{ matrix.name }}.rpm --clobber\n      env:\n        GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }}\n\n    - name: Store package as build artifact\n      uses: actions/upload-artifact@v4\n      if:   github.event_name == 'push'\n      with:\n        name: cadabra2-fedora42-${{ matrix.name }}.rpm\n        path: build/cadabra2-${{ env.VERSION }}-fedora42-${{ matrix.name }}.rpm\n\n  test:\n    needs: build\n    runs-on: ubuntu-latest\n    if:   github.event_name == 'release' # only test release builds\n    \n    steps:\n    - name: Set up Docker Buildx\n      uses: docker/setup-buildx-action@master\n\n    - name: Pull Fedora image\n      run: docker pull fedora:42\n\n    - name: Download package and run inside Fedora container\n      run: |\n        docker run --rm \\\n           -v ${{ github.workspace }}:/workspace \\\n           -w /workspace \\\n           fedora:42 \\\n           bash -c \" \n             dnf install -y xorg-x11-server-Xvfb wget curl jq\n             export VERSION=\\$(curl -s https://api.github.com/repos/kpeeters/cadabra2/releases|& jq .[0].tag_name -r)\n             export RPMNAME=cadabra2-\\${VERSION}-fedora42-x86_64.rpm\n             wget https://github.com/kpeeters/cadabra2/releases/download/\\${VERSION}/\\${RPMNAME}\n             dnf install -y \\${RPMNAME}\n             printf 'import sys\\nprint(sys.path)\\nimport cdb.main\\nex:=(A+B) (C+D);\\ndistribute(ex);\\nquit()\\n' > tst.cdb\n             cadabra2 tst.cdb\n             \n             xvfb-run -a cadabra2-gtk &\n             APP_PID=\\$!\n             sleep 10\n             if kill -0 \\$APP_PID 2>/dev/null; then\n                echo 'cadabra2-gtk started successfully'\n                kill \\$APP_PID\n                exit 0\n             else\n                echo 'cadabra2-gtk failed to start'\n                exit 1\n             fi\n           \"\n"
  },
  {
    "path": ".github/workflows/freebsd.yml",
    "content": "# This is a build which gets triggered on every commit push, to\n# ensure that we get some warnings when we push code that does\n# not build on Linux.\n\nname: FreeBSD\n\non: [push]\n\njobs:\n  build:\n\n    runs-on: ubuntu-latest\n    \n    steps:\n    - uses: actions/checkout@v4\n\n    - name: Build and test in FreeBSD\n      id: test\n      uses: vmactions/freebsd-vm@v1\n      with:\n        usesh: true\n        prepare: |\n          pkg install -y curl cmake python311 gettext-runtime pkgconf boost-libs\n          pkg install -y fontconfig harfbuzz pcre jsoncpp gmp atkmm cairomm glibmm gtkmm30 pangomm\n          pkg install -y git py311-sympy py311-numpy\n\n        run: |\n          pwd\n          env\n          freebsd-version\n          sysctl hw.model\n          sysctl hw.ncpu\n          sysctl hw.physmem\n          sysctl hw.usermem\n          mkdir build && cd build && cmake -DENABLE_MATHEMATICA=OFF ..\n          make\n          make install\n          make check\n"
  },
  {
    "path": ".github/workflows/homebrew-devel.yml",
    "content": "# This is a build which gets triggered on every push to the\n# 'devel' branch, to update the homebrew-repo the cadabra2-devel\n# package.\n\nname: Homebrew-devel\n\non:\n  push:\n    branches:\n      - devel\n      \njobs:\n  build:\n\n    runs-on: ubuntu-latest\n    \n    steps:\n    - name: Checkout Cadabra\n      uses: actions/checkout@v4\n      with:\n        ref: 'devel'\n      \n    - name: Checkout Homebrew repo\n      uses: actions/checkout@v4\n      with:\n        repository: kpeeters/homebrew-repo\n        path: homebrew-repo\n        token:  ${{ secrets.ACTIONS_HOMEBREW_REPO_TOKEN }}\n    \n    - name: Set up GitHub CLI\n      run: |\n        sudo apt-get update\n        sudo apt-get install -y gh\n\n    - name: Authenticate GitHub CLI\n      run: gh auth setup-git\n      env:\n        GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }}\n          \n    - name: Get dependencies\n      run:  sudo apt-get update && sudo DEBIAN_FRONTEND=noninteractive apt-get install git cmake jq python3-dev g++ libpcre3 libpcre3-dev libgmp3-dev libgtkmm-3.0-dev libboost-all-dev libgmp-dev libsqlite3-dev uuid-dev libmpfr-dev libmpc-dev\n\n    - name: Configure\n      run:  mkdir build && cd build && cmake -DPACKAGING_MODE=ON -DENABLE_MATHEMATICA=OFF -DCMAKE_INSTALL_PREFIX=/usr ..\n\n    - name: Set variables\n      run: |\n        export VERSION=$(cat build/VERSION)\n        export COMMIT=$(curl -s https://api.github.com/repos/kpeeters/cadabra2/commits/devel | jq -r .sha)\n        wget  https://github.com/kpeeters/cadabra2/archive/${COMMIT}.tar.gz\n        export SHA=`cat ${COMMIT}.tar.gz | sha256sum -b | cut -d \" \" -f 1`\n        echo \"SHA=${SHA}\" >> $GITHUB_ENV\n        echo \"VERSION=$VERSION\" >> $GITHUB_ENV\n        echo \"COMMIT=$COMMIT\" >> $GITHUB_ENV\n      \n    - name: Update Homebrew repo\n      run: |\n        cd homebrew-repo\n        cat cadabra2-devel.rb | sed -e 's/^  url .*/  url \"https:\\/\\/github.com\\/kpeeters\\/cadabra2\\/archive\\/${{ env.COMMIT }}.tar.gz\"/'  | sed -e 's/^  sha256.*/  sha256 \"${{ env.SHA }}\"/' | sed -e 's/^  version.*/  version \"${{ env.VERSION }}.${{ env.COMMIT }}\"/' > out.rb\n        mv out.rb cadabra2-devel.rb\n        cat cadabra2-devel.rb\n        git config user.name \"Kasper Peeters\"\n        git config user.email \"info@cadabra.science\"\n        git add cadabra2-devel.rb\n        git diff-index --quiet HEAD || (git commit -a -m \"Update to release ${{ env.VERSION }} commit ${{ env.COMMIT }}.\" && git push)\n\n        \n  test:\n    needs: build\n    runs-on: macos-latest\n    \n    steps:\n    - name: get dependencies\n      run:  brew update && brew upgrade && brew tap kpeeters/repo && brew install --verbose cadabra2-devel\n\n    - name: show where cadabra is located\n      run:  cat `which cadabra2`\n      \n    - name: test simple cli run\n      run:  printf \"import sys\\nprint(sys.path)\\nimport cdb.main\\nex:=(A+B) (C+D);\\ndistribute(ex);\\nquit()\\n\" > tst.cdb && cadabra2 tst.cdb\n    \n    - name: test gtk app launch\n      run: |\n        cadabra2-gtk &\n        APP_PID=$!\n        sleep 10\n        \n        if kill -0 $APP_PID 2>/dev/null; then\n          echo \"cadabra2-gtk started successfully\"\n          kill $APP_PID\n          exit 0\n        else\n          echo \"cadabra2-gtk failed to start\"\n          exit 1\n        fi\n\n    - name: Upload build logs\n      if: always()  \n      uses: actions/upload-artifact@v4\n      with:\n        name: brew-build-logs\n        path: |\n          ~/Library/Logs/Homebrew/\n        retention-days: 2\n\n        \n"
  },
  {
    "path": ".github/workflows/homebrew.yml",
    "content": "# This is a build which gets triggered on every release, to\n# update the homebrew-repo.\n\nname: Homebrew\n\non:\n  release:\n    types: [released]\n\n# on: [push]\n\njobs:\n  build:\n\n    runs-on: ubuntu-latest\n    \n    steps:\n    - name: Checkout Cadabra\n      uses: actions/checkout@v4\n\n    - name: Checkout Homebrew repo\n      uses: actions/checkout@v4\n      with:\n        repository: kpeeters/homebrew-repo\n        path: homebrew-repo\n        token:  ${{ secrets.ACTIONS_HOMEBREW_REPO_TOKEN }}\n    \n    - name: Set up GitHub CLI\n      run: |\n        sudo apt-get update\n        sudo apt-get install -y gh\n\n    - name: Authenticate GitHub CLI\n      run: gh auth setup-git\n      env:\n        GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }}\n          \n    - name: Get dependencies\n      run:  sudo apt-get update && sudo DEBIAN_FRONTEND=noninteractive apt-get install git cmake jq python3-dev g++ libpcre3 libpcre3-dev libgmp3-dev libgtkmm-3.0-dev libboost-all-dev libgmp-dev libsqlite3-dev uuid-dev libmpfr-dev libmpc-dev\n\n    - name: Configure\n      run:  mkdir build && cd build && cmake -DPACKAGING_MODE=ON -DENABLE_MATHEMATICA=OFF -DCMAKE_INSTALL_PREFIX=/usr ..\n\n    - name: Set variables\n      run: |\n        export VERSION=$(cat build/VERSION)\n        echo \"VERSION=$VERSION\" >> $GITHUB_ENV\n        wget https://github.com/kpeeters/cadabra2/archive/refs/tags/${VERSION}.tar.gz\n        export SHA=`cat ${VERSION}.tar.gz | sha256sum -b | cut -d \" \" -f 1`\n        echo \"SHA=${SHA}\" >> $GITHUB_ENV\n      \n    - name: Update Homebrew repo\n      run: |\n        cd homebrew-repo\n        cat cadabra2.rb | sed -e 's/^  url .*/  url \"https:\\/\\/github.com\\/kpeeters\\/cadabra2\\/archive\\/refs\\/tags\\/${{ env.VERSION }}.tar.gz\"/'  | sed -e 's/^  sha256.*/  sha256 \"${{ env.SHA }}\"/' | sed -e 's/^  version.*/  version \"${{ env.VERSION }}\"/' > out.rb\n        mv out.rb cadabra2.rb\n        cat cadabra2.rb\n        git config user.name \"Kasper Peeters\"\n        git config user.email \"info@cadabra.science\"\n        git add cadabra2.rb\n        git diff-index --quiet HEAD || (git commit -a -m \"Update to release ${{ env.VERSION }}.\" && git push)\n\n\n  test:\n    needs: build\n    runs-on: macos-latest\n    \n    steps:\n    - name: get dependencies\n      run:  brew update && brew upgrade && brew tap kpeeters/repo && brew install cadabra2\n\n    - name: show where cadabra is located\n      run:  cat `which cadabra2`\n      \n    - name: test simple cli run\n      run:  printf \"ex:=(A+B) (C+D);\\ndistribute(ex);\\nquit()\\n\" > tst.cdb && cadabra2 tst.cdb\n\n    - name: test gtk app launch\n      run: |\n        cadabra2-gtk &\n        APP_PID=$!\n        sleep 10\n        \n        if kill -0 $APP_PID 2>/dev/null; then\n          echo \"Application started successfully\"\n          kill $APP_PID\n          exit 0\n        else\n          echo \"Application failed to start\"\n          exit 1\n        fi\n\n"
  },
  {
    "path": ".github/workflows/linux.yml",
    "content": "# This is a build which gets triggered on every commit push, to\n# ensure that we get some warnings when we push code that does\n# not build on Linux.\n\nname: Linux\n\non: [push]\n\njobs:\n  build:\n\n    runs-on: ubuntu-latest\n    \n    steps:\n    - uses: actions/checkout@v3\n\n#     - name: Exit if not on devel branch\n#       if: github.ref != 'refs/heads/devel'\n#       run: exit 1\n      \n#    - name: setup python\n#      uses: actions/setup-python@v4\n#      with:\n#          python-version: 3.11\n\n    - name: get dependencies\n      run:  sudo apt-get update && sudo DEBIAN_FRONTEND=noninteractive apt-get install ninja-build git cmake python3-dev g++ libpcre3 libpcre3-dev libgmp3-dev libgtkmm-3.0-dev libboost-all-dev libgmp-dev libsqlite3-dev uuid-dev libmpfr-dev libmpc-dev libtbb-dev catch2 && python3 --version && which python3 && python3 -m pip install --upgrade pip && python3 -m pip install wheel && python3 -m pip install sympy gmpy2 numpy\n\n    - name: configure\n      run:  mkdir build && cd build && cmake -G Ninja -DENABLE_MATHEMATICA=OFF ..\n      \n    - name: build\n      run:  cd build && cmake --build .\n      \n    - name: test\n      env:\n        CTEST_OUTPUT_ON_FAILURE: 1\n      run:  cd build && ctest ARGS=\"-V\"\n"
  },
  {
    "path": ".github/workflows/macos.yml",
    "content": "# This is a build which gets triggered on every commit push, to\n# ensure that we get some warnings when we push code that does\n# not build on macOS.\n\nname: macOS\n\non: [push]\n\njobs:\n  build:\n\n    runs-on: macos-latest\n    \n    steps:\n    - uses: actions/checkout@v4\n\n#     - name: Exit if not on devel branch\n#       if: github.ref != 'refs/heads/devel'\n#       run: exit 1\n      \n#    - name: remove python 3.12\n#      run:  brew uninstall python@3.12\n          \n    - name: get dependencies\n      run:  brew install cmake ninja boost pcre gmp python@3.13 pkgconfig gtkmm3 adwaita-icon-theme catch2 tbb && python3 -m pip install --break-system-packages --user sympy gmpy2 numpy\n\n    - name: configure\n      run:  mkdir build && cd build && cmake -G Ninja -DENABLE_MATHEMATICA=OFF -DPython_EXECUTABLE=python3.12 ..\n      \n    - name: build\n      run:  cd build && cmake --build .\n      \n    - name: test\n      env:\n        CTEST_OUTPUT_ON_FAILURE: 1\n      run:  cd build && ctest ARGS=\"-V\"\n"
  },
  {
    "path": ".github/workflows/opensuse-tumbleweed-package.yml",
    "content": "# Create a OpenSUSE Tumbleweed package on a github release event.\n# This assumes that the cadabra version is the same as the\n# release name, and it will attempt to add the .rpm file\n# to the release assets.\n\nname: OpenSUSE-Tumbleweed package\n\n# on: [push]\n\non:\n  release:\n    types: [created]\n\n\njobs:\n  build:\n\n    runs-on: ubuntu-24.04\n    \n    steps:\n    - uses: actions/checkout@v3\n\n#    - name: Exit if not on devel branch\n#      if: github.ref != 'refs/heads/devel'\n#      run: exit 1\n      \n    - name: Set up Docker Buildx\n      uses: docker/setup-buildx-action@master\n\n    - name: Pull OpenSUSE image\n      run: docker pull opensuse/tumbleweed:latest\n\n    - name: Set up GitHub CLI\n      run: |\n        sudo apt-get update\n        sudo apt-get install -y gh\n\n    - name: Authenticate GitHub CLI\n      run: gh auth setup-git\n      env:\n        GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }}\n          \n    - name: Build RPM\n      run: |\n        docker run --rm \\\n           -v ${{ github.workspace }}:/workspace \\\n           -w /workspace \\\n           opensuse/tumbleweed:latest \\\n           bash -c \"\n             zypper refresh\n             zypper update\n             zypper -n install --no-recommends rpmbuild git cmake python313-devel gcc-c++ \\\n                  gmp-devel libuuid-devel  \\\n                  gtkmm3-devel sqlite3-devel \\\n                  python313-matplotlib libopenssl-devel \\\n                  libboost_system-devel libboost_filesystem-devel \\\n                  libboost_date_time-devel libboost_program_options-devel             \n             git config --global --add safe.directory /workspace\n             mkdir build \n             cd build \n             cmake -DPACKAGING_MODE=ON -DENABLE_MATHEMATICA=OFF -DCMAKE_INSTALL_PREFIX=/usr .. \n             make \n             cpack \n           \"\n\n    - name: Set version variables from output of cmake\n      run: |\n        VER=$(cat ${{ github.workspace }}/build/VERSION)\n        echo \"VERSION=$VER\" >> $GITHUB_ENV\n\n    - name: Upload Release Assets\n      run: |\n        gh release upload \"${{ env.VERSION }}\" build/cadabra2-${{ env.VERSION }}-tumbleweed.rpm --clobber\n      env:\n        GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }}\n\n  test:\n    needs: build\n    runs-on: ubuntu-24.04\n    \n    steps:\n    - name: Set up Docker Buildx\n      uses: docker/setup-buildx-action@master\n\n    - name: Pull OpenSUSE image\n      run: docker pull opensuse/tumbleweed:latest\n\n    - name: Download package and run inside OpenSUSE container\n      run: |\n        docker run --rm \\\n           -v ${{ github.workspace }}:/workspace \\\n           -w /workspace \\\n           opensuse/tumbleweed:latest \\\n           bash -c \"\n             zypper clean --all\n             zypper refresh\n             zypper update\n             zypper se -s libboost_filesystem\n             zypper -n install xvfb-run wget curl jq\n             export VERSION=\\$(curl -s https://api.github.com/repos/kpeeters/cadabra2/releases|& jq .[0].tag_name -r)\n             export RPMNAME=cadabra2-\\${VERSION}-tumbleweed.rpm\n             wget https://github.com/kpeeters/cadabra2/releases/download/\\${VERSION}/\\${RPMNAME}\n             zypper --no-gpg-checks -n install \\${RPMNAME}\n             printf 'import sys\\nprint(sys.path)\\nimport cdb.main\\nex:=(A+B) (C+D);\\ndistribute(ex);\\nquit()\\n' > tst.cdb\n             cadabra2 tst.cdb\n             \n             xvfb-run -a cadabra2-gtk &\n             APP_PID=\\$!\n             sleep 10\n             if kill -0 \\$APP_PID 2>/dev/null; then\n                echo 'cadabra2-gtk started successfully'\n                kill \\$APP_PID\n                exit 0\n             else\n                echo 'cadabra2-gtk failed to start'\n                exit 1\n             fi\n           \"\n"
  },
  {
    "path": ".github/workflows/tarball.yml",
    "content": "# This is a build which gets triggered on every release, to\n# generate a tarball which includes all submodules.\n\nname: Tarball\n\non:\n  release:\n    types: [released]\n\n# on: [push]\n\njobs:\n  build:\n\n    runs-on: ubuntu-latest\n    \n    steps:\n    - name: Checkout Cadabra\n      uses: actions/checkout@v4\n\n    - name: Set up GitHub CLI\n      run: |\n        sudo apt-get update\n        sudo apt-get install -y gh\n\n    - name: Authenticate GitHub CLI\n      run: gh auth setup-git\n      env:\n        GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }}\n          \n    - name: Create tarball\n      run: |\n        export CDB_MAJOR=`cat cmake/version.cmake |grep 'MAJOR '|sed -e 's/[^ ]* \\([0-9]*\\).*/\\1/'`\n        export CDB_MINOR=`cat cmake/version.cmake |grep 'MINOR '|sed -e 's/[^ ]* \\([0-9]*\\).*/\\1/'`\n        export CDB_PATCH=`cat cmake/version.cmake |grep 'PATCH '|sed -e 's/[^ ]* \\([0-9]*\\).*/\\1/'`\n        export VERSION=${CDB_MAJOR}.${CDB_MINOR}.${CDB_PATCH}\n        echo \"VERSION=$VERSION\" >> $GITHUB_ENV\n        mkdir -p submodules\n        cd submodules\n        git clone -b kpeeters/cadabra https://github.com/kpeeters/MicroTeX.git microtex\n        cd ../..\n        mv cadabra2 cadabra2-${VERSION}\n        tar zcf cadabra2-${VERSION}-source-inclusive.tar.gz --exclude \".git\" cadabra2-${VERSION}\n        mv cadabra2-${VERSION} cadabra2 \n      \n    - name: Upload tarball to assets\n      run: |\n        gh release upload \"${{ env.VERSION }}\" ${{ github.workspace }}/../cadabra2-${VERSION}-source-inclusive.tar.gz --clobber\n      env:\n        GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }}\n      \n"
  },
  {
    "path": ".github/workflows/ubuntu-22.04-package.yml",
    "content": "# Create an Ubuntu 22.04 package on a github release event.\n# This assumes that the cadabra version is the same as the\n# release name, and it will attempt to add the .deb file\n# to the release assets.\n\nname: Ubuntu-22.04 package\n\n# on: [push]\n\non:\n release:\n   types: [created]\n\njobs:\n  build:\n\n    strategy:\n      matrix:\n        include:\n          - os: ubuntu-22.04\n            name: x86_64\n            display-name: \"Ubuntu 22.04 x86_64\"\n          - os: ubuntu-22.04-arm\n            name: arm64\n            display-name: \"Ubuntu 22.04 arm64\"\n    runs-on: ${{ matrix.os }}\n    \n    steps:\n    - uses: actions/checkout@v3\n\n#    - name: Exit if not on devel branch\n#      if: github.ref != 'refs/heads/devel'\n#      run: exit 1\n      \n    - name: Set up GitHub CLI\n      run: |\n        sudo apt-get update\n        sudo apt-get install -y gh\n\n    - name: Authenticate GitHub CLI\n      run: gh auth setup-git\n      env:\n        GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }}\n          \n    - name: Get dependencies\n      run:  sudo apt-get update && sudo DEBIAN_FRONTEND=noninteractive apt-get install git cmake ninja-build python3-dev g++ libpcre3 libpcre3-dev libgmp3-dev libgtkmm-3.0-dev libboost-all-dev libgmp-dev libsqlite3-dev uuid-dev libmpfr-dev libmpc-dev libtbb-dev catch2 && python3 --version && which python3 && python3 -m pip install --upgrade pip && python3 -m pip install wheel && python3 -m pip install sympy gmpy2 numpy\n\n    - name: Configure\n      run:  mkdir build && cd build && cmake -G Ninja -DPACKAGING_MODE=ON -DENABLE_MATHEMATICA=OFF -DCMAKE_INSTALL_PREFIX=/usr ..\n      \n    - name: Build\n      run:  cd build && cmake --build .\n      \n    - name: Create the .deb package\n      run:  cd build && cpack\n      \n    - name: Set version variables from output of cmake\n      run: |\n        VER=$(cat build/VERSION)\n        echo \"VERSION=$VER\" >> $GITHUB_ENV\n\n    - name: Upload Release Assets\n      run: |\n        gh release upload \"${{ env.VERSION }}\" build/cadabra2-${{ env.VERSION }}-ubuntu-22.04-jammy-${{ matrix.name }}.deb --clobber\n      env:\n        GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }}\n\n\n  test:\n    needs: build\n    runs-on: ubuntu-22.04\n\n    steps:\n    - name: Get and install package\n      run: |\n        sudo apt install xvfb\n        export VERSION=$(curl -s https://api.github.com/repos/kpeeters/cadabra2/releases|& jq .[0].tag_name -r)\n        export DEBNAME=cadabra2-${VERSION}-ubuntu-22.04-jammy-x86_64.deb\n        wget https://github.com/kpeeters/cadabra2/releases/download/${VERSION}/${DEBNAME}\n        sudo apt -y update\n        sudo apt -y upgrade\n        sudo apt -y install ./${DEBNAME}\n\n    - name: Test simple cli run\n      run:  printf \"import sys\\nprint(sys.path)\\nimport cdb.main\\nex:=(A+B) (C+D);\\ndistribute(ex);\\nquit()\\n\" > tst.cdb && cadabra2 tst.cdb\n\n    - name: Test gtk app launch\n      run: |\n        xvfb-run -a cadabra2-gtk &\n        APP_PID=$!\n        sleep 10\n        \n        if kill -0 $APP_PID 2>/dev/null; then\n          echo \"Application started successfully\"\n          kill $APP_PID\n          exit 0\n        else\n          echo \"Application failed to start\"\n          exit 1\n        fi\n"
  },
  {
    "path": ".github/workflows/ubuntu-24.04-package.yml",
    "content": "# Create an Ubuntu 24.04 package on a github release event.\n# This assumes that the cadabra version is the same as the\n# release name, and it will attempt to add the .deb file\n# to the release assets.\n\nname: Ubuntu-24.04 package\n\n# on: [push]\n\non:\n  release:\n    types: [created]\n\njobs:\n  build:\n\n    strategy:\n      matrix:\n        include:\n          - os: ubuntu-24.04\n            name: x86_64\n            display-name: \"Ubuntu 24.04 x86_64\"\n          - os: ubuntu-24.04-arm\n            name: arm64\n            display-name: \"Ubuntu 24.04 arm64\"\n    runs-on: ${{ matrix.os }}\n    \n    steps:\n    - uses: actions/checkout@v3\n\n#    - name: Exit if not on devel branch\n#      if: github.ref != 'refs/heads/devel'\n#      run: exit 1\n      \n    - name: Set up GitHub CLI\n      run: |\n        sudo apt-get update\n        sudo apt-get install -y gh\n\n    - name: Authenticate GitHub CLI\n      run: gh auth setup-git\n      env:\n        GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }}\n          \n    - name: Get dependencies\n      run:  sudo apt-get update && sudo DEBIAN_FRONTEND=noninteractive apt-get install git cmake ninja-build python3-dev g++ libpcre3 libpcre3-dev libgmp3-dev libgtkmm-3.0-dev libboost-all-dev libgmp-dev libsqlite3-dev uuid-dev libmpfr-dev libmpc-dev libtbb-dev catch2 && python3 --version && which python3 && python3 -m pip install --upgrade pip && python3 -m pip install wheel && python3 -m pip install sympy gmpy2 numpy\n\n    - name: configure\n      run:  mkdir build && cd build && cmake -G Ninja -DPACKAGING_MODE=ON -DENABLE_MATHEMATICA=OFF -DCMAKE_INSTALL_PREFIX=/usr ..\n      \n    - name: Make\n      run:  cd build && cmake --build .\n      \n    - name: Create the .deb package\n      run:  cd build && cpack\n      \n    - name: Set version variables from output of cmake\n      run: |\n        VER=$(cat build/VERSION)\n        echo \"VERSION=$VER\" >> $GITHUB_ENV\n\n    - name: Upload Release Assets\n      if:   github.event_name == 'release'\n      run: |\n        gh release upload \"${{ env.VERSION }}\" build/cadabra2-${{ env.VERSION }}-ubuntu-24.04-noble-${{ matrix.name }}.deb --clobber\n      env:\n        GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }}\n\n    - name: Store package as build artifact\n      uses: actions/upload-artifact@v4\n      if:   github.event_name == 'push'\n      with:\n        name: cadabra2-ubuntu-24.04-noble-${{ matrix.name }}.deb\n        path: build/cadabra2-${{ env.VERSION }}-ubuntu-24.04-noble.deb\n\n\n  test:\n    needs: build\n    runs-on: ubuntu-24.04\n\n    steps:\n    - name: Install prerequisites for testing\n      run: |\n        sudo apt install xvfb imagemagick\n        sudo apt-mark hold firefox\n        \n    - name: Get and install package (release mode)\n      if:   github.event_name == 'release'\n      run: |\n        export VERSION=$(curl -s https://api.github.com/repos/kpeeters/cadabra2/releases|& jq .[0].tag_name -r)\n        export DEBNAME=cadabra2-${VERSION}-ubuntu-24.04-noble-x86_64.deb\n        wget https://github.com/kpeeters/cadabra2/releases/download/${VERSION}/${DEBNAME}\n        sudo apt -y update\n        sudo apt -y upgrade\n        sudo apt -y install ./${DEBNAME}\n\n    - name: Download package (push mode)\n      uses: actions/download-artifact@v4\n      if:   github.event_name == 'push'\n      with:\n        name: cadabra2-ubuntu-24.04-noble-x86_64.deb\n\n    - name: Install package (push mode)\n      if:   github.event_name == 'push'\n      run: |\n        ls -la\n        sudo apt -y update\n        sudo apt -y upgrade\n        sudo apt -y install ./cadabra2*.deb\n\n    - name: Test simple cli run\n      run:  printf \"import sys\\nprint(sys.path)\\nimport cdb.main\\nex:=(A+B) (C+D);\\ndistribute(ex);\\nquit()\\n\" > tst.cdb && cadabra2 tst.cdb\n\n    - name: Test gtk app launch and take screenshot\n      run: |\n        MESA_LOADER_DRIVER_OVERRIDE=llvmpipe LIBGL_ALWAYS_SOFTWARE=1 xvfb-run -a -s \"-screen 0 1920x1080x24 -ac\" cadabra2-gtk -n &\n        APP_PID=$!\n        sleep 10\n        \n        if kill -0 $APP_PID 2>/dev/null; then\n          echo \"Application started successfully\"\n          DISPLAY=:99 import -window root screenshot.png\n          kill $APP_PID\n          exit 0\n        else\n          echo \"Application failed to start\"\n          exit 1\n        fi\n\n    - name: Upload screenshot\n      uses: actions/upload-artifact@v4\n      with:\n        name: app-screenshot-ubuntu-24.04\n        path: screenshot.png\n"
  },
  {
    "path": ".github/workflows/windows-installer.yml",
    "content": "# Create Windows installer on a github release event.  This assumes\n# that the cadabra version is the same as the release name, and it\n# will attempt to add the installer file to the release assets.\n\nname: Windows 11 installer\n\n# on: [push]\n\non:\n  release:\n    types: [created]\n\ndefaults:\n    run:\n      shell: msys2 {0}\n\njobs:\n  msys2-ucrt64:\n    strategy:\n      matrix:\n        include:\n          - os: windows-2022\n            name: x86_64\n            display-name: \"Windows 11 x86_64\"\n            msystem: ucrt64\n            midfix: ucrt-x86_64\n          - os: windows-11-arm\n            name: arm64\n            msystem: clangarm64\n            midfix: clang-aarch64\n            display-name: \"Windows 11 arm64\"\n    runs-on: ${{ matrix.os }}\n    name: Windows 11\n    defaults:\n      run:\n        shell: msys2 {0}\n\n    steps:\n    - name: Install WiX v4/v5 Tool\n      run: |\n        dotnet tool install --tool-path c:\\WiX\\bin wix --version 5.0.2\n        c:\\WiX\\bin\\wix extension add --global WixToolset.UI.wixext/5.0.2\n      shell: pwsh\n\n    - name: Add WiX toolkit to PATH\n      shell: bash\n      run: |\n        echo \"WiX installed at ${WIX}, hopefully...\"\n        echo \"Listing C:/WiX/bin\"\n        ls \"C:/WiX/bin\"\n        echo \"Listing Program Files (x86):\"\n        ls \"C:/Program Files (x86)/\"\n        echo \"Listing Program Files:\"        \n        ls \"C:/Program Files/\"\n        echo \"${WIX}bin\" >> $GITHUB_PATH\n\n    - uses: msys2/setup-msys2@v2\n      with:\n        msystem: ${{ matrix.msystem }}\n        update: true\n        install: >-\n          curl\n          git\n          mingw-w64-${{ matrix.midfix }}-gcc\n          mingw-w64-${{ matrix.midfix }}-python\n          mingw-w64-${{ matrix.midfix }}-gtkmm3\n          mingw-w64-${{ matrix.midfix }}-boost    \n          mingw-w64-${{ matrix.midfix }}-sqlite3\n          mingw-w64-${{ matrix.midfix }}-cmake\n          mingw-w64-${{ matrix.midfix }}-python-matplotlib\n          mingw-w64-${{ matrix.midfix }}-python-sympy\n          mingw-w64-${{ matrix.midfix }}-github-cli\n          \n    - name: Authenticate GitHub CLI\n      run: gh auth setup-git\n      env:\n        GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }}\n          \n    - uses: actions/checkout@master\n      name: Checkout source\n      \n    - name: Build\n      run: |\n        mkdir build\n        cd build\n        # Turn off searching Python in the registry, as that contains the\n        # windows Python which is not the MSYS python that we want to use.\n        cmake -DPython_FIND_REGISTRY=NEVER ..\n        ninja\n        ninja install\n        cpack\n\n    - name: Upload WiX log file\n      if: always()\n      uses: actions/upload-artifact@v4\n      with:\n        name: wix-${{ matrix.name }}.log\n        path: build/_CPack_Packages/win64/WIX/wix.log\n        retention-days: 2\n\n    - name: Set version variables from output of cmake\n      run: |\n        VER=$(cat build/VERSION)\n        echo \"VERSION=$VER\" >> $GITHUB_ENV\n        GITVER=$(cat build/GIT_TAG_VERSION)\n        echo \"GIT_TAG_VERSION=$GITVER\" >> $GITHUB_ENV\n\n    - name: Upload release assets\n      run: |\n        gh release upload \"${{ env.GIT_TAG_VERSION }}\" build/cadabra2-${{ env.VERSION }}-win64.msi --clobber\n      env:\n        GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }}\n\n"
  },
  {
    "path": ".github/workflows/windows.yml",
    "content": "# Create Windows installer on a github push or release event\n# (upload to the release assets in the latter case).\n\nname: Windows 11\n\non: [push]\n\n#on:\n#  release:\n#    types: [created]\n\ndefaults:\n    run:\n      shell: msys2 {0}\n\njobs:\n  msys2-ucrt64:\n    strategy:\n      matrix:\n        include:\n          - os: windows-2022\n            name: x86_64\n            display-name: \"Windows 11 x86_64\"\n            msystem: ucrt64\n            midfix: ucrt-x86_64\n          - os: windows-11-arm\n            name: arm64\n            msystem: clangarm64\n            midfix: clang-aarch64\n            display-name: \"Windows 11 arm64\"\n    runs-on: ${{ matrix.os }}\n    name: Windows build\n    defaults:\n      run:\n        shell: msys2 {0}\n\n    steps:\n    - name: Install WiX v4/v5 Tool\n      run: |\n        dotnet tool install --tool-path c:\\WiX\\bin wix --version 5.0.2\n        c:\\WiX\\bin\\wix extension add --global WixToolset.UI.wixext/5.0.2\n      shell: pwsh\n\n    - name: Add WiX toolkit to PATH\n      shell: bash\n      run: |\n        echo \"WiX installed at ${WIX}, hopefully...\"\n        echo \"Listing C:/WiX/bin\"\n        ls \"C:/WiX/bin\"\n        echo \"Listing Program Files (x86):\"\n        ls \"C:/Program Files (x86)/\"\n        echo \"Listing Program Files:\"        \n        ls \"C:/Program Files/\"\n        echo \"${WIX}bin\" >> $GITHUB_PATH\n\n    - uses: msys2/setup-msys2@v2\n      with:\n        msystem: ${{ matrix.msystem }}\n        update: true\n        install: >-\n          curl\n          git\n          mingw-w64-${{ matrix.midfix }}-gcc\n          mingw-w64-${{ matrix.midfix }}-python\n          mingw-w64-${{ matrix.midfix }}-gtkmm3\n          mingw-w64-${{ matrix.midfix }}-boost    \n          mingw-w64-${{ matrix.midfix }}-sqlite3\n          mingw-w64-${{ matrix.midfix }}-cmake\n          mingw-w64-${{ matrix.midfix }}-python-matplotlib\n          mingw-w64-${{ matrix.midfix }}-python-sympy\n          mingw-w64-${{ matrix.midfix }}-github-cli\n          \n    - name: Authenticate GitHub CLI\n      run: gh auth setup-git\n      env:\n        GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }}\n          \n    - uses: actions/checkout@master\n      name: Checkout source\n      \n    - name: Build\n      run: |\n        mkdir build\n        cd build\n        # Turn off searching Python in the registry, as that contains the\n        # windows Python which is not the MSYS python that we want to use.\n        cmake -DPython_FIND_REGISTRY=NEVER ..\n        ninja\n        ninja install\n        cpack\n\n    - name: Upload cmake_install.cmake file\n      if: always()\n      uses: actions/upload-artifact@v4\n      with:\n        name: cmake_install-${{ matrix.name }}.cmake\n        path: build/cmake_install.cmake\n        retention-days: 2\n\n    - name: Upload frontend/cmake_install.cmake file\n      if: always()\n      uses: actions/upload-artifact@v4\n      with:\n        name: frontend-cmake_install-${{ matrix.name }}.cmake\n        path: build/frontend/cmake_install.cmake\n        retention-days: 2\n        \n    - name: Upload frontend/gtkmm/cmake_install.cmake file\n      if: always()\n      uses: actions/upload-artifact@v4\n      with:\n        name: frontend-gtkmm-cmake_install-${{ matrix.name }}.cmake\n        path: build/frontend/gtkmm/cmake_install.cmake\n        retention-days: 2\n        \n    - name: Upload WiX log file\n      if: always()\n      uses: actions/upload-artifact@v4\n      with:\n        name: wix-${{ matrix.name }}.log\n        path: build/_CPack_Packages/win64/WIX/wix.log\n        retention-days: 2\n\n    - name: Set version variables from output of cmake\n      run: |\n        VER=$(cat build/VERSION)\n        echo \"VERSION=$VER\" >> $GITHUB_ENV\n        GITVER=$(cat build/GIT_TAG_VERSION)\n        echo \"GIT_TAG_VERSION=$GITVER\" >> $GITHUB_ENV\n\n    - name: Upload installer as build artifact\n      uses: actions/upload-artifact@v4\n      with:\n        name: cadabra2-windows-${{ matrix.name }}.msi\n        path: build/cadabra2-${{ env.VERSION }}-win64.msi\n        retention-days: 2\n\n    - name: Upload release assets\n      if:   github.event_name == 'release'\n      run: |\n        mv build/cadabra2-${{ env.VERSION }}-win64.msi build/cadabra2-${{ env.GIT_TAG_VERSION }}-windows-${{ matrix.name }}.msi\n        gh release upload \"${{ env.GIT_TAG_VERSION }}\" build/cadabra2-${{ env.GIT_TAG_VERSION }}-windows-${{ matrix.name }}.msi --clobber\n      env:\n        GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }}\n\n  test:\n    needs: msys2-ucrt64\n    strategy:\n      fail-fast: false\n      matrix:\n        include:\n          - os: windows-2022\n            name: x86_64\n            display-name: \"Windows 11 x86_64\"\n          - os: windows-11-arm\n            name: arm64\n            display-name: \"Windows 11 arm64\"\n    runs-on: ${{ matrix.os }}\n    \n    steps:\n    - name: Download installer\n      uses: actions/download-artifact@v4\n      with:\n        name: cadabra2-windows-${{ matrix.name }}.msi\n\n    - name: Install silently\n      shell: pwsh\n      run: |\n        dir\n        $installer = Get-ChildItem -Filter \"cadabra*.msi\" | Select-Object -First 1 -ExpandProperty Name\n        if (-not $installer) {\n            Write-Error \"No installer found\"\n            exit 1\n        }\n        $installerPath = (Get-Item -Path \".\\$installer\").FullName        \n        Write-Host \"Installing $installerPath\"\n        Start-Process -FilePath \"msiexec\" -ArgumentList \"/i\", \"$installerPath\", \"/qn\", \"/l*v\", \"install.log\" -Wait\n        Write-Host \"Installer finished\"\n\n    - name: Upload installation log\n      uses: actions/upload-artifact@v4\n      with:\n        name: install-${{ matrix.os }}.log\n        path: install.log\n\n    - name: Check installation location\n      shell: cmd\n      run: |\n        echo \"Main folder:\"\n        dir \"C:\\Program Files\\Cadabra\" \n        \n    - name: Start GUI and take screenshot\n      shell: pwsh\n      run: |\n        # Attempt to start the notebook\n        if (-not (Test-Path \"C:\\Program Files\\Cadabra\\cadabra2-gtk.exe\")) {\n        Write-Host \"Executable not found\"\n        exit 1\n        }\n        $process = Start-Process \"C:\\Program Files\\Cadabra\\cadabra2-gtk.exe\" -ArgumentList \"-n\", \"Examples\\schwarzschild.cnb\" -WorkingDirectory \"C:\\Program Files\\Cadabra\" -PassThru\n        Start-Sleep -Seconds 120\n\n        # Take screenshot\n        Add-Type -AssemblyName System.Windows.Forms\n        Add-Type -AssemblyName System.Drawing\n        \n        $screen = [System.Windows.Forms.Screen]::PrimaryScreen.Bounds\n        $bitmap = New-Object System.Drawing.Bitmap($screen.Width, $screen.Height)\n        $graphics = [System.Drawing.Graphics]::FromImage($bitmap)\n        $graphics.CopyFromScreen($screen.Location, [System.Drawing.Point]::Empty, $screen.Size)\n        $bitmap.Save(\"screenshot.png\")\n        $graphics.Dispose()\n        $bitmap.Dispose()\n\n        # Cleanup\n        Stop-Process -Id $process.Id -Force\n      \n    - name: Upload cadabra_log.txt\n      if: always()\n      uses: actions/upload-artifact@v4\n      with:\n        name: cadabra_log-${{ matrix.os }}.txt\n        path: C:\\Windows\\Temp\\cadabra_log.txt\n\n    - name: Upload screenshot\n      uses: actions/upload-artifact@v4\n      with:\n        name: app-screenshot-${{ matrix.os }}\n        path: screenshot.png\n        \n"
  },
  {
    "path": ".gitignore",
    "content": ".cache\nweb2/cadabra2/source/book\n*.orig\n*.bak\ndoxygen\n.DS_Store\n*~\n*.o\nbuild\nbuild-lib\njbuild\ninstall\n.ipynb_checkpoints\n__pycache__\n.vscode\n.vs\nCMakeSettings.json\nconfig/pre_install.rtf\n.ccls-cache\n*appdata.xml\nconfig/install_script.iss\nconfig/science.cadabra.cadabra2-gtk.desktop\n"
  },
  {
    "path": ".gitmodules",
    "content": "[submodule \"submodules/microtex\"]\n\tpath = submodules/microtex\n\turl = https://github.com/kpeeters/MicroTeX\n\tbranch = kpeeters/cadabra\n"
  },
  {
    "path": ".travis.yml",
    "content": "branches:\n  only:\n  - master\n  - feature/pybind\n  \nos:\n   - linux\n     addons:\n        apt:\n          sources:\n            - ubuntu-toolchain-r-test\n          packages:\n            - g++-6\n     env:\n        - MATRIX_EVAL=\"CC=gcc-6 && CXX=g++-6\"\t\n   - osx\n\ncompiler:\n   - gcc\n\nlanguage: cpp\n\nsudo: required\n\ndist: trusty\n\nenv:\n  global:\n    - CTEST_EXT_COLOR_OUTPUT=TRUE\n    - CTEST_BUILD_FLAGS=-j4\n\nmatrix:\n   exclude:\n     - os: osx\n       compiler: gcc\nscript:\n   - cmake --build .\n   - ctest -VV .\n\nbefore_script:\n   - mkdir build\n   - cd build\n   - cmake ..\n\nbefore_install:\n   - if [ \"$TRAVIS_PULL_REQUEST\" == \"false\" ]; then openssl aes-256-cbc -K $encrypted_0c0fd3a7dbd0_key -iv $encrypted_0c0fd3a7dbd0_iv -in config/travisci_rsa.enc -out config/travisci_rsa -d; fi\n   - if [ \"$TRAVIS_PULL_REQUEST\" == \"false\" ]; then chmod 0600 config/travisci_rsa; cp config/travisci_rsa ~/.ssh/id_rsa; fi\n   - if [[ \"$TRAVIS_OS_NAME\" == \"linux\" ]]; then sudo apt-get -qq update; fi\n   - if [[ \"$TRAVIS_OS_NAME\" == \"linux\" ]]; then sudo apt-get install -y cmake python3-dev\n     g++ libpcre3 libpcre3-dev libgmp3-dev uuid-dev python3-pip; fi\n   - if [[ \"$TRAVIS_OS_NAME\" == \"linux\" ]]; then sudo apt-get install -y libgtkmm-3.0-dev\n     libjsoncpp-dev libboost-regex-dev libboost-system-dev libboost-program-options-dev libboost-date-time-dev libboost-filesystem-dev libgmp-dev libsqlite3-dev; fi\n   - if [[ \"$TRAVIS_OS_NAME\" == \"osx\" ]]; then brew update; brew unlink json-c; fi\n   - if [[ \"$TRAVIS_OS_NAME\" == \"osx\" ]]; then brew outdated cmake || brew upgrade cmake; fi\n   - if [[ \"$TRAVIS_OS_NAME\" == \"osx\" ]]; then brew outdated boost || travis_wait brew upgrade boost; fi\n   - if [[ \"$TRAVIS_OS_NAME\" == \"osx\" ]]; then brew outdated gmp || brew upgrade gmp; fi\n   - if [[ \"$TRAVIS_OS_NAME\" == \"osx\" ]]; then brew outdated pkgconfig || brew upgrade pkgconfig; fi\n   - if [[ \"$TRAVIS_OS_NAME\" == \"osx\" ]]; then brew install jsoncpp python3 gtkmm3 gnome-icon-theme; fi\n   - if [[ \"$TRAVIS_OS_NAME\" == \"osx\" ]]; then sudo pip3 install matplotlib sympy; fi\n   - if [ \"$TRAVIS_PULL_REQUEST\" == \"false\" ]; then if [[ \"$TRAVIS_OS_NAME\" == \"linux\" ]]; then if [[ \"`${CC} --version |grep gcc`\" != \"\" ]]; then sudo apt-get install --yes doxygen graphviz texlive-font-utils; ./config/publish-doxygen; fi; fi; fi\n\ninstall:\n   - pip3 install --user sympy\n\n\nnotifications:\n  email:\n    recipients:\n      - kasper.peeters@phi-sci.com\n    on_success: always\n    on_failure: always\n"
  },
  {
    "path": "CITATION.cff",
    "content": "cff-version: 1.2.0\nmessage: \"If you use this software, please cite it as below.\"\nauthors:\n- family-names: \"Peeters\"\n  given-names: \"Kasper\"\n  orcid: \"https://orcid.org/0000-0002-3077-8193\"\ntitle: \"My Research Software\"\nversion: 2.0.4\ndoi: 10.5281/zenodo.2500762\ndate-released: 2017-12-18\nurl: \"https://github.com/kpeeters/cadabra2\"\npreferred-citation:\n  type: article\n  authors:\n  - family-names: \"Peeters\"\n    given-names: \"Kasper\"\n    orcid: \"https://orcid.org/0000-0002-3077-8193\"\n  doi: doi.org/10.21105/joss.01118\n  journal: \"The Journal of Open Source Software\"\n  start: 1118 # First page number\n  end: 1119 # Last page number\n  title: \"Cadabra2: computer algebra for field theory revisited\"\n  issue: 3\n  volume: 32\n  year: 2018"
  },
  {
    "path": "CMakeLists.txt",
    "content": "set(CMAKE_LEGACY_CYGWIN_WIN32 0)\nif(WIN32)\n  # We want to use WiX 4.x but cpack only supports that from 3.30.\n  set(CADABRA_CMAKE_VERSION 3.30)\nelse()\n  set(CADABRA_CMAKE_VERSION 3.12)\nendif()\n\n# Policy settings for CMake to resolve ambiguities.\n\nif(POLICY CMP0042)\n  cmake_policy(SET CMP0042 NEW)\n  message(STATUS \"Set CMake policy CMP0042 to NEW\")\nendif()\nif(POLICY CMP0054)\n  cmake_policy(SET CMP0054 NEW)\n  message(STATUS \"Set CMake policy CMP0054 to NEW\")\nendif()\nif(POLICY CMP0127)\n  cmake_policy(SET CMP0127 NEW)\n  message(STATUS \"Set CMake policy CMP0127 to NEW\")\nendif()\nif(POLICY CMP0148)\n  cmake_policy(SET CMP0148 NEW)\n  message(STATUS \"Set CMake policy CMP0148 to NEW\")\nendif()\nif(POLICY CMP0167)\n  cmake_policy(SET CMP0167 NEW)\n  message(STATUS \"Set CMake policy CMP0167 to NEW\")\nendif()\nif(POLICY CMP0094)\n  cmake_policy(SET CMP0094 NEW)\n  message(STATUS \"Set CMake policy CMP0094 to NEW (use first Python found)\")\nendif()\nif(POLICY CMP0169)\n  cmake_policy(SET CMP0169 NEW)\n  message(STATUS \"Set CMake policy CMP0169 to NEW (use new FetchContent)\")\n  # CMake 3.30: call FetchContent_Populate() with just the name of a\n  # dependency. This modern alternative was introduced in cmake 3.14\n  # but we still support 3.12; we call the old behaviour in\n  # frontend/gtkmm/CMakeLists.txt\nendif()\nif(POLICY CMP0177)\n  cmake_policy(SET CMP0177 NEW)\n  message(STATUS \"Set CMake policy CMP0177 to NEW (destination paths are normalised)\")\nendif()\nif(POLICY CMP0087)\n  cmake_policy(SET CMP0087 NEW)\n  message(STATUS \"Set CMake policy CMP0089 to NEW (evaluate generator expressions in install(CODE))\")\nendif()\n\ncmake_minimum_required(VERSION ${CADABRA_CMAKE_VERSION})\nset(CMAKE_CXX_STANDARD 17)\nset(CMAKE_CXX_STANDARD_REQUIRED ON)\n\nproject(Cadabra)\n\nif (${CMAKE_SYSTEM_NAME} MATCHES \"Darwin\")\n    set(MACOS TRUE)\nendif()\n\n#---------------------------------------------------------------------------\n# Preamble\n#---------------------------------------------------------------------------\n\nset(CMAKE_EXPORT_COMPILE_COMMANDS ON)\n\n# Aliases for directories\nset(CADABRA_ROOT_DIR ${CMAKE_SOURCE_DIR})\nset(CADABRA_CLIENT_SERVER_DIR ${CADABRA_ROOT_DIR}/client_server)\nset(CADABRA_CORE_DIR ${CADABRA_ROOT_DIR}/core)\nset(CADABRA_FRONTEND_DIR ${CADABRA_ROOT_DIR}/frontend)\nset(CADABRA_IMAGES_DIR ${CADABRA_ROOT_DIR}/images)\nset(CADABRA_LIBS_DIR ${CADABRA_ROOT_DIR}/libs)\n\ninclude(cmake/functions.cmake)\n\n# Include Visual Studio specific build commands\nif (MSVC)\n  # https://developercommunity.visualstudio.com/content/problem/618088/cmake-msvc-toolset-version-is-incorrect-in-visual.html\n  if ((MSVC_VERSION EQUAL 1921 OR MSVC_VERSION EQUAL 1922) AND MSVC_TOOLSET_VERSION EQUAL 141)\n\t set(MSVC_TOOLSET_VERSION 142)\n  endif()\n  message(STATUS \"MSVC_VERSION = ${MSVC_VERSION}, MSVC_TOOLSET_VERSION = ${MSVC_TOOLSET_VERSION}\")\n  include(cmake/windows.cmake)\nendif()\n\n# Make sure the build type is non-empty.\nif(NOT DEFINED CMAKE_BUILD_TYPE OR CMAKE_BUILD_TYPE STREQUAL \"\")\n  set(CMAKE_BUILD_TYPE \"Release\")\nendif()\nset(CADABRA_BUILD_TYPE \"${CMAKE_BUILD_TYPE}\")\nif (CMAKE_BUILD_TYPE MATCHES \"^Debug$\")\n  set(CADABRA_DEBUG_BUILD TRUE)\nendif()\nmessage(STATUS \"Build type = ${CMAKE_BUILD_TYPE}\")\n\n# Set path to additional cmake files\nset(CMAKE_MODULE_PATH ${CMAKE_MODULE_PATH} \"${CMAKE_SOURCE_DIR}/cmake/modules\")\nif (APPLE)\n   set(ENV{PKG_CONFIG_PATH} \"/usr/local/opt/libffi/lib/pkgconfig:\")\nendif()\n\nset(PKG_CONFIG_USE_STATIC_LIBS OFF)\n\nif(NOT APPLE)\n  find_package(TBB QUIET)  \n  if(TBB_FOUND)\n    message(STATUS \"TBB found, will make some operations parallel\")\n  else()\n    message(STATUS \"TBB not found, parallel operations disabled\")\n  endif()\nelse()\n  message(STATUS \"Apple's toolchain not yet supporting TBB properly, disabled\")\nendif()\n\n# Get version information.\ninclude(cmake/version.cmake)\nprint_header(\"Building Cadabra version ${CADABRA_VERSION_SEM} (${SYSTEM_BITS}-bit)\")\nmessage(STATUS \"Build id '${CADABRA_VERSION_BUILD}' dated ${CADABRA_VERSION_DATE}\")\nmessage(STATUS \"Build mode is set to '${CMAKE_BUILD_TYPE}'\")\nstring(TOLOWER ${CMAKE_SYSTEM_PROCESSOR} STANDARD_ARCH_NAME)\nif(STANDARD_ARCH_NAME STREQUAL \"aarch64\")\n  set(STANDARD_ARCH_NAME \"arm64\")\nendif()\nif(STANDARD_ARCH_NAME STREQUAL \"amd64\")\n  set(STANDARD_ARCH_NAME \"x86_64\")\nendif()\nmessage(STATUS \"Architecture is '${CMAKE_SYSTEM_PROCESSOR}' (package names will use '${STANDARD_ARCH_NAME}')\")\nif(WIN32)\n  if(\"${STANDARD_ARCH_NAME}\" STREQUAL \"x86_64\")\n    set(MSYS_ENV \"ucrt64\")\n    set(WIX_SHORT_ARCH \"x64\")\n  else()\n    set(MSYS_ENV \"clangarm64\")\n    set(WIX_SHORT_ARCH \"arm64\")\n  endif()\n  message(STATUS \"MSYS environment set to ${MSYS_ENV}\")\nendif()\n\n# Store the version number in a build/VERSION file (so that e.g. github\n# actions can pick it up).\nfile(WRITE build/VERSION         \"${CADABRA_VERSION_SEM}\")\nfile(WRITE build/GIT_TAG_VERSION \"${CADABRA_VERSION_GITHUB_TAG}\")\n\n# Notify about install directory\nif (\"${CMAKE_INSTALL_PREFIX}\" STREQUAL \"\")\n\tmessage(STATUS \"Install directory not set\")\nelse()\n\tmessage(STATUS \"Install directory set to ${CMAKE_INSTALL_PREFIX}\")\nendif()\n\n# Turn Mathematica support on/off.\noption(ENABLE_MATHEMATICA \"Enable Mathematica support\" OFF)\n\n# Are we trying to build cadabra as a c++ library?\noption(BUILD_AS_CPP_LIBRARY \"Build cadabra as a C++ library\" OFF)\nif (BUILD_AS_CPP_LIBRARY)\n  enable_testing()\n  add_subdirectory(c++lib)\n  configure_file(\n\t \"${PROJECT_SOURCE_DIR}/core/Config.hh.in\"\n\t \"${PROJECT_SOURCE_DIR}/core/Config.hh\"\n    )\n  # Bail out early.\n  return()\nendif()\n\n# Switch between GTK4 and GTK3.\noption(USE_GTK4 \"Build for GTK4 (instead of GTK3)\" OFF)\n\n# Include packaging logic.\ninclude(cmake/packaging.cmake)\n\n#---------------------------------------------------------------------------\n# User options and other notifications\n#---------------------------------------------------------------------------\n\n#\noption(MSVC_TARGET_CONSOLE \"Force Release book on MSVC to display a console window\" OFF)\n\noption(APPIMAGE_MODE \"Run in AppImage mode, overriding path settings\" OFF)\nif(APPIMAGE_MODE)\n  message(STATUS \"Building for AppImage packaging (Debian paths, MicroTeX)\")\n  if(\"${CMAKE_INSTALL_PREFIX}\" STREQUAL \"/usr\")\n  else()\n    MESSAGE(FATAL_ERROR \"Building with -DAPPIMAGE_MODE=ON also requires -DCMAKE_INSTALL_PREFIX=/usr\")\n  endif()\nendif()\n\noption(PACKAGING_MODE \"Run in packaging mode, overriding path settings\" OFF)\nif (PACKAGING_MODE)\n\tmessage(STATUS \"Building in packaging mode\")\n\tif(\"${CMAKE_INSTALL_PREFIX}\" STREQUAL \"/usr\")\n\telse()\n\t\tMESSAGE(FATAL_ERROR \"Building with -DPACKAGING_MODE=ON also requires -DCMAKE_INSTALL_PREFIX=/usr\")\n\tendif()\nelse()\n\tmessage(STATUS \"Building in user mode\")\nendif()\n\noption(ENABLE_JUPYTER    \"Enable building the Xeus-based Jupyter kernel\" OFF)\noption(ENABLE_PY_JUPYTER \"Enable building the default Jupyter kernel\"    ON)\n\nif(ENABLE_JUPYTER)\n  # Currently only possible when building against Conda.\n  set(CONDA_FOUND TRUE)\nelse()\n   set(CONDA_FOUND FALSE)\nendif()\n\noption(BUILD_TESTS \"Build tests\" ON)\nif (BUILD_TESTS)\n  message(STATUS \"Building tests\")\n  # Allows tests to be built in all subdirectories.\n  enable_testing()\nendif()\n\noption(ENABLE_FRONTEND    \"Enable the UI frontend\" ON)\n\noption(ENABLE_SYSTEM_JSONCPP \"Use the system-provided jsoncpp library\" OFF)\n\noption(INSTALL_TARGETS_ONLY \"Only install targets; skipping icons, shared libraries etc...\" OFF)\nif (INSTALL_TARGETS_ONLY)\n\tmessage(STATUS \"INSTALL_TARGETS_ONLY is enabled, please make sure all auxillary files and programs Cadabra requires are already installed\")\nendif()\n\n#---------------------------------------------------------------------------\n# Compiler flags.\n#---------------------------------------------------------------------------\n\n# - Set the C++ standard to C++17\n# - Turn optimizations on\n# - Turn off warnings we don't need\n\ninclude(CheckIPOSupported)\ncheck_ipo_supported(RESULT IPO_SUPPORTED OUTPUT error)\nif( IPO_SUPPORTED )\n    message(STATUS \"IPO / LTO enabled\")\nelse()\n    message(STATUS \"IPO / LTO not supported: <${error}>\")\nendif()\n\n\n\n# GCC\nif(CMAKE_COMPILER_IS_GNUCC OR CMAKE_COMPILER_IS_GNUCXX)\n  if (ENABLE_FRONTEND)\n    if (CMAKE_CXX_COMPILER_VERSION VERSION_LESS 4.9)\n      message(FATAL_ERROR \"GCC version must be at least 4.9 for regex support! See http://askubuntu.com/questions/428198/getting-installing-gcc-g-4-9-on-ubuntu and then set the environment variables CXX to g++-4.9 and CC to gcc-4.9. You may have to erase the build directory before re-running cmake.\")\n    endif()\n    if (CMAKE_CXX_COMPILER_VERSION VERSION_LESS 14.0)\n      message(STATUS \"This version of g++ (${CMAKE_CXX_COMPILER_VERSION}) incorrectly warns about possibly uninitialised memory when using std::variant containing a std::shared_ptr. Disabling this warning.\")\n      set(CMAKE_CXX_FLAGS \"${CMAKE_CXX_FLAGS} -Wno-maybe-uninitialized\")\n    endif()\n  endif()\n  set(CMAKE_CXX_FLAGS \"${CMAKE_CXX_FLAGS} -g -O2 -Wall -Wextra -Wunused -Wno-psabi -Wno-unknown-pragmas -Wno-misleading-indentation -fvisibility=hidden -Wno-unused-but-set-variable -Wno-unused-parameter\")\nendif()\n\n# Clang\nif(\"${CMAKE_CXX_COMPILER_ID}\" STREQUAL \"Clang\")\n  # For Clang, need to additionally check version to avoid compiler bugs\n  if (CMAKE_CXX_COMPILER_VERSION VERSION_LESS 3.5)\n    message(FATAL_ERROR \"Clang version must be at least 3.5 to avoid known bugs.\")\n  endif()\n  set(CMAKE_CXX_FLAGS \"${CMAKE_CXX_FLAGS} -g -O2 -fvisibility=hidden -Wall -Wextra -Wunused -Wno-unused-parameter -Wno-null-pointer-subtraction\")\nendif()\n\n# Visual Studio\nif(MSVC)\n  set(CMAKE_WINDOWS_EXPORT_ALL_SYMBOLS ON)\n  # Disable specific warnings\n  set(MSVC_FLAGS\n    \"/wd4250\"\t\t\t\t\t\t# inherits via dominance (rampant in the GTKMM codebase)\n    \"/wd4101\"\t\t\t\t\t\t# unreferenced local variable\n    \"/wd4244\"\t\t\t\t\t\t# conversion from x to y, possible loss of data\n    \"/wd4267\"\t\t\t\t\t\t# same as 4244\n    \"/wd4305\"\t\t\t\t\t\t# truncation from '' to 'char'\n    \"/wd4309\"\t\t\t\t\t\t# truncation of constant value\n    \"/wd4390\"\t\t\t\t\t\t# empty control statement, due to a DEBUG macro which requires trailing ;\n    \"/wd4996\"\t\t\t\t\t\t# deprecated POSIX functions\n    \"-D_CRT_SECURE_NO_WARNINGS\"\t\t# don't warn about deprecated functions\n    \"-D_SCL_SECURE_NO_WARNINGS\"\t\t# don't warn about unsafe function calls (e.g. std::copy with raw pointers)\n    \"-DNOMINMAX\"\t\t\t\t\t# prevent windows headers from defining min and max macros\n    \"-DWIN32_LEAN_AND_MEAN\"\t\t\t# stop windows from including a bunch of garbage\n    \"-DBOOST_ALL_DYN_LINK\"\t\t\t# ensure boost's auto-linking is enabled\n  )\n  foreach(FLAG ${MSVC_FLAGS})\n    set(CMAKE_CXX_FLAGS \"${CMAKE_CXX_FLAGS} ${FLAG}\")\n  endforeach()\nendif()\n\n\n#---------------------------------------------------------------------------\n# Configure the various parts of Cadabra.\n#---------------------------------------------------------------------------\n\n# if(MATHEMATICA_FOUND)\n#    # To avoid issues finding Mathematica's libWSTP64i4,\n#    # when linking to Mathematica we set the RPATH.\n#    # That's not something we want to do in general, as e.g. Debian's\n#    # packages are not supposed to set RPATH.\n#    SET(CMAKE_SKIP_BUILD_RPATH  FALSE)\n#    SET(CMAKE_BUILD_WITH_INSTALL_RPATH FALSE)\n#    SET(CMAKE_INSTALL_RPATH \"${CMAKE_INSTALL_PREFIX}/lib\")\n#    SET(CMAKE_INSTALL_RPATH_USE_LINK_PATH TRUE)\n# endif()\n\nconfigure_file(\n\t\"${CMAKE_CURRENT_SOURCE_DIR}/config/postinst.in\"\n\t\"${CMAKE_CURRENT_BINARY_DIR}/postinst\"\n\t@ONLY\n)\nconfigure_file(\n   \"${CMAKE_CURRENT_SOURCE_DIR}/config/install_script.iss.in\"\n   \"${CMAKE_CURRENT_SOURCE_DIR}/config/install_script.iss\"\n   )\nconfigure_file(\n   \"${CMAKE_CURRENT_SOURCE_DIR}/config/pre_install.rtf.in\"\n   \"${CMAKE_CURRENT_SOURCE_DIR}/config/pre_install.rtf\"\n   )\nconfigure_file(\n   \"${CMAKE_CURRENT_SOURCE_DIR}/config/science.cadabra.cadabra2-gtk.desktop.in\"\n   \"${CMAKE_CURRENT_SOURCE_DIR}/config/science.cadabra.cadabra2-gtk.desktop\"\n   )\nconfigure_file(\n  \"${CMAKE_CURRENT_SOURCE_DIR}/frontend/gtkmm/science.cadabra.cadabra2-gtk.appdata.xml.in\"\n  \"${CMAKE_CURRENT_SOURCE_DIR}/frontend/gtkmm/science.cadabra.cadabra2-gtk.appdata.xml\"  \n)\n\n\n#---------------------------------------------------------------------------\n# Configure Mathematica (if enabled).\n#---------------------------------------------------------------------------\n\nif(ENABLE_MATHEMATICA)\n   print_header(\"Configuring Mathematica\")\n   cmake_policy(SET CMP0077 NEW)\n   set(Mathematica_USE_STATIC_LIBRARIES TRUE)\n   find_package(Mathematica COMPONENTS WSTP)\nendif()\n\n\n#---------------------------------------------------------------------------\n# Configure Python.\n#---------------------------------------------------------------------------\n\nprint_header(\"Configuring Python\")\n\ninclude(GNUInstallDirs)\n\nset(Python_POSTFIX \"3\")\nfind_package(Python REQUIRED COMPONENTS Interpreter Development)\nset(PYTHON_EXECUTABLE ${Python_EXECUTABLE} CACHE INTERNAL \"\")\nset(PYBIND11_PYTHON_VERSION ${Python_VERSION} CACHE INTERNAL \"\")\nfind_package(pybind11 CONFIG)\nif (NOT pybind11_FOUND OR pybind11_VERSION VERSION_LESS 2.13.6)\n  if(pybind11_FOUND)\n    message(STATUS \"Found pybind11 with version ${pybind11_VERSION} < 2.13.6, using included pybind11 instead.\")\n  else()\n    message(STATUS \"System-supplied pybind11 not found, using included pybind11.\")\n  endif()\n  add_subdirectory(libs/pybind11)\nendif()\n\nmessage(STATUS \"Found python ${Python_LIBRARIES}\")\nmessage(STATUS \"Python version is ${Python_VERSION_MAJOR}.${Python_VERSION_MINOR}.\")\n\n# The PYTHON_SITE_PATH variable is used for installation purposes\n# only. It is ideally a path relative to CMAKE_INSTALL_PREFIX, not an\n# absolute path which uses this variable explictly. See the CMake docs\n# for `install`.\nif(WIN32)\n  set(PYTHON_SITE_PATH lib/python${Python_VERSION_MAJOR}.${Python_VERSION_MINOR}/site-packages)\n  # NOTE: if you change the CDB_BIN_PATH, you also need to change the stripping\n  # logic in InstallPrefix.cc. Note that CDB_BIN_PATH needs to be a relative path.\n  set(CDB_BIN_PATH .)\nelse()\n  set(CDB_BIN_PATH bin)\n  if(PACKAGING_MODE AND IS_DEBIAN_PACKAGE)\n    # Debian packages install all their Python things in 'dist-packages', not 'site-packages'.\n    set(PYTHON_SITE_PATH lib/python${Python_VERSION_MAJOR}.${Python_VERSION_MINOR}/dist-packages)\n    # set(Python_SITE_DIST \"dist-packages\")\n  elseif(APPIMAGE_MODE)\n    set(PYTHON_SITE_PATH lib/python${Python_VERSION_MAJOR}.${Python_VERSION_MINOR}/dist-packages)\n    set(Python_SITE_DIST \"dist-packages\")\n  else()\n    # The builder can override the path by setting it externally.\n    if(NOT DEFINED PYTHON_SITE_PATH)\n      # set(PYTHON_SITE_PATH ${Python_SITEARCH})\n      # For everyone else there is 'site-packages' which we get from\n      # calling into python's 'site' package (and hoping that the 0th\n      # element is where we should be writing).\n      execute_process(\n\tCOMMAND ${Python_EXECUTABLE} -c \"import site; print(site.getsitepackages()[0])\"\n\tOUTPUT_VARIABLE PYTHON_SITE_PATH\n\tOUTPUT_STRIP_TRAILING_WHITESPACE\n      )\n    endif()\n  endif()\nendif()\nif(IS_ABSOLUTE ${PYTHON_SITE_PATH})\n  # CPack on windows complains if `install` commands contain absolute paths,\n  # so we do our best to make PYTHON_SITE_PATH relative to CMAKE_INSTALL_PREFIX.\n  # Of course, the net effect will be the same, as `install` with a relative\n  # DESTINATION will prepend CMAKE_INSTALL_PREFIX.\n  message(STATUS \"Making PYTHON_SITE_PATH relative if possible\")\n  string(REPLACE \"${CMAKE_INSTALL_PREFIX}/\" \"\" PYTHON_SITE_PATH_REL \"${PYTHON_SITE_PATH}\")\n  set(PYTHON_SITE_PATH ${PYTHON_SITE_PATH_REL})\nelse()\n  message(STATUS \"PYTHON_SITE_PATH is already relative\")\nendif()\n\nmessage(STATUS \"PYTHON_SITE_PATH = ${PYTHON_SITE_PATH}\")\nif(IS_ABSOLUTE ${PYTHON_SITE_PATH})\n  message(STATUS \"Installing Cadabra Python module in ${PYTHON_SITE_PATH}\")\n  message(STATUS \"Installing Cadabra packages in ${PYTHON_SITE_PATH}/cdb/\")\nelse()\n  message(STATUS \"Installing Cadabra Python module in ${CMAKE_INSTALL_PREFIX}/${PYTHON_SITE_PATH}\")\n  message(STATUS \"Installing Cadabra packages in ${CMAKE_INSTALL_PREFIX}/${PYTHON_SITE_PATH}/cdb/\")\nendif()\nmessage(STATUS \"Installing binaries in ${CMAKE_INSTALL_PREFIX}/bin/\")\nmessage(STATUS \"Installing manual pages in ${CMAKE_INSTALL_PREFIX}/share/man/\")\nmessage(STATUS \"Installing fonts/icons in ${CMAKE_INSTALL_PREFIX}/share/cadabra2/\")\nif(\"${Python_CDB_EXECUTABLE}\" STREQUAL \"\")\n  # We start the cadabra2 python script by using the current environment,\n  # so that e.g. Fedora 42 does not hard-code the python path as a\n  # dependency. However, on macOS with Homebrew, we need to be able\n  # to override this because otherwise we will not be running in the\n  # venv which homebrew created for our package. See cadabra2.rb and\n  # cadabra2-devel.rb where this is used.\n  set(Python_CDB_EXECUTABLE \"/usr/bin/env python3\")\nendif()\nmessage(STATUS \"Starting cadabra2 using '${Python_CDB_EXECUTABLE}'\")\nmessage(STATUS \"For reference:\")\nmessage(STATUS \"  Python executable (Python_EXECUTABLE)                                          ${Python_EXECUTABLE}\")\nmessage(STATUS \"  Python standard  platform-independent installation directory (Python_STDLIB)   ${Python_STDLIB}\")\nmessage(STATUS \"  Python standard  platform-dependent   installation directory (Python_STDARCH)  ${Python_STDARCH}\")\nmessage(STATUS \"  Python 3rd-party platform-independent installation directory (Python_SITELIB)  ${Python_SITELIB}\")\nmessage(STATUS \"  Python 3rd-party platform-dependent   installation directory (Python_SITEARCH) ${Python_SITEARCH}\")\n# We need to give our Python module an abi-name extension\n# so that it can be installed in a folder which does not\n# contain the abi name. See\n# https://www.python.org/dev/peps/pep-3149/\nexecute_process(\n\tCOMMAND ${Python_EXECUTABLE} -c \"import sysconfig; print(sysconfig.get_config_var('SOABI'))\"\n\tOUTPUT_VARIABLE Python_SOABI\n\tOUTPUT_STRIP_TRAILING_WHITESPACE\n\t)\nmessage(STATUS \"Python abi name ${Python_SOABI}\")\n\n# Suffixes\nif(WIN32)\n\tset(STATIC_LIB_SUFFIX \"lib\")\n\tset(SHARED_LIB_SUFFIX \"dll\")\n\tset(Python_MOD_SUFFIX \"pyd\")\n\tset(CMAKE_FIND_LIBRARY_PREFIXES \"lib\" ${CMAKE_FIND_LIBRARY_PREFIXES})\n\tset(CMAKE_SHARED_LIBRARY_SUFFIX \".dll\")\n\tset(CMAKE_FIND_LIBRARY_SUFFIXES \".dll.a\")\nelse()\n\tset(STATIC_LIB_SUFFIX \"a\")\n\tset(SHARED_LIB_SUFFIX \"so\")\n\tset(Python_MOD_EXT    \"so\")   \n\tset(Python_MOD_SUFFIX \"${Python_SOABI}.so\")\nendif()\n\nmessage(STATUS \"Python module extension ${Python_MOD_SUFFIX}\")\n\n\n#---------------------------------------------------------------------------\n# Add subdirectories to project.\n#---------------------------------------------------------------------------\n\nprint_header(\"Build tools and options\")\n# Mimalloc makes the cadabra2 module crash when run\n# as jupyter kernel, so disable for now.\n#find_package(mimalloc 2.0 QUIET)\nif(mimalloc_FOUND)\n  message(STATUS \"Using mimalloc allocator\")\nelse()\n  message(STATUS \"Using glibc allocator\")\nendif()\nfind_package(Catch2 3 QUIET) # This is optional; we will not run the C++ tests if Catch2 is not found\nif(Catch2_FOUND)\n  message(STATUS \"Will run C++ tests with Catch2\")\n  include(Catch)\nelse()\n  message(STATUS \"Catch2 not found, will not run C++ tests\")\nendif()\n\n# Jupyter kernel\nprint_header(\"Configuring Jupyter kernel\")\nif(ENABLE_JUPYTER)\n  message(STATUS \"Building the Xeus-based Jupyter kernel\")\n  # Currently only possible when building against Conda.\n  set(CONDA_FOUND TRUE)\nelse()\n   set(CONDA_FOUND FALSE)\n   if(ENABLE_PY_JUPYTER)\n      message(STATUS \"Building the default Jupyter kernel\")\n   else()\n      message(STATUS \"Not building a Jupyter kernel\")\n   endif()\nendif()\nif(ENABLE_PY_JUPYTER)\n   add_subdirectory(jupyterkernel)\nendif()\n\n# Core/packages\nadd_subdirectory(client_server)\nadd_subdirectory(core)\n\n# Frontend\nif(ENABLE_FRONTEND)\n  set(ENABLE_MICROTEX TRUE)\n  if(ENABLE_MICROTEX)\n    set(USE_MICROTEX TRUE)\n    set(tinyxml2_BUILD_TESTING FALSE)\n  endif()\n  add_subdirectory(frontend)\nendif()\n\n# Tests\nif(BUILD_TESTS)\n  add_subdirectory(tests)\nendif()\n\nadd_subdirectory(web2 EXCLUDE_FROM_ALL)\n\n# Generate the core/Config.hh file; this needs to come as late as possible\n# in this CMakeLists.txt to ensure that all variables have been set.\nconfigure_file(\n\t\"${PROJECT_SOURCE_DIR}/core/Config.hh.in\"\n\t\"${PROJECT_SOURCE_DIR}/core/Config.hh\"\n)\n\n# Some additional logic to install all runtime dependencies of our binaries\n# into the target installation directory on windows. \nif(WIN32)\n  set(EXECUTABLES\n    core/cadabra2-cli\n    core/cdb-nbtool\n    client_server/cadabra-server\n    frontend/gtkmm/cadabra2-gtk\n  )\n  list(JOIN EXECUTABLES \" \" LEXECUTABLES)\n  # Custom command to run ldd, get dependencies, and install these in a\n  # folder ready to be processed by `install`. The 'ldd' command does not\n  # run on the '*.pyd' file, but if we rename or copy it to have extension '.dll'\n  # all goes through fine...\n  set(LDDSTR \"ldd /${MSYS_ENV}/lib/gdk-pixbuf-2.0/2.10.0/loaders/pixbufloader_svg.dll core/cadabra2.dll ${LEXECUTABLES} | sed -e '/not found/d' -e '/Windows/d' -e '/System32/d' -e '/SysWOW64/d' | grep '=>' | sed -e 's/^[^=]*=>[ ]*\\\\([^ ]*\\\\).*/\\\\1/' | sort | uniq > ${CMAKE_BINARY_DIR}/ldd_dependencies.txt\")\n  message(STATUS \"Determining dependencies using command ${LDDSTR}\")\n  add_custom_command(\n    OUTPUT  dummy1\n    COMMAND cp core/cadabra2.pyd core/cadabra2.dll\n    COMMAND ${CMAKE_COMMAND} -E env bash -c \"${LDDSTR}\"\n    COMMAND touch dummy1\n    VERBATIM\n    DEPENDS  core/cadabra2.pyd ${EXECUTABLES}\n    COMMENT \"Using ldd to determine dependencies of ${EXECUTABLES}\"\n  )\n  add_custom_command(\n    OUTPUT dummy2\n    DEPENDS dummy1\n    COMMAND ${CMAKE_COMMAND} -E env bash -c \"cat ${CMAKE_BINARY_DIR}/ldd_dependencies.txt && mkdir -p ${CMAKE_SOURCE_DIR}/deps && for f in `cat ${CMAKE_BINARY_DIR}/ldd_dependencies.txt`; do cp \\${f} ${CMAKE_SOURCE_DIR}/deps/; done\"\n    COMMAND touch dummy2\n    VERBATIM\n    COMMENT \"Copying dependencies into ${CMAKE_SOURCE_DIR}/deps\"\n  )\n  add_custom_target(\"do_deps\" ALL DEPENDS dummy2)\n  \n  # Install all the dependencies into the root destination folder.\n  install(DIRECTORY deps/ DESTINATION . FILES_MATCHING PATTERN \"*.dll\")      \n\n  # And install a few more which, for reasons unknown, are not reported by dll.\n  install(CODE \"execute_process(COMMAND ls \\\"/${MSYS_ENV}/bin\\\") \" )\n  winstall(FILES /${MSYS_ENV}/bin/libcharset-1.dll                DESTINATION .)\n  winstall(FILES /${MSYS_ENV}/bin/librsvg-2-2.dll                 DESTINATION .)  \n  winstall(FILES /${MSYS_ENV}/bin/libxml2-2.dll                   DESTINATION .)  \n  winstall(FILES /${MSYS_ENV}/bin/liblzma-5.dll                   DESTINATION .)\n  # FIXME: these can be found by running ldd on numpy and matplotlib dlls.\n  winstall(FILES /${MSYS_ENV}/bin/libopenblas.dll                 DESTINATION .)  \n  winstall(FILES /${MSYS_ENV}/bin/libgomp-1.dll                   DESTINATION .)  \n  winstall(FILES /${MSYS_ENV}/bin/libgfortran-5.dll               DESTINATION .)  \n  winstall(FILES /${MSYS_ENV}/bin/libquadmath-0.dll               DESTINATION .)  \n  winstall(FILES /${MSYS_ENV}/bin/libsharpyuv-0.dll               DESTINATION .)  \n  winstall(FILES /${MSYS_ENV}/bin/libjpeg-8.dll                   DESTINATION .)  \n  winstall(FILES /${MSYS_ENV}/bin/libtiff-6.dll                   DESTINATION .)  \n  winstall(FILES /${MSYS_ENV}/bin/libdeflate.dll                  DESTINATION .)  \n  winstall(FILES /${MSYS_ENV}/bin/libjbig-0.dll                   DESTINATION .)  \n  winstall(FILES /${MSYS_ENV}/bin/libLerc.dll                     DESTINATION .)  \n  winstall(FILES /${MSYS_ENV}/bin/libwebp-7.dll                   DESTINATION .)  \n  winstall(FILES /${MSYS_ENV}/bin/libzstd.dll                     DESTINATION .)  \n  winstall(FILES /${MSYS_ENV}/bin/libimagequant.dll               DESTINATION .)  \n  winstall(FILES /${MSYS_ENV}/bin/libopenjp2-7.dll                DESTINATION .)  \n\n  # These are necessary only on ARM64.\n  winstall(FILES /${MSYS_ENV}/bin/libgmp-10.dll                   DESTINATION .)  \n  winstall(FILES /${MSYS_ENV}/bin/libgmpxx-4.dll                  DESTINATION .)  \n  \n  # We need gdbus to setup the dbus, needed by Glib, otherwise anything\n  # gtk-related will just bail out at start. We also need the helper\n  # program to spawn programs using Glib.\n  winstall(FILES /${MSYS_ENV}/bin/gdbus.exe                       DESTINATION .)\n  winstall(FILES /${MSYS_ENV}/bin/gspawn-win64-helper.exe         DESTINATION .)\n  winstall(FILES /${MSYS_ENV}/bin/gspawn-win64-helper-console.exe DESTINATION .)\n  winstall(FILES /${MSYS_ENV}/bin/gdk-pixbuf-query-loaders.exe    DESTINATION .)\nendif()\n    \n#---------------------------------------------------------------------------\n# Provide uninstall target.\n#---------------------------------------------------------------------------\n\nconfigure_file(\n\t\"${CMAKE_CURRENT_SOURCE_DIR}/cmake/cmake_uninstall.cmake.in\"\n\t\"${CMAKE_CURRENT_BINARY_DIR}/cmake/cmake_uninstall.cmake\"\n\tIMMEDIATE @ONLY\n)\n\nadd_custom_target(uninstall\n\t\"${CMAKE_COMMAND}\" -P \"${CMAKE_CURRENT_BINARY_DIR}/cmake/cmake_uninstall.cmake\"\n)\n\n#---------------------------------------------------------------------------\n# Provide target to build AppImage.\n#---------------------------------------------------------------------------\n\n# if(APPIMAGE_MODE)\n#   add_custom_target(appimage\n#     COMMAND mkdir -p AppDir/${Python_SITELIB}\n#     COMMAND cp -a ${CMAKE_SOURCE_DIR}/config/AppRun AppDir/\n#     COMMAND chmod gou+x ${CMAKE_SOURCE_DIR}/config/AppRun AppDir/AppRun\n#     COMMAND cp -a ${Python_SITELIB}/setuptools AppDir/${Python_SITELIB}/\n#     COMMAND cp -a ${Python_STDARCH}/* AppDir/${Python_STDARCH}/\n#   )\n# endif()\n\nif(WIN32)\n  add_custom_target(windows-installer\n    COMMAND cpack\n#    COMMAND osslsigncode sign -pkcs12 \"/mnt/c/path/to/certificate.p12\" -pass \"certificate password\" -n \"Cadabra2\" -i \"https://cadabra.science\" -t \"http://timestamp.comodoca.com/authenticode\" -in \"cadabra2-${CADABRA_VERSION_SEM}-win64.exe\" -out \"cadabra2-${CADABRA_VERSION_SEM}-win64-installer.exe\"\n    COMMAND gh auth setup-git\n    COMMAND release upload \"${CADABRA_VERSION_SEM}\" cadabra2-${CADABRA_VERSION_SEM}-win64.msi --clobber\n  )\nendif()\n\nprint_header(\"All scripts completed\")\n"
  },
  {
    "path": "CODE_OF_CONDUCT.md",
    "content": "# Contributor Covenant Code of Conduct\n\n## Our Pledge\n\nIn the interest of fostering an open and welcoming environment, we as contributors and maintainers pledge to making participation in our project and our community a harassment-free experience for everyone, regardless of age, body size, disability, ethnicity, gender identity and expression, level of experience, nationality, personal appearance, race, religion, or sexual identity and orientation.\n\n## Our Standards\n\nExamples of behavior that contributes to creating a positive environment include:\n\n* Using welcoming and inclusive language\n* Being respectful of differing viewpoints and experiences\n* Gracefully accepting constructive criticism\n* Focusing on what is best for the community\n* Showing empathy towards other community members\n\nExamples of unacceptable behavior by participants include:\n\n* The use of sexualized language or imagery and unwelcome sexual attention or advances\n* Trolling, insulting/derogatory comments, and personal or political attacks\n* Public or private harassment\n* Publishing others' private information, such as a physical or electronic address, without explicit permission\n* Other conduct which could reasonably be considered inappropriate in a professional setting\n\n## Our Responsibilities\n\nProject maintainers are responsible for clarifying the standards of acceptable behavior and are expected to take appropriate and fair corrective action in response to any instances of unacceptable behavior.\n\nProject maintainers have the right and responsibility to remove, edit, or reject comments, commits, code, wiki edits, issues, and other contributions that are not aligned to this Code of Conduct, or to ban temporarily or permanently any contributor for other behaviors that they deem inappropriate, threatening, offensive, or harmful.\n\n## Scope\n\nThis Code of Conduct applies both within project spaces and in public spaces when an individual is representing the project or its community. Examples of representing a project or community include using an official project e-mail address, posting via an official social media account, or acting as an appointed representative at an online or offline event. Representation of a project may be further defined and clarified by project maintainers.\n\n## Enforcement\n\nInstances of abusive, harassing, or otherwise unacceptable behavior may be reported by contacting the project team at kasper.peeters@phi-sci.com. The project team will review and investigate all complaints, and will respond in a way that it deems appropriate to the circumstances. The project team is obligated to maintain confidentiality with regard to the reporter of an incident. Further details of specific enforcement policies may be posted separately.\n\nProject maintainers who do not follow or enforce the Code of Conduct in good faith may face temporary or permanent repercussions as determined by other members of the project's leadership.\n\n## Attribution\n\nThis Code of Conduct is adapted from the [Contributor Covenant][homepage], version 1.4, available at [http://contributor-covenant.org/version/1/4][version]\n\n[homepage]: http://contributor-covenant.org\n[version]: http://contributor-covenant.org/version/1/4/\n"
  },
  {
    "path": "CONTRIBUTING.md",
    "content": "How to contribute\n=================\n\nIf you want to help out with Cadabra, or think you can contribute a\nuseful add-on package or perhaps just a sample notebook or a bit of\ndocumentation, you are more than welcome! Even just dropping us a\nnote with some details about what computations you do with Cadabra\nis a useful contribution, and helps to get a better idea of what\npeople expect from the software. \n\nBelow are some tips on how to get started contributing to Cadabra. For\nany questions, please post in the [questions and answers][1] forum or\nget in touch directly via [email][2]\n\n\nGet familiar with the software\n------------------------------\n\nThe first thing to do is to get familiar with how the software works,\nby playing with the [tutorials][3] Details of the software, including\nsome of the logic that is behind its inner workings, are described in\nthe [reference guide][4], and documentation is available separately\nfor all [properties and algorithms][5]. If you get stuck, do not\nhesitate to post a question on the [questions and answers][1] site. If\nyou want to contribute at the level of the C++ core, or if you are\nsimply interested in how things work behind the scenes, you will find\nthe [doxygen][6] documentation useful.\n\n\nIdentify something to work on\n-----------------------------\n\nMost likely you will have used (or will have tried to use) Cadabra for\na concrete project, and found that you see room for improvement. This\ncan be as simple as reporting a bug, perhaps even fixing it, or adding\na tutorial or other documentation, providing add-on functionality in\nthe form of packages, or helping with the core. We are also always\ninterested to hear about issues installing Cadabra on new systems.\n\n\nSetup your development environment\n----------------------------------\n\nContributions in any form are welcome, but if you want to submit\nsubstantial code contributions, it is useful to get familiar with the\ngit version control system. This is used to track software changes\nover time and to effectively manage contributions from different\nauthors. We also utilise [github][7], a web interface to git,\nextensively and use it for communication, issue tracking, merging\npatches (pull requests) and so on. Check out the source code from\nthere and follow the instructions on how to build it.\n\n\nCode conventions\n----------------\n\nTo generate debug output, we use the [dbg][8] facility. To turn this\non for a particular source file, comment out the `DBG_MACRO_DISABLE`\ndefinition at the top. You will then get nicely formatted debug output\nwhile running.\n\nCode is formatted using tabs for indentation, K&R style braces,\nwith some fine-tuning. All is taken care of by `make format` in the\ntop-level directory, which runs through the entire source tree and\ndoes a reformat using `astyle`.\n\n\nDocumentation\n-------------\n\nWe have tutorials, manual pages and reference documentation. In\naddition, there are user-contributed notebooks. In this sense, we try\nto follow [divio][9]. Contributions to all of these parts of the\ndocumentation are welcome.\n\n\n[1] https://cadabra.science/qa/\n[2] mailto:info@cadabra.science\n[3] https://cadabra.science/tutorials.html\n[4] https://cadabra.science/help.html\n[5] https://cadabra.science/man.html\n[6] https://cadabra.science/doxygen/html/\n[7] https://github.com/kpeeters/cadabra2\n[8] https://github.com/sharkdp/dbg-macro\n[9] https://www.divio.com/blog/documentation/\n"
  },
  {
    "path": "JUPYTER.rst",
    "content": "Building the Cadabra Jupyter kernel\n===================================\n\nThe Cadabra build scripts can now build a Jupyter kernel, so that you\ncan use the Jupyter notebook to write Cadabra code (using all of the\nCadabra notation, i.e. without having to resort to the much more ugly\nPython interface). At the moment this is only supported by compiling\nagainst a Conda python, simply because that enables us to build on the\n'xeus' library more easily.\n\nBuilding a Conda package\n------------------------\n\nAfter installation, first activate your miniconda distribution::\n\n    source ~/miniconda3/bin/activate\n\nAll dependencies to build a Conda package of Cadabra can then be\ninstalled from Conda directly, with::\n\n    conda install conda-build\n\nThen build with::\n\n    cd conda\n    conda-build .\n    \nTo install::\n\n    conda install --use-local cadabra2\n\n\n\n    \n\nBuilding using Conda (old)\n--------------------------\n\nThe following instructions have been tested on a clean Ubuntu 18.04\ninstallation.\n\nThe Cadabra Jupyter kernel uses the Xeus library, which is most easily\nobtained by getting it from Conda. If you do not have Conda yet, get\na minimal installation (MiniConda) from\n\n  https://docs.conda.io/en/latest/miniconda.html\n\n(install a Python3.x version).  \n\nWhen building against Conda, Cadabra will build only the Python module\nand the cadabra-jupyter-kernel binary. It is not possible to build\nmany of the other parts of Cadabra using Conda, for various reasons:\nConda's glibmm is not built with C++11 enabled, there is no gtkmm\nlibrary, and probably others. For a discussion on this, see\n\n  https://groups.google.com/a/continuum.io/d/msg/anaconda/oHtExJU9oiM/oMZLGpn1CAAJ\n\nand if you don't think this is a problem, see e.g.\n\n  https://unix.stackexchange.com/questions/414904/anaconda-qt-vs-system-qt\n\nAfter installation, first activate your miniconda distribution::\n\n    source ~/miniconda3/bin/activate\n\nAll dependencies for Cadabra's Jupyter kernel can then be installed from\nConda directly, with::\n\n    conda install cmake pkg-config glibmm zeromq cppzmq xtl cryptopp \\\n\t               sqlite util-linux xeus nlohmann_json sympy \\\n\t\t\t\t\t\tjupyter -c conda-forge\n\t \nNow it is time to do the Cadabra build. Configure with options which\nensure that CMake picks up the Conda libraries first, and make it\ninstall the Cadabra things in a place which does not interfere with\nany 'normal' build you may have sitting around::\n\n    cd cadabra2\n    mkdir build\n    cd build\n    cmake -DENABLE_JUPYTER=ON -DENABLE_FRONTEND=OFF \\\n                              -DCMAKE_INCLUDE_PATH=${HOME}/miniconda3/include \\\n                              -DCMAKE_LIBRARY_PATH=${HOME}/miniconda3/lib \\\n                              -DCMAKE_INSTALL_PREFIX=${HOME}/miniconda3 \\\n                              ..\n\nYou should see that it has configured using the Conda Python; look for\nthe `Configuring Python` block, which should be something like::\n\n    -------------------------------------------\n      Configuring Python\n    -------------------------------------------\n    -- Building for use with Python 3 (good!)\n    -- Found PythonInterp: /home/kasper/miniconda3/bin/python3.7 (found version \"3.7.1\") \n    -- Found PythonLibs: /home/kasper/miniconda3/lib/libpython3.7m.so\n    -- pybind11 v2.3.dev0\n    -- Found python /home/kasper/miniconda3/lib/libpython3.7m.so\n\nNote the reference to the Conda installation path. Further down you\nshould then also see a block for the Jupyter kernel::\n\n    -------------------------------------------\n      Configuring Jupyter kernel build\n    -------------------------------------------\n \nIf that's all ok, you can build with the standard::\n\n    make\n    sudo make install\n\nThis will install the kernel in::\n\n    ${HOME}/miniconda3/bin/\n\nand the JSON configuration files in::\n\n    ${HOME}/miniconda3/share/jupyter/kernels/cadabra/\n\nIf you now start Jupyter, you should be able to choose a Cadabra\nkernel::\n\n    ${HOME}/miniconda3/bin/jupyter notebook\n\nThere is a sample `schwarzschild.ipynb` in the `examples` directory.\t\n\n\n\nSetting up a Jupyterhub server for Cadabra\n------------------------------------------\n\nThe following instructions setup a JupyterHub installation using 'The\nLittlest JupyterHub' (TLJH). These instructions have been tested on a\nclean Ubuntu 18.04 installation.\n\nFirst install TLJH as per the instructions at::\n\n    https://the-littlest-jupyterhub.readthedocs.io/en/latest/install/custom-server.html\n\n(note that you *first* need to do a sudo command, otherwise the\ninstaller will ask for the password but you won't see that prompt,\nmaking it look like the installation process hangs).\n\n*New*: it should now also be possible to simply install the conda\npackage for the Jupyter kernel. *New*\n\nBecome root (you cannot write into `/opt/tljh` otherwise) and set the\nconda path using::\n\n    sudo su\n    export PATH=/opt/tljh/user/bin:${PATH}\n\nInstall the prerequisites with::\n\n    conda install cmake pkg-config glibmm zeromq cppzmq xtl cryptopp \\\n\t               sqlite util-linux xeus nlohmann_json sympy \\\n\t\t\t\t\t\t-c conda-forge\n\t \nBuild the Cadabra Jupyter kernel with::\n  \n    cd cadabra2\n    mkdir build\n    cd build\n    cmake -DENABLE_JUPYTER=ON -DENABLE_FRONTEND=OFF \\\n                              -DCMAKE_INCLUDE_PATH=/opt/tljh/user/include \\\n                              -DCMAKE_LIBRARY_PATH=/opt/tljh/user/lib \\\n                              -DCMAKE_INSTALL_PREFIX=/opt/tljh/user/ \\\n                              ..\n    make install\n\nThe 'new' button in the Jupyterhub file browser should now offer you\nthe option of creating a new Cadabra notebook.\n\n\nCreating a Conda package of the Cadabra Jupyter kernel\n------------------------------------------------------\n\nTo build a Conda package of the Cadabra Jupyter kernel from scratch,\nfirst install miniconda as above, and activate::\n\n    source ~/miniconda3/bin/activate\n\nNow the fun starts. Conda is an absolutely horrendous packaging\nsystem, which absolutely does *not* get dependencies right, but we\nwill have to live with it. First, update the base conda distribution::\n\n    conda update -n base -c defaults conda     \n    conda update --all\n\nThen activate the `conda-forge` channel, and update to the latest of\neverything::\n\n    conda config --add channels conda-forge\n    conda update --all\n\nDo *not* use `conda config --set channel_priority strict` as that\n*will* break the build with an endless list of package conflicts.\nThere are other ways to add the conda-forge channel, all subtly\ndifferent; avoid adding `-c conda-forge` as that is just broken beyond\nbelief too. Now install the prerequisites for building conda\npackages::\n\n    conda install conda-build anaconda-client \\\n         xeus pkg-config glibmm\n\nThat last line should not have been necessary, as build requirements\nin `meta.yaml` should have taken care of it, but alas, it does not\nwork that way. It spits out various messages about packages being\n*downgraded*; don't ask, I told you the system was broken.\n\nNow change to the `conda` directory and build the package::\n\n    cd cadabra2/conda\n    export PKG_CONFIG_PATH=${HOME}/miniconda3/lib/pkgconfig\n    conda build .\n\nAgain, that path setting should have been handled automatically...\nTo upload::\n\n    anaconda login\n    anaconda upload /path/to/conda-package.tar.bz2\n\n\n"
  },
  {
    "path": "LICENSE",
    "content": "                    GNU GENERAL PUBLIC LICENSE\n                       Version 3, 29 June 2007\n\n Copyright (C) 2007 Free Software Foundation, Inc. <http://fsf.org/>\n Everyone is permitted to copy and distribute verbatim copies\n of this license document, but changing it is not allowed.\n\n                            Preamble\n\n  The GNU General Public License is a free, copyleft license for\nsoftware and other kinds of works.\n\n  The licenses for most software and other practical works are designed\nto take away your freedom to share and change the works.  By contrast,\nthe GNU General Public License is intended to guarantee your freedom to\nshare and change all versions of a program--to make sure it remains free\nsoftware for all its users.  We, the Free Software Foundation, use the\nGNU General Public License for most of our software; it applies also to\nany other work released this way by its authors.  You can apply it to\nyour programs, too.\n\n  When we speak of free software, we are referring to freedom, not\nprice.  Our General Public Licenses are designed to make sure that you\nhave the freedom to distribute copies of free software (and charge for\nthem if you wish), that you receive source code or can get it if you\nwant it, that you can change the software or use pieces of it in new\nfree programs, and that you know you can do these things.\n\n  To protect your rights, we need to prevent others from denying you\nthese rights or asking you to surrender the rights.  Therefore, you have\ncertain responsibilities if you distribute copies of the software, or if\nyou modify it: responsibilities to respect the freedom of others.\n\n  For example, if you distribute copies of such a program, whether\ngratis or for a fee, you must pass on to the recipients the same\nfreedoms that you received.  You must make sure that they, too, receive\nor can get the source code.  And you must show them these terms so they\nknow their rights.\n\n  Developers that use the GNU GPL protect your rights with two steps:\n(1) assert copyright on the software, and (2) offer you this License\ngiving you legal permission to copy, distribute and/or modify it.\n\n  For the developers' and authors' protection, the GPL clearly explains\nthat there is no warranty for this free software.  For both users' and\nauthors' sake, the GPL requires that modified versions be marked as\nchanged, so that their problems will not be attributed erroneously to\nauthors of previous versions.\n\n  Some devices are designed to deny users access to install or run\nmodified versions of the software inside them, although the manufacturer\ncan do so.  This is fundamentally incompatible with the aim of\nprotecting users' freedom to change the software.  The systematic\npattern of such abuse occurs in the area of products for individuals to\nuse, which is precisely where it is most unacceptable.  Therefore, we\nhave designed this version of the GPL to prohibit the practice for those\nproducts.  If such problems arise substantially in other domains, we\nstand ready to extend this provision to those domains in future versions\nof the GPL, as needed to protect the freedom of users.\n\n  Finally, every program is threatened constantly by software patents.\nStates should not allow patents to restrict development and use of\nsoftware on general-purpose computers, but in those that do, we wish to\navoid the special danger that patents applied to a free program could\nmake it effectively proprietary.  To prevent this, the GPL assures that\npatents cannot be used to render the program non-free.\n\n  The precise terms and conditions for copying, distribution and\nmodification follow.\n\n                       TERMS AND CONDITIONS\n\n  0. Definitions.\n\n  \"This License\" refers to version 3 of the GNU General Public License.\n\n  \"Copyright\" also means copyright-like laws that apply to other kinds of\nworks, such as semiconductor masks.\n\n  \"The Program\" refers to any copyrightable work licensed under this\nLicense.  Each licensee is addressed as \"you\".  \"Licensees\" and\n\"recipients\" may be individuals or organizations.\n\n  To \"modify\" a work means to copy from or adapt all or part of the work\nin a fashion requiring copyright permission, other than the making of an\nexact copy.  The resulting work is called a \"modified version\" of the\nearlier work or a work \"based on\" the earlier work.\n\n  A \"covered work\" means either the unmodified Program or a work based\non the Program.\n\n  To \"propagate\" a work means to do anything with it that, without\npermission, would make you directly or secondarily liable for\ninfringement under applicable copyright law, except executing it on a\ncomputer or modifying a private copy.  Propagation includes copying,\ndistribution (with or without modification), making available to the\npublic, and in some countries other activities as well.\n\n  To \"convey\" a work means any kind of propagation that enables other\nparties to make or receive copies.  Mere interaction with a user through\na computer network, with no transfer of a copy, is not conveying.\n\n  An interactive user interface displays \"Appropriate Legal Notices\"\nto the extent that it includes a convenient and prominently visible\nfeature that (1) displays an appropriate copyright notice, and (2)\ntells the user that there is no warranty for the work (except to the\nextent that warranties are provided), that licensees may convey the\nwork under this License, and how to view a copy of this License.  If\nthe interface presents a list of user commands or options, such as a\nmenu, a prominent item in the list meets this criterion.\n\n  1. Source Code.\n\n  The \"source code\" for a work means the preferred form of the work\nfor making modifications to it.  \"Object code\" means any non-source\nform of a work.\n\n  A \"Standard Interface\" means an interface that either is an official\nstandard defined by a recognized standards body, or, in the case of\ninterfaces specified for a particular programming language, one that\nis widely used among developers working in that language.\n\n  The \"System Libraries\" of an executable work include anything, other\nthan the work as a whole, that (a) is included in the normal form of\npackaging a Major Component, but which is not part of that Major\nComponent, and (b) serves only to enable use of the work with that\nMajor Component, or to implement a Standard Interface for which an\nimplementation is available to the public in source code form.  A\n\"Major Component\", in this context, means a major essential component\n(kernel, window system, and so on) of the specific operating system\n(if any) on which the executable work runs, or a compiler used to\nproduce the work, or an object code interpreter used to run it.\n\n  The \"Corresponding Source\" for a work in object code form means all\nthe source code needed to generate, install, and (for an executable\nwork) run the object code and to modify the work, including scripts to\ncontrol those activities.  However, it does not include the work's\nSystem Libraries, or general-purpose tools or generally available free\nprograms which are used unmodified in performing those activities but\nwhich are not part of the work.  For example, Corresponding Source\nincludes interface definition files associated with source files for\nthe work, and the source code for shared libraries and dynamically\nlinked subprograms that the work is specifically designed to require,\nsuch as by intimate data communication or control flow between those\nsubprograms and other parts of the work.\n\n  The Corresponding Source need not include anything that users\ncan regenerate automatically from other parts of the Corresponding\nSource.\n\n  The Corresponding Source for a work in source code form is that\nsame work.\n\n  2. Basic Permissions.\n\n  All rights granted under this License are granted for the term of\ncopyright on the Program, and are irrevocable provided the stated\nconditions are met.  This License explicitly affirms your unlimited\npermission to run the unmodified Program.  The output from running a\ncovered work is covered by this License only if the output, given its\ncontent, constitutes a covered work.  This License acknowledges your\nrights of fair use or other equivalent, as provided by copyright law.\n\n  You may make, run and propagate covered works that you do not\nconvey, without conditions so long as your license otherwise remains\nin force.  You may convey covered works to others for the sole purpose\nof having them make modifications exclusively for you, or provide you\nwith facilities for running those works, provided that you comply with\nthe terms of this License in conveying all material for which you do\nnot control copyright.  Those thus making or running the covered works\nfor you must do so exclusively on your behalf, under your direction\nand control, on terms that prohibit them from making any copies of\nyour copyrighted material outside their relationship with you.\n\n  Conveying under any other circumstances is permitted solely under\nthe conditions stated below.  Sublicensing is not allowed; section 10\nmakes it unnecessary.\n\n  3. Protecting Users' Legal Rights From Anti-Circumvention Law.\n\n  No covered work shall be deemed part of an effective technological\nmeasure under any applicable law fulfilling obligations under article\n11 of the WIPO copyright treaty adopted on 20 December 1996, or\nsimilar laws prohibiting or restricting circumvention of such\nmeasures.\n\n  When you convey a covered work, you waive any legal power to forbid\ncircumvention of technological measures to the extent such circumvention\nis effected by exercising rights under this License with respect to\nthe covered work, and you disclaim any intention to limit operation or\nmodification of the work as a means of enforcing, against the work's\nusers, your or third parties' legal rights to forbid circumvention of\ntechnological measures.\n\n  4. Conveying Verbatim Copies.\n\n  You may convey verbatim copies of the Program's source code as you\nreceive it, in any medium, provided that you conspicuously and\nappropriately publish on each copy an appropriate copyright notice;\nkeep intact all notices stating that this License and any\nnon-permissive terms added in accord with section 7 apply to the code;\nkeep intact all notices of the absence of any warranty; and give all\nrecipients a copy of this License along with the Program.\n\n  You may charge any price or no price for each copy that you convey,\nand you may offer support or warranty protection for a fee.\n\n  5. Conveying Modified Source Versions.\n\n  You may convey a work based on the Program, or the modifications to\nproduce it from the Program, in the form of source code under the\nterms of section 4, provided that you also meet all of these conditions:\n\n    a) The work must carry prominent notices stating that you modified\n    it, and giving a relevant date.\n\n    b) The work must carry prominent notices stating that it is\n    released under this License and any conditions added under section\n    7.  This requirement modifies the requirement in section 4 to\n    \"keep intact all notices\".\n\n    c) You must license the entire work, as a whole, under this\n    License to anyone who comes into possession of a copy.  This\n    License will therefore apply, along with any applicable section 7\n    additional terms, to the whole of the work, and all its parts,\n    regardless of how they are packaged.  This License gives no\n    permission to license the work in any other way, but it does not\n    invalidate such permission if you have separately received it.\n\n    d) If the work has interactive user interfaces, each must display\n    Appropriate Legal Notices; however, if the Program has interactive\n    interfaces that do not display Appropriate Legal Notices, your\n    work need not make them do so.\n\n  A compilation of a covered work with other separate and independent\nworks, which are not by their nature extensions of the covered work,\nand which are not combined with it such as to form a larger program,\nin or on a volume of a storage or distribution medium, is called an\n\"aggregate\" if the compilation and its resulting copyright are not\nused to limit the access or legal rights of the compilation's users\nbeyond what the individual works permit.  Inclusion of a covered work\nin an aggregate does not cause this License to apply to the other\nparts of the aggregate.\n\n  6. Conveying Non-Source Forms.\n\n  You may convey a covered work in object code form under the terms\nof sections 4 and 5, provided that you also convey the\nmachine-readable Corresponding Source under the terms of this License,\nin one of these ways:\n\n    a) Convey the object code in, or embodied in, a physical product\n    (including a physical distribution medium), accompanied by the\n    Corresponding Source fixed on a durable physical medium\n    customarily used for software interchange.\n\n    b) Convey the object code in, or embodied in, a physical product\n    (including a physical distribution medium), accompanied by a\n    written offer, valid for at least three years and valid for as\n    long as you offer spare parts or customer support for that product\n    model, to give anyone who possesses the object code either (1) a\n    copy of the Corresponding Source for all the software in the\n    product that is covered by this License, on a durable physical\n    medium customarily used for software interchange, for a price no\n    more than your reasonable cost of physically performing this\n    conveying of source, or (2) access to copy the\n    Corresponding Source from a network server at no charge.\n\n    c) Convey individual copies of the object code with a copy of the\n    written offer to provide the Corresponding Source.  This\n    alternative is allowed only occasionally and noncommercially, and\n    only if you received the object code with such an offer, in accord\n    with subsection 6b.\n\n    d) Convey the object code by offering access from a designated\n    place (gratis or for a charge), and offer equivalent access to the\n    Corresponding Source in the same way through the same place at no\n    further charge.  You need not require recipients to copy the\n    Corresponding Source along with the object code.  If the place to\n    copy the object code is a network server, the Corresponding Source\n    may be on a different server (operated by you or a third party)\n    that supports equivalent copying facilities, provided you maintain\n    clear directions next to the object code saying where to find the\n    Corresponding Source.  Regardless of what server hosts the\n    Corresponding Source, you remain obligated to ensure that it is\n    available for as long as needed to satisfy these requirements.\n\n    e) Convey the object code using peer-to-peer transmission, provided\n    you inform other peers where the object code and Corresponding\n    Source of the work are being offered to the general public at no\n    charge under subsection 6d.\n\n  A separable portion of the object code, whose source code is excluded\nfrom the Corresponding Source as a System Library, need not be\nincluded in conveying the object code work.\n\n  A \"User Product\" is either (1) a \"consumer product\", which means any\ntangible personal property which is normally used for personal, family,\nor household purposes, or (2) anything designed or sold for incorporation\ninto a dwelling.  In determining whether a product is a consumer product,\ndoubtful cases shall be resolved in favor of coverage.  For a particular\nproduct received by a particular user, \"normally used\" refers to a\ntypical or common use of that class of product, regardless of the status\nof the particular user or of the way in which the particular user\nactually uses, or expects or is expected to use, the product.  A product\nis a consumer product regardless of whether the product has substantial\ncommercial, industrial or non-consumer uses, unless such uses represent\nthe only significant mode of use of the product.\n\n  \"Installation Information\" for a User Product means any methods,\nprocedures, authorization keys, or other information required to install\nand execute modified versions of a covered work in that User Product from\na modified version of its Corresponding Source.  The information must\nsuffice to ensure that the continued functioning of the modified object\ncode is in no case prevented or interfered with solely because\nmodification has been made.\n\n  If you convey an object code work under this section in, or with, or\nspecifically for use in, a User Product, and the conveying occurs as\npart of a transaction in which the right of possession and use of the\nUser Product is transferred to the recipient in perpetuity or for a\nfixed term (regardless of how the transaction is characterized), the\nCorresponding Source conveyed under this section must be accompanied\nby the Installation Information.  But this requirement does not apply\nif neither you nor any third party retains the ability to install\nmodified object code on the User Product (for example, the work has\nbeen installed in ROM).\n\n  The requirement to provide Installation Information does not include a\nrequirement to continue to provide support service, warranty, or updates\nfor a work that has been modified or installed by the recipient, or for\nthe User Product in which it has been modified or installed.  Access to a\nnetwork may be denied when the modification itself materially and\nadversely affects the operation of the network or violates the rules and\nprotocols for communication across the network.\n\n  Corresponding Source conveyed, and Installation Information provided,\nin accord with this section must be in a format that is publicly\ndocumented (and with an implementation available to the public in\nsource code form), and must require no special password or key for\nunpacking, reading or copying.\n\n  7. Additional Terms.\n\n  \"Additional permissions\" are terms that supplement the terms of this\nLicense by making exceptions from one or more of its conditions.\nAdditional permissions that are applicable to the entire Program shall\nbe treated as though they were included in this License, to the extent\nthat they are valid under applicable law.  If additional permissions\napply only to part of the Program, that part may be used separately\nunder those permissions, but the entire Program remains governed by\nthis License without regard to the additional permissions.\n\n  When you convey a copy of a covered work, you may at your option\nremove any additional permissions from that copy, or from any part of\nit.  (Additional permissions may be written to require their own\nremoval in certain cases when you modify the work.)  You may place\nadditional permissions on material, added by you to a covered work,\nfor which you have or can give appropriate copyright permission.\n\n  Notwithstanding any other provision of this License, for material you\nadd to a covered work, you may (if authorized by the copyright holders of\nthat material) supplement the terms of this License with terms:\n\n    a) Disclaiming warranty or limiting liability differently from the\n    terms of sections 15 and 16 of this License; or\n\n    b) Requiring preservation of specified reasonable legal notices or\n    author attributions in that material or in the Appropriate Legal\n    Notices displayed by works containing it; or\n\n    c) Prohibiting misrepresentation of the origin of that material, or\n    requiring that modified versions of such material be marked in\n    reasonable ways as different from the original version; or\n\n    d) Limiting the use for publicity purposes of names of licensors or\n    authors of the material; or\n\n    e) Declining to grant rights under trademark law for use of some\n    trade names, trademarks, or service marks; or\n\n    f) Requiring indemnification of licensors and authors of that\n    material by anyone who conveys the material (or modified versions of\n    it) with contractual assumptions of liability to the recipient, for\n    any liability that these contractual assumptions directly impose on\n    those licensors and authors.\n\n  All other non-permissive additional terms are considered \"further\nrestrictions\" within the meaning of section 10.  If the Program as you\nreceived it, or any part of it, contains a notice stating that it is\ngoverned by this License along with a term that is a further\nrestriction, you may remove that term.  If a license document contains\na further restriction but permits relicensing or conveying under this\nLicense, you may add to a covered work material governed by the terms\nof that license document, provided that the further restriction does\nnot survive such relicensing or conveying.\n\n  If you add terms to a covered work in accord with this section, you\nmust place, in the relevant source files, a statement of the\nadditional terms that apply to those files, or a notice indicating\nwhere to find the applicable terms.\n\n  Additional terms, permissive or non-permissive, may be stated in the\nform of a separately written license, or stated as exceptions;\nthe above requirements apply either way.\n\n  8. Termination.\n\n  You may not propagate or modify a covered work except as expressly\nprovided under this License.  Any attempt otherwise to propagate or\nmodify it is void, and will automatically terminate your rights under\nthis License (including any patent licenses granted under the third\nparagraph of section 11).\n\n  However, if you cease all violation of this License, then your\nlicense from a particular copyright holder is reinstated (a)\nprovisionally, unless and until the copyright holder explicitly and\nfinally terminates your license, and (b) permanently, if the copyright\nholder fails to notify you of the violation by some reasonable means\nprior to 60 days after the cessation.\n\n  Moreover, your license from a particular copyright holder is\nreinstated permanently if the copyright holder notifies you of the\nviolation by some reasonable means, this is the first time you have\nreceived notice of violation of this License (for any work) from that\ncopyright holder, and you cure the violation prior to 30 days after\nyour receipt of the notice.\n\n  Termination of your rights under this section does not terminate the\nlicenses of parties who have received copies or rights from you under\nthis License.  If your rights have been terminated and not permanently\nreinstated, you do not qualify to receive new licenses for the same\nmaterial under section 10.\n\n  9. Acceptance Not Required for Having Copies.\n\n  You are not required to accept this License in order to receive or\nrun a copy of the Program.  Ancillary propagation of a covered work\noccurring solely as a consequence of using peer-to-peer transmission\nto receive a copy likewise does not require acceptance.  However,\nnothing other than this License grants you permission to propagate or\nmodify any covered work.  These actions infringe copyright if you do\nnot accept this License.  Therefore, by modifying or propagating a\ncovered work, you indicate your acceptance of this License to do so.\n\n  10. Automatic Licensing of Downstream Recipients.\n\n  Each time you convey a covered work, the recipient automatically\nreceives a license from the original licensors, to run, modify and\npropagate that work, subject to this License.  You are not responsible\nfor enforcing compliance by third parties with this License.\n\n  An \"entity transaction\" is a transaction transferring control of an\norganization, or substantially all assets of one, or subdividing an\norganization, or merging organizations.  If propagation of a covered\nwork results from an entity transaction, each party to that\ntransaction who receives a copy of the work also receives whatever\nlicenses to the work the party's predecessor in interest had or could\ngive under the previous paragraph, plus a right to possession of the\nCorresponding Source of the work from the predecessor in interest, if\nthe predecessor has it or can get it with reasonable efforts.\n\n  You may not impose any further restrictions on the exercise of the\nrights granted or affirmed under this License.  For example, you may\nnot impose a license fee, royalty, or other charge for exercise of\nrights granted under this License, and you may not initiate litigation\n(including a cross-claim or counterclaim in a lawsuit) alleging that\nany patent claim is infringed by making, using, selling, offering for\nsale, or importing the Program or any portion of it.\n\n  11. Patents.\n\n  A \"contributor\" is a copyright holder who authorizes use under this\nLicense of the Program or a work on which the Program is based.  The\nwork thus licensed is called the contributor's \"contributor version\".\n\n  A contributor's \"essential patent claims\" are all patent claims\nowned or controlled by the contributor, whether already acquired or\nhereafter acquired, that would be infringed by some manner, permitted\nby this License, of making, using, or selling its contributor version,\nbut do not include claims that would be infringed only as a\nconsequence of further modification of the contributor version.  For\npurposes of this definition, \"control\" includes the right to grant\npatent sublicenses in a manner consistent with the requirements of\nthis License.\n\n  Each contributor grants you a non-exclusive, worldwide, royalty-free\npatent license under the contributor's essential patent claims, to\nmake, use, sell, offer for sale, import and otherwise run, modify and\npropagate the contents of its contributor version.\n\n  In the following three paragraphs, a \"patent license\" is any express\nagreement or commitment, however denominated, not to enforce a patent\n(such as an express permission to practice a patent or covenant not to\nsue for patent infringement).  To \"grant\" such a patent license to a\nparty means to make such an agreement or commitment not to enforce a\npatent against the party.\n\n  If you convey a covered work, knowingly relying on a patent license,\nand the Corresponding Source of the work is not available for anyone\nto copy, free of charge and under the terms of this License, through a\npublicly available network server or other readily accessible means,\nthen you must either (1) cause the Corresponding Source to be so\navailable, or (2) arrange to deprive yourself of the benefit of the\npatent license for this particular work, or (3) arrange, in a manner\nconsistent with the requirements of this License, to extend the patent\nlicense to downstream recipients.  \"Knowingly relying\" means you have\nactual knowledge that, but for the patent license, your conveying the\ncovered work in a country, or your recipient's use of the covered work\nin a country, would infringe one or more identifiable patents in that\ncountry that you have reason to believe are valid.\n\n  If, pursuant to or in connection with a single transaction or\narrangement, you convey, or propagate by procuring conveyance of, a\ncovered work, and grant a patent license to some of the parties\nreceiving the covered work authorizing them to use, propagate, modify\nor convey a specific copy of the covered work, then the patent license\nyou grant is automatically extended to all recipients of the covered\nwork and works based on it.\n\n  A patent license is \"discriminatory\" if it does not include within\nthe scope of its coverage, prohibits the exercise of, or is\nconditioned on the non-exercise of one or more of the rights that are\nspecifically granted under this License.  You may not convey a covered\nwork if you are a party to an arrangement with a third party that is\nin the business of distributing software, under which you make payment\nto the third party based on the extent of your activity of conveying\nthe work, and under which the third party grants, to any of the\nparties who would receive the covered work from you, a discriminatory\npatent license (a) in connection with copies of the covered work\nconveyed by you (or copies made from those copies), or (b) primarily\nfor and in connection with specific products or compilations that\ncontain the covered work, unless you entered into that arrangement,\nor that patent license was granted, prior to 28 March 2007.\n\n  Nothing in this License shall be construed as excluding or limiting\nany implied license or other defenses to infringement that may\notherwise be available to you under applicable patent law.\n\n  12. No Surrender of Others' Freedom.\n\n  If conditions are imposed on you (whether by court order, agreement or\notherwise) that contradict the conditions of this License, they do not\nexcuse you from the conditions of this License.  If you cannot convey a\ncovered work so as to satisfy simultaneously your obligations under this\nLicense and any other pertinent obligations, then as a consequence you may\nnot convey it at all.  For example, if you agree to terms that obligate you\nto collect a royalty for further conveying from those to whom you convey\nthe Program, the only way you could satisfy both those terms and this\nLicense would be to refrain entirely from conveying the Program.\n\n  13. Use with the GNU Affero General Public License.\n\n  Notwithstanding any other provision of this License, you have\npermission to link or combine any covered work with a work licensed\nunder version 3 of the GNU Affero General Public License into a single\ncombined work, and to convey the resulting work.  The terms of this\nLicense will continue to apply to the part which is the covered work,\nbut the special requirements of the GNU Affero General Public License,\nsection 13, concerning interaction through a network will apply to the\ncombination as such.\n\n  14. Revised Versions of this License.\n\n  The Free Software Foundation may publish revised and/or new versions of\nthe GNU General Public License from time to time.  Such new versions will\nbe similar in spirit to the present version, but may differ in detail to\naddress new problems or concerns.\n\n  Each version is given a distinguishing version number.  If the\nProgram specifies that a certain numbered version of the GNU General\nPublic License \"or any later version\" applies to it, you have the\noption of following the terms and conditions either of that numbered\nversion or of any later version published by the Free Software\nFoundation.  If the Program does not specify a version number of the\nGNU General Public License, you may choose any version ever published\nby the Free Software Foundation.\n\n  If the Program specifies that a proxy can decide which future\nversions of the GNU General Public License can be used, that proxy's\npublic statement of acceptance of a version permanently authorizes you\nto choose that version for the Program.\n\n  Later license versions may give you additional or different\npermissions.  However, no additional obligations are imposed on any\nauthor or copyright holder as a result of your choosing to follow a\nlater version.\n\n  15. Disclaimer of Warranty.\n\n  THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY\nAPPLICABLE LAW.  EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT\nHOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM \"AS IS\" WITHOUT WARRANTY\nOF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO,\nTHE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR\nPURPOSE.  THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM\nIS WITH YOU.  SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF\nALL NECESSARY SERVICING, REPAIR OR CORRECTION.\n\n  16. Limitation of Liability.\n\n  IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING\nWILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS\nTHE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY\nGENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE\nUSE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF\nDATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD\nPARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS),\nEVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF\nSUCH DAMAGES.\n\n  17. Interpretation of Sections 15 and 16.\n\n  If the disclaimer of warranty and limitation of liability provided\nabove cannot be given local legal effect according to their terms,\nreviewing courts shall apply local law that most closely approximates\nan absolute waiver of all civil liability in connection with the\nProgram, unless a warranty or assumption of liability accompanies a\ncopy of the Program in return for a fee.\n\n                     END OF TERMS AND CONDITIONS\n\n            How to Apply These Terms to Your New Programs\n\n  If you develop a new program, and you want it to be of the greatest\npossible use to the public, the best way to achieve this is to make it\nfree software which everyone can redistribute and change under these terms.\n\n  To do so, attach the following notices to the program.  It is safest\nto attach them to the start of each source file to most effectively\nstate the exclusion of warranty; and each file should have at least\nthe \"copyright\" line and a pointer to where the full notice is found.\n\n    {one line to give the program's name and a brief idea of what it does.}\n    Copyright (C) {year}  {name of author}\n\n    This program is free software: you can redistribute it and/or modify\n    it under the terms of the GNU General Public License as published by\n    the Free Software Foundation, either version 3 of the License, or\n    (at your option) any later version.\n\n    This program is distributed in the hope that it will be useful,\n    but WITHOUT ANY WARRANTY; without even the implied warranty of\n    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n    GNU General Public License for more details.\n\n    You should have received a copy of the GNU General Public License\n    along with this program.  If not, see <http://www.gnu.org/licenses/>.\n\nAlso add information on how to contact you by electronic and paper mail.\n\n  If the program does terminal interaction, make it output a short\nnotice like this when it starts in an interactive mode:\n\n    {project}  Copyright (C) {year}  {fullname}\n    This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'.\n    This is free software, and you are welcome to redistribute it\n    under certain conditions; type `show c' for details.\n\nThe hypothetical commands `show w' and `show c' should show the appropriate\nparts of the General Public License.  Of course, your program's commands\nmight be different; for a GUI interface, you would use an \"about box\".\n\n  You should also get your employer (if you work as a programmer) or school,\nif any, to sign a \"copyright disclaimer\" for the program, if necessary.\nFor more information on this, and how to apply and follow the GNU GPL, see\n<http://www.gnu.org/licenses/>.\n\n  The GNU General Public License does not permit incorporating your program\ninto proprietary programs.  If your program is a subroutine library, you\nmay consider it more useful to permit linking proprietary applications with\nthe library.  If this is what you want to do, use the GNU Lesser General\nPublic License instead of this License.  But first, please read\n<http://www.gnu.org/philosophy/why-not-lgpl.html>.\n"
  },
  {
    "path": "Makefile",
    "content": "\nall:\n\t@echo -n \"\\nTo build Cadabra, \\n\\n   mkdir build\\n   cd build\\n   cmake ..\\n   make\\n\\nThe other targets here are (for maintainer purposes only)\\n\\n   tarball:     build a tarball cadabra2-latest.tar.gz of current HEAD\\n   doc:         generate doxygen docs in doc\\n   webup:       build web pages/tutorials/man pages and upload to server\\n   updatesnoop: sync snoop repo\\n   packages:    create deb/rpm packages on buildbot\\n\\nIf you need help, email info@cadabra.science\\n\\n\"\n\n.PHONY: doc tarball findclay webbuild claybuild webup format packages updatesnoop\n\ntarball:\n\tgit archive --format=tar --prefix=cadabra2-latest/ HEAD | gzip > ${HOME}/tmp/cadabra2-latest.tar.gz\n\ndoc:\n\tdoxygen config/Doxyfile\n\nwebbuild:\n\tcd build; make -f web2/Makefile\n\nclaybuild:\n\tcd web2/cadabra2/source; rm -Rf build; clay build\n\nCMD_NOT_FOUND = $(error $(1) is required for this rule)\nCHECK_CMD = $(if $(shell command -v $(1)),,$(call CMD_NOT_FOUND,$(1)))\n\nfindclay:\n\t$(call CHECK_CMD, clay)\n\nwebup: findclay webbuild claybuild\n\tdoxygen config/Doxyfile\n\trsync -avz --chmod=+rx doxygen/ cadabra_web:/var/www/cadabra2/doxygen/\n\tcd web2/cadabra2/source; rsync -avz --chmod=+rx build/ cadabra_web:/var/www/cadabra2/;  rsync -avz --chmod=+rx static/styles/ cadabra_web:/var/www/cadabra2/static/styles;   scp static/cadabra_in* cadabra_web:/var/www/cadabra2/static/; rsync -avz --chmod=+rx static/fonts/ cadabra_web:/var/www/cadabra2/static/fonts; rsync -avz --chmod=+rx static/images/ cadabra_web:/var/www/cadabra2/static/images/; rsync -avz --chmod=+rx static/icons/ cadabra_web:/var/www/cadabra2/static/icons/; rsync -avz --chmod=+rx static/pdf/ cadabra_web:/var/www/cadabra2/static/pdf/; rsync -avz --chmod=+rx static/js/ cadabra_web:/var/www/cadabra2/static/js/; rsync -avz --chmod=+r static/robots.txt cadabra_web:/var/www/cadabra2\n\nformat:\n\tastyle --style=k/r --indent=tab=3 --recursive --attach-classes --attach-namespaces --indent-classes --indent-namespaces --indent-switches --break-closing-braces '*.hh'\n\tastyle --style=k/r --indent=tab=3 --recursive --attach-classes --attach-namespaces --indent-classes --indent-namespaces --indent-switches --break-closing-braces '*.cc'\n\tfind . -name \"*.cc\" -exec sed -i -e 's/^\\([ \\t]*\\)\\([\\{\\}]\\)/\\1\\t\\2/' '{}' ';'\n\tfind . -name \"*.hh\" -exec sed -i -e 's/^\\([ \\t]*\\)\\([\\{\\}]\\)/\\1\\t\\2/' '{}' ';'\n\npackages:\n\tbash config/buildbot.sh\n\nappimage:\n\t(mkdir build-appimage; cd build-appimage; cmake -DAPPIMAGE_MODE=ON -DCMAKE_INSTALL_PREFIX=/usr ..; make; make install DESTDIR=AppDir; make appimage)\n\nupdatesnoop:\n\tcp ../snoop/src/Snoop.cc ../snoop/src/SnoopPrivate.hh ../snoop/src/Snoop.hh client_server/\n"
  },
  {
    "path": "README.rst",
    "content": "Cadabra\n=======\n\n.. image:: https://joss.theoj.org/papers/10.21105/joss.01118/status.svg\n   :target: https://doi.org/10.21105/joss.01118\n\n.. image:: https://zenodo.org/badge/DOI/10.5281/zenodo.2500762.svg\n   :target: https://doi.org/10.5281/zenodo.2500762\n\n.. image:: https://github.com/kpeeters/cadabra2/workflows/Linux/badge.svg\n   :target: https://github.com/kpeeters/cadabra2/actions?query=workflow%3ALinux\n\n.. image:: https://github.com/kpeeters/cadabra2/workflows/macOS/badge.svg\n   :target: https://github.com/kpeeters/cadabra2/actions?query=workflow%3AmacOS\n\n.. image:: https://github.com/kpeeters/cadabra2/workflows/Docker/badge.svg\n   :target: https://github.com/kpeeters/cadabra2/actions?query=workflow%3ADocker\n\n.. image:: https://github.com/kpeeters/cadabra2/workflows/Windows%2011/badge.svg\n   :target: https://github.com/kpeeters/cadabra2/actions?query=workflow%3AWindows%2011\n\n.. image:: https://github.com/kpeeters/cadabra2/workflows/FreeBSD/badge.svg\n   :target: https://github.com/kpeeters/cadabra2/actions?query=workflow%3AFreeBSD\n\n*A field-theory motivated approach to computer algebra.*\n\nKasper Peeters <info@cadabra.science>\n\n- End-user documentation at https://cadabra.science/\n- Source code documentation at https://cadabra.science/doxygen/html\n\nThis repository holds the 2.x series of the Cadabra computer algebra\nsystem. It supersedes the 1.x series, which can still be found at\nhttps://github.com/kpeeters/cadabra.\n\nCadabra is a symbolic computer algebra system, designed specifically\nfor the solution of problems encountered in quantum and classical\nfield theory. It has extensive functionality for tensor computer\nalgebra, tensor polynomial simplification including multi-term\nsymmetries, fermions and anti-commuting variables, Clifford algebras\nand Fierz transformations, implicit coordinate dependence, multiple\nindex types and many more. The input format is a subset of TeX. Both a\ncommand-line and a graphical interface are available, and there is a\nkernel for Jupyter.\n\n\nInstallation\n-------------\n\nCadabra builds on Linux, macOS, OpenBSD, FreeBSD and Windows. Select\nyour system from the list below for detailed instructions.\n\n- `Linux (Debian/Ubuntu/Mint)`_\n- `Linux (Fedora 24 and later)`_\n- `Linux (CentOS/Scientific Linux)`_\n- `Linux (openSUSE)`_\n- `Linux (Arch/Manjaro)`_\n- `Linux (Solus)`_\n- `OpenBSD`_\n- `FreeBSD`_\n- `macOS`_\n- `Windows`_\n\nBinaries for most of these platforms are provided from the download\npage at https://cadabra.science/download.html, which links to\nhttps://github.com/kpeeters/cadabra2/releases/latest.  These binaries\nare automatically generated on every release.\n\nSee `Building Cadabra as C++ library`_ for instructions on how to\nbuild the entire Cadabra functionality as a library which you can use\nin a C++ program.\n\nSee `Building a Jupyter kernel`_ for information on the Jupyter kernel\nfor Cadabra sessions.\n\nSee `Notes on Python paths`_ for some remarks on where Cadabra\ninstalls its Python modules and how this plays with various types of\nPython installations.\n\n\nLinux (Debian/Ubuntu/Mint)\n~~~~~~~~~~~~~~~~~~~~~~~~~~\n\nOn Debian/Ubuntu you can install all that is needed with::\n\n    sudo apt install git cmake libpython3-dev python3-dev g++ libgmp3-dev \\\n          libgtkmm-3.0-dev libboost-all-dev libssl-dev libgmp-dev libsqlite3-dev uuid-dev  \\\n          python3-matplotlib python3-mpmath python3-sympy python3-gmpy2\n\n(on Ubuntu 14.04 you need to replace `cmake` with `cmake3` and also\ninstall g++-4.9; get in touch if you don't know how to do this). On\nolder systems you may want to install `sympy` using `sudo pip3 install\nsympy`, but that is discouraged in general.\n\t \nThis is the development platform and issues are typically first fixed\nhere. You can use either g++ or the clang++ compiler to build. You need to\nclone the cadabra2 git repository (if you download the .zip file you\nwill not have all data necessary to build). So first do::\n\n    git clone https://github.com/kpeeters/cadabra2\n\nBuilding is then done with the standard::\n\n    cd cadabra2\n    mkdir build\n    cd build\n    cmake ..\n    make\n    sudo make install\n\nThis will produce the command line app ``cadabra2`` and the Gtk\nnotebook interface ``cadabra2-gtk``. You can also find the latter in\nthe 'Education' menu.\n\nLinux (Fedora 24 and later)\n~~~~~~~~~~~~~~~~~~~~~~~~~~~\n\nFedora 24 is the first Fedora to have Python 3; you can build Cadabra\nusing Python 2 but you are strongly encouraged to upgrade. The Fedora\nplatform receives less testing so please get in touch if you run into\nany issues. You can use either g++ or the clang++ compiler.\n\nInstall the dependencies with::\n\n    sudo dnf install git python3-devel make cmake gcc-c++ \\\n         gmp-devel libuuid-devel sqlite-devel \\\n         gtkmm30-devel boost-devel \\\n         python3-matplotlib \\\n         python3-pip\n    sudo pip3 install sympy\n\nYou need to clone the cadabra2 git repository (if you download the\n.zip file you will not have all data necessary to build). So first do::\n\n    git clone https://github.com/kpeeters/cadabra2\n\nBuilding is then done with the standard::\n\n    cd cadabra2\n    mkdir build\n    cd build\n    cmake ..\n    make\n    sudo make install\n\nThis will produce the command line app ``cadabra2`` and the Gtk\nnotebook interface ``cadabra2-gtk``. You can also find the latter\nwhen searching for the 'Cadabra' app from the 'Activities' menu.\n\nLinux (CentOS/Scientific Linux)\n~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n\nOn CentOS/Scientific Linux you need to activate The Software\nCollections (SCL) and Extra Packages for Enterprise Linux (EPEL) to\nget access to a modern C++ compiler, Python3 and all required build\ntools.\n\nOn *CentOS* first do::\n\n    sudo yum install centos-release-scl epel-release\n\nOn *Scientific Linux* the equivalent is::\n\n    sudo yum install yum-conf-softwarecollections epel-release\n\t \nNow install all build dependencies with::\n  \n    sudo yum install devtoolset-7 rh-python36 cmake3 \\\n\t          gmp-devel libuuid-devel sqlite-devel \\\n                  gtkmm30-devel boost-devel git \\\n\t          python-matplotlib \n\nYou need to enable the Python3 and C++ compiler which you just\ninstalled with::\n\n    scl enable rh-python36 bash\t\t\t\t\t\n    scl enable devtoolset-7 bash\n\n(note: do *not* use sudo here!).\n\t \nYou also need to install sympy by hand::\n\n    sudo pip3 install sympy\n\nNow need to clone the cadabra2 git repository (if you download the\n.zip file you will not have all data necessary to build)::\n\n    git clone https://github.com/kpeeters/cadabra2\n\nBuilding is then done with the standard::\n\n    cd cadabra2\n    mkdir build\n    cd build\n    cmake3 .. \n    make\n    sudo make install\n\nThis will produce the command line app ``cadabra2`` and the Gtk\nnotebook interface ``cadabra2-gtk``. You can also find the latter in\nthe 'Education' menu.\n\n\nLinux (openSUSE)\n~~~~~~~~~~~~~~~~\n\nFor openSUSE (tested on 'Leap 15.2', probably also fine with minor\nchanges for 'Tumbleweed') you first need to install the dependencies\nwith::\n\n    sudo zypper install --no-recommends git cmake python3-devel gcc-c++ \\\n                  gmp-devel libuuid-devel sqlite-devel \\\n                  gtkmm3-devel  \\\n                  python3-matplotlib \\\n                  python3-sympy \\\n                  libboost_system1_71_0-devel libboost_filesystem1_71_0-devel \\\n                  libboost_date_time1_71_0-devel libboost_program_options1_71_0-devel\n\nThis platform receives less testing so please get in touch if you run\ninto any issues. You need to clone the cadabra2 git repository (if you\ndownload the .zip file you will not have all data necessary to\nbuild). So first do::\n\n    git clone https://github.com/kpeeters/cadabra2\n\nBuilding is then done with the standard::\n\n    cd cadabra2\n    mkdir build\n    cd build\n    cmake .. \n    make\n    sudo make install\n\nThis will produce the command line app ``cadabra2`` and the Gtk\nnotebook interface ``cadabra2-gtk``. \n\n\nLinux (Arch/Manjaro)\n~~~~~~~~~~~~~~~~~~~~\n\nThe package for Arch Linux is cadabra2\nhttps://aur.archlinux.org/packages/cadabra2/  Building and\ninstalling (including dependencies) can be accomplished with::\n\n    yay -S cadabra2\n\nAlternatively use ``makepkg``::\n\n    git clone https://aur.archlinux.org/cadabra2.git\n    cd cadabra2\n    makepkg -si\n\nPlease consult the Arch Wiki\nhttps://wiki.archlinux.org/index.php/Arch_User_Repository#Installing_packages\nfor more information regarding installing packages from the AUR.\n\n\nLinux (Solus)\n~~~~~~~~~~~~~\n\nSupport for Solux Linux is experimental. To build from source on Solus\nLinux, first install the dependencies by doing::\n\n    sudo eopkg install -c system.devel\n    sudo eopkg install libboost-devel gmp-devel libgtkmm-3-devel \n    sudo eopkg install sqlite3-devel python3-devel\n    sudo eopkg install git cmake make g++\n\nThen configure and build with::\n\n    cd cadabra2\n    mkdir build\n    cd build\n    cmake .. -DCMAKE_INSTALL_PREFIX=/usr\n    make\n    sudo make install\n\nThis installs below ``/usr`` (instead of ``/usr/local`` on other\nplatforms) because I could not figure out how to make it pick up\nlibraries there.\n\nAny feedback on these instructions is welcome.\n\n\nOpenBSD\n~~~~~~~\n\nInstall the dependencies with::\n\n  pkg_add git cmake boost python-3.6.2 gtk3mm gmp gmpxx py3-sympy\n\nWe will build using the default clang-4.0.0 compiler; building with\nthe alternative g++-4.9.4 leads to trouble when linking against the\nlibraries added with pkg_add.\n\nConfigure and build with::\n\n  cd cadabra2\n  mkdir build\n  cd build\n  cmake -DENABLE_MATHEMATICA=OFF ..\n  make\n  su\n  make install\n\nThe command-line version is now available as ``cadabra2`` and the\nnotebook interface as ``cadabra2-gtk``.\n\nAny feedback on this platform is welcome as this is not our\ndevelopment platform and testing is done only occasionally.\n\n\nFreeBSD\n~~~~~~~\n\nThe recommended way to install Cadabra is through::\n\n  pkg install cadabra2\n\nIt is also possible to build and install Cadabra from the port::\n\n  cd /usr/ports/math/cadabra2 && make install clean\n\nThe command-line version is now available as ``cadabra2`` and the\nnotebook interface as ``cadabra2-gtk``.\n\nAny feedback on this platform is welcome as this is not our\ndevelopment platform.\n\n\nmacOS\n~~~~~\n\nCadabra builds with the standard Apple compiler, on both Intel and\nApple silicon, but you do need a number of packages from Homebrew (see\nhttps://brew.sh). Install the required dependencies with::\n\n    brew install cmake boost gmp python3 \n    brew install pkgconfig \n    brew install gtkmm3 adwaita-icon-theme\n    pip3 install sympy gmpy2\n\nIf the lines above prompt you to install XCode, go ahead and let it do\nthat.\n\nYou can build against an Anaconda Python installation (in case you\nprefer Anaconda over the Homebrew Python); cmake will automatically\npick this up if available.\n\nYou need to clone the cadabra2 git repository (if you download the\n.zip file you will not have all data necessary to build). So do::\n\n    git clone https://github.com/kpeeters/cadabra2\n\nAfter that you can build with the standard::\n\n    cd cadabra2\n    mkdir build\n    cd build\n    cmake -DENABLE_MATHEMATICA=OFF ..\n    make\n    sudo make install\n\n(*note* the `-DENABLE_MATHEMATICA=OFF` in the `cmake` line above; the\nMathematica scalar backend does not yet work on macOS).\n  \nThis will produce the command line app ``cadabra2`` and the Gtk\nnotebook interface ``cadabra2-gtk``. \n\nFeedback from macOS users is *very* welcome because this is not the main\ndevelopment platform.\n\n\nWindows\n~~~~~~~\n\nOn Windows compilation is easiest by using the MSYS2 system, as their\ngtkmm-3.0 packages just work and the whole system can be driven from the\ncommand line. We used to build Cadabra using the vcpkg packages, but\nthey no longer provide packages for gtkmm-3.0, and in general the lack\nof binary packages means that build times are on the order of many, many\nhours, instead of just a few minutes with MSYS2. More info on building and\npackaging gtk apps on windows at https://www.gtk.org/docs/installations/windows/.\n\nInstall MSYS2 from https://www.msys2.org and start a UCRT64 shell.\nFirst update with (if you don't do this you may end up not being able\nto install some of the required packages due to version conflicts)::\n\n    pacman -Suy\n\nThen install a compiler and the dependencies of Cadabra with::\n\n    pacman -S mingw-w64-ucrt-x86_64-gcc\n    pacman -S mingw-w64-ucrt-x86_64-gtkmm3\n    pacman -S mingw-w64-ucrt-x86_64-boost    \n    pacman -S mingw-w64-ucrt-x86_64-sqlite3\n    pacman -S mingw-w64-ucrt-x86_64-cmake\n    pacman -S mingw-w64-ucrt-x86_64-python\n    pacman -S mingw-w64-ucrt-x86_64-python-matplotlib\n    pacman -S mingw-w64-ucrt-x86_64-python-sympy\n    pacman -S mingw-w64-ucrt-x86_64-osslsigncode\n    pacman -S git\n\nCheckout Cadabra and build::\n\n    git clone https://github.com/kpeeters/cadabra2\n    cd cadabra2\n    mkdir build\n    cd build\n    cmake ..\n    ninja\n    ninja install\n\nThis will leave an installation in `Program Files (x86)/Cadabra`, from where\nyou can start `cadabra2-gtk`. \n\nTo build an installer, simply run `cpack` after having built\nCadabra. \n    \n\nBuilding a Jupyter kernel\n-------------------------\n\nAs of version 2.3.4 the standard build process (as described above)\nalso creates a Jupyter kernel, which is written in Python on top of\n`ipykernel` (thanks to Fergus Baker). This should work on most\nplatforms out-of-the-box; you do not need to do anything else. The\nJupyter kernel allows you to use Cadabra notation inside a Jupyter\nnotebook session.\n\nThe distribution also still contains code for the 'old' Jupyter\nkernel, which is written in C++ on top of `xeus`. Building this kernel\nis more complicated mainly because of this dependency, and there is\nnot much of an advantage over the Python kernel; it's mainly left in\nthe tree for future reference, For full instructions on how to build\nthe old `xeus`-based kernel, see\nhttps://github.com/kpeeters/cadabra2/blob/master/JUPYTER.rst.\n\n\nCreating an AppImage\n--------------------\n\nThe Cadabra build system can create an AppImage for use on a wide\nvariety of Linux distributions (this is used to create the AppImage\nwhich is available from the `releases` on github). This build process\nhas been tested by using Ubuntu 20.04 as base system. Install the\nprerequisites as above,::\n\n    sudo apt install git cmake libpython3-dev python3-dev g++ libgmp3-dev \\\n          libgtkmm-3.0-dev libboost-all-dev libssl-dev libgmp-dev libsqlite3-dev uuid-dev  \\\n          python3-matplotlib python3-mpmath python3-sympy python3-gmpy2\n\nNow configure and build with::\n\n    cmake -DAPPIMAGE_MODE=ON -DCMAKE_INSTALL_PREFIX=/usr ..\n    make\n    make install DESTDIR=AppDir\n\nThis installs everything in the `AppDir` folder ready for packaging.\nThen run::\n\n    make appimage\n\nto create the AppImage itself. If you run into trouble with this,\nplease first consult the comments in the top-level `CMakeLists.txt`\nfile about `linuxdeploy` and friends.\n\n\n\nTutorials and other help\n------------------------\n\nPlease consult https://cadabra.science/ for tutorial-style notebooks\nand all other documentation, and https://cadabra.science/doxygen/html/\nfor doxygen documentation of the current master branch. The latter can\nalso be generated locally; you will need (on Debian and derivatives)::\n\n    sudo apt-get install doxygen libjs-mathjax  \n\nFor any questions, please contact info@cadabra.science .\n\n\nBuilding Cadabra as C++ library\n-------------------------------\n\nIf you want to use the functionality of Cadabra inside your own C++\nprograms, you can build Cadabra as a shared library. To do this::\n\n    mkdir build-lib\n    cd build-lib\n    cmake -DBUILD_AS_CPP_LIBRARY=ON ..\n    make\n    sudo make install\n\nThere is a sample program `simple.cc\n<https://github.com/kpeeters/cadabra2/blob/master/c%2B%2Blib/simple.cc>`_\nin the `c++lib` directory which shows how to use the Cadabra library.\n\n\nNotes on Python paths\n---------------------\n\nCadabra tries to play nice with a large variety of Python\ninstallations, which is not an easy task. In general, it will try to\ninstall in such a way that the Python interpreter which is specified\nat build time will be able to import the `cadabra2` Python module\nwithout any change to its path.  This is necessary so that e.g. a\nJupyter notebook will be able to find this module.  Cadabra will\ntherefore install its Python module in\n`site.getsitepackages()[0]`. Since this module constructs its\ndocstrings dynamically on load, the manual pages are also stored\nrelative to this module.\n\nHowever, Cadabra will install its binaries according to standard\nCMake logic in `$CMAKE_INSTALL_PREFIX/bin/`. On systems that have\nPython installed in subtree which is not below `$CMAKE_INSTALL_PREFIX`,\nthis means that the Cadabra binaries and the Cadabra Python module\nwill not be in the same subtree. This typically happens on systems\nwith Python coming from Homebrew, as these will have Python somewhere\nbelow `/opt/homebrew` even when `$CMAKE_INSTALL_PREFIX` is `/usr/local/`.\n\nOn some systems, users or package managers prefer that\n`site.getsitepackages()[0]` remains under control of the package\nmanager (Homebrew is the typical example). In this case, if you do not\nwant to write there, your only option is to first create a virtual\nenvironment before you run Cadabra's `cmake`.\n\n\nSpecial thanks\n--------------\n\nSpecial thanks to José M. Martín-García (for the xPerm\ncanonicalisation code), James Allen (for writing much of the factoring\ncode), Dominic Price (for the meld algorithm implementation, many\nadditions to the notebook interface, the conversion to pybind and the\nWindows port), Fergus Baker (for the new Jupyter kernel), Isuru\nFernando (for the Conda packaging), the Software Sustainability\nInstitute and the Institute of Advanced Study. Thanks to the many\npeople who have sent me bug reports (keep 'm coming), and thanks to\nall of you who use Cadabra, sent feedback or cited the Cadabra\npapers.\n\nLicenses\n--------\n\nCadabra itself is licensed under the GPL-3.0. It includes some dependencies\nwhich have the following licenses:\n\n* tiny-process-lib [https://gitlab.com/eidheim/tiny-process-library/]\n  MIT license\n\n   \n"
  },
  {
    "path": "c++lib/.gitignore",
    "content": "Makefile\ntreetracker\n"
  },
  {
    "path": "c++lib/CMakeLists.txt",
    "content": "cmake_minimum_required(VERSION 3.12)\n\nset(CMAKE_CXX_STANDARD 17)\nproject(Cadabra)\n\n#---------------------------------------------------------------------------\n# Preamble.\n#---------------------------------------------------------------------------\n\n# Set path to additional cmake files\nset(CMAKE_MODULE_PATH ${CMAKE_MODULE_PATH} \"${CMAKE_CURRENT_SOURCE_DIR}/../cmake/modules\")\n\n# Disable warning 'MACOSX_RPATH is enabled by default'\nif (POLICY CMP0042)\n  cmake_policy(SET CMP0042 NEW)\nendif(POLICY CMP0042)\n\n# Disable warning 'Only interpret if() arguments as variables or keywords when unquoted'\nif (POLICY CMP0054)\n  cmake_policy(SET CMP0054 NEW)\nendif()\n\n# Ensure that we can build the library and install it without having to\n# build the samples.\nset(CMAKE_SKIP_INSTALL_ALL_DEPENDENCY TRUE)\n\nfind_package(Python REQUIRED COMPONENTS Interpreter Development)\nmessage(STATUS \"Found python library: ${Python_LIBRARIES}\")\nmessage(STATUS \"Found python headers: ${Python_INCLUDE_DIRS}\")\nmessage(STATUS \"Python version is ${Python_VERSION_MAJOR}.${Python_VERSION_MINOR}.\")\n\n#---------------------------------------------------------------------------\n# User options.\n#---------------------------------------------------------------------------\n\nset(INSTALL_LIB_DIR     lib                CACHE PATH \"Installation directory for library\")\nset(INSTALL_INCLUDE_DIR include/cadabra2++ CACHE PATH \"Installation directory for header files\")\n\n# Scalar backend options\noption(USE_TREETRACKER \"Use the TreeTracker scalar backend\" OFF)\nset(PATH_TREETRACKER   \"./treetracker\" CACHE STRING \"Path to the TreeTracker library\")\n\n\n#---------------------------------------------------------------------------\n# Compiler flags.\n#---------------------------------------------------------------------------\n\nadd_definitions(\"-DNO_SYMPY\")\nif(CMAKE_COMPILER_IS_GNUCXX)\n  add_definitions(\"-Wall -g -Wno-unused-but-set-variable\")\nendif()\n\nif(CMAKE_COMPILER_IS_GNUCC OR CMAKE_COMPILER_IS_GNUCXX)\n  if (CMAKE_CXX_COMPILER_VERSION VERSION_LESS 14.0)\n    message(STATUS \"This version of g++ (${CMAKE_CXX_COMPILER_VERSION}) incorrectly warns about possibly uninitialised memory when using std::variant containing a std::shared_ptr. Disabling this warning.\")\n    set(CMAKE_CXX_FLAGS \"${CMAKE_CXX_FLAGS} -Wno-maybe-uninitialized\")\n  endif()\n  set(CMAKE_CXX_FLAGS \"${CMAKE_CXX_FLAGS} -O2\")\nendif()\n\nif(\"${CMAKE_CXX_COMPILER_ID}\" STREQUAL \"Clang\")\n   set(CMAKE_CXX_FLAGS \"${CMAKE_CXX_FLAGS} -O2\")\nendif()\n\nif(MSVC)\n\tset(CMAKE_WINDOWS_EXPORT_ALL_SYMBOLS ON)\n\tset(MSVC_FLAGS\n\t\t\"/wd4101\"\t\t\t\t\t\t# unreferenced local variable\n\t\t\"/wd4250\"\t\t\t\t\t\t# inherits via dominance\n\t\t\"/wd4244\"\t\t\t\t\t\t# conversion from x to y, possible loss of data\n\t\t\"/wd4267\"\t\t\t\t\t\t# same as 4244\n\t\t\"/wd4996\"\t\t\t\t\t\t# deprecated POSIX functions\n\t\t\"-D_CRT_SECURE_NO_WARNINGS\"\t\t# don't warn about deprecated functions\n\t)\n\tforeach(FLAG ${MSVC_FLAGS})\n\t\tset(CMAKE_CXX_FLAGS \"${CMAKE_CXX_FLAGS} ${FLAG}\")\n\tendforeach()\n\nendif()\n\n\n#---------------------------------------------------------------------------\n# Find libraries.\n#---------------------------------------------------------------------------\n\n# Locate gmpxx. On Homebrew there seems to be constantly something wrong with\n# the pkgconfig for gmpxx. So we just add the include path by hand.\nif(APPLE)\n   add_definitions(\"-I/usr/local/include -I/opt/local/include\")\nendif()\nif(MSVC)\n  find_package(GMPXX REQUIRED)\n  set(GMP_LIB \"${GMPXX_LIBRARIES}\")\n  set(GMPXX_LIB \"${GMPXX_LIBRARIES}\")\n  include_directories(\"${VCPKG_INCLUDE_DIRS}\")\nelse()\n  find_library(GMP_LIB gmp REQUIRED)\n  find_library(GMPXX_LIB gmpxx REQUIRED)\n  message(STATUS \"Found gmp ${GMP_LIB}\")\n  message(STATUS \"Found gmpxx ${GMPXX_LIB}\")\nendif()\n\n\n#---------------------------------------------------------------------------\n# Enumerate source files.\n#---------------------------------------------------------------------------\n\nSET(RESERVED_NODE_SRC_FILES\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/ReservedNode.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/Equals.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/Sum.cc\n)\n\nset(LOCAL_SRC_FILES\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/Adjform.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/Algorithm.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/Cleanup.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/Combinatorics.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/Compare.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/DisplayBase.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/DisplayTeX.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/DisplaySympy.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/DisplayTerminal.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/Grouping.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/TerminalStream.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/Multiplier.cc  \n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/NDSolver.cc  \n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/NEvaluator.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/NTensor.cc  \n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/NInterpolatingFunction.cc  \n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/Exceptions.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/Exchange.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/ExManip.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/Functional.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/IndexIterator.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/IndexClassifier.cc  \n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/Hash.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/Kernel.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/Parser.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/PreClean.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/PreProcessor.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/ProgressMonitor.cc  \n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/Props.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/Stopwatch.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/Storage.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/Symbols.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/YoungTab.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/properties/Accent.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/properties/AntiCommuting.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/properties/AntiSymmetric.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/properties/Commuting.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/properties/CommutingAsProduct.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/properties/CommutingAsSum.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/properties/CommutingBehaviour.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/properties/Coordinate.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/properties/DAntiSymmetric.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/properties/Depends.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/properties/DependsInherit.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/properties/Derivative.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/properties/DerivativeOp.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/properties/Determinant.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/properties/Diagonal.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/properties/DifferentialForm.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/properties/DiracBar.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/properties/Distributable.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/properties/EpsilonTensor.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/properties/ExteriorDerivative.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/properties/FilledTableau.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/properties/GammaMatrix.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/properties/GammaTraceless.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/properties/ImaginaryI.cc  \n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/properties/ImplicitIndex.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/properties/Indices.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/properties/Integer.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/properties/InverseMetric.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/properties/KroneckerDelta.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/properties/LaTeXForm.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/properties/Matrix.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/properties/Metric.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/properties/NonCommuting.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/properties/NumericalFlat.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/properties/PartialDerivative.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/properties/RiemannTensor.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/properties/SatisfiesBianchi.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/properties/SelfAntiCommuting.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/properties/SelfCommuting.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/properties/SelfNonCommuting.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/properties/SortOrder.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/properties/Spinor.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/properties/Symbol.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/properties/Symmetric.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/properties/Tableau.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/properties/TableauBase.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/properties/TableauInherit.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/properties/TableauSymmetry.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/properties/Trace.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/properties/Traceless.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/properties/Weight.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/properties/WeightInherit.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/properties/WeylTensor.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/modules/xperm_new.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/algorithms/canonicalise.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/algorithms/collect_components.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/algorithms/collect_factors.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/algorithms/collect_terms.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/algorithms/combine.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/algorithms/complete.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/algorithms/decompose_product.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/algorithms/distribute.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/algorithms/drop_weight.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/algorithms/einsteinify.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/algorithms/eliminate_kronecker.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/algorithms/eliminate_metric.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/algorithms/epsilon_to_delta.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/algorithms/evaluate.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/algorithms/expand.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/algorithms/expand_delta.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/algorithms/expand_diracbar.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/algorithms/expand_power.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/algorithms/factor_in.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/algorithms/factor_out.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/algorithms/fierz.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/algorithms/first_order_form.cc  \n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/algorithms/flatten_product.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/algorithms/flatten_sum.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/algorithms/indexsort.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/algorithms/integrate_by_parts.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/algorithms/join_gamma.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/algorithms/keep_terms.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/algorithms/lr_tensor.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/algorithms/order.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/algorithms/product_rule.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/algorithms/reduce_delta.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/algorithms/rename_dummies.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/algorithms/rewrite_indices.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/algorithms/simplify.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/algorithms/sort_product.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/algorithms/sort_sum.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/algorithms/split_gamma.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/algorithms/split_index.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/algorithms/substitute.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/algorithms/sym.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/algorithms/tab_basics.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/algorithms/take_match.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/algorithms/replace_match.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/algorithms/unwrap.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/algorithms/vary.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/algorithms/young_project.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/algorithms/young_project_product.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/algorithms/young_project_tensor.cc\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/algorithms/meld.cc\n  SympyDummy.cc\n)\nset(MAIN_HEADERS\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/Adjform.hh\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/Algorithm.hh\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/Combinatorics.hh\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/Compare.hh\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/DisplayBase.hh\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/DisplayTerminal.hh\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/NEvaluator.hh\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/Equals.hh  \n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/Exceptions.hh\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/ExManip.hh\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/IndexClassifier.hh\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/IndexIterator.hh\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/Kernel.hh\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/lru_cache.hh\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/Hash.hh\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/Multiplier.hh  \n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/NTensor.hh  \n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/Parser.hh\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/ProgressMonitor.hh\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/Props.hh\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/ReservedNode.hh\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/Storage.hh\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/Stopwatch.hh\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/Sum.hh\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/TerminalStream.hh\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/tree.hh\n  ${CMAKE_CURRENT_SOURCE_DIR}/../core/YoungTab.hh\n  )\nFILE(GLOB ALGO_HEADERS ${CMAKE_CURRENT_SOURCE_DIR}/../core/algorithms/*.hh)\nFILE(GLOB PROP_HEADERS ${CMAKE_CURRENT_SOURCE_DIR}/../core/properties/*.hh)\n\n# Copy relevant header files to the binary directory\nfile(COPY ${MAIN_HEADERS} DESTINATION ${CMAKE_BINARY_DIR}/include/cadabra2++)\nfile(COPY ${ALGO_HEADERS} DESTINATION ${CMAKE_BINARY_DIR}/include/cadabra2++/algorithms)\nfile(COPY ${PROP_HEADERS} DESTINATION ${CMAKE_BINARY_DIR}/include/cadabra2++/properties)\n\n# Create a 'master' header which includes all the above for convenience\nfile(WRITE \"${CMAKE_BINARY_DIR}/include/cadabra2++.hh\" \"// Main headers\\n\")\nforeach(HEADER ${MAIN_HEADERS})\n\tget_filename_component(FILENAME \"${HEADER}\" NAME)\n\tfile(APPEND \"${CMAKE_BINARY_DIR}/include/cadabra2++.hh\" \"#include \\\"cadabra2++/${FILENAME}\\\"\\n\")\nendforeach()\nfile(APPEND \"${CMAKE_BINARY_DIR}/include/cadabra2++.hh\" \"\\n// Properties\\n\")\nforeach(HEADER ${PROP_HEADERS})\n\tget_filename_component(FILENAME \"${HEADER}\" NAME)\n\tfile(APPEND \"${CMAKE_BINARY_DIR}/include/cadabra2++.hh\" \"#include \\\"cadabra2++/properties/${FILENAME}\\\"\\n\")\nendforeach()\nfile(APPEND \"${CMAKE_BINARY_DIR}/include/cadabra2++.hh\" \"\\n// Algorithms\\n\")\nforeach(HEADER ${ALGO_HEADERS})\n\tget_filename_component(FILENAME \"${HEADER}\" NAME)\n\tfile(APPEND \"${CMAKE_BINARY_DIR}/include/cadabra2++.hh\" \"#include \\\"cadabra2++/algorithms/${FILENAME}\\\"\\n\")\nendforeach()\nfile(READ ${CMAKE_CURRENT_SOURCE_DIR}/cpplib.hh.in CPPLIB_HH_IN)\nfile(APPEND \"${CMAKE_BINARY_DIR}/include/cadabra2++.hh\" \"\\n//Helper functions\\n${CPPLIB_HH_IN}\")\n\nset(LIB_INCLUDE_DIRS\n\t\".\" \n\t\"${CADABRA_CORE_DIR}\"\n\t\"${CADABRA_LIBS_DIR}/pybind11/include\"\n\t\"${CADABRA_LIBS_DIR}/internal/include\"\n\t\"${CADABRA_LIBS_DIR}/dbg\"\n\t${Python_INCLUDE_DIRS}\n)\nmessage(\"${LIB_INCLUDE_DIRS}\")\n\nif(USE_TREETRACKER)\n  add_definitions(-DUSE_TREETRACKER)\n  if(EXISTS \"${PATH_TREETRACKER}/treetracker.h\" OR EXISTS \"${CMAKE_CURRENT_SOURCE_DIR}/${PATH_TREETRACKER}/treetracker.h\")\n\t include_directories(${PATH_TREETRACKER})\n\t message(\"-- Using the TreeTracker scalar backend at ${PATH_TREETRACKER}\")\n  else()\n\t message(FATAL_ERROR \"-- Cannot find the 'treetracker.h' file in '${PATH_TREETRACKER}'\")\n  endif()\nelse()\n  message(\"-- Not using the TreeTracker scalar backend\")\nendif()\n\n\n#---------------------------------------------------------------------------\n# Targets\n#---------------------------------------------------------------------------\n\nadd_library(cadabra2++objects         OBJECT ${LOCAL_SRC_FILES} ${RESERVED_NODE_SRC_FILES})\nset_property(TARGET cadabra2++objects PROPERTY POSITION_INDEPENDENT_CODE 1)\ntarget_include_directories(cadabra2++objects PUBLIC \"${LIB_INCLUDE_DIRS}\")\n\nadd_library(cadabra2++         SHARED $<TARGET_OBJECTS:cadabra2++objects>)\nset_target_properties(cadabra2++        PROPERTIES PUBLIC_HEADER \"${PUBLIC_HEADER_FILES}\")\n\ntarget_link_libraries(cadabra2++        ${GMPXX_LIB} ${GMP_LIB} ${Python_LIBRARIES})\n\nadd_library(cadabra2++_static  STATIC $<TARGET_OBJECTS:cadabra2++objects>)\ntarget_link_libraries(cadabra2++_static ${GMPXX_LIB} ${GMP_LIB} ${Python_LIBRARIES})\n\nif(TBB_FOUND)\n  target_link_libraries(cadabra2++ TBB::tbb)\n  target_compile_definitions(cadabra2++objects PRIVATE HAS_TBB)\nendif()\n\n# Trivial example\nadd_executable(trivial trivial.cc)\ntarget_include_directories(trivial PUBLIC\n  \"${CADABRA_LIBS_DIR}/pybind11/include\"\n  \"${CMAKE_BINARY_DIR}/include\"\n  \"${CMAKE_BINARY_DIR}/include/cadabra2++\"\n  ${Python_INCLUDE_DIRS}\n)\ntarget_link_libraries(trivial cadabra2++)\n\n# Sample executable\nadd_executable(simple simple.cc)\ntarget_include_directories(simple PUBLIC\n  \"${CADABRA_LIBS_DIR}/pybind11/include\"\n  \"${CMAKE_BINARY_DIR}/include\"\n  \"${CMAKE_BINARY_DIR}/include/cadabra2++\"\n  ${Python_INCLUDE_DIRS}\n)\ntarget_link_libraries(simple cadabra2++)\n \n# Test for adjform\nadd_executable(adjform adjform.cc)\ntarget_include_directories(adjform PUBLIC\n  \"${CADABRA_LIBS_DIR}/pybind11/include\"\n  \"${CMAKE_BINARY_DIR}/include\"\n  \"${CMAKE_BINARY_DIR}/include/cadabra2++\"\n  ${Python_INCLUDE_DIRS}\n)\ntarget_link_libraries(adjform cadabra2++)\n \n# Test for numerical evaluation\nadd_executable(nevaluate nevaluate.cc)\ntarget_include_directories(nevaluate PUBLIC\n  \"${CADABRA_LIBS_DIR}/pybind11/include\"\n  \"${CMAKE_BINARY_DIR}/include\"\n  \"${CMAKE_BINARY_DIR}/include/cadabra2++\"\n  ${Python_INCLUDE_DIRS}\n)\ntarget_link_libraries(nevaluate cadabra2++)\n \n\n#---------------------------------------------------------------------------\n# Installation\n#---------------------------------------------------------------------------\n\ninstall(TARGETS  cadabra2++        LIBRARY DESTINATION \"${INSTALL_LIB_DIR}\")\ninstall(TARGETS  cadabra2++_static LIBRARY DESTINATION \"${INSTALL_LIB_DIR}\" ARCHIVE DESTINATION \"${INSTALL_LIB_DIR}\")\ninstall(DIRECTORY ${CMAKE_BINARY_DIR}/include DESTINATION \"${INSTALL_INCLUDE_DIR}\")\n\ninstall(DIRECTORY \n\tDESTINATION bin \n\tDIRECTORY_PERMISSIONS \n\t\tOWNER_READ \n\t\tOWNER_WRITE \n\t\tOWNER_EXECUTE\n\t\tGROUP_READ \n\t\tGROUP_EXECUTE\n\t\tWORLD_READ \n\t\tWORLD_EXECUTE\n)\n\ninstall(DIRECTORY \n\tDESTINATION lib\n\tDIRECTORY_PERMISSIONS \n\t\tOWNER_READ \n\t\tOWNER_WRITE \n\t\tOWNER_EXECUTE\n\t\tGROUP_READ \n\t\tGROUP_EXECUTE\n\t\tWORLD_READ \n\t\tWORLD_EXECUTE\n)\n"
  },
  {
    "path": "c++lib/README.txt",
    "content": "This directory contains code to illustrate the use of Cadabra from\nwithin C++ programs.\n"
  },
  {
    "path": "c++lib/SympyDummy.cc",
    "content": "\n#include \"Parser.hh\"\n#include \"Cleanup.hh\"\n#include \"PreClean.hh\"\n#include \"SympyCdb.hh\"\n#include \"DisplaySympy.hh\"\n#ifdef USE_TREETRACKER\n#include \"treetracker.h\"\n#endif\n#include <sstream>\n\ncadabra::Ex::iterator sympy::apply(const cadabra::Kernel& kernel, cadabra::Ex& ex, cadabra::Ex::iterator& it,\n                                   const std::vector<std::string>& head, std::vector<std::string> args,\n                                   const std::string& method)\n\t{\n\tstd::ostringstream str;\n\n\tif(head.size()>0)\n\t\tstr << head[0] << \"(\";\n\n\tcadabra::DisplaySympy ds(kernel, ex);\n\tds.output(str, it);\n\n\tif(head.size()>0)\n\t\tif(args.size()>0)\n\t\t\tstr << \", \" << args[0] << \")\";\n\tstr << method;\n\n\tif(head.size()>0)\n\t\tstr << \")\";\n\n\t//\tstd::cerr << \"Send: \" << str.str() << std::endl;\n\n#ifdef USE_TREETRACKER\n\n\tauto res = TreeTracker::FromString(str.str());\n\tres.RecursiveSimplify();\n\tstd::stringstream istr;\n\tres.ShowTree(istr, 0, false, true);\n\t//\tstd::cerr << \"Return: \" << istr.str() << std::endl;\n\tauto ptr = std::make_shared<cadabra::Ex>();\n\tcadabra::Parser parser(ptr);\n\tistr >> parser;\n\tpre_clean_dispatch_deep(kernel, *parser.tree);\n\tcleanup_dispatch_deep(kernel, *parser.tree);\n\t//parser.tree->print_recursive_treeform(std::cerr, parser.tree->begin());\n\tds.import(*parser.tree);\n\n\tcadabra::Ex::iterator first=parser.tree->begin();\n\tit = ex.move_ontop(it, first);\n#endif\n\n\treturn it;\n\t}\n\nvoid sympy::invert_matrix(const cadabra::Kernel& kernel, cadabra::Ex& ex,\n\t\t\t\t\t\t\t\t  cadabra::Ex& rules, const cadabra::Ex& tocompute)\n\t{\n\tthrow std::logic_error(\"Not implemented: sympy::invert_matrix\");\n\t}\n\nvoid sympy::determinant(const cadabra::Kernel&, cadabra::Ex& ex, cadabra::Ex& rules, const cadabra::Ex& tocompute)\n\t{\n\tthrow std::logic_error(\"Not implemented: sympy::determinant\");\n\t}\n\nvoid sympy::trace(const cadabra::Kernel&, cadabra::Ex& ex, cadabra::Ex& rules, const cadabra::Ex& tocompute)\n\t{\n\tthrow std::logic_error(\"Not implemented: sympy::trace\");\n\t}\n"
  },
  {
    "path": "c++lib/adjform.cc",
    "content": "#include \"cadabra2++.hh\"\n#include <iostream>\n\nusing namespace cadabra;\nusing namespace cadabra::cpplib;\n\nint main(int, char**)\n{\n\tKernel k(true);\n\tpprint_enable_utf8();\n    //{\\mu,\\nu}::Indices(vector).\n    //tr{#}::Trace.\n    //u^{\\mu}::SelfNonCommuting.\n    //u^{\\mu}::ImplicitIndex.\n    //ex:=tr{A u^{\\nu} u^{\\mu} u^{\\mu} u^{\\nu} + B u^{\\mu} u^{\\mu} u^{\\nu} u^{\\nu}}:\n    //meld(_);\n\n\tinject_property<SelfNonCommuting>(k, \"{A,B,C,D }\");\n\tinject_property<Trace>(k, \"tr{#}\");\n\n\tauto ex = R\"(tr(A B C D + B C D A)\"_ex(k);\n\tmeld m(k, *ex);\n\tstd::cout << pprint(k, ex) << '\\n';\n\tm.apply_pre_order();\n\tstd::cout << pprint(k, ex) << '\\n';\n\t// assert ex == $2 * Tr{ A B C D }$\n\t\n}\n"
  },
  {
    "path": "c++lib/cpplib.hh.in",
    "content": "#ifdef _MSC_VER\n#define WIN32_LEAN_AND_MEAN\n#include <Windows.h>\n#endif\n\nnamespace cadabra {\n\tnamespace cpplib {\n\n\t\tusing ExPtr = std::shared_ptr<Ex>;\n\n\t\tnamespace detail {\n\t\t\tstruct ExConstructorProxy\n\t\t\t{\n\t\t\t\tExConstructorProxy(const char* data) : data(data) {}\n\t\t\t\tExPtr operator () (Kernel& kernel)\n\t\t\t\t{\n\t\t\t\t\treturn kernel.ex_from_string(data);\n\t\t\t\t}\n\t\t\t\tstd::string data;\n\t\t\t};\n\n\t\t\tstruct ExPrettyPrinter\n\t\t\t{\n\t\t\t\tExPrettyPrinter(const Kernel& kernel, Ex::iterator it, bool use_unicode = true)\n\t\t\t\t\t: kernel(kernel)\n\t\t\t\t\t, ex(it)\n\t\t\t\t\t, use_unicode(use_unicode) {}\n\t\t\t\tconst Kernel& kernel;\n\t\t\t\tEx ex;\n\t\t\t\tbool use_unicode;\n\t\t\t};\n\t\t}\n\n\t\tExPtr copy(const ExPtr& ex)\n\t\t{\n\t\t\treturn std::make_shared<Ex>(*ex);\n\t\t}\n\n\t\ttemplate <typename Prop>\n\t\tvoid inject_property(Kernel& kernel, const ExPtr& pattern, const ExPtr& args = nullptr)\n\t\t{\n\t\t\tkernel.inject_property(new Prop(), pattern, args);\n\t\t}\n\n\t\ttemplate <typename Prop>\n\t\tvoid inject_property(Kernel& kernel, const char* pattern, const ExPtr& args = nullptr)\n\t\t{\n\t\t\tinject_property<Prop>(kernel, kernel.ex_from_string(pattern), args);\n\t\t}\n\n\t\ttemplate <typename Prop>\n\t\tvoid inject_property(Kernel& kernel, const ExPtr& pattern, const char* args)\n\t\t{\n\t\t\tinject_property<Prop>(kernel, pattern, kernel.ex_from_string(args));\n\t\t}\n\n\t\ttemplate <typename Prop>\n\t\tvoid inject_property(Kernel& kernel, const char* pattern, const char* args)\n\t\t{\n\t\t\tinject_property<Prop>(kernel, kernel.ex_from_string(pattern), kernel.ex_from_string(args));\n\t\t}\n\n\t\ttemplate <typename Algo, typename... Args>\n\t\tExPtr apply(const Kernel& kernel, const ExPtr& ex, Args&&... args,  bool deep = true, bool repeat = false, unsigned int depth = 0)\n\t\t{\n\t\t\tAlgo algo(kernel, *ex, std::forward<Args>(args)...);\n\t\t\talgo.apply_generic(deep, repeat, depth);\n\t\t\treturn ex;\n\t\t}\n\n\t\ttemplate <typename Algo, typename... Args>\n\t\tExPtr apply(const Kernel& kernel, const ExPtr& ex, Ex::iterator it, Args&&... args, bool deep = true, bool repeat = false, unsigned int depth = 0)\n\t\t{\n\t\t\tAlgo algo(kernel, *ex, std::forward<Args>(args)...);\n\t\t\talgo.apply_generic(it, deep, repeat, depth);\n\t\t\treturn ex;\n\t\t}\n\n\t\ttemplate <typename Algo, typename... Args>\n\t\tExPtr apply_preorder(const Kernel& kernel, const ExPtr& ex, Args&&... args)\n\t\t{\n\t\t\tAlgo algo(kernel, *ex, std::forward<Args>(args)...);\n\t\t\talgo.apply_pre_order();\n\t\t\treturn ex;\n\t\t}\n\n\t\tinline void pprint_enable_utf8()\n\t\t{\n\t\t\t// Set the codepage on windows to utf8\n#ifdef _MSC_VER\n\t\t\tSetConsoleOutputCP(65001);\n#endif\n\t\t}\n\n\t\tinline detail::ExConstructorProxy operator \"\" _ex(const char* ex, std::size_t n)\n\t\t{\n\t\t\treturn detail::ExConstructorProxy(ex);\n\t\t}\n\n\t\tinline detail::ExPrettyPrinter pprint(const Kernel& kernel, const ExPtr& ex, bool use_unicode = true)\n\t\t{\n\t\t\treturn detail::ExPrettyPrinter(kernel, ex->begin(), use_unicode);\n\t\t}\n\n\t\tinline detail::ExPrettyPrinter pprint(const Kernel& kernel, const Ex& ex, bool use_unicode = true)\n\t\t{\n\t\t\treturn detail::ExPrettyPrinter(kernel, ex.begin(), use_unicode);\n\t\t}\n\n\t\tinline detail::ExPrettyPrinter pprint(const Kernel& kernel, Ex::iterator it, bool use_unicode = true)\n\t\t{\n\t\t\treturn detail::ExPrettyPrinter(kernel, it, use_unicode);\n\t\t}\n\n\t\tinline std::ostream& operator << (std::ostream& stream, const detail::ExPrettyPrinter& pretty_printer)\n\t\t{\n\t\t\tDisplayTerminal dt(pretty_printer.kernel, pretty_printer.ex, pretty_printer.use_unicode);\n\t\t\tdt.output(stream);\n\t\t\treturn stream;\n\t\t}\n\t}\n}\n"
  },
  {
    "path": "c++lib/nevaluate.cc",
    "content": "#include \"cadabra2++.hh\"\n#include <iostream>\n\nusing namespace cadabra;\nusing namespace cadabra::cpplib;\n\nint main(int, char **)\n\t{\n\tKernel k(true);\n\tpprint_enable_utf8();\n\t//{\\mu,\\nu}::Indices(vector).\n\t// tr{#}::Trace.\n\t// u^{\\mu}::SelfNonCommuting.\n\t// u^{\\mu}::ImplicitIndex.\n\t// ex:=tr{A u^{\\nu} u^{\\mu} u^{\\mu} u^{\\nu} + B u^{\\mu} u^{\\mu} u^{\\nu}\n\t// u^{\\nu}}: meld(_);\n\n//\tinject_property<SelfNonCommuting>(k, \"{A,B,C,D }\");\n//\tinject_property<Trace>(k, \"tr{#}\");\n\n\t// Scalar broadcast\n\tNTensor t3a( { 2.0 } );\n\tstd::cerr << \"t3a.shape.size() = \" << t3a.shape.size() << std::endl;\n\tstd::cerr << \"t3a.shape[0]     = \" << t3a.shape[0] << std::endl;\t\n\tNTensor t432a=t3a.broadcast( {4, 1}, 1 );\n\tstd::cerr << t432a << std::endl;\n\n\t// NTensor broadcast\n\tNTensor t3( { 1.0, 2.0, 3.0 } );\n\tNTensor t432=t3.broadcast( {4,3,2}, 1 );\n\tstd::cerr << t432 << std::endl;\n\n\tNTensor t3c( { 1.0, 2.0, 3.0 } );\n\tNTensor t432c1=t3c.broadcast( {3,3,2}, 1 );\n\tstd::cerr << t432c1 << std::endl;\n\tNTensor t432c2=t3c.broadcast( {3,3,2}, 0 );\n\tstd::cerr << t432c2 << std::endl;\n\n\n\t// Multiplying two scalar variables which each take\n\t// an array of values leads to an outer product.\n\n\tauto ex1b = \"B*A + A\"_ex(k);\n\tNEvaluator ev1b(ex1b->begin());\n\tev1b.set_variable(Ex(\"A\"), NTensor({1.0, 2.0, 3.0}));\n\tev1b.set_variable(Ex(\"B\"), NTensor({0.5, 1.0, 5.0, 10.0}));\n\t// This should give a {3, 4} tensor.\n\tauto res1b = ev1b.evaluate();\n\tstd::cout << \"B*A + A = \" << res1b << \"\\n\\n\";\n\n\tauto ex1 = \"B*A + C\"_ex(k);\n\tNEvaluator ev1(ex1->begin());\n\tev1.set_variable(Ex(\"A\"), NTensor({1.0, 2.0, 3.0}));\n\tev1.set_variable(Ex(\"B\"), NTensor({0.5, 1.0, 5.0, 10.0}));\n\tev1.set_variable(Ex(\"C\"), NTensor({1.0, -1.0}));\n\t// This should give a {3, 4, 2} tensor.\n\tauto res1 = ev1.evaluate();\n\tstd::cout << \"B*A + C = \" << res1 << \"\\n\\n\";\n\n\t// Trigonometric functions.\n\n\tauto ex2 = R\"( A + B \\cos( C ) )\"_ex(k);\n\tstd::cout << pprint(k, ex2) << '\\n';\n\tNTensor nt2({2,4}, 0.0);\n\tnt2.at({1,2}) = 3.1415;\n\tfor(auto& v: nt2.values)\n\t\tstd::cout << v << \", \";\n\tstd::cout << \"\\n\\n\";\n\tstd::cout << nt2 << std::endl;\n\n\tNEvaluator ev(ex2->begin());\n\tev.set_variable(Ex(\"C\"), { 3.0 });\n\tev.set_variable(Ex(\"B\"), { 2.3 });\n\tev.set_variable(Ex(\"A\"), { 1.2 });\n\tauto res2 = ev.evaluate();\n\tstd::cout << \"A + B cos(C) = \" << res2 << \"\\n\\n\";\n\n\t// Double trig.\n\tStopwatch sw;\n\tauto ex3 = R\"( \\cos(x) \\sin(y) )\"_ex(k);\n\tNEvaluator ev3(ex3->begin());\n\tev3.set_variable(Ex(\"x\"), NTensor::linspace(0.0, 3.14, 1000));\n\tev3.set_variable(Ex(\"y\"), NTensor::linspace(0.0, 3.14, 1000));\n\tsw.start();\n\tint num=100;\n\tfor(int i=0; i<num; ++i) {\n\t\tauto res3 = ev3.evaluate();\n\t\t}\n\tsw.stop();\n\tsw /= num;\n\tstd::cout << \"cos(x) sin(y) over a 1000x1000 grid took \" << sw << \" on average\\n\\n\";\n\n\t// Array indexing.\n\n\tNTensor nt({2,4,3}, 0.0);\n\tnt.at({1,2,0}) = 6.2830;\n\tnt.at({0,3,2}) = -6.2830;\n\tstd::cout << nt << std::endl;\n\n\tstd::cout << \"is this real? \" << nt.is_real() << std::endl;\n\t}\n"
  },
  {
    "path": "c++lib/nevaluate.py",
    "content": "#!/usr/bin/python3\n#\n# Test program to determine the speed of sympy/numpy numerical\n# evaluation of functions, to compare with our C++ implementation (see\n# nevaluate.cc for details; we about 1.5 faster for this example,\n# provided we force numpy to do the computations over the complex\n# numbers, like we do in Cadabra).\n\nfrom sympy import *\nfrom sympy.abc import x,y\nimport numpy\nimport time\n\nexpr = cos(x)*sin(y)\nf = lambdify([x,y], expr, \"numpy\")\nxl = numpy.linspace(0, 3.14, 1000, dtype=complex)\nyl = numpy.linspace(0, 3.14, 1000, dtype=complex)\nX, Y = numpy.meshgrid(xl, yl)\n#F = numpy.vectorize(f)\n\ntotal = 0\nnum = 100\nfor i in range(num):\n    start = time.time()\n    q = f(X, Y)\n    end = time.time()\n    total += (end - start)\n\nprint(\"cos(x)*sin(y) with numpy over a 1000x1000 grid took\", total/num, \"seconds on average\")\n\n"
  },
  {
    "path": "c++lib/simple.cc",
    "content": "#include \"cadabra2++/Parser.hh\"\n#include \"cadabra2++/Storage.hh\"\n#include \"cadabra2++/DisplayTerminal.hh\"\n#include \"cadabra2++/algorithms/substitute.hh\"\n#include \"cadabra2++/algorithms/evaluate.hh\"\n#include \"cadabra2++/TerminalStream.hh\"\n#include \"cadabra2++/properties/PartialDerivative.hh\"\n#include \"cadabra2++/properties/Coordinate.hh\"\n\n#include <iostream>\n#include <sstream>\n\n/// \\file simple.cc\n/// \\ingroup libcadabra\n///\n/// Sample program to demonstrate the use of Cadabra directly from C++ code.\n\nvoid test1()\n\t{\n\t// The following few lines are equivalent to entering\n\t//\n\t//    {r,t}::Coordinate.\n\t//    {m,n}::Indices(values={t,r}, position=free).\n\t//    ex:= A_{m} A^{m};\n\t//    rl:= A_{t} = 3 + a;\n\t//    evaluate(ex, rl);\n\t//\n\t// in the Cadabra notebook.\n\n\tcadabra::Kernel kernel;\n\n\tkernel.inject_property(new cadabra::Coordinate(), kernel.ex_from_string(\"{r,t}\"), 0);\n\tkernel.inject_property(new cadabra::Indices(),    kernel.ex_from_string(\"{m,n}\"),\n\t                       kernel.ex_from_string(\"values={t,r}, position=free\"));\n\n\tauto ex = kernel.ex_from_string(\"A_{m} A^{m}\");\n\tauto rl = kernel.ex_from_string(\"A_{t} = 3 + a \");\n\tcadabra::evaluate ev(kernel, *ex, *rl);\n\tev.apply_generic();\n\n\t// Pretty-printing stream object.\n\tcadabra::TerminalStream ss(kernel, std::cerr);\n\tss << ex << std::endl;\n\t}\n\nvoid test2()\n\t{\n\t// The following few lines are equivalent to entering\n\t//\n\t//    {m,n,p,q}::Indices(position=free).\n\t//    \\partial{#}::PartialDerivative;\n\t//    ex:= \\int{ F_{m n} F^{m n} }{x};\n\t//    rl:= F_{m n} = \\\\partial_{m}{A_{n}} - \\\\partial_{n}{A_{m}};\n\t//    substitute(ex, rl, deep=True);\n\t//\n\t// in the Cadabra notebook.\n\n\tcadabra::Kernel kernel;\n\n\tauto ind1 = kernel.ex_from_string(\"{m,n,p,q}\");\n\tauto ind2 = kernel.ex_from_string(\"position=free\");\n\tkernel.inject_property(new cadabra::Indices(), ind1, ind2);\n\n\tauto pd   = kernel.ex_from_string(\"\\\\partial{#}\");\n\tkernel.inject_property(new cadabra::PartialDerivative(), pd, 0);\n\n\tauto ex = kernel.ex_from_string(\"\\\\int{ F_{m n} F^{m n} }{x}\");\n\tauto rl = kernel.ex_from_string(\"F_{m n} = \\\\partial_{m}{A_{n}} - \\\\partial_{n}{A_{m}}\");\n\n\t// Pretty-printing stream object.\n\tcadabra::TerminalStream ss(kernel, std::cerr);\n\n\tss << ex << std::endl;\n\tss << rl << std::endl;\n\n\t// Apply the 'substitute' algorithm.\n\tcadabra::substitute subs(kernel, *ex, *rl);\n\tsubs.apply_generic();\n\n\tss << ex << std::endl;\n\t}\n\n\nint main(int argc, char **argv)\n\t{\n\ttest1();\n\ttest2();\n\t}\n"
  },
  {
    "path": "c++lib/trivial.cc",
    "content": "#include \"cadabra2++.hh\"\n#include <iostream>\n\nusing namespace cadabra;\nusing namespace cadabra::cpplib;\n\nint main() {\n   Kernel k(true);\n   inject_property<AntiCommuting>(k, \"{A,B}\");\n   auto ex = \"A B - B A\"_ex(k);\n   sort_product sp(k, *ex);\n   sp.apply_generic();\n\n\tcollect_terms ct(k, *ex);\n\tct.apply_generic();\n\t\n   std::cout << pprint(k, ex) << std::endl;\n}\n"
  },
  {
    "path": "client_server/Actions.cc",
    "content": "\n\n#include \"Actions.hh\"\n#include \"DataCell.hh\"\n#include \"DocumentThread.hh\"\n#include \"GUIBase.hh\"\n\n#include <boost/core/demangle.hpp>\n#include <iostream>\n#include <fstream>\n\nusing namespace cadabra;\n\n#define DEBUG(ln)\n// #define DEBUG(ln) ln\n\n\nActionBase::ActionBase(DataCell::id_t id)\n\t: ref_id(id)\n\t{\n\t}\n\nbool ActionBase::undoable() const\n\t{\n\treturn true;\n\t}\n\nvoid ActionBase::execute(DocumentThread& cl, GUIBase& )\n\t{\n\tif(ref_id.id==0) {\n\t\t// A zero ID means the current cell.\n\t\tref = cl.current_cell;\n\t\treturn;\n\t\t}\n\telse {\n\t\t// Lookup the cell with the given ID.\n\t\tauto it=cl.doc.begin();\n\t\twhile(it!=cl.doc.end()) {\n\t\t\tif((*it).id().id==ref_id.id) {\n\t\t\t\tref=it;\n\t\t\t\treturn;\n\t\t\t\t}\n\t\t\t++it;\n\t\t\t}\n\t\t}\n\n\t// Not found, throw exception.\n\tstd::string class_name = boost::core::demangle(typeid(*this).name());\n\tthrow std::logic_error(class_name + \": cannot find cell with id \"+std::to_string(ref_id.id));\n\t}\n\nActionAddCell::ActionAddCell(DataCell cell, DataCell::id_t ref_id, Position pos_, bool activate_)\n\t: ActionBase(ref_id)\n\t, newcell(cell)\n\t, pos(pos_)\n\t, activate(activate_)\n\t, is_replacement(false)\n\t, is_input_form(false)\n\t{\n\t}\n\nvoid ActionAddCell::execute(DocumentThread& cl, GUIBase& gb)\n\t{\n\tActionBase::execute(cl, gb);\n\n\t// Insert this DataCell into the DTree document. We first need\n\t// to figure out whether we already have a cell with the DataCell's\n\t// cell_id; in this case we have to replace, not append/insert.\n\tauto it=cl.doc.begin();\n\twhile(it!=cl.doc.end()) {\n\t\tif((*it).id().id==newcell.id().id) {\n\t\t\t// FIXME: right now we only change textbuf.\n\t\t\tDEBUG( std::cerr << \"found! \" << it->id().id << \", \" << static_cast<int>(it->cell_type) << std::endl; )\n\t\t\tit->textbuf=newcell.textbuf;\n\t\t\tgb.update_cell(cl.doc, it);\n\t\t\tis_replacement=true;\n\t\t\treturn;\n\t\t\t}\n\t\t++it;\n\t\t}\n\n\t// If we get here we have to append/insert.\n\tDEBUG( std::cerr << \"ActionAddCell::execute: add cell with id \" << newcell.id().id; )\n\tswitch(pos) {\n\t\tcase Position::before:\n\t\t\tnewref = cl.doc.insert(ref, newcell);\n\t\t\tDEBUG( std::cerr << \" before \"; )\n\t\t\tbreak;\n\t\tcase Position::after:\n\t\t\tnewref = cl.doc.insert_after(ref, newcell);\n\t\t\tDEBUG( std::cerr << \" after \"; )\t\t\t\n\t\t\tbreak;\n\t\tcase Position::child:\n\t\t\tnewref = cl.doc.append_child(ref, newcell);\n\t\t\tDEBUG( std::cerr << \" as child of \"; )\t\t\t\n\t\t\tbreak;\n\t\t}\n\tDEBUG( std::cerr << \"  \" << ref->id().id << std::endl; )\n\t\t\n\tchild_num=cl.doc.index(newref);\n\tDEBUG( std::cerr << \"ActionAddCell::execute: added as child \" << child_num <<\n\t\t\t \": |\" << newcell.textbuf << \"|\" << std::endl; )\n\tgb.add_cell(cl.doc, newref, true);\n\tif(activate)\n\t\tgb.position_cursor(cl.doc, newref, -1);\n\t\n\tif(newcell.cell_type == DataCell::CellType::input_form)\n\t\tis_input_form=true;\n\t}\n\nvoid ActionAddCell::revert(DocumentThread& cl, GUIBase& gb)\n\t{\n\t// Remove the GUI cell from the notebook and then\n\t// remove the corresponding DataCell from the DTree.\n\n\tDEBUG( std::cerr << \"ActionAddCell::revert: removing child \" << child_num << std::endl; )\n\n\tDTree::sibling_iterator ch;\n\tswitch(pos) {\n\t\tcase Position::before:\n\t\t\t// `ref` is a cell after our cell.\n\t\t\tch = cl.doc.child(cl.doc.parent(ref), child_num);\n\t\t\tbreak;\n\t\tcase Position::after:\n\t\t\t// `ref` is a cell before our cell.\n\t\t\tch = cl.doc.child(cl.doc.parent(ref), child_num);\n\t\t\tbreak;\n\t\tcase Position::child:\n\t\t\t// `ref` is a parent of our cell.\n\t\t\tch = cl.doc.child(ref, child_num);\n\t\t\tbreak;\n\t\t}\n\tDEBUG( std::cerr << \"ActionAddCell::revert: removing cell \" << ch->textbuf << std::endl; )\n\tgb.remove_cell(cl.doc, ch);\n\t// std::cerr << \"ActionAddCell::revert: finally erase datacell\" << std::endl;\n\tcl.doc.erase(ch);\n\t}\n\nbool ActionAddCell::undoable() const\n\t{\n\treturn !(is_replacement || is_input_form);\n\t}\n\nActionPositionCursor::ActionPositionCursor(DataCell::id_t ref_id, Position pos_)\n\t: ActionBase(ref_id), needed_new_cell_with_id(0), pos(pos_)\n\t{\n\t}\n\nvoid ActionPositionCursor::execute(DocumentThread& cl, GUIBase& gb)\n\t{\n\tActionBase::execute(cl, gb);\n\n\tswitch(pos) {\n\t\tcase Position::in:\n\t\t\t// std::cerr << \"in\" << std::endl;\n\t\t\tnewref = ref;\n\t\t\tbreak;\n\t\tcase Position::next: {\n\t\t\tDTree::sibling_iterator sib=ref;\n\t\t\tbool found=false;\n\t\t\twhile(cl.doc.is_valid(++sib)) {\n\t\t\t\tif(sib->cell_type==DataCell::CellType::python || sib->cell_type==DataCell::CellType::latex) {\n\t\t\t\t\tif(!sib->hidden) {\n\t\t\t\t\t\tnewref=sib;\n\t\t\t\t\t\tfound=true;\n\t\t\t\t\t\tbreak;\n\t\t\t\t\t\t}\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\tif(!found) {\n\t\t\t\tif(ref->textbuf==\"\") { // If the last cell is empty, stay where we are.\n\t\t\t\t\tnewref=ref;\n\t\t\t\t\t}\n\t\t\t\telse {\n\t\t\t\t\t// Make sure that we store the generated cell id so we\n\t\t\t\t\t// can re-use it if we execute this in redo.\n\t\t\t\t\tif(needed_new_cell_with_id > 0) {\n\t\t\t\t\t\tDataCell::id_t id;\n\t\t\t\t\t\tid.id = needed_new_cell_with_id;\n\t\t\t\t\t\tDataCell newcell(id, DataCell::CellType::python, \"\");\n\t\t\t\t\t\tnewref = cl.doc.insert(sib, newcell);\n\t\t\t\t\t\t}\n\t\t\t\t\telse {\n\t\t\t\t\t\tDataCell newcell(DataCell::CellType::python, \"\");\n\t\t\t\t\t\tneeded_new_cell_with_id=newcell.id().id;\n\t\t\t\t\t\tnewref = cl.doc.insert(sib, newcell);\n\t\t\t\t\t\t}\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\tbreak;\n\t\t\t}\n\t\tcase Position::previous: {\n\t\t\tbool found=false;\n\t\t\tDTree::sibling_iterator sib=ref;\n\t\t\twhile(cl.doc.is_valid(--sib)) {\n\t\t\t\tif(sib->cell_type==DataCell::CellType::python || sib->cell_type==DataCell::CellType::latex) {\n\t\t\t\t\tif(!sib->hidden) {\n\t\t\t\t\t\tnewref=sib;\n\t\t\t\t\t\tfound=true;\n\t\t\t\t\t\tbreak;\n\t\t\t\t\t\t}\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\tif(!found)\n\t\t\t\tnewref=ref; // No previous sibling cell. FIXME: walk tree structure\n\t\t\tbreak;\n\t\t\t}\n\t\t}\n\n\t// Update GUI.\n\tif(needed_new_cell_with_id > 0) {\n\t\t// std::cerr << \"cadabra-client: adding new visual cell before positioning cursor\" << std::endl;\n\t\tgb.add_cell(cl.doc, newref, true);\n\t\t}\n\t// std::cerr << \"cadabra-client: positioning cursor\" << std::endl;\n\tgb.position_cursor(cl.doc, newref, -1);\n\tDEBUG( std::cerr << \"ActionPositionCursor::execute: done\" << std::endl; )\n\t}\n\nvoid ActionPositionCursor::revert(DocumentThread& cl, GUIBase& gb)\n\t{\n\tif(needed_new_cell_with_id > 0) {\n\t\tgb.remove_cell(cl.doc, newref);\n\t\tcl.doc.erase(newref);\n\t\t}\n\tgb.position_cursor(cl.doc, ref, -1);\n\tDEBUG( std::cerr << \"ActionPositionCursor::revert: done\" << std::endl; )\n\t}\n\nActionRemoveCell::ActionRemoveCell(DataCell::id_t ref_id)\n\t: ActionBase(ref_id)\n\t{\n\t}\n\nActionRemoveCell::~ActionRemoveCell()\n\t{\n\t}\n\nvoid ActionRemoveCell::execute(DocumentThread& cl, GUIBase& gb)\n\t{\n\tActionBase::execute(cl, gb);\n\n\tgb.remove_cell(cl.doc, ref);\n\n\treference_parent_cell = cl.doc.parent(ref);\n\treference_child_index = cl.doc.index(ref);\n\tremoved_tree=DTree(ref);\n\tDEBUG( std::cerr << \"removed has \" << cl.doc.number_of_children(ref) << \" children\" << std::endl; )\n\tcl.doc.erase(ref);\n\t}\n\nvoid ActionRemoveCell::revert(DocumentThread& cl, GUIBase& gb)\n\t{\n\tDEBUG( std::cerr << \"need to undo a remove cell at index \" << reference_child_index << std::endl; )\n\tDTree::iterator newcell;\n\tif(cl.doc.number_of_children(reference_parent_cell)==0) {\n\t\tnewcell = cl.doc.append_child(reference_parent_cell, removed_tree.begin());\n\t\t}\n\telse {\n\t\tauto it = cl.doc.child(reference_parent_cell, reference_child_index);\n\t\t//\t\t++it;\n\t\tnewcell = cl.doc.insert_subtree(it, removed_tree.begin());\n\t\tDEBUG( std::cerr << \"added doc cell \" << newcell->textbuf << \" at \" << &(*newcell) << \" before \" << it->textbuf << std::endl; )\n\t\t}\n\tgb.add_cell(cl.doc, newcell, true);\n\tDEBUG( std::cerr << \"added vis rep\" << std::endl; )\n\t}\n\n\nActionReplaceCell::ActionReplaceCell(DataCell::id_t ref_id)\n\t: ActionBase(ref_id)\n\t{\n\t}\n\nActionReplaceCell::~ActionReplaceCell()\n\t{\n\t}\n\nvoid ActionReplaceCell::execute(DocumentThread& cl, GUIBase& gb)\n\t{\n\t}\n\nvoid ActionReplaceCell::revert(DocumentThread& cl, GUIBase& gb)\n\t{\n\t}\n\nbool ActionReplaceCell::undoable() const\n\t{\n\treturn false;\n\t}\n\nActionSplitCell::ActionSplitCell(DataCell::id_t ref_id)\n\t: ActionBase(ref_id)\n\t{\n\t}\n\nActionSplitCell::~ActionSplitCell()\n\t{\n\t}\n\nvoid ActionSplitCell::execute(DocumentThread& cl, GUIBase& gb)\n\t{\n\tActionBase::execute(cl, gb);\n\n\tsize_t pos = gb.get_cursor_position(cl.doc, ref);\n\n\tstd::string segment1=ref->textbuf.substr(0, pos);\n\tstd::string segment2=ref->textbuf.substr(pos);\n\n\t// Strip leading newline in 2nd segment, if any.\n\tif(segment2.size()>0) {\n\t\tif(segment2[0]=='\\n')\n\t\t\tsegment2=segment2.substr(1);\n\t\t}\n\n\tDataCell newcell(ref->cell_type, segment2);\n\tnewref = cl.doc.insert_after(ref, newcell);\n\tref->textbuf=segment1;\n\n\tgb.add_cell(cl.doc, newref, true);\n\tgb.update_cell(cl.doc, ref);\n\t}\n\nvoid ActionSplitCell::revert(DocumentThread&, GUIBase& )\n\t{\n\t// FIXME: implement\n\t}\n\n\n\nActionSetRunStatus::ActionSetRunStatus(DataCell::id_t ref_id, bool running)\n\t: ActionBase(ref_id), new_running_(running)\n\t{\n\t}\n\nbool ActionSetRunStatus::undoable() const\n\t{\n\treturn false;\n\t}\n\nvoid ActionSetRunStatus::execute(DocumentThread& cl, GUIBase& gb)\n\t{\n\tActionBase::execute(cl, gb);\n\n\tgb.update_cell(cl.doc, ref);\n\n\twas_running_=ref->running;\n\tref->running=new_running_;\n\t}\n\nvoid ActionSetRunStatus::revert(DocumentThread&, GUIBase& )\n\t{\n\t}\n\n\nActionRunCell::ActionRunCell(DataCell::id_t ref_id)\n\t: ActionBase(ref_id), run_all_cells(false)\n\t{\n\t}\n\nActionRunCell::ActionRunCell()\n\t: ActionBase(DataCell::id_t()), run_all_cells(true)\n\t{\n\t}\n\nActionRunCell::~ActionRunCell()\n\t{\n\t}\n\nbool ActionRunCell::undoable() const\n\t{\n\treturn false;\n\t}\n\nvoid ActionRunCell::execute(DocumentThread& cl, GUIBase& gb)\n\t{\n\tif(!run_all_cells) {\n\t\tActionBase::execute(cl, gb);\n\t\tcl.run_cell(ref, false);\n\t\t}\n\telse {\n\t\tcl.run_all_cells();\n\t\t}\n\t}\n\nvoid ActionRunCell::revert(DocumentThread&, GUIBase& )\n\t{\n\t}\n\n\nActionOpen::ActionOpen(const std::string& n)\n\t: ActionBase(DataCell::id_t()), notebook_name(n)\n\t{\n\t}\n\nActionOpen::~ActionOpen()\n\t{\n\t}\n\nbool ActionOpen::undoable() const\n\t{\n\treturn false;\n\t}\n\nvoid ActionOpen::execute(DocumentThread& cl, GUIBase& gb)\n\t{\n\tstd::ifstream file(notebook_name);\n\tstd::string content, line;\n\t\n\twhile(std::getline(file, line))\n\t\tcontent+=line;\n\n\tcl.load_from_string(content);\n\t}\n\nvoid ActionOpen::revert(DocumentThread&, GUIBase& )\n\t{\n\t}\n\n\nActionSetVariableList::ActionSetVariableList(DataCell::id_t ref_id, std::set<std::string> variables)\n\t: ActionBase(ref_id), new_variables_(variables)\n\t{\n\t}\n\nbool ActionSetVariableList::undoable() const\n\t{\n\treturn false;\n\t}\n\nvoid ActionSetVariableList::execute(DocumentThread& cl, GUIBase& gb)\n\t{\n\tActionBase::execute(cl, gb);\n\n\tref->variables_referenced=new_variables_;\n\t}\n\nvoid ActionSetVariableList::revert(DocumentThread&, GUIBase& )\n\t{\n\t}\n\n\nActionInsertText::ActionInsertText(DataCell::id_t ref_id, int pos, const std::string& content)\n\t: ActionBase(ref_id), insert_pos(pos), text(content)\n\t{\n\t}\n\nvoid ActionInsertText::execute(DocumentThread& cl, GUIBase& gb)\n\t{\n\tActionBase::execute(cl, gb);\n\n\tref->textbuf.insert(insert_pos, text);\n\tDEBUG( std::cerr << \"ActionInsertText::execute: textbuf now |\" << ref->textbuf << \"|\" << std::endl; )\n\tgb.update_cell(cl.doc, ref);\n\t}\n\nvoid ActionInsertText::revert(DocumentThread& cl, GUIBase& gb)\n\t{\n\tref->textbuf.erase(insert_pos, text.size());\n\tDEBUG( std::cerr << \"ActionInsertText::revert: textbuf now |\" << ref->textbuf << \"|\" << std::endl; )\n\tgb.update_cell(cl.doc, ref);\n\t}\n\n\nActionCompleteText::ActionCompleteText(DataCell::id_t ref_id, int pos, const std::string& content, int alt)\n\t: ActionBase(ref_id), insert_pos(pos), text(content), alternative_(alt)\n\t{\n\t}\n\nvoid ActionCompleteText::execute(DocumentThread& cl, GUIBase& gb)\n\t{\n\tActionBase::execute(cl, gb);\n\n\tauto endpos = ref->textbuf.insert(insert_pos, text);\n\t// std::cerr << \"complete: textbuf now |\" << ref->textbuf << \"|\" << std::endl;\n\tgb.update_cell(cl.doc, ref);\n\tgb.position_cursor(cl.doc, ref, insert_pos+text.size());\n\t}\n\nvoid ActionCompleteText::revert(DocumentThread& cl, GUIBase& gb)\n\t{\n\tref->textbuf.erase(insert_pos, text.size());\n\tgb.update_cell(cl.doc, ref);\n\tgb.position_cursor(cl.doc, ref, insert_pos);\n\t}\n\nint ActionCompleteText::length() const\n\t{\n\treturn text.size();\n\t}\n\nint ActionCompleteText::alternative() const\n\t{\n\treturn alternative_;\n\t}\n\nActionEraseText::ActionEraseText(DataCell::id_t ref_id, int start, int end)\n\t: ActionBase(ref_id), from_pos(start), to_pos(end)\n\t{\n\t}\n\nvoid ActionEraseText::execute(DocumentThread& cl, GUIBase& gb)\n\t{\n\tActionBase::execute(cl, gb);\n\n\tDEBUG( std::cerr << from_pos << \", \" << to_pos << std::endl; )\n\tremoved_text=ref->textbuf.substr(from_pos, to_pos-from_pos);\n\tref->textbuf.erase(from_pos, to_pos-from_pos);\n\t}\n\nvoid ActionEraseText::revert(DocumentThread& cl, GUIBase& gb)\n\t{\n\tref->textbuf.insert(from_pos, removed_text);\n\tgb.update_cell(cl.doc, ref);\n\tgb.position_cursor(cl.doc, ref, from_pos+removed_text.size());\n\t}\n\n"
  },
  {
    "path": "client_server/Actions.hh",
    "content": "\n#pragma once\n\n#include \"DataCell.hh\"\n#include \"DocumentThread.hh\"\n\n#include <memory>\n\nnamespace cadabra {\n\n\tclass DocumentThread;\n\tclass GUIBase;\n\n\t/// \\ingroup clientserver\n\t///\n\t/// All actions derive from the ActionBase object, which defines\n\t/// the interface they need to implement. These objects are used to\n\t/// pass (user) action instructions around.  They can be stored in\n\t/// undo/redo stacks. All actions run on the GUI thread. The\n\t/// update_gui members typically call members of the GUIBase class.\n\t/// Action objects are allowed to modify the DTree document doc,\n\t/// since they essentially contain code which is part of the\n\t/// DocumentThread object.\n\t///\n\t/// All modifications to the document are done by calling 'perform' with an\n\t/// action object. This enables us to implement an undo stack. This method\n\t/// will take care of making the actual change to the DTree document, and\n\t/// call back on the 'change' methods above to inform the derived class\n\t/// that a change has been made.\n\n\n\tclass ActionBase {\n\t\tpublic:\n\t\t\tActionBase(DataCell::id_t ref_id);\n\n\t\t\t/// Perform the action. This should update both the document\n\t\t\t/// tree data structure and the GUI. The latter is updated\n\t\t\t/// by calling relevant methods on the GUIBase object passed\n\t\t\t/// in.\n\t\t\t///\n\t\t\t/// The base class just looks up the cell given its `id_t`.\n\t\t\t/// If your action does not refer to a cell at all, you do\n\t\t\t/// not need to call the base class `execute`.\n\n\t\t\tvirtual void execute(DocumentThread&, GUIBase&);\n\n\t\t\t/// Revert the change to the DTree document and the GUI.\n\n\t\t\tvirtual void revert(DocumentThread&, GUIBase&)=0;\n\n\t\t\t/// Can this action be undone?\n\t\t\tvirtual bool undoable() const;\n\n\t\t\tDataCell::id_t  ref_id;\n\n\t\t\t/// If you want a callback once this action has finished,\n\t\t\t/// set it here before queuing.\n\t\t\tstd::function<void()> callback;\n\t\t\t\n\t\tprotected:\n\t\t\tDTree::iterator ref;\n\t\t};\n\n\t/// \\ingroup clientserver\n\t///\n\t/// Add a cell to the notebook.\n\n\tclass ActionAddCell : public ActionBase {\n\t\tpublic:\n\t\t\tenum class Position { before, after, child };\n\n\t\t\tActionAddCell(DataCell, DataCell::id_t  ref_, Position pos_, bool activate=false);\n\t\t\tvirtual ~ActionAddCell() {};\n\n\t\t\tvirtual void execute(DocumentThread&, GUIBase&) override;\n\t\t\tvirtual void revert(DocumentThread&,  GUIBase&) override;\n\n\t\t\t/// Can this action be undone?\n\t\t\tvirtual bool undoable() const override;\n\t\tprivate:\n\t\t\t// Keep track of the location where this cell is inserted into\n\t\t\t// the notebook.\n\n\t\t\tDataCell          newcell;\n\t\t\tDTree::iterator   newref;\n\t\t\tPosition          pos;\n\t\t\tint               child_num;\n\t\t\tbool              activate;\n\n\t\t\t// If we are replacing a cell, keep track of that so we\n\t\t\t// report that we are not undoable.\n\t\t\tbool              is_replacement;\n\n\t\t\t// For input-form cells, we want no undo, as they will go\n\t\t\t// when the owner cell will be reverted.\n\t\t\tbool              is_input_form;\n\t\t};\n\n\n\t/// \\ingroup clientserver\n\t///\n\t/// Position the cursor relative to the indicated cell. If position is 'next' and\n\t/// there is no input cell following the indicated one, create a new one.\n\n\tclass ActionPositionCursor : public ActionBase {\n\t\tpublic:\n\t\t\tenum class Position { in, next, previous };\n\n\t\t\tActionPositionCursor(DataCell::id_t ref_id_, Position pos_);\n\t\t\tvirtual ~ActionPositionCursor() {};\n\n\t\t\tvirtual void execute(DocumentThread&, GUIBase&) override;\n\t\t\tvirtual void revert(DocumentThread&,  GUIBase&) override;\n\n\t\tprivate:\n\t\t\tuint64_t          needed_new_cell_with_id;\n\t\t\tDTree::iterator   newref;\n\t\t\tPosition          pos;\n\t\t};\n\n\t/// \\ingroup clientserver\n\t///\n\t/// Update the running status of the indicated cell.\n\n\tclass ActionSetRunStatus : public ActionBase {\n\t\tpublic:\n\t\t\tActionSetRunStatus(DataCell::id_t ref_id_, bool running);\n\t\t\tvirtual ~ActionSetRunStatus() {};\n\n\t\t\tvirtual void execute(DocumentThread&, GUIBase&) override;\n\t\t\tvirtual void revert(DocumentThread&,  GUIBase&) override;\n\n\t\t\tvirtual bool undoable() const override;\n\t\tprivate:\n\t\t\tDTree::iterator this_cell;\n\t\t\tbool            was_running_, new_running_;\n\t\t};\n\n\t/// \\ingroup clientserver\n\t///\n\t/// Update the list of referenced variables in this cell.\n\n\tclass ActionSetVariableList : public ActionBase {\n\t\tpublic:\n\t\t\tActionSetVariableList(DataCell::id_t ref_id_, std::set<std::string>);\n\t\t\tvirtual ~ActionSetVariableList() {};\n\n\t\t\tvirtual void execute(DocumentThread&, GUIBase&) override;\n\t\t\tvirtual void revert(DocumentThread&,  GUIBase&) override;\n\n\t\t\tvirtual bool undoable() const override;\n\t\tprivate:\n\t\t\tDTree::iterator this_cell;\n\t\t\tstd::set<std::string> new_variables_;\n\t\t};\n\n\n\t/// \\ingroup clientserver\n\t///\n\t/// Remove a cell and all its child cells from the document.\n\n\tclass ActionRemoveCell : public ActionBase {\n\t\tpublic:\n\t\t\tActionRemoveCell(DataCell::id_t ref_id_);\n\t\t\tvirtual ~ActionRemoveCell();\n\n\t\t\tvirtual void execute(DocumentThread&, GUIBase&) override;\n\t\t\tvirtual void revert(DocumentThread&,  GUIBase&) override;\n\n\t\tprivate:\n\t\t\t// Keep track of the location where this cell (and its child\n\t\t\t// cells) was in the notebook.  We keep a reference to the\n\t\t\t// parent cell and the index of the current cell as child of\n\t\t\t// that parent.\n\n\t\t\tDTree             removed_tree;\n\t\t\tDTree::iterator   reference_parent_cell;\n\t\t\tsize_t            reference_child_index;\n\t\t};\n\n\t/// \\ingroup clientserver\n\t///\n\t/// Replace the contents of a cell. Not undo-able.\n\n\tclass ActionReplaceCell : public ActionBase {\n\t\tpublic:\n\t\t\tActionReplaceCell(DataCell::id_t ref_id_);\n\t\t\tvirtual ~ActionReplaceCell();\n\n\t\t\tvirtual void execute(DocumentThread&, GUIBase&) override;\n\t\t\tvirtual void revert(DocumentThread&,  GUIBase&) override;\n\n\t\t\tvirtual bool undoable() const override;\n\t\tprivate:\n\t\t};\n\t\n\t/// \\ingroup clientserver\n\t///\n\t/// Split a cell into two separate cells, at the point of the cursor.\n\n\tclass ActionSplitCell : public ActionBase {\n\t\tpublic:\n\t\t\tActionSplitCell(DataCell::id_t ref_id);\n\t\t\tvirtual ~ActionSplitCell();\n\n\t\t\tvirtual void execute(DocumentThread&, GUIBase&) override;\n\t\t\tvirtual void revert(DocumentThread&,  GUIBase&) override;\n\n\t\tprivate:\n\t\t\tDTree::iterator newref; // the newly created cell\n\t\t};\n\n\n\t/// \\ingroup clientserver\n\t///\n\t/// Run a cell or run all cells. \n\n\tclass ActionRunCell : public ActionBase {\n\t\tpublic:\n\t\t\t// Run a particular cell.\n\t\t\tActionRunCell(DataCell::id_t ref_id);\n\t\t\t// Run all cells.\n\t\t\tActionRunCell();\n\t\t\t\n\t\t\tvirtual ~ActionRunCell();\n\t\t\t\n\t\t\tvirtual void execute(DocumentThread&, GUIBase&) override;\n\t\t\tvirtual void revert(DocumentThread&,  GUIBase&) override;\n\t\t\t\n\t\t\tvirtual bool undoable() const override;\n\t\tprivate:\n\t\t\tbool run_all_cells;\n\t};\n\n\t/// \\ingroup clientserver\n\t///\n\t/// Open a notebook from a file, in the current window.\n\n\tclass ActionOpen : public ActionBase {\n\t\tpublic:\n\t\t\tActionOpen(const std::string&);\n\t\t\tvirtual ~ActionOpen();\n\t\t\t\n\t\t\tvirtual void execute(DocumentThread&, GUIBase&) override;\n\t\t\tvirtual void revert(DocumentThread&,  GUIBase&) override;\n\t\t\t\n\t\t\tvirtual bool undoable() const override;\n\t\tprivate:\n\t\t\tstd::string notebook_name;\n\t};\n\n\n\t/// \\ingroup clientserver\n\t///\n\t/// Add a text string (can be just a single character) at the point\n\t/// of the cursor.\n\t/// This action is assumed to be triggered from a user change to\n\t/// the GUI cells, so will not update the GUI itself, only the\n\t/// underlying DTree. However, the revert method will need to\n\t/// update the GUI representation.\n\n\tclass ActionInsertText : public ActionBase {\n\t\tpublic:\n\t\t\tActionInsertText(DataCell::id_t ref_id, int pos, const std::string&);\n\t\t\tvirtual ~ActionInsertText() {};\n\n\t\t\tvirtual void execute(DocumentThread&, GUIBase&) override;\n\t\t\tvirtual void revert(DocumentThread&,  GUIBase&) override;\n\n\t\tprivate:\n\t\t\tDTree::iterator   this_cell;\n\t\t\tint         insert_pos;\n\t\t\tstd::string text;\n\t\t};\n\n\t/// \\ingroup clientserver\n\t///\n\t/// Complete text at a point in a GUI cell with one or more\n\t/// alternative.\n\t/// In contrast to ActionInsertText, this one is triggered from\n\t/// the server-side, so will update the GUI both for execute\n\t/// and revert.\n\n\tclass ActionCompleteText : public ActionBase {\n\t\tpublic:\n\t\t\tActionCompleteText(DataCell::id_t ref_id, int pos, const std::string&, int alternative);\n\t\t\tvirtual ~ActionCompleteText() {};\n\n\t\t\tvirtual void execute(DocumentThread&, GUIBase&) override;\n\t\t\tvirtual void revert(DocumentThread&,  GUIBase&) override;\n\n\t\t\tint length() const;\n\t\t\tint alternative() const;\n\t\t\t\n\t\tprivate:\n\t\t\tDTree::iterator   this_cell;\n\t\t\tint         insert_pos;\n\t\t\tstd::string text;\n\t\t\tint         alternative_; // in case there is more than one completion alternative\n\t\t};\n\n\t/// \\ingroup clientserver\n\t///\n\t/// Remove a text string starting at the indicated position, and\n\t/// with the indicated length, from the indicated cell.\n\t/// This action is assumed to be triggered from a user change to\n\t/// the GUI cells, so will not update the GUI itself, only the\n\t/// underlying DTree. However, the revert method will need to\n\t/// update the GUI representation.\n\n\tclass ActionEraseText : public ActionBase {\n\t\tpublic:\n\t\t\tActionEraseText(DataCell::id_t ref_id, int, int);\n\t\t\tvirtual ~ActionEraseText() {};\n\n\t\t\tvirtual void execute(DocumentThread&, GUIBase&) override;\n\t\t\tvirtual void revert(DocumentThread&,  GUIBase&) override;\n\n\t\tprivate:\n\t\t\tDTree::iterator   this_cell;\n\t\t\tint from_pos, to_pos;\n\t\t\tstd::string removed_text;\n\t\t};\n\n\t}\n\n\n//\n//       class ActionMergeCells\n\n\n\n"
  },
  {
    "path": "client_server/CMakeLists.txt",
    "content": "# cmake_minimum_required(VERSION ${CADABRA_CMAKE_VERSION})\nproject(Cadabra)\n\nif(POLICY CMP0167)\n  cmake_policy(SET CMP0167 NEW)\nendif()\n\n#---------------------------------------------------------------------------\n# Preamble.\n#---------------------------------------------------------------------------\n\nprint_header(\"Configuring client-server\")\n\nset(INSTALL_LATEX_DIR \"share/cadabra2\")\n\n\n#---------------------------------------------------------------------------\n# Locate libraries.\n#---------------------------------------------------------------------------\n\nif(USE_GTK4)\n  find_package(GLIBMM4  REQUIRED)\nelse()\n  find_package(GLIBMM3  REQUIRED)\nendif()\n  \nfind_package(SQLITE3 REQUIRED)\n# Don't set pthreads to required. Either we're on a platform where explict\n# linking with -lpthread is the norm (e.g. Linux) and it'll be found, or we're\n# on a platform that include pthreads by default (e.g. BSD, macOS) where this\n# won't find anything, or we're on a road-much-less-traveled OS where the user\n# can figure out what's wrong without a hard error here.\nfind_package(Threads)\n\n# We need at least Boost 1.71.0 because we now use `beast` (for the\n# websocket functionality) which was not stable before that version.\n# Actually, it is probably not stable before 1.75.0, but if we go that\n# high we cannot build on Ubuntu 20.04 anymore.\nfind_package(Boost 1.71.0 COMPONENTS program_options date_time filesystem REQUIRED)\n\n# OpenSSL needs to be linked in explicitly (probably because the boost\n# material referring to it is all in headers?). If you use a cmake module,\n# you will run into issues on MSYS2, so do *not* be tempted to do that\n# unless you test on MSYS2 first.\nset(OpenSSL_USE_STATIC_LIBS OFF)\nfind_package(OpenSSL REQUIRED)\nmessage(STATUS \"OPENSSL_LIBRARIES:      ${OPENSSL_LIBRARIES}\")\nmessage(STATUS \"OPENSSL_SSL_LIBRARY:    ${OPENSSL_SSL_LIBRARY}\")\nmessage(STATUS \"OPENSSL_CRYPTO_LIBRARY: ${OPENSSL_CRYPTO_LIBRARY}\")\nmessage(STATUS \"OPENSSL_INCLUDE_DIR:    ${OPENSSL_INCLUDE_DIR}\")\n\n#---------------------------------------------------------------------------\n# Enumerate input files.\n#---------------------------------------------------------------------------\n\nset(CADABRA_SERVER_SRC\n  cadabra-server.cc\n  Server.cc\n  Snoop.cc\n  websocket_client.cc\n  websocket_server.cc\n  ${CADABRA_CORE_DIR}/InstallPrefix.cc\n  ${CADABRA_CORE_DIR}/DataCell.cc\n  ${CADABRA_CORE_DIR}/Exceptions.cc\n  ${CADABRA_CORE_DIR}/CdbPython.cc \n  ${CADABRA_CORE_DIR}/Stopwatch.cc \n  ${CADABRA_CORE_DIR}/pythoncdb/py_helpers.cc\n  ${CADABRA_LIBS_DIR}/whereami/whereami.c\n  ${CADABRA_LIBS_DIR}/base64/base64.cc\n)\n\nset(CADABRA_CLIENT_SRC\n  ScriptThread.cc\n  ComputeThread.cc \n  DocumentThread.cc \n  Actions.cc \n  Snoop.cc\n  websocket_client.cc\n  websocket_server.cc\n  ${CADABRA_CORE_DIR}/DataCell.cc \n  ${CADABRA_CORE_DIR}/Exceptions.cc \n  ${CADABRA_CORE_DIR}/InstallPrefix.cc\n  ${CADABRA_CORE_DIR}/Stopwatch.cc\n  ${CADABRA_LIBS_DIR}/whereami/whereami.c\n)\n \nset(JUPYTER_KERNEL_SRC\n  cadabra-jupyter-kernel.cc\n  cadabra-jupyter-kernel.hh\n  cadabra-jupyter-main.cc\n  Server.cc\n  ${CADABRA_CORE_DIR}/InstallPrefix.cc\n  ${CADABRA_CORE_DIR}/DataCell.cc\n  ${CADABRA_CORE_DIR}/Exceptions.cc \n  ${CADABRA_CORE_DIR}/CdbPython.cc \n  ${CADABRA_CORE_DIR}/Stopwatch.cc \n  ${CADABRA_LIBS_DIR}/whereami/whereami.c\n  ${CADABRA_LIBS_DIR}/base64/base64.cc\n)\n  \n\n# set(CONNECTION_FILE ${CMAKE_CURRENT_SOURCE_DIR}/connection.json)\n# \n# add_custom_command(TARGET echo_kernel POST_BUILD\n#                    COMMAND ${CMAKE_COMMAND} -E\n#                    copy \"${CONNECTION_FILE}\" \"${CMAKE_CURRENT_BINARY_DIR}/\")\n# \n# add_custom_command(TARGET echo_kernel POST_BUILD\n#                    COMMAND ${CMAKE_COMMAND} -E\n#                  copy \"${CMAKE_BINARY_DIR}/${XEUS_RUNTIME_FILE}\" \"${CMAKE_CURRENT_BINARY_DIR}/\")\n\n#---------------------------------------------------------------------------\n# Include directories and preprocessor directives.\n#---------------------------------------------------------------------------\n\ninclude_directories(\n   \".\" \n   \"${CADABRA_CORE_DIR}\"\n   \"${CADABRA_LIBS_DIR}/pybind11/include\"\n#   \"${CADABRA_LIBS_DIR}/websocketpp\" \n   \"${CADABRA_LIBS_DIR}/internal/include\"\n   \"${CADABRA_LIBS_DIR}/whereami\"\n   \"${CADABRA_LIBS_DIR}/base64\"\n   \"${CADABRA_LIBS_DIR}/nlohmann\"\n   ${OPENSSL_INCLUDE_DIR}\n   ${Boost_INCLUDE_DIRS}\n   ${Python_INCLUDE_DIRS}\n   ${SQLITE3_INCLUDE_DIR}\n)\n\n# add_definitions(\n#    -D_WEBSOCKETPP_CPP11_STL_\n#    -DBOOST_ASIO_HAS_STD_CHRONO\n#    -DBOOST_BIND_GLOBAL_PLACEHOLDERS\n#  )\n\n#---------------------------------------------------------------------------\n# Make targets.\n#---------------------------------------------------------------------------\n\n# add_executable(tst tst.cc)\n# target_link_libraries(tst\n#  ${Boost_LIBRARIES}\n#  Threads::Threads\n#  )\n\n# Server executable\nif(WIN32)\n   message(STATUS \"Using the win32 subsystem for cadabra-server\")\n   add_executable(cadabra-server WIN32 ${CADABRA_SERVER_SRC}) \nelse()\n   add_executable(cadabra-server ${CADABRA_SERVER_SRC})\nendif()\n\n# target_link_libraries(cadabra-server cadabra_server)\ntarget_link_libraries(cadabra-server\n   pybind11::embed\n   ${Boost_LIBRARIES}\n   ${SQLITE3_LIBRARIES}\n   ${Python_LIBRARIES}\n   ${GLIBMM_LIBRARIES} \n   ${OPENSSL_LIBRARIES}\n   Threads::Threads\n   pthread\n   )\nif(WIN32)\n   target_link_libraries(cadabra-server ws2_32 mswsock bcrypt)\n endif()\n if(UNIX)\n    if(${CMAKE_SYSTEM_NAME} MATCHES \".*BSD|DragonFly\")\n       target_link_libraries(cadabra-server util)\n    else()\n       target_link_libraries(cadabra-server dl util)\n    endif()\n endif()\n\n# Client library\nadd_library(cadabra_client STATIC ${CADABRA_CLIENT_SRC})\ntarget_link_libraries(cadabra_client\n  ${Boost_LIBRARIES}\n  ${SQLITE3_LIBRARIES}\n  ${Python_LIBRARIES}\n  ${GLIBMM_LIBRARIES}\n  Threads::Threads\n  ${OPENSSL_LIBRARIES}\n  )\nif(WIN32)\n  target_link_libraries(cadabra_client ws2_32 bcrypt)\nendif()\n\n# cadabra2html\nadd_executable(cadabra2html \n  cadabra2html.cc \n  ${CADABRA_LIBS_DIR}/base64/base64.cc\n  )\ntarget_link_libraries(cadabra2html cadabra_client)\n\n# cadabra2latex\nadd_executable(cadabra2latex \n  cadabra2latex.cc \n  ${CADABRA_LIBS_DIR}/base64/base64.cc\n  )\ntarget_link_libraries(cadabra2latex cadabra_client)\n\n# Make sure sqlite3.dll is copied into the build directory on Windows.\nif (WIN32)\n   add_custom_command(TARGET cadabra_client POST_BUILD \n      COMMAND ${CMAKE_COMMAND} -E copy_if_different\n      ${SQLITE3_LIBRARIES}\n      ${PROJECT_BINARY_DIR}/${CADABRA_BUILD_TYPE}/sqlite3.dll\n   )\nendif()\n\n\n#---------------------------------------------------------------------------\n# Installation.\n#---------------------------------------------------------------------------\n\n# The preamble 'notebook.tex' should be kept in sync with the one in\n# ../frontend/common/texengine; this one is meant for printing so\n# slightly different, but cadabra-specific macros should be copied.\n\nif (NOT INSTALL_TARGETS_ONLY)\n   install(FILES  notebook.tex  DESTINATION ${INSTALL_LATEX_DIR})\n   install(FILES  notebook.html DESTINATION ${INSTALL_LATEX_DIR})\nendif()\n#set(INSTALL_LIB_DIR     lib           CACHE PATH \"Installation directory for libraries\")\n\ninstall(TARGETS cadabra-server             DESTINATION ${CDB_BIN_PATH})\ninstall(TARGETS cadabra2html cadabra2latex DESTINATION ${CDB_BIN_PATH})\n\n# We don't need to install the libcadabra_client library as it is statically\n# linked with our binaries anyway.\n# install(\n#  TARGETS cadabra_client \n#  RUNTIME DESTINATION bin COMPONENT runtime \n#  LIBRARY ARCHIVE DESTINATION lib \n#  LIBRARY DESTINATION lib\n# )\n# install(TARGETS cadabra_server LIBRARY ARCHIVE DESTINATION lib LIBRARY DESTINATION lib)\n\nif(ENABLE_JUPYTER)\n  install(TARGETS cadabra-jupyter-kernel      DESTINATION ${CDB_BIN_PATH})\n  install(FILES   kernel.json connection.json DESTINATION share/jupyter/kernels/cadabra)\nendif()\n\nif (MSVC AND NOT INSTALL_TARGETS_ONLY)\n   # GTK helpers\n   install(\n      FILES\n         \"${_VCPKG_ROOT_DIR}/installed/x64-windows/tools/glib/gspawn-win64-helper.exe\"    \n         \"${_VCPKG_ROOT_DIR}/installed/x64-windows/tools/glib/gspawn-win64-helper-console.exe\"\n      DESTINATION\n         ${CDB_BIN_PATH}\n         )\n   # Python (for some reason this is not copied in)\n   get_filename_component(CDB_PYTHON_BASE ${Python_LIBRARIES} NAME_WE)\n   get_filename_component(CDB_PYTHON_PATH ${Python_LIBRARIES} DIRECTORY)\n   message(\"--- Python directory: ${CDB_PYTHON_PATH}\")\n   string(TOLOWER ${CDB_PYTHON_BASE} CDB_PYTHON_BASE)\n   message(\"--- Python library:   ${CDB_PYTHON_BASE}.dll\")\n   install(FILES \"${CDB_PYTHON_PATH}/../${CDB_PYTHON_BASE}.dll\"\n     DESTINATION    ${CDB_BIN_PATH}\n   )\nendif()\n\n# manual pages\nif(NOT MSVC)\n  install(\n    FILES\n    ../man/man1/cadabra-server.1\n    DESTINATION\n    share/man/man1\n    )\nendif()\n"
  },
  {
    "path": "client_server/ComputeThread.cc",
    "content": "\n#include <string>\n#include <iostream>\n#include <sstream>\n#include \"ComputeThread.hh\"\n#include \"DocumentThread.hh\"\n#include \"GUIBase.hh\"\n#include \"Actions.hh\"\n#include \"InstallPrefix.hh\"\n#include \"popen2.hh\"\n#include <sys/types.h>\n#include <glibmm/spawn.h>\n#include \"internal/unistd.h\"\n#include \"CdbPython.hh\"\n\nusing namespace cadabra;\n\nComputeThread::ComputeThread(int server_port, std::string token, std::string ip_address)\n\t: gui(0), docthread(0), connection_is_open(false), restarting_kernel(false), server_pid(0),\n\t  server_stdout(0), server_stderr(0), forced_server_port(server_port), forced_server_token(token),\n\t  forced_server_ip_address(ip_address)\n\t{\n\t// The ComputeThread constructor (but _not_ the run() member!) is\n\t// always run on the gui thread, so we can grab the gui thread id\n\t// here.\n\n\tgui_thread_id=std::this_thread::get_id();\n\t}\n\nComputeThread::~ComputeThread()\n\t{\n\tif(server_stdout!=0) {\n\t\tclose(server_stdout);\n\t\t// close(server_stderr);\n\t\tGlib::spawn_close_pid(server_pid);\n\t\tserver_pid=0;\n\t\tserver_stdout=0;\n\t\tserver_stderr=0;\n\t\t}\n\t}\n\nvoid ComputeThread::set_master(GUIBase *b, DocumentThread *d)\n\t{\n\tgui=b;\n\tdocthread=d;\n\t}\n\nvoid ComputeThread::init()\n\t{\n\t// Setup the WebSockets client.\n\t}\n\nvoid ComputeThread::try_connect()\n\t{\n\twsclient.set_connect_handler(std::bind(&ComputeThread::on_open, this));\n\twsclient.set_fail_handler(std::bind(&ComputeThread::on_fail, this, std::placeholders::_1));\n\twsclient.set_close_handler(std::bind(&ComputeThread::on_close, this));\n\twsclient.set_message_handler(std::bind(&ComputeThread::on_message, this, std::placeholders::_1));\n\n\tstd::ostringstream uristr;\n\turistr << \"ws://\" << (forced_server_ip_address.empty() ? \"127.0.0.1\" : forced_server_ip_address) << \":\" << port;\n\twsclient.connect(uristr.str());\n\n\t// std::cerr << \"cadabra-client: connect done\" << std::endl;\n\t}\n\nvoid ComputeThread::run()\n\t{\n\t// This does *not* run on the GUI thread.\n\t\n\tinit();\n\ttry_spawn_server();\n\ttry_connect();\n\n\t// Enter run loop, which will never terminate anymore. The on_fail and on_close\n\t// handlers will re-try to establish connections when they go bad.\n\n\twsclient.run();\n\t}\n\nvoid ComputeThread::terminate()\n\t{\n\twsclient.stop();\n\n\t// If we have started the server ourselves, stop it now so we do\n\t// not leave mess behind.\n\t// http://riccomini.name/posts/linux/2012-09-25-kill-subprocesses-linux-bash/\n\n\tif(server_pid!=0) {\n\t\tstd::cerr << \"cadabra-client: killing server\" << std::endl;\n\n\t\tif(server_stdout!=0) {\n\t\t\tclose(server_stdout);\n\t\t\t// close(server_stderr);\n\t\t\tGlib::spawn_close_pid(server_pid);\n\t\t\tserver_pid=0;\n\t\t\tserver_stdout=0;\n\t\t\tserver_stderr=0;\n\t\t\t}\n\t\t//\t\tkill(server_pid, SIGKILL);\n\t\t// \t\tif(server_stdout)\n\t\t//\t\t\tpclose2(server_stdout, server_pid);\n\t\t}\n\t}\n\nbool ComputeThread::kernel_is_connected() const\n\t{\n\treturn connection_is_open;\n\t}\n\nvoid ComputeThread::all_cells_nonrunning()\n\t{\n\tfor(auto it: running_cells) {\n\t\tstd::shared_ptr<ActionBase> rs_action =\n\t\t   std::make_shared<ActionSetRunStatus>(it.first, false);\n\t\tdocthread->queue_action(rs_action);\n\t\t}\n\tif(gui) {\n\t\tgui->process_data();\n\t\tgui->on_kernel_runstatus(false);\n\t\t}\n\trunning_cells.clear();\n\t}\n\nvoid ComputeThread::on_fail(const boost::beast::error_code& ec)\n\t{\n\tif(!restarting_kernel) {\n\t\tstd::cerr << \"cadabra-client: connection to server on port \" << port << \" failed, \" << ec.message() << std::endl;\n\t\t}\n\tconnection_is_open=false;\n\tall_cells_nonrunning();\n\tif(gui && server_pid!=0) {\n\t\t// When a kernel restart is in progress, server_pid will be zero\n\t\t// and this block never runs.\n\t\tclose(server_stdout);\n\t\t// close(server_stderr);\n\t\t// std::cerr << \"closing connetion to terminated server\" << std::endl;\n\t\tGlib::spawn_close_pid(server_pid);\n\t\t//\t\tkill(server_pid, SIGKILL);\n\t\tserver_pid=0;\n\t\tserver_stdout=0;\n\t\tserver_stderr=0;\n\t\tgui->on_network_error();\n\t\t}\n\n\ttry_spawn_server();\n\ttry_connect();\n\t}\n\nusing SlotSpawnChildSetup = sigc::slot<void()>;\n\nvoid ComputeThread::try_spawn_server()\n\t{\n\t// Startup the server. First generate a UUID, pass this to the\n\t// starting server, then use this UUID to get access to the server\n\t// port.\n\n\t// std::cerr << \"cadabra-client: spawning server\" << std::endl;\n\n\tif(forced_server_port!=0) {\n\t\tport=forced_server_port;\n\t\tauthentication_token=forced_server_token;\n\t\treturn;\n\t\t}\n\n\tstd::vector<std::string> argv, envp;\n#if defined(_WIN32) || defined(_WIN64)\n\targv.push_back(\"cadabra-server.exe\");\n#else\n\tconst char *appdir = getenv(\"APPDIR\");\n\tif(appdir) {\n\t\t// std::cerr << \"This is an AppImage, APPDIR = \" << appdir << std::endl;\n\t\targv.push_back(std::string(appdir)+\"/usr/bin/cadabra-server\");\n\t\t}\n\telse {\n\t\t// std::cerr << \"Not an AppImage.\" << std::endl;\n\t\targv.push_back(\"cadabra-server\");\n\t\t}\n#endif\n\tGlib::Pid pid;\n\tstd::string wd(\"\");\n\n\t// See https://bugs.launchpad.net/inkscape/+bug/1662531 for things related to\n\t// the 'envp' argument in the call below.\n\ttry {\n#ifdef _WIN32\n\t\tGlib::SpawnFlags flags = Glib::SPAWN_DO_NOT_REAP_CHILD | Glib::SPAWN_SEARCH_PATH | Glib::SpawnFlags::SPAWN_STDERR_TO_DEV_NULL;\n#else\n  #if GLIBMM_MAJOR_VERSION > 2 || (GLIBMM_MAJOR_VERSION == 2 && GLIBMM_MINOR_VERSION >= 68)\n\t\tGlib::SpawnFlags flags = Glib::SpawnFlags::DEFAULT | Glib::SpawnFlags::SEARCH_PATH,\n  #else\n\t\tGlib::SpawnFlags flags = Glib::SPAWN_DO_NOT_REAP_CHILD | Glib::SPAWN_SEARCH_PATH;\n  #endif\n#endif\n\t\t\n\t\tGlib::spawn_async_with_pipes(wd, argv, /* envp, WITH envp, Fedora 27 fails to start python properly */\n\t\t\t\t\t\t\t\t\t\t\t  flags,\n\t\t                             sigc::slot<void()>(),\n\t\t                             &pid,\n\t\t                             0,\n\t\t                             &server_stdout,\n\t\t                             0); // We need to see stderr on the console\n\t\t//\t\t\t\t\t\t\t\t\t\t  &server_stderr);\n\n//#if GLIBMM_MAJOR_VERSION > 2 || (GLIBMM_MAJOR_VERSION == 2 && GLIBMM_MINOR_VERSION >= 68)\n//\t\t\t\t\t\t\t\t\t\t\t  Glib::SpawnFlags::DEFAULT | Glib::SpawnFlags::SEARCH_PATH,\n//\t\t                             sigc::slot<void()>(),\n//#else\n//\t\t                             flags,\n//\t\t                             sigc::slot<void>([](){ FreeConsole(); }),\n//#endif\n//\t\t                             &pid,\n//\t\t                             0,\n//\t\t                             &server_stdout,\n//\t\t                             0); // We need to see stderr on the console\n//\t\t//\t\t\t\t\t\t\t\t\t\t  &server_stderr);\n\n\t\tchar buffer[100];\n\t\tFILE *f = fdopen(server_stdout, \"r\");\n\t\tif(fscanf(f, \"%99s\", buffer)!=1) {\n\t\t\tthrow std::logic_error(\"Failed to read port from server.\");\n\t\t\t}\n\t\tport = atoi(buffer);\n\t\tif(fscanf(f, \"%99s\", buffer)!=1) {\n\t\t\tthrow std::logic_error(\"Failed to read authentication token from server.\");\n\t\t\t}\n\t\tauthentication_token=std::string(buffer);\n\t\t// std::cerr << \"auth token: \" << authentication_token << std::endl;\n\t\t}\n\tcatch(Glib::SpawnError& err) {\n\t\tstd::cerr << \"Failed to start server \" << argv[0] << \": \" << err.what() << std::endl;\n\t\t// FIXME: cannot just fall through, the server is not up!\n\t\t}\n\t}\n\nvoid ComputeThread::on_open()\n\t{\n\tconnection_is_open=true;\n\trestarting_kernel=false;\n\tif(gui) {\n\t\tgui->on_connect();\n\t\tgui->on_kernel_runstatus(false);\n\t\t}\n\n\t//\t// now it is safe to use the connection\n\t//\tstd::string msg;\n\t//\n\t////\tif(stopit) {\n\t////\t\tmsg =\n\t////\t\t\t\"{ \\\"header\\\":   { \\\"uuid\\\": \\\"none\\\", \\\"msg_type\\\": \\\"execute_interrupt\\\" },\"\n\t////\t\t\t\"  \\\"content\\\":  { \\\"code\\\": \\\"print(42)\\n\\\"} \"\n\t////\t\t\t\"}\";\n\t////\t\t}\n\t////\telse {\n\t//\t\tmsg =\n\t//\t\t\t\"{ \\\"header\\\":   { \\\"uuid\\\": \\\"none\\\", \\\"msg_type\\\": \\\"execute_request\\\" },\"\n\t//\t\t\t\"  \\\"content\\\":  { \\\"code\\\": \\\"import time\\nprint(42)\\ntime.sleep(10)\\n\\\"} \"\n\t//\t\t\t\"}\";\n\t////\t\t}\n\t//\n\t////\tc->send(hdl, \"import time\\nfor i in range(0,10):\\n   print('this is python talking '+str(i))\\nex=Ex('A_{m n}')\\nprint(str(ex))\", websocketpp::frame::opcode::text);\n\t//\tc->send(hdl, msg, websocketpp::frame::opcode::text);\n\t}\n\nvoid ComputeThread::on_close()\n\t{\n\t// std::cerr << \"cadabra-client: connection closed\" << std::endl;\n\tconnection_is_open=false;\n\tall_cells_nonrunning();\n\tif(gui) {\n\t\tif(restarting_kernel) {\n\t\t\tgui->on_disconnect(\"restarting kernel\");\n\t\t\tgui->on_kernel_runstatus(true);\n\t\t\t}\n\t\telse {\n\t\t\tgui->on_disconnect(\"not connected\");\n\t\t\t}\n\t\t}\n\n\tsleep(1); // do not cause a torrent...\n\ttry_connect();\n\t}\n\nvoid ComputeThread::cell_finished_running(DataCell::id_t id)\n\t{\n\tif(id.id==0) {\n\t\t// This was code without a cell representation (run in\n\t\t// response to e.g. a slider update). Ignore.\n\t\t}\n\telse {\n\t\tauto it=running_cells.find(id);\n\t\tif(it==running_cells.end()) {\n\t\t\tthrow std::logic_error(\"Cannot find cell with id = \"+std::to_string(id.id));\n\t\t\t}\n\t\t\n\t\tif(it->second==1) {\n\t\t\t// Mark this cell as no longer running.\n\t\t\tstd::shared_ptr<ActionBase> rs_action =\n\t\t\t\tstd::make_shared<ActionSetRunStatus>(id, false);\n\t\t\tdocthread->queue_action(rs_action);\n\n\t\t\trunning_cells.erase(it);\n\t\t\t}\n\t\telse\n\t\t\tit->second -= 1;\n\t\t}\n\t}\n\nvoid ComputeThread::on_message(const std::string& msg)\n\t{\n\t// Parse the JSON message.\n\tnlohmann::json root;\n\n\ttry {\n\t\troot=nlohmann::json::parse(msg);\n\t\t}\n\tcatch(nlohmann::json::exception& e) {\n\t\tstd::cerr << \"cadabra-client: cannot parse message.\" << std::endl;\n\t\treturn;\n\t\t}\n\tif(getenv(\"CADABRA_SHOW_RECEIVED\")) {\n\t\tstd::cerr << \"RECV: \" << root.dump(3) << std::endl;\n\t\t}\n\t\n\tif(root.count(\"header\")==0) {\n\t\tstd::cerr << \"cadabra-client: received message without 'header'.\" << std::endl;\n\t\treturn;\n\t\t}\n\tif(root.count(\"content\")==0) {\n\t\tstd::cerr << \"cadabra-client: received message without 'content'.\" << std::endl;\n\t\treturn;\n\t\t}\n\tconst nlohmann::json& header  = root[\"header\"];\n\tconst nlohmann::json& content = root[\"content\"];\n\tconst std::string msg_type    = root.value(\"msg_type\", \"\");\n\n\tDataCell::id_t parent_id;\n\tparent_id.id = header.value(\"parent_id\", uint64_t(0));\n\tif(header.value(\"parent_origin\", \"\")==\"client\")\n\t\tparent_id.created_by_client=true;\n\telse\n\t\tparent_id.created_by_client=false;\n\tDataCell::id_t cell_id;\n\tcell_id.id = header[\"cell_id\"].get<uint64_t>();\n\tif(header.value(\"cell_origin\", \"\")==\"client\")\n\t\tcell_id.created_by_client=true;\n\telse\n\t\tcell_id.created_by_client=false;\n\t// std::cerr << \"received cell with id \" << cell_id.id << std::endl;\n\n\t// Determine if this refers to a special cell in the interactive console.\n\tif (interactive_cells.find(parent_id.id) != interactive_cells.end()) {\n\t\tinteractive_cells.insert(cell_id.id);\n\t\tdocthread->on_interactive_output(root);\n\t}\n\telse if (interactive_cells.find(cell_id.id) != interactive_cells.end()) {\n\t\tdocthread->on_interactive_output(root);\n\t\t}\n\telse if (msg_type.find(\"csl_\") == 0) {\n\t\troot[\"header\"][\"from_server\"] = true;\n\t\tdocthread->on_interactive_output(root);\n\t\t}\n\telse if (msg_type == \"progress_update\") {\n\t\tstd::string msg = content.value<std::string>(\"msg\", \"Idle\");\n\t\tint n = content.value<int>(\"n\", 0);\n\t\tint total = content.value<int>(\"total\", 0);\n\t\t// FIXME: do something with 'pulse':\n\t\t// int pulse = content.value<bool>(\"pulse\", false);\n\t\tdocthread->set_progress(msg, n, total);\n\t}\n\telse if(msg_type==\"completed\") {\n\t\t// std::cerr << \"received completion of \" << content[\"original\"] << \" -> \" << content[\"completed\"] << std::endl;\n\n\t\t// Finally, the action to add the output cell.\n\t\tstd::string toadd=content[\"completed\"].get<std::string>();\n\t\tif(toadd.size()>0) {\n\t\t\ttoadd=toadd.substr(content[\"original\"].get<std::string>().size());\n\t\t\tint pos=content[\"position\"].get<int>();\n\t\t\tint alternative=content[\"alternative\"].get<int>();\n\t\t\tstd::shared_ptr<ActionBase> action =\n\t\t\t\tstd::make_shared<ActionCompleteText>(cell_id, pos, toadd, alternative);\n\t\t\tdocthread->queue_action(action);\n\t\t\t}\n\t\t}\n\telse {\n\t\ttry {\n\t\t\tbool finished = header[\"last_in_sequence\"].get<bool>();\n\n\t\t\tif (finished) {\n\t\t\t\tif(parent_id.id!=0) {\n\t\t\t\t\t// If this cell references variables, store them in the DataCell.\n\t\t\t\t\tif(content.count(\"variables\")>0) {\n\t\t\t\t\t\tstd::set<std::string> vars;\n\t\t\t\t\t\tfor(const auto& var: content[\"variables\"])\n\t\t\t\t\t\t\tvars.insert(var);\n\t\t\t\t\t\t\n\t\t\t\t\t\tstd::shared_ptr<ActionBase> action =\n\t\t\t\t\t\t\tstd::make_shared<ActionSetVariableList>(parent_id, vars);\n\t\t\t\t\t\tdocthread->queue_action(action);\n\t\t\t\t\t\t}\n\t\t\t\t\t}\n\t\t\t\tcell_finished_running(parent_id);\n\t\t\t\t}\n\n\t\t\tif (content.count(\"output\")>0 && content[\"output\"].get<std::string>().size() > 0) {\n\t\t\t\tif (msg_type == \"output\") {\n\t\t\t\t\tstd::string output = \"\\\\begin{verbatim}\" + content[\"output\"].get<std::string>() + \"\\\\end{verbatim}\";\n\n\t\t\t\t\t// Stick an AddCell action onto the stack. We instruct the\n\t\t\t\t\t// action to add this result output cell as a child of the\n\t\t\t\t\t// corresponding input cell.\n\t\t\t\t\tDataCell result(cell_id, DataCell::CellType::output, output);\n\n\t\t\t\t\t// Finally, the action to add the output cell.\n\t\t\t\t\tstd::shared_ptr<ActionBase> action =\n\t\t\t\t\t   std::make_shared<ActionAddCell>(result, parent_id, ActionAddCell::Position::child);\n\t\t\t\t\tdocthread->queue_action(action);\n\t\t\t\t\t}\n\t\t\t\telse if (msg_type == \"verbatim\") {\n\t\t\t\t\tstd::string output = \"\\\\begin{verbatim}\" + content[\"output\"].get<std::string>() + \"\\\\end{verbatim}\";\n\n\t\t\t\t\t// Stick an AddCell action onto the stack. We instruct the\n\t\t\t\t\t// action to add this result output cell as a child of the\n\t\t\t\t\t// corresponding input cell.\n\t\t\t\t\tDataCell result(cell_id, DataCell::CellType::verbatim, output);\n\n\t\t\t\t\t// Finally, the action to add the output cell.\n\t\t\t\t\tstd::shared_ptr<ActionBase> action =\n\t\t\t\t\t   std::make_shared<ActionAddCell>(result, parent_id, ActionAddCell::Position::child);\n\t\t\t\t\tdocthread->queue_action(action);\n\t\t\t\t\t}\n\t\t\t\telse if (msg_type == \"latex_view\") {\n\t\t\t\t\t// std::cerr << \"received latex cell \" << content[\"output\"].asString() << std::endl;\n\t\t\t\t\tDataCell result(cell_id, DataCell::CellType::latex_view, content[\"output\"].get<std::string>());\n\t\t\t\t\tstd::shared_ptr<ActionBase> action =\n\t\t\t\t\t   std::make_shared<ActionAddCell>(result, parent_id, ActionAddCell::Position::child);\n\t\t\t\t\tdocthread->queue_action(action);\n\t\t\t\t\t}\n\t\t\t\telse if (msg_type == \"input_form\") {\n\t\t\t\t\tDataCell result(cell_id, DataCell::CellType::input_form, content[\"output\"].get<std::string>());\n\t\t\t\t\tstd::shared_ptr<ActionBase> action =\n\t\t\t\t\t   std::make_shared<ActionAddCell>(result, parent_id, ActionAddCell::Position::child);\n\t\t\t\t\tdocthread->queue_action(action);\n\t\t\t\t\t}\n\t\t\t\telse if (msg_type == \"error\" || msg_type==\"fault\") {\n\t\t\t\t\tstd::string error = \"\\\\begin{verbatim}\" + content[\"output\"].get<std::string>()\n\t\t\t\t\t                    + \"\\\\end{verbatim}\";\n\t\t\t\t\t//if (msg_type == \"fault\") {\n\t\t\t\t\t//\terror = \"Kernel fault\\\\begin{small}\" + error + \"\\\\end{small}\";\n\t\t\t\t\t//\t}\n\n\t\t\t\t\t// Stick an AddCell action onto the stack. We instruct the\n\t\t\t\t\t// action to add this result output cell as a child of the\n\t\t\t\t\t// corresponding input cell.\n\t\t\t\t\tDataCell result(cell_id, DataCell::CellType::error, error);\n\n\t\t\t\t\t// Finally, the action.\n\t\t\t\t\tstd::shared_ptr<ActionBase> action =\n\t\t\t\t\t   std::make_shared<ActionAddCell>(result, parent_id, ActionAddCell::Position::child);\n\t\t\t\t\tdocthread->queue_action(action);\n\n\t\t\t\t\t// Position the cursor in the cell that generated the error. All other cells on\n\t\t\t\t\t// the execute queue have been cancelled by the server.\n\t\t\t\t\tstd::shared_ptr<ActionBase> actionpos =\n\t\t\t\t\t   std::make_shared<ActionPositionCursor>(parent_id, ActionPositionCursor::Position::in);\n\t\t\t\t\tdocthread->queue_action(actionpos);\n\n\t\t\t\t\t// Action has stopped, so mark all cells as non-running.\n\t\t\t\t\tall_cells_nonrunning();\n\t\t\t\t\t}\n\t\t\t\telse if (msg_type == \"image_png\") {\n\t\t\t\t\tDataCell result(cell_id, DataCell::CellType::image_png, content[\"output\"].get<std::string>());\n\t\t\t\t\tstd::shared_ptr<ActionBase> action =\n\t\t\t\t\t   std::make_shared<ActionAddCell>(result, parent_id, ActionAddCell::Position::child);\n\t\t\t\t\tdocthread->queue_action(action);\n\t\t\t\t\t}\n\t\t\t\telse if (msg_type == \"image_svg\") {\n\t\t\t\t\tDataCell result(cell_id, DataCell::CellType::image_svg, content[\"output\"].get<std::string>());\n\t\t\t\t\tstd::shared_ptr<ActionBase> action =\n\t\t\t\t\t   std::make_shared<ActionAddCell>(result, parent_id, ActionAddCell::Position::child);\n\t\t\t\t\tdocthread->queue_action(action);\n\t\t\t\t\t}\n\t\t\t\telse if (msg_type == \"slider\") {\n\t\t\t\t\tDataCell result(cell_id, DataCell::CellType::slider, content[\"output\"].get<std::string>());\n\t\t\t\t\tstd::shared_ptr<ActionBase> action =\n\t\t\t\t\t   std::make_shared<ActionAddCell>(result, parent_id, ActionAddCell::Position::child);\n\t\t\t\t\tdocthread->queue_action(action);\n\t\t\t\t\t}\n\t\t\t\telse {\n\t\t\t\t\tstd::cerr << \"cadabra-client: received cell we did not expect: \"\n\t\t\t\t\t          << msg_type << \": \" << content << std::endl;\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t}\n\t\tcatch (std::logic_error& ex) {\n\t\t\t// WARNING: if the server sends\n\t\t\tstd::cerr << \"cadabra-client: trouble processing server response: \" << ex.what() << std::endl;\n\t\t\t}\n\t\t}\n\n\t// Update kernel busy indicator depending on number of running cells.\n\tif(number_of_cells_executing()>0)\n\t\tgui->on_kernel_runstatus(true);\n\telse\n\t\tgui->on_kernel_runstatus(false);\n\n\tgui->process_data();\n\t}\n\nvoid ComputeThread::execute_interactive(uint64_t id, const std::string& code)\n\t{\n\tassert(gui_thread_id == std::this_thread::get_id());\n\n\tif (!connection_is_open)\n\t\treturn;\n\n\tif (code.substr(0, 7) == \"reset()\")\n\t\treturn restart_kernel();\n\n\tnlohmann::json req, header, content;\n\n\theader[\"msg_type\"]    = \"execute_request\";\n\theader[\"cell_id\"]     = id;\n\theader[\"interactive\"] = true;\n\tcontent[\"code\"]       = code.c_str();\n\n\treq[\"auth_token\"] = authentication_token;\n\treq[\"header\"]     = header;\n\treq[\"content\"]    = content;\n\n\tstd::ostringstream oss;\n\toss << req << std::endl;\n\tif(getenv(\"CADABRA_SHOW_SENT\")) {\n\t\tstd::cerr << \"SENT: \" << req.dump(3) << std::endl;\n\t\t}\n\twsclient.send(oss.str());\n\tinteractive_cells.insert(id);\n\t}\n\nvoid ComputeThread::execute_cell(DTree::iterator it, std::string no_assign, std::vector<uint64_t> output_cell_ids)\n\t{\n\t// This absolutely has to be run on the main GUI thread.\n\tassert(gui_thread_id==std::this_thread::get_id());\n\n\tif(connection_is_open==false)\n\t\treturn;\n\n\tconst DataCell& dc=(*it);\n\n\t// std::cout << \"cadabra-client: ComputeThread going to execute \" << dc.textbuf << std::endl;\n\n\tif((it->textbuf).substr(0,7)==\"reset()\") {\n\t\trestart_kernel();\n\n\t\tstd::shared_ptr<ActionBase> action =\n\t\t   std::make_shared<ActionPositionCursor>(it->id(), ActionPositionCursor::Position::next);\n\n\t\tdocthread->queue_action(action);\n\t\treturn;\n\t\t}\n\n\t// Position the cursor in the next cell so this one will not\n\t// accidentally get executed twice. This runs synchronously!\n\tstd::shared_ptr<ActionBase> actionpos =\n\t   std::make_shared<ActionPositionCursor>(it->id(), ActionPositionCursor::Position::next);\n\tdocthread->queue_action(actionpos);\n\tgui->process_data();\n\n\t// For a code cell, construct a server request message and then\n\t// send the cell to the server.\n\tif(it->cell_type==DataCell::CellType::python) {\n\t\tauto rit=running_cells.find(dc.id());\n\t\tif(rit==running_cells.end())\n\t\t\trunning_cells[dc.id()]=1;\n\t\telse\n\t\t\trit->second += 1;\n\n\t\t// Schedule an action to update the running status of this cell.\n\t\tstd::shared_ptr<ActionBase> rs_action =\n\t\t   std::make_shared<ActionSetRunStatus>(it->id(), true);\n\t\tdocthread->queue_action(rs_action);\n\n\t\tnlohmann::json req, header, content;\n\t\theader[\"uuid\"]=\"none\";\n\t\theader[\"cell_id\"]=dc.id().id;\n\t\tif(dc.id().created_by_client)\n\t\t\theader[\"cell_origin\"]=\"client\";\n\t\telse\n\t\t\theader[\"cell_origin\"]=\"server\";\n\t\theader[\"msg_type\"]=\"execute_request\";\n\t\theader[\"output_cell_ids\"]=output_cell_ids;\n\t\treq[\"auth_token\"]=authentication_token;\n\t\treq[\"header\"]=header;\n\t\tcontent[\"remove_variable_assignments\"]=no_assign;\n\t\tcontent[\"code\"]=dc.textbuf;\n\t\treq[\"content\"]=content;\n\n\t\tgui->on_kernel_runstatus(true);\n\t\tstd::ostringstream str;\n\t\tstr << req << std::endl;\n\t\tif(getenv(\"CADABRA_SHOW_SENT\")) {\n\t\t\tstd::cerr << \"SENT: \" << req.dump(3) << std::endl;\n\t\t\t}\n\t\twsclient.send(str.str());\n\t\t// NOTE: we can get a return message in on_message at any point after this,\n\t\t// it will come in on a different thread!\n\t\t}\n\n\t// For a LaTeX cell, immediately request a new latex output cell to be displayed.\n\tif(it->cell_type==DataCell::CellType::latex) {\n\t\t// Stick an AddCell action onto the stack. We instruct the\n\t\t// action to add this result output cell as a child of the\n\t\t// corresponding input cell.\n\t\tDataCell result(DataCell::CellType::latex_view, it->textbuf);\n\n\t\tstd::shared_ptr<ActionBase> action =\n\t\t   std::make_shared<ActionAddCell>(result, it->id(), ActionAddCell::Position::child);\n\t\tdocthread->queue_action(action);\n\t\t}\n\t}\n\nvoid ComputeThread::update_variable_on_server(std::string variable, double value)\n\t{\n\tnlohmann::json req, header, content;\n\theader[\"uuid\"]=\"none\";\n\theader[\"cell_id\"]=0;\n\theader[\"cell_origin\"]=\"client\";\n\theader[\"msg_type\"]=\"execute_request\";\n\treq[\"auth_token\"]=authentication_token;\n\treq[\"header\"]=header;\n\tcontent[\"code\"]=variable + \"=\" + std::to_string(value);\n\treq[\"content\"]=content;\n\t\n\tstd::ostringstream str;\n\tstr << req << std::endl;\n\tif(getenv(\"CADABRA_SHOW_SENT\")) {\n\t\tstd::cerr << \"SENT: \" << req.dump(3) << std::endl;\n\t\t}\n\twsclient.send(str.str());\n\t}\n\n\nint ComputeThread::number_of_cells_executing() const\n\t{\n\treturn running_cells.size();\n\t}\n\nvoid ComputeThread::stop()\n\t{\n\tif(connection_is_open==false)\n\t\treturn;\n\n\t// std::cerr << \"stopping existing kernel\" << std::endl;\n\t\n\tnlohmann::json req, header, content;\n\theader[\"uuid\"]=\"none\";\n\theader[\"msg_type\"]=\"execute_interrupt\";\n\treq[\"auth_token\"]=authentication_token;\n\treq[\"header\"]=header;\n\n\tstd::ostringstream str;\n\tstr << req << std::endl;\n\n\t//\tstd::cerr << str.str() << std::endl;\n\n\tserver_pid=0;\n\tif(getenv(\"CADABRA_SHOW_SENT\")) {\n\t\tstd::cerr << \"SENT: \" << req.dump(3) << std::endl;\n\t\t}\n\twsclient.send(str.str());\n\t// Do not yet mark cells non-running, otherwise we are unable to\n\t// process any error messages. Do this once the stop comes through.\n\t// all_cells_nonrunning();\t\n\t}\n\nvoid ComputeThread::restart_kernel()\n\t{\n\tif(connection_is_open==false)\n\t\treturn;\n\n\trestarting_kernel=true;\n\n\t// Restarting the kernel means all previously running blocks have stopped running.\n\t// Inform the GUI about this.\n\t// FIXME: set all running flags to false\n\tgui->on_kernel_runstatus(false);\n\n\t// std::cerr << \"cadabra-client: restarting kernel\" << std::endl;\n\tnlohmann::json req, header, content;\n\theader[\"uuid\"]=\"none\";\n\theader[\"msg_type\"]=\"exit\";\n\theader[\"from_server\"] = true;\n\treq[\"auth_token\"]=authentication_token;\n\treq[\"header\"]=header;\n\n\tstd::ostringstream str;\n\tstr << req << std::endl;\n\n\t//\tstd::cerr << str.str() << std::endl;\n\n\tif(getenv(\"CADABRA_SHOW_SENT\")) {\n\t\tstd::cerr << \"SENT: \" << req.dump(3) << std::endl;\n\t\t}\n\twsclient.send(str.str());\n\tdocthread->on_interactive_output(req);\n\t}\n\nbool ComputeThread::complete(DTree::iterator it, int pos, int alternative)\n\t{\n\tif(connection_is_open==false)\n\t\treturn false;\n\n\tconst DataCell& dc=(*it);\n\n\tnlohmann::json req, header, content;\n\theader[\"uuid\"]=\"none\";\n\theader[\"cell_id\"]=dc.id().id;\n\tif(dc.id().created_by_client)\n\t\theader[\"cell_origin\"]=\"client\";\n\telse\n\t\theader[\"cell_origin\"]=\"server\";\n\theader[\"msg_type\"]=\"complete\";\n\treq[\"auth_token\"]=authentication_token;\n\treq[\"header\"]=header;\n\tstd::string todo = it->textbuf.substr(0,pos);\n//\tif(todo.size()>0 && todo[todo.size()-1]=='\\n')\n//\t\ttodo=todo.substr(0, todo.size()-1);\n\t// std::cerr << \"to complete full: \" << todo << std::endl;\n\tsize_t lst=todo.find_last_of(\"\\n(){}[]:\\t \");\n\tif(lst!=std::string::npos)\n\t\ttodo=todo.substr(lst+1);\n\t// std::cerr << \"to complete strip: \" << todo << std::endl;\n\n\tif(todo.size()==0)\n\t\treturn false;\n\n\treq[\"string\"]=todo;\n\treq[\"position\"]=pos;\n\treq[\"alternative\"]=alternative;\n\n\tstd::ostringstream str;\n\tstr << req << std::endl;\n\n\t// std::cerr << str.str() << std::endl;\n\n\tserver_pid=0;\n\tif(getenv(\"CADABRA_SHOW_SENT\")) {\n\t\tstd::cerr << \"SENT: \" << req.dump(3) << std::endl;\n\t\t}\n\twsclient.send(str.str());\n\n\treturn true;\n\t}\n"
  },
  {
    "path": "client_server/ComputeThread.hh",
    "content": "\n#pragma once\n\n#include <signal.h>\n#include <thread>\n#include <set>\n#include <glibmm/spawn.h>\n#include \"websocket_client.hh\"\n\n#include \"DataCell.hh\"\n\nnamespace cadabra {\n\n\tclass GUIBase;\n\tclass DocumentThread;\n\n\t/// \\ingroup clientserver\n\t///\n\t/// Base class which talks to the server and sends Action objects back to the\n\t/// DocumentThread.\n\t///\n\t/// ComputeThread is the base class which takes care of doing actual\n\t/// computations with the cells in a document. It handles talking to\n\t/// the server backend. It knows how to pass cells to the server and\n\t/// ask them to be executed. Results are reported back to the GUI by\n\t/// putting ActionBase objects onto its todo stack. ComputeThread never\n\t/// directly modifies the document tree.\n\n\tclass ComputeThread {\n\t\tpublic:\n\t\t\t/// If the ComputeThread is constructed with a null pointer to the\n\t\t\t/// gui, there will be no gui updates, just DTree updates.\n\n\t\t\tComputeThread(int server_port=0, std::string token=\"\", std::string ip_address=\"127.0.0.1\");\n\t\t\tComputeThread(const ComputeThread& )=delete; // You cannot copy this object\n\t\t\t~ComputeThread();\n\n\t\t\t/// Determine the objects that this compute thread should be\n\t\t\t/// talking to.\n\t\t\tvoid set_master(GUIBase *, DocumentThread *);\n\n\t\t\t/// Main entry point, which will connect to the server and\n\t\t\t/// then start an event loop to handle communication with the\n\t\t\t/// server. Only terminates when the connection drops, so run\n\t\t\t/// your GUI on a different thread.\n\n\t\t\tvoid run();\n\n\t\t\t/// In order to execute code on the server, call the\n\t\t\t/// following from the GUI thread.  This method returns as\n\t\t\t/// soon as the request has been put on the network queue. If\n\t\t\t/// no communication with the server is necessary, this\n\t\t\t/// returns immediately. The ComputeThread will report the\n\t\t\t/// result of the computation/processing by adding actions to\n\t\t\t/// the DocumentThread owned pending_actions stack, by\n\t\t\t/// calling queue_action. It will never modify the cell\n\t\t\t/// directly, and will also never modify any other cells in\n\t\t\t/// the document tree.\n\n\t\t\tvoid execute_cell(DTree::iterator, std::string no_assign=\"\",\n\t\t\t\t\t\t\t\t\tstd::vector<uint64_t> output_cell_ids=std::vector<uint64_t>() );\n\n\t\t\tvoid execute_interactive(uint64_t id, const std::string& code);\n\n\t\t\t/// Update a variable in the kernel. This does essentially the\n\t\t\t/// same thing as execute_cell, but will not refer to any\n\t\t\t/// cell as it creates the code itself.\n\n\t\t\tvoid update_variable_on_server(std::string variable, double value);\n\t\t\t\n\t\t\t/// Stop the current cell execution on the server and remove\n\t\t\t/// all other cells from the run queue as well.\n\n\t\t\tvoid stop();\n\n\t\t\t/// Restart the kernel.\n\n\t\t\tvoid restart_kernel();\n\n\t\t\t/// Request completion of a string. Returns `false` if the current\n\t\t\t/// cell cannot be completed, in which case the TAB which led to\n\t\t\t/// the request should be interpreted literally and used for spacing.\n\t\t\t/// The `alternative` argument is the serial number of the requested\n\t\t\t/// completion, in case there is more than one possible completion.\n\n\t\t\tbool complete(DTree::iterator, int pos, int alternative);\n\n\t\t\t// Determine if there are still cells running on the server.\n\t\t\t// FIXME: this does not guarantee thread-safety but at the moment\n\t\t\t// is only used for updating status bars etc.\n\t\t\t// FIXME: can be moved to DocumentThread.\n\n\t\t\tint number_of_cells_executing(void) const;\n\n\t\t\t/// Terminate the compute thread, in preparation for shutting\n\t\t\t/// down the client altogether.\n\n\t\t\tvoid terminate();\n\n\t\t\t/// Return the status of the connection to the kernel.\n\t\t\tbool kernel_is_connected() const;\n\t\t\t\n\t\tprivate:\n\t\t\tGUIBase        *gui;\n\t\t\tDocumentThread *docthread;\n\n\t\t\t// For debugging purposes, we keep record of the gui thread id,\n\t\t\t// so that we can flag when code runs on the wrong thread.\n\t\t\t// Gets initialised in the ComputeThread constructor.\n\t\t\tstd::thread::id  gui_thread_id;\n\n\t\t\t// Keeping track of cells which are running on the server, in\n\t\t\t// a form which allows us to look them up quickly based only\n\t\t\t// on the id (which is all that the server knows about). A\n\t\t\t// cell can be queued multiple times for running; this is the\n\t\t\t// integer in the map.\n\n\t\t\tstd::map<DataCell::id_t, int> running_cells;\n\n\t\t\t// WebSocket++ things.\n\t\t\twebsocket_client            wsclient;\n\t\t\tbool                        connection_is_open, restarting_kernel;\n\n\t\t\tvoid init();\n\t\t\tvoid try_connect();\n\t\t\tvoid try_spawn_server();\n\t\t\tvoid on_open();\n\t\t\tvoid on_fail(const boost::beast::error_code&);\n\t\t\tvoid on_close();\n\t\t\tvoid on_message(const std::string& msg);\n\n\t\t\tvoid cell_finished_running(DataCell::id_t);\n\n\t\t\t/// Set all cells to be non-running (e.g. after a kernel failure) and\n\t\t\t/// report the status of each cell to the GUI.\n\t\t\tvoid all_cells_nonrunning();\n\n\t\t\tstd::set<uint64_t> interactive_cells;\n\n\t\t\t// Self-started server\n\t\t\tGlib::Pid       server_pid;\n\t\t\tint             server_stdout, server_stderr;\n\t\t\tunsigned short  port;\n\t\t\tstd::string     authentication_token;\n\t\t\tint             forced_server_port;\n\t\t\tstd::string     forced_server_token;\n\t\t\tstd::string     forced_server_ip_address;\n\t\t};\n\n\t}\n"
  },
  {
    "path": "client_server/DocumentThread.cc",
    "content": "\n#include \"Actions.hh\"\n#include \"DocumentThread.hh\"\n#include \"GUIBase.hh\"\n#include \"ComputeThread.hh\"\n#include \"CdbPython.hh\"\n\n#include <typeinfo>\n#include <iostream>\n#include <set>\n#include <string>\n#include <fstream>\n\n//#include <boost/config.hpp>\n\n#include <internal/unistd.h>\n#include <sys/types.h>\n#ifndef EMSCRIPTEN\n#include <glibmm/miscutils.h>\n#include \"Snoop.hh\"\n#endif\n#include \"Config.hh\"\n\nusing namespace cadabra;\n\nDocumentThread::DocumentThread(GUIBase* g)\n\t: gui(g)\n\t, compute(0)\n\t, current_cell(doc.end())\n\t, follow_mode(false)\n\t, follow_cell(doc.end())\n\t, follow_last_cell(doc.end())\n\t, disable_stacks(false)\n\t{\n\t// Setup logging.\n\tstd::string version=std::string(CADABRA_VERSION_SEM);\n#ifndef EMSCRIPTEN\n\tsnoop::log.init(\"Cadabra\", version, \"log.cadabra.science\");\n\tsnoop::log.set_sync_immediately(true);\n#endif\n\t//\tsnoop::log(snoop::warn) << \"Starting\" << snoop::flush;\n\n\t}\n\nvoid DocumentThread::on_interactive_output(const nlohmann::json& )\n\t{\n\n\t}\n\nvoid DocumentThread::set_progress(const std::string& msg, int cur_step, int total_steps)\n\t{\n\n\t}\n\nvoid DocumentThread::set_compute_thread(ComputeThread *cl)\n\t{\n\tcompute = cl;\n\t}\n\nvoid DocumentThread::new_document()\n\t{\n\t// Setup a single-cell document. This operation itself cannot be undone,\n\t// so we do it directly on the doc, not using Actions.\n\n\tDataCell top(DataCell::CellType::document);\n\tDTree::iterator doc_it = doc.set_head(top);\n\tgui->add_cell(doc, doc_it, false);\n\n\t// One Python input cell in the empty document.\n\n\tDataCell one(DataCell::CellType::python, \"\");\n\tDTree::iterator one_it = doc.append_child(doc_it, one);\n\tgui->add_cell(doc, one_it, false);\n\n\t// Put a 'position cursor' action on the stack to be executed as\n\t// soon as the GUI is up.\n\n\tstd::shared_ptr<ActionBase> actionpos =\n\t   std::make_shared<ActionPositionCursor>(one_it->id(), ActionPositionCursor::Position::in);\n\tqueue_action(actionpos);\n\t}\n\nvoid DocumentThread::load_from_string(const std::string& json)\n\t{\n\tstd::lock_guard<std::mutex> guard(stack_mutex);\n\tpending_actions=std::queue<std::shared_ptr<ActionBase> >();\n\tdoc.clear();\n\tJSON_deserialise(json, doc);\n\tgui->remove_all_cells();\n\tbuild_visual_representation();\n\t}\n\nvoid DocumentThread::undo()\n\t{\n\tstack_mutex.lock();\n\tif(undo_stack.size()==0) {\n\t\t//std::cerr << \"no entries left on the stack\" << std::endl;\n\t\tstack_mutex.unlock();\n\t\treturn;\n\t\t}\n\n\tdisable_stacks=true;\n\tauto ua = undo_stack.top();\n\t//std::cerr << \"Undo action \" << typeid(*ua).name() << std::endl;\n\n\tredo_stack.push(ua);\n\tundo_stack.pop();\n\t// std::cerr << \"DocumentThread::undo: undo_stack.size() == \" << undo_stack.size() << std::endl;\n\tua->revert(*this, *gui);\n\tdisable_stacks=false;\n\n\tstack_mutex.unlock();\n\t}\n\nvoid DocumentThread::redo()\n\t{\n\tstack_mutex.lock();\n\tif(redo_stack.size()==0) {\n\t\t//std::cerr << \"no entries left on the stack\" << std::endl;\n\t\tstack_mutex.unlock();\n\t\treturn;\n\t\t}\n\n\tdisable_stacks=true;\n\tauto ua = redo_stack.top();\n\t//std::cerr << \"Undo action \" << typeid(*ua).name() << std::endl;\n\n\tundo_stack.push(ua);\n\tredo_stack.pop();\n\tua->execute(*this, *gui);\n\tdisable_stacks=false;\n\n\tstack_mutex.unlock();\n\t}\n\nvoid DocumentThread::build_visual_representation()\n\t{\n\t// Because the add_cell method figures out by itself where to generate the VisualCell,\n\t// we only have feed all cells in turn.\n\n\tDTree::iterator doc_it=doc.begin();\n\twhile(doc_it!=doc.end()) {\n\t\t// std::cout << \"ADDING:\" << doc_it->textbuf << std::endl;\n\t\tgui->add_cell(doc, doc_it, false);\n\t\t++doc_it;\n\t\t}\n\t}\n\n//const DTree& DocumentThread::dtree()\n//\t{\n//\treturn doc;\n//\t}\n\ntemplate<typename charT>\nstruct ci_equal {\n\t\tbool operator()(charT ch1, charT ch2) {\n\t\treturn std::toupper(ch1) == std::toupper(ch2);\n\t\t}\n};\n\ntemplate<typename T>\nint ci_find_substr( const T& str1, const T& str2, int start_pos )\n\t{\n\tauto start=str1.begin();\n\tstart+=start_pos;\n\ttypename T::const_iterator it = std::search( start, str1.end(),\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tstr2.begin(), str2.end(), ci_equal<typename T::value_type>() );\n\tif ( it != str1.end() ) return it - str1.begin();\n\telse return -1;\n\t}\n\nstd::pair<DTree::iterator, size_t> DocumentThread::find_string(DTree::iterator start_it, size_t start_pos, const std::string& f, bool case_ins) const\n\t{\n\t// std::cerr << \"finding from pos \" << start_pos << \", \" << &(*start_it) << \": \" << start_it->textbuf.substr(0,30) << std::endl;\n\tDTree::iterator doc_it=start_it;\n\twhile(doc_it!=doc.end()) {\n\t\t//\t\tstd::cout << doc_it->textbuf << std::endl;\n\t\t// FIXME: re-enable searching in output cells.\n\t\tif(doc_it->hidden==false && (doc_it->cell_type==DataCell::CellType::python || doc_it->cell_type==DataCell::CellType::latex)) {\n\t\t\tsize_t pos;\n\t\t\tif(case_ins)\n\t\t\t\tpos = ci_find_substr(doc_it->textbuf, f, start_pos);\n\t\t\telse\n\t\t\t\tpos = doc_it->textbuf.find(f, start_pos);\n\n\t\t\tif(pos!=std::string::npos)\n\t\t\t\treturn std::make_pair(doc_it, pos);\n\t\t\t}\n\t\tstart_pos=0; // after one fail, start next cell at zero\n\t\t++doc_it;\n\t\t}\n\treturn std::make_pair(doc.end(), std::string::npos);\n\t}\n\nvoid DocumentThread::queue_action(std::shared_ptr<ActionBase> ab)\n\t{\n\tstd::lock_guard<std::mutex> guard(stack_mutex);\n\tpending_actions.push(ab);\n\t}\n\nvoid DocumentThread::run_all_cells()\n\t{\n\tfollow_mode=true;\n\tDTree::sibling_iterator sib=doc.begin(doc.begin());\n\twhile(sib!=doc.end(doc.begin())) {\n\t\tif(sib->cell_type==DataCell::CellType::python) {\n\t\t\trun_cell(DTree::iterator(sib), false);\n\t\t\tfollow_last_cell=DTree::iterator(sib);\n\t\t\t}\t\t\t\n\t\t++sib;\n\t\t}\n\t}\n\nvoid DocumentThread::run_cell(DTree::iterator it, bool shift_pressed)\n\t{\n\t// First ensure that this cell is not already running, otherwise all hell\n\t// will break loose when we try to double-remove the existing output cell etc.\n\n\tif(it->running)\n\t\treturn;\n\n\t// Ensure this cell is not empty either.\n\n\tif(it->textbuf.size()==0)\n\t\treturn;\n\n\t// Remove child nodes, if any.\n\t// FIXME: Does it make more sense to do this only after the\n\t// execution result comes back from the server?\n\n\tDTree::sibling_iterator sib=doc.begin(it);\n\tgui->dim_output_cells(it);\n\twhile(sib!=doc.end(it)) {\n\t\t// std::cout << \"cadabra-client: scheduling output cell for removal: \" << sib->id().id << std::endl;\n\t\tstd::shared_ptr<ActionBase> action = std::make_shared<ActionRemoveCell>(sib->id());\n\t\tqueue_action(action);\n\t\t++sib;\n\t\t}\n\n\t// Since the user has initiated this cell execution, we can\n\t// turn on cell follow mode.\n\tfollow_cell=it;\n\tfollow_mode=true;\n\n\t// Execute the cell.\n\t// std::cerr << \"Executing cell \" << it->id().id << std::endl;\n\n\t// If this is a LaTeX input cell, and auto-close is turned on, close\n\t// the input cell. Make sure to also feed that into the document\n\t// itself!\n\tif(it->cell_type==DataCell::CellType::latex) \n\t\tif(prefs.auto_close_latex) \n\t\t\tgui->hide_visual_cells(it);\n\t\n\t// Execute the cell. Make sure this comes after the hiding logic above.\n\tcompute->execute_cell(it);\n\t}\n\n\nvoid DocumentThread::run_cells_referencing_variable(std::string variable, double value)\n\t{\n\t// First update the variable itself.\n\tcompute->update_variable_on_server(variable, value);\n\n\t// Re-run all cells referencing this variable.\n\tfollow_mode=false;\n\tDTree::iterator it = doc.begin();\n\twhile(it!=doc.end()) {\n\t\tif(it->cell_type==DataCell::CellType::python) {\n\t\t\tif(it->variables_referenced.count(variable)==1) {\n\t\t\t\tif(it->textbuf.find(\"slider(\")==std::string::npos) {\n\t\t\t\t\t// We have found a cell which depends on the variable.\n\t\t\t\t\t// Collect the cell_id's of the current output cells,\n\t\t\t\t\t// so that we can re-use these.\n\t\t\t\t\tstd::vector<uint64_t> output_cell_ids;\n\t\t\t\t\tDTree::iterator sib = doc.begin(it);\n\t\t\t\t\twhile(sib != doc.end(it)) {\n\t\t\t\t\t\toutput_cell_ids.push_back(sib->id().id);\n\t\t\t\t\t\t++sib;\n\t\t\t\t\t\t}\n\t\t\t\t\t\n\t\t\t\t\t// Now execute.\n\t\t\t\t\tcompute->execute_cell(it, variable, output_cell_ids);\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t}\n\t\t++it;\n\t\t}\n\t}\n\nvoid DocumentThread::process_action_queue()\n\t{\n\t// This routine *absolutely* has to be run on the main GUI thread. Anything\n\t// else is a bug.\n\n\tif(main_thread_id != std::this_thread::get_id())\n\t\tstd::cerr << \"INTERNAL ERROR: DocumentThread::process_action_queue not running on main thread.\"\n\t\t\t\t\t << std::endl;\n\n\tstack_mutex.lock();\n\twhile(pending_actions.size()>0) {\n\t\t// std::cerr << \"pending_actions.size() == \" << pending_actions.size() << std::endl;\n\t\tstd::shared_ptr<ActionBase> ab = pending_actions.front();\n\t\t// Unlock the action queue while we are processing this particular action,\n\t\t// so that other actions can be added which we run.\n\t\tstack_mutex.unlock();\n\t\t// std::cerr << \"Executing action \" << typeid(*ab).name() << \" for \" << ab->ref_id.id << std::endl;\n\t\t// Execute the action; this will run synchronously, so after\n\t\t// this returns the doc and visual representation have both been\n\t\t// updated.\n\t\ttry {\n\t\t\tab->execute(*this, *gui);\n\t\t}\n\t\tcatch (const std::exception& err) {\n\t\t\ton_unhandled_error(err);\n\t\t}\n\t\t// Lock the queue to remove the action just executed, and\n\t\t// add it to the undo stack.\n\t\tstack_mutex.lock();\n\t\tif(ab->undoable())\n\t\t\tundo_stack.push(ab);\n\t\tif(ab->callback != nullptr)\n\t\t\tab->callback();\n\t\tif(pending_actions.size()>0) // some actions clear the queue\n\t\t\tpending_actions.pop();\n\t\t}\n\tstack_mutex.unlock();\n\t}\n\nbool DocumentThread::on_unhandled_error(const std::exception& err)\n\t{\n\treturn true;\n\t}\n\nDocumentThread::Prefs::Prefs(bool use_defaults)\n\t{\n#ifndef EMSCRIPTEN\n\tconfig_path=std::string(Glib::get_user_config_dir()) + \"/cadabra2.conf\";\n\ttry {\n\n\t\tif (!use_defaults) {\n\t\t\tstd::ifstream f(config_path);\n\t\t\tif (f) {\n\t\t\t\ttry {\n\t\t\t\t\tf >> data;\n\t\t\t\t\t}\n\t\t\t\tcatch(nlohmann::json::exception& ex) {\n\t\t\t\t\tstd::cerr << \"Config file \" << config_path << \" is not JSON; ignoring.\" << std::endl;\n\t\t\t\t\tdata = nlohmann::json::object();\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\telse {\n\t\t\t\tdata = nlohmann::json::object();\n\n\t\t\t\t// Backwards compatibility, check to see if cadabra.conf exists\n\t\t\t\t// and if so take the is_registered variable from there\n\t\t\t\tstd::ifstream old_f(std::string(Glib::get_user_config_dir()) + \"/cadabra.conf\");\n\t\t\t\tif (old_f) {\n\t\t\t\t\tstd::string line;\n\t\t\t\t\twhile (old_f.good()) {\n\t\t\t\t\t\tstd::getline(old_f, line);\n\t\t\t\t\t\tif (line.find(\"registered=true\") != std::string::npos) {\n\t\t\t\t\t\t\tdata[\"is_registered\"] = true;\n\t\t\t\t\t\t\tbreak;\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\t}\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t}\n\t\t}\n\tcatch(std::exception& ex) {\n\t\tdata = nlohmann::json::object();\n\t\t}\n\n\tfont_step          = data.value(\"font_step\", 0);\n\thighlight          = data.value(\"highlight\", false);\n\tis_registered      = data.value(\"is_registered\", false);\n\tis_anonymous       = data.value(\"is_anonymous\", false);\n\tgit_path           = data.value(\"git_path\", \"\");\n\tpython_path        = data.value(\"python_path\", \"\");\n\tmove_into_new_cell = data.value(\"move_into_new_cell\", false);\n\ttab_completion     = data.value(\"tab_completion\", true);\n\tmicrotex           = data.value(\"microtex\", true);\n\tauto_close_latex   = data.value(\"auto_close_latex\", true);\n\n\t// Force microtex when this is an AppImage.\n\tconst char *appdir = getenv(\"APPDIR\");\n\tif(appdir)\n\t\tmicrotex=true;\n\t// Force microtex when we are on Windows.\n#if(_WIN32)\n\tmicrotex = true;\n#endif\n\n\tif(git_path==\"\")\n\t\tgit_path=\"/usr/bin/git\";\n\n\t// Get the colours for syntax highlighting.\n\tif(data.count(\"colours\")==0)\n\t\tdata[\"colours\"]={ {\"python\", nlohmann::json::object() }, {\"latex\", nlohmann::json::object() } };\n\n\tconst auto& python_colours = data[\"colours\"][\"python\"];\n\n\tcolours[\"python\"][\"keyword\"]   = python_colours.value(\"keyword\", \"RoyalBlue\");\n\tcolours[\"python\"][\"operator\"]  = python_colours.value(\"operator\", \"SlateGray\");\n\tcolours[\"python\"][\"brace\"]     = python_colours.value(\"brace\", \"SlateGray\");\n\tcolours[\"python\"][\"string\"]    = python_colours.value(\"string\", \"ForestGreen\");\n\tcolours[\"python\"][\"comment\"]   = python_colours.value(\"comment\", \"Silver\");\n\tcolours[\"python\"][\"object\"]    = python_colours.value(\"object\", \"DarkGray\");\n\tcolours[\"python\"][\"number\"]    = python_colours.value(\"number\", \"Sienna\");\n\tcolours[\"python\"][\"maths\"]     = python_colours.value(\"maths\", \"Olive\");\n\tcolours[\"python\"][\"function\"]  = python_colours.value(\"function\", \"FireBrick\");\n\tcolours[\"python\"][\"decorator\"] = python_colours.value(\"decorator\", \"DarkViolet\");\n\tcolours[\"python\"][\"class\"]     = python_colours.value(\"class\", \"MediumOrchid\");\n\n\tconst auto& latex_colours = data[\"colours\"][\"latex\"];\n\tcolours[\"latex\"][\"command\"]    = latex_colours.value(\"command\", \"rgb(52,101,164)\");\n\tcolours[\"latex\"][\"parameter\"]  = latex_colours.value(\"brace\", \"rgb(245,121,0)\");\n\tcolours[\"latex\"][\"comment\"]    = latex_colours.value(\"comment\", \"Silver\");\n\tcolours[\"latex\"][\"maths\"]      = latex_colours.value(\"maths\", \"Sienna\");\n#endif\n\t}\n\nvoid DocumentThread::Prefs::save()\n\t{\n\tstd::ofstream f(config_path);\n\tif (f) {\n\t\tdata[\"font_step\"] = font_step;\n\t\tdata[\"highlight\"] = highlight;\n\t\tdata[\"is_registered\"] = is_registered;\n\t\tdata[\"is_anonymous\"] = is_anonymous;\n\t\tdata[\"python_path\"] = python_path;\n\t\tdata[\"move_into_new_cell\"] = move_into_new_cell;\n\t\tdata[\"tab_completion\"] = tab_completion;\n\t\tdata[\"microtex\"] = microtex;\n\t\tdata[\"auto_close_latex\"] = auto_close_latex;\n\t\tfor (const auto& lang : colours) {\n\t\t\tfor (const auto& kw : lang.second)\n\t\t\t\tdata[\"colours\"][lang.first][kw.first] = kw.second;\n\t\t\t}\n\t\tdata[\"git_path\"] = git_path;\n\t\tf << data << '\\n';\n\t\t}\n\telse\n\t\tstd::cerr << \"Warning: could not write to config file\\n\";\n\t}\n\nvoid DocumentThread::set_user_details(const std::string& name, const std::string& email, const std::string& affiliation)\n\t{\n#ifndef EMSCRIPTEN\n\tsnoop::log(\"name\") << name << snoop::flush;\n\tsnoop::log(\"email\") << email << snoop::flush;\n\tsnoop::log(\"affiliation\") << affiliation << snoop::flush;\n#endif\n\t}\n\nbool DocumentThread::help_type_and_topic(const std::string& before, const std::string& after,\n      help_t& help_type, std::string& help_topic) const\n\t{\n\thelp_t objtype=help_t::algorithm;\n\tif(! (before.size()==0 && after.size()==0) ) {\n\t\t// We provide help for properties, algorithms and reserved node\n\t\t// names.  Properties are delimited to the left by '::' and to\n\t\t// the right by anything non-alnum. Algorithms are delimited to\n\t\t// the left by non-alnum except '_' and to the right by '('. Reserved node\n\t\t// names are TeX symbols, starting with '\\'.\n\t\t//\n\t\t// So scan the 'before' string for a left-delimiter and the 'after' string\n\t\t// for a right-delimiter.\n\n\t\tint lpos=before.size()-1;\n\t\twhile(lpos>=0) {\n\t\t\tif(before[lpos]==':' && lpos>0 && before[lpos-1]==':') {\n\t\t\t\tobjtype=help_t::property;\n\t\t\t\tbreak;\n\t\t\t\t}\n\t\t\tif(before[lpos]=='\\\\') {\n\t\t\t\tobjtype=help_t::latex;\n\t\t\t\tbreak;\n\t\t\t\t}\n\t\t\tif(isalnum(before[lpos])==0 && before[lpos]!='_') {\n\t\t\t\tobjtype=help_t::algorithm;\n\t\t\t\tbreak;\n\t\t\t\t}\n\t\t\t--lpos;\n\t\t\t}\n\t\tif(objtype==help_t::none) return false;\n\t\t++lpos;\n\n\t\tsize_t rpos=0;\n\t\twhile(rpos<after.size()) {\n\t\t\tif(objtype==help_t::property) {\n\t\t\t\tif(isalnum(after[rpos])==0)\n\t\t\t\t\tbreak;\n\t\t\t\t}\n\t\t\telse if(objtype==help_t::algorithm) {\n\t\t\t\tif(after[rpos]=='(')\n\t\t\t\t\tbreak;\n\t\t\t\t}\n\t\t\telse if(objtype==help_t::latex) {\n\t\t\t\tif(isalnum(after[rpos])==0 && after[rpos]!='_')\n\t\t\t\t\tbreak;\n\t\t\t\t}\n\t\t\t++rpos;\n\t\t\t}\n\t\thelp_topic=before.substr(lpos)+after.substr(0,rpos);\n\t\t}\n\n\thelp_type=objtype;\n\treturn true;\n\t}\n"
  },
  {
    "path": "client_server/DocumentThread.hh",
    "content": "\n#pragma once\n\n#include <queue>\n#include <mutex>\n#include <stack>\n#include <map>\n#include <thread>\n\n#include \"DataCell.hh\"\n#include \"tree.hh\"\n\nnamespace cadabra {\n\n\tclass ActionBase;\n\tclass ActionAddCell;\n\tclass ActionPositionCursor;\n\tclass ActionRemoveCell;\n\tclass ActionSetRunStatus;\n\tclass ActionSplitCell;\n\tclass ActionInsertText;\n\tclass ActionCompleteText;\n\tclass ActionEraseText;\n\tclass ComputeThread;\n\tclass GUIBase;\n\n\t/// \\ingroup clientserver\n\t///\n\t/// A base class with all the logic to manipulate a Cadabra\n\t/// notebook document. Relies on the various objects derived from\n\t/// ActionBase in order to get actual work done. All methods here\n\t/// will always run on the GUI thread.\n\t///\n\t/// In order to implement a GUI, derive from both DocumentThread\n\t/// and GUIBase and then implement the virtual functions of the\n\t/// latter (those implement basic insertion/removal of notebook\n\t/// cells; the logic to figure out which ones and to implement the\n\t/// undo/redo stack is all in the GUI-agnostic DocumentThread).\n\n\n\tclass DocumentThread {\n\t\tpublic:\n\t\t\tDocumentThread(GUIBase *);\n\n\t\t\t/// It is not possible to copy-construct a DocumentThread as\n\t\t\t/// it holds on to resources which are not easily copied\n\t\t\t/// (such as GUI elements).\n\n\t\t\tDocumentThread(const DocumentThread&)=delete;\n\n\t\t\t/// Let the notebook know about the ComputeThread so that it\n\t\t\t/// can send cells for evaluation. Notebook does NOT own this\n\t\t\t/// pointer.\n\n\t\t\tvirtual void set_compute_thread(ComputeThread *);\n\n\t\t\t/// Ensure that the gui has an up-to-date representation of the\n\t\t\t/// dtree. Traverses the entire tree so is expensive to run and\n\t\t\t/// should only be used when loading new documents or creating\n\t\t\t/// a new canvas view.\n\n\t\t\tvoid build_visual_representation();\n\n\t\t\t/// All changes to the document should be made by submitting\n\t\t\t/// ActionBase derived objects to the 'queue_action' function,\n\t\t\t/// so that an undo stack can be kept. They are then processed\n\t\t\t/// by calling the 'process_action_queue' method (only\n\t\t\t/// available from this thread).\n\n\t\t\tvoid queue_action(std::shared_ptr<ActionBase>);\n\n\t\t\t/// Run all cells in the document. Only execute this on the\n\t\t\t/// main (GUI) thread!\n\n\t\t\tvoid run_all_cells();\n\t\t\t\n\t\t\t/// Run a single cell in the document. Only execute this on the\n\t\t\t/// main (GUI) thread!\n\n\t\t\tvoid run_cell(DTree::iterator, bool shift_pressed);\n\t\t\t\n\t\t\t/// Run all cells containing references to a given variable.\n\t\t\t/// This will eventually call compute->execute on the\n\t\t\t/// relevant cells, but is part of DocumentThread because\n\t\t\t/// this function takes care of scanning through the document\n\t\t\t/// to find out *which* cells to run.\n\n\t\t\tvoid run_cells_referencing_variable(std::string variable, double value);\n\t\t\t\n\t\t\t/// Setup an empty new document with a single Python input cell.\n\n\t\t\tvoid new_document();\n\n\t\t\t/// Load a new notebook from a JSON string. Should only be called\n\t\t\t/// from the GUI thread. Will cancel any pending operations on the\n\t\t\t/// existing notebook (if present) first.\n\n\t\t\tvirtual void load_from_string(const std::string&);\n\n\t\t\tvirtual void on_interactive_output(const nlohmann::json& msg);\n\n\t\t\tvirtual void set_progress(const std::string& msg, int cur_step, int total_steps);\n\n\t\t\t/// One undo step.\n\t\t\tvoid undo();\n\n\t\t\t/// One redo step.\n\t\t\tvoid redo();\n\n\t\t\t/// Find string, return match, or a (doc.end(), std::string::npos).\n\t\t\tstd::pair<DTree::iterator, size_t> find_string(DTree::iterator start_it, size_t start_pos, const std::string& f, bool case_ins) const;\n\n\t\t\t/// All actions are considered pieces of code which are part of\n\t\t\t/// DocumentThread, so they should be able to access its private\n\t\t\t/// variables.\n\t\t\t\n\t\t\tfriend ActionBase;\n\t\t\tfriend ActionAddCell;\n\t\t\tfriend ActionPositionCursor;\n\t\t\tfriend ActionRemoveCell;\n\t\t\tfriend ActionSplitCell;\n\t\t\tfriend ActionSetRunStatus;\n\t\t\tfriend ActionInsertText;\n\t\t\tfriend ActionCompleteText;\t\t\t\n\t\t\tfriend ActionEraseText;\n\n\t\t\tclass Prefs {\n\t\t\t\tpublic:\n\t\t\t\t\tusing ColorMap = std::map<std::string, std::string>;\n\t\t\t\t\tPrefs(bool use_defaults = false);\n\t\t\t\t\tvoid save();\n\t\t\t\t\tint font_step;\n\t\t\t\t\tbool highlight;\n\t\t\t\t\tbool is_registered;\n\t\t\t\t\tbool is_anonymous;\n\t\t\t\t\tstd::map<std::string, ColorMap> colours;\n\t\t\t\t\tstd::string git_path;\n\t\t\t\t\tstd::string python_path;\n\t\t\t\t\tbool move_into_new_cell;\n\t\t\t\t\tbool tab_completion;\n\t\t\t\t\tbool microtex;\n\t\t\t\t\tbool auto_close_latex;\n\t\t\t\tprivate:\n\t\t\t\t\tnlohmann::json data;\n\t\t\t\t\tstd::string    config_path;\n\t\t\t\t};\n\t\t\tPrefs prefs;\n\n\t\t\t/// Set user details which will be sent to the Cadabra log\n\t\t\t/// server.\n\n\t\t\tvoid set_user_details(const std::string& name, const std::string& email, const std::string& affiliation);\n\n\t\t\t/// For debugging purposes we store the main thread idea here (the\n\t\t\t/// main Cadabra class sets it).\n\t\t\tstd::thread::id main_thread_id;\n\t\t\t\n\t\tprotected:\n\t\t\tGUIBase       *gui;\n\t\t\tComputeThread *compute;\n\n\t\t\t/// The actual document tree. This object is only modified on\n\t\t\t/// the GUI thread, either directly by code in\n\t\t\t/// DocumentThread, or by code in the various objects derived\n\t\t\t/// from ActionBase. In particular, ComputeThread cannot\n\t\t\t/// access this tree directly.\n\n\t\t\tDTree          doc;\n\n\t\t\t/// Iterator to the currently active cell in the notebook, or\n\t\t\t/// doc.end() if nothing active.\n\t\t\t\n\t\t\tDTree::iterator current_cell;\n\n\t\t\t/// If `follow_mode` is true, the `follow_cell` can be set,\n\t\t\t/// and this will make the canvas view follow the indicated\n\t\t\t/// cell.\n\t\t\tbool            follow_mode;\n\t\t\tDTree::iterator follow_cell, follow_last_cell;\n\t\t\t\n\t\t\t/// The action undo/redo/todo stacks and logic to execute\n\t\t\t/// them. These stacks can be accessed from both the\n\t\t\t/// DocumentThread as well as the ComputeThread (the latter\n\t\t\t/// does it through the DocumentThread::queue_action method),\n\t\t\t/// so they need a mutex to access them.\n\n\t\t\tstd::mutex                                       stack_mutex;\n\t\t\ttypedef std::stack<std::shared_ptr<ActionBase> > ActionStack;\n\t\t\tActionStack                                      undo_stack, redo_stack;\n\t\t\tstd::queue<std::shared_ptr<ActionBase> >         pending_actions;\n\t\t\tbool                                             disable_stacks;\n\n\t\t\t/// Process the action queue. It is allowed to call queue_action() above\n\t\t\t/// while this is running. So a running action can add more actions.\n\t\t\t/// Needs to be called on the GUI thread!\n\n\t\t\tvoid         process_action_queue();\n\t\t\tvirtual bool on_unhandled_error(const std::exception& err);\n\n\n\n\t\t\t/// Help system\n\t\t\tenum class help_t { algorithm, property, latex, none };\n\t\t\tbool help_type_and_topic(const std::string& before, const std::string& after,\n\t\t\t                         help_t& help_type, std::string& help_topic) const;\n\n\t\t};\n\n\t}\n"
  },
  {
    "path": "client_server/GUIBase.hh",
    "content": "\n#pragma once\n\n#include <deque>\n\n#include \"DataCell.hh\"\n\nnamespace cadabra {\n\n\t/// \\ingroup clientserver\n\t///\n\t/// Abstract base class with methods that need to be implemented\n\t/// by any GUI. You need to derive from this class as well as from\n\t/// the DocumentThread class.\n\n\tclass GUIBase {\n\t\tpublic:\n\t\t\t/// The basic manipulations that a GUI needs to implement are\n\t\t\t/// adding, removing and updating (refreshing the display of)\n\t\t\t/// a cell. The code in DocumentThread will call these to make\n\t\t\t/// the GUI update its display. Called on the document thread.\n\n\t\t\tvirtual void update_cell(const DTree&, DTree::iterator)=0;\n\n\t\t\t/// Remove a single cell together with all its child cells.\n\t\t\t/// Some toolkits (e.g. Gtk) will take care of that entire\n\t\t\t/// child tree removal automatically, in which case the only\n\t\t\t/// thing that needs done for the child cells is to remove\n\t\t\t/// any reference to their VisualCells.\n\n\t\t\tvirtual void remove_cell(const DTree&, DTree::iterator)=0;\n\n\t\t\t/// Remove all GUI cells from the display (used as a quick way\n\t\t\t/// to clear all before loading a new document).\n\n\t\t\tvirtual void remove_all_cells()=0;\n\n\t\t\t/// Add a GUI cell corresponding to the document cell at the\n\t\t\t/// iterator. The GUI needs to figure out from the location of\n\t\t\t/// this cell in the DTree where to insert the cell in the visual\n\t\t\t/// display. If the 'visible' flag is false, hide the cell from\n\t\t\t/// view independent of whether its hidden flag is set (this\n\t\t\t/// is only used when constructing a document on load time and\n\t\t\t/// we do not want to show cells until they have all been added\n\t\t\t/// to the document).\n\n\t\t\tvirtual void add_cell(const DTree&, DTree::iterator, bool visible)=0;\n\n\t\t\t/// Position the cursor in the current canvas in the widget\n\t\t\t/// corresponding to the indicated cell.\n\n\t\t\tvirtual void position_cursor(const DTree&, DTree::iterator, int)=0;\n\n\t\t\t/// Retrieve the position of the cursor in the current cell.\n\n\t\t\tvirtual size_t get_cursor_position(const DTree&, DTree::iterator)=0;\n\n\t\t\t/// Hide all visual cells (on all canvasses) corresponding to\n\t\t\t/// a given document cell.\n\n\t\t\tvirtual void hide_visual_cells(DTree::iterator)=0;\n\t\t\t\n\t\t\t/// Dim all output cells of the visual cells corresponding to the\n\t\t\t/// given document cell.\n\n\t\t\tvirtual void dim_output_cells(DTree::iterator)=0;\n\t\t\t\n\t\t\t/// Network status is propagated from the ComputeThread to the\n\t\t\t/// GUI using the following methods. These get called on the\n\t\t\t/// compute thread (as opposed to the functions above, which get\n\t\t\t/// called on the gui thread).\n\n\t\t\t//@{\n\n\t\t\tvirtual void on_connect()=0;\n\t\t\tvirtual void on_disconnect(const std::string& reason)=0;\n\t\t\tvirtual void on_network_error()=0;\n\t\t\tvirtual void on_kernel_runstatus(bool)=0;\n\n\t\t\t//@}\n\n\t\t\t/// When the ComputeThread needs to modify the document, it\n\t\t\t/// stores an ActionBase object on the stack (see the\n\t\t\t/// DocumenThread class) and then wakes up the GUI thread\n\t\t\t/// signalling it to process this action. The following member\n\t\t\t/// should wake up the GUI thread and make it enter the\n\t\t\t/// processing part. You can call this from *any* thread.\n\n\t\t\tvirtual void process_data()=0;\n\n\t\t};\n\n\t};\n"
  },
  {
    "path": "client_server/ScriptThread.cc",
    "content": "\n#include \"ScriptThread.hh\"\n#include \"DocumentThread.hh\"\n#include \"GUIBase.hh\"\n#include \"Actions.hh\"\n\n#include <boost/uuid/uuid_generators.hpp> // generators\n#include <boost/uuid/uuid_io.hpp>         // streaming operators etc.\n#include <boost/algorithm/string/replace.hpp>\n\n#include <internal/uuid.h>\n#include <internal/string_tools.h>\n\n#include \"nlohmann/json.hpp\"\n\nusing namespace cadabra;\n\nScriptThread::ScriptThread(DocumentThread *d, GUIBase *g)\n\t: document(d), gui(g), local_port(0)\n\t{\n\t// Lock the URL (port and auth token) until the thread is\n\t// properly spun up.\n\turl_mutex.lock();\n\t\n\tboost::uuids::uuid authentication_uuid = boost::uuids::random_generator()();\n\tauthentication_token = boost::uuids::to_string( authentication_uuid );\n\t}\n\nScriptThread::~ScriptThread()\n\t{\n\turl_mutex.unlock();\n\t}\n\nvoid ScriptThread::on_open(websocket_server::id_type ws_id)\n\t{\n\tstd::cerr << \"on_open\" << std::endl;\n\n//\tstd::lock_guard<std::mutex> lock(ws_mutex);\n//\tConnection con;\n//\tcon.ws_id = ws_id;\n//\t// snoop::log(snoop::info) << \"Connection \" << con.uuid << \" open.\" << snoop::flush;\n//\tconnections[ws_id]=con;\n\t}\n\nvoid ScriptThread::on_close(websocket_server::id_type ws_id)\n\t{\n\tstd::cerr << \"on_close\" << std::endl;\n\n//\tstd::lock_guard<std::mutex> lock(ws_mutex);\n//\t//\tauto it = connections.find(hdl);\n//\t// snoop::log(snoop::info) << \"Connection \" << it->second.uuid << \" close.\" << snoop::flush;\n//\tconnections.erase(ws_id);\n//\n//\tif(exit_on_disconnect)\n//\t\texit(-1);\n\t}\n\nvoid ScriptThread::on_message(websocket_server::id_type ws_id, const std::string& msg,\n\t\t\t\t\t\t\t\t\t\tconst websocket_server::request_type& req, const std::string& ip_address)\n\t{\n\t// std::cerr << \"received: \" << msg << std::endl;\n\tif(req.target().substr(1) != authentication_token) {\n\t\t// Unauthorised.\n\t\treturn;\n\t\t}\n\n\ttry {\n\t\tauto jmsg = nlohmann::json::parse(msg);\n\t\tstd::cerr << \"received message: \" << jmsg.dump(3) << std::endl;\n\t\tstd::string msg_action = jmsg.value(\"action\", \"\");\n\t\tsize_t      msg_serial = jmsg.value(\"serial\", 0);\n\t\tif(msg_action==\"run_all_cells\") {\n\t\t\t// We cannot call directly into the document methods here,\n\t\t\t// because we are not on the main thread. So we queue an\n\t\t\t// action, to be dispatched later.\n\t\t\t\n\t\t\tstd::shared_ptr<ActionBase> action = std::make_shared<ActionRunCell>();\n\t\t\taction->callback = [this, ws_id, msg_serial, msg_action]() {\n\t\t\t\tnlohmann::json msg;\n\t\t\t\tmsg[\"status\"]=\"completed\";\n\t\t\t\tmsg[\"serial\"]=msg_serial;\n\t\t\t\tmsg[\"action\"]=msg_action;\n\t\t\t\twserver.send(ws_id, msg.dump());\n\t\t\t\t};\n\t\t\tdocument->queue_action(action);\n\t\t\tgui->process_data();\n\t\t\t}\n\t\telse if(msg_action==\"run_cell\") {\n\t\t\tuint64_t msg_cell_id = jmsg.value(\"cell_id\", uint64_t(0));\n\t\t\tDataCell::id_t id;\n\t\t\tid.id=msg_cell_id;\n\t\t\tstd::shared_ptr<ActionBase> action = std::make_shared<ActionRunCell>(id);\n\t\t\taction->callback = [this, ws_id, msg_serial, msg_action]() {\n\t\t\t\tnlohmann::json msg;\n\t\t\t\tmsg[\"status\"]=\"completed\";\n\t\t\t\tmsg[\"serial\"]=msg_serial;\n\t\t\t\tmsg[\"action\"]=msg_action;\n\t\t\t\twserver.send(ws_id, msg.dump());\n\t\t\t\t};\n\t\t\tdocument->queue_action(action);\n\t\t\tgui->process_data();\n\t\t\t}\n\t\telse if(msg_action==\"open\") {\n\t\t\tstd::string notebook = jmsg.value(\"notebook\", \"\");\n\t\t\t\n\t\t\tstd::shared_ptr<ActionBase> action = std::make_shared<ActionOpen>(notebook);\n\t\t\taction->callback = [this, ws_id, msg_serial, msg_action]() {\n\t\t\t\tnlohmann::json msg;\n\t\t\t\tmsg[\"status\"]=\"completed\";\n\t\t\t\tmsg[\"serial\"]=msg_serial;\n\t\t\t\tmsg[\"action\"]=msg_action;\n\t\t\t\twserver.send(ws_id, msg.dump());\n\t\t\t\t};\n\t\t\tdocument->queue_action(action);\n\t\t\tgui->process_data();\n\t\t\t}\n\t\telse if(msg_action==\"insert_text\") {\n\t\t\tstd::string content = jmsg.value(\"content\", \"\");\n\t\t\tDataCell::id_t id;\n\t\t\tid.id=0;\n\t\t\tstd::shared_ptr<ActionBase> action = std::make_shared<ActionInsertText>(id, 0, content);\n\t\t\taction->callback = [this, ws_id, msg_serial, msg_action]() {\n\t\t\t\tnlohmann::json msg;\n\t\t\t\tmsg[\"status\"]=\"completed\";\n\t\t\t\tmsg[\"serial\"]=msg_serial;\n\t\t\t\tmsg[\"action\"]=msg_action;\n\t\t\t\twserver.send(ws_id, msg.dump());\n\t\t\t\t};\n\t\t\tdocument->queue_action(action);\n\t\t\tgui->process_data();\n\t\t\t}\n\t\telse if(msg_action==\"add_cell\") {\n\t\t\tstd::string content = jmsg.value(\"content\", \"\");\n\t\t\tuint64_t cell_id = jmsg.value(\"cell_id\", uint64_t(0));\n\n\t\t\tDataCell::id_t this_id;\n\t\t\tif(cell_id!=0)\n\t\t\t\tthis_id.id=cell_id;\n\t\t\tDataCell dc(this_id, DataCell::CellType::python, content);\n\t\t\tDataCell::id_t ref_id;\n\t\t\tref_id.id=0; // relative to current cell\n\t\t\t\n\t\t\tstd::shared_ptr<ActionAddCell> action =\n\t\t\t\tstd::make_shared<ActionAddCell>(dc, ref_id, ActionAddCell::Position::before, true);\n\t\t\t\n\t\t\tnlohmann::json reply_msg;\n\t\t\treply_msg[\"status\"]=\"completed\";\n\t\t\treply_msg[\"serial\"]=msg_serial;\n\t\t\treply_msg[\"action\"]=msg_action;\n\t\t\treply_msg[\"cell_id\"]=dc.id().id;\n\t\t\taction->callback = [this, ws_id, reply_msg]() {\n\t\t\t\twserver.send(ws_id, reply_msg.dump());\n\t\t\t\t};\n\t\t\tdocument->queue_action(action);\n\t\t\tgui->process_data();\n\t\t\t}\n\t\t}\n\tcatch(nlohmann::json::exception& ex) {\n\t\tstd::cerr << \"Received unparsable message: \" << msg << std::endl;\n\t\t}\n\t}\n\nvoid ScriptThread::run()\n\t{\n\twserver.set_message_handler(std::bind(&ScriptThread::on_message, this,\n\t\t\t\t\t\t\t\t\t\t\t\t\t  std::placeholders::_1, std::placeholders::_2, std::placeholders::_3, std::placeholders::_4));\n\twserver.set_connect_handler(std::bind(&ScriptThread::on_open, this,     std::placeholders::_1));\n\twserver.set_disconnect_handler(std::bind(&ScriptThread::on_close, this, std::placeholders::_1));\n\t\n\twserver.listen(0); \n\tlocal_port = wserver.get_local_port();\n\t\n\turl_mutex.unlock();\n\twserver.run();\n\t}\n\nuint16_t ScriptThread::get_local_port() const\n\t{\n\tstd::lock_guard<std::mutex> guard(url_mutex);\n\treturn local_port;\n\t}\n\nstd::string ScriptThread::get_authentication_token() const\n\t{\n\tstd::lock_guard<std::mutex> guard(url_mutex);\n\treturn authentication_token;\n\t}\n\nvoid ScriptThread::terminate()\n\t{\n\twserver.stop();\n\t}\n"
  },
  {
    "path": "client_server/ScriptThread.hh",
    "content": "\n#pragma once\n\n#include \"websocket_server.hh\"\n\n\nnamespace cadabra {\n\n\t/// \\ingroup scripting\n\t///\n   /// Class containing all functionality which allows users to\n\t/// control a running notebook client by sending it commands\n\t/// via a websocket port. This can be used to script its\n\t/// operations.\n\t///\n\t/// This runs as a separate thread, so it is neither on the\n\t/// main thread (GUI, DocumentThread) nor on the thread that\n\t/// handles communication with the cadabra-server.\n\n\tclass DocumentThread;\n\tclass GUIBase;\n\t\n\tclass ScriptThread {\n\t\tpublic:\n\t\t\tScriptThread(DocumentThread *, GUIBase *);\n\t\t\t~ScriptThread();\n\n\t\t\tScriptThread(const ScriptThread&) = delete;\n\t\t\t\n\t\t\tvoid run();\n\t\t\tvoid terminate();\n\n\t\t\tuint16_t    get_local_port() const;\n\t\t\tstd::string get_authentication_token() const;\n\t\t\t\n\t\tprivate:\n\t\t\tvoid on_message(websocket_server::id_type id, const std::string& msg,\n\t\t\t\t\t\t\t\t const websocket_server::request_type& req, const std::string& ip_address);\n\t\t\tvoid on_open(websocket_server::id_type id);\n\t\t\tvoid on_close(websocket_server::id_type id);\n\t\t\t\n\t\t\twebsocket_server  wserver;\n\t\t\tDocumentThread   *document;\n\t\t\tGUIBase          *gui;\n\n\t\t\t// Authentication token, needs to be sent along with any message.\n\t\t\t// Gets shown when we start up.\n\t\t\tmutable std::mutex url_mutex;\n\t\t\tstd::string        authentication_token;\n\t\t\tuint16_t           local_port;\n\t};\n\t\n}\n"
  },
  {
    "path": "client_server/Server.cc",
    "content": "\n#include <signal.h>\n#include \"Server.hh\"\n#include \"InstallPrefix.hh\"\n\n#include <iostream>\n#include <fstream>\n#include <sstream>\n#include <thread>\n#include <regex>\n\n#include <boost/uuid/uuid_generators.hpp> // generators\n#include <boost/uuid/uuid_io.hpp>         // streaming operators etc.\n#include <boost/algorithm/string/replace.hpp>\n\n#include <internal/uuid.h>\n#include <internal/string_tools.h>\n\n#include \"Config.hh\"\n//#ifndef ENABLE_JUPYTER\n//#include \"Snoop.hh\"\n//#endif\n#include \"CdbPython.hh\"\n#include \"SympyCdb.hh\"\n#include \"pythoncdb/py_helpers.hh\"\n\n// #define DEBUG 1\n\n\nbool interrupt_block=false;\n\nServer::Server()\n//\t: return_cell_id(std::numeric_limits<uint64_t>::max()/2)\n\t{\n\tboost::uuids::uuid authentication_uuid = boost::uuids::random_generator()();\n\tauthentication_token = boost::uuids::to_string( authentication_uuid );\n\t// FIXME: we do not actually do anything with this.\n\tinit();\n\t}\n\nServer::Server(const std::string& socket)\n//\t: return_cell_id(std::numeric_limits<uint64_t>::max()/2)\n\t{\n\tinit();\n\t}\n\nServer::~Server()\n\t{\n\n\t}\n\nServer::CatchOutput::CatchOutput()\n\t{\n\t}\n\nServer::CatchOutput::CatchOutput(const CatchOutput&)\n\t{\n\t}\n\nvoid Server::CatchOutput::write(const std::string& str)\n\t{\n\t// std::cerr << \"Python wrote: \" << str << std::endl;\n\tcollect+=str;\n\t}\n\nvoid Server::CatchOutput::clear()\n\t{\n\t// std::cerr << \"Python clear\" << std::endl;\n\tcollect=\"\";\n\t}\n\nstd::string Server::CatchOutput::str() const\n\t{\n\treturn collect;\n\t}\n\nstd::string Server::architecture() const\n\t{\n\treturn \"client-server\";\n\t}\n\nPYBIND11_EMBEDDED_MODULE(cadabra2_internal, m)\n\t{\n\t//   auto cadabra_module = pybind11::module::import(\"cadabra2\");\n\n\tpybind11::class_<Server::CatchOutput>(m, \"CatchOutput\")\n\t.def(\"write\", &Server::CatchOutput::write)\n\t.def(\"clear\", &Server::CatchOutput::clear)\n\t;\n\n\tpybind11::class_<Server>(m, \"Server\")\n\t.def(\"send\", &Server::send)\n\t.def(\"handles\", &Server::handles)\n\t.def(\"architecture\", &Server::architecture)\n\t.def(\"send_progress_update\", &Server::send_progress_update);\n\t}\n\nstd::string parse_error(const std::string& error, const std::string& input)\n{\n\ttry {\n\t\t// Find syntax errors\n\t\tstd::regex syntax_error(R\"(SyntaxError: \\('([^']+)', \\('<string>', (\\d+), (\\d+),.*)\");\n\t\tstd::smatch sm;\n\t\tif (std::regex_match(error, sm, syntax_error)) {\n\t\t\tstd::string error_type = sm[1];\n\t\t\tsize_t line_no = stoi(sm[2]) - 1;\n\t\t\tsize_t col_no = stoi(sm[3]);\n\t\t\treturn\n\t\t\t\t\"SyntaxError: \" + error_type + \"\\n\" +\n\t\t\t\t\"Line \" + std::to_string(line_no) + \", column \" + std::to_string(col_no) + \"\\n\" +\n\t\t\t\tnth_line(input, line_no - 1) + \"\\n\" +\n\t\t\t\tstd::string(col_no > 1 ? col_no - 2 : 0, ' ') + \"^\";\n\t\t}\n\n\t\t// Find other errors\n\t\tstd::regex exception_name(R\"(([a-zA-Z_][a-zA-Z0-9_]*):.*)\");\n\t\tstd::string first_line = nth_line(error, 0);\n\t\tif (std::regex_match(first_line, sm, exception_name)) {\n\t\t\tstd::string name = sm[1];\n\t\t\tstd::regex line_no(R\"(<string>\\((\\d+)\\): <module>)\");\n\t\t\tstd::smatch lm;\n\t\t\tif (std::regex_search(error, lm, line_no)) {\n\t\t\t\tsize_t l = stoi(lm[1]) - 1;\n\t\t\t\treturn std::regex_replace(error, line_no, \"Notebook Cell (Line \" + std::to_string(l) + \"): \" + nth_line(input, l - 1));\n\t\t\t}\n\t\t}\n\n\t\treturn error;\n\t}\n\tcatch (std::exception& e) {\n\t\treturn error;\n\t}\n}\n\nvoid Server::init()\n\t{\n\tstarted=false;\n\n\tmain_module = pybind11::module::import(\"__main__\");\n\tmain_namespace = main_module.attr(\"__dict__\");\n\n\t// Make the C++ CatchOutput class visible on the Python side.\n\n\tauto python_path = cadabra::install_prefix_of_module();\n\n\t// FIXME: since the logic above *requires* that we can find the\n\t// `cdb.main` module, we will already have the correct path\n\t// set. So appending it once more below is useless.\n\t\n\tstd::string stdOutErr =\n\t   \"import sys\\n\"\n\t   \"sys.path.append(r'\"+python_path+\"')\\n\"\n\n\t   \"from cadabra2_internal import Server, CatchOutput\\n\"\n\t   \"server=0\\n\"\n\t   \"def setup_catch(cO, cE, sE):\\n\"\n\t   \"   global server\\n\"\n\t   \"   sys.stdout=cO\\n\"\n\t   \"   sys.stderr=cE\\n\"\n\t   \"   server=sE\\n\";\n\trun_string(stdOutErr, false);\n\n\t// Setup the C++ output catching objects and setup the Python side to\n\t// use these as stdout and stderr streams.\n\n\tpybind11::object setup_catch = main_module.attr(\"setup_catch\");\n\ttry {\n\t\tsetup_catch(std::ref(catchOut), std::ref(catchErr), std::ref(*this));\n\t\t}\n\tcatch(pybind11::error_already_set& ex) {\n//#ifndef ENABLE_JUPYTER\n//\t\tsnoop::log(snoop::fatal) << \"Failed to initialise Python bridge.\" << snoop::flush;\n//#endif\n\t\tPyErr_Print();\n\t\tthrow;\n\t\t}\n\n\t// Get the Python thread id.\n\tstd::string code_get_id = \"import threading; print(threading.get_native_id())\";\n\tstd::string main_thread_id_str = run_string(code_get_id);\n\tmain_thread_id = std::stol(main_thread_id_str);\n\t// std::cerr << \"Server: main python thread id = \" << main_thread_id << std::endl;\n\t// std::cerr << \"Server: python_path = \" << python_path << std::endl;\n\t\n\t// Call the Cadabra default initialisation script.\n\n\t//\tpybind11::eval_file(python_path + \"/cadabra2_defaults.py\");\n\t//\tHERE: should use pybind11::eval_file instead, much simpler.\n\t//\n\tstd::string startup =\n\t   \"f=open(r'\" + python_path + \"/cadabra2_defaults.py'); \"\n\t   \"code=compile(f.read(), 'cadabra2_defaults.py', 'exec'); \"\n\t   \"exec(code); f.close() \";\n\trun_string(startup);\n\n#ifdef DEBUG\n\tstd::cerr << \"Server::init: completed\" << std::endl;\n#endif\n\t}\n\nint InterruptCheck(PyObject* obj, _frame* frame, int what, PyObject* arg)\n\t{\n\tstd::cerr << \"Server: interruptcheck\" << std::endl;\n\tif(interrupt_block) {\n\t\tPyErr_SetString(PyExc_KeyboardInterrupt, \"Stop script\");\n\t\tinterrupt_block = false;\n\t\t}\n\t\n\treturn 0;\n\t}\n\nstd::string Server::run_string(const std::string& blk, bool handle_output, bool extract_variables,\n\t\t\t\t\t\t\t\t\t\t std::set<std::string> remove_assignments)\n\t{\n\t//std::cerr << \"RUN_STRING\" << std::endl;\n\t// snoop::log(\"run\") << blk << snoop::flush;\n\n\tstd::string result, newblk;\n\t\n\t// Run block. Catch output.\n\ttry {\n\t\t// Preparse input block.\n\t\t// std::cerr << \"RAW:\\n\" << blk << std::endl;\n\t\tstd::string error;\n\t\tnewblk = cadabra::cdb2python_string(blk, true, error);\n\t\t\n\t\t// std::cerr << \"PREPARSED:\\n\" << newblk << std::endl;\n\t\t// snoop::log(\"preparsed\") << newblk << snoop::flush;\n\t\t\n\t\trun_string_variables.clear();\n\t\tif(error.size()==0) {\n\t\t\t// If the preparsing found an error, do not attempt anything\n\t\t\t// else; just run it and let Python report the error.\n\t\t\tif(extract_variables) {\n\t\t\t\tcadabra::variables_in_code(newblk, run_string_variables);\n\t\t\t\tcadabra::variables_to_pull_in(newblk, run_string_variables);\n\t\t\t\t// std::cerr << \"----\" << std::endl;\n\t\t\t\t// for(const auto& name: run_string_variables)\n\t\t\t\t// \tstd::cerr << \"contains \" << name << std::endl;\n\t\t\t\t}\n\t\t\tfor(const std::string& var: remove_assignments) {\n\t\t\t\tnewblk = cadabra::remove_variable_assignments(newblk, var);\n\t\t\t\t}\n\t\t\t// std::cerr << \"REMOVED:\\n\" << newblk << std::endl;\n\t\t\t}\n\t\t\n#ifdef DEBUG\n\t\tstd::cerr << \"executing...\" << std::endl;\n\t\tstd::cerr << newblk << std::endl;\n#endif\n\t\tPyErr_Clear();\n//\t\tPyEval_SetTrace(InterruptCheck, NULL);\t\t\n\t\tpybind11::exec(newblk.c_str(), main_namespace);\n//\t\tPyEval_SetTrace(NULL, NULL);\t\t\n#ifdef DEBUG\n\t\tstd::cerr << \"exec done\" << std::endl;\n#endif\n\t\t//\t\tstd::string object_classname = ignored.attr(\"__class__\").attr(\"__name__\").cast<std::string>();\n\t\t//\t\tstd::cerr << \"\" << std::endl;\n\n\t\tif(handle_output) {\n\t\t\tresult = catchOut.str();\n\t\t\tcatchOut.clear();\n\t\t\tstd::string result_err = catchErr.str();\n\t\t\tif(result_err!=\"\") \n\t\t\t\tstd::cerr << \"catchErr: \" << result_err << std::endl;\n\t\t\tcatchErr.clear();\n\t\t\t}\n\t\t}\n\tcatch(pybind11::error_already_set& ex) {\n#ifdef DEBUG\n\t\tstd::cerr << \"Server::run_string: exception \" << ex.what() << std::endl;\n#endif\n\t\t// On macOS and with the current conda tools,\n\t\t// you can never exit from this block: throwing or simply\n\t\t// exiting with 'return \"\"' makes things hang.\n\t\t// The solution is to ex.restore(), see\n\t\t//    https://github.com/pybind/pybind11/issues/1490\n\t\t// Note: the restore() has the side effect of making the\n\t\t// error come back on any future pybind11::exec() call.\n\t\tstd::string reason=parse_error(ex.what(), newblk);\n\t\tex.restore();\n\t\tif(reason.substr(0, 17)==\"KeyboardInterrupt\") {\n\t\t\tauto loc = reason.find(\"At:\");\n\t\t\treason = \"Interrupted a\" + reason.substr(loc+1);\n\t\t\t}\n//\t\tstd::cerr << \"gobbling \" << catchOut.str() << std::endl;\n//\t\tcatchOut.clear();\n\t\tthrow std::runtime_error(reason);\n\t\t}\n\n\tserver_stopwatch.stop();\n\treturn result;\n\t}\n\n//void Server::on_socket_init(websocketpp::connection_hdl, boost::asio::ip::tcp::socket & /* s */)\n//\t{\n//\tboost::asio::ip::tcp::no_delay option(true);\n//\t// FIXME: this used to work in older websocketpp\n////\ts.lowest_layer().set_option(option);\n//\t}\n\nServer::Connection::Connection()\n\t{\n\tuuid = boost::uuids::random_generator()();\n\t}\n\nvoid Server::on_open(websocket_server::id_type ws_id)\n\t{\n\tstd::lock_guard<std::mutex> lock(ws_mutex);\n\tConnection con;\n\tcon.ws_id = ws_id;\n\t// snoop::log(snoop::info) << \"Connection \" << con.uuid << \" open.\" << snoop::flush;\n\tconnections[ws_id]=con;\n\t}\n\nvoid Server::on_close(websocket_server::id_type ws_id)\n\t{\n\tstd::lock_guard<std::mutex> lock(ws_mutex);\n\t//\tauto it = connections.find(hdl);\n\t// snoop::log(snoop::info) << \"Connection \" << it->second.uuid << \" close.\" << snoop::flush;\n\tconnections.erase(ws_id);\n\n\tif(exit_on_disconnect)\n\t\texit(-1);\n\t}\n\nint quit(void *)\n\t{\n//\tstd::cerr << \"Server: setting python interrupt.\" << std::endl;\n\tPyErr_SetInterrupt();\n//\tstd::cerr << \"Server: python interrupt set.\" << std::endl;\n\treturn -1;\n\t}\n\nvoid Server::wait_for_websocket()\n\t{\n\ttry {\n\t\twserver.set_message_handler(std::bind(&Server::on_message, this,\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t std::placeholders::_1, std::placeholders::_2, std::placeholders::_3, std::placeholders::_4));\n\t\twserver.set_connect_handler(std::bind(&Server::on_open, this,     std::placeholders::_1));\n\t\twserver.set_disconnect_handler(std::bind(&Server::on_close, this, std::placeholders::_1));\n\n\t\twserver.listen(run_on_port);\n\n\t\tauto p = wserver.get_local_port();\n\t\tstd::cout << p  << std::endl;\n\t\tstd::cout << authentication_token << std::endl;\n\t\twserver.run();\n\t\t}\n\tcatch(std::exception& ex) {\n\t\tstd::cerr << \"Server::wait_for_websocket: exception \" << ex.what() << std::endl;\n\t\tthrow;\n\t\t}\n\t}\n\nvoid Server::wait_for_job()\n\t{\n\t// Infinite loop, waiting for the master thread to signal that a new block is\n\t// available, and processing it. Blocks are always processed sequentially\n\t// even though new ones may come in before previous ones have finished.\n\n\t// snoop::log(snoop::info) << \"Waiting for blocks\" << snoop::flush;\n\n#ifdef DEBUG\n\tstd::cerr << \"Server::wait_for__job: start\" << std::endl;\n#endif\n\n#ifndef CDB_DONT_ACQUIRE_GIL\n\t// FIXME: why do we need this for the normal Cadabra server, but does\n\t// it hang in the Jupyter server? If you drop this from the normal\n\t// server, it will crash soon below.\n\tpybind11::gil_scoped_acquire acquire;\n#endif\n\n\twhile(true) {\n#ifdef DEBUG\n\t\tstd::cerr << \"Server::wait_for__job: locking\" << std::endl;\n#endif\n\t\tstd::unique_lock<std::mutex> lock(block_available_mutex);\n\t\twhile(block_queue.size()==0) {\n#ifdef DEBUG\n\t\t\tstd::cerr << \"Server::wait_for__job: waiting\" << std::endl;\n#endif\n\t\t\tblock_available.wait(lock);\n\t\t\t}\n\n\t\tcurrent_block = block_queue.front();\n\t\tblock_queue.pop();\n\t\tlock.unlock();\n\n\t\tserver_stopwatch.reset();\n\t\tserver_stopwatch.start();\n\n\t\ttry {\n\t\t\t// We are done with the block_queue; release the lock so that the\n\t\t\t// master thread can push new blocks onto it.\n\t\t\t// snoop::log(snoop::info) << \"Block finished running\" << snoop::flush;\n\t\t\tserver_stopwatch.stop();\n\t\t\tcurrent_ws_id   = current_block.ws_id;\n\t\t\tcurrent_id      = current_block.cell_id;\n\t\t\tcurrent_block.output    = run_string(current_block.input, true, true, current_block.remove_variable_assignments);\n\t\t\tcurrent_block.variables = run_string_variables;\n\t\t\ton_block_finished(current_block);\n\t\t\t}\n\t\tcatch(std::runtime_error& ex) {\n#ifdef DEBUG\n\t\t\tstd::cerr << \"Exception caught, acquiring lock\" << std::endl;\n#endif\n\t\t\tserver_stopwatch.stop();\n\t\t\t// snoop::log(snoop::info) << \"Python runtime exception\" << snoop::flush;\n\t\t\t// On error we remove all other blocks from the queue.\n\t\t\tlock.lock();\n#ifdef DEBUG\n\t\t\tstd::cerr << \"Lock acquired\" << std::endl;\n#endif\n\t\t\tstd::queue<Block> empty;\n\t\t\tstd::swap(block_queue, empty);\n\t\t\tlock.unlock();\n\t\t\tcurrent_block.output = catchOut.str();\n\t\t\tcatchOut.clear();\n\t\t\tcurrent_block.error = ex.what();\n\t\t\ton_block_error(current_block);\n\t\t\t}\n\t\tcatch(std::exception& ex) {\n\t\t\tserver_stopwatch.stop();\n\t\t\t// snoop::log(snoop::info) << \"System exception\" << snoop::flush;\n\t\t\tlock.lock();\n\t\t\tstd::queue<Block> empty;\n\t\t\tstd::swap(block_queue, empty);\n\t\t\tlock.unlock();\n\t\t\tcurrent_block.output=catchOut.str();\n\t\t\tcatchOut.clear();\n\t\t\tcurrent_block.error=ex.what();\n\t\t\ton_kernel_fault(current_block);\n\t\t\t// Keep running\n\t\t\t}\n\t\t}\n\t}\n\nvoid Server::stop_block()\n\t{\n//\tinterrupt_block=true;\n//\tstd::cerr << \"Server: sending SIGINT to python thread.\" << std::endl;\n\tPyErr_SetInterrupt();\n\n\t// PyGILState_STATE state = PyGILState_Ensure();\n\t// //\tPyThreadState_SetAsyncExc ?\n\t// Py_AddPendingCall(&quit, NULL);\n\t// PyGILState_Release(state);\n\n//\tPyGILState_STATE state = PyGILState_Ensure();\n//\tstd::cerr << \"Server: make thread \" << main_thread_id << \" raise exception\" << std::endl;\n//\tPyThreadState_SetAsyncExc(main_thread_id, PyExc_Exception);\n//\tPyGILState_Release(state);\n\t}\n\nServer::Block::Block()\n\t: ws_id(-1), cell_id(0)\n\t{\n\t}\n\nServer::Block::Block(websocket_server::id_type ws_id_, const std::string& str, uint64_t id_, const std::string& msg_type_)\n\t: ws_id(ws_id_), msg_type(msg_type_), input(str), cell_id(id_)\n\t{\n\tnlohmann::json content, header;\n\tresponse[\"header\"]=header;\n\tresponse[\"content\"]=content;\n\tresponse[\"msg_type\"]=msg_type;\n\t}\n\nvoid Server::on_message(websocket_server::id_type ws_id, const std::string& msg,\n\t\t\t\t\t\t\t\tconst websocket_server::request_type& req, const std::string& ip_address)\n\t{\n\tstd::lock_guard<std::mutex> lock(ws_mutex);\n\n\tauto it = connections.find(ws_id);\n\tif(it==connections.end()) {\n//#ifndef ENABLE_JUPYTER\n//\t\tsnoop::log(snoop::warn) << \"Message from unknown connection.\" << snoop::flush;\n//#endif\n\t\treturn;\n\t\t}\n\n\t//\tstd::cout << \"Message from \" << it->second.uuid << std::endl;\n\n\tdispatch_message(ws_id, msg);\n\t}\n\nvoid Server::dispatch_message(websocket_server::id_type ws_id, const std::string& json_msg)\n\t{\n\t//\tstd::cout << json_msg << std::endl;\n\n\tnlohmann::json root;\n\ttry {\n\t\troot = nlohmann::json::parse(json_msg);\n\t\t}\n\tcatch(nlohmann::json::exception& ex) {\n//#ifndef ENABLE_JUPYTER\n//\t\tsnoop::log(snoop::error) << \"Cannot parse message \" << json_msg << snoop::flush;\n//#endif\n\t\treturn;\n\t\t}\n\n\t// Check that this message is authenticated.\n\tstd::string auth_token = root.value(\"auth_token\", \"\");\n\tif(auth_token!=authentication_token) {\n\t\tstd::cerr << \"Received block with incorrect authentication token: \" << auth_token << \".\" << std::endl;\n\t\treturn;\n\t\t}\n\n\tconst auto& content    = root[\"content\"];\n\tconst auto& header     = root[\"header\"];\n\tstd::string msg_type = header[\"msg_type\"].get<std::string>();\n\t// std::cerr << \"received msg_type |\" << msg_type << \"|\" << std::endl;\n\n\tif(msg_type==\"execute_request\") {\n\t\tstd::string code = content.value(\"code\",\"\");\n\t\t// std::cerr << code << std::endl;\n\t\tuint64_t id = header.value(\"cell_id\", uint64_t(0));\n\t\tstd::unique_lock<std::mutex> lock(block_available_mutex);\n\t\tBlock block(ws_id, code, id, msg_type);\n\t\tif(content.count(\"remove_variable_assignments\")==1) {\n\t\t\tblock.remove_variable_assignments.insert(content.value(\"remove_variable_assignments\", \"\"));\n\t\t\t}\n\t\tif(header.count(\"output_cell_ids\")==1) {\n\t\t\tblock.reuse_output_cell_ids = header.value(\"output_cell_ids\", std::deque<uint64_t>());\n\t\t\t}\n\t\tblock.response[\"header\"][\"parent_origin\"]=\"client\";\n\t\tblock.response[\"header\"][\"parent_id\"]=id;\n\t\tblock_queue.push(block);\n\t\tblock_available.notify_one();\n\t\t}\n\telse if(msg_type==\"execute_interrupt\") {\n\t\tstd::unique_lock<std::mutex> lock(block_available_mutex);\n\t\t// std::cerr << \"Server: requesting python thread stop.\" << std::endl;\n\t\tstop_block();\n\t\t// std::cerr << \"Server: clearing block queue.\" << std::endl;\n\t\tstd::queue<Block> empty;\n\t\tstd::swap(block_queue, empty);\n\t\t// std::cerr << \"Server: block queue cleared.\" << std::endl;\n\t\t//snoop::log(snoop::warn) << \"Job stop requested.\" << snoop::flush;\n\t\t}\n\telse if(msg_type==\"init\") {\n\t\t// Stop any running blocks.\n\t\tstd::unique_lock<std::mutex> lock(block_available_mutex);\n\t\tstop_block();\n\t\tstd::queue<Block> empty;\n\t\tstd::swap(block_queue, empty);\n\t\t}\n\telse if(msg_type==\"complete\") {\n\t\t// Schedule a block which runs code to complete the given string.\n\t\tstd::string str=root[\"string\"].get<std::string>();\n\t\tint alternative=root[\"alternative\"].get<int>();\n\t\tstd::string todo=\"print(__cdbkernel__.completer.complete(\\\"\"+str+\"\\\", \"+std::to_string(alternative)+\"))\";\n\n\t\tuint64_t id = header.value(\"cell_id\", uint64_t(0));\n\t\tBlock blk(ws_id, todo, id, \"completed\");\n\t\tblk.response[\"header\"][\"cell_id\"]=id;\n\t\tblk.response[\"content\"][\"original\"]=str;\n\t\tblk.response[\"content\"][\"position\"]=root[\"position\"].get<int>();\n\t\tblk.response[\"content\"][\"alternative\"]=alternative;\n\n\t\tstd::unique_lock<std::mutex> lock(block_available_mutex);\n\t\tblock_queue.push(blk);\n\t\tblock_available.notify_one();\n\t\t}\n\telse if(msg_type==\"exit\") {\n\t\texit(-1);\n\t\t}\n\t}\n\nvoid Server::on_block_finished(Block block)\n\t{\n\tauto& header  = block.response[\"header\"];\n\tauto& content = block.response[\"content\"];\n\n\tif(block.msg_type==\"completed\") {\n\t\t// FIXME: need a better way to get the result out of python, so we can spot None\n\t\t// while keeping the possibility to complete 'No' -> 'None'.\n\t\tstd::string res=block.output;\n\t\tif(res.size()>0 && res[res.size()-1]=='\\n')\n\t\t\tres=res.substr(0, res.size()-1);\n\t\tif(res==\"None\")\n\t\t\tres=\"\";\n\t\tblock.response[\"content\"][\"completed\"]=res;\n\t\t}\n\telse {\n\t\theader[\"cell_origin\"]=\"server\";\n\t\theader[\"cell_id\"]=cadabra::generate_uuid<uint64_t>();\n\t\theader[\"time_total_microseconds\"]=std::to_string(server_stopwatch.seconds()*1e6L + server_stopwatch.useconds());\n\t\theader[\"time_sympy_microseconds\"]=std::to_string(sympy_stopwatch.seconds()*1e6L  + sympy_stopwatch.useconds());\n\t\theader[\"last_in_sequence\"]=block.error.empty(); // If this is the output followed by an error, it's not the last output cell for the running block.\n\t\tcontent[\"output\"]=block.output;\n\t\tblock.response[\"msg_type\"]=\"output\";\n\t\t}\n\n\t// Inform the notebook about the variables referenced in this block.\n\tcontent[\"variables\"]=block.variables;\n\n\tstd::ostringstream str;\n\tstr << block.response << std::endl;\n\tsend_json(str.str());\n\t}\n\nbool Server::handles(const std::string& otype) const\n\t{\n\tif(otype==\"latex_view\" || otype==\"image_png\" || otype==\"image_svg\" || otype==\"verbatim\") return true;\n\treturn false;\n\t}\n\nuint64_t Server::send(const std::string& output, const std::string& msg_type,\n\t\t\t\t\t\t\t uint64_t parent_id, uint64_t cell_id, bool last)\n\t{\n\t// This is the function exposed to the Python side; not used\n\t// directly in the server to send block output back to the client\n\t// (that's all handled by on_block_finished above).\n\n\t// std::cerr << \"Send: \" << msg_type << \", \" << output.substr(0, std::min(size_t(40), output.size())) << std::endl;\n\t\n\tnlohmann::json json, header, content;\n\n\tuint64_t return_cell_id=cell_id;\n\tif(return_cell_id==0) {\n\t\tif(current_block.reuse_output_cell_ids.size()>0) {\n\t\t\t// std::cerr << \"Re-using existing output cell.\" << std::endl;\n\t\t\treturn_cell_id=current_block.reuse_output_cell_ids.front();\n\t\t\tcurrent_block.reuse_output_cell_ids.pop_front();\n\t\t\t}\n\t\telse {\n\t\t\treturn_cell_id=cadabra::generate_uuid<uint64_t>();\n\t\t\t}\n\t\t}\n\t\n\tif(parent_id==0)\n\t\theader[\"parent_id\"]=current_id;\n\telse\n\t\theader[\"parent_id\"]=parent_id;\n\n\theader[\"parent_origin\"]=\"client\";\n\theader[\"cell_id\"]=return_cell_id;\n\theader[\"cell_origin\"]=\"server\";\n\theader[\"time_total_microseconds\"]=std::to_string(server_stopwatch.seconds()*1e6L + server_stopwatch.useconds());\n\theader[\"time_sympy_microseconds\"]=std::to_string(sympy_stopwatch.seconds()*1e6L  + sympy_stopwatch.useconds());\n\theader[\"last_in_sequence\"]=last;\n\n\tcontent[\"output\"]=output;\n\n\tjson[\"header\"]=header;\n\tjson[\"content\"]=content;\n\tjson[\"msg_type\"]=msg_type;\n\n\tstd::ostringstream str;\n\tstr << json << std::endl;\n\n\tsend_json(str.str());\n\n\treturn return_cell_id;\n\t}\n\nvoid Server::send_progress_update(const std::string& msg, int n, int total)\n\t{\n\tnlohmann::json json, content, header;\n\n\theader[\"parent_id\"] = 0;\n\theader[\"parent_origin\"] = \"client\";\n\theader[\"cell_id\"] = 0;\n\theader[\"cell_origin\"] = \"server\";\n\n\tcontent[\"msg\"] = msg;\n\tcontent[\"n\"] = n;\n\tcontent[\"total\"] = total;\n\n\tjson[\"header\"] = header;\n\tjson[\"content\"] = content;\n\tjson[\"msg_type\"] = \"progress_update\";\n\n\tstd::ostringstream str;\n\tstr << json << std::endl;\n\n\tsend_json(str.str());\n\t}\n\nvoid Server::send_json(const std::string& msg)\n\t{\n\t//\tstd::cerr << \"*** sending message \" << msg << std::endl;\n\tstd::lock_guard<std::mutex> lock(ws_mutex);\n\twserver.send(current_ws_id, msg);\n\t}\n\nvoid Server::on_block_error(Block blk)\n\t{\n\tif(blk.output!=\"\")\n\t\ton_block_finished(blk);\n\t\n\tstd::lock_guard<std::mutex> lock(ws_mutex);\n\n\t// Make a JSON message.\n\tnlohmann::json json, content, header;\n\n\tauto return_cell_id=cadabra::generate_uuid<uint64_t>();\n\theader[\"parent_id\"]=blk.cell_id;\n\theader[\"parent_origin\"]=\"client\";\n\theader[\"cell_id\"]=return_cell_id;\n\theader[\"cell_origin\"]=\"server\";\n\theader[\"last_in_sequence\"]=true;\n\tcontent[\"output\"]=blk.error;\n\n\tjson[\"header\"]=header;\n\tjson[\"content\"]=content;\n\tjson[\"msg_type\"]=\"error\";\n\n\tstd::ostringstream str;\n\tstr << json << std::endl;\n\t// std::cerr << \"cadabra-server: sending error, \" << str.str() << std::endl;\n\n\twserver.send(blk.ws_id, str.str());\n\t}\n\nvoid Server::on_kernel_fault(Block blk)\n\t{\n\tif(blk.output!=\"\")\n\t\ton_block_finished(blk);\n\t\n\tstd::lock_guard<std::mutex> lock(ws_mutex);\n\n\t// Make a JSON message.\n\tnlohmann::json json, content, header;\n\n\tauto return_cell_id=cadabra::generate_uuid<uint64_t>();\n\theader[\"parent_id\"]=blk.cell_id;\n\theader[\"parent_origin\"]=\"client\";\n\theader[\"cell_id\"]=return_cell_id;\n\theader[\"cell_origin\"]=\"server\";\n\theader[\"last_in_sequence\"]=true;\n\tcontent[\"output\"]=blk.error;\n\n\tjson[\"header\"]=header;\n\tjson[\"content\"]=content;\n\tjson[\"msg_type\"]=\"fault\";\n\n\tstd::ostringstream str;\n\tstr << json << std::endl;\n\t// std::cerr << \"cadabra-server: sending kernel crash report, \" << str.str() << std::endl;\n\n\twserver.send(blk.ws_id, str.str());\n\t}\n\nvoid Server::run(int port, bool eod)\n\t{\n\texit_on_disconnect = eod;\n\trun_on_port = port;\n\n\t// Python has to be running on the main thread, otherwise\n\t// it cannot receive signals. So we spawn the websocket\n\t// listener on a separate thread, and then do the blocking\n\t// \"wait for python code to execute\" loop on the main\n\t// thread.\n\n//\tstd::thread::id tmp= std::this_thread::get_id();\t\n//\tmain_thread_id = *(unsigned *)&tmp;\n//\tstd::cerr << \"Server: main_thread_id = \" << main_thread_id << std::endl;\n\trunner = std::thread(std::bind(&Server::wait_for_websocket, this));\n\n\twait_for_job();\n//\t\tpybind11::gil_scoped_release release;\n\t}\n"
  },
  {
    "path": "client_server/Server.hh",
    "content": "\n#pragma once\n\n#include <string>\n#include <set>\n#include <deque>\n#include <signal.h>\n#include <boost/uuid/uuid.hpp>\n#include <future>\n#include <pybind11/pybind11.h>\n#include <pybind11/embed.h>\n#include \"nlohmann/json.hpp\"\n#include \"websocket_server.hh\"\n\n#include \"Stopwatch.hh\"\n\n/// \\ingroup clientserver\n///\n/// Object representing a Cadabra server, capable of receiving messages\n/// on a websocket, running Python code, and sending output back to the\n/// client.\n///\n/// Contains the logic to intercept raw Python output but also provides\n/// functionality to the Python side which enables clients to send\n/// various objects in JSON encoded form. See Server::on_block_finished\n/// for the format of these messages.\n///\n/// Every block is run on the same Python scope. They run sequentially,\n/// one at a time, on a thread separate from the websocket++ main loop.\n/// When the Python code finishes (or when it is interrupted), this thread\n/// locks the socket_mutex and calls on_block_finished().\n\nclass Server {\n\tpublic:\n\t\tServer();\n\t\tServer(const Server&)=delete;\n\t\tServer(const std::string& socket);\n\t\tvirtual ~Server();\n\n\t\t/// The only user-visible part: just instantiate a server object and\n\t\t/// start it with run(). This will not return until the server has\n\t\t/// been shut down. Picks a random port when port==0. If\n\t\t/// `exit_on_disconnect==false`, keep the server alive on the\n\t\t/// same port and with the same authentication token when\n\t\t/// the connection drops (so you can reconnect).\n\n\t\tvoid run(int port=0, bool exit_on_disconnect=true);\n\n\n\t\t/// Python output catching. We implement this in a C++ class\n\t\t/// because we want to be able to catch each line of output\n\t\t/// separately, and perhaps add additional functionality to send\n\t\t/// out-of-band messages to the client later.\n\n\t\tclass CatchOutput {\n\t\t\tpublic:\n\t\t\t\tCatchOutput();\n\t\t\t\tCatchOutput(const CatchOutput&);\n\n\t\t\t\tvoid        write(const std::string& txt);\n\t\t\t\tvoid        clear();\n\t\t\t\tstd::string str() const;\n\t\t\tprivate:\n\t\t\t\tstd::string collect;\n\t\t\t};\n\n\t\tCatchOutput catchOut, catchErr;\n\n\t\tStopwatch server_stopwatch;\n\t\tStopwatch sympy_stopwatch;\n\n\t\t/// Raw code to send a string (which must be JSON formatted) as\n\t\t/// a message to the client. Handles communication of the result\n\t\t/// back to the client in JSON format. This is always of the\n\t\t/// form\n\t\t///\n\t\t///      { \"header\":   { \"parent_id\":     \"...\",\n\t\t///                      \"parent_origin\": \"client\" | \"server\",\n\t\t///                      \"cell_id\":       \"...\",\n\t\t///                      \"cell_origin\":   \"client\" | \"server\"\n\t\t///                    },\n\t\t///        \"content\":  { \"output\":  \"...\",\n\t\t///                      \"width\":   int (optional),\n\t\t///                      \"height\":  int (optional)\n      ///                    },\n\t\t///        \"msg_type\": \"...\"\n\t\t///      }\n\t\t///\n\t\t/// msg_type can be \"output\", \"latex\", \"image_png\" and so on,\n\t\t/// corresponding to the possible values of DataCell::CellType.\n\t\t///\n\t\t/// Returns the serial number of the new cell sent.\n\n\t\tvirtual uint64_t         send(const std::string& output, const std::string& msg_type,\n\t\t\t\t\t\t\t\t\t\t\t\tuint64_t parent_id=0, uint64_t cell_id=0, bool last_in_sequence=false);\n\n\t\tvoid                     send_progress_update(const std::string& msg, int n, int total);\n\t\tvoid                     send_json(const std::string&);\n\n\t\tbool                     handles(const std::string& otype) const;\n\t\tstd::string              architecture() const;\n\n\t\t/// Thread entry point for the code that waits for blocks to\n\t\t/// appear on the block queue, and executes them in turn.\n\t\t/// In practice we run this on the main thread.\n\t\tvoid wait_for_job();\n\n\t\t/// Thread entry point for code that sets up and runs the\n\t\t/// websocket listener.\n\t\tvoid wait_for_websocket();\n\n\tprotected:\n\t\tvoid init();\n\n\t\t// WebSocket++ dependent parts below.\n\t\tvoid on_message(websocket_server::id_type id, const std::string& msg,\n\t\t\t\t\t\t\t const websocket_server::request_type& req, const std::string& ip_address);\n\t\tvoid on_open(websocket_server::id_type id);\n\t\tvoid on_close(websocket_server::id_type id);\n\t\twebsocket_server wserver;\n\n\t\t// Connection tracking.  There can be multiple connections to\n\t\t// the server, but they all have access to the same Python\n\t\t// scope. With multiple connections, one can inspect the Python\n\t\t// stack from a different client (e.g. for debugging purposes).\n\t\t// All connections share the same authentication token.\n\n\t\tclass Connection {\n\t\t\tpublic:\n\t\t\t\tConnection();\n\n\t\t\t\twebsocket_server::id_type ws_id;\n\t\t\t\tboost::uuids::uuid        uuid;\n\t\t\t};\n\t\ttypedef std::map<websocket_server::id_type, Connection> ConnectionMap;\n\t\tConnectionMap connections;\n\t\t\n\t\t// Authentication token, needs to be sent along with any message.\n\t\t// Gets set when the server announces its port.\n\t\tstd::string  authentication_token;\n\n\t\t// Mutex to be able to use the websocket layer from both the\n\t\t// main loop and the python-running thread.\n\t\tstd::mutex ws_mutex;\n\n\n\t\t// Basics for the working thread that processes blocks.\n\t\tstd::thread             runner;\n\t\tstd::mutex              block_available_mutex;\n\t\tstd::condition_variable block_available;\n\t\tbool                    exit_on_disconnect;\n\t\tint                     run_on_port;\n\t\tunsigned long           main_thread_id;\n\n\t\t// Data and connection info for a single block of code.\n\t\tclass Block {\n\t\t\tpublic:\n\t\t\t\tBlock();\n\t\t\t\tBlock(websocket_server::id_type, const std::string&, uint64_t id, const std::string& msg_type);\n\t\t\t\t\n\t\t\t\twebsocket_server::id_type   ws_id; // FIXME: decouple from websocket?\n\t\t\t\tstd::string                 msg_type;\n\t\t\t\tstd::string                 input;\n\t\t\t\tstd::string                 output;\n\t\t\t\tstd::string                 error;\n\t\t\t\tuint64_t                    cell_id;\n\t\t\t\tstd::set<std::string>       variables;\n\t\t\t\tstd::set<std::string>       remove_variable_assignments;\n\n\t\t\t\t// When a cell is re-run on variable change, we re-use the output cells of the\n\t\t\t\t// previous run. The IDs of these cells are sent to us by the frontend. We\n\t\t\t\t// store them here, and then pop them off the front for each call to `send`.\n\n\t\t\t\tstd::deque<uint64_t>        reuse_output_cell_ids; \n\n\t\t\t\t// Response message, partially filled in when the\n\t\t\t\t// request comes in.\n\n\t\t\t\tnlohmann::json              response;\n\t\t\t};\n\t\tstd::queue<Block>           block_queue;\n\t\tBlock                       current_block;\n\t\twebsocket_server::id_type   current_ws_id;\n\t\tuint64_t                    current_id;    // id of the block given to us by the client.\n\n\t\t// Run a piece of Python code. This is called from a separate\n\t\t// thread constructed by on_message().\n\t\tstd::string              run_string(const std::string&,\n\t\t\t\t\t\t\t\t\t\t\t\t\t\tbool handle_output=true,\n\t\t\t\t\t\t\t\t\t\t\t\t\t\tbool extract_variables=false,\n\t\t\t\t\t\t\t\t\t\t\t\t\t\tstd::set<std::string> remove_variable_assignments=std::set<std::string>());\n\n\t\tstd::set<std::string> run_string_variables;\n\n\t\t/// Called by the run_block() thread upon completion of the\n\t\t/// task. This will send any output generated by printing directly\n\t\t/// to stdout or stderr from Python (so, output not generated by\n\t\t/// using the 'display' function). Indicates to the client that\n\t\t/// this block has finished executing. Will send an empty string\n\t\t/// if there has been no output 'print'ed.\n\n\t\tvirtual void             on_block_finished(Block);\n\t\tvirtual void             on_block_error(Block);\n\t\tvirtual void             on_kernel_fault(Block);\n\n\t\t/// Halt the currently running block and prevent execution of any\n\t\t/// further blocks that may still be on the queue.\n\n\t\tvoid                     stop_block();\n\t\tbool                     started;\n\t\tstd::future<std::string> job;\n\n\t\t/// Takes a JSON encoded message and performs the required action to process it.\n\t\t/// Where applicable these messages are compatible with IPython's message types,\n\t\t/// http://ipython.org/ipython-doc/dev/development/messaging.html\n\n\t\tvoid dispatch_message(websocket_server::id_type, const std::string& json_string);\n\n\t\t// Python global info.\n\t\tpybind11::scoped_interpreter guard;\n\t\tpybind11::module             main_module;\n\t\tpybind11::object             main_namespace;\n\t};\n"
  },
  {
    "path": "client_server/Snoop.cc",
    "content": "\n#include \"Snoop.hh\"\n\n#include <iostream>\n#include <string.h>\n#include <regex>\n#include <iostream>\n#include <chrono>\n#include <ctime>\n#include <memory.h>\n#ifndef _WIN32\n  #ifndef _WIN64\n     #include <sys/utsname.h>\n  #endif\n#endif\n#include <time.h>\n#ifdef _WIN32\n    #define timegm _mkgmtime\n#endif\n#include <stdint.h>\n#include <set>\n#include \"nlohmann/json.hpp\"\n#include \"Stopwatch.hh\"\n#ifdef ENCRYPT_PASSWORDS\n  #include <libscrypt.h>\n#endif\n\nstd::string snoop_base64_encode(unsigned char const* bytes_to_encode, unsigned int in_len);\nstd::string snoop_base64_decode(std::string const& encoded_string);\n\n#include <signal.h>\n#include <sys/types.h>\n#if !defined(_WIN32) && !defined(_WIN64)\n   #include <pwd.h>\n   #include <unistd.h>\n#else\n   #include <windows.h>\n   #include <io.h>\n   #include <process.h>\n   #include <direct.h>\n#endif\n\n#ifdef __APPLE__\n   #include <pwd.h>\n   #include \"TargetConditionals.h\"\n#else\n   #include <glibmm/miscutils.h>\n#endif\n\n   #define BOOST_SPIRIT_THREADSAFE\n   #include <boost/signals2.hpp>\n   #include <boost/property_tree/ptree.hpp>\n   #include <boost/property_tree/json_parser.hpp>\n   #include <boost/config.hpp>\n#if !defined(TARGET_OS_IPHONE)\n   #include <boost/program_options/detail/config_file.hpp>\n   #include <boost/program_options/parsers.hpp>\n#endif\n   #include <boost/uuid/uuid.hpp>\n   #include <boost/uuid/uuid_generators.hpp> // generators\n   #include <boost/uuid/uuid_io.hpp>         // streaming operators etc.\n\n#define SNOOPDEBUG(ln) \n//#define SNOOPDEBUG(ln) ln\n\nusing namespace snoop;\n\n// Global instance.\n\nsnoop::Snoop snoop::log;\nsnoop::Flush snoop::flush;\n\nusing u64_millis = std::chrono::duration<uint64_t, std::milli>;\nstatic std::chrono::time_point<std::chrono::system_clock, u64_millis> u64_to_time(uint64_t timestamp) {\n    return std::chrono::time_point<std::chrono::system_clock, u64_millis>{u64_millis{timestamp}};\n}\n\n// Until we have widespread C++20 support, we will need to get\n// the timezone offset using old-style code. This code returns\n// the offset in minutes the same as Javascript's\n// Date.getTimezoneOffset(); so if you are in zone GMT+2,\n// it returns -120.\n\nint local_utc_offset_minutes()\n\t{\n\ttime_t t  = time ( NULL );\n\tstruct tm * locg = localtime ( &t );\n\tstruct tm locl;\n\tmemcpy ( &locl, locg, sizeof ( struct tm ) );\n\treturn -1 * (int)( timegm ( locg ) - mktime ( &locl ) ) / 60;\n\t}\n\nstd::string safestring(const unsigned char *c)\n\t{\n\tif(c==0) return \"\";\n\telse     return std::string((const char *)c);\n\t}\n\nSnoop::Snoop()\n   : sync_immediately_(false)\n\t, db(0)\n\t, payload_db(0)\n\t, auth_db(0)\n\t, insert_statement(0)\n\t, id_for_uuid_statement(0)\n\t, payload_insert_statement(0)\n\t, testq_statement(0)\n\t, connection_is_open(false)\n\t, connection_attempt_failed(false)\n   {\n   }\n\nSnoop::ParseError::ParseError(const std::string& m)\n\t: std::logic_error(m)\n\t{\n\t}\n\nvoid Snoop::init(const std::string& app_name, const std::string& app_version, std::string server, std::string dbname, std::string machine_id)\n   {\n\tassert(app_name.size()>0);\n\t\n\tif(db==0) { // Only initialise if database has not been opened before\n\t\tthis_app_.app_name=app_name;\n\t\tthis_app_.app_version=app_version;\n\t\tthis_app_.pid = getpid();\n#if defined(_WIN32) || defined(_WIN64) \n\t\tDWORD dwVersion = 0; \n\t\tDWORD dwMajorVersion = 0;\n\t\tDWORD dwMinorVersion = 0; \n\t\tDWORD dwBuild = 0;\n\t\t\n\t\tdwVersion = GetVersion();\n\t\t\n\t\t// Get the Windows version.\n\t\t\n\t\tdwMajorVersion = (DWORD)(LOBYTE(LOWORD(dwVersion)));\n\t\tdwMinorVersion = (DWORD)(HIBYTE(LOWORD(dwVersion)));\n\t\t\n\t\t// Get the build number.\n\t\t\n\t\tif (dwVersion < 0x80000000)              \n\t\t\tdwBuild = (DWORD)(HIWORD(dwVersion));\n\t\t\n\t\tthis_app_.machine_id = \"Windows \"+std::to_string(dwMajorVersion)+\".\"+std::to_string(dwMinorVersion);\n#else\n\t\tstruct utsname buf;\n\t\tif(uname(&buf)==0) {\n\t\t\tthis_app_.machine_id = std::string(buf.sysname)\n\t\t\t\t+\", \"+buf.nodename+\", \"+buf.release+\", \"+buf.version+\", \"+buf.machine;\n#ifdef __linux__\n\t\t\tthis_app_.machine_id += std::string(\", \")+buf.domainname;\n#endif\n\t\t\t}\n#endif\n        if(machine_id!=\"\")\n            this_app_.machine_id = machine_id; // override (used in Objective-C backend).\n        \n\t\tthis_app_.user_id = get_user_uuid(app_name);\n\n\t\tauto duration =  std::chrono::system_clock::now().time_since_epoch();\n\t\tthis_app_.create_millis   = std::chrono::duration_cast<std::chrono::milliseconds>(duration).count();\n\t\tthis_app_.create_timezone = local_utc_offset_minutes();\n\n\t\tif(server.find(\"ws://\")==std::string::npos && server.find(\"wss://\")==std::string::npos)\n\t\t\tserver_=\"wss://\"+server;\n\t\telse\n\t\t\tserver_=server;\n\n\t\tstd::string payload_dbname, auth_dbname;\n\t\tif(dbname.size()==0) {\n#if defined(_WIN32) || defined(_WIN64)\n\t\t\t// On Windoze, we store in 'user_data_dir' provided by Glib.\n         std::string logdir = Glib::get_user_data_dir();\n         mkdir(logdir.c_str());\n#elif defined(TARGET_OS_IPHONE)\n         // On iOS, we store in '~/Library/.log/'.\n         std::string homedir=getenv(\"HOME\");\n         homedir+=\"/Library\";\n\t\t\tstd::string logdir = homedir+std::string(\"/.log\");\n\t\t\tmkdir(logdir.c_str(), 0700);\n#else\n\t\t\t// On Unix, we store in '~/.log/'.\n\t\t\tstruct passwd *pw = getpwuid(getuid());\n\t\t\tconst char *homedir = pw->pw_dir;\n\t\t\tstd::string logdir = homedir+std::string(\"/.log\");\n\t\t\tmkdir(logdir.c_str(), 0700);\n#endif\n\t\t\tSNOOPDEBUG( std::cerr << \"Snoop::init: storing databases in \" << logdir << std::endl; )\n\t\t\tdbname=logdir+\"/\"+app_name+\".db\";\n\t\t\tpayload_dbname=logdir+\"/\"+app_name+\"_payload.db\";\n\t\t\tauth_dbname=logdir+\"/\"+app_name+\"_auth.db\";\n\t\t\t}\n\t\telse {\n\t\t\tpayload_dbname=dbname+\"_payload.db\";\n\t\t\tauth_dbname=dbname+\"_auth.db\";\t\t\t\n\t\t\tdbname+=\".db\";\n\t\t\t}\n\n\t\t// Open the main database.\n\t\tint ret = sqlite3_open_v2(dbname.c_str(), &db, SQLITE_OPEN_READWRITE | SQLITE_OPEN_CREATE, NULL);\n\t\tif(ret) \n\t\t\tthrow std::logic_error(\"Snoop::init: Cannot open main snoop database\");\n\t\tSNOOPDEBUG( std::cerr << \"Snoop::init: main snoop database '\" << dbname << \"' open\" << std::endl; );\n\t\tsqlite3_exec(db, \"PRAGMA synchronous  = NORMAL\", NULL, NULL, NULL);\n\t\tsqlite3_exec(db, \"PRAGMA journal_mode = WAL\", NULL, NULL, NULL);\n\t\tsqlite3_exec(db, \"PRAGMA busy_timeout = 5000\", NULL, NULL, NULL);\n\n\t\t// Open the payload database.\n\t\tret = sqlite3_open_v2(payload_dbname.c_str(), &payload_db, SQLITE_OPEN_READWRITE | SQLITE_OPEN_CREATE, NULL);\n\t\tif(ret) \n\t\t\tthrow std::logic_error(\"Snoop::init: Cannot open payload database\");\n\t\tSNOOPDEBUG( std::cerr << \"Snoop::init: payload database open\" << std::endl; );\n\t\tsqlite3_exec(payload_db, \"PRAGMA synchronous  = NORMAL\", NULL, NULL, NULL);\n\t\tsqlite3_exec(payload_db, \"PRAGMA journal_mode = WAL\", NULL, NULL, NULL);\n\t\tsqlite3_exec(payload_db, \"PRAGMA busy_timeout = 5000\", NULL, NULL, NULL);\n\t\tSNOOPDEBUG( std::cerr << \"Snoop::init: payload database configured\" << std::endl; );\n\n\t\tcreate_tables();\n\t\tSNOOPDEBUG( std::cerr << \"Snoop::init: logging and payload tables created\" << std::endl; );\n\n\t\t// Open the auth database.\n\t\tret = sqlite3_open_v2(auth_dbname.c_str(), &auth_db, SQLITE_OPEN_READWRITE | SQLITE_OPEN_CREATE, NULL);\n\t\tif(ret) \n\t\t\tthrow std::logic_error(\"Snoop::init: Cannot open authentication database\");\n\t\tSNOOPDEBUG( std::cerr << \"Snoop::init: auth database open\" << std::endl; );\n\t\tsqlite3_exec(auth_db, \"PRAGMA synchronous  = NORMAL\", NULL, NULL, NULL);\n\t\tsqlite3_exec(auth_db, \"PRAGMA journal_mode = WAL\", NULL, NULL, NULL);\n\t\tsqlite3_exec(auth_db, \"PRAGMA busy_timeout = 5000\", NULL, NULL, NULL);\n\t\tSNOOPDEBUG( std::cerr << \"Snoop::init: auth database configured\" << std::endl; );\n\t\tcreate_authentication_tables();\n\t\tSNOOPDEBUG( std::cerr << \"Snoop::init: auth database tables created\" << std::endl; );\n\n\t\t// Turn off synchronous writes as they seriously degrade performance (by orders of magnitude)\n\t\t// for our single-row inserts. See\n\t\t// http://stackoverflow.com/questions/1711631/improve-insert-per-second-performance-of-sqlite?rq=1\n\t\t// for more options to speed things up.\n\t\t// The busy_timeout is to be compatible with litestream.\n\t\t// sqlite3_exec(db, \"PRAGMA synchronous  = OFF\", NULL, NULL, NULL);\n\n\t\t// If this is a client, i.e. not a SnoopServer: obtain a uuid, start the websocket listener,\n\t\t// and sync with the remote server whatever has not yet been synced in previous runs.\n\n\t\tif(this_app_.app_name!=\"SnoopServer\") {\n\t\t\tobtain_uuid();\n\t\t\tstart_websocket_client();\n\t\t\t// Once started, the websocket client thread will call a sync\n\t\t\t// in the on_client_open callback, and then set the\n\t\t\t// connection_is_open flag.\n\t\t\t}\n\t\t}\n   }\n\nstd::string Snoop::get_user_uuid(const std::string& appname) \n\t{\n\tstd::string user_uuid=\"\";\n\n#ifdef TARGET_OS_IPHONE\n\t// On iOS, config files go in '~/Library/.config/'\n\tstd::string configdir=getenv(\"HOME\");\n\tconfigdir+=\"/Library/.config\";\n#else\n\t// on Unix/Windoze, Glib knows where to store config data.\n\tstd::string configdir = Glib::get_user_config_dir();\n#endif\n\n\tstd::string configpath=configdir + std::string(\"/snoop/\"+appname+\".conf\");\n\tstd::ifstream config(configpath);\n\tbool need_to_write=true;\n#ifndef TARGET_OS_IPHONE\n\tif(config) {\n\t\tstd::set<std::string> options;\n\t\toptions.insert(\"user\");\n\n\t\tfor(boost::program_options::detail::config_file_iterator i(config, options), e ; i != e; ++i) {\n\t\t\t// FIXME: http://stackoverflow.com/questions/24701547/how-to-parse-boolean-option-in-config-file\n\t\t\tif(i->string_key==\"user\") {\n\t\t\t\tuser_uuid=i->value[0];\n\t\t\t\tneed_to_write=false;\n\t\t\t\t}\n\t\t\t}\n\t\t}\n#endif\n\tif(need_to_write) {\n\t\t// First time run; create config subdirectory for snoop.\n\t\tstd::string configsubdir = configdir+std::string(\"/snoop\");\n#if defined(_WIN32) || defined(_WIN64)\n\t\tmkdir(configdir.c_str());\n\t\tmkdir(configsubdir.c_str());\n#else\n\t\tmkdir(configdir.c_str(), 0700);\n\t\tmkdir(configsubdir.c_str(), 0700);\n#endif\n\t\t\n\t\tstd::ofstream config(configpath);\n\t\tif(config) {\n\t\t\tauto tmp = boost::uuids::random_generator()();\n\t\t\tstd::ostringstream str;\n\t\t\tstr << tmp;\n\t\t\tuser_uuid = str.str();\n\n\t\t\tconfig << \"user = \" << user_uuid << std::endl;\n\t\t\t}\n\t\telse {\n\t\t\tSNOOPDEBUG( std::cerr << \"Snoop: cannot write \" << configpath << std::endl; )\n\t\t\t}\n\t\t}\n\treturn user_uuid;\n\t}\n\nvoid Snoop::set_sync_immediately(bool s)\n\t{\n\tsync_immediately_=s;\n\t}\n\nvoid Snoop::create_tables()\n\t{\n\tassert(db!=0);\n\tassert(payload_db!=0);\n\n\tstd::lock_guard<std::recursive_mutex> lock(sqlite_mutex);\n\n\tchar *errmsg;\n\t// Create the `runs` table.\n\tif(sqlite3_exec(db, \"create table if not exists runs (\"\n\t\t\t\t\t\t \"id              integer primary key autoincrement,\"\n\t\t\t\t\t\t \"uuid            text,\"\n\t\t\t\t\t\t \"create_millis   unsigned big int,\"\n\t\t\t\t\t\t \"receive_millis  unsigned big int,\"\n\t\t\t\t\t\t \"pid             int,\"\n\t\t\t\t\t\t \"ip_address      text,\"\n\t\t\t\t\t\t \"machine_id      text,\"\n\t\t\t\t\t\t \"app_name        text,\"\n\t\t\t\t\t\t \"app_version     text,\"\n\t\t\t\t\t\t \"user_id         text,\"\n\t\t\t\t\t\t \"server_status   int,\"\n                   \"create_timezone int default -1);\"\n\t\t\t\t\t\t , NULL, NULL, &errmsg) != SQLITE_OK) {\n\t\tsqlite3_free(errmsg);\n\t\tthrow std::logic_error(\"Failed to create table runs\");\n\t\t}\n\t// Add the create_timezone column, ignore any errors.\n\tif(sqlite3_exec(db, \"alter table runs add column create_timezone int default -1;\"\n\t\t\t\t\t\t , NULL, NULL, &errmsg) != SQLITE_OK) {\n\t\tstd::string err(errmsg);\n\t\tsqlite3_free(errmsg);\n\t\t}\n\n\t// Create the `logs` table.\n\tif(sqlite3_exec(db, \"create table if not exists logs (\"\n\t\t\t\t\t\t \"log_id          integer primary key autoincrement,\"\n\t\t\t\t\t\t \"client_log_id   integer,\"\n\t\t\t\t\t\t \"id              integer references login,\"\n\t\t\t\t\t\t \"create_millis   unsigned big int,\"\n\t\t\t\t\t\t \"receive_millis  unsigned big int,\"\n\t\t\t\t\t\t \"loc_file        text,\"\n\t\t\t\t\t\t \"loc_line        integer,\"\n\t\t\t\t\t\t \"loc_method      text,\"\n\t\t\t\t\t\t \"type            text,\"\n\t\t\t\t\t\t \"message         text,\"\n\t\t\t\t\t\t \"server_status   int,\"\n\t\t\t\t\t\t \"session_uuid    text,\"\n\t\t\t\t\t\t \"create_timezone int default -1);\"\n\t\t\t\t\t\t , NULL, NULL, &errmsg) != SQLITE_OK) {\n\t\tsqlite3_free(errmsg);\n\t\tthrow std::logic_error(\"Failed to create table logs\");\n\t\t}\n\t// Add new session_uuid to existing table if we do not have it already.\n\tif(sqlite3_exec(db, \"alter table logs add column session_uuid text;\"\n\t\t\t\t\t\t , NULL, NULL, &errmsg) != SQLITE_OK) {\n\t\tstd::string err(errmsg);\n\t\tsqlite3_free(errmsg);\n\t\t}\n\t// Add the create_timezone column, ignore any errors.\n\tif(sqlite3_exec(db, \"alter table logs add column create_timezone int default -1;\"\n\t\t\t\t\t\t , NULL, NULL, &errmsg) != SQLITE_OK) {\n\t\tstd::string err(errmsg);\n\t\tsqlite3_free(errmsg);\n\t\t}\n\n\t// Create the `payload` table.\n\tif(sqlite3_exec(payload_db, \"create table if not exists payload (\"\n\t\t\t\t\t\t \"payload_id         integer primary key autoincrement,\"\n\t\t\t\t\t\t \"client_payload_id  integer,\"\t\t\t\t\t\t \n\t\t\t\t\t\t \"id                 integer,\"  /* 'references login', but that's not possible across databases */\n\t\t\t\t\t\t \"create_millis      unsigned big int,\"\n\t\t\t\t\t\t \"receive_millis     unsigned big int,\"\n\t\t\t\t\t\t \"payload            text,\"\n\t\t\t\t\t\t \"server_status      int,\"\n\t\t\t\t\t\t \"create_timezone    int default -1);\"\n\t\t\t\t\t\t , NULL, NULL, &errmsg) != SQLITE_OK) {\n\t\tsqlite3_free(errmsg);\n\t\tthrow std::logic_error(\"Failed to create table payload\");\n\t\t}\n\t// Add the create_timezone column, ignore any errors.\n\tif(sqlite3_exec(payload_db, \"alter table payload add column create_timezone int default -1;\"\n\t\t\t\t\t\t , NULL, NULL, &errmsg) != SQLITE_OK) {\n\t\tstd::string err(errmsg);\n\t\tsqlite3_free(errmsg);\n\t\t}\n\t\n\tif(sqlite3_exec(db, \"create index if not exists logs_id_idx on logs(id);\", NULL, NULL, &errmsg) != SQLITE_OK) {\n\t\tstd::string err(errmsg);\n\t\tsqlite3_free(errmsg);\n\t\tthrow std::logic_error(\"Failed to create index on logs.id: \"+err);\n\t\t}\n\tif(sqlite3_exec(db, \"create index if not exists logs_client_log_id_idx on logs(client_log_id);\", NULL, NULL, &errmsg) != SQLITE_OK) {\n\t\tstd::string err(errmsg);\n\t\tsqlite3_free(errmsg);\n\t\tthrow std::logic_error(\"Failed to create index on logs.client_log_id: \"+err);\n\t\t}\n\tif(sqlite3_exec(db, \"create index if not exists logs_create_millis_idx on logs(create_millis);\", NULL, NULL, &errmsg) != SQLITE_OK) {\n\t\tstd::string err(errmsg);\n\t\tsqlite3_free(errmsg);\n\t\tthrow std::logic_error(\"Failed to create index on logs.create_millis: \"+err);\n\t\t}\n\tif(sqlite3_exec(db, \"create index if not exists logs_type_idx on logs(type);\", NULL, NULL, &errmsg) != SQLITE_OK) {\n\t\tstd::string err(errmsg);\n\t\tsqlite3_free(errmsg);\n\t\tthrow std::logic_error(\"Failed to create index on logs.type: \"+err);\n\t\t}\n\tif(sqlite3_exec(db, \"create index if not exists runs_uuid_idx on runs(uuid);\", NULL, NULL, &errmsg) != SQLITE_OK) {\n\t\tstd::string err(errmsg);\n\t\tsqlite3_free(errmsg);\n\t\tthrow std::logic_error(\"Failed to create index on runs.uuid: \"+err);\n\t\t}\n\tif(sqlite3_exec(db, \"create index if not exists runs_machine_id_idx on runs(machine_id);\", NULL, NULL, &errmsg) != SQLITE_OK) {\n\t\tstd::string err(errmsg);\n\t\tsqlite3_free(errmsg);\n\t\tthrow std::logic_error(\"Failed to create index on runs.machine_id: \"+err);\n\t\t}\n\tif(sqlite3_exec(db, \"create index if not exists runs_app_version_idx on runs(app_version);\", NULL, NULL, &errmsg) != SQLITE_OK) {\n\t\tstd::string err(errmsg);\n\t\tsqlite3_free(errmsg);\n\t\tthrow std::logic_error(\"Failed to create index on runs.app_version: \"+err);\n\t\t}\n\tif(sqlite3_exec(db, \"create index if not exists runs_app_name_idx on runs(app_name);\", NULL, NULL, &errmsg) != SQLITE_OK) {\n\t\tstd::string err(errmsg);\n\t\tsqlite3_free(errmsg);\n\t\tthrow std::logic_error(\"Failed to create index on runs.app_name: \"+err);\n\t\t}\n\t}\n\nvoid Snoop::create_authentication_tables()\n\t{\n\t// We need two tables: one for the username/salted-password\n\t// combo (together with some other user info, probably)\n\t// and one for authorisation tickets issued after a successful\n\t// login. \n\n\tassert(auth_db!=0);\n\n\tstd::lock_guard<std::recursive_mutex> lock(sqlite_mutex);\n\n\tchar *errmsg;\n\tif(sqlite3_exec(auth_db, \"create table if not exists users (\"\n\t\t\t\t\t\t \"id              integer primary key autoincrement,\"\n\t\t\t\t\t\t \"username        text unique,\"\n\t                \"password        text,\"\n\t\t\t\t\t\t \"enabled         int,\"\n\t\t\t\t\t\t \"\\\"group\\\"           int,\"\n\t\t\t\t\t\t \"email           text,\"\n\t\t\t\t\t\t \"device          text);\"\n\t                , NULL, NULL, &errmsg) != SQLITE_OK) {\n\t\tstd::string err(\"Failed to create table users: \");\n\t\terr += std::string(errmsg);\n\t\tsqlite3_free(errmsg);\n\t\tthrow std::logic_error(err);\n\t\t}\n\tif(sqlite3_exec(auth_db, \"create table if not exists groups (\"\n\t\t\t\t\t\t \"id              integer primary key autoincrement,\"\n\t\t\t\t\t\t \"\\\"group\\\"       text unique,\"\n      \t                \"description        text,\"\n\t\t\t\"enabled            int);\"\n\t                , NULL, NULL, &errmsg) != SQLITE_OK) {\n\t\tstd::string err(\"Failed to create table groups: \");\n\t\terr += std::string(errmsg);\n\t\tsqlite3_free(errmsg);\n\t\tthrow std::logic_error(err);\n\t\t}\n\t// The following table is fairly trivial right now but can be used\n\t// to add other information at a later stage. Mainly introduced\n\t// so we can handle multiple user_detail records for each user.\n//\tif(sqlite3_exec(auth_db, \"create table if not exists user_details (\"\n//\t\t\t\t\t\t \"id              integer primary key autoincrement,\"\n//\t\t\t\t\t\t \"user_id         integer,\"\n//\t                \"device          text);\"\n//\t                , NULL, NULL, &errmsg) != SQLITE_OK) {\n//\t\tsqlite3_free(errmsg);\n//\t\tthrow std::logic_error(\"Failed to create table user_details\");\n//\t\t}\n\tif(sqlite3_exec(auth_db, \"create table if not exists tickets (\"\n\t\t\t\t\t\t \"id              integer primary key autoincrement,\"\n\t\t\t\t\t\t \"user_id         integer,\"\n\t\t\t\t\t\t \"ticket_uuid     text,\"\n\t                \"valid           integer);\"\n\t                , NULL, NULL, &errmsg) != SQLITE_OK) {\n\t\tstd::string err(\"Failed to create table tickets: \");\n\t\terr += std::string(errmsg);\n\t\tsqlite3_free(errmsg);\n\t\tthrow std::logic_error(err);\n\t\t}\n\tif(sqlite3_exec(auth_db, \"create table if not exists auth_attempts (\"\n\t\t\t\t\t\t \"id              integer primary key autoincrement,\"\n\t\t\t\t\t\t \"time_millis     unsigned big int,\"\n\t\t\t\t\t\t \"user_id         integer,\"\n\t\t\t\t\t\t \"ticket_id       integer,\"\n\t                \"success         integer,\"\n\t\t\t\t\t\t \"msg             text);\"\n\t                , NULL, NULL, &errmsg) != SQLITE_OK) {\n\t\tstd::string err(\"Failed to create table auth_attempts: \");\n\t\terr += std::string(errmsg);\n\t\tsqlite3_free(errmsg);\n\t\tthrow std::logic_error(err);\n\t\t}\n\t}\n\n\nvoid Snoop::obtain_uuid()\n\t{\n\tassert(db!=0);\n\n\tstd::lock_guard<std::recursive_mutex> lock(sqlite_mutex);\n\n\tsqlite3_stmt *statement=0;\n\tstd::ostringstream ss;\n//\tss << \"select uuid from runs where pid=\" << getpid() << \" order by create_millis desc limit 1\";\n\tss << \"select uuid from runs where pid=\" << getpid() << \" order by create_millis desc limit 1\";\n\t\n\tint res = sqlite3_prepare(db, ss.str().c_str(), -1, &statement, NULL);\n\tif(res==SQLITE_OK) {\n\t\tint ret = sqlite3_step(statement);\n\t\tif(ret==SQLITE_ROW) {\n\t\t\tif(sqlite3_column_type(statement, 0)==SQLITE3_TEXT) \n\t\t\t\tthis_app_.uuid=safestring(sqlite3_column_text(statement, 0));\n\t\t\telse throw std::logic_error(\"Database inconsistency for obtain_uuid\");\n\t\t\t}\n\t\t}\n\tsqlite3_finalize(statement);\n\n\t// Generate and insert a new uuid if there is no existing entry for the current pid.\n\n\tif(this_app_.uuid.size()==0) {\n\t\tauto tmp = boost::uuids::random_generator()();\n\t\tstd::ostringstream str;\n\t\tstr << tmp;\n\t\tthis_app_.uuid = str.str();\n\n\t\tSNOOPDEBUG( std::cerr << \"Snoop: registering run with uuid \" << this_app_.uuid << std::endl; );\n\t\tbool stored = store_app_entry_without_lock(this_app_);\n\t\tif(!stored) {\n  \t\t   SNOOPDEBUG( std::cerr << \"Snoop: uuid already registered\" << std::endl; );\n\t\t   }\n\t\telse {\n  \t\t   SNOOPDEBUG( std::cerr << \"Snoop: app run for this uuid stored\" << std::endl; );\n\t\t   }\n\t\t}\n\telse {\n\t   SNOOPDEBUG( std::cerr << \"Snoop: pid already has a uuid, not re-registering\" << std::endl; );\n\t   }\n\t}\n\n/// Get the app_version string for the last run on the given device.\n\nstd::string Snoop::last_seen_version(std::string machine_id)\n\t{\n\tassert(db!=0);\n\n\tstd::lock_guard<std::recursive_mutex> lock(sqlite_mutex);\n\n\tsqlite3_stmt *statement=0;\n\tstd::ostringstream ss;\n\tss << \"select app_version from runs where machine_id=? order by id desc limit 1\";\n\n\tstd::string last_version=\"\";\n\tint res = sqlite3_prepare(db, ss.str().c_str(), -1, &statement, NULL);\n\tif(res==SQLITE_OK) {\n\t\tsqlite3_bind_text(statement, 1, machine_id.c_str(), machine_id.size(), 0);\n\t\tint ret = sqlite3_step(statement);\n\t\tif(ret==SQLITE_ROW) {\n\t\t\tif(sqlite3_column_type(statement, 0)==SQLITE3_TEXT) \n\t\t\t\tlast_version=safestring(sqlite3_column_text(statement, 0));\n\t\t\t}\n\t\t}\n\tsqlite3_finalize(statement);\n\n\treturn last_version;\n\t}\n\nbool Snoop::authenticate(std::function<void (std::string, bool)> f, std::string user, std::string pass, bool always_reauth)\n   {\n   // Wait for the websocket client thread to have spun up.\n\tstd::unique_lock<std::mutex> lock(connection_mutex);\n\tif(connection_is_open==false && connection_attempt_failed==false) {\n\t\tconnection_cv.wait(lock);\n\t\t}\n\n\tauthentication_callback=f;\n\t\n   // If we have a ticket, setup check request and return true; \n   // If we do not have a ticket, and user and pass are not empty, setup login check, return false.\n\n   // First check if we have a ticket from a previous session.\n\n\tstd::string ticket_uuid;\n\tif(always_reauth==false)\n\t\tticket_uuid=get_local_ticket();\n\t\n\t// Check ticket validity with server, or do password login.\n\t                     \n\tif(ticket_uuid.size()!=0 && user==\"\" && pass==\"\") { // have ticket and want to login without name/pass\n\t\tSNOOPDEBUG( std::cerr << \"Have a ticket already, re-validating.\" << std::endl; );\n\t   std::ostringstream pack;\n\t   pack << \"{ \\\"authenticate\\\": {\"\n\t        << \"     \\\"ticket_uuid\\\": \\\"\" << ticket_uuid << \"\\\"} } \\n\";\n\t   if(!connection_is_open) {\n\t\t   SNOOPDEBUG( std::cerr << \"Connection not open, cannot verify ticket, allowed through.\" << std::endl; );\n\t\t   }\n\t   else {\n\t\t   wsclient.send(pack.str());\n\t\t   }\n\t   return true;\n\t   }\n   else {\n\t\tticket_uuid=\"\"; // FIXME: should we also remove it from the local database?\n\n\t\t// Store the user in the local database.\n\t\tSNOOPDEBUG( std::cerr << \"Snoop::authenticate: storing user '\" << user\n\t\t\t\t\t\t<< \"' (but not password) in local database.\" << std::endl; );\n\t\tif(!add_user(user, \"\", true)) {\n\t\t\tSNOOPDEBUG( std::cerr << \"Snoop::authenticate: error storing user.\" << std::endl; );\n\t\t\t}\n\n\t\t// Test:\n\t\tstd::string local_user_vrfy = local_user();\n\t\tSNOOPDEBUG( std::cerr << \"Snoop::authenticate: local_user = \" << local_user_vrfy << std::endl; );\n\n\t\t// Send authentication request to server, asking for ticket. Then exit, as\n\t\t// the ticket will come back async.\n\t   SNOOPDEBUG( std::cerr << \"No ticket yet, requesting one with login/pass.\" << std::endl; );\n\t   std::ostringstream pack;\n\t   pack << \"{ \\\"authenticate\\\": {\"\n\t        << \"     \\\"user\\\": \\\"\" << user << \"\\\", \\\"password\\\": \\\"\" << pass << \"\\\" } } \\n\";\n\n\t   if(!connection_is_open) {\n\t\t   SNOOPDEBUG( std::cerr << \"No connection, cannot verify login credentials\" << std::endl; );\n\t\t   // FIXME: need a 'false' which also shows that we have not been able to verify.\n\t\t   }\n\t   else {\n\t\t   wsclient.send(pack.str());\n\t\t   }\n\t   return false;\n\t   }\n   }\n\nvoid Snoop::set_error_handler(std::function<bool (std::string)> f)\n\t{\n\terror_callback=f;\n\t}\n\nvoid Snoop::set_session_uuid(const std::string& s)\n\t{\n\tsession_uuid_=s;\n\t}\n\nstd::string Snoop::get_local_ticket()\n   {\n\tstd::lock_guard<std::recursive_mutex> lock(sqlite_mutex);\n\n\t// Prepare the query for the ticket_uuid. This always\n\t// queries for the ticket with user number 0 (as the local\n\t// client storage does not store user details). \n\n\tsqlite3_stmt *statement=0;\n\tstd::ostringstream ss;\n\tss << \"select ticket_uuid from tickets where user_id=0 and valid=1\";\n\tint res = sqlite3_prepare(auth_db, ss.str().c_str(), -1, &statement, NULL);\n\tif(res!=SQLITE_OK)\n\t\treturn \"\";\n\n\tint ret = sqlite3_step(statement);\n\tstd::string ticket_uuid;\n\tif(ret==SQLITE_ROW) {\n\t\tticket_uuid=safestring(sqlite3_column_text(statement, 0));\t\t\n\t\t}\n\tsqlite3_finalize(statement);\n\n\treturn ticket_uuid;\n   }\n\nvoid Snoop::set_local_ticket(std::string ticket_uuid)\n   {\n   // First delete local ticket.\n   \n   std::ostringstream ss;\n\tsqlite3_stmt *statement=0;   \n   ss << \"delete from tickets\";\n   int res = sqlite3_prepare(auth_db, ss.str().c_str(), -1, &statement, NULL);\n   if(res!=SQLITE_OK)\n\t   throw std::logic_error(\"Snoop::delete_local_ticket: sqlite3_prepare failed error \"+std::to_string(res));\n   \n   res = sqlite3_step(statement);\n   if(res!=SQLITE_DONE)\n\t   throw std::logic_error(\"Snoop::store_ticket: sqlite3_step failed error \"+std::to_string(res));\n\n   sqlite3_finalize(statement);\n   \n   // Now store.\n   if(ticket_uuid.size()!=0)\n\t   store_ticket(ticket_uuid, 0, 1);\n   }\n\nSnoop::Ticket::Ticket()\n\t{\n\tticket_id=-1;\n\tuser_id=-1;\n\tvalid=false;\n\t}\n\nSnoop::Ticket Snoop::is_ticket_valid(std::string ticket_uuid) \n   {\n\tstd::lock_guard<std::recursive_mutex> lock(sqlite_mutex);\n\n\t// Prepare the query for the ticket_uuid.\n\n\tTicket tret;\n\ttret.ticket_uuid=ticket_uuid;\n\ttret.valid = false;\n\t\n\tsqlite3_stmt *statement=0;\n\tstd::ostringstream ss;\n\tss << \"select valid, users.enabled, ifnull(groups.enabled,1) as groupsenabled, tickets.id, users.id from tickets join users on tickets.user_id=users.id left join groups on users.\\\"group\\\"=groups.id where ticket_uuid=?\";\n\tint res = sqlite3_prepare(auth_db, ss.str().c_str(), -1, &statement, NULL);\n\tif(res != SQLITE_OK) \n\t\treturn tret;\n\n\tsqlite3_bind_text(statement, 1, ticket_uuid.c_str(), ticket_uuid.size(), 0);\n\n\t// Query database.\n\n\tint valid=0;\n\tint enabled=0;\n\tint groupsenabled=0;\n\tint ret = sqlite3_step(statement);\n\tif(ret==SQLITE_ROW) {\n\t  valid=sqlite3_column_int(statement, 0);\n\t  enabled=sqlite3_column_int(statement, 1);\n\t  groupsenabled=sqlite3_column_int(statement, 2);\n\t  tret.ticket_id=sqlite3_column_int(statement, 3);\n\t  tret.user_id=sqlite3_column_int(statement, 4);\t  \n\t}\n\tsqlite3_finalize(statement);\n\n\ttret.valid = (valid==1 && enabled==1 && groupsenabled==1);\n\t\n\treturn tret;\n   }\n\nint Snoop::store_ticket(std::string ticket_uuid, int user_id, bool valid)\n   {\n   assert(auth_db!=0);\n\n   std::ostringstream ss;\n\tsqlite3_stmt *statement=0;   \n   ss << \"insert into tickets (user_id, ticket_uuid, valid) values (?, ?, ?)\";\n   int res = sqlite3_prepare(auth_db, ss.str().c_str(), -1, &statement, NULL);\n   if(res!=SQLITE_OK)\n\t   throw std::logic_error(\"Snoop::store_ticket: sqlite3_prepare failed error \"+std::to_string(res));\n   \n   sqlite3_bind_int(statement,  1, user_id);\n   sqlite3_bind_text(statement, 2, ticket_uuid.c_str(), ticket_uuid.size(), 0);\n   sqlite3_bind_int(statement,  3, valid?1:0);\n   res = sqlite3_step(statement);\n   if(res!=SQLITE_DONE)\n\t   throw std::logic_error(\"Snoop::store_ticket: sqlite3_step failed error \"+std::to_string(res));\n\n   sqlite3_finalize(statement);\n\treturn sqlite3_last_insert_rowid(auth_db);\t\n   }\n\nbool Snoop::store_app_entry(Snoop::AppEntry& app)\n\t{\n\tassert(db!=0);\n\n\tstd::lock_guard<std::recursive_mutex> lock(sqlite_mutex);\n\n\treturn store_app_entry_without_lock(app);\n\t}\n\nbool Snoop::store_app_entry_without_lock(Snoop::AppEntry& app)\n\t{\n\t// Do we already have a record with this uuid?\n\tsqlite3_stmt *testq=0;\n\tint testq_res = sqlite3_prepare(db, \"select count(*) from runs where uuid=?\", -1, &testq, NULL);\n\tif(testq_res!=SQLITE_OK) \n\t\tthrow std::logic_error(\"Snoop::store_app_entry_without_lock: failed to test for row presence\");\n\n\tsqlite3_bind_text(testq, 1, app.uuid.c_str(), app.uuid.size(), 0);\n\tsqlite3_step(testq);\n\tint64_t num = sqlite3_column_int64(testq, 0);\n\tsqlite3_finalize(testq);\n\tif(num>0) \n\t\treturn false;\n\t\n\t// No entry yet, we need to store it.\n\tsqlite3_stmt *statement=0;\n\tint res = sqlite3_prepare(db, \"insert into runs (uuid, create_millis, receive_millis, pid, ip_address, machine_id, \"\n\t\t\t\t\t\t\t\t\t  \"app_name, app_version, user_id, server_status, create_timezone) \"\n\t\t\t\t\t\t\t\t\t  \"values (?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?)\",\n\t\t\t\t\t\t\t\t\t  -1, &statement, NULL);\n\t\n\tif(res==SQLITE_OK) {\n\t\tsqlite3_bind_text(statement,   1, app.uuid.c_str(), app.uuid.size(), 0);\n\t\tsqlite3_bind_int64(statement,  2, app.create_millis);\n\t\tsqlite3_bind_int64(statement,  3, app.receive_millis);\n\t\tsqlite3_bind_int64(statement,  4, app.pid);\n\t\tsqlite3_bind_text(statement,   5, app.ip_address.c_str(), app.ip_address.size(), 0);\n\t\tsqlite3_bind_text(statement,   6, app.machine_id.c_str(), app.machine_id.size(), 0);\n\t\tsqlite3_bind_text(statement,   7, app.app_name.c_str(), app.app_name.size(), 0);\n\t\tsqlite3_bind_text(statement,   8, app.app_version.c_str(), app.app_version.size(), 0);\n\t\tsqlite3_bind_text(statement,   9, app.user_id.c_str(), app.user_id.size(), 0);\n\t\tsqlite3_bind_int(statement,   10, app.server_status);\t\t\n//\t\tsqlite3_bind_text(statement,  11, app.uuid.c_str(), app.uuid.size(), 0);\n\t\tsqlite3_bind_int(statement,   11, app.create_timezone);\n\n\t\tsqlite3_step(statement);\n\t\tsqlite3_finalize(statement);\n\n\t\tapp.id = sqlite3_last_insert_rowid(db);\n\n\t\treturn true;\n\t\t}\n\telse {\n\t\tthrow std::logic_error(\"Failed to prepare insertion\");\n\t\t}\n\t}\n\nbool Snoop::store_log_entry(Snoop::LogEntry& log_entry, bool avoid_server_duplicates)\n\t{\n\tassert(db!=0);\n\t\n\tstd::lock_guard<std::recursive_mutex> lock(sqlite_mutex);\n\n\tif(false && avoid_server_duplicates) {\n\t\t// This can take 0.3s on a 15Gb database. We cannot afford that.\n\n\t\t// Do we already have a record with this client_log_id and id?\n\t\tif(testq_statement==0) {\n\t\t\tint testq_res = sqlite3_prepare(db, \"select exists (select 1 from (select client_log_id from logs where id=?) where client_log_id=?)\",\n\t\t\t\t\t\t\t\t\t\t\t\t\t  -1, &testq_statement, NULL);\n\t\t\tif(testq_res!=SQLITE_OK) \n\t\t\t\tthrow std::logic_error(\"Snoop::store_log_entry_without_lock: failed to prepare query for duplicate check\");\n\t\t\t}\n\n\t\tstd::cerr << log_entry.id << \", \" << log_entry.client_log_id << std::endl;\n\t\tsqlite3_bind_int64(testq_statement, 1, log_entry.id);\n\t\tsqlite3_bind_int64(testq_statement, 2, log_entry.client_log_id);\n\t\tsqlite3_step(testq_statement);\n\t\tint64_t num = sqlite3_column_int64(testq_statement, 0);\n\t\tsqlite3_reset(testq_statement);\n\t\tif(num>0) \n\t\t\treturn false;\n\n\t\t}\n\t\n\t// Need to store this entry.\n\n\tauto duration =  std::chrono::system_clock::now().time_since_epoch();\n\tlog_entry.receive_millis   = std::chrono::duration_cast<std::chrono::milliseconds>(duration).count();\n\n\tint res=SQLITE_OK;\n\tif(insert_statement==0) {\n\t\tres=sqlite3_prepare_v2(db, \"insert into logs \"\n\t\t\t\t\t\t\t\t\t  \"(client_log_id, id, create_millis, receive_millis, loc_file, loc_line, loc_method, \"\n\t\t\t\t\t\t\t\t\t  \" type, message, server_status, session_uuid, create_timezone) \"\n\t\t\t\t\t\t\t\t\t  \"values (?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?)\",\n\t\t\t\t\t\t\t\t\t  -1, &insert_statement, NULL);\n\t\t}\n\n\tif(res==SQLITE_OK ) {\n\t\tsqlite3_bind_int(insert_statement,    1, log_entry.client_log_id);\n\t\tsqlite3_bind_int(insert_statement,    2, log_entry.id);\n\t\tsqlite3_bind_int64(insert_statement,  3, log_entry.create_millis);\n\t\tsqlite3_bind_int64(insert_statement,  4, log_entry.receive_millis);\n\t\tsqlite3_bind_text(insert_statement,   5, log_entry.loc_file.c_str(), log_entry.loc_file.size(), 0);\n\t\tsqlite3_bind_int(insert_statement,    6, log_entry.loc_line);\n\t\tsqlite3_bind_text(insert_statement,   7, log_entry.loc_method.c_str(), log_entry.loc_method.size(), 0);\n\t\tsqlite3_bind_text(insert_statement,   8, log_entry.type.c_str(),    log_entry.type.size(), 0);\n\t\tsqlite3_bind_text(insert_statement,   9, log_entry.message.c_str(), log_entry.message.size(), 0);\n\t\tsqlite3_bind_int(insert_statement,   10, log_entry.server_status);\n\t\tsqlite3_bind_text(insert_statement,  11, log_entry.session_uuid.c_str(), log_entry.session_uuid.size(), 0);\t\t\n\t\tsqlite3_bind_int(insert_statement,   12, log_entry.create_timezone);\n\n\t\tsqlite3_step(insert_statement);\n\n\t\tlog_entry.log_id = sqlite3_last_insert_rowid(db);\n\t\tsqlite3_reset(insert_statement);\n\n\t\treturn true;\n\t\t}\n\telse {\n\t\tthrow std::logic_error(\"Failed to insert log entry\");\n\t\t}\n\t}\n\nbool Snoop::store_auth_attempt_entry(int user_id, int ticket_id, int valid, std::string msg)\n\t{\n\tstd::lock_guard<std::recursive_mutex> lock(sqlite_mutex);\n\n\tsqlite3_stmt *statement=0;\n\tint res = sqlite3_prepare(auth_db, \"insert into auth_attempts (time_millis, user_id, ticket_id, success, msg) \"\n\t\t\t\t\t\t\t\t\t  \"values (?, ?, ?, ?, ?)\",\n\t\t\t\t\t\t\t\t\t  -1, &statement, NULL);\n\n\tauto duration =  std::chrono::system_clock::now().time_since_epoch();\n\tuint64_t time_millis = std::chrono::duration_cast<std::chrono::milliseconds>(duration).count();\n\t\n\tif(res==SQLITE_OK) {\n\t\tsqlite3_bind_int64(statement,  1, time_millis);\n\t\tsqlite3_bind_int(statement,    2, user_id);\n\t\tsqlite3_bind_int(statement,    3, ticket_id);\n\t\tsqlite3_bind_int(statement,    4, valid);\n\t\tsqlite3_bind_text(statement,   5, msg.c_str(), msg.size(), 0);\t\t\n\t\t\n\t\tsqlite3_step(statement);\n\t\tsqlite3_finalize(statement);\n\n\t\treturn true;\n\t\t}\n\telse {\n\t\tthrow std::logic_error(\"Failed to prepare insertion for auth_attempts\");\n\t\t}\n\t}\n\nbool Snoop::store_payload_entry(Snoop::PayLoad& payload)\n\t{\n\tassert(payload_db!=0);\n\t\n\tstd::lock_guard<std::recursive_mutex> lock(sqlite_mutex);\n\n\t// Payload can be large, so we always first check if we have this entry already.\n\tsqlite3_stmt *testq=0;\n\tint testq_res = sqlite3_prepare(payload_db, \"select count(*) from payload where client_payload_id=? and id=? and client_payload_id!=-1\", -1, &testq, NULL);\n\tif(testq_res!=SQLITE_OK) \n\t\tthrow std::logic_error(\"Snoop::store_payload_entry_without_lock: failed to test for row presence\");\n\t\n\tsqlite3_bind_int64(testq, 1, payload.client_payload_id);\n\tsqlite3_bind_int64(testq, 2, payload.id);\n\tsqlite3_step(testq);\n\tint64_t num = sqlite3_column_int64(testq, 0);\n\tsqlite3_finalize(testq);\n\tif(num>0) {\n\t\tSNOOPDEBUG( std::cerr << \"Already have payload with client_payload_id=\" << payload.client_payload_id << \" and id=\" << payload.id << std::endl; );\n\t  return false;\n\t}\n\t\n\t// Need to store this entry.\n\n\tSNOOPDEBUG( std::cerr << \"Storing payload entry\" << std::endl; );\n\tint res=SQLITE_OK;\n\tif(payload_insert_statement==0) {\n\t\tres=sqlite3_prepare_v2(payload_db, \"insert into payload \"\n\t\t\t\t\t\t\t\t\t  \"(client_payload_id, id, create_millis, receive_millis, payload, server_status, create_timezone) \"\n\t\t\t\t\t\t\t\t\t  \"values (?, ?, ?, ?, ?, ?, ?)\",\n\t\t\t\t\t\t\t\t\t  -1, &payload_insert_statement, NULL);\n\t\t}\n\n\tif(res==SQLITE_OK ) {\n\t\tsqlite3_bind_int(payload_insert_statement,    1, payload.client_payload_id);\n\t\tsqlite3_bind_int(payload_insert_statement,    2, payload.id);\n\t\tsqlite3_bind_int64(payload_insert_statement,  3, payload.create_millis);\n\t\tsqlite3_bind_int64(payload_insert_statement,  4, payload.receive_millis);\n\t\tsqlite3_bind_text(payload_insert_statement,   5, payload.payload.c_str(), payload.payload.size(), 0);\n\t\tsqlite3_bind_int(payload_insert_statement,    6, payload.server_status);\n\t\tsqlite3_bind_int(payload_insert_statement,    7, payload.create_timezone);\t\t\n\n\t\tsqlite3_step(payload_insert_statement);\n\n\t\tpayload.payload_id = sqlite3_last_insert_rowid(db);\n\t\tsqlite3_reset(payload_insert_statement);\n\n\t\treturn true;\n\t\t}\n\telse {\n\t\tthrow std::logic_error(\"Failed to insert payload entry\");\n\t\t}\n\n\t}\n\nvoid Snoop::start_websocket_client()\n\t{\n\tSNOOPDEBUG( std::cerr << \"Snoop: attempting open\" << std::endl; );\n\t{ \tstd::unique_lock<std::mutex> lock(connection_mutex);\n\t\tconnection_attempt_failed=false;\n\t\t//std::cerr << \"Snoop: attempting open\" << std::endl;\n\t\t}\n\tSNOOPDEBUG( std::cerr << \"Snoop: got connection_mutex\" << std::endl; );\n\n//\twsclient.start_perpetual();\n\n\t// Start I/O thread. All actual connection work runs there,\n\t// and is also re-started there on connection failure/loss.\n\twsclient_thread=std::thread([this]{\n\t     io_thread_run();\n        SNOOPDEBUG( std::cerr << \"Snoop: client stopped running, thread will end\" << std::endl; );\n    });\n\t}\n\nvoid Snoop::try_connect()\n   {\n\t// This code runs in the separate thread which handles I/O.\n\n\twsclient.set_connect_handler(std::bind(&Snoop::on_client_open,    this));\n\twsclient.set_fail_handler(std::bind(&Snoop::on_client_fail,       this, std::placeholders::_1));\n\twsclient.set_close_handler(std::bind(&Snoop::on_client_close,     this));\n\twsclient.set_message_handler(std::bind(&Snoop::on_client_message, this, std::placeholders::_1));\n\n\tstd::string uri = server_;\n\tSNOOPDEBUG( std::cerr << \"Snoop: uri = \" << uri << std::endl; );\n\n\t// Attempt the connection. Failure is reported on the `on_fail` handler.\n\twsclient.connect(uri);\n\n\t// FIXME: we need to retry the connection, and handle when the connection\n\t// is down!!!\n   }\n\nvoid Snoop::io_thread_run()\n   {\n\t// This code runs in the separate thread which handles I/O.\n\n\tSNOOPDEBUG( std::cerr << \"Snoop: I/O thread starting.\" << std::endl; );\n\n\ttry_connect();\n   wsclient.run();\n\n   SNOOPDEBUG( std::cerr << \"Snoop: I/O thread up and running.\" << std::endl; );\n   }\n\nvoid Snoop::sync_with_server(bool from_wsthread)\n\t{\n\tassert(server_.size()>0);\n\n\tif(!from_wsthread)\n\t\tif(!connection_is_open) \n\t\t\treturn;\n\n\tsync_runs_with_server(from_wsthread);\n\tsync_logs_with_server(from_wsthread);\n\tsync_payloads_with_server(from_wsthread);\t\n\t}\n\nvoid Snoop::sync_runs_with_server(bool from_wsthread)\n\t{\n\tif(!from_wsthread)\n\t\tif(!connection_is_open) \n\t\t\treturn;\n\n\tstd::lock_guard<std::recursive_mutex> lock(sqlite_mutex);\n\n\t// Create a JSON text with all locally stored entries which have\n\t// a server_status field negative or zero.\n\n\tsqlite3_stmt *statement=0;\n\tstd::ostringstream ssc;\n\tstd::ostringstream pack;\n\tpack << \"{ \\\"run\\\": [\";\n\tssc << \"select id, uuid, create_millis, receive_millis, pid, ip_address, machine_id, app_name, app_version, user_id, server_status, create_timezone \"\n\t\t << \"from runs where server_status=0\";\n\n\tint sres = sqlite3_prepare(db, ssc.str().c_str(), -1, &statement, NULL);\n\tif(sres==SQLITE_OK) {\n\t\tbool first=true;\n\t\tbool go=true;\n\t\twhile(go) {\n\t\t\tint ret = sqlite3_step(statement);\n\t\t\tswitch(ret) {\n\t\t\t\tcase SQLITE_BUSY: \n\t\t\t\t\tthrow std::logic_error(\"Unexpected SQLITE_BUSY in sync_runs_with_server\");\n\t\t\t\t\tbreak;\n\t\t\t\tcase SQLITE_ROW: {\n\t\t\t\t\tSnoop::AppEntry ae;\n\t\t\t\t\t// FIXME: isolate this in a separate function so we can fetch individual records more easily\n\t\t\t\t\tae.id               = sqlite3_column_int(statement, 0);\n\t\t\t\t\tae.uuid             = safestring(sqlite3_column_text(statement, 1));\n\t\t\t\t\tae.create_millis    = sqlite3_column_int64(statement, 2);\n\t\t\t\t\tae.receive_millis   = sqlite3_column_int64(statement, 3);\n\t\t\t\t\tae.pid              = sqlite3_column_int(statement, 4);\n\t\t\t\t\tae.ip_address       = safestring(sqlite3_column_text(statement, 5));\n\t\t\t\t\tae.machine_id       = safestring(sqlite3_column_text(statement, 6));\n\t\t\t\t\tae.app_name         = safestring(sqlite3_column_text(statement, 7));\n\t\t\t\t\tae.app_version      = safestring(sqlite3_column_text(statement, 8));\n\t\t\t\t\tae.user_id          = safestring(sqlite3_column_text(statement, 9));\n\t\t\t\t\tae.server_status    = sqlite3_column_int(statement, 10);\n\t\t\t\t\tae.create_timezone  = sqlite3_column_int(statement, 11);\n\t\t\t\t\tif(!first) pack << \", \\n\";\n\t\t\t\t\telse       first=false;\n\t\t\t\t\tpack << ae.to_json(false);\n\t\t\t\t\tbreak;\n\t\t\t\t\t}\n\t\t\t\tcase SQLITE_DONE: {\n\t\t\t\t\tgo=false;\n\t\t\t\t\tbreak;\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t}\n\t\t}\n\tpack << \"] }\";\n\tsqlite3_finalize(statement);\n\n\t// Before we upload, decrease the server_status flag of all these\n\t// rows to indicate that we have started an attempt to get the info\n\t// to the server.\n\n\tssc.str(\"\");\n\tssc << \"update runs set server_status=server_status-1 where server_status=0\";\n\tsres = sqlite3_prepare(db, ssc.str().c_str(), -1, &statement, NULL);\n\tif(sres==SQLITE_OK) {\n\t\tsqlite3_step(statement);\n\t\tsqlite3_finalize(statement);\n\t\t}\n\telse {\n\t\tsqlite3_finalize(statement);\n\t\treturn;\n\t\t}\n\n\t// Upload to the server.\n   SNOOPDEBUG( std::cerr << \"Snoop::sync_logs_with_server: \" << pack.str() << std::endl; )\n\twsclient.send(pack.str());\n\t}\n\nvoid Snoop::sync_logs_with_server(bool from_wsthread)\n\t{\n\tif(!from_wsthread)\n\t\tif(!connection_is_open) \n\t\t\treturn;\n\n\tstd::lock_guard<std::recursive_mutex> lock(sqlite_mutex);\n\n\t// Create a JSON text with all locally stored entries which have\n\t// a server_status field negative or zero.\n\n\tsqlite3_stmt *statement=0;\n\tstd::ostringstream ssc;\n\tstd::ostringstream pack;\n\tpack << \"{ \\\"log\\\": [\";\n\tssc << \"select log_id, client_log_id, id, create_millis, loc_file, loc_line, loc_method, type, message, server_status, session_uuid, create_timezone \"\n\t\t << \"from logs where server_status=0\";\n\tif(local_types.size()>0) {\n\t\tssc << \" and type not in (\";\n\t\tbool first=true;\n\t\tfor(const auto& lt: local_types) {\n\t\t\tif(first) first=false;\n\t\t\telse      ssc << \", \";\n\t\t\t// FIXME: sql injection!\n\t\t\tssc << \"'\" << lt << \"'\";\n\t\t\t}\n\t\tssc << \")\";\n\t\t}\n\n\tint sres = sqlite3_prepare(db, ssc.str().c_str(), -1, &statement, NULL);\n\tif(sres==SQLITE_OK) {\n\t\tbool first=true;\n\t\tbool go=true;\n\t\twhile(go) {\n\t\t\tint ret = sqlite3_step(statement);\n\t\t\tswitch(ret) {\n\t\t\t\tcase SQLITE_BUSY: \n\t\t\t\t\tthrow std::logic_error(\"Unexpected SQLITE_BUSY in sync_runs_with_server\");\n\t\t\t\t\tbreak;\n\t\t\t\tcase SQLITE_ROW: {\n\t\t\t\t\tSnoop::LogEntry le;\n\t\t\t\t\tle.log_id           = sqlite3_column_int(statement, 0);\n\t\t\t\t\tle.client_log_id    = sqlite3_column_int(statement, 1);\n\t\t\t\t\tle.id               = sqlite3_column_int(statement, 2);\n\t\t\t\t\tle.uuid             = this_app_.uuid; // FIXME: this is wrong, we may still have log entries from a previous run!\n\t\t\t\t\t// See 'sync_payload_with_server' in Snoop.java for the query to handle this properly.\n\t\t\t\t\tle.create_millis    = sqlite3_column_int64(statement, 3);\n\t\t\t\t\tle.loc_file         = safestring(sqlite3_column_text(statement, 4));\n\t\t\t\t\tle.loc_line         = sqlite3_column_int(statement, 5);\n\t\t\t\t\tle.loc_method       = safestring(sqlite3_column_text(statement, 6));\n\t\t\t\t\tle.type             = safestring(sqlite3_column_text(statement, 7));\n\t\t\t\t\tle.message          = safestring(sqlite3_column_text(statement, 8));\n\t\t\t\t\tle.server_status    = sqlite3_column_int(statement, 9);\n\t\t\t\t\tle.session_uuid     = safestring(sqlite3_column_text(statement, 10));\n\t\t\t\t\tle.create_timezone  = sqlite3_column_int(statement, 11);\n\t\t\t\t\tif(!first) pack << \", \\n\";\n\t\t\t\t\telse       first=false;\n\t\t\t\t\tpack << le.to_json(false);\n\t\t\t\t\tbreak;\n\t\t\t\t\t}\n\t\t\t\tcase SQLITE_DONE: {\n\t\t\t\t\tgo=false;\n\t\t\t\t\tbreak;\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t}\n\t\t}\n\tpack << \"] }\";\n\tsqlite3_finalize(statement);\n\n\t// Before we upload, decrease the server_status flag of all these\n\t// rows to indicate that we have started an attempt to get the info\n\t// to the server.\n\n\tssc.str(\"\");\n\tssc << \"update logs set server_status=server_status-1 where server_status=0\";\n\tsres = sqlite3_prepare(db, ssc.str().c_str(), -1, &statement, NULL);\n\tif(sres==SQLITE_OK) {\n\t\tsqlite3_step(statement);\n\t\tsqlite3_finalize(statement);\n\t\t}\n\telse {\n\t\tsqlite3_finalize(statement);\n\t\treturn;\n\t\t}\n\n\t// Upload to the server.\n   SNOOPDEBUG( std::cerr << \"Snoop::sync_logs_with_server: \" << pack.str() << std::endl; )\n\twsclient.send(pack.str());\n\t}\n\nbool Snoop::is_connected() const\n   {\n   return connection_is_open;\n   }\n\nvoid Snoop::sync_payloads_with_server(bool from_wsthread)\n\t{\n\tif(!from_wsthread)\n\t\tif(!connection_is_open) \n\t\t\treturn;\n\n\tstd::lock_guard<std::recursive_mutex> lock(sqlite_mutex);\n\n\t// Create a JSON text with all locally stored entries which have\n\t// a server_status field negative or zero.\n\n\t// std::cerr << \"Syncing payloads\" << std::endl;\n\t\n\tsqlite3_stmt *statement=0;\n\tstd::ostringstream ssc;\n\tstd::ostringstream pack;\n\tpack << \"{ \\\"payload\\\": [\";\n\tssc << \"select payload_id, client_payload_id, id, create_millis, payload, server_status, create_timezone \"\n\t\t << \"from payload where server_status=0\";\n\n\tint sres = sqlite3_prepare(payload_db, ssc.str().c_str(), -1, &statement, NULL);\n\tif(sres==SQLITE_OK) {\n\t\tbool first=true;\n\t\tbool go=true;\n\t\twhile(go) {\n\t\t\tint ret = sqlite3_step(statement);\n\t\t\tswitch(ret) {\n\t\t\t\tcase SQLITE_BUSY: \n\t\t\t\t\tthrow std::logic_error(\"Unexpected SQLITE_BUSY in sync_payloads_with_server\");\n\t\t\t\t\tbreak;\n\t\t\t\tcase SQLITE_ROW: {\n\t\t\t\t\tSnoop::PayLoad payload;\n\t\t\t\t\tpayload.uuid             = this_app_.uuid; // FIXME: this is wrong, we may still have log entries from a previous run!\n\t\t\t\t\tpayload.payload_id       = sqlite3_column_int(statement,   0);\n\t\t\t\t\tpayload.client_payload_id= sqlite3_column_int(statement,   1);\n\t\t\t\t\tpayload.id               = sqlite3_column_int(statement,   2);\n\t\t\t\t\tpayload.create_millis    = sqlite3_column_int64(statement, 3);\n\t\t\t\t\tpayload.payload          = safestring(sqlite3_column_text(statement, 4));\n\t\t\t\t\tpayload.server_status    = sqlite3_column_int(statement,   5);\n\t\t\t\t\tpayload.create_timezone  = sqlite3_column_int(statement,   6);\t\t\t\t\t\n\t\t\t\t\tif(!first) pack << \", \\n\";\n\t\t\t\t\telse       first=false;\n\t\t\t\t\tpack << payload.to_json(false);\n\t\t\t\t\tbreak;\n\t\t\t\t\t}\n\t\t\t\tcase SQLITE_DONE: {\n\t\t\t\t\tgo=false;\n\t\t\t\t\tbreak;\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t}\n\t\t}\n\telse {\n\t\tthrow std::logic_error(\"Failed to prepare statement for payload select\");\n\t\t}\n\tpack << \"] }\";\n\tsqlite3_finalize(statement);\n\n\t// Before we upload, decrease the server_status flag of all these\n\t// rows to indicate that we have started an attempt to get the info\n\t// to the server.\n\n\tssc.str(\"\");\n\tssc << \"update payload set server_status=server_status-1 where server_status=0\";\n\tsres = sqlite3_prepare(payload_db, ssc.str().c_str(), -1, &statement, NULL);\n\tif(sres==SQLITE_OK) {\n\t\tsqlite3_step(statement);\n\t\tsqlite3_finalize(statement);\n\t\t}\n\telse {\n\t\tsqlite3_finalize(statement);\n\t\treturn;\n\t\t}\n\n\t// std::cerr << \"Syncing payloads almost done\" << std::endl;\n\n\n   // Upload to the server.\n\n\twsclient.send(pack.str());\n\t}\n\nstd::vector<Snoop::AppEntry> Snoop::get_app_registrations(std::string uuid_filter)\n\t{\n\tStopwatch sw;\n\tsw.start();\n\t\n\tstd::lock_guard<std::recursive_mutex> lock(sqlite_mutex);\n\n\tsqlite3_stmt *statement=0;\n\n\tstd::ostringstream ssc;\n\tssc << \"select id, uuid, create_millis, receive_millis, pid, ip_address, machine_id, \"\n\t\t\"app_name, app_version, user_id, server_status, create_timezone from runs\";\n\tif(uuid_filter.size()>0) \n\t\tssc << \" where uuid=?\";\n\n\tint sres = sqlite3_prepare(db, ssc.str().c_str(), -1, &statement, NULL);\n\tif(uuid_filter.size()>0) \n\t\tsqlite3_bind_text(statement, 1, uuid_filter.c_str(), uuid_filter.size(), 0);\n\n\tstd::vector<Snoop::AppEntry> entries;\n\tif(sres==SQLITE_OK) {\n\t\tbool go=true;\n\t\twhile(go) {\n\t\t\tint ret = sqlite3_step(statement);\n\t\t\tswitch(ret) {\n\t\t\t\tcase SQLITE_ROW: {\n\t\t\t\t\tSnoop::AppEntry ae;\n\t\t\t\t\tae.id               = sqlite3_column_int(statement, 0);\n\t\t\t\t\tae.uuid             = safestring(sqlite3_column_text(statement, 1));\n\t\t\t\t\tae.create_millis    = sqlite3_column_int64(statement, 2);\n\t\t\t\t\tae.receive_millis   = sqlite3_column_int64(statement, 3);\n\t\t\t\t\tae.pid              = sqlite3_column_int(statement, 4);\n\t\t\t\t\tae.ip_address       = safestring(sqlite3_column_text(statement, 5));\n\t\t\t\t\tae.machine_id       = safestring(sqlite3_column_text(statement, 6));\n\t\t\t\t\tae.app_name         = safestring(sqlite3_column_text(statement, 7));\n\t\t\t\t\tae.app_version      = safestring(sqlite3_column_text(statement, 8));\n\t\t\t\t\tae.user_id          = safestring(sqlite3_column_text(statement, 9));\n\t\t\t\t\tae.server_status    = sqlite3_column_int(statement, 10);\n\t\t\t\t\tae.create_timezone  = sqlite3_column_int(statement, 11);\n\t\t\t\t\tentries.push_back(ae);\n\t\t\t\t\tbreak;\n\t\t\t\t\t}\n\t\t\t\tcase SQLITE_DONE: {\n\t\t\t\t\tgo=false;\n\t\t\t\t\tbreak;\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t}\n\t\t}\n\telse throw std::logic_error(\"Failed to prepare statement for get_app_registrations\");\n\n\tsqlite3_finalize(statement);\n\n\tsw.stop();\n\t// This is now fast because we have added an index on `uuid`.\n   //\tstd::cerr << \"get_app_registrations: \" << uuid_filter << sw << std::endl;\n\t\n\treturn entries;\n\t}\n\nvoid Snoop::on_client_open()\n\t{\n\tSNOOPDEBUG( std::cerr << \"Snoop: connection to \" << server_  << \" open \" << std::this_thread::get_id() << std::endl; );\n\tsync_with_server(true);\n\tstd::unique_lock<std::mutex> lock(connection_mutex);\n\tconnection_is_open=true;\n\tconnection_attempt_failed=false;\n\tconnection_cv.notify_all();\n\tSNOOPDEBUG( std::cerr << \"Snoop: synced after open, ready to roll\" << std::endl; );\n\t}\n\nvoid Snoop::on_client_fail(const boost::beast::error_code& ec)\n\t{\n\t// This runs in the I/O thread.\n\tstd::string error_reason = ec.message();\n\t\n\tSNOOPDEBUG( std::cerr << \"Snoop: connection failed: \" << error_reason << std::endl;\t);\n\t// Clients may be waiting for the connection to open, but we may\n\t// never get to that stage. Signal them to move on.\n\tstd::unique_lock<std::mutex> lock(connection_mutex);\n\tconnection_attempt_failed=true;\n\tconnection_cv.notify_all();\n\n\t// Run the callback\n\tbool retry=true;\n\tif(error_callback) {\n\t\tretry = error_callback(error_reason);\n\t\tif(authentication_callback)\n\t\t\tauthentication_callback(\"\", false);\n\t\t}\n\t\n\t// Attempt to re-open.\n\tif(retry && this_app_.app_name!=\"SnoopServer\") {\n\t  SNOOPDEBUG( std::cerr << \"Snoop: sleeping a little before attempting reconnect\" << std::endl;\t);\n\t  sleep(3);\n\t  SNOOPDEBUG( std::cerr << \"Snoop: attempting to re-open connection\" << std::endl; );\n\t  try_connect();\n\t  }\n\t}\n\nvoid Snoop::on_client_close()\n\t{\n\t// Clients may be waiting for the connection to open, but we may\n\t// never get to that stage. Signal them to move on.\n\t  {\n\t\t std::unique_lock<std::mutex> lock(connection_mutex);\n\t\t connection_is_open=false;\n\t\t connection_attempt_failed=true;\n\t\t connection_cv.notify_all();\n\t\t SNOOPDEBUG( std::cerr << \"Snoop: connection closed\" << std::endl; );\n\t  }\n\n\t// Attempt to re-open.\n\tif(this_app_.app_name!=\"SnoopServer\") {\n\t  SNOOPDEBUG( std::cerr << \"Snoop: attempting to re-open connection\" << std::endl; );\n\t  try_connect();\n\t  }\n\t}\n\nvoid Snoop::on_client_message(const std::string& msg)\n\t{\n\tnlohmann::json root;\n\n\t// std::cerr << msg->get_payload() << std::endl;\n\ttry {\n\t\troot=nlohmann::json::parse(msg);\n\t\t}\n\tcatch(nlohmann::json::exception& ex) {\n\t\tSNOOPDEBUG( std::cerr << \"Snoop::on_client_message: Cannot parse LogEntry from JSON: \" << ex.what() << std::endl; );\n\t\treturn;\n\t\t}\n\t\n\t// Determine what type of message this is, and take corresponding action.\n\n\tstd::lock_guard<std::recursive_mutex> lock(sqlite_mutex);\n\n\ttry {\n\t\t\n\t\tif(root.count(\"log_stored\")>0) {\n\t\t\t// Mark all log entries for which we have received confirmation from the \n\t\t\t// server that they have been stored with 'server_status=1', to prevent\n\t\t\t// us from re-uploading them again. \n\n\t\t\tSNOOPDEBUG( std::cerr << \"server ack'ed storing log entries \" << root[\"log_stored\"] << std::endl; );\n\t\t\t\n\t\t\tsqlite3_exec(db, \"BEGIN TRANSACTION\", NULL, NULL, NULL);\n\n\t\t\tsqlite3_stmt *statement=0;\n\t\t\tstd::ostringstream ssc;\n\t\t\tssc << \"update logs set server_status=1 where log_id=?\";\n\t\t\tint ret = sqlite3_prepare(db, ssc.str().c_str(), -1, &statement, NULL);\n\t\t\tif(ret!=SQLITE_OK) \n\t\t\t\tthrow std::logic_error(\"Failed to prepare statement for on_client_message\");\n\t\t\n\t\t\tconst auto& entries=root[\"log_stored\"];\n\t\t\tfor(auto entry: entries) {\n\t\t\t\tsqlite3_bind_int(statement, 1, entry.get<int>() );\n\t\t\t\tsqlite3_step(statement);\n\t\t\t\tsqlite3_reset(statement);\n\t\t\t\t}\n\t\t\tsqlite3_finalize(statement);\n\n\t\t\tsqlite3_exec(db, \"END TRANSACTION\", NULL, NULL, NULL);\n\t\t\t}\n\n\t\tif(root.count(\"app_stored\")>0) {\n\t\t\t// Mark all app entries for which we have received confirmation from the \n\t\t\t// server that they have been stored with 'server_status=1', to prevent\n\t\t\t// us from re-uploading them again. \n\n\t\t\tSNOOPDEBUG( std::cerr << \"server ack'ed storing run entries \" << root[\"app_stored\"] << std::endl; );\n\n\t\t\tsqlite3_exec(db, \"BEGIN TRANSACTION\", NULL, NULL, NULL);\n\n\t\t\tsqlite3_stmt *statement=0;\n\t\t\tstd::ostringstream ssc;\n\t\t\tssc << \"update runs set server_status=1 where id=?\";\n\t\t\tint ret = sqlite3_prepare(db, ssc.str().c_str(), -1, &statement, NULL);\n\t\t\tif(ret!=SQLITE_OK) \n\t\t\t\tthrow std::logic_error(\"Failed to prepare statement for on_client_message\");\n\t\t\n\t\t\tconst auto& entries=root[\"app_stored\"];\n\t\t\tfor(auto entry: entries) {\n\t\t\t\tsqlite3_bind_int(statement, 1, entry.get<int>());\n\t\t\t\tsqlite3_step(statement);\n\t\t\t\tsqlite3_reset(statement);\n\t\t\t\t}\n\t\t\tsqlite3_finalize(statement);\n\n\t\t\tsqlite3_exec(db, \"END TRANSACTION\", NULL, NULL, NULL);\n\t\t\t}\n\t\n\t\tif(root.count(\"payload_stored\")>0) {\n\t\t\t// Mark all payload entries for which we have received confirmation from the \n\t\t\t// server that they have been stored with 'server_status=1', to prevent\n\t\t\t// us from re-uploading them again. \n\n\t\t\tsqlite3_exec(payload_db, \"BEGIN TRANSACTION\", NULL, NULL, NULL);\n\n\t\t\tsqlite3_stmt *statement=0;\n\t\t\tstd::ostringstream ssc;\n\t\t\tssc << \"update payload set server_status=1 where id=?\";\n\t\t\tint ret = sqlite3_prepare(payload_db, ssc.str().c_str(), -1, &statement, NULL);\n\t\t\tif(ret!=SQLITE_OK) \n\t\t\t\tthrow std::logic_error(\"Failed to prepare statement for on_client_message\");\n\t\t\n\t\t\tconst auto& entries=root[\"payload_stored\"];\n\t\t\tfor(auto entry: entries) {\n\t\t\t\tsqlite3_bind_int(statement, 1, entry.get<int>());\n\t\t\t\tsqlite3_step(statement);\n\t\t\t\tsqlite3_reset(statement);\n\t\t\t\t}\n\t\t\tsqlite3_finalize(statement);\n\n\t\t\tsqlite3_exec(payload_db, \"END TRANSACTION\", NULL, NULL, NULL);\n\t\t\t}\n\t\n\t\tif(root.count(\"authenticate\")>0) {\n\t\t\tSNOOPDEBUG( std::cerr << \"Received authentication response message from server.\" << std::endl; );\n\t\t\tconst auto& auth=root[\"authenticate\"];\n\t\t\tstd::string ticket_uuid = auth.value(\"ticket_uuid\", \"\");\n\t\t\tbool valid              = auth.value(\"valid\", false);\n\t\t\tif(valid)\n\t\t\t\tset_local_ticket(ticket_uuid);\n\t\t\telse\n\t\t\t\tset_local_ticket(\"\");\n\t\t\tauthentication_callback(ticket_uuid, valid);\n\t\t\tauthentication_callback=nullptr;\n\t\t\t}\n\t\t}\n\tcatch(nlohmann::json::exception& ex) {\n\t\tSNOOPDEBUG( std::cerr << \"Discarding message, JSON malformed: \" << ex.what() << std::endl; );\n\t\t}\n\t}\n\n\nSnoop::~Snoop()\n   {\n\t// If a program runs for only a very short time, the connection to the logging \n\t// server may not be open yet when we reach this destructor. In that case,\n\t// we will want to wait for the connection to open, so that we can do a final\n\t// sync before we terminate.\n\n\t// However, if the connection was attempted but failed (e.g. no server), we\n\t// can skip all that.\n\n   // std::cerr << \"|\" << this_app_.app_name << \"|\" << std::endl;\n\tstd::unique_lock<std::mutex> lock(connection_mutex);\n\t// std::cerr << \"unlocked\" << std::endl;\n\t\n\tif(this_app_.app_name!=\"\" && this_app_.app_name!=\"SnoopServer\") {\n\t\tif(connection_is_open==false && connection_attempt_failed==false) {\n\t\t\tconnection_cv.wait(lock);\n\t\t\t}\n\t\t\n\t\tsync_with_server();\n\t\t\n\t\tif(db!=0) { // If the database is not open the wsclient won't be running either\n\t\t\twsclient.stop();\n\t\t\twsclient_thread.join();\n\t\t\t}\n\t\t}\n\n\tif(insert_statement!=0) {\n\t\tsqlite3_finalize(insert_statement);\n\t\t}\n\tif(id_for_uuid_statement!=0) {\n\t\tsqlite3_finalize(id_for_uuid_statement);\n\t\t}\n\tif(db!=0) {\n\t\tsqlite3_close(db);\n\t\tdb=0;\n\t\t}\n\tif(payload_db!=0) {\n\t\tsqlite3_close(payload_db);\n\t\tpayload_db=0;\n\t\t}\n   }\n\nvoid Snoop::set_local_type(const std::string& t)\n   {\n   local_types.insert(t);\n   }\n\nSnoop& Snoop::operator()(const std::string& type, std::string fl, int loc, std::string method) \n\t{\n\tstd::lock_guard<std::recursive_mutex> lock(call_mutex);\n\n\tassert(this_app_.app_name.size()>0);\n\n\tif(type!=\"\") \n\t\tthis_log_.type=type;\n\tthis_log_.loc_file=fl;\n\tthis_log_.loc_line=loc;\n\tthis_log_.loc_method=method;\n\n\treturn *this;\n\t}\n\nSnoop& Snoop::operator<<(const Flush&)\n   {\n    // SNOOPDEBUG(std::cerr << \"================= Flush\" << std::endl;)\n\tstd::lock_guard<std::recursive_mutex> lock(call_mutex);\n       \n\tassert(this_app_.app_name.size()>0);\n\n\t// Fill in the remaining fields of the LogEntry to be stored/sent.\n\n\tauto duration =  std::chrono::system_clock::now().time_since_epoch();\n\tauto millis   = std::chrono::duration_cast<std::chrono::milliseconds>(duration).count();\n\tthis_log_.create_millis = millis;\n\tthis_log_.create_timezone = local_utc_offset_minutes();\n\tthis_log_.message       = out_.str();\n\tthis_log_.server_status = 0;\n\tthis_log_.session_uuid  = session_uuid_;\n\n\tstore_log_entry(this_log_, false);\n\tif(sync_immediately_)\n\t\tsync_logs_with_server();\n\n   out_.str(\"\");\n\n\tthis_log_.loc_file=\"\";\n\tthis_log_.loc_line=-1;\n\tthis_log_.loc_method=\"\";\n\tthis_log_.type=\"\";\n\tthis_log_.message=\"\";\n\n\treturn *this;\n   }\n\nSnoop& Snoop::payload(const std::vector<char>& data)\n   {\n\tstd::lock_guard<std::recursive_mutex> lock(call_mutex);\n\n\tassert(this_app_.app_name.size()>0);\n\n\t// Fill in the remaining fields of the PayLoad to be stored/sent.\n\n\tSnoop::PayLoad pl(data);\n\tauto duration =  std::chrono::system_clock::now().time_since_epoch();\n\tauto millis   = std::chrono::duration_cast<std::chrono::milliseconds>(duration).count();\n\tpl.create_millis   = millis;\n\tpl.create_timezone = local_utc_offset_minutes();\n\tpl.server_status   = 0;\n\n\tstore_payload_entry(pl);\n\tsync_payloads_with_server();\n\n\treturn *this;\n   }\n\nSnoop::LogEntry::LogEntry()\n\t: log_id(0), client_log_id(0), id(0), create_millis(0), receive_millis(0), loc_line(0), server_status(0), create_timezone(-1)\n\t{\n\t}\n\nSnoop::LogEntry::LogEntry(int log_id_, int client_log_id_, int c1, const std::string& c1b,\n\t\t\t\t\t\t\t\t  uint64_t c2, uint64_t c2b, const std::string& c3, int c4, const std::string& c5,\n\t\t\t\t\t\t\t\t  const std::string& c6, const std::string& c7, int c8, const std::string& c9, int create_timezone_)\n\t: log_id(log_id_), client_log_id(client_log_id_), id(c1), uuid(c1b), \n\t  create_millis(c2), receive_millis(c2b), loc_file(c3), loc_line(c4), loc_method(c5), \n\t  type(c6), message(c7), server_status(c8), session_uuid(c9), create_timezone(create_timezone_)\n\t{\n\t}\n\nstd::string Snoop::LogEntry::to_json(bool human_readable) const\n\t{\n\tnlohmann::json json;\n\t\n\tjson[\"log_id\"]=log_id;\n\tjson[\"client_log_id\"]=client_log_id;\n\tjson[\"id\"]=id;\n\tjson[\"uuid\"]=uuid;\n\tif(human_readable) {\t\n\t\ttime_t tt = std::chrono::system_clock::to_time_t(u64_to_time(create_millis));\n\t\ttm utc_tm = *localtime(&tt);\n\t\tstd::ostringstream str;\n\t\tstr << std::setfill('0') \n\t\t\t << std::setw(2) << utc_tm.tm_hour << \":\" \n\t\t\t << std::setw(2) << utc_tm.tm_min << \":\" \n\t\t\t << std::setw(2) << utc_tm.tm_sec;\n\t\tjson[\"time\"]=str.str();\n\t\tstr.str(\"\");\n\t\tstr << std::setw(2) << utc_tm.tm_mday << \"/\" \n\t\t\t << std::setw(2) << utc_tm.tm_mon+1 << \"/\" \n\t\t\t << std::setw(4) << utc_tm.tm_year+1900;\n\t\tjson[\"date\"]=str.str();\n\t\t}\n\tjson[\"create_millis\"]=create_millis;\n\tjson[\"create_timezone\"]=create_timezone;\n\tjson[\"receive_millis\"]=receive_millis;\n\tjson[\"loc_file\"]=loc_file;\n\tjson[\"loc_line\"]=loc_line;\n\tjson[\"loc_method\"]=loc_method;\n\tjson[\"type\"]=type;\n\tjson[\"message\"]=message;\n\tjson[\"server_status\"]=server_status;\n\tjson[\"session_uuid\"]=session_uuid;\n\n\tstd::ostringstream str;\n\tstr << json;\n\n//\tSNOOPDEBUG( std::cerr << \"Snoop::LogEntry::to_json: \" << str.str() << std::endl; )\n\t\n\treturn str.str();\n\t}\n\nSnoop::AppEntry::AppEntry()\n\t: id(0), create_millis(0), receive_millis(0), pid(0), server_status(0), connected(false), create_timezone(-1)\n\t{\n\t}\n\nSnoop::AppEntry::AppEntry(const std::string& uuid_, uint64_t create_millis_, uint64_t receive_millis_, uint64_t pid_, \n\t\t\t\t\t\t\t\t  const std::string& ip_address_, const std::string& machine_id_, \n\t\t\t\t\t\t\t\t  const std::string& app_name_,   const std::string& app_version_,\n\t\t\t\t\t\t\t\t  const std::string& user_id_,\n\t\t\t\t\t\t\t\t  int server_status_, int create_timezone_)\n\t: uuid(uuid_), create_millis(create_millis_), receive_millis(receive_millis_), pid(pid_), ip_address(ip_address_),\n\t  machine_id(machine_id_), app_name(app_name_), app_version(app_version_), \n\t  user_id(user_id_), server_status(server_status_), create_timezone(create_timezone_)\n\t{\n\t}\n\nstd::string Snoop::AppEntry::to_json(bool human_readable) const\n\t{\n\tstd::ostringstream str;\n\tstr << \"{ \\\"id\\\": \" << id  \n\t\t << \", \\\"uuid\\\": \\\"\" << uuid << \"\\\"\";\n\tif(human_readable) {\t\n\t\ttime_t tt = std::chrono::system_clock::to_time_t(u64_to_time(create_millis));\n\t\ttm utc_tm = *localtime(&tt);\n\t\tstr << \", \\\"time\\\": \\\"\" \n\t\t\t << std::setfill('0') \n\t\t\t << std::setw(2) << utc_tm.tm_hour << \":\" \n\t\t\t << std::setw(2) << utc_tm.tm_min << \":\" \n\t\t\t << std::setw(2) << utc_tm.tm_sec << \"\\\"\"\n\t\t\t << \", \\\"date\\\": \\\"\"\n\t\t\t << std::setw(2) << utc_tm.tm_mday << \"/\" \n\t\t\t << std::setw(2) << utc_tm.tm_mon+1 << \"/\" \n\t\t\t << std::setw(4) << utc_tm.tm_year+1900\n\t\t\t << \"\\\"\";\n\t\t}\n\tstr << \", \\\"create_millis\\\": \" << create_millis\n\t\t << \", \\\"create_timezone\\\": \" << create_timezone\n\t\t << \", \\\"receive_millis\\\": \" << receive_millis\n\t\t << \", \\\"pid\\\": \" << pid \n\t\t << \", \\\"ip_address\\\": \\\"\" << ip_address << \"\\\"\"\n\t\t << \", \\\"machine_id\\\": \\\"\" << machine_id << \"\\\"\"\n\t\t << \", \\\"app_name\\\": \\\"\" << app_name << \"\\\"\"\n\t\t << \", \\\"app_version\\\": \\\"\" << app_version << \"\\\"\"\n\t\t << \", \\\"user_id\\\": \\\"\" << user_id << \"\\\"\"\n\t\t << \", \\\"server_status\\\": \" << server_status\n\t\t << \", \\\"connected\\\": \" << connected\n\t\t << \"}\";\n\n\treturn str.str();\n\t}\n\nSnoop::PayLoad::PayLoad()\n\t{\n\tclient_payload_id=-1;\n\tauto duration =  std::chrono::system_clock::now().time_since_epoch();\n\treceive_millis   = std::chrono::duration_cast<std::chrono::milliseconds>(duration).count();\n\t}\n\nSnoop::PayLoad::PayLoad(const std::vector<char>& data)\n\t: PayLoad()\n\t{\n\tpayload=snoop_base64_encode(reinterpret_cast<const unsigned char*>(data.data()), data.size());\n\t}\n\nstd::string Snoop::PayLoad::to_json(bool) const\n\t{\n\tnlohmann::json json;\n\n\tjson[\"payload_id\"]=payload_id;\n\tjson[\"id\"]=id;\n\tjson[\"create_millis\"]=create_millis;\n\tjson[\"create_timezone\"]=create_timezone;\n\tjson[\"receive_millis\"]=receive_millis;\n\tjson[\"payload\"]=payload;\n\tjson[\"server_status\"]=server_status;\n\tjson[\"uuid\"]=uuid;\n\t\n\tstd::ostringstream str;\n\tstr << json;\n\n\treturn str.str();\n\t}\n\nvoid Snoop::LogEntry::from_json(const nlohmann::json& entry) \n\t{\n\t// std::cerr << \"logentry: \" << entry << std::endl;\n\n\tif(entry.count(\"log_id\")==0 ||\n\t\tentry.count(\"id\")==0 ||\n\t\tentry.count(\"uuid\")==0 ||\n\t\tentry.count(\"type\")==0 ||\n\t\tentry.count(\"message\")==0) {\n\t\tthrow ParseError(\"Incomplete log entry\");\n\t\t}\n\t\t\t\t\t\t\t\t\t\t\t\t\t  \n\ttry {\n\t\tlog_id          = entry[\"log_id\"].get<int>();\n\t\tid              = entry[\"id\"].get<int>();\n\t\tuuid            = entry[\"uuid\"].get<std::string>();\n\t\tif(entry.count(\"create_millis\")>0)\n\t\t\tcreate_millis   = entry[\"create_millis\"].get<uint64_t>();\n\t\tloc_file        = entry.value(\"loc_file\", \"\");\n\t\tloc_line        = entry.value(\"loc_line\", 0);\n\t\tloc_method      = entry.value(\"loc_method\", \"\");\n\t\ttype            = entry[\"type\"].get<std::string>();\n\t\tmessage         = entry.value(\"message\", \"\");\n\t\tserver_status   = entry.value(\"server_status\", 0);\n\t\tsession_uuid    = entry.value(\"session_uuid\", \"\");\n\t\tcreate_timezone = entry.value(\"create_timezone\", -1);\n\t\t}\n\tcatch(nlohmann::json::exception& ex) {\n\t\tSNOOPDEBUG( std::cerr << \"Snoop::LogEntry::from_json: \" << ex.what() << std::endl; );\t\t\n\t\t}\n\n\t// std::cerr << \"LogEntry parsed\" << std::endl;\n\t}\n\nvoid Snoop::AppEntry::from_json(const nlohmann::json& entry)\n\t{\n\t// std::cerr << entry.dump() << std::endl;\n\t\n\ttry {\n\t\tid              = entry[\"id\"].get<int>();\n\t\tuuid            = entry[\"uuid\"].get<std::string>();\n\t\tcreate_millis   = entry[\"create_millis\"].get<uint64_t>();\n\t\tif(entry.count(\"pid\")>0)\n\t\t\tpid             = entry[\"pid\"].get<uint64_t>();\n\t\tif(entry.count(\"ip_address\")>0) \n\t\t\tip_address      = entry[\"ip_address\"].get<std::string>();\n\t\t\n\t\tmachine_id      = entry[\"machine_id\"].get<std::string>();\n\t\tapp_name        = entry[\"app_name\"].get<std::string>();\n\t\tapp_version     = entry[\"app_version\"].get<std::string>();\n\t\tif(entry.count(\"user_id\")>0) \n\t\t\tuser_id         = entry[\"user_id\"].get<std::string>();\n\t\tif(entry.count(\"server_status\")>0)\n\t\t\tserver_status   = entry[\"server_status\"].get<int>();\n\t\t\n\t\tcreate_timezone = entry.value(\"create_timezone\", -1);\n\t\t}\n\tcatch(nlohmann::json::exception& ex) {\n\t\tSNOOPDEBUG( std::cerr << \"Snoop::AppEntry::from_json: \" << ex.what() << std::endl; );\t\t\n\t\t}\n\n\t// std::cerr << \"AppEntry parsed\" << std::endl;\n\t}\n\nvoid Snoop::PayLoad::from_json(const nlohmann::json& entry)\n\t{\n\ttry {\n\t\tpayload_id      = entry[\"payload_id\"].get<int>();\n\t\tid              = entry[\"id\"].get<int>();\n\t\tcreate_millis   = entry[\"create_millis\"].get<uint64_t>();\n\t\tpayload         = entry[\"payload\"].get<std::string>();\n\t\tserver_status   = entry[\"server_status\"].get<int>();\n\t\tcreate_timezone = entry.value(\"create_timezone\", -1);\n\t\t}\n\tcatch(nlohmann::json::exception& ex) {\n\t\tSNOOPDEBUG( std::cerr << \"Snoop::LogEntry::from_json: \" << ex.what() << std::endl; );\t\t\n\t\t}\n\t}\n\nbool Snoop::add_user(std::string user, std::string password, bool single)\n   {\n\tstd::lock_guard<std::recursive_mutex> lock(sqlite_mutex);\n\n\tassert(auth_db!=0);\n\n#ifdef ENCRYPT_PASSWORDS\n\tchar outbuf[SCRYPT_MCF_LEN+1];\n\t// std::cerr << SCRYPT_N << \", \" << SCRYPT_r << \", \" << SCRYPT_p << \", \" << SCRYPT_MCF_LEN << std::endl;\n   libscrypt_hash(outbuf, password.c_str(), SCRYPT_N, SCRYPT_r, SCRYPT_p);\n#else\n\tconst char *outbuf = password.c_str();\n#endif\n\t\n\t// If `single`, flush the database.\n\tif(single) {\n\t\tint res = sqlite3_exec(auth_db, \"delete from users\", NULL, NULL, NULL);\n\t\tif(res!=SQLITE_OK) {\n\t\t\tSNOOPDEBUG( std::cerr << \"Snoop::add_user: problem erasing users table.\" << std::endl; )\n\t\t\t}\n\t\t}\n\t\n\tsqlite3_stmt *statement=0;\n\tstd::ostringstream ss;\n\tss << \"insert into users (username, password) values (?,?)\";\n\tint res = sqlite3_prepare(auth_db, ss.str().c_str(), -1, &statement, NULL);\n\tassert(res==SQLITE_OK);\n\tsqlite3_bind_text(statement, 1, user.c_str(), user.size(), 0);\n\tsqlite3_bind_text(statement, 2, outbuf, strlen(outbuf), 0);\t\t\n\tres=sqlite3_step(statement);\n\tsqlite3_finalize(statement);\n\n\tif(res!=SQLITE_DONE) {\n\t\tSNOOPDEBUG( std::cerr << \"Snoop::add_user: error \" << sqlite3_errmsg(db) << std::endl; )\n\t\treturn false;\n\t\t}\n\t\n   return true;\n   }\n\nstd::string Snoop::local_user() const\n\t{\n\tstd::string name=\"\";\n\n\tsqlite3_stmt *statement=0;\n\tstd::ostringstream ss;\n\tint res = sqlite3_prepare(auth_db, \"select username from users where username!=\\\"\\\"\", -1, &statement, NULL);\n\tif(res!=SQLITE_OK)\n\t\treturn \"\";\n\t\n\tint ret = sqlite3_step(statement);\n\tif(ret==SQLITE_ROW) {\n\t\tname = safestring(sqlite3_column_text(statement, 0));\n\t\tSNOOPDEBUG( std::cerr << \"Snoop::init: localUser = \" << name << std::endl; );\t\t\n\t\t}\n\telse {\n\t\tSNOOPDEBUG( std::cerr << \"Snoop::init: no localUser set (yet)\" << std::endl; );\t\t\n\t\t}\n\t\n\tsqlite3_finalize(statement);\n\treturn name;\n\t}\n\n\nstatic const std::string base64_chars = \n             \"ABCDEFGHIJKLMNOPQRSTUVWXYZ\"\n             \"abcdefghijklmnopqrstuvwxyz\"\n             \"0123456789+/\";\n\n\nstatic inline bool is_base64(unsigned char c) {\n  return (isalnum(c) || (c == '+') || (c == '/'));\n}\n\nstd::string snoop_base64_encode(unsigned char const* bytes_to_encode, unsigned int in_len) {\n  std::string ret;\n  int i = 0;\n  int j = 0;\n  unsigned char char_array_3[3];\n  unsigned char char_array_4[4];\n\n  while (in_len--) {\n    char_array_3[i++] = *(bytes_to_encode++);\n    if (i == 3) {\n      char_array_4[0] = (char_array_3[0] & 0xfc) >> 2;\n      char_array_4[1] = ((char_array_3[0] & 0x03) << 4) + ((char_array_3[1] & 0xf0) >> 4);\n      char_array_4[2] = ((char_array_3[1] & 0x0f) << 2) + ((char_array_3[2] & 0xc0) >> 6);\n      char_array_4[3] = char_array_3[2] & 0x3f;\n\n      for(i = 0; (i <4) ; i++)\n        ret += base64_chars[char_array_4[i]];\n      i = 0;\n    }\n  }\n\n  if (i)\n  {\n    for(j = i; j < 3; j++)\n      char_array_3[j] = '\\0';\n\n    char_array_4[0] = (char_array_3[0] & 0xfc) >> 2;\n    char_array_4[1] = ((char_array_3[0] & 0x03) << 4) + ((char_array_3[1] & 0xf0) >> 4);\n    char_array_4[2] = ((char_array_3[1] & 0x0f) << 2) + ((char_array_3[2] & 0xc0) >> 6);\n    char_array_4[3] = char_array_3[2] & 0x3f;\n\n    for (j = 0; (j < i + 1); j++)\n      ret += base64_chars[char_array_4[j]];\n\n    while((i++ < 3))\n      ret += '=';\n\n  }\n\n  return ret;\n\n}\nstd::string snoop_base64_decode(std::string const& encoded_string) {\n  int in_len = encoded_string.size();\n  int i = 0;\n  int j = 0;\n  int in_ = 0;\n  unsigned char char_array_4[4], char_array_3[3];\n  std::string ret;\n\n  while (in_len-- && ( encoded_string[in_] != '=') && is_base64(encoded_string[in_])) {\n    char_array_4[i++] = encoded_string[in_]; in_++;\n    if (i ==4) {\n      for (i = 0; i <4; i++)\n        char_array_4[i] = base64_chars.find(char_array_4[i]);\n\n      char_array_3[0] = (char_array_4[0] << 2) + ((char_array_4[1] & 0x30) >> 4);\n      char_array_3[1] = ((char_array_4[1] & 0xf) << 4) + ((char_array_4[2] & 0x3c) >> 2);\n      char_array_3[2] = ((char_array_4[2] & 0x3) << 6) + char_array_4[3];\n\n      for (i = 0; (i < 3); i++)\n        ret += char_array_3[i];\n      i = 0;\n    }\n  }\n\n  if (i) {\n    for (j = i; j <4; j++)\n      char_array_4[j] = 0;\n\n    for (j = 0; j <4; j++)\n      char_array_4[j] = base64_chars.find(char_array_4[j]);\n\n    char_array_3[0] = (char_array_4[0] << 2) + ((char_array_4[1] & 0x30) >> 4);\n    char_array_3[1] = ((char_array_4[1] & 0xf) << 4) + ((char_array_4[2] & 0x3c) >> 2);\n    char_array_3[2] = ((char_array_4[2] & 0x3) << 6) + char_array_4[3];\n\n    for (j = 0; (j < i - 1); j++) ret += char_array_3[j];\n  }\n\n  return ret;\n}\n\n"
  },
  {
    "path": "client_server/Snoop.hh",
    "content": "\n/*\n\n   Snoop\n   Copyright (C) 2015-2024  Kasper Peeters\n   Available under the terms of the GPL v3.\n\n   Snoop is a lightweight logging library which stores its log entries in\n\ta local SQLite database or on a remote server.\n\n */\n\n#pragma once\n\n#ifndef __ANDROID__\n   // Android uses Java/Kotlin networking, don't attempt to do it native.\n   #define SNOOP_SSL\n#endif\n\n#include <string>\n#include <sstream>\n#include <sqlite3.h>\n#include <stdint.h>\n#include <mutex>\n#include \"nlohmann/json.hpp\"\n#include <thread>\n#include <condition_variable>\n#include <set>\n\n#include \"websocket_client.hh\"\n\n#ifndef _MSC_VER\n  #include <unistd.h>\n#endif\n\nstd::string safestring(const unsigned char *c);\n\nnamespace snoop {\n\n\tclass SnoopImpl;\n   class Flush {};\n   extern Flush flush;\n\n\t/// Logging class with functionality to send log information to a\n\t/// remote server using a websocket connection.\n\n   class Snoop {\n      public:\n         Snoop();\n         ~Snoop();\n\n\t\t\t/// Initialise the logging stream. Should be called once at\n         /// program startup, but can be called multiple times without\n         /// causing problems.\n\n\t\t\tvoid init(const std::string& app_name, const std::string& app_version, \n                      std::string server=\"\", std::string local_log_file=\"\", std::string machine_id=\"\");\n\n\t\t\t/// Get a string which uniquely identifies the current user. This is\n\t\t\t/// stored in ~/.config/snoop/appname.conf, and in the 'user_id' field\n\t\t\t/// in each LogEntry. Note that this is different from the 'uuid' field,\n\t\t\t/// which will change from one run to the next.\n\n\t\t\tstd::string get_user_uuid(const std::string& app_name);\n\n\t\t\t/// Operator to initialise a logging entry with the type of\n\t\t\t/// the log message as well as (optionally) the file, line\n\t\t\t/// number and method.\n\n\t\t\tSnoop& operator()(const std::string& type=\"\", std::string fl=\"\", int loc=-1, std::string method=\"\");\n       \n         /// Determine the 'type' field of records which should not be\n         /// sent to the remote logging server. Can be called multiple times.\n\n         void set_local_type(const std::string& type);\n\n         /// Generic operator to log an object to the log message being constructed.\n\n\t\t\ttemplate<class T>\n\t\t\tSnoop& operator<<(const T& obj) {\n\t\t\t   out_ <<(obj);\n\t\t\t   return *this;\n\t\t\t}\n\n\t\t\t/// Log payload data.\n\n\t\t\tSnoop& payload(const std::vector<char>&);\n\t\t\t\n\t\t\t/// Flush the log entry to disk/server.\n\n         Snoop& operator<<(const Flush&);\n\n\t\t\t/// Set to sync with server after every log line.\n\n\t\t\tvoid set_sync_immediately(bool);\n\n\t\t\t/// Ensure that the local database is synchronised with the\n\t\t\t/// server (this sends multiple app or log entries in one\n\t\t\t/// websocket message). Leave the bool argument at its\n\t\t\t/// default argument under all normal circumstances.\n\n\t\t\tvoid sync_with_server(bool from_wsthread=false);\n\t\t\t\n\t\t\t/// As above, but only for run entries. \n\n\t\t\tvoid sync_runs_with_server(bool from_wsthread=false);\n\t\t\t\n\t\t\t/// As above, but only for log entries. \n\n\t\t\tvoid sync_logs_with_server(bool from_wsthread=false);\n\t\t\t\n\t\t\t/// As above, but only for payload data. \n\n\t\t\tvoid sync_payloads_with_server(bool from_wsthread=false);\n\n         /// Are we connected to the log server?\n\n         bool is_connected() const;         \n\n         /// Return version of last run seen on given device.\n         \n         std::string last_seen_version(std::string machine_id);\n\n         /// Authentication logic; passes ticket or credentials\n         /// to server, and registers callback function for when\n         /// the response comes back. If the `always_reauth` flag\n\t\t\t/// is true, always ask the server for a new ticket using\n\t\t\t/// the user/password combo.\n\n         bool authenticate(std::function<void (std::string, bool)>, std::string user=\"\", std::string pass=\"\", bool always_reauth=false);\n\t\t\t/// Set error handler for clients; will be called on\n\t\t\t/// any networking errors. When this function returns\n\t\t\t/// false, no further attempts will be made to connect\n\t\t\t/// or send, and if authentication was in progress, a\n\t\t\t/// final call to the authentication callback will be\n\t\t\t/// made, with 'false' as argument.\n\n\t\t\tvoid set_error_handler(std::function<bool (std::string)>);\n\t\t\t\n\t\t\t/// Exception used to flag invalid/unparseable data received on the wire.\n\n\t\t\tclass ParseError : public std::logic_error {\n\t\t\t\tpublic:\n\t\t\t\t\tParseError(const std::string&);\n\t\t\t};\n\t\t\t\n         /// Get status of a given authentication ticket.\n\n\t\t\tclass Ticket {\n\t\t\t\tpublic:\n\t\t\t\t\tTicket();\n\t\t\t\t\tint         ticket_id;\n\t\t\t\t\tint         user_id;\n\t\t\t\t\tstd::string ticket_uuid;\n\t\t\t\t\tbool        valid;\n\t\t\t};\n         Ticket is_ticket_valid(std::string ticket_uuid);\n\n         /// C++ representation of a run entry.\n\n\t\t\tclass AppEntry {\n\t\t\t\tpublic:\n\t\t\t\t\tAppEntry();\n\t\t\t\t\tAppEntry(const std::string& uuid_, uint64_t create_millis_, uint64_t receive_millis_, uint64_t pid_, \n\t\t\t\t\t\t\t\tconst std::string& ip_address_, const std::string& machine_id_, \n\t\t\t\t\t\t\t\tconst std::string& app_name_,   const std::string& app_version_,\n\t\t\t\t\t\t\t\tconst std::string& user_id_,\n\t\t\t\t\t\t\t\tint server_status_, int create_timezone);\n\n\t\t\t\t\tstd::string to_json(bool human_readable) const;\n\t\t\t\t\tvoid        from_json(const nlohmann::json&);\n\n\t\t\t\t\tint         id;\n\t\t\t\t\tstd::string uuid;\n\t\t\t\t\tuint64_t    create_millis;\n\t\t\t\t\tuint64_t    receive_millis;\n\t\t\t\t\tuint64_t    pid;\n\t\t\t\t\tstd::string ip_address;\n\t\t\t\t\tstd::string machine_id;\n\t\t\t\t\tstd::string app_name;\n\t\t\t\t\tstd::string app_version;\n\t\t\t\t\tstd::string user_id;\n\t\t\t\t\tint         server_status; // 1: synced, 0 and negative: number of attempts at syncing made\n\t\t\t\t\tbool        connected;\n\t\t\t\t\tint         create_timezone;\t\t\t\t\t\n\t\t\t};\n\n\t\t\t/// C++ representation of a log entry.\n\n\t\t\tclass LogEntry {\n\t\t\t\tpublic:\n\t\t\t\t\tLogEntry();\n\t\t\t\t\tLogEntry(int log_id_, int client_log_id_, int id_, const std::string&, \n\t\t\t\t\t\t\t\tuint64_t, uint64_t, const std::string&, int, const std::string&, \n\t\t\t\t\t\t\t\tconst std::string& , const std::string&, int status, const std::string&,\n\t\t\t\t\t\t\t\tint create_timezone);\n\n\t\t\t\t\tstd::string to_json(bool human_readable) const;\n\t\t\t\t\tvoid        from_json(const nlohmann::json&);\n\t\t\t\t\t\n\t\t\t\t\tint         log_id;\n\t\t\t\t\tint         client_log_id;\n\t\t\t\t\tint         id;\n\t\t\t\t\tstd::string uuid;              // this goes on the wire, but is not stored on disk.\n\t\t\t\t\tuint64_t    create_millis;\n\t\t\t\t\tuint64_t    receive_millis;\n\t\t\t\t\tstd::string loc_file;\n\t\t\t\t\tint         loc_line;\n\t\t\t\t\tstd::string loc_method;\n\t\t\t\t\tstd::string type;\n\t\t\t\t\tstd::string message;\n\t\t\t\t\tint         server_status;     // 1: synced, 0 and negative: number of attempts at syncing made\n\t\t\t\t\tstd::string session_uuid;\n\t\t\t\t\tint         create_timezone;\n\t\t\t};\n\n\t\t\t/// C++ representation of a payload entry.\n\n\t\t\tclass PayLoad {\n\t\t\t\tpublic:\n\t\t\t\t\tPayLoad();\n\t\t\t\t\tPayLoad(const std::vector<char>& data);\n\n\t\t\t\t\tstd::string to_json(bool human_readable) const;\n\t\t\t\t\tvoid        from_json(const nlohmann::json&);\n\n\t\t\t\t\tint         payload_id;\n\t\t\t\t\tint         client_payload_id;\n\t\t\t\t\tint         id;\n\t\t\t\t\tstd::string uuid;              // this goes on the wire, but is not stored on disk.\n\t\t\t\t\tuint64_t    create_millis;\n\t\t\t\t\tuint64_t    receive_millis;\n\t\t\t\t\tstd::string payload;\n\t\t\t\t\tint         server_status;     // 1: synced, 0 and negative: number of attempts at syncing made\n\t\t\t\t\tint         create_timezone;\n\t\t\t};\n       \n          /// Client-side fetching of ticket.\n       \n          std::string get_local_ticket();\n\n\t\t\t/// Retrieve the (single) local username from the database, empty string\n\t\t\t/// if no such row exists.\n\n\t\t\tstd::string local_user() const;\n\n\t\t\t/// Set the session uuid so log entries can be easily grouped by session.\n\t\t\t\n\t\t\tvoid set_session_uuid(const std::string&);\n\t\t\t\n         /// Add a user/password combo to the user database. This can also be used\n\t\t\t/// locally (client mode, not server) to save a username to persistent\n\t\t\t/// storage. If `single` is true, first flush the local user database (so\n\t\t\t/// at any time only one record is present). \n\n         bool add_user(std::string user, std::string password, bool single=false);\n\n      protected:\n\t\t\t/// Start the websocket client. This tries to connect to the server and then\n         /// waits in a separate thread until the server sends us something (typically\n         /// in response to something the main thread makes by calling wsclient.send).\n\n\t\t\tvoid start_websocket_client();\n\n\t\t\t/// Ensure that the required tables are present in the\n\t\t\t/// database file.\n\n\t\t\tvoid create_tables();\n\n\t      /// Ensure that the required authentication tables are present\n\t      /// in the authentication database. Only used on the server.\n\n\t      void create_authentication_tables();\n\n\t\t\t/// Obtain a uuid by finding the last AppEntry stored in the\n\t\t\t/// local database. Will attempt to re-turn a previously\n\t\t\t/// generated uuid but will do so only if one is stored for\n\t\t\t/// the current pid; if no entry with the current pid is\n\t\t\t/// stored then a new one will always be generated.\n\n\t\t\tvoid obtain_uuid();\n\n\t\t\t/// Store an app entry in the database. Will update the 'id'\n\t\t\t/// field in the AppEntry.\n\n\t\t\tbool store_app_entry(Snoop::AppEntry&);\n\t\t\tbool store_app_entry_without_lock(Snoop::AppEntry&);\n\n\t\t\t/// Store a log entry in the local database. Generates its\n\t\t\t/// own receive_millis field (the one given gets\n\t\t\t/// overwritten). Will update the 'id' field in the LogEntry.\n\t\t\t/// Returns 'true' if the entry was stored, or 'false' if an\n\t\t\t/// entry with this client_log_id was already present (except\n\t\t\t/// when it is 0).\n\n\t\t\tbool store_log_entry(Snoop::LogEntry&, bool avoid_server_duplicates);\n\n\t\t\t/// Store payload data in the local database.\n\n\t\t\tbool store_payload_entry(Snoop::PayLoad&);\n\n\t\t\t/// Store an attempt to login into the authentication database.\n\t\t\t\n\t\t\tbool store_auth_attempt_entry(int user_id, int ticket_id, int valid, std::string msg);\n\t\t\t\n\t\t\t/// Return a vector of all aps registered in the database. If\n\t\t\t/// the uuid filter is non-empty, will filter on the given\n\t\t\t/// uuid.\n\n\t\t\tstd::vector<Snoop::AppEntry> get_app_registrations(std::string uuid_filter=\"\");\n\n         /// Store an authentication ticket in the database.\n         \n\t      int store_ticket(std::string ticket_uuid, int user_id, bool valid);\n\n         /// Client-side storing of ticket (simpler than store_ticket above).\n         /// If ticket is empty, only deletes current ticket.\n\n         void set_local_ticket(std::string ticket_uuid);\n\t\t\t\n         /// Variables\n         \n         bool          sync_immediately_;\n\t      sqlite3      *db, *payload_db, *auth_db;\n\t\t\tsqlite3_stmt *insert_statement, *id_for_uuid_statement, *payload_insert_statement, *testq_statement;\n\t\t\tstd::recursive_mutex    sqlite_mutex;\n\t\t\t\n      private:\n\t\t\t/// Websocket client to talk to a remote logging server.\n\t\t\t\n\t\t\twebsocket_client                wsclient;\n\t\t\tstd::thread                     wsclient_thread;\n\t\t\tstd::mutex                      connection_mutex;\n\t\t\tstd::condition_variable         connection_cv;\n\t\t\tbool                            connection_is_open, connection_attempt_failed;\n\n\t      // Main entry point for the I/O thread.\n\t      void io_thread_run();\n\t      void try_connect();\n\t  \n\t\t\tvoid on_client_open();\n\t\t\tvoid on_client_fail(const boost::beast::error_code& ec);\n\t\t\tvoid on_client_close();\n\t\t\tvoid on_client_message(const std::string& msg);\n\n\t\t\tstd::ostringstream out_;\n\t\t\t\n\t\t\tSnoop::AppEntry    this_app_;\n\t\t\tSnoop::LogEntry    this_log_;\n\t\t\tstd::string        server_;\n\t\t\tstd::string        session_uuid_; // gets copied into every LogEntry.\n\n         std::recursive_mutex   call_mutex;\n\n\t      std::set<std::string> local_types;\n         std::function<void (std::string, bool)> authentication_callback;\n\t\t\tstd::function<bool (std::string)>       error_callback;\n\n   };\n\n\textern Snoop log;\n\n\tconst char info[] =\"info\";\n\tconst char warn[] =\"warning\";\n\tconst char error[]=\"error\";\n\tconst char fatal[]=\"fatal\";\n\tconst char email[]=\"email\";\n}\n\n// set(CMAKE_CXX_FLAGS \"${CMAKE_CXX_FLAGS} -D__FILENAME__='\\\"$(subst\n//  ${CMAKE_SOURCE_DIR}/,,$(abspath $<))\\\"'\")\n\n#define LOC __FILE__, __LINE__, __func__\n\n"
  },
  {
    "path": "client_server/TODO",
    "content": "\nCan it ever happen that e.g. the user selects a cell, clicks delete, but before\nthe Action can be 'perform'ed, the client has already removed it?\n\n\nThe problem is that the user interface can fire off a Delete action and then happily\nrequest other things to that cell before the delete has happened. Or can it? With\ncalling perform, you always run on the gui thread. This thread should just execute\nall actions immediately, all the way down to the gui update.\n\nLATER: It's worse: you can set a cell to execute, then delete it while the cell\nis still running. When the return data comes in and the computethread wants to\nadd the child output cell, the original one has gone and the pointer is stale => segfault.\nYou can't avoid this with doing actions in sync. You can prevent it by requiring that\na delete can only happen on cells which are not executing.\n\n\n -> maybe the best is to make 'perform' execute all the way through, and make\n    a separate member, only accessible to the client, which does actions by\n    waking.\n\n    perform_sync();\n\n\n    perform_async();\n\n -> No, let the GUI thread do all updates. The client can only request updates, the\n    gui thread executes them. Then it becomes easy to force the gui to first run the\n    outstanding requests before doing its own.\n\n    HOWEVER, in this case we have to worry about how the client stores ActionBase.\n    The GUIThread holds the action stack, but the NetThread can lock it and write\n    into it.\n\n\nMake sure to keep the GUIBase and Client classes separating the thread actions.\nSome stuff should probably move out from Client -> GUIBase. Also: rename to\nGUIThread and NetThread.  Or maybe add SharedData to separate it out even cleaner.\n\n\n* We are passing around all data in the form of shared ptrs, but that ignores\n  the tree structure. Perhaps change this?"
  },
  {
    "path": "client_server/cadabra-jupyter-kernel.cc",
    "content": "\n#include \"Config.hh\"\n#include <iostream>\n#include \"cadabra-jupyter-kernel.hh\"\n#include \"xeus/xguid.hpp\"\n#include <boost/algorithm/string.hpp>\n\n// #define DEBUG 1\n\ncadabra::CadabraJupyter::CadabraJupyter()\n\t: Server()\n\t{\n\trunner = std::thread(std::bind(&Server::wait_for_job, this));\n\tpybind11::gil_scoped_release release;\n\t}\n\nvoid cadabra::CadabraJupyter::configure_impl()\n\t{\n\tauto handle_comm_opened = [](xeus::xcomm&& comm, const xeus::xmessage&) {\n\t\tstd::cerr << \"Comm opened for target: \" << comm.target().name() << std::endl;\n\t\t};\n\tcomm_manager().register_comm_target(\"echo_target\", handle_comm_opened);\n//\tusing function_type = std::function<void(xeus::xcomm&&, const xeus::xmessage&)>;\n#ifdef DEBUG\n\tstd::cerr << \"CadabraJupyter configured\" << std::endl;\n#endif\n\t}\n\nxjson cadabra::CadabraJupyter::execute_request_impl(int execution_counter,\n      const std::string& code,\n      bool silent,\n      bool store_history,\n      xjson /* user_expressions */,\n      bool allow_stdin)\n\t{\n#ifdef DEBUG\n\tstd::cerr << \"Received execute_request\" << std::endl;\n\tstd::cerr << \"execution_counter: \" << execution_counter << std::endl;\n\tstd::cerr << \"code: \" << code << std::endl;\n\tstd::cerr << \"silent: \" << silent << std::endl;\n\tstd::cerr << \"store_history: \" << store_history << std::endl;\n\tstd::cerr << \"allow_stdin: \" << allow_stdin << std::endl;\n\tstd::cerr << std::endl;\n#endif\n\n\tstd::unique_lock<std::mutex> lock(block_available_mutex);\n\twebsocketpp::connection_hdl hdl;\n\tblock_queue.push(Block(hdl, code, execution_counter));\n\tblock_available.notify_one();\n\n\t// The 'wait_for_job' function which runs in a separate thread will take\n\t// care of executing the 'code'. If anything in 'code' uses 'display',\n\t// it will run the 'send' function below. At the end of the code\n\t// execution, a final output block will be sent by 'Server::on_block_finished'.\n\n\txjson result;\n\tresult[\"status\"] = \"ok\";\n\treturn result;\n\t}\n\nvoid cadabra::CadabraJupyter::on_block_error(Block blk)\n\t{\n#ifdef DEBUG\n\tstd::cerr << \"error: \" << blk.error << std::endl;\n#endif\n\tstd::vector<std::string> traceback;\n\t// FIXME: This does not show the error, for some reason...\n\tpublish_execution_error(\"Exception\", blk.error, traceback);\n\txjson pub_data;\n\tpub_data[\"text/markdown\"] = blk.error;\n//\txjson extra_data;\n//\textra_data[\"dummy\"] = \"dummy\";\n\t// FIXME: ... so we send it again as a message.\n\tpublish_execution_result(current_id, std::move(pub_data), 0); // std::move(extra_data));\n\t}\n\nuint64_t cadabra::CadabraJupyter::send(const std::string& output, const std::string& msg_type, uint64_t parent_id, bool last)\n\t{\n#ifdef DEBUG\n\tstd::cerr << \"received: \" << msg_type << \" \" << output << std::endl;\n#endif\n\tif(output.size()>0) {\n\t\tif(msg_type==\"verbatim\" || msg_type==\"output\") {\n\t\t\txjson pub_data;\n\t\t\tpub_data[\"text/markdown\"] = output;\n//\t\t\txjson extra_data;\n//\t\t\textra_data[\"dummy\"] = \"dummy\";\n\t\t\tpublish_execution_result(current_id, std::move(pub_data), 0); // std::move(extra_data));\n\t\t\t}\n\t\telse if(msg_type==\"latex_view\") {\n\t\t\txjson pub_data;\n\t\t\tstd::string tmp=output;\n\t\t\tboost::replace_all(tmp, \"\\\\begin{dmath*}\", \"$\");\n\t\t\tboost::replace_all(tmp, \"\\\\end{dmath*}\", \"$\");\n\t\t\tpub_data[\"text/markdown\"] = tmp;\n//\t\t\txjson extra_data;\n//\t\t\textra_data[\"dummy\"] = \"dummy\";\n\t\t\tpublish_execution_result(current_id, std::move(pub_data), 0); // std::move(extra_data));\n\t\t\t}\n\t\t}\n\treturn current_id;\n\t}\n\nxjson cadabra::CadabraJupyter::complete_request_impl(const std::string& code,\n      int cursor_pos)\n\t{\n#ifdef DEBUG\n\tstd::cerr << \"Received complete_request\" << std::endl;\n\tstd::cerr << \"code: \" << code << std::endl;\n\tstd::cerr << \"cursor_pos: \" << cursor_pos << std::endl;\n\tstd::cerr << std::endl;\n#endif\n\txjson result;\n\tresult[\"status\"] = \"ok\";\n\tresult[\"matches\"] = {\"a.echo1\"};\n\tresult[\"cursor_start\"] = 2;\n\tresult[\"cursor_end\"] = 6;\n\treturn result;\n\t}\n\nxjson cadabra::CadabraJupyter::inspect_request_impl(const std::string& code,\n      int cursor_pos,\n      int detail_level)\n\t{\n#ifdef DEBUG\n\tstd::cerr << \"Received inspect_request\" << std::endl;\n\tstd::cerr << \"code: \" << code << std::endl;\n\tstd::cerr << \"cursor_pos: \" << cursor_pos << std::endl;\n\tstd::cerr << \"detail_level: \" << detail_level << std::endl;\n\tstd::cerr << std::endl;\n#endif\n\txjson result;\n\tresult[\"status\"] = \"ok\";\n\tresult[\"found\"] = false;\n\treturn result;\n\t}\n\nxjson cadabra::CadabraJupyter::is_complete_request_impl(const std::string& code)\n\t{\n#ifdef DEBUG\n\tstd::cerr << \"Received is_complete_request\" << std::endl;\n\tstd::cerr << \"code: \" << code << std::endl;\n\tstd::cerr << std::endl;\n#endif\n\txjson result;\n\tresult[\"status\"] = \"complete\";\n\treturn result;\n\t}\n\nxjson cadabra::CadabraJupyter::kernel_info_request_impl()\n\t{\n\txjson result;\n\tresult[\"implementation\"] = \"Cadabra\";\n\tresult[\"implementation_version\"] = std::string(CADABRA_VERSION_SEM);\n\tresult[\"language_info\"][\"name\"] = \"cadabra\";\n\tresult[\"language_info\"][\"version\"] = \"2.0.0\";\n\tresult[\"language_info\"][\"mimetype\"] = \"text/cadabra\";\n\tresult[\"language_info\"][\"file_extension\"] = \".cdb\";\n\treturn result;\n\t}\n\nvoid cadabra::CadabraJupyter::shutdown_request_impl() {}\n\n\n"
  },
  {
    "path": "client_server/cadabra-jupyter-kernel.hh",
    "content": "\n#pragma once\n\n#include \"xeus/xinterpreter.hpp\"\n#include \"xeus/xjson.hpp\"\n#include \"Server.hh\"\n\nusing xeus::xinterpreter;\nusing xeus::xjson;\n\nnamespace cadabra {\n\n\t/// \\ingroup clientserver\n\t///\n\t/// A Jupyter kernel for Cadabra, which provides the Cadabra\n\t/// pre-processor to enable input as in the Gtk notebook frontend.\n\t/// Built using Xeus.\n\n\tclass CadabraJupyter : public xinterpreter, public Server {\n\t\tpublic:\n\n\t\t\tCadabraJupyter();\n\t\t\tvirtual ~CadabraJupyter() = default;\n\n\t\t\tvirtual uint64_t send(const std::string& output, const std::string& msg_type, uint64_t parent_id, bool last) override;\n\n\t\t\tint current_counter;\n\t\t\tbool finished=true;\n\n\t\tprotected:\n\t\t\tvirtual void   on_block_error(Block) override;\n\n\t\tprivate:\n\n\t\t\tvoid configure_impl() override;\n\n\t\t\txjson execute_request_impl(int execution_counter,\n\t\t\t                           const std::string& code,\n\t\t\t                           bool silent,\n\t\t\t                           bool store_history,\n\t\t\t                           xjson user_expressions,\n\t\t\t                           bool allow_stdin) override;\n\n\t\t\txjson complete_request_impl(const std::string& code,\n\t\t\t                            int cursor_pos) override;\n\n\t\t\txjson inspect_request_impl(const std::string& code,\n\t\t\t                           int cursor_pos,\n\t\t\t                           int detail_level) override;\n\n\t\t\txjson is_complete_request_impl(const std::string& code) override;\n\n\t\t\txjson kernel_info_request_impl() override;\n\n\t\t\tvoid shutdown_request_impl() override;\n\t\t};\n\t}\n"
  },
  {
    "path": "client_server/cadabra-jupyter-main.cc",
    "content": "#include <iostream>\n#include <memory>\n\n#include \"cadabra-jupyter-kernel.hh\"\n#include \"xeus/xkernel.hpp\"\n#include \"xeus/xkernel_configuration.hpp\"\n\nint main(int argc, char* argv[])\n\t{\n\tstd::string file_name = (argc == 1) ? \"connection.json\" : argv[2];\n\txeus::xconfiguration config = xeus::load_configuration(file_name);\n\n\tusing interpreter_ptr = std::unique_ptr<cadabra::CadabraJupyter>;\n\tinterpreter_ptr interpreter = interpreter_ptr(new cadabra::CadabraJupyter());\n\txeus::xkernel kernel(config, \"kpeeters\", std::move(interpreter));\n\tstd::cout << \"starting kernel\" << std::endl;\n\tkernel.start();\n\n\treturn 0;\n\t}\n"
  },
  {
    "path": "client_server/cadabra-server.cc",
    "content": "\n#include \"Config.hh\"\n#include \"Snoop.hh\"\n#include \"Server.hh\"\n#include <glibmm/miscutils.h>\n\n#define NDEBUG 1\n\n#ifdef _WIN32\n#include <Windows.h>\n#endif\n\n#ifdef _WIN32\n\nstd::string getRegKey(const std::string& location, const std::string& name, bool system)\n\t{\n\tHKEY key;\n\tTCHAR value[1024];\n\tDWORD bufLen = 1024*sizeof(TCHAR);\n\tlong ret;\n\tret = RegOpenKeyExA(system?HKEY_LOCAL_MACHINE:HKEY_CURRENT_USER, location.c_str(), 0, KEY_QUERY_VALUE, &key);\n\tif( ret != ERROR_SUCCESS ){\n\t\treturn std::string();\n\t\t}\n\tret = RegQueryValueExA(key, name.c_str(), 0, 0, (LPBYTE) value, &bufLen);\n\tRegCloseKey(key);\n\tif ( (ret != ERROR_SUCCESS) || (bufLen > 1024*sizeof(TCHAR)) ){\n\t\treturn std::string();\n\t\t}\n\tstd::string stringValue = std::string(value, (size_t)bufLen - 1);\n\tsize_t i = stringValue.length();\n\twhile( i > 0 && stringValue[i-1] == '\\0' ){\n\t\t--i;\n\t\t}\n\treturn stringValue.substr(0,i);\n\t}\n\n#endif\n\n// Run a simple Cadabra server on a local port.\n\nint main(int argc, char **argv)\n\t{\n#ifndef ENABLE_JUPYTER\n \tsnoop::log.init(\"CadabraServer\", CADABRA_VERSION_FULL, \"log.cadabra.science\");\n \tsnoop::log.set_sync_immediately(true);\n#endif\n\t\n#ifdef _WIN32\n\tsnoop::log(\"platform\") << \"windows\" << snoop::flush;\n#else\n#ifdef __APPLE__\n\tsnoop::log(\"platform\") << \"macos\" << snoop::flush;\n#else\n\tsnoop::log(\"platform\") << \"linux\" << snoop::flush;\n#endif\n#endif\n\t\n\tint port=0;\n\tbool eod=true;\n\tif(argc>1)\n\t\tport=atoi(argv[1]);\n\tif(argc>2)\n\t\teod=(atoi(argv[2])==1);\n\n\tServer server;\n\tserver.run(port, eod);\n\n\treturn 0;\n\t}\n\n\n#if defined(_WIN32) && defined(NDEBUG)\nint WinMain(HINSTANCE hInstance, HINSTANCE hPrevInstance, LPSTR lpCmdLine, int nCmdShow)\n\t{\n\tFreeConsole();\n\treturn main(__argc, __argv);\n\t}\n#endif\n"
  },
  {
    "path": "client_server/cadabra2html.cc",
    "content": "#include <fstream>\n#include <iostream>\n#include \"DataCell.hh\"\n\nint main(int argc, char **argv)\n\t{\n\tif(argc<2) {\n\t\tstd::cerr << \"Usage: cadabra2html [--segment] [--strip-code] [cadabra notebook] [html file]\\n\\n\";\n\t\tstd::cerr << \"Convert a Cadabra notebook to an HTML segment or standalone HTML file.\\n\"\n\t\t\t\t\t << \"  --segment:          generate output for the cadabra web site.\\n\"\n\t\t\t\t\t << \"  --strip-code:       suppress Python cells with 'def' or 'from' lines.\\n\"\n\t\t\t\t\t << \"  --hide-input-cells: suppress all input cells (overrides notebook setting).\\n\"\n\t\t          << \"If the HTML file name is not given, output goes to standard out.\\n\";\n\t\treturn -1;\n\t\t}\n\n\tstd::string cdb_file, html_file;\n\tbool segment_only=false;\n\tbool strip_code=false;\n\tbool hide_input_cells=false;\n\tint n=1;\n\twhile(n<argc) {\n\t\tif(std::string(argv[n])==\"--segment\")\n\t\t\tsegment_only=true;\n\t\telse if(std::string(argv[n])==\"--strip-code\")\n\t\t\tstrip_code=true;\n\t\telse if(std::string(argv[n])==\"--hide-input-cells\")\n\t\t\thide_input_cells=true;\n\t\telse if(cdb_file==\"\")\n\t\t\tcdb_file=argv[n];\n\t\telse\n\t\t\thtml_file=argv[n];\n\t\t++n;\n\t\t}\n\t//std::cerr << \"stripping code: \" << strip_code << std::endl;\n\n\tauto from=cdb_file.find_last_of(\"/\");\n\t++from;\n\tauto to  =cdb_file.find_last_of(\".\");\n\tstd::string t=cdb_file.substr(from, to-from);\n\tt[0]=toupper(t[0]);\n\tstd::string title=\"Cadabra manual: \"+t;\n\n\tstd::ifstream file(cdb_file);\n\tif(!file.is_open()) {\n\t\tstd::cerr << \"cadabra2html: cannot open \" << cdb_file << std::endl;\n\t\treturn -1;\n\t\t}\n\t\n\tstd::string content, line;\n\twhile(std::getline(file, line))\n\t\tcontent+=line;\n\n\tcadabra::DTree doc;\n\tJSON_deserialise(content, doc);\n\tif(hide_input_cells)\n\t\tdoc.hide_input_cells=hide_input_cells;\n\tstd::string html = export_as_HTML(doc, segment_only, strip_code, title);\n\n\tif(html_file!=\"\") {\n\t\tstd::ofstream htmlfile(html_file);\n\t\thtmlfile << html;\n\t\t}\n\telse {\n\t\tstd::cout << html;\n\t\t}\n\n\treturn 0;\n\t}\n"
  },
  {
    "path": "client_server/cadabra2latex.cc",
    "content": "#include <fstream>\n#include <iostream>\n#include <regex>\n#include \"DataCell.hh\"\n\nint main(int argc, char **argv)\n\t{\n\tif(argc<3) {\n\t\tstd::cerr << \"Usage: cadabra2latex [--segment] [cadabra notebook] [latex file]\\n\\n\";\n\t\tstd::cerr << \"Convert a Cadabra v2 notebook to a standalone LaTeX file (plus images).\\n\";\n\t\treturn -1;\n\t\t}\n\n\tint i=1;\n\tbool for_embedding=false;\n\tif(argc==4) {\n\t\tif(std::string(argv[1])==\"--segment\") {\n\t\t\tfor_embedding=true;\n\t\t\t}\n\t\t++i;\n\t\t}\n\tstd::string cdb_file=argv[i], latex_file=argv[i+1];\n\n\tstd::ifstream file(cdb_file);\n\tstd::string content, line;\n\twhile(std::getline(file, line))\n\t\tcontent+=line;\n\n\tcadabra::DTree doc;\n\tJSON_deserialise(content, doc);\n\tstd::size_t dotpos = latex_file.rfind('.');\n\tstd::string base = latex_file.substr(0, dotpos);\n\tstd::string latex = export_as_LaTeX(doc, base, for_embedding);\n\n\tif(for_embedding) {\n\t\t// Ensure all sections are numbered if this will be embedded in a larger\n\t\t// document.\n\t\tlatex=std::regex_replace(latex, std::regex(R\"(\\\\section\\*\\{)\"), \"\\\\section\\{\");\n\t\tlatex=std::regex_replace(latex, std::regex(R\"(\\\\subsection\\*\\{)\"), \"\\\\subsection\\{\");\n\t\tlatex=std::regex_replace(latex, std::regex(R\"(\\\\LaTeX\\{\\})\"), \"LaTeX{}\");\t\t\t\t\n\t\t}\n\n\tstd::ofstream latexfile(latex_file);\n\tlatexfile << latex;\n\n\treturn 0;\n\t}\n"
  },
  {
    "path": "client_server/connection.json",
    "content": "{\n    \"transport\": \"tcp\",\n    \"ip\": \"127.0.0.1\",\n    \"control_port\": 50160,\n    \"shell_port\": 57503,\n    \"stdin_port\": 52597,\n    \"iopub_port\": 40885,\n    \"hb_port\": 42540,\n    \"signature_scheme\": \"hmac-sha256\",\n    \"key\": \"a0436f6c-1916-498b-8eb9-e81ab9368e84\"\n}\n"
  },
  {
    "path": "client_server/kernel.json",
    "content": "{\n    \"display_name\": \"Cadabra\",\n    \"language\" : \"python\",\n    \"argv\": [\n        \"cadabra-jupyter-kernel\",\n        \"-f\",\n        \"{connection_file}\"\n    ]\n}\n"
  },
  {
    "path": "client_server/notebook.html",
    "content": "<!doctype html>\n<html>\n  <head>\n    <meta name=\"generator\"     content=\"Cadabra 2.5.11\">\n    <meta name=\"generator-url\" content=\"https://cadabra.science/\">\n    \n    <script id=\"MathJax-script\"\n\t    async\n\t    src=\"https://cdn.jsdelivr.net/npm/mathjax@2/MathJax.js?config=TeX-AMS_SVG\"></script>\n\n    <style>\n      @font-face {\n          font-family: cmr;\n          src: url(\"https://cadabra.science/static/fonts/cmunrm.otf\") format(\"opentype\");\n      }\n      @font-face {\n          font-family: cmbx;\n          src: url(\"https://cadabra.science/static/fonts/cmunbx.otf\") format(\"opentype\");\n      }\n      body { tab-size: 3; }\n      div.image_png { width: 400px; }\n      div.output { font-family: monospace; }\n      h1, h2, h3 { font-family: cmbx; font-weight: normal; }\n      div.latex_view { font-family: cmr; color: black; font-size: 16px; line-height: 23px; margin-left: 40px; margin-right: 40px; padding-left: 10px; margin-bottom: 10px; }\n      div.python div.latex_view { margin-left: 0px; margin-top: 5px; margin-bottom: -18px; padding-left: 0px; }\n      div.image_png img { width: 100%; }\n      div.python { font-family: monospace; font-size: 13px; padding-left: 10px; margin-left: 40px; margin-right; 40px; margin-bottom: 10px; margin-top: 10px; white-space: pre; color: blue; }\n      div.input_form { display: none; }\n      pre.output { color: black; }\n      code { font-size: 13px; }\n      div.author { font-weight: bold; }\n      div.email  { font-family: monospace; }\n    </style>\n    <script>\n      MathJax = {\n\t tex2jax: {\n\t    inlineMath: [['$','$'], ['\\\\(','\\\\)']],\n\t    processEscapes: true,\n\t    displayAlign: \"left\",\n\t    ignoreClass: \"python\",\n\t    processClass: \"latex_view\",\n\t    linebreaks: { automatic: true }\n\t },\n\t \"HTML-CSS\": {\n\t    scale: 100,\n\t    preferredFont: \"TeX\",\n\t    webFont: \"TeX\",\n\t    mtextFontInherit: true,\n\t    matchFontHeight: false,\n\t    linebreaks: { automatic: true }\n\t },\n\t SVG: {\n\t    linebreaks: { automatic: true },\n\t    matchFontHeight: false,\n\t    font: \"TeX\"\n\t }\n      };\n    </script>\n  </head>\n  \n"
  },
  {
    "path": "client_server/notebook.tex",
    "content": "% This is the bit of LaTeX style information that DataCell.cc needs in\n% order to write notebooks out in standalone LaTeX form. It is very\n% similar to ../frontend/common/preamble.tex; keep them in sync.\n\n\\documentclass[10pt]{article}\n\\usepackage[scale=.8]{geometry}\n\\usepackage{setspace}\n\\usepackage{fancyhdr}\n\\usepackage{ytableau}\n\\usepackage{listings}\n\\usepackage[fleqn]{amsmath}\n\\usepackage{color}\n\\usepackage{changepage}\n\\usepackage[colorlinks=true, urlcolor=black, plainpages=false, pdfpagelabels]{hyperref}\n\\usepackage{etoolbox}\n\\usepackage{amssymb}\n\\usepackage[parfill]{parskip}\n\\usepackage{graphicx}\n%\\usepackage{tableaux}\n\\def\\specialcolon{\\mathrel{\\mathop{:}}\\hspace{-.5em}}\n\\renewcommand{\\bar}[1]{\\overline{#1}}\n\\newcommand{\\algorithm}[2]{{\\tt\\Large\\detokenize{#1}}\\\\[1ex]\n{\\emph{#2}}\\\\[1ex]\n}\n\\newcommand{\\property}[2]{{\\tt\\Large\\detokenize{#1}}\\\\[1ex]\n{\\emph{#2}}\\\\[1ex]\n}\n\\newcommand{\\algo}[1]{{\\tt \\detokenize{#1}}}\n\\newcommand{\\prop}[1]{{\\tt \\detokenize{#1}}}\n\\renewcommand{\\author}[1]{{\\bfseries #1}}\n\\newcommand{\\email}[1]{, {\\tt #1}}\n%\\makeatletter\\def\\old@comma{,}\\catcode`\\,=13 \\def,{%\n%\\ifmmode\\old@comma\\discretionary{}{}{}\\else\\old@comma\\fi}\\makeatother\n\n\\newcommand{\\bigO}{{\\cal O}}\n\n% Math expressions wrapped in \\brwrap will get typeset with\n% round brackets around them, which have the appropriate size.\n% The expression itself can still be broken over multiple lines.\n\n\\newcommand\\brwrap[3]{%\n  \\setbox0=\\hbox{$#2$}\n  \\left#1\\vbox to \\the\\ht0{\\hbox to 0pt{}}\\right.\\kern-.2em\n  \\begingroup #2\\endgroup\\kern-.15em\n  \\left.\\vbox to \\the\\ht0{\\hbox to 0pt{}}\\right#3\n}\n\n\\renewcommand{\\arraystretch}{1.2}\n\\tolerance=10000\n\\relpenalty=10\n\\binoppenalty=10\n\\hyphenpenalty=10\n\\raggedright\n\n\\lstnewenvironment{python}[1][]{\\lstset{language=python,\n   columns=fullflexible,\n   xleftmargin=1em,\n   belowskip=0pt,\n   tabsize=3,\n   commentstyle={}, % otherwise {#} cadabra arguments look ugly\n   breaklines=true,   \n   basicstyle=\\small\\ttfamily\\color{blue},\n   keywordstyle={}\n}}{}\n  \n\n\\everymath{\\displaystyle}\n\n% Page numbers\n\\pagestyle{fancy}\n\\fancyhf{} % clear all header and footer fields\n\\renewcommand{\\headrulewidth}{0pt}\n\\renewcommand{\\footrulewidth}{0pt}\n\\fancyfoot[LE,RO]{{\\small\\thepage}}\n\\fancyfoot[LO,RE]{{\\tiny\\href{https://cadabra.science}{{\\tt https://cadabra.science}}}}\n\n% \\makeatletter\\def\\old@comma{,}\\catcode`\\,=13 \\def,{%\n% \\ifmmode\\old@comma\\discretionary{}{}{}\\else\\old@comma\\fi}\\makeatother\n\n% Ensure that maths broken over multiple lines has a bit of spacing\n% between lines.\n\\lineskiplimit=0mm\n\\lineskip=1.5ex\n\n% % Typesetting Young tableaux, originally in a separate style\n% % file, now included to avoid path searching problems. \n% % Some internals for the typesetting macros below; nothing\n% % user-servicable here; please read on.\n% \n% \\def\\@tabforc#1#2#3{\\expandafter\\tabf@rc\\expandafter#1{#2 \\^}{#3}}\n% \\def\\tabf@@rc#1#2#3\\tabf@@rc#4{\\def#1{#2}#4\\tabf@rc#1{#3}{#4}}\n% \\long\\def\\ReturnAfterFi#1\\fi{\\fi#1}\n%     \\def\\tabf@rc#1#2#3{%\n%       \\def\\temp@ty{#2}%\n%       \\ifx\\@empty\\temp@ty\n%       \\else\n%         \\ReturnAfterFi{%\n%           \\tabf@@rc#1#2\\tabf@@rc{#3}%\n%         }%\n%       \\fi\n%     }%\n% \n% % Sorry, some global registers for sizes and keeping track of\n% % measurements.\n%     \n% \\newdimen\\ytsize\\ytsize=2mm\n% \\newdimen\\ytfsize\\ytfsize=4mm\n% \\newcount\\repcnt\n% \\newdimen\\acchspace\n% \\newdimen\\accvspace\n% \\newdimen\\raiseh\n% \\newdimen\\maxw\n% \n% \\newcommand\\phrule[1]{\\hbox{\\vbox to0pt{\\hrule height .2pt width#1\\vss}}}\n% \n% % Typeset a Young tableau with filled boxes. Takes a single \n% % argument which is a string of symbols for each row,\n% % separated by commas. Examples:\n% %\n% %   \\ftableau{abc,de}\n% %   \\ftableau{ab{d_2},f{g_3}}\n% \n% \\newcommand\\ftableau[1]{%\n% \\def\\ctest{,}\n% \\def\\Ktest{\\^}\n% \\acchspace=0ex\n% \\accvspace=0ex\n% \\maxw=0ex\n% \\vbox{\\hbox{%\n% \\@tabforc\\thisel{#1}{%\n%  \\ifx\\thisel\\Ktest{%\n%      \\ifnum\\maxw=0\\maxw=\\acchspace\\fi%\n%      \\raisebox{\\accvspace}{\\vbox to \\ytfsize{\\hbox to\n% \t\t 0pt{\\vrule height \\ytfsize\\hss}}}\\kern\\acchspace\\kern-\\maxw}\n%  \\else\\ifx\\thisel\\ctest\n%      \\ifnum\\maxw=0\\maxw=\\acchspace\\fi%\n%      \\raisebox{\\accvspace}{\\vbox to \\ytfsize{\\hbox to 0pt{\\vrule height \\ytfsize\\hss}}}%\n%      \\kern\\acchspace\\acchspace=0ex\n% \t  \\advance\\accvspace by -\\ytfsize\n%  \\else\n%      \\setbox3=\\hbox{$\\thisel$}%\n% \t  \\raiseh=\\ytfsize%\n% \t  \\advance\\raiseh by -1ex%\n% \t  \\divide\\raiseh by 2%\n%      \\advance\\acchspace by-\\ytfsize%\n%      \\raisebox{\\accvspace}{\\vbox to \\ytfsize{\\hrule\\hbox to%\n%         \\ytfsize{\\vrule height \\ytfsize\\hskip.5ex%\n%          \\raisebox{\\raiseh}{\\tiny$\\thisel$}\\hss}\\vss\\phrule{\\ytfsize}}}%\n%  \\fi\\fi}}}}\n% \n% % Typeset a Young tableau with unlabelled boxes. Takes a single \n% % argument which is a string of numbers, one for the length of\n% % each row of the tableau. Example:\n% %\n% %   \\tableau{{10}{8}{3}}\n% %\n% % typesets a tableau with 10 boxes in the 1st row, 8 in the 2nd\n% % and 3 in the 3rd. Curly brackets can be omitted if numbers\n% % are less than 10.\n% \n% \\newcommand\\tableau[1]{%\n% \\def\\stest{ }\n% \\def\\Ktest{\\^}\n% \\acchspace=0ex\n% \\accvspace=0ex\n% \\maxw=0ex\n% \\hbox{%\n% \\@tabforc\\thisel{#1}{%\n%  \\ifx\\thisel\\Ktest{}\n%  \\else\n%      \\repcnt=\\thisel%\n%      \\loop{}%\n%      \\advance\\acchspace by-\\ytsize%\n%      \\raisebox{\\accvspace}{\\vbox to \\ytsize{\\hrule \\hbox to%\n% \t\t\t\\ytsize{\\vrule height \\ytsize\\hss}\\vss\\phrule{\\ytsize}}}%\n%      \\advance\\repcnt by -1\\ifnum\\repcnt>1{}\\repeat%\n%      \\ifnum\\maxw=0\\maxw=\\acchspace\\fi%\n%      \\raisebox{\\accvspace}{\\vbox to \\ytsize{\\hbox to 0pt{\\vrule height \\ytsize\\hss}}}%\n%      \\kern\\acchspace\\acchspace=0ex%\n% \t  \\advance\\accvspace by -\\ytsize%\n%  \\fi}\\kern-\\maxw}}\n \n\\ytableausetup{centertableaux} % smalltableaux\n"
  },
  {
    "path": "client_server/popen2.cc",
    "content": "\n// http://stackoverflow.com/questions/26852198/getting-the-pid-from-popen\n\n#include \"popen2.hh\"\n#include <sys/wait.h>\n#include <stdexcept>\n\n#define READ   0\n#define WRITE  1\n\nFILE * popen2(std::string command, std::string type, int & pid)\n\t{\n\tpid_t child_pid;\n\tint fd[2];\n\tif(pipe(fd)==-1)\n\t\tthrow std::logic_error(\"popen2 failed constructing pipe\");\n\n\tif((child_pid = fork()) == -1) {\n\t\tperror(\"fork\");\n\t\texit(1);\n\t\t}\n\n\t/* child process */\n\tif (child_pid == 0) {\n\t\tif (type == \"r\") {\n\t\t\tclose(fd[READ]);    //Close the READ end of the pipe since the child's fd is write-only\n\t\t\tdup2(fd[WRITE], 1); //Redirect stdout to pipe\n\t\t\t}\n\t\telse {\n\t\t\tclose(fd[WRITE]);    //Close the WRITE end of the pipe since the child's fd is read-only\n\t\t\tdup2(fd[READ], 0);   //Redirect stdin to pipe\n\t\t\t}\n\n\t\texecl(\"/bin/sh\", \"/bin/sh\", \"-c\", command.c_str(), NULL);\n\t\texit(0);\n\t\t}\n\telse {\n\t\tif (type == \"r\") {\n\t\t\tclose(fd[WRITE]); //Close the WRITE end of the pipe since parent's fd is read-only\n\t\t\t}\n\t\telse {\n\t\t\tclose(fd[READ]); //Close the READ end of the pipe since parent's fd is write-only\n\t\t\t}\n\t\t}\n\n\tpid = child_pid;\n\n\tif (type == \"r\") {\n\t\treturn fdopen(fd[READ], \"r\");\n\t\t}\n\n\treturn fdopen(fd[WRITE], \"w\");\n\t}\n\nint pclose2(FILE * fp, pid_t pid)\n\t{\n\tint stat;\n\n\tfclose(fp);\n\twhile (waitpid(pid, &stat, 0) == -1) {\n\t\tif (errno != EINTR) {\n\t\t\tstat = -1;\n\t\t\tbreak;\n\t\t\t}\n\t\t}\n\n\treturn stat;\n\t}\n\n"
  },
  {
    "path": "client_server/popen2.hh",
    "content": "\n#pragma once\n\n#include <internal/unistd.h>\n#include <errno.h>\n#include <stdio.h>\n#include <stdlib.h>\n#include <sys/types.h>\n#include <string>\n\nFILE * popen2(std::string command, std::string type, int & pid);\nint    pclose2(FILE * fp, pid_t pid);\n"
  },
  {
    "path": "client_server/regexp_tester.cc",
    "content": "\n#include <iostream>\n#include <string>\n#include <regex>\n\nint main(int argc, char **argv)\n\t{\n\tif(argc<3) {\n\t\tstd::cerr << \"Usage: regexp_tester [regex] [string]\" << std::endl;\n\t\treturn -1;\n\t\t}\n\n\ttry {\n\t\tstd::regex match(argv[1]);\n\t\tstd::smatch res;\n\t\tstd::string arg = argv[2];\n\t\tif(std::regex_search(arg, res, match)) {\n\t\t\tfor(unsigned int i=0; i<res.size(); ++i) {\n\t\t\t\tstd::cout << i << \":\\t |\" << res[i] << \"|\" << std::endl;\n\t\t\t\t}\n\t\t\t}\n\t\telse {\n\t\t\tstd::cout << \"no match\" << std::endl;\n\t\t\t}\n\t\t}\n\tcatch(std::exception& ex) {\n\t\tstd::cout << \"exception: \" << ex.what() << std::endl;\n\t\t}\n\t}\n"
  },
  {
    "path": "client_server/test_client.cc",
    "content": "\n// A test client to do some basic manipulation of a notebook and\n// some I/O with a cadabra server.\n\n#include \"Client.hh\"\n#include <thread>\n#include <system_error>\n\nclass MyClient : public cadabra::Client {\n\tpublic:\n\t\tMyClient();\n\n\t\tvoid on_connect();\n\t\tvoid on_disconnect();\n\t\tvoid on_network_error();\n\t\tvoid on_progress();\n\t\tvoid before_tree_change(ActionBase&);\n\t\tvoid after_tree_change(ActionBase&);\n\t};\n\nclass UI {\n\tpublic:\n\t\tvoid run();\n\t};\n\nMyClient client;\nUI       ui;\n\n\nMyClient::MyClient()\n\t: Client(0)\n\t{\n\t}\n\nvoid MyClient::on_connect()\n\t{\n\tstd::cout << \"connected to server\" << std::endl;\n\t}\n\nvoid MyClient::on_disconnect()\n\t{\n\tstd::cout << \"disconnected from server\" << std::endl;\n\t}\n\nvoid MyClient::on_network_error()\n\t{\n\tstd::cout << \"network error\" << std::endl;\n\t}\n\nvoid MyClient::on_progress()\n\t{\n\t}\n\nvoid MyClient::before_tree_change(ActionBase& ab)\n\t{\n\t}\n\nvoid MyClient::after_tree_change(ActionBase& ab)\n\t{\n\t}\n\nvoid UI::run()\n\t{\n\tint i;\n\tstd::cin >> i;\n\n\tcadabra::Client::iterator it=client.dtree().begin();\n\tauto cell = std::make_shared<cadabra::Client::DataCell>();\n\tauto ac = std::make_shared<cadabra::Client::ActionAddCell>(cell, it, cadabra::Client::ActionAddCell::Position::child);\n\n\ttry {\n\t\tstd::cout << \"calling perform\" << std::endl;\n\t\tclient.perform(ac);\n\t\t}\n\tcatch(std::error_code& ex) {\n\t\tstd::cout << ex.message() << std::endl;\n\t\t}\n\tstd::cout << \"perform called\" << std::endl;\n\n\tsleep(10);\n\t}\n\nint main(int, char **)\n\t{\n\t//\tclient.init();\n\tstd::cout << \"client connected\" << std::endl;\n\n\ttry {\n\t\t// Spawn two threads.\n\t\tstd::thread client_thread(&MyClient::run, std::ref(client));\n\t\tstd::thread ui_thread(&UI::run, ui);\n\n\t\t// Wait for all threads to finish.\n\t\tclient_thread.join();\n\t\tui_thread.join();\n\t\t}\n\tcatch(std::error_code& ex) {\n\t\tstd::cout << ex.message() << std::endl;\n\t\t}\n\n\t}\n"
  },
  {
    "path": "client_server/test_talk_to_server.cc",
    "content": "\n#include <websocketpp/client.hpp>\n#include <websocketpp/config/asio_no_tls_client.hpp>\n#include <websocketpp/common/functional.hpp>\n\n// Simple test program to talk to a cadabra server.\n\nusing websocketpp::lib::placeholders::_1;\nusing websocketpp::lib::placeholders::_2;\nusing websocketpp::lib::bind;\ntypedef websocketpp::client<websocketpp::config::asio_client> client;\ntypedef websocketpp::config::asio_client::message_type::ptr message_ptr;\n\nbool stopit=false;\n\nvoid on_open(client* c, websocketpp::connection_hdl hdl)\n\t{\n\t// now it is safe to use the connection\n\tstd::cout << \"connection ready\" << std::endl;\n\n\tstd::string msg;\n\n\tif(stopit) {\n\t\tmsg =\n\t\t   \"{ \\\"header\\\":   { \\\"uuid\\\": \\\"none\\\", \\\"msg_type\\\": \\\"execute_interrupt\\\" },\"\n\t\t   \"  \\\"content\\\":  { \\\"code\\\": \\\"print(42)\\n\\\"} \"\n\t\t   \"}\";\n\t\t}\n\telse {\n\t\tmsg =\n\t\t   \"{ \\\"header\\\":   { \\\"uuid\\\": \\\"none\\\", \\\"msg_type\\\": \\\"execute_request\\\" },\"\n\t\t   \"  \\\"content\\\":  { \\\"code\\\": \\\"import time\\nprint(42)\\ntime.sleep(10)\\n\\\"} \"\n\t\t   \"}\";\n\t\t}\n\n\t//\tc->send(hdl, \"import time\\nfor i in range(0,10):\\n   print('this is python talking '+str(i))\\nex=Ex('A_{m n}')\\nprint(str(ex))\", websocketpp::frame::opcode::text);\n\tc->send(hdl, msg, websocketpp::frame::opcode::text);\n\t}\n\nvoid on_message(client* c, websocketpp::connection_hdl hdl, message_ptr msg)\n\t{\n\tclient::connection_ptr con = c->get_con_from_hdl(hdl);\n\n\tstd::cout << \"received message on channel \" << con->get_resource() << std::endl;\n\tstd::cout << msg->get_payload() << std::endl;\n\t}\n\n\nint main(int argc, char **argv)\n\t{\n\tif(argc>1) stopit=true;\n\n\tclient c;\n\tc.clear_access_channels(websocketpp::log::alevel::all);\n\tc.clear_error_channels(websocketpp::log::elevel::all);\n\n\tstd::string uri = \"ws://localhost:9002\";\n\n\tc.init_asio();\n\tc.set_open_handler(bind(&on_open,&c,::_1));\n\tc.set_message_handler(bind(&on_message,&c,::_1,::_2));\n\n\twebsocketpp::lib::error_code ec;\n\tclient::connection_ptr con = c.get_connection(uri, ec);\n\tc.connect(con);\n\n\tstd::cout << \"connected\" << std::endl;\n\n\t// Start the ASIO io_service run loop\n\tc.run();\n\n\tstd::cout << \"run loop terminated\" << std::endl;\n\t}\n"
  },
  {
    "path": "client_server/tree.hh",
    "content": "\n//\tSTL-like templated tree class.\n//\n// Copyright (C) 2001-2014 Kasper Peeters <kasper@phi-sci.com>\n// Distributed under the GNU General Public License version 3.\n//\n// Special permission to use tree.hh under the conditions of a\n// different license can be requested from the author.\n\n/** \\mainpage tree.hh\n \t\t\t\\author   Kasper Peeters\n \t\t\t\\version  3.0\n \t\t\t\\date     25-Dec-2014\n \t\t\t\\see      http://tree.phi-sci.com/\n \t\t\t\\see      http://tree.phi-sci.com/ChangeLog\n\nThe tree.hh library for C++ provides an STL-like container class\nfor n-ary trees, templated over the data stored at the\n\tnodes. Various types of iterators are provided (post-order,\npre-order, and others). Where possible the access methods are\n\tcompatible with the STL or alternative algorithms are\navailable.\n*/\n\n\n#ifndef tree_hh_\n#define tree_hh_\n\n#include <cassert>\n#include <memory>\n#include <stdexcept>\n#include <iterator>\n#include <set>\n#include <queue>\n#include <algorithm>\n#include <cstddef>\n\n\n/// A node in the tree, combining links to other nodes as well as the actual data.\ntemplate<class T>\nclass tree_node_ { // size: 5*4=20 bytes (on 32 bit arch), can be reduced by 8.\n\tpublic:\n\t\ttree_node_();\n\t\ttree_node_(const T&);\n\n\t\ttree_node_<T> *parent;\n\t\ttree_node_<T> *first_child, *last_child;\n\t\ttree_node_<T> *prev_sibling, *next_sibling;\n\t\tT data;\n\t}; // __attribute__((packed));\n\ntemplate<class T>\ntree_node_<T>::tree_node_()\n\t: parent(0), first_child(0), last_child(0), prev_sibling(0), next_sibling(0)\n\t{\n\t}\n\ntemplate<class T>\ntree_node_<T>::tree_node_(const T& val)\n\t: parent(0), first_child(0), last_child(0), prev_sibling(0), next_sibling(0), data(val)\n\t{\n\t}\n\ntemplate <class T, class tree_node_allocator = std::allocator<tree_node_<T> > >\nclass tree {\n\tprotected:\n\t\ttypedef tree_node_<T> tree_node;\n\tpublic:\n\t\t/// Value of the data stored at a node.\n\t\ttypedef T value_type;\n\n\t\tclass iterator_base;\n\t\tclass pre_order_iterator;\n\t\tclass post_order_iterator;\n\t\tclass sibling_iterator;\n\t\tclass leaf_iterator;\n\n\t\ttree();                                         // empty constructor\n\t\ttree(const T&);                                 // constructor setting given element as head\n\t\ttree(const iterator_base&);\n\t\ttree(const tree<T, tree_node_allocator>&);      // copy constructor\n\t\ttree(tree<T, tree_node_allocator>&&);           // move constructor\n\t\t~tree();\n\t\ttree<T,tree_node_allocator>& operator=(const tree<T, tree_node_allocator>&);   // copy assignment\n\t\ttree<T,tree_node_allocator>& operator=(tree<T, tree_node_allocator>&&);        // move assignment\n\n\t\t/// Base class for iterators, only pointers stored, no traversal logic.\n#ifdef __SGI_STL_PORT\n\t\tclass iterator_base : public stlport::bidirectional_iterator<T, ptrdiff_t> {\n#else\n\t\tclass iterator_base {\n#endif\n\t\t\tpublic:\n\t\t\t\ttypedef T                               value_type;\n\t\t\t\ttypedef T*                              pointer;\n\t\t\t\ttypedef T&                              reference;\n\t\t\t\ttypedef size_t                          size_type;\n\t\t\t\ttypedef ptrdiff_t                       difference_type;\n\t\t\t\ttypedef std::bidirectional_iterator_tag iterator_category;\n\n\t\t\t\titerator_base();\n\t\t\t\titerator_base(tree_node *);\n\n\t\t\t\tT&             operator*() const;\n\t\t\t\tT*             operator->() const;\n\n\t\t\t\t/// When called, the next increment/decrement skips children of this node.\n\t\t\t\tvoid         skip_children();\n\t\t\t\tvoid         skip_children(bool skip);\n\t\t\t\t/// Number of children of the node pointed to by the iterator.\n\t\t\t\tunsigned int number_of_children() const;\n\n\t\t\t\tsibling_iterator begin() const;\n\t\t\t\tsibling_iterator end() const;\n\n\t\t\t\ttree_node *node;\n\t\t\tprotected:\n\t\t\t\tbool skip_current_children_;\n\t\t\t};\n\n\t\t/// Depth-first iterator, first accessing the node, then its children.\n\t\tclass pre_order_iterator : public iterator_base {\n\t\t\tpublic:\n\t\t\t\tpre_order_iterator();\n\t\t\t\tpre_order_iterator(tree_node *);\n\t\t\t\tpre_order_iterator(const iterator_base&);\n\t\t\t\tpre_order_iterator(const sibling_iterator&);\n\n\t\t\t\tbool    operator==(const pre_order_iterator&) const;\n\t\t\t\tbool    operator!=(const pre_order_iterator&) const;\n\t\t\t\tpre_order_iterator&  operator++();\n\t\t\t\tpre_order_iterator&  operator--();\n\t\t\t\tpre_order_iterator   operator++(int);\n\t\t\t\tpre_order_iterator   operator--(int);\n\t\t\t\tpre_order_iterator&  operator+=(unsigned int);\n\t\t\t\tpre_order_iterator&  operator-=(unsigned int);\n\n\t\t\t\tpre_order_iterator&  next_skip_children();\n\t\t\t};\n\n\t\t/// Depth-first iterator, first accessing the children, then the node itself.\n\t\tclass post_order_iterator : public iterator_base {\n\t\t\tpublic:\n\t\t\t\tpost_order_iterator();\n\t\t\t\tpost_order_iterator(tree_node *);\n\t\t\t\tpost_order_iterator(const iterator_base&);\n\t\t\t\tpost_order_iterator(const sibling_iterator&);\n\n\t\t\t\tbool    operator==(const post_order_iterator&) const;\n\t\t\t\tbool    operator!=(const post_order_iterator&) const;\n\t\t\t\tpost_order_iterator&  operator++();\n\t\t\t\tpost_order_iterator&  operator--();\n\t\t\t\tpost_order_iterator   operator++(int);\n\t\t\t\tpost_order_iterator   operator--(int);\n\t\t\t\tpost_order_iterator&  operator+=(unsigned int);\n\t\t\t\tpost_order_iterator&  operator-=(unsigned int);\n\n\t\t\t\t/// Set iterator to the first child as deep as possible down the tree.\n\t\t\t\tvoid descend_all();\n\t\t\t};\n\n\t\t/// Breadth-first iterator, using a queue\n\t\tclass breadth_first_queued_iterator : public iterator_base {\n\t\t\tpublic:\n\t\t\t\tbreadth_first_queued_iterator();\n\t\t\t\tbreadth_first_queued_iterator(tree_node *);\n\t\t\t\tbreadth_first_queued_iterator(const iterator_base&);\n\n\t\t\t\tbool    operator==(const breadth_first_queued_iterator&) const;\n\t\t\t\tbool    operator!=(const breadth_first_queued_iterator&) const;\n\t\t\t\tbreadth_first_queued_iterator&  operator++();\n\t\t\t\tbreadth_first_queued_iterator   operator++(int);\n\t\t\t\tbreadth_first_queued_iterator&  operator+=(unsigned int);\n\n\t\t\tprivate:\n\t\t\t\tstd::queue<tree_node *> traversal_queue;\n\t\t\t};\n\n\t\t/// The default iterator types throughout the tree class.\n\t\ttypedef pre_order_iterator            iterator;\n\t\ttypedef breadth_first_queued_iterator breadth_first_iterator;\n\n\t\t/// Iterator which traverses only the nodes at a given depth from the root.\n\t\tclass fixed_depth_iterator : public iterator_base {\n\t\t\tpublic:\n\t\t\t\tfixed_depth_iterator();\n\t\t\t\tfixed_depth_iterator(tree_node *);\n\t\t\t\tfixed_depth_iterator(const iterator_base&);\n\t\t\t\tfixed_depth_iterator(const sibling_iterator&);\n\t\t\t\tfixed_depth_iterator(const fixed_depth_iterator&);\n\n\t\t\t\tbool    operator==(const fixed_depth_iterator&) const;\n\t\t\t\tbool    operator!=(const fixed_depth_iterator&) const;\n\t\t\t\tfixed_depth_iterator&  operator++();\n\t\t\t\tfixed_depth_iterator&  operator--();\n\t\t\t\tfixed_depth_iterator   operator++(int);\n\t\t\t\tfixed_depth_iterator   operator--(int);\n\t\t\t\tfixed_depth_iterator&  operator+=(unsigned int);\n\t\t\t\tfixed_depth_iterator&  operator-=(unsigned int);\n\n\t\t\t\ttree_node *top_node;\n\t\t\t};\n\n\t\t/// Iterator which traverses only the nodes which are siblings of each other.\n\t\tclass sibling_iterator : public iterator_base {\n\t\t\tpublic:\n\t\t\t\tsibling_iterator();\n\t\t\t\tsibling_iterator(tree_node *);\n\t\t\t\tsibling_iterator(const sibling_iterator&);\n\t\t\t\tsibling_iterator(const iterator_base&);\n\n\t\t\t\tbool    operator==(const sibling_iterator&) const;\n\t\t\t\tbool    operator!=(const sibling_iterator&) const;\n\t\t\t\tsibling_iterator&  operator++();\n\t\t\t\tsibling_iterator&  operator--();\n\t\t\t\tsibling_iterator   operator++(int);\n\t\t\t\tsibling_iterator   operator--(int);\n\t\t\t\tsibling_iterator&  operator+=(unsigned int);\n\t\t\t\tsibling_iterator&  operator-=(unsigned int);\n\n\t\t\t\ttree_node *range_first() const;\n\t\t\t\ttree_node *range_last() const;\n\t\t\t\ttree_node *parent_;\n\t\t\tprivate:\n\t\t\t\tvoid set_parent_();\n\t\t\t};\n\n\t\t/// Iterator which traverses only the leaves.\n\t\tclass leaf_iterator : public iterator_base {\n\t\t\tpublic:\n\t\t\t\tleaf_iterator();\n\t\t\t\tleaf_iterator(tree_node *, tree_node *top=0);\n\t\t\t\tleaf_iterator(const sibling_iterator&);\n\t\t\t\tleaf_iterator(const iterator_base&);\n\n\t\t\t\tbool    operator==(const leaf_iterator&) const;\n\t\t\t\tbool    operator!=(const leaf_iterator&) const;\n\t\t\t\tleaf_iterator&  operator++();\n\t\t\t\tleaf_iterator&  operator--();\n\t\t\t\tleaf_iterator   operator++(int);\n\t\t\t\tleaf_iterator   operator--(int);\n\t\t\t\tleaf_iterator&  operator+=(unsigned int);\n\t\t\t\tleaf_iterator&  operator-=(unsigned int);\n\t\t\tprivate:\n\t\t\t\ttree_node *top_node;\n\t\t\t};\n\n\t\t/// Return iterator to the beginning of the tree.\n\t\tinline pre_order_iterator   begin() const;\n\t\t/// Return iterator to the end of the tree.\n\t\tinline pre_order_iterator   end() const;\n\t\t/// Return post-order iterator to the beginning of the tree.\n\t\tpost_order_iterator  begin_post() const;\n\t\t/// Return post-order end iterator of the tree.\n\t\tpost_order_iterator  end_post() const;\n\t\t/// Return fixed-depth iterator to the first node at a given depth from the given iterator.\n\t\tfixed_depth_iterator begin_fixed(const iterator_base&, unsigned int) const;\n\t\t/// Return fixed-depth end iterator.\n\t\tfixed_depth_iterator end_fixed(const iterator_base&, unsigned int) const;\n\t\t/// Return breadth-first iterator to the first node at a given depth.\n\t\tbreadth_first_queued_iterator begin_breadth_first() const;\n\t\t/// Return breadth-first end iterator.\n\t\tbreadth_first_queued_iterator end_breadth_first() const;\n\t\t/// Return sibling iterator to the first child of given node.\n\t\tsibling_iterator     begin(const iterator_base&) const;\n\t\t/// Return sibling end iterator for children of given node.\n\t\tsibling_iterator     end(const iterator_base&) const;\n\t\t/// Return leaf iterator to the first leaf of the tree.\n\t\tleaf_iterator   begin_leaf() const;\n\t\t/// Return leaf end iterator for entire tree.\n\t\tleaf_iterator   end_leaf() const;\n\t\t/// Return leaf iterator to the first leaf of the subtree at the given node.\n\t\tleaf_iterator   begin_leaf(const iterator_base& top) const;\n\t\t/// Return leaf end iterator for the subtree at the given node.\n\t\tleaf_iterator   end_leaf(const iterator_base& top) const;\n\n\t\t/// Return iterator to the parent of a node.\n\t\ttemplate<typename\titer> static iter parent(iter);\n\t\t/// Return iterator to the previous sibling of a node.\n\t\ttemplate<typename iter> static iter previous_sibling(iter);\n\t\t/// Return iterator to the next sibling of a node.\n\t\ttemplate<typename iter> static iter next_sibling(iter);\n\t\t/// Return iterator to the next node at a given depth.\n\t\ttemplate<typename iter> iter next_at_same_depth(iter) const;\n\n\t\t/// Erase all nodes of the tree.\n\t\tvoid     clear();\n\t\t/// Erase element at position pointed to by iterator, return incremented iterator.\n\t\ttemplate<typename iter> iter erase(iter);\n\t\t/// Erase all children of the node pointed to by iterator.\n\t\tvoid     erase_children(const iterator_base&);\n\n\t\t/// Insert empty node as last/first child of node pointed to by position.\n\t\ttemplate<typename iter> iter append_child(iter position);\n\t\ttemplate<typename iter> iter prepend_child(iter position);\n\t\t/// Insert node as last/first child of node pointed to by position.\n\t\ttemplate<typename iter> iter append_child(iter position, const T& x);\n\t\ttemplate<typename iter> iter prepend_child(iter position, const T& x);\n\t\t/// Append the node (plus its children) at other_position as last/first child of position.\n\t\ttemplate<typename iter> iter append_child(iter position, iter other_position);\n\t\ttemplate<typename iter> iter prepend_child(iter position, iter other_position);\n\t\t/// Append the nodes in the from-to range (plus their children) as last/first children of position.\n\t\ttemplate<typename iter> iter append_children(iter position, sibling_iterator from, sibling_iterator to);\n\t\ttemplate<typename iter> iter prepend_children(iter position, sibling_iterator from, sibling_iterator to);\n\n\t\t/// Short-hand to insert topmost node in otherwise empty tree.\n\t\tpre_order_iterator set_head(const T& x);\n\t\t/// Insert node as previous sibling of node pointed to by position.\n\t\ttemplate<typename iter> iter insert(iter position, const T& x);\n\t\t/// Specialisation of previous member.\n\t\tsibling_iterator insert(sibling_iterator position, const T& x);\n\t\t/// Insert node (with children) pointed to by subtree as previous sibling of node pointed to by position.\n\t\t/// Does not change the subtree itself (use move_in or move_in_below for that).\n\t\ttemplate<typename iter> iter insert_subtree(iter position, const iterator_base& subtree);\n\t\t/// Insert node as next sibling of node pointed to by position.\n\t\ttemplate<typename iter> iter insert_after(iter position, const T& x);\n\t\t/// Insert node (with children) pointed to by subtree as next sibling of node pointed to by position.\n\t\ttemplate<typename iter> iter insert_subtree_after(iter position, const iterator_base& subtree);\n\n\t\t/// Replace node at 'position' with other node (keeping same children); 'position' becomes invalid.\n\t\ttemplate<typename iter> iter replace(iter position, const T& x);\n\t\t/// Replace node at 'position' with subtree starting at 'from' (do not erase subtree at 'from'); see above.\n\t\ttemplate<typename iter> iter replace(iter position, const iterator_base& from);\n\t\t/// Replace string of siblings (plus their children) with copy of a new string (with children); see above\n\t\tsibling_iterator replace(sibling_iterator orig_begin, sibling_iterator orig_end,\n\t\t                         sibling_iterator new_begin,  sibling_iterator new_end);\n\n\t\t/// Move all children of node at 'position' to be siblings, returns position.\n\t\ttemplate<typename iter> iter flatten(iter position);\n\t\t/// Move nodes in range to be children of 'position'.\n\t\ttemplate<typename iter> iter reparent(iter position, sibling_iterator begin, sibling_iterator end);\n\t\t/// Move all child nodes of 'from' to be children of 'position'.\n\t\ttemplate<typename iter> iter reparent(iter position, iter from);\n\n\t\t/// Replace node with a new node, making the old node a child of the new node.\n\t\ttemplate<typename iter> iter wrap(iter position, const T& x);\n\n\t\t/// Move 'source' node (plus its children) to become the next sibling of 'target'.\n\t\ttemplate<typename iter> iter move_after(iter target, iter source);\n\t\t/// Move 'source' node (plus its children) to become the previous sibling of 'target'.\n\t\ttemplate<typename iter> iter move_before(iter target, iter source);\n\t\tsibling_iterator move_before(sibling_iterator target, sibling_iterator source);\n\t\t/// Move 'source' node (plus its children) to become the node at 'target' (erasing the node at 'target').\n\t\ttemplate<typename iter> iter move_ontop(iter target, iter source);\n\n\t\t/// Extract the subtree starting at the indicated node, removing it from the original tree.\n\t\ttree                         move_out(iterator);\n\t\t/// Inverse of take_out: inserts the given tree as previous sibling of indicated node by a\n\t\t/// move operation, that is, the given tree becomes empty. Returns iterator to the top node.\n\t\ttemplate<typename iter> iter move_in(iter, tree&);\n\t\t/// As above, but now make the tree a child of the indicated node.\n\t\ttemplate<typename iter> iter move_in_below(iter, tree&);\n\t\t/// As above, but now make the tree the nth child of the indicated node (if possible).\n\t\ttemplate<typename iter> iter move_in_as_nth_child(iter, size_t, tree&);\n\n\t\t/// Merge with other tree, creating new branches and leaves only if they are not already present.\n\t\tvoid     merge(sibling_iterator, sibling_iterator, sibling_iterator, sibling_iterator,\n\t\t               bool duplicate_leaves=false);\n\t\t/// Sort (std::sort only moves values of nodes, this one moves children as well).\n\t\tvoid     sort(sibling_iterator from, sibling_iterator to, bool deep=false);\n\t\ttemplate<class StrictWeakOrdering>\n\t\tvoid     sort(sibling_iterator from, sibling_iterator to, StrictWeakOrdering comp, bool deep=false);\n\t\t/// Compare two ranges of nodes (compares nodes as well as tree structure).\n\t\ttemplate<typename iter>\n\t\tbool     equal(const iter& one, const iter& two, const iter& three) const;\n\t\ttemplate<typename iter, class BinaryPredicate>\n\t\tbool     equal(const iter& one, const iter& two, const iter& three, BinaryPredicate) const;\n\t\ttemplate<typename iter>\n\t\tbool     equal_subtree(const iter& one, const iter& two) const;\n\t\ttemplate<typename iter, class BinaryPredicate>\n\t\tbool     equal_subtree(const iter& one, const iter& two, BinaryPredicate) const;\n\t\t/// Extract a new tree formed by the range of siblings plus all their children.\n\t\ttree     subtree(sibling_iterator from, sibling_iterator to) const;\n\t\tvoid     subtree(tree&, sibling_iterator from, sibling_iterator to) const;\n\t\t/// Exchange the node (plus subtree) with its sibling node (do nothing if no sibling present).\n\t\tvoid     swap(sibling_iterator it);\n\t\t/// Exchange two nodes (plus subtrees)\n\t\tvoid     swap(iterator, iterator);\n\n\t\t/// Count the total number of nodes.\n\t\tsize_t   size() const;\n\t\t/// Count the total number of nodes below the indicated node (plus one).\n\t\tsize_t   size(const iterator_base&) const;\n\t\t/// Check if tree is empty.\n\t\tbool     empty() const;\n\t\t/// Compute the depth to the root or to a fixed other iterator.\n\t\tstatic int depth(const iterator_base&);\n\t\tstatic int depth(const iterator_base&, const iterator_base&);\n\t\t/// Determine the maximal depth of the tree. An empty tree has max_depth=-1.\n\t\tint      max_depth() const;\n\t\t/// Determine the maximal depth of the tree with top node at the given position.\n\t\tint      max_depth(const iterator_base&) const;\n\t\t/// Count the number of children of node at position.\n\t\tstatic unsigned int number_of_children(const iterator_base&);\n\t\t/// Count the number of siblings (left and right) of node at iterator. Total nodes at this level is +1.\n\t\tunsigned int number_of_siblings(const iterator_base&) const;\n\t\t/// Determine whether node at position is in the subtrees with root in the range.\n\t\tbool     is_in_subtree(const iterator_base& position, const iterator_base& begin,\n\t\t                       const iterator_base& end) const;\n\t\t/// Determine whether the iterator is an 'end' iterator and thus not actually pointing to a node.\n\t\tbool     is_valid(const iterator_base&) const;\n\t\t/// Find the lowest common ancestor of two nodes, that is, the deepest node such that\n\t\t/// both nodes are descendants of it.\n\t\titerator lowest_common_ancestor(const iterator_base&, const iterator_base &) const;\n\n\t\t/// Determine the index of a node in the range of siblings to which it belongs.\n\t\tunsigned int index(sibling_iterator it) const;\n\t\t/// Inverse of 'index': return the n-th child of the node at position.\n\t\tstatic sibling_iterator child(const iterator_base& position, unsigned int);\n\t\t/// Return iterator to the sibling indicated by index\n\t\tsibling_iterator sibling(const iterator_base& position, unsigned int);\n\n\t\t/// For debugging only: verify internal consistency by inspecting all pointers in the tree\n\t\t/// (which will also trigger a valgrind error in case something got corrupted).\n\t\tvoid debug_verify_consistency() const;\n\n\t\t/// Comparator class for iterators (compares pointer values; why doesn't this work automatically?)\n\t\tclass iterator_base_less {\n\t\t\tpublic:\n\t\t\t\tbool operator()(const typename tree<T, tree_node_allocator>::iterator_base& one,\n\t\t\t\t                const typename tree<T, tree_node_allocator>::iterator_base& two) const\n\t\t\t\t\t{\n\t\t\t\t\treturn one.node < two.node;\n\t\t\t\t\t}\n\t\t\t};\n\t\ttree_node *head, *feet;    // head/feet are always dummy; if an iterator points to them it is invalid\n\tprivate:\n\t\ttree_node_allocator alloc_;\n\t\tvoid head_initialise_();\n\t\tvoid copy_(const tree<T, tree_node_allocator>& other);\n\n\t\t/// Comparator class for two nodes of a tree (used for sorting and searching).\n\t\ttemplate<class StrictWeakOrdering>\n\t\tclass compare_nodes {\n\t\t\tpublic:\n\t\t\t\tcompare_nodes(StrictWeakOrdering comp) : comp_(comp) {};\n\n\t\t\t\tbool operator()(const tree_node *a, const tree_node *b)\n\t\t\t\t\t{\n\t\t\t\t\treturn comp_(a->data, b->data);\n\t\t\t\t\t}\n\t\t\tprivate:\n\t\t\t\tStrictWeakOrdering comp_;\n\t\t\t};\n\t};\n\n//template <class T, class tree_node_allocator>\n//class iterator_base_less {\n//\tpublic:\n//\t\tbool operator()(const typename tree<T, tree_node_allocator>::iterator_base& one,\n//\t\t\t\t\t\t  const typename tree<T, tree_node_allocator>::iterator_base& two) const\n//\t\t\t{\n//\t\t\ttxtout << \"operatorclass<\" << one.node < two.node << std::endl;\n//\t\t\treturn one.node < two.node;\n//\t\t\t}\n//};\n\n// template <class T, class tree_node_allocator>\n// bool operator<(const typename tree<T, tree_node_allocator>::iterator& one,\n// \t\t\t\t\tconst typename tree<T, tree_node_allocator>::iterator& two)\n// \t{\n// \ttxtout << \"operator< \" << one.node < two.node << std::endl;\n// \tif(one.node < two.node) return true;\n// \treturn false;\n// \t}\n//\n// template <class T, class tree_node_allocator>\n// bool operator==(const typename tree<T, tree_node_allocator>::iterator& one,\n// \t\t\t\t\tconst typename tree<T, tree_node_allocator>::iterator& two)\n// \t{\n// \ttxtout << \"operator== \" << one.node == two.node << std::endl;\n// \tif(one.node == two.node) return true;\n// \treturn false;\n// \t}\n//\n// template <class T, class tree_node_allocator>\n// bool operator>(const typename tree<T, tree_node_allocator>::iterator_base& one,\n// \t\t\t\t\tconst typename tree<T, tree_node_allocator>::iterator_base& two)\n// \t{\n// \ttxtout << \"operator> \" << one.node < two.node << std::endl;\n// \tif(one.node > two.node) return true;\n// \treturn false;\n// \t}\n\n\n\n// Tree\n\ntemplate <class T, class tree_node_allocator>\ntree<T, tree_node_allocator>::tree()\n\t{\n\thead_initialise_();\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntree<T, tree_node_allocator>::tree(const T& x)\n\t{\n\thead_initialise_();\n\tset_head(x);\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntree<T, tree_node_allocator>::tree(tree<T, tree_node_allocator>&& x)\n\t{\n\thead_initialise_();\n\thead->next_sibling=x.head->next_sibling;\n\tfeet->prev_sibling=x.head->prev_sibling;\n\tx.head->next_sibling->prev_sibling=head;\n\tx.feet->prev_sibling->next_sibling=feet;\n\tx.head->next_sibling=x.feet;\n\tx.feet->prev_sibling=x.head;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntree<T, tree_node_allocator>::tree(const iterator_base& other)\n\t{\n\thead_initialise_();\n\tset_head((*other));\n\treplace(begin(), other);\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntree<T, tree_node_allocator>::~tree()\n\t{\n\tclear();\n\talloc_.destroy(head);\n\talloc_.destroy(feet);\n\talloc_.deallocate(head,1);\n\talloc_.deallocate(feet,1);\n\t}\n\ntemplate <class T, class tree_node_allocator>\nvoid tree<T, tree_node_allocator>::head_initialise_()\n\t{\n\thead = alloc_.allocate(1,0); // MSVC does not have default second argument\n\tfeet = alloc_.allocate(1,0);\n\talloc_.construct(head, tree_node_<T>());\n\talloc_.construct(feet, tree_node_<T>());\n\n\thead->parent=0;\n\thead->first_child=0;\n\thead->last_child=0;\n\thead->prev_sibling=0; //head;\n\thead->next_sibling=feet; //head;\n\n\tfeet->parent=0;\n\tfeet->first_child=0;\n\tfeet->last_child=0;\n\tfeet->prev_sibling=head;\n\tfeet->next_sibling=0;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntree<T,tree_node_allocator>& tree<T, tree_node_allocator>::operator=(const tree<T, tree_node_allocator>& other)\n\t{\n\tif(this != &other)\n\t\tcopy_(other);\n\treturn *this;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntree<T,tree_node_allocator>& tree<T, tree_node_allocator>::operator=(tree<T, tree_node_allocator>&& x)\n\t{\n\tif(this != &x) {\n\t\thead->next_sibling=x.head->next_sibling;\n\t\tfeet->prev_sibling=x.head->prev_sibling;\n\t\tx.head->next_sibling->prev_sibling=head;\n\t\tx.feet->prev_sibling->next_sibling=feet;\n\t\tx.head->next_sibling=x.feet;\n\t\tx.feet->prev_sibling=x.head;\n\t\t}\n\treturn *this;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntree<T, tree_node_allocator>::tree(const tree<T, tree_node_allocator>& other)\n\t{\n\thead_initialise_();\n\tcopy_(other);\n\t}\n\ntemplate <class T, class tree_node_allocator>\nvoid tree<T, tree_node_allocator>::copy_(const tree<T, tree_node_allocator>& other)\n\t{\n\tclear();\n\tpre_order_iterator it=other.begin(), to=begin();\n\twhile(it!=other.end()) {\n\t\tto=insert(to, (*it));\n\t\tit.skip_children();\n\t\t++it;\n\t\t}\n\tto=begin();\n\tit=other.begin();\n\twhile(it!=other.end()) {\n\t\tto=replace(to, it);\n\t\tto.skip_children();\n\t\tit.skip_children();\n\t\t++to;\n\t\t++it;\n\t\t}\n\t}\n\ntemplate <class T, class tree_node_allocator>\nvoid tree<T, tree_node_allocator>::clear()\n\t{\n\tif(head)\n\t\twhile(head->next_sibling!=feet)\n\t\t\terase(pre_order_iterator(head->next_sibling));\n\t}\n\ntemplate<class T, class tree_node_allocator>\nvoid tree<T, tree_node_allocator>::erase_children(const iterator_base& it)\n\t{\n\t//\tstd::cout << \"erase_children \" << it.node << std::endl;\n\tif(it.node==0) return;\n\n\ttree_node *cur=it.node->first_child;\n\ttree_node *prev=0;\n\n\twhile(cur!=0) {\n\t\tprev=cur;\n\t\tcur=cur->next_sibling;\n\t\terase_children(pre_order_iterator(prev));\n\t\t//\t\tkp::destructor(&prev->data);\n\t\talloc_.destroy(prev);\n\t\talloc_.deallocate(prev,1);\n\t\t}\n\tit.node->first_child=0;\n\tit.node->last_child=0;\n\t//\tstd::cout << \"exit\" << std::endl;\n\t}\n\ntemplate<class T, class tree_node_allocator>\ntemplate<class iter>\niter tree<T, tree_node_allocator>::erase(iter it)\n\t{\n\ttree_node *cur=it.node;\n\tassert(cur!=head);\n\titer ret=it;\n\tret.skip_children();\n\t++ret;\n\terase_children(it);\n\tif(cur->prev_sibling==0) {\n\t\tcur->parent->first_child=cur->next_sibling;\n\t\t}\n\telse {\n\t\tcur->prev_sibling->next_sibling=cur->next_sibling;\n\t\t}\n\tif(cur->next_sibling==0) {\n\t\tcur->parent->last_child=cur->prev_sibling;\n\t\t}\n\telse {\n\t\tcur->next_sibling->prev_sibling=cur->prev_sibling;\n\t\t}\n\n\t//\tkp::destructor(&cur->data);\n\talloc_.destroy(cur);\n\talloc_.deallocate(cur,1);\n\treturn ret;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::pre_order_iterator tree<T, tree_node_allocator>::begin() const\n\t{\n\treturn pre_order_iterator(head->next_sibling);\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::pre_order_iterator tree<T, tree_node_allocator>::end() const\n\t{\n\treturn pre_order_iterator(feet);\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::breadth_first_queued_iterator tree<T, tree_node_allocator>::begin_breadth_first() const\n\t{\n\treturn breadth_first_queued_iterator(head->next_sibling);\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::breadth_first_queued_iterator tree<T, tree_node_allocator>::end_breadth_first() const\n\t{\n\treturn breadth_first_queued_iterator();\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::post_order_iterator tree<T, tree_node_allocator>::begin_post() const\n\t{\n\ttree_node *tmp=head->next_sibling;\n\tif(tmp!=feet) {\n\t\twhile(tmp->first_child)\n\t\t\ttmp=tmp->first_child;\n\t\t}\n\treturn post_order_iterator(tmp);\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::post_order_iterator tree<T, tree_node_allocator>::end_post() const\n\t{\n\treturn post_order_iterator(feet);\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::fixed_depth_iterator tree<T, tree_node_allocator>::begin_fixed(const iterator_base& pos, unsigned int dp) const\n\t{\n\ttypename tree<T, tree_node_allocator>::fixed_depth_iterator ret;\n\tret.top_node=pos.node;\n\n\ttree_node *tmp=pos.node;\n\tunsigned int curdepth=0;\n\twhile(curdepth<dp) { // go down one level\n\t\twhile(tmp->first_child==0) {\n\t\t\tif(tmp->next_sibling==0) {\n\t\t\t\t// try to walk up and then right again\n\t\t\t\tdo {\n\t\t\t\t\tif(tmp==ret.top_node)\n\t\t\t\t\t\tthrow std::range_error(\"tree: begin_fixed out of range\");\n\t\t\t\t\ttmp=tmp->parent;\n\t\t\t\t\tif(tmp==0)\n\t\t\t\t\t\tthrow std::range_error(\"tree: begin_fixed out of range\");\n\t\t\t\t\t--curdepth;\n\t\t\t\t\t}\n\t\t\t\twhile(tmp->next_sibling==0);\n\t\t\t\t}\n\t\t\ttmp=tmp->next_sibling;\n\t\t\t}\n\t\ttmp=tmp->first_child;\n\t\t++curdepth;\n\t\t}\n\n\tret.node=tmp;\n\treturn ret;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::fixed_depth_iterator tree<T, tree_node_allocator>::end_fixed(const iterator_base& pos, unsigned int dp) const\n\t{\n\tassert(1==0); // FIXME: not correct yet: use is_valid() as a temporary workaround\n\ttree_node *tmp=pos.node;\n\tunsigned int curdepth=1;\n\twhile(curdepth<dp) { // go down one level\n\t\twhile(tmp->first_child==0) {\n\t\t\ttmp=tmp->next_sibling;\n\t\t\tif(tmp==0)\n\t\t\t\tthrow std::range_error(\"tree: end_fixed out of range\");\n\t\t\t}\n\t\ttmp=tmp->first_child;\n\t\t++curdepth;\n\t\t}\n\treturn tmp;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::sibling_iterator tree<T, tree_node_allocator>::begin(const iterator_base& pos) const\n\t{\n\tassert(pos.node!=0);\n\tif(pos.node->first_child==0) {\n\t\treturn end(pos);\n\t\t}\n\treturn pos.node->first_child;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::sibling_iterator tree<T, tree_node_allocator>::end(const iterator_base& pos) const\n\t{\n\tsibling_iterator ret(0);\n\tret.parent_=pos.node;\n\treturn ret;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::leaf_iterator tree<T, tree_node_allocator>::begin_leaf() const\n\t{\n\ttree_node *tmp=head->next_sibling;\n\tif(tmp!=feet) {\n\t\twhile(tmp->first_child)\n\t\t\ttmp=tmp->first_child;\n\t\t}\n\treturn leaf_iterator(tmp);\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::leaf_iterator tree<T, tree_node_allocator>::end_leaf() const\n\t{\n\treturn leaf_iterator(feet);\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::leaf_iterator tree<T, tree_node_allocator>::begin_leaf(const iterator_base& top) const\n\t{\n\ttree_node *tmp=top.node;\n\twhile(tmp->first_child)\n\t\ttmp=tmp->first_child;\n\treturn leaf_iterator(tmp, top.node);\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::leaf_iterator tree<T, tree_node_allocator>::end_leaf(const iterator_base& top) const\n\t{\n\treturn leaf_iterator(top.node, top.node);\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntemplate <typename iter>\niter tree<T, tree_node_allocator>::parent(iter position)\n\t{\n\tassert(position.node!=0);\n\treturn iter(position.node->parent);\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntemplate <typename iter>\niter tree<T, tree_node_allocator>::previous_sibling(iter position)\n\t{\n\tassert(position.node!=0);\n\titer ret(position);\n\tret.node=position.node->prev_sibling;\n\treturn ret;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntemplate <typename iter>\niter tree<T, tree_node_allocator>::next_sibling(iter position)\n\t{\n\tassert(position.node!=0);\n\titer ret(position);\n\tret.node=position.node->next_sibling;\n\treturn ret;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntemplate <typename iter>\niter tree<T, tree_node_allocator>::next_at_same_depth(iter position) const\n\t{\n\t// We make use of a temporary fixed_depth iterator to implement this.\n\n\ttypename tree<T, tree_node_allocator>::fixed_depth_iterator tmp(position.node);\n\n\t++tmp;\n\treturn iter(tmp);\n\n\t//\tassert(position.node!=0);\n\t//\titer ret(position);\n\t//\n\t//\tif(position.node->next_sibling) {\n\t//\t\tret.node=position.node->next_sibling;\n\t//\t\t}\n\t//\telse {\n\t//\t\tint relative_depth=0;\n\t//\t   upper:\n\t//\t\tdo {\n\t//\t\t\tret.node=ret.node->parent;\n\t//\t\t\tif(ret.node==0) return ret;\n\t//\t\t\t--relative_depth;\n\t//\t\t\t} while(ret.node->next_sibling==0);\n\t//\t   lower:\n\t//\t\tret.node=ret.node->next_sibling;\n\t//\t\twhile(ret.node->first_child==0) {\n\t//\t\t\tif(ret.node->next_sibling==0)\n\t//\t\t\t\tgoto upper;\n\t//\t\t\tret.node=ret.node->next_sibling;\n\t//\t\t\tif(ret.node==0) return ret;\n\t//\t\t\t}\n\t//\t\twhile(relative_depth<0 && ret.node->first_child!=0) {\n\t//\t\t\tret.node=ret.node->first_child;\n\t//\t\t\t++relative_depth;\n\t//\t\t\t}\n\t//\t\tif(relative_depth<0) {\n\t//\t\t\tif(ret.node->next_sibling==0) goto upper;\n\t//\t\t\telse                          goto lower;\n\t//\t\t\t}\n\t//\t\t}\n\t//\treturn ret;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntemplate <typename iter>\niter tree<T, tree_node_allocator>::append_child(iter position)\n\t{\n\tassert(position.node!=head);\n\tassert(position.node!=feet);\n\tassert(position.node);\n\n\ttree_node *tmp=alloc_.allocate(1,0);\n\talloc_.construct(tmp, tree_node_<T>());\n\t//\tkp::constructor(&tmp->data);\n\ttmp->first_child=0;\n\ttmp->last_child=0;\n\n\ttmp->parent=position.node;\n\tif(position.node->last_child!=0) {\n\t\tposition.node->last_child->next_sibling=tmp;\n\t\t}\n\telse {\n\t\tposition.node->first_child=tmp;\n\t\t}\n\ttmp->prev_sibling=position.node->last_child;\n\tposition.node->last_child=tmp;\n\ttmp->next_sibling=0;\n\treturn tmp;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntemplate <typename iter>\niter tree<T, tree_node_allocator>::prepend_child(iter position)\n\t{\n\tassert(position.node!=head);\n\tassert(position.node!=feet);\n\tassert(position.node);\n\n\ttree_node *tmp=alloc_.allocate(1,0);\n\talloc_.construct(tmp, tree_node_<T>());\n\t//\tkp::constructor(&tmp->data);\n\ttmp->first_child=0;\n\ttmp->last_child=0;\n\n\ttmp->parent=position.node;\n\tif(position.node->first_child!=0) {\n\t\tposition.node->first_child->prev_sibling=tmp;\n\t\t}\n\telse {\n\t\tposition.node->last_child=tmp;\n\t\t}\n\ttmp->next_sibling=position.node->first_child;\n\tposition.node->prev_child=tmp;\n\ttmp->prev_sibling=0;\n\treturn tmp;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntemplate <class iter>\niter tree<T, tree_node_allocator>::append_child(iter position, const T& x)\n\t{\n\t// If your program fails here you probably used 'append_child' to add the top\n\t// node to an empty tree. From version 1.45 the top element should be added\n\t// using 'insert'. See the documentation for further information, and sorry about\n\t// the API change.\n\tassert(position.node!=head);\n\tassert(position.node!=feet);\n\tassert(position.node);\n\n\ttree_node* tmp = alloc_.allocate(1,0);\n\talloc_.construct(tmp, x);\n\t//\tkp::constructor(&tmp->data, x);\n\ttmp->first_child=0;\n\ttmp->last_child=0;\n\n\ttmp->parent=position.node;\n\tif(position.node->last_child!=0) {\n\t\tposition.node->last_child->next_sibling=tmp;\n\t\t}\n\telse {\n\t\tposition.node->first_child=tmp;\n\t\t}\n\ttmp->prev_sibling=position.node->last_child;\n\tposition.node->last_child=tmp;\n\ttmp->next_sibling=0;\n\treturn tmp;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntemplate <class iter>\niter tree<T, tree_node_allocator>::prepend_child(iter position, const T& x)\n\t{\n\tassert(position.node!=head);\n\tassert(position.node!=feet);\n\tassert(position.node);\n\n\ttree_node* tmp = alloc_.allocate(1,0);\n\talloc_.construct(tmp, x);\n\t//\tkp::constructor(&tmp->data, x);\n\ttmp->first_child=0;\n\ttmp->last_child=0;\n\n\ttmp->parent=position.node;\n\tif(position.node->first_child!=0) {\n\t\tposition.node->first_child->prev_sibling=tmp;\n\t\t}\n\telse {\n\t\tposition.node->last_child=tmp;\n\t\t}\n\ttmp->next_sibling=position.node->first_child;\n\tposition.node->first_child=tmp;\n\ttmp->prev_sibling=0;\n\treturn tmp;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntemplate <class iter>\niter tree<T, tree_node_allocator>::append_child(iter position, iter other)\n\t{\n\tassert(position.node!=head);\n\tassert(position.node!=feet);\n\tassert(position.node);\n\n\tsibling_iterator aargh=append_child(position, value_type());\n\treturn replace(aargh, other);\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntemplate <class iter>\niter tree<T, tree_node_allocator>::prepend_child(iter position, iter other)\n\t{\n\tassert(position.node!=head);\n\tassert(position.node!=feet);\n\tassert(position.node);\n\n\tsibling_iterator aargh=prepend_child(position, value_type());\n\treturn replace(aargh, other);\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntemplate <class iter>\niter tree<T, tree_node_allocator>::append_children(iter position, sibling_iterator from, sibling_iterator to)\n\t{\n\tassert(position.node!=head);\n\tassert(position.node!=feet);\n\tassert(position.node);\n\n\titer ret=from;\n\n\twhile(from!=to) {\n\t\tinsert_subtree(position.end(), from);\n\t\t++from;\n\t\t}\n\treturn ret;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntemplate <class iter>\niter tree<T, tree_node_allocator>::prepend_children(iter position, sibling_iterator from, sibling_iterator to)\n\t{\n\tassert(position.node!=head);\n\tassert(position.node!=feet);\n\tassert(position.node);\n\n\titer ret=from;\n\n\twhile(from!=to) {\n\t\tinsert_subtree(position.begin(), from);\n\t\t++from;\n\t\t}\n\treturn ret;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::pre_order_iterator tree<T, tree_node_allocator>::set_head(const T& x)\n\t{\n\tassert(head->next_sibling==feet);\n\treturn insert(iterator(feet), x);\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntemplate <class iter>\niter tree<T, tree_node_allocator>::insert(iter position, const T& x)\n\t{\n\tif(position.node==0) {\n\t\tposition.node=feet; // Backward compatibility: when calling insert on a null node,\n\t\t// insert before the feet.\n\t\t}\n\ttree_node* tmp = alloc_.allocate(1,0);\n\talloc_.construct(tmp, x);\n\t//\tkp::constructor(&tmp->data, x);\n\ttmp->first_child=0;\n\ttmp->last_child=0;\n\n\ttmp->parent=position.node->parent;\n\ttmp->next_sibling=position.node;\n\ttmp->prev_sibling=position.node->prev_sibling;\n\tposition.node->prev_sibling=tmp;\n\n\tif(tmp->prev_sibling==0) {\n\t\tif(tmp->parent) // when inserting nodes at the head, there is no parent\n\t\t\ttmp->parent->first_child=tmp;\n\t\t}\n\telse\n\t\ttmp->prev_sibling->next_sibling=tmp;\n\treturn tmp;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::sibling_iterator tree<T, tree_node_allocator>::insert(sibling_iterator position, const T& x)\n\t{\n\ttree_node* tmp = alloc_.allocate(1,0);\n\talloc_.construct(tmp, x);\n\t//\tkp::constructor(&tmp->data, x);\n\ttmp->first_child=0;\n\ttmp->last_child=0;\n\n\ttmp->next_sibling=position.node;\n\tif(position.node==0) { // iterator points to end of a subtree\n\t\ttmp->parent=position.parent_;\n\t\ttmp->prev_sibling=position.range_last();\n\t\ttmp->parent->last_child=tmp;\n\t\t}\n\telse {\n\t\ttmp->parent=position.node->parent;\n\t\ttmp->prev_sibling=position.node->prev_sibling;\n\t\tposition.node->prev_sibling=tmp;\n\t\t}\n\n\tif(tmp->prev_sibling==0) {\n\t\tif(tmp->parent) // when inserting nodes at the head, there is no parent\n\t\t\ttmp->parent->first_child=tmp;\n\t\t}\n\telse\n\t\ttmp->prev_sibling->next_sibling=tmp;\n\treturn tmp;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntemplate <class iter>\niter tree<T, tree_node_allocator>::insert_after(iter position, const T& x)\n\t{\n\ttree_node* tmp = alloc_.allocate(1,0);\n\talloc_.construct(tmp, x);\n\t//\tkp::constructor(&tmp->data, x);\n\ttmp->first_child=0;\n\ttmp->last_child=0;\n\n\ttmp->parent=position.node->parent;\n\ttmp->prev_sibling=position.node;\n\ttmp->next_sibling=position.node->next_sibling;\n\tposition.node->next_sibling=tmp;\n\n\tif(tmp->next_sibling==0) {\n\t\tif(tmp->parent) // when inserting nodes at the head, there is no parent\n\t\t\ttmp->parent->last_child=tmp;\n\t\t}\n\telse {\n\t\ttmp->next_sibling->prev_sibling=tmp;\n\t\t}\n\treturn tmp;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntemplate <class iter>\niter tree<T, tree_node_allocator>::insert_subtree(iter position, const iterator_base& subtree)\n\t{\n\t// insert dummy\n\titer it=insert(position, value_type());\n\t// replace dummy with subtree\n\treturn replace(it, subtree);\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntemplate <class iter>\niter tree<T, tree_node_allocator>::insert_subtree_after(iter position, const iterator_base& subtree)\n\t{\n\t// insert dummy\n\titer it=insert_after(position, value_type());\n\t// replace dummy with subtree\n\treturn replace(it, subtree);\n\t}\n\n// template <class T, class tree_node_allocator>\n// template <class iter>\n// iter tree<T, tree_node_allocator>::insert_subtree(sibling_iterator position, iter subtree)\n// \t{\n// \t// insert dummy\n// \titer it(insert(position, value_type()));\n// \t// replace dummy with subtree\n// \treturn replace(it, subtree);\n// \t}\n\ntemplate <class T, class tree_node_allocator>\ntemplate <class iter>\niter tree<T, tree_node_allocator>::replace(iter position, const T& x)\n\t{\n\t//\tkp::destructor(&position.node->data);\n\t//\tkp::constructor(&position.node->data, x);\n\tposition.node->data=x;\n\t//\talloc_.destroy(position.node);\n\t//\talloc_.construct(position.node, x);\n\treturn position;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntemplate <class iter>\niter tree<T, tree_node_allocator>::replace(iter position, const iterator_base& from)\n\t{\n\tassert(position.node!=head);\n\ttree_node *current_from=from.node;\n\ttree_node *start_from=from.node;\n\ttree_node *current_to  =position.node;\n\n\t// replace the node at position with head of the replacement tree at from\n\t//\tstd::cout << \"warning!\" << position.node << std::endl;\n\terase_children(position);\n\t//\tstd::cout << \"no warning!\" << std::endl;\n\ttree_node* tmp = alloc_.allocate(1,0);\n\talloc_.construct(tmp, (*from));\n\t//\tkp::constructor(&tmp->data, (*from));\n\ttmp->first_child=0;\n\ttmp->last_child=0;\n\tif(current_to->prev_sibling==0) {\n\t\tif(current_to->parent!=0)\n\t\t\tcurrent_to->parent->first_child=tmp;\n\t\t}\n\telse {\n\t\tcurrent_to->prev_sibling->next_sibling=tmp;\n\t\t}\n\ttmp->prev_sibling=current_to->prev_sibling;\n\tif(current_to->next_sibling==0) {\n\t\tif(current_to->parent!=0)\n\t\t\tcurrent_to->parent->last_child=tmp;\n\t\t}\n\telse {\n\t\tcurrent_to->next_sibling->prev_sibling=tmp;\n\t\t}\n\ttmp->next_sibling=current_to->next_sibling;\n\ttmp->parent=current_to->parent;\n\t//\tkp::destructor(&current_to->data);\n\talloc_.destroy(current_to);\n\talloc_.deallocate(current_to,1);\n\tcurrent_to=tmp;\n\n\t// only at this stage can we fix 'last'\n\ttree_node *last=from.node->next_sibling;\n\n\tpre_order_iterator toit=tmp;\n\t// copy all children\n\tdo {\n\t\tassert(current_from!=0);\n\t\tif(current_from->first_child != 0) {\n\t\t\tcurrent_from=current_from->first_child;\n\t\t\ttoit=append_child(toit, current_from->data);\n\t\t\t}\n\t\telse {\n\t\t\twhile(current_from->next_sibling==0 && current_from!=start_from) {\n\t\t\t\tcurrent_from=current_from->parent;\n\t\t\t\ttoit=parent(toit);\n\t\t\t\tassert(current_from!=0);\n\t\t\t\t}\n\t\t\tcurrent_from=current_from->next_sibling;\n\t\t\tif(current_from!=last) {\n\t\t\t\ttoit=append_child(parent(toit), current_from->data);\n\t\t\t\t}\n\t\t\t}\n\t\t}\n\twhile(current_from!=last);\n\n\treturn current_to;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::sibling_iterator tree<T, tree_node_allocator>::replace(\n   sibling_iterator orig_begin,\n   sibling_iterator orig_end,\n   sibling_iterator new_begin,\n   sibling_iterator new_end)\n\t{\n\ttree_node *orig_first=orig_begin.node;\n\ttree_node *new_first=new_begin.node;\n\ttree_node *orig_last=orig_first;\n\twhile((++orig_begin)!=orig_end)\n\t\torig_last=orig_last->next_sibling;\n\ttree_node *new_last=new_first;\n\twhile((++new_begin)!=new_end)\n\t\tnew_last=new_last->next_sibling;\n\n\t// insert all siblings in new_first..new_last before orig_first\n\tbool first=true;\n\tpre_order_iterator ret;\n\twhile(1==1) {\n\t\tpre_order_iterator tt=insert_subtree(pre_order_iterator(orig_first), pre_order_iterator(new_first));\n\t\tif(first) {\n\t\t\tret=tt;\n\t\t\tfirst=false;\n\t\t\t}\n\t\tif(new_first==new_last)\n\t\t\tbreak;\n\t\tnew_first=new_first->next_sibling;\n\t\t}\n\n\t// erase old range of siblings\n\tbool last=false;\n\ttree_node *next=orig_first;\n\twhile(1==1) {\n\t\tif(next==orig_last)\n\t\t\tlast=true;\n\t\tnext=next->next_sibling;\n\t\terase((pre_order_iterator)orig_first);\n\t\tif(last)\n\t\t\tbreak;\n\t\torig_first=next;\n\t\t}\n\treturn ret;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntemplate <typename iter>\niter tree<T, tree_node_allocator>::flatten(iter position)\n\t{\n\tif(position.node->first_child==0)\n\t\treturn position;\n\n\ttree_node *tmp=position.node->first_child;\n\twhile(tmp) {\n\t\ttmp->parent=position.node->parent;\n\t\ttmp=tmp->next_sibling;\n\t\t}\n\tif(position.node->next_sibling) {\n\t\tposition.node->last_child->next_sibling=position.node->next_sibling;\n\t\tposition.node->next_sibling->prev_sibling=position.node->last_child;\n\t\t}\n\telse {\n\t\tposition.node->parent->last_child=position.node->last_child;\n\t\t}\n\tposition.node->next_sibling=position.node->first_child;\n\tposition.node->next_sibling->prev_sibling=position.node;\n\tposition.node->first_child=0;\n\tposition.node->last_child=0;\n\n\treturn position;\n\t}\n\n\ntemplate <class T, class tree_node_allocator>\ntemplate <typename iter>\niter tree<T, tree_node_allocator>::reparent(iter position, sibling_iterator begin, sibling_iterator end)\n\t{\n\ttree_node *first=begin.node;\n\ttree_node *last=first;\n\n\tassert(first!=position.node);\n\n\tif(begin==end) return begin;\n\t// determine last node\n\twhile((++begin)!=end) {\n\t\tlast=last->next_sibling;\n\t\t}\n\t// move subtree\n\tif(first->prev_sibling==0) {\n\t\tfirst->parent->first_child=last->next_sibling;\n\t\t}\n\telse {\n\t\tfirst->prev_sibling->next_sibling=last->next_sibling;\n\t\t}\n\tif(last->next_sibling==0) {\n\t\tlast->parent->last_child=first->prev_sibling;\n\t\t}\n\telse {\n\t\tlast->next_sibling->prev_sibling=first->prev_sibling;\n\t\t}\n\tif(position.node->first_child==0) {\n\t\tposition.node->first_child=first;\n\t\tposition.node->last_child=last;\n\t\tfirst->prev_sibling=0;\n\t\t}\n\telse {\n\t\tposition.node->last_child->next_sibling=first;\n\t\tfirst->prev_sibling=position.node->last_child;\n\t\tposition.node->last_child=last;\n\t\t}\n\tlast->next_sibling=0;\n\n\ttree_node *pos=first;\n\tfor(;;) {\n\t\tpos->parent=position.node;\n\t\tif(pos==last) break;\n\t\tpos=pos->next_sibling;\n\t\t}\n\n\treturn first;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntemplate <typename iter> iter tree<T, tree_node_allocator>::reparent(iter position, iter from)\n\t{\n\tif(from.node->first_child==0) return position;\n\treturn reparent(position, from.node->first_child, end(from));\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntemplate <typename iter> iter tree<T, tree_node_allocator>::wrap(iter position, const T& x)\n\t{\n\tassert(position.node!=0);\n\tsibling_iterator fr=position, to=position;\n\t++to;\n\titer ret = insert(position, x);\n\treparent(ret, fr, to);\n\treturn ret;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntemplate <typename iter> iter tree<T, tree_node_allocator>::move_after(iter target, iter source)\n\t{\n\ttree_node *dst=target.node;\n\ttree_node *src=source.node;\n\tassert(dst);\n\tassert(src);\n\n\tif(dst==src) return source;\n\tif(dst->next_sibling)\n\t\tif(dst->next_sibling==src) // already in the right spot\n\t\t\treturn source;\n\n\t// take src out of the tree\n\tif(src->prev_sibling!=0) src->prev_sibling->next_sibling=src->next_sibling;\n\telse                     src->parent->first_child=src->next_sibling;\n\tif(src->next_sibling!=0) src->next_sibling->prev_sibling=src->prev_sibling;\n\telse                     src->parent->last_child=src->prev_sibling;\n\n\t// connect it to the new point\n\tif(dst->next_sibling!=0) dst->next_sibling->prev_sibling=src;\n\telse                     dst->parent->last_child=src;\n\tsrc->next_sibling=dst->next_sibling;\n\tdst->next_sibling=src;\n\tsrc->prev_sibling=dst;\n\tsrc->parent=dst->parent;\n\treturn src;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntemplate <typename iter> iter tree<T, tree_node_allocator>::move_before(iter target, iter source)\n\t{\n\ttree_node *dst=target.node;\n\ttree_node *src=source.node;\n\tassert(dst);\n\tassert(src);\n\n\tif(dst==src) return source;\n\tif(dst->prev_sibling)\n\t\tif(dst->prev_sibling==src) // already in the right spot\n\t\t\treturn source;\n\n\t// take src out of the tree\n\tif(src->prev_sibling!=0) src->prev_sibling->next_sibling=src->next_sibling;\n\telse                     src->parent->first_child=src->next_sibling;\n\tif(src->next_sibling!=0) src->next_sibling->prev_sibling=src->prev_sibling;\n\telse                     src->parent->last_child=src->prev_sibling;\n\n\t// connect it to the new point\n\tif(dst->prev_sibling!=0) dst->prev_sibling->next_sibling=src;\n\telse                     dst->parent->first_child=src;\n\tsrc->prev_sibling=dst->prev_sibling;\n\tdst->prev_sibling=src;\n\tsrc->next_sibling=dst;\n\tsrc->parent=dst->parent;\n\treturn src;\n\t}\n\n// specialisation for sibling_iterators\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::sibling_iterator tree<T, tree_node_allocator>::move_before(sibling_iterator target,\n      sibling_iterator source)\n\t{\n\ttree_node *dst=target.node;\n\ttree_node *src=source.node;\n\ttree_node *dst_prev_sibling;\n\tif(dst==0) { // must then be an end iterator\n\t\tdst_prev_sibling=target.parent_->last_child;\n\t\tassert(dst_prev_sibling);\n\t\t}\n\telse dst_prev_sibling=dst->prev_sibling;\n\tassert(src);\n\n\tif(dst==src) return source;\n\tif(dst_prev_sibling)\n\t\tif(dst_prev_sibling==src) // already in the right spot\n\t\t\treturn source;\n\n\t// take src out of the tree\n\tif(src->prev_sibling!=0) src->prev_sibling->next_sibling=src->next_sibling;\n\telse                     src->parent->first_child=src->next_sibling;\n\tif(src->next_sibling!=0) src->next_sibling->prev_sibling=src->prev_sibling;\n\telse                     src->parent->last_child=src->prev_sibling;\n\n\t// connect it to the new point\n\tif(dst_prev_sibling!=0) dst_prev_sibling->next_sibling=src;\n\telse                    target.parent_->first_child=src;\n\tsrc->prev_sibling=dst_prev_sibling;\n\tif(dst) {\n\t\tdst->prev_sibling=src;\n\t\tsrc->parent=dst->parent;\n\t\t}\n\tsrc->next_sibling=dst;\n\treturn src;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntemplate <typename iter> iter tree<T, tree_node_allocator>::move_ontop(iter target, iter source)\n\t{\n\ttree_node *dst=target.node;\n\ttree_node *src=source.node;\n\tassert(dst);\n\tassert(src);\n\n\tif(dst==src) return source;\n\n\t//\tif(dst==src->prev_sibling) {\n\t//\n\t//\t\t}\n\n\t// remember connection points\n\ttree_node *b_prev_sibling=dst->prev_sibling;\n\ttree_node *b_next_sibling=dst->next_sibling;\n\ttree_node *b_parent=dst->parent;\n\n\t// remove target\n\terase(target);\n\n\t// take src out of the tree\n\tif(src->prev_sibling!=0) src->prev_sibling->next_sibling=src->next_sibling;\n\telse                     src->parent->first_child=src->next_sibling;\n\tif(src->next_sibling!=0) src->next_sibling->prev_sibling=src->prev_sibling;\n\telse                     src->parent->last_child=src->prev_sibling;\n\n\t// connect it to the new point\n\tif(b_prev_sibling!=0) b_prev_sibling->next_sibling=src;\n\telse                  b_parent->first_child=src;\n\tif(b_next_sibling!=0) b_next_sibling->prev_sibling=src;\n\telse                  b_parent->last_child=src;\n\tsrc->prev_sibling=b_prev_sibling;\n\tsrc->next_sibling=b_next_sibling;\n\tsrc->parent=b_parent;\n\treturn src;\n\t}\n\n\ntemplate <class T, class tree_node_allocator>\ntree<T, tree_node_allocator> tree<T, tree_node_allocator>::move_out(iterator source)\n\t{\n\ttree ret;\n\n\t// Move source node into the 'ret' tree.\n\tret.head->next_sibling = source.node;\n\tret.feet->prev_sibling = source.node;\n\tsource.node->parent=0;\n\n\t// Close the links in the current tree.\n\tif(source.node->prev_sibling!=0)\n\t\tsource.node->prev_sibling->next_sibling = source.node->next_sibling;\n\n\tif(source.node->next_sibling!=0)\n\t\tsource.node->next_sibling->prev_sibling = source.node->prev_sibling;\n\n\t// Fix source prev/next links.\n\tsource.node->prev_sibling = ret.head;\n\tsource.node->next_sibling = ret.feet;\n\n\treturn ret; // A good compiler will move this, not copy.\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntemplate<typename iter> iter tree<T, tree_node_allocator>::move_in(iter loc, tree& other)\n\t{\n\tif(other.head->next_sibling==other.feet) return loc; // other tree is empty\n\n\ttree_node *other_first_head = other.head->next_sibling;\n\ttree_node *other_last_head  = other.feet->prev_sibling;\n\n\tsibling_iterator prev(loc);\n\t--prev;\n\n\tprev.node->next_sibling = other_first_head;\n\tloc.node->prev_sibling  = other_last_head;\n\tother_first_head->prev_sibling = prev.node;\n\tother_last_head->next_sibling  = loc.node;\n\n\t// Adjust parent pointers.\n\ttree_node *walk=other_first_head;\n\twhile(true) {\n\t\twalk->parent=loc.node->parent;\n\t\tif(walk==other_last_head)\n\t\t\tbreak;\n\t\twalk=walk->next_sibling;\n\t\t}\n\n\t// Close other tree.\n\tother.head->next_sibling=other.feet;\n\tother.feet->prev_sibling=other.head;\n\n\treturn other_first_head;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntemplate<typename iter> iter tree<T, tree_node_allocator>::move_in_as_nth_child(iter loc, size_t n, tree& other)\n\t{\n\tif(other.head->next_sibling==other.feet) return loc; // other tree is empty\n\n\ttree_node *other_first_head = other.head->next_sibling;\n\ttree_node *other_last_head  = other.feet->prev_sibling;\n\n\tif(n==0) {\n\t\tif(loc.node->first_child==0) {\n\t\t\tloc.node->first_child=other_first_head;\n\t\t\tloc.node->last_child=other_last_head;\n\t\t\tother_last_head->next_sibling=0;\n\t\t\tother_first_head->prev_sibling=0;\n\t\t\t}\n\t\telse {\n\t\t\tloc.node->first_child->prev_sibling=other_last_head;\n\t\t\tother_last_head->next_sibling=loc.node->first_child;\n\t\t\tloc.node->first_child=other_first_head;\n\t\t\tother_first_head->prev_sibling=0;\n\t\t\t}\n\t\t}\n\telse {\n\t\t--n;\n\t\ttree_node *walk = loc.node->first_child;\n\t\twhile(true) {\n\t\t\tif(walk==0)\n\t\t\t\tthrow std::range_error(\"tree: move_in_as_nth_child position \"\n\t\t\t\t                       +std::to_string(n+1)\n\t\t\t\t                       +\" out of range; only \"\n\t\t\t\t                       +std::to_string(number_of_children(loc))\n\t\t\t\t                       +\" child nodes present\");\n\t\t\tif(n==0)\n\t\t\t\tbreak;\n\t\t\t--n;\n\t\t\twalk = walk->next_sibling;\n\t\t\t}\n\t\tif(walk->next_sibling==0)\n\t\t\tloc.node->last_child=other_last_head;\n\t\telse\n\t\t\twalk->next_sibling->prev_sibling=other_last_head;\n\t\tother_last_head->next_sibling=walk->next_sibling;\n\t\twalk->next_sibling=other_first_head;\n\t\tother_first_head->prev_sibling=walk;\n\t\t}\n\n\t// Adjust parent pointers.\n\ttree_node *walk=other_first_head;\n\twhile(true) {\n\t\twalk->parent=loc.node;\n\t\tif(walk==other_last_head)\n\t\t\tbreak;\n\t\twalk=walk->next_sibling;\n\t\t}\n\n\t// Close other tree.\n\tother.head->next_sibling=other.feet;\n\tother.feet->prev_sibling=other.head;\n\n\treturn other_first_head;\n\t}\n\n\ntemplate <class T, class tree_node_allocator>\nvoid tree<T, tree_node_allocator>::merge(sibling_iterator to1,   sibling_iterator to2,\n      sibling_iterator from1, sibling_iterator from2,\n      bool duplicate_leaves)\n\t{\n\tsibling_iterator fnd;\n\twhile(from1!=from2) {\n\t\tif((fnd=std::find(to1, to2, (*from1))) != to2) { // element found\n\t\t\tif(from1.begin()==from1.end()) { // full depth reached\n\t\t\t\tif(duplicate_leaves)\n\t\t\t\t\tappend_child(parent(to1), (*from1));\n\t\t\t\t}\n\t\t\telse {   // descend further\n\t\t\t\tmerge(fnd.begin(), fnd.end(), from1.begin(), from1.end(), duplicate_leaves);\n\t\t\t\t}\n\t\t\t}\n\t\telse {   // element missing\n\t\t\tinsert_subtree(to2, from1);\n\t\t\t}\n\t\t++from1;\n\t\t}\n\t}\n\n\ntemplate <class T, class tree_node_allocator>\nvoid tree<T, tree_node_allocator>::sort(sibling_iterator from, sibling_iterator to, bool deep)\n\t{\n\tstd::less<T> comp;\n\tsort(from, to, comp, deep);\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntemplate <class StrictWeakOrdering>\nvoid tree<T, tree_node_allocator>::sort(sibling_iterator from, sibling_iterator to,\n                                        StrictWeakOrdering comp, bool deep)\n\t{\n\tif(from==to) return;\n\t// make list of sorted nodes\n\t// CHECK: if multiset stores equivalent nodes in the order in which they\n\t// are inserted, then this routine should be called 'stable_sort'.\n\tstd::multiset<tree_node *, compare_nodes<StrictWeakOrdering> > nodes(comp);\n\tsibling_iterator it=from, it2=to;\n\twhile(it != to) {\n\t\tnodes.insert(it.node);\n\t\t++it;\n\t\t}\n\t// reassemble\n\t--it2;\n\n\t// prev and next are the nodes before and after the sorted range\n\ttree_node *prev=from.node->prev_sibling;\n\ttree_node *next=it2.node->next_sibling;\n\ttypename std::multiset<tree_node *, compare_nodes<StrictWeakOrdering> >::iterator nit=nodes.begin(), eit=nodes.end();\n\tif(prev==0) {\n\t\tif((*nit)->parent!=0) // to catch \"sorting the head\" situations, when there is no parent\n\t\t\t(*nit)->parent->first_child=(*nit);\n\t\t}\n\telse prev->next_sibling=(*nit);\n\n\t--eit;\n\twhile(nit!=eit) {\n\t\t(*nit)->prev_sibling=prev;\n\t\tif(prev)\n\t\t\tprev->next_sibling=(*nit);\n\t\tprev=(*nit);\n\t\t++nit;\n\t\t}\n\t// prev now points to the last-but-one node in the sorted range\n\tif(prev)\n\t\tprev->next_sibling=(*eit);\n\n\t// eit points to the last node in the sorted range.\n\t(*eit)->next_sibling=next;\n\t(*eit)->prev_sibling=prev; // missed in the loop above\n\tif(next==0) {\n\t\tif((*eit)->parent!=0) // to catch \"sorting the head\" situations, when there is no parent\n\t\t\t(*eit)->parent->last_child=(*eit);\n\t\t}\n\telse next->prev_sibling=(*eit);\n\n\tif(deep) {\t// sort the children of each node too\n\t\tsibling_iterator bcs(*nodes.begin());\n\t\tsibling_iterator ecs(*eit);\n\t\t++ecs;\n\t\twhile(bcs!=ecs) {\n\t\t\tsort(begin(bcs), end(bcs), comp, deep);\n\t\t\t++bcs;\n\t\t\t}\n\t\t}\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntemplate <typename iter>\nbool tree<T, tree_node_allocator>::equal(const iter& one_, const iter& two, const iter& three_) const\n\t{\n\tstd::equal_to<T> comp;\n\treturn equal(one_, two, three_, comp);\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntemplate <typename iter>\nbool tree<T, tree_node_allocator>::equal_subtree(const iter& one_, const iter& two_) const\n\t{\n\tstd::equal_to<T> comp;\n\treturn equal_subtree(one_, two_, comp);\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntemplate <typename iter, class BinaryPredicate>\nbool tree<T, tree_node_allocator>::equal(const iter& one_, const iter& two, const iter& three_, BinaryPredicate fun) const\n\t{\n\tpre_order_iterator one(one_), three(three_);\n\n\t//\tif(one==two && is_valid(three) && three.number_of_children()!=0)\n\t//\t\treturn false;\n\twhile(one!=two && is_valid(three)) {\n\t\tif(!fun(*one,*three))\n\t\t\treturn false;\n\t\tif(one.number_of_children()!=three.number_of_children())\n\t\t\treturn false;\n\t\t++one;\n\t\t++three;\n\t\t}\n\treturn true;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntemplate <typename iter, class BinaryPredicate>\nbool tree<T, tree_node_allocator>::equal_subtree(const iter& one_, const iter& two_, BinaryPredicate fun) const\n\t{\n\tpre_order_iterator one(one_), two(two_);\n\n\tif(!fun(*one,*two)) return false;\n\tif(number_of_children(one)!=number_of_children(two)) return false;\n\treturn equal(begin(one),end(one),begin(two),fun);\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntree<T, tree_node_allocator> tree<T, tree_node_allocator>::subtree(sibling_iterator from, sibling_iterator to) const\n\t{\n\ttree tmp;\n\ttmp.set_head(value_type());\n\ttmp.replace(tmp.begin(), tmp.end(), from, to);\n\treturn tmp;\n\t}\n\ntemplate <class T, class tree_node_allocator>\nvoid tree<T, tree_node_allocator>::subtree(tree& tmp, sibling_iterator from, sibling_iterator to) const\n\t{\n\ttmp.set_head(value_type());\n\ttmp.replace(tmp.begin(), tmp.end(), from, to);\n\t}\n\ntemplate <class T, class tree_node_allocator>\nsize_t tree<T, tree_node_allocator>::size() const\n\t{\n\tsize_t i=0;\n\tpre_order_iterator it=begin(), eit=end();\n\twhile(it!=eit) {\n\t\t++i;\n\t\t++it;\n\t\t}\n\treturn i;\n\t}\n\ntemplate <class T, class tree_node_allocator>\nsize_t tree<T, tree_node_allocator>::size(const iterator_base& top) const\n\t{\n\tsize_t i=0;\n\tpre_order_iterator it=top, eit=top;\n\teit.skip_children();\n\t++eit;\n\twhile(it!=eit) {\n\t\t++i;\n\t\t++it;\n\t\t}\n\treturn i;\n\t}\n\ntemplate <class T, class tree_node_allocator>\nbool tree<T, tree_node_allocator>::empty() const\n\t{\n\tpre_order_iterator it=begin(), eit=end();\n\treturn (it==eit);\n\t}\n\ntemplate <class T, class tree_node_allocator>\nint tree<T, tree_node_allocator>::depth(const iterator_base& it)\n\t{\n\ttree_node* pos=it.node;\n\tassert(pos!=0);\n\tint ret=0;\n\twhile(pos->parent!=0) {\n\t\tpos=pos->parent;\n\t\t++ret;\n\t\t}\n\treturn ret;\n\t}\n\ntemplate <class T, class tree_node_allocator>\nint tree<T, tree_node_allocator>::depth(const iterator_base& it, const iterator_base& root)\n\t{\n\ttree_node* pos=it.node;\n\tassert(pos!=0);\n\tint ret=0;\n\twhile(pos->parent!=0 && pos!=root.node) {\n\t\tpos=pos->parent;\n\t\t++ret;\n\t\t}\n\treturn ret;\n\t}\n\ntemplate <class T, class tree_node_allocator>\nint tree<T, tree_node_allocator>::max_depth() const\n\t{\n\tint maxd=-1;\n\tfor(tree_node *it = head->next_sibling; it!=feet; it=it->next_sibling)\n\t\tmaxd=std::max(maxd, max_depth(it));\n\n\treturn maxd;\n\t}\n\n\ntemplate <class T, class tree_node_allocator>\nint tree<T, tree_node_allocator>::max_depth(const iterator_base& pos) const\n\t{\n\ttree_node *tmp=pos.node;\n\n\tif(tmp==0 || tmp==head || tmp==feet) return -1;\n\n\tint curdepth=0, maxdepth=0;\n\twhile(true) { // try to walk the bottom of the tree\n\t\twhile(tmp->first_child==0) {\n\t\t\tif(tmp==pos.node) return maxdepth;\n\t\t\tif(tmp->next_sibling==0) {\n\t\t\t\t// try to walk up and then right again\n\t\t\t\tdo {\n\t\t\t\t\ttmp=tmp->parent;\n\t\t\t\t\tif(tmp==0) return maxdepth;\n\t\t\t\t\t--curdepth;\n\t\t\t\t\t}\n\t\t\t\twhile(tmp->next_sibling==0);\n\t\t\t\t}\n\t\t\tif(tmp==pos.node) return maxdepth;\n\t\t\ttmp=tmp->next_sibling;\n\t\t\t}\n\t\ttmp=tmp->first_child;\n\t\t++curdepth;\n\t\tmaxdepth=std::max(curdepth, maxdepth);\n\t\t}\n\t}\n\ntemplate <class T, class tree_node_allocator>\nunsigned int tree<T, tree_node_allocator>::number_of_children(const iterator_base& it)\n\t{\n\ttree_node *pos=it.node->first_child;\n\tif(pos==0) return 0;\n\n\tunsigned int ret=1;\n\t//\t  while(pos!=it.node->last_child) {\n\t//\t\t  ++ret;\n\t//\t\t  pos=pos->next_sibling;\n\t//\t\t  }\n\twhile((pos=pos->next_sibling))\n\t\t++ret;\n\treturn ret;\n\t}\n\ntemplate <class T, class tree_node_allocator>\nunsigned int tree<T, tree_node_allocator>::number_of_siblings(const iterator_base& it) const\n\t{\n\ttree_node *pos=it.node;\n\tunsigned int ret=0;\n\t// count forward\n\twhile(pos->next_sibling &&\n\t      pos->next_sibling!=head &&\n\t      pos->next_sibling!=feet) {\n\t\t++ret;\n\t\tpos=pos->next_sibling;\n\t\t}\n\t// count backward\n\tpos=it.node;\n\twhile(pos->prev_sibling &&\n\t      pos->prev_sibling!=head &&\n\t      pos->prev_sibling!=feet) {\n\t\t++ret;\n\t\tpos=pos->prev_sibling;\n\t\t}\n\n\treturn ret;\n\t}\n\ntemplate <class T, class tree_node_allocator>\nvoid tree<T, tree_node_allocator>::swap(sibling_iterator it)\n\t{\n\ttree_node *nxt=it.node->next_sibling;\n\tif(nxt) {\n\t\tif(it.node->prev_sibling)\n\t\t\tit.node->prev_sibling->next_sibling=nxt;\n\t\telse\n\t\t\tit.node->parent->first_child=nxt;\n\t\tnxt->prev_sibling=it.node->prev_sibling;\n\t\ttree_node *nxtnxt=nxt->next_sibling;\n\t\tif(nxtnxt)\n\t\t\tnxtnxt->prev_sibling=it.node;\n\t\telse\n\t\t\tit.node->parent->last_child=it.node;\n\t\tnxt->next_sibling=it.node;\n\t\tit.node->prev_sibling=nxt;\n\t\tit.node->next_sibling=nxtnxt;\n\t\t}\n\t}\n\ntemplate <class T, class tree_node_allocator>\nvoid tree<T, tree_node_allocator>::swap(iterator one, iterator two)\n\t{\n\t// if one and two are adjacent siblings, use the sibling swap\n\tif(one.node->next_sibling==two.node) swap(one);\n\telse if(two.node->next_sibling==one.node) swap(two);\n\telse {\n\t\ttree_node *nxt1=one.node->next_sibling;\n\t\ttree_node *nxt2=two.node->next_sibling;\n\t\ttree_node *pre1=one.node->prev_sibling;\n\t\ttree_node *pre2=two.node->prev_sibling;\n\t\ttree_node *par1=one.node->parent;\n\t\ttree_node *par2=two.node->parent;\n\n\t\t// reconnect\n\t\tone.node->parent=par2;\n\t\tone.node->next_sibling=nxt2;\n\t\tif(nxt2) nxt2->prev_sibling=one.node;\n\t\telse     par2->last_child=one.node;\n\t\tone.node->prev_sibling=pre2;\n\t\tif(pre2) pre2->next_sibling=one.node;\n\t\telse     par2->first_child=one.node;\n\n\t\ttwo.node->parent=par1;\n\t\ttwo.node->next_sibling=nxt1;\n\t\tif(nxt1) nxt1->prev_sibling=two.node;\n\t\telse     par1->last_child=two.node;\n\t\ttwo.node->prev_sibling=pre1;\n\t\tif(pre1) pre1->next_sibling=two.node;\n\t\telse     par1->first_child=two.node;\n\t\t}\n\t}\n\n// template <class BinaryPredicate>\n// tree<T, tree_node_allocator>::iterator tree<T, tree_node_allocator>::find_subtree(\n// \tsibling_iterator subfrom, sibling_iterator subto, iterator from, iterator to,\n// \tBinaryPredicate fun) const\n// \t{\n// \tassert(1==0); // this routine is not finished yet.\n// \twhile(from!=to) {\n// \t\tif(fun(*subfrom, *from)) {\n//\n// \t\t\t}\n// \t\t}\n// \treturn to;\n// \t}\n\ntemplate <class T, class tree_node_allocator>\nbool tree<T, tree_node_allocator>::is_in_subtree(const iterator_base& it, const iterator_base& begin,\n      const iterator_base& end) const\n\t{\n\t// FIXME: this should be optimised.\n\tpre_order_iterator tmp=begin;\n\twhile(tmp!=end) {\n\t\tif(tmp==it) return true;\n\t\t++tmp;\n\t\t}\n\treturn false;\n\t}\n\ntemplate <class T, class tree_node_allocator>\nbool tree<T, tree_node_allocator>::is_valid(const iterator_base& it) const\n\t{\n\tif(it.node==0 || it.node==feet || it.node==head) return false;\n\telse return true;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::iterator tree<T, tree_node_allocator>::lowest_common_ancestor(\n   const iterator_base& one, const iterator_base& two) const\n\t{\n\tstd::set<iterator, iterator_base_less> parents;\n\n\t// Walk up from 'one' storing all parents.\n\titerator walk=one;\n\tdo {\n\t\twalk=parent(walk);\n\t\tparents.insert(walk);\n\t\t}\n\twhile( is_valid(parent(walk)) );\n\n\t// Walk up from 'two' until we encounter a node in parents.\n\twalk=two;\n\tdo {\n\t\twalk=parent(walk);\n\t\tif(parents.find(walk) != parents.end()) break;\n\t\t}\n\twhile( is_valid(parent(walk)) );\n\n\treturn walk;\n\t}\n\ntemplate <class T, class tree_node_allocator>\nunsigned int tree<T, tree_node_allocator>::index(sibling_iterator it) const\n\t{\n\tunsigned int ind=0;\n\tif(it.node->parent==0) {\n\t\twhile(it.node->prev_sibling!=head) {\n\t\t\tit.node=it.node->prev_sibling;\n\t\t\t++ind;\n\t\t\t}\n\t\t}\n\telse {\n\t\twhile(it.node->prev_sibling!=0) {\n\t\t\tit.node=it.node->prev_sibling;\n\t\t\t++ind;\n\t\t\t}\n\t\t}\n\treturn ind;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::sibling_iterator tree<T, tree_node_allocator>::sibling(const iterator_base& it, unsigned int num)\n\t{\n\ttree_node *tmp;\n\tif(it.node->parent==0) {\n\t\ttmp=head->next_sibling;\n\t\twhile(num) {\n\t\t\ttmp = tmp->next_sibling;\n\t\t\t--num;\n\t\t\t}\n\t\t}\n\telse {\n\t\ttmp=it.node->parent->first_child;\n\t\twhile(num) {\n\t\t\tassert(tmp!=0);\n\t\t\ttmp = tmp->next_sibling;\n\t\t\t--num;\n\t\t\t}\n\t\t}\n\treturn tmp;\n\t}\n\ntemplate <class T, class tree_node_allocator>\nvoid tree<T, tree_node_allocator>::debug_verify_consistency() const\n\t{\n\titerator it=begin();\n\twhile(it!=end()) {\n\t\tif(it.node->parent!=0) {\n\t\t\tif(it.node->prev_sibling==0)\n\t\t\t\tassert(it.node->parent->first_child==it.node);\n\t\t\telse\n\t\t\t\tassert(it.node->prev_sibling->next_sibling==it.node);\n\t\t\tif(it.node->next_sibling==0)\n\t\t\t\tassert(it.node->parent->last_child==it.node);\n\t\t\telse\n\t\t\t\tassert(it.node->next_sibling->prev_sibling==it.node);\n\t\t\t}\n\t\t++it;\n\t\t}\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::sibling_iterator tree<T, tree_node_allocator>::child(const iterator_base& it, unsigned int num)\n\t{\n\ttree_node *tmp=it.node->first_child;\n\twhile(num--) {\n\t\tassert(tmp!=0);\n\t\ttmp=tmp->next_sibling;\n\t\t}\n\treturn tmp;\n\t}\n\n\n\n\n// Iterator base\n\ntemplate <class T, class tree_node_allocator>\ntree<T, tree_node_allocator>::iterator_base::iterator_base()\n\t: node(0), skip_current_children_(false)\n\t{\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntree<T, tree_node_allocator>::iterator_base::iterator_base(tree_node *tn)\n\t: node(tn), skip_current_children_(false)\n\t{\n\t}\n\ntemplate <class T, class tree_node_allocator>\nT& tree<T, tree_node_allocator>::iterator_base::operator*() const\n\t{\n\treturn node->data;\n\t}\n\ntemplate <class T, class tree_node_allocator>\nT* tree<T, tree_node_allocator>::iterator_base::operator->() const\n\t{\n\treturn &(node->data);\n\t}\n\ntemplate <class T, class tree_node_allocator>\nbool tree<T, tree_node_allocator>::post_order_iterator::operator!=(const post_order_iterator& other) const\n\t{\n\tif(other.node!=this->node) return true;\n\telse return false;\n\t}\n\ntemplate <class T, class tree_node_allocator>\nbool tree<T, tree_node_allocator>::post_order_iterator::operator==(const post_order_iterator& other) const\n\t{\n\tif(other.node==this->node) return true;\n\telse return false;\n\t}\n\ntemplate <class T, class tree_node_allocator>\nbool tree<T, tree_node_allocator>::pre_order_iterator::operator!=(const pre_order_iterator& other) const\n\t{\n\tif(other.node!=this->node) return true;\n\telse return false;\n\t}\n\ntemplate <class T, class tree_node_allocator>\nbool tree<T, tree_node_allocator>::pre_order_iterator::operator==(const pre_order_iterator& other) const\n\t{\n\tif(other.node==this->node) return true;\n\telse return false;\n\t}\n\ntemplate <class T, class tree_node_allocator>\nbool tree<T, tree_node_allocator>::sibling_iterator::operator!=(const sibling_iterator& other) const\n\t{\n\tif(other.node!=this->node) return true;\n\telse return false;\n\t}\n\ntemplate <class T, class tree_node_allocator>\nbool tree<T, tree_node_allocator>::sibling_iterator::operator==(const sibling_iterator& other) const\n\t{\n\tif(other.node==this->node) return true;\n\telse return false;\n\t}\n\ntemplate <class T, class tree_node_allocator>\nbool tree<T, tree_node_allocator>::leaf_iterator::operator!=(const leaf_iterator& other) const\n\t{\n\tif(other.node!=this->node) return true;\n\telse return false;\n\t}\n\ntemplate <class T, class tree_node_allocator>\nbool tree<T, tree_node_allocator>::leaf_iterator::operator==(const leaf_iterator& other) const\n\t{\n\tif(other.node==this->node && other.top_node==this->top_node) return true;\n\telse return false;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::sibling_iterator tree<T, tree_node_allocator>::iterator_base::begin() const\n\t{\n\tif(node->first_child==0)\n\t\treturn end();\n\n\tsibling_iterator ret(node->first_child);\n\tret.parent_=this->node;\n\treturn ret;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::sibling_iterator tree<T, tree_node_allocator>::iterator_base::end() const\n\t{\n\tsibling_iterator ret(0);\n\tret.parent_=node;\n\treturn ret;\n\t}\n\ntemplate <class T, class tree_node_allocator>\nvoid tree<T, tree_node_allocator>::iterator_base::skip_children()\n\t{\n\tskip_current_children_=true;\n\t}\n\ntemplate <class T, class tree_node_allocator>\nvoid tree<T, tree_node_allocator>::iterator_base::skip_children(bool skip)\n\t{\n\tskip_current_children_=skip;\n\t}\n\ntemplate <class T, class tree_node_allocator>\nunsigned int tree<T, tree_node_allocator>::iterator_base::number_of_children() const\n\t{\n\ttree_node *pos=node->first_child;\n\tif(pos==0) return 0;\n\n\tunsigned int ret=1;\n\twhile(pos!=node->last_child) {\n\t\t++ret;\n\t\tpos=pos->next_sibling;\n\t\t}\n\treturn ret;\n\t}\n\n\n\n// Pre-order iterator\n\ntemplate <class T, class tree_node_allocator>\ntree<T, tree_node_allocator>::pre_order_iterator::pre_order_iterator()\n\t: iterator_base(0)\n\t{\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntree<T, tree_node_allocator>::pre_order_iterator::pre_order_iterator(tree_node *tn)\n\t: iterator_base(tn)\n\t{\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntree<T, tree_node_allocator>::pre_order_iterator::pre_order_iterator(const iterator_base &other)\n\t: iterator_base(other.node)\n\t{\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntree<T, tree_node_allocator>::pre_order_iterator::pre_order_iterator(const sibling_iterator& other)\n\t: iterator_base(other.node)\n\t{\n\tif(this->node==0) {\n\t\tif(other.range_last()!=0)\n\t\t\tthis->node=other.range_last();\n\t\telse\n\t\t\tthis->node=other.parent_;\n\t\tthis->skip_children();\n\t\t++(*this);\n\t\t}\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::pre_order_iterator& tree<T, tree_node_allocator>::pre_order_iterator::operator++()\n\t{\n\tassert(this->node!=0);\n\tif(!this->skip_current_children_ && this->node->first_child != 0) {\n\t\tthis->node=this->node->first_child;\n\t\t}\n\telse {\n\t\tthis->skip_current_children_=false;\n\t\twhile(this->node->next_sibling==0) {\n\t\t\tthis->node=this->node->parent;\n\t\t\tif(this->node==0)\n\t\t\t\treturn *this;\n\t\t\t}\n\t\tthis->node=this->node->next_sibling;\n\t\t}\n\treturn *this;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::pre_order_iterator& tree<T, tree_node_allocator>::pre_order_iterator::operator--()\n\t{\n\tassert(this->node!=0);\n\tif(this->node->prev_sibling) {\n\t\tthis->node=this->node->prev_sibling;\n\t\twhile(this->node->last_child)\n\t\t\tthis->node=this->node->last_child;\n\t\t}\n\telse {\n\t\tthis->node=this->node->parent;\n\t\tif(this->node==0)\n\t\t\treturn *this;\n\t\t}\n\treturn *this;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::pre_order_iterator tree<T, tree_node_allocator>::pre_order_iterator::operator++(int)\n\t{\n\tpre_order_iterator copy = *this;\n\t++(*this);\n\treturn copy;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::pre_order_iterator& tree<T, tree_node_allocator>::pre_order_iterator::next_skip_children()\n\t{\n\t(*this).skip_children();\n\t(*this)++;\n\treturn *this;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::pre_order_iterator tree<T, tree_node_allocator>::pre_order_iterator::operator--(int)\n\t{\n\tpre_order_iterator copy = *this;\n\t--(*this);\n\treturn copy;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::pre_order_iterator& tree<T, tree_node_allocator>::pre_order_iterator::operator+=(unsigned int num)\n\t{\n\twhile(num>0) {\n\t\t++(*this);\n\t\t--num;\n\t\t}\n\treturn (*this);\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::pre_order_iterator& tree<T, tree_node_allocator>::pre_order_iterator::operator-=(unsigned int num)\n\t{\n\twhile(num>0) {\n\t\t--(*this);\n\t\t--num;\n\t\t}\n\treturn (*this);\n\t}\n\n\n\n// Post-order iterator\n\ntemplate <class T, class tree_node_allocator>\ntree<T, tree_node_allocator>::post_order_iterator::post_order_iterator()\n\t: iterator_base(0)\n\t{\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntree<T, tree_node_allocator>::post_order_iterator::post_order_iterator(tree_node *tn)\n\t: iterator_base(tn)\n\t{\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntree<T, tree_node_allocator>::post_order_iterator::post_order_iterator(const iterator_base &other)\n\t: iterator_base(other.node)\n\t{\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntree<T, tree_node_allocator>::post_order_iterator::post_order_iterator(const sibling_iterator& other)\n\t: iterator_base(other.node)\n\t{\n\tif(this->node==0) {\n\t\tif(other.range_last()!=0)\n\t\t\tthis->node=other.range_last();\n\t\telse\n\t\t\tthis->node=other.parent_;\n\t\tthis->skip_children();\n\t\t++(*this);\n\t\t}\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::post_order_iterator& tree<T, tree_node_allocator>::post_order_iterator::operator++()\n\t{\n\tassert(this->node!=0);\n\tif(this->node->next_sibling==0) {\n\t\tthis->node=this->node->parent;\n\t\tthis->skip_current_children_=false;\n\t\t}\n\telse {\n\t\tthis->node=this->node->next_sibling;\n\t\tif(this->skip_current_children_) {\n\t\t\tthis->skip_current_children_=false;\n\t\t\t}\n\t\telse {\n\t\t\twhile(this->node->first_child)\n\t\t\t\tthis->node=this->node->first_child;\n\t\t\t}\n\t\t}\n\treturn *this;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::post_order_iterator& tree<T, tree_node_allocator>::post_order_iterator::operator--()\n\t{\n\tassert(this->node!=0);\n\tif(this->skip_current_children_ || this->node->last_child==0) {\n\t\tthis->skip_current_children_=false;\n\t\twhile(this->node->prev_sibling==0)\n\t\t\tthis->node=this->node->parent;\n\t\tthis->node=this->node->prev_sibling;\n\t\t}\n\telse {\n\t\tthis->node=this->node->last_child;\n\t\t}\n\treturn *this;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::post_order_iterator tree<T, tree_node_allocator>::post_order_iterator::operator++(int)\n\t{\n\tpost_order_iterator copy = *this;\n\t++(*this);\n\treturn copy;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::post_order_iterator tree<T, tree_node_allocator>::post_order_iterator::operator--(int)\n\t{\n\tpost_order_iterator copy = *this;\n\t--(*this);\n\treturn copy;\n\t}\n\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::post_order_iterator& tree<T, tree_node_allocator>::post_order_iterator::operator+=(unsigned int num)\n\t{\n\twhile(num>0) {\n\t\t++(*this);\n\t\t--num;\n\t\t}\n\treturn (*this);\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::post_order_iterator& tree<T, tree_node_allocator>::post_order_iterator::operator-=(unsigned int num)\n\t{\n\twhile(num>0) {\n\t\t--(*this);\n\t\t--num;\n\t\t}\n\treturn (*this);\n\t}\n\ntemplate <class T, class tree_node_allocator>\nvoid tree<T, tree_node_allocator>::post_order_iterator::descend_all()\n\t{\n\tassert(this->node!=0);\n\twhile(this->node->first_child)\n\t\tthis->node=this->node->first_child;\n\t}\n\n\n// Breadth-first iterator\n\ntemplate <class T, class tree_node_allocator>\ntree<T, tree_node_allocator>::breadth_first_queued_iterator::breadth_first_queued_iterator()\n\t: iterator_base()\n\t{\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntree<T, tree_node_allocator>::breadth_first_queued_iterator::breadth_first_queued_iterator(tree_node *tn)\n\t: iterator_base(tn)\n\t{\n\ttraversal_queue.push(tn);\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntree<T, tree_node_allocator>::breadth_first_queued_iterator::breadth_first_queued_iterator(const iterator_base& other)\n\t: iterator_base(other.node)\n\t{\n\ttraversal_queue.push(other.node);\n\t}\n\ntemplate <class T, class tree_node_allocator>\nbool tree<T, tree_node_allocator>::breadth_first_queued_iterator::operator!=(const breadth_first_queued_iterator& other) const\n\t{\n\tif(other.node!=this->node) return true;\n\telse return false;\n\t}\n\ntemplate <class T, class tree_node_allocator>\nbool tree<T, tree_node_allocator>::breadth_first_queued_iterator::operator==(const breadth_first_queued_iterator& other) const\n\t{\n\tif(other.node==this->node) return true;\n\telse return false;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::breadth_first_queued_iterator& tree<T, tree_node_allocator>::breadth_first_queued_iterator::operator++()\n\t{\n\tassert(this->node!=0);\n\n\t// Add child nodes and pop current node\n\tsibling_iterator sib=this->begin();\n\twhile(sib!=this->end()) {\n\t\ttraversal_queue.push(sib.node);\n\t\t++sib;\n\t\t}\n\ttraversal_queue.pop();\n\tif(traversal_queue.size()>0)\n\t\tthis->node=traversal_queue.front();\n\telse\n\t\tthis->node=0;\n\treturn (*this);\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::breadth_first_queued_iterator tree<T, tree_node_allocator>::breadth_first_queued_iterator::operator++(int)\n\t{\n\tbreadth_first_queued_iterator copy = *this;\n\t++(*this);\n\treturn copy;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::breadth_first_queued_iterator& tree<T, tree_node_allocator>::breadth_first_queued_iterator::operator+=(unsigned int num)\n\t{\n\twhile(num>0) {\n\t\t++(*this);\n\t\t--num;\n\t\t}\n\treturn (*this);\n\t}\n\n\n\n// Fixed depth iterator\n\ntemplate <class T, class tree_node_allocator>\ntree<T, tree_node_allocator>::fixed_depth_iterator::fixed_depth_iterator()\n\t: iterator_base()\n\t{\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntree<T, tree_node_allocator>::fixed_depth_iterator::fixed_depth_iterator(tree_node *tn)\n\t: iterator_base(tn), top_node(0)\n\t{\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntree<T, tree_node_allocator>::fixed_depth_iterator::fixed_depth_iterator(const iterator_base& other)\n\t: iterator_base(other.node), top_node(0)\n\t{\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntree<T, tree_node_allocator>::fixed_depth_iterator::fixed_depth_iterator(const sibling_iterator& other)\n\t: iterator_base(other.node), top_node(0)\n\t{\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntree<T, tree_node_allocator>::fixed_depth_iterator::fixed_depth_iterator(const fixed_depth_iterator& other)\n\t: iterator_base(other.node), top_node(other.top_node)\n\t{\n\t}\n\ntemplate <class T, class tree_node_allocator>\nbool tree<T, tree_node_allocator>::fixed_depth_iterator::operator==(const fixed_depth_iterator& other) const\n\t{\n\tif(other.node==this->node && other.top_node==top_node) return true;\n\telse return false;\n\t}\n\ntemplate <class T, class tree_node_allocator>\nbool tree<T, tree_node_allocator>::fixed_depth_iterator::operator!=(const fixed_depth_iterator& other) const\n\t{\n\tif(other.node!=this->node || other.top_node!=top_node) return true;\n\telse return false;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::fixed_depth_iterator& tree<T, tree_node_allocator>::fixed_depth_iterator::operator++()\n\t{\n\tassert(this->node!=0);\n\n\tif(this->node->next_sibling) {\n\t\tthis->node=this->node->next_sibling;\n\t\t}\n\telse {\n\t\tint relative_depth=0;\nupper:\n\t\tdo {\n\t\t\tif(this->node==this->top_node) {\n\t\t\t\tthis->node=0; // FIXME: return a proper fixed_depth end iterator once implemented\n\t\t\t\treturn *this;\n\t\t\t\t}\n\t\t\tthis->node=this->node->parent;\n\t\t\tif(this->node==0) return *this;\n\t\t\t--relative_depth;\n\t\t\t}\n\t\twhile(this->node->next_sibling==0);\nlower:\n\t\tthis->node=this->node->next_sibling;\n\t\twhile(this->node->first_child==0) {\n\t\t\tif(this->node->next_sibling==0)\n\t\t\t\tgoto upper;\n\t\t\tthis->node=this->node->next_sibling;\n\t\t\tif(this->node==0) return *this;\n\t\t\t}\n\t\twhile(relative_depth<0 && this->node->first_child!=0) {\n\t\t\tthis->node=this->node->first_child;\n\t\t\t++relative_depth;\n\t\t\t}\n\t\tif(relative_depth<0) {\n\t\t\tif(this->node->next_sibling==0) goto upper;\n\t\t\telse                          goto lower;\n\t\t\t}\n\t\t}\n\treturn *this;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::fixed_depth_iterator& tree<T, tree_node_allocator>::fixed_depth_iterator::operator--()\n\t{\n\tassert(this->node!=0);\n\n\tif(this->node->prev_sibling) {\n\t\tthis->node=this->node->prev_sibling;\n\t\t}\n\telse {\n\t\tint relative_depth=0;\nupper:\n\t\tdo {\n\t\t\tif(this->node==this->top_node) {\n\t\t\t\tthis->node=0;\n\t\t\t\treturn *this;\n\t\t\t\t}\n\t\t\tthis->node=this->node->parent;\n\t\t\tif(this->node==0) return *this;\n\t\t\t--relative_depth;\n\t\t\t}\n\t\twhile(this->node->prev_sibling==0);\nlower:\n\t\tthis->node=this->node->prev_sibling;\n\t\twhile(this->node->last_child==0) {\n\t\t\tif(this->node->prev_sibling==0)\n\t\t\t\tgoto upper;\n\t\t\tthis->node=this->node->prev_sibling;\n\t\t\tif(this->node==0) return *this;\n\t\t\t}\n\t\twhile(relative_depth<0 && this->node->last_child!=0) {\n\t\t\tthis->node=this->node->last_child;\n\t\t\t++relative_depth;\n\t\t\t}\n\t\tif(relative_depth<0) {\n\t\t\tif(this->node->prev_sibling==0) goto upper;\n\t\t\telse                            goto lower;\n\t\t\t}\n\t\t}\n\treturn *this;\n\n\t//\n\t//\n\t//\tassert(this->node!=0);\n\t//\tif(this->node->prev_sibling!=0) {\n\t//\t\tthis->node=this->node->prev_sibling;\n\t//\t\tassert(this->node!=0);\n\t//\t\tif(this->node->parent==0 && this->node->prev_sibling==0) // head element\n\t//\t\t\tthis->node=0;\n\t//\t\t}\n\t//\telse {\n\t//\t\ttree_node *par=this->node->parent;\n\t//\t\tdo {\n\t//\t\t\tpar=par->prev_sibling;\n\t//\t\t\tif(par==0) { // FIXME: need to keep track of this!\n\t//\t\t\t\tthis->node=0;\n\t//\t\t\t\treturn *this;\n\t//\t\t\t\t}\n\t//\t\t\t} while(par->last_child==0);\n\t//\t\tthis->node=par->last_child;\n\t//\t\t}\n\t//\treturn *this;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::fixed_depth_iterator tree<T, tree_node_allocator>::fixed_depth_iterator::operator++(int)\n\t{\n\tfixed_depth_iterator copy = *this;\n\t++(*this);\n\treturn copy;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::fixed_depth_iterator tree<T, tree_node_allocator>::fixed_depth_iterator::operator--(int)\n\t{\n\tfixed_depth_iterator copy = *this;\n\t--(*this);\n\treturn copy;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::fixed_depth_iterator& tree<T, tree_node_allocator>::fixed_depth_iterator::operator-=(unsigned int num)\n\t{\n\twhile(num>0) {\n\t\t--(*this);\n\t\t--(num);\n\t\t}\n\treturn (*this);\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::fixed_depth_iterator& tree<T, tree_node_allocator>::fixed_depth_iterator::operator+=(unsigned int num)\n\t{\n\twhile(num>0) {\n\t\t++(*this);\n\t\t--(num);\n\t\t}\n\treturn *this;\n\t}\n\n\n// Sibling iterator\n\ntemplate <class T, class tree_node_allocator>\ntree<T, tree_node_allocator>::sibling_iterator::sibling_iterator()\n\t: iterator_base()\n\t{\n\tset_parent_();\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntree<T, tree_node_allocator>::sibling_iterator::sibling_iterator(tree_node *tn)\n\t: iterator_base(tn)\n\t{\n\tset_parent_();\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntree<T, tree_node_allocator>::sibling_iterator::sibling_iterator(const iterator_base& other)\n\t: iterator_base(other.node)\n\t{\n\tset_parent_();\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntree<T, tree_node_allocator>::sibling_iterator::sibling_iterator(const sibling_iterator& other)\n\t: iterator_base(other), parent_(other.parent_)\n\t{\n\t}\n\ntemplate <class T, class tree_node_allocator>\nvoid tree<T, tree_node_allocator>::sibling_iterator::set_parent_()\n\t{\n\tparent_=0;\n\tif(this->node==0) return;\n\tif(this->node->parent!=0)\n\t\tparent_=this->node->parent;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::sibling_iterator& tree<T, tree_node_allocator>::sibling_iterator::operator++()\n\t{\n\tif(this->node)\n\t\tthis->node=this->node->next_sibling;\n\treturn *this;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::sibling_iterator& tree<T, tree_node_allocator>::sibling_iterator::operator--()\n\t{\n\tif(this->node) this->node=this->node->prev_sibling;\n\telse {\n\t\tassert(parent_);\n\t\tthis->node=parent_->last_child;\n\t\t}\n\treturn *this;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::sibling_iterator tree<T, tree_node_allocator>::sibling_iterator::operator++(int)\n\t{\n\tsibling_iterator copy = *this;\n\t++(*this);\n\treturn copy;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::sibling_iterator tree<T, tree_node_allocator>::sibling_iterator::operator--(int)\n\t{\n\tsibling_iterator copy = *this;\n\t--(*this);\n\treturn copy;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::sibling_iterator& tree<T, tree_node_allocator>::sibling_iterator::operator+=(unsigned int num)\n\t{\n\twhile(num>0) {\n\t\t++(*this);\n\t\t--num;\n\t\t}\n\treturn (*this);\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::sibling_iterator& tree<T, tree_node_allocator>::sibling_iterator::operator-=(unsigned int num)\n\t{\n\twhile(num>0) {\n\t\t--(*this);\n\t\t--num;\n\t\t}\n\treturn (*this);\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::tree_node *tree<T, tree_node_allocator>::sibling_iterator::range_first() const\n\t{\n\ttree_node *tmp=parent_->first_child;\n\treturn tmp;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::tree_node *tree<T, tree_node_allocator>::sibling_iterator::range_last() const\n\t{\n\treturn parent_->last_child;\n\t}\n\n// Leaf iterator\n\ntemplate <class T, class tree_node_allocator>\ntree<T, tree_node_allocator>::leaf_iterator::leaf_iterator()\n\t: iterator_base(0), top_node(0)\n\t{\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntree<T, tree_node_allocator>::leaf_iterator::leaf_iterator(tree_node *tn, tree_node *top)\n\t: iterator_base(tn), top_node(top)\n\t{\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntree<T, tree_node_allocator>::leaf_iterator::leaf_iterator(const iterator_base &other)\n\t: iterator_base(other.node), top_node(0)\n\t{\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntree<T, tree_node_allocator>::leaf_iterator::leaf_iterator(const sibling_iterator& other)\n\t: iterator_base(other.node), top_node(0)\n\t{\n\tif(this->node==0) {\n\t\tif(other.range_last()!=0)\n\t\t\tthis->node=other.range_last();\n\t\telse\n\t\t\tthis->node=other.parent_;\n\t\t++(*this);\n\t\t}\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::leaf_iterator& tree<T, tree_node_allocator>::leaf_iterator::operator++()\n\t{\n\tassert(this->node!=0);\n\tif(this->node->first_child!=0) { // current node is no longer leaf (children got added)\n\t\twhile(this->node->first_child)\n\t\t\tthis->node=this->node->first_child;\n\t\t}\n\telse {\n\t\twhile(this->node->next_sibling==0) {\n\t\t\tif (this->node->parent==0) return *this;\n\t\t\tthis->node=this->node->parent;\n\t\t\tif (top_node != 0 && this->node==top_node) return *this;\n\t\t\t}\n\t\tthis->node=this->node->next_sibling;\n\t\twhile(this->node->first_child)\n\t\t\tthis->node=this->node->first_child;\n\t\t}\n\treturn *this;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::leaf_iterator& tree<T, tree_node_allocator>::leaf_iterator::operator--()\n\t{\n\tassert(this->node!=0);\n\twhile (this->node->prev_sibling==0) {\n\t\tif (this->node->parent==0) return *this;\n\t\tthis->node=this->node->parent;\n\t\tif (top_node !=0 && this->node==top_node) return *this;\n\t\t}\n\tthis->node=this->node->prev_sibling;\n\twhile(this->node->last_child)\n\t\tthis->node=this->node->last_child;\n\treturn *this;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::leaf_iterator tree<T, tree_node_allocator>::leaf_iterator::operator++(int)\n\t{\n\tleaf_iterator copy = *this;\n\t++(*this);\n\treturn copy;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::leaf_iterator tree<T, tree_node_allocator>::leaf_iterator::operator--(int)\n\t{\n\tleaf_iterator copy = *this;\n\t--(*this);\n\treturn copy;\n\t}\n\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::leaf_iterator& tree<T, tree_node_allocator>::leaf_iterator::operator+=(unsigned int num)\n\t{\n\twhile(num>0) {\n\t\t++(*this);\n\t\t--num;\n\t\t}\n\treturn (*this);\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::leaf_iterator& tree<T, tree_node_allocator>::leaf_iterator::operator-=(unsigned int num)\n\t{\n\twhile(num>0) {\n\t\t--(*this);\n\t\t--num;\n\t\t}\n\treturn (*this);\n\t}\n\n#endif\n\n// Local variables:\n// default-tab-width: 3\n// End:\n"
  },
  {
    "path": "client_server/websocket_client.cc",
    "content": "#include \"websocket_client.hh\"\n#include <iostream>\n\nwebsocket_client::websocket_client()\n\t: ssl_ctx_(boost::asio::ssl::context::sslv23_client) // tlsv12_client)\n\t, resolver_(ioc_)\n\t, is_ssl_(false)\n\t{\n\tssl_ctx_.set_default_verify_paths();\n#ifdef __APPLE__\n  #include <TargetConditionals.h>\n  #if TARGET_OS_IPHONE\n\tssl_ctx_.set_verify_mode(boost::asio::ssl::verify_none);\n  #else\n\t// on MacOS or related, include the system certificate chain.\n\tssl_ctx_.set_verify_mode(boost::asio::ssl::verify_none);\n//\tssl_ctx_.load_verify_file(\"/etc/ssl/cert.pem\");\n//\tssl_ctx_.set_verify_mode(boost::asio::ssl::verify_peer);\n\t// Configure SSL context to be more permissive\n  #endif\n//  ssl_ctx_.set_options(boost::asio::ssl::context::default_workarounds |\n//\t\t\t\t\t\t\t  boost::asio::ssl::context::no_sslv2 |\n//\t\t\t\t\t\t\t  boost::asio::ssl::context::no_sslv3);\n#else\n\tssl_ctx_.set_verify_mode(boost::asio::ssl::verify_peer);\n#endif\n//\tssl_ctx_.set_verify_callback([](bool preverified, ssl::verify_context& ctx) {\n//\t\t// Log verification details for debugging\n//\t\tchar subject_name[256];\n//\t\tX509* cert = X509_STORE_CTX_get_current_cert(ctx.native_handle());\n//\t\tX509_NAME_oneline(X509_get_subject_name(cert), subject_name, 256);\n//\t\tstd::cerr << \"websocket_client::verify_callback: \" << subject_name << \"\\n\";\n//\t\treturn preverified;\n//\t\t});\n\t}\n\nwebsocket_client::~websocket_client()\n\t{\n   boost::beast::error_code ec;  // ignored errors\n\t\n\tif (ws_stream_) {\n\t\tws_stream_->close(boost::beast::websocket::close_code::normal, ec);\n\t\tboost::beast::get_lowest_layer(*ws_stream_).shutdown(boost::asio::ip::tcp::socket::shutdown_both, ec);\n\t\t}\n\t\n\tif (wss_stream_) {\n\t\twss_stream_->close(boost::beast::websocket::close_code::normal, ec);\n\t\twss_stream_->next_layer().shutdown(ec);\n\t\tboost::beast::get_lowest_layer(*wss_stream_).shutdown(boost::asio::ip::tcp::socket::shutdown_both, ec);\n\t\t}\n\t\n\tioc_.stop();\n\t}\n\nvoid websocket_client::set_message_handler(message_handler h) { message_handler_ = std::move(h); }\nvoid websocket_client::set_connect_handler(connect_handler h) { connect_handler_ = std::move(h); }\nvoid websocket_client::set_close_handler(close_handler h) { close_handler_ = std::move(h); }\nvoid websocket_client::set_fail_handler(fail_handler h) { fail_handler_ = std::move(h); }\n\nvoid websocket_client::connect(const std::string& uri_string)\n\t{\n\t// Parse URI (basic)\n\tUri uri(uri_string);\n\tis_ssl_ = uri.protocol==\"wss\";\n\thost_   = uri.host;\n\tport_   = uri.port.empty() ? (is_ssl_ ? \"443\" : \"80\") : uri.port;\n\tpath_   = uri.path;\n\t\n\t// Create appropriate stream\n\tif (is_ssl_) {\n\t\twss_stream_ = std::make_unique<boost::beast::websocket::stream<\n\t\t\tboost::beast::ssl_stream<boost::asio::ip::tcp::socket>>>(ioc_, ssl_ctx_);\n\t\twss_stream_->binary(false);  // Set to text mode\n\t\twss_stream_->auto_fragment(false);  // Don't fragment messages\n\t\twss_stream_->read_message_max(64 * 1024 * 1024);  // 64MB max message size\n//\t\tssl_ctx_.set_verify_callback(\n//\t\t\t[host](bool preverified, ssl::verify_context& ctx) {\n//\t\t\t// You can add debug logging here to see verification attempts\n//\t\t\tstd::cerr << \"Verifying certificate: \" << preverified << std::endl;\n//\t\t\treturn preverified;\n//\t\t\t});\n//\t\twss_stream_->next_layer().set_server_hostname(host_);\n\t\twss_stream_->set_option(boost::beast::websocket::stream_base::decorator(\n\t\t\t\t\t\t\t\t\t\t\t[](boost::beast::websocket::request_type& req) {\n\t\t\t\t\t\t\t\t\t\t\treq.version(11); \n\t\t\t\t\t\t\t\t\t\t\treq.set(boost::beast::http::field::user_agent, \"WebSocket-Client/1.0\");\n\t\t\t\t\t\t\t\t\t\t\t// Log all headers\n\t\t\t\t\t\t\t\t\t\t\t// for (auto const& field : req) {\n\t\t\t\t\t\t\t\t\t\t\t// \tstd::cerr << field.name_string() << \": \" \n\t\t\t\t\t\t\t\t\t\t\t// \t\t\t\t << field.value() << \"\\n\";\n\t\t\t\t\t\t\t\t\t\t\t// \t}\n\t\t\t\t\t\t\t\t\t\t\t}));\n\t\t}\n\telse {\n\t\tws_stream_ = std::make_unique<boost::beast::websocket::stream<\n\t\t\tboost::asio::ip::tcp::socket>>(ioc_);\n\t\tws_stream_->binary(false);  // Set to text mode\n\t\tws_stream_->auto_fragment(false);  // Don't fragment messages\n\t\tws_stream_->read_message_max(64 * 1024 * 1024);  // 64MB max message size\n\t\t}\n\t\n\t// Start the connection process\n\tresolver_.async_resolve(host_, port_,\n\t\t\t\t\t\t\t\t\t[this](const boost::beast::error_code& ec,\n\t\t\t\t\t\t\t\t\t\t\t boost::asio::ip::tcp::resolver::results_type results) {\n\t\t\t\t\t\t\t\t\ton_resolve(ec, results);\n\t\t\t\t\t\t\t\t\t});\n\t}\n\nvoid websocket_client::on_resolve(const boost::beast::error_code& ec,\n\t\t\t\t\t\t\t\t\t\t\t boost::asio::ip::tcp::resolver::results_type results)\n\t{\n\tif (ec) return fail(ec);\n\t\n\tif (is_ssl_) {\n\t\tboost::asio::async_connect(\n\t\t\twss_stream_->next_layer().next_layer(),\n\t\t\tresults,\n\t\t\t[this](const boost::beast::error_code& ec,\n\t\t\t\t\t const boost::asio::ip::tcp::endpoint& /*endpoint*/) {\n\t\t\ton_connect(ec);\n\t\t\t});\n\t\t}\n\telse {\n\t\tboost::asio::async_connect(\n\t\t\tws_stream_->next_layer(),\n\t\t\tresults,\n\t\t\t[this](const boost::beast::error_code& ec,\n\t\t\t\t\t const boost::asio::ip::tcp::endpoint& /*endpoint*/) {\n\t\t\ton_connect(ec);\n\t\t\t});\n\t\t}\n\t}\n\nvoid websocket_client::on_connect(const boost::beast::error_code& ec)\n\t{\n\tif (ec) return fail(ec);\n\t\n\tif (is_ssl_) {\n\t\tif (!SSL_set_tlsext_host_name(\n\t\t\t\t wss_stream_->next_layer().native_handle(), host_.c_str())) {\n\t\t\tthrow boost::beast::system_error{\n\t\t\t\tboost::beast::error_code{\n\t\t\t\t\tstatic_cast<int>(::ERR_get_error()),\n\t\t\t\t\tboost::beast::net::error::get_ssl_category()}};\n\t\t\t}\n\t\t\n\t\twss_stream_->next_layer().async_handshake(\n\t\t\tboost::asio::ssl::stream_base::client,\n\t\t\t[this](const boost::beast::error_code& ec) {\n\t\t\ton_ssl_handshake(ec);\n\t\t\t});\n\t\t}\n\telse {\n\t\tws_stream_->async_handshake(host_, path_,\n\t\t\t\t\t\t\t\t\t\t\t [this](const boost::beast::error_code& ec) {\n\t\t\t\t\t\t\t\t\t\t\t on_handshake(ec);\n\t\t\t\t\t\t\t\t\t\t\t });\n\t\t}\n\t}\n\nvoid websocket_client::on_ssl_handshake(const boost::beast::error_code& ec)\n\t{\n\tif (ec) return fail(ec);\n\t\n\twss_stream_->async_handshake(host_, path_,\n\t\t\t\t\t\t\t\t\t\t  [this](const boost::beast::error_code& ec) {\n\t\t\t\t\t\t\t\t\t\t  on_handshake(ec);\n\t\t\t\t\t\t\t\t\t\t  });\n\t}\n\nvoid websocket_client::on_handshake(const boost::beast::error_code& ec)\n\t{\n\tif (ec) return fail(ec);\n\t\n\tif (connect_handler_) {\n\t\tconnect_handler_();\n\t\t}\n\t\n\tdo_read();\n\t}\n\n\n\nvoid websocket_client::send(const std::string& message)\n\t{\n\t// Beast does not allow us to run two `async_write` at the\n\t// same time; we have to wait for the completion handler\n\t// to be called.\n\t\n\t// Create a new buffer for this message\n\tqueued_message msg;\n\tmsg.data   = message;\n\tmsg.buffer = std::make_shared<boost::beast::flat_buffer>();\n\tboost::beast::ostream(*msg.buffer) << msg.data;\n\t\n\tmessage_queue_.push(msg);\n\tif (!writing_)\n\t\tdo_write();\n\t}\n\nvoid websocket_client::on_write(const boost::beast::error_code& ec, std::size_t /* bytes_transferred */)\n\t{\n\tif(ec) {\n\t\tif(fail_handler_) {\n\t\t\tfail_handler_(ec);\n\t\t\t}\n\t\treturn;\n\t\t}\n\t\n\t// Remove the message and the associated beast buffer.\n\tmessage_queue_.pop();  \n\t\n\t// Write next message, if any.\n\tdo_write();\n\t}\n\nvoid websocket_client::do_write()\n\t{\n\tif (message_queue_.empty()) {\n\t\twriting_ = false;\n\t\treturn;\n\t\t}\n\t\n\twriting_ = true;\n\tauto& msg = message_queue_.front();\n   \n\tif (is_ssl_) {\n\t\twss_stream_->async_write(\n\t\t\tmsg.buffer->data(),\n                [this](boost::beast::error_code ec, std::size_t bytes_transferred) {\n\t\t\t\t\t on_write(ec, bytes_transferred);\n                });\n\t\t}\n\telse {\n\t\tws_stream_->async_write(\n\t\t\tmsg.buffer->data(),\n\t\t\t[this](boost::beast::error_code ec, std::size_t bytes_transferred) {\n\t\t\ton_write(ec, bytes_transferred);\n\t\t\t});\n\t\t}\n\t}\n\nvoid websocket_client::do_read()\n\t{\n\tif (is_ssl_) {\n\t\twss_stream_->async_read(\n\t\t\tbuffer_,\n\t\t\t[this](const boost::beast::error_code& ec, std::size_t bytes) {\n\t\t\ton_read(ec, bytes);\n\t\t\t});\n\t\t}\n\telse {\n\t\tws_stream_->async_read(\n\t\t\tbuffer_,\n\t\t\t[this](const boost::beast::error_code& ec, std::size_t bytes) {\n\t\t\ton_read(ec, bytes);\n\t\t\t});\n\t\t}\n\t}\n\nvoid websocket_client::on_read(const boost::beast::error_code& ec, std::size_t /* bytes_transferred */)\n\t{\n\tif (ec) return fail(ec);\n\t\n\tif (message_handler_) {\n\t\tmessage_handler_(boost::beast::buffers_to_string(buffer_.data()));\n\t\t}\n\t\n\tbuffer_.consume(buffer_.size());\n\tdo_read();\n\t}\n\nvoid websocket_client::close()\n\t{\n\tif (is_ssl_) {\n\t\twss_stream_->async_close(\n\t\t\tboost::beast::websocket::close_code::normal,\n\t\t\t[this](const boost::beast::error_code& ec) {\n\t\t\ton_close(ec);\n\t\t\t});\n\t\t}\n\telse {\n\t\tws_stream_->async_close(\n\t\t\tboost::beast::websocket::close_code::normal,\n\t\t\t[this](const boost::beast::error_code& ec) {\n\t\t\ton_close(ec);\n\t\t\t});\n\t\t}\n\t}\n\nvoid websocket_client::on_close(const boost::beast::error_code& ec)\n\t{\n\tif (ec) return fail(ec);\n\t\n\tif (close_handler_) {\n\t\tclose_handler_();\n\t\t}\n\t}\n\nvoid websocket_client::fail(const boost::beast::error_code& ec)\n\t{\n\tif (fail_handler_) {\n\t\tfail_handler_(ec);\n\t\t}\n\t}\n\nvoid websocket_client::run()\n\t{\n\tioc_.run();\n\t}\n\nvoid websocket_client::stop()\n\t{\n\tioc_.stop();\n\t}\n\n\nUri::Uri(const std::string& uri)\n\t{\n\tpath = \"/\";  // default path\n\tstd::regex pattern(\"^([^:]+)://([^/:]+)(?::(\\\\d+))?(/.*)?\");\n\tstd::smatch matches;\n   \n\tif (std::regex_match(uri, matches, pattern)) {\n\t\tprotocol = matches[1];\n\t\thost = matches[2];\n\t\tif (matches[3].matched) port = matches[3];\n\t\tif (matches[4].matched) path = matches[4];\n\t\t}\n\t}\n\nstd::string Uri::to_string() const\n\t{\n\tstd::string result = protocol + \"://\" + host;\n\tif (!port.empty()) result += \":\" + port;\n\tresult += path;\n\treturn result;\n\t}\n"
  },
  {
    "path": "client_server/websocket_client.hh",
    "content": "#pragma once\n\n#include <boost/beast/core.hpp>\n#include <boost/beast/websocket.hpp>\n#include <boost/beast/ssl.hpp>\n#include <boost/asio/connect.hpp>\n#include <boost/asio/ip/tcp.hpp>\n#include <boost/asio/ssl/stream.hpp>\n#include <functional>\n#include <memory>\n#include <string>\n#include <queue>\n#include <regex>\n\nclass websocket_client {\n\tpublic:\n\t\t// Callback handlers\n\t\tusing message_handler = std::function<void(const std::string&)>;\n\t\tusing connect_handler = std::function<void()>;\n\t\tusing close_handler = std::function<void()>;\n\t\tusing fail_handler = std::function<void(const boost::beast::error_code&)>;\n\n\t\twebsocket_client();\n\t\t~websocket_client();\n\n\t\t// No copying\n\t\twebsocket_client(const websocket_client&) = delete;\n\t\twebsocket_client& operator=(const websocket_client&) = delete;\n\n\t\t// Set handlers (all optional)\n\t\tvoid set_message_handler(message_handler h);\n\t\tvoid set_connect_handler(connect_handler h);\n\t\tvoid set_close_handler(close_handler h);\n\t\tvoid set_fail_handler(fail_handler h);\n\n\t\t// Async operations (all return immediately)\n\t\tvoid connect(const std::string& uri);  // ws:// or wss://\n\t\tvoid send(const std::string& message);\n\t\tvoid close();\n    \n\t\tvoid run();\n\t\tvoid stop();\n\n\tprivate:\n\t\tvoid on_resolve(const boost::beast::error_code& ec, \n\t\t\t\t\t\t\t boost::asio::ip::tcp::resolver::results_type results);\n\t\tvoid on_connect(const boost::beast::error_code& ec);\n\t\tvoid on_ssl_handshake(const boost::beast::error_code& ec);\n\t\tvoid on_handshake(const boost::beast::error_code& ec);\n\t\tvoid on_write(const boost::beast::error_code& ec, std::size_t bytes_transferred);\n\t\tvoid on_read(const boost::beast::error_code& ec, std::size_t bytes_transferred);\n\t\tvoid on_close(const boost::beast::error_code& ec);\n\t\tvoid do_read();\n\t\tvoid do_write();\n\t\tvoid fail(const boost::beast::error_code& ec);\n\n\t\t// State\n\t\tboost::asio::io_context        ioc_;\n\t\tboost::asio::ssl::context      ssl_ctx_;\n\t\tboost::asio::ip::tcp::resolver resolver_;\n\t\tstd::unique_ptr<boost::beast::websocket::stream<boost::beast::ssl_stream<boost::asio::ip::tcp::socket>>> wss_stream_;\n\t\tstd::unique_ptr<boost::beast::websocket::stream<boost::asio::ip::tcp::socket>> ws_stream_;\n\t\tboost::beast::flat_buffer buffer_;\n\t\tbool is_ssl_;\n\t\tstd::string host_, port_, path_;\n\n\t\t// Handlers\n\t\tmessage_handler message_handler_;\n\t\tconnect_handler connect_handler_;\n\t\tclose_handler   close_handler_;\n\t\tfail_handler    fail_handler_;\n\n\t\t// Message queue.\n\t\tstruct queued_message {\n\t\t\t\tstd::string data;\n\t\t\t\tstd::shared_ptr<boost::beast::flat_buffer> buffer;\n\t\t};\n\t\tstd::queue<queued_message> message_queue_;\n\n\t\tbool writing_{false};\n};\n\n\nclass Uri {\n\tpublic:\n\t\tUri(const std::string& uri);\n\n\t\tstd::string to_string() const;\n\n\t\tstd::string protocol;\n\t\tstd::string host;\n\t\tstd::string port;\n\t\tstd::string path;\n\n};\n"
  },
  {
    "path": "client_server/websocket_server.cc",
    "content": "#include \"websocket_server.hh\"\n#include <iostream>\n\nwebsocket_server::connection::connection(boost::asio::io_context& ioc, websocket_server& server, id_type id)\n\t: socket_(ioc)\n\t, server_(server)\n\t, id_(id)\n\t{\n\t}\n\nvoid websocket_server::connection::start()\n\t{\n\t// First read as HTTP\n\tboost::beast::http::async_read(\n\t\tsocket_,\n\t\tbuffer_,\n\t\thttp_request_,\n\t\t[self = shared_from_this()](\n\t\t\tboost::beast::error_code ec, std::size_t bytes_transferred) {\n\t\tself->on_read_request(ec, bytes_transferred);\n\t\t});\n\t}\n\nvoid websocket_server::connection::on_read_request(boost::beast::error_code ec, std::size_t)\n\t{\n\tif (ec) {\n\t\tserver_.remove_connection(id_);\n\t\treturn;\n\t\t}\n\n\tif (boost::beast::websocket::is_upgrade(http_request_)) {\n\t\t// Handle as WebSocket\n\t\tis_websocket_ = true;\n\t\tws_stream_.emplace(socket_);\n\t\tws_stream_->async_accept(\n\t\t\thttp_request_,\n\t\t\t[self = shared_from_this()](boost::beast::error_code ec) {\n\t\t\tself->on_websocket_accept(ec);\n\t\t\t});\n\t\t}\n\telse {\n\t\t// Handle as HTTP\n\t\thandle_http_request();\n\t\t}\n\t}\n\nvoid websocket_server::connection::handle_http_request()\n\t{\n\t// Create response that lives through the async operation\n\tauto response = std::make_shared<boost::beast::http::response<boost::beast::http::string_body>>();\n   \n\tif (server_.http_handler_) {\n\t\tserver_.http_handler_(http_request_, *response);\n\t\t}\n\telse {\n\t\tresponse->result(boost::beast::http::status::not_found);\n\t\tresponse->version(http_request_.version());\n\t\tresponse->set(boost::beast::http::field::server, \"Beast\");\n\t\tresponse->set(boost::beast::http::field::content_type, \"text/plain\");\n\t\tresponse->body() = \"404 Not Found\\r\\n\";\n\t\t}\n\t\n\tresponse->prepare_payload();\n   \n\tboost::beast::http::async_write(\n\t\tsocket_,\n\t\t*response,\n\t\t[self = shared_from_this(), response](  // Keep response alive in lambda\n\t\t\tboost::beast::error_code ec, std::size_t) {\n\t\tif (ec) {\n\t\t\tself->server_.remove_connection(self->id_);\n\t\t\treturn;\n\t\t\t}\n\t\t// HTTP is done, close the connection\n\t\tboost::beast::error_code sec;\n\t\tself->socket_.shutdown(boost::asio::ip::tcp::socket::shutdown_send, sec);\n\t\tself->server_.remove_connection(self->id_);\n\t\t});\n\t}\n\nvoid websocket_server::connection::on_websocket_accept(boost::beast::error_code ec)\n\t{\n\tif (ec) {\n\t\tserver_.remove_connection(id_);\n\t\treturn;\n\t\t}\n\t\n\tif (server_.connect_handler_) {\n\t\tserver_.connect_handler_(id_);\n\t\t}\n\t\n\tdo_read_websocket();\n\t}\n\nvoid websocket_server::connection::do_read_websocket()\n\t{\n\tws_stream_->async_read(\n\t\tbuffer_,\n\t\t[self = shared_from_this()](\n\t\t\tboost::beast::error_code ec, std::size_t bytes_transferred) {\n\t\tself->on_read_websocket(ec, bytes_transferred);\n\t\t});\n\t}\n\nvoid websocket_server::connection::on_read_websocket(boost::beast::error_code ec, std::size_t)\n\t{\n\tif (ec) {\n\t\tserver_.remove_connection(id_);\n\t\treturn;\n\t\t}\n\t\n\tif (server_.message_handler_) {\n\t\tserver_.message_handler_(id_,\n\t\t\t\t\t\t\t\t\t\t boost::beast::buffers_to_string(buffer_.data()),\n\t\t\t\t\t\t\t\t\t\t http_request_,\n\t\t\t\t\t\t\t\t\t\t socket_.remote_endpoint().address().to_string());\n\t\t}\n\t\n\tbuffer_.consume(buffer_.size());\n\tdo_read_websocket();\n\t}\n\nvoid websocket_server::connection::send(const std::string& message)\n\t{\n\tstatic int msg_number=0;\n\t\n\tif (!is_websocket_) return;\n   \n\t// std::cerr << \"SEND CALLED on thread \" << pthread_self() << std::endl;\n\n\tqueued_message msg;\n\tmsg.data   = message;\n\tmsg.buffer = std::make_shared<boost::beast::flat_buffer>();\n\tmsg.seq    = ++msg_number;\n\tboost::beast::ostream(*msg.buffer) << msg.data;\n\n\tstd::unique_lock<std::mutex> lock(queue_mutex_);\n\tmessage_queue_.push(msg);\n\n\t// std::cerr << \"QUEUE size after push \" << message_queue_.size() << std::endl;\n\tif(!writing_) {\n\t\tlock.unlock();\n\t\tdo_write();\n\t\t}\n\t}\n\nvoid websocket_server::connection::do_write()\n\t{\n\tstd::unique_lock<std::mutex> lock(queue_mutex_);\n\tif(message_queue_.empty() || !is_websocket_) {\n\t\twriting_ = false;\n\t\tlock.unlock();\n\t\treturn;\n\t\t}\n\t\n\twriting_ = true;\n\tqueued_message msg = message_queue_.front();\n\tlock.unlock();\n\t\n\t// std::cerr << \"going to send msg \" << msg.seq << std::endl;\n\tws_stream_->async_write(\n\t\tmsg.buffer->data(),\n\t\t[self = shared_from_this()](\n\t\t\tboost::beast::error_code ec, std::size_t bytes_transferred) {\n\t\tself->on_write(ec, bytes_transferred);\n\t\t});\n\t}\n\nvoid websocket_server::connection::close()\n\t{\n\tif (!is_websocket_) {\n\t\tsocket_.shutdown(boost::asio::ip::tcp::socket::shutdown_both);\n\t\tserver_.remove_connection(id_);\n\t\treturn;\n\t\t}\n\t\n\tws_stream_->async_close(\n\t\tboost::beast::websocket::close_code::normal,\n\t\t[self = shared_from_this()](boost::beast::error_code ec) {\n\t\tself->on_close(ec);\n\t\t});\n\t}\n\nvoid websocket_server::connection::on_write(boost::beast::error_code ec, std::size_t)\n\t{\n\t//std::cerr << \"sent msg \" << message_queue_.front().seq\n//\t\t\t\t << \"; queue size on_write \" << message_queue_.size() << std::endl;\n\tstd::unique_lock<std::mutex> lock(queue_mutex_);\n\tmessage_queue_.pop();\n\tlock.unlock();\n\t\n\tif(ec) {\n\t\tserver_.remove_connection(id_);\n\t\treturn;\n\t\t}\n\t\n\tdo_write();\n\t}\n\nvoid websocket_server::connection::on_close(boost::beast::error_code ec)\n\t{\n\tserver_.remove_connection(id_);\n\t}\n\nwebsocket_server::websocket_server(uint16_t port)\n\t{\n\tlisten(port);\n\t}\n\nwebsocket_server::~websocket_server()\n\t{\n\tstop();\n\t}\n\nvoid websocket_server::listen(uint16_t port)\n\t{\n\tboost::asio::ip::tcp::endpoint endpoint{boost::asio::ip::tcp::v4(), port};\n   \n\tacceptor_.emplace(ioc_);\n\tacceptor_->open(endpoint.protocol());\n\tacceptor_->set_option(boost::asio::socket_base::reuse_address(true));\n\tacceptor_->bind(endpoint);\n\tacceptor_->listen(64 /* backlog */);\n\t\n\tdo_accept();\n\t}\n\nuint16_t websocket_server::get_local_port() const\n\t{\n\treturn acceptor_->local_endpoint().port();\n\t}\n\nvoid websocket_server::set_message_handler(message_handler h)\n\t{\n\tmessage_handler_ = std::move(h);\n\t}\n\nvoid websocket_server::set_connect_handler(connect_handler h)\n\t{\n\tconnect_handler_ = std::move(h);\n\t}\n\nvoid websocket_server::set_disconnect_handler(disconnect_handler h)\n\t{\n\tdisconnect_handler_ = std::move(h);\n\t}\n\nvoid websocket_server::set_http_handler(http_handler h)\n\t{\n\thttp_handler_ = std::move(h);\n\t}\n\nvoid websocket_server::do_accept()\n\t{\n\tif(!acceptor_) return;\n\t\n\tacceptor_->async_accept(\n\t\t[this](boost::beast::error_code ec, boost::asio::ip::tcp::socket socket) {\n\t\tif (!ec) {\n\t\t\tauto id = next_connection_id_++;\n\t\t\tauto conn = std::make_shared<connection>(ioc_, *this, id);\n\t\t\tsocket.set_option(boost::asio::ip::tcp::no_delay(true));\n\t\t\tconn->socket_ = std::move(socket);\n\t\t\tconnections_[id] = conn;\n\t\t\tconn->start();\n\t\t\t}\n\t\telse {\n\t\t\tstd::cerr << \"websocket::server::do_accept: error on accept, \" << ec << std::endl;\n\t\t\t}\n\n\t\t// restart for the next connection\n\t\tdo_accept();\n\t\t});\n\t}\n\nvoid websocket_server::send(id_type id, const std::string& message)\n\t{\n\tif (auto it = connections_.find(id); it != connections_.end()) {\n\t\tit->second->send(message);\n\t\t}\n\t}\n\nvoid websocket_server::close(id_type id)\n\t{\n\tif (auto it = connections_.find(id); it != connections_.end()) {\n\t\tit->second->close();\n\t\t}\n\t}\n\nvoid websocket_server::remove_connection(id_type id)\n\t{\n\tif (disconnect_handler_) {\n\t\tdisconnect_handler_(id);\n\t\t}\n\tconnections_.erase(id);\n\t}\n\nvoid websocket_server::run()\n\t{\n\tstatic int calls=0;\n\t// std::cerr << \"RUN CALLED on thread \" << pthread_self() << std::endl;\n\n\tif(++calls>1)\n\t\tthrow std::logic_error(\"Cannot call websocket_server::run multiple times.\");\n\t\n\tioc_.run();\n\t}\n\nvoid websocket_server::stop()\n\t{\n\tboost::beast::error_code ec;\n\tif(acceptor_)\n\t\tacceptor_->close(ec);\n\t\n\tfor (auto& [_, conn] : connections_) {\n\t\tconn->close();\n\t\t}\n\t\n\tconnections_.clear();\n\tioc_.stop();\n\t}\n"
  },
  {
    "path": "client_server/websocket_server.hh",
    "content": "#pragma once\n\n#include <boost/beast/core.hpp>\n#include <boost/beast/websocket.hpp>\n#include <boost/beast/http.hpp>\n#include <boost/asio/ip/tcp.hpp>\n#include <functional>\n#include <memory>\n#include <string>\n#include <queue>\n#include <optional>\n#include <unordered_map>\n#include <iostream>\n#include <pthread.h>\n\nclass websocket_server {\n\tpublic:\n\t\tusing id_type = std::size_t;\n\t\tusing request_type  = boost::beast::http::request<boost::beast::http::string_body>;\n\t\tusing response_type = boost::beast::http::response<boost::beast::http::string_body>;\n\t\t\n\t\tusing message_handler = std::function<void(id_type, const std::string&, const request_type&, const std::string& ip_address)>;\n\t\tusing connect_handler = std::function<void(id_type)>;\n\t\tusing disconnect_handler = std::function<void(id_type)>;\n\t\tusing http_handler = std::function<void(request_type&, response_type&)>;\n\n\t\twebsocket_server() = default;\n\t\texplicit websocket_server(uint16_t port);\n\t\t~websocket_server();\n\n\t\twebsocket_server(const websocket_server&) = delete;\n\t\twebsocket_server& operator=(const websocket_server&) = delete;\n\n\t\t// Change the port on which to listen.\n\t\tvoid listen(uint16_t port);\n\n\t\tvoid set_message_handler(message_handler h);\n\t\tvoid set_connect_handler(connect_handler h);\n\t\tvoid set_disconnect_handler(disconnect_handler h);\n\t\tvoid set_http_handler(http_handler h);\n\n\t\t// You should call `run` on a separate thread to start the\n\t\t// listening process.  All callbacks on the message handlers will\n\t\t// come on this thread. It is safe to call `send` below from a\n\t\t// different thread.\n\t\tvoid run();\n\t\tvoid stop();\n\n\t\t// Send a message. This is safe on a thread which is not the\n\t\t// thread which called `run`.\n\t\tvoid send(id_type id, const std::string& message);\n\t\tvoid close(id_type id);\n\n\t\tuint16_t get_local_port() const;\n\t\t\n\tprivate:\n\t\t// The connection class handles all actual communication. There\n\t\t// is one instance for each connection. Connections are\n\t\t// identified by the single `id_type` stored as `id`.\n\t\t\n\t\tclass connection : public std::enable_shared_from_this<connection> {\n\t\t\tpublic:\n\t\t\t\tconnection(boost::asio::io_context& ioc, websocket_server& server, id_type id);\n\n\t\t\t\tvoid start();\n\t\t\t\tvoid send(const std::string& message);\n\t\t\t\tvoid close();\n\n\t\t\t\tfriend websocket_server;\n\n\t\t\tprivate:\n\t\t\t\tvoid on_read_request(boost::beast::error_code ec, std::size_t);\n\t\t\t\tvoid on_websocket_accept(boost::beast::error_code ec);\n\t\t\t\tvoid do_read_websocket();\n\t\t\t\tvoid on_read_websocket(boost::beast::error_code ec, std::size_t);\n\t\t\t\tvoid do_write();\n\t\t\t\tvoid on_write(boost::beast::error_code ec, std::size_t);\n\t\t\t\tvoid on_close(boost::beast::error_code ec);\n\t\t\t\tvoid handle_http_request();\n\n\t\t\t\tboost::asio::ip::tcp::socket   socket_;\n\t\t\t\tstd::optional<boost::beast::websocket::stream<boost::asio::ip::tcp::socket&>> ws_stream_;\n\t\t\t\tboost::beast::flat_buffer      buffer_;\n\t\t\t\twebsocket_server::request_type http_request_;\n\t\t\t\twebsocket_server&              server_;\n\n\t\t\t\tid_type id_;\n\t\t\t\tclass queued_message {\n\t\t\t\t\tpublic:\n\t\t\t\t\t\tqueued_message() {\n\t\t\t\t\t\t// std::cerr << \"Thread \" << pthread_self() << \" queued_message constructor \" << (void*)this << std::endl;\n\t\t\t\t\t\t}\n\t\t\t\t\t\t~queued_message() {\n\t\t\t\t\t\t// std::cerr << \"Thread \" << pthread_self() << \" queued_message destructor \" << (void*)this << std::endl;\n\t\t\t\t\t\t}\n\t\t\t\t\t\t\n\t\t\t\t\t\tstd::string data;\n\t\t\t\t\t\tstd::shared_ptr<boost::beast::flat_buffer> buffer;\n\t\t\t\t\t\tint seq;\n\t\t\t\t};\n\t\t\t\tbool is_websocket_{false};\n\n\t\t\t\tstd::mutex queue_mutex_; // lock this for access to the variables below\n\t\t\t\tstd::queue<queued_message> message_queue_;\n\t\t\t\tbool writing_{false};\n\t\t};\n\n\t\tvoid do_accept();\n\t\tvoid remove_connection(id_type id);\n\n\t\tboost::asio::io_context                                  ioc_;\n\t\tstd::optional<boost::asio::ip::tcp::acceptor>            acceptor_;\n\t\tstd::unordered_map<id_type, std::shared_ptr<connection>> connections_;\n\t\tid_type                                                  next_connection_id_{0};\n\n\t\tmessage_handler    message_handler_;\n\t\tconnect_handler    connect_handler_;\n\t\tdisconnect_handler disconnect_handler_;\n\t\thttp_handler       http_handler_;\n};\n\n"
  },
  {
    "path": "cmake/cmake_uninstall.cmake.in",
    "content": "if(NOT EXISTS \"@CMAKE_CURRENT_BINARY_DIR@/install_manifest.txt\")\n  message(FATAL_ERROR \"Cannot find install manifest: @CMAKE_CURRENT_BINARY_DIR@/install_manifest.txt\")\nendif()\n\nfile(READ \"@CMAKE_CURRENT_BINARY_DIR@/install_manifest.txt\" files)\nstring(REGEX REPLACE \"\\n\" \";\" files \"${files}\")\nforeach(file ${files})\n  message(STATUS \"Uninstalling $ENV{DESTDIR}${file}\")\n  if(IS_SYMLINK \"$ENV{DESTDIR}${file}\" OR EXISTS \"$ENV{DESTDIR}${file}\")\n    execute_process(\n      COMMAND         \"@CMAKE_COMMAND@\" \"-E\" \"remove\" \"$ENV{DESTDIR}${file}\"\n      OUTPUT_VARIABLE rm_out\n      RESULT_VARIABLE rm_retval\n      )\n    if(NOT \"${rm_retval}\" EQUAL 0)\n      message(FATAL_ERROR \"Problem when removing $ENV{DESTDIR}${file}\")\n    endif()\n  else()\n    message(STATUS \"File $ENV{DESTDIR}${file} does not exist.\")\n  endif()\nendforeach(file)\n"
  },
  {
    "path": "cmake/functions.cmake",
    "content": "# Prints section headers\nmacro(print_header TEXT)\n  message(\"\")\n  message(\"-------------------------------------------\")\n  message(\"  ${TEXT}\")\n  message(\"-------------------------------------------\")\nendmacro()\n\n# Install directory permissions\nmacro(install_directory_permissions DIR)\n  install(\n    DIRECTORY DESTINATION ${DIR}\n    DIRECTORY_PERMISSIONS \n    OWNER_READ \n    OWNER_WRITE \n    OWNER_EXECUTE \n    GROUP_READ \n    GROUP_EXECUTE \n    WORLD_READ \n    WORLD_EXECUTE\n  )\nendmacro()\n\n# Macro just like `install`, but converting the path from a unix\n# path to a windows path using `cygpath`.\nmacro(winstall TYPE FILE TMP2 DEST)\n  execute_process(COMMAND cygpath -m ${FILE} OUTPUT_VARIABLE WFILE OUTPUT_STRIP_TRAILING_WHITESPACE)\n  if(EXISTS ${WFILE})\n    install(${TYPE} ${WFILE} DESTINATION ${DEST})\n  else()\n    message(STATUS \"WARNING: file/dir ${WFILE} not present, skipping installation\")\n  endif()\nendmacro()\n"
  },
  {
    "path": "cmake/modules/FindGLIBMM3.cmake",
    "content": "if(WIN33)\n  windows_find_library(GLIBMM3_LIBRARIES REQUIRED glibmm sigc glib gobject)\n  if (GLIBMM3_LIBRARIES)\n    set(GLIBMM3_FOUND TRUE)\n  endif()\nelse()\n  find_package(PkgConfig REQUIRED)\n  if(MACOS)\n    execute_process(COMMAND brew --prefix glibmm@2.64  OUTPUT_STRIP_TRAILING_WHITESPACE OUTPUT_VARIABLE GLIBMM_PREFIX)\n    execute_process(COMMAND brew --prefix cairomm@1.14 OUTPUT_STRIP_TRAILING_WHITESPACE OUTPUT_VARIABLE CAIROMM_PREFIX)\n    execute_process(COMMAND brew --prefix pangomm@2.42 OUTPUT_STRIP_TRAILING_WHITESPACE OUTPUT_VARIABLE PANGOMM_PREFIX)\n    execute_process(COMMAND brew --prefix atkmm@2.28   OUTPUT_STRIP_TRAILING_WHITESPACE OUTPUT_VARIABLE ATKMM_PREFIX)\n    set( ENV{PKG_CONFIG_PATH} \"${GLIBMM_PREFIX}/lib/pkgconfig:${CAIROMM_PREFIX}/lib/pkgconfig:${PANGOMM_PREFIX}/lib/pkgconfig:${ATKMM_PREFIX}/lib/pkgconfig:$ENV{PKG_CONFIG_PATH}\" )\n    message(STATUS \"Using PKG_CONFIG_PATH = $ENV{PKG_CONFIG_PATH}\")\n  endif()\n  pkg_check_modules(GLIBMM REQUIRED glibmm-2.4)\n  include_directories(${GLIBMM_INCLUDE_DIRS})\n  link_directories(${GLIBMM_LIBRARY_DIRS})\n  add_definitions(${GLIBMM_CFLAGS_OTHER})\nendif()\n\nif (GLIBMM_FOUND)\n  message(STATUS \"Found glibmm; include path ${GLIBMM_INCLUDE_DIRS}\")\n  message(STATUS \"Found glibmm; lib ${GLIBMM_LIBRARIES}\")\nendif()\n"
  },
  {
    "path": "cmake/modules/FindGLIBMM4.cmake",
    "content": "if(WIN33)\n  windows_find_library(GLIBMM4_LIBRARIES REQUIRED glibmm sigc glib gobject)\n  if (GLIBMM4_LIBRARIES)\n    set(GLIBMM4_FOUND TRUE)\n  endif()\nelse()\n  find_package(PkgConfig REQUIRED)\n  if(MACOS)\n    execute_process(COMMAND brew --prefix glibmm@2.68  OUTPUT_STRIP_TRAILING_WHITESPACE OUTPUT_VARIABLE GLIBMM_PREFIX)\n    execute_process(COMMAND brew --prefix cairomm@1.16 OUTPUT_STRIP_TRAILING_WHITESPACE OUTPUT_VARIABLE CAIROMM_PREFIX)\n    execute_process(COMMAND brew --prefix pangomm@2.48 OUTPUT_STRIP_TRAILING_WHITESPACE OUTPUT_VARIABLE PANGOMM_PREFIX)\n    execute_process(COMMAND brew --prefix atkmm@2.28   OUTPUT_STRIP_TRAILING_WHITESPACE OUTPUT_VARIABLE ATKMM_PREFIX)\n    set( ENV{PKG_CONFIG_PATH} \"${GLIBMM_PREFIX}/lib/pkgconfig:${CAIROMM_PREFIX}/lib/pkgconfig:${PANGOMM_PREFIX}/lib/pkgconfig:${ATKMM_PREFIX}/lib/pkgconfig:$ENV{PKG_CONFIG_PATH}\" )\n    message(STATUS \"Using PKG_CONFIG_PATH = $ENV{PKG_CONFIG_PATH}\")\n  endif()\n  pkg_check_modules(GLIBMM REQUIRED glibmm-2.68)\n  include_directories(${GLIBMM_INCLUDE_DIRS})\n  link_directories(${GLIBMM_LIBRARY_DIRS})\n  add_definitions(${GLIBMM_CFLAGS_OTHER})\nendif()\n\nif (GLIBMM_FOUND)\n  message(STATUS \"Found glibmm; include path ${GLIBMM_INCLUDE_DIRS}\")\n  message(STATUS \"Found glibmm; lib ${GLIBMM_LIBRARIES}\")\nendif()\n"
  },
  {
    "path": "cmake/modules/FindGMPXX.cmake",
    "content": "\n# Find the GMPXX library and its GMP dependency.\n# Simply looks for the shared libraries on Linux/OSX.\n# On Windows, finds MPIR using the logic in\n# ../winlibs.cmake (which works for building against\n# vcpkg).\n\nif (WIN323)\n  windows_find_library(GMP_LIBRARIES mpir)\n  if (GMP_LIBRARIES)\n    set(GMP_FOUND TRUE)\n  endif()\n  windows_find_library(GMPXX_LIBRARIES mpir)\n  if (GMPXX_LIBRARIES)\n    set(GMPXX_FOUND TRUE)\n  endif()\nelse()\n  find_path(GMP_INCLUDE_DIRS NAMES gmp.h REQUIRED)\n  find_library(GMP_LIBRARIES   gmp   REQUIRED)\n  find_library(GMPXX_LIBRARIES gmpxx REQUIRED)\n  message(\"-- Found gmp header at  ${GMP_INCLUDE_DIRS}\")\n  message(\"-- Found gmp library at ${GMP_LIBRARIES}\")\n  set(GMP_FOUND 1)\n  set(GMPXX_FOUND 1)  \nendif()\n\nif (GMP_FOUND)\n  message(STATUS \"Found gmp\")\nelse()\n  message(FATAL_ERROR \"Gmp not found\")\nendif()\n\nif (GMPXX_FOUND)\n  message(STATUS \"Found gmpxx\")\nelse()\n  message(FATAL_ERROR \"Gmpxx not found\")\nendif()\n"
  },
  {
    "path": "cmake/modules/FindGTKMM3.cmake",
    "content": "if(MSVC)\n  windows_find_library(GTKMM_LIBRARIES\n\tgtk gdk gdk_pixbuf pangocairo pango atk gio gobject\n\tgmodule glib cairo-gobject cairo intl atkmm cairomm\n\tgdkmm giomm glibmm gtkmm pangomm\n  )\n  if (GTKMM_LIBRARIES)\n    set(GTKMM3_FOUND TRUE)\n  endif()\nelse()\n  find_package(PkgConfig REQUIRED)\n  pkg_check_modules(GTKMM   REQUIRED IMPORTED_TARGET gtkmm-3.0)\n  pkg_check_modules(GLIBMM  REQUIRED IMPORTED_TARGET glibmm-2.4)\n  pkg_check_modules(GLIB    REQUIRED IMPORTED_TARGET glib-2.0)  \n  pkg_check_modules(PangoMM REQUIRED IMPORTED_TARGET pangomm-1.4)  \n  pkg_check_modules(CairoMM REQUIRED IMPORTED_TARGET cairomm-1.0)\n  include_directories(${GTKMM_INCLUDE_DIRS} ${CairoMM_INCLUDE_DIRS} ${PangoMM_INCLUDE_DIRS})\n  link_directories(${GTKMM_LIBRARY_DIRS})\n  add_definitions(${GTKMM_CFLAGS_OTHER})\n  if(GTKMM_FOUND)\n    set(GTKMM3_FOUND TRUE)\n  endif()\nendif()\n\nif(GTKMM3_FOUND)\n  message(STATUS \"Found gtkmm3\")\nendif()\n"
  },
  {
    "path": "cmake/modules/FindGTKMM4.cmake",
    "content": "if(MSVC)\n  windows_find_library(GTKMM_LIBRARIES\n\tgtk gdk gdk_pixbuf pangocairo pango atk gio gobject\n\tgmodule glib cairo-gobject cairo intl atkmm cairomm\n\tgdkmm giomm glibmm gtkmm pangomm\n  )\n  if (GTKMM_LIBRARIES)\n    set(GTKMM4_FOUND TRUE)\n  endif()\nelse()\n  find_package(PkgConfig REQUIRED)\n  pkg_check_modules(GTKMM   REQUIRED IMPORTED_TARGET gtkmm-4.0)\n  pkg_check_modules(GLIBMM  REQUIRED IMPORTED_TARGET glibmm-2.68)\n  pkg_check_modules(PangoMM REQUIRED IMPORTED_TARGET pangomm-2.48)  \n  pkg_check_modules(CairoMM REQUIRED IMPORTED_TARGET cairomm-1.16)\n  include_directories(${GTKMM_INCLUDE_DIRS})\n  link_directories(${GTKMM_LIBRARY_DIRS})\n  add_definitions(${GTKMM_CFLAGS_OTHER})\n  if(GTKMM_FOUND)\n    set(GTKMM4_FOUND TRUE)\n  endif()\nendif()\n\nif(GTKMM4_FOUND)\n  message(STATUS \"Found gtkmm4\")\nendif()\n"
  },
  {
    "path": "cmake/modules/FindJSONCPP.cmake",
    "content": "find_package(PkgConfig REQUIRED)\npkg_check_modules(JSONCPP jsoncpp)\n#message(\"**** ${JSONCPP_INCLUDE_DIRS}\")\n#message(\"**** ${JSONCPP_LIBRARIES}\")\n"
  },
  {
    "path": "cmake/modules/FindLibPythonOSX.py",
    "content": "# Note by Nikolaus Demmel 28.03.2014: My contributions are licensend under the\n# same as CMake (BSD). My adaptations are in part based\n# https://github.com/qgis/QGIS/tree/master/cmake which has the following\n# copyright note:\n\n# FindLibPython.py\n# Copyright (c) 2007, Simon Edwards <simon@simonzone.com>\n# Redistribution and use is allowed according to the terms of the BSD license.\n# For details see the accompanying COPYING-CMAKE-SCRIPTS file.\n\nimport sys\nimport distutils.sysconfig\n\nprint(\"exec_prefix:%s\" % sys.exec_prefix)\nprint(\"major_version:%s\" % str(sys.version_info[0]))\nprint(\"minor_version:%s\" % str(sys.version_info[1]))\nprint(\"patch_version:%s\" % str(sys.version_info[2]))\nprint(\"short_version:%s\" % '.'.join(map(lambda x:str(x), sys.version_info[0:2])))\nprint(\"long_version:%s\" % '.'.join(map(lambda x:str(x), sys.version_info[0:3])))\nprint(\"py_inc_dir:%s\" % distutils.sysconfig.get_python_inc())\nprint(\"site_packages_dir:%s\" % distutils.sysconfig.get_python_lib(plat_specific=1))\nfor e in distutils.sysconfig.get_config_vars ('LIBDIR'):\n    if e != None:\n        print(\"py_lib_dir:%s\" % e)\n        break\n"
  },
  {
    "path": "cmake/modules/FindMathematica.cmake",
    "content": "# - Try to find Mathematica installation and provide CMake functions for its C/C++ interface\n#\n# See the FindMathematica manual for usage hints.\n#\n#=============================================================================\n# Copyright 2010-2021 Sascha Kratky\n#\n# Permission is hereby granted, free of charge, to any person)\n# obtaining a copy of this software and associated documentation)\n# files (the \"Software\"), to deal in the Software without)\n# restriction, including without limitation the rights to use,)\n# copy, modify, merge, publish, distribute, sublicense, and/or sell)\n# copies of the Software, and to permit persons to whom the)\n# Software is furnished to do so, subject to the following)\n# conditions:)\n#\n# The above copyright notice and this permission notice shall be)\n# included in all copies or substantial portions of the Software.)\n#\n# THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND,)\n# EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES)\n# OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND)\n# NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT)\n# HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,)\n# WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING)\n# FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR)\n# OTHER DEALINGS IN THE SOFTWARE.)\n#=============================================================================\n\n# we need the CMakeParseArguments module\n# call cmake_minimum_required, but prevent modification of the CMake policy stack\ncmake_policy(PUSH)\ncmake_minimum_required(VERSION 2.8.12)\ncmake_policy(POP)\n\nset (Mathematica_CMAKE_MODULE_DIR \"${CMAKE_CURRENT_LIST_DIR}\")\nset (Mathematica_CMAKE_MODULE_VERSION \"3.8.0\")\n\n# activate select policies\nif (POLICY CMP0025)\n\t# Compiler id for Apple Clang is now AppleClang\n\tcmake_policy(SET CMP0025 NEW)\nendif()\n\nif (POLICY CMP0026)\n\t# disallow use of the LOCATION target property\n\tif (CYGWIN OR MSYS)\n\t\t# Cygwin and MSYS do not produce workable Mathematica paths using\n\t\t# the $<TARGET_FILE:...> notation\n\t\tcmake_policy(SET CMP0026 OLD)\n\telse()\n\t\tcmake_policy(SET CMP0026 NEW)\n\tendif()\nendif()\n\nif (POLICY CMP0038)\n\t# targets may not link directly to themselves\n\tcmake_policy(SET CMP0038 NEW)\nendif()\n\nif (POLICY CMP0039)\n\t# utility targets may not have link dependencies\n\tcmake_policy(SET CMP0039 NEW)\nendif()\n\nif (POLICY CMP0040)\n\t# target in the TARGET signature of add_custom_command() must exist\n\tcmake_policy(SET CMP0040 NEW)\nendif()\n\nif (POLICY CMP0045)\n\t# error on non-existent target in get_target_property\n\tcmake_policy(SET CMP0045 NEW)\nendif()\n\nif (POLICY CMP0046)\n\t# error on non-existent dependency in add_dependencies\n\tcmake_policy(SET CMP0046 NEW)\nendif()\n\nif (POLICY CMP0049)\n\t# do not expand variables in target source entries\n\tcmake_policy(SET CMP0049 NEW)\nendif()\n\nif (POLICY CMP0050)\n\t# disallow add_custom_command SOURCE signatures\n\tcmake_policy(SET CMP0050 NEW)\nendif()\n\nif (POLICY CMP0051)\n\t# include TARGET_OBJECTS expressions in a target's SOURCES property\n\tcmake_policy(SET CMP0051 NEW)\nendif()\n\nif (POLICY CMP0053)\n\t# simplify variable reference and escape sequence evaluation\n\tcmake_policy(SET CMP0053 NEW)\nendif()\n\nif (POLICY CMP0054)\n\t# only interpret if() arguments as variables or keywords when unquoted\n\tcmake_policy(SET CMP0054 NEW)\nendif()\n\ninclude(TestBigEndian)\ninclude(CMakeParseArguments)\ninclude(FindPackageHandleStandardArgs)\ninclude(CMakeFindFrameworks)\n\n# internal function to convert Windows path to Cygwin workable CMake path\n# E.g., \"C:\\Program Files\" is converted to \"/cygdrive/c/Program Files\"\n# file(TO_CMAKE_PATH \"C:\\Program Files\" ...) would result in unworkable \"C;/Program Files\"\nfunction (_to_cmake_path _inPath _outPathVariable)\n\tif (CYGWIN)\n\t\tfind_program(Mathematica_CYGPATH_EXECUTABLE \"cygpath\")\n\t\tmark_as_advanced(Mathematica_CYGPATH_EXECUTABLE)\n\t\texecute_process(\n\t\t\tCOMMAND \"${Mathematica_CYGPATH_EXECUTABLE}\" \"--unix\" \"${_inPath}\" TIMEOUT 5\n\t\t\tOUTPUT_VARIABLE ${_outPathVariable} OUTPUT_STRIP_TRAILING_WHITESPACE)\n\telse()\n\t\tfile(TO_CMAKE_PATH \"${_inPath}\" ${_outPathVariable})\n\tendif()\n\tset (${_outPathVariable} \"${${_outPathVariable}}\" PARENT_SCOPE)\nendfunction()\n\n# internal function to convert CMake path to \"pure\" native path without escapes\nfunction (_to_native_path _inPath _outPathVariable)\n\t# do not use the built-in function file (TO_NATIVE_PATH ...),\n\t# which does too much or the wrong thing:\n\t# it converts a CMake path to a native path but then also escapes all blanks\n\t# and special characters\n\t# under MinGW it produces unworkable paths with forward slashes\n\tif (CYGWIN)\n\t\tfind_program(Mathematica_CYGPATH_EXECUTABLE \"cygpath\")\n\t\tmark_as_advanced(Mathematica_CYGPATH_EXECUTABLE)\n\t\texecute_process(\n\t\t\tCOMMAND \"${Mathematica_CYGPATH_EXECUTABLE}\" \"--mixed\" \"${_inPath}\" TIMEOUT 5\n\t\t\tOUTPUT_VARIABLE ${_outPathVariable} OUTPUT_STRIP_TRAILING_WHITESPACE)\n\telseif (CMAKE_HOST_UNIX)\n\t\t# use CMake path literally under UNIX\n\t\tset (${_outPathVariable} \"${_inPath}\")\n\telseif (CMAKE_HOST_WIN32)\n\t\tstring (REPLACE \"/\" \"\\\\\" ${_outPathVariable} \"${_inPath}\")\n\telse()\n\t\tmessage (FATAL_ERROR \"Unsupported host platform ${CMAKE_HOST_SYSTEM_NAME}\")\n\tendif()\n\tset (${_outPathVariable} \"${${_outPathVariable}}\" PARENT_SCOPE)\nendfunction()\n\n# internal macro to set a file's executable bit under UNIX\nmacro (_make_file_executable _inPath)\n\tif (CMAKE_HOST_UNIX)\n\t\t_to_native_path (\"${_inPath}\" _nativePath)\n\t\texecute_process(\n\t\t\tCOMMAND chmod \"-f\" \"+x\" \"${_nativePath}\" TIMEOUT 5)\n\tendif()\nendmacro()\n\n# internal macro to convert list to command string with quoting\nmacro (_list_to_cmd_str _outCmd)\n\tset (_str \"\")\n\tforeach (_arg ${ARGN})\n\t\tif (\"${_arg}\" MATCHES \" \")\n\t\t\tset (_arg \"\\\"${_arg}\\\"\")\n\t\tendif()\n\t\tif (_str)\n\t\t\tset (_str \"${_str} ${_arg}\")\n\t\telse()\n\t\t\tset (_str \"${_arg}\")\n\t\tendif()\n\tendforeach()\n\tset (${_outCmd} \"${_str}\")\nendmacro()\n\n# internal macro to compute kernel paths (relative to installation directory)\nmacro (_get_host_kernel_names _outKernelNames)\n\tif (Mathematica_FIND_VERSION AND Mathematica_FIND_VERSION_EXACT)\n\t\tif (Mathematica_FIND_VERSION VERSION_LESS \"10.0.0\")\n\t\t\tif (CMAKE_HOST_WIN32 OR CYGWIN)\n\t\t\t\tset (${_outKernelNames} \"math.exe\")\n\t\t\telseif (CMAKE_HOST_APPLE)\n\t\t\t\tset (${_outKernelNames} \"Contents/MacOS/MathKernel\")\n\t\t\telseif (CMAKE_HOST_UNIX)\n\t\t\t\tset (${_outKernelNames} \"Executables/MathKernel\" \"Executables/math\")\n\t\t\tendif()\n\t\telse()\n\t\t\tif (CMAKE_HOST_WIN32 OR CYGWIN)\n\t\t\t\tset (${_outKernelNames} \"wolfram.exe\")\n\t\t\telseif (CMAKE_HOST_APPLE)\n\t\t\t\tset (${_outKernelNames} \"Contents/MacOS/WolframKernel\")\n\t\t\telseif (CMAKE_HOST_UNIX)\n\t\t\t\tset (${_outKernelNames} \"Executables/WolframKernel\")\n\t\t\tendif()\n\t\tendif()\n\telse()\n\t\tif (CMAKE_HOST_WIN32 OR CYGWIN)\n\t\t\tset (${_outKernelNames} \"wolfram.exe\" \"math.exe\")\n\t\telseif (CMAKE_HOST_APPLE)\n\t\t\tset (${_outKernelNames} \"Contents/MacOS/WolframKernel\" \"Contents/MacOS/MathKernel\")\n\t\telseif (CMAKE_HOST_UNIX)\n\t\t\tset (${_outKernelNames} \"Executables/WolframKernel\" \"Executables/MathKernel\" \"Executables/math\")\n\t\tendif()\n\tendif()\nendmacro()\n\n# internal macro to to compute front end paths (relative to installation directory)\nmacro (_get_host_frontend_names _outFrontEndNames)\n\tif (CMAKE_HOST_WIN32 OR CYGWIN)\n\t\tset (${_outFrontEndNames} \"Mathematica.exe\")\n\telseif (CMAKE_HOST_APPLE)\n\t\tset (${_outFrontEndNames} \"Contents/MacOS/Mathematica\")\n\telseif (CMAKE_HOST_UNIX)\n\t\tset (${_outFrontEndNames}\n\t\t\t\"Executables/mathematica\" \"Executables/Mathematica\")\n\tendif()\nendmacro()\n\n# internal macro to compute program name from product name and version\n# E.g., \"Mathematica\" and \"7.0\" gives \"Mathematica 7.0.app\" for Mac OS X\nmacro (_append_program_names _product _version _outProgramNames)\n\tstring (REPLACE \" \" \"\" _productWithoutBlanks \"${_product}\")\n\tif (CMAKE_HOST_APPLE)\n\t\tif (${_version})\n\t\t\t# under Mac OS X the application name may contain the version number as a suffix\n\t\t\tlist (APPEND ${_outProgramNames} \"${_product} ${_version}.app\")\n\t\t\tlist (APPEND ${_outProgramNames} \"${_productWithoutBlanks} ${_version}.app\")\n\t\telse()\n\t\t\tlist (APPEND ${_outProgramNames} \"${_product}.app\")\n\t\t\tlist (APPEND ${_outProgramNames} \"${_productWithoutBlanks}.app\")\n\t\tendif()\n\telse()\n\t\tif (${_version})\n\t\t\t# other platforms have a sub-directory named after the version number\n\t\t\tlist (APPEND ${_outProgramNames} \"${_product}/${_version}\")\n\t\t\tlist (APPEND ${_outProgramNames} \"${_productWithoutBlanks}/${_version}\")\n\t\tendif()\n\tendif()\nendmacro()\n\n# internal macro to determine search order for different versions of Mathematica\nmacro (_get_program_names _outProgramNames)\n\tset (${_outProgramNames} \"\")\n\t# Mathematica products in order of preference\n\tset (_MathematicaApps\n\t\t\"Mathematica\" \"mathematica\"\n\t\t\"Wolfram Desktop\" \"Wolfram Engine\"\n\t\t\"gridMathematica Server\")\n\t# Mathematica product versions in order of preference\n\tset (_MathematicaVersions\n\t\t\"13.2\" \"13.1\" \"13.0\"\n\t\t\"12.3\" \"12.2\" \"12.1\" \"12.0\"\n\t\t\"11.3\" \"11.2\" \"11.1\" \"11.0\"\n\t\t\"10.4\" \"10.3\" \"10.2\" \"10.1\" \"10.0\"\n\t\t\"9.0\" \"8.0\" \"7.0\" \"6.0\" \"5.2\")\n\t# search for explicitly requested application version first\n\tif (Mathematica_FIND_VERSION AND Mathematica_FIND_VERSION_EXACT)\n\t\tforeach (_product IN LISTS _MathematicaApps)\n\t\t\t_append_program_names(\"${_product}\"\n\t\t\t\t\"${Mathematica_FIND_VERSION_MAJOR}.${Mathematica_FIND_VERSION_MINOR}\"\n\t\t\t\t${_outProgramNames})\n\t\tendforeach()\n\tendif()\n\t# then try all qualified application names\n\tforeach (_product IN LISTS _MathematicaApps)\n\t\tforeach (_version IN LISTS _MathematicaVersions)\n\t\t\t_append_program_names(\"${_product}\" \"${_version}\" ${_outProgramNames})\n\t\tendforeach()\n\tendforeach()\n\t# then try unqualified application names\n\tforeach (_product IN LISTS _MathematicaApps)\n\t\t_append_program_names(\"${_product}\" \"\" ${_outProgramNames})\n\tendforeach()\n\tlist (REMOVE_DUPLICATES ${_outProgramNames})\nendmacro()\n\n# internal function to get Mathematica Windows installation directory for a registry entry\nfunction (_add_registry_search_path _registryKey _outSearchPaths)\n\tset (_ProductNamePatterns\n\t\t\"Wolfram Mathematica [0-9.]+\" \"Wolfram Desktop [0-9.]+\"\n\t\t\"Wolfram Engine [0-9.]+\" \"Wolfram Finance Platform\")\n\tget_filename_component (\n\t\t_productName \"[${_registryKey};ProductName]\" NAME)\n\tget_filename_component (\n\t\t_productVersion \"[${_registryKey};ProductVersion]\" NAME)\n\tget_filename_component (\n\t\t_productPath \"[${_registryKey};ExecutablePath]\" PATH)\n\tif (Mathematica_DEBUG)\n\t\tmessage (STATUS \"[${_registryKey};ProductName]=${_productName}\")\n\t\tmessage (STATUS \"[${_registryKey};ProductVersion]=${_productVersion}\")\n\t\tmessage (STATUS \"[${_registryKey};ExecutablePath]=${_productPath}\")\n\tendif()\n\tset (_qualified False)\n\tforeach (_Pattern IN LISTS _ProductNamePatterns)\n\t\tif (\"${_productName}\" MATCHES \"${_Pattern}\")\n\t\t\tset (_qualified True)\n\t\t\tbreak()\n\t\tendif()\n\tendforeach()\n\tif (_qualified)\n\t\tif (EXISTS \"${_productPath}\")\n\t\t\t_to_cmake_path(\"${_productPath}\" _path)\n\t\t\tif (Mathematica_FIND_VERSION AND Mathematica_FIND_VERSION_EXACT)\n\t\t\t\tif (\"${_productVersion}\" MATCHES \"${Mathematica_FIND_VERSION}\")\n\t\t\t\t\t# prepend if version matches requested one\n\t\t\t\t\tlist (INSERT ${_outSearchPaths} 0 \"${_path}\")\n\t\t\t\telse()\n\t\t\t\t\tlist (APPEND ${_outSearchPaths} \"${_path}\")\n\t\t\t\tendif()\n\t\t\telse()\n\t\t\t\tlist (APPEND ${_outSearchPaths} \"${_path}\")\n\t\t\tendif()\n\t\tendif()\n\tendif()\n\tset (${_outSearchPaths} ${${_outSearchPaths}} PARENT_SCOPE)\nendfunction()\n\n# internal function to determine Mathematica installation paths from Windows registry\nfunction (_add_registry_search_paths _outSearchPaths)\n\tif (CMAKE_HOST_WIN32)\n\t\tforeach (_registryKey IN ITEMS ${ARGN})\n\t\t\tset (_regExe \"reg.exe\")\n\t\t\tif (DEFINED ENV{windir})\n\t\t\t\t# use 64-bit reg.exe under WoW64 to make sure we search all keys\n\t\t\t\tif (EXISTS \"$ENV{windir}/sysnative/reg.exe\")\n\t\t\t\t\tset (_regExe \"$ENV{windir}/sysnative/reg.exe\")\n\t\t\t\tendif()\n\t\t\tendif()\n\t\t\texecute_process(\n\t\t\t\tCOMMAND \"${_regExe}\" query \"${_registryKey}\" \"/s\"\n\t\t\t\tCOMMAND findstr \"${_registryKey}\"\n\t\t\t\tTIMEOUT 5 OUTPUT_VARIABLE _queryResult ERROR_QUIET)\n\t\t\tstring (REGEX MATCHALL \"[0-9]+\" _installIDs \"${_queryResult}\")\n\t\t\tif (_installIDs)\n\t\t\t\t# _installIDs sorted from oldest to newest version\n\t\t\t\tlist (REVERSE _installIDs)\n\t\t\t\tset (_paths \"\")\n\t\t\t\tforeach (_installID IN LISTS _installIDs)\n\t\t\t\t\t_add_registry_search_path(\"${_registryKey}\\\\${_installID}\" _paths)\n\t\t\t\tendforeach()\n\t\t\t\tlist (APPEND ${_outSearchPaths} ${_paths})\n\t\t\tendif()\n\t\tendforeach()\n\t\tset (${_outSearchPaths} ${${_outSearchPaths}} PARENT_SCOPE)\n\tendif()\nendfunction()\n\n# internal function to determine Mathematica installation paths from Mac OS X LaunchServices database\nfunction (_add_launch_services_search_paths _outSearchPaths)\n\tif (CMAKE_HOST_APPLE)\n\t\t# the lsregister executable is needed to search the LaunchServices database\n\t\t# the executable usually resides in the LaunchServices framework Support directory\n\t\t# The LaunchServices framework is a sub-framework of the CoreServices umbrella framework\n\t\tcmake_find_frameworks(CoreServices)\n\t\tfind_program (Mathematica_LSRegister_EXECUTABLE\n\t\t\tNAMES \"lsregister\"\n\t\t\tPATH_SUFFIXES \"/Frameworks/LaunchServices.framework/Support\"\n\t\t\tHINTS ${CoreServices_FRAMEWORKS})\n\t\tmark_as_advanced(\n\t\t\tMathematica_CoreServices_DIR\n\t\t\tMathematica_LaunchServices_DIR\n\t\t\tMathematica_LSRegister_EXECUTABLE)\n\t\tif (NOT Mathematica_LSRegister_EXECUTABLE)\n\t\t\tmessage (STATUS \"Skipping search of the LaunchServices database, because the lsregister executable could not be found.\")\n\t\t\treturn()\n\t\tendif()\n\t\tforeach (_bundleID IN ITEMS ${ARGN})\n\t\t\texecute_process(\n\t\t\t\tCOMMAND \"${Mathematica_LSRegister_EXECUTABLE}\" \"-dump\"\n\t\t\t\tCOMMAND \"grep\" \"--before-context=20\" \"--after-context=20\" \"${_bundleID}\"\n\t\t\t\tCOMMAND \"grep\" \"--only-matching\" \"/.*\\\\.app\"\n\t\t\t\tTIMEOUT 10 OUTPUT_VARIABLE _queryResult ERROR_QUIET)\n\t\t\tstring (REPLACE \";\" \"\\\\;\" _queryResult \"${_queryResult}\")\n\t\t\tstring (REPLACE \"\\n\" \";\" _appPaths \"${_queryResult}\")\n\t\t\tif (_appPaths)\n\t\t\t\t# put paths into canonical order\n\t\t\t\tlist (SORT _appPaths)\n\t\t\t\tlist (REVERSE _appPaths)\n\t\t\telse()\n\t\t\t\tmessage (STATUS \"No Mathematica apps registered in Mac OS X LaunchServices database.\")\n\t\t\tendif()\n\t\t\tif (Mathematica_DEBUG)\n\t\t\t\tmessage (STATUS \"Mac OS X LaunchServices database registered apps=${_appPaths}\")\n\t\t\tendif()\n\t\t\tif (_appPaths)\n\t\t\t\tset (_paths \"\")\n\t\t\t\tset (_insertIndex 0)\n\t\t\t\tforeach (_appPath IN LISTS _appPaths)\n\t\t\t\t\t# ignore paths that no longer exist\n\t\t\t\t\tif (EXISTS \"${_appPath}\")\n\t\t\t\t\t\t_to_cmake_path(\"${_appPath}\" _appPath)\n\t\t\t\t\t\tif (Mathematica_FIND_VERSION AND Mathematica_FIND_VERSION_EXACT)\n\t\t\t\t\t\t\tif (\"${_appPath}\" MATCHES \"${Mathematica_FIND_VERSION_MAJOR}.${Mathematica_FIND_VERSION_MINOR}\")\n\t\t\t\t\t\t\t\t# insert in front of other versions if version matches requested one\n\t\t\t\t\t\t\t\tlist (LENGTH _paths _len)\n\t\t\t\t\t\t\t\tif (_len EQUAL _insertIndex)\n\t\t\t\t\t\t\t\t\tlist (APPEND _paths \"${_appPath}\")\n\t\t\t\t\t\t\t\telse()\n\t\t\t\t\t\t\t\t\tlist (INSERT _paths ${_insertIndex} \"${_appPath}\")\n\t\t\t\t\t\t\t\tendif()\n\t\t\t\t\t\t\t\tmath(EXPR _insertIndex \"${_insertIndex} + 1\")\n\t\t\t\t\t\t\telse()\n\t\t\t\t\t\t\t\tlist (APPEND _paths \"${_appPath}\")\n\t\t\t\t\t\t\tendif()\n\t\t\t\t\t\telse()\n\t\t\t\t\t\t\tlist (APPEND _paths \"${_appPath}\")\n\t\t\t\t\t\tendif()\n\t\t\t\t\tendif()\n\t\t\t\tendforeach()\n\t\t\t\tlist (APPEND ${_outSearchPaths} ${_paths})\n\t\t\tendif()\n\t\tendforeach()\n\t\tset (${_outSearchPaths} ${${_outSearchPaths}} PARENT_SCOPE)\n\tendif()\nendfunction()\n\n# internal macro to determine default Mathematica installation (the one which is on the system search path)\nmacro (_add_default_search_path _outSearchPaths)\n\tset (_searchPaths \"\")\n\tif (DEFINED ENV{PATH})\n\t\tfile (TO_CMAKE_PATH \"$ENV{PATH}\" _searchPaths)\n\tendif()\n\t_get_host_kernel_names(_kernelNames)\n\tforeach (_searchPath IN LISTS _searchPaths)\n\t\tif (CMAKE_HOST_WIN32 OR CYGWIN)\n\t\t\tset (_executable \"${_searchPath}/math.exe\")\n\t\telse()\n\t\t\tset (_executable \"${_searchPath}/math\")\n\t\tendif()\n\t\tif (EXISTS \"${_executable}\")\n\t\t\t# resolve symlinks\n\t\t\tget_filename_component (_executable \"${_executable}\" REALPATH)\n\t\t\tforeach (_kernelName IN LISTS _kernelNames)\n\t\t\t\tstring (REPLACE \"${_kernelName}\" \"\" _executableDir \"${_executable}\")\n\t\t\t\tif (NOT \"${_executable}\" STREQUAL \"${_executableDir}\" AND\n\t\t\t\t\tIS_DIRECTORY ${_executableDir})\n\t\t\t\t\tif (Mathematica_FIND_VERSION)\n\t\t\t\t\t\tlist (APPEND ${_outSearchPaths} \"${_executableDir}\")\n\t\t\t\t\telse()\n\t\t\t\t\t\t# prefer default installation if not searching for version explicitly\n\t\t\t\t\t\tlist (INSERT ${_outSearchPaths} 0 \"${_executableDir}\")\n\t\t\t\t\tendif()\n\t\t\t\tendif()\n\t\t\tendforeach()\n\t\tendif()\n\tendforeach()\nendmacro()\n\n# internal macro to determine platform specific Mathematica installation search paths\nmacro (_get_search_paths _outSearchPaths)\n\tset (${_outSearchPaths} \"\")\n\tif (CMAKE_HOST_WIN32 OR CYGWIN)\n\t\t# add non-standard installation paths from Windows registry\n\t\t_add_registry_search_paths(${_outSearchPaths}\n\t\t\t\"HKEY_LOCAL_MACHINE\\\\SOFTWARE\\\\Wolfram Research\\\\Installations\"\n\t\t\t\"HKEY_LOCAL_MACHINE\\\\SOFTWARE\\\\Wow6432Node\\\\Wolfram Research\\\\Installations\")\n\t\t# environment variable locations where Mathematica may be installed\n\t\tset (_WindowsProgramFilesEnvVars to \"ProgramW6432\" \"ProgramFiles(x86)\" \"ProgramFiles\" )\n\t\tif (CYGWIN)\n\t\t\t# Cygwin may be configured to convert all environment variables to all-uppercase\n\t\t\tlist (APPEND _WindowsProgramFilesEnvVars \"PROGRAMW6432\" \"PROGRAMFILES(X86)\" \"PROGRAMFILES\")\n\t\tendif()\n\t\t# add standard Mathematica Windows installation paths\n\t\tforeach (_envVar IN LISTS _WindowsProgramFilesEnvVars)\n\t\t\tif (DEFINED ENV{${_envVar})\n\t\t\t\t_to_cmake_path(\"$ENV{${_envVar}}\" _unixPath)\n\t\t\t\tlist (APPEND ${_outSearchPaths} \"${_unixPath}/Wolfram Research\" )\n\t\t\tendif()\n\t\tendforeach()\n\t\t# add default installation path\n\t\tif (IS_DIRECTORY \"C:/Program Files/Wolfram Research\")\n\t\t\tlist (APPEND ${_outSearchPaths} \"C:/Program Files/Wolfram Research\" )\n\t\tendif()\n\t\t# Windows container paths may be lowercase\n\t\tif (IS_DIRECTORY \"C:/Program Files/wolfram research\")\n\t\t\tlist (APPEND ${_outSearchPaths} \"C:/Program Files/wolfram research\" )\n\t\tendif()\n\telseif (CMAKE_HOST_APPLE)\n\t\t# add standard Mathematica Mac OS X installation paths\n\t\tlist (APPEND ${_outSearchPaths} \"~/Applications;/Applications\")\n\t\tif (CMAKE_SYSTEM_APPBUNDLE_PATH)\n\t\t\tlist (APPEND ${_outSearchPaths} ${CMAKE_SYSTEM_APPBUNDLE_PATH})\n\t\tendif()\n\t\t# add non-standard installation paths from Mac OS X LaunchServices database\n\t\t_add_launch_services_search_paths(${_outSearchPaths} \"com.wolfram.Mathematica\")\n\telseif (CMAKE_HOST_UNIX)\n\t\t# add standard Mathematica Unix installation paths\n\t\tlist (APPEND ${_outSearchPaths} \"/usr/local/Wolfram\" \"/opt/Wolfram\")\n\tendif()\n\t_add_default_search_path(${_outSearchPaths})\n\tif (${_outSearchPaths})\n\t\tlist (REMOVE_DUPLICATES ${_outSearchPaths})\n\tendif()\nendmacro()\n\n# internal macro to compute Mathematica SystemIDs from system name\nmacro (_systemNameToSystemID _systemName _systemProcessor _outSystemIDs)\n\tif (\"${_systemName}\" STREQUAL \"Windows\")\n\t\tif (\"${_systemProcessor}\" STREQUAL \"AMD64\")\n\t\t\tset (${_outSystemIDs} \"Windows-x86-64\")\n\t\telse()\n\t\t\t# default to 32-bit Windows\n\t\t\tset (${_outSystemIDs} \"Windows\")\n\t\tendif()\n\telseif (\"${_systemName}\" STREQUAL \"CYGWIN\")\n\t\tif (\"${_systemProcessor}\" STREQUAL \"x86_64\")\n\t\t\tset (${_outSystemIDs} \"Windows-x86-64\")\n\t\telse()\n\t\t\t# default to 32-bit Windows\n\t\t\tset (${_outSystemIDs} \"Windows\")\n\t\tendif()\n\telseif (\"${_systemName}\" STREQUAL \"Darwin\")\n\t\tif (\"${_systemProcessor}\" STREQUAL \"i386\")\n\t\t\tset (${_outSystemIDs} \"MacOSX-x86\")\n\t\telseif (\"${_systemProcessor}\" STREQUAL \"x86_64\")\n\t\t\tset (${_outSystemIDs} \"MacOSX-x86-64\")\n\t\telseif (\"${_systemProcessor}\" STREQUAL \"arm64\")\n\t\t\tset (${_outSystemIDs} \"MacOSX-ARM64\")\n\t\telseif (\"${_systemProcessor}\" MATCHES \"ppc64|powerpc64\")\n\t\t\tset (${_outSystemIDs} \"Darwin-PowerPC64\")\n\t\telseif (\"${_systemProcessor}\" MATCHES \"ppc|powerpc\")\n\t\t\tif (Mathematica_VERSION)\n\t\t\t\t# Mathematica versions before 6 used \"Darwin\" as system ID for ppc32\n\t\t\t\tif (NOT \"${Mathematica_VERSION}\" VERSION_LESS \"6.0\")\n\t\t\t\t\tset (${_outSystemIDs} \"MacOSX\")\n\t\t\t\telse()\n\t\t\t\t\tset (${_outSystemIDs} \"Darwin\")\n\t\t\t\tendif()\n\t\t\telse ()\n\t\t\t\tset (${_outSystemIDs} \"MacOSX\" \"Darwin\")\n\t\t\tendif()\n\t\tendif()\n\telseif (\"${_systemName}\" STREQUAL \"Linux\")\n\t\tif (\"${_systemProcessor}\" MATCHES \"^i.86$\")\n\t\t\tset (${_outSystemIDs} \"Linux\")\n\t\telseif (\"${_systemProcessor}\" MATCHES \"x86_64|amd64\")\n\t\t\tset (${_outSystemIDs} \"Linux-x86-64\")\n\t\telseif (\"${_systemProcessor}\" STREQUAL \"ia64\")\n\t\t\tset (${_outSystemIDs} \"Linux-IA64\")\n\t\telseif (\"${_systemProcessor}\" MATCHES \"^arm\")\n\t\t\tset (${_outSystemIDs} \"Linux-ARM\")\n\t\tendif()\n\telseif (\"${_systemName}\" STREQUAL \"SunOS\")\n\t\tif (\"${_systemProcessor}\" MATCHES \"^sparc\")\n\t\t\tif (Mathematica_VERSION)\n\t\t\t\t# Mathematica versions before 6 used \"UltraSPARC\" as system ID for Solaris\n\t\t\t\tif (NOT \"${Mathematica_VERSION}\" VERSION_LESS \"6.0\")\n\t\t\t\t\tset (${_outSystemIDs} \"Solaris-SPARC\")\n\t\t\t\telse()\n\t\t\t\t\tset (${_outSystemIDs} \"UltraSPARC\")\n\t\t\t\tendif()\n\t\t\telse ()\n\t\t\t\tset (${_outSystemIDs} \"Solaris-SPARC\" \"UltraSPARC\")\n\t\t\tendif()\n\t\telseif (\"${_systemProcessor}\" STREQUAL \"x86_64\")\n\t\t\tset (${_outSystemIDs} \"Solaris-x86-64\")\n\t\tendif()\n\telseif (\"${_systemName}\" STREQUAL \"AIX\")\n\t\tset (${_outSystemIDs} \"AIX-Power64\")\n\telseif (\"${_systemName}\" STREQUAL \"HP-UX\")\n\t\tset (${_outSystemIDs} \"HPUX-PA64\")\n\telseif (\"${_systemName}\" STREQUAL \"IRIX\")\n\t\tset (${_outSystemIDs} \"IRIX-MIPS64\")\n\tendif()\nendmacro(_systemNameToSystemID)\n\n# internal macro to compute target Mathematica SystemIDs\nmacro (_get_system_IDs _outSystemIDs)\n\tif (WIN32 OR CYGWIN)\n\t\t# pointer size check is more reliable than CMAKE_SYSTEM_PROCESSOR\n\t\tif (CMAKE_SIZEOF_VOID_P EQUAL 8)\n\t\t\tset (${_outSystemIDs} \"Windows-x86-64\")\n\t\telse()\n\t\t\tset (${_outSystemIDs} \"Windows\")\n\t\tendif()\n\telseif (APPLE)\n\t\tset (${_outSystemIDs} \"\")\n\t\tif (CMAKE_OSX_ARCHITECTURES)\n\t\t\t# determine System ID from specified architectures\n\t\t\tforeach (_arch ${CMAKE_OSX_ARCHITECTURES})\n\t\t\t\tset (_systemID \"\")\n\t\t\t\t_systemNameToSystemID(\"${CMAKE_SYSTEM_NAME}\" \"${_arch}\" _systemID)\n\t\t\t\tif (_systemID)\n\t\t\t\t\tlist (APPEND ${_outSystemIDs} ${_systemID})\n\t\t\t\telse()\n\t\t\t\t\tmessage (FATAL_ERROR \"Unsupported Mac OS X architecture ${_arch}\")\n\t\t\t\tendif()\n\t\t\tendforeach()\n\t\telse()\n\t\t\t# determine System ID by checking endianness and pointer size\n\t\t\tTEST_BIG_ENDIAN(_isBigEndian)\n\t\t\tif (_isBigEndian)\n\t\t\t\tif (CMAKE_SIZEOF_VOID_P EQUAL 8)\n\t\t\t\t\tset (${_outSystemIDs} \"Darwin-PowerPC64\")\n\t\t\t\telse()\n\t\t\t\t\tif (Mathematica_VERSION)\n\t\t\t\t\t\t# Mathematica versions before 6 used \"Darwin\" as system ID for ppc32\n\t\t\t\t\t\tif (NOT \"${Mathematica_VERSION}\" VERSION_LESS \"6.0\")\n\t\t\t\t\t\t\tset (${_outSystemIDs} \"MacOSX\")\n\t\t\t\t\t\telse()\n\t\t\t\t\t\t\tset (${_outSystemIDs} \"Darwin\")\n\t\t\t\t\t\tendif()\n\t\t\t\t\telse ()\n\t\t\t\t\t\tset (${_outSystemIDs} \"MacOSX\" \"Darwin\")\n\t\t\t\t\tendif()\n\t\t\t\tendif()\n\t\t\telse()\n\t\t\t\tif (CMAKE_SIZEOF_VOID_P EQUAL 8)\n\t\t\t\t\tset (${_outSystemIDs} \"MacOSX-x86-64\")\n\t\t\t\telse()\n\t\t\t\t\tset (${_outSystemIDs} \"MacOSX-x86\")\n\t\t\t\tendif()\n\t\t\tendif()\n\t\tendif()\n\telseif (UNIX)\n\t\tif (\"${CMAKE_SYSTEM_NAME}\" STREQUAL \"Linux\")\n\t\t\t# pointer size check is more reliable than CMAKE_SYSTEM_PROCESSOR\n\t\t\tif (CMAKE_SIZEOF_VOID_P EQUAL 8)\n\t\t\t\tset (${_outSystemIDs} \"Linux-x86-64\")\n\t\t\telse()\n\t\t\t\tset (${_outSystemIDs} \"Linux\")\n\t\t\tendif()\n\t\telse()\n\t\t\t_systemNameToSystemID(\"${CMAKE_SYSTEM_NAME}\" \"${CMAKE_SYSTEM_PROCESSOR}\" ${_outSystemIDs})\n\t\tendif()\n\telse()\n\t\tset (${_outSystemIDs} \"Generic\")\n\tendif()\n\tlist (REMOVE_DUPLICATES ${_outSystemIDs})\nendmacro(_get_system_IDs)\n\n# internal macro to compute host Mathematica SystemIDs\nmacro (_get_host_system_IDs _outSystemIDs)\n\tif (CMAKE_HOST_WIN32)\n\t\tset (${_outSystemIDs} \"Windows\")\n\t\tif (DEFINED ENV{PROCESSOR_ARCHITEW6432})\n\t\t\tif (\"$ENV{PROCESSOR_ARCHITEW6432}\" STREQUAL \"AMD64\")\n\t\t\t\t# running of WoW64, host is native 64-bit Windows\n\t\t\t\tset (${_outSystemIDs} \"Windows-x86-64\")\n\t\t\tendif()\n\t\telseif (DEFINED ENV{PROCESSOR_ARCHITECTURE})\n\t\t\tif (\"$ENV{PROCESSOR_ARCHITECTURE}\" STREQUAL \"AMD64\")\n\t\t\t\t# host is native 64-bit Windows\n\t\t\t\tset (${_outSystemIDs} \"Windows-x86-64\")\n\t\t\tendif()\n\t\tendif()\n\telse()\n\t\t# always determine host system ID from\n\t\t# CMAKE_HOST_SYSTEM_NAME and CMAKE_HOST_SYSTEM_PROCESSOR\n\t\tif (_CMAKE_OSX_MACHINE)\n\t\t\t# work-around for Mac OS X, where CMAKE_HOST_SYSTEM_PROCESSOR is not always accurate\n\t\t\tset (_hostSystemProcessor \"${_CMAKE_OSX_MACHINE}\")\n\t\telse()\n\t\t\tset (_hostSystemProcessor \"${CMAKE_HOST_SYSTEM_PROCESSOR}\")\n\t\tendif()\n\t\t_systemNameToSystemID(\n\t\t\t\"${CMAKE_HOST_SYSTEM_NAME}\" \"${_hostSystemProcessor}\"\n\t\t\t_hostSystemID)\n\t\tif (NOT DEFINED _hostSystemID)\n\t\t\tmessage (FATAL_ERROR \"Unsupported host platform ${CMAKE_HOST_SYSTEM_NAME}\")\n\t\tendif()\n\t\t_get_compatible_system_IDs(${_hostSystemID} ${_outSystemIDs})\n\tendif()\nendmacro()\n\nmacro (_get_supported_systemIDs _version _outSystemIDs)\n\tif (NOT \"${_version}\" VERSION_LESS \"12.3\")\n\t\tset (${_outSystemIDs}\n\t\t\t\"Windows-x86-64\"\n\t\t\t\"Linux-x86-64\" \"Linux-ARM\"\n\t\t\t\"MacOSX-x86-64\" \"MacOSX-ARM64\")\n\telseif (NOT \"${_version}\" VERSION_LESS \"12.1\")\n\t\tset (${_outSystemIDs}\n\t\t\t\"Windows-x86-64\"\n\t\t\t\"Linux-x86-64\" \"Linux-ARM\"\n\t\t\t\"MacOSX-x86-64\")\n\telseif (NOT \"${_version}\" VERSION_LESS \"11.3\")\n\t\tset (${_outSystemIDs}\n\t\t\t\"Windows\" \"Windows-x86-64\"\n\t\t\t\"Linux-x86-64\" \"Linux-ARM\"\n\t\t\t\"MacOSX-x86-64\")\n\telseif (NOT \"${_version}\" VERSION_LESS \"10.0\")\n\t\tset (${_outSystemIDs}\n\t\t\t\"Windows\" \"Windows-x86-64\"\n\t\t\t\"Linux\" \"Linux-x86-64\" \"Linux-ARM\"\n\t\t\t\"MacOSX-x86-64\")\n\telseif (NOT \"${_version}\" VERSION_LESS \"9.0\")\n\t\tset (${_outSystemIDs}\n\t\t\t\"Windows\" \"Windows-x86-64\"\n\t\t\t\"Linux\" \"Linux-x86-64\"\n\t\t\t\"MacOSX-x86-64\")\n\telseif (NOT \"${_version}\" VERSION_LESS \"8.0\")\n\t\tset (${_outSystemIDs}\n\t\t\t\"Windows\" \"Windows-x86-64\"\n\t\t\t\"Linux\" \"Linux-x86-64\"\n\t\t\t\"MacOSX-x86\" \"MacOSX-x86-64\")\n\telseif (NOT \"${_version}\" VERSION_LESS \"7.0\")\n\t\tset (${_outSystemIDs}\n\t\t\t\"Windows\" \"Windows-x86-64\"\n\t\t\t\"Linux\" \"Linux-x86-64\"\n\t\t\t\"MacOSX-x86\" \"MacOSX-x86-64\" \"MacOSX\"\n\t\t\t\"Solaris-SPARC\" \"Solaris-x86-64\")\n\telseif (NOT \"${_version}\" VERSION_LESS \"6.0\")\n\t\tset (${_outSystemIDs}\n\t\t\t\"Windows\" \"Windows-x86-64\"\n\t\t\t\"Linux\" \"Linux-x86-64\" \"Linux-IA64\"\n\t\t\t\"MacOSX-x86\" \"MacOSX-x86-64\" \"MacOSX\"\n\t\t\t\"Solaris-SPARC\" \"Solaris-x86-64\"\n\t\t\t\"AIX-Power64\")\n\telseif (NOT \"${_version}\" VERSION_LESS \"5.2\")\n\t\tset (${_outSystemIDs}\n\t\t\t\"Windows\" \"Windows-x86-64\"\n\t\t\t\"Linux\" \"Linux-x86-64\" \"Linux-IA64\"\n\t\t\t\"MacOSX-x86\" \"Darwin-PowerPC64\" \"Darwin\"\n\t\t\t\"UltraSPARC\" \"Solaris-x86-64\"\n\t\t\t\"AIX-Power64\" \"DEC-AXP\" \"HPUX-PA64\" \"IRIX-MIPS64\")\n\telse()\n\t\t# platforms probably supported before 5.2?\n\t\tset (${_outSystemIDs}\n\t\t\t\"Windows\"\n\t\t\t\"Linux\" \"Linux-x86-64\" \"Linux-IA64\" \"Linux-PPC\"\n\t\t\t\"Darwin\"\n\t\t\t\"Solaris\" \"SGI\"\n\t\t\t\"IBM-RISC\" \"DEC-AXP\" \"HP-RISC\" \"IRIX-MIPS32\" \"IRIX-MIPS64\")\n\tendif()\nendmacro()\n\nmacro (_get_compatible_system_IDs _systemID _outSystemIDs)\n\tset (${_outSystemIDs} \"\")\n\tif (\"${_systemID}\" STREQUAL \"Windows-x86-64\")\n\t\tif (Mathematica_VERSION)\n\t\t\tif (NOT \"${Mathematica_VERSION}\" VERSION_LESS \"5.2\")\n\t\t\t\t# Mathematica 5.2 added support for Windows-x86-64\n\t\t\t\tlist (APPEND ${_outSystemIDs} \"Windows-x86-64\")\n\t\t\tendif()\n\t\telse()\n\t\t\tlist (APPEND ${_outSystemIDs} \"Windows-x86-64\")\n\t\tendif()\n\t\tif (Mathematica_VERSION)\n\t\t\t# Mathematica 12.1 dropped support for x86\n\t\t\tif (\"${Mathematica_VERSION}\" VERSION_LESS \"12.1\")\n\t\t\t\t# Windows x64 can run x86 through WoW64\n\t\t\t\tlist (APPEND ${_outSystemIDs} \"Windows\")\n\t\t\tendif()\n\t\telse()\n\t\t\t# Windows x64 can run x86 through WoW64\n\t\t\tlist (APPEND ${_outSystemIDs} \"Windows\")\n\t\tendif()\n\telseif (\"${_systemID}\" MATCHES \"MacOSX|Darwin\")\n\t\tif (\"${_systemID}\" MATCHES \"MacOSX-x86\")\n\t\t\tif (Mathematica_VERSION)\n\t\t\t\t# Mathematica 6 added support for MacOSX-x86-64\n\t\t\t\tif (NOT \"${Mathematica_VERSION}\" VERSION_LESS \"6.0\")\n\t\t\t\t\tlist (APPEND ${_outSystemIDs} \"MacOSX-x86-64\")\n\t\t\t\tendif()\n\t\t\t\t# Mathematica 5.2 added support for MacOSX-x86\n\t\t\t\t# Mathematica 9.0 dropped support for MacOSX-x86\n\t\t\t\tif (NOT \"${Mathematica_VERSION}\" VERSION_LESS \"5.2\" AND\n\t\t\t\t\t\"${Mathematica_VERSION}\" VERSION_LESS \"9.0\")\n\t\t\t\t\tlist (APPEND ${_outSystemIDs} \"MacOSX-x86\")\n\t\t\t\tendif()\n\t\t\telse()\n\t\t\t\tlist (APPEND ${_outSystemIDs} \"MacOSX-x86-64\" \"MacOSX-x86\")\n\t\t\tendif()\n\t\telseif (\"${_systemID}\" MATCHES \"MacOSX-ARM64\")\n\t\t\tif (Mathematica_VERSION)\n\t\t\t\t# Mathematica 12.3 added support for MacOSX-ARM64\n\t\t\t\tif (NOT \"${Mathematica_VERSION}\" VERSION_LESS \"12.3\")\n\t\t\t\t\tlist (APPEND ${_outSystemIDs} \"MacOSX-ARM64\")\n\t\t\t\tendif()\n\t\t\t\t# Mathematica 6 added support for MacOSX-x86-64\n\t\t\t\tif (NOT \"${Mathematica_VERSION}\" VERSION_LESS \"6.0\")\n\t\t\t\t\tlist (APPEND ${_outSystemIDs} \"MacOSX-x86-64\")\n\t\t\t\tendif()\n\t\t\telse()\n\t\t\t\tlist (APPEND ${_outSystemIDs} \"MacOSX-ARM64\" \"MacOSX-x86-64\")\n\t\t\tendif()\n\t\telseif (\"${_systemID}\" STREQUAL \"Darwin-PowerPC64\")\n\t\t\tif (Mathematica_VERSION)\n\t\t\t\tif (NOT \"${Mathematica_VERSION}\" VERSION_LESS \"5.2\" AND\n\t\t\t\t\t\"${Mathematica_VERSION}\" VERSION_LESS \"6.0\")\n\t\t\t\t\t# Only Mathematica 5.2 supports Darwin-PowerPC64\n\t\t\t\t\tlist (APPEND ${_outSystemIDs} \"Darwin-PowerPC64\")\n\t\t\t\tendif()\n\t\t\telse()\n\t\t\t\tlist (APPEND ${_outSystemIDs} \"Darwin-PowerPC64\")\n\t\t\tendif()\n\t\tendif()\n\t\t# handle ppc32 (Darwin or MacOSX)\n\t\t# Mac OS X versions before Lion support ppc32 natively or through Rosetta\n\t\t# (Mac OS X 10.7.0 is Darwin 11.0.0)\n\t\tif (\"${CMAKE_HOST_SYSTEM_VERSION}\" VERSION_LESS \"11.0.0\")\n\t\t\tif (Mathematica_VERSION)\n\t\t\t\tif (\"${Mathematica_VERSION}\" VERSION_LESS \"6.0\")\n\t\t\t\t\t# Mathematica versions before 6 used \"Darwin\" as system ID for ppc32\n\t\t\t\t\tlist (APPEND ${_outSystemIDs} \"Darwin\")\n\t\t\t\telseif (\"${Mathematica_VERSION}\" VERSION_LESS \"8.0\")\n\t\t\t\t\t# Mathematica 8 dropped support for ppc32\n\t\t\t\t\tlist (APPEND ${_outSystemIDs} \"MacOSX\")\n\t\t\t\tendif()\n\t\t\telse()\n\t\t\t\tlist (APPEND ${_outSystemIDs} \"MacOSX\" \"Darwin\")\n\t\t\tendif()\n\t\tendif()\n\telseif (\"${_systemID}\" MATCHES \"Linux-x86-64|Linux-IA64\")\n\t\tif (Mathematica_VERSION)\n\t\t\tif (NOT \"${Mathematica_VERSION}\" VERSION_LESS \"5.2\")\n\t\t\t\t# Mathematica 5.2 added support for 64-bit\n\t\t\t\tlist (APPEND ${_outSystemIDs} ${_systemID})\n\t\t\tendif()\n\t\telse()\n\t\t\tlist (APPEND ${_outSystemIDs} ${_systemID})\n\t\tendif()\n\t\t# Linux 64-bit can run x86 through ia32-libs package\n\t\tif (Mathematica_VERSION)\n\t\t\tif (\"${Mathematica_VERSION}\" VERSION_LESS \"11.3\")\n\t\t\t\t# Mathematica 11.3 dropped support for 32-bit Linux\n\t\t\t\tlist (APPEND ${_outSystemIDs} \"Linux\")\n\t\t\tendif()\n\t\telse()\n\t\t\tlist (APPEND ${_outSystemIDs} \"Linux\")\n\t\tendif()\n\telse()\n\t\tlist (APPEND ${_outSystemIDs} ${_systemID})\n\tendif()\n\tlist (REMOVE_DUPLICATES ${_outSystemIDs})\nendmacro()\n\n# internal macro to compute target MathLink / WSTP DeveloperKit system ID\nmacro(_get_developer_kit_system_IDs _outSystemIDs)\n\tif (APPLE)\n\t\tif (Mathematica_VERSION)\n\t\t\tif (\"${Mathematica_VERSION}\" VERSION_LESS \"9.0\")\n\t\t\t\t# Mathematica versions before 9 did not have a system ID subdirectory\n\t\t\t\tset (${_outSystemIDs} \"\")\n\t\t\telse()\n\t\t\t\t# Mathematica versions after 9 have a system ID subdirectory\n\t\t\t\tset (${_outSystemIDs} \"MacOSX-x86-64\" \"MacOSX-ARM64\")\n\t\t\tendif()\n\t\telse()\n\t\t\t_get_system_IDs(${_outSystemIDs})\n\t\tendif()\n\telse()\n\t\t_get_system_IDs(${_outSystemIDs})\n\tendif()\nendmacro()\n\n# internal macro to compute host MathLink / WSTP DeveloperKit system ID\nmacro(_get_host_developer_kit_system_IDs _outSystemIDs)\n\tif (CMAKE_HOST_APPLE)\n\t\tif (Mathematica_VERSION)\n\t\t\t# Mathematica versions before 9 did not have a system ID subdirectory\n\t\t\tif (\"${Mathematica_VERSION}\" VERSION_LESS \"9.0\")\n\t\t\t\tset (${_outSystemIDs} \"\")\n\t\t\telse()\n\t\t\t\t# Mathematica versions after 9 have a system ID subdirectory\n\t\t\t\tset (${_outSystemIDs} \"MacOSX-x86-64\" \"MacOSX-ARM64\")\n\t\t\tendif()\n\t\telse()\n\t\t\t_get_host_system_IDs(${_outSystemIDs})\n\t\tendif()\n\telse()\n\t\t_get_host_system_IDs(${_outSystemIDs})\n\tendif()\nendmacro()\n\n# internal macro to compute target development flavor\nmacro (_get_target_flavor _outFlavor)\n\tif (CYGWIN)\n\t\tset (${_outFlavor} \"cygwin\")\n\telseif (WIN32)\n\t\tif (CMAKE_SIZEOF_VOID_P EQUAL 8)\n\t\t\tset (${_outFlavor} \"mldev64\")\n\t\telse()\n\t\t\tset (${_outFlavor} \"mldev32\")\n\t\tendif()\n\telseif (APPLE)\n\t\tset (${_outFlavor} \"\")\n\t\tif (Mathematica_VERSION)\n\t\t\tif (Mathematica_USE_LIBCXX_LIBRARIES AND\n\t\t\t\tNOT \"${Mathematica_VERSION}\" VERSION_LESS \"10.0\" AND\n\t\t\t\t\"${Mathematica_VERSION}\" VERSION_LESS \"10.4\")\n\t\t\t\t# Mathematica 10 added LLVM libc++ compiled version in AlternativeLibraries directory\n\t\t\t\t# Mathematica 10.4 and later only ship with LLVM libc++ compiled version\n\t\t\t\tset (${_outFlavor} \"AlternativeLibraries\")\n\t\t\tendif()\n\t\tendif()\n\telse()\n\t\t# no flavors on non-Windows platforms\n\t\tset (${_outFlavor} \"\")\n\tendif()\nendmacro()\n\n# internal macro to compute host development flavor\nmacro (_get_host_flavor _outFlavor)\n\tif (CYGWIN)\n\t\tset (${_outFlavor} \"cygwin\")\n\telseif (CMAKE_HOST_WIN32)\n\t\tset (${_outFlavor} \"mldev32\")\n\t\tif (DEFINED ENV{PROCESSOR_ARCHITEW6432})\n\t\t\tif (\"$ENV{PROCESSOR_ARCHITEW6432}\" STREQUAL \"AMD64\")\n\t\t\t\t# running of WoW64, host is native 64-bit Windows\n\t\t\t\tset (${_outFlavor} \"mldev64\")\n\t\t\tendif()\n\t\telseif (DEFINED ENV{PROCESSOR_ARCHITECTURE})\n\t\t\tif (\"$ENV{PROCESSOR_ARCHITECTURE}\" STREQUAL \"AMD64\")\n\t\t\t\t# host is native 64-bit Windows\n\t\t\t\tset (${_outFlavor} \"mldev64\")\n\t\t\tendif()\n\t\tendif()\n\telseif (CMAKE_HOST_APPLE)\n\t\tset (${_outFlavor} \"\")\n\t\tif (Mathematica_VERSION)\n\t\t\tif (Mathematica_USE_LIBCXX_LIBRARIES AND\n\t\t\t\tNOT \"${Mathematica_VERSION}\" VERSION_LESS \"10.0\" AND\n\t\t\t\t\"${Mathematica_VERSION}\" VERSION_LESS \"10.4\")\n\t\t\t\t# Mathematica 10 added LLVM libc++ compiled version in AlternativeLibraries directory\n\t\t\t\t# Mathematica 10.4 and later only ship with LLVM libc++ compiled version\n\t\t\t\tset (${_outFlavor} \"AlternativeLibraries\")\n\t\t\tendif()\n\t\tendif()\n\telse()\n\t\t# no flavors on non-Windows platforms\n\t\tset (${_outFlavor} \"\")\n\tendif()\nendmacro()\n\n# internal macro to compute WolframRTL library names\nmacro (_get_wolfram_runtime_library_names _outLibraryNames)\n\tif (Mathematica_USE_STATIC_LIBRARIES)\n\t\tset (${_outLibraryNames} \"WolframRTL_Static_Minimal\" )\n\telse()\n\t\tif (Mathematica_USE_MINIMAL_LIBRARIES)\n\t\t\tset (${_outLibraryNames} \"WolframRTL_Minimal\" )\n\t\telse()\n\t\t\tset (${_outLibraryNames} \"WolframRTL\" )\n\t\tendif()\n\tendif()\nendmacro()\n\n# internal macro to compute MathLink library names\nmacro (_get_mathlink_library_names _outLibraryNames)\n\tif (CYGWIN)\n\t\tif (DEFINED Mathematica_MathLink_FIND_VERSION_MAJOR)\n\t\t\tset (${_outLibraryNames} \"ML32i${Mathematica_MathLink_FIND_VERSION_MAJOR}\")\n\t\telse()\n\t\t\tset (${_outLibraryNames} \"ML32i4\" \"ML32i3\" \"ML32i2\" \"ML32i1\")\n\t\tendif()\n\telseif (WIN32)\n\t\tif (CMAKE_SIZEOF_VOID_P EQUAL 8)\n\t\t\tif (BORLAND)\n\t\t\t\tset (${_outLibraryNames} \"ml64i3b\" \"ml64i2b\")\n\t\t\telseif (WATCOM)\n\t\t\t\tset (${_outLibraryNames} \"ml64i3w\" \"ml64i2w\")\n\t\t\tendif()\n\t\t\t# always add default Microsoft 64-bit PE libraries\n\t\t\tif (DEFINED Mathematica_MathLink_FIND_VERSION_MAJOR)\n\t\t\t\tif (Mathematica_USE_STATIC_LIBRARIES)\n\t\t\t\t\tlist (APPEND ${_outLibraryNames} \"ml64i${Mathematica_MathLink_FIND_VERSION_MAJOR}s\")\n\t\t\t\telse()\n\t\t\t\t\tlist (APPEND ${_outLibraryNames} \"ml64i${Mathematica_MathLink_FIND_VERSION_MAJOR}m\")\n\t\t\t\tendif()\n\t\t\telse()\n\t\t\t\tif (Mathematica_USE_STATIC_LIBRARIES)\n\t\t\t\t\tlist (APPEND ${_outLibraryNames} \"ml64i4s\" \"ml64i3s\")\n\t\t\t\telse()\n\t\t\t\t\tlist (APPEND ${_outLibraryNames} \"ml64i4m\" \"ml64i3m\" \"ml64i2m\")\n\t\t\t\tendif()\n\t\t\tendif()\n\t\telse()\n\t\t\tif (BORLAND)\n\t\t\t\tset (${_outLibraryNames} \"ml32i3b\" \"ml32i2b\" \"ml32i1b\")\n\t\t\telseif (WATCOM)\n\t\t\t\tset (${_outLibraryNames} \"ml32i3w\" \"ml32i2w\" \"ml32i1w\")\n\t\t\tendif()\n\t\t\t# always add default Microsoft 32-bit PE libraries\n\t\t\tif (DEFINED Mathematica_MathLink_FIND_VERSION_MAJOR)\n\t\t\t\tif (Mathematica_USE_STATIC_LIBRARIES)\n\t\t\t\t\tlist (APPEND ${_outLibraryNames} \"ml32i${Mathematica_MathLink_FIND_VERSION_MAJOR}s\")\n\t\t\t\telse()\n\t\t\t\t\tlist (APPEND ${_outLibraryNames} \"ml32i${Mathematica_MathLink_FIND_VERSION_MAJOR}m\")\n\t\t\t\tendif()\n\t\t\telse()\n\t\t\t\tif (Mathematica_USE_STATIC_LIBRARIES)\n\t\t\t\t\tlist (APPEND ${_outLibraryNames} \"ml32i4s\" \"ml32i3s\")\n\t\t\t\telse()\n\t\t\t\t\tlist (APPEND ${_outLibraryNames} \"ml32i4m\" \"ml32i3m\" \"ml32i2m\" \"ml32i1m\")\n\t\t\t\tendif()\n\t\t\tendif()\n\t\tendif()\n\telseif (APPLE)\n\t\tif (Mathematica_USE_STATIC_LIBRARIES)\n\t\t\tif (DEFINED Mathematica_MathLink_FIND_VERSION_MAJOR AND DEFINED Mathematica_MathLink_FIND_VERSION_MINOR)\n\t\t\t\tset (${_outLibraryNames} \"libMLi${Mathematica_MathLink_FIND_VERSION_MAJOR}.${Mathematica_MathLink_FIND_VERSION_MINOR}.a\")\n\t\t\telseif (DEFINED Mathematica_MathLink_FIND_VERSION_MAJOR)\n\t\t\t\tset (${_outLibraryNames} \"libMLi${Mathematica_MathLink_FIND_VERSION_MAJOR}.a\")\n\t\t\telse()\n\t\t\t\tset (${_outLibraryNames} \"libMLi4.a\" \"libMLi3.a\" \"libML.a\")\n\t\t\tendif()\n\t\telse()\n\t\t\t# search for mathlink.framework\n\t\t\tset (${_outLibraryNames} \"mathlink\" \"ML\")\n\t\tendif()\n\telseif (UNIX)\n\t\tif (Mathematica_USE_STATIC_LIBRARIES)\n\t\t\tset (_ext \".a\")\n\t\telse()\n\t\t\tset (_ext \".so\")\n\t\tendif()\n\t\tif (CMAKE_SIZEOF_VOID_P EQUAL 8)\n\t\t\tset (_arch \"64\")\n\t\telse()\n\t\t\tset (_arch \"32\")\n\t\tendif()\n\t\tif (DEFINED Mathematica_MathLink_FIND_VERSION_MAJOR)\n\t\t\tset (${_outLibraryNames} \"libML${_arch}i${Mathematica_MathLink_FIND_VERSION_MAJOR}${_ext}\")\n\t\telse()\n\t\t\tset (${_outLibraryNames} \"libML${_arch}i4${_ext}\" \"libML${_arch}i3${_ext}\" \"libML${_ext}\")\n\t\tendif()\n\tendif()\nendmacro(_get_mathlink_library_names)\n\nfunction (_get_mprep_output_file _templateFile _outfile)\n\tget_filename_component(_templateFile_name ${_templateFile} NAME)\n\tget_filename_component(_templateFile_ext \"${_templateFile}\" EXT)\n\tif (_templateFile_ext STREQUAL \".tmpp\")\n\t\tset (${_outfile} \"${_templateFile_name}.cpp\" PARENT_SCOPE)\n\telseif (_templateFile_ext STREQUAL \".tm++\")\n\t\tset (${_outfile} \"${_templateFile_name}.c++\" PARENT_SCOPE)\n\telseif (_templateFile_ext STREQUAL \".tmxx\")\n\t\tset (${_outfile} \"${_templateFile_name}.cxx\" PARENT_SCOPE)\n\telse()\n\t\tset (${_outfile} \"${_templateFile_name}.c\" PARENT_SCOPE)\n\tendif()\nendfunction()\n\n# internal macro to compute WSTP library names\nmacro (_get_WSTP_library_names _outLibraryNames)\n\tif (CYGWIN)\n\t\tif (DEFINED Mathematica_WSTP_FIND_VERSION_MAJOR)\n\t\t\tset (${_outLibraryNames} \"WSTP32i${Mathematica_WSTP_FIND_VERSION_MAJOR}\")\n\t\telse()\n\t\t\tset (${_outLibraryNames} \"WSTP32i4\" \"WSTP32i3\" \"WSTP32i2\" \"WSTP32i1\")\n\t\tendif()\n\telseif (WIN32)\n\t\tif (CMAKE_SIZEOF_VOID_P EQUAL 8)\n\t\t\tset (_arch \"64\")\n\t\telse()\n\t\t\tset (_arch \"32\")\n\t\tendif()\n\t\tif (DEFINED Mathematica_WSTP_FIND_VERSION_MAJOR)\n\t\t\tif (Mathematica_USE_STATIC_LIBRARIES)\n\t\t\t\tlist (APPEND ${_outLibraryNames} \"wstp${_arch}i${Mathematica_WSTP_FIND_VERSION_MAJOR}s\")\n\t\t\telse()\n\t\t\t\tlist (APPEND ${_outLibraryNames} \"wstp${_arch}i${Mathematica_WSTP_FIND_VERSION_MAJOR}m\")\n\t\t\tendif()\n\t\telse()\n\t\t\tif (Mathematica_USE_STATIC_LIBRARIES)\n\t\t\t\tlist (APPEND ${_outLibraryNames} \"wstp${_arch}i4s\" \"wstp${_arch}i3s\")\n\t\t\telse()\n\t\t\t\tlist (APPEND ${_outLibraryNames} \"wstp${_arch}i4m\" \"wstp${_arch}i3m\" \"wstp${_arch}i2m\" \"wstp${_arch}i1m\")\n\t\t\tendif()\n\t\tendif()\n\telseif (APPLE)\n\t\tif (Mathematica_USE_STATIC_LIBRARIES)\n\t\t\tif (DEFINED Mathematica_WSTP_FIND_VERSION_MAJOR AND DEFINED Mathematica_WSTP_FIND_VERSION_MINOR)\n\t\t\t\tset (${_outLibraryNames} \"libWSTPi${Mathematica_WSTP_FIND_VERSION_MAJOR}.${Mathematica_WSTP_FIND_VERSION_MINOR}.a\")\n\t\t\telseif (DEFINED Mathematica_WSTP_FIND_VERSION_MAJOR)\n\t\t\t\tset (${_outLibraryNames} \"libWSTPi${Mathematica_WSTP_FIND_VERSION_MAJOR}.a\")\n\t\t\telse()\n\t\t\t\tset (${_outLibraryNames} \"libWSTPi4.a\" \"libWSTPi3.a\")\n\t\t\tendif()\n\t\telse()\n\t\t\t# search for wstp.framework\n\t\t\tset (${_outLibraryNames} \"wstp\")\n\t\tendif()\n\telseif (UNIX)\n\t\tif (Mathematica_USE_STATIC_LIBRARIES)\n\t\t\tset (_ext \".a\")\n\t\telse()\n\t\t\tset (_ext \".so\")\n\t\tendif()\n\t\tif (CMAKE_SIZEOF_VOID_P EQUAL 8)\n\t\t\tset (_arch \"64\")\n\t\telse()\n\t\t\tset (_arch \"32\")\n\t\tendif()\n\t\tif (DEFINED Mathematica_WSTP_FIND_VERSION_MAJOR)\n\t\t\tset (${_outLibraryNames} \"libWSTP${_arch}i${Mathematica_WSTP_FIND_VERSION_MAJOR}${_ext}\")\n\t\telse()\n\t\t\tset (${_outLibraryNames} \"libWSTP${_arch}i4${_ext}\" \"libWSTP${_arch}i3${_ext}\")\n\t\tendif()\n\tendif()\nendmacro(_get_WSTP_library_names)\n\n# internal macro to compute Java launcher name\nmacro (_get_jlink_java_name _outExecutabeName)\n\tif (CMAKE_HOST_WIN32)\n\t\tset (${_outExecutabeName} \"java.exe\")\n\telseif (CMAKE_HOST_UNIX)\n\t\tset (${_outExecutabeName} \"java\")\n\tendif()\nendmacro()\n\n# internal macro to compute required WolframRTL system libraries\nmacro (_append_wolframlibrary_needed_system_libraries _outLibraries)\n\tif (UNIX)\n\t\tif (CMAKE_SYSTEM_NAME STREQUAL \"Linux\")\n\t\t\tlist (APPEND ${_outLibraries} pthread m )\n\t\tendif()\n\tendif()\nendmacro()\n\n# internal macro to compute required MathLink system libraries\nmacro (_append_mathlink_needed_system_libraries _outLibraries)\n\tif (APPLE)\n\t\tif (DEFINED Mathematica_MathLink_VERSION_MINOR)\n\t\t\tif (\"${Mathematica_MathLink_VERSION_MINOR}\" GREATER 18)\n\t\t\t\t# OS X MathLink API revision >= 19 has dependency on C++ standard library\n\t\t\t\tif (Mathematica_USE_LIBCXX_LIBRARIES)\n\t\t\t\t\t# LLVM libc++\n\t\t\t\t\tlist (APPEND ${_outLibraries} c++ )\n\t\t\t\telse()\n\t\t\t\t\t# GNU libstdc++\n\t\t\t\t\tlist (APPEND ${_outLibraries} stdc++ )\n\t\t\t\tendif()\n\t\t\tendif()\n\t\t\tif (\"${Mathematica_MathLink_VERSION_MINOR}\" GREATER 20)\n\t\t\t\t# Mac OS X MathLink API revision >= 21 has dependency on Core Foundation framework\n\t\t\t\tlist (APPEND ${_outLibraries} \"-framework Foundation\" )\n\t\t\tendif()\n\t\tendif()\n\telseif (UNIX)\n\t\tif (DEFINED Mathematica_MathLink_VERSION_MINOR)\n\t\t\tif (\"${Mathematica_MathLink_VERSION_MINOR}\" GREATER 18)\n\t\t\t\t# UNIX MathLink API revision >= 19 has dependency on GNU libstdc++\n\t\t\t\tlist (APPEND ${_outLibraries} stdc++ )\n\t\t\tendif()\n\t\tendif()\n\t\tif (CMAKE_SYSTEM_NAME STREQUAL \"Linux\")\n\t\t\tlist (APPEND ${_outLibraries} m)\n\t\t\tset (CMAKE_THREAD_PREFER_PTHREAD TRUE)\n\t\t\tfind_package(Threads REQUIRED)\n\t\t\tlist (APPEND ${_outLibraries} \"${CMAKE_THREAD_LIBS_INIT}\")\n\t\t\tfind_library(Mathematica_rt_LIBRARY rt)\n\t\t\tmark_as_advanced(Mathematica_rt_LIBRARY)\n\t\t\tlist (APPEND ${_outLibraries} ${Mathematica_rt_LIBRARY})\n\t\t\tif (DEFINED Mathematica_MathLink_VERSION_MINOR)\n\t\t\t\tif (\"${Mathematica_MathLink_VERSION_MINOR}\" GREATER 24)\n\t\t\t\t\t# Linux MathLink API revision >= 25 has dependency on libdl and libuuid\n\t\t\t\t\tlist (APPEND ${_outLibraries} ${CMAKE_DL_LIBS})\n\t\t\t\t\tfind_library (Mathematica_uuid_LIBRARY uuid)\n\t\t\t\t\tmark_as_advanced(Mathematica_uuid_LIBRARY)\n\t\t\t\t\tlist (APPEND ${_outLibraries} ${Mathematica_uuid_LIBRARY})\n\t\t\t\tendif()\n\t\t\tendif()\n\t\telseif (CMAKE_SYSTEM_NAME STREQUAL \"SunOS\")\n\t\t\tlist (APPEND ${_outLibraries} m socket nsl rt )\n\t\telseif (CMAKE_SYSTEM_NAME STREQUAL \"AIX\")\n\t\t\tlist (APPEND ${_outLibraries} m pthread )\n\t\telseif (CMAKE_SYSTEM_NAME STREQUAL \"HP-UX\")\n\t\t\tlist (APPEND ${_outLibraries}\n\t\t\t\tm /usr/lib/pa20_64/libdld.sl /usr/lib/pa20_64/libm.a pthread rt )\n\t\telseif (CMAKE_SYSTEM_NAME STREQUAL \"IRIX\")\n\t\t\tlist (APPEND ${_outLibraries} m pthread )\n\t\tendif()\n\telseif (WIN32)\n\t\tif (DEFINED Mathematica_MathLink_VERSION_MINOR)\n\t\t\tif (\"${Mathematica_MathLink_VERSION_MINOR}\" GREATER 19)\n\t\t\t\t# Windows MathLink API revision >= 20 has dependency on Winsock 2\n\t\t\t\tlist (APPEND ${_outLibraries} Ws2_32.lib )\n\t\t\tendif()\n\t\t\tif (\"${Mathematica_MathLink_VERSION_MINOR}\" GREATER 24)\n\t\t\t\t# Windows MathLink API interface >= 25 has dependency on RPC\n\t\t\t\tlist (APPEND ${_outLibraries} Rpcrt4.lib )\n\t\t\tendif()\n\t\tendif()\n\tendif()\nendmacro()\n\n# internal macro to compute required WSTP system libraries\nmacro (_append_WSTP_needed_system_libraries _outLibraries)\n\tif (APPLE)\n\t\tif (DEFINED Mathematica_WSTP_VERSION_MINOR)\n\t\t\tif (\"${Mathematica_WSTP_VERSION_MINOR}\" GREATER 18)\n\t\t\t\t# OS X WSTP API revision >= 19 has dependency on C++ standard library\n\t\t\t\tif (Mathematica_USE_LIBCXX_LIBRARIES)\n\t\t\t\t\t# LLVM libc++\n\t\t\t\t\tlist (APPEND ${_outLibraries} c++ )\n\t\t\t\telse()\n\t\t\t\t\t# GNU libstdc++\n\t\t\t\t\tlist (APPEND ${_outLibraries} stdc++ )\n\t\t\t\tendif()\n\t\t\tendif()\n\t\t\tif (\"${Mathematica_WSTP_VERSION_MINOR}\" GREATER 20)\n\t\t\t\t# Mac OS X WSTP API revision >= 21 has dependency on Core Foundation framework\n\t\t\t\tlist (APPEND ${_outLibraries} \"-framework Foundation\" )\n\t\t\tendif()\n\t\tendif()\n\telseif (UNIX)\n\t\tif (CMAKE_SYSTEM_NAME STREQUAL \"Linux\")\n\t\t\tif (DEFINED Mathematica_WSTP_VERSION_MINOR)\n\t\t\t\tif (\"${Mathematica_WSTP_VERSION_MINOR}\" GREATER 18)\n\t\t\t\t\t# UNIX WSTP API revision >= 19 has dependency on GNU libstdc++\n\t\t\t\t\tlist (APPEND ${_outLibraries} stdc++ )\n\t\t\t\tendif()\n\t\t\tendif()\n\t\t\tlist (APPEND ${_outLibraries} m pthread rt )\n\t\t\tif (DEFINED Mathematica_WSTP_VERSION_MINOR)\n\t\t\t\tif (\"${Mathematica_WSTP_VERSION_MINOR}\" GREATER 24)\n\t\t\t\t\t# Linux WSTP API revision >= 25 has dependency on libdl and libuuid\n\t\t\t\t\tlist (APPEND ${_outLibraries} ${CMAKE_DL_LIBS})\n\t\t\t\t\tfind_library (Mathematica_uuid_LIBRARY uuid)\n\t\t\t\t\tmark_as_advanced(Mathematica_uuid_LIBRARY)\n\t\t\t\t\tlist (APPEND ${_outLibraries} ${Mathematica_uuid_LIBRARY})\n\t\t\t\tendif()\n\t\t\tendif()\n\t\tendif()\n\telseif (WIN32)\n\t\tif (DEFINED Mathematica_WSTP_VERSION_MINOR)\n\t\t\tif (\"${Mathematica_WSTP_VERSION_MINOR}\" GREATER 19)\n\t\t\t\t# Windows WSTP API revision >= 20 has dependency on Winsock 2\n\t\t\t\tlist (APPEND ${_outLibraries} Ws2_32.lib )\n\t\t\tendif()\n\t\t\tif (\"${Mathematica_WSTP_VERSION_MINOR}\" GREATER 24)\n\t\t\t\t# Windows WSTP API interface >= 25 has dependency on RPC\n\t\t\t\tlist (APPEND ${_outLibraries} Rpcrt4.lib )\n\t\t\tendif()\n\t\tendif()\n\tendif()\nendmacro()\n\n# internal macro to return dynamic library search path environment variables on host platform\nmacro (_get_host_library_search_path_envvars _outVariableNames)\n\tset (${_outVariableNames} \"\")\n\tif (CMAKE_HOST_APPLE)\n\t\tlist (APPEND ${_outVariableNames} \"DYLD_FRAMEWORK_PATH\" \"DYLD_LIBRARY_PATH\")\n\telseif (CYGWIN)\n\t\tlist (APPEND ${_outVariableNames} \"PATH\" \"LD_LIBRARY_PATH\")\n\telseif (CMAKE_HOST_WIN32)\n\t\tlist (APPEND ${_outVariableNames} \"PATH\")\n\telseif (CMAKE_HOST_UNIX)\n\t\tif (\"${CMAKE_HOST_SYSTEM_NAME}\" STREQUAL \"SunOS\")\n\t\t\tlist (APPEND ${_outVariableNames} \"LD_LIBRARY_PATH_64\")\n\t\telseif (\"${CMAKE_HOST_SYSTEM_NAME}\" STREQUAL \"AIX\")\n\t\t\tlist (APPEND ${_outVariableNames} \"LIBPATH\")\n\t\telseif (\"${CMAKE_HOST_SYSTEM_NAME}\" STREQUAL \"HP-UX\")\n\t\t\tlist (APPEND ${_outVariableNames} \"SHLIB_PATH\")\n\t\telseif (\"${CMAKE_HOST_SYSTEM_NAME}\" STREQUAL \"IRIX\")\n\t\t\tlist (APPEND ${_outVariableNames} \"LD_LIBRARY64_PATH\")\n\t\tendif()\n\t\tlist (APPEND ${_outVariableNames} \"LD_LIBRARY_PATH\")\n\tendif()\nendmacro()\n\n# internal macro to convert list to a search path list for host platform\nfunction (_to_native_path_list _outPathList)\n\tset (_nativePathList \"\")\n\tforeach (_path ${ARGN})\n\t\t_to_native_path(\"${_path}\" _nativePath)\n\t\tlist (APPEND _nativePathList \"${_nativePath}\")\n\tendforeach()\n\tif (CMAKE_HOST_UNIX)\n\t\tstring (REPLACE \";\" \":\" _nativePathList \"${_nativePathList}\")\n\telseif (CMAKE_HOST_WIN32)\n\t\t# prevent CMake from interpreting ; as a list separator\n\t\tstring (REPLACE \";\" \"\\\\;\" _nativePathList \"${_nativePathList}\")\n\tendif()\n\tset (${_outPathList} \"${_nativePathList}\" PARENT_SCOPE)\nendfunction()\n\nfunction (_to_cmake_path_list _outPathList)\n\tset (_cmakePathList \"\")\n\tforeach (_path ${ARGN})\n\t\t_to_cmake_path(\"${_path}\" _cmakePath)\n\t\tlist (APPEND _cmakePathList \"${_cmakePath}\")\n\tendforeach()\n\tif (CMAKE_HOST_UNIX)\n\t\tstring (REPLACE \";\" \":\" _cmakePathList \"${_cmakePathList}\")\n\telseif (CMAKE_HOST_WIN32)\n\t\t# prevent CMake from interpreting ; as a list separator\n\t\tstring (REPLACE \";\" \"\\\\;\" _cmakePathList \"${_cmakePathList}\")\n\tendif()\n\tset (${_outPathList} \"${_cmakePathList}\" PARENT_SCOPE)\nendfunction()\n\n# internal macro to select runtime libraries according to build type\nmacro (_select_configuration_run_time_dirs _outRuntimeDirs)\n\tset (${_outRuntimeDirs} ${Mathematica_RUNTIME_LIBRARY_DIRS})\n\tif (DEFINED CMAKE_BUILD_TYPE)\n\t\tif (\"${CMAKE_BUILD_TYPE}\" STREQUAL \"Debug\")\n\t\t\tset (${_outRuntimeDirs} ${Mathematica_RUNTIME_LIBRARY_DIRS_DEBUG})\n\t\tendif()\n\tendif()\nendmacro()\n\n# internal macro to set up Mathematica host system IDs\nmacro (_setup_mathematica_systemIDs)\n\t_get_system_IDs(Mathematica_SYSTEM_IDS)\n\t# default target platform system ID is first one in Mathematica_SYSTEM_IDS\n\tlist(GET Mathematica_SYSTEM_IDS 0 Mathematica_SYSTEM_ID)\n\tif (Mathematica_RUN_KERNEL_ON_CONFIGURE AND COMMAND Mathematica_EXECUTE)\n\t\t# determine true host system ID which depends on both Mathematica version\n\t\t# and OS variant by running Mathematica kernel\n\t\tMathematica_EXECUTE(\n\t\t\tCODE \"Print[StandardForm[$SystemID]]\"\n\t\t\tOUTPUT_VARIABLE Mathematica_KERNEL_HOST_SYSTEM_ID\n\t\t\tCACHE DOC \"Actual Mathematica host system ID.\"\n\t\t\tTIMEOUT 10)\n\t\tif (NOT Mathematica_KERNEL_HOST_SYSTEM_ID)\n\t\t\tmessage (WARNING \"Cannot accurately determine Mathematica host system ID.\")\n\t\tendif()\n\tendif()\n\tif (Mathematica_KERNEL_HOST_SYSTEM_ID)\n\t\tif (Mathematica_KERNEL_HOST_SYSTEM_ID MATCHES \"[a-zA-Z0-9_-]+\")\n\t\t\tset (Mathematica_HOST_SYSTEM_ID \"${Mathematica_KERNEL_HOST_SYSTEM_ID}\")\n\t\telse()\n\t\t\tunset (Mathematica_KERNEL_HOST_SYSTEM_ID CACHE)\n\t\tendif()\n\telse()\n\t\t# guess host system ID from the environment\n\t\t_get_host_system_IDs(_HostSystemIDs)\n\t\t# default to first ID in _HostSystemIDs\n\t\tlist (GET _HostSystemIDs 0 Mathematica_HOST_SYSTEM_ID)\n\tendif()\n\t_get_compatible_system_IDs(${Mathematica_HOST_SYSTEM_ID} Mathematica_HOST_SYSTEM_IDS)\nendmacro()\n\n# internal macro to set up Mathematica creation ID\nmacro (_setup_mathematica_creationID)\n\tif (DEFINED Mathematica_ROOT_DIR)\n\t\tif (EXISTS \"${Mathematica_ROOT_DIR}/.CreationID\")\n\t\t\t# parse hidden CreationID file\n\t\t\tfile (STRINGS \"${Mathematica_ROOT_DIR}/.CreationID\" Mathematica_CREATION_ID REGEX \"[0-9]+\")\n\t\telseif (CMAKE_HOST_APPLE AND EXISTS \"${Mathematica_ROOT_DIR}/Contents/Info.plist\")\n\t\t\texecute_process(\n\t\t\t\tCOMMAND \"grep\" \"--after-context=1\" \"CFBundleShortVersionString\"\n\t\t\t\t\t\"${Mathematica_ROOT_DIR}/Contents/Info.plist\"\n\t\t\t\tTIMEOUT 10 OUTPUT_VARIABLE _versionStr ERROR_QUIET)\n\t\t\tif (_versionStr MATCHES \"\\\\.([0-9]+)</string>\")\n\t\t\t\t# OS X Info.plist CFBundleShortVersionString has Creation ID as last version component\n\t\t\t\tset (Mathematica_CREATION_ID \"${CMAKE_MATCH_1}\")\n\t\t\telse()\n\t\t\t\tset (_versionLine \"\")\n\t\t\tendif()\n\t\tendif()\n\tendif()\n\tif (NOT DEFINED Mathematica_CREATION_ID AND DEFINED Mathematica_CREATION_ID_LAST)\n\t\tset (Mathematica_CREATION_ID ${Mathematica_CREATION_ID_LAST})\n\tendif()\nendmacro()\n\n# internal macro to set up Mathematica base directory variable\nmacro (_setup_mathematica_base_directory)\n\tif (Mathematica_RUN_KERNEL_ON_CONFIGURE AND COMMAND Mathematica_EXECUTE)\n\t\t# determine true $BaseDirectory\n\t\tMathematica_EXECUTE(\n\t\t\tCODE \"Print[StandardForm[$BaseDirectory]]\"\n\t\t\tOUTPUT_VARIABLE Mathematica_KERNEL_BASE_DIR\n\t\t\tCACHE DOC \"Actual Mathematica $BaseDirectory.\"\n\t\t\tTIMEOUT 10)\n\t\tif (NOT Mathematica_KERNEL_BASE_DIR)\n\t\t\tmessage (WARNING \"Cannot accurately determine Mathematica $BaseDirectory.\")\n\t\tendif()\n\tendif()\n\tif (Mathematica_KERNEL_BASE_DIR)\n\t\tif (IS_ABSOLUTE \"${Mathematica_KERNEL_BASE_DIR}\")\n\t\t\tset (Mathematica_BASE_DIR \"${Mathematica_KERNEL_BASE_DIR}\")\n\t\telse()\n\t\t\tunset (Mathematica_KERNEL_BASE_DIR CACHE)\n\t\tendif()\n\telse ()\n\t\t# guess Mathematica_BASE_DIR from environment\n\t\t# environment variable MATHEMATICA_BASE may override default\n\t\t# $BaseDirectory, see\n\t\t# https://reference.wolfram.com/language/tutorial/ConfigurationFiles.html\n\t\tif (DEFINED ENV{MATHEMATICA_BASE})\n\t\t\tset (Mathematica_BASE_DIR \"$ENV{MATHEMATICA_BASE}\")\n\t\telseif (CMAKE_HOST_WIN32 OR CYGWIN)\n\t\t\tif (DEFINED $ENV{PROGRAMDATA})\n\t\t\t\tset (Mathematica_BASE_DIR \"$ENV{PROGRAMDATA}\\\\Mathematica\")\n\t\t\telseif (DEFINED ENV{ALLUSERSAPPDATA})\n\t\t\t\tset (Mathematica_BASE_DIR \"$ENV{ALLUSERSAPPDATA}\\\\Mathematica\")\n\t\t\telseif (DEFINED ENV{USERPROFILE} AND\n\t\t\t\t\tDEFINED ENV{ALLUSERSPROFILE} AND\n\t\t\t\t\tDEFINED ENV{APPDATA})\n\t\t\t\tstring (REPLACE \"$ENV{USERPROFILE}\" \"$ENV{ALLUSERSPROFILE}\"\n\t\t\t\t\tMathematica_BASE_DIR \"$ENV{APPDATA}\\\\Mathematica\")\n\t\t\tendif()\n\t\telseif (CMAKE_HOST_APPLE)\n\t\t\tset (Mathematica_BASE_DIR \"/Library/Mathematica\")\n\t\telseif (CMAKE_HOST_UNIX)\n\t\t\tset (Mathematica_BASE_DIR \"/usr/share/Mathematica\")\n\t\tendif()\n\tendif()\n\tif (Mathematica_BASE_DIR)\n\t\tget_filename_component(Mathematica_BASE_DIR \"${Mathematica_BASE_DIR}\" ABSOLUTE)\n\t\t_to_cmake_path(\"${Mathematica_BASE_DIR}\" Mathematica_BASE_DIR)\n\telse()\n\t\tset (Mathematica_BASE_DIR \"Mathematica_BASE_DIR-NOTFOUND\")\n\t\tmessage (WARNING \"Cannot determine Mathematica base directory.\")\n\tendif()\nendmacro()\n\n# internal macro to set up Mathematica user base directory variable\nmacro (_setup_mathematica_userbase_directory)\n\tif (Mathematica_RUN_KERNEL_ON_CONFIGURE AND COMMAND Mathematica_EXECUTE)\n\t\t# determine true $UserBaseDirectory\n\t\tMathematica_EXECUTE(\n\t\t\tCODE \"Print[StandardForm[$UserBaseDirectory]]\"\n\t\t\tOUTPUT_VARIABLE Mathematica_KERNEL_USERBASE_DIR\n\t\t\tCACHE DOC \"Actual Mathematica $UserBaseDirectory.\"\n\t\t\tTIMEOUT 10)\n\t\tif (NOT Mathematica_KERNEL_USERBASE_DIR)\n\t\t\tmessage (WARNING \"Cannot accurately determine Mathematica $UserBaseDirectory.\")\n\t\tendif()\n\tendif()\n\tif (Mathematica_KERNEL_USERBASE_DIR)\n\t\tif (IS_ABSOLUTE \"${Mathematica_KERNEL_USERBASE_DIR}\")\n\t\t\tset (Mathematica_USERBASE_DIR \"${Mathematica_KERNEL_USERBASE_DIR}\")\n\t\telse()\n\t\t\tunset (Mathematica_KERNEL_USERBASE_DIR CACHE)\n\t\tendif()\n\telse ()\n\t\t# guess Mathematica_USERBASE_DIR from environment\n\t\t# environment variable MATHEMATICA_USERBASE may override default\n\t\t# $UserBaseDirectory, see\n\t\t# https://reference.wolfram.com/language/tutorial/ConfigurationFiles.html\n\t\tif (DEFINED ENV{MATHEMATICA_USERBASE})\n\t\t\tset (Mathematica_USERBASE_DIR \"$ENV{MATHEMATICA_USERBASE}\")\n\t\telseif (CMAKE_HOST_WIN32 OR CYGWIN)\n\t\t\tif (DEFINED ENV{APPDATA})\n\t\t\t\tset (Mathematica_USERBASE_DIR \"$ENV{APPDATA}\\\\Mathematica\")\n\t\t\tendif()\n\t\telseif (CMAKE_HOST_APPLE)\n\t\t\tif (DEFINED ENV{HOME})\n\t\t\t\tset (Mathematica_USERBASE_DIR \"$ENV{HOME}/Library/Mathematica\")\n\t\t\tendif()\n\t\telseif (CMAKE_HOST_UNIX)\n\t\t\tif (DEFINED ENV{HOME})\n\t\t\t\tset (Mathematica_USERBASE_DIR \"$ENV{HOME}/.Mathematica\")\n\t\t\tendif()\n\t\tendif()\n\tendif()\n\tif (Mathematica_USERBASE_DIR)\n\t\tget_filename_component(Mathematica_USERBASE_DIR \"${Mathematica_USERBASE_DIR}\" ABSOLUTE)\n\t\t_to_cmake_path(\"${Mathematica_USERBASE_DIR}\" Mathematica_USERBASE_DIR)\n\telse()\n\t\tset (Mathematica_USERBASE_DIR \"Mathematica_USERBASE_DIR-NOTFOUND\")\n\t\tmessage (WARNING \"Cannot determine Mathematica user base directory.\")\n\tendif()\nendmacro()\n\n# internal macro to setup FindMathematica option variables\nmacro (_setup_findmathematica_options)\n\tif (NOT DEFINED Mathematica_USE_STATIC_LIBRARIES_INIT)\n\t\tif (DEFINED Mathematica_USE_STATIC_LIBRARIES)\n\t\t\tset (Mathematica_USE_STATIC_LIBRARIES_INIT ${Mathematica_USE_STATIC_LIBRARIES})\n\t\telse()\n\t\t\tset (Mathematica_USE_STATIC_LIBRARIES_INIT FALSE)\n\t\tendif()\n\tendif()\n\toption (Mathematica_USE_STATIC_LIBRARIES\n\t\t\"prefer static Mathematica libraries to dynamic libraries?\"\n\t\t${Mathematica_USE_STATIC_LIBRARIES_INIT})\n\tif (NOT DEFINED Mathematica_USE_MINIMAL_LIBRARIES_INIT)\n\t\tif (DEFINED Mathematica_USE_MINIMAL_LIBRARIES)\n\t\t\tset (Mathematica_USE_MINIMAL_LIBRARIES_INIT ${Mathematica_USE_MINIMAL_LIBRARIES})\n\t\telse()\n\t\t\tset (Mathematica_USE_MINIMAL_LIBRARIES_INIT FALSE)\n\t\tendif()\n\tendif()\n\toption (Mathematica_USE_MINIMAL_LIBRARIES\n\t\t\"prefer minimal Mathematica libraries to full libraries?\"\n\t\t${Mathematica_USE_MINIMAL_LIBRARIES_INIT})\n\tif (NOT DEFINED Mathematica_USE_LIBCXX_LIBRARIES_INIT)\n\t\tif (DEFINED Mathematica_USE_LIBCXX_LIBRARIES)\n\t\t\tset (Mathematica_USE_LIBCXX_LIBRARIES_INIT ${Mathematica_USE_LIBCXX_LIBRARIES})\n\t\telse()\n\t\t\t# starting with OS X 10.9, Clang uses libc++ by default\n\t\t\tif (APPLE AND NOT \"${CMAKE_SYSTEM_VERSION}\" VERSION_LESS \"13.0.0\" AND \"${CMAKE_CXX_COMPILER_ID}\" MATCHES \"Clang\")\n\t\t\t\tset (Mathematica_USE_LIBCXX_LIBRARIES_INIT TRUE)\n\t\t\telse()\n\t\t\t\tset (Mathematica_USE_LIBCXX_LIBRARIES_INIT FALSE)\n\t\t\tendif()\n\t\tendif()\n\tendif()\n\toption (Mathematica_USE_LIBCXX_LIBRARIES\n\t\t\"prefer Mathematica libraries linked with LLVM libc++ to those linked with GNU libstdc++?\"\n\t\t${Mathematica_USE_LIBCXX_LIBRARIES_INIT})\n\tif (NOT DEFINED Mathematica_DEBUG_INIT)\n\t\tif (DEFINED Mathematica_DEBUG)\n\t\t\tset (Mathematica_DEBUG_INIT ${Mathematica_DEBUG})\n\t\telse()\n\t\t\tset (Mathematica_DEBUG_INIT FALSE)\n\t\tendif()\n\tendif()\n\toption (Mathematica_DEBUG\n\t\t\"enable FindMathematica debugging output?\"\n\t\t${Mathematica_DEBUG_INIT})\n\tif (NOT DEFINED Mathematica_RUN_KERNEL_ON_CONFIGURE_INIT)\n\t\tif (DEFINED Mathematica_RUN_KERNEL_ON_CONFIGURE)\n\t\t\tset (Mathematica_RUN_KERNEL_ON_CONFIGURE_INIT ${Mathematica_RUN_KERNEL_ON_CONFIGURE})\n\t\telse()\n\t\t\tset (Mathematica_RUN_KERNEL_ON_CONFIGURE_INIT TRUE)\n\t\tendif()\n\tendif()\n\toption (Mathematica_RUN_KERNEL_ON_CONFIGURE\n\t\t\"allow FindMathematica to implicitly run the Mathematica kernel at CMake configure time?\"\n\t\t${Mathematica_RUN_KERNEL_ON_CONFIGURE_INIT})\nendmacro()\n\n# internal macro to find Mathematica installation\nmacro (_find_mathematica)\n\t_get_host_frontend_names(_FrontEndExecutables)\n\t_get_host_kernel_names(_KernelExecutables)\n\tif (Mathematica_DEBUG)\n\t\tmessage (STATUS \"FrontEndExecutables ${_FrontEndExecutables}\")\n\t\tmessage (STATUS \"KernelExecutables ${_KernelExecutables}\")\n\tendif()\n\tset (_helpStr \"Mathematica host installation root directory.\")\n\tif (NOT DEFINED Mathematica_HOST_ROOT_DIR)\n\t\tset (_doSearch TRUE)\n\telseif (NOT EXISTS \"${Mathematica_HOST_ROOT_DIR}\")\n\t\tset (_doSearch TRUE)\n\telse()\n\t\tset (_doSearch FALSE)\n\tendif()\n\tif (_doSearch)\n\t\t_get_search_paths(_SearchPaths)\n\t\t_get_program_names(_ProgramNames)\n\t\tif (Mathematica_DEBUG)\n\t\t\tmessage (STATUS \"SearchPaths ${_SearchPaths}\")\n\t\t\tmessage (STATUS \"ProgramNames ${_ProgramNames}\")\n\t\t\tmessage (STATUS \"KernelExecutables ${_KernelExecutables}\")\n\t\tendif()\n\t\tfind_path (Mathematica_HOST_ROOT_DIR\n\t\t\tNAMES ${_KernelExecutables}\n\t\t\tPATH_SUFFIXES ${_ProgramNames}\n\t\t\tPATHS ${_SearchPaths} ENV MATHEMATICA_HOME\n\t\t\tDOC \"${_helpStr}\"\n\t\t\tNO_DEFAULT_PATH NO_CMAKE_FIND_ROOT_PATH\n\t\t)\n\telse()\n\t\t# preserve pre-defined value, but set correct type and help string\n\t\tset_property(CACHE Mathematica_HOST_ROOT_DIR PROPERTY TYPE PATH)\n\t\tset_property(CACHE Mathematica_HOST_ROOT_DIR PROPERTY HELPSTRING \"${_helpStr}\")\n\tendif()\n\t# Mathematica_ROOT_DIR is initialized to Mathematica_HOST_ROOT_DIR by default\n\t# upon cross-compiling Mathematica_ROOT_DIR needs to be manually set to the correct\n\t# Mathematica installation folder for the target platform\n\tset (_helpStr \"Mathematica target installation root directory.\")\n\tif (NOT DEFINED Mathematica_ROOT_DIR)\n\t\tset (Mathematica_ROOT_DIR ${Mathematica_HOST_ROOT_DIR} CACHE PATH \"${_helpStr}\")\n\telseif (NOT EXISTS \"${Mathematica_ROOT_DIR}\")\n\t\tset (Mathematica_ROOT_DIR ${Mathematica_HOST_ROOT_DIR} CACHE PATH \"${_helpStr}\")\n\telse()\n\t\t# preserve pre-defined value, but set correct type and help string\n\t\tset_property(CACHE Mathematica_ROOT_DIR PROPERTY TYPE PATH)\n\t\tset_property(CACHE Mathematica_ROOT_DIR PROPERTY HELPSTRING \"${_helpStr}\")\n\tendif()\n\tfind_program (Mathematica_KERNEL_EXECUTABLE\n\t\tNAMES ${_KernelExecutables}\n\t\tHINTS ${Mathematica_HOST_ROOT_DIR}\n\t\tDOC \"Mathematica kernel executable.\"\n\t\tNO_DEFAULT_PATH NO_CMAKE_FIND_ROOT_PATH\n\t)\n\tfind_program (Mathematica_FRONTEND_EXECUTABLE\n\t\tNAMES ${_FrontEndExecutables}\n\t\tHINTS ${Mathematica_HOST_ROOT_DIR}\n\t\tDOC \"Mathematica front end executable.\"\n\t\tNO_DEFAULT_PATH NO_CMAKE_FIND_ROOT_PATH\n\t)\n\tfind_path (Mathematica_INCLUDE_DIR\n\t\tNAMES \"mdefs.h\"\n\t\tHINTS\n\t\t\t\"${Mathematica_ROOT_DIR}/SystemFiles/IncludeFiles\"\n\t\t\t\"${Mathematica_ROOT_DIR}/Contents/SystemFiles/IncludeFiles\"\n\t\t\t\"${Mathematica_ROOT_DIR}/Contents/Resources/Wolfram Player.app/Contents/SystemFiles/IncludeFiles\"\n\t\tPATH_SUFFIXES \"C\"\n\t\tDOC \"Mathematica C language definitions include directory.\"\n\t\tNO_DEFAULT_PATH NO_CMAKE_FIND_ROOT_PATH\n\t)\n\tif (Mathematica_INCLUDE_DIR)\n\t\tset (Mathematica_INCLUDE_DIRS ${Mathematica_INCLUDE_DIR})\n\telse()\n\t\tset (Mathematica_INCLUDE_DIRS \"\")\n\tendif()\n\tset (Mathematica_LIBRARIES \"\")\n\tset (Mathematica_LIBRARY_DIRS \"\")\n\tset (Mathematica_RUNTIME_LIBRARY_DIRS \"\")\n\tset (Mathematica_RUNTIME_LIBRARY_DIRS_DEBUG \"\")\nendmacro(_find_mathematica)\n\n# internal macro to init _LIBRARIES variable from given _LIBRARY variable\nmacro (_setup_libraries_var _library_var _libraries_var)\n\tif (APPLE)\n\t\t# handle universal builds under Mac OS X\n\t\t# we need to add a library for each architecture\n\t\t_get_system_IDs(_SystemIDs)\n\t\tforeach (_systemID IN LISTS _SystemIDs)\n\t\t\tif (\"${${_library_var}}\" MATCHES \"/${_systemID}/\")\n\t\t\t\tset (_primarySystemID \"${_systemID}\")\n\t\t\tendif()\n\t\tendforeach()\n\t\tif (_primarySystemID)\n\t\t\tset (${_libraries_var} \"\")\n\t\t\tforeach (_systemID IN LISTS _SystemIDs)\n\t\t\t\tstring (REPLACE \"/${_primarySystemID}/\" \"/${_systemID}/\" _library\n\t\t\t\t\t\"${${_library_var}}\")\n\t\t\t\tif (EXISTS \"${_library}\")\n\t\t\t\t\tlist (APPEND ${_libraries_var} \"${_library}\")\n\t\t\t\tendif()\n\t\t\tendforeach()\n\t\telse()\n\t\t\tset (${_libraries_var} ${${_library_var}})\n\t\tendif()\n\telse()\n\t\tset (${_libraries_var} ${${_library_var}})\n\tendif()\nendmacro()\n\n# internal macro to find Wolfram Library inside Mathematica installation\nmacro (_find_wolframlibrary)\n\tif (NOT DEFINED Mathematica_ROOT_DIR)\n\t\t_find_mathematica()\n\tendif()\n\t_get_system_IDs(_SystemIDs)\n\t_get_wolfram_runtime_library_names(_WolframRuntimeLibraryNames)\n\tif (Mathematica_DEBUG)\n\t\tmessage (STATUS \"WolframLibrary SystemID ${_SystemIDs}\")\n\t\tmessage (STATUS \"WolframRuntimeLibraryNames ${_WolframRuntimeLibraryNames}\")\n\tendif()\n\tset (_findLibraryPrefixesSave \"${CMAKE_FIND_LIBRARY_PREFIXES}\")\n\tset (_findLibrarySuffixesSave \"${CMAKE_FIND_LIBRARY_SUFFIXES}\")\n\tif (CYGWIN)\n\t\t# Wolfram RTL library names do not follow UNIX conventions under Cygwin\n\t\tset (CMAKE_FIND_LIBRARY_PREFIXES \"\")\n\t\tset (CMAKE_FIND_LIBRARY_SUFFIXES \".lib\")\n\tendif()\n\tfind_library (Mathematica_WolframLibrary_LIBRARY\n\t\tNAMES ${_WolframRuntimeLibraryNames}\n\t\tHINTS\n\t\t\t\"${Mathematica_ROOT_DIR}/SystemFiles/Libraries\"\n\t\t\t\"${Mathematica_ROOT_DIR}/Contents/SystemFiles/Libraries\"\n\t\t\t\"${Mathematica_ROOT_DIR}/Contents/Resources/Wolfram Player.app/Contents/SystemFiles/Libraries\"\n\t\tPATH_SUFFIXES ${_SystemIDs}\n\t\tDOC \"Mathematica Wolfram Runtime Library.\"\n\t\tNO_DEFAULT_PATH NO_CMAKE_FIND_ROOT_PATH\n\t)\n\tfind_path (Mathematica_WolframLibrary_INCLUDE_DIR\n\t\tNAMES \"WolframLibrary.h\" \"WolframRTL.h\"\n\t\tHINTS\n\t\t\t\"${Mathematica_ROOT_DIR}/SystemFiles/IncludeFiles\"\n\t\t\t\"${Mathematica_ROOT_DIR}/Contents/SystemFiles/IncludeFiles\"\n\t\t\t\"${Mathematica_ROOT_DIR}/Contents/Resources/Wolfram Player.app/Contents/SystemFiles/IncludeFiles\"\n\t\tPATH_SUFFIXES \"C\"\n\t\tDOC \"Mathematica WolframLibrary include directory.\"\n\t\tNO_DEFAULT_PATH NO_CMAKE_FIND_ROOT_PATH\n\t)\n\tif (Mathematica_WolframLibrary_INCLUDE_DIR)\n\t\tlist (APPEND Mathematica_INCLUDE_DIRS ${Mathematica_WolframLibrary_INCLUDE_DIR})\n\tendif()\n\tset (CMAKE_FIND_LIBRARY_PREFIXES \"${_findLibraryPrefixesSave}\")\n\tset (CMAKE_FIND_LIBRARY_SUFFIXES \"${_findLibrarySuffixesSave}\")\nendmacro()\n\n# internal macro to find MathLink SDK inside Mathematica installation\nmacro (_find_mathlink)\n\t_get_developer_kit_system_IDs(_SystemIDs)\n\t_get_host_developer_kit_system_IDs(_HostSystemIDs)\n\t_get_target_flavor(_MathLinkFlavor)\n\t_get_host_flavor(_HostMathLinkFlavor)\n\t_get_mathlink_library_names(_MathLinkLibraryNames)\n\tif (NOT DEFINED Mathematica_ROOT_DIR OR\n\t\tNOT DEFINED Mathematica_HOST_ROOT_DIR)\n\t\t_find_mathematica()\n\tendif()\n\tif (Mathematica_DEBUG)\n\t\tmessage (STATUS \"MathLink Target DeveloperKit SystemID ${_SystemIDs} ${_MathLinkFlavor}\")\n\t\tmessage (STATUS \"MathLink Host DeveloperKit SystemID ${_HostSystemIDs} ${_HostMathLinkFlavor}\")\n\t\tmessage (STATUS \"MathLink Library Names ${_MathLinkLibraryNames}\")\n\tendif()\n\tfind_path (Mathematica_MathLink_ROOT_DIR\n\t\tNAMES \"CompilerAdditions\"\n\t\tHINTS\n\t\t\t\"${Mathematica_ROOT_DIR}/SystemFiles/Links/MathLink/DeveloperKit\"\n\t\t\t\"${Mathematica_ROOT_DIR}/Contents/SystemFiles/Links/MathLink/DeveloperKit\"\n\t\t\t\"${Mathematica_ROOT_DIR}/Contents/Resources/Wolfram Player.app/Contents/SystemFiles/Links/MathLink/DeveloperKit\"\n\t\t\t\"${Mathematica_ROOT_DIR}/AddOns/MathLink/DeveloperKit\"\n\t\tPATH_SUFFIXES ${_SystemIDs}\n\t\tDOC \"MathLink target SDK root directory.\"\n\t\tNO_DEFAULT_PATH NO_CMAKE_FIND_ROOT_PATH\n\t)\n\tif (_MathLinkFlavor)\n\t\tset (_CompilerAdditions\n\t\t\t\"${Mathematica_MathLink_ROOT_DIR}/CompilerAdditions/${_MathLinkFlavor}\"\n\t\t\t\"${Mathematica_MathLink_ROOT_DIR}/CompilerAdditions\")\n\telse()\n\t\tset (_CompilerAdditions \"${Mathematica_MathLink_ROOT_DIR}/CompilerAdditions\")\n\tendif()\n\tfind_path (Mathematica_MathLink_HOST_ROOT_DIR\n\t\tNAMES \"CompilerAdditions\"\n\t\tHINTS\n\t\t\t\"${Mathematica_HOST_ROOT_DIR}/SystemFiles/Links/MathLink/DeveloperKit\"\n\t\t\t\"${Mathematica_HOST_ROOT_DIR}/Contents/SystemFiles/Links/MathLink/DeveloperKit\"\n\t\t\t\"${Mathematica_HOST_ROOT_DIR}/Contents/Resources/Wolfram Player.app/Contents/SystemFiles/Links/MathLink/DeveloperKit\"\n\t\t\t\"${Mathematica_HOST_ROOT_DIR}/AddOns/MathLink/DeveloperKit\"\n\t\tPATH_SUFFIXES ${_HostSystemIDs}\n\t\tDOC \"MathLink host SDK root directory.\"\n\t\tNO_DEFAULT_PATH NO_CMAKE_FIND_ROOT_PATH\n\t)\n\tif (_HostMathLinkFlavor)\n\t\tset (_HostCompilerAdditions\n\t\t\t\"${Mathematica_MathLink_HOST_ROOT_DIR}/CompilerAdditions/${_HostMathLinkFlavor}\"\n\t\t\t\"${Mathematica_MathLink_HOST_ROOT_DIR}/CompilerAdditions\")\n\telse()\n\t\tset (_HostCompilerAdditions \"${Mathematica_MathLink_HOST_ROOT_DIR}/CompilerAdditions\")\n\tendif()\n\tif (Mathematica_DEBUG)\n\t\tmessage (STATUS \"MathLink CompilerAdditions ${_CompilerAdditions}\")\n\t\tmessage (STATUS \"MathLink HostCompilerAdditions ${_HostCompilerAdditions}\")\n\tendif()\n\tif (APPLE)\n\t\tset (_findFrameWorkSave \"${CMAKE_FIND_FRAMEWORK}\")\n\t\tif (Mathematica_USE_STATIC_LIBRARIES)\n\t\t\tset (CMAKE_FIND_FRAMEWORK \"LAST\")\n\t\telse()\n\t\t\tset (CMAKE_FIND_FRAMEWORK \"FIRST\")\n\t\tendif()\n\tendif()\n\tfind_program (Mathematica_MathLink_MPREP_EXECUTABLE\n\t\tNAMES \"mprep\"\n\t\tHINTS ${_HostCompilerAdditions}\n\t\tPATH_SUFFIXES \"bin\"\n\t\tDOC \"MathLink template file preprocessor executable.\"\n\t\tNO_DEFAULT_PATH NO_CMAKE_FIND_ROOT_PATH\n\t)\n\tfind_library (Mathematica_MathLink_LIBRARY\n\t\tNAMES ${_MathLinkLibraryNames}\n\t\tHINTS ${_CompilerAdditions}\n\t\tPATH_SUFFIXES \"lib\"\n\t\tDOC \"MathLink library to link against.\"\n\t\tNO_DEFAULT_PATH NO_CMAKE_FIND_ROOT_PATH\n\t)\n\tfind_path (Mathematica_MathLink_INCLUDE_DIR\n\t\tNAMES \"mathlink.h\"\n\t\tHINTS ${_CompilerAdditions}\n\t\tPATH_SUFFIXES \"include\"\n\t\tDOC \"Path to the MathLink include directory.\"\n\t\tNO_DEFAULT_PATH NO_CMAKE_FIND_ROOT_PATH\n\t)\n\tif (APPLE AND DEFINED Mathematica_MathLink_FIND_VERSION_MAJOR AND IS_DIRECTORY \"${Mathematica_MathLink_LIBRARY}\")\n\t\tif (DEFINED Mathematica_MathLink_FIND_VERSION_MINOR)\n\t\t\tset (_frameworkVersionSubDir \"${Mathematica_MathLink_LIBRARY}/Versions/${Mathematica_MathLink_FIND_VERSION_MAJOR}.${Mathematica_MathLink_FIND_VERSION_MINOR}\")\n\t\telse()\n\t\t\tset (_frameworkVersionSubDir \"${Mathematica_MathLink_LIBRARY}/Versions/${Mathematica_MathLink_FIND_VERSION_MAJOR}.[0-9]+\")\n\t\tendif()\n\t\tfile (GLOB _versionedLibrary \"${_frameworkVersionSubDir}/mathlink\")\n\t\tif (_versionedLibrary)\n\t\t\t# use last if there are multiple\n\t\t\tlist (GET _versionedLibrary -1 _versionedLibrary)\n\t\t\tset (Mathematica_MathLink_LIBRARY \"${_versionedLibrary}\" CACHE FILEPATH \"MathLink library to link against.\" FORCE)\n\t\tendif()\n\t\tfile (GLOB _versionedHeaderDir \"${_frameworkVersionSubDir}/Headers\")\n\t\tif (_versionedHeaderDir)\n\t\t\tset (Mathematica_MathLink_INCLUDE_DIR \"${_versionedHeaderDir}\" CACHE FILEPATH \"Path to the MathLink include directory.\" FORCE)\n\t\tendif()\n\tendif()\n\tfind_path (Mathematica_MathLink_HOST_INCLUDE_DIR\n\t\tNAMES \"mathlink.h\"\n\t\tHINTS ${_HostCompilerAdditions}\n\t\tPATH_SUFFIXES \"include\"\n\t\tDOC \"Path to the MathLink host include directory.\"\n\t\tNO_DEFAULT_PATH NO_CMAKE_FIND_ROOT_PATH\n\t)\n\tif (APPLE)\n\t\tset (CMAKE_FIND_FRAMEWORK \"${_findFrameWorkSave}\")\n\tendif()\n\tif (Mathematica_MathLink_INCLUDE_DIR)\n\t\tlist (APPEND Mathematica_INCLUDE_DIRS ${Mathematica_MathLink_INCLUDE_DIR})\n\tendif()\nendmacro(_find_mathlink)\n\n# internal macro to find WSTP SDK inside Mathematica installation\nmacro (_find_WSTP)\n\t_get_developer_kit_system_IDs(_SystemIDs)\n\t_get_host_developer_kit_system_IDs(_HostSystemIDs)\n\t_get_target_flavor(_WSTPFlavor)\n\t_get_host_flavor(_HostWSTPFlavor)\n\t_get_WSTP_library_names(_WSTPLibraryNames)\n\tif (NOT DEFINED Mathematica_ROOT_DIR OR\n\t\tNOT DEFINED Mathematica_HOST_ROOT_DIR)\n\t\t_find_mathematica()\n\tendif()\n\tif (Mathematica_DEBUG)\n\t\tmessage (STATUS \"WSTP Target DeveloperKit SystemID ${_SystemIDs} ${_WSTPFlavor}\")\n\t\tmessage (STATUS \"WSTP Host DeveloperKit SystemID ${_HostSystemIDs} ${_HostWSTPFlavor}\")\n\t\tmessage (STATUS \"WSTP Library Names ${_WSTPLibraryNames}\")\n\tendif()\n\tfind_path (Mathematica_WSTP_ROOT_DIR\n\t\tNAMES \"CompilerAdditions\"\n\t\tHINTS\n\t\t\t\"${Mathematica_ROOT_DIR}/SystemFiles/Links/WSTP/DeveloperKit\"\n\t\t\t\"${Mathematica_ROOT_DIR}/Contents/SystemFiles/Links/WSTP/DeveloperKit\"\n\t\t\t\"${Mathematica_ROOT_DIR}/Contents/Resources/Wolfram Player.app/Contents/SystemFiles/Links/WSTP/DeveloperKit\"\n\t\tPATH_SUFFIXES ${_SystemIDs}\n\t\tDOC \"WSTP target SDK root directory.\"\n\t\tNO_DEFAULT_PATH NO_CMAKE_FIND_ROOT_PATH\n\t)\n\tif (_WSTPFlavor)\n\t\tset (_CompilerAdditions\n\t\t\t\"${Mathematica_WSTP_ROOT_DIR}/CompilerAdditions/${_WSTPFlavor}\"\n\t\t\t\"${Mathematica_WSTP_ROOT_DIR}/CompilerAdditions\")\n\telse()\n\t\tset (_CompilerAdditions \"${Mathematica_WSTP_ROOT_DIR}/CompilerAdditions\")\n\tendif()\n\tfind_path (Mathematica_WSTP_HOST_ROOT_DIR\n\t\tNAMES \"CompilerAdditions\"\n\t\tHINTS\n\t\t\t\"${Mathematica_HOST_ROOT_DIR}/SystemFiles/Links/WSTP/DeveloperKit\"\n\t\t\t\"${Mathematica_HOST_ROOT_DIR}/Contents/SystemFiles/Links/WSTP/DeveloperKit\"\n\t\t\t\"${Mathematica_HOST_ROOT_DIR}/Contents/Resources/Wolfram Player.app/Contents/SystemFiles/Links/WSTP/DeveloperKit\"\n\t\tPATH_SUFFIXES ${_HostSystemIDs}\n\t\tDOC \"WSTP host SDK root directory.\"\n\t\tNO_DEFAULT_PATH NO_CMAKE_FIND_ROOT_PATH\n\t)\n\tif (_HostWSTPFlavor)\n\t\tset (_HostCompilerAdditions\n\t\t\t\"${Mathematica_WSTP_HOST_ROOT_DIR}/CompilerAdditions/${_HostWSTPFlavor}\"\n\t\t\t\"${Mathematica_WSTP_HOST_ROOT_DIR}/CompilerAdditions\")\n\telse()\n\t\tset (_HostCompilerAdditions \"${Mathematica_WSTP_HOST_ROOT_DIR}/CompilerAdditions\")\n\tendif()\n\tif (Mathematica_DEBUG)\n\t\tmessage (STATUS \"WSTP CompilerAdditions ${_CompilerAdditions}\")\n\t\tmessage (STATUS \"WSTP HostCompilerAdditions ${_HostCompilerAdditions}\")\n\tendif()\n\tif (APPLE)\n\t\tset (_findFrameWorkSave \"${CMAKE_FIND_FRAMEWORK}\")\n\t\tif (Mathematica_USE_STATIC_LIBRARIES)\n\t\t\tset (CMAKE_FIND_FRAMEWORK \"LAST\")\n\t\telse()\n\t\t\tset (CMAKE_FIND_FRAMEWORK \"FIRST\")\n\t\tendif()\n\tendif()\n\tfind_program (Mathematica_WSTP_WSPREP_EXECUTABLE\n\t\tNAMES \"wsprep\"\n\t\tHINTS ${_HostCompilerAdditions}\n\t\tPATH_SUFFIXES \"bin\"\n\t\tDOC \"WSTP template file preprocessor executable.\"\n\t\tNO_DEFAULT_PATH NO_CMAKE_FIND_ROOT_PATH\n\t)\n\tfind_library (Mathematica_WSTP_LIBRARY\n\t\tNAMES ${_WSTPLibraryNames}\n\t\tHINTS ${_CompilerAdditions}\n\t\tPATH_SUFFIXES \"lib\"\n\t\tDOC \"WSTP library to link against.\"\n\t\tNO_DEFAULT_PATH NO_CMAKE_FIND_ROOT_PATH\n\t)\n\tfind_path (Mathematica_WSTP_INCLUDE_DIR\n\t\tNAMES \"wstp.h\"\n\t\tHINTS ${_CompilerAdditions}\n\t\tPATH_SUFFIXES \"include\"\n\t\tDOC \"Path to the WSTP include directory.\"\n\t\tNO_DEFAULT_PATH NO_CMAKE_FIND_ROOT_PATH\n\t)\n\tif (APPLE AND DEFINED Mathematica_WSTP_FIND_VERSION_MAJOR AND IS_DIRECTORY \"${Mathematica_WSTP_LIBRARY}\")\n\t\tif (DEFINED Mathematica_WSTP_FIND_VERSION_MINOR)\n\t\t\tset (_frameworkVersionSubDir \"${Mathematica_WSTP_LIBRARY}/Versions/${Mathematica_WSTP_FIND_VERSION_MAJOR}.${Mathematica_WSTP_FIND_VERSION_MINOR}\")\n\t\telse()\n\t\t\tset (_frameworkVersionSubDir \"${Mathematica_WSTP_LIBRARY}/Versions/${Mathematica_WSTP_FIND_VERSION_MAJOR}.[0-9]+\")\n\t\tendif()\n\t\tfile (GLOB _versionedLibrary \"${_frameworkVersionSubDir}/wstp\")\n\t\tif (_versionedLibrary)\n\t\t\t# use last if there are multiple\n\t\t\tlist (GET _versionedLibrary -1 _versionedLibrary)\n\t\t\tset (Mathematica_WSTP_LIBRARY \"${_versionedLibrary}\" CACHE FILEPATH \"WSTP library to link against.\" FORCE)\n\t\tendif()\n\t\tfile (GLOB _versionedHeaderDir \"${_frameworkVersionSubDir}/Headers\")\n\t\tif (_versionedHeaderDir)\n\t\t\tset (Mathematica_WSTP_INCLUDE_DIR \"${_versionedHeaderDir}\" CACHE FILEPATH \"Path to the WSTP include directory.\" FORCE)\n\t\tendif()\n\tendif()\n\tfind_path (Mathematica_WSTP_HOST_INCLUDE_DIR\n\t\tNAMES \"wstp.h\"\n\t\tHINTS ${_HostCompilerAdditions}\n\t\tPATH_SUFFIXES \"include\"\n\t\tDOC \"Path to the WSTP host include directory.\"\n\t\tNO_DEFAULT_PATH NO_CMAKE_FIND_ROOT_PATH\n\t)\n\tif (APPLE)\n\t\tset (CMAKE_FIND_FRAMEWORK \"${_findFrameWorkSave}\")\n\tendif()\n\tif (Mathematica_WSTP_INCLUDE_DIR)\n\t\tlist (APPEND Mathematica_INCLUDE_DIRS ${Mathematica_WSTP_INCLUDE_DIR})\n\tendif()\nendmacro(_find_WSTP)\n\n# internal macro to find J/Link SDK inside Mathematica installation\nmacro (_find_jlink)\n\tif (NOT DEFINED Mathematica_ROOT_DIR)\n\t\t_find_mathematica()\n\tendif()\n\t_get_system_IDs(_SystemIDs)\n\t_get_host_system_IDs(_HostSystemIDs)\n\t_get_jlink_java_name(_JLinkJavaNames)\n\tif (Mathematica_DEBUG)\n\t\tmessage (STATUS \"J/Link Target SystemID ${_SystemIDs}\")\n\t\tmessage (STATUS \"J/Link Host SystemID ${_HostSystemIDs}\")\n\t\tmessage (STATUS \"JLinkJavaName ${_JLinkJavaNames}\")\n\tendif()\n\tfind_path (Mathematica_JLink_PACKAGE_DIR\n\t\tNAMES \"JLink.jar\"\n\t\tHINTS\n\t\t\t\"${Mathematica_ROOT_DIR}/SystemFiles/Links/JLink\"\n\t\t\t\"${Mathematica_ROOT_DIR}/Contents/SystemFiles/Links/JLink\"\n\t\t\t\"${Mathematica_ROOT_DIR}/Contents/Resources/Wolfram Player.app/Contents/SystemFiles/Links/JLink\"\n\t\t\t\"${Mathematica_ROOT_DIR}/AddOns/JLink\"\n\t\tDOC \"J/Link SDK root directory.\"\n\t\tNO_DEFAULT_PATH NO_CMAKE_FIND_ROOT_PATH\n\t)\n\tif (EXISTS \"${Mathematica_JLink_PACKAGE_DIR}\")\n\t\tset (Mathematica_JLink_JAR_FILE \"${Mathematica_JLink_PACKAGE_DIR}/JLink.jar\")\n\telse()\n\t\tset (Mathematica_JLink_JAR_FILE \"Mathematica_JLink_JAR_FILE-NOTFOUND\")\n\tendif()\n\tset (_findLibraryPrefixesSave \"${CMAKE_FIND_LIBRARY_PREFIXES}\")\n\tset (_findLibrarySuffixesSave \"${CMAKE_FIND_LIBRARY_SUFFIXES}\")\n\tif (APPLE)\n\t\tset (CMAKE_FIND_LIBRARY_PREFIXES \"lib\")\n\t\tset (CMAKE_FIND_LIBRARY_SUFFIXES \".jnilib\")\n\telseif (WIN32)\n\t\tset (CMAKE_FIND_LIBRARY_PREFIXES \"\")\n\t\tset (CMAKE_FIND_LIBRARY_SUFFIXES \".dll\")\n\tendif()\n\tfind_library (Mathematica_JLink_RUNTIME_LIBRARY\n\t\tNAMES \"JLinkNativeLibrary\"\n\t\tHINTS \"${Mathematica_JLink_PACKAGE_DIR}/SystemFiles/Libraries\"\n\t\tPATHS ENV JLINK_LIB_DIR\n\t\tPATH_SUFFIXES ${_SystemIDs}\n\t\tDOC \"J/Link native library.\"\n\t\tNO_DEFAULT_PATH NO_CMAKE_FIND_ROOT_PATH\n\t)\n\tset (CMAKE_FIND_LIBRARY_PREFIXES \"${_findLibraryPrefixesSave}\")\n\tset (CMAKE_FIND_LIBRARY_SUFFIXES \"${_findLibrarySuffixesSave}\")\n\tif (CMAKE_HOST_APPLE)\n\t\tif (EXISTS \"${Mathematica_HOST_ROOT_DIR}/Contents/SystemFiles/Java\")\n\t\t\tset (_mmaJavaHome \"${Mathematica_HOST_ROOT_DIR}/Contents/SystemFiles/Java\")\n\t\telseif (EXISTS \"${Mathematica_HOST_ROOT_DIR}/Contents/Resources/Wolfram Player.app/Contents/SystemFiles/Java\")\n\t\t\tset (_mmaJavaHome \"${Mathematica_HOST_ROOT_DIR}/Contents/Resources/Wolfram Player.app/Contents/SystemFiles/Java\")\n\t\telse()\n\t\t\t# OS X versions of Mathematica earlier than 10 did not have a JVM bundled\n\t\t\t# but used the Java JVM pre-installed on system\n\t\t\tset (_mmaJavaHome \"${Mathematica_HOST_ROOT_DIR}/SystemFiles/Java\")\n\t\t\tif (DEFINED Mathematica_VERSION)\n\t\t\t\tif (\"${Mathematica_VERSION}\" VERSION_LESS \"10.0\")\n\t\t\t\t\t# use java_home to find path to JVM installed on system\n\t\t\t\t\tfind_program(Mathematica_JAVA_HOME_EXECUTABLE \"java_home\" PATHS \"/usr/libexec/\")\n\t\t\t\t\tmark_as_advanced(Mathematica_JAVA_HOME_EXECUTABLE)\n\t\t\t\t\tif (Mathematica_JAVA_HOME_EXECUTABLE)\n\t\t\t\t\t\texecute_process(\n\t\t\t\t\t\t\tCOMMAND \"${Mathematica_JAVA_HOME_EXECUTABLE}\" \"--version\" \"1.6\"\n\t\t\t\t\t\t\tTIMEOUT 10 OUTPUT_VARIABLE _mmaJavaHome ERROR_QUIET OUTPUT_STRIP_TRAILING_WHITESPACE)\n\t\t\t\t\tendif()\n\t\t\t\tendif()\n\t\t\tendif()\n\t\tendif()\n\telse()\n\t\tset (_mmaJavaHome \"${Mathematica_HOST_ROOT_DIR}/SystemFiles/Java\")\n\tendif()\n\tfind_program (Mathematica_JLink_JAVA_EXECUTABLE\n\t\tNAMES \"bin/${_JLinkJavaNames}\"\n\t\tHINTS \"${_mmaJavaHome}\"\n\t\tPATH_SUFFIXES ${_HostSystemIDs}\n\t\tDOC \"J/Link Java launcher.\"\n\t\tNO_DEFAULT_PATH NO_CMAKE_FIND_ROOT_PATH\n\t)\n\tfind_path (Mathematica_JLink_JAVA_HOME\n\t\tNAMES \"bin/${_JLinkJavaNames}\"\n\t\tHINTS \"${_mmaJavaHome}\"\n\t\tPATH_SUFFIXES ${_HostSystemIDs}\n\t\tDOC \"J/Link Java home directory.\"\n\t\tNO_DEFAULT_PATH NO_CMAKE_FIND_ROOT_PATH\n\t)\nendmacro()\n\n# internal macro to find MUnit package\nmacro (_find_munit_package)\n\tif (Mathematica_RUN_KERNEL_ON_CONFIGURE AND COMMAND Mathematica_FIND_PACKAGE)\n\t\tMathematica_FIND_PACKAGE(Mathematica_MUnit_PACKAGE_FILE \"MUnit`MUnit`\")\n\t\t# determine enclosing MUnit package directory\n\t\tif (Mathematica_MUnit_PACKAGE_FILE)\n\t\t\tMathematica_GET_PACKAGE_DIR(Mathematica_MUnit_PACKAGE_DIR \"${Mathematica_MUnit_PACKAGE_FILE}\")\n\t\tendif()\n\tendif()\n\tif (NOT DEFINED Mathematica_MUnit_PACKAGE_DIR)\n\t\tset (Mathematica_MUnit_PACKAGE_DIR \"Mathematica_MUnit_PACKAGE_DIR-NOTFOUND\")\n\tendif()\nendmacro()\n\n# internal macro to find LibaryLink package\nmacro (_find_librarylink_package)\n\tif (Mathematica_RUN_KERNEL_ON_CONFIGURE AND COMMAND Mathematica_FIND_PACKAGE)\n\t\tMathematica_FIND_PACKAGE(Mathematica_LibraryLink_PACKAGE_FILE \"LibraryLink`LibraryLink`\")\n\t\t# determine enclosing LibraryLink package directory\n\t\tif (Mathematica_LibraryLink_PACKAGE_FILE)\n\t\t\tMathematica_GET_PACKAGE_DIR(Mathematica_LibraryLink_PACKAGE_DIR \"${Mathematica_LibraryLink_PACKAGE_FILE}\")\n\t\tendif()\n\tendif()\n\tif (NOT DEFINED Mathematica_LibraryLink_PACKAGE_DIR)\n\t\tset (Mathematica_LibraryLink_PACKAGE_DIR \"Mathematica_LibraryLink_PACKAGE_DIR-NOTFOUND\")\n\tendif()\nendmacro()\n\n# internal helper macro to setup version related variables from existing _VERSION variable\nmacro (_setup_package_version_variables _packageName)\n\tif (DEFINED ${_packageName}_VERSION)\n\t\tstring (REGEX MATCHALL \"[0-9]+\" _versionComponents \"${${_packageName}_VERSION}\")\n\t\tlist (LENGTH _versionComponents _len)\n\t\tif (_len GREATER 0)\n\t\t\tlist(GET _versionComponents 0 ${_packageName}_VERSION_MAJOR)\n\t\tendif()\n\t\tif (_len GREATER 1)\n\t\t\tlist(GET _versionComponents 1 ${_packageName}_VERSION_MINOR)\n\t\tendif()\n\t\tif (_len GREATER 2)\n\t\t\tlist(GET _versionComponents 2 ${_packageName}_VERSION_PATCH)\n\t\tendif()\n\t\tif (_len GREATER 3)\n\t\t\tlist(GET _versionComponents 3 ${_packageName}_VERSION_TWEAK)\n\t\tendif()\n\t\tset (${_packageName}_VERSION_COUNT ${_len})\n\t\tif (NOT DEFINED ${_packageName}_VERSION_STRING)\n\t\t\tset (${_packageName}_VERSION_STRING ${${_packageName}_VERSION})\n\t\tendif()\n\tendif()\nendmacro()\n\n# internal macro to setup Mathematica version related variables\nmacro (_setup_mathematica_version_variables)\n\tif (NOT Mathematica_VERSION)\n\t\tset (_versionLine \"\")\n\t\tif (DEFINED Mathematica_ROOT_DIR)\n\t\t\tif (Mathematica_ROOT_DIR AND EXISTS \"${Mathematica_ROOT_DIR}/.VersionID\")\n\t\t\t\t# parse version number from hidden VersionID and PatchLevel files\n\t\t\t\tfile (STRINGS \"${Mathematica_ROOT_DIR}/.VersionID\" _versionLine)\n\t\t\t\tif (EXISTS \"${Mathematica_ROOT_DIR}/.PatchLevel\")\n\t\t\t\t\tfile (STRINGS \"${Mathematica_ROOT_DIR}/.PatchLevel\" _patchLevel)\n\t\t\t\t\tif (_versionLine MATCHES \".+\" AND _patchLevel MATCHES \".+\")\n\t\t\t\t\t\tset (_versionLine \"${_versionLine}.${_patchLevel}\")\n\t\t\t\t\tendif()\n\t\t\t\tendif()\n\t\t\telseif (CMAKE_HOST_APPLE AND Mathematica_ROOT_DIR AND\n\t\t\t\tEXISTS \"${Mathematica_ROOT_DIR}/Contents/Info.plist\")\n\t\t\t\texecute_process(\n\t\t\t\t\tCOMMAND \"grep\" \"--after-context=1\" \"CFBundleShortVersionString\"\n\t\t\t\t\t\"${Mathematica_ROOT_DIR}/Contents/Info.plist\"\n\t\t\t\t\tTIMEOUT 10 OUTPUT_VARIABLE _versionStr ERROR_QUIET)\n\t\t\t\tif (_versionStr MATCHES \"<string>([0-9]+\\\\.[0-9]+\\\\.[0-9]+)\")\n\t\t\t\t\tset (_versionLine \"${CMAKE_MATCH_1}\")\n\t\t\t\telse()\n\t\t\t\t\tset (_versionLine \"\")\n\t\t\t\tendif()\n\t\t\tendif()\n\t\tendif()\n\t\tif (NOT _versionLine AND DEFINED Mathematica_MathLink_INCLUDE_DIR)\n\t\t\tif (Mathematica_MathLink_INCLUDE_DIR AND\n\t\t\t\tEXISTS \"${Mathematica_MathLink_INCLUDE_DIR}/mathlink.h\")\n\t\t\t\t# parse version number from mathlink.h\n\t\t\t\tfile (STRINGS \"${Mathematica_MathLink_INCLUDE_DIR}/mathlink.h\" _versionLine\n\t\t\t\t\tREGEX \".*define.*MLMATHVERSION.*\")\n\t\t\tendif()\n\t\tendif()\n\t\tif (NOT _versionLine AND DEFINED Mathematica_MathLink_HOST_INCLUDE_DIR)\n\t\t\tif (Mathematica_MathLink_HOST_INCLUDE_DIR AND\n\t\t\t\tEXISTS \"${Mathematica_MathLink_HOST_INCLUDE_DIR}/mathlink.h\")\n\t\t\t\t# parse version number from mathlink.h\n\t\t\t\tfile (STRINGS \"${Mathematica_MathLink_HOST_INCLUDE_DIR}/mathlink.h\" _versionLine\n\t\t\t\t\tREGEX \".*define.*MLMATHVERSION.*\")\n\t\t\tendif()\n\t\tendif()\n\t\tif (_versionLine MATCHES \".+\")\n\t\t\tstring (REGEX REPLACE \"[^0-9]*([0-9]+(\\\\.[0-9]+)*).*\" \"\\\\1\" _versionStr \"${_versionLine}\")\n\t\t\tif (DEFINED _versionStr)\n\t\t\t\tset (Mathematica_VERSION \"${_versionStr}\"\n\t\t\t\t\tCACHE INTERNAL \"Mathematica version.\" FORCE)\n\t\t\tendif()\n\t\tendif()\n\tendif()\n\t_setup_package_version_variables(Mathematica)\nendmacro()\n\n# internal macro to setup WolframLibrary version related variables\nmacro (_setup_wolframlibrary_version_variables)\n\tif (NOT Mathematica_WolframLibrary_VERSION AND Mathematica_WolframLibrary_INCLUDE_DIR)\n\t\tset (_file \"${Mathematica_WolframLibrary_INCLUDE_DIR}/WolframLibrary.h\")\n\t\tif (EXISTS \"${_file}\")\n\t\t\tfile (STRINGS \"${_file}\" _versionLine REGEX \".*define.*WolframLibraryVersion.*\")\n\t\t\tif (_versionLine)\n\t\t\t\tstring (REGEX REPLACE \"[^0-9]*([0-9]+(\\\\.[0-9]+)*).*\" \"\\\\1\" _versionStr \"${_versionLine}\")\n\t\t\t\tif (DEFINED _versionStr)\n\t\t\t\t\tset (Mathematica_WolframLibrary_VERSION \"${_versionStr}\"\n\t\t\t\t\t\tCACHE INTERNAL \"WolframLibrary version.\" FORCE)\n\t\t\t\tendif()\n\t\t\tendif()\n\t\tendif()\n\tendif()\n\t_setup_package_version_variables(Mathematica_WolframLibrary)\nendmacro()\n\n# internal macro to setup MathLink version related variables\nmacro (_setup_mathlink_version_variables)\n\tif (NOT Mathematica_MathLink_VERSION AND Mathematica_MathLink_INCLUDE_DIR)\n\t\tset (_file \"${Mathematica_MathLink_INCLUDE_DIR}/mathlink.h\")\n\t\tif (EXISTS \"${_file}\")\n\t\t\tif (DEFINED Mathematica_MathLink_FIND_VERSION_MAJOR)\n\t\t\t\tset (_mlInterface \"${Mathematica_MathLink_FIND_VERSION_MAJOR}\")\n\t\t\telse()\n\t\t\t\tfile (STRINGS \"${_file}\" _mlInterfaceLine REGEX \".*define.*MLINTERFACE.*\")\n\t\t\t\tstring (REGEX REPLACE \"[^0-9]*([0-9]+).*\" \"\\\\1\" _mlInterface\n\t\t\t\t\t${_mlInterfaceLine})\n\t\t\tendif()\n\t\t\tfile (STRINGS \"${_file}\" _mlRevisionLine REGEX \".*define.*MLREVISION.*\")\n\t\t\tstring (REGEX REPLACE \"[^0-9]*([0-9]+).*\" \"\\\\1\" _mlRevision\n\t\t\t\t${_mlRevisionLine})\n\t\t\tif (DEFINED _mlInterface AND DEFINED _mlRevision)\n\t\t\t\tset (_versionStr \"${_mlInterface}.${_mlRevision}\")\n\t\t\t\tset (Mathematica_MathLink_VERSION \"${_versionStr}\"\n\t\t\t\t\tCACHE INTERNAL \"MathLink version.\" FORCE)\n\t\t\tendif()\n\t\tendif()\n\tendif()\n\t_setup_package_version_variables(Mathematica_MathLink)\nendmacro()\n\n# internal macro to setup WSTP version related variables\nmacro (_setup_WSTP_version_variables)\n\tif (NOT Mathematica_WSTP_VERSION AND Mathematica_WSTP_INCLUDE_DIR)\n\t\tset (_file \"${Mathematica_WSTP_INCLUDE_DIR}/wstp.h\")\n\t\tif (EXISTS \"${_file}\")\n\t\t\tif (DEFINED Mathematica_WSTP_FIND_VERSION_MAJOR)\n\t\t\t\tset (_wstpInterface \"${Mathematica_WSTP_FIND_VERSION_MAJOR}\")\n\t\t\telse()\n\t\t\t\tfile (STRINGS \"${_file}\" _wstpInterfaceLine REGEX \".*define.*(WS|ML)INTERFACE.*\")\n\t\t\t\tif (_wstpInterfaceLine)\n\t\t\t\t\tstring (REGEX REPLACE \"[^0-9]*([0-9]+).*\" \"\\\\1\" _wstpInterface\n\t\t\t\t\t\t${_wstpInterfaceLine})\n\t\t\t\tendif()\n\t\t\tendif()\n\t\t\tfile (STRINGS \"${_file}\" _wstpRevisionLine REGEX \".*define.*(WS|ML)REVISION.*\")\n\t\t\tstring (REGEX REPLACE \"[^0-9]*([0-9]+).*\" \"\\\\1\" _wstpRevision\n\t\t\t\t${_wstpRevisionLine})\n\t\t\tif (DEFINED _wstpInterface AND DEFINED _wstpRevision)\n\t\t\t\tset (_versionStr \"${_wstpInterface}.${_wstpRevision}\")\n\t\t\t\tset (Mathematica_WSTP_VERSION \"${_versionStr}\"\n\t\t\t\t\tCACHE INTERNAL \"WSTP version.\" FORCE)\n\t\t\tendif()\n\t\tendif()\n\tendif()\n\t_setup_package_version_variables(Mathematica_WSTP)\nendmacro()\n\n# internal macro to setup J/Link version related variables\nmacro (_setup_jlink_version_variables)\n\tif (NOT Mathematica_JLink_VERSION AND Mathematica_JLink_PACKAGE_DIR)\n\t\tset (_file \"${Mathematica_JLink_PACKAGE_DIR}/Source/Java/com/wolfram/jlink/KernelLink.java\")\n\t\tif (EXISTS \"${_file}\")\n\t\t\tfile (STRINGS \"${_file}\" _versionLine REGEX \".*String.*VERSION.*\")\n\t\t\tstring (REGEX REPLACE \"[^0-9]*([0-9]+(\\\\.[0-9]+)*).*\" \"\\\\1\" _versionStr \"${_versionLine}\")\n\t\t\tif (DEFINED _versionStr)\n\t\t\t\tset (Mathematica_JLink_VERSION \"${_versionStr}\"\n\t\t\t\t\tCACHE INTERNAL \"J/Link version.\" FORCE)\n\t\t\tendif()\n\t\tendif()\n\tendif()\n\t_setup_package_version_variables(Mathematica_JLink)\nendmacro()\n\n# internal macro to setup MUnit version related variables\nmacro (_setup_munit_package_version_variables)\n\tif (NOT Mathematica_MUnit_VERSION AND Mathematica_MUnit_PACKAGE_FILE)\n\t\tset (_file \"${Mathematica_MUnit_PACKAGE_FILE}\")\n\t\tif (EXISTS \"${_file}\")\n\t\t\tfile (STRINGS \"${_file}\" _mUnitVersionNumberLine REGEX \".*`\\\\$VersionNumber.*\")\n\t\t\tfile (STRINGS \"${_file}\" _mUnitReleaseNumberLine REGEX \".*`\\\\$ReleaseNumber.*\")\n\t\t\tfile (STRINGS \"${_file}\" _mUnitVersionLine REGEX \".*`\\\\$Version.*\")\n\t\t\tstring (REGEX REPLACE \"[^0-9]*([0-9]+\\\\.[0-9]+).*\" \"\\\\1\" _mUnitVersionNumber\n\t\t\t\t${_mUnitVersionNumberLine})\n\t\t\tstring (REGEX REPLACE \"[^0-9]*([0-9]+).*\" \"\\\\1\" _mUnitReleaseNumber\n\t\t\t\t${_mUnitReleaseNumberLine})\n\t\t\tif (DEFINED _mUnitVersionNumber AND DEFINED _mUnitReleaseNumber)\n\t\t\t\tset (_versionStr \"${_mUnitVersionNumber}.${_mUnitReleaseNumber}\")\n\t\t\t\tset (Mathematica_MUnit_VERSION \"${_versionStr}\"\n\t\t\t\t\tCACHE INTERNAL \"MUnit version.\" FORCE)\n\t\t\tendif()\n\t\tendif()\n\tendif()\n\t_setup_package_version_variables(Mathematica_MUnit)\nendmacro()\n\n# internal macro to setup WolframLibrary library related variables\nmacro (_setup_wolframlibrary_library_variables)\n\tif (Mathematica_WolframLibrary_LIBRARY)\n\t\tset (Mathematica_WolframLibrary_RUNTIME_LIBRARY_DIRS \"\")\n\t\tset (Mathematica_WolframLibrary_RUNTIME_LIBRARY_DIRS_DEBUG \"\")\n\t\t_setup_libraries_var(Mathematica_WolframLibrary_LIBRARY Mathematica_WolframLibrary_LIBRARIES)\n\t\tforeach (_library ${Mathematica_WolframLibrary_LIBRARIES})\n\t\t\tget_filename_component (_libraryDir ${_library} DIRECTORY)\n\t\t\tlist (APPEND Mathematica_LIBRARY_DIRS ${_libraryDir})\n\t\t\tif (NOT Mathematica_USE_STATIC_LIBRARIES)\n\t\t\t\tlist (APPEND Mathematica_WolframLibrary_RUNTIME_LIBRARY_DIRS ${_libraryDir})\n\t\t\t\tlist (APPEND Mathematica_WolframLibrary_RUNTIME_LIBRARY_DIRS_DEBUG ${_libraryDir})\n\t\t\t\tlist (APPEND Mathematica_RUNTIME_LIBRARY_DIRS ${_libraryDir})\n\t\t\t\tlist (APPEND Mathematica_RUNTIME_LIBRARY_DIRS_DEBUG ${_libraryDir})\n\t\t\tendif()\n\t\tendforeach()\n\t\tif (NOT APPLE)\n\t\t\t# kernel binaries dir on Windows and Linux contains additional runtime libraries (e.g., Intel MKL)\n\t\t\tforeach (_systemID ${Mathematica_SYSTEM_IDS})\n\t\t\t\tset (_kernelBinariesDir \"${Mathematica_ROOT_DIR}/SystemFiles/Kernel/Binaries/${_systemID}\")\n\t\t\t\tif (EXISTS \"${_kernelBinariesDir}\")\n\t\t\t\t\tlist (APPEND Mathematica_LIBRARY_DIRS ${_kernelBinariesDir})\n\t\t\t\t\tif (NOT Mathematica_USE_STATIC_LIBRARIES)\n\t\t\t\t\t\tlist (APPEND Mathematica_WolframLibrary_RUNTIME_LIBRARY_DIRS \"${_kernelBinariesDir}\")\n\t\t\t\t\t\tlist (APPEND Mathematica_WolframLibrary_RUNTIME_LIBRARY_DIRS_DEBUG \"${_kernelBinariesDir}\")\n\t\t\t\t\t\tlist (APPEND Mathematica_RUNTIME_LIBRARY_DIRS \"${_kernelBinariesDir}\")\n\t\t\t\t\t\tlist (APPEND Mathematica_RUNTIME_LIBRARY_DIRS_DEBUG \"${_kernelBinariesDir}\")\n\t\t\t\t\tendif()\n\t\t\t\tendif()\n\t\t\tendforeach()\n\t\tendif()\n\t\t_append_wolframlibrary_needed_system_libraries(Mathematica_WolframLibrary_LIBRARIES)\n\t\tlist (REMOVE_DUPLICATES Mathematica_WolframLibrary_RUNTIME_LIBRARY_DIRS)\n\t\tlist (REMOVE_DUPLICATES Mathematica_WolframLibrary_RUNTIME_LIBRARY_DIRS_DEBUG)\n\t\tlist (APPEND Mathematica_LIBRARIES ${Mathematica_WolframLibrary_LIBRARIES})\n\tendif()\nendmacro()\n\n# internal macro to setup MathLink library related variables\nmacro (_setup_mathlink_library_variables)\n\tif (Mathematica_MathLink_LIBRARY)\n\t\t_setup_libraries_var(Mathematica_MathLink_LIBRARY Mathematica_MathLink_LIBRARIES)\n\t\tif (DEFINED Mathematica_MathLink_VERSION_MAJOR)\n\t\t\tset (Mathematica_MathLink_DEFINITIONS \"-DMLINTERFACE=${Mathematica_MathLink_VERSION_MAJOR}\")\n\t\telseif (DEFINED Mathematica_MathLink_FIND_VERSION_MAJOR)\n\t\t\tset (Mathematica_MathLink_DEFINITIONS \"-DMLINTERFACE=${Mathematica_MathLink_FIND_VERSION_MAJOR}\")\n\t\telse()\n\t\t\tset (Mathematica_MathLink_DEFINITIONS \"\")\n\t\tendif()\n\t\tset (Mathematica_MathLink_RUNTIME_LIBRARY_DIRS \"\")\n\t\tset (Mathematica_MathLink_RUNTIME_LIBRARY_DIRS_DEBUG \"\")\n\t\tif (APPLE)\n\t\t\tset (Mathematica_MathLink_LINKER_FLAGS \"\")\n\t\t\tforeach (_library ${Mathematica_MathLink_LIBRARIES})\n\t\t\t\tget_filename_component (_libraryDir ${_library} DIRECTORY)\n\t\t\t\tlist (APPEND Mathematica_LIBRARY_DIRS ${_libraryDir})\n\t\t\tendforeach()\n\t\t\t# for OS X we have to add the MathLink CompilerAdditions directory which contains the MathLink framework\n\t\t\t_get_target_flavor(_MathLinkFlavor)\n\t\t\tif (_MathLinkFlavor)\n\t\t\t\tset (_CompilerAdditions \"${Mathematica_MathLink_ROOT_DIR}/CompilerAdditions/${_MathLinkFlavor}\")\n\t\t\telse()\n\t\t\t\tset (_CompilerAdditions \"${Mathematica_MathLink_ROOT_DIR}/CompilerAdditions\")\n\t\t\tendif()\n\t\t\tif (IS_DIRECTORY \"${_CompilerAdditions}\")\n\t\t\t\tlist (APPEND Mathematica_MathLink_RUNTIME_LIBRARY_DIRS \"${_CompilerAdditions}\")\n\t\t\t\tlist (APPEND Mathematica_MathLink_RUNTIME_LIBRARY_DIRS_DEBUG \"${_CompilerAdditions}\")\n\t\t\t\tlist (APPEND Mathematica_RUNTIME_LIBRARY_DIRS \"${_CompilerAdditions}\")\n\t\t\t\tlist (APPEND Mathematica_RUNTIME_LIBRARY_DIRS_DEBUG \"${_CompilerAdditions}\")\n\t\t\tendif()\n\t\telseif (UNIX)\n\t\t\tset (Mathematica_MathLink_LINKER_FLAGS \"\")\n\t\t\tforeach (_library ${Mathematica_MathLink_LIBRARIES})\n\t\t\t\tget_filename_component (_libraryDir ${_library} DIRECTORY)\n\t\t\t\tlist (APPEND Mathematica_LIBRARY_DIRS ${_libraryDir})\n\t\t\t\tif (NOT Mathematica_USE_STATIC_LIBRARIES)\n\t\t\t\t\tlist (APPEND Mathematica_MathLink_RUNTIME_LIBRARY_DIRS ${_libraryDir})\n\t\t\t\t\tlist (APPEND Mathematica_MathLink_RUNTIME_LIBRARY_DIRS_DEBUG ${_libraryDir})\n\t\t\t\t\tlist (APPEND Mathematica_RUNTIME_LIBRARY_DIRS ${_libraryDir})\n\t\t\t\t\tlist (APPEND Mathematica_RUNTIME_LIBRARY_DIRS_DEBUG ${_libraryDir})\n\t\t\t\tendif()\n\t\t\tendforeach()\n\t\telseif (WIN32)\n\t\t\tset (Mathematica_MathLink_LINKER_FLAGS \"\")\n\t\t\tforeach (_library ${Mathematica_MathLink_LIBRARIES})\n\t\t\t\tget_filename_component (_libraryDir ${_library} DIRECTORY)\n\t\t\t\tlist (APPEND Mathematica_LIBRARY_DIRS ${_libraryDir})\n\t\t\tendforeach()\n\t\t\t# Windows MathLink SDK has runtime DLLs in a separate directory\n\t\t\tset (_runtimeDir \"${Mathematica_MathLink_ROOT_DIR}/SystemAdditions\")\n\t\t\tif (IS_DIRECTORY \"${_runtimeDir}\")\n\t\t\t\tlist (APPEND Mathematica_MathLink_RUNTIME_LIBRARY_DIRS \"${_runtimeDir}\")\n\t\t\t\tlist (APPEND Mathematica_RUNTIME_LIBRARY_DIRS \"${_runtimeDir}\")\n\t\t\tendif()\n\t\t\t# Windows MathLink SDK also ships with debug DLLs in AlternativeComponents\n\t\t\tset (_runtimeDir \"${Mathematica_MathLink_ROOT_DIR}/AlternativeComponents/DebugLibraries\")\n\t\t\tif (IS_DIRECTORY \"${_runtimeDir}\")\n\t\t\t\tlist (APPEND Mathematica_MathLink_RUNTIME_LIBRARY_DIRS_DEBUG \"${_runtimeDir}\")\n\t\t\t\tlist (APPEND Mathematica_RUNTIME_LIBRARY_DIRS_DEBUG \"${_runtimeDir}\")\n\t\t\tendif()\n\t\tendif()\n\t\t_append_mathlink_needed_system_libraries(Mathematica_MathLink_LIBRARIES)\n\t\tlist (REMOVE_DUPLICATES Mathematica_MathLink_RUNTIME_LIBRARY_DIRS)\n\t\tlist (REMOVE_DUPLICATES Mathematica_MathLink_RUNTIME_LIBRARY_DIRS_DEBUG)\n\t\tlist (APPEND Mathematica_LIBRARIES ${Mathematica_MathLink_LIBRARIES})\n\tendif()\nendmacro()\n\n# internal macro to setup WSTP library related variables\nmacro (_setup_WSTP_library_variables)\n\tif (Mathematica_WSTP_LIBRARY)\n\t\t_setup_libraries_var(Mathematica_WSTP_LIBRARY Mathematica_WSTP_LIBRARIES)\n\t\tif (DEFINED Mathematica_WSTP_VERSION_MAJOR)\n\t\t\tset (Mathematica_WSTP_DEFINITIONS \"-DWSINTERFACE=${Mathematica_WSTP_VERSION_MAJOR}\")\n\t\telseif (DEFINED Mathematica_WSTP_FIND_VERSION_MAJOR)\n\t\t\tset (Mathematica_WSTP_DEFINITIONS \"-DWSINTERFACE=${Mathematica_WSTP_FIND_VERSION_MAJOR}\")\n\t\telse()\n\t\t\tset (Mathematica_WSTP_DEFINITIONS \"\")\n\t\tendif()\n\t\tset (Mathematica_WSTP_RUNTIME_LIBRARY_DIRS \"\")\n\t\tset (Mathematica_WSTP_RUNTIME_LIBRARY_DIRS_DEBUG \"\")\n\t\tif (APPLE)\n\t\t\tset (Mathematica_WSTP_LINKER_FLAGS \"\")\n\t\t\tforeach (_library ${Mathematica_WSTP_LIBRARIES})\n\t\t\t\tget_filename_component (_libraryDir ${_library} DIRECTORY)\n\t\t\t\tlist (APPEND Mathematica_LIBRARY_DIRS ${_libraryDir})\n\t\t\tendforeach()\n\t\t\t# for OS X we have to add the WSTP CompilerAdditions directory which contains the WSTP framework\n\t\t\t_get_target_flavor(_WSTPFlavor)\n\t\t\tif (_WSTPFlavor)\n\t\t\t\tset (_CompilerAdditions \"${Mathematica_WSTP_ROOT_DIR}/CompilerAdditions/${_WSTPFlavor}\")\n\t\t\telse()\n\t\t\t\tset (_CompilerAdditions \"${Mathematica_WSTP_ROOT_DIR}/CompilerAdditions\")\n\t\t\tendif()\n\t\t\tif (IS_DIRECTORY \"${_CompilerAdditions}\")\n\t\t\t\tlist (APPEND Mathematica_WSTP_RUNTIME_LIBRARY_DIRS ${_libraryDir})\n\t\t\t\tlist (APPEND Mathematica_WSTP_RUNTIME_LIBRARY_DIRS_DEBUG ${_libraryDir})\n\t\t\t\tlist (APPEND Mathematica_RUNTIME_LIBRARY_DIRS \"${_CompilerAdditions}\")\n\t\t\t\tlist (APPEND Mathematica_RUNTIME_LIBRARY_DIRS_DEBUG \"${_CompilerAdditions}\")\n\t\t\tendif()\n\t\telseif (UNIX)\n\t\t\tset (Mathematica_WSTP_LINKER_FLAGS \"\")\n\t\t\tforeach (_library ${Mathematica_WSTP_LIBRARIES})\n\t\t\t\tget_filename_component (_libraryDir ${_library} DIRECTORY)\n\t\t\t\tlist (APPEND Mathematica_LIBRARY_DIRS ${_libraryDir})\n\t\t\t\tif (NOT Mathematica_USE_STATIC_LIBRARIES)\n\t\t\t\t\tlist (APPEND Mathematica_WSTP_RUNTIME_LIBRARY_DIRS ${_libraryDir})\n\t\t\t\t\tlist (APPEND MathematicaWSTP_RUNTIME_LIBRARY_DIRS_DEBUG ${_libraryDir})\n\t\t\t\t\tlist (APPEND Mathematica_RUNTIME_LIBRARY_DIRS ${_libraryDir})\n\t\t\t\t\tlist (APPEND Mathematica_RUNTIME_LIBRARY_DIRS_DEBUG ${_libraryDir})\n\t\t\t\tendif()\n\t\t\tendforeach()\n\t\telseif (WIN32)\n\t\t\tset (Mathematica_WSTP_LINKER_FLAGS \"\")\n\t\t\tforeach (_library ${Mathematica_WSTP_LIBRARIES})\n\t\t\t\tget_filename_component (_libraryDir ${_library} DIRECTORY)\n\t\t\t\tlist (APPEND Mathematica_LIBRARY_DIRS ${_libraryDir})\n\t\t\tendforeach()\n\t\t\t# Windows WSTP SDK has runtime DLLs in a separate directory\n\t\t\tset (_runtimeDir \"${Mathematica_WSTP_ROOT_DIR}/SystemAdditions\")\n\t\t\tif (IS_DIRECTORY \"${_runtimeDir}\")\n\t\t\t\tlist (APPEND Mathematica_WSTP_RUNTIME_LIBRARY_DIRS \"${_runtimeDir}\")\n\t\t\t\tlist (APPEND Mathematica_RUNTIME_LIBRARY_DIRS \"${_runtimeDir}\")\n\t\t\tendif()\n\t\t\t# Windows WSTP SDK also ships with debug DLLs in AlternativeComponents\n\t\t\tset (_runtimeDir \"${Mathematica_WSTP_ROOT_DIR}/AlternativeComponents/DebugLibraries\")\n\t\t\tif (IS_DIRECTORY \"${_runtimeDir}\")\n\t\t\t\tlist (APPEND Mathematica_WSTP_RUNTIME_LIBRARY_DIRS_DEBUG \"${_runtimeDir}\")\n\t\t\t\tlist (APPEND Mathematica_RUNTIME_LIBRARY_DIRS_DEBUG \"${_runtimeDir}\")\n\t\t\tendif()\n\t\tendif()\n\t\t_append_WSTP_needed_system_libraries(Mathematica_WSTP_LIBRARIES)\n\t\tlist (REMOVE_DUPLICATES Mathematica_WSTP_RUNTIME_LIBRARY_DIRS)\n\t\tlist (REMOVE_DUPLICATES Mathematica_WSTP_RUNTIME_LIBRARY_DIRS_DEBUG)\n\t\tlist (APPEND Mathematica_LIBRARIES ${Mathematica_WSTP_LIBRARIES})\n\tendif()\nendmacro()\n\n# internal macro to log used variables\nmacro (_log_used_variables)\n\tif (Mathematica_DEBUG)\n\t\tmessage (STATUS \"Executing on ${CMAKE_HOST_SYSTEM}, ${CMAKE_HOST_SYSTEM_NAME}, ${CMAKE_HOST_SYSTEM_PROCESSOR}, ${CMAKE_HOST_SYSTEM_VERSION}\")\n\t\tmessage (STATUS \"Compiling for ${CMAKE_SYSTEM}, ${CMAKE_SYSTEM_NAME}, ${CMAKE_SYSTEM_PROCESSOR}, ${CMAKE_SYSTEM_VERSION}\")\n\t\tmessage (STATUS \"Configuration: ${CMAKE_BUILD_TYPE}, ${CMAKE_CONFIGURATION_TYPES}\")\n\t\tmessage (STATUS \"Configuration directory: ${CMAKE_CFG_INTDIR}\")\n\t\tmessage (STATUS \"Project source dir: ${PROJECT_SOURCE_DIR}\")\n\t\tmessage (STATUS \"Project binary dir: ${PROJECT_BINARY_DIR}\")\n\t\tmessage (STATUS \"Cross compiling: ${CMAKE_CROSSCOMPILING}\")\n\t\tmessage (STATUS \"Library prefixes: ${CMAKE_FIND_LIBRARY_PREFIXES}\")\n\t\tmessage (STATUS \"Library suffixes: ${CMAKE_FIND_LIBRARY_SUFFIXES}\")\n\t\tmessage (STATUS \"Current file: ${CMAKE_CURRENT_LIST_FILE}:${CMAKE_CURRENT_LIST_LINE}\")\n\t\tmessage (STATUS \"Parent file: ${CMAKE_PARENT_LIST_FILE}\")\n\t\tmessage (STATUS \"Find version: ${Mathematica_FIND_VERSION}\")\n\t\tmessage (STATUS \"Find exact: ${Mathematica_FIND_VERSION_EXACT}\")\n\t\tmessage (STATUS \"Find quietly: ${Mathematica_FIND_QUIETLY}\")\n\t\tmessage (STATUS \"Find required: ${Mathematica_FIND_REQUIRED}\")\n\t\tmessage (STATUS \"Find components: ${Mathematica_FIND_COMPONENTS}\")\n\t\tmessage (STATUS \"Find required MathLink: ${Mathematica_FIND_REQUIRED_MathLink}\")\n\t\tmessage (STATUS \"Find MathLink interface version: ${Mathematica_MathLink_FIND_VERSION_MAJOR}\")\n\t\tmessage (STATUS \"Find MathLink revision number: ${Mathematica_MathLink_FIND_VERSION_MINOR}\")\n\t\tmessage (STATUS \"Find required WSTP: ${Mathematica_FIND_REQUIRED_WSTP}\")\n\t\tmessage (STATUS \"Find WSTP interface version: ${Mathematica_WSTP_FIND_VERSION_MAJOR}\")\n\t\tmessage (STATUS \"Find WSTP revision number: ${Mathematica_WSTP_FIND_VERSION_MINOR}\")\n\t\tmessage (STATUS \"Find required WolframLibrary: ${Mathematica_FIND_REQUIRED_WolframLibrary}\")\n\t\tmessage (STATUS \"Find required J/Link: ${Mathematica_FIND_REQUIRED_JLink}\")\n\t\tmessage (STATUS \"Find required MUnit: ${Mathematica_FIND_REQUIRED_MUnit}\")\n\t\tmessage (STATUS \"Use static libraries: ${Mathematica_USE_STATIC_LIBRARIES}\")\n\t\tmessage (STATUS \"Use minimal libraries: ${Mathematica_USE_MINIMAL_LIBRARIES}\")\n\tendif()\nendmacro()\n\n# internal macro to log found variables\nmacro (_log_found_variables)\n\tif (Mathematica_DEBUG)\n\t\tmessage (STATUS \"Mathematica CMake module dir ${Mathematica_CMAKE_MODULE_DIR}\")\n\t\tif (Mathematica_FOUND)\n\t\t\tmessage (STATUS \"Mathematica ${Mathematica_VERSION} found\")\n\t\t\tmessage (STATUS \"Mathematica creation ID ${Mathematica_CREATION_ID}\")\n\t\t\tmessage (STATUS \"Mathematica target root dir ${Mathematica_ROOT_DIR}\")\n\t\t\tmessage (STATUS \"Mathematica host root dir ${Mathematica_HOST_ROOT_DIR}\")\n\t\t\tmessage (STATUS \"Mathematica host MathLink include dir ${Mathematica_MathLink_HOST_INCLUDE_DIR}\")\n\t\t\tmessage (STATUS \"Mathematica host WSTP include dir ${Mathematica_WSTP_HOST_INCLUDE_DIR}\")\n\t\t\tmessage (STATUS \"Mathematica kernel executable ${Mathematica_KERNEL_EXECUTABLE}\")\n\t\t\tmessage (STATUS \"Mathematica frontend executable ${Mathematica_FRONTEND_EXECUTABLE}\")\n\t\t\tmessage (STATUS \"Mathematica target system ID ${Mathematica_SYSTEM_ID}\")\n\t\t\tmessage (STATUS \"Mathematica target system IDs ${Mathematica_SYSTEM_IDS}\")\n\t\t\tmessage (STATUS \"Mathematica host system ID ${Mathematica_HOST_SYSTEM_ID}\")\n\t\t\tmessage (STATUS \"Mathematica host system IDs ${Mathematica_HOST_SYSTEM_IDS}\")\n\t\t\tmessage (STATUS \"Mathematica base directory ${Mathematica_BASE_DIR}\")\n\t\t\tmessage (STATUS \"Mathematica user base directory ${Mathematica_USERBASE_DIR}\")\n\t\t\tmessage (STATUS \"Mathematica include dir ${Mathematica_INCLUDE_DIR}\")\n\t\t\tmessage (STATUS \"Mathematica include dirs ${Mathematica_INCLUDE_DIRS}\")\n\t\t\tmessage (STATUS \"Mathematica libraries ${Mathematica_LIBRARIES}\")\n\t\t\tmessage (STATUS \"Mathematica library dirs ${Mathematica_LIBRARY_DIRS}\")\n\t\t\tmessage (STATUS \"Mathematica runtime library dirs ${Mathematica_RUNTIME_LIBRARY_DIRS}\")\n\t\t\tmessage (STATUS \"Mathematica runtime debug library dirs ${Mathematica_RUNTIME_LIBRARY_DIRS_DEBUG}\")\n\t\telse()\n\t\t\tmessage (STATUS \"Mathematica not found\")\n\t\tendif()\n\t\tif (Mathematica_WolframLibrary_FOUND)\n\t\t\tmessage (STATUS \"WolframLibrary ${Mathematica_WolframLibrary_VERSION} found\")\n\t\t\tmessage (STATUS \"WolframLibrary include dir ${Mathematica_WolframLibrary_INCLUDE_DIR}\")\n\t\t\tmessage (STATUS \"WolframLibrary library ${Mathematica_WolframLibrary_LIBRARY}\")\n\t\t\tmessage (STATUS \"WolframLibrary libraries ${Mathematica_WolframLibrary_LIBRARIES}\")\n\t\t\tmessage (STATUS \"WolframLibrary runtime library dirs ${Mathematica_WolframLibrary_RUNTIME_LIBRARY_DIRS}\")\n\t\t\tmessage (STATUS \"WolframLibrary runtime debug library dirs ${Mathematica_WolframLibrary_RUNTIME_LIBRARY_DIRS_DEBUG}\")\n\t\t\tmessage (STATUS \"LibraryLink package dir ${Mathematica_LibraryLink_PACKAGE_DIR}\")\n\t\telse()\n\t\t\tmessage (STATUS \"WolframLibrary not found\")\n\t\tendif()\n\t\tif (Mathematica_MathLink_FOUND)\n\t\t\tmessage (STATUS \"MathLink ${Mathematica_MathLink_VERSION} found\")\n\t\t\tmessage (STATUS \"MathLink target root dir ${Mathematica_MathLink_ROOT_DIR}\")\n\t\t\tmessage (STATUS \"MathLink host root dir ${Mathematica_MathLink_HOST_ROOT_DIR}\")\n\t\t\tmessage (STATUS \"MathLink include dir ${Mathematica_MathLink_INCLUDE_DIR}\")\n\t\t\tmessage (STATUS \"MathLink library ${Mathematica_MathLink_LIBRARY}\")\n\t\t\tmessage (STATUS \"MathLink libraries ${Mathematica_MathLink_LIBRARIES}\")\n\t\t\tmessage (STATUS \"MathLink mprep executable ${Mathematica_MathLink_MPREP_EXECUTABLE}\")\n\t\t\tmessage (STATUS \"MathLink definitions ${Mathematica_MathLink_DEFINITIONS}\")\n\t\t\tmessage (STATUS \"MathLink linker flags ${Mathematica_MathLink_LINKER_FLAGS}\")\n\t\t\tmessage (STATUS \"MathLink runtime library dirs ${Mathematica_MathLink_RUNTIME_LIBRARY_DIRS}\")\n\t\t\tmessage (STATUS \"MathLink runtime debug library dirs ${Mathematica_MathLink_RUNTIME_LIBRARY_DIRS_DEBUG}\")\n\t\telse()\n\t\t\tmessage (STATUS \"MathLink not found\")\n\t\tendif()\n\t\tif (Mathematica_WSTP_FOUND)\n\t\t\tmessage (STATUS \"WSTP ${Mathematica_WSTP_VERSION} found\")\n\t\t\tmessage (STATUS \"WSTP target root dir ${Mathematica_WSTP_ROOT_DIR}\")\n\t\t\tmessage (STATUS \"WSTP host root dir ${Mathematica_WSTP_HOST_ROOT_DIR}\")\n\t\t\tmessage (STATUS \"WSTP include dir ${Mathematica_WSTP_INCLUDE_DIR}\")\n\t\t\tmessage (STATUS \"WSTP library ${Mathematica_WSTP_LIBRARY}\")\n\t\t\tmessage (STATUS \"WSTP libraries ${Mathematica_WSTP_LIBRARIES}\")\n\t\t\tmessage (STATUS \"WSTP wsprep executable ${Mathematica_WSTP_WSPREP_EXECUTABLE}\")\n\t\t\tmessage (STATUS \"WSTP definitions ${Mathematica_WSTP_DEFINITIONS}\")\n\t\t\tmessage (STATUS \"WSTP linker flags ${Mathematica_WSTP_LINKER_FLAGS}\")\n\t\t\tmessage (STATUS \"WSTP runtime library dirs ${Mathematica_WSTP_RUNTIME_LIBRARY_DIRS}\")\n\t\t\tmessage (STATUS \"WSTP runtime debug library dirs ${Mathematica_WSTP_RUNTIME_LIBRARY_DIRS_DEBUG}\")\n\t\telse()\n\t\t\tmessage (STATUS \"WSTP not found\")\n\t\tendif()\n\t\tif (Mathematica_JLink_FOUND)\n\t\t\tmessage (STATUS \"J/Link ${Mathematica_JLink_VERSION} found\")\n\t\t\tmessage (STATUS \"J/Link package dir ${Mathematica_JLink_PACKAGE_DIR}\")\n\t\t\tmessage (STATUS \"J/Link JAR file ${Mathematica_JLink_JAR_FILE}\")\n\t\t\tmessage (STATUS \"J/Link native library ${Mathematica_JLink_RUNTIME_LIBRARY}\")\n\t\t\tmessage (STATUS \"J/Link java launcher ${Mathematica_JLink_JAVA_EXECUTABLE}\")\n\t\t\tmessage (STATUS \"J/Link java home directory ${Mathematica_JLink_JAVA_HOME}\")\n\t\telse()\n\t\t\tmessage (STATUS \"J/Link not found\")\n\t\tendif()\n\t\tif (Mathematica_MUnit_FOUND)\n\t\t\tmessage (STATUS \"MUnit ${Mathematica_MUnit_VERSION} found\")\n\t\t\tmessage (STATUS \"MUnit package dir ${Mathematica_MUnit_PACKAGE_DIR}\")\n\t\telse()\n\t\t\tmessage (STATUS \"MUnit not found\")\n\t\tendif()\n\tendif()\n\t# warn explicitly about common mistakes users make\n\tif (UNIX AND NOT APPLE)\n\t\tif (DEFINED Mathematica_uuid_LIBRARY)\n\t\t\tif (Mathematica_uuid_LIBRARY MATCHES \"-NOTFOUND$\")\n\t\t\t\tmessage (WARNING \"WSTP and MathLink require libuuid. Install libuuid with the system package manager.\")\n\t\t\tendif()\n\t\tendif()\n\tendif()\n\tif (DEFINED Mathematica_VERSION)\n\t\tif (CMAKE_SIZEOF_VOID_P EQUAL 4)\n\t\t\tif (WINDOWS)\n\t\t\t\tif (NOT \"${Mathematica_VERSION}\" VERSION_LESS \"12.1\")\n\t\t\t\t\tmessage (WARNING \"Windows Mathematica ${Mathematica_VERSION} does not support 32-bit.\")\n\t\t\t\tendif()\n\t\t\telseif (APPLE)\n\t\t\t\tif (NOT \"${Mathematica_VERSION}\" VERSION_LESS \"9.0\")\n\t\t\t\t\tmessage (WARNING \"Mac Mathematica ${Mathematica_VERSION} does not support 32-bit.\")\n\t\t\t\tendif()\n\t\t\telseif (UNIX)\n\t\t\t\tif (NOT \"${Mathematica_VERSION}\" VERSION_LESS \"11.3\")\n\t\t\t\t\tmessage (WARNING \"Linux Mathematica ${Mathematica_VERSION} does not support 32-bit.\")\n\t\t\t\tendif()\n\t\t\tendif()\n\t\tendif()\n\tendif()\n\tif (DEFINED Mathematica_VERSION_MAJOR AND\n\t\tDEFINED Mathematica_VERSION_MINOR AND\n\t\tDEFINED Mathematica_SYSTEM_IDS)\n\t\tif (APPLE AND \"${Mathematica_VERSION_MAJOR}\" EQUAL 5 AND \"${Mathematica_VERSION_MINOR}\" EQUAL 2)\n\t\t\tforeach (_systemID ${Mathematica_SYSTEM_IDS})\n\t\t\t\tif (\"${_systemID}\" STREQUAL \"MacOSX-x86-64\")\n\t\t\t\t\tmessage (WARNING \"Mathematica 5.2 for Mac OS X does not support x86_64, run cmake with option -DCMAKE_OSX_ARCHITECTURES=i386.\")\n\t\t\t\tendif()\n\t\t\tendforeach()\n\t\tendif()\n\tendif()\n\tif (CYGWIN AND CMAKE_COMPILER_IS_GNUCC AND Mathematica_WolframLibrary_FOUND)\n\t\tif (\"${CMAKE_C_COMPILER_VERSION}\" VERSION_LESS \"3.0.0\" OR NOT \"${CMAKE_C_COMPILER_VERSION}\" VERSION_LESS \"4.0.0\")\n\t\t\tmessage (WARNING\n\t\t\t\t\"LibraryLink DLL generation requires the -mno-cygwin compiler flag, which is not supported by gcc ${CMAKE_C_COMPILER_VERSION}.\"\n\t\t\t\t\" Run cmake with options -DCMAKE_CXX_COMPILER=/usr/bin/g++-3.exe -DCMAKE_C_COMPILER=/usr/bin/gcc-3.exe.\")\n\t\tendif()\n\tendif()\nendmacro(_log_found_variables)\n\n# internal macro returns cache variables that determine search result\nmacro (_get_cache_variables _CacheVariables)\n\tset (${_CacheVariables}\n\t\tMathematica_FIND_VERSION\n\t\tMathematica_FIND_VERSION_EXACT\n\t\tMathematica_USE_STATIC_LIBRARIES\n\t\tMathematica_USE_MINIMAL_LIBRARIES\n\t\tMathematica_USE_LIBCXX_LIBRARIES\n\t\tMathematica_SYSTEM_IDS\n\t\tMathematica_CREATION_ID\n\t\tMathematica_ROOT_DIR\n\t\tMathematica_HOST_ROOT_DIR\n\t\tMathematica_MathLink_FIND_VERSION_MAJOR\n\t\tMathematica_MathLink_FIND_VERSION_MINOR\n\t\tMathematica_MathLink_ROOT_DIR\n\t\tMathematica_MathLink_HOST_ROOT_DIR\n\t\tMathematica_WSTP_FIND_VERSION_MAJOR\n\t\tMathematica_WSTP_FIND_VERSION_MINOR\n\t\tMathematica_WSTP_ROOT_DIR\n\t\tMathematica_WSTP_HOST_ROOT_DIR\n\t\tMathematica_JLink_PACKAGE_DIR\n\t\tMathematica_MUnit_PACKAGE_FILE\n\t\tMathematica_LibraryLink_PACKAGE_FILE\n\t\tMathematica_CMAKE_MODULE_VERSION)\nendmacro()\n\n# internal macro returns cache variables that are dependent on the given variable\nmacro (_get_dependent_cache_variables _var _outDependentVars)\n\t# do comparisons with an underscore prefix to prevent CMake from automatically\n\t# resolving the left and right hand arguments to STREQUAL\n\tif (\"_${_var}\" STREQUAL \"_Mathematica_FIND_VERSION\" OR\n\t\t\"_${_var}\" STREQUAL \"_Mathematica_FIND_VERSION_EXACT\")\n\t\tlist (APPEND ${_outDependentVars}\n\t\t\tMathematica_ROOT_DIR Mathematica_HOST_ROOT_DIR Mathematica_VERSION)\n\t\t_get_dependent_cache_variables(\"Mathematica_ROOT_DIR\" ${_outDependentVars})\n\t\t_get_dependent_cache_variables(\"Mathematica_HOST_ROOT_DIR\" ${_outDependentVars})\n\telseif (\"_${_var}\" STREQUAL \"_Mathematica_ROOT_DIR\" OR\n\t\t\t\"_${_var}\" STREQUAL \"_Mathematica_SYSTEM_IDS\")\n\t\tlist (APPEND ${_outDependentVars}\n\t\t\tMathematica_VERSION\n\t\t\tMathematica_INCLUDE_DIR\n\t\t\tMathematica_WolframLibrary_VERSION\n\t\t\tMathematica_WolframLibrary_INCLUDE_DIR\n\t\t\tMathematica_WolframLibrary_LIBRARY\n\t\t\tMathematica_KERNEL_HOST_SYSTEM_ID\n\t\t\tMathematica_MathLink_ROOT_DIR\n\t\t\tMathematica_WSTP_ROOT_DIR\n\t\t\tMathematica_KERNEL_BASE_DIR\n\t\t\tMathematica_KERNEL_USERBASE_DIR)\n\t\t_get_dependent_cache_variables(\"Mathematica_MathLink_ROOT_DIR\" ${_outDependentVars})\n\t\t_get_dependent_cache_variables(\"Mathematica_WSTP_ROOT_DIR\" ${_outDependentVars})\n\telseif (\"_${_var}\" STREQUAL \"_Mathematica_CREATION_ID\")\n\t\t# all cached Mathematica version variables are dependent on the cached creation ID\n\t\tlist (APPEND ${_outDependentVars}\n\t\t\tMathematica_VERSION\n\t\t\tMathematica_WolframLibrary_VERSION\n\t\t\tMathematica_MathLink_VERSION\n\t\t\tMathematica_WSTP_VERSION\n\t\t\tMathematica_JLink_VERSION\n\t\t\tMathematica_MUnit_VERSION)\n\telseif (\"_${_var}\" STREQUAL \"_Mathematica_HOST_ROOT_DIR\" OR\n\t\t\t\"_${_var}\" STREQUAL \"_Mathematica_HOST_SYSTEM_IDS\")\n\t\tlist (APPEND ${_outDependentVars}\n\t\t\tMathematica_FRONTEND_EXECUTABLE\n\t\t\tMathematica_KERNEL_EXECUTABLE\n\t\t\tMathematica_KERNEL_HOST_SYSTEM_ID\n\t\t\tMathematica_MathLink_HOST_ROOT_DIR\n\t\t\tMathematica_WSTP_HOST_ROOT_DIR\n\t\t\tMathematica_KERNEL_BASE_DIR\n\t\t\tMathematica_KERNEL_USERBASE_DIR\n\t\t\tMathematica_JLink_PACKAGE_DIR\n\t\t\tMathematica_MUnit_PACKAGE_FILE\n\t\t\tMathematica_LibraryLink_PACKAGE_FILE\n\t\t\tMathematica_JLink_JAVA_EXECUTABLE\n\t\t\tMathematica_JLink_JAVA_HOME)\n\t\t_get_dependent_cache_variables(\"Mathematica_MathLink_HOST_ROOT_DIR\" ${_outDependentVars})\n\t\t_get_dependent_cache_variables(\"Mathematica_WSTP_HOST_ROOT_DIR\" ${_outDependentVars})\n\t\t_get_dependent_cache_variables(\"Mathematica_JLink_PACKAGE_DIR\" ${_outDependentVars})\n\t\t_get_dependent_cache_variables(\"Mathematica_MUnit_PACKAGE_FILE\" ${_outDependentVars})\n\telseif (\"_${_var}\" STREQUAL \"_Mathematica_MathLink_ROOT_DIR\")\n\t\tlist (APPEND ${_outDependentVars}\n\t\t\tMathematica_MathLink_VERSION\n\t\t\tMathematica_MathLink_INCLUDE_DIR\n\t\t\tMathematica_MathLink_LIBRARY)\n\telseif (\"_${_var}\" STREQUAL \"_Mathematica_MathLink_HOST_ROOT_DIR\")\n\t\tlist (APPEND ${_outDependentVars}\n\t\t\tMathematica_MathLink_HOST_INCLUDE_DIR\n\t\t\tMathematica_MathLink_MPREP_EXECUTABLE)\n\telseif (\"_${_var}\" STREQUAL \"_Mathematica_MathLink_FIND_VERSION_MAJOR\" OR\n\t\t\t\"_${_var}\" STREQUAL \"_Mathematica_MathLink_FIND_VERSION_MINOR\")\n\t\tlist (APPEND ${_outDependentVars}\n\t\t\tMathematica_MathLink_VERSION\n\t\t\tMathematica_MathLink_INCLUDE_DIR\n\t\t\tMathematica_MathLink_LIBRARY\n\t\t\tMathematica_MathLink_HOST_INCLUDE_DIR\n\t\t\tMathematica_MathLink_MPREP_EXECUTABLE)\n\telseif (\"_${_var}\" STREQUAL \"_Mathematica_WSTP_ROOT_DIR\")\n\t\tlist (APPEND ${_outDependentVars}\n\t\t\tMathematica_WSTP_VERSION\n\t\t\tMathematica_WSTP_INCLUDE_DIR\n\t\t\tMathematica_WSTP_LIBRARY)\n\telseif (\"_${_var}\" STREQUAL \"_Mathematica_WSTP_HOST_ROOT_DIR\")\n\t\tlist (APPEND ${_outDependentVars}\n\t\t\tMathematica_WSTP_HOST_INCLUDE_DIR\n\t\t\tMathematica_WSTP_WSPREP_EXECUTABLE)\n\telseif (\"_${_var}\" STREQUAL \"_Mathematica_WSTP_FIND_VERSION_MAJOR\" OR\n\t\t\t\"_${_var}\" STREQUAL \"_Mathematica_WSTP_FIND_VERSION_MINOR\")\n\t\tlist (APPEND ${_outDependentVars}\n\t\t\tMathematica_WSTP_VERSION\n\t\t\tMathematica_WSTP_INCLUDE_DIR\n\t\t\tMathematica_WSTP_LIBRARY\n\t\t\tMathematica_WSTP_HOST_INCLUDE_DIR\n\t\t\tMathematica_WSTP_WSPREP_EXECUTABLE)\n\telseif (\"_${_var}\" STREQUAL \"_Mathematica_USE_STATIC_LIBRARIES\")\n\t\tlist (APPEND ${_outDependentVars}\n\t\t\tMathematica_WolframLibrary_LIBRARY\n\t\t\tMathematica_MathLink_LIBRARY\n\t\t\tMathematica_MathLink_INCLUDE_DIR\n\t\t\tMathematica_MathLink_HOST_INCLUDE_DIR\n\t\t\tMathematica_WSTP_LIBRARY\n\t\t\tMathematica_WSTP_INCLUDE_DIR\n\t\t\tMathematica_WSTP_HOST_INCLUDE_DIR)\n\telseif (\"_${_var}\" STREQUAL \"_Mathematica_USE_MINIMAL_LIBRARIES\")\n\t\tlist (APPEND ${_outDependentVars}\n\t\t\tMathematica_WolframLibrary_LIBRARY)\n\telseif (\"_${_var}\" STREQUAL \"_Mathematica_USE_LIBCXX_LIBRARIES\")\n\t\tlist (APPEND ${_outDependentVars}\n\t\t\tMathematica_MathLink_LIBRARY\n\t\t\tMathematica_WSTP_LIBRARY)\n\telseif (\"_${_var}\" STREQUAL \"_Mathematica_JLink_PACKAGE_DIR\")\n\t\tlist (APPEND ${_outDependentVars}\n\t\t\tMathematica_JLink_VERSION Mathematica_JLink_RUNTIME_LIBRARY)\n\telseif (\"_${_var}\" STREQUAL \"_Mathematica_MUnit_PACKAGE_FILE\")\n\t\tlist (APPEND ${_outDependentVars}\n\t\t\tMathematica_MUnit_VERSION)\n\tendif()\nendmacro(_get_dependent_cache_variables)\n\n# internal macro to cleanup outdated cache variables\nmacro (_cleanup_cache)\n\t_get_cache_variables(_CacheVariables)\n\tset (_vars_to_clean \"\")\n\tforeach (_CacheVariable IN LISTS _CacheVariables)\n\t\tget_property(_cacheVariableType CACHE \"${_CacheVariable}\" PROPERTY TYPE)\n\t\tif (DEFINED ${_CacheVariable} AND DEFINED ${_CacheVariable}_LAST)\n\t\t\tif (NOT \"${${_CacheVariable}}\" STREQUAL \"${${_CacheVariable}_LAST}\")\n\t\t\t\t# search var has changed\n\t\t\t\t_get_dependent_cache_variables(${_CacheVariable} _vars_to_clean)\n\t\t\t\tif (Mathematica_DEBUG)\n\t\t\t\t\tmessage (STATUS \"${_CacheVariable} changed from ${${_CacheVariable}_LAST} to ${${_CacheVariable}}\")\n\t\t\t\tendif()\n\t\t\telseif (\"${_cacheVariableType}\" MATCHES \"PATH\" AND\n\t\t\t\tNOT \"${${_CacheVariable}}\" MATCHES \"-NOTFOUND$\" AND\n\t\t\t\tNOT EXISTS \"${${_CacheVariable}}\")\n\t\t\t\t# original var path no longer exists\n\t\t\t\tlist (APPEND _vars_to_clean \"${_CacheVariable}\")\n\t\t\t\t_get_dependent_cache_variables(${_CacheVariable} _vars_to_clean)\n\t\t\t\tif (Mathematica_DEBUG)\n\t\t\t\t\tmessage (STATUS \"${_CacheVariable} path ${${_CacheVariable}} no longer exists\")\n\t\t\t\tendif()\n\t\t\telseif (\"${_cacheVariableType}\" MATCHES \"PATH\" AND\n\t\t\t\tEXISTS \"${${_CacheVariable}}\" AND\n\t\t\t\t\"${${_CacheVariable}}\" IS_NEWER_THAN \"${CMAKE_CACHEFILE_DIR}/CMakeCache.txt\")\n\t\t\t\t# search var path has changed\n\t\t\t\t_get_dependent_cache_variables(${_CacheVariable} _vars_to_clean)\n\t\t\t\tif (Mathematica_DEBUG)\n\t\t\t\t\tmessage (STATUS \"${_CacheVariable} path ${${_CacheVariable}} modified since last CMake run\")\n\t\t\t\tendif()\n\t\t\tendif()\n\t\telseif (DEFINED ${_CacheVariable} OR DEFINED ${_CacheVariable}_LAST)\n\t\t\t# search var presence changed\n\t\t\t_get_dependent_cache_variables(${_CacheVariable} _vars_to_clean)\n\t\t\tif (Mathematica_DEBUG)\n\t\t\t\tmessage (STATUS \"${_CacheVariable} presence changed\")\n\t\t\tendif()\n\t\tendif()\n\tendforeach()\n\tif (_vars_to_clean)\n\t\tlist (REMOVE_DUPLICATES _vars_to_clean)\n\t\tmessage (STATUS \"Mathematica environment changed, restart search ...\")\n\t\tif (Mathematica_DEBUG)\n\t\t\tmessage (STATUS \"Unset ${_vars_to_clean}\")\n\t\tendif()\n\t\tforeach (_CacheVariable IN LISTS _vars_to_clean)\n\t\t\tunset(${_CacheVariable} CACHE)\n\t\t\tunset(${_CacheVariable})\n\t\tendforeach()\n\tendif()\nendmacro()\n\n# internal macro to update cache variables\nmacro (_update_cache)\n\tmark_as_advanced(\n\t\tMathematica_INCLUDE_DIR\n\t\tMathematica_KERNEL_EXECUTABLE\n\t\tMathematica_FRONTEND_EXECUTABLE\n\t\tMathematica_WolframLibrary_INCLUDE_DIR\n\t\tMathematica_WolframLibrary_LIBRARY\n\t\tMathematica_MathLink_INCLUDE_DIR\n\t\tMathematica_MathLink_LIBRARY\n\t\tMathematica_MathLink_HOST_INCLUDE_DIR\n\t\tMathematica_MathLink_MPREP_EXECUTABLE\n\t\tMathematica_WSTP_INCLUDE_DIR\n\t\tMathematica_WSTP_LIBRARY\n\t\tMathematica_WSTP_HOST_INCLUDE_DIR\n\t\tMathematica_WSTP_WSPREP_EXECUTABLE\n\t\tMathematica_KERNEL_HOST_SYSTEM_ID\n\t\tMathematica_KERNEL_BASE_DIR\n\t\tMathematica_KERNEL_USERBASE_DIR\n\t\tMathematica_MUnit_PACKAGE_FILE\n\t\tMathematica_LibraryLink_PACKAGE_FILE\n\t\tMathematica_JLink_RUNTIME_LIBRARY\n\t\tMathematica_JLink_JAVA_EXECUTABLE\n\t\tMathematica_JLink_JAVA_HOME\n\t)\n\t_get_cache_variables(_CacheVariables)\n\tforeach (_CacheVariable IN LISTS _CacheVariables)\n\t\tif (DEFINED ${_CacheVariable})\n\t\t\tset (${_CacheVariable}_LAST ${${_CacheVariable}}\n\t\t\t\tCACHE INTERNAL \"Last value of ${_CacheVariable}.\" FORCE)\n\t\telse()\n\t\t\tunset(${_CacheVariable}_LAST CACHE)\n\t\tendif()\n\tendforeach()\nendmacro()\n\n# internal macro to return variables that need to exist in order for component\n# to be considered found successfully\nmacro (_get_required_vars _component _outVars)\n\tif (\"${_component}\" STREQUAL \"Mathematica\")\n\t\tset (${_outVars}\n\t\t\tMathematica_ROOT_DIR\n\t\t\tMathematica_KERNEL_EXECUTABLE)\n\telseif (\"${_component}\" STREQUAL \"MathLink\")\n\t\tset (${_outVars}\n\t\t\tMathematica_MathLink_LIBRARY Mathematica_MathLink_INCLUDE_DIR)\n\telseif (\"${_component}\" STREQUAL \"WSTP\")\n\t\tset (${_outVars}\n\t\t\tMathematica_WSTP_LIBRARY Mathematica_WSTP_INCLUDE_DIR)\n\telseif (\"${_component}\" STREQUAL \"WolframLibrary\")\n\t\tset (${_outVars}\n\t\t\tMathematica_WolframLibrary_LIBRARY Mathematica_WolframLibrary_INCLUDE_DIR)\n\telseif (\"${_component}\" STREQUAL \"JLink\")\n\t\tset (${_outVars}\n\t\t\tMathematica_JLink_PACKAGE_DIR Mathematica_JLink_JAR_FILE)\n\telseif (\"${_component}\" STREQUAL \"MUnit\")\n\t\tset (${_outVars}\n\t\t\tMathematica_MUnit_PACKAGE_DIR)\n\tendif()\nendmacro()\n\nmacro (_get_components_to_find _outComponents)\n\tif (Mathematica_FIND_COMPONENTS)\n\t\tlist (APPEND ${_outComponents} ${Mathematica_FIND_COMPONENTS})\n\telse()\n\t\tif (DEFINED Mathematica_FIND_VERSION_MAJOR)\n\t\t\tset (_versionMajor \"${Mathematica_FIND_VERSION_MAJOR}\")\n\t\telseif (DEFINED Mathematica_VERSION_MAJOR)\n\t\t\tset (_versionMajor \"${Mathematica_VERSION_MAJOR}\")\n\t\telse()\n\t\t\tset (_versionMajor \"\")\n\t\tendif()\n\t\tif (_versionMajor)\n\t\t\tif (_versionMajor GREATER 9)\n\t\t\t\tlist (APPEND ${_outComponents} \"WSTP\" \"MathLink\" \"WolframLibrary\" \"JLink\" \"MUnit\")\n\t\t\telseif (_versionMajor GREATER 7)\n\t\t\t\tlist (APPEND ${_outComponents} \"MathLink\" \"WolframLibrary\" \"JLink\" \"MUnit\")\n\t\t\telse()\n\t\t\t\tlist (APPEND ${_outComponents} \"MathLink\" \"JLink\" \"MUnit\")\n\t\t\tendif()\n\t\telse()\n\t\t\tlist (APPEND ${_outComponents} \"WSTP\" \"MathLink\" \"WolframLibrary\" \"JLink\" \"MUnit\")\n\t\tendif()\n\tendif()\n\tlist (REMOVE_DUPLICATES ${_outComponents})\nendmacro()\n\n# internal macro to handle the QUIETLY and REQUIRED arguments and set *_FOUND variables\nmacro (_setup_found_variables)\n\t# determine required Mathematica components\n\t_get_required_vars(\"Mathematica\" _requiredVars)\n\t_get_components_to_find(_components)\n\tforeach(_component IN LISTS _components)\n\t\t_get_required_vars(${_component} _requiredComponentVars)\n\t\t# suppress find_package_handle_standard_args warning on mismatching names\n\t\tset (FPHSA_NAME_MISMATCHED On)\n\t\tfind_package_handle_standard_args(\n\t\t\tMathematica_${_component}\n\t\t\tREQUIRED_VARS ${_requiredComponentVars}\n\t\t\tVERSION_VAR Mathematica_${_component}_VERSION)\n\t\tstring(TOUPPER ${_component} _UpperCaseComponent)\n\t\t# find_package_handle_standard_args only sets upper case _FOUND variable\n\t\tset (Mathematica_${_component}_FOUND ${MATHEMATICA_${_UpperCaseComponent}_FOUND})\n\t\tif (Mathematica_FIND_REQUIRED_${_component})\n\t\t\tlist (APPEND _requiredVars ${_requiredComponentVars} )\n\t\tendif()\n\tendforeach()\n\tfind_package_handle_standard_args(\n\t\tMathematica\n\t\tREQUIRED_VARS ${_requiredVars}\n\t\tVERSION_VAR Mathematica_VERSION)\n\t# find_package_handle_standard_args only sets upper case _FOUND variable\n\tset (Mathematica_FOUND ${MATHEMATICA_FOUND})\nendmacro()\n\n# internal macro that searches for requested components\nmacro (_find_components)\n\t_get_components_to_find(_components)\n\tforeach(_component IN LISTS _components)\n\t\tif (\"${_component}\" STREQUAL \"MathLink\")\n\t\t\t_find_mathlink()\n\t\t\t_setup_mathlink_version_variables()\n\t\t\t_setup_mathlink_library_variables()\n\t\telseif (\"${_component}\" STREQUAL \"WSTP\")\n\t\t\t_find_wstp()\n\t\t\t_setup_wstp_version_variables()\n\t\t\t_setup_wstp_library_variables()\n\t\telseif (\"${_component}\" STREQUAL \"WolframLibrary\")\n\t\t\t_find_wolframlibrary()\n\t\t\t_setup_wolframlibrary_version_variables()\n\t\t\t_setup_wolframlibrary_library_variables()\n\t\t\t_find_librarylink_package()\n\t\telseif (\"${_component}\" STREQUAL \"JLink\")\n\t\t\t_find_jlink()\n\t\t\t_setup_jlink_version_variables()\n\t\telseif (\"${_component}\" STREQUAL \"MUnit\")\n\t\t\t_find_munit_package()\n\t\t\t_setup_munit_package_version_variables()\n\t\telse()\n\t\t\tmessage (FATAL_ERROR \"Unknown Mathematica component ${_component}\")\n\t\tendif()\n\tendforeach()\n\tlist (REMOVE_DUPLICATES Mathematica_INCLUDE_DIRS)\n\tlist (REMOVE_DUPLICATES Mathematica_LIBRARIES)\n\tlist (REMOVE_DUPLICATES Mathematica_LIBRARY_DIRS)\n\tlist (REMOVE_DUPLICATES Mathematica_RUNTIME_LIBRARY_DIRS)\n\tlist (REMOVE_DUPLICATES Mathematica_RUNTIME_LIBRARY_DIRS_DEBUG)\nendmacro()\n\n# internal helper function to compute the install name of a shared library under Mac OS X\nmacro (_get_install_name _libraryPath _libraryInstallName _libraryAbsPath)\n\tif (APPLE)\n\t\tset (${_libraryInstallName} \"\")\n\t\tset (${_libraryAbsPath} \"\")\n\t\tif (IS_DIRECTORY \"${_libraryPath}\")\n\t\t\t# framework folder\n\t\t\tget_filename_component(_name \"${_libraryPath}\" NAME_WE)\n\t\t\tset (_path \"${_libraryPath}/${_name}\")\n\t\telse()\n\t\t\tset (_path \"${_libraryPath}\")\n\t\tendif()\n\t\tif (EXISTS \"${_path}\")\n\t\t\tfind_program(Mathematica_OTOOL_EXECUTABLE \"otool\")\n\t\t\tmark_as_advanced(Mathematica_OTOOL_EXECUTABLE)\n\t\t\tget_filename_component(${_libraryAbsPath} ${_path} ABSOLUTE)\n\t\t\tset (_otoolOutput \"\")\n\t\t\tif (Mathematica_OTOOL_EXECUTABLE)\n\t\t\t\texecute_process(\n\t\t\t\t\tCOMMAND \"${Mathematica_OTOOL_EXECUTABLE}\" \"-D\" \"-X\" \"${${_libraryAbsPath}}\" TIMEOUT 5\n\t\t\t\t\tOUTPUT_VARIABLE _otoolOutput OUTPUT_STRIP_TRAILING_WHITESPACE)\n\t\t\t\t# install name is in last line of otool output\n\t\t\t\tstring (REPLACE \"\\n\" \";\" _otoolOutput \"${_otoolOutput}\")\n\t\t\tendif()\n\t\t\tif (_otoolOutput)\n\t\t\t\tlist (GET _otoolOutput -1 ${_libraryInstallName})\n\t\t\telse()\n\t\t\t\tset (${_libraryInstallName} \"\")\n\t\t\tendif()\n\t\tendif()\n\tendif()\nendmacro()\n\n# FindMathematica \"main\" starts here\n_setup_findmathematica_options()\n_log_used_variables()\n_setup_mathematica_systemIDs()\n_setup_mathematica_creationID()\nif (DEFINED Mathematica_SYSTEM_IDS_LAST)\n\t# not the initial find invocation\n\t_cleanup_cache()\nendif()\n_setup_mathematica_base_directory()\n_setup_mathematica_userbase_directory()\n_find_mathematica()\n_setup_mathematica_version_variables()\n\n# now setup public functions based on found components\n\n# public function to convert a CMake string to a Mathematica string\nfunction (Mathematica_TO_NATIVE_STRING _inStr _outStr)\n\tstring (REPLACE \"\\\\\" \"\\\\\\\\\" _str ${_inStr})\n\tstring (REPLACE \"\\\"\" \"\\\\\\\"\" _str ${_str})\n\tset (${_outStr} \"\\\"${_str}\\\"\" PARENT_SCOPE)\nendfunction()\n\n# public function to convert a CMake list to a Mathematica list\nfunction (Mathematica_TO_NATIVE_LIST _outList)\n\tset (_list \"{\")\n\tforeach (_elem ${ARGN})\n\t\tMathematica_TO_NATIVE_STRING(${_elem} _elemStr)\n\t\tif (\"${_list}\" STREQUAL \"{\")\n\t\t\tset (_list \"{${_elemStr}\")\n\t\telse()\n\t\t\tset (_list \"${_list},${_elemStr}\")\n\t\tendif()\n\tendforeach()\n\tset (${_outList} \"${_list}}\" PARENT_SCOPE)\nendfunction()\n\n# public function to convert CMake paths to Mathematica paths\nfunction (Mathematica_TO_NATIVE_PATH _inPathStr _outPathStr)\n\tlist (LENGTH _inPathStr _len)\n\tif (_len EQUAL 0)\n\t\tset (${_outPathStr} \"\" PARENT_SCOPE)\n\telseif (_len EQUAL 1)\n\t\t_to_native_path(\"${_inPathStr}\" _nativePath)\n\t\tMathematica_TO_NATIVE_STRING(\"${_nativePath}\" _pathMma)\n\t\tset (${_outPathStr} \"${_pathMma}\" PARENT_SCOPE)\n\telse()\n\t\tset (_lastDir \"\")\n\t\tset (_names \"\")\n\t\tset (_nativePathsMma \"\")\n\t\tset (_hasMapPaths FALSE)\n\t\tset (_requiresList FALSE)\n\t\tforeach (_path IN LISTS _inPathStr ITEMS \"\")\n\t\t\tget_filename_component(_dir \"${_path}\" DIRECTORY)\n\t\t\tget_filename_component(_name \"${_path}\" NAME)\n\t\t\tif (_lastDir AND NOT \"${_dir}\" STREQUAL \"${_lastDir}\")\n\t\t\t\tlist (LENGTH _names _nameCount)\n\t\t\t\tif (_nameCount GREATER 1)\n\t\t\t\t\tMathematica_TO_NATIVE_PATH(\"${_lastDir}\" _commonDirMma)\n\t\t\t\t\tMathematica_TO_NATIVE_LIST(_namesMma ${_names})\n\t\t\t\t\tset (_code \"Map[ToFileName[${_commonDirMma},#]&,${_namesMma}]\")\n\t\t\t\t\tset (_hasMapPaths TRUE)\n\t\t\t\telse()\n\t\t\t\t\tMathematica_TO_NATIVE_PATH(\"${_lastDir}/${_names}\" _code)\n\t\t\t\tendif()\n\t\t\t\tif (_nativePathsMma)\n\t\t\t\t\tset (_nativePathsMma \"${_nativePathsMma},${_code}\")\n\t\t\t\t\tset (_requiresList TRUE)\n\t\t\t\telse()\n\t\t\t\t\tset (_nativePathsMma \"${_code}\")\n\t\t\t\tendif()\n\t\t\t\tset (_names \"\")\n\t\t\tendif()\n\t\t\tset (_lastDir \"${_dir}\")\n\t\t\tlist (APPEND _names \"${_name}\")\n\t\tendforeach()\n\t\tif (_requiresList AND _hasMapPaths)\n\t\t\tset (_nativePathsMma \"Flatten[{${_nativePathsMma}}]\")\n\t\telseif (_requiresList)\n\t\t\tset (_nativePathsMma \"{${_nativePathsMma}}\")\n\t\tendif()\n\t\tset (${_outPathStr} \"${_nativePathsMma}\" PARENT_SCOPE)\n\tendif()\nendfunction()\n\n# public function to initialize Mathematica test properties\nfunction (Mathematica_SET_TESTS_PROPERTIES)\n\t_select_configuration_run_time_dirs(_configRuntimeDirs)\n\t_get_host_library_search_path_envvars(_envVars)\n\tforeach (_envVar IN LISTS _envVars)\n\t\tif (DEFINED ENV{${_envVar}})\n\t\t\tfile (TO_CMAKE_PATH \"$ENV{${_envVar}}\" _envRuntimeDirs)\n\t\t\t# prepend Mathematica runtime directories to system ones\n\t\t\tset (_runtimeDirs ${_configRuntimeDirs} ${_envRuntimeDirs})\n\t\telse()\n\t\t\tset (_runtimeDirs ${_configRuntimeDirs})\n\t\tendif()\n\t\tif (_runtimeDirs)\n\t\t\tlist (REMOVE_DUPLICATES _runtimeDirs)\n\t\t\tif (CYGWIN)\n\t\t\t\t# CYGWIN path list requires UNIX syntax\n\t\t\t\t_to_cmake_path_list(_nativeRuntimeDirs ${_runtimeDirs})\n\t\t\telse()\n\t\t\t\t_to_native_path_list(_nativeRuntimeDirs ${_runtimeDirs})\n\t\t\tendif()\n\t\t\tforeach (_testName ${ARGV})\n\t\t\t\tif (\"${_testName}\" STREQUAL \"PROPERTIES\")\n\t\t\t\t\tbreak()\n\t\t\t\tendif()\n\t\t\t\tset_property (TEST ${_testName} APPEND PROPERTY\n\t\t\t\t\tENVIRONMENT \"${_envVar}=${_nativeRuntimeDirs}\" )\n\t\t\tendforeach()\n\t\tendif()\n\tendforeach()\n\tset (_haveProperties False)\n\tforeach (_testName IN ITEMS ${ARGV})\n\t\tif (\"${_testName}\" STREQUAL \"PROPERTIES\")\n\t\t\tset (_haveProperties True)\n\t\t\tbreak()\n\t\tendif()\n\t\tset_property (TEST ${_testName} APPEND PROPERTY LABELS \"Mathematica\")\n\tendforeach()\n\tif (_haveProperties)\n\t\tset_tests_properties (${ARGV})\n\tendif()\nendfunction(Mathematica_SET_TESTS_PROPERTIES)\n\n# internal macro to return test driver for host platform\nfunction (_add_test_driver _cmdVar _testName _inputVar _inputFileVar)\n\tif (CMAKE_HOST_UNIX)\n\t\tset (_testDriver \"${Mathematica_CMAKE_MODULE_DIR}/FindMathematicaTestDriver.sh\")\n\telseif (CMAKE_HOST_WIN32)\n\t\tset (_testDriver \"${Mathematica_CMAKE_MODULE_DIR}/FindMathematicaTestDriver.cmd\")\n\tendif()\n\tif (NOT EXISTS \"${_testDriver}\")\n\t\tmessage (FATAL_ERROR \"FindMathematica test driver script ${_testDriver} is missing.\")\n\tendif()\n\t_make_file_executable(${_testDriver})\n\tif (CYGWIN)\n\t\t_to_cmake_path(\"${_testDriver}\" _testDriver)\n\telse()\n\t\t_to_native_path(\"${_testDriver}\" _testDriver)\n\tendif()\n\tlist (APPEND ${_cmdVar} \"${_testDriver}\" \"${_testName}\" \"$<CONFIGURATION>\")\n\tif (DEFINED ${_inputVar})\n\t\tlist (APPEND ${_cmdVar} \"input\" \"${${_inputVar}}\")\n\telseif (DEFINED ${_inputFileVar})\n\t\tlist (APPEND ${_cmdVar} \"inputfile\" \"${${_inputFileVar}}\")\n\telse()\n\t\tlist (APPEND ${_cmdVar} \"noinput\")\n\tendif()\n\tset (${_cmdVar} ${${_cmdVar}} PARENT_SCOPE)\nendfunction()\n\n# internal macro to add platform specific executable launch prefix\nmacro (_add_launch_prefix _cmdVar _systemIDVar)\n\tif (DEFINED ${_systemIDVar})\n\t\tif (CMAKE_HOST_APPLE)\n\t\t\tif (NOT \"${${_systemIDVar}}\" STREQUAL \"${Mathematica_HOST_SYSTEM_ID}\")\n\t\t\t\t# under Mac OS X, run appropriate target architecture of executable universal binary\n\t\t\t\t# by using the the /usr/bin/arch tool which is available since Leopard\n\t\t\t\t# (Mac OS X 10.5.0 is Darwin 9.0.0)\n\t\t\t\tif (\"${CMAKE_HOST_SYSTEM_VERSION}\" VERSION_LESS \"9.0.0\")\n\t\t\t\t\tmessage (STATUS \"Executable system ID selection of ${${_systemIDVar}} is not supported, running default.\")\n\t\t\t\telseif (\"${${_systemIDVar}}\" STREQUAL \"MacOSX-x86\")\n\t\t\t\t\tlist (APPEND ${_cmdVar} \"/usr/bin/arch\" \"-i386\")\n\t\t\t\telseif(\"${${_systemIDVar}}\" STREQUAL \"MacOSX-x86-64\")\n\t\t\t\t\tlist (APPEND ${_cmdVar} \"/usr/bin/arch\" \"-x86_64\")\n\t\t\t\telseif(\"${${_systemIDVar}}\" STREQUAL \"MacOSX-ARM64\")\n\t\t\t\t\tlist (APPEND ${_cmdVar} \"/usr/bin/arch\" \"-arm64\")\n\t\t\t\telseif(\"${${_systemIDVar}}\" MATCHES \"Darwin|MacOSX\")\n\t\t\t\t\tlist (APPEND ${_cmdVar} \"/usr/bin/arch\" \"-ppc\")\n\t\t\t\telseif(\"${${_systemIDVar}}\" STREQUAL \"Darwin-PowerPC64\")\n\t\t\t\t\tlist (APPEND ${_cmdVar} \"/usr/bin/arch\" \"-ppc64\")\n\t\t\t\telse()\n\t\t\t\t\tmessage (STATUS \"Executable system ID ${${_systemIDVar}} is not supported, running default.\")\n\t\t\t\tendif()\n\t\t\tendif()\n\t\tendif()\n\tendif()\nendmacro()\n\n# internal macro to set up kernel launch command\nmacro (_add_kernel_launch_code _cmdVar _systemIDVar _kernelOptionsVar)\n\tif (CMAKE_HOST_WIN32 OR CYGWIN)\n\t\tset (_kernelExecutable \"${Mathematica_KERNEL_EXECUTABLE}\")\n\t\tif (DEFINED ${_systemIDVar})\n\t\t\t# under Windows, run alternate binary for given system ID\n\t\t\tget_filename_component(_kernelName \"${_kernelExecutable}\" NAME)\n\t\t\tset (_kernelExecutable\n\t\t\t\t\"${Mathematica_HOST_ROOT_DIR}/SystemFiles/Kernel/Binaries/${${_systemIDVar}}/${_kernelName}\")\n\t\t\tif (NOT EXISTS \"${_kernelExecutable}\")\n\t\t\t\tset (_kernelExecutable \"${Mathematica_KERNEL_EXECUTABLE}\")\n\t\t\t\tif (NOT \"${_systemIDVar}\" STREQUAL \"${Mathematica_HOST_SYSTEM_ID}\")\n\t\t\t\t\tmessage (STATUS \"Kernel executable for ${${_systemIDVar}} is not available, running default ${Mathematica_HOST_SYSTEM_ID}.\")\n\t\t\t\tendif()\n\t\t\tendif()\n\t\tendif()\n\t\t_to_native_path(\"${_kernelExecutable}\" _kernelExecutable)\n\t\tlist (APPEND ${_cmdVar} \"${_kernelExecutable}\")\n\telseif (CMAKE_HOST_APPLE)\n\t\t_add_launch_prefix(${_cmdVar} ${_systemIDVar})\n\t\t_to_native_path(\"${Mathematica_KERNEL_EXECUTABLE}\" _kernelExecutable)\n\t\tlist (APPEND ${_cmdVar} \"${_kernelExecutable}\")\n\telseif (CMAKE_HOST_UNIX)\n\t\t_to_native_path(\"${Mathematica_KERNEL_EXECUTABLE}\" _kernelExecutable)\n\t\tlist (APPEND ${_cmdVar} \"${_kernelExecutable}\")\n\t\tif (DEFINED ${_systemIDVar})\n\t\t\tif (Mathematica_VERSION)\n\t\t\t\tif (NOT \"${Mathematica_VERSION}\" VERSION_LESS \"8.0\")\n\t\t\t\t\t# Mathematica 8 kernel wrapper shell script supports option -SystemID\n\t\t\t\t\tlist (APPEND ${_cmdVar} \"-SystemID\" \"${${_systemIDVar}}\")\n\t\t\t\telseif (NOT \"${_systemIDVar}\" STREQUAL \"${Mathematica_HOST_SYSTEM_ID}\")\n\t\t\t\t\tmessage (STATUS \"Kernel system ID selection of ${${_systemIDVar}} is not supported, running default ${Mathematica_HOST_SYSTEM_ID}.\")\n\t\t\t\tendif()\n\t\t\tendif()\n\t\tendif()\n\telse()\n\t\tmessage (FATAL_ERROR \"Unsupported host platform ${CMAKE_HOST_SYSTEM_NAME}\")\n\tendif()\n\tif (DEFINED ${_kernelOptionsVar})\n\t\tlist (APPEND ${_cmdVar} ${${_kernelOptionsVar}})\n\telse()\n\t\tlist (APPEND ${_cmdVar} \"-noinit\" \"-noprompt\")\n\tendif()\nendmacro(_add_kernel_launch_code)\n\nmacro (_test_use_tempfile_for_code_segments _codeVar _useTempFileVar)\n\tset (_codeLength 0)\n\tset (_codeSegmentCount 1)\n\tset (_usesReservedChars FALSE)\n\tforeach (_codeSegment IN LISTS ${_codeVar})\n\t\tstring (LENGTH \"${_codeSegment}\" _codeSegmentLength)\n\t\tmath (EXPR _codeLength \"${_codeLength} + ${_codeSegmentLength}\")\n\t\tif (_codeSegment MATCHES \"(Get|Needs|Install|Sequence)\\\\[[^]]*\\\\]\")\n\t\t\t# start new code segment\n\t\t\tmath (EXPR _codeSegmentCount \"${_codeSegmentCount} + 1\")\n\t\tendif()\n\t\tif (NOT _usesReservedChars)\n\t\t\tif (_codeSegment MATCHES \"[<>|&!%^]\")\n\t\t\t\tset (_usesReservedChars TRUE)\n\t\t\tendif()\n\t\tendif()\n\tendforeach()\n\tif (CMAKE_HOST_WIN32 AND (_usesReservedChars OR _codeLength GREATER 1000 OR _codeSegmentCount GREATER 3))\n\t\t# under Windows XP or later cmd.exe has a command line length limit of 8191 characters.\n\t\t# we do not use inline statements if the approximate command line length\n\t\t# might exceed that limit or there are too many individual arguments.\n\t\t# we write the inline statements to a temporary script instead\n\t\tset (${_useTempFileVar} TRUE)\n\telseif (CMAKE_HOST_UNIX AND (_codeLength GREATER 10000 OR _codeSegmentCount GREATER 10))\n\t\t# for UNIX use a temp file if command line becomes confusing\n\t\tset (${_useTempFileVar} TRUE)\n\telse()\n\t\tset (${_useTempFileVar} FALSE)\n\tendif()\nendmacro()\n\nmacro (_code_segments_to_compound_expressions _codeVar _codeSegments)\n\t# collect all CODE sections into CompoundExpressions\n\tset (${_codeSegments} \"\")\n\tset (_currentCodeSegment \"\")\n\tset (_currentCodeSegmentCompound False)\n\tforeach (_codeSegment IN LISTS ${_codeVar} ITEMS \"Sequence[]\")\n\t\tif (_codeSegment MATCHES \"\\n\")\n\t\t\t# remove indentation with tabs\n\t\t\tstring (REGEX REPLACE \"\\t+\" \"\" _codeSegment \"${_codeSegment}\")\n\t\t\t# separate multiple lines via commas\n\t\t\tstring (REPLACE \"\\n\" \",\" _codeSegment \"${_codeSegment}\")\n\t\tendif()\n\t\t# prevent CMake from interpreting ; as a list separator\n\t\tstring (REPLACE \";\" \"\\\\;\" _codeSegment \"${_codeSegment}\")\n\t\tif (_currentCodeSegment)\n\t\t\tif (NOT _codeSegment STREQUAL \"Sequence[]\")\n\t\t\t\tset (_currentCodeSegmentCompound True)\n\t\t\t\tset (_currentCodeSegment \"${_currentCodeSegment},${_codeSegment}\")\n\t\t\tendif()\n\t\telse()\n\t\t\tset (_currentCodeSegment \"${_codeSegment}\")\n\t\tendif()\n\t\t# flush current CompoundExpression when a Get[...], Needs[...] or Install[...]\n\t\t# expression is encountered, so that new context definitions become effective\n\t\t# immediately for subsequent commands\n\t\t# Sequence[] can be used to explicitly flush the current CompoundExpression\n\t\tif (_codeSegment MATCHES \"(Get|Needs|Install|Sequence)\\\\[[^]]*\\\\]\")\n\t\t\tif (_currentCodeSegmentCompound OR\n\t\t\t\t(CMAKE_HOST_WIN32 AND NOT _currentCodeSegment MATCHES \" \"))\n\t\t\t\t# note that the blanks around the CompoundExpression argument below are necessary\n\t\t\t\t# to force CMake to do proper cmd.exe quoting of the resulting parameter under Windows\n\t\t\t\t# (a comma in the parameter may be misinterpreted as a separator otherwise)\n\t\t\t\tlist (APPEND ${_codeSegments} \"-run\" \"CompoundExpression[ ${_currentCodeSegment} ]\")\n\t\t\telseif (NOT _currentCodeSegment STREQUAL \"Sequence[]\")\n\t\t\t\t# flush single code segment, but only if it is not a NOP\n\t\t\t\tlist (APPEND ${_codeSegments} \"-run\" \"${_currentCodeSegment}\")\n\t\t\tendif()\n\t\t\tset (_currentCodeSegment \"\")\n\t\t\tset (_currentCodeSegmentCompound False)\n\t\tendif()\n\tendforeach()\nendmacro(_code_segments_to_compound_expressions)\n\nmacro (_code_segments_to_tempfile _codeVar _tempScriptFile)\n\t# check for use of CMake generator expressions in inline code\n\tset (_contentsHasGeneratorExpressions FALSE)\n\tset (_contents \"\")\n\tforeach (_codeSegment IN LISTS ${_codeVar})\n\t\tstring (REPLACE \";\" \"\\\\;\" _line \"${_codeSegment}\")\n\t\tlist (APPEND _contents \"${_line}\")\n\t\tif (NOT _contentsHasGeneratorExpressions)\n\t\t\tif (\"${_line}\" MATCHES \"\\\\$<.*>\")\n\t\t\t\tset (_contentsHasGeneratorExpressions TRUE)\n\t\t\tendif()\n\t\tendif()\n\tendforeach()\n\tstring (REPLACE \";\" \"\\n\" _contents \"${_contents}\")\n\t# use script content MD5 as temporary file name\n\tstring (MD5 _scriptName \"${_contents}\")\n\tset (_tempScript \"${CMAKE_CURRENT_BINARY_DIR}/FindMathematica/${_scriptName}.m\")\n\tfile (WRITE \"${_tempScript}\" \"${_contents}\")\n\tif (_contentsHasGeneratorExpressions)\n\t\tset (_configNameOrNoneGeneratorExpression \"$<$<CONFIG:>:None>$<$<NOT:$<CONFIG:>>:$<CONFIGURATION>>\")\n\t\tset (_tempConfigScript \"${CMAKE_CURRENT_BINARY_DIR}/FindMathematica/${_scriptName}_${_configNameOrNoneGeneratorExpression}.m\")\n\t\tfile (GENERATE OUTPUT \"${_tempConfigScript}\" INPUT \"${_tempScript}\")\n\telse()\n\t\tset (_tempConfigScript \"${_tempScript}\")\n\tendif()\n\tset (${_tempScriptFile} \"${_tempConfigScript}\")\nendmacro(_code_segments_to_tempfile)\n\n# internal macro to translate CODE or SCRIPT option to Mathematica launch command\nmacro (_add_script_or_code _cmdVar _scriptVar _codeVar)\n\tif (DEFINED ${_codeVar} OR DEFINED ${_scriptVar})\n\t\t# start with code to prepend the FindMathematica module directory to the Mathematica $Path\n\t\tMathematica_TO_NATIVE_PATH(\"${Mathematica_CMAKE_MODULE_DIR}\" _cmakeModuleDirMma)\n\t\tset (_code \"PrependTo[$Path, ${_cmakeModuleDirMma}]\")\n\t\t# add given inline code statements\n\t\tif (DEFINED ${_codeVar})\n\t\t\tlist (APPEND _code ${${_codeVar}})\n\t\tendif()\n\t\t# compute absolute path to given script\n\t\tif (DEFINED ${_scriptVar})\n\t\t\tif (IS_ABSOLUTE \"${${_scriptVar}}\")\n\t\t\t\t_to_cmake_path(\"${${_scriptVar}}\" _scriptFileAbs)\n\t\t\telse()\n\t\t\t\t_to_cmake_path(\"${CMAKE_CURRENT_SOURCE_DIR}/${${_scriptVar}}\" _scriptFileAbs)\n\t\t\tendif()\n\t\tendif()\n\t\tif (NOT DEFINED ${_scriptVar})\n\t\t\t# no given script, quit kernel explicitly unless last code statement already does it\n\t\t\tlist (GET _code -1 _lastStatement)\n\t\t\tif (NOT _lastStatement MATCHES \"^(Quit|Exit)\\\\[\")\n\t\t\t\tlist (APPEND _code \"Quit[]\")\n\t\t\tendif()\n\t\telseif (\"${Mathematica_VERSION}\" VERSION_LESS \"10.0\")\n\t\t\t# Although the -script option is supported since Mathematica 8, under Mathematica 9\n\t\t\t# using the -script option does not work as expected, if it is preceded by multiple inline\n\t\t\t# Mathematica commands using the -run option.\n\t\t\t# Thus we use the Get function instead, which should work with all versions.\n\t\t\t# According to https://reference.wolfram.com/language/tutorial/WolframLanguageScripts.html\n\t\t\t# running the kernel with the -script option is equivalent to reading the file using the Get function\n\t\t\t# with a single difference: after the last command in the file is evaluated, the kernel terminates\n\t\t\tMathematica_TO_NATIVE_PATH(\"${_scriptFileAbs}\" _scriptFileMma)\n\t\t\tlist (APPEND _code \"Get[${_scriptFileMma}]\" \"Quit[]\")\n\t\tendif()\n\t\t# convert resulting code to kernel inline code segments or if necessary to a temporary script file\n\t\t_test_use_tempfile_for_code_segments(_code _useTempFile)\n\t\tif (_useTempFile)\n\t\t\t_code_segments_to_tempfile(_code _tempScriptFile)\n\t\t\tMathematica_TO_NATIVE_PATH(\"${_tempScriptFile}\" _tempScriptFileMma)\n\t\t\tlist (APPEND ${_cmdVar} \"-run\" \"Get[${_tempScriptFileMma}]\")\n\t\telse()\n\t\t\t_code_segments_to_compound_expressions(_code _codeSegments)\n\t\t\tlist (APPEND ${_cmdVar} ${_codeSegments})\n\t\tendif()\n\t\t# finally, run given script with -script option if using Mathematica 10 or later\n\t\tif (DEFINED ${_scriptVar})\n\t\t\tif (NOT \"${Mathematica_VERSION}\" VERSION_LESS \"10.0\")\n\t\t\t\tlist (APPEND ${_cmdVar} \"-script\" \"${_scriptFileAbs}\")\n\t\t\t\t# after the last command in the script file is evaluated, the kernel terminates automatically\n\t\t\tendif()\n\t\tendif()\n\tendif()\nendmacro(_add_script_or_code)\n\n# internal macro to set up linkmode launch command\nmacro (_add_linkmode_launch_code _cmdVar _protocolKind _systemIDVar _kernelOptionsVar _linkProtocolVar _scriptVar _codeVar)\n\tlist (APPEND ${_cmdVar} \"-linkmode\" \"launch\")\n\tif (DEFINED ${_linkProtocolVar})\n\t\tlist (APPEND ${_cmdVar} \"-linkprotocol\" \"${${_linkProtocolVar}}\")\n\tendif()\n\tlist (APPEND ${_cmdVar} \"-linkname\")\n\tif (UNIX AND NOT CYGWIN)\n\t\t# UNIX (except for Cygwin) requires quoted link name path and -mathlink or -wstp\n\t\tset (_kernelLaunchArgs \"\")\n\t\t_add_kernel_launch_code(_kernelLaunchArgs ${_systemIDVar} ${_kernelOptionsVar})\n\t\t_add_script_or_code(_kernelLaunchArgs ${_scriptVar} ${_codeVar})\n\t\t_list_to_cmd_str(_kernelLaunchStr ${_kernelLaunchArgs})\n\t\tlist (APPEND ${_cmdVar} \"${_kernelLaunchStr} ${_protocolKind}\")\n\telse ()\n\t\t_add_kernel_launch_code(${_cmdVar} ${_systemIDVar} ${_kernelOptionsVar})\n\tendif()\nendmacro()\n\nif (Mathematica_KERNEL_EXECUTABLE)\n\n# public function for executing Mathematica code file at configuration time\nfunction (Mathematica_EXECUTE)\n\tset(_options \"\")\n\tlist(APPEND _options CACHE)\n\tset(_oneValueArgs\n\t\tSCRIPT SYSTEM_ID\n\t\tINPUT_FILE OUTPUT_FILE ERROR_FILE\n\t\tRESULT_VARIABLE OUTPUT_VARIABLE ERROR_VARIABLE\n\t\tTIMEOUT DOC)\n\tset(_multiValueArgs CODE KERNEL_OPTIONS)\n\tcmake_parse_arguments(_option \"${_options}\" \"${_oneValueArgs}\" \"${_multiValueArgs}\" ${ARGN})\n\tif(_option_UNPARSED_ARGUMENTS)\n\t\tmessage (FATAL_ERROR \"Unknown keywords: ${_option_UNPARSED_ARGUMENTS}\")\n\telseif (NOT _option_CODE AND NOT _option_SCRIPT)\n\t\tmessage (FATAL_ERROR \"Either the keyword CODE or SCRIPT must be present.\")\n\tendif()\n\tif (_option_CACHE AND _option_OUTPUT_VARIABLE)\n\t\tif (DEFINED \"${_option_OUTPUT_VARIABLE}\")\n\t\t\tset (_var \"${${_option_OUTPUT_VARIABLE}}\")\n\t\t\tif (_var AND NOT \"${_var}\" MATCHES \"\\\\$Failed|\\\\$Aborted|Mathematica cannot find a valid password\")\n\t\t\t\t# use result from cache if is not a false constant, $Failed, $Aborted or not properly registered\n\t\t\t\treturn()\n\t\t\tendif()\n\t\tendif()\n\tendif()\n\tset (_cmd COMMAND)\n\t_add_kernel_launch_code(_cmd _option_SYSTEM_ID _option_KERNEL_OPTIONS)\n\t_add_script_or_code(_cmd _option_SCRIPT _option_CODE)\n\tif (_option_CODE)\n\t\tlist (APPEND _cmd OUTPUT_STRIP_TRAILING_WHITESPACE)\n\t\tlist (APPEND _cmd ERROR_STRIP_TRAILING_WHITESPACE)\n\tendif()\n\tforeach (_key IN LISTS _oneValueArgs)\n\t\tset (_value \"_option_${_key}\")\n\t\tif (DEFINED ${_value})\n\t\t\tif (_key MATCHES \"_VARIABLE$\")\n\t\t\t\tlist (APPEND _cmd ${_key} \"${${_value}}\")\n\t\t\t\tlist (APPEND _variables \"${${_value}}\")\n\t\t\telseif (NOT _key MATCHES \"SCRIPT|CODE|SYSTEM_ID|DOC\")\n\t\t\t\tlist (APPEND _cmd ${_key} \"${${_value}}\")\n\t\t\tendif()\n\t\tendif()\n\tendforeach()\n\tlist (APPEND _cmd WORKING_DIRECTORY \"${CMAKE_CURRENT_BINARY_DIR}\")\n\tif (Mathematica_DEBUG)\n\t\tmessage (STATUS \"execute_process: ${_cmd}\")\n\tendif()\n\texecute_process (${_cmd})\n\t# put result to cache\n\tif (_option_OUTPUT_VARIABLE)\n\t\t# if Mathematica is not registered properly, print a warning\n\t\tif (\"${${_option_OUTPUT_VARIABLE}}\" MATCHES \"Mathematica cannot find a valid password\")\n\t\t\tmessage (WARNING \"${${_option_OUTPUT_VARIABLE}}\")\n\t\t\treturn()\n\t\tendif()\n\tendif()\n\tif (_option_CACHE AND _option_OUTPUT_VARIABLE)\n\t\tif (NOT _option_DOC)\n\t\t\tset (_option_DOC \"Mathematica_EXECUTE kernel output.\")\n\t\tendif()\n\t\tset (${_option_OUTPUT_VARIABLE}\n\t\t\t\"${${_option_OUTPUT_VARIABLE}}\" CACHE STRING \"${_option_DOC}\" FORCE)\n\tendif()\n\t# propagate variables to parent scope\n\tforeach (_var IN LISTS _variables)\n\t\tif (DEFINED ${_var})\n\t\t\tset (${_var} ${${_var}} PARENT_SCOPE)\n\t\tendif()\n\tendforeach()\nendfunction(Mathematica_EXECUTE)\n\n# public function for executing Mathematica code at build time as a standalone target\nfunction (Mathematica_ADD_CUSTOM_TARGET _targetName)\n\tset(_options ALL)\n\tset(_oneValueArgs SCRIPT COMMENT SYSTEM_ID)\n\tset(_multiValueArgs CODE DEPENDS SOURCES KERNEL_OPTIONS)\n\tcmake_parse_arguments(_option \"${_options}\" \"${_oneValueArgs}\" \"${_multiValueArgs}\" ${ARGN})\n\tif(_option_UNPARSED_ARGUMENTS)\n\t\tmessage (FATAL_ERROR \"Unknown keywords: ${_option_UNPARSED_ARGUMENTS}\")\n\telseif (NOT _option_CODE AND NOT _option_SCRIPT)\n\t\tmessage (FATAL_ERROR \"Either the keyword CODE or SCRIPT must be present.\")\n\tendif()\n\tset (_cmd \"${_targetName}\")\n\tif (_option_ALL)\n\t\tlist(APPEND _cmd \"ALL\")\n\tendif()\n\tlist(APPEND _cmd COMMAND)\n\t_add_kernel_launch_code(_cmd _option_SYSTEM_ID _option_KERNEL_OPTIONS)\n\t_add_script_or_code(_cmd _option_SCRIPT _option_CODE)\n\tif (_option_SCRIPT)\n\t\tlist (APPEND _option_DEPENDS ${_option_SCRIPT})\n\tendif()\n\tif (_option_DEPENDS)\n\t\tlist (APPEND _cmd DEPENDS ${_option_DEPENDS})\n\tendif()\n\tif (_option_COMMENT)\n\t\tlist(APPEND _cmd COMMENT ${_option_COMMENT})\n\tendif()\n\tif (_option_SOURCES)\n\t\tlist(APPEND _cmd SOURCES ${_option_SOURCES})\n\tendif()\n\tlist (APPEND _cmd WORKING_DIRECTORY \"${CMAKE_CURRENT_BINARY_DIR}\" VERBATIM)\n\tif (Mathematica_DEBUG)\n\t\tmessage (STATUS \"add_custom_target: ${_cmd}\")\n\tendif()\n\tadd_custom_target(${_cmd})\nendfunction(Mathematica_ADD_CUSTOM_TARGET)\n\n# public function for executing Mathematica code at build time to produce output files\nfunction (Mathematica_ADD_CUSTOM_COMMAND)\n\tset(_options PRE_BUILD PRE_LINK POST_BUILD APPEND)\n\tset(_oneValueArgs SCRIPT COMMENT MAIN_DEPENDENCY TARGET SYSTEM_ID)\n\tset(_multiValueArgs CODE OUTPUT DEPENDS KERNEL_OPTIONS)\n\tcmake_parse_arguments(_option \"${_options}\" \"${_oneValueArgs}\" \"${_multiValueArgs}\" ${ARGN})\n\tif(_option_UNPARSED_ARGUMENTS)\n\t\tmessage (FATAL_ERROR \"Unknown keywords: ${_option_UNPARSED_ARGUMENTS}\")\n\telseif (NOT _option_CODE AND NOT _option_SCRIPT)\n\t\tmessage (FATAL_ERROR \"Either the keyword CODE or SCRIPT must be present.\")\n\telseif (NOT _option_OUTPUT AND NOT _option_TARGET)\n\t\tmessage (FATAL_ERROR \"Either the keyword OUTPUT or TARGET must be present.\")\n\telseif (_option_OUTPUT AND _option_TARGET)\n\t\tmessage (FATAL_ERROR \"Keywords OUTPUT and TARGET are mutually exclusive.\")\n\tendif()\n\tif (_option_OUTPUT)\n\t\tset (_cmd OUTPUT ${_option_OUTPUT})\n\tendif()\n\tif (_option_TARGET)\n\t\tset (_cmd TARGET ${_option_TARGET})\n\tendif()\n\tif (_option_PRE_BUILD)\n\t\tlist(APPEND _cmd PRE_BUILD)\n\tendif()\n\tif (_option_PRE_LINK)\n\t\tlist(APPEND _cmd PRE_LINK)\n\tendif()\n\tif (_option_POST_BUILD)\n\t\tlist(APPEND _cmd POST_BUILD)\n\tendif()\n\tlist(APPEND _cmd COMMAND)\n\t_add_kernel_launch_code(_cmd _option_SYSTEM_ID _option_KERNEL_OPTIONS)\n\t_add_script_or_code(_cmd _option_SCRIPT _option_CODE)\n\tif (_option_MAIN_DEPENDENCY)\n\t\tlist(APPEND _cmd MAIN_DEPENDENCY ${_option_MAIN_DEPENDENCY})\n\tendif()\n\tif (_option_SCRIPT AND _option_OUTPUT)\n\t\tlist (APPEND _option_DEPENDS ${_option_SCRIPT})\n\tendif()\n\tif (_option_DEPENDS)\n\t\tlist(APPEND _cmd DEPENDS ${_option_DEPENDS})\n\tendif()\n\tif (_option_COMMENT)\n\t\tlist(APPEND _cmd COMMENT ${_option_COMMENT})\n\tendif()\n\tlist (APPEND _cmd WORKING_DIRECTORY \"${CMAKE_CURRENT_BINARY_DIR}\" VERBATIM)\n\tif (_option_APPEND)\n\t\tlist(APPEND _cmd APPEND)\n\tendif()\n\tif (Mathematica_DEBUG)\n\t\tmessage (STATUS \"add_custom_command: ${_cmd}\")\n\tendif()\n\tadd_custom_command(${_cmd})\nendfunction(Mathematica_ADD_CUSTOM_COMMAND)\n\n# public function to simplify testing Mathematica commands\nfunction (Mathematica_ADD_TEST)\n\tset(_options \"\")\n\tset(_oneValueArgs NAME SCRIPT INPUT INPUT_FILE SYSTEM_ID)\n\tset(_multiValueArgs CODE CONFIGURATIONS COMMAND KERNEL_OPTIONS)\n\tcmake_parse_arguments(_option \"${_options}\" \"${_oneValueArgs}\" \"${_multiValueArgs}\" ${ARGN})\n\tif(_option_UNPARSED_ARGUMENTS)\n\t\tmessage (FATAL_ERROR \"Unknown keywords: ${_option_UNPARSED_ARGUMENTS}\")\n\telseif (NOT _option_NAME)\n\t\tmessage (FATAL_ERROR \"Mandatory parameter NAME is missing.\")\n\telseif (NOT _option_CODE AND NOT _option_SCRIPT AND NOT _option_COMMAND)\n\t\tmessage (FATAL_ERROR \"Either the keyword CODE, SCRIPT or COMMAND must be present.\")\n\tendif()\n\tset (_cmd NAME \"${_option_NAME}\" COMMAND)\n\t_add_test_driver(_cmd \"${_option_NAME}\" _option_INPUT _option_INPUT_FILE)\n\tif (_option_COMMAND)\n\t\t_add_launch_prefix(_cmd _option_SYSTEM_ID)\n\t\tlist (APPEND _cmd ${_option_COMMAND})\n\telse()\n\t\t_add_kernel_launch_code(_cmd _option_SYSTEM_ID _option_KERNEL_OPTIONS)\n\t\t_add_script_or_code(_cmd _option_SCRIPT _option_CODE)\n\tendif()\n\tif (_option_CONFIGURATIONS)\n\t\tlist (APPEND _cmd CONFIGURATIONS ${_option_CONFIGURATIONS})\n\tendif()\n\tif (Mathematica_DEBUG)\n\t\tmessage (STATUS \"add_test: ${_cmd}\")\n\tendif()\n\tadd_test (${_cmd})\nendfunction (Mathematica_ADD_TEST)\n\n# public function to add target that runs Mathematica Encode function on input files\nfunction (Mathematica_ENCODE)\n\tset(_options \"CHECK_TIMESTAMPS\")\n\tset(_oneValueArgs \"COMMENT\" \"KEY\" \"MACHINE_ID\")\n\tset(_multiValueArgs \"OUTPUT\")\n\tcmake_parse_arguments(_option \"${_options}\" \"${_oneValueArgs}\" \"${_multiValueArgs}\" ${ARGN})\n\tset (_inputFiles ${_option_UNPARSED_ARGUMENTS})\n\tlist (LENGTH _inputFiles _inputFileCount)\n\tif (_inputFileCount EQUAL 0)\n\t\tmessage (WARNING \"No input files to encode given.\")\n\t\treturn()\n\tendif()\n\tif (_option_OUTPUT)\n\t\tset (_outputFiles ${_option_OUTPUT})\n\telse()\n\t\t# no output option given, write encoded files to CMAKE_CURRENT_BINARY_DIR\n\t\tset (_outputFiles ${CMAKE_CURRENT_BINARY_DIR})\n\tendif()\n\tlist (LENGTH _outputFiles _outputFileCount)\n\tif (_outputFileCount EQUAL 1 AND _inputFileCount GREATER 1 AND IS_DIRECTORY \"${_outputFiles}\")\n\t\t# OUTPUT option is a single existing directory, write encoded files to it\n\t\tset (_outputDir \"${_outputFiles}\")\n\t\tmath(EXPR _lastIndex \"${_inputFileCount} - 2\")\n\t\tforeach(_index RANGE ${_lastIndex})\n\t\t\tlist (APPEND _outputFiles \"${_outputDir}\")\n\t\tendforeach()\n\t\tset (_outputFileCount ${_inputFileCount})\n\tendif()\n\tset (_outputFilesAbs \"\")\n\tset (_inputFilesAbs \"\")\n\tset (_outputDirs \"\")\n\tif (_outputFileCount EQUAL _inputFileCount)\n\t\tmath(EXPR _lastIndex \"${_inputFileCount} - 1\")\n\t\tforeach(_index RANGE ${_lastIndex})\n\t\t\tlist (GET _inputFiles ${_index} _inputFile)\n\t\t\tget_filename_component(_inputFileAbs \"${_inputFile}\" ABSOLUTE)\n\t\t\tlist (APPEND _inputFilesAbs \"${_inputFileAbs}\")\n\t\t\tlist (GET _outputFiles ${_index} _outputFile)\n\t\t\tif (IS_DIRECTORY \"${_outputFile}\")\n\t\t\t\tfile (RELATIVE_PATH _inputFileRel ${CMAKE_CURRENT_SOURCE_DIR} \"${_inputFileAbs}\")\n\t\t\t\tif (NOT IS_ABSOLUTE \"${_inputFileRel}\" AND NOT \"${_inputFileRel}\" MATCHES \"^\\\\.\\\\.\")\n\t\t\t\t\tset (_outputFile \"${_outputFile}/${_inputFileRel}\")\n\t\t\t\telse()\n\t\t\t\t\tget_filename_component(_inputFileName \"${_inputFile}\" NAME)\n\t\t\t\t\tset (_outputFile \"${_outputFile}/${_inputFileName}\")\n\t\t\t\tendif()\n\t\t\tendif()\n\t\t\tif (IS_ABSOLUTE \"${_outputFile}\")\n\t\t\t\tlist (APPEND _outputFilesAbs \"${_outputFile}\")\n\t\t\telse()\n\t\t\t\tlist (APPEND _outputFilesAbs \"${CMAKE_CURRENT_BINARY_DIR}/${_outputFile}\")\n\t\t\tendif()\n\t\t\tget_filename_component(_outputFileDir \"${_outputFile}\" DIRECTORY)\n\t\t\tif (NOT _outputFileDir STREQUAL \"${CMAKE_CURRENT_BINARY_DIR}\")\n\t\t\t\tlist (APPEND _outputDirs \"${_outputFileDir}\")\n\t\t\tendif()\n\t\tendforeach()\n\telse()\n\t\t# OUTPUT option must have exactly one entry for each input file\n\t\tmessage (FATAL_ERROR\n\t\t\t\"Number of output files (${_outputFileCount}) does not match number of input files (${_inputFileCount}).\")\n\tendif()\n\tMathematica_TO_NATIVE_PATH(\"${_inputFilesAbs}\" _inputFilesAbsMma)\n\tMathematica_TO_NATIVE_PATH(\"${_outputFilesAbs}\" _outputFilesAbsMma)\n\tset (_cmdOptionsMma \"\")\n\tif (_option_KEY)\n\t\tMathematica_TO_NATIVE_STRING(\"${_option_KEY}\" _keyMma)\n\t\tset (_cmdOptionsMma \"${_cmdOptionsMma},${_keyMma}\")\n\tendif()\n\tif (_option_MACHINE_ID)\n\t\tMathematica_TO_NATIVE_STRING(\"${_option_MACHINE_ID}\" _machineIDMma)\n\t\tset (_cmdOptionsMma \"${_cmdOptionsMma},MachineID->${_machineIDMma}\")\n\tendif()\n\tif (_option_CHECK_TIMESTAMPS)\n\t\tset (_encodeFunc \"If[FileType[#2]==None||OrderedQ[{FileDate[#2],FileDate[#1]}],Encode[#1,#2${_cmdOptionsMma}]]&\")\n\telse()\n\t\tset (_encodeFunc \"Encode[#1,#2${_cmdOptionsMma}]&\")\n\tendif()\n\tif (_inputFileCount EQUAL 1)\n\t\tset (_func \"Apply\")\n\telse()\n\t\tset (_func \"MapThread\")\n\tendif()\n\tset (_cmds \"\")\n\tif (_outputDirs)\n\t\tlist (SORT _outputDirs)\n\t\tlist (REMOVE_DUPLICATES _outputDirs)\n\t\tMathematica_TO_NATIVE_PATH(\"${_outputDirs}\" _outputDirsMma)\n\t\tlist (APPEND _cmds \"Quiet[CreateDirectory[${_outputDirsMma}]]\")\n\tendif()\n\tlist (APPEND _cmds \"${_func}[${_encodeFunc},{${_inputFilesAbsMma},${_outputFilesAbsMma}}]\")\n\tif (NOT _option_COMMENT)\n\t\tif (_inputFileCount EQUAL 1)\n\t\t\tset (_option_COMMENT \"Encoding ${_inputFiles}\")\n\t\telse()\n\t\t\tset (_option_COMMENT \"Encoding ${_inputFileCount} Mathematica files\")\n\t\tendif()\n\tendif()\n\tMathematica_ADD_CUSTOM_COMMAND(\n\t\tCODE ${_cmds}\n\t\tOUTPUT ${_outputFilesAbs}\n\t\tDEPENDS ${_inputFilesAbs}\n\t\tCOMMENT \"${_option_COMMENT}\")\n\tset_source_files_properties(${_outputFilesAbs} PROPERTIES GENERATED TRUE LABELS \"Mathematica\")\nendfunction(Mathematica_ENCODE)\n\n# public function to find Mathematica package\nfunction (Mathematica_FIND_PACKAGE _var _packageName)\n\tset(_options \"\")\n\tset(_oneValueArgs DOC SYSTEM_ID)\n\tset(_multiValueArgs KERNEL_OPTIONS)\n\tcmake_parse_arguments(_option \"${_options}\" \"${_oneValueArgs}\" \"${_multiValueArgs}\" ${ARGN})\n\tif(_option_UNPARSED_ARGUMENTS)\n\t\tmessage (FATAL_ERROR \"Unknown keywords: ${_option_UNPARSED_ARGUMENTS}\")\n\tendif()\n\t# determine MUnit package directory\n\tMathematica_TO_NATIVE_STRING(\"${_packageName}\" _packageNameMma)\n\t# default to using FileNames function\n\tset (_findPackage \"Print[StandardForm[Check[First[FileNames[ContextToFileName[${_packageNameMma}],$Path]],$Failed]]]\")\n\tif (DEFINED Mathematica_VERSION)\n\t\tif (NOT \"${Mathematica_VERSION}\" VERSION_LESS \"7.0\")\n\t\t\t# function FindFile available since Mathematica 7\n\t\t\tset (_findPackage \"Print[StandardForm[FindFile[${_packageNameMma}]]]\")\n\t\tendif()\n\tendif()\n\tif (NOT _option_DOC)\n\t\tset (_option_DOC \"Mathematica package file path.\")\n\tendif()\n\tset (_cmd\n\t\tCODE \"${_findPackage}\"\n\t\tOUTPUT_VARIABLE ${_var}\n\t\tCACHE DOC \"${_option_DOC}\"\n\t\tTIMEOUT 10)\n\tif (_option_KERNEL_FLAGS)\n\t\tlist (APPEND _cmd KERNEL_OPTIONS ${_option_KERNEL_FLAGS})\n\tendif()\n\tif (_option_SYSTEM_ID)\n\t\tlist (APPEND _cmd SYSTEM_ID ${_option_SYSTEM_ID})\n\tendif()\n\t# if package file variable already defined, verify package file existence\n\tif (DEFINED ${_var})\n\t\tif (NOT EXISTS \"${${_var}}\")\n\t\t\tunset(${_var} CACHE)\n\t\t\tunset(${_var})\n\t\tendif()\n\tendif()\n\tMathematica_EXECUTE(${_cmd})\n\t# verify package file existence\n\tif (DEFINED ${_var})\n\t\tif (EXISTS \"${${_var}}\")\n\t\t\t_to_cmake_path(\"${${_var}}\" ${_var})\n\t\telse()\n\t\t\tset (${_var} \"${_var}-NOTFOUND\")\n\t\tendif()\n\telse()\n\t\tset (${_var} \"${_var}-NOTFOUND\")\n\tendif()\n\tset (${_var} \"${${_var}}\" CACHE FILEPATH \"${_option_DOC}\" FORCE)\n\tset (${_var} \"${${_var}}\" PARENT_SCOPE)\nendfunction()\n\n# public function to get root Mathematica package directory from a package file\nfunction (Mathematica_GET_PACKAGE_DIR _var _packageFile)\n\t_get_supported_systemIDs(\"${Mathematica_VERSION}\" _intermediateDirs)\n\tlist (APPEND _intermediateDirs\n\t\t\"Kernel\" \"SystemResources\" \"SystemFiles\" \"Binaries\"\n\t\t\"Libraries\" \"LibraryResources\" \"Java\" \"CSource\")\n\tif (NOT EXISTS \"${_packageFile}\")\n\t\tset (${_var} \"${_var}-NOTFOUND\" PARENT_SCOPE)\n\t\treturn()\n\tendif()\n\t# walk up directory tree until we find package root dir\n\tset (_packageFileDir \"${_packageFile}\")\n\tset (_index 0)\n\twhile (NOT ${_index} EQUAL -1)\n\t\tget_filename_component(_packageFileDir \"${_packageFileDir}\" DIRECTORY)\n\t\tget_filename_component(_name \"${_packageFileDir}\" NAME)\n\t\tlist (FIND _intermediateDirs \"${_name}\" _index)\n\tendwhile()\n\tset (${_var} ${_packageFileDir} PARENT_SCOPE)\nendfunction()\n\nendif (Mathematica_KERNEL_EXECUTABLE)\n\n# re-compute system IDs and base directories, now that we can query the kernel\n_setup_mathematica_systemIDs()\n_setup_mathematica_creationID()\n_setup_mathematica_base_directory()\n_setup_mathematica_userbase_directory()\n\n# find Mathematica components\n_find_components()\n_setup_mathematica_version_variables()\n_update_cache()\n_setup_found_variables()\n_log_found_variables()\n\n# public function for fixing shared library references to dynamic Mathematica runtime libraries under Mac OS X\nfunction (Mathematica_ABSOLUTIZE_LIBRARY_DEPENDENCIES)\n\tif (APPLE)\n\t\tforeach(_target ${ARGV})\n\t\t\tget_target_property(_targetType ${_target} TYPE)\n\t\t\tif (_targetType MATCHES \"MODULE_LIBRARY|SHARED_LIBRARY|EXECUTABLE\")\n\t\t\t\tforeach(_library Mathematica_WolframLibrary_LIBRARY Mathematica_MathLink_LIBRARY Mathematica_WSTP_LIBRARY)\n\t\t\t\t\tif (DEFINED ${_library})\n\t\t\t\t\t\t_get_install_name(\"${${_library}}\" _libraryInstallName _libraryAbsPath)\n\t\t\t\t\t\tif (_libraryInstallName)\n\t\t\t\t\t\t\tadd_custom_command (TARGET ${_target}\n\t\t\t\t\t\t\t\tPOST_BUILD COMMAND \"${CMAKE_INSTALL_NAME_TOOL}\"\n\t\t\t\t\t\t\t\t\t\"-change\" \"${_libraryInstallName}\" \"${_libraryAbsPath}\"\n\t\t\t\t\t\t\t\t\"$<TARGET_FILE:${_target}>\" VERBATIM)\n\t\t\t\t\t\tendif()\n\t\t\t\t\tendif()\n\t\t\t\tendforeach()\n\t\t\tendif()\n\t\tendforeach()\n\tendif()\nendfunction()\n\nif (Mathematica_KERNEL_EXECUTABLE AND Mathematica_MathLink_FOUND)\n\n# public function to simplify testing MathLink programs\nfunction (Mathematica_MathLink_ADD_TEST)\n\tset(_options \"\")\n\tset(_oneValueArgs NAME SCRIPT TARGET INPUT INPUT_FILE SYSTEM_ID LINK_PROTOCOL LINK_MODE)\n\tset(_multiValueArgs CODE CONFIGURATIONS KERNEL_OPTIONS)\n\tcmake_parse_arguments(_option \"${_options}\" \"${_oneValueArgs}\" \"${_multiValueArgs}\" ${ARGN})\n\tif(_option_UNPARSED_ARGUMENTS)\n\t\tmessage (FATAL_ERROR \"Unknown keywords: ${_option_UNPARSED_ARGUMENTS}\")\n\telseif (NOT _option_TARGET)\n\t\tmessage (FATAL_ERROR \"Mandatory parameter TARGET is missing.\")\n\telseif (NOT _option_NAME)\n\t\tmessage (FATAL_ERROR \"Mandatory parameter NAME is missing.\")\n\tendif()\n\tif (NOT _option_LINK_MODE)\n\t\tif (_option_CODE OR _option_SCRIPT)\n\t\t\tset (_option_LINK_MODE \"ParentConnect\")\n\t\telse()\n\t\t\tset (_option_LINK_MODE \"Launch\")\n\t\tendif()\n\tendif()\n\tset (_cmd NAME \"${_option_NAME}\" COMMAND)\n\t_add_test_driver(_cmd \"${_option_NAME}\" _option_INPUT _option_INPUT_FILE)\n\tif (_option_LINK_MODE MATCHES \"^ParentConnect$\")\n\t\t# run Mathematica kernel and launch MathLink executable as a child process that connects with ParentConnect\n\t\tif (CYGWIN OR MSYS)\n\t\t\tget_target_property (_targetFile ${_option_TARGET} LOCATION)\n\t\t\tMathematica_TO_NATIVE_PATH(\"${_targetFile}\" _installCmdMma)\n\t\telse()\n\t\t\tset (_installCmdMma \"\\\"$<TARGET_FILE:${_option_TARGET}>\\\"\")\n\t\tendif()\n\t\tset (_launch_prefix \"\")\n\t\t_add_launch_prefix(_launch_prefix _option_SYSTEM_ID)\n\t\tif (_launch_prefix)\n\t\t\tMathematica_TO_NATIVE_LIST(_launch_prefixMma ${_launch_prefix})\n\t\t\tset (_installCmdMma\n\t\t\t\t\"StringJoin[StringInsert[${_launch_prefixMma},\\\" \\\",-1],StringInsert[${_installCmdMma},\\\"\\\\\\\"\\\",{1,-1}]]\" )\n\t\tendif()\n\t\tif (_option_LINK_PROTOCOL)\n\t\t\tset (_installCmd \"link=Install[${_installCmdMma},LinkProtocol->\\\"${_option_LINK_PROTOCOL}\\\"]\")\n\t\telse()\n\t\t\tset (_installCmd \"link=Install[${_installCmdMma}]\")\n\t\tendif()\n\t\tif (_option_CODE)\n\t\t\tlist (APPEND _installCmd ${_option_CODE})\n\t\tendif()\n\t\tif (NOT _option_SCRIPT)\n\t\t\tlist (APPEND _installCmd \"Uninstall[link]\")\n\t\tendif()\n\t\t_add_kernel_launch_code(_cmd _option_SYSTEM_ID _option_KERNEL_OPTIONS)\n\t\t_add_script_or_code(_cmd _option_SCRIPT _installCmd)\n\telseif (_option_LINK_MODE MATCHES \"^Launch$\")\n\t\t# run MathLink executable as front-end to Mathematica kernel\n\t\t_add_launch_prefix(_cmd _option_SYSTEM_ID)\n\t\tlist (APPEND _cmd \"$<TARGET_FILE:${_option_TARGET}>\")\n\t\t_add_linkmode_launch_code(_cmd \"-mathlink\"\n\t\t\t_option_SYSTEM_ID _option_KERNEL_OPTIONS _option_LINK_PROTOCOL\n\t\t\t_option_SCRIPT _option_CODE)\n\telse()\n\t\tmessage (FATAL_ERROR \"Parameter LINK_MODE must be either \\\"Launch\\\" or \\\"ParentConnect\\\".\")\n\tendif()\n\tif (_option_CONFIGURATIONS)\n\t\tlist (APPEND _cmd CONFIGURATIONS ${_option_CONFIGURATIONS})\n\tendif()\n\tif (Mathematica_DEBUG)\n\t\tmessage (STATUS \"add_test: ${_cmd}\")\n\tendif()\n\tadd_test (${_cmd})\nendfunction(Mathematica_MathLink_ADD_TEST)\n\nendif (Mathematica_KERNEL_EXECUTABLE AND Mathematica_MathLink_FOUND)\n\nif (Mathematica_KERNEL_EXECUTABLE AND Mathematica_WSTP_FOUND)\n\n# public function to simplify testing WSTP programs\nfunction (Mathematica_WSTP_ADD_TEST)\n\tset(_options \"\")\n\tset(_oneValueArgs NAME SCRIPT TARGET INPUT INPUT_FILE SYSTEM_ID LINK_PROTOCOL)\n\tset(_multiValueArgs CODE CONFIGURATIONS KERNEL_OPTIONS)\n\tcmake_parse_arguments(_option \"${_options}\" \"${_oneValueArgs}\" \"${_multiValueArgs}\" ${ARGN})\n\tif(_option_UNPARSED_ARGUMENTS)\n\t\tmessage (FATAL_ERROR \"Unknown keywords: ${_option_UNPARSED_ARGUMENTS}\")\n\telseif (NOT _option_TARGET)\n\t\tmessage (FATAL_ERROR \"Mandatory parameter TARGET is missing.\")\n\telseif (NOT _option_NAME)\n\t\tmessage (FATAL_ERROR \"Mandatory parameter NAME is missing.\")\n\tendif()\n\tset (_cmd NAME \"${_option_NAME}\" COMMAND)\n\t_add_test_driver(_cmd \"${_option_NAME}\" _option_INPUT _option_INPUT_FILE)\n\tif (_option_CODE OR _option_SCRIPT)\n\t\t# run Mathematica kernel and install WSTP executable\n\t\tif (CYGWIN OR MSYS)\n\t\t\tget_target_property (_targetFile ${_option_TARGET} LOCATION)\n\t\t\tMathematica_TO_NATIVE_PATH(\"${_targetFile}\" _installCmdMma)\n\t\telse()\n\t\t\tset (_installCmdMma \"\\\"$<TARGET_FILE:${_option_TARGET}>\\\"\")\n\t\tendif()\n\t\tset (_launch_prefix \"\")\n\t\t_add_launch_prefix(_launch_prefix _option_SYSTEM_ID)\n\t\tif (_launch_prefix)\n\t\t\tMathematica_TO_NATIVE_LIST(_launch_prefixMma ${_launch_prefix})\n\t\t\tset (_installCmdMma\n\t\t\t\t\"StringJoin[StringInsert[${_launch_prefixMma},\\\" \\\",-1],StringInsert[${_installCmdMma},\\\"\\\\\\\"\\\",{1,-1}]]\" )\n\t\tendif()\n\t\tif (_option_LINK_PROTOCOL)\n\t\t\tset (_installCmd \"link=Install[${_installCmdMma},LinkProtocol->\\\"${_option_LINK_PROTOCOL}\\\"]\")\n\t\telse()\n\t\t\tset (_installCmd \"link=Install[${_installCmdMma}]\")\n\t\tendif()\n\t\tif (_option_CODE)\n\t\t\tlist (APPEND _installCmd ${_option_CODE})\n\t\tendif()\n\t\tif (NOT _option_SCRIPT)\n\t\t\tlist (APPEND _installCmd \"Uninstall[link]\")\n\t\tendif()\n\t\t_add_kernel_launch_code(_cmd _option_SYSTEM_ID _option_KERNEL_OPTIONS)\n\t\t_add_script_or_code(_cmd _option_SCRIPT _installCmd)\n\telse()\n\t\t# run WSTP executable as front-end to Mathematica kernel\n\t\t_add_launch_prefix(_cmd _option_SYSTEM_ID)\n\t\tlist (APPEND _cmd \"$<TARGET_FILE:${_option_TARGET}>\")\n\t\t_add_linkmode_launch_code(_cmd \"-wstp\"\n\t\t\t_option_SYSTEM_ID _option_KERNEL_OPTIONS _option_LINK_PROTOCOL\n\t\t\t_option_SCRIPT _option_CODE)\n\tendif()\n\tif (_option_CONFIGURATIONS)\n\t\tlist (APPEND _cmd CONFIGURATIONS ${_option_CONFIGURATIONS})\n\tendif()\n\tif (Mathematica_DEBUG)\n\t\tmessage (STATUS \"add_test: ${_cmd}\")\n\tendif()\n\tadd_test (${_cmd})\nendfunction(Mathematica_WSTP_ADD_TEST)\n\nendif (Mathematica_KERNEL_EXECUTABLE AND Mathematica_WSTP_FOUND)\n\nif (Mathematica_KERNEL_EXECUTABLE AND Mathematica_WolframLibrary_FOUND)\n\n# public function to add target that creates C code from Mathematica code\nfunction (Mathematica_GENERATE_C_CODE _packageFile)\n\tget_filename_component(_packageFileBaseName ${_packageFile} NAME_WE)\n\tget_filename_component(_packageFileName ${_packageFile} NAME)\n\tget_filename_component(_packageFileAbs ${_packageFile} ABSOLUTE)\n\tset(_options \"\")\n\tset(_oneValueArgs \"OUTPUT\")\n\tset(_multiValueArgs \"DEPENDS\")\n\tcmake_parse_arguments(_option \"${_options}\" \"${_oneValueArgs}\" \"${_multiValueArgs}\" ${ARGN})\n\tif(_option_UNPARSED_ARGUMENTS)\n\t\tmessage (FATAL_ERROR \"Unknown keywords: ${_option_UNPARSED_ARGUMENTS}\")\n\tendif()\n\tif (_option_OUTPUT)\n\t\tset (_cSource \"${_option_OUTPUT}\")\n\t\tget_filename_component(_cHeaderBaseName ${_cSource} NAME_WE)\n\t\tset (_cHeader \"${_cHeaderBaseName}.h\")\n\telse()\n\t\tset (_cSource \"${_packageFileName}.c\")\n\t\tset (_cHeader \"${_packageFileName}.h\")\n\t\tset (_cHeaderBaseName \"${_packageFileName}\")\n\tendif()\n\tMathematica_TO_NATIVE_PATH(${_packageFileAbs} _packageFileAbsMma)\n\tMathematica_TO_NATIVE_PATH(${_cSource} _cSourceMma)\n\tMathematica_TO_NATIVE_PATH(${_cHeader} _cHeaderMma)\n\tMathematica_TO_NATIVE_STRING(${_cHeaderBaseName} _cHeaderBaseNameMma)\n\tMathematica_TO_NATIVE_STRING(${_packageFileBaseName} _packageFileBaseNameMma)\n\tstring (REGEX REPLACE \"\\n|\\t\" \"\" _codeGenerate\n\t\t\"Module[{functions=Get[${_packageFileAbsMma}]},\n\t\t\tIf[ListQ[functions],\n\t\t\t\tCompoundExpression[\n\t\t\t\t\tCCodeGenerate[Sequence@@functions,${_cSourceMma},\n\t\t\t\t\t\t\\\"CodeTarget\\\"->\\\"WolframRTL\\\",\n\t\t\t\t\t\t\\\"HeaderName\\\"->${_cHeaderBaseNameMma},\n\t\t\t\t\t\t\\\"LifeCycleFunctionNames\\\"->${_packageFileBaseNameMma}],\n\t\t\t\t\tCCodeGenerate[Sequence@@functions,${_cHeaderMma},\n\t\t\t\t\t\t\\\"CodeTarget\\\"->\\\"WolframRTLHeader\\\",\n\t\t\t\t\t\t\\\"LifeCycleFunctionNames\\\"->${_packageFileBaseNameMma}]\n\t\t\t\t]\n\t\t\t]\n\t\t]\")\n\tlist (INSERT _codeGenerate 0 \"Needs[\\\"CCodeGenerator`\\\"]\")\n\tset (_msg \"Generating source ${_cSource} and header ${_cHeader} from ${_packageFile}\")\n\tlist (INSERT _option_DEPENDS 0 \"${_packageFileAbs}\")\n\tMathematica_ADD_CUSTOM_COMMAND(\n\t\tOUTPUT \"${_cSource}\" \"${_cHeader}\"\n\t\tCODE ${_codeGenerate}\n\t\tDEPENDS ${_option_DEPENDS}\n\t\tCOMMENT \"${_msg}\")\n\tset_source_files_properties(\"${_cSource}\" \"${_cHeader}\"\n\t\tPROPERTIES GENERATED TRUE LABELS \"Mathematica\")\nendfunction(Mathematica_GENERATE_C_CODE)\n\n# public function to simplify testing WolframLibrary targets\nfunction (Mathematica_WolframLibrary_ADD_TEST)\n\tset(_options \"\")\n\tset(_oneValueArgs NAME SCRIPT TARGET INPUT INPUT_FILE SYSTEM_ID)\n\tset(_multiValueArgs CODE CONFIGURATIONS KERNEL_OPTIONS)\n\tcmake_parse_arguments(_option \"${_options}\" \"${_oneValueArgs}\" \"${_multiValueArgs}\" ${ARGN})\n\tif(_option_UNPARSED_ARGUMENTS)\n\t\tmessage (FATAL_ERROR \"Unknown keywords: ${_option_UNPARSED_ARGUMENTS}\")\n\telseif (NOT _option_TARGET)\n\t\tmessage (FATAL_ERROR \"Mandatory parameter TARGET is missing.\")\n\telseif (NOT _option_NAME)\n\t\tmessage (FATAL_ERROR \"Mandatory parameter NAME is missing.\")\n\telseif (NOT _option_CODE AND NOT _option_SCRIPT)\n\t\tmessage (FATAL_ERROR \"Either the keyword CODE or SCRIPT must be present.\")\n\tendif()\n\tset (_cmd NAME \"${_option_NAME}\" COMMAND)\n\t_add_test_driver(_cmd \"${_option_NAME}\" _option_INPUT _option_INPUT_FILE)\n\t# run Mathematica kernel and load Wolfram library\n\tif (CYGWIN OR MSYS)\n\t\tget_target_property (_targetFile ${_option_TARGET} LOCATION)\n\t\tMathematica_TO_NATIVE_PATH(\"${_targetFile}\" _targetFileMma)\n\telse()\n\t\tset (_targetFileMma \"\\\"$<TARGET_FILE:${_option_TARGET}>\\\"\")\n\tendif()\n\tset (_installCmd\n\t\t\"libPath = ${_targetFileMma}\"\n\t\t\"LibraryLoad[libPath]\"\n\t\t\"Print[LibraryLink`$LibraryError]\" )\n\tif (_option_CODE)\n\t\tlist (APPEND _installCmd ${_option_CODE})\n\tendif()\n\tif (NOT _option_SCRIPT)\n\t\tlist (APPEND _installCmd \"LibraryUnload[libPath]\")\n\tendif()\n\t_add_kernel_launch_code(_cmd _option_SYSTEM_ID _option_KERNEL_OPTIONS)\n\t_add_script_or_code(_cmd _option_SCRIPT _installCmd)\n\tif (_option_CONFIGURATIONS)\n\t\tlist (APPEND _cmd CONFIGURATIONS ${_option_CONFIGURATIONS})\n\tendif()\n\tif (Mathematica_DEBUG)\n\t\tmessage (STATUS \"add_test: ${_cmd}\")\n\tendif()\n\tadd_test (${_cmd})\nendfunction(Mathematica_WolframLibrary_ADD_TEST)\n\nendif (Mathematica_KERNEL_EXECUTABLE AND Mathematica_WolframLibrary_FOUND)\n\nif (Mathematica_WolframLibrary_FOUND)\n\n# public function that sets dynamic library names according to LibraryLink naming conventions\nfunction (Mathematica_WolframLibrary_SET_PROPERTIES)\n\tset (_haveProperties False)\n\tforeach (_libraryName ${ARGV})\n\t\tif (\"${_libraryName}\" STREQUAL \"PROPERTIES\")\n\t\t\tset (_haveProperties True)\n\t\t\tbreak()\n\t\tendif()\n\t\tset_target_properties (${_libraryName} PROPERTIES PREFIX \"\")\n\t\tif (WIN32 OR CYGWIN)\n\t\t\tset_target_properties (${_libraryName} PROPERTIES SUFFIX \".dll\")\n\t\telseif (APPLE)\n\t\t\tset_target_properties (${_libraryName} PROPERTIES SUFFIX \".dylib\")\n\t\telseif (UNIX)\n\t\t\tset_target_properties (${_libraryName} PROPERTIES SUFFIX \".so\")\n\t\tendif()\n\t\tset_target_properties (${_libraryName} PROPERTIES LABELS \"Mathematica\")\n\t\tif (CYGWIN AND CMAKE_COMPILER_IS_GNUCC)\n\t\t\t# Mathematica kernel cannot load Cygwin generated libraries linked with Cygwin runtime DLL\n\t\t\t# a work-around is to use the -mno-cygwin flag, which is only supported by gcc 3.x, not by gcc 4.x\n\t\t\tif (NOT \"${CMAKE_C_COMPILER_VERSION}\" VERSION_LESS \"3.0.0\" AND \"${CMAKE_C_COMPILER_VERSION}\" VERSION_LESS \"4.0.0\")\n\t\t\t\tset_target_properties (${_libraryName} PROPERTIES COMPILE_OPTIONS \"-mno-cygwin\")\n\t\t\t\tset_target_properties (${_libraryName} PROPERTIES LINK_FLAGS \"-mno-cygwin\")\n\t\t\tendif()\n\t\tendif()\n\tendforeach()\n\tif (_haveProperties)\n\t\tset_target_properties (${ARGV})\n\tendif()\nendfunction(Mathematica_WolframLibrary_SET_PROPERTIES)\n\n# public function for creating dynamic library loadable with LibraryLink\nfunction (Mathematica_ADD_LIBRARY _libraryName)\n\tadd_library (${_libraryName} MODULE ${ARGN})\n\tMathematica_WolframLibrary_SET_PROPERTIES(${_libraryName})\nendfunction()\n\nendif (Mathematica_WolframLibrary_FOUND)\n\nif (Mathematica_MathLink_MPREP_EXECUTABLE)\n\n# public function for creating source file from template file using mprep\nfunction (Mathematica_MathLink_MPREP_TARGET _templateFile)\n\tget_filename_component(_templateFileName ${_templateFile} NAME)\n\tget_filename_component(_templateFileAbs ${_templateFile} ABSOLUTE)\n\tset(_options LINE_DIRECTIVES)\n\tset(_oneValueArgs OUTPUT CUSTOM_HEADER CUSTOM_TRAILER)\n\tset(_multiValueArgs \"\")\n\tcmake_parse_arguments(_option \"${_options}\" \"${_oneValueArgs}\" \"${_multiValueArgs}\" ${ARGN})\n\tif(_option_UNPARSED_ARGUMENTS)\n\t\tmessage (FATAL_ERROR \"Unknown keywords: ${_option_UNPARSED_ARGUMENTS}\")\n\tendif()\n\tif (_option_OUTPUT)\n\t\tset (_outfile ${_option_OUTPUT})\n\telse()\n\t\t_get_mprep_output_file(\"${_templateFile}\" _outfile)\n\tendif()\n\t_to_native_path (\"${Mathematica_MathLink_MPREP_EXECUTABLE}\" _mprepExeNative)\n\t_to_native_path (\"${_outfile}\" _outfileNative)\n\tset (_command \"${_mprepExeNative}\" \"-o\" \"${_outfileNative}\")\n\tset (_dependencies \"${Mathematica_MathLink_MPREP_EXECUTABLE}\")\n\tif (_option_CUSTOM_HEADER)\n\t\t_to_native_path (\"${_option_CUSTOM_HEADER}\" _customHeaderNative)\n\t\tlist (APPEND _command \"-h\" \"${_customHeaderNative}\")\n\t\tlist (APPEND _dependencies \"${_option_CUSTOM_HEADER}\")\n\tendif()\n\tif (_option_CUSTOM_TRAILER)\n\t\t_to_native_path (\"${_option_CUSTOM_TRAILER}\" _customTrailerNative)\n\t\tlist (APPEND _command \"-t\" \"${_customTrailerNative}\")\n\t\tlist (APPEND _dependencies \"${_option_CUSTOM_TRAILER}\")\n\tendif()\n\tif (_option_LINE_DIRECTIVES)\n\t\tlist (APPEND _command \"-lines\")\n\telse()\n\t\tlist (APPEND _command \"-nolines\")\n\tendif()\n\tif (CYGWIN)\n\t\t# under Cygwin invoke mprep.exe with template file argument specified as\n\t\t# a relative path because it cannot handle absolute Cygwin UNIX paths\n\t\tfile (RELATIVE_PATH _templateFileRel ${CMAKE_CURRENT_BINARY_DIR} ${_templateFileAbs})\n\t\tlist (APPEND _command \"${_templateFileRel}\")\n\telse()\n\t\t_to_native_path (\"${_templateFileAbs}\" _templateFileAbsNative)\n\t\tlist (APPEND _command \"${_templateFileAbsNative}\")\n\tendif()\n\tset (_msg \"Generating MathLink source ${_outfile} from ${_templateFileName}\")\n\tadd_custom_command(\n\t\tOUTPUT ${_outfile}\n\t\tCOMMAND ${_command}\n\t\tMAIN_DEPENDENCY ${_templateFileAbs}\n\t\tDEPENDS ${_dependencies}\n\t\tWORKING_DIRECTORY ${CMAKE_CURRENT_BINARY_DIR}\n\t\tCOMMENT ${_msg}\n\t\tVERBATIM)\n\tset_source_files_properties(${_outfile} PROPERTIES GENERATED TRUE LABELS \"Mathematica\")\nendfunction(Mathematica_MathLink_MPREP_TARGET)\n\n# public function for creating MathLink executable from template file and source files\nfunction (Mathematica_MathLink_ADD_EXECUTABLE _executableName _templateFile)\n\t_get_mprep_output_file(${_templateFile} _outfile)\n\tMathematica_MathLink_MPREP_TARGET(${_templateFile} OUTPUT ${_outfile})\n\tadd_executable (${_executableName} WIN32 ${_outfile} ${ARGN})\n\ttarget_link_libraries(${_executableName} PRIVATE ${Mathematica_MathLink_LIBRARIES})\n\tif (Mathematica_MathLink_LINKER_FLAGS)\n\t\tset_target_properties(${_executableName} PROPERTIES LINK_FLAGS \"${Mathematica_MathLink_LINKER_FLAGS}\")\n\tendif()\n\tset_target_properties (${_executableName} PROPERTIES LABELS \"Mathematica\")\nendfunction()\n\n# public function for exporting standard mprep header and trailer code\nfunction (Mathematica_MathLink_MPREP_EXPORT_FRAMES)\n\tset(_options FORCE)\n\tset(_oneValueArgs OUTPUT_DIRECTORY SYSTEM_ID)\n\tset(_multiValueArgs \"\")\n\tcmake_parse_arguments(_option \"${_options}\" \"${_oneValueArgs}\" \"${_multiValueArgs}\" ${ARGN})\n\tif (NOT _option_OUTPUT_DIRECTORY)\n\t\tset (_option_OUTPUT_DIRECTORY \"${CMAKE_CURRENT_BINARY_DIR}\")\n\tendif()\n\tif (NOT _option_SYSTEM_ID)\n\t\tset (_option_SYSTEM_ID \"${Mathematica_HOST_SYSTEM_ID}\")\n\tendif()\n\tset (_headerFileName \"${_option_OUTPUT_DIRECTORY}/mprep_header_${_option_SYSTEM_ID}.txt\")\n\tset (_trailerFileName \"${_option_OUTPUT_DIRECTORY}/mprep_trailer_${_option_SYSTEM_ID}.txt\")\n\tif (NOT _option_FORCE AND\n\t\tEXISTS \"${_headerFileName}\" AND EXISTS \"${_trailerFileName}\")\n\t\tmessage (STATUS \"Mprep header file mprep_header_${_option_SYSTEM_ID}.txt already exists\")\n\t\tmessage (STATUS \"Mprep trailer file mprep_trailer_${_option_SYSTEM_ID}.txt already exists\")\n\t\treturn()\n\tendif()\n\tif (WIN32)\n\t\tset (_input_file \"NUL\")\n\telse()\n\t\tset (_input_file \"/dev/null\")\n\tendif()\n\texecute_process(\n\t\tCOMMAND \"${Mathematica_MathLink_MPREP_EXECUTABLE}\"\n\t\tWORKING_DIRECTORY ${CMAKE_CURRENT_BINARY_DIR}\n\t\tINPUT_FILE \"${_input_file}\"\n\t\tOUTPUT_VARIABLE _mprep_frame\n\t\tOUTPUT_STRIP_TRAILING_WHITESPACE)\n\t# prevent CMake from interpreting ; as a list separator\n\tstring (REPLACE \";\" \"\\\\;\" _mprep_frame \"${_mprep_frame}\")\n\tstring (REPLACE \"\\n\" \";\" _mprep_frame \"${_mprep_frame}\")\n\tset (_header \"\")\n\tset (_trailer \"\")\n\tforeach (_line IN LISTS _mprep_frame)\n\t\tif (\"${_line}\" MATCHES \"MPREP_REVISION ([0-9]+)\")\n\t\t\tset (_mprep_revision \"${CMAKE_MATCH_1}\")\n\t\t\tset (_appendToVar _header)\n\t\telseif (\"${_line}\" MATCHES \"/.*end header.*/\")\n\t\t\tunset (_appendToVar)\n\t\telseif (\"${_line}\" MATCHES \"/.*begin trailer.*/\")\n\t\t\tset (_appendToVar _trailer)\n\t\telseif (DEFINED _appendToVar)\n\t\t\tset (${_appendToVar} \"${${_appendToVar}}${_line}\\n\")\n\t\tendif()\n\tendforeach()\n\tif (\"${_header}\" MATCHES \".+\")\n\t\tmessage (STATUS \"Mprep header revision ${_mprep_revision} exported to ${_headerFileName}\")\n\t\tfile (WRITE \"${_headerFileName}\" \"${_header}\")\n\tendif()\n\tif (\"${_trailer}\" MATCHES \".+\")\n\t\tmessage (STATUS \"Mprep trailer revision ${_mprep_revision} exported to ${_trailerFileName}\")\n\t\tfile (WRITE \"${_trailerFileName}\" \"${_trailer}\")\n\tendif()\nendfunction(Mathematica_MathLink_MPREP_EXPORT_FRAMES)\n\nendif (Mathematica_MathLink_MPREP_EXECUTABLE)\n\nif (Mathematica_WSTP_WSPREP_EXECUTABLE)\n\n# public function for creating source file from template file using mprep\nfunction (Mathematica_WSTP_WSPREP_TARGET _templateFile)\n\tget_filename_component(_templateFileName ${_templateFile} NAME)\n\tget_filename_component(_templateFileAbs ${_templateFile} ABSOLUTE)\n\tset(_options LINE_DIRECTIVES)\n\tset(_oneValueArgs OUTPUT CUSTOM_HEADER CUSTOM_TRAILER)\n\tset(_multiValueArgs \"\")\n\tcmake_parse_arguments(_option \"${_options}\" \"${_oneValueArgs}\" \"${_multiValueArgs}\" ${ARGN})\n\tif(_option_UNPARSED_ARGUMENTS)\n\t\tmessage (FATAL_ERROR \"Unknown keywords: ${_option_UNPARSED_ARGUMENTS}\")\n\tendif()\n\tif (_option_OUTPUT)\n\t\tset (_outfile ${_option_OUTPUT})\n\telse()\n\t\t_get_mprep_output_file(\"${_templateFile}\" _outfile)\n\tendif()\n\t_to_native_path (\"${Mathematica_WSTP_WSPREP_EXECUTABLE}\" _mprepExeNative)\n\t_to_native_path (\"${_outfile}\" _outfileNative)\n\tset (_command \"${_mprepExeNative}\" \"-o\" \"${_outfileNative}\")\n\tset (_dependencies \"${Mathematica_WSTP_WSPREP_EXECUTABLE}\")\n\tif (_option_CUSTOM_HEADER)\n\t\t_to_native_path (\"${_option_CUSTOM_HEADER}\" _customHeaderNative)\n\t\tlist (APPEND _command \"-h\" \"${_customHeaderNative}\")\n\t\tlist (APPEND _dependencies \"${_option_CUSTOM_HEADER}\")\n\tendif()\n\tif (_option_CUSTOM_TRAILER)\n\t\t_to_native_path (\"${_option_CUSTOM_TRAILER}\" _customTrailerNative)\n\t\tlist (APPEND _command \"-t\" \"${_customTrailerNative}\")\n\t\tlist (APPEND _dependencies \"${_option_CUSTOM_TRAILER}\")\n\tendif()\n\tif (_option_LINE_DIRECTIVES)\n\t\tlist (APPEND _command \"-lines\")\n\telse()\n\t\tlist (APPEND _command \"-nolines\")\n\tendif()\n\tif (CYGWIN)\n\t\t# under Cygwin invoke mprep.exe with template file argument specified as\n\t\t# a relative path because it cannot handle absolute Cygwin UNIX paths\n\t\tfile (RELATIVE_PATH _templateFileRel ${CMAKE_CURRENT_BINARY_DIR} ${_templateFileAbs})\n\t\tlist (APPEND _command \"${_templateFileRel}\")\n\telse()\n\t\t_to_native_path (\"${_templateFileAbs}\" _templateFileAbsNative)\n\t\tlist (APPEND _command \"${_templateFileAbsNative}\")\n\tendif()\n\tset (_msg \"Generating WSTP source ${_outfile} from ${_templateFileName}\")\n\tadd_custom_command(\n\t\tOUTPUT ${_outfile}\n\t\tCOMMAND ${_command}\n\t\tMAIN_DEPENDENCY ${_templateFileAbs}\n\t\tDEPENDS ${_dependencies}\n\t\tWORKING_DIRECTORY ${CMAKE_CURRENT_BINARY_DIR}\n\t\tCOMMENT ${_msg}\n\t\tVERBATIM)\n\tset_source_files_properties(${_outfile} PROPERTIES GENERATED TRUE LABELS \"Mathematica\")\nendfunction(Mathematica_WSTP_WSPREP_TARGET)\n\n# public function for creating WSTP executable from template file and source files\nfunction (Mathematica_WSTP_ADD_EXECUTABLE _executableName _templateFile)\n\t_get_mprep_output_file(\"${_templateFile}\" _outfile)\n\tMathematica_WSTP_WSPREP_TARGET(${_templateFile} OUTPUT ${_outfile})\n\tadd_executable (${_executableName} WIN32 ${_outfile} ${ARGN})\n\ttarget_link_libraries(${_executableName} PRIVATE ${Mathematica_WSTP_LIBRARIES})\n\tif (Mathematica_WSTP_LINKER_FLAGS)\n\t\tset_target_properties(${_executableName} PROPERTIES LINK_FLAGS \"${Mathematica_WSTP_LINKER_FLAGS}\")\n\tendif()\n\tset_target_properties (${_executableName} PROPERTIES LABELS \"Mathematica\")\nendfunction()\n\n# public function for exporting standard mprep header and trailer code\nfunction (Mathematica_WSTP_WSPREP_EXPORT_FRAMES)\n\tset(_options FORCE)\n\tset(_oneValueArgs OUTPUT_DIRECTORY SYSTEM_ID)\n\tset(_multiValueArgs \"\")\n\tcmake_parse_arguments(_option \"${_options}\" \"${_oneValueArgs}\" \"${_multiValueArgs}\" ${ARGN})\n\tif (NOT _option_OUTPUT_DIRECTORY)\n\t\tset (_option_OUTPUT_DIRECTORY \"${CMAKE_CURRENT_BINARY_DIR}\")\n\tendif()\n\tif (NOT _option_SYSTEM_ID)\n\t\tset (_option_SYSTEM_ID \"${Mathematica_HOST_SYSTEM_ID}\")\n\tendif()\n\tset (_headerFileName \"${_option_OUTPUT_DIRECTORY}/wsprep_header_${_option_SYSTEM_ID}.txt\")\n\tset (_trailerFileName \"${_option_OUTPUT_DIRECTORY}/wsprep_trailer_${_option_SYSTEM_ID}.txt\")\n\tif (NOT _option_FORCE AND\n\t\tEXISTS \"${_headerFileName}\" AND EXISTS \"${_trailerFileName}\")\n\t\tmessage (STATUS \"wsprep header file wsprep_header_${_option_SYSTEM_ID}.txt already exists\")\n\t\tmessage (STATUS \"wsprep trailer file wsprep_trailer_${_option_SYSTEM_ID}.txt already exists\")\n\t\treturn()\n\tendif()\n\tif (WIN32)\n\t\tset (_input_file \"NUL\")\n\telse()\n\t\tset (_input_file \"/dev/null\")\n\tendif()\n\texecute_process(\n\t\tCOMMAND \"${Mathematica_WSTP_WSPREP_EXECUTABLE}\"\n\t\tWORKING_DIRECTORY ${CMAKE_CURRENT_BINARY_DIR}\n\t\tINPUT_FILE \"${_input_file}\"\n\t\tOUTPUT_VARIABLE _wsprep_frame\n\t\tOUTPUT_STRIP_TRAILING_WHITESPACE)\n\t# prevent CMake from interpreting ; as a list separator\n\tstring (REPLACE \";\" \"\\\\;\" _wsprep_frame \"${_wsprep_frame}\")\n\tstring (REPLACE \"\\n\" \";\" _wsprep_frame \"${_wsprep_frame}\")\n\tset (_header \"\")\n\tset (_trailer \"\")\n\tforeach (_line IN LISTS _wsprep_frame)\n\t\tif (\"${_line}\" MATCHES \"PREP_REVISION ([0-9]+)\")\n\t\t\tset (_wsprep_revision \"${CMAKE_MATCH_1}\")\n\t\t\tset (_appendToVar _header)\n\t\telseif (\"${_line}\" MATCHES \"/.*end header.*/\")\n\t\t\tunset (_appendToVar)\n\t\telseif (\"${_line}\" MATCHES \"/.*begin trailer.*/\")\n\t\t\tset (_appendToVar _trailer)\n\t\telseif (DEFINED _appendToVar)\n\t\t\tset (${_appendToVar} \"${${_appendToVar}}${_line}\\n\")\n\t\tendif()\n\tendforeach()\n\tif (\"${_header}\" MATCHES \".+\")\n\t\tmessage (STATUS \"wsprep header revision ${_wsprep_revision} exported to ${_headerFileName}\")\n\t\tfile (WRITE \"${_headerFileName}\" \"${_header}\")\n\tendif()\n\tif (\"${_trailer}\" MATCHES \".+\")\n\t\tmessage (STATUS \"wsprep trailer revision ${_wsprep_revision} exported to ${_trailerFileName}\")\n\t\tfile (WRITE \"${_trailerFileName}\" \"${_trailer}\")\n\tendif()\nendfunction(Mathematica_WSTP_WSPREP_EXPORT_FRAMES)\n\nendif (Mathematica_WSTP_WSPREP_EXECUTABLE)\n\nif (Mathematica_MUnit_FOUND)\n\n# public function for resolving a TestSuite declaration in a Mathematica unit test file\nfunction (Mathematica_MUnit_RESOLVE_SUITE _var)\n\tset(_options \"\")\n\tset(_oneValueArgs RELATIVE)\n\tset(_multiValueArgs \"\")\n\tcmake_parse_arguments(_option \"${_options}\" \"${_oneValueArgs}\" \"${_multiValueArgs}\" ${ARGN})\n\tset (${_var} \"\")\n\tforeach (_testSuiteFile IN LISTS _option_UNPARSED_ARGUMENTS)\n\t\t# parse test file names from TestSuite[{ ... }]\n\t\tfile (STRINGS \"${_testSuiteFile}\" _testSuite NEWLINE_CONSUME)\n\t\tif (\"${_testSuite}\" MATCHES \"TestSuite\\\\[\")\n\t\t\tstring (REPLACE \"\\n\" \"\" _testSuite \"${_testSuite}\")\n\t\t\tstring (REGEX REPLACE \".*TestSuite\\\\[.*{(.*)}.*\\\\].*\" \"\\\\1\" _testSuite \"${_testSuite}\")\n\t\t\tstring (REPLACE \",\" \";\" _testSuite \"${_testSuite}\")\n\t\t\tget_filename_component(_testSuiteDir \"${_testSuiteFile}\" DIRECTORY)\n\t\t\tforeach (_testSuiteItem IN LISTS _testSuite)\n\t\t\t\t# parse quoted test file name\n\t\t\t\tstring (REGEX REPLACE \"[^\\\"]*\\\"(.*)\\\"[^\\\"]*\" \"\\\\1\" _testSuiteItem \"${_testSuiteItem}\")\n\t\t\t\t_to_cmake_path(\"${_testSuiteDir}/${_testSuiteItem}\" _testFile)\n\t\t\t\tif (_option_RELATIVE)\n\t\t\t\t\tfile (RELATIVE_PATH _testFile \"${_option_RELATIVE}\" \"${_testFile}\")\n\t\t\t\tendif()\n\t\t\t\tlist (APPEND ${_var} \"${_testFile}\")\n\t\t\tendforeach()\n\t\telse()\n\t\t\t# not a test suite file, return test suite file path itself\n\t\t\tget_filename_component(_testSuiteFile \"${_testSuiteFile}\" ABSOLUTE)\n\t\t\tif (_option_RELATIVE)\n\t\t\t\tfile (RELATIVE_PATH _testSuiteFile \"${_option_RELATIVE}\" \"${_testSuiteFile}\")\n\t\t\tendif()\n\t\t\tlist (APPEND ${_var} \"${_testSuiteFile}\")\n\t\tendif()\n\tendforeach()\n\tlist (REMOVE_DUPLICATES ${_var})\n\tset (${_var} \"${${_var}}\" PARENT_SCOPE)\nendfunction()\n\n# public function for adding a CMake test that runs a Mathematica MUnit test file or notebook\nfunction (Mathematica_MUnit_ADD_TEST)\n\tset(_options \"\")\n\tset(_oneValueArgs NAME LOGGERS SCRIPT INPUT INPUT_FILE TIMEOUT SYSTEM_ID)\n\tset(_multiValueArgs CODE CONFIGURATIONS KERNEL_OPTIONS)\n\tcmake_parse_arguments(_option \"${_options}\" \"${_oneValueArgs}\" \"${_multiValueArgs}\" ${ARGN})\n\tif(_option_UNPARSED_ARGUMENTS)\n\t\tmessage (FATAL_ERROR \"Unknown keywords: ${_option_UNPARSED_ARGUMENTS}\")\n\telseif (NOT _option_NAME)\n\t\tmessage (FATAL_ERROR \"Mandatory parameter NAME is missing.\")\n\telseif (NOT _option_SCRIPT)\n\t\tmessage (FATAL_ERROR \"Mandatory parameter SCRIPT is missing.\")\n\tendif()\n\tset (_cmd NAME \"${_option_NAME}\" COMMAND)\n\t_add_test_driver(_cmd \"${_option_NAME}\" _option_INPUT _option_INPUT_FILE)\n\tif (NOT _option_LOGGERS)\n\t\t# default to VerbosePrintLogger which prints detailed information for failed tests\n\t\tset (_option_LOGGERS \"{VerbosePrintLogger[]}\")\n\tendif()\n\tset (_testCmds \"If[Needs[\\\"MUnit`\\\"]===$Failed,Exit[]]\")\n\tif (_option_CODE)\n\t\tlist (APPEND _testCmds ${_option_CODE})\n\tendif()\n\tif (IS_ABSOLUTE \"${_option_SCRIPT}\")\n\t\t_to_cmake_path(\"${_option_SCRIPT}\" _testScript)\n\telse()\n\t\t_to_cmake_path(\"${CMAKE_CURRENT_SOURCE_DIR}/${_option_SCRIPT}\" _testScript)\n\tendif()\n\tget_filename_component(_testScriptExt \"${_testScript}\" EXT)\n\tget_filename_component(_testScriptDir \"${_testScript}\" DIRECTORY)\n\tMathematica_TO_NATIVE_STRING(\"${_option_NAME}\" _testNameMma)\n\tif (\"${_testScriptExt}\" MATCHES \"\\\\.(nb|cdf)$\")\n\t\t# notebook test run requires Mathematica front end\n\t\tif (DEFINED Mathematica_VERSION)\n\t\t\tif (\"${Mathematica_VERSION}\" VERSION_LESS \"7.0\")\n\t\t\t\t# default to using undocumented function Developer`UseFrontEnd\n\t\t\t\t# available in Mathematica 5.1 and newer\n\t\t\t\tset (_useFrontEndFunc \"Developer`UseFrontEnd\")\n\t\t\telse()\n\t\t\t\t# documented function UsingFrontEnd available since Mathematica 7\n\t\t\t\tset (_useFrontEndFunc \"UsingFrontEnd\")\n\t\t\tendif()\n\t\tendif()\n\t\tMathematica_TO_NATIVE_PATH(\"${_testScript}\" _testScriptMma)\n\t\tstring (REGEX REPLACE \"\\n|\\t\" \"\" _testCmd\n\t\t\t\"${_useFrontEndFunc}[\n\t\t\t\tCompoundExpression[\n\t\t\t\t\tnb=NotebookOpen[${_testScriptMma},Visible->False],\n\t\t\t\t\tmUnitResult=TestRun[nb,TestRunTitle->${_testNameMma},Loggers:>${_option_LOGGERS}],\n\t\t\t\t\tNotebookClose[nb]]]\")\n\t\tlist (APPEND _testCmds \"${_testCmd}\")\n\telse()\n\t\tMathematica_MUnit_RESOLVE_SUITE(_testFiles \"${_testScript}\")\n\t\tMathematica_TO_NATIVE_PATH(\"${_testFiles}\" _testFilesMma)\n\t\tlist (LENGTH _testFiles _fileCount)\n\t\tif (_fileCount GREATER 1)\n\t\t\tif (DEFINED Mathematica_VERSION)\n\t\t\t\tif (\"${Mathematica_VERSION}\" VERSION_LESS \"7.0\")\n\t\t\t\t\t# default to using DirectoryName\n\t\t\t\t\tset (_titleExtractFunc \"StringDrop[#,StringLength[DirectoryName[#]]]\")\n\t\t\t\telse()\n\t\t\t\t\t# function FileNameTake available since Mathematica 7\n\t\t\t\t\tset (_titleExtractFunc \"FileNameTake[#]\")\n\t\t\t\tendif()\n\t\t\tendif()\n\t\t\tMathematica_TO_NATIVE_PATH(\"${_testScriptDir}\" _testScriptDirMma)\n\t\t\tstring (REGEX REPLACE \"\\n|\\t\" \"\" _testCmd\n\t\t\t\t\"mUnitResult=And@@Map[\n\t\t\t\t\tTestRun[#,TestRunTitle->${_titleExtractFunc},Loggers:>${_option_LOGGERS}]&,\n\t\t\t\t\t${_testFilesMma}]\")\n\t\telse()\n\t\t\tstring (REGEX REPLACE \"\\n|\\t\" \"\" _testCmd\n\t\t\t\t\"mUnitResult=TestRun[\n\t\t\t\t\t${_testFilesMma},TestRunTitle->${_testNameMma},Loggers:>${_option_LOGGERS}]\")\n\t\tendif()\n\t\tlist (APPEND _testCmds \"${_testCmd}\")\n\tendif()\n\t# use MUnit TestRun result as exit code to signal CTest success or failure\n\tlist (APPEND _testCmds \"Exit[Boole[Not[mUnitResult]]]\")\n\t_add_kernel_launch_code(_cmd _option_SYSTEM_ID _option_KERNEL_OPTIONS)\n\t_add_script_or_code(_cmd _noScript _testCmds)\n\tif (_option_CONFIGURATIONS)\n\t\tlist (APPEND _cmd CONFIGURATIONS ${_option_CONFIGURATIONS})\n\tendif()\n\tif (Mathematica_DEBUG)\n\t\tmessage (STATUS \"add_test: ${_cmd}\")\n\tendif()\n\tadd_test (${_cmd})\n\tset_property (TEST ${_option_NAME} PROPERTY LABELS \"Mathematica\")\n\tif (_option_TIMEOUT)\n\t\tset_tests_properties (${_option_NAME} PROPERTIES TIMEOUT ${_option_TIMEOUT})\n\tendif()\nendfunction (Mathematica_MUnit_ADD_TEST)\n\nendif (Mathematica_MUnit_FOUND)\n\nif (Mathematica_KERNEL_EXECUTABLE AND Mathematica_JLink_FOUND)\n\n# public function for adding a target which builds Mathematica documentation\nfunction (Mathematica_ADD_DOCUMENTATION _targetName)\n\t# documentation build requires Apache Ant\n\tif (CMAKE_HOST_WIN32)\n\t\tset (_antExecutableName \"ant.bat\")\n\telse()\n\t\tset (_antExecutableName \"ant\")\n\tendif()\n\tfind_program(Mathematica_ANT_EXECUTABLE \"${_antExecutableName}\" PATHS ENV ANT_HOME PATH_SUFFIXES \"bin\")\n\tif (NOT Mathematica_ANT_EXECUTABLE)\n\t\tmessage (WARNING \"Mathematica documentation build required Apache Ant executable \\\"ant\\\" cannot be found.\")\n\tendif()\n\t# find DocumentationBuild package\n\tMathematica_FIND_PACKAGE(Mathematica_DocumentationBuild_PACKAGE_FILE \"DocumentationBuild`\"\n\t\tDOC \"Mathematica DocumentationBuild package.\")\n\tif (NOT Mathematica_DocumentationBuild_PACKAGE_FILE)\n\t\tmessage (STATUS \"Mathematica documentation build required package \\\"DocumentationBuild`\\\" cannot be found.\")\n\tendif()\n\tMathematica_GET_PACKAGE_DIR(Mathematica_DocumentationBuild_PACKAGE_DIR\n\t\t\"${Mathematica_DocumentationBuild_PACKAGE_FILE}\")\n\t# find Transmogrify package required by DocumentationBuild package\n\tMathematica_FIND_PACKAGE(Mathematica_Transmogrify_PACKAGE_FILE \"Transmogrify`\"\n\t\tDOC \"Mathematica Transmogrify package.\")\n\tif (NOT Mathematica_Transmogrify_PACKAGE_FILE)\n\t\tmessage (STATUS \"Mathematica documentation build required package \\\"Transmogrify`\\\" cannot be found.\")\n\tendif()\n\tmark_as_advanced(\n\t\tMathematica_ANT_EXECUTABLE\n\t\tMathematica_DocumentationBuild_PACKAGE_FILE\n\t\tMathematica_Transmogrify_PACKAGE_FILE\n\t)\n\t# build command from options\n\tset(_options \"ALL\" \"CHECK_TIMESTAMPS\" \"INCLUDE_NOTEBOOKS\")\n\tset(_oneValueArgs DOCUMENTATION_TYPE INPUT_DIRECTORY OUTPUT_DIRECTORY APPLICATION_NAME LANGUAGE COMMENT JAVACMD)\n\tset(_multiValueArgs SOURCES)\n\tcmake_parse_arguments(_option \"${_options}\" \"${_oneValueArgs}\" \"${_multiValueArgs}\" ${ARGN})\n\tif(_option_UNPARSED_ARGUMENTS)\n\t\tmessage (FATAL_ERROR \"Unknown keywords: ${_option_UNPARSED_ARGUMENTS}\")\n\tendif()\n\tif (NOT _option_DOCUMENTATION_TYPE)\n\t\tset (_option_DOCUMENTATION_TYPE \"Notebook\")\n\tendif()\n\tif (NOT _option_APPLICATION_NAME)\n\t\tset (_option_APPLICATION_NAME \"${PROJECT_NAME}\")\n\tendif()\n\tif (NOT _option_LANGUAGE)\n\t\tset (_option_LANGUAGE \"English\")\n\tendif()\n\tif (NOT _option_INPUT_DIRECTORY)\n\t\tset (_option_INPUT_DIRECTORY \"${CMAKE_CURRENT_SOURCE_DIR}\")\n\tendif()\n\tif (NOT _option_JAVACMD)\n\t\tif (Mathematica_JLink_JAVA_EXECUTABLE)\n\t\t\tset (_option_JAVACMD \"${Mathematica_JLink_JAVA_EXECUTABLE}\")\n\t\telseif (Java_JAVA_EXECUTABLE)\n\t\t\tset (_option_JAVACMD \"${Java_JAVA_EXECUTABLE}\")\n\t\telse()\n\t\t\tif (CMAKE_HOST_WIN32)\n\t\t\t\tset (_option_JAVACMD \"java.exe\")\n\t\t\telse()\n\t\t\t\tset (_option_JAVACMD \"java\")\n\t\t\tendif()\n\t\tendif()\n\tendif()\n\tif (NOT _option_OUTPUT_DIRECTORY)\n\t\tif (_option_DOCUMENTATION_TYPE STREQUAL \"Notebook\")\n\t\t\tset (_option_OUTPUT_DIRECTORY\n\t\t\t\t\"${CMAKE_CURRENT_BINARY_DIR}/${_option_APPLICATION_NAME}/Documentation\")\n\t\telse()\n\t\t\tset (_option_OUTPUT_DIRECTORY\n\t\t\t\t\"${CMAKE_CURRENT_BINARY_DIR}/${_option_APPLICATION_NAME}-${_option_DOCUMENTATION_TYPE}\")\n\t\tendif()\n\tendif()\n\tif (NOT _option_COMMENT)\n\t\tset (_option_COMMENT\n\t\t\t\"Building ${_option_APPLICATION_NAME} Mathematica ${_option_DOCUMENTATION_TYPE} documentation\")\n\tendif()\n\t# set up custom target\n\tset (_cmd \"${_targetName}\")\n\tif (_option_ALL)\n\t\tlist (APPEND _cmd ALL)\n\tendif()\n\tif (Mathematica_ANT_EXECUTABLE AND\n\t\tMathematica_DocumentationBuild_PACKAGE_FILE AND\n\t\tMathematica_Transmogrify_PACKAGE_FILE)\n\t\t# set up documentation generation script if all requirements are met\n\t\tset (_templateBuildScript \"${Mathematica_CMAKE_MODULE_DIR}/FindMathematicaDocumentationBuild.cmake.in\")\n\t\tset (_buildScriptName \"${_option_APPLICATION_NAME}Mathematica${_option_DOCUMENTATION_TYPE}DocumentationBuild.cmake\")\n\t\tif (NOT EXISTS \"${_templateBuildScript}\")\n\t\t\tmessage (FATAL_ERROR \"FindMathematica documentation build script template ${_templateBuildScript} is missing.\")\n\t\tendif()\n\t\tconfigure_file(\"${_templateBuildScript}\" \"${_buildScriptName}\" @ONLY)\n\t\tlist (APPEND _cmd COMMAND \"${CMAKE_COMMAND}\" \"-P\" \"${CMAKE_CURRENT_BINARY_DIR}/${_buildScriptName}\")\n\t\tlist (APPEND _cmd DEPENDS \"${CMAKE_CURRENT_BINARY_DIR}/${_buildScriptName}\")\n\telse()\n\t\t# just generate empty documentation directory and print message\n\t\tlist (APPEND _cmd COMMAND \"${CMAKE_COMMAND}\" \"-E\" \"make_directory\" \"${_option_OUTPUT_DIRECTORY}\")\n\t\tlist (APPEND _cmd COMMAND \"${CMAKE_COMMAND}\" \"-E\" \"echo\" \"Required Mathematica packages for documentation building are not available.\")\n\tendif()\n\tlist (APPEND _cmd WORKING_DIRECTORY \"${CMAKE_CURRENT_BINARY_DIR}\")\n\tlist (APPEND _cmd COMMENT ${_option_COMMENT} VERBATIM)\n\tif (_option_SOURCES)\n\t\tlist (APPEND _cmd SOURCES ${_option_SOURCES})\n\tendif()\n\tif (_option_INCLUDE_NOTEBOOKS)\n\t\tfile (GLOB_RECURSE _docuSourceNBs \"${_option_INPUT_DIRECTORY}/*.nb\")\n\t\tif (_docuSourceNBs)\n\t\t\tif (_option_SOURCES)\n\t\t\t\tlist (APPEND _cmd ${_docuSourceNBs})\n\t\t\telse()\n\t\t\t\tlist (APPEND _cmd SOURCES ${_docuSourceNBs})\n\t\t\tendif()\n\t\tendif()\n\tendif()\n\tif (Mathematica_DEBUG)\n\t\tmessage (STATUS \"add_custom_target: ${_cmd}\")\n\tendif()\n\tadd_custom_target(${_cmd})\nendfunction (Mathematica_ADD_DOCUMENTATION)\n\nendif (Mathematica_KERNEL_EXECUTABLE AND Mathematica_JLink_FOUND)\n\nif (Mathematica_KERNEL_EXECUTABLE AND Mathematica_JLink_FOUND)\n\n# public function to simplify testing J/Link programs\nfunction (Mathematica_JLink_ADD_TEST)\n\tset(_options \"\")\n\tset(_oneValueArgs NAME MAIN_CLASS SCRIPT TARGET INPUT INPUT_FILE SYSTEM_ID LINK_PROTOCOL)\n\tset(_multiValueArgs CODE CONFIGURATIONS KERNEL_OPTIONS CLASSPATH)\n\tcmake_parse_arguments(_option \"${_options}\" \"${_oneValueArgs}\" \"${_multiValueArgs}\" ${ARGN})\n\tif(_option_UNPARSED_ARGUMENTS)\n\t\tmessage (FATAL_ERROR \"Unknown keywords: ${_option_UNPARSED_ARGUMENTS}\")\n\telseif (NOT _option_TARGET)\n\t\tmessage (FATAL_ERROR \"Mandatory parameter TARGET is missing.\")\n\telseif (NOT _option_NAME)\n\t\tmessage (FATAL_ERROR \"Mandatory parameter NAME is missing.\")\n\tendif()\n\tset (_cmd NAME \"${_option_NAME}\" COMMAND)\n\t_add_test_driver(_cmd \"${_option_NAME}\" _option_INPUT _option_INPUT_FILE)\n\tif (TARGET ${_option_TARGET})\n\t\tget_target_property (_targetJarFile ${_option_TARGET} JAR_FILE)\n\telse()\n\t\t_to_cmake_path(\"${_option_TARGET}\" _targetJarFile)\n\tendif()\n\tif (_option_CODE OR _option_SCRIPT)\n\t\t# run Mathematica kernel and load JAR file\n\t\tMathematica_TO_NATIVE_PATH(\"${_targetJarFile}\" _targetJarFileMma)\n\t\tset (_installCmd \"Needs[\\\"JLink`\\\"]\" \"AddToClassPath[${_targetJarFileMma}]\")\n\t\tif (_option_CODE)\n\t\t\tlist (INSERT _option_CODE 0 ${_installCmd})\n\t\telse()\n\t\t\tset (_option_CODE ${_installCmd})\n\t\tendif()\n\t\t_add_kernel_launch_code(_cmd _option_SYSTEM_ID _option_KERNEL_OPTIONS)\n\t\t_add_script_or_code(_cmd _option_SCRIPT _option_CODE)\n\telse()\n\t\t# run JAR file as front-end to Mathematica kernel\n\t\tif (NOT _option_MAIN_CLASS)\n\t\t\tget_filename_component(_option_MAIN_CLASS ${_targetJarFile} NAME_WE)\n\t\tendif()\n\t\t_to_native_path (\"${Mathematica_JLink_JAR_FILE}\" _jlinkJarNative)\n\t\t_to_native_path (\"${_targetJarFile}\" _targetJarFileNative)\n\t\t_to_native_path_list(_classPath \"${_jlinkJarNative}\" \"${_targetJarFileNative}\" ${_option_CLASSPATH})\n\t\tif (Mathematica_JLink_JAVA_EXECUTABLE)\n\t\t\tlist (APPEND _cmd \"${Mathematica_JLink_JAVA_EXECUTABLE}\")\n\t\telseif (Java_JAVA_EXECUTABLE)\n\t\t\tlist (APPEND _cmd \"${Java_JAVA_EXECUTABLE}\")\n\t\telse()\n\t\t\tif (CMAKE_HOST_WIN32)\n\t\t\t\tlist (APPEND _cmd \"java.exe\")\n\t\t\telse()\n\t\t\t\tlist (APPEND _cmd \"java\")\n\t\t\tendif()\n\t\tendif()\n\t\tif (Mathematica_JLink_RUNTIME_LIBRARY)\n\t\t\tget_filename_component(_jlinkLibraryDir ${Mathematica_JLink_RUNTIME_LIBRARY} DIRECTORY)\n\t\t\t_to_native_path (\"${_jlinkLibraryDir}\" _jlinkLibraryDirNative)\n\t\t\tlist (APPEND _cmd \"-Dcom.wolfram.jlink.libdir=${_jlinkLibraryDirNative}\")\n\t\tendif()\n\t\tlist (APPEND _cmd \"-cp\" \"${_classPath}\" \"${_option_MAIN_CLASS}\")\n\t\t_add_linkmode_launch_code(_cmd \"-mathlink\"\n\t\t\t_option_SYSTEM_ID _option_KERNEL_OPTIONS _option_LINK_PROTOCOL\n\t\t\t_option_SCRIPT _option_CODE)\n\tendif()\n\tif (_option_CONFIGURATIONS)\n\t\tlist (APPEND _cmd CONFIGURATIONS ${_option_CONFIGURATIONS})\n\tendif()\n\tif (Mathematica_DEBUG)\n\t\tmessage (STATUS \"add_test: ${_cmd}\")\n\tendif()\n\tadd_test (${_cmd})\nendfunction(Mathematica_JLink_ADD_TEST)\n\nendif(Mathematica_KERNEL_EXECUTABLE AND Mathematica_JLink_FOUND)\n"
  },
  {
    "path": "cmake/modules/FindMathematicaDocumentationBuild.cmake.in",
    "content": "# FindMathematica @Mathematica_CMAKE_MODULE_VERSION@ documentation build script\n\n# JAVACMD is an environment variable that points to the full path to the Java runtime executable\n# used by the Apache Ant wrapper scripts\nset (ENV{JAVACMD} \"@_option_JAVACMD@\")\n\nset (Mathematica_KERNEL_EXECUTABLE \"@Mathematica_KERNEL_EXECUTABLE@\")\nset (Mathematica_ANT_EXECUTABLE \"@Mathematica_ANT_EXECUTABLE@\")\nset (Mathematica_JLink_PACKAGE_DIR \"@Mathematica_JLink_PACKAGE_DIR@\")\nset (Mathematica_DocumentationBuild_PACKAGE_DIR \"@Mathematica_DocumentationBuild_PACKAGE_DIR@\")\nset (Mathematica_DEBUG \"@Mathematica_DEBUG@\")\n\nset (DOCU_INPUT_DIRECTORY \"@_option_INPUT_DIRECTORY@\")\nset (DOCU_OUTPUT_DIRECTORY \"@_option_OUTPUT_DIRECTORY@\")\nset (DOCU_TYPE \"@_option_DOCUMENTATION_TYPE@\")\nset (DOCU_LANGUAGE \"@_option_LANGUAGE@\")\nset (DOCU_APP_NAME \"@_option_APPLICATION_NAME@\")\nset (CHECK_TIMESTAMPS \"@_option_CHECK_TIMESTAMPS@\")\n\nfunction(_to_native_path _inPath _outPathVariable)\n\tif (CYGWIN)\n\t\texecute_process(\n\t\t\tCOMMAND cygpath \"--mixed\" \"${_inPath}\" TIMEOUT 5\n\t\t\tOUTPUT_VARIABLE ${_outPathVariable} OUTPUT_STRIP_TRAILING_WHITESPACE)\n\telseif (CMAKE_HOST_WIN32)\n\t\tstring (REPLACE \"/\" \"\\\\\" ${_outPathVariable} \"${_inPath}\")\n\telse()\n\t\t# use CMake path literally\n\t\tset (${_outPathVariable} \"${_inPath}\")\n\tendif()\n\tset (${_outPathVariable} \"${${_outPathVariable}}\" PARENT_SCOPE)\nendfunction()\n\nset (_buildDocu TRUE)\n# handle CHECK_TIMESTAMPS option\nif (CHECK_TIMESTAMPS AND EXISTS \"${DOCU_OUTPUT_DIRECTORY}\")\n\tif (DOCU_TYPE MATCHES \"[Nn]otebook\")\n\t\tfile (GLOB_RECURSE _docuSourceNBs RELATIVE \"${DOCU_INPUT_DIRECTORY}\" \"${DOCU_INPUT_DIRECTORY}/*.nb\")\n\t\tfile (GLOB_RECURSE _docuBinaryNBs RELATIVE \"${DOCU_OUTPUT_DIRECTORY}\" \"${DOCU_OUTPUT_DIRECTORY}/*.nb\")\n\t\tif (_docuBinaryNBs)\n\t\t\tset (_docuNBs ${_docuSourceNBs} ${_docuBinaryNBs})\n\t\t\tlist (REMOVE_DUPLICATES _docuNBs)\n\t\t\tset (_docuNBTrigger \"\")\n\t\t\tforeach (_docuNB ${_docuNBs})\n\t\t\t\tif (\"${DOCU_INPUT_DIRECTORY}/${_docuNB}\" IS_NEWER_THAN \"${DOCU_OUTPUT_DIRECTORY}/${_docuNB}\")\n\t\t\t\t\tlist (APPEND _docuNBTrigger \"${_docuNB}\")\n\t\t\t\t\tlist (LENGTH _docuNBTrigger _len)\n\t\t\t\t\tif (_len GREATER 10)\n\t\t\t\t\t\t# stop if many out-of-date files have been found\n\t\t\t\t\t\tbreak()\n\t\t\t\t\tendif()\n\t\t\t\tendif()\n\t\t\tendforeach()\n\t\t\tif (_docuNBTrigger)\n\t\t\t\tmessage (STATUS \"Out-of-date ${DOCU_APP_NAME} Mathematica documentation notebooks: ${_docuNBTrigger}\")\n\t\t\telse()\n\t\t\t\tmessage (STATUS \"Built ${DOCU_APP_NAME} Mathematica ${DOCU_TYPE} documentation is up-to-date\")\n\t\t\t\tset (_buildDocu FALSE)\n\t\t\tendif()\n\t\tendif()\n\telseif (DOCU_TYPE MATCHES \"HTML\")\n\t\tfile (GLOB_RECURSE _docuSourceNBs RELATIVE \"${DOCU_INPUT_DIRECTORY}\" \"${DOCU_INPUT_DIRECTORY}/*.nb\")\n\t\tfile (GLOB_RECURSE _docuBinaryHTMLs RELATIVE \"${DOCU_OUTPUT_DIRECTORY}\" \"${DOCU_OUTPUT_DIRECTORY}/*.html\")\n\t\tif (_docuBinaryHTMLs)\n\t\t\tset (_docuNBTrigger \"\")\n\t\t\tforeach (_docuNB ${_docuSourceNBs})\n\t\t\t\tget_filename_component(_docuBaseName \"${_docuNB}\" NAME_WE)\n\t\t\t\tstring (REGEX MATCHALL \"[^;]+/${_docuBaseName}\\\\.html\" _docuHTMLNames \"${_docuBinaryHTMLs}\")\n\t\t\t\tif (_docuHTMLNames)\n\t\t\t\t\tforeach (_docuHTMLName ${_docuHTMLNames})\n\t\t\t\t\t\tif (\"${DOCU_INPUT_DIRECTORY}/${_docuNB}\" IS_NEWER_THAN \"${DOCU_OUTPUT_DIRECTORY}/${_docuHTMLName}\")\n\t\t\t\t\t\t\tlist (APPEND _docuNBTrigger \"${_docuNB}\")\n\t\t\t\t\t\t\tbreak()\n\t\t\t\t\t\tendif()\n\t\t\t\t\tendforeach()\n\t\t\t\telse()\n\t\t\t\t\t# no corresponding HTML document\n\t\t\t\t\tlist (APPEND _docuNBTrigger \"${_docuNB}\")\n\t\t\t\tendif()\n\t\t\t\tlist (LENGTH _docuNBTrigger _len)\n\t\t\t\tif (_len GREATER 10)\n\t\t\t\t\t# stop if many out-of-date files have been found\n\t\t\t\t\tbreak()\n\t\t\t\tendif()\n\t\t\tendforeach()\n\t\t\tif (_docuNBTrigger)\n\t\t\t\tmessage (STATUS \"Out-of-date ${DOCU_APP_NAME} Mathematica documentation notebooks: ${_docuNBTrigger}\")\n\t\t\telse()\n\t\t\t\tmessage (STATUS \"Built ${DOCU_APP_NAME} Mathematica ${DOCU_TYPE} documentation is up-to-date\")\n\t\t\t\tset (_buildDocu FALSE)\n\t\t\tendif()\n\t\tendif()\n\tendif()\nendif()\n\nif (_buildDocu)\n\t# clean previously built documentation files\n\tfile (REMOVE_RECURSE \"${DOCU_OUTPUT_DIRECTORY}\")\n\tfile (MAKE_DIRECTORY \"${DOCU_OUTPUT_DIRECTORY}\")\n\tget_filename_component(_appPath \"${Mathematica_DocumentationBuild_PACKAGE_DIR}\" DIRECTORY)\n\tstring (TOLOWER \"${DOCU_TYPE}.xml\" _buildFileName)\n\tset (_buildFile \"${Mathematica_DocumentationBuild_PACKAGE_DIR}/SystemFiles/ant/Build/${_buildFileName}\")\n\t_to_native_path (\"${Mathematica_ANT_EXECUTABLE}\" _antExecutableNative)\n\t_to_native_path (\"${_buildFile}\" _buildFileNative)\n\t_to_native_path (\"${_appPath}\" _appPathNative)\n\t_to_native_path (\"${Mathematica_KERNEL_EXECUTABLE}\" _kernelExecutableNative)\n\t_to_native_path (\"${Mathematica_JLink_PACKAGE_DIR}\" _jlinkPathNative)\n\t_to_native_path (\"${DOCU_INPUT_DIRECTORY}\" _inputDirNative)\n\t_to_native_path (\"${DOCU_OUTPUT_DIRECTORY}\" _outputDirNative)\n\tset (_cmd COMMAND \"${_antExecutableNative}\")\n\tlist (APPEND _cmd \"-buildfile\" \"${_buildFileNative}\")\n\tlist (APPEND _cmd \"-DappPath=${_appPathNative}\")\n\tlist (APPEND _cmd \"-Dapp.name=${DOCU_APP_NAME}\")\n\tlist (APPEND _cmd \"-DmathExe=${_kernelExecutableNative}\")\n\tlist (APPEND _cmd \"-Djlinkpath=${_jlinkPathNative}\")\n\tlist (APPEND _cmd \"-DinputDir=${_inputDirNative}\")\n\tlist (APPEND _cmd \"-DoutputDir=${_outputDirNative}\")\n\tlist (APPEND _cmd \"-Dlanguage=${DOCU_LANGUAGE}\")\n\tlist (APPEND _cmd \"-DincludeLinkTrails=False\")\n\tlist (APPEND _cmd \"-Dlocal=True\")\n\tlist (APPEND _cmd \"-DcompleteHTMLQ=True\")\n\tif (Mathematica_DEBUG)\n\t\tlist (APPEND _cmd \"-Ddebug=True\")\n\telse()\n\t\tlist (APPEND _cmd \"-Ddebug=False\")\n\tendif()\n\tlist (APPEND _cmd RESULT_VARIABLE _result)\n\tif (Mathematica_DEBUG)\n\t\tmessage (STATUS \"execute_process: ${_cmd}\")\n\tendif()\n\texecute_process(${_cmd})\n\tmessage(STATUS \"${DOCU_APP_NAME} ${DOCU_TYPE} generation result=${_result}\")\nendif()\n"
  },
  {
    "path": "cmake/modules/FindMathematicaTestDriver.cmd",
    "content": "@echo off\r\nrem FindMathematica test driver script for Windows\r\n\r\nsetlocal enabledelayedexpansion\r\n\r\nrem echo !CMDCMDLINE!\r\nrem echo !PATH!\r\n\r\nset \"TEST_NAME=%~1\"\r\nset \"TEST_CONFIGURATION=%~2\"\r\nset \"TEST_INPUT_OPTION=%~3\"\r\nif \"!TEST_INPUT_OPTION!\" == \"input\" (\r\n\tset \"TEST_INPUT=%~4\"\r\n\tset \"TEST_EXECUTABLE=%~5\"\r\n\tshift\r\n\tshift\r\n\tshift\r\n\tshift\r\n\tshift\r\n\tshift\r\n) else if \"!TEST_INPUT_OPTION!\" == \"inputfile\" (\r\n\tset \"TEST_INPUT_FILE=%~4\"\r\n\tset \"TEST_EXECUTABLE=%~5\"\r\n\tshift\r\n\tshift\r\n\tshift\r\n\tshift\r\n\tshift\r\n\tshift\r\n) else (\r\n\tset \"TEST_EXECUTABLE=%~4\"\r\n\tshift\r\n\tshift\r\n\tshift\r\n\tshift\r\n\tshift\r\n)\r\n\r\nif \"!TEST_INPUT_OPTION!\" == \"input\" (\r\n\techo !TEST_INPUT! | \"!TEST_EXECUTABLE!\" %0 %1 %2 %3 %4 %5 %6 %7 %8 %9\r\n) else if \"!TEST_INPUT_OPTION!\" == \"inputfile\" (\r\n\t\"!TEST_EXECUTABLE!\" < \"!TEST_INPUT_FILE!\" %0 %1 %2 %3 %4 %5 %6 %7 %8 %9\r\n) else (\r\n\t\"!TEST_EXECUTABLE!\" %0 %1 %2 %3 %4 %5 %6 %7 %8 %9\r\n)\r\n"
  },
  {
    "path": "cmake/modules/FindMathematicaTestDriver.sh",
    "content": "#!/bin/bash\n# FindMathematica test driver script for UNIX systems\n\n#logger -- $# \"$@\"\n#logger -- LD_LIBRARY_PATH=$LD_LIBRARY_PATH\n#logger -- DYLD_FRAMEWORK_PATH=$DYLD_FRAMEWORK_PATH\n#logger -- DYLD_LIBRARY_PATH=$DYLD_LIBRARY_PATH\n\nexport TEST_NAME=$1\nexport TEST_CONFIGURATION=$2\nexport TEST_INPUT_OPTION=$3\n\nif [ \"$TEST_INPUT_OPTION\" = \"input\" ]\nthen\n\texport TEST_INPUT=$4\n\texport TEST_EXECUTABLE=$5\nelif [ \"$TEST_INPUT_OPTION\" = \"inputfile\" ]\nthen\n\texport TEST_INPUT_FILE=$4\n\texport TEST_EXECUTABLE=$5\nelse\n\texport TEST_EXECUTABLE=$4\nfi\n\nif [ \"$OSTYPE\" = \"cygwin\" ]\nthen\n\t# make sure that executable has the right format under Cygwin\n\texport TEST_EXECUTABLE=\"$(/usr/bin/cygpath --unix \"$TEST_EXECUTABLE\")\"\nfi\n\nif [ \"$TEST_INPUT_OPTION\" = \"input\" ]\nthen\n\techo \"$TEST_INPUT\" | exec \"$TEST_EXECUTABLE\" \"${@:6}\"\nelif [ \"$TEST_INPUT_OPTION\" = \"inputfile\" ]\nthen\n\texec < \"$TEST_INPUT_FILE\" \"$TEST_EXECUTABLE\" \"${@:6}\"\nelse\n\texec \"$TEST_EXECUTABLE\" \"${@:5}\"\nfi\n"
  },
  {
    "path": "cmake/modules/FindPythonLibsOSX.cmake",
    "content": "# - Find python libraries\n# This module finds if Python is installed and determines where the\n# include files and libraries are. It also determines what the name of\n# the library is. This code sets the following variables:\n#\n#  PYTHONLIBS_FOUND           - have the Python libs been found\n#  PYTHON_LIBRARIES           - path to the python library\n#  PYTHON_INCLUDE_PATH        - path to where Python.h is found (deprecated)\n#  PYTHON_INCLUDE_DIRS        - path to where Python.h is found\n#  PYTHON_DEBUG_LIBRARIES     - path to the debug library (deprecated)\n#  PYTHONLIBS_VERSION_STRING  - version of the Python libs found (since CMake 2.8.8)\n#\n# The Python_ADDITIONAL_VERSIONS variable can be used to specify a list of\n# version numbers that should be taken into account when searching for Python.\n# You need to set this variable before calling find_package(PythonLibs).\n#\n# If you'd like to specify the installation of Python to use, you should modify\n# the following cache variables:\n#  PYTHON_LIBRARY             - path to the python library\n#  PYTHON_INCLUDE_DIR         - path to where Python.h is found\n\n#=============================================================================\n# Copyright 2001-2009 Kitware, Inc.\n#\n# Distributed under the OSI-approved BSD License (the \"License\");\n# see accompanying file Copyright.txt for details.\n#\n# This software is distributed WITHOUT ANY WARRANTY; without even the\n# implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.\n# See the License for more information.\n#=============================================================================\n# (To distribute this file outside of CMake, substitute the full\n#  License text for the above reference.)\n\n# Note by Nikolaus Demmel 28.03.2014: My contributions are licensend under the\n# same as CMake (BSD). My adaptations are in part based\n# https://github.com/qgis/QGIS/tree/master/cmake which has the following\n# copyright note:\n\n# Copyright (c) 2007, Simon Edwards <simon@simonzone.com>\n# Redistribution and use is allowed according to the terms of the BSD license.\n# For details see the accompanying COPYING-CMAKE-SCRIPTS file.\n\n\nif(NOT DEFINED PYTHON_INCLUDE_DIR)\n  if(DEFINED PYTHON_INCLUDE_PATH)\n    # For backward compatibility, repect PYTHON_INCLUDE_PATH.\n    set(PYTHON_INCLUDE_DIR \"${PYTHON_INCLUDE_PATH}\" CACHE PATH\n      \"Path to where Python.h is found\" FORCE)\n  else()\n    set(PYTHON_INCLUDE_DIR \"\" CACHE PATH\n      \"Path to where Python.h is found\" FORCE)\n  endif()\nendif()\n\nif(EXISTS \"${PYTHON_INCLUDE_DIR}\" AND EXISTS \"${PYTHON_LIBRARY}\")\n  if(EXISTS \"${PYTHON_INCLUDE_DIR}/patchlevel.h\")\n    file(STRINGS \"${PYTHON_INCLUDE_DIR}/patchlevel.h\" _PYTHON_VERSION_STR\n      REGEX \"^#define[ \\t]+PY_VERSION[ \\t]+\\\"[^\\\"]+\\\"\")\n    string(REGEX REPLACE \"^#define[ \\t]+PY_VERSION[ \\t]+\\\"([^\\\"]+)\\\".*\" \"\\\\1\"\n      PYTHONLIBS_VERSION_STRING \"${_PYTHON_VERSION_STR}\")\n    unset(_PYTHON_VERSION_STR)\n  endif()\nelse()\n  set(_PYTHON1_VERSIONS 1.6 1.5)\n  set(_PYTHON2_VERSIONS 2.7 2.6 2.5 2.4 2.3 2.2 2.1 2.0)\n  set(_PYTHON3_VERSIONS 3.4 3.3 3.2 3.1 3.0)\n\n  unset(_PYTHON_FIND_OTHER_VERSIONS)\n  if(PythonLibs_FIND_VERSION)\n    if(PythonLibs_FIND_VERSION_COUNT GREATER 1)\n      set(_PYTHON_FIND_MAJ_MIN \"${PythonLibs_FIND_VERSION_MAJOR}.${PythonLibs_FIND_VERSION_MINOR}\")\n      if(NOT PythonLibs_FIND_VERSION_EXACT)\n        foreach(_PYTHON_V ${_PYTHON${PythonLibs_FIND_VERSION_MAJOR}_VERSIONS})\n          if(NOT _PYTHON_V VERSION_LESS _PYTHON_FIND_MAJ_MIN)\n            if(NOT _PYTHON_V STREQUAL PythonLibs_FIND_VERSION)\n              list(APPEND _PYTHON_FIND_OTHER_VERSIONS ${_PYTHON_V})\n            endif()\n          endif()\n        endforeach()\n      endif()\n      unset(_PYTHON_FIND_MAJ_MIN)\n    else()\n      set(_PYTHON_FIND_OTHER_VERSIONS ${_PYTHON${PythonLibs_FIND_VERSION_MAJOR}_VERSIONS})\n    endif()\n  else()\n    # add an empty version to check the `python` executable first in case no version is requested\n    set(_PYTHON_FIND_OTHER_VERSIONS ${_PYTHON3_VERSIONS} ${_PYTHON2_VERSIONS} ${_PYTHON1_VERSIONS})\n  endif()\n\n  unset(_PYTHON1_VERSIONS)\n  unset(_PYTHON2_VERSIONS)\n  unset(_PYTHON3_VERSIONS)\n\n  # Set up the versions we know about, in the order we will search. Always add\n  # the user supplied additional versions to the front.\n  # If FindPythonInterp has already found the major and minor version,\n  # insert that version between the user supplied versions and the stock\n  # version list.\n  # If no specific version is requested or suggested by PythonInterp, always look\n  # for \"python\" executable first\n  set(_PYTHON_VERSIONS ${PythonLibs_FIND_VERSION} ${PythonLibs_ADDITIONAL_VERSIONS} )\n  if(DEFINED PYTHON_VERSION_MAJOR AND DEFINED PYTHON_VERSION_MINOR)\n    list(APPEND _PYTHON_VERSIONS ${PYTHON_VERSION_MAJOR}.${PYTHON_VERSION_MINOR})\n  endif()\n  if (NOT _PYTHON_VERSIONS)\n    set(_PYTHON_VERSIONS \";\") # empty entry at the front makeing sure we search for \"python\" first\n  endif()\n  list(APPEND _PYTHON_VERSIONS ${_PYTHON_FIND_OTHER_VERSIONS})\n\n  unset(_PYTHON_FIND_OTHER_VERSIONS)\n\n  message(STATUS \"Looking for versions: ${_PYTHON_VERSIONS}\")\n\n  FIND_FILE(_FIND_LIB_PYTHON_PY FindLibPythonOSX.py PATHS ${CMAKE_MODULE_PATH} ${CMAKE_ROOT}/Modules)\n\n  if(NOT _FIND_LIB_PYTHON_PY)\n    message(FATAL_ERROR \"Could not find required file 'FindLibPythonOSX.py'\")\n  endif()\n\n  unset(PYTHONLIBS_VERSION_STRING)\n  foreach(_CURRENT_VERSION IN LISTS _PYTHON_VERSIONS)\n\n    STRING(REGEX REPLACE \"^([0-9]+).*$\"          \"\\\\1\" _VERSION_MAJOR \"${_CURRENT_VERSION}\")\n    STRING(REGEX REPLACE \"^[0-9]+\\\\.([0-9]+).*$\" \"\\\\1\" _VERSION_MINOR \"${_CURRENT_VERSION}\")\n\n    set(_PYTHON_NAMES python)\n\n    if (_CURRENT_VERSION MATCHES \"^[0-9]+.*$\")\n      list(APPEND _PYTHON_NAMES \"python${_VERSION_MAJOR}\")\n      if (_CURRENT_VERSION MATCHES \"^[0-9]+\\\\.[0-9].*$\")\n        list(APPEND _PYTHON_NAMES \"python${_VERSION_MAJOR}.${_VERSION_MINOR}\")\n      endif()\n    endif()\n\n    message(STATUS \"Looking for python version '${_CURRENT_VERSION}' by checking executables: ${_PYTHON_NAMES}.\")\n\n    foreach(_CURRENT_PYTHON_NAME IN LISTS _PYTHON_NAMES)\n\n      unset(_PYTHON_EXECUTABLE CACHE)\n      find_program(_PYTHON_EXECUTABLE ${_CURRENT_PYTHON_NAME}\n        PATHS [HKEY_LOCAL_MACHINE\\\\SOFTWARE\\\\Python\\\\PythonCore\\\\${_CURRENT_VERSION}\\\\InstallPath])\n\n      if(_PYTHON_EXECUTABLE)\n\n        EXECUTE_PROCESS(\n          COMMAND ${_PYTHON_EXECUTABLE} \"${_FIND_LIB_PYTHON_PY}\"\n          OUTPUT_VARIABLE _PYTHON_CONFIG\n          RESULT_VARIABLE _PYTHON_CONFIG_RESULT\n          ERROR_QUIET)\n\n        if(NOT ${_PYTHON_CONFIG_RESULT} AND (NOT ${_PYTHON_CONFIG} STREQUAL \"\"))\n          STRING(REGEX REPLACE \".*\\nmajor_version:([0-9]+).*$\" \"\\\\1\" _PYTHON_MAJOR_VERSION ${_PYTHON_CONFIG})\n          STRING(REGEX REPLACE \".*\\nminor_version:([0-9]+).*$\" \"\\\\1\" _PYTHON_MINOR_VERSION ${_PYTHON_CONFIG})\n          STRING(REGEX REPLACE \".*\\npatch_version:([0-9]+).*$\" \"\\\\1\" _PYTHON_PATCH_VERSION ${_PYTHON_CONFIG})\n          STRING(REGEX REPLACE \".*\\nshort_version:([^\\n]+).*$\" \"\\\\1\" _PYTHON_SHORT_VERSION ${_PYTHON_CONFIG})\n          STRING(REGEX REPLACE \".*\\nlong_version:([^\\n]+).*$\"  \"\\\\1\" _PYTHON_LONG_VERSION  ${_PYTHON_CONFIG})\n          STRING(REGEX REPLACE \".*\\npy_inc_dir:([^\\n]+).*$\"    \"\\\\1\" _PYTHON_INCLUDE_DIR   ${_PYTHON_CONFIG})\n          STRING(REGEX REPLACE \".*\\npy_lib_dir:([^\\n]+).*$\"    \"\\\\1\" _PYTHON_LIBRARY_DIR   ${_PYTHON_CONFIG})\n          STRING(REGEX REPLACE \".*\\nexec_prefix:(^\\n+).*$\"     \"\\\\1\" _PYTHON_PREFIX        ${_PYTHON_CONFIG})\n\n          if (\"${_CURRENT_VERSION}\" STREQUAL \"\"                         OR\n              \"${_CURRENT_VERSION}\" STREQUAL \"${_PYTHON_MAJOR_VERSION}\" OR\n              \"${_CURRENT_VERSION}\" STREQUAL \"${_PYTHON_SHORT_VERSION}\" OR\n              \"${_CURRENT_VERSION}\" STREQUAL \"${_PYTHON_LONG_VERSION}\")\n\n            message(STATUS \"Found executable ${_PYTHON_EXECUTABLE} with suitable version ${_PYTHON_LONG_VERSION}\")\n\n            if(NOT EXISTS \"${PYTHON_INCLUDE_DIR}\")\n              set(PYTHON_INCLUDE_DIR \"${_PYTHON_INCLUDE_DIR}\")\n            endif()\n\n            if(NOT EXISTS \"${PYTHON_LIBRARY}\")\n              set(_PYTHON_SHORT_VERSION_NO_DOT \"${_PYTHON_MAJOR_VERSION}${_PYTHON_MINOR_VERSION}\")\n              set(_PYTHON_LIBRARY_NAMES python${_PYTHON_SHORT_VERSION} python${_PYTHON_SHORT_VERSION_NO_DOT})\n              FIND_LIBRARY(PYTHON_LIBRARY\n                NAMES ${_PYTHON_LIBRARY_NAMES}\n                PATH_SUFFIXES\n                python${_PYTHON_SHORT_VERSION}/config\n                python${_PYTHON_SHORT_VERSION_NO_DOT}/config\n                PATHS\n                ${_PYTHON_LIBRARY_DIR}\n                ${_PYTHON_PREFIX}/lib $\n                {_PYTHON_PREFIX}/libs\n                NO_DEFAULT_PATH)\n\n              if(WIN32)\n                find_library(PYTHON_DEBUG_LIBRARY\n                  NAMES python${_PYTHON_SHORT_VERSION_NO_DOT}_d python\n                  PATHS\n                  [HKEY_LOCAL_MACHINE\\\\SOFTWARE\\\\Python\\\\PythonCore\\\\${_CURRENT_VERSION}\\\\InstallPath]/libs/Debug\n                  [HKEY_CURRENT_USER\\\\SOFTWARE\\\\Python\\\\PythonCore\\\\${_CURRENT_VERSION}\\\\InstallPath]/libs/Debug\n                  [HKEY_LOCAL_MACHINE\\\\SOFTWARE\\\\Python\\\\PythonCore\\\\${_CURRENT_VERSION}\\\\InstallPath]/libs\n                  [HKEY_CURRENT_USER\\\\SOFTWARE\\\\Python\\\\PythonCore\\\\${_CURRENT_VERSION}\\\\InstallPath]/libs\n                  )\n              endif()\n            endif()\n\n            set(PYTHONLIBS_VERSION_STRING ${_PYTHON_LONG_VERSION})\n            if(_PYTHON_PATCH_VERSION STREQUAL \"0\")\n              # it's called \"Python 2.7\", not \"2.7.0\"\n              string(REGEX REPLACE \"\\\\.0$\" \"\" PYTHONLIBS_VERSION_STRING \"${PYTHONLIBS_VERSION_STRING}\")\n            endif()\n\n            break()\n          else()\n            message(STATUS \"Found executable ${_PYTHON_EXECUTABLE} with UNsuitable version ${_PYTHON_LONG_VERSION}\")\n          endif() # version ok\n        else()\n          message(WARNING \"Found executable ${_PYTHON_EXECUTABLE}, but could not extract version info.\")\n        endif() # could extract config\n      endif() # found executable\n    endforeach() # python names\n    if (PYTHONLIBS_VERSION_STRING)\n      break()\n    endif()\n  endforeach() # python versions\nendif()\n\nunset(_PYTHON_NAMES)\nunset(_PYTHON_VERSIONS)\nunset(_PYTHON_EXECUTABLE CACHE)\nunset(_PYTHON_MAJOR_VERSION)\nunset(_PYTHON_MINOR_VERSION)\nunset(_PYTHON_PATCH_VERSION)\nunset(_PYTHON_SHORT_VERSION)\nunset(_PYTHON_LONG_VERSION)\nunset(_PYTHON_LIBRARY_DIR)\nunset(_PYTHON_INCLUDE_DIR)\nunset(_PYTHON_PREFIX)\nunset(_PYTHON_SHORT_VERSION_NO_DOT)\nunset(_PYTHON_LIBRARY_NAMES)\n\n\n# For backward compatibility, set PYTHON_INCLUDE_PATH.\nset(PYTHON_INCLUDE_PATH \"${PYTHON_INCLUDE_DIR}\")\n\nmark_as_advanced(\n  PYTHON_DEBUG_LIBRARY\n  PYTHON_LIBRARY\n  PYTHON_INCLUDE_DIR\n)\n\n# We use PYTHON_INCLUDE_DIR, PYTHON_LIBRARY and PYTHON_DEBUG_LIBRARY for the\n# cache entries because they are meant to specify the location of a single\n# library. We now set the variables listed by the documentation for this\n# module.\nset(PYTHON_INCLUDE_DIRS \"${PYTHON_INCLUDE_DIR}\")\nset(PYTHON_DEBUG_LIBRARIES \"${PYTHON_DEBUG_LIBRARY}\")\n\n# These variables have been historically named in this module different from\n# what SELECT_LIBRARY_CONFIGURATIONS() expects.\nset(PYTHON_LIBRARY_DEBUG \"${PYTHON_DEBUG_LIBRARY}\")\nset(PYTHON_LIBRARY_RELEASE \"${PYTHON_LIBRARY}\")\n#include(${CMAKE_CURRENT_LIST_DIR}/SelectLibraryConfigurations.cmake)\ninclude(SelectLibraryConfigurations)\nSELECT_LIBRARY_CONFIGURATIONS(PYTHON)\n# SELECT_LIBRARY_CONFIGURATIONS() sets ${PREFIX}_FOUND if it has a library.\n# Unset this, this prefix doesn't match the module prefix, they are different\n# for historical reasons.\nunset(PYTHON_FOUND)\n\n#include(${CMAKE_CURRENT_LIST_DIR}/FindPackageHandleStandardArgs.cmake)\ninclude(FindPackageHandleStandardArgs)\nFIND_PACKAGE_HANDLE_STANDARD_ARGS(PythonLibs\n                                  REQUIRED_VARS PYTHON_LIBRARIES PYTHON_INCLUDE_DIRS\n                                  VERSION_VAR PYTHONLIBS_VERSION_STRING)\n\n# PYTHON_ADD_MODULE(<name> src1 src2 ... srcN) is used to build modules for python.\n# PYTHON_WRITE_MODULES_HEADER(<filename>) writes a header file you can include\n# in your sources to initialize the static python modules\nfunction(PYTHON_ADD_MODULE _NAME )\n  get_property(_TARGET_SUPPORTS_SHARED_LIBS\n    GLOBAL PROPERTY TARGET_SUPPORTS_SHARED_LIBS)\n  option(PYTHON_ENABLE_MODULE_${_NAME} \"Add module ${_NAME}\" TRUE)\n  option(PYTHON_MODULE_${_NAME}_BUILD_SHARED\n    \"Add module ${_NAME} shared\" ${_TARGET_SUPPORTS_SHARED_LIBS})\n\n  # Mark these options as advanced\n  mark_as_advanced(PYTHON_ENABLE_MODULE_${_NAME}\n    PYTHON_MODULE_${_NAME}_BUILD_SHARED)\n\n  if(PYTHON_ENABLE_MODULE_${_NAME})\n    if(PYTHON_MODULE_${_NAME}_BUILD_SHARED)\n      set(PY_MODULE_TYPE MODULE)\n    else()\n      set(PY_MODULE_TYPE STATIC)\n      set_property(GLOBAL  APPEND  PROPERTY  PY_STATIC_MODULES_LIST ${_NAME})\n    endif()\n\n    set_property(GLOBAL  APPEND  PROPERTY  PY_MODULES_LIST ${_NAME})\n    add_library(${_NAME} ${PY_MODULE_TYPE} ${ARGN})\n#    target_link_libraries(${_NAME} ${PYTHON_LIBRARIES})\n\n    if(PYTHON_MODULE_${_NAME}_BUILD_SHARED)\n      set_target_properties(${_NAME} PROPERTIES PREFIX \"${PYTHON_MODULE_PREFIX}\")\n      if(WIN32 AND NOT CYGWIN)\n        set_target_properties(${_NAME} PROPERTIES SUFFIX \".pyd\")\n      endif()\n    endif()\n\n  endif()\nendfunction()\n\nfunction(PYTHON_WRITE_MODULES_HEADER _filename)\n\n  get_property(PY_STATIC_MODULES_LIST  GLOBAL  PROPERTY PY_STATIC_MODULES_LIST)\n\n  get_filename_component(_name \"${_filename}\" NAME)\n  string(REPLACE \".\" \"_\" _name \"${_name}\")\n  string(TOUPPER ${_name} _nameUpper)\n  set(_filename ${CMAKE_CURRENT_BINARY_DIR}/${_filename})\n\n  set(_filenameTmp \"${_filename}.in\")\n  file(WRITE ${_filenameTmp} \"/*Created by cmake, do not edit, changes will be lost*/\\n\")\n  file(APPEND ${_filenameTmp}\n\"#ifndef ${_nameUpper}\n#define ${_nameUpper}\n\n#include <Python.h>\n\n#ifdef __cplusplus\nextern \\\"C\\\" {\n#endif /* __cplusplus */\n\n\")\n\n  foreach(_currentModule ${PY_STATIC_MODULES_LIST})\n    file(APPEND ${_filenameTmp} \"extern void init${PYTHON_MODULE_PREFIX}${_currentModule}(void);\\n\\n\")\n  endforeach()\n\n  file(APPEND ${_filenameTmp}\n\"#ifdef __cplusplus\n}\n#endif /* __cplusplus */\n\n\")\n\n\n  foreach(_currentModule ${PY_STATIC_MODULES_LIST})\n    file(APPEND ${_filenameTmp} \"int ${_name}_${_currentModule}(void) \\n{\\n  static char name[]=\\\"${PYTHON_MODULE_PREFIX}${_currentModule}\\\"; return PyImport_AppendInittab(name, init${PYTHON_MODULE_PREFIX}${_currentModule});\\n}\\n\\n\")\n  endforeach()\n\n  file(APPEND ${_filenameTmp} \"void ${_name}_LoadAllPythonModules(void)\\n{\\n\")\n  foreach(_currentModule ${PY_STATIC_MODULES_LIST})\n    file(APPEND ${_filenameTmp} \"  ${_name}_${_currentModule}();\\n\")\n  endforeach()\n  file(APPEND ${_filenameTmp} \"}\\n\\n\")\n  file(APPEND ${_filenameTmp} \"#ifndef EXCLUDE_LOAD_ALL_FUNCTION\\nvoid CMakeLoadAllPythonModules(void)\\n{\\n  ${_name}_LoadAllPythonModules();\\n}\\n#endif\\n\\n#endif\\n\")\n\n# with configure_file() cmake complains that you may not use a file created using file(WRITE) as input file for configure_file()\n  execute_process(COMMAND ${CMAKE_COMMAND} -E copy_if_different \"${_filenameTmp}\" \"${_filename}\" OUTPUT_QUIET ERROR_QUIET)\n\nendfunction()\n"
  },
  {
    "path": "cmake/modules/FindSQLITE3.cmake",
    "content": "# Copyright (C) 2007-2009 LuaDist.\n# Created by Peter Kapec <kapecp@gmail.com>\n# Redistribution and use of this file is allowed according to the terms of the MIT license.\n# For details see the COPYRIGHT file distributed with LuaDist.\n#\tNote:\n#\t\tSearching headers and libraries is very simple and is NOT as powerful as scripts\n#\t\tdistributed with CMake, because LuaDist defines directories to search for.\n#\t\tEveryone is encouraged to contact the author with improvements. Maybe this file\n#\t\tbecomes part of CMake distribution sometimes.\n\n# - Find sqlite3\n# Find the native SQLITE3 headers and libraries.\n#\n# SQLITE3_INCLUDE_DIR\t- where to find sqlite3.h, etc.\n# SQLITE3_LIBRARIES\t- List of libraries when using sqlite.\n# SQLITE3_FOUND\t- True if sqlite found.\n\n\nif(WIN32)\n  # Look for the header file.\n  FIND_PATH(SQLITE3_INCLUDE_DIR NAMES sqlite3.h)\n  # Look for the library.\n  FIND_LIBRARY(SQLITE3_LIBRARY NAMES sqlite3)\nelse()\n  find_package(PkgConfig REQUIRED)\n  pkg_check_modules(SQLITE3 REQUIRED sqlite3)\n  message(\"-- Found sqlite3 library path ${SQLITE3_LIBRARIES}\")\n  message(\"-- Found sqlite3 include path ${SQLITE3_INCLUDE_DIRS}\") \n  set(SQLITE3_LIBRARY ${SQLITE3_LIBRARIES})\n  set(SQLITE3_INCLUDE_DIR ${SQLITE3_INCLUDE_DIR})\n  set(SQLITE3_FOUND)\nendif()\n\n# Handle the QUIETLY and REQUIRED arguments and set SQLITE3_FOUND to TRUE if all listed variables are TRUE.\nINCLUDE(FindPackageHandleStandardArgs)\nFIND_PACKAGE_HANDLE_STANDARD_ARGS(SQLITE3 DEFAULT_MSG SQLITE3_LIBRARY) # SQLITE3_INCLUDE_DIR)\n\n\n# Copy the results to the output variables.\nIF(SQLITE3_FOUND)\n\tSET(SQLITE3_LIBRARIES ${SQLITE3_LIBRARY})\n\tSET(SQLITE3_INCLUDE_DIR ${SQLITE3_INCLUDE_DIR})\nELSE(SQLITE3_FOUND)\n\tSET(SQLITE3_LIBRARIES)\n\tSET(SQLITE3_INCLUDE_DIR)\nENDIF(SQLITE3_FOUND)\n\n\nMARK_AS_ADVANCED(SQLITE3_INCLUDE_DIR SQLITE3_LIBRARIES)\n\n\n"
  },
  {
    "path": "cmake/modules/FindZeroMQ.cmake",
    "content": "# - Find zeromq libraries\r\n# This module finds zeromq if it is installed and determines where the\r\n# include files and libraries are. It also determines what the name of\r\n# the library is. This code sets the following variables:\r\n#\r\n#  ZEROMQ_FOUND               - have the zeromq libs been found\r\n#  ZEROMQ_LIBRARIES           - path to the zeromq library\r\n#  ZEROMQ_INCLUDE_DIRS        - path to where zmq.h is found\r\n#  ZEROMQ_DEBUG_LIBRARIES     - path to the debug library\r\n\r\n#INCLUDE(CMakeFindFrameworks)\r\n# Search for the zeromq framework on Apple.\r\n#CMAKE_FIND_FRAMEWORKS(ZeroMQ)\r\n\r\nIF(WIN32)\r\n\tFIND_LIBRARY(ZEROMQ_DEBUG_LIBRARY\r\n\t\tNAMES libzmq_d zmq_d\r\n\t\tPATHS\r\n\t\t\t${ZEROMQ_LIBRARIES}\r\n\t)\r\nENDIF(WIN32)\r\n\r\nFIND_LIBRARY(ZEROMQ_LIBRARY\r\n\tNAMES libzmq zmq \r\n\tPATHS\r\n\t\t${ZEROMQ_LIBRARIES}\r\n\t\t${NSCP_LIBRARYDIR}\r\n)\r\n\r\n#  IF(ZeroMQ_FRAMEWORKS AND NOT ZEROMQ_INCLUDE_DIR)\r\n#    FOREACH(dir ${ZeroMQ_FRAMEWORKS})\r\n#      SET(ZEROMQ_FRAMEWORK_INCLUDES ${ZEROMQ_FRAMEWORK_INCLUDES}\r\n#        ${dir}/Versions/${_CURRENT_VERSION}/include/zeromq${_CURRENT_VERSION})\r\n#    ENDFOREACH(dir)\r\n#  ENDIF(ZeroMQ_FRAMEWORKS AND NOT ZEROMQ_INCLUDE_DIR)\r\n\r\nFIND_PATH(ZEROMQ_INCLUDE_DIR\r\n\tNAMES zmq.hpp\r\n\tPATHS\r\n#\t\t${ZEROMQ_FRAMEWORK_INCLUDES}\r\n\t\t${ZEROMQ_INCLUDE_DIRS}\r\n\t\t${NSCP_INCLUDEDIR}\r\n\t\t${ZEROMQ_INCLUDE_DIR}\r\n)\r\n\r\nMARK_AS_ADVANCED(\r\n  ZEROMQ_DEBUG_LIBRARY\r\n  ZEROMQ_LIBRARY\r\n  ZEROMQ_INCLUDE_DIR\r\n)\r\nSET(ZEROMQ_INCLUDE_DIRS \"${ZEROMQ_INCLUDE_DIR}\")\r\nSET(ZEROMQ_LIBRARIES \"${ZEROMQ_LIBRARY}\")\r\nSET(ZEROMQ_DEBUG_LIBRARIES \"${ZEROMQ_DEBUG_LIBRARY}\")\r\n\r\nINCLUDE(FindPackageHandleStandardArgs)\r\nFIND_PACKAGE_HANDLE_STANDARD_ARGS(ZeroMQ DEFAULT_MSG ZEROMQ_LIBRARIES ZEROMQ_INCLUDE_DIRS)\r\n"
  },
  {
    "path": "cmake/modules/cotire.cmake",
    "content": "# - cotire (compile time reducer)\n#\n# See the cotire manual for usage hints.\n#\n#=============================================================================\n# Copyright 2012-2014 Sascha Kratky\n#\n# Permission is hereby granted, free of charge, to any person\n# obtaining a copy of this software and associated documentation\n# files (the \"Software\"), to deal in the Software without\n# restriction, including without limitation the rights to use,\n# copy, modify, merge, publish, distribute, sublicense, and/or sell\n# copies of the Software, and to permit persons to whom the\n# Software is furnished to do so, subject to the following\n# conditions:\n#\n# The above copyright notice and this permission notice shall be\n# included in all copies or substantial portions of the Software.\n#\n# THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND,\n# EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES\n# OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND\n# NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT\n# HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,\n# WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n# FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR\n# OTHER DEALINGS IN THE SOFTWARE.\n#=============================================================================\n\nif(__COTIRE_INCLUDED)\n\treturn()\nendif()\nset(__COTIRE_INCLUDED TRUE)\n\n# call cmake_minimum_required, but prevent modification of the CMake policy stack in include mode\n# cmake_minimum_required also sets the policy version as a side effect, which we have to avoid\nif (NOT CMAKE_SCRIPT_MODE_FILE)\n\tcmake_policy(PUSH)\nendif()\n# we need the CMake variables CMAKE_SCRIPT_MODE_FILE and CMAKE_ARGV available since 2.8.5\n# we need APPEND_STRING option for set_property available since 2.8.6\ncmake_minimum_required(VERSION 2.8.6)\nif (NOT CMAKE_SCRIPT_MODE_FILE)\n\tcmake_policy(POP)\nendif()\n\nif (NOT CMAKE_VERSION VERSION_LESS \"3.1.0\")\n\t# include TARGET_OBJECTS expressions in a target's SOURCES property\n\tcmake_policy(SET CMP0051 NEW)\n\t# only interpret if() arguments as variables or keywords when unquoted\n\tcmake_policy(SET CMP0054 NEW)\nendif()\n\nset (COTIRE_CMAKE_MODULE_FILE \"${CMAKE_CURRENT_LIST_FILE}\")\nset (COTIRE_CMAKE_MODULE_VERSION \"1.6.9\")\n\ninclude(CMakeParseArguments)\ninclude(ProcessorCount)\n\nfunction (cotire_determine_compiler_version _language _versionPrefix)\n\tif (NOT ${_versionPrefix}_VERSION)\n\t\t# use CMake's predefined compiler version variable (available since CMake 2.8.8)\n\t\tif (DEFINED CMAKE_${_language}_COMPILER_VERSION)\n\t\t\tset (${_versionPrefix}_VERSION \"${CMAKE_${_language}_COMPILER_VERSION}\")\n\t\telseif (WIN32)\n\t\t\t# cl.exe messes with the output streams unless the environment variable VS_UNICODE_OUTPUT is cleared\n\t\t\tunset (ENV{VS_UNICODE_OUTPUT})\n\t\t\tstring (STRIP \"${CMAKE_${_language}_COMPILER_ARG1}\" _compilerArg1)\n\t\t\texecute_process (\n\t\t\t\tCOMMAND ${CMAKE_${_language}_COMPILER} ${_compilerArg1}\n\t\t\t\tERROR_VARIABLE _versionLine OUTPUT_QUIET TIMEOUT 10)\n\t\t\tstring (REGEX REPLACE \".*Version *([0-9]+(\\\\.[0-9]+)*).*\" \"\\\\1\" ${_versionPrefix}_VERSION \"${_versionLine}\")\n\t\telse()\n\t\t\t# assume GCC like command line interface\n\t\t\tstring (STRIP \"${CMAKE_${_language}_COMPILER_ARG1}\" _compilerArg1)\n\t\t\texecute_process (\n\t\t\t\tCOMMAND ${CMAKE_${_language}_COMPILER} ${_compilerArg1} \"-dumpversion\"\n\t\t\t\tOUTPUT_VARIABLE ${_versionPrefix}_VERSION\n\t\t\t\tRESULT_VARIABLE _result\n\t\t\t\tOUTPUT_STRIP_TRAILING_WHITESPACE TIMEOUT 10)\n\t\t\tif (_result)\n\t\t\t\tset (${_versionPrefix}_VERSION \"\")\n\t\t\tendif()\n\t\tendif()\n\t\tif (${_versionPrefix}_VERSION)\n\t\t\tset (${_versionPrefix}_VERSION \"${${_versionPrefix}_VERSION}\" CACHE INTERNAL \"${_language} compiler version\")\n\t\tendif()\n\t\tset (${_versionPrefix}_VERSION \"${${_versionPrefix}_VERSION}\" PARENT_SCOPE)\n\t\tif (COTIRE_DEBUG)\n\t\t\tmessage (STATUS \"${CMAKE_${_language}_COMPILER} version ${${_versionPrefix}_VERSION}\")\n\t\tendif()\n\tendif()\nendfunction()\n\nfunction (cotire_get_configuration_types _configsVar)\n\tset (_configs \"\")\n\tif (CMAKE_CONFIGURATION_TYPES)\n\t\tlist (APPEND _configs ${CMAKE_CONFIGURATION_TYPES})\n\tendif()\n\tif (CMAKE_BUILD_TYPE)\n\t\tlist (APPEND _configs \"${CMAKE_BUILD_TYPE}\")\n\tendif()\n\tif (_configs)\n\t\tlist (REMOVE_DUPLICATES _configs)\n\t\tset (${_configsVar} ${_configs} PARENT_SCOPE)\n\telse()\n\t\tset (${_configsVar} \"None\" PARENT_SCOPE)\n\tendif()\nendfunction()\n\nfunction (cotire_get_source_file_extension _sourceFile _extVar)\n\t# get_filename_component returns extension from first occurrence of . in file name\n\t# this function computes the extension from last occurrence of . in file name\n\tstring (FIND \"${_sourceFile}\" \".\" _index REVERSE)\n\tif (_index GREATER -1)\n\t\tmath (EXPR _index \"${_index} + 1\")\n\t\tstring (SUBSTRING \"${_sourceFile}\" ${_index} -1 _sourceExt)\n\telse()\n\t\tset (_sourceExt \"\")\n\tendif()\n\tset (${_extVar} \"${_sourceExt}\" PARENT_SCOPE)\nendfunction()\n\nmacro (cotire_check_is_path_relative_to _path _isRelativeVar)\n\tset (${_isRelativeVar} FALSE)\n\tif (IS_ABSOLUTE \"${_path}\")\n\t\tforeach (_dir ${ARGN})\n\t\t\tfile (RELATIVE_PATH _relPath \"${_dir}\" \"${_path}\")\n\t\t\tif (NOT _relPath OR (NOT IS_ABSOLUTE \"${_relPath}\" AND NOT \"${_relPath}\" MATCHES \"^\\\\.\\\\.\"))\n\t\t\t\tset (${_isRelativeVar} TRUE)\n\t\t\t\tbreak()\n\t\t\tendif()\n\t\tendforeach()\n\tendif()\nendmacro()\n\nfunction (cotire_filter_language_source_files _language _sourceFilesVar _excludedSourceFilesVar _cotiredSourceFilesVar)\n\tset (_sourceFiles \"\")\n\tset (_excludedSourceFiles \"\")\n\tset (_cotiredSourceFiles \"\")\n\tif (CMAKE_${_language}_SOURCE_FILE_EXTENSIONS)\n\t\tset (_languageExtensions \"${CMAKE_${_language}_SOURCE_FILE_EXTENSIONS}\")\n\telse()\n\t\tset (_languageExtensions \"\")\n\tendif()\n\tif (CMAKE_${_language}_IGNORE_EXTENSIONS)\n\t\tset (_ignoreExtensions \"${CMAKE_${_language}_IGNORE_EXTENSIONS}\")\n\telse()\n\t\tset (_ignoreExtensions \"\")\n\tendif()\n\tif (COTIRE_UNITY_SOURCE_EXCLUDE_EXTENSIONS)\n\t\tset (_excludeExtensions \"${COTIRE_UNITY_SOURCE_EXCLUDE_EXTENSIONS}\")\n\telse()\n\t\tset (_excludeExtensions \"\")\n\tendif()\n\tif (COTIRE_DEBUG)\n\t\tmessage (STATUS \"${_language} source file extensions: ${_languageExtensions}\")\n\t\tmessage (STATUS \"${_language} ignore extensions: ${_ignoreExtensions}\")\n\t\tmessage (STATUS \"${_language} exclude extensions: ${_excludeExtensions}\")\n\tendif()\n\tif (CMAKE_VERSION VERSION_LESS \"3.1.0\")\n\t\tset (_allSourceFiles ${ARGN})\n\telse()\n\t\t# as of CMake 3.1 target sources may contain generator expressions\n\t\t# since we cannot obtain required property information about source files added\n\t\t# through generator expressions at configure time, we filter them out\n\t\tstring (GENEX_STRIP \"${ARGN}\" _allSourceFiles)\n\tendif()\n\tforeach (_sourceFile ${_allSourceFiles})\n\t\tget_source_file_property(_sourceIsHeaderOnly \"${_sourceFile}\" HEADER_FILE_ONLY)\n\t\tget_source_file_property(_sourceIsExternal \"${_sourceFile}\" EXTERNAL_OBJECT)\n\t\tget_source_file_property(_sourceIsSymbolic \"${_sourceFile}\" SYMBOLIC)\n\t\tget_source_file_property(_sourceLanguage \"${_sourceFile}\" LANGUAGE)\n\t\tset (_sourceIsFiltered FALSE)\n\t\tif (NOT _sourceIsHeaderOnly AND NOT _sourceIsExternal AND NOT _sourceIsSymbolic)\n\t\t\tcotire_get_source_file_extension(\"${_sourceFile}\" _sourceExt)\n\t\t\tif (_sourceExt)\n\t\t\t\tlist (FIND _ignoreExtensions \"${_sourceExt}\" _ignoreIndex)\n\t\t\t\tif (_ignoreIndex LESS 0)\n\t\t\t\t\tlist (FIND _excludeExtensions \"${_sourceExt}\" _excludeIndex)\n\t\t\t\t\tif (_excludeIndex GREATER -1)\n\t\t\t\t\t\tlist (APPEND _excludedSourceFiles \"${_sourceFile}\")\n\t\t\t\t\telse()\n\t\t\t\t\t\tlist (FIND _languageExtensions \"${_sourceExt}\" _sourceIndex)\n\t\t\t\t\t\tif (_sourceIndex GREATER -1)\n\t\t\t\t\t\t\tset (_sourceIsFiltered TRUE)\n\t\t\t\t\t\telseif (\"${_sourceLanguage}\" STREQUAL \"${_language}\")\n\t\t\t\t\t\t\t# add to excluded sources, if file is not ignored and has correct language without having the correct extension\n\t\t\t\t\t\t\tlist (APPEND _excludedSourceFiles \"${_sourceFile}\")\n\t\t\t\t\t\tendif()\n\t\t\t\t\tendif()\n\t\t\t\tendif()\n\t\t\tendif()\n\t\tendif()\n\t\tif (COTIRE_DEBUG)\n\t\t\tmessage (STATUS \"${_sourceFile} filtered=${_sourceIsFiltered} language=${_sourceLanguage} header=${_sourceIsHeaderOnly}\")\n\t\tendif()\n\t\tif (_sourceIsFiltered)\n\t\t\tget_source_file_property(_sourceIsExcluded \"${_sourceFile}\" COTIRE_EXCLUDED)\n\t\t\tget_source_file_property(_sourceIsCotired \"${_sourceFile}\" COTIRE_TARGET)\n\t\t\tget_source_file_property(_sourceCompileFlags \"${_sourceFile}\" COMPILE_FLAGS)\n\t\t\tif (COTIRE_DEBUG)\n\t\t\t\tmessage (STATUS \"${_sourceFile} excluded=${_sourceIsExcluded} cotired=${_sourceIsCotired} compileFlags=${_sourceCompileFlags}\")\n\t\t\tendif()\n\t\t\tif (_sourceIsCotired)\n\t\t\t\tlist (APPEND _cotiredSourceFiles \"${_sourceFile}\")\n\t\t\telseif (_sourceIsExcluded OR _sourceCompileFlags)\n\t\t\t\tlist (APPEND _excludedSourceFiles \"${_sourceFile}\")\n\t\t\telse()\n\t\t\t\tlist (APPEND _sourceFiles \"${_sourceFile}\")\n\t\t\tendif()\n\t\tendif()\n\tendforeach()\n\tif (COTIRE_DEBUG)\n\t\tmessage (STATUS \"All: ${ARGN}\")\n\t\tmessage (STATUS \"${_language}: ${_sourceFiles}\")\n\t\tmessage (STATUS \"Excluded: ${_excludedSourceFiles}\")\n\t\tmessage (STATUS \"Cotired: ${_cotiredSourceFiles}\")\n\tendif()\n\tset (${_sourceFilesVar} ${_sourceFiles} PARENT_SCOPE)\n\tset (${_excludedSourceFilesVar} ${_excludedSourceFiles} PARENT_SCOPE)\n\tset (${_cotiredSourceFilesVar} ${_cotiredSourceFiles} PARENT_SCOPE)\nendfunction()\n\nfunction (cotire_get_objects_with_property_on _filteredObjectsVar _property _type)\n\tset (_filteredObjects \"\")\n\tforeach (_object ${ARGN})\n\t\tget_property(_isSet ${_type} \"${_object}\" PROPERTY ${_property} SET)\n\t\tif (_isSet)\n\t\t\tget_property(_propertyValue ${_type} \"${_object}\" PROPERTY ${_property})\n\t\t\tif (_propertyValue)\n\t\t\t\tlist (APPEND _filteredObjects \"${_object}\")\n\t\t\tendif()\n\t\tendif()\n\tendforeach()\n\tset (${_filteredObjectsVar} ${_filteredObjects} PARENT_SCOPE)\nendfunction()\n\nfunction (cotire_get_objects_with_property_off _filteredObjectsVar _property _type)\n\tset (_filteredObjects \"\")\n\tforeach (_object ${ARGN})\n\t\tget_property(_isSet ${_type} \"${_object}\" PROPERTY ${_property} SET)\n\t\tif (_isSet)\n\t\t\tget_property(_propertyValue ${_type} \"${_object}\" PROPERTY ${_property})\n\t\t\tif (NOT _propertyValue)\n\t\t\t\tlist (APPEND _filteredObjects \"${_object}\")\n\t\t\tendif()\n\t\tendif()\n\tendforeach()\n\tset (${_filteredObjectsVar} ${_filteredObjects} PARENT_SCOPE)\nendfunction()\n\nfunction (cotire_get_source_file_property_values _valuesVar _property)\n\tset (_values \"\")\n\tforeach (_sourceFile ${ARGN})\n\t\tget_source_file_property(_propertyValue \"${_sourceFile}\" ${_property})\n\t\tif (_propertyValue)\n\t\t\tlist (APPEND _values \"${_propertyValue}\")\n\t\tendif()\n\tendforeach()\n\tset (${_valuesVar} ${_values} PARENT_SCOPE)\nendfunction()\n\nfunction (cotire_resolve_config_properites _configurations _propertiesVar)\n\tset (_properties \"\")\n\tforeach (_property ${ARGN})\n\t\tif (\"${_property}\" MATCHES \"<CONFIG>\")\n\t\t\tforeach (_config ${_configurations})\n\t\t\t\tstring (TOUPPER \"${_config}\" _upperConfig)\n\t\t\t\tstring (REPLACE \"<CONFIG>\" \"${_upperConfig}\" _configProperty \"${_property}\")\n\t\t\t\tlist (APPEND _properties ${_configProperty})\n\t\t\tendforeach()\n\t\telse()\n\t\t\tlist (APPEND _properties ${_property})\n\t\tendif()\n\tendforeach()\n\tset (${_propertiesVar} ${_properties} PARENT_SCOPE)\nendfunction()\n\nfunction (cotire_copy_set_properites _configurations _type _source _target)\n\tcotire_resolve_config_properites(\"${_configurations}\" _properties ${ARGN})\n\tforeach (_property ${_properties})\n\t\tget_property(_isSet ${_type} ${_source} PROPERTY ${_property} SET)\n\t\tif (_isSet)\n\t\t\tget_property(_propertyValue ${_type} ${_source} PROPERTY ${_property})\n\t\t\tset_property(${_type} ${_target} PROPERTY ${_property} \"${_propertyValue}\")\n\t\tendif()\n\tendforeach()\nendfunction()\n\nfunction (cotire_get_target_link_libraries_for_usage_requirements _target _targetLinkLibrariesVar)\n\tset (_targetLinkLibraries \"\")\n\tget_target_property(_librariesToProcess ${_target} LINK_LIBRARIES)\n\twhile (_librariesToProcess)\n\t\t# remove from head\n\t\tlist (GET _librariesToProcess 0 _library)\n\t\tlist (REMOVE_AT _librariesToProcess 0)\n\t\tlist (FIND _targetLinkLibraries ${_library} _index)\n\t\tif (_index LESS 0)\n\t\t\tlist (APPEND _targetLinkLibraries ${_library})\n\t\t\t# process transitive libraries\n\t\t\tif (TARGET ${_library})\n\t\t\t\tget_target_property(_libraries ${_library} INTERFACE_LINK_LIBRARIES)\n\t\t\t\tif (_libraries)\n\t\t\t\t\tlist (APPEND _librariesToProcess ${_libraries})\n\t\t\t\tendif()\n\t\t\tendif()\n\t\tendif()\n\tendwhile()\n\tset (${_targetLinkLibrariesVar} ${_targetLinkLibraries} PARENT_SCOPE)\nendfunction()\n\nfunction (cotire_filter_compile_flags _language _flagFilter _matchedOptionsVar _unmatchedOptionsVar)\n\tif (WIN32 AND CMAKE_${_language}_COMPILER_ID MATCHES \"MSVC|Intel\")\n\t\tset (_flagPrefix \"[/-]\")\n\telse()\n\t\tset (_flagPrefix \"--?\")\n\tendif()\n\tset (_optionFlag \"\")\n\tset (_matchedOptions \"\")\n\tset (_unmatchedOptions \"\")\n\tforeach (_compileFlag ${ARGN})\n\t\tif (_compileFlag)\n\t\t\tif (_optionFlag AND NOT \"${_compileFlag}\" MATCHES \"^${_flagPrefix}\")\n\t\t\t\t# option with separate argument\n\t\t\t\tlist (APPEND _matchedOptions \"${_compileFlag}\")\n\t\t\t\tset (_optionFlag \"\")\n\t\t\telseif (\"${_compileFlag}\" MATCHES \"^(${_flagPrefix})(${_flagFilter})$\")\n\t\t\t\t# remember option\n\t\t\t\tset (_optionFlag \"${CMAKE_MATCH_2}\")\n\t\t\telseif (\"${_compileFlag}\" MATCHES \"^(${_flagPrefix})(${_flagFilter})(.+)$\")\n\t\t\t\t# option with joined argument\n\t\t\t\tlist (APPEND _matchedOptions \"${CMAKE_MATCH_3}\")\n\t\t\t\tset (_optionFlag \"\")\n\t\t\telse()\n\t\t\t\t# flush remembered option\n\t\t\t\tif (_optionFlag)\n\t\t\t\t\tlist (APPEND _matchedOptions \"${_optionFlag}\")\n\t\t\t\t\tset (_optionFlag \"\")\n\t\t\t\tendif()\n\t\t\t\t# add to unfiltered options\n\t\t\t\tlist (APPEND _unmatchedOptions \"${_compileFlag}\")\n\t\t\tendif()\n\t\tendif()\n\tendforeach()\n\tif (_optionFlag)\n\t\tlist (APPEND _matchedOptions \"${_optionFlag}\")\n\tendif()\n\tif (COTIRE_DEBUG)\n\t\tmessage (STATUS \"Filter ${_flagFilter}\")\n\t\tif (_matchedOptions)\n\t\t\tmessage (STATUS \"Matched ${_matchedOptions}\")\n\t\tendif()\n\t\tif (_unmatchedOptions)\n\t\t\tmessage (STATUS \"Unmatched ${_unmatchedOptions}\")\n\t\tendif()\n\tendif()\n\tset (${_matchedOptionsVar} ${_matchedOptions} PARENT_SCOPE)\n\tset (${_unmatchedOptionsVar} ${_unmatchedOptions} PARENT_SCOPE)\nendfunction()\n\nfunction (cotire_get_target_compile_flags _config _language _directory _target _flagsVar)\n\tstring (TOUPPER \"${_config}\" _upperConfig)\n\t# collect options from CMake language variables\n\tset (_compileFlags \"\")\n\tif (CMAKE_${_language}_FLAGS)\n\t\tset (_compileFlags \"${_compileFlags} ${CMAKE_${_language}_FLAGS}\")\n\tendif()\n\tif (CMAKE_${_language}_FLAGS_${_upperConfig})\n\t\tset (_compileFlags \"${_compileFlags} ${CMAKE_${_language}_FLAGS_${_upperConfig}}\")\n\tendif()\n\tif (_target)\n\t\t# add option from CMake target type variable\n\t\tget_target_property(_targetType ${_target} TYPE)\n\t\tif (POLICY CMP0018)\n\t\t\t# handle POSITION_INDEPENDENT_CODE property introduced with CMake 2.8.9 if policy CMP0018 is turned on\n\t\t\tcmake_policy(GET CMP0018 _PIC_Policy)\n\t\telse()\n\t\t\t# default to old behavior\n\t\t\tset (_PIC_Policy \"OLD\")\n\t\tendif()\n\t\tif (COTIRE_DEBUG)\n\t\t\tmessage(STATUS \"CMP0018=${_PIC_Policy}\")\n\t\tendif()\n\t\tif (_PIC_Policy STREQUAL \"NEW\")\n\t\t\t# NEW behavior: honor the POSITION_INDEPENDENT_CODE target property\n\t\t\tget_target_property(_targetPIC ${_target} POSITION_INDEPENDENT_CODE)\n\t\t\tif (_targetPIC)\n\t\t\t\tif (_targetType STREQUAL \"EXECUTABLE\" AND CMAKE_${_language}_COMPILE_OPTIONS_PIE)\n\t\t\t\t\tset (_compileFlags \"${_compileFlags} ${CMAKE_${_language}_COMPILE_OPTIONS_PIE}\")\n\t\t\t\telseif (CMAKE_${_language}_COMPILE_OPTIONS_PIC)\n\t\t\t\t\tset (_compileFlags \"${_compileFlags} ${CMAKE_${_language}_COMPILE_OPTIONS_PIC}\")\n\t\t\t\tendif()\n\t\t\tendif()\n\t\telse()\n\t\t\t# OLD behavior or policy not set: use the value of CMAKE_SHARED_LIBRARY_<Lang>_FLAGS\n\t\t\tif (_targetType STREQUAL \"MODULE_LIBRARY\")\n\t\t\t\t# flags variable for module library uses different name SHARED_MODULE\n\t\t\t\t# (e.g., CMAKE_SHARED_MODULE_C_FLAGS)\n\t\t\t\tset (_targetType SHARED_MODULE)\n\t\t\tendif()\n\t\t\tif (CMAKE_${_targetType}_${_language}_FLAGS)\n\t\t\t\tset (_compileFlags \"${_compileFlags} ${CMAKE_${_targetType}_${_language}_FLAGS}\")\n\t\t\tendif()\n\t\tendif()\n\tendif()\n\tif (_directory)\n\t\t# add_definitions may have been used to add flags to the compiler command\n\t\tget_directory_property(_dirDefinitions DIRECTORY \"${_directory}\" DEFINITIONS)\n\t\tif (_dirDefinitions)\n\t\t\tset (_compileFlags \"${_compileFlags} ${_dirDefinitions}\")\n\t\tendif()\n\tendif()\n\tif (_target)\n\t\t# add target compile options\n\t\tget_target_property(_targetflags ${_target} COMPILE_FLAGS)\n\t\tif (_targetflags)\n\t\t\tset (_compileFlags \"${_compileFlags} ${_targetflags}\")\n\t\tendif()\n\t\tget_target_property(_targetOptions ${_target} COMPILE_OPTIONS)\n\t\tif (_targetOptions)\n\t\t\tset (_compileFlags \"${_compileFlags} ${_targetOptions}\")\n\t\tendif()\n\t\t# interface compile options from linked library targets\n\t\tcotire_get_target_link_libraries_for_usage_requirements(${_target} _linkLibraries)\n\t\tforeach (_library ${_linkLibraries})\n\t\t\tif (TARGET ${_library})\n\t\t\t\tget_target_property(_targetOptions ${_library} INTERFACE_COMPILE_OPTIONS)\n\t\t\t\tif (_targetOptions)\n\t\t\t\t\tset (_compileFlags \"${_compileFlags} ${_targetOptions}\")\n\t\t\t\tendif()\n\t\t\tendif()\n\t\tendforeach()\n\tendif()\n\tif (UNIX)\n\t\tseparate_arguments(_compileFlags UNIX_COMMAND \"${_compileFlags}\")\n\telseif(WIN32)\n\t\tseparate_arguments(_compileFlags WINDOWS_COMMAND \"${_compileFlags}\")\n\telse()\n\t\tseparate_arguments(_compileFlags)\n\tendif()\n\t# platform specific flags\n\tif (APPLE)\n\t\tget_target_property(_architectures ${_target} OSX_ARCHITECTURES_${_upperConfig})\n\t\tif (NOT _architectures)\n\t\t\tget_target_property(_architectures ${_target} OSX_ARCHITECTURES)\n\t\tendif()\n\t\tif (_architectures)\n\t\t\tforeach (_arch ${_architectures})\n\t\t\t\tlist (APPEND _compileFlags \"-arch\" \"${_arch}\")\n\t\t\tendforeach()\n\t\tendif()\n\t\tif (CMAKE_OSX_SYSROOT)\n\t\t\tif (CMAKE_${_language}_SYSROOT_FLAG)\n\t\t\t\tlist (APPEND _compileFlags \"${CMAKE_${_language}_SYSROOT_FLAG}\" \"${CMAKE_OSX_SYSROOT}\")\n\t\t\telse()\n\t\t\t\tlist (APPEND _compileFlags \"-isysroot\" \"${CMAKE_OSX_SYSROOT}\")\n\t\t\tendif()\n\t\tendif()\n\t\tif (CMAKE_OSX_DEPLOYMENT_TARGET)\n\t\t\tif (CMAKE_${_language}_OSX_DEPLOYMENT_TARGET_FLAG)\n\t\t\t\tlist (APPEND _compileFlags \"${CMAKE_${_language}_OSX_DEPLOYMENT_TARGET_FLAG}${CMAKE_OSX_DEPLOYMENT_TARGET}\")\n\t\t\telse()\n\t\t\t\tlist (APPEND _compileFlags \"-mmacosx-version-min=${CMAKE_OSX_DEPLOYMENT_TARGET}\")\n\t\t\tendif()\n\t\tendif()\n\tendif()\n\tif (COTIRE_DEBUG AND _compileFlags)\n\t\tmessage (STATUS \"Target ${_target} compile flags ${_compileFlags}\")\n\tendif()\n\tset (${_flagsVar} ${_compileFlags} PARENT_SCOPE)\nendfunction()\n\nfunction (cotire_get_target_include_directories _config _language _targetSourceDir _targetBinaryDir _target _includeDirsVar _systemIncludeDirsVar)\n\tset (_includeDirs \"\")\n\tset (_systemIncludeDirs \"\")\n\t# default include dirs\n\tif (CMAKE_INCLUDE_CURRENT_DIR)\n\t\tlist (APPEND _includeDirs \"${_targetBinaryDir}\")\n\t\tlist (APPEND _includeDirs \"${_targetSourceDir}\")\n\tendif()\n\t# parse additional include directories from target compile flags\n\tset (_targetFlags \"\")\n\tcotire_get_target_compile_flags(\"${_config}\" \"${_language}\" \"${_targetSourceDir}\" \"${_target}\" _targetFlags)\n\tcotire_filter_compile_flags(\"${_language}\" \"I\" _dirs _ignore ${_targetFlags})\n\tif (_dirs)\n\t\tlist (APPEND _includeDirs ${_dirs})\n\tendif()\n\t# target include directories\n\tget_directory_property(_dirs DIRECTORY \"${_targetSourceDir}\" INCLUDE_DIRECTORIES)\n\tif (_target)\n\t\tget_target_property(_targetDirs ${_target} INCLUDE_DIRECTORIES)\n\t\tif (_targetDirs)\n\t\t\tlist (APPEND _dirs ${_targetDirs})\n\t\tendif()\n\t\tget_target_property(_targetDirs ${_target} INTERFACE_SYSTEM_INCLUDE_DIRECTORIES)\n\t\tif (_targetDirs)\n\t\t\tlist (APPEND _systemIncludeDirs ${_targetDirs})\n\t\tendif()\n\t\t# interface include directories from linked library targets\n\t\tcotire_get_target_link_libraries_for_usage_requirements(${_target} _linkLibraries)\n\t\tforeach (_library ${_linkLibraries})\n\t\t\tif (TARGET ${_library})\n\t\t\t\tget_target_property(_targetDirs ${_library} INTERFACE_INCLUDE_DIRECTORIES)\n\t\t\t\tif (_targetDirs)\n\t\t\t\t\tlist (APPEND _dirs ${_targetDirs})\n\t\t\t\tendif()\n\t\t\t\tget_target_property(_targetDirs ${_library} INTERFACE_SYSTEM_INCLUDE_DIRECTORIES)\n\t\t\t\tif (_targetDirs)\n\t\t\t\t\tlist (APPEND _systemIncludeDirs ${_targetDirs})\n\t\t\t\tendif()\n\t\t\tendif()\n\t\tendforeach()\n\tendif()\n\tif (dirs)\n\t\tlist (REMOVE_DUPLICATES _dirs)\n\tendif()\n\tlist (LENGTH _includeDirs _projectInsertIndex)\n\tforeach (_dir ${_dirs})\n\t\tif (CMAKE_INCLUDE_DIRECTORIES_PROJECT_BEFORE)\n\t\t\tcotire_check_is_path_relative_to(\"${_dir}\" _isRelative \"${CMAKE_SOURCE_DIR}\" \"${CMAKE_BINARY_DIR}\")\n\t\t\tif (_isRelative)\n\t\t\t\tlist (LENGTH _includeDirs _len)\n\t\t\t\tif (_len EQUAL _projectInsertIndex)\n\t\t\t\t\tlist (APPEND _includeDirs \"${_dir}\")\n\t\t\t\telse()\n\t\t\t\t\tlist (INSERT _includeDirs _projectInsertIndex \"${_dir}\")\n\t\t\t\tendif()\n\t\t\t\tmath (EXPR _projectInsertIndex \"${_projectInsertIndex} + 1\")\n\t\t\telse()\n\t\t\t\tlist (APPEND _includeDirs \"${_dir}\")\n\t\t\tendif()\n\t\telse()\n\t\t\tlist (APPEND _includeDirs \"${_dir}\")\n\t\tendif()\n\tendforeach()\n\tlist (REMOVE_DUPLICATES _includeDirs)\n\tlist (REMOVE_DUPLICATES _systemIncludeDirs)\n\tif (CMAKE_${_language}_IMPLICIT_INCLUDE_DIRECTORIES)\n\t\tlist (REMOVE_ITEM _includeDirs ${CMAKE_${_language}_IMPLICIT_INCLUDE_DIRECTORIES})\n\tendif()\n\tif (COTIRE_DEBUG AND _includeDirs)\n\t\tmessage (STATUS \"Target ${_target} include dirs ${_includeDirs}\")\n\tendif()\n\tset (${_includeDirsVar} ${_includeDirs} PARENT_SCOPE)\n\tif (COTIRE_DEBUG AND _systemIncludeDirs)\n\t\tmessage (STATUS \"Target ${_target} system include dirs ${_systemIncludeDirs}\")\n\tendif()\n\tset (${_systemIncludeDirsVar} ${_systemIncludeDirs} PARENT_SCOPE)\nendfunction()\n\nmacro (cotire_make_C_identifier _identifierVar _str)\n\tif (CMAKE_VERSION VERSION_LESS \"2.8.12\")\n\t\t# mimic CMake SystemTools::MakeCindentifier behavior\n\t\tif (\"${_str}\" MATCHES \"^[0-9].+$\")\n\t\t\tset (_str \"_${str}\")\n\t\tendif()\n\t\tstring (REGEX REPLACE \"[^a-zA-Z0-9]\" \"_\" ${_identifierVar} \"${_str}\")\n\telse()\n\t\tstring (MAKE_C_IDENTIFIER \"${_str}\" \"${_identifierVar}\")\n\tendif()\nendmacro()\n\nfunction (cotire_get_target_export_symbol _target _exportSymbolVar)\n\tset (_exportSymbol \"\")\n\tget_target_property(_targetType ${_target} TYPE)\n\tget_target_property(_enableExports ${_target} ENABLE_EXPORTS)\n\tif (_targetType MATCHES \"(SHARED|MODULE)_LIBRARY\" OR\n\t\t(_targetType STREQUAL \"EXECUTABLE\" AND _enableExports))\n\t\tget_target_property(_exportSymbol ${_target} DEFINE_SYMBOL)\n\t\tif (NOT _exportSymbol)\n\t\t\tset (_exportSymbol \"${_target}_EXPORTS\")\n\t\tendif()\n\t\tcotire_make_C_identifier(_exportSymbol \"${_exportSymbol}\")\n\tendif()\n\tset (${_exportSymbolVar} ${_exportSymbol} PARENT_SCOPE)\nendfunction()\n\nfunction (cotire_get_target_compile_definitions _config _language _directory _target _definitionsVar)\n\tstring (TOUPPER \"${_config}\" _upperConfig)\n\tset (_configDefinitions \"\")\n\t# CMAKE_INTDIR for multi-configuration build systems\n\tif (NOT \"${CMAKE_CFG_INTDIR}\" STREQUAL \".\")\n\t\tlist (APPEND _configDefinitions \"CMAKE_INTDIR=\\\"${_config}\\\"\")\n\tendif()\n\t# target export define symbol\n\tcotire_get_target_export_symbol(\"${_target}\" _defineSymbol)\n\tif (_defineSymbol)\n\t\tlist (APPEND _configDefinitions \"${_defineSymbol}\")\n\tendif()\n\t# directory compile definitions\n\tget_directory_property(_definitions DIRECTORY \"${_directory}\" COMPILE_DEFINITIONS)\n\tif (_definitions)\n\t\tlist (APPEND _configDefinitions ${_definitions})\n\tendif()\n\tget_directory_property(_definitions DIRECTORY \"${_directory}\" COMPILE_DEFINITIONS_${_upperConfig})\n\tif (_definitions)\n\t\tlist (APPEND _configDefinitions ${_definitions})\n\tendif()\n\t# target compile definitions\n\tget_target_property(_definitions ${_target} COMPILE_DEFINITIONS)\n\tif (_definitions)\n\t\tlist (APPEND _configDefinitions ${_definitions})\n\tendif()\n\tget_target_property(_definitions ${_target} COMPILE_DEFINITIONS_${_upperConfig})\n\tif (_definitions)\n\t\tlist (APPEND _configDefinitions ${_definitions})\n\tendif()\n\t# interface compile definitions from linked library targets\n\tcotire_get_target_link_libraries_for_usage_requirements(${_target} _linkLibraries)\n\tforeach (_library ${_linkLibraries})\n\t\tif (TARGET ${_library})\n\t\t\tget_target_property(_definitions ${_library} INTERFACE_COMPILE_DEFINITIONS)\n\t\t\tif (_definitions)\n\t\t\t\tlist (APPEND _configDefinitions ${_definitions})\n\t\t\tendif()\n\t\tendif()\n\tendforeach()\n\t# parse additional compile definitions from target compile flags\n\t# and don't look at directory compile definitions, which we already handled\n\tset (_targetFlags \"\")\n\tcotire_get_target_compile_flags(\"${_config}\" \"${_language}\" \"\" \"${_target}\" _targetFlags)\n\tcotire_filter_compile_flags(\"${_language}\" \"D\" _definitions _ignore ${_targetFlags})\n\tif (_definitions)\n\t\tlist (APPEND _configDefinitions ${_definitions})\n\tendif()\n\tlist (REMOVE_DUPLICATES _configDefinitions)\n\tif (COTIRE_DEBUG AND _configDefinitions)\n\t\tmessage (STATUS \"Target ${_target} compile definitions ${_configDefinitions}\")\n\tendif()\n\tset (${_definitionsVar} ${_configDefinitions} PARENT_SCOPE)\nendfunction()\n\nfunction (cotire_get_target_compiler_flags _config _language _directory _target _compilerFlagsVar)\n\t# parse target compile flags omitting compile definitions and include directives\n\tset (_targetFlags \"\")\n\tcotire_get_target_compile_flags(\"${_config}\" \"${_language}\" \"${_directory}\" \"${_target}\" _targetFlags)\n\tset (_compilerFlags \"\")\n\tcotire_filter_compile_flags(\"${_language}\" \"[ID]\" _ignore _compilerFlags ${_targetFlags})\n\tif (COTIRE_DEBUG AND _compilerFlags)\n\t\tmessage (STATUS \"Target ${_target} compiler flags ${_compilerFlags}\")\n\tendif()\n\tset (${_compilerFlagsVar} ${_compilerFlags} PARENT_SCOPE)\nendfunction()\n\nfunction (cotire_add_sys_root_paths _pathsVar)\n\tif (APPLE)\n\t\tif (CMAKE_OSX_SYSROOT AND CMAKE_${_language}_HAS_ISYSROOT)\n\t\t\tforeach (_path IN LISTS ${_pathsVar})\n\t\t\t\tif (IS_ABSOLUTE \"${_path}\")\n\t\t\t\t\tget_filename_component(_path \"${CMAKE_OSX_SYSROOT}/${_path}\" ABSOLUTE)\n\t\t\t\t\tif (EXISTS \"${_path}\")\n\t\t\t\t\t\tlist (APPEND ${_pathsVar} \"${_path}\")\n\t\t\t\t\tendif()\n\t\t\t\tendif()\n\t\t\tendforeach()\n\t\tendif()\n\tendif()\n\tset (${_pathsVar} ${${_pathsVar}} PARENT_SCOPE)\n\tif (COTIRE_DEBUG)\n\t\tmessage (STATUS \"${_pathsVar}=${${_pathsVar}}\")\n\tendif()\nendfunction()\n\nfunction (cotire_get_source_extra_properties _sourceFile _pattern _resultVar)\n\tset (_extraProperties ${ARGN})\n\tset (_result \"\")\n\tif (_extraProperties)\n\t\tlist (FIND _extraProperties \"${_sourceFile}\" _index)\n\t\tif (_index GREATER -1)\n\t\t\tmath (EXPR _index \"${_index} + 1\")\n\t\t\tlist (LENGTH _extraProperties _len)\n\t\t\tmath (EXPR _len \"${_len} - 1\")\n\t\t\tforeach (_index RANGE ${_index} ${_len})\n\t\t\t\tlist (GET _extraProperties ${_index} _value)\n\t\t\t\tif (_value MATCHES \"${_pattern}\")\n\t\t\t\t\tlist (APPEND _result \"${_value}\")\n\t\t\t\telse()\n\t\t\t\t\tbreak()\n\t\t\t\tendif()\n\t\t\tendforeach()\n\t\tendif()\n\tendif()\n\tset (${_resultVar} ${_result} PARENT_SCOPE)\nendfunction()\n\nfunction (cotire_get_source_compile_definitions _config _language _sourceFile _definitionsVar)\n\tset (_compileDefinitions \"\")\n\tif (NOT CMAKE_SCRIPT_MODE_FILE)\n\t\tstring (TOUPPER \"${_config}\" _upperConfig)\n\t\tget_source_file_property(_definitions \"${_sourceFile}\" COMPILE_DEFINITIONS)\n\t\tif (_definitions)\n\t\t\tlist (APPEND _compileDefinitions ${_definitions})\n\t\tendif()\n\t\tget_source_file_property(_definitions \"${_sourceFile}\" COMPILE_DEFINITIONS_${_upperConfig})\n\t\tif (_definitions)\n\t\t\tlist (APPEND _compileDefinitions ${_definitions})\n\t\tendif()\n\tendif()\n\tcotire_get_source_extra_properties(\"${_sourceFile}\" \"^[a-zA-Z0-9_]+(=.*)?$\" _definitions ${ARGN})\n\tif (_definitions)\n\t\tlist (APPEND _compileDefinitions ${_definitions})\n\tendif()\n\tif (COTIRE_DEBUG AND _compileDefinitions)\n\t\tmessage (STATUS \"Source ${_sourceFile} compile definitions ${_compileDefinitions}\")\n\tendif()\n\tset (${_definitionsVar} ${_compileDefinitions} PARENT_SCOPE)\nendfunction()\n\nfunction (cotire_get_source_files_compile_definitions _config _language _definitionsVar)\n\tset (_configDefinitions \"\")\n\tforeach (_sourceFile ${ARGN})\n\t\tcotire_get_source_compile_definitions(\"${_config}\" \"${_language}\" \"${_sourceFile}\" _sourceDefinitions)\n\t\tif (_sourceDefinitions)\n\t\t\tlist (APPEND _configDefinitions \"${_sourceFile}\" ${_sourceDefinitions} \"-\")\n\t\tendif()\n\tendforeach()\n\tset (${_definitionsVar} ${_configDefinitions} PARENT_SCOPE)\nendfunction()\n\nfunction (cotire_get_source_undefs _sourceFile _property _sourceUndefsVar)\n\tset (_sourceUndefs \"\")\n\tif (NOT CMAKE_SCRIPT_MODE_FILE)\n\t\tget_source_file_property(_undefs \"${_sourceFile}\" ${_property})\n\t\tif (_undefs)\n\t\t\tlist (APPEND _sourceUndefs ${_undefs})\n\t\tendif()\n\tendif()\n\tcotire_get_source_extra_properties(\"${_sourceFile}\" \"^[a-zA-Z0-9_]+$\" _undefs ${ARGN})\n\tif (_undefs)\n\t\tlist (APPEND _sourceUndefs ${_undefs})\n\tendif()\n\tif (COTIRE_DEBUG AND _sourceUndefs)\n\t\tmessage (STATUS \"Source ${_sourceFile} ${_property} undefs ${_sourceUndefs}\")\n\tendif()\n\tset (${_sourceUndefsVar} ${_sourceUndefs} PARENT_SCOPE)\nendfunction()\n\nfunction (cotire_get_source_files_undefs _property _sourceUndefsVar)\n\tset (_sourceUndefs \"\")\n\tforeach (_sourceFile ${ARGN})\n\t\tcotire_get_source_undefs(\"${_sourceFile}\" ${_property} _undefs)\n\t\tif (_undefs)\n\t\t\tlist (APPEND _sourceUndefs \"${_sourceFile}\" ${_undefs} \"-\")\n\t\tendif()\n\tendforeach()\n\tset (${_sourceUndefsVar} ${_sourceUndefs} PARENT_SCOPE)\nendfunction()\n\nmacro (cotire_set_cmd_to_prologue _cmdVar)\n\tset (${_cmdVar} \"${CMAKE_COMMAND}\")\n\tif (COTIRE_DEBUG)\n\t\tlist (APPEND ${_cmdVar} \"--warn-uninitialized\")\n\tendif()\n\tlist (APPEND ${_cmdVar} \"-DCOTIRE_BUILD_TYPE:STRING=$<CONFIGURATION>\")\n\tif (COTIRE_VERBOSE)\n\t\tlist (APPEND ${_cmdVar} \"-DCOTIRE_VERBOSE:BOOL=ON\")\n\telseif(\"${CMAKE_GENERATOR}\" MATCHES \"Makefiles\")\n\t\tlist (APPEND ${_cmdVar} \"-DCOTIRE_VERBOSE:BOOL=$(VERBOSE)\")\n\tendif()\nendmacro()\n\nfunction (cotire_init_compile_cmd _cmdVar _language _compilerExe _compilerArg1)\n\tif (NOT _compilerExe)\n\t\tset (_compilerExe \"${CMAKE_${_language}_COMPILER}\")\n\tendif()\n\tif (NOT _compilerArg1)\n\t\tset (_compilerArg1 ${CMAKE_${_language}_COMPILER_ARG1})\n\tendif()\n\tstring (STRIP \"${_compilerArg1}\" _compilerArg1)\n\tset (${_cmdVar} \"${_compilerExe}\" ${_compilerArg1} PARENT_SCOPE)\nendfunction()\n\nmacro (cotire_add_definitions_to_cmd _cmdVar _language)\n\tforeach (_definition ${ARGN})\n\t\tif (WIN32 AND CMAKE_${_language}_COMPILER_ID MATCHES \"MSVC|Intel\")\n\t\t\tlist (APPEND ${_cmdVar} \"/D${_definition}\")\n\t\telse()\n\t\t\tlist (APPEND ${_cmdVar} \"-D${_definition}\")\n\t\tendif()\n\tendforeach()\nendmacro()\n\nmacro (cotire_add_includes_to_cmd _cmdVar _language _includeSystemFlag _includesVar _systemIncludesVar)\n\tforeach (_include ${${_includesVar}})\n\t\tif (WIN32 AND CMAKE_${_language}_COMPILER_ID MATCHES \"MSVC|Intel\")\n\t\t\tfile (TO_NATIVE_PATH \"${_include}\" _include)\n\t\t\tlist (APPEND ${_cmdVar} \"/I${_include}\")\n\t\telse()\n\t\t\tlist (FIND ${_systemIncludesVar} ${_include} _index)\n\t\t\tif(_index GREATER -1 AND NOT \"${_includeSystemFlag}\" STREQUAL \"\")\n\t\t\t\tlist (APPEND ${_cmdVar} \"${_includeSystemFlag}${_include}\")\n\t\t\telse()\n\t\t\t\tlist (APPEND ${_cmdVar} \"-I${_include}\")\n\t\t\tendif()\n\t\tendif()\n\tendforeach()\nendmacro()\n\nmacro (cotire_add_frameworks_to_cmd _cmdVar _language)\n\tif (APPLE)\n\t\tset (_frameWorkDirs \"\")\n\t\tforeach (_include ${ARGN})\n\t\t\tif (IS_ABSOLUTE \"${_include}\" AND _include MATCHES \"\\\\.framework$\")\n\t\t\t\tget_filename_component(_frameWorkDir \"${_include}\" PATH)\n\t\t\t\tlist (APPEND _frameWorkDirs \"${_frameWorkDir}\")\n\t\t\tendif()\n\t\tendforeach()\n\t\tif (_frameWorkDirs)\n\t\t\tlist (REMOVE_DUPLICATES _frameWorkDirs)\n\t\t\tforeach (_frameWorkDir ${_frameWorkDirs})\n\t\t\t\tlist (APPEND ${_cmdVar} \"-F${_frameWorkDir}\")\n\t\t\tendforeach()\n\t\tendif()\n\tendif()\nendmacro()\n\nmacro (cotire_add_compile_flags_to_cmd _cmdVar)\n\tforeach (_flag ${ARGN})\n\t\tlist (APPEND ${_cmdVar} \"${_flag}\")\n\tendforeach()\nendmacro()\n\nfunction (cotire_check_file_up_to_date _fileIsUpToDateVar _file)\n\tset (${_fileIsUpToDateVar} FALSE PARENT_SCOPE)\n\tset (_triggerFile \"\")\n\tforeach (_dependencyFile ${ARGN})\n\t\tif (EXISTS \"${_dependencyFile}\" AND \"${_dependencyFile}\" IS_NEWER_THAN \"${_file}\")\n\t\t\tset (_triggerFile \"${_dependencyFile}\")\n\t\t\tbreak()\n\t\tendif()\n\tendforeach()\n\tget_filename_component(_fileName \"${_file}\" NAME)\n\tif (EXISTS \"${_file}\")\n\t\tif (_triggerFile)\n\t\t\tif (COTIRE_VERBOSE)\n\t\t\t\tmessage (STATUS \"${_fileName} update triggered by ${_triggerFile} change.\")\n\t\t\tendif()\n\t\telse()\n\t\t\tif (COTIRE_VERBOSE)\n\t\t\t\tmessage (STATUS \"${_fileName} is up-to-date.\")\n\t\t\tendif()\n\t\t\tset (${_fileIsUpToDateVar} TRUE PARENT_SCOPE)\n\t\tendif()\n\telse()\n\t\tif (COTIRE_VERBOSE)\n\t\t\tmessage (STATUS \"${_fileName} does not exist yet.\")\n\t\tendif()\n\tendif()\nendfunction()\n\nmacro (cotire_find_closest_relative_path _headerFile _includeDirs _relPathVar)\n\tset (${_relPathVar} \"\")\n\tforeach (_includeDir ${_includeDirs})\n\t\tif (IS_DIRECTORY \"${_includeDir}\")\n\t\t\tfile (RELATIVE_PATH _relPath \"${_includeDir}\" \"${_headerFile}\")\n\t\t\tif (NOT IS_ABSOLUTE \"${_relPath}\" AND NOT \"${_relPath}\" MATCHES \"^\\\\.\\\\.\")\n\t\t\t\tstring (LENGTH \"${${_relPathVar}}\" _closestLen)\n\t\t\t\tstring (LENGTH \"${_relPath}\" _relLen)\n\t\t\t\tif (_closestLen EQUAL 0 OR _relLen LESS _closestLen)\n\t\t\t\t\tset (${_relPathVar} \"${_relPath}\")\n\t\t\t\tendif()\n\t\t\tendif()\n\t\telseif (\"${_includeDir}\" STREQUAL \"${_headerFile}\")\n\t\t\t# if path matches exactly, return short non-empty string\n\t\t\tset (${_relPathVar} \"1\")\n\t\t\tbreak()\n\t\tendif()\n\tendforeach()\nendmacro()\n\nmacro (cotire_check_header_file_location _headerFile _insideIncudeDirs _outsideIncudeDirs _headerIsInside)\n\t# check header path against ignored and honored include directories\n\tcotire_find_closest_relative_path(\"${_headerFile}\" \"${_insideIncudeDirs}\" _insideRelPath)\n\tif (_insideRelPath)\n\t\t# header is inside, but could be become outside if there is a shorter outside match\n\t\tcotire_find_closest_relative_path(\"${_headerFile}\" \"${_outsideIncudeDirs}\" _outsideRelPath)\n\t\tif (_outsideRelPath)\n\t\t\tstring (LENGTH \"${_insideRelPath}\" _insideRelPathLen)\n\t\t\tstring (LENGTH \"${_outsideRelPath}\" _outsideRelPathLen)\n\t\t\tif (_outsideRelPathLen LESS _insideRelPathLen)\n\t\t\t\tset (${_headerIsInside} FALSE)\n\t\t\telse()\n\t\t\t\tset (${_headerIsInside} TRUE)\n\t\t\tendif()\n\t\telse()\n\t\t\tset (${_headerIsInside} TRUE)\n\t\tendif()\n\telse()\n\t\t# header is outside\n\t\tset (${_headerIsInside} FALSE)\n\tendif()\nendmacro()\n\nmacro (cotire_check_ignore_header_file_path _headerFile _headerIsIgnoredVar)\n\tif (NOT EXISTS \"${_headerFile}\")\n\t\tset (${_headerIsIgnoredVar} TRUE)\n\telseif (IS_DIRECTORY \"${_headerFile}\")\n\t\tset (${_headerIsIgnoredVar} TRUE)\n\telseif (\"${_headerFile}\" MATCHES \"\\\\.\\\\.|[_-]fixed\" AND \"${_headerFile}\" MATCHES \"\\\\.h$\")\n\t\t# heuristic: ignore C headers with embedded parent directory references or \"-fixed\" or \"_fixed\" in path\n\t\t# these often stem from using GCC #include_next tricks, which may break the precompiled header compilation\n\t\t# with the error message \"error: no include path in which to search for header.h\"\n\t\tset (${_headerIsIgnoredVar} TRUE)\n\telse()\n\t\tset (${_headerIsIgnoredVar} FALSE)\n\tendif()\nendmacro()\n\nmacro (cotire_check_ignore_header_file_ext _headerFile _ignoreExtensionsVar _headerIsIgnoredVar)\n\t# check header file extension\n\tcotire_get_source_file_extension(\"${_headerFile}\" _headerFileExt)\n\tset (${_headerIsIgnoredVar} FALSE)\n\tif (_headerFileExt)\n\t\tlist (FIND ${_ignoreExtensionsVar} \"${_headerFileExt}\" _index)\n\t\tif (_index GREATER -1)\n\t\t\tset (${_headerIsIgnoredVar} TRUE)\n\t\tendif()\n\tendif()\nendmacro()\n\nmacro (cotire_parse_line _line _headerFileVar _headerDepthVar)\n\tif (MSVC)\n\t\t# cl.exe /showIncludes output looks different depending on the language pack used, e.g.:\n\t\t# English: \"Note: including file:   C:\\directory\\file\"\n\t\t# German: \"Hinweis: Einlesen der Datei:   C:\\directory\\file\"\n\t\t# We use a very general regular expression, relying on the presence of the : characters\n\t\tif (_line MATCHES \"( +)([a-zA-Z]:[^:]+)$\")\n\t\t\t# Visual Studio compiler output\n\t\t\tstring (LENGTH \"${CMAKE_MATCH_1}\" ${_headerDepthVar})\n\t\t\tget_filename_component(${_headerFileVar} \"${CMAKE_MATCH_2}\" ABSOLUTE)\n\t\telse()\n\t\t\tset (${_headerFileVar} \"\")\n\t\t\tset (${_headerDepthVar} 0)\n\t\tendif()\n\telse()\n\t\tif (_line MATCHES \"^(\\\\.+) (.*)$\")\n\t\t\t# GCC like output\n\t\t\tstring (LENGTH \"${CMAKE_MATCH_1}\" ${_headerDepthVar})\n\t\t\tif (IS_ABSOLUTE \"${CMAKE_MATCH_2}\")\n\t\t\t\tset (${_headerFileVar} \"${CMAKE_MATCH_2}\")\n\t\t\telse()\n\t\t\t\tget_filename_component(${_headerFileVar} \"${CMAKE_MATCH_2}\" REALPATH)\n\t\t\tendif()\n\t\telse()\n\t\t\tset (${_headerFileVar} \"\")\n\t\t\tset (${_headerDepthVar} 0)\n\t\tendif()\n\tendif()\nendmacro()\n\nfunction (cotire_parse_includes _language _scanOutput _ignoredIncudeDirs _honoredIncudeDirs _ignoredExtensions _selectedIncludesVar _unparsedLinesVar)\n\tif (WIN32)\n\t\t# prevent CMake macro invocation errors due to backslash characters in Windows paths\n\t\tstring (REPLACE \"\\\\\" \"/\" _scanOutput \"${_scanOutput}\")\n\tendif()\n\t# canonize slashes\n\tstring (REPLACE \"//\" \"/\" _scanOutput \"${_scanOutput}\")\n\t# prevent semicolon from being interpreted as a line separator\n\tstring (REPLACE \";\" \"\\\\;\" _scanOutput \"${_scanOutput}\")\n\t# then separate lines\n\tstring (REGEX REPLACE \"\\n\" \";\" _scanOutput \"${_scanOutput}\")\n\tlist (LENGTH _scanOutput _len)\n\t# remove duplicate lines to speed up parsing\n\tlist (REMOVE_DUPLICATES _scanOutput)\n\tlist (LENGTH _scanOutput _uniqueLen)\n\tif (COTIRE_VERBOSE OR COTIRE_DEBUG)\n\t\tmessage (STATUS \"Scanning ${_uniqueLen} unique lines of ${_len} for includes\")\n\t\tif (_ignoredExtensions)\n\t\t\tmessage (STATUS \"Ignored extensions: ${_ignoredExtensions}\")\n\t\tendif()\n\t\tif (_ignoredIncudeDirs)\n\t\t\tmessage (STATUS \"Ignored paths: ${_ignoredIncudeDirs}\")\n\t\tendif()\n\t\tif (_honoredIncudeDirs)\n\t\t\tmessage (STATUS \"Included paths: ${_honoredIncudeDirs}\")\n\t\tendif()\n\tendif()\n\tset (_sourceFiles ${ARGN})\n\tset (_selectedIncludes \"\")\n\tset (_unparsedLines \"\")\n\t# stack keeps track of inside/outside project status of processed header files\n\tset (_headerIsInsideStack \"\")\n\tforeach (_line IN LISTS _scanOutput)\n\t\tif (_line)\n\t\t\tcotire_parse_line(\"${_line}\" _headerFile _headerDepth)\n\t\t\tif (_headerFile)\n\t\t\t\tcotire_check_header_file_location(\"${_headerFile}\" \"${_ignoredIncudeDirs}\" \"${_honoredIncudeDirs}\" _headerIsInside)\n\t\t\t\tif (COTIRE_DEBUG)\n\t\t\t\t\tmessage (STATUS \"${_headerDepth}: ${_headerFile} ${_headerIsInside}\")\n\t\t\t\tendif()\n\t\t\t\t# update stack\n\t\t\t\tlist (LENGTH _headerIsInsideStack _stackLen)\n\t\t\t\tif (_headerDepth GREATER _stackLen)\n\t\t\t\t\tmath (EXPR _stackLen \"${_stackLen} + 1\")\n\t\t\t\t\tforeach (_index RANGE ${_stackLen} ${_headerDepth})\n\t\t\t\t\t\tlist (APPEND _headerIsInsideStack ${_headerIsInside})\n\t\t\t\t\tendforeach()\n\t\t\t\telse()\n\t\t\t\t\tforeach (_index RANGE ${_headerDepth} ${_stackLen})\n\t\t\t\t\t\tlist (REMOVE_AT _headerIsInsideStack -1)\n\t\t\t\t\tendforeach()\n\t\t\t\t\tlist (APPEND _headerIsInsideStack ${_headerIsInside})\n\t\t\t\tendif()\n\t\t\t\tif (COTIRE_DEBUG)\n\t\t\t\t\tmessage (STATUS \"${_headerIsInsideStack}\")\n\t\t\t\tendif()\n\t\t\t\t# header is a candidate if it is outside project\n\t\t\t\tif (NOT _headerIsInside)\n\t\t\t\t\t# get parent header file's inside/outside status\n\t\t\t\t\tif (_headerDepth GREATER 1)\n\t\t\t\t\t\tmath (EXPR _index \"${_headerDepth} - 2\")\n\t\t\t\t\t\tlist (GET _headerIsInsideStack ${_index} _parentHeaderIsInside)\n\t\t\t\t\telse()\n\t\t\t\t\t\tset (_parentHeaderIsInside TRUE)\n\t\t\t\t\tendif()\n\t\t\t\t\t# select header file if parent header file is inside project\n\t\t\t\t\t# (e.g., a project header file that includes a standard header file)\n\t\t\t\t\tif (_parentHeaderIsInside)\n\t\t\t\t\t\tcotire_check_ignore_header_file_path(\"${_headerFile}\" _headerIsIgnored)\n\t\t\t\t\t\tif (NOT _headerIsIgnored)\n\t\t\t\t\t\t\tcotire_check_ignore_header_file_ext(\"${_headerFile}\" _ignoredExtensions _headerIsIgnored)\n\t\t\t\t\t\t\tif (NOT _headerIsIgnored)\n\t\t\t\t\t\t\t\tlist (APPEND _selectedIncludes \"${_headerFile}\")\n\t\t\t\t\t\t\telse()\n\t\t\t\t\t\t\t\t# fix header's inside status on stack, it is ignored by extension now\n\t\t\t\t\t\t\t\tlist (REMOVE_AT _headerIsInsideStack -1)\n\t\t\t\t\t\t\t\tlist (APPEND _headerIsInsideStack TRUE)\n\t\t\t\t\t\t\tendif()\n\t\t\t\t\t\tendif()\n\t\t\t\t\t\tif (COTIRE_DEBUG)\n\t\t\t\t\t\t\tmessage (STATUS \"${_headerFile} ${_ignoredExtensions} ${_headerIsIgnored}\")\n\t\t\t\t\t\tendif()\n\t\t\t\t\tendif()\n\t\t\t\tendif()\n\t\t\telse()\n\t\t\t\tif (MSVC)\n\t\t\t\t\t# for cl.exe do not keep unparsed lines which solely consist of a source file name\n\t\t\t\t\tstring (FIND \"${_sourceFiles}\" \"${_line}\" _index)\n\t\t\t\t\tif (_index LESS 0)\n\t\t\t\t\t\tlist (APPEND _unparsedLines \"${_line}\")\n\t\t\t\t\tendif()\n\t\t\t\telse()\n\t\t\t\t\tlist (APPEND _unparsedLines \"${_line}\")\n\t\t\t\tendif()\n\t\t\tendif()\n\t\tendif()\n\tendforeach()\n\tlist (REMOVE_DUPLICATES _selectedIncludes)\n\tset (${_selectedIncludesVar} ${_selectedIncludes} PARENT_SCOPE)\n\tset (${_unparsedLinesVar} ${_unparsedLines} PARENT_SCOPE)\nendfunction()\n\nfunction (cotire_scan_includes _includesVar)\n\tset(_options \"\")\n\tset(_oneValueArgs COMPILER_ID COMPILER_EXECUTABLE COMPILER_VERSION INCLUDE_SYSTEM_FLAG LANGUAGE UNPARSED_LINES)\n\tset(_multiValueArgs COMPILE_DEFINITIONS COMPILE_FLAGS INCLUDE_DIRECTORIES SYSTEM_INCLUDE_DIRECTORIES IGNORE_PATH INCLUDE_PATH IGNORE_EXTENSIONS)\n\tcmake_parse_arguments(_option \"${_options}\" \"${_oneValueArgs}\" \"${_multiValueArgs}\" ${ARGN})\n\tset (_sourceFiles ${_option_UNPARSED_ARGUMENTS})\n\tif (NOT _option_LANGUAGE)\n\t\tset (_option_LANGUAGE \"CXX\")\n\tendif()\n\tif (NOT _option_COMPILER_ID)\n\t\tset (_option_COMPILER_ID \"${CMAKE_${_option_LANGUAGE}_ID}\")\n\tendif()\n\tset (_cmd \"${_option_COMPILER_EXECUTABLE}\" ${_option_COMPILER_ARG1})\n\tcotire_init_compile_cmd(_cmd \"${_option_LANGUAGE}\" \"${_option_COMPILER_EXECUTABLE}\" \"${_option_COMPILER_ARG1}\")\n\tcotire_add_definitions_to_cmd(_cmd \"${_option_LANGUAGE}\" ${_option_COMPILE_DEFINITIONS})\n\tcotire_add_compile_flags_to_cmd(_cmd ${_option_COMPILE_FLAGS})\n\tcotire_add_includes_to_cmd(_cmd \"${_option_LANGUAGE}\" \"${_option_INCLUDE_SYSTEM_FLAG}\" _option_INCLUDE_DIRECTORIES _option_SYSTEM_INCLUDE_DIRECTORIES)\n\tcotire_add_frameworks_to_cmd(_cmd \"${_option_LANGUAGE}\" ${_option_INCLUDE_DIRECTORIES})\n\tcotire_add_makedep_flags(\"${_option_LANGUAGE}\" \"${_option_COMPILER_ID}\" \"${_option_COMPILER_VERSION}\" _cmd)\n\t# only consider existing source files for scanning\n\tset (_existingSourceFiles \"\")\n\tforeach (_sourceFile ${_sourceFiles})\n\t\tif (EXISTS \"${_sourceFile}\")\n\t\t\tlist (APPEND _existingSourceFiles \"${_sourceFile}\")\n\t\tendif()\n\tendforeach()\n\tif (NOT _existingSourceFiles)\n\t\tset (${_includesVar} \"\" PARENT_SCOPE)\n\t\treturn()\n\tendif()\n\tlist (APPEND _cmd ${_existingSourceFiles})\n\tif (COTIRE_VERBOSE)\n\t\tmessage (STATUS \"execute_process: ${_cmd}\")\n\tendif()\n\tif (_option_COMPILER_ID MATCHES \"MSVC\")\n\t\tif (COTIRE_DEBUG)\n\t\t\tmessage (STATUS \"clearing VS_UNICODE_OUTPUT\")\n\t\tendif()\n\t\t# cl.exe messes with the output streams unless the environment variable VS_UNICODE_OUTPUT is cleared\n\t\tunset (ENV{VS_UNICODE_OUTPUT})\n\tendif()\n\texecute_process(\n\t\tCOMMAND ${_cmd} WORKING_DIRECTORY \"${CMAKE_CURRENT_SOURCE_DIR}\"\n\t\tRESULT_VARIABLE _result OUTPUT_QUIET ERROR_VARIABLE _output)\n\tif (_result)\n\t\tmessage (STATUS \"Result ${_result} scanning includes of ${_existingSourceFiles}.\")\n\tendif()\n\tcotire_parse_includes(\n\t\t\"${_option_LANGUAGE}\" \"${_output}\"\n\t\t\"${_option_IGNORE_PATH}\" \"${_option_INCLUDE_PATH}\"\n\t\t\"${_option_IGNORE_EXTENSIONS}\"\n\t\t_includes _unparsedLines\n\t\t${_sourceFiles})\n\tset (${_includesVar} ${_includes} PARENT_SCOPE)\n\tif (_option_UNPARSED_LINES)\n\t\tset (${_option_UNPARSED_LINES} ${_unparsedLines} PARENT_SCOPE)\n\tendif()\nendfunction()\n\nmacro (cotire_append_undefs _contentsVar)\n\tset (_undefs ${ARGN})\n\tif (_undefs)\n\t\tlist (REMOVE_DUPLICATES _undefs)\n\t\tforeach (_definition ${_undefs})\n\t\t\tlist (APPEND ${_contentsVar} \"#undef ${_definition}\")\n\t\tendforeach()\n\tendif()\nendmacro()\n\nmacro (cotire_comment_str _language _commentText _commentVar)\n\tif (\"${_language}\" STREQUAL \"CMAKE\")\n\t\tset (${_commentVar} \"# ${_commentText}\")\n\telse()\n\t\tset (${_commentVar} \"/* ${_commentText} */\")\n\tendif()\nendmacro()\n\nfunction (cotire_write_file _language _file _contents _force)\n\tget_filename_component(_moduleName \"${COTIRE_CMAKE_MODULE_FILE}\" NAME)\n\tcotire_comment_str(\"${_language}\" \"${_moduleName} ${COTIRE_CMAKE_MODULE_VERSION} generated file\" _header1)\n\tcotire_comment_str(\"${_language}\" \"${_file}\" _header2)\n\tset (_contents \"${_header1}\\n${_header2}\\n${_contents}\")\n\tif (COTIRE_DEBUG)\n\t\tmessage (STATUS \"${_contents}\")\n\tendif()\n\tif (_force OR NOT EXISTS \"${_file}\")\n\t\tfile (WRITE \"${_file}\" \"${_contents}\")\n\telse()\n\t\tfile (READ \"${_file}\" _oldContents)\n\t\tif (NOT \"${_oldContents}\" STREQUAL \"${_contents}\")\n\t\t\tfile (WRITE \"${_file}\" \"${_contents}\")\n\t\telse()\n\t\t\tif (COTIRE_DEBUG)\n\t\t\t\tmessage (STATUS \"${_file} unchanged\")\n\t\t\tendif()\n\t\tendif()\n\tendif()\nendfunction()\n\nfunction (cotire_generate_unity_source _unityFile)\n\tset(_options \"\")\n\tset(_oneValueArgs LANGUAGE)\n\tset(_multiValueArgs\n\t\tDEPENDS SOURCE_LOCATIONS SOURCES_COMPILE_DEFINITIONS\n\t\tPRE_UNDEFS SOURCES_PRE_UNDEFS POST_UNDEFS SOURCES_POST_UNDEFS PROLOGUE EPILOGUE)\n\tcmake_parse_arguments(_option \"${_options}\" \"${_oneValueArgs}\" \"${_multiValueArgs}\" ${ARGN})\n\tif (_option_DEPENDS)\n\t\tcotire_check_file_up_to_date(_unityFileIsUpToDate \"${_unityFile}\" ${_option_DEPENDS})\n\t\tif (_unityFileIsUpToDate)\n\t\t\treturn()\n\t\tendif()\n\tendif()\n\tset (_sourceFiles ${_option_UNPARSED_ARGUMENTS})\n\tif (NOT _option_PRE_UNDEFS)\n\t\tset (_option_PRE_UNDEFS \"\")\n\tendif()\n\tif (NOT _option_SOURCES_PRE_UNDEFS)\n\t\tset (_option_SOURCES_PRE_UNDEFS \"\")\n\tendif()\n\tif (NOT _option_POST_UNDEFS)\n\t\tset (_option_POST_UNDEFS \"\")\n\tendif()\n\tif (NOT _option_SOURCES_POST_UNDEFS)\n\t\tset (_option_SOURCES_POST_UNDEFS \"\")\n\tendif()\n\tset (_contents \"\")\n\tif (_option_PROLOGUE)\n\t\tlist (APPEND _contents ${_option_PROLOGUE})\n\tendif()\n\tif (_option_LANGUAGE AND _sourceFiles)\n\t\tif (\"${_option_LANGUAGE}\" STREQUAL \"CXX\")\n\t\t\tlist (APPEND _contents \"#ifdef __cplusplus\")\n\t\telseif (\"${_option_LANGUAGE}\" STREQUAL \"C\")\n\t\t\tlist (APPEND _contents \"#ifndef __cplusplus\")\n\t\tendif()\n\tendif()\n\tset (_compileUndefinitions \"\")\n\tset (_index 0)\n\tforeach (_sourceFile ${_sourceFiles})\n\t\tcotire_get_source_compile_definitions(\n\t\t\t\"${_option_CONFIGURATION}\" \"${_option_LANGUAGE}\" \"${_sourceFile}\" _compileDefinitions\n\t\t\t${_option_SOURCES_COMPILE_DEFINITIONS})\n\t\tcotire_get_source_undefs(\"${_sourceFile}\" COTIRE_UNITY_SOURCE_PRE_UNDEFS _sourcePreUndefs ${_option_SOURCES_PRE_UNDEFS})\n\t\tcotire_get_source_undefs(\"${_sourceFile}\" COTIRE_UNITY_SOURCE_POST_UNDEFS _sourcePostUndefs ${_option_SOURCES_POST_UNDEFS})\n\t\tif (_option_PRE_UNDEFS)\n\t\t\tlist (APPEND _compileUndefinitions ${_option_PRE_UNDEFS})\n\t\tendif()\n\t\tif (_sourcePreUndefs)\n\t\t\tlist (APPEND _compileUndefinitions ${_sourcePreUndefs})\n\t\tendif()\n\t\tif (_compileUndefinitions)\n\t\t\tcotire_append_undefs(_contents ${_compileUndefinitions})\n\t\t\tset (_compileUndefinitions \"\")\n\t\tendif()\n\t\tif (_sourcePostUndefs)\n\t\t\tlist (APPEND _compileUndefinitions ${_sourcePostUndefs})\n\t\tendif()\n\t\tif (_option_POST_UNDEFS)\n\t\t\tlist (APPEND _compileUndefinitions ${_option_POST_UNDEFS})\n\t\tendif()\n\t\tforeach (_definition ${_compileDefinitions})\n\t\t\tif (_definition MATCHES \"^([a-zA-Z0-9_]+)=(.+)$\")\n\t\t\t\tlist (APPEND _contents \"#define ${CMAKE_MATCH_1} ${CMAKE_MATCH_2}\")\n\t\t\t\tlist (INSERT _compileUndefinitions 0 \"${CMAKE_MATCH_1}\")\n\t\t\telse()\n\t\t\t\tlist (APPEND _contents \"#define ${_definition}\")\n\t\t\t\tlist (INSERT _compileUndefinitions 0 \"${_definition}\")\n\t\t\tendif()\n\t\tendforeach()\n\t\tif (_option_SOURCE_LOCATIONS)\n\t\t\t# use explicitly provided source file location\n\t\t\tlist (GET _option_SOURCE_LOCATIONS ${_index} _sourceFileLocation)\n\t\telse()\n\t\t\t# use absolute path as source file location\n\t\t\tget_filename_component(_sourceFileLocation \"${_sourceFile}\" ABSOLUTE)\n\t\tendif()\n\t\tif (WIN32)\n\t\t\tfile (TO_NATIVE_PATH \"${_sourceFileLocation}\" _sourceFileLocation)\n\t\tendif()\n\t\tlist (APPEND _contents \"#include \\\"${_sourceFileLocation}\\\"\")\n\t\tmath (EXPR _index \"${_index} + 1\")\n\tendforeach()\n\tif (_compileUndefinitions)\n\t\tcotire_append_undefs(_contents ${_compileUndefinitions})\n\t\tset (_compileUndefinitions \"\")\n\tendif()\n\tif (_option_LANGUAGE AND _sourceFiles)\n\t\tlist (APPEND _contents \"#endif\")\n\tendif()\n\tif (_option_EPILOGUE)\n\t\tlist (APPEND _contents ${_option_EPILOGUE})\n\tendif()\n\tlist (APPEND _contents \"\")\n\tstring (REPLACE \";\" \"\\n\" _contents \"${_contents}\")\n\tif (COTIRE_VERBOSE)\n\t\tmessage (\"${_contents}\")\n\tendif()\n\tcotire_write_file(\"${_option_LANGUAGE}\" \"${_unityFile}\" \"${_contents}\" TRUE)\nendfunction()\n\nfunction (cotire_generate_prefix_header _prefixFile)\n\tset(_options \"\")\n\tset(_oneValueArgs LANGUAGE COMPILER_EXECUTABLE COMPILER_ID COMPILER_VERSION INCLUDE_SYSTEM_FLAG)\n\tset(_multiValueArgs DEPENDS COMPILE_DEFINITIONS COMPILE_FLAGS\n\t\tINCLUDE_DIRECTORIES SYSTEM_INCLUDE_DIRECTORIES IGNORE_PATH INCLUDE_PATH IGNORE_EXTENSIONS)\n\tcmake_parse_arguments(_option \"${_options}\" \"${_oneValueArgs}\" \"${_multiValueArgs}\" ${ARGN})\n\tif (_option_DEPENDS)\n\t\tcotire_check_file_up_to_date(_prefixFileIsUpToDate \"${_prefixFile}\" ${_option_DEPENDS})\n\t\tif (_prefixFileIsUpToDate)\n\t\t\tset (_unparsedLinesFile \"${_prefixFile}.log\")\n\t\t\tfile (WRITE \"${_unparsedLinesFile}\" \"\")\n\t\t\treturn()\n\t\tendif()\n\tendif()\n\tset (_prologue \"\")\n\tset (_epilogue \"\")\n\tif (_option_COMPILER_ID MATCHES \"Clang\")\n\t\tset (_prologue \"#pragma clang system_header\")\n\telseif (_option_COMPILER_ID MATCHES \"GNU\")\n\t\tset (_prologue \"#pragma GCC system_header\")\n\telseif (_option_COMPILER_ID MATCHES \"MSVC\")\n\t\tset (_prologue \"#pragma warning(push, 0)\")\n\t\tset (_epilogue \"#pragma warning(pop)\")\n\telseif (_option_COMPILER_ID MATCHES \"Intel\")\n\t\t# Intel compiler requires hdrstop pragma to stop generating PCH file\n\t\tset (_epilogue \"#pragma hdrstop\")\n\tendif()\n\tset (_sourceFiles ${_option_UNPARSED_ARGUMENTS})\n\tcotire_scan_includes(_selectedHeaders ${_sourceFiles}\n\t\tLANGUAGE \"${_option_LANGUAGE}\"\n\t\tCOMPILER_EXECUTABLE \"${_option_COMPILER_EXECUTABLE}\"\n\t\tCOMPILER_ID \"${_option_COMPILER_ID}\"\n\t\tCOMPILER_VERSION \"${_option_COMPILER_VERSION}\"\n\t\tCOMPILE_DEFINITIONS ${_option_COMPILE_DEFINITIONS}\n\t\tCOMPILE_FLAGS ${_option_COMPILE_FLAGS}\n\t\tINCLUDE_DIRECTORIES ${_option_INCLUDE_DIRECTORIES}\n\t\tINCLUDE_SYSTEM_FLAG ${_option_INCLUDE_SYSTEM_FLAG}\n\t\tSYSTEM_INCLUDE_DIRECTORIES ${_option_SYSTEM_INCLUDE_DIRECTORIES}\n\t\tIGNORE_PATH ${_option_IGNORE_PATH}\n\t\tINCLUDE_PATH ${_option_INCLUDE_PATH}\n\t\tIGNORE_EXTENSIONS ${_option_IGNORE_EXTENSIONS}\n\t\tUNPARSED_LINES _unparsedLines)\n\tcotire_generate_unity_source(\"${_prefixFile}\"\n\t\tPROLOGUE ${_prologue} EPILOGUE ${_epilogue} LANGUAGE \"${_option_LANGUAGE}\" ${_selectedHeaders})\n\tset (_unparsedLinesFile \"${_prefixFile}.log\")\n\tif (_unparsedLines)\n\t\tif (COTIRE_VERBOSE OR NOT _selectedHeaders)\n\t\t\tlist (LENGTH _unparsedLines _skippedLineCount)\n\t\t\tfile (RELATIVE_PATH _unparsedLinesFileRelPath \"${CMAKE_BINARY_DIR}\" \"${_unparsedLinesFile}\")\n\t\t\tmessage (STATUS \"${_skippedLineCount} line(s) skipped, see ${_unparsedLinesFileRelPath}\")\n\t\tendif()\n\t\tstring (REPLACE \";\" \"\\n\" _unparsedLines \"${_unparsedLines}\")\n\tendif()\n\tfile (WRITE \"${_unparsedLinesFile}\" \"${_unparsedLines}\")\nendfunction()\n\nfunction (cotire_add_makedep_flags _language _compilerID _compilerVersion _flagsVar)\n\tset (_flags ${${_flagsVar}})\n\tif (_compilerID MATCHES \"MSVC\")\n\t\t# cl.exe options used\n\t\t# /nologo suppresses display of sign-on banner\n\t\t# /TC treat all files named on the command line as C source files\n\t\t# /TP treat all files named on the command line as C++ source files\n\t\t# /EP preprocess to stdout without #line directives\n\t\t# /showIncludes list include files\n\t\tset (_sourceFileTypeC \"/TC\")\n\t\tset (_sourceFileTypeCXX \"/TP\")\n\t\tif (_flags)\n\t\t\t# append to list\n\t\t\tlist (APPEND _flags /nologo \"${_sourceFileType${_language}}\" /EP /showIncludes)\n\t\telse()\n\t\t\t# return as a flag string\n\t\t\tset (_flags \"${_sourceFileType${_language}} /EP /showIncludes\")\n\t\tendif()\n\telseif (_compilerID MATCHES \"GNU\")\n\t\t# GCC options used\n\t\t# -H print the name of each header file used\n\t\t# -E invoke preprocessor\n\t\t# -fdirectives-only do not expand macros, requires GCC >= 4.3\n\t\tif (_flags)\n\t\t\t# append to list\n\t\t\tlist (APPEND _flags -H -E)\n\t\t\tif (NOT \"${_compilerVersion}\" VERSION_LESS \"4.3.0\")\n\t\t\t\tlist (APPEND _flags \"-fdirectives-only\")\n\t\t\tendif()\n\t\telse()\n\t\t\t# return as a flag string\n\t\t\tset (_flags \"-H -E\")\n\t\t\tif (NOT \"${_compilerVersion}\" VERSION_LESS \"4.3.0\")\n\t\t\t\tset (_flags \"${_flags} -fdirectives-only\")\n\t\t\tendif()\n\t\tendif()\n\telseif (_compilerID MATCHES \"Clang\")\n\t\t# Clang options used\n\t\t# -H print the name of each header file used\n\t\t# -E invoke preprocessor\n\t\tif (_flags)\n\t\t\t# append to list\n\t\t\tlist (APPEND _flags -H -E)\n\t\telse()\n\t\t\t# return as a flag string\n\t\t\tset (_flags \"-H -E\")\n\t\tendif()\n\telseif (_compilerID MATCHES \"Intel\")\n\t\tif (WIN32)\n\t\t\t# Windows Intel options used\n\t\t\t# /nologo do not display compiler version information\n\t\t\t# /QH display the include file order\n\t\t\t# /EP preprocess to stdout, omitting #line directives\n\t\t\t# /TC process all source or unrecognized file types as C source files\n\t\t\t# /TP process all source or unrecognized file types as C++ source files\n\t\t\tset (_sourceFileTypeC \"/TC\")\n\t\t\tset (_sourceFileTypeCXX \"/TP\")\n\t\t\tif (_flags)\n\t\t\t\t# append to list\n\t\t\t\tlist (APPEND _flags /nologo \"${_sourceFileType${_language}}\" /EP /QH)\n\t\t\telse()\n\t\t\t\t# return as a flag string\n\t\t\t\tset (_flags \"${_sourceFileType${_language}} /EP /QH\")\n\t\t\tendif()\n\t\telse()\n\t\t\t# Linux / Mac OS X Intel options used\n\t\t\t# -H print the name of each header file used\n\t\t\t# -EP preprocess to stdout, omitting #line directives\n\t\t\t# -Kc++ process all source or unrecognized file types as C++ source files\n\t\t\tif (_flags)\n\t\t\t\t# append to list\n\t\t\t\tif (\"${_language}\" STREQUAL \"CXX\")\n\t\t\t\t\tlist (APPEND _flags -Kc++)\n\t\t\t\tendif()\n\t\t\t\tlist (APPEND _flags -H -EP)\n\t\t\telse()\n\t\t\t\t# return as a flag string\n\t\t\t\tif (\"${_language}\" STREQUAL \"CXX\")\n\t\t\t\t\tset (_flags \"-Kc++ \")\n\t\t\t\tendif()\n\t\t\t\tset (_flags \"${_flags}-H -EP\")\n\t\t\tendif()\n\t\tendif()\n\telse()\n\t\tmessage (FATAL_ERROR \"cotire: unsupported ${_language} compiler ${_compilerID} version ${_compilerVersion}.\")\n\tendif()\n\tset (${_flagsVar} ${_flags} PARENT_SCOPE)\nendfunction()\n\nfunction (cotire_add_pch_compilation_flags _language _compilerID _compilerVersion _prefixFile _pchFile _hostFile _flagsVar)\n\tset (_flags ${${_flagsVar}})\n\tif (_compilerID MATCHES \"MSVC\")\n\t\tfile (TO_NATIVE_PATH \"${_prefixFile}\" _prefixFileNative)\n\t\tfile (TO_NATIVE_PATH \"${_pchFile}\" _pchFileNative)\n\t\tfile (TO_NATIVE_PATH \"${_hostFile}\" _hostFileNative)\n\t\t# cl.exe options used\n\t\t# /Yc creates a precompiled header file\n\t\t# /Fp specifies precompiled header binary file name\n\t\t# /FI forces inclusion of file\n\t\t# /TC treat all files named on the command line as C source files\n\t\t# /TP treat all files named on the command line as C++ source files\n\t\t# /Zs syntax check only\n\t\tset (_sourceFileTypeC \"/TC\")\n\t\tset (_sourceFileTypeCXX \"/TP\")\n\t\tif (_flags)\n\t\t\t# append to list\n\t\t\tlist (APPEND _flags /nologo \"${_sourceFileType${_language}}\"\n\t\t\t\t\"/Yc${_prefixFileNative}\" \"/Fp${_pchFileNative}\" \"/FI${_prefixFileNative}\" /Zs \"${_hostFileNative}\")\n\t\telse()\n\t\t\t# return as a flag string\n\t\t\tset (_flags \"/Yc\\\"${_prefixFileNative}\\\" /Fp\\\"${_pchFileNative}\\\" /FI\\\"${_prefixFileNative}\\\"\")\n\t\tendif()\n\telseif (_compilerID MATCHES \"GNU|Clang\")\n\t\t# GCC / Clang options used\n\t\t# -x specify the source language\n\t\t# -c compile but do not link\n\t\t# -o place output in file\n\t\t# note that we cannot use -w to suppress all warnings upon pre-compiling, because turning off a warning may\n\t\t# alter compile flags as a side effect (e.g., -Wwrite-string implies -fconst-strings)\n\t\tset (_xLanguage_C \"c-header\")\n\t\tset (_xLanguage_CXX \"c++-header\")\n\t\tif (_flags)\n\t\t\t# append to list\n\t\t\tlist (APPEND _flags \"-x\" \"${_xLanguage_${_language}}\" \"-c\" \"${_prefixFile}\" -o \"${_pchFile}\")\n\t\telse()\n\t\t\t# return as a flag string\n\t\t\tset (_flags \"-x ${_xLanguage_${_language}} -c \\\"${_prefixFile}\\\" -o \\\"${_pchFile}\\\"\")\n\t\tendif()\n\telseif (_compilerID MATCHES \"Intel\")\n\t\tif (WIN32)\n\t\t\tfile (TO_NATIVE_PATH \"${_prefixFile}\" _prefixFileNative)\n\t\t\tfile (TO_NATIVE_PATH \"${_pchFile}\" _pchFileNative)\n\t\t\tfile (TO_NATIVE_PATH \"${_hostFile}\" _hostFileNative)\n\t\t\t# Windows Intel options used\n\t\t\t# /nologo do not display compiler version information\n\t\t\t# /Yc create a precompiled header (PCH) file\n\t\t\t# /Fp specify a path or file name for precompiled header files\n\t\t\t# /FI tells the preprocessor to include a specified file name as the header file\n\t\t\t# /TC process all source or unrecognized file types as C source files\n\t\t\t# /TP process all source or unrecognized file types as C++ source files\n\t\t\t# /Zs syntax check only\n\t\t\t# /Wpch-messages enable diagnostics related to pre-compiled headers (requires Intel XE 2013 Update 2)\n\t\t\tset (_sourceFileTypeC \"/TC\")\n\t\t\tset (_sourceFileTypeCXX \"/TP\")\n\t\t\tif (_flags)\n\t\t\t\t# append to list\n\t\t\t\tlist (APPEND _flags /nologo \"${_sourceFileType${_language}}\"\n\t\t\t\t\t\"/Yc\" \"/Fp${_pchFileNative}\" \"/FI${_prefixFileNative}\" /Zs \"${_hostFileNative}\")\n\t\t\t\tif (NOT \"${_compilerVersion}\" VERSION_LESS \"13.1.0\")\n\t\t\t\t\tlist (APPEND _flags \"/Wpch-messages\")\n\t\t\t\tendif()\n\t\t\telse()\n\t\t\t\t# return as a flag string\n\t\t\t\tset (_flags \"/Yc /Fp\\\"${_pchFileNative}\\\" /FI\\\"${_prefixFileNative}\\\"\")\n\t\t\t\tif (NOT \"${_compilerVersion}\" VERSION_LESS \"13.1.0\")\n\t\t\t\t\tset (_flags \"${_flags} /Wpch-messages\")\n\t\t\t\tendif()\n\t\t\tendif()\n\t\telse()\n\t\t\t# Linux / Mac OS X Intel options used\n\t\t\t# -pch-dir location for precompiled header files\n\t\t\t# -pch-create name of the precompiled header (PCH) to create\n\t\t\t# -Kc++ process all source or unrecognized file types as C++ source files\n\t\t\t# -fsyntax-only check only for correct syntax\n\t\t\t# -Wpch-messages enable diagnostics related to pre-compiled headers (requires Intel XE 2013 Update 2)\n\t\t\tget_filename_component(_pchDir \"${_pchFile}\" PATH)\n\t\t\tget_filename_component(_pchName \"${_pchFile}\" NAME)\n\t\t\tset (_xLanguage_C \"c-header\")\n\t\t\tset (_xLanguage_CXX \"c++-header\")\n\t\t\tif (_flags)\n\t\t\t\t# append to list\n\t\t\t\tif (\"${_language}\" STREQUAL \"CXX\")\n\t\t\t\t\tlist (APPEND _flags -Kc++)\n\t\t\t\tendif()\n\t\t\t\tlist (APPEND _flags \"-include\" \"${_prefixFile}\" \"-pch-dir\" \"${_pchDir}\" \"-pch-create\" \"${_pchName}\" \"-fsyntax-only\" \"${_hostFile}\")\n\t\t\t\tif (NOT \"${_compilerVersion}\" VERSION_LESS \"13.1.0\")\n\t\t\t\t\tlist (APPEND _flags \"-Wpch-messages\")\n\t\t\t\tendif()\n\t\t\telse()\n\t\t\t\t# return as a flag string\n\t\t\t\tset (_flags \"-include \\\"${_prefixFile}\\\" -pch-dir \\\"${_pchDir}\\\" -pch-create \\\"${_pchName}\\\"\")\n\t\t\t\tif (NOT \"${_compilerVersion}\" VERSION_LESS \"13.1.0\")\n\t\t\t\t\tset (_flags \"${_flags} -Wpch-messages\")\n\t\t\t\tendif()\n\t\t\tendif()\n\t\tendif()\n\telse()\n\t\tmessage (FATAL_ERROR \"cotire: unsupported ${_language} compiler ${_compilerID} version ${_compilerVersion}.\")\n\tendif()\n\tset (${_flagsVar} ${_flags} PARENT_SCOPE)\nendfunction()\n\nfunction (cotire_add_prefix_pch_inclusion_flags _language _compilerID _compilerVersion _prefixFile _pchFile _flagsVar)\n\tset (_flags ${${_flagsVar}})\n\tif (_compilerID MATCHES \"MSVC\")\n\t\tfile (TO_NATIVE_PATH \"${_prefixFile}\" _prefixFileNative)\n\t\t# cl.exe options used\n\t\t# /Yu uses a precompiled header file during build\n\t\t# /Fp specifies precompiled header binary file name\n\t\t# /FI forces inclusion of file\n\t\tif (_pchFile)\n\t\t\tfile (TO_NATIVE_PATH \"${_pchFile}\" _pchFileNative)\n\t\t\tif (_flags)\n\t\t\t\t# append to list\n\t\t\t\tlist (APPEND _flags \"/Yu${_prefixFileNative}\" \"/Fp${_pchFileNative}\" \"/FI${_prefixFileNative}\")\n\t\t\telse()\n\t\t\t\t# return as a flag string\n\t\t\t\tset (_flags \"/Yu\\\"${_prefixFileNative}\\\" /Fp\\\"${_pchFileNative}\\\" /FI\\\"${_prefixFileNative}\\\"\")\n\t\t\tendif()\n\t\telse()\n\t\t\t# no precompiled header, force inclusion of prefix header\n\t\t\tif (_flags)\n\t\t\t\t# append to list\n\t\t\t\tlist (APPEND _flags \"/FI${_prefixFileNative}\")\n\t\t\telse()\n\t\t\t\t# return as a flag string\n\t\t\t\tset (_flags \"/FI\\\"${_prefixFileNative}\\\"\")\n\t\t\tendif()\n\t\tendif()\n\telseif (_compilerID MATCHES \"GNU\")\n\t\t# GCC options used\n\t\t# -include process include file as the first line of the primary source file\n\t\t# -Winvalid-pch warns if precompiled header is found but cannot be used\n\t\t# note: ccache requires the -include flag to be used in order to process precompiled header correctly\n\t\tif (_flags)\n\t\t\t# append to list\n\t\t\tlist (APPEND _flags \"-Winvalid-pch\" \"-include\" \"${_prefixFile}\")\n\t\telse()\n\t\t\t# return as a flag string\n\t\t\tset (_flags \"-Winvalid-pch -include \\\"${_prefixFile}\\\"\")\n\t\tendif()\n\telseif (_compilerID MATCHES \"Clang\")\n\t\t# Clang options used\n\t\t# -include process include file as the first line of the primary source file\n\t\t# -include-pch include precompiled header file\n\t\t# -Qunused-arguments don't emit warning for unused driver arguments\n\t\t# note: ccache requires the -include flag to be used in order to process precompiled header correctly\n\t\tif (_flags)\n\t\t\t# append to list\n\t\t\tlist (APPEND _flags \"-Qunused-arguments\" \"-include\" \"${_prefixFile}\")\n\t\telse()\n\t\t\t# return as a flag string\n\t\t\tset (_flags \"-Qunused-arguments -include \\\"${_prefixFile}\\\"\")\n\t\tendif()\n\telseif (_compilerID MATCHES \"Intel\")\n\t\tif (WIN32)\n\t\t\tfile (TO_NATIVE_PATH \"${_prefixFile}\" _prefixFileNative)\n\t\t\t# Windows Intel options used\n\t\t\t# /Yu use a precompiled header (PCH) file\n\t\t\t# /Fp specify a path or file name for precompiled header files\n\t\t\t# /FI tells the preprocessor to include a specified file name as the header file\n\t\t\t# /Wpch-messages enable diagnostics related to pre-compiled headers (requires Intel XE 2013 Update 2)\n\t\t\tif (_pchFile)\n\t\t\t\tfile (TO_NATIVE_PATH \"${_pchFile}\" _pchFileNative)\n\t\t\t\tif (_flags)\n\t\t\t\t\t# append to list\n\t\t\t\t\tlist (APPEND _flags \"/Yu\" \"/Fp${_pchFileNative}\" \"/FI${_prefixFileNative}\")\n\t\t\t\t\tif (NOT \"${_compilerVersion}\" VERSION_LESS \"13.1.0\")\n\t\t\t\t\t\tlist (APPEND _flags \"/Wpch-messages\")\n\t\t\t\t\tendif()\n\t\t\t\telse()\n\t\t\t\t\t# return as a flag string\n\t\t\t\t\tset (_flags \"/Yu /Fp\\\"${_pchFileNative}\\\" /FI\\\"${_prefixFileNative}\\\"\")\n\t\t\t\t\tif (NOT \"${_compilerVersion}\" VERSION_LESS \"13.1.0\")\n\t\t\t\t\t\tset (_flags \"${_flags} /Wpch-messages\")\n\t\t\t\t\tendif()\n\t\t\t\tendif()\n\t\t\telse()\n\t\t\t\t# no precompiled header, force inclusion of prefix header\n\t\t\t\tif (_flags)\n\t\t\t\t\t# append to list\n\t\t\t\t\tlist (APPEND _flags \"/FI${_prefixFileNative}\")\n\t\t\t\telse()\n\t\t\t\t\t# return as a flag string\n\t\t\t\t\tset (_flags \"/FI\\\"${_prefixFileNative}\\\"\")\n\t\t\t\tendif()\n\t\t\tendif()\n\t\telse()\n\t\t\t# Linux / Mac OS X Intel options used\n\t\t\t# -pch-dir location for precompiled header files\n\t\t\t# -pch-use name of the precompiled header (PCH) to use\n\t\t\t# -include process include file as the first line of the primary source file\n\t\t\t# -Wpch-messages enable diagnostics related to pre-compiled headers (requires Intel XE 2013 Update 2)\n\t\t\tif (_pchFile)\n\t\t\t\tget_filename_component(_pchDir \"${_pchFile}\" PATH)\n\t\t\t\tget_filename_component(_pchName \"${_pchFile}\" NAME)\n\t\t\t\tif (_flags)\n\t\t\t\t\t# append to list\n\t\t\t\t\tlist (APPEND _flags \"-include\" \"${_prefixFile}\" \"-pch-dir\" \"${_pchDir}\" \"-pch-use\" \"${_pchName}\")\n\t\t\t\t\tif (NOT \"${_compilerVersion}\" VERSION_LESS \"13.1.0\")\n\t\t\t\t\t\tlist (APPEND _flags \"-Wpch-messages\")\n\t\t\t\t\tendif()\n\t\t\t\telse()\n\t\t\t\t\t# return as a flag string\n\t\t\t\t\tset (_flags \"-include \\\"${_prefixFile}\\\" -pch-dir \\\"${_pchDir}\\\" -pch-use \\\"${_pchName}\\\"\")\n\t\t\t\t\tif (NOT \"${_compilerVersion}\" VERSION_LESS \"13.1.0\")\n\t\t\t\t\t\tset (_flags \"${_flags} -Wpch-messages\")\n\t\t\t\t\tendif()\n\t\t\t\tendif()\n\t\t\telse()\n\t\t\t\t# no precompiled header, force inclusion of prefix header\n\t\t\t\tif (_flags)\n\t\t\t\t\t# append to list\n\t\t\t\t\tlist (APPEND _flags \"-include\" \"${_prefixFile}\")\n\t\t\t\telse()\n\t\t\t\t\t# return as a flag string\n\t\t\t\t\tset (_flags \"-include \\\"${_prefixFile}\\\"\")\n\t\t\t\tendif()\n\t\t\tendif()\n\t\tendif()\n\telse()\n\t\tmessage (FATAL_ERROR \"cotire: unsupported ${_language} compiler ${_compilerID} version ${_compilerVersion}.\")\n\tendif()\n\tset (${_flagsVar} ${_flags} PARENT_SCOPE)\nendfunction()\n\nfunction (cotire_precompile_prefix_header _prefixFile _pchFile _hostFile)\n\tset(_options \"\")\n\tset(_oneValueArgs COMPILER_EXECUTABLE COMPILER_ID COMPILER_VERSION INCLUDE_SYSTEM_FLAG LANGUAGE)\n\tset(_multiValueArgs COMPILE_DEFINITIONS COMPILE_FLAGS INCLUDE_DIRECTORIES SYSTEM_INCLUDE_DIRECTORIES SYS)\n\tcmake_parse_arguments(_option \"${_options}\" \"${_oneValueArgs}\" \"${_multiValueArgs}\" ${ARGN})\n\tif (NOT _option_LANGUAGE)\n\t\tset (_option_LANGUAGE \"CXX\")\n\tendif()\n\tif (NOT _option_COMPILER_ID)\n\t\tset (_option_COMPILER_ID \"${CMAKE_${_option_LANGUAGE}_ID}\")\n\tendif()\n\tcotire_init_compile_cmd(_cmd \"${_option_LANGUAGE}\" \"${_option_COMPILER_EXECUTABLE}\" \"${_option_COMPILER_ARG1}\")\n\tcotire_add_definitions_to_cmd(_cmd \"${_option_LANGUAGE}\" ${_option_COMPILE_DEFINITIONS})\n\tcotire_add_compile_flags_to_cmd(_cmd ${_option_COMPILE_FLAGS})\n\tcotire_add_includes_to_cmd(_cmd \"${_option_LANGUAGE}\" \"${_option_INCLUDE_SYSTEM_FLAG}\" _option_INCLUDE_DIRECTORIES _option_SYSTEM_INCLUDE_DIRECTORIES)\n\tcotire_add_frameworks_to_cmd(_cmd \"${_option_LANGUAGE}\" ${_option_INCLUDE_DIRECTORIES})\n\tcotire_add_pch_compilation_flags(\n\t\t\"${_option_LANGUAGE}\" \"${_option_COMPILER_ID}\" \"${_option_COMPILER_VERSION}\"\n\t\t\"${_prefixFile}\" \"${_pchFile}\" \"${_hostFile}\" _cmd)\n\tif (COTIRE_VERBOSE)\n\t\tmessage (STATUS \"execute_process: ${_cmd}\")\n\tendif()\n\tif (_option_COMPILER_ID MATCHES \"MSVC\")\n\t\tif (COTIRE_DEBUG)\n\t\t\tmessage (STATUS \"clearing VS_UNICODE_OUTPUT\")\n\t\tendif()\n\t\t# cl.exe messes with the output streams unless the environment variable VS_UNICODE_OUTPUT is cleared\n\t\tunset (ENV{VS_UNICODE_OUTPUT})\n\tendif()\n\texecute_process(\n\t\tCOMMAND ${_cmd}\n\t\tWORKING_DIRECTORY \"${CMAKE_CURRENT_SOURCE_DIR}\"\n\t\tRESULT_VARIABLE _result)\n\tif (_result)\n\t\tmessage (FATAL_ERROR \"cotire: error ${_result} precompiling ${_prefixFile}.\")\n\tendif()\nendfunction()\n\nfunction (cotire_check_precompiled_header_support _language _targetSourceDir _target _msgVar)\n\tset (_unsupportedCompiler\n\t\t\"Precompiled headers not supported for ${_language} compiler ${CMAKE_${_language}_COMPILER_ID}\")\n\tif (CMAKE_${_language}_COMPILER_ID MATCHES \"MSVC\")\n\t\t# supported since Visual Studio C++ 6.0\n\t\t# and CMake does not support an earlier version\n\t\tset (${_msgVar} \"\" PARENT_SCOPE)\n\telseif (CMAKE_${_language}_COMPILER_ID MATCHES \"GNU\")\n\t\t# GCC PCH support requires version >= 3.4\n\t\tcotire_determine_compiler_version(\"${_language}\" COTIRE_${_language}_COMPILER)\n\t\tif (\"${COTIRE_${_language}_COMPILER_VERSION}\" MATCHES \".+\" AND\n\t\t\t\"${COTIRE_${_language}_COMPILER_VERSION}\" VERSION_LESS \"3.4.0\")\n\t\t\tset (${_msgVar} \"${_unsupportedCompiler} version ${COTIRE_${_language}_COMPILER_VERSION}.\" PARENT_SCOPE)\n\t\telse()\n\t\t\tset (${_msgVar} \"\" PARENT_SCOPE)\n\t\tendif()\n\telseif (CMAKE_${_language}_COMPILER_ID MATCHES \"Clang\")\n\t\t# all Clang versions have PCH support\n\t\tset (${_msgVar} \"\" PARENT_SCOPE)\n\telseif (CMAKE_${_language}_COMPILER_ID MATCHES \"Intel\")\n\t\t# Intel PCH support requires version >= 8.0.0\n\t\tcotire_determine_compiler_version(\"${_language}\" COTIRE_${_language}_COMPILER)\n\t\tif (\"${COTIRE_${_language}_COMPILER_VERSION}\" MATCHES \".+\" AND\n\t\t\t\"${COTIRE_${_language}_COMPILER_VERSION}\" VERSION_LESS \"8.0.0\")\n\t\t\tset (${_msgVar} \"${_unsupportedCompiler} version ${COTIRE_${_language}_COMPILER_VERSION}.\" PARENT_SCOPE)\n\t\telse()\n\t\t\tset (${_msgVar} \"\" PARENT_SCOPE)\n\t\tendif()\n\telse()\n\t\tset (${_msgVar} \"${_unsupportedCompiler}.\" PARENT_SCOPE)\n\tendif()\n\tif (CMAKE_${_language}_COMPILER MATCHES \"ccache\")\n\t\tif (NOT \"$ENV{CCACHE_SLOPPINESS}\" MATCHES \"time_macros|pch_defines\")\n\t\t\tset (${_msgVar}\n\t\t\t\t\"ccache requires the environment variable CCACHE_SLOPPINESS to be set to \\\"pch_defines,time_macros\\\".\"\n\t\t\t\tPARENT_SCOPE)\n\t\tendif()\n\tendif()\n\tif (APPLE)\n\t\t# PCH compilation not supported by GCC / Clang for multi-architecture builds (e.g., i386, x86_64)\n\t\tcotire_get_configuration_types(_configs)\n\t\tforeach (_config ${_configs})\n\t\t\tset (_targetFlags \"\")\n\t\t\tcotire_get_target_compile_flags(\"${_config}\" \"${_language}\" \"${_targetSourceDir}\" \"${_target}\" _targetFlags)\n\t\t\tcotire_filter_compile_flags(\"${_language}\" \"arch\" _architectures _ignore ${_targetFlags})\n\t\t\tlist (LENGTH _architectures _numberOfArchitectures)\n\t\t\tif (_numberOfArchitectures GREATER 1)\n\t\t\t\tstring (REPLACE \";\" \", \" _architectureStr \"${_architectures}\")\n\t\t\t\tset (${_msgVar}\n\t\t\t\t\t\"Precompiled headers not supported on Darwin for multi-architecture builds (${_architectureStr}).\"\n\t\t\t\t\tPARENT_SCOPE)\n\t\t\t\tbreak()\n\t\t\tendif()\n\t\tendforeach()\n\tendif()\nendfunction()\n\nmacro (cotire_get_intermediate_dir _cotireDir)\n\tget_filename_component(${_cotireDir} \"${CMAKE_CURRENT_BINARY_DIR}/${CMAKE_CFG_INTDIR}/${COTIRE_INTDIR}\" ABSOLUTE)\nendmacro()\n\nmacro (cotire_setup_file_extension_variables)\n\tset (_unityFileExt_C \".c\")\n\tset (_unityFileExt_CXX \".cxx\")\n\tset (_prefixFileExt_C \".h\")\n\tset (_prefixFileExt_CXX \".hxx\")\n\tset (_prefixSourceFileExt_C \".c\")\n\tset (_prefixSourceFileExt_CXX \".cxx\")\nendmacro()\n\nfunction (cotire_make_single_unity_source_file_path _language _target _unityFileVar)\n\tcotire_setup_file_extension_variables()\n\tif (NOT DEFINED _unityFileExt_${_language})\n\t\tset (${_unityFileVar} \"\" PARENT_SCOPE)\n\t\treturn()\n\tendif()\n\tset (_unityFileBaseName \"${_target}_${_language}${COTIRE_UNITY_SOURCE_FILENAME_SUFFIX}\")\n\tset (_unityFileName \"${_unityFileBaseName}${_unityFileExt_${_language}}\")\n\tcotire_get_intermediate_dir(_baseDir)\n\tset (_unityFile \"${_baseDir}/${_unityFileName}\")\n\tset (${_unityFileVar} \"${_unityFile}\" PARENT_SCOPE)\n\tif (COTIRE_DEBUG)\n\t\tmessage(STATUS \"${_unityFile}\")\n\tendif()\nendfunction()\n\nfunction (cotire_make_unity_source_file_paths _language _target _maxIncludes _unityFilesVar)\n\tcotire_setup_file_extension_variables()\n\tif (NOT DEFINED _unityFileExt_${_language})\n\t\tset (${_unityFileVar} \"\" PARENT_SCOPE)\n\t\treturn()\n\tendif()\n\tset (_unityFileBaseName \"${_target}_${_language}${COTIRE_UNITY_SOURCE_FILENAME_SUFFIX}\")\n\tcotire_get_intermediate_dir(_baseDir)\n\tset (_startIndex 0)\n\tset (_index 0)\n\tset (_unityFiles \"\")\n\tset (_sourceFiles ${ARGN})\n\tforeach (_sourceFile ${_sourceFiles})\n\t\tget_source_file_property(_startNew \"${_sourceFile}\" COTIRE_START_NEW_UNITY_SOURCE)\n\t\tmath (EXPR _unityFileCount \"${_index} - ${_startIndex}\")\n\t\tif (_startNew OR (_maxIncludes GREATER 0 AND NOT _unityFileCount LESS _maxIncludes))\n\t\t\tif (_index GREATER 0)\n\t\t\t\t# start new unity file segment\n\t\t\t\tmath (EXPR _endIndex \"${_index} - 1\")\n\t\t\t\tset (_unityFileName \"${_unityFileBaseName}_${_startIndex}_${_endIndex}${_unityFileExt_${_language}}\")\n\t\t\t\tlist (APPEND _unityFiles \"${_baseDir}/${_unityFileName}\")\n\t\t\tendif()\n\t\t\tset (_startIndex ${_index})\n\t\tendif()\n\t\tmath (EXPR _index \"${_index} + 1\")\n\tendforeach()\n\tlist (LENGTH _sourceFiles _numberOfSources)\n\tif (_startIndex EQUAL 0)\n\t\t# there is only a single unity file\n\t\tcotire_make_single_unity_source_file_path(${_language} ${_target} _unityFiles)\n\telseif (_startIndex LESS _numberOfSources)\n\t\t# end with final unity file segment\n\t\tmath (EXPR _endIndex \"${_index} - 1\")\n\t\tset (_unityFileName \"${_unityFileBaseName}_${_startIndex}_${_endIndex}${_unityFileExt_${_language}}\")\n\t\tlist (APPEND _unityFiles \"${_baseDir}/${_unityFileName}\")\n\tendif()\n\tset (${_unityFilesVar} ${_unityFiles} PARENT_SCOPE)\n\tif (COTIRE_DEBUG)\n\t\tmessage(STATUS \"${_unityFiles}\")\n\tendif()\nendfunction()\n\nfunction (cotire_unity_to_prefix_file_path _language _target _unityFile _prefixFileVar)\n\tcotire_setup_file_extension_variables()\n\tif (NOT DEFINED _unityFileExt_${_language})\n\t\tset (${_prefixFileVar} \"\" PARENT_SCOPE)\n\t\treturn()\n\tendif()\n\tset (_unityFileBaseName \"${_target}_${_language}${COTIRE_UNITY_SOURCE_FILENAME_SUFFIX}\")\n\tset (_prefixFileBaseName \"${_target}_${_language}${COTIRE_PREFIX_HEADER_FILENAME_SUFFIX}\")\n\tstring (REPLACE \"${_unityFileBaseName}\" \"${_prefixFileBaseName}\" _prefixFile \"${_unityFile}\")\n\tstring (REGEX REPLACE \"${_unityFileExt_${_language}}$\" \"${_prefixFileExt_${_language}}\" _prefixFile \"${_prefixFile}\")\n\tset (${_prefixFileVar} \"${_prefixFile}\" PARENT_SCOPE)\nendfunction()\n\nfunction (cotire_prefix_header_to_source_file_path _language _prefixHeaderFile _prefixSourceFileVar)\n\tcotire_setup_file_extension_variables()\n\tif (NOT DEFINED _prefixSourceFileExt_${_language})\n\t\tset (${_prefixSourceFileVar} \"\" PARENT_SCOPE)\n\t\treturn()\n\tendif()\n\tstring (REGEX REPLACE \"${_prefixFileExt_${_language}}$\" \"${_prefixSourceFileExt_${_language}}\" _prefixSourceFile \"${_prefixHeaderFile}\")\n\tset (${_prefixSourceFileVar} \"${_prefixSourceFile}\" PARENT_SCOPE)\nendfunction()\n\nfunction (cotire_make_prefix_file_name _language _target _prefixFileBaseNameVar _prefixFileNameVar)\n\tcotire_setup_file_extension_variables()\n\tif (NOT _language)\n\t\tset (_prefixFileBaseName \"${_target}${COTIRE_PREFIX_HEADER_FILENAME_SUFFIX}\")\n\t\tset (_prefixFileName \"${_prefixFileBaseName}${_prefixFileExt_C}\")\n\telseif (DEFINED _prefixFileExt_${_language})\n\t\tset (_prefixFileBaseName \"${_target}_${_language}${COTIRE_PREFIX_HEADER_FILENAME_SUFFIX}\")\n\t\tset (_prefixFileName \"${_prefixFileBaseName}${_prefixFileExt_${_language}}\")\n\telse()\n\t\tset (_prefixFileBaseName \"\")\n\t\tset (_prefixFileName \"\")\n\tendif()\n\tset (${_prefixFileBaseNameVar} \"${_prefixFileBaseName}\" PARENT_SCOPE)\n\tset (${_prefixFileNameVar} \"${_prefixFileName}\" PARENT_SCOPE)\nendfunction()\n\nfunction (cotire_make_prefix_file_path _language _target _prefixFileVar)\n\tcotire_make_prefix_file_name(\"${_language}\" \"${_target}\" _prefixFileBaseName _prefixFileName)\n\tset (${_prefixFileVar} \"\" PARENT_SCOPE)\n\tif (_prefixFileName)\n\t\tif (NOT _language)\n\t\t\tset (_language \"C\")\n\t\tendif()\n\t\tif (MSVC OR CMAKE_${_language}_COMPILER_ID MATCHES \"GNU|Clang|Intel\")\n\t\t\tcotire_get_intermediate_dir(_baseDir)\n\t\t\tset (${_prefixFileVar} \"${_baseDir}/${_prefixFileName}\" PARENT_SCOPE)\n\t\tendif()\n\tendif()\nendfunction()\n\nfunction (cotire_make_pch_file_path _language _targetSourceDir _target _pchFileVar)\n\tcotire_make_prefix_file_name(\"${_language}\" \"${_target}\" _prefixFileBaseName _prefixFileName)\n\tset (${_pchFileVar} \"\" PARENT_SCOPE)\n\tif (_prefixFileBaseName AND _prefixFileName)\n\t\tcotire_check_precompiled_header_support(\"${_language}\" \"${_targetSourceDir}\" \"${_target}\" _msg)\n\t\tif (NOT _msg)\n\t\t\tif (XCODE)\n\t\t\t\t# For Xcode, we completely hand off the compilation of the prefix header to the IDE\n\t\t\t\treturn()\n\t\t\tendif()\n\t\t\tcotire_get_intermediate_dir(_baseDir)\n\t\t\tif (CMAKE_${_language}_COMPILER_ID MATCHES \"MSVC\")\n\t\t\t\t# MSVC uses the extension .pch added to the prefix header base name\n\t\t\t\tset (${_pchFileVar} \"${_baseDir}/${_prefixFileBaseName}.pch\" PARENT_SCOPE)\n\t\t\telseif (CMAKE_${_language}_COMPILER_ID MATCHES \"Clang\")\n\t\t\t\t# Clang looks for a precompiled header corresponding to the prefix header with the extension .pch appended\n\t\t\t\tset (${_pchFileVar} \"${_baseDir}/${_prefixFileName}.pch\" PARENT_SCOPE)\n\t\t\telseif (CMAKE_${_language}_COMPILER_ID MATCHES \"GNU\")\n\t\t\t\t# GCC looks for a precompiled header corresponding to the prefix header with the extension .gch appended\n\t\t\t\tset (${_pchFileVar} \"${_baseDir}/${_prefixFileName}.gch\" PARENT_SCOPE)\n\t\t\telseif (CMAKE_${_language}_COMPILER_ID MATCHES \"Intel\")\n\t\t\t\t# Intel uses the extension .pchi added to the prefix header base name\n\t\t\t\tset (${_pchFileVar} \"${_baseDir}/${_prefixFileBaseName}.pchi\" PARENT_SCOPE)\n\t\t\tendif()\n\t\tendif()\n\tendif()\nendfunction()\n\nfunction (cotire_select_unity_source_files _unityFile _sourcesVar)\n\tset (_sourceFiles ${ARGN})\n\tif (_sourceFiles AND \"${_unityFile}\" MATCHES \"${COTIRE_UNITY_SOURCE_FILENAME_SUFFIX}_([0-9]+)_([0-9]+)\")\n\t\tset (_startIndex ${CMAKE_MATCH_1})\n\t\tset (_endIndex ${CMAKE_MATCH_2})\n\t\tlist (LENGTH _sourceFiles _numberOfSources)\n\t\tif (NOT _startIndex LESS _numberOfSources)\n\t\t\tmath (EXPR _startIndex \"${_numberOfSources} - 1\")\n\t\tendif()\n\t\tif (NOT _endIndex LESS _numberOfSources)\n\t\t\tmath (EXPR _endIndex \"${_numberOfSources} - 1\")\n\t\tendif()\n\t\tset (_files \"\")\n\t\tforeach (_index RANGE ${_startIndex} ${_endIndex})\n\t\t\tlist (GET _sourceFiles ${_index} _file)\n\t\t\tlist (APPEND _files \"${_file}\")\n\t\tendforeach()\n\telse()\n\t\tset (_files ${_sourceFiles})\n\tendif()\n\tset (${_sourcesVar} ${_files} PARENT_SCOPE)\nendfunction()\n\nfunction (cotire_get_unity_source_dependencies _language _target _dependencySourcesVar)\n\tset (_dependencySources \"\")\n\t# depend on target's generated source files\n\tcotire_get_objects_with_property_on(_generatedSources GENERATED SOURCE ${ARGN})\n\tif (_generatedSources)\n\t\t# but omit all generated source files that have the COTIRE_EXCLUDED property set to true\n\t\tcotire_get_objects_with_property_on(_excludedGeneratedSources COTIRE_EXCLUDED SOURCE ${_generatedSources})\n\t\tif (_excludedGeneratedSources)\n\t\t\tlist (REMOVE_ITEM _generatedSources ${_excludedGeneratedSources})\n\t\tendif()\n\t\t# and omit all generated source files that have the COTIRE_DEPENDENCY property set to false explicitly\n\t\tcotire_get_objects_with_property_off(_excludedNonDependencySources COTIRE_DEPENDENCY SOURCE ${_generatedSources})\n\t\tif (_excludedNonDependencySources)\n\t\t\tlist (REMOVE_ITEM _generatedSources ${_excludedNonDependencySources})\n\t\tendif()\n\t\tif (_generatedSources)\n\t\t\tlist (APPEND _dependencySources ${_generatedSources})\n\t\tendif()\n\tendif()\n\tif (COTIRE_DEBUG AND _dependencySources)\n\t\tmessage (STATUS \"${_language} ${_target} unity source depends on ${_dependencySources}\")\n\tendif()\n\tset (${_dependencySourcesVar} ${_dependencySources} PARENT_SCOPE)\nendfunction()\n\nfunction (cotire_get_prefix_header_dependencies _language _target _dependencySourcesVar)\n\t# depend on target source files marked with custom COTIRE_DEPENDENCY property\n\tset (_dependencySources \"\")\n\tcotire_get_objects_with_property_on(_dependencySources COTIRE_DEPENDENCY SOURCE ${ARGN})\n\tif (CMAKE_${_language}_COMPILER_ID MATCHES \"GNU|Clang\")\n\t\t# GCC and clang raise a fatal error if a file is not found during preprocessing\n\t\t# thus we depend on target's generated source files for prefix header generation\n\t\tcotire_get_objects_with_property_on(_generatedSources GENERATED SOURCE ${ARGN})\n\t\tif (_generatedSources)\n\t\t\tlist (APPEND _dependencySources ${_generatedSources})\n\t\tendif()\n\tendif()\n\tif (COTIRE_DEBUG AND _dependencySources)\n\t\tmessage (STATUS \"${_language} ${_target} prefix header DEPENDS ${_dependencySources}\")\n\tendif()\n\tset (${_dependencySourcesVar} ${_dependencySources} PARENT_SCOPE)\nendfunction()\n\nfunction (cotire_generate_target_script _language _configurations _targetSourceDir _targetBinaryDir _target _targetScriptVar _targetConfigScriptVar)\n\tset (COTIRE_TARGET_SOURCES ${ARGN})\n\tcotire_get_source_file_property_values(COTIRE_TARGET_SOURCE_LOCATIONS LOCATION ${COTIRE_TARGET_SOURCES})\n\tcotire_get_prefix_header_dependencies(${_language} ${_target} COTIRE_TARGET_PREFIX_DEPENDS ${COTIRE_TARGET_SOURCES})\n\tcotire_get_unity_source_dependencies(${_language} ${_target} COTIRE_TARGET_UNITY_DEPENDS ${COTIRE_TARGET_SOURCES})\n\t# set up variables to be configured\n\tset (COTIRE_TARGET_LANGUAGE \"${_language}\")\n\tcotire_determine_compiler_version(\"${COTIRE_TARGET_LANGUAGE}\" COTIRE_${_language}_COMPILER)\n\tget_target_property(COTIRE_TARGET_IGNORE_PATH ${_target} COTIRE_PREFIX_HEADER_IGNORE_PATH)\n\tcotire_add_sys_root_paths(COTIRE_TARGET_IGNORE_PATH)\n\tget_target_property(COTIRE_TARGET_INCLUDE_PATH ${_target} COTIRE_PREFIX_HEADER_INCLUDE_PATH)\n\tcotire_add_sys_root_paths(COTIRE_TARGET_INCLUDE_PATH)\n\tget_target_property(COTIRE_TARGET_PRE_UNDEFS ${_target} COTIRE_UNITY_SOURCE_PRE_UNDEFS)\n\tget_target_property(COTIRE_TARGET_POST_UNDEFS ${_target} COTIRE_UNITY_SOURCE_POST_UNDEFS)\n\tget_target_property(COTIRE_TARGET_MAXIMUM_NUMBER_OF_INCLUDES ${_target} COTIRE_UNITY_SOURCE_MAXIMUM_NUMBER_OF_INCLUDES)\n\tcotire_get_source_files_undefs(COTIRE_UNITY_SOURCE_PRE_UNDEFS COTIRE_TARGET_SOURCES_PRE_UNDEFS ${COTIRE_TARGET_SOURCES})\n\tcotire_get_source_files_undefs(COTIRE_UNITY_SOURCE_POST_UNDEFS COTIRE_TARGET_SOURCES_POST_UNDEFS ${COTIRE_TARGET_SOURCES})\n\tstring (STRIP \"${CMAKE_INCLUDE_SYSTEM_FLAG_${_language}}\" COTIRE_INCLUDE_SYSTEM_FLAG)\n\tset (COTIRE_TARGET_CONFIGURATION_TYPES \"${_configurations}\")\n\tforeach (_config ${_configurations})\n\t\tstring (TOUPPER \"${_config}\" _upperConfig)\n\t\tcotire_get_target_include_directories(\n\t\t\t\"${_config}\" \"${_language}\" \"${_targetSourceDir}\" \"${_targetBinaryDir}\" \"${_target}\" COTIRE_TARGET_INCLUDE_DIRECTORIES_${_upperConfig} COTIRE_TARGET_SYSTEM_INCLUDE_DIRECTORIES_${_upperConfig})\n\t\tcotire_get_target_compile_definitions(\n\t\t\t\"${_config}\" \"${_language}\" \"${_targetSourceDir}\" \"${_target}\" COTIRE_TARGET_COMPILE_DEFINITIONS_${_upperConfig})\n\t\tcotire_get_target_compiler_flags(\n\t\t\t\"${_config}\" \"${_language}\" \"${_targetSourceDir}\" \"${_target}\" COTIRE_TARGET_COMPILE_FLAGS_${_upperConfig})\n\t\tcotire_get_source_files_compile_definitions(\n\t\t\t\"${_config}\" \"${_language}\" COTIRE_TARGET_SOURCES_COMPILE_DEFINITIONS_${_upperConfig} ${COTIRE_TARGET_SOURCES})\n\tendforeach()\n\tget_cmake_property(_vars VARIABLES)\n\tstring (REGEX MATCHALL \"COTIRE_[A-Za-z0-9_]+\" _matchVars \"${_vars}\")\n\t# remove COTIRE_VERBOSE which is passed as a CMake define on command line\n\tlist (REMOVE_ITEM _matchVars COTIRE_VERBOSE)\n\tset (_contents \"\")\n\tset (_contentsHasGeneratorExpressions FALSE)\n\tforeach (_var IN LISTS _matchVars ITEMS\n\t\tXCODE MSVC CMAKE_GENERATOR CMAKE_BUILD_TYPE CMAKE_CONFIGURATION_TYPES\n\t\tCMAKE_${_language}_COMPILER_ID CMAKE_${_language}_COMPILER CMAKE_${_language}_COMPILER_ARG1\n\t\tCMAKE_${_language}_SOURCE_FILE_EXTENSIONS)\n\t\tif (DEFINED ${_var})\n\t\t\tstring (REPLACE \"\\\"\" \"\\\\\\\"\" _value \"${${_var}}\")\n\t\t\tset (_contents \"${_contents}set (${_var} \\\"${_value}\\\")\\n\")\n\t\t\tif (NOT _contentsHasGeneratorExpressions)\n\t\t\t\tif (\"${_value}\" MATCHES \"\\\\$<.*>\")\n\t\t\t\t\tset (_contentsHasGeneratorExpressions TRUE)\n\t\t\t\tendif()\n\t\t\tendif()\n\t\tendif()\n\tendforeach()\n\tget_filename_component(_moduleName \"${COTIRE_CMAKE_MODULE_FILE}\" NAME)\n\tset (_targetCotireScript \"${CMAKE_CURRENT_BINARY_DIR}/${_target}_${_language}_${_moduleName}\")\n\tcotire_write_file(\"CMAKE\" \"${_targetCotireScript}\" \"${_contents}\" FALSE)\n\tif (_contentsHasGeneratorExpressions)\n\t\t# use file(GENERATE ...) to expand generator expressions in the target script at CMake generate-time\n\t\tif (NOT CMAKE_VERSION VERSION_LESS \"2.8.12\")\n\t\t\t# the file(GENERATE ...) command requires cmake 2.8.12 or later\n\t\t\tset (_configNameOrNoneGeneratorExpression \"$<$<CONFIG:>:None>$<$<NOT:$<CONFIG:>>:$<CONFIGURATION>>\")\n\t\t\tset (_targetCotireConfigScript \"${CMAKE_CURRENT_BINARY_DIR}/${_target}_${_language}_${_configNameOrNoneGeneratorExpression}_${_moduleName}\")\n\t\t\tfile (GENERATE OUTPUT \"${_targetCotireConfigScript}\" INPUT \"${_targetCotireScript}\")\n\t\telse()\n\t\t\tmessage (WARNING \"cotire: generator expression used in target ${_target}. This requires CMake 2.8.12 or later.\")\n\t\t\tset (_targetCotireConfigScript \"${_targetCotireScript}\")\n\t\tendif()\n\telse()\n\t\tset (_targetCotireConfigScript \"${_targetCotireScript}\")\n\tendif()\n\tset (${_targetScriptVar} \"${_targetCotireScript}\" PARENT_SCOPE)\n\tset (${_targetConfigScriptVar} \"${_targetCotireConfigScript}\" PARENT_SCOPE)\nendfunction()\n\nfunction (cotire_setup_pch_file_compilation _language _target _targetSourceDir _targetScript _prefixFile _pchFile)\n\tset (_sourceFiles ${ARGN})\n\tif (CMAKE_${_language}_COMPILER_ID MATCHES \"MSVC|Intel\")\n\t\t# for Visual Studio and Intel, we attach the precompiled header compilation to the first source file\n\t\t# the remaining files include the precompiled header, see cotire_setup_pch_file_inclusion\n\t\tif (_sourceFiles)\n\t\t\tfile (TO_NATIVE_PATH \"${_prefixFile}\" _prefixFileNative)\n\t\t\tfile (TO_NATIVE_PATH \"${_pchFile}\" _pchFileNative)\n\t\t\tlist (GET _sourceFiles 0 _hostFile)\n\t\t\tset (_flags \"\")\n\t\t\tcotire_determine_compiler_version(\"${_language}\" COTIRE_${_language}_COMPILER)\n\t\t\tcotire_add_pch_compilation_flags(\n\t\t\t\t\"${_language}\" \"${CMAKE_${_language}_COMPILER_ID}\" \"${COTIRE_${_language}_COMPILER_VERSION}\"\n\t\t\t\t\"${_prefixFile}\" \"${_pchFile}\" \"${_hostFile}\" _flags)\n\t\t\tset_property (SOURCE ${_hostFile} APPEND_STRING PROPERTY COMPILE_FLAGS \" ${_flags} \")\n\t\t\tset_property (SOURCE ${_hostFile} APPEND PROPERTY OBJECT_OUTPUTS \"${_pchFile}\")\n\t\t\t# make first source file depend on prefix header\n\t\t\tset_property (SOURCE ${_hostFile} APPEND PROPERTY OBJECT_DEPENDS \"${_prefixFile}\")\n\t\t\t# mark first source file as cotired to prevent it from being used in another cotired target\n\t\t\tset_property (SOURCE ${_hostFile} PROPERTY COTIRE_TARGET \"${_target}\")\n\t\tendif()\n\telseif (\"${CMAKE_GENERATOR}\" MATCHES \"Makefiles|Ninja\")\n\t\t# for makefile based generator, we add a custom command to precompile the prefix header\n\t\tif (_targetScript)\n\t\t\tcotire_set_cmd_to_prologue(_cmds)\n\t\t\tlist (GET _sourceFiles 0 _hostFile)\n\t\t\tlist (APPEND _cmds -P \"${COTIRE_CMAKE_MODULE_FILE}\" \"precompile\" \"${_targetScript}\" \"${_prefixFile}\" \"${_pchFile}\" \"${_hostFile}\")\n\t\t\tfile (RELATIVE_PATH _pchFileRelPath \"${CMAKE_BINARY_DIR}\" \"${_pchFile}\")\n\t\t\tif (COTIRE_DEBUG)\n\t\t\t\tmessage (STATUS \"add_custom_command: OUTPUT ${_pchFile} ${_cmds} DEPENDS ${_prefixFile} IMPLICIT_DEPENDS ${_language} ${_prefixFile}\")\n\t\t\tendif()\n\t\t\tset_property (SOURCE \"${_pchFile}\" PROPERTY GENERATED TRUE)\n\t\t\tadd_custom_command(\n\t\t\t\tOUTPUT \"${_pchFile}\"\n\t\t\t\tCOMMAND ${_cmds}\n\t\t\t\tDEPENDS \"${_prefixFile}\"\n\t\t\t\tIMPLICIT_DEPENDS ${_language} \"${_prefixFile}\"\n\t\t\t\tWORKING_DIRECTORY \"${_targetSourceDir}\"\n\t\t\t\tCOMMENT \"Building ${_language} precompiled header ${_pchFileRelPath}\" VERBATIM)\n\t\tendif()\n\tendif()\nendfunction()\n\nfunction (cotire_setup_pch_file_inclusion _language _target _wholeTarget _prefixFile _pchFile)\n\tset (_sourceFiles ${ARGN})\n\tif (CMAKE_${_language}_COMPILER_ID MATCHES \"MSVC|Intel\")\n\t\t# for Visual Studio and Intel, we include the precompiled header in all but the first source file\n\t\t# the first source file does the precompiled header compilation, see cotire_setup_pch_file_compilation\n\t\tlist (LENGTH _sourceFiles _numberOfSourceFiles)\n\t\tif (_numberOfSourceFiles GREATER 1)\n\t\t\t# mark sources as cotired to prevent them from being used in another cotired target\n\t\t\tset_source_files_properties(${_sourceFiles} PROPERTIES COTIRE_TARGET \"${_target}\")\n\t\t\tlist (REMOVE_AT _sourceFiles 0)\n\t\t\tset (_flags \"\")\n\t\t\tcotire_determine_compiler_version(\"${_language}\" COTIRE_${_language}_COMPILER)\n\t\t\tcotire_add_prefix_pch_inclusion_flags(\n\t\t\t\t\"${_language}\" \"${CMAKE_${_language}_COMPILER_ID}\" \"${COTIRE_${_language}_COMPILER_VERSION}\"\n\t\t\t\t\"${_prefixFile}\" \"${_pchFile}\" _flags)\n\t\t\tset_property (SOURCE ${_sourceFiles} APPEND_STRING PROPERTY COMPILE_FLAGS \" ${_flags} \")\n\t\t\t# make source files depend on precompiled header\n\t\t\tset_property (SOURCE ${_sourceFiles} APPEND PROPERTY OBJECT_DEPENDS \"${_pchFile}\")\n\t\tendif()\n\telseif (\"${CMAKE_GENERATOR}\" MATCHES \"Makefiles|Ninja\")\n\t\tif (NOT _wholeTarget)\n\t\t\t# for makefile based generator, we force the inclusion of the prefix header for a subset\n\t\t\t# of the source files, if this is a multi-language target or has excluded files\n\t\t\tset (_flags \"\")\n\t\t\tcotire_determine_compiler_version(\"${_language}\" COTIRE_${_language}_COMPILER)\n\t\t\tcotire_add_prefix_pch_inclusion_flags(\n\t\t\t\t\"${_language}\" \"${CMAKE_${_language}_COMPILER_ID}\" \"${COTIRE_${_language}_COMPILER_VERSION}\"\n\t\t\t\t\"${_prefixFile}\" \"${_pchFile}\" _flags)\n\t\t\tset_property (SOURCE ${_sourceFiles} APPEND_STRING PROPERTY COMPILE_FLAGS \" ${_flags} \")\n\t\t\t# mark sources as cotired to prevent them from being used in another cotired target\n\t\t\tset_source_files_properties(${_sourceFiles} PROPERTIES COTIRE_TARGET \"${_target}\")\n\t\tendif()\n\t\t# make source files depend on precompiled header\n\t\tset_property (SOURCE ${_sourceFiles} APPEND PROPERTY OBJECT_DEPENDS \"${_pchFile}\")\n\tendif()\nendfunction()\n\nfunction (cotire_setup_prefix_file_inclusion _language _target _prefixFile)\n\tset (_sourceFiles ${ARGN})\n\t# force the inclusion of the prefix header for the given source files\n\tset (_flags \"\")\n\tcotire_determine_compiler_version(\"${_language}\" COTIRE_${_language}_COMPILER)\n\tcotire_add_prefix_pch_inclusion_flags(\n\t\t\"${_language}\" \"${CMAKE_${_language}_COMPILER_ID}\" \"${COTIRE_${_language}_COMPILER_VERSION}\"\n\t\t\"${_prefixFile}\" \"\" _flags)\n\tset_property (SOURCE ${_sourceFiles} APPEND_STRING PROPERTY COMPILE_FLAGS \" ${_flags} \")\n\t# mark sources as cotired to prevent them from being used in another cotired target\n\tset_source_files_properties(${_sourceFiles} PROPERTIES COTIRE_TARGET \"${_target}\")\n\t# make source files depend on prefix header\n\tset_property (SOURCE ${_sourceFiles} APPEND PROPERTY OBJECT_DEPENDS \"${_prefixFile}\")\nendfunction()\n\nfunction (cotire_get_first_set_property_value _propertyValueVar _type _object)\n\tset (_properties ${ARGN})\n\tforeach (_property ${_properties})\n\t\tget_property(_propertyValue ${_type} \"${_object}\" PROPERTY ${_property})\n\t\tif (_propertyValue)\n\t\t\tset (${_propertyValueVar} ${_propertyValue} PARENT_SCOPE)\n\t\t\treturn()\n\t\tendif()\n\tendforeach()\n\tset (${_propertyValueVar} \"\" PARENT_SCOPE)\nendfunction()\n\nfunction (cotire_setup_combine_command _language _sourceDir _targetScript _joinedFile _cmdsVar)\n\tset (_files ${ARGN})\n\tset (_filesPaths \"\")\n\tforeach (_file ${_files})\n\t\tif (IS_ABSOLUTE \"${_file}\")\n\t\t\tset (_filePath \"${_file}\")\n\t\telse()\n\t\t\tget_filename_component(_filePath \"${_sourceDir}/${_file}\" ABSOLUTE)\n\t\tendif()\n\t\tfile (RELATIVE_PATH _fileRelPath \"${_sourceDir}\" \"${_filePath}\")\n\t\tif (NOT IS_ABSOLUTE \"${_fileRelPath}\" AND NOT \"${_fileRelPath}\" MATCHES \"^\\\\.\\\\.\")\n\t\t\tlist (APPEND _filesPaths \"${_fileRelPath}\")\n\t\telse()\n\t\t\tlist (APPEND _filesPaths \"${_filePath}\")\n\t\tendif()\n\tendforeach()\n\tcotire_set_cmd_to_prologue(_prefixCmd)\n\tlist (APPEND _prefixCmd -P \"${COTIRE_CMAKE_MODULE_FILE}\" \"combine\")\n\tif (_targetScript)\n\t\tlist (APPEND _prefixCmd \"${_targetScript}\")\n\tendif()\n\tlist (APPEND _prefixCmd \"${_joinedFile}\" ${_filesPaths})\n\tif (COTIRE_DEBUG)\n\t\tmessage (STATUS \"add_custom_command: OUTPUT ${_joinedFile} COMMAND ${_prefixCmd} DEPENDS ${_files}\")\n\tendif()\n\tset_property (SOURCE \"${_joinedFile}\" PROPERTY GENERATED TRUE)\n\tfile (RELATIVE_PATH _joinedFileRelPath \"${CMAKE_BINARY_DIR}\" \"${_joinedFile}\")\n\tget_filename_component(_joinedFileBaseName \"${_joinedFile}\" NAME_WE)\n\tget_filename_component(_joinedFileExt \"${_joinedFile}\" EXT)\n\tif (_language AND _joinedFileBaseName MATCHES \"${COTIRE_UNITY_SOURCE_FILENAME_SUFFIX}$\")\n\t\tset (_comment \"Generating ${_language} unity source ${_joinedFileRelPath}\")\n\telseif (_language AND _joinedFileBaseName MATCHES \"${COTIRE_PREFIX_HEADER_FILENAME_SUFFIX}$\")\n\t\tif (_joinedFileExt MATCHES \"^\\\\.c\")\n\t\t\tset (_comment \"Generating ${_language} prefix source ${_joinedFileRelPath}\")\n\t\telse()\n\t\t\tset (_comment \"Generating ${_language} prefix header ${_joinedFileRelPath}\")\n\t\tendif()\n\telse()\n\t\tset (_comment \"Generating ${_joinedFileRelPath}\")\n\tendif()\n\tadd_custom_command(\n\t\tOUTPUT \"${_joinedFile}\"\n\t\tCOMMAND ${_prefixCmd}\n\t\tDEPENDS ${_files}\n\t\tCOMMENT \"${_comment}\"\n\t\tWORKING_DIRECTORY \"${_sourceDir}\" VERBATIM)\n\tlist (APPEND ${_cmdsVar} COMMAND ${_prefixCmd})\n\tset (${_cmdsVar} ${${_cmdsVar}} PARENT_SCOPE)\nendfunction()\n\nfunction (cotire_setup_target_pch_usage _languages _targetSourceDir _target _wholeTarget)\n\tif (XCODE)\n\t\t# for Xcode, we attach a pre-build action to generate the unity sources and prefix headers\n\t\t# if necessary, we also generate a single prefix header which includes all language specific prefix headers\n\t\tset (_prefixFiles \"\")\n\t\tforeach (_language ${_languages})\n\t\t\tget_property(_prefixFile TARGET ${_target} PROPERTY COTIRE_${_language}_PREFIX_HEADER)\n\t\t\tif (_prefixFile)\n\t\t\t\tlist (APPEND _prefixFiles \"${_prefixFile}\")\n\t\t\tendif()\n\t\tendforeach()\n\t\tset (_cmds ${ARGN})\n\t\tlist (LENGTH _prefixFiles _numberOfPrefixFiles)\n\t\tif (_numberOfPrefixFiles GREATER 1)\n\t\t\tcotire_make_prefix_file_path(\"\" ${_target} _prefixHeader)\n\t\t\tcotire_setup_combine_command(\"\" \"${_targetSourceDir}\" \"\" \"${_prefixHeader}\" _cmds ${_prefixFiles})\n\t\telse()\n\t\t\tset (_prefixHeader \"${_prefixFiles}\")\n\t\tendif()\n\t\tif (COTIRE_DEBUG)\n\t\t\tmessage (STATUS \"add_custom_command: TARGET ${_target} PRE_BUILD ${_cmds}\")\n\t\tendif()\n\t\tadd_custom_command(TARGET \"${_target}\"\n\t\t\tPRE_BUILD ${_cmds}\n\t\t\tWORKING_DIRECTORY \"${_targetSourceDir}\"\n\t\t\tCOMMENT \"Updating target ${_target} prefix headers\" VERBATIM)\n\t\t# make Xcode precompile the generated prefix header with ProcessPCH and ProcessPCH++\n\t\tset_target_properties(${_target} PROPERTIES XCODE_ATTRIBUTE_GCC_PRECOMPILE_PREFIX_HEADER \"YES\")\n\t\tset_target_properties(${_target} PROPERTIES XCODE_ATTRIBUTE_GCC_PREFIX_HEADER \"${_prefixHeader}\")\n\telseif (\"${CMAKE_GENERATOR}\" MATCHES \"Makefiles|Ninja\")\n\t\t# for makefile based generator, we force inclusion of the prefix header for all target source files\n\t\t# if this is a single-language target without any excluded files\n\t\tif (_wholeTarget)\n\t\t\tset (_language \"${_languages}\")\n\t\t\t# for Visual Studio and Intel, precompiled header inclusion is always done on the source file level\n\t\t\t# see cotire_setup_pch_file_inclusion\n\t\t\tif (NOT CMAKE_${_language}_COMPILER_ID MATCHES \"MSVC|Intel\")\n\t\t\t\tget_property(_prefixFile TARGET ${_target} PROPERTY COTIRE_${_language}_PREFIX_HEADER)\n\t\t\t\tif (_prefixFile)\n\t\t\t\t\tset (_flags \"\")\n\t\t\t\t\tcotire_determine_compiler_version(\"${_language}\" COTIRE_${_language}_COMPILER)\n\t\t\t\t\tget_property(_pchFile TARGET ${_target} PROPERTY COTIRE_${_language}_PRECOMPILED_HEADER)\n\t\t\t\t\tcotire_add_prefix_pch_inclusion_flags(\n\t\t\t\t\t\t\"${_language}\" \"${CMAKE_${_language}_COMPILER_ID}\" \"${COTIRE_${_language}_COMPILER_VERSION}\"\n\t\t\t\t\t\t\"${_prefixFile}\" \"${_pchFile}\" _flags)\n\t\t\t\t\tset_property(TARGET ${_target} APPEND_STRING PROPERTY COMPILE_FLAGS \" ${_flags} \")\n\t\t\t\tendif()\n\t\t\tendif()\n\t\tendif()\n\tendif()\nendfunction()\n\nfunction (cotire_setup_unity_generation_commands _language _targetSourceDir _target _targetScript _targetConfigScript _unityFiles _cmdsVar)\n\tset (_dependencySources \"\")\n\tcotire_get_unity_source_dependencies(${_language} ${_target} _dependencySources ${ARGN})\n\tforeach (_unityFile ${_unityFiles})\n\t\tfile (RELATIVE_PATH _unityFileRelPath \"${CMAKE_BINARY_DIR}\" \"${_unityFile}\")\n\t\tset_property (SOURCE \"${_unityFile}\" PROPERTY GENERATED TRUE)\n\t\t# set up compiled unity source dependencies via OBJECT_DEPENDS\n\t\t# this ensures that missing source files are generated before the unity file is compiled\n\t\tif (COTIRE_DEBUG AND _dependencySources)\n\t\t\tmessage (STATUS \"${_unityFile} OBJECT_DEPENDS ${_dependencySources}\")\n\t\tendif()\n\t\tif (_dependencySources)\n\t\t\t# the OBJECT_DEPENDS property requires a list of full paths\n\t\t\tset (_objectDependsPaths \"\")\n\t\t\tforeach (_sourceFile ${_dependencySources})\n\t\t\t\tget_source_file_property(_sourceLocation \"${_sourceFile}\" LOCATION)\n\t\t\t\tlist (APPEND _objectDependsPaths \"${_sourceLocation}\")\n\t\t\tendforeach()\n\t\t\tset_property (SOURCE \"${_unityFile}\" PROPERTY OBJECT_DEPENDS ${_objectDependsPaths})\n\t\tendif()\n\t\tif (WIN32 AND CMAKE_${_language}_COMPILER_ID MATCHES \"MSVC|Intel\")\n\t\t\t# unity file compilation results in potentially huge object file, thus use /bigobj by default unter MSVC and Windows Intel\n\t\t\tset_property (SOURCE \"${_unityFile}\" APPEND_STRING PROPERTY COMPILE_FLAGS \"/bigobj\")\n\t\tendif()\n\t\tcotire_set_cmd_to_prologue(_unityCmd)\n\t\tlist (APPEND _unityCmd -P \"${COTIRE_CMAKE_MODULE_FILE}\" \"unity\" \"${_targetConfigScript}\" \"${_unityFile}\")\n\t\tif (CMAKE_VERSION VERSION_LESS \"3.1.0\")\n\t\t\tset (_unityCmdDepends \"${_targetScript}\")\n\t\telse()\n\t\t\t# CMake 3.1.0 supports generator expressions in arguments to DEPENDS\n\t\t\tset (_unityCmdDepends \"${_targetConfigScript}\")\n\t\tendif()\n\t\tif (COTIRE_DEBUG)\n\t\t\tmessage (STATUS \"add_custom_command: OUTPUT ${_unityFile} COMMAND ${_unityCmd} DEPENDS ${_unityCmdDepends}\")\n\t\tendif()\n\t\tadd_custom_command(\n\t\t\tOUTPUT \"${_unityFile}\"\n\t\t\tCOMMAND ${_unityCmd}\n\t\t\tDEPENDS ${_unityCmdDepends}\n\t\t\tCOMMENT \"Generating ${_language} unity source ${_unityFileRelPath}\"\n\t\t\tWORKING_DIRECTORY \"${_targetSourceDir}\" VERBATIM)\n\t\tlist (APPEND ${_cmdsVar} COMMAND ${_unityCmd})\n\tendforeach()\n\tlist (LENGTH _unityFiles _numberOfUnityFiles)\n\tif (_numberOfUnityFiles GREATER 1)\n\t\t# create a joint unity file from all unity file segments\n\t\tcotire_make_single_unity_source_file_path(${_language} ${_target} _unityFile)\n\t\tcotire_setup_combine_command(${_language} \"${_targetSourceDir}\" \"${_targetConfigScript}\" \"${_unityFile}\" ${_cmdsVar} ${_unityFiles})\n\tendif()\n\tset (${_cmdsVar} ${${_cmdsVar}} PARENT_SCOPE)\nendfunction()\n\nfunction (cotire_setup_prefix_generation_command _language _target _targetSourceDir _targetScript _prefixFile _unityFile _cmdsVar)\n\tset (_sourceFiles ${ARGN})\n\tset (_dependencySources \"\")\n\tcotire_get_prefix_header_dependencies(${_language} ${_target} _dependencySources ${_sourceFiles})\n\tcotire_set_cmd_to_prologue(_prefixCmd)\n\tlist (APPEND _prefixCmd -P \"${COTIRE_CMAKE_MODULE_FILE}\" \"prefix\" \"${_targetScript}\" \"${_prefixFile}\" \"${_unityFile}\")\n\tset_property (SOURCE \"${_prefixFile}\" PROPERTY GENERATED TRUE)\n\tif (COTIRE_DEBUG)\n\t\tmessage (STATUS \"add_custom_command: OUTPUT ${_prefixFile} COMMAND ${_prefixCmd} DEPENDS ${_unityFile} ${_dependencySources}\")\n\tendif()\n\tfile (RELATIVE_PATH _prefixFileRelPath \"${CMAKE_BINARY_DIR}\" \"${_prefixFile}\")\n\tget_filename_component(_prefixFileExt \"${_prefixFile}\" EXT)\n\tif (_prefixFileExt MATCHES \"^\\\\.c\")\n\t\tset (_comment \"Generating ${_language} prefix source ${_prefixFileRelPath}\")\n\telse()\n\t\tset (_comment \"Generating ${_language} prefix header ${_prefixFileRelPath}\")\n\tendif()\n\tadd_custom_command(\n\t\tOUTPUT \"${_prefixFile}\" \"${_prefixFile}.log\"\n\t\tCOMMAND ${_prefixCmd}\n\t\tDEPENDS \"${_unityFile}\" ${_dependencySources}\n\t\tCOMMENT \"${_comment}\"\n\t\tWORKING_DIRECTORY \"${CMAKE_BINARY_DIR}\" VERBATIM)\n\tlist (APPEND ${_cmdsVar} COMMAND ${_prefixCmd})\n\tset (${_cmdsVar} ${${_cmdsVar}} PARENT_SCOPE)\nendfunction()\n\nfunction (cotire_setup_prefix_generation_from_unity_command _language _target _targetSourceDir _targetScript _prefixFile _unityFiles _cmdsVar)\n\tset (_sourceFiles ${ARGN})\n\tif (CMAKE_${_language}_COMPILER_ID MATCHES \"GNU|Clang\")\n\t\t# GNU and Clang require indirect compilation of the prefix header to make them honor the system_header pragma\n\t\tcotire_prefix_header_to_source_file_path(${_language} \"${_prefixFile}\" _prefixSourceFile)\n\telse()\n\t\tset (_prefixSourceFile \"${_prefixFile}\")\n\tendif()\n\tlist (LENGTH _unityFiles _numberOfUnityFiles)\n\tif (_numberOfUnityFiles GREATER 1)\n\t\tcotire_make_single_unity_source_file_path(${_language} ${_target} _unityFile)\n\t\tcotire_setup_prefix_generation_command(\n\t\t\t${_language} ${_target} \"${_targetSourceDir}\" \"${_targetScript}\"\n\t\t\t\"${_prefixSourceFile}\" \"${_unityFile}\" ${_cmdsVar} ${_sourceFiles})\n\telse()\n\t\tcotire_setup_prefix_generation_command(\n\t\t\t${_language} ${_target} \"${_targetSourceDir}\" \"${_targetScript}\"\n\t\t\t\"${_prefixSourceFile}\" \"${_unityFiles}\" ${_cmdsVar} ${_sourceFiles})\n\tendif()\n\tif (CMAKE_${_language}_COMPILER_ID MATCHES \"GNU|Clang\")\n\t\tcotire_setup_combine_command(${_language} \"${_targetSourceDir}\" \"${_targetScript}\" \"${_prefixFile}\" ${_cmdsVar} ${_prefixSourceFile})\n\tendif()\n\tset (${_cmdsVar} ${${_cmdsVar}} PARENT_SCOPE)\nendfunction()\n\nfunction (cotire_setup_prefix_generation_from_provided_command _language _target _targetSourceDir _targetScript _prefixFile _cmdsVar)\n\tset (_prefixHeaderFiles ${ARGN})\n\tif (CMAKE_${_language}_COMPILER_ID MATCHES \"GNU|Clang\")\n\t\t# GNU and Clang require indirect compilation of the prefix header to make them honor the system_header pragma\n\t\tcotire_prefix_header_to_source_file_path(${_language} \"${_prefixFile}\" _prefixSourceFile)\n\telse()\n\t\tset (_prefixSourceFile \"${_prefixFile}\")\n\tendif()\n\tcotire_setup_combine_command(${_language} \"${_targetSourceDir}\" \"${_targetScript}\" \"${_prefixSourceFile}\" _cmds ${_prefixHeaderFiles})\n\tif (CMAKE_${_language}_COMPILER_ID MATCHES \"GNU|Clang\")\n\t\tcotire_setup_combine_command(${_language} \"${_targetSourceDir}\" \"${_targetScript}\" \"${_prefixFile}\" _cmds ${_prefixSourceFile})\n\tendif()\n\tset (${_cmdsVar} ${${_cmdsVar}} PARENT_SCOPE)\nendfunction()\n\nfunction (cotire_init_cotire_target_properties _target)\n\tget_property(_isSet TARGET ${_target} PROPERTY COTIRE_ENABLE_PRECOMPILED_HEADER SET)\n\tif (NOT _isSet)\n\t\tset_property(TARGET ${_target} PROPERTY COTIRE_ENABLE_PRECOMPILED_HEADER TRUE)\n\tendif()\n\tget_property(_isSet TARGET ${_target} PROPERTY COTIRE_ADD_UNITY_BUILD SET)\n\tif (NOT _isSet)\n\t\tset_property(TARGET ${_target} PROPERTY COTIRE_ADD_UNITY_BUILD TRUE)\n\tendif()\n\tget_property(_isSet TARGET ${_target} PROPERTY COTIRE_ADD_CLEAN SET)\n\tif (NOT _isSet)\n\t\tset_property(TARGET ${_target} PROPERTY COTIRE_ADD_CLEAN FALSE)\n\tendif()\n\tget_property(_isSet TARGET ${_target} PROPERTY COTIRE_PREFIX_HEADER_IGNORE_PATH SET)\n\tif (NOT _isSet)\n\t\tset_property(TARGET ${_target} PROPERTY COTIRE_PREFIX_HEADER_IGNORE_PATH \"${CMAKE_SOURCE_DIR}\")\n\t\tcotire_check_is_path_relative_to(\"${CMAKE_BINARY_DIR}\" _isRelative \"${CMAKE_SOURCE_DIR}\")\n\t\tif (NOT _isRelative)\n\t\t\tset_property(TARGET ${_target} APPEND PROPERTY COTIRE_PREFIX_HEADER_IGNORE_PATH \"${CMAKE_BINARY_DIR}\")\n\t\tendif()\n\tendif()\n\tget_property(_isSet TARGET ${_target} PROPERTY COTIRE_PREFIX_HEADER_INCLUDE_PATH SET)\n\tif (NOT _isSet)\n\t\tset_property(TARGET ${_target} PROPERTY COTIRE_PREFIX_HEADER_INCLUDE_PATH \"\")\n\tendif()\n\tget_property(_isSet TARGET ${_target} PROPERTY COTIRE_UNITY_SOURCE_PRE_UNDEFS SET)\n\tif (NOT _isSet)\n\t\tset_property(TARGET ${_target} PROPERTY COTIRE_UNITY_SOURCE_PRE_UNDEFS \"\")\n\tendif()\n\tget_property(_isSet TARGET ${_target} PROPERTY COTIRE_UNITY_SOURCE_POST_UNDEFS SET)\n\tif (NOT _isSet)\n\t\tset_property(TARGET ${_target} PROPERTY COTIRE_UNITY_SOURCE_POST_UNDEFS \"\")\n\tendif()\n\tget_property(_isSet TARGET ${_target} PROPERTY COTIRE_UNITY_LINK_LIBRARIES_INIT SET)\n\tif (NOT _isSet)\n\t\tset_property(TARGET ${_target} PROPERTY COTIRE_UNITY_LINK_LIBRARIES_INIT \"\")\n\tendif()\n\tget_property(_isSet TARGET ${_target} PROPERTY COTIRE_UNITY_SOURCE_MAXIMUM_NUMBER_OF_INCLUDES SET)\n\tif (NOT _isSet)\n\t\tif (COTIRE_MAXIMUM_NUMBER_OF_UNITY_INCLUDES)\n\t\t\tset_property(TARGET ${_target} PROPERTY COTIRE_UNITY_SOURCE_MAXIMUM_NUMBER_OF_INCLUDES \"${COTIRE_MAXIMUM_NUMBER_OF_UNITY_INCLUDES}\")\n\t\telse()\n\t\t\tset_property(TARGET ${_target} PROPERTY COTIRE_UNITY_SOURCE_MAXIMUM_NUMBER_OF_INCLUDES \"\")\n\t\tendif()\n\tendif()\nendfunction()\n\nfunction (cotire_make_target_message _target _languages _disableMsg _targetMsgVar)\n\tget_target_property(_targetUsePCH ${_target} COTIRE_ENABLE_PRECOMPILED_HEADER)\n\tget_target_property(_targetAddSCU ${_target} COTIRE_ADD_UNITY_BUILD)\n\tstring (REPLACE \";\" \" \" _languagesStr \"${_languages}\")\n\tmath (EXPR _numberOfExcludedFiles \"${ARGC} - 4\")\n\tif (_numberOfExcludedFiles EQUAL 0)\n\t\tset (_excludedStr \"\")\n\telseif (COTIRE_VERBOSE OR _numberOfExcludedFiles LESS 4)\n\t\tstring (REPLACE \";\" \", \" _excludedStr \"excluding ${ARGN}\")\n\telse()\n\t\tset (_excludedStr \"excluding ${_numberOfExcludedFiles} files\")\n\tendif()\n\tset (_targetMsg \"\")\n\tif (NOT _languages)\n\t\tset (_targetMsg \"Target ${_target} cannot be cotired.\")\n\t\tif (_disableMsg)\n\t\t\tset (_targetMsg \"${_targetMsg} ${_disableMsg}\")\n\t\tendif()\n\telseif (NOT _targetUsePCH AND NOT _targetAddSCU)\n\t\tset (_targetMsg \"${_languagesStr} target ${_target} cotired without unity build and precompiled header.\")\n\t\tif (_disableMsg)\n\t\t\tset (_targetMsg \"${_targetMsg} ${_disableMsg}\")\n\t\tendif()\n\telseif (NOT _targetUsePCH)\n\t\tif (_excludedStr)\n\t\t\tset (_targetMsg \"${_languagesStr} target ${_target} cotired without precompiled header ${_excludedStr}.\")\n\t\telse()\n\t\t\tset (_targetMsg \"${_languagesStr} target ${_target} cotired without precompiled header.\")\n\t\tendif()\n\t\tif (_disableMsg)\n\t\t\tset (_targetMsg \"${_targetMsg} ${_disableMsg}\")\n\t\tendif()\n\telseif (NOT _targetAddSCU)\n\t\tif (_excludedStr)\n\t\t\tset (_targetMsg \"${_languagesStr} target ${_target} cotired without unity build ${_excludedStr}.\")\n\t\telse()\n\t\t\tset (_targetMsg \"${_languagesStr} target ${_target} cotired without unity build.\")\n\t\tendif()\n\telse()\n\t\tif (_excludedStr)\n\t\t\tset (_targetMsg \"${_languagesStr} target ${_target} cotired ${_excludedStr}.\")\n\t\telse()\n\t\t\tset (_targetMsg \"${_languagesStr} target ${_target} cotired.\")\n\t\tendif()\n\tendif()\n\tset (${_targetMsgVar} \"${_targetMsg}\" PARENT_SCOPE)\nendfunction()\n\nfunction (cotire_choose_target_languages _targetSourceDir _target _targetLanguagesVar _wholeTargetVar)\n\tset (_languages ${ARGN})\n\tset (_allSourceFiles \"\")\n\tset (_allExcludedSourceFiles \"\")\n\tset (_allCotiredSourceFiles \"\")\n\tset (_targetLanguages \"\")\n\tset (_pchEligibleTargetLanguages \"\")\n\tget_target_property(_targetType ${_target} TYPE)\n\tget_target_property(_targetSourceFiles ${_target} SOURCES)\n\tget_target_property(_targetUsePCH ${_target} COTIRE_ENABLE_PRECOMPILED_HEADER)\n\tget_target_property(_targetAddSCU ${_target} COTIRE_ADD_UNITY_BUILD)\n\tset (_disableMsg \"\")\n\tforeach (_language ${_languages})\n\t\tget_target_property(_prefixHeader ${_target} COTIRE_${_language}_PREFIX_HEADER)\n\t\tget_target_property(_unityBuildFile ${_target} COTIRE_${_language}_UNITY_SOURCE)\n\t\tif (_prefixHeader OR _unityBuildFile)\n\t\t\tmessage (STATUS \"cotire: target ${_target} has already been cotired.\")\n\t\t\tset (${_targetLanguagesVar} \"\" PARENT_SCOPE)\n\t\t\treturn()\n\t\tendif()\n\t\tif (_targetUsePCH AND \"${_language}\" MATCHES \"^C|CXX$\")\n\t\t\tcotire_check_precompiled_header_support(\"${_language}\" \"${_targetSourceDir}\" \"${_target}\" _disableMsg)\n\t\t\tif (_disableMsg)\n\t\t\t\tset (_targetUsePCH FALSE)\n\t\t\tendif()\n\t\tendif()\n\t\tset (_sourceFiles \"\")\n\t\tset (_excludedSources \"\")\n\t\tset (_cotiredSources \"\")\n\t\tcotire_filter_language_source_files(${_language} _sourceFiles _excludedSources _cotiredSources ${_targetSourceFiles})\n\t\tif (_sourceFiles OR _excludedSources OR _cotiredSources)\n\t\t\tlist (APPEND _targetLanguages ${_language})\n\t\tendif()\n\t\tif (_sourceFiles)\n\t\t\tlist (APPEND _allSourceFiles ${_sourceFiles})\n\t\tendif()\n\t\tlist (LENGTH _sourceFiles _numberOfSources)\n\t\tif (NOT _numberOfSources LESS ${COTIRE_MINIMUM_NUMBER_OF_TARGET_SOURCES})\n\t\t\tlist (APPEND _pchEligibleTargetLanguages ${_language})\n\t\tendif()\n\t\tif (_excludedSources)\n\t\t\tlist (APPEND _allExcludedSourceFiles ${_excludedSources})\n\t\tendif()\n\t\tif (_cotiredSources)\n\t\t\tlist (APPEND _allCotiredSourceFiles ${_cotiredSources})\n\t\tendif()\n\tendforeach()\n\tset (_targetMsgLevel STATUS)\n\tif (NOT _targetLanguages)\n\t\tstring (REPLACE \";\" \" or \" _languagesStr \"${_languages}\")\n\t\tset (_disableMsg \"No ${_languagesStr} source files.\")\n\t\tset (_targetUsePCH FALSE)\n\t\tset (_targetAddSCU FALSE)\n\tendif()\n\tif (_targetUsePCH)\n\t\tif (_allCotiredSourceFiles)\n\t\t\tcotire_get_source_file_property_values(_cotireTargets COTIRE_TARGET ${_allCotiredSourceFiles})\n\t\t\tlist (REMOVE_DUPLICATES _cotireTargets)\n\t\t\tstring (REPLACE \";\" \", \" _cotireTargetsStr \"${_cotireTargets}\")\n\t\t\tset (_disableMsg \"Target sources already include a precompiled header for target(s) ${_cotireTargets}.\")\n\t\t\tset (_disableMsg \"${_disableMsg} Set target property COTIRE_ENABLE_PRECOMPILED_HEADER to FALSE for targets ${_target},\")\n\t\t\tset (_disableMsg \"${_disableMsg} ${_cotireTargetsStr} to get a workable build system.\")\n\t\t\tset (_targetMsgLevel SEND_ERROR)\n\t\t\tset (_targetUsePCH FALSE)\n\t\telseif (NOT _pchEligibleTargetLanguages)\n\t\t\tset (_disableMsg \"Too few applicable sources.\")\n\t\t\tset (_targetUsePCH FALSE)\n\t\telseif (XCODE AND _allExcludedSourceFiles)\n\t\t\t# for Xcode, we cannot apply the precompiled header to individual sources, only to the whole target\n\t\t\tset (_disableMsg \"Exclusion of source files not supported for generator Xcode.\")\n\t\t\tset (_targetUsePCH FALSE)\n\t\telseif (XCODE AND \"${_targetType}\" STREQUAL \"OBJECT_LIBRARY\")\n\t\t\t# for Xcode, we cannot apply the required PRE_BUILD action to generate the prefix header to an OBJECT_LIBRARY target\n\t\t\tset (_disableMsg \"Required PRE_BUILD action not supported for OBJECT_LIBRARY targets for generator Xcode.\")\n\t\t\tset (_targetUsePCH FALSE)\n\t\tendif()\n\tendif()\n\tset_property(TARGET ${_target} PROPERTY COTIRE_ENABLE_PRECOMPILED_HEADER ${_targetUsePCH})\n\tset_property(TARGET ${_target} PROPERTY COTIRE_ADD_UNITY_BUILD ${_targetAddSCU})\n\tcotire_make_target_message(${_target} \"${_targetLanguages}\" \"${_disableMsg}\" _targetMsg ${_allExcludedSourceFiles})\n\tif (_targetMsg)\n\t\tif (NOT DEFINED COTIREMSG_${_target})\n\t\t\tset (COTIREMSG_${_target} \"\")\n\t\tendif()\n\t\tif (COTIRE_VERBOSE OR NOT \"${_targetMsgLevel}\" STREQUAL \"STATUS\" OR\n\t\t\tNOT \"${COTIREMSG_${_target}}\" STREQUAL \"${_targetMsg}\")\n\t\t\t# cache message to avoid redundant messages on re-configure\n\t\t\tset (COTIREMSG_${_target} \"${_targetMsg}\" CACHE INTERNAL \"${_target} cotire message.\")\n\t\t\tmessage (${_targetMsgLevel} \"${_targetMsg}\")\n\t\tendif()\n\tendif()\n\tlist (LENGTH _targetLanguages _numberOfLanguages)\n\tif (_numberOfLanguages GREATER 1 OR _allExcludedSourceFiles)\n\t\tset (${_wholeTargetVar} FALSE PARENT_SCOPE)\n\telse()\n\t\tset (${_wholeTargetVar} TRUE PARENT_SCOPE)\n\tendif()\n\tset (${_targetLanguagesVar} ${_targetLanguages} PARENT_SCOPE)\nendfunction()\n\nfunction (cotire_compute_unity_max_number_of_includes _target _maxIncludesVar)\n\tset (_sourceFiles ${ARGN})\n\tget_target_property(_maxIncludes ${_target} COTIRE_UNITY_SOURCE_MAXIMUM_NUMBER_OF_INCLUDES)\n\tif (_maxIncludes MATCHES \"(-j|--parallel|--jobs) ?([0-9]*)\")\n\t\tset (_numberOfThreads \"${CMAKE_MATCH_2}\")\n\t\tif (NOT _numberOfThreads)\n\t\t\t# use all available cores\n\t\t\tProcessorCount(_numberOfThreads)\n\t\tendif()\n\t\tlist (LENGTH _sourceFiles _numberOfSources)\n\t\tmath (EXPR _maxIncludes \"(${_numberOfSources} + ${_numberOfThreads} - 1) / ${_numberOfThreads}\")\n\t\t# a unity source segment must not contain less than COTIRE_MINIMUM_NUMBER_OF_TARGET_SOURCES files\n\t\tif (_maxIncludes LESS ${COTIRE_MINIMUM_NUMBER_OF_TARGET_SOURCES})\n\t\t\tset (_maxIncludes ${COTIRE_MINIMUM_NUMBER_OF_TARGET_SOURCES})\n\t\tendif()\n\telseif (NOT _maxIncludes MATCHES \"[0-9]+\")\n\t\tset (_maxIncludes 0)\n\tendif()\n\tif (COTIRE_DEBUG)\n\t\tmessage (STATUS \"${_target} unity source max includes = ${_maxIncludes}\")\n\tendif()\n\tset (${_maxIncludesVar} ${_maxIncludes} PARENT_SCOPE)\nendfunction()\n\nfunction (cotire_process_target_language _language _configurations _targetSourceDir _targetBinaryDir _target _wholeTarget _cmdsVar)\n\tset (${_cmdsVar} \"\" PARENT_SCOPE)\n\tget_target_property(_targetSourceFiles ${_target} SOURCES)\n\tset (_sourceFiles \"\")\n\tset (_excludedSources \"\")\n\tset (_cotiredSources \"\")\n\tcotire_filter_language_source_files(${_language} _sourceFiles _excludedSources _cotiredSources ${_targetSourceFiles})\n\tif (NOT _sourceFiles AND NOT _cotiredSources)\n\t\treturn()\n\tendif()\n\tset (_cmds \"\")\n\t# check for user provided unity source file list\n\tget_property(_unitySourceFiles TARGET ${_target} PROPERTY COTIRE_${_language}_UNITY_SOURCE_INIT)\n\tif (NOT _unitySourceFiles)\n\t\tset (_unitySourceFiles ${_sourceFiles} ${_cotiredSources})\n\tendif()\n\tcotire_generate_target_script(\n\t\t${_language} \"${_configurations}\" \"${_targetSourceDir}\" \"${_targetBinaryDir}\" ${_target} _targetScript _targetConfigScript ${_unitySourceFiles})\n\tcotire_compute_unity_max_number_of_includes(${_target} _maxIncludes ${_unitySourceFiles})\n\tcotire_make_unity_source_file_paths(${_language} ${_target} ${_maxIncludes} _unityFiles ${_unitySourceFiles})\n\tif (NOT _unityFiles)\n\t\treturn()\n\tendif()\n\tcotire_setup_unity_generation_commands(\n\t\t${_language} \"${_targetSourceDir}\" ${_target} \"${_targetScript}\" \"${_targetConfigScript}\" \"${_unityFiles}\" _cmds ${_unitySourceFiles})\n\tcotire_make_prefix_file_path(${_language} ${_target} _prefixFile)\n\tif (_prefixFile)\n\t\t# check for user provided prefix header files\n\t\tget_property(_prefixHeaderFiles TARGET ${_target} PROPERTY COTIRE_${_language}_PREFIX_HEADER_INIT)\n\t\tif (_prefixHeaderFiles)\n\t\t\tcotire_setup_prefix_generation_from_provided_command(\n\t\t\t\t${_language} ${_target} \"${_targetSourceDir}\" \"${_targetConfigScript}\" \"${_prefixFile}\" _cmds ${_prefixHeaderFiles})\n\t\telse()\n\t\t\tcotire_setup_prefix_generation_from_unity_command(\n\t\t\t\t${_language} ${_target} \"${_targetSourceDir}\" \"${_targetConfigScript}\" \"${_prefixFile}\" \"${_unityFiles}\" _cmds ${_unitySourceFiles})\n\t\tendif()\n\t\t# check if selected language has enough sources at all\n\t\tlist (LENGTH _sourceFiles _numberOfSources)\n\t\tif (_numberOfSources LESS ${COTIRE_MINIMUM_NUMBER_OF_TARGET_SOURCES})\n\t\t\tset (_targetUsePCH FALSE)\n\t\telse()\n\t\t\tget_target_property(_targetUsePCH ${_target} COTIRE_ENABLE_PRECOMPILED_HEADER)\n\t\tendif()\n\t\tif (_targetUsePCH)\n\t\t\tcotire_make_pch_file_path(${_language} \"${_targetSourceDir}\" ${_target} _pchFile)\n\t\t\tif (_pchFile)\n\t\t\t\tcotire_setup_pch_file_compilation(\n\t\t\t\t\t${_language} ${_target} \"${_targetSourceDir}\" \"${_targetConfigScript}\" \"${_prefixFile}\" \"${_pchFile}\" ${_sourceFiles})\n\t\t\t\tcotire_setup_pch_file_inclusion(\n\t\t\t\t\t${_language} ${_target} ${_wholeTarget} \"${_prefixFile}\" \"${_pchFile}\" ${_sourceFiles})\n\t\t\tendif()\n\t\telseif (_prefixHeaderFiles)\n\t\t\t# user provided prefix header must be included unconditionally\n\t\t\tcotire_setup_prefix_file_inclusion(${_language} ${_target} \"${_prefixFile}\" ${_sourceFiles})\n\t\tendif()\n\tendif()\n\t# mark target as cotired for language\n\tset_property(TARGET ${_target} PROPERTY COTIRE_${_language}_UNITY_SOURCE \"${_unityFiles}\")\n\tif (_prefixFile)\n\t\tset_property(TARGET ${_target} PROPERTY COTIRE_${_language}_PREFIX_HEADER \"${_prefixFile}\")\n\t\tif (_targetUsePCH AND _pchFile)\n\t\t\tset_property(TARGET ${_target} PROPERTY COTIRE_${_language}_PRECOMPILED_HEADER \"${_pchFile}\")\n\t\tendif()\n\tendif()\n\tset (${_cmdsVar} ${_cmds} PARENT_SCOPE)\nendfunction()\n\nfunction (cotire_setup_clean_target _target)\n\tset (_cleanTargetName \"${_target}${COTIRE_CLEAN_TARGET_SUFFIX}\")\n\tif (NOT TARGET \"${_cleanTargetName}\")\n\t\tcotire_set_cmd_to_prologue(_cmds)\n\t\tget_filename_component(_outputDir \"${CMAKE_CURRENT_BINARY_DIR}/${CMAKE_CFG_INTDIR}\" ABSOLUTE)\n\t\tlist (APPEND _cmds -P \"${COTIRE_CMAKE_MODULE_FILE}\" \"cleanup\" \"${_outputDir}\" \"${COTIRE_INTDIR}\" \"${_target}\")\n\t\tadd_custom_target(${_cleanTargetName} COMMAND ${_cmds} WORKING_DIRECTORY \"${CMAKE_BINARY_DIR}\"\n\t\t\tCOMMENT \"Cleaning up target ${_target} cotire generated files\" VERBATIM)\n\t\tcotire_init_target(\"${_cleanTargetName}\")\n\tendif()\nendfunction()\n\nfunction (cotire_setup_pch_target _languages _configurations _target)\n\tif (\"${CMAKE_GENERATOR}\" MATCHES \"Makefiles|Ninja\")\n\t\t# for makefile based generators, we add a custom target to trigger the generation of the cotire related files\n\t\tset (_dependsFiles \"\")\n\t\tforeach (_language ${_languages})\n\t\t\tset (_props COTIRE_${_language}_PREFIX_HEADER COTIRE_${_language}_UNITY_SOURCE)\n\t\t\tif (NOT CMAKE_${_language}_COMPILER_ID MATCHES \"MSVC|Intel\")\n\t\t\t\t# Visual Studio and Intel only create precompiled header as a side effect\n\t\t\t\tlist (INSERT _props 0 COTIRE_${_language}_PRECOMPILED_HEADER)\n\t\t\tendif()\n\t\t\tcotire_get_first_set_property_value(_dependsFile TARGET ${_target} ${_props})\n\t\t\tif (_dependsFile)\n\t\t\t\tlist (APPEND _dependsFiles \"${_dependsFile}\")\n\t\t\tendif()\n\t\tendforeach()\n\t\tif (_dependsFiles)\n\t\t\tset (_pchTargetName \"${_target}${COTIRE_PCH_TARGET_SUFFIX}\")\n\t\t\tadd_custom_target(\"${_pchTargetName}\" DEPENDS ${_dependsFiles})\n\t\t\tcotire_init_target(\"${_pchTargetName}\")\n\t\t\tcotire_add_to_pch_all_target(${_pchTargetName})\n\t\tendif()\n\telse()\n\t\t# for other generators, we add the \"clean all\" target to clean up the precompiled header\n\t\tcotire_setup_clean_all_target()\n\tendif()\nendfunction()\n\nfunction (cotire_setup_unity_build_target _languages _configurations _targetSourceDir _target)\n\tget_target_property(_unityTargetName ${_target} COTIRE_UNITY_TARGET_NAME)\n\tif (NOT _unityTargetName)\n\t\tset (_unityTargetName \"${_target}${COTIRE_UNITY_BUILD_TARGET_SUFFIX}\")\n\tendif()\n\t# determine unity target sub type\n\tget_target_property(_targetType ${_target} TYPE)\n\tif (\"${_targetType}\" STREQUAL \"EXECUTABLE\")\n\t\tset (_unityTargetSubType \"\")\n\telseif (_targetType MATCHES \"(STATIC|SHARED|MODULE|OBJECT)_LIBRARY\")\n\t\tset (_unityTargetSubType \"${CMAKE_MATCH_1}\")\n\telse()\n\t\tmessage (WARNING \"cotire: target ${_target} has unknown target type ${_targetType}.\")\n\t\treturn()\n\tendif()\n\t# determine unity target sources\n\tget_target_property(_targetSourceFiles ${_target} SOURCES)\n\tset (_unityTargetSources ${_targetSourceFiles})\n\tforeach (_language ${_languages})\n\t\tget_property(_unityFiles TARGET ${_target} PROPERTY COTIRE_${_language}_UNITY_SOURCE)\n\t\tif (_unityFiles)\n\t\t\t# remove source files that are included in the unity source\n\t\t\tset (_sourceFiles \"\")\n\t\t\tset (_excludedSources \"\")\n\t\t\tset (_cotiredSources \"\")\n\t\t\tcotire_filter_language_source_files(${_language} _sourceFiles _excludedSources _cotiredSources ${_targetSourceFiles})\n\t\t\tif (_sourceFiles OR _cotiredSources)\n\t\t\t\tlist (REMOVE_ITEM _unityTargetSources ${_sourceFiles} ${_cotiredSources})\n\t\t\tendif()\n\t\t\t# if cotire is applied to a target which has not been added in the current source dir,\n\t\t\t# non-existing files cannot be referenced from the unity build target (this is a CMake restriction)\n\t\t\tif (NOT \"${_targetSourceDir}\" STREQUAL \"${CMAKE_CURRENT_SOURCE_DIR}\")\n\t\t\t\tset (_nonExistingFiles \"\")\n\t\t\t\tforeach (_file ${_unityTargetSources})\n\t\t\t\t\tif (NOT EXISTS \"${_file}\")\n\t\t\t\t\t\tlist (APPEND _nonExistingFiles \"${_file}\")\n\t\t\t\t\tendif()\n\t\t\t\tendforeach()\n\t\t\t\tif (_nonExistingFiles)\n\t\t\t\t\tif (COTIRE_VERBOSE)\n\t\t\t\t\t\tmessage (STATUS \"removing non-existing ${_nonExistingFiles} from ${_unityTargetName}\")\n\t\t\t\t\tendif()\n\t\t\t\t\tlist (REMOVE_ITEM _unityTargetSources ${_nonExistingFiles})\n\t\t\t\tendif()\n\t\t\tendif()\n\t\t\t# add unity source files instead\n\t\t\tlist (APPEND _unityTargetSources ${_unityFiles})\n\t\tendif()\n\tendforeach()\n\tif (COTIRE_DEBUG)\n\t\tmessage (STATUS \"add ${_targetType} ${_unityTargetName} ${_unityTargetSubType} EXCLUDE_FROM_ALL ${_unityTargetSources}\")\n\tendif()\n\t# generate unity target\n\tif (\"${_targetType}\" STREQUAL \"EXECUTABLE\")\n\t\tadd_executable(${_unityTargetName} ${_unityTargetSubType} EXCLUDE_FROM_ALL ${_unityTargetSources})\n\telse()\n\t\tadd_library(${_unityTargetName} ${_unityTargetSubType} EXCLUDE_FROM_ALL ${_unityTargetSources})\n\tendif()\n\tset (_outputDirProperties\n\t\tARCHIVE_OUTPUT_DIRECTORY ARCHIVE_OUTPUT_DIRECTORY_<CONFIG>\n\t\tLIBRARY_OUTPUT_DIRECTORY LIBRARY_OUTPUT_DIRECTORY_<CONFIG>\n\t\tRUNTIME_OUTPUT_DIRECTORY RUNTIME_OUTPUT_DIRECTORY_<CONFIG>)\n\t# copy output location properties\n\tif (COTIRE_UNITY_OUTPUT_DIRECTORY)\n\t\tset (_setDefaultOutputDir TRUE)\n\t\tif (IS_ABSOLUTE \"${COTIRE_UNITY_OUTPUT_DIRECTORY}\")\n\t\t\tset (_outputDir \"${COTIRE_UNITY_OUTPUT_DIRECTORY}\")\n\t\telse()\n\t\t\tcotire_copy_set_properites(\"${_configurations}\" TARGET ${_target} ${_unityTargetName} ${_outputDirProperties})\n\t\t\tcotire_resolve_config_properites(\"${_configurations}\" _properties ${_outputDirProperties})\n\t\t\tforeach (_property ${_properties})\n\t\t\t\tget_property(_outputDir TARGET ${_target} PROPERTY ${_property})\n\t\t\t\tif (_outputDir)\n\t\t\t\t\tget_filename_component(_outputDir \"${_outputDir}/${COTIRE_UNITY_OUTPUT_DIRECTORY}\" ABSOLUTE)\n\t\t\t\t\tset_property(TARGET ${_unityTargetName} PROPERTY ${_property} \"${_outputDir}\")\n\t\t\t\t\tset (_setDefaultOutputDir FALSE)\n\t\t\t\tendif()\n\t\t\tendforeach()\n\t\t\tif (_setDefaultOutputDir)\n\t\t\t\tget_filename_component(_outputDir \"${CMAKE_CURRENT_BINARY_DIR}/${COTIRE_UNITY_OUTPUT_DIRECTORY}\" ABSOLUTE)\n\t\t\tendif()\n\t\tendif()\n\t\tif (_setDefaultOutputDir)\n\t\t\tset_target_properties(${_unityTargetName} PROPERTIES\n\t\t\t\tARCHIVE_OUTPUT_DIRECTORY \"${_outputDir}\"\n\t\t\t\tLIBRARY_OUTPUT_DIRECTORY \"${_outputDir}\"\n\t\t\t\tRUNTIME_OUTPUT_DIRECTORY \"${_outputDir}\")\n\t\tendif()\n\telse()\n\t\tcotire_copy_set_properites(\"${_configurations}\" TARGET ${_target} ${_unityTargetName} ${_outputDirProperties})\n\tendif()\n\t# copy output name\n\tcotire_copy_set_properites(\"${_configurations}\" TARGET ${_target} ${_unityTargetName}\n\t\tARCHIVE_OUTPUT_NAME ARCHIVE_OUTPUT_NAME_<CONFIG>\n\t\tLIBRARY_OUTPUT_NAME LIBRARY_OUTPUT_NAME_<CONFIG>\n\t\tOUTPUT_NAME OUTPUT_NAME_<CONFIG>\n\t\tRUNTIME_OUTPUT_NAME RUNTIME_OUTPUT_NAME_<CONFIG>\n\t\tPREFIX <CONFIG>_POSTFIX SUFFIX\n\t\tIMPORT_PREFIX IMPORT_SUFFIX)\n\t# copy compile stuff\n\tcotire_copy_set_properites(\"${_configurations}\" TARGET ${_target} ${_unityTargetName}\n\t\tCOMPILE_DEFINITIONS COMPILE_DEFINITIONS_<CONFIG>\n\t\tCOMPILE_FLAGS COMPILE_OPTIONS\n\t\tFortran_FORMAT Fortran_MODULE_DIRECTORY\n\t\tINCLUDE_DIRECTORIES\n\t\tINTERPROCEDURAL_OPTIMIZATION INTERPROCEDURAL_OPTIMIZATION_<CONFIG>\n\t\tPOSITION_INDEPENDENT_CODE\n\t\tC_VISIBILITY_PRESET CXX_VISIBILITY_PRESET VISIBILITY_INLINES_HIDDEN)\n\t# copy interface stuff\n\tcotire_copy_set_properites(\"${_configurations}\" TARGET ${_target} ${_unityTargetName}\n\t\tCOMPATIBLE_INTERFACE_BOOL COMPATIBLE_INTERFACE_NUMBER_MAX COMPATIBLE_INTERFACE_NUMBER_MIN COMPATIBLE_INTERFACE_STRING\n\t\tINTERFACE_COMPILE_DEFINITIONS INTERFACE_COMPILE_OPTIONS INTERFACE_INCLUDE_DIRECTORIES\n\t\tINTERFACE_POSITION_INDEPENDENT_CODE INTERFACE_SYSTEM_INCLUDE_DIRECTORIES\n\t\tINTERFACE_AUTOUIC_OPTIONS)\n\t# copy link stuff\n\tcotire_copy_set_properites(\"${_configurations}\" TARGET ${_target} ${_unityTargetName}\n\t\tBUILD_WITH_INSTALL_RPATH INSTALL_RPATH INSTALL_RPATH_USE_LINK_PATH SKIP_BUILD_RPATH\n\t\tLINKER_LANGUAGE LINK_DEPENDS LINK_DEPENDS_NO_SHARED\n\t\tLINK_FLAGS LINK_FLAGS_<CONFIG>\n\t\tLINK_INTERFACE_LIBRARIES LINK_INTERFACE_LIBRARIES_<CONFIG>\n\t\tLINK_INTERFACE_MULTIPLICITY LINK_INTERFACE_MULTIPLICITY_<CONFIG>\n\t\tLINK_SEARCH_START_STATIC LINK_SEARCH_END_STATIC\n\t\tSTATIC_LIBRARY_FLAGS STATIC_LIBRARY_FLAGS_<CONFIG>\n\t\tNO_SONAME SOVERSION VERSION)\n\t# copy Qt stuff\n\tcotire_copy_set_properites(\"${_configurations}\" TARGET ${_target} ${_unityTargetName}\n\t\tAUTOMOC AUTOMOC_MOC_OPTIONS AUTOUIC AUTOUIC_OPTIONS AUTORCC AUTORCC_OPTIONS\n\t\tAUTOGEN_TARGET_DEPENDS)\n\t# copy cmake stuff\n\tcotire_copy_set_properites(\"${_configurations}\" TARGET ${_target} ${_unityTargetName}\n\t\tIMPLICIT_DEPENDS_INCLUDE_TRANSFORM RULE_LAUNCH_COMPILE RULE_LAUNCH_CUSTOM RULE_LAUNCH_LINK)\n\t# copy Apple platform specific stuff\n\tcotire_copy_set_properites(\"${_configurations}\" TARGET ${_target} ${_unityTargetName}\n\t\tBUNDLE BUNDLE_EXTENSION FRAMEWORK INSTALL_NAME_DIR MACOSX_BUNDLE MACOSX_BUNDLE_INFO_PLIST MACOSX_FRAMEWORK_INFO_PLIST\n\t\tMACOSX_RPATH OSX_ARCHITECTURES OSX_ARCHITECTURES_<CONFIG> PRIVATE_HEADER PUBLIC_HEADER RESOURCE)\n\t# copy Windows platform specific stuff\n\tcotire_copy_set_properites(\"${_configurations}\" TARGET ${_target} ${_unityTargetName}\n\t\tGNUtoMS\n\t\tPDB_NAME PDB_NAME_<CONFIG> PDB_OUTPUT_DIRECTORY PDB_OUTPUT_DIRECTORY_<CONFIG>\n\t\tVS_DOTNET_REFERENCES VS_GLOBAL_KEYWORD VS_GLOBAL_PROJECT_TYPES VS_GLOBAL_ROOTNAMESPACE VS_KEYWORD\n\t\tVS_SCC_AUXPATH VS_SCC_LOCALPATH VS_SCC_PROJECTNAME VS_SCC_PROVIDER\n\t\tVS_WINRT_EXTENSIONS VS_WINRT_REFERENCES WIN32_EXECUTABLE)\n\t# use output name from original target\n\tget_target_property(_targetOutputName ${_unityTargetName} OUTPUT_NAME)\n\tif (NOT _targetOutputName)\n\t\tset_property(TARGET ${_unityTargetName} PROPERTY OUTPUT_NAME \"${_target}\")\n\tendif()\n\t# use export symbol from original target\n\tcotire_get_target_export_symbol(\"${_target}\" _defineSymbol)\n\tif (_defineSymbol)\n\t\tset_property(TARGET ${_unityTargetName} PROPERTY DEFINE_SYMBOL \"${_defineSymbol}\")\n\t\tif (\"${_targetType}\" STREQUAL \"EXECUTABLE\")\n\t\t\tset_property(TARGET ${_unityTargetName} PROPERTY ENABLE_EXPORTS TRUE)\n\t\tendif()\n\tendif()\n\tcotire_init_target(${_unityTargetName})\n\tcotire_add_to_unity_all_target(${_unityTargetName})\n\tset_property(TARGET ${_target} PROPERTY COTIRE_UNITY_TARGET_NAME \"${_unityTargetName}\")\nendfunction(cotire_setup_unity_build_target)\n\nfunction (cotire_target _target)\n\tset(_options \"\")\n\tset(_oneValueArgs SOURCE_DIR BINARY_DIR)\n\tset(_multiValueArgs LANGUAGES CONFIGURATIONS)\n\tcmake_parse_arguments(_option \"${_options}\" \"${_oneValueArgs}\" \"${_multiValueArgs}\" ${ARGN})\n\tif (NOT _option_SOURCE_DIR)\n\t\tset (_option_SOURCE_DIR \"${CMAKE_CURRENT_SOURCE_DIR}\")\n\tendif()\n\tif (NOT _option_BINARY_DIR)\n\t\tset (_option_BINARY_DIR \"${CMAKE_CURRENT_BINARY_DIR}\")\n\tendif()\n\tif (NOT _option_LANGUAGES)\n\t\tget_property (_option_LANGUAGES GLOBAL PROPERTY ENABLED_LANGUAGES)\n\tendif()\n\tif (NOT _option_CONFIGURATIONS)\n\t\tcotire_get_configuration_types(_option_CONFIGURATIONS)\n\tendif()\n\t# trivial checks\n\tget_target_property(_imported ${_target} IMPORTED)\n\tif (_imported)\n\t\tmessage (WARNING \"cotire: imported target ${_target} cannot be cotired.\")\n\t\treturn()\n\tendif()\n\t# resolve alias\n\tget_target_property(_aliasName ${_target} ALIASED_TARGET)\n\tif (_aliasName)\n\t\tif (COTIRE_DEBUG)\n\t\t\tmessage (STATUS \"${_target} is an alias. Applying cotire to aliased target ${_aliasName} instead.\")\n\t\tendif()\n\t\tset (_target ${_aliasName})\n\tendif()\n\t# check if target needs to be cotired for build type\n\t# when using configuration types, the test is performed at build time\n\tcotire_init_cotire_target_properties(${_target})\n\tif (NOT CMAKE_CONFIGURATION_TYPES)\n\t\tif (CMAKE_BUILD_TYPE)\n\t\t\tlist (FIND _option_CONFIGURATIONS \"${CMAKE_BUILD_TYPE}\" _index)\n\t\telse()\n\t\t\tlist (FIND _option_CONFIGURATIONS \"None\" _index)\n\t\tendif()\n\t\tif (_index EQUAL -1)\n\t\t\tif (COTIRE_DEBUG)\n\t\t\t\tmessage (STATUS \"CMAKE_BUILD_TYPE=${CMAKE_BUILD_TYPE} not cotired (${_option_CONFIGURATIONS})\")\n\t\t\tendif()\n\t\t\treturn()\n\t\tendif()\n\tendif()\n\t# choose languages that apply to the target\n\tcotire_choose_target_languages(\"${_option_SOURCE_DIR}\" \"${_target}\" _targetLanguages _wholeTarget ${_option_LANGUAGES})\n\tif (NOT _targetLanguages)\n\t\treturn()\n\tendif()\n\tset (_cmds \"\")\n\tforeach (_language ${_targetLanguages})\n\t\tcotire_process_target_language(\"${_language}\" \"${_option_CONFIGURATIONS}\"\n\t\t\t\"${_option_SOURCE_DIR}\" \"${_option_BINARY_DIR}\" ${_target} ${_wholeTarget} _cmd)\n\t\tif (_cmd)\n\t\t\tlist (APPEND _cmds ${_cmd})\n\t\tendif()\n\tendforeach()\n\tget_target_property(_targetAddSCU ${_target} COTIRE_ADD_UNITY_BUILD)\n\tif (_targetAddSCU)\n\t\tcotire_setup_unity_build_target(\"${_targetLanguages}\" \"${_option_CONFIGURATIONS}\" \"${_option_SOURCE_DIR}\" ${_target})\n\tendif()\n\tget_target_property(_targetUsePCH ${_target} COTIRE_ENABLE_PRECOMPILED_HEADER)\n\tif (_targetUsePCH)\n\t\tcotire_setup_target_pch_usage(\"${_targetLanguages}\" \"${_option_SOURCE_DIR}\" ${_target} ${_wholeTarget} ${_cmds})\n\t\tcotire_setup_pch_target(\"${_targetLanguages}\" \"${_option_CONFIGURATIONS}\" ${_target})\n\tendif()\n\tget_target_property(_targetAddCleanTarget ${_target} COTIRE_ADD_CLEAN)\n\tif (_targetAddCleanTarget)\n\t\tcotire_setup_clean_target(${_target})\n\tendif()\nendfunction(cotire_target)\n\nfunction (cotire_map_libraries _strategy _mappedLibrariesVar)\n\tset (_mappedLibraries \"\")\n\tforeach (_library ${ARGN})\n\t\tif (TARGET \"${_library}\" AND \"${_strategy}\" MATCHES \"COPY_UNITY\")\n\t\t\t# use target's corresponding unity target, if available\n\t\t\tget_target_property(_libraryUnityTargetName ${_library} COTIRE_UNITY_TARGET_NAME)\n\t\t\tif (TARGET \"${_libraryUnityTargetName}\")\n\t\t\t\tlist (APPEND _mappedLibraries \"${_libraryUnityTargetName}\")\n\t\t\telse()\n\t\t\t\tlist (APPEND _mappedLibraries \"${_library}\")\n\t\t\tendif()\n\t\telse()\n\t\t\tlist (APPEND _mappedLibraries \"${_library}\")\n\t\tendif()\n\tendforeach()\n\tlist (REMOVE_DUPLICATES _mappedLibraries)\n\tset (${_mappedLibrariesVar} ${_mappedLibraries} PARENT_SCOPE)\nendfunction()\n\nfunction (cotire_target_link_libraries _target)\n\tget_target_property(_unityTargetName ${_target} COTIRE_UNITY_TARGET_NAME)\n\tif (TARGET \"${_unityTargetName}\")\n\t\tget_target_property(_linkLibrariesStrategy ${_target} COTIRE_UNITY_LINK_LIBRARIES_INIT)\n\t\tif (COTIRE_DEBUG)\n\t\t\tmessage (STATUS \"unity target ${_unityTargetName} link strategy: ${_linkLibrariesStrategy}\")\n\t\tendif()\n\t\tif (\"${_linkLibrariesStrategy}\" MATCHES \"^(COPY|COPY_UNITY)$\")\n\t\t\tif (CMAKE_VERSION VERSION_LESS \"2.8.11\")\n\t\t\t\tmessage (WARNING \"cotire: unity target link strategy ${_linkLibrariesStrategy} requires CMake 2.8.11 or later. Defaulting to NONE for ${_target}.\")\n\t\t\telse()\n\t\t\t\tset (_unityLinkLibraries \"\")\n\t\t\t\tget_target_property(_linkLibraries ${_target} LINK_LIBRARIES)\n\t\t\t\tif (_linkLibraries)\n\t\t\t\t\tlist (APPEND _unityLinkLibraries ${_linkLibraries})\n\t\t\t\tendif()\n\t\t\t\tget_target_property(_interfaceLinkLibraries ${_target} INTERFACE_LINK_LIBRARIES)\n\t\t\t\tif (_interfaceLinkLibraries)\n\t\t\t\t\tlist (APPEND _unityLinkLibraries ${_interfaceLinkLibraries})\n\t\t\t\tendif()\n\t\t\t\tcotire_map_libraries(\"${_linkLibrariesStrategy}\" _unityLinkLibraries ${_unityLinkLibraries})\n\t\t\t\tif (COTIRE_DEBUG)\n\t\t\t\t\tmessage (STATUS \"unity target ${_unityTargetName} libraries: ${_unityLinkLibraries}\")\n\t\t\t\tendif()\n\t\t\t\tif (_unityLinkLibraries)\n\t\t\t\t\ttarget_link_libraries(${_unityTargetName} ${_unityLinkLibraries})\n\t\t\t\tendif()\n\t\t\tendif()\n\t\tendif()\n\tendif()\nendfunction(cotire_target_link_libraries)\n\nfunction (cotire_cleanup _binaryDir _cotireIntermediateDirName _targetName)\n\tif (_targetName)\n\t\tfile (GLOB_RECURSE _cotireFiles \"${_binaryDir}/${_targetName}*.*\")\n\telse()\n\t\tfile (GLOB_RECURSE _cotireFiles \"${_binaryDir}/*.*\")\n\tendif()\n\t# filter files in intermediate directory\n\tset (_filesToRemove \"\")\n\tforeach (_file ${_cotireFiles})\n\t\tget_filename_component(_dir \"${_file}\" PATH)\n\t\tget_filename_component(_dirName \"${_dir}\" NAME)\n\t\tif (\"${_dirName}\" STREQUAL \"${_cotireIntermediateDirName}\")\n\t\t\tlist (APPEND _filesToRemove \"${_file}\")\n\t\tendif()\n\tendforeach()\n\tif (_filesToRemove)\n\t\tif (COTIRE_VERBOSE)\n\t\t\tmessage (STATUS \"removing ${_filesToRemove}\")\n\t\tendif()\n\t\tfile (REMOVE ${_filesToRemove})\n\tendif()\nendfunction()\n\nfunction (cotire_init_target _targetName)\n\tif (COTIRE_TARGETS_FOLDER)\n\t\tset_target_properties(${_targetName} PROPERTIES FOLDER \"${COTIRE_TARGETS_FOLDER}\")\n\tendif()\n\tif (MSVC_IDE)\n\t\tset_target_properties(${_targetName} PROPERTIES EXCLUDE_FROM_DEFAULT_BUILD TRUE)\n\tendif()\nendfunction()\n\nfunction (cotire_add_to_pch_all_target _pchTargetName)\n\tset (_targetName \"${COTIRE_PCH_ALL_TARGET_NAME}\")\n\tif (NOT TARGET \"${_targetName}\")\n\t\tadd_custom_target(\"${_targetName}\" WORKING_DIRECTORY \"${CMAKE_BINARY_DIR}\" VERBATIM)\n\t\tcotire_init_target(\"${_targetName}\")\n\tendif()\n\tcotire_setup_clean_all_target()\n\tadd_dependencies(${_targetName} ${_pchTargetName})\nendfunction()\n\nfunction (cotire_add_to_unity_all_target _unityTargetName)\n\tset (_targetName \"${COTIRE_UNITY_BUILD_ALL_TARGET_NAME}\")\n\tif (NOT TARGET \"${_targetName}\")\n\t\tadd_custom_target(\"${_targetName}\" WORKING_DIRECTORY \"${CMAKE_BINARY_DIR}\" VERBATIM)\n\t\tcotire_init_target(\"${_targetName}\")\n\tendif()\n\tcotire_setup_clean_all_target()\n\tadd_dependencies(${_targetName} ${_unityTargetName})\nendfunction()\n\nfunction (cotire_setup_clean_all_target)\n\tset (_targetName \"${COTIRE_CLEAN_ALL_TARGET_NAME}\")\n\tif (NOT TARGET \"${_targetName}\")\n\t\tcotire_set_cmd_to_prologue(_cmds)\n\t\tlist (APPEND _cmds -P \"${COTIRE_CMAKE_MODULE_FILE}\" \"cleanup\" \"${CMAKE_BINARY_DIR}\" \"${COTIRE_INTDIR}\")\n\t\tadd_custom_target(${_targetName} COMMAND ${_cmds}\n\t\t\tWORKING_DIRECTORY \"${CMAKE_BINARY_DIR}\" COMMENT \"Cleaning up all cotire generated files\" VERBATIM)\n\t\tcotire_init_target(\"${_targetName}\")\n\tendif()\nendfunction()\n\nfunction (cotire)\n\tset(_options \"\")\n\tset(_oneValueArgs SOURCE_DIR BINARY_DIR)\n\tset(_multiValueArgs LANGUAGES CONFIGURATIONS)\n\tcmake_parse_arguments(_option \"${_options}\" \"${_oneValueArgs}\" \"${_multiValueArgs}\" ${ARGN})\n\tset (_targets ${_option_UNPARSED_ARGUMENTS})\n\tif (NOT _option_SOURCE_DIR)\n\t\tset (_option_SOURCE_DIR \"${CMAKE_CURRENT_SOURCE_DIR}\")\n\tendif()\n\tif (NOT _option_BINARY_DIR)\n\t\tset (_option_BINARY_DIR \"${CMAKE_CURRENT_BINARY_DIR}\")\n\tendif()\n\tforeach (_target ${_targets})\n\t\tif (TARGET ${_target})\n\t\t\tcotire_target(${_target} LANGUAGES ${_option_LANGUAGES} CONFIGURATIONS ${_option_CONFIGURATIONS}\n\t\t\t\tSOURCE_DIR \"${_option_SOURCE_DIR}\" BINARY_DIR \"${_option_BINARY_DIR}\")\n\t\telse()\n\t\t\tmessage (WARNING \"cotire: ${_target} is not a target.\")\n\t\tendif()\n\tendforeach()\n\tforeach (_target ${_targets})\n\t\tif (TARGET ${_target})\n\t\t\tcotire_target_link_libraries(${_target})\n\t\tendif()\n\tendforeach()\nendfunction()\n\nif (CMAKE_SCRIPT_MODE_FILE)\n\n\t# cotire is being run in script mode\n\t# locate -P on command args\n\tset (COTIRE_ARGC -1)\n\tforeach (_index RANGE ${CMAKE_ARGC})\n\t\tif (COTIRE_ARGC GREATER -1)\n\t\t\tset (COTIRE_ARGV${COTIRE_ARGC} \"${CMAKE_ARGV${_index}}\")\n\t\t\tmath (EXPR COTIRE_ARGC \"${COTIRE_ARGC} + 1\")\n\t\telseif (\"${CMAKE_ARGV${_index}}\" STREQUAL \"-P\")\n\t\t\tset (COTIRE_ARGC 0)\n\t\tendif()\n\tendforeach()\n\n\t# include target script if available\n\tif (\"${COTIRE_ARGV2}\" MATCHES \"\\\\.cmake$\")\n\t\t# the included target scripts sets up additional variables relating to the target (e.g., COTIRE_TARGET_SOURCES)\n\t\tinclude(\"${COTIRE_ARGV2}\")\n\tendif()\n\n\tif (COTIRE_DEBUG)\n\t\tmessage (STATUS \"${COTIRE_ARGV0} ${COTIRE_ARGV1} ${COTIRE_ARGV2} ${COTIRE_ARGV3} ${COTIRE_ARGV4} ${COTIRE_ARGV5}\")\n\tendif()\n\n\tif (WIN32)\n\t\t# for MSVC, compiler IDs may not always be set correctly\n\t\tif (MSVC)\n\t\t\tset (CMAKE_C_COMPILER_ID \"MSVC\")\n\t\t\tset (CMAKE_CXX_COMPILER_ID \"MSVC\")\n\t\tendif()\n\tendif()\n\n\tif (NOT COTIRE_BUILD_TYPE)\n\t\tset (COTIRE_BUILD_TYPE \"None\")\n\tendif()\n\tstring (TOUPPER \"${COTIRE_BUILD_TYPE}\" _upperConfig)\n\tset (_includeDirs ${COTIRE_TARGET_INCLUDE_DIRECTORIES_${_upperConfig}})\n\tset (_systemIncludeDirs ${COTIRE_TARGET_SYSTEM_INCLUDE_DIRECTORIES_${_upperConfig}})\n\tset (_compileDefinitions ${COTIRE_TARGET_COMPILE_DEFINITIONS_${_upperConfig}})\n\tset (_compileFlags ${COTIRE_TARGET_COMPILE_FLAGS_${_upperConfig}})\n\t# check if target has been cotired for actual build type COTIRE_BUILD_TYPE\n\tlist (FIND COTIRE_TARGET_CONFIGURATION_TYPES \"${COTIRE_BUILD_TYPE}\" _index)\n\tif (_index GREATER -1)\n\t\tset (_sources ${COTIRE_TARGET_SOURCES})\n\t\tset (_sourceLocations ${COTIRE_TARGET_SOURCE_LOCATIONS})\n\t\tset (_sourcesDefinitions ${COTIRE_TARGET_SOURCES_COMPILE_DEFINITIONS_${_upperConfig}})\n\telse()\n\t\tif (COTIRE_DEBUG)\n\t\t\tmessage (STATUS \"COTIRE_BUILD_TYPE=${COTIRE_BUILD_TYPE} not cotired (${COTIRE_TARGET_CONFIGURATION_TYPES})\")\n\t\tendif()\n\t\tset (_sources \"\")\n\t\tset (_sourceLocations \"\")\n\t\tset (_sourcesDefinitions \"\")\n\tendif()\n\tset (_targetPreUndefs ${COTIRE_TARGET_PRE_UNDEFS})\n\tset (_targetPostUndefs ${COTIRE_TARGET_POST_UNDEFS})\n\tset (_sourcesPreUndefs ${COTIRE_TARGET_SOURCES_PRE_UNDEFS})\n\tset (_sourcesPostUndefs ${COTIRE_TARGET_SOURCES_POST_UNDEFS})\n\n\tif (\"${COTIRE_ARGV1}\" STREQUAL \"unity\")\n\n\t\tif (XCODE)\n\t\t\t# executing pre-build action under Xcode, check dependency on target script\n\t\t\tset (_dependsOption DEPENDS \"${COTIRE_ARGV2}\")\n\t\telse()\n\t\t\t# executing custom command, no need to re-check for dependencies\n\t\t\tset (_dependsOption \"\")\n\t\tendif()\n\n\t\tcotire_select_unity_source_files(\"${COTIRE_ARGV3}\" _sources ${_sources})\n\t\tcotire_select_unity_source_files(\"${COTIRE_ARGV3}\" _sourceLocations ${_sourceLocations})\n\n\t\tcotire_generate_unity_source(\n\t\t\t\"${COTIRE_ARGV3}\" ${_sources}\n\t\t\tLANGUAGE \"${COTIRE_TARGET_LANGUAGE}\"\n\t\t\tSOURCE_LOCATIONS ${_sourceLocations}\n\t\t\tSOURCES_COMPILE_DEFINITIONS ${_sourcesDefinitions}\n\t\t\tPRE_UNDEFS ${_targetPreUndefs}\n\t\t\tPOST_UNDEFS ${_targetPostUndefs}\n\t\t\tSOURCES_PRE_UNDEFS ${_sourcesPreUndefs}\n\t\t\tSOURCES_POST_UNDEFS ${_sourcesPostUndefs}\n\t\t\t${_dependsOption})\n\n\telseif (\"${COTIRE_ARGV1}\" STREQUAL \"prefix\")\n\n\t\tif (XCODE)\n\t\t\t# executing pre-build action under Xcode, check dependency on unity file and prefix dependencies\n\t\t\tset (_dependsOption DEPENDS \"${COTIRE_ARGV4}\" ${COTIRE_TARGET_PREFIX_DEPENDS})\n\t\telse()\n\t\t\t# executing custom command, no need to re-check for dependencies\n\t\t\tset (_dependsOption \"\")\n\t\tendif()\n\n\t\tset (_files \"\")\n\t\tforeach (_index RANGE 4 ${COTIRE_ARGC})\n\t\t\tif (COTIRE_ARGV${_index})\n\t\t\t\tlist (APPEND _files \"${COTIRE_ARGV${_index}}\")\n\t\t\tendif()\n\t\tendforeach()\n\n\t\tcotire_generate_prefix_header(\n\t\t\t\"${COTIRE_ARGV3}\" ${_files}\n\t\t\tCOMPILER_EXECUTABLE \"${CMAKE_${COTIRE_TARGET_LANGUAGE}_COMPILER}\"\n\t\t\tCOMPILER_ARG1 ${CMAKE_${COTIRE_TARGET_LANGUAGE}_COMPILER_ARG1}\n\t\t\tCOMPILER_ID \"${CMAKE_${COTIRE_TARGET_LANGUAGE}_COMPILER_ID}\"\n\t\t\tCOMPILER_VERSION \"${COTIRE_${COTIRE_TARGET_LANGUAGE}_COMPILER_VERSION}\"\n\t\t\tLANGUAGE \"${COTIRE_TARGET_LANGUAGE}\"\n\t\t\tIGNORE_PATH \"${COTIRE_TARGET_IGNORE_PATH};${COTIRE_ADDITIONAL_PREFIX_HEADER_IGNORE_PATH}\"\n\t\t\tINCLUDE_PATH ${COTIRE_TARGET_INCLUDE_PATH}\n\t\t\tIGNORE_EXTENSIONS \"${CMAKE_${COTIRE_TARGET_LANGUAGE}_SOURCE_FILE_EXTENSIONS};${COTIRE_ADDITIONAL_PREFIX_HEADER_IGNORE_EXTENSIONS}\"\n\t\t\tINCLUDE_SYSTEM_FLAG \"${COTIRE_INCLUDE_SYSTEM_FLAG}\"\n\t\t\tINCLUDE_DIRECTORIES ${_includeDirs}\n\t\t\tSYSTEM_INCLUDE_DIRECTORIES ${_systemIncludeDirs}\n\t\t\tCOMPILE_DEFINITIONS ${_compileDefinitions}\n\t\t\tCOMPILE_FLAGS ${_compileFlags}\n\t\t\t${_dependsOption})\n\n\telseif (\"${COTIRE_ARGV1}\" STREQUAL \"precompile\")\n\n\t\tset (_files \"\")\n\t\tforeach (_index RANGE 5 ${COTIRE_ARGC})\n\t\t\tif (COTIRE_ARGV${_index})\n\t\t\t\tlist (APPEND _files \"${COTIRE_ARGV${_index}}\")\n\t\t\tendif()\n\t\tendforeach()\n\n\t\tcotire_precompile_prefix_header(\n\t\t\t\"${COTIRE_ARGV3}\" \"${COTIRE_ARGV4}\" \"${COTIRE_ARGV5}\"\n\t\t\tCOMPILER_EXECUTABLE \"${CMAKE_${COTIRE_TARGET_LANGUAGE}_COMPILER}\"\n\t\t\tCOMPILER_ARG1 ${CMAKE_${COTIRE_TARGET_LANGUAGE}_COMPILER_ARG1}\n\t\t\tCOMPILER_ID \"${CMAKE_${COTIRE_TARGET_LANGUAGE}_COMPILER_ID}\"\n\t\t\tCOMPILER_VERSION \"${COTIRE_${COTIRE_TARGET_LANGUAGE}_COMPILER_VERSION}\"\n\t\t\tLANGUAGE \"${COTIRE_TARGET_LANGUAGE}\"\n\t\t\tINCLUDE_SYSTEM_FLAG \"${COTIRE_INCLUDE_SYSTEM_FLAG}\"\n\t\t\tINCLUDE_DIRECTORIES ${_includeDirs}\n\t\t\tSYSTEM_INCLUDE_DIRECTORIES ${_systemIncludeDirs}\n\t\t\tCOMPILE_DEFINITIONS ${_compileDefinitions}\n\t\t\tCOMPILE_FLAGS ${_compileFlags})\n\n\telseif (\"${COTIRE_ARGV1}\" STREQUAL \"combine\")\n\n\t\tif (COTIRE_TARGET_LANGUAGE)\n\t\t\tset (_startIndex 3)\n\t\telse()\n\t\t\tset (_startIndex 2)\n\t\tendif()\n\t\tset (_files \"\")\n\t\tforeach (_index RANGE ${_startIndex} ${COTIRE_ARGC})\n\t\t\tif (COTIRE_ARGV${_index})\n\t\t\t\tlist (APPEND _files \"${COTIRE_ARGV${_index}}\")\n\t\t\tendif()\n\t\tendforeach()\n\n\t\tif (COTIRE_TARGET_LANGUAGE)\n\t\t\tcotire_generate_unity_source(${_files} LANGUAGE \"${COTIRE_TARGET_LANGUAGE}\")\n\t\telse()\n\t\t\tcotire_generate_unity_source(${_files})\n\t\tendif()\n\n\telseif (\"${COTIRE_ARGV1}\" STREQUAL \"cleanup\")\n\n\t\tcotire_cleanup(\"${COTIRE_ARGV2}\" \"${COTIRE_ARGV3}\" \"${COTIRE_ARGV4}\")\n\n\telse()\n\t\tmessage (FATAL_ERROR \"cotire: unknown command \\\"${COTIRE_ARGV1}\\\".\")\n\tendif()\n\nelse()\n\n\t# cotire is being run in include mode\n\t# set up all variable and property definitions\n\n\tunset (COTIRE_C_COMPILER_VERSION CACHE)\n\tunset (COTIRE_CXX_COMPILER_VERSION CACHE)\n\n\tif (NOT DEFINED COTIRE_DEBUG_INIT)\n\t\tif (DEFINED COTIRE_DEBUG)\n\t\t\tset (COTIRE_DEBUG_INIT ${COTIRE_DEBUG})\n\t\telse()\n\t\t\tset (COTIRE_DEBUG_INIT FALSE)\n\t\tendif()\n\tendif()\n\toption (COTIRE_DEBUG \"Enable cotire debugging output?\" ${COTIRE_DEBUG_INIT})\n\n\tif (NOT DEFINED COTIRE_VERBOSE_INIT)\n\t\tif (DEFINED COTIRE_VERBOSE)\n\t\t\tset (COTIRE_VERBOSE_INIT ${COTIRE_VERBOSE})\n\t\telse()\n\t\t\tset (COTIRE_VERBOSE_INIT FALSE)\n\t\tendif()\n\tendif()\n\toption (COTIRE_VERBOSE \"Enable cotire verbose output?\" ${COTIRE_VERBOSE_INIT})\n\n\tset (COTIRE_ADDITIONAL_PREFIX_HEADER_IGNORE_EXTENSIONS \"inc;inl;ipp\" CACHE STRING\n\t\t\"Ignore headers with the listed file extensions from the generated prefix header.\")\n\n\tset (COTIRE_ADDITIONAL_PREFIX_HEADER_IGNORE_PATH \"\" CACHE STRING\n\t\t\"Ignore headers from these directories when generating the prefix header.\")\n\n\tset (COTIRE_UNITY_SOURCE_EXCLUDE_EXTENSIONS \"m;mm\" CACHE STRING\n\t\t\"Ignore sources with the listed file extensions from the generated unity source.\")\n\n\tset (COTIRE_MINIMUM_NUMBER_OF_TARGET_SOURCES \"3\" CACHE STRING\n\t\t\"Minimum number of sources in target required to enable use of precompiled header.\")\n\n\tif (NOT DEFINED COTIRE_MAXIMUM_NUMBER_OF_UNITY_INCLUDES_INIT)\n\t\tif (DEFINED COTIRE_MAXIMUM_NUMBER_OF_UNITY_INCLUDES)\n\t\t\tset (COTIRE_MAXIMUM_NUMBER_OF_UNITY_INCLUDES_INIT ${COTIRE_MAXIMUM_NUMBER_OF_UNITY_INCLUDES})\n\t\telseif (\"${CMAKE_GENERATOR}\" MATCHES \"JOM|Ninja|Visual Studio\")\n\t\t\t# enable parallelization for generators that run multiple jobs by default\n\t\t\tset (COTIRE_MAXIMUM_NUMBER_OF_UNITY_INCLUDES_INIT \"-j\")\n\t\telse()\n\t\t\tset (COTIRE_MAXIMUM_NUMBER_OF_UNITY_INCLUDES_INIT \"0\")\n\t\tendif()\n\tendif()\n\tset (COTIRE_MAXIMUM_NUMBER_OF_UNITY_INCLUDES \"${COTIRE_MAXIMUM_NUMBER_OF_UNITY_INCLUDES_INIT}\" CACHE STRING\n\t\t\"Maximum number of source files to include in a single unity source file.\")\n\n\tif (NOT COTIRE_PREFIX_HEADER_FILENAME_SUFFIX)\n\t\tset (COTIRE_PREFIX_HEADER_FILENAME_SUFFIX \"_prefix\")\n\tendif()\n\tif (NOT COTIRE_UNITY_SOURCE_FILENAME_SUFFIX)\n\t\tset (COTIRE_UNITY_SOURCE_FILENAME_SUFFIX \"_unity\")\n\tendif()\n\tif (NOT COTIRE_INTDIR)\n\t\tset (COTIRE_INTDIR \"cotire\")\n\tendif()\n\tif (NOT COTIRE_PCH_ALL_TARGET_NAME)\n\t\tset (COTIRE_PCH_ALL_TARGET_NAME \"all_pch\")\n\tendif()\n\tif (NOT COTIRE_UNITY_BUILD_ALL_TARGET_NAME)\n\t\tset (COTIRE_UNITY_BUILD_ALL_TARGET_NAME \"all_unity\")\n\tendif()\n\tif (NOT COTIRE_CLEAN_ALL_TARGET_NAME)\n\t\tset (COTIRE_CLEAN_ALL_TARGET_NAME \"clean_cotire\")\n\tendif()\n\tif (NOT COTIRE_CLEAN_TARGET_SUFFIX)\n\t\tset (COTIRE_CLEAN_TARGET_SUFFIX \"_clean_cotire\")\n\tendif()\n\tif (NOT COTIRE_PCH_TARGET_SUFFIX)\n\t\tset (COTIRE_PCH_TARGET_SUFFIX \"_pch\")\n\tendif()\n\tif (NOT COTIRE_UNITY_BUILD_TARGET_SUFFIX)\n\t\tset (COTIRE_UNITY_BUILD_TARGET_SUFFIX \"_unity\")\n\tendif()\n\tif (NOT DEFINED COTIRE_TARGETS_FOLDER)\n\t\tset (COTIRE_TARGETS_FOLDER \"cotire\")\n\tendif()\n\tif (NOT DEFINED COTIRE_UNITY_OUTPUT_DIRECTORY)\n\t\tif (\"${CMAKE_GENERATOR}\" MATCHES \"Ninja\")\n\t\t\t# generated Ninja build files do not work if the unity target produces the same output file as the cotired target\n\t\t\tset (COTIRE_UNITY_OUTPUT_DIRECTORY \"unity\")\n\t\telse()\n\t\t\tset (COTIRE_UNITY_OUTPUT_DIRECTORY \"\")\n\t\tendif()\n\tendif()\n\n\t# define cotire cache variables\n\n\tdefine_property(\n\t\tCACHED_VARIABLE PROPERTY \"COTIRE_ADDITIONAL_PREFIX_HEADER_IGNORE_PATH\"\n\t\tBRIEF_DOCS \"Ignore headers from these directories when generating the prefix header.\"\n\t\tFULL_DOCS\n\t\t\t\"The variable can be set to a semicolon separated list of include directories.\"\n\t\t\t\"If a header file is found in one of these directories or sub-directories, it will be excluded from the generated prefix header.\"\n\t\t\t\"If not defined, defaults to empty list.\"\n\t)\n\n\tdefine_property(\n\t\tCACHED_VARIABLE PROPERTY \"COTIRE_ADDITIONAL_PREFIX_HEADER_IGNORE_EXTENSIONS\"\n\t\tBRIEF_DOCS \"Ignore includes with the listed file extensions from the generated prefix header.\"\n\t\tFULL_DOCS\n\t\t\t\"The variable can be set to a semicolon separated list of file extensions.\"\n\t\t\t\"If a header file extension matches one in the list, it will be excluded from the generated prefix header.\"\n\t\t\t\"Includes with an extension in CMAKE_<LANG>_SOURCE_FILE_EXTENSIONS are always ignored.\"\n\t\t\t\"If not defined, defaults to inc;inl;ipp.\"\n\t)\n\n\tdefine_property(\n\t\tCACHED_VARIABLE PROPERTY \"COTIRE_UNITY_SOURCE_EXCLUDE_EXTENSIONS\"\n\t\tBRIEF_DOCS \"Exclude sources with the listed file extensions from the generated unity source.\"\n\t\tFULL_DOCS\n\t\t\t\"The variable can be set to a semicolon separated list of file extensions.\"\n\t\t\t\"If a source file extension matches one in the list, it will be excluded from the generated unity source file.\"\n\t\t\t\"Source files with an extension in CMAKE_<LANG>_IGNORE_EXTENSIONS are always excluded.\"\n\t\t\t\"If not defined, defaults to m;mm.\"\n\t)\n\n\tdefine_property(\n\t\tCACHED_VARIABLE PROPERTY \"COTIRE_MINIMUM_NUMBER_OF_TARGET_SOURCES\"\n\t\tBRIEF_DOCS \"Minimum number of sources in target required to enable use of precompiled header.\"\n\t\tFULL_DOCS\n\t\t\t\"The variable can be set to an integer > 0.\"\n\t\t\t\"If a target contains less than that number of source files, cotire will not enable the use of the precompiled header for the target.\"\n\t\t\t\"If not defined, defaults to 3.\"\n\t)\n\n\tdefine_property(\n\t\tCACHED_VARIABLE PROPERTY \"COTIRE_MAXIMUM_NUMBER_OF_UNITY_INCLUDES\"\n\t\tBRIEF_DOCS \"Maximum number of source files to include in a single unity source file.\"\n\t\tFULL_DOCS\n\t\t\t\"This may be set to an integer >= 0.\"\n\t\t\t\"If 0, cotire will only create a single unity source file.\"\n\t\t\t\"If a target contains more than that number of source files, cotire will create multiple unity source files for it.\"\n\t\t\t\"Can be set to \\\"-j\\\" to optimize the count of unity source files for the number of available processor cores.\"\n\t\t\t\"Can be set to \\\"-j jobs\\\" to optimize the number of unity source files for the given number of simultaneous jobs.\"\n\t\t\t\"Is used to initialize the target property COTIRE_UNITY_SOURCE_MAXIMUM_NUMBER_OF_INCLUDES.\"\n\t\t\t\"Defaults to \\\"-j\\\" for the generators Visual Studio, JOM or Ninja. Defaults to 0 otherwise.\"\n\t)\n\n\t# define cotire directory properties\n\n\tdefine_property(\n\t\tDIRECTORY PROPERTY \"COTIRE_ENABLE_PRECOMPILED_HEADER\"\n\t\tBRIEF_DOCS \"Modify build command of cotired targets added in this directory to make use of the generated precompiled header.\"\n\t\tFULL_DOCS\n\t\t\t\"See target property COTIRE_ENABLE_PRECOMPILED_HEADER.\"\n\t)\n\n\tdefine_property(\n\t\tDIRECTORY PROPERTY \"COTIRE_ADD_UNITY_BUILD\"\n\t\tBRIEF_DOCS \"Add a new target that performs a unity build for cotired targets added in this directory.\"\n\t\tFULL_DOCS\n\t\t\t\"See target property COTIRE_ADD_UNITY_BUILD.\"\n\t)\n\n\tdefine_property(\n\t\tDIRECTORY PROPERTY \"COTIRE_ADD_CLEAN\"\n\t\tBRIEF_DOCS \"Add a new target that cleans all cotire generated files for cotired targets added in this directory.\"\n\t\tFULL_DOCS\n\t\t\t\"See target property COTIRE_ADD_CLEAN.\"\n\t)\n\n\tdefine_property(\n\t\tDIRECTORY PROPERTY \"COTIRE_PREFIX_HEADER_IGNORE_PATH\"\n\t\tBRIEF_DOCS \"Ignore headers from these directories when generating the prefix header.\"\n\t\tFULL_DOCS\n\t\t\t\"See target property COTIRE_PREFIX_HEADER_IGNORE_PATH.\"\n\t)\n\n\tdefine_property(\n\t\tDIRECTORY PROPERTY \"COTIRE_PREFIX_HEADER_INCLUDE_PATH\"\n\t\tBRIEF_DOCS \"Honor headers from these directories when generating the prefix header.\"\n\t\tFULL_DOCS\n\t\t\t\"See target property COTIRE_PREFIX_HEADER_INCLUDE_PATH.\"\n\t)\n\n\tdefine_property(\n\t\tDIRECTORY PROPERTY \"COTIRE_UNITY_SOURCE_PRE_UNDEFS\"\n\t\tBRIEF_DOCS \"Preprocessor undefs to place in the generated unity source file before the inclusion of each source file.\"\n\t\tFULL_DOCS\n\t\t\t\"See target property COTIRE_UNITY_SOURCE_PRE_UNDEFS.\"\n\t)\n\n\tdefine_property(\n\t\tDIRECTORY PROPERTY \"COTIRE_UNITY_SOURCE_POST_UNDEFS\"\n\t\tBRIEF_DOCS \"Preprocessor undefs to place in the generated unity source file after the inclusion of each source file.\"\n\t\tFULL_DOCS\n\t\t\t\"See target property COTIRE_UNITY_SOURCE_POST_UNDEFS.\"\n\t)\n\n\tdefine_property(\n\t\tDIRECTORY PROPERTY \"COTIRE_UNITY_SOURCE_MAXIMUM_NUMBER_OF_INCLUDES\"\n\t\tBRIEF_DOCS \"Maximum number of source files to include in a single unity source file.\"\n\t\tFULL_DOCS\n\t\t\t\"See target property COTIRE_UNITY_SOURCE_MAXIMUM_NUMBER_OF_INCLUDES.\"\n\t)\n\n\tdefine_property(\n\t\tDIRECTORY PROPERTY \"COTIRE_UNITY_LINK_LIBRARIES_INIT\"\n\t\tBRIEF_DOCS \"Define strategy for setting up the unity target's link libraries.\"\n\t\tFULL_DOCS\n\t\t\t\"See target property COTIRE_UNITY_LINK_LIBRARIES_INIT.\"\n\t)\n\n\t# define cotire target properties\n\n\tdefine_property(\n\t\tTARGET PROPERTY \"COTIRE_ENABLE_PRECOMPILED_HEADER\" INHERITED\n\t\tBRIEF_DOCS \"Modify this target's build command to make use of the generated precompiled header.\"\n\t\tFULL_DOCS\n\t\t\t\"If this property is set to TRUE, cotire will modify the build command to make use of the generated precompiled header.\"\n\t\t\t\"Irrespective of the value of this property, cotire will setup custom commands to generate the unity source and prefix header for the target.\"\n\t\t\t\"For makefile based generators cotire will also set up a custom target to manually invoke the generation of the precompiled header.\"\n\t\t\t\"The target name will be set to this target's name with the suffix _pch appended.\"\n\t\t\t\"Inherited from directory.\"\n\t\t\t\"Defaults to TRUE.\"\n\t)\n\n\tdefine_property(\n\t\tTARGET PROPERTY \"COTIRE_ADD_UNITY_BUILD\" INHERITED\n\t\tBRIEF_DOCS \"Add a new target that performs a unity build for this target.\"\n\t\tFULL_DOCS\n\t\t\t\"If this property is set to TRUE, cotire creates a new target of the same type that uses the generated unity source file instead of the target sources.\"\n\t\t\t\"Most of the relevant target properties will be copied from this target to the new unity build target.\"\n\t\t\t\"Target dependencies and linked libraries have to be manually set up for the new unity build target.\"\n\t\t\t\"The unity target name will be set to this target's name with the suffix _unity appended.\"\n\t\t\t\"Inherited from directory.\"\n\t\t\t\"Defaults to TRUE.\"\n\t)\n\n\tdefine_property(\n\t\tTARGET PROPERTY \"COTIRE_ADD_CLEAN\" INHERITED\n\t\tBRIEF_DOCS \"Add a new target that cleans all cotire generated files for this target.\"\n\t\tFULL_DOCS\n\t\t\t\"If this property is set to TRUE, cotire creates a new target that clean all files (unity source, prefix header, precompiled header).\"\n\t\t\t\"The clean target name will be set to this target's name with the suffix _clean_cotire appended.\"\n\t\t\t\"Inherited from directory.\"\n\t\t\t\"Defaults to FALSE.\"\n\t)\n\n\tdefine_property(\n\t\tTARGET PROPERTY \"COTIRE_PREFIX_HEADER_IGNORE_PATH\" INHERITED\n\t\tBRIEF_DOCS \"Ignore headers from these directories when generating the prefix header.\"\n\t\tFULL_DOCS\n\t\t\t\"The property can be set to a list of directories.\"\n\t\t\t\"If a header file is found in one of these directories or sub-directories, it will be excluded from the generated prefix header.\"\n\t\t\t\"Inherited from directory.\"\n\t\t\t\"If not set, this property is initialized to \\${CMAKE_SOURCE_DIR};\\${CMAKE_BINARY_DIR}.\"\n\t)\n\n\tdefine_property(\n\t\tTARGET PROPERTY \"COTIRE_PREFIX_HEADER_INCLUDE_PATH\" INHERITED\n\t\tBRIEF_DOCS \"Honor headers from these directories when generating the prefix header.\"\n\t\tFULL_DOCS\n\t\t\t\"The property can be set to a list of directories.\"\n\t\t\t\"If a header file is found in one of these directories or sub-directories, it will be included in the generated prefix header.\"\n\t\t\t\"If a header file is both selected by COTIRE_PREFIX_HEADER_IGNORE_PATH and COTIRE_PREFIX_HEADER_INCLUDE_PATH,\"\n\t\t\t\"the option which yields the closer relative path match wins.\"\n\t\t\t\"Inherited from directory.\"\n\t\t\t\"If not set, this property is initialized to the empty list.\"\n\t)\n\n\tdefine_property(\n\t\tTARGET PROPERTY \"COTIRE_UNITY_SOURCE_PRE_UNDEFS\" INHERITED\n\t\tBRIEF_DOCS \"Preprocessor undefs to place in the generated unity source file before the inclusion of each target source file.\"\n\t\tFULL_DOCS\n\t\t\t\"This may be set to a semicolon-separated list of preprocessor symbols.\"\n\t\t\t\"cotire will add corresponding #undef directives to the generated unit source file before each target source file.\"\n\t\t\t\"Inherited from directory.\"\n\t\t\t\"Defaults to empty string.\"\n\t)\n\n\tdefine_property(\n\t\tTARGET PROPERTY \"COTIRE_UNITY_SOURCE_POST_UNDEFS\" INHERITED\n\t\tBRIEF_DOCS \"Preprocessor undefs to place in the generated unity source file after the inclusion of each target source file.\"\n\t\tFULL_DOCS\n\t\t\t\"This may be set to a semicolon-separated list of preprocessor symbols.\"\n\t\t\t\"cotire will add corresponding #undef directives to the generated unit source file after each target source file.\"\n\t\t\t\"Inherited from directory.\"\n\t\t\t\"Defaults to empty string.\"\n\t)\n\n\tdefine_property(\n\t\tTARGET PROPERTY \"COTIRE_UNITY_SOURCE_MAXIMUM_NUMBER_OF_INCLUDES\" INHERITED\n\t\tBRIEF_DOCS \"Maximum number of source files to include in a single unity source file.\"\n\t\tFULL_DOCS\n\t\t\t\"This may be set to an integer > 0.\"\n\t\t\t\"If a target contains more than that number of source files, cotire will create multiple unity build files for it.\"\n\t\t\t\"If not set, cotire will only create a single unity source file.\"\n\t\t\t\"Inherited from directory.\"\n\t\t\t\"Defaults to empty.\"\n\t)\n\n\tdefine_property(\n\t\tTARGET PROPERTY \"COTIRE_<LANG>_UNITY_SOURCE_INIT\"\n\t\tBRIEF_DOCS \"User provided unity source file to be used instead of the automatically generated one.\"\n\t\tFULL_DOCS\n\t\t\t\"If set, cotire will only add the given file(s) to the generated unity source file.\"\n\t\t\t\"If not set, cotire will add all the target source files to the generated unity source file.\"\n\t\t\t\"The property can be set to a user provided unity source file.\"\n\t\t\t\"Defaults to empty.\"\n\t)\n\n\tdefine_property(\n\t\tTARGET PROPERTY \"COTIRE_<LANG>_PREFIX_HEADER_INIT\"\n\t\tBRIEF_DOCS \"User provided prefix header file to be used instead of the automatically generated one.\"\n\t\tFULL_DOCS\n\t\t\t\"If set, cotire will add the given header file(s) to the generated prefix header file.\"\n\t\t\t\"If not set, cotire will generate a prefix header by tracking the header files included by the unity source file.\"\n\t\t\t\"The property can be set to a user provided prefix header file (e.g., stdafx.h).\"\n\t\t\t\"Defaults to empty.\"\n\t)\n\n\tdefine_property(\n\t\tTARGET PROPERTY \"COTIRE_UNITY_LINK_LIBRARIES_INIT\" INHERITED\n\t\tBRIEF_DOCS \"Define strategy for setting up unity target's link libraries.\"\n\t\tFULL_DOCS\n\t\t\t\"If this property is empty, the generated unity target's link libraries have to be set up manually.\"\n\t\t\t\"If this property is set to COPY, the unity target's link libraries will be copied from this target.\"\n\t\t\t\"If this property is set to COPY_UNITY, the unity target's link libraries will be copied from this target with considering existing unity targets.\"\n\t\t\t\"Inherited from directory.\"\n\t\t\t\"Defaults to empty.\"\n\t)\n\n\tdefine_property(\n\t\tTARGET PROPERTY \"COTIRE_<LANG>_UNITY_SOURCE\"\n\t\tBRIEF_DOCS \"Read-only property. The generated <LANG> unity source file(s).\"\n\t\tFULL_DOCS\n\t\t\t\"cotire sets this property to the path of the generated <LANG> single computation unit source file for the target.\"\n\t\t\t\"Defaults to empty string.\"\n\t)\n\n\tdefine_property(\n\t\tTARGET PROPERTY \"COTIRE_<LANG>_PREFIX_HEADER\"\n\t\tBRIEF_DOCS \"Read-only property. The generated <LANG> prefix header file.\"\n\t\tFULL_DOCS\n\t\t\t\"cotire sets this property to the full path of the generated <LANG> language prefix header for the target.\"\n\t\t\t\"Defaults to empty string.\"\n\t)\n\n\tdefine_property(\n\t\tTARGET PROPERTY \"COTIRE_<LANG>_PRECOMPILED_HEADER\"\n\t\tBRIEF_DOCS \"Read-only property. The generated <LANG> precompiled header file.\"\n\t\tFULL_DOCS\n\t\t\t\"cotire sets this property to the full path of the generated <LANG> language precompiled header binary for the target.\"\n\t\t\t\"Defaults to empty string.\"\n\t)\n\n\tdefine_property(\n\t\tTARGET PROPERTY \"COTIRE_UNITY_TARGET_NAME\"\n\t\tBRIEF_DOCS \"The name of the generated unity build target corresponding to this target.\"\n\t\tFULL_DOCS\n\t\t\t\"This property can be set to the desired name of the unity target that will be created by cotire.\"\n\t\t\t\"If not set, the unity target name will be set to this target's name with the suffix _unity appended.\"\n\t\t\t\"After this target has been processed by cotire, the property is set to the actual name of the generated unity target.\"\n\t\t\t\"Defaults to empty string.\"\n\t)\n\n\t# define cotire source properties\n\n\tdefine_property(\n\t\tSOURCE PROPERTY \"COTIRE_EXCLUDED\"\n\t\tBRIEF_DOCS \"Do not modify source file's build command.\"\n\t\tFULL_DOCS\n\t\t\t\"If this property is set to TRUE, the source file's build command will not be modified to make use of the precompiled header.\"\n\t\t\t\"The source file will also be excluded from the generated unity source file.\"\n\t\t\t\"Source files that have their COMPILE_FLAGS property set will be excluded by default.\"\n\t\t\t\"Defaults to FALSE.\"\n\t)\n\n\tdefine_property(\n\t\tSOURCE PROPERTY \"COTIRE_DEPENDENCY\"\n\t\tBRIEF_DOCS \"Add this source file to dependencies of the automatically generated prefix header file.\"\n\t\tFULL_DOCS\n\t\t\t\"If this property is set to TRUE, the source file is added to dependencies of the generated prefix header file.\"\n\t\t\t\"If the file is modified, cotire will re-generate the prefix header source upon build.\"\n\t\t\t\"Defaults to FALSE.\"\n\t)\n\n\tdefine_property(\n\t\tSOURCE PROPERTY \"COTIRE_UNITY_SOURCE_PRE_UNDEFS\"\n\t\tBRIEF_DOCS \"Preprocessor undefs to place in the generated unity source file before the inclusion of this source file.\"\n\t\tFULL_DOCS\n\t\t\t\"This may be set to a semicolon-separated list of preprocessor symbols.\"\n\t\t\t\"cotire will add corresponding #undef directives to the generated unit source file before this file is included.\"\n\t\t\t\"Defaults to empty string.\"\n\t)\n\n\tdefine_property(\n\t\tSOURCE PROPERTY \"COTIRE_UNITY_SOURCE_POST_UNDEFS\"\n\t\tBRIEF_DOCS \"Preprocessor undefs to place in the generated unity source file after the inclusion of this source file.\"\n\t\tFULL_DOCS\n\t\t\t\"This may be set to a semicolon-separated list of preprocessor symbols.\"\n\t\t\t\"cotire will add corresponding #undef directives to the generated unit source file after this file is included.\"\n\t\t\t\"Defaults to empty string.\"\n\t)\n\n\tdefine_property(\n\t\tSOURCE PROPERTY \"COTIRE_START_NEW_UNITY_SOURCE\"\n\t\tBRIEF_DOCS \"Start a new unity source file which includes this source file as the first one.\"\n\t\tFULL_DOCS\n\t\t\t\"If this property is set to TRUE, cotire will complete the current unity file and start a new one.\"\n\t\t\t\"The new unity source file will include this source file as the first one.\"\n\t\t\t\"This property essentially works as a separator for unity source files.\"\n\t\t\t\"Defaults to FALSE.\"\n\t)\n\n\tdefine_property(\n\t\tSOURCE PROPERTY \"COTIRE_TARGET\"\n\t\tBRIEF_DOCS \"Read-only property. Mark this source file as cotired for the given target.\"\n\t\tFULL_DOCS\n\t\t\t\"cotire sets this property to the name of target, that the source file's build command has been altered for.\"\n\t\t\t\"Defaults to empty string.\"\n\t)\n\n\tmessage (STATUS \"cotire ${COTIRE_CMAKE_MODULE_VERSION} loaded.\")\n\nendif()\n"
  },
  {
    "path": "cmake/packaging.cmake",
    "content": "# Logic to build packages (RPM/DEB) using CPack; see https://cmake.org/Wiki/CMake:Packaging_With_CPack\n# \n\nset(LINUX_NAME \"\")\nset(IS_DEBIAN_PACKAGE FALSE)\nif(EXISTS \"/etc/redhat-release\")\n  file(READ \"/etc/redhat-release\" LINUX_ISSUE)\n  if(LINUX_ISSUE MATCHES \"CentOS\")\n    set(CPACK_GENERATOR \"RPM\")\n    set(CPACK_SYSTEM_NAME \"centos\")\n    set(CPACK_RPM_PACKAGE_REQUIRES   \"centos-release-scl, epel-release, rh-python36, gmp, libuuid, sqlite, gtkmm30, boost-system, boost-filesystem, boost-program-options, boost-regex, libstdc++\")\n    message(\"-- This is a CentOS system\")\n  endif()\n  if(LINUX_ISSUE MATCHES \"Scientific Linux\")\n    set(CPACK_GENERATOR \"RPM\")\n    set(CPACK_SYSTEM_NAME \"scientific7x\")\n    set(CPACK_RPM_PACKAGE_REQUIRES   \"yum-conf-softwarecollections, epel-release, rh-python36, gmp, libuuid, sqlite, gtkmm30, boost-system, boost-filesystem, boost-program-options, boost-regex, libstdc++\")\n    message(\"-- This is a CentOS system\")\n  endif()\n  if(LINUX_ISSUE MATCHES \"Fedora\")\n    set(CPACK_GENERATOR   \"RPM\")\n    if(LINUX_ISSUE MATCHES \"40\")\n      message(\"-- This is a Fedora 40 system\")\n      set(CPACK_RPM_PACKAGE_REQUIRES   \"python3, python3-libs, gmp, libuuid, sqlite, gtkmm30, openssl, boost-system, boost-filesystem, boost-program-options, boost-regex, libstdc++, python3-matplotlib, python3-sympy\")\n      set(CPACK_SYSTEM_NAME \"fedora40-${STANDARD_ARCH_NAME}\")\n    elseif(LINUX_ISSUE MATCHES \"41\")\n      message(\"-- This is a Fedora 41 system\")\n      set(CPACK_RPM_PACKAGE_REQUIRES   \"python3, python3-libs, gmp, libuuid, sqlite, gtkmm30, openssl, boost-system, boost-filesystem, boost-program-options, boost-regex, libstdc++, python3-matplotlib, python3-sympy\")\n      set(CPACK_SYSTEM_NAME \"fedora41-${STANDARD_ARCH_NAME}\")\n    elseif(LINUX_ISSUE MATCHES \"42\")\n      message(\"-- This is a Fedora 42 system\")\n      set(CPACK_RPM_PACKAGE_REQUIRES   \"python3, python3-libs, gmp, libuuid, sqlite, gtkmm30, openssl, boost-system, boost-filesystem, boost-program-options, boost-regex, libstdc++, python3-matplotlib, python3-sympy\")\n      set(CPACK_SYSTEM_NAME \"fedora42-${STANDARD_ARCH_NAME}\")\n    else()\t\n      message(FATAL_ERROR \"-- This is an old Fedora system <40, we do not support packaging for this anymore.\")\n    endif()\n  endif()\nelse()\n  if(EXISTS \"/etc/os-release\")\n    file(READ \"/etc/os-release\" LINUX_ISSUE)\n    if(LINUX_ISSUE MATCHES \"15.0\")\n      set(CPACK_SYSTEM_NAME \"leap150\")\n      set(CPACK_GENERATOR   \"RPM\")\n      message(\"-- This is an openSUSE Leap 15.0 system (UNSUPPORTED)\")\n      set(CPACK_RPM_PACKAGE_REQUIRES   \"libpython3_6m1_0, libgmp10, libuuid1, libsqlite3-0, libgtkmm-3_0-1, libboost_system1_66_0, libboost_filesystem1_66_0, libboost_program_options1_66_0, libboost_regex1_66_0, libstdc++6, python3-matplotlib, python3-sympy\")\n    endif()\n    if(LINUX_ISSUE MATCHES \"Tumbleweed\")\n      set(CPACK_SYSTEM_NAME \"tumbleweed\")\n      set(CPACK_GENERATOR   \"RPM\")\n      message(\"-- This is an openSUSE Tumbleweed system\")\n      set(CPACK_RPM_PACKAGE_REQUIRES   \"libpython3_13-1_0, libgmp10, libuuid1, libgtkmm-3_0-1, openssl, libboost_system1_88_0, libboost_filesystem1_88_0, libboost_program_options1_88_0, libboost_regex1_88_0, libstdc++6, python313-matplotlib, python313-sympy\")\n    endif()\n  endif()\n  if(EXISTS \"/etc/issue\")\n    file(READ \"/etc/issue\" LINUX_ISSUE)\n    if(LINUX_ISSUE MATCHES \"openSUSE\")\n      if(LINUX_ISSUE MATCHES \"42.1\")\n   \tset(CPACK_SYSTEM_NAME \"leap421\")\n\tset(CPACK_GENERATOR   \"RPM\")\n\tmessage(\"-- This is an openSUSE Leap 42.1 system (UNSUPPORTED)\")\n\tset(CPACK_RPM_PACKAGE_REQUIRES   \"libpython3_4m1_0, libgmp10, libuuid1, libsqlite3-0, libgtkmm-3_0-1, libboost_system1_61_0, libboost_filesystem1_61_0, libboost_program_options1_61_0, libboost_regex1_61_0, libstdc++6, python3-matplotlib\")\n      endif()\n    endif()\n    if(LINUX_ISSUE MATCHES \"Debian\")\n      set(CPACK_GENERATOR   \"DEB\")\n      set(IS_DEBIAN_PACKAGE TRUE)\n      if(PACKAGING_MODE)\n\tset(PYTHON_SITE_PATH  \"/usr/lib/python3/dist-packages\")\n\tset(INSTALL_LATEX_DIR  \"/usr/share/texmf\")\n      endif()\n      if(LINUX_ISSUE MATCHES \"8\")\n   \tset(CPACK_SYSTEM_NAME \"jessie\")\n\tset(CPACK_DEBIAN_PACKAGE_DEPENDS \"python3, libgmpxx4ldbl, libboost-system1.55.0, libboost-filesystem1.55.0, libboost-program-options1.55.0, libboost-regex1.55.0, libstdc++6, uuid-runtime, libgtkmm-3.0-1, python3-matplotlib, python3-mpmath, python3-sympy, python3-gmpy2\")\n   \tmessage(\"-- This is a Debian Jessie 8.x system\")\n      endif()\n      if(LINUX_ISSUE MATCHES \"9\")\n   \tset(CPACK_SYSTEM_NAME \"stretch\")\n\tset(CPACK_DEBIAN_PACKAGE_DEPENDS \"python3, libgmpxx4ldbl, libboost-system1.62.0, libboost-filesystem1.62.0, libboost-program-options1.62.0, libboost-regex1.62.0, libstdc++6, uuid-runtime, libgtkmm-3.0-1v5, python3-matplotlib, python3-mpmath, python3-sympy, python3-gmpy2\")\n   \tmessage(\"-- This is a Debian Stretch 9.x system\")\n      endif()\n      if(LINUX_ISSUE MATCHES \"buster\")\n   \tset(CPACK_SYSTEM_NAME \"buster\")\n\tset(CPACK_DEBIAN_PACKAGE_DEPENDS \"python3, libgmpxx4ldbl, libboost-system1.67.0, libboost-filesystem1.67.0, libboost-program-options1.67.0, libboost-regex1.67.0, libstdc++6, uuid-runtime, libgtkmm-3.0-1v5, python3-matplotlib, python3-mpmath, python3-sympy, python3-gmpy2\")\n   \tmessage(\"-- This is a Debian Buster 10.x system\")\n      endif()\n      if(LINUX_ISSUE MATCHES \"10\")\n   \tset(CPACK_SYSTEM_NAME \"buster\")\n\tset(CPACK_DEBIAN_PACKAGE_DEPENDS \"python3, libgmpxx4ldbl, libboost-system1.67.0, libboost-filesystem1.67.0, libboost-program-options1.67.0, libboost-regex1.67.0, libstdc++6, uuid-runtime, libgtkmm-3.0-1v5, python3-matplotlib, python3-mpmath, python3-sympy, python3-gmpy2\")\n   \tmessage(\"-- This is a Debian Buster 10.x system\")\n      endif()\n    endif()\n    if(LINUX_ISSUE MATCHES \"Ubuntu\")\n      set(CPACK_GENERATOR   \"DEB\")\n      set(IS_DEBIAN_PACKAGE TRUE)\n      if(PACKAGING_MODE)\n\tset(PYTHON_SITE_PATH  \"/usr/lib/python3/dist-packages\")\n\tset(INSTALL_LATEX_DIR  \"/usr/share/texmf\")\n      endif()\n      if(LINUX_ISSUE MATCHES \"20.04\")\n   \tset(CPACK_SYSTEM_NAME \"focal-${STANDARD_ARCH_NAME}\")\n\tset(CPACK_DEBIAN_PACKAGE_DEPENDS \"python3, libgmpxx4ldbl, libssl3, libboost-system1.71.0, libboost-filesystem1.71.0, libboost-program-options1.71.0, libboost-regex1.71.0, libstdc++6, uuid-runtime, libgtkmm-3.0-1v5, python3-matplotlib, python3-mpmath, python3-sympy, python3-gmpy2\")\n   \tmessage(\"-- This is an Ubuntu 20.04 system\")\n      endif()\n      if(LINUX_ISSUE MATCHES \"22.04\")\n   \tset(CPACK_SYSTEM_NAME \"ubuntu-22.04-jammy-${STANDARD_ARCH_NAME}\")\n\tset(CPACK_DEBIAN_PACKAGE_DEPENDS \"python3, libtbb12, libgmpxx4ldbl, libssl3, libboost-system1.74.0, libboost-filesystem1.74.0, libboost-program-options1.74.0, libboost-regex1.74.0, libstdc++6, uuid-runtime, libgtkmm-3.0-1v5, python3-matplotlib, python3-mpmath, python3-sympy, python3-gmpy2\")\n   \tmessage(\"-- This is an Ubuntu 22.04 system\")\n      endif()\n      if(LINUX_ISSUE MATCHES \"24.04\")\n   \tset(CPACK_SYSTEM_NAME \"ubuntu-24.04-noble-${STANDARD_ARCH_NAME}\")\n\tset(CPACK_DEBIAN_PACKAGE_DEPENDS \"python3, libtbb12, libgmpxx4ldbl, libssl3, libboost-system1.83.0, libboost-filesystem1.83.0, libboost-program-options1.83.0, libboost-regex1.83.0, libstdc++6, uuid-runtime, libgtkmm-3.0-1t64, librsvg2-2, librsvg2-common, python3-matplotlib, python3-mpmath, python3-sympy, python3-gmpy2\")\n   \tmessage(\"-- This is an Ubuntu 24.04 system\")\n      endif()\n    endif()\n    if(LINUX_ISSUE MATCHES \"Mint\")\n      set(CPACK_GENERATOR \"DEB\")\n      set(IS_DEBIAN_PACKAGE TRUE)\n      if(PACKAGING_MODE)\n\tset(PYTHON_SITE_PATH   \"/usr/lib/python3/dist-packages\")\n\tset(INSTALL_LATEX_DIR  \"/usr/share/texmf\")\n      endif()\n      if(LINUX_ISSUE MATCHES \"19\")\n   \tmessage(\"-- This is a Linux Mint 19 system\")\n   \tset(CPACK_SYSTEM_NAME \"tessa\")\n\tset(CPACK_DEBIAN_PACKAGE_DEPENDS \"python3, libgmpxx4ldbl, libboost-system1.65.1, libboost-filesystem1.65.1, libboost-program-options1.65.1, libboost-regex1.65.1, libstdc++6, uuid-runtime, libgtkmm-3.0-1v5, python3-matplotlib, python3-mpmath, python3-sympy, python3-gmpy2\")\n      endif()\n      if(LINUX_ISSUE MATCHES \"20\")\n   \tmessage(\"-- This is a Linux Mint 20 system\")\n   \tset(CPACK_SYSTEM_NAME \"ulyana\")\n\tset(CPACK_DEBIAN_PACKAGE_DEPENDS \"python3, libgmpxx4ldbl, libboost-system1.71.0, libboost-filesystem1.71.0, libboost-program-options1.71.0, libboost-regex1.71.0, libstdc++6, uuid-runtime, libgtkmm-3.0-1v5, python3-matplotlib, python3-mpmath, python3-sympy, python3-gmpy2\")\n      endif()\n      if(LINUX_ISSUE MATCHES \"21\")\n   \tmessage(\"-- This is a Linux Mint 21 system\")\n   \tset(CPACK_SYSTEM_NAME \"vanessa\")\n\tset(CPACK_DEBIAN_PACKAGE_DEPENDS \"python3, libgmpxx4ldbl, libboost-system1.74.0, libboost-filesystem1.74.0, libboost-program-options1.74.0, libboost-regex1.74.0, libstdc++6, uuid-runtime, libgtkmm-3.0-1v5, python3-matplotlib, python3-mpmath, python3-sympy, python3-gmpy2\")\n      endif()\n    endif()\n  endif()\nendif()\n\nif(WIN32)\n  message(\"-- This is a Windows system, creating WIX installer\")\n  # A good resource (though not complete) for CPack on various platforms is\n  # https://martin-fieber.de/blog/cmake-cpack-cross-platform-distributables/\n  #   set(CPACK_GENERATOR NSIS)\n  #   set(CPACK_PACKAGE_INSTALL_DIRECTORY \"Cadabra\")\n  #   set(CPACK_NSIS_MODIFY_PATH OFF)\n  #   set(CPACK_NSIS_EXECUTABLES_DIRECTORY .)\n  #   set(CPACK_NSIS_URL_INFO_ABOUT \"https://cadabra.science/\")\n  #   set(CPACK_NSIS_CONTACT \"Kasper Peeters <info@cadabra.science>\")\n  set(CPACK_GENERATOR WIX)\n  set(CPACK_WIX_ROOT \"C:/WiX\")\n  set(CPACK_WIX_VERSION 4)\n  set(CPACK_WIX_ARCHITECTURE \"${WIX_SHORT_ARCH}\")\n  set(CPACK_WIX_LIGHT_EXTRA_FLAGS \"-sw1076\")\n  set(CPACK_WIX_DESKTOP_SHORTCUTS TRUE)\n  set(CPACK_WIX_PROGRAM_MENU_FOLDER \"Cadabra\")\n  set(CPACK_PACKAGE_INSTALL_DIRECTORY \"Cadabra\")\n  set(CPACK_WIX_PROPERTY_ARPURLINFOABOUT \"https://cadabra.science/\")\n  set(CPACK_WIX_PROPERTY_ARPCONTACT \"Kasper Peeters <info@cadabra.science>\")\n  set(CPACK_WIX_UPGRADE_GUID \"7CD938BA-C9E0-4CF0-8649-B44F292C01B5\")\n  set(CPACK_WIX_UI_BANNER \"${CMAKE_SOURCE_DIR}/doc/msi_banner.png\")\n  set(CPACK_WIX_UI_DIALOG \"${CMAKE_SOURCE_DIR}/doc/msi_dialog.png\")\n  set(CPACK_WIX_PRODUCT_ICON \"${CMAKE_SOURCE_DIR}/config/cadabra2.ico\") \n  set(CPACK_PACKAGE_EXECUTABLES \"cadabra2-gtk\" \"Cadabra\") \n  set(CPACK_CREATE_DESKTOP_LINKS \"cadabra2-gtk\")\n#  set(CPACK_WIX_EXTRA_SOURCES \"${CMAKE_SOURCE_DIR}/config/shortcuts.wxs\")\n  set(CPACK_START_MENU_SHORTCUTS \"Cadabra\")\nendif()\n\n# Ensure that on Windows we also install the libraries provided\n# by Visual Studio, e.g. MSVCnnn.DLL. This does mean that the installer\n# will now contain both the normal and the debug libraries, but better\n# to have both than to have none.\n#   set(CMAKE_INSTALL_DEBUG_LIBRARIES TRUE)\n# That didn't work... Commented out for future reference.\n\ninclude (InstallRequiredSystemLibraries)\n\nif(NOT WIN32)\n  set(CPACK_SET_DESTDIR true)\nendif()\nset(CPACK_INSTALL_PREFIX /usr)\nset(CPACK_PACKAGE_NAME           \"cadabra2\")\nset(CPACK_RESOURCE_FILE_LICENSE  \"${CMAKE_CURRENT_SOURCE_DIR}/doc/license.txt\")\nset(CPACK_RPM_PACKAGE_LICENSE    \"GPLv3\")\nset(CPACK_PACKAGE_VERSION_MAJOR  \"${CADABRA_VERSION_MAJOR}\")\nset(CPACK_PACKAGE_VERSION_MINOR  \"${CADABRA_VERSION_MINOR}\")\nset(CPACK_PACKAGE_VERSION_PATCH  \"${CADABRA_VERSION_PATCH}\")\nset(CPACK_PACKAGE_VERSION        \"${CADABRA_VERSION_SEM}\")\nset(CPACK_PACKAGE_VENDOR         \"Kasper Peeters\")\nset(CPACK_PACKAGE_CONTACT        \"Kasper Peeters <info@cadabra.science>\")\nset(CPACK_STRIP_FILES            ON)\nset(CPACK_DEBIAN_PACKAGE_CONTROL_EXTRA ${CMAKE_CURRENT_BINARY_DIR}/postinst)\nset(CPACK_RPM_POST_INSTALL_SCRIPT_FILE ${CMAKE_CURRENT_BINARY_DIR}/postinst)\nunset(CPACK_RPM_PACKAGE_RELOCATABLE)\n\n#xdg-desktop-menu install <install>/share/applications/MyApp.desktop\n\nset(CPACK_DEBIAN_PACKAGE_SECTION \"math\")\nset(CPACK_RPM_PACKAGE_GROUP      \"Applications/Productivity\")\n\nset(CPACK_PACKAGE_DESCRIPTION_SUMMARY \"field-theory motivated computer algebra system\")\nset(CPACK_PACKAGE_DESCRIPTION_FILE ${CMAKE_CURRENT_SOURCE_DIR}/doc/description)\ninclude(CPack)\n"
  },
  {
    "path": "cmake/policies.cmake",
    "content": "\n# Policy settings for CMake to resolve ambiguities.\n\nif (POLICY CMP0042)\n  cmake_policy(SET CMP0042 NEW)\nendif()\nif (POLICY CMP0054)\n  cmake_policy(SET CMP0054 NEW)\nendif()\nif (POLICY CMP0127)\n  cmake_policy(SET CMP0127 NEW)\nendif()"
  },
  {
    "path": "cmake/version.cmake",
    "content": "set(CADABRA_VERSION_MAJOR 2)\nset(CADABRA_VERSION_MINOR 5)\nset(CADABRA_VERSION_PATCH 15)\nset(CADABRA_VERSION_RC    \"\")  # do *not* use rcX here, just use X\nset(CADABRA_VERSION_SEM   ${CADABRA_VERSION_MAJOR}.${CADABRA_VERSION_MINOR}.${CADABRA_VERSION_PATCH})\nset(CADABRA_VERSION_GITHUB_TAG   ${CADABRA_VERSION_SEM})\nif(NOT \"${CADABRA_VERSION_RC}\" STREQUAL \"\")\n  set(CADABRA_VERSION_GITHUB_TAG   ${CADABRA_VERSION_SEM}-rc${CADABRA_VERSION_RC})\n  if(WIN32)\n    # WiX does not like x.y.z-rcX versions, it wants x.y.z.X\n    set(CADABRA_VERSION_SEM   ${CADABRA_VERSION_SEM}.${CADABRA_VERSION_RC})\n  else()\n    # The rest of the world is normal.\n    set(CADABRA_VERSION_SEM   ${CADABRA_VERSION_SEM}-rc${CADABRA_VERSION_RC})\n  endif()\nendif()\nset(COPYRIGHT_YEARS \"2001-2025\")\nmath(EXPR SYSTEM_BITS \"${CMAKE_SIZEOF_VOID_P} * 8\")\nfind_program(GIT git PATHS ${GIT_DIR})\nif(GIT)\n  message(\"-- Git found: ${GIT}\")\n  execute_process(COMMAND git rev-parse --short HEAD OUTPUT_VARIABLE GIT_SHORT_SHA     OUTPUT_STRIP_TRAILING_WHITESPACE)\n  execute_process(COMMAND git rev-list --count HEAD  OUTPUT_VARIABLE GIT_COMMIT_SERIAL OUTPUT_STRIP_TRAILING_WHITESPACE)\n  execute_process(COMMAND git log -1 --date=short --pretty=format:%cd  OUTPUT_VARIABLE GIT_COMMIT_DATE OUTPUT_STRIP_TRAILING_WHITESPACE)\nelse()\n  message(\"-- Git not found, not including commit SHA\")\nendif()\nif(GIT_SHORT_SHA)\n  set(CADABRA_VERSION_BUILD \"${GIT_COMMIT_SERIAL}.${GIT_SHORT_SHA}\")\nelse()\n  set(CADABRA_VERSION_BUILD \"private\")\nendif()\nif(GIT_COMMIT_DATE)\n  set(CADABRA_VERSION_DATE \"${GIT_COMMIT_DATE}\")\nelse()\n  string(TIMESTAMP THE_DATE \"%Y-%m-%d\" UTC)\n  set(CADABRA_VERSION_DATE \"${THE_DATE}\") \nendif()\n"
  },
  {
    "path": "cmake/windows.cmake",
    "content": "# Collection of utilities for using\n# vcpkg to find libraries in CMake\n\nlist(LENGTH CMAKE_CONFIGURATION_TYPES N_CONFIGURATION_TYPES)\nif (${N_CONFIGURATION_TYPES} EQUAL 1)\n  set(CMAKE_BUILD_TYPE ${CMAKE_CONFIGURATION_TYPES})\nendif()\n\n# Attempts to find the vcpkg.cmake toolchain file and include it\n# if it has not been supplied.\nif (NOT VCPKG_TOOLCHAIN)\n  find_file(CMAKE_TOOLCHAIN_FILE vcpkg.cmake HINTS $ENV{userprofile} $ENV{systemdrive} PATH_SUFFIXES vcpkg/scripts/buildsystems)\n  if (CMAKE_TOOLCHAIN_FILE)\n    include(${CMAKE_TOOLCHAIN_FILE}) \n  endif()\nendif()\nif (VCPKG_TOOLCHAIN)\n  if(NOT _VCPKG_ROOT_DIR)\n    set(_VCPKG_ROOT_DIR ${Z_VCPKG_ROOT_DIR})\n  endif()\n  message(STATUS \"Found vcpkg at ${Z_VCPKG_ROOT_DIR}\")\nelse()\n  message(FATAL_ERROR \"Could not find vcpkg (required for building on Visual Studio)\")\nendif()\n\nif (VCPKG_TOOLCHAIN)\n  # Location of include files\n  set(VCPKG_INCLUDE_DIRS ${_VCPKG_INSTALLED_DIR}/${VCPKG_TARGET_TRIPLET}/include)\n\n  if(CMAKE_BUILD_TYPE MATCHES \"^Debug$\" OR NOT DEFINED CMAKE_BUILD_TYPE)\n    set(VCPKG_LIB_DIRS \n      ${_VCPKG_INSTALLED_DIR}/${VCPKG_TARGET_TRIPLET}/debug/lib\n      ${_VCPKG_INSTALLED_DIR}/${VCPKG_TARGET_TRIPLET}/debug/lib/manual-link\n      ${_VCPKG_INSTALLED_DIR}/${VCPKG_TARGET_TRIPLET}/lib\n      ${_VCPKG_INSTALLED_DIR}/${VCPKG_TARGET_TRIPLET}/lib/manual-link\n    )\n    set(VCPKG_BIN_DIRS \n      ${_VCPKG_INSTALLED_DIR}/${VCPKG_TARGET_TRIPLET}/debug/bin\n      ${_VCPKG_INSTALLED_DIR}/${VCPKG_TARGET_TRIPLET}/bin\n    )\n  else()\n    set(VCPKG_LIB_DIRS \n      ${_VCPKG_INSTALLED_DIR}/${VCPKG_TARGET_TRIPLET}/lib\n      ${_VCPKG_INSTALLED_DIR}/${VCPKG_TARGET_TRIPLET}/lib/manual-link\n    )\n    set(VCPKG_BIN_DIRS \n      ${_VCPKG_INSTALLED_DIR}/${VCPKG_TARGET_TRIPLET}/bin\n    )\n  endif()\n\n  message(STATUS \"VCPKG_LIB_DIRS = ${VCPKG_LIB_DIRS}\")\n  message(STATUS \"VCPKG_BIN_DIRS = ${VCPKG_BIN_DIRS}\")   \n\n  function(windows_find_file VAR FNAME FEXT)\n    set(TMPVAR \"\")\n    foreach (DIR ${VCPKG_LIB_DIRS})\n      # If a debug build is specified, first try and find the library name\n      # with a debug marker\n      if(CMAKE_BUILD_TYPE MATCHES \"^Debug$\" OR NOT DEFINED CMAKE_BUILD_TYPE)\n\tif (\"${TMPVAR}\" STREQUAL \"\") # name-d.lib\n\t  file(GLOB TMPVAR \"${DIR}/${FNAME}-d.${FEXT}\")\n\tendif()\n\tif (\"${TMPVAR}\" STREQUAL \"\") # named.lib\n\t  file(GLOB TMPVAR \"${DIR}/${FNAME}d.${FEXT}\")\n\tendif()\n\tif (\"${TMPVAR}\" STREQUAL \"\") # name-<version-number>-d.lib\n\t  file(GLOB TMPVAR \"${DIR}/${FNAME}-[0-9]*-d.${FEXT}\")\n\tendif()\n\tif (\"${TMPVAR}\" STREQUAL \"\") # name-<version-number>d.lib\n\t  file(GLOB TMPVAR \"${DIR}/${FNAME}-[0-9]*-d.${FEXT}\")\n\tendif()\n\tif (\"${TMPVAR}\" STREQUAL \"\") # name<version-number>-d.lib\n\t  file(GLOB TMPVAR \"${DIR}/${FNAME}[0-9]*-d.${FEXT}\")\n\tendif()\n\tif (\"${TMPVAR}\" STREQUAL \"\") # name<version-number>d.lib\n\t  file(GLOB TMPVAR \"${DIR}/${FNAME}[0-9]*d.${FEXT}\")\n\tendif()\n\tif (\"${TMPVAR}\" STREQUAL \"\") # name-d-<version-number>.lib\n\t  file(GLOB TMPVAR \"${DIR}/${FNAME}-d-[0-9]*.${FEXT}\")\n\tendif()\n\tif (\"${TMPVAR}\" STREQUAL \"\") # named-<version-number>.lib\n\t  file(GLOB TMPVAR \"${DIR}/${FNAME}d-[0-9]*.${FEXT}\")\n\tendif()\n\tif (\"${TMPVAR}\" STREQUAL \"\") # name-d<version-number>.lib\n\t  file(GLOB TMPVAR \"${DIR}/${FNAME}-d[0-9]*.${FEXT}\")\n\tendif()\n\tif (\"${TMPVAR}\" STREQUAL \"\") # named<version-number>.lib\n\t  file(GLOB TMPVAR \"${DIR}/${FNAME}d[0-9]*.${FEXT}\")\n\tendif()\n      endif()\n      # Attempt to find library name without debug marker\n      if (\"${TMPVAR}\" STREQUAL \"\") # name.lib\n\tfile(GLOB TMPVAR \"${DIR}/${FNAME}.${FEXT}\")\n      endif()\n      if (\"${TMPVAR}\" STREQUAL \"\") # name-<version-number>.lib\n\tfile(GLOB TMPVAR \"${DIR}/${FNAME}-[0-9]*.${FEXT}\")\n      endif()\n      if (\"${TMPVAR}\" STREQUAL \"\") # name<version-number>.lib\n\tfile(GLOB TMPVAR \"${DIR}/${FNAME}[0-9]*.${FEXT}\")\n      endif()\n    endforeach()\n    # Assign the result of the search to VAR\n    if (\"${TMPVAR}\" STREQUAL \"\")\n      # Couldn't find it, set to NOTFOUND\n      set(${VAR} \"${VAR}-NOTFOUND\" PARENT_SCOPE)\n    else()\n      # GLOB could return a list of matching filenames, in which case\n      # we choose the latest version (i.e. the one which is alphabetically\n      # last)\n      list(SORT TMPVAR)\n      list(REVERSE TMPVAR)\n      list(GET TMPVAR 0 TMPVAR)\n      set(${VAR} \"${TMPVAR}\")\n    endif()\n  endfunction()\n\n  function(windows_find_library VAR)\n    # Avoid some horrible indirections by using a local variable\n    set(OUTVAR \"${${VAR}}\")\n\n    # If the variable is already specified, don't attempt to \n    # find it again\n    if (\"${OUTVAR}\" STREQUAL \"\")\n    else()\n      return()\n    endif()\n\n    # Attempt to find the REQUIRED flag\n    foreach(FLAG ${ARGN})\n      if (FLAG STREQUAL \"REQUIRED\")\n\tset(IS_REQUIRED TRUE)\n      endif()\n    endforeach()\n\n    # Loop over all the library names\n    foreach(LIBNAME ${ARGN})\n      set(TMPVAR \"\")\n      # Could be the required flag\n      if (LIBNAME STREQUAL \"REQUIRED\")\n\tcontinue()\n      endif()\n      # Loop over all library directories, searching for the\n      # library name\n      foreach (DIR ${VCPKG_LIB_DIRS})\n\t# If a debug build is specified, first try and find the library name\n\t# with a debug marker\n\tif(CMAKE_BUILD_TYPE MATCHES \"^Debug$\" OR NOT DEFINED CMAKE_BUILD_TYPE)\n\t  if (\"${TMPVAR}\" STREQUAL \"\") # name-d.lib\n\t    file(GLOB TMPVAR \"${DIR}/${LIBNAME}-d.lib\")\n\t  endif()\n\t  if (\"${TMPVAR}\" STREQUAL \"\") # named.lib\n\t    file(GLOB TMPVAR \"${DIR}/${LIBNAME}d.lib\")\n\t  endif()\n\t  if (\"${TMPVAR}\" STREQUAL \"\") # name-<version-number>-d.lib\n\t    file(GLOB TMPVAR \"${DIR}/${LIBNAME}-[0-9]*-d.lib\")\n\t  endif()\n\t  if (\"${TMPVAR}\" STREQUAL \"\") # name-<version-number>d.lib\n\t    file(GLOB TMPVAR \"${DIR}/${LIBNAME}-[0-9]*-d.lib\")\n\t  endif()\n\t  if (\"${TMPVAR}\" STREQUAL \"\") # name<version-number>-d.lib\n\t    file(GLOB TMPVAR \"${DIR}/${LIBNAME}[0-9]*-d.lib\")\n\t  endif()\n\t  if (\"${TMPVAR}\" STREQUAL \"\") # name<version-number>d.lib\n\t    file(GLOB TMPVAR \"${DIR}/${LIBNAME}[0-9]*d.lib\")\n\t  endif()\n\t  if (\"${TMPVAR}\" STREQUAL \"\") # name-d-<version-number>.lib\n\t    file(GLOB TMPVAR \"${DIR}/${LIBNAME}-d-[0-9]*.lib\")\n\t  endif()\n\t  if (\"${TMPVAR}\" STREQUAL \"\") # named-<version-number>.lib\n\t    file(GLOB TMPVAR \"${DIR}/${LIBNAME}d-[0-9]*.lib\")\n\t  endif()\n\t  if (\"${TMPVAR}\" STREQUAL \"\") # name-d<version-number>.lib\n\t    file(GLOB TMPVAR \"${DIR}/${LIBNAME}-d[0-9]*.lib\")\n\t  endif()\n\t  if (\"${TMPVAR}\" STREQUAL \"\") # named<version-number>.lib\n\t    file(GLOB TMPVAR \"${DIR}/${LIBNAME}d[0-9]*.lib\")\n\t  endif()\n\tendif()\n\t# Attempt to find library name without debug marker\n\tif (\"${TMPVAR}\" STREQUAL \"\") # name.lib\n\t  file(GLOB TMPVAR \"${DIR}/${LIBNAME}.lib\")\n\tendif()\n\tif (\"${TMPVAR}\" STREQUAL \"\") # name-<version-number>.lib\n\t  file(GLOB TMPVAR \"${DIR}/${LIBNAME}-[0-9]*.lib\")\n\tendif()\n\tif (\"${TMPVAR}\" STREQUAL \"\") # name<version-number>.lib\n\t  file(GLOB TMPVAR \"${DIR}/${LIBNAME}[0-9]*.lib\")\n\tendif()\n      endforeach()\n      # Assign the result of the search to VAR\n      if (\"${TMPVAR}\" STREQUAL \"\")\n\t# Couldn't find it, set to NOTFOUND\n\tset(${VAR} \"${VAR}-NOTFOUND\" PARENT_SCOPE)\n\tif (IS_REQUIRED)\n\t  message(FATAL_ERROR \"Could NOT find REQUIRED library ${LIBNAME} required for ${VAR}\")\n\telse()\n\t  message(SEND_ERROR \"Could NOT find library ${LIBNAME} required for ${VAR}\")\n\tendif()\n      else()\n\t# GLOB could return a list of matching filenames, in which case\n\t# we choose the latest version (i.e. the one which is alphabetically\n\t# last)\n\tlist(SORT TMPVAR)\n\tlist(REVERSE TMPVAR)\n\tlist(GET TMPVAR 0 TMPVAR)\n\tlist(APPEND OUTVAR \"${TMPVAR}\")\n      endif()\n    endforeach()\n    set(${VAR} \"${OUTVAR}\" PARENT_SCOPE)\n  endfunction()\nendif()\n"
  },
  {
    "path": "codemeta.json",
    "content": "{\n  \"@context\": \"https://raw.githubusercontent.com/codemeta/codemeta/master/codemeta.jsonld\",\n  \"@type\": \"Code\",\n  \"author\": [\n\t\t\"Kasper Peeters\"\n  ],\n  \"identifier\": \"\",\n  \"codeRepository\": \"https://github.com/kpeeters/cadabra2\",\n  \"datePublished\": \"2018-12-05\",\n  \"dateModified\": \"2018-12-05\",\n  \"dateCreated\": \"2018-12-05\",\n  \"description\": \"Computer algebra for field theory revisited\",\n  \"keywords\": \"physics, field theory, tensors, computer algebra\",\n  \"license\": \"GPL v3.0\",\n  \"title\": \"Cadabra2\",\n  \"version\": \"https://doi.org/10.5281/zenodo.1842262\"\n}\n"
  },
  {
    "path": "conda/build.sh",
    "content": "#!/bin/bash\n\nREL_SP_DIR=$(python -c \"import os;print(os.path.relpath(os.getenv('SP_DIR'), os.getenv('PREFIX')))\")\nsed -i.bak \"s@set(PYTHON_SITE_PATH.*@set(PYTHON_SITE_PATH $REL_SP_DIR)@g\" CMakeLists.txt\n\nmkdir build\ncd build\n\ncmake \\\n  -DCMAKE_PREFIX_PATH=$PREFIX \\\n  -DCMAKE_INSTALL_PREFIX=$PREFIX \\\n  -DCMAKE_BUILD_TYPE=Release \\\n  -DENABLE_SYSTEM_JSONCPP=ON \\\n  -DENABLE_MATHEMATICA=OFF \\\n  -DENABLE_JUPYTER=ON \\\n  -DPYTHON_EXECUTABLE=$PYTHON \\\n  ..\n\nmake -j${CPU_COUNT}\nmake install\n\nmkdir -p $PREFIX/share/cadabra2\nln -s $SP_DIR $PREFIX/share/cadabra2/python\n\n# Following test fails with no module named `module03` found.\nTESTS_TO_SKIP=\"modules\"\nif [[ \"$target_platform\" == osx* ]]; then\n    # The following test segfaults on OSX\n    TESTS_TO_SKIP=\"${TESTS_TO_SKIP}|implicit\"\nfi\n\nctest --output-on-failure -E \"${TESTS_TO_SKIP}\" -j${CPU_COUNT}\n"
  },
  {
    "path": "conda/meta.yaml",
    "content": "{% set name = \"cadabra2\" %}\n{% set version = \"2.2.9\" %}\n\npackage:\n  name: {{ name|lower }}\n  version: {{ version }}\n\nsource:\n  path: ../\n#   url: https://github.com/kpeeters/cadabra2/archive/{{ version }}.tar.gz\n#   sha256: 72786423b2ff847e8e0035326a8f1b2cdcf76a68c77f95588276bbccfaa74d7e\n#   patches:\n#     - cdd2fb45dc3e280d6f3834b54d9f7d612b604155.patch\n\nbuild:\n  number: 0\n  skip: True  # [win]\n\nrequirements:\n  build:\n    - {{ compiler('c') }}\n    - {{ compiler('cxx') }}\n    - cmake\n    - make\n    - pkg-config\n    - {{ cdt('libice-devel') }}  # [linux]\n    - {{ cdt('libsm-devel') }}  # [linux]\n    - {{ cdt('libx11-devel') }}  # [linux]\n    - {{ cdt('libxcomposite-devel') }}  # [linux]\n    - {{ cdt('libxcursor-devel') }}  # [linux]\n    - {{ cdt('libxdamage-devel') }}  # [linux]\n    - {{ cdt('libxext-devel') }}  # [linux]\n    - {{ cdt('libxi-devel') }}  # [linux]\n    - {{ cdt('libxinerama-devel') }}  # [linux]\n    - {{ cdt('libxfixes-devel') }}  # [linux]\n    - {{ cdt('libxrandr-devel') }}  # [linux]\n    - {{ cdt('libxrender-devel') }}  # [linux]\n    - {{ cdt('libxtst-devel') }}  # [linux]\n    - {{ cdt('mesa-libEGL-devel') }}  # [linux]\n    - {{ cdt('mesa-libGL-devel') }}  # [linux]\n    - {{ cdt('xorg-x11-proto-devel') }}  # [linux]\n\n  host:\n    - python\n    - gmp\n    - boost-cpp\n    - libuuid\n    - sqlite\n    - gtkmm-3.0\n    - glibmm\n    - cairomm-1.0\n    - glib\n    - sigcpp-2.0\n    - pangomm-1.4\n    - cairo\n    - atkmm-1.6\n    - nlohmann_json\n    - xtl\n    - jsoncpp\n    - xeus\n    - zeromq\n    - cppzmq\n    - gtkmm\n    - pybind11\n    # Needed for ctest\n    - sympy\n  run:\n    - boost-cpp\n    - python\n    - sympy\n    - matplotlib-base\n    - xeus\n    # Remove these when they get run_exports\n    - {{ pin_compatible(\"cairo\") }}\n    - {{ pin_compatible(\"glibmm\") }}\n    - {{ pin_compatible(\"glib\") }}\n\ntest:\n  imports:\n    - cadabra2\n\nabout:\n  home: https://github.com/kpeeters/cadabra2\n  license: GPL-3.0-only\n  license_family: GPL\n  license_file: LICENSE\n  summary: 'a field-theory motivated approach to computer algebra'\n\nextra:\n  recipe-maintainers:\n    - isuruf\n    - kpeeters\n"
  },
  {
    "path": "config/AppRun",
    "content": "#!/bin/bash\n#\n# Set the PYTHONHOME and PYTHONPATH variables to ensure that Cadabra\n# inside the AppImage can find the Python installation.\n#\nexport PYTHONHOME=$APPDIR/usr\nexport PYTHONPATH=$APPDIR/usr/lib/python3.8:$APPDIR/usr/lib/python3.8/site-packages:$APPDIR/usr/lib/python3.8/dist-packages:$APPDIR/usr/lib/python3/site-packages:$APPDIR/usr/lib/python3/dist-packages\nexport LD_LIBRARY_PATH=$APPDIR/usr/lib:$LD_LIBRARY_PATH\nexport LANG=en_US.UTF-8\n\nexec $APPDIR/usr/bin/cadabra2-gtk \"$@\"\n"
  },
  {
    "path": "config/Doxyfile",
    "content": "# Doxyfile 1.8.11\n\n# This file describes the settings to be used by the documentation system\n# doxygen (www.doxygen.org) for a project.\n#\n# All text after a double hash (##) is considered a comment and is placed in\n# front of the TAG it is preceding.\n#\n# All text after a single hash (#) is considered a comment and will be ignored.\n# The format is:\n# TAG = value [value, ...]\n# For lists, items can also be appended using:\n# TAG += value [value, ...]\n# Values that contain spaces should be placed between quotes (\\\" \\\").\n\n#---------------------------------------------------------------------------\n# Project related configuration options\n#---------------------------------------------------------------------------\n\n# This tag specifies the encoding used for all characters in the config file\n# that follow. The default is UTF-8 which is also the encoding used for all text\n# before the first occurrence of this tag. Doxygen uses libiconv (or the iconv\n# built into libc) for the transcoding. See http://www.gnu.org/software/libiconv\n# for the list of possible encodings.\n# The default value is: UTF-8.\n\nDOXYFILE_ENCODING      = UTF-8\n\n# The PROJECT_NAME tag is a single word (or a sequence of words surrounded by\n# double-quotes, unless you are using Doxywizard) that should identify the\n# project for which the documentation is generated. This name is used in the\n# title of most generated pages and in a few other places.\n# The default value is: My Project.\n\nPROJECT_NAME           = \"Cadabra\"\n\n# The PROJECT_NUMBER tag can be used to enter a project or revision number. This\n# could be handy for archiving the generated documentation or if some version\n# control system is used.\n\nPROJECT_NUMBER         =\n\n# Using the PROJECT_BRIEF tag one can provide an optional one line description\n# for a project that appears at the top of each page and should give viewer a\n# quick idea about the purpose of the project. Keep the description short.\n\nPROJECT_BRIEF          = \"Computer algebra system for field theory problems\"\n\n# With the PROJECT_LOGO tag one can specify a logo or an icon that is included\n# in the documentation. The maximum height of the logo should not exceed 55\n# pixels and the maximum width should not exceed 200 pixels. Doxygen will copy\n# the logo to the output directory.\n\nPROJECT_LOGO           = images/64x64/cadabra2-gtk.png\n\n# The OUTPUT_DIRECTORY tag is used to specify the (relative or absolute) path\n# into which the generated documentation will be written. If a relative path is\n# entered, it will be relative to the location where doxygen was started. If\n# left blank the current directory will be used.\n\nOUTPUT_DIRECTORY       = doxygen\n\n# If the CREATE_SUBDIRS tag is set to YES then doxygen will create 4096 sub-\n# directories (in 2 levels) under the output directory of each output format and\n# will distribute the generated files over these directories. Enabling this\n# option can be useful when feeding doxygen a huge amount of source files, where\n# putting all generated files in the same directory would otherwise causes\n# performance problems for the file system.\n# The default value is: NO.\n\nCREATE_SUBDIRS         = NO\n\n# If the ALLOW_UNICODE_NAMES tag is set to YES, doxygen will allow non-ASCII\n# characters to appear in the names of generated files. If set to NO, non-ASCII\n# characters will be escaped, for example _xE3_x81_x84 will be used for Unicode\n# U+3044.\n# The default value is: NO.\n\nALLOW_UNICODE_NAMES    = NO\n\n# The OUTPUT_LANGUAGE tag is used to specify the language in which all\n# documentation generated by doxygen is written. Doxygen will use this\n# information to generate all constant output in the proper language.\n# Possible values are: Afrikaans, Arabic, Armenian, Brazilian, Catalan, Chinese,\n# Chinese-Traditional, Croatian, Czech, Danish, Dutch, English (United States),\n# Esperanto, Farsi (Persian), Finnish, French, German, Greek, Hungarian,\n# Indonesian, Italian, Japanese, Japanese-en (Japanese with English messages),\n# Korean, Korean-en (Korean with English messages), Latvian, Lithuanian,\n# Macedonian, Norwegian, Persian (Farsi), Polish, Portuguese, Romanian, Russian,\n# Serbian, Serbian-Cyrillic, Slovak, Slovene, Spanish, Swedish, Turkish,\n# Ukrainian and Vietnamese.\n# The default value is: English.\n\nOUTPUT_LANGUAGE        = English\n\n# If the BRIEF_MEMBER_DESC tag is set to YES, doxygen will include brief member\n# descriptions after the members that are listed in the file and class\n# documentation (similar to Javadoc). Set to NO to disable this.\n# The default value is: YES.\n\nBRIEF_MEMBER_DESC      = YES\n\n# If the REPEAT_BRIEF tag is set to YES, doxygen will prepend the brief\n# description of a member or function before the detailed description\n#\n# Note: If both HIDE_UNDOC_MEMBERS and BRIEF_MEMBER_DESC are set to NO, the\n# brief descriptions will be completely suppressed.\n# The default value is: YES.\n\nREPEAT_BRIEF           = YES\n\n# This tag implements a quasi-intelligent brief description abbreviator that is\n# used to form the text in various listings. Each string in this list, if found\n# as the leading text of the brief description, will be stripped from the text\n# and the result, after processing the whole list, is used as the annotated\n# text. Otherwise, the brief description is used as-is. If left blank, the\n# following values are used ($name is automatically replaced with the name of\n# the entity):The $name class, The $name widget, The $name file, is, provides,\n# specifies, contains, represents, a, an and the.\n\nABBREVIATE_BRIEF       =\n\n# If the ALWAYS_DETAILED_SEC and REPEAT_BRIEF tags are both set to YES then\n# doxygen will generate a detailed section even if there is only a brief\n# description.\n# The default value is: NO.\n\nALWAYS_DETAILED_SEC    = NO\n\n# If the INLINE_INHERITED_MEMB tag is set to YES, doxygen will show all\n# inherited members of a class in the documentation of that class as if those\n# members were ordinary class members. Constructors, destructors and assignment\n# operators of the base classes will not be shown.\n# The default value is: NO.\n\nINLINE_INHERITED_MEMB  = NO\n\n# If the FULL_PATH_NAMES tag is set to YES, doxygen will prepend the full path\n# before files name in the file list and in the header files. If set to NO the\n# shortest path that makes the file name unique will be used\n# The default value is: YES.\n\nFULL_PATH_NAMES        = YES\n\n# The STRIP_FROM_PATH tag can be used to strip a user-defined part of the path.\n# Stripping is only done if one of the specified strings matches the left-hand\n# part of the path. The tag can be used to show relative paths in the file list.\n# If left blank the directory from which doxygen is run is used as the path to\n# strip.\n#\n# Note that you can specify absolute paths here, but also relative paths, which\n# will be relative from the directory where doxygen is started.\n# This tag requires that the tag FULL_PATH_NAMES is set to YES.\n\nSTRIP_FROM_PATH        =\n\n# The STRIP_FROM_INC_PATH tag can be used to strip a user-defined part of the\n# path mentioned in the documentation of a class, which tells the reader which\n# header file to include in order to use a class. If left blank only the name of\n# the header file containing the class definition is used. Otherwise one should\n# specify the list of include paths that are normally passed to the compiler\n# using the -I flag.\n\nSTRIP_FROM_INC_PATH    =\n\n# If the SHORT_NAMES tag is set to YES, doxygen will generate much shorter (but\n# less readable) file names. This can be useful is your file systems doesn't\n# support long names like on DOS, Mac, or CD-ROM.\n# The default value is: NO.\n\nSHORT_NAMES            = NO\n\n# If the JAVADOC_AUTOBRIEF tag is set to YES then doxygen will interpret the\n# first line (until the first dot) of a Javadoc-style comment as the brief\n# description. If set to NO, the Javadoc-style will behave just like regular Qt-\n# style comments (thus requiring an explicit @brief command for a brief\n# description.)\n# The default value is: NO.\n\nJAVADOC_AUTOBRIEF      = YES\n\n# If the QT_AUTOBRIEF tag is set to YES then doxygen will interpret the first\n# line (until the first dot) of a Qt-style comment as the brief description. If\n# set to NO, the Qt-style will behave just like regular Qt-style comments (thus\n# requiring an explicit \\brief command for a brief description.)\n# The default value is: NO.\n\nQT_AUTOBRIEF           = NO\n\n# The MULTILINE_CPP_IS_BRIEF tag can be set to YES to make doxygen treat a\n# multi-line C++ special comment block (i.e. a block of //! or /// comments) as\n# a brief description. This used to be the default behavior. The new default is\n# to treat a multi-line C++ comment block as a detailed description. Set this\n# tag to YES if you prefer the old behavior instead.\n#\n# Note that setting this tag to YES also means that rational rose comments are\n# not recognized any more.\n# The default value is: NO.\n\nMULTILINE_CPP_IS_BRIEF = NO\n\n# If the INHERIT_DOCS tag is set to YES then an undocumented member inherits the\n# documentation from any documented member that it re-implements.\n# The default value is: YES.\n\nINHERIT_DOCS           = YES\n\n# If the SEPARATE_MEMBER_PAGES tag is set to YES then doxygen will produce a new\n# page for each member. If set to NO, the documentation of a member will be part\n# of the file/class/namespace that contains it.\n# The default value is: NO.\n\nSEPARATE_MEMBER_PAGES  = NO\n\n# The TAB_SIZE tag can be used to set the number of spaces in a tab. Doxygen\n# uses this value to replace tabs by spaces in code fragments.\n# Minimum value: 1, maximum value: 16, default value: 4.\n\nTAB_SIZE               = 4\n\n# This tag can be used to specify a number of aliases that act as commands in\n# the documentation. An alias has the form:\n# name=value\n# For example adding\n# \"sideeffect=@par Side Effects:\\n\"\n# will allow you to put the command \\sideeffect (or @sideeffect) in the\n# documentation, which will result in a user-defined paragraph with heading\n# \"Side Effects:\". You can put \\n's in the value part of an alias to insert\n# newlines.\n\nALIASES                =\n\n# This tag can be used to specify a number of word-keyword mappings (TCL only).\n# A mapping has the form \"name=value\". For example adding \"class=itcl::class\"\n# will allow you to use the command class in the itcl::class meaning.\n\nTCL_SUBST              =\n\n# Set the OPTIMIZE_OUTPUT_FOR_C tag to YES if your project consists of C sources\n# only. Doxygen will then generate output that is more tailored for C. For\n# instance, some of the names that are used will be different. The list of all\n# members will be omitted, etc.\n# The default value is: NO.\n\nOPTIMIZE_OUTPUT_FOR_C  = NO\n\n# Set the OPTIMIZE_OUTPUT_JAVA tag to YES if your project consists of Java or\n# Python sources only. Doxygen will then generate output that is more tailored\n# for that language. For instance, namespaces will be presented as packages,\n# qualified scopes will look different, etc.\n# The default value is: NO.\n\nOPTIMIZE_OUTPUT_JAVA   = NO\n\n# Set the OPTIMIZE_FOR_FORTRAN tag to YES if your project consists of Fortran\n# sources. Doxygen will then generate output that is tailored for Fortran.\n# The default value is: NO.\n\nOPTIMIZE_FOR_FORTRAN   = NO\n\n# Set the OPTIMIZE_OUTPUT_VHDL tag to YES if your project consists of VHDL\n# sources. Doxygen will then generate output that is tailored for VHDL.\n# The default value is: NO.\n\nOPTIMIZE_OUTPUT_VHDL   = NO\n\n# Doxygen selects the parser to use depending on the extension of the files it\n# parses. With this tag you can assign which parser to use for a given\n# extension. Doxygen has a built-in mapping, but you can override or extend it\n# using this tag. The format is ext=language, where ext is a file extension, and\n# language is one of the parsers supported by doxygen: IDL, Java, Javascript,\n# C#, C, C++, D, PHP, Objective-C, Python, Fortran (fixed format Fortran:\n# FortranFixed, free formatted Fortran: FortranFree, unknown formatted Fortran:\n# Fortran. In the later case the parser tries to guess whether the code is fixed\n# or free formatted code, this is the default for Fortran type files), VHDL. For\n# instance to make doxygen treat .inc files as Fortran files (default is PHP),\n# and .f files as C (default is Fortran), use: inc=Fortran f=C.\n#\n# Note: For files without extension you can use no_extension as a placeholder.\n#\n# Note that for custom extensions you also need to set FILE_PATTERNS otherwise\n# the files are not read by doxygen.\n\nEXTENSION_MAPPING      =\n\n# If the MARKDOWN_SUPPORT tag is enabled then doxygen pre-processes all comments\n# according to the Markdown format, which allows for more readable\n# documentation. See http://daringfireball.net/projects/markdown/ for details.\n# The output of markdown processing is further processed by doxygen, so you can\n# mix doxygen, HTML, and XML commands with Markdown formatting. Disable only in\n# case of backward compatibilities issues.\n# The default value is: YES.\n\nMARKDOWN_SUPPORT       = YES\n\n# When enabled doxygen tries to link words that correspond to documented\n# classes, or namespaces to their corresponding documentation. Such a link can\n# be prevented in individual cases by putting a % sign in front of the word or\n# globally by setting AUTOLINK_SUPPORT to NO.\n# The default value is: YES.\n\nAUTOLINK_SUPPORT       = YES\n\n# If you use STL classes (i.e. std::string, std::vector, etc.) but do not want\n# to include (a tag file for) the STL sources as input, then you should set this\n# tag to YES in order to let doxygen match functions declarations and\n# definitions whose arguments contain STL classes (e.g. func(std::string);\n# versus func(std::string) {}). This also make the inheritance and collaboration\n# diagrams that involve STL classes more complete and accurate.\n# The default value is: NO.\n\nBUILTIN_STL_SUPPORT    = NO\n\n# If you use Microsoft's C++/CLI language, you should set this option to YES to\n# enable parsing support.\n# The default value is: NO.\n\nCPP_CLI_SUPPORT        = NO\n\n# Set the SIP_SUPPORT tag to YES if your project consists of sip (see:\n# http://www.riverbankcomputing.co.uk/software/sip/intro) sources only. Doxygen\n# will parse them like normal C++ but will assume all classes use public instead\n# of private inheritance when no explicit protection keyword is present.\n# The default value is: NO.\n\nSIP_SUPPORT            = NO\n\n# For Microsoft's IDL there are propget and propput attributes to indicate\n# getter and setter methods for a property. Setting this option to YES will make\n# doxygen to replace the get and set methods by a property in the documentation.\n# This will only work if the methods are indeed getting or setting a simple\n# type. If this is not the case, or you want to show the methods anyway, you\n# should set this option to NO.\n# The default value is: YES.\n\nIDL_PROPERTY_SUPPORT   = YES\n\n# If member grouping is used in the documentation and the DISTRIBUTE_GROUP_DOC\n# tag is set to YES then doxygen will reuse the documentation of the first\n# member in the group (if any) for the other members of the group. By default\n# all members of a group must be documented explicitly.\n# The default value is: NO.\n\nDISTRIBUTE_GROUP_DOC   = NO\n\n# If one adds a struct or class to a group and this option is enabled, then also\n# any nested class or struct is added to the same group. By default this option\n# is disabled and one has to add nested compounds explicitly via \\ingroup.\n# The default value is: NO.\n\nGROUP_NESTED_COMPOUNDS = NO\n\n# Set the SUBGROUPING tag to YES to allow class member groups of the same type\n# (for instance a group of public functions) to be put as a subgroup of that\n# type (e.g. under the Public Functions section). Set it to NO to prevent\n# subgrouping. Alternatively, this can be done per class using the\n# \\nosubgrouping command.\n# The default value is: YES.\n\nSUBGROUPING            = YES\n\n# When the INLINE_GROUPED_CLASSES tag is set to YES, classes, structs and unions\n# are shown inside the group in which they are included (e.g. using \\ingroup)\n# instead of on a separate page (for HTML and Man pages) or section (for LaTeX\n# and RTF).\n#\n# Note that this feature does not work in combination with\n# SEPARATE_MEMBER_PAGES.\n# The default value is: NO.\n\nINLINE_GROUPED_CLASSES = NO\n\n# When the INLINE_SIMPLE_STRUCTS tag is set to YES, structs, classes, and unions\n# with only public data fields or simple typedef fields will be shown inline in\n# the documentation of the scope in which they are defined (i.e. file,\n# namespace, or group documentation), provided this scope is documented. If set\n# to NO, structs, classes, and unions are shown on a separate page (for HTML and\n# Man pages) or section (for LaTeX and RTF).\n# The default value is: NO.\n\nINLINE_SIMPLE_STRUCTS  = NO\n\n# When TYPEDEF_HIDES_STRUCT tag is enabled, a typedef of a struct, union, or\n# enum is documented as struct, union, or enum with the name of the typedef. So\n# typedef struct TypeS {} TypeT, will appear in the documentation as a struct\n# with name TypeT. When disabled the typedef will appear as a member of a file,\n# namespace, or class. And the struct will be named TypeS. This can typically be\n# useful for C code in case the coding convention dictates that all compound\n# types are typedef'ed and only the typedef is referenced, never the tag name.\n# The default value is: NO.\n\nTYPEDEF_HIDES_STRUCT   = NO\n\n# The size of the symbol lookup cache can be set using LOOKUP_CACHE_SIZE. This\n# cache is used to resolve symbols given their name and scope. Since this can be\n# an expensive process and often the same symbol appears multiple times in the\n# code, doxygen keeps a cache of pre-resolved symbols. If the cache is too small\n# doxygen will become slower. If the cache is too large, memory is wasted. The\n# cache size is given by this formula: 2^(16+LOOKUP_CACHE_SIZE). The valid range\n# is 0..9, the default is 0, corresponding to a cache size of 2^16=65536\n# symbols. At the end of a run doxygen will report the cache usage and suggest\n# the optimal cache size from a speed point of view.\n# Minimum value: 0, maximum value: 9, default value: 0.\n\nLOOKUP_CACHE_SIZE      = 0\n\n#---------------------------------------------------------------------------\n# Build related configuration options\n#---------------------------------------------------------------------------\n\n# If the EXTRACT_ALL tag is set to YES, doxygen will assume all entities in\n# documentation are documented, even if no documentation was available. Private\n# class members and static file members will be hidden unless the\n# EXTRACT_PRIVATE respectively EXTRACT_STATIC tags are set to YES.\n# Note: This will also disable the warnings about undocumented members that are\n# normally produced when WARNINGS is set to YES.\n# The default value is: NO.\n\nEXTRACT_ALL            = YES\n\n# If the EXTRACT_PRIVATE tag is set to YES, all private members of a class will\n# be included in the documentation.\n# The default value is: NO.\n\nEXTRACT_PRIVATE        = YES\n\n# If the EXTRACT_PACKAGE tag is set to YES, all members with package or internal\n# scope will be included in the documentation.\n# The default value is: NO.\n\nEXTRACT_PACKAGE        = NO\n\n# If the EXTRACT_STATIC tag is set to YES, all static members of a file will be\n# included in the documentation.\n# The default value is: NO.\n\nEXTRACT_STATIC         = NO\n\n# If the EXTRACT_LOCAL_CLASSES tag is set to YES, classes (and structs) defined\n# locally in source files will be included in the documentation. If set to NO,\n# only classes defined in header files are included. Does not have any effect\n# for Java sources.\n# The default value is: YES.\n\nEXTRACT_LOCAL_CLASSES  = YES\n\n# This flag is only useful for Objective-C code. If set to YES, local methods,\n# which are defined in the implementation section but not in the interface are\n# included in the documentation. If set to NO, only methods in the interface are\n# included.\n# The default value is: NO.\n\nEXTRACT_LOCAL_METHODS  = NO\n\n# If this flag is set to YES, the members of anonymous namespaces will be\n# extracted and appear in the documentation as a namespace called\n# 'anonymous_namespace{file}', where file will be replaced with the base name of\n# the file that contains the anonymous namespace. By default anonymous namespace\n# are hidden.\n# The default value is: NO.\n\nEXTRACT_ANON_NSPACES   = NO\n\n# If the HIDE_UNDOC_MEMBERS tag is set to YES, doxygen will hide all\n# undocumented members inside documented classes or files. If set to NO these\n# members will be included in the various overviews, but no documentation\n# section is generated. This option has no effect if EXTRACT_ALL is enabled.\n# The default value is: NO.\n\nHIDE_UNDOC_MEMBERS     = NO\n\n# If the HIDE_UNDOC_CLASSES tag is set to YES, doxygen will hide all\n# undocumented classes that are normally visible in the class hierarchy. If set\n# to NO, these classes will be included in the various overviews. This option\n# has no effect if EXTRACT_ALL is enabled.\n# The default value is: NO.\n\nHIDE_UNDOC_CLASSES     = NO\n\n# If the HIDE_FRIEND_COMPOUNDS tag is set to YES, doxygen will hide all friend\n# (class|struct|union) declarations. If set to NO, these declarations will be\n# included in the documentation.\n# The default value is: NO.\n\nHIDE_FRIEND_COMPOUNDS  = NO\n\n# If the HIDE_IN_BODY_DOCS tag is set to YES, doxygen will hide any\n# documentation blocks found inside the body of a function. If set to NO, these\n# blocks will be appended to the function's detailed documentation block.\n# The default value is: NO.\n\nHIDE_IN_BODY_DOCS      = NO\n\n# The INTERNAL_DOCS tag determines if documentation that is typed after a\n# \\internal command is included. If the tag is set to NO then the documentation\n# will be excluded. Set it to YES to include the internal documentation.\n# The default value is: NO.\n\nINTERNAL_DOCS          = NO\n\n# If the CASE_SENSE_NAMES tag is set to NO then doxygen will only generate file\n# names in lower-case letters. If set to YES, upper-case letters are also\n# allowed. This is useful if you have classes or files whose names only differ\n# in case and if your file system supports case sensitive file names. Windows\n# and Mac users are advised to set this option to NO.\n# The default value is: system dependent.\n\nCASE_SENSE_NAMES       = NO\n\n# If the HIDE_SCOPE_NAMES tag is set to NO then doxygen will show members with\n# their full class and namespace scopes in the documentation. If set to YES, the\n# scope will be hidden.\n# The default value is: NO.\n\nHIDE_SCOPE_NAMES       = NO\n\n# If the HIDE_COMPOUND_REFERENCE tag is set to NO (default) then doxygen will\n# append additional text to a page's title, such as Class Reference. If set to\n# YES the compound reference will be hidden.\n# The default value is: NO.\n\nHIDE_COMPOUND_REFERENCE= NO\n\n# If the SHOW_INCLUDE_FILES tag is set to YES then doxygen will put a list of\n# the files that are included by a file in the documentation of that file.\n# The default value is: YES.\n\nSHOW_INCLUDE_FILES     = YES\n\n# If the SHOW_GROUPED_MEMB_INC tag is set to YES then Doxygen will add for each\n# grouped member an include statement to the documentation, telling the reader\n# which file to include in order to use the member.\n# The default value is: NO.\n\nSHOW_GROUPED_MEMB_INC  = NO\n\n# If the FORCE_LOCAL_INCLUDES tag is set to YES then doxygen will list include\n# files with double quotes in the documentation rather than with sharp brackets.\n# The default value is: NO.\n\nFORCE_LOCAL_INCLUDES   = NO\n\n# If the INLINE_INFO tag is set to YES then a tag [inline] is inserted in the\n# documentation for inline members.\n# The default value is: YES.\n\nINLINE_INFO            = YES\n\n# If the SORT_MEMBER_DOCS tag is set to YES then doxygen will sort the\n# (detailed) documentation of file and class members alphabetically by member\n# name. If set to NO, the members will appear in declaration order.\n# The default value is: YES.\n\nSORT_MEMBER_DOCS       = YES\n\n# If the SORT_BRIEF_DOCS tag is set to YES then doxygen will sort the brief\n# descriptions of file, namespace and class members alphabetically by member\n# name. If set to NO, the members will appear in declaration order. Note that\n# this will also influence the order of the classes in the class list.\n# The default value is: NO.\n\nSORT_BRIEF_DOCS        = NO\n\n# If the SORT_MEMBERS_CTORS_1ST tag is set to YES then doxygen will sort the\n# (brief and detailed) documentation of class members so that constructors and\n# destructors are listed first. If set to NO the constructors will appear in the\n# respective orders defined by SORT_BRIEF_DOCS and SORT_MEMBER_DOCS.\n# Note: If SORT_BRIEF_DOCS is set to NO this option is ignored for sorting brief\n# member documentation.\n# Note: If SORT_MEMBER_DOCS is set to NO this option is ignored for sorting\n# detailed member documentation.\n# The default value is: NO.\n\nSORT_MEMBERS_CTORS_1ST = NO\n\n# If the SORT_GROUP_NAMES tag is set to YES then doxygen will sort the hierarchy\n# of group names into alphabetical order. If set to NO the group names will\n# appear in their defined order.\n# The default value is: NO.\n\nSORT_GROUP_NAMES       = NO\n\n# If the SORT_BY_SCOPE_NAME tag is set to YES, the class list will be sorted by\n# fully-qualified names, including namespaces. If set to NO, the class list will\n# be sorted only by class name, not including the namespace part.\n# Note: This option is not very useful if HIDE_SCOPE_NAMES is set to YES.\n# Note: This option applies only to the class list, not to the alphabetical\n# list.\n# The default value is: NO.\n\nSORT_BY_SCOPE_NAME     = NO\n\n# If the STRICT_PROTO_MATCHING option is enabled and doxygen fails to do proper\n# type resolution of all parameters of a function it will reject a match between\n# the prototype and the implementation of a member function even if there is\n# only one candidate or it is obvious which candidate to choose by doing a\n# simple string match. By disabling STRICT_PROTO_MATCHING doxygen will still\n# accept a match between prototype and implementation in such cases.\n# The default value is: NO.\n\nSTRICT_PROTO_MATCHING  = NO\n\n# The GENERATE_TODOLIST tag can be used to enable (YES) or disable (NO) the todo\n# list. This list is created by putting \\todo commands in the documentation.\n# The default value is: YES.\n\nGENERATE_TODOLIST      = YES\n\n# The GENERATE_TESTLIST tag can be used to enable (YES) or disable (NO) the test\n# list. This list is created by putting \\test commands in the documentation.\n# The default value is: YES.\n\nGENERATE_TESTLIST      = YES\n\n# The GENERATE_BUGLIST tag can be used to enable (YES) or disable (NO) the bug\n# list. This list is created by putting \\bug commands in the documentation.\n# The default value is: YES.\n\nGENERATE_BUGLIST       = YES\n\n# The GENERATE_DEPRECATEDLIST tag can be used to enable (YES) or disable (NO)\n# the deprecated list. This list is created by putting \\deprecated commands in\n# the documentation.\n# The default value is: YES.\n\nGENERATE_DEPRECATEDLIST= YES\n\n# The ENABLED_SECTIONS tag can be used to enable conditional documentation\n# sections, marked by \\if <section_label> ... \\endif and \\cond <section_label>\n# ... \\endcond blocks.\n\nENABLED_SECTIONS       =\n\n# The MAX_INITIALIZER_LINES tag determines the maximum number of lines that the\n# initial value of a variable or macro / define can have for it to appear in the\n# documentation. If the initializer consists of more lines than specified here\n# it will be hidden. Use a value of 0 to hide initializers completely. The\n# appearance of the value of individual variables and macros / defines can be\n# controlled using \\showinitializer or \\hideinitializer command in the\n# documentation regardless of this setting.\n# Minimum value: 0, maximum value: 10000, default value: 30.\n\nMAX_INITIALIZER_LINES  = 30\n\n# Set the SHOW_USED_FILES tag to NO to disable the list of files generated at\n# the bottom of the documentation of classes and structs. If set to YES, the\n# list will mention the files that were used to generate the documentation.\n# The default value is: YES.\n\nSHOW_USED_FILES        = YES\n\n# Set the SHOW_FILES tag to NO to disable the generation of the Files page. This\n# will remove the Files entry from the Quick Index and from the Folder Tree View\n# (if specified).\n# The default value is: YES.\n\nSHOW_FILES             = YES\n\n# Set the SHOW_NAMESPACES tag to NO to disable the generation of the Namespaces\n# page. This will remove the Namespaces entry from the Quick Index and from the\n# Folder Tree View (if specified).\n# The default value is: YES.\n\nSHOW_NAMESPACES        = YES\n\n# The FILE_VERSION_FILTER tag can be used to specify a program or script that\n# doxygen should invoke to get the current version for each file (typically from\n# the version control system). Doxygen will invoke the program by executing (via\n# popen()) the command command input-file, where command is the value of the\n# FILE_VERSION_FILTER tag, and input-file is the name of an input file provided\n# by doxygen. Whatever the program writes to standard output is used as the file\n# version. For an example see the documentation.\n\nFILE_VERSION_FILTER    =\n\n# The LAYOUT_FILE tag can be used to specify a layout file which will be parsed\n# by doxygen. The layout file controls the global structure of the generated\n# output files in an output format independent way. To create the layout file\n# that represents doxygen's defaults, run doxygen with the -l option. You can\n# optionally specify a file name after the option, if omitted DoxygenLayout.xml\n# will be used as the name of the layout file.\n#\n# Note that if you run doxygen from a directory containing a file called\n# DoxygenLayout.xml, doxygen will parse it automatically even if the LAYOUT_FILE\n# tag is left empty.\n\nLAYOUT_FILE            = config/DoxygenLayout.xml\n\n# The CITE_BIB_FILES tag can be used to specify one or more bib files containing\n# the reference definitions. This must be a list of .bib files. The .bib\n# extension is automatically appended if omitted. This requires the bibtex tool\n# to be installed. See also http://en.wikipedia.org/wiki/BibTeX for more info.\n# For LaTeX the style of the bibliography can be controlled using\n# LATEX_BIB_STYLE. To use this feature you need bibtex and perl available in the\n# search path. See also \\cite for info how to create references.\n\nCITE_BIB_FILES         =\n\n#---------------------------------------------------------------------------\n# Configuration options related to warning and progress messages\n#---------------------------------------------------------------------------\n\n# The QUIET tag can be used to turn on/off the messages that are generated to\n# standard output by doxygen. If QUIET is set to YES this implies that the\n# messages are off.\n# The default value is: NO.\n\nQUIET                  = YES\n\n# The WARNINGS tag can be used to turn on/off the warning messages that are\n# generated to standard error (stderr) by doxygen. If WARNINGS is set to YES\n# this implies that the warnings are on.\n#\n# Tip: Turn warnings on while writing the documentation.\n# The default value is: YES.\n\nWARNINGS               = YES\n\n# If the WARN_IF_UNDOCUMENTED tag is set to YES then doxygen will generate\n# warnings for undocumented members. If EXTRACT_ALL is set to YES then this flag\n# will automatically be disabled.\n# The default value is: YES.\n\nWARN_IF_UNDOCUMENTED   = YES\n\n# If the WARN_IF_DOC_ERROR tag is set to YES, doxygen will generate warnings for\n# potential errors in the documentation, such as not documenting some parameters\n# in a documented function, or documenting parameters that don't exist or using\n# markup commands wrongly.\n# The default value is: YES.\n\nWARN_IF_DOC_ERROR      = YES\n\n# This WARN_NO_PARAMDOC option can be enabled to get warnings for functions that\n# are documented, but have no documentation for their parameters or return\n# value. If set to NO, doxygen will only warn about wrong or incomplete\n# parameter documentation, but not about the absence of documentation.\n# The default value is: NO.\n\nWARN_NO_PARAMDOC       = NO\n\n# If the WARN_AS_ERROR tag is set to YES then doxygen will immediately stop when\n# a warning is encountered.\n# The default value is: NO.\n\nWARN_AS_ERROR          = NO\n\n# The WARN_FORMAT tag determines the format of the warning messages that doxygen\n# can produce. The string should contain the $file, $line, and $text tags, which\n# will be replaced by the file and line number from which the warning originated\n# and the warning text. Optionally the format may contain $version, which will\n# be replaced by the version of the file (if it could be obtained via\n# FILE_VERSION_FILTER)\n# The default value is: $file:$line: $text.\n\nWARN_FORMAT            = \"$file:$line: $text\"\n\n# The WARN_LOGFILE tag can be used to specify a file to which warning and error\n# messages should be written. If left blank the output is written to standard\n# error (stderr).\n\nWARN_LOGFILE           =\n\n#---------------------------------------------------------------------------\n# Configuration options related to the input files\n#---------------------------------------------------------------------------\n\n# The INPUT tag is used to specify the files and/or directories that contain\n# documented source files. You may enter file names like myfile.cpp or\n# directories like /usr/src/myproject. Separate the files or directories with\n# spaces. See also FILE_PATTERNS and EXTENSION_MAPPING\n# Note: If this tag is empty the current directory is searched.\n\nINPUT                  = doc/main.md \\\n                         c++lib \\\n                         core \\\n                         core/pythoncdb \\\n                         core/cadabra2 \\\n                         doc/modules.dox \\\n                         core/cadabra2_defaults.py \\\n                         core/algorithms \\\n                         core/properties \\\n                         client_server \\\n                         frontend/common \\\n                         frontend/gtkmm \\\n                         frontend/osx/Cadabra \\\n                         frontend/osx/Cadabra/Cadabra\n\n# This tag can be used to specify the character encoding of the source files\n# that doxygen parses. Internally doxygen uses the UTF-8 encoding. Doxygen uses\n# libiconv (or the iconv built into libc) for the transcoding. See the libiconv\n# documentation (see: http://www.gnu.org/software/libiconv) for the list of\n# possible encodings.\n# The default value is: UTF-8.\n\nINPUT_ENCODING         = UTF-8\n\n# If the value of the INPUT tag contains directories, you can use the\n# FILE_PATTERNS tag to specify one or more wildcard patterns (like *.cpp and\n# *.h) to filter out the source-files in the directories.\n#\n# Note that for custom extensions or not directly supported extensions you also\n# need to set EXTENSION_MAPPING for the extension otherwise the files are not\n# read by doxygen.\n#\n# If left blank the following patterns are tested:*.c, *.cc, *.cxx, *.cpp,\n# *.c++, *.java, *.ii, *.ixx, *.ipp, *.i++, *.inl, *.idl, *.ddl, *.odl, *.h,\n# *.hh, *.hxx, *.hpp, *.h++, *.cs, *.d, *.php, *.php4, *.php5, *.phtml, *.inc,\n# *.m, *.markdown, *.md, *.mm, *.dox, *.py, *.pyw, *.f90, *.f, *.for, *.tcl,\n# *.vhd, *.vhdl, *.ucf, *.qsf, *.as and *.js.\n\nFILE_PATTERNS          =\n\n# The RECURSIVE tag can be used to specify whether or not subdirectories should\n# be searched for input files as well.\n# The default value is: NO.\n\nRECURSIVE              = NO\n\n# The EXCLUDE tag can be used to specify files and/or directories that should be\n# excluded from the INPUT source files. This way you can easily exclude a\n# subdirectory from a directory tree whose root is specified with the INPUT tag.\n#\n# Note that relative paths are relative to the directory from which doxygen is\n# run.\n\nEXCLUDE                = core/tree.hh \\\n                         client_server/tree.hh \\\n                         frontend/common/lodepng.cc \\\n                         frontend/common/lodepng.h\n\n# The EXCLUDE_SYMLINKS tag can be used to select whether or not files or\n# directories that are symbolic links (a Unix file system feature) are excluded\n# from the input.\n# The default value is: NO.\n\nEXCLUDE_SYMLINKS       = NO\n\n# If the value of the INPUT tag contains directories, you can use the\n# EXCLUDE_PATTERNS tag to specify one or more wildcard patterns to exclude\n# certain files from those directories.\n#\n# Note that the wildcards are matched against the file with absolute path, so to\n# exclude all test directories for example use the pattern */test/*\n\nEXCLUDE_PATTERNS       =\n\n# The EXCLUDE_SYMBOLS tag can be used to specify one or more symbol names\n# (namespaces, classes, functions, etc.) that should be excluded from the\n# output. The symbol name can be a fully qualified name, a word, or if the\n# wildcard * is used, a substring. Examples: ANamespace, AClass,\n# AClass::ANamespace, ANamespace::*Test\n#\n# Note that the wildcards are matched against the file with absolute path, so to\n# exclude all test directories use the pattern */test/*\n\nEXCLUDE_SYMBOLS        =\n\n# The EXAMPLE_PATH tag can be used to specify one or more files or directories\n# that contain example code fragments that are included (see the \\include\n# command).\n\nEXAMPLE_PATH           = .\n\n# If the value of the EXAMPLE_PATH tag contains directories, you can use the\n# EXAMPLE_PATTERNS tag to specify one or more wildcard pattern (like *.cpp and\n# *.h) to filter out the source-files in the directories. If left blank all\n# files are included.\n\nEXAMPLE_PATTERNS       =\n\n# If the EXAMPLE_RECURSIVE tag is set to YES then subdirectories will be\n# searched for input files to be used with the \\include or \\dontinclude commands\n# irrespective of the value of the RECURSIVE tag.\n# The default value is: NO.\n\nEXAMPLE_RECURSIVE      = NO\n\n# The IMAGE_PATH tag can be used to specify one or more files or directories\n# that contain images that are to be included in the documentation (see the\n# \\image command).\n\nIMAGE_PATH             =\n\n# The INPUT_FILTER tag can be used to specify a program that doxygen should\n# invoke to filter for each input file. Doxygen will invoke the filter program\n# by executing (via popen()) the command:\n#\n# <filter> <input-file>\n#\n# where <filter> is the value of the INPUT_FILTER tag, and <input-file> is the\n# name of an input file. Doxygen will then use the output that the filter\n# program writes to standard output. If FILTER_PATTERNS is specified, this tag\n# will be ignored.\n#\n# Note that the filter must not add or remove lines; it is applied before the\n# code is scanned, but not when the output code is generated. If lines are added\n# or removed, the anchors will not be placed correctly.\n#\n# Note that for custom extensions or not directly supported extensions you also\n# need to set EXTENSION_MAPPING for the extension otherwise the files are not\n# properly processed by doxygen.\n\nINPUT_FILTER           =\n\n# The FILTER_PATTERNS tag can be used to specify filters on a per file pattern\n# basis. Doxygen will compare the file name with each pattern and apply the\n# filter if there is a match. The filters are a list of the form: pattern=filter\n# (like *.cpp=my_cpp_filter). See INPUT_FILTER for further information on how\n# filters are used. If the FILTER_PATTERNS tag is empty or if none of the\n# patterns match the file name, INPUT_FILTER is applied.\n#\n# Note that for custom extensions or not directly supported extensions you also\n# need to set EXTENSION_MAPPING for the extension otherwise the files are not\n# properly processed by doxygen.\n\nFILTER_PATTERNS        =\n\n# If the FILTER_SOURCE_FILES tag is set to YES, the input filter (if set using\n# INPUT_FILTER) will also be used to filter the input files that are used for\n# producing the source files to browse (i.e. when SOURCE_BROWSER is set to YES).\n# The default value is: NO.\n\nFILTER_SOURCE_FILES    = NO\n\n# The FILTER_SOURCE_PATTERNS tag can be used to specify source filters per file\n# pattern. A pattern will override the setting for FILTER_PATTERN (if any) and\n# it is also possible to disable source filtering for a specific pattern using\n# *.ext= (so without naming a filter).\n# This tag requires that the tag FILTER_SOURCE_FILES is set to YES.\n\nFILTER_SOURCE_PATTERNS =\n\n# If the USE_MDFILE_AS_MAINPAGE tag refers to the name of a markdown file that\n# is part of the input, its contents will be placed on the main page\n# (index.html). This can be useful if you have a project on for instance GitHub\n# and want to reuse the introduction page also for the doxygen output.\n\nUSE_MDFILE_AS_MAINPAGE =\n\n#---------------------------------------------------------------------------\n# Configuration options related to source browsing\n#---------------------------------------------------------------------------\n\n# If the SOURCE_BROWSER tag is set to YES then a list of source files will be\n# generated. Documented entities will be cross-referenced with these sources.\n#\n# Note: To get rid of all source code in the generated output, make sure that\n# also VERBATIM_HEADERS is set to NO.\n# The default value is: NO.\n\nSOURCE_BROWSER         = NO\n\n# Setting the INLINE_SOURCES tag to YES will include the body of functions,\n# classes and enums directly into the documentation.\n# The default value is: NO.\n\nINLINE_SOURCES         = NO\n\n# Setting the STRIP_CODE_COMMENTS tag to YES will instruct doxygen to hide any\n# special comment blocks from generated source code fragments. Normal C, C++ and\n# Fortran comments will always remain visible.\n# The default value is: YES.\n\nSTRIP_CODE_COMMENTS    = YES\n\n# If the REFERENCED_BY_RELATION tag is set to YES then for each documented\n# function all documented functions referencing it will be listed.\n# The default value is: NO.\n\nREFERENCED_BY_RELATION = NO\n\n# If the REFERENCES_RELATION tag is set to YES then for each documented function\n# all documented entities called/used by that function will be listed.\n# The default value is: NO.\n\nREFERENCES_RELATION    = NO\n\n# If the REFERENCES_LINK_SOURCE tag is set to YES and SOURCE_BROWSER tag is set\n# to YES then the hyperlinks from functions in REFERENCES_RELATION and\n# REFERENCED_BY_RELATION lists will link to the source code. Otherwise they will\n# link to the documentation.\n# The default value is: YES.\n\nREFERENCES_LINK_SOURCE = YES\n\n# If SOURCE_TOOLTIPS is enabled (the default) then hovering a hyperlink in the\n# source code will show a tooltip with additional information such as prototype,\n# brief description and links to the definition and documentation. Since this\n# will make the HTML file larger and loading of large files a bit slower, you\n# can opt to disable this feature.\n# The default value is: YES.\n# This tag requires that the tag SOURCE_BROWSER is set to YES.\n\nSOURCE_TOOLTIPS        = YES\n\n# If the USE_HTAGS tag is set to YES then the references to source code will\n# point to the HTML generated by the htags(1) tool instead of doxygen built-in\n# source browser. The htags tool is part of GNU's global source tagging system\n# (see http://www.gnu.org/software/global/global.html). You will need version\n# 4.8.6 or higher.\n#\n# To use it do the following:\n# - Install the latest version of global\n# - Enable SOURCE_BROWSER and USE_HTAGS in the config file\n# - Make sure the INPUT points to the root of the source tree\n# - Run doxygen as normal\n#\n# Doxygen will invoke htags (and that will in turn invoke gtags), so these\n# tools must be available from the command line (i.e. in the search path).\n#\n# The result: instead of the source browser generated by doxygen, the links to\n# source code will now point to the output of htags.\n# The default value is: NO.\n# This tag requires that the tag SOURCE_BROWSER is set to YES.\n\nUSE_HTAGS              = NO\n\n# If the VERBATIM_HEADERS tag is set the YES then doxygen will generate a\n# verbatim copy of the header file for each class for which an include is\n# specified. Set to NO to disable this.\n# See also: Section \\class.\n# The default value is: YES.\n\nVERBATIM_HEADERS       = YES\n\n# If the CLANG_ASSISTED_PARSING tag is set to YES then doxygen will use the\n# clang parser (see: http://clang.llvm.org/) for more accurate parsing at the\n# cost of reduced performance. This can be particularly helpful with template\n# rich C++ code for which doxygen's built-in parser lacks the necessary type\n# information.\n# Note: The availability of this option depends on whether or not doxygen was\n# generated with the -Duse-libclang=ON option for CMake.\n# The default value is: NO.\n\nCLANG_ASSISTED_PARSING = NO\n\n# If clang assisted parsing is enabled you can provide the compiler with command\n# line options that you would normally use when invoking the compiler. Note that\n# the include paths will already be set by doxygen for the files and directories\n# specified with INPUT and INCLUDE_PATH.\n# This tag requires that the tag CLANG_ASSISTED_PARSING is set to YES.\n\nCLANG_OPTIONS          =\n\n#---------------------------------------------------------------------------\n# Configuration options related to the alphabetical class index\n#---------------------------------------------------------------------------\n\n# If the ALPHABETICAL_INDEX tag is set to YES, an alphabetical index of all\n# compounds will be generated. Enable this if the project contains a lot of\n# classes, structs, unions or interfaces.\n# The default value is: YES.\n\nALPHABETICAL_INDEX     = YES\n\n# The COLS_IN_ALPHA_INDEX tag can be used to specify the number of columns in\n# which the alphabetical index list will be split.\n# Minimum value: 1, maximum value: 20, default value: 5.\n# This tag requires that the tag ALPHABETICAL_INDEX is set to YES.\n\nCOLS_IN_ALPHA_INDEX    = 5\n\n# In case all classes in a project start with a common prefix, all classes will\n# be put under the same header in the alphabetical index. The IGNORE_PREFIX tag\n# can be used to specify a prefix (or a list of prefixes) that should be ignored\n# while generating the index headers.\n# This tag requires that the tag ALPHABETICAL_INDEX is set to YES.\n\nIGNORE_PREFIX          =\n\n#---------------------------------------------------------------------------\n# Configuration options related to the HTML output\n#---------------------------------------------------------------------------\n\n# If the GENERATE_HTML tag is set to YES, doxygen will generate HTML output\n# The default value is: YES.\n\nGENERATE_HTML          = YES\n\n# The HTML_OUTPUT tag is used to specify where the HTML docs will be put. If a\n# relative path is entered the value of OUTPUT_DIRECTORY will be put in front of\n# it.\n# The default directory is: html.\n# This tag requires that the tag GENERATE_HTML is set to YES.\n\nHTML_OUTPUT            = html\n\n# The HTML_FILE_EXTENSION tag can be used to specify the file extension for each\n# generated HTML page (for example: .htm, .php, .asp).\n# The default value is: .html.\n# This tag requires that the tag GENERATE_HTML is set to YES.\n\nHTML_FILE_EXTENSION    = .html\n\n# The HTML_HEADER tag can be used to specify a user-defined HTML header file for\n# each generated HTML page. If the tag is left blank doxygen will generate a\n# standard header.\n#\n# To get valid HTML the header file that includes any scripts and style sheets\n# that doxygen needs, which is dependent on the configuration options used (e.g.\n# the setting GENERATE_TREEVIEW). It is highly recommended to start with a\n# default header using\n# doxygen -w html new_header.html new_footer.html new_stylesheet.css\n# YourConfigFile\n# and then modify the file new_header.html. See also section \"Doxygen usage\"\n# for information on how to generate the default header that doxygen normally\n# uses.\n# Note: The header is subject to change so you typically have to regenerate the\n# default header when upgrading to a newer version of doxygen. For a description\n# of the possible markers and block names see the documentation.\n# This tag requires that the tag GENERATE_HTML is set to YES.\n\nHTML_HEADER            =\n\n# The HTML_FOOTER tag can be used to specify a user-defined HTML footer for each\n# generated HTML page. If the tag is left blank doxygen will generate a standard\n# footer. See HTML_HEADER for more information on how to generate a default\n# footer and what special commands can be used inside the footer. See also\n# section \"Doxygen usage\" for information on how to generate the default footer\n# that doxygen normally uses.\n# This tag requires that the tag GENERATE_HTML is set to YES.\n\nHTML_FOOTER            =\n\n# The HTML_STYLESHEET tag can be used to specify a user-defined cascading style\n# sheet that is used by each HTML page. It can be used to fine-tune the look of\n# the HTML output. If left blank doxygen will generate a default style sheet.\n# See also section \"Doxygen usage\" for information on how to generate the style\n# sheet that doxygen normally uses.\n# Note: It is recommended to use HTML_EXTRA_STYLESHEET instead of this tag, as\n# it is more robust and this tag (HTML_STYLESHEET) will in the future become\n# obsolete.\n# This tag requires that the tag GENERATE_HTML is set to YES.\n\nHTML_STYLESHEET        =\n\n# The HTML_EXTRA_STYLESHEET tag can be used to specify additional user-defined\n# cascading style sheets that are included after the standard style sheets\n# created by doxygen. Using this option one can overrule certain style aspects.\n# This is preferred over using HTML_STYLESHEET since it does not replace the\n# standard style sheet and is therefore more robust against future updates.\n# Doxygen will copy the style sheet files to the output directory.\n# Note: The order of the extra style sheet files is of importance (e.g. the last\n# style sheet in the list overrules the setting of the previous ones in the\n# list). For an example see the documentation.\n# This tag requires that the tag GENERATE_HTML is set to YES.\n\nHTML_EXTRA_STYLESHEET  = config/DoxygenStyle.css\n\n# The HTML_EXTRA_FILES tag can be used to specify one or more extra images or\n# other source files which should be copied to the HTML output directory. Note\n# that these files will be copied to the base HTML output directory. Use the\n# $relpath^ marker in the HTML_HEADER and/or HTML_FOOTER files to load these\n# files. In the HTML_STYLESHEET file, use the file name only. Also note that the\n# files will be copied as-is; there are no commands or markers available.\n# This tag requires that the tag GENERATE_HTML is set to YES.\n\nHTML_EXTRA_FILES       =\n\n# The HTML_COLORSTYLE_HUE tag controls the color of the HTML output. Doxygen\n# will adjust the colors in the style sheet and background images according to\n# this color. Hue is specified as an angle on a colorwheel, see\n# http://en.wikipedia.org/wiki/Hue for more information. For instance the value\n# 0 represents red, 60 is yellow, 120 is green, 180 is cyan, 240 is blue, 300\n# purple, and 360 is red again.\n# Minimum value: 0, maximum value: 359, default value: 220.\n# This tag requires that the tag GENERATE_HTML is set to YES.\n\nHTML_COLORSTYLE_HUE    = 220\n\n# The HTML_COLORSTYLE_SAT tag controls the purity (or saturation) of the colors\n# in the HTML output. For a value of 0 the output will use grayscales only. A\n# value of 255 will produce the most vivid colors.\n# Minimum value: 0, maximum value: 255, default value: 100.\n# This tag requires that the tag GENERATE_HTML is set to YES.\n\nHTML_COLORSTYLE_SAT    = 100\n\n# The HTML_COLORSTYLE_GAMMA tag controls the gamma correction applied to the\n# luminance component of the colors in the HTML output. Values below 100\n# gradually make the output lighter, whereas values above 100 make the output\n# darker. The value divided by 100 is the actual gamma applied, so 80 represents\n# a gamma of 0.8, The value 220 represents a gamma of 2.2, and 100 does not\n# change the gamma.\n# Minimum value: 40, maximum value: 240, default value: 80.\n# This tag requires that the tag GENERATE_HTML is set to YES.\n\nHTML_COLORSTYLE_GAMMA  = 80\n\n# If the HTML_TIMESTAMP tag is set to YES then the footer of each generated HTML\n# page will contain the date and time when the page was generated. Setting this\n# to YES can help to show when doxygen was last run and thus if the\n# documentation is up to date.\n# The default value is: NO.\n# This tag requires that the tag GENERATE_HTML is set to YES.\n\nHTML_TIMESTAMP         = YES\n\n# If the HTML_DYNAMIC_SECTIONS tag is set to YES then the generated HTML\n# documentation will contain sections that can be hidden and shown after the\n# page has loaded.\n# The default value is: NO.\n# This tag requires that the tag GENERATE_HTML is set to YES.\n\nHTML_DYNAMIC_SECTIONS  = NO\n\n# With HTML_INDEX_NUM_ENTRIES one can control the preferred number of entries\n# shown in the various tree structured indices initially; the user can expand\n# and collapse entries dynamically later on. Doxygen will expand the tree to\n# such a level that at most the specified number of entries are visible (unless\n# a fully collapsed tree already exceeds this amount). So setting the number of\n# entries 1 will produce a full collapsed tree by default. 0 is a special value\n# representing an infinite number of entries and will result in a full expanded\n# tree by default.\n# Minimum value: 0, maximum value: 9999, default value: 100.\n# This tag requires that the tag GENERATE_HTML is set to YES.\n\nHTML_INDEX_NUM_ENTRIES = 100\n\n# If the GENERATE_DOCSET tag is set to YES, additional index files will be\n# generated that can be used as input for Apple's Xcode 3 integrated development\n# environment (see: http://developer.apple.com/tools/xcode/), introduced with\n# OSX 10.5 (Leopard). To create a documentation set, doxygen will generate a\n# Makefile in the HTML output directory. Running make will produce the docset in\n# that directory and running make install will install the docset in\n# ~/Library/Developer/Shared/Documentation/DocSets so that Xcode will find it at\n# startup. See http://developer.apple.com/tools/creatingdocsetswithdoxygen.html\n# for more information.\n# The default value is: NO.\n# This tag requires that the tag GENERATE_HTML is set to YES.\n\nGENERATE_DOCSET        = NO\n\n# This tag determines the name of the docset feed. A documentation feed provides\n# an umbrella under which multiple documentation sets from a single provider\n# (such as a company or product suite) can be grouped.\n# The default value is: Doxygen generated docs.\n# This tag requires that the tag GENERATE_DOCSET is set to YES.\n\nDOCSET_FEEDNAME        = \"Doxygen generated docs\"\n\n# This tag specifies a string that should uniquely identify the documentation\n# set bundle. This should be a reverse domain-name style string, e.g.\n# com.mycompany.MyDocSet. Doxygen will append .docset to the name.\n# The default value is: org.doxygen.Project.\n# This tag requires that the tag GENERATE_DOCSET is set to YES.\n\nDOCSET_BUNDLE_ID       = org.doxygen.Project\n\n# The DOCSET_PUBLISHER_ID tag specifies a string that should uniquely identify\n# the documentation publisher. This should be a reverse domain-name style\n# string, e.g. com.mycompany.MyDocSet.documentation.\n# The default value is: org.doxygen.Publisher.\n# This tag requires that the tag GENERATE_DOCSET is set to YES.\n\nDOCSET_PUBLISHER_ID    = org.doxygen.Publisher\n\n# The DOCSET_PUBLISHER_NAME tag identifies the documentation publisher.\n# The default value is: Publisher.\n# This tag requires that the tag GENERATE_DOCSET is set to YES.\n\nDOCSET_PUBLISHER_NAME  = Publisher\n\n# If the GENERATE_HTMLHELP tag is set to YES then doxygen generates three\n# additional HTML index files: index.hhp, index.hhc, and index.hhk. The\n# index.hhp is a project file that can be read by Microsoft's HTML Help Workshop\n# (see: http://www.microsoft.com/en-us/download/details.aspx?id=21138) on\n# Windows.\n#\n# The HTML Help Workshop contains a compiler that can convert all HTML output\n# generated by doxygen into a single compiled HTML file (.chm). Compiled HTML\n# files are now used as the Windows 98 help format, and will replace the old\n# Windows help format (.hlp) on all Windows platforms in the future. Compressed\n# HTML files also contain an index, a table of contents, and you can search for\n# words in the documentation. The HTML workshop also contains a viewer for\n# compressed HTML files.\n# The default value is: NO.\n# This tag requires that the tag GENERATE_HTML is set to YES.\n\nGENERATE_HTMLHELP      = NO\n\n# The CHM_FILE tag can be used to specify the file name of the resulting .chm\n# file. You can add a path in front of the file if the result should not be\n# written to the html output directory.\n# This tag requires that the tag GENERATE_HTMLHELP is set to YES.\n\nCHM_FILE               =\n\n# The HHC_LOCATION tag can be used to specify the location (absolute path\n# including file name) of the HTML help compiler (hhc.exe). If non-empty,\n# doxygen will try to run the HTML help compiler on the generated index.hhp.\n# The file has to be specified with full path.\n# This tag requires that the tag GENERATE_HTMLHELP is set to YES.\n\nHHC_LOCATION           =\n\n# The GENERATE_CHI flag controls if a separate .chi index file is generated\n# (YES) or that it should be included in the master .chm file (NO).\n# The default value is: NO.\n# This tag requires that the tag GENERATE_HTMLHELP is set to YES.\n\nGENERATE_CHI           = NO\n\n# The CHM_INDEX_ENCODING is used to encode HtmlHelp index (hhk), content (hhc)\n# and project file content.\n# This tag requires that the tag GENERATE_HTMLHELP is set to YES.\n\nCHM_INDEX_ENCODING     =\n\n# The BINARY_TOC flag controls whether a binary table of contents is generated\n# (YES) or a normal table of contents (NO) in the .chm file. Furthermore it\n# enables the Previous and Next buttons.\n# The default value is: NO.\n# This tag requires that the tag GENERATE_HTMLHELP is set to YES.\n\nBINARY_TOC             = NO\n\n# The TOC_EXPAND flag can be set to YES to add extra items for group members to\n# the table of contents of the HTML help documentation and to the tree view.\n# The default value is: NO.\n# This tag requires that the tag GENERATE_HTMLHELP is set to YES.\n\nTOC_EXPAND             = NO\n\n# If the GENERATE_QHP tag is set to YES and both QHP_NAMESPACE and\n# QHP_VIRTUAL_FOLDER are set, an additional index file will be generated that\n# can be used as input for Qt's qhelpgenerator to generate a Qt Compressed Help\n# (.qch) of the generated HTML documentation.\n# The default value is: NO.\n# This tag requires that the tag GENERATE_HTML is set to YES.\n\nGENERATE_QHP           = NO\n\n# If the QHG_LOCATION tag is specified, the QCH_FILE tag can be used to specify\n# the file name of the resulting .qch file. The path specified is relative to\n# the HTML output folder.\n# This tag requires that the tag GENERATE_QHP is set to YES.\n\nQCH_FILE               =\n\n# The QHP_NAMESPACE tag specifies the namespace to use when generating Qt Help\n# Project output. For more information please see Qt Help Project / Namespace\n# (see: http://qt-project.org/doc/qt-4.8/qthelpproject.html#namespace).\n# The default value is: org.doxygen.Project.\n# This tag requires that the tag GENERATE_QHP is set to YES.\n\nQHP_NAMESPACE          = org.doxygen.Project\n\n# The QHP_VIRTUAL_FOLDER tag specifies the namespace to use when generating Qt\n# Help Project output. For more information please see Qt Help Project / Virtual\n# Folders (see: http://qt-project.org/doc/qt-4.8/qthelpproject.html#virtual-\n# folders).\n# The default value is: doc.\n# This tag requires that the tag GENERATE_QHP is set to YES.\n\nQHP_VIRTUAL_FOLDER     = doc\n\n# If the QHP_CUST_FILTER_NAME tag is set, it specifies the name of a custom\n# filter to add. For more information please see Qt Help Project / Custom\n# Filters (see: http://qt-project.org/doc/qt-4.8/qthelpproject.html#custom-\n# filters).\n# This tag requires that the tag GENERATE_QHP is set to YES.\n\nQHP_CUST_FILTER_NAME   =\n\n# The QHP_CUST_FILTER_ATTRS tag specifies the list of the attributes of the\n# custom filter to add. For more information please see Qt Help Project / Custom\n# Filters (see: http://qt-project.org/doc/qt-4.8/qthelpproject.html#custom-\n# filters).\n# This tag requires that the tag GENERATE_QHP is set to YES.\n\nQHP_CUST_FILTER_ATTRS  =\n\n# The QHP_SECT_FILTER_ATTRS tag specifies the list of the attributes this\n# project's filter section matches. Qt Help Project / Filter Attributes (see:\n# http://qt-project.org/doc/qt-4.8/qthelpproject.html#filter-attributes).\n# This tag requires that the tag GENERATE_QHP is set to YES.\n\nQHP_SECT_FILTER_ATTRS  =\n\n# The QHG_LOCATION tag can be used to specify the location of Qt's\n# qhelpgenerator. If non-empty doxygen will try to run qhelpgenerator on the\n# generated .qhp file.\n# This tag requires that the tag GENERATE_QHP is set to YES.\n\nQHG_LOCATION           =\n\n# If the GENERATE_ECLIPSEHELP tag is set to YES, additional index files will be\n# generated, together with the HTML files, they form an Eclipse help plugin. To\n# install this plugin and make it available under the help contents menu in\n# Eclipse, the contents of the directory containing the HTML and XML files needs\n# to be copied into the plugins directory of eclipse. The name of the directory\n# within the plugins directory should be the same as the ECLIPSE_DOC_ID value.\n# After copying Eclipse needs to be restarted before the help appears.\n# The default value is: NO.\n# This tag requires that the tag GENERATE_HTML is set to YES.\n\nGENERATE_ECLIPSEHELP   = NO\n\n# A unique identifier for the Eclipse help plugin. When installing the plugin\n# the directory name containing the HTML and XML files should also have this\n# name. Each documentation set should have its own identifier.\n# The default value is: org.doxygen.Project.\n# This tag requires that the tag GENERATE_ECLIPSEHELP is set to YES.\n\nECLIPSE_DOC_ID         = org.doxygen.Project\n\n# If you want full control over the layout of the generated HTML pages it might\n# be necessary to disable the index and replace it with your own. The\n# DISABLE_INDEX tag can be used to turn on/off the condensed index (tabs) at top\n# of each HTML page. A value of NO enables the index and the value YES disables\n# it. Since the tabs in the index contain the same information as the navigation\n# tree, you can set this option to YES if you also set GENERATE_TREEVIEW to YES.\n# The default value is: NO.\n# This tag requires that the tag GENERATE_HTML is set to YES.\n\nDISABLE_INDEX          = NO\n\n# The GENERATE_TREEVIEW tag is used to specify whether a tree-like index\n# structure should be generated to display hierarchical information. If the tag\n# value is set to YES, a side panel will be generated containing a tree-like\n# index structure (just like the one that is generated for HTML Help). For this\n# to work a browser that supports JavaScript, DHTML, CSS and frames is required\n# (i.e. any modern browser). Windows users are probably better off using the\n# HTML help feature. Via custom style sheets (see HTML_EXTRA_STYLESHEET) one can\n# further fine-tune the look of the index. As an example, the default style\n# sheet generated by doxygen has an example that shows how to put an image at\n# the root of the tree instead of the PROJECT_NAME. Since the tree basically has\n# the same information as the tab index, you could consider setting\n# DISABLE_INDEX to YES when enabling this option.\n# The default value is: NO.\n# This tag requires that the tag GENERATE_HTML is set to YES.\n\nGENERATE_TREEVIEW      = NO\n\n# The ENUM_VALUES_PER_LINE tag can be used to set the number of enum values that\n# doxygen will group on one line in the generated HTML documentation.\n#\n# Note that a value of 0 will completely suppress the enum values from appearing\n# in the overview section.\n# Minimum value: 0, maximum value: 20, default value: 4.\n# This tag requires that the tag GENERATE_HTML is set to YES.\n\nENUM_VALUES_PER_LINE   = 4\n\n# If the treeview is enabled (see GENERATE_TREEVIEW) then this tag can be used\n# to set the initial width (in pixels) of the frame in which the tree is shown.\n# Minimum value: 0, maximum value: 1500, default value: 250.\n# This tag requires that the tag GENERATE_HTML is set to YES.\n\nTREEVIEW_WIDTH         = 250\n\n# If the EXT_LINKS_IN_WINDOW option is set to YES, doxygen will open links to\n# external symbols imported via tag files in a separate window.\n# The default value is: NO.\n# This tag requires that the tag GENERATE_HTML is set to YES.\n\nEXT_LINKS_IN_WINDOW    = NO\n\n# Use this tag to change the font size of LaTeX formulas included as images in\n# the HTML documentation. When you change the font size after a successful\n# doxygen run you need to manually remove any form_*.png images from the HTML\n# output directory to force them to be regenerated.\n# Minimum value: 8, maximum value: 50, default value: 10.\n# This tag requires that the tag GENERATE_HTML is set to YES.\n\nFORMULA_FONTSIZE       = 10\n\n# Use the FORMULA_TRANPARENT tag to determine whether or not the images\n# generated for formulas are transparent PNGs. Transparent PNGs are not\n# supported properly for IE 6.0, but are supported on all modern browsers.\n#\n# Note that when changing this option you need to delete any form_*.png files in\n# the HTML output directory before the changes have effect.\n# The default value is: YES.\n# This tag requires that the tag GENERATE_HTML is set to YES.\n\nFORMULA_TRANSPARENT    = YES\n\n# Enable the USE_MATHJAX option to render LaTeX formulas using MathJax (see\n# http://www.mathjax.org) which uses client side Javascript for the rendering\n# instead of using pre-rendered bitmaps. Use this if you do not have LaTeX\n# installed or if you want to formulas look prettier in the HTML output. When\n# enabled you may also need to install MathJax separately and configure the path\n# to it using the MATHJAX_RELPATH option.\n# The default value is: NO.\n# This tag requires that the tag GENERATE_HTML is set to YES.\n\nUSE_MATHJAX            = YES\n\n# When MathJax is enabled you can set the default output format to be used for\n# the MathJax output. See the MathJax site (see:\n# http://docs.mathjax.org/en/latest/output.html) for more details.\n# Possible values are: HTML-CSS (which is slower, but has the best\n# compatibility), NativeMML (i.e. MathML) and SVG.\n# The default value is: HTML-CSS.\n# This tag requires that the tag USE_MATHJAX is set to YES.\n\nMATHJAX_FORMAT         = HTML-CSS\n\n# When MathJax is enabled you need to specify the location relative to the HTML\n# output directory using the MATHJAX_RELPATH option. The destination directory\n# should contain the MathJax.js script. For instance, if the mathjax directory\n# is located at the same level as the HTML output directory, then\n# MATHJAX_RELPATH should be ../mathjax. The default value points to the MathJax\n# Content Delivery Network so you can quickly see the result without installing\n# MathJax. However, it is strongly recommended to install a local copy of\n# MathJax from http://www.mathjax.org before deployment.\n# The default value is: http://cdn.mathjax.org/mathjax/latest.\n# This tag requires that the tag USE_MATHJAX is set to YES.\n\nMATHJAX_RELPATH        = http://cdn.mathjax.org/mathjax/latest\n\n# The MATHJAX_EXTENSIONS tag can be used to specify one or more MathJax\n# extension names that should be enabled during MathJax rendering. For example\n# MATHJAX_EXTENSIONS = TeX/AMSmath TeX/AMSsymbols\n# This tag requires that the tag USE_MATHJAX is set to YES.\n\nMATHJAX_EXTENSIONS     =\n\n# The MATHJAX_CODEFILE tag can be used to specify a file with javascript pieces\n# of code that will be used on startup of the MathJax code. See the MathJax site\n# (see: http://docs.mathjax.org/en/latest/output.html) for more details. For an\n# example see the documentation.\n# This tag requires that the tag USE_MATHJAX is set to YES.\n\nMATHJAX_CODEFILE       =\n\n# When the SEARCHENGINE tag is enabled doxygen will generate a search box for\n# the HTML output. The underlying search engine uses javascript and DHTML and\n# should work on any modern browser. Note that when using HTML help\n# (GENERATE_HTMLHELP), Qt help (GENERATE_QHP), or docsets (GENERATE_DOCSET)\n# there is already a search function so this one should typically be disabled.\n# For large projects the javascript based search engine can be slow, then\n# enabling SERVER_BASED_SEARCH may provide a better solution. It is possible to\n# search using the keyboard; to jump to the search box use <access key> + S\n# (what the <access key> is depends on the OS and browser, but it is typically\n# <CTRL>, <ALT>/<option>, or both). Inside the search box use the <cursor down\n# key> to jump into the search results window, the results can be navigated\n# using the <cursor keys>. Press <Enter> to select an item or <escape> to cancel\n# the search. The filter options can be selected when the cursor is inside the\n# search box by pressing <Shift>+<cursor down>. Also here use the <cursor keys>\n# to select a filter and <Enter> or <escape> to activate or cancel the filter\n# option.\n# The default value is: YES.\n# This tag requires that the tag GENERATE_HTML is set to YES.\n\nSEARCHENGINE           = YES\n\n# When the SERVER_BASED_SEARCH tag is enabled the search engine will be\n# implemented using a web server instead of a web client using Javascript. There\n# are two flavors of web server based searching depending on the EXTERNAL_SEARCH\n# setting. When disabled, doxygen will generate a PHP script for searching and\n# an index file used by the script. When EXTERNAL_SEARCH is enabled the indexing\n# and searching needs to be provided by external tools. See the section\n# \"External Indexing and Searching\" for details.\n# The default value is: NO.\n# This tag requires that the tag SEARCHENGINE is set to YES.\n\nSERVER_BASED_SEARCH    = NO\n\n# When EXTERNAL_SEARCH tag is enabled doxygen will no longer generate the PHP\n# script for searching. Instead the search results are written to an XML file\n# which needs to be processed by an external indexer. Doxygen will invoke an\n# external search engine pointed to by the SEARCHENGINE_URL option to obtain the\n# search results.\n#\n# Doxygen ships with an example indexer (doxyindexer) and search engine\n# (doxysearch.cgi) which are based on the open source search engine library\n# Xapian (see: http://xapian.org/).\n#\n# See the section \"External Indexing and Searching\" for details.\n# The default value is: NO.\n# This tag requires that the tag SEARCHENGINE is set to YES.\n\nEXTERNAL_SEARCH        = NO\n\n# The SEARCHENGINE_URL should point to a search engine hosted by a web server\n# which will return the search results when EXTERNAL_SEARCH is enabled.\n#\n# Doxygen ships with an example indexer (doxyindexer) and search engine\n# (doxysearch.cgi) which are based on the open source search engine library\n# Xapian (see: http://xapian.org/). See the section \"External Indexing and\n# Searching\" for details.\n# This tag requires that the tag SEARCHENGINE is set to YES.\n\nSEARCHENGINE_URL       =\n\n# When SERVER_BASED_SEARCH and EXTERNAL_SEARCH are both enabled the unindexed\n# search data is written to a file for indexing by an external tool. With the\n# SEARCHDATA_FILE tag the name of this file can be specified.\n# The default file is: searchdata.xml.\n# This tag requires that the tag SEARCHENGINE is set to YES.\n\nSEARCHDATA_FILE        = searchdata.xml\n\n# When SERVER_BASED_SEARCH and EXTERNAL_SEARCH are both enabled the\n# EXTERNAL_SEARCH_ID tag can be used as an identifier for the project. This is\n# useful in combination with EXTRA_SEARCH_MAPPINGS to search through multiple\n# projects and redirect the results back to the right project.\n# This tag requires that the tag SEARCHENGINE is set to YES.\n\nEXTERNAL_SEARCH_ID     =\n\n# The EXTRA_SEARCH_MAPPINGS tag can be used to enable searching through doxygen\n# projects other than the one defined by this configuration file, but that are\n# all added to the same external search index. Each project needs to have a\n# unique id set via EXTERNAL_SEARCH_ID. The search mapping then maps the id of\n# to a relative location where the documentation can be found. The format is:\n# EXTRA_SEARCH_MAPPINGS = tagname1=loc1 tagname2=loc2 ...\n# This tag requires that the tag SEARCHENGINE is set to YES.\n\nEXTRA_SEARCH_MAPPINGS  =\n\n#---------------------------------------------------------------------------\n# Configuration options related to the LaTeX output\n#---------------------------------------------------------------------------\n\n# If the GENERATE_LATEX tag is set to YES, doxygen will generate LaTeX output.\n# The default value is: YES.\n\nGENERATE_LATEX         = NO\n\n# The LATEX_OUTPUT tag is used to specify where the LaTeX docs will be put. If a\n# relative path is entered the value of OUTPUT_DIRECTORY will be put in front of\n# it.\n# The default directory is: latex.\n# This tag requires that the tag GENERATE_LATEX is set to YES.\n\nLATEX_OUTPUT           = latex\n\n# The LATEX_CMD_NAME tag can be used to specify the LaTeX command name to be\n# invoked.\n#\n# Note that when enabling USE_PDFLATEX this option is only used for generating\n# bitmaps for formulas in the HTML output, but not in the Makefile that is\n# written to the output directory.\n# The default file is: latex.\n# This tag requires that the tag GENERATE_LATEX is set to YES.\n\nLATEX_CMD_NAME         = latex\n\n# The MAKEINDEX_CMD_NAME tag can be used to specify the command name to generate\n# index for LaTeX.\n# The default file is: makeindex.\n# This tag requires that the tag GENERATE_LATEX is set to YES.\n\nMAKEINDEX_CMD_NAME     = makeindex\n\n# If the COMPACT_LATEX tag is set to YES, doxygen generates more compact LaTeX\n# documents. This may be useful for small projects and may help to save some\n# trees in general.\n# The default value is: NO.\n# This tag requires that the tag GENERATE_LATEX is set to YES.\n\nCOMPACT_LATEX          = NO\n\n# The PAPER_TYPE tag can be used to set the paper type that is used by the\n# printer.\n# Possible values are: a4 (210 x 297 mm), letter (8.5 x 11 inches), legal (8.5 x\n# 14 inches) and executive (7.25 x 10.5 inches).\n# The default value is: a4.\n# This tag requires that the tag GENERATE_LATEX is set to YES.\n\nPAPER_TYPE             = a4\n\n# The EXTRA_PACKAGES tag can be used to specify one or more LaTeX package names\n# that should be included in the LaTeX output. The package can be specified just\n# by its name or with the correct syntax as to be used with the LaTeX\n# \\usepackage command. To get the times font for instance you can specify :\n# EXTRA_PACKAGES=times or EXTRA_PACKAGES={times}\n# To use the option intlimits with the amsmath package you can specify:\n# EXTRA_PACKAGES=[intlimits]{amsmath}\n# If left blank no extra packages will be included.\n# This tag requires that the tag GENERATE_LATEX is set to YES.\n\nEXTRA_PACKAGES         =\n\n# The LATEX_HEADER tag can be used to specify a personal LaTeX header for the\n# generated LaTeX document. The header should contain everything until the first\n# chapter. If it is left blank doxygen will generate a standard header. See\n# section \"Doxygen usage\" for information on how to let doxygen write the\n# default header to a separate file.\n#\n# Note: Only use a user-defined header if you know what you are doing! The\n# following commands have a special meaning inside the header: $title,\n# $datetime, $date, $doxygenversion, $projectname, $projectnumber,\n# $projectbrief, $projectlogo. Doxygen will replace $title with the empty\n# string, for the replacement values of the other commands the user is referred\n# to HTML_HEADER.\n# This tag requires that the tag GENERATE_LATEX is set to YES.\n\nLATEX_HEADER           =\n\n# The LATEX_FOOTER tag can be used to specify a personal LaTeX footer for the\n# generated LaTeX document. The footer should contain everything after the last\n# chapter. If it is left blank doxygen will generate a standard footer. See\n# LATEX_HEADER for more information on how to generate a default footer and what\n# special commands can be used inside the footer.\n#\n# Note: Only use a user-defined footer if you know what you are doing!\n# This tag requires that the tag GENERATE_LATEX is set to YES.\n\nLATEX_FOOTER           =\n\n# The LATEX_EXTRA_STYLESHEET tag can be used to specify additional user-defined\n# LaTeX style sheets that are included after the standard style sheets created\n# by doxygen. Using this option one can overrule certain style aspects. Doxygen\n# will copy the style sheet files to the output directory.\n# Note: The order of the extra style sheet files is of importance (e.g. the last\n# style sheet in the list overrules the setting of the previous ones in the\n# list).\n# This tag requires that the tag GENERATE_LATEX is set to YES.\n\nLATEX_EXTRA_STYLESHEET =\n\n# The LATEX_EXTRA_FILES tag can be used to specify one or more extra images or\n# other source files which should be copied to the LATEX_OUTPUT output\n# directory. Note that the files will be copied as-is; there are no commands or\n# markers available.\n# This tag requires that the tag GENERATE_LATEX is set to YES.\n\nLATEX_EXTRA_FILES      =\n\n# If the PDF_HYPERLINKS tag is set to YES, the LaTeX that is generated is\n# prepared for conversion to PDF (using ps2pdf or pdflatex). The PDF file will\n# contain links (just like the HTML output) instead of page references. This\n# makes the output suitable for online browsing using a PDF viewer.\n# The default value is: YES.\n# This tag requires that the tag GENERATE_LATEX is set to YES.\n\nPDF_HYPERLINKS         = YES\n\n# If the USE_PDFLATEX tag is set to YES, doxygen will use pdflatex to generate\n# the PDF file directly from the LaTeX files. Set this option to YES, to get a\n# higher quality PDF documentation.\n# The default value is: YES.\n# This tag requires that the tag GENERATE_LATEX is set to YES.\n\nUSE_PDFLATEX           = YES\n\n# If the LATEX_BATCHMODE tag is set to YES, doxygen will add the \\batchmode\n# command to the generated LaTeX files. This will instruct LaTeX to keep running\n# if errors occur, instead of asking the user for help. This option is also used\n# when generating formulas in HTML.\n# The default value is: NO.\n# This tag requires that the tag GENERATE_LATEX is set to YES.\n\nLATEX_BATCHMODE        = NO\n\n# If the LATEX_HIDE_INDICES tag is set to YES then doxygen will not include the\n# index chapters (such as File Index, Compound Index, etc.) in the output.\n# The default value is: NO.\n# This tag requires that the tag GENERATE_LATEX is set to YES.\n\nLATEX_HIDE_INDICES     = NO\n\n# If the LATEX_SOURCE_CODE tag is set to YES then doxygen will include source\n# code with syntax highlighting in the LaTeX output.\n#\n# Note that which sources are shown also depends on other settings such as\n# SOURCE_BROWSER.\n# The default value is: NO.\n# This tag requires that the tag GENERATE_LATEX is set to YES.\n\nLATEX_SOURCE_CODE      = NO\n\n# The LATEX_BIB_STYLE tag can be used to specify the style to use for the\n# bibliography, e.g. plainnat, or ieeetr. See\n# http://en.wikipedia.org/wiki/BibTeX and \\cite for more info.\n# The default value is: plain.\n# This tag requires that the tag GENERATE_LATEX is set to YES.\n\nLATEX_BIB_STYLE        = plain\n\n# If the LATEX_TIMESTAMP tag is set to YES then the footer of each generated\n# page will contain the date and time when the page was generated. Setting this\n# to NO can help when comparing the output of multiple runs.\n# The default value is: NO.\n# This tag requires that the tag GENERATE_LATEX is set to YES.\n\nLATEX_TIMESTAMP        = NO\n\n#---------------------------------------------------------------------------\n# Configuration options related to the RTF output\n#---------------------------------------------------------------------------\n\n# If the GENERATE_RTF tag is set to YES, doxygen will generate RTF output. The\n# RTF output is optimized for Word 97 and may not look too pretty with other RTF\n# readers/editors.\n# The default value is: NO.\n\nGENERATE_RTF           = NO\n\n# The RTF_OUTPUT tag is used to specify where the RTF docs will be put. If a\n# relative path is entered the value of OUTPUT_DIRECTORY will be put in front of\n# it.\n# The default directory is: rtf.\n# This tag requires that the tag GENERATE_RTF is set to YES.\n\nRTF_OUTPUT             = rtf\n\n# If the COMPACT_RTF tag is set to YES, doxygen generates more compact RTF\n# documents. This may be useful for small projects and may help to save some\n# trees in general.\n# The default value is: NO.\n# This tag requires that the tag GENERATE_RTF is set to YES.\n\nCOMPACT_RTF            = NO\n\n# If the RTF_HYPERLINKS tag is set to YES, the RTF that is generated will\n# contain hyperlink fields. The RTF file will contain links (just like the HTML\n# output) instead of page references. This makes the output suitable for online\n# browsing using Word or some other Word compatible readers that support those\n# fields.\n#\n# Note: WordPad (write) and others do not support links.\n# The default value is: NO.\n# This tag requires that the tag GENERATE_RTF is set to YES.\n\nRTF_HYPERLINKS         = NO\n\n# Load stylesheet definitions from file. Syntax is similar to doxygen's config\n# file, i.e. a series of assignments. You only have to provide replacements,\n# missing definitions are set to their default value.\n#\n# See also section \"Doxygen usage\" for information on how to generate the\n# default style sheet that doxygen normally uses.\n# This tag requires that the tag GENERATE_RTF is set to YES.\n\nRTF_STYLESHEET_FILE    =\n\n# Set optional variables used in the generation of an RTF document. Syntax is\n# similar to doxygen's config file. A template extensions file can be generated\n# using doxygen -e rtf extensionFile.\n# This tag requires that the tag GENERATE_RTF is set to YES.\n\nRTF_EXTENSIONS_FILE    =\n\n# If the RTF_SOURCE_CODE tag is set to YES then doxygen will include source code\n# with syntax highlighting in the RTF output.\n#\n# Note that which sources are shown also depends on other settings such as\n# SOURCE_BROWSER.\n# The default value is: NO.\n# This tag requires that the tag GENERATE_RTF is set to YES.\n\nRTF_SOURCE_CODE        = NO\n\n#---------------------------------------------------------------------------\n# Configuration options related to the man page output\n#---------------------------------------------------------------------------\n\n# If the GENERATE_MAN tag is set to YES, doxygen will generate man pages for\n# classes and files.\n# The default value is: NO.\n\nGENERATE_MAN           = NO\n\n# The MAN_OUTPUT tag is used to specify where the man pages will be put. If a\n# relative path is entered the value of OUTPUT_DIRECTORY will be put in front of\n# it. A directory man3 will be created inside the directory specified by\n# MAN_OUTPUT.\n# The default directory is: man.\n# This tag requires that the tag GENERATE_MAN is set to YES.\n\nMAN_OUTPUT             = man\n\n# The MAN_EXTENSION tag determines the extension that is added to the generated\n# man pages. In case the manual section does not start with a number, the number\n# 3 is prepended. The dot (.) at the beginning of the MAN_EXTENSION tag is\n# optional.\n# The default value is: .3.\n# This tag requires that the tag GENERATE_MAN is set to YES.\n\nMAN_EXTENSION          = .3\n\n# The MAN_SUBDIR tag determines the name of the directory created within\n# MAN_OUTPUT in which the man pages are placed. If defaults to man followed by\n# MAN_EXTENSION with the initial . removed.\n# This tag requires that the tag GENERATE_MAN is set to YES.\n\nMAN_SUBDIR             =\n\n# If the MAN_LINKS tag is set to YES and doxygen generates man output, then it\n# will generate one additional man file for each entity documented in the real\n# man page(s). These additional files only source the real man page, but without\n# them the man command would be unable to find the correct page.\n# The default value is: NO.\n# This tag requires that the tag GENERATE_MAN is set to YES.\n\nMAN_LINKS              = NO\n\n#---------------------------------------------------------------------------\n# Configuration options related to the XML output\n#---------------------------------------------------------------------------\n\n# If the GENERATE_XML tag is set to YES, doxygen will generate an XML file that\n# captures the structure of the code including all documentation.\n# The default value is: NO.\n\nGENERATE_XML           = YES\n\n# The XML_OUTPUT tag is used to specify where the XML pages will be put. If a\n# relative path is entered the value of OUTPUT_DIRECTORY will be put in front of\n# it.\n# The default directory is: xml.\n# This tag requires that the tag GENERATE_XML is set to YES.\n\nXML_OUTPUT             = xml\n\n# If the XML_PROGRAMLISTING tag is set to YES, doxygen will dump the program\n# listings (including syntax highlighting and cross-referencing information) to\n# the XML output. Note that enabling this will significantly increase the size\n# of the XML output.\n# The default value is: YES.\n# This tag requires that the tag GENERATE_XML is set to YES.\n\nXML_PROGRAMLISTING     = NO\n\n#---------------------------------------------------------------------------\n# Configuration options related to the DOCBOOK output\n#---------------------------------------------------------------------------\n\n# If the GENERATE_DOCBOOK tag is set to YES, doxygen will generate Docbook files\n# that can be used to generate PDF.\n# The default value is: NO.\n\nGENERATE_DOCBOOK       = NO\n\n# The DOCBOOK_OUTPUT tag is used to specify where the Docbook pages will be put.\n# If a relative path is entered the value of OUTPUT_DIRECTORY will be put in\n# front of it.\n# The default directory is: docbook.\n# This tag requires that the tag GENERATE_DOCBOOK is set to YES.\n\nDOCBOOK_OUTPUT         = docbook\n\n# If the DOCBOOK_PROGRAMLISTING tag is set to YES, doxygen will include the\n# program listings (including syntax highlighting and cross-referencing\n# information) to the DOCBOOK output. Note that enabling this will significantly\n# increase the size of the DOCBOOK output.\n# The default value is: NO.\n# This tag requires that the tag GENERATE_DOCBOOK is set to YES.\n\nDOCBOOK_PROGRAMLISTING = NO\n\n#---------------------------------------------------------------------------\n# Configuration options for the AutoGen Definitions output\n#---------------------------------------------------------------------------\n\n# If the GENERATE_AUTOGEN_DEF tag is set to YES, doxygen will generate an\n# AutoGen Definitions (see http://autogen.sf.net) file that captures the\n# structure of the code including all documentation. Note that this feature is\n# still experimental and incomplete at the moment.\n# The default value is: NO.\n\nGENERATE_AUTOGEN_DEF   = NO\n\n#---------------------------------------------------------------------------\n# Configuration options related to the Perl module output\n#---------------------------------------------------------------------------\n\n# If the GENERATE_PERLMOD tag is set to YES, doxygen will generate a Perl module\n# file that captures the structure of the code including all documentation.\n#\n# Note that this feature is still experimental and incomplete at the moment.\n# The default value is: NO.\n\nGENERATE_PERLMOD       = NO\n\n# If the PERLMOD_LATEX tag is set to YES, doxygen will generate the necessary\n# Makefile rules, Perl scripts and LaTeX code to be able to generate PDF and DVI\n# output from the Perl module output.\n# The default value is: NO.\n# This tag requires that the tag GENERATE_PERLMOD is set to YES.\n\nPERLMOD_LATEX          = NO\n\n# If the PERLMOD_PRETTY tag is set to YES, the Perl module output will be nicely\n# formatted so it can be parsed by a human reader. This is useful if you want to\n# understand what is going on. On the other hand, if this tag is set to NO, the\n# size of the Perl module output will be much smaller and Perl will parse it\n# just the same.\n# The default value is: YES.\n# This tag requires that the tag GENERATE_PERLMOD is set to YES.\n\nPERLMOD_PRETTY         = YES\n\n# The names of the make variables in the generated doxyrules.make file are\n# prefixed with the string contained in PERLMOD_MAKEVAR_PREFIX. This is useful\n# so different doxyrules.make files included by the same Makefile don't\n# overwrite each other's variables.\n# This tag requires that the tag GENERATE_PERLMOD is set to YES.\n\nPERLMOD_MAKEVAR_PREFIX =\n\n#---------------------------------------------------------------------------\n# Configuration options related to the preprocessor\n#---------------------------------------------------------------------------\n\n# If the ENABLE_PREPROCESSING tag is set to YES, doxygen will evaluate all\n# C-preprocessor directives found in the sources and include files.\n# The default value is: YES.\n\nENABLE_PREPROCESSING   = YES\n\n# If the MACRO_EXPANSION tag is set to YES, doxygen will expand all macro names\n# in the source code. If set to NO, only conditional compilation will be\n# performed. Macro expansion can be done in a controlled way by setting\n# EXPAND_ONLY_PREDEF to YES.\n# The default value is: NO.\n# This tag requires that the tag ENABLE_PREPROCESSING is set to YES.\n\nMACRO_EXPANSION        = NO\n\n# If the EXPAND_ONLY_PREDEF and MACRO_EXPANSION tags are both set to YES then\n# the macro expansion is limited to the macros specified with the PREDEFINED and\n# EXPAND_AS_DEFINED tags.\n# The default value is: NO.\n# This tag requires that the tag ENABLE_PREPROCESSING is set to YES.\n\nEXPAND_ONLY_PREDEF     = NO\n\n# If the SEARCH_INCLUDES tag is set to YES, the include files in the\n# INCLUDE_PATH will be searched if a #include is found.\n# The default value is: YES.\n# This tag requires that the tag ENABLE_PREPROCESSING is set to YES.\n\nSEARCH_INCLUDES        = YES\n\n# The INCLUDE_PATH tag can be used to specify one or more directories that\n# contain include files that are not input files but should be processed by the\n# preprocessor.\n# This tag requires that the tag SEARCH_INCLUDES is set to YES.\n\nINCLUDE_PATH           =\n\n# You can use the INCLUDE_FILE_PATTERNS tag to specify one or more wildcard\n# patterns (like *.h and *.hpp) to filter out the header-files in the\n# directories. If left blank, the patterns specified with FILE_PATTERNS will be\n# used.\n# This tag requires that the tag ENABLE_PREPROCESSING is set to YES.\n\nINCLUDE_FILE_PATTERNS  =\n\n# The PREDEFINED tag can be used to specify one or more macro names that are\n# defined before the preprocessor is started (similar to the -D option of e.g.\n# gcc). The argument of the tag is a list of macros of the form: name or\n# name=definition (no spaces). If the definition and the \"=\" are omitted, \"=1\"\n# is assumed. To prevent a macro definition from being undefined via #undef or\n# recursively expanded use the := operator instead of the = operator.\n# This tag requires that the tag ENABLE_PREPROCESSING is set to YES.\n\nPREDEFINED             =\n\n# If the MACRO_EXPANSION and EXPAND_ONLY_PREDEF tags are set to YES then this\n# tag can be used to specify a list of macro names that should be expanded. The\n# macro definition that is found in the sources will be used. Use the PREDEFINED\n# tag if you want to use a different macro definition that overrules the\n# definition found in the source code.\n# This tag requires that the tag ENABLE_PREPROCESSING is set to YES.\n\nEXPAND_AS_DEFINED      =\n\n# If the SKIP_FUNCTION_MACROS tag is set to YES then doxygen's preprocessor will\n# remove all references to function-like macros that are alone on a line, have\n# an all uppercase name, and do not end with a semicolon. Such function macros\n# are typically used for boiler-plate code, and will confuse the parser if not\n# removed.\n# The default value is: YES.\n# This tag requires that the tag ENABLE_PREPROCESSING is set to YES.\n\nSKIP_FUNCTION_MACROS   = YES\n\n#---------------------------------------------------------------------------\n# Configuration options related to external references\n#---------------------------------------------------------------------------\n\n# The TAGFILES tag can be used to specify one or more tag files. For each tag\n# file the location of the external documentation should be added. The format of\n# a tag file without this location is as follows:\n# TAGFILES = file1 file2 ...\n# Adding location for the tag files is done as follows:\n# TAGFILES = file1=loc1 \"file2 = loc2\" ...\n# where loc1 and loc2 can be relative or absolute paths or URLs. See the\n# section \"Linking to external documentation\" for more information about the use\n# of tag files.\n# Note: Each tag file must have a unique name (where the name does NOT include\n# the path). If a tag file is not located in the directory in which doxygen is\n# run, you must also specify the path to the tagfile here.\n\nTAGFILES               =\n\n# When a file name is specified after GENERATE_TAGFILE, doxygen will create a\n# tag file that is based on the input files it reads. See section \"Linking to\n# external documentation\" for more information about the usage of tag files.\n\nGENERATE_TAGFILE       =\n\n# If the ALLEXTERNALS tag is set to YES, all external class will be listed in\n# the class index. If set to NO, only the inherited external classes will be\n# listed.\n# The default value is: NO.\n\nALLEXTERNALS           = NO\n\n# If the EXTERNAL_GROUPS tag is set to YES, all external groups will be listed\n# in the modules index. If set to NO, only the current project's groups will be\n# listed.\n# The default value is: YES.\n\nEXTERNAL_GROUPS        = YES\n\n# If the EXTERNAL_PAGES tag is set to YES, all external pages will be listed in\n# the related pages index. If set to NO, only the current project's pages will\n# be listed.\n# The default value is: YES.\n\nEXTERNAL_PAGES         = YES\n\n\n#---------------------------------------------------------------------------\n# Configuration options related to the dot tool\n#---------------------------------------------------------------------------\n\n# If the CLASS_DIAGRAMS tag is set to YES, doxygen will generate a class diagram\n# (in HTML and LaTeX) for classes with base or super classes. Setting the tag to\n# NO turns the diagrams off. Note that this option also works with HAVE_DOT\n# disabled, but it is recommended to install and use dot, since it yields more\n# powerful graphs.\n# The default value is: YES.\n\nCLASS_DIAGRAMS         = YES\n\n# You can include diagrams made with dia in doxygen documentation. Doxygen will\n# then run dia to produce the diagram and insert it in the documentation. The\n# DIA_PATH tag allows you to specify the directory where the dia binary resides.\n# If left empty dia is assumed to be found in the default search path.\n\nDIA_PATH               =\n\n# If set to YES the inheritance and collaboration graphs will hide inheritance\n# and usage relations if the target is undocumented or is not a class.\n# The default value is: YES.\n\nHIDE_UNDOC_RELATIONS   = YES\n\n# If you set the HAVE_DOT tag to YES then doxygen will assume the dot tool is\n# available from the path. This tool is part of Graphviz (see:\n# http://www.graphviz.org/), a graph visualization toolkit from AT&T and Lucent\n# Bell Labs. The other options in this section have no effect if this option is\n# set to NO\n# The default value is: YES.\n\nHAVE_DOT               = NO\n\n# The DOT_NUM_THREADS specifies the number of dot invocations doxygen is allowed\n# to run in parallel. When set to 0 doxygen will base this on the number of\n# processors available in the system. You can set it explicitly to a value\n# larger than 0 to get control over the balance between CPU load and processing\n# speed.\n# Minimum value: 0, maximum value: 32, default value: 0.\n# This tag requires that the tag HAVE_DOT is set to YES.\n\nDOT_NUM_THREADS        = 0\n\n# When you want a differently looking font in the dot files that doxygen\n# generates you can specify the font name using DOT_FONTNAME. You need to make\n# sure dot is able to find the font, which can be done by putting it in a\n# standard location or by setting the DOTFONTPATH environment variable or by\n# setting DOT_FONTPATH to the directory containing the font.\n# The default value is: Helvetica.\n# This tag requires that the tag HAVE_DOT is set to YES.\n\nDOT_FONTNAME           = Helvetica\n\n# The DOT_FONTSIZE tag can be used to set the size (in points) of the font of\n# dot graphs.\n# Minimum value: 4, maximum value: 24, default value: 10.\n# This tag requires that the tag HAVE_DOT is set to YES.\n\nDOT_FONTSIZE           = 10\n\n# By default doxygen will tell dot to use the default font as specified with\n# DOT_FONTNAME. If you specify a different font using DOT_FONTNAME you can set\n# the path where dot can find it using this tag.\n# This tag requires that the tag HAVE_DOT is set to YES.\n\nDOT_FONTPATH           =\n\n# If the CLASS_GRAPH tag is set to YES then doxygen will generate a graph for\n# each documented class showing the direct and indirect inheritance relations.\n# Setting this tag to YES will force the CLASS_DIAGRAMS tag to NO.\n# The default value is: YES.\n# This tag requires that the tag HAVE_DOT is set to YES.\n\nCLASS_GRAPH            = YES\n\n# If the COLLABORATION_GRAPH tag is set to YES then doxygen will generate a\n# graph for each documented class showing the direct and indirect implementation\n# dependencies (inheritance, containment, and class references variables) of the\n# class with other documented classes.\n# The default value is: YES.\n# This tag requires that the tag HAVE_DOT is set to YES.\n\nCOLLABORATION_GRAPH    = YES\n\n# If the GROUP_GRAPHS tag is set to YES then doxygen will generate a graph for\n# groups, showing the direct groups dependencies.\n# The default value is: YES.\n# This tag requires that the tag HAVE_DOT is set to YES.\n\nGROUP_GRAPHS           = YES\n\n# If the UML_LOOK tag is set to YES, doxygen will generate inheritance and\n# collaboration diagrams in a style similar to the OMG's Unified Modeling\n# Language.\n# The default value is: NO.\n# This tag requires that the tag HAVE_DOT is set to YES.\n\nUML_LOOK               = NO\n\n# If the UML_LOOK tag is enabled, the fields and methods are shown inside the\n# class node. If there are many fields or methods and many nodes the graph may\n# become too big to be useful. The UML_LIMIT_NUM_FIELDS threshold limits the\n# number of items for each type to make the size more manageable. Set this to 0\n# for no limit. Note that the threshold may be exceeded by 50% before the limit\n# is enforced. So when you set the threshold to 10, up to 15 fields may appear,\n# but if the number exceeds 15, the total amount of fields shown is limited to\n# 10.\n# Minimum value: 0, maximum value: 100, default value: 10.\n# This tag requires that the tag HAVE_DOT is set to YES.\n\nUML_LIMIT_NUM_FIELDS   = 10\n\n# If the TEMPLATE_RELATIONS tag is set to YES then the inheritance and\n# collaboration graphs will show the relations between templates and their\n# instances.\n# The default value is: NO.\n# This tag requires that the tag HAVE_DOT is set to YES.\n\nTEMPLATE_RELATIONS     = NO\n\n# If the INCLUDE_GRAPH, ENABLE_PREPROCESSING and SEARCH_INCLUDES tags are set to\n# YES then doxygen will generate a graph for each documented file showing the\n# direct and indirect include dependencies of the file with other documented\n# files.\n# The default value is: YES.\n# This tag requires that the tag HAVE_DOT is set to YES.\n\nINCLUDE_GRAPH          = YES\n\n# If the INCLUDED_BY_GRAPH, ENABLE_PREPROCESSING and SEARCH_INCLUDES tags are\n# set to YES then doxygen will generate a graph for each documented file showing\n# the direct and indirect include dependencies of the file with other documented\n# files.\n# The default value is: YES.\n# This tag requires that the tag HAVE_DOT is set to YES.\n\nINCLUDED_BY_GRAPH      = YES\n\n# If the CALL_GRAPH tag is set to YES then doxygen will generate a call\n# dependency graph for every global function or class method.\n#\n# Note that enabling this option will significantly increase the time of a run.\n# So in most cases it will be better to enable call graphs for selected\n# functions only using the \\callgraph command. Disabling a call graph can be\n# accomplished by means of the command \\hidecallgraph.\n# The default value is: NO.\n# This tag requires that the tag HAVE_DOT is set to YES.\n\nCALL_GRAPH             = NO\n\n# If the CALLER_GRAPH tag is set to YES then doxygen will generate a caller\n# dependency graph for every global function or class method.\n#\n# Note that enabling this option will significantly increase the time of a run.\n# So in most cases it will be better to enable caller graphs for selected\n# functions only using the \\callergraph command. Disabling a caller graph can be\n# accomplished by means of the command \\hidecallergraph.\n# The default value is: NO.\n# This tag requires that the tag HAVE_DOT is set to YES.\n\nCALLER_GRAPH           = NO\n\n# If the GRAPHICAL_HIERARCHY tag is set to YES then doxygen will graphical\n# hierarchy of all classes instead of a textual one.\n# The default value is: YES.\n# This tag requires that the tag HAVE_DOT is set to YES.\n\nGRAPHICAL_HIERARCHY    = YES\n\n# If the DIRECTORY_GRAPH tag is set to YES then doxygen will show the\n# dependencies a directory has on other directories in a graphical way. The\n# dependency relations are determined by the #include relations between the\n# files in the directories.\n# The default value is: YES.\n# This tag requires that the tag HAVE_DOT is set to YES.\n\nDIRECTORY_GRAPH        = YES\n\n# The DOT_IMAGE_FORMAT tag can be used to set the image format of the images\n# generated by dot. For an explanation of the image formats see the section\n# output formats in the documentation of the dot tool (Graphviz (see:\n# http://www.graphviz.org/)).\n# Note: If you choose svg you need to set HTML_FILE_EXTENSION to xhtml in order\n# to make the SVG files visible in IE 9+ (other browsers do not have this\n# requirement).\n# Possible values are: png, png:cairo, png:cairo:cairo, png:cairo:gd, png:gd,\n# png:gd:gd, jpg, jpg:cairo, jpg:cairo:gd, jpg:gd, jpg:gd:gd, gif, gif:cairo,\n# gif:cairo:gd, gif:gd, gif:gd:gd, svg, png:gd, png:gd:gd, png:cairo,\n# png:cairo:gd, png:cairo:cairo, png:cairo:gdiplus, png:gdiplus and\n# png:gdiplus:gdiplus.\n# The default value is: png.\n# This tag requires that the tag HAVE_DOT is set to YES.\n\nDOT_IMAGE_FORMAT       = png\n\n# If DOT_IMAGE_FORMAT is set to svg, then this option can be set to YES to\n# enable generation of interactive SVG images that allow zooming and panning.\n#\n# Note that this requires a modern browser other than Internet Explorer. Tested\n# and working are Firefox, Chrome, Safari, and Opera.\n# Note: For IE 9+ you need to set HTML_FILE_EXTENSION to xhtml in order to make\n# the SVG files visible. Older versions of IE do not have SVG support.\n# The default value is: NO.\n# This tag requires that the tag HAVE_DOT is set to YES.\n\nINTERACTIVE_SVG        = NO\n\n# The DOT_PATH tag can be used to specify the path where the dot tool can be\n# found. If left blank, it is assumed the dot tool can be found in the path.\n# This tag requires that the tag HAVE_DOT is set to YES.\n\nDOT_PATH               =\n\n# The DOTFILE_DIRS tag can be used to specify one or more directories that\n# contain dot files that are included in the documentation (see the \\dotfile\n# command).\n# This tag requires that the tag HAVE_DOT is set to YES.\n\nDOTFILE_DIRS           =\n\n# The MSCFILE_DIRS tag can be used to specify one or more directories that\n# contain msc files that are included in the documentation (see the \\mscfile\n# command).\n\nMSCFILE_DIRS           =\n\n# The DIAFILE_DIRS tag can be used to specify one or more directories that\n# contain dia files that are included in the documentation (see the \\diafile\n# command).\n\nDIAFILE_DIRS           =\n\n# When using plantuml, the PLANTUML_JAR_PATH tag should be used to specify the\n# path where java can find the plantuml.jar file. If left blank, it is assumed\n# PlantUML is not used or called during a preprocessing step. Doxygen will\n# generate a warning when it encounters a \\startuml command in this case and\n# will not generate output for the diagram.\n\nPLANTUML_JAR_PATH      =\n\n# When using plantuml, the specified paths are searched for files specified by\n# the !include statement in a plantuml block.\n\nPLANTUML_INCLUDE_PATH  =\n\n# The DOT_GRAPH_MAX_NODES tag can be used to set the maximum number of nodes\n# that will be shown in the graph. If the number of nodes in a graph becomes\n# larger than this value, doxygen will truncate the graph, which is visualized\n# by representing a node as a red box. Note that doxygen if the number of direct\n# children of the root node in a graph is already larger than\n# DOT_GRAPH_MAX_NODES then the graph will not be shown at all. Also note that\n# the size of a graph can be further restricted by MAX_DOT_GRAPH_DEPTH.\n# Minimum value: 0, maximum value: 10000, default value: 50.\n# This tag requires that the tag HAVE_DOT is set to YES.\n\nDOT_GRAPH_MAX_NODES    = 50\n\n# The MAX_DOT_GRAPH_DEPTH tag can be used to set the maximum depth of the graphs\n# generated by dot. A depth value of 3 means that only nodes reachable from the\n# root by following a path via at most 3 edges will be shown. Nodes that lay\n# further from the root node will be omitted. Note that setting this option to 1\n# or 2 may greatly reduce the computation time needed for large code bases. Also\n# note that the size of a graph can be further restricted by\n# DOT_GRAPH_MAX_NODES. Using a depth of 0 means no depth restriction.\n# Minimum value: 0, maximum value: 1000, default value: 0.\n# This tag requires that the tag HAVE_DOT is set to YES.\n\nMAX_DOT_GRAPH_DEPTH    = 0\n\n# Set the DOT_TRANSPARENT tag to YES to generate images with a transparent\n# background. This is disabled by default, because dot on Windows does not seem\n# to support this out of the box.\n#\n# Warning: Depending on the platform used, enabling this option may lead to\n# badly anti-aliased labels on the edges of a graph (i.e. they become hard to\n# read).\n# The default value is: NO.\n# This tag requires that the tag HAVE_DOT is set to YES.\n\nDOT_TRANSPARENT        = NO\n\n# Set the DOT_MULTI_TARGETS tag to YES to allow dot to generate multiple output\n# files in one run (i.e. multiple -o and -T options on the command line). This\n# makes dot run faster, but since only newer versions of dot (>1.8.10) support\n# this, this feature is disabled by default.\n# The default value is: NO.\n# This tag requires that the tag HAVE_DOT is set to YES.\n\nDOT_MULTI_TARGETS      = YES\n\n# If the GENERATE_LEGEND tag is set to YES doxygen will generate a legend page\n# explaining the meaning of the various boxes and arrows in the dot generated\n# graphs.\n# The default value is: YES.\n# This tag requires that the tag HAVE_DOT is set to YES.\n\nGENERATE_LEGEND        = YES\n\n# If the DOT_CLEANUP tag is set to YES, doxygen will remove the intermediate dot\n# files that are used to generate the various graphs.\n# The default value is: YES.\n# This tag requires that the tag HAVE_DOT is set to YES.\n\nDOT_CLEANUP            = YES\n"
  },
  {
    "path": "config/DoxygenLayout.xml",
    "content": "<doxygenlayout version=\"1.0\">\n  <!-- Generated by doxygen 1.8.6 -->\n  <!-- Navigation index tabs for HTML output -->\n  <navindex>\n    <tab type=\"mainpage\" visible=\"yes\" title=\"\"/>\n    <tab type=\"pages\" visible=\"yes\" title=\"\" intro=\"\"/>\n    <tab type=\"modules\" visible=\"yes\" title=\"\" intro=\"\"/>\n    <tab type=\"namespaces\" visible=\"yes\" title=\"\">\n      <tab type=\"namespacelist\" visible=\"yes\" title=\"\" intro=\"\"/>\n      <tab type=\"namespacemembers\" visible=\"yes\" title=\"\" intro=\"\"/>\n    </tab>\n    <tab type=\"classes\" visible=\"yes\" title=\"\">\n      <tab type=\"classlist\" visible=\"yes\" title=\"\" intro=\"\"/>\n      <tab type=\"classindex\" visible=\"$ALPHABETICAL_INDEX\" title=\"\"/> \n      <tab type=\"hierarchy\" visible=\"yes\" title=\"\" intro=\"\"/>\n      <tab type=\"classmembers\" visible=\"yes\" title=\"\" intro=\"\"/>\n    </tab>\n    <tab type=\"files\" visible=\"yes\" title=\"\">\n      <tab type=\"filelist\" visible=\"yes\" title=\"\" intro=\"\"/>\n      <tab type=\"globals\" visible=\"yes\" title=\"\" intro=\"\"/>\n    </tab>\n    <tab type=\"examples\" visible=\"yes\" title=\"\" intro=\"\"/>  \n  </navindex>\n\n  <!-- Layout definition for a class page -->\n  <class>\n    <briefdescription visible=\"no\"/>\n    <detaileddescription title=\"Description\"/>\n    <includes visible=\"$SHOW_INCLUDE_FILES\"/>\n    <inheritancegraph visible=\"$CLASS_GRAPH\"/>\n    <collaborationgraph visible=\"$COLLABORATION_GRAPH\"/>\n    <memberdecl>\n      <nestedclasses visible=\"yes\" title=\"\"/>\n      <publictypes title=\"\"/>\n      <services title=\"\"/>\n      <interfaces title=\"\"/>\n      <publicslots title=\"\"/>\n      <signals title=\"\"/>\n      <publicmethods title=\"\"/>\n      <publicstaticmethods title=\"\"/>\n      <publicattributes title=\"\"/>\n      <publicstaticattributes title=\"\"/>\n      <protectedtypes title=\"\"/>\n      <protectedslots title=\"\"/>\n      <protectedmethods title=\"\"/>\n      <protectedstaticmethods title=\"\"/>\n      <protectedattributes title=\"\"/>\n      <protectedstaticattributes title=\"\"/>\n      <packagetypes title=\"\"/>\n      <packagemethods title=\"\"/>\n      <packagestaticmethods title=\"\"/>\n      <packageattributes title=\"\"/>\n      <packagestaticattributes title=\"\"/>\n      <properties title=\"\"/>\n      <events title=\"\"/>\n      <privatetypes title=\"\"/>\n      <privateslots title=\"\"/>\n      <privatemethods title=\"\"/>\n      <privatestaticmethods title=\"\"/>\n      <privateattributes title=\"\"/>\n      <privatestaticattributes title=\"\"/>\n      <friends title=\"\"/>\n      <related title=\"\" subtitle=\"\"/>\n      <membergroups visible=\"yes\"/>\n    </memberdecl>\n    <memberdef>\n      <inlineclasses title=\"\"/>\n      <typedefs title=\"\"/>\n      <enums title=\"\"/>\n      <services title=\"\"/>\n      <interfaces title=\"\"/>\n      <constructors title=\"\"/>\n      <functions title=\"\"/>\n      <related title=\"\"/>\n      <variables title=\"\"/>\n      <properties title=\"\"/>\n      <events title=\"\"/>\n    </memberdef>\n    <allmemberslink visible=\"yes\"/>\n    <usedfiles visible=\"$SHOW_USED_FILES\"/>\n    <authorsection visible=\"yes\"/>\n  </class>\n\n  <!-- Layout definition for a namespace page -->\n  <namespace>\n    <briefdescription visible=\"yes\"/>\n    <memberdecl>\n      <nestednamespaces visible=\"yes\" title=\"\"/>\n      <constantgroups visible=\"yes\" title=\"\"/>\n      <classes visible=\"yes\" title=\"\"/>\n      <typedefs title=\"\"/>\n      <enums title=\"\"/>\n      <functions title=\"\"/>\n      <variables title=\"\"/>\n      <membergroups visible=\"yes\"/>\n    </memberdecl>\n    <detaileddescription title=\"\"/>\n    <memberdef>\n      <inlineclasses title=\"\"/>\n      <typedefs title=\"\"/>\n      <enums title=\"\"/>\n      <functions title=\"\"/>\n      <variables title=\"\"/>\n    </memberdef>\n    <authorsection visible=\"yes\"/>\n  </namespace>\n\n  <!-- Layout definition for a file page -->\n  <file>\n    <briefdescription visible=\"yes\"/>\n    <includes visible=\"$SHOW_INCLUDE_FILES\"/>\n    <includegraph visible=\"$INCLUDE_GRAPH\"/>\n    <includedbygraph visible=\"$INCLUDED_BY_GRAPH\"/>\n    <sourcelink visible=\"yes\"/>\n    <memberdecl>\n      <classes visible=\"yes\" title=\"\"/>\n      <namespaces visible=\"yes\" title=\"\"/>\n      <constantgroups visible=\"yes\" title=\"\"/>\n      <defines title=\"\"/>\n      <typedefs title=\"\"/>\n      <enums title=\"\"/>\n      <functions title=\"\"/>\n      <variables title=\"\"/>\n      <membergroups visible=\"yes\"/>\n    </memberdecl>\n    <detaileddescription title=\"\"/>\n    <memberdef>\n      <inlineclasses title=\"\"/>\n      <defines title=\"\"/>\n      <typedefs title=\"\"/>\n      <enums title=\"\"/>\n      <functions title=\"\"/>\n      <variables title=\"\"/>\n    </memberdef>\n    <authorsection/>\n  </file>\n\n  <!-- Layout definition for a group page -->\n  <group>\n    <briefdescription visible=\"no\"/>\n    <detaileddescription title=\"Module Description\"/>\n    <groupgraph visible=\"$GROUP_GRAPHS\"/>\n    <memberdecl>\n      <nestedgroups visible=\"yes\" title=\"\"/>\n      <dirs visible=\"yes\" title=\"\"/>\n      <files visible=\"yes\" title=\"\"/>\n      <namespaces visible=\"yes\" title=\"\"/>\n      <classes visible=\"yes\" title=\"\"/>\n      <defines title=\"\"/>\n      <typedefs title=\"\"/>\n      <enums title=\"\"/>\n      <enumvalues title=\"\"/>\n      <functions title=\"\"/>\n      <variables title=\"\"/>\n      <signals title=\"\"/>\n      <publicslots title=\"\"/>\n      <protectedslots title=\"\"/>\n      <privateslots title=\"\"/>\n      <events title=\"\"/>\n      <properties title=\"\"/>\n      <friends title=\"\"/>\n      <membergroups visible=\"yes\"/>\n    </memberdecl>\n    <memberdef>\n      <pagedocs/>\n      <inlineclasses title=\"\"/>\n      <defines title=\"\"/>\n      <typedefs title=\"\"/>\n      <enums title=\"\"/>\n      <enumvalues title=\"\"/>\n      <functions title=\"\"/>\n      <variables title=\"\"/>\n      <signals title=\"\"/>\n      <publicslots title=\"\"/>\n      <protectedslots title=\"\"/>\n      <privateslots title=\"\"/>\n      <events title=\"\"/>\n      <properties title=\"\"/>\n      <friends title=\"\"/>\n    </memberdef>\n    <authorsection visible=\"yes\"/>\n  </group>\n\n  <!-- Layout definition for a directory page -->\n  <directory>\n    <briefdescription visible=\"yes\"/>\n    <directorygraph visible=\"yes\"/>\n    <memberdecl>\n      <dirs visible=\"yes\"/>\n      <files visible=\"yes\"/>\n    </memberdecl>\n    <detaileddescription title=\"\"/>\n  </directory>\n</doxygenlayout>\n"
  },
  {
    "path": "config/DoxygenStyle.css",
    "content": "div.contents p {\n\t font-size: 16px;\n\t margin-left: 15px;\n    width: 80%;\n    background-color: white;\n}\ndiv.fragment {\n\t margin-left: 20px;\n}"
  },
  {
    "path": "config/README.txt",
    "content": "Building a Windows binary requires the 'rcedit.exe' tool available\nfrom https://github.com/electron/rcedit/releases.\n"
  },
  {
    "path": "config/buildbot.sh",
    "content": "#!/bin/bash\n# set -e\n\nDIR=\"$( cd \"$( dirname \"${BASH_SOURCE[0]}\" )\" && pwd )\"\n\nexport CDB_TAG=$1\nexport CDB_PLATFORM=$2\nif [ \"${CDB_TAG}\" = \"\" -o \"${CDB_TAG}\" = \"-h\" ]; then\n    echo \"Usage: bash buildbot.sh [tag|HEAD] [platform|ALL]\"\n    exit\nfi\nif [ \"${CDB_PLATFORM}\" = \"\" ]; then\n    echo \"Please specify a platform, or 'ALL' for all platforms.\"\n    exit\nfi\n\nfunction runbuild {\n    # Want this platform?\n    if [ \"${CDB_PLATFORM}\" != \"ALL\" -a \"${CDB_PLATFORM}\" != \"$1\" ]; then\n        echo \"Not building $1.\"\n        return 0\n    fi\n\t # Start the VM and wait for it to come up.\n\t echo \"Starting build bot for $1, ssh port $3\"\n\t ssh buildbothost \"nohup VBoxHeadless -s '$1' > /tmp/buildbot.out 2> /tmp/buildbot.err < /dev/null &\"\n\t echo \"Waiting 20 seconds for VM to start up...\"\n\t sleep 20\n\n\t # Setup the tunnel to the VM; a local port $3 gets mapped\n\t # to a port $3 on the build host, which is forwarded by \n\t # virtualbox to the ssh port of the build bot.\n\n\t echo 'Going to start build process...'\n\t ssh -M -S my-ctrl-socket -fnNT -L $3:localhost:$3 buildbothost\n\t \n\t # Execute build commands on the VM, using the build script\n\t # on the local machine (as the build bot may not have an\n\t # up-to-date build script yet).\n\n\t ssh -tt -p $3 buildbot CDB_TAG=${CDB_TAG} \"bash -s\" -- < ${DIR}/buildpkg.sh\n\t \n\t # Copy the generated package to the web server.\n\n\t echo 'Going to copy the package to the web server'\n\t scp -P $3 'buildbot:cadabra2/build/cadabra*' .\n\t scp cadabra*$2 \"cadabra_web:/var/www/cadabra2/packages/$4\"\n\t rm -f cadabra*$2\n\t \n\t # Take down the VM gracefully.\n\n\t echo 'Shutting down build bot...'\n\t ssh -tt -p $3 buildbot 'sudo shutdown now'\n\t \n\t # Close the tunnel to the VM.\n\n\t ssh -S my-ctrl-socket -O exit buildbot\n}\n\n# To setup a new build bot, install a basic system, install\n# openssh-server, and setup a tunnel from a local port (to be given\n# below) to the ssh port on the build bot. Put\n#\n#   kasper ALL=(ALL) NOPASSWD: ALL\n#\n# at the bottom of the file edited with 'sudo visudo' (to avoid\n# scripts asking for passwords). Copy the ~/.ssh/buildbots_rsa.pub to\n# ~/.ssh/authorized_keys on the build VM.\n#\n# For RPM-based systems, install rpm-build.\n#\n# Then install 'git', install all cadabra2 dependencies, and clone the\n# github repo into ~/cadabra2.\n\n# Parameters: VM name, package type, local ssh port, folder name on web server.\n\nrunbuild \"Mint_21\"             \".deb\" 7035 mint21\n# runbuild \"Mint_20\"             \".deb\" 7026 mint20\nrunbuild \"Ubuntu_22.04\"        \".deb\" 7033 ubuntu2204\n# runbuild \"Ubuntu_20.04\"        \".deb\" 7030 ubuntu2004\n#runbuild \"Ubuntu_18.04\"        \".deb\" 7017 ubuntu1804\n#runbuild \"Fedora_28\"           \".rpm\" 7020 fedora28\n#runbuild \"Fedora_29\"           \".rpm\" 7025 fedora29               \n#runbuild \"Fedora_32\"           \".rpm\" 7027 fedora32\n#runbuild \"Fedora_33\"           \".rpm\" 7031 fedora33\nrunbuild \"Fedora_35\"           \".rpm\" 7032 fedora35\n#runbuild \"Mint_19\"             \".deb\" 7022 mint19\n#runbuild \"OpenSUSE_15\"         \".rpm\" 7024 opensuse150\nrunbuild \"OpenSUSE_Tumbleweed\" \".rpm\" 7023 opensusetw\n#runbuild \"Debian_921\"          \".deb\" 7014 debian9\n#runbuild \"Debian_Buster\"       \".deb\" 7021 debian10\n# runbuild \"CentOS_7\"            \".rpm\" 7004 centos7      cmake/packaging clash\n# runbuild \"Scientific_Linux_74\" \".rpm\" 7013 scientific7x\n\n\n# Outdated versions:\n# runbuild \"Mint_18\" \".deb\" 7002 mint18                   ERROR\n# runbuild \"Fedora_27\" \".rpm\" 7015 fedora27               ERROR\n# runbuild \"Fedora_24_build\" \".rpm\" 7001 fedora24\n# runbuild \"Fedora_26\" \".rpm\" 7011 fedora26\n# runbuild \"Ubuntu_14.04_build\" \".deb\" 7005 ubuntu1404\n# runbuild \"Ubuntu_16.04_build\" \".deb\" 7000 ubuntu1604\n# runbuild \"Ubuntu_17.10\" \".deb\" 7012 ubuntu1710\n# runbuild \"Debian86\"            \".deb\" 7006 debian86     ERROR\n# runbuild \"OpenSUSE_Leap\" \".rpm\" 7003 opensuse421\n"
  },
  {
    "path": "config/buildpkg.sh",
    "content": "#!/bin/bash\n\n#sudo rm -Rf ${HOME}/cadabra2\n#git clone https://github.com/kpeeters/cadabra2\n# if [ -f /etc/redhat-release ]; then\n#     echo \"Updating .rpm system...\"\n#     sudo yum update -y\n# else\n#     echo \"Updating .deb system...\"\n#     sudo apt update\n#     sudo apt upgrade -y\n# fi\n\ncd ${HOME}/cadabra2\n#sudo ls\nrm -f config/install_script.iss config/pre_install.rtf\ngit pull origin\ngit checkout ${CDB_TAG}\nls\n# Weird: using sudo no longer works?!\nrm -Rf build\nmkdir build\ncd build\nif [ -f /etc/redhat-release ]; then\n\t sudo dnf -y install rpm-build\n    centos=\"`cat /etc/redhat-release | grep CentOS`\"\n    scilin=\"`cat /etc/redhat-release | grep Scientific`\"\n    if [ -n \"${centos}\" -o -n \"${scilin}\" ]; then\n        source /opt/rh/rh-python36/enable\n        source /opt/rh/devtoolset-7/enable\n        sudo alternatives --install /usr/bin/python python /usr/bin/python3.6 60\n        cmake3 -DPACKAGING_MODE=ON -DENABLE_MATHEMATICA=OFF -DCMAKE_INSTALL_PREFIX=/usr ..\n    else\n        cmake -DPACKAGING_MODE=ON -DENABLE_MATHEMATICA=OFF -DCMAKE_INSTALL_PREFIX=/usr ..\n    fi\nelse\n    cmake -DPACKAGING_MODE=ON -DENABLE_MATHEMATICA=OFF -DCMAKE_INSTALL_PREFIX=/usr ..\nfi\nmake\nif [ -n \"${centos}\" -o -n \"${scilin}\"  ]; then\n    sudo cpack3\nelse\n\t sudo cpack\nfi\nexit\n"
  },
  {
    "path": "config/doxyrest-config.lua",
    "content": "--------------------------------------------------------------------------------\n--\n--  This file is part of the Doxyrest toolkit.\n--\n--  Doxyrest is distributed under the MIT license.\n--  For details see accompanying license.txt file,\n--  the public copy of which is also available at:\n--  http://tibbo.com/downloads/archive/doxyrest/license.txt\n--\n--------------------------------------------------------------------------------\n\n--!\n--! \\defgroup frame-config\n--! \\grouporder 2\n--! \\title Frame Settings\n--!\n--! This section describes frame settings controlling input and output paths,\n--! titles, force-includes, declaration coding style, etc.\n--!\n--! A default ``doxyrest-config.lua`` file for standard frames can be found at\n--! ``$DOXYREST_FRAME_DIR/doxyrest-config.lua``. Copy it to your project\n--! directory and then adjust all the necessary parameters.\n--!\n--! @{\n--!\n\n--!\n--! Table containing a list of frame directories. All frame files will be\n--! searched in directories -- and in the sequence -- specified here.\n--!\n\nFRAME_DIR_LIST = { \"/usr/local/share/doxyrest/frame/cfamily\", \"/usr/local/share/doxyrest/frame/common\" }\n\n--!\n--! The output master (index) reStructuredText file. Usually, the index frame\n--! also generates auxillary files -- they will be placed next to the master\n--! file. The command line option ``-f`` *overrides* this value.\n--! If neither ``FRAME_FILE`` nor ``-f`` is specified, ``index.rst.in`` will be\n--! used as the default frame file.\n--!\n\nFRAME_FILE = \"index.rst.in\"\n\n--!\n--! The input master (index) XML file. Specifying it here allows calling\n--! ``doxyrest`` without parameters; otherwise, the master XML *must* be passed\n--! via the command line. If both ``INPUT_FILE`` and command line parameter are\n--! specified, the command line takes precedence.\n--!\n\nINPUT_FILE = \"doxygen/xml/index.xml\"\n\n--!\n--! The output master (index) reStructuredText file. Usually, the index frame\n--! also generates auxillary files -- they will be placed next to the master\n--! file. The command line option ``-o`` *overrides* this value. If neither\n--! ``OUTPUT_FILE`` nor ``-o`` is specified, ``index.rst`` will be used as\n--! the default output master file.\n--!\n\nOUTPUT_FILE = \"doxygen/rst/index.rst\"\n\n--!\n--! File with project-specific reStructuredText definitions. When non``nil``,\n--! this file will be included at the top of every generated ``.rst`` file.\n--!\n\nFORCE_INCLUDE_FILE = nil\n\n--!\n--! If you want to add extra reStructuredText documentation pages, do so\n--! by adding them to this list.\n--!\n\nEXTRA_PAGE_LIST = {}\n\n--!\n--! The title of the main (index) page. This only is used when ``INTRO_FILE``\n--! is not set (otherwise, the title of intro file will be used).\n--!\n\nINDEX_TITLE = \"My Project Documentation\"\n\n--!\n--! File with project introduction (reStructuredText). When non-nil, this file\n--! will be included into ``index.rst`` file and NOT added to the list of other\n--! documentation pages.\n--!\n\nINTRO_FILE = \"page_index.rst\"\n\n--!\n--! Specify whether to sort groups lexicographically (by ``title``) or\n--! logically (by ``id``). To maintain the original order (in which a group has\n--! been seen in the XML database), use ``originalIdx``.\n--!\n--! Omitting ``SORT_GROUPS_BY`` (or setting it to ``nil``) results in groups\n--! being sorted by ``title``.\n--!\n\nSORT_GROUPS_BY = \"title\"\n\n--[[!\n\tBy default, the page for the global namespace page will be called\n\t\"Global Namespace\" and will contain no description except that for the\n\tglobal compounds and members.\n\n\tIt's possible to override this behaviour by defining an auxillary compound\n\t(page or group) with a special ``id``; this page/group may contain a\n\tuser-defined title,  a brief description and a detailed description. Use\n\t``GLOBAL_AUX_COMPOUND_ID`` to define this special id.\n\n\t.. note::\n\n\t\tTo make sure you use the correct **Doxygen** XML ID of the group/page,\n\t\tfind the definition of the group in one of ``.xml`` files and copy\n\t\tthe value of ``id`` attribute.\n\n\t\tFor example, if the group was declared as ``\\defgroup global`` then\n\t\tthe its ``id`` will probably be either ``group_<your-group-name>`` or\n\t\t``group__<your-group-name>``.\n]]\n\nGLOBAL_AUX_COMPOUND_ID = \"group_global\"\n\n--[[!\n\tDoxyrest offers a workaround for the lack of footnotes in Doxygen by\n\tgetting documentation blocks for specially named pseudo-members and\n\tconverting those into footnotes.\n\n\t``FOOTNOTE_MEMBER_PREFIX`` specifies the name prefix for such\n\tpseudo-members. If it is set to ``nil`` or an empty string, Doxyrest\n\twill not attempt to convert any members to footnotes.\n\n\t\\sa :ref:`footnotes`\n]]\n\nFOOTNOTE_MEMBER_PREFIX = nil\n\n--!\n--! Specify the main language of your project; this string will be used for\n--! the reStructuredText ``.. code-block::`` sections and for conditional\n--! formatting of module item declarations.\n--!\n\nLANGUAGE = cpp\n\n--!\n--! Convert ``\\verbatim`` sections in doxy-comments to ``.. code-block::``\n--! sections in the output reStructuredText. The string value of\n--! ``VERBATIM_TO_CODE_BLOCK`` will be used as the language of\n--! ``.. code-block::`` section. By default, it's ``\"none\"`` which results in\n--! no syntax highlighting. To disable conversion at all, use ``nil``.\n--!\n\nVERBATIM_TO_CODE_BLOCK = \"cpp\"\n\n--!\n--! If the original doxy comments contain asterisks, they have to be escaped in\n--! reStructuredText (asterisks are used to mark **bold** or *italic* blocks).\n--!\n\nESCAPE_ASTERISKS = true\n\n--!\n--! If the original doxy comments contain pipe characters ``|``, they have to be\n--! escaped in reStructuredText (pipes are used for substitution references).\n--!\n\nESCAPE_PIPES = true\n\n--!\n--! If the original doxy comments contain trailingasterisks, they have to be\n--! escaped in reStructuredText (trailing underscores are used for internal\n--! links).\n--!\n\nESCAPE_TRAILING_UNDERSCORES = true\n\n--!\n--! Exclude items declared in specific locations. Use a regular expression to\n--! define a mask of directories/source files to completely exclude from the\n--! final documentation. For example, ``.*/impl/.*lua$`` will exclude all\n--! ``.lua`` files located in ``impl/`` directory.\n--!\n\nEXCLUDE_LOCATION_PATTERN = nil\n\n--!\n--! Exclude variables and functions without any documentation (no doxy-comments).\n--!\n\nEXCLUDE_UNDOCUMENTED_ITEMS = false\n\n--!\n--! \\subgroup\n--!\n--! By default, Doxyrest tries to translate Doxygen ``\\section``,\n--! ``\\subsection``, and ``\\subsubsection`` commands (as well as the\n--! ``<heading level=\"n\">`` blocks generated by Doxygen from Markdown titles\n--! inside comments) into reStructuredText titles.\n--!\n--! This sometimes leads to problems because Doxygen headings may appear outside\n--! of the global scope (e.g. inside lists) while reStructuredText titles are\n--! only allowed at the global scope. Another issue is Doxygen headings may\n--! yield inconsistent title structure (e.g. a title level 1 followed by level\n--! 3).\n--!\n--! If you run into these issues, use ``SECTION_TO_RUBRIC`` or\n--! ``HEADING_TO_RUBRIC``  to always convert Doxygen sections or ``<heading>``\n--! blocks or into reStructuredText ``.. rubric::`` directives. This yields\n--! uni-level headings, but solves both aforementioned problems.\n--!\n\nSECTION_TO_RUBRIC = false\nHEADING_TO_RUBRIC = false\n\n--[[!\n\tBy default, Doxyrest frames build a Python dictionary to be used later on by\n\tthe ``:cref:`` (code-reference) role. This database maps language-specific\n\tqualified names of items to their IDs.\n\n\tThis, together with setting the Sphinx ``default_role`` to ``cref``, allows\n\tto conveniently reference items from Doxy-comments or regular ``.rst`` files\n\tas such:\n\n\t.. code-block:: none\n\n\t\tThe `ui::Dialog` class is a base to the `ui::FileDialog` class.\n\n\tHowever, if this facility is not used, building (and loading) of the\n\tcref-database can be omitted to save both space and time.\n]]\n\nCREF_DB = false\n\n--[[!\n\tExclude items with higher protection level than ``PROTECTION_FILTER``:\n\n\t\t1. ``public``\n\t\t2. ``protected``\n\t\t3. ``private``\n\t\t4. ``package``\n\n\tBy default, only public items are included into documentation.\n]]\n\nPROTECTION_FILTER = \"public\"\n\n--!\n--! In many projects empty defines are *only* used as include-guards (and as\n--! such, should be excluded from the documentation). If this is not the case\n--! and empty defines should be kept in the final documentation, change this\n--! setting to ``false``.\n--!\n\nEXCLUDE_EMPTY_DEFINES = true\n\n--!\n--! If non-``nil``, each define will be checked using this regular expression\n--! and if its name matches, this define will be excluded from the documentation.\n--!\n\nEXCLUDE_DEFINE_PATTERN = nil\n\n--!\n--! Usually providing documentation blocks for default constructors is\n--! not necessary (as to avoid redundant meaningless \"Constructs a new object\"\n--! paragraphs). Change this to ``false`` if default constructors *should* be\n--! included.\n--!\n\nEXCLUDE_DEFAULT_CONSTRUCTORS = true\n\n--!\n--! Usually providing documentation blocks for a destructors is\n--! not necessary (as to avoid redundant meaningless \"Destructs an object\"\n--! paragraphs). Change this to ``false`` if destructors *should* be\n--! included.\n--!\n\nEXCLUDE_DESTRUCTORS = true\n\n--[[!\n\tUsually providing documentation blocks for primitive C typedefs such as:\n\n\t.. code-block:: C\n\n\t\ttypedef struct S S;\n\n\tis not necessary. Change this to ``false`` if such typedefs *should* be\n\tincluded.\n]]\n\nEXCLUDE_PRIMITIVE_TYPEDEFS = true\n\n--!\n--! For a base class/struct, show all the types directly derived from it.\n--!\n\nSHOW_DIRECT_DESCENDANTS = true\n\n--[[!\n\t\\subgroup\n\n\tInsert space between function name and parameter list like this:\n\n\t.. code-block:: C\n\n\t\tvoid foo ();\n\n\tBy default, ``PRE_PARAM_LIST_SPACE`` is ``false`` which yields:\n\n\t.. code-block:: C\n\n\t\tvoid foo();\n]]\n\nPRE_PARAM_LIST_SPACE = false\nPRE_OPERATOR_NAME_SPACE = true\nPRE_OPERATOR_PARAM_LIST_SPACE = true\n\n--[[!\n\tInsert a new line before the body of a enum, struct, class, etc.\n\n\tWhen ``PRE_BODY_NL`` is ``false``:\n\n\t.. code-block:: cpp\n\n\t\tclass MyClass {\n\t\t\t...\n\t\t}\n\n\tWhen ``PRE_BODY_NL`` is ``true``:\n\n\t.. code-block:: cpp\n\n\t\tclass MyClass\n\t\t{\n\t\t\t...\n\t\t}\n]]\n\nPRE_BODY_NL = true\n\n--[[!\n\tUse multi-line parameter lists in function declarations if parameter count is\n\tgreater than this threshold. ``nil`` means don't use parameter count\n\tthreshold.\n\n\tFor example, when ``ML_PARAM_LIST_COUNT_THRESHOLD`` is ``2``, the function\n\tdeclarations will look as such:\n\n\t.. code-block:: C\n\n\t\tvoid fn0();\n\t\tvoid fn1(int a);\n\t\tvoid fn2(int a, int b);\n\n\t\tvoid fn3(\n\t\t\tint a,\n\t\t\tint b\n\t\t\tint c\n\t\t\t);\n]]\n\nML_PARAM_LIST_COUNT_THRESHOLD = nil\n\n--[[!\n\tUse multi-line parameter lists in function declarations if single-line\n\tdeclaration length parameter count is greater than this threshold.\n\t``nil`` means don't use length threshold.\n\n\tSimilar to ``ML_PARAM_LIST_COUNT_THRESHOLD``, but the threshold parameter\n\there is *declaration length* and not *declaration parameter count*.\n\n\tExample:\n\n\t.. code-block:: C\n\n\t\tvoid foo(int a, int b, int c);\n\n\t\tvoid bar(\n\t\t\tint veryLongParameterName,\n\t\t\tint anotherVeryLongParameterName\n\t\t\t);\n\n]]\n\nML_PARAM_LIST_LENGTH_THRESHOLD = 80\n\n--[[!\n\tUse multi-line specifier-modifier lists in function declarations, i.e\n\tallocate a dedicated line for each type specifier/morifier.\n\n\tFor example, when ``ML_SPECIFIER_MODIFIER_LIST`` is ``true``, the function\n\tdeclarations will look as such:\n\n\t.. code-block:: C\n\n\t\tvoid\n\t\tfoo();\n\n\t\tstatic\n\t\tbool\n\t\t__cdecl\n\t\tbar(int a);\n]]\n\nML_SPECIFIER_MODIFIER_LIST = false\n\n--[[!\n\tUse the new C++11 syntax for ``typedef``-s:\n\n\tWhen ``TYPEDEF_TO_USING`` is ``false``:\n\n\t.. code-block:: cpp\n\n\t\ttypedef unsigned int uint_t;\n\t\ttypedef void Foo(int);\n\t\ttypedef void (*FooPtr)(int);\n\n\tWhen ``TYPEDEF_TO_USING`` is ``true``:\n\n\t.. code-block:: cpp\n\n\t\tusing uint_t = unsigned int;\n\t\tusing Foo typedef void (int);\n\t\tusing FooPtr typedef void (*)(int);\n]]\n\nTYPEDEF_TO_USING = false\n\n--[[!\n\tSometimes, it's required to redirect a Doxygen link to some external location.\n\tIn this case, add an entry to ``EXTERNAL_CREF_DB`` with the target URL, e.g.:\n\n\t.. code-block:: lua\n\n\t\tEXTERNAL_CREF_DB =\n\t\t{\n\t\t\t[ \"jnc.Scheduler\" ] = \"https://vovkos.github.io/jancy/stdlib/class_jnc_Scheduler.html\",\n\t\t\t[ \"strlen\"] = \"https://vovkos.github.io/jancy/stdlib/group_crt.html#doxid-function-strlen\"\n\n\t\t\t-- ...\n\t\t}\n\n\tThe key of the map is an ``importid`` attribute. This is a non-standard Doxygen\n\tattribute; Jancy compiler generates is when a referenced item is contained in an\n\timported extensions library (``.jncx``)\n]]\n\nEXTERNAL_CREF_DB = {}\n\n--[[!\n\tUsually providing documentation blocks for Lua ``local`` variables or\n\tfunctions is not desired. Change this to ``false`` if local items\n\t*should* be included in the final documentation.\n]]\n\nEXCLUDE_LUA_LOCALS = true\n\n--! @}\n"
  },
  {
    "path": "config/generate_keywords.py",
    "content": "import inspect\nimport importlib\nimport keyword\n\ndef get_functions(module):\n\tisfunc = lambda x: inspect.isfunction(x) or inspect.ismethod(x) or inspect.isbuiltin(x)\n\treturn [x[0] for x in inspect.getmembers(module, isfunc)]\n\ndef get_classes(module):\n\tisclass = lambda x: inspect.isclass(x)\n\treturn [x[0] for x in inspect.getmembers(module, isclass)]\n\ndef generate_set(name, items, line_begin = '\\t', line_size = 80):\n\tprint('const std::unordered_set<std::string> {} = {{'.format(name))\n\tcurline = ''\n\tfor item in ('\"{}\", '.format(item) for item in sorted(items)):\n\t\tif len(curline) + len(item) > line_size:\n\t\t\tprint(line_begin + curline)\n\t\t\tcurline = ''\n\t\tcurline += item\n\tif curline:\n\t\tprint(line_begin + curline)\n\tprint('};\\n')\n\ndef generate_find_func(*sets):\n\tprint('const char* get_keyword_group(const std::string& name)')\n\tprint('{')\n\tfor set in sets:\n\t\tprint('\\tif ({}.find(name) != {}.end())'.format(set[0], set[0]))\n\t\tprint('\\t\\treturn \"{}\";'.format(set[1]))\n\tprint('\\treturn nullptr;')\n\tprint('}')\n\n\n\nif __name__ == \"__main__\":\n\timport importlib\n\timport os\n\timport sys\n\n\tmodules = [\"builtins\"]\n\toutdir = '../frontend/gtkmm'\n\tif len(sys.argv) == 1:\n\t\tprint(\"Usage: {} [module1 [module2 [...]]] [--outdir] [--path]\".format(sys.argv[0]))\n\t\tprint(f\"\\tSpecify the output directory for the Keywords.hh and Keywords.cc files with --outdir=path/to/outdir (defaults to {outdir})\")\n\t\tprint(\"\\tSpecify additional search paths for modules with --path=your/import/directory. Specify multiple times for different paths.\")\n\t\texit(-1)\n\tfor arg in sys.argv[1:]:\n\t\tif arg.startswith(\"--outdir=\"):\n\t\t\toutdir = arg[len(\"--outdir=\"):]\n\t\telif arg.startswith(\"--path=\"):\n\t\t\tsys.path.append(os.path.abspath(arg[len(\"--path=\"):]))\n\t\telse:\n\t\t\tmodules.append(arg)\n\n\toutdir = os.path.abspath(outdir)\n\tfor i in range(len(modules)):\n\t\ttry:\n\t\t\tmodules[i] = importlib.import_module(modules[i])\n\t\texcept ImportError:\n\t\t\tprint(\"Could not import module {}. Used path:\".format(modules[i]))\n\t\t\tfor path in sys.path:\n\t\t\t\tprint(f\"\\t{path}\")\n\t\t\texit(-1)\n\n\tfunctions = set()\n\tclasses = set()\n\n\tfor module in modules:\n\t\tfor f in get_functions(module):\n\t\t\tfunctions.add(f)\n\t\tfor c in get_classes(module):\n\t\t\tclasses.add(c)\n\n\tprint(\"Generating in directory '{}'\".format(outdir))\n\n\t# Generate header file\n\tsys.stdout = open(os.path.join(outdir, 'Keywords.hh'), 'w+')\n\tprint(\"#pragma once\\n\\n#include <string>\\n\")\n\tprint(\"// Returns the group name belongs to, or nullptr if not found\")\n\tprint(\"const char* get_keyword_group(const std::string& name);\")\n\n\t#Generate code file\n\tsys.stdout = open(os.path.join(outdir, 'Keywords.cc'), 'w+')\n\n\tprint('#include <unordered_set>')\n\tprint('#include \"Keywords.hh\"\\n\\n')\n\n\tgenerate_set(\"functions\", functions)\n\tgenerate_set(\"classes\", classes)\n\tgenerate_set(\"keywords\", keyword.kwlist)\n\n\tgenerate_find_func(\n\t\t(\"functions\", \"function\"),\n\t\t(\"classes\", \"class\"),\n\t\t(\"keywords\", \"keyword\")\n\t)\n\t\n\tsys.stdout = sys.__stdout__\n\tprint(\"Generated Keywords.hh and Keywords.cc\")\n"
  },
  {
    "path": "config/init-cadabra2.scm",
    "content": "\n;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;\n;;\n;; MODULE      : cadabra2.scm\n;; DESCRIPTION : Initialize cadabra2 plugin\n;; COPYRIGHT   : (C) 2025 Kasper Peeters\n;;\n;; This software falls under the GNU general public license and comes WITHOUT\n;; ANY WARRANTY WHATSOEVER. See the file $TEXMACS_PATH/LICENSE for details.\n;; If you don't have this file, write to the Free Software Foundation, Inc.,\n;; 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.\n;;\n;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;\n\n;; As in the python plugin, we need a way to make TeXmacs send\n;; multi-line input without stripping newlines.\n\n(define (cadabra-serialize lan t)\n  (with u (pre-serialize lan t)\n    (with s (texmacs->code (stree->tree u) \"SourceCode\")\n\t  (string-append  s  \"\\n<EOF>\\n\"))))\n\n(plugin-configure cadabra\n  (:require (url-exists-in-path? \"cadabra2\"))\n  (:launch \"cadabra2 --texmacs\")\n  (:serializer ,cadabra-serialize)\n  (:session \"Cadabra2\"))\n"
  },
  {
    "path": "config/install_python_windows.cmake.in",
    "content": "execute_process(COMMAND cygpath -m @PYLIBDIR@ OUTPUT_VARIABLE WINPYTHON OUTPUT_STRIP_TRAILING_WHITESPACE)\nmessage(STATUS \"Copying python runtime from @PYLIBDIR@ aka ${WINPYTHON}\")\n#file(INSTALL \"${WINPYTHON}\" DESTINATION \"@CMAKE_INSTALL_PREFIX@/lib\")\ninstall(DIRECTORY \"${WINPYTHON}\" DESTINATION \"@CMAKE_INSTALL_PREFIX@/lib\")\n"
  },
  {
    "path": "config/install_script.iss.in",
    "content": "; Script generated by the Inno Setup Script Wizard.\r\n; SEE THE DOCUMENTATION FOR DETAILS ON CREATING INNO SETUP SCRIPT FILES!\r\n\r\n#define MyAppName \"Cadabra2\"\r\n#define MyAppVersion \"@CADABRA_VERSION_SEM@\"\r\n#define MyAppPublisher \"Kasper Peeters\"\r\n#define MyAppURL \"https://www.cadabra.science/\"\r\n#define MyAppExeName \"cadabra2-gtk.exe\"\r\n\r\n[Setup]\r\n; NOTE: The value of AppId uniquely identifies this application.\r\n; Do not use the same AppId value in installers for other applications.\r\n; (To generate a new GUID, click Tools | Generate GUID inside the IDE.)\r\nAppId={{1ADE9581-27A2-43EA-9A22-CE05177883B4}\r\nAppName={#MyAppName}\r\nAppVersion={#MyAppVersion}\r\n;AppVerName={#MyAppName} {#MyAppVersion}\r\nAppPublisher={#MyAppPublisher}\r\nAppPublisherURL={#MyAppURL}\r\nAppSupportURL={#MyAppURL}\r\nAppUpdatesURL={#MyAppURL}\r\nDefaultDirName={pf}\\{#MyAppName}\r\nDisableProgramGroupPage=yes\r\nLicenseFile=..\\LICENSE\r\n; File showing the prerequesties etc...\r\nInfoBeforeFile=pre_install.rtf \r\n; File shown after installation, linking to docs etc...\r\nInfoAfterFile=post_install.rtf\r\nOutputDir=build\r\nOutputBaseFilename=cadabra2-installer\r\n; Icon of the installer. If this causes a compilation error, just \r\n; comment it out\r\nSetupIconFile=cadabra2.ico\r\nCompression=lzma\r\nSolidCompression=yes\r\nArchitecturesInstallIn64BitMode=x64\r\n\r\n[Languages]\r\nName: \"english\"; MessagesFile: \"compiler:Default.isl\"\r\n\r\n[Tasks]\r\nName: \"desktopicon\"; Description: \"{cm:CreateDesktopIcon}\"; GroupDescription: \"{cm:AdditionalIcons}\"; Flags: unchecked\r\n\r\n[Files]\r\nSource: \"C:\\Cadabra\\bin\\cadabra2-gtk.exe\"; DestDir: \"{app}\\bin\"; Flags: ignoreversion\r\nSource: \"C:\\Cadabra\\*\"; DestDir: \"{app}\"; Flags: ignoreversion recursesubdirs createallsubdirs\r\n; Source: \"C:\\Users\\kasper\\Anaconda3\\DLLs\\sqlite3.dll\"; DestDir: \"{app}\\bin\"; Flags: ignoreversion\r\n; NOTE: Don't use \"Flags: ignoreversion\" on any shared system files\r\n; VC++ redistributable runtime. Extracted by VC2019RedistNeedsInstall(), if needed.\r\nSource: \"vcredist_x64.exe\"; DestDir: {tmp}; Flags: dontcopy\r\n\r\n[Run]\r\nFilename: \"{tmp}\\vcredist_x64.exe\"; StatusMsg: \"Installing VC++ redistributables...\"; Parameters: \"/quiet\"; Check: VC2019RedistNeedsInstall ; Flags: waituntilterminated\r\n\r\n; https://stackoverflow.com/questions/24574035/how-to-install-microsoft-vc-redistributables-silently-in-inno-setup\r\n[Code]\r\nfunction VC2019RedistNeedsInstall: Boolean;\r\nvar \r\n  Version: String;\r\nbegin\r\n  if (RegQueryStringValue(HKEY_LOCAL_MACHINE, 'SOFTWARE\\Microsoft\\VisualStudio\\14.0\\VC\\Runtimes\\x64', 'Version', Version)) then\r\n  begin\r\n    // Is the installed version at least 14.23 ? \r\n    Log('VC Redist Version check : found ' + Version);\r\n    Result := (CompareStr(Version, 'v14.23.27820.00')<0);\r\n  end\r\n  else \r\n  begin\r\n    // Not even an old version installed\r\n    Result := True;\r\n  end;\r\n  if (Result) then\r\n  begin\r\n    ExtractTemporaryFile('vcredist_x64.exe');\r\n  end;\r\nend;\r\n\r\n\r\n[Icons]\r\nName: \"{commonprograms}\\{#MyAppName}\"; Filename: \"{app}\\bin\\{#MyAppExeName}\"\r\nName: \"{commondesktop}\\{#MyAppName}\"; Filename: \"{app}\\bin\\{#MyAppExeName}\"; Tasks: desktopicon\r\n\r\n[Run]\r\nFilename: \"{app}\\bin\\{#MyAppExeName}\"; Description: \"{cm:LaunchProgram,{#StringChange(MyAppName, '&', '&&')}}\"; Flags: nowait postinstall skipifsilent\r\n\r\n"
  },
  {
    "path": "config/make.bat",
    "content": "rcedit.exe C:\\Cadabra\\bin\\cadabra2-gtk.exe --set-icon cadabra2.ico\r\n\"C:\\Program Files (x86)\\Inno Setup 6\\ISCC.exe\" install_script.iss\r\n"
  },
  {
    "path": "config/post_install.rtf",
    "content": "If you are a new user of Cadabra, then you may wish to read the tutorials and documentation at http://cadabra.science/tutorials.html"
  },
  {
    "path": "config/postinst.in",
    "content": "#!/bin/sh\n#\n# Script to be included in the cadabra2 packages (deb/rpm) and to be\n# run after installation, to make TeX pick up our style sheets and\n# the desktop pickup our menu entry/icon.\n\n/sbin/ldconfig -v\n\n# texhash\n\nif hash gtk-update-icon-cache-3.0 2>/dev/null; then \n   gtk-update-icon-cache-3.0 -t /usr/share/icons/hicolor\nelse\n   gtk-update-icon-cache -t /usr/share/icons/hicolor\nfi\n"
  },
  {
    "path": "config/pre_install.rtf.in",
    "content": "No requirements.\r\n"
  },
  {
    "path": "config/publish-doxygen",
    "content": "#!/bin/bash -e\n#\n# Courtesy of http://blog.gockelhut.com/2014/09/automatic-documentation-publishing-with.html\n\n# Settings\nREPO_PATH=git@github.com:kpeeters/cadabra2.git\nHTML_PATH=doxygen/html\nCOMMIT_USER=\"Documentation Builder\"\nCOMMIT_EMAIL=\"kasper.peeters@phi-sci.com\"\nCHANGESET=$(git rev-parse --verify HEAD)\n\n# Get a clean version of the HTML documentation repo.\nrm -rf ${HTML_PATH}\nmkdir -p ${HTML_PATH}\ngit clone -b gh-pages \"${REPO_PATH}\" --single-branch ${HTML_PATH}\n\n# rm all the files through git to prevent stale files.\ncd ${HTML_PATH}\ngit rm -rf .\ncd -\n\n# Generate the HTML documentation.\ndoxygen\n\n# Create and commit the documentation repo.\ncd ${HTML_PATH}\ngit add .\ngit config user.name \"${COMMIT_USER}\"\ngit config user.email \"${COMMIT_EMAIL}\"\ngit commit -m \"Automated documentation build for changeset ${CHANGESET}.\"\ngit push origin gh-pages\ncd -\n"
  },
  {
    "path": "config/science.cadabra.cadabra2-gtk.desktop.in",
    "content": "[Desktop Entry]\nVersion=1.0\nType=Application\nName=Cadabra 2\nGenericName=Computer algebra system\nComment=Computer algebra system for field theory problems\nIcon=cadabra2-gtk\nCategories=Math;Science;Education;\nExec=cadabra2-gtk %f\nTerminal=false\nKeywords=\"Computer Algebra\";Physics;Mathematics\nMimeType=application/cadabra;application/x-cadabra;\nX-AppImage-Name=\"Cadabra 2\"\nX-AppImage-Version=@CADABRA_VERSION_SEM@\n"
  },
  {
    "path": "config/shortcuts.wxs",
    "content": "<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n<Wix xmlns=\"http://schemas.microsoft.com/wix/2006/wi\">\n  <Fragment>\n    <DirectoryRef Id=\"PROGRAM_MENU_FOLDER\">\n      <Component Id=\"CadabraShortcuts\" Guid=\"*\">\n        <Shortcut Id=\"CadabraStartMenuShortcut\" \n                  Name=\"Cadabra\" \n                  Description=\"Computer algebra system for field theory\"\n                  Target=\"[#cadabra2-gtk.exe]\"\n                  WorkingDirectory=\"INSTALLDIR\"/>\n        <RemoveFolder Id=\"CleanupShortcut\" On=\"uninstall\"/>\n        <RegistryValue Root=\"HKCU\" Key=\"Software\\Cadabra\" Name=\"installed\" Type=\"integer\" Value=\"1\" KeyPath=\"yes\"/>\n      </Component>\n    </DirectoryRef>\n  </Fragment>\n</Wix>\n"
  },
  {
    "path": "config/travisci_rsa.pub",
    "content": "ssh-rsa AAAAB3NzaC1yc2EAAAADAQABAAABAQC6TwMFIylqHAK5LHUzFQou6SvzLlMt4QriGh6NCbsdSydaiH4NRAoaWXi7lVH3DJgp+w4TKeGvAzLsIoRANxEXKUnET9E1lqFYmlC0R5QE790wCx9NxwusvxHuuHPv+H78UbVR+8gmoXztUEozmgx55M8/VZqnueoLv/Y/j7vbfLBTjYZLaumnDqfd71EewjTdZ/WW5+mJZWYgTsFH2d8ZwESMaweYshSCkSaqGcBdtuLOmeRXUdC/zptsD19oCiHbs+pwRdfO7NthwOXKeTWfrSxDIUdTUzfldORKRdb6+77H5VghWYvYsZk9acrQs/cju1dI6/43GehOITGDnFWn kasper.peeters@phi-sci.com\n"
  },
  {
    "path": "contrib/einstein_equations.cnb",
    "content": "{\n\t\"cells\" : \n\t[\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\section*{Einstein equations from a variational principle}\\n\\n\\\\author{Mattia Scomparin}\\\\email{mattia.scompa@gmail.com}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\section*{Einstein equations from a variational principle}\\n\\n\\\\author{Mattia Scomparin}\\\\email{mattia.scompa@gmail.com}\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"This notebook derives the Einstein equations by starting from the Einstein-Hilbert action, and requiring that\\nits variational derivative with respect to the metric vanishes. \"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"This notebook derives the Einstein equations by starting from the Einstein-Hilbert action, and requiring that\\nits variational derivative with respect to the metric vanishes. \"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"import cdb.core.manip as manip\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"We first of all need to declare the indices which we will use, as well as the symbols we use for the metric and Kronecker delta.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"We first of all need to declare the indices which we will use, as well as the symbols we use for the metric and Kronecker delta.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Indices(position=independent) to~}\\\\left[\\\\mu,~\\\\discretionary{}{}{} \\\\nu,~\\\\discretionary{}{}{} \\\\rho,~\\\\discretionary{}{}{} \\\\sigma,~\\\\discretionary{}{}{} \\\\alpha,~\\\\discretionary{}{}{} \\\\beta,~\\\\discretionary{}{}{} \\\\gamma,~\\\\discretionary{}{}{} \\\\lambda,~\\\\discretionary{}{}{} \\\\tau,~\\\\discretionary{}{}{} \\\\pi,~\\\\discretionary{}{}{} \\\\xi,~\\\\discretionary{}{}{} \\\\iota,~\\\\discretionary{}{}{} \\\\omega,~\\\\discretionary{}{}{} \\\\kappa,~\\\\discretionary{}{}{} \\\\psi,~\\\\discretionary{}{}{} \\\\chi,~\\\\discretionary{}{}{} \\\\epsilon,~\\\\discretionary{}{}{} \\\\upsilon\\\\right].\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"{\\\\mu,\\\\nu,\\\\rho,\\\\sigma,\\\\alpha,\\\\beta,\\\\gamma,\\\\lambda,\\\\tau,\\\\pi,\\\\xi,\\\\iota,\\\\omega,\\\\kappa,\\\\psi,\\\\chi,\\\\epsilon,\\\\upsilon}::Indices(position=independent);\\ng_{\\\\mu\\\\nu}::Metric.\\ng^{\\\\mu\\\\nu}::InverseMetric.\\n{\\\\delta{#},g_{\\\\mu}^{\\\\nu},g^{\\\\mu}_{\\\\nu}}::KroneckerDelta.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"Make various symbols display in a more readable form,\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"Make various symbols display in a more readable form,\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\\\\Lm::LaTeXForm(\\\"\\\\mathcal{L}_{\\\\text{mat}}\\\").    \\t\\t\\n\\\\Dg::LaTeXForm(\\\"\\\\sqrt{-g}\\\").          \\n\\\\dg{#}::LaTeXForm(\\\"\\\\delta g\\\").  \\t\\t\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\\\\dLm::LaTeXForm(\\\"\\\\delta\\\\mathcal{L}_{\\\\text{mat}}\\\").  \\n\\\\d::LaTeXForm(\\\"\\\\delta\\\").\\n\\\\dDg::LaTeXForm(\\\"\\\\delta\\\\sqrt{-g}\\\").   \\n\\\\dCn{#}::LaTeXForm(\\\"\\\\delta\\\\Gamma\\\").         \\n\\\\dR{#}::LaTeXForm(\\\"\\\\delta R\\\").\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"The Christoffel symbols and their variations are symmetric in the two lower indices,\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"The Christoffel symbols and their variations are symmetric in the two lower indices,\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\\\\Gamma^{\\\\alpha}_{\\\\mu\\\\nu}::TableauSymmetry(shape={2}, indices={1,2}).\\n\\\\dGamma^{\\\\alpha}_{\\\\mu\\\\nu}::TableauSymmetry(shape={2}, indices={1,2}).\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"We need to declare which symbols to use for derivatives,\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"We need to declare which symbols to use for derivatives,\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property PartialDerivative to~}\\\\partial{\\\\#}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Derivative to~}\\\\left[\\\\nabla{\\\\#},~\\\\discretionary{}{}{} \\\\delta{\\\\#}\\\\right].\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"{\\\\partial{#}}::PartialDerivative;\\n{\\\\nabla{#},\\\\delta{#}}::Derivative;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"We now need to define the Christoffel connection in terms of the metric, and the Riemann tensor in terms of the Christoffel connection,\\nas well as the Ricci tensor and scalar and Einstein tensor. These are also available in a Cadabra package, but for clarity we spell\\nthem out here.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"We now need to define the Christoffel connection in terms of the metric, and the Riemann tensor in terms of the Christoffel connection,\\nas well as the Ricci tensor and scalar and Einstein tensor. These are also available in a Cadabra package, but for clarity we spell\\nthem out here.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"\\\\Gamma^{\\\\mu}_{\\\\nu \\\\rho} =  1/2 g^{\\\\mu \\\\sigma} (\\\\partial_{\\\\rho}(g_{\\\\nu \\\\sigma}) + \\\\partial_{\\\\nu}(g_{\\\\rho \\\\sigma})-\\\\partial_{\\\\sigma}(g_{\\\\nu \\\\rho}))\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\Gamma^{\\\\mu}\\\\,_{\\\\nu \\\\rho} = \\\\frac{1}{2}g^{\\\\mu \\\\sigma} \\\\left(\\\\partial_{\\\\rho}{g_{\\\\nu \\\\sigma}}+\\\\partial_{\\\\nu}{g_{\\\\rho \\\\sigma}}-\\\\partial_{\\\\sigma}{g_{\\\\nu \\\\rho}}\\\\right)\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"R^{\\\\rho}_{\\\\sigma \\\\mu \\\\nu} = \\\\partial_{\\\\mu}(\\\\Gamma^{\\\\rho}_{\\\\nu \\\\sigma})-\\\\partial_{\\\\nu}(\\\\Gamma^{\\\\rho}_{\\\\mu \\\\sigma}) + \\\\Gamma^{\\\\rho}_{\\\\mu \\\\lambda} \\\\Gamma^{\\\\lambda}_{\\\\nu \\\\sigma}-\\\\Gamma^{\\\\rho}_{\\\\nu \\\\lambda} \\\\Gamma^{\\\\lambda}_{\\\\mu \\\\sigma}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}R^{\\\\rho}\\\\,_{\\\\sigma \\\\mu \\\\nu} = \\\\partial_{\\\\mu}{\\\\Gamma^{\\\\rho}\\\\,_{\\\\nu \\\\sigma}}-\\\\partial_{\\\\nu}{\\\\Gamma^{\\\\rho}\\\\,_{\\\\mu \\\\sigma}}+\\\\Gamma^{\\\\rho}\\\\,_{\\\\mu \\\\lambda} \\\\Gamma^{\\\\lambda}\\\\,_{\\\\nu \\\\sigma}-\\\\Gamma^{\\\\rho}\\\\,_{\\\\nu \\\\lambda} \\\\Gamma^{\\\\lambda}\\\\,_{\\\\mu \\\\sigma}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"R_{\\\\sigma \\\\nu} = R^{\\\\rho}_{\\\\sigma \\\\rho \\\\nu}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}R_{\\\\sigma \\\\nu} = R^{\\\\rho}\\\\,_{\\\\sigma \\\\rho \\\\nu}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"R = R_{\\\\sigma \\\\nu} g^{\\\\sigma \\\\nu}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}R = R_{\\\\sigma \\\\nu} g^{\\\\sigma \\\\nu}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"G_{\\\\mu \\\\nu} = R_{\\\\mu \\\\nu} -  1/2 g_{\\\\mu \\\\nu} R\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}G_{\\\\mu \\\\nu} = R_{\\\\mu \\\\nu} - \\\\frac{1}{2}g_{\\\\mu \\\\nu} R\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"connection       := \\\\Gamma^{\\\\mu}_{\\\\nu\\\\rho} = 1/2 g^{\\\\mu\\\\sigma} ( \\\\partial_{\\\\rho}{g_{\\\\nu\\\\sigma}} +\\\\partial_{\\\\nu}{g_{\\\\rho\\\\sigma}} -\\\\partial_{\\\\sigma}{g_{\\\\nu\\\\rho}} );\\nriemannTensor    := R^{\\\\rho}_{\\\\sigma\\\\mu\\\\nu} = \\\\partial_{\\\\mu}{\\\\Gamma^{\\\\rho}_{\\\\nu\\\\sigma}} -\\\\partial_{\\\\nu}{\\\\Gamma^{\\\\rho}_{\\\\mu\\\\sigma}} \\n                                              +\\\\Gamma^{\\\\rho}_{\\\\mu\\\\lambda} \\\\Gamma^{\\\\lambda}_{\\\\nu\\\\sigma} -\\\\Gamma^{\\\\rho}_{\\\\nu\\\\lambda} \\\\Gamma^{\\\\lambda}_{\\\\mu\\\\sigma};\\nricciTensor      := R_{\\\\sigma\\\\nu} = R^{\\\\rho}_{\\\\sigma\\\\rho\\\\nu};\\nscalarCurvature  := R = R_{\\\\sigma\\\\nu} g^{\\\\sigma\\\\nu};      \\neinsteinTensor   := G_{\\\\mu\\\\nu} = R_{\\\\mu\\\\nu} - 1/2 g_{\\\\mu\\\\nu} R;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"We are now ready to address the variational problem. The action we use is the Einstein-Hilbert action, amended with \\na cosmological constant term.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"We are now ready to address the variational problem. The action we use is the Einstein-Hilbert action, amended with \\na cosmological constant term.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"S = \\\\int{\\\\Dg ( 1/2 (\\\\kappa)**(-1) (R-2\\\\Lambda) + \\\\Lm)}{x}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}S = \\\\int \\\\sqrt{-g} \\\\left(\\\\frac{1}{2}{\\\\kappa}^{-1} \\\\left(R-2\\\\Lambda\\\\right)+\\\\mathcal{L}_{\\\\text{mat}}\\\\right)\\\\,\\\\,{\\\\rm d}x\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"S = \\\\int{ 1/2 \\\\Dg (\\\\kappa)**(-1) R-\\\\Dg (\\\\kappa)**(-1) \\\\Lambda + \\\\Dg \\\\Lm}{x}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}S = \\\\int \\\\left(\\\\frac{1}{2}\\\\sqrt{-g} {\\\\kappa}^{-1} R-\\\\sqrt{-g} {\\\\kappa}^{-1} \\\\Lambda+\\\\sqrt{-g} \\\\mathcal{L}_{\\\\text{mat}}\\\\right)\\\\,\\\\,{\\\\rm d}x\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"action := S = \\\\int{\\\\Dg*[1/2*1/\\\\kappa*(R-2\\\\Lambda)+\\\\Lm]}{x};\\ndistribute(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"Before we vary this, we need to construct the variation of the various objects in this action step by step. The variation of the metric determinant is given by\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"Before we vary this, we need to construct the variation of the various objects in this action step by step. The variation of the metric determinant is given by\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"\\\\delta(\\\\Dg) =  -  1/2 \\\\Dg g_{\\\\mu \\\\nu} \\\\dg^{\\\\mu \\\\nu}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\delta{\\\\sqrt{-g}} =  - \\\\frac{1}{2}\\\\sqrt{-g} g_{\\\\mu \\\\nu} \\\\delta g^{\\\\mu \\\\nu}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"deltaMetricDeterminant := \\\\delta(\\\\Dg) = -\\\\frac{1}{2}*\\\\Dg*g_{\\\\mu\\\\nu}\\\\dg^{\\\\mu\\\\nu}; \"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"By definition the variation of the matter Lagrangian gives the stress tensor; we rewrite it here slightly for later purposes.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"By definition the variation of the matter Lagrangian gives the stress tensor; we rewrite it here slightly for later purposes.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"\\\\Dg T_{\\\\mu \\\\nu} \\\\dg^{\\\\mu \\\\nu} = -2\\\\delta(\\\\Dg \\\\Lm)\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\sqrt{-g} T_{\\\\mu \\\\nu} \\\\delta g^{\\\\mu \\\\nu} = -2\\\\delta\\\\left(\\\\sqrt{-g} \\\\mathcal{L}_{\\\\text{mat}}\\\\right)\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"\\\\Dg g_{\\\\mu \\\\nu} \\\\dg^{\\\\mu \\\\nu} \\\\Lm-2\\\\Dg \\\\delta(\\\\Lm) = \\\\Dg T_{\\\\mu \\\\nu} \\\\dg^{\\\\mu \\\\nu}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\sqrt{-g} g_{\\\\mu \\\\nu} \\\\delta g^{\\\\mu \\\\nu} \\\\mathcal{L}_{\\\\text{mat}}-2\\\\sqrt{-g} \\\\delta{\\\\mathcal{L}_{\\\\text{mat}}} = \\\\sqrt{-g} T_{\\\\mu \\\\nu} \\\\delta g^{\\\\mu \\\\nu}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"energyMomentumTensor := \\\\Dg T_{\\\\mu\\\\nu}\\\\dg^{\\\\mu\\\\nu} = -2\\\\delta(\\\\Dg*\\\\Lm);\\nproduct_rule(_)\\ndistribute(_)\\nsubstitute(_,deltaMetricDeterminant)\\nmatterLagrangianVariation = manip.swap_sides(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"Next comes the variation of the Christoffel symbols. We then rewrite these in such a way that we isolate the derivative\\nof the variation, as that object will appear once we start varying the Riemann tensor.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"Next comes the variation of the Christoffel symbols. We then rewrite these in such a way that we isolate the derivative\\nof the variation, as that object will appear once we start varying the Riemann tensor.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"\\\\nabla_{\\\\sigma}(\\\\dCn^{\\\\mu}_{\\\\nu \\\\rho}) = \\\\partial_{\\\\sigma}(\\\\dCn^{\\\\mu}_{\\\\nu \\\\rho}) + \\\\Gamma^{\\\\mu}_{\\\\sigma \\\\alpha} \\\\dCn^{\\\\alpha}_{\\\\nu \\\\rho}-\\\\Gamma^{\\\\alpha}_{\\\\sigma \\\\nu} \\\\dCn^{\\\\mu}_{\\\\alpha \\\\rho}-\\\\Gamma^{\\\\alpha}_{\\\\sigma \\\\rho} \\\\dCn^{\\\\mu}_{\\\\nu \\\\alpha}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\nabla_{\\\\sigma}{\\\\delta\\\\Gamma^{\\\\mu}\\\\,_{\\\\nu \\\\rho}} = \\\\partial_{\\\\sigma}{\\\\delta\\\\Gamma^{\\\\mu}\\\\,_{\\\\nu \\\\rho}}+\\\\Gamma^{\\\\mu}\\\\,_{\\\\sigma \\\\alpha} \\\\delta\\\\Gamma^{\\\\alpha}\\\\,_{\\\\nu \\\\rho}-\\\\Gamma^{\\\\alpha}\\\\,_{\\\\sigma \\\\nu} \\\\delta\\\\Gamma^{\\\\mu}\\\\,_{\\\\alpha \\\\rho}-\\\\Gamma^{\\\\alpha}\\\\,_{\\\\sigma \\\\rho} \\\\delta\\\\Gamma^{\\\\mu}\\\\,_{\\\\nu \\\\alpha}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"0 = \\\\partial_{\\\\sigma}(\\\\dCn^{\\\\mu}_{\\\\nu \\\\rho}) + \\\\Gamma^{\\\\mu}_{\\\\sigma \\\\alpha} \\\\dCn^{\\\\alpha}_{\\\\nu \\\\rho}-\\\\Gamma^{\\\\alpha}_{\\\\sigma \\\\nu} \\\\dCn^{\\\\mu}_{\\\\alpha \\\\rho}-\\\\Gamma^{\\\\alpha}_{\\\\sigma \\\\rho} \\\\dCn^{\\\\mu}_{\\\\nu \\\\alpha}-\\\\nabla_{\\\\sigma}(\\\\dCn^{\\\\mu}_{\\\\nu \\\\rho})\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}0 = \\\\partial_{\\\\sigma}{\\\\delta\\\\Gamma^{\\\\mu}\\\\,_{\\\\nu \\\\rho}}+\\\\Gamma^{\\\\mu}\\\\,_{\\\\sigma \\\\alpha} \\\\delta\\\\Gamma^{\\\\alpha}\\\\,_{\\\\nu \\\\rho}-\\\\Gamma^{\\\\alpha}\\\\,_{\\\\sigma \\\\nu} \\\\delta\\\\Gamma^{\\\\mu}\\\\,_{\\\\alpha \\\\rho}-\\\\Gamma^{\\\\alpha}\\\\,_{\\\\sigma \\\\rho} \\\\delta\\\\Gamma^{\\\\mu}\\\\,_{\\\\nu \\\\alpha}-\\\\nabla_{\\\\sigma}{\\\\delta\\\\Gamma^{\\\\mu}\\\\,_{\\\\nu \\\\rho}}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"-\\\\partial_{\\\\sigma}(\\\\dCn^{\\\\mu}_{\\\\nu \\\\rho}) = \\\\Gamma^{\\\\mu}_{\\\\sigma \\\\alpha} \\\\dCn^{\\\\alpha}_{\\\\nu \\\\rho}-\\\\Gamma^{\\\\alpha}_{\\\\sigma \\\\nu} \\\\dCn^{\\\\mu}_{\\\\alpha \\\\rho}-\\\\Gamma^{\\\\alpha}_{\\\\sigma \\\\rho} \\\\dCn^{\\\\mu}_{\\\\nu \\\\alpha}-\\\\nabla_{\\\\sigma}(\\\\dCn^{\\\\mu}_{\\\\nu \\\\rho})\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}-\\\\partial_{\\\\sigma}{\\\\delta\\\\Gamma^{\\\\mu}\\\\,_{\\\\nu \\\\rho}} = \\\\Gamma^{\\\\mu}\\\\,_{\\\\sigma \\\\alpha} \\\\delta\\\\Gamma^{\\\\alpha}\\\\,_{\\\\nu \\\\rho}-\\\\Gamma^{\\\\alpha}\\\\,_{\\\\sigma \\\\nu} \\\\delta\\\\Gamma^{\\\\mu}\\\\,_{\\\\alpha \\\\rho}-\\\\Gamma^{\\\\alpha}\\\\,_{\\\\sigma \\\\rho} \\\\delta\\\\Gamma^{\\\\mu}\\\\,_{\\\\nu \\\\alpha}-\\\\nabla_{\\\\sigma}{\\\\delta\\\\Gamma^{\\\\mu}\\\\,_{\\\\nu \\\\rho}}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"\\\\partial_{\\\\sigma}(\\\\dCn^{\\\\mu}_{\\\\nu \\\\rho}) = -\\\\Gamma^{\\\\mu}_{\\\\sigma \\\\alpha} \\\\dCn^{\\\\alpha}_{\\\\nu \\\\rho} + \\\\Gamma^{\\\\alpha}_{\\\\sigma \\\\nu} \\\\dCn^{\\\\mu}_{\\\\alpha \\\\rho} + \\\\Gamma^{\\\\alpha}_{\\\\sigma \\\\rho} \\\\dCn^{\\\\mu}_{\\\\nu \\\\alpha} + \\\\nabla_{\\\\sigma}(\\\\dCn^{\\\\mu}_{\\\\nu \\\\rho})\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\partial_{\\\\sigma}{\\\\delta\\\\Gamma^{\\\\mu}\\\\,_{\\\\nu \\\\rho}} = -\\\\Gamma^{\\\\mu}\\\\,_{\\\\sigma \\\\alpha} \\\\delta\\\\Gamma^{\\\\alpha}\\\\,_{\\\\nu \\\\rho}+\\\\Gamma^{\\\\alpha}\\\\,_{\\\\sigma \\\\nu} \\\\delta\\\\Gamma^{\\\\mu}\\\\,_{\\\\alpha \\\\rho}+\\\\Gamma^{\\\\alpha}\\\\,_{\\\\sigma \\\\rho} \\\\delta\\\\Gamma^{\\\\mu}\\\\,_{\\\\nu \\\\alpha}+\\\\nabla_{\\\\sigma}{\\\\delta\\\\Gamma^{\\\\mu}\\\\,_{\\\\nu \\\\rho}}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"covariantDerivativeCn := \\\\nabla_{\\\\sigma}(\\\\dCn^{\\\\mu}_{\\\\nu\\\\rho}) = \\\\partial_{\\\\sigma}(\\\\dCn^{\\\\mu}_{\\\\nu\\\\rho})\\n                        +\\\\Gamma^{\\\\mu}_{\\\\sigma\\\\alpha}\\\\dCn^{\\\\alpha}_{\\\\nu\\\\rho}-\\\\Gamma^{\\\\alpha}_{\\\\sigma\\\\nu}\\\\dCn^{\\\\mu}_{\\\\alpha\\\\rho}\\n                        -\\\\Gamma^{\\\\alpha}_{\\\\sigma\\\\rho}\\\\dCn^{\\\\mu}_{\\\\nu\\\\alpha}; \\ncovariantDerivativeCn1 = manip.to_rhs(_, $\\\\nabla_{\\\\sigma}{A??}$);\\ncovariantDerivativeCn2 = manip.to_lhs(_, $\\\\partial_{\\\\sigma}{A??}$);\\npartialDerivativeCn = manip.multiply_through(covariantDerivativeCn2, $-1$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"The variation of the Riemann tensor comes next. With a few steps this is rewritten to a form which only \\ninvolves covariant derivatives of the variation of the Christoffel connection.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"The variation of the Riemann tensor comes next. With a few steps this is rewritten to a form which only \\ninvolves covariant derivatives of the variation of the Christoffel connection.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"\\\\dR^{\\\\rho}_{\\\\sigma \\\\mu \\\\nu} = \\\\partial_{\\\\mu}(\\\\dCn^{\\\\rho}_{\\\\nu \\\\sigma})-\\\\partial_{\\\\nu}(\\\\dCn^{\\\\rho}_{\\\\mu \\\\sigma}) + \\\\dCn^{\\\\rho}_{\\\\mu \\\\lambda} \\\\Gamma^{\\\\lambda}_{\\\\nu \\\\sigma} + \\\\Gamma^{\\\\rho}_{\\\\mu \\\\lambda} \\\\dCn^{\\\\lambda}_{\\\\nu \\\\sigma}-\\\\dCn^{\\\\rho}_{\\\\nu \\\\lambda} \\\\Gamma^{\\\\lambda}_{\\\\mu \\\\sigma}-\\\\Gamma^{\\\\rho}_{\\\\nu \\\\lambda} \\\\dCn^{\\\\lambda}_{\\\\mu \\\\sigma}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\delta R^{\\\\rho}\\\\,_{\\\\sigma \\\\mu \\\\nu} = \\\\partial_{\\\\mu}{\\\\delta\\\\Gamma^{\\\\rho}\\\\,_{\\\\nu \\\\sigma}}-\\\\partial_{\\\\nu}{\\\\delta\\\\Gamma^{\\\\rho}\\\\,_{\\\\mu \\\\sigma}}+\\\\delta\\\\Gamma^{\\\\rho}\\\\,_{\\\\mu \\\\lambda} \\\\Gamma^{\\\\lambda}\\\\,_{\\\\nu \\\\sigma}+\\\\Gamma^{\\\\rho}\\\\,_{\\\\mu \\\\lambda} \\\\delta\\\\Gamma^{\\\\lambda}\\\\,_{\\\\nu \\\\sigma}-\\\\delta\\\\Gamma^{\\\\rho}\\\\,_{\\\\nu \\\\lambda} \\\\Gamma^{\\\\lambda}\\\\,_{\\\\mu \\\\sigma}-\\\\Gamma^{\\\\rho}\\\\,_{\\\\nu \\\\lambda} \\\\delta\\\\Gamma^{\\\\lambda}\\\\,_{\\\\mu \\\\sigma}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"\\\\dR^{\\\\rho}_{\\\\sigma \\\\mu \\\\nu} = \\\\partial_{\\\\mu}(\\\\dCn^{\\\\rho}_{\\\\nu \\\\sigma})-\\\\partial_{\\\\nu}(\\\\dCn^{\\\\rho}_{\\\\mu \\\\sigma}) + \\\\Gamma^{\\\\lambda}_{\\\\nu \\\\sigma} \\\\dCn^{\\\\rho}_{\\\\mu \\\\lambda} + \\\\Gamma^{\\\\rho}_{\\\\mu \\\\lambda} \\\\dCn^{\\\\lambda}_{\\\\nu \\\\sigma}-\\\\Gamma^{\\\\lambda}_{\\\\mu \\\\sigma} \\\\dCn^{\\\\rho}_{\\\\nu \\\\lambda}-\\\\Gamma^{\\\\rho}_{\\\\nu \\\\lambda} \\\\dCn^{\\\\lambda}_{\\\\mu \\\\sigma}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\delta R^{\\\\rho}\\\\,_{\\\\sigma \\\\mu \\\\nu} = \\\\partial_{\\\\mu}{\\\\delta\\\\Gamma^{\\\\rho}\\\\,_{\\\\nu \\\\sigma}}-\\\\partial_{\\\\nu}{\\\\delta\\\\Gamma^{\\\\rho}\\\\,_{\\\\mu \\\\sigma}}+\\\\Gamma^{\\\\lambda}\\\\,_{\\\\nu \\\\sigma} \\\\delta\\\\Gamma^{\\\\rho}\\\\,_{\\\\mu \\\\lambda}+\\\\Gamma^{\\\\rho}\\\\,_{\\\\mu \\\\lambda} \\\\delta\\\\Gamma^{\\\\lambda}\\\\,_{\\\\nu \\\\sigma}-\\\\Gamma^{\\\\lambda}\\\\,_{\\\\mu \\\\sigma} \\\\delta\\\\Gamma^{\\\\rho}\\\\,_{\\\\nu \\\\lambda}-\\\\Gamma^{\\\\rho}\\\\,_{\\\\nu \\\\lambda} \\\\delta\\\\Gamma^{\\\\lambda}\\\\,_{\\\\mu \\\\sigma}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"\\\\dR^{\\\\rho}_{\\\\sigma \\\\mu \\\\nu} = -\\\\Gamma^{\\\\rho}_{\\\\mu \\\\alpha} \\\\dCn^{\\\\alpha}_{\\\\nu \\\\sigma} + \\\\Gamma^{\\\\alpha}_{\\\\mu \\\\nu} \\\\dCn^{\\\\rho}_{\\\\alpha \\\\sigma} + \\\\Gamma^{\\\\alpha}_{\\\\mu \\\\sigma} \\\\dCn^{\\\\rho}_{\\\\nu \\\\alpha} + \\\\nabla_{\\\\mu}(\\\\dCn^{\\\\rho}_{\\\\nu \\\\sigma}) + \\\\Gamma^{\\\\rho}_{\\\\nu \\\\alpha} \\\\dCn^{\\\\alpha}_{\\\\mu \\\\sigma}-\\\\Gamma^{\\\\alpha}_{\\\\nu \\\\mu} \\\\dCn^{\\\\rho}_{\\\\alpha \\\\sigma}-\\\\Gamma^{\\\\alpha}_{\\\\nu \\\\sigma} \\\\dCn^{\\\\rho}_{\\\\mu \\\\alpha}-\\\\nabla_{\\\\nu}(\\\\dCn^{\\\\rho}_{\\\\mu \\\\sigma}) + \\\\Gamma^{\\\\lambda}_{\\\\nu \\\\sigma} \\\\dCn^{\\\\rho}_{\\\\mu \\\\lambda} + \\\\Gamma^{\\\\rho}_{\\\\mu \\\\lambda} \\\\dCn^{\\\\lambda}_{\\\\nu \\\\sigma}-\\\\Gamma^{\\\\lambda}_{\\\\mu \\\\sigma} \\\\dCn^{\\\\rho}_{\\\\nu \\\\lambda}-\\\\Gamma^{\\\\rho}_{\\\\nu \\\\lambda} \\\\dCn^{\\\\lambda}_{\\\\mu \\\\sigma}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\delta R^{\\\\rho}\\\\,_{\\\\sigma \\\\mu \\\\nu} = -\\\\Gamma^{\\\\rho}\\\\,_{\\\\mu \\\\alpha} \\\\delta\\\\Gamma^{\\\\alpha}\\\\,_{\\\\nu \\\\sigma}+\\\\Gamma^{\\\\alpha}\\\\,_{\\\\mu \\\\nu} \\\\delta\\\\Gamma^{\\\\rho}\\\\,_{\\\\alpha \\\\sigma}+\\\\Gamma^{\\\\alpha}\\\\,_{\\\\mu \\\\sigma} \\\\delta\\\\Gamma^{\\\\rho}\\\\,_{\\\\nu \\\\alpha}+\\\\nabla_{\\\\mu}{\\\\delta\\\\Gamma^{\\\\rho}\\\\,_{\\\\nu \\\\sigma}}+\\\\Gamma^{\\\\rho}\\\\,_{\\\\nu \\\\alpha} \\\\delta\\\\Gamma^{\\\\alpha}\\\\,_{\\\\mu \\\\sigma}-\\\\Gamma^{\\\\alpha}\\\\,_{\\\\nu \\\\mu} \\\\delta\\\\Gamma^{\\\\rho}\\\\,_{\\\\alpha \\\\sigma}-\\\\Gamma^{\\\\alpha}\\\\,_{\\\\nu \\\\sigma} \\\\delta\\\\Gamma^{\\\\rho}\\\\,_{\\\\mu \\\\alpha}-\\\\nabla_{\\\\nu}{\\\\delta\\\\Gamma^{\\\\rho}\\\\,_{\\\\mu \\\\sigma}}+\\\\Gamma^{\\\\lambda}\\\\,_{\\\\nu \\\\sigma} \\\\delta\\\\Gamma^{\\\\rho}\\\\,_{\\\\mu \\\\lambda}+\\\\Gamma^{\\\\rho}\\\\,_{\\\\mu \\\\lambda} \\\\delta\\\\Gamma^{\\\\lambda}\\\\,_{\\\\nu \\\\sigma}-\\\\Gamma^{\\\\lambda}\\\\,_{\\\\mu \\\\sigma} \\\\delta\\\\Gamma^{\\\\rho}\\\\,_{\\\\nu \\\\lambda}-\\\\Gamma^{\\\\rho}\\\\,_{\\\\nu \\\\lambda} \\\\delta\\\\Gamma^{\\\\lambda}\\\\,_{\\\\mu \\\\sigma}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"\\\\dR^{\\\\rho}_{\\\\sigma \\\\mu \\\\nu} = \\\\Gamma^{\\\\alpha}_{\\\\mu \\\\nu} \\\\dCn^{\\\\rho}_{\\\\alpha \\\\sigma} + \\\\nabla_{\\\\mu}(\\\\dCn^{\\\\rho}_{\\\\nu \\\\sigma})-\\\\Gamma^{\\\\alpha}_{\\\\nu \\\\mu} \\\\dCn^{\\\\rho}_{\\\\alpha \\\\sigma}-\\\\nabla_{\\\\nu}(\\\\dCn^{\\\\rho}_{\\\\mu \\\\sigma})\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\delta R^{\\\\rho}\\\\,_{\\\\sigma \\\\mu \\\\nu} = \\\\Gamma^{\\\\alpha}\\\\,_{\\\\mu \\\\nu} \\\\delta\\\\Gamma^{\\\\rho}\\\\,_{\\\\alpha \\\\sigma}+\\\\nabla_{\\\\mu}{\\\\delta\\\\Gamma^{\\\\rho}\\\\,_{\\\\nu \\\\sigma}}-\\\\Gamma^{\\\\alpha}\\\\,_{\\\\nu \\\\mu} \\\\delta\\\\Gamma^{\\\\rho}\\\\,_{\\\\alpha \\\\sigma}-\\\\nabla_{\\\\nu}{\\\\delta\\\\Gamma^{\\\\rho}\\\\,_{\\\\mu \\\\sigma}}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"\\\\dR^{\\\\rho}_{\\\\sigma \\\\mu \\\\nu} = \\\\nabla_{\\\\mu}(\\\\dCn^{\\\\rho}_{\\\\nu \\\\sigma})-\\\\nabla_{\\\\nu}(\\\\dCn^{\\\\rho}_{\\\\mu \\\\sigma})\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\delta R^{\\\\rho}\\\\,_{\\\\sigma \\\\mu \\\\nu} = \\\\nabla_{\\\\mu}{\\\\delta\\\\Gamma^{\\\\rho}\\\\,_{\\\\nu \\\\sigma}}-\\\\nabla_{\\\\nu}{\\\\delta\\\\Gamma^{\\\\rho}\\\\,_{\\\\mu \\\\sigma}}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"deltaRiemannTensor = vary(riemannTensor, $\\\\Gamma^{\\\\mu}_{\\\\nu\\\\rho}->\\\\dCn^{\\\\mu}_{\\\\nu\\\\rho}, R^{\\\\rho}_{\\\\sigma\\\\mu\\\\nu} -> \\\\dR^{\\\\rho}_{\\\\sigma\\\\mu\\\\nu}$);\\nsort_product(_);\\nsubstitute(_,partialDerivativeCn);\\nrename_dummies(_);\\ncanonicalise(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"The variation of the Ricci tensor leads to the so-called Palatini identity:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"The variation of the Ricci tensor leads to the so-called Palatini identity:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"\\\\dR_{\\\\sigma \\\\nu} = \\\\dR^{\\\\rho}_{\\\\sigma \\\\rho \\\\nu}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\delta R_{\\\\sigma \\\\nu} = \\\\delta R^{\\\\rho}\\\\,_{\\\\sigma \\\\rho \\\\nu}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"\\\\dR_{\\\\sigma \\\\nu} = \\\\nabla_{\\\\rho}(\\\\dCn^{\\\\rho}_{\\\\nu \\\\sigma})-\\\\nabla_{\\\\nu}(\\\\dCn^{\\\\rho}_{\\\\rho \\\\sigma})\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\delta R_{\\\\sigma \\\\nu} = \\\\nabla_{\\\\rho}{\\\\delta\\\\Gamma^{\\\\rho}\\\\,_{\\\\nu \\\\sigma}}-\\\\nabla_{\\\\nu}{\\\\delta\\\\Gamma^{\\\\rho}\\\\,_{\\\\rho \\\\sigma}}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"deltaRicciTensor = vary(ricciTensor, $R^{\\\\rho}_{\\\\sigma\\\\rho\\\\nu}->\\\\dR^{\\\\rho}_{\\\\sigma\\\\rho\\\\nu}, R_{\\\\sigma\\\\nu} -> \\\\dR_{\\\\sigma\\\\nu}$);\\nsubstitute(_,deltaRiemannTensor);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"We can now vary the scalar curvature.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"We can now vary the scalar curvature.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"\\\\dR = \\\\dR_{\\\\sigma \\\\nu} g^{\\\\sigma \\\\nu} + R_{\\\\sigma \\\\nu} \\\\dg^{\\\\sigma \\\\nu}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\delta R = \\\\delta R_{\\\\sigma \\\\nu} g^{\\\\sigma \\\\nu}+R_{\\\\sigma \\\\nu} \\\\delta g^{\\\\sigma \\\\nu}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"\\\\dR = (\\\\nabla_{\\\\rho}(\\\\dCn^{\\\\rho}_{\\\\nu \\\\sigma})-\\\\nabla_{\\\\nu}(\\\\dCn^{\\\\rho}_{\\\\rho \\\\sigma})) g^{\\\\sigma \\\\nu} + R_{\\\\sigma \\\\nu} \\\\dg^{\\\\sigma \\\\nu}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\delta R = \\\\left(\\\\nabla_{\\\\rho}{\\\\delta\\\\Gamma^{\\\\rho}\\\\,_{\\\\nu \\\\sigma}}-\\\\nabla_{\\\\nu}{\\\\delta\\\\Gamma^{\\\\rho}\\\\,_{\\\\rho \\\\sigma}}\\\\right) g^{\\\\sigma \\\\nu}+R_{\\\\sigma \\\\nu} \\\\delta g^{\\\\sigma \\\\nu}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"\\\\dR = \\\\nabla_{\\\\rho}(\\\\dCn^{\\\\rho}_{\\\\nu \\\\sigma}) g^{\\\\sigma \\\\nu}-\\\\nabla_{\\\\nu}(\\\\dCn^{\\\\rho}_{\\\\rho \\\\sigma}) g^{\\\\sigma \\\\nu} + R_{\\\\sigma \\\\nu} \\\\dg^{\\\\sigma \\\\nu}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\delta R = \\\\nabla_{\\\\rho}{\\\\delta\\\\Gamma^{\\\\rho}\\\\,_{\\\\nu \\\\sigma}} g^{\\\\sigma \\\\nu}-\\\\nabla_{\\\\nu}{\\\\delta\\\\Gamma^{\\\\rho}\\\\,_{\\\\rho \\\\sigma}} g^{\\\\sigma \\\\nu}+R_{\\\\sigma \\\\nu} \\\\delta g^{\\\\sigma \\\\nu}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"\\\\dR = \\\\nabla_{\\\\rho}(\\\\dCn^{\\\\rho}_{\\\\nu \\\\sigma} g^{\\\\sigma \\\\nu})-\\\\nabla_{\\\\nu}(\\\\dCn^{\\\\rho}_{\\\\rho \\\\sigma} g^{\\\\sigma \\\\nu}) + R_{\\\\sigma \\\\nu} \\\\dg^{\\\\sigma \\\\nu}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\delta R = \\\\nabla_{\\\\rho}\\\\left(\\\\delta\\\\Gamma^{\\\\rho}\\\\,_{\\\\nu \\\\sigma} g^{\\\\sigma \\\\nu}\\\\right)-\\\\nabla_{\\\\nu}\\\\left(\\\\delta\\\\Gamma^{\\\\rho}\\\\,_{\\\\rho \\\\sigma} g^{\\\\sigma \\\\nu}\\\\right)+R_{\\\\sigma \\\\nu} \\\\delta g^{\\\\sigma \\\\nu}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"\\\\dR = \\\\nabla_{\\\\nu}(\\\\dCn^{\\\\nu}_{\\\\rho \\\\sigma} g^{\\\\rho \\\\sigma})-\\\\nabla_{\\\\nu}(\\\\dCn^{\\\\rho}_{\\\\rho \\\\sigma} g^{\\\\nu \\\\sigma}) + R_{\\\\nu \\\\sigma} \\\\dg^{\\\\nu \\\\sigma}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\delta R = \\\\nabla_{\\\\nu}\\\\left(\\\\delta\\\\Gamma^{\\\\nu}\\\\,_{\\\\rho \\\\sigma} g^{\\\\rho \\\\sigma}\\\\right)-\\\\nabla_{\\\\nu}\\\\left(\\\\delta\\\\Gamma^{\\\\rho}\\\\,_{\\\\rho \\\\sigma} g^{\\\\nu \\\\sigma}\\\\right)+R_{\\\\nu \\\\sigma} \\\\delta g^{\\\\nu \\\\sigma}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"deltaScalarCurvature = vary(scalarCurvature, $R-> \\\\dR, R_{\\\\sigma\\\\nu} -> \\\\dR_{\\\\sigma\\\\nu}, g^{\\\\mu\\\\nu}->\\\\dg^{\\\\mu\\\\nu}$);\\nsubstitute(_,deltaRicciTensor);\\ndistribute(_);\\nsubstitute(_,$\\\\nabla_{\\\\sigma}(\\\\dCn^{\\\\mu}_{\\\\nu\\\\rho})g^{\\\\alpha\\\\beta}->\\\\nabla_{\\\\sigma}(\\\\dCn^{\\\\mu}_{\\\\nu\\\\rho}g^{\\\\alpha\\\\beta})$);\\ncanonicalise(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"With these ingredients we can now vary the action: simply vary all ingredients and then substitute what we have found\\nabove for the variations of the metric, connection and curvature tensors.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"With these ingredients we can now vary the action: simply vary all ingredients and then substitute what we have found\\nabove for the variations of the metric, connection and curvature tensors.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"\\\\delta(S) = \\\\int{ 1/2 \\\\delta(\\\\Dg) (\\\\kappa)**(-1) R +  1/2 \\\\Dg (\\\\kappa)**(-1) \\\\dR-\\\\delta(\\\\Dg) (\\\\kappa)**(-1) \\\\Lambda + \\\\delta(\\\\Dg) \\\\Lm + \\\\Dg \\\\delta(\\\\Lm)}{x}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\delta{S} = \\\\int \\\\left(\\\\frac{1}{2}\\\\delta{\\\\sqrt{-g}} {\\\\kappa}^{-1} R+\\\\frac{1}{2}\\\\sqrt{-g} {\\\\kappa}^{-1} \\\\delta R-\\\\delta{\\\\sqrt{-g}} {\\\\kappa}^{-1} \\\\Lambda+\\\\delta{\\\\sqrt{-g}} \\\\mathcal{L}_{\\\\text{mat}}+\\\\sqrt{-g} \\\\delta{\\\\mathcal{L}_{\\\\text{mat}}}\\\\right)\\\\,\\\\,{\\\\rm d}x\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"\\\\delta(S) = \\\\int{ -  1/4 \\\\Dg g_{\\\\mu \\\\nu} \\\\dg^{\\\\mu \\\\nu} (\\\\kappa)**(-1) R +  1/2 \\\\Dg (\\\\kappa)**(-1) \\\\dR +  1/2 \\\\Dg g_{\\\\mu \\\\nu} \\\\dg^{\\\\mu \\\\nu} (\\\\kappa)**(-1) \\\\Lambda -  1/2 \\\\Dg g_{\\\\mu \\\\nu} \\\\dg^{\\\\mu \\\\nu} \\\\Lm + \\\\Dg \\\\delta(\\\\Lm)}{x}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\delta{S} = \\\\int \\\\left( - \\\\frac{1}{4}\\\\sqrt{-g} g_{\\\\mu \\\\nu} \\\\delta g^{\\\\mu \\\\nu} {\\\\kappa}^{-1} R+\\\\frac{1}{2}\\\\sqrt{-g} {\\\\kappa}^{-1} \\\\delta R+\\\\frac{1}{2}\\\\sqrt{-g} g_{\\\\mu \\\\nu} \\\\delta g^{\\\\mu \\\\nu} {\\\\kappa}^{-1} \\\\Lambda - \\\\frac{1}{2}\\\\sqrt{-g} g_{\\\\mu \\\\nu} \\\\delta g^{\\\\mu \\\\nu} \\\\mathcal{L}_{\\\\text{mat}}+\\\\sqrt{-g} \\\\delta{\\\\mathcal{L}_{\\\\text{mat}}}\\\\right)\\\\,\\\\,{\\\\rm d}x\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"\\\\delta(S) = \\\\int{ -  1/4 \\\\Dg g_{\\\\mu \\\\nu} \\\\dg^{\\\\mu \\\\nu} (\\\\kappa)**(-1) R +  1/2 \\\\Dg (\\\\kappa)**(-1) \\\\dR +  1/2 \\\\Dg g_{\\\\mu \\\\nu} \\\\dg^{\\\\mu \\\\nu} (\\\\kappa)**(-1) \\\\Lambda -  1/2 \\\\Dg T_{\\\\mu \\\\nu} \\\\dg^{\\\\mu \\\\nu}}{x}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\delta{S} = \\\\int \\\\left( - \\\\frac{1}{4}\\\\sqrt{-g} g_{\\\\mu \\\\nu} \\\\delta g^{\\\\mu \\\\nu} {\\\\kappa}^{-1} R+\\\\frac{1}{2}\\\\sqrt{-g} {\\\\kappa}^{-1} \\\\delta R+\\\\frac{1}{2}\\\\sqrt{-g} g_{\\\\mu \\\\nu} \\\\delta g^{\\\\mu \\\\nu} {\\\\kappa}^{-1} \\\\Lambda - \\\\frac{1}{2}\\\\sqrt{-g} T_{\\\\mu \\\\nu} \\\\delta g^{\\\\mu \\\\nu}\\\\right)\\\\,\\\\,{\\\\rm d}x\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"\\\\delta(S) = \\\\int{ -  1/4 \\\\Dg g_{\\\\mu \\\\nu} \\\\dg^{\\\\mu \\\\nu} (\\\\kappa)**(-1) R +  1/2 \\\\Dg (\\\\kappa)**(-1) (\\\\nabla_{\\\\nu}(\\\\dCn^{\\\\nu}_{\\\\rho \\\\sigma} g^{\\\\rho \\\\sigma})-\\\\nabla_{\\\\nu}(\\\\dCn^{\\\\rho}_{\\\\rho \\\\sigma} g^{\\\\nu \\\\sigma}) + R_{\\\\nu \\\\sigma} \\\\dg^{\\\\nu \\\\sigma}) +  1/2 \\\\Dg g_{\\\\mu \\\\nu} \\\\dg^{\\\\mu \\\\nu} (\\\\kappa)**(-1) \\\\Lambda -  1/2 \\\\Dg T_{\\\\mu \\\\nu} \\\\dg^{\\\\mu \\\\nu}}{x}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\delta{S} = \\\\int \\\\left( - \\\\frac{1}{4}\\\\sqrt{-g} g_{\\\\mu \\\\nu} \\\\delta g^{\\\\mu \\\\nu} {\\\\kappa}^{-1} R+\\\\frac{1}{2}\\\\sqrt{-g} {\\\\kappa}^{-1} \\\\left(\\\\nabla_{\\\\nu}\\\\left(\\\\delta\\\\Gamma^{\\\\nu}\\\\,_{\\\\rho \\\\sigma} g^{\\\\rho \\\\sigma}\\\\right)-\\\\nabla_{\\\\nu}\\\\left(\\\\delta\\\\Gamma^{\\\\rho}\\\\,_{\\\\rho \\\\sigma} g^{\\\\nu \\\\sigma}\\\\right)+R_{\\\\nu \\\\sigma} \\\\delta g^{\\\\nu \\\\sigma}\\\\right)+\\\\frac{1}{2}\\\\sqrt{-g} g_{\\\\mu \\\\nu} \\\\delta g^{\\\\mu \\\\nu} {\\\\kappa}^{-1} \\\\Lambda - \\\\frac{1}{2}\\\\sqrt{-g} T_{\\\\mu \\\\nu} \\\\delta g^{\\\\mu \\\\nu}\\\\right)\\\\,\\\\,{\\\\rm d}x\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"\\\\delta(S) = \\\\int{ -  1/4 \\\\Dg g_{\\\\mu \\\\nu} \\\\dg^{\\\\mu \\\\nu} (\\\\kappa)**(-1) R +  1/2 \\\\Dg (\\\\kappa)**(-1) \\\\nabla_{\\\\nu}(\\\\dCn^{\\\\nu}_{\\\\rho \\\\sigma} g^{\\\\rho \\\\sigma}) -  1/2 \\\\Dg (\\\\kappa)**(-1) \\\\nabla_{\\\\nu}(\\\\dCn^{\\\\rho}_{\\\\rho \\\\sigma} g^{\\\\nu \\\\sigma}) +  1/2 \\\\Dg (\\\\kappa)**(-1) R_{\\\\nu \\\\sigma} \\\\dg^{\\\\nu \\\\sigma} +  1/2 \\\\Dg g_{\\\\mu \\\\nu} \\\\dg^{\\\\mu \\\\nu} (\\\\kappa)**(-1) \\\\Lambda -  1/2 \\\\Dg T_{\\\\mu \\\\nu} \\\\dg^{\\\\mu \\\\nu}}{x}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\delta{S} = \\\\int \\\\left( - \\\\frac{1}{4}\\\\sqrt{-g} g_{\\\\mu \\\\nu} \\\\delta g^{\\\\mu \\\\nu} {\\\\kappa}^{-1} R+\\\\frac{1}{2}\\\\sqrt{-g} {\\\\kappa}^{-1} \\\\nabla_{\\\\nu}\\\\left(\\\\delta\\\\Gamma^{\\\\nu}\\\\,_{\\\\rho \\\\sigma} g^{\\\\rho \\\\sigma}\\\\right) - \\\\frac{1}{2}\\\\sqrt{-g} {\\\\kappa}^{-1} \\\\nabla_{\\\\nu}\\\\left(\\\\delta\\\\Gamma^{\\\\rho}\\\\,_{\\\\rho \\\\sigma} g^{\\\\nu \\\\sigma}\\\\right)+\\\\frac{1}{2}\\\\sqrt{-g} {\\\\kappa}^{-1} R_{\\\\nu \\\\sigma} \\\\delta g^{\\\\nu \\\\sigma}+\\\\frac{1}{2}\\\\sqrt{-g} g_{\\\\mu \\\\nu} \\\\delta g^{\\\\mu \\\\nu} {\\\\kappa}^{-1} \\\\Lambda - \\\\frac{1}{2}\\\\sqrt{-g} T_{\\\\mu \\\\nu} \\\\delta g^{\\\\mu \\\\nu}\\\\right)\\\\,\\\\,{\\\\rm d}x\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"\\\\delta(S) = \\\\int{ -  1/4 \\\\Dg g_{\\\\mu \\\\nu} \\\\dg^{\\\\mu \\\\nu} (\\\\kappa)**(-1) R +  1/2 \\\\Dg (\\\\kappa)**(-1) \\\\nabla_{\\\\mu}(\\\\dCn^{\\\\mu}_{\\\\nu \\\\rho} g^{\\\\nu \\\\rho}) -  1/2 \\\\Dg (\\\\kappa)**(-1) \\\\nabla_{\\\\rho}(\\\\dCn^{\\\\mu}_{\\\\mu \\\\nu} g^{\\\\rho \\\\nu}) +  1/2 \\\\Dg (\\\\kappa)**(-1) R_{\\\\mu \\\\nu} \\\\dg^{\\\\mu \\\\nu} +  1/2 \\\\Dg g_{\\\\mu \\\\nu} \\\\dg^{\\\\mu \\\\nu} (\\\\kappa)**(-1) \\\\Lambda -  1/2 \\\\Dg T_{\\\\mu \\\\nu} \\\\dg^{\\\\mu \\\\nu}}{x}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\delta{S} = \\\\int \\\\left( - \\\\frac{1}{4}\\\\sqrt{-g} g_{\\\\mu \\\\nu} \\\\delta g^{\\\\mu \\\\nu} {\\\\kappa}^{-1} R+\\\\frac{1}{2}\\\\sqrt{-g} {\\\\kappa}^{-1} \\\\nabla_{\\\\mu}\\\\left(\\\\delta\\\\Gamma^{\\\\mu}\\\\,_{\\\\nu \\\\rho} g^{\\\\nu \\\\rho}\\\\right) - \\\\frac{1}{2}\\\\sqrt{-g} {\\\\kappa}^{-1} \\\\nabla_{\\\\rho}\\\\left(\\\\delta\\\\Gamma^{\\\\mu}\\\\,_{\\\\mu \\\\nu} g^{\\\\rho \\\\nu}\\\\right)+\\\\frac{1}{2}\\\\sqrt{-g} {\\\\kappa}^{-1} R_{\\\\mu \\\\nu} \\\\delta g^{\\\\mu \\\\nu}+\\\\frac{1}{2}\\\\sqrt{-g} g_{\\\\mu \\\\nu} \\\\delta g^{\\\\mu \\\\nu} {\\\\kappa}^{-1} \\\\Lambda - \\\\frac{1}{2}\\\\sqrt{-g} T_{\\\\mu \\\\nu} \\\\delta g^{\\\\mu \\\\nu}\\\\right)\\\\,\\\\,{\\\\rm d}x\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"\\\\delta(S) = \\\\int{\\\\Dg \\\\dg^{\\\\mu \\\\nu} ( -  1/4 g_{\\\\mu \\\\nu} (\\\\kappa)**(-1) R +  1/2 (\\\\kappa)**(-1) R_{\\\\mu \\\\nu} +  1/2 g_{\\\\mu \\\\nu} (\\\\kappa)**(-1) \\\\Lambda -  1/2 T_{\\\\mu \\\\nu}) + \\\\Dg ( 1/2 (\\\\kappa)**(-1) \\\\nabla_{\\\\mu}(\\\\dCn^{\\\\mu}_{\\\\nu \\\\rho} g^{\\\\nu \\\\rho}) -  1/2 (\\\\kappa)**(-1) \\\\nabla_{\\\\rho}(\\\\dCn^{\\\\mu}_{\\\\mu \\\\nu} g^{\\\\rho \\\\nu}))}{x}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\delta{S} = \\\\int \\\\left(\\\\sqrt{-g} \\\\delta g^{\\\\mu \\\\nu} \\\\left( - \\\\frac{1}{4}g_{\\\\mu \\\\nu} {\\\\kappa}^{-1} R+\\\\frac{1}{2}{\\\\kappa}^{-1} R_{\\\\mu \\\\nu}+\\\\frac{1}{2}g_{\\\\mu \\\\nu} {\\\\kappa}^{-1} \\\\Lambda - \\\\frac{1}{2}T_{\\\\mu \\\\nu}\\\\right)+\\\\sqrt{-g} \\\\left(\\\\frac{1}{2}{\\\\kappa}^{-1} \\\\nabla_{\\\\mu}\\\\left(\\\\delta\\\\Gamma^{\\\\mu}\\\\,_{\\\\nu \\\\rho} g^{\\\\nu \\\\rho}\\\\right) - \\\\frac{1}{2}{\\\\kappa}^{-1} \\\\nabla_{\\\\rho}\\\\left(\\\\delta\\\\Gamma^{\\\\mu}\\\\,_{\\\\mu \\\\nu} g^{\\\\rho \\\\nu}\\\\right)\\\\right)\\\\right)\\\\,\\\\,{\\\\rm d}x\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"vary(action, $\\\\Dg->\\\\delta(\\\\Dg), R -> \\\\dR, \\\\Lm->\\\\delta(\\\\Lm), S->\\\\delta(S)$);\\nsubstitute(action, deltaMetricDeterminant);\\nsubstitute(action, matterLagrangianVariation);\\nsubstitute(action, deltaScalarCurvature);\\ndistribute(action);\\nrename_dummies(action);\\nfactor_out(action, $\\\\dg^{\\\\mu\\\\nu}, \\\\Dg$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"The terms proportional to $\\\\delta g^{\\\\mu\\\\nu}$ are the Einstein equations, the rest is a total derivative.\\nWe can rewrite this a bit further to get the familiar form:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"The terms proportional to $\\\\delta g^{\\\\mu\\\\nu}$ are the Einstein equations, the rest is a total derivative.\\nWe can rewrite this a bit further to get the familiar form:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"2\\\\kappa ( -  1/4 g_{\\\\mu \\\\nu} (\\\\kappa)**(-1) R +  1/2 (\\\\kappa)**(-1) R_{\\\\mu \\\\nu} +  1/2 g_{\\\\mu \\\\nu} (\\\\kappa)**(-1) \\\\Lambda -  1/2 T_{\\\\mu \\\\nu}) = 0\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}2\\\\kappa \\\\left( - \\\\frac{1}{4}g_{\\\\mu \\\\nu} {\\\\kappa}^{-1} R+\\\\frac{1}{2}{\\\\kappa}^{-1} R_{\\\\mu \\\\nu}+\\\\frac{1}{2}g_{\\\\mu \\\\nu} {\\\\kappa}^{-1} \\\\Lambda - \\\\frac{1}{2}T_{\\\\mu \\\\nu}\\\\right) = 0\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \" -  1/2 g_{\\\\mu \\\\nu} R + R_{\\\\mu \\\\nu} + g_{\\\\mu \\\\nu} \\\\Lambda = \\\\kappa T_{\\\\mu \\\\nu}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{} - \\\\frac{1}{2}g_{\\\\mu \\\\nu} R+R_{\\\\mu \\\\nu}+g_{\\\\mu \\\\nu} \\\\Lambda = \\\\kappa T_{\\\\mu \\\\nu}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"G_{\\\\mu \\\\nu} + g_{\\\\mu \\\\nu} \\\\Lambda = \\\\kappa T_{\\\\mu \\\\nu}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}G_{\\\\mu \\\\nu}+g_{\\\\mu \\\\nu} \\\\Lambda = \\\\kappa T_{\\\\mu \\\\nu}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"t1 = action[1][0][0][2]\\neom:= 2\\\\kappa @(t1) = 0;\\ndistribute(_)\\ncollect_factors(_)\\nmanip.to_rhs(_, $- \\\\kappa T_{\\\\mu\\\\nu}$);\\nsubstitute(_, manip.swap_sides(einsteinTensor));\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1\n}\n"
  },
  {
    "path": "contrib/structure_equations_and_bianchi.cnb",
    "content": "{\n\t\"cell_id\" : 2082837756733559988,\n\t\"cells\" : \n\t[\n\t\t{\n\t\t\t\"cell_id\" : 1525272859004475730,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 6179245722104386386,\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\section*{Cartan structural equations and Bianchi identity}\\n\\n\\\\author{Oscar Castillo-Felisola}\\n\\n\\\\section*{Theoretical background}\\n\\nLet $M$ be a manifold, and $g$ a (semi)Riemannian metric defined on $M$. Then the line element for the metric $g$ is\\n\\\\begin{equation*}\\n  \\\\mathrm{d}{s}^2(g) = g_{\\\\mu\\\\nu} \\\\mathrm{d}{x}^\\\\mu \\\\otimes \\\\mathrm{d}{x}^\\\\nu.\\n\\\\end{equation*}\\nNonetheless, the information about the metric structure of the manifold can be translated to the language of frames,\\n\\\\begin{equation*}\\n  \\\\begin{split}\\n    \\\\mathrm{d}{s}^2(g)\\n    & = g_{\\\\mu\\\\nu} \\\\mathrm{d}{x}^\\\\mu \\\\otimes \\\\mathrm{d}{x}^\\\\nu \\\\\\\\\\n    & = \\\\eta_{ab} \\\\; e^{a}_{\\\\mu}(x) \\\\, e^{b}_{\\\\nu}(x) \\\\; \\\\mathrm{d}{x}^\\\\mu \\\\otimes \\\\mathrm{d}{x}^\\\\nu \\\\\\\\\\n    & = \\\\eta_{ab} \\\\; \\\\mathrm{e}^{a} \\\\otimes \\\\mathrm{e}^{b}.\\n  \\\\end{split}\\n\\\\end{equation*}\\nTherefore, the vielbein 1-form, $\\\\mathrm{e}^{a} \\\\equiv e^{a}_{\\\\mu}(x) \\\\mathrm{d}{x}^\\\\mu$, encodes the information of the metric tensor.\\nIn order to complete the structure, one needs information about the transport of geometrical objects lying on bundles\\nbased on $M$. That information is encoded on the spin connection 1-form, $\\\\omega^{a}{}_{b}$. Using these quantities one finds\\nthe generalisation of the structure equations of Cartan,\\n\\\\begin{align}\\n  \\\\mathrm{d}{\\\\mathrm{e}^{a}} + \\\\omega^{a}{}_{b} \\\\wedge \\\\mathrm{e}^{b} & = \\\\mathrm{T}^{a},\\n  \\\\label{firstSE}\\\\\\\\\\n  \\\\mathrm{d}{\\\\omega^{a}{}_{c}} + \\\\omega^{a}{}_{b} \\\\wedge \\\\omega^{b}{}_{c} & = \\\\mathrm{R}^{a}{}_{c}\\n  \\\\label{secondSE}.\\n\\\\end{align}\\nThe torsion 2-form, $\\\\mathrm{T}^{a}$, and the curvature 2-form, $\\\\mathrm{R}^{a}{}_{c}$, measure the impossibility of endowing $M$ with\\nan Euclidean structure.\\n\\n\\\\section*{Manipulation of the structural equations}\\n\\n\\\\subsection*{Definitions}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\section*{Cartan structural equations and Bianchi identity}\\n\\n\\\\author{Oscar Castillo-Felisola}\\n\\n\\\\section*{Theoretical background}\\n\\nLet $M$ be a manifold, and $g$ a (semi)Riemannian metric defined on $M$. Then the line element for the metric $g$ is\\n\\\\begin{equation*}\\n  \\\\mathrm{d}{s}^2(g) = g_{\\\\mu\\\\nu} \\\\mathrm{d}{x}^\\\\mu \\\\otimes \\\\mathrm{d}{x}^\\\\nu.\\n\\\\end{equation*}\\nNonetheless, the information about the metric structure of the manifold can be translated to the language of frames,\\n\\\\begin{equation*}\\n  \\\\begin{split}\\n    \\\\mathrm{d}{s}^2(g)\\n    & = g_{\\\\mu\\\\nu} \\\\mathrm{d}{x}^\\\\mu \\\\otimes \\\\mathrm{d}{x}^\\\\nu \\\\\\\\\\n    & = \\\\eta_{ab} \\\\; e^{a}_{\\\\mu}(x) \\\\, e^{b}_{\\\\nu}(x) \\\\; \\\\mathrm{d}{x}^\\\\mu \\\\otimes \\\\mathrm{d}{x}^\\\\nu \\\\\\\\\\n    & = \\\\eta_{ab} \\\\; \\\\mathrm{e}^{a} \\\\otimes \\\\mathrm{e}^{b}.\\n  \\\\end{split}\\n\\\\end{equation*}\\nTherefore, the vielbein 1-form, $\\\\mathrm{e}^{a} \\\\equiv e^{a}_{\\\\mu}(x) \\\\mathrm{d}{x}^\\\\mu$, encodes the information of the metric tensor.\\nIn order to complete the structure, one needs information about the transport of geometrical objects lying on bundles\\nbased on $M$. That information is encoded on the spin connection 1-form, $\\\\omega^{a}{}_{b}$. Using these quantities one finds\\nthe generalisation of the structure equations of Cartan,\\n\\\\begin{align}\\n  \\\\mathrm{d}{\\\\mathrm{e}^{a}} + \\\\omega^{a}{}_{b} \\\\wedge \\\\mathrm{e}^{b} & = \\\\mathrm{T}^{a},\\n  \\\\label{firstSE}\\\\\\\\\\n  \\\\mathrm{d}{\\\\omega^{a}{}_{c}} + \\\\omega^{a}{}_{b} \\\\wedge \\\\omega^{b}{}_{c} & = \\\\mathrm{R}^{a}{}_{c}\\n  \\\\label{secondSE}.\\n\\\\end{align}\\nThe torsion 2-form, $\\\\mathrm{T}^{a}$, and the curvature 2-form, $\\\\mathrm{R}^{a}{}_{c}$, measure the impossibility of endowing $M$ with\\nan Euclidean structure.\\n\\n\\\\section*{Manipulation of the structural equations}\\n\\n\\\\subsection*{Definitions}\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 13528271774984453456,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 9223372036854775809,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property DifferentialForm to~}\\\\left[e^{a},~\\\\discretionary{}{}{} \\\\omega^{a}\\\\,_{b}\\\\right].\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 9223372036854775810,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property DifferentialForm to~}\\\\left[\\\\mathrm{T}^{a},~\\\\discretionary{}{}{} \\\\mathrm{R}^{a}\\\\,_{b}\\\\right].\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"{a,b,c,l,m,n}::Indices.\\nd{#}::ExteriorDerivative;.\\nd{#}::LaTeXForm(\\\"\\\\mathrm{d}\\\").\\nT{#}::LaTeXForm(\\\"\\\\mathrm{T}\\\").\\nR{#}::LaTeXForm(\\\"\\\\mathrm{R}\\\").\\n{e^{a}, \\\\omega^{a}_{b}}::DifferentialForm(degree=1); \\n{T^{a}, R^{a}_{b}}::DifferentialForm(degree=2);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 12238953187398236596,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 3573955577442069632,\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\subsection*{Cartan structural equations}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\subsection*{Cartan structural equations}\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 17296288306406801707,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 9223372036854775812,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\" : 9223372036854775813,\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"d(e^{a}) + \\\\omega^{a}_{b} ^ e^{b}-T^{a} = 0\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\mathrm{d}{e^{a}}+\\\\omega^{a}\\\\,_{b}\\\\wedge e^{b}-\\\\mathrm{T}^{a} = 0\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"struc1 := d{e^{a}} + \\\\omega^{a}_{b} ^ e^{b} - T^{a} = 0;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 12676826774600030559,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 9223372036854775815,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\" : 9223372036854775816,\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"d(\\\\omega^{a}_{b}) + \\\\omega^{a}_{m} ^ \\\\omega^{m}_{b}-R^{a}_{b} = 0\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\mathrm{d}{\\\\omega^{a}\\\\,_{b}}+\\\\omega^{a}\\\\,_{m}\\\\wedge \\\\omega^{m}\\\\,_{b}-\\\\mathrm{R}^{a}\\\\,_{b} = 0\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"struc2 := d{\\\\omega^{a}_{b}} + \\\\omega^{a}_{m} ^ \\\\omega^{m}_{b} - R^{a}_{b} = 0;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 5906705874232891115,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 7464233204901409597,\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"In the following, we will also use the structural equations as definitions of the\\nexterior derivatives of the vielbein and spin connection 1-forms. Therefore, we shall\\nutilise the \\\\algo{isolate} algorithm---from the \\\\algo{cdb.core.manip} library---to \\ndefine substitution rules.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"In the following, we will also use the structural equations as definitions of the\\nexterior derivatives of the vielbein and spin connection 1-forms. Therefore, we shall\\nutilise the \\\\algo{isolate} algorithm---from the \\\\algo{cdb.core.manip} library---to \\ndefine substitution rules.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 14872820092824926673,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 9223372036854775818,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\" : 9223372036854775819,\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"d(e^{a}) = -\\\\omega^{a}_{b} ^ e^{b} + T^{a}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\mathrm{d}{e^{a}} = -\\\\omega^{a}\\\\,_{b}\\\\wedge e^{b}+\\\\mathrm{T}^{a}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"from cdb.core.manip import *\\nde:= @(struc1):\\nisolate(de, $d{e^{a}}$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 11514586735070898136,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 9223372036854775821,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\" : 9223372036854775822,\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"d(\\\\omega^{a}_{b}) = -\\\\omega^{a}_{m} ^ \\\\omega^{m}_{b} + R^{a}_{b}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\mathrm{d}{\\\\omega^{a}\\\\,_{b}} = -\\\\omega^{a}\\\\,_{m}\\\\wedge \\\\omega^{m}\\\\,_{b}+\\\\mathrm{R}^{a}\\\\,_{b}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"domega := @(struc2):\\nisolate(domega, $d{\\\\omega^{a}_{b}}$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 13650837369708637637,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 13513964711918699242,\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\section*{Bianchi identities}\\n\\nThe bianchi identities are obtained by applying the exterior derivative to the structural\\n equations.\\n\\n\\\\subsection*{First Bianchi identity}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\section*{Bianchi identities}\\n\\nThe bianchi identities are obtained by applying the exterior derivative to the structural\\n equations.\\n\\n\\\\subsection*{First Bianchi identity}\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 10781709412135246056,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 9223372036854775824,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\" : 9223372036854775825,\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"d(d(e^{a}) + \\\\omega^{a}_{b} ^ e^{b}-T^{a}) = 0\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\mathrm{d}\\\\left(\\\\mathrm{d}{e^{a}}+\\\\omega^{a}\\\\,_{b}\\\\wedge e^{b}-\\\\mathrm{T}^{a}\\\\right) = 0\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"Bianchi1 :=  d{ @(struc1) };\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 13200781608660800209,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 9223372036854775827,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\" : 9223372036854775828,\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"d(\\\\omega^{a}_{b}) ^ e^{b}-\\\\omega^{a}_{b} ^ d(e^{b})-d(T^{a}) = 0\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\mathrm{d}{\\\\omega^{a}\\\\,_{b}}\\\\wedge e^{b}-\\\\omega^{a}\\\\,_{b}\\\\wedge \\\\mathrm{d}{e^{b}}-\\\\mathrm{d}{\\\\mathrm{T}^{a}} = 0\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"distribute(Bianchi1)\\nproduct_rule(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 5318681466055967294,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 9223372036854775830,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\" : 9223372036854775831,\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"-\\\\omega^{a}_{m} ^ \\\\omega^{m}_{b} ^ e^{b} + R^{a}_{b} ^ e^{b} + \\\\omega^{a}_{b} ^ \\\\omega^{b}_{c} ^ e^{c}-\\\\omega^{a}_{b} ^ T^{b}-d(T^{a}) = 0\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}-\\\\omega^{a}\\\\,_{m}\\\\wedge \\\\omega^{m}\\\\,_{b}\\\\wedge e^{b}+\\\\mathrm{R}^{a}\\\\,_{b}\\\\wedge e^{b}+\\\\omega^{a}\\\\,_{b}\\\\wedge \\\\omega^{b}\\\\,_{c}\\\\wedge e^{c}-\\\\omega^{a}\\\\,_{b}\\\\wedge \\\\mathrm{T}^{b}-\\\\mathrm{d}{\\\\mathrm{T}^{a}} = 0\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"substitute(Bianchi1, de, repeat=True)\\nsubstitute(Bianchi1, domega, repeat=True)\\ndistribute(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 12361525078320634286,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 9223372036854775833,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\" : 9223372036854775834,\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"R^{a}_{b} ^ e^{b}-\\\\omega^{a}_{b} ^ T^{b}-d(T^{a}) = 0\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\mathrm{R}^{a}\\\\,_{b}\\\\wedge e^{b}-\\\\omega^{a}\\\\,_{b}\\\\wedge \\\\mathrm{T}^{b}-\\\\mathrm{d}{\\\\mathrm{T}^{a}} = 0\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"rename_dummies(Bianchi1);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 3384034677461271825,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 13291494998090488942,\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"In the absence of torsion, the above expression is the well-known \\\\emph{algebraic} Bianchi identity\\n\\\\begin{equation*}\\nR^\\\\mu{}_{\\\\nu\\\\lambda\\\\rho} + R^\\\\mu{}_{\\\\lambda\\\\rho\\\\nu} + R^\\\\mu{}_{\\\\rho\\\\nu\\\\lambda} = 0.\\n\\\\end{equation*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"In the absence of torsion, the above expression is the well-known \\\\emph{algebraic} Bianchi identity\\n\\\\begin{equation*}\\nR^\\\\mu{}_{\\\\nu\\\\lambda\\\\rho} + R^\\\\mu{}_{\\\\lambda\\\\rho\\\\nu} + R^\\\\mu{}_{\\\\rho\\\\nu\\\\lambda} = 0.\\n\\\\end{equation*}\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 3283601467486312560,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 9810454215356752931,\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\subsection*{Second Bianchi identity}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\subsection*{Second Bianchi identity}\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 10044568257557969795,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 9223372036854775836,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\" : 9223372036854775837,\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"d(d(\\\\omega^{a}_{b}) + \\\\omega^{a}_{m} ^ \\\\omega^{m}_{b}-R^{a}_{b}) = 0\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\mathrm{d}\\\\left(\\\\mathrm{d}{\\\\omega^{a}\\\\,_{b}}+\\\\omega^{a}\\\\,_{m}\\\\wedge \\\\omega^{m}\\\\,_{b}-\\\\mathrm{R}^{a}\\\\,_{b}\\\\right) = 0\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"Bianchi2 := d{ @(struc2) };\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 7450601817332024218,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 9223372036854775839,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\" : 9223372036854775840,\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"d(\\\\omega^{a}_{m}) ^ \\\\omega^{m}_{b}-\\\\omega^{a}_{m} ^ d(\\\\omega^{m}_{b})-d(R^{a}_{b}) = 0\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\mathrm{d}{\\\\omega^{a}\\\\,_{m}}\\\\wedge \\\\omega^{m}\\\\,_{b}-\\\\omega^{a}\\\\,_{m}\\\\wedge \\\\mathrm{d}{\\\\omega^{m}\\\\,_{b}}-\\\\mathrm{d}{\\\\mathrm{R}^{a}\\\\,_{b}} = 0\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"distribute(Bianchi2)\\nproduct_rule(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 17474571898667354088,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 9223372036854775842,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\" : 9223372036854775843,\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"R^{a}_{c} ^ \\\\omega^{c}_{b}-\\\\omega^{a}_{c} ^ R^{c}_{b}-d(R^{a}_{b}) = 0\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\mathrm{R}^{a}\\\\,_{c}\\\\wedge \\\\omega^{c}\\\\,_{b}-\\\\omega^{a}\\\\,_{c}\\\\wedge \\\\mathrm{R}^{c}\\\\,_{b}-\\\\mathrm{d}{\\\\mathrm{R}^{a}\\\\,_{b}} = 0\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"substitute(Bianchi2, domega, repeat=True)\\ndistribute(_)\\nrename_dummies(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 4167877586568113468,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 4549200947217648772,\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"The above result, when written in tensorial components, is the well-known\\n\\\\emph{differential} Bianchi identity:\\n\\\\begin{equation*}\\n  R^\\\\mu{}_{\\\\nu\\\\lambda\\\\rho;\\\\sigma} + R^\\\\mu{}_{\\\\nu\\\\sigma\\\\lambda;\\\\rho} + R^\\\\mu{}_{\\\\nu\\\\rho\\\\sigma;\\\\lambda} = 0.\\n\\\\end{equation*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"The above result, when written in tensorial components, is the well-known\\n\\\\emph{differential} Bianchi identity:\\n\\\\begin{equation*}\\n  R^\\\\mu{}_{\\\\nu\\\\lambda\\\\rho;\\\\sigma} + R^\\\\mu{}_{\\\\nu\\\\sigma\\\\lambda;\\\\rho} + R^\\\\mu{}_{\\\\nu\\\\rho\\\\sigma;\\\\lambda} = 0.\\n\\\\end{equation*}\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 13682950063533411677,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1\n}\n"
  },
  {
    "path": "core/.gitignore",
    "content": "cadabra2_defaults.py\nConfig.hh\ncadabra2\nConfig.hh"
  },
  {
    "path": "core/Adjform.cc",
    "content": "#include <algorithm>\n#include <iostream>\n#include <limits>\n#include <numeric>\n#include \"Adjform.hh\"\n#include \"Cleanup.hh\"\n#include \"Compare.hh\"\n#include \"properties/IndexInherit.hh\"\n#include \"properties/Symbol.hh\"\n#include \"properties/Coordinate.hh\"\n#include \"properties/Trace.hh\"\n\n// Get the next permutation of term and return the number of swaps\n// required for the transformation\nint next_perm(std::vector<size_t>& term)\n{\n\tint n = term.size();\n\n\t// Find longest non-increasing suffix to get pivot\n\tint pivot = n - 2;\n\twhile (pivot > -1) {\n\t\tif (term[pivot + 1] > term[pivot])\n\t\t\tbreak;\n\t\t--pivot;\n\t}\n\n\t// Entire sequence is already sorted, return\n\tif (pivot == -1)\n\t\treturn 0;\n\n\t// Find rightmost element greater than pivot\n\tint idx = n - 1;\n\twhile (idx > pivot) {\n\t\tif (term[idx] > term[pivot])\n\t\t\tbreak;\n\t\t--idx;\n\t}\n\n\t// Swap with pivot\n\tstd::swap(term[pivot], term[idx]);\n\n\t// Reverse the suffix\n\tint swaps = 1;\n\tint maxswaps = (n - pivot - 1) / 2;\n\tfor (int i = 0; i < maxswaps; ++i) {\n\t\tif (term[pivot + i + 1] != term[n - i - 1]) {\n\t\t\tstd::swap(term[pivot + i + 1], term[n - i - 1]);\n\t\t\t++swaps;\n\t\t}\n\t}\n\n\treturn swaps;\n}\n\n// Returns the position of 'val' between 'begin' and 'end', starting\n// the search at 'offset'\ntemplate <typename It, typename T>\nsize_t index_of(It begin, It end, const T& val, size_t offset = 0)\n{\n\tauto pos = std::find(begin + offset, end, val);\n\treturn std::distance(begin, pos);\n}\n\nsize_t slots_to_pairs(size_t slots)\n{\n\tsize_t res = 1;\n\tfor (size_t i = 3; i < slots; i += 2)\n\t\tres *= i;\n\treturn res;\n}\n\nsize_t ifactorial(size_t n, size_t den = 1)\n{\n\tif (n < 2)\n\t\treturn 1;\n\n\tsize_t res = 1;\n\tfor (size_t k = den + 1; k <= n; ++k)\n\t\tres *= k;\n\treturn res;\n}\n\nnamespace cadabra {\n\n\tbool is_coordinate(const Kernel& kernel, Ex::iterator it)\n\t{\n\t\tif (it->is_index()) {\n\t\t\tauto coord = kernel.properties.get<Coordinate>(it, true);\n\t\t\tauto integer = it->is_integer();\n\t\t\treturn coord != nullptr || integer;\n\t\t}\n\t\treturn false;\n\t}\n\n\tbool is_index(const Kernel& kernel, Ex::iterator it, bool include_coordinates)\n\t{\n\t\tif (it->is_index()) {\n\t\t\t// Ignore things defined with the symbol property, and rational numbers\n\t\t\tauto symbol = kernel.properties.get<Symbol>(it, true);\n\t\t\tauto rational = it->is_rational() && !it->is_integer();\n\t\t\treturn\n\t\t\t\tsymbol == nullptr &&\n\t\t\t\t!rational &&\n\t\t\t\t(include_coordinates || !is_coordinate(kernel, it));\n\t\t}\n\t\treturn false;\n\t}\n\n\tAdjform::Adjform()\n\t{\n\n\t}\n\n\tAdjform::const_iterator Adjform::begin() const\n\t{\n\t\treturn data.cbegin();\n\t}\n\n\tAdjform::const_iterator Adjform::end() const\n\t{\n\t\treturn data.cend();\n\t}\n\n\tAdjform::size_type Adjform::index_of(value_type index, size_type offset) const\n\t{\n\t\tauto pos = std::find(begin() + offset, end(), index);\n\t\treturn std::distance(begin(), pos);\n\t}\n\n\tbool Adjform::operator < (const Adjform& other) const\n\t{\n\t\treturn data < other.data;\n\t}\n\n\tbool Adjform::operator == (const Adjform& other) const\n\t{\n\t\treturn data == other.data;\n\t}\n\n\tbool Adjform::operator != (const Adjform& other) const\n\t{\n\t\treturn data != other.data;\n\t}\n\n\tAdjform::const_reference Adjform::operator [] (Adjform::size_type idx) const\n\t{\n\t\treturn data[idx];\n\t}\n\n\tAdjform::size_type Adjform::size() const\n\t{\n\t\treturn (size_type)data.size();\n\t}\n\n\tAdjform::size_type Adjform::max_size() const\n\t{\n\t\treturn std::numeric_limits<value_type>::max();\n\t}\n\n\tbool Adjform::empty() const\n\t{\n\t\treturn data.empty();\n\t}\n\n\n\tbool Adjform::is_free_index(Adjform::size_type pos) const\n\t{\n\t\treturn data[pos] < 0;\n\t}\n\n\tbool Adjform::is_dummy_index(Adjform::size_type pos) const\n\t{\n\t\treturn data[pos] >= 0;\n\t}\n\n\tAdjform::size_type Adjform::n_free_indices() const\n\t{\n\t\treturn std::count_if(data.begin(), data.end(), [](value_type idx) { return idx < 0; });\n\t}\n\n\tAdjform::size_type Adjform::n_dummy_indices() const\n\t{\n\t\treturn size() - n_free_indices();\n\t}\n\n\tbool Adjform::resolve_dummy(value_type value)\n\t{\n\t\t// Find positions of both indices\n\t\tsize_type posA = index_of(value);\n\t\tif (posA == size())\n\t\t\treturn false;\n\t\tsize_type posB = index_of(value, posA + 1);\n\t\tif (posB == size())\n\t\t\treturn false;\n\n\t\t// Contract\n\t\tdata[posA] = posB;\n\t\tdata[posB] = posA;\n\t\treturn true;\n\t}\n\n\tvoid Adjform::push_index(value_type value)\n\t{\n\t\tauto pos = std::find(data.begin(), data.end(), value);\n\t\tif (pos == data.end()) {\n\t\t\tdata.push_back(value);\n\t\t}\n\t\telse {\n\t\t\t*pos = data.size();\n\t\t\tdata.push_back(std::distance(data.begin(), pos));\n\t\t}\n\t}\n\n\tvoid Adjform::push_indices(const Adjform& other)\n\t{\n\t\tsize_t start_size = size();\n\t\tfor (auto index : other) {\n\t\t\tif (index > 0)\n\t\t\t\tpush_coordinate(index + start_size);\n\t\t\telse\n\t\t\t\tpush_index(index);\n\t\t}\n\t}\n\n\tvoid Adjform::push_coordinate(value_type value)\n\t{\n\t\tdata.push_back(value);\n\t}\n\n\tvoid Adjform::push_coordinates(const Adjform& other)\n\t{\n\t\tsize_t start_size = size();\n\t\tfor (auto index : other) {\n\t\t\tif (index > 0)\n\t\t\t\tpush_coordinate(index + start_size);\n\t\t\telse\n\t\t\t\tpush_coordinate(index);\n\t\t}\n\t}\n\n\tvoid Adjform::push(Ex::iterator it, IndexMap& index_map, const Kernel& kernel)\n\t{\n\t\tauto val = index_map.get_free_index(it);\n\t\tif (IndexMap::is_coordinate(kernel, it))\n\t\t\tpush_coordinate(val);\n\t\telse\n\t\t\tpush_index(val);\n\t}\n\n\tvoid Adjform::swap(size_type a, size_type b)\n\t{\n\t\t// do nothing if they point to each other\n\t\tif (data[a] == b && data[b] == a)\n\t\t\treturn;\n\n\t\t// update pointed-to positions\n\t\tif (is_dummy_index(a))\n\t\t\tdata[data[a]] = b;\n\t\tif (is_dummy_index(b))\n\t\t\tdata[data[b]] = a;\n\n\t\tstd::swap(data[a], data[b]);\n\t}\n\n\tvoid Adjform::rotate(size_type n)\n\t{\n\t\tif (size() < 2)\n\t\t\treturn;\n\t\tn = (n % size() + size()) % size();\n\n\t\tstd::rotate(data.begin(), data.end() - n, data.end());\n\t\tfor (auto& idx : data) {\n\t\t\tif (idx >= 0)\n\t\t\t\tidx = (idx + n) % data.size();\n\t\t}\n\t}\n\n\tvoid Adjform::sort()\n\t{\n\t\tstd::sort(data.begin(), data.end());\n\t\tauto dummy_start = std::find_if(data.begin(), data.end(), [](value_type v) { return v >= 0; });\n\t\tfor (size_t pos = std::distance(data.begin(), dummy_start); pos < data.size(); pos += 2) {\n\t\t\tdata[pos] = pos + 1;\n\t\t\tdata[pos + 1] = pos;\n\t\t}\n\t}\n\n\tuint64_t Adjform::to_lehmer_code() const\n\t{\n\t\tstd::vector<size_t> counts = { 0 };\n\t\tuint64_t dummy_idx = 0;\n\t\tsize_t n_dummies = n_dummy_indices();\n\t\tsize_t remaining_dummies = n_dummies;\n\t\tarray_type perm(size());\n\n\t\tfor (value_type i = 0; i < size(); ++i) {\n\t\t\tif (data[i] < 0) {\n\t\t\t\tperm[i] = -data[i];\n\t\t\t\tassert(counts.size() < std::numeric_limits<size_type>::max());\n\t\t\t\tif((size_type)counts.size() <= perm[i])\n\t\t\t\t\tcounts.resize(perm[i] + 1, 0);\n\t\t\t\t++counts[perm[i]];\n\t\t\t}\n\t\t\telse {\n\t\t\t\tif (data[i] > i) {\n\t\t\t\t\tsize_t dist = 0;\n\t\t\t\t\tfor (value_type j = i + 1; j < size(); ++j) {\n\t\t\t\t\t\tif (data[j] == i) {\n\t\t\t\t\t\t\tremaining_dummies -= 2;\n\t\t\t\t\t\t\tdummy_idx += dist * slots_to_pairs(remaining_dummies);\n\t\t\t\t\t\t}\n\t\t\t\t\t\telse if (data[j] > i) {\n\t\t\t\t\t\t\tdist += 1;\n\t\t\t\t\t\t}\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t\tperm[i] = 0;\n\t\t\t\t++counts[0];\n\t\t\t}\n\t\t}\n\n\t\tfor (size_t i = 0; i < counts.size(); ++i) {\n\t\t\tif (counts[i] == 0) {\n\t\t\t\tfor (auto& elem : perm) {\n\t\t\t\t\tassert(elem > 0);\n\t\t\t\t\tif((size_t)elem > i)\n\t\t\t\t\t\t--elem;\n\t\t\t\t}\n\t\t\t\tcounts.erase(counts.begin() + i);\n\t\t\t\t--i;\n\t\t\t}\n\t\t}\n\n\t\tsize_t perm_idx = 0;\n\t\tfor (size_t i = 0; i < perm.size() - 1; ++i) {\n\t\t\tsize_t num = ifactorial(perm.size() - i - 1);\n\t\t\tfor (size_type j = 0; j < perm[i]; ++j) {\n\t\t\t\tif (counts[j] == 0)\n\t\t\t\t\tcontinue;\n\t\t\t\t--counts[j];\n\t\t\t\tsize_t den = 1;\n\t\t\t\tfor (size_t k = 0; k < counts.size(); ++k)\n\t\t\t\t\tden *= ifactorial(counts[k]);\n\t\t\t\tperm_idx += num / den;\n\t\t\t\t++counts[j];\n\t\t\t}\n\t\t\t--counts[perm[i]];\n\t\t}\n\t\treturn perm_idx * slots_to_pairs(n_dummies) + dummy_idx;\n\t}\n\n\tuint64_t Adjform::max_lehmer_code() const\n\t{\n\t\tauto dummies = n_dummy_indices();\n\t\tuint64_t res = ifactorial(data.size(), dummies);\n\t\tres *= slots_to_pairs(dummies);\n\t\treturn res;\n\t}\n\n\tstd::string Adjform::to_string() const\n\t{\n\t\tstd::string res(data.size(), ' ');\n\t\tsize_type next_free_index = size();\n\t\tfor (size_t i = 0; i < data.size(); ++i) {\n\t\t\tif (data[i] < 0) {\n\t\t\t\tres[i] = 'a' - data[i] - 1;\n\t\t\t}\n\t\t\telse if ((size_t)(data[i]) > i) {\n\t\t\t\tres[i] = 'a' + next_free_index;\n\t\t\t\t++next_free_index;\n\t\t\t}\n\t\t\telse {\n\t\t\t\tres[i] = res[data[i]];\n\t\t\t}\n\t\t}\n\t\treturn res;\n\t}\n\n\n\tIndexMap::IndexMap(const Kernel& kernel)\n\t\t: comp(std::make_unique<Ex_comparator>(kernel.properties))\n\t\t, data(std::make_unique<Ex>(\"T\"))\n\t{\n\n\t}\n\n\tIndexMap::~IndexMap()\n\t{\n\t\t\n\t}\n\n\tAdjform::value_type IndexMap::get_free_index(Ex::iterator index)\n\t{\n\t\tAdjform::value_type i = 0;\n\t\tEx::iterator head = data->begin();\n\t\tfor (Ex::sibling_iterator beg = head.begin(), end = head.end(); beg != end; ++beg) {\n\t\t\tcomp->clear();\n\t\t\tauto res = comp->equal_subtree(index, beg, Ex_comparator::useprops_t::never, true);\n\t\t\tif (res == Ex_comparator::match_t::subtree_match)\n\t\t\t\treturn -(i + 1);\n\t\t\t++i;\n\t\t}\n\t\tdata->append_child(head, index);\n\t\treturn -(Adjform::value_type)data->begin().number_of_children();\n\t}\n\n\tbool IndexMap::is_coordinate(const Kernel& kernel, Ex::iterator index)\n\t{\n\t\tif (index->is_integer())\n\t\t\treturn true;\n\t\tauto symb = kernel.properties.get<Symbol>(index, true);\n\t\tif (symb)\n\t\t\treturn true;\n\t\tauto coord = kernel.properties.get<Coordinate>(index, true);\n\t\tif (coord)\n\t\t\treturn true;\n\t\treturn false;\n\t}\n\n\tProjectedAdjform::integer_type ProjectedAdjform::zero = 0;\n\n\tProjectedAdjform::ProjectedAdjform()\n\t{\n\n\t}\n\n\tProjectedAdjform::ProjectedAdjform(const Adjform& adjform, const ProjectedAdjform::integer_type& value)\n\t{\n\t\tset(adjform, value);\n\t}\n\n\tvoid ProjectedAdjform::combine(const ProjectedAdjform& other)\n\t{\n\t\tfor (const auto& kv : other.data)\n\t\t\tadd(kv.first, kv.second);\n\t}\n\n\tvoid ProjectedAdjform::combine(const ProjectedAdjform& other, integer_type factor)\n\t{\n\t\tfor (const auto& kv : other.data)\n\t\t\tadd(kv.first, kv.second * factor);\n\t}\n\n\tProjectedAdjform& ProjectedAdjform::operator += (const ProjectedAdjform& other)\n\t{\n\t\tcombine(other);\n\t\treturn *this;\n\t}\n\n\tProjectedAdjform operator + (ProjectedAdjform lhs, const ProjectedAdjform& rhs)\n\t{\n\t\treturn lhs += rhs;\n\t}\n\n\tvoid ProjectedAdjform::multiply(const integer_type& k)\n\t{\n\t\tfor (auto& kv : data)\n\t\t\tkv.second *= k;\n\t}\n\n\tProjectedAdjform& ProjectedAdjform::operator *= (const integer_type& k)\n\t{\n\t\tmultiply(k);\n\t\treturn *this;\n\t}\n\n\tProjectedAdjform operator * (ProjectedAdjform lhs, const ProjectedAdjform::integer_type& rhs)\n\t{\n\t\tlhs.multiply(rhs);\n\t\treturn lhs;\n\t}\n\n\tProjectedAdjform::iterator ProjectedAdjform::begin()\n\t{\n\t\treturn data.begin();\n\t}\n\n\tProjectedAdjform::const_iterator ProjectedAdjform::begin() const\n\t{\n\t\treturn data.begin();\n\t}\n\n\tProjectedAdjform::iterator ProjectedAdjform::end()\n\t{\n\t\treturn data.end();\n\t}\n\n\tProjectedAdjform::const_iterator ProjectedAdjform::end() const\n\t{\n\t\treturn data.end();\n\t}\n\n\tvoid ProjectedAdjform::clear()\n\t{\n\t\tdata.clear();\n\t}\n\n\tsize_t ProjectedAdjform::size() const\n\t{\n\t\treturn data.size();\n\t}\n\n\tsize_t ProjectedAdjform::max_size() const\n\t{\n\t\tif (empty())\n\t\t\treturn 0;\n\t\treturn begin()->first.max_lehmer_code();\n\t}\n\n\tsize_t ProjectedAdjform::n_indices() const\n\t{\n\t\tif (empty())\n\t\t\treturn 0;\n\t\treturn begin()->first.size();\n\t}\n\n\tbool ProjectedAdjform::empty() const\n\t{\n\t\treturn data.empty();\n\t}\n\n\tconst ProjectedAdjform::integer_type& ProjectedAdjform::get(const Adjform& adjform) const\n\t{\n\t\tauto pos = data.find(adjform);\n\t\treturn (pos == data.end()) ? zero : pos->second;\n\t}\n\n\tvoid ProjectedAdjform::set(const Adjform& term, const ProjectedAdjform::integer_type& value)\n\t{\n\t\tif (!term.empty())\n\t\t\tset_(term, value);\n\t}\n\n\tvoid ProjectedAdjform::set_(const Adjform& term, const ProjectedAdjform::integer_type& value)\n\t{\n\t\tif (value != 0)\n\t\t\tdata[term] = value;\n\t\telse\n\t\t\tdata.erase(term);\n\t}\n\n\tvoid ProjectedAdjform::add(const Adjform& term, const ProjectedAdjform::integer_type& value)\n\t{\n\t\tif (!term.empty())\n\t\t\tadd_(term, value);\n\t}\n\n\tvoid ProjectedAdjform::add_(const Adjform& term, const ProjectedAdjform::integer_type& value)\n\t{\n\t\tauto elem = data.find(term);\n\t\tif (elem == data.end() && value != 0) {\n\t\t\tdata[term] = value;\n\t\t}\n\t\telse {\n\t\t\telem->second += value;\n\t\t\tif (elem->second == 0)\n\t\t\t\tdata.erase(elem);\n\t\t}\n\t}\n\n\tvoid ProjectedAdjform::apply_young_symmetry(const std::vector<size_t>& indices, bool antisymmetric)\n\t{\n\t\tmap_t old_data = data;\n\n\t\tfor (const auto& kv : old_data) {\n\t\t\tstd::vector<int> values(indices.size());\n\t\t\tstd::iota(values.begin(), values.end(), 1);\n\t\t\tstd::vector<int> positions(indices.size() + 1);\n\t\t\tstd::iota(positions.begin(), positions.end(), -1);\n\t\t\tstd::vector<int> directions(indices.size() + 1, -1);\n\t\t\tint sign = -1;\n\t\t\tauto term = kv.first;\n\t\t\twhile (true) {\n\t\t\t\tint r = 0;\n\t\t\t\tfor (int rk = values.size(); rk > 0; --rk) {\n\t\t\t\t\tsize_t loc = positions[rk] + directions[rk];\n\t\t\t\t\tif (loc >= 0 && loc < values.size() && values[loc] < rk) {\n\t\t\t\t\t\tr = rk;\n\t\t\t\t\t\tbreak;\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t\tif (r == 0)\n\t\t\t\t\tbreak;\n\n\t\t\t\tint r_loc = positions[r];\n\t\t\t\tint l_loc = r_loc + directions[r];\n\t\t\t\tint l = values[l_loc];\n\n\t\t\t\tterm.swap(indices[values[l_loc] - 1], indices[values[r_loc] - 1]);\n\t\t\t\tadd_(term, kv.second * (antisymmetric ? sign : 1));\n\n\t\t\t\tstd::swap(values[l_loc], values[r_loc]);\n\t\t\t\tstd::swap(positions[l], positions[r]);\n\t\t\t\tsign *= -1;\n\t\t\t\tfor (size_t i = r + 1; i < directions.size(); ++i)\n\t\t\t\t\tdirections[i] = -directions[i];\n\t\t\t}\n\t\t}\n\t}\n\n\tvoid ProjectedAdjform::apply_ident_symmetry(const std::vector<size_t>& positions, size_t n_indices)\n\t{\n\t\tapply_ident_symmetry(positions, n_indices, std::vector<std::vector<int>>(positions.size(), std::vector<int>(positions.size(), 1)));\n\t}\n\n\tvoid ProjectedAdjform::apply_ident_symmetry(const std::vector<size_t>& positions, size_t n_indices, const std::vector<std::vector<int>>& commutation_matrix)\n\t{\n\t\tfor (size_t i = 0; i < positions.size() - 1; ++i) {\n\t\t\tauto old_data = data;\n\t\t\tfor (size_t j = i + 1; j < positions.size(); ++j) {\n\t\t\t\tint sign = commutation_matrix[i][j];\n\t\t\t\tif (sign != 0) {\n\t\t\t\t\tfor (const auto& kv : old_data) {\n\t\t\t\t\t\tauto term = kv.first;\n\t\t\t\t\t\tfor (size_t k = 0; k < n_indices; ++k)\n\t\t\t\t\t\t\tterm.swap(positions[i] + k, positions[j] + k);\n\t\t\t\t\t\tadd_(term, kv.second * sign);\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t}\n\t\t}\n\t}\n\n\tvoid ProjectedAdjform::apply_cyclic_symmetry()\n\t{\n\t\tif (data.empty())\n\t\t\treturn;\n\n\t\tsize_t n_indices = data.begin()->first.size();\n\t\tsize_t n_steps = n_indices - 1;\n\t\tmap_t old_data = data;\n\n\t\tfor (const auto& kv : old_data) {\n\t\t\tauto perm = kv.first;\n\t\t\tfor (size_t step = 0; step < n_steps; ++step) {\n\t\t\t\tperm.rotate(1);\n\t\t\t\tadd_(perm, kv.second);\n\t\t\t}\n\t\t}\n\t}\n\n}\n\nstd::ostream& operator << (std::ostream& os, const cadabra::Adjform& adjform)\n{\n\tfor (const auto& idx : adjform)\n\t\tos << idx << ' ';\n\treturn os;\n}\n\nstd::ostream& operator << (std::ostream& os, const cadabra::ProjectedAdjform& adjex)\n{\n\tsize_t i = 0;\n\tsize_t max = std::min(std::size_t(200), adjex.size());\n\tauto it = adjex.begin();\n\twhile (i < max) {\n\t\tos << it->first << '\\t' << it->second << '\\n';\n\t\t++i;\n\t\t++it;\n\t}\n\tif (max < adjex.size()) {\n\t\tos << \"(skipped \" << (adjex.size() - max) << \" terms)\\n\";\n\t}\n\treturn os;\n}\n\n"
  },
  {
    "path": "core/Adjform.hh",
    "content": "#pragma once\n\n#include <vector>\n#include <map>\n#include <iosfwd>\n#include <cstdint>\n#include <string>\n#include \"Compare.hh\"\n#include \"Kernel.hh\"\n#include \"Storage.hh\"\n\nnamespace cadabra {\n\n\tclass IndexMap;\n\n\t/// Representation of the index structure of a tensor monomial,\n\t/// using a storage format which resembles an adjacency matrix. The\n\t/// structure is stored as a vector of integers.  Negative integers\n\t/// denote free indices. Positive indices denote a contraction with\n\t/// an index at the indicated position.\n\t///\n\t/// Example:\n\t///\n\t///    A_{m n} B_{p n}   ->   -1 3 -2 1\n\t///       0 1     2 3\n\t///\n\t/// The tensor names themselves ('A' and 'B' above) are not stored.\n\t\n\tclass Adjform\n\t\t{\n\t\tpublic:\n\t\t\t/// The maximal number of index slots is set by `value_type`: for a\n\t\t\t/// short, the maximal number of slots is 127.\n\t\t\tusing value_type = short;\n\t\t\tusing size_type = value_type;\n\t\t\tusing difference_type = value_type;\n\t\t\tusing array_type = std::vector<value_type>;\n\t\t\tusing const_reference = array_type::const_reference;\n\t\t\tusing const_iterator = array_type::const_iterator;\n\n\t\t\tAdjform();\n\t\t\ttemplate <typename IndexIterator>\n\t\t\tAdjform(IndexIterator beg, IndexIterator end, IndexMap& index_map, const Kernel& kernel);\n\t\t\ttemplate <typename ValueIterator>\n\t\t\tAdjform(ValueIterator beg, ValueIterator end, bool push_as_coordinates);\n\n\t\t\tconst_iterator begin() const;\n\t\t\tconst_iterator end() const;\n\n\t\t\t// Return the position of the given index starting from the given\n\t\t\t// offset (but returning the position from the actual start). Returns\n\t\t\t// this->size() if not found.\n\t\t\tsize_type index_of(value_type index, size_type offset = 0) const;\n\n\t\t\tbool operator < (const Adjform& other) const;\n\t\t\tbool operator == (const Adjform& other) const;\n\t\t\tbool operator != (const Adjform& other) const;\n\n\t\t\tconst_reference operator [] (size_type idx) const;\n\n\t\t\tsize_type size() const;\n\t\t\tsize_type max_size() const;\n\t\t\tbool empty() const;\n\n\t\t\t// Return true if the value at 'pos' is < 0\n\t\t\tbool is_free_index(size_type pos) const;\n\t\t\t// Return true if the value at pos is >= 0\n\t\t\tbool is_dummy_index(size_type pos) const;\n\t\n\t\t\tsize_type n_free_indices() const;\n\t\t\tsize_type n_dummy_indices() const;\n\n\t\t\t// Contract pairs of this type of index, e.g. with value=-1 '-1 -2 -3 -1' -> '3 -2 -3 0'.\n\t\t\t// Returns true if the index was found and replaced.\n\t\t\tbool resolve_dummy(value_type value);\n\n\t\t\t// Push value(s) to the end and contract it if a eqivalent is found, e.g. with\n\t\t\t// value=-1 '-1 -2 -3' -> '3 -2 -3 0'\n\t\t\tvoid push_index(value_type value);\n\t\t\tvoid push_indices(const Adjform& other);\n\n\t\t\t// PUsh value to the end, but do not attempt to contract it, e.g. with\n\t\t\t// value=-1 '-1 -2 -3' -> '-1 -2 -3 -1'\n\t\t\tvoid push_coordinate(value_type value);\n\t\t\tvoid push_coordinates(const Adjform& other);\n\n\t\t\t// Push an iterator by calling IndexMap::is_coordinate to see if push_index or \n\t\t\t// push_coordinate should be used\n\t\t\tvoid push(Ex::iterator iterator, IndexMap& index_map, const Kernel& kernel);\n\n\t\t\t// Swap the values at positions a and b\n\t\t\tvoid swap(size_type a, size_type b);\n\n\t\t\t// Cycle the values by moving the last element to the front n times,\n\t\t\t// e.g. with n=1 '3 -2 -3 0' -> '1 0 -2 -3'\n\t\t\tvoid rotate(size_type n);\n\n\t\t\t// Sort indices so that all free indices are at the beginning and all contracted\n\t\t\t// pairs at the end and next to each other, e.g. '3 -2 -3 0' -> '-3 -2 3 2'\n\t\t\tvoid sort();\n\n\t\t\t// Produce a unique integer to represent the current permutation\n\t\t\tuint64_t to_lehmer_code() const;\n\t\t\t// The total number of possible permutations of values\n\t\t\tuint64_t max_lehmer_code() const;\n\t\t\t// String representation where indices are named 'a-z' in the order they appear\n\t\t\tstd::string to_string() const;\n\n\t\tprivate:\n\t\t\t// Storage of an index configuration; has a maximal size\n\t\t\t// equal to size_type (not size_t).\n\t\t\tarray_type data;\n\t\t};\n\n\t/// To ensure consistency when creating adjforms out of two\n\t/// different Ex objects an IndexMap object is required which\n\t/// keeps track of which numeric index represents which index\n\t/// name.\n\t\n\tclass IndexMap\n\t\t{\n\t\tpublic:\n\t\t\tIndexMap(const Kernel& kernel);\n\t\t\t~IndexMap();\n\t\t\t// Return a negative integer for each unique index\n\t\t\tAdjform::value_type get_free_index(Ex::iterator index);\n\t\t\t// Return true if index has the Coordinate or Symbol property, or is an integer\n\t\t\tstatic bool is_coordinate(const Kernel& kernel, Ex::iterator index);\n\t\tprivate:\n\t\t\tstd::unique_ptr<Ex_comparator> comp;\n\t\t\tstd::unique_ptr<Ex> data;\n\t\t};\n\n\t/// Representation of a sum of tensor monomials, each having the\n\t/// same tensor names, but with different index positions. As with\n\t/// AdjForm, the names of the tensors are not stored, only the\n\t/// index structure and the coefficient of each term.\n\t\n\tclass ProjectedAdjform\n\t\t{\n\t\tpublic:\n\t\t\tusing integer_type = int32_t;\n\t\t\tusing map_t = std::map<Adjform, integer_type>;\n\t\t\tusing iterator = map_t::iterator;\n\t\t\tusing const_iterator = map_t::const_iterator;\n\n\t\t\tProjectedAdjform();\n\t\t\tProjectedAdjform(const Adjform& adjform, const integer_type& value = 1);\n\n\t\t\t// Add all contributions from 'other' into 'this'\n\t\t\tvoid combine(const ProjectedAdjform& other); \n\t\t\tvoid combine(const ProjectedAdjform& other, integer_type factor);\n\t\t\tProjectedAdjform& operator += (const ProjectedAdjform& other);\n\t\t\tfriend ProjectedAdjform operator + (ProjectedAdjform lhs, const ProjectedAdjform& rhs);\n\n\t\t\t// Multiply all terms by a scalar factor\n\t\t\tvoid multiply(const integer_type& k);\n\t\t\tProjectedAdjform& operator *= (const integer_type& k);\n\t\t\tfriend ProjectedAdjform operator * (ProjectedAdjform lhs, const integer_type& rhs);\n\n\t\t\titerator begin();\n\t\t\tconst_iterator begin() const;\n\t\t\titerator end();\n\t\t\tconst_iterator end() const;\n\n\t\t\tvoid clear(); // Remove all entries\n\t\t\tsize_t size() const; // Number of entries\n\t\t\tsize_t max_size() const; // Returns the number of terms there would be if fully symmetrized\n\t\t\tsize_t n_indices() const; // Returns the number of indices each adjform has\n\t\t\tbool empty() const; // True if there are no entries\n\n\t\t\t// Get the value of the term, or zero if it doesn't exist\n\t\t\tconst integer_type& get(const Adjform& adjform) const;\n\t\t\t// Sets the given term to value, creating/removing the term if required\n\t\t\tvoid set(const Adjform& adjform, const integer_type& value = 1);\n\t\t\t// Adds value to the given term, creating/removing the term if required\n\t\t\tvoid add(const Adjform& adjform, const integer_type& value = 1);\n\n\t\t\t// Symmetrise or anti-symmetrise in the given indices\n\t\t\t// e.g. if the only term is abcd then\n\t\t\t//        apply_young_symmetry({0, 1, 2}, false) -> abcd + acbd + bacd + bcad + cabd + cbad\n\t\t\t//        apply_young_symmetry({2, 3, 4}, true) -> abcd - abdc - acbd + acdb - adcb + adbc\n\t\t\tvoid apply_young_symmetry(const std::vector<size_t>& indices, bool antisymmetric);\n\n\t\t\t// Symmetrize in indices starting at the indices in 'positions' with each group\n\t\t\t// 'n_indices' long.\n\t\t\t// e.g. if the only term is abcdefg then apply_ident_symmetry({0, 2, 4}, 2) ->\n\t\t\t//      abcdefg + abefcdg + cdabefg + cdefabg + efabcdg + efcdabg\n\t\t\tvoid apply_ident_symmetry(const std::vector<size_t>& positions, size_t n_indices);\n\t\t\tvoid apply_ident_symmetry(const std::vector<size_t>& positions, size_t n_indices, const std::vector<std::vector<int>>& commutation_matrix);\n\n\t\t\t// Symmetrize cyclically so abc -> abc + bca + cab\n\t\t\tvoid apply_cyclic_symmetry();\n\n\t\tprivate:\n\t\t\t// Unsafe (but faster) versions of the public functions\n\t\t\tvoid set_(const Adjform& adjform, const integer_type& value = 1);\n\t\t\tvoid add_(const Adjform& adjform, const integer_type& value = 1);\n\n\t\t\tmap_t data;\n\t\t\tstatic integer_type zero;\n\t\t};\n\n\ttemplate <typename IndexIterator>\n\tAdjform::Adjform(IndexIterator beg, IndexIterator end, IndexMap& index_map, const Kernel& kernel)\n\t\t{\n\t\twhile (beg != end) {\n\t\t\tpush(beg, index_map, kernel);\n\t\t\t++beg;\n\t\t\t}\n\t\t}\n\n\ttemplate <typename ValueIterator>\n\tAdjform::Adjform(ValueIterator beg, ValueIterator end, bool push_as_coordinates)\n\t\t{\n\t\twhile (beg != end) {\n\t\t\tauto val = *beg;\n\t\t\tif (push_as_coordinates)\n\t\t\t\tpush_coordinate(val);\n\t\t\telse\n\t\t\t\tpush_index(val);\n\t\t\t++beg;\n\t\t\t}\n\t\t}\n\t}\n\n\nstd::ostream& operator << (std::ostream& os, const cadabra::Adjform& adjform);\nstd::ostream& operator << (std::ostream& os, const cadabra::ProjectedAdjform& adjex);\n"
  },
  {
    "path": "core/Algorithm.cc",
    "content": "/*\n\nCadabra: a field-theory motivated computer algebra system.\nCopyright (C) 2001-2015  Kasper Peeters <kasper.peeters@phi-sci.com>\n\nThis program is free software: you can redistribute it and/or\n\tmodify it under the terms of the GNU General Public License as\npublished by the Free Software Foundation, either version 3 of the\nLicense, or (at your option) any later version.\n\nThis program is distributed in the hope that it will be useful,\nbut WITHOUT ANY WARRANTY; without even the implied warranty of\nMERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU\nGeneral Public License for more details.\n\nYou should have received a copy of the GNU General Public License\nalong with this program.  If not, see <http://www.gnu.org/licenses/>.\n\n*/\n\n#include <stddef.h>\n#include \"Algorithm.hh\"\n#include \"IndexClassifier.hh\"\n#include \"Storage.hh\"\n#include \"Props.hh\"\n#include \"Cleanup.hh\"\n#include \"Exceptions.hh\"\n#include \"Functional.hh\"\n#include \"properties/PartialDerivative.hh\"\n#include <typeinfo>\n#include <boost/version.hpp>\n#if BOOST_VERSION > 105500\n#include <boost/core/demangle.hpp>\n#endif\n//#include <boost/stacktrace.hpp>\n\n#include \"properties/Accent.hh\"\n#include \"properties/Coordinate.hh\"\n#include \"properties/Derivative.hh\"\n#include \"properties/Indices.hh\"\n#include \"properties/Trace.hh\"\n#include \"properties/DependsBase.hh\"\n#include \"properties/NonCommuting.hh\"\n#include \"properties/AntiCommuting.hh\"\n#include \"properties/SelfNonCommuting.hh\"\n#include \"properties/SelfAntiCommuting.hh\"\n\n//#define DEBUG\n\nusing namespace cadabra;\n\nAlgorithm::Algorithm(const Kernel& k, Ex& tr_)\n\t: ExManip(k, tr_),\n//\t  IndexClassifier(k),\n\t  interrupted(false),\n\t  number_of_calls(0), number_of_modifications(0),\n\t  suppress_normal_output(false),\n\t  discard_command_node(false),\n\t  pm(0),\n\t  traverse_ldots(false)\n\t{\n\t}\n\nAlgorithm::~Algorithm()\n\t{\n\t}\n\nvoid Algorithm::set_progress_monitor(ProgressMonitor *pm_)\n\t{\n\tpm=pm_;\n\t}\n\nAlgorithm::result_t Algorithm::apply_pre_order(bool repeat)\n\t{\n#if BOOST_VERSION > 105500\n\tScopedProgressGroup sp(pm, boost::core::demangle(typeid(*this).name()));\n#else\n\tScopedProgressGroup sp(typeid(*this).name());\n#endif\n\t\n\tresult_t ret=result_t::l_no_action;\n\tEx::iterator start=tr.begin();\n\twhile(start!=tr.end()) {\n\t\tif(traverse_ldots || !tr.is_hidden(start)) {\n\t\t\tif(start->is_index()==false) {\n\t\t\t\tauto aor=apply_once(start);\n\t\t\t\tif(aor==result_t::l_applied || aor==result_t::l_applied_no_new_dummies) {\n\t\t\t\t\tret=result_t::l_applied;\n\t\t\t\t\t// Need to cleanup on the entire tree above us.\n\t\t\t\t\t\n\t\t\t\t\tif(!repeat) {\n\t\t\t\t\t\tstart.skip_children();\n\t\t\t\t\t\t++start;\n\t\t\t\t\t\t}\n\t\t\t\t\t}\n\t\t\t\telse ++start;\n\t\t\t\t}\n\t\t\telse ++start;\n\t\t\t}\n\t\telse {\n\t\t\t++start;\n\t\t\t}\n\t\t}\n\n\tcleanup_dispatch_deep(kernel, tr);\n\n\treturn ret;\n\t}\n\nAlgorithm::result_t Algorithm::apply_generic(bool deep, bool repeat, unsigned int depth)\n\t{\n\tauto it = tr.begin();\n\treturn apply_generic(it, deep, repeat, depth);\n\t}\n\nAlgorithm::result_t Algorithm::apply_generic(Ex::iterator& it, bool deep, bool repeat, unsigned int depth)\n\t{\n#if BOOST_VERSION > 105500\n\tScopedProgressGroup sp(pm, boost::core::demangle(typeid(*this).name()));\n#else\n\tScopedProgressGroup sp(typeid(*this).name());\n#endif\n\n\tresult_t ret=result_t::l_no_action;\n\n\tEx::fixed_depth_iterator start=tr.begin_fixed(it, depth, false);\n#ifdef DEBUG\n\tstd::cerr << \"apply_generic at \" << it.node << \" \" << *it->name << \" \" << *start->name << std::endl;\n#endif\n\n\twhile(tr.is_valid(start)) {\n\t\t//\t\tstd::cerr << \"evaluate main loop at \" << *start->name << std::endl;\n#ifdef DEBUG\n\t\tstd::cerr << \"main loop for \" << typeid(*this).name() << \":\\n\" << Ex(start) << std::endl;\n#endif\n\n\t\tresult_t thisret=result_t::l_no_action;\n\t\tEx::iterator enter(start);\n\t\tEx::fixed_depth_iterator next(start);\n\t\t++next;\n\t\t//\t\tif(tr.is_valid(next))\n\t\t//\t\t\tstd::cerr << \"next = \" << *next->name << std::endl;\n\t\tdo {\n\t\t\t//\t\t\tstd::cout << \"apply at \" << *enter->name << std::endl;\n\t\t\tbool work_is_topnode=(enter==it);\n\t\t\tif(deep && depth==0)\n\t\t\t\tthisret = apply_deep(enter);\n\t\t\telse\n\t\t\t\tthisret = apply_once(enter);\n\n\t\t\tif(work_is_topnode)\n\t\t\t\tit=enter;\n\n\t\t\t// FIXME: handle l_error or remove\n\t\t\tif(thisret==result_t::l_applied || thisret==result_t::l_applied_no_new_dummies)\n\t\t\t\tret=result_t::l_applied;\n\t\t\t}\n\t\twhile(depth==0 && repeat && (thisret==result_t::l_applied || thisret==result_t::l_applied_no_new_dummies));\n\n\t\tif(depth==0) {\n\t\t\t// std::cerr << \"break \" << std::endl;\n\t\t\tbreak;\n\t\t\t}\n\t\telse {\n\t\t\t// std::cerr << \"no break \" << std::endl;\n\t\t\t}\n\t\tstart=next;\n\t\t}\n\n\t// std::cerr << \"pre-exit node \" << it.node << std::endl;\n\n\t// If we are acting at fixed depth, we will not have gone up in the\n\t// tree, so missed one cleanup action. Do it now.\n\tif(depth>0) {\n\t\tEx::fixed_depth_iterator start=tr.begin_fixed(it, depth-1, false);\n\t\twhile(tr.is_valid(start)) {\n\t\t\tEx::iterator work=start;\n\t\t\t++start;\n\t\t\tbool cpy=false;\n\t\t\tif(work==it) cpy=true;\n\t\t\tcleanup_dispatch(kernel, tr, work);\n\t\t\tif(cpy) it=work;\n\t\t\t}\n\t\t}\n\n\t// std::cerr << \"exit node \" << it.node << std::endl;\n\n\t//\tif(tr.is_valid(it)) {\n\t//\t\tstd::cerr << \"exit \" << *it->name << std::endl;\n\t//\t\tstd::cerr << \"exit apply_generic\\n\" << Ex(it) << std::endl;\n\t//\t\t}\n\n\treturn ret;\n\t}\n\nAlgorithm::result_t Algorithm::apply_once(Ex::iterator& it)\n\t{\n\t// std::cerr << \"=== apply_once ===\" << std::endl;\n\tif(traverse_ldots || !tr.is_hidden(it)) {\n\t\tif(can_apply(it)) {\n\t\t\tresult_t res=apply(it);\n\t\t\t// std::cerr << \"apply algorithm at \" << *it->name << std::endl;\n\t\t\tif(res==result_t::l_applied || res==result_t::l_applied_no_new_dummies) {\n\t\t\t\tcleanup_dispatch(kernel, tr, it);\n\t\t\t\treturn res;\n\t\t\t\t}\n\t\t\t}\n\t\t}\n\n\treturn result_t::l_no_action;\n\t}\n\nAlgorithm::result_t Algorithm::apply_deep(Ex::iterator& it)\n\t{\n\t// This recursive algorithm walks the tree depth-first\n\t// (parent-after-child). The algorithm is applied on each node if\n\t// can_apply returns true. When the iterator goes up one level\n\t// (i.e. from a child to a parent), and any changes have been made\n\t// so far at the child level level, cleanup and simplification\n\t// routines will be called. The only nodes that can be removed from\n\t// the tree are nodes at a lower level than the simplification\n\t// node.\n\n\t// std::cout << \"=== apply_deep ===\" << std::endl;\n\t//\ttr.print_recursive_treeform(std::cout, it);\n\n\tpost_order_iterator current=it;\n\tcurrent.descend_all();\n\tpost_order_iterator last=it;\n\tint deepest_action = -1;\n\t//\tstd::cout << \"apply_deep: it = \" << *it->name << std::endl;\n\tbool stop_after_this_one=false;\n\tresult_t some_changes_somewhere=result_t::l_no_action;\n\n\tfor(;;) {\n\t\t//\t\tstd::cout << \"reached \" << *current->name << std::endl;\n#ifdef DEBUG\n\t\tstd::cout << \"apply_deep \" << typeid(*this).name() << \": current = \" << *current->name << std::endl;\n#endif\n\n\t\tif(current.node==last.node) {\n\t\t\t//\t\t\tstd::cout << \"stop after this one\" << std::endl;\n\t\t\tstop_after_this_one=true;\n\t\t\t}\n\n\t\tif(deepest_action > tr.depth(current)) {\n#ifdef DEBUG\n\t\t\tstd::cerr << \"simplify; we are at \" << *(current->name) << std::endl;\n#endif\n\t\t\titerator work=current;\n\t\t\tbool work_is_topnode=(work==it);\n\t\t\tcleanup_dispatch(kernel, tr, work);\n\t\t\tcurrent=work;\n\t\t\tif(work_is_topnode)\n\t\t\t\tit=work;\n#ifdef DEBUG\n\t\t\tstd::cerr << \"current now \" << *(current->name) << std::endl;\n\t\t\ttr.print_recursive_treeform(std::cerr, current);\n#endif\n\t\t\tdeepest_action = tr.depth(current); // needs to propagate upwards\n\t\t\t}\n\n\t\tif((traverse_ldots || !tr.is_hidden(current)) && can_apply(current)) {\n#ifdef DEBUG\n\t\t\tstd::cout << \"acting at \" << *current->name << std::endl;\n#endif\n\t\t\titerator work=current;\n\t\t\tpost_order_iterator next(current);\n\t\t\t++next;\n\t\t\tbool work_is_topnode=(work==it);\n\t\t\tresult_t res = apply(work);\n\t\t\tif(res==Algorithm::result_t::l_applied || res==Algorithm::result_t::l_applied_no_new_dummies) {\n\t\t\t\tsome_changes_somewhere=result_t::l_applied;\n\t\t\t\tif(res==Algorithm::result_t::l_applied) {\n//\t\t\t\t\tstd::cerr << \"rename replacement on \" << work << std::endl;\n\t\t\t\t\trename_replacement_dummies(work, true);\n\t\t\t\t\t}\n\t\t\t\tdeepest_action=tr.depth(work);\n\t\t\t\t// If we got a zero at 'work', we need to propagate this up the tree and\n\t\t\t\t// then restart our post-order traversal such that everything that has\n\t\t\t\t// been removed from the tree by this zero will no longer be considered.\n\t\t\t\tif(*work->multiplier==0) {\n#ifdef DEBUG\n\t\t\t\t\tstd::cerr << \"propagate zero up the tree\" << std::endl;\n\t\t\t\t\ttr.print_recursive_treeform(std::cerr, it);\n#endif\n\t\t\t\t\tpost_order_iterator moved_next=work;\n\t\t\t\t\tpropagate_zeroes(moved_next, it);\n#ifdef DEBUG\n\t\t\t\t\ttr.print_recursive_treeform(std::cerr, it);\n\t\t\t\t\tstd::cerr << Ex(it) << std::endl;\n#endif\n\t\t\t\t\tnext=moved_next;\n\t\t\t\t\t}\n\n\t\t\t\t// The 'work' iterator can now point to a new node. If we were acting at the\n\t\t\t\t// top node, we need to propagate the change in 'work' to 'it' so the caller\n\t\t\t\t// knows where the new top node is.\n\t\t\t\tif(work_is_topnode)\n\t\t\t\t\tit=work;\n\t\t\t\t}\n\t\t\t// The algorithm may have replaced the 'work' node, so instead of walking from\n\t\t\t// there, we continue at the node which was next in line before we called 'apply'.\n\t\t\tcurrent=next;\n\t\t\t}\n\t\telse {\n\t\t\t++current;\n\t\t\t}\n\n\t\tif(stop_after_this_one)\n\t\t\tbreak;\n\n\t\t}\n\n#ifdef DEBUG\n\tstd::cerr << \"recursive end **\" << std::endl;\n#endif\n\n\treturn some_changes_somewhere;\n\t}\n\nvoid Algorithm::propagate_zeroes(post_order_iterator& it, const iterator& topnode)\n\t{\n\tassert(*it->multiplier==0);\n\tif(it==topnode) return;\n\tif(tr.is_head(it)) return;\n\t\n\titerator walk=tr.parent(it);\n#ifdef DEBUG\n\tstd::cerr << \"propagate_zeroes at \" << *walk->name << std::endl;\n#endif\n//\tif(!tr.is_valid(walk))\n//\t\treturn;\n\n\tconst Derivative *der=kernel.properties.get<Derivative>(walk);\n\tconst Trace *trace=kernel.properties.get<Trace>(walk);\n\tif(*walk->name==\"\\\\prod\" || der || trace) {\n\t\tif(der && it->is_index()) return;\n\t\twalk->multiplier=rat_set.insert(0).first;\n\t\tit=walk;\n\t\tpropagate_zeroes(it, topnode);\n\t\t// Removing happens in the next step.\n\t\t}\n\telse if(*walk->name==\"\\\\pow\") {\n\t\tif(tr.index(it)==0) { // the argument is zero\n\t\t\tsibling_iterator arg=it;\n\t\t\t++arg;\n\t\t\tif(*arg->multiplier<0) \n\t\t\t\tthrow RuntimeException(\"Division by zero encountered.\");\n\t\t\t\n\t\t\twalk->multiplier=rat_set.insert(0).first;\n\t\t\tit=walk;\n\t\t\tpropagate_zeroes(it, topnode);\n\t\t\t}\n\t\telse {   // the exponent\n\t\t\trset_t::iterator rem=walk->multiplier;\n\t\t\ttr.erase(it);\n\t\t\ttr.flatten(walk);\n\t\t\tit=tr.erase(walk);\n\t\t\tnode_one(it);\n\t\t\tit->multiplier=rem;\n\t\t\t}\n\t\t}\n\telse if(*walk->name==\"\\\\sum\") {\n\t\tif(tr.number_of_children(walk)>2) {\n\t\t\tif(tr.is_valid(tr.next_sibling(it))) {\n\t\t\t\tit=tr.erase(it);\n\t\t\t\tit.descend_all();\n\t\t\t\t}\n\t\t\telse {\n\t\t\t\titerator ret=tr.parent(it);\n\t\t\t\ttr.erase(it);\n\t\t\t\tit=ret;\n\t\t\t\t}\n\t\t\t}\n\t\telse {\n\t\t\t// If the sum is the top node, we cannot flatten it because\n\t\t\t// we are not allowed to invalidate the topnode iterator\n\t\t\tif(walk==topnode) {\n#ifdef DEBUG\n\t\t\t\tstd::cerr << \"\\\\sum at top, cannot flatten\" << std::endl;\n#endif\n\t\t\t\t//\t\t\t\tit=tr.next_sibling(it); // Added but wrong?\n\t\t\t\treturn;\n\t\t\t\t}\n\n\t\t\ttr.erase(it);\n\t\t\titerator singlearg=tr.begin(walk);\n\t\t\tif(singlearg!=tr.end(walk)) {\n\t\t\t\tsinglearg->fl.bracket=walk->fl.bracket; // to remove brackets of the sum\n\t\t\t\tif(*tr.parent(walk)->name==\"\\\\prod\") {\n\t\t\t\t\tmultiply(tr.parent(walk)->multiplier, *singlearg->multiplier);\n\t\t\t\t\tcadabra::one(singlearg->multiplier);\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\ttr.flatten(walk);\n\t\t\tit=tr.erase(walk);\n\t\t\tif(*it->name==\"\\\\prod\" && *tr.parent(it)->name==\"\\\\prod\") {\n\t\t\t\ttr.flatten(it);\n\t\t\t\tit=tr.erase(it);\n\t\t\t\t}\n\t\t\t}\n\t\t}\n\telse {\n\t\titerator nn=tr.insert_after(it, str_node(\"1\"));\n\t\tnn->fl.parent_rel=it->fl.parent_rel;\n\t\tnn->fl.bracket=it->fl.bracket;\n\t\tit=tr.erase(it);\n\t\tzero(it->multiplier);\n\t\t}\n\n\treturn;\n\t}\n\nvoid Algorithm::pushup_multiplier(iterator it)\n\t{\n\tif(!tr.is_valid(it)) return;\n\tif(*it->multiplier!=1) {\n\t\tif(*it->name==\"\\\\sum\") {\n\t\t\t//\t\t\ttxtout << \"SUM\" << std::endl;\n\t\t\tsibling_iterator sib=tr.begin(it);\n\t\t\twhile(sib!=tr.end(it)) {\n\t\t\t\tmultiply(sib->multiplier, *it->multiplier);\n\t\t\t\t//\t\t\t\ttxtout << \"going up\" << std::endl;\n\t\t\t\tif(tr.is_head(it)==false)\n\t\t\t\t\tpushup_multiplier(tr.parent(it));\n\t\t\t\t//\t\t\t\ttxtout << \"back and back up\" << std::endl;\n\t\t\t\tpushup_multiplier(sib);\n\t\t\t\t//\t\t\t\ttxtout << \"back\" << std::endl;\n\t\t\t\t++sib;\n\t\t\t\t}\n\t\t\t::one(it->multiplier);\n\t\t\t}\n\t\telse {\n\t\t\t//\t\t\ttxtout << \"PUSHUP: \" << *it->name << std::endl;\n\t\t\tif(tr.is_head(it)==false) {\n\t\t\t\t//\t\t\t\ttxtout << \"test propinherit\" << std::endl;\n\t\t\t\t//\t\t\t\titerator tmp=tr.parent(it);\n\t\t\t\t// tmp not always valid?!? This one crashes hard with a loop!?!\n\t\t\t\t//\t\t\t\ttxtout << \" of \" << *tmp->name << std::endl;\n\t\t\t\tconst PropertyInherit *pin=kernel.properties.get<PropertyInherit>(tr.parent(it));\n\t\t\t\tif(pin || *(tr.parent(it)->name)==\"\\\\prod\") {\n\t\t\t\t\tmultiply(tr.parent(it)->multiplier, *it->multiplier);\n\t\t\t\t\t::one(it->multiplier); // moved up, was at end of block, correct?\n\t\t\t\t\t//\t\t\t\t\ttxtout << \"going up\" << std::endl;\n\t\t\t\t\tpushup_multiplier(tr.parent(it));\n\t\t\t\t\t//\t\t\t\t\ttxtout << \"back\" << std::endl;\n\t\t\t\t\t}\n\t\t\t\t//\t\t\t\telse txtout << \"not relevant\" << std::endl;\n\t\t\t\t}\n\t\t\t}\n\t\t}\n\t}\n\nvoid Algorithm::node_zero(iterator it)\n\t{\n\t::zero(it->multiplier);\n\ttr.erase_children(it);\n\tit->name=name_set.insert(\"1\").first;\n\t}\n\nvoid Algorithm::node_one(iterator it)\n\t{\n\t::one(it->multiplier);\n\ttr.erase_children(it);\n\tit->name=name_set.insert(\"1\").first;\n\t}\n\nvoid Algorithm::node_integer(iterator it, int num)\n\t{\n\t::one(it->multiplier);\n\ttr.erase_children(it);\n\tit->name=name_set.insert(\"1\").first;\n\t::multiply(it->multiplier, num);\n\t}\n\n// int Algorithm::index_parity(iterator it) const\n// \t{\n// \tsibling_iterator frst=tr.begin(tr.parent(it));\n// \tsibling_iterator fnd(it);\n// \tint sgn=1;\n// \twhile(frst!=fnd) {\n// \t\tsgn=-sgn;\n// \t\t++frst;\n// \t\t}\n// \treturn sgn;\n// \t}\n// \n\nunsigned int Algorithm::number_of_indices(iterator it)\n\t{\n\tunsigned int res=0;\n\tindex_iterator indit=begin_index(it);\n\twhile(indit!=end_index(it)) {\n\t\t++res;\n\t\t++indit;\n\t\t}\n\treturn res;\n\t}\n\nstd::string Algorithm::get_index_set_name(iterator it) const\n\t{\n\tconst Indices *ind=kernel.properties.get<Indices>(it, true);\n\tif(ind) {\n\t\treturn ind->set_name;\n\t\t// TODO: The logic was once as below, but it is no longer clear to\n\t\t// me why that would ever make sense.\n\t\t//\t\tif(ind->parent_name!=\"\") return ind->parent_name;\n\t\t//\t\telse                     return ind->set_name;\n\t\t}\n\telse return \" undeclared\";\n\t}\n\nindex_iterator Algorithm::begin_index(iterator it) const\n\t{\n\treturn index_iterator::begin(kernel.properties, it);\n\t}\n\nindex_iterator Algorithm::end_index(iterator it) const\n\t{\n\treturn index_iterator::end(kernel.properties, it);\n\t}\n\n\n\n\nbool Algorithm::check_index_consistency(iterator it) const\n\t{\n\tIndexClassifier ic(kernel);\n\t\n\tIndexClassifier::index_map_t ind_free, ind_dummy;\n\tic.classify_indices(it,ind_free,ind_dummy);\n\treturn true;\n\t}\n\nbool Algorithm::check_degree_consistency(iterator ) const\n\t{\n\treturn true; // FIXME: this needs to be implemented.\n\t}\n\nbool Algorithm::check_consistency(iterator it) const\n\t{\n\tStopwatch w1;\n\tw1.start();\n\t//\tdebugout << \"checking consistency ... \" << std::flush;\n\tassert(tr.is_head(it)==false);\n\t//\titerator entry=it;\n\titerator end=it;\n\tend.skip_children();\n\t++end;\n\twhile(it!=end) {\n\t\tif(interrupted)\n\t\t\tthrow InterruptionException(\"check_consistency\");\n\n\t\tif(*it->name==\"\\\\sum\") {\n\t\t\tif(*it->multiplier!=1)\n\t\t\t\tthrow ConsistencyException(\"Found \\\\sum node with non-unit multiplier.\");\n\t\t\telse if(Ex::number_of_children(it)<2)\n\t\t\t\tthrow ConsistencyException(\"Found a \\\\sum node with 0 or 1 child nodes.\");\n\t\t\telse {\n\t\t\t\tsibling_iterator sumch=it.begin();\n\t\t\t\tstr_node::bracket_t firstbracket=sumch->fl.bracket;\n\t\t\t\twhile(*sumch->name==\"\\\\sum\" || *sumch->name==\"\\\\prod\") {\n\t\t\t\t\t++sumch;\n\t\t\t\t\tif(sumch==it.end()) break;\n\t\t\t\t\telse                  firstbracket=sumch->fl.bracket;\n\t\t\t\t\t}\n\t\t\t\tsumch=it.begin();\n\t\t\t\twhile(sumch!=it.end()) {\n\t\t\t\t\tif(*sumch->name!=\"\\\\sum\" && *sumch->name!=\"\\\\prod\") {\n\t\t\t\t\t\tif(sumch->fl.bracket!=firstbracket)\n\t\t\t\t\t\t\tthrow ConsistencyException(\"Found a \\\\sum node with different brackets on its children.\");\n\t\t\t\t\t\t}\n\t\t\t\t\t//\t\t\t\t\telse if(*sumch->name==\"\\\\sum\") {\n\t\t\t\t\t//\t\t\t\t\t\tsibling_iterator sumchch=sumch.begin();\n\t\t\t\t\t//\t\t\t\t\t\twhile(sumchch!=sumch.end()) {\n\t\t\t\t\t//\t\t\t\t\t\t\tif(sumchch->fl.bracket==str_node::b_none) {\n\t\t\t\t\t//\t\t\t\t\t\t\t\ttr.print_recursive_treeform(debugout, entry);\n\t\t\t\t\t//\t\t\t\t\t\t\t\tthrow ConsistencyException(\"Found a sum node with \\\\sum child without bracketed children.\");\n\t\t\t\t\t//\t\t\t\t\t\t\t\t}\n\t\t\t\t\t//\t\t\t\t\t\t\t++sumchch;\n\t\t\t\t\t//\t\t\t\t\t\t\t}\n\t\t\t\t\t//\t\t\t\t\t\t}\n\t\t\t\t\t++sumch;\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t}\n\t\telse if(*it->name==\"\\\\prod\") {\n\t\t\tif(Ex::number_of_children(it)<=1)\n\t\t\t\tthrow ConsistencyException(\"Found \\\\prod node with only 0 or 1 children.\");\n\t\t\tsibling_iterator ch=it.begin();\n\t\t\tstr_node::bracket_t firstbracket=ch->fl.bracket;\n\t\t\twhile(*ch->name==\"\\\\sum\" || *ch->name==\"\\\\prod\") {\n\t\t\t\t++ch;\n\t\t\t\tif(ch==it.end())   break;\n\t\t\t\telse               firstbracket=ch->fl.bracket;\n\t\t\t\t}\n\t\t\tch=it.begin();\n\t\t\twhile(ch!=it.end()) {\n\t\t\t\tif(*ch->name!=\"\\\\prod\" && *ch->name!=\"\\\\sum\") {\n\t\t\t\t\tif(ch->fl.bracket!=firstbracket)\n\t\t\t\t\t\tthrow ConsistencyException(\"Found \\\\prod node with different brackets on its children.\");\n\t\t\t\t\t}\n\t\t\t\tif(*ch->multiplier!=1) {\n\t\t\t\t\tthrow ConsistencyException(\"Found \\\\prod child with non-unit multiplier.\");\n\t\t\t\t\t//\t\t\t\t\tdebugout << \"node name \" << *ch->name << \", multiplier \" << *ch->multiplier << std::endl;\n\t\t\t\t\t//\t\t\t\t\tinconsistent=true;\n\t\t\t\t\t//\t\t\t\t\tbreak;\n\t\t\t\t\t}\n\t\t\t\t++ch;\n\t\t\t\t}\n\t\t\t}\n\t\telse if(*it->name==\"\\\\sequence\") {\n\t\t\tif(Ex::number_of_children(it)!=2)\n\t\t\t\tthrow ConsistencyException(\"Found \\\\sequence node with incorrect (non-2) number of children.\");\n\t\t\t}\n\t\t++it;\n\t\t}\n\n\tw1.stop();\n\t//\tdebugout << \"checking done...\" << w1 << std::endl;\n\treturn true;\n\t}\n\nvoid Algorithm::report_progress(const std::string&, int, int, int count)\n\t{\n//\tbool display=false;\n//\tif(count==2) display=true;\n//\telse {\n//\t\tif(report_progress_stopwatch.stopped()) {\n//\t\t\tdisplay=true;\n//\t\t\treport_progress_stopwatch.start();\n//\t\t\t}\n//\t\telse {\n//\t\t\tif(report_progress_stopwatch.seconds()>0 || report_progress_stopwatch.useconds()>300000L) {\n//\t\t\t\tdisplay=true;\n//\t\t\t\treport_progress_stopwatch.reset();\n//\t\t\t\t}\n//\t\t\t}\n//\t\t}\n\n\t//\tif(display) { // prevents updates at a rate of more than one per second\n\t//\t\tif(eo->output_format==Ex_output::out_xcadabra) {\n\t//\t\t\ttxtout << \"<progress>\" << std::endl\n\t//\t\t\t\t\t << str << std::endl\n\t//\t\t\t\t\t << todo << std::endl\n\t//\t\t\t\t\t << done << std::endl\n\t//\t\t\t\t\t << count << std::endl\n\t//\t\t\t\t\t << \"</progress>\" << std::endl;\n\t//\t\t\t}\n\t//\t\telse {\n\t//\t\t\tif(count==2)\n\t//\t\t\t\ttxtout << str << \" (\" << done << \" of \" << todo << \" completed)\" << std::endl;\n\t//\t\t\t}\n\t//\t\t}\n\t}\n\nbool Algorithm::rename_replacement_dummies(iterator two, bool still_inside_algo)\n\t{\n#ifdef DEBUG\n\tstd::cerr << \"renaming in \" << two << std::endl;\n#endif\n\t//\tstd::cout << \"full story \" << *two->name << std::endl;\n\t//\tprint_classify_indices(two);\n\t//\tstd::cout << \"replacement\" << std::endl;\n\t//\tprint_classify_indices(std::cout, two);\n\n\tIndexClassifier ic(kernel);\n\tIndexClassifier::index_map_t ind_free, ind_dummy;\n\tIndexClassifier::index_map_t ind_free_full, ind_dummy_full;\n\n\tif(false && still_inside_algo) {\n\t\tif(tr.is_head(two)==false)\n\t\t\tic.classify_indices_up(tr.parent(two), ind_free_full, ind_dummy_full);\n\t\t}\n\telse {\n\t\tic.classify_indices_up(two, ind_free_full, ind_dummy_full); // the indices in everything except the replacement\n\t\t}\n\tic.classify_indices(two, ind_free, ind_dummy); // the indices in the replacement subtree\n#ifdef DEBUG\n\tstd::cerr << \"dummies of \" << *two->name << std::endl;\n\tfor(auto& ii: ind_dummy)\n\t\tstd::cerr << ii.first << std::endl;\n\tstd::cerr << \"free indices above us\" << std::endl;\n\tfor(auto& ii: ind_free_full)\n\t\tstd::cerr << ii.first << std::endl;\n\tstd::cerr << \"dummy indices above us\" << std::endl;\n\tfor(auto& ii: ind_dummy_full)\n\t\tstd::cerr << ii.first << std::endl;\n#endif\n\n\tIndexClassifier::index_map_t must_be_empty;\n\tIndexClassifier::index_map_t newly_generated;\n\n\t// Catch double index pairs\n\tic.determine_intersection(ind_dummy_full, ind_dummy, must_be_empty);\n\tIndexClassifier::index_map_t::iterator it=must_be_empty.begin();\n\twhile(it!=must_be_empty.end()) {\n#ifdef DEBUG\n\t\tstd::cerr << \"double index pair\" << std::endl;\n#endif\n\t\tEx the_key=(*it).first;\n\t\tconst Indices *dums=kernel.properties.get<Indices>(it->second, true);\n\t\tif(!dums)\n\t\t\tthrow ConsistencyException(\"Failed to find dummy property for $\"+*it->second->name+\"$ while renaming dummies.\");\n\t\t//\t\t\ttxtout << \"failed to find dummy property for \" << *it->second->name << std::endl;\n\t\tassert(dums);\n\t\tEx relabel\n\t\t   =ic.get_dummy(dums, &ind_dummy_full, &ind_dummy, &ind_free_full, &ind_free, &newly_generated);\n\t\tnewly_generated.insert(IndexClassifier::index_map_t::value_type(Ex(relabel),(*it).second));\n\t\t//\t\ttxtout << \" renamed to \" << *relabel << std::endl;\n\t\tdo {\n\t\t\ttr.replace_index((*it).second, relabel.begin(), true);\n\t\t\t//\t\t\t(*it).second->name=relabel;\n\t\t\t++it;\n\t\t\t}\n\t\twhile(it!=must_be_empty.end() && tree_exact_equal(&kernel.properties, (*it).first,the_key, 1, true, -2, true));\n\t\t}\n\n\t// Catch triple indices (two cases: dummy pair in replacement, free index elsewhere and\n\t// dummy elsewhere, free index in replacement)\n\tmust_be_empty.clear();\n\t//\tnewly_generated.clear(); // DO NOT ERASE, IDIOT!\n\n\tic.determine_intersection(ind_free_full, ind_dummy, must_be_empty);\n\t//for(auto& ii: must_be_empty) {\n\t//\tstd::cerr << ii.first << std::endl;\n\t//\t}\n\tit=must_be_empty.begin();\n\twhile(it!=must_be_empty.end()) {\n\t\t//std::cerr << \"triple index pair \" << it->first << std::endl;\n\t\tEx the_key=(*it).first;\n\t\tconst Indices *dums=kernel.properties.get<Indices>(it->second, true);\n\t\tif(!dums)\n\t\t\tthrow ConsistencyException(\"Failed to find dummy property for $\"+*it->second->name+\"$ while renaming dummies.\");\n\t\tassert(dums);\n\t\tEx relabel\n\t\t   =ic.get_dummy(dums, &ind_dummy_full, &ind_dummy, &ind_free_full, &ind_free, &newly_generated);\n\t\trelabel.begin()->fl.parent_rel=it->second->fl.parent_rel;\n\t\tnewly_generated.insert(IndexClassifier::index_map_t::value_type(relabel,(*it).second));\n\t\tdo {\n\t\t\ttr.replace_index((*it).second, relabel.begin(), true);\n\t\t\t++it;\n\t\t\t}\n\t\twhile(it!=must_be_empty.end() && tree_exact_equal(&kernel.properties, (*it).first,the_key, 1, true, -2, true));\n\t\t}\n\n\tmust_be_empty.clear();\n\t//\tnewly_generated.clear();\n\tic.determine_intersection(ind_free, ind_dummy_full, must_be_empty);\n\tit=must_be_empty.begin();\n\twhile(it!=must_be_empty.end()) {\n\t\t// std::cerr << \"triple index pair 2\" << std::endl;\n\t\tEx the_key=(*it).first;\n\t\tconst Indices *dums=kernel.properties.get<Indices>(it->second, true);\n\t\tif(!dums)\n\t\t\tthrow ConsistencyException(\"Failed to find dummy property for $\"+*it->second->name+\"$ while renaming dummies.\");\n\t\tassert(dums);\n\t\tEx relabel\n\t\t   =ic.get_dummy(dums, &ind_dummy_full, &ind_dummy, &ind_free_full, &ind_free, &newly_generated);\n\t\trelabel.begin()->fl.parent_rel=it->second->fl.parent_rel;\n\t\tnewly_generated.insert(IndexClassifier::index_map_t::value_type(relabel,(*it).second));\n\t\tdo {\n\t\t\ttr.replace_index((*it).second, relabel.begin(), true);\n\t\t\t++it;\n\t\t\t}\n\t\twhile(it!=must_be_empty.end() && tree_exact_equal(&kernel.properties, (*it).first,the_key, 1, true, -2, true));\n\t\t}\n\n\treturn true;\n\t}\n\n\n\nbool Algorithm::contains(sibling_iterator from, sibling_iterator to, sibling_iterator arg)\n\t{\n\twhile(from!=to) {\n\t\tif(from->name==arg->name) return true;\n\t\t++from;\n\t\t}\n\treturn false;\n\t}\n\nAlgorithm::range_vector_t::iterator Algorithm::find_arg_superset(range_vector_t& ran,\n      sibling_iterator it)\n\t{\n\tsibling_iterator nxt=it;\n\t++nxt;\n\treturn find_arg_superset(ran, it, nxt);\n\t}\n\n//void Algorithm::find_argument_lists(range_vector_t& ran, bool only_comma_lists) const\n//\t{\n//\tsibling_iterator argit=args_begin();\n//\twhile(argit!=args_end()) {\n//\t\tif(*argit->name==\"\\\\comma\") {\n//\t\t\tran.push_back(range_t(tr.begin(argit), tr.end(argit)));\n//\t\t\t}\n//\t\telse if(!only_comma_lists) {\n//\t\t\tsibling_iterator argnxt=argit; ++argnxt;\n//\t\t\tran.push_back(range_t(argit, argnxt));\n//\t\t\t}\n//\t\t++argit;\n//\t\t}\n//\t}\n\ntemplate<class Iter>\nAlgorithm::range_vector_t::iterator Algorithm::find_arg_superset(range_vector_t& ran, Iter st, Iter nd)\n\t{\n\trange_vector_t::iterator ranit=ran.begin();\n\twhile(ranit!=ran.end()) {\n\t\tsibling_iterator findthese=st;\n\t\tbool contained=true;\n\t\twhile(findthese!=nd) {\n\t\t\tif(contains((*ranit).first, (*ranit).second, findthese)) {\n\t\t\t\t++findthese;\n\t\t\t\t}\n\t\t\telse {\n\t\t\t\tcontained=false;\n\t\t\t\tbreak;\n\t\t\t\t}\n\t\t\t}\n\t\tif(contained) return ranit;\n\t\t++ranit;\n\t\t}\n\treturn ran.end();\n\t}\n\nbool Algorithm::is_termlike(iterator it)\n\t{\n\tif(*it->name==\"\\\\equals\") return false;\n\n\tif(!is_factorlike(it))\n\t\tif(*it->name!=\"\\\\sum\")\n\t\t\tif(it->fl.parent_rel==str_node::p_none)\n\t\t\t\treturn true;\n\n\treturn false;\n\t}\n\nbool Algorithm::is_factorlike(iterator it)\n\t{\n\tif(Ex::is_head(it)) return false;\n\tif(*Ex::parent(it)->name==\"\\\\prod\")\n\t\treturn true;\n\treturn false;\n\t}\n\nbool Algorithm::is_noncommuting(const Properties& properties, iterator it)\n\t{\n\tauto nc = properties.get<NonCommuting>(it);\n\tif(nc) return true;\n\n\tauto ac = properties.get<AntiCommuting>(it);\n\tif(ac) return true;\n\t\n\tauto snc = properties.get<SelfNonCommuting>(it);\n\tif(snc) return true;\n\t\n\tauto sac = properties.get<SelfAntiCommuting>(it);\n\tif(sac) return true;\n\n\treturn false;\n\t}\n\nbool Algorithm::separated_by_derivative(iterator i1, iterator i2, iterator check_dependence) const\n\t{\n\titerator lca = tr.lowest_common_ancestor(i1, i2);\n\n\t// Walk up the tree from the first node until the LCA, flag any derivatives\n\t// with which we do not commute.\n\n\tstruct {\n\t\tbool operator()(const Kernel& kernel, Ex& tr, iterator walk, iterator lca, iterator check_dependence)\n\t\t\t{\n\t\t\tconst Properties& pr=kernel.properties;\n\t\t\tdo {\n\t\t\t\twalk=Ex::parent(walk);\n\t\t\t\tif(walk == lca) break;\n\t\t\t\tconst Derivative *der=pr.get<Derivative>(walk);\n\t\t\t\tif(der) {\n\t\t\t\t\tif(tr.is_valid(check_dependence) ) {\n\t\t\t\t\t\tconst DependsBase *dep = pr.get<DependsBase>(check_dependence);\n\t\t\t\t\t\tif(dep) {\n\t\t\t\t\t\t\tEx deps=dep->dependencies(kernel, check_dependence);\n\t\t\t\t\t\t\tsibling_iterator depobjs=deps.begin(deps.begin());\n\t\t\t\t\t\t\twhile(depobjs!=deps.end(deps.begin())) {\n\t\t\t\t\t\t\t\tif(walk->name == depobjs->name) {\n\t\t\t\t\t\t\t\t\treturn true;\n\t\t\t\t\t\t\t\t\t}\n\t\t\t\t\t\t\t\telse {\n\t\t\t\t\t\t\t\t\t// compare all indices\n\t\t\t\t\t\t\t\t\tsibling_iterator indit=tr.begin(walk);\n\t\t\t\t\t\t\t\t\twhile(indit!=tr.end(walk)) {\n\t\t\t\t\t\t\t\t\t\tif(indit->is_index()) {\n\t\t\t\t\t\t\t\t\t\t\tif(subtree_exact_equal(&pr, indit, depobjs))\n\t\t\t\t\t\t\t\t\t\t\t\treturn true;\n\t\t\t\t\t\t\t\t\t\t\t}\n\t\t\t\t\t\t\t\t\t\t++indit;\n\t\t\t\t\t\t\t\t\t\t}\n\t\t\t\t\t\t\t\t\t}\n\t\t\t\t\t\t\t\t++depobjs;\n\t\t\t\t\t\t\t\t}\n\t\t\t\t\t\t\treturn false; // Dependence found but not relevant here.\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\telse return false;   // No dependence property found at all.\n\t\t\t\t\t\t}\n\t\t\t\t\telse return true;   // Should not check for dependence.\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\twhile(walk != lca);\n\t\t\treturn false;\n\t\t\t}\n\t\t} one_run;\n\n\tif(one_run(kernel, tr, i1, lca, check_dependence)) return true;\n\tif(one_run(kernel, tr, i2, lca, check_dependence)) return true;\n\n\treturn false;\n\t}\n\n\n// bool Algorithm::cleanup_anomalous_products(Ex& tr, Ex::iterator& it)\n// \t{\n// \tif(*(it->name)==\"\\\\prod\") {\n// \t\t if(tr.number_of_children(it)==0) {\n// \t\t\t  it->name=name_set.insert(\"1\").first;\n// \t\t\t  return true;\n// \t\t\t  }\n// \t\t else if(tr.number_of_children(it)==1) {\n// \t\t\t  tr.begin(it)->fl.bracket=it->fl.bracket;\n// \t\t\t  tr.begin(it)->multiplier=it->multiplier;\n// \t\t\t  tr.flatten(it);\n// \t\t\t  Ex::iterator tmp=tr.erase(it);\n// //\t\t\t  txtout << \"HERRE?\" << std::endl;\n// \t\t\t  pushup_multiplier(tmp);\n// \t\t\t  it=tmp;\n// \t\t\t  return true;\n// \t\t\t  }\n// \t\t }\n// \treturn false;\n// \t}\n//\n\nunsigned int Algorithm::locate_single_object(Ex::iterator obj_to_find,\n      Ex::iterator st, Ex::iterator nd,\n      std::vector<unsigned int>& store)\n\t{\n\tunsigned int count=0;\n\tunsigned int index=0;\n\twhile(st!=nd) {\n\t\tEx::iterator it1=st;\n\t\tit1.skip_children();\n\t\t++it1;\n\t\tif(tr.equal(st, it1, obj_to_find, Algorithm::compare_)) {\n\t\t\t++count;\n\t\t\tstore.push_back(index);\n\t\t\t}\n\t\t++st;\n\t\t++index;\n\t\t}\n\treturn count;\n\t}\n\nbool Algorithm::locate_object_set(const Ex& objs,\n                                  Ex::iterator st, Ex::iterator nd,\n                                  std::vector<unsigned int>& store)\n\t{\n\t// Locate the objects in which to symmetrise. We use an integer\n\t// index (offset wrt. 'st') rather than an iterator because the\n\t// latter only apply to a single tree, not to its copies.\n\n\t// We accept only a tree with a \\comma node at the top.\n\tEx::iterator top=objs.begin();\n\tif(*top->name!=\"\\\\comma\")\n\t\ttop = objs.begin(objs.begin());\n\n\tassert(*top->name==\"\\\\comma\");\n\n\tEx::sibling_iterator fst=objs.begin(top);\n\tEx::sibling_iterator fnd=objs.end(top);\n\twhile(fst!=fnd) {\n\t\tEx::iterator aim=fst;\n\t\tif((*aim->name)==\"\\\\comma\") {\n\t\t\t// Objects can themselves be lists of other objects (for instance\n\t\t\t// when we want to symmetrise in index pairs).\n\t\t\tif(locate_object_set(Ex(aim), st, nd, store)==false)\n\t\t\t\treturn false;\n\t\t\t}\n\t\telse {\n\t\t\tif((*aim->name).size()==0 && tr.number_of_children(aim)==1)\n\t\t\t\taim=tr.begin(aim);\n\t\t\tif(locate_single_object(aim, st, nd, store)!=1)\n\t\t\t\treturn false;\n\t\t\t}\n\t\t++fst;\n\t\t}\n\treturn true;\n\t}\n\nbool Algorithm::derivative_acts_on(iterator it) const\n\t{\n\tif(tr.is_head(it)) return false;\n\tconst auto *pd = kernel.properties.get<PartialDerivative>(tr.parent(it));\n\tif(pd) return true;\n\n\treturn false;\n\t}\n\nstd::set<Ex, tree_exact_less_obj> Algorithm::dependencies(iterator it, bool include_derivatives_of) const\n\t{\n\ttree_exact_less_obj comp(&kernel.properties);\n\tstd::set<Ex, tree_exact_less_obj> ret(comp);\n\n\t// Is this node a coordinate itself? If so, add it.\n\tconst Coordinate *cd = kernel.properties.get<Coordinate>(it, true);\n\tif(cd) {\n\t\tif(include_derivatives_of || derivative_acts_on(it)==false) {\n\t\t\tEx cpy(it);\n\t\t\tcpy.begin()->fl.bracket=str_node::b_none;\n\t\t\tcpy.begin()->fl.parent_rel=str_node::p_none;\n\t\t\tone(cpy.begin()->multiplier);\n\t\t\tret.insert(cpy);\n\t\t\t}\n\t\t}\n\n\t// Determine explicit dependence on Coordinates, that is, collect\n\t// parent_rel=p_none arguments, and add them directly if they\n\t// carry a Coordinate property, or run the algorithm recursively\n\t// if not (to catch e.g. exp(F(r)) depending on 'r'.\n\n\tcadabra::do_subtree(tr, it, [&](Ex::iterator nd) -> Ex::iterator {\n\t\tif(nd==it) return nd; // skip node itself, leads to indefinite recursion\n\t\tif(nd->fl.parent_rel==str_node::p_none)\n\t\t\t{\n\t\t\tconst Coordinate *cd = kernel.properties.get<Coordinate>(nd, true);\n\t\t\tif(cd) {\n\t\t\t\tif(include_derivatives_of || derivative_acts_on(nd)==false) {\n\t\t\t\t\tEx cpy(nd);\n\t\t\t\t\tcpy.begin()->fl.bracket=str_node::b_none;\n\t\t\t\t\tcpy.begin()->fl.parent_rel=str_node::p_none;\n\t\t\t\t\tone(cpy.begin()->multiplier);\n\t\t\t\t\tret.insert(cpy);\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\telse {\n\t\t\t\tauto arg_deps=dependencies(nd);\n\t\t\t\tif(arg_deps.size()>0)\n\t\t\t\t\tfor(const auto& new_dep: arg_deps)\n\t\t\t\t\t\tret.insert(new_dep);\n\t\t\t\t}\n\t\t\t}\n\t\treturn nd;\n\t\t});\n\n\t// Determine implicit dependence via Depends.\n#ifdef DEBUG\n\tstd::cerr << \"deps for \" << Ex(it) << std::endl;\n#endif\n\n\tconst DependsBase *dep = kernel.properties.get<DependsBase>(it, true);\n\tif(dep) {\n#ifdef DEBUG\n\t\tstd::cerr << \"implicit deps\" << std::endl;\n#endif\n\t\tEx deps(dep->dependencies(kernel, it));\n\t\tcadabra::do_list(deps, deps.begin(), [&](Ex::iterator nd) {\n\t\t\tif(include_derivatives_of || derivative_acts_on(nd)==false) {\n\t\t\t\tEx cpy(nd);\n\t\t\t\tcpy.begin()->fl.bracket=str_node::b_none;\n\t\t\t\tcpy.begin()->fl.parent_rel=str_node::p_none;\n\t\t\t\tret.insert(cpy);\n\t\t\t\t}\n\t\t\treturn true;\n\t\t\t});\n#ifdef DEBUG\n\t\tfor(auto& e: ret)\n\t\t\tstd::cerr << e << std::endl;\n#endif\n\t\t}\n\n\treturn ret;\n\t}\n\n\nnamespace cadabra {\n\n\t// static functions\n\n\tunsigned int Algorithm::number_of_indices(const Properties& pr, iterator it)\n\t\t{\n\t\tunsigned int res=0;\n\t\tindex_iterator indit=index_iterator::begin(pr, it);\n\t\twhile(indit!=index_iterator::end(pr, it)) {\n\t\t\t++res;\n\t\t\t++indit;\n\t\t\t}\n\t\treturn res;\n\t\t}\n\n\tunsigned int Algorithm::number_of_direct_indices(iterator it)\n\t\t{\n\t\tunsigned int res=0;\n\t\tsibling_iterator sib=Ex::begin(it);\n\t\twhile(sib!=Ex::end(it)) {\n\t\t\tif(sib->fl.parent_rel==str_node::p_sub || sib->fl.parent_rel==str_node::p_super)\n\t\t\t\t++res;\n\t\t\t++sib;\n\t\t\t}\n\t\treturn res;\n\t\t}\n\n//\tbool Algorithm::less_without_numbers(nset_t::iterator it1, nset_t::iterator it2)\n//\t\t{\n//\t\tstd::string::const_iterator ch1=(*it1).begin();\n//\t\tstd::string::const_iterator ch2=(*it2).begin();\n//\n//\t\twhile(ch1!=(*it1).end() && ch2!=(*it2).end()) {\n//\t\t\tif(isdigit(*ch1)) return true;   // bla1  < blaq\n//\t\t\tif(isdigit(*ch2)) return false;  // blaa !< bla1\n//\t\t\tif(*ch1>=*ch2)    return false;\n//\t\t\t++ch1;\n//\t\t\t++ch2;\n//\t\t\t}\n//\t\tif(ch1==(*it1).end()) {\n//\t\t\tif(ch2==(*it2).end())\n//\t\t\t\treturn false;\n//\t\t\telse\n//\t\t\t\treturn true;\n//\t\t\t}\n//\t\treturn false;\n//\t\t}\n//\n//\tbool Algorithm::equal_without_numbers(nset_t::iterator it1, nset_t::iterator it2)\n//\t\t{\n//\t\tstd::string::const_iterator ch1=(*it1).begin();\n//\t\tstd::string::const_iterator ch2=(*it2).begin();\n//\n//\t\twhile(ch1!=(*it1).end() && ch2!=(*it2).end()) {\n//\t\t\tif(isdigit(*ch1)) {\n//\t\t\t\tif(isdigit(*ch2))\n//\t\t\t\t\treturn true;\n//\t\t\t\telse\n//\t\t\t\t\treturn false;\n//\t\t\t\t}\n//\t\t\tif(*ch1!=*ch2) return false;\n//\t\t\t++ch1;\n//\t\t\t++ch2;\n//\t\t\t}\n//\t\tif(ch1==(*it1).end()) {\n//\t\t\tif(ch2==(*it2).end())\n//\t\t\t\treturn true;\n//\t\t\telse\n//\t\t\t\treturn false;\n//\t\t\t}\n//\t\treturn false;\n//\t\t}\n\n\tbool Algorithm::compare_(const str_node& one, const str_node& two)\n\t\t{\n\t\t// If the obj->name is empty, this means that we look for a tree with\n\t\t// anything as root, but the required index structure in obj.  This\n\t\t// requires a slightly different 'equal_to' (one that always matches\n\t\t// an empty node with a non-empty node).\n\n\t\tif(/* one.fl.bracket!=two.fl.bracket || */ one.fl.parent_rel!=two.fl.parent_rel)\n\t\t\treturn false;\n\n\t\tif((*two.name).size()==0)\n\t\t\treturn true;\n\t\telse if(one.name==two.name)\n\t\t\treturn true;\n\t\treturn false;\n\t\t}\n\n\t}\n"
  },
  {
    "path": "core/Algorithm.hh",
    "content": "/*\n\nCadabra: a field-theory motivated computer algebra system.\nCopyright (C) 2001-2014  Kasper Peeters <kasper.peeters@phi-sci.com>\n\nThis program is free software: you can redistribute it and/or\n\tmodify it under the terms of the GNU General Public License as\npublished by the Free Software Foundation, either version 3 of the\nLicense, or (at your option) any later version.\n\nThis program is distributed in the hope that it will be useful,\nbut WITHOUT ANY WARRANTY; without even the implied warranty of\nMERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU\nGeneral Public License for more details.\n\nYou should have received a copy of the GNU General Public License\nalong with this program.  If not, see <http://www.gnu.org/licenses/>.\n\n*/\n\n#pragma once\n\n#include \"Stopwatch.hh\"\n#include \"Storage.hh\"\n#include \"Props.hh\"\n#include \"Kernel.hh\"\n#include \"IndexIterator.hh\"\n#include \"ProgressMonitor.hh\"\n#include \"ExManip.hh\"\n#include \"Compare.hh\"\n\nnamespace cadabra {\n\n\t/// \\ingroup core\n\t///\n\t/// Base class for all algorithms, containing generic routines and in\n\t/// particular the logic for index classification. Also contains static\n\t/// algorithms acting on Ex objects which require property\n\t/// information and can therefore not be a member of Ex.\n\t///\n\t/// In order to implement a new algorithm, subclass Algorithm and\n\t/// implement the abstract members Algorithm::can_apply and\n\t/// Algorithm::apply (see there for further documentation).  The\n\t/// general logic is that the implementation of\n\t/// Algorithm::apply(iterator&) is not allowed to make the node pointed\n\t/// at by the iterator invalid. If the algorithm makes the node vanish,\n\t/// it should indicate so by setting its multiplier to zero; the\n\t/// calling logic will then take care of cleaning up the subtree\n\t/// at the node.\n\t///\n\t/// The algorithm is, however, allowed to change the node itself or\n\t/// replace it with another one, as long as it updates the iterator.\n\n\tclass Algorithm : public ExManip /* , public IndexClassifier */ {\n\t\tpublic:\n\t\t\t/// Initialise the algorithm with a reference to the expression\n\t\t\t/// tree, but do not yet do anything with this tree. Algorithms\n\t\t\t/// are not typically allowed to mess with the settings in the\n\t\t\t/// Kernel, so it is passed const.\n\n\t\t\tAlgorithm(const Kernel&, Ex&);\n\t\t\tvirtual ~Algorithm();\n\n\t\t\ttypedef std::set<Ex, tree_exact_less_obj> Ex_set_t;\n\t\t\ttypedef Ex::result_t                      result_t;\n\n\t\t\tbool interrupted;\n\n\t\t\t/// Provide the algorithm with a ProgressMonitor object on which to register\n\t\t\t/// (nested) progress information, to be reported out-of-band to a client.\n\n\t\t\tvoid set_progress_monitor(ProgressMonitor *);\n\n\t\t\t/// The main entry points for running algorithms, which traverse\n\t\t\t/// the tree post-order ('child before parent'). The 'deep' flag\n\t\t\t/// indicates whether sub-expressions should be acted on\n\t\t\t/// too. The 'repeat' flag indicates whether the algorithm\n\t\t\t/// should be applied until the expression no longer\n\t\t\t/// changes. The 'depth' flag, if not equal to -1, indicates the\n\t\t\t/// depth in the tree where the algorithm should start applying.\n\n\t\t\tresult_t  apply_generic(bool deep=true, bool repeat=false, unsigned int depth=0);\n\t\t\tresult_t  apply_generic(iterator&, bool deep, bool repeat, unsigned int depth);\n\n\t\t\t/// Apply algorithm with alternative traversal: starting from\n\t\t\t/// the top node, traverse the tree pre-order ('parent before\n\t\t\t/// child') and once the algorithm acts at a given node, do not\n\t\t\t/// traverse the subtree below anymore.\n\n\t\t\tresult_t  apply_pre_order(bool repeat=false);\n\n\t\t\t// Global information\n\t\t\tunsigned int     number_of_calls;\n\t\t\tunsigned int     number_of_modifications;\n\t\t\tbool             suppress_normal_output;\n\t\t\tbool             discard_command_node;\n\n\t\t\t/// Given an expression top node, check index consistency.\n\t\t\tbool      check_consistency(iterator) const;\n\t\t\tbool      check_index_consistency(iterator) const;\n\t\t\t/// Given an expression top node, check differential form degree consistency.\n\t\t\tbool      check_degree_consistency(iterator) const;\n\n\t\t\tvoid report_progress(const std::string&, int todo, int done, int count=2);\n\n\t\t\tmutable Stopwatch index_sw;\n\t\t\tmutable Stopwatch get_dummy_sw;\n\t\t\tmutable Stopwatch report_progress_stopwatch;\n\n\t\t\tindex_iterator begin_index(iterator it) const;\n\t\t\tindex_iterator end_index(iterator it) const;\n\n\t\t\t// The number of indices of a node, taking into account IndexInherit-ance. These\n\t\t\t// indices do therefore not all have to be direct child nodes of 'it', they can\n\t\t\t// sit deeper down the tree.\n\t\t\tunsigned int number_of_indices(iterator it);\n\t\t\tstatic unsigned int number_of_indices(const Properties&, iterator it);\n\n\t\t\t// The number of indices of a node, counting only the direct ones (i.e. not those\n\t\t\t// inherited from child nodes).\n\t\t\tstatic unsigned int number_of_direct_indices(iterator it);\n\n\t\t\t// The set to which the first index belongs..\n\t\t\tstd::string get_index_set_name(iterator it) const;\n\n\t\t\t/// Rename the dummies in the sub-tree starting with head at the given iterator.\n\t\t\t/// Ensures that no dummies in this sub-tree overlap with the indices elsewhere\n\t\t\t/// in the tree.\t\t\t\n\t\t\tbool     rename_replacement_dummies(iterator, bool still_inside_algo=false);\n\n\t\t\t/// Determines whether the indicated node is 'like a term in a\n\t\t\t/// sum'.  This requires that the node is not a `\\sum` node, not\n\t\t\t/// a child of a `\\prod` node, and that its parent rel is of\n\t\t\t/// argument-type (p_none).\n\t\t\tstatic bool     is_termlike(iterator);\n\n\t\t\t/// Determines whether the indicated node is 'like a factor in a product'.\n\t\t\t/// This requires that the parent is a `\\prod' node.\n\t\t\tstatic bool     is_factorlike(iterator);\n\n\t\t\t/// Generic function to determine if there is any kind of non-commutativity\n\t\t\t/// associated to the given object. Useful as quick check for algorithms that\n\t\t\t/// do not (yet) handle non-commuting behaviour.\n\t\t\tstatic bool is_noncommuting(const Properties&, iterator);\n\n\t\t\t/// Determine all the Coordinate dependencies of the object at 'it'. If\n\t\t\t/// the flag is false, do not include derivatives of these coordinates\n\t\t\t/// (e.g. when coordinates are dependent on parameters and derivatives\n\t\t\t/// wrt. these parameters are present, do not include these as dependencies).\n\t\t\tEx_set_t dependencies(iterator it, bool include_derivatives_of=true) const;\n\n\t\t\t/// Is this a symbol on which a derivative acts?\n\t\t\tbool derivative_acts_on(iterator it) const;\n\t\t\t\n\t\tprotected:\n\t\t\tProgressMonitor *pm;\n\n\t\t\t// The main entry point which is used by the public entry points listed\n\t\t\t// above. Override these in any subclass.\n\t\t\t//\n\t\t\tvirtual bool can_apply(iterator)=0;\n\t\t\tvirtual result_t apply(iterator&)=0;\n\n\t\t\t// Index stuff\n\t\t\t// int      index_parity(iterator) const;\n\t\t\t// static bool less_without_numbers(nset_t::iterator, nset_t::iterator);\n\t\t\t// static bool equal_without_numbers(nset_t::iterator, nset_t::iterator);\n\n\t\t\t/// Finding objects in sets.\n\t\t\ttypedef std::pair<sibling_iterator, sibling_iterator> range_t;\n\t\t\ttypedef std::vector<range_t>                          range_vector_t;\n\n\t\t\tbool     contains(sibling_iterator from, sibling_iterator to, sibling_iterator arg);\n\t\t\tvoid     find_argument_lists(range_vector_t&, bool only_comma_lists=true) const;\n\t\t\ttemplate<class Iter>\n\t\t\trange_vector_t::iterator find_arg_superset(range_vector_t&, Iter st, Iter nd);\n\t\t\trange_vector_t::iterator find_arg_superset(range_vector_t&, sibling_iterator it);\n\n\t\t\t// Locate objects inside the tree (formerly in the 'locate' algorithm).\n\t\t\tunsigned int locate_single_object(Ex::iterator obj_to_find,\n\t\t\t                                  Ex::iterator st, Ex::iterator nd,\n\t\t\t                                  std::vector<unsigned int>& store);\n\t\t\tbool         locate_object_set(const Ex& objs,\n\t\t\t                               Ex::iterator st, Ex::iterator nd,\n\t\t\t                               std::vector<unsigned int>& store);\n\t\t\tstatic bool  compare_(const str_node&, const str_node&);\n\n\n\t\t\t/// Figure out whether two objects (commonly indices) are separated by a derivative\n\t\t\t/// operator, as in \\f[ \\partial_{a}{A_{b}} C^{b} \\f].\n\t\t\t/// If the last iterator is pointing to a valid node, check whether it is\n\t\t\t/// independent of the derivative (using the Depends property).\n\t\t\tbool     separated_by_derivative(iterator, iterator, iterator check_dependence) const;\n\n\t\t\t// Given a node with non-zero multiplier, distribute this\n\t\t\t// multiplier up the tree when the node is a \\sum node, or push it into the\n\t\t\t// `\\prod` node if that is the parent. Do this recursively\n\t\t\t// in case a child is a sum as well. Note that 'pushup' is actually 'pushdown'\n\t\t\t// in the case of sums.\n\t\t\t// This never changes the tree structure, only the distribution of multipliers.\n\n\t\t\t// FIXME: this is now superseded by code in Cleanup.cc, and the generic way\n\t\t\t// to make a tree consistent is to call cleanup_dispatch, not pick-and-match from\n\t\t\t// the various algorithms.\n\t\t\tvoid     pushup_multiplier(iterator);\n\n\t\t\t// Return the number of elements in the first range for which an identical element\n\t\t\t// is present in the second range.\n\t\t\ttemplate<class BinaryPredicate>\n\t\t\tunsigned int intersection_number(sibling_iterator, sibling_iterator,\n\t\t\t                                 sibling_iterator, sibling_iterator, BinaryPredicate) const;\n\n\t\t\t// Turn a node into a '1' or '0' node.\n\t\t\tvoid     node_zero(iterator);\n\t\t\tvoid     node_one(iterator);\n\t\t\tvoid     node_integer(iterator, int);\n\n\n\n\t\tprotected:\n\t\t\tbool traverse_ldots;\n\n\t\tprivate:\n\n\t\t\t// Single or deep-scan apply operations. Do not call directly.\n\t\t\tresult_t apply_once(Ex::iterator& it);\n\t\t\tresult_t apply_deep(Ex::iterator& it);\n\n\t\t\t/// Given a node with zero multiplier, propagate this zero\n\t\t\t/// upwards in the tree.  Changes the iterator so that it points\n\t\t\t/// to the next node in a post_order traversal (post_order:\n\t\t\t/// children first, then node). The second node is the topmost\n\t\t\t/// node, beyond which this routine is not allowed to touch the\n\t\t\t/// tree (i.e. the 2nd iterator will always remain valid).\n\t\t\tvoid     propagate_zeroes(post_order_iterator&, const iterator&);\n\n\t\t\t//\t\tbool cleanup_anomalous_products(Ex& tr, Ex::iterator& it);\n\t\t};\n\n\n\t/// Determine the number of elements in the first range which also occur in the\n\t/// second range.\n\ttemplate<class BinaryPredicate>\n\tunsigned int Algorithm::intersection_number(sibling_iterator from1, sibling_iterator to1,\n\t      sibling_iterator from2, sibling_iterator to2,\n\t      BinaryPredicate fun) const\n\t\t{\n\t\tunsigned int ret=0;\n\t\tsibling_iterator it1=from1;\n\t\twhile(it1!=to1) {\n\t\t\tsibling_iterator it2=from2;\n\t\t\twhile(it2!=to2) {\n\t\t\t\tif(fun(*it1,*it2))\n\t\t\t\t\t++ret;\n\t\t\t\t++it2;\n\t\t\t\t}\n\t\t\t++it1;\n\t\t\t}\n\t\treturn ret;\n\t\t}\n\n\n\t}\n"
  },
  {
    "path": "core/Bridge.cc",
    "content": "\n#include \"pythoncdb/py_ex.hh\"\n#include \"pythoncdb/py_helpers.hh\"\n#include \"Bridge.hh\"\n#include \"algorithms/collect_terms.hh\"\n#include \"Exceptions.hh\"\n\nusing namespace cadabra;\nnamespace py = pybind11;\n\nvoid pull_in(std::shared_ptr<Ex> ex, Kernel *kernel)\n\t{\n\tcollect_terms rr(*kernel, *ex);\n\n//\tbool acted=false;\n\tEx::iterator it=ex->begin();\n\twhile(it!=ex->end()) {\n\t\tif(*it->name==\"@\") {\n\t\t\tstd::string pobj = *(Ex::begin(it)->name);\n\t\t\tstd::shared_ptr<Ex> pull_ex = fetch_from_python(pobj);\n\t\t\tif(pull_ex) {\n//\t\t\t\tacted=true;\n\t\t\t\tmultiplier_t mult           = *(it->multiplier);\n\t\t\t\tstr_node::parent_rel_t prel = (it->fl.parent_rel);\n\t\t\t\tauto topnode_it   = pull_ex->begin();\n\t\t\t\tauto at_arg       = ex->begin(it);\n\n\t\t\t\tex->erase(at_arg);           // erase argument of @\n\t\t\t\tit=ex->replace(it, *(topnode_it));     // replace @ with head of ex\n\t\t\t\tif(ex->number_of_children(topnode_it)>0) {\n\t\t\t\t\tEx::sibling_iterator walk=ex->end(topnode_it);\n\t\t\t\t\tdo {\n\t\t\t\t\t\t--walk;\n\t\t\t\t\t\tex->prepend_child(it, (Ex::iterator)walk);\n\t\t\t\t\t\t}\n\t\t\t\t\twhile(walk!=ex->begin(topnode_it));\n\t\t\t\t\t}\n\t\t\t\t// FIXME: prepend_children is broken!\n\t\t\t\t//\t\t\t\tex->prepend_children(it, ex->begin(topnode_it), ex->end(topnode_it)); // add children of ex\n\t\t\t\tmultiply(it->multiplier, mult);\n\t\t\t\tit->fl.parent_rel=prel;\n\t\t\t\trr.rename_replacement_dummies(it, false);\n\t\t\t\t}\n//\t\t\telse {\n//\t\t\t\t// Perhaps this object is a float or int?\n//\t\t\t\tif(py::isinstance<py::int_>(pobj))\n//\t\t\t\t\tstd::cerr << \"it's a float!\" << std::endl;\n//\t\t\t\telse if(py::isinstance<py::float_>(pobj))\n//\t\t\t\t\tstd::cerr << \"it's an int!\" << std::endl;\n//\t\t\t\t}\n\t\t\t\n\t\t\tif(!pull_ex)\n\t\t\t\tthrow ArgumentException(\"Python object '\"+pobj+\"' does not exist.\");\n\t\t\t}\n\t\t++it;\n\t\t}\n\n\t//\tif(acted)\n\t//\t\tstd::cerr << \"pull_in done: \" << *ex << std::endl;\n\n\treturn;\n\t}\n\nvoid run_python_functions(std::shared_ptr<Ex> ex, Kernel *kernel)\n\t{\n\tif(kernel->call_embedded_python_functions==false)\n\t\treturn;\n\t\n\tEx::post_order_iterator it = ex->begin_post();\n\tauto locals=get_locals();\n\twhile(it!=ex->end_post()) {\n\t\tauto nxt=it;\n\t\t++nxt;\n\n\t\t// Do not call single-letter functions; assume those are\n\t\t// always mathematics, not python. Also do not even attempt\n\t\t// to call functions which start with a backslash (those\n\t\t// are TeX).\n\t\tif((*it->name).size()==1 || (*it->name)[0]=='\\\\') {\n\t\t\tit=nxt;\n\t\t\tcontinue;\n\t\t\t}\n\t\t\n\t\t// Only call functions if the cadabra symbols have one or\n\t\t// more child nodes which all have bracket_t::b_none.\n\t\tEx::sibling_iterator sib=ex->begin(it);\n\t\tif(sib==ex->end(it)) {\n\t\t\tit=nxt;\n\t\t\tcontinue;\n\t\t\t}\n\t\t\n\t\tbool cancall=true;\n\t\twhile(sib!=ex->end(it)) {\n\t\t\tif(sib->fl.parent_rel!=str_node::parent_rel_t::p_none) {\n\t\t\t\tcancall=false;\n\t\t\t\tbreak;\n\t\t\t\t}\n\t\t\t++sib;\n\t\t\t}\n\t\tif(!cancall) {\n\t\t\tit=nxt;\n\t\t\tcontinue;\n\t\t\t}\n\t\t\n\t\tif(scope_has(locals, *it->name)) {\n\t\t\t// std::cerr << \"can run function \" << *it->name << std::endl;\n\t\t\tpy::object fun=locals[(*it->name).c_str()];\n\t\t\tEx::sibling_iterator sib=ex->begin(it);\n\t\t\tpy::object res;\n\t\t\t\n\t\t\tif(sib!=ex->end(it)) {\n\t\t\t\tEx tmp1(sib);\n\t\t\t\t++sib;\n\t\t\t\tif(sib!=ex->end(it)) {\n\t\t\t\t\tEx tmp2(sib);\n\t\t\t\t\t++sib;\n\t\t\t\t\tif(sib!=ex->end(it)) {\n\t\t\t\t\t\tEx tmp3(sib);\n\t\t\t\t\t\tres = fun(tmp1, tmp2, tmp3);\n\t\t\t\t\t\t++sib;\n\t\t\t\t\t\tif(sib!=ex->end(it)) {\n\t\t\t\t\t\t\tthrow RuntimeException(\"Cannot yet call inline functions with more than 3 arguments.\");\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\t}\n\t\t\t\t\telse res = fun(tmp1, tmp2);\n\t\t\t\t\t}\n\t\t\t\telse res = fun(tmp1);\n\t\t\t\t}\n\t\t\telse res = fun();\n\t\t\t\n\t\t\tEx repl = res.cast<Ex>();\n\t\t\tEx::iterator tmpit=it;\n\t\t\trset_t::iterator mult=tmpit->multiplier;\n\t\t\tex->move_ontop(tmpit, repl.begin())->multiplier=mult;\n\t\t\t}\n\t\tit=nxt;\n\t\t}\n\t}\n"
  },
  {
    "path": "core/Bridge.hh",
    "content": "\n#pragma once\n\n#include \"Storage.hh\"\n#include \"Kernel.hh\"\n\n/// \\ingroup pythoncore\n///\n/// Replace any objects of the form '@(...)' in the expression tree by the\n/// python expression '...' if it exists. Rename dummies to avoid clashes.\n\nvoid pull_in(std::shared_ptr<cadabra::Ex> ex, cadabra::Kernel *);\n\n\n/// \\ingroup pythoncore\n///\n/// Run all functions in the given expression which are available \n/// in the Python scope.\n\nvoid run_python_functions(std::shared_ptr<cadabra::Ex> ex, cadabra::Kernel *);\n"
  },
  {
    "path": "core/CMakeLists.txt",
    "content": "# cmake_minimum_required(VERSION ${CADABRA_CMAKE_VERSION}) # Required for various macros\nproject(Cadabra)\nif(POLICY CMP0167)\n  cmake_policy(SET CMP0167 NEW)\nendif()\n\n#---------------------------------------------------------------------------\n# Preamble.\n#---------------------------------------------------------------------------\n\nprint_header(\"Configuring core\")\n\n# configure_file(\n#    \"${PROJECT_SOURCE_DIR}/cadabra2.in\"\n#    \"${PROJECT_BINARY_DIR}/cadabra2\"\n# )\nconfigure_file(\n   \"${PROJECT_SOURCE_DIR}/cadabra2_defaults.py.in\"\n   \"${PROJECT_BINARY_DIR}/packages/cadabra2_defaults.py\"\n)\n\n\n#---------------------------------------------------------------------------\n# Locate libraries.\n#---------------------------------------------------------------------------\n#SET(CMAKE_FIND_LIBRARY_SUFFIXES .a ${CMAKE_FIND_LIBRARY_SUFFIXES})\n\n# Boost.regex, Boost.system\n# if(ENABLE_JUPYTER)\n#   # To avoid issues building the Jupyter kernel on Conda, link boost\n#   # statically, to avoid version mismatch. Unfortunately, this cannot work,\n#   # as you cannot link a static library into a shared one. But fortunately,\n#   # for the Jupyter kernel, cadabra2.so only uses header-only Boost stuff,\n#   # so no linking takes place\n#   set(Boost_USE_STATIC_LIBS   ON)\n# endif()\nfind_package(Boost 1.71.0 COMPONENTS filesystem REQUIRED)\nmessage(STATUS \"Boost version ${Boost_VERSION}\")\n\n# Find glibmm (for base64)\nif(USE_GTK4)\n  find_package(GLIBMM4  REQUIRED)\nelse()\n  find_package(GLIBMM3  REQUIRED)\nendif()\n\n# GMPXX\n# In order to distribute as a PyPl wheel, we need to link\n# statically; the line below picks up the right library,\n# but then things fail because gmp/gmpxx are not built\n# with -fPIC. Postponed for now.\n# set(CMAKE_FIND_LIBRARY_SUFFIXES \".a\")\n#find_package(GMPXX REQUIRED STATIC)\nfind_package(GMPXX REQUIRED STATIC)\n\nmessage(STATUS \"Linking to GMP   library ${GMP_LIBRARIES}\")\nmessage(STATUS \"Linking to GMPXX library ${GMPXX_LIBRARIES}\")\nmessage(STATUS \"Include dir for GMP/GMPXX ${GMP_INCLUDE_DIRS}\")\n\n# Dependency of TinyProcessLib\nfind_package(Threads)\n\n\n#---------------------------------------------------------------------------\n# Enumerate input files and directories.\n#---------------------------------------------------------------------------\n\nSET(RESERVED_NODE_SRC_FILES\n  ReservedNode.cc\n  Equals.cc\n  Sum.cc\n)\n\nSET(ALGORITHM_SRC_FILES\n   algorithms/canonicalise.cc\n   algorithms/collect_components.cc\n   algorithms/collect_factors.cc\n   algorithms/collect_terms.cc\n   algorithms/combine.cc\n   algorithms/complete.cc\n   algorithms/decompose.cc\n   algorithms/decompose_product.cc\n   algorithms/distribute.cc\n   algorithms/drop_weight.cc\n   algorithms/einsteinify.cc\n   algorithms/eliminate_kronecker.cc\n   algorithms/eliminate_metric.cc\n   algorithms/eliminate_vielbein.cc   \n   algorithms/epsilon_to_delta.cc\n   algorithms/evaluate.cc\n   algorithms/expand.cc\n   algorithms/expand_delta.cc\n   algorithms/expand_diracbar.cc\n   algorithms/expand_dummies.cc\n   algorithms/expand_power.cc\n   algorithms/explicit_indices.cc\n   algorithms/factor_in.cc\n   algorithms/factor_out.cc\n   algorithms/fierz.cc\n   algorithms/first_order_form.cc\n   algorithms/flatten_product.cc\n   algorithms/flatten_sum.cc\n   algorithms/indexsort.cc\n   algorithms/integrate_by_parts.cc\n   algorithms/join_gamma.cc\n   algorithms/keep_terms.cc\n   algorithms/lower_free_indices.cc\n   algorithms/lr_tensor.cc\n   algorithms/map_sympy.cc\n   algorithms/meld.cc\n   algorithms/nevaluate.cc\n   algorithms/nval.cc\n   algorithms/order.cc\n   algorithms/product_rule.cc\n   algorithms/reduce_delta.cc\n   algorithms/rename_dummies.cc\n   algorithms/rewrite_indices.cc\n   algorithms/simplify.cc\n   algorithms/sort_product.cc\n   algorithms/sort_spinors.cc\n   algorithms/sort_sum.cc\n   algorithms/split_gamma.cc\n   algorithms/split_index.cc\n   algorithms/substitute.cc\n   algorithms/sym.cc\n   algorithms/tab_dimension.cc  \n   algorithms/tab_basics.cc\n   algorithms/take_match.cc\n   algorithms/replace_match.cc\n   algorithms/unwrap.cc\n   algorithms/unzoom.cc\n   algorithms/untrace.cc\n   algorithms/vary.cc\n   algorithms/young_project.cc\n   algorithms/young_project_product.cc\n   algorithms/young_project_tensor.cc\n   algorithms/zoom.cc  \n)\n\nset(PROPERTY_SRC_FILES\n   properties/Accent.cc\n   properties/AntiCommuting.cc\n   properties/AntiSymmetric.cc\n   properties/Commuting.cc\n   properties/CommutingAsProduct.cc\n   properties/CommutingAsSum.cc\n   properties/CommutingBehaviour.cc\n   properties/Coordinate.cc\n   properties/DAntiSymmetric.cc\n   properties/Depends.cc\n   properties/DependsInherit.cc\n   properties/Derivative.cc\n   properties/DerivativeOp.cc   \n   properties/Determinant.cc\n   properties/Diagonal.cc\n   properties/DifferentialForm.cc\n   properties/DiracBar.cc\n   properties/Distributable.cc\n   properties/EpsilonTensor.cc\n   properties/ExteriorDerivative.cc\n   properties/FilledTableau.cc\n   properties/GammaMatrix.cc\n   properties/GammaTraceless.cc\n   properties/ImaginaryI.cc\n   properties/ImplicitIndex.cc\n   properties/Indices.cc\n   properties/Integer.cc\n   properties/InverseMetric.cc\n   properties/KroneckerDelta.cc\n   properties/LaTeXForm.cc\n   properties/Matrix.cc\n   properties/Metric.cc\n   properties/NonCommuting.cc\n   properties/NumericalFlat.cc\n   properties/PartialDerivative.cc\n   properties/RiemannTensor.cc\n   properties/SatisfiesBianchi.cc\n   properties/SelfAntiCommuting.cc\n   properties/SelfCommuting.cc\n   properties/SelfNonCommuting.cc\n   properties/SortOrder.cc\n   properties/Spinor.cc\n   properties/Symbol.cc\n   properties/Symmetric.cc\n   properties/Tableau.cc\n   properties/TableauBase.cc\n   properties/TableauInherit.cc   \n   properties/TableauSymmetry.cc\n   properties/Trace.cc  \n   properties/Traceless.cc\n   properties/Vielbein.cc\n   properties/Weight.cc\n   properties/WeightInherit.cc\n   properties/WeylTensor.cc\n)\n\n# Packages are now handled by a CMakeLists.txt in the\n# packages directory.\n#\n# set(PACKAGES\n#   core/manip\n#   relativity/__init__\n#   relativity/schwarzschild\n#   gauge_theory/__init__\n#   gauge_theory/instantons\n#   )\n\nset(MODULE_SRC_FILES\n  pythoncdb/py_media.cc\n  pythoncdb/py_ntensor.cc\n  pythoncdb/py_algorithms.cc\n  pythoncdb/py_ex.cc\n  pythoncdb/py_globals.cc\n  pythoncdb/py_helpers.cc\n  pythoncdb/py_kernel.cc\n  pythoncdb/py_module.cc\n  pythoncdb/py_packages.cc\n  pythoncdb/py_progress.cc\n  pythoncdb/py_properties.cc\n  pythoncdb/py_stopwatch.cc\n  pythoncdb/py_tableau.cc\n)\n\nset(LOCAL_SRC_FILES\n  NDSolver.cc\n  NIntegrator.cc  \n  NEvaluator.cc\n  NTensor.cc\n  NInterpolatingFunction.cc  \n  InstallPrefix.cc\n  DataCell.cc\n  CdbPython.cc\n  ExNode.cc\n  ProgressMonitor.cc\n  Bridge.cc\n  Adjform.cc\n  Algorithm.cc\n  Cleanup.cc\n  Combinatorics.cc\n  Compare.cc\n  DisplayBase.cc\n  DisplayMMA.cc\n  DisplayTeX.cc\n  DisplaySympy.cc\n  DisplayTerminal.cc\n  TerminalStream.cc\n  Exceptions.cc\n  Exchange.cc\n  ExManip.cc\n  Functional.cc\n  Grouping.cc\n  Hash.cc\n  IndexIterator.cc\n  IndexClassifier.cc\n  Kernel.cc\n  Linear.cc\n  Media.cc\n  Multiplier.cc\n  Parser.cc\n  PreClean.cc\n  PreProcessor.cc\n  Props.cc\n  PythonException.cc\n  Stopwatch.cc\n  Storage.cc\n  Symbols.cc\n  SympyCdb.cc\n  YoungTab.cc\n  modules/xperm_new.cc\n  ${CADABRA_LIBS_DIR}/whereami/whereami.c\n  ${CADABRA_LIBS_DIR}/base64/base64.cc\n  ${RESERVED_NODE_SRC_FILES}\n  ${ALGORITHM_SRC_FILES}\n  ${PROPERTY_SRC_FILES}\n)\nif(MATHEMATICA_FOUND)\n   set(LOCAL_SRC_FILES \n      ${LOCAL_SRC_FILES}\n      MMACdb.cc  \n      algorithms/map_mma.cc\n      )\nendif()\n\nset(IMAGES\n   ../images/cadabra.png\n)\n\n\n#---------------------------------------------------------------------------\n# Include directories and preprocessor definitions.\n#---------------------------------------------------------------------------\n\ninclude_directories(\n   \".\"\n   \"${CADABRA_LIBS_DIR}/pybind11/include\"\n   \"${CADABRA_LIBS_DIR}/internal/include\"\n   \"${CADABRA_LIBS_DIR}/whereami\"\n   \"${CADABRA_LIBS_DIR}/base64\"   \n   \"${CADABRA_LIBS_DIR}/dbg\"   \n   \"${CADABRA_LIBS_DIR}/linenoise\"\n   \"${CADABRA_LIBS_DIR}/nlohmann\"\n   ${GMP_INCLUDE_DIRS}\n   ${Boost_INCLUDE_DIRS}\n   ${Python_INCLUDE_DIRS}\n   )\n\n\n#---------------------------------------------------------------------------\n# Targets.\n#---------------------------------------------------------------------------\n\n# Cadabra2 python module\npybind11_add_module(cadabra2 SHARED\n  ${LOCAL_SRC_FILES}\n  ${MODULE_SRC_FILES}\n)\nset_target_properties(cadabra2 PROPERTIES \n  SUFFIX \".${Python_MOD_SUFFIX}\" \n  CXX_VISIBILITY_PRESET default\n)\n\ntarget_link_libraries(cadabra2 PRIVATE\n  ${GMPXX_LIBRARIES}\n  ${GMP_LIBRARIES}   \n  ${Boost_LIBRARIES}\n  #  ${Python_LIBRARIES}\n  #  ${GLIBMM_LIBRARIES}    \n)\nif(mimalloc_FOUND)\n  target_link_libraries(cadabra2 PUBLIC mimalloc)\nendif()\n\nif(IPO_SUPPORTED)\n  message(STATUS \"IPO / LTO for cadabra2 enabled\")     \n  set_property(TARGET cadabra2 PROPERTY INTERPROCEDURAL_OPTIMIZATION TRUE)\n  set_target_properties(cadabra2 PROPERTIES COMPILE_FLAGS \"-flto=auto\")\n  set_target_properties(cadabra2 PROPERTIES LINK_FLAGS \"-flto=auto\")  \nendif()\n\nif(TBB_FOUND)\n  target_link_libraries(cadabra2 PRIVATE TBB::tbb)\n  target_compile_definitions(cadabra2 PRIVATE HAS_TBB)\nendif()\n   \n# On Unix, don't link the extension module to libpython*.so\n# because some python executables are link to python static library for performance\n# and if an extension is linked to python shared library, symbol clashes occur.\nif(${CMAKE_SYSTEM_NAME} MATCHES \"Darwin\")\n  set_target_properties(cadabra2 PROPERTIES LINK_FLAGS \"-undefined dynamic_lookup\")\nelseif(${CMAKE_SYSTEM_NAME} MATCHES \"Windows\")\n  target_link_libraries(cadabra2 PRIVATE ${Python_LIBRARIES})\nelseif(CMAKE_SHARED_LINKER_FLAGS MATCHES \".*-Wl,--no-undefined.*\")\n  # Exception for systems that require no undefined symbols present\n  # in shared libraries (e.g. openSUSE).\n  message(\"-- Linking cadabra2.so to libpython.so because of default linker flags.\")\n  target_link_libraries(cadabra2 PRIVATE ${Python_LIBRARIES})\nendif()\n\n# Make the python module pick up elements from two parents up.\nset(CMAKE_BUILD_WITH_INSTALL_RPATH TRUE)\nset_target_properties(cadabra2 PROPERTIES INSTALL_RPATH \"$ORIGIN/../../:$ORIGIN\")\n\nif(MATHEMATICA_FOUND)\n   target_link_libraries(cadabra2 PRIVATE ${Mathematica_WSTP_LIBRARIES})\nendif()\n\n# cadabra2 CLI\nadd_executable(cadabra2-cli\n   cadabra2-cli.cc\n   CdbPython.cc\n   Exceptions.cc\n   InstallPrefix.cc\n   pythoncdb/py_helpers.cc\n   ${CADABRA_LIBS_DIR}/whereami/whereami.c\n)\ntarget_compile_definitions(cadabra2-cli PRIVATE CDBPYTHON_NO_NOTEBOOK)\ntarget_include_directories(cadabra2-cli PRIVATE pybind11::pybind11)\ntarget_link_libraries(cadabra2-cli PRIVATE pybind11::embed ${GLIBMM_LIBRARIES} ${Boost_LIBRARIES})\n\n# Notebook diff tool\nadd_executable(cdb-nbtool\n  cdb-nbtool.cc\n  ${CADABRA_LIBS_DIR}/tiny-process-library/process.cpp\n)\nif(WIN32)\n  target_sources(cdb-nbtool PRIVATE ${CADABRA_LIBS_DIR}/tiny-process-library/process_win.cpp)\nelse()\n  target_sources(cdb-nbtool PRIVATE ${CADABRA_LIBS_DIR}/tiny-process-library/process_unix.cpp)\n  target_link_libraries(cdb-nbtool PRIVATE Threads::Threads)\nendif()\ntarget_include_directories(cdb-nbtool PRIVATE ${CADABRA_LIBS_DIR}/tiny-process-library)\n\n# Test preprocessor executable\nadd_executable(test_preprocessor \n   test_preprocessor.cc \n   PreProcessor.cc\n   ${CADABRA_LIBS_DIR}/base64/base64.cc  \n)\n\n# cadabra2python executable\nadd_executable(cadabra2python \n   cadabra2python.cc \n   CdbPython.cc\n   InstallPrefix.cc    \n   DataCell.cc\n   Exceptions.cc   \n   ${CADABRA_LIBS_DIR}/whereami/whereami.c\n   ${CADABRA_LIBS_DIR}/base64/base64.cc\n   )\ntarget_link_libraries(cadabra2python \n   ${Boost_LIBRARIES}\n   #    ${GLIBMM_LIBRARIES}     \n   ${Python_LIBRARIES}\n   )\n\n# cadabra2ipynb executable\nadd_executable(cadabra2ipynb\n   cadabra2ipynb.cc \n   CdbPython.cc\n   InstallPrefix.cc    \n   DataCell.cc\n   Exceptions.cc   \n   ${CADABRA_LIBS_DIR}/whereami/whereami.c\n   ${CADABRA_LIBS_DIR}/base64/base64.cc\n   )\ntarget_link_libraries(cadabra2ipynb\n   ${Boost_LIBRARIES}\n   #    ${GLIBMM_LIBRARIES}     \n   ${Python_LIBRARIES}\n   )\n\n# cadabra2cadabra\nadd_executable(cadabra2cadabra \n   cadabra2cadabra.cc \n   DataCell.cc \n   InstallPrefix.cc\n   Exceptions.cc\n   ${CADABRA_LIBS_DIR}/whereami/whereami.c\n   ${CADABRA_LIBS_DIR}/base64/base64.cc\n   )\ntarget_link_libraries(cadabra2cadabra\n   ${Boost_LIBRARIES}\n   )\n\n# Mathematica WSTP test\nif(MATHEMATICA_FOUND)\n   message(STATUS \"Building with Mathematica support (linking against ${Mathematica_VERSION})\")\n   include_directories(${Mathematica_WSTP_INCLUDE_DIR})\n   add_executable(test_wstp         test_wstp.cc)\n   target_link_libraries(test_wstp ${Mathematica_WSTP_LIBRARIES})\nelse()\n   message(STATUS \"Building without Mathematica support\")\nendif()\n\n#---------------------------------------------------------------------------\n# Tests run purely in C++ (no python).\n#---------------------------------------------------------------------------\n\nif(WIN32)\n  message(STATUS \"Not building C++ tests on Windows\")\nelse()\n  # We are linking the test with the full python module, which is a bit\n  # wasteful, but splitting out the ${LOCAL_SRC_FILES} into a separate\n  # library turned out to lead to linking errors with the algorithm\n  # modules in `packages/` (missing typeinfo things). For now this works.\n  if(Catch2_FOUND)\n    add_executable(test_internals\n      test_internals.cc\n    )\n    add_executable(test_multiplier\n      test_multiplier.cc\n      Multiplier.cc\n    )\n    target_link_libraries(test_internals PRIVATE\n      cadabra2\n      ${GMPXX_LIBRARIES}\n      ${GMP_LIBRARIES}\n      ${Python_LIBRARIES}\n      PRIVATE Catch2::Catch2WithMain\n    )\n    target_link_libraries(test_multiplier PRIVATE\n      ${GMPXX_LIBRARIES}\n      ${GMP_LIBRARIES}\n      PRIVATE Catch2::Catch2WithMain\n    )\n    catch_discover_tests(test_internals DL_PATHS \"${CMAKE_CURRENT_BINARY_DIR}\")\n    catch_discover_tests(test_multiplier)\n    set_target_properties(test_internals PROPERTIES\n      RPATH \"${CMAKE_CURRENT_BINARY_DIR}\"\n    )\n  endif()\n\n  # Some other tests which are more for diagnostics, not actual tests,\n  # so they do not run under control of catch2.\n  add_executable(test_benchmark\n    test_benchmark.cc\n  )\n  target_link_libraries(test_benchmark PRIVATE\n    cadabra2\n    ${GMPXX_LIBRARIES}\n    ${GMP_LIBRARIES}\n    ${Python_LIBRARIES}\n  )\nendif()\n\n\n# Profiling mode\nif(CMAKE_BUILD_TYPE STREQUAL \"Profile\")\n  find_library(GPERFTOOLS_PROFILER profiler REQUIRED)\n  message(STATUS \"Building with profiling enabled: ${GPERFTOOLS_PROFILER}\")\n  set(CMAKE_CXX_FLAGS_PROFILE \"${CMAKE_CXX_FLAGS_RELEASE} -g\")\n  target_link_libraries(cadabra2 PRIVATE -Wl,--no-as-needed ${GPERFTOOLS_PROFILER})\nendif()\n\n#---------------------------------------------------------------------------\n# Packages.\n#---------------------------------------------------------------------------\n\nadd_subdirectory(packages)\n\n\n#---------------------------------------------------------------------------\n# Installation.\n#---------------------------------------------------------------------------\n\n# Python module\n# \n# https://stackoverflow.com/questions/21198030/installfiles-cmake-cfg-intdir-abc-win-dll-destination-bin\n\ninstall_directory_permissions(${PYTHON_SITE_PATH})\n\nif(WIN32)\n  install(\n    TARGETS\n    cadabra2\n    DESTINATION \n    .\n    )\nelse()\n  install(\n    TARGETS\n    cadabra2\n    DESTINATION \n    ${PYTHON_SITE_PATH}\n    )\nendif()\n\nif(WIN32)\n  # Install the Python runtime packages.\n  set(PYLIBDIR \"/${MSYS_ENV}/lib/python${Python_VERSION_MAJOR}.${Python_VERSION_MINOR}\")\n  execute_process(\n    COMMAND         cygpath -m ${PYLIBDIR}\n    OUTPUT_VARIABLE WINPYTHON\n    OUTPUT_STRIP_TRAILING_WHITESPACE)\n  message(STATUS \"Copying python runtime from ${PYLIBDIR} aka ${WINPYTHON}\")\n  install(DIRECTORY ${WINPYTHON} DESTINATION lib)\nendif()\n\ninstall(TARGETS cadabra2-cli DESTINATION ${CDB_BIN_PATH})\ninstall(TARGETS cdb-nbtool DESTINATION ${CDB_BIN_PATH})\nmessage(STATUS \"Triple-check binary install path ${CMAKE_INSTALL_PREFIX}/${CDB_BIN_PATH}\")\nif(NOT WIN32)\n  # Windows cmake followed by wix leads to symbolic link issues, so don't.\n  install(CODE \"\n    set(CDB_BIN_PATH \\\"${CDB_BIN_PATH}\\\")\n\n    # Remove old binary if it exists\n    file(REMOVE \\\"\\$ENV{DESTDIR}\\${CMAKE_INSTALL_PREFIX}/\\${CDB_BIN_PATH}/cadabra2\\\")\n    \n    # Create symbolic link\n    execute_process(\n        COMMAND ${CMAKE_COMMAND} -E create_symlink cadabra2-cli cadabra2\n        WORKING_DIRECTORY \\\"\\$ENV{DESTDIR}\\${CMAKE_INSTALL_PREFIX}/\\${CDB_BIN_PATH}\\\"\n    )\n   \")\nendif()\ninstall(\n   FILES \n      \"${PROJECT_BINARY_DIR}/packages/cadabra2_defaults.py\" \n      \"${CADABRA_LIBS_DIR}/appdirs/cdb_appdirs.py\"\n   DESTINATION \n      \"${PYTHON_SITE_PATH}\"\n)\n\n# CLI\n# install(\n#   PROGRAMS \n#     \"${PROJECT_BINARY_DIR}/cadabra2\" \n#   DESTINATION \n#     ${CDB_BIN_PATH}\n# )\n\n# cadabra2python\ninstall(\n  TARGETS \n    cadabra2python \n  DESTINATION \n    ${CDB_BIN_PATH}\n)\ninstall_directory_permissions(\"bin\")\n\n# cadabra2ipynb\ninstall(\n  TARGETS \n    cadabra2ipynb\n  DESTINATION \n    ${CDB_BIN_PATH}\n)\n\n# cadabra2cadabra\ninstall(\n   TARGETS \n   cadabra2cadabra\n   DESTINATION \n   ${CDB_BIN_PATH}\n )\n\nif(NOT WIN32)\n   if(CMAKE_GENERATOR MATCHES \"Ninja\")\n      set(destdir_expr \"\\$\\${DESTDIR}\")\n   else()\n      set(destdir_expr \"\\$(DESTDIR)\")\n   endif()\nendif()             \n\n# manual pages\nif(NOT WIN32)\n  install(\n    FILES\n    ../man/man1/cadabra2.1\n    ../man/man1/cadabra2-cli.1    \n    ../man/man1/cadabra2cadabra.1\n    ../man/man1/cadabra2ipynb.1\n    ../man/man1/cadabra2html.1 \n    ../man/man1/cadabra2latex.1\n    ../man/man1/cadabra2python.1  \n    DESTINATION\n    share/man/man1\n    )\nendif()\n\n# if(APPIMAGE_MODE)\n#   # Install sympy. Matplotlib would be nice, but that pulls in blas and fortran and zillions of other things,\n#   # which then don't link properly anymore either.\n#   install(CODE      \"execute_process(COMMAND echo \\\"Installing python things in \\$ENV{DESTDIR}|${CMAKE_INSTALL_PREFIX}|${PYTHON_SITE_PATH}\\\")\")\n#   install(CODE      \"execute_process(COMMAND pip3 install --target \\$ENV{DESTDIR}${CMAKE_INSTALL_PREFIX}/${PYTHON_SITE_PATH} sympy matplotlib)\")\n# endif()\n"
  },
  {
    "path": "core/CdbPython.cc",
    "content": "\n#include <regex>\n#include <sstream>\n#include <sys/stat.h>\n#include <fstream>\n#include <iomanip>\n#include <iostream>\n#include \"CdbPython.hh\"\n#include <pybind11/pybind11.h>\n#include <pybind11/embed.h>\n#include <pybind11/stl.h>\n#include \"Exceptions.hh\"\n\n#ifndef CDBPYTHON_NO_NOTEBOOK\n#include \"DataCell.hh\"\n#endif\n\n// #define DEBUG __FILE__\n#include \"Debug.hh\"\n\nstd::string cadabra::escape_quotes(const std::string& line)\n\t{\n\treturn \"''\"+line+\"''\";\n\t//\tstd::string ret=std::replace_all_copy(line, \"'\", \"\\\\'\");\n\t//\tstd::replace_all(ret, \"\\\"\", \"\\\\\\\"\");\n\t//\treturn ret;\n\t}\n\nstd::string cadabra::cdb2python(const std::string& in_name, bool display)\n\t{\n\t// Read the file into a string.\n\tstd::ifstream ifs(in_name);\n\tstd::stringstream buffer;\n\tbuffer << ifs.rdbuf();\n\n\tstd::time_t t = std::time(nullptr);\n\tstd::tm tm = *std::localtime(&t);\n\n\tstd::ostringstream ofs;\n\tofs << \"# cadabra2 package, auto-compiled \" << std::put_time(&tm, \"%F %T\") << '\\n'\n\t    << \"# Do not modify - changing the timestamp of this file may cause import errors\\n\"\n\t    << \"# Original file location: \" << in_name << '\\n'\n\t    << \"import cadabra2\\n\"\n\t    << \"from cadabra2 import *\\n\"\n\t\t << \"from cadabra2_defaults import *\\n\"\n\t    << \"__cdbkernel__ = cadabra2.__cdbkernel__\\n\"\n\t    << \"temp__all__ = dir() + ['temp__all__']\\n\\n\"\n\t    << \"def display(ex):\\n\"\n\t    << \"   pass\\n\\n\";\n\n\tstd::string error;\n\tofs << cdb2python_string(buffer.str(), display, error);\n\n\tofs << '\\n'\n\t    << \"del locals()['display']\\n\\n\"\n\t    << \"try:\\n\"\n\t    << \"    __all__\\n\"\n\t    << \"except NameError:\\n\"\n\t    << \"    __all__  = list(set(dir()) - set(temp__all__))\\n\";\n\n\treturn ofs.str();\n\t}\n\nstd::string cadabra::insert_prefix(const std::string& tmpblk, const std::string& tmpprefix, size_t tmpprefixloc)\n\t{\n\t// Search backwards for \"[^\\\\]\\n[\\w]+\" and insert the\n\t// prefix immediately after that.\n\tstd::regex pattern_rx(\"([^\\\\\\\\])\\n[ \\t]+\");\n\tauto last = tmpblk.begin();\n\tlast += tmpprefixloc;\n\tstd::sregex_iterator it(tmpblk.begin(), last, pattern_rx);\n\tstd::sregex_iterator end;\n\tsize_t lastpos = std::string::npos;\n\twhile (it != end) {\n\t\tlastpos = it->position() + it->length();\n\t\t++it;\n\t\t}\n\tstd::string ret;\n\tif(lastpos!=std::string::npos) {\n\t\tret = tmpblk.substr(0, lastpos) + tmpprefix + tmpblk.substr(lastpos);\n#ifdef DEBUG\n\t\tstd::cerr << \"tmpblk now: \" << ret << std::endl;\n#endif\n\t\t}\n\telse {\n#ifdef DEBUG\n\t\tstd::cerr << \"cannot find a place to insert prefix\" << std::endl;\n#endif\n\t\tret = tmpblk;\n\t\t}\n\t\n\treturn ret;\n\t}\n\nstd::string cadabra::cdb2python_string(const std::string& blk, bool display, std::string& report_error)\n\t{\n\tstd::stringstream str(blk);\n\tstd::string line;\n\tstd::string tmpblk;\n\tstd::vector<std::string> newblks;\n\tConvertData cv;\n\n\tstd::pair<std::string, std::string> res;\n\n\t// We collect lines into blocks until they pass python\n\t// validation. If we ever hit an indentation error, we add\n\t// previous successful blocks and re-try, successively,\n\t// until the block compiles again.\n\n\tbool early_exit=false;\n\tstd::string error;\n\t\t\n\twhile(!early_exit && std::getline(str, line, '\\n')) {\n\t\tres = cadabra::convert_line(line, cv, display);\n\n//\t\tif(res.second!=\"::empty\")\n//\t\t\ttmpblk += res.first + res.second + \"\\n\";\n\n\t\tif(res.second!=\"::empty\")\n\t\t\ttmpblk += res.second;\n\n\t\tbool previous_step_removed=false; // avoid removing a line, then adding again.\n\t\twhile(true) {\n\t\t\tint ic = is_python_code_complete(tmpblk, error);\n#ifdef DEBUG\n\t\t\tstd::cerr << \"CHECK:---\\n\" << tmpblk << \"\\n---: \" << ic << \", \" << res.first << std::endl;\n#endif\n\t\t\tif(ic==1) { // complete\n\t\t\t\tnewblks.push_back(res.first + tmpblk + \"\\n\");\n\t\t\t\ttmpblk = \"\";\n\t\t\t\tbreak;\n\t\t\t\t}\n\t\t\tif(ic==0) { // incomplete\n\t\t\t\tif(res.first.size()>0)\n\t\t\t\t\ttmpblk = insert_prefix(tmpblk, res.first, tmpblk.size());\n\t\t\t\ttmpblk += \"\\n\";\n\t\t\t\tbreak;\n\t\t\t\t}\n\t\t\tif(ic==-1) { // indentation error\n\t\t\t\tif(newblks.size()==0) {\n\t\t\t\t\tearly_exit=true;\n\t\t\t\t\tbreak;\n\t\t\t\t\t}\n\t\t\t\t// Grow block by adding previously ok block,\n\t\t\t\t// then try compiling again.\n\n\t\t\t\ttmpblk = newblks.back() + tmpblk;\n\t\t\t\tnewblks.pop_back();\n\t\t\t\tif(previous_step_removed) {\n\t\t\t\t\t// We are about to add a line which we just removed. This is a genuine\n\t\t\t\t\t// indentation error. Return what we have so far and let the code runner\n\t\t\t\t\t// fail with proper exception info for the user (if we just throw an\n\t\t\t\t\t// exception with the content of 'error' it will refer to 'codeop').\n\t\t\t\t\tearly_exit=true;\n\t\t\t\t\tbreak;\n\t\t\t\t\t}\n\t\t\t\tprevious_step_removed=false;\n\t\t\t\t}\n\t\t\tif(ic==-2) { \n\t\t\t\t// This is either a genuine syntax error, or one line\n\t\t\t\t// added too many (after a previous 'incomplete' result).\n\t\t\t\t// Remove the line from the block, then re-run that line\n\t\t\t\t// separately.\n\t\t\t\tif(tmpblk != \"\") {\n\t\t\t\t\tif(size_t pos = tmpblk.rfind('\\n'); pos != std::string::npos) {\n\t\t\t\t\t\tnewblks.push_back(tmpblk.substr(0, pos)+\"\\n\");\n\t\t\t\t\t\ttmpblk = tmpblk.substr(pos+1);\n\t\t\t\t\t\tprevious_step_removed=true;\n\t\t\t\t\t\t// re-run\n\t\t\t\t\t\t}\n\t\t\t\t\telse {\n\t\t\t\t\t\tearly_exit=true;\n\t\t\t\t\t\tbreak;\n\t\t\t\t\t\t}\n\t\t\t\t\t}\n\t\t\t\telse {\n\t\t\t\t\tearly_exit=true;\n\t\t\t\t\tbreak;\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t}\n\t\t}\n\n\t// Collect.\n#ifdef DEBUG\n\tstd::cerr << \"** at exit:\" << std::endl;\n\tfor(const auto& blk: newblks)\n\t\tstd::cerr << \"blk: \" << blk << std::endl;\n\tstd::cerr << \"tmpblk    = \" << tmpblk << std::endl;\n#endif\n\n\tstd::string newblk;\n\tfor(const auto& blk: newblks)\n\t\tnewblk += blk;\n\n\t// Add anything still left and cross fingers.\n\tnewblk += tmpblk+\"\\n\";\n\n\tif(early_exit) {\n\t\tstd::cerr << \"** EARLY EXIT: \" << error << std::endl;\n\t\treport_error=error;\n\t\t}\n\n\treturn newblk;\n\t}\n\n//  1: complete\n//  0: incomplete\n// -1: indentation error, need backtracking\n// -2: syntax error\n\nint cadabra::is_python_code_complete(const std::string& code, std::string& error)\n\t{\n\t// The following code prints None, <code object> and <code object>.\n\t// Make sure that the string you feed here does *not* include the\n\t// newline on the last line.\n\t//\n\t// \n   //  from codeop import *\n   //  \n   //  str1='''def fun():\n   //     print(\"hello\")'''\n   //  str2='''def fun():\n   //     print(\"hello\")\n   //  '''\n   //  str3='''print(\"hello\")'''\n   //  \n   //  print(compile_command(str1, \"<string>\", \"single\"))\n   //  print(compile_command(str2, \"<string>\", \"single\"))\n   //  print(compile_command(str3, \"<string>\", \"single\"))\n\n   //\tpybind11::scoped_interpreter guard{}; // Ensures the Python interpreter is initialized.\n\t\n\t// Import the 'codeop' module.\n\tpybind11::object codeop = pybind11::module_::import(\"codeop\");\n\tpybind11::object compile_command = codeop.attr(\"compile_command\");\n\n\t// std::cerr << \"CHECK:\\n\" << code << \"END\" << std::endl;\n\ttry {\n\t\tpybind11::object result = compile_command(code, \"<string>\", \"single\");\n\t\tif( result.is_none() ) return 0;\n\t\telse                   return 1;\n\t\t}\n\tcatch (pybind11::error_already_set& e) {\n//\t\tstd::cerr << \"EXCEPTION: \" << e.what() << std::endl;\n\t\terror=e.what();\n\t\t// if (std::string(e.what()).find(\"multiple statements found while compiling a single\") != std::string::npos) {\n\t\t// \treturn 0;\n\t\t// \t}\n\t\tif (std::string(e.what()).find(\"unexpected EOF\") != std::string::npos) {\n\t\t\treturn -1;\n\t\t\t}\n\t\tif (std::string(e.what()).find(\"Indentation\") != std::string::npos) {\n\t\t\treturn -1;\n\t\t\t}\n\t\tif (std::string(e.what()).find(\"SyntaxError\") != std::string::npos) {\n\t\t\t// std::cerr << e.what() << std::endl;\n\t\t\treturn -2;\n\t\t\t}\n\t\t\n\t\tthrow; // pass all other exceptions through\n\t\t}\n\t}\n\nstd::string cadabra::remove_variable_assignments(const std::string& code, const std::string& variable)\n\t{\n//\tpybind11::scoped_interpreter guard{};\n\nstatic std::string removal_code = R\"PYTHON(\nimport ast\n\nclass AssignmentRemover(ast.NodeTransformer):\n    def __init__(self, var_name):\n        self.var_name = var_name\n\n    def visit_Assign(self, node):\n        for target in node.targets:\n            if isinstance(target, ast.Name) and target.id == self.var_name:\n                return ast.Pass()\n        return node\n\n    def visit_AnnAssign(self, node):\n        if isinstance(node.target, ast.Name) and node.target.id == self.var_name:\n            return ast.Pass()\n        return node\n\n    def visit_AugAssign(self, node):\n        if isinstance(node.target, ast.Name) and node.target.id == self.var_name:\n            return ast.Pass()\n        return node\n\ndef remove_assignments(code: str, var_name: str) -> str:\n    try:\n        # Python 3.9+\n        unparse = ast.unparse\n    except AttributeError:\n        # Python < 3.9\n        import astunparse\n        unparse = astunparse.unparse\n\n    tree = ast.parse(code)\n    transformer = AssignmentRemover(var_name)\n    modified_tree = transformer.visit(tree)\n    ast.fix_missing_locations(modified_tree)\n    return unparse(modified_tree)\n)PYTHON\";\n\n\t\n\ttry {\n\t\tpybind11::exec(removal_code);\n\t\tpybind11::object remove_assignments = pybind11::globals()[\"remove_assignments\"];\n\t\tpybind11::object result = remove_assignments(code, variable);\n\t\treturn result.cast<std::string>();\n\t\t}\n\tcatch(const pybind11::error_already_set& e) {\n\t\tstd::cerr << \"Python error: \" << e.what() << std::endl;\n\t\treturn code;\n\t\t}\n\t}\n\nbool cadabra::code_contains_variable(const std::string& code, const std::string& variable)\n\t{\n\tpybind11::scoped_interpreter guard{};\t\n\t\t\n\tstatic std::string testcode = R\"PYTHON(\ndef contains_variable(code_str, variable_name):\n    import ast\n\n    class VariableVisitor(ast.NodeVisitor):\n        def __init__(self):\n            self.found = False\n        \n        def visit_Name(self, node):\n            if node.id == variable_name:\n                self.found = True\n\n    try:\n        tree = ast.parse(code_str)\n        visitor = VariableVisitor()\n        visitor.visit(tree)\n        return visitor.found\n    except SyntaxError:\n        return False\n   )PYTHON\";\n\n\ttry {\n\t\tpybind11::exec(testcode);\n\t\tpybind11::object contains_variable = pybind11::globals()[\"contains_variable\"];\n\t\tpybind11::object result = contains_variable(code, variable);\n\t\treturn result.cast<bool>();\n\t\t}\n\tcatch(const pybind11::error_already_set& e) {\n\t\tstd::cerr << \"Python error: \" << e.what() << std::endl;\n\t\treturn false;\n\t\t}\n\t}\n\nbool cadabra::variables_to_pull_in(const std::string& code, std::set<std::string>& variables)\n\t{\n\tstd::regex pullin_rx(R\"(@\\(([^\\)]*)\\))\");\n\n\tauto it = std::sregex_iterator(code.begin(), code.end(), pullin_rx);\n\twhile(it != std::sregex_iterator()) {\n\t\tstd::smatch m = *it;\n\t\tvariables.insert(m[1].str());\n\t\t++it;\n\t\t}\n\n\treturn true;\n\t}\n\n\nbool cadabra::variables_in_code(const std::string& code, std::set<std::string>& variables)\n\t{\n\t// It would be great if we could parse Python code and then walk\n\t// the AST directly using the Python C API. However, that does not\n\t// seem to exist (or rather, it seems to have been removed, as the\n\t// `ast.h` header is no longer public). So we have to do all this\n\t// in Python using the `ast` module, and then move the resulting\n\t// variable list to the C++ side.\n\t\n\tstatic std::string testcode = R\"CODE(\ndef variable_set(code_str):\n    \"\"\"\n    Collect all variable names in a piece of Python code.\n    Returns a set of names.\n    \"\"\"\n    import ast\n\n    class VariableVisitor(ast.NodeVisitor):\n        def __init__(self):\n            self.names = set()\n        \n        def generic_visit(self, node):\n            # We still need to visit all children even if parent assignment fails\n            for child in ast.iter_child_nodes(node):\n                try:\n                    child.parent = node\n                except (TypeError, AttributeError):\n                    # If we can't set parent, continue without it\n                    pass\n                self.visit(child)\n        \n        def visit_Name(self, node):\n            # For names, if we can check the context do so, otherwise include the name\n            try:\n                parent = getattr(node, 'parent', None)\n                if parent is not None:\n                    # Only exclude if we're certain it's a function call\n                    if isinstance(parent, ast.Call) and parent.func == node:\n                        return\n\n            except (TypeError, AttributeError):\n                pass\n            \n            # Include the name unless we explicitly determined it's a function call\n            self.names.add(node.id)\n\n    try:\n        # Parse the code into an AST\n        tree = ast.parse(code_str)\n        visitor = VariableVisitor()\n        visitor.visit(tree)\n        return visitor.names\n    except SyntaxError:\n        # Handle invalid Python code\n        return False\n)CODE\";\n\n\ttry {\n\t\tpybind11::exec(testcode);\n\t\tpybind11::object variable_set = pybind11::globals()[\"variable_set\"];\n\t\tpybind11::object result = variable_set(code);\n\n\t\tvariables = result.cast<std::set<std::string>>();\n\n\t\t// Add the variables inside '@(...)' wrappers.\n\t\t\n\t\t\n\t\treturn true;\n\t\t}\n\tcatch(const pybind11::error_already_set& e) {\n\t\tstd::cerr << \"Python error: \" << e.what() << std::endl;\n\t\treturn false;\n\t\t}\n\t}\n\n\ncadabra::ConvertData::ConvertData()\n\t{\n\t}\n\ncadabra::ConvertData::ConvertData(const std::string& lhs_, const std::string& rhs_,\n\t\t\t\t\t\t\t\t\t\t\t const std::string& op_, const std::string& indent_)\n\t: lhs(lhs_), rhs(rhs_), op(op_), indent(indent_)\n\t{\n\t}\n\nstd::string replace_dollar_expressions(const std::string& input, \n\t\t\t\t\t\t\t\t\t\t\t\t\tconst std::function<std::string(const std::string&)>& replacer)\n\t{\n\tstd::ostringstream result;\n\tbool in_single_quote = false;\n\tbool in_double_quote = false;\n\tsize_t dollar_start = std::string::npos;\n\t\n\tfor (size_t i = 0; i < input.length(); ++i) {\n\t\tchar c = input[i];\n      \n\t\t// Toggle quote state\n\t\tif (c == '\"' && !in_single_quote && dollar_start == std::string::npos) {\n\t\t\tin_double_quote = !in_double_quote;\n\t\t\tresult << c;\n        }\n\t\telse if (c == '\\'' && !in_double_quote && dollar_start == std::string::npos) {\n\t\t\tin_single_quote = !in_single_quote;\n\t\t\tresult << c;\n\t\t\t}\n\t\t// Handle dollar signs outside of quotes\n\t\telse if (c == '$' && !in_single_quote && !in_double_quote) {\n\t\t\tif (dollar_start == std::string::npos) {\n\t\t\t\t// First dollar sign\n\t\t\t\tdollar_start = i;\n\t\t\t\t// Don't append the $ yet, wait until we find the matching one\n            }\n\t\t\telse {\n\t\t\t\t// Second dollar sign, found a match\n\t\t\t\tstd::string content = input.substr(dollar_start + 1, i - dollar_start - 1);\n\t\t\t\tresult << replacer(content);\n\t\t\t\tdollar_start = std::string::npos;\n            }\n        }\n\t\telse {\n\t\t\t// Regular character\n\t\t\tif (dollar_start == std::string::npos) {\n\t\t\t\t// Not in the middle of a $...$ expression\n\t\t\t\tresult << c;\n            }\n\t\t\t// If we're between $...$, don't add anything yet\n\t\t\t}\n\t\t}\n\t\n\t// Handle unclosed dollar\n\tif (dollar_start != std::string::npos) {\n\t\tresult << input.substr(dollar_start);\n\t\t}\n\t\n\treturn result.str();\n\t}\n\nstd::pair<std::string, std::string> cadabra::convert_line(const std::string& line, ConvertData& cv, bool display)\n\t{\n\tstd::string ret, prefix;\n\n\tauto& lhs    = cv.lhs;\n\tauto& rhs    = cv.rhs;\n\tauto& op     = cv.op;\n\tauto& indent = cv.indent;\n\n\tstd::regex imatch(\"([\\\\s]*)([^\\\\s].*[^\\\\s])([\\\\s]*)\");\n\tstd::cmatch mres;\n\n\tstd::string indent_line, end_of_line, line_stripped;\n\tif(std::regex_match(line.c_str(), mres, imatch)) {\n\t\tindent_line=std::string(mres[1].first, mres[1].second);\n\t\tend_of_line=std::string(mres[3].first, mres[3].second);\n\t\tline_stripped=std::string(mres[2]);\n\t\t}\n\telse {\n\t\tindent_line=\"\";\n\t\tend_of_line=\"\\n\";\n\t\tline_stripped=line;\n\t\t}\n\n\tif(line_stripped.size()==0) {\n\t\treturn std::make_pair(prefix, \"\");\n\t\t}\n\n\t// Do not do anything with comment lines.\n\tif(line_stripped[0]=='#') return std::make_pair(prefix, line);\n\n\t// Bare ';' gets replaced with 'display(_)' but *only* if we have no\n\t// preceding lines which have not finished parsing.\n\tif(line_stripped==\";\" && lhs==\"\") {\n\t\tif(display)\n\t\t\treturn std::make_pair(prefix, indent_line+\"display(_)\");\n\t\telse\n\t\t\treturn std::make_pair(prefix, indent_line);\n\t\t}\n\n\t// 'lastchar' is either a Cadabra termination character, or empty.\n\t// 'line_stripped' will have that character stripped, if present.\n\tstd::string lastchar = line_stripped.substr(line_stripped.size()-1,1);\n\tif(lastchar==\".\" || lastchar==\";\" || lastchar==\":\") {\n\t\tif(lhs!=\"\") {\n\t\t\tline_stripped=line_stripped.substr(0,line_stripped.size()-1);\n\t\t\trhs += \" \"+line_stripped;\n\t\t\tif(lhs.find('(')==std::string::npos) {\n\t\t\t\tret = indent + lhs + \" = Ex(r'\" + escape_quotes(rhs) + \"')\";\n\t\t\t\t}\n\t\t\telse {\n\t\t\t\tret = indent + \"def \" + lhs + \": return Ex(r'\" + escape_quotes(rhs) + \"')\";\n\t\t\t\t}\n\t\t\tif(op==\":=\") {\n\t\t\t\tif(ret[ret.size()-1]!=';')\n\t\t\t\t\tret+=\";\";\n\t\t\t\tret+=\" _=\"+lhs;\n\t\t\t\t}\n\t\t\tif(lastchar!=\".\")\n\t\t\t\tif(display)\n\t\t\t\t\tret = ret + \"; display(\"+lhs+\")\";\n\t\t\tindent=\"\";\n\t\t\tlhs=\"\";\n\t\t\trhs=\"\";\n\t\t\top=\"\";\n\t\t\treturn std::make_pair(prefix, ret);\n\t\t\t}\n\t\t}\n\telse {\n\t\t// If we are a Cadabra continuation, add to the rhs without further processing\n\t\t// and return an empty line immediately.\n\t\tif(lhs!=\"\") {\n\t\t\trhs += line_stripped+\" \";\n\t\t\treturn std::make_pair(prefix, \"::empty\");\n\t\t\t}\n\t\t}\n\n\t// Add '__cdbkernel__' as first argument of post_process if it doesn't have that already.\n\tstd::regex postprocmatch(R\"(def post_process\\(([^_]))\");\n\tline_stripped = std::regex_replace(line_stripped, postprocmatch, \"def post_process(__cdbkernel__, $1\");\n\n\t// Replace $...$ with Ex(...).\n\tauto replacement = [](const std::string& content) {\n\t\treturn \"Ex(r'''\" + content + \"''', False)\";\n\t\t};\n    \n\tline_stripped = replace_dollar_expressions(line_stripped, replacement);\n\tDEBUGLN( std::cerr << \"line_stripped = \" << line_stripped << std::endl; );\n\t\n// \tstd::regex dollarmatch(R\"(\\$([^\\$]*)\\$)\");\n// \tline_stripped = std::regex_replace(line_stripped, dollarmatch, \"Ex(r'''$1''', False)\", std::regex_constants::match_default | std::regex_constants::format_default );\n\n\t// Replace 'converge(ex):' with 'server.progress('converge'); ex.reset(); while ex.changed(): server.progress(); server.end_progress();' properly indented.\n\tstd::regex converge_match(R\"(([ ]*)converge\\(([^\\)]*)\\):)\");\n\tstd::smatch converge_res;\n\tif(std::regex_match(line_stripped, converge_res, converge_match)) {\n\t\tret = indent_line+std::string(converge_res[1])+std::string(converge_res[2])+\".reset(); _=\"+std::string(converge_res[2])+\"\\n\"\n\t\t      + indent_line+std::string(converge_res[1])+\"while \"+std::string(converge_res[2])+\".changed():\";\n\t\treturn std::make_pair(prefix, ret);\n\t\t}\n\n\tsize_t found = line_stripped.find(\":=\");\n\tif(found!=std::string::npos) {\n\t\t// If the last character is not a Cadabra terminator, start a capture process.\n\t\tif(lastchar!=\".\" && lastchar!=\";\" && lastchar!=\":\") {\n\t\t\tindent=indent_line;\n\t\t\tlhs=line_stripped.substr(0,found);\n\t\t\trhs=line_stripped.substr(found+2);\n\t\t\top=\":=\";\n\t\t\treturn std::make_pair(prefix, \"::empty\");\n\t\t\t}\n\t\telse {\n\t\t\tline_stripped=line_stripped.substr(0,line_stripped.size()-1);\n\t\t\tif(line_stripped.substr(0, found).find('(')==std::string::npos) {\n\t\t\t\tret = indent_line + line_stripped.substr(0,found) + \" = Ex(r'\"\n\t\t\t\t\t+ escape_quotes(line_stripped.substr(found+2)) + \"')\";\n\t\t\t\t}\n\t\t\telse {\n\t\t\t\tret = indent_line + \"def \" + line_stripped.substr(0,found) + \": return Ex(r'\"\n\t\t\t      + escape_quotes(line_stripped.substr(found+2)) + \"')\";\n\t\t\t\t}\n\t\t\tstd::string objname = line_stripped.substr(0,found);\n\t\t\tret = ret + \"; _=\"+objname;\n\t\t\tif(lastchar==\";\" && /* indent_line.size()==0 && */ display)\n\t\t\t\tret = ret + \"; display(\"+objname+\")\";\n\t\t\t}\n\t\t}\n\telse {   // {a,b,c}::Indices(real, parent=holo);\n\t\tfound = line_stripped.find(\"::\");\n\t\tif(found!=std::string::npos) {\n\t\t\tstd::regex amatch(R\"(([a-zA-Z]+)(\\(.*\\))?[ ]*[;\\.:]*)\");\n\t\t\tstd::smatch ares;\n\t\t\tstd::string subline=line_stripped.substr(found+2); // need to store the copy, not feed it straight into regex_match!\n\t\t\tif(std::regex_match(subline, ares, amatch)) {\n\t\t\t\tauto propname = std::string(ares[1]);\n\t\t\t\tauto argument = std::string(ares[2]);\n\t\t\t\tif(argument.size()>0) { // declaration with arguments\n\t\t\t\t\targument=argument.substr(1,argument.size()-2);\n\t\t\t\t\tret = indent_line + \"__cdbtmp__ = \"+propname\n\t\t\t\t\t      +\"(Ex(r'\"+escape_quotes(line_stripped.substr(0,found))\n\t\t\t\t\t      +\"'), Ex(r'\" +escape_quotes(argument) + \"') )\";\n\t\t\t\t\t}\n\t\t\t\telse {\n\t\t\t\t\t// no arguments\n\t\t\t\t\tline_stripped=line_stripped.substr(0,line_stripped.size()-1);\n\t\t\t\t\tret = indent_line + \"__cdbtmp__ = \" + line_stripped.substr(found+2)\n\t\t\t\t\t      + \"(Ex(r'\"+escape_quotes(line_stripped.substr(0,found))+\"'), Ex(r''))\";\n\t\t\t\t\t}\n\t\t\t\tif(lastchar==\";\" && display)\n\t\t\t\t\tret += \"; display(__cdbtmp__)\";\n\t\t\t\t}\n\t\t\telse {\n\t\t\t\t// inconsistent, who knows what will happen...\n\t\t\t\tret = line; // inconsistent; you are asking for trouble.\n\t\t\t\t}\n\t\t\t}\n\t\telse {\n\t\t\tif(lastchar==\";\" && display) {\n\t\t\t\tprefix = \"_ = \" + prefix;\n\t\t\t\tret = indent_line + line_stripped + \" display(_)\";\n\t\t\t\t}\n\t\t\telse {\n\t\t\t\tret = indent_line + line_stripped;\n\t\t\t\t}\n\t\t\t}\n\t\t}\n\treturn std::make_pair(prefix, ret+end_of_line);\n\t}\n\n#ifndef CDBPYTHON_NO_NOTEBOOK\n\nstd::string cadabra::cnb2python(const std::string& in_name, bool for_standalone)\n\t{\n\t// Read the file into a Json object and get the cells. We go through\n\t// a proper notebook read because that way we can benefit from automatic\n\t// Jupyter -> Cadabra conversion.\n\tstd::ifstream ifs(in_name);\n\tstd::string content, line;\n\twhile(std::getline(ifs, line))\n\t\tcontent+=line;\n\tcadabra::DTree doc;\n\tcadabra::JSON_deserialise(content, doc);\n\n\tstd::time_t t = std::time(nullptr);\n\tstd::tm tm = *std::localtime(&t);\n\n\t// Loop over input cells, compile them and write to python file\n\tstd::ostringstream ofs;\n\tofs << \"# cadabra2 package, auto-compiled \" << std::put_time(&tm, \"%F %T\") << '\\n'\n\t    << \"# Do not modify - changing the timestamp of this file may cause import errors\\n\"\n\t    << \"# Original file location: \" << in_name << '\\n'\n\t    << \"import cadabra2\\n\"\n\t    << \"from cadabra2 import *\\n\"\n\t\t << \"from cadabra2_defaults import *\\n\"\n\t    << \"__cdbkernel__ = cadabra2.__cdbkernel__\\n\"\n\t    << \"temp__all__ = dir() + ['temp__all__']\\n\\n\"\n\t    << \"def display(ex):\\n\"\n\t    << \"   pass\\n\\n\";\n\n\n\t// FIXME: this only does a single layer of cells below the top-level\n\t// 'document' cell; need recursing, in principle.\n\tauto docit=doc.begin();\n\tfor(auto cell=doc.begin(docit); cell!=doc.end(docit); ++cell) {\n\t\tbool ioi = cell->ignore_on_import;\n\t\tif(for_standalone || !ioi) {\n\t\t\tif(cell->cell_type==cadabra::DataCell::CellType::python) {\n\t\t\t\tstd::stringstream s, temp;\n\t\t\t\ts << cell->textbuf; // cell[\"source\"].asString();\n\t\t\t\tConvertData cv;\n//\t\t\t\tstd::string line, lhs, rhs, op, indent;\n\t\t\t\twhile (std::getline(s, line)) {\n\t\t\t\t\tstd::pair<std::string, std::string> res\n\t\t\t\t\t\t= convert_line(line, cv, for_standalone); // lhs, rhs, op, indent, for_standalone);\n\t\t\t\t\tif(res.second!=\"::empty\")\n\t\t\t\t\t\tofs << res.second << '\\n';\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t}\n\t\tcell.skip_children();\n\t\t}\n\t// Ensure only symbols defined in this file get exported\n\tofs << '\\n'\n\t    << \"del locals()['display']\\n\\n\"\n\t    << \"try:\\n\"\n\t    << \"    __all__\\n\"\n\t    << \"except NameError:\\n\"\n\t    << \"    __all__  = list(set(dir()) - set(temp__all__))\\n\";\n\n\treturn ofs.str();\n\t}\n\n\n// std::string cadabra::cnb2python(const std::string& name)\n// \t{\n// \t// Only compile if the notebook is newer than the compiled package\n// \tstruct stat f1, f2;\n// \tif (stat(std::string(name + \".cnb\").c_str(), &f1) == 0 && stat(std::string(name + \".py\").c_str(), &f2) == 0) {\n// \t\tif (f1.st_mtime < f2.st_mtime)\n// \t\t\treturn \"\";\n// \t\t}\n//\n// \t// Read the file into a Json object and get the cells\n// \tstd::ifstream ifs(name + \".cnb\");\n// \tJson::Value nb;\n// \tifs >> nb;\n// \tJson::Value& cells = nb[\"cells\"];\n//\n// \t// Loop over input cells, compile them and write to python file\n//\n// \tstd::ostringstream ofs;\n// \tstd::time_t t = std::time(nullptr);\n// \tstd::tm tm = *std::localtime(&t);\n// \tofs << \"# cadabra2 package, auto-compiled \" << std::put_time(&tm, \"%F %T\") << '\\n'\n// \t    << \"import cadabra2\\n\"\n// \t    << \"import imp\\n\"\n// \t    << \"from cadabra2 import *\\n\"\n// \t    << \"__cdbkernel__ = cadabra2.__cdbkernel__\\n\"\n// \t    << \"temp__all__ = dir() + ['temp__all__']\\n\\n\"\n// \t    << \"def display(ex):\\n\"\n// \t    << \"   pass\\n\\n\";\n//\n// //\t    << \"with open(imp.find_module('cadabra2_defaults')[1]) as f:\\n\"\n// //\t    << \"   code = compile(f.read(), 'cadabra2_defaults.py', 'exec')\\n\"\n// //\t    << \"   exec(code)\\n\\n\";\n//\n// \tfor (auto cell : cells) {\n// \t\tif (cell[\"cell_type\"] == \"input\") {\n// \t\t\tstd::stringstream s, temp;\n// \t\t\ts << cell[\"source\"].asString();\n// \t\t\tstd::string line, lhs, rhs, op, indent;\n// \t\t\twhile (std::getline(s, line))\n// \t\t\t\tofs << convert_line(line, lhs, rhs, op, indent) << '\\n';\n// \t\t}\n// \t}\n// \t// Ensure only symbols defined in this file get exported\n// \tofs << '\\n'\n// \t    << \"del locals()['display']\\n\\n\"\n// \t    << \"try:\\n\"\n// \t    << \"    __all__\\n\"\n// \t    << \"except NameError:\\n\"\n// \t    << \"    __all__  = list(set(dir()) - set(temp__all__))\\n\";\n//\n// \treturn ofs.str();\n// \t}\n//\n\n#endif\n"
  },
  {
    "path": "core/CdbPython.hh",
    "content": "\n#pragma once\n\n#include <string>\n#include <set>\n#include <pybind11/pybind11.h>\n\nnamespace cadabra {\n\n\tstd::string escape_quotes(const std::string&);\n\n\t/// \\ingroup files\n\t/// Convert a block of Cadabra notation into pure Python. Mimics\n\t/// the functionality in the python script 'cadabra2'\n\t/// If display is false, this will not make ';' characters \n\t/// generate 'display' statements (used in the conversion of\n\t/// notebooks to python packages).\n\n\tstd::string cdb2python(const std::string&, bool display);\n\n\t/// Helper function to insert a prefix.\n\tstd::string insert_prefix(const std::string&, const std::string& prefix, size_t prefixloc);\n\t\n\tstd::string cdb2python_string(const std::string&, bool display, std::string& error);\t\n\n\t/// Test whether a block of Python code is complete or requires\n\t/// more input lines. This uses `codeop.compile_command`.\n\t///     1: complete\n   ///     0: incomplete\n   ///    -1: indentation error, need backtracking\n\t///    -2: overcomplete\n\n\tint         is_python_code_complete(const std::string&, std::string& error);\n\t\n\t/// Determine if the python code `code` contains a reference to\n\t/// the variable `variable` by parsing it into an AST.\n\tbool code_contains_variable(const std::string& code, const std::string& variable);\n\n\t/// Fill a set with all variables references in the given piece of Python code.\n\t/// This needs to be proper Python, not a mixture of Python and Cadabra input which\n\t/// still needs to be pre-processed.\n\tbool variables_in_code(const std::string& code, std::set<std::string>& variables);\n\n\t/// Fill a set with all variables references inside of Cadabra pull-in constructions,\n\t/// that is, constructions of the form \"@(var)\". This just does regex matching, no\n\t/// Python AST walking (we cannot, as this pull-in logic only happens when a\n\t/// string gets parsed into a Cadabra Ex, but that's all inside Ex, not visible\n\t/// to the server that runs the code.\n\tbool variables_to_pull_in(const std::string& code, std::set<std::string>& variables);\n\n\t/// Given a piece of Python code, remove all lines which assign a value to\n\t/// the given variable. Return the modified code.\n\tstd::string remove_variable_assignments(const std::string& code, const std::string& variable);\n\n\t/// \\ingroup files\n\t/// Object to store pre-parsing intermediate results. Necessary\n\t/// to keep things tidy but also in order to avoid the fact that\n\t/// we cannot pass strings by reference between C++ and Python.\n\tclass ConvertData {\n\t\tpublic:\n\t\t\tConvertData();\n\t\t\tConvertData(const std::string&, const std::string&, const std::string&, const std::string&);\n\t\t\t\n\t\t\tstd::string lhs, rhs, op, indent;\n\t};\n\t\n\t/// \\ingroup files\n   /// Detect Cadabra expression statements and rewrite to Python form.\n   ///  \n   /// Lines containing ':=' are interpreted as expression declarations.\n   /// Lines containing '::' are interpreted as property declarations.\n   /// \n   /// These need to end on '.', ':' or ';'. If not, keep track of the\n   /// input so far and store that in self.convert_data.lhs, self.convert_data.op, self.convert_data.rhs, and\n   /// then return an empty string.\n   /// \n   /// TODO: make ';' at the end of '::' line result the print statement printing \n   /// property objects using their readable form; addresses one issue report).\n\t///\n\t/// Returns two strings, one which should be prefixed to the block so far, the other postfixed.\n\n\tstd::pair<std::string, std::string> convert_line(const std::string&, ConvertData& cv, bool display);\n\n\t/// \\ingroup files\n\t/// Convert a Cadabra notebook file to pure Python. This gets\n\t/// called on-the-fly when importing Cadabra notebooks written by\n\t/// users, and at install time for all system-supplied packages.\n\t/// If for_standalone is false, this will not make ';' characters \n\t/// generate 'display' statements (used in the conversion of\n\t/// notebooks to python packages), and it will not convert\n\t/// any cells which have their `ignore_on_import` flag set.\n\n\t#ifndef CDBPYTHON_NO_NOTEBOOK\n\n\tstd::string cnb2python(const std::string&, bool for_standalone);\n\n\t#endif\n\t}\n"
  },
  {
    "path": "core/Cleanup.cc",
    "content": "\n#include \"Cleanup.hh\"\n#include \"Functional.hh\"\n#include \"Exceptions.hh\"\n#include \"Algorithm.hh\"\n#include \"algorithms/collect_terms.hh\"\n#include \"properties/Coordinate.hh\"\n#include \"properties/SelfAntiCommuting.hh\"\n#include \"properties/Integer.hh\"\n#include \"properties/Diagonal.hh\"\n#include \"properties/ExteriorDerivative.hh\"\n#include \"properties/DifferentialForm.hh\"\n#include \"properties/KroneckerDelta.hh\"\n#include \"properties/Matrix.hh\"\n#include \"properties/NumericalFlat.hh\"\n#include \"properties/PartialDerivative.hh\"\n#include \"properties/ImaginaryI.hh\"\n#include \"NTensor.hh\"\n\n// #define DEBUG 1\n\nnamespace cadabra {\n\n\tvoid cleanup_dispatch(const Kernel& kernel, Ex& tr, Ex::iterator& it)\n\t\t{\n#ifdef DEBUG\n\t\tstd::cerr << \"cleanup at \" << *it->name << std::endl;\n#endif\n\n\t\t// Run the cleanup as long as the expression changes.\n\n\t\tbool changed;\n\t\tdo {\n\t\t\tchanged=false;\n\t\t\tbool res=false;\n\n\t\t\tif(std::holds_alternative<std::shared_ptr<NTensor>>(it->content)) {\n\t\t\t\tauto ntp = std::get<std::shared_ptr<NTensor>>(it->content);\n\t\t\t\tif(ntp->shape.size()==1 && ntp->shape[0]==1 && ntp->is_real()) {\n\t\t\t\t\tmultiply(it->multiplier, ntp->at().real());\n\t\t\t\t\tit->content = std::monostate();\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t\n\t\t\tif(it->is_zero() && (tr.number_of_children(it)!=0 || *it->name!=\"1\")) {\n\t\t\t\tcadabra::zero(it->multiplier);\n\t\t\t\ttr.erase_children(it);\n\t\t\t\tit->name=name_set.insert(\"1\").first;\n\t\t\t\t// once we hit zero, there is nothing to simplify anymore\n\t\t\t\tbreak;\n\t\t\t\t}\n\t\t\tif(*it->name==\"\\\\frac\")                          res = cleanup_fraclike(kernel, tr, it);\n\t\t\tchanged = changed || res;\n\t\t\tif(*it->name==\"\\\\pow\")                           res = cleanup_powlike(kernel, tr, it);\n\t\t\tchanged = changed || res;\n\t\t\tif(*it->name==\"\\\\prod\" || *it->name==\"\\\\wedge\")  res = cleanup_productlike(kernel, tr, it);\n\t\t\tchanged = changed || res;\n\t\t\tif(*it->name==\"\\\\sum\")                           res = cleanup_sumlike(kernel, tr, it);\n\t\t\tchanged = changed || res;\n\t\t\tif(*it->name==\"\\\\comma\")                         res = cleanup_comma(kernel, tr, it);\n\t\t\tchanged = changed || res;\n\t\t\tif(*it->name==\"\\\\tie\")                           res = cleanup_tie(kernel, tr, it);\n\t\t\tchanged = changed || res;\n\t\t\tif(*it->name==\"\\\\components\")                    res = cleanup_components(kernel, tr, it);\n\t\t\tchanged = changed || res;\n\n\t\t\tconst Derivative *der = kernel.properties.get<Derivative>(it);\n\t\t\tif(der) {\n\t\t\t\tres = cleanup_derivative(kernel, tr, it);\n\t\t\t\tchanged = changed || res;\n\t\t\t\t}\n\t\t\tconst PartialDerivative *pder = kernel.properties.get<PartialDerivative>(it);\n\t\t\tif(pder) {\n\t\t\t\tres = cleanup_partialderivative(kernel, tr, it);\n\t\t\t\tchanged = changed || res;\n\t\t\t\t}\n\t\t\t// std::cerr << \"derivative \" << changed << std::endl;\n\n\t\t\tconst NumericalFlat *nf = kernel.properties.get<NumericalFlat>(it);\n\t\t\tif(nf) {\n\t\t\t\tres = cleanup_numericalflat(kernel, tr, it);\n\t\t\t\tchanged = changed || res;\n\t\t\t\t}\n\t\t\t// std::cerr << \"numerical \" << changed << std::endl;\n\n\t\t\tconst Diagonal *diag = kernel.properties.get<Diagonal>(it);\n\t\t\tif(diag) {\n\t\t\t\tres = cleanup_diagonal(kernel, tr, it);\n\t\t\t\tchanged = changed || res;\n\t\t\t\t}\n\t\t\t// std::cerr << \"diagonal \" << changed << std::endl;\n\n\t\t\t//std::cerr << \"Is symbol \" << Ex(it) << \" a KD?\" << std::endl;\n\t\t\tconst KroneckerDelta *kr = kernel.properties.get<KroneckerDelta>(it);\n\t\t\tif(kr) {\n\t\t\t\t//std::cerr << \"Symbol \" << Ex(it) << \" is a KD\" << std::endl;\n\t\t\t\tres = cleanup_kronecker(kernel, tr, it);\n\t\t\t\tchanged = changed || res;\n\t\t\t\t}\n\t\t\t// std::cerr << \"delta \" << changed << std::endl;\n\n\t\t\tconst ExteriorDerivative *ed = kernel.properties.get<ExteriorDerivative>(it);\n\t\t\tif(ed) {\n\t\t\t\tres = cleanup_exterior_derivative(kernel, tr, it);\n\t\t\t\tchanged = changed || res;\n\t\t\t\t}\n\n\t\t\t}\n\t\twhile(changed);\n\n\t\t//\tstd::cerr << Ex(it) << std::endl;\n\t\t}\n\n\tvoid check_index_consistency(const Kernel& k, Ex& tr, Ex::iterator it)\n\t\t{\n\t\tif(it==tr.end()) return;\n\t\tcollect_terms ct(k, tr);\n\t\tct.check_index_consistency(it);\n\t\tct.check_degree_consistency(it); // FIXME: needs to be implemented in Algorithm.\n\t\t}\n\n\tbool cleanup_fraclike(const Kernel& k, Ex&tr, Ex::iterator& it)\n\t\t{\n\t\tauto arg=tr.begin(it);\n\t\tif(*arg->name==\"\\\\equals\") {\n\t\t\t// When dividing an equation by something else, divide both sides.\n\n\t\t\tauto div=arg;\n\t\t\t++div;\n\n\t\t\tauto lhs=tr.begin(arg);\n\t\t\tauto rhs=lhs;\n\t\t\trhs.skip_children();\n\t\t\t++rhs;\n\n\t\t\tauto lhsfrac=tr.wrap(lhs, str_node(\"\\\\frac\"));\n\t\t\tauto rhsfrac=tr.wrap(rhs, str_node(\"\\\\frac\"));\n\t\t\ttr.append_child(lhsfrac, div);\n\t\t\ttr.append_child(rhsfrac, div);\n\n\t\t\tit=tr.flatten_and_erase(it);\n\n\t\t\treturn true;\n\t\t\t}\n\n\t\treturn false;\n\t\t}\n\n\tbool cleanup_powlike(const Kernel& k, Ex&tr, Ex::iterator& it)\n\t\t{\n\t\tauto arg=tr.begin(it);\n\t\tauto exp=arg;\n\t\t++exp;\n\t\tif(exp==tr.end(it)) return false;\n\n\t\t// (anything)^1 = anything\n\t\tif(exp->is_integer() && *exp->multiplier==1) {\n\t\t\ttr.erase(exp);\n\t\t\tit = tr.flatten_and_erase(it);\n\t\t\treturn true;\n\t\t\t}\n\t\t\n\t\tif(*arg->multiplier==0) { // 0**positive = 0, 0**negative=undefined\n\t\t\tif(*exp->multiplier<0)\n\t\t\t\tthrow RuntimeException(\"Division by zero encountered.\");\n\t\t\tzero(it->multiplier);\n\t\t\treturn true;\n\t\t\t}\n\t\t\n\t\tif(*arg->name==\"1\") {\n\t\t\tif(*arg->multiplier==1) { // 1**anything = 1\n\t\t\t\ttr.erase_children(it);\n\t\t\t\tit->name=name_set.insert(\"1\").first;\n\t\t\t\treturn true;\n\t\t\t\t}\n\t\t\tif(*exp->name==\"1\" && *exp->multiplier==-1) {    // Turn (numerical)**(-1) into a multiplier.\n\t\t\t\tmultiply(it->multiplier, multiplier_t(1)/(*arg->multiplier));\n\t\t\t\ttr.erase_children(it);\n\t\t\t\tit->name = name_set.insert(\"1\").first;\n\t\t\t\treturn true;\n\t\t\t\t}\n\t\t\t}\n\n\t\t// Turn \\pow{mA A}{B} with mA the multiplier for A into mA^B \\pow{A}{B}\n\t\tif(exp->is_integer() && exp->multiplier->is_rational()\n\t\t\t&& arg->multiplier->is_rational() && *arg->multiplier!=1 && *arg->name!=\"1\") {\n\t\t\tmpz_class nw_n, nw_d;\n\t\t\t// std::cerr << \"also doing \" << arg << \", \" << *arg->multiplier << \"**\" << *exp->multiplier << \"***\" << std::endl;\n\t\t\tlong Cexp=to_long(exp->multiplier->get_rational());\n\t\t\tmpz_pow_ui(nw_n.get_mpz_t(), arg->multiplier->get_rational().get_num().get_mpz_t(), std::abs(Cexp));\n\t\t\tmpz_pow_ui(nw_d.get_mpz_t(), arg->multiplier->get_rational().get_den().get_mpz_t(), std::abs(Cexp));\n\t\t\t// std::cerr << nw_n << \", \" << nw_d << std::endl;\n\t\t\tif(Cexp<0)\n\t\t\t\tstd::swap(nw_n, nw_d);\n\t\t\tmpq_class newmult=mpq_class(nw_n, nw_d);\n\t\t\tnewmult.canonicalize();\n\t\t\t// std::cerr << newmult << std::endl;\n\t\t\tmultiply(it->multiplier, *rat_set.insert(newmult).first);\n\t\t\tone(arg->multiplier);\n\t\t\treturn true;\n\t\t\t}\n\n\t\t// Turn \\pow{mult \\pow{A}{B}}{C} into \\pow{mult}{C} \\pow{A}{B*C} if C is an integer.\n\t\t// A bit tricky with the multiplier of \\pow{A}{B}, as that becomes mult^C\n\t\t// and can then either be absorbed into the overall multiplier, or needs\n\t\t// a second factor.\n\t\tauto ipow=tr.begin(it);\n\t\tif(*ipow->name==\"\\\\pow\") {\n\t\t\t// std::cerr << \"*POW\" << std::endl;\n\t\t\t// tr.print_recursive_treeform(std::cerr, it);\n\t\t\tauto iA=tr.begin(ipow);\n\t\t\tauto iB=iA;\n\t\t\t++iB;\n\t\t\tauto iC=ipow;\n\t\t\t++iC;\n\t\t\t// std::cerr << it << std::endl;\n\t\t\tif(ipow->multiplier->is_rational() && (iC->is_integer() || k.properties.get<Integer>(iC))) {\n\t\t\t\tif(iC->is_integer() && iC->multiplier->is_rational()) { // newmult = (mult)^C;\n\t\t\t\t\tmpz_class nw_n, nw_d;\n\t\t\t\t\t// std::cerr << \"doing \" << *ipow->multiplier << \"**\" << *iC->multiplier << std::endl;\n\t\t\t\t\tlong Cexp=to_long(iC->multiplier->get_rational());\n\t\t\t\t\tmpz_pow_ui(nw_n.get_mpz_t(), ipow->multiplier->get_rational().get_num().get_mpz_t(), std::abs(Cexp));\n\t\t\t\t\tmpz_pow_ui(nw_d.get_mpz_t(), ipow->multiplier->get_rational().get_den().get_mpz_t(), std::abs(Cexp));\n\t\t\t\t\tif(Cexp<0)\n\t\t\t\t\t\tstd::swap(nw_n, nw_d);\n\t\t\t\t\tmpq_class newmult(nw_n, nw_d);\n\t\t\t\t\tnewmult.canonicalize();\n\t\t\t\t\t// std::cerr << \"new multiplier \" << newmult << std::endl;\n\t\t\t\t\tipow->multiplier=rat_set.insert(newmult).first;\n\t\t\t\t\t}\n\t\t\t\telse {   // need to generate (mult)^C as a separate factor, if mult!=1.\n\t\t\t\t\tif(*ipow->multiplier!=1) {\n\t\t\t\t\t\t// std::cerr << \"generate separate factor for \" << *ipow->multiplier << \"**\" << iC << std::endl;\n\t\t\t\t\t\tEx nw(\"\\\\pow\");\n\t\t\t\t\t\tnw.append_child(nw.begin(), str_node(\"1\"))->multiplier=ipow->multiplier;\n\t\t\t\t\t\tnw.append_child(nw.begin(), Ex::iterator(iC));\n\t\t\t\t\t\ttr.wrap(it, str_node(\"\\\\prod\"));\n\t\t\t\t\t\ttr.insert_subtree(it, nw.begin());\n\t\t\t\t\t\tone(ipow->multiplier);\n\t\t\t\t\t\t}\n\t\t\t\t\t}\n\t\t\t\tEx::iterator expprod=tr.wrap(iB, str_node(\"\\\\prod\"));\n\t\t\t\ttr.move_after(iB, iC);\n\t\t\t\tit=tr.flatten_and_erase(it);\n\t\t\t\tcleanup_productlike(k, tr, expprod);\n\t\t\t\t// std::cerr << \"after: \" << it << std::endl;\n\t\t\t\treturn true;\n\t\t\t\t}\n\t\t\t}\n\n\t\treturn false;\n\t\t}\n\n\tbool cleanup_productlike(const Kernel& k, Ex&tr, Ex::iterator& it)\n\t\t{\n\t\tbool ret=false;\n\n\t\tassert(*it->name==\"\\\\prod\" || *it->name==\"\\\\wedge\");\n\t\tstd::string nm = *it->name;\n\n\t\t// Flatten prod children inside this prod node.\n\t\tauto sib=tr.begin(it);\n\t\twhile(sib!=tr.end(it)) {\n\t\t\tif(*sib->name==nm) {\n\t\t\t\tmultiply(it->multiplier, *sib->multiplier);\n\t\t\t\ttr.flatten(sib);\n\t\t\t\tsib=tr.erase(sib);\n\t\t\t\tret=true;\n\t\t\t\t}\n\t\t\telse ++sib;\n\t\t\t}\n\n\t\tif(tr.number_of_children(it)==1)\n\t\t\tif(tr.begin(it)->is_range_wildcard())\n\t\t\t\treturn ret;\n\n\t\tbool tmp = cleanup_numericalflat(k, tr, it);\n\t\tret = ret || tmp;\n\n\t\t// Turn products of ImaginaryI into -1 factors.\n\t\tif(tr.number_of_children(it)>1) {\n\t\t\tstd::vector<Ex::sibling_iterator> fs;\n\t\t\tauto sib=tr.begin(it);\n\t\t\twhile(sib!=tr.end(it)) {\n\t\t\t\tif(k.properties.get<ImaginaryI>(sib))\n\t\t\t\t\tfs.push_back(sib);\n\t\t\t\t++sib;\n\t\t\t\t}\n\t\t\tmultiplier_t mult=1;\n\t\t\tfor(size_t i=0; i<fs.size()/2; ++i) {\n\t\t\t\ttr.erase(fs[2*i]);\n\t\t\t\ttr.erase(fs[2*i+1]);\n\t\t\t\tmult*=-1;\n\t\t\t\t}\n\t\t\tmultiply(it->multiplier, mult);\n\t\t\t}\n\n\t\t// Turn products with two adjacent identical anti-commuting siblings to zero.\n\t\tif(nm==\"\\\\prod\") {\n\t\t\tauto s1=tr.begin(it);\n\t\t\tauto s2=s1;\n\t\t\t++s2;\n\t\t\twhile(s2!=tr.end(it)) {\n\t\t\t\tauto ac = k.properties.get<SelfAntiCommuting>(s1);\n\t\t\t\tif(ac) {\n\t\t\t\t\tif(subtree_compare(0, s1, s2)==0) {\n\t\t\t\t\t\ttr.erase_children(it);\n\t\t\t\t\t\tzero(it->multiplier);\n\t\t\t\t\t\tret=true;\n\t\t\t\t\t\tbreak;\n\t\t\t\t\t\t}\n\t\t\t\t\t}\n\t\t\t\t++s2;\n\t\t\t\t++s1;\n\t\t\t\t}\n\t\t\t}\n\n\t\t// Turn wedge products containing two identical siblings of odd degree to zero\n\t\t// if they are not matrix objects.\n\t\tif(nm==\"\\\\wedge\") {\n\t\t\tauto s1=tr.begin(it);\n\t\t\tauto s2=s1;\n\t\t\t++s2;\n\t\t\twhile(s2!=tr.end(it)) {\n\t\t\t\tif(subtree_compare(0, s1, s2)==0) {\n\t\t\t\t\tauto df1 = k.properties.get<DifferentialForm>(s1);\n\t\t\t\t\tauto df2 = k.properties.get<DifferentialForm>(s2);\n\t\t\t\t\tauto mat1 = k.properties.get<Matrix>(s1);\n\t\t\t\t\tauto mat2 = k.properties.get<Matrix>(s2);\n\t\t\t\t\tif(df1 && df2 && !(mat1 && mat2) ) {\n\t\t\t\t\t\tauto degree1 = df1->degree(k.properties, s1);\n\t\t\t\t\t\tauto degree2 = df2->degree(k.properties, s2);\n\t\t\t\t\t\tif(degree1.is_rational() && degree2.is_rational()) {\n\t\t\t\t\t\t\tlong d1 = to_long(degree1.to_rational());\n\t\t\t\t\t\t\tlong d2 = to_long(degree2.to_rational());\n\t\t\t\t\t\t\tif(d1==d2 && d1%2==1) {\n\t\t\t\t\t\t\t\ttr.erase_children(it);\n\t\t\t\t\t\t\t\tzero(it->multiplier);\n\t\t\t\t\t\t\t\tret=true;\n\t\t\t\t\t\t\t\tbreak;\n\t\t\t\t\t\t\t\t}\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\t}\n\t\t\t\t\t}\n\t\t\t\t++s2;\n\t\t\t\t++s1;\n\t\t\t\t}\n\t\t\t}\n\n\t\t// Handle edge cases where the product should collapse to a single node,\n\t\t// e.g. when we have just a single factor, or when the product vanishes.\n\n\t\tif(tr.number_of_children(it)==1) { // i.e. from '3*4*7*a*9'\n\t\t\tret=true;\n\t\t\ttr.begin(it)->fl.bracket=it->fl.bracket;\n\t\t\ttr.begin(it)->fl.parent_rel=it->fl.parent_rel;\n\t\t\ttr.begin(it)->multiplier=it->multiplier;\n\t\t\ttr.flatten(it);\n\t\t\tit=tr.erase(it);\n\t\t\tpush_down_multiplier(k, tr, it);\n\t\t\t}\n\t\telse if(tr.number_of_children(it)==0) {   // i.e. from '3*4*7*9'\n\t\t\tret=true;\n\t\t\tit->name=name_set.insert(\"1\").first;\n\t\t\t}\n\n\n\t\t// If any of the elements is an `\\equals`, multiply the rest of the\n\t\t// terms through on both sides. If there is more than one `\\equals`, throw\n\t\t// an error.\n\n\t\tsib=tr.begin(it);\n\t\tEx::sibling_iterator equals_node=tr.end(it);\n\t\twhile(sib!=tr.end(it)) {\n\t\t\tif(*sib->name==\"\\\\equals\") {\n\t\t\t\tif(equals_node!=tr.end(it))\n\t\t\t\t\tthrow ConsistencyException(\"Encountered more than one equalities in a product; undefined.\");\n\t\t\t\telse\n\t\t\t\t\tequals_node=sib;\n\t\t\t\t}\n\t\t\t++sib;\n\t\t\t}\n\t\tif(equals_node!=tr.end(it)) {\n\t\t\tEx::sibling_iterator lhs=tr.begin(equals_node);\n\t\t\tEx::sibling_iterator rhs=lhs;\n\t\t\t++rhs;\n\n\t\t\tauto lhsprod=tr.wrap(lhs, str_node(\"\\\\prod\"));\n\t\t\tauto rhsprod=tr.wrap(rhs, str_node(\"\\\\prod\"));\n\t\t\tsib=tr.begin(it);\n\t\t\tbool left=true;\n\t\t\twhile(sib!=tr.end(it)) {\n\t\t\t\tif(sib!=equals_node) {\n\t\t\t\t\tif(left) {\n\t\t\t\t\t\ttr.prepend_child(lhsprod, sib);\n\t\t\t\t\t\ttr.prepend_child(rhsprod, sib);\n\t\t\t\t\t\t}\n\t\t\t\t\telse {\n\t\t\t\t\t\ttr.append_child(lhsprod, sib);\n\t\t\t\t\t\ttr.append_child(rhsprod, sib);\n\t\t\t\t\t\t}\n\t\t\t\t\tsib=tr.erase(sib);\n\t\t\t\t\t}\n\t\t\t\telse {\n\t\t\t\t\tleft=false;\n\t\t\t\t\t++sib;\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\tEx::iterator tmp1(lhsprod), tmp2(rhsprod);\n\t\t\tcleanup_dispatch(k, tr, tmp1);\n\t\t\tcleanup_dispatch(k, tr, tmp2);\n\t\t\tit=tr.flatten_and_erase(it);\n\t\t\tret=true;\n\t\t\t}\n\n\t\treturn ret;\n\t\t}\n\n\tbool cleanup_sumlike(const Kernel& k, Ex&tr, Ex::iterator& it)\n\t\t{\n#ifdef DEBUG\n\t\tstd::cerr << \"cleanup_sumlike, before: \" << it << std::endl;\n\t\tif(tr.number_of_children(it)==0)\n\t\t\tstd::cerr << \"zero children on sum; \" << it.node << \", tree = \" << tr.begin() << std::endl;\n#endif\n\t\tassert(*it->name==\"\\\\sum\");\n\t\tbool ret=false;\n\n\t\t// Remove children which are 0\n\t\tEx::sibling_iterator sib=tr.begin(it);\n\t\twhile(sib!=tr.end(it)) {\n\t\t\tif(sib->is_zero()) {\n\t\t\t\tret=true;\n\t\t\t\tsib=tr.erase(sib);\n\t\t\t\t}\n\t\t\telse\n\t\t\t\t++sib;\n\t\t\t}\n\n\t\t// Do not allow equalities as terms inside a sum if there are\n\t\t// other terms present as well.\n\t\tsib=tr.begin(it);\n\t\tint equalities=0;\n\t\tint nonequalities=0;\n\t\twhile(sib!=tr.end(it)) {\n\t\t\tif(*sib->name==\"\\\\equals\") ++equalities;\n\t\t\telse                       ++nonequalities;\n\t\t\tif(equalities!=0 && nonequalities!=0)\n\t\t\t\tthrow ConsistencyException(\"Encountered an equality and a normal term in the same sum; not allowed.\");\n\t\t\t++sib;\n\t\t\t}\n\t\tif(equalities>1) { // This is a sum of at least 2 equalities.\n\t\t\t// Combine all lhs and all rhs.\n\t\t\tauto frst=tr.begin(it);\n\t\t\tEx::sibling_iterator lhs=tr.begin(frst);\n\t\t\tEx::sibling_iterator rhs=lhs;\n\t\t\t++rhs;\n\t\t\t// Ensure both lhs and rhs are sums.\n\t\t\tif(*lhs->name!=\"\\\\sum\")\n\t\t\t\tlhs=tr.wrap(lhs, str_node(\"\\\\sum\"));\n\t\t\tif(*rhs->name!=\"\\\\sum\")\n\t\t\t\trhs=tr.wrap(rhs, str_node(\"\\\\sum\"));\n\t\t\tEx::sibling_iterator lhsend=tr.end(lhs);\n\t\t\tEx::sibling_iterator rhsend=tr.end(rhs);\n\t\t\tsib=frst;\n\t\t\t++sib;\n\t\t\twhile(sib!=tr.end(it)) {\n            // sib is an `\\equals` node\n\t\t\t\tEx::sibling_iterator side=tr.begin(sib);\n\t\t\t\tmultiply(side->multiplier, *sib->multiplier);\n\t\t\t\ttr.move_before(lhsend, side);\n\t\t\t\tside=tr.begin(sib);\n\t\t\t\tmultiply(side->multiplier, *sib->multiplier);\n\t\t\t\ttr.move_before(rhsend, side);\n\t\t\t\tsib=tr.erase(sib);\n\t\t\t\t}\n#ifdef DEBUG\n\t\t\tstd::cerr << \"got through equals cleanup\" << std::endl;\n\t\t\tstd::cerr << it << std::endl;\n#endif\n\t\t\tEx::iterator tmp1=lhs, tmp2=rhs;\n\t\t\tcleanup_sumlike(k, tr, tmp1);\n\t\t\tcleanup_sumlike(k, tr, tmp2);\n\t\t\t}\n\n\t\t// Flatten sums which are supposed to be flat.\n\t\tlong num=tr.number_of_children(it);\n\t\tif(num==0) {\n\t\t\tret=true;\n\t\t\tcadabra::zero(it->multiplier);\n\t\t\treturn ret;\n\t\t\t}\n\n\t\tif(num==1) {\n\t\t\tif(tr.begin(it)->is_range_wildcard())\n\t\t\t\treturn ret;\n\n\t\t\tret=true;\n\t\t\tmultiply(tr.begin(it)->multiplier, *it->multiplier);\n\t\t\ttr.flatten(it);\n\t\t\tit=tr.erase(it);\n\t\t\t}\n\t\telse {\n\t\t\tauto facs=tr.begin(it);\n\t\t\tstr_node::bracket_t btype_par=facs->fl.bracket;\n\t\t\twhile(facs!=tr.end(it)) {\n\t\t\t\tif(facs->fl.bracket!=str_node::b_none) {\n\t\t\t\t\tbtype_par=facs->fl.bracket;\n\t\t\t\t\t}\n\t\t\t\t++facs;\n\t\t\t\t}\n\t\t\tfacs=tr.begin(it);\n\t\t\twhile(facs!=tr.end(it)) {\n\t\t\t\tif(*facs->name==\"\\\\sum\") {\n\t\t\t\t\tauto terms=tr.begin(facs);\n\t\t\t\t\tauto tmp=facs;\n\t\t\t\t\t++tmp;\n\t\t\t\t\twhile(terms!=tr.end(facs)) {\n\t\t\t\t\t\tmultiply(terms->multiplier,*facs->multiplier);\n\t\t\t\t\t\tterms->fl.bracket=btype_par;\n\t\t\t\t\t\t++terms;\n\t\t\t\t\t\t}\n\t\t\t\t\tret=true;\n\t\t\t\t\ttr.flatten(facs);\n\t\t\t\t\ttr.erase(facs);\n\t\t\t\t\tfacs=tmp;\n\t\t\t\t\t}\n\t\t\t\telse ++facs;\n\t\t\t\t}\n\t\t\t}\n\n\t\tbool tmp = push_down_multiplier(k, tr, it);\n\t\tret = ret || tmp;\n\n#ifdef DEBUG\n\t\tstd::cerr << \"cleanup_sumlike, after, \" << ret << \": \" << it << std::endl;\n#endif\n\t\treturn ret;\n\t\t}\n\n\tbool push_down_multiplier(const Kernel& k, Ex& tr, Ex::iterator it)\n\t\t{\n\t\tbool ret=false;\n\n\t\tauto mult=*it->multiplier;\n\t\tif(mult==1)\n\t\t\treturn ret;\n\n\t\tif(*it->name==\"\\\\sum\" || *it->name==\"\\\\equals\") {\n\t\t\tauto sib=tr.begin(it);\n\t\t\twhile(sib!=tr.end(it)) {\n\t\t\t\tret=true;\n\t\t\t\tmultiply(sib->multiplier, mult);\n\t\t\t\tpush_down_multiplier(k, tr, sib);\n\t\t\t\t++sib;\n\t\t\t\t}\n\t\t\tif(*it->multiplier!=1)\n\t\t\t\tret=true;\n\t\t\tone(it->multiplier);\n\t\t\t}\n\t\telse if(*it->name==\"\\\\components\") {\n\t\t\tEx::sibling_iterator sib=tr.end(it);\n\t\t\t--sib;\n\t\t\t// Examine all index value sets and push the multiplier\n\t\t\t// in there.\n\t\t\tcadabra::do_list(tr, sib, [&](Ex::iterator nd) {\n\t\t\t\tEx::sibling_iterator val=tr.begin(nd);\n\t\t\t\t++val;\n\t\t\t\tif(mult!=1) {\n\t\t\t\t\tret=true;\n\t\t\t\t\tmultiply(val->multiplier, mult);\n\t\t\t\t\t}\n\t\t\t\t// Need to evaluate it; just putting it in '||' may lead to the compiler not evaluating it if\n\t\t\t\t// 'ret' is already true!\n\t\t\t\tbool tmp = push_down_multiplier(k, tr, val);\n\t\t\t\tret = ret || tmp;\n\t\t\t\treturn true;\n\t\t\t\t});\n\t\t\tif(*it->multiplier!=1)\n\t\t\t\tret=true;\n\t\t\tone(it->multiplier);\n\t\t\t}\n\n\t\treturn ret;\n\t\t}\n\n\tbool cleanup_components(const Kernel& k, Ex&tr, Ex::iterator& it)\n\t\t{\n\t\tassert(*it->name==\"\\\\components\");\n\n\t\tbool ret=push_down_multiplier(k, tr, it);\n\n\t\t// If this component node has no free indices, get rid of all\n\t\t// the baggage and turn into a normal expression.\n\n\t\t// std::cerr << \"components cleanup: \" << Ex(it) << std::endl;\n\n\t\tauto comma=tr.begin(it);\n\t\tif(*comma->name==\"\\\\comma\") { // If the first child is \\comma, there are no indices: scalar.\n\t\t\tif(tr.number_of_children(comma)==0) {\n\t\t\t\t// Totally empty component node, can happen after an\n\t\t\t\t// evaluate with no rules matching.\n\t\t\t\tzero(it->multiplier);\n\t\t\t\tret=true;\n\t\t\t\treturn ret;\n\t\t\t\t}\n\t\t\tret=true;\n\t\t\t// std::cerr << \"components node for a scalar\" << std::endl;\n\t\t\ttr.flatten(comma);     // unwrap comma\n\t\t\tcomma=tr.erase(comma); // erase comma\n\t\t\ttr.flatten(comma);     // unwrap equals\n\t\t\tcomma=tr.erase(comma); // erase equals\n\t\t\tcomma=tr.erase(comma); // remove empty comma for index values\n\t\t\ttr.flatten(it); // remove components node\n\t\t\tit=tr.erase(it);\n\t\t\t// std::cerr << Ex(it) << std::endl;\n\t\t\t}\n\t\telse {\n\t\t\twhile(comma!=tr.end(it)) {\n\t\t\t\tif(*comma->name==\"\\\\comma\") {\n\t\t\t\t\tif(tr.number_of_children(comma)==0) {\n\t\t\t\t\t\tret=true;\n\t\t\t\t\t\tzero(it->multiplier);\n\t\t\t\t\t\t}\n\t\t\t\t\t// Still check if there is a component value for which the index\n\t\t\t\t\t// values exactly match the index names. In that case, replace\n\t\t\t\t\t// the entire components node with the component value.\n\t\t\t\t\tauto equals   = tr.begin(comma);\n\t\t\t\t\twhile(equals != tr.end(comma)) {\n\t\t\t\t\t\tauto valcomma = tr.begin(equals);\n\t\t\t\t\t\tauto valindices=tr.begin(valcomma);\n\t\t\t\t\t\tauto expindices=tr.begin(it);\n\t\t\t\t\t\tEx_comparator comp(k.properties);\n\t\t\t\t\t\tbool foundmatch=true;\n\t\t\t\t\t\twhile(valindices!=tr.end(valcomma)) {\n\t\t\t\t\t\t\tauto match = comp.equal_subtree(valindices, expindices, Ex_comparator::useprops_t::not_at_top, true);\n\t\t\t\t\t\t\tif(! (match==Ex_comparator::match_t::node_match || match==Ex_comparator::match_t::subtree_match)) {\n\t\t\t\t\t\t\t\tfoundmatch=false;\n\t\t\t\t\t\t\t\tbreak;\n\t\t\t\t\t\t\t\t}\n\t\t\t\t\t\t\t++expindices;\n\t\t\t\t\t\t\t++valindices;\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\tif(foundmatch) {\n\t\t\t\t\t\t\t// Yep, we can unwrap this component and replace it with the\n\t\t\t\t\t\t\t// single value.\n\t\t\t\t\t\t\tauto erase=tr.begin(it);\n\t\t\t\t\t\t\twhile(erase!=comma)    // erase indices from \\components\n\t\t\t\t\t\t\t\terase=tr.erase(erase);\n\t\t\t\t\t\t\tauto eit=tr.begin(comma);\n\t\t\t\t\t\t\twhile(eit!=tr.end(comma)) { // erase all component values which we do not need.\n\t\t\t\t\t\t\t\tif(eit==equals) ++eit;\n\t\t\t\t\t\t\t\telse            eit=tr.erase(eit);\n\t\t\t\t\t\t\t\t}\n\t\t\t\t\t\t\ttr.flatten(comma);     // unwrap comma\n\t\t\t\t\t\t\tcomma=tr.erase(comma); // erase comma\n\t\t\t\t\t\t\ttr.flatten(comma);     // unwrap equals\n\t\t\t\t\t\t\tcomma=tr.erase(comma); // erase equals\n\t\t\t\t\t\t\tcomma=tr.erase(comma); // remove comma node (plus its children) for index values\n\t\t\t\t\t\t\ttr.flatten(it); // remove components node\n\t\t\t\t\t\t\tit=tr.erase(it);\n\t\t\t\t\t\t\treturn true;\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\t++equals;\n\t\t\t\t\t\t}\n\t\t\t\t\t// None of the index value sets match the index names. If the index names are\n\t\t\t\t\t// coordinates, this means that the value of this component is zero.\n\t\t\t\t\tauto expindices=tr.begin(it);\n\t\t\t\t\tbool all_coordinates=true;\n\t\t\t\t\twhile(*expindices->name!=\"\\\\comma\") {\n\t\t\t\t\t\tif(expindices->is_integer()==false && k.properties.get<Coordinate>(expindices, true)==0) {\n\t\t\t\t\t\t\tall_coordinates=false;\n\t\t\t\t\t\t\tbreak;\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\t++expindices;\n\t\t\t\t\t\t}\n\t\t\t\t\tif(all_coordinates) {\n\t\t\t\t\t\tzero(it->multiplier);\n\t\t\t\t\t\treturn true;\n\t\t\t\t\t\t}\n\t\t\t\t\treturn ret;\n\t\t\t\t\t}\n\t\t\t\t++comma;\n\t\t\t\t}\n\t\t\t// Anonymous tensor with all components vanishing.\n\t\t\tret=true;\n\t\t\tzero(it->multiplier);\n\t\t\t}\n\n\t\treturn ret;\n\t\t}\n\n\tbool cleanup_partialderivative(const Kernel&, Ex& tr, Ex::iterator& it)\n\t\t{\n\t\t// Nested derivatives with the same name should be flattened, but\n\t\t// only if both the outer derivative and the inner derivative have\n\t\t// an index (otherwise D(D(A)) becomes D(A) which is wrong).\n\n\t\t// Find first non-index child.\n\n\t\tbool ret=false;\n\n\t\tEx::sibling_iterator sib=tr.begin(it);\n\t\tif(sib==tr.end(it)) return ret;\n\n\t\twhile(sib->is_index()) {\n\t\t\t++sib;\n\t\t\tif(sib==tr.end(it)) {\n\t\t\t\tzero(it->multiplier);\n\t\t\t\treturn true;\n\t\t\t\t}\n\t\t\tif(sib==tr.end(it))\n\t\t\t\tthrow ConsistencyException(\"Encountered PartialDerivative object without argument on which to act.\");\n\t\t\t}\n\n\t\t// FIXME: this ignores that derivatives can have functional child\n\t\t// nodes which are interpreted as 'object wrt. with derivative should be taken'.\n\n\t\tif(it->name == sib->name) {\n\t\t\tif(Algorithm::number_of_direct_indices(it)>0 && Algorithm::number_of_direct_indices(sib)>0) {\n\t\t\t\tmultiply(it->multiplier, *sib->multiplier);\n\t\t\t\ttr.flatten(sib);\n\t\t\t\ttr.erase(sib);\n\t\t\t\tret=true;\n\t\t\t\t}\n\t\t\t}\n\n\t\treturn ret;\n\t\t}\n\n\tbool cleanup_derivative(const Kernel& k, Ex& tr, Ex::iterator& it)\n\t\t{\n\t\tbool ret=false;\n\n\t\tif(Algorithm::number_of_direct_indices(it) == tr.number_of_children(it)) {\n\t\t\t// This is a derivative acting on nothing, always occurs\n\t\t\t// when all constants have been moved out.\n\t\t\tzero(it->multiplier);\n\t\t\tret=true;\n\t\t\treturn ret;\n\t\t\t}\n\n\t\tauto sib=tr.begin(it);\n\t\twhile(sib!=tr.end(it)) {\n\t\t\tif(sib->fl.parent_rel==str_node::p_none) {\n\t\t\t\tif(*sib->name==\"\\\\equals\") {\n\t\t\t\t\t// FIXME: this should probably be taken out for generalisation.\n\t\t\t\t\tauto lhs = tr.begin(sib);\n\t\t\t\t\tauto rhs = lhs;\n\t\t\t\t\t++rhs;\n\n\t\t\t\t\tauto lhswrap = tr.wrap(lhs, *it);\n\t\t\t\t\tauto rhswrap = tr.wrap(rhs, *it);\n\t\t\t\t\tmultiply(lhswrap->multiplier, *it->multiplier);\n\t\t\t\t\tmultiply(rhswrap->multiplier, *it->multiplier);\n\n\t\t\t\t\tauto sib2=tr.begin(it);\n\t\t\t\t\twhile(sib2!=tr.end(it)) {\n\t\t\t\t\t\tif(sib2!=sib) {\n\t\t\t\t\t\t\ttr.insert_subtree(lhs, sib2);\n\t\t\t\t\t\t\ttr.insert_subtree(rhs, sib2);\n\t\t\t\t\t\t\tsib2=tr.erase(sib2);\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\telse ++sib2;\n\t\t\t\t\t\t}\n\n\t\t\t\t\tit=tr.flatten(it);\n\t\t\t\t\tit=tr.erase(it);\n\n\t\t\t\t\tEx::iterator tmp1(lhswrap), tmp2(rhswrap);\n\t\t\t\t\tcleanup_dispatch(k, tr, tmp1);\n\t\t\t\t\tcleanup_dispatch(k, tr, tmp2);\n\n\t\t\t\t\tret=true;\n\t\t\t\t\tbreak;\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t++sib;\n\t\t\t}\n\n\t\treturn ret;\n\t\t}\n\n\tbool cleanup_numericalflat(const Kernel&, Ex& tr, Ex::iterator& it)\n\t\t{\n\t\tbool ret=false;\n\n\t\t//tr.print_recursive_treeform(std::cerr, it);\n\t\t// Collect all multipliers and remove resulting '1' nodes.\n\t\tauto facs=tr.begin(it);\n\t\tmultiplier_t factor=1;\n\t\twhile(facs!=tr.end(it)) {\n\t\t\t// std::cerr << \"at \" << *facs << std::endl;\n\t\t\tif(facs->is_index()==false) { // Do not collect the number in e.g. \\partial_{4}{A}.\n\t\t\t\tfactor*=*facs->multiplier;\n\t\t\t\tif(facs->is_rational()) {\n\t\t\t\t\tmultiplier_t tmp; // FIXME: there is a bug in gmp which means we have to put init on next line.\n\t\t\t\t\ttmp=mpq_class((*facs->name).c_str());\n\t\t\t\t\tret=true;\n\t\t\t\t\tfactor*=tmp;\n\t\t\t\t\tfacs=tr.erase(facs);\n\t\t\t\t\tif(facs==tr.end())\n\t\t\t\t\t\tfacs=tr.end(it);\n\t\t\t\t\t}\n\t\t\t\telse {\n\t\t\t\t\tif(*facs->multiplier!=1)\n\t\t\t\t\t\tret=true;\n\t\t\t\t\tone(facs->multiplier);\n\t\t\t\t\t++facs;\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\telse ++facs;\n\t\t\t}\n\t\tif(factor!=1)\n\t\t\tret=true;\n\n\t\tmultiply(it->multiplier,factor);\n\t\treturn ret;\n\t\t}\n\n\tbool cleanup_diagonal(const Kernel& k, Ex& tr, Ex::iterator& it)\n\t\t{\n\t\tbool ret=false;\n\n\t\tif(tr.number_of_children(it)!=2) return ret;\n\n\t\tauto c1=tr.begin(it);\n\t\tauto c2(c1);\n\t\t++c2;\n\n\t\t// Two different numerical indices will lead to zero.\n\t\tif(c1->is_rational() && c2->is_rational())\n\t\t\tif(c1->multiplier != c2->multiplier) {\n\t\t\t\tret=true;\n\t\t\t\tzero(it->multiplier);\n\t\t\t\t}\n\t\t// Two different Coordinate indices will lead to zero.\n \t\tif(!(c1->is_rational() && c2->is_rational())) {\n\t\t\tauto *c1coord = k.properties.get<Coordinate>(c1, true);\n\t\t\tauto *c2coord = k.properties.get<Coordinate>(c2, true);\n\t\t\tif(c1coord!=0 && c2coord!=0) {\n\t\t\t\tif(subtree_compare(0, c1, c2)!=0) {\n\t\t\t\t\tret=true;\n\t\t\t\t\tzero(it->multiplier);\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t}\n\n\t\treturn ret;\n\t\t}\n\n\tbool cleanup_kronecker(const Kernel&, Ex& tr, Ex::iterator& it)\n\t\t{\n\t\tbool ret=false;\n\n\t\tif(tr.number_of_children(it)!=2) return ret;\n\n\t\tauto c1=tr.begin(it);\n\t\tauto c2(c1);\n\t\t++c2;\n\n\t\tif(c1->is_rational() && c2->is_rational()) {\n\t\t\tif(c1->multiplier != c2->multiplier) {\n\t\t\t\tret=true;\n\t\t\t\tzero(it->multiplier);\n\t\t\t\t}\n\t\t\telse {\n\t\t\t\t//\t\t\t::one(it->multiplier);\n\t\t\t\ttr.erase_children(it);\n\t\t\t\tret=true;\n\t\t\t\tit->name=name_set.insert(\"1\").first;\n\t\t\t\t}\n\t\t\t}\n\n\t\treturn ret;\n\t\t}\n\n\tbool cleanup_exterior_derivative(const Kernel& k, Ex& tr, Ex::iterator& it)\n\t\t{\n\t\t// FIXME: could have this act on a sum as well.\n\t\tif(tr.number_of_children(it)==1) {\n\t\t\tauto sib=tr.begin(it);\n\t\t\tconst ExteriorDerivative *ed1=k.properties.get<ExteriorDerivative>(it);\n\t\t\tconst ExteriorDerivative *ed2=k.properties.get<ExteriorDerivative>(sib);\n\t\t\tif(ed1==ed2) {\n\t\t\t\tzero(it->multiplier);\n\t\t\t\treturn true;\n\t\t\t\t}\n\t\t\t}\n\t\treturn false;\n\t\t}\n\n\tbool cleanup_comma(const Kernel& k, Ex& tr, Ex::iterator& it)\n\t\t{\n\t\tif(*it->multiplier!=1) {\n\t\t\tEx::sibling_iterator sib = tr.begin(it);\n\t\t\twhile(sib!=tr.end(it)) {\n\t\t\t\tmultiply(sib->multiplier, *it->multiplier);\n\t\t\t\t++sib;\n\t\t\t\t}\n\t\t\tone(it->multiplier);\n\t\t\treturn true;\n\t\t\t}\n\t\telse return false;\n\t\t}\n\n\tbool cleanup_tie(const Kernel& k, Ex& tr, Ex::iterator& it)\n\t\t{\n\t\t// Are all siblings lists?\n\t\tEx::sibling_iterator sib = tr.begin(it);\n\t\twhile(sib!=tr.end(it)) {\n\t\t\tif(*sib->name!=\"\\\\comma\")\n\t\t\t\treturn false;\n\t\t\t++sib;\n\t\t\t}\n\t\t\n\t\t// All siblings are lists. Join them together into one\n\t\t// long list.\n\t\tit->name = name_set.insert(\"\\\\comma\").first;\n\t\tsib=tr.begin(it);\n\t\twhile(sib!=tr.end(it)) {\n\t\t\tauto nxt = sib;\n\t\t\t++nxt;\n\t\t\ttr.flatten_and_erase(sib);\n\t\t\tsib=nxt;\n\t\t\t}\n\t\treturn true;\n\t\t}\n\n\tvoid cleanup_dispatch_deep(const Kernel& k, Ex& tr, dispatcher_t dispatch)\n\t\t{\n\t\tEx::iterator top=tr.begin();\n\t\tcleanup_dispatch_deep(k, tr, top, dispatch);\n\t\t}\n\n\tvoid cleanup_dispatch_deep(const Kernel& k, Ex& tr, Ex::iterator&, dispatcher_t dispatch)\n\t\t{\n\t\t// Cleanup the entire tree starting from the deepest nodes and\n\t\t// working upwards.\n\n\t\t// This duplicates work of Algorithm::apply, but we want to have an\n\t\t// independent cleanup unit which does not rely on things we may\n\t\t// want to change in Algorithm::apply in the future, and we do not\n\t\t// want to make recursive calls into that function either. And it is\n\t\t// simple enough anyway.\n\n\t\t//\tdo_subtree(tr, top, [&dispatch, &tr, &k](Ex::iterator it) {\n\t\t//\t\t\tdispatch(k, tr, it);\n\t\t//\t\t\treturn it;\n\t\t//\t\t\t});\n\n\t\tEx::post_order_iterator it=tr.begin();\n\t\tit.descend_all();\n\t\twhile(it!=tr.end()) {\n\t\t\tEx::post_order_iterator next=it;\n\t\t\t++next;\n\t\t\tEx::iterator tmp=it;\n\t\t\tdispatch(k, tr, tmp);\n\t\t\tit=next;\n\t\t\t}\n\n\t\t}\n\n\t}\n"
  },
  {
    "path": "core/Cleanup.hh",
    "content": "/*\n\n\tCadabra: a field-theory motivated computer algebra system.\n\tCopyright (C) 2001-2014  Kasper Peeters <kasper.peeters@phi-sci.com>\n\nThis program is free software: you can redistribute it and/or\nmodify it under the terms of the GNU General Public License as\n\tpublished by the Free Software Foundation, either version 3 of the\nLicense, or (at your option) any later version.\n\nThis program is distributed in the hope that it will be useful,\nbut WITHOUT ANY WARRANTY; without even the implied warranty of\nMERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU\nGeneral Public License for more details.\n\nYou should have received a copy of the GNU General Public License\n\talong with this program.  If not, see <http://www.gnu.org/licenses/>.\n\n*/\n\n\n#pragma once\n\n#include \"Storage.hh\"\n#include \"Kernel.hh\"\n\nnamespace cadabra {\n\n\ttypedef void (*dispatcher_t)(const Kernel& k, Ex&, Ex::iterator& it);\n\n\t/// \\ingroup cleanup\n\t///\n\t/// Central cleanup dispatch routine, which calls the other cleanup\n\t/// functions defined later.\n\t///\n\t/// These cleanup routines do NOT use normal cadabra algorithms; they\n\t/// are completely independent of them to prevent circular dependence\n\t/// or infinite recursion.\n\t///\n\t/// These algorithms clean up the tree at the current node and the\n\t/// first layer of child nodes, but do NOT descend deeper down the\n\t/// tree, UNLESS that would leave the tree in an inconsistent\n\t/// state. An example is acting at the top node of\n\t/// `\\prod{4}{\\sum{a}{b}}`, which would push the 4 to the multiplier of\n\t/// the sum, but that is not allowed, so it needs to go further down.\n\t/// Sibling nodes of 'it' remain untouched as well.\n\n\tvoid cleanup_dispatch(const Kernel& k, Ex&, Ex::iterator& it);\n\n\t/// \\ingroup cleanup\n\t///\n\t/// More general cleanup of an entire tree. Walks depth-first along the\n\t/// entire tree and call cleanup_dispatch at every node.\n\n\tvoid cleanup_dispatch_deep(const Kernel& k, Ex&, dispatcher_t disp=&cleanup_dispatch);\n\tvoid cleanup_dispatch_deep(const Kernel& k, Ex&, Ex::iterator& it, dispatcher_t disp=&cleanup_dispatch);\n\n\t/// Individual node cleanup routines. Do not call these yourself.\n\t///\n\t/// Once more, these algorithms clean up the tree at the current node\n\t/// and the first layer of child nodes, but do NOT descend deeper down\n\t/// the tree, except when that is necessary to ensure that the tree\n\t/// remains consistent.  As with any algorithms, the iterator pointing\n\t/// to the starting node may be changed, but these functions are not\n\t/// allowed to modify anything except the node and nodes below (in\n\t/// particular, they will leave sibling nodes untouched).\n\n\tbool cleanup_fraclike(const Kernel& k, Ex&, Ex::iterator& it);\n\tbool cleanup_powlike(const Kernel& k, Ex&, Ex::iterator& it);\n\tbool cleanup_productlike(const Kernel& k, Ex&, Ex::iterator& it);\n\tbool cleanup_sumlike(const Kernel& k, Ex&, Ex::iterator& it);\n\tbool cleanup_derivative(const Kernel& k, Ex&, Ex::iterator& it);\n\tbool cleanup_partialderivative(const Kernel& k, Ex&, Ex::iterator& it);\n\tbool cleanup_components(const Kernel& k, Ex&, Ex::iterator& it);\n\tbool cleanup_numericalflat(const Kernel& k, Ex&, Ex::iterator& it);\n\tbool cleanup_diagonal(const Kernel& k, Ex&, Ex::iterator& it);\n\tbool cleanup_kronecker(const Kernel& k, Ex&, Ex::iterator& it);\n\tbool cleanup_exterior_derivative(const Kernel& k, Ex&, Ex::iterator& it);\n\tbool cleanup_comma(const Kernel&k, Ex&, Ex::iterator& it);\n\tbool cleanup_tie(const Kernel&k, Ex&, Ex::iterator& it);\t\n\n\t/// Given a node with a non-unit multiplier, push this multiplier\n\t/// down the tree if the node is not allowed to have a non-unit\n\t/// multiplier. This is a recursive procedure as the node onto\n\t/// which the multiplier gets pushed may itself not allow for\n\t/// a non-unit multiplier.\n\t/// Note that some nodes disallow non-unit multipliers on their\n\t/// children, but that should be handled individually (see cleanup\n\t/// of product nodes for an example).\n\n\tbool push_down_multiplier(const Kernel& k, Ex& tr, Ex::iterator it);\n\n\t/// Generic tool to check for index inconsistencies independent of\n\t/// running any algorithm.\n\n\tvoid check_index_consistency(const Kernel& k, Ex& tr, Ex::iterator it);\n\n\t}\n"
  },
  {
    "path": "core/Combinatorics.cc",
    "content": "/*\n\n\tCadabra: a field-theory motivated computer algebra system.\n\tCopyright (C) 2001-2014  Kasper Peeters <kasper.peeters@phi-sci.com>\n\nThis program is free software: you can redistribute it and/or\n\tmodify it under the terms of the GNU General Public License as\npublished by the Free Software Foundation, either version 3 of the\nLicense, or (at your option) any later version.\n\nThis program is distributed in the hope that it will be useful,\n\tbut WITHOUT ANY WARRANTY; without even the implied warranty of\nMERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU\nGeneral Public License for more details.\n\nYou should have received a copy of the GNU General Public License\n\talong with this program.  If not, see <http://www.gnu.org/licenses/>.\n\n*/\n\n#include \"Combinatorics.hh\"\n\nunsigned long combin::factorial(unsigned int x)\n\t{\n\tunsigned long ret=1;\n\twhile(x) {\n\t\tret*=x--;\n\t\t}\n\treturn ret;\n\t}\n\nint combin::determine_intersection_ranges(const combin::range_vector_t& prod,\n      const combin::range_vector_t& indv,\n      combin::range_vector_t& target)\n\t{\n\tint ret=1;\n\tfor(unsigned int i=0; i<prod.size(); ++i) { // all ranges in prod\n\t\tfor(unsigned int k=0; k<indv.size(); ++k) { // all ranges in indv\n\t\t\tcombin::range_t newrange;\n\t\t\tfor(unsigned int ic=0; ic<prod[i].size(); ++ic) {\n\t\t\t\tfor(unsigned int kc=0; kc<indv[k].size(); ++kc) {\n\t\t\t\t\tif(prod[i][ic] == indv[k][kc])\n\t\t\t\t\t\tnewrange.push_back(indv[k][kc]);\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\tif(newrange.size()>=2) {\n\t\t\t\tret*=factorial(newrange.size());\n\t\t\t\ttarget.push_back(newrange);\n\t\t\t\t}\n\t\t\t}\n\t\t}\n\n\treturn ret;\n\t}\n\nlong combin::vector_sum(const std::vector<int>& v)\n\t{\n\tlong ret=0;\n\tfor(unsigned int i=0; i<v.size(); ++i)\n\t\tret+=v[i];\n\treturn ret;\n\t}\n\nunsigned long combin::vector_prod(const std::vector<unsigned int>& v)\n\t{\n\tunsigned long ret=1;\n\tfor(unsigned int i=0; i<v.size(); ++i)\n\t\tret*=v[i];\n\treturn ret;\n\t}\n\nunsigned long combin::vector_prod_fact(const std::vector<unsigned int>& v)\n\t{\n\tunsigned long ret=1;\n\tfor(unsigned int i=0; i<v.size(); ++i)\n\t\tret*=fact(v[i]);\n\treturn ret;\n\t}\n\nbool combin::operator==(const std::vector<unsigned int>& one, const std::vector<unsigned int>& two)\n\t{\n\tif(one.size()!=two.size()) return false;\n\n\tfor(unsigned int k=0; k<one.size(); ++k)\n\t\tif(one[k]!=two[k]) return false;\n\n\treturn true;\n\t}\n\nlong combin::hash(const std::vector<unsigned int>& one)\n\t{\n\tlong ret=1;\n\tfor(unsigned int k=0; k<one.size(); ++k) {\n\t\tret*=17;\n\t\tret+=one[k];\n\t\t}\n\treturn ret;\n\t}\n"
  },
  {
    "path": "core/Combinatorics.hh",
    "content": "/*\n\n\tCadabra: a field-theory motivated computer algebra system.\n\tCopyright (C) 2001-2014  Kasper Peeters <kasper.peeters@phi-sci.com>\n\nThis program is free software: you can redistribute it and/or\n\tmodify it under the terms of the GNU General Public License as\npublished by the Free Software Foundation, either version 3 of the\nLicense, or (at your option) any later version.\n\nThis program is distributed in the hope that it will be useful,\n\tbut WITHOUT ANY WARRANTY; without even the implied warranty of\nMERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU\nGeneral Public License for more details.\n\nYou should have received a copy of the GNU General Public License\n\talong with this program.  If not, see <http://www.gnu.org/licenses/>.\n\n*/\n\n/*\n                               length vector\n\tnormal combinations:     one element, value=total length.\n\tnormal permutations:     n elements, each equal to 1.\n\n*/\n\n#pragma once\n\n#include <vector>\n#include <cassert>\n#include <algorithm>\n#include <iomanip>\n#include <iostream>\n#include <map>\n\nnamespace combin {\n\n\ttypedef std::vector<unsigned int>  range_t;\n\ttypedef std::vector<range_t>       range_vector_t;\n\ttypedef std::vector<int>           weights_t;\n\n\tunsigned long factorial(unsigned int x);\n\t/// sum of elements\n\tlong          vector_sum(const std::vector<int>&);\n\t/// product of elements\n\tunsigned long vector_prod(const std::vector<unsigned int>&);\n\t/// product of factorials of elements\n\tunsigned long vector_prod_fact(const std::vector<unsigned int>&);\n\n\tbool operator==(const std::vector<unsigned int>&, const std::vector<unsigned int>&);\n\n\t/// compute a hash value for a vector of unsigned ints\n\tlong hash(const std::vector<unsigned int>&);\n\n\ttemplate<class T>\n\tclass combinations_base {\n\t\tpublic:\n\t\t\tcombinations_base();\n\t\t\tcombinations_base(const std::vector<T>&);\n\t\t\tvirtual ~combinations_base();\n\n\t\t\tvoid         permute(long start=-1, long end=-1);\n\t\t\tvirtual void clear();\n\t\t\tvirtual void clear_results();\n\t\t\tunsigned int sum_of_sublengths() const;\n\t\t\tvoid         set_unit_sublengths();\n\t\t\tunsigned int multiplier(const std::vector<T>&) const;\n\t\t\tunsigned int total_permutations() const; // including the ones not stored\n\n\t\t\tenum weight_cond { weight_equals, weight_less, weight_greater };\n\n\t\t\tunsigned int               block_length;\n\t\t\tstd::vector<unsigned int>  sublengths;\n\t\t\trange_vector_t             input_asym;\n\t\t\tstd::vector<T>             original;\n\t\t\tbool                       multiple_pick;\n\t\t\tstd::vector<weights_t>     weights;\n\t\t\tstd::vector<int>           max_weights;\n\t\t\tstd::vector<weight_cond>   weight_conditions;\n\t\t\tunsigned int               sub_problem_blocksize; // when non-zero, do permutations within\n\n\t\tprotected:\n\t\t\tvirtual void   vector_generated(const std::vector<unsigned int>&)=0;\n\t\t\tvirtual bool   entry_accepted(unsigned int current) const;\n\t\t\tstd::vector<unsigned int>  temparr;\n\n\t\t\tlong                       start_, end_, vector_generated_called_;\n\t\t\tstd::vector<int>           current_weight;\n\t\tprivate:\n\t\t\tbool is_allowed_by_weight_constraints(unsigned int i);\n\t\t\tbool final_weight_constraints_check() const;\n\t\t\tvoid update_weights(unsigned int i);\n\t\t\tvoid restore_weights(unsigned int i);\n\t\t\tvoid nextstep(unsigned int current, unsigned int fromalgehad, unsigned int groupindex,\n\t\t\t              std::vector<bool> algehad);\n\n\t\t};\n\n\ttemplate<class T>\n\tclass combinations : public combinations_base<T> {\n\t\tpublic:\n\t\t\ttypedef typename std::vector<std::vector<T> >    permuted_sets_t;\n\t\t\ttypedef typename permuted_sets_t::const_iterator const_iterator;\n\n\t\t\tcombinations();\n\t\t\tcombinations(const std::vector<T>&);\n\t\t\tvirtual ~combinations();\n\n\t\t\tvirtual void           clear();\n\t\t\tvirtual void           clear_results();\n\t\t\tconst std::vector<T>&  operator[](unsigned int) const;\n\t\t\tint                    ordersign(unsigned int) const;\n\t\t\tunsigned int           size() const;\n\t\t\tunsigned int           multiplier(unsigned int) const;\n\n\t\tprotected:\n\t\t\tvirtual void vector_generated(const std::vector<unsigned int>&);\n\n\t\tprivate:\n\t\t\tpermuted_sets_t storage;\n\t\t};\n\n\ttemplate<class T>\n\tclass symmetriser;\n\n\ttemplate<class T>\n\tclass symm_helper : public combinations_base<T> {\n\t\tpublic:\n\t\t\tsymm_helper(symmetriser<T>&);\n\t\t\tvirtual void clear();\n\n\t\t\tint             current_multiplicity;\n\t\tprotected:\n\t\t\tbool            first_one;\n\t\t\tsymmetriser<T>& owner_;\n\t\t\tvirtual void vector_generated(const std::vector<unsigned int>&);\n\t\t};\n\n\ttemplate<class T>\n\tclass symm_val_helper : public combinations_base<T> {\n\t\tpublic:\n\t\t\tsymm_val_helper(symmetriser<T>&);\n\t\t\tvirtual void clear();\n\n\t\t\tint             current_multiplicity;\n\t\tprotected:\n\t\t\tbool            first_one;\n\t\t\tsymmetriser<T>& owner_;\n\t\t\tvirtual void vector_generated(const std::vector<unsigned int>&);\n\t\t};\n\n\ttemplate<class T>\n\tclass symmetriser {\n\t\tpublic:\n\t\t\tsymmetriser();\n\t\t\tvoid apply_symmetry(long start=-1, long end=-1);\n\n\t\t\tstd::vector<T>            original;\n\t\t\tunsigned int              block_length;\n\t\t\tstd::vector<unsigned int> permute_blocks;   // offset in unit elements! (not in blocks)\n\t\t\tstd::vector<T>            value_permute;\n\t\t\tint                       permutation_sign;\n\n\t\t\tstd::vector<unsigned int> sublengths; // refers to position within permute_blocks\n\t\t\trange_vector_t            input_asym; // as in combinations_base\n\t\t\trange_vector_t            sublengths_scattered; // sublengths, in original, but not connected.\n\n\t\t\t/// Convert vectors of values to vectors of locations in the original\n\t\t\t/// (mainly useful to create input_asym for permutation by value).\n\t\t\trange_t                   values_to_locations(const std::vector<T>& values) const;\n\n\t\t\tconst std::vector<T>&     operator[](unsigned int) const;\n\t\t\tint                       signature(unsigned int) const;\n\t\t\tvoid                      set_multiplicity(unsigned int pos, int val);\n\t\t\tunsigned int              size() const;\n\t\t\tvoid                      clear();\n\t\t\t/// Collect equal entries, and adjust the multiplier field accordingly.\n\t\t\tvoid                      collect();\n\t\t\tvoid                      remove_multiplicity_zero();\n\n\t\t\tfriend class symm_helper<T>;\n\t\t\tfriend class symm_val_helper<T>;\n\t\tprivate:\n\t\t\tsymm_helper<T>               sh_;\n\t\t\tsymm_val_helper<T>           svh_;\n\t\t\tunsigned int                 current_;\n\t\t\tstd::vector<std::vector<T> > originals;\n\t\t\tstd::vector<int>             multiplicity;\n\t\t};\n\n\tint determine_intersection_ranges(const range_vector_t& prod,\n\t                                  const range_vector_t& indv,\n\t                                  range_vector_t& target);\n\n\ttemplate<class iterator1, class iterator2>\n\tint ordersign(iterator1 b1, iterator1 e1, iterator2 b2, iterator2 e2, int stepsize=1);\n\n\ttemplate<class iterator1>\n\tint ordersign(iterator1 b1, iterator1 e1);\n\n\ttemplate<class T>\n\tT fact(T x);\n\n\ttemplate<class T>\n\tstd::ostream& operator<<(std::ostream& str, const symmetriser<T>& sym);\n\n\n\t/*\n\tI assume PI consists of the integers 1 to N.\n\tIt can be done with O(N) comparisons and transpositions of integers\n\tin the list.\n\n\tsign:= 1;\n\tfor i from 1 to N do\n\twhile PI[i] <> i do\n\t  \tinterchange PI[i] and PI[PI[i]];\n\t  \tsign:= -sign\n\t\tod\n\tod\n\t*/\n\n\ttemplate<class iterator1, class iterator2>\n\tint ordersign(iterator1 b1, iterator1 e1, iterator2 b2, iterator2 e2, int stepsize)\n\t\t{\n\t\tint sign=1;\n\t\tstd::vector<bool> crossedoff(std::distance(b1,e1),false);\n\t\twhile(b1!=e1) {\n\t\t\tint otherpos=0;\n\t\t\titerator2 it=b2;\n\t\t\twhile(it!=e2) {\n\t\t\t\tif( (*it)==(*b1) && crossedoff[otherpos]==false) {\n\t\t\t\t\tcrossedoff[otherpos]=true;\n\t\t\t\t\tbreak;\n\t\t\t\t\t}\n\t\t\t\telse {\n\t\t\t\t\tif(!crossedoff[otherpos])\n\t\t\t\t\t\tsign=-sign;\n\t\t\t\t\t}\n\t\t\t\tit+=stepsize;\n\t\t\t\t++otherpos;\n\t\t\t\t}\n\t\t\tb1+=stepsize;\n\t\t\t}\n\t\treturn sign;\n\t\t}\n\n\t//template<class iterator1, class iterator2, class comparator>\n\t//int ordersign(iterator1 b1, iterator1 e1, iterator2 b2, iterator2 e2, comparator cmp, int stepsize)\n\t//\t{\n\t//\tint sign=1;\n\t//\tstd::vector<bool> crossedoff(std::distance(b1,e1),false);\n\t//\twhile(b1!=e1) {\n\t//\t\tint otherpos=0;\n\t//\t\titerator2 it=b2;\n\t//\t\twhile(it!=e2) {\n\t//\t\t\tif(cmp((*it), (*b1)) && crossedoff[otherpos]==false) {\n\t//\t\t\t\tcrossedoff[otherpos]=true;\n\t//\t\t\t\tbreak;\n\t//\t\t\t\t}\n\t//\t\t\telse {\n\t//\t\t\t\tif(!crossedoff[otherpos])\n\t//\t\t\t\t\tsign=-sign;\n\t//\t\t\t\t}\n\t//\t\t\tit+=stepsize;\n\t//\t\t\t++otherpos;\n\t//\t\t\t}\n\t//\t\tb1+=stepsize;\n\t//\t\t}\n\t//\treturn sign;\n\t//\t}\n\n\ttemplate<class iterator1>\n\tint ordersign(iterator1 b1, iterator1 e1)\n\t\t{\n\t\tstd::vector<unsigned int> fil;\n\t\tfor(int k=0; k<distance(b1,e1); ++k)\n\t\t\tfil.push_back(k);\n\t\treturn ordersign(fil.begin(), fil.end(), b1, e1);\n\t\t}\n\n\ttemplate<class T>\n\tT fact(T x)\n\t\t{\n\t\tT ret=1;\n\t\tassert(x>=0);\n\t\twhile(x!=0) {\n\t\t\tret*=x--;\n\t\t\t}\n\t\treturn ret;\n\t\t}\n\n\n\t// Implementations\n\n\ttemplate<class T>\n\tcombinations_base<T>::combinations_base()\n\t\t: block_length(1), multiple_pick(false), sub_problem_blocksize(0)\n\t\t{\n\t\t}\n\n\ttemplate<class T>\n\tcombinations_base<T>::combinations_base(const std::vector<T>& oa)\n\t\t: block_length(1), original(oa), multiple_pick(false), sub_problem_blocksize(0)\n\t\t{\n\t\t}\n\n\ttemplate<class T>\n\tcombinations<T>::combinations()\n\t\t: combinations_base<T>()\n\t\t{\n\t\t}\n\n\ttemplate<class T>\n\tcombinations<T>::combinations(const std::vector<T>& oa)\n\t\t: combinations_base<T>(oa)\n\t\t{\n\t\t}\n\n\ttemplate<class T>\n\tcombinations_base<T>::~combinations_base()\n\t\t{\n\t\t}\n\n\ttemplate<class T>\n\tcombinations<T>::~combinations()\n\t\t{\n\t\t}\n\n\ttemplate<class T>\n\tvoid combinations<T>::vector_generated(const std::vector<unsigned int>& toadd)\n\t\t{\n\t\t++this->vector_generated_called_;\n\t\tif((this->start_==-1 || this->vector_generated_called_ >= this->start_) &&\n\t\t      (this->end_==-1   || this->vector_generated_called_ < this->end_)) {\n\t\t\tstd::vector<T> newone(toadd.size()*this->block_length);\n\t\t\tfor(unsigned int i=0; i<toadd.size(); ++i)\n\t\t\t\tfor(unsigned int bl=0; bl<this->block_length; ++bl)\n\t\t\t\t\tnewone[i*this->block_length+bl]=this->original[toadd[i]*this->block_length+bl];\n\t\t\tstorage.push_back(newone);\n\t\t\t}\n\t\t}\n\n\ttemplate<class T>\n\tbool combinations_base<T>::entry_accepted(unsigned int) const\n\t\t{\n\t\treturn true;\n\t\t}\n\n\ttemplate<class T>\n\tvoid combinations_base<T>::permute(long start, long end)\n\t\t{\n\t\tstart_=start;\n\t\tend_=end;\n\t\tvector_generated_called_=-1;\n\n\t\t// Initialise weight handling.\n\t\tcurrent_weight.clear();\n\t\tcurrent_weight.resize(weights.size(), 0);\n\t\tfor(unsigned int i=0; i<weights.size(); ++i)\n\t\t\tassert(weights[i].size() == original.size()/block_length);\n\t\tif(weights.size()>0) {\n\t\t\tif(weight_conditions.size()==0)\n\t\t\t\tweight_conditions.resize(weights.size(), weight_equals);\n\t\t\telse assert(weight_conditions.size()==weights.size());\n\t\t\t}\n\t\telse assert(weight_conditions.size()==0);\n\n\t\t// Sublength handling.\n\t\tassert(sublengths.size()!=0);\n\t\tunsigned int len=sum_of_sublengths();\n\n\t\t// Consistency checks.\n\t\tassert(original.size()%block_length==0);\n\t\tif(!multiple_pick)\n\t\t\tassert(len*block_length<=original.size());\n\n\t\tfor(unsigned int i=0; i<this->input_asym.size(); ++i)\n\t\t\tstd::sort(this->input_asym[i].begin(), this->input_asym[i].end());\n\n\t\ttemparr=std::vector<unsigned int>(len/* *block_length*/);\n\t\tstd::vector<bool> algehad(original.size()/block_length,false);\n\t\tnextstep(0,0,0,algehad);\n\t\t}\n\n\ttemplate<class T>\n\tvoid combinations_base<T>::clear()\n\t\t{\n\t\tblock_length=1;\n\t\tsublengths.clear();\n\t\tthis->input_asym.clear();\n\t\toriginal.clear();\n\t\tweights.clear();\n\t\tmax_weights.clear();\n\t\tweight_conditions.clear();\n\t\tsub_problem_blocksize=0;\n\t\ttemparr.clear();\n\t\tcurrent_weight.clear();\n\t\t}\n\n\ttemplate<class T>\n\tvoid combinations_base<T>::clear_results()\n\t\t{\n\t\ttemparr.clear();\n\t\t}\n\n\ttemplate<class T>\n\tvoid combinations<T>::clear()\n\t\t{\n\t\tstorage.clear();\n\t\tcombinations_base<T>::clear();\n\t\t}\n\n\ttemplate<class T>\n\tvoid combinations<T>::clear_results()\n\t\t{\n\t\tstorage.clear();\n\t\tcombinations_base<T>::clear_results();\n\t\t}\n\n\ttemplate<class T>\n\tconst std::vector<T>& combinations<T>::operator[](unsigned int i) const\n\t\t{\n\t\tassert(i<storage.size());\n\t\treturn storage[i];\n\t\t}\n\n\ttemplate<class T>\n\tunsigned int combinations<T>::size() const\n\t\t{\n\t\treturn storage.size();\n\t\t}\n\n\ttemplate<class T>\n\tunsigned int combinations_base<T>::sum_of_sublengths() const\n\t\t{\n\t\tunsigned int ret=0;\n\t\tfor(unsigned int i=0; i<sublengths.size(); ++i)\n\t\t\tret+=sublengths[i];\n\t\treturn ret;\n\t\t}\n\n\ttemplate<class T>\n\tunsigned int combinations_base<T>::total_permutations() const\n\t\t{\n\t\treturn vector_generated_called_+1;\n\t\t}\n\n\ttemplate<class T>\n\tvoid combinations_base<T>::set_unit_sublengths()\n\t\t{\n\t\tsublengths.clear();\n\t\tfor(unsigned int i=0; i<original.size()/block_length; ++i)\n\t\t\tsublengths.push_back(1);\n\t\t}\n\n\ttemplate<class T>\n\tint combinations<T>::ordersign(unsigned int num) const\n\t\t{\n\t\tassert(num<storage.size());\n\t\treturn combin::ordersign(storage[0].begin(), storage[0].end(),\n\t\t                         storage[num].begin(), storage[num].end(), this->block_length);\n\t\t}\n\n\ttemplate<class T>\n\tunsigned int combinations<T>::multiplier(unsigned int num) const\n\t\t{\n\t\treturn combinations_base<T>::multiplier(this->storage[num]);\n\t\t}\n\n\ttemplate<class T>\n\tunsigned int combinations_base<T>::multiplier(const std::vector<T>& stor) const\n\t\t{\n\t\tunsigned long numerator=1;\n\t\tfor(unsigned int i=0; i<this->input_asym.size(); ++i)\n\t\t\tnumerator*=fact(this->input_asym[i].size());\n\n\t\tunsigned long denominator=1;\n\t\tfor(unsigned int i=0; i<this->input_asym.size(); ++i) {\n\t\t\t// for each input asym, and for each output asym, count\n\t\t\t// the number of overlap elements.\n\t\t\tunsigned int current=0;\n\t\t\tfor(unsigned int k=0; k<this->sublengths.size(); ++k) {\n\t\t\t\tif(this->sublengths[k]>1) {\n\t\t\t\t\tunsigned int overlap=0;\n\t\t\t\t\tfor(unsigned int slc=0; slc<this->sublengths[k]; ++slc) {\n\t\t\t\t\t\tfor(unsigned int j=0; j<this->input_asym[i].size(); ++j) {\n\t\t\t\t\t\t\tunsigned int index=0;\n\t\t\t\t\t\t\twhile(!(stor[current]==this->original[index]))\n\t\t\t\t\t\t\t\t++index;\n\t\t\t\t\t\t\tif(index==this->input_asym[i][j])\n\t\t\t\t\t\t\t\t++overlap;\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\t++current;\n\t\t\t\t\t\t}\n\t\t\t\t\tif(overlap>0)\n\t\t\t\t\t\tdenominator*=fact(overlap);\n\t\t\t\t\t// FIXME: for each overlap thus found, divide out by a factor\n\t\t\t\t\t// due to the fact that output asym ranges can overlap.\n\t\t\t\t\t// well, that's not right either.\n\t\t\t\t\t}\n\t\t\t\telse ++current;\n\t\t\t\t}\n\t\t\t}\n\n\t\treturn numerator/denominator;\n\t\t}\n\n\ttemplate<class T>\n\tbool combinations_base<T>::is_allowed_by_weight_constraints(unsigned int i)\n\t\t{\n\t\tif(weights.size()==0) return true;\n\t\tfor(unsigned int cn=0; cn<current_weight.size(); ++cn) {\n\t\t\tif(weight_conditions[cn]==weight_less)\n\t\t\t\tif(current_weight[cn]+weights[cn][i] >= max_weights[cn])\n\t\t\t\t\treturn false;\n\t\t\t}\n\t\treturn true;\n\t\t}\n\n\ttemplate<class T>\n\tbool combinations_base<T>::final_weight_constraints_check() const\n\t\t{\n\t\tfor(unsigned int cn=0; cn<current_weight.size(); ++cn) {\n\t\t\tswitch(weight_conditions[cn]) {\n\t\t\t\tcase weight_equals:\n\t\t\t\t\tif(current_weight[cn]!=max_weights[cn])\n\t\t\t\t\t\treturn false;\n\t\t\t\t\tbreak;\n\t\t\t\tcase weight_less:\n\t\t\t\t\tbreak;\n\t\t\t\tcase weight_greater:\n\t\t\t\t\tif(current_weight[cn]<=max_weights[cn])\n\t\t\t\t\t\treturn false;\n\t\t\t\t\tbreak;\n\t\t\t\t}\n\t\t\t}\n\t\treturn true;\n\t\t}\n\n\ttemplate<class T>\n\tvoid combinations_base<T>::update_weights(unsigned int i)\n\t\t{\n\t\tif(weights.size()==0) return;\n\t\tfor(unsigned int cn=0; cn<current_weight.size(); ++cn)\n\t\t\tcurrent_weight[cn]+=weights[cn][i];\n\t\t}\n\n\ttemplate<class T>\n\tvoid combinations_base<T>::restore_weights(unsigned int i)\n\t\t{\n\t\tif(weights.size()==0) return;\n\t\tfor(unsigned int cn=0; cn<current_weight.size(); ++cn)\n\t\t\tcurrent_weight[cn]-=weights[cn][i];\n\t\t}\n\n\ttemplate<class T>\n\tvoid combinations_base<T>::nextstep(unsigned int current, unsigned int lowest_in_group, unsigned int groupindex,\n\t                                    std::vector<bool> algehad)\n\t\t{\n\t\tunsigned int grouplen=0;\n\t\tfor(unsigned int i=0; i<=groupindex; ++i)\n\t\t\tgrouplen+=sublengths[i];\n\t\tif(current==grouplen) { // group is filled\n\t\t\t++groupindex;\n\t\t\tif(groupindex==sublengths.size()) {\n\t\t\t\tif(final_weight_constraints_check())\n\t\t\t\t\tvector_generated(temparr);\n\t\t\t\treturn;\n\t\t\t\t}\n\t\t\tlowest_in_group=0;\n\t\t\t}\n\n\t\tunsigned int starti=0, endi=original.size()/block_length;\n\t\tif(sub_problem_blocksize>0) {\n\t\t\tstarti=current-current%sub_problem_blocksize;\n\t\t\tendi=starti+sub_problem_blocksize;\n\t\t\t}\n\t\tfor(unsigned int i=starti; i<endi; i++) {\n\t\t\tif(!algehad[i] || multiple_pick) {\n\t\t\t\tbool discard=false;\n\t\t\t\tif(is_allowed_by_weight_constraints(i)) {\n\t\t\t\t\t// handle input_asym\n\t\t\t\t\tfor(unsigned k=0; k<this->input_asym.size(); ++k) {\n\t\t\t\t\t\tfor(unsigned int kk=0; kk<this->input_asym[k].size(); ++kk) {\n\t\t\t\t\t\t\tif(i==this->input_asym[k][kk]) {\n\t\t\t\t\t\t\t\tunsigned int k2=kk;\n\t\t\t\t\t\t\t\twhile(k2!=0) {\n\t\t\t\t\t\t\t\t\t--k2;\n\t\t\t\t\t\t\t\t\tif(!algehad[this->input_asym[k][k2]]) {\n\t\t\t\t\t\t\t\t\t\t//\t\t\t\t\t\t\t\t\tstd::cout << \"discarding \" << std::endl;\n\t\t\t\t\t\t\t\t\t\tdiscard=true;\n\t\t\t\t\t\t\t\t\t\tbreak;\n\t\t\t\t\t\t\t\t\t\t}\n\t\t\t\t\t\t\t\t\t}\n\t\t\t\t\t\t\t\t}\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\tif(discard) break;\n\t\t\t\t\t\t}\n\t\t\t\t\t}\n\t\t\t\telse discard=true;\n\t\t\t\tif(!discard)\n\t\t\t\t\tif(i+1>lowest_in_group) {\n\t\t\t\t\t\talgehad[i]=true;\n\t\t\t\t\t\tupdate_weights(i);\n\t\t\t\t\t\ttemparr[current]=i;\n\t\t\t\t\t\t//\t\t\t\t\tfor(unsigned bl=0; bl<block_length; ++bl)\n\t\t\t\t\t\t//\t\t\t\t\t\ttemparr[current*block_length+bl]=original[i*block_length+bl];\n\t\t\t\t\t\tif(entry_accepted(current)) {\n\t\t\t\t\t\t\tnextstep(current+1, i, groupindex, algehad);\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\talgehad[i]=false;\n\t\t\t\t\t\trestore_weights(i);\n\t\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t}\n\t\t}\n\n\ttemplate<class T>\n\tsymmetriser<T>::symmetriser()\n\t\t: block_length(1), permutation_sign(1), sh_(*this), svh_(*this)\n\t\t{\n\t\t}\n\n\ttemplate<class T>\n\tvoid symmetriser<T>::clear()\n\t\t{\n\t\toriginal.clear();\n\t\tblock_length=1;\n\t\tpermute_blocks.clear();\n\t\tvalue_permute.clear();\n\t\tpermutation_sign=1;\n\t\tsublengths.clear();\n\t\tinput_asym.clear();\n\t\tsublengths_scattered.clear();\n\t\toriginals.clear();\n\t\tmultiplicity.clear();\n\t\t}\n\n\ttemplate<class T>\n\tvoid symmetriser<T>::collect()\n\t\t{\n\t\tstd::cout << \"collecting\" << std::endl;\n\t\t// Fill the hash map: entries which are equal have to sit in the same\n\t\t// bin, but there may be other entries in that bin which still have to\n\t\t// be separated.\n\t\tstd::multimap<long, unsigned int> hashmap;\n\t\tfor(unsigned int i=0; i<originals.size(); ++i)\n\t\t\thashmap.insert(std::pair<long, unsigned int>(hash(originals[i]), i));\n\n\t\t// Collect equal vectors.\n\t\tstd::multimap<long, unsigned int>::iterator it=hashmap.begin(), thisbin1, thisbin2, tmpit;\n\t\twhile(it!=hashmap.end()) {\n\t\t\tlong current_hash=it->first;\n\t\t\tthisbin1=it;\n\t\t\twhile(thisbin1!=hashmap.end() && thisbin1->first==current_hash) {\n\t\t\t\tthisbin2=thisbin1;\n\t\t\t\t++thisbin2;\n\t\t\t\twhile(thisbin2!=hashmap.end() && thisbin2->first==current_hash) {\n\t\t\t\t\tif(originals[(*thisbin1).second]==originals[(*thisbin2).second]) {\n\t\t\t\t\t\tmultiplicity[(*thisbin1).second]+=multiplicity[(*thisbin2).second];\n\t\t\t\t\t\tmultiplicity[(*thisbin2).second]=0;\n\t\t\t\t\t\ttmpit=thisbin2;\n\t\t\t\t\t\t++tmpit;\n\t\t\t\t\t\thashmap.erase(thisbin2);\n\t\t\t\t\t\tthisbin2=tmpit;\n\t\t\t\t\t\t}\n\t\t\t\t\telse ++thisbin2;\n\t\t\t\t\t}\n\t\t\t\t++thisbin1;\n\t\t\t\t}\n\t\t\tit=thisbin1;\n\t\t\t}\n\n\t\tremove_multiplicity_zero();\n\t\t}\n\n\ttemplate<class T>\n\tvoid symmetriser<T>::remove_multiplicity_zero()\n\t\t{\n\t\tstd::vector<std::vector<T> > new_originals;\n\t\tstd::vector<int>             new_multiplicity;\n\t\tfor(unsigned int k=0; k<originals.size(); ++k) {\n\t\t\tif(multiplicity[k]!=0) {\n\t\t\t\tnew_originals.push_back(originals[k]);\n\t\t\t\tnew_multiplicity.push_back(multiplicity[k]);\n\t\t\t\t}\n\t\t\t}\n\t\toriginals=new_originals;\n\t\tmultiplicity=new_multiplicity;\n\t\t}\n\n\n\ttemplate<class T>\n\tvoid symmetriser<T>::apply_symmetry(long start, long end)\n\t\t{\n\t\tunsigned int current_length=originals.size();\n\t\tif(current_length==0) {\n\t\t\toriginals.push_back(original);\n\t\t\tmultiplicity.push_back(1);\n\t\t\tcurrent_length=1;\n\t\t\t}\n\n\t\t// Some options are mutually exclusive.\n\t\tassert(permute_blocks.size()>0 || value_permute.size()>0);\n\t\tassert(sublengths.size()==0 || sublengths_scattered.size()==0);\n\n\t\tif(permute_blocks.size()==0) { // permute by value\n\t\t\tassert(value_permute.size()!=0);\n\n\t\t\tif(input_asym.size()==0 && sublengths_scattered.size()==0) {\n\t\t\t\t// When permuting by value, we can do the permutation once,\n\t\t\t\t// and then figure out (see vector_generated of symm_val_helper),\n\t\t\t\t// for each permutation which is already stored in the symmetriser,\n\t\t\t\t// how the objects are moved.\n\n\t\t\t\tcurrent_=current_length;\n\t\t\t\tsvh_.clear();\n\t\t\t\tsvh_.original=value_permute;\n\t\t\t\tsvh_.input_asym.clear();\n\t\t\t\tsvh_.sublengths=sublengths;\n\t\t\t\tsvh_.current_multiplicity=combin::vector_prod_fact(sublengths);\n\t\t\t\tif(svh_.sublengths.size()==0)\n\t\t\t\t\tsvh_.set_unit_sublengths();\n\n\t\t\t\tsvh_.permute(start, end);\n\t\t\t\t// Since we do not divide by the number of permutations, we need\n\t\t\t\t// to adjust the multiplicity of all the originals.\n\t\t\t\t//\t\tfor(unsigned int i=0; i<current_; ++i)\n\t\t\t\t//\t\t\t\tmultiplicity[i] *= svh_.current_multiplicity;\n\t\t\t\t}\n\t\t\telse {\n\t\t\t\t// However, when there is input_asym or sublength_scattered\n\t\t\t\t// are present, we cannot just do the permutation on the\n\t\t\t\t// values and then put them into all existing sets, since the\n\t\t\t\t// overlap of input_asym with the objects to be permuted will\n\t\t\t\t// be different for every set.  Therefore, we have to apply\n\t\t\t\t// the permutation algorithm separately to each and every set\n\t\t\t\t// which is already stored in the symmetriser.  We convert\n\t\t\t\t// the problem to a permute-by-location problem.\n\n\t\t\t\tfor(unsigned int i=0; i<current_length; ++i) {\n\t\t\t\t\tcurrent_=i;\n\t\t\t\t\tsh_.clear();\n\t\t\t\t\tassert(sublengths.size()==0); // not yet implemented\n\t\t\t\t\tstd::vector<unsigned int> my_permute_blocks;\n\n\t\t\t\t\t// Determine the location of the values.\n\t\t\t\t\tfor(unsigned int k=0; k<value_permute.size(); ++k) {\n\t\t\t\t\t\tfor(unsigned int m=0; m<originals[i].size(); ++m) {\n\t\t\t\t\t\t\tif(originals[i][m]==value_permute[k]) {\n\t\t\t\t\t\t\t\tmy_permute_blocks.push_back(m); // FIXME: non-unit block length?\n\t\t\t\t\t\t\t\tbreak;\n\t\t\t\t\t\t\t\t}\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\t}\n\n\t\t\t\t\t//\t\t\t\tstd::cout << \"handling sublengths\" << std::endl;\n\t\t\t\t\tif(sublengths_scattered.size()>0) {\n\t\t\t\t\t\t// Re-order my_permute_blocks in such a way that the objects which sit\n\t\t\t\t\t\t// in one sublength_scattered range are consecutive. This does not make\n\t\t\t\t\t\t// any difference for the sign.\n\t\t\t\t\t\tsh_.sublengths.clear();\n\t\t\t\t\t\tstd::vector<unsigned int> reordered_permute_blocks;\n\t\t\t\t\t\tfor(unsigned int m=0; m<sublengths_scattered.size(); ++m) {\n\t\t\t\t\t\t\tint overlap=0;\n\t\t\t\t\t\t\tfor(unsigned int mm=0; mm<sublengths_scattered[m].size(); ++mm) {\n\t\t\t\t\t\t\t\t//\t\t\t\t\t\t\tstd::cout << \"trying to find \" << sublengths_scattered[m][mm] << \" \" << std::flush;\n\t\t\t\t\t\t\t\tstd::vector<unsigned int>::iterator it=my_permute_blocks.begin();\n\t\t\t\t\t\t\t\twhile(it!=my_permute_blocks.end()) {\n\t\t\t\t\t\t\t\t\tif((*it)==sublengths_scattered[m][mm]) {\n\t\t\t\t\t\t\t\t\t\t//\t\t\t\t\t\t\t\t\tstd::cout << \" found \" << std::endl;\n\t\t\t\t\t\t\t\t\t\treordered_permute_blocks.push_back(*it);\n\t\t\t\t\t\t\t\t\t\tmy_permute_blocks.erase(it);\n\t\t\t\t\t\t\t\t\t\t++overlap;\n\t\t\t\t\t\t\t\t\t\tbreak;\n\t\t\t\t\t\t\t\t\t\t}\n\t\t\t\t\t\t\t\t\t++it;\n\t\t\t\t\t\t\t\t\t}\n\t\t\t\t\t\t\t\t//\t\t\t\t\t\t\tstd::cout << std::endl;\n\t\t\t\t\t\t\t\t}\n\t\t\t\t\t\t\tif(overlap>0)\n\t\t\t\t\t\t\t\tsh_.sublengths.push_back(overlap);\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\tstd::vector<unsigned int>::iterator it=my_permute_blocks.begin();\n\t\t\t\t\t\twhile(it!=my_permute_blocks.end()) {\n\t\t\t\t\t\t\treordered_permute_blocks.push_back(*it);\n\t\t\t\t\t\t\t//\t\t\t\t\t\tstd::cout << \"adding one\" << std::endl;\n\t\t\t\t\t\t\tsh_.sublengths.push_back(1);\n\t\t\t\t\t\t\t++it;\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\tmy_permute_blocks=reordered_permute_blocks;\n\t\t\t\t\t\t//\t\t\t\t\tstd::cout << \"handled sublengths\" << std::endl;\n\t\t\t\t\t\t}\n\n\t\t\t\t\t// Put to-be-permuted data in originals.\n\t\t\t\t\tfor(unsigned int k=0; k<my_permute_blocks.size(); ++k) {\n\t\t\t\t\t\tfor(unsigned int kk=0; kk<block_length; ++kk) {\n\t\t\t\t\t\t\tsh_.original.push_back(originals[i][my_permute_blocks[k]+kk]);\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\t}\n\n\t\t\t\t\tcombin::range_vector_t subprob_input_asym;\n\t\t\t\t\tsh_.current_multiplicity=1;\n\t\t\t\t\tif(input_asym.size()>0) {\n\t\t\t\t\t\t// Make a proper input_asym which refers to object locations\n\t\t\t\t\t\t// in the permute blocks array, rather than in the original\n\t\t\t\t\t\t// array.\n\t\t\t\t\t\tfor(unsigned int k=0; k<input_asym.size(); ++k) {\n\t\t\t\t\t\t\trange_t newrange;\n\t\t\t\t\t\t\tfor(unsigned int m=0; m<input_asym[k].size(); ++m) {\n\t\t\t\t\t\t\t\t// search in my_permute_blocks\n\t\t\t\t\t\t\t\tfor(unsigned int kk=0; kk<my_permute_blocks.size(); ++kk)\n\t\t\t\t\t\t\t\t\tif(my_permute_blocks[kk]==input_asym[k][m]) {\n\t\t\t\t\t\t\t\t\t\tnewrange.push_back(kk);\n\t\t\t\t\t\t\t\t\t\tbreak;\n\t\t\t\t\t\t\t\t\t\t}\n\t\t\t\t\t\t\t\t}\n\t\t\t\t\t\t\tif(newrange.size()>1) {\n\t\t\t\t\t\t\t\tsubprob_input_asym.push_back(newrange);\n\t\t\t\t\t\t\t\tsh_.current_multiplicity*=fact(newrange.size());\n\t\t\t\t\t\t\t\t}\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\t}\n\t\t\t\t\tif(sh_.sublengths.size()==0)\n\t\t\t\t\t\tsh_.set_unit_sublengths();\n\t\t\t\t\tsh_.current_multiplicity*=combin::vector_prod_fact(sh_.sublengths);\n\n\t\t\t\t\t// debugging\n\t\t\t\t\t//\t\t\t\tstd::cout << \"my_permute_blocks: \";\n\t\t\t\t\t//\t\t\t\tfor(unsigned int ii=0; ii<my_permute_blocks.size(); ++ii)\n\t\t\t\t\t//\t\t\t\t\tstd::cout << my_permute_blocks[ii] << \" \";\n\t\t\t\t\t//\t\t\t\tstd::cout << std::endl;\n\t\t\t\t\t//\t\t\t\tstd::cout << \"sublengths: \";\n\t\t\t\t\t//\t\t\t\tfor(unsigned int ii=0; ii<sh_.sublengths.size(); ++ii)\n\t\t\t\t\t//\t\t\t\t\tstd::cout << sh_.sublengths[ii] << \" \";\n\t\t\t\t\t//\t\t\t\tstd::cout << std::endl;\n\n\t\t\t\t\t// Debugging output:\n\t\t\t\t\t//\t\t\t\tstd::cout << sh_.current_multiplicity << \" asym: \";\n\t\t\t\t\t//\t\t\t\tif(subprob_input_asym.size()>0) {\n\t\t\t\t\t//\t\t\t\t\tfor(unsigned int k=0; k<subprob_input_asym[0].size(); ++k)\n\t\t\t\t\t//\t\t\t\t\t\tstd::cout << subprob_input_asym[0][k] << \" \";\n\t\t\t\t\t//\t\t\t\t\tstd::cout << std::endl;\n\t\t\t\t\t//\t\t\t\t\tstd::cout << subprob_input_asym.size() << std::endl;\n\t\t\t\t\t//\t\t\t\t\t}\n\t\t\t\t\t//\t\t\t\telse std::cout << \"no asym\" << std::endl;\n\n\t\t\t\t\tpermute_blocks=my_permute_blocks;\n\t\t\t\t\tsh_.block_length=block_length;\n\t\t\t\t\tsh_.input_asym=subprob_input_asym;\n\t\t\t\t\tsh_.permute(start, end);\n\n\t\t\t\t\t// Since we do not divide by the number of permutations, we need\n\t\t\t\t\t// to adjust the multiplicity of the original.\n\t\t\t\t\tmultiplicity[i]*=sh_.current_multiplicity;\n\t\t\t\t\tpermute_blocks.clear(); // restore just in case\n\t\t\t\t\t//\t\t\t\tfor(unsigned int m=0; m<originals.size(); ++m) {\n\t\t\t\t\t//\t\t\t\t\tfor(unsigned int mm=0; mm<originals[m].size(); ++mm)\n\t\t\t\t\t//\t\t\t\t\t\tstd::cout << originals[m][mm] << \" \";\n\t\t\t\t\t//\t\t\t\t\tstd::cout << std::endl;\n\t\t\t\t\t//\t\t\t\t\t}\n\t\t\t\t\t//\t\t\t\tbreak;\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t}\n\t\telse {                         // permute by location\n\t\t\tassert(value_permute.size()==0);\n\t\t\tassert(permute_blocks.size()>0);\n\t\t\t// When permuting by location, we have to apply the permutation\n\t\t\t// algorithm separately to each and every permutation which is\n\t\t\t// already stored in the symmetriser.\n\t\t\tfor(unsigned int i=0; i<current_length; ++i) {\n\t\t\t\tcurrent_=i;\n\t\t\t\tsh_.clear();\n\t\t\t\tfor(unsigned int k=0; k<permute_blocks.size(); ++k) {\n\t\t\t\t\tfor(unsigned int kk=0; kk<block_length; ++kk) {\n\t\t\t\t\t\tsh_.original.push_back(originals[i][permute_blocks[k]+kk]);\n\t\t\t\t\t\t}\n\t\t\t\t\t//\t\t\t\tsh_.sublengths.push_back(1);\n\t\t\t\t\t}\n\t\t\t\tassert(sublengths.size()==0); // not yet implemented\n\t\t\t\t// sh_.sublengths=sublengths;\n\t\t\t\tif(sh_.sublengths.size()==0)\n\t\t\t\t\tsh_.set_unit_sublengths();\n\t\t\t\tsh_.block_length=block_length;\n\t\t\t\tsh_.input_asym=input_asym;\n\t\t\t\tsh_.permute(start, end);\n\t\t\t\t}\n\t\t\t}\n\n\t\tif(start!=-1) { // if start is not the first, have to erase the first\n\t\t\toriginals.erase(originals.begin());\n\t\t\tmultiplicity.erase(multiplicity.begin());\n\t\t\t}\n\t\t}\n\n\ttemplate<class T>\n\tconst std::vector<T>& symmetriser<T>::operator[](unsigned int i) const\n\t\t{\n\t\tassert(i<originals.size());\n\t\treturn originals[i];\n\t\t}\n\n\ttemplate<class T>\n\tunsigned int symmetriser<T>::size() const\n\t\t{\n\t\treturn originals.size();\n\t\t}\n\n\ttemplate<class T>\n\trange_t symmetriser<T>::values_to_locations(const std::vector<T>& values) const\n\t\t{\n\t\trange_t ret;\n\t\tfor(unsigned int i=0; i<values.size(); ++i) {\n\t\t\t//\t\tstd::cout << \"finding \" << values[i] << std::endl;\n\t\t\tfor(unsigned int j=0; j<value_permute.size(); ++j) {\n\t\t\t\t//\t\t\tstd::cout << value_permute[j] << \" \";\n\t\t\t\tif(value_permute[i]==value_permute[j]) {\n\t\t\t\t\t//\t\t\t\tstd::cout << \"found\" << std::endl;\n\t\t\t\t\tret.push_back(j);\n\t\t\t\t\tbreak;\n\t\t\t\t\t}\n\t\t\t\t//\t\t\tstd::cout << std::endl;\n\t\t\t\t}\n\t\t\t}\n\t\treturn ret;\n\t\t}\n\n\ttemplate<class T>\n\tsymm_val_helper<T>::symm_val_helper(symmetriser<T>& tt)\n\t\t: current_multiplicity(1), first_one(true), owner_(tt)\n\t\t{\n\t\t}\n\n\ttemplate<class T>\n\tvoid symm_val_helper<T>::clear()\n\t\t{\n\t\tfirst_one=true;\n\t\tcombinations_base<T>::clear();\n\t\t}\n\n\ttemplate<class T>\n\tvoid symm_val_helper<T>::vector_generated(const std::vector<unsigned int>& vec)\n\t\t{\n\t\t++this->vector_generated_called_;\n\t\tif(first_one) {\n\t\t\tfirst_one=false;\n\t\t\t}\n\t\telse {\n\t\t\tif((this->start_==-1 || this->vector_generated_called_ >= this->start_) &&\n\t\t\t      (this->end_==-1   || this->vector_generated_called_ < this->end_)) {\n\n\t\t\t\t// Since we permuted by value, we can do this permutation in one\n\t\t\t\t// shot on all previously generated sets.\n\t\t\t\tfor(unsigned int i=0; i<owner_.current_; ++i) {\n\t\t\t\t\t//\t\t\t\towner_.multiplicity[i] *= current_multiplicity;\n\t\t\t\t\towner_.originals.push_back(owner_.originals[i]);\n\n\t\t\t\t\t// Take care of the multiplicity & sign.\n\t\t\t\t\tint multiplicity=owner_.multiplicity[i] * current_multiplicity;\n\t\t\t\t\tif(owner_.permutation_sign==-1)\n\t\t\t\t\t\tmultiplicity*=ordersign(vec.begin(), vec.end());\n\t\t\t\t\towner_.multiplicity.push_back(multiplicity); //sign==1?true:false);\n\n\t\t\t\t\t// We now have to find the permuted objects in the larger\n\t\t\t\t\t// \"original\" set, and re-order these appropriately.\n\t\t\t\t\tunsigned int loc=owner_.originals.size()-1;\n\t\t\t\t\tfor(unsigned int j=0; j<vec.size(); ++j) {\n\t\t\t\t\t\tfor(unsigned int k=0; k<owner_.originals[i].size(); ++k) {\n\t\t\t\t\t\t\tif(owner_.originals[i][k]==this->original[j]) {\n\t\t\t\t\t\t\t\towner_.originals[loc][k]=this->original[vec[j]];\n\t\t\t\t\t\t\t\tbreak;\n\t\t\t\t\t\t\t\t}\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\t}\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t}\n\t\t}\n\n\ttemplate<class T>\n\tsymm_helper<T>::symm_helper(symmetriser<T>& tt)\n\t\t: current_multiplicity(1), first_one(true), owner_(tt)\n\t\t{\n\t\t}\n\n\ttemplate<class T>\n\tvoid symm_helper<T>::clear()\n\t\t{\n\t\tfirst_one=true;\n\t\tcombinations_base<T>::clear();\n\t\t}\n\n\ttemplate<class T>\n\tint symmetriser<T>::signature(unsigned int i) const\n\t\t{\n\t\tassert(i<multiplicity.size());\n\t\treturn multiplicity[i]; //?1:-1;\n\t\t}\n\n\ttemplate<class T>\n\tvoid symmetriser<T>::set_multiplicity(unsigned int i, int val)\n\t\t{\n\t\tassert(i<multiplicity.size());\n\t\tmultiplicity[i]=val;\n\t\t}\n\n\ttemplate<class T>\n\tvoid symm_helper<T>::vector_generated(const std::vector<unsigned int>& vec)\n\t\t{\n\t\t++this->vector_generated_called_;\n\t\tif(first_one) {\n\t\t\tfirst_one=false;\n\t\t\t}\n\t\telse {\n\t\t\tif((this->start_==-1 || this->vector_generated_called_ >= this->start_) &&\n\t\t\t      (this->end_==-1   || this->vector_generated_called_ < this->end_)) {\n\n\t\t\t\t//\t\t\tstd::cout << \"produced \";\n\t\t\t\t//\t\t\tfor(unsigned int m=0; m<vec.size(); ++m)\n\t\t\t\t//\t\t\tstd::cout << vec[m] << \" \";\n\t\t\t\t//\t\t\tstd::cout << std::endl;\n\n\t\t\t\t//\t\t\towner_.multiplicity[owner_.current_] *= current_multiplicity;\n\t\t\t\towner_.originals.push_back(owner_.originals[owner_.current_]);\n\t\t\t\tunsigned int siz=owner_.originals.size()-1;\n\n\t\t\t\t// Take care of the permutation sign.\n\t\t\t\tint multiplicity=owner_.multiplicity[owner_.current_] * current_multiplicity;\n\t\t\t\tif(owner_.permutation_sign==-1)\n\t\t\t\t\tmultiplicity*=ordersign(vec.begin(), vec.end());\n\t\t\t\towner_.multiplicity.push_back(multiplicity);\n\n\t\t\t\tfor(unsigned int k=0; k<owner_.permute_blocks.size(); ++k) {\n\t\t\t\t\tfor(unsigned int kk=0; kk<owner_.block_length; ++kk) {\n\t\t\t\t\t\tassert(owner_.permute_blocks[k]+kk<owner_.originals[0].size());\n\t\t\t\t\t\towner_.originals[siz][owner_.permute_blocks[k]+kk]=\n\t\t\t\t\t\t   owner_.originals[owner_.current_][owner_.permute_blocks[vec[k]]+kk];\n\t\t\t\t\t\t}\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t}\n\t\t}\n\n\ttemplate<class T>\n\tstd::ostream& operator<<(std::ostream& str, const symmetriser<T>& sym)\n\t\t{\n\t\tfor(unsigned int i=0; i<sym.size(); ++i) {\n\t\t\tfor(unsigned int j=0; j<sym[i].size(); ++j) {\n\t\t\t\tstr << sym[i][j] << \" \";\n\t\t\t\t}\n\t\t\tstr << \" \";\n\t\t\tstr.setf(std::ios::right, std::ios::adjustfield);\n\t\t\tstr << std::setw(2) << sym.signature(i) << std::endl;\n\t\t\t}\n\t\treturn str;\n\t\t}\n\n\t}\n\n\n\n"
  },
  {
    "path": "core/Compare.cc",
    "content": "\n#include <typeinfo>\n\n#include \"Compare.hh\"\n#include \"Algorithm.hh\" // FIXME: only needed because index_iterator is in there\n#include \"Exceptions.hh\"\n#include <sstream>\n#include <regex>\n#include \"properties/Indices.hh\"\n#include \"properties/Coordinate.hh\"\n#include \"properties/ImplicitIndex.hh\"\n#include \"properties/SelfCommutingBehaviour.hh\"\n#include \"properties/CommutingAsSum.hh\"\n#include \"properties/CommutingAsProduct.hh\"\n#include \"properties/CommutingBehaviour.hh\"\n#include \"properties/DifferentialForm.hh\"\n#include \"properties/DiracBar.hh\"\n#include \"properties/Integer.hh\"\n#include \"properties/SortOrder.hh\"\n\n// #define DEBUG \"Compare.cc\"\n#include \"Debug.hh\"\n\nnamespace cadabra {\n\n\tint Ex_comparator::offset=0;\n\n\tint subtree_compare(const Properties *properties,\n\t                    Ex::iterator one, Ex::iterator two,\n\t                    int mod_prel, bool, int compare_multiplier, bool literal_wildcards)\n\t\t{\n\t\t//\tstd::cerr << \"comparing \" << Ex(one) << \" with \" << Ex(two) << \" \" << mod_prel << \", \" << checksets << std::endl;\n\n\t\t// The logic is to compare successive aspects of the two objects, returning a\n\t\t// no-match code if a difference is found at a particular level, or continuing\n\t\t// further down the line if there still is a match.\n\n\t\t// Compare multipliers. Skip this step if one of the objects is a rational and the\n\t\t// other not, as in that case we are matching values to symbols.\n\t\tif( one->is_rational()==two->is_rational() ) {\n\t\t\tif(compare_multiplier==-2 && !two->is_name_wildcard() && !one->is_name_wildcard())\n\t\t\t\tif(one->multiplier != two->multiplier) {\n\t\t\t\t\tif(*one->multiplier < *two->multiplier) return 2;\n\t\t\t\t\telse return -2;\n\t\t\t\t\t}\n\t\t\t}\n\n\t\tint  mult=2;\n\t\t// Handle object wildcards and comparison\n\t\tif(!literal_wildcards) {\n\t\t\tif(one->is_object_wildcard() || two->is_object_wildcard())\n\t\t\t\treturn 0;\n\t\t\t}\n\n\t\t// Handle mismatching node names.\n\t\tif(one->name!=two->name) {\n\t\t\t//\t\tstd::cerr << *one->name << \" != \" << *two->name << std::endl;\n\t\t\tif(literal_wildcards) {\n\t\t\t\tif(*one->name < *two->name) return mult;\n\t\t\t\telse return -mult;\n\t\t\t\t}\n\n\t\t\tDEBUGLN( std::cerr << \"auto? \" << one->is_autodeclare_wildcard() << \", \" << two->is_numbered_symbol() << std::endl; );\n\t\t\tif( (one->is_autodeclare_wildcard() && two->is_numbered_symbol()) ||\n\t\t\t      (two->is_autodeclare_wildcard() && one->is_numbered_symbol()) ) {\n\t\t\t\tif( one->name_only() != two->name_only() ) {\n\t\t\t\t\tif(*one->name < *two->name) return mult;\n\t\t\t\t\telse return -mult;\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\telse if( one->is_name_wildcard()==false && two->is_name_wildcard()==false ) {\n\t\t\t\tif(*one->name < *two->name) return mult;\n\t\t\t\telse return -mult;\n\t\t\t\t}\n\n\t\t\tDEBUGLN( std::cerr << \"match despite difference: \" << *one->name << \" and \" << *two->name << std::endl; );\t\t\t\n\t\t\t}\n\n\t\t// Compare parent relations.\n\t\tif(mod_prel<=-2) {\n\t\t\tstr_node::parent_rel_t p1=one->fl.parent_rel;\n\t\t\tstr_node::parent_rel_t p2=two->fl.parent_rel;\n\t\t\tif(p1!=p2) {\n\t\t\t\treturn (p1<p2)?2:-2;\n\t\t\t\t}\n\t\t\t}\n\n\t\t// Now turn to the child nodes. Before comparing them directly, first compare\n\t\t// the number of children, taking into account range wildcards.\n\t\tint numch1=Ex::number_of_children(one);\n\t\tint numch2=Ex::number_of_children(two);\n\n\t\t// FIXME: handle range wildcards as in Props.cc\n\n\t\tif(numch1!=numch2) {\n\t\t\tif(numch1<numch2) return 2;\n\t\t\telse return -2;\n\t\t\t}\n\n\t\t// Compare actual children. We run through this twice: first\n\t\t// consider all non-index children, then all index children. This\n\t\t// is because we want products of tensors which differ only by\n\t\t// index position to be sorted by the names of the tensors first,\n\t\t// not first by their index positions. Otherwise canonicalise cannot\n\t\t// do its raising/lowering job.\n\n\t\tbool do_indices=false;\n\t\tint remember_ret=0;\n\t\tif(mod_prel==0) mod_prel=-2;\n\t\telse if(mod_prel>0)  --mod_prel;\n\t\tif(compare_multiplier==0) compare_multiplier=-2;\n\t\telse if(compare_multiplier>0)  --compare_multiplier;\n\n\t\tfor(;;) {\n\t\t\tEx::sibling_iterator sib1=one.begin(), sib2=two.begin();\n\n\t\t\twhile(sib1!=one.end()) {\n\t\t\t\tif(sib1->is_index() == do_indices) {\n\t\t\t\t\tint ret=subtree_compare(properties, sib1,sib2, mod_prel, true /* checksets */,\n\t\t\t\t\t                        compare_multiplier, literal_wildcards);\n\t\t\t\t\t// std::cerr << \"result \" << ret << std::endl;\n\t\t\t\t\tif(abs(ret)>1)\n\t\t\t\t\t\treturn ret/abs(ret)*mult;\n\t\t\t\t\tif(ret!=0 && remember_ret==0)\n\t\t\t\t\t\tremember_ret=ret;\n\t\t\t\t\t}\n\t\t\t\t++sib1;\n\t\t\t\t++sib2;\n\t\t\t\t}\n\n\t\t\tif(remember_ret!=0) break;\n\n\t\t\tif(!do_indices) do_indices=true;\n\t\t\telse break;\n\t\t\t}\n\n\t\treturn remember_ret;\n\t\t}\n\n\tbool tree_less(const Properties* properties, const Ex& one, const Ex& two, int mod_prel, bool checksets, int compare_multiplier)\n\t\t{\n\t\treturn subtree_less(properties, one.begin(), two.begin(), mod_prel, checksets, compare_multiplier);\n\t\t}\n\n\tbool tree_equal(const Properties* properties, const Ex& one, const Ex& two, int mod_prel, bool checksets, int compare_multiplier)\n\t\t{\n\t\treturn subtree_equal(properties, one.begin(), two.begin(), mod_prel, checksets, compare_multiplier);\n\t\t}\n\n\tbool tree_exact_less(const Properties* properties, const Ex& one, const Ex& two, int mod_prel, bool checksets, int compare_multiplier, bool literal_wildcards)\n\t\t{\n\t\treturn subtree_exact_less(properties, one.begin(), two.begin(), mod_prel, checksets, compare_multiplier, literal_wildcards);\n\t\t}\n\n\tbool tree_exact_less(const Properties* properties, Ex::iterator one, Ex::iterator two, int mod_prel, bool checksets, int compare_multiplier, bool literal_wildcards)\n\t\t{\n\t\treturn subtree_exact_less(properties, one, two, mod_prel, checksets, compare_multiplier, literal_wildcards);\n\t\t}\n\n\tbool tree_exact_equal(const Properties* properties, const Ex& one, const Ex& two, int mod_prel, bool checksets, int compare_multiplier, bool literal_wildcards)\n\t\t{\n\t\treturn subtree_exact_equal(properties, one.begin(), two.begin(), mod_prel, checksets, compare_multiplier, literal_wildcards);\n\t\t}\n\n\tbool subtree_less(const Properties* properties, Ex::iterator one, Ex::iterator two, int mod_prel, bool checksets, int compare_multiplier)\n\t\t{\n\t\tint cmp=subtree_compare(properties, one, two, mod_prel, checksets, compare_multiplier);\n\t\tif(cmp==2) return true;\n\t\treturn false;\n\t\t}\n\n\tbool subtree_equal(const Properties* properties, Ex::iterator one, Ex::iterator two, int mod_prel, bool checksets, int compare_multiplier)\n\t\t{\n\t\tint cmp=subtree_compare(properties, one, two, mod_prel, checksets, compare_multiplier);\n\t\tif(abs(cmp)<=1) return true;\n\t\treturn false;\n\t\t}\n\n\tbool subtree_exact_less(const Properties* properties, Ex::iterator one, Ex::iterator two, int mod_prel, bool checksets, int compare_multiplier, bool literal_wildcards)\n\t\t{\n\t\tint cmp=subtree_compare(properties, one, two, mod_prel, checksets, compare_multiplier, literal_wildcards);\n\t\t//std::cerr << \"comparing \" << Ex(one) << \" with \" << Ex(two) << \" = \" << cmp << std::endl;\n\t\tif(cmp>0) return true;\n\t\treturn false;\n\t\t}\n\n\tbool subtree_exact_equal(const Properties* properties, Ex::iterator one, Ex::iterator two, int mod_prel, bool checksets, int compare_multiplier, bool literal_wildcards)\n\t\t{\n\t\tint cmp=subtree_compare(properties, one, two, mod_prel, checksets, compare_multiplier, literal_wildcards);\n\t\t//\tstd::cout << *one->name << \" == \" << *two->name << \" : \" << cmp << std::endl;\n\t\tif(cmp==0) return true;\n\t\treturn false;\n\t\t}\n\n\ttree_less_obj::tree_less_obj(const Properties* k)\n\t\t: properties(k)\n\t\t{\n\t\t}\n\n\tbool tree_less_obj::operator()(const Ex& one, const Ex& two) const\n\t\t{\n\t\treturn tree_less(properties, one, two);\n\t\t}\n\n\ttree_less_modprel_obj::tree_less_modprel_obj(const Properties* k)\n\t\t: properties(k)\n\t\t{\n\t\t}\n\n\tbool tree_less_modprel_obj::operator()(const Ex& one, const Ex& two) const\n\t\t{\n\t\treturn tree_less(properties, one, two, 0);\n\t\t}\n\n\ttree_equal_obj::tree_equal_obj(const Properties* k)\n\t\t: properties(k)\n\t\t{\n\t\t}\n\n\tbool tree_equal_obj::operator()(const Ex& one, const Ex& two) const\n\t\t{\n\t\treturn tree_equal(properties, one, two);\n\t\t}\n\n\ttree_exact_less_obj::tree_exact_less_obj(const Properties *p)\n\t\t: properties(p)\n\t\t{\n\t\t}\n\n\tbool tree_exact_less_obj::operator()(const Ex& one, const Ex& two) const\n\t\t{\n\t\treturn tree_exact_less(properties, one, two);\n\t\t}\n\n\tbool tree_exact_less_obj::operator()(Ex::iterator one, Ex::iterator two) const\n\t\t{\n\t\treturn tree_exact_less(properties, one, two);\n\t\t}\n\n\ttree_exact_less_no_wildcards_obj::tree_exact_less_no_wildcards_obj()\n\t\t{\n\t\tproperties=0;\n\t\t}\n\n\tbool tree_exact_less_no_wildcards_obj::operator()(const Ex& one, const Ex& two) const\n\t\t{\n\t\treturn tree_exact_less(properties, one, two, -2, true, 0, true);\n\t\t}\n\n\tbool tree_exact_less_no_wildcards_mod_prel_obj::operator()(const Ex& one, const Ex& two) const\n\t\t{\n\t\treturn tree_exact_less(properties, one, two, 0, true, -2, true);\n\t\t}\n\n\tbool tree_exact_equal_obj::operator()(const Ex& one, const Ex& two) const\n\t\t{\n\t\treturn tree_exact_equal(properties, one, two);\n\t\t}\n\n\ttree_exact_less_mod_prel_obj::tree_exact_less_mod_prel_obj(const Properties *p)\n\t\t: properties(p)\n\t\t{\n\t\t}\n\n\tbool tree_exact_less_mod_prel_obj::operator()(const Ex& one, const Ex& two) const\n\t\t{\n\t\treturn tree_exact_less(properties, one, two, 0, true, -2, true);\n\t\t}\n\n\tbool tree_exact_equal_mod_prel_obj::operator()(const Ex& one, const Ex& two) const\n\t\t{\n\t\treturn tree_exact_equal(properties, one, two, 0, true, -2, true);\n\t\t}\n\n\tbool tree_exact_less_for_indexmap_obj::operator()(const Ex& one, const Ex& two) const\n\t\t{\n\t\treturn tree_exact_less(0, one, two, -2 /* mod_prel, was 0 */, true, -2 /* compare_multiplier, was 0 */, true);\n\t\t}\n\n\t//bool operator==(const Ex& first, const Ex& second)\n\t//\t{\n\t//\treturn tree_exact_equal(properties, first, second, 0, true, -2, true);\n\t//\t}\n\t//\n\n\tvoid Ex_comparator::clear()\n\t\t{\n\t\treplacement_map.clear();\n\t\tsubtree_replacement_map.clear();\n\t\tindex_value_map.clear();\n\t\tfactor_locations.clear();\n\t\tfactor_moving_signs.clear();\n\t\t}\n\n\tEx_comparator::match_t Ex_comparator::match_subtree(const Ex& tr, Ex::iterator i1, Ex::iterator i2, Ex::iterator conditions)\n\t\t{\n\t\tauto ret = equal_subtree(i1, i2);\n\t\tif(ret==match_t::subtree_match || ret==match_t::node_match) {\n\t\t\tif(conditions==tr.end()) return ret;\n\t\t\tstd::string error;\n\t\t\tif(satisfies_conditions(conditions, error))\n\t\t\t\treturn ret;\n\t\t\telse\n\t\t\t\treturn match_t::no_match_greater; // FIXME: is that the right thing to do?\n\t\t\t}\n\t\telse return ret;\n\t\t}\n\n\tEx_comparator::match_t Ex_comparator::equal_subtree(Ex::iterator i1, Ex::iterator i2,\n\t      useprops_t use_props, bool ignore_parent_rel)\n\t\t{\n\t\t// FIXME: Ex_comparator should really know about the tree,\n\t\t// so that we can do safety checks like the ones below.\n\t\t// \n\t\t// if(!i1.is_valid() && i2.is_valid())\n\t\t// \treturn match_t::no_match_less;\n\t\t// \n\t\t// if(i1.is_valid() && !i2.is_valid())\n\t\t// \treturn match_t::no_match_greater;\n\t\t// \n\t\t// if(!i1.is_valid() && !i2.is_valid())\n\t\t// \treturn match_t::subtree_match;\n\t\t\n\t\tDEBUGLN( std::cerr << tab() << \"equal_subtree with use_props = \" << use_props << std::endl; );\n\t\t++offset;\n\n\t\tEx::sibling_iterator i1end(i1);\n\t\tEx::sibling_iterator i2end(i2);\n\t\t++i1end;\n\t\t++i2end;\n\n\t\t// When measuring depth (to determine if we need to use\n\t\t// properties or not), things like \\dot{\\alpha} should give the\n\t\t// same depth for \\dot and for \\alpha, because \\dot is an\n\t\t// Accent. We use a predicate function to take care of this.\n\t\tauto depth_predicate = [this,use_props](const Ex::iterator& i) {\n\t\t\tif(use_props!=useprops_t::not_at_top) return true;\n\t\t\tconst Accent *accent = properties.get<Accent>(i);\n\t\t\treturn (accent==0);\n\t\t};\n\t\t\n\t\tbool first_call=true;\n\t\tmatch_t worst_mismatch=match_t::subtree_match;\n\t\tEx::iterator rememberi1=i1;\n\n\t\twhile(i1!=i1end && i2!=i2end) {\n\t\t\tuseprops_t up = use_props;\n\t\t\tauto dist = Ex::distance(rememberi1, i1, depth_predicate);\n\t\t\tif(use_props==useprops_t::not_at_top) {\n\t\t\t\tif(dist!=0) up=useprops_t::always;\n\t\t\t\telse        up=useprops_t::never;\n\t\t\t\t}\n\t\t\tbool    ip = ignore_parent_rel && (dist==0);\n\t\t\tmatch_t mm=compare(i1, i2, first_call, up, ip);\n\t\t\t//\t\tDEBUGLN( std::cerr << \"COMPARE \" << *i1->name << \", \" << *i2->name << \" = \" << static_cast<int>(mm) << std::endl; )\n\t\t\tfirst_call=false;\n\t\t\tswitch(mm) {\n\t\t\t\tcase match_t::no_match_indexpos_less:\n\t\t\t\tcase match_t::no_match_indexpos_greater:\n\t\t\t\t\tworst_mismatch=mm;\n\t\t\t\t\t// FIXME: at the moment skipping children is the right thing to do\n\t\t\t\t\t// as we are assuming that the no_match_indexpos_... is the worst\n\t\t\t\t\t// thing that could have happened for this child subtree. See\n\t\t\t\t\t// also the FIXME below.\n\t\t\t\t\ti1.skip_children();\n\t\t\t\t\ti2.skip_children();\n\t\t\t\t\tbreak;\n\t\t\t\tcase match_t::no_match_less:\n\t\t\t\tcase match_t::no_match_greater:\n\t\t\t\t\t// As soon as we get a mismatch, return.\n\t\t\t\t\treturn report(mm);\n\t\t\t\tcase match_t::node_match: {\n\t\t\t\t\tsize_t num1=Ex::number_of_children(i1);\n\t\t\t\t\tsize_t num2=Ex::number_of_children(i2);\n\n\t\t\t\t\tif(num1==1 && i1.begin()->is_range_wildcard()) {\n\t\t\t\t\t\t//\t\t\t\tstd::cerr << \"comparing \" << *i1->name << \" with \" << *i2->name << \" \" << num1 << \" \" << num2 << std::endl;\n\t\t\t\t\t\treturn match_t::subtree_match;\n\t\t\t\t\t\t}\n\n\t\t\t\t\t// TODO: this is where we should decide what to do with\n\t\t\t\t\t// nodes which have sibling wildcards. Make a\n\t\t\t\t\t// 'compare_siblings'. We also need a\n\t\t\t\t\t// siblings_replacement_map in which we can store a\n\t\t\t\t\t// sibling range for a given sibling wildcard symbol,\n\t\t\t\t\t// e.g. a... -> i j k.  This matching routine should walk\n\t\t\t\t\t// to the first non-range object in the pattern, and match\n\t\t\t\t\t// that. Once it is matched, it should store the resulting\n\t\t\t\t\t// map for any range object to the left. Then continue,\n\t\t\t\t\t// recursively, finding the second non-range object, and\n\t\t\t\t\t// again storing the range object map.  Once a no-match\n\t\t\t\t\t// comes back, pop the match objects from the stack and\n\t\t\t\t\t// try to find the non-range object to the right of the match\n\t\t\t\t\t// reported earlier.\n\n\t\t\t\t\t// This slightly oversearches (we could keep track of how\n\t\t\t\t\t// many non-range objects are still to be matched in order\n\t\t\t\t\t// to restrict how far to the right a search should go), but in\n\t\t\t\t\t// practise this is probably not relevant (and can always be added).\n\n\t\t\t\t\tif(num1 < num2)      return report(match_t::no_match_less);\n\t\t\t\t\telse if(num1 > num2) return report(match_t::no_match_greater);\n\t\t\t\t\tbreak;\n\t\t\t\t\t}\n\t\t\t\tcase match_t::match_index_less:\n\t\t\t\tcase match_t::match_index_greater:\n\t\t\t\t\t// If we have a match but different index names, remember this\n\t\t\t\t\t// mismatch, because it will determine our total result value.\n\t\t\t\t\tif(worst_mismatch==match_t::subtree_match)\n\t\t\t\t\t\tworst_mismatch=mm;\n\t\t\t\t\t// If indices by type but not name, we do not need to go\n\t\t\t\t\t// further down the tree. E.g. W_{\\hat{\\theta_1}} vs\n\t\t\t\t\t// W_{\\hat{\\theta_2}} compared at the index position.\n\t\t\t\t\t// The 'compare' has done a comparison of the entire\n\t\t\t\t\t// tree of the indices, no need to go down.\n\t\t\t\t\ti1.skip_children();\n\t\t\t\t\ti2.skip_children();\n\t\t\t\t\tbreak;\n\t\t\t\tcase match_t::subtree_match:\n\t\t\t\t\t// If a match of the entire subtrees at i1 and i2 has been found,\n\t\t\t\t\t// we do not need to go down the child nodes of i1 and i2 anymore.\n\t\t\t\t\ti1.skip_children();\n\t\t\t\t\ti2.skip_children();\n\t\t\t\t\tbreak;\n\t\t\t\t}\n\t\t\t// Continue walking the tree downwards.\n\t\t\tDEBUGLN( std::cerr << tab() << \"one down\" << std::endl; );\n\t\t\t++i1;\n\t\t\t++i2;\n\t\t\t}\n\t\tDEBUGLN( std::cerr << tab() << \"equal_subtree done\" << std::endl; );\n\t\t\n\t\treturn report(worst_mismatch);\n\t\t}\n\n\tEx_comparator::Ex_comparator(const Properties& k)\n\t\t: properties(k), value_matches_index(false)\n\t\t{\n\t\t}\n\n\tvoid Ex_comparator::set_value_matches_index(bool v)\n\t\t{\n\t\tvalue_matches_index=v;\n\t\t}\n\n\tstd::string Ex_comparator::tab() const\n\t\t{\n\t\tstd::string ret;\n\t\tfor(int i=0; i<offset; ++i)\n\t\t\tret+=\"   \";\n\t\treturn ret;\n\t\t}\n\n\tEx_comparator::match_t Ex_comparator::report(Ex_comparator::match_t r) const\n\t\t{\n#ifndef DEBUG\t\t\n\t\treturn r;\n#endif\n\n\t\tDEBUGLN( std::cerr << tab() << \"result = \"; );\n\t\tDEBUGLN( \n\t\t\tswitch(r) {\n\t\t\t\tcase match_t::node_match:\n\t\t\t\t\tstd::cerr << \"node_match\";\n\t\t\t\t\tbreak;\n\t\t\t\tcase match_t::subtree_match:\n\t\t\t\t\tstd::cerr << \"subtree_match\";\n\t\t\t\t\tbreak;\n\t\t\t\tcase match_t::match_index_less:\n\t\t\t\t\tstd::cerr << \"match_index_less\";\n\t\t\t\t\tbreak;\n\t\t\t\tcase match_t::match_index_greater:\n\t\t\t\t\tstd::cerr << \"match_index_greater\";\n\t\t\t\t\tbreak;\n\t\t\t\tcase match_t::no_match_indexpos_less:\n\t\t\t\t\tstd::cerr << \"no_match_indexpos_less\";\n\t\t\t\t\tbreak;\n\t\t\t\tcase match_t::no_match_indexpos_greater:\n\t\t\t\t\tstd::cerr << \"no_match_indexpos_greater\";\n\t\t\t\t\tbreak;\n\t\t\t\tcase match_t::no_match_less:\n\t\t\t\t\tstd::cerr << \"no_match_less\";\n\t\t\t\t\tbreak;\n\t\t\t\tcase match_t::no_match_greater:\n\t\t\t\t\tstd::cerr << \"no_match_greater\";\n\t\t\t\t\tbreak;\n\t\t\t\t}\n\t\t\tstd::cerr << std::endl; );\n\t\t\n\t\t--offset;\n\t\treturn r;\n\t\t}\n\n\tEx_comparator::match_t Ex_comparator::compare(const Ex::iterator& one,\n\t      const Ex::iterator& two,\n\t      bool nobrackets,\n\t      useprops_t use_props, bool ignore_parent_rel)\n\t\t{\n\t\t++offset;\n\n\t\t// nobrackets also implies 'no multiplier', i.e. 'toplevel'.\n\t\t// 'one' is the substitute pattern, 'two' the expression under consideration.\n\n\t\tDEBUGLN( std::cerr << tab() << \"matching \" << Ex(one) << tab() << \"to \" << Ex(two) << tab() << \"using props = \" << use_props << \", ignore_parent_rel = \" << ignore_parent_rel << std::endl; );\n\n\t\tif(nobrackets==false && one->fl.bracket != two->fl.bracket)\n\t\t\treturn report( (one->fl.bracket < two->fl.bracket)?match_t::no_match_less:match_t::no_match_greater );\n\n\t\t// Determine whether we are dealing with one of the pattern types.\n\t\tbool pattern=false;\n\t\tbool objectpattern=false;\n\t\tbool implicit_pattern=false; // anything in _{..} or ^{..} that is not an integer or coordinate\n\t\tbool is_index=false;\n\t\tbool is_sibling_pattern=false;\n\t\tbool is_coordinate=false;\n\t\tbool is_number=false;\n\t\tbool two_is_value=false;\n\n\t\tif(one->fl.bracket==str_node::b_none && one->is_index() )\n\t\t\tis_index=true;\n\t\tif(one->is_name_wildcard())\n\t\t\tpattern=true;\n\t\telse if(one->is_object_wildcard())\n\t\t\tobjectpattern=true;\n\t\telse if(one->is_siblings_wildcard())\n\t\t\tis_sibling_pattern=true;\n\t\telse if(is_index && one->is_integer()==false) {\n\t\t\t// Things in _{..} or ^{..} are either indices (implicit patterns), or coordinates (as\n\t\t\t// numbers are treated in the last branch below).\n\t\t\tconst Coordinate *cdn1=0;\n\t\t\tif(use_props==useprops_t::always) {\n\t\t\t\tDEBUGLN( std::cerr << tab() << \"is \" << *one->name << \" a coordinate?\" << std::endl; );\n\t\t\t\tcdn1=properties.get<Coordinate>(one, true);\n\t\t\t\tDEBUGLN( std::cerr << tab() << cdn1 << std::endl; );\n\t\t\t\t}\n\n\t\t\tif(cdn1==0)\n\t\t\t\timplicit_pattern=true;\n\t\t\telse\n\t\t\t\tis_coordinate=true;\n\t\t\t}\n\t\telse if(one->is_integer())\n\t\t\tis_number=true;\n\n\t\t// Various cases to be distinguished now:\n\t\t//   - match index pattern to object\n\t\t//   - match object pattern to object\n\t\t//   - match coordinate to index\n\t\t//   - everything else, which does not involve patterns/wildcards\n\n\t\tif(pattern || implicit_pattern) {\n\n\t\t\t// It is possible to match integers to implicit patterns (indices), provided\n\t\t\t// we know that the given index can take the found numerical value.\n\t\t\t// See basic.cdb/test26 for a simple example.\n\t\t\t// If we have a proper 'question mark' pattern, we always match to integers.\n\n\t\t\tif(two->is_rational() && implicit_pattern) {\n\t\t\t\t// Determine whether 'one' can take the value 'two'.\n\t\t\t\tDEBUGLN( std::cerr << tab() << \"can one take value two (use props = \" << use_props  << \")\" << std::endl; );\n\t\t\t\tconst Integer *ip = 0;\n\t\t\t\tif(use_props==useprops_t::always) {\n\t\t\t\t\tDEBUGLN( std::cerr << tab() << \"is \" << *one->name << \" an integer?\" << std::endl; );\n\t\t\t\t\tip = properties.get<Integer>(one, true); // 'true' to ignore parent rel.\n\t\t\t\t\tDEBUGLN( std::cerr << tab() << ip << std::endl; );\n\t\t\t\t\t}\n\n\t\t\t\tif(ip==0) return report(match_t::no_match_less);\n\t\t\t\t\n\t\t\t\tDEBUGLN( std::cerr << tab() << \"yes, potentially, check the range\" << std::endl; );\n\n\t\t\t\tbool lower_bdy=true, upper_bdy=true;\n\t\t\t\tmultiplier_t from, to;\n\t\t\t\tif(ip->from.begin()==ip->from.end()) lower_bdy=false;\n\t\t\t\telse {\n\t\t\t\t\tif(!ip->from.begin()->is_rational()) return report(match_t::no_match_less);\n\t\t\t\t\tfrom = *ip->from.begin()->multiplier;\n\t\t\t\t\t}\n\t\t\t\tif(ip->to.begin()==ip->to.end())     upper_bdy=false;\n\t\t\t\telse {\n\t\t\t\t\tif(!ip->to.begin()->is_rational()) return report(match_t::no_match_less);\n\t\t\t\t\tto   = *ip->to.begin()->multiplier;\n\t\t\t\t\t}\n\t\t\t\tif((lower_bdy && *two->multiplier < from) || (upper_bdy && *two->multiplier > to))\n\t\t\t\t\treturn report(match_t::no_match_less);\n\n\t\t\t\tDEBUGLN( std::cerr << tab() << Ex(one) << tab() << \"can take value \" << *two->multiplier << std::endl );\n\t\t\t\t}\n\n\t\t\t// We want to search the replacement map for replacement rules which we have\n\t\t\t// constructed earlier, and discard the current match if it conflicts those\n\t\t\t// rules. This is to make sure that e.g. a pattern k1_a k2_a does not match\n\t\t\t// an expression k1_c k2_d.\n\t\t\t//\n\t\t\t// In order to ensure that a replacement rule for a lower index is also\n\t\t\t// triggering a rule for an upper index, we simply store both rules (see\n\t\t\t// below) so that searching for rules can remain simple.\n\n\t\t\treplacement_map_t::iterator loc=replacement_map.find(Ex(one));\n\n\t\t\tbool tested_full=true;\n\n\t\t\t// If this is a pattern with a non-zero number of children,\n\t\t\t// also search the pattern without the children (but not if\n\t\t\t// this node is an Accent, because then the child nodes are\n\t\t\t// very relevant).\n\t\t\tif(loc == replacement_map.end() && Ex::number_of_children(one)!=0) {\n\t\t\t\tDEBUGLN( std::cerr << tab() << \"**** not found, trying without child nodes\" << std::endl; );\n\t\t\t\tif(properties.get<Accent>(one)==0 ) {\n\t\t\t\t\tEx tmp1(one);\n\t\t\t\t\ttmp1.erase_children(tmp1.begin());\n\t\t\t\t\tloc = replacement_map.find(tmp1);\n\t\t\t\t\ttested_full=false;\n\t\t\t\t\t}\n\t\t\t\t}\n\n\t\t\tif(loc!=replacement_map.end()) {\n\t\t\t\t// We constructed a replacement rule for this node already at an earlier\n\t\t\t\t// stage. Need to make sure that that rule is consistent with what we\n\t\t\t\t// found now.\n\n\t\t\t\tint cmp;\n\n\t\t\t\t// If this is an index/pattern, try to match the whole index/pattern.\n\t\t\t\tif(tested_full)\n\t\t\t\t\tcmp=subtree_compare(&properties, (*loc).second.begin(), two, -2);\n\t\t\t\telse {\n\t\t\t\t\tEx tmp2(two);\n\t\t\t\t\ttmp2.erase_children(tmp2.begin());\n\t\t\t\t\tcmp=subtree_compare(&properties, (*loc).second.begin(), tmp2.begin(), -2);\n\t\t\t\t\t}\n\t\t\t\tDEBUGLN(std::cerr << \" pattern \" << two\n\t\t\t\t\t\t<< \" should be \" << (*loc).second.begin()\n\t\t\t\t\t\t<< \" because that's what \" << one\n\t\t\t\t\t\t<< \" was set to previously; result \" << cmp << std::endl;  );\n\t\t\t\t\t\n\t\t\t\tif(cmp==0)      return report(match_t::subtree_match);\n\t\t\t\telse if(cmp>0)  return report(match_t::no_match_less);\n\t\t\t\telse            return report(match_t::no_match_greater);\n\t\t\t\t}\n\t\t\telse {\n\t\t\t\t// This index/pattern was not encountered earlier. If this node is an index,\n\t\t\t\t// check that the index types in pattern and object agree (if known,\n\t\t\t\t// otherwise assume they match).\n\t\t\t\t// If two is a rational, we have already checked that one can take this value.\n\n\t\t\t\tif(two->is_index() && !one->is_index() && !one->is_range_wildcard())\n\t\t\t\t\treturn report(match_t::no_match_indexpos_greater);\n\t\t\t\t\n\t\t\t\tif(one->is_index()) {\n\t\t\t\t\tDEBUGLN( std::cerr << tab() << \"object one is index\" << std::endl; );\n\n\t\t\t\t\tconst Indices *t1=0;\n\t\t\t\t\tconst Indices *t2=0;\n\t\t\t\t\tif(use_props==useprops_t::always) {\n\t\t\t\t\t\tDEBUGLN( std::cerr << tab() << \"is \" << *one->name << \" an index?\" << std::endl; );\n\t\t\t\t\t\tDEBUGSTOP(true);\n\t\t\t\t\t\tt1=properties.get<Indices>(one, false);\n\t\t\t\t\t\tDEBUGSTOP(false);\n\t\t\t\t\t\tDEBUGLN( std::cerr << tab() << \"found index property for one: \" << t1 << std::endl; );\n\t\t\t\t\t\tif(two->is_rational()==false) {\n\t\t\t\t\t\t\tDEBUGLN( std::cerr << tab() << \"is \" << *two->name << \" an index?\" << std::endl; );\n\t\t\t\t\t\t\tDEBUGSTOP(true);\n\t\t\t\t\t\t\tt2=properties.get<Indices>(two, false);\n\t\t\t\t\t\t\tDEBUGSTOP(false);\n\t\t\t\t\t\t\tDEBUGLN( std::cerr << tab() << \"found index property for two: \" << t2 << std::endl; );\n\t\t\t\t\t\t\t// It is still possible that t2 is a Coordinate and\n\t\t\t\t\t\t\t// t1 an Index which can take the value of the\n\t\t\t\t\t\t\t// coordinate. This happens when 'm' is an index\n\t\t\t\t\t\t\t// taking values {t,...}, you declare X^{m} to have\n\t\t\t\t\t\t\t// a property and then later ask if X^{t} has that\n\t\t\t\t\t\t\t// property. In that case X^{m} is object 1 and\n\t\t\t\t\t\t\t// X^{t} object 2, and we end up here (NOT in the\n\t\t\t\t\t\t\t// branch with both exchanged, which happens when\n\t\t\t\t\t\t\t// evaluate tries to determine if a rule for X^{t}\n\t\t\t\t\t\t\t// applies to an expression X^{m}).\n\t\t\t\t\t\t\tif(t1!=0 && t2!=t1) {\n\t\t\t\t\t\t\t\tconst auto& values = t1->values(properties, one);\n\t\t\t\t\t\t\t\tauto ivals = std::find_if(values.begin(), values.end(),\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t  [&](const Ex& a) {\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t  if(subtree_compare(&properties, a.begin(), two, 0)==0)\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t  return true;\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t  else return false;\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t  });\n\t\t\t\t\t\t\t\tif(ivals!=values.end()) {\n\t\t\t\t\t\t\t\t\tt2=t1;\n\t\t\t\t\t\t\t\t\ttwo_is_value=true;\n\t\t\t\t\t\t\t\t\t}\n\t\t\t\t\t\t\t\t}\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\t\telse {\n\t\t\t\t\t\t\t\tt2=t1; // We already know 'one' can take the value 'two', so in a sense t2 is in the same set as t1.\n\t\t\t\t\t\t\t\tDEBUGLN( std::cerr << tab() << two << \" is rational\" << std::endl; );\n\t\t\t\t\t\t\t\t}\n\t\t\t\t\t\t}\n\n\t\t\t\t\t// Check parent rel if a) there is no Indices property for the indices, b) the index positions\n\t\t\t\t\t// are not free. Effectively this means that indices without property info get treated as\n\t\t\t\t\t// fixed-position indices.\n\n\t\t\t\t\t// FIXME: this is not entirely correct. If the indexpos does not match, going deeper may\n\t\t\t\t\t// still reveal that the mismatch is even worse.\n\n\t\t\t\t\tif(!ignore_parent_rel)\n\t\t\t\t\t\tif(t1==0 || t2==0 || (t1->position_type!=Indices::free && t2->position_type!=Indices::free))\n\t\t\t\t\t\t\tif(one->fl.parent_rel != two->fl.parent_rel) {\n\t\t\t\t\t\t\t\tDEBUGLN( std::cerr << tab() << \"parent_rels not the same\" << std::endl;);\n\t\t\t\t\t\t\t\treturn report( (one->fl.parent_rel < two->fl.parent_rel)\n\t\t\t\t\t\t\t\t               ?match_t::no_match_indexpos_less:match_t::no_match_indexpos_greater );\n\t\t\t\t\t\t\t\t}\n\n\t\t\t\t\t// If both indices have no Indices property, compare them by name and pretend they are\n\t\t\t\t\t// both in the same Indices set.\n\n\t\t\t\t\tif(two->is_rational()==false && !(t1==0 && t2==0)) {\n\t\t\t\t\t\tif( (t1 || t2) && implicit_pattern ) {\n\t\t\t\t\t\t\tif(t1 && t2) {\n\t\t\t\t\t\t\t\tif((*t1).set_name != (*t2).set_name) {\n\t\t\t\t\t\t\t\t\tif((*t1).set_name < (*t2).set_name) return report(match_t::no_match_less);\n\t\t\t\t\t\t\t\t\telse                                return report(match_t::no_match_greater);\n\t\t\t\t\t\t\t\t\t}\n\t\t\t\t\t\t\t\t}\n\t\t\t\t\t\t\telse {\n\t\t\t\t\t\t\t\t// If we get here, 'one' or 'two' has an Indices property, and\n\t\t\t\t\t\t\t\t// the other one doesn't. So we do not know how to compare them,\n\t\t\t\t\t\t\t\t// except by name. Note that we should return something which is\n\t\t\t\t\t\t\t\t// symmetric if 'two' and 'one' had been exchanged!\n\t\t\t\t\t\t\t\tint dc = subtree_compare(&properties, one, two, 0);\n\t\t\t\t\t\t\t\tif(dc<0) return report(match_t::no_match_less);\n\t\t\t\t\t\t\t\telse     return report(match_t::no_match_greater);\n\t\t\t\t\t\t\t\t}\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\t}\n\t\t\t\t\t}\n\t\t\t\t\t\n\t\t\t\t// See the documentation of substitute::can_apply for details about\n\t\t\t\t// how the replacement_map is supposed to work. In general, if we want\n\t\t\t\t// that e.g a found _{z} also leads to a replacement rule for (z), or\n\t\t\t\t// if we want that a found _{z} also leads to a replacement for ^{z},\n\t\t\t\t// this needs to be added to the replacement map explicitly.\n\t\t\t\t\n\t\t\t\tDEBUGLN( std::cerr << \"adding \" << one << \" -> \" << two << \" to replacement map \" << std::endl; );\n\n\t\t\t\t// We absolutely need to keep the multiplier here. If we don't, then it\n\t\t\t\t// becomes very messy to restore multipliers of child nodes in the pattern,\n\t\t\t\t// e.g A?_{m n} matching Q_{1 -1}. Do not set the multiplier to one!\n\t\t\t\tEx tmp(two);\n            // cadabra::one(tmp.begin()->multiplier);\n\t\t\t\treplacement_map[Ex(one)]=tmp;\n\n\t\t\t\t// if this is an index, also store the pattern with the parent_rel flipped\n\n\t\t\t\tif(one->is_index()) {\n\t\t\t\t\tEx cmptree1(one);\n\t\t\t\t\tEx cmptree2(two);\n\t\t\t\t\tcmptree1.begin()->flip_parent_rel();\n\t\t\t\t\tif(two->is_index())\n\t\t\t\t\t\tcmptree2.begin()->flip_parent_rel();\n\t\t\t\t\treplacement_map[cmptree1]=cmptree2;\n\t\t\t\t\t}\n\n\t\t\t\t// if this is a pattern and the pattern has a non-zero number of children,\n\t\t\t\t// also add the pattern without the children\n\t\t\t\tif(Ex::number_of_children(one)!=0) {\n\t\t\t\t\tEx tmp1(one), tmp2(two);\n\t\t\t\t\ttmp1.erase_children(tmp1.begin());\n\t\t\t\t\ttmp2.erase_children(tmp2.begin());\n\t\t\t\t\treplacement_map[tmp1]=tmp2;\n\t\t\t\t\t}\n\t\t\t\t// and if this is a pattern also insert the one without the parent_rel\n\t\t\t\tif( /* one->is_name_wildcard()  &&  */ one->is_index()) {\n\t\t\t\t\t//std::cerr << \"storing pattern without pattern rel \" << replacement_map.size() << std::endl;\n\t\t\t\t\tEx tmp1(one), tmp2(two);\n\t\t\t\t\ttmp1.begin()->fl.parent_rel=str_node::p_none;\n\t\t\t\t\ttmp2.begin()->fl.parent_rel=str_node::p_none;\n\t\t\t\t\t// We do not want this pattern to be present already.\n\t\t\t\t\tauto fnd=replacement_map.find(tmp1);\n\t\t\t\t\tif(fnd!=replacement_map.end()) {\n\t\t\t\t\t\tthrow InternalError(\"Attempting to duplicate replacement rule.\");\n\t\t\t\t\t\t}\n\t\t\t\t\t//\t\t\t\tassert(replacement_map.find(tmp1)!=replacement_map.end());\n\t\t\t\t\t// std::cerr << \"storing \" << Ex(tmp1) << \" -> \" << Ex(tmp2) << std::endl;\n\t\t\t\t\treplacement_map[tmp1]=tmp2;\n\t\t\t\t\t}\n\n\t\t\t\tDEBUGLN( std::cerr << \"Replacement map is now:\" << std::endl; \n\t\t\t\t\t\t for(auto& rule: replacement_map)\n\t\t\t\t\t\t\t std::cerr << \"* \" << rule.first << \" -> \" << rule.second << std::endl;\n\t\t\t\t\t\t );\n\t\t\t\t\t\t \n\t\t\t\t}\n\n\t\t\t// Return a match of the appropriate type. If we are comparing indices and\n\t\t\t// they matched because they are from the same set but do not have the same\n\t\t\t// name, we still need to let the caller know about this.\n\t\t\tif(is_index) {\n\t\t\t\tif(two->is_rational() || two_is_value) {\n\t\t\t\t\t// We matched an index in 'one' to a value in 'two', report as matching.\n\t\t\t\t\tDEBUGLN( std::cerr << \"Matched index to numerical value.\" << std::endl; );\n\t\t\t\t\treturn report(match_t::subtree_match);\n\t\t\t\t\t}\n\t\t\t\telse {\n\t\t\t\t\tDEBUGLN( std::cerr << \"Index type matches, report whether names match too.\" << std::endl; );\n\t\t\t\t\tint xc = subtree_compare(0, one, two, ignore_parent_rel?(-1):(-2));\n\t\t\t\t\tif(xc==0) return report(match_t::subtree_match);\n\t\t\t\t\tif(xc>0)  return report(match_t::match_index_less);\n\t\t\t\t\treturn report(match_t::match_index_greater);\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\telse return report(match_t::node_match);\n\t\t\t}\n\t\telse if(objectpattern) {\n\t\t\tDEBUGLN( std::cerr << \"object pattern \" << one << std::endl; );\n\t\t\t// Even for object patterns, if we do not ignore the parent rel, we need to test them.\n\t\t\tif(!ignore_parent_rel)\n\t\t\t\tif( one->fl.parent_rel != two->fl.parent_rel )\n\t\t\t\t\treturn report( (one->fl.parent_rel < two->fl.parent_rel)\n\t\t\t\t\t\t\t\t\t\t?match_t::no_match_indexpos_less:match_t::no_match_indexpos_greater );\n\t\t\t\n\t\t\tsubtree_replacement_map_t::iterator loc=subtree_replacement_map.find(one->name);\n\t\t\tif(loc!=subtree_replacement_map.end()) {\n\t\t\t\treturn report(equal_subtree((*loc).second,two,use_props));\n\t\t\t\t}\n\t\t\telse {\n\t\t\t\tDEBUGLN( std::cerr << \"storing subtree replacement \" << one\n\t\t\t\t\t\t\t<< \" -> \" << two << std::endl; );\n\t\t\t\tsubtree_replacement_map[one->name]=two;\n\t\t\t\t}\n\n\t\t\treturn report(match_t::subtree_match);\n\t\t\t}\n\t\telse if(is_coordinate || is_number) {   // Check if the coordinate can come from an index.\n\t\t\tconst Indices *t2=0;\n\t\t\tif(use_props==useprops_t::always) {\n\t\t\t\tDEBUGLN( std::cerr << tab() << \"is \" << *two->name << \" an index?\" << std::endl; );\n\t\t\t\tt2=properties.get<Indices>(two, true);\n\t\t\t\tDEBUGLN( std::cerr << tab() << t2 << std::endl; );\n\t\t\t\t}\n\n\t\t\tif(value_matches_index && t2) {\n\t\t\t\t// std::cerr << \"coordinate \" << *one->name << \" versus index \" << *two->name << std::endl;\n\t\t\t\t// If the 'two' index type is fixed or independent, ensure\n\t\t\t\t// that the parent relation matches!\n\n\t\t\t\tif(!ignore_parent_rel)\n\t\t\t\t\tif(t2->position_type==Indices::fixed || t2->position_type==Indices::independent) {\n\t\t\t\t\t\tif( one->fl.parent_rel != two->fl.parent_rel ) {\n\t\t\t\t\t\t\tDEBUGLN( std::cerr << tab() << \"parent_rels not the same\" << std::endl;);\n\t\t\t\t\t\t\treturn report( (one->fl.parent_rel < two->fl.parent_rel)\n\t\t\t\t\t\t\t               ?match_t::no_match_indexpos_less:match_t::no_match_indexpos_greater );\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\t}\n\n\t\t\t\t// Look through values attribute of Indices object to see if the 'two' index\n\t\t\t\t// can take the 'one' value.\n\n\t\t\t\tconst auto& values = t2->values(properties, two);\n\t\t\t\tauto ivals = std::find_if(values.begin(), values.end(),\n\t\t\t\t\t\t\t\t\t\t\t\t  [&](const Ex& a) {\n\t\t\t\t\t\t\t\t\t\t\t\t  if(subtree_compare(&properties, a.begin(), one, 0)==0) return true;\n\t\t\t\t\t\t\t\t\t\t\t\t  else return false;\n\t\t\t\t\t\t\t\t\t\t\t\t  });\n\t\t\t\tif(ivals!=values.end()) {\n\t\t\t\t\t// Verify that the 'two' index has not already been matched to a value\n\t\t\t\t\t// different from 'one'.\n\t\t\t\t\tEx t1(two), t2(two), o1(one), o2(one);\n\t\t\t\t\tt2.begin()->flip_parent_rel();\n\t\t\t\t\to2.begin()->flip_parent_rel();\n\t\t\t\t\tauto prev1 = index_value_map.find(t1);\n\t\t\t\t\tauto prev2 = index_value_map.find(t2);\n\t\t\t\t\tif(prev1!=index_value_map.end() && ! (prev1->second==o1) ) {\n\t\t\t\t\t\t//\t\t\t\t\tstd::cerr << \"Previously 1 \" << Ex(two) << \" was \" << Ex(prev1->second) << std::endl;\n\t\t\t\t\t\treturn report(match_t::no_match_less);\n\t\t\t\t\t\t}\n\t\t\t\t\tif(prev2!=index_value_map.end() && ! (prev2->second==o2) ) {\n\t\t\t\t\t\t//\t\t\t\t\tstd::cerr << \"Previously 2 \" << Ex(two) << \" was \" << Ex(prev2->second) << std::endl;\n\t\t\t\t\t\treturn report(match_t::no_match_less);\n\t\t\t\t\t\t}\n\n\t\t\t\t\tindex_value_map[Ex(two)]=Ex(one);\n\t\t\t\t\treturn report(match_t::node_match);\n\t\t\t\t\t}\n\t\t\t\telse {\n\t\t\t\t\t// The index 'one' is not known to be able to take value 'two'. So this is not\n\t\t\t\t\t// a match. Compare lexographically; this should be symmetric if one and two had\n\t\t\t\t\t// been exchanged.\n\t\t\t\t\tint dc = subtree_compare(&properties, one, two, 0);\n\t\t\t\t\tif(dc<0) return report(match_t::no_match_less);\n\t\t\t\t\telse     return report(match_t::no_match_greater);\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\telse {\n\t\t\t\t// What's left is the possibility that both indices are Coordinates, in which case they\n\t\t\t\t// need to match exactly.\n\t\t\t\tint cmp=subtree_compare(&properties, one, two, -2);\n\t\t\t\tif(cmp==0)      return report(match_t::subtree_match);\n\t\t\t\telse if(cmp>0)  return report(match_t::no_match_less);\n\t\t\t\telse            return report(match_t::no_match_greater);\n\t\t\t\t}\n\t\t\t}\n\t\telse {   // object is not dummy nor objectpattern nor coordinate\n\n\t\t\tif(one->is_rational() && two->is_rational()) {\n\t\t\t\tif(one->multiplier!=two->multiplier) {\n\t\t\t\t\tif(*one->multiplier < *two->multiplier) return report(match_t::no_match_less);\n\t\t\t\t\telse                                    return report(match_t::no_match_greater);\n\t\t\t\t\t}\n\t\t\t\telse {\n\t\t\t\t\t// Equal numerical factors with different parent rel _never_ match, because\n\t\t\t\t\t// we cannot determine if index raising/lowering is allowed if we do not\n\t\t\t\t\t// know the bundle type.\n\t\t\t\t\tif(!ignore_parent_rel)\n\t\t\t\t\t\tif(one->fl.parent_rel != two->fl.parent_rel)\n\t\t\t\t\t\t\treturn report( (one->fl.parent_rel < two->fl.parent_rel)\n\t\t\t\t\t\t\t               ?match_t::no_match_indexpos_less:match_t::no_match_indexpos_greater );\n\t\t\t\t\t}\n\t\t\t\t}\n\n\t\t\tif(name_match_with_autodeclare(one, two)) {\n\t\t\t\tif(nobrackets || (one->multiplier == two->multiplier) ) {\n\t\t\t\t\tif(ignore_parent_rel || one->fl.parent_rel==two->fl.parent_rel) return report( match_t::node_match );\n\t\t\t\t\treport( (one->fl.parent_rel < two->fl.parent_rel)\n\t\t\t\t\t        ?match_t::no_match_indexpos_less:match_t::no_match_indexpos_greater );\n\t\t\t\t\t}\n\n\t\t\t\tif(*one->multiplier < *two->multiplier) return report(match_t::no_match_less);\n\t\t\t\telse                                    return report(match_t::no_match_greater);\n\t\t\t\t}\n\t\t\telse if( ((one->is_autodeclare_wildcard() && two->is_numbered_symbol()) ||\n\t\t\t\t\t\t (two->is_autodeclare_wildcard() && one->is_numbered_symbol()) ) && one->name_only()==two->name_only() ) {\n\t\t\t\treturn report(match_t::node_match);\n\t\t\t\t}\n\t\t\telse {\n\t\t\t\tif( *one->name < *two->name ) return report(match_t::no_match_less);\n\t\t\t\telse                          return report(match_t::no_match_greater);\n\t\t\t\t}\n\t\t\t}\n\n\t\tassert(1==0); // should never be reached\n\n\t\treturn report(match_t::no_match_less);\n\t\t}\n\n\tbool Ex_comparator::name_match_with_autodeclare(Ex::sibling_iterator one, Ex::sibling_iterator two) const\n\t\t{\n\t\tif(one->name==two->name) return true;\n\t\tif((one->is_autodeclare_wildcard() && two->is_numbered_symbol()) ||\n\t\t\t(two->is_autodeclare_wildcard() && one->is_numbered_symbol()) ) {\n\t\t\tif( one->name_only()==two->name_only() )\n\t\t\t\treturn true;\n\t\t\t}\n\t\treturn false;\n\t\t}\n\n\tEx_comparator::match_t Ex_comparator::match_subproduct(const Ex& tr,\n\t      Ex::sibling_iterator lhs,\n\t      Ex::sibling_iterator tofind,\n\t      Ex::sibling_iterator st,\n\t      Ex::iterator conditions)\n\t\t{\n\t\treplacement_map_t         backup_replacements(replacement_map);\n\t\tsubtree_replacement_map_t backup_subtree_replacements(subtree_replacement_map);\n\n\t\t// 'Start' iterates over all factors, trying to find 'tofind'. It may happen that the\n\t\t// first match is such that the entire subproduct matches, but it may be that we have\n\t\t// to iterate 'start' over more factors (typically when non-commutative objects are\n\t\t// concerned).\n\n\t\tEx::sibling_iterator start=st.begin();\n\t\twhile(start!=st.end()) {\n\n\t\t\t// The factor 'tofind' can only be matched against a factor in the subproduct if we\n\t\t\t// have not already previously matched part of the lhs to this factor. We check that first.\n\n\t\t\tif(std::find(factor_locations.begin(), factor_locations.end(), start)==factor_locations.end()) {\n\n\t\t\t\t// Compare this factor with 'tofind'.\n\n\t\t\t\tauto match = equal_subtree(tofind, start);\n\t\t\t\tif(match==match_t::subtree_match || match==match_t::match_index_less || match==match_t::match_index_greater) {\n\n\t\t\t\t\t// The factor has been found. Verify that it can be moved\n\t\t\t\t\t// next to the previous factor, if applicable (nontrivial\n\t\t\t\t\t// if factors do not commute).\n\n\t\t\t\t\tint sign=1;\n\t\t\t\t\tif(factor_locations.size()>0) {\n\t\t\t\t\t\tDEBUGLN(std::cerr << \"--- can move?     ---\" << std::endl; );\n\t\t\t\t\t\t// Determining the sign is non-trivial to do step-by step.\n\t\t\t\t\t\t// Consider an expression\n\t\t\t\t\t\t//   A B C D E\n\t\t\t\t\t\t// and a pattern\n\t\t\t\t\t\t//   D A B\n\t\t\t\t\t\t// (D, A, B anti-commuting). A can be moved to the right of D\n\t\t\t\t\t\t// picking up two signs, and B can moved to the right of A with\n\t\t\t\t\t\t// no sign.\n\t\t\t\t\t\tEx_comparator comparator(properties);\n\t\t\t\t\t\tsign=comparator.can_move_adjacent(st, factor_locations, start);\n\t\t\t\t\t\tDEBUGLN(std::cerr << \"--- done can move ---\" << sign << std::endl; );\n\t\t\t\t\t\t}\n\t\t\t\t\tif(sign==0) { // object found, but we cannot move it in the right order\n\t\t\t\t\t\treplacement_map=backup_replacements;\n\t\t\t\t\t\tsubtree_replacement_map=backup_subtree_replacements;\n\t\t\t\t\t\t}\n\t\t\t\t\telse {\n\t\t\t\t\t\tfactor_locations.push_back(start);\n\t\t\t\t\t\tfactor_moving_signs.push_back(sign);\n\n\t\t\t\t\t\tEx::sibling_iterator nxt=tofind;\n\t\t\t\t\t\t++nxt;\n\t\t\t\t\t\tif(nxt!=lhs.end()) {\n\t\t\t\t\t\t\tmatch_t res=match_subproduct(tr, lhs, nxt, st, conditions);\n\t\t\t\t\t\t\tif(res==match_t::subtree_match) return res;\n\t\t\t\t\t\t\telse {\n\t\t\t\t\t\t\t\t//\t\t\t\t\t\ttxtout << tofind.node << \"found factor useless \" << start.node << std::endl;\n\t\t\t\t\t\t\t\tfactor_locations.pop_back();\n\t\t\t\t\t\t\t\tfactor_moving_signs.pop_back();\n\t\t\t\t\t\t\t\treplacement_map=backup_replacements;\n\t\t\t\t\t\t\t\tsubtree_replacement_map=backup_subtree_replacements;\n\t\t\t\t\t\t\t\t}\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\telse {\n\t\t\t\t\t\t\t// Found all factors in sub-product, now check the conditions.\n\t\t\t\t\t\t\tstd::string error;\n\t\t\t\t\t\t\tif(conditions==tr.end()) return match_t::subtree_match;\n\t\t\t\t\t\t\tif(satisfies_conditions(conditions, error)) {\n\t\t\t\t\t\t\t\treturn match_t::subtree_match;\n\t\t\t\t\t\t\t\t}\n\t\t\t\t\t\t\telse {\n\t\t\t\t\t\t\t\tfactor_locations.pop_back();\n\t\t\t\t\t\t\t\tfactor_moving_signs.pop_back();\n\t\t\t\t\t\t\t\treplacement_map=backup_replacements;\n\t\t\t\t\t\t\t\tsubtree_replacement_map=backup_subtree_replacements;\n\t\t\t\t\t\t\t\t}\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\t}\n\t\t\t\t\t}\n\t\t\t\telse {\n\t\t\t\t\t//\t\t\t\ttxtout << tofind.node << \"does not match\" << std::endl;\n\t\t\t\t\treplacement_map=backup_replacements;\n\t\t\t\t\tsubtree_replacement_map=backup_subtree_replacements;\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t++start;\n\t\t\t}\n\t\treturn match_t::no_match_less; // FIXME not entirely true\n\t\t}\n\n\tEx_comparator::match_t Ex_comparator::match_subsum(const Ex& tr,\n\t      Ex::sibling_iterator lhs,\n\t      Ex::sibling_iterator tofind,\n\t      Ex::sibling_iterator st,\n\t      Ex::iterator conditions)\n\t\t{\n\t\treplacement_map_t         backup_replacements(replacement_map);\n\t\tsubtree_replacement_map_t backup_subtree_replacements(subtree_replacement_map);\n\n\t\t// 'Start' iterates over all terms, trying to find 'tofind'. It may happen that the\n\t\t// first match is such that the entire sub-sum matches, but it may be that we have\n\t\t// to iterate 'start' over more terms (typically when relative factors of terms\n\t\t// do not match).\n\n\t\tEx::sibling_iterator start=st.begin();\n\t\twhile(start!=st.end()) {\n\n\t\t\t// The term 'tofind' can only be matched against a term in the sub-sum if we\n\t\t\t// have not already previously matched part of the lhs to this term. We check that first.\n\n\t\t\tif(std::find(factor_locations.begin(), factor_locations.end(), start)==factor_locations.end()) {\n\n\t\t\t\t// Compare this factor with 'tofind'.\n\n\t\t\t\tauto match = equal_subtree(tofind, start);\n\t\t\t\tif(match==match_t::subtree_match || match==match_t::match_index_less || match==match_t::match_index_greater) {\n\n\t\t\t\t\t// The term has been found. If this is not the 1st term, verify\n\t\t\t\t\t// that the ratio of its multiplier to the multiplier of the search term\n\t\t\t\t\t// agrees with that ratio for the first term.\n\n\t\t\t\t\tif(tr.index(tofind)==0) {\n\t\t\t\t\t\tterm_ratio = (*tofind->multiplier)/(*start->multiplier);\n\t\t\t\t\t\t}\n\t\t\t\t\tauto this_ratio = (*tofind->multiplier)/(*start->multiplier);\n\t\t\t\t\tif(this_ratio!=term_ratio) {\n\t\t\t\t\t\treplacement_map=backup_replacements;\n\t\t\t\t\t\tsubtree_replacement_map=backup_subtree_replacements;\n\t\t\t\t\t\t}\n\t\t\t\t\telse {\n\t\t\t\t\t\tfactor_locations.push_back(start);\n\n\t\t\t\t\t\tEx::sibling_iterator nxt=tofind;\n\t\t\t\t\t\t++nxt;\n\t\t\t\t\t\tif(nxt!=lhs.end()) {\n\t\t\t\t\t\t\tmatch_t res=match_subsum(tr, lhs, nxt, st, conditions);\n\t\t\t\t\t\t\tif(res==match_t::subtree_match) return res;\n\t\t\t\t\t\t\telse {\n\t\t\t\t\t\t\t\tfactor_locations.pop_back();\n\t\t\t\t\t\t\t\treplacement_map=backup_replacements;\n\t\t\t\t\t\t\t\tsubtree_replacement_map=backup_subtree_replacements;\n\t\t\t\t\t\t\t\t}\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\telse {\n\t\t\t\t\t\t\t// Found all factors in sub-product, now check the conditions.\n\t\t\t\t\t\t\tstd::string error;\n\t\t\t\t\t\t\tif(conditions==tr.end()) return match_t::subtree_match;\n\t\t\t\t\t\t\tif(satisfies_conditions(conditions, error)) {\n\t\t\t\t\t\t\t\treturn match_t::subtree_match;\n\t\t\t\t\t\t\t\t}\n\t\t\t\t\t\t\telse {\n\t\t\t\t\t\t\t\tfactor_locations.pop_back();\n\t\t\t\t\t\t\t\treplacement_map=backup_replacements;\n\t\t\t\t\t\t\t\tsubtree_replacement_map=backup_subtree_replacements;\n\t\t\t\t\t\t\t\t}\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\t}\n\t\t\t\t\t}\n\t\t\t\telse {\n\t\t\t\t\t//\t\t\t\ttxtout << tofind.node << \"does not match\" << std::endl;\n\t\t\t\t\treplacement_map=backup_replacements;\n\t\t\t\t\tsubtree_replacement_map=backup_subtree_replacements;\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t++start;\n\t\t\t}\n\t\treturn match_t::no_match_less; // FIXME not entirely true\n\t\t}\n\n\t//Ex_comparator::match_t Ex_comparator::match_subsum(const Ex& tr,\n\t//\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t Ex::sibling_iterator lhs,\n\t//\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t Ex::sibling_iterator tofind,\n\t//\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t Ex::sibling_iterator st,\n\t//\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t Ex::iterator conditions)\n\t//\t{\n\t//\t// 'Start' iterates over all terms, trying to find 'tofind'.\n\t//\n\t//\tEx::sibling_iterator start=st.begin();\n\t//\twhile(start!=st.end()) {\n\t//\n\t//\t\t// The term 'tofind' can only be matched against a term in the\n\t//\t\t// subsum if we have not already previously matched part of the\n\t//\t\t// lhs to this factor. We check that first.\n\t//\n\t//\t\tif(std::find(factor_locations.begin(), factor_locations.end(), start)==factor_locations.end()) {\n\t//\n\t//\t\t\t// Compare this term with 'tofind'.\n\t//\n\t//\t\t\tauto match = equal_subtree(tofind, start);\n\t//\t\t\tif(match==match_t::subtree_match || match==match_t::match_index_less || match==match_t::match_index_greater) {\n\t//\t\t\t\tfactor_locations.push_back(start);\n\t//\n\t//\t\t\t\tEx::sibling_iterator nxt=tofind;\n\t//\t\t\t\t++nxt;\n\t//\t\t\t\tif(nxt!=lhs.end()) {\n\t//\t\t\t\t\tmatch_t res=match_subsum(tr, lhs, nxt, st, conditions);\n\t//\t\t\t\t\treturn res;\n\t//\t\t\t\t\t}\n\t//\t\t\t\telse {\n\t//\t\t\t\t\t// Found all factors in sub-product.\n\t//\t\t\t\t\tauto sib=lhs.begin();\n\t//\t\t\t\t\tfor(size_t i=0; i<factor_locations.size(); ++i) {\n\t//\t\t\t\t\t\tstd::cerr << *factor_locations[i]->multiplier << \" (vs \" << *sib->multiplier << \"), \";\n\t//\t\t\t\t\t\t++sib;\n\t//\t\t\t\t\t\t}\n\t//\t\t\t\t\tstd::cerr << std::endl;\n\t//\n\t//\t\t\t\t\t// Now check the conditions.\n\t//\t\t\t\t\tstd::string error;\n\t//\t\t\t\t\tif(conditions==tr.end()) return match_t::subtree_match;\n\t//\t\t\t\t\tif(satisfies_conditions(conditions, error)) {\n\t//\t\t\t\t\t\treturn match_t::subtree_match;\n\t//\t\t\t\t\t\t}\n\t//\t\t\t\t\t}\n\t//\t\t\t\t}\n\t//\t\t\t}\n\t//\t\t++start;\n\t//\t\t}\n\t//\treturn match_t::no_match_less;\n\t//\t}\n\n\n\tint Ex_comparator::can_move_adjacent(Ex::iterator prod,\n\t                                     Ex::sibling_iterator one, Ex::sibling_iterator two, bool fix_one)\n\t\t{\n\t\tassert(Ex::parent(one)==Ex::parent(two));\n\t\tassert(Ex::parent(one)==prod);\n\n\t\t// Make sure that 'one' points to the object which occurs first in 'prod'.\n\t\tbool onefirst=false;\n\t\tEx::sibling_iterator probe=one;\n\t\twhile(probe!=prod.end()) {\n\t\t\tif(probe==two) {\n\t\t\t\tonefirst=true;\n\t\t\t\tbreak;\n\t\t\t\t}\n\t\t\t++probe;\n\t\t\t}\n\t\tint sign=1;\n\t\tif(!onefirst) {\n\t\t\tstd::swap(one,two);\n\t\t\tauto es=equal_subtree(one,two);\n\t\t\tsign*=can_swap(one,two,es);\n\t\t\t//\t\ttxtout << \"swapping one and two: \" << sign << std::endl;\n\t\t\t}\n\n\t\tif(sign!=0) {\n\t\t\t// Loop over all pair flips which are necessary to move one to the left of two.\n\t\t\t// Keep one fixed if fix_one is true.\n\n\t\t\tif(fix_one) {\n\t\t\t\tprobe=two;\n\t\t\t\t--probe;\n\t\t\t\twhile(probe!=one) {\n\t\t\t\t\tauto es=equal_subtree(two,probe);\n\t\t\t\t\t// std::cerr << \"swapping \" << Ex(two) << \" and \" << Ex(probe) << std::endl;\n\t\t\t\t\tsign*=can_swap(two,probe,es);\n\t\t\t\t\tif(sign==0) break;\n\t\t\t\t\t--probe;\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\telse {\n\t\t\t\tprobe=one;\n\t\t\t\t++probe;\n\t\t\t\twhile(probe!=two) {\n\t\t\t\t\tassert(probe!=prod.end());\n\t\t\t\t\tauto es=equal_subtree(one,probe);\n\t\t\t\t\t// std::cerr << \"swapping \" << Ex(one) << \" and \" << Ex(probe) << std::endl;\n\t\t\t\t\tsign*=can_swap(one,probe,es);\n\t\t\t\t\tif(sign==0) break;\n\t\t\t\t\t++probe;\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t}\n\t\treturn sign;\n\t\t}\n\n\tint Ex_comparator::can_move_to_front(Ex& tr, Ex::iterator prod, Ex::sibling_iterator one)\n\t\t{\n\t\t// Insert a dummy, determine whether we can move\n\t\t// next to the dummy, then erase the dummy again.\n\t\tauto dummy = tr.prepend_child(prod, str_node(\"dummy\"));\t\t\n\t\tint sign=can_move_adjacent(prod, dummy, one, true);\n\t\ttr.erase(dummy);\n\t\treturn sign;\n\t\t}\n\n\tint Ex_comparator::can_swap_components(Ex::iterator one, Ex::iterator two, match_t subtree_comparison)\n\t\t{\n\t\tint tmp;\n\t\tauto impi=properties.get_with_pattern<ImplicitIndex>(one, tmp, \"\");\n\t\tif(impi.first) {\n\t\t\tif(impi.first->explicit_form.size()>0) {\n\t\t\t\tone=impi.first->explicit_form.begin();\n\t\t\t\t}\n\t\t\t}\n\t\timpi=properties.get_with_pattern<ImplicitIndex>(two, tmp, \"\");\n\t\tif(impi.first) {\n\t\t\tif(impi.first->explicit_form.size()>0) {\n\t\t\t\ttwo=impi.first->explicit_form.begin();\n\t\t\t\t}\n\t\t\t}\n\t\treturn can_swap(one, two, subtree_comparison, true);\n\t\t}\n\n\t// Determine the sign required to move the last factor in 'factors' to\n\t// the right of the first.  If moving left, do not count signs from\n\t// moving past any of the other factors.  If moving right, do count\n\t// those signs. In effect, the logic is that we count signs as if\n\t// all other factors have already been moved to the right of the first.\n\n\tint Ex_comparator::can_move_adjacent(Ex::iterator prod, const std::vector<Ex::sibling_iterator>& factors, Ex::sibling_iterator i2)\n\t\t{\n\t\tif(factors.size()==0) return 1;\n\n\t\tEx::sibling_iterator i1=factors[0];\n\n\t\t// Determine whether to move right or left.\n\t\tbool move_right=true;\n\t\tEx::sibling_iterator probe=i1;\n\t\twhile(probe!=prod.end()) {\n\t\t\tif(probe==i2) {\n\t\t\t\tmove_right=false;\n\t\t\t\tbreak;\n\t\t\t\t}\n\t\t\t++probe;\n\t\t\t}\n\n\t\t// Move through all factors.\n\t\tprobe=i2;\n\t\tint sign=1;\n\t\tdo {\n\t\t\tif(move_right) ++probe;\n\t\t\telse           --probe;\n\t\t\tif(probe==i1)\n\t\t\t\tbreak;\n\n\t\t\tif(std::find(factors.begin(), factors.end(), probe)!=factors.end())\n\t\t\t\tcontinue;\n\t\t\tauto es=equal_subtree(i2, probe);\n\t\t\tsign*=can_swap(i2, probe, es);\n\n\t\t\t}\n\t\twhile(sign!=0);\n\n\t\tif(move_right) {\n\t\t\t// When moving right, all factors which we have already ordered\n\t\t\t// sit to the right of the moving one, so we need to swap with them\n\t\t\t// all.\n\t\t\tauto f=factors.begin();\n\t\t\twhile(f!=factors.end()) {\n\t\t\t\tauto es=equal_subtree(i2, *f);\n\t\t\t\tsign*=can_swap(i2, *f, es);\n\t\t\t\t++f;\n\t\t\t\t}\n\t\t\t}\n\n\t\treturn sign;\n\t\t}\n\n\n\t// Should obj and obj+1 be swapped, according to the SortOrder\n\t// properties?\n\t//\n\tbool Ex_comparator::should_swap(Ex::iterator obj, match_t subtree_comparison)\n\t\t{\n\t\tEx::sibling_iterator one=obj, two=obj;\n\t\t++two;\n\n\t\t// If the two objects are the same up to index names, we do not care\n\t\t// whether it sits in a SortOrder list; just compare alpha.\n\t\tif(subtree_comparison==match_t::match_index_less)    return false;\n\t\tif(subtree_comparison==match_t::match_index_greater) return true;\n\n\t\t// Find a SortOrder property which contains both one and two.\n\t\tint num1, num2;\n\t\tconst SortOrder *so1=properties.get<SortOrder>(one,num1);\n\t\tconst SortOrder *so2=properties.get<SortOrder>(two,num2);\n\n\t\tif(so1==0 || so2==0 || so1!=so2) {\n\t\t\tDEBUGLN( std::cerr << \"No sort order between \" << Ex(one) << \" and \" << Ex(two); );\n\t\t\treport(subtree_comparison);\n\t\t\t// No explicit sort order known; use whatever we know from the comparison.\n\t\t\tswitch(subtree_comparison) {\n\t\t\t\tcase match_t::node_match:\n\t\t\t\tcase match_t::subtree_match:\n\t\t\t\tcase match_t::no_match_less:\n\t\t\t\tcase match_t::no_match_indexpos_less:\n\t\t\t\tcase match_t::match_index_less:\n\t\t\t\t\treturn false;\n\t\t\t\tcase match_t::no_match_greater:\n\t\t\t\tcase match_t::no_match_indexpos_greater:\n\t\t\t\tcase match_t::match_index_greater:\t\t\t\t\t\n\t\t\t\t\treturn true;\n\t\t\t\t}\n\t\t\treturn false;\n\t\t\t}\n\n\t\tassert(so1==so2);\n\t\treturn num1>num2;\n\t\t}\n\n\t// Various tests about whether two non-elementary objects can be swapped.\n\t//\n\tint Ex_comparator::can_swap_prod_obj(Ex::iterator prod, Ex::iterator obj,\n\t                                     bool ignore_implicit_indices)\n\t\t{\n\t\t//\tstd::cout << \"prod_obj \" << *prod->name << \" \" << *obj->name << std::endl;\n\t\t// Warning: no check is made that prod is actually a product!\n\t\tint sign=1;\n\t\tEx::sibling_iterator sib=prod.begin();\n\t\twhile(sib!=prod.end()) {\n\t\t\tconst Indices *ind1=properties.get<Indices>(sib, true);\n\t\t\tconst Indices *ind2=properties.get<Indices>(obj, true);\n\t\t\tif(! (ind1!=0 && ind2!=0) ) { // If both objects are actually real indices,\n\t\t\t\t// then we do not include their commutativity property\n\t\t\t\t// in the sign. This is because the routines that use\n\t\t\t\t// can_swap_prod_obj all test for such index-index\n\t\t\t\t// swaps separately.\n\t\t\t\tauto es=equal_subtree(sib, obj);\n\t\t\t\t//\t\t\tstd::cout << \"  \" << *sib->name << \" \" << *obj->name << \" \" << es << std::endl;\n\t\t\t\tsign*=can_swap(sib, obj, es, ignore_implicit_indices);\n\t\t\t\tif(sign==0) break;\n\t\t\t\t}\n\t\t\t++sib;\n\t\t\t}\n\t\treturn sign;\n\t\t}\n\n\tint Ex_comparator::can_swap_prod_prod(Ex::iterator prod1, Ex::iterator prod2,\n\t                                      bool ignore_implicit_indices)\n\t\t{\n\t\t//\tstd::cout << \"prod_prod \" << *prod1->name << \" \" << *prod2->name;\n\t\t// Warning: no check is made that prod1,2 are actually products!\n\t\tint sign=1;\n\t\tEx::sibling_iterator sib=prod2.begin();\n\t\twhile(sib!=prod2.end()) {\n\t\t\tsign*=can_swap_prod_obj(prod1, sib, ignore_implicit_indices);\n\t\t\tif(sign==0) break;\n\t\t\t++sib;\n\t\t\t}\n\t\t//\tstd::cout << \"  -> \" << sign << std::endl;\n\t\treturn sign;\n\t\t}\n\n\tint Ex_comparator::can_swap_sum_obj(Ex::iterator sum, Ex::iterator obj,\n\t                                    bool ignore_implicit_indices)\n\t\t{\n\t\t// Warning: no check is made that sum is actually a sum!\n\t\tint sofar=2;\n\t\tEx::sibling_iterator sib=sum.begin();\n\t\twhile(sib!=sum.end()) {\n\t\t\tauto es=equal_subtree(sib, obj);\n\t\t\tint thissign=can_swap(sib, obj, es, ignore_implicit_indices);\n\t\t\tif(sofar==2) sofar=thissign;\n\t\t\telse if(thissign!=sofar) {\n\t\t\t\tsofar=0;\n\t\t\t\tbreak;\n\t\t\t\t}\n\t\t\t++sib;\n\t\t\t}\n\t\treturn sofar;\n\t\t}\n\n\tint Ex_comparator::can_swap_prod_sum(Ex::iterator prod, Ex::iterator sum,\n\t                                     bool ignore_implicit_indices)\n\t\t{\n\t\t// Warning: no check is made that sum is actually a sum or prod is a prod!\n\t\tint sign=1;\n\t\tEx::sibling_iterator sib=prod.begin();\n\t\twhile(sib!=prod.end()) {\n\t\t\t//\t\tconst Indices *ind=kernel.properties->get<Indices>(sib);\n\t\t\t//\t\tif(ind==0) {\n\t\t\tsign*=can_swap_sum_obj(sum, sib, ignore_implicit_indices);\n\t\t\tif(sign==0) break;\n\t\t\t//\t\t\t}\n\t\t\t++sib;\n\t\t\t}\n\t\treturn sign;\n\t\t}\n\n\tint Ex_comparator::can_swap_sum_sum(Ex::iterator sum1, Ex::iterator sum2,\n\t                                    bool ignore_implicit_indices)\n\t\t{\n\t\tint sofar=2;\n\t\tEx::sibling_iterator sib=sum1.begin();\n\t\twhile(sib!=sum1.end()) {\n\t\t\tint thissign=can_swap_sum_obj(sum2, sib, ignore_implicit_indices);\n\t\t\tif(sofar==2) sofar=thissign;\n\t\t\telse if(thissign!=sofar) {\n\t\t\t\tsofar=0;\n\t\t\t\tbreak;\n\t\t\t\t}\n\t\t\t++sib;\n\t\t\t}\n\t\treturn sofar;\n\t\t}\n\n\tint Ex_comparator::can_swap_ilist_ilist(Ex::iterator obj1, Ex::iterator obj2)\n\t\t{\n\t\tint sign=1;\n\n\t\tindex_iterator it1=index_iterator::begin(properties, obj1);\n\t\twhile(it1!=index_iterator::end(properties, obj1)) {\n\t\t\tindex_iterator it2=index_iterator::begin(properties, obj2);\n\t\t\twhile(it2!=index_iterator::end(properties, obj2)) {\n\t\t\t\t// Only deal with real indices here, i.e. those carrying an Indices property.\n\t\t\t\tconst Indices *ind1=properties.get<Indices>(it1, true);\n\t\t\t\tconst Indices *ind2=properties.get<Indices>(it2, true);\n\t\t\t\tif(ind1!=0 && ind2!=0) {\n\t\t\t\t\tconst CommutingBehaviour *com1 =properties.get<CommutingBehaviour>(it1, true);\n\t\t\t\t\tconst CommutingBehaviour *com2 =properties.get<CommutingBehaviour>(it2, true);\n\n\t\t\t\t\tif(com1!=0  &&  com1 == com2)\n\t\t\t\t\t\tsign *= com1->sign();\n\n\t\t\t\t\tif(sign==0) break;\n\t\t\t\t\t}\n\t\t\t\t++it2;\n\t\t\t\t}\n\t\t\tif(sign==0) break;\n\t\t\t++it1;\n\t\t\t}\n\n\t\treturn sign;\n\t\t}\n\n\tbool Ex_comparator::can_swap_different_indexsets(Ex::iterator obj1, Ex::iterator obj2)\n\t\t{\n\t\tstd::set<const Indices *> index_sets1;\n\t\t// std::cerr << \"Are \" << obj1 << \" and \" << obj2 << \" swappable?\" << std::endl;\n\n\t\tindex_iterator it1=index_iterator::begin(properties, obj1);\n\t\twhile(it1!=index_iterator::end(properties, obj1)) {\n\t\t\tauto ind = properties.get<Indices>(it1, true);\n\t\t\tif(!ind) return false;\n\t\t\tindex_sets1.insert(ind);\n\t\t\t++it1;\n\t\t\t}\n\t\tindex_iterator it2=index_iterator::begin(properties, obj2);\n\t\twhile(it2!=index_iterator::end(properties, obj2)) {\n\t\t\tauto ind = properties.get<Indices>(it2, true);\n\t\t\tif(!ind) return false;\n\t\t\tif(index_sets1.find(ind)!=index_sets1.end()) {\n\t\t\t\t// std::cerr << \"NO\" << std::endl;\n\t\t\t\treturn false;\n\t\t\t\t}\n\t\t\t++it2;\n\t\t\t}\n\t\t// std::cerr << \"YES\" << std::endl;\n\t\treturn true;\n\t\t}\n\n\tint Ex_comparator::can_swap(Ex::iterator one, Ex::iterator two, match_t,\n\t                            bool ignore_implicit_indices)\n\t\t{\n\t\t// std::cerr << \"can_swap \" << *one->name << \" \" << *two->name << \" \" << ignore_implicit_indices << std::endl;\n\n\t\t// Explicitly declared commutation behaviour goes first.\n\t\tconst CommutingBehaviour *com = properties.get<CommutingBehaviour>(one, two, true);\n\t\tif(com)\n\t\t\treturn com->sign();\n\n\n\t\t// If both objects have implicit indices, we cannot swap the\n\t\t// objects because that would re-order the index line. The sole\n\t\t// exception is when these indices are explicitly stated to be in\n\t\t// different sets.\n\n\t\tconst ImplicitIndex *ii1 = properties.get<ImplicitIndex>(one);\n\t\tconst ImplicitIndex *ii2 = properties.get<ImplicitIndex>(two);\n\t\tif(!ignore_implicit_indices) {\n\t\t\tif(ii1) {\n\t\t\t\tif(ii1->explicit_form.size()==0) {\n\t\t\t\t\tif(ii2) return 0; // nothing known about explicit form\n\t\t\t\t\t}\n\t\t\t\telse one=ii1->explicit_form.begin();\n\t\t\t\t}\n\t\t\tif(ii2) {\n\t\t\t\tif(ii2->explicit_form.size()==0) {\n\t\t\t\t\tif(ii1) return 0; // nothing known about explicit form\n\t\t\t\t\t}\n\t\t\t\telse two=ii2->explicit_form.begin();\n\t\t\t\t}\n\t\t\t// Check that indices in one and two are in mutually exclusive sets.\n\t\t\tif(ii1 && ii2)\n\t\t\t\tif(!can_swap_different_indexsets(one, two))\n\t\t\t\t\treturn false;\n\t\t\t}\n\n\t\t// Differential forms in a product cannot be moved through each\n\t\t// other except when the degree of one of them is zero.  In a wedge\n\t\t// product, we can move them and potentially pick up a sign.\n\n\t\tconst DifferentialFormBase *df1 = properties.get<DifferentialFormBase>(one);\n\t\tconst DifferentialFormBase *df2 = properties.get<DifferentialFormBase>(two);\n\n\t\tif(df1 && df2) {\n\t\t\tif(df1->degree(properties,one).begin()->is_zero() || df2->degree(properties,two).begin()->is_zero())\n\t\t\t\treturn 1;\n\t\t\telse {\n\t\t\t\tif(Ex::is_head(one) || *(Ex::parent(one)->name)==\"\\\\wedge\") {\n\t\t\t\t\tif(df1->degree(properties, one).is_rational()==false ||\n\t\t\t\t\t      df2->degree(properties, two).is_rational()==false)\n\t\t\t\t\t\treturn 0; // Cannot yet order forms with non-numerical degrees.\n\t\t\t\t\tlong d1 = to_long(df1->degree(properties, one).to_rational());\n\t\t\t\t\tlong d2 = to_long(df2->degree(properties, two).to_rational());\n\t\t\t\t\tif( (d1*d2) % 2 == 1) return -1;\n\t\t\t\t\treturn 1;\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t}\n\n\t\t// Do we need to use Self* properties?\n\t\tconst SelfCommutingBehaviour *sc1 =properties.get<SelfCommutingBehaviour>(one, true);\n\t\tconst SelfCommutingBehaviour *sc2 =properties.get<SelfCommutingBehaviour>(two, true);\n\t\tif( (sc1!=0 && sc1==sc2) )\n\t\t\treturn sc1->sign();\n\n\t\t// One or both of the objects are not in an explicit list. So now comes the generic\n\t\t// part. The first step is to look at all explicit indices of the two objects and determine\n\t\t// their commutativity.\n\t\t// Note: this does not yet look at arguments (non-index children).\n\n\t\tint tmpsign=can_swap_ilist_ilist(one, two);\n\t\tif(tmpsign==0) return 0;\n\n\t\t// The second step is to check for product-like and sum-like behaviour. The following\n\t\t// take into account all commutativity properties of explict with implicit indices,\n\t\t// as well as hard-specified commutativity of factors.\n\n\t\tconst CommutingAsProduct *comap1 = properties.get<CommutingAsProduct>(one);\n\t\tconst CommutingAsProduct *comap2 = properties.get<CommutingAsProduct>(two);\n\t\tconst CommutingAsSum     *comas1 = properties.get<CommutingAsSum>(one);\n\t\tconst CommutingAsSum     *comas2 = properties.get<CommutingAsSum>(two);\n\n\t\tif(comap1 && comap2) return tmpsign*can_swap_prod_prod(one,two,ignore_implicit_indices);\n\t\tif(comap1 && comas2) return tmpsign*can_swap_prod_sum(one,two,ignore_implicit_indices);\n\t\tif(comap2 && comas1) return tmpsign*can_swap_prod_sum(two,one,ignore_implicit_indices);\n\t\tif(comas1 && comas2) return tmpsign*can_swap_sum_sum(one,two,ignore_implicit_indices);\n\t\tif(comap1)           return tmpsign*can_swap_prod_obj(one,two,ignore_implicit_indices);\n\t\tif(comap2)           return tmpsign*can_swap_prod_obj(two,one,ignore_implicit_indices);\n\t\tif(comas1)           return tmpsign*can_swap_sum_obj(one,two,ignore_implicit_indices);\n\t\tif(comas2)           return tmpsign*can_swap_sum_obj(two,one,ignore_implicit_indices);\n\n\t\treturn 1; // default: commuting.\n\t\t}\n\n\tbool Ex_comparator::satisfies_conditions(Ex::iterator conditions, std::string& error)\n\t\t{\n//\t\tstd::cerr << \"satisfies_conditions\" << std::endl;\n\t\tfor(unsigned int i=0; i<Ex::arg_size(conditions); ++i) {\n\t\t\tEx::iterator cond=Ex::arg(conditions, i);\n//\t\t\tstd::cerr << \"condition \" << cond << std::endl;\n\t\t\tif(*cond->name==\"\\\\unequals\") {\n\t\t\t\tEx::sibling_iterator lhs=cond.begin();\n\t\t\t\tEx::sibling_iterator rhs=lhs;\n\t\t\t\t++rhs;\n\t\t\t\t// Lookup the replacement rules for the two given objects, and return true if\n\t\t\t\t// those rules give a different result. But first check that there are rules\n\t\t\t\t// to start with.\n\t\t\t\t//\t\t\tstd::cerr << *lhs->name  << \" !=? \" << *rhs->name << std::endl;\n\t\t\t\tif(replacement_map.find(Ex(lhs))==replacement_map.end() ||\n\t\t\t\t      replacement_map.find(Ex(rhs))==replacement_map.end()) return true;\n\t\t\t\t//\t\t\tstd::cerr << *lhs->name  << \" !=?? \" << *rhs->name << std::endl;\n\t\t\t\tif(tree_exact_equal(&properties, replacement_map[Ex(lhs)], replacement_map[Ex(rhs)])) {\n\t\t\t\t\treturn false;\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\telse if(*cond->name==\"\\\\greater\" || *cond->name==\"\\\\less\") {\n\t\t\t\tEx::sibling_iterator lhs=cond.begin();\n\t\t\t\tEx::sibling_iterator rhs=lhs;\n\t\t\t\t++rhs;\n\n\t\t\t\tmultiplier_t mlhs;\n\t\t\t\tif(lhs->is_rational()==false) {\n\t\t\t\t\tauto fnd=replacement_map.find(Ex(lhs));\n//\t\t\t\t\tstd::cerr << \"finding \" << lhs << std::endl;\n\t\t\t\t\tif(fnd!=replacement_map.end()) {\n\t\t\t\t\t\tauto tn=fnd->second.begin();\n//\t\t\t\t\t\tstd::cerr << tn << std::endl;\n\t\t\t\t\t\tif(tn->is_rational())\n\t\t\t\t\t\t\tmlhs=*tn->multiplier;\n\t\t\t\t\t\telse {\n\t\t\t\t\t\t\terror=\"Replacement not numerical.\";\n\t\t\t\t\t\t\treturn false;\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\t}\n\t\t\t\t\telse {\n\t\t\t\t\t\terror=\"Can only compare objects which evaluate to numbers.\";\n\t\t\t\t\t\treturn false;\n\t\t\t\t\t\t}\n\t\t\t\t\t}\n\t\t\t\telse mlhs=*lhs->multiplier;\n\n\t\t\t\t// FIXME: abstract into Storage\n\t\t\t\tmultiplier_t mrhs;\n\t\t\t\tif(rhs->is_rational()==false) {\n\t\t\t\t\tauto fnd=replacement_map.find(Ex(rhs));\n\t\t\t\t\tif(fnd!=replacement_map.end()) {\n\t\t\t\t\t\tauto tn=fnd->second.begin();\n\t\t\t\t\t\tif(tn->is_rational())\n\t\t\t\t\t\t\tmrhs=*tn->multiplier;\n\t\t\t\t\t\telse {\n\t\t\t\t\t\t\terror=\"Replacement not numerical.\";\n\t\t\t\t\t\t\treturn false;\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\t}\n\t\t\t\t\telse {\n\t\t\t\t\t\terror=\"Can only compare objects which evaluate to numbers.\";\n\t\t\t\t\t\treturn false;\n\t\t\t\t\t\t}\n\t\t\t\t\t}\n\t\t\t\telse mrhs=*rhs->multiplier;\n\n\t\t\t\tif(*cond->name==\"\\\\greater\" && mlhs <= mrhs) return false;\n\t\t\t\tif(*cond->name==\"\\\\less\"    && mlhs >= mrhs) return false;\n\t\t\t\t}\n\t\t\telse if(*cond->name==\"\\\\indexpairs\") {\n\t\t\t\tint countpairs=0;\n\t\t\t\treplacement_map_t::const_iterator it=replacement_map.begin(),it2;\n\t\t\t\twhile(it!=replacement_map.end()) {\n\t\t\t\t\tit2=it;\n\t\t\t\t\t++it2;\n\t\t\t\t\twhile(it2!=replacement_map.end()) {\n\t\t\t\t\t\tif(tree_exact_equal(&properties, it->second, it2->second)) {\n\t\t\t\t\t\t\t++countpairs;\n\t\t\t\t\t\t\tbreak;\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\t++it2;\n\t\t\t\t\t\t}\n\t\t\t\t\t++it;\n\t\t\t\t\t}\n\t\t\t\t//\t\t\ttxtout << countpairs << \" pairs\" << std::endl;\n\t\t\t\tif(countpairs!=cond.begin()->multiplier->get_rational())\n\t\t\t\t\treturn false;\n\t\t\t\t}\n\t\t\telse if(*cond->name==\"\\\\regex\") {\n\t\t\t\t//\t\t\ttxtout << \"regex matching...\" << std::endl;\n\t\t\t\tEx::sibling_iterator lhs=cond.begin();\n\t\t\t\tEx::sibling_iterator rhs=lhs;\n\t\t\t\t++rhs;\n\t\t\t\t// If we have a match, all indices have replacement rules.\n\t\t\t\tstd::string pat=(*rhs->name).substr(1,(*rhs->name).size()-2);\n\t\t\t\t//\t\t\ttxtout << \"matching \" << *comp.replacement_map[lhs->name]\n\t\t\t\t//\t\t\t\t\t << \" with pattern \" << pat << std::endl;\n\t\t\t\tstd::regex reg(pat);\n\t\t\t\tif (!std::regex_match(*(replacement_map[Ex(lhs)].begin()->name), reg))\n\t\t\t\t\treturn false;\n\t\t\t\t}\n\t\t\t// V2: FIXME: re-enable searching for properties\n\t\t\t//\t\telse if(*cond->name==\"\\\\hasprop\") {\n\t\t\t//\t\t\tEx::sibling_iterator lhs=cond.begin();\n\t\t\t//\t\t\tEx::sibling_iterator rhs=lhs;\n\t\t\t//\t\t\t++rhs;\n\t\t\t//\t\t\tProperties::registered_property_map_t::iterator pit=properties->store.find(*rhs->name);\n\t\t\t//\t\t\tif(pit==properties->store.end()) {\n\t\t\t//\t\t\t\tstd::ostringstream str;\n\t\t\t//\t\t\t\tstr << \"Property \\\"\" << *rhs->name << \"\\\" not registered.\" << std::endl;\n\t\t\t//\t\t\t\terror=str.str();\n\t\t\t//\t\t\t\treturn false;\n\t\t\t//\t\t\t\t}\n\t\t\t//\t\t\tconst property_base *aprop=pit->second();\n\t\t\t//\n\t\t\t//\t\t\tsubtree_replacement_map_t::iterator subfind=subtree_replacement_map.find(lhs->name);\n\t\t\t//\t\t\treplacement_map_t::iterator         patfind=replacement_map.find(Ex(lhs));\n\t\t\t//\n\t\t\t//\t\t\tif(subfind==subtree_replacement_map.end() && patfind==replacement_map.end()) {\n\t\t\t//\t\t\t\tstd::ostringstream str;\n\t\t\t//\t\t\t\tstr << \"Pattern \" << *lhs->name << \" in \\\\hasprop did not occur in match.\" << std::endl;\n\t\t\t//\t\t\t\tdelete aprop;\n\t\t\t//\t\t\t\terror=str.str();\n\t\t\t//\t\t\t\treturn false;\n\t\t\t//\t\t\t\t}\n\t\t\t//\n\t\t\t//\t\t\tbool ret=false;\n\t\t\t//\t\t\tif(subfind==subtree_replacement_map.end())\n\t\t\t//\t\t\t\t ret=properties->has(aprop, (*patfind).second.begin());\n\t\t\t//\t\t\telse\n\t\t\t//\t\t\t\t ret=properties->has(aprop, (*subfind).second);\n\t\t\t//\t\t\tdelete aprop;\n\t\t\t//\t\t\treturn ret;\n\t\t\t//\t\t\t}\n\t\t\telse {\n\t\t\t\tstd::ostringstream str;\n\t\t\t\tstr << \"substitute: condition involving \" << *cond->name << \" not understood.\" << std::endl;\n\t\t\t\terror=str.str();\n\t\t\t\treturn false;\n\t\t\t\t}\n\t\t\t}\n\t\treturn true;\n\t\t}\n\n\tEx_is_equivalent::Ex_is_equivalent(const Properties& k)\n\t\t: properties(k)\n\t\t{\n\t\t}\n\n\tbool Ex_is_equivalent::operator()(const Ex& one, const Ex& two)\n\t\t{\n\t\tint ret=subtree_compare(&properties, one.begin(), two.begin());\n\t\tif(ret==0) return true;\n\t\telse       return false;\n\t\t}\n\n\tEx_is_less::Ex_is_less(const Properties& k, int mp)\n\t\t: properties(k), mod_prel(mp)\n\t\t{\n\t\t}\n\n\tbool Ex_is_less::operator()(const Ex& one, const Ex& two)\n\t\t{\n\t\tint ret=subtree_compare(&properties, one.begin(), two.begin(), mod_prel);\n\t\tif(ret < 0) return true;\n\t\telse        return false;\n\t\t}\n\n\t}\n\nbool operator<(const cadabra::Ex::iterator& i1, const cadabra::Ex::iterator& i2)\n\t{\n\treturn i1.node < i2.node;\n\t}\n\nbool operator<(const cadabra::Ex& e1, const cadabra::Ex& e2)\n\t{\n\treturn e1.begin().node < e2.begin().node;\n\t}\n\nstd::ostream& operator<<(std::ostream& s, cadabra::Ex_comparator::useprops_t up)\n\t{\n\tswitch(up) {\n\t\tcase cadabra::Ex_comparator::useprops_t::always:\n\t\t\ts << \"always\";\n\t\t\tbreak;\n\t\tcase cadabra::Ex_comparator::useprops_t::not_at_top:\n\t\t\ts << \"not_at_top\";\n\t\t\tbreak;\n\t\tcase cadabra::Ex_comparator::useprops_t::never:\n\t\t\ts << \"never\";\n\t\t\tbreak;\n\t\t}\n\treturn s;\n\t}\n\n\n"
  },
  {
    "path": "core/Compare.hh",
    "content": "\n#pragma once\n\n#include \"Storage.hh\"\n#include \"Props.hh\"\n#include \"properties/Indices.hh\"\n\nnamespace cadabra {\n\n\t/// \\ingroup compare\n\t///\n\t/// Basic building block subtree comparison function for tensors\n\t/// without dummy indices, which determines whether two tensor\n\t/// subtrees are equal up to the names of indices. This uses NO\n\t/// property information whatsoever; when indices are compared,\n\t/// they are simply compared based on their name, not on the\n\t/// index set they may belong to. In most cases, this is NOT what\n\t/// you want.\n\t///\n\t/// In MOST cases, the use of Ex_comparator below is recommended\n\t/// instead, as it can do much more complicated matching and will\n\t/// also keep track of the relation between symbols in the pattern\n\t/// and symbols in the object to be matched.\n\t///\n\t/// Examples:\n\t///\n\t///     A_m                        equals  A_n                       up to index names\n\t///     \\diff{A*B_g*\\diff{C}_k}_m  equals  \\diff{A*B_h*\\diff{C}_r}_s up to index names\n\t///\n\t///  return | meaning\n\t///  -------|-----------------------------------------------\n\t///  0      | structure equal, and all indices the same name\n\t///  1      | structure equal, index names of one < two\n\t/// -1      | structure equal, index names of one > two\n\t///  2      | structure different, one < two\n\t/// -2      | structure different, one > two\n\t///\n\t/// @param one                 object\n\t/// @param two                 pattern\n\t/// @param mod_prel            see below\n\t/// @param checksets           ignored FIXME: remove\n\t/// @param compare_multiplier  whether to match the multiplier field too.\n\t/// @param literal_wildcards   whether to treat wildcard names as ordinary names.\n\t///\n\t/// The mod_prel variable determines whether parent relations are taken into\n\t/// account when comparing:\n\t/// FIXME: now that subtree_compare does not use properties anymore, a lot can be simplified.\n\t///\n\t///        -3: require that parent relations match, unless indexpos=free.\n\t///        -2: require that parent relations match (even when indexpos = free)\n\t///        -1: do not require that parent relations match\n\t///       >=0: do not require parent relations to match up to and including this level\n\t///\n\t/// Similar logic holds for the compare_multiplier parameter.\n\n\tint subtree_compare(const Properties*,\n\t                    Ex::iterator one, Ex::iterator two,\n\t                    int mod_prel=-2, bool checksets=true, int compare_multiplier=-2,\n\t                    bool literal_wildcards=false);\n\n\t/// Various comparison functions, some exact, some with pattern logic.\n\n\tbool tree_less(const Properties*,\n\t               const Ex& one, const Ex& two,\n\t               int mod_prel=-2, bool checksets=true, int compare_multiplier=-2);\n\tbool tree_equal(const Properties*,\n\t                const Ex& one, const Ex& two,\n\t                int mod_prel=-2, bool checksets=true, int compare_multiplier=-2);\n\tbool tree_exact_less(const Properties*,\n\t                     const Ex& one, const Ex& two,\n\t                     int mod_prel=-2, bool checksets=true, int compare_multiplier=-2,\n\t                     bool literal_wildcards=false);\n\tbool tree_exact_less(const Properties*,\n\t                     Ex::iterator one, Ex::iterator two,\n\t                     int mod_prel=-2, bool checksets=true, int compare_multiplier=-2,\n\t                     bool literal_wildcards=false);\n\tbool tree_exact_equal(const Properties*,\n\t                      const Ex& one, const Ex& two,\n\t                      int mod_prel=-2, bool checksets=true, int compare_multiplier=-2,\n\t                      bool literal_wildcards=false);\n\n\tbool subtree_less(const Properties*,\n\t                  Ex::iterator one, Ex::iterator two,\n\t                  int mod_prel=-2, bool checksets=true, int compare_multiplier=-2);\n\tbool subtree_equal(const Properties*,\n\t                   Ex::iterator one, Ex::iterator two,\n\t                   int mod_prel=-2, bool checksets=true, int compare_multiplier=-2);\n\tbool subtree_exact_less(const Properties*,\n\t                        Ex::iterator one, Ex::iterator two,\n\t                        int mod_prel=-2, bool checksets=true, int compare_multiplier=-2,\n\t                        bool literal_wildcards=false);\n\tbool subtree_exact_equal(const Properties*,\n\t                         Ex::iterator one, Ex::iterator two,\n\t                         int mod_prel=-2, bool checksets=true, int compare_multiplier=-2,\n\t                         bool literal_wildcards=false);\n\n\t/// Compare two trees by pattern logic, i.e. modulo index names.\n\t//\n\tclass tree_less_obj {\n\t\tpublic:\n\t\t\ttree_less_obj(const Properties*);\n\t\t\tbool operator()(const Ex& first, const Ex& second) const;\n\t\tprivate:\n\t\t\tconst Properties* properties;\n\t\t};\n\n\tclass tree_less_modprel_obj {\n\t\tpublic:\n\t\t\ttree_less_modprel_obj(const Properties*);\n\t\t\tbool operator()(const Ex& first, const Ex& second) const;\n\t\tprivate:\n\t\t\tconst Properties* properties;\n\t\t};\n\n\tclass tree_equal_obj {\n\t\tpublic:\n\t\t\ttree_equal_obj(const Properties*);\n\t\t\tbool operator()(const Ex& first, const Ex& second) const;\n\t\tprivate:\n\t\t\tconst Properties* properties;\n\t\t};\n\n\t/// Compare two trees exactly, i.e. including exact index names.\n\t//\n\tclass tree_exact_less_obj {\n\t\tpublic:\n\t\t\ttree_exact_less_obj(const Properties*);\n\t\t\tbool operator()(const Ex& first, const Ex& second) const;\n\t\t\tbool operator()(Ex::iterator first, Ex::iterator second) const;\n\t\tprivate:\n\t\t\tconst Properties* properties;\n\t\t};\n\n\tclass tree_exact_less_mod_prel_obj {\n\t\tpublic:\n\t\t\ttree_exact_less_mod_prel_obj(const Properties*);\n\t\t\tbool operator()(const Ex& first, const Ex& second) const;\n\t\tprivate:\n\t\t\tconst Properties* properties;\n\t\t};\n\n\tclass tree_exact_equal_obj {\n\t\tpublic:\n\t\t\ttree_exact_equal_obj(const Properties*);\n\t\t\tbool operator()(const Ex& first, const Ex& second) const;\n\t\tprivate:\n\t\t\tconst Properties* properties;\n\t\t};\n\n\tclass tree_exact_equal_mod_prel_obj {\n\t\tpublic:\n\t\t\ttree_exact_equal_mod_prel_obj(const Properties*);\n\t\t\tbool operator()(const Ex& first, const Ex& second) const;\n\t\tprivate:\n\t\t\tconst Properties* properties;\n\t\t};\n\n\t/// Compare for indexmap_t. The only comparator object that does not use\n\t/// properties info to lookup properties. This one compares exactly (it cannot\n\t/// do any matching which requires knowledge about index sets because it does\n\t/// not know about properties). It requires parent relations to match including\n\t/// at top level. It requires multipliers to match including at top level.\n\t/// Names with '?' or '??' suffixes are matched literally, not as patterns.\n\n\tclass tree_exact_less_for_indexmap_obj {\n\t\tpublic:\n\t\t\tbool operator()(const Ex& first, const Ex& second) const;\n\t\t};\n\n\t/// Compare two trees exactly, treat wildcard names as ordinary names.\n\t//\n\tclass tree_exact_less_no_wildcards_obj {\n\t\tpublic:\n\t\t\ttree_exact_less_no_wildcards_obj(); // disables property handling\n\t\t\ttree_exact_less_no_wildcards_obj(const Properties*);\n\t\t\tbool operator()(const Ex& first, const Ex& second) const;\n\t\tprivate:\n\t\t\tconst Properties* properties;\n\t\t};\n\n\tclass tree_exact_less_no_wildcards_mod_prel_obj {\n\t\tpublic:\n\t\t\ttree_exact_less_no_wildcards_mod_prel_obj(const Properties*);\n\t\t\tbool operator()(const Ex& first, const Ex& second) const;\n\t\tprivate:\n\t\t\tconst Properties* properties;\n\t\t};\n\n\n\t/// \\ingroup compare\n\t///\n\t/// A generic tree comparison class which will take into account index\n\t/// contractions and will also keep track of a replacement list for\n\t/// all types of cadabra wildcards. The entry point is typically\n\t/// 'equal_subtree' or 'match_subproduct'.\n\n\tclass Ex_comparator {\n\t\tpublic:\n\t\t\tEx_comparator(const Properties&);\n\n\t\t\tenum class match_t {\n\t\t\t\tnode_match=0,                 // a single node matches\n\t\t\t\tsubtree_match=1,              // identical match, including index names\n\t\t\t\tmatch_index_less=2,           // structure match, indices in same set, but different names\n\t\t\t\tmatch_index_greater=3,\n\t\t\t\tno_match_indexpos_less=4,     // mismatch but only for index positions\n\t\t\t\tno_match_indexpos_greater=5,\n\t\t\t\tno_match_less=6,              // more serious mismatch\n\t\t\t\tno_match_greater=7\n\t\t\t\t};\n\n\t\t\tenum class useprops_t {\n\t\t\t\talways=0,         // always use property info\n\t\t\t\tnot_at_top,       // don't use property info at top level of the expression\n\t\t\t\tnever=2           // never use property info\n\t\t\t\t};\n\n\t\t\t/// Reset the object for a new match.\n\n\t\t\tvoid    clear();\n\n\t\t\t/// Determine whether Coordinates in the pattern (first argument\n\t\t\t/// to functions below) can match against Indices in the object\n\t\t\t/// (second argument). That is to say, whether the pattern\n\t\t\t/// `\\partial_{t}{A}` matches against the expression\n\t\t\t/// `\\partial_{\\mu}{A}` when `\\mu` can take the value `t`. This is\n\t\t\t/// used in 'evaluate', but should generically be turned off for\n\t\t\t/// 'substitute'.\n\n\t\t\tvoid    set_value_matches_index(bool);\n\n\t\t\t/// Match two subtrees taking into account symbol\n\t\t\t/// properties. 'i1' can be a pattern.\n\t\t\t/// Returns subtree_match or one of the no_match\n\t\t\t/// results.  You need to fill lhs_contains_dummies before\n\t\t\t/// calling!\n\t\t\t/// If use_props is false, it will not try to fetch any property\n\t\t\t/// information at the TOP level of the comparison. Properties\n\t\t\t/// will always be used at  levels.\n\n\t\t\tmatch_t equal_subtree(Ex::iterator i1, Ex::iterator i2,\n\t\t\t                      useprops_t use_props=useprops_t::always, bool ignore_parent_rel=false);\n\n\t\t\t/// Match two subtrees, new-style equal_subtree that handles conditions; this is\n\t\t\t/// what substitute uses.\n\n\t\t\tmatch_t match_subtree(const Ex&, Ex::iterator i1, Ex::iterator i2, Ex::iterator conditions);\n\n\t\t\t/// Find a sub-product in a product. The 'lhs' iterator points to the product which\n\t\t\t/// we want to find, the 'tofind' iterator to the current factor which we are looking\n\t\t\t/// for. The product in which to search is pointed to by 'st'.\n\t\t\t/// Once 'tofind' is found, this routine calls itself to find the next factor in\n\t\t\t/// 'lhs'. If the next factor cannot be found, we backtrack and try to find the\n\t\t\t/// previous factor again (it may have appeared multiple times).\n\n\t\t\tmatch_t match_subproduct(const Ex&,\n\t\t\t                         Ex::sibling_iterator lhs, Ex::sibling_iterator tofind,\n\t\t\t                         Ex::sibling_iterator st, Ex::iterator conditions);\n\n\t\t\t/// Find a sub-sum in a sum. The 'lhs' iterator points to the sum which\n\t\t\t/// we want to find, the 'tofind' iterator to the current term which we are looking\n\t\t\t/// for. The sum in which to search is pointed to by 'st'.\n\t\t\t/// Once 'tofind' is found, this routine calls itself to find the next term in\n\t\t\t/// 'lhs'. Since Cadabra assumes all terms in a sum commute, we do not\n\t\t\t/// need the backtracking logic of subproduct.\n\n\t\t\tmatch_t match_subsum(const Ex&,\n\t\t\t                     Ex::sibling_iterator lhs, Ex::sibling_iterator tofind,\n\t\t\t                     Ex::sibling_iterator st, Ex::iterator conditions);\n\n\t\t\t/// Check whether the a match found by calling equal_subtree or match_subproduct\n\t\t\t/// satisfies the conditions as stated.\n\t\t\t/// FIXME: document possible conditions.\n\n\t\t\tbool    satisfies_conditions(Ex::iterator conditions, std::string& error);\n\n\t\t\t/// Map for the replacement of nodes (indices, patterns).\n\n\t\t\ttypedef std::map<Ex, Ex, tree_exact_less_no_wildcards_obj>     replacement_map_t;\n\t\t\treplacement_map_t                                              replacement_map;\n\n\t\t\t/// Map for the replacement of entire subtrees (object patterns).\n\n\t\t\ttypedef std::map<nset_t::iterator, Ex::iterator, nset_it_less> subtree_replacement_map_t;\n\t\t\tsubtree_replacement_map_t                                      subtree_replacement_map;\n\n\t\t\t/// Map for matching of index names to index values. Note: this is in the opposite order\n\t\t\t/// from replacement_map!\n\n\t\t\treplacement_map_t                                              index_value_map;\n\n\t\t\t/// Information to keep track of where individual factors/terms\n\t\t\t/// in a sub-product/sub-sum were found, and (for sub-products)\n\t\t\t/// whether moving them into the searched-for order leads to\n\t\t\t/// sign flips.\n\n\t\t\tstd::vector<Ex::sibling_iterator> factor_locations;\n\t\t\tstd::vector<int>                  factor_moving_signs;\n\t\t\tmultiplier_t                      term_ratio;\n\n\t\t\t/// Flag to indicate whether additional care must be taken to handle dummies in the\n\t\t\t/// lhs of the pattern.\n\t\t\t/// FIXME: would be better if this were automatic.\n\t\t\tbool lhs_contains_dummies;\n\n\t\t\t/// Determine whether two objects should be swapped according to\n\t\t\t/// the available SortOrder properties.\n\n\t\t\tbool should_swap(Ex::iterator obj, match_t subtree_comparison) ;\n\n\t\t\t/// Determine whether obj and obj+1 be exchanged? If yes, return\n\t\t\t/// the sign, if no return zero. This is the general entry point\n\t\t\t/// for two arbitrary nodes (which may be a product or sum).\n\t\t\t///\n\t\t\t/// The last flag ('ignore_implicit_indices') is used to disable\n\t\t\t/// all checks dealing with implicit indices (this is useful for\n\t\t\t/// algorithms which re-order objects with implicit indices,\n\t\t\t/// which would otherwise always receive a 0 from this\n\t\t\t/// function).\n\n\t\t\tint  can_swap(Ex::iterator one, Ex::iterator two, match_t subtree_comparison,\n\t\t\t              bool ignore_implicit_indices=false);\n\n\t\t\t/// Wrapper for can_swap which is meant for objects that have implicit\n\t\t\t/// indices. This checks whether a single component of A commutes or\n\t\t\t/// anticommutes with a single component of B, saying nothing about\n\t\t\t/// whether A and B commute under matrix multiplication.\n\n\t\t\tint  can_swap_components(Ex::iterator one, Ex::iterator two,\n\t\t\t\t\t\t match_t subtree_comparison);\n\n\t\t\t/// Determine whether object 'one' and 'two' can be moved next\n\t\t\t/// to each other by moving either one or the other: if fix_one==true\n\t\t\t/// the first node is kept fixed, otherwise the second node is kept fixed.\n\n\t\t\tint  can_move_adjacent(Ex::iterator prod, Ex::sibling_iterator one,\n\t\t\t                       Ex::sibling_iterator two, bool fix_one=false) ;\n\n\n\t\t\t/// Determine whether object 'one' can be moved to be the first\n\t\t\t/// factor in the given product.\n\t\t\tint  can_move_to_front(Ex&, Ex::iterator prod, Ex::sibling_iterator one);\n\t\t\t\n\t\t\t/// Alternative to the above, which handles more complicated versions where we\n\t\t\t/// need to keep track of previously moved factors (used by algorithms/substitute.cc).\n\n\t\t\tint  can_move_adjacent(Ex::iterator prod, const std::vector<Ex::sibling_iterator>& factors, Ex::sibling_iterator to_move);\n\n\t\tprotected:\n\t\t\tconst Properties& properties;\n\n\t\t\tbool value_matches_index;\n\n\t\t\t/// Internal entry point. This comparison function tries to match\n\t\t\t/// a single node in the tree, except when the node is an\n\t\t\t/// index. Indices are considered to be leaf-nodes, and for these\n\t\t\t/// a full subtree match will be attempted (using subtree_compare).\n\n\t\t\tmatch_t compare(const Ex::iterator&, const Ex::iterator&,\n\t\t\t                bool       nobrackets=false,\n\t\t\t                useprops_t use_props=useprops_t::always,\n\t\t\t                bool       ignore_parent_rel=false);\n\n\t\t\t// Internal functions used by can_swap.\n\t\t\tint  can_swap_prod_obj(Ex::iterator prod, Ex::iterator obj, bool) ;\n\t\t\tint  can_swap_prod_prod(Ex::iterator prod1, Ex::iterator prod2, bool) ;\n\t\t\tint  can_swap_sum_obj(Ex::iterator sum, Ex::iterator obj, bool) ;\n\t\t\tint  can_swap_prod_sum(Ex::iterator prod, Ex::iterator sum, bool) ;\n\t\t\tint  can_swap_sum_sum(Ex::iterator sum1, Ex::iterator sum2, bool) ;\n\t\t\tint  can_swap_ilist_ilist(Ex::iterator obj1, Ex::iterator obj2);\n\t\t\tbool can_swap_different_indexsets(Ex::iterator obj1, Ex::iterator obj2);\n\n\t\t\tstd::string tab() const;\n\t\t\tmatch_t     report(match_t r) const;\n\n\t\t\t/// Match the `name` elements of a node, but take into account that\n\t\t\t/// one of them can be an autodeclare name `XXX#`.\n\t\t\tbool name_match_with_autodeclare(Ex::sibling_iterator one, Ex::sibling_iterator two) const;\n\t\t\t\n\t\t\tstatic int offset;\n\t\t};\n\n\t/// \\ingroup core\n\t///\n\t/// Basic comparison operator for tree iterators, so we can use them as keys in maps.\n\n\tclass Ex_is_equivalent {\n\t\tpublic:\n\t\t\tEx_is_equivalent(const Properties&);\n\t\t\tbool operator()(const Ex&, const Ex&);\n\t\tprivate:\n\t\t\tconst Properties& properties;\n\t\t};\n\n\tclass Ex_is_less {\n\t\tpublic:\n\t\t\tEx_is_less(const Properties&, int mod_prel);\n\t\t\tbool operator()(const Ex&, const Ex&);\n\t\tprivate:\n\t\t\tconst Properties& properties;\n\t\t\tint mod_prel;\n\t\t};\n\n\n\n\t}\n\nbool operator<(const cadabra::Ex::iterator&, const cadabra::Ex::iterator&);\nbool operator<(const cadabra::Ex&, const cadabra::Ex&);\nstd::ostream& operator<<(std::ostream&, cadabra::Ex_comparator::useprops_t up);\n"
  },
  {
    "path": "core/Config.hh.in",
    "content": "\n#pragma once\n\n/// This file contains settings which are imported from the CMake\n/// configuration (installation path and version numbers)\n\n#define CADABRA_VERSION_MAJOR \"@CADABRA_VERSION_MAJOR@\"\n#define CADABRA_VERSION_MINOR \"@CADABRA_VERSION_MINOR@\"\n#define CADABRA_VERSION_PATCH \"@CADABRA_VERSION_PATCH@\"\n#define CADABRA_VERSION_FULL  \"@CADABRA_VERSION_MAJOR@.@CADABRA_VERSION_MINOR@.@CADABRA_VERSION_PATCH@\"\n#define CADABRA_VERSION_SEM   \"@CADABRA_VERSION_SEM@\"\n#define CADABRA_VERSION_DATE  \"@CADABRA_VERSION_DATE@\"\n#define CADABRA_VERSION_BUILD \"@CADABRA_VERSION_BUILD@\"\n#define COPYRIGHT_YEARS       \"@COPYRIGHT_YEARS@\"\n\n#cmakedefine CONDA_FOUND\n#cmakedefine ENABLE_JUPYTER\n#cmakedefine USE_GTK4\n#cmakedefine mimalloc_FOUND\n\n#cmakedefine MATHEMATICA_FOUND\n#define Mathematica_KERNEL_EXECUTABLE \"@Mathematica_KERNEL_EXECUTABLE@\"\n\n#define Python_VERSION_MAJOR  \"@Python_VERSION_MAJOR@\"\n#define Python_VERSION_MINOR  \"@Python_VERSION_MINOR@\"\n\n#cmakedefine USE_MICROTEX\n\n#cmakedefine APPIMAGE_MODE\n"
  },
  {
    "path": "core/DataCell.cc",
    "content": "\n#include \"InstallPrefix.hh\"\n#include \"Config.hh\"\n#include \"DataCell.hh\"\n#include \"Exceptions.hh\"\n#include <sstream>\n#include <fstream>\n#include <regex>\n//#include <boost/filesystem.hpp>\n//#include <boost/algorithm/string.hpp>\n#include <iostream>\n#include \"base64.hh\"\n#include <internal/uuid.h>\n#include <iomanip>\n\n\nusing namespace cadabra;\n\n// General tool to strip spaces from both ends\nstatic std::string trim(const std::string& s)\n\t{\n\tif(s.length() == 0)\n\t\treturn s;\n\tint b = s.find_first_not_of(\" \\t\\n\");\n\tint e = s.find_last_not_of(\" \\t\\n\");\n\tif(b == -1) // No non-spaces\n\t\treturn \"\";\n\treturn std::string(s, b, e - b + 1);\n\t}\n\nDTree::DTree()\n\t: tree<DataCell>(), hide_input_cells(false)\n\t{\n\t}\n\nDTree::DTree(const iterator& it)\n\t: tree<DataCell>(it), hide_input_cells(false)\n\t{\n\t}\n\nbool DataCell::id_t::operator<(const DataCell::id_t& other) const\n\t{\n\tif(created_by_client != other.created_by_client) return created_by_client;\n\n\treturn (id < other.id);\n\t}\n\nDataCell::id_t::id_t()\n\t: id(generate_uuid<uint64_t>())\n\t, created_by_client(true)\n\t{\n\t}\n\nDataCell::DataCell(CellType t, const std::string& str, bool cell_hidden)\n\t{\n\tcell_type = t;\n\ttextbuf = str;\n\thidden = cell_hidden;\n\trunning=false;\n\tignore_on_import=false;\n\t}\n\nDataCell::DataCell(id_t id_, CellType t, const std::string& str, bool cell_hidden)\n\t{\n\tcell_type = t;\n\ttextbuf = str;\n\thidden = cell_hidden;\n\trunning=false;\n\tserial_number=id_;\n\tignore_on_import=false;\t\n\t}\n\nDataCell::DataCell(const DataCell& other)\n\t{\n\trunning = other.running;\n\tcell_type = other.cell_type;\n\ttextbuf = other.textbuf;\n\thidden = other.hidden;\n\tsensitive = other.sensitive;\n\tserial_number = other.serial_number;\n\tignore_on_import = other.ignore_on_import;\n\t}\n\nstd::string cadabra::export_as_HTML(const DTree& doc, bool for_embedding, bool strip_code, std::string title)\n\t{\n\t// Load the pre-amble from file.\n\tstd::string pname = cadabra::install_prefix()+\"/share/cadabra2/notebook.html\";\n\tstd::ifstream preamble(pname);\n\tif(!preamble)\n\t\tthrow std::logic_error(\"Cannot open HTML preamble at \"+pname);\n\tstd::stringstream buffer;\n\tbuffer << preamble.rdbuf();\n\t// std::cerr << \"Using preamble at \" << pname << std::endl;\n\tstd::string preamble_string = buffer.str();\n\n\tstd::ostringstream str;\n\tHTML_recurse(doc, doc.begin(), str, preamble_string, for_embedding, strip_code, title);\n\n\treturn str.str();\n\t}\n\nstd::string cadabra::latex_to_html(const std::string& str)\n\t{\n\t// std::cerr << \"converting \" << str << std::endl;\n\tstd::regex section(R\"(\\\\section\\*\\{([^\\}]*)\\})\");\n\tstd::regex author(R\"(\\\\author\\{([^\\}]*)\\})\");\n\tstd::regex email(R\"(\\\\email\\{([^\\}]*)\\})\");\n\tstd::regex discretionary(R\"(\\\\discretionary\\{\\}\\{\\}\\{\\})\");\n\tstd::regex subsection(R\"(\\\\subsection\\*\\{([^\\}]*)\\})\");\n\tstd::regex subsubsection(R\"(\\\\subsubsection\\*\\{([^\\}]*)\\})\");\n\tstd::regex emph(R\"(\\\\emph\\{([^\\}]*)\\})\");\t\n\tstd::regex verb(R\"(\\\\verb\\|([^\\|]*)\\|)\");\n\tstd::regex url(R\"(\\\\url\\{([^\\}]*)\\})\");\n\tstd::regex href(R\"(\\\\href\\{([^\\}]*)\\}\\{([^\\}]*)\\})\");\n\tstd::regex begin_verbatim(R\"(\\\\begin\\{verbatim\\})\");\n\tstd::regex end_verbatim(R\"(\\\\end\\{verbatim\\})\");\n\tstd::regex begin_dmath(R\"(\\\\begin\\{dmath\\*\\})\");\n\tstd::regex end_dmath(R\"(\\\\end\\{dmath\\*\\})\");\n\tstd::regex tilde(\"~\");\n\tstd::regex less(\"<\");\n\tstd::regex greater(\">\");\n\tstd::regex bigO(R\"(\\\\bigO)\");\n\tstd::regex latex(R\"(\\\\LaTeX\\{\\})\");\n\tstd::regex tex(R\"(\\\\TeX\\{\\})\");\n\tstd::regex algorithm(R\"(\\\\algorithm\\{([^\\}]*)\\}\\{([^\\}]*)\\})\");\n\tstd::regex property(R\"(\\\\property\\{([^\\}]*)\\}\\{([^\\}]*)\\})\");\n\tstd::regex package(R\"(\\\\package\\{([^\\}]*)\\}\\{([^\\}]*)\\})\");\n\tstd::regex algo(R\"(\\\\algo\\{([^\\}]*)\\})\");\n\tstd::regex prop(R\"(\\\\prop\\{([^\\}]*)\\})\");\n\tstd::regex underscore(R\"(\\\\_)\");\n\tstd::regex e_aigu(R\"(\\\\'e)\");\n\tstd::regex ldots(R\"(\\\\ldots)\");\n\tstd::regex dquote(R\"(``([^']*)'')\");\n\tstd::regex squote(R\"(`([^']*)')\");\n\tstd::regex linebreak(R\"(\\\\linebreak\\[0\\])\");\n\tstd::regex tableau(R\"(\\\\tableau\\{(\\{[^\\}]*\\})*\\})\");\n\tstd::regex ftableau(R\"(\\\\ftableau\\{(\\{[^\\}]*\\}[,]?)*\\})\");\n\tstd::regex begin_tabular(R\"(\\\\begin\\{tabular\\}\\{[^\\}]*\\})\");\n\tstd::regex end_tabular(R\"(\\\\end\\{tabular\\})\");\n\tstd::regex hash_in_math(R\"((\\\\begin\\{dmath\\*\\}.*)\\\\#(\\\\end\\{dmath\\*\\}))\");\n\tstd::regex verbatim_symbol(R\"(\\{\\\\texttt\\{\\\\backslash\\{\\}([^\\}]*)\\}\\})\");\n//\tstd::regex verbatim_symbol(R\"(\\\\texttt\\{([^\\}]*)\\})\");\n\tstd::string res;\n\n\ttry {\n\t\tres = std::regex_replace(str, hash_in_math, \"$1#$2\");\n      res = std::regex_replace(res, verbatim_symbol, \"$\\\\setminus\\\\texttt{$1}$\");\n\t\tres = std::regex_replace(res, begin_dmath, R\"(\\(\\displaystyle)\");\n\t\tres = std::regex_replace(res, discretionary, \" \");\n\t\tres = std::regex_replace(res, end_dmath, R\"(\\))\");\n\t\tres = std::regex_replace(res, tilde, \" \");\n\t\tres = std::regex_replace(res, less, \"&lt;\");\n\t\tres = std::regex_replace(res, greater, \"&gt;\");\n\t\tres = std::regex_replace(res, bigO, \"{\\\\cal O}\");\t\t\n\t\tres = std::regex_replace(res, begin_verbatim, \"<pre class='output'>\");\n\t\tres = std::regex_replace(res, end_verbatim, \"</pre>\");\n\t\tres = std::regex_replace(res, section, \"<h1>$1</h1>\");\n\t\tres = std::regex_replace(res, subsection, \"<h2>$1</h2>\");\n\t\tres = std::regex_replace(res, subsubsection, \"<h3>$1</h3>\");\n\t\tres = std::regex_replace(res, emph, \"<i>$1</i>\");\n\t\tres = std::regex_replace(res, author, \"<div class='author'>$1</div>\");\n\t\tres = std::regex_replace(res, email, \"<div class='email'>$1</div>\");\n\t\tres = std::regex_replace(res, verb, \"<code>$1</code>\");\n\t\tres = std::regex_replace(res, url, \"<a href=\\\"$1\\\">$1</a>\");\n\t\tres = std::regex_replace(res, href, \"<a href=\\\"$1\\\">$2</a>\");\n\t\tres = std::regex_replace(res, algorithm, \"<h2>$1</h2><div class=\\\"summary\\\">$2</div>\");\n\t\tres = std::regex_replace(res, property, \"<h2>$1</h2><div class=\\\"summary\\\">$2</div>\");\n\t\tres = std::regex_replace(res, package, \"<h1>$1</h1><div class=\\\"summary\\\">$2</div>\");\n\t\tres = std::regex_replace(res, algo, \"<a href=\\\"/manual/$1.html\\\"><code>$1</code></a>\");\n\t\tres = std::regex_replace(res, prop, \"<a href=\\\"/manual/$1.html\\\"><code>$1</code></a>\");\n\t\tres = std::regex_replace(res, underscore, \"_\");\n\t\tres = std::regex_replace(res, latex, \"LaTeX\");\n\t\tres = std::regex_replace(res, tex, \"TeX\");\n\t\tres = std::regex_replace(res, e_aigu, \"é\");\n\t\tres = std::regex_replace(res, ldots, \"...\");\n\t\tres = std::regex_replace(res, dquote, \"\\\"$1\\\"\");\n\t\tres = std::regex_replace(res, squote,  \"'$1'\");\n\t\tres = std::regex_replace(res, linebreak, \"\\\\mmlToken{mo}[linebreak=\\\"goodbreak\\\"]{}\");\n\t\tres = std::regex_replace(res, tableau, \"\\\\)<div class=\\\"young_box\\\"></div>\\\\(\\\\displaystyle\");\n\t\tres = std::regex_replace(res, ftableau, \"\\\\)<div class=\\\"young_box filled\\\"></div>\\\\(\\\\displaystyle\");\n\t\tres = std::regex_replace(res, begin_tabular, \"<table>\");\n\t\tres = std::regex_replace(res, end_tabular, \"</table>\");\n\t\tres = std::regex_replace(res, std::regex(R\"(\\{\\\\tt ([^\\}]*)\\})\"), \"<tt>$1</tt>\");\n\t\t}\n\tcatch(std::regex_error& ex) {\n\t\tstd::cerr << \"regex error on \" << str << std::endl;\n\t\t}\n\n\t// std::cerr << \"to \" << res << std::endl;\n\treturn res;\n\t}\n\nvoid cadabra::HTML_recurse(const DTree& doc, DTree::iterator it, std::ostringstream& str,\n                           const std::string& preamble_string,\n                           bool for_embedding, bool strip_code,\n                           std::string title)\n\t{\n\tbool strip_this=false;\n\n\tif(doc.hide_input_cells)\n\t\tif(it->cell_type==DataCell::CellType::python || it->cell_type==DataCell::CellType::latex)\n\t\t\tstrip_this=true;\n\n\tswitch(it->cell_type) {\n\t\tcase DataCell::CellType::document:\n\t\t\tif(!for_embedding) {\n\t\t\t\tstr << preamble_string << \"\\n<body>\\n\";\n\t\t\t\t}\n\t\t\telse {\n\t\t\t\tstr << \"{% extends \\\"notebook_layout.html\\\" %}\\n\"\n\t\t\t\t    << \"{% block head %}\\n\"\n\t\t\t\t    << \" <meta name=\\\"keywords\\\" content=\\\"cadabra, manual\\\"/>\\n\"\n\t\t\t\t    << \"{%- endblock %}\\n\"\n\t\t\t\t    << \"{% block main %}\\n\"\n\t\t\t\t    << \"{% raw %}\\n\";\n\t\t\t\t}\n\t\t\tbreak;\n\t\tcase DataCell::CellType::python:\n\t\t\tif(strip_code && (it->textbuf.substr(0,4)==\"def \" || it->textbuf.substr(0,5)==\"from \"))\n\t\t\t\tstrip_this=true;\n\t\t\tstr << \"<div class='python'>\";\n\t\t\tbreak;\n\t\tcase DataCell::CellType::output:\n\t\t\tstr << \"<div class='output'>\";\n\t\t\tbreak;\n\t\tcase DataCell::CellType::verbatim:\n\t\t\tstr << \"<div class='verbatim'>\";\n\t\t\tbreak;\n\t\tcase DataCell::CellType::latex:\n\t\t\tstr << \"<div class='latex'>\";\n\t\t\tbreak;\n\t\tcase DataCell::CellType::latex_view:\n\t\t\tstr << \"<div class='latex_view hyphenate'>\";\n\t\t\tbreak;\n\t\tcase DataCell::CellType::error:\n\t\t\tstr << \"<div class='error'>\";\n\t\t\tbreak;\n\t\tcase DataCell::CellType::image_png:\n\t\t\tstr << \"<div class='image_png'><img src='data:image/png;base64,\";\n\t\t\tbreak;\n\t\tcase DataCell::CellType::image_svg:\n\t\t\tstr << \"<div class='image_svg'><img src='data:image/svg+xml;base64,\";\n\t\t\tbreak;\n\t\tcase DataCell::CellType::slider:\n\t\t\tstrip_this=true;\n\t\t\tbreak;\n\t\tcase DataCell::CellType::input_form:\n\t\t\t// str << \"<div class='input_form'>\";\n\t\t\tstrip_this=true;\n\t\t\tbreak;\n\t\t}\n\n\tif(!strip_this) {\n\t\ttry {\n\t\t\tif(it->textbuf.size()>0) {\n\t\t\t\tif(it->cell_type==DataCell::CellType::image_png)\n\t\t\t\t\tstr << it->textbuf;\n\t\t\t\telse if(it->cell_type==DataCell::CellType::image_svg)\n\t\t\t\t\tstr << it->textbuf;\n\t\t\t\telse if(it->cell_type==DataCell::CellType::slider) {\n\t\t\t\t\t}\n\t\t\t\telse if(it->cell_type!=DataCell::CellType::document && it->cell_type!=DataCell::CellType::latex) {\n\t\t\t\t\tstd::string out;\n\t\t\t\t\tif(it->cell_type==DataCell::CellType::python)\n\t\t\t\t\t\tout=it->textbuf;\n\t\t\t\t\telse\n\t\t\t\t\t\tout=latex_to_html(it->textbuf);\n\t\t\t\t\tif(out.size()>0) {\n\t\t\t\t\t\tif(it->cell_type==DataCell::CellType::python) {\n\t\t\t\t\t\t\tout = std::regex_replace(out, std::regex(\"<\"), \"&lt;\");\n\t\t\t\t\t\t\tout = std::regex_replace(out, std::regex(\">\"), \"&gt;\");\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\tstr << \"<div class=\\\"source donthyphenate\\\">\"+out+\"</div>\";\n\t\t\t\t\t\t}\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t}\n\t\tcatch(std::regex_error& ex) {\n\t\t\tstd::cerr << \"regex error doing latex_to_html on \" << it->textbuf << std::endl;\n\t\t\tthrow;\n\t\t\t}\n\t\t}\n\n\tif(doc.number_of_children(it)>0) {\n\t\tDTree::sibling_iterator sib=doc.begin(it);\n\t\twhile(sib!=doc.end(it)) {\n\t\t\tHTML_recurse(doc, sib, str, preamble_string, false, strip_code);\n\t\t\t++sib;\n\t\t\t}\n\t\t}\n\n\tswitch(it->cell_type) {\n\t\tcase DataCell::CellType::document:\n\t\t\tif(!for_embedding) {\n\t\t\t\tstr << \"</body>\\n\";\n\t\t\t\tstr << \"</html>\\n\";\n\t\t\t\t}\n\t\t\telse {\n\t\t\t\tstr << \"{% endraw %}\\n\"\n\t\t\t\t    << \"{%- endblock %}\\n\"\n\t\t\t\t    << \"{% block title %}\" << title << \"{% endblock %}\\n\";\n\t\t\t\t}\n\t\t\tbreak;\n\t\tcase DataCell::CellType::python:\n\t\t\tstr << \"</div>\\n\";\n\t\t\tbreak;\n\t\tcase DataCell::CellType::output:\n\t\t\tstr << \"</div>\\n\";\n\t\t\tbreak;\n\t\tcase DataCell::CellType::verbatim:\n\t\t\tstr << \"</div>\\n\";\n\t\t\tbreak;\n\t\tcase DataCell::CellType::latex:\n\t\t\tstr << \"</div>\\n\";\n\t\t\tbreak;\n\t\tcase DataCell::CellType::latex_view:\n\t\t\tstr << \"</div>\\n\";\n\t\t\tbreak;\n\t\tcase DataCell::CellType::error:\n\t\t\tstr << \"</div>\\n\";\n\t\t\tbreak;\n\t\tcase DataCell::CellType::image_png:\n\t\t\tstr << \"' /></div>\\n\";\n\t\t\tbreak;\n\t\tcase DataCell::CellType::image_svg:\n\t\t\tstr << \"' /></div>\\n\";\n\t\t\tbreak;\n\t\tcase DataCell::CellType::slider:\n\t\t\tbreak;\n\t\tcase DataCell::CellType::input_form:\n\t\t\t// str << \"</div>\\n\";\n\t\t\tbreak;\n\t\t}\n\t}\n\nstd::string cadabra::JSON_serialise(const DTree& doc)\n\t{\n\tnlohmann::json json;\n\tJSON_recurse(doc, doc.begin(), json);\n\n\tstd::ostringstream str;\n\tstr << std::setfill('\\t') << std::setw(1) << json;\n\n\treturn str.str();\n\t}\n\nvoid cadabra::JSON_recurse(const DTree& doc, DTree::iterator it, nlohmann::json& json)\n\t{\n\tswitch(it->cell_type) {\n\t\tcase DataCell::CellType::document: {\n\t\t\tjson[\"description\"]=\"Cadabra JSON notebook format\";\n\t\t\tjson[\"version\"]=1.0;\n\t\t\tnlohmann::json flags;\n\t\t\tflags[\"hide_input_cells\"] = doc.hide_input_cells;\n\t\t\tjson[\"flags\"]=flags;\n\t\t\tbreak;\n\t\t\t}\n\t\tcase DataCell::CellType::python:\n\t\t\tjson[\"cell_type\"]=\"input\";\n\t\t\tbreak;\n\t\tcase DataCell::CellType::output:\n\t\t\tjson[\"cell_type\"]=\"output\";\n\t\t\tbreak;\n\t\tcase DataCell::CellType::verbatim:\n\t\t\tjson[\"cell_type\"]=\"verbatim\";\n\t\t\tbreak;\n\t\tcase DataCell::CellType::latex:\n\t\t\tjson[\"cell_type\"]=\"latex\";\n\t\t\tbreak;\n\t\tcase DataCell::CellType::latex_view:\n\t\t\tjson[\"cell_type\"]=\"latex_view\";\n\t\t\tbreak;\n\t\tcase DataCell::CellType::error:\n\t\t\tjson[\"cell_type\"]=\"error\";\n\t\t\tbreak;\n\t\tcase DataCell::CellType::image_png:\n\t\t\tjson[\"cell_type\"]=\"image_png\";\n\t\t\tbreak;\n\t\tcase DataCell::CellType::image_svg:\n\t\t\tjson[\"cell_type\"]=\"image_svg\";\n\t\t\tbreak;\n\t\tcase DataCell::CellType::slider:\n\t\t\tjson[\"cell_type\"]=\"slider\";\n\t\t\tbreak;\n\t\tcase DataCell::CellType::input_form:\n\t\t\tjson[\"cell_type\"]=\"input_form\";\n\t\t\tbreak;\n\t\t\t//\t\tcase DataCell::CellType::section: {\n\t\t\t//\t\t\tassert(1==0);\n\t\t\t//\t\t\t// NOT YET FUNCTIONAL\n\t\t\t//\t\t\tjson[\"cell_type\"]=\"section\";\n\t\t\t//\t\t\tnlohmann::json child;\n\t\t\t//\t\t\tchild[\"content\"]=\"test\";\n\t\t\t//\t\t\tjson.append(child);\n\t\t\t//\t\t\tbreak;\n\t\t\t//\t\t\t}\n\t\t}\n\tif(it->hidden)\n\t\tjson[\"hidden\"]=true;\n\tif(it->ignore_on_import)\n\t\tjson[\"ignore_on_import\"]=true;\n\n\tjson[\"cell_id\"] = it->id().id;\n\n\tif(it->cell_type!=DataCell::CellType::document) {\n\t\tjson[\"source\"]  =it->textbuf;\n\t\tif(it->id().created_by_client)\n\t\t\tjson[\"cell_origin\"] = \"client\";\n\t\telse\n\t\t\tjson[\"cell_origin\"] = \"server\";\n\t\t//json[\"cell_id\"]       =(Json::UInt64)it->id().id;\n\t\t}\n\n\tif(doc.number_of_children(it)>0) {\n\t\tnlohmann::json cells=nlohmann::json::array();\n\t\tDTree::sibling_iterator sib=doc.begin(it);\n\t\twhile(sib!=doc.end(it)) {\n\t\t\tnlohmann::json thiscell;\n\t\t\tJSON_recurse(doc, sib, thiscell);\n\t\t\tcells.push_back(thiscell);\n\t\t\t++sib;\n\t\t\t}\n\t\tjson[\"cells\"]=cells;\n\t\t}\n\t}\n\nvoid cadabra::JSON_deserialise(const std::string& cj, DTree& doc)\n\t{\n\tnlohmann::json  root;\n\n\ttry {\n\t\troot=nlohmann::json::parse(cj);\n\t\t}\n\tcatch(nlohmann::json::exception& e) {\n\t\tstd::cerr << \"Cannot parse json file.\" << std::endl;\n\t\treturn;\n\t\t}\n\n\t// Setup main document.\n\tDataCell::id_t id;\n\ttry {\n\t\tid.id=root.value(\"cell_id\", generate_uuid<uint64_t>());\n\t\t}\n\tcatch(nlohmann::json::exception& e) {\n\t\tstd::cerr << \"Failed to find root-level 'cell_id' element (must be an integer).\" << std::endl;\n\t\treturn;\n\t\t}\n\tDataCell top(id, DataCell::CellType::document);\n\tDTree::iterator doc_it = doc.set_head(top);\n\n\t// Determine whether this is a Jupyter notebook or a Cadabra\n\t// notebook.\n\tif(root.count(\"description\") == 0) {\n\t\troot = cadabra::ipynb2cnb(root);\n\t\t}\n\t\n\t// Scan through json file.\n\tconst nlohmann::json& cells = root[\"cells\"];\n\tif(root.count(\"flags\")>0) {\n\t\tconst nlohmann::json& flags = root[\"flags\"];\n\t\tdoc.hide_input_cells = flags.value(\"hide_input_cells\", false);\n\t\t}\n\tJSON_in_recurse(doc, doc_it, cells);\n\t}\n\nvoid cadabra::JSON_in_recurse(DTree& doc, DTree::iterator loc, const nlohmann::json& cells)\n\t{\n\ttry {\n\t\tfor(const auto& cell: cells) {\n\t\t\tconst nlohmann::json& textbuf = cell[\"source\"];\n\n\t\t\tDTree::iterator last=doc.end();\n\t\t\tDataCell::id_t id;\n\t\t\tid.id=cell.value(\"cell_id\", generate_uuid<uint64_t>());\n\n\t\t\tif(cell.value(\"cell_origin\", \"\")==\"server\")\n\t\t\t\tid.created_by_client=false;\n\t\t\telse\n\t\t\t\tid.created_by_client=true;\n\t\t\t\n\t\t\tbool hide=false;\n\t\t\tif(cell.value(\"hidden\", false))\n\t\t\t\thide=true;\n\n\t\t\tstd::string cell_type = cell.value(\"cell_type\", \"\");\n\t\t\tif(cell_type==\"input\" || cell_type==\"code\") {\n\t\t\t\tstd::string res;\n\t\t\t\tif(textbuf.is_array()) {\n\t\t\t\t\tfor(const auto& el: textbuf)\n\t\t\t\t\t\tres+=el.get<std::string>();\n\t\t\t\t\t}\n\t\t\t\telse {\n\t\t\t\t\tres=textbuf.get<std::string>();\n\t\t\t\t\t}\n\t\t\t\tDataCell dc(id, cadabra::DataCell::CellType::python, res, hide);\n\t\t\t\tlast=doc.append_child(loc, dc);\n\t\t\t\t}\n\t\t\telse if(cell_type==\"output\") {\n\t\t\t\tDataCell dc(id, cadabra::DataCell::CellType::output, textbuf.get<std::string>(), hide);\n\t\t\t\tlast=doc.append_child(loc, dc);\n\t\t\t\t}\n\t\t\telse if(cell_type==\"error\") {\n\t\t\t\tDataCell dc(id, cadabra::DataCell::CellType::error, textbuf.get<std::string>(), hide);\n\t\t\t\tlast=doc.append_child(loc, dc);\n\t\t\t\t}\n\t\t\telse if(cell_type==\"verbatim\") {\n\t\t\t\tDataCell dc(id, cadabra::DataCell::CellType::verbatim, textbuf.get<std::string>(), hide);\n\t\t\t\tlast=doc.append_child(loc, dc);\n\t\t\t\t}\n\t\t\telse if(cell_type==\"input_form\") {\n\t\t\t\tDataCell dc(id, cadabra::DataCell::CellType::input_form, textbuf.get<std::string>(), hide);\n\t\t\t\tlast=doc.append_child(loc, dc);\n\t\t\t\t}\n\t\t\telse if(cell_type==\"latex_view\") {\n\t\t\t\tstd::string res;\n\t\t\t\tif(textbuf.is_array()) {\n\t\t\t\t\tfor(auto& el: textbuf)\n\t\t\t\t\t\tres+=el.get<std::string>();\n\t\t\t\t\t}\n\t\t\t\telse {\n\t\t\t\t\tres=textbuf.get<std::string>();\n\t\t\t\t\t}\n\t\t\t\tDataCell dc(id, cadabra::DataCell::CellType::latex_view, res, false);\n\t\t\t\tlast=doc.append_child(loc, dc);\n\t\t\t\t}\n\t\t\telse if(cell_type==\"latex\" || cell_type==\"markdown\") {\n\t\t\t\tstd::string res;\n\t\t\t\tif(textbuf.is_array()) {\n\t\t\t\t\tfor(auto& el: textbuf)\n\t\t\t\t\t\tres+=el.get<std::string>();\n\t\t\t\t\t}\n\t\t\t\telse {\n\t\t\t\t\tres=textbuf.get<std::string>();\n\t\t\t\t\t}\n\t\t\t\tbool hide_jupyter=hide;\n\t\t\t\tif(cell.count(\"cells\")==0) hide_jupyter=true;\n\n\t\t\t\tDataCell dc(id, cadabra::DataCell::CellType::latex, res, hide_jupyter);\n\t\t\t\tlast=doc.append_child(loc, dc);\n\n\t\t\t\t// IPython/Jupyter notebooks only have the input LaTeX cell, not the output cell,\n\t\t\t\t// which we need.\n\t\t\t\tif(cell.count(\"cells\")==0) {\n\t\t\t\t\tDataCell dc(id, cadabra::DataCell::CellType::latex_view, res, hide);\n\t\t\t\t\tdoc.append_child(last, dc);\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\telse if(cell_type==\"image_png\") {\n\t\t\t\tDataCell dc(id, cadabra::DataCell::CellType::image_png, textbuf.get<std::string>(), hide);\n\t\t\t\tlast=doc.append_child(loc, dc);\n\t\t\t\t}\n\t\t\telse if(cell_type==\"image_svg\") {\n\t\t\t\tDataCell dc(id, cadabra::DataCell::CellType::image_svg, textbuf.get<std::string>(), hide);\n\t\t\t\tlast=doc.append_child(loc, dc);\n\t\t\t\t}\n\t\t\telse if(cell_type==\"slider\") {\n\t\t\t\tDataCell dc(id, cadabra::DataCell::CellType::slider, textbuf.get<std::string>(), hide);\n\t\t\t\tlast=doc.append_child(loc, dc);\n\t\t\t\t}\n\t\t\telse {\n\t\t\t\tstd::cerr << \"cadabra-client: found unknown cell type '\"+cell_type+\"', ignoring\" << std::endl;\n\t\t\t\tcontinue;\n\t\t\t\t}\n\n\t\t\tif(last!=doc.end()) {\n\t\t\t\tif(cell.value(\"ignore_on_import\", false))\n\t\t\t\t\tlast->ignore_on_import=true;\n\t\t\t\tif(cell.count(\"cells\")>0) {\n\t\t\t\t\tconst nlohmann::json& subcells = cell[\"cells\"];\n\t\t\t\t\tJSON_in_recurse(doc, last, subcells);\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t}\n\t\t}\n\tcatch(std::exception& ex) {\n\t\tstd::cerr << \"cadabra-client: exception reading notebook: \" << ex.what() << std::endl;\n\t\t}\n\t}\n\nDataCell::id_t DataCell::id() const\n\t{\n\treturn serial_number;\n\t}\n\nstd::string cadabra::export_as_LaTeX(const DTree& doc, const std::string& image_file_base, bool for_embedding)\n\t{\n\t// Load the pre-amble from file.\n\tstd::string preamble_string;\n\tif(!for_embedding) {\n\t\tstd::string pname = cadabra::install_prefix()+\"/share/cadabra2/notebook.tex\";\n\t\tstd::ifstream preamble(pname);\n\t\tif(!preamble)\n\t\t\tthrow std::logic_error(\"Cannot open LaTeX preamble at \"+pname);\n\t\tstd::stringstream buffer;\n\t\tbuffer << preamble.rdbuf();\n\t\t// std::cerr << \"Using preamble at \" << pname << std::endl;\n\t\tpreamble_string = buffer.str();\n\t\t}\n\n\t// Open the LaTeX file for writing.\n\tstd::ostringstream str;\n\tint image_num=0;\n\tLaTeX_recurse(doc, doc.begin(), str, preamble_string, image_file_base, image_num, for_embedding);\n\n\treturn str.str();\n\t}\n\nvoid cadabra::LaTeX_recurse(const DTree& doc, DTree::iterator it, std::ostringstream& str,\n                            const std::string& preamble_string, const std::string& image_file_base,\n                            int& image_num, bool for_embedding)\n\t{\n\tswitch(it->cell_type) {\n\t\tcase DataCell::CellType::document:\n\t\t\tif(!for_embedding) {\n\t\t\t\tstr << preamble_string;\n\t\t\t\tstr << \"\\\\begin{document}\\n\";\n\t\t\t\t}\n\t\t\tbreak;\n\t\tcase DataCell::CellType::python:\n\t\t\tstr << \"\\\\begin{python}\\n\";\n\t\t\tbreak;\n\t\tcase DataCell::CellType::output:\n\t\t\tstr << \"\\\\begin{python}\\n\";\n\t\t\tbreak;\n\t\tcase DataCell::CellType::verbatim:\n//\t\t\tstr << \"\\\\begin{verbatim}\\n\";\n\t\t\tbreak;\n\t\tcase DataCell::CellType::latex:\n\t\t\tbreak;\n\t\tcase DataCell::CellType::latex_view:\n\t\t\tbreak;\n\t\tcase DataCell::CellType::error:\n\t\t\tstr << \"{\\\\color{red}\";\n\t\t\tbreak;\n\t\tcase DataCell::CellType::slider:\n\t\t\tbreak;\n\t\tcase DataCell::CellType::input_form:\n\t\t\tbreak;\n \t\tcase DataCell::CellType::image_png:\n \t\tcase DataCell::CellType::image_svg:\n\t\t\tstd::size_t pos=image_file_base.rfind('/');\n\t\t\tstd::string fileonly=image_file_base.substr(pos+1);\n\t\t\tstr << \"\\\\begin{minipage}{\\\\textwidth}\\n\\\\includegraphics[width=.6\\\\textwidth]{\"\n\t\t\t    << fileonly+std::to_string(image_num)+\"}\\n\"\n\t\t\t    << \"\\\\end{minipage}\\n\";\n\t\t\tbreak;\n\t\t}\n\n\tif(it->cell_type==DataCell::CellType::image_png) {\n\t\t// Images have to be saved to disk as separate files as\n\t\t// LaTeX has no concept of images embedded in the .tex file.\n\t\tstd::ofstream out(image_file_base+std::to_string(image_num)+\".png\");\n\t\tout << base64_decode(it->textbuf);\n\t\t++image_num;\n\t\t}\n\telse if(it->cell_type==DataCell::CellType::image_svg) {\n\t\t// Images have to be saved to disk as separate files as\n\t\t// LaTeX has no concept of images embedded in the .tex file.\n\t\tstd::string basename=image_file_base+std::to_string(image_num);\n\t\tstd::ofstream out(basename+\".svg\");\n\t\tout << base64_decode(it->textbuf);\n\t\tout.close();\n\t\t// Convert to pdf, otherwise LaTeX cannot include it.\n      //\t\tinkscape t.svg --export-pdf=t.pdf\n\t\tint res = system((std::string(\"inkscape \")+basename+std::string(\".svg --export-type=pdf --export-filename=\")+basename+std::string(\".pdf\")).c_str());\n\t\tif(res!=0)\n\t\t\tthrow std::logic_error(\"DataCell::LaTeX_recurse: failed to run 'convert' to convert svg to pdf.\");\n\t\t++image_num;\n\t\t}\n\telse {\n\t\tif(it->textbuf.size()>0) {\n\t\t\tif(it->cell_type!=DataCell::CellType::document\n\t\t\t\t&& it->cell_type!=DataCell::CellType::latex\n\t\t\t\t&& it->cell_type!=DataCell::CellType::slider\n\t\t\t\t&& it->cell_type!=DataCell::CellType::input_form) {\n\n\t\t\t\tif(!doc.hide_input_cells ||\n\t\t\t\t\t(it->cell_type!=DataCell::CellType::python && it->cell_type!=DataCell::CellType::latex)) {\n\t\t\t\t\t\t\n\t\t\t\t\tstd::string lr(it->textbuf);\n\t\t\t\t\t// Make sure to sync these with the same in TeXEngine.cc !!!\n\t\t\t\t\tlr=std::regex_replace(lr, std::regex(R\"(\\\\left\\()\"),            \"\\\\brwrap{(}{\");\n\t\t\t\t\tlr=std::regex_replace(lr, std::regex(R\"(\\\\right\\))\"),           \"}{)}\");\n\t\t\t\t\tlr=std::regex_replace(lr, std::regex(R\"(\\\\left\\[)\"),            \"\\\\brwrap{[}{\");\n\t\t\t\t\tlr=std::regex_replace(lr, std::regex(R\"(\\\\left\\.)\"),            \"\\\\brwrap{.}{\");\n\t\t\t\t\tlr=std::regex_replace(lr, std::regex(R\"(\\\\right\\])\"),           \"}{]}\");\n\t\t\t\t\tlr=std::regex_replace(lr, std::regex(R\"(\\\\left\\\\\\{)\"),            \"\\\\brwrap{\\\\{}{\");\n\t\t\t\t\tlr=std::regex_replace(lr, std::regex(R\"(\\\\right\\\\\\})\"),           \"}{\\\\}}\");\n\t\t\t\t\tlr=std::regex_replace(lr, std::regex(R\"(\\\\right\\.)\"),            \"}{.}\");\n//\t\t\t\tlr=std::regex_replace(lr, std::regex(R\"(\\\\begin\\{verbatim\\})\"), \"\");\n//\t\t\t\tlr=std::regex_replace(lr, std::regex(R\"(\\\\end\\{verbatim\\})\"),   \"\");\n\t\t\t\t\tlr=std::regex_replace(lr, std::regex(R\"(\\\\begin\\{dmath\\*\\})\"),  \"\\\\begin{adjustwidth}{1em}{0cm}$\");\n\t\t\t\t\tlr=std::regex_replace(lr, std::regex(R\"(\\\\end\\{dmath\\*\\})\"),    \"$\\\\end{adjustwidth}\");\n\t\t\t\t\tlr=std::regex_replace(lr, std::regex(R\"(\\\\algorithm\\{(.*)_(.*)\\})\"), \"\\\\algorithm{$1\\\\textunderscore{}$2}\");\n\t\t\t\t\tlr=std::regex_replace(lr, std::regex(R\"(\\\\algorithm\\{(.*)_(.*)\\})\"), \"\\\\algorithm{$1\\\\textunderscore{}$2}\");\n\t\t\t\t\tlr=std::regex_replace(lr, std::regex(R\"(🍅)\"), \"*\");\n\t\t\t\t\tstr << lr << \"\\n\";\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t}\n\t\t}\n\t\n\tswitch(it->cell_type) {\n\t\tcase DataCell::CellType::python:\n\t\tcase DataCell::CellType::output:\n\t\t\tstr << \"\\\\end{python}\\n\";\n\t\t\tbreak;\n\t\tcase DataCell::CellType::verbatim:\n//\t\t\tstr << \"\\\\end{verbatim}\\n\";\n\t\t\tbreak;\n\t\tcase DataCell::CellType::document:\n\t\t\tbreak;\n\t\tcase DataCell::CellType::latex:\n\t\t\tbreak;\n\t\tcase DataCell::CellType::latex_view:\n\t\t\tbreak;\n\t\tcase DataCell::CellType::input_form:\n\t\t\tbreak;\n\t\tcase DataCell::CellType::error:\n\t\t\tstr << \"}\";\n\t\t\tbreak;\n\t\tcase DataCell::CellType::image_png:\n\t\t\tbreak;\n\t\tcase DataCell::CellType::image_svg:\n\t\t\tbreak;\n\t\tcase DataCell::CellType::slider:\n\t\t\tbreak;\n\t\t}\n\n\tif(doc.number_of_children(it)>0) {\n\t\tDTree::sibling_iterator sib=doc.begin(it);\n\t\twhile(sib!=doc.end(it)) {\n\t\t\tLaTeX_recurse(doc, sib, str, preamble_string, image_file_base, image_num, for_embedding);\n\t\t\t++sib;\n\t\t\t}\n\t\t}\n\n\tswitch(it->cell_type) {\n\t\tcase DataCell::CellType::document:\n\t\t\tif(!for_embedding) {\n\t\t\t\tstr << \"\\\\end{document}\\n\";\n\t\t\t\t}\n\t\t\tbreak;\n\t\tcase DataCell::CellType::python:\n\t\tcase DataCell::CellType::output:\n\t\tcase DataCell::CellType::verbatim:\n\t\tcase DataCell::CellType::latex:\n\t\tcase DataCell::CellType::latex_view:\n\t\tcase DataCell::CellType::input_form:\n\t\tcase DataCell::CellType::error:\n\t\tcase DataCell::CellType::image_png:\n\t\tcase DataCell::CellType::image_svg:\n\t\tcase DataCell::CellType::slider:\n\t\t\tbreak;\n\t\t}\n\n\t}\n\nstd::string cadabra::export_as_python(const DTree& doc)\n\t{\n\tstd::ostringstream str;\n\tpython_recurse(doc, doc.begin(), str);\n\n\treturn str.str();\n\t}\n\nvoid cadabra::python_recurse(const DTree& doc, DTree::iterator it, std::ostringstream& str)\n\t{\n\tif(it->cell_type==DataCell::CellType::document)\n\t\tstr << \"#!/usr/bin/env cadabra2\\n\";\n\telse {\n\t\tif(it->cell_type==DataCell::CellType::python) {\n\t\t\tif(it->textbuf.size()>0) {\n\t\t\t\tstr << it->textbuf << \"\\n\";\n\t\t\t\t}\n\t\t\t}\n\t\t}\n\n\tif(doc.number_of_children(it)>0) {\n\t\tDTree::sibling_iterator sib=doc.begin(it);\n\t\twhile(sib!=doc.end(it)) {\n\t\t\tpython_recurse(doc, sib, str);\n\t\t\t++sib;\n\t\t\t}\n\t\t}\n\t}\n\n// std::string cadabra::replace_all(std::string str, const std::string& old, const std::string& new_s)\n//    {\n//    if(!old.empty()){\n// \t   size_t pos = 0;\n// \t   while ((pos = str.find(old, pos)) != std::string::npos) {\n// \t\t   str=str.replace(pos, old.length(), new_s);\n// \t\t   pos += new_s.length();\n// \t\t   }\n// \t   }\n//    return str;\n//    }\n\nnlohmann::json cadabra::ipynb2cnb(const nlohmann::json& root)\n\t{\n\tint nbf = root.value(\"nbformat\", 0);\n\tnlohmann::json json;\n\n\tif(nbf==0)\n\t\tthrow RuntimeException(\"Not a Jupyter notebook.\");\n\n\tjson[\"description\"]=\"Cadabra JSON notebook format\";\n\tjson[\"version\"]=1.0;\n\n\tnlohmann::json cells=nlohmann::json::array();\n\tconst nlohmann::json& jucells=root[\"cells\"];\n\t\n\t// Jupyter notebooks just have a single array of cells; walk\n\t// through and add to our \"cells\" array.\n\n\tfor(unsigned int c=0; c<jucells.size(); ++c) {\n\t\tnlohmann::json cell;\n\t\tif(jucells[c][\"cell_type\"].get<std::string>()==\"markdown\")\n\t\t\tcell[\"cell_type\"]=\"latex\";\n\t\telse\n\t\t\tcell[\"cell_type\"]=\"input\";\n\t\tcell[\"hidden\"]=false;\n\t\tconst nlohmann::json& source=jucells[c][\"source\"];\n\t\t// Jupyter stores the source line-by-line in an array 'source'.\n\t\tstd::string block;\n\t\tfor(unsigned int l=0; l<source.size(); ++l) {\n\t\t\tstd::string line=source[l].get<std::string>();\n\t\t\tif(line.size()>0) {\n\t\t\t\tif(line[0]=='#') {\n\t\t\t\t\tstd::string sub=\"\";\n\t\t\t\t\tline=line.substr(1);\n\t\t\t\t\tint inc=0;\n\t\t\t\t\twhile(line.size()>0 && line[0]=='#') {\n\t\t\t\t\t\tif(inc<2) {\n\t\t\t\t\t\t\tsub+=\"sub\";\n\t\t\t\t\t\t\tinc+=1;\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\tline=line.substr(1);\n\t\t\t\t\t\t}\n\t\t\t\t\tif(line.size()==0)\n\t\t\t\t\t\tcontinue;\n\t\t\t\t\tif(line[line.size()-1]=='\\n')\n\t\t\t\t\t\tline=line.substr(0,line.size()-1);\n\t\t\t\t\tblock+=\"\\\\\"+sub+\"section*{\"+trim(line)+\"}\\n\";\n\t\t\t\t\t}\n\t\t\t\telse\n\t\t\t\t\tblock+=line;\n\t\t\t\t}\n\t\t\t}\n\t\tcell[\"source\"]=block;\n\t\tcells.push_back(cell);\n\t\t}\n\n\tjson[\"cells\"] = cells;\n\t\n\treturn json;\n\t}\n\nnlohmann::json cadabra::cnb2ipynb(const nlohmann::json& root)\n\t{\n\tnlohmann::json ipynb, kernelspec, lang;\n\n\tipynb[\"nbformat\"]=4;\n\tipynb[\"nbformat_minor\"]=4;\n\n\tkernelspec[\"display_name\"]=\"Cadabra2\";\n\tkernelspec[\"language\"]=\"python\";\n\tkernelspec[\"name\"]=\"cadabra2\";\n\n\tlang[\"codemirror_mode\"]=\"cadabra\";\n\tlang[\"file_extension\"]=\".ipynb\";\n\tlang[\"mimetype\"]=\"text/cadabra\";\n\tlang[\"name\"]=\"cadabra2\";\n\tlang[\"pygments_lexer\"]=\"cadabra\";\n\t\n\tipynb[\"metadata\"] = {\n\t\t{\"kernelspec\", kernelspec},\n\t\t{\"language_info\", lang}\n\t};\n\n\tnlohmann::json cells=nlohmann::json::array();\n\t\n\t// Jupyter notebooks just have a single array of cells; walk\n\t// through and setup our cells array.\n\n\tfor(const auto& cdb: root[\"cells\"]) {\n\t\tnlohmann::json cell;\n\t\tif(cdb[\"cell_type\"]==\"python\") {\n\t\t\tcell[\"cell_type\"]=\"code\";\n\t\t\tcell[\"source\"]=nlohmann::json::array();\n\t\t\tcell[\"source\"].push_back(cdb[\"source\"]);\n\t\t\tcell[\"metadata\"]=nlohmann::json::object();\n\t\t\tcell[\"outputs\"]=nlohmann::json::array();\n\t\t\tcell[\"execution_count\"]={};\t\t\t\n\t\t\t}\n\t\tif(cdb[\"cell_type\"]==\"input\") {\n\t\t\tcell[\"cell_type\"]=\"code\";\n\t\t\tcell[\"source\"]=nlohmann::json::array();\n\t\t\tcell[\"source\"].push_back(cdb[\"source\"]);\n\t\t\tcell[\"metadata\"]=nlohmann::json::object();\n\t\t\tcell[\"outputs\"]=nlohmann::json::array();\n\t\t\tcell[\"execution_count\"]={};\n\t\t\t}\n\t\telse if(cdb[\"cell_type\"]==\"latex\") {\n\t\t\tcell[\"cell_type\"]=\"markdown\";\n\t\t\tcell[\"source\"]=nlohmann::json::array();\n\t\t\tcell[\"source\"].push_back(cdb[\"source\"]);\n\t\t\tcell[\"metadata\"]=nlohmann::json::object();\n\t\t\t}\n\n\t\tif(cell.is_null()==false)\n\t\t\tcells.push_back(cell);\n\t\t\n\t\t}\n\n\tipynb[\"cells\"] = cells;\n\t\n\treturn ipynb;\n\t}\n"
  },
  {
    "path": "core/DataCell.hh",
    "content": "\n#pragma once\n\n#include <string>\n#include <mutex>\n\n#include \"tree.hh\"\n#include \"nlohmann/json.hpp\"\n\nnamespace cadabra {\n\n\t/// \\ingroup files\n\t///\n\t/// DataCells are the basic building blocks for a document. They\n\t/// represent visual units in the notebook interface. They\n\t/// are stored in a tree inside the client, and can be transmitted\n\t/// over the wire between server and client in JSON format (see the\n\t/// documentation of the cadabra::JSON_serialise and cadabra::JSON_deserialise\n\t/// methods below for details on this representation). The notebook\n\t/// user interface reads these cells and construct corresponding\n\t/// graphical output for them.\n\t///\n\t/// The cadabra.display method of the cadabra python library knows\n\t/// how to turn various Python objects into the corresponding JSON\n\t/// representation of a DataCell.\n\n\tclass DataCell {\n\t\tpublic:\n\n\t\t\t/// Cells are labelled with the data type of its contents, which is\n\t\t\t/// stored in a textural representation but may need processing for\n\t\t\t/// proper display.\n\n\t\t\tenum class CellType {\n\t\t\t\tdocument,   ///< head node, only one per document\n\t\t\t\tpython,     ///< input : editor cell for code in python\n\t\t\t\tlatex,      ///< input : editor cell for code in latex\n\t\t\t\toutput,     ///< output: cell showing python stdout, verbatim\n\t\t\t\tverbatim,   ///< output: cell showing other verbatim output\n\t\t\t\tlatex_view, ///< output: cell showing LaTeX text formatted using LaTeX\n\t\t\t\tinput_form, ///< output: cell containing input form of preceding output cell\n\t\t\t\timage_png,  ///< output: cell showing a base64 encoded PNG image\n\t\t\t\timage_svg,  ///< output: cell showing an SVG image\n\t\t\t\tslider,     ///< output: cell showing a slider\n\t\t\t\terror,      ///< output: cell showing LaTeX text for errors\n\t\t\t\t// section\n\t\t\t\t};\n\n\t\t\t/// Each cell is identified by a serial number 'id' which is used\n\t\t\t/// to keep track of it across network calls, and a bool indicating\n\t\t\t/// whether the client or the server has created this cell.\n\n\t\t\tclass id_t {\n\t\t\t\tpublic:\n\t\t\t\t\tid_t();\n\n\t\t\t\t\tuint64_t  id;\n\t\t\t\t\tbool      created_by_client;\n\n\t\t\t\t\tbool operator<(const id_t& other) const;\n\t\t\t\t};\n\n\t\t\t/// Standard constructor, generates a new unique id for this DataCell.\n\n\t\t\tDataCell(CellType t=CellType::python, const std::string& str=\"\", bool hidden=false);\n\n\t\t\t/// Initialise a cell with an already determined id (it is the caller's responsibility\n\t\t\t/// to ensure that this id does not clash with any other DataCell's id).\n\n\t\t\tDataCell(id_t, CellType t=CellType::python, const std::string& str=\"\", bool hidden=false);\n\n\t\t\t/// Copy constructor; preserves all information including id.\n\n\t\t\tDataCell(const DataCell&);\n\n\t\t\tCellType                      cell_type;\n\n\t\t\t/// Textual representation of the cell content. For e.g. latex cells it is a bit of a\n\t\t\t/// waste to store this representation both in the input and in the output cell.\n\t\t\t/// However, this gives us the flexibility to do manipulations on the input (e.g.\n\t\t\t/// resolving equation references) before feeding it to LaTeX.\n\n\t\t\tstd::string                   textbuf;\n\n\t\t\t/// Flag indicating whether this cell should be hidden from\n\t\t\t/// view. The GUI should have a way to bring the cells back\n\t\t\t/// into view, typically by clicking on the output cell\n\t\t\t/// corresponding to the input cell.\n\n\t\t\tbool                          hidden;\n\t\t\tbool                          sensitive;\n\n\t\t\t/// Flag indicating whether this cell should be ignored in case the \n\t\t\t/// notebook is imported. Essentially the equivalent of `if __name__==\"__main__\"`.\n\n\t\t\tbool                          ignore_on_import;\n\n\t\t\t/// Indicator whether this cell is currently being evaluated by the server.\n\t\t\t/// Currently only has a meaning for cells of type 'python'.\n\t\t\t/// This flag is set/reset using the ActionSetRunStatus action.\n\n\t\t\tbool                          running;\n\n\t\t\t/// Return the cell ID. This is essentially a random UUID.\n\t\t\tid_t                          id() const;\n\n\t\t\t/// List of all variables referenced in this cell. This gets updated as\n\t\t\t/// soon as the cell is run by the server and the output comes back.\n\n\t\t\tstd::set<std::string>         variables_referenced;\n\n\t\tprivate:\n\t\t\tid_t                          serial_number;\n\t\t};\n\n\tclass DTree : public tree<DataCell> {\n\t\tpublic:\n\t\t\tDTree();\n\t\t\tDTree(const iterator&);\n\t\t\t\t\n\t\t\tbool hide_input_cells;\n\t};\n\n\t/// Serialise a document into .cj format, which is a JSON version of\n\t/// the document tree.\n\n\tstd::string JSON_serialise(const DTree&);\n\tvoid        JSON_recurse(const DTree&, DTree::iterator, nlohmann::json&);\n\n\t/// Load a document from .cnb format, i.e. the inverse of the above.\n\n\tvoid        JSON_deserialise(const std::string&, DTree&);\n\tvoid        JSON_in_recurse(DTree& doc, DTree::iterator loc, const nlohmann::json& cells);\n\n\t/// Export a document to a single self-contained HTML file containing inline CSS.\n\n\tstd::string export_as_HTML(const DTree& doc, bool for_embedding=false, bool\n\t                           strip_code=false, std::string title=\"\");\n\tvoid        HTML_recurse(const DTree& doc, DTree::iterator it, std::ostringstream& str,\n\t                         const std::string& preamble_string,\n\t                         bool for_embedding=false, bool strip_code=false, std::string title=\"\");\n\n\t/// Convert various LaTeX constructions to HTML-with-Mathjax, e.g. \\\\section{...},\n\t/// \\\\begin{verbatim}...\\\\end{verbatim}, \\\\verb.\n\n\tstd::string latex_to_html(const std::string&);\n\n\t/// Export a document to a single self-contained LaTeX file, with the exception of\n\t/// images which get saved as separate numbered files.\n\n\tstd::string export_as_LaTeX(const DTree& doc, const std::string& image_file_base, bool for_embedding=false);\n\tvoid        LaTeX_recurse(const DTree& doc, DTree::iterator it, std::ostringstream& str,\n\t                          const std::string& preamble_string, const std::string& image_file_base,\n\t                          int& image_num, bool for_embedding);\n\n\t/// Export a document to a python-like file (converting text cells to comments\n\t/// and python cells to python code, dropping output cells).\n\n\tstd::string export_as_python(const DTree& doc);\n\tvoid        python_recurse(const DTree& doc, DTree::iterator it, std::ostringstream& str);\n\n\t/// Replace all occurrences of a substring in the original string.\n\t// std::string replace_all(std::string, const std::string& old, const std::string& nw);\n\n\t/// Convert the JSON of a Jupyter notebook (with Cadabra contents)\n\t/// to the JSON of a Cadabra notebook.\n\t\n\tnlohmann::json ipynb2cnb(const nlohmann::json&);\n\n\t/// Convert the JSON of a Cadabra notebook to a Jupyter notebook.\n\n\tnlohmann::json cnb2ipynb(const nlohmann::json&);\n}\n"
  },
  {
    "path": "core/Debug.hh",
    "content": "\n// Include this *only* in .cc files. Then define DEBUG in such .cc file\n// to enable debugging. Use DEBUGLN to wrap around statements which should\n// only execute when debugging is active.\n\n#ifdef DEBUG\n#pragma message(\"DEBUG enabled for \" DEBUG)\nstatic bool debug_stop = false;\n#define DEBUGLN(ln) if(!debug_stop) { ln; }\n#define DEBUGSTOP(fl) { debug_stop = fl; }\n#else\n#define DEBUGLN(ln)\n#define DEBUGSTOP(fl)\n#endif\n"
  },
  {
    "path": "core/DisplayBase.cc",
    "content": "\n#include \"DisplayBase.hh\"\n\nusing namespace cadabra;\n\nDisplayBase::DisplayBase(const Kernel& k, const Ex& e)\n\t: tree(e), kernel(k)\n\t{\n\t}\n\nvoid DisplayBase::output(std::ostream& str)\n\t{\n\tEx::iterator it=tree.begin();\n\tif(it==tree.end()) return;\n\n\toutput(str, it);\n\t}\n\nvoid DisplayBase::output(std::ostream& str, Ex::iterator it)\n\t{\n\tdispatch(str, it);\n\t}\n\n"
  },
  {
    "path": "core/DisplayBase.hh",
    "content": "#pragma once\n\n#include <string>\n#include <sstream>\n#include \"Props.hh\"\n#include \"Storage.hh\"\n\nnamespace cadabra {\n\n\t/// \\ingroup display\n\t///\n\t/// Base class for all display classes.  A key difficulty with\n\t/// printing is to figure out when to print additional brackets for\n\t/// objects which would otherwise not render correctly. For example, a\n\t/// sum inside a product need brackets, but it does not need brackets\n\t/// when it is given as an argument to a function, because then the\n\t/// brackets are already there from the function call.\n\n\tclass DisplayBase {\n\t\tpublic:\n\t\t\tDisplayBase(const Kernel&, const Ex&);\n\n\t\t\tvoid output(std::ostream&);\n\t\t\tvoid output(std::ostream&, Ex::iterator);\n\n\t\t\tvirtual void dispatch(std::ostream&, Ex::iterator)=0;\n\n\t\tprotected:\n\t\t\t/// Determine if a node needs extra brackets around it. Uses context from the\n\t\t\t/// parent node if necessary. Has to be implemented in a derived class, because\n\t\t\t/// the answer depends on the printing method (e.g. `(a+b)/c` needs brackets\n\t\t\t/// when printed like this, but does not need brackets when printed as\n\t\t\t/// `\\frac{a+b}{c}`).\n\n\t\t\tvirtual bool needs_brackets(Ex::iterator it)=0;\n\n\t\t\tconst Ex&     tree;\n\t\t\tconst Kernel& kernel;\n\n\t\t};\n\n\ttemplate <typename DisplayType> std::string ex_to_string(const Kernel& kernel, const Ex& ex)\n\t{\n\t\tstd::ostringstream ss;\n\t\tDisplayType dt(kernel, ex);\n\t\tdt.output(ss);\n\t\treturn ss.str();\n\t}\n\n\ttemplate <typename DisplayType> std::string ex_to_string(const Kernel& kernel, Ex::iterator it)\n\t{\n\t\treturn ex_to_string<DisplayType>(kernel, Ex(it));\n\t}\n\n\n\t}\n"
  },
  {
    "path": "core/DisplayMMA.cc",
    "content": "\n#include \"Storage.hh\"\n#include \"Exceptions.hh\"\n#include \"Functional.hh\"\n#include \"DisplayMMA.hh\"\n#include \"PreClean.hh\"\n#include \"properties/Depends.hh\"\n\nusing namespace cadabra;\n\nDisplayMMA::DisplayMMA(const Kernel& kernel, const Ex& e, bool uuc)\n\t: DisplayBase(kernel, e), use_unicode(uuc)\n\t{\n\tsymmap = {\n\t\t\t{\"\\\\cos\",  \"Cos\"},\n\t\t\t{\"\\\\sin\",  \"Sin\"},\n\t\t\t{\"\\\\tan\",  \"Tan\"},\n\t\t\t{\"\\\\sec\",  \"Sec\"},\n\t\t\t{\"\\\\csc\",  \"Csc\"},\n\t\t\t{\"\\\\cot\",  \"Cot\"},\n\n\t\t\t{\"\\\\cosh\", \"Cosh\"},\n\t\t\t{\"\\\\sinh\", \"Sinh\"},\n\t\t\t{\"\\\\tanh\", \"Tanh\"},\n\n\t\t\t{\"\\\\scsh\", \"Sech\"},\n\t\t\t{\"\\\\csch\", \"Csch\"},\n\t\t\t{\"\\\\coth\", \"Coth\"},\n\n\t\t\t{\"\\\\log\", \"Log\"},\n\t\t\t{\"\\\\int\", \"Integrate\" },\n\t\t\t{\"\\\\matrix\", \"Matrix\" },\n\t\t\t{\"\\\\sum\", \"Plus\" },\n\t\t\t{\"\\\\exp\", \"Exp\" },\n\t\t\t{\"\\\\sqrt\", \"Sqrt\" },\n\t\t\t{\"\\\\prod\", \"Times\" },\n\t\t\t{\"\\\\pow\",  \"Power\" },\n\t\t\t{\"\\\\frac\", \"Rational\" },\n\n\t\t\t{\"\\\\infty\",   \"Infinity\"},\n\n\t\t\t{\"\\\\alpha\",   \"α\" },\n\t\t\t{\"\\\\beta\",    \"β\" },  // beta seems to be reserved\n\t\t\t{\"\\\\gamma\",   \"γ\" }, // gamma seems to be reserved\n\t\t\t{\"\\\\delta\",   \"δ\" },\n\t\t\t{\"\\\\epsilon\", \"ε\" },\n\t\t\t{\"\\\\zeta\",    \"ζ\" },\n\t\t\t{\"\\\\eta\",     \"η\" },\n\t\t\t{\"\\\\theta\",   \"θ\" },\n\t\t\t{\"\\\\iota\",    \"ι\" },\n\t\t\t{\"\\\\kappa\",   \"κ\" },\n\t\t\t{\"\\\\lambda\",  \"λ\" }, // lambda is reserved\n\t\t\t{\"\\\\mu\",      \"μ\" },\n\t\t\t{\"\\\\nu\",      \"ν\" },\n\t\t\t{\"\\\\xi\",      \"ξ\" },\n\t\t\t{\"\\\\omicron\", \"ο\" },\n\t\t\t{\"\\\\pi\",      \"π\" },\n\t\t\t{\"\\\\rho\",     \"ρ\" },\n\t\t\t{\"\\\\sigma\",   \"σ\" },\n\t\t\t{\"\\\\tau\",     \"τ\" },\n\t\t\t{\"\\\\upsilon\", \"υ\" },\n\t\t\t{\"\\\\phi\",     \"ϕ\" },\n\t\t\t{\"\\\\chi\",     \"χ\" },\n\t\t\t{\"\\\\psi\",     \"ψ\" },\n\t\t\t{\"\\\\omega\",   \"ω\" },\n\n\t\t\t{\"\\\\Alpha\",   \"Α\" },\n\t\t\t{\"\\\\Beta\",    \"Β\" },\n\t\t\t{\"\\\\Gamma\",   \"Γ\" },\n\t\t\t{\"\\\\Delta\",   \"Δ\" },\n\t\t\t{\"\\\\Epsilon\", \"Ε\" },\n\t\t\t{\"\\\\Zeta\",    \"Ζ\" },\n\t\t\t{\"\\\\Eta\",     \"Η\" },\n\t\t\t{\"\\\\Theta\",   \"ϴ\" },\n\t\t\t{\"\\\\Iota\",    \"Ι\" },\n\t\t\t{\"\\\\Kappa\",   \"Κ\" },\n\t\t\t{\"\\\\Lambda\",  \"Λ\" },\n\t\t\t{\"\\\\Mu\",      \"Μ\" },\n\t\t\t{\"\\\\Nu\",      \"Ν\" },\n\t\t\t{\"\\\\Xi\",      \"Ξ\" },\n\t\t\t{\"\\\\Omicron\", \"Ο\" },\n\t\t\t{\"\\\\Pi\",      \"Π\" },\n\t\t\t{\"\\\\Rho\",     \"Ρ\" },\n\t\t\t{\"\\\\Sigma\",   \"Σ\" },\n\t\t\t{\"\\\\Tau\",     \"Τ\" },\n\t\t\t{\"\\\\Upsilon\", \"Υ\" },\n\t\t\t{\"\\\\Phi\",     \"Φ\" },\n\t\t\t{\"\\\\Chi\",     \"Χ\" },\n\t\t\t{\"\\\\Psi\",     \"Ψ\" },\n\t\t\t{\"\\\\Omega\",   \"Ω\" },\n\n\t\t\t{\"\\\\partial\", \"Derivative\"}\n\t\t};\n\n\tregex_map = {\n\t\t\t{\"\\\\alpha\",   R\"(\\[Alpha])\"   },\n\t\t\t{\"\\\\beta\",    R\"(\\[Beta])\"    },\n\t\t\t{\"\\\\gamma\",   R\"(\\[Gamma])\"   },\n\t\t\t{\"\\\\delta\",   R\"(\\[Delta])\"   },\n\t\t\t{\"\\\\epsilon\", R\"(\\[Epsilon])\" },\n\t\t\t{\"\\\\zeta\",    R\"(\\[Zeta])\"    },\n\t\t\t{\"\\\\eta\",     R\"(\\[Eta])\"     },\n\t\t\t{\"\\\\theta\",   R\"(\\[Theta])\"   },\n\t\t\t{\"\\\\iota\",    R\"(\\[Iota])\"    },\n\t\t\t{\"\\\\kappa\",   R\"(\\[Kappa])\"   },\n\t\t\t{\"\\\\lambda\",  R\"(\\[Lamda])\"   },\n\t\t\t{\"\\\\mu\",      R\"(\\[Mu])\"      },\n\t\t\t{\"\\\\nu\",      R\"(\\[Nu])\"      },\n\t\t\t{\"\\\\xi\",      R\"(\\[Xi])\"      },\n\t\t\t{\"\\\\omicron\", R\"(\\[Omicron])\" },\n\t\t\t{\"\\\\pi\",      R\"(\\[Pi])\"      },\n\t\t\t{\"\\\\pi\",      R\"(Pi)\"              },\n\t\t\t{\"\\\\rho\",     R\"(\\[Rho])\"     },\n\t\t\t{\"\\\\sigma\",   R\"(\\[Sigma])\"   },\n\t\t\t{\"\\\\tau\",     R\"(\\[Tau])\"     },\n\t\t\t{\"\\\\upsilon\", R\"(\\[Upsilon])\" },\n\t\t\t{\"\\\\phi\",     R\"(\\[Phi])\"     },\n\t\t\t{\"\\\\varphi\",  R\"(\\[CurlyPhi])\"},\n\t\t\t{\"\\\\chi\",     R\"(\\[Chi])\"     },\n\t\t\t{\"\\\\psi\",     R\"(\\[Psi])\"     },\n\t\t\t{\"\\\\omega\",   R\"(\\[Omega])\"   },\n\n\t\t\t{\"\\\\Alpha\",   R\"(\\[CapitalAlpha])\"   },\n\t\t\t{\"\\\\Beta\",    R\"(\\[CapitalBeta])\"    },\n\t\t\t{\"\\\\Gamma\",   R\"(\\[CapitalGamma])\"   },\n\t\t\t{\"\\\\Delta\",   R\"(\\[CapitalDelta])\"   },\n\t\t\t{\"\\\\Epsilon\", R\"(\\[CapitalEpsilon])\" },\n\t\t\t{\"\\\\Zeta\",    R\"(\\[CapitalZeta])\"    },\n\t\t\t{\"\\\\Eta\",     R\"(\\[CapitalEta])\"     },\n\t\t\t{\"\\\\Theta\",   R\"(\\[CapitalTheta])\"   },\n\t\t\t{\"\\\\Iota\",    R\"(\\[CapitalIota])\"    },\n\t\t\t{\"\\\\Kappa\",   R\"(\\[CapitalKappa])\"   },\n\t\t\t{\"\\\\Lambda\",  R\"(\\[CapitalLamda])\"   },\n\t\t\t{\"\\\\Mu\",      R\"(\\[CapitalMu])\"      },\n\t\t\t{\"\\\\Nu\",      R\"(\\[CapitalNu])\"      },\n\t\t\t{\"\\\\Xi\",      R\"(\\[CapitalXi])\"      },\n\t\t\t{\"\\\\Omicron\", R\"(\\[CapitalOmicron])\" },\n\t\t\t{\"\\\\Pi\",      R\"(\\[CapitalPi])\"      },\n\t\t\t{\"\\\\Rho\",     R\"(\\[CapitalRho])\"     },\n\t\t\t{\"\\\\Sigma\",   R\"(\\[CapitalSigma])\"   },\n\t\t\t{\"\\\\Tau\",     R\"(\\[CapitalTau])\"     },\n\t\t\t{\"\\\\Upsilon\", R\"(\\[CapitalUpsilon])\" },\n\t\t\t{\"\\\\Phi\",     R\"(\\[CapitalPhi])\"     },\n\t\t\t{\"\\\\Chi\",     R\"(\\[CapitalChi])\"     },\n\t\t\t{\"\\\\Psi\",     R\"(\\[CapitalPsi])\"     },\n\t\t\t{\"\\\\Omega\",   R\"(\\[CapitalOmega])\"   },\n\t\t};\n\t}\n\n//TODO: complete this list\n\nbool DisplayMMA::needs_brackets(Ex::iterator it)\n\t{\n\t// FIXME: may need looking at properties\n\t// FIXME: write as individual parent/current tests\n\tif(tree.is_head(it)) return false;\n\n\tstd::string parent=*tree.parent(it)->name;\n\tstd::string child =*it->name;\n\n\n\tif(*tree.parent(it)->name==\"\\\\prod\" || *tree.parent(it)->name==\"\\\\frac\" || *tree.parent(it)->name==\"\\\\pow\") {\n\t\tif(*it->name==\"\\\\sum\" || *it->name==\"\\\\prod\") return true;\n\t\tif(parent==\"\\\\pow\" && ( (tree.index(it)==0 && !it->is_integer()) || child==\"\\\\sum\" || child==\"\\\\prod\" || child==\"\\\\pow\")  ) return true;\n\t\t}\n\telse if(it->fl.parent_rel==str_node::p_none) {\n\t\tif(*it->name==\"\\\\sum\") return false;\n\t\t}\n\telse {\n\t\tif(*it->name==\"\\\\sum\")  return true;\n\t\tif(*it->name==\"\\\\prod\") return true;\n\t\t}\n\treturn false;\n\t}\n\n\nvoid DisplayMMA::print_other(std::ostream& str, Ex::iterator it)\n\t{\n\tif(needs_brackets(it))\n\t\tstr << \"(\";\n\n\t// print multiplier and object name\n\tif(*it->multiplier!=1)\n\t\tprint_multiplier(str, it);\n\n\tif(*it->name==\"1\") {\n\t\tif(*it->multiplier==1 || (*it->multiplier==-1)) // this would print nothing altogether.\n\t\t\tstr << \"1\";\n\n\t\tif(needs_brackets(it))\n\t\t\tstr << \")\";\n\t\treturn;\n\t\t}\n\n\t//\tconst Accent *ac=properties.get<Accent>(it);\n\t//\tif(!ac) { // accents should never get additional curly brackets, {\\bar}{g} does not print.\n\t//\t\tEx::sibling_iterator sib=tree.begin(it);\n\t//\t\twhile(sib!=tree.end(it)) {\n\t//\t\t\tif(sib->is_index())\n\t//\t\t\t\tneeds_extra_brackets=true;\n\t//\t\t\t++sib;\n\t//\t\t\t}\n\t//\t\t}\n\n\tauto sbit=*it->name;\n\tif(!use_unicode) {\n\t\tauto rn = regex_map.find(sbit);\n\t\tif(rn!=regex_map.end())\n\t\t\tsbit = rn->second;\n\t\t}\n\tauto rn = symmap.find(sbit);\n\tif(rn!=symmap.end())\n\t\tstr << rn->second;\n\telse\n\t\tstr << sbit;\n\n\tprint_children(str, it);\n\n\tif(needs_brackets(it))\n\t\tstr << \")\";\n\t}\n\nvoid DisplayMMA::print_children(std::ostream& str, Ex::iterator it, int )\n\t{\n\t// Mathematica has no notion of children with different parent relations; it's all\n\t// functions of functions kind of stuff. What we will do is print upper and\n\t// lower indices as 'UP(..)' and 'DN(..)' type arguments, and then convert\n\t// them back later.\n\n\t// We need to know if the symbol has implicit dependence on other symbols,\n\t// as this needs to be made explicit for sympy. We need to strip this\n\t// dependence off later again.\n\n\tconst Depends *dep=kernel.properties.get<Depends>(it);\n\tif(dep) {\n\t\tdepsyms[it->name]=dep->dependencies(kernel, it);\n\t\t//\t\tstd::cerr << *it->name << \"depends on \" << depsyms[it->name] << std::endl;\n\t\t}\n\n\tEx::sibling_iterator ch=tree.begin(it);\n\tif(ch!=tree.end(it) || dep!=0) {\n\t\tstr << \"[\";\n\t\tbool first=true;\n\t\twhile(ch!=tree.end(it)) {\n\t\t\tif(first) first=false;\n\t\t\telse      str << \", \";\n\t\t\tif(ch->fl.parent_rel==str_node::p_super)\n\t\t\t\tstr << \"UP\";\n\t\t\tif(ch->fl.parent_rel==str_node::p_sub)\n\t\t\t\tstr << \"DN\";\n\n\t\t\tdispatch(str, ch);\n\n\t\t\t//\t\t\tif(ch->fl.parent_rel==str_node::p_super || ch->fl.parent_rel==str_node::p_sub)\n\t\t\t//\t\t\t\tstr << \"]\";\n\t\t\t++ch;\n\t\t\t}\n\t\tif(dep) {\n\t\t\tif(!first) str << \", \";\n\t\t\tEx deplist=dep->dependencies(kernel, it);\n\t\t\t// deplist is always a \\comma node\n\t\t\tauto sib=tree.begin(deplist.begin());\n\t\t\twhile(sib!=tree.end(deplist.begin())) {\n\t\t\t\tdispatch(str, sib);\n\t\t\t\t++sib;\n\t\t\t\tif(sib!=tree.end(deplist.begin()))\n\t\t\t\t\tstr << \", \";\n\t\t\t\t}\n\t\t\t//\n\t\t\t//\t\t\tDisplayMMA ds(kernel, deplist);\n\t\t\t//\t\t\tds.output(str);\n\t\t\t}\n\t\tstr << \"]\";\n\t\t}\n\t}\n\nvoid DisplayMMA::print_multiplier(std::ostream& str, Ex::iterator it)\n\t{\n\tbool suppress_star=false;\n\tif(it->multiplier->is_rational()) {\n\t\tmpz_class denom=it->multiplier->get_rational().get_den();\n\t\tmpz_class numer=it->multiplier->get_rational().get_num();\n\t\t\n\t\tif(denom!=1) {\n\t\t\tif(false && numer<0)\n\t\t\t\tstr << \"(\" << numer << \")\";\n\t\t\telse\n\t\t\t\tstr << numer;\n\t\t\tstr << \"/\" << denom;\n\t\t\t}\n\t\telse if(*it->multiplier==-1) {\n\t\t\tstr << \"-\";\n\t\t\tsuppress_star=true;\n\t\t\t}\n\t\telse {\n\t\t\tstr << *it->multiplier;\n\t\t\t}\n\t\t}\n\telse {\n\t\tstr << it->multiplier->get_double();\n\t\t}\n\t\n\tif(!suppress_star && !(*it->name==\"1\"))\n\t\tstr << \"*\";\n\t}\n\nvoid DisplayMMA::print_opening_bracket(std::ostream& str, str_node::bracket_t br)\n\t{\n\tswitch(br) {\n\t\tcase str_node::b_pointy:\n\t\tcase str_node::b_curly:\n\t\t\tthrow NotYetImplemented(\"curly/pointy bracket type\");\n\t\tcase str_node::b_none:\n\t\t\tstr << \"[\";\n\t\t\tbreak;\n\t\tcase str_node::b_round:\n\t\t\tstr << \"[\";\n\t\t\tbreak;\n\t\tcase str_node::b_square:\n\t\t\tstr << \"[\";\n\t\t\tbreak;\n\t\tdefault :\n\t\t\treturn;\n\t\t}\n\t}\n\nvoid DisplayMMA::print_closing_bracket(std::ostream& str, str_node::bracket_t br)\n\t{\n\tswitch(br) {\n\t\tcase str_node::b_pointy:\n\t\tcase str_node::b_curly:\n\t\t\tthrow NotYetImplemented(\"curly/pointy bracket type\");\n\t\tcase str_node::b_none:\n\t\t\tstr << \"]\";\n\t\t\tbreak;\n\t\tcase str_node::b_round:\n\t\t\tstr << \"]\";\n\t\t\tbreak;\n\t\tcase str_node::b_square:\n\t\t\tstr << \"]\";\n\t\t\tbreak;\n\t\tdefault :\n\t\t\treturn;\n\t\t}\n\t}\n\nvoid DisplayMMA::print_parent_rel(std::ostream& str, str_node::parent_rel_t pr, bool )\n\t{\n\tswitch(pr) {\n\t\tcase str_node::p_super:\n\t\tcase str_node::p_sub:\n\t\t\tthrow NotYetImplemented(\"MMA print of indices\");\n\t\tcase str_node::p_property:\n\t\t\tthrow NotYetImplemented(\"MMA print of properties\");\n\t\tcase str_node::p_exponent:\n\t\t\tstr << \"^\";\n\t\t\tbreak;\n\t\tcase str_node::p_none:\n\t\t\tbreak;\n\t\tcase str_node::p_components:\n\t\t\tbreak;\n\t\tcase str_node::p_invalid:\n\t\t\tthrow std::logic_error(\"DisplayMMA: p_invalid not handled.\");\n\t\t}\n\t}\n\nvoid DisplayMMA::dispatch(std::ostream& str, Ex::iterator it)\n\t{\n\t// The node names below should only be reserved node names; all others\n\t// should be looked up using properties. FIXME\n\tif(*it->name==\"\\\\prod\")        print_productlike(str, it, \"*\");\n\telse if(*it->name==\"\\\\sum\")    print_sumlike(str, it);\n\telse if(*it->name==\"\\\\frac\")   print_fraclike(str, it);\n\telse if(*it->name==\"\\\\comma\")  print_commalike(str, it);\n\telse if(*it->name==\"\\\\arrow\")  print_arrowlike(str, it);\n\telse if(*it->name==\"\\\\pow\")    print_powlike(str, it);\n\telse if(*it->name==\"\\\\int\")    print_intlike(str, it);\n\telse if(*it->name==\"\\\\sum\")    print_intlike(str, it);\n\telse if(*it->name==\"\\\\equals\") print_equalitylike(str, it);\n\telse if(*it->name==\"\\\\components\") print_components(str, it);\n\telse if(*it->name==\"\\\\partial\") print_partial(str, it);\n\telse if(*it->name==\"\\\\matrix\") print_matrix(str, it);\n\telse                           print_other(str, it);\n\t}\n\nvoid DisplayMMA::print_commalike(std::ostream& str, Ex::iterator it)\n\t{\n\tEx::sibling_iterator sib=tree.begin(it);\n\tbool first=true;\n\tstr << \"{\";\n\twhile(sib!=tree.end(it)) {\n\t\tif(first)\n\t\t\tfirst=false;\n\t\telse\n\t\t\tstr << \", \";\n\t\tdispatch(str, sib);\n\t\t++sib;\n\t\t}\n\tstr << \"}\";\n\t//print_closing_bracket(str, (*it).fl.bracket, str_node::p_none);\n\t}\n\nvoid DisplayMMA::print_arrowlike(std::ostream& str, Ex::iterator it)\n\t{\n\tEx::sibling_iterator sib=tree.begin(it);\n\tdispatch(str, sib);\n\tstr << \" -> \";\n\t++sib;\n\tdispatch(str, sib);\n\t}\n\nvoid DisplayMMA::print_fraclike(std::ostream& str, Ex::iterator it)\n\t{\n\tEx::sibling_iterator num=tree.begin(it), den=num;\n\t++den;\n\n\tif(*it->multiplier!=1) {\n\t\tprint_multiplier(str, it);\n\t\t}\n\tdispatch(str, num);\n\n\tstr << \"/(\";\n\n\tdispatch(str, den);\n\n\tstr << \")\";\n\t}\n\nvoid DisplayMMA::print_productlike(std::ostream& str, Ex::iterator it, const std::string& inbetween)\n\t{\n\tif(needs_brackets(it))\n\t\tstr << \"(\";\n\n\tif(*it->multiplier!=1) {\n\t\tprint_multiplier(str, it);\n\t\t//\t\tEx::sibling_iterator st=tree.begin(it);\n\t\t}\n\n\t// To print \\prod{\\sum{a}{b}}{\\sum{c}{d}} correctly:\n\t// If there is any sum as child, and if the sum children do not\n\t// all have the same bracket type (different from b_none or b_no),\n\t// then print brackets.\n\n\tstr_node::bracket_t previous_bracket_=str_node::b_invalid;\n//\tbool beginning_of_group=true;\n\tEx::sibling_iterator ch=tree.begin(it);\n\twhile(ch!=tree.end(it)) {\n\t\tstr_node::bracket_t current_bracket_=(*ch).fl.bracket;\n\t\tif(previous_bracket_!=current_bracket_) {\n\t\t\tif(current_bracket_!=str_node::b_none) {\n\t\t\t\tprint_opening_bracket(str, current_bracket_);\n//\t\t\t\tbeginning_of_group=true;\n\t\t\t\t}\n\t\t\t}\n\t\tdispatch(str, ch);\n\t\t++ch;\n\t\tif(ch==tree.end(it)) {\n\t\t\tif(current_bracket_!=str_node::b_none)\n\t\t\t\tprint_closing_bracket(str, current_bracket_);\n\t\t\t}\n\n\t\tif(ch!=tree.end(it)) {\n\t\t\tstr << inbetween;\n\t\t\t}\n\t\tprevious_bracket_=current_bracket_;\n\t\t}\n\n\tif(needs_brackets(it))\n\t\tstr << \")\";\n\t//\tif(close_bracket) str << \")\";\n\t}\n\nvoid DisplayMMA::print_sumlike(std::ostream& str, Ex::iterator it)\n\t{\n\tassert(*it->multiplier==1);\n\n\tif(needs_brackets(it))\n\t\tstr << \"(\";\n\n\tunsigned int steps=0;\n\n\tEx::sibling_iterator ch=tree.begin(it);\n\twhile(ch!=tree.end(it)) {\n\t\tif(++steps==20) {\n\t\t\tsteps=0;\n\t\t\t}\n\t\tif(*ch->multiplier>=0 && ch!=tree.begin(it))\n\t\t\tstr << \"+\";\n\n\t\tdispatch(str, ch);\n\t\t++ch;\n\t\t}\n\n\tif(needs_brackets(it))\n\t\tstr << \")\";\n\tstr << std::flush;\n\t}\n\nvoid DisplayMMA::print_powlike(std::ostream& str, Ex::iterator it)\n\t{\n\tif(needs_brackets(it))\n\t\tstr << \"(\";\n\n\tEx::sibling_iterator sib=tree.begin(it);\n\tif(*it->multiplier!=1)\n\t\tprint_multiplier(str, it);\n\tdispatch(str, sib);\n\tstr << \"^(\";\n\t++sib;\n\tdispatch(str, sib);\n\tstr << \")\";\n\n\tif(needs_brackets(it))\n\t\tstr << \")\";\n\t}\n\nvoid DisplayMMA::print_intlike(std::ostream& str, Ex::iterator it)\n\t{\n\tif(*it->multiplier!=1)\n\t\tprint_multiplier(str, it);\n\tstr << symmap[*it->name] << \"[\";\n\tEx::sibling_iterator sib=tree.begin(it);\n\tdispatch(str, sib);\n\t++sib;\n\tif(tree.is_valid(sib)) {\n\t\tstr << \", \";\n\t\tdispatch(str, sib);\n\t\t}\n\tstr << \"]\";\n\t}\n\nvoid DisplayMMA::print_equalitylike(std::ostream& str, Ex::iterator it)\n\t{\n\tEx::sibling_iterator sib=tree.begin(it);\n\tdispatch(str, sib);\n\tstr << \" == \";\n\t++sib;\n\tif(sib==tree.end(it))\n\t\tthrow ConsistencyException(\"Found equals node with only one child node.\");\n\tdispatch(str, sib);\n\t}\n\nvoid DisplayMMA::print_components(std::ostream& str, Ex::iterator it)\n\t{\n\tstr << *it->name;\n\tauto sib=tree.begin(it);\n\tauto end=tree.end(it);\n\t--end;\n\twhile(sib!=end) {\n\t\tdispatch(str, sib);\n\t\t++sib;\n\t\t}\n\tstr << \"\\n\";\n\tsib=tree.begin(end);\n\twhile(sib!=tree.end(end)) {\n\t\tstr << \"    \";\n\t\tdispatch(str, sib);\n\t\tstr << \"\\n\";\n\t\t++sib;\n\t\t}\n\t}\n\nvoid DisplayMMA::print_partial(std::ostream& str, Ex::iterator it)\n\t{\n\tif(*it->multiplier!=1)\n\t\tprint_multiplier(str, it);\n\n\tstr << \"D[\";\n\tEx::sibling_iterator sib=tree.begin(it);\n\twhile(sib!=tree.end(it)) {\n\t\tif(sib->fl.parent_rel==str_node::p_none) {\n\t\t\tdispatch(str, sib);\n\t\t\tbreak;\n\t\t\t}\n\t\t++sib;\n\t\t}\n\tsib=tree.begin(it);\n\twhile(sib!=tree.end(it)) {\n\t\tif(sib->fl.parent_rel!=str_node::p_none) {\n\t\t\tstr << \", \";\n\t\t\tdispatch(str, sib);\n\t\t\t}\n\t\t++sib;\n\t\t}\n\tstr << \"]\";\n\t}\n\nvoid DisplayMMA::print_matrix(std::ostream& str, Ex::iterator it)\n\t{\n\tstr << \"Matrix([\";\n\tauto comma=tree.begin(it);\n\tEx::sibling_iterator row_it = tree.begin(comma);\n\twhile(row_it!=tree.end(comma)) {\n\t\tif(row_it!=tree.begin(comma)) str << \", \";\n\t\tEx::sibling_iterator col_it = tree.begin(row_it);\n\t\tstr << \"[\";\n\t\twhile(col_it!=tree.end(row_it)) {\n\t\t\tif(col_it!=tree.begin(row_it)) str << \", \";\n\t\t\tdispatch(str, col_it);\n\t\t\t++col_it;\n\t\t\t}\n\t\tstr << \"]\";\n\t\t++row_it;\n\t\t}\n\tstr << \"])\";\n\t}\n\nbool DisplayMMA::children_have_brackets(Ex::iterator ch) const\n\t{\n\tEx::sibling_iterator chlds=tree.begin(ch);\n\tstr_node::bracket_t childbr=chlds->fl.bracket;\n\tif(childbr==str_node::b_none || childbr==str_node::b_no)\n\t\treturn false;\n\telse return true;\n\t}\n\nstd::string DisplayMMA::preparse_import(const std::string& in)\n\t{\n\tstd::string ret = in;\n\t// MMA sends doubled backslash characters, reduce them first.\n\tret = replace_all(ret, \"\\\\\\\\\", \"\\\\\");\n\tfor(auto& r: regex_map) {\n\t\tret = replace_all(ret, r.second, r.first);\n\t\t}\n\treturn ret;\n\t}\n\nvoid DisplayMMA::import(Ex& ex)\n\t{\n\tcadabra::do_subtree<Ex>(ex, ex.begin(), [&](Ex::iterator it) -> Ex::iterator {\n\t\t// Mathematica wraps everything in square brackets, set these to\n\t\t// b_none;\n\t\tit->fl.bracket=str_node::b_none;\n\n\t\t// Convert symbols.\n\t\tfor(auto& m: symmap)\n\t\t\t{\n\t\t\t// If we have converted the name of this symbol, convert back.\n\t\t\tif(m.second==*it->name) {\n\t\t\t\tit->name=name_set.insert(m.first).first;\n\t\t\t\tbreak;\n\t\t\t\t}\n\t\t\t}\n\n\t\t// Move child nodes of partial to the right place.\n\t\t// We have to fix the notation for Derivative. A derivative\n\t\t// of the type\n\t\t//    \\partial_{r t t}{f}\n\t\t// gets produced as\n\t\t//    Derivative[1][2][f][r][t]\n\t\t// which at first instance reads\n\t\t//    \\partial{1}{2}{f}{r}{t}\n\t\t// This is even true for simple 1st order derivatives.\n\t\t// For 'm' arguments, we have '(m-1)/2' variables.\n\t\t\n\t\tif(*it->name==\"\\\\partial\")\n\t\t\t{\n//\t\t\tstd::cerr << \"to convert: \" << Ex(it) << std::endl;\n\t\t\tint n=ex.number_of_children(it);\n\t\t\tif(n<3 || n%2!=1)\n\t\t\t\tthrow ConsistencyException(\"Returned unparseable derivative.\");\n\t\t\t\n\t\t\tn=(n-1)/2;\n\t\t\tstd::vector<int> nums;\n\t\t\tauto args = ex.begin(it);\n\t\t\tfor(int i=0; i<n; ++i) {\n\t\t\t\tnums.push_back( to_long(*(args->multiplier)) );\n\t\t\t\targs=ex.erase(args);\n\t\t\t\t}\n\n\t\t\targs=ex.begin(it);\n\t\t\t++args;\n\t\t\tint p=0;\n\t\t\twhile(args!=ex.end(it)) {\n\t\t\t\tauto nxt=args;\n\t\t\t\t++nxt;\n\t\t\t\tfor(int i=0; i<nums[p]; ++i)\n\t\t\t\t\tex.insert_subtree(ex.begin(it), args)->fl.parent_rel=str_node::p_sub;\n\t\t\t\targs=ex.erase(args);\n\t\t\t\t++p;\n\t\t\t\t}\n\t\t\t}\n\n\t\t// See if we have added dependencies to this symbol (lookup in map).\n\t\t// If yes, strip them off again.\n\t\tauto fnd = depsyms.find(it->name);\n\t\tif(fnd!=depsyms.end())\n\t\t\t{\n\t\t\tauto args=ex.begin(it);\n\t\t\t// Strip out only those symbols which have been added.\n\t\t\twhile(args!=ex.end(it)) {\n\t\t\t\tif(args->fl.parent_rel==str_node::p_none) {\n\t\t\t\t\tauto findsib=fnd->second.begin(fnd->second.begin());\n\t\t\t\t\tbool removed=false;\n\t\t\t\t\twhile(findsib!=fnd->second.end(fnd->second.begin())) {\n\t\t\t\t\t\tif(subtree_equal(0, findsib, args)) {\n\t\t\t\t\t\t\targs=ex.erase(args);\n\t\t\t\t\t\t\tremoved=true;\n\t\t\t\t\t\t\tbreak;\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\t++findsib;\n\t\t\t\t\t\t}\n\t\t\t\t\tif(!removed)\n\t\t\t\t\t\t++args;\n\t\t\t\t\t}\n\t\t\t\telse\n\t\t\t\t\t++args;\n\t\t\t\t}\n\t\t\t//\t\t\t\tstd::cerr << \"stripping from \" << *it->name << std::endl;\n\t\t\t////\t\t\t\tif(*ex.begin(it)->name==\"\\\\comma\")\n\t\t\t//\t\t\t\tex.erase(ex.begin(it));\n\t\t\t}\n\n\n\t\treturn it;\n\t\t});\n\t}\n"
  },
  {
    "path": "core/DisplayMMA.hh",
    "content": "\n#pragma once\n\n#include \"DisplayBase.hh\"\n#include <ostream>\n#include <map>\n#include <set>\n\ntypedef uint32_t kunichar;\n\nnamespace cadabra {\n\n\t/// \\ingroup display\n\t///\n\t/// Class to display expressions in a format that Mathematica can\n\t/// parse. Will throw an exception if a Cadabra Ex object cannot be\n\t/// understood by Mathematica. Can also convert expressions back to\n\t/// Cadabra notation.\n\n\tclass DisplayMMA : public DisplayBase {\n\t\tpublic:\n\t\t\tDisplayMMA(const Kernel&, const Ex&, bool use_unicode = true);\n\n\t\t\t/// Rewrite the output of mathematica back into a notation used by\n\t\t\t/// Cadabra. This in particular involves converting 'Sin' and\n\t\t\t/// friends to `\\sin` and so on, as well as converting all the\n\t\t\t/// greek symbols.  Currently only acts node-by-node, does not\n\t\t\t/// do anything complicated with trees.\n\n\t\t\tvoid import(Ex&);\n\n\t\t\tstd::string preparse_import(const std::string&);\n\n\t\tprotected:\n\t\t\tbool use_unicode;\n\n\t\t\tvirtual bool needs_brackets(Ex::iterator it) override;\n\n\t\tprivate:\n\t\t\t/// Output the expression to a mathematica-readable form. For symbols\n\t\t\t/// which cannot be parsed by mathematica, this can convert to an\n\t\t\t/// alternative, Such rewrites can then be undone by the\n\t\t\t/// 'import' member above.\n\n\t\t\tvoid print_multiplier(std::ostream&, Ex::iterator);\n\t\t\tvoid print_opening_bracket(std::ostream&, str_node::bracket_t);\n\t\t\tvoid print_closing_bracket(std::ostream&, str_node::bracket_t);\n\t\t\tvoid print_parent_rel(std::ostream&, str_node::parent_rel_t, bool first);\n\t\t\tvoid print_children(std::ostream&, Ex::iterator, int skip=0);\n\n\n\t\t\t/// For every object encountered, dispatch will figure out the\n\t\t\t/// most appropriate way to convert it into a LaTeX\n\t\t\t/// expression. This may be done by simply looking at the\n\t\t\t/// object's name (e.g. `\\prod` will print as a product) but may\n\t\t\t/// also involve looking up properties and deciding on the best\n\t\t\t/// course of action based on the attached properties.\n\n\t\t\tvirtual void dispatch(std::ostream&, Ex::iterator) override;\n\n\t\t\t/// Printing members for various standard constructions,\n\t\t\t/// e.g. print as a list, or as a decorated symbol with\n\t\t\t/// super/subscripts etc. The names reflect the structure of the\n\t\t\t/// output, not necessarily the meaning or name of the object\n\t\t\t/// that is being printed.\n\n\t\t\tvoid print_productlike(std::ostream&, Ex::iterator, const std::string& inbetween);\n\t\t\tvoid print_sumlike(std::ostream&, Ex::iterator);\n\t\t\tvoid print_fraclike(std::ostream&, Ex::iterator);\n\t\t\tvoid print_commalike(std::ostream&, Ex::iterator);\n\t\t\tvoid print_arrowlike(std::ostream&, Ex::iterator);\n\t\t\tvoid print_powlike(std::ostream&, Ex::iterator);\n\t\t\tvoid print_intlike(std::ostream&, Ex::iterator);\n\t\t\tvoid print_equalitylike(std::ostream&, Ex::iterator);\n\t\t\tvoid print_components(std::ostream&, Ex::iterator);\n\t\t\tvoid print_partial(std::ostream& str, Ex::iterator it);\n\t\t\tvoid print_matrix(std::ostream& str, Ex::iterator it);\n\t\t\tvoid print_other(std::ostream& str, Ex::iterator it);\n\n\t\t\tbool children_have_brackets(Ex::iterator ch) const;\n\n\t\t\t/// Map from Cadabra symbols to Mathematica symbols.\n\t\t\t/// This is a bit tricky because MathLink does not pass\n\t\t\t/// `\\[Alpha]` and friends transparently. So we feed it UTF8\n\t\t\t/// α and so on, but then we get `\\[Alpha]` back, and that\n\t\t\t/// needs to be regex-replaced before we feed it to our\n\t\t\t/// parser as ours does not swallow that kind of bracketing.\n\t\t\tstd::map<std::string, std::string>      symmap;\n\t\t\tstd::multimap<std::string, std::string> regex_map;\n\n\t\t\t/// Map from symbols which have had dependencies added\n\t\t\t/// to an expression containing these dependencies.\n\t\t\tstd::map<nset_t::iterator, Ex, nset_it_less> depsyms;\n\t\t};\n\n\tconst char *unichar(kunichar c);\n\n\t}\n"
  },
  {
    "path": "core/DisplaySympy.cc",
    "content": "\n#include \"Algorithm.hh\"\n#include \"Functional.hh\"\n#include \"DisplaySympy.hh\"\n#include \"properties/Depends.hh\"\n#include \"properties/Accent.hh\"\n#include \"Exceptions.hh\"\n#include \"properties/Derivative.hh\"\n#include <regex>\n\n// #define DEBUG __FILE__\n#include \"Debug.hh\"\n\nusing namespace cadabra;\n\nDisplaySympy::DisplaySympy(const Kernel& kernel, const Ex& e)\n\t: DisplayBase(kernel, e)\n\t{\n\tsymmap = {\n\t\t\t{\"\\\\cos\", \"cos\"},\n\t\t\t{\"\\\\sin\", \"sin\"},\n\t\t\t{\"\\\\tan\", \"tan\"},\n\t\t\t{\"\\\\arccos\", \"acos\"},\n\t\t\t{\"\\\\arcsin\", \"asin\"},\n\t\t\t{\"\\\\arctan\", \"atan\"},\n\t\t\t{\"\\\\cosh\", \"cosh\"},\n\t\t\t{\"\\\\sinh\", \"sinh\"},\n\t\t\t{\"\\\\tanh\", \"tanh\"},\n         {\"\\\\coth\", \"coth\"},\n         {\"\\\\sech\", \"sech\"},\n         {\"\\\\csch\", \"csch\"},\n\t\t\t{\"\\\\arccosh\", \"acosh\"},\n\t\t\t{\"\\\\arcsinh\", \"asinh\"},\n\t\t\t{\"\\\\arctanh\", \"atanh\"},\n         {\"\\\\arccoth\", \"acoth\"},\n         {\"\\\\arcsech\", \"asech\"},\n         {\"\\\\arccsch\", \"acsch\"},\n\t\t\t{\"\\\\log\", \"log\"},\n\t\t\t{\"\\\\int\", \"integrate\" },\n\t\t\t{\"\\\\matrix\", \"Matrix\" },\n\t\t\t{\"\\\\sum\", \"Sum\" },\n\t\t\t{\"\\\\exp\", \"exp\" },\n\t\t\t{\"\\\\sqrt\", \"sqrt\" },\n\t\t\t{\"\\\\equals\", \"Eq\" },\n\n\t\t\t{\"\\\\infty\", \"oo\"},\n\t\t\t{\"\\\\hbar\",   \"hbar\"},\n\n\t\t\t{\"\\\\alpha\",   \"alpha\" },\n\t\t\t{\"\\\\beta\",    \"bbeta\" },  // beta seems to be reserved\n\t\t\t{\"\\\\gamma\",   \"ggamma\" }, // gamma seems to be reserved\n\t\t\t{\"\\\\delta\",   \"delta\" },\n\t\t\t{\"\\\\epsilon\", \"epsilon\" },\n\t\t\t{\"\\\\zeta\",    \"zeta\" },\n\t\t\t{\"\\\\eta\",     \"eta\" },\n\t\t\t{\"\\\\theta\",   \"theta\" },\n\t\t\t{\"\\\\iota\",    \"iota\" },\n\t\t\t{\"\\\\kappa\",   \"kappa\" },\n\t\t\t{\"\\\\lambda\",  \"lamda\" }, // lambda is reserved\n\t\t\t{\"\\\\mu\",      \"mu\" },\n\t\t\t{\"\\\\nu\",      \"nu\" },\n\t\t\t{\"\\\\xi\",      \"xi\" },\n\t\t\t{\"\\\\omicron\", \"omicron\" },\n\t\t\t{\"\\\\pi\",      \"pi\" },\n\t\t\t{\"\\\\rho\",     \"rho\" },\n\t\t\t{\"\\\\sigma\",   \"sigma\" },\n\t\t\t{\"\\\\tau\",     \"tau\" },\n\t\t\t{\"\\\\upsilon\", \"upsilon\" },\n\t\t\t{\"\\\\phi\",     \"phi\" },\n\t\t\t{\"\\\\varphi\",  \"varphi\" },\n\t\t\t{\"\\\\chi\",     \"chi\" },\n\t\t\t{\"\\\\psi\",     \"psi\" },\n\t\t\t{\"\\\\omega\",   \"omega\" },\n\n\t\t\t{\"\\\\Alpha\",   \"Alpha\" },\n\t\t\t{\"\\\\Beta\",    \"Beta\" },\n\t\t\t{\"\\\\Gamma\",   \"Gamma\" },\n\t\t\t{\"\\\\Delta\",   \"Delta\" },\n\t\t\t{\"\\\\Epsilon\", \"Epsilon\" },\n\t\t\t{\"\\\\Zeta\",    \"Zeta\" },\n\t\t\t{\"\\\\Eta\",     \"Eta\" },\n\t\t\t{\"\\\\Theta\",   \"Theta\" },\n\t\t\t{\"\\\\Iota\",    \"Iota\" },\n\t\t\t{\"\\\\Kappa\",   \"Kappa\" },\n\t\t\t{\"\\\\Lambda\",  \"Lamda\" },\n\t\t\t{\"\\\\Mu\",      \"Mu\" },\n\t\t\t{\"\\\\Nu\",      \"Nu\" },\n\t\t\t{\"\\\\Xi\",      \"Xi\" },\n\t\t\t{\"\\\\Omicron\", \"Omicron\" },\n\t\t\t{\"\\\\Pi\",      \"Pi\" },\n\t\t\t{\"\\\\Rho\",     \"Rho\" },\n\t\t\t{\"\\\\Sigma\",   \"Sigma\" },\n\t\t\t{\"\\\\Tau\",     \"Tau\" },\n\t\t\t{\"\\\\Upsilon\", \"Upsilon\" },\n\t\t\t{\"\\\\Phi\",     \"Phi\" },\n\t\t\t{\"\\\\Chi\",     \"Chi\" },\n\t\t\t{\"\\\\Psi\",     \"Psi\" },\n\t\t\t{\"\\\\Omega\",   \"Omega\" },\n\n\t\t\t{\"\\\\partial\", \"Derivative\"},\n\t\t\t{\"\\\\dot\",     \"dot\"},\n\t\t\t{\"\\\\ddot\",    \"ddot\"},\n\n\t\t\t{\"\\\\Im\",      \"im\"},\n\t\t\t{\"\\\\Re\",      \"re\"},\n\n\t\t// A few symbols are reserved by sympy.\n\t\t\t{\"N\", \"sympyN\"},\n\t\t\t{\"O\", \"sympyO\"},\n\t\t\t{\"S\", \"sympyS\"},\n\t\t\t{\"Q\", \"sympyQ\"}\n\t\t};\n\n\tregex_map = {\n\t\t\t{\"Integral\",   \"\\\\int\"   }\n\t\t};\n\n\t}\n\n//TODO: complete this list (take from Sympy)\n\nbool DisplaySympy::needs_brackets(Ex::iterator it)\n\t{\n\t// FIXME: may need looking at properties\n\t// FIXME: write as individual parent/current tests\n\tif(tree.is_head(it)) return false;\n\n\tstd::string parent=*tree.parent(it)->name;\n\tstd::string child =*it->name;\n\n\tif(parent==\"\\\\prod\" || parent==\"\\\\frac\" || parent==\"\\\\pow\") {\n\t\tif(parent==\"\\\\pow\" && *it->multiplier<0) return true;\n\t\tif(child==\"\\\\sum\") return true;\n\t\tif(parent==\"\\\\pow\" && ( (tree.index(it)==0 && !it->is_integer()) || child==\"\\\\sum\" || child==\"\\\\prod\" || child==\"\\\\pow\")  ) return true;\n\t\t}\n\telse if(it->fl.parent_rel==str_node::p_none) {\n\t\tif(*it->name==\"\\\\sum\") return false;\n\t\t}\n\telse {\n\t\tif(*it->name==\"\\\\sum\")  return true;\n\t\tif(*it->name==\"\\\\prod\") return true;\n\t\t}\n\treturn false;\n\t}\n\n\nvoid DisplaySympy::print_other(std::ostream& str, Ex::iterator it)\n\t{\n\tif(needs_brackets(it))\n\t\tstr << \"(\";\n\n\t// print multiplier and object name\n\tif(*it->multiplier!=1)\n\t\tprint_multiplier(str, it);\n\n\tif(*it->name==\"1\") {\n\t\tif(*it->multiplier==1 || (*it->multiplier==-1)) // this would print nothing altogether.\n\t\t\tstr << \"1\";\n\n\t\tif(needs_brackets(it))\n\t\t\tstr << \")\";\n\t\treturn;\n\t\t}\n\n\t//\tconst Accent *ac=properties.get<Accent>(it);\n\t//\tif(!ac) { // accents should never get additional curly brackets, {\\bar}{g} does not print.\n\t//\t\tEx::sibling_iterator sib=tree.begin(it);\n\t//\t\twhile(sib!=tree.end(it)) {\n\t//\t\t\tif(sib->is_index())\n\t//\t\t\t\tneeds_extra_brackets=true;\n\t//\t\t\t++sib;\n\t//\t\t\t}\n\t//\t\t}\n\n\tauto rn = symmap.find(*it->name);\n\tif(rn!=symmap.end())\n\t\tstr << rn->second;\n\telse\n\t\tstr << *it->name;\n\n\tprint_children(str, it);\n\n\tif(needs_brackets(it))\n\t\tstr << \")\";\n\t}\n\nvoid DisplaySympy::print_children(std::ostream& str, Ex::iterator it, int )\n\t{\n\t// Sympy has no notion of children with different parent relations; it's all\n\t// functions of functions kind of stuff. What we will do is print upper and\n\t// lower indices as 'UP(..)' and 'DN(..)' type arguments, and then convert\n\t// them back later.\n\n\t// We need to know if the symbol has implicit dependence on other symbols,\n\t// as this needs to be made explicit for sympy. We need to strip this\n\t// dependence off later again.\n\n\tconst Depends *dep=kernel.properties.get<Depends>(it);\n\tif(dep) {\n\t\tdepsyms[it->name]=dep->dependencies(kernel, it);\n\t\t//\t\tstd::cerr << *it->name << \"depends on \" << depsyms[it->name] << std::endl;\n\t\t}\n\n\tEx::sibling_iterator ch=tree.begin(it);\n\tif(ch!=tree.end(it) || dep!=0) {\n\t\tstr << \"(\";\n\t\tbool first=true;\n\t\twhile(ch!=tree.end(it)) {\n\t\t\tif(first) first=false;\n\t\t\telse      str << \", \";\n\t\t\tif(ch->fl.parent_rel==str_node::p_super)\n\t\t\t\tstr << \"UP\";\n\t\t\tif(ch->fl.parent_rel==str_node::p_sub)\n\t\t\t\tstr << \"DN\";\n\n\t\t\tdispatch(str, ch);\n\n\t\t\t//\t\t\tif(ch->fl.parent_rel==str_node::p_super || ch->fl.parent_rel==str_node::p_sub)\n\t\t\t//\t\t\t\tstr << \")\";\n\t\t\t++ch;\n\t\t\t}\n\t\tif(dep) {\n\t\t\tif(!first) str << \", \";\n\t\t\tEx deplist=dep->dependencies(kernel, it);\n\t\t\t// deplist is always a \\comma node\n\t\t\tauto sib=tree.begin(deplist.begin());\n\t\t\twhile(sib!=tree.end(deplist.begin())) {\n\t\t\t\tconst Derivative *dep_is_derivative=kernel.properties.get<Derivative>(sib);\n\t\t\t\tif(dep_is_derivative)\n\t\t\t\t\tthrow RuntimeException(\"Dependencies on derivatives are not yet handled in the SymPy bridge\");\n\t\t\t\tdispatch(str, sib);\n\t\t\t\t++sib;\n\t\t\t\tif(sib!=tree.end(deplist.begin()))\n\t\t\t\t\tstr << \", \";\n\t\t\t\t}\n\t\t\t//\n\t\t\t//\t\t\tDisplaySympy ds(kernel, deplist);\n\t\t\t//\t\t\tds.output(str);\n\t\t\t}\n\t\tstr << \")\";\n\t\t}\n\t}\n\nvoid DisplaySympy::print_multiplier(std::ostream& str, Ex::iterator it)\n\t{\n\tbool suppress_star=false;\n\tif(it->multiplier->is_rational()) {\n\t\tmpq_class q = it->multiplier->get_rational();\n\t\tmpz_class denom=q.get_den();\n\t\tmpz_class numer=q.get_num();\n\n\t\tif(denom!=1) {\n\t\t\tif(false && numer<0)\n\t\t\t\tstr << \"(\" << numer << \")\";\n\t\t\telse\n\t\t\t\tstr << numer;\n\t\t\tstr << \"/\" << denom;\n\t\t\t}\n\t\telse if(*it->multiplier==-1) {\n\t\t\tstr << \"-\";\n\t\t\tsuppress_star=true;\n\t\t\t}\n\t\telse {\n\t\t\tstr << *it->multiplier;\n\t\t\t}\n\t\t}\n\telse {\n\t\tstr << it->multiplier->get_double();\n\t\t}\n\n\tif(!suppress_star && !(*it->name==\"1\"))\n\t\tstr << \"*\";\n\t}\n\nvoid DisplaySympy::print_opening_bracket(std::ostream& str, str_node::bracket_t br)\n\t{\n\tswitch(br) {\n\t\tcase str_node::b_none:\n\t\t\tstr << \")\";\n\t\t\tbreak;\n\t\tcase str_node::b_pointy:\n\t\t\tstr << \"\\\\<\";\n\t\t\tbreak;\n\t\tcase str_node::b_curly:\n\t\t\tstr << \"\\\\{\";\n\t\t\tbreak;\n\t\tcase str_node::b_round:\n\t\t\tstr << \"(\";\n\t\t\tbreak;\n\t\tcase str_node::b_square:\n\t\t\tstr << \"[\";\n\t\t\tbreak;\n\t\tdefault :\n\t\t\treturn;\n\t\t}\n\t}\n\nvoid DisplaySympy::print_closing_bracket(std::ostream& str, str_node::bracket_t br)\n\t{\n\tswitch(br) {\n\t\tcase str_node::b_none:\n\t\t\tstr << \")\";\n\t\t\tbreak;\n\t\tcase str_node::b_pointy:\n\t\t\tstr << \"\\\\>\";\n\t\t\tbreak;\n\t\tcase str_node::b_curly:\n\t\t\tstr << \"\\\\}\";\n\t\t\tbreak;\n\t\tcase str_node::b_round:\n\t\t\tstr << \")\";\n\t\t\tbreak;\n\t\tcase str_node::b_square:\n\t\t\tstr << \"]\";\n\t\t\tbreak;\n\t\tdefault :\n\t\t\treturn;\n\t\t}\n\t}\n\nvoid DisplaySympy::print_parent_rel(std::ostream& str, str_node::parent_rel_t pr, bool )\n\t{\n\tswitch(pr) {\n\t\tcase str_node::p_super:\n\t\t\tstr << \"^\";\n\t\t\tbreak;\n\t\tcase str_node::p_sub:\n\t\t\tstr << \"_\";\n\t\t\tbreak;\n\t\tcase str_node::p_property:\n\t\t\tstr << \"$\";\n\t\t\tbreak;\n\t\tcase str_node::p_exponent:\n\t\t\tstr << \"**\";\n\t\t\tbreak;\n\t\tcase str_node::p_none:\n\t\t\tbreak;\n\t\tcase str_node::p_components:\n\t\t\tbreak;\n\t\tcase str_node::p_invalid:\n\t\t\tthrow std::logic_error(\"DisplaySympy: p_invalid not handled.\");\n\t\t}\n\t}\n\nvoid DisplaySympy::dispatch(std::ostream& str, Ex::iterator it)\n\t{\n\tif(std::holds_alternative<std::shared_ptr<NTensor>>(it->content)) {\n\t\tthrow ArgumentException(\"Cannot yet convert NTensor to SymPy expression.\");\n\t\t}\n\telse if(std::holds_alternative<std::shared_ptr<NInterpolatingFunction>>(it->content)) {\n\t\tthrow ArgumentException(\"Cannot yet convert NInterpolatingFunction to SymPy expression.\");\n\t\t}\n\n\tauto der = kernel.properties.get<Derivative>(it);\n\t\n   // The node names below should only be reserved node names; all others\n\t// should be looked up using properties. FIXME\n\tif(*it->name==\"\\\\prod\")        print_productlike(str, it, \"*\");\n\telse if(*it->name==\"\\\\sum\")    print_sumlike(str, it);\n\telse if(*it->name==\"\\\\frac\")   print_fraclike(str, it);\n\telse if(*it->name==\"\\\\comma\")  print_commalike(str, it);\n\telse if(*it->name==\"\\\\arrow\")  print_arrowlike(str, it);\n\telse if(*it->name==\"\\\\pow\")    print_powlike(str, it);\n\telse if(*it->name==\"\\\\int\")    print_intlike(str, it);\n\telse if(*it->name==\"\\\\sum\")    print_intlike(str, it);\n\telse if(*it->name==\"\\\\equals\") print_equalitylike(str, it);\n\telse if(*it->name==\"\\\\components\") print_components(str, it);\n\telse if(*it->name==\"\\\\matrix\") print_matrix(str, it);\n\telse if(der)                   print_derivative(str, it, der);\n\telse                           print_other(str, it);\n\t}\n\nvoid DisplaySympy::print_commalike(std::ostream& str, Ex::iterator it)\n\t{\n\tEx::sibling_iterator sib=tree.begin(it);\n\tbool first=true;\n\tstr << \"[\";\n\twhile(sib!=tree.end(it)) {\n\t\tif(first)\n\t\t\tfirst=false;\n\t\telse\n\t\t\tstr << \", \";\n\t\tdispatch(str, sib);\n\t\t++sib;\n\t\t}\n\tstr << \"]\";\n\t//print_closing_bracket(str, (*it).fl.bracket, str_node::p_none);\n\t}\n\nvoid DisplaySympy::print_arrowlike(std::ostream& str, Ex::iterator it)\n\t{\n\tEx::sibling_iterator sib=tree.begin(it);\n\tstr << \"rule(\";\n\tdispatch(str, sib);\n\tstr << \", \";\n\t++sib;\n\tdispatch(str, sib);\n\tstr << \")\";\n\t}\n\nvoid DisplaySympy::print_fraclike(std::ostream& str, Ex::iterator it)\n\t{\n\tEx::sibling_iterator num=tree.begin(it), den=num;\n\t++den;\n\n\tif(*it->multiplier!=1) {\n\t\tprint_multiplier(str, it);\n\t\t}\n\tdispatch(str, num);\n\n\tstr << \"/(\";\n\n\tdispatch(str, den);\n\n\tstr << \")\";\n\t}\n\nvoid DisplaySympy::print_productlike(std::ostream& str, Ex::iterator it, const std::string& inbetween)\n\t{\n\tif(needs_brackets(it))\n\t\tstr << \"(\";\n\n\tif(*it->multiplier!=1) {\n\t\tprint_multiplier(str, it);\n\t\t//\t\tEx::sibling_iterator st=tree.begin(it);\n\t\t}\n\n\t// To print \\prod{\\sum{a}{b}}{\\sum{c}{d}} correctly:\n\t// If there is any sum as child, and if the sum children do not\n\t// all have the same bracket type (different from b_none or b_no),\n\t// then print brackets.\n\n\tstr_node::bracket_t previous_bracket_=str_node::b_invalid;\n//\tbool beginning_of_group=true;\n\tEx::sibling_iterator ch=tree.begin(it);\n\twhile(ch!=tree.end(it)) {\n\t\tstr_node::bracket_t current_bracket_=(*ch).fl.bracket;\n\t\tif(previous_bracket_!=current_bracket_) {\n\t\t\tif(current_bracket_!=str_node::b_none) {\n\t\t\t\tprint_opening_bracket(str, current_bracket_);\n//\t\t\t\tbeginning_of_group=true;\n\t\t\t\t}\n\t\t\t}\n\t\tdispatch(str, ch);\n\t\t++ch;\n\t\tif(ch==tree.end(it)) {\n\t\t\tif(current_bracket_!=str_node::b_none)\n\t\t\t\tprint_closing_bracket(str, current_bracket_);\n\t\t\t}\n\n\t\tif(ch!=tree.end(it)) {\n\t\t\tstr << inbetween;\n\t\t\t}\n\t\tprevious_bracket_=current_bracket_;\n\t\t}\n\n\tif(needs_brackets(it))\n\t\tstr << \")\";\n\t//\tif(close_bracket) str << \")\";\n\t}\n\nvoid DisplaySympy::print_sumlike(std::ostream& str, Ex::iterator it)\n\t{\n\tassert(*it->multiplier==1);\n\n\tif(needs_brackets(it))\n\t\tstr << \"(\";\n\n\tunsigned int steps=0;\n\n\tEx::sibling_iterator ch=tree.begin(it);\n\twhile(ch!=tree.end(it)) {\n\t\tif(++steps==20) {\n\t\t\tsteps=0;\n\t\t\t}\n\t\tif(*ch->multiplier>=0 && ch!=tree.begin(it))\n\t\t\tstr << \"+\";\n\n\t\tdispatch(str, ch);\n\t\t++ch;\n\t\t}\n\n\tif(needs_brackets(it))\n\t\tstr << \")\";\n\tstr << std::flush;\n\t}\n\nvoid DisplaySympy::print_powlike(std::ostream& str, Ex::iterator it)\n\t{\n\tif(needs_brackets(it))\n\t\tstr << \"(\";\n\n\tEx::sibling_iterator sib=tree.begin(it);\n\tif(*it->multiplier!=1)\n\t\tprint_multiplier(str, it);\n\tdispatch(str, sib);\n\tstr << \"**(\";\n\t++sib;\n\tdispatch(str, sib);\n\tstr << \")\";\n\n\tif(needs_brackets(it))\n\t\tstr << \")\";\n\t}\n\nvoid DisplaySympy::print_intlike(std::ostream& str, Ex::iterator it)\n\t{\n\tif(*it->multiplier!=1)\n\t\tprint_multiplier(str, it);\n\tstr << symmap[*it->name] << \"(\";\n\tEx::sibling_iterator sib=tree.begin(it);\n\tdispatch(str, sib);\n\t++sib;\n\twhile(tree.is_valid(sib)) {\n\t\tstr << \", \";\n\t\tdispatch(str, sib);\n\t\t++sib;\n\t\t}\n\tstr << \")\";\n\t}\n\nvoid DisplaySympy::print_equalitylike(std::ostream& str, Ex::iterator it)\n\t{\n\tstr << \"Eq(\";\n\tEx::sibling_iterator sib=tree.begin(it);\n\tdispatch(str, sib);\n\tstr << \", \";\n\t++sib;\n\tif(sib==tree.end(it))\n\t\tthrow ConsistencyException(\"Found equals node with only one child node.\");\n\tdispatch(str, sib);\n\tstr << \")\";\n\t}\n\nvoid DisplaySympy::print_components(std::ostream& str, Ex::iterator it)\n\t{\n\tstr << *it->name;\n\tauto sib=tree.begin(it);\n\tauto end=tree.end(it);\n\t--end;\n\twhile(sib!=end) {\n\t\tdispatch(str, sib);\n\t\t++sib;\n\t\t}\n\tstr << \"\\n\";\n\tsib=tree.begin(end);\n\twhile(sib!=tree.end(end)) {\n\t\tstr << \"    \";\n\t\tdispatch(str, sib);\n\t\tstr << \"\\n\";\n\t\t++sib;\n\t\t}\n\t}\n\nvoid DisplaySympy::print_derivative(std::ostream& str, Ex::iterator it, const Derivative *der)\n\t{\n\tif(*it->multiplier!=1)\n\t\tprint_multiplier(str, it);\n\n\tstr << \"diff(\";\n\tEx::sibling_iterator sib=tree.begin(it);\n\twhile(sib!=tree.end(it)) {\n\t\tif(sib->fl.parent_rel==str_node::p_none) {\n\t\t\tdispatch(str, sib);\n\t\t\tbreak;\n\t\t\t}\n\t\t++sib;\n\t\t}\n\t// write the implicit direction of the derivative, if any.\n\tconst Derivative *derivative = kernel.properties.get<Derivative>(it);\n\tif(derivative) {\n\t\tDEBUGLN( std::cerr << *it->name << \" is a derivative\" << std::endl; );\n\t\tif(derivative->with_respect_to.size()>0) {\n\t\t\tDEBUGLN( std::cerr << *it->name << \" has coordinates set\" << std::endl; );\n\t\t\tstr << \", \";\n\t\t\tdispatch(str, derivative->with_respect_to.begin());\n\t\t\t}\n\t\t}\n\telse {\n\t\tDEBUGLN( std::cerr << *it->name << \" is NOT a derivative\" << std::endl; );\n\t\t}\n\t\n\t// write the explicit direction(s) of the derivative.\n\tsib=tree.begin(it);\n\twhile(sib!=tree.end(it)) {\n\t\tif(sib->fl.parent_rel!=str_node::p_none) {\n\t\t\tstr << \", \";\n\t\t\tdispatch(str, sib);\n\t\t\t}\n\t\t++sib;\n\t\t}\n\tstr << \")\";\n\t}\n\nvoid DisplaySympy::print_matrix(std::ostream& str, Ex::iterator it)\n\t{\n\tstr << \"Matrix([\";\n\tauto comma=tree.begin(it);\n\tEx::sibling_iterator row_it = tree.begin(comma);\n\twhile(row_it!=tree.end(comma)) {\n\t\tif(row_it!=tree.begin(comma)) str << \", \";\n\t\tEx::sibling_iterator col_it = tree.begin(row_it);\n\t\tstr << \"[\";\n\t\twhile(col_it!=tree.end(row_it)) {\n\t\t\tif(col_it!=tree.begin(row_it)) str << \", \";\n\t\t\tdispatch(str, col_it);\n\t\t\t++col_it;\n\t\t\t}\n\t\tstr << \"]\";\n\t\t++row_it;\n\t\t}\n\tstr << \"])\";\n\t}\n\nbool DisplaySympy::children_have_brackets(Ex::iterator ch) const\n\t{\n\tEx::sibling_iterator chlds=tree.begin(ch);\n\tstr_node::bracket_t childbr=chlds->fl.bracket;\n\tif(childbr==str_node::b_none || childbr==str_node::b_no)\n\t\treturn false;\n\telse return true;\n\t}\n\nstd::string DisplaySympy::preparse_import(const std::string& in)\n\t{\n#ifdef DEBUG\n\tstd::cerr << \"DisplaySympy::preparse_import\" << std::endl;\n#endif\n\tstd::string ret = in;\n\tfor(auto& r: regex_map) {\n#ifdef DEBUG\n\t\tstd::cerr << \"Replacing \" << r.first << \" with \" << r.second << std::endl;\n#endif\n\t\tret = std::regex_replace(ret, std::regex(r.first), r.second);\n\t\t}\n\treturn ret;\n\t}\n\nvoid DisplaySympy::import(Ex& ex)\n\t{\n\tcadabra::do_subtree(ex, ex.begin(), [&](Ex::iterator it) -> Ex::iterator {\n\t\tfor(auto& m: symmap)\n\t\t\t{\n\t\t\t// If we have converted the name of this symbol, convert back.\n\t\t\tif(m.second==*it->name) {\n\t\t\t\tit->name=name_set.insert(m.first).first;\n\t\t\t\tbreak;\n\t\t\t\t}\n\t\t\t}\n\t\t// See if we have added dependencies to this symbol (lookup in map).\n\t\t// If yes, strip them off again.\n\t\tauto fnd = depsyms.find(it->name);\n\t\tif(fnd!=depsyms.end())\n\t\t\t{\n\t\t\tauto args=ex.begin(it);\n\t\t\t// Strip out only those symbols which have been added.\n\t\t\twhile(args!=ex.end(it)) {\n\t\t\t\tif(args->fl.parent_rel==str_node::p_none) {\n\t\t\t\t\tauto findsib=fnd->second.begin(fnd->second.begin());\n\t\t\t\t\tbool removed=false;\n\t\t\t\t\twhile(findsib!=fnd->second.end(fnd->second.begin())) {\n\t\t\t\t\t\tif(subtree_equal(0, findsib, args)) {\n\t\t\t\t\t\t\targs=ex.erase(args);\n\t\t\t\t\t\t\tremoved=true;\n\t\t\t\t\t\t\tbreak;\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\t++findsib;\n\t\t\t\t\t\t}\n\t\t\t\t\tif(!removed)\n\t\t\t\t\t\t++args;\n\t\t\t\t\t}\n\t\t\t\telse\n\t\t\t\t\t++args;\n\t\t\t\t}\n\t\t\t//\t\t\t\tstd::cerr << \"stripping from \" << *it->name << std::endl;\n\t\t\t////\t\t\t\tif(*ex.begin(it)->name==\"\\\\comma\")\n\t\t\t//\t\t\t\tex.erase(ex.begin(it));\n\t\t\t}\n\n\t\t// Move child nodes of partial to the right place.\n\t\tif(*it->name==\"\\\\partial\")\n\t\t\t{\n\t\t\tauto args = ex.begin(it);\n\t\t\t++args;\n\t\t\twhile(args!=ex.end(it)) {\n\t\t\t\tauto nxt=args;\n\t\t\t\t++nxt;\n\t\t\t\tauto loc = ex.move_before(ex.begin(it), args);\n\t\t\t\tloc->fl.parent_rel=str_node::p_sub;\n\n\t\t\t\t// If the argument is \\comma{x}{n} expand this to 'n' arguments 'x'.\n\t\t\t\t// This is to handle Sympy returning 'Derivative(f(x), (x,2))' for the\n\t\t\t\t// 2nd order derivative.\n\n\t\t\t\tif(*loc->name==\"\\\\comma\") {\n#ifdef DEBUG\n\t\t\t\t\tstd::cerr << loc << std::endl;\n#endif\n\t\t\t\t\tauto x=ex.begin(loc);\n\t\t\t\t\tauto n=x;\n\t\t\t\t\t++n;\n\t\t\t\t\tif(! n->is_integer())\n\t\t\t\t\t\tthrow RuntimeException(\"DisplaySympy::import received un-parseable Derivative expression.\");\n\t\t\t\t\tint nn=to_long(*n->multiplier);\n\t\t\t\t\tfor(int k=0; k<nn; ++k)\n\t\t\t\t\t\tex.insert_subtree(loc, x)->fl.parent_rel=str_node::p_sub;\n\t\t\t\t\tex.erase(loc);\n#ifdef DEBUG\n\t\t\t\t\tstd::cerr << it << std::endl;\n#endif\n\t\t\t\t\t}\n\n\n\t\t\t\targs=nxt;\n\t\t\t\t}\n\n\t\t\t// Strip subscripts which are the same as the 'with_respect_to' member of the\n\t\t\t// derivative (if any), as these are implicit in Cadabra. This is tricky, because\n\t\t\t// a multiple derivative with respect to this argument needs to be replaced\n\t\t\t// with a multiple nesting of the derivative operator itself, e.g.\n\t\t\t//   \\partial{\\partial{r}} -> diff(diff(r(t),t),t) -> diff(r(t),t,t)\n\t\t  \n\t\t\tconst Derivative *derivative = kernel.properties.get<Derivative>(it);\n\t\t\tif(derivative) {\n#ifdef DEBUG\n\t\t\t\tstd::cerr << \"is proper derivative\" << std::endl;\n#endif\n\t\t\t\tif(derivative->with_respect_to.size()>0) {\n\t\t\t\t\tauto it_copy=it;\n\t\t\t\t\targs=ex.begin(it_copy);\n\t\t\t\t\tbool first=true;\n\t\t\t\t\twhile(args!=ex.end(it_copy)) {\n#ifdef DEBUG\n\t\t\t\t\t\tstd::cerr << \"Comparing: \" << args << std::endl\n\t\t\t\t\t\t\t\t\t << \"and \" << derivative->with_respect_to.begin()\n\t\t\t\t\t\t\t\t\t << std::endl;\n#endif\n\t\t\t\t\t\t \n\t\t\t\t\t\tif(subtree_equal(0, args, derivative->with_respect_to.begin(), 0) ) {\n\t\t\t\t\t\t\targs=ex.erase(args);\n\t\t\t\t\t\t\tif(first) {\n\t\t\t\t\t\t\t\tfirst=false;\n\t\t\t\t\t\t\t\t}\n\t\t\t\t\t\t\telse {\n\t\t\t\t\t\t\t\tit=ex.wrap(it, str_node(it->name));\n\t\t\t\t\t\t\t\t}\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\telse\n\t\t\t\t\t\t\t++args;\n\t\t\t\t\t\t}\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\telse {\n#ifdef DEBUG\n\t\t\t\tstd::cerr << it << \" is not a proper derivative\" << std::endl;\n#endif\n\t\t\t\t\n\t\t\t\t}\n\t\t\t\n\t\t\t//\t\t\t\tex.flatten(comma);\n\t\t\t//\t\t\t\tex.erase(comma);\n\t\t\t//\t\t\t\t}\n\t\t\t}\n\n\t\treturn it;\n\t\t\t});\n\t}\n"
  },
  {
    "path": "core/DisplaySympy.hh",
    "content": "\n#pragma once\n\n#include \"DisplayBase.hh\"\n#include <ostream>\n#include <map>\n#include <set>\n\ntypedef uint32_t kunichar;\n\nnamespace cadabra {\n\n\tclass Derivative;\n\t\n\t/// \\ingroup display\n\t///\n\t/// Class to display expressions in a format that Sympy can\n\t/// parse. Will throw an exception if a Cadabra Ex object cannot be\n\t/// understood by Sympy. Can also convert expressions back to Cadabra\n\t/// notation. This class contains the printing logic that you see in\n\t/// action when you call the `__sympy__` method on an Ex object.\n\n\tclass DisplaySympy : public DisplayBase {\n\t\tpublic:\n\t\t\tDisplaySympy(const Kernel&, const Ex&);\n\n\t\t\t/// Rewrite the output of sympy back into a notation used by\n\t\t\t/// Cadabra. This in particular involves converting 'sin' and\n\t\t\t/// friends to `\\sin` and so on, as well as converting all the\n\t\t\t/// greek symbols.  Currently only acts node-by-node, does not\n\t\t\t/// do anything complicated with trees.\n\n\t\t\tvoid import(Ex&);\n\n\t\t\tstd::string preparse_import(const std::string&);\n\n\t\tprotected:\n\t\t\tvirtual bool needs_brackets(Ex::iterator it) override;\n\n\t\tprivate:\n\t\t\t/// Output the expression to a sympy-readable form. For symbols\n\t\t\t/// which cannot be parsed by sympy, this can convert to an\n\t\t\t/// alternative, Such rewrites can then be undone by the\n\t\t\t/// 'import' member above.\n\n\t\t\tvoid print_multiplier(std::ostream&, Ex::iterator);\n\t\t\tvoid print_opening_bracket(std::ostream&, str_node::bracket_t);\n\t\t\tvoid print_closing_bracket(std::ostream&, str_node::bracket_t);\n\t\t\tvoid print_parent_rel(std::ostream&, str_node::parent_rel_t, bool first);\n\t\t\tvoid print_children(std::ostream&, Ex::iterator, int skip=0);\n\n\n\t\t\t/// For every object encountered, dispatch will figure out the\n\t\t\t/// most appropriate way to convert it into a LaTeX\n\t\t\t/// expression. This may be done by simply looking at the\n\t\t\t/// object's name (e.g. `\\prod` will print as a product) but may\n\t\t\t/// also involve looking up properties and deciding on the best\n\t\t\t/// course of action based on the attached properties.\n\n\t\t\tvirtual void dispatch(std::ostream&, Ex::iterator) override;\n\n\t\t\t/// Printing members for various standard constructions,\n\t\t\t/// e.g. print as a list, or as a decorated symbol with\n\t\t\t/// super/subscripts etc. The names reflect the structure of the\n\t\t\t/// output, not necessarily the meaning or name of the object\n\t\t\t/// that is being printed.\n\n\t\t\tvoid print_productlike(std::ostream&, Ex::iterator, const std::string& inbetween);\n\t\t\tvoid print_sumlike(std::ostream&, Ex::iterator);\n\t\t\tvoid print_fraclike(std::ostream&, Ex::iterator);\n\t\t\tvoid print_commalike(std::ostream&, Ex::iterator);\n\t\t\tvoid print_arrowlike(std::ostream&, Ex::iterator);\n\t\t\tvoid print_powlike(std::ostream&, Ex::iterator);\n\t\t\tvoid print_intlike(std::ostream&, Ex::iterator);\n\t\t\tvoid print_equalitylike(std::ostream&, Ex::iterator);\n\t\t\tvoid print_components(std::ostream&, Ex::iterator);\n\t\t\tvoid print_matrix(std::ostream& str, Ex::iterator it);\n\t\t\tvoid print_derivative(std::ostream& str, Ex::iterator it, const Derivative *der);\n\t\t\tvoid print_other(std::ostream& str, Ex::iterator it);\n\n\t\t\tbool children_have_brackets(Ex::iterator ch) const;\n\n\t\t\t/// Map from Cadabra symbols to Sympy symbols.\n\t\t\tstd::map<std::string, std::string> symmap;\n\t\t\tstd::multimap<std::string, std::string> regex_map;\n\n\t\t\t/// Map from symbols which have had dependencies added\n\t\t\t/// to an expression containing these dependencies.\n\t\t\tstd::map<nset_t::iterator, Ex, nset_it_less> depsyms;\n\t\t};\n\n\tconst char *unichar(kunichar c);\n\n\t}\n"
  },
  {
    "path": "core/DisplayTeX.cc",
    "content": "\n#include \"Config.hh\"\n#include \"Exceptions.hh\"\n#include \"Symbols.hh\"\n#include \"Grouping.hh\"\n#include \"DisplayTeX.hh\"\n#include \"Algorithm.hh\"\n#include \"algorithms/substitute.hh\"\n#include \"properties/LaTeXForm.hh\"\n#include \"properties/Derivative.hh\"\n#include \"properties/Accent.hh\"\n#include \"properties/Tableau.hh\"\n#include \"properties/FilledTableau.hh\"\n#include \"properties/TableauInherit.hh\"\n#include \"NTensor.hh\"\n#include \"NInterpolatingFunction.hh\"\n\n#include <regex>\n\n#define nbsp   \" \"\n//(( parent.utf8_output?(unichar(0x00a0)):\" \"))\n#define zwnbsp \"\"\n//(( parent.utf8_output?(unichar(0xfeff)):\"\"))\n\nusing namespace cadabra;\n\n#ifdef ENABLE_JUPYTER\nconst std::string discr = \"\";\n#else\nconst std::string discr = \"\\\\discretionary{}{}{}\";\n#endif\n\nDisplayTeX::DisplayTeX(const Kernel& k, const Ex& e)\n\t: DisplayBase(k, e)\n\t{\n\tsymmap = {\n\t\t\t{\"\\\\hat\", \"\\\\widehat\"},\n\t\t\t{\"\\\\tilde\", \"\\\\widetilde\"}\n\t\t};\n\n\tcurly_bracket_operators = {\n\t\t\"\\\\sqrt\",\n\t\t\"\\\\dot\"\n\t\t};\n\t}\n\nbool DisplayTeX::needs_brackets(Ex::iterator it)\n\t{\n\t// FIXME: may need looking at properties\n\t// FIXME: write as individual parent/current tests\n\tif(tree.is_head(it)) return false;\n\n\tstd::string parent=*tree.parent(it)->name;\n\tstd::string child =*it->name;\n\n\tif(parent==\"\\\\partial\" && (child==\"\\\\sum\" || child==\"\\\\oplus\")) return false; // Always handled by the functional argument. Was: true;\n\n\tif(parent==\"\\\\int\" && (child==\"\\\\sum\" || child==\"\\\\oplus\")) return true;\n\n\tif(parent==\"\\\\indexbracket\" && child==\"\\\\prod\") return false;\n\n\tconst Derivative *der=kernel.properties.get<Derivative>(it);\n\n\tif(parent==\"\\\\pow\") {\n\t\tEx::sibling_iterator sib=it;\n\t\t++sib;\n\t\tif(tree.index(it)==0 && *sib->name==\"1\" && *sib->multiplier==multiplier_t(1)/2) return false; // \\sqrt{this}\n\t\tif(tree.index(it)==0 && !it->is_integer() && *it->multiplier!=1) return true;\n\t\tint nc = Ex::number_of_children(it);\n\t\tint ic = Algorithm::number_of_direct_indices(it);\n\t\tif(nc-ic>0) {\n\t\t\tEx::sibling_iterator ch = Ex::begin(it);\n\t\t\twhile(ch->is_index())\n\t\t\t\t++ch;\n\t\t\tbool rao = reads_as_operator(it, ch);\n\t\t\tif(rao)\n\t\t\t\treturn true;\n\t\t\t}\n\t\t}\n\n\tif(parent==\"\\\\oplus\" && child==\"\\\\otimes\") return true;\n\n\tif(parent==\"\\\\pow\" && (child==\"\\\\prod\" || child==\"\\\\sum\" || child==\"\\\\oplus\" || der)) return  true;\n\n\tif(parent==\"\\\\wedge\" && child==\"\\\\prod\") return true;\n\t\n\tif(parent==\"\\\\prod\" || parent==\"\\\\frac\" || parent==\"\\\\pow\" || parent==\"\\\\wedge\") {\n\t\tif(*tree.parent(it)->name!=\"\\\\frac\" && (*it->name==\"\\\\sum\" || *it->name==\"\\\\oplus\")) return true;\n\t\t//\t\tif(*tree.parent(it)->name==\"\\\\pow\" && (*it->multiplier<0 || (*it->multiplier!=1 && *it->name!=\"1\")) ) return true;\n\t\t}\n\telse if(it->fl.parent_rel==str_node::p_none) {   // function argument\n\t\tif(*it->name==\"\\\\sum\" || *it->name==\"\\\\oplus\" || *it->name==\"\\\\pow\") return false;\n\t\t}\n\telse {\n\t\tif(*it->name==\"\\\\sum\")  return true;\n\t\tif(*it->name==\"\\\\oplus\")  return true;\n\t\tif(*it->name==\"\\\\prod\") return true;\n\t\t}\n\treturn false;\n\t}\n\nbool DisplayTeX::reads_as_operator(Ex::iterator obj, Ex::iterator arg) const\n\t{\n\tconst Derivative *der=kernel.properties.get<Derivative>(obj);\n\tif(der) {\n\t\tif(*arg->name==\"\\\\pow\") return true;\n\t\t// FIXME: this needs fine-tuning; there are more cases where\n\t\t// no brackets are needed.\n\t\tconst LaTeXForm *lf = kernel.properties.get<LaTeXForm>(arg);\n\t\tif((*arg->name).size()==1 || lf || cadabra::symbols::greekmap.find(*arg->name)!=cadabra::symbols::greekmap.end()) return true;\n\t\t}\n\n\tif(*obj->name==\"\\\\cos\" || *obj->name==\"\\\\sin\" || *obj->name==\"\\\\tan\" || *obj->name==\"\\\\exp\") {\n\t\tconst LaTeXForm *lf = kernel.properties.get<LaTeXForm>(arg);\n\t\tif(*arg->multiplier==1)\n\t\t\tif((*arg->name).size()==1 || lf || cadabra::symbols::greekmap.find(*arg->name)!=cadabra::symbols::greekmap.end()) return true;\n\t\t}\n\n\tauto it=curly_bracket_operators.find(*obj->name);\n\tif(it!=curly_bracket_operators.end()) return true;\n\n\treturn false;\n\t}\n\nvoid DisplayTeX::print_other(std::ostream& str, Ex::iterator it)\n\t{\n\tif(needs_brackets(it))\n\t\tstr << \"\\\\left(\";\n\n\t// print multiplier and object name\n\tif(*it->multiplier!=1)\n\t\tprint_multiplier(str, it);\n\n\tif(*it->name==\"1\") {\n\t\tif(*it->multiplier==1 || (*it->multiplier==-1)) // this would print nothing altogether.\n\t\t\tstr << \"1\";\n\t\tif(needs_brackets(it))\n\t\t\tstr << \"\\\\right)\";\n\t\treturn;\n\t\t}\n\n\tEx_comparator comp(kernel.properties);\n\tint num;\n\tauto prop=kernel.properties.get_with_pattern_ext<LaTeXForm>(it, comp, num, \"\", false, true);  // get property, ignore parent rel!\n\tconst LaTeXForm *lf=prop.first;\n\tbool needs_extra_brackets=false;\n\tconst Accent *ac=kernel.properties.get<Accent>(it);\n\tif(!ac && extra_brackets_for_symbols) { // accents should never get additional curly brackets, {\\bar}{g} does not print.\n\t\tEx::sibling_iterator sib=tree.begin(it);\n\t\twhile(sib!=tree.end(it)) {\n\t\t\tif(sib->is_index())\n\t\t\t\tneeds_extra_brackets=true;\n\t\t\t++sib;\n\t\t\t}\n\t\t}\n\n\tif(needs_extra_brackets) str << \"{\"; // to prevent double sup/sub script errors\n\tif(lf) {\n\t\t// Use the pattern as the lhs, and one-by-one the elements in\n\t\t// latex as the rhs. So\n\t\t//\n\t\t//     ket(A??) -> \"|\"\n\t\t//     ket(A??) -> A??\n\t\t//     ...\n\t\t// Then apply this to the original expression to be printed, e.g. ket(1).\n\n\t\tfor(auto lt: lf->latex) {\n\t\t\tauto s = *(lt.begin()->name);\n\t\t\tif(s[0]=='\\\"') {\n\t\t\t\ts=s.substr(1,s.size()-2);\n\t\t\t\tstr << s;\n\t\t\t\tif(lf->latex.size()==1)\n\t\t\t\t\tprint_children(str, it);\n\t\t\t\t}\n\t\t\telse {\n\t\t\t\tEx replacement(\"\\\\arrow\");\n\t\t\t\treplacement.append_child(replacement.begin(), prop.second->obj.begin());\n\t\t\t\treplacement.append_child(replacement.begin(), lt.begin());\n\t\t\t\tEx tmp(it);\n\t\t\t\t// The overall multiplier has already been printed, so set to one now.\n\t\t\t\tone(tmp.begin()->multiplier);\n\t\t\t\tsubstitute subs(kernel, tmp, replacement);\n\t\t\t\tauto lti=tmp.begin();\n\t\t\t\tif(subs.can_apply(lti))\n\t\t\t\t\tsubs.apply(lti);\n\t\t\t\t// std::cerr << tmp << std::endl;\n\t\t\t\tdispatch(str, tmp.begin());\n\t\t\t\t}\n\t\t\t}\n\t\t}\n\telse {\n\t\tstr << texify(*it->name);\n\t\tprint_children(str, it);\n\t\t}\n\n\tif(needs_extra_brackets)\n\t\tstr << \"}\";\n\n\tif(needs_brackets(it))\n\t\tstr << \"\\\\right)\";\n\t}\n\nvoid DisplayTeX::print_tableau(std::ostream& str, Ex::iterator it)\n\t{\n\tif(needs_brackets(it))\n\t\tstr << \"\\\\left(\";\n\n\t// print multiplier and object name\n\tif(*it->multiplier!=1) {\n\t\tprint_multiplier(str, it);\n\t\tstr << \"\\\\, \";\n\t\t}\n\n\tstr << \"\\\\ydiagram{\";\n\tauto sib=tree.begin(it);\n\twhile(sib!=tree.end(it)) {\n\t\tstr << *sib->multiplier;\n\t\t++sib;\n\t\tif(sib!=tree.end(it))\n\t\t\tstr << \",\";\n\t\t}\n\tstr << \"}\";\n\t\n\tif(needs_brackets(it))\n\t\tstr << \"\\\\right)\";\n\t}\n\nvoid DisplayTeX::print_ftableau(std::ostream& str, Ex::iterator it)\n\t{\n\tif(needs_brackets(it))\n\t\tstr << \"\\\\left(\";\n\n\t// print multiplier and object name\n\tif(*it->multiplier!=1) {\n\t\tprint_multiplier(str, it);\n\t\tstr << \"\\\\, \";\n\t\t}\n\n\tstr << \"\\\\ytableaushort{\";\n\tauto sib=tree.begin(it);\n\twhile(sib!=tree.end(it)) {\n\t\tif(*sib->name!=\"\\\\comma\") {\n\t\t\tstr << \"{\";\n\t\t\tdispatch(str, sib);\n\t\t\tstr << \"}\";\n\t\t\t}\n\t\telse {\n\t\t\tauto sib2=tree.begin(sib);\n\t\t\twhile(sib2!=tree.end(sib)) {\n\t\t\t\tstr << \"{\";\n\t\t\t\tdispatch(str, sib2);\n\t\t\t\tstr << \"}\";\n\t\t\t\t++sib2;\n\t\t\t\t}\n\t\t\t}\n\t\t++sib;\n\t\tif(sib!=tree.end(it))\n\t\t\tstr << \",\";\n\t\t}\n\tstr << \"}\";\n\n\tif(needs_brackets(it))\n\t\tstr << \"\\\\right)\";\n\t}\n\nstd::string DisplayTeX::texify(std::string str) const\n\t{\n\tauto rn = symmap.find(str);\n\tif(rn!=symmap.end())\n\t\tstr = rn->second;\n\n\t// Convert symbols which need to be escaped for TeX.\n\tstd::string res;\n\tfor(unsigned int i=0; i<str.size(); ++i) {\n\t\tif(str[i]=='#') res+=\"\\\\#\";\n\t\telse res+=str[i];\n\t\t}\n\n\t// Make symbols like \"a13\" print as \"a_{13}\" automatically.\n\tif(res.size()>1) {\n\t\tstd::string nondigit;\n\t\tstd::string digit;\n\t\tbool nd=true;\n\t\tfor(size_t i=0; i<str.size(); ++i) {\n\t\t\tif(nd) {\n\t\t\t\tif(isdigit(str[i])) {\n\t\t\t\t\tnd=false;\n\t\t\t\t\tdigit+=str[i];\n\t\t\t\t\t}\n\t\t\t\telse nondigit+=str[i];\n\t\t\t\t}\n\t\t\telse {\n\t\t\t\tif(isdigit(str[i])==false) {\n\t\t\t\t\tdigit=\"\";\n\t\t\t\t\tbreak; // nothing we can do here\n\t\t\t\t\t}\n\t\t\t\telse digit+=str[i];\n\t\t\t\t}\n\t\t\t}\n\t\tif(digit.size()>0 && nondigit.size()>0)\n\t\t\tres=\"{\"+nondigit+\"_{\"+digit+\"}}\";\n\t\t}\n\t\n\treturn res;\n\t}\n\nvoid DisplayTeX::print_children(std::ostream& str, Ex::iterator it, int skip)\n\t{\n\tstr_node::bracket_t    previous_bracket_   =str_node::b_invalid;\n\tstr_node::parent_rel_t previous_parent_rel_=str_node::p_none;\n\n\tint number_of_nonindex_children=0;\n\tint number_of_index_children=0;\n\tEx::sibling_iterator ch=tree.begin(it);\n\twhile(ch!=tree.end(it)) {\n\t\tif(ch->is_index()==false) {\n\t\t\t++number_of_nonindex_children;\n\t\t\tif(*ch->name==\"\\\\prod\")\n\t\t\t\t++number_of_nonindex_children;\n\t\t\t}\n\t\telse ++number_of_index_children;\n\t\t++ch;\n\t\t}\n\n\tch=tree.begin(it);\n\tch+=skip;\n\tunsigned int chnum=0;\n\twhile(ch!=tree.end(it)) {\n\t\tstr_node::bracket_t    current_bracket_   =(*ch).fl.bracket;\n\t\tstr_node::parent_rel_t current_parent_rel_=(*ch).fl.parent_rel;\n\t\tconst Accent *is_accent=kernel.properties.get<Accent>(it);\n\n\t\tbool function_bracket_needed=true;\n\t\tif(current_bracket_==str_node::b_none) {\n\t\t\tif(previous_bracket_==str_node::b_none && current_parent_rel_==previous_parent_rel_ && current_parent_rel_==str_node::p_none)\n\t\t\t\tstr << \", \" << discr;\n\t\t\tfunction_bracket_needed=!reads_as_operator(it, ch);\n\t\t\t}\n\n\t\tif(current_bracket_!=str_node::b_none || previous_bracket_!=current_bracket_ || previous_parent_rel_!=current_parent_rel_) {\n\t\t\tif(previous_parent_rel_!=current_parent_rel_) \n\t\t\t\tif(previous_parent_rel_==str_node::p_sub || previous_parent_rel_==str_node::p_super)\n\t\t\t\t\tif(current_bracket_!=str_node::b_none)\n\t\t\t\t\t\tstr << \"\\\\!\";\n\t\t\t\n\t\t\tprint_parent_rel(str, current_parent_rel_, ch==tree.begin(it));\n\n\t\t\tif(is_accent==0 && function_bracket_needed) {\n\t\t\t\t// FIXME: the line below was there originally to make function brackets sit a bit\n\t\t\t\t// closer to the function name. However, it gets triggered for\n\t\t\t\t//   `\\alpha_{n}^{\\mu}::SelfNonCommuting;`\n\t\t\t\t// and then messes up the superscript. That's worse than wrong spacing.\n\t\t\t\tprint_opening_bracket(str, (number_of_nonindex_children>1 /* &&number_of_index_children>0 */ &&\n\t\t\t\t                            current_parent_rel_!=str_node::p_sub &&\n\t\t\t\t                            current_parent_rel_!=str_node::p_super ? str_node::b_round:current_bracket_),\n\t\t\t\t                      current_parent_rel_);\n\t\t\t\t}\n\t\t\telse str << \"{\";\n\t\t\t}\n\n\t\t// print this child depending on its name or meaning\n\t\tdispatch(str, ch);\n\n\t\t++ch;\n\t\tif(ch==tree.end(it) || current_bracket_!=str_node::b_none || current_bracket_!=(*ch).fl.bracket || current_parent_rel_!=(*ch).fl.parent_rel) {\n\t\t\tif(is_accent==0 && function_bracket_needed)\n\t\t\t\tprint_closing_bracket(str,  (number_of_nonindex_children>1 /* &&number_of_index_children>0 */ &&\n\t\t\t\t                             current_parent_rel_!=str_node::p_sub &&\n\t\t\t\t                             current_parent_rel_!=str_node::p_super ? str_node::b_round:current_bracket_),\n\t\t\t\t                      current_parent_rel_);\n\t\t\telse str  << \"}\";\n\t\t\t}\n\t\telse str << nbsp;\n\n\t\tprevious_bracket_=current_bracket_;\n\t\tprevious_parent_rel_=current_parent_rel_;\n\t\t++chnum;\n\t\t}\n\t}\n\nvoid DisplayTeX::print_multiplier(std::ostream& str, Ex::iterator it, int mult)\n\t{\n\tif(it->multiplier->is_rational()) {\n\t\tmpq_class q = it->multiplier->get_rational();\n\t\tmpz_class denom=q.get_den();\n\t\tmpz_class numer=q.get_num();\n\t\t\n\t\tif(denom!=1) {\n\t\t\tif(mult*numer<0) {\n\t\t\t\tstr << \" - \";\n\t\t\t\tmult *= -1;\n\t\t\t\t}\n\t\t\tstr << \"\\\\frac{\" << mult * numer << \"}{\" << denom << \"}\";\n\t\t\t}\n\t\telse if(mult * q==-1) {\n\t\t\tstr << \"-\";\n\t\t\t}\n\t\telse {\n\t\t\tstr << mult * q;\n\t\t\t}\n\t\t}\n\telse {\n\t\tstd::ostringstream str2;\n\t\tstr2 << it->multiplier->get_double();\n\t\tstd::string s = str2.str();\n\t\tstd::string s2 = std::regex_replace(s, std::regex(\"(\\\\d+\\\\.?\\\\d*|\\\\.\\\\d+)e([+-]?\\\\d+)\"), \"$1 \\\\times 10^{$2}\");\n\t\tstr << s2;\n\t\t}\n\tstr << \"\\\\,\";\n\t}\n\nvoid DisplayTeX::print_opening_bracket(std::ostream& str, str_node::bracket_t br, str_node::parent_rel_t pr)\n\t{\n\tswitch(br) {\n\t\tcase str_node::b_none:\n\t\t\tif(pr==str_node::p_none)     str << \"\\\\left(\";\n\t\t\telse                         str << \"{\";\n\t\t\tbreak;\n\t\tcase str_node::b_pointy:\n\t\t\tstr << \"\\\\<\";\n\t\t\tbreak;\n\t\tcase str_node::b_curly:\n\t\t\tstr << \"\\\\left\\\\{\";\n\t\t\tbreak;\n\t\tcase str_node::b_round:\n\t\t\tstr << \"\\\\left(\";\n\t\t\tbreak;\n\t\tcase str_node::b_square:\n\t\t\tstr << \"\\\\left[\";\n\t\t\tbreak;\n\t\tdefault :\n\t\t\treturn;\n\t\t}\n\t++(bracket_level);\n\t}\n\nvoid DisplayTeX::print_closing_bracket(std::ostream& str, str_node::bracket_t br, str_node::parent_rel_t pr)\n\t{\n\tswitch(br) {\n\t\tcase str_node::b_none:\n\t\t\tif(pr==str_node::p_none)     str << \"\\\\right)\";\n\t\t\telse                         str << \"}\";\n\t\t\tbreak;\n\t\tcase str_node::b_pointy:\n\t\t\tstr << \"\\\\>\";\n\t\t\tbreak;\n\t\tcase str_node::b_curly:\n\t\t\tstr << \"\\\\right\\\\}\";\n\t\t\tbreak;\n\t\tcase str_node::b_round:\n\t\t\tstr << \"\\\\right)\";\n\t\t\tbreak;\n\t\tcase str_node::b_square:\n\t\t\tstr << \"\\\\right]\";\n\t\t\tbreak;\n\t\tdefault :\n\t\t\treturn;\n\t\t}\n\t--(bracket_level);\n\t}\n\nvoid DisplayTeX::print_parent_rel(std::ostream& str, str_node::parent_rel_t pr, bool first)\n\t{\n\tswitch(pr) {\n\t\tcase str_node::p_super:\n\t\t\tif(!first && latex_spacing) str << \"\\\\,\";\n\t\t\tstr << \"^\";\n\t\t\tbreak;\n\t\tcase str_node::p_sub:\n\t\t\tif(!first && latex_spacing) str << \"\\\\,\";\n\t\t\tstr << \"_\";\n\t\t\tbreak;\n\t\tcase str_node::p_property:\n\t\t\tstr << \"$\";\n\t\t\tbreak;\n\t\tcase str_node::p_exponent:\n\t\t\tstr << \"**\";\n\t\t\tbreak;\n\t\tcase str_node::p_none:\n\t\t\tbreak;\n\t\tcase str_node::p_components:\n\t\t\tbreak;\n\t\tcase str_node::p_invalid:\n\t\t\tthrow std::logic_error(\"DisplayTeX: p_invalid not handled.\");\n\t\t}\n\t// Prevent line break after this character.\n\tstr << zwnbsp;\n\t}\n\nvoid DisplayTeX::dispatch(std::ostream& str, Ex::iterator it)\n\t{\n\tif(handle_unprintable_wildcards(str, it))\n\t\treturn;\n\n\tif(std::holds_alternative<std::shared_ptr<NTensor>>(it->content)) {\n\t\tstd::ostringstream str2;\n\t\tauto nt = std::get<std::shared_ptr<NTensor>>(it->content);\n\t\tstr2 << *nt;\n\t\tstd::string s = str2.str();\n\t\tstd::string s2 = std::regex_replace(s, std::regex(\"(\\\\d+\\\\.?\\\\d*|\\\\.\\\\d+)e([+-]?\\\\d+)\"), \"$1 \\\\times 10^{$2}\");\n\t\tif(nt->shape.size()==1 && nt->shape[0]==1) {\n\t\t\tif(!nt->is_real())\n\t\t\t\tstr << \"(\" << s2.substr(1, s2.size()-2) << \")\";\n\t\t\telse\n\t\t\t\tstr << s2.substr(1, s2.size()-2);\n\t\t\t}\n\t\telse\n\t\t\tstr << s2;\n\n\t\tif(*it->name==\"1\" && tree.number_of_children(it)==0)\n\t\t\treturn;\n//\t\treturn; // FIXME: always just ignore the subtree?\n\t\t}\n\telse if(std::holds_alternative<std::shared_ptr<NInterpolatingFunction>>(it->content)) {\n\t\tstr << \"\\\\square{}\" << std::endl;\n\t\tauto ni = std::get<std::shared_ptr<NInterpolatingFunction>>(it->content);\n\t\tstr << \"(\";\n\t\tdispatch(str, ni->var.begin());\n\t\tstr << \")\";\n\t\treturn;\n\t\t}\n\t\n\tif(*it->name==\"\\\\prod\")                                   print_productlike(str, it, \" \");\n\telse if(*it->name==\"\\\\sum\" || *it->name==\"\\\\oplus\")       print_sumlike(str, it);\n\telse if(*it->name==\"\\\\frac\")                              print_fraclike(str, it);\n\telse if(*it->name==\"\\\\comma\")                             print_commalike(str, it);\n\telse if(*it->name==\"\\\\arrow\")                             print_arrowlike(str, it);\n\telse if(*it->name==\"\\\\inner\")                             print_dot(str, it);\n\telse if(*it->name==\"\\\\pow\")                               print_powlike(str, it);\n\telse if(*it->name==\"\\\\int\")                               print_intlike(str, it);\n\telse if(*it->name==\"\\\\equals\" || *it->name==\"\\\\unequals\") print_equalitylike(str, it);\n\telse if(*it->name==\"\\\\commutator\")                        print_commutator(str, it, true);\n\telse if(*it->name==\"\\\\anticommutator\")                    print_commutator(str, it, false);\n\telse if(*it->name==\"\\\\components\")                        print_components(str, it);\n\telse if(*it->name==\"\\\\wedge\")                             print_wedgeproduct(str, it);\n\telse if(*it->name==\"\\\\conditional\")                       print_conditional(str, it);\n\telse if(*it->name==\"\\\\greater\" || *it->name==\"\\\\less\")    print_relation(str, it);\n\telse if(*it->name==\"\\\\indexbracket\")                      print_indexbracket(str, it);\n\telse if(*it->name==\"\\\\ldots\")                             print_dots(str, it);\n\telse if(kernel.properties.get<Tableau>(it))               print_tableau(str, it);\n\telse if(kernel.properties.get<FilledTableau>(it))         print_ftableau(str, it);\n\telse                                                      print_other(str, it);\n\t}\n\nvoid DisplayTeX::print_commalike(std::ostream& str, Ex::iterator it)\n\t{\n\tEx::sibling_iterator sib=tree.begin(it);\n\tbool first=true;\n\tstr << \"\\\\left[\";\n\twhile(sib!=tree.end(it)) {\n\t\tif(first)\n\t\t\tfirst=false;\n\t\telse\n\t\t\tstr << \", \" << discr; // << \" \";\n\t\tdispatch(str, sib);\n\t\t++sib;\n\t\t}\n\tstr << \"\\\\right]\";\n\t}\n\nvoid DisplayTeX::print_wedgeproduct(std::ostream& str, Ex::iterator it)\n\t{\n\tif(*it->multiplier!=1) {\n\t\tprint_multiplier(str, it);\n\t\t}\n\n\tif(needs_brackets(it))\n\t\tstr << \"\\\\left(\";\n\n\tEx::sibling_iterator sib=tree.begin(it);\n\tdispatch(str, sib);\n\t++sib;\n\twhile(sib!=tree.end(it)) {\n\t\tstr << \"\\\\wedge \";\n\t\tdispatch(str, sib);\n\t\t++sib;\n\t\t}\n\n\tif(needs_brackets(it))\n\t\tstr << \"\\\\right)\";\n\t}\n\nvoid DisplayTeX::print_arrowlike(std::ostream& str, Ex::iterator it)\n\t{\n\tEx::sibling_iterator sib=tree.begin(it);\n\tdispatch(str, sib);\n\tstr << \" \\\\rightarrow \";\n\t++sib;\n\tdispatch(str, sib);\n\t}\n\nvoid DisplayTeX::print_dot(std::ostream& str, Ex::iterator it)\n\t{\n\tEx::sibling_iterator sib=tree.begin(it);\n\tdispatch(str, sib);\n\tstr << \" \\\\cdot \";\n\t++sib;\n\tdispatch(str, sib);\n\t}\n\nvoid DisplayTeX::print_fraclike(std::ostream& str, Ex::iterator it)\n\t{\n\tEx::sibling_iterator num=tree.begin(it), den=num;\n\t++den;\n\n\tint mult=1;\n\tif(*it->multiplier<0) {\n\t\tstr << \" - \";\n\t\tmult=-1;\n\t\t}\n\n\tstr << \"\\\\frac{\";\n\tif(it->multiplier->is_rational()) {\n\t\tif(mult * (it->multiplier->get_rational())!=1) {\n\t\t\tprint_multiplier(str, it, mult);\n\t\t\t}\n\t\t}\n\telse {\n\t\tprint_multiplier(str, it, mult);\n\t\t}\n\t\n\tif(num->is_rational()==false || (mult * (it->multiplier->get_rational()))==1)\n\t\tdispatch(str, num);\n\tstr << \"}{\";\n\tdispatch(str, den);\n\tstr << \"}\";\n\t}\n\nvoid DisplayTeX::print_productlike(std::ostream& str, Ex::iterator it, const std::string& inbetween)\n\t{\n\tif(needs_brackets(it))\n\t\tstr << \"\\\\left(\";\n\n\tif (kernel.display_fractions) {\n\t\t// If one (or more) of the factors is a negative power, split into top and\n\t\t// bottom parts and print as a fraction\n\t\tEx pos(\"\\\\prod\"), neg(\"\\\\prod\");\n\t\tfor (Ex::sibling_iterator beg = it.begin(), end = it.end(); beg != end; ++beg) {\n\t\t\tbool is_negexp = false;\n\t\t\tif (*beg->name == \"\\\\pow\") {\n\t\t\t\tEx::sibling_iterator exponent = beg.begin();\n\t\t\t\t++exponent;\n\t\t\t\tif (*exponent->name == \"1\" && *exponent->multiplier < 0) {\n\t\t\t\t\tis_negexp = true;\n\t\t\t\t\tif (*exponent->multiplier == -1) {\n\t\t\t\t\t\tneg.append_child(neg.begin(), (Ex::iterator)beg.begin());\n\t\t\t\t\t}\n\t\t\t\t\telse {\n\t\t\t\t\t\tauto pos = neg.append_child(neg.begin(), (Ex::iterator)beg);\n\t\t\t\t\t\texponent = pos.begin();\n\t\t\t\t\t\t++exponent;\n\t\t\t\t\t\tmultiply(exponent->multiplier, -1);\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t}\n\t\t\tif (!is_negexp) {\n\t\t\t\tpos.append_child(pos.begin(), (Ex::iterator)beg);\n\t\t\t}\n\t\t}\n\n\t\tif (neg.begin().begin() != neg.begin().end()) {\n\t\t\tauto mult = *it->multiplier;\n\t\t\tif (mult < 0) {\n\t\t\t\tstr << \"-\";\n\t\t\t\tmult *= -1;\n\t\t\t}\n\t\t\tif (mult.is_rational()) {\n\t\t\t\tauto rmult = mult.get_rational();\n\t\t\t\tif(mult.get_rational().get_den() == 1) {\n\t\t\t\t\tmultiply(pos.begin()->multiplier, rmult);\n\t\t\t\t\t}\n\t\t\t\telse {\n\t\t\t\t\tmultiply(pos.begin()->multiplier, rmult.get_num());\n\t\t\t\t\tmultiply(neg.begin()->multiplier, rmult.get_den());\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\telse {\n\t\t\t\tmultiply(pos.begin()->multiplier, mult);\n\t\t\t\t}\n\t\t\t\n\t\t\tstr << \"\\\\frac{\";\n\t\t\tif (pos.begin().begin() == pos.begin().end()) {\n\t\t\t\tpos.begin()->name = name_set.insert(\"1\").first;\n\t\t\t\tprint_other(str, pos.begin());\n\t\t\t}\n\t\t\telse {\n\t\t\t\tprint_productlike(str, pos.begin(), inbetween);\n\t\t\t}\n\t\t\tstr << \"}{\";\n\t\t\tprint_productlike(str, neg.begin(), inbetween);\n\t\t\tstr << \"}\";\n\n\t\t\tif (needs_brackets(it))\n\t\t\t\tstr << \"\\\\right)\";\n\t\t\treturn;\n\t\t}\n\t}\n\n\t// The multiplier needs to be inside the brackets, otherwise things like\n\t// \\pow{ 2/3 \\prod{a}{b} }{c} do not print correctly.\n\n\tif(*it->multiplier!=1)\n\t\tprint_multiplier(str, it);\n\n\t// To print \\prod{\\sum{a}{b}}{\\sum{c}{d}} correctly:\n\t// If there is any sum as child, and if the sum children do not\n\t// all have the same bracket type (different from b_none or b_no),\n\t// then print brackets.\n\n\tstr_node::bracket_t previous_bracket_=str_node::b_invalid;\n//\tbool beginning_of_group=true;\n\tEx::sibling_iterator ch=tree.begin(it);\n\tbool prev_is_tableau=false;\n\tif(ch!=tree.end(it)) {\n\t\tconst Tableau        *tab =kernel.properties.get<Tableau>(ch);\n\t\tconst FilledTableau  *ftab=kernel.properties.get<FilledTableau>(ch);\n\t\tif(tab || ftab)\n\t\t\tprev_is_tableau=true;\n\t\t}\n\twhile(ch!=tree.end(it)) {\n\t\tstr_node::bracket_t current_bracket_=(*ch).fl.bracket;\n\t\tif(previous_bracket_!=current_bracket_) {\n\t\t\tif(current_bracket_!=str_node::b_none) {\n\t\t\t\tprint_opening_bracket(str, current_bracket_, str_node::p_none);\n//\t\t\t\tbeginning_of_group=true;\n\t\t\t\t}\n\t\t\t}\n\t\tdispatch(str, ch);\n\t\t++ch;\n\t\tif(ch==tree.end(it)) {\n\t\t\tif(current_bracket_!=str_node::b_none)\n\t\t\t\tprint_closing_bracket(str, current_bracket_, str_node::p_none);\n\t\t\t}\n\t\telse {\n\t\t\tconst Tableau       *tab =kernel.properties.get<Tableau>(ch);\n\t\t\tconst FilledTableau *ftab=kernel.properties.get<FilledTableau>(ch);\n\t\t\tif(tab || ftab) {\n\t\t\t\tif(prev_is_tableau)\n\t\t\t\t\tstr << \" \\\\otimes \";\n\t\t\t\telse\n\t\t\t\t\tstr << \" \";\n\t\t\t\tprev_is_tableau=true;\n\t\t\t\t}\n\t\t\telse {\n\t\t\t\tprev_is_tableau=false;\n\t\t\t\tif(print_star) {\n\t\t\t\t\tif(tight_star) str << inbetween;\n\t\t\t\t\telse str << \" \" << inbetween << \" \";\n\t\t\t\t\t}\n\t\t\t\telse {\n\t\t\t\t\tstr << \" \";\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t}\n\t\tprevious_bracket_=current_bracket_;\n\t\t}\n\n\tif(needs_brackets(it))\n\t\tstr << \"\\\\right)\";\n\n\t}\n\nvoid DisplayTeX::print_sumlike(std::ostream& str, Ex::iterator it)\n\t{\n\tassert(*it->multiplier==1);\n\n\tif(needs_brackets(it))\n\t\tstr << \"\\\\left(\";\n\n\tunsigned int steps=0;\n\n\tEx::sibling_iterator ch=tree.begin(it);\n\tbool prev_is_tableau=false;\n\tif(ch!=tree.end(it)) {\n\t\tconst Tableau        *tab =kernel.properties.get<Tableau>(ch);\n\t\tconst FilledTableau  *ftab=kernel.properties.get<FilledTableau>(ch);\n\t\tif(tab || ftab)\n\t\t\tprev_is_tableau=true;\n\t\t}\n\twhile(ch!=tree.end(it)) {\n\t\t//\t\tif(ch!=tree.begin(it))\n\t\t//\t\t\tstr << \"%\\n\"; // prevent LaTeX overflow.\n\t\tif(steps>0)\n\t\t\tstr << discr;\n\t\tif(++steps==20) {\n\t\t\tsteps=1;\n\t\t\tstr << \"%\\n\"; // prevent LaTeX overflow.\n\t\t\t}\n\t\tif(*ch->multiplier>=0 && ch!=tree.begin(it)) {\n\t\t\tif(*it->name==\"\\\\sum\") {\n\t\t\t\tconst Tableau       *tab =kernel.properties.get<Tableau>(ch);\n\t\t\t\tconst FilledTableau *ftab=kernel.properties.get<FilledTableau>(ch);\n\t\t\t\tif(tab || ftab) {\n\t\t\t\t\tif(prev_is_tableau)\n\t\t\t\t\t\tstr << \" \\\\oplus \";\n\t\t\t\t\telse\n\t\t\t\t\t\tstr << \"+\";\n\t\t\t\t\tprev_is_tableau=true;\n\t\t\t\t\t}\n\t\t\t\telse\n\t\t\t\t\tstr << \"+\";\n\t\t\t\t}\n\t\t\telse\n\t\t\t\tstr << *it->name << \"{}\";\n\t\t\t}\n\n\t\tdispatch(str, ch);\n\t\t++ch;\n\t\t}\n\n\tif(needs_brackets(it))\n\t\tstr << \"\\\\right)\";\n\tstr << std::flush;\n\t}\n\nbool DisplayTeX::handle_unprintable_wildcards(std::ostream& str, Ex::iterator it) const\n\t{\n\t// Catch `\\pow{#}` and other wildcard constructions, these\n\t// need to print verbatim.\n\n\tif(it.number_of_children()==1) {\n\t\tconst std::string& name = (*it->name);\n\t\tif(name.size()>0 && name[0]=='\\\\' && *(it.begin()->name)==\"#\") {\n\t\t\tstr << \"\\\\backslash\\\\texttt{\" << name.substr(1) << \"}\\\\{\\\\#\\\\}\";\n\t\t\treturn true;\n\t\t\t}\n\t\t}\n\treturn false;\n\t}\n\nvoid DisplayTeX::print_powlike(std::ostream& str, Ex::iterator it)\n\t{\n\tauto arg=tree.begin(it);\n\tassert(arg!=tree.end(it));\n\tauto exp=arg;\n\t++exp;\n\n\tassert(exp!=tree.end(it));\n\n\tif (kernel.display_fractions && exp->is_rational() && *exp->multiplier < 0) {\n\t\tauto mult = *it->multiplier;\n\t\tbool mult_is_int = mult.is_rational() && (mult.get_rational().get_den() == 1);\n\t\tif (mult < 0) {\n\t\t\tstr << \"-\";\n\t\t\tmult *= -1;\n\t\t}\n\t\tstr << \"\\\\frac{\";\n\t\tif (mult_is_int)\n\t\t\tstr << mult;\n\t\telse {\n\t\t\tif(mult.is_rational())\n\t\t\t\tstr << mult.get_rational().get_num();\n\t\t\telse\n\t\t\t\tstr << mult;\n\t\t\t}\n\t\tstr << \"}{\";\n\t\tif (*exp->multiplier == -1) {\n\t\t\tEx copy(arg);\n\t\t\tif(mult.is_rational()) {\n\t\t\t\tif (!mult_is_int) {\n\t\t\t\t\tmultiply(copy.begin()->multiplier, mult.get_rational().get_den());\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\telse multiply(copy.begin()->multiplier, mult);\n\t\t\t\n\t\t\tdispatch(str, copy.begin());\n\t\t}\n\t\telse {\n\t\t\tEx copy(it);\n\t\t\texp = copy.begin().begin();\n\t\t\t++exp;\n\t\t\tmultiply(exp->multiplier, -1);\n\t\t\tif(mult.is_rational()) {\n\t\t\t\tif (!mult_is_int)\n\t\t\t\t\tcopy.begin()->multiplier = rat_set.insert(mult.get_rational().get_den()).first;\n\t\t\t\t}\n\t\t\telse copy.begin()->multiplier = rat_set.insert(mult).first;\n\t\t\t\n\t\t\tprint_powlike(str, copy.begin());\n\t\t}\n\t\tstr << \"}\";\n\t\treturn;\n\t}\n\n\tif(*it->multiplier!=1)\n\t\tprint_multiplier(str, it);\n\n\tbool is_sqrt=false;\n\tif(exp->is_rational() && *exp->multiplier==multiplier_t(1)/2) {\n\t\tstr << \"\\\\sqrt\";\n\t\tis_sqrt=true;\n\t\t}\n\n\tstr << \"{\";\n\tdispatch(str, arg);\n\tstr << \"}\";\n\n\tif(!is_sqrt) {\n\t\tstr << \"^{\";\n\t\tdispatch(str, exp);\n\t\tstr << \"}\";\n\t\t}\n\t}\n\nvoid DisplayTeX::print_intlike(std::ostream& str, Ex::iterator it)\n\t{\n\tif(*it->multiplier!=1)\n\t\tprint_multiplier(str, it);\n\tstr << *it->name;\n\n\t// The first argument is the integrand. Subsequent arguments are\n\t// either integration variables, or lists consisting of an\n\t// integration variable, a start value and an end value.\n\t// Since the integration ranges need to be attached to the\n\t// integral symbols, we need to scan for them first.\n\n\tauto sib=tree.begin(it);\n\t++sib;\n\twhile(sib!=tree.end(it)) {\n\t\tif(*sib->name==\"\\\\comma\") {\n\t\t\tauto bvalue = tree.child(sib, 1);\n\t\t\tauto evalue = tree.child(sib, 2);\n\t\t\tstr << \"_{\";\n\t\t\tdispatch(str, bvalue);\n\t\t\tstr << \"}^{\";\n\t\t\tdispatch(str, evalue);\n\t\t\tstr << \"}\";\n\t\t\t}\n\t\t++sib;\n\t\tif(sib!=tree.end(it))\n\t\t\tstr << *it->name;\n\t\t}\n\n\tstr << \" \";\n\tsib=tree.begin(it);\n\tdispatch(str, sib);\n\t++sib;\n\tbool first=true;\n\n\twhile(sib!=tree.end(it)) {\n\t\tif(first) {\n\t\t\tstr << \"\\\\,\";\n\t\t\tfirst=false;\n\t\t\t}\n\t\tstr << \"\\\\,{\\\\rm d}\";\n\t\tif(*sib->name==\"\\\\comma\") {\n\t\t\tdispatch(str, tree.child(sib,0));\n\t\t\t}\n\t\telse {\n\t\t\tdispatch(str, sib);\n\t\t\t}\n\t\t++sib;\n\t\t}\n\t}\n\nvoid DisplayTeX::print_equalitylike(std::ostream& str, Ex::iterator it)\n\t{\n\tEx::sibling_iterator sib=tree.begin(it);\n\tdispatch(str, sib);\n\tstr << \" \";\n\tif(*it->name==\"\\\\unequals\") str << \"\\\\not\";\n\tstr << \"= \";\n\t++sib;\n\tif(sib==tree.end(it))\n\t\tthrow ConsistencyException(\"Found equals node with only one child node.\");\n\tdispatch(str, sib);\n\t}\n\nvoid DisplayTeX::print_commutator(std::ostream& str, Ex::iterator it, bool comm)\n\t{\n\tif(*it->multiplier!=1)\n\t\tprint_multiplier(str, it);\n\n\tif(comm) str << \"{}\\\\left[\";\n\telse     str << \"{}\\\\left\\\\{\";\n\tauto sib=tree.begin(it);\n\tbool first=true;\n\twhile(sib!=tree.end(it)) {\n\t\tif(!first) str << \", \" << discr;\n\t\telse       first=false;\n\t\tdispatch(str, sib);\n\t\t++sib;\n\t\t}\n\tif(comm) str << \"\\\\right]{}\";\n\telse     str << \"\\\\right\\\\}{}\";\n\t}\n\nvoid DisplayTeX::print_dots(std::ostream& str, Ex::iterator it)\n\t{\n\tif(tree.is_head(it)==false) {\n\t\tif(*tree.parent(it)->name==\"\\\\sum\")\n\t\t\tstr << \" \\\\ldots \";\n\t\telse\n\t\t\tstr << \" \\\\cdots \";\n\t\t}\n\telse\n\t\tstr << \" \\\\ldots \";\n\t}\n\nvoid DisplayTeX::print_components(std::ostream& str, Ex::iterator it)\n\t{\n\tassert(*it->multiplier==1);\n\n\tauto ind_names=tree.begin(it);\n\tauto ind_values=tree.end(it);\n\t--ind_values;\n\n\tstr << \"\\\\square\";\n\tauto sib=ind_names;\n\twhile(sib!=ind_values) {\n\t\tif(sib->fl.parent_rel==str_node::p_sub)   str << \"{}_{\";\n\t\tif(sib->fl.parent_rel==str_node::p_super) str << \"{}^{\";\n\t\tdispatch(str, sib);\n\t\tstr << \"}\";\n\t\t++sib;\n\t\t}\n\n\t// Find duplicates.\n\tequiv_fun_t component_equiv = [](const Ex& ex, Ex::iterator it1, Ex::iterator it2) {\n\t\tit1 = ex.child(it1, 1);\n\t\tit2 = ex.child(it2, 1);\n\t\treturn ex.equal_subtree(it1, it2);\n\t\t};\n\tauto grp = group_by_equivalence(tree, ind_values, component_equiv);\n\n\t// Function to display anonymous tensor.\n\tauto display_anon = [this, &str, &ind_names](Ex::sibling_iterator c) {\n\t\tauto iv = tree.begin(c);\n\t\tauto in = ind_names;\n\t\tstr << \"\\\\square\";\n\t\twhile(iv!=tree.end(c)) {\n\t\t\tif(in->fl.parent_rel==str_node::p_sub)   str << \"{}_{\";\n\t\t\tif(in->fl.parent_rel==str_node::p_super) str << \"{}^{\";\n\t\t\tdispatch(str, iv);\n\t\t\tstr << \"}\";\n\t\t\t++in;\n\t\t\t++iv;\n\t\t\t}\n\t\t};\n\n\t// Display all unique components.\n\tstr << \"\\\\left\\\\{\\\\begin{aligned}\";\n\tsib=tree.begin(ind_values);\n\twhile(sib!=tree.end(ind_values)) {\n\t\tif( grp.find( sib ) == grp.end() ) {\n\t\t\tEx::sibling_iterator c=tree.begin(sib);\n\t\t\tdisplay_anon(c);\n\t\t\tstr << \"& = \";\n\n\t\t\tfor(const auto& equal_tensor: grp) {\n\t\t\t\t// std::cerr << equal_tensor.second.second << std::endl;\n\t\t\t\tif( equal_tensor.second.second == sib ) {\n\t\t\t\t\tdisplay_anon(tree.begin(equal_tensor.first));\n\t\t\t\t\tstr << \" = \";\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t\n\t\t\t++c;\n\t\t\tdispatch(str, c);\n\t\t\tstr << \"\\\\\\\\[-.5ex]\\n\";\n\t\t\t}\n\t\t++sib;\n\t\t}\n\tstr << \"\\\\end{aligned}\\\\right\\\\}\\n\";\n\t}\n\nvoid DisplayTeX::print_conditional(std::ostream& str, Ex::iterator it)\n\t{\n\tauto sib=tree.begin(it);\n\tdispatch(str, sib);\n\tstr << \"\\\\quad\\\\text{with}\\\\quad{}\";\n\t++sib;\n\tdispatch(str, sib);\n\t}\n\nvoid DisplayTeX::print_relation(std::ostream& str, Ex::iterator it)\n\t{\n\tauto sib=tree.begin(it);\n\tdispatch(str, sib);\n\tif(*it->name==\"\\\\greater\") str << \" > \";\n\tif(*it->name==\"\\\\less\")    str << \" < \";\n\t++sib;\n\tdispatch(str, sib);\n\t}\n\nvoid DisplayTeX::print_indexbracket(std::ostream& str, Ex::iterator it)\n\t{\n\tif(*it->multiplier!=1)\n\t\tprint_multiplier(str, it);\n\n\tauto sib=tree.begin(it);\n\tstr << \"\\\\left(\";\n\tdispatch(str, sib);\n\tstr << \"\\\\right)\";\n\tprint_children(str, it, 1);\n\t}\n\nbool DisplayTeX::children_have_brackets(Ex::iterator ch) const\n\t{\n\tEx::sibling_iterator chlds=tree.begin(ch);\n\tstr_node::bracket_t childbr=chlds->fl.bracket;\n\tif(childbr==str_node::b_none || childbr==str_node::b_no)\n\t\treturn false;\n\telse return true;\n\t}\n\n\n// Thanks to Behdad Esfahbod\nint k_unichar_to_utf8(kunichar c, char *buf)\n\t{\n\tbuf[0]=(c) < 0x00000080 ?   (c)                  :\n\t       (c) < 0x00000800 ?  ((c) >>  6)         | 0xC0 :\n\t       (c) < 0x00010000 ?  ((c) >> 12)         | 0xE0 :\n\t       (c) < 0x00200000 ?  ((c) >> 18)         | 0xF0 :\n\t       (c) < 0x04000000 ?  ((c) >> 24)         | 0xF8 :\n\t       ((c) >> 30)         | 0xFC;\n\n\tbuf[1]=(c) < 0x00000080 ?    0 /* null-terminator */     :\n\t       (c) < 0x00000800 ?  ((c)        & 0x3F) | 0x80 :\n\t       (c) < 0x00010000 ? (((c) >>  6) & 0x3F) | 0x80 :\n\t       (c) < 0x00200000 ? (((c) >> 12) & 0x3F) | 0x80 :\n\t       (c) < 0x04000000 ? (((c) >> 18) & 0x3F) | 0x80 :\n\t       (((c) >> 24) & 0x3F) | 0x80;\n\n\tbuf[2]=(c) < 0x00000800 ?    0 /* null-terminator */     :\n\t       (c) < 0x00010000 ?  ((c)        & 0x3F) | 0x80 :\n\t       (c) < 0x00200000 ? (((c) >>  6) & 0x3F) | 0x80 :\n\t       (c) < 0x04000000 ? (((c) >> 12) & 0x3F) | 0x80 :\n\t       (((c) >> 18) & 0x3F) | 0x80;\n\n\tbuf[3]=(c) < 0x00010000 ?    0 /* null-terminator */     :\n\t       (c) < 0x00200000 ?  ((c)        & 0x3F) | 0x80 :\n\t       (c) < 0x04000000 ? (((c) >>  6) & 0x3F) | 0x80 :\n\t       (((c) >> 12) & 0x3F) | 0x80;\n\n\tbuf[4]=(c) < 0x00200000 ?    0 /* null-terminator */     :\n\t       (c) < 0x04000000 ?  ((c)        & 0x3F) | 0x80 :\n\t       (((c) >>  6) & 0x3F) | 0x80;\n\n\tbuf[5]=(c) < 0x04000000 ?    0 /* null-terminator */     :\n\t       ((c)        & 0x3F) | 0x80;\n\n\tbuf[6]=0;\n\treturn 6;\n\t}\n\nconst char *unichar(kunichar c)\n\t{\n\tstatic char buffer[7];\n\tint pos=k_unichar_to_utf8(c, buffer);\n\tbuffer[pos]=0;\n\treturn buffer;\n\t}\n"
  },
  {
    "path": "core/DisplayTeX.hh",
    "content": "\n#pragma once\n\n#include \"Props.hh\"\n#include \"Storage.hh\"\n#include \"DisplayBase.hh\"\n#include <ostream>\n\ntypedef uint32_t kunichar;\n\nnamespace cadabra {\n\n\t/// \\ingroup display\n\t///\n\t/// Class to handle display of expressions using LaTeX notation. This\n\t/// is a very non-local bit of logic, in the sense that it will try to\n\t/// look around the property assignments in order to figure out the\n\t/// best way to print any given object. See the DisplayTeX::dispatch\n\t/// method to see how this works in more detail.\n\n\tclass DisplayTeX : public DisplayBase {\n\t\tpublic:\n\t\t\tDisplayTeX(const Kernel&, const Ex&);\n\n\t\tprotected:\n\t\t\tvirtual bool needs_brackets(Ex::iterator it) override;\n\n\t\tprivate:\n\t\t\t// FIXME: just make this take the multiplier, instead of the node. Then mult can go away.\n\t\t\tvoid print_multiplier(std::ostream&, Ex::iterator, int mult=1);\n\t\t\tvoid print_opening_bracket(std::ostream&, str_node::bracket_t, str_node::parent_rel_t);\n\t\t\tvoid print_closing_bracket(std::ostream&, str_node::bracket_t, str_node::parent_rel_t);\n\t\t\tvoid print_parent_rel(std::ostream&, str_node::parent_rel_t, bool first);\n\t\t\tvoid print_children(std::ostream&, Ex::iterator, int skip=0);\n\n\t\t\tstd::string texify(std::string) const;\n\n\t\t\tbool print_star=false;\n\t\t\tbool tight_star=false;\n\t\t\t//\t\tbool tight_plus=false;\n\t\t\t//\t\tbool utf8_output=false;\n\t\t\tbool latex_spacing=true;\n\t\t\t//\t\tbool latex_linefeeds=true;             // to prevent buffer overflows in TeX\n\t\t\tbool extra_brackets_for_symbols=false; // wrap extra {} around symbols to ensure typesetting safety\n\n\t\t\tint bracket_level=0;\n\n\t\t\t/// For every object encountered, dispatch will figure out the\n\t\t\t/// most appropriate way to convert it into a LaTeX\n\t\t\t/// expression. This may be done by simply looking at the\n\t\t\t/// object's name (e.g. `\\prod` will print as a product) but may\n\t\t\t/// also involve looking up properties and deciding on the best\n\t\t\t/// course of action based on the attached properties.\n\n\t\t\tvirtual void dispatch(std::ostream&, Ex::iterator) override;\n\n\t\t\t/// Printing members for various standard constructions,\n\t\t\t/// e.g. print as a list, or as a decorated symbol with\n\t\t\t/// super/subscripts etc. The names reflect the structure of the\n\t\t\t/// output, not necessarily the meaning or name of the object\n\t\t\t/// that is being printed.\n\n\t\t\tvoid print_productlike(std::ostream&, Ex::iterator, const std::string& inbetween);\n\t\t\tvoid print_sumlike(std::ostream&, Ex::iterator);\n\t\t\tvoid print_fraclike(std::ostream&, Ex::iterator);\n\t\t\tvoid print_commalike(std::ostream&, Ex::iterator);\n\t\t\tvoid print_arrowlike(std::ostream&, Ex::iterator);\n\t\t\tvoid print_powlike(std::ostream&, Ex::iterator);\n\t\t\tvoid print_intlike(std::ostream&, Ex::iterator);\n\t\t\tvoid print_equalitylike(std::ostream&, Ex::iterator);\n\t\t\tvoid print_commutator(std::ostream& str, Ex::iterator it, bool comm);\n\t\t\tvoid print_components(std::ostream&, Ex::iterator);\n\t\t\tvoid print_conditional(std::ostream&, Ex::iterator);\n\t\t\tvoid print_relation(std::ostream&, Ex::iterator);\n\t\t\tvoid print_indexbracket(std::ostream&, Ex::iterator);\n\t\t\tvoid print_wedgeproduct(std::ostream&, Ex::iterator);\n\t\t\tvoid print_tableau(std::ostream&, Ex::iterator);\n\t\t\tvoid print_ftableau(std::ostream&, Ex::iterator);\n\t\t\tvoid print_dot(std::ostream& str, Ex::iterator it);\n\t\t\tvoid print_dots(std::ostream& str, Ex::iterator it);\n\t\t\tvoid print_other(std::ostream& str, Ex::iterator it);\n\n\t\t\tbool children_have_brackets(Ex::iterator ch) const;\n\n\t\t\t/// Handle unprintable constructions like `\\pow{#}`, which need\n\t\t\t/// to print verbatim. Pass it the top-level iterator, will return\n\t\t\t/// true if printing has been taken care of.\n\t\t\tbool handle_unprintable_wildcards(std::ostream&, Ex::iterator it) const;\n\t\t\t\n\t\t\t/// Determine whether the indicated object 'obj', when acting on\n\t\t\t/// the single argument 'arg', reads as an operator, and therefore\n\t\t\t/// 'arg' does not need to be wrapped in brackets.\n\t\t\t/// Example: the tree `\\partial{A}` can be displayed as `\\partial A`\n\t\t\t/// (or rather, `\\partial{A}`, instead of `\\partial(A)`.\n\n\t\t\tbool reads_as_operator(Ex::iterator obj, Ex::iterator arg) const;\n\n\t\t\t/// Map from Cadabra symbols to LaTeX symbols (for some typographic cleanup).\n\t\t\tstd::map<std::string, std::string> symmap;\n\n\t\t\t/// List of operators which need all arguments fed with curly brackets, not\n\t\t\t/// round ones (e.g. `\\sqrt`).\n\t\t\tstd::set<std::string> curly_bracket_operators;\n\n\t\t};\n\n\tconst char *unichar(kunichar c);\n\n\t}\n"
  },
  {
    "path": "core/DisplayTerminal.cc",
    "content": "\n#include \"Algorithm.hh\"\n#include \"DisplayTerminal.hh\"\n#include \"Symbols.hh\"\n#include \"Exceptions.hh\"\n#include \"properties/Accent.hh\"\n#include \"NTensor.hh\"\n#include <variant>\n\nusing namespace cadabra;\n\nDisplayTerminal::DisplayTerminal(const Kernel& k, const Ex& e, bool uuc)\n\t: DisplayBase(k, e), use_unicode(uuc)\n\t{\n\tsymmap = {\n\t\t\t{\"\\\\cos\",  \"cos\"},\n\t\t\t{\"\\\\sin\",  \"sin\"},\n\t\t\t{\"\\\\tan\",  \"tan\"},\n\t\t\t{\"\\\\cosh\", \"cosh\"},\n\t\t\t{\"\\\\sinh\", \"sinh\"},\n\t\t\t{\"\\\\tanh\", \"tanh\"},\n\t\t\t{\"\\\\int\",  \"∫\" },\n\t\t\t{\"\\\\sum\",  \"∑\" },\n\t\t\t{\"\\\\iu\",   \"i\" }\n\t\t};\n\t}\n\n// Logic: each node should check whether it needs to have brackets printed around\n// all of itself. The function below will determine that by inspecting the parent\n// node. Nodes should NOT print brackets for children.\n\nbool DisplayTerminal::needs_brackets(Ex::iterator it)\n\t{\n\t// FIXME: may need looking at properties\n\t// FIXME: write as individual parent/current tests\n\tif(tree.is_head(it)) return false;\n\n\t//\tEx::iterator parent_it = tree.parent(it);\n\tEx::iterator child_it  = it;\n\tint child_num = tree.index(it);\n\n\tstd::string parent=*tree.parent(it)->name;\n\tstd::string child =*it->name;\n\n\tif(parent==\"\\\\partial\" && child==\"\\\\sum\") return true;\n\n\tif(parent==\"\\\\frac\" && ( child==\"\\\\sum\" || child==\"\\\\prod\" || (*child_it->multiplier!=1 && child_num>0) )) return true;\n\n\tif(parent==\"\\\\pow\" && ( !it->is_integer() || child==\"\\\\prod\" || child==\"\\\\sum\" || child==\"\\\\pow\")  ) return true;\n\n\t// negative and fractional exponents need brackets.\n\tif(parent==\"\\\\pow\" && (*it->multiplier < 0 || !it->is_integer()) ) return true;\n\n\t//\tif(parent==\"\\\\pow\" && child_num>0 && *child_it->multiplier!=1 ) return true;\n\n\tif(parent==\"\\\\prod\" && child==\"\\\\sum\") return true;\n\n\t//\tif(it->fl.parent_rel==str_node::p_none && (child==\"\\\\sum\" || child==\"\\\\prod\") ) return true;\n\n\treturn false;\n\t}\n\n//void DisplayTerminal::dispatch(std::ostream& str, Ex::iterator it)\n//\t{\n//\n//\t// print multiplier and object name\n//\tif(*it->multiplier!=1)\n//\t\tprint_multiplier(str, it);\n//\n//\tif(*it->name==\"1\") {\n//\t\tif(*it->multiplier==1 || (*it->multiplier==-1)) // this would print nothing altogether.\n//\t\t\tstr << \"1\";\n//\t\treturn;\n//\t\t}\n//\n//\tbool needs_extra_brackets=false;\n//\tconst Accent *ac=kernel.properties.get<Accent>(it);\n//\tif(!ac) { // accents should never get additional curly brackets, {\\bar}{g} does not print.\n//\t\tEx::sibling_iterator sib=tree.begin(it);\n//\t\twhile(sib!=tree.end(it)) {\n//\t\t\tif(sib->is_index())\n//\t\t\t\tneeds_extra_brackets=true;\n//\t\t\t++sib;\n//\t\t\t}\n//\t\t}\n//\n//\tif(needs_extra_brackets) str << \"{\"; // to prevent double sup/sub script errors\n//\tauto rn = symmap.find(*it->name);\n//\tif(rn!=symmap.end())\n//\t\tstr << rn->second;\n//\telse\n//\t\tstr << *it->name;\n//\tif(needs_extra_brackets) str << \"}\";\n//\n//\tprint_children(str, it);\n//\t}\n\nvoid DisplayTerminal::print_children(std::ostream& str, Ex::iterator it, int skip)\n\t{\n\tstr_node::bracket_t    previous_bracket_   =str_node::b_invalid;\n\tstr_node::parent_rel_t previous_parent_rel_=str_node::p_invalid;\n\n\tint number_of_nonindex_children=0;\n\tint number_of_index_children=0;\n\tEx::sibling_iterator ch=tree.begin(it);\n\twhile(ch!=tree.end(it)) {\n\t\tif(ch->is_index()==false) {\n\t\t\t++number_of_nonindex_children;\n\t\t\tif(*ch->name==\"\\\\prod\")\n\t\t\t\t++number_of_nonindex_children;\n\t\t\t}\n\t\telse ++number_of_index_children;\n\t\t++ch;\n\t\t}\n\n\tch=tree.begin(it);\n\tch+=skip;\n\tunsigned int chnum=0;\n\twhile(ch!=tree.end(it)) {\n\t\tstr_node::bracket_t    current_bracket_   =(*ch).fl.bracket;\n\t\tstr_node::parent_rel_t current_parent_rel_=(*ch).fl.parent_rel;\n\t\tconst Accent *is_accent=kernel.properties.get<Accent>(it);\n\n\t\tif(current_bracket_==str_node::b_none) {\n\t\t\tif(previous_bracket_==str_node::b_none && current_parent_rel_==previous_parent_rel_ && current_parent_rel_==str_node::p_none)\n\t\t\t\tstr << \", \";\n\t\t\t}\n\n\t\tif(current_bracket_!=str_node::b_none || previous_bracket_!=current_bracket_ || previous_parent_rel_!=current_parent_rel_) {\n\t\t\tprint_parent_rel(str, current_parent_rel_, ch==tree.begin(it));\n\t\t\tif(is_accent==0)\n\t\t\t\tprint_opening_bracket(str, (number_of_nonindex_children>1 /* &&number_of_index_children>0 */ &&\n\t\t\t\t                            current_parent_rel_!=str_node::p_sub &&\n\t\t\t\t                            current_parent_rel_!=str_node::p_super ? str_node::b_round:current_bracket_),\n\t\t\t\t                      current_parent_rel_);\n\t\t\telse str << \"{\";\n\t\t\t}\n\n\t\t// print this child depending on its name or meaning\n\t\tdispatch(str, ch);\n\n\t\t++ch;\n\t\tif(ch==tree.end(it) || current_bracket_!=str_node::b_none || current_bracket_!=(*ch).fl.bracket || current_parent_rel_!=(*ch).fl.parent_rel) {\n\t\t\tif(is_accent==0)\n\t\t\t\tprint_closing_bracket(str,  (number_of_nonindex_children>1 /* &&number_of_index_children>0 */ &&\n\t\t\t\t                             current_parent_rel_!=str_node::p_sub &&\n\t\t\t\t                             current_parent_rel_!=str_node::p_super ? str_node::b_round:current_bracket_),\n\t\t\t\t                      current_parent_rel_);\n\t\t\telse str  << \"}\";\n\t\t\t}\n\t\telse str << \" \";\n\n\t\tprevious_bracket_=current_bracket_;\n\t\tprevious_parent_rel_=current_parent_rel_;\n\t\t++chnum;\n\t\t}\n\t}\n\nvoid DisplayTerminal::print_multiplier(std::ostream& str, Ex::iterator it, int mult)\n\t{\n\tif(it->multiplier->is_rational()) {\n\t\tmpq_class q = it->multiplier->get_rational();\n\t\tmpz_class denom=q.get_den();\n\t\tmpz_class numer=q.get_num();\n\t\t\n\t\tif(denom!=1) {\n\t\t\tif(mult*numer<0) {\n\t\t\t\tstr << \" - \";\n\t\t\t\tmult *= -1;\n\t\t\t\t}\n\t\t\tstr << \" \" << mult * numer << \"/\" << denom << \" \";\n\t\t\t}\n\t\telse if(mult * it->multiplier->get_rational()==-1) {\n\t\t\tstr << \"-\";\n\t\t\t}\n\t\telse {\n\t\t\tstr << mult * (it->multiplier->get_rational());\n\t\t\t}\n\t\t}\n\telse {\n\t\tstr << *it->multiplier;\n\t\t}\n\t}\n\nvoid DisplayTerminal::print_opening_bracket(std::ostream& str, str_node::bracket_t br, str_node::parent_rel_t pr)\n\t{\n\tswitch(br) {\n\t\tcase str_node::b_none:\n\t\t\tif(pr==str_node::p_none)     str << \"(\";\n\t\t\telse                         str << \"{\";\n\t\t\tbreak;\n\t\tcase str_node::b_pointy:\n\t\t\tstr << \"<\";\n\t\t\tbreak;\n\t\tcase str_node::b_curly:\n\t\t\tstr << \"{\";\n\t\t\tbreak;\n\t\tcase str_node::b_round:\n\t\t\tstr << \"(\";\n\t\t\tbreak;\n\t\tcase str_node::b_square:\n\t\t\tstr << \"[\";\n\t\t\tbreak;\n\t\tdefault :\n\t\t\treturn;\n\t\t}\n\t++(bracket_level);\n\t}\n\nvoid DisplayTerminal::print_closing_bracket(std::ostream& str, str_node::bracket_t br, str_node::parent_rel_t pr)\n\t{\n\tswitch(br) {\n\t\tcase str_node::b_none:\n\t\t\tif(pr==str_node::p_none)     str << \")\";\n\t\t\telse                         str << \"}\";\n\t\t\tbreak;\n\t\tcase str_node::b_pointy:\n\t\t\tstr << \">\";\n\t\t\tbreak;\n\t\tcase str_node::b_curly:\n\t\t\tstr << \"}\";\n\t\t\tbreak;\n\t\tcase str_node::b_round:\n\t\t\tstr << \")\";\n\t\t\tbreak;\n\t\tcase str_node::b_square:\n\t\t\tstr << \"]\";\n\t\t\tbreak;\n\t\tdefault :\n\t\t\treturn;\n\t\t}\n\t--(bracket_level);\n\t}\n\nvoid DisplayTerminal::print_parent_rel(std::ostream& str, str_node::parent_rel_t pr, bool)\n\t{\n\tswitch(pr) {\n\t\tcase str_node::p_super:\n\t\t\tstr << \"^\";\n\t\t\tbreak;\n\t\tcase str_node::p_sub:\n\t\t\tstr << \"_\";\n\t\t\tbreak;\n\t\tcase str_node::p_property:\n\t\t\tstr << \"$\";\n\t\t\tbreak;\n\t\tcase str_node::p_exponent:\n\t\t\tstr << \"**\";\n\t\t\tbreak;\n\t\tcase str_node::p_none:\n\t\t\tbreak;\n\t\tcase str_node::p_components:\n\t\t\tbreak;\n\t\tcase str_node::p_invalid:\n\t\t\tbreak;\n\t\t}\n\t}\n\nvoid DisplayTerminal::dispatch(std::ostream& str, Ex::iterator it)\n\t{\n\tif(handle_unprintable_wildcards(str, it))\n\t\treturn;\n\t\n\tif(std::holds_alternative<std::shared_ptr<NTensor>>(it->content)) {\n\t\tauto nt = std::get<std::shared_ptr<NTensor>>(it->content);\n\t\tstr << (*nt);\n//\t\tstd::string s = str2.str();\n//\t\tstr << std::regex_replace(s, std::regex(\"(\\\\d+\\\\.?\\\\d*|\\\\.\\\\d+)e([+-]?\\\\d+)\"), \"$1 \\\\times 10^{$2}\");\n\t\treturn; // FIXME: always just ignore the subtree?\n\t\t}\n\telse if(std::holds_alternative<std::shared_ptr<NInterpolatingFunction>>(it->content)) {\n\t\tstr << \" (NInterpolatingFunction)\";\n\t\treturn;\n\t\t}\n\t\n\tif(*it->name==\"\\\\prod\")            print_productlike(str, it, \" \");\n\telse if(*it->name==\"\\\\sum\")        print_sumlike(str, it);\n\telse if(*it->name==\"\\\\frac\")       print_fraclike(str, it);\n\telse if(*it->name==\"\\\\comma\")      print_commalike(str, it);\n\telse if(*it->name==\"\\\\commutator\") print_commutator(str, it, true);\n\telse if(*it->name==\"\\\\anticommutator\") print_commutator(str, it, false);\n\telse if(*it->name==\"\\\\arrow\")      print_arrowlike(str, it);\n\telse if(*it->name==\"\\\\inner\")      print_dot(str, it);\n\telse if(*it->name==\"\\\\pow\")        print_powlike(str, it);\n\telse if(*it->name==\"\\\\wedge\")      print_productlike(str, it, \" ^ \");\n\telse if(*it->name==\"\\\\conditional\")    print_conditional(str, it);\n\telse if(*it->name==\"\\\\greater\" || *it->name==\"\\\\less\")  print_relation(str, it);\n\telse if(*it->name==\"\\\\int\")        print_intlike(str, it);\n\telse if(*it->name==\"\\\\sum\")        print_intlike(str, it);\n\telse if(*it->name==\"\\\\equals\")     print_equalitylike(str, it);\n\telse if(*it->name==\"\\\\components\") print_components(str, it);\n\telse if(*it->name==\"\\\\ldots\")      print_dots(str, it);\n\telse                               print_other(str, it);\n\t}\n\nbool DisplayTerminal::handle_unprintable_wildcards(std::ostream& str, Ex::iterator it) const\n\t{\n\t// Catch `\\pow{#}` and other wildcard constructions, these\n\t// need to print verbatim.\n\n\tif(it.number_of_children()==1) {\n\t\tif(*(it.begin()->name)==\"#\") {\n\t\t\tstr << (*(it->name)) << \"{#}\";\n\t\t\treturn true;\n\t\t\t}\n\t\t}\n\treturn false;\n\t}\n\nvoid DisplayTerminal::print_commalike(std::ostream& str, Ex::iterator it)\n\t{\n\tEx::sibling_iterator sib=tree.begin(it);\n\tbool first=true;\n\tstr << \"{\";\n\twhile(sib!=tree.end(it)) {\n\t\tif(first)\n\t\t\tfirst=false;\n\t\telse\n\t\t\tstr << \", \";\n\t\tdispatch(str, sib);\n\t\t++sib;\n\t\t}\n\tstr << \"}\";\n\t}\n\nvoid DisplayTerminal::print_arrowlike(std::ostream& str, Ex::iterator it)\n\t{\n\tEx::sibling_iterator sib=tree.begin(it);\n\tdispatch(str, sib);\n\tif(use_unicode)\n\t\tstr << \" → \";\n\telse\n\t\tstr << \" -> \";\n\t++sib;\n\tdispatch(str, sib);\n\t}\n\nvoid DisplayTerminal::print_dot(std::ostream& str, Ex::iterator it)\n\t{\n\tEx::sibling_iterator sib=tree.begin(it);\n\tdispatch(str, sib);\n\tif(use_unicode)\n\t\tstr << \"·\";\n\telse\n\t\tstr << \".\";\n\t++sib;\n\tdispatch(str, sib);\n\t}\n\nvoid DisplayTerminal::print_fraclike(std::ostream& str, Ex::iterator it)\n\t{\n\tEx::sibling_iterator num=tree.begin(it), den=num;\n\t++den;\n\n\tif(*it->multiplier!=1)\n\t\tprint_multiplier(str, it);\n\n\t//\tif(needs_brackets(num))\n\t//\t\tstr << \"(\";\n\n\tif(num->is_rational()==false || (*it->multiplier)==1)\n\t\tdispatch(str, num);\n\n\t//\tif(needs_brackets(num))\n\t//\t\tstr << \")\";\n\n\tstr << \"/\";\n\n\t//\tif(needs_brackets(den))\n\t//\t\tstr << \"(\";\n\n\tdispatch(str, den);\n\n\t//\tif(needs_brackets(den))\n\t//\t\tstr << \")\";\n\t}\n\nvoid DisplayTerminal::print_productlike(std::ostream& str, Ex::iterator it, const std::string& inbetween)\n\t{\n\tif(needs_brackets(it))\n\t\tstr << \"(\";\n\n\tif(*it->multiplier!=1) {\n\t\tprint_multiplier(str, it);\n\t\t//\t\tEx::sibling_iterator st=tree.begin(it);\n\t\t}\n\n\t// To print \\prod{\\sum{a}{b}}{\\sum{c}{d}} correctly:\n\t// If there is any sum as child, and if the sum children do not\n\t// all have the same bracket type (different from b_none or b_no),\n\t// then print brackets.\n\n\tstr_node::bracket_t previous_bracket_=str_node::b_invalid;\n//\tbool beginning_of_group=true;\n\tEx::sibling_iterator ch=tree.begin(it);\n\twhile(ch!=tree.end(it)) {\n\t\tstr_node::bracket_t current_bracket_=(*ch).fl.bracket;\n\t\tif(previous_bracket_!=current_bracket_) {\n\t\t\tif(current_bracket_!=str_node::b_none) {\n\t\t\t\tprint_opening_bracket(str, current_bracket_, str_node::p_none);\n//\t\t\t\tbeginning_of_group=true;\n\t\t\t\t}\n\t\t\t}\n\t\tdispatch(str, ch);\n\t\t++ch;\n\t\tif(ch==tree.end(it)) {\n\t\t\tif(current_bracket_!=str_node::b_none)\n\t\t\t\tprint_closing_bracket(str, current_bracket_, str_node::p_none);\n\t\t\t}\n\n\t\tif(ch!=tree.end(it)) {\n\t\t\tstr << inbetween;\n\t\t\t}\n\t\tprevious_bracket_=current_bracket_;\n\t\t}\n\n\tif(needs_brackets(it))\n\t\tstr << \")\";\n\t}\n\nvoid DisplayTerminal::print_sumlike(std::ostream& str, Ex::iterator it)\n\t{\n\tassert(*it->multiplier==1);\n\n\tif(needs_brackets(it))\n\t\tstr << \"(\";\n\n\tEx::sibling_iterator ch=tree.begin(it);\n\twhile(ch!=tree.end(it)) {\n\t\tif(*ch->multiplier>=0 && ch!=tree.begin(it))\n\t\t\tstr << \" + \";\n\n\t\tdispatch(str, ch);\n\t\t++ch;\n\t\t}\n\n\tif(needs_brackets(it))\n\t\tstr << \")\";\n\tstr << std::flush;\n\t}\n\nvoid DisplayTerminal::print_powlike(std::ostream& str, Ex::iterator it)\n\t{\n\tif(needs_brackets(it))\n\t\tstr << \"(\";\n\n\tEx::sibling_iterator sib=tree.begin(it);\n\tif(*it->multiplier!=1)\n\t\tprint_multiplier(str, it);\n\tdispatch(str, sib);\n\t//\tif(needs_brackets(sib))\n\t//\t\tstr << \")\";\n\tstr << \"**\";\n\t++sib;\n\t//\tif(needs_brackets(sib))\n\t//\t\tstr << \"(\";\n\tdispatch(str, sib);\n\n\tif(needs_brackets(it))\n\t\tstr << \")\";\n\t}\n\nvoid DisplayTerminal::print_conditional(std::ostream& str, Ex::iterator it)\n\t{\n\tauto sib=tree.begin(it);\n\tdispatch(str, sib);\n\tstr << \" with \";\n\t++sib;\n\tdispatch(str, sib);\n\t}\n\nvoid DisplayTerminal::print_relation(std::ostream& str, Ex::iterator it)\n\t{\n\tauto sib=tree.begin(it);\n\tdispatch(str, sib);\n\tif(*it->name==\"\\\\greater\") str << \" > \";\n\tif(*it->name==\"\\\\less\")    str << \" < \";\n\t++sib;\n\tdispatch(str, sib);\n\t}\n\nvoid DisplayTerminal::print_intlike(std::ostream& str, Ex::iterator it)\n\t{\n\tif(*it->multiplier!=1)\n\t\tprint_multiplier(str, it);\n\tif(!use_unicode || getenv(\"CADABRA_NO_UNICODE\")!=0)\n\t\tstr << *it->name << \"{\";\n\telse\n\t\tstr << symmap[*it->name] << \"(\";\n\tEx::sibling_iterator sib=tree.begin(it);\n\tdispatch(str, sib);\n\t++sib;\n\tif(tree.is_valid(sib)) {\n\t\tstr << \"}{\";\n\t\tdispatch(str, sib);\n\t\t}\n\tstr << \"}\";\n\t}\n\nvoid DisplayTerminal::print_equalitylike(std::ostream& str, Ex::iterator it)\n\t{\n\tEx::sibling_iterator sib=tree.begin(it);\n\tdispatch(str, sib);\n\tstr << \" = \";\n\t++sib;\n\tif(sib==tree.end(it))\n\t\tthrow ConsistencyException(\"Found equals node with only one child node.\");\n\tdispatch(str, sib);\n\t}\n\nvoid DisplayTerminal::print_commutator(std::ostream& str, Ex::iterator it, bool comm)\n\t{\n\tif(comm) str << \"[\";\n\telse     str << \"{\";\n\tauto sib=tree.begin(it);\n\tbool first=true;\n\twhile(sib!=tree.end(it)) {\n\t\tif(!first) str << \", \";\n\t\telse       first=false;\n\t\tdispatch(str, sib);\n\t\t++sib;\n\t\t}\n\tif(comm) str << \"]\";\n\telse     str << \"}\";\n\t}\n\nvoid DisplayTerminal::print_components(std::ostream& str, Ex::iterator it)\n\t{\n\tif( ! (use_unicode && getenv(\"CADABRA_NO_UNICODE\")==0) ) {\n\t\tprint_other(str, it);\n\t\treturn;\n\t\t}\n\n\tstr << R\"(□)\";\n\tauto sib=tree.begin(it);\n\tauto end=tree.end(it);\n\t--end;\n\tif(sib!=end) {\n\t\tbool needs_close=false;\n\t\tstr_node::parent_rel_t prel=str_node::parent_rel_t::p_none;\n\t\twhile(sib!=end) {\n\t\t\tif(sib->fl.parent_rel!=prel) {\n\t\t\t\tif(needs_close)\n\t\t\t\t\tstr << \"}\";\n\t\t\t\tneeds_close=true;\n\t\t\t\tprel=sib->fl.parent_rel;\n\t\t\t\tif(prel==str_node::p_sub)   str << \"_{\";\n\t\t\t\tif(prel==str_node::p_super) str << \"^{\";\n\t\t\t\t}\n\t\t\tdispatch(str, sib);\n\t\t\t++sib;\n\t\t\t}\n\t\tif(needs_close)\n\t\t\tstr << \"}\";\n\t\t}\n\tstr << \"\\n\";\n\tsib=tree.begin(end);\n\twhile(sib!=tree.end(end)) {\n\t\tstr << \"    \";\n\t\tdispatch(str, sib);\n\t\tstr << \"\\n\";\n\t\t++sib;\n\t\t}\n\t}\n\nbool DisplayTerminal::children_have_brackets(Ex::iterator ch) const\n\t{\n\tEx::sibling_iterator chlds=tree.begin(ch);\n\tstr_node::bracket_t childbr=chlds->fl.bracket;\n\tif(childbr==str_node::b_none || childbr==str_node::b_no)\n\t\treturn false;\n\telse return true;\n\t}\n\nvoid DisplayTerminal::print_dots(std::ostream& str, Ex::iterator )\n\t{\n\tstr << \" ... \";\n\t}\n\nvoid DisplayTerminal::print_other(std::ostream& str, Ex::iterator it)\n\t{\n\tif(needs_brackets(it))\n\t\tstr << \"(\";\n\n\t// print multiplier and object name\n\tif(*it->multiplier!=1)\n\t\tprint_multiplier(str, it);\n\n\tif(*it->name==\"1\") {\n\t\tif(*it->multiplier==1 || (*it->multiplier==-1)) // this would print nothing altogether.\n\t\t\tstr << \"1\";\n\t\tif(needs_brackets(it))\n\t\t\tstr << \")\";\n\t\treturn;\n\t\t}\n\n\tbool needs_extra_brackets=false;\n\t//\tconst Accent *ac=kernel.properties.get<Accent>(it);\n\t//\tif(!ac) { // accents should never get additional curly brackets, {\\bar}{g} does not print.\n\t//\t\tEx::sibling_iterator sib=tree.begin(it);\n\t//\t\twhile(sib!=tree.end(it)) {\n\t//\t\t\tif(sib->is_index())\n\t//\t\t\t\tneeds_extra_brackets=true;\n\t//\t\t\t++sib;\n\t//\t\t\t}\n\t//\t\t}\n\n\tif(needs_extra_brackets) str << \"{\"; // to prevent double sup/sub script errors\n\tstd::string sbit=*it->name;\n\tif(sbit!=\"\\\\indexbracket\") {\n\t\tif(use_unicode && getenv(\"CADABRA_NO_UNICODE\")==0) {\n\t\t\tauto rn1 = symmap.find(sbit);\n\t\t\tif(rn1!=symmap.end())\n\t\t\t\tsbit = rn1->second;\n\t\t\tauto rn = cadabra::symbols::greekmap.find(sbit);\n\t\t\tif(rn!=cadabra::symbols::greekmap.end())\n\t\t\t\tsbit = rn->second;\n\t\t\t}\n\t\tstr << sbit;\n\t\t}\n\t\n\tif(needs_extra_brackets) str << \"}\";\n\n\tprint_children(str, it);\n\n\n\tif(needs_brackets(it))\n\t\tstr << \")\";\n\t}\n"
  },
  {
    "path": "core/DisplayTerminal.hh",
    "content": "\n#pragma once\n\n#include \"Props.hh\"\n#include \"Storage.hh\"\n#include \"DisplayBase.hh\"\n#include <ostream>\n#include <map>\n#include <string>\n\ntypedef uint32_t kunichar;\n\nnamespace cadabra {\n\n\t/// \\ingroup display\n\t///\n\t/// Class to display expressions to the terminal. This is used in the\n\t/// PythonCdb bridge to provide 'str' type python printing for Ex\n\t/// objects. The cadabra2 command line application uses this class for\n\t/// all its output. This class does not necessarily produce output which\n\t/// is readable by sympy; for that, use the DisplaySympy class (as an\n\t/// example, partial derivatives will display using a LaTeX notation using\n\t/// the present class, but be printed as 'sympy.diff' by the DisplaySympy\n\t/// class).\n\n\tclass DisplayTerminal : public DisplayBase {\n\t\tpublic:\n\t\t\tDisplayTerminal(const Kernel&, const Ex&, bool use_unicode = true);\n\n\t\tprotected:\n\t\t\tbool use_unicode;\n\n\t\t\tvirtual void dispatch(std::ostream&, Ex::iterator) override;\n\t\t\tvirtual bool needs_brackets(Ex::iterator it) override;\n\n\t\tprivate:\n\t\t\tvoid print_multiplier(std::ostream&, Ex::iterator, int mult=1);\n\t\t\tvoid print_opening_bracket(std::ostream&, str_node::bracket_t, str_node::parent_rel_t);\n\t\t\tvoid print_closing_bracket(std::ostream&, str_node::bracket_t, str_node::parent_rel_t);\n\t\t\tvoid print_parent_rel(std::ostream&, str_node::parent_rel_t, bool first);\n\t\t\tvoid print_children(std::ostream&, Ex::iterator, int skip=0);\n\n\t\t\tint bracket_level=0;\n\n\t\t\t/// Printing members for various standard constructions,\n\t\t\t/// e.g. print as a list, or as a decorated symbol with\n\t\t\t/// super/subscripts etc. The names reflect the structure of the\n\t\t\t/// output, not necessarily the meaning or name of the object\n\t\t\t/// that is being printed.\n\n\t\t\tvoid print_productlike(std::ostream&, Ex::iterator, const std::string& inbetween);\n\t\t\tvoid print_sumlike(std::ostream&, Ex::iterator);\n\t\t\tvoid print_fraclike(std::ostream&, Ex::iterator);\n\t\t\tvoid print_commalike(std::ostream&, Ex::iterator);\n\t\t\tvoid print_arrowlike(std::ostream&, Ex::iterator);\n\t\t\tvoid print_dot(std::ostream&, Ex::iterator);\n\t\t\tvoid print_powlike(std::ostream&, Ex::iterator);\n\t\t\tvoid print_intlike(std::ostream&, Ex::iterator);\n\t\t\tvoid print_conditional(std::ostream&, Ex::iterator);\n\t\t\tvoid print_relation(std::ostream&, Ex::iterator);\n\t\t\tvoid print_equalitylike(std::ostream&, Ex::iterator);\n\t\t\tvoid print_commutator(std::ostream& str, Ex::iterator it, bool comm);\n\t\t\tvoid print_components(std::ostream&, Ex::iterator);\n\t\t\tvoid print_dots(std::ostream&, Ex::iterator);\n\t\t\tvoid print_other(std::ostream&, Ex::iterator);\n\n\t\t\t/// Handle unprintable constructions like `\\pow{#}`, which need\n\t\t\t/// to print verbatim. Pass it the top-level iterator, will return\n\t\t\t/// true if printing has been taken care of.\n\t\t\tbool handle_unprintable_wildcards(std::ostream&, Ex::iterator it) const;\n\n\t\t\tbool children_have_brackets(Ex::iterator ch) const;\n\n\t\t\tstd::map<std::string, std::string> symmap;\n\t\t};\n\n\tconst char *unichar(kunichar c);\n\n\t}\n"
  },
  {
    "path": "core/Dummies.hh",
    "content": "/*\n\nCadabra: a field-theory motivated computer algebra system.\nCopyright (C) 2001-2011  Kasper Peeters <kasper.peeters@aei.mpg.de>\n\nThis program is free software: you can redistribute it and/or\n\tmodify it under the terms of the GNU General Public License as\npublished by the Free Software Foundation, either version 3 of the\nLicense, or (at your option) any later version.\n\nThis program is distributed in the hope that it will be useful,\nbut WITHOUT ANY WARRANTY; without even the implied warranty of\nMERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU\nGeneral Public License for more details.\n\nYou should have received a copy of the GNU General Public License\nalong with this program.  If not, see <http://www.gnu.org/licenses/>.\n\n*/\n\n#ifndef dummies_hh_\n#define dummies_hh_\n\n#include \"algorithm.hh\"\n#include \"props.hh\"\n\nclass rename_dummies : public algorithm {\n\tpublic:\n\t\trename_dummies(Ex&, iterator);\n\n\t\tvirtual bool     can_apply(iterator);\n\t\tvirtual result_t apply(iterator&);\n\t};\n\n\n#endif\n"
  },
  {
    "path": "core/Equals.cc",
    "content": "\n#include \"Equals.hh\"\n#include \"Exceptions.hh\"\n\nusing namespace cadabra;\n\nvisit::Equals::Equals(const Kernel &k, Ex &e, Ex::iterator i)\n\t: ReservedNode(k, e, i)\n\t{\n\tif(*top->name != \"\\\\equals\")\n\t\tthrow ConsistencyException(\"Top not not an equality.\");\n\t}\n\nEx::iterator visit::Equals::lhs() const\n\t{\n\treturn tr.begin(top);\n\t}\n\nEx::iterator visit::Equals::rhs() const\n\t{\n\tsibling_iterator it = tr.begin(top);\n\t++it;\n\treturn it;\n\t}\n\nvoid visit::Equals::move_all_to_lhs()\n\t{\n\tEx::iterator lhs_ = lhs();\n\tEx::iterator rhs_ = rhs();\n\n\tif(*lhs_->name!=\"\\\\sum\")\n\t\tforce_node_wrap(lhs_, \"\\\\sum\");\n\tif(*rhs_->name!=\"\\\\sum\")\n\t\tforce_node_wrap(rhs_, \"\\\\sum\");\n\n\tEx::iterator last = tr.end(lhs_);\n\tlast.skip_children();\n\t--last;\n\n\ttr.reparent(lhs_, rhs_);\n\n\tlast.skip_children();\n\t++last;\n\twhile(last != tr.end(lhs_)) {\n\t\tmultiply(last->multiplier, -1);\n\t\tlast.skip_children();\n\t\t++last;\n\t\t}\n\n\ttr.append_child(rhs_, Ex(0).begin());\n\t}\n"
  },
  {
    "path": "core/Equals.hh",
    "content": "#pragma once\n\n#include \"Storage.hh\"\n#include \"Kernel.hh\"\n#include \"ReservedNode.hh\"\n\nnamespace cadabra {\n\n\tnamespace visit {\n\t\n\t\tclass Equals : public cadabra::visit::ReservedNode {\n\t\t\tpublic:\n\t\t\t\tEquals(const Kernel&, Ex&, Ex::iterator);\n\t\t\t\t\n\t\t\t\t/// Left-hand side.\n\t\t\t\tEx::iterator lhs() const;\n\t\t\t\tEx::iterator rhs() const;\n\t\t\t\t\n\t\t\t\t/// Move all terms in an equality to the left-hand side.\n\t\t\t\tvoid move_all_to_lhs();\n\t\t};\n\t};\n};\n        \n"
  },
  {
    "path": "core/ExManip.cc",
    "content": "\n#include \"ExManip.hh\"\n#include \"Kernel.hh\"\n#include \"properties/Accent.hh\"\n\nusing namespace cadabra;\n\nExManip::ExManip(const Kernel &k, Ex &e)\n\t: kernel(k)\n\t, tr(e)\n\t{\n\t}\n\nbool ExManip::prod_wrap_single_term(iterator& it)\n\t{\n\tif(is_single_term(it)) {\n\t\tforce_node_wrap(it, \"\\\\prod\");\n\t\treturn true;\n\t\t}\n\telse return false;\n\t}\n\nbool ExManip::sum_wrap_single_term(iterator& it)\n\t{\n\tif(is_single_term(it)) {\n\t\tforce_node_wrap(it, \"\\\\sum\");\n\t\treturn true;\n\t\t}\n\telse return false;\n\t}\n\nvoid ExManip::force_node_wrap(iterator& it, std::string nm)\n\t{\n\titerator prodnode=tr.insert(it, str_node(nm));\n\tsibling_iterator fr=it, to=it;\n\t++to;\n\ttr.reparent(prodnode, fr, to);\n\tprodnode->fl.bracket=it->fl.bracket;\n\tit->fl.bracket=str_node::b_none;\n\tif(nm!=\"\\\\sum\") { // multipliers should sit on terms in a sum\n\t\tprodnode->multiplier=it->multiplier;\n\t\tone(it->multiplier);\n\t\t}\n\tit=prodnode;\n\t}\n\nbool ExManip::prod_unwrap_single_term(iterator& it)\n\t{\n\tif((*it->name)==\"\\\\prod\") {\n\t\tif(tr.number_of_children(it)==1) {\n\t\t\tmultiply(tr.begin(it)->multiplier, *it->multiplier);\n\t\t\ttr.begin(it)->fl.bracket=it->fl.bracket;\n\t\t\ttr.begin(it)->multiplier=it->multiplier;\n\t\t\ttr.flatten(it);\n\t\t\tit=tr.erase(it);\n\t\t\treturn true;\n\t\t\t}\n\t\t}\n\treturn false;\n\t}\n\nbool ExManip::sum_unwrap_single_term(iterator& it)\n\t{\n\tif((*it->name)==\"\\\\sum\") {\n\t\tif(tr.number_of_children(it)==1) {\n\t\t\tmultiply(tr.begin(it)->multiplier, *it->multiplier);\n\t\t\ttr.begin(it)->fl.bracket=it->fl.bracket;\n\t\t\ttr.begin(it)->multiplier=it->multiplier;\n\t\t\ttr.flatten(it);\n\t\t\tit=tr.erase(it);\n\t\t\treturn true;\n\t\t\t}\n\t\t}\n\treturn false;\n\t}\n\nbool ExManip::is_single_term(iterator it)\n\t{\n\tif(*it->name!=\"\\\\prod\" && *it->name!=\"\\\\sum\" && *it->name!=\"\\\\asymimplicit\"\n\t      && *it->name!=\"\\\\comma\" && *it->name!=\"\\\\equals\" && *it->name!=\"\\\\arrow\") {\n\n\t\tif(tr.is_head(it) || *tr.parent(it)->name==\"\\\\equals\" || *tr.parent(it)->name==\"\\\\int\") return true;\n\t\telse if(*tr.parent(it)->name==\"\\\\sum\")\n\t\t\treturn true;\n\t\telse if(*tr.parent(it)->name!=\"\\\\prod\" && it->fl.parent_rel==str_node::parent_rel_t::p_none\n\t\t        && kernel.properties.get<Accent>(tr.parent(it))==0 ) {\n#ifdef DEBUG\n\t\t\tstd::cerr << \"Found single term in \" << tr.parent(it) << std::endl;\n#endif\n\t\t\treturn true;\n\t\t\t}\n\t\t}\n\treturn false;\n\t}\n\nbool ExManip::is_nonprod_factor_in_prod(iterator it)\n\t{\n\tif(*it->name!=\"\\\\prod\" && *it->name!=\"\\\\sum\" && *it->name!=\"\\\\asymimplicit\" && *it->name!=\"\\\\comma\"\n\t      && *it->name!=\"\\\\equals\") {\n\t\ttry {\n\t\t\tif(tr.is_head(it)==false && *tr.parent(it)->name==\"\\\\prod\")\n\t\t\t\treturn true;\n\t\t\t}\n\t\tcatch(navigation_error& ex) {\n\t\t\t// no parent, ignore\n\t\t\t}\n\t\t//\t\telse return true;\n\t\t}\n\treturn false;\n\t}\n\n        \n"
  },
  {
    "path": "core/ExManip.hh",
    "content": "#pragma once\n\n#include \"Storage.hh\"\n\nnamespace cadabra {\n\n\tclass Kernel;\n\n\tclass ExManip {\n\t\tpublic:\n\t\t\ttypedef Ex::iterator_base       iterator_base;\n\t\t\ttypedef Ex::iterator            iterator;\n\t\t\ttypedef Ex::post_order_iterator post_order_iterator;\n\t\t\ttypedef Ex::sibling_iterator    sibling_iterator;\n\n\t\t\tExManip(const Kernel&, Ex&);\n\t\t\t\n\t\t\t/// Take a single non-product node in a sum and wrap it in a\n\t\t\t/// product node, so it can be handled on the same footing as a proper product.\n\t\t\tbool prod_wrap_single_term(iterator&);\n\t\t\tbool prod_unwrap_single_term(iterator&);\n\t\t\tbool sum_wrap_single_term(iterator&);\n\t\t\tbool sum_unwrap_single_term(iterator&);\n\n\t\t\t/// Is the indicated node a single term in an expression?\n         /// Returns true if the indicated node is a single\n         /// non-reserved node (non-prod, non-sum, ...)  at the top\n         /// level of an expression (real top, top of equation\n         /// lhs/rhs, top of integral argument, ...).\n\t\t\tbool  is_single_term(iterator);\n\n\t\t\t/// \n\t\t\tbool  is_nonprod_factor_in_prod(iterator);\n\n\t\t\t/// Wrap a term in a product or sum in a node with indicated\n\t\t\t/// name, irrespective of its parent (it usually makes more\n\t\t\t/// sense to call the safer prod_wrap_single_term or\n\t\t\t/// sum_wrap_single_term above). Sets the iterator to the\n\t\t\t/// new node.\n\t\t\tvoid  force_node_wrap(iterator&, std::string);\n\n\t\tprotected:\n\t\t\tconst Kernel& kernel;\n\t\t\tEx&           tr;\n\t};\n\t\n};\n"
  },
  {
    "path": "core/ExNode.cc",
    "content": "\n#include \"ExNode.hh\"\n#include \"Cleanup.hh\"\n#include \"Exceptions.hh\"\n#include \"Algorithm.hh\"\n#include \"pythoncdb/py_kernel.hh\"\n#include <pybind11/pybind11.h>\n#include <pybind11/embed.h>\n#include <pybind11/operators.h>\n#include <pybind11/stl.h>\n#include \"DisplayTeX.hh\"\n#include \"DisplaySympy.hh\"\n#include \"DisplayTerminal.hh\"\n#include \"pythoncdb/py_ex.hh\"\n#include <sstream>\n\n//#define DEBUG 1\n\nusing namespace cadabra;\n\nExNode::ExNode(const Kernel& k, std::shared_ptr<Ex> ex_)\n\t: IndexClassifier(k), ex(ex_), indices_only(false), args_only(false), terms_only(false), factors_only(false),\n\t  indnxtit(get_kernel_from_scope()->properties), use_sibling_iterator(false), use_index_iterator(false)\n\t{\n\t}\n\nbool ExNode::is_valid() const\n\t{\n\treturn ex->is_valid(it);\n\t}  \n\nExNode ExNode::copy() const\n\t{\n\tExNode ret(kernel, ex);\n\n\tret.it=it;\n\tret.tag=tag;\n\tret.indices_only=indices_only;\n\tret.args_only=args_only;\n\tret.terms_only=terms_only;\n\tret.factors_only=factors_only;\n\n\tret.nxtit=nxtit;\n\tret.sibnxtit=sibnxtit;\n\tret.indnxtit=indnxtit;\n\n\tret.use_sibling_iterator=use_sibling_iterator;\n\tret.use_index_iterator=use_index_iterator;\n\n\tret.topit=topit;\n\tret.stopit=stopit;\n\n\tret.ind_free=ind_free;\n\tret.ind_dummy=ind_dummy;\n\tret.ind_pos_dummy=ind_pos_dummy;\n\n\treturn ret;\n\t}\n\nstd::string ExNode::input_form() const\n   {\n\t\t// FIXME: this is a duplicate of Ex_as_string; unify the logic.\n\t\tstd::ostringstream str;\n\n\t\tDisplayTerminal dt(*get_kernel_from_scope(), get_ex(), false);\n\t\tdt.output(str);\n\n\t\treturn str.str();\n   }\n\nExNode ExNode::getitem_string(std::string tag)\n\t{\n\tExNode ret(kernel, ex);\n\tret.tag=tag;\n\tret.ex=ex;\n\tret.topit=it;\n\tret.stopit=it;\n\tret.stopit.skip_children();\n\t++ret.stopit;\n\tret.update(true);\n\treturn ret;\n\t}\n\nExNode ExNode::getitem_iterator(ExNode it)\n\t{\n\tif(it.ex!=ex) {\n\n\t\tstd::cerr << \"Need to convert iterator\" << std::endl;\n\t\t}\n\n\tExNode ret=it;\n\treturn ret;\n\t}\n\nvoid ExNode::setitem_string(std::string, std::shared_ptr<Ex>)\n\t{\n\t//   ExNode ret(ex);\n\t//   ret.tag=tag;\n\t//   ret.ex=ex;\n\t//   ret.topit=it;\n\t//   ret.stopit=it;\n\t//   ret.stopit.skip_children();\n\t//   ++ret.stopit;\n\t//   ret.update(true);\n\t//\n\tstd::cerr << \"will set iterator range to value\" << std::endl;\n\t////\tEx::iterator it=ex->begin();\n\t////\n\t////\tsize_t num=ex->number_of_children(it);\n\t////\tif(index>=0 && (size_t)index<num)\n\t////\t\tex->replace(ex->child(it, index), val.begin());\n\t////\telse\n\t////\t\tthrow ArgumentException(\"index \"+std::to_string(index)+\" out of range, must be smaller than \"+std::to_string(num));\n\t//\n\t//   return ret;\n\t}\n\nvoid ExNode::setitem_iterator(ExNode en, std::shared_ptr<Ex> val)\n\t{\n\tstd::cerr << \"Setitem iterator\" << std::endl;\n\n\tEx::iterator use;\n\tif(en.ex!=ex) {\n\t\tstd::cerr << \"Setitem need to convert iterator\" << std::endl;\n\t\tauto path=en.ex->path_from_iterator(en.it, en.topit);\n\t\tuse=ex->iterator_from_path(path, topit);\n\t\t}\n\telse use=en.it;\n\n\tEx::iterator top=val->begin();\n\tif(*top->name==\"\") {\n\t\t// std::cerr << \"top is empty\" << std::endl;\n\t\ttop=val->begin(top);\n\t\t}\n\tex->replace(use, top);\n\t}\n\nExNode ExNode::terms()\n\t{\n\tExNode ret(kernel, ex);\n\tret.topit=it;\n\tret.terms_only=true;\n\tret.factors_only=false;\n\tret.use_sibling_iterator=true;\n\tret.update(true);\n\treturn ret;\n\t}\n\nExNode ExNode::factors()\n\t{\n\tExNode ret(kernel, ex);\n\tret.topit=it;\n\tret.terms_only=false;\n\tret.factors_only=true;\n\tret.use_sibling_iterator=true;\n\tret.update(true);\n\treturn ret;\n\t}\n\nExNode ExNode::own_indices()\n\t{\n\tExNode ret(kernel, ex);\n\tret.topit=it;\n\tret.indices_only=true;\n\tret.use_sibling_iterator=true;\n\tret.update(true);\n\treturn ret;\n\t}\n\nExNode ExNode::indices()\n\t{\n\tExNode ret(kernel, ex);\n\tret.topit=it;\n\tret.ind_free.clear();\n\tret.ind_dummy.clear();\n\tret.indices_only=true;\n\tret.use_index_iterator=true;\n\tret.update(true);\n\treturn ret;\n\t}\n\nExNode ExNode::free_indices()\n\t{\n\tExNode ret(kernel, ex);\n\tret.topit=it;\n\tret.ind_free.clear();\n\tret.ind_dummy.clear();\n\tclassify_indices(it, ret.ind_free, ret.ind_dummy);\n\tfill_index_position_map(it, ret.ind_dummy, ret.ind_pos_dummy);\n\tret.indices_only=true;\n\tret.use_index_iterator=true;\n\tret.update(true);\n\treturn ret;\n\t}\n\nExNode ExNode::components()\n\t{\n\tif(*(ex->begin()->name) != \"\\\\components\")\n\t\tthrow ConsistencyException(\"ExNode::components: node not a components node.\");\n\t\n\tExNode ret(kernel, ex);\n   cadabra::Ex::sibling_iterator sib=ex->begin(it);\n\twhile(*sib->name!=\"\\\\comma\") {\n\t\t++sib;\n\t\tif(sib==ex->end(it))\n\t\t\tthrow InternalError(\"ExNode::components: inconsistent internals structure.\");\n\t\t}\n\tret.topit=sib;\n\tret.use_sibling_iterator=true;\n\tret.update(true);\n\treturn ret;\n\t}\n\nExNode ExNode::args()\n\t{\n\tExNode ret(kernel, ex);\n\tret.topit=it;\n\tret.args_only=true;\n\tret.use_sibling_iterator=true;\n\tret.update(true);\n\treturn ret;\n\t}\n\nExNode ExNode::children()\n\t{\n\tExNode ret(kernel, ex);\n\tret.topit=it;\n\tret.use_sibling_iterator=true;\n\tret.update(true);\n\treturn ret;\n\t}\n\nvoid ExNode::replace(std::shared_ptr<Ex> rep)\n\t{\n#ifdef DEBUG\n\tstd::cerr << \"next at \" << nxtit << std::endl;\n#endif\n\twhile(nxtit!=stopit && ex->is_in_subtree(nxtit, it))\n\t\tupdate(false);\n#ifdef DEBUG\n\tstd::cerr << nxtit.node << std::endl;\n\tstd::cerr << stopit.node << std::endl;\n\tif(nxtit==stopit)\n\t\tstd::cerr << \"updated next to be at stopit\" << std::endl;\n\telse\n\t\tstd::cerr << \"updated next at \" << nxtit << std::endl;\n#endif\n\tit=ex->replace(it, rep->begin());\n\t}\n\nExNode ExNode::insert(std::shared_ptr<Ex> rep)\n\t{\n\tExNode ret(kernel, ex);\n\tret.it=ex->insert_subtree(it, rep->begin());\n\treturn ret;\n\t}\n\nExNode ExNode::insert_it(ExNode rep)\n\t{\n\tExNode ret(kernel, ex);\n\tret.it=ex->insert_subtree(it, rep.it);\n\treturn ret;\n\t}\n\nExNode ExNode::append_child(std::shared_ptr<Ex> rep)\n\t{\n\tExNode ret(kernel, ex);\n\tret.it=ex->append_child(it, rep->begin());\n\treturn ret;\n\t}\n\nExNode ExNode::append_child_it(ExNode rep)\n\t{\n\tExNode ret(kernel, ex);\n\tret.it=ex->append_child(it, rep.it);\n\treturn ret;\n\t}\n\nExNode ExNode::add_ex(std::shared_ptr<cadabra::Ex> other)\n\t{\n\t// std::cerr << it << std::endl;\n\t// std::cerr << \"- - - \" << std::endl;\n\t// std::cerr << ex->begin() << std::endl;\n\tif(ex->is_head(it) || *(ex->parent(it)->name)!=\"\\\\sum\")\n\t\tex->wrap(it, str_node(\"\\\\sum\"));\n\tauto sumnode=ex->parent(it);\n\tExNode ret(kernel, ex);\n\t// std::cerr << ex->begin() << std::endl;\n\tret.it=ex->insert_subtree_after(it, other->begin());\n\tcleanup_dispatch(*get_kernel_from_scope(), *ex, sumnode);\n\t// std::cerr << \"----\" << std::endl;\n\t// std::cerr << ex->begin() << std::endl;\n\t// std::cerr << \"====\" << std::endl;\n\treturn *this;\n\t}\n\nvoid ExNode::erase()\n\t{\n\tex->erase(it);\n\t}\n\nstd::string ExNode::get_name() const\n\t{\n\tif(!ex->is_valid(it))\n\t\tthrow ConsistencyException(\"Cannot print the value of an iterator before the first 'next'.\");\n\treturn *it->name;\n\t}\n\nvoid ExNode::set_name(std::string nm)\n\t{\n\tif(!ex->is_valid(it))\n\t\tthrow ConsistencyException(\"Cannot set the value of an iterator before the first 'next'.\");\n\tit->name = name_set.insert(nm).first;\n\t}\n\ncadabra::Ex ExNode::get_ex() const\n\t{\n\treturn Ex(it);\n\t}\n\nstr_node::parent_rel_t ExNode::get_parent_rel() const\n\t{\n\tif(!ex->is_valid(it))\n\t\tthrow ConsistencyException(\"Cannot get the value of an iterator before the first 'next'.\");\n\treturn it->fl.parent_rel;\n\t}\n\nvoid ExNode::set_parent_rel(str_node::parent_rel_t pr)\n\t{\n\tif(!ex->is_valid(it))\n\t\tthrow ConsistencyException(\"Cannot set the value of an iterator before the first 'next'.\");\n\tit->fl.parent_rel=pr;\n\t}\n\n\nExNode& ExNode::iter()\n\t{\n\treturn *this;\n\t}\n\nvoid ExNode::update(bool first)\n\t{\n\tif(use_sibling_iterator) {\n\t\tif(terms_only) {\n\t\t\tif(*topit->name==\"\\\\sum\") {\n\t\t\t\tif(first) sibnxtit=ex->begin(topit);\n\t\t\t\telse      ++sibnxtit;\n\t\t\t\t}\n\t\t\telse {\n\t\t\t\tif(Algorithm::is_termlike(topit)) {\n\t\t\t\t\tif(Ex::is_head(topit)==false && *Ex::parent(topit)->name==\"\\\\sum\")\n\t\t\t\t\t\tsibnxtit=ex->end(topit);\n\t\t\t\t\telse {\n\t\t\t\t\t\tif(first) sibnxtit=topit;\n\t\t\t\t\t\telse      sibnxtit=ex->end(topit);\n\t\t\t\t\t\t}\n\t\t\t\t\t}\n\t\t\t\telse sibnxtit=ex->end(topit);\n\t\t\t\t}\n\t\t\t}\n\t\telse if(factors_only) {\n\t\t\tif(*topit->name==\"\\\\prod\") {\n\t\t\t\tif(first) sibnxtit=ex->begin(topit);\n\t\t\t\telse      ++sibnxtit;\n\t\t\t\t}\n\t\t\telse {\n\t\t\t\tif(first) sibnxtit=topit;\n\t\t\t\telse      sibnxtit=ex->end(topit);\n\t\t\t\t}\n\t\t\t}\n\t\telse {\n\t\t\tif(first) sibnxtit=ex->begin(topit);\n\t\t\telse      ++sibnxtit;\n\t\t\t}\n\n\t\tif(!indices_only && !args_only) return; // any sibling is ok.\n\n\t\twhile(sibnxtit!=ex->end(topit)) {\n\t\t\tif(indices_only)\n\t\t\t\tif(sibnxtit->fl.parent_rel==str_node::p_sub || sibnxtit->fl.parent_rel==str_node::p_super)\n\t\t\t\t\treturn;\n\t\t\tif(args_only)\n\t\t\t\tif(sibnxtit->fl.parent_rel==str_node::p_none)\n\t\t\t\t\treturn;\n\t\t\t++sibnxtit;\n\t\t\t}\n\t\t}\n\telse if(use_index_iterator) {\n\t\tif(first) indnxtit=cadabra::index_iterator::begin(get_kernel_from_scope()->properties, topit);\n\t\telse      ++indnxtit;\n\t\t// Test if this is a dummy index.\n\t\tEx::iterator tofind=indnxtit;\n\t\twhile(ind_pos_dummy.find(tofind)!=ind_pos_dummy.end()) {\n#ifdef DEBUG\n\t\t\tstd::cerr << \"considered \" << tofind << \" but that's a dummy\" << std::endl;\n#endif\n\t\t\t++indnxtit;\n\t\t\ttofind=indnxtit;\n\t\t\tif(indnxtit==cadabra::index_iterator::end(get_kernel_from_scope()->properties, topit))\n\t\t\t\tbreak;\n\t\t\t}\n\t\t}\n\telse {\n#ifdef DEBUG\n\t\tstd::cerr << \"update normal iterator\" << std::endl;\n#endif\n\t\tif(first) nxtit=topit;\n\t\telse      ++nxtit;\n\n#ifdef DEBUG\n\t\tif(nxtit==stopit)\n\t\t\tstd::cerr << \"update reached end\" << std::endl;\n#endif\n\t\twhile(nxtit!=stopit) {\n#ifdef DEBUG\n\t\t\tstd::cerr << \"update at \" << nxtit << std::endl;\n#endif\n\t\t\tif(*nxtit->name==\"\\\\ldots\") {\n\t\t\t\tnxtit.skip_children();\n\t\t\t\t}\n\t\t\telse {\n\t\t\t\tif(tag==\"\" || *nxtit->name==tag)\n\t\t\t\t\treturn;\n\t\t\t\t}\n\t\t\t++nxtit;\n\t\t\t}\n\t\t}\n\t}\n\nExNode& ExNode::next()\n\t{\n\tif(use_sibling_iterator) {\n\t\tif(sibnxtit==ex->end(topit))\n\t\t\tthrow pybind11::stop_iteration();\n\t\tit=sibnxtit;\n\t\t}\n\telse if(use_index_iterator) {\n\t\tif(indnxtit==cadabra::index_iterator::end(get_kernel_from_scope()->properties, topit))\n\t\t\tthrow pybind11::stop_iteration();\n\t\tit=indnxtit;\n\t\t}\n\telse {\n\t\tif(nxtit==stopit)\n\t\t\tthrow pybind11::stop_iteration();\n\t\tit=nxtit;\n\t\t}\n\n\tupdate(false);\n\treturn *this;\n\t}\n\nstd::string ExNode::__str__() const\n\t{\n\tif(!ex->is_valid(it))\n\t\tthrow ConsistencyException(\"Cannot print iterator before the first 'next'.\");\n\t\n\tstd::ostringstream str;\n\t//\n\t// //\tif(state()==Algorithm::result_t::l_no_action)\n\t// //\t\tstr << \"(unchanged)\" << std::endl;\n\t// \tDisplayTeX dt(get_kernel_from_scope()->properties, ex);\n\n\tDisplayTerminal dt(*get_kernel_from_scope(), Ex(it), true);\n\tdt.output(str, it);\n\n\treturn str.str();\n\t}\n\nstd::string ExNode::_latex_() const\n\t{\n\tif(!ex->is_valid(it))\n\t\tthrow ConsistencyException(\"Cannot print iterator LaTeX form before the first 'next'.\");\n\n\tstd::ostringstream str;\n\tDisplayTeX dt(*get_kernel_from_scope(), Ex(it));\n\tdt.output(str, it);\n\treturn str.str();\n\t}\n\n\nExNode Ex_iter(std::shared_ptr<Ex> ex)\n\t{\n\tExNode ret(*get_kernel_from_scope(), ex);\n\tret.ex=ex;\n\tret.topit=ex->begin();\n\tret.stopit=ex->end();\n\tret.update(true);\n\treturn ret;\n\t}\n\nExNode Ex_top(std::shared_ptr<Ex> ex)\n\t{\n\tExNode ret(*get_kernel_from_scope(), ex);\n\tret.ex=ex;\n\tret.topit=ex->begin();\n\tret.stopit=ex->end();\n\tret.it=ret.topit;\n\treturn ret;\n\t}\n\nbool Ex_matches(std::shared_ptr<Ex> ex, ExNode& other)\n\t{\n\tEx_comparator comp(get_kernel_from_scope()->properties);\n\tauto ret=comp.equal_subtree(ex->begin(), other.it);\n\tif(ret<=Ex_comparator::match_t::match_index_greater) return true;\n\treturn false;\n\t}\n\nbool Ex_matches_Ex(std::shared_ptr<Ex> ex, std::shared_ptr<Ex> other)\n\t{\n\tEx_comparator comp(get_kernel_from_scope()->properties);\n\tif(ex->begin()==ex->end() && other->begin()==other->end()) return true;\n\tif(ex->begin()==ex->end() || other->begin()==other->end()) return false;\n\n\tauto ret=comp.equal_subtree(ex->begin(), other->begin());\n\tif(ret<=Ex_comparator::match_t::match_index_greater) return true;\n\treturn false;\n\t}\n\nbool ExNode_less(ExNode& one, ExNode& two)\n\t{\n\tEx_comparator comp(get_kernel_from_scope()->properties);\n\tauto ret=comp.equal_subtree(one.it, two.it);\n\tif(ret==Ex_comparator::match_t::no_match_less) return true;\n\treturn false;\n\t}\n\nbool ExNode_greater(ExNode& one, ExNode& two)\n\t{\n\tEx_comparator comp(get_kernel_from_scope()->properties);\n\tauto ret=comp.equal_subtree(one.it, two.it);\n\tif(ret==Ex_comparator::match_t::no_match_greater) return true;\n\treturn false;\n\t}\n\nExNode Ex_getitem_string(std::shared_ptr<Ex> ex, std::string tag)\n\t{\n\tExNode ret(*get_kernel_from_scope(), ex);\n\tret.tag=tag;\n\tret.ex=ex;\n\tret.topit=ex->begin();\n\tret.stopit=ex->end();\n\tret.update(true);\n\treturn ret;\n\t}\n\nExNode Ex_getitem_iterator(std::shared_ptr<Ex> ex, ExNode en)\n\t{\n\tEx::iterator use;\n\tif(en.ex!=ex) {\n\t\t//\t\tstd::cerr << \"Need to convert iterator \" << en.it << std::endl;\n\t\t//\t\tstd::cerr << \"for \" << en.topit << std::endl;\n\t\t//\t\tstd::cerr << \"to one for \" << ex->begin() << std::endl;\n\t\tauto path=en.ex->path_from_iterator(en.it, en.topit);\n\t\tuse=ex->iterator_from_path(path, ex->begin());\n\t\t}\n\telse use=en.it;\n\t//\tuse=ex->begin();  This does not help\n\n\tExNode ret(*get_kernel_from_scope(), ex);\n\tret.ex=ex;\n\tret.topit=use;\n\tret.it=use;\n\tuse.skip_children();\n\t++use;\n\tret.stopit=use;\n\tret.update(true);\n\t//\tstd::cerr << \"Set to go\" << std::endl;\n\t//\tstd::cerr << ret.topit << std::endl;\n\treturn ret;\n\t}\n\n"
  },
  {
    "path": "core/ExNode.hh",
    "content": "\n#pragma once\n\n#include \"Kernel.hh\"\n#include \"Storage.hh\"\n#include \"IndexIterator.hh\"\n#include \"IndexClassifier.hh\"\n#include <memory>\n#include <pybind11/pybind11.h>\n\n/// ExNode is a combination of an Ex::iterator and an interface which\n/// we can use to manipulate the data pointed to by this iterator.\n/// In this way, we can use\n///\n///   for it in ex:\n///      ...\n///\n/// loops and still use 'it' to do things like insertion etc.\n/// which requires knowing the Ex::iterator.\n///\n/// Iterators are much safer than in C++, because they carry the\n/// tree modification interface themselves, and can thus compute\n/// their next value for any destructive operation.\n///\n/// Note that ExNode does not really behave like a Python iterator\n/// in the strict sense: it does not return copies of nodes in the\n/// tree, but rather objects which know how to modify the tree.\n\nclass ExNode : public cadabra::IndexClassifier {\n\tpublic:\n\t\tExNode(const cadabra::Kernel&, std::shared_ptr<cadabra::Ex>);\n\n\t\tstd::shared_ptr<cadabra::Ex>          ex;\n\t\tcadabra::Ex::iterator it;\n\n\t\tExNode& iter();\n\t\tExNode& next();\n\n\t\tExNode copy() const;\n\n\t\tstd::string __str__() const;\n\t\tstd::string _latex_() const;\n\t   std::string input_form() const;\n\t\n\t\tstd::string get_name() const;\n\t\tvoid        set_name(std::string);\n\n\t\t/// Is the ExNode a valid pointer into an Ex?\n\t\tbool is_valid() const;\n\t\t\n\t\t/// Create a copy of the Ex pointed to by this iterator.\n\t\tcadabra::Ex get_ex() const;\n\t\t\n\t\tcadabra::str_node::parent_rel_t get_parent_rel() const;\n\t\tvoid                            set_parent_rel(cadabra::str_node::parent_rel_t);\n\n\t\t/// Take a child argument out of the node and\n\t\t/// add as child of current.\n\t\t//      ExNode      unwrap(ExNode child);\n\n\t\t/// Replace the subtree at the current node with the given\n\t\t/// expression. Updates the iterator so that it points to the\n\t\t/// replacement subtree.\n\t\tvoid        replace(std::shared_ptr<cadabra::Ex> rep);\n\n\t\t/// Insert a subtree as previous sibling of the current node.\n\t\tExNode      insert(std::shared_ptr<cadabra::Ex>    ins);\n\t\tExNode      insert_it(ExNode ins);\n\n\t\t/// Append a subtree as a child. Return an ExNode pointing to the new child.\n\t\tExNode      append_child(std::shared_ptr<cadabra::Ex>);\n\t\tExNode      append_child_it(ExNode ins);\n\n\t\t/// Add an expression to the given node, adding a sum parent if necessary.\n\t\tExNode      add_ex(std::shared_ptr<cadabra::Ex>);\n\n\t\t/// Erase the current node, iterator becomes invalid!\n\t\tvoid        erase();\n\n\t\t/// Get a new iterator which always stays\n\t\t/// below the current one.\n\t\tExNode      getitem_string(std::string tag);\n\t\tExNode      getitem_iterator(ExNode);\n\n\t\t/// Set all elements with the indicated tag to the given value.\n\t\tvoid        setitem_string(std::string tag, std::shared_ptr<cadabra::Ex> val);\n\t\tvoid        setitem_iterator(ExNode, std::shared_ptr<cadabra::Ex> val);\n\n\t\t/// Get a new iterator which only iterates over all first-level\n\t\t/// terms. If the first-level is not a sum, the iterator will\n\t\t/// only return the single node and then end.\n\t\tExNode      terms();\n\n\t\t/// Get a new iterator which only iterates over all first-level\n\t\t/// factors. If the first-level is not a product, the iterator will\n\t\t/// only return the single node and then end.\n\t\tExNode      factors();\n\n\t\t/// Get a new iterator which only iterates over all first-level indices\n\t\t/// (that is, does not iterate over inherited indices; use 'indices' for that).\n\t\tExNode      own_indices();\n\n\t\t/// Get a new iterator which only iterates over all indices (whether direct\n\t\t/// or inherited). Uses an index_iterator internally (see its documentation\n\t\t/// for details on behaviour).\n\t\tExNode      indices();\n\n\t\t/// Get a new iterator which only iterates over all free indices (whether direct\n\t\t/// or inherited). Uses an index_iterator internally (see its documentation\n\t\t/// for details on behaviour).\n\t\tExNode      free_indices();\n\n\t\t///\n\t\tExNode      components();\n\t\t\n\t\t/// Get a new iterator which only iterates over all first-level\n\t\t/// arguments (non-indices).\n\t\tExNode      args();\n\n\t\t/// Get a new iterator which iterates over all first-level\n\t\t/// children (a sibling iterator, in other words).\n\t\tExNode      children();\n\n\t\tstd::string tag;\n\t\tbool        indices_only, args_only, terms_only, factors_only;\n\n\t\t/// Internal function to update the iterator to the next value.\n\t\t/// Switches behaviour depending on use_sibling_iterator, use_index_iterator,\n\t\t/// indices_only, args_only, terms_only, factors_only;\n\t\tvoid update(bool first);\n\n\t\tcadabra::Ex::iterator         nxtit;\n\t\tcadabra::Ex::sibling_iterator sibnxtit;\n\t\tcadabra::index_iterator       indnxtit;\n\n\t\tbool                          use_sibling_iterator;\n\t\tbool                          use_index_iterator;\n\t\tcadabra::Ex::iterator         topit, stopit;\n\n\t\tindex_map_t                   ind_free, ind_dummy;\n\t\tindex_position_map_t          ind_pos_dummy;\n\n\tprivate:\n\t};\n\n\nExNode Ex_iter(std::shared_ptr<cadabra::Ex> ex);\nExNode Ex_top(std::shared_ptr<cadabra::Ex> ex);\nbool   Ex_matches(std::shared_ptr<cadabra::Ex> ex, ExNode& other);\nbool   Ex_matches_Ex(std::shared_ptr<cadabra::Ex> ex, std::shared_ptr<cadabra::Ex> other);\nbool   ExNode_less(ExNode& one, ExNode& two);\nbool   ExNode_greater(ExNode& one, ExNode& two);\nExNode Ex_getitem_string(std::shared_ptr<cadabra::Ex> ex, std::string tag);\nExNode Ex_getitem_iterator(std::shared_ptr<cadabra::Ex> ex, ExNode);\n\n\n\n"
  },
  {
    "path": "core/Exceptions.cc",
    "content": "\n#include \"Exceptions.hh\"\n#include <iostream>\n\nCadabraException::CadabraException(std::string s)\n\t: std::logic_error(s)\n\t{\n\t}\n\nParseException::ParseException(std::string s)\n\t: CadabraException(s)\n\t{\n\t}\n\nConsistencyException::ConsistencyException(std::string s)\n\t: CadabraException(s)\n\t{\n\t}\n\nInterruptionException::InterruptionException(std::string s)\n\t: CadabraException(s)\n\t{\n\t}\n\nArgumentException::ArgumentException(std::string s)\n\t: CadabraException(s)\n\t{\n\t}\n\nstd::string ArgumentException::py_what() const\n\t{\n\tstd::cerr << what() << std::endl;\n\treturn what();\n\t}\n\nNonScalarException::NonScalarException(std::string s)\n\t: CadabraException(s)\n\t{\n\t}\n\nstd::string NonScalarException::py_what() const\n\t{\n\tstd::cerr << what() << std::endl;\n\treturn what();\n\t}\n\nRuntimeException::RuntimeException(std::string s)\n\t: CadabraException(s)\n\t{\n\t}\n\nInternalError::InternalError(std::string s)\n\t: CadabraException(s)\n\t{\n\t}\n\nstd::string InternalError::py_what() const\n\t{\n\tstd::cerr << \"Internal error: \" << what() << \"Please report a bug to info@cadabra.science.\" << std::endl;\n\treturn what();\n\t}\n\nNotYetImplemented::NotYetImplemented(std::string s)\n\t: CadabraException(s)\n\t{\n\t}\n\nstd::string NotYetImplemented::py_what() const\n\t{\n\tstd::cerr << \"Not yet implemented: \" << what() << std::endl;\n\treturn what();\n\t}\n\n"
  },
  {
    "path": "core/Exceptions.hh",
    "content": "\n#pragma once\n\n#include <stdexcept>\n#include <string>\n\nclass CadabraException : public std::logic_error {\n\tpublic:\n\t\tCadabraException(std::string);\n\t};\n\n// Exception thrown when an inconsist expression or argument is encountered.\n\nclass ConsistencyException : public CadabraException {\n\tpublic:\n\t\tConsistencyException(std::string);\n\t};\n\n// Exception thrown when the parser cannot parse an input expression.\n\nclass ParseException : public CadabraException {\n\tpublic:\n\t\tParseException(std::string);\n\t};\n\n// Exception thrown when an algorithm determines that it was interrupted.\n\nclass InterruptionException : public CadabraException {\n\tpublic:\n\t\tInterruptionException(std::string=\"\");\n\t};\n\n/// Exception thrown when arguments to an algorithm or property are not correct.\n\nclass ArgumentException : public CadabraException {\n\tpublic:\n\t\tArgumentException(std::string=\"\");\n\n\t\tstd::string py_what() const;\n\t};\n\n/// Exception thrown when something requires that an expression is a pure scalar\n/// (i.e. no free indices and no dummy indices), but isn't.\n\nclass NonScalarException : public CadabraException {\n\tpublic:\n\t\tNonScalarException(std::string=\"\");\n\n\t\tstd::string py_what() const;\n\t};\n\n/// Exception thrown when an algorithm cannot complete, e.g. because it does not\n/// yet know how to process a particular expression. This gets thrown if returning\n/// the original expression would be a mathematical error.\n\nclass RuntimeException : public CadabraException {\n\tpublic:\n\t\tRuntimeException(std::string=\"\");\n\t};\n\n\n/// Exception thrown when there the Cadabra code detects an internal inconsistency;\n/// this should never happen, but is better than bailing out with an assert.\n\nclass InternalError : public CadabraException {\n\tpublic:\n\t\tInternalError(std::string=\"\");\n\n\t\tstd::string py_what() const;\n\t};\n\n/// Exception thrown when there the Cadabra code detects an internal inconsistency;\n/// this should never happen, but is better than bailing out with an assert.\n\nclass NotYetImplemented : public CadabraException {\n\tpublic:\n\t\tNotYetImplemented(std::string=\"\");\n\n\t\tstd::string py_what() const;\n\t};\n\n"
  },
  {
    "path": "core/Exchange.cc",
    "content": "/*\n\nCadabra: a field-theory motivated computer algebra system.\nCopyright (C) 2001-2011  Kasper Peeters <kasper.peeters@aei.mpg.de>\n\nThis program is free software: you can redistribute it and/or\nmodify it under the terms of the GNU General Public License as\npublished by the Free Software Foundation, either version 3 of the\nLicense, or (at your option) any later version.\n\nThis program is distributed in the hope that it will be useful,\nbut WITHOUT ANY WARRANTY; without even the implied warranty of\nMERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU\nGeneral Public License for more details.\n\nYou should have received a copy of the GNU General Public License\n\talong with this program.  If not, see <http://www.gnu.org/licenses/>.\n\n*/\n\n// #define XPERM_DEBUG 1\n\n#include <map>\n\n#include \"Exchange.hh\"\n#include \"Compare.hh\"\n#include \"Algorithm.hh\"\n#include \"properties/DiracBar.hh\"\n\nusing namespace cadabra;\n\n// Find groups of identical tensors.\n//\nint exchange::collect_identical_tensors(const Properties& properties, Ex& tr, Ex::iterator it,\n                                        std::vector<identical_tensors_t>& idts)\n\t{\n\tassert(*it->name==\"\\\\prod\");\n\n\tint total_number_of_indices=0; // refers to number of indices on gamma matrices\n\tEx::sibling_iterator sib=it.begin();\n\twhile(sib!=it.end()) {\n\t\tunsigned int i=0;\n\t\tif(Algorithm::number_of_indices(properties, sib)==0) {\n\t\t\t++sib;\n\t\t\tcontinue;\n\t\t\t}\n\t\tif(properties.get<GammaMatrix>(sib)) {\n\t\t\ttotal_number_of_indices+=Algorithm::number_of_indices(properties, sib);\n\t\t\t++sib;\n\t\t\tcontinue;\n\t\t\t}\n\n\t\t// In case of spinors, the name may be hidden inside a Dirac bar.\n\t\tEx::sibling_iterator truetensor=sib;\n\t\tconst DiracBar *db=properties.get<DiracBar>(truetensor);\n\t\tif(db)\n\t\t\ttruetensor=tr.begin(truetensor);\n\n\t\tEx_comparator comp(properties);\n\n\t\t// Compare the current tensor with all other tensors encountered so far.\n\t\tfor(; i<idts.size(); ++i) {\n\t\t\tEx::sibling_iterator truetensor2=idts[i].tensors[0];\n\t\t\tconst DiracBar *db2=properties.get<DiracBar>(truetensor2);\n\t\t\tif(db2)\n\t\t\t\ttruetensor2=tr.begin(truetensor2);\n\n\t\t\tcomp.clear();\n\t\t\tauto match = comp.equal_subtree(truetensor2, truetensor);\n\t\t\tif(match==Ex_comparator::match_t::subtree_match ||\n\t\t\t      match==Ex_comparator::match_t::match_index_less ||\n\t\t\t      match==Ex_comparator::match_t::match_index_greater) {\n\t\t\t\t// If this is a spinor, check that it's connected to the one already stored\n\t\t\t\t// by a Gamma matrix, or that it is connected directly.\n\t\t\t\tif(idts[i].spino) {\n\t\t\t\t\tEx::sibling_iterator tmpit=idts[i].tensors[0];\n\t\t\t\t\tconst GammaMatrix *gmnxt=0;\n\t\t\t\t\tconst Spinor      *spnxt=0;\n\t\t\t\t\t// skip objects without spinor line\n\t\t\t\t\tdo {\n\t\t\t\t\t\t++tmpit;\n\t\t\t\t\t\tgmnxt=properties.get<GammaMatrix>(tmpit);\n\t\t\t\t\t\tspnxt=properties.get<Spinor>(tmpit);\n\t\t\t\t\t\t} while(gmnxt==0 && spnxt==0);\n\t\t\t\t\t\n\t\t\t\t\tif(tmpit==sib) {\n\t\t\t\t\t\t// Found a pair of adjacent spinors with the same name.\n\t\t\t\t\t\t// Now make sure that it is *not* of the type \\psi^a\\bar{\\psi^b},\n\t\t\t\t\t\t// because that's not a contracted spinor line!\n\t\t\t\t\t\t// Note: db2 is the DiracBar property of the *previously*\n\t\t\t\t\t\t// found spinor, so of the first one, not the second.\n\t\t\t\t\t\t// std::cerr << \"DiracBar: \" << db2 << \", \" << db << std::endl;\n\t\t\t\t\t\tif(! ((db2!=0 && db==0) || (db2==0 && db==0)) ) {\n\t\t\t\t\t\t\ti=idts.size();\n\t\t\t\t\t\t\tbreak;\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\t//\t\t\t\t\t\ttxtout << \"using fermi exchange\" << std::endl;\n\t\t\t\t\t\tidts[i].extra_sign++;\n\t\t\t\t\t\tbreak;\n\t\t\t\t\t\t}\n\t\t\t\t\tif(gmnxt) {\n\t\t\t\t\t\t//\t\t\t\t\t\ttxtout << \"gamma next \" << std::endl;\n\t\t\t\t\t\tint numind=Algorithm::number_of_indices(properties, tmpit);\n\t\t\t\t\t\t// skip objects without spinor line\n\t\t\t\t\t\tdo {\n\t\t\t\t\t\t\t++tmpit;\n\t\t\t\t\t\t\tgmnxt=properties.get<GammaMatrix>(tmpit);\n\t\t\t\t\t\t\tspnxt=properties.get<Spinor>(tmpit);\n\t\t\t\t\t\t\t} while(gmnxt==0 && spnxt==0);\n\t\t\t\t\t\t\n\t\t\t\t\t\tif(tmpit==sib) { // yes, it's a proper Majorana spinor pair.\n\t\t\t\t\t\t\t// Again, it has to be \\bar{...}\\gamma{...}, the bar\n\t\t\t\t\t\t\t// should *not* sit on the 2nd object.\n\t\t\t\t\t\t\tif(! ((db2!=0 && db==0) || (db2==0 && db==0)) ) {\n\t\t\t\t\t\t\t\ti=idts.size();\n\t\t\t\t\t\t\t\tbreak;\n\t\t\t\t\t\t\t\t}\n\t\t\t\t\t\t\t//\ttxtout << \"using fermi exchange with gamma \" << numind << std::endl;\n\t\t\t\t\t\t\tif( ((numind*(numind+1))/2)%2 == 0 )\n\t\t\t\t\t\t\t\tidts[i].extra_sign++;\n\t\t\t\t\t\t\tbreak;\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\t}\n\t\t\t\t\t}\n\t\t\t\telse break;\n\t\t\t\t}\n\t\t\t}\n\t\tif(i==idts.size()) {\n\t\t\tidentical_tensors_t ngr;\n\t\t\tngr.comm=properties.get<SelfCommutingBehaviour>(sib, true);\n\t\t\t//\t\t\tif(ngr.comm)\n\t\t\t//\t\t\t\tstd::cerr << \"selfcomm \" << ngr.comm->sign() << \" for \" << sib << std::endl;\n\t\t\tngr.spino=properties.get<Spinor>(sib);\n\t\t\tngr.tab=properties.get<TableauBase>(sib);\n\t\t\tngr.traceless=properties.get<Traceless>(sib);\n\t\t\tngr.gammatraceless=properties.get<GammaTraceless>(sib);\n\t\t\tngr.extra_sign=0;\n\t\t\tngr.number_of_indices=Algorithm::number_of_indices(properties, truetensor);\n\t\t\tngr.tensors.push_back(sib);\n\t\t\tngr.seq_numbers_of_first_indices.push_back(total_number_of_indices);\n\t\t\ttotal_number_of_indices+=ngr.number_of_indices;\n\t\t\tif(ngr.spino==0 || ngr.spino->majorana==true)\n\t\t\t\tidts.push_back(ngr);\n\t\t\t}\n\t\telse {\n\t\t\tidts[i].tensors.push_back(sib);\n\t\t\tidts[i].seq_numbers_of_first_indices.push_back(total_number_of_indices);\n\t\t\ttotal_number_of_indices+=idts[i].number_of_indices;\n\t\t\t}\n\t\t++sib;\n\t\t}\n\treturn total_number_of_indices;\n\t}\n\n\nbool exchange::get_node_gs(const Properties& properties, Ex& tr, Ex::iterator it, std::vector<std::vector<int> >& gs)\n\t{\n\tstd::vector<identical_tensors_t> idts;\n\tint total_number_of_indices=collect_identical_tensors(properties, tr, it, idts);\n#ifdef XPERM_DEBUG\n\tstd::cerr << \"exchange::get_node_gs: indices returned by collect_identical_tensors = \"\n\t\t\t\t << total_number_of_indices << std::endl;\n#endif\n\tif(idts.size()==0) return true; // no indices, so nothing to permute\n\n\t// Make a strong generating set for the permutation of identical tensors.\n\n\tfor(unsigned int i=0; i<idts.size(); ++i) {\n\t\tunsigned int num=idts[i].tensors.size();\n\t\tif(idts[i].comm)\n\t\t\tif(idts[i].comm->sign()==0) continue;\n\n\t\tif(num>1) {\n\t\t\tstd::vector<int> gsel(total_number_of_indices+2);\n\n\t\t\tfor(unsigned int sobj=0; sobj<num-1; ++sobj) {\n\t\t\t\tfor(int kk=0; kk<total_number_of_indices+2; ++kk)\n\t\t\t\t\tgsel[kk]=kk+1;\n\n\t\t\t\t// permutation of sobj & obj for all sobj and obj > sobj.\n\t\t\t\tfor(unsigned int obj=sobj; obj<num-1; ++obj) {\n\t\t\t\t\tfor(unsigned int kk=0; kk<idts[i].number_of_indices; ++kk)\n\t\t\t\t\t\tstd::swap(gsel[idts[i].seq_numbers_of_first_indices[obj]+kk],\n\t\t\t\t\t\t          gsel[idts[i].seq_numbers_of_first_indices[obj+1]+kk]);\n\t\t\t\t\tif(idts[i].spino) {\n\t\t\t\t\t\tassert(num==2); // FIXME: cannot yet do more than two fermions\n\t\t\t\t\t\tif(idts[i].extra_sign%2==1) {\n\t\t\t\t\t\t\tstd::swap(gsel[total_number_of_indices], gsel[total_number_of_indices+1]);\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\t}\n\t\t\t\t\tif(idts[i].comm) {\n\t\t\t\t\t\tif(idts[i].comm->sign()==-1)\n\t\t\t\t\t\t\tstd::swap(gsel[total_number_of_indices], gsel[total_number_of_indices+1]);\n\t\t\t\t\t\t}\n\t\t\t\t\tif(idts[i].spino && idts[i].number_of_indices==0) {\n\t\t\t\t\t\tif(gsel[total_number_of_indices+1]==total_number_of_indices+1)\n\t\t\t\t\t\t\treturn false;\n\t\t\t\t\t\t}\n\t\t\t\t\telse gs.push_back(gsel);\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t}\n\t\t}\n\n\t//  \tfor(unsigned int i=0; i<idts.size(); ++i) {\n\t//  \t\tint num=idts[i].tensors.size();\n\t//  \t\tif(num>1) {\n\t//  \t\t\tfor(int t1=0; t1<num-1; ++t1) {\n\t//  \t\t\t\tfor(int t2=t1+1; t2<num; ++t2) {\n\t//  \t\t\t\t\tstd::vector<int> gsel(total_number_of_indices+2);\n\t//  \t\t\t\t\tfor(int kk=0; kk<total_number_of_indices+2; ++kk)\n\t//  \t\t\t\t\t\tgsel[kk]=kk+1;\n\t//\n\t//  \t\t\t\t\tif(idts[i].spino) {\n\t//  \t\t\t\t\t\tassert(num==2); // FIXME: cannot yet do more than two fermions\n\t//  \t\t\t\t\t\tif(idts[i].extra_sign%2==1) {\n\t//  //\t\t\t\t\t\t\ttxtout << \"extra sign\" << std::endl;\n\t//  \t\t\t\t\t\t\tstd::swap(gsel[total_number_of_indices], gsel[total_number_of_indices+1]);\n\t//  \t\t\t\t\t\t\t}\n\t//  \t\t\t\t\t\t}\n\t//  \t\t\t\t\tfor(unsigned int kk=0; kk<idts[i].number_of_indices; ++kk)\n\t//  \t\t\t\t\t\tstd::swap(gsel[idts[i].seq_numbers_of_first_indices[t1]+kk],\n\t//  \t\t\t\t\t\t\t\t\t gsel[idts[i].seq_numbers_of_first_indices[t2]+kk]);\n\t//  //\t\t\t\t\t\tfor(int kk=0; kk<total_number_of_indices+2; ++kk) {\n\t//  //\t\t\t\t\t\t\ttxtout << gsel[kk] << \" \";\n\t//  //\t\t\t\t\t\t\t}\n\t//  //\t\t\t\t\t\ttxtout << std::endl;\n\t//  //\t\t\t\t\t\ttxtout << \"adding gs element\" << std::endl;\n\t//\n\t//  \t\t\t\t\tif(idts[i].comm) {\n\t//  \t\t\t\t\t\tif(idts[i].comm->sign()==-1) {\n\t//  //\t\t\t\t\t\t\ttxtout << \"anticommuting\" << std::endl;\n\t//  \t\t\t\t\t\t\tstd::swap(gsel[total_number_of_indices], gsel[total_number_of_indices+1]);\n\t//  \t\t\t\t\t\t\t}\n\t//  \t\t\t\t\t\telse if(idts[i].comm->sign()==0)\n\t//  \t\t\t\t\t\t\treturn false;\n\t//  \t\t\t\t\t\t}\n\t//\n\t//  \t\t\t\t\tif(idts[i].spino && idts[i].number_of_indices==0) {\n\t//  \t\t\t\t\t\tif(gsel[total_number_of_indices+1]==total_number_of_indices+1)\n\t//  \t\t\t\t\t\t\treturn false;\n\t//  \t\t\t\t\t\t}\n\t//  \t\t\t\t\telse gs.push_back(gsel);\n\t//  \t\t\t\t\t}\n\t//  \t\t\t\t}\n\t//  \t\t\t}\n\t//  \t\t}\n\treturn true;\n\t}\n\nbool operator<(const exchange::tensor_type_t& one, const exchange::tensor_type_t& two)\n\t{\n\tif(*one.name < *two.name) return true;\n\tif(one.name == two.name)\n\t\tif(one.number_of_indices < two.number_of_indices) return true;\n\treturn false;\n\t}\n"
  },
  {
    "path": "core/Exchange.hh",
    "content": "/*\n\nCadabra: a field-theory motivated computer algebra system.\nCopyright (C) 2001-2014  Kasper Peeters <kasper.peeters@phi-sci.com>\n\nThis program is free software: you can redistribute it and/or\nmodify it under the terms of the GNU General Public License as\npublished by the Free Software Foundation, either version 3 of the\nLicense, or (at your option) any later version.\n\nThis program is distributed in the hope that it will be useful,\nbut WITHOUT ANY WARRANTY; without even the implied warranty of\nMERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU\nGeneral Public License for more details.\n\nYou should have received a copy of the GNU General Public License\n\talong with this program.  If not, see <http://www.gnu.org/licenses/>.\n\n*/\n\n/**\n\nFunctions to handle the exchange properties of two or more symbols\nin a product. This module is only concerned with the exchange\nproperties of tensors as a whole, not with index permutation symmetries\n(which are handled in the canonicalise class of algebra.cc).\n\n*/\n\n#pragma once\n\n#include <vector>\n\n#include \"Storage.hh\"\n\n#include \"properties/GammaMatrix.hh\"\n#include \"properties/Spinor.hh\"\n#include \"properties/Traceless.hh\"\n#include \"properties/GammaTraceless.hh\"\n#include \"properties/SelfCommutingBehaviour.hh\"\n#include \"properties/CommutingBehaviour.hh\"\n\nnamespace cadabra {\n\n\tclass exchange {\n\t\tpublic:\n\t\t\tstruct identical_tensors_t {\n\t\t\t\tunsigned int                           number_of_indices;\n\t\t\t\tstd::vector<Ex::sibling_iterator> tensors;\n\t\t\t\tstd::vector<int>                       seq_numbers_of_first_indices;\n\n\t\t\t\tconst SelfCommutingBehaviour *comm;\n\t\t\t\tconst Spinor                 *spino;\n\t\t\t\tconst TableauBase            *tab;\n\t\t\t\tconst Traceless              *traceless;\n\t\t\t\tconst GammaTraceless         *gammatraceless;\n\t\t\t\tint                           extra_sign;\n\t\t\t\t};\n\n\t\t\t// Obtain index exchange symmetries under tensor permutation. Returns 'false' if\n\t\t\t// an identically zero expression is encountered.\n\t\t\tstatic int          collect_identical_tensors(const Properties& pr, Ex& tr, Ex::iterator it,\n\t\t\t      std::vector<identical_tensors_t>& idts);\n\t\t\tstatic unsigned int possible_singlets(Ex&, Ex::iterator);\n\t\t\tstatic bool         get_node_gs(const Properties&, Ex&, Ex::iterator, std::vector<std::vector<int> >& );\n\n\t\t\t//\t\tstatic void get_index_gs(Ex::iterator, std::vector<std::vector<int> >& );\n\n\t\t\tstruct tensor_type_t {\n\t\t\t\tnset_t::iterator name;\n\t\t\t\tunsigned int     number_of_indices;\n\t\t\t\t};\n\n\t\t};\n\n\tbool operator<(const exchange::tensor_type_t& one, const exchange::tensor_type_t& two);\n\n\n\t}\n"
  },
  {
    "path": "core/Functional.cc",
    "content": "\n#include \"Functional.hh\"\n\nnamespace cadabra {\n\n\tvoid do_list(const Ex& tr, Ex::iterator it, std::function<bool(Ex::iterator)> f)\n\t\t{\n\t\tif(it==tr.end()) return;\n\n\t\tif(*it->name==\"\\\\comma\") {\n\t\t\tEx::sibling_iterator sib=tr.begin(it);\n\t\t\twhile(sib!=tr.end(it)) {\n\t\t\t\tEx::sibling_iterator nxt=sib;\n\t\t\t\t++nxt;\n\t\t\t\tif(f(sib)==false)\n\t\t\t\t\treturn;\n\t\t\t\tsib=nxt;\n\t\t\t\t}\n\t\t\t}\n\t\telse {\n\t\t\tf(it);\n\t\t\t}\n\t\t}\n\n\tvoid do_sum(const Ex& tr, Ex::iterator it, std::function<bool(Ex::iterator)> f)\n\t\t{\n\t\tif(it==tr.end()) return;\n\n\t\tif(*it->name==\"\\\\sum\") {\n\t\t\tEx::sibling_iterator sib=tr.begin(it);\n\t\t\twhile(sib!=tr.end(it)) {\n\t\t\t\tEx::sibling_iterator nxt=sib;\n\t\t\t\t++nxt;\n\t\t\t\tif(f(sib)==false)\n\t\t\t\t\treturn;\n\t\t\t\tsib=nxt;\n\t\t\t\t}\n\t\t\t}\n\t\telse {\n\t\t\tf(it);\n\t\t\t}\n\t\t}\n\n\tint list_size(const Ex& tr, Ex::iterator it)\n\t\t{\n\t\tif(*it->name==\"\\\\comma\")\n\t\t\treturn tr.number_of_children(it);\n\t\telse\n\t\t\treturn 1;\n\t\t}\n\n\tEx::iterator find_in_subtree(const Ex& tr, Ex::iterator it, std::function<bool(Ex::iterator)> f, bool including_head)\n\t\t{\n\t\tif(it==tr.end()) return it;\n\n\t\tEx::post_order_iterator walk=it, last=it;\n\t\t++last;\n\t\twalk.descend_all();\n\n\t\tdo {\n\t\t\tauto nxt=walk;\n\t\t\t++nxt;\n\n\t\t\tif(f(walk))\n\t\t\t\treturn walk;\n\n\t\t\twalk=nxt;\n\n\t\t\tif(including_head==false && walk==it)\n\t\t\t\tbreak;\n\t\t\t}\n\t\twhile(walk!=last);\n\n\t\treturn tr.end();\n\t\t}\n\n\n\tEx::iterator find_in_list(const Ex& tr, Ex::iterator it, std::function<Ex::iterator(Ex::iterator)> f)\n\t\t{\n\t\tif(*it->name==\"\\\\comma\") {\n\t\t\tEx::sibling_iterator sib=tr.begin(it);\n\t\t\twhile(sib!=tr.end(it)) {\n\t\t\t\tEx::iterator ret = f(sib);\n\t\t\t\tif(ret!=tr.end())\n\t\t\t\t\treturn ret;\n\t\t\t\t++sib;\n\t\t\t\t}\n\t\t\treturn tr.end();\n\t\t\t}\n\t\telse {\n\t\t\treturn f(it);\n\t\t\t}\n\t\t}\n\n\tEx make_list(Ex el)\n\t\t{\n\t\tauto it=el.begin();\n\n\t\tif(*it->name!=\"\\\\comma\")\n\t\t\tel.wrap(it, str_node(\"\\\\comma\"));\n\n\t\treturn el;\n\t\t}\n\n\t}\n\n"
  },
  {
    "path": "core/Functional.hh",
    "content": "\n#pragma once\n\n#include <functional>\n#include \"Storage.hh\"\n\nnamespace cadabra {\n\n\t/// \\ingroup core\n\t///\n\t/// Apply a function to every element of a list, or if the iterator\n\t/// 'it' does not point to a list, only on that single\n\t/// element. Handles lists wrapped in an \\expression node as well.\n\t/// It is safe to remove the node pointed to by 'it' in 'f'.\n\t/// If your 'f' returns false, the loop is aborted immediately.\n\n\tvoid do_list(const Ex& tr, Ex::iterator it, std::function<bool(Ex::iterator)> f);\n\n   /// \\ingroup core\n\t///\n\t/// Apply a function to every term in a sum, or if the iterator does\n\t/// not point to a sum, only on that single term. As in `do_list`, terminates\n\t/// immediately if the function returns `false`.\n\t\n\tvoid do_sum(const Ex& sum, Ex::iterator it, std::function<bool(Ex::iterator)> f);\n\t\n\t/// \\ingroup core\n\t///\n\t/// For lists as defined above for 'do_list', return their size (in case you\n\t/// really need to know the size before iterating over the elements).\n\n\tint list_size(const Ex& tr, Ex::iterator it);\n\n\t/// \\ingroup core\n\t///\n\t/// Returns an iterator to the first element for which 'f' does not return tr.end().\n\n\tEx::iterator find_in_list(const Ex& tr, Ex::iterator it, std::function<Ex::iterator(Ex::iterator)> f);\n\n\t/// \\ingroup core\n\t///\n\t/// Returns an iterator to the first element for which 'f' returns 'true', or 'tr.end()'.\n\n\tEx::iterator find_in_subtree(const Ex& tr, Ex::iterator it, std::function<bool(Ex::iterator)> f, bool including_head=true);\n\n\t/// \n\n\tstd::vector<Ex::iterator> find_in_sum_multiple();\n\t\n\t/// \\ingroup core\n\t///\n\t/// Ensure that the tree is a list, even if it contains only a single element.\n\n\tEx make_list(Ex el);\n\n\t/// \\ingroup core\n\t///\n\t/// Apply a function on every node in the tree at and below the\n\t/// given node, depth-first. Return an iterator to the top node,\n\t/// which replaces 'it' (may be the same).\n\n\ttemplate<typename T>\n\ttypename T::iterator do_subtree(const T& tr, typename T::iterator it, std::function<typename T::iterator(typename T::iterator)> f)\n\t\t{\n\t\tif(it==tr.end()) return it;\n\n\t\tclass T::post_order_iterator walk=it, last=it;\n\t\t++last;\n\t\twalk.descend_all();\n\n\t\tdo {\n\t\t\tauto nxt=walk;\n\t\t\t++nxt;\n\n\t\t\tbool cpy=false;\n\t\t\tif(walk==it) cpy=true;\n\t\t\twalk = f(walk);\n\t\t\tif(cpy) it=walk;\n\n\t\t\twalk=nxt;\n\t\t\t}\n\t\twhile(walk!=last);\n\n\t\treturn it;\n\t\t}\n\n\t// Iterate over the children of 'it' if the node is named 'delim', otherwise only\n\t// iterate over the single node. Note: this yields iterators, not str_nodes.\n\tstruct split_it\n\t{\n\t\tstruct iterator {\n\t\t\tusing value_type = Ex::sibling_iterator;\n\t\t\tusing difference_type = ptrdiff_t;\n\t\t\tusing reference = value_type&;\n\t\t\tusing const_reference = const value_type&;\n\t\t\tusing pointer = value_type*;\n\t\t\tusing const_pointer = const value_type*;\n\t\t\tusing iterator_category = std::input_iterator_tag;\n\n\t\t\titerator() {}\n\t\t\titerator(Ex::sibling_iterator it) : it(it) {}\n\n\t\t\tbool operator == (const iterator& other) { return it == other.it; }\n\t\t\tbool operator != (const iterator& other) { return !(*this == other); }\n\t\t\treference operator* () { return it; }\n\t\t\tpointer operator-> () { return &it; }\n\t\t\treference operator ++ () { return ++it; }\n\t\t\tvalue_type operator ++ (int) { return it++; }\n\n\n\t\t\tEx::sibling_iterator it;\n\t\t};\n\n\t\tsplit_it(Ex::iterator it, const std::string& delim = \"\")\n\t\t{\n\t\t\tif (delim == \"\" || *it->name == delim) {\n\t\t\t\tbegin_ = it.begin();\n\t\t\t\tend_ = it.end();\n\t\t\t}\n\t\t\telse {\n\t\t\t\tbegin_ = it;\n\t\t\t\tend_ = it;\n\t\t\t\t++end_;\n\t\t\t}\n\t\t}\n\n\t\titerator begin() { return iterator(begin_); }\n\t\titerator end() { return iterator(end_); }\n\n\tprivate:\n\t\tEx::sibling_iterator begin_, end_;\n\t};\n\n\t};\n"
  },
  {
    "path": "core/Grouping.cc",
    "content": "#include \"Grouping.hh\"\n#include \"Exceptions.hh\"\n#include \"Compare.hh\"\n#include <map>\n\ncadabra::equiv_map_t cadabra::group_by_equivalence(const Ex& ex, Ex::sibling_iterator first, Ex::sibling_iterator last)\n\t{\n\tequiv_fun_t comp = [](const Ex& ex, Ex::iterator it1, Ex::iterator it2) {\n\t\treturn ex.equal_subtree(it1, it2);\n\t\t};\n\n\treturn group_by_equivalence(ex, first, last, comp);\n\t}\n\ncadabra::equiv_map_t cadabra::group_by_equivalence(const Ex& ex, Ex::sibling_iterator first, Ex::sibling_iterator last, equiv_fun_t& comp)\n\t{\n\tequiv_map_t equivs;\n\t\n\tfor(auto it = first; it != last; ++it) {\n\t\t// std::cerr << it << std::endl;\n\t\tif( equivs.find(it) != equivs.end() )\n\t\t\tcontinue;\n\t\t\n\t\tauto it2=it;\n\t\t++it2;\n\t\tfor(; it2!=last; ++it2) {\n\t\t\tif( equivs.find(it2) != equivs.end() )\n\t\t\t\tcontinue;\n\t\t\t\n\t\t\tif( comp(ex, it, it2) )\n\t\t\t\tequivs[it2] = std::make_pair( 1, it ); // FIXME: handle multiplier\n\t\t\t}\n\t\t}\n\t\treturn equivs;\n\t}\n\ncadabra::equiv_map_t cadabra::group_by_equivalence(const Ex& ex, Ex::iterator comma_top)\n\t{\n\tequiv_fun_t comp = [](const Ex& ex, Ex::iterator it1, Ex::iterator it2) {\n\t\treturn ex.equal_subtree(it1, it2);\n\t\t};\n\n\treturn group_by_equivalence(ex, comma_top, comp);\n\t}\n\ncadabra::equiv_map_t cadabra::group_by_equivalence(const Ex& ex, Ex::iterator comma_top, equiv_fun_t& comp)\n\t{\n\tif(*comma_top->name!=\"\\\\comma\")\n\t\tthrow InternalError(\"cadabra::group_by_equivalence: top node not a list\");\n\n\treturn group_by_equivalence(ex, comma_top.begin(), comma_top.end(), comp);\n\t}\n        \n"
  },
  {
    "path": "core/Grouping.hh",
    "content": "\n#pragma once\n\n#include \"Storage.hh\"\n#include <functional>\n\nnamespace cadabra {\n\n\t/// \\ingroup algorithms\n\t///\n\t/// Given an ExNode iterator, find all expressions in its\n\t/// range which are equal up to a numerical multiplier.\n\t/// Return a structure which summarises these equivalencies,\n\n\ttypedef std::map<Ex::iterator, std::pair<multiplier_t, Ex::sibling_iterator>, Ex::iterator_base_less> equiv_map_t;\n\ttypedef std::function<bool(const Ex&, Ex::iterator, Ex::iterator)> equiv_fun_t;\n\t\n\tequiv_map_t group_by_equivalence(const Ex&, Ex::sibling_iterator first, Ex::sibling_iterator last);\n\tequiv_map_t group_by_equivalence(const Ex&, Ex::iterator comma_top);\n\n\tequiv_map_t group_by_equivalence(const Ex&, Ex::sibling_iterator first, Ex::sibling_iterator last, equiv_fun_t&);\n\tequiv_map_t group_by_equivalence(const Ex&, Ex::iterator comma_top, equiv_fun_t&);\n\n}\n"
  },
  {
    "path": "core/Hash.cc",
    "content": "#include \"Hash.hh\"\n\n// Based on boost's implementation of hash_combine\n// <https://www.boost.org/doc/libs/1_54_0/doc/html/hash/reference.html#boost.hash_combine>\nvoid hash_combine(size_t& seed, size_t modifier)\n{\n\tseed ^= (modifier + 0x9e3779b9 + (seed << 6) + (seed >> 2));\n}\n\ntemplate <typename T>\nsize_t do_hash(const T& t)\n{\n\tstd::hash<T> h;\n\treturn h(t);\n};\n\nnamespace cadabra\n{\n\tEx_hasher::Ex_hasher()\n\t\t: flags(HASH_DEFAULT)\n\t{\n\n\t}\n\n\tEx_hasher::Ex_hasher(HashFlags flags)\n\t\t: flags(flags)\n\t{\n\n\t}\n\n\tEx_hasher::result_t Ex_hasher::operator () (const Ex& ex) const\n\t{\n\t\treturn hash(ex.begin(), true);\n\t}\n\n\tEx_hasher::result_t Ex_hasher::operator () (Ex::iterator it) const\n\t{\n\t\treturn hash(it, true);\n\t}\n\n\tEx_hasher::result_t Ex_hasher::hash (Ex::iterator it, bool toplevel) const\n\t{\n\t\tsize_t seed = 0;\n\n\t\t// Hash the underlying str_node\n\t\tif (!flag_set(HASH_IGNORE_NAMES))\n\t\t\thash_combine(seed, do_hash(*it->name));\n\t\tif (!flag_set(HASH_IGNORE_MULTIPLIER) && !(toplevel && flag_set(HASH_IGNORE_TOP_MULTIPLIER))) {\n\t\t\tif(it->multiplier->is_rational())\n\t\t\t\thash_combine(seed, do_hash(it->multiplier->get_rational().get_str()));\n\t\t\telse\n\t\t\t\thash_combine(seed, do_hash(it->multiplier->get_double()));\n\t\t\t}\n\t\t// Offset the flags by different amounts to reduce collisions\n\t\tif (!flag_set(HASH_IGNORE_BRACKET_TYPE))\n\t\t\thash_combine(seed, do_hash((it->fl.bracket + 1) << 4));\n\t\tif (!flag_set(HASH_IGNORE_PARENT_REL))\n\t\t\thash_combine(seed, do_hash((it->fl.parent_rel + 1) << 8));\n\n\t\tif (!flag_set(HASH_IGNORE_CHILDREN) && it.number_of_children() > 0) {\n\n\t\t\tif (\n\t\t\t\tflag_set(HASH_IGNORE_CHILD_ORDER) ||\n\t\t\t\t(flag_set(HASH_IGNORE_SUM_ORDER) && *it->name == \"\\\\sum\") ||\n\t\t\t\t(flag_set(HASH_IGNORE_PRODUCT_ORDER) && *it->name == \"\\\\prod\")) {\n\t\t\t\tstd::set<size_t> hashes;\n\t\t\t\tfor (Ex::sibling_iterator beg = it.begin(), end = it.end(); beg != end; ++beg) {\n\t\t\t\t\tif (!flag_set(HASH_IGNORE_INDICES) && beg->is_index())\n\t\t\t\t\t\thashes.insert(hash(beg, false));\n\t\t\t\t}\n\t\t\t\tfor (size_t hash : hashes)\n\t\t\t\t\thash_combine(seed, hash);\n\t\t\t}\n\t\t\telse {\n\t\t\t\tif (flag_set(HASH_IGNORE_INDICES)) {\n\t\t\t\t\tfor (Ex::sibling_iterator beg = it.begin(), end = it.end(); beg != end; ++beg) {\n\t\t\t\t\t\tif (beg->is_index())\n\t\t\t\t\t\t\tcontinue;\n\t\t\t\t\t\thash_combine(seed, hash(beg, false));\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t\telse if (flag_set(HASH_IGNORE_INDEX_ORDER)) {\n\t\t\t\t\tstd::set<size_t> hashes;\n\t\t\t\t\tfor (Ex::sibling_iterator beg = it.begin(), end = it.end(); beg != end; ++beg) {\n\t\t\t\t\t\tif (beg->is_index())\n\t\t\t\t\t\t\thashes.insert(hash(beg, false));\n\t\t\t\t\t\telse\n\t\t\t\t\t\t\thash_combine(seed, hash(beg, false));\n\t\t\t\t\t}\n\t\t\t\t\tfor (size_t hash : hashes)\n\t\t\t\t\t\thash_combine(seed, hash);\n\t\t\t\t}\n\t\t\t\telse {\n\t\t\t\t\tfor (Ex::sibling_iterator beg = it.begin(), end = it.end(); beg != end; ++beg) {\n\t\t\t\t\t\thash_combine(seed, hash(beg, false));\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t}\n\t\t}\n\t\treturn seed;\n\t}\n\n\tbool Ex_hasher::flag_set(HashFlags flag) const\n\t{\n\t\treturn (flags & flag);\n\t}\n\n\tusing flags_base_t = std::underlying_type_t<HashFlags>;\n\n\tHashFlags operator ~ (HashFlags flags)\n\t{\n\t\treturn (HashFlags)~(flags_base_t)(flags);\n\t}\n\n\tHashFlags operator | (HashFlags lhs, HashFlags rhs)\n\t{\n\t\treturn (HashFlags)((flags_base_t)lhs | (flags_base_t)rhs);\n\t}\n\n\tHashFlags operator & (HashFlags lhs, HashFlags rhs)\n\t{\n\t\treturn (HashFlags)((flags_base_t)lhs & (flags_base_t)rhs);\n\t}\n\n\tHashFlags& operator |= (HashFlags& lhs, HashFlags rhs)\n\t{\n\t\treturn (HashFlags&)((flags_base_t&)lhs |= (flags_base_t)rhs);\n\t}\n\n\tHashFlags& operator &= (HashFlags& lhs, HashFlags rhs)\n\t{\n\t\treturn (HashFlags&)((flags_base_t&)lhs &= (flags_base_t)rhs);\n\t}\n\n\tEx_hasher::result_t hash_ex(Ex::iterator it, HashFlags flags)\n\t{\n\t\tEx_hasher hasher(flags);\n\t\treturn hasher(it);\n\t}\n\n\tbool hash_compare(Ex::iterator lhs, Ex::iterator rhs, HashFlags flags)\n\t{\n\t\tEx_hasher hasher(flags);\n\t\treturn hasher(lhs) == hasher(rhs);\n\t}\n}\n"
  },
  {
    "path": "core/Hash.hh",
    "content": "#pragma once\n\n#include \"Storage.hh\"\n\nnamespace cadabra\n{\n\tenum HashFlags : unsigned int\n\t{\n\t\tHASH_DEFAULT = 0x0,\n\t\tHASH_IGNORE_TOP_MULTIPLIER = 0x1,\n\t\tHASH_IGNORE_MULTIPLIER = 0x2,\n\t\tHASH_IGNORE_PRODUCT_ORDER = 0x4,\n\t\tHASH_IGNORE_SUM_ORDER = 0x8,\n\t\tHASH_IGNORE_INDEX_ORDER = 0x10,\n\t\tHASH_IGNORE_PARENT_REL = 0x20,\n\t\tHASH_IGNORE_BRACKET_TYPE = 0x40,\n\t\tHASH_IGNORE_CHILDREN = 0x80,\n\t\tHASH_IGNORE_NAMES = 0x100,\n\t\tHASH_IGNORE_INDICES = 0x200,\n\t\tHASH_IGNORE_CHILD_ORDER = 0x400\n\t};\n\n\tclass Ex_hasher\n\t{\n\tpublic:\n\t\tusing result_t = size_t;\n\t\tEx_hasher();\n\t\tEx_hasher(HashFlags flags);\n\n\t\tresult_t operator () (const Ex& ex) const;\n\t\tresult_t operator () (Ex::iterator it) const;\n\n\t\tvoid set_flags(HashFlags flags);\n\t\tHashFlags get_flags() const;\n\t\tvoid add_flags(HashFlags flags);\n\t\tvoid remove_flags(HashFlags flags);\n\n\tprivate:\n\t\tresult_t hash(Ex::iterator it, bool toplevel) const;\n\t\tbool flag_set(HashFlags flag) const;\n\n\t\tHashFlags flags;\n\t};\n\n\tHashFlags operator ~ (HashFlags flags);\n\tHashFlags operator | (HashFlags lhs, HashFlags rhs);\n\tHashFlags operator & (HashFlags lhs, HashFlags rhs);\n\tHashFlags& operator |= (HashFlags& lhs, HashFlags rhs);\n\tHashFlags& operator &= (HashFlags& lhs, HashFlags rhs);\n\n\tEx_hasher::result_t hash_ex(Ex::iterator it, HashFlags flags = HASH_DEFAULT);\n\tbool hash_compare(Ex::iterator lhs, Ex::iterator rhs, HashFlags flags = HASH_DEFAULT);\n}\n"
  },
  {
    "path": "core/IndexClassifier.cc",
    "content": "\n#include \"IndexClassifier.hh\"\n#include \"IndexIterator.hh\"\n#include \"Exceptions.hh\"\n#include \"Kernel.hh\"\n#include \"properties/Symbol.hh\"\n#include \"properties/Coordinate.hh\"\n#include \"properties/IndexInherit.hh\"\n#include <sstream>\n\n// #define DEBUG 1\n\nusing namespace cadabra;\n\nIndexClassifier::IndexClassifier(const Kernel& k)\n\t: kernel(k)\n\t{\n\t}\n\n// For each iterator in the original map, find the sequential position of the index.\n// That is, the index 'd' has position '3' in A_{a b} C_{c} D_{d}.\n// WARNING: expensive operation.\n//\nvoid IndexClassifier::fill_index_position_map(Ex::iterator prodnode, const index_map_t& im, index_position_map_t& ipm) const\n\t{\n\tipm.clear();\n\tindex_map_t::const_iterator imit=im.begin();\n\twhile(imit!=im.end()) {\n\t\tint current_pos=0;\n\t\tbool found=false;\n\t\tindex_iterator indexit=index_iterator::begin(kernel.properties, prodnode);\n\t\twhile(indexit!=index_iterator::end(kernel.properties, prodnode)) {\n\t\t\tif(imit->second==(Ex::iterator)(indexit)) {\n\t\t\t\tipm.insert(index_position_map_t::value_type(imit->second, current_pos));\n\t\t\t\tfound=true;\n\t\t\t\tbreak;\n\t\t\t\t}\n\t\t\t++current_pos;\n\t\t\t++indexit;\n\t\t\t}\n\t\tif(!found)\n\t\t\tthrow ConsistencyException(\"Internal error in fill_index_position_map; cannot find index \"\n\t\t\t                           + *(imit->first.begin()->name)+\".\");\n\t\t++imit;\n\t\t}\n\t}\n\nvoid IndexClassifier::fill_map(index_map_t& mp, Ex::sibling_iterator st, Ex::sibling_iterator nd) const\n\t{\n\twhile(st!=nd) {\n\t\tmp.insert(index_map_t::value_type(Ex(st), Ex::iterator(st)));\n\t\t++st;\n\t\t}\n\t}\n\nvoid IndexClassifier::determine_intersection(index_map_t& one, index_map_t& two, index_map_t& target, bool move_out)  const\n\t{\n\tindex_map_t::iterator it1=one.begin();\n\twhile(it1!=one.end()) {\n\t\tconst Coordinate *cdn=kernel.properties.get<Coordinate>(it1->second, true);\n\t\tconst Symbol     *smb=Symbol::get(kernel.properties, it1->second, true);\n\t\tif(it1->second->is_integer()==false && !cdn && !smb && !it1->second->is_name_wildcard() && !it1->second->is_object_wildcard() &&\n\t\t      !(*it1->second->name==\"\\\\sum\")) {\n\t\t\tbool move_this_one=false;\n\t\t\tindex_map_t::iterator it2=two.begin();\n\t\t\twhile(it2!=two.end()) {\n\t\t\t\tif(tree_exact_equal(&kernel.properties, (*it1).first,(*it2).first,1,true,-2,true)) {\n\t\t\t\t\t//\t\t\t\t\tconst Indices *ind=kernel.properties.get<Indices>(it1->second);\n\t\t\t\t\t//\t\t\t\t\tif(ind && ind->position_type==Indices::fixed && it1->second->fl.parent_rel==it2->second->fl.parent_rel) {\n\t\t\t\t\t//\t\t\t\t\t\tstd::cerr << tr << std::endl;\n\t\t\t\t\t//\t\t\t\t\t\tthrow ConsistencyException(\"Fixed index pair with two upper or two lower indices \"+ *it1->second->name + \" found.\");\n\t\t\t\t\t//\t\t\t\t\t\t}\n\t\t\t\t\ttarget.insert((*it2));\n\t\t\t\t\tif(move_out) {\n\t\t\t\t\t\tindex_map_t::iterator nxt=it2;\n\t\t\t\t\t\t++nxt;\n\t\t\t\t\t\ttwo.erase(it2);\n\t\t\t\t\t\tit2=nxt;\n\t\t\t\t\t\tmove_this_one=true;\n\t\t\t\t\t\t}\n\t\t\t\t\telse ++it2;\n\t\t\t\t\t}\n\t\t\t\telse ++it2;\n\t\t\t\t}\n\t\t\tEx the_key=(*it1).first;\n\t\t\tif(move_this_one && move_out) {\n\t\t\t\tindex_map_t::iterator nxt=it1;\n\t\t\t\t++nxt;\n\t\t\t\ttarget.insert(*it1);\n\t\t\t\tone.erase(it1);\n\t\t\t\tit1=nxt;\n\t\t\t\t}\n\t\t\telse ++it1;\n\t\t\t// skip all indices in two with the same name\n\t\t\twhile(it1!=one.end() && tree_exact_equal(&kernel.properties, (*it1).first,the_key,1,true,-2,true)) {\n\t\t\t\tif(move_this_one && move_out) {\n\t\t\t\t\tindex_map_t::iterator nxt=it1;\n\t\t\t\t\t++nxt;\n\t\t\t\t\ttarget.insert(*it1);\n\t\t\t\t\tone.erase(it1);\n\t\t\t\t\tit1=nxt;\n\t\t\t\t\t}\n\t\t\t\telse ++it1;\n\t\t\t\t}\n\t\t\t}\n\t\telse ++it1;\n\t\t}\n\t}\n\nIndexClassifier::index_map_t::iterator IndexClassifier::find_modulo_parent_rel(Ex::iterator it, index_map_t& imap)  const\n\t{\n\tauto fnd=imap.find(Ex(it));\n\tif(fnd==imap.end()) {\n\t\tit->flip_parent_rel();\n\t\tfnd=imap.find(Ex(it));\n\t\tit->flip_parent_rel();\n\t\treturn fnd;\n\t\t}\n\treturn fnd;\n\t}\n\n// Directly add an index to the free/dummy sets, as appropriate (only add if this really is an\n// index!)\n\nvoid IndexClassifier::classify_add_index(Ex::iterator it, index_map_t& ind_free, index_map_t& ind_dummy) const\n\t{\n\tif((it->fl.parent_rel==str_node::p_sub || it->fl.parent_rel==str_node::p_super) &&\n\t      it->fl.bracket==str_node::b_none /* && it->is_integer()==false */) {\n\t\tconst Coordinate *cdn=kernel.properties.get<Coordinate>(it, true);\n\t\tconst Symbol     *smb=Symbol::get(kernel.properties, it, true);\n\t\tif(it->is_integer() || cdn || smb)\n\t\t\tind_free.insert(index_map_t::value_type(Ex(it), it));\n\t\telse {\n\t\t\tindex_map_t::iterator fnd=find_modulo_parent_rel(it, ind_free);\n\t\t\tif(fnd!=ind_free.end()) {\n\t\t\t\t// std::cerr << \"found in free indices\" << std::endl;\n\t\t\t\t// check consistency: one up and one down if index position is fixed.\n\t\t\t\tconst Indices *ind=kernel.properties.get<Indices>(it);\n\t\t\t\tif(ind && ind->position_type==Indices::fixed && it->fl.parent_rel==fnd->second->fl.parent_rel) {\n\t\t\t\t\tthrow ConsistencyException(\"Fixed index pair with two upper or two lower indices found.\");\n\t\t\t\t\t}\n\t\t\t\tind_dummy.insert(*fnd);\n\t\t\t\tind_dummy.insert(index_map_t::value_type(Ex(it), it));\n\t\t\t\tind_free.erase(fnd);\n\t\t\t\t}\n\t\t\telse {\n\t\t\t\t// std::cerr << \"not yet found; after insertion\" << std::endl;\n\t\t\t\tif(ind_dummy.count(Ex(it))>0) {\n\t\t\t\t\tthrow ConsistencyException(\"Triple index occurred.\");\n\t\t\t\t\t}\n\t\t\t\tind_free.insert(index_map_t::value_type(Ex(it), it));\n\t\t\t\t// for(auto& n: ind_free)\n\t\t\t\t//\t std::cerr << n.first << std::endl;\n\t\t\t\t}\n\t\t\t}\n\t\t}\n\t}\n\nvoid IndexClassifier::classify_indices_up(Ex::iterator it, index_map_t& ind_free, index_map_t& ind_dummy)  const\n\t{\n#ifdef DEBUG\n\tstd::cerr << \"classify_indices_up at \" << it << std::endl;\n#endif\nloopie:\n\tif(Ex::is_head(it)) return;\n\tEx::iterator par=Ex::parent(it);\n\t//\tif(Ex::is_valid(par)==false || par==tr.end()) { // reached the top\n\t//\t\treturn;\n\t//\t\t}\n\tconst IndexInherit *inh=kernel.properties.get<IndexInherit>(par);\n\n\tif(*par->name==\"\\\\sum\" || *par->name==\"\\\\equals\") {\n\t\t// sums or equal signs are no problem since the other terms do not end up in our\n\t\t// factor; therefore, just go up.\n\t\tit=par;\n\t\tgoto loopie;\n\t\t}\n\telse if(*par->name==\"\\\\fermibilinear\" || inh) {\n\t\t// For each _other_ child in this product, do a top-down classify for all non-sub/super\n\t\t// children; add the indices thus found to the maps since they will end up in our factor.\n\t\tEx::sibling_iterator sit=par.begin();\n\t\twhile(sit!=par.end()) {\n#ifdef DEBUG\n\t\t\tstd::cerr << \"checking \" << sit << std::endl;\n#endif\n\t\t\tif(sit!=Ex::sibling_iterator(it)) {\n\t\t\t\tif(sit->is_index()==false) {\n#ifdef DEBUG\n\t\t\t\t\tstd::cerr << \"classifying at \" << sit << std::endl;\n#endif\n\t\t\t\t\tindex_map_t factor_free, factor_dummy;\n\t\t\t\t\tclassify_indices(sit, factor_free, factor_dummy);\n\n\t\t\t\t\t// Test for absence of triple or quadruple indices\n\t\t\t\t\tindex_map_t must_be_empty;\n\t\t\t\t\tdetermine_intersection(factor_free, ind_dummy, must_be_empty);\n\t\t\t\t\tif(must_be_empty.size()>0)\n\t\t\t\t\t\tthrow ConsistencyException(\"Triple index occurred.\");\n\n\t\t\t\t\t// Test for absence of double index pairs\n\t\t\t\t\tmust_be_empty.clear();\n\t\t\t\t\tdetermine_intersection(factor_dummy, ind_dummy, must_be_empty);\n\t\t\t\t\tif(must_be_empty.size()>0)\n\t\t\t\t\t\tthrow ConsistencyException(\"Double index pair occurred.\");\n\n\t\t\t\t\tind_dummy.insert(factor_dummy.begin(), factor_dummy.end());\n\t\t\t\t\tindex_map_t new_dummy;\n\t\t\t\t\tdetermine_intersection(factor_free, ind_free, new_dummy, true);\n\t\t\t\t\tind_free.insert(factor_free.begin(), factor_free.end());\n\t\t\t\t\tind_dummy.insert(new_dummy.begin(), new_dummy.end());\n\t\t\t\t\t}\n\t\t\t\telse {\n\t\t\t\t\t//\t\t\t\t\tind_free.insert(free_so_far.begin(), free_so_far.end());\n\t\t\t\t\t//\t\t\t\t\tfree_so_far.clear();\n\t\t\t\t\tclassify_add_index(sit, ind_free, ind_dummy);\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t++sit;\n\t\t\t}\n\t\tit=par;\n\t\tgoto loopie;\n\t\t}\n\telse if((*par->name).size()>0 && (*par->name)[0]=='@') {   // command nodes swallow everything\n\t\treturn;\n\t\t}\n\telse if(*par->name==\"\\\\tie\") {   // tie lists do not care about indices\n\t\tind_free.clear();\n\t\tind_dummy.clear();\n\t\tit=par;\n\t\tgoto loopie;\n\t\t}\n\telse if(*par->name==\"\\\\arrow\") {   // rules can have different indices on lhs and rhs\n\t\t//\t\tind_free.clear();\n\t\t//\t\tind_dummy.clear();\n\t\tit=par;\n\t\tgoto loopie;\n\t\t}\n\t//\telse if(*par->name==\"\\\\indexbracket\") { // it's really just a bracket, so go up\n\t//\t\tEx::sibling_iterator sit=tr.begin(par);\n\t//\t\t++sit;\n\t//\t\twhile(sit!=tr.end(par)) {\n\t//\t\t\t++sit;\n\t//\t\t\t}\n\t//\t\tit=par;\n\t//\t\tgoto loopie;\n\t//\t\t}\n\telse if(*par->name==\"\\\\comma\") { // comma lists can contain anything NO: [a_{mu}, b_{nu}]\n\t\t// reaching a comma node is like reaching the top of an expression.\n\t\treturn;\n\t\t}\n\telse if(!inh) {\n\t\treturn;\n\t\t}\n\n\t// FIXME: do something with these warnings!!\n\t//\ttxtout << \"Index classification for this expression failed because of \"\n\t//\t\t\t << *par->name << \" node, disabling index checking.\" << std::endl;\n\t//\tassert(1==0);\n\tind_free.clear();\n\tind_dummy.clear();\n\t}\n\nvoid IndexClassifier::dumpmap(std::ostream& str, const index_map_t& mp) const\n\t{\n\tindex_map_t::const_iterator dpr=mp.begin();\n\twhile(dpr!=mp.end()) {\n\t\tstr << *(dpr->first.begin()->name) << \" \";\n\t\t++dpr;\n\t\t}\n\tstr << std::endl;\n\t}\n\nvoid IndexClassifier::classify_indices(Ex::iterator it, index_map_t& ind_free, index_map_t& ind_dummy) const\n\t{\n\tconst IndexInherit *inh=kernel.properties.get<IndexInherit>(it);\n\tif(*it->name==\"\\\\sum\" || *it->name==\"\\\\equals\") {\n\t\tindex_map_t first_free;\n\t\tEx::sibling_iterator sit=it.begin();\n\t\tbool is_first_term=true;\n\n\t\t// Determine whether all indices in 'one' are also present in 'two' (but not the\n\t\t// other way around). Takes care of matching non-equal parent_rel if the index\n\t\t// is free. Indices in 'one' which are integers, symbols, coordinates or patterns do not\n\t\t// need to match indices in 'two'.\n\n\t\tauto free_index_set_contains = [&](const index_map_t& one, const index_map_t& two) {\n\t\t\tindex_map_t::const_iterator i1=one.begin();\n\t\t\twhile(i1!=one.end()) {\n\t\t\t\tconst Coordinate *cdn=kernel.properties.get<Coordinate>(i1->second, true);\n\t\t\t\tconst Symbol     *smb=kernel.properties.get<Symbol>(i1->second, true);\n\t\t\t\t// Integer, coordinate or symbol indices, or pattern objects, or '\\sum' nodes, are always ok.\n\t\t\t\tif(i1->second->is_integer()==false && !cdn && !smb && !i1->second->is_name_wildcard() && !i1->second->is_object_wildcard()\n\t\t\t\t      && !(*i1->second->name==\"\\\\sum\")) {\n\t\t\t\t\t// Check whether there is a corresponding free index in the current term.\n\t\t\t\t\tif(two.count((*i1).first)==0) {\n\t\t\t\t\t\t// std::cerr << \"did not find Symbol for \" << i1->second << std::endl;\n\t\t\t\t\t\t// Not found. However, if this index is free, it is\n\t\t\t\t\t\t// allowed to appear with opposite parent rel. Check\n\t\t\t\t\t\t// that too.\n\t\t\t\t\t\tconst Indices *idc = kernel.properties.get<Indices>(i1->second, true);\n\t\t\t\t\t\tbool trouble=true;\n\t\t\t\t\t\t// if(idc)\n\t\t\t\t\t\t// \tstd::cerr << \"Have indices \" << idc->position_type << std::endl;\n\t\t\t\t\t\tif(idc && idc->position_type==Indices::position_t::free) {\n\t\t\t\t\t\t\tEx cpy((*i1).first);\n\t\t\t\t\t\t\tcpy.begin()->flip_parent_rel();\n\t\t\t\t\t\t\tif(two.count(cpy)!=0) {\n\t\t\t\t\t\t\t\ttrouble=false;\n\t\t\t\t\t\t\t\t// std::cerr << \"Narrow escape\" << std::endl;\n\t\t\t\t\t\t\t\t}\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\tif(trouble) return false;\n\t\t\t\t\t\t}\n\t\t\t\t\t}\n\t\t\t\t++i1;\n\t\t\t\t}\n\t\t\treturn true;\n\t\t\t};\n\n\t\t// Look at the first term to determine the free index\n\t\t// content. Then consider all other terms in turn, and check\n\t\t// that their free index content matches.\n\t\twhile(sit!=it.end()) {\n\t\t\tif(*sit->multiplier!=0) { // A zero term is always ok.\n\t\t\t\t// Classify the indices of this term in the sum.\n\t\t\t\tindex_map_t term_free, term_dummy;\n\t\t\t\tclassify_indices(sit, term_free, term_dummy);\n\t\t\t\tif(!is_first_term) {\n\t\t\t\t\tbool ok=true;\n\t\t\t\t\tok = ok && free_index_set_contains(first_free, term_free);\n\t\t\t\t\tok = ok && free_index_set_contains(term_free, first_free);\n\t\t\t\t\tif(!ok) {\n\t\t\t\t\t\tif(*it->name==\"\\\\sum\") {\n#ifdef DEBUG\n\t\t\t\t\t\t\tstd::cerr << \"--- first:\" << std::endl;\n\t\t\t\t\t\t\tfor(auto& ii: first_free)\n\t\t\t\t\t\t\t\tstd::cerr << ii.first << std::endl;\n\t\t\t\t\t\t\tstd::cerr << \"--- term:\" << std::endl;\n\t\t\t\t\t\t\tfor(auto& ii: term_free)\n\t\t\t\t\t\t\t\tstd::cerr << ii.first << std::endl;\n#endif\n\t\t\t\t\t\t\tthrow ConsistencyException(\"Free indices in different terms in a sum do not match.\");\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\telse\n\t\t\t\t\t\t\tthrow ConsistencyException(\"Free indices on lhs and rhs do not match.\");\n\t\t\t\t\t\t}\n\t\t\t\t\t}\n\t\t\t\telse {\n\t\t\t\t\t// This is the first term; remember the free indices as we need\n\t\t\t\t\t// to check that all other terms have the same indices free.\n\t\t\t\t\tfirst_free=term_free;\n\t\t\t\t\tis_first_term=false;\n\t\t\t\t\t}\n\n\t\t\t\tind_dummy.insert(term_dummy.begin(), term_dummy.end());\n\t\t\t\tind_free.insert(term_free.begin(), term_free.end());\n\t\t\t\t}\n\t\t\t++sit; // next term in sum or \\equals node\n\t\t\t}\n\t\t}\n\telse if(inh) {\n\t\t// std::cerr << \"classify inherit at \" << it << std::endl;\t\t\n\t\tindex_map_t free_so_far;\n\t\tEx::sibling_iterator sit=it.begin();\n\t\twhile(sit!=it.end()) {\n\t\t\t// std::cerr << \"testing\" << std::endl;\n\t\t\tif(sit->is_index()==false) {\n\t\t\t\tindex_map_t factor_free, factor_dummy;\n\t\t\t\tclassify_indices(sit, factor_free, factor_dummy);\n\n\t\t\t\t// Test for absence of triple or quadruple indices\n\t\t\t\tindex_map_t must_be_empty;\n\t\t\t\tdetermine_intersection(factor_free, ind_dummy, must_be_empty);\n\t\t\t\tif(must_be_empty.size()>0)\n\t\t\t\t\tthrow ConsistencyException(\"Triple index \"\n\t\t\t\t\t                           + *(must_be_empty.begin()->second->name)\n\t\t\t\t\t                           + \" inside a single factor found.\");\n\n\t\t\t\t// Test for absence of double index pairs\n\t\t\t\tmust_be_empty.clear();\n\t\t\t\tdetermine_intersection(factor_dummy, ind_dummy, must_be_empty);\n\t\t\t\tif(must_be_empty.size()>0)\n\t\t\t\t\tthrow ConsistencyException(\"Double index pair \"\n\t\t\t\t\t                           + *(must_be_empty.begin()->second->name)\n\t\t\t\t\t                           + \" inside a single factor found.\");\n\n\t\t\t\tind_dummy.insert(factor_dummy.begin(), factor_dummy.end());\n\t\t\t\tindex_map_t new_dummy;\n\t\t\t\tdetermine_intersection(factor_free, free_so_far, new_dummy, true);\n\t\t\t\tfree_so_far.insert(factor_free.begin(), factor_free.end());\n\t\t\t\tind_dummy.insert(new_dummy.begin(), new_dummy.end());\n\t\t\t\t}\n\t\t\telse {\n\t\t\t\tclassify_add_index(sit, free_so_far, ind_dummy);\n\t\t\t\t}\n\t\t\t++sit;\n\t\t\t}\n\t\tind_free.insert(free_so_far.begin(), free_so_far.end());\n\t\t}\n\t//\telse if(tr.is_valid(tr.parent(it))==false) {\n\t//\t\tclassify_indices(it.begin(), ind_free, ind_dummy);\n\t//\t\t}\n\telse if(*it->name==\"\\\\tie\") {\n\t\tind_free.clear();\n\t\tind_dummy.clear();\n\t\t}\n\telse if(*it->name==\"\\\\pow\") {\n\t\t// Power nodes can have dummies in all arguments, but no free indices. We allow for\n\t\t// \\pow{ A_{m} A^{m} }{2} type of things, in the understanding that any algorithm that\n\t\t// does something with this (e.g. product_rule) will need to relabel once the expression\n\t\t// gets down to A_{m} A^{m} itself. Note that the classifier will mark numerical indices\n\t\t// and coordinate indices as free.\n\t\tauto sib=it.begin();\n\t\twhile(sib!=it.end()) {\n\t\t\tindex_map_t ind_free_here, ind_dummy_here;\n\t\t\tclassify_indices(sib, ind_free_here, ind_dummy_here);\n\t\t\tif(ind_free_here.size()>0) {\n\t\t\t\tfor(auto& di: ind_free_here) {\n\t\t\t\t\tconst Coordinate *cdn=kernel.properties.get<Coordinate>(di.second, true);\n\t\t\t\t\tconst Symbol     *smb=kernel.properties.get<Symbol>(di.second, true);\n\t\t\t\t\tif(! (cdn || smb || di.second->is_integer()) ) {\n#ifdef DEBUG\n\t\t\t\t\t\tstd::cerr << di.first << std::endl;\n#endif\n\t\t\t\t\t\tthrow ConsistencyException(\"Power with free indices not allowed.\");\n\t\t\t\t\t\t}\n\t\t\t\t\t}\n\t\t\t\t//\t\t\t\tind_free_here.clear();\n\t\t\t\t}\n\t\t\t// FIXME: add test for overlap\n//\t\t\tind_free.insert(ind_free_here.begin(), ind_free_here.end());\n//\t\t\tind_dummy.insert(ind_dummy_here.begin(), ind_dummy_here.end());\n\t\t\t++sib;\n\t\t\t}\n\t\t}\n\telse if((*it->name).size()>0 && (*it->name)[0]=='@') {\n\t\t// This is an active node that has not been replaced yet; since\n\t\t// we do not know anything about what this will become, do not return\n\t\t// any index information (clashes will be resolved when the active\n\t\t// node gets replaced).\n\t\t}\n\telse {\n\t\t// std::cerr << \"classify ordinary at \" << it << std::endl;\n\t\tEx::sibling_iterator sit=it.begin();\n\t\tindex_map_t item_free;\n\t\tindex_map_t item_dummy;\n\t\twhile(sit!=it.end()) {\n\t\t\tif((sit->fl.parent_rel==str_node::p_sub || sit->fl.parent_rel==str_node::p_super) && sit->fl.bracket==str_node::b_none) {\n\t\t\t\tif(*sit->name!=\"??\") {\n\t\t\t\t\tconst Coordinate *cdn=kernel.properties.get<Coordinate>(sit, true);\n\t\t\t\t\tconst Symbol     *smb=kernel.properties.get<Symbol>(sit, true);\n\t\t\t\t\t// integer, coordinate or symbol indices always ok\n\t\t\t\t\tif(sit->is_integer() || cdn || smb) {\n\t\t\t\t\t\t// Note: even integers need to be stored as indices, because we expect e.g. canonicalise\n\t\t\t\t\t\t// to re-order even numerical indices. They should just never be flagged as dummies.\n\t\t\t\t\t\titem_free.insert(index_map_t::value_type(Ex(sit), Ex::iterator(sit)));\n\t\t\t\t\t\t}\n\t\t\t\t\telse {\n\t\t\t\t\t\tindex_map_t::iterator fnd=find_modulo_parent_rel(sit, item_free);\n\t\t\t\t\t\tif(fnd!=item_free.end()) {\n\t\t\t\t\t\t\tif(find_modulo_parent_rel(sit, item_dummy)!=item_dummy.end())\n\t\t\t\t\t\t\t\tthrow ConsistencyException(\"Triple index \" + *sit->name + \" inside a single factor found.\");\n\t\t\t\t\t\t\titem_dummy.insert(*fnd);\n\t\t\t\t\t\t\titem_free.erase(fnd);\n\t\t\t\t\t\t\titem_dummy.insert(index_map_t::value_type(Ex(sit), Ex::iterator(sit)));\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\telse {\n\t\t\t\t\t\t\titem_free.insert(index_map_t::value_type(Ex(sit), Ex::iterator(sit)));\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\t}\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t//\t\t\telse {\n\t\t\t//\t\t\t\titem_free.insert(index_map_t::value_type(sit->name, Ex::iterator(sit)));\n\t\t\t//\t\t\t\t}\n\t\t\t++sit;\n\t\t\t}\n\t\tind_free.insert(item_free.begin(), item_free.end());\n\t\tind_dummy.insert(item_dummy.begin(), item_dummy.end());\n\t\t}\n\n\t// std::cerr << \"ind_free: \"  << ind_free.size() << std::endl;\n\t// std::cerr << \"ind_dummy: \" << ind_dummy.size() << std::endl;\n\t}\n\nEx IndexClassifier::get_dummy(const list_property *dums,\n                              const index_map_t * one,\n                              const index_map_t * two,\n                              const index_map_t * three,\n                              const index_map_t * four,\n                              const index_map_t * five) const\n\t{\n\tstd::pair<Properties::pattern_map_t::const_iterator, Properties::pattern_map_t::const_iterator>\n\tpr=kernel.properties.pats.equal_range(dums);\n\n\t// std::cerr << \"finding index not in: \" << std::endl;\n\t// if(one)\n\t// \tfor(auto& i: *one)\n\t// \t\tstd::cerr << i.first << std::endl;\n\t// if(two)\n\t// \tfor(auto& i: *two)\n\t// \t\tstd::cerr << i.first << std::endl;\n\t// if(three)\n\t// \tfor(auto& i: *three)\n\t// \t\tstd::cerr << i.first << std::endl;\n\t// if(four)\n\t// \tfor(auto& i: *four)\n\t// \t\tstd::cerr << i.first << std::endl;\n\t// if(five)\n\t// \tfor(auto& i: *five)\n\t// \t\tstd::cerr << i.first << std::endl;\n\n\twhile(pr.first!=pr.second) {\n\t\t// std::cerr << \"trying: \" << std::endl;\n\t\t// std::cerr << pr.first->second->obj << std::endl;\n\t\tif(pr.first->second->obj.begin()->is_autodeclare_wildcard()) {\n\t\t\t// std::cerr << \"is autodeclare wildcard\" << std::endl;\n\t\t\tstd::string base=*pr.first->second->obj.begin()->name_only();\n\t\t\tint used=max_numbered_name(base, one, two, three, four, five);\n\t\t\tstd::ostringstream str;\n\t\t\tstr << base << used+1;\n\t\t\t//\t\t\ttxtout << \"going to use \" << str.str() << std::endl;\n\t\t\tnset_t::iterator newnm=name_set.insert(str.str()).first;\n\t\t\tEx ret;\n\t\t\tret.set_head(str_node(newnm));\n\t\t\treturn ret;\n\t\t\t}\n\t\telse {\n\t\t\t// std::cerr << \"is NOT autodeclare\" << std::endl;\n\t\t\tconst Ex& inm=(*pr.first).second->obj;\n\t\t\t// BUG: even if only _{a} is in the used map, we should not\n\t\t\t// accept ^{a}. But since ...\n\t\t\tif(index_in_set(inm, one)==false   &&\n\t\t\t      index_in_set(inm, two)==false   &&\n\t\t\t      index_in_set(inm, three)==false &&\n\t\t\t      index_in_set(inm, four)==false  &&\n\t\t\t      index_in_set(inm, five)==false) {\n\t\t\t\t// std::cerr << \"ok to use \" << inm << std::endl;\n\t\t\t\treturn inm;\n\t\t\t\t}\n\t\t\t}\n\t\t++pr.first;\n\t\t}\n\n\tconst Indices *dd=dynamic_cast<const Indices *>(dums);\n\tassert(dd);\n\tthrow ConsistencyException(\"Ran out of dummy indices for type \\\"\"+dd->set_name+\"\\\".\");\n\t}\n\nEx IndexClassifier::get_dummy(const list_property *dums, Ex::iterator it) const\n\t{\n\tindex_map_t one, two, three, four, five;\n\tclassify_indices_up(it, one, two);\n\tclassify_indices(it, three, four);\n\n\treturn get_dummy(dums, &one, &two, &three, &four, 0);\n\t}\n\n// Find a dummy index of the type given in \"nm\", making sure that this index\n// name does not class with the object in it1 nor it2.\n\nEx IndexClassifier::get_dummy(const list_property *dums, Ex::iterator it1, Ex::iterator it2) const\n\t{\n\tindex_map_t one, two, three, four, five;\n\tclassify_indices_up(it1, one, two);\n\tclassify_indices_up(it2, one, two);\n\tclassify_indices(it1, three, four);\n\tclassify_indices(it2, three, four);\n\n\treturn get_dummy(dums, &one, &two, &three, &four, 0);\n\t}\n\nvoid IndexClassifier::print_classify_indices(std::ostream& str, Ex::iterator st) const\n\t{\n\tstr << \"for node \" << Ex(st) << std::endl;\n\tindex_map_t ind_free, ind_dummy;\n\tclassify_indices(st, ind_free, ind_dummy);\n\n\tindex_map_t::iterator it=ind_free.begin();\n\tindex_map_t::iterator prev=ind_free.end();\n\tstr << \"free indices: \" << std::endl;\n\twhile(it!=ind_free.end()) {\n\t\tif(prev==ind_free.end() || tree_exact_equal(&kernel.properties, (*it).first,(*prev).first,1,true,-2,true)==false)\n\t\t\tstr << *(*it).first.begin()->name << \" (\" << ind_free.count((*it).first) << \") \";\n\t\tprev=it;\n\t\t++it;\n\t\t}\n\tstr << std::endl;\n\tit=ind_dummy.begin();\n\tprev=ind_dummy.end();\n\tstr << \"dummy indices: \";\n\twhile(it!=ind_dummy.end()) {\n\t\tif(prev==ind_dummy.end() || tree_exact_equal(&kernel.properties, (*it).first,(*prev).first,1,true,-2,true)==false)\n\t\t\tstr << *(*it).first.begin()->name << \" (\" << ind_dummy.count((*it).first) << \") \";\n\t\tprev=it;\n\t\t++it;\n\t\t}\n\tstr << \"---\" << std::endl;\n\t}\n\nint IndexClassifier::max_numbered_name_one(const std::string& nm, const index_map_t * one) const\n\t{\n\tassert(one);\n\n\tint themax=0;\n\tindex_map_t::const_iterator it=one->begin();\n\twhile(it!=one->end()) {\n\t\tsize_t pos=(*it->first.begin()->name).find_first_of(\"0123456789\");\n\t\tif(pos!=std::string::npos) {\n\t\t\t//\t\t\ttxtout << (*it->first).substr(0,pos) << std::endl;\n\t\t\tif((*it->first.begin()->name).substr(0,pos) == nm) {\n\t\t\t\tint thenum=atoi((*it->first.begin()->name).substr(pos).c_str());\n\t\t\t\t//\t\t\t\ttxtout << \"num = \" << thenum << std::endl;\n\t\t\t\tthemax=std::max(themax, thenum);\n\t\t\t\t}\n\t\t\t}\n\t\t++it;\n\t\t}\n\treturn themax;\n\t}\n\nint IndexClassifier::max_numbered_name(const std::string& nm,\n                                       const index_map_t * one,\n                                       const index_map_t * two,\n                                       const index_map_t * three,\n                                       const index_map_t * four,\n                                       const index_map_t * five) const\n\t{\n\tint themax=0;\n\tif(one) {\n\t\tthemax=std::max(themax, max_numbered_name_one(nm, one));\n\t\tif(two) {\n\t\t\tthemax=std::max(themax, max_numbered_name_one(nm, two));\n\t\t\tif(three) {\n\t\t\t\tthemax=std::max(themax, max_numbered_name_one(nm, three));\n\t\t\t\tif(four) {\n\t\t\t\t\tthemax=std::max(themax, max_numbered_name_one(nm, four));\n\t\t\t\t\tif(five) {\n\t\t\t\t\t\tthemax=std::max(themax, max_numbered_name_one(nm, five));\n\t\t\t\t\t\t}\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t}\n\t\t}\n\treturn themax;\n\t}\n\n\nbool IndexClassifier::index_in_set(Ex ex, const index_map_t *im) const\n\t{\n\tif(im==0) return false;\n\n\tif(im->count(ex)>0) return true;\n\n\tif(ex.begin()->fl.parent_rel==str_node::p_super) {\n\t\tex.begin()->fl.parent_rel=str_node::p_sub;\n\t\tint c=im->count(ex);\n\t\tif(c>0) return true;\n\t\t}\n\tif(ex.begin()->fl.parent_rel==str_node::p_sub) {\n\t\tex.begin()->fl.parent_rel=str_node::p_super;\n\t\tint c=im->count(ex);\n\t\tif(c>0) return true;\n\t\t}\n\treturn false;\n\t}\n"
  },
  {
    "path": "core/IndexClassifier.hh",
    "content": "\n#pragma once\n\n#include \"Kernel.hh\"\n#include \"Storage.hh\"\n#include \"Props.hh\"\n#include \"Compare.hh\"\n\n/// Class to deal with index scanning and classification.\n\nnamespace cadabra {\n\n\tclass IndexClassifier {\n\n\t\tpublic:\n\t\t\tIndexClassifier(const Kernel&);\n\n\t\t\t/// A map from a pattern to the position where it occurs in the tree. The comparator\n\t\t\t/// is such that we store indices exactly, apart from their multiplicative factor.\n\t\t\t/// This means that the index in A_{n} and in A_{-n} are stored in the same way,\n\t\t\t/// and one needs to lookup the expression in the tree to find this multiplier.\n\t\t\t/// See basic.cdb test 26 for an example that uses this.\n\t\t\ttypedef std::multimap<Ex, Ex::iterator, tree_exact_less_for_indexmap_obj> index_map_t;\n\n\t\t\t/// A map from the position of each index to the sequential index.\n\t\t\ttypedef std::map<Ex::iterator, int, Ex::iterator_base_less>    index_position_map_t;\n\n\n\t\t\t/// Routines to find and classify all indices in an expression, taking into account\n\t\t\t/// sums and products. Note that dummy indices do not always come in pairs, for\n\t\t\t/// instance in expressions like\n\t\t\t///            a_{m n} ( b^{n p} + q^{n p} ) .\n\t\t\t/// Similarly, free indices can appear multiple times, as in\n\t\t\t///            a_{m} + b_{m} .\n\t\t\tvoid     fill_index_position_map(Ex::iterator, const index_map_t&, index_position_map_t&) const;\n\t\t\tvoid     fill_map(index_map_t&, Ex::sibling_iterator, Ex::sibling_iterator) const;\n\t\t\tvoid     print_classify_indices(std::ostream&, Ex::iterator) const;\n\n\t\t\t/// Determine those indices in 'two' which have a name which is identical to\n\t\t\t/// an index name occurring in 'one'. Store these indices of 'two' in target.\n\t\t\t/// If 'move_out' is true, instead move both the indices in 'one' and 'two'\n\t\t\t/// (i.e. move instead of copy, and also store the 'one' index).\n\t\t\t/// One exception: numerical, coordinate and symbol indices are always kept in 'one'.\n\n\t\t\tvoid     determine_intersection(index_map_t& one, index_map_t& two, index_map_t& target,\n\t\t\t                                bool move_out=false) const;\n\n\t\t\tvoid     classify_add_index(Ex::iterator it, index_map_t& ind_free, index_map_t& ind_dummy) const;\n\n\t\t\t/// Classify indices bottom-up, that is, given a node, it goes up the tree to find\n         /// all free and dummy indices in the product in which this node would end up if a full\n         /// distribute would be done on the entire expression.\n\n\t\t\tvoid     classify_indices_up(Ex::iterator, index_map_t& ind_free, index_map_t& ind_dummy) const;\n\n         /// Classify indices top-down, that is, finds the free indices and all dummy\n         /// index pairs used in the full subtree below a given node.\n\n\t\t\tvoid     classify_indices(Ex::iterator, index_map_t& ind_free, index_map_t& ind_dummy) const;\n\t\t\t\n\t\t\tint      max_numbered_name_one(const std::string& nm, const index_map_t * one) const;\n\t\t\tint      max_numbered_name(const std::string&, const index_map_t *m1, const index_map_t *m2=0,\n\t\t\t                           const index_map_t *m3=0, const index_map_t *m4=0, const index_map_t *m5=0) const;\n\t\t\tEx get_dummy(const list_property *, const index_map_t *m1, const index_map_t *m2=0,\n\t\t\t             const index_map_t *m3=0, const index_map_t *m4=0, const index_map_t *m5=0) const;\n\t\t\tEx get_dummy(const list_property *, Ex::iterator) const;\n\t\t\tEx get_dummy(const list_property *, Ex::iterator, Ex::iterator) const;\n\n\t\t\tbool index_in_set(Ex, const index_map_t *) const;\n\t\t\tvoid     dumpmap(std::ostream&, const index_map_t&) const;\n\n\t\t\t/// Find an index in the set, not taking into account index position.\n\t\t\tindex_map_t::iterator find_modulo_parent_rel(Ex::iterator it, index_map_t& imap) const;\n\n\t\tprotected:\n\t\t\tconst Kernel& kernel;\n\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/IndexIterator.cc",
    "content": "\n#include \"IndexIterator.hh\"\n#include \"properties/IndexInherit.hh\"\n\nusing namespace cadabra;\n\nindex_iterator::index_iterator(const Properties& k)\n\t: iterator_base(), properties(&k)\n\t{\n\t}\n\nindex_iterator index_iterator::create(const Properties& k, const iterator_base& other)\n\t{\n\tindex_iterator ret(k);\n\tret.node=other.node;\n\tret.halt=other;\n\tret.walk=other;\n\tret.roof=other;\n\n\tret.halt.skip_children();\n\t++ret.halt;\n\tret.operator++();\n\treturn ret;\n\t}\n\nindex_iterator::index_iterator(const index_iterator& other)\n\t: iterator_base(other.node), halt(other.halt), walk(other.walk), roof(other.roof), properties(other.properties)\n\t{\n\t}\n\nbool index_iterator::operator!=(const index_iterator& other) const\n\t{\n\tif(other.node!=this->node) return true;\n\telse return false;\n\t}\n\nbool index_iterator::operator==(const index_iterator& other) const\n\t{\n\tif(other.node==this->node) return true;\n\telse return false;\n\t}\n\n// \\bar{\\prod{A}{B}} 's indices are undefined, as \\bar inherits\n// the Product property of \\prod. So the worst-case scenario is\n// of the type \\bar{\\hat{A_\\mu}} in which the objects with Inherit\n// property are strictly nested. However, we can also have\n// things like \\bar{\\diff{\\diff{A_\\mu}_{\\nu}}_{\\rho}}, for which\n// we have to collect indices at multiple levels.\n\n/*\n\t\t\t\\bar{?}::Accent.\n\t\t\t\\bar{\\diff{\\diff{A_\\mu}_{\\nu}}_{\\rho}};\n@indexlist(%);\n\t\t\t\\diff{\\diff{A_{\\mu}}_{\\nu}}_{\\rho};\n@indexlist(%);\n\t\t\t\\diff{\\diff{A}_{\\nu}}_{\\rho};\n@indexlist(%);\n\t\t\t\\bar{\\psi_{m}} * \\Gamma_{q n p} * \\psi_{m} * H_{n p q};\n@indexlist(%);\nq*A_{d c b a};\n@indexlist(%);\nA_{d c b a}*q;\n@indexlist(%);\n\t\t\t\\diff{\\phi}_s A_\\mu \\diff{\\phi}_t;\n@indexlist(%);\n\t\t\t\\Gamma_{a b c};\n@indexlist(%);\n\t\t\t\\diff{\\sin(x_\\mu)}_{\\nu};\n@indexlist(%);\n\t\t\t\\equals{A_{i}}{B_{i j} Z_{j}};\n@indexlist(%);\n\n*/\nindex_iterator& index_iterator::operator+=(unsigned int num)\n\t{\n\twhile(num != 0) {\n\t\t--num;\n\t\toperator++();\n\t\t}\n\treturn *this;\n\t}\n\n\nindex_iterator& index_iterator::operator++()\n\t{\n\tassert(this->node!=0);\n\n\t// Increment the iterator. As long as we are at an inherit\n\t// node, keep incrementing. As long as the parent does not inherit,\n\t// and as long as we are not at the top node,\n\t// skip children. As long as we are not at an index, keep incrementing.\n\n\tconst IndexInherit *this_inh=0, *parent_inh=0;\n\twhile(walk!=halt) {\n\t\tthis_inh=properties->get<IndexInherit>(walk);\n\n\t\tif(this_inh==0 && (walk!=roof && walk.node->parent!=0)) {\n\t\t\tparent_inh=properties->get<IndexInherit>(walk.node->parent);\n\t\t\tif(parent_inh==0)\n\t\t\t\twalk.skip_children();\n\t\t\t}\n\n\t\t++walk;\n\n\t\tif(walk!=halt)\n\t\t\tif(walk->is_index())\n\t\t\t\tbreak;\n\t\t//\t\tif(this_inh==false && walk->is_index())\n\t\t//\t\t\tbreak;\n\t\t}\n\tif(walk==halt) {\n\t\tthis->node=0;\n\t\treturn *this;\n\t\t}\n\telse {\n\t\tthis->node=walk.node;\n\t\t}\n\n\treturn *this;\n\t}\n\nindex_iterator index_iterator::begin(const Properties& properties, const iterator_base& it, int offset)\n\t{\n\tindex_iterator ret=index_iterator::create(properties,it);\n\tif(offset>0)\n\t\tret+=offset;\n\treturn ret;\n\t}\n\nindex_iterator index_iterator::end(const Properties& properties, const iterator_base& it)\n\t{\n\tindex_iterator tmp=create(properties, it);\n\ttmp.node=0;\n\n\treturn tmp;\n\t}\n\nindex_iterator& index_iterator::operator=(const index_iterator& other)\n\t{\n\titerator_base::operator=(other);\n\thalt=other.halt;\n\twalk=other.walk;\n\troof=other.roof;\n\tproperties=other.properties;\n\treturn *this;\n\t}\n\n//size_t number_of_indices(const Properties& pr, Ex::iterator it)\n//\t{\n//\tunsigned int res=0;\n//\tindex_iterator indit=index_iterator::begin(pr, it);\n//\twhile(indit!=index_iterator::end(pr, it)) {\n//\t\t++res;\n//\t\t++indit;\n//\t\t}\n//\treturn res;\n//\t}\n"
  },
  {
    "path": "core/IndexIterator.hh",
    "content": "\n#pragma once\n\n#include \"Storage.hh\"\n#include \"Props.hh\"\n\nnamespace cadabra {\n\n\t/// \\ingroup core\n\t///\n\t/// An iterator which iterates over indices even if they are at lower\n\t/// levels, i.e. taking into account the \"Inherit\" property of\n\t/// nodes. Needs access to Properties in the current scope in order to\n\t/// determine which objects are indices.\n\t///\n\t/// Example use:\n\t///\n\t///    \n\n\tclass index_iterator : public Ex::iterator_base {\n\t\tpublic:\n\t\t\tindex_iterator(const Properties&);\n\t\t\tindex_iterator(const index_iterator&);\n\n\t\t\tstatic index_iterator create(const Properties&, const iterator_base&);\n\n\t\t\tstatic index_iterator begin(const Properties&, const iterator_base&, int offset=0);\n\t\t\tstatic index_iterator end(const Properties&, const iterator_base&);\n\n\t\t\tindex_iterator& operator=(const index_iterator&);\n\t\t\tbool    operator==(const index_iterator&) const;\n\t\t\tbool    operator!=(const index_iterator&) const;\n\t\t\tindex_iterator&  operator++();\n\t\t\tindex_iterator   operator++(int);\n\t\t\tindex_iterator&  operator+=(unsigned int);\n\n\t\t\tEx::iterator halt, walk, roof;\n\t\tprivate:\n\t\t\tconst Properties *properties;\n\n\t\t\tbool is_index(Ex::iterator) const;\n\t\t};\n\n\tstruct iter_indices\n\t{\n\t\tstruct iterator {\n\t\t\tusing value_type = index_iterator;\n\t\t\tusing difference_type = ptrdiff_t;\n\t\t\tusing reference = value_type&;\n\t\t\tusing const_reference = const value_type&;\n\t\t\tusing pointer = value_type*;\n\t\t\tusing const_pointer = const value_type*;\n\t\t\tusing iterator_category = std::input_iterator_tag;\n\n\t\t\titerator(index_iterator it) : it(it) {}\n\n\t\t\tbool operator == (const iterator& other) { return it == other.it; }\n\t\t\tbool operator != (const iterator& other) { return !(*this == other); }\n\t\t\treference operator* () { return it; }\n\t\t\tpointer operator-> () { return &it; }\n\t\t\treference operator ++ () { return ++it; }\n\t\t\tvalue_type operator ++ (int) { return it++; }\n\n\n\t\t\tindex_iterator it;\n\t\t};\n\n\t\titer_indices(const Properties& properties, Ex::iterator it)\n\t\t\t: it(it)\n\t\t\t, properties(properties) { }\n\n\t\titerator begin() { return index_iterator::begin(properties, it); }\n\t\titerator begin(int offset) { return index_iterator::begin(properties, it, offset); }\n\t\titerator end() { return index_iterator::end(properties, it); }\n\t\tsize_t size() { return std::distance(begin(), end()); }\n\n\tprivate:\n\t\tEx::iterator it;\n\t\tconst Properties& properties;\n\t};\n\t//size_t number_of_indices(const Properties&, Ex::iterator);\n\t}\n"
  },
  {
    "path": "core/InstallPrefix.cc",
    "content": "\n#include \"Config.hh\"\n#include \"InstallPrefix.hh\"\n#include \"whereami.h\"\n#include <stdexcept>\n\nstd::string cadabra::install_prefix()\n\t{\n\tstd::string ret;\n\tint dirname_length;\n\tauto length = wai_getExecutablePath(NULL, 0, &dirname_length);\n\tif(length > 0) {\n\t\tchar *path = (char*)malloc(length + 1);\n\t\tif (!path)\n\t\t\tthrow std::logic_error(\"Cannot determine installation path.\");\n\t\twai_getExecutablePath(path, length, &dirname_length);\n\t\tpath[length] = '\\0';\n\t\tpath[dirname_length] = '\\0';\n\t\tret=std::string(path);\n\t\tfree(path);\n#if !defined(_WIN32)\n\t\tret=ret.substr(0, ret.size()-4); // strip '/bin'\n#endif\n\t\t}\n\treturn ret;\n\t}\n\n//const char *cadabra::cmake_install_prefix()\n//\t{\n//\tstatic const char prefix[]=CMAKE_INSTALL_PREFIX;\n//\n//\treturn prefix;\n//\t}\n"
  },
  {
    "path": "core/InstallPrefix.hh",
    "content": "\n#pragma once\n\n#include <string>\n\nnamespace cadabra {\n\n\t/// Return an absolute path to the installation path. This is\n\t/// determined at runtime, to allow for binary distributions to be\n\t/// installed at any location. Note that this cannot be used if the\n\t/// binary running the code was a python interpreter.  In that\n\t/// case, use `py_helpers.cc` method `install_prefix_of_module`\n\t/// and take the appropriate parent of that.\n\n\tstd::string install_prefix();\n\n\t/// Just get a constant char array with the install prefix.\n\n//\tconst char *cmake_install_prefix();\n\t\n\t}\n"
  },
  {
    "path": "core/Kernel.cc",
    "content": "#include \"Kernel.hh\"\n#include \"PreClean.hh\"\n#include \"Cleanup.hh\"\n#include \"Parser.hh\"\n#include \"Config.hh\"\n\n// Default properties\n#include \"properties/Distributable.hh\"\n#include \"properties/IndexInherit.hh\"\n#include \"properties/TableauInherit.hh\"\n#include \"properties/CommutingAsProduct.hh\"\n#include \"properties/DependsInherit.hh\"\n#include \"properties/NumericalFlat.hh\"\n#include \"properties/WeightInherit.hh\"\n#include \"properties/CommutingAsSum.hh\"\n#include \"properties/Derivative.hh\"\n#include \"properties/Accent.hh\"\n#include \"properties/Tableau.hh\"\n#include \"properties/FilledTableau.hh\"\n#include \"properties/ImaginaryI.hh\"\n#include \"properties/LaTeXForm.hh\"\n\nusing namespace cadabra;\n\nconst std::string Kernel::version = CADABRA_VERSION_FULL;\nconst std::string Kernel::build   = CADABRA_VERSION_BUILD;\n\nKernel::Kernel(bool inject_defaults)\n\t: scalar_backend(scalar_backend_t::sympy)\n\t, call_embedded_python_functions(false)\n\t, display_fractions(false)\n\t, warning_level(warn_t::warning)\n\t, warning_callback(nullptr)\n\t{\n\tif (inject_defaults) {\n\t\tinject_property(new Distributable(),          ex_from_string(\"\\\\prod{#}\"), 0);\n\t\tinject_property(new IndexInherit(),           ex_from_string(\"\\\\prod{#}\"), 0);\n\t\tinject_property(new TableauInherit(),         ex_from_string(\"\\\\prod{#}\"), 0);\n\t\tinject_property(new CommutingAsProduct(),     ex_from_string(\"\\\\prod{#}\"), 0);\n\t\tinject_property(new DependsInherit(),         ex_from_string(\"\\\\prod{#}\"), 0);\n\t\tinject_property(new NumericalFlat(),          ex_from_string(\"\\\\prod{#}\"), 0);\n\t\tinject_property(new Inherit<Tableau>(),       ex_from_string(\"\\\\prod{#}\"), 0);\n\t\tinject_property(new Inherit<FilledTableau>(), ex_from_string(\"\\\\prod{#}\"), 0);\n\n\t\tauto wi2 = new WeightInherit();\n\t\twi2->combination_type = WeightInherit::multiplicative;\n\t\tauto wa2 = ex_from_string(\"label=all, type=multiplicative\");\n\t\tinject_property(wi2,                          ex_from_string(\"\\\\prod{#}\"), wa2);\n\n\t\tinject_property(new IndexInherit(),           ex_from_string(\"\\\\frac{#}\"), 0);\n\t\tinject_property(new DependsInherit(),         ex_from_string(\"\\\\frac{#}\"), 0);\n\n\t\tinject_property(new Distributable(),          ex_from_string(\"\\\\wedge{#}\"), 0);\n\t\tinject_property(new IndexInherit(),           ex_from_string(\"\\\\wedge{#}\"), 0);\n\n\t\tinject_property(new DependsInherit(),         ex_from_string(\"\\\\wedge{#}\"), 0);\n\t\tinject_property(new NumericalFlat(),          ex_from_string(\"\\\\wedge{#}\"), 0);\n\t\tauto wi4 = new WeightInherit();\n\t\twi4->combination_type = WeightInherit::multiplicative;\n\t\tauto wa4 = ex_from_string(\"label=all, type=multiplicative\");\n\t\tinject_property(wi4,                          ex_from_string(\"\\\\wedge{#}\"), wa4);\n\n\t\tinject_property(new IndexInherit(),           ex_from_string(\"\\\\sum{#}\"), 0);\n\t\tinject_property(new Inherit<Tableau>(),       ex_from_string(\"\\\\sum{#}\"), 0);\n\t\tinject_property(new Inherit<FilledTableau>(), ex_from_string(\"\\\\sum{#}\"), 0);\n\t\tinject_property(new CommutingAsSum(),         ex_from_string(\"\\\\sum{#}\"), 0);\n\t\tinject_property(new DependsInherit(),         ex_from_string(\"\\\\sum{#}\"), 0);\n\t\tauto wi = new WeightInherit();\n\t\tauto wa = ex_from_string(\"label=all, type=additive\");\n\t\tinject_property(wi,                           ex_from_string(\"\\\\sum{#}\"), wa);\n\n\t\tauto d = new Derivative();\n\t\td->hidden(true);\n\t\tinject_property(d, ex_from_string(\"\\\\cdbDerivative{#}\"), 0);\n\n\t\tinject_property(new Derivative(), ex_from_string(\"\\\\commutator{#}\"), 0);\n\t\tinject_property(new IndexInherit(), ex_from_string(\"\\\\commutator{#}\"), 0);\n\n\t\tinject_property(new Derivative(), ex_from_string(\"\\\\anticommutator{#}\"), 0);\n\t\tinject_property(new IndexInherit(), ex_from_string(\"\\\\anticommutator{#}\"), 0);\n\n\t\tinject_property(new Distributable(), ex_from_string(\"\\\\indexbracket{#}\"), 0);\n\t\tinject_property(new IndexInherit(), ex_from_string(\"\\\\indexbracket{#}\"), 0);\n\n\t\tinject_property(new DependsInherit(), ex_from_string(\"\\\\pow{#}\"), 0);\n\t\tauto wi3 = new WeightInherit();\n\t\tauto wa3 = ex_from_string(\"label=all, type=power\");\n\t\tinject_property(wi3, ex_from_string(\"\\\\pow{#}\"), wa3);\n\n\t\tinject_property(new NumericalFlat(), ex_from_string(\"\\\\int{#}\"), 0);\n\t\tinject_property(new IndexInherit(), ex_from_string(\"\\\\int{#}\"), 0);\n\n\t\t// Hidden nodes.\n\t\tinject_property(new Accent(), ex_from_string(\"\\\\ldots{#}\"), 0);\n\n\t\t// Accents, necessary for proper display.\n\t\tinject_property(new Accent(), ex_from_string(\"\\\\hat{#}\"), 0);\n\t\tinject_property(new Accent(), ex_from_string(\"\\\\bar{#}\"), 0);\n\t\tinject_property(new Accent(), ex_from_string(\"\\\\overline{#}\"), 0);\n\t\tinject_property(new Accent(), ex_from_string(\"\\\\tilde{#}\"), 0);\n\n\t\t// ImaginaryI\n\t\tinject_property(new ImaginaryI(), ex_from_string(\"\\\\iu}\"), 0);\n\t\tauto iu = new LaTeXForm();\n\t\tiu->latex.push_back(Ex(\"i\"));\n\t\tinject_property(iu, ex_from_string(\"\\\\iu}\"), 0);\n\t\t}\n\t}\n\nKernel::~Kernel()\n\t{\n\t//\tstd::cerr << \"~Kernel() \" << this << std::endl;\n\t}\n\nvoid Kernel::inject_property(property *prop, std::shared_ptr<Ex> ex, std::shared_ptr<Ex> param)\n\t{\n\tEx::iterator it=ex->begin();\n\n\tif(param) {\n\t\t// std::cerr << \"property with \" << *param << std::endl;\n\t\tkeyval_t keyvals;\n\t\tprop->parse_to_keyvals(*param, keyvals);\n\t\tprop->parse(*this, ex, keyvals);\n\t\t}\n\t// Validate and insert a copy of the property.\n\tprop->validate(*this, ex);\n\tproperties.master_insert(Ex(it), prop);\n\t}\n\nstd::shared_ptr<cadabra::Ex> Kernel::ex_from_string(const std::string& s)\n\t{\n\tauto ex = std::make_shared<cadabra::Ex>();\n\tcadabra::Parser parser1(ex, s);\n\n\tpre_clean_dispatch_deep(*this, *ex);\n\tcleanup_dispatch_deep(*this, *ex);\n\tcheck_index_consistency(*this, *ex, ex->begin());\n\n\treturn ex;\n\t}\n\nvoid Kernel::warn(const std::string& msg, Kernel::warn_t level) const\n\t{\n\tif (warning_callback && warning_level != warn_t::notset && level > warning_level)\n\t\twarning_callback(msg);\n\t}\n"
  },
  {
    "path": "core/Kernel.hh",
    "content": "\n#pragma once\n\n#include <functional>\n#include \"Props.hh\"\n\n/// \\ingroup core\n///\n/// Cadabra kernel that keeps all state information that needs to be passed\n/// around to algorithms and properties. Stores property information and\n/// global settings.\n\nnamespace cadabra {\n\n\tclass Kernel {\n\t\tpublic:\n\t\t\tKernel(bool inject_defaults=true);\n\t\t\tKernel(const Kernel& other) = delete;\n\t\t\t~Kernel();\n\n\t\t\t/// Inject a property into the system and attach it to the given pattern.\n\t\t\t/// Transfers property ownership to the kernel.\n\t\t\tvoid inject_property(property *prop, std::shared_ptr<Ex> pattern, std::shared_ptr<Ex> property_arguments);\n\n\t\t\t/// Create an Ex expression object from a string, which will be parsed.\n\t\t\tstd::shared_ptr<Ex> ex_from_string(const std::string&);\n\n\t\t\t\n\t\t\tProperties properties;\n\n\t\t\t/// Settings.\n\t\t\tenum class scalar_backend_t { sympy, mathematica } scalar_backend;\n\t\t\tbool                                               call_embedded_python_functions;\n\t\t\tbool                                               display_fractions;\n\n\n\t\t\tconst static std::string version;\n\t\t\tconst static std::string build  ;\n\n\t\t\t// Warnings \n\t\t\tenum class warn_t {\n\t\t\t\tnotset   = 0,\n\t\t\t\tdebug    = 10,\n\t\t\t\tinfo     = 20,\n\t\t\t\twarning  = 30,\n\t\t\t\terror    = 40,\n\t\t\t\tcritical = 50\n\t\t\t};\n\t\t\twarn_t warning_level;\n\t\t\tstd::function<void(const std::string&)> warning_callback;\n\t\t\tvoid warn(const std::string& msg, warn_t level = warn_t::warning) const;\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/Linear.cc",
    "content": "\n#include \"Linear.hh\"\n\ntypedef cadabra::multiplier_t multiplier_t;\n\nbool linear::gaussian_elimination_inplace(std::vector<std::vector<multiplier_t> >& a,\n      std::vector<multiplier_t>& b)\n\t{\n\tassert(a.size() == b.size());\n\n\t// If there are more equations than unknowns, we first reduce the form to\n\t//  xxx = x\n\t//   xx = x\n\t//    x = x\n\t//  000 = 0\n\t//  000 = 0\n\n\tunsigned int number_of_eqs = a.size();\n\tunsigned int number_of_unk = a[0].size();\n\tunsigned int mineu=std::min(number_of_eqs, number_of_unk);\n\n\t// Loop over rows, creating upper-triangular matrix 'a'\n\tfor(unsigned row=0; row<mineu; ++row) {\n\t\tmultiplier_t pivot = a[row][row];\n\t\tif(pivot == 0) {\n\t\t\tunsigned int nrow;\n\t\t\tfor(nrow=row+1; nrow<number_of_eqs; ++nrow)\n\t\t\t\tif((pivot = a[nrow][row]) != 0)\n\t\t\t\t\tbreak;\n\t\t\tif(pivot == 0)\n\t\t\t\treturn true; // undetermined system FIXME: still minimalise\n\t\t\tstd::swap(a[nrow],a[row]);\n\t\t\tstd::swap(b[nrow],b[row]);\n\t\t\t}\n\n\t\t// Gaussian elimination of column\n\t\tfor(unsigned int nrow=row+1; nrow<number_of_eqs; ++nrow) {\n\t\t\tmultiplier_t tmp = a[nrow][row]/pivot;\n\t\t\ta[nrow][row]=0;\n\t\t\tfor(unsigned int col=row+1; col<number_of_unk; ++col)\n\t\t\t\ta[nrow][col] -= tmp*a[row][col];\n\t\t\tb[nrow] -= tmp*b[row];\n\t\t\t}\n\t\t}\n\t//\tfor(unsigned int i=0; i<a.size(); ++i) {\n\t//\t\tfor(unsigned int j=0; j<a[i].size(); ++j)\n\t//\t\t\ttxtout << a[i][j] << \" \";\n\t//\t\ttxtout <<  \" = \" << b[i] << std::endl;\n\t//\t\t}\n\n\t// Check that there are no inconsistencies\n\tfor(unsigned int i=number_of_unk; i<number_of_eqs; ++i)\n\t\tif(b[i]!=0)\n\t\t\treturn false;\n\n\t//\ttxtout << \"consistent\" << std::endl;\n\n\t// Back substitution\n\tfor(int row=mineu-1; row>=0; --row) {\n\t\tassert(a[row][row]!=0);\n\t\tfor(int col=mineu-1; col>row; --col) {\n\t\t\tb[row]      -= a[row][col]*b[col];\n\t\t\tfor(unsigned allcol=col; allcol<number_of_unk; ++allcol)\n\t\t\t\ta[row][allcol] -= a[row][allcol]*a[row][row];\n\t\t\t}\n\t\tassert(a[row][row]!=0);\n\t\tb[row]      /= a[row][row];\n\t\ta[row][row]  = (a[row][row]!=0?1:0);\n\t\t}\n\treturn true;\n\t}\n"
  },
  {
    "path": "core/Linear.hh",
    "content": "\n#pragma once\n\n#include <numeric>\n#include <vector>\n#include <boost/numeric/ublas/matrix.hpp> \n#include <boost/numeric/ublas/vector.hpp>\n#include <boost/numeric/ublas/matrix_proxy.hpp>\n#include <boost/numeric/ublas/lu.hpp>\n#include \"Storage.hh\"\n\nnamespace linear {\n\t//\tbool gaussian_elimination(const std::vector<std::vector<multiplier_t> >&, const std::vector<multiplier_t>& );\n\tbool gaussian_elimination_inplace(std::vector<std::vector<cadabra::multiplier_t> >&, std::vector<cadabra::multiplier_t>& );\n\n\t// Class for solving equations of the form Ax = y for x. First call\n\t// factorize with the matrix A and then call solve as many times as needed\n\ttemplate <typename T>\n\tstruct Solver\n\t{\n\tpublic:\n\t\tusing matrix_type = boost::numeric::ublas::matrix<T>;\n\t\tusing vector_type = boost::numeric::ublas::vector<T>;\n\n\t\t// Initialise the solver with the matrix A\n\t\tbool factorize(const matrix_type& A_);\n\n\t\t// Solve for Ax = y\n\t\tvector_type solve(const vector_type& y);\n\n\tprivate:\n\t\tmatrix_type A;\n\t\tboost::numeric::ublas::vector<size_t> P;\n\t\tvector_type x;\n\t\tsize_t N;\n\t};\n\n\ttemplate <typename T>\n\tbool Solver<T>::factorize(const matrix_type& A_)\n\t{\n\t\tassert(A_.size1() == A_.size2());\n\t\tN = A_.size1();\n\t\tA = A_;\n\t\tP.resize(N);\n\n\t\t// Bring swap and abs into namespace\n\t\tusing namespace std;\n\t\tusing namespace boost::numeric::ublas;\n\n\t\tstd::iota(P.begin(), P.end(), 0);\n\n\t\tfor (size_t i = 0; i < N; ++i) {\n\t\t\tT maxA = 0;\n\t\t\tsize_t imax = i;\n\t\t\tfor (size_t k = i; k < N; ++k) {\n\t\t\t\tT absA = abs(A(k, i));\n\t\t\t\tif (absA > maxA) {\n\t\t\t\t\tmaxA = absA;\n\t\t\t\t\timax = k;\n\t\t\t\t}\n\t\t\t}\n\n\t\t\tif (imax != i) {\n\t\t\t\tswap(P(i), P(imax)); //pivoting P\n\t\t\t\tswap(row(A, i), row(A, imax)); //pivoting rows of A\n\t\t\t}\n\n\t\t\tif (A(i, i) == 0)\n\t\t\t\treturn false;\n\n\t\t\tfor (size_t j = i + 1; j < N; ++j) {\n\t\t\t\tA(j, i) /= A(i, i);\n\t\t\t\tfor (size_t k = i + 1; k < N; ++k)\n\t\t\t\t\tA(j, k) -= A(j, i) * A(i, k);\n\t\t\t}\n\t\t}\n\n\t\treturn true;\n\t}\n\n\n\ttemplate <typename T>\n\ttypename Solver<T>::vector_type Solver<T>::solve(const vector_type& y)\n\t{\n\t\tx.resize(y.size());\n\t\tfor (size_t i = 0; i < N; ++i) {\n\t\t\tx(i) = y(P(i));\n\t\t\tfor (size_t k = 0; k < i; ++k)\n\t\t\t\tx(i) -= A(i, k) * x(k);\n\t\t}\n\n\t\tfor (size_t i = N; i > 0; --i) {\n\t\t\tfor (size_t k = i; k < N; ++k)\n\t\t\t\tx(i - 1) -= A(i - 1, k) * x(k);\n\t\t\tx(i - 1) = x(i - 1) / A(i - 1, i - 1);\n\t\t}\n\n\t\treturn x;\n\t}\n\n\t}\n\n"
  },
  {
    "path": "core/MMACdb.cc",
    "content": "\n\n#include \"Config.hh\"\n#include <boost/python.hpp>\n#include \"Functional.hh\"\n#include \"MMACdb.hh\"\n#include \"PreClean.hh\"\n#include \"Cleanup.hh\"\n#include \"Parser.hh\"\n#include \"Kernel.hh\"\n#include \"DisplayMMA.hh\"\n#include \"algorithms/substitute.hh\"\n\nusing namespace cadabra;\n\nWSLINK        MMA::lp = 0;\nWSEnvironment MMA::stdenv = 0;\n\n//#define DEBUG 1\n\nEx::iterator MMA::apply_mma(const Kernel& kernel, Ex& ex, Ex::iterator& it, const std::vector<std::string>& wrap,\n                            std::vector<std::string> args, const std::string& method)\n\t{\n\t// We first need to print the sub-expression using DisplaySympy,\n\t// optionally with the head wrapped around it and the args added\n\t// (if present).\n\tstd::ostringstream str;\n\n\tfor(size_t i=0; i<wrap.size(); ++i) {\n\t\tstr << wrap[i] << \"[\";\n\t\t}\n\n\tDisplayMMA ds(kernel, ex, true);\n\tds.output(str, it);\n\n\tif(wrap.size()>0)\n\t\tif(args.size()>0)\n\t\t\tfor(size_t i=0; i<args.size(); ++i)\n\t\t\t\tstr << \", \" << args[i];\n\tfor(size_t i=1; i<wrap.size(); ++i)\n\t\tstr << \"]\";\n\tstr << method;\n\n\tif(wrap.size()>0)\n\t\tstr << \"]\";\n\n\t// We then execute the expression in Python.\n\n\t//ex.print_recursive_treeform(std::cerr, it);\n#ifdef DEBUG\n\tstd::cerr << \"feeding \" << str.str() << std::endl;\n#endif\n\n\tstd::string result;\n\n\t// ---------------------\n\tsetup_link();\n\n\tWSPutFunction(lp, \"EvaluatePacket\", 1L);\n\tWSPutFunction(lp, \"ToString\", 1L);\n\tWSPutFunction(lp, \"FullForm\", 1L);\n\tWSPutFunction(lp, \"ToExpression\", 1L);\n\tWSPutUTF8String(lp, (const unsigned char *)str.str().c_str(), str.str().size());\n\tWSEndPacket(lp);\n\tWSFlush(lp);\n\n\t// std::cerr << \"flushed\" << std::endl;\n\n\tint pkt=0;\n\twhile( (pkt = WSNextPacket(lp), pkt) && pkt != RETURNPKT ) {\n\t\t// std::cerr << \"received packet \" << pkt << std::endl;\n\t\tWSNewPacket(lp);\n\t\tif (WSError(lp)) {\n\t\t\tstd::cerr << \"error\" << std::endl;\n\t\t\t}\n\t\t}\n\t// std::cerr << \"packet now \" << pkt << std::endl;\n\n\tconst char *out;\n\tif(! WSGetString(lp, &out)) {\n\t\tthrow InternalError(\"Unable to read from WSTP link\");\n\t\t}\n\telse {\n\t\tresult=out;\n\t\tWSReleaseString(lp, out);\n\t\tif(result==\"$Failed\") {\n\t\t\tthrow RuntimeException(\"Mathematica failed to handle expression.\");\n\t\t\t}\n\t\t}\n\t// -------------------------------\n\n\t// After that, we construct a new sub-expression from this string by using our\n\t// own parser, and replace the original.\n\n#ifdef DEBUG\n\tstd::cerr << \"result: \" << result << std::endl;\n#endif\n\n\tresult = ds.preparse_import(result);\n\n#ifdef DEBUG\n\tstd::cerr << \"preparsed: \" << result << std::endl;\n#endif\n\n\tauto ptr = std::make_shared<Ex>();\n\tcadabra::Parser parser(ptr);\n\tstd::stringstream istr(result);\n\tistr >> parser;\n\n\tpre_clean_dispatch_deep(kernel, *parser.tree);\n\tcleanup_dispatch_deep(kernel, *parser.tree);\n\n\t//parser.tree->print_recursive_treeform(std::cerr, parser.tree->begin());\n\n#ifdef DEBUG\n\tstd::cerr << \"cleaned up: \" << *parser.tree << std::endl;\n#endif\n\t\n\tds.import(*parser.tree);\n\n#ifdef DEBUG\n\tstd::cerr << \"imported: \" << *parser.tree << std::endl;\n#endif\n\n\tpre_clean_dispatch_deep(kernel, *parser.tree);\n\tcleanup_dispatch_deep(kernel, *parser.tree);\n\n\tEx::iterator first=parser.tree->begin();\n\t// std::cerr << \"reparsed \" << Ex(first) << std::endl;\n\tit = ex.move_ontop(it, first);\n\n\treturn it;\n\t}\n\nvoid MMA::setup_link()\n\t{\n\tif(lp!=0) return; // already setup\n\n\tchar argvi[4][512] = { \"-linkname\", Mathematica_KERNEL_EXECUTABLE \" -mathlink\", \"-linkmode\", \"launch\" };\n\tchar *argv[4];\n\tfor (size_t i=0; i<4; ++i)\n\t\targv[i] = argvi[i];\n\tint  argc = 4;\n\n\tint errno;\n\tstdenv = WSInitialize((WSEnvironmentParameter)0);\n\tif(stdenv==0)\n\t\tthrow InternalError(\"Failed to initialise WSTP\");\n\n\t// std::cerr << \"initialised\" << std::endl;\n\n\ttry {\n\t\tlp = WSOpenArgcArgv(stdenv, argc, argv, &errno);\n\t\tif(lp==0 || errno!=WSEOK) {\n\t\t\t// std::cerr << errno << \", \" << WSErrorMessage(lp) << \";\" << std::endl;\n\t\t\tlp=0;\n\t\t\tWSDeinitialize(stdenv);\n\t\t\tthrow InternalError(\"Failed to open Mathematica link\");\n\t\t\t}\n\t\t}\n\tcatch(std::exception& ex) {\n\t\tlp=0;\n\t\tWSDeinitialize(stdenv);\n\t\tthrow InternalError(\"Failed to open Mathematica link\");\n\t\t}\n\n\t// std::cerr << \"loopback link open\" << std::endl;\n\n\tWSActivate(lp);\n\t}\n\nvoid MMA::teardown_link()\n\t{\n\tif(lp!=0) {\n\t\tWSClose(lp);\n\t\tWSDeinitialize(stdenv);\n\t\tlp=0;\n\t\t}\n\t}\n"
  },
  {
    "path": "core/MMACdb.hh",
    "content": "\n#pragma once\n\n#include \"Props.hh\"\n#include \"Storage.hh\"\n#include \"Kernel.hh\"\n#include \"Stopwatch.hh\"\n\n#include \"wstp.h\"\n\nclass MMA {\n\tpublic:\n\n\t\t/// \\ingroup scalar\n\t\t///\n\t\t/// Functionality to act with Mathematica functions on (parts of)\n\t\t/// Cadabra Ex expressions and read the result back into the same\n\t\t/// Ex. This duplicates some of the logic in PythonCdb.hh, in\n\t\t/// particular make_Ex_from_string, but it is best to keep these\n\t\t/// two completely separate.\n\n\t\tstatic cadabra::Ex::iterator apply_mma(const cadabra::Kernel&, cadabra::Ex&, cadabra::Ex::iterator&,\n\t\t                                       const std::vector<std::string>& wrap, std::vector<std::string> args,\n\t\t                                       const std::string& method);\n\n\n\tprivate:\n\t\tstatic WSEnvironment stdenv;\n\t\tstatic WSLINK        lp;\n\n\t\tstatic void setup_link();\n\t\tstatic void teardown_link();\n\t};\n"
  },
  {
    "path": "core/Media.cc",
    "content": "\n#include \"Media.hh\"\n\nLaTeXString::LaTeXString(const std::string& s)\n   : content(s)\n\t{\n\t}\n\nstd::string LaTeXString::latex() const\n\t{\n\treturn content;\n\t}\n"
  },
  {
    "path": "core/Media.hh",
    "content": "#pragma once\n\n#include <string>\n\nclass LaTeXString {\n\tpublic:\n\t\tLaTeXString(const std::string& );\n\t\t\n\t\tstd::string latex() const;\n\tprivate:\n\t\tstd::string content;\n};\n"
  },
  {
    "path": "core/MultiIndex.hh",
    "content": "\n#pragma once\n\n#include <vector>\n\n/// A class to help iterating over all values of multiple objects.\n/// Templated over the type of the values. See test_multiindex.cc\n/// for a sample use case.\n\ntemplate<class T>\nclass MultiIndex {\n\tpublic:\n\t\ttypedef std::vector<T> values_type;\n\t\tstd::vector<values_type> values;\n\n\t\tvoid start()\n\t\t\t{\n\t\t\tcurrent_pos=std::vector<std::size_t>(values.size(), 0);\n\t\t\tend_=false;\n\t\t\t}\n\n\t\tbool end() const\n\t\t\t{\n\t\t\treturn end_;\n\t\t\t}\n\n\t\tMultiIndex& operator++()\n\t\t\t{\n\t\t\tcurrent_pos[0]++;\n\t\t\tstd::size_t ci=0;\n\t\t\twhile(current_pos[ci] == values[ci].size()) {\n\t\t\t\tif(ci==current_pos.size()-1) {\n\t\t\t\t\tend_=true;\n\t\t\t\t\treturn *this;\n\t\t\t\t\t}\n\t\t\t\tcurrent_pos[ci++]=0;\n\t\t\t\tcurrent_pos[ci]++;\n\t\t\t\t}\n\t\t\treturn *this;\n\t\t\t}\n\n\t\tconst T& operator[](std::size_t i)\n\t\t\t{\n\t\t\treturn values[i][current_pos[i]];\n\t\t\t}\n\n\tprivate:\n\t\tstd::vector<std::size_t> current_pos;\n\t\tbool end_;\n\t};\n\n\n"
  },
  {
    "path": "core/Multiplier.cc",
    "content": "#include \"Multiplier.hh\"\n#include <exception>\n\nnamespace cadabra {\n\n\tMultiplier::Multiplier()\n\t\t: value(mpq_class(0))\n\t\t{\n\t\t}\n\n\tMultiplier::Multiplier(mpz_class n, mpz_class d)\n\t\t: value(mpq_class(n, d))\n\t\t{\n\t\t}\n\t\n\tMultiplier::Multiplier(const mpq_class& v)\n\t\t: value(v)\n\t\t{\n\t\t}\n\n\tMultiplier::Multiplier(int v)\n\t\t: value(mpq_class(v))\n\t\t{\n\t\t}\n\n\tMultiplier::Multiplier(unsigned int v)\n\t\t: value(mpq_class(v))\n\t\t{\n\t\t}\n\n\tMultiplier::Multiplier(long v)\n\t\t: value(mpq_class(v))\n\t\t{\n\t\t}\n\n\tMultiplier::Multiplier(unsigned long v)\n\t\t: value(mpq_class(v))\n\t\t{\n\t\t}\n\n\tMultiplier::Multiplier(double v)\n\t\t: value(v)\n\t\t{\n\t\t}\n\n\tMultiplier& Multiplier::operator=(const mpq_class& v)\n\t\t{\n\t\tvalue = v;\n\t\treturn *this;\n\t\t}\n\n\tMultiplier& Multiplier::operator=(const double& v)\n\t\t{\n\t\tvalue = v;\n\t\treturn *this;\n\t\t}\n\n\tbool Multiplier::is_rational() const\n\t\t{\n\t\treturn std::holds_alternative<mpq_class>(value);\n\t\t}\n\n\tbool Multiplier::is_double() const\n\t\t{\n\t\treturn std::holds_alternative<double>(value);\n\t\t}\n\n\tconst mpq_class& Multiplier::get_rational() const\n\t\t{\n\t\tif (is_rational()) {\n\t\t\treturn std::get<mpq_class>(value);\n\t\t\t}\n\t\telse throw std::logic_error(\"Multiplier::get_rational: cannot convert double to rational.\");\n\t\t}\n\n\tdouble Multiplier::get_double() const\n\t\t{\n\t\tif (is_double()) {\n\t\t\treturn std::get<double>(value);\n\t\t\t}\n\t\telse {\n\t\t\treturn std::get<mpq_class>(value).get_d();\n\t\t\t}\n\t\t}\n\t\n\tbool Multiplier::result_is_double(const Multiplier& a, const Multiplier& b)\n\t\t{\n\t\treturn a.is_double() || b.is_double();\n\t\t}\n\n\tvoid Multiplier::canonicalize()\n\t\t{\n\t\tif(is_rational()) {\n\t\t\tmpq_class rat = get_rational();\n\t\t\trat.canonicalize();\n\t\t\tvalue = rat;\n\t\t\t}\n\t\t}\n\t\n\tMultiplier Multiplier::operator+(const Multiplier& other) const\n\t\t{\n\t\tif (result_is_double(*this, other)) {\n\t\t\treturn Multiplier(this->get_double() + other.get_double());\n\t\t\t}\n\t\telse {\n\t\t\treturn Multiplier(this->get_rational() + other.get_rational());\n\t\t\t}\n\t\t}\n\n\tMultiplier Multiplier::operator-(const Multiplier& other) const\n\t\t{\n\t\tif (result_is_double(*this, other)) {\n\t\t\treturn Multiplier(this->get_double() - other.get_double());\n\t\t\t}\n\t\telse {\n\t\t\treturn Multiplier(this->get_rational() - other.get_rational());\n\t\t\t}\n\t\t}\n\n\tMultiplier Multiplier::operator*(const Multiplier& other) const\n\t\t{\n\t\tif (result_is_double(*this, other)) {\n\t\t\treturn Multiplier(this->get_double() * other.get_double());\n\t\t\t}\n\t\telse {\n\t\t\treturn Multiplier(this->get_rational() * other.get_rational());\n\t\t\t}\n\t\t}\n\t\n\tMultiplier Multiplier::operator/(const Multiplier& other) const\n\t\t{\n\t\tif (result_is_double(*this, other)) {\n\t\t\treturn Multiplier(this->get_double() / other.get_double());\n\t\t\t}\n\t\telse {\n\t\t\treturn Multiplier(this->get_rational() / other.get_rational());\n\t\t\t}\n\t\t}\n\t\n\tMultiplier& Multiplier::operator+=(const Multiplier& other)\n\t\t{\n\t\t*this = *this + other;\n\t\treturn *this;\n\t\t}\n\n\tMultiplier& Multiplier::operator-=(const Multiplier& other)\n\t\t{\n\t\t*this = *this - other;\n\t\treturn *this;\n\t\t}\n\n\tMultiplier& Multiplier::operator*=(const Multiplier& other)\n\t\t{\n\t\t*this = *this * other;\n\t\treturn *this;\n\t\t}\n\n\tMultiplier& Multiplier::operator/=(const Multiplier& other)\n\t\t{\n\t\t*this = *this / other;\n\t\treturn *this;\n\t\t}\n\n\tbool Multiplier::operator==(const Multiplier& other) const\n\t\t{\n\t\tif (is_rational() && other.is_rational()) {\n\t\t\treturn get_rational() == other.get_rational();\n\t\t\t} else {\n\t\t\treturn get_double() == other.get_double();\n\t\t\t}\n\t\t}\n\n\tbool Multiplier::operator!=(const Multiplier& other) const\n\t\t{\n\t\treturn !(*this == other);\n\t\t}\n\t\n\tbool Multiplier::operator<(const Multiplier& other) const\n\t\t{\n\t\tif(is_rational() && other.is_rational()) {\n\t\t\treturn get_rational() < other.get_rational();\n\t\t\t}\n\t\telse {\n\t\t\treturn get_double() < other.get_double();\n\t\t\t}\n\t\t}\n\n\tbool Multiplier::operator<=(const Multiplier& other) const\n\t\t{\n\t\tif (is_rational() && other.is_rational()) {\n\t\t\treturn get_rational() <= other.get_rational();\n\t\t\t}\n\t\telse {\n\t\t\treturn get_double() <= other.get_double();\n\t\t\t}\n\t\t}\n\t\n\tbool Multiplier::operator>(const Multiplier& other) const\n\t\t{\n\t\treturn !(*this <= other);\n\t\t}\n\n\tbool Multiplier::operator>=(const Multiplier& other) const\n\t\t{\n\t\treturn !(*this < other);\n\t\t}\n\n\tstd::ostream& operator<<(std::ostream& os, const Multiplier& m)\n\t\t{\n\t\tif (m.is_rational()) {\n\t\t\tos << std::get<mpq_class>(m.value);\n\t\t\t}\n\t\telse {\n\t\t\tos << std::get<double>(m.value);\n\t\t\t}\n\t\treturn os;\n\t\t}\n}\n"
  },
  {
    "path": "core/Multiplier.hh",
    "content": "#pragma once\n\n#include <iostream>\n#include <variant>\n#include <gmpxx.h>\n\nnamespace cadabra {\n\n\tclass Multiplier {\n\t\tprivate:\n\t\t\tstd::variant<mpq_class, double> value;\n\n\t\tpublic:\n\t\t\t// Constructors\n\t\t\tMultiplier();\n\t\t\tMultiplier(mpz_class numerator, mpz_class denominator=1);\n\t\t\tMultiplier(const mpq_class& v);\n\t\t\tMultiplier(int v);\n\t\t\tMultiplier(unsigned int v);\n\t\t\tMultiplier(long v);\n\t\t\tMultiplier(unsigned long v);\n\t\t\tMultiplier(double v);\n    \n\t\t\t// Copy constructor\n\t\t\tMultiplier(const Multiplier& other) = default;\n    \n\t\t\t// Assignment operators\n\t\t\tMultiplier& operator=(const Multiplier& other) = default;\n\t\t\tMultiplier& operator=(const mpq_class& v);\n\t\t\tMultiplier& operator=(const double& v);\n    \n\t\t\t// Type checking\n\t\t\tbool is_rational() const;\n\t\t\tbool is_double() const;\n    \n\t\t\t// Value getters\n\t\t\tconst mpq_class& get_rational() const;\n\t\t\tdouble get_double() const;\n    \n\t\t\t// Helper method to determine result type\n\t\t\tstatic bool result_is_double(const Multiplier& a, const Multiplier& b);\n\n\t\t\t// Canonicalize if rational.\n\t\t\tvoid canonicalize();\n\t\t\t\n\t\t\t// Arithmetic operators\n\t\t\tMultiplier operator+(const Multiplier& other) const;\n\t\t\tMultiplier operator-(const Multiplier& other) const;\n\t\t\tMultiplier operator*(const Multiplier& other) const;\n\t\t\tMultiplier operator/(const Multiplier& other) const;\n    \n\t\t\t// Compound assignment operators\n\t\t\tMultiplier& operator+=(const Multiplier& other);\n\t\t\tMultiplier& operator-=(const Multiplier& other);\n\t\t\tMultiplier& operator*=(const Multiplier& other);\n\t\t\tMultiplier& operator/=(const Multiplier& other);\n    \n\t\t\t// Comparison operators\n\t\t\tbool operator==(const Multiplier& other) const;\n\t\t\tbool operator!=(const Multiplier& other) const;\n\t\t\tbool operator<(const Multiplier& other) const;\n\t\t\tbool operator<=(const Multiplier& other) const;\n\t\t\tbool operator>(const Multiplier& other) const;\n\t\t\tbool operator>=(const Multiplier& other) const;\n    \n\t\t\t// Stream output\n\t\t\tfriend std::ostream& operator<<(std::ostream& os, const Multiplier& m);\n\t};\n\n}\n"
  },
  {
    "path": "core/NDSolver.cc",
    "content": "\n#include \"NDSolver.hh\"\n#include \"Exceptions.hh\"\n#include \"Functional.hh\"\n#include \"NEvaluator.hh\"\n#include <boost/numeric/odeint.hpp>\n#include <boost/numeric/odeint/integrate/integrate_const.hpp>\n\nusing namespace cadabra;\n\nNDSolver::EventException::EventException(std::string reason)\n\t: CadabraException(reason)\n\t{\n\t}\n\nNDSolver::NDSolver(const Ex& odes)\n\t: ODEs(odes), time_variable(Ex(\"t\")), range_from(0), range_to(1)\n\t{\n\t}\n\nvoid NDSolver::operator()(const state_type& x, state_type& dxdt, const double t)\n\t{\n\t// Evaluate the right-hand sides of the ODEs at the given point in\n\t// x's and t.\n\n\tfor(size_t e=0; e<evaluators.size(); ++e) {\n\t\tNEvaluator& evaluator = evaluators[e];\n\t\tevaluator.set_variable(time_variable, NTensor(t));\n\t\tfor(size_t i=0; i<x.size(); ++i) {\n\t\t\tevaluator.set_variable(variables[i], NTensor(x[i]));\n\t\t\t}\n\t\tNTensor res = evaluator.evaluate();\n//\t\tstd::cerr << \"size = \" << res.shape.size() << std::endl;\n//\t\tstd::cerr << res << std::endl;\n//\t\tstd::cerr << shape\n\t\tdxdt[e] = evaluator.evaluate().at().real(); // FIXME: solve over C?\n\t\t// std::cerr << x[0] << \", \" << x[1] << \" -> \"\n\t\t//\t\t\t << dxdt[0] << \", \" << dxdt[1] << std::endl;\n\t\t}\n\t}\n\nbool NDSolver::evaluate_stop(const state_type& x, const double t)\n\t{\n\tfor(size_t e=0; e<stop_conditions.size(); ++e) {\n\t\tNEvaluator& lhs_evaluator = stop_lhs_evaluators[e];\n\t\tNEvaluator& rhs_evaluator = stop_rhs_evaluators[e];\n\t\tlhs_evaluator.set_variable(time_variable, NTensor(t));\n\t\tfor(size_t i=0; i<x.size(); ++i) {\n\t\t\tlhs_evaluator.set_variable(variables[i], NTensor(x[i]));\n\t\t\trhs_evaluator.set_variable(variables[i], NTensor(x[i]));\n\t\t\t}\n\t\tauto lhs = lhs_evaluator.evaluate().at().real();\n\t\tauto rhs = rhs_evaluator.evaluate().at().real();\n\t\tif(stop_conditions[e]) {\n\t\t\tif(lhs < rhs)\n\t\t\t\treturn true;\n\t\t\t}\n\t\telse {\n\t\t\tif(lhs > rhs)\n\t\t\t\treturn true;\n\t\t\t}\n\t\t// FIXME: handle <= and >=.\n\t\t}\n\t\n\treturn false;\n\t}\n\nvoid NDSolver::operator()(const state_type&x, const double t)\n\t{\n\t// This is the observer function, which can also be used to stop\n\t// integration when a condition is met (to stop iteration before\n\t// the final t-value has been reached, simply throw an\n\t// EventException here).\n\n\t// std::cerr << this << \", t=\" << t << \": \" << x[0] << \", \" << x[1] << std::endl;\n\ttimes.push_back(t);\n\tfor(size_t i=0; i<x.size(); ++i) \n\t\tstates[i].push_back( x[i] );\n\n\tif(evaluate_stop(x, t))\n\t\tthrow EventException(\"NDSolve::evaluate: stop condition triggered.\");\n\t}\n\nvoid NDSolver::set_ODEs(const Ex& odes)\n\t{\n\tODEs=odes;\n\t}\n\nvoid NDSolver::set_initial_value(const Ex& var, double val)\n\t{\n\tauto it = initial_values.find(var);\n\tif(it == initial_values.end()) {\n\t\tinitial_values[var] = val;\n\t\t}\n\telse {\n\t\tit->second = val;\n\t\t}\n\t}\n\nvoid NDSolver::set_range(const Ex& var, double f, double t)\n\t{\n\ttime_variable = var;\n\trange_from = f;\n\trange_to   = t;\n\t}\n\nvoid NDSolver::set_stop(const Ex& stop_)\n\t{\n\tstop = stop_;\n\t}\n\nvoid NDSolver::extract_from_ODEs()\n\t{\n\tevaluators.clear();\n\tstop_lhs_evaluators.clear();\n\tstop_rhs_evaluators.clear();\t\n\t\n\tdo_list(ODEs, ODEs.begin(), [this](Ex::iterator it) {\n\t\tif(*it->name!=\"\\\\equals\")\n\t\t\tthrow ConsistencyException(\"NDSolver: found a non-equation.\");\n\n\t\tauto lhs = ODEs.begin(it);\n\t\tif(*lhs->name!=\"\\\\dot\")\n\t\t\tthrow ConsistencyException(\"NDSolver: all left-hand sides must be first-order derivatives.\");\n\n\t\tauto var = ODEs.begin(lhs);\n\t\tvariables.push_back(Ex(var));\n\t\t// std::cerr << \"found variable \" << var << std::endl;\n\n\t\t++lhs;\n\t\tevaluators.push_back(NEvaluator(lhs));\n\t\t// std::cerr << \"found rhs \" << lhs << std::endl;\n\t\t\n\t\treturn true;\n\t\t});\n\n\tdo_list(stop, stop.begin(), [this](Ex::iterator it) {\n\t\tif(*it->name!=\"\\\\less\" && *it->name!=\"\\\\greater\")\n\t\t\tthrow ConsistencyException(\"NDSolver: stopping conditions have to be inequalities.\");\n\n\t\tstop_conditions.push_back( *it->name==\"\\\\less\" );\n\t\t\n\t\tauto lhs = stop.begin(it);\n\t\tstop_lhs_evaluators.push_back(NEvaluator(lhs));\n\n\t\tauto rhs = lhs;\n\t\t++rhs;\n\t\tstop_rhs_evaluators.push_back(NEvaluator(rhs));\n\n\t\treturn true;\n\t\t});\n\t}\n\nconst std::vector<Ex>& NDSolver::functions() const\n\t{\n\treturn variables;\n\t}\n\nstd::vector<NTensor> NDSolver::integrate()\n\t{\n\textract_from_ODEs();\n\tstates.resize(variables.size());\n\ttimes.clear();\n\tstates.clear();\n\n\t// Setup initial values.\n\tstate_type ivs;\n\tfor(size_t i=0; i<variables.size(); ++i) {\n\t\tauto it = initial_values.find( variables[i] );\n\t\tif(it != initial_values.end()) \n\t\t\tivs.push_back(it->second);\n\t\telse \n\t\t\tivs.push_back(0);\n\t\t}\n\n\tsize_t steps=0;\n\ttry {\n\t\t// FIXME: use integrate_const (see gemini chat) to use an event observer,\n\t\t// so that we can stop integration precisely at the point where the event\n\t\t// occurs. Right now, we typically overshoot.\n\t\tsteps = boost::numeric::odeint::integrate(std::ref(*this),\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tivs,    // initial values\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\trange_from,\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\trange_to,\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t0.01, // initial step size, adjusts itself\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tstd::ref(*this));\n\t\t}\n\tcatch(const EventException& ex) {\n\t\t// Integration has been stopped by the observer function.\n\t\t}\n\n\t// Create a vector of NTensors to return.\n\tNTensor ts( times );\n\tstd::vector<NTensor> ret;\n\tret.push_back(ts);\n\tfor(size_t i=0; i<variables.size(); ++i) {\n\t\tNTensor vs( states[i] );\n\t\tret.push_back(vs);\n\t\t}\n\n\treturn ret;\n\t}\n"
  },
  {
    "path": "core/NDSolver.hh",
    "content": "#pragma once\n\n#include \"Storage.hh\"\n#include \"Compare.hh\"\n#include \"Exceptions.hh\"\n#include \"NTensor.hh\"\n#include \"NEvaluator.hh\"\n\nnamespace cadabra {\n\n\t/// \\ingroup numerical\n\t///\n\t/// Functionality to numerically integrate a set of first-order\n\t/// ODEs. Currently only supports initial value problems.\n\t///\n\t/// The ODEs should be stored in the Ex as a list of equations\n\t/// of the form\n\t///\n\t///   \\dot{x} = f(t,x,y),  \\dot{y} = g(t,x,y), ...\n\t///\n\t/// Here '\\dot' needs to be a Derivative, with the 'to' parameter\n\t/// set to the ODE parameter (which can also appear explictly\n\t/// on the right-hand sides).\n\t\n\tclass NDSolver {\n\t\tpublic:\n\t\t\t// Initialise with an Ex containing the ODEs in standard form\n\t\t\t// (that is, only 1st order derivatives on the lhs).\n\t\t\tNDSolver(const Ex&);\n\n\t\t\ttypedef std::vector<double> state_type;\n\n\t\t\t// Integration function.\n\t\t\tvoid operator()(const state_type &x, state_type &dxdt, const double t);\n\n\t\t\t// Observer function.\n\t\t\tvoid operator()( const state_type &x , double t );\n\n\t\t\t// Set and check ODE(s).\n\t\t\tvoid set_ODEs(const Ex&);\n\n\t\t\t// Set initial values.\n\t\t\tvoid set_initial_value(const Ex&, double val);\n\n\t\t\t// Set integration range for the independent variable.\n\t\t\tvoid set_range(const Ex&, double from, double to);\n\n\t\t\t// Set a condition which, when satisfied, will stop the integration.\n\t\t\tvoid set_stop(const Ex&);\n\t\t\t\n\t\t\t// Entry point.\n\t\t\tstd::vector<NTensor> integrate();\n\n\t\t\t// Functions.\n\t\t\tconst std::vector<Ex>& functions() const;\n\t\t\t\n\t\tprivate:\n\t\t\t// Exception used by the observer function to terminate\n\t\t\t// iteration in case an event happens.\n\t\t\t\n\t\t\tclass EventException : public CadabraException {\n\t\t\t\tpublic:\n\t\t\t\t\tEventException(std::string reason=\"\");\n\t\t\t};\n\t\t\t\n\t\t\tEx ODEs, stop;\n\n\t\t\t// Information extracted from `ODEs`.\n\t\t\tstd::vector<Ex>           variables;\n\n\t\t\t// For each function in the ODEs we have one evaluator.\n\t\t\tstd::vector<NEvaluator>   evaluators;\n\n\t\t\t// For each condition in the `stop` expression we also have one evaluator.\n\t\t\tstd::vector<NEvaluator>   stop_lhs_evaluators, stop_rhs_evaluators;\n\t\t\tstd::vector<bool>         stop_conditions;\n\n\t\t\t// Extract from `ODEs` the right-hand side expressions as\n\t\t\t// well as the names of the functions to solve for.\n\t\t\tvoid extract_from_ODEs();\n\n\t\t\t// Evaluate the stop condition.\n\t\t\tbool evaluate_stop(const state_type& x, const double t);\n\n\t\t\t// Storage of the result of the integration.\n\t\t\tstd::vector<std::vector<double>> states;\n\t\t\tstd::vector<double>              times;\n\t\t\tstd::map<Ex, double, tree_exact_less_no_wildcards_obj>  initial_values;\n\t\t\tEx                               time_variable;\n\t\t\tdouble                           range_from, range_to;\n};\n\t\n};\n"
  },
  {
    "path": "core/NEvaluator.cc",
    "content": "\n#include \"Compare.hh\"\n#include \"NEvaluator.hh\"\n#include \"NInterpolatingFunction.hh\"\n#include \"Exceptions.hh\"\n#include <cmath>\n\nusing namespace cadabra;\n\n\n// void NEvaluator::find_common_subexpressions(std::vector<Ex *>)\n// \t{\n// \t// Compute the hash value of every subtree, and collect matches.\n// \t// Then compare subtrees with equal hash to find common subtrees.\n// \t}\n\n// #define DEBUG __FILE__\n#include \"Debug.hh\"\n\nconstexpr double const_pi = 3.14159265358979323846;\n\nNEvaluator::NEvaluator()\n\t{\n\t}\n\nNEvaluator::NEvaluator(Ex::iterator ex_it)\n\t: ex(ex_it)\n\t{\n\t}\n\nvoid NEvaluator::set_function(Ex::iterator ex_it)\n\t{\n\tex = Ex(ex_it);\n\t}\n\nvoid NEvaluator::set_lookup_function(lookup_function_t f)\n\t{\n\tlookup_function = f;\n\t}\n\nNTensor NEvaluator::evaluate()\n\t{\n\tfind_variable_locations();\n\n\t// The vector below pairs LaTeX strings which can appear in the\n\t// cadabra input to function names in the C++ standard library.\n\n\tusing complex_func = std::complex<double>(*)(const std::complex<double>&);\n\t// const double eps = 1e-10;\n\n\tconst std::map<nset_t::iterator, complex_func, nset_it_less> elementary\n\t\t= { // Trigonometric functions.\n\n\t\t{ name_set.find(\"\\\\sin\"), std::sin<double> },\n\t\t{ name_set.find(\"\\\\cos\"), std::cos<double> },\n\t\t{ name_set.find(\"\\\\tan\"), std::tan<double> },\n\n\t\t{ name_set.find(\"\\\\csc\"), [](const std::complex<double>& x) { return 1.0/std::sin<double>(x); } },\n\t\t{ name_set.find(\"\\\\sec\"), [](const std::complex<double>& x) { return 1.0/std::cos<double>(x); } },\n\t\t{ name_set.find(\"\\\\cot\"), [](const std::complex<double>& x) { return std::cos<double>(x)/std::sin<double>(x); } },\n\n\t\t{ name_set.find(\"\\\\arcsin\"), std::asin<double>},\n\t\t{ name_set.find(\"\\\\arccos\"), std::acos<double>},\n\t\t{ name_set.find(\"\\\\arctan\"), std::atan<double>},\n\t\t\n\t\t// Hyperbolic functions.\n\t\t\n\t\t{ name_set.find(\"\\\\sinh\"), std::sinh<double>},\n\t\t{ name_set.find(\"\\\\cosh\"), std::cosh<double>},\n\t\t{ name_set.find(\"\\\\tanh\"), std::tanh<double>},\n\t\t\n\t\t{ name_set.find(\"\\\\csch\"), [](const std::complex<double>& x) { return 1.0/std::sinh<double>(x); } },\n\t\t{ name_set.find(\"\\\\sech\"), [](const std::complex<double>& x) { return 1.0/std::cosh<double>(x); } },\n\t\t{ name_set.find(\"\\\\coth\"), [](const std::complex<double>& x) { return std::cosh<double>(x)/std::sinh<double>(x); } },\n\t\t\n\t\t{ name_set.find(\"\\\\arcsinh\"), std::asinh<double>},\n\t\t{ name_set.find(\"\\\\arccosh\"), std::acosh<double>},\n\t\t{ name_set.find(\"\\\\arctanh\"), std::atanh<double>},\n\n\t\t// Logarithmic and exponential functions.\n\t\t\n\t\t{ name_set.find(\"\\\\log\"),     std::log10<double>},\n\t\t{ name_set.find(\"\\\\log2\"),    [](const std::complex<double>& x) { return std::log<double>(x) / std::log<double>(2.0); } },\n\t\t{ name_set.find(\"\\\\ln\"),      std::log<double>  },\n\t\t{ name_set.find(\"\\\\exp\"),     std::exp<double>  },\n\t\t{ name_set.find(\"\\\\sqrt\"),    std::sqrt<double> },\n\n\t\t// Real and imaginary parts.\n\n\t\t{ name_set.find(\"\\\\Re\"),      [](const std::complex<double>& x) { return std::complex<double>(x.real(), 0); } },\n\t\t{ name_set.find(\"\\\\Im\"),      [](const std::complex<double>& x) { return std::complex<double>(x.imag(), 0); } },\n\n\t\t// Steps, absolute values and so on.\n\t\t\n\t\t{ name_set.find(\"\\\\abs\"),    [](const std::complex<double>& x) { return std::complex<double>(std::abs<double>(x), 0.0); } } ,\n//\t\t{ name_set.find(\"\\\\floor\"),  [eps](const std::complex<double>& x) {\n//\t\t\tif(std::abs(x.imag()) > eps)\n//\t\t\t\tthrow ConsistencyException(\"Function floor called on complex number.\");\n//\t\t\treturn std::complex<double>(std::floor(x.real()), 0.0);\n//\t\t\t} },\n\t\t{ name_set.find(\"\\\\sign\"),   [](const std::complex<double>& x) {\n\t\t\tif(x.real()==0)     return  std::complex<double>(0.0,  0.0);\n\t\t\telse if(x.real()<0) return  std::complex<double>(-1.0, 0.0);\n\t\t\telse                return  std::complex<double>(1.0,  0.0);\n\t\t\t} }\n\t}; \n\n\tconst auto n_pow  = name_set.find(\"\\\\pow\");\n\tconst auto n_prod = name_set.find(\"\\\\prod\");\n\tconst auto n_sum  = name_set.find(\"\\\\sum\");\n\tconst auto n_pi   = name_set.find(\"\\\\pi\");\n\tconst auto n_bigO = name_set.find(\"\\\\bigO\");\n\n\tNTensor lastval(0);\n\n\tauto it = ex.begin_post();\n\twhile(it != ex.end_post()) {\n\n\t\t// First check interpolating functions.\n\t\t\n\t\tif(std::holds_alternative<std::shared_ptr<NInterpolatingFunction>>(it->content)) {\n\t\t\tauto nif = std::get<std::shared_ptr<NInterpolatingFunction>>(it->content);\n\t\t\tif(lastval.is_real()==false)\n\t\t\t\tthrow ConsistencyException(\"NEvaluator: cannot feed complex number to NInterpolatingFunction.\");\n\n\t\t\tlastval = variable_values[0].values.broadcast(fullshape, 0);\n#ifdef DEBUG\n\t\t\tstd::cerr << \"Evaluating interpolating function for \" << lastval.values.size() << \" values\" << std::endl;\n#endif\n\t\t\t// Feed all values in the NTensor lastval through the interpolating function.\n\t\t\tfor(size_t i=0; i<lastval.values.size(); ++i) {\n\t\t\t\tlastval.values[i] = nif->evaluate(lastval.values[i].real());\n\t\t\t\t}\n\t\t\tsubtree_values.insert(std::make_pair(it, lastval) );\n\t\t\t++it;\n\t\t\tcontinue;\n\t\t\t}\n\n\t\t// Either this node is known in the subtree value map,\n\t\t// or this node is a function which combines the values\n\t\t// of child nodes.\n\n\t\tauto fnd = subtree_values.find(Ex::iterator(it));\n\t\tif(fnd!=subtree_values.end()) {\n#ifdef DEBUG\n\t\t\tstd::cerr << it << \" has value \" << fnd->second << std::endl;\n\t\t\t// Note: the above will, for a scalar value, display the\n\t\t\t// broadcast value for `fullshape` as computed below\n\t\t\t// in `find_variable_locations`; so [[[1]]] is perfectly\n\t\t\t// normal if there are three variables defined.\n#endif\n\t\t\tlastval  = fnd->second;\n\t\t\t}\n\t\telse {\n\t\t\tbool found_elementary=false;\n\t\t\tif(it->is_rational() || it->is_double()) {\n\t\t\t\tlastval = NTensor(to_double(*it->multiplier));\n\t\t\t\tfound_elementary=true;\n\t\t\t\t}\n\t\t\telse {\n\t\t\t\tauto elementary_it = elementary.find(it->name);\n\t\t\t\tif(elementary_it != elementary.end()) {\n\t\t\t\t\tauto arg    = ex.begin(it);\n#ifdef DEBUG\n\t\t\t\t\tstd::cerr << *el.first << \" has \" << ex.number_of_children(it) << \" child nodes\" << std::endl;\n\t\t\t\t\tstd::cerr << \"need to apply \" << *el.first << \" to \" << arg << std::endl;\n#endif\n\t\t\t\t\tauto argit  = subtree_values.find(arg);\n\t\t\t\t   lastval = NTensor(argit->second);\n#ifdef DEBUG\n\t\t\t\t\tstd::cerr << \" argument equals \" << argval\n\t\t\t\t\t\t\t\t << \"; stored had multiplier \" << *(argit->first->multiplier) << std::endl;\n#endif\n\t\t\t\t\t// Any expressions are stored without multiplier, so we\n\t\t\t\t\t// now need to first multiply-through with the current\n\t\t\t\t\t// multiplier.\n\t\t\t\t\tmultiplier_t tomult = (*arg->multiplier)/(*argit->first->multiplier);\n\t\t\t\t\tif(tomult != 1) {\n\t\t\t\t\t\t// std::cerr << \"MULT!\" << std::endl;\n\t\t\t\t\t\tlastval *= to_double(tomult);\n\t\t\t\t\t\t}\n\t\t\t\t\t\n\t\t\t\t\tlastval.apply(elementary_it->second);\n\t\t\t\t\tlastval *= to_double(*it->multiplier);\n\t\t\t\t\tfound_elementary=true;\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t\n\t\t\tif(found_elementary==false) {\n\t\t\t\tif(it->name==n_prod) {\n\t\t\t\t\tfor(auto cit = ex.begin(it); cit!=ex.end(it); ++cit) {\n\t\t\t\t\t\tauto cfnd = subtree_values.find(Ex::iterator(cit));\n\t\t\t\t\t\tif(cfnd==subtree_values.end())\n\t\t\t\t\t\t\tthrow std::logic_error(\"Inconsistent value tree.\");\n\t\t\t\t\t\tif(cit==ex.begin(it))\n\t\t\t\t\t\t\tlastval = cfnd->second;\n\t\t\t\t\t\telse\n\t\t\t\t\t\t\tlastval *= cfnd->second;\n\t\t\t\t\t\t}\n\t\t\t\t\tlastval *= to_double(*it->multiplier);\n\t\t\t\t\t}\n\t\t\t\telse if(it->name==n_sum) {\n\t\t\t\t\tfor(auto cit = ex.begin(it); cit!=ex.end(it); ++cit) {\n\t\t\t\t\t\tauto cfnd = subtree_values.find(Ex::iterator(cit));\n\t\t\t\t\t\tif(cfnd==subtree_values.end())\n\t\t\t\t\t\t\tthrow std::logic_error(\"Inconsistent value tree.\");\n\t\t\t\t\t\t\n\t\t\t\t\t\tif(cit==ex.begin(it)) \n\t\t\t\t\t\t\tlastval = cfnd->second;\n\t\t\t\t\t\telse\n\t\t\t\t\t\t\tlastval += cfnd->second;\n\t\t\t\t\t\t}\n\t\t\t\t\tlastval *= to_double(*it->multiplier);\n\t\t\t\t\t}\n\t\t\t\telse if(it->name==n_pow) {\n\t\t\t\t\tauto cit1  = Ex::begin(it);\n\t\t\t\t\tauto cit2  = cit1;\n\t\t\t\t\t++cit2;\n\t\t\t\t\t\n\t\t\t\t\tauto cfnd1 = subtree_values.find(Ex::iterator(cit1));\n\t\t\t\t\tauto cfnd2 = subtree_values.find(Ex::iterator(cit2));\n\t\t\t\t\tif(cfnd1==subtree_values.end() || cfnd2==subtree_values.end())\n\t\t\t\t\t\tthrow std::logic_error(\"Inconsistent value tree at exponentiation node.\");\n\n\t\t\t\t\tlastval = cfnd1->second.pow( cfnd2->second );\n\t\t\t\t\tlastval *= to_double(*it->multiplier);\n\t\t\t\t\t// throw std::logic_error(\"Value unknown for subtree special function.\");\n\t\t\t\t\t}\n\t\t\t\telse if(it->name==n_pi) {\n#ifdef DEBUG\n\t\t\t\t\tstd::cerr << \"found \\\\pi\" << std::endl;\n#endif \n\t\t\t\t\tlastval  = NTensor(const_pi * to_double(*it->multiplier));\n\t\t\t\t\t}\n\t\t\t\telse if(it->name==n_bigO) {\n\t\t\t\t\tlastval = NTensor(0);\n\t\t\t\t\t}\n\t\t\t\telse {\n\t\t\t\t\t// Try variable substitution rules.\n\t\t\t\t\tbool found=false;\n\t\t\t\t\tfor(const auto& var: variable_values) {\n\t\t\t\t\t\t// std::cerr << \"Comparing \" << var.first << \" with \" << *it << std::endl;\n\t\t\t\t\t\tEx no_multiplier(it);\n\t\t\t\t\t\tauto mult = *it->multiplier;\n\t\t\t\t\t\tone( no_multiplier.begin()->multiplier );\n\t\t\t\t\t\tno_multiplier.begin()->fl.parent_rel = str_node::p_none;\n\t\t\t\t\t\tif(var.variable == no_multiplier) {\n#ifdef DEBUG\n\t\t\t\t\t\t\tstd::cerr << \"found \" << *(no_multiplier.begin()->name) << \" with multiplier \"\n\t\t\t\t\t\t\t\t\t\t << mult << std::endl;\n#endif\n\t\t\t\t\t\t\tlastval = var.values;\n\t\t\t\t\t\t\tlastval *= to_double(mult);\n\t\t\t\t\t\t\tsubtree_values.insert(std::make_pair(it, lastval) );\n\t\t\t\t\t\t\t// std::cerr << \"We know the value of \" << *it << std::endl;\n\t\t\t\t\t\t\tfound=true;\n\t\t\t\t\t\t\tbreak;\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\t}\n\n\t\t\t\t\t// Is this perhaps a string representing a float?\n\t\t\t\t\tif(!found) {\n\t\t\t\t\t\ttry {\n\t\t\t\t\t\t\tlastval = NTensor(std::stod(*it->name));\n\t\t\t\t\t\t\tsubtree_values.insert(std::make_pair(it, lastval));\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\tcatch(const std::invalid_argument& err) {\n\t\t\t\t\t\t\t// Last resort: lookup value using the external lookup function.\n\t\t\t\t\t\t\ttry {\n\t\t\t\t\t\t\t\tif(lookup_function)\n\t\t\t\t\t\t\t\t\tlastval = NTensor(lookup_function(Ex(it)));\n\t\t\t\t\t\t\t\telse \n\t\t\t\t\t\t\t\t\tthrow std::logic_error(\"Value unknown for subtree with head \"+(*it->name)+\".\");\n\t\t\t\t\t\t\t\t}\n\t\t\t\t\t\t\tcatch(const std::exception& ex) {\n\t\t\t\t\t\t\t\tthrow std::logic_error(\"Value unknown for subtree with head \"+(*it->name)+\".\");\n\t\t\t\t\t\t\t\t}\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\tcatch(const std::out_of_range& err) {\n\t\t\t\t\t\t\tthrow std::logic_error(\"Value \"+(*it->name)+\" does not fit in a float.\");\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\t}\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\tsubtree_values.insert(std::make_pair(it, lastval));\n\t\t\t}\n\n\t\t++it;\n\t\t}\n\n\tDEBUGLN( if(lastval.shape.size()==1 && lastval.shape[0]==1)\n\t\t\t\t\tstd::cerr << \"lastval needs broadcasting, shape[0] = \" << lastval.shape[0] << std::endl; );\n\n\tif(lastval.is_scalar()) {\n\t\t// The evaluation code above never pulled in any of the variables,\n\t\t// so the numerical value was never broadcast to the shape of the\n\t\t// output that we want. Do that now.\n\t\tlastval = NTensor(fullshape, lastval.at());\n\t\t}\n\t\t\n\tDEBUGLN( std::cerr << \"evaluate returns \" << lastval << std::endl; );\n\n\treturn lastval;\n\t}\n\nvoid NEvaluator::set_variable(const Ex& var, const NTensor& val)\n\t{\n\t// Ensure that we only store one entry in variable_values for\n\t// every variable.\n\n\tif(*var.begin()->multiplier != 1)\n\t\tthrow ConsistencyException(\"NEvaluator::set_variable: variables should not have multipliers.\");\n\t\n\tauto it = variable_values_locs.find(var);\n\tif(it == variable_values_locs.end()) {\n\t\t// Create new entry.\n\t\tvariable_values_locs[var] = variable_values.size();\n\t\tvariable_values.push_back( VariableValues({var, NTensor(val), {} }) );\n\t\t}\n\telse {\n\t\t// Overwrite if the variable was already present.\n\t\tvariable_values[it->second] = VariableValues({var, NTensor(val), {} });\n\t\t}\n\t}\n\nvoid NEvaluator::find_variable_locations()\n\t{\n#ifdef DEBUG\n\tfor(auto& var: variable_values) {\n\t\tstd::cerr << \"variable \" << var.variable << std::endl;\n\t\tstd::cerr << \"values \";\n\t\tfor(const auto& val: var.values.values)\n\t\t\tstd::cerr << val << \", \";\n\t\tstd::cerr << std::endl;\n\t\t}\n#endif\n\t// FIXME: we don't really need this anymore, as we do everything\n\t// with broadcasting. Well, not quite true. We do use the\n\t// subtree_values below to fetch the value of variables, as\n\t// subtree_values is the place where these have been broadcast\n\t// to the full shape. \n\tfor(auto& var: variable_values) {\n\t\tvar.locations.clear();\n\t\tauto it = ex.begin_post();\n\t\twhile(it != ex.end_post()) {\n\t\t\t// FIXME: also find variables in NInterpolatingFunctions.\n\t\t\tEx no_multiplier(it);\n\t\t\tauto mult = *it->multiplier;\n\t\t\tone( no_multiplier.begin()->multiplier );\n\t\t\tno_multiplier.begin()->fl.parent_rel = str_node::p_none;\n\t\t\tif(var.variable == no_multiplier)\n\t\t\t\tvar.locations.push_back(it);\n\t\t\t++it;\n\t\t\t}\n\t\t// std::cerr << \"Variable \" << var.variable << \" at \" << var.locations.size() << \" places\" << std::endl;\n\t\t}\n\n\t// Now insert subtree values which are such that for every\n\t// variable node we have an NTensor which is broadcast to the\n\t// shape of the full variable set NTensor.\n\n\tfullshape.clear();\n\tfor(const auto& var: variable_values) {\n\t\tif(var.values.shape.size()!=1)\n\t\t\tthrow ConsistencyException(\"NTensor: all variables should be specified as one-dimensional arrays.\");\n\n\t\tfullshape.push_back(var.values.shape[0]);\n\t\t// std::cerr << var.values.shape[0] << \", \";\n\t\t}\n\t// std::cerr << std::endl;\n\n\tsubtree_values.clear();\n\tfor(size_t v=0; v<variable_values.size(); ++v) {\n\t\tconst auto& var = variable_values[v];\n\t\tfor(const auto& it: var.locations) {\n\t\t\tauto bc_val = var.values.broadcast( fullshape, v );\n\t\t\tbc_val *= to_double(*it->multiplier);\n\t\t\tsubtree_values.insert(std::make_pair(it, bc_val ) );\n\t\t\t// std::cerr << bc_val << std::endl;\n\t\t\t}\n\t\t}\n\n\t// std::cerr << \"ready\" << std::endl;\n\t}\n"
  },
  {
    "path": "core/NEvaluator.hh",
    "content": "\n#pragma once\n\n#include \"Storage.hh\"\n#include \"NTensor.hh\"\n#include \"Compare.hh\"\n#include <functional>\n\nnamespace cadabra {\n\n\t/// \\ingroup numerical\n\t///\n\t/// Functionality to numerically evaluate a scalar expression,\n\t/// give the values of its building blocks.\n\t///\n\t/// The input is a map which relates subtrees in the expression\n\t/// to numerical values. The `evaluate` function will then do a\n\t/// post-order iteration over the tree, collecting and combining\n\t/// the values thus obtained.\n\t///\n\t/// Currently needs the leaf nodes to have an entry in the\n\t/// `subtree_values` map; may be extended later to cover values\n\t/// of non-elementary subtrees.\n\t///\n\t/// If there are 'n' variables, then at any stage the tree will\n\t/// be an n-tensor, with the dimension of each index set by the\n\t/// length of the value array for the corresponding variable.\n\n\tclass NEvaluator {\n\t\tpublic:\n\t\t\tNEvaluator();\n\t\t\tNEvaluator(Ex::iterator);\n\n\t\t\t/// If we know the value of a subtree explicitly as a number,\n\t\t\t/// it is stored in this map. These are computed nodes. Note that\n\t\t\t/// keys are compared as pointers, so two identical expressions at\n\t\t\t/// two different locations in the tree will have two entries in\n\t\t\t/// this map.\n\t\t\tstd::map<Ex::iterator, NTensor, Ex::iterator_base_less> subtree_values;\n\n\t\t\t/// If we know the value of a subtree is equal to another subtree\n\t\t\t/// (either in the same expression or another one), it is stored\n\t\t\t/// in the map below. This then still needs a lookup in the\n\t\t\t/// `subtree_values` map.\n\t\t\t/// FIXME: not used right now. The idea was that if we find two subtrees\n\t\t\t/// which are equal symbolically, we only have to evaluate one, and can\n\t\t\t/// then read off the value of the other one by referring to the first.\n\t\t\tstd::map<Ex::iterator, Ex::iterator, Ex::iterator_base_less> subtree_equalities;\n\n\t\t\t/// The expression will get evaluated for a range of values for\n\t\t\t/// each unknown sub-expression (variable). These are set in\n\t\t\t/// the map below.\n\t\t\tclass VariableValues {\n\t\t\t\tpublic:\n\t\t\t\t\tEx                        variable;\n\t\t\t\t\tNTensor                   values;\n\t\t\t\t\tstd::vector<Ex::iterator> locations;\n\t\t\t};\n\t\t\tstd::vector<VariableValues> variable_values;\n\t\t\tstd::map<Ex, size_t, tree_exact_less_no_wildcards_obj> variable_values_locs;\n\n\t\t\t/// Set function to evaluate. Can also be passed in the constructor.\n\t\t\tvoid    set_function(Ex::iterator);\n\t\t\t\n\t\t\t/// Set the range of values which we want to insert into the\n\t\t\t/// indicated variable. Fills the map above.\n\t\t\tvoid    set_variable(const Ex&, const NTensor& val);\n\n\t\t\t/// Set an external function which will be used by `evaluate` to lookup\n\t\t\t/// values of objects as a last resort, if they do not resolve using\n\t\t\t/// the `variable_values` list above.\n\t\t\ttypedef std::function<std::complex<double>(const Ex&)> lookup_function_t;\n\t\t\tvoid    set_lookup_function(lookup_function_t);\n\t\t\t\n\t\t\t/// Evaluate the expression, using the variable values set in\n\t\t\t/// `set_variable`. This will only work if the expression evaluates\n\t\t\t/// to a complex double.\n\t\t\tNTensor evaluate();\n\n\t\t\t/// PRIVATE:\n\n\t\t\tvoid find_variable_locations();\n\n\t\tprivate:\n\t\t\tEx                ex;\n\t\t\tlookup_function_t lookup_function;\n\n\t\t\t// The shape of the tensor that we will produce.\n\t\t\tstd::vector<size_t> fullshape;\n\t};\n\n};\n"
  },
  {
    "path": "core/NIntegrator.cc",
    "content": "\n#include \"NIntegrator.hh\"\n#include <boost/math/quadrature/gauss_kronrod.hpp>\n\nusing namespace cadabra;\n\nNIntegrator::NIntegrator(Ex::iterator ex_it)\n\t: evaluator(NEvaluator(ex_it)), integrand(ex_it)\n\t{\n\t}\n\nvoid NIntegrator::set_range(const Ex& x, double from_, double to_)\n\t{\n\tivar=x;\n\trange_from=from_;\n\trange_to=to_;\n\t}\n\nstd::complex<double> NIntegrator::integrate()\n\t{\n\tdouble abs_error = 1e-12;\n\tdouble error;\n\t\n\t// Maximum number of iterations\n\tsize_t max_depth = 15;\n\n\tauto eval = [this](double x) -> std::complex<double> {\n\t\tevaluator.set_variable(ivar, NTensor(x));\n\t\treturn evaluator.evaluate().at();\n\t\t};\n\n\t\n\t// Perform the integration\n\tstd::complex<double> result =\n\t\tboost::math::quadrature::gauss_kronrod<double, 15>::integrate(\n\t\t\teval, range_from, range_to, max_depth, abs_error, &error);\n\n\treturn result;\n\t}\n"
  },
  {
    "path": "core/NIntegrator.hh",
    "content": "#pragma once\n\n#include \"Storage.hh\"\n#include \"Compare.hh\"\n#include \"Exceptions.hh\"\n#include \"NTensor.hh\"\n#include \"NEvaluator.hh\"\n\nnamespace cadabra {\n\n\t/// \\ingroup numerical\n\t///\n\t/// Functionality to numerically integrate definite integrals.\n\t\n\tclass NIntegrator {\n\t\tpublic:\n\t\t\t// Initialise with an Ex subtree containing the integrand.\n\t\t\tNIntegrator(Ex::iterator);\n\n\t\t\t// Set integration range.\n\t\t\tvoid set_range(const Ex&, double from, double to);\n\t\t\t\n\t\t\t// Entry point.\n\t\t\tstd::complex<double> integrate();\n\n\t\t\t// Object to evaluate the expression. Users of `NIntegrator`\n\t\t\t// can set values for variables in this evaluator.\n\t\t\tNEvaluator evaluator;\n\t\t\t\n\t\tprivate:\n\t\t\tEx::iterator integrand;\n         Ex           ivar;\n\t\t\tdouble       range_from, range_to;\n};\n\t\n};\n"
  },
  {
    "path": "core/NInterpolatingFunction.cc",
    "content": "\n#include \"NInterpolatingFunction.hh\"\n#include \"Exceptions.hh\"\n\n// #define DEBUG 1\n\n#ifdef DEBUG\n#warning \"DEBUG enabled for NInterpolatingFunction.cc\"\nstatic bool debug_stop = false;\n#define DEBUGLN(ln) if(!debug_stop) { ln; }\n#else\n#define DEBUGLN(ln)\n#endif\n\n\nusing namespace cadabra;\n\nNInterpolatingFunction::NInterpolatingFunction()\n\t: var_values(0), fun_values(0), slope_values(0), last_index(0), precomputed(false)\n\t{\n\t}\n\nsize_t NInterpolatingFunction::find_interval(double v) const\n\t{\n\t// Same interval as previously?\n\tif(v >= var_values.values[last_index].real() && v<= var_values.values[last_index+1].real())\n\t\treturn last_index;\n\n\t// Hope that 'v' has just rolled into the next interval...\n\t++last_index;\n\tif(v >= var_values.values[last_index].real() && v<= var_values.values[last_index+1].real())\n\t\treturn last_index;\n\n\t// Exhaustive search.\n\tfor(last_index=0; last_index<var_values.values.size()-1; ++last_index)\n\t\tif(v >= var_values.values[last_index].real() && v<= var_values.values[last_index+1].real())\n\t\t\treturn last_index;\n\n\tthrow InternalError(\"NInterpolatingFunction: internal error, please report a bug.\");\n\t}\n\nvoid NInterpolatingFunction::compute_slopes() const\n\t{\n\tif(var_values.values.size() != fun_values.values.size())\n\t\tthrow ConsistencyException(\"NInterpolatingFunction: number of variable values != number of function values\");\n\n\tslope_values.shape = fun_values.shape;\n\tslope_values.values.clear();\n\tslope_values.values.resize(var_values.values.size()-1);\n\t\n\tfor(size_t i=0; i<var_values.values.size()-1; ++i) {\n\t\tdouble dx               = var_values.values[i+1].real() - var_values.values[i].real();\n\t\tstd::complex<double> dy = fun_values.values[i+1]        - fun_values.values[i];\n\t\tslope_values.values[i] = dy / dx;\n\t\t}\n\n\tprecomputed=true;\n\t}\n\nstd::pair<double, double> NInterpolatingFunction::range() const\n\t{\n\treturn std::make_pair( var_values.values.front().real(),\n\t\t\t\t\t\t\t\t  var_values.values.back().real() );\n\t}\n\nstd::complex<double> NInterpolatingFunction::evaluate(double v) const\n\t{\n\tif(!precomputed) {\n\t\tcompute_slopes();\n//\t\tspline = boost::math::cubic_b_spline<std::complex<double>>(\n//\t\t\tfun_values.values.begin(), fun_values.values.end(),\n//\t\t\tvar_values.values.front(),\n//\t\t\t[&x](size_t i) {\n//\t\t\treturn var_values.values[i+1].real() - var_values.values[i].real();\n//\t\t\t});\n\t\t}\n\t\n\tif(v < var_values.values.front().real() || v > var_values.values.back().real())\n\t\tthrow ArgumentException(\"NInterpolatingFunction: evaluated outside domain.\");\n\n\tsize_t i = find_interval(v);\n\tauto ret = fun_values.values[i] + (v - var_values.values[i].real()) * slope_values.values[i];\n\n\tDEBUGLN( std::cerr << \"InterpolatingFunction::evaluate: returning \" << ret << std::endl; );\n\treturn ret;\n\t}\n\nvariable_ranges_t cadabra::function_domain(const Ex& ex)\n\t{\n\tvariable_ranges_t ret;\n\n\t// Walk the whole tree, collecting ranges from\n\t// NInterpolatingFunctions (and possibly others\n\t// at some later stage).\n\n\tauto it = ex.begin();\n\twhile(it!=ex.end()) {\n\t\tif(std::holds_alternative<std::shared_ptr<NInterpolatingFunction>>(it->content)) {\n\t\t\tauto nif = std::get<std::shared_ptr<NInterpolatingFunction>>(it->content);\n\t\t\tauto rit = ret.find(nif->var);\n\t\t\tif(rit!=ret.end()) {\n\t\t\t\tstd::pair<double, double> oldrange = rit->second;\n\t\t\t\toldrange.first  = std::max(nif->range().first, oldrange.first);\n\t\t\t\toldrange.second = std::min(nif->range().second, oldrange.second);\n\t\t\t\tif(oldrange.first > oldrange.second)\n\t\t\t\t\tthrow ArgumentException(\"NInterpolatingFunction: domain intersection is empty.\");\n\t\t\t\trit->second = oldrange;\n\t\t\t\t}\n\t\t\telse {\n\t\t\t\tret[nif->var] = nif->range();\n\t\t\t\t}\n\t\t}\n\t\t\n\t\t++it;\n\t\t}\n\t\n\treturn ret;\n\t}\n"
  },
  {
    "path": "core/NInterpolatingFunction.hh",
    "content": "#pragma once\n\n#include \"NTensor.hh\"\n#include \"Storage.hh\"\n#include \"Compare.hh\"\n#include <vector>\n\nnamespace cadabra {\n\n\t/// An object representing a one-variable function (for now), which\n\t/// is computed from an interpolation of numerical data points.\n\t/// FIXME: generalise to functions of more than one variable.\n\t\n\tclass NInterpolatingFunction {\n\t\tpublic:\n\t\t\tNInterpolatingFunction();\n\n\t\t\t// FIXME: use NTensor as argument?\n\t\t\tstd::complex<double> evaluate(double) const;\n\t\t\t\n \t\t\tEx          var;\n\t\t\tNTensor     var_values;\n\t\t\tNTensor     fun_values;\n\n\t\t\t// Return the range over which the function is\n\t\t\t// defined/computable without extrapolation.\n\t\t\tstd::pair<double, double> range() const;\n\n\t\tprivate:\n\t\t\tmutable NTensor slope_values;\n\t\t\tmutable size_t  last_index;\n\t\t\tmutable bool    precomputed;\n\n\t\t\tsize_t find_interval(double) const;\n\t\t\tvoid   compute_slopes() const;\n\t};\n\n\t/// Data structure which, for a set of variables/expressions,\n\t/// holds a real range.\n\ttypedef std::map<Ex, std::pair<double, double>, tree_exact_less_no_wildcards_obj> variable_ranges_t;\n\t\n\t/// Return the range of definition of a given expression.\n\tvariable_ranges_t function_domain(const Ex&);\n\n};\n"
  },
  {
    "path": "core/NTensor.cc",
    "content": "#include \"NTensor.hh\"\n#include <stdexcept>\n#include \"Stopwatch.hh\"\n#include <cassert>\n#include <cmath>\n#include <string>\n#ifdef HAS_TBB\n#include <execution>\n#endif\n#include <algorithm>\n\nusing namespace cadabra;\n\n// #define DEBUG 1\n\n#ifdef DEBUG\n#warning \"DEBUG enabled for NTensor.cc\"\nstatic bool debug_stop = false;\n#define DEBUGLN(ln) if(!debug_stop) { ln; }\n#else\n#define DEBUGLN(ln)\n#endif\n\nNTensor::NTensor(const std::vector<size_t>& shape_, std::complex<double> val)\n\t: shape(shape_)\n\t{\n\tsize_t len=1;\n\tfor(auto dim: shape)\n\t\tlen *= dim;\n\n\tvalues.resize(len);\n\tfor(auto& v: values)\n\t\tv=val;\n\t}\n\nNTensor::NTensor(const std::vector<std::complex<double>>& vals)\n\t: values(vals)\n\t{\n\tshape.push_back(values.size());\n\t}\n\nNTensor::NTensor(const std::vector<double>& vals)\n\t{\n\tfor(size_t i=0; i<vals.size(); ++i)\n\t\tvalues.push_back(vals[i]);\n\tshape.push_back(values.size());\n\t}\n\nNTensor::NTensor(std::initializer_list<std::complex<double>> vals)\n\t: NTensor(std::vector<std::complex<double>>(vals.begin(), vals.end()))\n\t{\n\t}\n\nNTensor::NTensor(std::initializer_list<double> vals)\n\t: NTensor(std::vector<double>(vals.begin(), vals.end()))\n\t{\n\t}\n\nNTensor::NTensor(std::complex<double> val)\n\t{\n\tvalues.push_back(val);\n\tshape.push_back(1);\n\t}\n\nNTensor::NTensor(double val)\n\t{\n\tvalues.push_back(std::complex<double>(val, 0));\n\tshape.push_back(1);\n\t}\n\nNTensor::NTensor(const NTensor& other)\n\t{\n//\tstd::cerr << \"copy-constructor \" << other.values.size() << std::endl;\n\tDEBUGLN( std::cerr << \"NTensor(const NTensor&): \" << other.shape.size()\n\t\t\t\t<< \", \" << other.values.size() << std::endl; );\n\tshape=other.shape;\n\tvalues=other.values;\n\t}\n\nNTensor::NTensor(NTensor&& other)\n\t: shape(std::move(other.shape))\n\t, values(std::move(other.values))\n\t{\n\t}\n\nNTensor& NTensor::operator=(NTensor&& other) noexcept\n\t{\n\tif(this != &other) {\n\t\tshape = std::move(other.shape);\n\t\tvalues = std::move(other.values);\n\t\t}\n\treturn *this;\n\t}\n\nNTensor& NTensor::operator=(const NTensor&& other) noexcept\n\t{\n\tif(this != &other) {\n\t\tshape = std::move(other.shape);\n\t\tvalues = std::move(other.values);\n\t\t}\n\treturn *this;\n\t}\n\nNTensor NTensor::linspace(std::complex<double> from, std::complex<double> to, size_t steps)\n\t{\n\tNTensor res(std::vector<size_t>({steps}), 0.0);\n\tif(steps <= 1)\n\t\tthrow std::range_error(\"NTensor::linspace: steps must be greater than 1\");\n\n\tfor(size_t i=0; i<steps; ++i) {\n\t\tres.values[i] = from + (double)(i)*(to-from)/(double(steps-1));\n\t\t}\n\treturn res;\n\t}\n\nNTensor& NTensor::operator=(const NTensor& other)\n\t{\n\tshape=other.shape;\n\tvalues=other.values;\n\treturn *this;\n\t}\n\nstd::complex<double> NTensor::at() const\n\t{\n//\tif(shape.size()!=1 || shape[0]!=1)\n//\t\tthrow std::range_error(\"NTensor::at: cannot convert tensor \"+std::to_string(shape.size())\n//\t\t\t\t\t\t\t\t\t  +\", \"+std::to_string(shape[0])+\" to single scalar.\");\n\n\tif(values.size()!=1)\n\t\tthrow std::range_error(\"NTensor::at: inconsistent value array.\");\n\t\n\treturn values[0];\n\t}\n\nstd::complex<double> NTensor::at(const std::vector<size_t>& indices) const\n\t{\n\tif(indices.size()!=shape.size())\n\t\tthrow std::range_error(\"NTensor::at: number of indices != shape length.\");\n\n\tsize_t idx = 0;\n\tsize_t stride=1;\n\n\tfor(size_t p=indices.size(); p-- != 0; ) {\n\t\tif(indices[p]>=shape[p])\n\t\t\tthrow std::range_error(\"NTensor::at: index out of range.\");\n\t\tidx += stride*indices[p];\n\t\tstride *= shape[p];\n\t\t}\n\n\tif(idx >= values.size())\n\t\tthrow std::range_error(\"NTensor::at: indices out of range.\");\n\n\treturn values[idx];\n\t}\n\nstd::complex<double>& NTensor::at(const std::vector<size_t>& indices)\n\t{\n\tif(indices.size()!=shape.size())\n\t\tthrow std::range_error(\"NTensor::at: number of indices != shape length.\");\n\n\tsize_t idx = 0;\n\tsize_t stride=1;\n\n\tfor(size_t p=indices.size(); p-- != 0; ) {\n\t\tif(indices[p]>=shape[p])\n\t\t\tthrow std::range_error(\"NTensor::at: index out of range.\");\n\t\tidx += stride*indices[p];\n\t\tstride *= shape[p];\n\t\t}\n\n\tif(idx >= values.size())\n\t\tthrow std::range_error(\"NTensor::at: indices out of range.\");\n\n\treturn values[idx];\n\t}\n\nstd::ostream& cadabra::operator<<(std::ostream &str, const NTensor &nt)\n\t{\n\t// For an {a,b} tensor, we display as a vector of size 'a', each\n\t// element of which is a vector of size 'b'. And so on.\n\n\tbool isreal = nt.is_real();\n\n\tfor(size_t p=0; p<nt.shape.size(); ++p)\n\t\tstr << \"[\";\n\n\tfor(size_t i=0; i<nt.values.size(); ++i) {\n\t\tif(isreal) str << nt.values[i].real();\n\t\telse       {\n\t\t\tstr << nt.values[i].real();\n\t\t\tif(nt.values[i].imag()<0) str << \" - \";\n\t\t\telse                      str << \" + \";\n\t\t\tstr << std::abs(nt.values[i].imag()) << \"i\";\n\t\t\t}\n\n\t\t// Closing/re-opening.\n\t\tsize_t mult=1;\n\t\tfor(size_t p=nt.shape.size(); p-- != 0; ) {\n\t\t\t// 2,4,3 -> 2, 8, 24\n\t\t\tmult *= nt.shape[p];\n\t\t\tif((i+1)%mult == 0)\n\t\t\t\tstr << \"]\";\n\t\t\t}\n\n\t\tif(i+1<nt.values.size()) {\n\t\t\tstr << \", \";\n\t\t\tmult=1;\n\t\t\tfor(size_t p=nt.shape.size(); p-- != 0; ) {\n\t\t\t\tmult *= nt.shape[p];\n\t\t\t\tif((i+1)%mult == 0)\n\t\t\t\t\tstr << \"[\";\n\t\t\t\t}\n\t\t\t}\n\t\t}\n\n\treturn str;\n\t}\n\nNTensor& NTensor::apply(std::complex<double> (*fun)(const std::complex<double>&))\n\t{\n#ifdef HAS_TBB\n\tstd::transform(std::execution::par_unseq,\n\t\t\t\t\t\tvalues.begin(), values.end(),\n\t\t\t\t\t\tvalues.begin(),\n\t\t\t\t\t\tfun);\n#else\n\tfor(auto& v: values)\n\t\tv = fun(v);\n#endif\n\n\treturn *this;\n\t}\n\nNTensor& NTensor::operator+=(const NTensor& other)\n\t{\n\tif(other.shape.size()==1 && other.shape[0]==1) {\n\t\t// Arbitrary size base plus a scalar; add it to all.\n\t\tfor(size_t i=0; i<values.size(); ++i)\n\t\t\tvalues[i] += other.values[0];\n\t\t}\n\telse if(shape.size()==1 && shape[0]==1) {\n\t\t// Scalar plus arbitrary size other.\n\t\tauto add = values[0];\n\t\tvalues = other.values;\n\t\tfor(size_t i=0; i<values.size(); ++i)\n\t\t\tvalues[i] += add;\n\t\tshape=other.shape;\n\t\t}\n\telse {\n\t\tif(shape.size() != other.shape.size())\n\t\t\tthrow std::range_error(\"NTensor::operator+=: shape lengths do not match, \"+std::to_string(shape.size())\n\t\t\t\t\t\t\t\t\t\t  + \" versus \" + std::to_string(other.shape.size()) + \".\");\n\t\t\n\t\tfor(size_t p=0; p<shape.size(); ++p)\n\t\t\tif(shape[p]!=other.shape[p])\n\t\t\t\tthrow std::range_error(\"NTensor::operator+=: shapes do not match.\");\n\t\t\n\t\tfor(size_t i=0; i<values.size(); ++i)\n\t\t\tvalues[i] += other.values[i];\n\t\t}\n\t\n\treturn *this;\n\t}\n\nNTensor& NTensor::operator*=(const NTensor& other)\n\t{\n\tif(other.shape.size()==1 && other.shape[0]==1) {\n\t\t// Arbitrary size base times a scalar.\n\t\tfor(size_t i=0; i<values.size(); ++i)\n\t\t\tvalues[i] *= other.values[0];\n\t\t}\n\telse if(shape.size()==1 && shape[0]==1) {\n\t\t// Scalar times arbitrary size other.\n\t\tauto mult = values[0];\n\t\tvalues = other.values;\n\t\tfor(size_t i=0; i<values.size(); ++i)\n\t\t\tvalues[i] *= mult;\n\t\tshape=other.shape;\n\t\t}\n\telse {\n\t\tif(shape.size() != other.shape.size()) {\n\t\t\tDEBUGLN( std::cerr << *this << \"\\n\" << other << std::endl; )\n\t\t\tthrow std::range_error(\"NTensor::operator*=: shape lengths do not match, \"+std::to_string(shape.size())\n\t\t\t\t\t\t\t\t\t\t  + \" versus \" + std::to_string(other.shape.size()) + \".\");\n\t\t\t}\n\t\t\n\t\tfor(size_t p=0; p<shape.size(); ++p)\n\t\t\tif(shape[p]!=other.shape[p])\n\t\t\t\tthrow std::range_error(\"NTensor::operator*=: shapes do not match.\");\n\t\t\n\t\tfor(size_t i=0; i<values.size(); ++i)\n\t\t\tvalues[i] *= other.values[i];\n\t\t}\n\n\treturn *this;\n\t}\n\nNTensor& NTensor::operator*=(const std::complex<double>& m)\n\t{\n\tfor(size_t i=0; i<values.size(); ++i)\n\t\tvalues[i] *= m;\n\treturn *this;\n\t}\n\nNTensor& NTensor::operator*=(double m)\n\t{\n\tfor(size_t i=0; i<values.size(); ++i)\n\t\tvalues[i] *= m;\n\treturn *this;\n\t}\n\nNTensor& NTensor::pow(const NTensor& other)\n\t{\n\tif(other.shape.size()==1 && other.shape[0]==1) {\n\t\t// Arbitrary size base to the power of a scalar.\n\t\tfor(size_t i=0; i<values.size(); ++i)\n\t\t\tvalues[i] = std::pow(values[i], other.values[0]);\n\t\t}\n\telse {\n\t\tif(shape.size() != other.shape.size())\n\t\t\tthrow std::range_error(\"NTensor::pow: shape lengths do not match, \"+std::to_string(shape.size())\n\t\t\t\t\t\t\t\t\t\t  + \" versus \" + std::to_string(other.shape.size()) + \".\");\n\n\t\tfor(size_t p=0; p<shape.size(); ++p)\n\t\t\tif(shape[p]!=other.shape[p])\n\t\t\t\tthrow std::range_error(\"NTensor::pow: shapes do not match; direction \"\n\t\t\t\t\t\t\t\t\t\t\t  +std::to_string(p)+\": \"\n\t\t\t\t\t\t\t\t\t\t\t  +std::to_string(shape[p])+\" vs. \"\n\t\t\t\t\t\t\t\t\t\t\t  +std::to_string(other.shape[p])+\".\");\n\t\t\n\t\tfor(size_t i=0; i<values.size(); ++i)\n\t\t\tvalues[i] = std::pow(values[i], other.values[i]);\n\t\t}\n\t\n\treturn *this;\n\t}\n\nNTensor NTensor::outer_product(const NTensor& a, const NTensor& b)\n\t{\n\t// std::cerr << \"multiplying \" << a << \"\\n\"\n\t// \t\t\t << \"       with \" << b << std::endl;\n\tstd::vector<size_t> res_shape;\n\tres_shape.insert(res_shape.end(), a.shape.begin(), a.shape.end());\n\tres_shape.insert(res_shape.end(), b.shape.begin(), b.shape.end());\n\n\tNTensor res( res_shape, 0.0 );\n\n\tfor(size_t i=0; i<res.values.size(); ++i) {\n\t\tsize_t idx_a = i / b.values.size();\n\t\tsize_t idx_b = i % b.values.size();\n\t\tif(idx_a >= a.values.size())\n\t\t\tthrow std::range_error(\"NTensor::outer_product: index a out of range\");\n\t\tif(idx_b >= b.values.size())\n\t\t\tthrow std::range_error(\"NTensor::outer_product: index b out of range\");\n\n\t\tres.values[i] = a.values[idx_a] * b.values[idx_b];\n\t\t}\n\n\treturn res;\n\t}\n\nbool NTensor::is_real() const\n\t{\n\tfor(const auto& value: values)\n\t\tif(std::abs(value.imag()) > std::numeric_limits<double>::epsilon())\n\t\t\treturn false;\n\treturn true;\n\t}\n\nbool NTensor::is_scalar() const\n\t{\n\treturn (shape.size()==1 && shape[0]==1);\n\t}\n\nNTensor NTensor::broadcast(std::vector<size_t> new_shape, size_t pos) const\n\t{\n\t// for(auto s: new_shape)\n\t// \tstd::cerr << s << \", \";\n\t// std::cerr << \"\\n\" << pos << std::endl;\n\tif(pos >= new_shape.size())\n\t\tthrow std::range_error(\"NTensor::broadcast: pos out of range\");\n\tif(shape.size() != 1)\n\t\tthrow std::range_error(\"NTensor::broadcast: tensor must be rank-1\");\n\tif(new_shape[pos] != shape[0])\n\t\tthrow std::range_error(\"NTensor::broadcast: shape mismatch\");\n\n\n\tNTensor res(new_shape, 0.);\n\n\tsize_t lower = 1, higher=1;\n\tfor(size_t s=pos+1; s<new_shape.size(); ++s)\n\t\tlower  *= new_shape[s];\n\thigher = lower * new_shape[pos];\n\n\t//  std::cerr << \"lower: \" << lower << \"\\nhigher: \" << higher << std::endl;\n\n\t// Stopwatch sw;\n\t// sw.start();\n\tfor(size_t i=0; i<res.values.size(); ++i) {\n\t\tsize_t orig_i = (i % higher) / lower;\n\t\t// std::cerr << i << \" -> \" << orig_i << std::endl;\n\t\tif(orig_i >= new_shape[pos])\n\t\t\tthrow std::range_error(\"NTensor::broadcast: computed index out of range\");\n\n\t\tres.values[i] = values[orig_i];\n\t\t}\n\n\t// sw.stop();\n\t// std::cerr << \"broadcast to \" << res.values.size() <<  \" took \" << sw << std::endl;\n\n\treturn res;\n\t}\n"
  },
  {
    "path": "core/NTensor.hh",
    "content": "\n#pragma once\n\n#include <vector>\n#include <iostream>\n#include <complex>\n\n/// \\ingroup numerical\n///\n/// Class to hold numerical values structured in tensor form, that is,\n/// a multi-dimensional array.\n\nnamespace cadabra {\n\n\tclass NTensor {\n\t\tpublic:\n\t\t\t/// Initialise by giving the dimension for each index.  Storage\n\t\t\t/// is generalised row-major.  Display follows that convention:\n\t\t\t/// we use maths matrix conventions for printing, that is,\n\t\t\t/// earlier indices are more major, and are iterated over in a\n\t\t\t/// more outer loop.\n\t\t\texplicit NTensor(const std::vector<size_t>& shape, std::complex<double> val);\n\n\t\t\t/// Initialise as a vector of std::complex<double>s; sets shape automatically\n\t\t\texplicit NTensor(const std::vector<std::complex<double>>& vals);\n\t\t\t/// As above, but with doubles instead of complex doubles.\n\t\t\texplicit NTensor(const std::vector<double>& vals);\n\n\t\t\t/// Helper functions to be able to initialise a tensor with an initialiser list.\n\t\t\tNTensor(std::initializer_list<std::complex<double>> vals);\n\t\t\tNTensor(std::initializer_list<double> vals);\n\n\t\t\t/// Initialise as a scalar; sets shape automatically.\n\t\t\texplicit NTensor(std::complex<double>);\n\t\t\texplicit NTensor(double);\n\n\t\t\t/// Copy constructor.\n\t\t\texplicit NTensor(const NTensor&);\n\n\t\t\t/// Move constructor.\n\t\t\tNTensor(NTensor&&);\n\n\t\t\t/// Create equally spaced values in a range.\n\t\t\tstatic NTensor linspace(std::complex<double> from, std::complex<double> to, size_t steps);\n\n\t\t\t/// Assignment operator.\n\t\t\tNTensor& operator=(const NTensor&);\n\n\t\t\t/// Move assignment operators.\n\t\t\tNTensor& operator=(NTensor&&) noexcept;\n\t\t\tNTensor& operator=(const NTensor&&) noexcept;\n\n\t\t\t/// Addition operator. This requires the shapes to match.\n\t\t\tNTensor& operator+=(const NTensor&);\n\n\t\t\t/// Element-wise multiplication operator. This requires the shapes to match.\n\t\t\tNTensor& operator*=(const NTensor&);\n\n\t\t\t/// Multiplyall elements with a scalar.\n\t\t\tNTensor& operator*=(const std::complex<double>&);\n\t\t\tNTensor& operator*=(double);\n\n\t\t\t/// Element-wise pow operator (self**b, or pow(self,b)). Requires the shapes to match.\n\t\t\tNTensor& pow(const NTensor&);\n\n\t\t\t/// Get the value of a scalar NTensor.\n\t\t\tstd::complex<double>  at() const;\n\t\t\t\n\t\t\t/// Get the value of the tensor at the indicated component.\n\t\t\tstd::complex<double>  at(const std::vector<size_t>& indices) const;\n\n\t\t\t/// Get the value of the tensor at the indicated component.\n\t\t\tstd::complex<double>& at(const std::vector<size_t>& indices);\n\n\t\t\t/// Expand the shape of the tensor to the specified shape\n\t\t\t/// by broadcasting to the other dimensions. Effectively,\n\t\t\t///\n\t\t\t///    A_{i} ->  A_{k i l}\n\t\t\t///\n\t\t\t/// E.g. shape {2} tensor [3,4] (vector) to shape {4,2} (two-tensor) pos 1:\n\t\t\t///\n\t\t\t///   -> [[3,4], [3,4]]\n\t\t\t///\n\t\t\t/// So no matter the value of the new indices, the component\n\t\t\t/// is always determined by the value of the `pos` index (`i` above).\n\t\t\t///\n\t\t\t/// For now only works if the original shape size is 1, so that\n\t\t\t/// the tensor is rank one, `that is, a vector (as in the example above).\n\n\t\t\tNTensor broadcast(std::vector<size_t> new_shape, size_t pos) const;\n\n\t\t\t/// Outer product of two NTensors. The shape becomes the\n\t\t\t/// concatenation of the two shapes, with the shape of `a`\n\t\t\t/// coming first.\n\t\t\t///\n\t\t\t///    a       b\n\t\t\t///  { 3 } x { 4 } ->  { 3, 4}.\n\n\t\t\tstatic NTensor outer_product(const NTensor& a, const NTensor& b);\n\n\t\t\t/// Apply a scalar function `fun` to all elements, return\n\t\t\t/// a reference to itself.\n\t\t\tNTensor& apply(std::complex<double> (*fun)(const std::complex<double>&));\n\n\t\t\t/// Test if all values of the tensor are real.\n\t\t\tbool is_real() const;\n\n\t\t\t/// Test if the shape is a single element equal to 1 (so the tensor\n\t\t\t/// is actually a scalar).\n\t\t\tbool is_scalar() const;\n\t\t\t\n\t\t\tfriend std::ostream& operator<<(std::ostream&, const NTensor&);\n\n\t\t\tstd::vector<size_t> shape;\n\t\t\tstd::vector<std::complex<double>> values;\n\t};\n\n\tstd::ostream& operator<<(std::ostream &, const NTensor &);\n\n}\n"
  },
  {
    "path": "core/Parser.cc",
    "content": "/*\n\nCadabra: a field-theory motivated computer algebra system.\nCopyright (C) 2001-2014  Kasper Peeters <kasper.peeters@phi-sci.com>\n\nThis program is free software: you can redistribute it and/or\nmodify it under the terms of the GNU General Public License as\npublished by the Free Software Foundation, either version 3 of the\nLicense, or (at your option) any later version.\n\nThis program is distributed in the hope that it will be useful,\nbut WITHOUT ANY WARRANTY; without even the implied warranty of\nMERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU\nGeneral Public License for more details.\n\nYou should have received a copy of the GNU General Public License\n\talong with this program.  If not, see <http://www.gnu.org/licenses/>.\n\n*/\n\n#include \"Parser.hh\"\n#include \"PreProcessor.hh\"\n#include \"Symbols.hh\"\n\n#include <sstream>\n#include <internal/uniconv.h>\n#include <iostream>\n#include <typeinfo>\n\n// #define DEBUG 1\n\nstd::istream& operator>>(std::istream& str, cadabra::Parser& pa)\n\t{\n\tstd::string inp;\n\twhile(std::getline(str >> std::ws, inp)) {\n\t\t// FIXME: This should all have been done in the manipulator, but when we\n\t\t// read the default settings from a string the input here is more than\n\t\t// just one line.\n\t\tif(inp[inp.size()-1]=='.') inp=inp.substr(0,inp.size()-1);\n\t\t//\t\tstd::cout << \"[\" << inp << \"]\" << std::endl;\n\n#ifdef DEBUG\n\t\tstd::cerr << inp << std::endl;\n#endif\n\t\t\n\t\tpa.string2tree(inp);\n\t\t}\n\t// Remove the expression head.\n\tpa.finalise();\n\n\treturn str;\n\t}\n\nusing namespace cadabra;\n\n//std::ostream& operator<<(std::ostream& str, Parser& pa)\n//\t{\n//\tEx_output eo(pa.tree);\n//\teo.print_infix(str, pa.tree.begin());\n//\treturn str;\n//\t}\n\nstr_node::bracket_t Parser::is_closing_bracket(const char32_t& br) const\n\t{\n\tif(br==')')     return str_node::b_none;\n\tif(br==']')     return str_node::b_square;\n\tif(br=='}')     return str_node::b_none;\n\tif(br=='}'+128) return str_node::b_curly;\n\tif(br=='>'+128) return str_node::b_pointy;\n\treturn str_node::b_no;\n\t}\n\nstr_node::bracket_t Parser::is_opening_bracket(const char32_t& br) const\n\t{\n\tif(br=='(')     return str_node::b_none;\n\tif(br=='[')     return str_node::b_square;\n\tif(br=='{')     return str_node::b_none;\n\tif(br=='{'+128) return str_node::b_curly;\n\tif(br=='<'+128) return str_node::b_pointy;\n\treturn str_node::b_no;\n\t}\n\nstr_node::parent_rel_t Parser::is_link(const char32_t& ln) const\n\t{\n\tif(ln=='^') return str_node::p_super;\n\tif(ln=='_') return str_node::p_sub;\n\tif(ln=='$') return str_node::p_property;\n\tif(ln=='&') return str_node::p_exponent;\n\treturn str_node::p_none;\n\t}\n\nParser::Parser()\n\t{\n\ttree = std::make_shared<Ex>();\n\ttree->set_head(str_node(\"\\\\expression\", str_node::b_none, str_node::p_none));\n\tparts=tree->begin();\n\t}\n\nParser::Parser(std::shared_ptr<Ex> t)\n\t: tree(t)\n\t{\n\ttree->clear();\n\ttree->set_head(str_node(\"\\\\expression\", str_node::b_none, str_node::p_none));\n\tparts=tree->begin();\n\t}\n\nParser::Parser(std::shared_ptr<Ex> t, const std::string& str)\n\t: tree(t)\n\t{\n\ttree->clear();\n\ttree->set_head(str_node(\"\\\\expression\", str_node::b_none, str_node::p_none));\n\tparts=tree->begin();\n\tstring2tree(str);\n\tfinalise();\n\t}\n\nvoid Parser::erase()\n\t{\n\tstr.clear();\n\ttree->clear();\n\ttree->insert(tree->begin(), str_node(\"\\\\expression\", str_node::b_none, str_node::p_none));\n\tparts=tree->begin();\n\tcurrent_mode.clear();\n\tcurrent_bracket.clear();\n\tcurrent_parent_rel.clear();\n\t}\n\nvoid Parser::remove_empty_nodes()\n\t{\n\tEx::iterator it=tree->begin();\n\twhile(it!=tree->end()) {\n\t\tif((*it->name).size()==0) {\n\t\t\ttree->flatten(it);\n\t\t\tit=tree->erase(it);\n\t\t\t}\n\t\t++it;\n\t\t}\n\t}\n\nvoid Parser::finalise()\n\t{\n\tif(tree->is_valid(tree->begin())==false) return;\n\n\tif(*(tree->begin()->name)==\"\\\\expression\") {\n\t\ttree->flatten(tree->begin());\n\t\ttree->erase(tree->begin());\n\t\t}\n\t}\n\nvoid Parser::advance(unsigned int& i)\n\t{\n//\tif(get_token(i)>128) ++i;\n\t++i;\n\t}\n\nchar32_t Parser::get_token(unsigned int i)\n\t{\n\tif(str[i]=='\\\\')\n\t\tif(is_opening_bracket(str[i+1])!=str_node::b_no || is_closing_bracket(str[i+1])!=str_node::b_no)\n\t\t\treturn str[i+1]+128;\n\treturn str[i];\n\t}\n\nbool Parser::string2tree(const std::string& inp)\n\t{\n\tif(inp.size()==0 || inp[0]=='#' || inp[0]=='%')\n\t\treturn true;\n\n\t// Run the preprocessor.\n#ifdef DEBUG\n\tstd::cout << \"running preprocessor\" << std::endl;\n#endif\n\tstd::stringstream ss(inp), ss2;\n\tpreprocessor pp;\n\tss >> pp;\n#ifdef DEBUG\n\tstd::cout << \"running preprocessor done\" << std::endl;\n#endif\n\tss2 << pp;\n\tstd::string str8=\"  \"+ss2.str()+\"  \"; // for lookahead\n\n#ifdef DEBUG\n\tstd::cout << \"converting Greek unicode to TeX\" << std::endl;\n#endif\n\tfor (auto const& c : cadabra::symbols::greekmap) {\n\t\tsize_t pos1 = 0;\n\t\tsize_t pos2;\n\t\twhile ((pos2 = str8.find(c.second, pos1)) != std::string::npos) {\n\t\t\tstr8.replace(pos2, c.second.length(), c.first);\n\t\t\tpos1 = pos2 + c.first.length();\n\t\t\t}\n\t\t}\n#ifdef DEBUG\n\tstd::cout << \"converting to utf32\" << std::endl;\n#endif\n\n\tutf_converter conv;\n\tstr=conv.to_utf32(str8);\n\n#ifdef DEBUG\n\tstd::cout << \"converted to utf32\" << std::endl;\n\tfor(size_t i=0; i<inp.size(); ++i)\n\t\tstd::cout << (int)inp[i] << \" \";\n\tstd::cout << std::endl;\n\tfor(size_t i=0; i<str.size(); ++i)\n\t\tstd::cout << (int)str[i] << \" \";\n\tstd::cout << std::endl;\n#endif\n\n\t// Initialise the parser.\n\tunsigned int i=0;\n\tcurrent_mode.push_back(m_initialgroup);\n\tcurrent_bracket.push_back((*parts).fl.bracket);\n\tcurrent_parent_rel.push_back((*parts).fl.parent_rel);\n\tstd::u32string tmp;  // buffer for object name\n\t//\tstr_node ss;\n\n\tEx::iterator current_parent=parts;\n\n\twhile(i<str.size()) {\n\t\tif(current_mode.size()==0) {\n\t\t\treturn false;\n\t\t\t}\n\t\tchar32_t c=get_token(i);\n#ifdef DEBUG\t\t\n\t\tstd::cerr << i << \" \" << (int)c << \" \" << (c>128 ? \"\\\\\":\"\")\n\t\t\t\t\t << (char)(c<128 ? c:(c-128)) << \" mode \"\n\t\t\t\t\t << static_cast<int>(current_mode.back()) << std::endl;\n#endif\n\t\tswitch(current_mode.back()) {\n\t\t\tcase m_skipwhite:\n\t\t\t\t// std::cerr << \"m_skipwhite\" << \" \" << c << std::endl;\n\t\t\t\tif(c!=' ' && c!='\\n') current_mode.pop_back();\n\t\t\t\telse                  advance(i);\n\t\t\t\tbreak;\n\t\t\tcase m_name: {\n\t\t\t\t// std::cerr << \"m_name\" << \" \" << c << std::endl;\n\t\t\t\tif(is_opening_bracket(c)!=str_node::b_no ||\n\t\t\t\t      ( is_link(c)!=str_node::p_none && ( tmp.size()==0 ||\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t!((tmp.size()>3 && tmp[0]!='\\\\' && is_opening_bracket(get_token(i+1))==str_node::b_no) || tmp[0]=='@' || (tmp[0]=='\\\\' && tmp[1]=='@'))) )) {\n\t\t\t\t\t// Note: the funky look-ahead above is to handle expressions of the form\n\t\t\t\t\t// somethinglong_{m}, which should trigger a child node, and\n\t\t\t\t\t// somethinglong_m, which should *not* (anything with more than 3 characters,\n\t\t\t\t\t// not started with a '\\', followed by an underscore, is assumed to be\n\t\t\t\t\t// a python function.\n\t\t\t\t\tcurrent_parent=tree->append_child(current_parent,str_node(tmp,\n\t\t\t\t\t                                  current_bracket.back(),\n\t\t\t\t\t                                  current_parent_rel.back()));\n\t\t\t\t\tcurrent_mode.push_back(m_findchildren);\n\t\t\t\t\ttmp.clear();\n\t\t\t\t\tbreak;\n\t\t\t\t\t}\n\t\t\t\tif(is_closing_bracket(c)!=str_node::b_no) {\n\t\t\t\t\tif(tmp.size()>0) {\n\t\t\t\t\t\ttree->append_child(current_parent,str_node(tmp,\n\t\t\t\t\t\t                   current_bracket.back(),\n\t\t\t\t\t\t                   current_parent_rel.back()));\n\t\t\t\t\t\ttmp.clear();\n\t\t\t\t\t\t}\n\t\t\t\t\tcurrent_mode.pop_back();\n\t\t\t\t\tbreak;\n\t\t\t\t\t}\n\t\t\t\tif(tmp.size()>0) {\n\t\t\t\t\tif(c=='+' || c=='-' || c=='*' || c=='/' || c=='\\\\' || c==' ' || c=='\\n') {\n\t\t\t\t\t\ttree->append_child(current_parent,str_node(tmp,\n\t\t\t\t\t\t                   current_bracket.back(),\n\t\t\t\t\t\t                   current_parent_rel.back()));\n\t\t\t\t\t\ttmp.clear();\n\t\t\t\t\t\tif(c==' ' || c=='\\n')\n\t\t\t\t\t\t\tadvance(i);\n\t\t\t\t\t\tcurrent_mode.pop_back();\n\t\t\t\t\t\tbreak;\n\t\t\t\t\t\t}\n\t\t\t\t\t}\n\t\t\t\tif(c=='+' || c=='-' || c=='*' || c=='/') {\n\t\t\t\t\ttmp+=c;\n\t\t\t\t\ttree->append_child(current_parent,str_node(tmp,\n\t\t\t\t\t                   current_bracket.back(),\n\t\t\t\t\t                   current_parent_rel.back()));\n\t\t\t\t\ttmp.clear();\n\t\t\t\t\tadvance(i);\n\t\t\t\t\tcurrent_mode.pop_back();\n\t\t\t\t\tbreak;\n\t\t\t\t\t}\n\t\t\t\tassert(c!=' ' && c!='\\n');\n\t\t\t\ttmp+=c;\n\t\t\t\tadvance(i);\n\t\t\t\tif(c=='\\\"')\n\t\t\t\t\tcurrent_mode.push_back(m_verbatim);\n\t\t\t\tbreak;\n\t\t\t\t}\n\t\t\tcase m_findchildren: {\n\t\t\t\t// std::cerr << \"m_findchildren\" << \" \" << c << std::endl;\n\t\t\t\tstr_node::parent_rel_t pr=is_link(c);\n\t\t\t\tif(pr!=str_node::p_none) {\n\t\t\t\t\tadvance(i);\n\t\t\t\t\tint cc=get_token(i);\n\t\t\t\t\tstr_node::bracket_t br=is_opening_bracket(cc);\n\t\t\t\t\tif(br!=str_node::b_no) {\n\t\t\t\t\t\tcurrent_bracket.push_back(br);\n\t\t\t\t\t\tcurrent_parent_rel.push_back(pr);\n\t\t\t\t\t\tcurrent_mode.push_back(m_childgroup);\n\t\t\t\t\t\tadvance(i);\n\t\t\t\t\t\t}\n\t\t\t\t\telse {\n\t\t\t\t\t\tcurrent_bracket.push_back(str_node::b_none);\n\t\t\t\t\t\tcurrent_parent_rel.push_back(pr);\n\t\t\t\t\t\tif(pr==str_node::p_property)\n\t\t\t\t\t\t\tcurrent_mode.push_back(m_property);\n\t\t\t\t\t\telse {\n\t\t\t\t\t\t\t// A '^' or '_' immediately followed by text, without bracket.\n\t\t\t\t\t\t\t// std::cerr << tmp[0] << std::endl;\n\t\t\t\t\t\t\tcurrent_mode.push_back(m_singlecharname);\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\t}\n\t\t\t\t\tbreak;\n\t\t\t\t\t}\n\t\t\t\telse {\n\t\t\t\t\tstr_node::bracket_t br=is_opening_bracket(c);\n\t\t\t\t\tif(br!=str_node::b_no) {\n\t\t\t\t\t\tcurrent_bracket.push_back(br);\n\t\t\t\t\t\tcurrent_parent_rel.push_back(str_node::p_none);\n\t\t\t\t\t\tcurrent_mode.push_back(m_childgroup);\n\t\t\t\t\t\tadvance(i);\n\t\t\t\t\t\tbreak;\n\t\t\t\t\t\t}\n\t\t\t\t\telse {\n\t\t\t\t\t\tcurrent_mode.pop_back();\n\t\t\t\t\t\tcurrent_mode.push_back(m_skipwhite);\n\t\t\t\t\t\tcurrent_parent=tree->parent(current_parent);\n\t\t\t\t\t\t//\t\t\t\t \t\tadvance(i);\n\t\t\t\t\t\tbreak;\n\t\t\t\t\t\t}\n\t\t\t\t\t}\n\t\t\t\tbreak;\n\t\t\t\t}\n\t\t\tcase m_singlecharname:\n\t\t\t\t// This is for names 'a' or '\\aaa' that appear as (...)^a\n\t\t\t\t// or (...)^\\aaa .\n\n\t\t\t\t// std::cerr << \"m_singlecharname\" << \" \" << c << std::endl;\n\t\t\t\ttmp+=c;\n\t\t\t\tif(c=='\\\\') {\n\t\t\t\t\tcurrent_mode.pop_back();\n\t\t\t\t\tcurrent_mode.push_back(m_backslashname);\n\t\t\t\t\tadvance(i);\n\t\t\t\t\tbreak;\n\t\t\t\t\t}\n\t\t\t\telse {\n\t\t\t\t\ttree->append_child(current_parent,str_node(tmp,\n\t\t\t\t\t                   str_node::b_none, /* current_bracket.back(), */\n\t\t\t\t\t                   current_parent_rel.back()));\n\t\t\t\t\tadvance(i);\n\t\t\t\t\ttmp.clear();\n\t\t\t\t\tcurrent_mode.pop_back();\n\t\t\t\t\tcurrent_bracket.pop_back();\n\t\t\t\t\tcurrent_parent_rel.pop_back();\n\t\t\t\t\tbreak;\n\t\t\t\t\t}\n\t\t\tcase m_property: // properties do not need brackets\n\t\t\t\tif(c==' ' || c=='\\n') {\n\t\t\t\t\tcurrent_mode.pop_back();\n\t\t\t\t\tcurrent_bracket.pop_back();\n\t\t\t\t\tcurrent_parent_rel.pop_back();\n\t\t\t\t\tcurrent_parent=tree->parent(current_parent);\n\t\t\t\t\t}\n\t\t\t\telse if(is_opening_bracket(c)) {\n\t\t\t\t\tif(tmp.size()>0) {\n\t\t\t\t\t\tcurrent_parent=tree->append_child(current_parent,str_node(tmp,\n\t\t\t\t\t\t                                  current_bracket.back(),\n\t\t\t\t\t\t                                  current_parent_rel.back()));\n\t\t\t\t\t\t}\n\t\t\t\t\tcurrent_mode.push_back(m_childgroup);\n\t\t\t\t\t}\n\t\t\t\tadvance(i);\n\t\t\t\ttmp+=c;\n\t\t\t\tbreak;\n\t\t\tcase m_verbatim:\n\t\t\t\tif(c=='\\\"')\n\t\t\t\t\tcurrent_mode.pop_back();\n\t\t\t\ttmp+=c;\n\t\t\t\tadvance(i);\n\t\t\t\tbreak;\n\t\t\tcase m_backslashname:\n#ifdef DEBUG\n\t\t\t\tstd::cerr << \"m_backslashname\" << \" \" << c << std::endl;\n#endif\n\t\t\t\tif(c==' ' || c=='\\n' || c=='\\\\' || is_link(c)!=str_node::p_none\n\t\t\t\t      || is_closing_bracket(c)!=str_node::b_no) {\n\t\t\t\t\tcurrent_mode.pop_back();\n\t\t\t\t\ttree->append_child(current_parent,str_node(tmp,\n\t\t\t\t\t                   current_bracket.back(),\n\t\t\t\t\t                   current_parent_rel.back()));\n\t\t\t\t\ttmp.clear();\n\t\t\t\t\tbreak;\n\t\t\t\t\t}\n\t\t\t\tif(is_opening_bracket(c)!=str_node::b_no) {\n\t\t\t\t\t// This happens with e.g. `\\partial_\\theta{f}`. The `\\theta`\n\t\t\t\t\t// is a backslashname, and should be terminated as soon as\n\t\t\t\t\t// the opening brace is found. If you want the whole thing\n\t\t\t\t\t// to go into the subscript you should use `\\partial_{\\theta{f}}`\n\t\t\t\t\t// and that will then not trigger backslashname (just ordinary name).\n\t\t\t\t\tcurrent_mode.pop_back();\n\t\t\t\t\ttree->append_child(current_parent,str_node(tmp,\n\t\t\t\t\t                   current_bracket.back(),\n\t\t\t\t\t                   current_parent_rel.back()));\n\t\t\t\t\ttmp.clear();\n\t\t\t\t\tbreak;\n\t\t\t\t\t}\n\t\t\t\ttmp+=c;\n\t\t\t\tadvance(i);\n\t\t\t\tif(c=='\\\"')\n\t\t\t\t\tcurrent_mode.push_back(m_verbatim);\n\t\t\t\tbreak;\n\t\t\tcase m_childgroup: {\n#ifdef DEBUG\n\t\t\t\tstd::cerr << \"m_childgroup\" << \" \" << c << std::endl;\n#endif\n\t\t\t\tstr_node::bracket_t cb = is_closing_bracket(c);\n\t\t\t\tif(cb!=str_node::b_no) {\n\t\t\t\t\t// std::cerr << \"leaving group\" << std::endl;\n\t\t\t\t\tcurrent_mode.pop_back();\n\t\t\t\t\tif(current_bracket.back()!=cb)\n\t\t\t\t\t\tthrow std::logic_error(\"Closing bracket not matching opening bracket, or spurious backslash.\");\n\t\t\t\t\tcurrent_bracket.pop_back();\n\t\t\t\t\tcurrent_parent_rel.pop_back();\n\t\t\t\t\tadvance(i);\n\t\t\t\t\tbreak;\n\t\t\t\t\t}\n\t\t\t\telse {\n#ifdef DEBUG\n\t\t\t\t\tstd::cerr << \"skip white then find name\" << std::endl;\n#endif\n\t\t\t\t\tcurrent_mode.push_back(m_name);\n\t\t\t\t\tcurrent_mode.push_back(m_skipwhite);\n\t\t\t\t\tbreak;\n\t\t\t\t\t}\n\t\t\t\tbreak;\n\t\t\t\t}\n\t\t\tcase m_initialgroup:\n\t\t\t\tcurrent_mode.push_back(m_name);\n\t\t\t\tcurrent_mode.push_back(m_skipwhite);\n\t\t\t\tbreak;\n\t\t\t}\n\t\t}\n\treturn true;\n\t}\n\nbool Parser::is_number(const std::u32string& str) const\n\t{\n\tfor(unsigned int i=0; i<str.size(); ++i)\n\t\tif(!isdigit(str[i])) return false;\n\treturn true;\n\t}\n\n"
  },
  {
    "path": "core/Parser.hh",
    "content": "/*\n\nCadabra: a field-theory motivated computer algebra system.\nCopyright (C) 2001-2014  Kasper Peeters <kasper.peeters@phi-sci.com>\n\nThis program is free software: you can redistribute it and/or\nmodify it under the terms of the GNU General Public License as\npublished by the Free Software Foundation, either version 3 of the\nLicense, or (at your option) any later version.\n\nThis program is distributed in the hope that it will be useful,\nbut WITHOUT ANY WARRANTY; without even the implied warranty of\nMERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU\nGeneral Public License for more details.\n\nYou should have received a copy of the GNU General Public License\n\talong with this program.  If not, see <http://www.gnu.org/licenses/>.\n\n*/\n\n#pragma once\n\n#include <string>\n#include <vector>\n#include <iostream>\n\n#include \"Storage.hh\"\n\nnamespace cadabra {\n\n   /// \\ingroup core\n   ///\n   /// Class which turns the string output of a `preprocessor`\n   /// object and turns it into an Ex expression tree. The output of\n   /// `preprocessor` is assumed to be valid and consistent, so the\n   /// code here is rather simple.\n\n\tclass Parser {\n\t\tpublic:\n\t\t\tParser();\n\t\t\tParser(std::shared_ptr<Ex>);\n\t\t\tParser(std::shared_ptr<Ex>, const std::string&);\n\n\t\t\tvoid erase();\n\n\t\t\tvoid remove_empty_nodes();\n\n\t\t\t/// Finalise the parsed expression. This function should be\n\t\t\t/// called when no further operator>> calls are going to be made,\n\t\t\t/// and is necessary to ensure that the tree is consistent.\n\t\t\tvoid finalise();\n\t\t\tbool string2tree(const std::string& inp);\n\n\t\t\tstd::shared_ptr<Ex> tree;\n\t\tprivate:\n\t\t\tEx::iterator   parts;\n\t\t\tstd::u32string str;\n\n\t\t\tenum mode_t { m_skipwhite=0, m_name=1, m_findchildren=2,\n\t\t\t              m_singlecharname=3, m_backslashname=4,\n\t\t\t              m_childgroup=5, m_initialgroup=6, m_verbatim=7, m_property=8\n\t\t\t};\n\n\t\t\tvoid                   advance(unsigned int& i);\n\t\t\tchar32_t               get_token(unsigned int i);\n\t\t\tbool                   is_number(const std::u32string& str) const;\n\t\t\tstr_node::bracket_t    is_closing_bracket(const char32_t& br) const;\n\t\t\tstr_node::bracket_t    is_opening_bracket(const char32_t& br) const;\n\t\t\tstr_node::parent_rel_t is_link(const char32_t& ln) const;\n\n\t\t\tstd::vector<mode_t>                 current_mode;\n\t\t\tstd::vector<str_node::bracket_t>    current_bracket;\n\t\t\tstd::vector<str_node::parent_rel_t> current_parent_rel;\n\t\t};\n\n\t}\n\nstd::istream& operator>>(std::istream&, cadabra::Parser&);\n\n\n//std::ostream& operator<<(std::ostream&, Parser&);\n"
  },
  {
    "path": "core/Permutations.hh",
    "content": "\n#pragma once\n\n#include <stdexcept>\n#include <vector>\n\n/// \\ingroup core\n///\n/// Generic permutation group material. Largely follows the notation of xperm to avoid\n/// confusion.\n///\n/// Example: 1->4, 4->3, 3->1, 5->6, 6->5\n///\n///    Perm(   3, 2, 4, 1, 6, 5 )\n///    Images( 4, 2, 1, 3, 6, 5 )\n\nclass PermutationException : std::logic_error {\n\tpublic:\n\t\tPermutationException(const std::string& ex) : std::logic_error(ex) {};\n\t};\n\nclass Perm {\n\tpublic:\n\t\tstd::vector<int> perm;\n\n\t\t/// Find the permutation that takes [start1, end1> to [start2, end2>.\n\t\t/// This will be available in 'perm' afterwards.\n\t\ttemplate<class iterator>\n\t\tvoid find(iterator start1, iterator end1, iterator start2, iterator end2);\n\n\t\t/// Apply the permutation 'perm' on the given range.\n\t\ttemplate<class iterator>\n\t\tvoid apply(iterator start1, iterator end1);\n\n\t};\n\nclass Images {\n\tpublic:\n\t\tstd::vector<int> images;\n\n\t\t/// Find the permutation that takes [start1, end1> to [start2, end2>.\n\t\ttemplate<class iterator>\n\t\tvoid find(iterator start1, iterator end1, iterator start2, iterator end2);\n\t};\n\n\n\n\ntemplate<class iterator>\nvoid Perm::find(iterator start1, iterator end1, iterator start2, iterator end2)\n\t{\n\tperm.clear();\n\n\twhile(start2!=end2) {\n\t\tauto it=start1;\n\t\tint num=0;\n\t\twhile(it!=end1) {\n\t\t\tif(*start2==*it) {\n\t\t\t\tperm.push_back(num);\n\t\t\t\tbreak;\n\t\t\t\t}\n\t\t\t++num;\n\t\t\t++it;\n\t\t\t}\n\t\tif(it==end1)\n\t\t\tthrow PermutationException(\"Sets do not contain the same elements.\");\n\n\t\t++start2;\n\t\t}\n\t}\n\ntemplate<class iterator>\nvoid Perm::apply(iterator start, iterator end)\n\t{\n\ttypedef typename std::remove_reference<decltype(*start)>::type value_type;\n\n\tstd::vector<value_type> orig;\n\tauto it=start;\n\twhile(it!=end) {\n\t\torig.push_back(*it);\n\t\t++it;\n\t\t}\n\n\t// std::cerr << orig.size() << \", \" << perm.size() << std::endl;\n\tif(orig.size()!=perm.size()) {\n\t\tstd::cerr << \"Perm::apply: orig.size()=\" << orig.size() << \", \"\n\t\t          << \"perm.size()=\" << perm.size() << std::endl;\n\t\tassert(orig.size()==perm.size());\n\t\t}\n\n\tfor(unsigned int i=0; i<orig.size(); ++i) {\n\t\t*start=orig[perm[i]];\n\t\t++start;\n\t\t}\n\t}\n\n\ntemplate<class iterator>\nvoid Images::find(iterator start1, iterator end1, iterator start2, iterator end2)\n\t{\n\timages.clear();\n\n\twhile(start1!=end1) {\n\t\tauto it=start2;\n\t\tint num=0;\n\t\twhile(it!=end2) {\n\t\t\tif(*start1==*it) {\n\t\t\t\timages.push_back(num);\n\t\t\t\tbreak;\n\t\t\t\t}\n\t\t\t++num;\n\t\t\t++it;\n\t\t\t}\n\t\tif(it==end2)\n\t\t\tthrow PermutationException(\"Sets do not contain the same elements.\");\n\n\t\t++start1;\n\t\t}\n\t}\n"
  },
  {
    "path": "core/PreClean.cc",
    "content": "\n#include \"PreClean.hh\"\n#include \"Cleanup.hh\"\n\nnamespace cadabra {\n\n\tvoid pre_clean_dispatch(const Kernel& kernel, Ex& ex, Ex::iterator& it)\n\t\t{\n\t\tif(*it->name!=\"1\" && it->is_unsimplified_rational()) cleanup_rational(kernel, ex, it);\n\t\tif(*it->name!=\"1\" && it->is_unsimplified_double())   cleanup_double(kernel, ex, it);\n\n\t\tif(*it->name==\"\\\\frac\")                      cleanup_frac(kernel, ex, it);\n\t\telse if(*it->name==\"\\\\sub\")                  cleanup_sub(kernel, ex, it);\n\t\telse if(*it->name==\"\\\\sqrt\")                 cleanup_sqrt(kernel, ex, it);\n\t\telse if(*it->name==\"\\\\prod\")                 cleanup_prod(kernel, ex, it);\n\t\telse if((*it->name).substr(0,2)==\"UP\" || (*it->name).substr(0,2)==\"DN\")  cleanup_updown(kernel, ex, it);\n\n\t\tcleanup_indexbracket(kernel, ex, it);\n\t\t}\n\n\tvoid pre_clean_dispatch_deep(const Kernel& k, Ex& tr)\n\t\t{\n\t\treturn cleanup_dispatch_deep(k, tr, &pre_clean_dispatch);\n\t\t}\n\n\tvoid cleanup_updown(const Kernel&, Ex&, Ex::iterator& st)\n\t\t{\n\t\tstd::string rn=*st->name;\n\t\tbool isup=true;\n\t\tif(rn.substr(0,2)==\"DN\")\n\t\t\tisup=false;\n\n\t\trn=rn.substr(2);\n\n\t\t//\ttr.flatten(st);\n\t\t//\tst=tr.erase(st);\n\t\tif(isup) st->fl.parent_rel=str_node::p_super;\n\t\telse     st->fl.parent_rel=str_node::p_sub;\n\t\tst->name=name_set.insert(rn).first;\n\t\t}\n\n\tvoid cleanup_rational(const Kernel&, Ex&, Ex::iterator& st)\n\t\t{\n\t\t// This is guaranteed to be a string rational, not a float.\n\t\tmpq_class num(*st->name);\n\t\tnum.canonicalize();\n\t\tst->name=name_set.insert(\"1\").first;\n\t\tmultiply(st->multiplier, num);\n\t\t}\n\n\tvoid cleanup_double(const Kernel&, Ex&, Ex::iterator& st)\n\t\t{\n\t\t// This is guaranteed to be a float, not an integer or rational.\n\t\tdouble num = std::stod(*st->name);\n\t\tst->name=name_set.insert(\"1\").first;\n\t\tmultiply(st->multiplier, num);\n\t\t}\n\n\tvoid cleanup_frac(const Kernel&, Ex& tr, Ex::iterator& st)\n\t\t{\n\t\t// Catch \\frac{} nodes with one argument; those are supposed to be read as 1/(...).\n\t\t// The only exception is \\frac{#}, which needs to stay as it is.\n\t\tif(tr.number_of_children(st)==1) {\n\t\t\tif(tr.begin(st)->is_range_wildcard()) return;\n\t\t\ttr.insert(tr.begin(st), str_node(\"1\"));\n\t\t\t}\n\n\t\t// Turn this into a \\prod node. Everything except the first child\n\t\t// should be wrapped in a \\pow{..}{-1} node.\n\n\t\tauto sib=tr.begin(st);\n\t\t++sib;\n\t\twhile(sib!=tr.end(st)) {\n\t\t\tsib = tr.wrap(sib, str_node(\"\\\\pow\"));\n\t\t\tmultiply( tr.append_child(sib, str_node(\"1\"))->multiplier, -1 );\n\t\t\t++sib;\n\t\t\t}\n\t\tst->name=name_set.insert(\"\\\\prod\").first;\n\n\n\t\t//\tassert(tr.number_of_children(st)>1);\n\t\t//\tEx::sibling_iterator it=tr.begin(st);\n\t\t//\tmultiplier_t rat;\n\t\t//\n\t\t//\tbool allnumerical=true;\n\t\t//\trat=*(it->multiplier);\n\t\t//\tif(it->is_rational()==false)\n\t\t//\t\tallnumerical=false;\n\t\t//\n\t\t//\tone(it->multiplier);\n\t\t//\t++it;\n\t\t//\twhile(it!=tr.end(st)) {\n\t\t//\t\tif(*it->multiplier==0) {\n\t\t//\t\t\t// CHECK: do these zeroes get handled correctly elsewhere?\n\t\t//\t\t\treturn;\n\t\t//\t\t\t}\n\t\t//\t\trat/=*it->multiplier;\n\t\t//\t\tone(it->multiplier);\n\t\t//\t\tif(it->is_rational()==false) allnumerical=false;\n\t\t//\t\t++it;\n\t\t//\t\t}\n\t\t//\tif(allnumerical) { // can remove the \\frac altogether\n\t\t//\t\ttr.erase_children(st);\n\t\t//\t\tst->name=name_set.insert(\"1\").first;\n\t\t//\t\t}\n\t\t//\telse { // just remove the all-numerical child nodes\n\t\t//\t\tit=tr.begin(st);\n\t\t//\t\t++it;\n\t\t//\t\twhile(it!=tr.end(st)) {\n\t\t//\t\t\tif(it->is_rational())\n\t\t//\t\t\t\tit=tr.erase(it);\n\t\t//\t\t\telse ++it;\n\t\t//\t\t\t}\n\t\t//\t\tif(tr.number_of_children(st)==1) {\n\t\t//\t\t\ttr.begin(st)->fl.bracket=st->fl.bracket;\n\t\t//\t\t\ttr.begin(st)->fl.parent_rel=st->fl.parent_rel;\n\t\t//\t\t\tmultiply(tr.begin(st)->multiplier, *st->multiplier);\n\t\t//\t\t\ttr.flatten(st);\n\t\t//\t\t\tst=tr.erase(st);\n\t\t//\t\t\t}\n\t\t//\t\t}\n\t\t//\tmultiply(st->multiplier, rat);\n\n\t\t}\n\n\tvoid cleanup_sqrt(const Kernel&, Ex& tr, Ex::iterator& st)\n\t\t{\n\t\tst->name=name_set.insert(\"\\\\pow\").first;\n\t\tmultiply(tr.append_child(st, str_node(\"1\"))->multiplier, multiplier_t(1)/2);\n\t\t}\n\n\tvoid cleanup_prod(const Kernel&, Ex& tr, Ex::iterator& st)\n\t\t{\n\t\tauto sib=tr.begin(st);\n\t\twhile(sib!=tr.end(st)) {\n\t\t\tif(*sib->name==\"\\\\\")\n\t\t\t\tthrow std::logic_error(\"Single backslash as name not allowed, did you mean to write a single slash but wrote two?\");\n\t\t\t++sib;\n\t\t\t}\n\t\t}\n\n\tvoid cleanup_sub(const Kernel&, Ex& tr, Ex::iterator& it)\n\t\t{\n\t\tassert(tr.number_of_children(it)>1); // To guarantee that we have really cleaned up that old stuff.\n\n\t\tit->name=name_set.insert(\"\\\\sum\").first;\n\t\tEx::sibling_iterator sit=tr.begin(it);\n\n\t\t// Make sure that all terms have the right sign, and zeroes are removed.\n\t\tif(*sit->multiplier==0) sit=tr.erase(sit);\n\t\telse                    ++sit;\n\n\t\twhile(sit!=tr.end(it)) {\n\t\t\tif(*sit->multiplier==0)\n\t\t\t\tsit=tr.erase(sit);\n\t\t\telse {\n\t\t\t\tflip_sign(sit->multiplier);\n\t\t\t\t++sit;\n\t\t\t\t}\n\t\t\t}\n\n\t\t// Single-term situation: remove the \\sum.\n\t\tif(tr.number_of_children(it)==0) {\n\t\t\tzero(it->multiplier);\n\t\t\tit->name=name_set.insert(\"1\").first;\n\t\t\t}\n\t\telse {\n\t\t\tif(tr.number_of_children(it)==1) {\n\t\t\t\tsit=tr.begin(it);\n\t\t\t\tsit->fl.parent_rel=it->fl.parent_rel;\n\t\t\t\tsit->fl.bracket=it->fl.bracket;\n\t\t\t\tmultiply(sit->multiplier, *it->multiplier);\n\t\t\t\ttr.flatten(it);\n\t\t\t\tit=tr.erase(it);\n\t\t\t\t}\n\t\t\t}\n\t\t}\n\n\tvoid cleanup_indexbracket(const Kernel&, Ex& tr, Ex::iterator& it)\n\t\t{\n\t\tif((*it->name).size()==0) {\n\t\t\tauto sib=tr.begin(it);\n\t\t\tif(sib->fl.parent_rel!=str_node::p_super && sib->fl.parent_rel!=str_node::p_sub) {\n\t\t\t\t++sib;\n\t\t\t\twhile(sib!=tr.end(it)) {\n\t\t\t\t\tif(sib->fl.parent_rel==str_node::p_super || sib->fl.parent_rel==str_node::p_sub) {\n\t\t\t\t\t\tit->name=name_set.insert(\"\\\\indexbracket\").first;\n\t\t\t\t\t\treturn;\n\t\t\t\t\t\t}\n\t\t\t\t\t++sib;\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t}\n\t\telse if(*it->name==\"\\\\prod\" || *it->name==\"\\\\sum\") {\n\t\t\tauto sib=tr.begin(it);\n\t\t\twhile(sib!=tr.end(it)) {\n\t\t\t\tif(sib->fl.parent_rel==str_node::p_super || sib->fl.parent_rel==str_node::p_sub) {\n\t\t\t\t\tauto ibrack=tr.insert(it,str_node(\"\\\\indexbracket\"));\n\t\t\t\t\tEx::sibling_iterator nxt=it;\n\t\t\t\t\t++nxt;\n\t\t\t\t\ttr.reparent(ibrack,Ex::sibling_iterator(it),nxt);\n\t\t\t\t\tit=tr.begin(ibrack);\n\t\t\t\t\tauto sib=tr.begin(it);\n\t\t\t\t\twhile(sib!=tr.end(it)) {\n\t\t\t\t\t\tif(sib->fl.parent_rel==str_node::p_super || sib->fl.parent_rel==str_node::p_sub) {\n\t\t\t\t\t\t\ttr.append_child(ibrack,*sib);\n\t\t\t\t\t\t\tsib=tr.erase(sib);\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\telse ++sib;\n\t\t\t\t\t\t}\n\t\t\t\t\tit=ibrack;\n\t\t\t\t\treturn;\n\t\t\t\t\t}\n\t\t\t\t++sib;\n\t\t\t\t}\n\t\t\t}\n\t\t}\n\n\tstd::string replace_all(std::string const& original, std::string const& from, std::string const& to )\n\t\t{\n\t\tstd::string results;\n\t\tstd::string::const_iterator end = original.end();\n\t\tstd::string::const_iterator current = original.begin();\n\t\tstd::string::const_iterator next = std::search( current, end, from.begin(), from.end() );\n\t\twhile ( next != end ) {\n\t\t\tresults.append( current, next );\n\t\t\tresults.append( to );\n\t\t\tcurrent = next + from.size();\n\t\t\tnext = std::search( current, end, from.begin(), from.end() );\n\t\t\t}\n\t\tresults.append( current, next );\n\t\treturn results;\n\t\t}\n\n\t}\n"
  },
  {
    "path": "core/PreClean.hh",
    "content": "\n#pragma once\n\n#include \"Algorithm.hh\"\n\n/// \\ingroup core\n///\n/// Handle the entire preclean stage, which turns a parsed expression\n/// into an expression which satisfies the Cadabra conventions. This\n/// does not involve the property system.\n///\n/// - All numerical multipliers in a product on the product node, no\n///   multiplier on a sum node or on the comma node.\n///\n/// - Any '\\\\frac' nodes with a purely numerical denominator should be\n///   rewritten as a rational multiplier for the numerator node.\n///\n/// - Any \\\\sub nodes get converted to \\\\sum nodes.\n\nnamespace cadabra {\n\n\tvoid pre_clean_dispatch(const Kernel& k, Ex&, Ex::iterator& it);\n\tvoid pre_clean_dispatch_deep(const Kernel& k, Ex&);\n\n\t/// Cleanup for individual node types.  These are not needed during any\n\t/// later stages of the manipulation of an expression (and are hence\n\t/// defined here, not in 'Cleanup.hh').\n\n\tvoid cleanup_updown(const Kernel& k, Ex&, Ex::iterator& it);\n\tvoid cleanup_rational(const Kernel& k, Ex&, Ex::iterator& it);\n\tvoid cleanup_double(const Kernel& k, Ex&, Ex::iterator& it);\n\tvoid cleanup_frac(const Kernel& k, Ex&, Ex::iterator& it);\n\tvoid cleanup_sqrt(const Kernel& k, Ex&, Ex::iterator& it);\n\tvoid cleanup_prod(const Kernel& k, Ex&, Ex::iterator& it);\n\tvoid cleanup_sub(const Kernel& k, Ex&, Ex::iterator& it);\n\n\t/// Convert parser output which indicates an indexbracket to an actual\n\t/// indexbracket node.\n\tvoid cleanup_indexbracket(const Kernel& k, Ex&, Ex::iterator& it);\n\n\t/// Replace all occurrances of 'from' with 'to', return result (does not replace in-place).\n\tstd::string replace_all(std::string const& original, std::string const& from, std::string const& to );\n\n\t}\n"
  },
  {
    "path": "core/PreProcessor.cc",
    "content": "/*\n\nCadabra: a field-theory motivated computer algebra system.\nCopyright (C) 2001-2015  Kasper Peeters <cadabra@phi-sci.com>\n\nThis program is free software: you can redistribute it and/or\nmodify it under the terms of the GNU General Public License as\npublished by the Free Software Foundation, either version 3 of the\nLicense, or (at your option) any later version.\n\nThis program is distributed in the hope that it will be useful,\nbut WITHOUT ANY WARRANTY; without even the implied warranty of\nMERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU\nGeneral Public License for more details.\n\nYou should have received a copy of the GNU General Public License\nalong with this program.  If not, see <http://www.gnu.org/licenses/>.\n\n*/\n\n/*\n\nBugs: - This code is ugly. Then again, this is only because human\n\t\t  beings cannot be bothered to type in prefix notation. Since\n\t\t  it ain't broke, I won't fix it. Should really be replaced by\n\t\t  a parser written using ANTLR or Bisonc++ or something like that.\n\nRemember: we want brackets around infix operators to be around every child,\n          not around the operator itself.\n\n*/\n\n#include <ctype.h>\n#include <stdexcept>\n#include <sstream>\n#include <internal/uniconv.h>\n#include \"PreProcessor.hh\"\n\nconst char32_t preprocessor::orders[]     = { '!', tok_pow, '/', '*', tok_wedge,\n                                                   '-', '+', tok_sequence, '=', tok_unequals,\n                                                   '<', '>', '|', tok_arrow, tok_set_option,\n                                                   tok_declare, ',', '~', 0\n                                                 \t};\nconst char32_t * const  preprocessor::order_names[]= { U\"\\\\factorial\",\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t U\"\\\\pow\", U\"\\\\frac\", U\"\\\\prod\", U\"\\\\wedge\",\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t U\"\\\\sub\", U\"\\\\sum\", U\"\\\\sequence\",\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t U\"\\\\equals\", U\"\\\\unequals\", U\"\\\\less\",\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t U\"\\\\greater\", U\"\\\\conditional\",\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t U\"\\\\arrow\", U\"\\\\setoption\", U\"\\\\declare\",\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t U\"\\\\comma\", U\"\\\\tie\", 0\n};\nconst char32_t preprocessor::open_brackets[]    = { '{', '(', '[' };\nconst char32_t preprocessor::close_brackets[]   = { '}', ')', ']' };\n\nstd::istream& operator>>(std::istream& s, preprocessor& p)\n\t{\n\tstd::string inp;\n\n\tutf_converter conv;\n\twhile(std::getline(s,inp)) {\n\t\tstd::u32string inp32=conv.to_utf32(inp);\n\t\tp.parse_(inp32);\n\t\t}\n\treturn s;\n\t}\n\nstd::ostream& operator<<(std::ostream& s, const preprocessor& p)\n\t{\n\twhile(p.accus.size()>0)\n\t\tp.unwind_(sizeof(preprocessor::orders)/sizeof(char32_t));\n\tp.unwind_(sizeof(preprocessor::orders)/sizeof(char32_t));\n\tp.strip_outer_brackets();\n\tutf_converter conv;\n\tauto ac8 = conv.to_utf8(p.cur.accu);\n\ts << ac8;\n\treturn s;\n\t}\n\npreprocessor::preprocessor()\n\t: verbatim_(false), next_is_product_(false), eat_initial_whitespace_(true), cur_pos(0)\n\t{\n\t}\n\nbool preprocessor::is_link_(char32_t c) const\n\t{\n\treturn (c=='_' || c=='^' || c=='$' || c=='&');\n\t}\n\nbool preprocessor::is_infix_operator_(char32_t c) const\n\t{\n\tfor(unsigned int i=0; i<sizeof(orders)/sizeof(char32_t); ++i)\n\t\tif(orders[i]==c) return true;\n\treturn false;\n\t}\n\nvoid preprocessor::print_stack() const\n\t{\n//\tfor(unsigned int i=0; i<accus.size(); ++i) {\n//\t\tstd::cerr << \"LEVEL \" << i << std::endl\n//\t\t          << \"  head gen= \" << accus[i].head_is_generated << std::endl\n//\t\t          << \"  bracket = \" << accus[i].bracket << std::endl\n//\t\t          << \"  order   = \" << accus[i].order << std::endl\n//\t\t          << \"  parts   = \" << accus[i].parts.size() << std::endl;\n//\t\tfor(unsigned int k=0; k<accus[i].parts.size(); ++k)\n//\t\t\tstd::cerr << \"             \" << accus[i].parts[k] << std::endl;\n//\t\tstd::cerr << \"  accu    = \" << accus[i].accu << std::endl;\n//\t\t}\n//\tstd::cerr << \"CURRENT \"  << std::endl\n//\t          << \"  head gen= \" << cur.head_is_generated << std::endl\n//\t          << \"  bracket = \" << cur.bracket << std::endl\n//\t          << \"  order   = \" << cur.order << std::endl\n//\t          << \"  parts   = \" << cur.parts.size() << std::endl;\n//\tfor(unsigned int k=0; k<cur.parts.size(); ++k)\n//\t\tstd::cerr << \"             \" << cur.parts[k] << std::endl;\n//\tstd::cerr << \"  accu    = \" << cur.accu << std::endl;\n\t}\n\nunsigned int preprocessor::current_bracket_(bool deep) const\n\t{\n\tunsigned int i;\n\tif((i=accus.size())>0) {\n\t\tdo {\n\t\t\tif(accus[--i].bracket)\n\t\t\t\treturn accus[i].bracket;\n\t\t\t}\n\t\twhile(i>0 && deep);\n\t\t}\n\treturn 0;\n\t}\n\nbool preprocessor::default_is_product_() const\n\t{\n\tif(cur.order==order_prod || cur.order==order_frac || cur.order==order_arrow || cur.order==order_comma ||\n\t      cur.order==order_minus || cur.order==order_plus || cur.order==order_equals ||\n\t      cur.order==order_unequals )\n\t\treturn true; // spaces in comma-separated lists/products are stars\n\tint n=current_bracket_(true);\n\treturn (n==2 || n==3 || n==0 || (n==1 && cur.is_index==false) );\n\t}\n\nbool preprocessor::is_digits_(const std::u32string& str) const\n\t{\n\tif(str.size()==0) return false;\n\tfor(unsigned int i=0; i<str.size(); ++i)\n\t\tif(!isdigit(str[i]) && str[i]!='.') return false;\n\treturn true;\n\t}\n\nunsigned int preprocessor::is_closing_bracket_(char32_t c) const\n\t{\n\tfor(unsigned int i=0; i<sizeof(close_brackets)/sizeof(char32_t); ++i) {\n\t\tif(c==close_brackets[i]) return i+1;\n\t\tif(c==close_brackets[i]+128) return i+1+128;\n\t\t}\n\treturn 0;\n\t}\n\nunsigned int preprocessor::is_opening_bracket_(char32_t c) const\n\t{\n\tfor(unsigned int i=0; i<sizeof(open_brackets)/sizeof(char32_t); ++i) {\n\t\tif(c==open_brackets[i])     return i+1;\n\t\tif(c==open_brackets[i]+128) return i+1+128;\n\t\t}\n\treturn 0;\n\t}\n\nunsigned int preprocessor::is_bracket_(char32_t c) const\n\t{\n\tunsigned int ret;\n\tif((ret=is_opening_bracket_(c))) return ret;\n\treturn is_closing_bracket_(c);\n\t}\n\nbool preprocessor::is_already_bracketed_(const std::u32string& str) const\n\t{\n\tif(str.size()>=2)\n\t\tif(is_bracket_(str[0])) // && str[0]!='{')\n\t\t\tif(is_opening_bracket_(str[0])==is_closing_bracket_(str[str.size()-1]))\n\t\t\t\treturn true;\n\treturn false;\n\t}\n\nchar32_t preprocessor::get_token_(char32_t prev_token)\n\t{\n\tchar32_t candidate=0;\n\t// Candidate is set to the code of an infix operator if\n\t// encountered. Because we have to treat spaces as multiplication\n\t// operators, yet these can also just denote spaces by themselves if\n\t// followed by an explicit operator, the loop below iterates until a\n\t// non-space character is found.\n\n\t//\tstd::cout << \"cur char=\" << cur_str[cur_pos] << \"\\n\";\n\n\tif(verbatim_) {\n\t\treturn cur_str[cur_pos];\n\t\t}\n\tif(next_is_product_) {\n\t\tnext_is_product_=false;\n\t\tcandidate='*';\n\t\t//\t\tif(cur_pos<cur_str.size()) {\n\t\t//\t\t\t--cur_pos;\n\t\t//\t\t\treturn '*';\n\t\t//\t\t\t}\n\t\t}\n\tif(is_opening_bracket_(prev_token)) {\n\t\twhile(cur_str[cur_pos]==' ' || cur_str[cur_pos]=='\\t' || cur_str[cur_pos]=='\\n' /* std::isblank(cur_str[cur_pos], std::locale(\"en_US.UTF-8\"))*/ ) {\n\t\t\t++cur_pos;\n\t\t\t}\n\t\t}\n\twhile(cur_pos<cur_str.size()) {\n\t\tchar32_t c=cur_str[cur_pos];\n\t\t//\t\tstd::cerr << \"|\" << c << \"|\" << std::endl;\n\t\tif(c==':' && cur_str[cur_pos+1]=='=') { // ':' and ':=' are the same thing\n\t\t\t++cur_pos;\n\t\t\tcur_str[cur_pos]=tok_declare;\n\t\t\tc=tok_declare;\n\t\t\t}\n\t\tif(c==':' && cur_str[cur_pos+1]==':') {\n\t\t\t++cur_pos;\n\t\t\tcur_str[cur_pos]='$';\n\t\t\tc='$'; // FIXME: Another hack... (property)\n\t\t\t}\n\t\tif(c=='*' && cur_str[cur_pos+1]=='*') {\n\t\t\t++cur_pos;\n\t\t\tcur_str[cur_pos]=tok_pow;\n\t\t\tc=tok_pow; // FIXME: Another hack... (exponent)\n\t\t\t}\n\t\tif(c=='-' && cur_str[cur_pos+1]=='>') {\n\t\t\t++cur_pos;\n\t\t\tcur_str[cur_pos]=tok_arrow;\n\t\t\tc=tok_arrow; // FIXME: Another hack... (arrow)\n\t\t\t}\n\t\tif(c==':' && cur_str[cur_pos+1]=='>') {\n\t\t\t++cur_pos;\n\t\t\tcur_str[cur_pos]=tok_set_option;\n\t\t\tc=tok_set_option; // FIXME: Another hack... (set_option)\n\t\t\t}\n\t\tif(c=='!' && cur_str[cur_pos+1]=='=') {\n\t\t\t++cur_pos;\n\t\t\tcur_str[cur_pos]=tok_unequals;\n\t\t\tc=tok_unequals; // FIXME: Another hack... (unequals)\n\t\t\t}\n\t\tif(c=='.') {\n\t\t\tif(cur_str[cur_pos+1]=='.') {\n\t\t\t\t++cur_pos;\n\t\t\t\tif(cur_str[cur_pos+1]=='.') {\n\t\t\t\t\tcur_str[cur_pos]=tok_siblings;\n\t\t\t\t\tcur_str[cur_pos+1]=tok_siblings;\n\t\t\t\t\t++cur_pos;\n\t\t\t\t\tc=tok_siblings;\n\t\t\t\t\treturn '@'; // FIXME: worst hack of them all, we're running out of tricks...\n\t\t\t\t\t}\n\t\t\t\telse {\n\t\t\t\t\tcur_str[cur_pos]=tok_sequence;\n\t\t\t\t\tc=tok_sequence; // FIXME: Another hack... (sequence)\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\telse return c;\n\t\t\t}\n\n\t\t//\tHERE: how do we force get_token to return a '*' for the space separating .... and b ?\n\n\t\tif(c==' ' || c=='\\t' || c=='\\n' /*std::isblank(c, std::locale(\"en_US.UTF-8\")*/ ) {\n\t\t\t//\t\t\tstd::cout << \"blank \" << (int)(c) << \"\\n\";\n\t\t\tif(candidate==0) candidate=' ';\n\t\t\t++cur_pos;\n\t\t\tcontinue;\n\t\t\t}\n\t\telse if(c=='^' && candidate==' ') {   // Isolated '^' with space prefixing it.\n\t\t\tcur_str[cur_pos]=tok_wedge;\n\t\t\t++cur_pos;\n\t\t\treturn tok_wedge;\n\t\t\t}\n\t\telse if(is_infix_operator_(c)) {\n\t\t\tif(candidate && candidate!=' ') {\n\t\t\t\t--cur_pos;\n\t\t\t\treturn candidate;\n\t\t\t\t// FIXME: have to test whether this operator allows for missing first child.\n\t\t\t\t//\t\t\t\tthrow std::logic_error(\"two subsequent operators without intermediate operand\");\n\t\t\t\t}\n\t\t\tcandidate=c;\n\t\t\t++cur_pos;\n\t\t\tcontinue;\n\t\t\t}\n\t\telse if(c=='@' && isdigit(cur_str[cur_pos+1]) ) {   // eat labels completely\n\t\t\twhile(isdigit(cur_str[++cur_pos]));\n\t\t\tcontinue;\n\t\t\t}\n\t\tif(candidate==0 && c=='\\\\' && is_bracket_(cur_str[cur_pos+1])) {\n\t\t\t++cur_pos;\n\t\t\tc=cur_str[cur_pos]+128;\n\t\t\t}\n\t\tif(candidate!=0) {\n\t\t\t//\t\t\tstd::cout << \"candidate \" << (int)candidate << \"\\n\";\n\t\t\t--cur_pos;\n\t\t\tif(candidate==' ' && default_is_product_()) return '*';\n\t\t\treturn candidate;\n\t\t\t}\n\t\telse {\n\t\t\tstd::u32string acplusone=cur.accu + (char32_t)(c);\n\t\t\tif( ( is_closing_bracket_(prev_token) && is_opening_bracket_(c) && cur.head_is_generated ) ||\n\t\t\t      ( is_closing_bracket_(prev_token) && !is_infix_operator_(c) && !is_bracket_(c) && !is_link_(c) ) ||\n\t\t\t      ( is_digits_(cur.accu) && !is_digits_(acplusone) && !is_link_(c) && !is_closing_bracket_(c) ) ||\n\t\t\t      ( !is_infix_operator_(prev_token) && !is_opening_bracket_(prev_token) && !is_link_(prev_token) && prev_token!=' ' && c=='\\\\' ) ) {\n\t\t\t\t--cur_pos;\n\t\t\t\tif( default_is_product_() ) return '*';\n\t\t\t\telse                        return ' ';\n\t\t\t\t}\n\t\t\tif(is_link_(prev_token) && !(is_opening_bracket_(c) || c=='\\\\' || prev_token=='$')) {\n\t\t\t\tif(cur.accu.size()==0 || ! (cur.accu.size()>3 || cur.accu[0]=='@' || (cur.accu[0]=='\\\\' && cur.accu[1]=='@'))) {\n\t\t\t\t\tnext_is_product_=true; // turn aaa_bbb into aaa_b bb (but keep @aaa_bbb)\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\treturn c;\n\t\t\t}\n\t\t}\n\tif(candidate) {\n\t\t--cur_pos;\n\t\treturn candidate;\n\t\t}\n\tthrow std::range_error(\"get_token out of range\");\n\t}\n\nvoid preprocessor::bracket_strings_(char32_t cb, std::u32string& obrack, std::u32string& cbrack) const\n\t{\n\tobrack=U\"\";\n\tcbrack=U\"\";\n\tif(cb==0) return;\n\tif(cb>128) {\n\t\tobrack=U\"\\\\\";\n\t\tcbrack=U\"\\\\\";\n\t\tcb-=128;\n\t\t}\n\tobrack+=open_brackets[cb-1];\n\tcbrack+=close_brackets[cb-1];\n\t}\n\n\n// unwind the \"stack\" until we reach infix operator level \"onum\" or bottom of stack.\n// if onum==sizeof(orders), unwind to the bracket level of the second (optional) argument.\n\nbool preprocessor::unwind_(unsigned int onum, unsigned int bracketgoal, bool usebracket) const\n\t{\n\t//\tstd::cout << \"unwinding to \" << onum << \" \" << usebracket << std::endl;\n\n\t//\tstatic long iters=0;\n\tbool generated_head=false;\n\tbool bracket_reached=false;\n\n\tdo {\n\t\tgenerated_head=false;\n\t\tbracket_reached=false;\n\n\t\tstd::u32string tmp;\n\t\tif(cur.accu.size()>0)\n\t\t\tcur.parts.push_back(cur.accu);\n\t\tunsigned int cb=current_bracket_();\n\n\t\t//\t\tstd::cout << \"current bracket = \" << cb << std::endl;\n\t\t//\t\tprint_stack();\n\n\t\tif(onum==sizeof(orders)/sizeof(char32_t) && bracketgoal) {\n\t\t\tif(cb!=0) {\n\t\t\t\tif(cb==bracketgoal)\n\t\t\t\t\tbracket_reached=true;\n\t\t\t\telse {\n\t\t\t\t\t//\t\t\t\t\tstd::cerr << \"wanted \" << bracketgoal << \" got \" << cb << std::endl;\n\t\t\t\t\tshow_and_throw_(\"Bracket mismatch.\");\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t}\n\t\telse {\n\t\t\t// if we are unwinding to reach a different operator level, never unwind beyond\n\t\t\t// a bracket (in that case, we have to push up again).\n\t\t\tif(current_bracket_())\n\t\t\t\tbracket_reached=true;\n\t\t\t}\n\n\n\t\tstd::u32string obrack, cbrack;\n\t\tif(cb==0 || !usebracket || (onum==sizeof(orders)/sizeof(char32_t) && bracket_reached && accus.back().accu.size()>0)) {\n\t\t\tobrack=U\"{\";\n\t\t\tcbrack=U\"}\";\n\t\t\t}\n\t\telse bracket_strings_(cb, obrack, cbrack);\n\n\t\tif(cur.parts.size()>1 || cur.order==order_factorial) { // More than one argument to the function.\n\t\t\tif(cur.order<sizeof(orders)/sizeof(char32_t)) {\n\t\t\t\tbool special=((cb==2 || cb==3) && std::u32string(order_names[cur.order])==U\"\\\\comma\" && accus.size()>0 && accus.back().accu.size()!=0);\n\t\t\t\tif(!special)\n\t\t\t\t\ttmp+=order_names[cur.order];\n\t\t\t\telse\n\t\t\t\t\tbracket_strings_(accus.back().bracket, obrack, cbrack);\n\n\t\t\t\tfor(unsigned int k=0; k<cur.parts.size(); ++k)\n\t\t\t\t\tif(cur.parts[k].size()>0) {\n\t\t\t\t\t\tif(is_already_bracketed_(cur.parts[k]) && (cur.parts[k][0]==obrack[0] || obrack[0]=='{'))\n\t\t\t\t\t\t\ttmp+=cur.parts[k];\n\t\t\t\t\t\telse {\n\t\t\t\t\t\t\tif(special) {\n\t\t\t\t\t\t\t\tif(k>0) tmp+=obrack;\n\t\t\t\t\t\t\t\t}\n\t\t\t\t\t\t\telse\n\t\t\t\t\t\t\t\ttmp+=obrack;\n\t\t\t\t\t\t\ttmp+=cur.parts[k];\n\t\t\t\t\t\t\tif(special) {\n\t\t\t\t\t\t\t\tif(k<cur.parts.size()-1) tmp+=cbrack;\n\t\t\t\t\t\t\t\t}\n\t\t\t\t\t\t\telse\n\t\t\t\t\t\t\t\ttmp+=cbrack;\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\t}\n\t\t\t\tgenerated_head=true;\n\t\t\t\t}\n\t\t\telse {\n\t\t\t\ttmp=obrack;\n\t\t\t\tfor(unsigned int k=0; k<cur.parts.size(); ++k) {\n\t\t\t\t\ttmp+=cur.parts[k];\n\t\t\t\t\tif(k!=cur.parts.size()-1) tmp+=U\" \";\n\t\t\t\t\t}\n\t\t\t\ttmp+=cbrack;\n\t\t\t\t}\n\t\t\t}\n\t\telse {   // Function with only one argument.\n\t\t\tif(cur.parts.size()>0) {\n\t\t\t\tbracket_strings_(cb, obrack, cbrack);\n\t\t\t\t//\t\t\t\tstd::cout << cur.parts[0] << \" : \" << is_already_bracketed_(cur.parts[0]) << std::endl;\n\t\t\t\tif(onum!=sizeof(orders)/sizeof(char32_t) ||\n\t\t\t\t      ( is_already_bracketed_(cur.parts[0]) && ( cur.parts[0][0]==obrack[0] || obrack[0]=='{')))\n\t\t\t\t\ttmp=cur.parts[0];\n\t\t\t\telse {\n\t\t\t\t\ttmp=obrack;\n\t\t\t\t\ttmp+=cur.parts[0];\n\t\t\t\t\ttmp+=cbrack;\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t}\n\t\t//\t\tstd::cerr << \"string to unwind: \" << tmp << std::endl;\n\t\tif(accus.size()==0) {\n\t\t\tcur.erase();\n\t\t\tcur.order=onum;\n\t\t\tcur.accu=tmp;\n\t\t\tbreak;\n\t\t\t}\n\t\tif(onum!=sizeof(orders)/sizeof(char32_t) && bracket_reached) {\n\t\t\tcur.accu=tmp;\n\t\t\tcur.parts.clear();\n\t\t\tbreak;\n\t\t\t}\n\t\tcur=accus.back();\n\t\taccus.pop_back();\n\t\t// if there was something at this level already, wrap the string just constructed\n\t\t// in brackets\n\t\tif(cur.accu.size()>0) {\n\t\t\tif(tmp.size()>0) {\n\t\t\t\tbracket_strings_(cb, obrack, cbrack);\n\t\t\t\t// FIXME: next line might want to check for {(aaa)} problems (like all other\n\t\t\t\t// lines that check for is_already_bracketed_)\n\t\t\t\tif(!is_opening_bracket_(tmp[0]) && !(tmp[0]=='\\\\' && is_opening_bracket_(tmp[1])) && ( !is_already_bracketed_(tmp) || tmp[0]!=obrack[0])) {\n\t\t\t\t\tcur.accu+=obrack;\n\t\t\t\t\tcur.accu+=tmp;\n\t\t\t\t\tcur.accu+=cbrack;\n\t\t\t\t\t}\n\t\t\t\telse\n\t\t\t\t\tcur.accu+=tmp;\n\t\t\t\t}\n\t\t\tgenerated_head=false;\n\t\t\t}\n\t\telse cur.accu+=tmp;\n\n\t\t}\n\twhile(cur.order<onum && !bracket_reached);\n\n\t// Reset the head_is_generated flag, otherwise we end up with\n\t// situations where e.g. a \\prod{}{} node pushed into the parts\n\t// vector sets this flag, then a '+' sign is read, and any\n\t// subsequent elements are automatically treated as if they got the\n\t// head generated too.\n\tcur.head_is_generated=false;\n\n\tif(onum!=sizeof(orders)/sizeof(char32_t) && cur.accu.size()>0 && onum>=cur.order && !bracket_reached) {\n\t\t//\t\tstd::cout << cur.accu.size() << std::endl;\n\t\tcur.parts.push_back(cur.accu);\n\t\tcur.accu.erase();\n\t\t}\n\tif(generated_head && cur.accu.size()>0)\n\t\tcur.head_is_generated=true;\n\treturn bracket_reached;\n\t}\n\npreprocessor::accu_t::accu_t()\n\t: head_is_generated(false), order(sizeof(orders)/sizeof(char32_t)), bracket(0), is_index(false)\n\t{\n\t}\n\nvoid preprocessor::accu_t::erase()\n\t{\n\thead_is_generated=false;\n\taccu.erase();\n\torder=sizeof(orders)/sizeof(char32_t);\n\tparts.clear();\n\tbracket=0;\n\t}\n\nvoid preprocessor::strip_outer_brackets() const\n\t{\n\tif(is_already_bracketed_(cur.accu))\n\t\tcur.accu=cur.accu.substr(1,cur.accu.size()-2);\n\t}\n\nvoid preprocessor::erase()\n\t{\n\tcur_pos=0;\n\tcur_str.erase();\n\tcur.erase();\n\taccus.clear();\n\tnext_is_product_=false;\n\t}\n\nvoid preprocessor::parse_(const std::u32string& str)\n\t{\n\tcur_str=str;\n\tparse_internal_();\n\t}\n\nvoid preprocessor::show_and_throw_(const std::string& str) const\n\t{\n\tstd::stringstream ss;\n\tutf_converter conv;\n\tss << std::endl << conv.to_utf8(cur_str) << std::endl;\n\tfor(unsigned int i=0; i<cur_pos; ++i)\n\t\tss << \" \";\n\tss << \"^\" << std::endl\n\t   << str;\n\tss << std::endl << cur.order << std::endl;\n\tthrow std::logic_error(ss.str());\n\tthrow std::logic_error(str);\n\t}\n\nvoid preprocessor::parse_internal_()\n\t{\n\tstatic long chars_parsed=0;\n\tcur_pos=0;\n\tchar32_t c=0, prev_token=0;\n\twhile(cur_pos<cur_str.size()) {\n\t\tunsigned onum=0;\n\t\tprev_token=c;\n\t\tc=get_token_(c);\n\t\tif(eat_initial_whitespace_ && c=='*')\n\t\t\tgoto loopdone;\n\t\teat_initial_whitespace_=false;\n\t\t//std::cerr << c << \", brac=\" << cur.bracket << \", order=\" << cur.order << std::endl;\n\t\tif(verbatim_) {\n\t\t\tif(c=='\\\"')\n\t\t\t\tverbatim_=false;\n\t\t\tcur.accu+=c;\n\t\t\tgoto loopdone;\n\t\t\t}\n\t\tfor(; onum<sizeof(orders)/sizeof(char32_t); ++onum) {\n\t\t\tif(c==orders[order_factorial] && cur.accu.size()>0 && cur.accu[0]=='@')\n\t\t\t\tbreak; // keep the '!' in '@command!(foobar)'\n\t\t\tif(c==orders[onum]) {\n\t\t\t\tif(cur.order==sizeof(orders)/sizeof(char32_t) || onum==cur.order) {\n\t\t\t\t\t//\t\t\t\t\tstd::cerr << \"same order, was \" << cur.order << \" now \" << onum << std::endl;\n\t\t\t\t\t// FIXME: this is a hack\n\t\t\t\t\tif(onum==order_minus && cur.accu.size()==0)\n\t\t\t\t\t\tcur.accu=U\"0\";\n\t\t\t\t\tcur.order=onum;\n\t\t\t\t\t++chars_parsed;\n\t\t\t\t\t//\t\t\t\t\tif(chars_parsed%(100L)==0)\n\t\t\t\t\t//\t\t\t\t\t\tstd::cout << chars_parsed << std::endl;\n\t\t\t\t\tcur.parts.push_back(cur.accu);\n\t\t\t\t\tcur.accu.erase();\n\t\t\t\t\tcur.head_is_generated=false;\n\t\t\t\t\t//\t\t\t\t\tprint_stack();\n\t\t\t\t\t}\n\t\t\t\telse if(onum<cur.order) {\n\t\t\t\t\tstd::u32string tmp=cur.accu;\n\t\t\t\t\tcur.accu.erase();\n\t\t\t\t\tcur.head_is_generated=false;\n\t\t\t\t\tif(tmp.size()==0 && onum==order_minus) // hack for \"foo: -a-b\"\n\t\t\t\t\t\ttmp=U\"0\";\n\t\t\t\t\t//\t\t\t\t\tstd::cerr << \"pushing up |\" << tmp << \"| to \" << orders[onum] << std::endl;\n\t\t\t\t\taccus.push_back(cur);\n\t\t\t\t\tcur.erase();\n\t\t\t\t\tcur.parts.push_back(tmp);\n\t\t\t\t\tcur.order=onum;\n\t\t\t\t\t//\t\t\t\t\tstd::cerr << \"next character:\" << cur_str[cur_pos+1] << std::endl;\n\t\t\t\t\t}\n\t\t\t\telse {\n\t\t\t\t\t//\t\t\t\t\tstd::cerr << \"need to unwind from \" << cur.order << \" to \" << onum << std::endl;\n\t\t\t\t\tif(unwind_(onum, 0, false) || onum<cur.order) {\n\t\t\t\t\t\t//\t\t\t\t\t\tstd::cerr << \"lifting up again, previous was \" << cur.accu << \", \" << cur.order << std::endl;\n\t\t\t\t\t\tstd::u32string tmp(cur.accu);\n\t\t\t\t\t\tcur.accu.erase();\n\t\t\t\t\t\t// for \"a = b c + e\" we need to push back\n\t\t\t\t\t\t// for \"[a b, c]\"    we don't.\n\t\t\t\t\t\tif(onum<cur.order)\n\t\t\t\t\t\t\taccus.push_back(cur);\n\t\t\t\t\t\tcur.parts.clear();\n\t\t\t\t\t\tcur.parts.push_back(tmp);\n\t\t\t\t\t\tcur.order=onum;\n\t\t\t\t\t\t//\t\t\t\t\t\tprint_stack();\n\t\t\t\t\t\tgoto loopdone;\n\t\t\t\t\t\t}\n\t\t\t\t\tif(cur.accu.size()>0)\n\t\t\t\t\t\tcur.parts.push_back(cur.accu);\n\t\t\t\t\tcur.accu.erase();\n\t\t\t\t\tcur.head_is_generated=false;\n\t\t\t\t\t}\n\t\t\t\tgoto loopdone;\n\t\t\t\t}\n\t\t\t}\n\t\tif(c==' ' && cur.order!=sizeof(orders)/sizeof(char32_t)) {\n\t\t\tif(cur_pos==cur_str.size()-1)\n\t\t\t\tgoto loopdone;\n\t\t\telse show_and_throw_(\"Whitespace encountered at unexpected location.\");\n\t\t\t}\n\t\tunsigned int ind;\n\t\tif((ind=is_opening_bracket_(c))) {\n\t\t\t//\t\t\t std::cerr << \"entering bracket level \" << ind << \" \" << prev_token << std::endl;\n\t\t\t//\t\t\t std::cerr << \"is index before entering: \" << cur.is_index << std::endl;\n\t\t\tcur.bracket=ind; // remember the bracket, so that we can add it when we return to this level.\n\t\t\t//\t\t\tstd::cerr << \"is index after entering: \" << cur.is_index << std::endl;\n\t\t\taccus.push_back(cur);\n\t\t\tif(is_link_(prev_token)) cur.is_index=true;\n\t\t\telse                     cur.is_index=false;\n\t\t\tcur.erase();\n\t\t\tcur.bracket=0;\n\t\t\t}\n\t\telse if((ind=is_closing_bracket_(c))) {\n\t\t\t//\t\t\tstd::cerr << \"closing bracket encountered \" << ind << \" \" << (char)cur.bracket << \" \" << (char)current_bracket_() << std::endl;\n\t\t\tif(ind==1 && cur.accu.size()==0 && cur.parts.size()==0)\n\t\t\t\tcur.parts.push_back(cur.accu); // empty lists count\n\t\t\t//\t\t\tstd::cerr << \"on accu: \" << accus.back().is_index << std::endl;\n\t\t\tunwind_(sizeof(orders)/sizeof(char32_t), ind);\n\t\t\t//\t\t\tstd::cerr << \"is index now \" << cur.is_index << std::endl;\n\t\t\tcur.bracket=0;\n\t\t\t//\t\t\tcur.is_index=false; // TEST\n\t\t\t}\n\t\telse if(c==' ') {\n\t\t\t//\t\t\tstd::cout << \"space\\n\";\n\t\t\tif(cur.accu.size()>0) {\n\t\t\t\tcur.parts.push_back(cur.accu);\n\t\t\t\tcur.accu.erase();\n\t\t\t\tcur.head_is_generated=false;\n\t\t\t\t}\n\t\t\t}\n\t\telse cur.accu+=c;\n\t\tif(c=='\\\"')\n\t\t\tverbatim_=true;\n\nloopdone:\n\t\t++cur_pos;\n\t\t}\n\t}\n\n"
  },
  {
    "path": "core/PreProcessor.hh",
    "content": "/*\n\nCadabra: a field-theory motivated computer algebra system.\nCopyright (C) 2001-2014  Kasper Peeters <kasper.peeters@phi-sci.com>\n\nThis program is free software: you can redistribute it and/or\nmodify it under the terms of the GNU General Public License as\npublished by the Free Software Foundation, either version 3 of the\nLicense, or (at your option) any later version.\n\nThis program is distributed in the hope that it will be useful,\nbut WITHOUT ANY WARRANTY; without even the implied warranty of\nMERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU\nGeneral Public License for more details.\n\nYou should have received a copy of the GNU General Public License\nalong with this program.  If not, see <http://www.gnu.org/licenses/>.\n\n*/\n\n#pragma once\n\n#include <iostream>\n#include <string>\n#include <vector>\n\nenum { tok_arrow=0xac, tok_unequals=0xad, tok_wedge=0xae, tok_pow=0xaf, tok_set_option=0xb0, tok_declare=0xb1, tok_sequence=0xb2, tok_siblings=0xb3 };\n\n/// \\ingroup core\n///\n/// Preprocessing class which takes infix mathematical notation with\n/// all sorts of maths shortcuts and transforms it into a string which\n/// is properly formatted in prefix notation. The Parser class then\n/// uses this result to turn the string into an Ex expression tree.\n\nclass preprocessor {\n\tpublic:\n\t\tpreprocessor();\n\t\tfriend std::istream& operator>>(std::istream&, preprocessor&);\n\t\tfriend std::ostream& operator<<(std::ostream&, const preprocessor&);\n\n\t\tvoid erase();\n\t\tvoid strip_outer_brackets() const;\n\n\t\tconst static char32_t  orders[];\n\n\t\tenum order_labels { order_factorial=0,\n\t\t                    order_pow,\n\t\t                    order_frac,\n\t\t                    order_prod,\n\t\t                    order_wedge,\n\t\t                    order_minus,\n\t\t                    order_plus,\n\t\t                    order_dot,\n\t\t                    order_equals,\n\t\t                    order_unequals,\n\t\t                    order_less_than,\n\t\t                    order_greater_than,\n\t\t                    order_conditions,\n\t\t                    order_arrow,\n\t\t                    order_set_option,\n\t\t                    order_colon,\n\t\t                    order_comma,\n\t\t                    order_tilde\n\t\t                  \t};\n\t\t// FIXME: we really need a way to associate multiple characters to a single operator,\n\t\t// since that would allow for \"..\" (sequence), \":=\" (define), \">=\" and so on. The current\n\t\t// '.' is a hack and is treated as such: when it occurs there is an additional check for\n\t\t// a followup '.'.\n\t\tconst static char32_t *const    order_names[];\n\tprivate:\n\t\tvoid parse_(const std::u32string&);\n\t\tvoid parse_internal_();\n\t\tbool verbatim_;\n\t\tbool next_is_product_;\n\t\tbool eat_initial_whitespace_;\n\t\tbool unwind_(unsigned int tolevel, unsigned int bracketgoal=0, bool usebracket=true) const;\n\t\tchar32_t get_token_(char32_t prev_token);\n\t\tvoid show_and_throw_(const std::string& str) const;\n\n\t\tvoid         bracket_strings_(char32_t cb, std::u32string& obrack, std::u32string& cbrack) const;\n\t\tbool         is_infix_operator_(char32_t c) const;\n\t\tbool         is_link_(char32_t c) const;\n\t\tunsigned int is_opening_bracket_(char32_t c) const;\n\t\tunsigned int is_closing_bracket_(char32_t c) const;\n\t\tunsigned int is_bracket_(char32_t c) const;\n\t\tbool         is_already_bracketed_(const std::u32string& str) const;\n\t\tbool         is_digits_(const std::u32string& str) const;\n\t\tunsigned int current_bracket_(bool deep=false) const;\n\t\tvoid         print_stack() const; // for debuggging purposes\n\n\t\tbool default_is_product_() const;\n\t\tunsigned int    cur_pos;\n\t\tstd::u32string  cur_str;\n\n\t\t// A backslash followed by a bracket is also a bracket (gets code\n\t\t// of the bracket plus 128).\n\t\tconst static char32_t open_brackets[];\n\t\tconst static char32_t close_brackets[];\n\n\t\tclass accu_t {\n\t\t\tpublic:\n\t\t\t\taccu_t();\n\t\t\t\tvoid erase();\n\n\t\t\t\tbool                     head_is_generated;  // when infix -> postfix has occurred\n\t\t\t\tstd::u32string           accu;\n\t\t\t\tunsigned int             order;\n\t\t\t\tstd::vector<std::u32string> parts;\n\t\t\t\tunsigned int             bracket;\n\t\t\t\tbool                     is_index; // whether the bracket was prefixed with ^ or _\n\t\t\t};\n\t\tmutable accu_t               cur;\n\t\tmutable std::vector<accu_t>  accus;\n\t};\n\nstd::ostream& operator<<(std::ostream&, const preprocessor&);\nstd::istream& operator>>(std::istream&, preprocessor&);\n\n\n"
  },
  {
    "path": "core/ProgressMonitor.cc",
    "content": "\n#include \"ProgressMonitor.hh\"\n#include <iostream>\n#include <sstream>\n#include <assert.h>\n\nProgressMonitor::ProgressMonitor(std::function<void(const std::string&, int, int)> report, int report_level)\n\t: report(report)\n\t, report_level(report_level)\n\t{\n\t}\n\nProgressMonitor::~ProgressMonitor()\n\t{\n\t}\n\nProgressMonitor::Block::Block(const std::string& name, int level)\n\t: name(name), step(0), total_steps(0), level(level)\n\t{\n\tstarted=std::chrono::duration_cast<std::chrono::milliseconds>(std::chrono::system_clock::now().time_since_epoch());\n\t}\n\nProgressMonitor::Total::Total()\n\t: call_count(0), time_spent(0), total_steps(0)\n\t{\n\t}\n\nstd::string ProgressMonitor::Total::str() const\n\t{\n\tstd::ostringstream s;\n\n\ts << name << \": \" << call_count << \" calls, \" << total_steps << \" steps, \" << time_spent.count() << \" ms\";\n\tfor(const auto& msg: messages)\n\t\ts << \"; \" << msg;\n\n\treturn s.str();\n\t}\n\nvoid ProgressMonitor::group(std::string name, int total, int level)\n\t{\n\tif(name==\"\") {\n\t\tBlock& blk=call_stack.top();\n\t\tlevel = blk.level;\n\t\tauto fnd = call_totals.find(blk.name);\n\t\tTotal& tot=fnd->second;\n\n\t\ttot.name=blk.name;\n\t\tauto now=std::chrono::duration_cast<std::chrono::milliseconds>(std::chrono::system_clock::now().time_since_epoch());\n\t\ttot.time_spent  += (now - blk.started);\n\t\ttot.total_steps += blk.total_steps;\n\t\ttot.messages.reserve(tot.messages.size() + std::distance(blk.messages.begin(), blk.messages.end()));\n\t\ttot.messages.insert(tot.messages.end(), blk.messages.begin(), blk.messages.end());\n\n\t\tcall_stack.pop();\n\t\t}\n\telse {\n\t\tif (level < 0) {\n\t\t\tif (call_stack.empty())\n\t\t\t\tlevel = report_level;\n\t\t\telse\n\t\t\t\tlevel = call_stack.top().level;\n\t\t}\n\n\t\t// Insert an entry on the call stack.\n\t\tBlock blk(name, level);\n\t\tblk.total_steps = total;\n\t\tcall_stack.push(blk);\n\n\t\t// Also insert an entry to the total stack for this group if there\n\t\t// isn't one already.\n\t\tauto fnd=call_totals.find(name);\n\t\tif(fnd==call_totals.end()) {\n\t\t\tTotal tot;\n\t\t\ttot.call_count=1;\n\t\t\ttot.name=name;\n\t\t\tcall_totals[name]=tot;\n\t\t\t}\n\t\telse {\n\t\t\tfnd->second.call_count++;\n\t\t\t}\n\t\t}\n\n\tif (report && level >= report_level) {\n\t\tif (call_stack.size() == 0)\n\t\t\treport(\"Idle\", 0, 0);\n\t\telse\n\t\t\treport(call_stack.top().name, call_stack.top().step, call_stack.top().total_steps);\n\t\t}\n\t}\n\nvoid ProgressMonitor::progress()\n\t{\n\tassert(!call_stack.empty());\n\tprogress(call_stack.top().step + 1);\n\t}\n\nvoid ProgressMonitor::progress(int n)\n\t{\n\tassert(!call_stack.empty());\n\tprogress(n, call_stack.top().total_steps);\n\t}\n\nvoid ProgressMonitor::progress(int n, int total)\n\t{\n\tassert(!call_stack.empty());\n\tcall_stack.top().step=n;\n\tcall_stack.top().total_steps=total;\n\n\tif (report && call_stack.top().level >= report_level)\n\t\treport(call_stack.top().name, n, total);\n\t}\n\nvoid ProgressMonitor::message(const std::string& msg)\n\t{\n\tcall_stack.top().messages.push_back(msg);\n\t}\n\nlong ProgressMonitor::Total::time_spent_as_long() const\n\t{\n\treturn time_spent.count();\n\t}\n\nvoid ProgressMonitor::print() const\n\t{\n\tfor(auto& t: call_totals) {\n\t\tconst Total& tot=t.second;\n\t\tstd::cerr << tot.name << \": \"\n\t\t          << tot.call_count << \" calls, \"\n\t\t          //\t\t\t\t\t << (long)tot.time_spent << \" ms, \"\n\t\t          << tot.total_steps << \" steps\" << std::endl;\n\t\tfor(const auto& msg: tot.messages)\n\t\t\tstd::cerr << \"  \" << msg << std::endl;\n\t\t}\n\t}\n\nstd::vector<ProgressMonitor::Total> ProgressMonitor::totals() const\n\t{\n\tstd::vector<Total> res;\n\tfor(auto& t: call_totals)\n\t\tres.push_back(t.second);\n\n\treturn res;\n\t}\n\nbool ProgressMonitor::Total::operator==(const Total& other) const\n\t{\n\tif(name==other.name &&\n\t      call_count==other.call_count &&\n\t      time_spent==other.time_spent &&\n\t      total_steps==other.total_steps) return true;\n\treturn false;\n\t}\n\nScopedProgressGroup::ScopedProgressGroup(ProgressMonitor* pm, const std::string& name, int total, int level)\n\t: pm(pm)\n\t{\n\tif (pm)\n\t\tpm->group(name, total, level);\n\t}\n\nScopedProgressGroup::~ScopedProgressGroup()\n\t{\n\tif (pm)\n\t\tpm->group();\n\t}\n\nvoid ScopedProgressGroup::progress()\n\t{\n\tif (pm)\n\t\tpm->progress();\n\t}\n\nvoid ScopedProgressGroup::progress(int n)\n\t{\n\tif (pm)\n\t\tpm->progress(n);\n\t}\n\nvoid ScopedProgressGroup::progress(int n, int total)\n\t{\n\tif (pm)\n\t\tpm->progress(n, total);\n\t}\n"
  },
  {
    "path": "core/ProgressMonitor.hh",
    "content": "\n#pragma once\n\n#include <string>\n#include <chrono>\n#include <stack>\n#include <map>\n#include <vector>\n#include <functional>\n\n/// \\ingroup core\n///\n/// Object keeping track of time spent in nested execution blocks,\n/// and keeping track of out-of-band messages produced by these\n/// blocks. The messaging facility is currently experimental.\n\nclass ProgressMonitor {\n\tpublic:\n\t\tProgressMonitor(std::function<void(const std::string&, int, int)> report = nullptr, int report_level = 2);\n\t\tvirtual ~ProgressMonitor();\n\n\t\t/// Start a new named group, or close the innermost one in case\n\t\t/// the `name` argument is empty. All time spent inbetween calls\n\t\t/// to group open/close calls is accumulated in a `Totals`\n\t\t/// object, one for each group name. These `Totals` blocks can\n\t\t/// be retrieved from the `totals` function.\n\t\t/// FIXME: call this `block`.\n\t\tvoid group(std::string name = \"\", int total = 0, int level = -1);\n\n\t\t/// Set the progress of the current top-level block to be `n`\n\t\t/// out of `total` steps. It is possible to change `totals` at\n\t\t/// every call (e.g. in situations where the algorithm cannot\n\t\t/// possibly figure out how many total steps there are to take.\n\t\tvoid progress(); // Increment current step by 1\n\t\tvoid progress(int n);\n\t\tvoid progress(int n, int total);\n\n\t\t/// Log out-of-band messages to the current block.\n\n\t\tvoid message(const std::string&);\n\t\t\n\t\t/// Generate debug output on `cerr`.\n\t\t\n\t\tvoid print() const;\n\n\t\t/// Callback for reporting a progress update\n\t\tstd::function<void(const std::string&, int, int)> report;\n\n\t\t// Level above which to report progress updates and not only add to totals\n\t\tint report_level;\n\n\t\t/// Object to accumulate total time and call counts for a\n\t\t/// particular named execution group.\n\t\t\n\t\tclass Total {\n\t\t\tpublic:\n\t\t\t\tTotal();\n\n\t\t\t\tstd::string               name;\n\t\t\t\tsize_t                    call_count;\n\t\t\t\tstd::chrono::milliseconds time_spent;\n\t\t\t\tint                       total_steps;\n\t\t\t\tstd::vector<std::string>  messages;\n\n\t\t\t\tlong                      time_spent_as_long() const;\n\n\t\t\t\tbool operator==(const Total& other) const;\n\n\t\t\t\tstd::string               str() const;\n\t\t\t};\n\n\t\tstd::vector<Total> totals() const;\n\n\tprivate:\n\t\t/// A single element of the nested `group` call stack.  Every\n\t\t/// time a `group` function is called with a non-empty name,\n\t\t/// a new `Block` is pushed onto the call stack. When `group`\n\t\t/// is called with an empty name, the topmost `Block` is popped\n\t\t/// from the stack, and its sub-totals added to the `Total`\n\t\t/// element which thus collects data from multiple executions\n\t\t/// of identically-named groups.\n\t\t\n\t\tclass Block {\n\t\t\tpublic:\n\t\t\t\tBlock(const std::string& name, int level);\n\n\t\t\t\tstd::string               name;\n\t\t\t\tstd::chrono::milliseconds started;\n\t\t\t\tint                       step, total_steps;\n\t\t\t\tstd::vector<std::string>  messages;\n\t\t\t\tint                       level;\n\t\t\t};\n\n\t\tstd::stack<Block>            call_stack;\n\t\tstd::map<std::string, Total> call_totals;\n\t};\n\n\nclass ScopedProgressGroup\n{\npublic:\n\tScopedProgressGroup(ProgressMonitor* pm, const std::string& name, int total = 0, int level = -1);\n\t~ScopedProgressGroup();\n\n\tvoid progress();\n\tvoid progress(int n);\n\tvoid progress(int n, int total);\n\nprivate:\n\tProgressMonitor* pm;\n};\n"
  },
  {
    "path": "core/Props.cc",
    "content": "/*\n\nCadabra: a field-theory motivated computer algebra system.\nCopyright (C) 2001-2014  Kasper Peeters <kasper.peeters@phi-sci.com>\n\nThis program is free software: you can redistribute it and/or\nmodify it under the terms of the GNU General Public License as\n\tpublished by the Free Software Foundation, either version 3 of the\nLicense, or (at your option) any later version.\n\nThis program is distributed in the hope that it will be useful,\nbut WITHOUT ANY WARRANTY; without even the implied warranty of\nMERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU\nGeneral Public License for more details.\n\nYou should have received a copy of the GNU General Public License\nalong with this program.  If not, see <http://www.gnu.org/licenses/>.\n\n*/\n\n#include \"Props.hh\"\n#include \"Exceptions.hh\"\n#include \"Compare.hh\"\n#include <stdlib.h>\n#include <typeinfo>\n#include <iostream>\n#include <sstream>\n#include \"properties/Indices.hh\"\n\n// #define DEBUG 1\n\nusing namespace cadabra;\n\npattern::pattern()\n\t{\n\t}\n\npattern::pattern(const Ex& o)\n\t: obj(o)\n\t{\n\t}\n\nbool pattern::match(const Properties& properties, const Ex::iterator& it, bool ignore_parent_rel, bool ignore_properties) const\n\t{\n\tEx_comparator comp(properties);\n\treturn match_ext(properties, it, comp, ignore_parent_rel, ignore_properties);\n\t}\n\nbool pattern::match_ext(const Properties& properties, const Ex::iterator& it, Ex_comparator& comp, bool ignore_parent_rel, bool ignore_properties) const\n\t{\n\t// Special case for range wildcards.\n\t// FIXME: move this to Compare.cc (see the FIXME there)\n\n\t// std::cerr << \"Attempting to match \" << Ex(it) << \" to \" << Ex(obj) << std::endl;\n\n\tif(it->name==obj.begin()->name && children_wildcard()) {\n\t\tEx::iterator hm=obj.begin(obj.begin());\n\t\tif(Ex::number_of_children(hm)==0) {\n\t\t\treturn true; // # without arguments\n\t\t\t}\n\t\tEx::iterator hmarg=hm.begin();\n\t\tEx::iterator seqarg=hm;\n\t\tconst Indices *ind=0;\n\n\t\tif(*hmarg->name==\"\\\\comma\" || *hmarg->name!=\"\\\\sequence\") {\n\t\t\tEx::iterator stt=hmarg;\n\t\t\tif(*hmarg->name==\"\\\\comma\") {\n\t\t\t\tstt=hmarg.begin();\n\t\t\t\tseqarg=hmarg.begin();\n\t\t\t\tseqarg.skip_children();\n\t\t\t\t++seqarg;\n\t\t\t\t}\n\t\t\tind=properties.get<Indices>(stt, true);\n\t\t\t}\n\t\telse seqarg=hmarg;\n\n\t\tif(seqarg!=hm) {\n\t\t\tEx::sibling_iterator seqit=seqarg.begin();\n\t\t\tunsigned int from=to_long(*seqit->multiplier);\n\t\t\t++seqit;\n\t\t\tunsigned int to  =to_long(*seqit->multiplier);\n\n\t\t\tif(Ex::number_of_children(it)<from ||\n\t\t\t      Ex::number_of_children(it)>to )\n\t\t\t\treturn false;\n\t\t\t}\n\n\t\tif(ind!=0) {\n\t\t\tEx::sibling_iterator indit=it.begin();\n\t\t\twhile(indit!=it.end()) {\n\t\t\t\tconst Indices *gi=properties.get<Indices>(indit, true);\n\t\t\t\tif(gi!=ind) {\n\t\t\t\t\treturn false;\n\t\t\t\t\t}\n\t\t\t\t++indit;\n\t\t\t\t}\n\t\t\t}\n\n\t\treturn true;\n\t\t}\n\n\t// Cases without range wildcard.  Compare making full use of\n\t// property information. Note the order of the arguments to\n\t// 'equal_subtree': the first argument is supposed to be a\n\t// pattern, the second an expression which is to be matched.\n\n#ifdef DEBUG\n\tstd::cerr << \"vvvvvvv \" << ignore_properties << std::endl;\n#endif\n\tcomp.clear();\n\tEx_comparator::match_t res=\n\t\tcomp.equal_subtree(obj.begin(), it,\n\t\t\t\t\t\t\t\t ignore_properties?Ex_comparator::useprops_t::never:Ex_comparator::useprops_t::not_at_top,\n\t\t\t\t\t\t\t\t ignore_parent_rel);\n#ifdef DEBUG\n\tstd::cerr << \"pattern::match: comparing\" << Ex(it) <<  \" with \" << Ex(obj) << \" = \" << static_cast<int>(res) << std::endl;\n\tstd::cerr << \"^^^^^^\" << std::endl;\n#endif\n\n\tif(is_in(res, {\n\tEx_comparator::match_t::subtree_match,\n\tEx_comparator::match_t::match_index_less,\n\tEx_comparator::match_t::match_index_greater,\n\tEx_comparator::match_t::node_match\n\t} )) {\n\t\treturn true;\n\t\t}\n\n\treturn false;\n\t}\n\nbool pattern::children_wildcard() const\n\t{\n\tif(Ex::number_of_children(obj.begin())==1)\n\t\tif(obj.begin(obj.begin())->is_range_wildcard())\n\t\t\treturn true;\n\treturn false;\n\t}\n\nbool Properties::has(const property *pb, Ex::iterator it)\n\t{\n\tstd::pair<property_map_t::iterator, property_map_t::iterator> pit=props.equal_range(it->name_only());\n\twhile(pit.first!=pit.second) {\n\t\t//\t\ttxtout << *it->name << std::endl;\n\t\t//\t\ttxtout << typeid(pit.first->second.second).name() << \" versus \"\n\t\t//\t\t\t\t << typeid(pb).name() << std::endl;\n\t\tconst property *tmp = (pit.first->second.second);\n\t\tif(typeid(*tmp)==typeid(*pb) &&\n\t\t      pit.first->second.first->match(*this, it))  // match found\n\t\t\treturn true;\n\t\t++pit.first;\n\t\t}\n\treturn false;\n\t}\n\nvoid Properties::clear()\n\t{\n\t// Clear and free the property lists. Since pointers to properties can\n\t// be shared, we use the pats map and make sure that we only free each\n\t// property* pointer once.\n\tpattern_map_t::const_iterator it=pats.begin();\n\tconst property *previous=0;\n\twhile(it!=pats.end()) {\n\t\tif(previous!=it->first) {\n\t\t\tprevious=it->first;\n\t\t\tdelete it->first;\n\t\t\t}\n\t\tdelete it->second;\n\t\t++it;\n\t\t}\n\tprops.clear();\n\tpats.clear();\n\t}\n\nProperties::registered_property_map_t::~registered_property_map_t()\n\t{\n\t// FIXME: V2\n\t}\n\nvoid Properties::register_property(property* (*fun)(), const std::string& name)\n\t{\n\tregistered_properties.store[name]=fun;\n\t}\n\nkeyval_t::const_iterator keyval_t::find(const std::string& key) const\n\t{\n\tkeyval_t::const_iterator it=keyvals.begin();\n\twhile(it!=keyvals.end()) {\n\t\tif(it->first==key)\n\t\t\tbreak;\n\t\t++it;\n\t\t}\n\treturn it;\n\t}\n\nkeyval_t::iterator keyval_t::find(const std::string& key)\n\t{\n\tkeyval_t::iterator it=keyvals.begin();\n\twhile(it!=keyvals.end()) {\n\t\tif(it->first==key)\n\t\t\tbreak;\n\t\t++it;\n\t\t}\n\treturn it;\n\t}\n\nkeyval_t::const_iterator keyval_t::begin() const\n\t{\n\treturn keyvals.begin();\n\t}\n\nkeyval_t::const_iterator keyval_t::end() const\n\t{\n\treturn keyvals.end();\n\t}\n\nvoid keyval_t::push_back(const kvpair_t& kv)\n\t{\n\tkeyvals.push_back(kv);\n\t}\n\nvoid keyval_t::erase(iterator it)\n\t{\n\tkeyvals.erase(it);\n\t}\n\n\nproperty::property(bool h)\n\t: hidden_(h)\n\t{\n\t}\n\nvoid property::hidden(bool h)\n\t{\n\thidden_=h;\n\t}\n\nbool property::hidden() const\n\t{\n\treturn hidden_;\n\t}\n\nbool property::parse(Kernel&, keyval_t&)\n\t{\n\treturn true;\n\t}\n\nbool property::parse(Kernel& kernel, std::shared_ptr<Ex>, keyval_t& keyvals)\n\t{\n\t// The default is to run the 'parse' without 'ex', as most properties\n\t// do not implement the new interface.\n\treturn parse(kernel, keyvals);\n\t}\n\nvoid property::validate(Kernel&, std::shared_ptr<Ex>) const\n\t{\n\t}\n\nbool property::parse_one_argument(Ex::iterator arg, keyval_t& keyvals)\n\t{\n\tif(*arg->name==\"\\\\equals\") {\n\t\tEx::sibling_iterator key=arg.begin();\n\t\tif(key==arg.end()) return false;\n\t\tEx::sibling_iterator val=key;\n\t\t++val;\n\t\tif(val==arg.end()) return false;\n\t\tkeyvals.push_back(keyval_t::value_type(*arg.begin()->name, Ex(val)));\n\t\t}\n\telse {\n\t\tif(unnamed_argument()!=\"\") {\n\t\t\t// std::cerr << unnamed_argument() << \" unnamed \" << *arg->name << std::endl;\n\t\t\tkeyvals.push_back(keyval_t::value_type(unnamed_argument(), Ex(arg)));\n\t\t\t}\n\t\telse return false;\n\t\t}\n\treturn true;\n\t}\n\nbool property::parse_to_keyvals(const Ex& tr, keyval_t& keyvals)\n\t{\n\tif(tr.begin()==tr.end()) return true;\n\n\tauto it=tr.begin();\n\n\t//\tstd::cout << \"parsing to keyvals\" << std::endl;\n\tif(*(it)->name!=\"\\\\comma\") { // one argument\n\t\tif(parse_one_argument(it, keyvals)==false)\n\t\t\treturn false;\n\t\t}\n\telse {\n\t\tEx::sibling_iterator sib=tr.begin(it);\n\t\twhile(sib!=tr.end(it)) {\n\t\t\tif(parse_one_argument(sib, keyvals)==false)\n\t\t\t\treturn false;\n\t\t\t++sib;\n\t\t\t}\n\t\t}\n\n\t// for(auto it=keyvals.begin(); it!=keyvals.end(); ++it)\n\t//   \tstd::cerr << (*it).first << \" = \" << *(*it).second->name << std::endl;\n\treturn true;\n\t}\n\n\nvoid property::latex(std::ostream& str) const\n\t{\n\tstr << name();\n\t}\n\nstd::string property::unnamed_argument() const\n\t{\n\treturn \"\";\n\t}\n\nproperty::match_t property::equals(const property *) const\n\t{\n\treturn exact_match;\n\t}\n\nbool labelled_property::parse(Kernel&, std::shared_ptr<Ex>, keyval_t& keyvals)\n\t{\n\tkeyval_t::const_iterator lit=keyvals.find(\"label\");\n\tif(lit!=keyvals.end()) {\n\t\tlabel=*lit->second.begin()->name;\n\t\treturn true;\n\t\t}\n\telse {\n\t\t// FIXME: not all labelled properties have an actual label, e.g.\n\t\t// Derivative derives from WeightBase but not all derivatives need\n\t\t// a label. If we throw an exception here, those properties fail\n\t\t// to run.\n\t\t//\t\tthrow ArgumentException(\"Need a 'label' parameter for property.\");\n\t\treturn false;\n\t\t}\n\t}\n\n//bool operator<(const pattern& one, const pattern& two)\n//\t{\n//\treturn tree_less(one.obj, two.obj);\n////\tif(*(one.obj.begin()->name)<*(two.obj.begin()->name)) return true;\n////\treturn false;\n//\t}\n\n//bool operator==(const pattern& one, const pattern& two)\n//\t  {\n//\t  return one.obj==two.obj; // FIXME: handle dummy indices\n//\t  }\n\nvoid Properties::insert_prop(const Ex& et, const property *pr)\n\t{\n\t//\tassert(pats.find(pr)==pats.end()); // identical properties have to be assigned through insert_list_prop\n\n\t// FIXME: is it really necessary to store this by pointer? We are in any case\n\t// not cleaning this up correctly yet.\n\tpattern *pat=new pattern(et);\n\n\tstd::pair<property_map_t::iterator, property_map_t::iterator> pit=\n\t   props.equal_range(pat->obj.begin()->name_only());\n\n\tproperty_map_t::iterator first_nonpattern=pit.first;\n\n\twhile(pit.first!=pit.second) {\n\t\t// keep track of the first non-pattern element\n\t\tif(Ex::number_of_children((*pit.first).second.first->obj.begin())==1)\n\t\t\tif((*pit.first).second.first->obj.begin().begin()->is_range_wildcard())\n\t\t\t\t++first_nonpattern;\n\n\t\t// A given pattern can only have one property of any given type. The following\n\t\t// triggers on entries in the props map which match the pattern to be inserted.\n\t\tif((*pit.first).second.first->match(*this, et.begin())) {\n\n\t\t\t// Does this entry in props give a property of the same type as the one we\n\t\t\t// are trying to insert?\n\t\t\tconst property *tmp = (*pit.first).second.second;\n\t\t\tif(typeid(*pr)==typeid(*tmp)) {\n\n\t\t\t\t// If this is a labelled property, is the label different from the one on the\n\t\t\t\t// property we are trying to insert?\n\t\t\t\tconst labelled_property *lp   =dynamic_cast<const labelled_property *>(pr);\n\t\t\t\tconst labelled_property *lpold=dynamic_cast<const labelled_property *>(pit.first->second.second);\n\n\t\t\t\tif(!lp || !lpold || lp->label==lpold->label) {\n\n\t\t\t\t\t// The to-be-inserted property cannot co-exist on this pattern with the\n\t\t\t\t\t// one that is currently associated to the pattern. Remove it.\n\n\t\t\t\t\tpattern        *oldpat =pit.first->second.first;\n\t\t\t\t\tconst property *oldprop=pit.first->second.second;\n\n\t\t\t\t\t// If the new property instance is the same as the old one, we can stop\n\t\t\t\t\t// (this happens if a pattern is accidentally repeated in a property assignment).\n\t\t\t\t\tif(oldprop==pr) {\n\t\t\t\t\t\tdelete pat;\n\t\t\t\t\t\treturn;\n\t\t\t\t\t\t}\n\n\t\t\t\t\t// Erase the pattern->property entry, and delete the pattern.\n\t\t\t\t\t// FIXME: store pattern by value.\n\t\t\t\t\tprops.erase(pit.first);\n\t\t\t\t\tdelete oldpat;\n\n\t\t\t\t\t// Remove the property->pattern entry. Only delete the property\n\t\t\t\t\t// if it is no longer associated to any other pattern.\n\t\t\t\t\t// FIXME:\n\t\t\t\t\t//   {A, B}::SelfAntiCommuting.\n\t\t\t\t\t//   {A}::SelfAntiCommuting.\n\t\t\t\t\t//   {B}::SelfAntiCommuting.\n\t\t\t\t\t// leads to two properties SelfAntiCommuting, which are identical.\n\t\t\t\t\t// We need a way to compare properties and decide when they are\n\t\t\t\t\t// identical, or when they can coexist, or something like that.\n\t\t\t\t\tfor(auto pi=pats.begin(); pi!=pats.end(); ++pi) {\n\t\t\t\t\t\tif((*pi).first==oldprop && (*pi).second==oldpat) {\n\t\t\t\t\t\t\t//\t\t\t\t\t\t\tstd::cerr << \"found old entry, deleting\" << std::endl;\n\t\t\t\t\t\t\tpats.erase(pi);\n\t\t\t\t\t\t\tbreak;\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\t}\n\t\t\t\t\tif(pats.find(oldprop)==pats.end()) {\n\t\t\t\t\t\t//\t\t\t\t\t\tstd::cerr << \"no other references\" << std::endl;\n\t\t\t\t\t\tdelete oldprop;\n\t\t\t\t\t\t}\n\n\t\t\t\t\tbreak;\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t}\n\t\t++pit.first;\n\t\t}\n\n\tpats.insert(pattern_map_t::value_type(pr, pat));\n\t// std::cerr << \"inserting for \" << *(pat->obj.begin()->name) << std::endl;\n\tprops.insert(property_map_t::value_type(pat->obj.begin()->name_only(), pat_prop_pair_t(pat,pr)));\n\t}\n\nvoid Properties::insert_list_prop(const std::vector<Ex>& its, const list_property *pr)\n\t{\n\tassert(pats.find(pr)==pats.end()); // identical properties have to be assigned through insert_list_prop\n\tassert(its.size()>0);\n\n\t// If 'pr' is exactly equal to an existing property, we should use that one instead of\n\t// introducing a duplicate.\n\tpattern_map_t::iterator fit=pats.begin();\n\twhile(fit!=pats.end()) {\n\t\tconst property *tmp = (*fit).first;\n\t\tif(typeid(*tmp)==typeid(*pr))\n\t\t\tif(pr->equals((*fit).first)==property::exact_match) {\n\t\t\t\tpr=static_cast<const list_property *>( (*fit).first );\n\t\t\t\tbreak;\n\t\t\t\t}\n\t\t++fit;\n\t\t}\n\n\t// If 'pr' has id_match with an existing property, we need to remove all property assignments\n\t// for the existing one, except when there is an exact_match.\n\tconst property *to_delete_property=0;\n\tpattern_map_t::iterator pit=pats.begin();\n\twhile(pit!=pats.end()) {\n\t\tconst property *tmp = (*pit).first;\n\t\tif(typeid(*tmp)==typeid(*pr))\n\t\t\tif(pr->equals((*pit).first)==property::id_match) {\n\t\t\t\tto_delete_property = (*pit).first;\n\t\t\t\tbreak;\n\t\t\t\t}\n\t\t++pit;\n\t\t}\n\tif(to_delete_property) {\n\t\tpats.erase(to_delete_property);\n\t\tproperty_map_t::iterator it=props.begin();\n\t\twhile(it!=props.end()) {\n\t\t\tproperty_map_t::iterator nxt=it;\n\t\t\t++nxt;\n\t\t\tif((*it).second.second==to_delete_property) props.erase(it);\n\t\t\tit=nxt;\n\t\t\t}\n\t\t}\n\n\n\t// Now register the list property.\n\n\tfor(unsigned int i=0; i<its.size(); ++i) {\n\t\tpattern *pat=new pattern(its[i]);\n\n\t\t// Removing properties causes more problems than it solves (the only reason\n\t\t// for overwriting a list property is to change the SortOrder, which is\n\t\t// rarely useful). So we just insert the new property regardless.\n\n\t\t//\t\t// Pointers to properties are shared, so we need to delete them only once.\n\t\t//\n\t\t//\t\tstd::pair<property_map_t::iterator, property_map_t::iterator> pit=\n\t\t//\t\t\tprops.equal_range(its[i]->name);\n\t\t//\n\t\t//\t\twhile(pit.first!=pit.second) {\n\t\t//\t\t\tif((*pit.first).second.first->match(its[i])) { // found the pattern 'its[i]' in the property list\n\t\t//\t\t\t\tif(typeid(*pr)==typeid(*(*pit.first).second.second)) {\n\t\t////\t\t\t\t\t\ttxtout << \"found a property for \" << *(its[i]->name) << std::endl;\n\t\t////\t\t\t\t\t\tEx::print_recursive_treeform(txtout, its[i]);\n\t\t//\n\t\t//\t\t\t\t\tpattern  *oldpat=pit.first->second.first;\n\t\t//\t\t\t\t\tconst property *oldprop=pit.first->second.second;\n\t\t//\n\t\t////\t\t\t\t\tprops.erase(pit.first); THIS\n\t\t//\n\t\t//\t\t\t\t\t// Delete only those entries in the pattern map which are related to\n\t\t//\t\t\t\t\t// this particular pattern _and_ this particular property\n\t\t//\t\t\t\t\tstd::pair<pattern_map_t::iterator, pattern_map_t::iterator> patrange=\n\t\t//\t\t\t\t\t\tpats.equal_range(oldprop);\n\t\t//\t\t\t\t\twhile(patrange.first!=patrange.second) {\n\t\t//\t\t\t\t\t\tif(patrange.first->first==oldprop && patrange.first->second==oldpat) {\n\t\t////\t\t\t\t\t\t\t\t  txtout << \"erasing property for \" << *(oldpat->headnode) << std::endl;\n\t\t////\t\t\t\t\t\t\tpats.erase(patrange.first); // THIS\n\t\t//\t\t\t\t\t\t\tbreak;\n\t\t//\t\t\t\t\t\t\t}\n\t\t//\t\t\t\t\t\t++patrange.first;\n\t\t//\t\t\t\t\t\t}\n\t\t////\t\t\t\t\tdelete oldpat; THIS\n\t\t//\t\t\t\t\tbreak;\n\t\t//\t\t\t\t\t}\n\t\t//\t\t\t\t}\n\t\t//\t\t\t++pit.first;\n\t\t//\t\t\t}\n\n\t\t// Now register the property.\n\t\t//\t\ttxtout << \"registering \" << *(pat->headnode) << std::endl;\n\t\tpats.insert(pattern_map_t::value_type(pr, pat));\n\t\tprops.insert(property_map_t::value_type(pat->obj.begin()->name_only(), pat_prop_pair_t(pat,pr)));\n\t\t}\n\t}\n\n\nint Properties::serial_number(const property *listprop, const pattern *pat) const\n\t{\n\tint serialnum=0;\n\n\tstd::pair<pattern_map_t::const_iterator, pattern_map_t::const_iterator>\n\tpm=pats.equal_range(listprop);\n\tserialnum=0;\n\twhile(pm.first!=pm.second) {\n\t\tif((*pm.first).second==pat)\n\t\t\tbreak;\n\t\t++serialnum;\n\t\t++pm.first;\n\t\t}\n\treturn serialnum;\n\t}\n\n\n/*\n\n\t\t\t{a,b,c,d,e}::Indices(vector).\n\t\t\t{a,b,c}::Indices(spinor).\n\nThis should make a,b,c spinor indices, and keep d,e as vector indices.\n\n\n\t\t\t{a,b,c}::Indices(vector).\n\t\t\t{d,e}::Indices(vector).\n\nThis should make all of a,b,c,d,e vector indices.\n\n\n\t\t\t{a,b,c}::Indices(vector).\n\t\t\t{a,b,c,d,e,f}::Indices(spinor).\n\nThis should make all indices spinor indices.\n\n\n\t\t\t{a,b,c,d,e}::Indices(vector, position=free).\n\t\t\t{a,b,c}::Indices(vector, position=fixed).\n\nYou can only have one type of index for each name, so this declaration implies that\nd,e should have their property removed.\n\n\n*/\n\n\n// Insert a property for the given pattern Ex. Determines whether the property\n// is a list property or a normal one, and dispatches accordingly.\n\nstd::string Properties::master_insert(Ex proptree, const property *thepropbase)\n\t{\n\tstd::ostringstream str;\n\n\tEx::sibling_iterator st=proptree.begin();\n\n\tconst list_property *thelistprop=dynamic_cast<const list_property *>(thepropbase);\n\tif(thelistprop) { // a list property\n\t\tstd::vector<Ex> objs;\n\t\tif(*st->name==\"\\\\comma\") {\n\t\t\tEx::sibling_iterator sib=proptree.begin(st);\n\t\t\twhile(sib!=proptree.end(st)) {\n\t\t\t\tif(sib->fl.parent_rel!=str_node::p_property) {\n\t\t\t\t\tobjs.push_back(Ex(sib));\n\t\t\t\t\t}\n\t\t\t\t++sib;\n\t\t\t\t}\n\t\t\t}\n\t\tif(objs.size()<2)\n\t\t\tthrow ConsistencyException(\"A list property cannot be assigned to a single object.\");\n\n\t\t// FIXME: we special-case Indices, as those pass a list of objects with parent_rel==p_none,\n\t\t// but we need the patterns to have parent_rel set to p_sub and p_super in order to avoid\n\t\t// special cases in the pattern matcher later.\n\t\t// DOCME: the above\n\t\tif(dynamic_cast<const Indices *>(thelistprop)) {\n\t\t\tstd::vector<Ex> objs2;\n\t\t\tfor(auto& obj: objs) {\n\t\t\t\tEx obj2(obj);\n\t\t\t\tobj2.begin()->fl.parent_rel=str_node::p_super;\n\t\t\t\tobjs2.push_back(obj2);\n\t\t\t\t}\n\t\t\tfor(auto& obj: objs) {\n\t\t\t\tEx obj2(obj);\n\t\t\t\tobj2.begin()->fl.parent_rel=str_node::p_sub;\n\t\t\t\tobjs2.push_back(obj2);\n\t\t\t\t}\n\t\t\tinsert_list_prop(objs2, thelistprop);\n\t\t\t}\n\t\telse {\n\t\t\tinsert_list_prop(objs, thelistprop);\n\t\t\t}\n\t\t}\n\telse {   // a normal property\n\t\tconst property *theprop=thepropbase;\n\t\tassert(theprop);\n\t\tif(*st->name==\"\\\\comma\") {\n\t\t\tEx::sibling_iterator sib=proptree.begin(st);\n\t\t\twhile(sib!=proptree.end(st)) {\n\t\t\t\tif(sib->fl.parent_rel!=str_node::p_property) {\n\t\t\t\t\t//\tstd::cerr << \"inserting property for \" << Ex(sib) << std::endl;\n\t\t\t\t\tinsert_prop(Ex(sib), theprop);\n\t\t\t\t\t}\n\t\t\t\t++sib;\n\t\t\t\t}\n\t\t\t}\n\t\telse {\n\t\t\tinsert_prop(Ex(st), theprop);\n\t\t\t}\n\t\t}\n\treturn str.str();\n\t}\n\nbool Properties::check_label(const property* p, const std::string& label) const\n\t{\n\treturn true;\n\t}\n\nbool Properties::check_label(const labelled_property* p, const std::string& label) const\n\t{\n\treturn (p->label==label || p->label==\"all\");\n\t}\n\t\nEx_comparator *Properties::create_comparator() const\n\t{\n\treturn new Ex_comparator(*this);\n\t}\n\nvoid Properties::destroy_comparator(Ex_comparator *c) const\n\t{\n\tdelete c;\n\t}\n"
  },
  {
    "path": "core/Props.hh",
    "content": "/*\n\nCadabra: a field-theory motivated computer algebra system.\nCopyright (C) 2001-2014  Kasper Peeters <kasper.peeters@phi-sci.com>\n\nThis program is free software: you can redistribute it and/or\nmodify it under the terms of the GNU General Public License as\n\tpublished by the Free Software Foundation, either version 3 of the\nLicense, or (at your option) any later version.\n\nThis program is distributed in the hope that it will be useful,\nbut WITHOUT ANY WARRANTY; without even the implied warranty of\nMERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU\nGeneral Public License for more details.\n\nYou should have received a copy of the GNU General Public License\nalong with this program.  If not, see <http://www.gnu.org/licenses/>.\n\n*/\n\n// Classes handling storage of property information. Actual property\n// implementations are in the properties directory in separate files.\n\n#pragma once\n\n#include <map>\n#include <list>\n#include <type_traits>\n#include \"Storage.hh\"\n\nnamespace cadabra {\n\n\tclass Properties;\n\tclass Kernel;\n\tclass Accent;\n\tclass LaTeXForm;\n\tclass Ex_comparator;\n\t\n\tclass pattern {\n\t\tpublic:\n\t\t\tpattern();\n\t\t\tpattern(const Ex&);\n\n\t\t\t/// Match a pattern to an expression. If ignore_parent_rel is\n\t\t\t/// true, this will match regardless of the parent_rel of the\n\t\t\t/// top node. If ignore_properties is true, property\n\t\t\t/// information will not be used to match symbols anywhere\n\t\t\t/// (in which case A_{a} and A_{b} will no longer match even\n\t\t\t/// when 'a' and 'b' have the same Indices property, for\n\t\t\t/// example). The latter feature is mostly used to do pattern\n\t\t\t/// matching when the property for which we need it cannot\n\t\t\t/// rely on such child node properties, e.g. Accent; see the\n\t\t\t/// specialisation in get below.\n\t\t\t\n\t\t\tbool match(const Properties&, const Ex::iterator&, bool ignore_parent_rel=false, bool ignore_properties=false) const;\n\t\t\tbool children_wildcard() const;\n\n\t\t\t/// As `match`, but using a comparator object which is\n\t\t\t/// externally provided, so that the caller can use\n\t\t\t/// the found pattern map.\n\t\t\tbool match_ext(const Properties&, const Ex::iterator&, Ex_comparator& comp, bool ignore_parent_rel=false, bool ignore_properties=false) const;\n\n\t\t\tEx obj;\n\t\t};\n\n\t/// Arguments to properties get parsed into a keyval_t structure.\n\n\tclass keyval_t {\n\t\tpublic:\n\t\t\ttypedef std::pair<std::string, Ex> kvpair_t;\n\t\t\ttypedef std::list<kvpair_t>        kvlist_t;\n\n\t\t\ttypedef kvlist_t::const_iterator const_iterator;\n\t\t\ttypedef kvlist_t::iterator       iterator;\n\t\t\ttypedef kvpair_t value_type;\n\n\t\t\tconst_iterator find(const std::string&) const;\n\t\t\titerator       find(const std::string&);\n\t\t\tconst_iterator begin() const;\n\t\t\tconst_iterator end() const;\n\t\t\tvoid           push_back(const kvpair_t&);\n\t\t\tvoid           erase(iterator);\n\n\t\tprivate:\n\t\t\tkvlist_t keyvals;\n\t\t};\n\n\t/// \\ingroup core\n\t///\n\t/// Base class for all properties, handling argument parsing and\n\t/// defining the interface.\n\t///\n\t/// Properties can have arguments. Parsing of these is done in the\n\t/// properties object itself, with the use of some helper functions.\n\t/// Parsing is done by implementing the virtual function\n\t/// property::parse(const Kernel&, keyval_t&). The argument is a\n\t/// container class which represents the arguments passed to the\n\t/// property as key/value pairs keyval_t type.\n\t///\n\t/// Properties will be asked to check that they can be associated to a\n\t/// given pattern through the virtual property::validate(const\n\t/// Properties&, const Ex&) function. The\n\t// default implementation returns true for any pattern.\n\t///\n\t/// FIXME: the above two need to be merged, because parse may need access\n\t/// to the actual pattern tree, and once we are there, we may as well\n\t/// do checking.\n\t/// HOWEVER: in TableauSymmetry.cc:\n\t/// FIXME: we get the wrong pattern in case of a list! We should have\n\t/// been fed each individual item in the list, not the list itself.\n\t///\n\t/// This suggests that we should be calling once for every pattern, but\n\t/// that is wasteful in case we are just parsing arguments. Can we really\n\t/// avoid calling parse for every pattern?\n\t///\n\t/// {A_{m n}, A_{m n p}, A_{m n p q}}::TableauSymmetry(shape={2,1}, indices={0,1,2}).\n\t///\n\t/// leads to a problem, because the property needs to setup its internal\n\t/// structures but also verify that these can match all objects in the\n\t/// same way.\n\t///\n\t///\n\t/// Make all identical properties point to the same property object, so\n\t/// that normal and list properties become pretty much identical.\n\n\n\tclass property {\n\t\tpublic:\n\t\t\tproperty(bool hidden=false);\n\t\t\tvirtual ~property() {};\n\n\t\t\t// Parse the argument tree into key-value pairs. Returns false on error.\n\t\t\tbool                parse_to_keyvals(const Ex&, keyval_t&);\n\n\t\t\t// Use the pre-parsed arguments in key/value form to set parameters.\n\t\t\t// Parses universal arguments by default. Will be called once for\n\t\t\t// every property; assigning a non-list property to multiple patterns\n\t\t\t// still calls this only once.\n\t\t\t// FIXME: failure to call\n\t\t\t// into superclass may lead to problems for labelled properties.\n\t\t\tvirtual bool        parse(Kernel&, keyval_t& keyvals);\n\n\t\t\t// New entry point, which also passes the Ex of the pattern, so that\n\t\t\t// the property itself can inject other properties automatically (e.g.\n\t\t\t// declare an InverseMetric if a Metric is declared).\n\t\t\tvirtual bool        parse(Kernel&, std::shared_ptr<Ex>, keyval_t& keyvals);\n\n\t\t\t// Check whether the property can be associated with the pattern.\n\t\t\t// Throw an error if validation fails. Needs access to all other\n\t\t\t// declared properties so that it can understand what the pattern\n\t\t\t// means (which objects are indices etc.).\n\t\t\t//\n\t\t\t// This is currently also the point where properties are allowed\n\t\t\t// to insert other, related properties (see e.g. `Indices`), and form\n\t\t\t// that reason the Kernel parameter is not const. FIXME: split and\n\t\t\t// then make Kernel const again).\n\t\t\tvirtual void        validate(Kernel&, std::shared_ptr<Ex>) const;\n\n\t\t\t/// Display the property on the stream\n\t\t\t//\t\tvirtual void        display(std::ostream&) const;\n\n\t\t\t/// Generate a LaTeX representation of the property, assuming LaTeX\n\t\t\t/// is in text mode (so it needs dollar symbols to switch to maths).\n\t\t\tvirtual void        latex(std::ostream&) const;\n\n\t\t\tvirtual std::string name() const=0;\n\t\t\tvirtual std::string unnamed_argument() const;\n\n\t\t\t// To compare properties we sometimes need to compare their variables, not only\n\t\t\t// their type. The following function needs to be overridden in all properties\n\t\t\t// for which comparison by type is not sufficient to establish equality.\n\t\t\t//\n\t\t\t//   id_match:    only one of these properties can be registered, but their data is not the same\n\t\t\t//   exact_match: these properties are exactly identical\n\t\t\tenum match_t { no_match, id_match, exact_match };\n\t\t\tvirtual match_t equals(const property *) const;\n\n\t\t\t/// Properties can be hidden because they only make sense to the\n\t\t\t/// system; they will not be printed when the user asks for a list\n\t\t\t/// of properties.\n\t\t\tvoid hidden(bool h);\n\t\t\tbool hidden(void) const;\n\n\t\tprivate:\n\t\t\tbool                parse_one_argument(Ex::iterator arg, keyval_t& keyvals);\n\t\t\tbool hidden_;\n\t\t};\n\n\tclass labelled_property : virtual public property {\n\t\tpublic:\n\t\t\tvirtual bool parse(Kernel&, std::shared_ptr<Ex>, keyval_t&) override;\n\t\t\tstd::string label;\n\t\t};\n\n\t/// Something cannot be both a list property and a normal property at\n\t/// the same time, so we can safely inherit without virtual.\n\n\tclass list_property : public property {\n\t\tpublic:\n\t\t};\n\n\t/// If a property X derives from Inherit<Y>, and get<Y> is called on\n\t/// an object which has an X property (but no Y property), then the\n\t/// get<Y> will look at the non-index child of the object to see if\n\t/// that has a Y property.  FIXME: need to decided what to do if there\n\t/// are more non-index children.\n\n\ttemplate<class T>\n\tclass Inherit : virtual public property {\n\t\tpublic:\n\t\t\tvirtual ~Inherit() {};\n\t\t\tvirtual std::string name() const\n\t\t\t\t{\n//\t\t\t\tT tmp;\n\t\t\t\t// T can be abstract, so we cannot instantiate. Maybe use typeid,\n\t\t\t\t// but then we need to be careful about name mangling.\n\t\t\t\treturn std::string(\"Inherit\");\n\t\t\t\t};\n\t\t};\n\n\t/// PropertyInherit is like Inherit<T> for all properties. This is very\n\t/// generic and almost never really useful.\n\n\tclass PropertyInherit : virtual public property {\n\t\tpublic:\n\t\t\tvirtual std::string name() const\n\t\t\t\t{\n\t\t\t\treturn std::string(\"PropertyInherit\");\n\t\t\t\t};\n\t\t};\n\n\t/// \\ingroup core\n\t///\n\t/// Class holding a collection of properties attached to expressions.\n\t/// Symbols and expressions do not have a default meaning in\n\t/// Cadabra. They get their meaning by attaching properties to\n\t/// them. When the core manipulator calls an algorithm object, it\n\t/// passes an instance of the Properties class along with the\n\t/// expression tree on which to act, so that the algorithm can figure\n\t/// out what the symbols in the expression tree mean.\n\n\tclass Properties {\n\t\tpublic:\n\t\t\t// Registering property types.\n\t\t\tclass registered_property_map_t {\n\t\t\t\tpublic:\n\t\t\t\t\t~registered_property_map_t();\n\n\t\t\t\t\ttypedef std::map<std::string, property* (*)()> internal_property_map_t;\n\t\t\t\t\ttypedef internal_property_map_t::iterator iterator;\n\n\t\t\t\t\tinternal_property_map_t store;\n\t\t\t\t};\n\n\t\t\t/// Registering properties.  When inserting a property or\n\t\t\t/// list_property, ownership of the property gets transferred to\n\t\t\t/// this class.\n\n\t\t\tvoid                          register_property(property* (*)(), const std::string& name);\n\t\t\tregistered_property_map_t     registered_properties;\n\t\t\ttypedef std::pair<pattern *, const property *>  pat_prop_pair_t;\n\n\t\t\t/// We keep two multi-maps: one from the pattern to the property (roughly) and\n\t\t\t/// one from the property to the pattern. These are both multi-maps because\n\t\t\t/// one pattern can have multiple properties assigned to it, and one property can\n\t\t\t/// be assigned to multiple properties.\n\t\t\t///\n\t\t\t/// When we delete properties, we check the pats map to see if the reference count\n\t\t\t/// for that property has dropped to zero.\n\t\t\ttypedef std::multimap<nset_t::iterator, pat_prop_pair_t, nset_it_less>  property_map_t;\n\t\t\ttypedef std::multimap<const property *, pattern *>                      pattern_map_t;\n\n\t\t\t/// Register a property for the indicated Ex. Takes both normal and list\n\t\t\t/// properties and works out which insert calls to make. The property ownership\n\t\t\t/// is transferred to us on using this call.\n\t\t\tstd::string master_insert(Ex proptree, const property *thepropbase);\n\n\t\t\tvoid        clear();\n\n\t\t\t/// The following two maps own the pointers to the properties and patterns stored\n\t\t\t/// in them; use clear() to clean up. Note that pointers can sit in in more than one\n\t\t\t/// entry in this map (when they are pointing to list_property objects, which are\n\t\t\t/// shared between patterns).\n\t\t\tproperty_map_t  props;  // pattern -> property\n\t\t\tpattern_map_t   pats;   // property -> pattern; for list properties, patterns are stored here in order\n\n\t\t\t/// Normal search: given a pattern, get its property if any.\n\t\t\ttemplate<class T> const T*  get(Ex::iterator, bool ignore_parent_rel=false) const;\n\t\t\ttemplate<class T> const T*  get(Ex::iterator, int& serialnum, bool doserial=true, bool ignore_parent_rel=false) const;\n\t\t\t/// Ditto for labelled properties\n\t\t\ttemplate<class T> const T*  get(Ex::iterator, const std::string& label) const;\n\t\t\ttemplate<class T> const T*  get(Ex::iterator, int& serialnum, const std::string& label, bool doserial=true) const;\n\t\t\t/// For list properties: given two patterns, get a common property.\n\t\t\ttemplate<class T> const T*  get(Ex::iterator, Ex::iterator, bool ignore_parent_rel=false) const;\n\t\t\ttemplate<class T> const T*  get(Ex::iterator, Ex::iterator, int&, int&, bool ignore_parent_rel=false) const;\n\n\t\t\t/// General property finder, which will return not only the property but also\n\t\t\t/// the pattern which matched the given node. All 'get' functions above call\n\t\t\t/// this function; all functionality is contained in here.\n\t\t\ttemplate<class T>\n\t\t\tstd::pair<const T*, const pattern *> get_with_pattern(Ex::iterator, int& serialnum,\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tconst std::string& label,\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tbool doserial=true, bool ignore_parent_rel=false) const;\n\n\t\t\ttemplate<class T>\n\t\t\tstd::pair<const T*, const pattern *> get_with_pattern_ext(Ex::iterator, Ex_comparator&, int& serialnum,\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tconst std::string& label,\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tbool doserial=true, bool ignore_parent_rel=false) const;\n\n\t\t\t// Get the outermost node which has the given property attached, i.e. go down through\n\t\t\t// all (if any) nodes which have just inherited the property.\n\t\t\ttemplate<class T> Ex::iterator head(Ex::iterator, bool ignore_parent_rel=false) const;\n\n\t\t\t// Inverse search: given a property type, get a pattern which has this property.\n\t\t\t// When given an iterator, it starts to search in the property\n\t\t\t// map from this particular point. Note: this searches on property type, not exact property.\n\t\t\t//\t\ttemplate<class T>\n\t\t\t//\t\tproperty_map_t::iterator      get_pattern(property_map_t::iterator=props.begin());\n\n\t\t\t// Equivalent search: given a node, get a pattern of equivalents.\n\t\t\t//\t\tproperty_map_t::iterator      get_equivalent(Ex::iterator,\n\t\t\t//\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t  property_map_t::iterator=props.begin());\n\n\t\tprivate:\n\t\t\t// Insert a property. Do not use this directly, use the public\n\t\t\t// interface `master_insert` instead.\n\t\t\tvoid insert_prop(const Ex&, const property *);\n\t\t\tvoid insert_list_prop(const std::vector<Ex>&, const list_property *);\n\t\t\tbool check_label(const property *, const std::string&) const;\n\t\t\tbool check_label(const labelled_property *, const std::string&) const;\t\t\t\n\t\t\t// Search through pointers\n\t\t\tbool has(const property *, Ex::iterator);\n\t\t\t// Find serial number of a pattern in a given list property\n\t\t\tint  serial_number(const property *, const pattern *) const;\n\t\t\tEx_comparator *create_comparator() const;\n\t\t\tvoid           destroy_comparator(Ex_comparator *) const;\t\t\t\n\t\t};\n\n\ttemplate<class T>\n\tconst T* Properties::get(Ex::iterator it, bool ignore_parent_rel) const\n\t\t{\n\t\tint tmp;\n\t\treturn get<T>(it, tmp, false, ignore_parent_rel);\n\t\t}\n\n\ttemplate<class T>\n\tconst T* Properties::get(Ex::iterator it, int& serialnum, bool doserial, bool ignore_parent_rel) const\n\t\t{\n\t\tauto ret = get_with_pattern<T>(it, serialnum, \"\", doserial, ignore_parent_rel);\n\t\treturn ret.first;\n\t\t}\n\n\ttemplate<class T>\n\tstd::pair<const T*, const pattern *> Properties::get_with_pattern(Ex::iterator it, int& serialnum, const std::string& label,\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tbool doserial, bool ignore_parent_rel) const\n\t\t{\n\t\tEx_comparator *compptr = create_comparator();\n\t\t// FIXME: catch and rethrow all exceptions so we do not leak memory\n\t\tauto ret = get_with_pattern_ext<T>(it, *compptr, serialnum, label, doserial, ignore_parent_rel);\n\t\tdestroy_comparator(compptr);\n\t\treturn ret;\n\t\t}\n\n\ttemplate<class T>\n\tstd::pair<const T*, const pattern *> Properties::get_with_pattern_ext(Ex::iterator it, Ex_comparator& comp,\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t int& serialnum, const std::string& label,\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t bool doserial, bool ignore_parent_rel) const\n\t\t{\n\t\tstd::pair<const T*, const pattern *> ret;\n\t\tret.first=0;\n\t\tret.second=0;\n\t\tbool inherits=false;\n\n\t\t//std::cerr << *it->name_only() << std::endl;\n\t\t//\tstd::cerr << props.size() << std::endl;\n\t\tstd::pair<property_map_t::const_iterator, property_map_t::const_iterator> pit=props.equal_range(it->name_only());\n\n\t\t// First look for properties of the node itself. Go through the loop twice:\n\t\t// once looking for patterns which do not have wildcards, and then looking\n\t\t// for wildcard patterns.\n\t\tbool wildcards=false;\n\n\t\t// For some properties, we cannot lookup properties lower down the\n\t\t// tree, because it would lead to an endless recursion (and it would\n\t\t// not make sense anyway). At the moment, this is only for Accent.\n\t\tbool ignore_properties=false;\n\t\tif(std::is_same<T, Accent>::value)\n\t\t\tignore_properties=true;\n\t\t\n\t\tfor(;;) {\n\t\t\tproperty_map_t::const_iterator walk=pit.first;\n\t\t\twhile(walk!=pit.second) {\n\t\t\t\tif(wildcards==(*walk).second.first->children_wildcard()) {\n\t\t\t\t\t// First check property type; a dynamic cast is much faster than a pattern match.\n\t\t\t\t\tret.first=dynamic_cast<const T *>((*walk).second.second);\n\t\t\t\t\tif(ret.first) {\n\t\t\t\t\t\tif((*walk).second.first->match_ext(*this, it, comp, ignore_parent_rel, ignore_properties)) {\n\t\t\t\t\t\t\tret.second=(*walk).second.first;\n\t\t\t\t\t\t\tif(!check_label(ret.first, label)) \n\t\t\t\t\t\t\t\tret.first=0;\n\t\t\t\t\t\t\telse {\n\t\t\t\t\t\t\t\tif(doserial) \n\t\t\t\t\t\t\t\t\tserialnum=serial_number( (*walk).second.second, (*walk).second.first );\n\t\t\t\t\t\t\t\tbreak;\n\t\t\t\t\t\t\t\t}\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\t}\n\t\t\t\t\tret.first=0;\n\t\t\t\t\tif(dynamic_cast<const PropertyInherit *>((*walk).second.second))\n\t\t\t\t\t\tinherits=true;\n\t\t\t\t\telse if(dynamic_cast<const Inherit<T> *>((*walk).second.second))\n\t\t\t\t\t\tinherits=true;\n\t\t\t\t\t}\n\t\t\t\t++walk;\n\t\t\t\t}\n\t\t\tif(!wildcards && !ret.first) {\n\t\t\t\t//\t\t\tstd::cerr << \"not yet found, switching to wildcards\" << std::endl;\n\t\t\t\twildcards=true;\n\t\t\t\t}\n\t\t\telse break;\n\t\t\t}\n\n\t\t// Do not walk down the tree if the property cannot be passed up the tree.\n\t\t// FIXME: see issue/259.\n\t\tif(std::is_same<T, LaTeXForm>::value)\n\t\t\tinherits=false;\n\t\t\n\t\t// If no property was found, figure out whether a property is inherited from a child node.\n\t\tif(!ret.first && inherits) {\n\t\t\t//\t\tstd::cout << \"no match but perhaps inheritance?\" << std::endl;\n\t\t\tEx::sibling_iterator sib=it.begin();\n\t\t\twhile(sib!=it.end()) {\n\t\t\t\tstd::pair<const T*, const pattern *> tmp=get_with_pattern<T>((Ex::iterator)(sib), serialnum, label, doserial);\n\t\t\t\tif(tmp.first) {\n\t\t\t\t\tret=tmp;\n\t\t\t\t\tbreak;\n\t\t\t\t\t}\n\t\t\t\t++sib;\n\t\t\t\t}\n\t\t\t}\n\n\t\t//\tstd::cout << ret << std::endl;\n\t\treturn ret;\n\t\t}\n\n\ttemplate<class T>\n\tconst T* Properties::get(Ex::iterator it, const std::string& label) const\n\t\t{\n\t\tint tmp;\n\t\treturn get<T>(it, tmp, label, false);\n\t\t}\n\n\ttemplate<class T>\n\tconst T* Properties::get(Ex::iterator it, int& serialnum, const std::string& label, bool doserial) const\n\t\t{\n\t\tauto ret=get_with_pattern<T>(it, serialnum, label, doserial, false);\n\t\treturn ret.first;\n\t\t}\n\n\ttemplate<class T>\n\tconst T* Properties::get(Ex::iterator it1, Ex::iterator it2, bool ignore_parent_rel) const\n\t\t{\n\t\tint tmp1, tmp2;\n\t\treturn get<T>(it1,it2,tmp1,tmp2, ignore_parent_rel);\n\t\t}\n\n\ttemplate<class T>\n\tconst T* Properties::get(Ex::iterator it1, Ex::iterator it2, int& serialnum1, int& serialnum2, bool ignore_parent_rel) const\n\t\t{\n\t\tconst T* ret1=0;\n\t\tconst T* ret2=0;\n\t\tbool found=false;\n\n\t\tbool inherits1=false, inherits2=false;\n\t\tstd::pair<property_map_t::const_iterator, property_map_t::const_iterator> pit1=props.equal_range(it1->name_only());\n\t\tstd::pair<property_map_t::const_iterator, property_map_t::const_iterator> pit2=props.equal_range(it2->name_only());\n\n\t\tproperty_map_t::const_iterator walk1=pit1.first;\n\t\twhile(walk1!=pit1.second) {\n\t\t\tif((*walk1).second.first->match(*this, it1, ignore_parent_rel)) { // match for object 1 found\n\t\t\t\tret1=dynamic_cast<const T *>((*walk1).second.second);\n\t\t\t\tif(ret1) { // property of the right type found for object 1\n\t\t\t\t\tproperty_map_t::const_iterator walk2=pit2.first;\n\t\t\t\t\twhile(walk2!=pit2.second) {\n\t\t\t\t\t\tif((*walk2).second.first->match(*this, it2, ignore_parent_rel)) { // match for object 2 found\n\t\t\t\t\t\t\tret2=dynamic_cast<const T *>((*walk2).second.second);\n\t\t\t\t\t\t\tif(ret2) { // property of the right type found for object 2\n\t\t\t\t\t\t\t\tif(ret1==ret2 && walk1!=walk2) { // accept if properties are the same and patterns are not\n\t\t\t\t\t\t\t\t\tserialnum1=serial_number( (*walk1).second.second, (*walk1).second.first );\n\t\t\t\t\t\t\t\t\tserialnum2=serial_number( (*walk2).second.second, (*walk2).second.first );\n\t\t\t\t\t\t\t\t\tfound=true;\n\t\t\t\t\t\t\t\t\tgoto done;\n\t\t\t\t\t\t\t\t\t}\n\t\t\t\t\t\t\t\t}\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\tif(dynamic_cast<const PropertyInherit *>((*walk2).second.second))\n\t\t\t\t\t\t\tinherits2=true;\n\t\t\t\t\t\t++walk2;\n\t\t\t\t\t\t}\n\t\t\t\t\t}\n\t\t\t\tif(dynamic_cast<const PropertyInherit *>((*walk1).second.second))\n\t\t\t\t\tinherits1=true;\n\t\t\t\t}\n\t\t\t++walk1;\n\t\t\t}\n\n\t\t// If no property was found, figure out whether a property is inherited from a child node.\n\t\tif(!found && (inherits1 || inherits2)) {\n\t\t\tEx::sibling_iterator sib1, sib2;\n\t\t\tif(inherits1) sib1=it1.begin();\n\t\t\telse          sib1=it1;\n\t\t\tbool keepgoing1=true;\n\t\t\tdo {    // 1\n\t\t\t\tbool keepgoing2=true;\n\t\t\t\tif(inherits2) sib2=it2.begin();\n\t\t\t\telse          sib2=it2;\n\t\t\t\tdo { // 2\n\t\t\t\t\tconst T* tmp=get<T>((Ex::iterator)(sib1), (Ex::iterator)(sib2), serialnum1, serialnum2, ignore_parent_rel);\n\t\t\t\t\tif(tmp) {\n\t\t\t\t\t\tret1=tmp;\n\t\t\t\t\t\tfound=true;\n\t\t\t\t\t\tgoto done;\n\t\t\t\t\t\t}\n\t\t\t\t\tif(!inherits2 || ++sib2==it2.end())\n\t\t\t\t\t\tkeepgoing2=false;\n\t\t\t\t\t}\n\t\t\t\twhile(keepgoing2);\n\t\t\t\tif(!inherits1 || ++sib1==it1.end())\n\t\t\t\t\tkeepgoing1=false;\n\t\t\t\t}\n\t\t\twhile(keepgoing1);\n\t\t\t}\n\ndone:\n\t\tif(!found) ret1=0;\n\t\treturn ret1;\n\t\t}\n\n\ttemplate<class T>\n\tEx::iterator Properties::head(Ex::iterator it, bool ignore_parent_rel) const\n\t\t{\n\t\tEx::iterator dn=it;\n\t\tfor(;;) {\n\t\t\tif(get<PropertyInherit>(dn, ignore_parent_rel)) {\n\t\t\t\tdn=dn.begin();\n\t\t\t\t}\n\t\t\telse {\n\t\t\t\tassert(get<T>(dn));\n\t\t\t\tbreak;\n\t\t\t\t}\n\t\t\t}\n\t\treturn dn;\n\t\t}\n\n\t}\n"
  },
  {
    "path": "core/PythonException.cc",
    "content": "\n#include <pybind11/pybind11.h>\n#include <stdexcept>\n#include \"PythonException.hh\"\n\nstd::string parse_python_exception()\n\t{\n\tPyObject *type_ptr = NULL, *value_ptr = NULL, *traceback_ptr = NULL;\n\n\t// Fetch the exception info from the Python C API\n\tPyErr_Fetch(&type_ptr, &value_ptr, &traceback_ptr);\n\n\tstd::string ret(\"Unfetchable Python error\");\n\tif(type_ptr != NULL) {\n\t\tpybind11::handle h_type(type_ptr);\n\t\tpybind11::str    type_pstr(h_type);\n\t\ttry {\n\t\t\tret = type_pstr.cast<std::string>();\n\t\t\t}\n\t\tcatch(const pybind11::value_error& e) {\n\t\t\tret = \"Unknown exception type\";\n\t\t\t}\n\t\t}\n\tif(value_ptr) {\n\t\tpybind11::handle h_val(value_ptr);\n\t\tpybind11::str    a(h_val);\n\t\ttry {\n\t\t\tret += a.cast<std::string>();\n\t\t\t}\n\t\tcatch(const pybind11::value_error &e) {\n\t\t\tret += \": Unparseable Python error: \";\n\t\t\t}\n\t\t}\n\n\t// Parse lines from the traceback using the Python traceback module\n\tif(traceback_ptr) {\n\t\tpybind11::handle h_tb(traceback_ptr);\n\t\t// Load the traceback module and the format_tb function\n\t\tpybind11::object tb(pybind11::module::import(\"traceback\"));\n\t\tpybind11::object fmt_tb(tb.attr(\"format_tb\"));\n\t\t// Call format_tb to get a list of traceback strings\n\t\tpybind11::object tb_list(fmt_tb(h_tb));\n\t\t// Extract the string, check the extraction, and fallback in necessary\n\t\ttry {\n\t\t\tfor(auto &s: tb_list)\n\t\t\t\tret += s.cast<std::string>();\n\t\t\t}\n\t\tcatch(const pybind11::value_error &e) {\n\t\t\tret += \": Unparseable Python traceback\";\n\t\t\t}\n\t\t}\n\n\treturn ret;\n\t}\n"
  },
  {
    "path": "core/PythonException.hh",
    "content": "\n#pragma once\n#include <string>\n\nstd::string parse_python_exception();\n\n//class PythonException;\n//\n//class PythonNameError : public PythonException;\n//class PythonTypeError : public PythonTypeError;\n"
  },
  {
    "path": "core/ReservedNode.cc",
    "content": "\n#include \"ReservedNode.hh\"\n\nusing namespace cadabra;\n\nvisit::ReservedNode::ReservedNode(const Kernel &k, Ex &e, Ex::iterator i)\n   : ExManip(k, e), top(i)\n\t{\n\t}\n\nEx::iterator visit::ReservedNode::node() const\n\t{\n\treturn top;\n\t}  \n"
  },
  {
    "path": "core/ReservedNode.hh",
    "content": "\n#pragma once\n\n#include \"ExManip.hh\"\n\nnamespace cadabra {\n\n\tnamespace visit {\n\t\n\t\tclass ReservedNode : public ExManip {\n\t\t\tpublic:\n\t\t\t\tReservedNode(const Kernel&, Ex&, Ex::iterator);\n\n\t\t\t\tEx::iterator node() const;\n\t\t\t\t\n\t\t\tprotected:\n\t\t\t\tEx::iterator   top;\n\t\t};\n\n\t}\n\n}\n\t\n"
  },
  {
    "path": "core/Stopwatch.cc",
    "content": "/*\n\nCadabra: a field-theory motivated computer algebra system.\nCopyright (C) 2001-2018  Kasper Peeters <kasper.peeters@aei.mpg.de>\n\nThis program is free software: you can redistribute it and/or\nmodify it under the terms of the GNU General Public License as\n\tpublished by the Free Software Foundation, either version 3 of the\nLicense, or (at your option) any later version.\n\nThis program is distributed in the hope that it will be useful,\nbut WITHOUT ANY WARRANTY; without even the implied warranty of\nMERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU\nGeneral Public License for more details.\n\nYou should have received a copy of the GNU General Public License\n\talong with this program.  If not, see <http://www.gnu.org/licenses/>.\n\n*/\n\n#include <ratio>\n#include \"Stopwatch.hh\"\n\nStopwatch::Stopwatch()\n\t: elapsed_(0), stopped_(true)\n\t{\n\t}\n\nvoid Stopwatch::reset()\n\t{\n\telapsed_=0;\n\tstart_=clock::now();\n\t}\n\nvoid Stopwatch::start()\n\t{\n\tstopped_=false;\n\tstart_=clock::now();\n\t}\n\nvoid Stopwatch::stop()\n\t{\n\tstopped_=true;\n\tcheckpoint_();\n\t}\n\nbool Stopwatch::stopped() const\n\t{\n\treturn stopped_;\n\t}\n\nvoid Stopwatch::checkpoint_() const\n\t{\n\tusing namespace std::chrono;\n\tclock::time_point stop_ = clock::now();\n\telapsed_ += duration_cast<duration<long, std::micro>>(stop_ - start_).count();\n\tstart_ = stop_;\n\t}\n\nlong Stopwatch::seconds() const\n\t{\n\tif(!stopped_) checkpoint_();\n\treturn elapsed_ / s_to_us;\n\t}\n\nlong Stopwatch::useconds() const\n\t{\n\tif(!stopped_) checkpoint_();\n\treturn elapsed_ % s_to_us;\n\t}\n\nStopwatch& Stopwatch::operator/=(int num)\n\t{\n\telapsed_ /= num;\n\treturn *this;\n\t}\n\nstd::ostream& operator<<(std::ostream& lhs, const Stopwatch& rhs)\n\t{\n\treturn lhs << rhs.seconds() << \"s and \" << rhs.useconds() << \"us\";\n\t}\n\n"
  },
  {
    "path": "core/Stopwatch.hh",
    "content": "/*\n\nCadabra: a field-theory motivated computer algebra system.\nCopyright (C) 2001-2011  Kasper Peeters <kasper.peeters@aei.mpg.de>\n\nThis program is free software: you can redistribute it and/or\nmodify it under the terms of the GNU General Public License as\n\tpublished by the Free Software Foundation, either version 3 of the\nLicense, or (at your option) any later version.\n\nThis program is distributed in the hope that it will be useful,\nbut WITHOUT ANY WARRANTY; without even the implied warranty of\nMERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU\nGeneral Public License for more details.\n\nYou should have received a copy of the GNU General Public License\n\talong with this program.  If not, see <http://www.gnu.org/licenses/>.\n\n*/\n\n#ifndef stopwatch_hh__\n#define stopwatch_hh__\n\n#include <chrono>\n#include <iosfwd>\n#include <iostream>\n\n/// \\class Stopwatch\n/// \\ingroup Client-Server\n///\n/// The Stopwach class provides a simple interace to allow\n/// timing function calls etc... It is possible to stop\n/// the stopwatch for an indefinite amount of time without\n/// losing the current elapsed time period, allowing it\n/// to be used to calculate the actual amount of time\n/// a function spends performing a task without taking\n/// into account e.g. time spent being blocked by a mutex.\n/// The class is exported to python in the cadabra2\n/// module as Stopwatch.\n///\n///\n/// Example C++ usage:\n///\n/// ~~~~~~~{.cc}\n/// #include <iostream>\n/// #include <vector>\n/// #include \"Stopwatch.hh\"\n///\n/// void do_other_stuff() { std::cout << \"Doing other stuff\\n\"; }\n///\n/// int main()\n/// {\n///   const int n = 1000;\n///   std::vector<int> v;\n///   Stopwatch s;\n///\n///   s.start();\n///   for (unsigned int i = 0; i < n; ++i)\n///     v.push_back(i);\n///   s.stop();\n///   do_other_stuff();\n///   s.start();\n///   for (unsigned int i = n; i > 0; --i)\n///     v.push_back(i);\n///   s.stop();\n///   std::cout << \"Total time spent pushing to vector and not spent doing other stuff: \" << s << '\\n';\n///\n///   s.reset();\n///   s.start();\n///   do_other_stuff();\n///   s.stop();\n///   std::cout << \"Doing other stuff takes \" << s.useconds() << \"us\\n\"; //Assuming do_other_stuff() takes < 1s\n///   return 0;\n/// }\n/// ~~~~~~~\n///\n/// Example python usage:\n///\n/// ~~~~~~~{.py}\n/// from cadabra2 import Stopwatch\n///\n/// def do_other_stuff():\n///   print(\"Doing other stuff\")\n///\n/// n = 1000\n/// v = []\n/// s = Stopwatch()\n///\n/// s.start()\n/// for i in range(n):\n///   v += [i]\n/// s.stop()\n/// do_other_stuff()\n/// s.start()\n/// for i in range(n, 0, -1):\n///   v += [i]\n/// s.stop()\n/// print(\"Total time spent pushing to vector and not spent doing other stuff: {}\".format(s))\n///\n/// s.reset()\n/// s.start()\n/// do_other_stuff()\n/// s.stop()\n/// print(\"Doing other stuff takes {}us\".format(s.useconds())) #Assuming do_other_stuff() takes < 1s\n/// ~~~~~~~\n\nclass Stopwatch {\n\tpublic:\n\t\tStopwatch();\n\n\t\ttypedef std::chrono::steady_clock clock;\n\n\t\t/// Reset to no-time-elapsed.\n\t\tvoid reset();\n\t\t/// Continue timing (does not reset).\n\t\tvoid start();\n\t\t/// Stop timing.\n\t\tvoid stop();\n\t\t/// Number of seconds elapsed.\n\t\tlong seconds() const;\n\t\t/// Number of micro-seconds elapsed (needs to be added to 'seconds').\n\t\tlong useconds() const;\n\t\t/// Is the stopwatch currently timing?\n\t\tbool stopped() const;\n\n\t\tfriend std::ostream& operator<<(std::ostream&, const Stopwatch&);\n\n\t\tStopwatch& operator/=(int);\n\n\tprivate:\n\t\tvoid checkpoint_() const;\n\n\t\tmutable clock::time_point start_;\n\t\tmutable long              elapsed_;\n\t\tbool                      stopped_;\n\n\t\tstatic const long s_to_us = 1000000L;\n\t};\n\n/// Print human-readable representation of the time elapsed.\nstd::ostream& operator<<(std::ostream&, const Stopwatch&);\n\n#endif\n"
  },
  {
    "path": "core/Storage.cc",
    "content": "/*\n\nCadabra: a field-theory motivated computer algebra system.\nCopyright (C) 2001-2014  Kasper Peeters <kasper.peeters@phi-sci.com>\n\nThis program is free software: you can redistribute it and/or\nmodify it under the terms of the GNU General Public License as\npublished by the Free Software Foundation, either version 3 of the\nLicense, or (at your option) any later version.\n\nThis program is distributed in the hope that it will be useful,\nbut WITHOUT ANY WARRANTY; without even the implied warranty of\nMERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU\nGeneral Public License for more details.\n\nYou should have received a copy of the GNU General Public License\n\talong with this program.  If not, see <http://www.gnu.org/licenses/>.\n\n*/\n\n#include \"Config.hh\"\n#ifdef mimalloc_FOUND\n  #include \"mimalloc-new-delete.h\"\n#endif\n\n#include \"Storage.hh\"\n#include \"Combinatorics.hh\"\n#include \"Compare.hh\"\n#include \"Exceptions.hh\"\n#include <iomanip>\n#include <sstream>\n#include <locale>\n#include <codecvt>\n#include \"NTensor.hh\"\n\n#include <boost/functional/hash.hpp>\n\n//#define DEBUG 1\n\nnamespace cadabra {\n\n\tnset_t    name_set;\n\trset_t    rat_set;\n\n   // Simple pool for memory allocation.\n\tstd::pmr::unsynchronized_pool_resource                pool;\n\t\n\tlong to_long(multiplier_t mul)\n\t\t{\n\t\tif(!mul.is_rational())\n\t\t\tthrow ConsistencyException(\"Cannot convert double to long.\");\n\t\t\n\t\treturn mul.get_rational().get_num().get_si();\n\t\t}\n\n\tdouble to_double(multiplier_t mul)\n\t\t{\n\t\tif(mul.is_rational())\n\t\t\treturn mul.get_rational().get_d();\n\t\telse\n\t\t\treturn mul.get_double();\n\t\t}\n\n\tstd::string to_string(long num)\n\t\t{\n\t\tstd::ostringstream str;\n\t\tstr << num;\n\t\treturn str.str();\n\t\t}\n\n\t// Expression constructor/destructor members.\n\n\tEx::Ex()\n\t\t: cdb_tree(&pool)\n\t\t, state_(result_t::l_no_action)\n\t\t{\n\t\t}\n\n\tEx::Ex(cdb_tree::iterator it)\n\t\t: cdb_tree(it, &pool)\n\t\t, state_(result_t::l_no_action)\n\t\t{\n\t\t}\n\n\tEx::Ex(const str_node& x)\n\t\t: cdb_tree(x, &pool)\n\t\t, state_(result_t::l_no_action)\n\t\t{\n\t\t}\n\n\tEx::Ex(const Ex& other)\n\t\t: std::enable_shared_from_this<Ex>(other)\n\t\t, cdb_tree(other, &pool)\n\t\t, state_(result_t::l_no_action)\n\t\t{\n\t\t//\tstd::cout << \"Ex copy constructor\" << std::endl;\n\t\t}\n\n\tEx& Ex::operator=(Ex other)\n\t\t{\n\t\tstd::swap(static_cast<cdb_tree&>(*this),\n\t\t\t\t\t static_cast<cdb_tree&>(other));\n\t\tstd::swap((*this).state_, other.state_);\n\t\tstd::swap((*this).history, other.history);\n\t\tstd::swap((*this).terms, other.terms);\n\n\t\treturn *this;\n\t\t}\n\n\tEx::Ex(const std::string& str)\n\t\t: cdb_tree(&pool)\n\t\t, state_(result_t::l_no_action)\n\t\t{\n\t\tset_head(str_node(str));\n\t\t}\n\n\tEx::Ex(int val)\n\t\t: cdb_tree(&pool)\n\t\t, state_(result_t::l_no_action)\n\t\t{\n\t\tset_head(str_node(\"1\"));\n\t\tmultiply(begin()->multiplier, val);\n\t\t}\n\n\tEx::Ex(int numer, int denom)\n\t\t: cdb_tree(&pool)\n\t\t, state_(result_t::l_no_action)\n\t\t{\n\t\tset_head(str_node(\"1\"));\n\t\tmultiply(begin()->multiplier, mpq_class(numer, denom));\n\t\t}\n\n\tEx::Ex(double val)\n\t\t: cdb_tree(&pool)\n\t\t, state_(result_t::l_no_action)\n\t\t{\n\t\tstd::ostringstream str;\n\t\tstr << val;\n\t\tset_head(str_node(str.str()));\n\t\t}\n\n\n\t\n\tEx::result_t Ex::state() const\n\t\t{\n\t\treturn state_;\n\t\t}\n\n\tvoid Ex::update_state(Ex::result_t newstate)\n\t\t{\n\t\tswitch(newstate) {\n\t\t\tcase Ex::result_t::l_applied:\n\t\t\tcase Ex::result_t::l_applied_no_new_dummies:\n\t\t\tcase Ex::result_t::l_cached:\n\t\t\tcase Ex::result_t::l_checkpointed:\n\t\t\t\t// If we are in error state, preserve this.\n\t\t\t\tif(state_!=Ex::result_t::l_error)\n\t\t\t\t\tstate_=newstate;\n\t\t\t\tbreak;\n\t\t\tcase Ex::result_t::l_error:\n\t\t\t\t// Changing to error state is always possible,\n\t\t\t\t// but it requires a reset_state to get out again.\n\t\t\t\tstate_=newstate;\n\t\t\t\tbreak;\n\t\t\tcase Ex::result_t::l_no_action:\n\t\t\t\tbreak;\n\t\t\t}\n\t\t}\n\n\tvoid Ex::reset_state()\n\t\t{\n\t\t// Always use reset_state to clear error states; you cannot\n\t\t// clear error states with update_state.\n\t\tstate_=Ex::result_t::l_checkpointed;\n\t\t}\n\n\tbool Ex::changed_state()\n\t\t{\n\t\tbool ret=false;\n\t\tif(state_==result_t::l_checkpointed || state_==result_t::l_applied) ret=true;\n\t\tstate_=result_t::l_no_action;\n\t\treturn ret;\n\t\t}\n\n\tbool Ex::is_rational() const\n\t\t{\n\t\tif(begin()!=end())\n\t\t\tif(begin()->is_rational())\n\t\t\t\treturn true;\n\t\treturn false;\n\t\t}\n\n\tmultiplier_t Ex::to_rational() const\n\t\t{\n\t\tif(!is_rational())\n\t\t\tthrow InternalError(\"Called to_rational() on non-rational Ex\");\n\t\treturn *(begin()->multiplier);\n\t\t}\n\n\tbool Ex::is_integer() const\n\t\t{\n\t\tif(begin()!=end())\n\t\t\tif(begin()->is_integer())\n\t\t\t\treturn true;\n\t\treturn false;\n\t\t}\n\n\tlong Ex::to_integer() const\n\t\t{\n\t\tif(!is_integer())\n\t\t\tthrow InternalError(\"Called to_integer() on non-integer Ex\");\n\t\treturn to_long(*(begin()->multiplier));\n\t\t}\n\n\tbool Ex::is_string() const\n\t\t{\n\t\titerator it=begin();\n\t\tif(it != end()) {\n\t\t\tmultiplier_t mult = *it->multiplier;\n\t\t\t++it;\n\t\t\tif(it==end() && mult==1)\n\t\t\t\treturn true;\n\t\t\t}\n\t\treturn false;\n\t\t}\n\n\tbool Ex::equals(const std::string& str) const\n\t\t{\n\t\tif(is_string())\n\t\t\treturn (*begin()->name == str);\n\t\tthrow ConsistencyException(\"Expected string, found maths expression.\");\n\t\t}\n\n\tbool Ex::is_empty() const\n\t\t{\n\t\treturn begin()==end();\n\t\t}\n\n\tstd::ostream& Ex::print_python(std::ostream& str, Ex::iterator it)\n\t\t{\n\t\tstd::string name(*(*it).name);\n\t\tstd::string res;\n\t\tif(*it->multiplier!=1)\n\t\t\tstr << *it->multiplier;\n\n\t\tfor(unsigned int i=0; i<name.size(); ++i) {\n\t\t\tif(name[i]=='#')       res+=\"\\\\#\";\n\t\t\t//\t\telse if(name[i]=='\\\\') res+=\"\\\\backslash{}\";\n\t\t\telse                   res+=name[i];\n\t\t\t}\n\t\tif(res!=\"1\")\n\t\t\tstr << res;\n\n\t\tEx::sibling_iterator beg=it.begin();\n\t\tEx::sibling_iterator fin=it.end();\n\t\tstr_node::bracket_t    current_bracket=str_node::b_invalid;\n\t\tstr_node::parent_rel_t current_parent_rel=str_node::p_invalid;\n\n\t\twhile(beg!=fin) {\n\t\t\tif(beg==it.begin() || current_parent_rel!=(*beg).fl.parent_rel) {\n\t\t\t\tswitch((*beg).fl.parent_rel) {\n\t\t\t\t\tcase str_node::p_super:\n\t\t\t\t\t\tstr << \"^\";\n\t\t\t\t\t\tbreak;\n\t\t\t\t\tcase str_node::p_sub:\n\t\t\t\t\t\tstr << \"_\";\n\t\t\t\t\t\tbreak;\n\t\t\t\t\tcase str_node::p_property:\n\t\t\t\t\t\tstr << \"$\";\n\t\t\t\t\t\tbreak;\n\t\t\t\t\tcase str_node::p_exponent:\n\t\t\t\t\t\tstr << \"&\";\n\t\t\t\t\t\tbreak;\n\t\t\t\t\tdefault:\n\t\t\t\t\t\tbreak;\n\t\t\t\t\t}\n\t\t\t\tcurrent_parent_rel=(*beg).fl.parent_rel;\n\t\t\t\t}\n\t\t\tif(beg==it.begin() || current_bracket!=(*beg).fl.bracket || current_parent_rel!=(*beg).fl.parent_rel) {\n\t\t\t\tswitch((*beg).fl.bracket) {\n\t\t\t\t\tcase str_node::b_round:\n\t\t\t\t\t\tstr << \"(\";\n\t\t\t\t\t\tbreak;\n\t\t\t\t\tcase str_node::b_square:\n\t\t\t\t\t\tstr << \"[\";\n\t\t\t\t\t\tbreak;\n\t\t\t\t\tcase str_node::b_curly:\n\t\t\t\t\t\tstr << \"{\";\n\t\t\t\t\t\tbreak;\n\t\t\t\t\tcase str_node::b_pointy:\n\t\t\t\t\t\tstr << \"<\";\n\t\t\t\t\t\tbreak;\n\t\t\t\t\tcase str_node::b_none: {\n\t\t\t\t\t\tif((*beg).fl.parent_rel==str_node::p_none) str << \"(\";\n\t\t\t\t\t\telse                                       str << \"{\";\n\t\t\t\t\t\t}\n\t\t\t\t\tbreak;\n\t\t\t\t\tdefault:\n\t\t\t\t\t\tbreak;\n\t\t\t\t\t}\n\t\t\t\tcurrent_bracket=(*beg).fl.bracket;\n\t\t\t\t}\n\n\t\t\tprint_python(str, beg);\n\n\t\t\tauto nxt=beg;\n\t\t\t++nxt;\n\t\t\tif(nxt!=fin) {\n\t\t\t\tif((*beg).fl.parent_rel!=str_node::p_none)\n\t\t\t\t\tstr << \" \";\n\t\t\t\t}\n\t\t\tif(nxt==fin || (*nxt).fl.bracket!=(*beg).fl.bracket || (*beg).fl.parent_rel==str_node::p_none) {\n\t\t\t\tcurrent_bracket=str_node::b_invalid;\n\t\t\t\tcurrent_parent_rel=str_node::p_invalid;\n\t\t\t\tswitch((*beg).fl.bracket) {\n\t\t\t\t\tcase str_node::b_round:\n\t\t\t\t\t\tstr << \")\";\n\t\t\t\t\t\tbreak;\n\t\t\t\t\tcase str_node::b_square:\n\t\t\t\t\t\tstr << \"]\";\n\t\t\t\t\t\tbreak;\n\t\t\t\t\tcase str_node::b_curly:\n\t\t\t\t\t\tstr << \"}\";\n\t\t\t\t\t\tbreak;\n\t\t\t\t\tcase str_node::b_pointy:\n\t\t\t\t\t\tstr << \">\";\n\t\t\t\t\t\tbreak;\n\t\t\t\t\tcase str_node::b_none: {\n\t\t\t\t\t\tif((*beg).fl.parent_rel==str_node::p_none) str << \")\";\n\t\t\t\t\t\telse                                       str << \"}\";\n\t\t\t\t\t\t}\n\t\t\t\t\tbreak;\n\t\t\t\t\tdefault:\n\t\t\t\t\t\tbreak;\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t++beg;\n\t\t\t}\n\n\t\treturn str;\n\t\t}\n\n\tstd::ostream& Ex::print_repr(std::ostream& str, Ex::iterator it) const\n\t\t{\n\t\tstr << *it->name;\n\t\tsibling_iterator sib=it.begin();\n\t\twhile(sib!=it.end()) {\n\t\t\tprint_repr(str, sib);\n\t\t\t++sib;\n\t\t\t}\n\t\treturn str;\n\t\t}\n\n\tstd::ostream& Ex::print_recursive_treeform(std::ostream& str, Ex::iterator it)\n\t\t{\n\t\tunsigned int num=1;\n\t\tswitch((*it).fl.parent_rel) {\n\t\t\tcase str_node::p_super:\n\t\t\t\tstr << \"^\";\n\t\t\t\tbreak;\n\t\t\tcase str_node::p_sub:\n\t\t\t\tstr << \"_\";\n\t\t\t\tbreak;\n\t\t\tcase str_node::p_property:\n\t\t\t\tstr << \"$\";\n\t\t\t\tbreak;\n\t\t\tcase str_node::p_exponent:\n\t\t\t\tstr << \"&\";\n\t\t\t\tbreak;\n\t\t\tdefault:\n\t\t\t\tbreak;\n\t\t\t}\n\t\treturn print_recursive_treeform(str, it, num);\n\t\t}\n\n\tstd::ostream& Ex::print_entire_tree(std::ostream& str) const\n\t\t{\n\t\tsibling_iterator sib=begin();\n\t\tunsigned int num=1;\n\t\twhile(sib!=end()) {\n\t\t\tprint_recursive_treeform(str, sib, num);\n\t\t\t++sib;\n\t\t\t++num;\n\t\t\t}\n\t\treturn str;\n\t\t}\n\n\tstd::ostream& Ex::print_recursive_treeform(std::ostream& str, Ex::iterator it, unsigned int& num)\n\t\t{\n\t\tbool compact_tree=getenv(\"CADABRA_COMPACT_TREE\");\n\n\t\tEx::sibling_iterator beg=it.begin();\n\t\tEx::sibling_iterator fin=it.end();\n\n\t\tif((*it).fl.bracket   ==str_node::b_round)       str << \"(\";\n\t\telse if((*it).fl.bracket   ==str_node::b_square) str << \"[\";\n\t\telse if((*it).fl.bracket   ==str_node::b_curly)  str << \"\\\\{\";\n\t\telse if((*it).fl.bracket   ==str_node::b_pointy) str << \"\\\\<\";\n\t\telse if((*it).fl.bracket   ==str_node::b_none)   str << \"{\";\n\t\t//\tif((*it).fl.mark) str << \"\\033[1m\";\n\t\tstr << *(*it).name;\n\t\t//\tif((*it).fl.mark) str << \"\\033[0m\";\n\t\tif((*it).fl.bracket   ==str_node::b_round)       str << \")\";\n\t\telse if((*it).fl.bracket   ==str_node::b_square) str << \"]\";\n\t\telse if((*it).fl.bracket   ==str_node::b_curly)  str << \"\\\\}\";\n\t\telse if((*it).fl.bracket   ==str_node::b_pointy) str << \"\\\\>\";\n\t\telse if((*it).fl.bracket   ==str_node::b_none)   str << \"}\";\n\n\t\tif(*it->multiplier!=multiplier_t(1)) {\n\t\t\tif(compact_tree)\n\t\t\t\tstr << \"#\" << *it->multiplier;\n\t\t\telse\n\t\t\t\tstr << \"  \" << *it->multiplier;\n\t\t\t}\n\t\tif(std::holds_alternative<std::shared_ptr<NTensor>>(it->content)) {\n\t\t\tstr << \" \" << *std::get<std::shared_ptr<NTensor>>(it->content);\n\t\t\t}\n\t\telse if(std::holds_alternative<std::shared_ptr<NInterpolatingFunction>>(it->content)) {\n\t\t\tstr << \" (NInterpolatingFunction)\";\n\t\t\t}\n\t\t//\tstr << \"  (\" << calc_hash(it) << \")\";\n\t\t//\tstr << \"  (\" << depth(it) << \")\";\n\t\t//\tstr << \"  (\" << it->fl.bracket << \" \" << &(*it) << \")\";\n//\t\tstr << \"  (\" << it->fl.bracket << \" \" << it.node << \")\";\n\t\tif(!compact_tree) str << std::endl;\n\n\t\twhile(beg!=fin) {\n\t\t\tint offset=1;\n\t\t\tif(num && !compact_tree) {\n\t\t\t\tstr << std::setw(3) << num << \":\";\n\t\t\t\toffset=1;\n\t\t\t\t}\n\t\t\tif(!compact_tree)\n\t\t\t\tfor(int i=offset; i<depth(beg); ++i)\n\t\t\t\t\tstr << \"  \";\n\t\t\tswitch((*beg).fl.parent_rel) {\n\t\t\t\tcase str_node::p_super:\n\t\t\t\t\tstr << \"^\";\n\t\t\t\t\tbreak;\n\t\t\t\tcase str_node::p_sub:\n\t\t\t\t\tstr << \"_\";\n\t\t\t\t\tbreak;\n\t\t\t\tcase str_node::p_property:\n\t\t\t\t\tstr << \"$\";\n\t\t\t\t\tbreak;\n\t\t\t\tcase str_node::p_exponent:\n\t\t\t\t\tstr << \"&\";\n\t\t\t\t\tbreak;\n\t\t\t\tdefault:\n\t\t\t\t\tbreak;\n\t\t\t\t}\n\t\t\tif(num) ++num;\n\t\t\tprint_recursive_treeform(str, beg, num);\n\t\t\t++beg;\n\t\t\t}\n\t\treturn str;\n\t\t}\n\n\n\t// std::ostream& operator<<(std::ostream& str, const Ex& tr)\n\t// \t{\n\t// \tunsigned int number=1;\n\t// \tEx::iterator it=tr.begin();\n\t// \twhile(it!=tr.end()) {\n\t// \t\ttr.print_recursive_infix(str, it, number, true);\n\t// \t\tit.skip_children();\n\t// \t\t++it;\n\t// \t\tif(it!=tr.end())\n\t// \t\t\tstr << std::endl;\n\t// \t\t}\n\t// \treturn str;\n\t// \t}\n\n\tEx::iterator Ex::named_parent(Ex::iterator it, const std::string& nm) const\n\t\t{\n\t\t//\tstd::cout << \"!!\" << *it->name << std::endl << std::flush;\n\t\tassert(is_valid(it));\n\t\twhile(*it->name!=nm /* && it->is_command()==false */) {\n\t\t\tit=parent(it);\n\t\t\tassert(is_valid(it));\n\t\t\t//\t\tstd::cout << \"  !!\" << *it->name << std::endl << std::flush;\n\t\t\t}\n\t\t//\tstd::cout << \"  out\" << std::endl;\n\t\treturn it;\n\t\t}\n\n\tEx::iterator Ex::erase_expression(Ex::iterator it)\n\t\t{\n\t\tit=named_parent(it, \"\\\\history\");\n\t\treturn erase(it);\n\t\t}\n\n\n\thashval_t Ex::calc_hash(iterator it) const\n\t\t{\n\t\t// Hash values do not contain info about the multiplier field,\n\t\t// nor do they know about the type of the links (FIXME: is the latter\n\t\t// the correct thing to do?)\n\t\t//\n\t\t// If this algorithm is changed, factorise::calc_restricted_hash in\n\t\t// core/algorithms/factor_in.cc should also be modified!\n\n\t\titerator end=it;\n\t\tend.skip_children();\n\t\t++end;\n\t\tit.skip_children(false);\n\n\t\thashval_t seed = 0;\n\t\twhile(it!=end) {\n\t\t\tboost::hash_combine(seed, *it->name);\n\t\t\t++it;\n\t\t\t}\n\n\t\treturn seed;\n\t\t}\n\n\tEx::sibling_iterator Ex::arg(iterator it, unsigned int num)\n\t\t{\n\t\tif(*it->name==\"\\\\comma\") {\n\t\t\tassert(Ex::number_of_children(it)>num);\n\t\t\treturn Ex::child(it,num);\n\t\t\t}\n\t\telse return it;\n\t\t}\n\n\tunsigned int Ex::arg_size(sibling_iterator sib)\n\t\t{\n\t\tif(*sib->name==\"\\\\comma\") return Ex::number_of_children(sib);\n\t\telse return 1;\n\t\t}\n\n\tmultiplier_t Ex::arg_to_num(sibling_iterator sib, unsigned int num) const\n\t\t{\n\t\tsibling_iterator nod;\n\t\tif(*sib->name==\"\\\\comma\") nod=child(sib,num);\n\t\telse                      nod=sib;\n\t\treturn *nod->multiplier;\n\t\t}\n\n//\tunsigned int Ex::equation_number(Ex::iterator it) const\n//\t\t{\n//\t\titerator historynode=named_parent(it, \"\\\\history\");\n//\t\tunsigned int num=0;\n//\t\titerator sit=begin();\n//\t\t//\tlong totravel=0;\n//\t\twhile(sit!=end()) {\n//\t\t\t//\t\t++totravel;\n//\t\t\tif(*sit->name==\"\\\\history\") {\n//\t\t\t\t++num;\n//\t\t\t\tif(historynode==sit) {\n//\t\t\t\t\t//\t\t\t\ttxtout << \"had to travel \" << totravel << std::endl;\n//\t\t\t\t\treturn num;\n//\t\t\t\t\t}\n//\t\t\t\t}\n//\t\t\tsit.skip_children();\n//\t\t\t++sit;\n//\t\t\t}\n//\t\treturn 0;\n//\t\t}\n//\n//\tnset_t::iterator Ex::equation_label(Ex::iterator it) const\n//\t\t{\n//\t\tnset_t::iterator ret=name_set.end();\n//\n//\t\titerator sit=begin();\n//\t\twhile(sit!=end()) {\n//\t\t\tif(*sit->name==\"\\\\history\") {\n//\t\t\t\tif(it==sit)\n//\t\t\t\t\tgoto found;\n//\t\t\t\titerator eit=begin(sit);\n//\t\t\t\titerator endit=sit;\n//\t\t\t\tendit.skip_children();\n//\t\t\t\t++endit;\n//\t\t\t\twhile(eit!=endit) {\n//\t\t\t\t\tif(it==eit)\n//\t\t\t\t\t\tgoto found;\n//\t\t\t\t\t++eit;\n//\t\t\t\t\t}\n//\t\t\t\tsit.skip_children();\n//\t\t\t\t}\n//\t\t\t++sit;\n//\t\t\t}\n//found:\n//\t\tif(sit!=end()) {\n//\t\t\tsibling_iterator lit=begin(sit);\n//\t\t\twhile(lit!=end(sit)) {\n//\t\t\t\tif(*lit->name==\"\\\\label\") {\n//\t\t\t\t\tret=begin(lit)->name;\n//\t\t\t\t\tbreak;\n//\t\t\t\t\t}\n//\t\t\t\t++lit;\n//\t\t\t\t}\n//\t\t\t}\n//\t\treturn ret;\n//\t\t}\n//\n//\t// Always returns the \\\\history node of the equation (i.e. the top node).\n//\tEx::iterator Ex::equation_by_number(unsigned int i) const\n//\t\t{\n//\t\titerator it=begin();\n//\t\tunsigned int num=1;\n//\t\twhile(it!=end()) {\n//\t\t\tif(*it->name==\"\\\\history\") {\n//\t\t\t\tif(num==i) return it;\n//\t\t\t\telse       ++num;\n//\t\t\t\t}\n//\t\t\tit.skip_children();\n//\t\t\t++it;\n//\t\t\t}\n//\t\treturn it;\n//\t\t//\tif(num==number_of_siblings(begin()))\n//\t\t//\t\treturn end();\n//\t\t//\treturn it;\n//\t\t}\n//\n//\tEx::iterator Ex::equation_by_name(nset_t::iterator nit) const\n//\t\t{\n//\t\tunsigned int tmp;\n//\t\treturn equation_by_name(nit, tmp);\n//\t\t}\n//\n//\tEx::iterator Ex::equation_by_name(nset_t::iterator nit, unsigned int& tmp) const\n//\t\t{\n//\t\tunsigned int num=0;\n//\t\titerator it=begin();\n//\t\twhile(it!=end()) {\n//\t\t\tif(*it->name==\"\\\\history\") {\n//\t\t\t\t++num;\n//\t\t\t\tsibling_iterator lit=begin(it);\n//\t\t\t\twhile(lit!=end(it)) {\n//\t\t\t\t\tif(*lit->name==\"\\\\label\") {\n//\t\t\t\t\t\tif(begin(lit)->name==nit) {\n//\t\t\t\t\t\t\ttmp=num;\n//\t\t\t\t\t\t\treturn it;\n//\t\t\t\t\t\t\t}\n//\t\t\t\t\t\t}\n//\t\t\t\t\t++lit;\n//\t\t\t\t\t}\n//\t\t\t\t}\n//\t\t\tit.skip_children();\n//\t\t\t++it;\n//\t\t\t}\n//\t\treturn end();\n//\t\t}\n\n\tbool Ex::is_hidden(iterator it) const\n\t\t{\n\t\tdo {\n\t\t\tif(*it->name==\"\\\\ldots\") return true;\n\t\t\tif(is_head(it)) break;\n\t\t\tit=parent(it);\n\t\t\t}\n\t\twhile(true);\n\t\treturn false;\n\t\t}\n\n//\tEx::iterator Ex::procedure_by_name(nset_t::iterator nit) const\n//\t\t{\n//\t\titerator it=begin();\n//\t\twhile(it!=end()) {\n//\t\t\tif(*it->name==\"\\\\procedure\") {\n//\t\t\t\tsibling_iterator lit=begin(it);\n//\t\t\t\twhile(lit!=end(it)) {\n//\t\t\t\t\tif(*lit->name==\"\\\\label\") {\n//\t\t\t\t\t\tif(begin(lit)->name==nit)\n//\t\t\t\t\t\t\treturn it;\n//\t\t\t\t\t\t}\n//\t\t\t\t\t++lit;\n//\t\t\t\t\t}\n//\t\t\t\t}\n//\t\t\tit.skip_children();\n//\t\t\t++it;\n//\t\t\t}\n//\t\treturn end();\n//\t\t}\n\n\tEx::iterator Ex::replace_index(iterator pos, const iterator& from, bool keep_parent_rel)\n\t\t{\n\t\t//\tassert(pos->fl.parent_rel==str_node::p_sub || pos->fl.parent_rel==str_node::p_super);\n\t\tstr_node::bracket_t    bt=pos->fl.bracket;\n\t\tstr_node::parent_rel_t pr=pos->fl.parent_rel;\n\t\titerator ret=replace(pos, from);\n\t\tret->fl.bracket=bt;\n\t\tif(keep_parent_rel)\n\t\t\tret->fl.parent_rel=pr;\n\t\treturn ret;\n\t\t}\n\n\tEx::iterator Ex::move_index(iterator pos, const iterator& from)\n\t\t{\n\t\t//\tassert(pos->fl.parent_rel==str_node::p_sub || pos->fl.parent_rel==str_node::p_super);\n\t\tstr_node::bracket_t    bt=pos->fl.bracket;\n\t\tstr_node::parent_rel_t pr=pos->fl.parent_rel;\n\t\tmove_ontop(pos, from);\n\t\tfrom->fl.bracket=bt;\n\t\tfrom->fl.parent_rel=pr;\n\t\treturn from;\n\t\t}\n\n\tvoid Ex::list_wrap_single_element(iterator& it)\n\t\t{\n\t\tif(*it->name!=\"\\\\comma\") {\n\t\t\titerator commanode=insert(it, str_node(\"\\\\comma\"));\n\t\t\tsibling_iterator fr=it, to=it;\n\t\t\t++to;\n\t\t\treparent(commanode, fr, to);\n\t\t\tit=commanode;\n\t\t\t}\n\t\t}\n\n\tvoid Ex::list_unwrap_single_element(iterator& it)\n\t\t{\n\t\tif(*it->name==\"\\\\comma\") {\n\t\t\tif(number_of_children(it)==1) {\n\t\t\t\tflatten(it);\n\t\t\t\tit=erase(it);\n\t\t\t\t}\n\t\t\t}\n\t\t}\n\n\tEx::iterator Ex::flatten_and_erase(iterator pos)\n\t\t{\n\t\t//\tassert(number_of_children(pos)==1);\n\n\t\tmultiplier_t tmp=*pos->multiplier;\n\t\tflatten(pos);\n\t\tpos=erase(pos);\n\t\tmultiply(pos->multiplier, tmp);\n\t\treturn pos;\n\t\t}\n\n//\tunsigned int Ex::number_of_equations() const\n//\t\t{\n//\t\tunsigned int last_eq=0;\n//\t\titerator eq=begin();\n//\t\twhile(eq!=end()) {\n//\t\t\tif(*eq->name==\"\\\\history\")\n//\t\t\t\t++last_eq;\n//\t\t\teq.skip_children();\n//\t\t\t++eq;\n//\t\t\t}\n//\t\treturn last_eq;\n//\t\t}\n\n//\tEx::iterator Ex::equation_by_number_or_name(iterator it, unsigned int last_used_equation,\n//\t      unsigned int& real_eqno) const\n//\t\t{\n//\t\titerator ret;\n//\t\tif(it->is_rational()) {\n//\t\t\tint eqno=static_cast<int>(it->multiplier->get_d());\n//\t\t\treal_eqno=eqno;\n//\t\t\tret=equation_by_number(eqno);\n//\t\t\t}\n//\t\telse {\n//\t\t\tif(*it->name==\"%\") {\n//\t\t\t\tret=equation_by_number(last_used_equation);\n//\t\t\t\treal_eqno=last_used_equation;\n//\t\t\t\t}\n//\t\t\telse {\n//\t\t\t\tret=equation_by_name(it->name, real_eqno);\n//\t\t\t\t}\n//\t\t\t}\n//\t\treturn ret;\n//\t\t}\n\n//\tEx::iterator Ex::equation_by_number_or_name(iterator it, unsigned int last_used_equation) const\n//\t\t{\n//\t\tunsigned int tmp;\n//\t\treturn equation_by_number_or_name(it, last_used_equation, tmp);\n//\t\t}\n//\n//\tstd::string Ex::equation_number_or_name(iterator it, unsigned int last_used_equation) const\n//\t\t{\n//\t\tstd::stringstream ss;\n//\t\tif(it->is_rational()) {\n//\t\t\tint eqno=static_cast<int>(it->multiplier->get_d());\n//\t\t\tss << eqno;\n//\t\t\t}\n//\t\telse {\n//\t\t\tif(*it->name==\"%\") ss << last_used_equation;\n//\t\t\telse               ss << *it->name;\n//\t\t\t}\n//\t\treturn ss.str();\n//\t\t}\n\n\tbool Ex::operator==(const Ex& other) const\n\t\t{\n\t\treturn equal_subtree(begin(), other.begin());\n\t\t}\n\n//\tbool Ex::operator<(const Ex& other) const\n//\t\t{\n//\t\tEx::iterator_base_less less;\n//\t\treturn less(begin(), other.begin());\n//\t\t}\n\n\tvoid Ex::push_history(const std::vector<Ex::path_t>& paths)\n\t\t{\n\t\thistory.push_back(*this);\n\t\tterms.push_back(paths);\n\t\t}\n\n\tstd::vector<Ex::path_t> Ex::pop_history()\n\t\t{\n\t\tcdb_tree::operator=(history.back());\n\t\thistory.pop_back();\n\t\tauto ret(terms.back());\n\t\tterms.pop_back();\n\t\treturn ret;\n\t\t}\n\n\tint Ex::history_size() const\n\t\t{\n\t\treturn history.size();\n\t\t}\n\n\tstr_node::str_node(void)\n\t\t: name(name_set.end())\n\t\t, content(std::monostate())\n\t\t{\n\t\tone(multiplier);\n\t\t//\tfl.modifier=m_none;\n\t\tfl.bracket=b_none;\n\t\tfl.parent_rel=p_none;\n\t\t//\tfl.mark=0;\n\t\t}\n\n//\tstr_node::str_node(const str_node& other)\n//\t\t: name(other.name)\n//\t\t, multiplier(other.multiplier)\n//\t\t, content(other.content)\n//\t\t, fl(other.fl)\n//\t\t{\n//\t\t}\n//\t\n//\tstr_node::str_node(str_node&& other)\n//\t\t: name(std::move(other.name))\n//\t\t, multiplier(std::move(other.multiplier))\n//\t\t, content(std::move(other.content))\n//\t\t, fl(std::move(other.fl))\n//\t\t{\n//\t\t}\n\t\n\tstr_node::str_node(nset_t::iterator nm, bracket_t br, parent_rel_t pr)\n\t\t: name(name_set.end())\n\t\t, content(std::monostate())\n\t\t{\n\t\tone(multiplier);\n\t\tname=nm;\n\t\t//\tfl.modifier=m_none;\n\t\tfl.bracket=br;\n\t\tfl.parent_rel=pr;\n\t\t//\tfl.mark=0;\n\t\t}\n\n\tstr_node::str_node(const std::u32string& nm, bracket_t br, parent_rel_t pr)\n\t\t: name(name_set.end())\n\t\t, content(std::monostate())\n\t\t{\n#ifdef _MSC_VER\n\t\tstd::wstring_convert<std::codecvt_utf8<int32_t>, int32_t> conv;\n\t\tauto p = reinterpret_cast<const int32_t*>(nm.data());\n\t\tstd::string nm8 = conv.to_bytes(p, p + nm.size());\n#else\n\t\tstd::wstring_convert<std::codecvt_utf8<char32_t>, char32_t> conv;\n\t\tstd::string nm8=conv.to_bytes(nm);\n#endif\n\n#ifdef DEBUG\n\t\tstd::cerr << \"str_node: \" << nm8 << std::endl;\n#endif\n\t\tone(multiplier);\n\t\tname=name_set.insert(nm8).first;\n\t\t//\tfl.modifier=m_none;\n\t\tfl.bracket=br;\n\t\tfl.parent_rel=pr;\n\t\t}\n\n\tstr_node::str_node(const std::string& nm, bracket_t br, parent_rel_t pr)\n\t\t: name(name_set.end())\n\t\t, content(std::monostate())\n\t\t{\n\t\tone(multiplier);\n\t\tname=name_set.insert(nm).first;\n\t\t//\tfl.modifier=m_none;\n\t\tfl.bracket=br;\n\t\tfl.parent_rel=pr;\n\t\t//\tfl.mark=0;\n\t\t}\n\n\tvoid str_node::flip_parent_rel()\n\t\t{\n\t\tif(fl.parent_rel==p_super)       fl.parent_rel=p_sub;\n\t\telse if(fl.parent_rel==p_sub)    fl.parent_rel=p_super;\n\t\telse throw std::logic_error(\"flip_parent_rel called on non-index\");\n\t\t}\n\n\tbool str_node::is_standard() const\n\t\t{\n\t\treturn std::holds_alternative<std::monostate>(content);\n\t\t}\n\n\tbool str_node::is_zero() const\n\t\t{\n\t\tif(*multiplier==0) return true;\n\t\treturn false;\n\t\t}\n\n\tbool str_node::is_identity() const\n\t\t{\n\t\tif(*name==\"1\" && *multiplier==1 && is_standard()) return true;\n\t\treturn false;\n\t\t}\n\n\tbool str_node::is_rational() const\n\t\t{\n\t\treturn (*name==\"1\" && multiplier->is_rational() && is_standard());\n\t\t}\n\n\tbool str_node::is_double() const\n\t\t{\n\t\treturn (*name==\"1\" && multiplier->is_double() && is_standard());\n\t\t}\n\n\tbool str_node::is_integer() const\n\t\t{\n\t\tif(*name==\"1\") {\n\t\t\tif(multiplier->is_rational() && is_standard()) {\n\t\t\t\tauto r = multiplier->get_rational();\n\t\t\t\tif(r.get_den()==1)\n\t\t\t\t\treturn true;\n\t\t\t\t}\n\t\t\t}\n\t\treturn false;\n\t\t}\n\n\tbool str_node::is_unsimplified_rational() const\n\t\t{\n\t\tif((*name).size()==0) return false;\n\t\tfor(unsigned int i=0; i<(*name).size(); ++i) {\n\t\t\tif(!isdigit((*name)[i]) && (*name)[i]!='/' && (*name)[i]!='-')\n\t\t\t\treturn false;\n\t\t\t}\n\t\treturn true;\n\t\t}\n\n\tbool str_node::is_unsimplified_double() const\n\t\t{\n\t\tif((*name).size()==0) return false;\n\t\tbool founddot=false;\n\t\tfor(unsigned int i=0; i<(*name).size(); ++i) {\n\t\t\tif(!isdigit((*name)[i]) && (*name)[i]!='.' && (*name)[i]!='e' && (*name)[i]!='-')\n\t\t\t\treturn false;\n\t\t\tif((*name)[i]=='.') founddot=true;\n\t\t\t}\n\t\treturn founddot;\n\t\t}\n\n\tbool str_node::is_unsimplified_integer() const\n\t\t{\n\t\tif((*name).size()==0) return false;\n\t\tfor(unsigned int i=0; i<(*name).size(); ++i) {\n\t\t\tif(!isdigit((*name)[i]) && (*name)[i]!='-')\n\t\t\t\treturn false;\n\t\t\t}\n\t\treturn true;\n\t\t}\n\n\tbool str_node::is_index() const\n\t\t{\n\t\tif(fl.parent_rel==p_sub || fl.parent_rel==p_super) return true;\n\t\treturn false;\n\t\t}\n\n\tbool str_node::is_quoted_string() const\n\t\t{\n\t\tif((*name).size()<2) return false;\n\t\tif((*name)[0]!='\\\"') return false;\n\t\tif((*name)[(*name).size()-1]!='\\\"') return false;\n\t\treturn true;\n\t\t}\n\n\tbool str_node::is_command() const\n\t\t{\n\t\tif(name == name_set.end()) return false;\n\n\t\tif((*name).size()>0)\n\t\t\tif((*name)[0]=='@') {\n\t\t\t\tif((*name).size()>1) {\n\t\t\t\t\tif((*name)[1]!='@')\n\t\t\t\t\t\treturn true;\n\t\t\t\t\t}\n\t\t\t\telse return true;\n\t\t\t\t}\n\t\treturn false;\n\t\t}\n\n\tbool str_node::is_inert_command() const\n\t\t{\n\t\tif(name == name_set.end()) return false;\n\n\t\tif((*name).size()>1)\n\t\t\tif((*name)[0]=='@')\n\t\t\t\tif((*name)[1]=='@')\n\t\t\t\t\treturn true;\n\t\treturn false;\n\t\t}\n\n\tbool str_node::is_name_wildcard() const\n\t\t{\n\t\tif(name == name_set.end()) return false;\n\t\t\n\t\tif((*name).size()>0)\n\t\t\tif((*name)[name->size()-1]=='?') {\n\t\t\t\tif(name->size()>1) {\n\t\t\t\t\tif((*name)[name->size()-2]!='?')\n\t\t\t\t\t\treturn true;\n\t\t\t\t\t}\n\t\t\t\telse return true;\n\t\t\t\t}\n\t\treturn false;\n\t\t}\n\n\tbool str_node::is_object_wildcard() const\n\t\t{\n\t\tif(name == name_set.end()) return false;\n\n\t\tif((*name).size()>1)\n\t\t\tif((*name)[name->size()-1]=='?')\n\t\t\t\tif((*name)[name->size()-2]=='?')\n\t\t\t\t\treturn true;\n\t\treturn false;\n\t\t}\n\n\tbool str_node::is_range_wildcard() const\n\t\t{\n\t\tif(name == name_set.end()) return false;\n\n\t\tif(name->size()>0) {\n\t\t\tif((*name)[0]=='#')\n\t\t\t\treturn true;\n\t\t\t}\n\t\treturn false;\n\t\t}\n\n\tbool str_node::is_siblings_wildcard() const\n\t\t{\n\t\tif(name == name_set.end()) return false;\n\n\t\tif(name->size()>0) {\n\t\t\tif((*name)[name->size()-1]=='@')\n\t\t\t\treturn true;\n\t\t\t}\n\t\treturn false;\n\t\t}\n\n\tbool str_node::is_autodeclare_wildcard() const\n\t\t{\n\t\tif(name == name_set.end()) return false;\n\n\t\tif(name->size()>0)\n\t\t\tif((*name)[name->size()-1]=='#')\n\t\t\t\treturn true;\n\t\treturn false;\n\t\t}\n\n\tbool str_node::is_indexstar_wildcard() const\n\t\t{\n\t\tif(name == name_set.end()) return false;\n\n\t\tif((*name).size()>1)\n\t\t\tif((*name)[name->size()-1]=='?')\n\t\t\t\tif((*name)[name->size()-2]=='*')\n\t\t\t\t\treturn true;\n\t\treturn false;\n\t\t}\n\n\tbool str_node::is_indexplus_wildcard() const\n\t\t{\n\t\tif(name == name_set.end()) return false;\n\n\t\tif((*name).size()>1)\n\t\t\tif((*name)[name->size()-1]=='?')\n\t\t\t\tif((*name)[name->size()-2]=='+')\n\t\t\t\t\treturn true;\n\t\treturn false;\n\t\t}\n\n\tbool str_node::is_numbered_symbol() const\n\t\t{\n\t\tif(name == name_set.end()) return false;\n\n\t\tint len=(*name).size();\n\t\tif(len>1)\n\t\t\tif(isdigit((*name)[len-1]))\n\t\t\t\treturn true;\n\t\treturn false;\n\t\t}\n\n\tnset_t::iterator str_node::name_only()\n\t\t{\n\t\tif(is_name_wildcard()) {\n\t\t\tstd::string tmp=(*name).substr(0, name->size()-1);\n\t\t\treturn name_set.insert(tmp).first;\n\t\t\t}\n\t\telse if(is_object_wildcard()) {\n\t\t\tstd::string tmp=(*name).substr(0, name->size()-2);\n\t\t\treturn name_set.insert(tmp).first;\n\t\t\t}\n\t\telse if(is_autodeclare_wildcard()) {\n\t\t\tsize_t pos=name->find('#');\n\t\t\tstd::string tmp=(*name).substr(0, pos);\n\t\t\treturn name_set.insert(tmp).first;\n\t\t\t}\n\t\telse if(is_numbered_symbol()) {\n\t\t\tsize_t pos=name->find_first_of(\"0123456789\");\n\t\t\tstd::string tmp=(*name).substr(0, pos);\n\t\t\treturn name_set.insert(tmp).first;\n\t\t\t}\n\t\treturn name;\n\t\t}\n\n\tbool str_node::operator==(const str_node& other) const\n\t\t{\n\t\tif(*name==*other.name &&\n\t\t      fl.bracket==other.fl.bracket &&\n\t\t      fl.parent_rel==other.fl.parent_rel &&\n\t\t      multiplier==other.multiplier)\n\t\t\treturn true;\n\t\telse return false;\n\t\t}\n\n\tbool str_node::compare_names_only(const str_node& one, const str_node& two)\n\t\t{\n\t\tif(one.name==two.name) return true;\n\t\telse                   return false;\n\t\t}\n\n\tbool str_node::compare_name_brack_par(const str_node& one, const str_node& two)\n\t\t{\n\t\tif(one.name==two.name &&\n\t\t      one.fl.bracket==two.fl.bracket &&\n\t\t      one.fl.parent_rel==two.fl.parent_rel) return true;\n\t\telse                                     return false;\n\t\t}\n\n\tbool str_node::compare_name_inverse_par(const str_node& one, const str_node& two)\n\t\t{\n\t\tif(one.name==two.name &&\n\t\t      ( (one.fl.parent_rel==str_node::p_super && two.fl.parent_rel==str_node::p_sub) ||\n\t\t        (one.fl.parent_rel==str_node::p_sub && two.fl.parent_rel==str_node::p_super)))\n\t\t\treturn true;\n\t\treturn false;\n\t\t}\n\n\tbool nset_it_less::operator()(nset_t::iterator first, nset_t::iterator second) const\n\t\t{\n\t\tif(*first < *second)\n\t\t\treturn true;\n\t\treturn false;\n\t\t}\n\n\n\tvoid multiply(rset_t::iterator& num, multiplier_t fac)\n\t\t{\n\t\tfac*=*num;\n\t\tfac.canonicalize();\n\t\tnum=rat_set.insert(fac).first;\n\t\t}\n\n\tvoid divide(rset_t::iterator& num, multiplier_t fac)\n\t\t{\n\t\tmultiplier_t tmp(*num);\n\t\ttmp /= fac;\n\t\ttmp.canonicalize();\n\t\tnum=rat_set.insert(tmp).first;\n\t\t}\n\n\tvoid set(rset_t::iterator& num, multiplier_t fac)\n\t\t{\n\t\tfac.canonicalize();\n\t\tnum=rat_set.insert(fac).first;\n\t\t}\n\n\tvoid add(rset_t::iterator& num, multiplier_t fac)\n\t\t{\n\t\tfac+=*num;\n\t\tfac.canonicalize();\n\t\tnum=rat_set.insert(fac).first;\n\t\t}\n\n\tvoid zero(rset_t::iterator& num)\n\t\t{\n\t\tstatic rset_t::iterator rat_it_zero=rat_set.end();\n\n\t\tif(rat_it_zero==rat_set.end())\n\t\t\trat_it_zero = rat_set.insert(0).first;\n\t\tnum=rat_it_zero;\n\t\t}\n\n\tvoid one(rset_t::iterator& num)\n\t\t{\n\t\tstatic rset_t::iterator rat_it_one=rat_set.end();\n\t\t\n\t\tif(rat_it_one==rat_set.end())\n\t\t\trat_it_one = rat_set.insert(1).first;\n\t\tnum=rat_it_one; \n\t\t}\n\n\tvoid flip_sign(rset_t::iterator& num)\n\t\t{\n\t\tmultiplier_t fac = multiplier_t(-1)*(*num);\n\t\tfac.canonicalize();\n\t\tnum=rat_set.insert(fac).first;\n\t\t}\n\n\tvoid half(rset_t::iterator& num)\n\t\t{\n\t\tmultiplier_t fac=(*num)/2;\n\t\tfac.canonicalize();\n\t\tnum=rat_set.insert(fac).first;\n\t\t}\n\n\tbool str_node::operator<(const cadabra::str_node& other) const\n\t\t{\n\t\tif(*name<*other.name) return true;\n\t\tif(*name==*other.name && *multiplier<*other.multiplier) return true;\n\t\treturn false;\n\t\t}\n\n\t}\n\n// Keep operator overloading outside of the cadabra namespace.\n\nstd::ostream& operator<<(std::ostream& str, const cadabra::Ex& ex)\n\t{\n\tif(ex.begin()==ex.end()) return str;\n\tex.print_recursive_treeform(str, ex.begin());\n\t//\tex.print_python(str, ex.begin());\n\treturn str;\n\t}\n\nstd::ostream& operator<<(std::ostream& str, cadabra::Ex::iterator it)\n\t{\n\tcadabra::Ex::print_recursive_treeform(str, it);\n\t//\tex.print_python(str, ex.begin());\n\treturn str;\n\t}\n"
  },
  {
    "path": "core/Storage.hh",
    "content": "/*\n\nCadabra: a field-theory motivated computer algebra system.\nCopyright (C) 2001-2014  Kasper Peeters <kasper.peeters@phi-sci.com>\n\nThis program is free software: you can redistribute it and/or\nmodify it under the terms of the GNU General Public License as\npublished by the Free Software Foundation, either version 3 of the\nLicense, or (at your option) any later version.\n\nThis program is distributed in the hope that it will be useful,\nbut WITHOUT ANY WARRANTY; without even the implied warranty of\nMERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU\nGeneral Public License for more details.\n\nYou should have received a copy of the GNU General Public License\n\talong with this program.  If not, see <http://www.gnu.org/licenses/>.\n\n*/\n\n#pragma once\n\n#include <cstddef>\n#include <iostream>\n#include <gmpxx.h>\n#include <string>\n#include <vector>\n#include <set>\n#include <map>\n#include <stdint.h>\n#include <assert.h>\n#include <initializer_list>\n#include <variant>\n#include <memory_resource>\n\n#include \"tree.hh\"\n#include \"Multiplier.hh\"\n\nnamespace cadabra {\n\n\tclass NTensor;\n\tclass NInterpolatingFunction;\n\t\n\ttypedef Multiplier              multiplier_t;\n\ttypedef std::set<std::string>   nset_t;\n\ttypedef std::set<multiplier_t>  rset_t;\n\ttypedef uintptr_t               hashval_t;\n\n\tlong        to_long(multiplier_t);\n\tdouble      to_double(multiplier_t);\n\tstd::string to_string(long);\n\n\textern nset_t name_set;\n\textern rset_t rat_set;\n\n\t/// \\ingroup core\n\t///\n\t/// Elementary building block for a mathematical expression. Contains information about the\n\t/// way in which the node is related to the parent node, and iterators into the global\n\t/// list of names and rationals.\n\n\tclass str_node { // size: 9 bytes (32 bit arch), can be reduced to 5 bytes.\n\t\tpublic:\n\t\t\tenum bracket_t     { b_round=0, b_square=1, b_curly=2, b_pointy=3, b_none=4, b_no=5, b_invalid=6 };\n\n\t\t\t/// Child nodes are related to their parent node by a so-called parent relation, which can\n\t\t\t/// be one of these values.\n\t\t\tenum parent_rel_t  { p_sub=0, p_super=1, p_none=2, p_property=3, p_exponent=4, p_components=5, p_invalid=7 };\n\n\t\t\tstr_node(void);\n//\t\t\tstr_node(const str_node&);\n//\t\t\tstr_node(str_node&&);\n\t\t\tstr_node(nset_t::iterator name, bracket_t btype=b_none, parent_rel_t ptype=p_none);\n\t\t\tstr_node(const std::string& name, bracket_t btype=b_none, parent_rel_t ptype=p_none);\n\t\t\tstr_node(const std::u32string& name, bracket_t btype=b_none, parent_rel_t ptype=p_none);\n\n\t\t\tbool operator==(const str_node&) const;\n\t\t\tbool operator<(const str_node&) const;\n\n\t\t\tnset_t::iterator name;\n\t\t\trset_t::iterator multiplier;\n\n\t\t\t// Special content which does not fit the AST structure, but still needs to\n\t\t\t// sit in the tree, is stored in the form of a shared pointer to data outside\n\t\t\t// the tree. If there is nothing, the std::monostate is set.\n\t\t\tstd::variant<std::monostate,\n\t\t\t\t\t\t\t std::shared_ptr<NTensor>,\n\t\t\t\t\t\t\t std::shared_ptr<NInterpolatingFunction>\n\t\t\t\t\t\t\t > content;\n\n#ifdef _WIN32\n\t\t\tstruct flag_t {\n\t\t\t\tbool            keep_after_eval ;\n\t\t\t\tbracket_t       bracket         ;\n\t\t\t\tparent_rel_t    parent_rel      ;\n\t\t\t\tbool            line_per_node   ;\n\t\t\t\t};\n#else\n\t\t\tstruct flag_t { // kept inside 8 bits for speed and size\n\t\t\t\tbool            keep_after_eval : 1;\n\t\t\t\tbracket_t       bracket         : 3;\n\t\t\t\tparent_rel_t    parent_rel      : 3;\n\t\t\t\tbool            line_per_node   : 1;\n\t\t\t\t};\n#endif\n\n\t\t\tflag_t fl;\n\n\t\t\t/// Change the parent relation from sub to super and vice versa (throws error\n\t\t\t/// when this is not an index).\n\t\t\tvoid flip_parent_rel();\n\n\t\t\t/// Standard nodes are nodes which do not hold special\n\t\t\t/// content in the `content` variable. Typical tree\n\t\t\t/// simplifications cannot apply to non-standard nodes.\n\t\t\tbool is_standard() const;\n\t\t\t\t\n\t\t\tbool is_zero() const;\n\t\t\tbool is_identity() const;\n\t\t\tbool is_rational() const;\n\t\t\tbool is_double() const;\n\t\t\tbool is_unsimplified_rational() const;\n\t\t\tbool is_unsimplified_double() const;\n\t\t\tbool is_integer() const;\n\t\t\tbool is_unsimplified_integer() const;\n\t\t\tbool is_index() const;            // _ or ^ parent_rel (does not query properties)\n\t\t\tbool is_quoted_string() const;\n\t\t\tbool is_command() const;\n\t\t\tbool is_inert_command() const;\n\t\t\tbool is_name_wildcard() const;    //  ?\n\t\t\tbool is_object_wildcard() const;  //  ??\n\t\t\tbool is_range_wildcard() const;   //  #{..}\n\t\t\tbool is_siblings_wildcard() const; // a...\n\t\t\tbool is_autodeclare_wildcard() const; // m#\n\t\t\tbool is_indexstar_wildcard() const; // ?* in sub/super\n\t\t\tbool is_indexplus_wildcard() const; // ?+ in sub/super\n\t\t\tbool is_numbered_symbol() const;  //  [a-zA-Z]+[0-9]+\n\n\t\t\tnset_t::iterator name_only();\n\n\t\t\tstatic bool compare_names_only(const str_node&, const str_node&);\n\t\t\tstatic bool compare_name_brack_par(const str_node&, const str_node&);\n\t\t\tstatic bool compare_name_inverse_par(const str_node&, const str_node&);\n\t\t};\n\n\t/// \\ingroup core\n\t///\n\t/// Helper functions for manipulation of multipliers.\n\tvoid     multiply(rset_t::iterator&, multiplier_t);\n\tvoid     divide(rset_t::iterator&, multiplier_t);\n\tvoid     add(rset_t::iterator&, multiplier_t);\n\tvoid     zero(rset_t::iterator&);\n\tvoid     one(rset_t::iterator&);\n\tvoid     flip_sign(rset_t::iterator&);\n\tvoid     half(rset_t::iterator&);\n\tvoid     set(rset_t::iterator&, multiplier_t);\n\t\n\n\t///\n\t/// Basic storage class for symbolic mathemematical expressions. The\n\t/// full meaning of an expression typically requires knowledge about\n\t/// properties of patterns in it, which this class does _not_\n\t/// contain. All property dependent algorithms acting on Ex\n\t/// objects are in Algorithm.hh.\n\n//\ttypedef tree<str_node, std::pmr::polymorphic_allocator<tree_node_<str_node>>> cdb_tree;\n//\textern std::pmr::polymorphic_allocator<tree_node_<str_node>> alloc;\n\ttypedef tree<str_node, std::pmr::polymorphic_allocator<tree_node_<str_node>>> cdb_tree;\n\t\n\tclass Ex : public std::enable_shared_from_this<Ex>, public cdb_tree {\n\t\tpublic:\n\t\t\tEx();\n\t\t\t/// Create a new Ex with a copy of the subtree at the given iterator.\n\t\t\texplicit Ex(cdb_tree::iterator);\n\t\t\t/// Create new Ex with single head node being a copy of the given node.\n\t\t\texplicit Ex(const str_node&);\n\t\t\t/// Copy constructor: create a full copy of the given other Ex.\n\t\t\tEx(const Ex&);\n\t\t\t/// Copy constructor: create a full copy of the given other Ex.\n\t\t\t// explicit Ex(Ex);\n\t\t\t/// Initialise with given string as head node (does not parse this string).\n\t\t\texplicit Ex(const std::string&);\n\t\t\t/// Create a single-node Ex representing the given integer.\n\t\t\texplicit Ex(int);\n\t\t\t/// Create a single-node Ex representing the given float.\n\t\t\texplicit Ex(double);\n\t\t\t/// Create a single-node Ex representing the given rational.\n\t\t\texplicit Ex(int, int);\n\n\t\t\tEx& operator=(Ex);\n\t\t\t\n\t\t\t/// Keeping track of what algorithms have done to this expression.\n\t\t\t/// After a reset_state (or at initialisation), the expression sits\n\t\t\t/// in the 'checkpointed' state. When an algorithm acts, it can then\n\t\t\t/// move to 'no_action' (unchanged), 'applied' (changed) or 'error'.\n\t\t\t/// Once it is in 'error', it will stay there until the next 'reset'.\n\t\t\t/// FIXME: the following should implement a stack of states,\n\t\t\t/// so that it can be used with nested functions.\n\n\t\t\tenum result_t {\n\t\t\t\tl_checkpointed,\n\t\t\t\tl_no_action,\n\t\t\t\tl_applied,\n\t\t\t\tl_applied_no_new_dummies,\n\t\t\t\tl_error,\n\t\t\t\tl_cached\n\t\t\t};\n\t\t\tresult_t state() const;\n\t\t\tvoid     update_state(result_t);\n\t\t\tvoid     reset_state();\n\n\t\t\t/// A status query method mainly to implement a simple method to\n\t\t\t/// apply algorithms until they converge. Returns true when the\n\t\t\t/// expression is in 'checkpointed' or 'applied' state. Will\n\t\t\t/// set the state to 'no_action'.\n\t\t\t///\n\t\t\t/// This is used in `cadabra::convert_line` defined in `CdbPython.cc`,\n\t\t\t/// which essentially defines `converge(ex): [block]` to mean\n\t\t\t///\n\t\t\t///   ex.reset_state()\n\t\t\t///   while ex.changed():\n\t\t\t///      [block]\n\t\t\t\n\t\t\tbool     changed_state();\n\n\t\t\t/// Test if the expression is a rational number.\n\t\t\t/// FIXME: add tests for integers as well.\n\t\t\tbool          is_rational() const;\n\t\t\tmultiplier_t  to_rational() const;\n\t\t\tbool          is_integer()  const;\n\t\t\tlong          to_integer()  const;\n\t\t\tbool          is_string()   const;\n\n\t\t\t/// Comparison operators with primitive types.\n\t\t\tbool          equals(const std::string&) const;\n\n\t\t\t/// Test if the expression is empty (no content at all).\n\t\t\tbool          is_empty() const;\n\n\t\t\t/// Display expression in Python/Cadabra input form. This is\n\t\t\t/// fairly straightforward so not handled with a separate\n\t\t\t/// DisplayBase derived class.\n\t\t\tstatic std::ostream& print_python(std::ostream& str, Ex::iterator it);\n\n\t\t\t/// Output helpers mainly for debugging purposes.\n\t\t\tstd::ostream& print_entire_tree(std::ostream& str) const;\n\t\t\tstatic std::ostream& print_recursive_treeform(std::ostream& str, Ex::iterator it);\n\t\t\tstatic std::ostream& print_recursive_treeform(std::ostream& str, Ex::iterator it, unsigned int& number);\n\n\t\t\t/// Print a representation like Python's 'repr'.\n\t\t\tstd::ostream& print_repr(std::ostream& str, Ex::iterator it) const;\n\n\t\t\t/// Step up until matching node is found (if current node matches, do nothing)\n\t\t\titerator     named_parent(iterator it, const std::string&) const;\n\t\t\titerator     erase_expression(iterator it);\n\n\t\t\t/// Calculate the hash value for the subtree starting at 'it'.\n\t\t\thashval_t    calc_hash(iterator it) const;\n\n\t\t\t/// Quick access to arguments or argument lists for A(B)(C,D) type nodes.\n\t\t\tstatic sibling_iterator arg(iterator, unsigned int);\n\t\t\tstatic unsigned int     arg_size(sibling_iterator);\n\n\t\t\tmultiplier_t     arg_to_num(sibling_iterator, unsigned int) const; // shorthand for numerical arguments\n\n\t\t\t// Like 'child', but using index iterators instead.\n\t\t\t//\t\tsibling_iterator tensor_index(const iterator_base& position, unsigned int) const;\n\n\t\t\t// Number of \\\\history nodes in an expression\n\t\t\tunsigned int     number_of_steps(iterator it) const;\n\t\t\t// Given an iterator pointing to any node in the tree, figure\n\t\t\t// out to which equation number it belongs.\n//\t\t\tunsigned int     number_of_equations() const;\n//\t\t\tunsigned int     equation_number(iterator it) const;\n//\t\t\tnset_t::iterator equation_label(iterator it) const;\n//\t\t\titerator         equation_by_number(unsigned int i) const;\n//\t\t\titerator         equation_by_name(nset_t::iterator it) const;\n//\t\t\titerator         equation_by_name(nset_t::iterator it, unsigned int& ) const;\n//\t\t\titerator         equation_by_number_or_name(iterator it, unsigned int last_used_equation) const;\n//\t\t\titerator         equation_by_number_or_name(iterator it, unsigned int last_used_equation,\n//\t\t\t      unsigned int&) const;\n//\t\t\tstd::string      equation_number_or_name(iterator it, unsigned int last_used_equation) const;\n//\t\t\titerator         procedure_by_name(nset_t::iterator it) const;\n\n\t\t\t// Determine whether a node has an '\\ldots' parent (not necessarily direct).\n\t\t\tbool is_hidden(iterator) const;\n\n\t\t\t/// Replace the index-like object (originally intended to\n\t\t\t/// replace indices only, but now used also for e.g. normal\n\t\t\t/// function arguments, as in \\f[ \\partial_{z}{ A(z) } \\f] with\n\t\t\t/// a replacement of z).\n\t\t\t///\n\t\t\t/// Note: this originally kept the bracket and parent_rel, but\n\t\t\t/// that is not a good idea, because it prevents us from\n\t\t\t/// changing those. If we want to use a _{z} pattern replacing a\n\t\t\t/// A(z) index, it is better to make a rule that matches (z) and\n\t\t\t/// at the time we find and match _{z}. So this should be\n\t\t\t/// handled by the replacement_map logic in Compare.cc.\n\t\t\titerator         replace_index(iterator position, const iterator& from, bool keep_parent_rel=false);\n\n\t\t\t/// As in replace_index, but moves the index rather than making a copy (so that iterators\n\t\t\t/// pointing to the original remain valid).\n\t\t\titerator         move_index(iterator position, const iterator& from);\n\n\t\t\t/// Make sure that the node pointed to is a \\\\comma object, i.e. wrap the node if not already\n\t\t\t/// inside such a \\\\comma.\n\t\t\t/// DEPRECATED: in favour of 'do_list' in Functional.hh.\n\t\t\tvoid             list_wrap_single_element(iterator&);\n\t\t\tvoid             list_unwrap_single_element(iterator&);\n\n\t\t\t/// Replace the node with the children of the node, useful for e.g.\n\t\t\t/// \\\\prod{A} -> A. This algorithm takes care of the multiplier of the\n\t\t\t/// top node, i.e. it does 2\\\\prod{A} -> 2 A. Returns an iterator\n\t\t\t/// to the new location of the first child of the original node.\n\t\t\titerator         flatten_and_erase(iterator position);\n\n\t\t\t/// Compare two Ex objects for exact equality; no dummy equivalence or other\n\t\t\t/// things that require property information.\n\n\t\t\tbool operator==(const Ex& other) const;\n\n\t\t\t/// Push a copy of the current Storstate of the expression onto the\n\t\t\t/// history stack.  Also pushes a set of paths to terms which\n\t\t\t/// will be kept in the next history step.\n\t\t\t/// DEPRECATED, only used by take_match/replace_match.\n\t\t\tvoid push_history(const std::vector<Ex::path_t>&);\n\n\t\t\t/// Pop the most recent state of the expression off the history stack; returns\n\t\t\t/// the set of paths that we are replacing.\n\t\t\t/// DEPRECATED, only used by take_match/replace_match.\n\t\t\tstd::vector<Ex::path_t> pop_history();\n\n\t\t\t/// Return the size of the history; 0 means no history, just the current\n\t\t\t/// expression.\n\t\t\tint  history_size() const;\n\n\t\tprivate:\n\t\t\tresult_t state_;\n\n\t\t\tstd::vector<cdb_tree> history;\n\t\t\t/// Patterns which describe how to get from one history step to the next.\n\t\t\tstd::vector<std::vector<Ex::path_t> > terms;\n\t\t};\n\n\n\t/// \\ingroup core\n\t///\n\t/// Compare two nset iterators by comparing the strings to which they point.\n\n\tclass nset_it_less {\n\t\tpublic:\n\t\t\tbool operator()(nset_t::iterator first, nset_t::iterator second) const;\n\t\t};\n\n\ttemplate <typename T>\n\tbool is_in(const T& val, const std::initializer_list<T>& list)\n\t\t{\n\t\tfor (const auto& i : list) {\n\t\t\tif (val == i) {\n\t\t\t\treturn true;\n\t\t\t\t}\n\t\t\t}\n\t\treturn false;\n\t\t}\n\n\t}\n\n/// \\ingroup core\n///\n/// Bare output operator for Ex objects, mainly to provide a simple\n/// way to generate debugging output. Does not do any fancy\n/// formatting; just prints a nested list representation.  For more\n/// fancy output, look at DisplayTeX, DisplaySympy and\n/// DisplayTerminal.\n\nstd::ostream& operator<<(std::ostream&, const cadabra::Ex&);\nstd::ostream& operator<<(std::ostream&, cadabra::Ex::iterator);\n"
  },
  {
    "path": "core/Sum.cc",
    "content": "\n#include \"Sum.hh\"\n#include \"Exceptions.hh\"\n#include \"Functional.hh\"\n#include \"Compare.hh\"\n\nusing namespace cadabra;\n\nvisit::Sum::Sum(const Kernel &k, Ex &e, Ex::iterator i)\n\t: ReservedNode(k, e, i)\n\t{\n\tif(*top->name != \"\\\\sum\")\n\t\tthrow ConsistencyException(\"Top not a sum.\");\n\t}\n\nstd::vector<Ex::iterator> visit::Sum::find_terms_containing(Ex::iterator fnd) const\n\t{\n\tstd::vector<Ex::iterator> ret;\n\n\tdo_list(tr, top,\n\t\t\t  [this, &fnd, &ret](iterator term)\n\t\t\t\t  {\n\t\t\t\t  do_subtree(tr, term,\n\t\t\t\t\t\t\t\t [this, &fnd, &ret](iterator el)\n\t\t\t\t\t\t\t\t\t {\n\t\t\t\t\t\t\t\t\t if(subtree_exact_equal(&kernel.properties, el, fnd)) {\n\t\t\t\t\t\t\t\t\t\t ret.push_back(el);\n\t\t\t\t\t\t\t\t\t\t }\n\t\t\t\t\t\t\t\t\t return el;\n\t\t\t\t\t\t\t\t\t }\n\t\t\t\t\t\t\t\t );\n\t\t\t\t  return true;\n\t\t\t\t  }\n\t\t\t  );\n\t\n\treturn ret;\n\t}\n"
  },
  {
    "path": "core/Sum.hh",
    "content": "#pragma once\n\n#include \"Storage.hh\"\n#include \"Kernel.hh\"\n#include \"ReservedNode.hh\"\n\nnamespace cadabra {\n\n\tnamespace visit {\n\t\n\t\tclass Sum : public cadabra::visit::ReservedNode {\n\t\t\tpublic:\n\t\t\t\tSum(const Kernel&, Ex&, Ex::iterator);\n\n\t\t\t\t/// Find all terms in the sum which contain the given sub-expression.\n\t\t\t\t/// Returns iterators pointing to terms.\n\t\t\t\tstd::vector<Ex::iterator> find_terms_containing(Ex::iterator) const;\n\t\t};\n\t};\n};\n        \n"
  },
  {
    "path": "core/Symbols.cc",
    "content": "\n#include \"Symbols.hh\"\n\n\nconst std::map<std::string, std::string> cadabra::symbols::greekmap {\n\t{\"\\\\alpha\",   \"α\" },\n\t{\"\\\\beta\",    \"β\" },  // beta seems to be reserved\n\t{\"\\\\gamma\",   \"γ\" }, // gamma seems to be reserved\n\t{\"\\\\delta\",   \"δ\" },\n\t{\"\\\\epsilon\", \"ε\" },\n\t{\"\\\\zeta\",    \"ζ\" },\n\t{\"\\\\eta\",     \"η\" },\n\t{\"\\\\theta\",   \"θ\" },\n\t{\"\\\\iota\",    \"ι\" },\n\t{\"\\\\kappa\",   \"κ\" },\n\t{\"\\\\lambda\",  \"λ\" }, // lambda is reserved\n\t{\"\\\\mu\",      \"μ\" },\n\t{\"\\\\nu\",      \"ν\" },\n\t{\"\\\\xi\",      \"ξ\" },\n\t{\"\\\\omicron\", \"ο\" },\n\t{\"\\\\pi\",      \"π\" },\n\t{\"\\\\rho\",     \"ρ\" },\n\t{\"\\\\sigma\",   \"σ\" },\n\t{\"\\\\tau\",     \"τ\" },\n\t{\"\\\\upsilon\", \"υ\" },\n\t{\"\\\\phi\",     \"φ\" },\n\t{\"\\\\varphi\",  \"ϕ\" },\n\t{\"\\\\chi\",     \"χ\" },\n\t{\"\\\\psi\",     \"ψ\" },\n\t{\"\\\\omega\",   \"ω\" },\n\n\t{\"\\\\Alpha\",   \"Α\" },\n\t{\"\\\\Beta\",    \"Β\" },\n\t{\"\\\\Gamma\",   \"Γ\" },\n\t{\"\\\\Delta\",   \"Δ\" },\n\t{\"\\\\Epsilon\", \"Ε\" },\n\t{\"\\\\Zeta\",    \"Ζ\" },\n\t{\"\\\\Eta\",     \"Η\" },\n\t{\"\\\\Theta\",   \"ϴ\" },\n\t{\"\\\\Iota\",    \"Ι\" },\n\t{\"\\\\Kappa\",   \"Κ\" },\n\t{\"\\\\Lambda\",  \"Λ\" },\n\t{\"\\\\Mu\",      \"Μ\" },\n\t{\"\\\\Nu\",      \"Ν\" },\n\t{\"\\\\Xi\",      \"Ξ\" },\n\t{\"\\\\Omicron\", \"Ο\" },\n\t{\"\\\\Pi\",      \"Π\" },\n\t{\"\\\\Rho\",     \"Ρ\" },\n\t{\"\\\\Sigma\",   \"Σ\" },\n\t{\"\\\\Tau\",     \"Τ\" },\n\t{\"\\\\Upsilon\", \"Υ\" },\n\t{\"\\\\Phi\",     \"Φ\" },\n\t{\"\\\\Chi\",     \"Χ\" },\n\t{\"\\\\Psi\",     \"Ψ\" },\n\t{\"\\\\Omega\",   \"Ω\" },\n\t};\n"
  },
  {
    "path": "core/Symbols.hh",
    "content": "\n#pragma once\n\n#include <map>\n#include <string>\n\nnamespace cadabra {\n\tnamespace symbols {\n\t\textern const std::map<std::string, std::string> greekmap;\n\t\t}\n\t}\n"
  },
  {
    "path": "core/SympyCdb.cc",
    "content": "\n#include \"Storage.hh\"\n#include <gmpxx.h>\n#define PYBIND11_DETAILED_ERROR_MESSAGES\n\n#include <pybind11/pybind11.h>\n#include <sstream>\n#include \"Functional.hh\"\n#include \"SympyCdb.hh\"\n#include \"Exceptions.hh\"\n#include \"PreClean.hh\"\n#include \"Cleanup.hh\"\n#include \"Parser.hh\"\n#include \"Kernel.hh\"\n#include \"DisplaySympy.hh\"\n#include \"algorithms/substitute.hh\"\n#include \"properties/AntiCommuting.hh\"\n#include \"properties/NonCommuting.hh\"\n#include \"properties/SelfAntiCommuting.hh\"\n#include \"properties/SelfNonCommuting.hh\"\n\nusing namespace cadabra;\n\n// #define DEBUG __FILE__\n#include \"Debug.hh\"\n\n#ifndef NO_SYMPY\n\nsympy::SympyBridge::SympyBridge(const Kernel& k, std::shared_ptr<Ex> ex)\n\t: DisplaySympy(k, *ex), ex(ex)\n\t{\n\tEx::iterator it=(*ex).begin();\n\twhile(it != (*ex).end()) {\n\t\tif(Algorithm::is_noncommuting(kernel.properties, it))\n\t\t\tthrow RuntimeException(\"Cannot handle NonCommuting/AntiCommuting objects in the SymPy bridge.\");\n\t\t\n\t\t++it;\n\t\t}\n\t}\n\nsympy::SympyBridge::~SympyBridge()\n\t{\n\t}\n\npybind11::object sympy::SympyBridge::export_ex()\n\t{\n\tstd::ostringstream str;\n\toutput(str);\n\tpybind11::module sympy_parser = pybind11::module::import(\"sympy.parsing.sympy_parser\");\n\tauto parse = sympy_parser.attr(\"parse_expr\");\n#ifdef DEBUG\n\tstd::cerr << \"sympy::SympyBridge::export_ex: \" << str.str() << std::endl;\n#endif\n\tpybind11::object ret = parse(str.str());\n#ifdef DEBUG\n\tstd::cerr << \"sympy::SympyBridge::export_ex: succes\" << std::endl;\n#endif\n\t\n\treturn ret;\n\t}\n\ncadabra::Ex sympy::SympyBridge::convert(pybind11::handle obj)\n\t{\n\tstatic std::map<std::string, std::function<Ex(pybind11::handle)>> known =\n\t\t{\n\t\t\t{ \"<class 'sympy.sets.sets.FiniteSet'>\",  [this](pybind11::handle node)\n\t\t\t\t\t{\n\t\t\t\t\tEx ex_tuple(\"\\\\comma\");\n\t\t\t\t\t\n\t\t\t\t\tpybind11::object py_args = node.attr(\"args\");\n\t\t\t\t\tfor(auto item: py_args)\n\t\t\t\t\t\tex_tuple.append_child(ex_tuple.begin(), convert(item).begin());\n\n\t\t\t\t\treturn ex_tuple;\n\t\t\t\t\t}\n\t\t\t},\n\t\t\t{ \"<class 'set'>\",  [this](pybind11::handle node)\n\t\t\t\t\t{\n\t\t\t\t\tEx ex_tuple(\"\\\\comma\");\n\t\t\t\t\t\n\t\t\t\t\tfor(auto item: node)\n\t\t\t\t\t\tex_tuple.append_child(ex_tuple.begin(), convert(item).begin());\n\n\t\t\t\t\treturn ex_tuple;\n\t\t\t\t\t}\n\t\t\t},\n\t\t\t{ \"<class 'list'>\",  [this](pybind11::handle node)\n\t\t\t\t\t{\n\t\t\t\t\tEx ex_tuple(\"\\\\comma\");\n\t\t\t\t\t\n\t\t\t\t\tfor(auto item: node)\n\t\t\t\t\t\tex_tuple.append_child(ex_tuple.begin(), convert(item).begin());\n\n\t\t\t\t\treturn ex_tuple;\n\t\t\t\t\t}\n\t\t\t},\n\t\t\t{ \"<class 'sympy.core.containers.Tuple'>\", [this](pybind11::handle node)\n\t\t\t\t\t{\n\t\t\t\t\tEx ex_tuple(\"\\\\comma\");\n\t\t\t\t\t\n\t\t\t\t\tpybind11::object py_args = node.attr(\"args\");\n\t\t\t\t\tfor(auto item: py_args)\n\t\t\t\t\t\tex_tuple.append_child(ex_tuple.begin(), convert(item).begin());\n\n\t\t\t\t\t\n\t\t\t\t\treturn ex_tuple;\n\t\t\t\t\t}\n\t\t\t},\n\t\t\t{ \"<class 'tuple'>\", [this](pybind11::handle node)\n\t\t\t\t\t{\n\t\t\t\t\tEx ex_tuple(\"\\\\comma\");\n\t\t\t\t\t\n\t\t\t\t\tpybind11::tuple py_vars_tuple = pybind11::reinterpret_borrow<pybind11::tuple>(node);\n\t\t\t\t\tsize_t num = pybind11::len(py_vars_tuple);\n\t\t\t\t\tfor(size_t i=0; i<num; ++i) \n\t\t\t\t\t\tex_tuple.append_child(ex_tuple.begin(), convert(py_vars_tuple[i]).begin());\n\n\t\t\t\t\treturn ex_tuple;\n\t\t\t\t\t}\n\t\t\t},\n\t\t\t{ \"<class 'sympy.core.add.Add'>\",          [this](pybind11::handle node)\n\t\t\t\t\t{\n\t\t\t\t\tEx ex_add(\"\\\\sum\");\n\n\t\t\t\t\t// The order of terms in `args` is some weird SymPy idea of canonical\n\t\t\t\t\t// form. We use StrPrinter()._as_ordered_terms(node) to get something\n\t\t\t\t\t// suitable for human consumption.\n\n\t\t\t\t\tpybind11::module sympy_printing = pybind11::module::import(\"sympy.printing.str\");\n\t\t\t\t\tauto StrPrinter_class = sympy_printing.attr(\"StrPrinter\");\n\t\t\t\t\tpybind11::object printer = StrPrinter_class();\n\t\t\t\t\tpybind11::object py_args = printer.attr(\"_as_ordered_terms\")(node);\n\t\t\t\t\t\n\t\t\t\t\tfor(auto item: py_args)\n\t\t\t\t\t\tex_add.append_child(ex_add.begin(), convert(item).begin());\n\n\t\t\t\t\treturn ex_add;\n\t\t\t\t\t}\n\t\t\t},\n\t\t\t{ \"<class 'sympy.core.mul.Mul'>\",          [this](pybind11::handle node)\n\t\t\t\t\t{\n\t\t\t\t\tEx ex_mul(\"\\\\prod\");\n\n\t\t\t\t\t// For `Mul`, SymPy uses *reverse* lexicographical ordering. That is just\n\t\t\t\t\t// madness.\n\t\t\t\t\tpybind11::tuple py_args = node.attr(\"args\");\n\t\t\t\t\tsize_t num = pybind11::len(py_args);\n\t\t\t\t\tfor(; num>0; --num) \n\t\t\t\t\t\tex_mul.append_child(ex_mul.begin(), convert(py_args[num-1]).begin());\n\n\t\t\t\t\treturn ex_mul;\n\t\t\t\t\t}\n\t\t\t},\n\t\t\t{ \"<class 'sympy.core.power.Pow'>\",          [this](pybind11::handle node)\n\t\t\t\t\t{\n\t\t\t\t\tEx ex_pow(\"\\\\pow\");\n\t\t\t\t\t\n\t\t\t\t\tpybind11::object py_base = node.attr(\"base\");\n\t\t\t\t\tpybind11::object py_exp  = node.attr(\"exp\");\n\n\t\t\t\t\tex_pow.append_child(ex_pow.begin(), convert(py_base).begin());\n\t\t\t\t\tex_pow.append_child(ex_pow.begin(), convert(py_exp).begin());\t\t\t\t\t\n\n\t\t\t\t\treturn ex_pow;\n\t\t\t\t\t}\n\t\t\t},\n\t\t\t{ \"<class 'sympy.core.function.Derivative'>\",          [this](pybind11::handle node)\n\t\t\t\t\t{\n\t\t\t\t\tEx ex_der(\"\\\\partial\"); // FIXME: use the original derivative!\n\t\t\t\t\t\n\t\t\t\t\tpybind11::object py_expr = node.attr(\"expr\");\n\t\t\t\t\tpybind11::object py_vars = node.attr(\"variables\");\n\n\t\t\t\t\tex_der.append_child(ex_der.begin(), convert(py_expr).begin());\n\n\t\t\t\t\tpybind11::tuple py_vars_tuple = pybind11::reinterpret_borrow<pybind11::tuple>(py_vars);\n\t\t\t\t\tsize_t num = pybind11::len(py_vars_tuple);\n\t\t\t\t\tfor(size_t i=0; i<num; ++i) {\n\t\t\t\t\t\tex_der.append_child(ex_der.begin(), convert(py_vars_tuple[i]).begin())->fl.parent_rel=str_node::p_sub;\n\t\t\t\t\t\t}\n\n\t\t\t\t\treturn ex_der;\n\t\t\t\t\t}\n\t\t\t},\n\t\t\t{ \"<class 'sympy.core.numbers.Integer'>\",   [](pybind11::handle node)\n\t\t\t\t\t{\n\t\t\t\t\t// Make sure to handle large integers: convert to string, then parse back into mpz_class.\n\t\t\t\t\tstd::string int_str = pybind11::str(node);\n\t\t\t\t\tEx res(1);\n\t\t\t\t\tmultiply(res.begin()->multiplier, Multiplier(mpz_class(int_str)));\n\t\t\t\t\treturn res;\n\t\t\t\t\t}\n\t\t\t},\n\t\t\t{ \"<class 'int'>\",   [](pybind11::handle node)\n\t\t\t\t\t{\n\t\t\t\t\t// Make sure to handle large integers: convert to string, then parse back into mpz_class.\n\t\t\t\t\tstd::string int_str = pybind11::str(node);\n\t\t\t\t\tEx res(1);\n\t\t\t\t\tmultiply(res.begin()->multiplier, Multiplier(mpz_class(int_str)));\n\t\t\t\t\treturn res;\n\t\t\t\t\t}\n\t\t\t},\n\t\t\t{ \"<class 'sympy.core.numbers.Float'>\",          [](pybind11::handle node)\n\t\t\t\t\t{\n\t\t\t\t\treturn Ex(node.cast<double>());\n\t\t\t\t\t}\n\t\t\t},\n\t\t\t{ \"<class 'sympy.core.numbers.Zero'>\",          [](pybind11::handle node)\n\t\t\t\t\t{\n\t\t\t\t\treturn Ex(0);\n\t\t\t\t\t}\n\t\t\t},\n\t\t\t{ \"<class 'sympy.core.numbers.One'>\",          [](pybind11::handle node)\n\t\t\t\t\t{\n\t\t\t\t\treturn Ex(1);\n\t\t\t\t\t}\n\t\t\t},\n\t\t\t{ \"<class 'sympy.core.numbers.Half'>\",          [](pybind11::handle node)\n\t\t\t\t\t{\n\t\t\t\t\treturn Ex(1,2);\n\t\t\t\t\t}\n\t\t\t},\n\t\t\t{ \"<class 'sympy.core.numbers.NegativeOne'>\",          [](pybind11::handle node)\n\t\t\t\t\t{\n\t\t\t\t\treturn Ex(-1);\n\t\t\t\t\t}\n\t\t\t},\n\t\t\t{ \"<class 'sympy.core.numbers.NegativeOne'>\",          [](pybind11::handle node)\n\t\t\t\t\t{\n\t\t\t\t\treturn Ex(-1);\n\t\t\t\t\t}\n\t\t\t},\n\t\t\t{ \"<class 'sympy.core.numbers.ImaginaryUnit'>\",          [](pybind11::handle node)\n\t\t\t\t\t{\n\t\t\t\t\treturn Ex(\"\\\\iu\");\n\t\t\t\t\t}\n\t\t\t},\n\t\t\t{ \"<class 'sympy.core.numbers.Pi'>\",          [](pybind11::handle node)\n\t\t\t\t\t{\n\t\t\t\t\treturn Ex(\"\\\\pi\");\n\t\t\t\t\t}\n\t\t\t},\n\t\t\t{ \"<class 'sympy.core.numbers.Infinity'>\",          [](pybind11::handle node)\n\t\t\t\t\t{\n\t\t\t\t\treturn Ex(\"\\\\infty\");\n\t\t\t\t\t}\n\t\t\t},\n\t\t\t{ \"<class 'sympy.core.numbers.NegativeInfinity'>\",          [](pybind11::handle node)\n\t\t\t\t\t{\n\t\t\t\t\tEx neginf(\"\\\\infty\");\n\t\t\t\t\tmultiply(neginf.begin()->multiplier, -1);\n\t\t\t\t\treturn neginf;\n\t\t\t\t\t}\n\t\t\t},\n\t\t\t{ \"<class 'sympy.series.order.Order'>\",          [this](pybind11::handle node)\n\t\t\t\t\t{\n\t\t\t\t\tEx ex_order(\"\\\\bigO\");\n\t\t\t\t\tpybind11::object py_expr = node.attr(\"expr\");\n\t\t\t\t\tpybind11::object py_vars = node.attr(\"variables\");\n\n\t\t\t\t\tex_order.append_child(ex_order.begin(), convert(py_expr).begin());\n\t\t\t\t\treturn ex_order;\n\t\t\t\t\t}\n\t\t\t},\n\t\t\t{ \"<class 'sympy.core.relational.Equality'>\",          [this](pybind11::handle node)\n\t\t\t\t\t{\n\t\t\t\t\tEx ex_equal(\"\\\\equals\");\n\t\t\t\t\t\n\t\t\t\t\tpybind11::object py_lhs = node.attr(\"lhs\");\n\t\t\t\t\tpybind11::object py_rhs = node.attr(\"rhs\");\n\n\t\t\t\t\tex_equal.append_child(ex_equal.begin(), convert(py_lhs).begin());\n\t\t\t\t\tex_equal.append_child(ex_equal.begin(), convert(py_rhs).begin());\t\t\t\t\t\n\n\t\t\t\t\treturn ex_equal;\n\t\t\t\t\t}\n\t\t\t},\n\t\t\t{ \"<class 'sympy.core.numbers.Rational'>\",          [this](pybind11::handle node)\n\t\t\t\t\t{\n\t\t\t\t\tEx ex_frac(\"\\\\frac\");\n\t\t\t\t\tpybind11::object py_numer = node.attr(\"numerator\");\n\t\t\t\t\tpybind11::object py_denom = node.attr(\"denominator\");\n\n\t\t\t\t\tex_frac.append_child(ex_frac.begin(), convert(py_numer).begin());\n\t\t\t\t\tex_frac.append_child(ex_frac.begin(), convert(py_denom).begin());\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\treturn ex_frac;\n\t\t\t\t\t}\n\t\t\t},\n\t\t\t{ \"<class 'sympy.core.symbol.Symbol'>\",          [](pybind11::handle node)\n\t\t\t\t\t{\n\t\t\t\t\tpybind11::handle py_name = node.attr(\"name\");\n\t\t\t\t\treturn Ex(pybind11::str(py_name));\n\t\t\t\t\t}\n\t\t\t}\n\t\t};\n\n\tpybind11::handle type_obj = obj.get_type();\n\tstd::string type_name = pybind11::str(type_obj);\n\n\tauto fun = known.find(type_name);\n\tif(fun != known.end()) {\n\t\t// std::cerr << type_name << std::endl;\n\t\treturn (fun->second)(obj);\n\t\t}\n\telse {\n\t\t// SymPy represents each function as a separate class. So the type of\n\t\t// `f(x)` will be `f`, and you need to walk the inheritance chain to\n\t\t// figure out that it is f -> AppliedUndef -> Function.\n\t\t// See https://github.com/sympy/sympy/issues/18028 for details.\n\n\t\tpybind11::object mro = type_obj.attr(\"__mro__\");\n//\t\tint depth=0;\n\t\tfor(pybind11::handle base_class: mro) {\n\t\t\tstd::string class_name = base_class.attr(\"__name__\").cast<std::string>();\n\t\t\tif(class_name == \"Function\") {\n\t\t\t\t// std::cerr << \" Function!\" << std::endl;\n\t\t\t\tEx ex_fun(type_name);\n\t\t\t\tpybind11::object py_args = obj.attr(\"args\");\n\t\t\t\tfor(pybind11::handle py_arg: py_args) {\n\t\t\t\t\tex_fun.append_child(ex_fun.begin(), convert(py_arg).begin())->fl.bracket=str_node::b_none;\n\t\t\t\t\t}\n\t\t\t\treturn ex_fun;\n\t\t\t\t}\n//\t\t\tif(++depth == 3)\n//\t\t\t\tbreak;\n\t\t\t}\n\t\tthrow InternalError(\"SympyBridge::convert: do not know (yet) how to handle \"+type_name);\n\t\t}\n\t}\n\nvoid sympy::SympyBridge::import_ex(pybind11::object obj)\n\t{\n\tif(pybind11::isinstance<pybind11::str>(obj))\n\t\tthrow ArgumentException(\"SympyBridge::from_sympy: passing as 'str' is now disabled, pass the sympy object instead.\");\n\t\n\tEx new_ex = convert(obj);\n\tpre_clean_dispatch_deep(kernel, new_ex);\n\tcleanup_dispatch_deep(kernel, new_ex);\n\timport(new_ex);\n\tEx::iterator first=new_ex.begin();\n\tEx::iterator orig=tree.begin();\n\tex->move_ontop(orig, first);\n\t}\n\n// void sympy::SympyBridge::import_ex(const std::string& s)\n// \t{\n// \tpreparse_import(s);\n// #ifdef DEBUG\n// \tstd::cerr << \"sympy::SympyBridge::import_ex: \" << s << std::endl;\n// #endif\n// \tauto ptr = std::make_shared<Ex>();\n// \tcadabra::Parser parser(ptr);\n// \tstd::stringstream istr(s);\n// \tistr >> parser;\n// \n// \tpre_clean_dispatch_deep(kernel, *parser.tree);\n// \tcleanup_dispatch_deep(kernel, *parser.tree);\n// #ifdef DEBUG\n// \tstd::cerr << \"importing \" << parser.tree->begin() << std::endl;\n// #endif\n// \timport(*parser.tree);\n// \tEx::iterator first=parser.tree->begin();\n// \tEx::iterator orig=tree.begin();\n// \tex->move_ontop(orig, first);\n// #ifdef DEBUG\n// \tstd::cerr << \"result \" << ex->begin() << std::endl;\n// #endif\n// \t}\n\n#endif\n\nEx::iterator sympy::apply(const Kernel& kernel, Ex& ex, Ex::iterator& it, const std::vector<std::string>& wrap, std::vector<std::string> args,\n                          const std::string& method)\n\t{\n\t// Safeguard against using noncommuting/anticommuting objects.\n\tEx::iterator cpy = it, nxt = it;\n\tnxt.skip_children();\n\t++nxt;\n\twhile(cpy != nxt) {\n\t\tif(Algorithm::is_noncommuting(kernel.properties, cpy))\n\t\t\tthrow RuntimeException(\"Cannot handle NonCommuting/AntiCommuting objects in the SymPy bridge.\");\n\t\t\n\t\t++cpy;\n\t\t}\n\n\t// We first need to print the sub-expression using DisplaySympy,\n\t// optionally with the head wrapped around it and the args added\n\t// (if present).\n\tstd::ostringstream str;\n\n\tfor(size_t i=0; i<wrap.size(); ++i) {\n\t\tstr << wrap[i] << \"(\";\n\t\t}\n\n\tDisplaySympy ds(kernel, ex);\n\tds.output(str, it);\n\n\tif(wrap.size()>0)\n\t\tif(args.size()>0) {\n\t\t\tfor(size_t i=0; i<args.size(); ++i)\n\t\t\t\tstr << \", \" << args[i];\n\t\t\t}\n\tfor(size_t i=1; i<wrap.size(); ++i)\n\t\tstr << \")\";\n\tstr << method;\n\n\tif(wrap.size()>0)\n\t\tstr << \")\";\n\n\t// We then execute the expression in Python.\n\n\t//ex.print_recursive_treeform(std::cerr, it);\n#ifdef DEBUG\n\tstd::cerr << \"feeding \" << str.str() << std::endl;\n\tstd::cerr << \"which is \" << it << std::endl;\n#endif\n\n\tauto module = pybind11::module::import(\"sympy.parsing.sympy_parser\");\n\tauto parse  = module.attr(\"parse_expr\");\n\tpybind11::object obj = parse(str.str());\n\t//std::cerr << \"converting result to string\" << std::endl;\n\tauto __str__ = obj.attr(\"__str__\");\n\tpybind11::object res = __str__();\n\tstd::string result = res.cast<std::string>();\n#ifdef DEBUG\n\tstd::cerr << \"result \" << result << std::endl;\n#endif\n\n\n\t// After that, we construct a new sub-expression from this string by using our\n\t// own parser, and replace the original.\n\n\tresult = ds.preparse_import(result);\n\n\tauto ptr = std::make_shared<Ex>();\n\tcadabra::Parser parser(ptr);\n\tstd::stringstream istr(result);\n\tistr >> parser;\n\n\tpre_clean_dispatch_deep(kernel, *parser.tree);\n\tcleanup_dispatch_deep(kernel, *parser.tree);\n\n\t//parser.tree->print_recursive_treeform(std::cerr, parser.tree->begin());\n\n\tds.import(*parser.tree);\n\n\n\tEx::iterator first=parser.tree->begin();\n#ifdef DEBUG\n\tstd::cerr << \"reparsed \" << first.node << \"\\n\" << Ex(first) << std::endl;\n\tstd::cerr << \"before \" << it.node << \"\\n\" << Ex(it) << std::endl;\n#endif\n\tstr_node::parent_rel_t pr = it->fl.parent_rel;\n\tit = ex.move_ontop(it, first);\n\tit->fl.parent_rel = pr;\n#ifdef DEBUG\n\tstd::cerr << \"after \" << Ex(it) << std::endl;\n\tstd::cerr << \"top node \" << it.node << std::endl;\n#endif\n\n\n\treturn it;\n\t}\n\nEx sympy::fill_matrix(const Kernel& kernel, Ex& ex, Ex& rules)\n\t{\n\t// check that object has two children only.\n\tif(ex.number_of_children(ex.begin())!=2) {\n\t\tthrow ConsistencyException(\"Object should have exactly two indices.\");\n\t\t}\n\n\tEx::iterator ind1=ex.child(ex.begin(), 0);\n\tEx::iterator ind2=ex.child(ex.begin(), 1);\n\n\t// Get Indices property and from there Coordinates.\n\n\tconst Indices *prop1 = kernel.properties.get<Indices>(ind1);\n\tconst Indices *prop2 = kernel.properties.get<Indices>(ind2);\n\n\tif(prop1!=prop2 || prop1==0)\n\t\tthrow ConsistencyException(\"Need the indices of object to be declared with Indices property.\");\n\n\t// Run over all values of Coordinates, construct matrix.\n\n\tEx matrix(\"\\\\matrix\");\n\tconst auto& values = prop1->values(kernel.properties, ind1);\n\tauto cols=matrix.append_child(matrix.begin(), str_node(\"\\\\comma\"));\n\tfor(unsigned c1=0; c1<values.size(); ++c1) {\n\t\tauto row=matrix.append_child(cols, str_node(\"\\\\comma\"));\n\t\tfor(unsigned c2=0; c2<values.size(); ++c2) {\n\t\t\t// Generate an expression with this component, apply substitution, then stick\n\t\t\t// the result into the string that will go to sympy.\n\n\t\t\tEx c(ex.begin());\n\t\t\tEx::iterator cit1=c.child(c.begin(), 0);\n\t\t\tEx::iterator cit2=c.child(c.begin(), 1);\n\t\t\tcit1=c.replace_index(cit1, values[c1].begin(), true);\n\t\t\tcit2=c.replace_index(cit2, values[c2].begin(), true);\n\n\t\t\tEx::iterator cit=c.begin();\n\t\t\tsubstitute subs(kernel, c, rules);\n\t\t\tif(subs.can_apply(cit)) {\n\t\t\t\tsubs.apply(cit);\n\t\t\t\tmatrix.append_child(row, cit);\n\t\t\t\t}\n\t\t\telse {\n\t\t\t\tzero( matrix.append_child(row, str_node(\"1\"))->multiplier );\n\t\t\t\t}\n\t\t\t}\n\t\t}\n\n\treturn matrix;\n\t}\n\nvoid sympy::invert_matrix(const Kernel& kernel, Ex& ex, Ex& rules, const Ex& tocompute)\n\t{\n\tif(ex.number_of_children(ex.begin())!=2) {\n\t\tthrow ConsistencyException(\"Object should have exactly two indices.\");\n\t\t}\n\n\tauto matrix = fill_matrix(kernel, ex, rules);\n\n\tauto top=matrix.begin();\n\tstd::vector<std::string> wrap;\n\tsympy::apply(kernel, matrix, top, wrap, std::vector<std::string>(), \".inv()\");\n\t//matrix.print_recursive_treeform(std::cerr, top);\n\n\tEx::iterator ind1=ex.child(ex.begin(), 0);\n\tEx::iterator ind2=ex.child(ex.begin(), 1);\n\tconst Indices *prop1 = kernel.properties.get<Indices>(ind1);\n\tconst Indices *prop2 = kernel.properties.get<Indices>(ind2);\n\n\tEx::iterator ruleslist=rules.begin();\n\tconst auto& values1 = prop1->values(kernel.properties, ind1);\n\tconst auto& values2 = prop2->values(kernel.properties, ind2);\t\n\n\t// Now we need to iterate over the components again and construct sparse rules.\n\tauto cols=matrix.begin(matrix.begin()); // outer comma\n\tauto row=matrix.begin(cols); // first inner comma\n\tfor(unsigned c1=0; c1<values1.size(); ++c1) {\n\t\tauto el =matrix.begin(row);  // first element of first inner comma\n\t\tfor(unsigned c2=0; c2<values2.size(); ++c2) {\n\t\t\tif(el->is_zero()==false) {\n\t\t\t\tEx rule(\"\\\\equals\");\n\t\t\t\tauto rit  = rule.append_child(rule.begin(), tocompute.begin());\n\t\t\t\t/* auto cvit = */ rule.append_child(rule.begin(), Ex::iterator(el));\n\t\t\t\tauto i = rule.begin(rit);\n\t\t\t\t//std::cerr << c1 << \", \" << c2 << std::endl;\n\t\t\t\ti = rule.replace_index(i, values1[c1].begin(), true);\n\t\t\t\t//\t\t\t\ti->fl.parent_rel=ind1->fl.parent_rel;\n\t\t\t\t++i;\n\t\t\t\ti = rule.replace_index(i, values2[c2].begin(), true);\n\t\t\t\t//\t\t\t\ti->fl.parent_rel=ind1->fl.parent_rel;\n\t\t\t\trules.append_child(ruleslist, rule.begin());\n\t\t\t\t//rule.print_recursive_treeform(std::cerr, rule.begin());\n\t\t\t\t}\n\t\t\t++el;\n\t\t\t}\n\t\t++row;\n\t\t}\n\t}\n\nvoid sympy::determinant(const Kernel& kernel, Ex& ex, Ex& rules, const Ex& tocompute)\n\t{\n\tauto matrix = fill_matrix(kernel, ex, rules);\n\n\tauto top=matrix.begin();\n\tstd::vector<std::string> wrap;\n\tsympy::apply(kernel, matrix, top, wrap, std::vector<std::string>(), \".det()\");\n\n\tEx rule(\"\\\\equals\");\n\trule.append_child(rule.begin(), tocompute.begin());\n\trule.append_child(rule.begin(), matrix.begin());\n\trules.append_child(rules.begin(), rule.begin());\n\t}\n\nvoid sympy::trace(const Kernel& kernel, Ex& ex, Ex& rules, const Ex& tocompute)\n\t{\n\tauto matrix = fill_matrix(kernel, ex, rules);\n\n\tauto top=matrix.begin();\n\tstd::vector<std::string> wrap;\n\tsympy::apply(kernel, matrix, top, wrap, std::vector<std::string>(), \".trace()\");\n\n\tEx rule(\"\\\\equals\");\n\trule.append_child(rule.begin(), tocompute.begin());\n\trule.append_child(rule.begin(), matrix.begin());\n\trules.append_child(rules.begin(), rule.begin());\n\t}\n"
  },
  {
    "path": "core/SympyCdb.hh",
    "content": "\n#pragma once\n\n#include \"Props.hh\"\n#include \"Storage.hh\"\n#include \"Kernel.hh\"\n#include \"Stopwatch.hh\"\n#include \"DisplaySympy.hh\"\n\n#ifndef NO_SYMPY\n#include <pybind11/pybind11.h>\n#endif\n\nnamespace sympy {\n\n#ifndef NO_SYMPY\n\t/// Helper class to enable conversion from/to sympy.\n\n\tclass SympyBridge : public cadabra::DisplaySympy {\n\t\tpublic:\n\t\t\tSympyBridge(const cadabra::Kernel&, std::shared_ptr<cadabra::Ex>);\n\t\t\tvirtual ~SympyBridge();\n\n\t\t\tpybind11::object export_ex();\n//\t\t\tvoid             import_ex(const std::string&);\n\t\t\tvoid             import_ex(pybind11::object obj);\n\n\t\tprivate:\n\t\t\tstd::shared_ptr<cadabra::Ex> ex;\n\n\t\t\tcadabra::Ex convert(pybind11::handle obj);\n\t\t};\n#endif\n\n\t/// \\ingroup scalar\n\t///\n\t/// Functionality to act with Sympy on all scalar parts of an expression, and\n\t/// keep the result in-place. This is a higher-level function than\n\t/// 'apply' below.\n\n\t//\tcadabra::Ex* map_sympy(const cadabra::Kernel&, cadabra::Ex&,\n\t//\t\t\t\t\t\t\t\t  const std::vector<std::string>& wrap, const std::string& args, const std::string& method);\n\n\t/// \\ingroup scalar\n\t///\n\t/// Functionality to act with Sympy functions on (parts of) Cadabra Ex expressions\n\t/// and read the result back into the same Ex. This duplicates some of the\n\t/// logic in PythonCdb.hh, in particular make_Ex_from_string, but it is best to\n\t/// keep these two completely separate.\n\n\tcadabra::Ex::iterator apply(const cadabra::Kernel&, cadabra::Ex&, cadabra::Ex::iterator&,\n\t                            const std::vector<std::string>& wrap, std::vector<std::string> args, const std::string& method);\n\n\t//    /// \\ingroup scalar\n\t//    ///\n\t//    /// Low-level function to feed a string to Python and read the result back in\n\t// \t/// as a Cadabra Ex. As compared to 'apply' above, this starts from a string rather\n\t// \t/// than an Ex, and hence gives more flexibility in constructing input.\n\t//\n\t// \tEx python(Kernel&, Ex&, Ex::iterator&, const std::string& head, const std::string& args);\n\n\n\t/// \\ingroup scalar\n\t///\n\t/// Use Sympy to invert a matrix, given a set of rules determining its\n\t/// sparse components. Will return a set of Cadabra rules for the\n\t/// inverse matrix.\n\n\tvoid invert_matrix(const cadabra::Kernel&, cadabra::Ex& ex, cadabra::Ex& rules, const cadabra::Ex& tocompute);\n\n\t/// \\ingroup scalar\n\t///\n\t/// Use Sympy to compute the determinant of a matrix, given a set of rules determining\n\t/// its sparse components. Will add the rules to the list.\n\n\tvoid determinant(const cadabra::Kernel&, cadabra::Ex& ex, cadabra::Ex& rules, const cadabra::Ex& tocompute);\n\tvoid trace(const cadabra::Kernel&, cadabra::Ex& ex, cadabra::Ex& rules, const cadabra::Ex& tocompute);\n\n\tcadabra::Ex fill_matrix(const cadabra::Kernel&, cadabra::Ex& ex, cadabra::Ex& rules);\n\t//\textern Stopwatch sympy_stopwatch;\n\n};\n"
  },
  {
    "path": "core/TerminalStream.cc",
    "content": "\n#include \"DisplayTerminal.hh\"\n#include \"TerminalStream.hh\"\n\nusing namespace cadabra;\n\nTerminalStream::TerminalStream(const Kernel& k, std::ostream& s)\n\t: kernel(k), out_(s)\n\t{\n\t}\n\nTerminalStream& TerminalStream::operator<<(const Ex& ex)\n\t{\n\tDisplayTerminal dt(kernel, ex, true);\n\tdt.output(out_);\n\treturn *this;\n\t}\n\nTerminalStream& TerminalStream::operator<<(std::shared_ptr<Ex> ex)\n\t{\n\tDisplayTerminal dt(kernel, *ex, true);\n\tdt.output(out_);\n\treturn *this;\n\t}\n"
  },
  {
    "path": "core/TerminalStream.hh",
    "content": "#pragma once\n\n#include \"Kernel.hh\"\n#include <ostream>\n\nnamespace cadabra {\n\n\tclass TerminalStream {\n\t\tpublic:\n\t\t\tTerminalStream(const Kernel&, std::ostream&);\n\n\t\t\tTerminalStream& operator<<(const Ex&);\n\t\t\tTerminalStream& operator<<(std::shared_ptr<Ex>);\n\n\t\t\ttemplate<class T>\n\t\t\tTerminalStream& operator<<(const T& obj)\n\t\t\t\t{\n\t\t\t\tout_ << obj;\n\t\t\t\treturn *this;\n\t\t\t\t}\n\n\t\t\tTerminalStream& operator <<(std::ostream& (*os)(std::ostream&))\n\t\t\t\t{\n\t\t\t\tout_ << os;\n\t\t\t\treturn *this;\n\t\t\t\t}\n\t\tprivate:\n\t\t\tconst Kernel& kernel;\n\t\t\tstd::ostream& out_;\n\t\t};\n\n\n\t}\n"
  },
  {
    "path": "core/YoungTab.cc",
    "content": "/*\n\nCadabra: a field-theory motivated computer algebra system.\nCopyright (C) 2001-2011  Kasper Peeters <kasper.peeters@aei.mpg.de>\n\n\tThis program is free software: you can redistribute it and/or\nmodify it under the terms of the GNU General Public License as\npublished by the Free Software Foundation, either version 3 of the\nLicense, or (at your option) any later version.\n\n\tThis program is distributed in the hope that it will be useful,\n\tbut WITHOUT ANY WARRANTY; without even the implied warranty of\nMERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU\nGeneral Public License for more details.\n\n\tYou should have received a copy of the GNU General Public License\n\talong with this program.  If not, see <http://www.gnu.org/licenses/>.\n\n*/\n\n#include \"YoungTab.hh\"\n#include <cassert>\n\nnamespace yngtab {\n\n\ttableau_base::tableau_base()\n\t\t: multiplicity(1), selfdual_column(0)\n\t\t{\n\t\t}\n\n\ttableau_base::~tableau_base()\n\t\t{\n\t\t}\n\n\ttableau::~tableau()\n\t\t{\n\t\t}\n\n\ttableau::tableau()\n\t\t: tableau_base()\n\t\t{\n\t\t}\n\n\ttableau::tableau(const tableau& other)\n\t\t{\n\t\trows=other.rows;\n\t\t}\n\n\tvoid tableau_base::add_row(unsigned int row_size)\n\t\t{\n\t\tassert(row_size>0);\n\t\tunsigned int row=number_of_rows();\n\t\tfor(unsigned int i=0; i<row_size; ++i)\n\t\t\tadd_box(row);\n\t\t}\n\n\tyngint_t tableau_base::dimension(unsigned int dim) const\n\t\t{\n\t\tyngint_t ret=1;\n\t\tfor(unsigned int r=0; r<number_of_rows(); ++r) {\n\t\t\tunsigned int backup=dim;\n\t\t\tfor(unsigned int c=0; c<row_size(r); ++c)\n\t\t\t\tret*=(dim++);\n\t\t\tdim=backup-1;\n\t\t\t}\n\t\tassert(ret%hook_length_prod()==0);\n\t\tret/=hook_length_prod();\n\t\treturn ret;\n\t\t}\n\n\tunsigned int tableau_base::column_size(unsigned int c) const\n\t\t{\n\t\tunsigned int r=0;\n\t\twhile(r<number_of_rows()) {\n\t\t\tif(row_size(r)-1<c)\n\t\t\t\tbreak;\n\t\t\t++r;\n\t\t\t}\n\t\treturn r;\n\t\t}\n\n\tunsigned long tableau_base::hook_length(unsigned int row, unsigned int col) const\n\t\t{\n\t\tassert(row<number_of_rows());\n\t\tassert(col<row_size(row));\n\t\tunsigned long hook=row_size(row)-col;\n\t\tfor(unsigned int i=row+1; i<number_of_rows() && col<row_size(i); ++i)\n\t\t\t++hook;\n\t\treturn hook;\n\t\t}\n\n\tyngint_t tableau_base::hook_length_prod() const\n\t\t{\n\t\tyngint_t hook=1;\n\t\tfor(unsigned int i=0; i<number_of_rows(); ++i)\n\t\t\tfor(unsigned int j=0; j<row_size(i); ++j)\n\t\t\t\thook*=hook_length(i,j);\n\t\treturn hook;\n\t\t}\n\n\tvoid tableau::add_box(unsigned int rownum)\n\t\t{\n\t\tif(rownum>=rows.size()) {\n\t\t\tunsigned int prevsize=rows.size();\n\t\t\trows.resize(rownum+1);\n\t\t\tfor(unsigned int i=prevsize; i<rows.size(); ++i)\n\t\t\t\trows[i]=0;\n\t\t\t}\n\t\t++rows[rownum];\n\t\t}\n\n\tvoid tableau::remove_box(unsigned int rownum)\n\t\t{\n\t\tassert(rownum<rows.size());\n\t\tassert(rows[rownum]>0);\n\t\tif((--rows[rownum])==0)\n\t\t\trows.pop_back();\n\t\t}\n\n\tunsigned int tableau::number_of_rows() const\n\t\t{\n\t\treturn rows.size();\n\t\t}\n\n\tunsigned int tableau::row_size(unsigned int num) const\n\t\t{\n\t\tassert(num<rows.size());\n\t\treturn rows[num];\n\t\t}\n\n\tvoid tableau::clear()\n\t\t{\n\t\trows.clear();\n\t\t}\n\n\ttableau& tableau::operator=(const tableau& other)\n\t\t{\n\t\trows=other.rows;\n\t\treturn (*this);\n\t\t}\n\n\tstd::ostream& operator<<(std::ostream& str, const tableau& tab)\n\t\t{\n\t\tfor(unsigned int i=0; i<tab.number_of_rows(); ++i) {\n\t\t\tfor(unsigned int j=0; j<tab.row_size(i); ++j) {\n\t\t\t\t//\t\t\tstr << \"|x|\";\n\t\t\t\tstr << \"x\";\n\t\t\t\t}\n\t\t\tif(i==0) str << \"  \" << tab.dimension(10) << \" \" << tab.hook_length_prod();\n\t\t\tif(i!=tab.number_of_rows()-1)\n\t\t\t\tstr << std::endl;\n\t\t\t}\n\t\treturn str;\n\t\t}\n\n\t//bool legal_box(const std::vector<std::pair<int,int> >& prev,\n\t//\t\t\t\t\tconst std::vector<std::pair<int,int> >& ths,\n\t//\t\t\t\t\tint colpos, int rowpos)\n\t//\t{\n\t//\t// Note the initial condition: upon startup, the prev vector contains as many -1,-1\n\t//   // pairs as boxes in the first row of tableau 2. So 'prevabove' will initially evaluate\n\t//\t// to this number.\n\t//\n\t//\tint prevabove=0; // number of boxes of the previous row added above the candidate position\n\t//\tint thisabove=0; // number of boxes of the current  row added above the candidate position\n\t//\tfor(unsigned int i=0; i<prev.size(); ++i) {\n\t//\t\tif(prev[i].second<rowpos)\n\t//\t\t\t++prevabove;\n\t//\t\t}\n\t//\tfor(unsigned int i=0; i<ths.size(); ++i) {\n\t//\t\tif(ths[i].first==colpos) return false; // would imply anti-symmetrisation of symmetrised boxes\n\t//\t\tif(ths[i].second<rowpos)\n\t//\t\t\t++thisabove;\n\t//\t\t}\n\t//\tif(prevabove>thisabove) return true;\n\t//\treturn false;\n\t//\t}\n\n#ifndef __CYGWIN__\n#ifndef _WIN32\n\ttemplate<>\n\tvoid add_box(tableau& tab1, unsigned int row1,\n\t             const tableau&, unsigned int, unsigned int)\n\t\t{\n\t\ttab1.add_box(row1);\n\t\t}\n#endif\n#endif\n\n\t};\n"
  },
  {
    "path": "core/YoungTab.hh",
    "content": "/*\n\nCadabra: a field-theory motivated computer algebra system.\nCopyright (C) 2001-2011  Kasper Peeters <kasper.peeters@aei.mpg.de>\n\n\tThis program is free software: you can redistribute it and/or\nmodify it under the terms of the GNU General Public License as\npublished by the Free Software Foundation, either version 3 of the\nLicense, or (at your option) any later version.\n\n\tThis program is distributed in the hope that it will be useful,\n\tbut WITHOUT ANY WARRANTY; without even the implied warranty of\nMERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU\nGeneral Public License for more details.\n\n\tYou should have received a copy of the GNU General Public License\n\talong with this program.  If not, see <http://www.gnu.org/licenses/>.\n\n*/\n\n/*\n- TODO: has_nullifying trace is wrong, but needs to be merged with the\n        input_asym code in order to be more useful.\n\n*/\n\n#pragma once\n\n#include <cstddef>\n#include <iostream>\n#include <iterator>\n#include <vector>\n#include <list>\n#include <gmpxx.h>\n#include \"Combinatorics.hh\"\n#include <cstddef>\n\ntypedef mpz_class yngint_t;\ntypedef mpq_class yngrat_t;\n\n/// Generic Young tableaux routines\nnamespace yngtab {\n\n\t// The tableau_base is the abstract interface; does not depend on the\n\t// actual storage format.\n\n\tclass tableau_base {\n\t\tpublic:\n\t\t\ttableau_base();\n\t\t\tvirtual ~tableau_base();\n\t\t\tvirtual unsigned int number_of_rows() const=0;\n\t\t\tvirtual unsigned int row_size(unsigned int row) const=0;\n\t\t\tvirtual unsigned int column_size(unsigned int col) const; // FIXME: maybe make pure virt too\n\t\t\tvirtual void         add_box(unsigned int row)=0;\n\t\t\tvirtual void         remove_box(unsigned int row)=0;\n\t\t\tvirtual void         add_row(unsigned int row_size);\n\t\t\tvirtual void         clear()=0;\n\n\t\t\tyngrat_t             multiplicity;    // also keeps track of signs\n\t\t\tint                  selfdual_column; // -n, 0, n  for antiselfdual, no, selfdual (count from 1)\n\t\t\tyngint_t             dimension(unsigned int) const;\n\t\t\tunsigned long        hook_length(unsigned int row, unsigned int col) const;\n\t\t\tyngint_t             hook_length_prod() const;\n\t\t};\n\n\tclass tableau : public tableau_base {\n\t\tpublic:\n\t\t\ttableau();\n\t\t\ttableau(const tableau&);\n\t\t\t\n\t\t\tvirtual ~tableau();\n\t\t\tvirtual unsigned int number_of_rows() const;\n\t\t\tvirtual unsigned int row_size(unsigned int row) const;\n\t\t\tvirtual void         add_box(unsigned int row);\n\t\t\tvirtual void         remove_box(unsigned int row);\n\t\t\tvirtual void         clear();\n\n\t\t\ttableau& operator=(const tableau&);\n\t\tprivate:\n\t\t\tstd::vector<int> rows;\n\t\t};\n\n\ttemplate<class T>\n\tclass tableaux;\n\n\ttemplate<class T>\n\tclass filled_tableau : public tableau {\n\t\tpublic:\n\t\t\ttypedef T value_type;\n\n\t\t\tfilled_tableau();\n\t\t\tfilled_tableau(const filled_tableau<T>&);\n\t\t\t\n\t\t\tvirtual ~filled_tableau();\n\t\t\tvirtual unsigned int number_of_rows() const;\n\t\t\tvirtual unsigned int row_size(unsigned int row) const;\n\t\t\tvirtual void         add_box(unsigned int row);\n\t\t\tvirtual void         remove_box(unsigned int row);\n\t\t\tstd::pair<int, int>  find(const T&) const;\n\t\t\tvirtual void         clear();\n\n\t\t\tvoid                 copy_shape(const tableau&);\n\n\t\t\tT&                   operator()(unsigned int row, unsigned int col);\n\t\t\tconst T&             operator()(unsigned int row, unsigned int col) const;\n\t\t\tconst T&             operator[](unsigned int boxnum) const;\n\t\t\tvoid                 add_box(unsigned int rownum, T val);\n\t\t\tvoid                 swap_columns(unsigned int c1, unsigned int c2);\n\n\t\t\tbool                 compare_without_multiplicity(const filled_tableau<T>& other) const;\n\t\t\tbool                 has_nullifying_trace() const;\n\t\t\tvoid                 sort_within_columns();\n\t\t\tvoid                 sort_columns();\n\t\t\t/// Sort equal-length columns and sort within columns.\n\t\t\tvoid                 canonicalise();\n\t\t\tstd::pair<int, int>  nonstandard_loc() const;\n\t\t\ttemplate<class StrictWeakOrdering> void sort_within_columns(StrictWeakOrdering comp);\n\t\t\ttemplate<class StrictWeakOrdering> void sort_columns(StrictWeakOrdering comp);\n\t\t\ttemplate<class StrictWeakOrdering> void canonicalise(StrictWeakOrdering comp, bool only_col_ex=false);\n\t\t\tvoid                 projector(combin::symmetriser<T>&, bool modulo_monoterm=false) const;\n\t\t\tvoid                 projector(combin::symmetriser<T>&, combin::range_vector_t&) const;\n\t\t\tyngrat_t             projector_normalisation() const;\n\n\t\t\tfilled_tableau<T>& operator=(const filled_tableau<T>&);\n\n\t\t\tclass iterator_base {\n\t\t\t\tpublic:\n\t\t\t\t\ttypedef T                               value_type;\n\t\t\t\t\ttypedef T*                              pointer;\n\t\t\t\t\ttypedef T&                              reference;\n\t\t\t\t\ttypedef size_t                          size_type;\n\t\t\t\t\ttypedef ptrdiff_t                       difference_type;\n\t\t\t\t\ttypedef std::random_access_iterator_tag iterator_category;\n\t\t\t\t};\n\n\t\t\tclass const_iterator_base {\n\t\t\tpublic:\n\t\t\t\ttypedef T                               value_type;\n\t\t\t\ttypedef const T* pointer;\n\t\t\t\ttypedef const T& reference;\n\t\t\t\ttypedef size_t                          size_type;\n\t\t\t\ttypedef ptrdiff_t                       difference_type;\n\t\t\t\ttypedef std::random_access_iterator_tag iterator_category;\n\t\t\t};\n\n\t\t\tclass const_iterator;\n\t\t\tclass in_column_iterator;\n\t\t\tclass in_column_const_iterator;\n\t\t\tclass in_row_iterator;\n\t\t\tclass in_row_const_iterator;\t\t\t\t\t\t\n\t\t\t\n\t\t\t/// An iterator which stays inside a given column of a tableau.\n\t\t\tclass in_column_iterator : public iterator_base {\n\t\t\t\tpublic:\n\t\t\t\t\tin_column_iterator(unsigned int r, unsigned int c, filled_tableau<T> *);\n\t\t\t\t\tT&                  operator*() const;\n\t\t\t\t\tT*                  operator->() const;\n\t\t\t\t\tin_column_iterator& operator++();\n\t\t\t\t\tin_column_iterator  operator++(int);\n\t\t\t\t\tin_column_iterator& operator--();\n\t\t\t\t\tin_column_iterator  operator--(int);\n\t\t\t\t\tin_column_iterator  operator+(unsigned int) const;\n\t\t\t\t\tin_column_iterator  operator-(unsigned int) const;\n\t\t\t\t\tin_column_iterator& operator+=(unsigned int);\n\t\t\t\t\tin_column_iterator& operator-=(unsigned int);\n\t\t\t\t\tT&                  operator[](int n) const;\n\t\t\t\t\tbool                operator<(const in_column_iterator& other) const;\n\t\t\t\t\tbool                operator>(const in_column_iterator& other) const;\n\t\t\t\t\tbool                operator<=(const in_column_iterator& other) const;\n\t\t\t\t\tbool                operator>=(const in_column_iterator& other) const;\n\t\t\t\t\tptrdiff_t           operator-(const in_column_iterator&) const;\n\t\t\t\t\tbool                operator==(const in_column_iterator&) const;\n\t\t\t\t\tbool                operator!=(const in_column_iterator&) const;\n\n\t\t\t\t\tfriend class filled_tableau<T>;\n\t\t\t\t\tfriend class filled_tableau<T>::in_column_const_iterator;\n\t\t\t\tprivate:\n\t\t\t\t\tfilled_tableau<T> *tab;\n\t\t\t\t\tunsigned int       column_number, row_number;\n\t\t\t\t};\n\n\t\t\t/// A const iterator which stays inside a given column of a tableau.\n\t\t\tclass in_column_const_iterator : public const_iterator_base {\n\t\t\tpublic:\n\t\t\t\tin_column_const_iterator(unsigned int r, unsigned int c, const filled_tableau<T>*);\n\t\t\t\tin_column_const_iterator(const in_column_iterator& other);\n\t\t\t\tconst T& operator*() const;\n\t\t\t\tconst T* operator->() const;\n\t\t\t\tin_column_const_iterator& operator++();\n\t\t\t\tin_column_const_iterator  operator++(int);\n\t\t\t\tin_column_const_iterator& operator--();\n\t\t\t\tin_column_const_iterator  operator--(int);\n\t\t\t\tin_column_const_iterator  operator+(unsigned int) const;\n\t\t\t\tin_column_const_iterator  operator-(unsigned int) const;\n\t\t\t\tin_column_const_iterator& operator+=(unsigned int);\n\t\t\t\tin_column_const_iterator& operator-=(unsigned int);\n\t\t\t\tbool                operator<(const in_column_const_iterator& other) const;\n\t\t\t\tbool                operator>(const in_column_const_iterator& other) const;\n\t\t\t\tbool                operator<=(const in_column_const_iterator& other) const;\n\t\t\t\tbool                operator>=(const in_column_const_iterator& other) const;\n\t\t\t\tptrdiff_t           operator-(const in_column_const_iterator&) const;\n\t\t\t\tbool                operator==(const in_column_const_iterator&) const;\n\t\t\t\tbool                operator!=(const in_column_const_iterator&) const;\n\n\t\t\t\tfriend class filled_tableau<T>;\n\t\t\tprivate:\n\t\t\t\tconst filled_tableau<T>* tab;\n\t\t\t\tunsigned int       column_number, row_number;\n\t\t\t};\n\n\t\t\t/// An iterator which stays inside a given row of a tableau.\n\t\t\tclass in_row_iterator : public iterator_base {\n\t\t\tpublic:\n\t\t\t\tin_row_iterator(unsigned int r, unsigned int c, filled_tableau<T>*);\n\t\t\t\tT& operator*() const;\n\t\t\t\tT* operator->() const;\n\t\t\t\tin_row_iterator& operator++();\n\t\t\t\tin_row_iterator  operator++(int);\n\t\t\t\tin_row_iterator& operator--();\n\t\t\t\tin_row_iterator  operator--(int);\n\t\t\t\tin_row_iterator  operator+(unsigned int) const;\n\t\t\t\tin_row_iterator  operator-(unsigned int) const;\n\t\t\t\tin_row_iterator& operator+=(unsigned int);\n\t\t\t\tin_row_iterator& operator-=(unsigned int);\n\t\t\t\tbool                operator<(const in_row_iterator& other) const;\n\t\t\t\tbool                operator>(const in_row_iterator& other) const;\n\t\t\t\tbool                operator<=(const in_row_iterator& other) const;\n\t\t\t\tbool                operator>=(const in_row_iterator& other) const;\n\t\t\t\tptrdiff_t           operator-(const in_row_iterator&) const;\n\t\t\t\tbool                operator==(const in_row_iterator&) const;\n\t\t\t\tbool                operator!=(const in_row_iterator&) const;\n\n\t\t\t\tfriend class filled_tableau<T>;\n\t\t\t\tfriend class filled_tableau<T>::in_row_const_iterator;\n\t\t\tprivate:\n\t\t\t\tfilled_tableau<T>* tab;\n\t\t\t\tunsigned int       column_number, row_number;\n\t\t\t};\n\n\t\t\tclass in_row_const_iterator : public const_iterator_base {\n\t\t\tpublic:\n\t\t\t\tin_row_const_iterator(unsigned int r, unsigned int c, const filled_tableau<T>*);\n\t\t\t\tin_row_const_iterator(const in_row_iterator& other);\n\t\t\t\tconst T& operator*() const;\n\t\t\t\tconst T* operator->() const;\n\t\t\t\tin_row_const_iterator& operator++();\n\t\t\t\tin_row_const_iterator  operator++(int);\n\t\t\t\tin_row_const_iterator& operator--();\n\t\t\t\tin_row_const_iterator  operator--(int);\n\t\t\t\tin_row_const_iterator  operator+(unsigned int) const;\n\t\t\t\tin_row_const_iterator  operator-(unsigned int) const;\n\t\t\t\tin_row_const_iterator& operator+=(unsigned int);\n\t\t\t\tin_row_const_iterator& operator-=(unsigned int);\n\t\t\t\tbool                operator<(const in_row_const_iterator& other) const;\n\t\t\t\tbool                operator>(const in_row_const_iterator& other) const;\n\t\t\t\tbool                operator<=(const in_row_const_iterator& other) const;\n\t\t\t\tbool                operator>=(const in_row_const_iterator& other) const;\n\t\t\t\tptrdiff_t           operator-(const in_row_const_iterator&) const;\n\t\t\t\tbool                operator==(const in_row_const_iterator&) const;\n\t\t\t\tbool                operator!=(const in_row_const_iterator&) const;\n\n\t\t\t\tfriend class filled_tableau<T>;\n\t\t\tprivate:\n\t\t\t\tconst filled_tableau<T>* tab;\n\t\t\t\tunsigned int       column_number, row_number;\n\t\t\t};\n\n\t\t\t/// An iterator over all boxes of a tableau, left to right, top to bottom.\n\t\t\tclass iterator : public iterator_base {\n\t\t\t\tpublic:\n\t\t\t\t\titerator(unsigned int r, unsigned int c, filled_tableau<T> *);\n\t\t\t\t\tT&                  operator*() const;\n\t\t\t\t\tT*                  operator->() const;\n\t\t\t\t\titerator&           operator++();\n\t\t\t\t\titerator            operator++(int);\n\t\t\t\t\titerator&           operator--();\n\t\t\t\t\titerator            operator--(int);\n\t\t\t\t\titerator            operator+(unsigned int) const;\n\t\t\t\t\titerator            operator-(unsigned int) const;\n\t\t\t\t\titerator&           operator+=(unsigned int);\n\t\t\t\t\titerator&           operator-=(unsigned int);\n\t\t\t\t\tbool                operator<(const iterator& other) const;\n\t\t\t\t\tbool                operator>(const iterator& other) const;\n\t\t\t\t\tptrdiff_t           operator-(const iterator&) const;\n\t\t\t\t\tbool                operator==(const iterator&) const;\n\t\t\t\t\tbool                operator!=(const iterator&) const;\n\n\t\t\t\t\tfriend class filled_tableau<T>;\n\t\t\t\t\tfriend class filled_tableau<T>::const_iterator;\n\t\t\t\tprivate:\n\t\t\t\t\tfilled_tableau<T> *tab;\n\t\t\t\t\tunsigned int       column_number, row_number;\n\t\t\t\t};\n\n\t\t\tclass const_iterator : public const_iterator_base {\n\t\t\tpublic:\n\t\t\t\tconst_iterator(unsigned int r, unsigned int c, const filled_tableau<T>*);\n\t\t\t\tconst_iterator(const iterator& other);\n\t\t\t\tconst T& operator*() const;\n\t\t\t\tconst T* operator->() const;\n\t\t\t\tconst_iterator&\t\t\t\toperator++();\n\t\t\t\tconst_iterator            operator++(int);\n\t\t\t\tconst_iterator&\t\t\t\toperator--();\n\t\t\t\tconst_iterator            operator--(int);\n\t\t\t\tconst_iterator            operator+(unsigned int) const;\n\t\t\t\tconst_iterator            operator-(unsigned int) const;\n\t\t\t\tconst_iterator&\t\t\t\t operator+=(unsigned int);\n\t\t\t\tconst_iterator&\t\t\t\toperator-=(unsigned int);\n\t\t\t\tbool\t\t\t               operator<(const const_iterator& other) const;\n\t\t\t\tbool\t\t\t\t\t        operator>(const const_iterator& other) const;\n\t\t\t\tptrdiff_t\t\t\t\t\t  operator-(const const_iterator&) const;\n\t\t\t\tbool\t\t\t             operator==(const const_iterator&) const;\n\t\t\t\tbool\t\t\t\t\t        operator!=(const const_iterator&) const;\n\n\t\t\t\tfriend class filled_tableau<T>;\n\t\t\tprivate:\n\t\t\t\tconst filled_tableau<T>* tab;\n\t\t\t\tunsigned int       column_number, row_number;\n\t\t\t};\n\n\n\t\t\tin_column_iterator   begin_column(unsigned int column_number);\n\t\t\tin_column_iterator   end_column(unsigned int column_number);\n\t\t\tin_column_const_iterator   begin_column(unsigned int column_number) const;\n\t\t\tin_column_const_iterator   end_column(unsigned int column_number) const;\n\t\t\tin_column_const_iterator   cbegin_column(unsigned int column_number) const;\n\t\t\tin_column_const_iterator   cend_column(unsigned int column_number) const;\n\t\t\tin_row_iterator\t\tbegin_row(unsigned int row_number);\n\t\t\tin_row_iterator\t\tend_row(unsigned int row_number);\n\t\t\tin_row_const_iterator\t\tbegin_row(unsigned int row_number) const;\n\t\t\tin_row_const_iterator\t\tend_row(unsigned int row_number) const;\n\t\t\tin_row_const_iterator\t\tcbegin_row(unsigned int row_number) const;\n\t\t\tin_row_const_iterator\t\tcend_row(unsigned int row_number) const;\n\t\t\titerator begin();\n\t\t\titerator end();\n\t\t\tconst_iterator             begin() const;\n\t\t\tconst_iterator             end() const;\n\t\t\tconst_iterator             cbegin() const;\n\t\t\tconst_iterator             cend() const;\n\n\t\t\ttemplate<class OutputIterator>\n\t\t\tOutputIterator       Garnir_set(OutputIterator, unsigned int, unsigned int) const;\n\t\tprivate:\n\t\t\ttypedef std::vector<T>       box_row;\n\t\t\ttypedef std::vector<box_row> row_stack;\n\t\t\trow_stack rows;\n\t\t};\n\n\ttemplate<class T>\n\tclass tableaux {\n\t\tpublic:\n\t\t\tyngint_t         total_dimension(unsigned int dim);\n\t\t\tvoid             remove_nullifying_traces();\n\t\t\t/// Put the set of tableaux into standard form by using Garnir symmetries.\n\t\t\t/// Return value indicates whether the tableaux were already all in standard form.\n\t\t\tbool             standard_form();\n\t\t\tvoid             add_tableau(const T&);\n\t\t\tvoid             symmetrise(const T& tabsym);\n\n\t\t\ttypedef std::list<T> tableau_container_t;\n\t\t\ttableau_container_t  storage;\n\n\t\t\ttypedef std::back_insert_iterator<tableau_container_t> back_insert_iterator;\n\n\t\t\tback_insert_iterator get_back_insert_iterator();\n\t\t};\n\n\tbool legal_box(const std::vector<std::pair<int,int> >& prev,\n\t               const std::vector<std::pair<int,int> >& ths,\n\t               int colpos, int trypos);\n\n\t// --------------------------------------\n\n\n\ttemplate<class T>\n\ttypename tableaux<T>::back_insert_iterator tableaux<T>::get_back_insert_iterator()\n\t\t{\n\t\treturn back_insert_iterator(storage);\n\t\t}\n\n\ttemplate<class T>\n\tvoid tableaux<T>::remove_nullifying_traces()\n\t\t{\n\t\ttypename tableau_container_t::iterator it=storage.begin();\n\t\twhile(it!=storage.end()) {\n\t\t\tif(it->has_nullifying_trace())\n\t\t\t\tit=storage.erase(it);\n\t\t\telse ++it;\n\t\t\t}\n\t\t}\n\n\ttemplate<class T>\n\tvoid tableaux<T>::symmetrise(const T&)\n\t\t{\n\t\t//\n\t\t//\ttypename tableau_container_t::iterator thetab=storage.begin();\n\t\t//\twhile(thetab!=storage.end()) {\n\t\t//\t\t(*thetab).sort_columns();\n\t\t//\t\tstd::pair<int,int> where=(*thetab).nonstandard_loc();\n\t\t//\t\tif(where.first!=-1) {\n\t\t//\t\t\tcombinations<typename T::value_type> com;\n\t\t//\n\n\t\t/*\n\t\tFIXME: we should have two LR_tensor routines, because if you do 'alltabs', you should\n\t\tkeep track of which boxes came from tableau 2. So do a LR_tensor with numbered boxes,\n\t\t\tand then after the LR_tensor apply the symmetries of the original tableaux, put back\n\t\tthe original index names, sort columns and determine whether the tableau is identically\n\t\t\tnon-zero. Then add to the product.\n\n\t\tAnother issue: adding to tableaux should have an option to not insert doubles.\n\n\t\t\tThere was something third, forgotten...\n\t\t*/\n\t\t}\n\n\ttemplate<class T>\n\tvoid filled_tableau<T>::copy_shape(const tableau& other)\n\t\t{\n\t\trows.clear();\n\t\tfor(unsigned int r=0; r<other.number_of_rows(); ++r) {\n\t\t\trows.push_back(box_row(other.row_size(r)));\n\t\t\t}\n\t\ttableau::operator=(other);\n\t\t}\n\n\ttemplate<class T>\n\tbool filled_tableau<T>::compare_without_multiplicity(const filled_tableau<T>& other) const\n\t\t{\n\t\treturn (rows==other.rows);\n\t\t}\n\n\ttemplate<class T>\n\tbool filled_tableau<T>::has_nullifying_trace() const\n\t\t{\n\t\treturn false;\n\n\t\t// Old, probably incorrect code:\n\t\t//\n\t\t//\tfor(unsigned int r1=0; r1<number_of_rows(); ++r1) {\n\t\t//\t\tfor(unsigned c1=0; c1<row_size(r1); ++c1) {\n\t\t//\t\t\tfor(unsigned int c2=c1+1; c2<row_size(r1); ++c2) {\n\t\t//\t\t\t\t// (r1,c1) and (r1,c2)\n\t\t//\t\t\t\tfor(unsigned int c3=0; c3<row_size(0); ++c3) {\n\t\t//\t\t\t\t\tunsigned int r3=0;\n\t\t//\t\t\t\t\twhile(r3<number_of_rows()-1 && c3<row_size(r3)) {\n\t\t//\t\t\t\t\t\tunsigned int r4=r3+1;\n\t\t//\t\t\t\t\t\twhile(r4<number_of_rows() && c3<row_size(r4)) {\n\t\t//\t\t\t\t\t\t\tif((rows[r1][c1]==rows[r3][c3] && rows[r1][c2]==rows[r4][c3]) ||\n\t\t//\t\t\t\t\t\t\t\t(rows[r1][c1]==rows[r4][c3] && rows[r1][c2]==rows[r3][c3]) )\n\t\t//\t\t\t\t\t\t\t\treturn true;\n\t\t//\t\t\t\t\t\t\t++r4;\n\t\t//\t\t\t\t\t\t\t}\n\t\t//\t\t\t\t\t\t++r3;\n\t\t//\t\t\t\t\t\t}\n\t\t//\t\t\t\t\t}\n\t\t//\t\t\t\t}\n\t\t//\t\t\t}\n\t\t//\t\t}\n\t\t//\treturn false;\n\t\t}\n\n\ttemplate<class T>\n\tstd::pair<int, int> filled_tableau<T>::find(const T& obj) const\n\t\t{\n\t\tfor(unsigned int ir=0; ir<rows.size(); ++ir) {\n\t\t\tfor(unsigned int ic=0; ic<rows[ir].size(); ++ic) {\n\t\t\t\tif(rows[ir][ic]==obj)\n\t\t\t\t\treturn std::pair<int,int>(ir, ic);\n\t\t\t\t}\n\t\t\t}\n\t\treturn std::pair<int,int>(-1,-1);\n\t\t}\n\n\ttemplate<class T>\n\tvoid filled_tableau<T>::sort_within_columns()\n\t\t{\n\t\tstd::less<T> comp;\n\t\tsort_within_columns(comp);\n\t\t}\n\n\ttemplate<class T>\n\tvoid filled_tableau<T>::sort_columns()\n\t\t{\n\t\tstd::less<T> comp;\n\t\tsort_columns(comp);\n\t\t}\n\n\ttemplate<class T>\n\tvoid filled_tableau<T>::canonicalise()\n\t\t{\n\t\tstd::less<T> comp;\n\t\tcanonicalise(comp);\n\t\t}\n\n\ttemplate<class T>\n\ttemplate<class StrictWeakOrdering>\n\tvoid filled_tableau<T>::sort_within_columns(StrictWeakOrdering comp)\n\t\t{\n\t\tfilled_tableau<T> tmp(*this);\n\t\tif(number_of_rows()==0) return;\n\t\tfor(unsigned int c=0; c<row_size(0); ++c) {\n\t\t\tstd::sort(begin_column(c), end_column(c), comp);\n\t\t\tmultiplicity*=combin::ordersign(begin_column(c), end_column(c), tmp.begin_column(c), tmp.end_column(c));\n\t\t\t}\n\t\t}\n\n\ttemplate<class T>\n\ttemplate<class StrictWeakOrdering>\n\tvoid filled_tableau<T>::sort_columns(StrictWeakOrdering comp)\n\t\t{\n\t\tfor(unsigned int c1=0; c1<row_size(0); ++c1) {\n\t\t\tfor(unsigned int c2=c1; c2<row_size(0); ++c2) {\n\t\t\t\tif(column_size(c1)==column_size(c2)) {\n\t\t\t\t\tif(comp((*this)(0,c2), (*this)(0,c1)))\n\t\t\t\t\t\tswap_columns(c1,c2);\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t}\n\t\t}\n\n\ttemplate<class T>\n\ttemplate<class StrictWeakOrdering>\n\tvoid filled_tableau<T>::canonicalise(StrictWeakOrdering comp, bool only_col_ex)\n\t\t{\n\t\tif(!only_col_ex)\n\t\t\tsort_within_columns(comp);\n\t\tsort_columns(comp);\n\t\t}\n\n\t//---------------------------------------------------------------------------\n\t// in_column_iterator\n\n\ttemplate<class T>\n\tfilled_tableau<T>::in_column_iterator::in_column_iterator(unsigned int r, unsigned int c, filled_tableau<T> *t)\n\t\t: tab(t), column_number(c), row_number(r)\n\t\t{\n\t\t}\n\n\ttemplate<class T>\n\ttypename filled_tableau<T>::in_column_iterator filled_tableau<T>::in_column_iterator::operator+(unsigned int n) const\n\t\t{\n\t\ttypename filled_tableau<T>::in_column_iterator it2(*this);\n\t\tit2+=n;\n\t\treturn it2;\n\t\t}\n\n\ttemplate<class T>\n\ttypename filled_tableau<T>::in_column_iterator filled_tableau<T>::in_column_iterator::operator-(unsigned int n) const\n\t\t{\n\t\ttypename filled_tableau<T>::in_column_iterator it2(*this);\n\t\tit2-=n;\n\t\treturn it2;\n\t\t}\n\n\ttemplate<class T>\n\tptrdiff_t filled_tableau<T>::in_column_iterator::operator-(const in_column_iterator& other) const\n\t\t{\n\t\treturn row_number-other.row_number;\n\t\t}\n\n\ttemplate<class T>\n\tT& filled_tableau<T>::in_column_iterator::operator[](int n) const\n\t\t{\n\t\treturn (*tab)(row_number + n, column_number);\n\t\t}\n\n\ttemplate<class T>\n\tT& filled_tableau<T>::in_column_iterator::operator*() const\n\t\t{\n\t\treturn (*tab)(row_number,column_number);\n\t\t}\n\n\ttemplate<class T>\n\tT* filled_tableau<T>::in_column_iterator::operator->() const\n\t\t{\n\t\treturn &((*tab)(row_number,column_number));\n\t\t}\n\n\ttemplate<class T>\n\ttypename filled_tableau<T>::in_column_iterator& filled_tableau<T>::in_column_iterator::operator++()\n\t\t{\n\t\t++row_number;\n\t\treturn (*this);\n\t\t}\n\n\ttemplate<class T>\n\ttypename filled_tableau<T>::in_column_iterator& filled_tableau<T>::in_column_iterator::operator+=(unsigned int n)\n\t\t{\n\t\trow_number+=n;\n\t\treturn (*this);\n\t\t}\n\n\ttemplate<class T>\n\ttypename filled_tableau<T>::in_column_iterator& filled_tableau<T>::in_column_iterator::operator--()\n\t\t{\n\t\t--row_number;\n\t\treturn (*this);\n\t\t}\n\n\ttemplate<class T>\n\ttypename filled_tableau<T>::in_column_iterator filled_tableau<T>::in_column_iterator::operator--(int)\n\t\t{\n\t\tin_column_iterator tmp(*this);\n\t\t--row_number;\n\t\treturn tmp;\n\t\t}\n\n\ttemplate<class T>\n\ttypename filled_tableau<T>::in_column_iterator filled_tableau<T>::in_column_iterator::operator++(int)\n\t\t{\n\t\tin_column_iterator tmp(*this);\n\t\t++row_number;\n\t\treturn tmp;\n\t\t}\n\n\ttemplate<class T>\n\ttypename filled_tableau<T>::in_column_iterator& filled_tableau<T>::in_column_iterator::operator-=(unsigned int n)\n\t\t{\n\t\trow_number-=n;\n\t\treturn (*this);\n\t\t}\n\n\ttemplate<class T>\n\tbool filled_tableau<T>::in_column_iterator::operator==(const in_column_iterator& other) const\n\t\t{\n\t\tif(tab==other.tab && row_number==other.row_number && column_number==other.column_number)\n\t\t\treturn true;\n\t\treturn false;\n\t\t}\n\n\ttemplate<class T>\n\tbool filled_tableau<T>::in_column_iterator::operator<=(const in_column_iterator& other) const\n\t\t{\n\t\tif(row_number<=other.row_number) return true;\n\t\treturn false;\n\t\t}\n\n\ttemplate<class T>\n\tbool filled_tableau<T>::in_column_iterator::operator>=(const in_column_iterator& other) const\n\t\t{\n\t\tif(row_number>=other.row_number) return true;\n\t\treturn false;\n\t\t}\n\n\ttemplate<class T>\n\tbool filled_tableau<T>::in_column_iterator::operator<(const in_column_iterator& other) const\n\t\t{\n\t\tif(row_number<other.row_number) return true;\n\t\treturn false;\n\t\t}\n\n\ttemplate<class T>\n\tbool filled_tableau<T>::in_column_iterator::operator>(const in_column_iterator& other) const\n\t\t{\n\t\tif(row_number>other.row_number) return true;\n\t\treturn false;\n\t\t}\n\n\ttemplate<class T>\n\tbool filled_tableau<T>::in_column_iterator::operator!=(const in_column_iterator& other) const\n\t\t{\n\t\treturn !((*this)==other);\n\t\t}\n\n\t//---------------------------------------------------------------------------\n// in_column_const_iterator\n\n\ttemplate<class T>\n\tfilled_tableau<T>::in_column_const_iterator::in_column_const_iterator(unsigned int r, unsigned int c, const filled_tableau<T>* t)\n\t\t: tab(t), column_number(c), row_number(r)\n\t{\n\t}\n\n\ttemplate<class T>\n\tfilled_tableau<T>::in_column_const_iterator::in_column_const_iterator(const filled_tableau<T>::in_column_iterator& other)\n\t\t: tab(other.tab), column_number(other.column_number), row_number(other.row_number)\n\t{\n\t}\n\n\ttemplate<class T>\n\ttypename filled_tableau<T>::in_column_const_iterator filled_tableau<T>::in_column_const_iterator::operator+(unsigned int n) const\n\t{\n\t\ttypename filled_tableau<T>::in_column_const_iterator it2(*this);\n\t\tit2 += n;\n\t\treturn it2;\n\t}\n\n\ttemplate<class T>\n\ttypename filled_tableau<T>::in_column_const_iterator filled_tableau<T>::in_column_const_iterator::operator-(unsigned int n) const\n\t{\n\t\ttypename filled_tableau<T>::in_column_const_iterator it2(*this);\n\t\tit2 -= n;\n\t\treturn it2;\n\t}\n\n\ttemplate<class T>\n\tptrdiff_t filled_tableau<T>::in_column_const_iterator::operator-(const in_column_const_iterator& other) const\n\t{\n\t\treturn row_number - other.row_number;\n\t}\n\n\ttemplate<class T>\n\tconst T& filled_tableau<T>::in_column_const_iterator::operator*() const\n\t{\n\t\treturn (*tab)(row_number, column_number);\n\t}\n\n\ttemplate<class T>\n\tconst T* filled_tableau<T>::in_column_const_iterator::operator->() const\n\t{\n\t\treturn &((*tab)(row_number, column_number));\n\t}\n\n\ttemplate<class T>\n\ttypename filled_tableau<T>::in_column_const_iterator& filled_tableau<T>::in_column_const_iterator::operator++()\n\t{\n\t\t++row_number;\n\t\treturn (*this);\n\t}\n\n\ttemplate<class T>\n\ttypename filled_tableau<T>::in_column_const_iterator& filled_tableau<T>::in_column_const_iterator::operator+=(unsigned int n)\n\t{\n\t\trow_number += n;\n\t\treturn (*this);\n\t}\n\n\ttemplate<class T>\n\ttypename filled_tableau<T>::in_column_const_iterator& filled_tableau<T>::in_column_const_iterator::operator--()\n\t{\n\t\t--row_number;\n\t\treturn (*this);\n\t}\n\n\ttemplate<class T>\n\ttypename filled_tableau<T>::in_column_const_iterator filled_tableau<T>::in_column_const_iterator::operator--(int)\n\t{\n\t\tin_column_const_iterator tmp(*this);\n\t\t--row_number;\n\t\treturn tmp;\n\t}\n\n\ttemplate<class T>\n\ttypename filled_tableau<T>::in_column_const_iterator filled_tableau<T>::in_column_const_iterator::operator++(int)\n\t{\n\t\tin_column_const_iterator tmp(*this);\n\t\t++row_number;\n\t\treturn tmp;\n\t}\n\n\ttemplate<class T>\n\ttypename filled_tableau<T>::in_column_const_iterator& filled_tableau<T>::in_column_const_iterator::operator-=(unsigned int n)\n\t{\n\t\trow_number -= n;\n\t\treturn (*this);\n\t}\n\n\ttemplate<class T>\n\tbool filled_tableau<T>::in_column_const_iterator::operator==(const in_column_const_iterator& other) const\n\t{\n\t\tif (tab == other.tab && row_number == other.row_number && column_number == other.column_number)\n\t\t\treturn true;\n\t\treturn false;\n\t}\n\n\ttemplate<class T>\n\tbool filled_tableau<T>::in_column_const_iterator::operator<=(const in_column_const_iterator & other) const\n\t{\n\t\tif (row_number <= other.row_number) return true;\n\t\treturn false;\n\t}\n\n\ttemplate<class T>\n\tbool filled_tableau<T>::in_column_const_iterator::operator>=(const in_column_const_iterator & other) const\n\t{\n\t\tif (row_number >= other.row_number) return true;\n\t\treturn false;\n\t}\n\n\ttemplate<class T>\n\tbool filled_tableau<T>::in_column_const_iterator::operator<(const in_column_const_iterator & other) const\n\t{\n\t\tif (row_number < other.row_number) return true;\n\t\treturn false;\n\t}\n\n\ttemplate<class T>\n\tbool filled_tableau<T>::in_column_const_iterator::operator>(const in_column_const_iterator & other) const\n\t{\n\t\tif (row_number > other.row_number) return true;\n\t\treturn false;\n\t}\n\n\ttemplate<class T>\n\tbool filled_tableau<T>::in_column_const_iterator::operator!=(const in_column_const_iterator & other) const\n\t{\n\t\treturn !((*this) == other);\n\t}\n\n\n\t//---------------------------------------------------------------------------\n\t// in_row_iterator\n\n\ttemplate<class T>\n\tfilled_tableau<T>::in_row_iterator::in_row_iterator(unsigned int r, unsigned int c, filled_tableau<T>* t)\n\t\t: tab(t), column_number(c), row_number(r)\n\t{\n\t}\n\n\ttemplate<class T>\n\ttypename filled_tableau<T>::in_row_iterator filled_tableau<T>::in_row_iterator::operator+(unsigned int n) const\n\t{\n\t\ttypename filled_tableau<T>::in_row_iterator it2(*this);\n\t\tit2 += n;\n\t\treturn it2;\n\t}\n\n\ttemplate<class T>\n\ttypename filled_tableau<T>::in_row_iterator filled_tableau<T>::in_row_iterator::operator-(unsigned int n) const\n\t{\n\t\ttypename filled_tableau<T>::in_row_iterator it2(*this);\n\t\tit2 -= n;\n\t\treturn it2;\n\t}\n\n\ttemplate<class T>\n\tptrdiff_t filled_tableau<T>::in_row_iterator::operator-(const in_row_iterator& other) const\n\t{\n\t\treturn column_number - other.column_number;\n\t}\n\n\ttemplate<class T>\n\tT& filled_tableau<T>::in_row_iterator::operator*() const\n\t{\n\t\treturn (*tab)(row_number, column_number);\n\t}\n\n\ttemplate<class T>\n\tT* filled_tableau<T>::in_row_iterator::operator->() const\n\t{\n\t\treturn &((*tab)(row_number, column_number));\n\t}\n\n\ttemplate<class T>\n\ttypename filled_tableau<T>::in_row_iterator& filled_tableau<T>::in_row_iterator::operator++()\n\t{\n\t\t++column_number;\n\t\treturn (*this);\n\t}\n\n\ttemplate<class T>\n\ttypename filled_tableau<T>::in_row_iterator& filled_tableau<T>::in_row_iterator::operator+=(unsigned int n)\n\t{\n\t\tcolumn_number += n;\n\t\treturn (*this);\n\t}\n\n\ttemplate<class T>\n\ttypename filled_tableau<T>::in_row_iterator& filled_tableau<T>::in_row_iterator::operator--()\n\t{\n\t\t--column_number;\n\t\treturn (*this);\n\t}\n\n\ttemplate<class T>\n\ttypename filled_tableau<T>::in_row_iterator filled_tableau<T>::in_row_iterator::operator--(int)\n\t{\n\t\tin_row_iterator tmp(*this);\n\t\t--column_number;\n\t\treturn tmp;\n\t}\n\n\ttemplate<class T>\n\ttypename filled_tableau<T>::in_row_iterator filled_tableau<T>::in_row_iterator::operator++(int)\n\t{\n\t\tin_row_iterator tmp(*this);\n\t\t++column_number;\n\t\treturn tmp;\n\t}\n\n\ttemplate<class T>\n\ttypename filled_tableau<T>::in_row_iterator& filled_tableau<T>::in_row_iterator::operator-=(unsigned int n)\n\t{\n\t\tcolumn_number -= n;\n\t\treturn (*this);\n\t}\n\n\ttemplate<class T>\n\tbool filled_tableau<T>::in_row_iterator::operator==(const in_row_iterator& other) const\n\t{\n\t\tif (tab == other.tab && row_number == other.row_number && column_number == other.column_number)\n\t\t\treturn true;\n\t\treturn false;\n\t}\n\n\ttemplate<class T>\n\tbool filled_tableau<T>::in_row_iterator::operator<=(const in_row_iterator & other) const\n\t{\n\t\tif (column_number <= other.column_number) return true;\n\t\treturn false;\n\t}\n\n\ttemplate<class T>\n\tbool filled_tableau<T>::in_row_iterator::operator>=(const in_row_iterator & other) const\n\t{\n\t\tif (column_number >= other.column_number) return true;\n\t\treturn false;\n\t}\n\n\ttemplate<class T>\n\tbool filled_tableau<T>::in_row_iterator::operator<(const in_row_iterator & other) const\n\t{\n\t\tif (column_number < other.column_number) return true;\n\t\treturn false;\n\t}\n\n\ttemplate<class T>\n\tbool filled_tableau<T>::in_row_iterator::operator>(const in_row_iterator & other) const\n\t{\n\t\tif (column_number > other.column_number) return true;\n\t\treturn false;\n\t}\n\n\ttemplate<class T>\n\tbool filled_tableau<T>::in_row_iterator::operator!=(const in_row_iterator & other) const\n\t{\n\t\treturn !((*this) == other);\n\t}\n\n\t//---------------------------------------------------------------------------\n// in_row_const_iterator\n\n\ttemplate<class T>\n\tfilled_tableau<T>::in_row_const_iterator::in_row_const_iterator(unsigned int r, unsigned int c, const filled_tableau<T>* t)\n\t\t: tab(t), column_number(c), row_number(r)\n\t{\n\t}\n\n\ttemplate<class T>\n\tfilled_tableau<T>::in_row_const_iterator::in_row_const_iterator(const filled_tableau<T>::in_row_iterator& other)\n\t\t: tab(other.tab), column_number(other.column_number), row_number(other.row_number)\n\t{\n\t}\n\n\n\ttemplate<class T>\n\ttypename filled_tableau<T>::in_row_const_iterator filled_tableau<T>::in_row_const_iterator::operator+(unsigned int n) const\n\t{\n\t\ttypename filled_tableau<T>::in_row_const_iterator it2(*this);\n\t\tit2 += n;\n\t\treturn it2;\n\t}\n\n\ttemplate<class T>\n\ttypename filled_tableau<T>::in_row_const_iterator filled_tableau<T>::in_row_const_iterator::operator-(unsigned int n) const\n\t{\n\t\ttypename filled_tableau<T>::in_row_const_iterator it2(*this);\n\t\tit2 -= n;\n\t\treturn it2;\n\t}\n\n\ttemplate<class T>\n\tptrdiff_t filled_tableau<T>::in_row_const_iterator::operator-(const in_row_const_iterator& other) const\n\t{\n\t\treturn column_number - other.column_number;\n\t}\n\n\ttemplate<class T>\n\tconst T& filled_tableau<T>::in_row_const_iterator::operator*() const\n\t{\n\t\treturn (*tab)(row_number, column_number);\n\t}\n\n\ttemplate<class T>\n\tconst T* filled_tableau<T>::in_row_const_iterator::operator->() const\n\t{\n\t\treturn &((*tab)(row_number, column_number));\n\t}\n\n\ttemplate<class T>\n\ttypename filled_tableau<T>::in_row_const_iterator& filled_tableau<T>::in_row_const_iterator::operator++()\n\t{\n\t\t++column_number;\n\t\treturn (*this);\n\t}\n\n\ttemplate<class T>\n\ttypename filled_tableau<T>::in_row_const_iterator& filled_tableau<T>::in_row_const_iterator::operator+=(unsigned int n)\n\t{\n\t\tcolumn_number += n;\n\t\treturn (*this);\n\t}\n\n\ttemplate<class T>\n\ttypename filled_tableau<T>::in_row_const_iterator& filled_tableau<T>::in_row_const_iterator::operator--()\n\t{\n\t\t--column_number;\n\t\treturn (*this);\n\t}\n\n\ttemplate<class T>\n\ttypename filled_tableau<T>::in_row_const_iterator filled_tableau<T>::in_row_const_iterator::operator--(int)\n\t{\n\t\tin_row_const_iterator tmp(*this);\n\t\t--column_number;\n\t\treturn tmp;\n\t}\n\n\ttemplate<class T>\n\ttypename filled_tableau<T>::in_row_const_iterator filled_tableau<T>::in_row_const_iterator::operator++(int)\n\t{\n\t\tin_row_const_iterator tmp(*this);\n\t\t++column_number;\n\t\treturn tmp;\n\t}\n\n\ttemplate<class T>\n\ttypename filled_tableau<T>::in_row_const_iterator& filled_tableau<T>::in_row_const_iterator::operator-=(unsigned int n)\n\t{\n\t\tcolumn_number -= n;\n\t\treturn (*this);\n\t}\n\n\ttemplate<class T>\n\tbool filled_tableau<T>::in_row_const_iterator::operator==(const in_row_const_iterator& other) const\n\t{\n\t\tif (tab == other.tab && row_number == other.row_number && column_number == other.column_number)\n\t\t\treturn true;\n\t\treturn false;\n\t}\n\n\ttemplate<class T>\n\tbool filled_tableau<T>::in_row_const_iterator::operator<=(const in_row_const_iterator & other) const\n\t{\n\t\tif (column_number <= other.column_number) return true;\n\t\treturn false;\n\t}\n\n\ttemplate<class T>\n\tbool filled_tableau<T>::in_row_const_iterator::operator>=(const in_row_const_iterator & other) const\n\t{\n\t\tif (column_number >= other.column_number) return true;\n\t\treturn false;\n\t}\n\n\ttemplate<class T>\n\tbool filled_tableau<T>::in_row_const_iterator::operator<(const in_row_const_iterator & other) const\n\t{\n\t\tif (column_number < other.column_number) return true;\n\t\treturn false;\n\t}\n\n\ttemplate<class T>\n\tbool filled_tableau<T>::in_row_const_iterator::operator>(const in_row_const_iterator & other) const\n\t{\n\t\tif (column_number > other.column_number) return true;\n\t\treturn false;\n\t}\n\n\ttemplate<class T>\n\tbool filled_tableau<T>::in_row_const_iterator::operator!=(const in_row_const_iterator & other) const\n\t{\n\t\treturn !((*this) == other);\n\t}\n\n\n\n\t//---------------------------------------------------------------------------\n\t// iterator\n\n\ttemplate<class T>\n\tfilled_tableau<T>::iterator::iterator(unsigned int r, unsigned int c, filled_tableau<T> *t)\n\t\t: tab(t), column_number(c), row_number(r)\n\t\t{\n\t\t}\n\n\ttemplate<class T>\n\ttypename filled_tableau<T>::iterator filled_tableau<T>::iterator::operator+(unsigned int n) const\n\t\t{\n\t\ttypename filled_tableau<T>::iterator it2(*this);\n\t\tit2+=n;\n\t\treturn it2;\n\t\t}\n\n\ttemplate<class T>\n\ttypename filled_tableau<T>::iterator filled_tableau<T>::iterator::operator-(unsigned int n) const\n\t\t{\n\t\ttypename filled_tableau<T>::iterator it2(*this);\n\t\tit2-=n;\n\t\treturn it2;\n\t\t}\n\n\ttemplate<class T>\n\tptrdiff_t filled_tableau<T>::iterator::operator-(const iterator& other) const\n\t\t{\n\t\treturn row_number-other.row_number;\n\t\t}\n\n\ttemplate<class T>\n\tT& filled_tableau<T>::iterator::operator*() const\n\t\t{\n\t\treturn (*tab)(row_number,column_number);\n\t\t}\n\n\ttemplate<class T>\n\tT* filled_tableau<T>::iterator::operator->() const\n\t\t{\n\t\treturn &((*tab)(row_number,column_number));\n\t\t}\n\n\ttemplate<class T>\n\ttypename filled_tableau<T>::iterator& filled_tableau<T>::iterator::operator++()\n\t\t{\n\t\tif(++column_number==tab->rows[row_number].size()) {\n\t\t\tcolumn_number=0;\n\t\t\t++row_number;\n\t\t\t}\n\t\treturn (*this);\n\t\t}\n\n\ttemplate<class T>\n\ttypename filled_tableau<T>::iterator& filled_tableau<T>::iterator::operator+=(unsigned int n)\n\t\t{\n\t\twhile(n>0) {\n\t\t\tif(++column_number==tab->rows[row_number]) {\n\t\t\t\tcolumn_number=0;\n\t\t\t\t++row_number;\n\t\t\t\t}\n\t\t\t--n;\n\t\t\t}\n\t\treturn (*this);\n\t\t}\n\n\ttemplate<class T>\n\ttypename filled_tableau<T>::iterator& filled_tableau<T>::iterator::operator--()\n\t\t{\n\t\tif(column_number==0) {\n\t\t\t--row_number;\n\t\t\tcolumn_number=tab->rows[row_number].size()-1;\n\t\t\t}\n\t\telse --column_number;\n\t\treturn (*this);\n\t\t}\n\n\ttemplate<class T>\n\ttypename filled_tableau<T>::iterator filled_tableau<T>::iterator::operator--(int)\n\t\t{\n\t\titerator tmp(*this);\n\t\tif(column_number==0) {\n\t\t\t--row_number;\n\t\t\tcolumn_number=tab->rows[row_number].size()-1;\n\t\t\t}\n\t\telse --column_number;\n\t\treturn tmp;\n\t\t}\n\n\ttemplate<class T>\n\ttypename filled_tableau<T>::iterator filled_tableau<T>::iterator::operator++(int)\n\t\t{\n\t\titerator tmp(*this);\n\t\twhile(this->n>0) {\n\t\t\tif(++column_number==tab->rows[row_number]) {\n\t\t\t\tcolumn_number=0;\n\t\t\t\t++row_number;\n\t\t\t\t}\n\t\t\t--this->n;\n\t\t\t}\n\t\treturn tmp;\n\t\t}\n\n\ttemplate<class T>\n\ttypename filled_tableau<T>::iterator& filled_tableau<T>::iterator::operator-=(unsigned int n)\n\t\t{\n\t\twhile(n>0) {\n\t\t\tif(column_number==0) {\n\t\t\t\t--row_number;\n\t\t\t\tcolumn_number=tab->rows[row_number].size()-1;\n\t\t\t\t}\n\t\t\telse --column_number;\n\t\t\t--n;\n\t\t\t}\n\t\treturn (*this);\n\t\t}\n\n\ttemplate<class T>\n\tbool filled_tableau<T>::iterator::operator==(const iterator& other) const\n\t\t{\n\t\tif(tab==other.tab && row_number==other.row_number && column_number==other.column_number)\n\t\t\treturn true;\n\t\treturn false;\n\t\t}\n\n\ttemplate<class T>\n\tbool filled_tableau<T>::iterator::operator<(const iterator& other) const\n\t\t{\n\t\tif(row_number<other.row_number) return true;\n\t\treturn false;\n\t\t}\n\n\ttemplate<class T>\n\tbool filled_tableau<T>::iterator::operator>(const iterator& other) const\n\t\t{\n\t\tif(row_number>other.row_number) return true;\n\t\treturn false;\n\t\t}\n\n\ttemplate<class T>\n\tbool filled_tableau<T>::iterator::operator!=(const iterator& other) const\n\t\t{\n\t\treturn !((*this)==other);\n\t\t}\n\n\n\n\t//---------------------------------------------------------------------------\n\t// const_iterator\n\n\ttemplate<class T>\n\tfilled_tableau<T>::const_iterator::const_iterator(unsigned int r, unsigned int c, const filled_tableau<T>* t)\n\t\t: tab(t), column_number(c), row_number(r)\n\t{\n\t}\n\n\ttemplate<class T>\n\tfilled_tableau<T>::const_iterator::const_iterator(const filled_tableau<T>::iterator& other)\n\t\t: tab(other.tab), column_number(other.column_number), row_number(other.row_number)\n\t{\n\t}\n\n\ttemplate<class T>\n\ttypename filled_tableau<T>::const_iterator filled_tableau<T>::const_iterator::operator+(unsigned int n) const\n\t{\n\t\ttypename filled_tableau<T>::const_iterator it2(*this);\n\t\tit2 += n;\n\t\treturn it2;\n\t}\n\n\ttemplate<class T>\n\ttypename filled_tableau<T>::const_iterator filled_tableau<T>::const_iterator::operator-(unsigned int n) const\n\t{\n\t\ttypename filled_tableau<T>::const_iterator it2(*this);\n\t\tit2 -= n;\n\t\treturn it2;\n\t}\n\n\ttemplate<class T>\n\tptrdiff_t filled_tableau<T>::const_iterator::operator-(const const_iterator& other) const\n\t{\n\t\treturn row_number - other.row_number;\n\t}\n\n\ttemplate<class T>\n\tconst T& filled_tableau<T>::const_iterator::operator*() const\n\t{\n\t\treturn (*tab)(row_number, column_number);\n\t}\n\n\ttemplate<class T>\n\tconst T* filled_tableau<T>::const_iterator::operator->() const\n\t{\n\t\treturn &((*tab)(row_number, column_number));\n\t}\n\n\ttemplate<class T>\n\ttypename filled_tableau<T>::const_iterator& filled_tableau<T>::const_iterator::operator++()\n\t{\n\t\tif (++column_number == tab->rows[row_number].size()) {\n\t\t\tcolumn_number = 0;\n\t\t\t++row_number;\n\t\t}\n\t\treturn (*this);\n\t}\n\n\ttemplate<class T>\n\ttypename filled_tableau<T>::const_iterator& filled_tableau<T>::const_iterator::operator+=(unsigned int n)\n\t{\n\t\twhile (n > 0) {\n\t\t\tif (++column_number == tab->rows[row_number]) {\n\t\t\t\tcolumn_number = 0;\n\t\t\t\t++row_number;\n\t\t\t}\n\t\t\t--n;\n\t\t}\n\t\treturn (*this);\n\t}\n\n\ttemplate<class T>\n\ttypename filled_tableau<T>::const_iterator& filled_tableau<T>::const_iterator::operator--()\n\t{\n\t\tif (column_number == 0) {\n\t\t\t--row_number;\n\t\t\tcolumn_number = tab->rows[row_number].size() - 1;\n\t\t}\n\t\telse --column_number;\n\t\treturn (*this);\n\t}\n\n\ttemplate<class T>\n\ttypename filled_tableau<T>::const_iterator filled_tableau<T>::const_iterator::operator--(int)\n\t{\n\t\tconst_iterator tmp(*this);\n\t\tif (column_number == 0) {\n\t\t\t--row_number;\n\t\t\tcolumn_number = tab->rows[row_number].size() - 1;\n\t\t}\n\t\telse --column_number;\n\t\treturn tmp;\n\t}\n\n\ttemplate<class T>\n\ttypename filled_tableau<T>::const_iterator filled_tableau<T>::const_iterator::operator++(int)\n\t{\n\t\tconst_iterator tmp(*this);\n\t\twhile (this->n > 0) {\n\t\t\tif (++column_number == tab->rows[row_number]) {\n\t\t\t\tcolumn_number = 0;\n\t\t\t\t++row_number;\n\t\t\t}\n\t\t\t--this->n;\n\t\t}\n\t\treturn tmp;\n\t}\n\n\ttemplate<class T>\n\ttypename filled_tableau<T>::const_iterator& filled_tableau<T>::const_iterator::operator-=(unsigned int n)\n\t{\n\t\twhile (n > 0) {\n\t\t\tif (column_number == 0) {\n\t\t\t\t--row_number;\n\t\t\t\tcolumn_number = tab->rows[row_number].size() - 1;\n\t\t\t}\n\t\t\telse --column_number;\n\t\t\t--n;\n\t\t}\n\t\treturn (*this);\n\t}\n\n\ttemplate<class T>\n\tbool filled_tableau<T>::const_iterator::operator==(const const_iterator& other) const\n\t{\n\t\tif (tab == other.tab && row_number == other.row_number && column_number == other.column_number)\n\t\t\treturn true;\n\t\treturn false;\n\t}\n\n\ttemplate<class T>\n\tbool filled_tableau<T>::const_iterator::operator<(const const_iterator & other) const\n\t{\n\t\tif (row_number < other.row_number) return true;\n\t\treturn false;\n\t}\n\n\ttemplate<class T>\n\tbool filled_tableau<T>::const_iterator::operator>(const const_iterator & other) const\n\t{\n\t\tif (row_number > other.row_number) return true;\n\t\treturn false;\n\t}\n\n\ttemplate<class T>\n\tbool filled_tableau<T>::const_iterator::operator!=(const const_iterator & other) const\n\t{\n\t\treturn !((*this) == other);\n\t}\n\n\n\t//---\n\t// other\n\n\ttemplate<class T>\n\ttypename filled_tableau<T>::iterator filled_tableau<T>::begin()\n\t{\n\t\treturn iterator(0, 0, this);\n\t}\n\n\ttemplate<class T>\n\ttypename filled_tableau<T>::iterator filled_tableau<T>::end()\n\t{\n\t\treturn iterator(rows.size(), 0, this);\n\t}\n\n\n\ttemplate<class T>\n\ttypename filled_tableau<T>::const_iterator filled_tableau<T>::cbegin() const\n\t\t{\n\t\treturn const_iterator(0,0,this);\n\t\t}\n\n\ttemplate<class T>\n\ttypename filled_tableau<T>::const_iterator filled_tableau<T>::cend() const\n\t\t{\n\t\treturn const_iterator(rows.size(), 0, this);\n\t\t}\n\n\ttemplate<class T>\n\ttypename filled_tableau<T>::const_iterator filled_tableau<T>::begin() const\n\t{\n\t\treturn cbegin();\n\t}\n\n\ttemplate<class T>\n\ttypename filled_tableau<T>::const_iterator filled_tableau<T>::end() const\n\t{\n\t\treturn cend();\n\t}\n\n\ttemplate<class T>\n\ttypename filled_tableau<T>::in_column_iterator filled_tableau<T>::begin_column(unsigned int column)\n\t\t{\n\t\ttypename filled_tableau<T>::in_column_iterator it(0,column,this);\n\t\tassert(number_of_rows()>0);\n\t\tassert(column<row_size(0));\n\t\treturn it;\n\t\t}\n\n\ttemplate<class T>\n\ttypename filled_tableau<T>::in_column_iterator filled_tableau<T>::end_column(unsigned int column)\n\t\t{\n\t\tunsigned int r=0;\n\t\twhile(r<number_of_rows()) {\n\t\t\tif(row_size(r)<=column)\n\t\t\t\tbreak;\n\t\t\t++r;\n\t\t\t}\n\t\ttypename filled_tableau<T>::in_column_iterator it(r,column,this);\n\t\treturn it;\n\t\t}\n\n\ttemplate<class T>\n\ttypename filled_tableau<T>::in_column_const_iterator filled_tableau<T>::cbegin_column(unsigned int column) const\n\t{\n\t\ttypename filled_tableau<T>::in_column_const_iterator it(0, column, this);\n\t\tassert(number_of_rows() > 0);\n\t\tassert(column < row_size(0));\n\t\treturn it;\n\t}\n\n\ttemplate<class T>\n\ttypename filled_tableau<T>::in_column_const_iterator filled_tableau<T>::cend_column(unsigned int column) const\n\t{\n\t\tunsigned int r = 0;\n\t\twhile (r < number_of_rows()) {\n\t\t\tif (row_size(r) <= column)\n\t\t\t\tbreak;\n\t\t\t++r;\n\t\t}\n\t\ttypename filled_tableau<T>::in_column_const_iterator it(r, column, this);\n\t\treturn it;\n\t}\n\n\ttemplate<class T>\n\ttypename filled_tableau<T>::in_column_const_iterator filled_tableau<T>::begin_column(unsigned int column) const\n\t{\n\t\treturn cbegin_column(column);\n\t}\n\n\ttemplate<class T>\n\ttypename filled_tableau<T>::in_column_const_iterator filled_tableau<T>::end_column(unsigned int column) const\n\t{\n\t\treturn cend_column(column);\n\t}\n\n\ttemplate<class T>\n\ttypename filled_tableau<T>::in_row_iterator filled_tableau<T>::begin_row(unsigned int row)\n\t{\n\t\treturn in_row_iterator{ row, 0, this };\n\t}\n\n\ttemplate<class T>\n\ttypename filled_tableau<T>::in_row_iterator filled_tableau<T>::end_row(unsigned int row)\n\t{\n\t\treturn in_row_iterator{ row, row_size(row), this };\n\t}\n\n\ttemplate<class T>\n\ttypename filled_tableau<T>::in_row_const_iterator filled_tableau<T>::cbegin_row(unsigned int row) const\n\t{\n\t\treturn in_row_const_iterator{ row, 0, this };\n\t}\n\n\ttemplate<class T>\n\ttypename filled_tableau<T>::in_row_const_iterator filled_tableau<T>::cend_row(unsigned int row) const\n\t{\n\t\treturn in_row_const_iterator{ row, row_size(row), this };\n\t}\n\n\ttemplate<class T>\n\ttypename filled_tableau<T>::in_row_const_iterator filled_tableau<T>::begin_row(unsigned int row) const\n\t{\n\t\treturn cbegin_row(row);\n\t}\n\n\ttemplate<class T>\n\ttypename filled_tableau<T>::in_row_const_iterator filled_tableau<T>::end_row(unsigned int row) const\n\t{\n\t\treturn cend_row(row);\n\t}\n\n\n\n\n\ttemplate<class T>\n\ttemplate<class OutputIterator>\n\tOutputIterator filled_tableau<T>::Garnir_set(OutputIterator it, unsigned int row, unsigned int col) const\n\t\t{\n\t\tassert(col>0);\n\t\tunsigned int r=row, c=col;\n\t\t*it=(*this)(r,c);\n\t\t++it;\n\t\twhile(r>0) {\n\t\t\t--r;\n\t\t\t*it=(*this)(r,c);\n\t\t\t++it;\n\t\t\t}\n\t\tr=row;\n\t\t--c;\n\t\t*it=(*this)(r,c);\n\t\t++it;\n\t\twhile(r+1<column_size(c)) {\n\t\t\t++r;\n\t\t\t*it=(*this)(r,c);\n\t\t\t++it;\n\t\t\t}\n\t\treturn it;\n\t\t}\n\n\ttemplate<class T>\n\tstd::pair<int, int> filled_tableau<T>::nonstandard_loc() const\n\t\t{\n\t\tunsigned int r=number_of_rows();\n\t\tassert(r>0);\n\t\tdo {\n\t\t\t--r;\n\t\t\tfor(unsigned int c=0; c<row_size(r)-1; ++c) {\n\t\t\t\tif((*this)(r,c) > (*this)(r,c+1) )\n\t\t\t\t\treturn std::pair<int, int>(r,c);\n\t\t\t\t}\n\t\t\t}\n\t\twhile(r>0);\n\t\treturn std::pair<int,int>(-1,-1);\n\t\t}\n\n\ttemplate<class T>\n\tbool tableaux<T>::standard_form()\n\t\t{\n\t\tbool already_standard=true;\n\n\t\ttypename tableau_container_t::iterator thetab=storage.begin();\n\t\twhile(thetab!=storage.end()) {\n\t\t\t(*thetab).sort_within_columns();\n\t\t\tstd::pair<int,int> where=(*thetab).nonstandard_loc();\n\t\t\tif(where.first!=-1) {\n\t\t\t\talready_standard=false;\n\t\t\t\tcombin::combinations<typename T::value_type> com;\n\t\t\t\tfor(unsigned int i1=where.first; i1<(*thetab).column_size(where.second); ++i1)\n\t\t\t\t\tcom.original.push_back((*thetab)(i1,where.second));\n\t\t\t\tfor(unsigned int i1=0; i1<=(unsigned int)(where.first); ++i1)\n\t\t\t\t\tcom.original.push_back((*thetab)(i1,where.second+1));\n\t\t\t\tcom.sublengths.push_back((*thetab).column_size(where.second)-where.first);\n\t\t\t\tcom.sublengths.push_back(where.first+1);\n\t\t\t\tcom.permute();\n\t\t\t\tfor(unsigned int tabi=1; tabi<com.size(); ++tabi) {\n\t\t\t\t\tT ntab((*thetab));\n\t\t\t\t\tunsigned int offset=0;\n\t\t\t\t\tfor(unsigned int i1=where.first; i1<(*thetab).column_size(where.second); ++i1, ++offset)\n\t\t\t\t\t\tntab(i1,where.second)=com[tabi][offset];\n\t\t\t\t\tfor(unsigned int i1=0; i1<=(unsigned int)(where.first); ++i1, ++offset)\n\t\t\t\t\t\tntab(i1,where.second+1)=com[tabi][offset];\n\t\t\t\t\tntab.multiplicity*=-1*com.ordersign(tabi);\n\t\t\t\t\tadd_tableau(ntab);\n\t\t\t\t\t}\n\t\t\t\tthetab=storage.erase(thetab);\n\t\t\t\t}\n\t\t\telse ++thetab;\n\t\t\t}\n\t\treturn already_standard;\n\t\t}\n\n\ttemplate<class T>\n\tvoid tableaux<T>::add_tableau(const T& ntab)\n\t\t{\n\t\ttypename tableau_container_t::iterator it=storage.begin();\n\t\twhile(it!=storage.end()) {\n\t\t\tif((*it).compare_without_multiplicity(ntab)) {\n\t\t\t\t(*it).multiplicity+=ntab.multiplicity;\n\t\t\t\tif((*it).multiplicity==0)\n\t\t\t\t\tstorage.erase(it);\n\t\t\t\treturn;\n\t\t\t\t}\n\t\t\t++it;\n\t\t\t}\n\t\tstorage.push_back(ntab);\n\t\t}\n\n\n\ttemplate<class T>\n\tyngrat_t filled_tableau<T>::projector_normalisation() const\n\t\t{\n\t\tyngrat_t norm=1;\n\t\tnorm/=hook_length_prod();\n\t\treturn norm;\n\t\t}\n\n\ttemplate<class T>\n\tvoid filled_tableau<T>::projector(combin::symmetriser<T>& sym, bool modulo_monoterm) const\n\t\t{\n\t\tfor(unsigned int r=0; r<number_of_rows(); ++r)\n\t\t\tfor(unsigned int c=0; c<row_size(r); ++c)\n\t\t\t\tsym.original.push_back(rows[r][c]);\n\n\t\tunsigned int offset=0;\n\t\t// symmetrise over boxes in rows\n\t\tfor(unsigned int r=0; r<number_of_rows(); ++r) {\n\t\t\tsym.permutation_sign=1;\n\t\t\tsym.permute_blocks.clear();\n\t\t\tsym.block_length=1;\n\t\t\tsym.input_asym.clear();\n\t\t\tfor(unsigned int c=0; c<row_size(r); ++c)\n\t\t\t\tsym.permute_blocks.push_back(offset++);\n\t\t\tsym.apply_symmetry();\n\t\t\t}\n\t\t//\tsym.collect();\n\t\t// anti-symmetrise over boxes in columns\n\t\tif(modulo_monoterm) {\n\t\t\tint newmult=1;\n\t\t\tfor(unsigned int c=0; c<row_size(0); ++c)\n\t\t\t\tnewmult*=combin::factorial(column_size(c));\n\t\t\tfor(unsigned int i=0; i<sym.size(); ++i)\n\t\t\t\tsym.set_multiplicity(i, sym.signature(i)*newmult);\n\t\t\t}\n\t\telse {\n\t\t\tsym.permute_blocks.clear();\n\t\t\tfor(unsigned int c=0; c<row_size(0); ++c) {\n\t\t\t\tunsigned int r=0;\n\t\t\t\tsym.value_permute.clear();\n\t\t\t\tsym.permutation_sign=-1;\n\t\t\t\tsym.input_asym.clear();\n\t\t\t\twhile(r<number_of_rows() && c<row_size(r))\n\t\t\t\t\tsym.value_permute.push_back(rows[r++][c]);\n\t\t\t\tif(sym.value_permute.size()>1)\n\t\t\t\t\tsym.apply_symmetry();\n\t\t\t\t}\n\t\t\t}\n\t\t//\tsym.collect();\n\t\t}\n\n\ttemplate<class T>\n\tvoid filled_tableau<T>::projector(combin::symmetriser<T>& sym,\n\t                                  combin::range_vector_t& sublengths_scattered) const\n\t\t{\n\t\tfor(unsigned int r=0; r<number_of_rows(); ++r)\n\t\t\tfor(unsigned int c=0; c<row_size(r); ++c)\n\t\t\t\tsym.original.push_back(rows[r][c]);\n\n\t\tunsigned int offset=0;\n\t\t// symmetrise over boxes in rows\n\t\tfor(unsigned int r=0; r<number_of_rows(); ++r) {\n\t\t\tsym.permutation_sign=1;\n\t\t\tsym.permute_blocks.clear();\n\t\t\tsym.block_length=1;\n\t\t\tsym.input_asym.clear();\n\t\t\tfor(unsigned int c=0; c<row_size(r); ++c)\n\t\t\t\tsym.permute_blocks.push_back(offset++);\n\t\t\tsym.apply_symmetry();\n\t\t\t}\n\t\t/// anti-symmetrise over boxes in columns\n\t\tsym.permute_blocks.clear();\n\t\tfor(unsigned int c=0; c<row_size(0); ++c) {\n\t\t\tunsigned int r=0;\n\t\t\tsym.value_permute.clear();\n\t\t\tsym.permutation_sign=-1;\n\t\t\twhile(r<number_of_rows() && c<row_size(r))\n\t\t\t\tsym.value_permute.push_back(rows[r++][c]);\n\n\t\t\tsym.sublengths_scattered=sublengths_scattered;\n\n\t\t\t//\t\t// Now setup sublengths_scattered to take into account\n\t\t\t//\t\t// asym_ranges.  These asym_ranges refer to values stored in the\n\t\t\t//\t\t// boxes of the full tableau. We need to find the locations of\n\t\t\t//\t\t// these values inside the full original, as that is what goes\n\t\t\t//\t\t// into sublengths_scattered.\n\t\t\t//\n\t\t\t//\t\tsym.input_asym.clear();\n\t\t\t//\t\tsym.sublengths.clear();\n\t\t\t//\t\tsym.sublengths_scattered.clear();\n\t\t\t//\t\tfor(unsigned int m=0; m<sym.value_permute.size(); ++m) {\n\t\t\t//\t\t\t// Try to find this value in an asym range.\n\t\t\t//\t\t\tunsigned int overlap=0;\n\t\t\t//\t\t\tfor(unsigned int n=0; n<asym_ranges.size(); ++n) {\n\t\t\t//\t\t\t\tfor(unsigned int nn=0; nn<asym_ranges[n].size(); ++nn) {\n\t\t\t//\t\t\t\t\tif(sym.value_permute[m]==asym_ranges[n][nn]) {\n\t\t\t//\t\t\t\t\t\tstd::cout << \"found \" << sym.value_permute[m] << \" in range\" << std::endl;\n\t\t\t//\t\t\t\t\t\t// FIXME: this assumes that even though asym_ranges[n] is a superset\n\t\t\t//\t\t\t\t\t\t// of the current part of value_permute, elements are in the same order.\n\t\t\t//\t\t\t\t\t\t++m; ++nn;\n\t\t\t//\t\t\t\t\t\twhile(nn<asym_ranges[n].size()) {\n\t\t\t//\t\t\t\t\t\t\tif(sym.value_permute[m]==asym_ranges[n][nn]) {\n\t\t\t//\t\t\t\t\t\t\t\tstd::cout << \"same range: \" << sym.value_permute[m] << std::endl;\n\t\t\t//\t\t\t\t\t\t\t\t++m;\n\t\t\t//\t\t\t\t\t\t\t\t++overlap;\n\t\t\t//\t\t\t\t\t\t\t\t}\n\t\t\t//\t\t\t\t\t\t\t++nn;\n\t\t\t//\t\t\t\t\t\t\t}\n\t\t\t//\t\t\t\t\t\tbreak;\n\t\t\t//\t\t\t\t\t\t}\n\t\t\t//\t\t\t\t\t}\n\t\t\t//\t\t\t\t}\n\t\t\t//\t\t\tif(overlap>0) --m;\n\t\t\t//\t\t\tsym.sublengths.push_back(overlap+1);\n\t\t\t//\t\t\t}\n\t\t\t//\t\tunsigned int sum=0;\n\t\t\t//\t\tfor(unsigned int m=0; m<sym.sublengths.size(); ++m)\n\t\t\t//\t\t\tsum+=sym.sublengths[m];\n\t\t\t//\n\t\t\t//\t\tstd::cout << sum << \" \" << sym.value_permute.size() << std::endl;\n\t\t\t//\t\tassert(sum==sym.value_permute.size());\n\n\t\t\t// All set to run...\n\t\t\tif(sym.value_permute.size()>1)\n\t\t\t\tsym.apply_symmetry();\n\t\t\t}\n\t\t}\n\n\ttemplate<class T>\n\tfilled_tableau<T>::filled_tableau()\n\t\t: tableau()\n\t\t{\n\t\t}\n\n\ttemplate<class T>\n\tfilled_tableau<T>::filled_tableau(const filled_tableau<T>& other)\n\t\t: tableau(other), rows(other.rows)\n\t\t{\n\t\t}\n\n\ttemplate<class T>\n\tfilled_tableau<T>& filled_tableau<T>::operator=(const filled_tableau<T>& other)\n\t\t{\n\t\trows=other.rows;\n\t\ttableau::operator=(other);\n\t\treturn (*this);\n\t\t}\n\n\ttemplate<class T>\n\tyngint_t tableaux<T>::total_dimension(unsigned int dim)\n\t\t{\n\t\tyngint_t totdim=0;\n\t\ttypename tableau_container_t::const_iterator it=storage.begin();\n\t\twhile(it!=storage.end()) {\n\t\t\ttotdim+=(*it).dimension(dim);\n\t\t\t++it;\n\t\t\t}\n\t\treturn totdim;\n\t\t}\n\n\ttemplate<class T, class OutputIterator>\n\tvoid LR_tensor(const tableaux<T>& tabs1, const T& tab2, unsigned int maxrows,\n\t               OutputIterator out, bool alltabs=false)\n\t\t{\n\t\ttypename tableaux<T>::tableau_container_t::const_iterator it=tabs1.storage.begin();\n\t\twhile(it!=tabs1.storage.end()) {\n\t\t\tLR_tensor((*it), tab2, maxrows, out, alltabs);\n\t\t\t++it;\n\t\t\t}\n\t\t}\n\n\ttemplate<class T1, class T2>\n\tvoid add_box(T1& tab1, unsigned int row1,\n\t             const T2& tab2, unsigned int row2, unsigned int col2)\n\t\t{\n\t\ttab1.add_box(row1, tab2(row2,col2));\n\t\t}\n\n\ttemplate<class T1>\n\tvoid add_box(T1& tab1, unsigned int row1,\n\t             const tableau&, unsigned int, unsigned int)\n\t\t{\n\t\ttab1.add_box(row1);\n\t\t}\n\n\ttypedef filled_tableau<std::pair<int, int> > keeptrack_tab_t;\n\n\ttemplate<class Tab, class OutputIterator>\n\tvoid LR_add_box(const Tab& tab2, Tab& newtab,\n\t                unsigned int currow2, unsigned int curcol2, unsigned int startrow,\n\t                unsigned int maxrows,\n\t                OutputIterator outit,\n\t                keeptrack_tab_t& Ycurrent,\n\t                bool alltabs)\n\t\t{\n\t\t// Are we at the end of the current row of boxes in tab2 ?\n\t\tif((++curcol2)==tab2.row_size(currow2)) {\n\t\t\t// Are we at the end of tab2 altogether?\n\t\t\tif((++currow2)==tab2.number_of_rows()) {\n\t\t\t\t*outit=newtab;  // Store the product tableau just created.\n\t\t\t\treturn;\n\t\t\t\t}\n\t\t\tcurcol2=0;\n\t\t\tstartrow=0;\n\t\t\t}\n\n\t\t// Rule \"row_by_row\".\n\t\tfor(unsigned int rowpos=startrow; rowpos<std::min(newtab.number_of_rows()+1,maxrows); ++rowpos) {\n\t\t\t// Rule \"always_young\".\n\t\t\tif(rowpos>0 && rowpos<newtab.number_of_rows())\n\t\t\t\tif(newtab.row_size(rowpos-1)==newtab.row_size(rowpos))\n\t\t\t\t\tcontinue; // No, would lead to non-Young tableau shape.\n\n\t\t\t// The column where the box will be added.\n\t\t\tunsigned int colpos=(rowpos==newtab.number_of_rows())?0:newtab.row_size(rowpos);\n\n\t\t\t// Rule \"avoid_sym2asym\".\n\t\t\tfor(unsigned int rr=0; rr<rowpos; ++rr)\n\t\t\t\tif(Ycurrent(rr,colpos).first==(int)(currow2))\n\t\t\t\t\tgoto rule_violated;\n\n\t\t\t// Rule \"avoid_asym2sym\".\n\t\t\tif(alltabs) // if not generating all tabs, ordered will take care of this already.\n\t\t\t\tfor(unsigned int cc=0; cc<colpos; ++cc)\n\t\t\t\t\tif(Ycurrent(rowpos,cc).second==(int)(curcol2))\n\t\t\t\t\t\tgoto rule_violated;\n\n\t\t\t// Rule \"ordered\".\n\t\t\tif(!alltabs && currow2>0) {\n\t\t\t\tint numi=0, numimin1=0;\n\t\t\t\tif(rowpos>0) {\n\t\t\t\t\tfor(unsigned int sr=0; sr<rowpos; ++sr)  // top to bottom\n\t\t\t\t\t\tfor(unsigned int sc=0; sc<Ycurrent.row_size(sr); ++sc) { // right to left\n\t\t\t\t\t\t\t// Count all boxes from currow2 and from currow2-1.\n\t\t\t\t\t\t\tif(Ycurrent(sr,sc).first==(int)(currow2))    ++numi;\n\t\t\t\t\t\t\tif(Ycurrent(sr,sc).first==(int)(currow2)-1)  ++numimin1;\n\t\t\t\t\t\t\t}\n\t\t\t\t\t}\n\t\t\t\t++numi; // the box to be added\n\t\t\t\tif(numi>numimin1)\n\t\t\t\t\tgoto rule_violated;\n\n\t\t\t\t// continue counting to see whether a previously valid box is now invalid\n\t\t\t\tfor(unsigned int sr=rowpos; sr<Ycurrent.number_of_rows(); ++sr)  // top to bottom\n\t\t\t\t\tfor(int sc=Ycurrent.row_size(sr)-1; sc>=0; --sc) { // right to left\n\t\t\t\t\t\tif(Ycurrent(sr,sc).first==(int)(currow2))    ++numi;\n\t\t\t\t\t\tif(Ycurrent(sr,sc).first==(int)(currow2)-1)  ++numimin1;\n\t\t\t\t\t\tif(numi>numimin1)\n\t\t\t\t\t\t\tgoto rule_violated;\n\t\t\t\t\t\t}\n\t\t\t\t}\n\n\t\t\t// Put the box at row 'rowpos' and call LR_add_box recursively\n\t\t\t// to add the other boxes.\n\t\t\tYcurrent.add_box(rowpos, std::pair<int,int>(currow2, curcol2));\n\t\t\tadd_box(newtab, rowpos, tab2, currow2, curcol2);\n\t\t\tLR_add_box(tab2, newtab, currow2, curcol2, alltabs?0:rowpos, maxrows,\n\t\t\t           outit, Ycurrent, alltabs);\n\n\t\t\t// Remove the box again in preparation for trying to add it to other rows.\n\t\t\tnewtab.remove_box(rowpos);\n\t\t\tYcurrent.remove_box(rowpos);\n\nrule_violated:\n\t\t\t;\n\t\t\t}\n\t\t}\n\n\ttemplate<class Tab, class OutputIterator>\n\tvoid LR_tensor(const Tab& tab1, const Tab& tab2, unsigned int maxrows,\n\t               OutputIterator outit, bool alltabs=false)\n\t\t{\n\t\t// Make a copy of tab1 because LR_add_box has to change it and\n\t\t// tab1 is const here.\n\t\tTab newtab(tab1);\n\n\t\t// Tableau which keeps track of the LR rules. It contains the\n\t\t// current (incomplete) shape of the tensor product, and for all boxes\n\t\t// which come from tab2 we store the row and column of tab2\n\t\t// from which they originated. Tab1 boxes have (-2,-2) stored.\n\t\tkeeptrack_tab_t Ycurrent;\n\t\tYcurrent.copy_shape(tab1);\n\t\tkeeptrack_tab_t::iterator yi=Ycurrent.begin();\n\t\twhile(yi!=Ycurrent.end()) {\n\t\t\t(*yi)=std::pair<int,int>(-2,-2);\n\t\t\t++yi;\n\t\t\t}\n\n\t\tLR_add_box(tab2, newtab, 0, -1, 0, maxrows, outit, Ycurrent, alltabs);\n\t\t}\n\n\ttemplate<class T, class OutputIterator>\n\tvoid LR_tensor(const tableaux<T>&, bool, unsigned int, OutputIterator )\n\t\t{\n\t\tassert(1==0);\n\t\t}\n\n\n\n\tstd::ostream& operator<<(std::ostream&, const tableau& );\n\n\ttemplate<class T>\n\tstd::ostream& operator<<(std::ostream&, const tableaux<T>& );\n\n\ttemplate<class T>\n\tstd::ostream& operator<<(std::ostream&, const filled_tableau<T>& );\n\n\ttemplate<class T>\n\tunsigned int filled_tableau<T>::number_of_rows() const\n\t\t{\n\t\treturn rows.size();\n\t\t}\n\n\ttemplate<class T>\n\tunsigned int filled_tableau<T>::row_size(unsigned int num) const\n\t\t{\n\t\tassert(num<rows.size());\n\t\treturn rows[num].size();\n\t\t}\n\n\ttemplate<class T>\n\tT& filled_tableau<T>::operator()(unsigned int row, unsigned int col)\n\t\t{\n\t\tassert(row<rows.size());\n\t\tassert(col<rows[row].size());\n\t\treturn rows[row][col];\n\t\t}\n\n\ttemplate<class T>\n\tconst T& filled_tableau<T>::operator()(unsigned int row, unsigned int col)  const\n\t\t{\n\t\tassert(row<rows.size());\n\t\tassert(col<rows[row].size());\n\t\treturn rows[row][col];\n\t\t}\n\n\ttemplate<class T>\n\tconst T& filled_tableau<T>::operator[](unsigned int boxnum) const\n\t\t{\n\t\tunsigned int row = 0;\n\t\twhile (true) {\n\t\t\tif (boxnum < row_size(row))\n\t\t\t\tbreak;\n\t\t\tboxnum -= row_size(row);\n\t\t\t++row;\n\t\t}\n\t\treturn rows[row][boxnum];\n\t\t}\n\n\ttemplate<class T>\n\tfilled_tableau<T>::~filled_tableau()\n\t\t{\n\t\t}\n\n\ttemplate<class T>\n\tvoid filled_tableau<T>::add_box(unsigned int rownum)\n\t\t{\n\t\tif(rownum>=rows.size())\n\t\t\trows.resize(rownum+1);\n\t\tassert(rownum<rows.size());\n\t\trows[rownum].push_back(T());\n\t\t}\n\n\ttemplate<class T>\n\tvoid filled_tableau<T>::add_box(unsigned int rownum, T val)\n\t\t{\n\t\tif(rownum>=rows.size())\n\t\t\trows.resize(rownum+1);\n\t\tassert(rownum<rows.size());\n\t\trows[rownum].push_back(val);\n\t\t}\n\n\ttemplate<class T>\n\tvoid filled_tableau<T>::swap_columns(unsigned int c1, unsigned int c2)\n\t\t{\n\t\tassert(c1<row_size(0) && c2<row_size(0));\n\t\tassert(column_size(c1)==column_size(c2));\n\t\tfor(unsigned int r=0; r<column_size(c1); ++r) {\n\t\t\tT tmp=(*this)(r,c1);\n\t\t\t(*this)(r,c1)=(*this)(r,c2);\n\t\t\t(*this)(r,c2)=tmp;\n\t\t\t}\n\t\t}\n\n\ttemplate<class T>\n\tvoid filled_tableau<T>::remove_box(unsigned int rownum)\n\t\t{\n\t\tassert(rownum<rows.size());\n\t\tassert(rows[rownum].size()>0);\n\t\trows[rownum].pop_back();\n\t\tif(rows[rownum].size()==0)\n\t\t\trows.pop_back();\n\t\t}\n\n\ttemplate<class T>\n\tvoid filled_tableau<T>::clear()\n\t\t{\n\t\trows.clear();\n\t\ttableau::clear();\n\t\t}\n\n\ttemplate<class T>\n\tstd::ostream& operator<<(std::ostream& str, const tableaux<T>& tabs)\n\t\t{\n\t\ttypename tableaux<T>::tableau_container_t::const_iterator it=tabs.storage.begin();\n\t\twhile(it!=tabs.storage.end()) {\n\t\t\tstr << (*it) << std::endl << std::endl;\n\t\t\t++it;\n\t\t\t}\n\t\treturn str;\n\t\t}\n\n\ttemplate<class T>\n\tstd::ostream& operator<<(std::ostream& str, const filled_tableau<T>& tab)\n\t\t{\n\t\tfor(unsigned int i=0; i<tab.number_of_rows(); ++i) {\n\t\t\tfor(unsigned int j=0; j<tab.row_size(i); ++j) {\n\t\t\t\t//\t\t\tstr << \"|\" << tab(i,j) << \"|\";\n\t\t\t\tstr << tab(i,j);\n\t\t\t\t}\n\t\t\tif(i==0) {\n\t\t\t\tstr << \"  \" << tab.dimension(10);\n\t\t\t\tif(tab.has_nullifying_trace()) str << \" null\";\n\t\t\t\t}\n\t\t\tif(i!=tab.number_of_rows()-1)\n\t\t\t\tstr << std::endl;\n\t\t\telse\n\t\t\t\tstr << \" (\" << tab.multiplicity << \")\" << std::endl;\n\t\t\t}\n\t\treturn str;\n\t\t}\n\n\t};\n\n\n"
  },
  {
    "path": "core/algorithms/all_contractions.tex",
    "content": "\\cdbalgorithm{all\\_contractions}{}\n\nConstruct all full contractions of the given tensors, taking into\naccount mono-term symmetries. Example,\n\\begin{screen}{1,2,3,4,5}\nA_{m n}::Symmetric.\nA_{m n}::Traceless.\n{m,n,p,q,r,s,t,u}::Indices(vector).\n{m,n,p,q,r,s,t,u}::Integer(0..9).\nobj14:= A_{m n} A_{p q} A_{r s} A_{t u};\n@all_contractions(%){2};\nA_{m n} A_{m n} A_{p q} A_{p q} + A_{m n} A_{m p} A_{n q} A_{p q};\n\\end{screen}\n\nThis command is not entirely correct at the moment: it determines the\ntotal number of singlets correctly, but does not generate parity-odd\ncontractions (the ones involving an epsilon tensor). It also does not\nknow about dimension-dependent identities. If this is a problem for\nyour application, contact the author for an experimental version of\ncadabra.\n\n\\cdbseeprop{Symmetric}\n\\cdbseeprop{Traceless}\n\\cdbseealgo{canonicalise}\n\n"
  },
  {
    "path": "core/algorithms/asym.cnb",
    "content": "{\n\t\"cells\" : \n\t[\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\algorithm{asym}{Anti-symmetrise or symmetrise an expression in indicated indices or arguments}\\n\\nAnti-symmetrise or symmetrise (depending on the \\\\verb|antisymmetric| flag) a product or tensor in the indicated objects.\\nThis works both with normal objects and with indices. An example of the former:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\algorithm{asym}{Anti-symmetrise or symmetrise an expression in indicated indices or arguments}\\n\\nAnti-symmetrise or symmetrise (depending on the \\\\verb|antisymmetric| flag) a product or tensor in the indicated objects.\\nThis works both with normal objects and with indices. An example of the former:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}A B C\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex:=A B C;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\frac{1}{6}A B C - \\\\frac{1}{6}A C B - \\\\frac{1}{6}B A C+\\\\frac{1}{6}B C A+\\\\frac{1}{6}C A B - \\\\frac{1}{6}C B A\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"asym(_, $A,B,C$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"When used with indices, remember to also\\nindicate whether you want to symmetrise upper or lower indices, as in\\nthe example below.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"When used with indices, remember to also\\nindicate whether you want to symmetrise upper or lower indices, as in\\nthe example below.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}A_{m n} B_{p}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex:=A_{m n} B_{p};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\frac{1}{6}A_{m n} B_{p} - \\\\frac{1}{6}A_{m p} B_{n} - \\\\frac{1}{6}A_{n m} B_{p}+\\\\frac{1}{6}A_{n p} B_{m}+\\\\frac{1}{6}A_{p m} B_{n} - \\\\frac{1}{6}A_{p n} B_{m}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"asym(_, $_{m}, _{n}, _{p}$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"If you want to \\\\emph{symmetrise} in the indicated objects instead, use the \\\\verb|antisymmetric=False| flag:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"If you want to \\\\emph{symmetrise} in the indicated objects instead, use the \\\\verb|antisymmetric=False| flag:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}A_{m n} B_{p}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\frac{1}{6}A_{m n} B_{p}+\\\\frac{1}{6}A_{m p} B_{n}+\\\\frac{1}{6}A_{n m} B_{p}+\\\\frac{1}{6}A_{n p} B_{m}+\\\\frac{1}{6}A_{p m} B_{n}+\\\\frac{1}{6}A_{p n} B_{m}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex:=A_{m n} B_{p};\\nasym(_, $_{m}, _{n}, _{p}$, antisymmetric=False);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1\n}\n"
  },
  {
    "path": "core/algorithms/canonicalise.cc",
    "content": "\n#include \"Cleanup.hh\"\n#include \"Exchange.hh\"\n#include \"Functional.hh\"\n#include \"IndexClassifier.hh\"\n#include \"algorithms/canonicalise.hh\"\n#include \"modules/xperm_new.h\"\n#include \"properties/Trace.hh\"\n#include \"properties/Traceless.hh\"\n#include \"properties/Diagonal.hh\"\n#include \"properties/Derivative.hh\"\n#include \"properties/AntiCommuting.hh\"\n\n// #define DEBUG 1\n// #define XPERM_DEBUG 1\n\nusing namespace cadabra;\n\ncanonicalise::canonicalise(const Kernel& k, Ex& tr)\n\t: Algorithm(k, tr), reuse_generating_set(false)\n\t{\n\t}\n\nbool canonicalise::can_apply(iterator it)\n\t{\n\tif(*(it->name)!=\"\\\\prod\")\n\t\tif(*(it->name)==\"\\\\pow\" || is_single_term(it)==false)\n\t\t\treturn false;\n\n\t//if(! (tr.is_head(it)==false && *tr.parent(it)->name==\"\\\\pow\" && tr.index(it)==0) )\n\n\t// Canonicalise requires strict monomial structure: no products which contain\n\t// sums as factors. Products as factors are ok, they do not lead to multiple\n\t// identically named free indices.\n\n\tauto sum_or_prod_or_pow = find_in_subtree(tr, it, [this](Ex::iterator tst) {\n\t\tif((*tst->name==\"\\\\sum\" || *tst->name==\"\\\\pow\") && number_of_indices(tst)>0) return true;\n\t\treturn false;\n\t\t}, false);\n\tif(sum_or_prod_or_pow!=tr.end()) {\n#ifdef DEBUG\n\t\tstd::cerr << \"trying to canonicalise nested product/sum/power \" << Ex(it) << \" \" << Ex(sum_or_prod_or_pow) << std::endl;\n#endif\n\t\treturn false;\n\t\t}\n\n#ifdef DEBUG\n\tstd::cerr << \"canonicalise::can_apply: at \" << it << std::endl;\n#endif\n\treturn true;\n\t}\n\nbool canonicalise::remove_traceless_traces(iterator& it)\n\t{\n\t// Remove any traces of traceless tensors (this is best done early).\n\tsibling_iterator facit=tr.begin(it);\n\twhile(facit!=tr.end(it)) {\n\t\tconst Traceless *trl=kernel.properties.get<Traceless>(facit);\n\t\tif(trl) {\n\t\t\tunsigned int ihits=0;\n\t\t\ttree_exact_less_mod_prel_obj comp(&kernel.properties);\n\t\t\tstd::set<Ex, tree_exact_less_mod_prel_obj> countmap(comp);\n\t\t\tindex_iterator indit=begin_index(facit);\n\t\t\twhile(indit!=end_index(facit)) {\n\t\t\t\tbool incremented_now=false;\n\t\t\t\tauto ind=kernel.properties.get<Indices>(indit, true);\n\t\t\t\tif(ind) {\n\t\t\t\t\t// The indexs need to be in the set for which the object is\n\t\t\t\t\t// traceless (if specified, otherwise accept all).\n\t\t\t\t\tif(trl->index_set_names.find(ind->set_name)!=trl->index_set_names.end() || trl->index_set_names.size()==0) {\n\t\t\t\t\t\tincremented_now=true;\n\t\t\t\t\t\t++ihits;\n\t\t\t\t\t\t}\n\t\t\t\t\t}\n\t\t\t\telse incremented_now=true;\n\t\t\t\t// Having no name is treated as having the right name\n\t\t\t\tif(countmap.find(Ex(indit))==countmap.end()) {\n\t\t\t\t\tcountmap.insert(Ex(indit));\n\t\t\t\t\t}\n\t\t\t\telse if(incremented_now) {\n\t\t\t\t\tzero(it->multiplier);\n\t\t\t\t\treturn true;\n\t\t\t\t\t}\n\t\t\t\t++indit;\n\t\t\t\t}\n\t\t\titerator parent=it;\n\t\t\tif (tr.number_of_children(it)==1 && !tr.is_head(it)) parent=tr.parent(it);\n\t\t\tconst Trace *trace=kernel.properties.get<Trace>(parent);\n\t\t\tif(trace) {\n\t\t\t\tint tmp;\n\t\t\t\tauto impi=kernel.properties.get_with_pattern<ImplicitIndex>(facit, tmp, \"\");\n\t\t\t\tif(impi.first->explicit_form.size()>0) {\n\t\t\t\t\t// Does the explicit form have two more indices of the right type?\n\t\t\t\t\tEx::iterator eform=impi.first->explicit_form.begin();\n\t\t\t\t\tunsigned int ehits=0;\n\t\t\t\t\tindit=begin_index(eform);\n\t\t\t\t\twhile(indit!=end_index(eform)) {\n\t\t\t\t\t\tauto ind=kernel.properties.get<Indices>(indit, true);\n\t\t\t\t\t\tif(trl->index_set_names.find(ind->set_name)!=trl->index_set_names.end() && ind->set_name==trace->index_set_name) ++ehits;\n\t\t\t\t\t\tif(ehits - ihits > 1) {\n\t\t\t\t\t\t\tzero(it->multiplier);\n\t\t\t\t\t\t\treturn true;\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\t++indit;\n\t\t\t\t\t\t}\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t}\n\t\t++facit;\n\t\t}\n\treturn false;\n\t}\n\nbool canonicalise::remove_vanishing_numericals(iterator& it)\n\t{\n\t// Remove Diagonal objects with numerical indices which are not all the same.\n\tsibling_iterator facit=tr.begin(it);\n\twhile(facit!=tr.end(it)) {\n\t\tconst Diagonal *dgl=kernel.properties.get<Diagonal>(facit);\n\t\tif(dgl) {\n\t\t\tindex_iterator indit=begin_index(facit);\n\t\t\tif(indit->is_rational()) {\n\t\t\t\tindex_iterator indit2=indit;\n\t\t\t\t++indit2;\n\t\t\t\twhile(indit2!=end_index(facit)) {\n\t\t\t\t\tif(indit2->is_rational()==false)\n\t\t\t\t\t\tbreak;\n\t\t\t\t\tif(indit2->multiplier!=indit->multiplier) {\n\t\t\t\t\t\tzero(it->multiplier);\n\t\t\t\t\t\treturn true;\n\t\t\t\t\t\t}\n\t\t\t\t\t++indit2;\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t}\n\t\t++facit;\n\t\t}\n\treturn false;\n\t}\n\nIndices::position_t canonicalise::position_type(iterator it) const\n\t{\n\tconst Indices *ind=kernel.properties.get<Indices>(it, true);\n\tif(ind)\n\t\treturn ind->position_type;\n\treturn Indices::free;\n\t}\n\nbool canonicalise::only_one_on_derivative(iterator i1, iterator i2) const\n\t{\n\tint num=0;\n\titerator p1=tr.parent(i1);\n\tconst Derivative *der1=kernel.properties.get<Derivative>(p1);\n\tif(der1) ++num;\n\n\titerator p2=tr.parent(i2);\n\tconst Derivative *der2=kernel.properties.get<Derivative>(p2);\n\tif(der2) ++num;\n\n\tif(num==1) return true;\n\telse return false;\n\t}\n\nAlgorithm::result_t canonicalise::apply(iterator& it)\n\t{\n#ifdef DEBUG\n\tstd::cerr << \"canonicalise at \" << it << std::endl;\n#endif\n\t// std::cerr << is_single_term(it) << std::endl;\n\n\tStopwatch totalsw;\n\ttotalsw.start();\n\tprod_wrap_single_term(it);\n\n\tif(remove_traceless_traces(it)) {\n\t\tcleanup_dispatch(kernel, tr, it);\n\t\treturn result_t::l_applied;\n\t\t}\n\n\tif(remove_vanishing_numericals(it)) {\n\t\tcleanup_dispatch(kernel, tr, it);\n\t\treturn result_t::l_applied;\n\t\t}\n\n\n\t// Now the real thing...\n\tIndexClassifier ic(kernel);\n\tIndexClassifier::index_map_t ind_free, ind_dummy;\n\tic.classify_indices(it, ind_free, ind_dummy);\n\tIndexClassifier::index_position_map_t ind_pos_free, ind_pos_dummy;\n\tic.fill_index_position_map(it, ind_free, ind_pos_free);\n\tic.fill_index_position_map(it, ind_dummy, ind_pos_dummy);\n\tconst unsigned int total_number_of_indices=ind_free.size()+ind_dummy.size();\n\n#ifdef DEBUG\n\t//\tstd::cerr << \"free index position map:\\n\";\n\t//\tfor(auto& ip: ind_pos_free)\n\t//\t\tstd::cerr << Ex(ip.first) << \" @ \" << ip.second << std::endl;;\n#endif\n\n\t// If there are no indices, there is nothing to do here...\n\tif(total_number_of_indices==0) {\n#ifdef DEBUG\n\t\tstd::cerr << \"no indices on \" << Ex(it) << std::endl;\n#endif\n\t\tprod_unwrap_single_term(it);\n\t\treturn result_t::l_no_action;\n\t\t}\n\n\t// We currently do not handle situations in which one of the\n\t// factors in a product is a sum. To be precise, we do not handle\n\t// situations in which one or both of the indices in a dummy\n\t// pair appear multiple times (in the different terms of the sum).\n\t// Ditto for free indices; these need to sit in one particular\n\t// place in the tree, not in multiple. For these situations, we\n\t// will bail out here, but the user can always distribute and then\n\t// canonicalise.\n\n#ifdef DEBUG\n\t//\tstd::cerr << \"dummies:\\n\";\n\t//\tfor(auto& dummy: ind_dummy)\n\t//\t\tstd::cerr << dummy.first;\n\t//\tstd::cerr << \"free:\\n\";\n\t//\tfor(auto& fr: ind_free)\n\t//\t\tstd::cerr << fr.first;\n#endif\n\n\tfor(auto& dummy: ind_dummy)\n\t\tif(ind_dummy.count(dummy.first)>2)\n\t\t\treturn result_t::l_no_action;\n\n\t// PROGRESS\n\t//\tfor(auto& free: ind_free)\n\t//\t\tif(ind_free.count(free.first)>1) {\n\t//\t\t\tstd::cerr << \"bailing out\" << std::endl;\n\t//\t\t\treturn result_t::l_no_action;\n\t//\t\t\t}\n\n\tresult_t res=result_t::l_no_action;\n\n\t// Construct the \"name to slot\" map from the order in ind_free & ind_dummy.\n\t// Also construct the free and dummy lists.\n\t// And a map from index number to iterator (for later).\n\tstd::vector<int> vec_perm;\n\n\n\t// We need two arrays: one which maps from the order in which slots appear in\n\t//\tthe tensor to the corresponding iterator (this is provided by the standard\n\t// index routines already), and one which maps from the order in which the indices\n\t// appear in the base map to an Ex object (so that we can replace).\n\n\tstd::vector<Ex::iterator> num_to_it_map(total_number_of_indices);\n\tstd::vector<Ex>           num_to_tree_map;\n\n#ifdef DEBUG\n\tstd::cerr << \"indices:\" << std::endl;\n\tauto ii=begin_index(it);\n\twhile(ii!=end_index(it)) {\n\t\tstd::cerr << ii << std::endl;\n\t\t++ii;\n\t\t}\n#endif\n\n\n\t// Handle free indices.\n\n#ifdef DEBUG\n\tstd::cerr << \"found \" << ind_free.size() << \" free indices\" << std::endl;\n#endif\n\tIndexClassifier::index_map_t::iterator sorted_it=ind_free.begin();\n\tint curr_index=0;\n\twhile(sorted_it!=ind_free.end()) {\n\t\tIndexClassifier::index_position_map_t::iterator ii=ind_pos_free.find(sorted_it->second);\n\t\tnum_to_it_map.at(ii->second)=ii->first;\n\t\tnum_to_tree_map.push_back(Ex(ii->first));\n#ifdef DEBUG\n\t\tstd::cerr << sorted_it->second << \" free at pos \" << ii->second+1 << std::endl;\n#endif\n\t\tvec_perm.push_back(ii->second+1);\n\n\t\t++sorted_it;\n\t\t}\n\tcurr_index=0;\n\n\n\t// Handle dummy indices\n\t// In order to ensure that dummy indices from different index types do not\n\t// get mixed up, we need to collect information about the types of all\n\t// dummy indices.\n\t// The key in the maps below is the set_name of the Indices property, or the\n\t// set_name of the parent if applicable. If none, it will be ' undeclared'.\n\n\ttypedef std::map<std::string, std::vector<int> > dummy_set_t;\n\tdummy_set_t dummy_sets;\n#ifdef DEBUG\n\tstd::cerr << \"found \" << ind_dummy.size() << \" dummies\" << std::endl;\n#endif\n\tsorted_it=ind_dummy.begin();\n\twhile(sorted_it!=ind_dummy.end()) {\n\t\t// We insert the dummy indices in pairs (canonicalise only acts on\n\t\t// expressions which have dummies coming in doublets, not the more\n\t\t// general cadabra dummy concept).\n\t\t// The lower index come first, and then the upper index.\n\n\t\tIndexClassifier::index_position_map_t::const_iterator ii=ind_pos_dummy.find(sorted_it->second);\n\t\tIndexClassifier::index_map_t::const_iterator          next_it=sorted_it;\n\t\t++next_it;\n\t\tIndexClassifier::index_position_map_t::const_iterator i2=ind_pos_dummy.find(next_it->second);\n\n#ifdef XPERM_DEBUG\n\t\tstd::cerr << *(ii->first->name) << \" at pos \" << ii->second+1 << \" \" << ii->first->fl.parent_rel << std::endl;\n#endif\n\n\t\tswitch(ii->first->fl.parent_rel) {\n\t\t\tcase str_node::p_super:\n\t\t\tcase str_node::p_none:\n\t\t\t\t//\t\t\t\tvec_perm.push_back(ii->second+1);\n\t\t\t\t//\t\t\t\tvec_perm.push_back(i2->second+1);\n\t\t\t\t//\t\t\t\tnum_to_tree_map.push_back(Ex(ii->first));\n\t\t\t\t//\t\t\t\tnum_to_tree_map.push_back(Ex(i2->first));\n\t\t\t\tbreak;\n\t\t\tcase str_node::p_sub:\n\t\t\t\tstd::swap(ii, i2);\n\t\t\t\t//\t\t\t\tvec_perm.push_back(i2->second+1);\n\t\t\t\t//\t\t\t\tvec_perm.push_back(ii->second+1);\n\t\t\t\t//\t\t\t\tnum_to_tree_map.push_back(Ex(i2->first));\n\t\t\t\t//\t\t\t\tnum_to_tree_map.push_back(Ex(ii->first));\n\t\t\t\tbreak;\n\t\t\tdefault:\n\t\t\t\tbreak;\n\t\t\t}\n\n\t\tvec_perm.push_back(ii->second+1);\n\t\tvec_perm.push_back(i2->second+1);\n\t\tnum_to_tree_map.push_back(Ex(ii->first));\n\t\tnum_to_tree_map.push_back(Ex(i2->first));\n\n\t\tnum_to_it_map[ii->second]=ii->first;\n\t\tnum_to_it_map[i2->second]=i2->first;\n\n\t\t// If the indices are not in canonical order and they are separated\n\t\t// by a Derivative, we cannot raise/lower, so they should stay in this order.\n\t\t// Have to do this by putting those indices in a different set and then\n\t\t// setting the metric flag to 0. Ditto when only one index is on a derivative\n\t\t// (canonicalising usually makes the expression uglier in that case).\n\t\titerator tmp;\n\t\tif( ( (separated_by_derivative(tr.parent(ii->first), tr.parent(i2->first),tmp)\n\t\t       || only_one_on_derivative(ii->first, i2->first) )\n\t\t      && position_type(ii->first)==Indices::fixed ) ||\n\t\t      position_type(ii->first)==Indices::independent ) {\n\t\t\tdummy_sets[\" NR \"+get_index_set_name(ii->first)].push_back(ii->second+1);\n\t\t\tdummy_sets[\" NR \"+get_index_set_name(i2->first)].push_back(i2->second+1);\n\t\t\t}\n\t\telse {\n\t\t\tif( kernel.properties.get<AntiCommuting>(ii->first, true) != 0 ) {\n\t\t\t\tdummy_sets[\" AC \"+get_index_set_name(ii->first)].push_back(ii->second+1);\n\t\t\t\tdummy_sets[\" AC \"+get_index_set_name(i2->first)].push_back(i2->second+1);\n\t\t\t\t}\n\t\t\telse {\n\t\t\t\tdummy_sets[get_index_set_name(ii->first)].push_back(ii->second+1);\n\t\t\t\tdummy_sets[get_index_set_name(i2->first)].push_back(i2->second+1);\n\t\t\t\t}\n\t\t\t}\n\n\t\t++sorted_it;\n\t\t++sorted_it;\n\t\t}\n\n\t// FIXME: kludge to handle numerical indices; should be done through lookup\n\t// in Integer properties. This one does NOT work when there is more than\n\t// one index set; we would need more clever logic to figure out which\n\t// index type the numerical index corresponds to.\n\t//\tdebugout << index_sets.size() << std::endl;\n\t//\tif(index_sets.size()==1) {\n\t//\t\tfor(unsigned int kk=0; kk<indexpos_to_indextype.size(); ++kk)\n\t//\t\t\tif(indexpos_to_indextype[kk]==\"numerical\")\n\t//\t\t\t\tindexpos_to_indextype[kk]=index_sets.begin()->first;\n\t//\t\t}\n\t//\n\n\t// TRACE: remove later THIS DOES NOT SOLVE THE PROBLEM, ITERATORS ABOVE SEEM TO BE WRONG.\n\t//\tprod_unwrap_single_term(it);\n\t//\treturn result_t::l_no_action;\n\n\n\t// Construct the generating set.\n\n\tstd::vector<unsigned int> base_here;\n\n\tif(!reuse_generating_set || generating_set.size()==0) {\n\t\tgenerating_set.clear();\n\t\t// Symmetry of individual tensors.\n\t\tsibling_iterator facit=tr.begin(it);\n\t\tint curr_pos=0;\n\t\twhile(facit!=tr.end(it)) {\n\t\t\tconst TableauBase *tba=kernel.properties.get<TableauBase>(facit);\n\t\t\t// std::cerr << Ex(facit) << \" has tableaubase \" << tba << std::endl;\n\t\t\tif(tba) {\n\t\t\t\tunsigned int num_ind=number_of_indices(facit);\n#ifdef XPERM_DEBUG\n\t\t\t\tstd::cerr << \"factor \" << *facit->name << \" has \" << num_ind << \" indices\" << std::endl;\n#endif\n\n\t\t\t\t// Add indices to the base. We used to add everything except the last one, but that\n\t\t\t\t// seems to be the wrong thing to do after the XPERM -> XPERM_EXT upgrade (see Jose's email).\n\t\t\t\tfor(unsigned int kk=0; kk<num_ind; ++kk)\n\t\t\t\t\tbase_here.push_back(curr_pos+kk+1);\n\n\t\t\t\t// loop over tabs\n\t\t\t\tfor(unsigned int ti=0; ti<tba->size(kernel.properties, tr, facit); ++ti) {\n\t\t\t\t\tTableauBase::tab_t tmptab=tba->get_tab(kernel.properties, tr,facit,ti);\n\t\t\t\t\t// std::cerr << tmptab << std::endl;\n\t\t\t\t\tif(tmptab.number_of_rows()>0) {\n\t\t\t\t\t\tfor(unsigned int col=0; col<tmptab.row_size(0); ++col) { // anti-symmetry in all inds in a col\n\t\t\t\t\t\t\tif(tmptab.column_size(col)>1) {\n\t\t\t\t\t\t\t\t// all pairs NEW: SGS\n\t\t\t\t\t\t\t\tfor(unsigned int indnum1=0; indnum1<tmptab.column_size(col)-1; ++indnum1) {\n\t\t\t\t\t\t\t\t\t//\t\t\t\t\t\t\t\tfor(unsigned int indnum2=indnum1+1; indnum2<tmptab.column_size(col); ++indnum2) {\n\t\t\t\t\t\t\t\t\tstd::vector<int> permute(total_number_of_indices+2);\n\t\t\t\t\t\t\t\t\tfor(unsigned int kk=0; kk<permute.size(); ++kk)\n\t\t\t\t\t\t\t\t\t\tpermute[kk]=kk+1;\n\t\t\t\t\t\t\t\t\tstd::swap(permute[tmptab(indnum1,col)+curr_pos],\n\t\t\t\t\t\t\t\t\t          permute[tmptab(indnum1+1,col)+curr_pos]);\n\t\t\t\t\t\t\t\t\tstd::swap(permute[total_number_of_indices+1],\n\t\t\t\t\t\t\t\t\t          permute[total_number_of_indices]); // anti-symmetry\n\t\t\t\t\t\t\t\t\tgenerating_set.push_back(permute);\n\t\t\t\t\t\t\t\t\t}\n\t\t\t\t\t\t\t\t}\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\t}\n\t\t\t\t\tif(tmptab.number_of_rows()==1 && tmptab.row_size(0)>1) { // symmetry, if all cols of size 1\n\t\t\t\t\t\t// all pairs\n\t\t\t\t\t\tfor(unsigned int indnum1=0; indnum1<tmptab.row_size(0)-1; ++indnum1) {\n\t\t\t\t\t\t\t//\t\t\t\t\t\tfor(unsigned int indnum2=indnum1+1; indnum2<tmptab.row_size(0); ++indnum2) {\n\t\t\t\t\t\t\tstd::vector<int> permute(total_number_of_indices+2);\n\t\t\t\t\t\t\tfor(unsigned int kk=0; kk<permute.size(); ++kk)\n\t\t\t\t\t\t\t\tpermute[kk]=kk+1;\n\t\t\t\t\t\t\tstd::swap(permute[tmptab(0,indnum1)+curr_pos],\n\t\t\t\t\t\t\t          permute[tmptab(0,indnum1+1)+curr_pos]);\n\t\t\t\t\t\t\tgenerating_set.push_back(permute);\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\t}\n\t\t\t\t\telse if(tmptab.number_of_rows()>0) {   // find symmetry under equal-length column exchange\n\t\t\t\t\t\tunsigned int column_height=tmptab.column_size(0);\n\t\t\t\t\t\tunsigned int this_set_start=0;\n\t\t\t\t\t\tfor(unsigned int col=1; col<=tmptab.row_size(0); ++col) {\n\t\t\t\t\t\t\tif(col==tmptab.row_size(0) || column_height!=tmptab.column_size(col)) {\n\t\t\t\t\t\t\t\tif(col-this_set_start>1) {\n\t\t\t\t\t\t\t\t\t// two or more equal-length columns found, make generating set\n\t\t\t\t\t\t\t\t\tfor(unsigned int col1=this_set_start; col1+1<=col-1; ++col1) {\n\t\t\t\t\t\t\t\t\t\t//\t\t\t\t\t\t\t\t\tfor(unsigned int col2=this_set_start+1; col2<col; ++col2) {\n\t\t\t\t\t\t\t\t\t\tstd::vector<int> permute(total_number_of_indices+2);\n\t\t\t\t\t\t\t\t\t\tfor(unsigned int kk=0; kk<permute.size(); ++kk)\n\t\t\t\t\t\t\t\t\t\t\tpermute[kk]=kk+1;\n\t\t\t\t\t\t\t\t\t\tfor(unsigned int row=0; row<column_height; ++row) {\n\t\t\t\t\t\t\t\t\t\t\t//\t\t\t\t\t\t\t\t\t\ttxtout << row << \" \" << col1 << std::endl;\n\t\t\t\t\t\t\t\t\t\t\tstd::swap(permute[tmptab(row,col1)+curr_pos],\n\t\t\t\t\t\t\t\t\t\t\t          permute[tmptab(row,col1+1)+curr_pos]);\n\t\t\t\t\t\t\t\t\t\t\t}\n\t\t\t\t\t\t\t\t\t\tgenerating_set.push_back(permute);\n\t\t\t\t\t\t\t\t\t\t}\n\t\t\t\t\t\t\t\t\t}\n\t\t\t\t\t\t\t\tthis_set_start=col;\n\t\t\t\t\t\t\t\tif(col<tmptab.row_size(0))\n\t\t\t\t\t\t\t\t\tcolumn_height=tmptab.column_size(col);\n\t\t\t\t\t\t\t\t}\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\t}\n\t\t\t\t\t}\n\t\t\t\t//\t\t\t\t\ttxtout << \"loop over tabs done\" << std::endl;\n\t\t\t\tcurr_pos+=num_ind;\n\t\t\t\t}\n\t\t\telse {\n\t\t\t\tunsigned int num_ind=number_of_indices(facit);\n\t\t\t\tif(num_ind==1)\n\t\t\t\t\tbase_here.push_back(curr_pos+1);\n\t\t\t\telse {\n\t\t\t\t\tfor(unsigned int kk=0; kk<num_ind; ++kk)\n\t\t\t\t\t\tbase_here.push_back(curr_pos+kk+1);\n\t\t\t\t\t}\n\t\t\t\tcurr_pos+=number_of_indices(facit); // even if tba=0, this factor may contain indices\n\t\t\t\t}\n\t\t\t++facit;\n\t\t\t}\n\t\t// Symmetry under tensor exchange.\n\t\tif(exchange::get_node_gs(kernel.properties, tr, it, generating_set)==false) {\n\t\t\tzero(it->multiplier);\n\t\t\tres=result_t::l_applied;\n\t\t\t}\n\t\t}\n\t// End of construction of generating set.\n\n#ifdef XPERM_DEBUG\n\tstd::cerr << \"generating set size = \" << generating_set.size() << \" multiplier \" << *it->multiplier << std::endl;\n#endif\n\n\t// Even if generating_set.size()==0 we still need to continue,\n\t// because we still need to do simple index relabelling.\n\t//\tif(generating_set.size()==0) {\n\t//\t\tprod_unwrap_single_term(it);\n\t//\t\treturn result_t::l_no_action;\n\t//\t\t}\n\n\tif(*it->multiplier!=0) {\n\t\t// Fill data for the xperm routines.\n\t\tint *gs=0;\n\n\t\tif(generating_set.size()>0) {\n\t\t\tgs=new int[generating_set.size()*generating_set[0].size()];\n\t\t\tfor(unsigned int i=0; i<generating_set.size(); ++i) {\n\t\t\t\tfor(unsigned int j=0; j<total_number_of_indices+2; ++j) {\n\t\t\t\t\tgs[i*(total_number_of_indices+2)+j]=generating_set[i][j];\n#ifdef XPERM_DEBUG\n\t\t\t\t\tstd::cerr << gs[i*(total_number_of_indices+2)+j] << \" \";\n#endif\n\t\t\t\t\t}\n#ifdef XPERM_DEBUG\n\t\t\t\tstd::cerr << std::endl;\n#endif\n\t\t\t\t}\n\t\t\t}\n\n\t\t// Setup the arrays for xperm from our own data structures.\n\n\t\tint    *base=new int[base_here.size()];\n\t\tint    *perm=new int[total_number_of_indices+2];\n\t\tint   *cperm=new int[total_number_of_indices+2];\n\n\t\tfor(unsigned int i=0; i<base_here.size(); ++i)\n\t\t\tbase[i]=base_here[i];\n\t\tassert(vec_perm.size()==total_number_of_indices);\n\t\tfor(unsigned int i=0; i<total_number_of_indices; ++i)\n\t\t\tperm[i]=vec_perm[i];\n\t\tperm[total_number_of_indices]=total_number_of_indices+1;\n\t\tperm[total_number_of_indices+1]=total_number_of_indices+2;\n\n\t\tint  *lengths_of_dummy_sets=new int[dummy_sets.size()];\n\t\tint  *dummies              =new int[ind_dummy.size()];\n\t\tint  *metric_signatures    =new int[dummy_sets.size()];\n\t\tint  dsi=0;\n\t\tint  cdi=0;\n\t\tdummy_set_t::iterator ds=dummy_sets.begin();\n\t\twhile(ds!=dummy_sets.end()) {\n\t\t\tlengths_of_dummy_sets[dsi]=ds->second.size();\n\t\t\tfor(unsigned int k=0; k<ds->second.size(); ++k)\n\t\t\t\tdummies[cdi++]=(ds->second)[k];\n\t\t\tif(ds->first.substr(0,4)==\" NR \")\n\t\t\t\tmetric_signatures[dsi]=0;\n\t\t\telse {\n\t\t\t\tif(ds->first.substr(0,4)==\" AC \")\n\t\t\t\t\tmetric_signatures[dsi]=-1;\n\t\t\t\telse\n\t\t\t\t\tmetric_signatures[dsi]=1;\n\t\t\t\t}\n\t\t\t++ds;\n\t\t\t++dsi;\n\t\t\t}\n\n\t\t// Setup repeated sets. These are free indices which appear more\n\t\t// than once (so these are coordinates or integers). Take them out\n\t\t// of the free set and store them in the repeated sets.\n\n#ifdef DEBUG\n\t\tstd::cerr << \"creating repeated sets\" << std::endl;\n#endif\n\t\tstd::vector<int>          ind_repeated_lengths;\n\t\tstd::vector<Ex::iterator> ind_repeated;\n\t\tauto fi = ind_free.begin();\n\t\tauto prev=fi;\n\t\tif(fi!=ind_free.end()) {\n\t\t\t++fi;\n\t\t\twhile(fi!=ind_free.end()) {\n\t\t\t\tint len=1;\n\t\t\t\twhile(fi!=ind_free.end() && fi->first==prev->first) {\n\t\t\t\t\tif(len==1)\n\t\t\t\t\t\tind_repeated.push_back(prev->second);\n\t\t\t\t\tind_repeated.push_back(fi->second);\n\t\t\t\t\t++len;\n\t\t\t\t\t++fi;\n\t\t\t\t\t}\n\t\t\t\tif(len!=1) {\n\t\t\t\t\tind_free.erase(prev, fi);\n\t\t\t\t\tind_repeated_lengths.push_back(len);\n\t\t\t\t\t}\n\t\t\t\tif(fi!=ind_free.end()) {\n\t\t\t\t\tprev=fi;\n\t\t\t\t\t++fi;\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t}\n\n\t\t// free_indices stores a list of index slots which contain a free\n\t\t// index.\n\t\tint              *free_indices=new int[ind_free.size()];\n\t\tsorted_it=ind_free.begin();\n\t\tcurr_index=0;\n\t\twhile(sorted_it!=ind_free.end()) {\n\t\t\tIndexClassifier::index_position_map_t::iterator ii=ind_pos_free.find(sorted_it->second);\n\t\t\tfree_indices[curr_index++]=ii->second+1;\n\t\t\t++sorted_it;\n\t\t\t}\n\n\t\t//\t\tstd::cerr << \"repeated sets:\\n\";\n\t\t//\t\tfor(auto& f: ind_repeated)\n\t\t//\t\t\tstd::cerr << *(f->multiplier) << \" \";\n\t\t//\t\tstd::cerr << \"\\nrepeated lengths:\\n\";\n\t\t//\t\tfor(auto& i: ind_repeated_lengths)\n\t\t//\t\t\tstd::cerr << i << \" \";\n\t\t//\t\tstd::cerr << std::endl;\n\n\t\tint *repeated_indices         = new int[ind_repeated.size()];\n\t\tint *lengths_of_repeated_sets = new int[ind_repeated_lengths.size()];\n\n\t\t// repeated_indices contains a list of slots which contain repeated indices.\n\t\tfor(size_t i=0; i<ind_repeated.size(); ++i) {\n\t\t\tauto pos=ind_pos_free.find(ind_repeated[i]);\n\t\t\trepeated_indices[i]=pos->second+1;\n\t\t\t}\n\t\tfor(size_t i=0; i<ind_repeated_lengths.size(); ++i)\n\t\t\tlengths_of_repeated_sets[i]=ind_repeated_lengths[i];\n\n#ifdef XPERM_DEBUG\n\t\tstd::cerr << \"perm:\" << std::endl;\n\t\tfor(unsigned int i=0; i<total_number_of_indices+2; ++i)\n\t\t\tstd::cerr << perm[i] << \" \";\n\t\tstd::cerr << std::endl;\n\t\tstd::cerr << \"base:\" << std::endl;\n\t\tfor(unsigned int i=0; i<base_here.size(); ++i)\n\t\t\tstd::cerr << base[i] << \" \";\n\t\tstd::cerr << std::endl;\n\t\tstd::cerr << \"free indices in slots:\" << std::endl;\n\t\tfor(unsigned int i=0; i<ind_free.size(); ++i)\n\t\t\tstd::cerr << free_indices[i] << \" \";\n\t\tstd::cerr << std::endl;\n\t\tstd::cerr << \"lengths_of_dummy_sets:\" << std::endl;\n\t\tfor(unsigned int i=0; i<dummy_sets.size(); ++i)\n\t\t\tstd::cerr << lengths_of_dummy_sets[i]\n\t\t\t          << \" (metric=\" << metric_signatures[i] << \") \";\n\t\tstd::cerr << std::endl;\n\t\tstd::cerr << \"dummies in slots:\" << std::endl;\n\t\tfor(unsigned int i=0; i<ind_dummy.size(); ++i)\n\t\t\tstd::cerr << dummies[i] << \" \";\n\t\tstd::cerr << std::endl;\n\t\tstd::cerr << \"lengths_of_repeated_sets:\" << std::endl;\n\t\tfor(unsigned int i=0; i<ind_repeated_lengths.size(); ++i)\n\t\t\tstd::cerr << lengths_of_repeated_sets[i];\n\t\tstd::cerr << std::endl;\n\t\tstd::cerr << \"repeated indices in slots:\" << std::endl;\n\t\tfor(unsigned int i=0; i<ind_repeated.size(); ++i)\n\t\t\tstd::cerr << repeated_indices[i];\n\t\tstd::cerr << std::endl;\n#endif\n\n\t\tStopwatch sw;\n\t\tsw.start();\n\n\t\t// JMM now uses a different convention.\n\t\tint *perm1 = new int[total_number_of_indices+2];\n\t\tint *perm2 = new int[total_number_of_indices+2];\n\t\tint *free_indices_new_order = new int[ind_free.size()];\n\t\tint *dummies_new_order      = new int[ind_dummy.size()];\n\t\tint *repeated_new_order     = new int[ind_repeated.size()];\n\n\t\tinverse(perm, perm1, total_number_of_indices+2);\n\t\tfor(size_t i=0; i<ind_free.size(); i++) {\n\t\t\tfree_indices_new_order[i] = onpoints(free_indices[i], perm1, total_number_of_indices+2);\n\t\t\t}\n\t\tfor(size_t i=0; i<ind_dummy.size(); i++) {\n\t\t\tdummies_new_order[i] = onpoints(dummies[i], perm1, total_number_of_indices+2);\n\t\t\t}\n\t\tfor(size_t i=0; i<ind_repeated.size(); i++) {\n\t\t\trepeated_new_order[i] = onpoints(repeated_indices[i], perm1, total_number_of_indices+2);\n\t\t\t}\n#ifdef XPERM_DEBUG\n\t\tstd::cerr << \"perm1: \";\n\t\tfor(unsigned int i=0; i<total_number_of_indices; ++i) {\n\t\t\tstd::cerr << perm1[i] << \" \";\n\t\t\t}\n\t\tstd::cerr << std::endl;\n#endif\n\t\t// Brief reminder of the meaning of the various arrays, using the example in\n\t\t// Jose's xPerm paper (not yet updated to reflect the _ext version which allows\n\t\t// for multiple dummy sets; see below for repeated (numerical) indices):\n\t\t//\n\t\t// expression        = R_{b}^{1d1} R_{c}^{bac}\n\t\t//\n\t\t// sorted_index_set  = {a,d,b,-b,c,-c,1,1}\n\t\t// base              = {1,2,3, 4,5, 6,7,8}\n\t\t// dummies           = {3,4,5,6}\n\t\t//    sorted_index_set[3] and [4] is a dummy pair\n\t\t//    sorted_index_set[5] and [6] is a dummy pair\n\t\t//    these can just be in sorted order, i.e. only referring\n\t\t//    to the sorted_index_set.\n\t\t//\n\t\t// frees             = {1,2}\n\t\t//    sorted_index_set[1] and [2] are free indices\n\t\t//\n\t\t// dummies_new_order = {dn[1], dn[2], ...}\n\t\t//    slot dn[1] and dn[2] form a dummy pair ?\n\t\t//\n\t\t// free_indices_new_order = {...}\n\t\t//    these slots contain free indices ?\n\t\t//\n\t\t// perm = {4,7,2,8,6,3,1,5,9,10}\n\t\t//    1st slot contains sorted_index_set[4] ( = -b )\n\t\t//    2nd slot contains sorted_index_set[7] ( = 1 )\n\t\t//    etc.\n\t\t//\n\t\t// perm1 = {p1[1], p1[2], ...}\n\t\t//\n\t\t//    1st index sits in slot p1[1] ?\n\t\t//\n\t\t// cperm = {1,3,4,5,2,7,6,8,9,10}\n\t\t//\n\t\t//    1st slot gets sorted_index_set[1] ( = a )\n\t\t//    2nd slot gets sorted_index_set[3] ( = b )\n\t\t//    ...\n\t\t//\n\t\t// for the repeated set logic:\n\t\t// (in both perm and free, numbers refer to index names (each index name has a separate number\n\t\t// even if it occurs multiple times).\n\t\t//\n\t\t// R_{3 3 m 3}\n\t\t//    perm: 6\n\t\t//    2 3 1 4 5 6  (slot 3 gets index name 1, slot 1 index 2, slot 3 index 3, slot 4 index 4)\n\t\t//    base: 4\n\t\t//    1 2 3 4\n\t\t//    free: 1\n\t\t//    1            (index name 1 is free)\n\t\t//    number of repes: 3\n\t\t//    2 3 4        (index names 2 to 4 are repeated);\n\n\t\t// R_{3 m 3 3}\n\t\t//    perm: 6\n\t\t//    2 1 3 4 5 6   (slot 2 gets index name 1, ...)\n\t\t//    base: 4\n\t\t//    1 2 3 4       (always the same)\n\t\t//    free: 1\n\t\t//    1             (index name 1 is free)\n\t\t//    number of repes: 3\n\t\t//    2 3 4         (2nd, 3rd and 4th index names are repeated: index 1, 3 and 4)\n\n\n\t\tcanonical_perm_ext(perm1,                       // permutation to be canonicalised\n\t\t                   total_number_of_indices+2,  // degree (+2 for the overall sign)\n\t\t                   1,                          // is this a strong generating set?\n\t\t                   base,                       // base for the strong generating set\n\t\t                   base_here.size(),           //    its length\n\t\t                   gs,                         // generating set\n\t\t                   generating_set.size(),      //    its size\n\t\t                   free_indices_new_order,     // free indices\n\t\t                   ind_free.size(),            // number of free indices\n\t\t                   lengths_of_dummy_sets,      // list of lengths of dummy sets\n\t\t                   dummy_sets.size(),          //    its length\n\t\t                   dummies_new_order,          // list with pairs of dummies\n\t\t                   ind_dummy.size(),           //    its length\n\t\t                   metric_signatures,          // list of symmetries of metric\n\t\t                   lengths_of_repeated_sets,   // list of lengths of repeated-sets\n\t\t                   ind_repeated_lengths.size(),//    its length\n\t\t                   repeated_new_order,         // list with repeated indices\n\t\t                   ind_repeated.size(),        //    its length\n\t\t                   perm2);                     // output\n\n\t\tif (perm2[0] != 0) inverse(perm2, cperm, total_number_of_indices+2);\n\t\telse copy_list(perm2, cperm, total_number_of_indices+2);\n\n\t\tdelete [] dummies_new_order;\n\t\tdelete [] free_indices_new_order;\n\t\tdelete [] repeated_new_order;\n\t\tdelete [] perm1;\n\t\tdelete [] perm2;\n\n\t\tsw.stop();\n\t\t//\t\tstd::cerr << \"xperm took \" << sw << std::endl;\n\n#ifdef XPERM_DEBUG\n\t\tstd::cerr << \"cperm:\" << std::endl;\n\t\tfor(unsigned int i=0; i<total_number_of_indices+2; ++i)\n\t\t\tstd::cerr << cperm[i] << \" \";\n\t\tstd::cerr << std::endl;\n#endif\n\n\t\tif(cperm[0]!=0) {\n\t\t\tbool has_changed=false;\n\t\t\tfor(unsigned int i=0; i<total_number_of_indices+1; ++i) {\n\t\t\t\tif(perm[i]!=cperm[i]) {\n\t\t\t\t\thas_changed=true;\n\t\t\t\t\tbreak;\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\tif(has_changed) {\n\t\t\t\tif(static_cast<unsigned int>(cperm[total_number_of_indices+1])==total_number_of_indices+1) {\n\t\t\t\t\tflip_sign(it->multiplier);\n\t\t\t\t\t}\n\t\t\t\tres = result_t::l_applied;\n\n\t\t\t\tfor(unsigned int i=0; i<total_number_of_indices; ++i) {\n\t\t\t\t\t// In the new final permutation, e.g.\n\t\t\t\t\t//\n\t\t\t\t\t// 1 5 6 8 7 2 3 4 10 9\n\t\t\t\t\t//\n\t\t\t\t\t// we place first the first index (m), which goes to the first slot. Then\n\t\t\t\t\t// we put n, which can only go the fifth slot. Then we put p, which can go\n\t\t\t\t\t// to 6,7,8, so that it goes to 6. Then we put r (not q), which can go to 7\n\t\t\t\t\t// and 8, and so we put it at 7, etc.\n\n#ifdef XPERM_DEBUG\n\t\t\t\t\tstd::cerr << \"putting index \" << i+1 << \"(\" << *num_to_tree_map[i].begin()->name\n\t\t\t\t\t          << \", \" << num_to_tree_map[i].begin()->fl.parent_rel\n\t\t\t\t\t          << \") in slot \" << cperm[i] << std::endl;\n#endif\n\n\t\t\t\t\titerator ri = tr.replace_index(num_to_it_map[cperm[i]-1], num_to_tree_map[i].begin());\n\t\t\t\t\t//\t\t\t\t\tassert(ri->fl.parent_rel==num_to_tree_map[i].begin()->fl.parent_rel);\n\t\t\t\t\tri->fl.parent_rel=num_to_tree_map[i].begin()->fl.parent_rel;\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t}\n\t\telse {\n\t\t\tzero(it->multiplier);\n\t\t\tres = result_t::l_applied;\n\t\t\t}\n\n\t\tif(gs)\n\t\t\tdelete [] gs;\n\t\tdelete [] base;\n\n\t\tdelete [] repeated_indices;\n\t\tdelete [] lengths_of_repeated_sets;\n\t\tdelete [] metric_signatures;\n\t\tdelete [] lengths_of_dummy_sets;\n\t\tdelete [] dummies;\n\t\tdelete [] cperm;\n\t\tdelete [] perm;\n\t\tdelete [] free_indices;\n\t\t}\n#ifdef DEBUG\n\tstd::cerr << \"=====\\n\";\n#endif\n\n\tcleanup_dispatch(kernel, tr, it);\n\n\n\ttotalsw.stop();\n\t//\tstd::cerr << \"total canonicalise took \" << totalsw << std::endl;\n\n\treturn res;\n\t}\n"
  },
  {
    "path": "core/algorithms/canonicalise.cnb",
    "content": "{\n\t\"cells\" : \n\t[\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\algorithm{canonicalise}{Bring a tensorial expression to canonical form by re-ordering indices.}\\n\\nCanonicalise a product of tensors, using the mono-term \\nindex symmetries of the individual tensors and the\\nexchange symmetries of identical tensors. Tensor exchange takes into\\naccount commutativity properties of identical tensors.\\n\\n\\nNote that this algorithm does not take into account multi-term\\nsymmetries such as the Ricci identity of the Riemann tensor; those\\ncanonicalisation procedures require the use\\nof \\\\algo{young\\\\_project\\\\_tensor}\\nor \\\\algo{young\\\\_project\\\\_product}. Similarly,\\ndimension-dependent identities are not taken into account, use\\n\\\\algo{decompose_product} for those.\\n\\n\\nIn order to specify symmetries of tensors you need to use symmetry\\nproperties such as \\\\prop{Symmetric}, \\\\prop{AntiSymmetric}\\nor \\\\prop{TableauSymmetry}. The following example illustrates this.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\algorithm{canonicalise}{Bring a tensorial expression to canonical form by re-ordering indices.}\\n\\nCanonicalise a product of tensors, using the mono-term \\nindex symmetries of the individual tensors and the\\nexchange symmetries of identical tensors. Tensor exchange takes into\\naccount commutativity properties of identical tensors.\\n\\n\\nNote that this algorithm does not take into account multi-term\\nsymmetries such as the Ricci identity of the Riemann tensor; those\\ncanonicalisation procedures require the use\\nof \\\\algo{young\\\\_project\\\\_tensor}\\nor \\\\algo{young\\\\_project\\\\_product}. Similarly,\\ndimension-dependent identities are not taken into account, use\\n\\\\algo{decompose_product} for those.\\n\\n\\nIn order to specify symmetries of tensors you need to use symmetry\\nproperties such as \\\\prop{Symmetric}, \\\\prop{AntiSymmetric}\\nor \\\\prop{TableauSymmetry}. The following example illustrates this.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}A_{m n} B_{m n}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}0\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"A_{m n}::AntiSymmetric.\\nB_{p q}::Symmetric.\\nex:=A_{m n} B_{m n};\\ncanonicalise(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"If the various terms in an expression use different index names, you\\nmay need an additional call to \\\\algo{rename\\\\_dummies}\\nbefore the terms get collected together:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"If the various terms in an expression use different index names, you\\nmay need an additional call to \\\\algo{rename\\\\_dummies}\\nbefore the terms get collected together:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}A_{m n} C_{m n q}+A_{s r} C_{s q r}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}A_{m n} C_{q m n}-A_{r s} C_{q r s}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"{m,n,p,q,r,s}::Indices.\\nA_{m n}::AntiSymmetric.\\nC_{p q r}::AntiSymmetric.\\nex:=A_{m n} C_{m n q} + A_{s r} C_{s q r};\\ncanonicalise(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}0\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"rename_dummies(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"If you have symmetric or anti-symmetric tensors with many indices, it\\nsometimes pays off to sort them to the end of the expression (this may\\nspeed up the canonicalisation process considerably).\\n\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"If you have symmetric or anti-symmetric tensors with many indices, it\\nsometimes pays off to sort them to the end of the expression (this may\\nspeed up the canonicalisation process considerably).\\n\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1\n}\n"
  },
  {
    "path": "core/algorithms/canonicalise.hh",
    "content": "#pragma once\n\n#include \"Algorithm.hh\"\n#include \"properties/Indices.hh\"\n#include <vector>\n\nnamespace cadabra {\n\n\t/// \\ingroup algorithms\n\t///\n\t/// Canonicalise the index structure of a tensorial expression.\n\n\tclass canonicalise : public Algorithm {\n\t\tpublic:\n\t\t\tcanonicalise(const Kernel&, Ex&);\n\n\t\t\tvirtual bool     can_apply(iterator);\n\t\t\tvirtual result_t apply(iterator&);\n\n\t\t\tstd::vector<std::vector<int> > generating_set;\n\t\t\tbool                           reuse_generating_set;\n\n\t\tprivate:\n\t\t\t// Sub-algorithms needed before going to the full fledged canonicaliser.\n\t\t\t// All return true if they have modified the expression.\n\t\t\tbool remove_traceless_traces(iterator&);\n\t\t\tbool remove_vanishing_numericals(iterator&);\n\t\t\tbool only_one_on_derivative(iterator index1, iterator index2) const;\n\n\t\t\tIndices::position_t  position_type(iterator) const;\n\t\t\t//\t\tvoid collect_dummy_info(const index_map_t&, const index_position_map_t&,\n\t\t\t//\t\t\t\t\t\t\t\t\t\tstd::vector<int>&, std::vector<int>&);\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/algorithms/canonicalorder.tex",
    "content": "\\cdbalgorithm{canonicalorder}{}\n\nOrders the indicated objects in the expression in canonical order. On\na simple product of objects it works as a partial product sort,\n\\begin{screen}{1,2}\nC B E D A;\n@canonicalorder!(%)(A, B, E);\nC A B D E;\n\\end{screen}\nIt can, however, also be used to sort indices. Thereby, it facilitates\nimposing index symmetry on a tensor with open indices, as the\nfollowing example illustrates.\n\\begin{screen}{1,2}\nA^{m n p} B^{q r} + A^{q m} B^{n p r};\n@canonicalorder!(%)( ^{m}, ^{n}, ^{p}, ^{r}, ^{q} );\nA^{m n p} B^{r q} + A^{m n} B^{p r q};\n\\end{screen}\n~\n\n\\cdbseealgo{acanonicalorder}\n\\cdbseealgo{prodsort}\n\\cdbseealgo{canonicalise}\n"
  },
  {
    "path": "core/algorithms/coefficients.tex",
    "content": "\\cdbalgorithm{coefficients}{}\n\nCreate a list of the coefficients of the powers of the indicated object.\n\\begin{screen}{1,2,3}\na + b x**2 + c x + d x**7;\n@coefficients(%){x};\n\\end{screen}\n\n\n\\cdbseealgo{range}\n\n"
  },
  {
    "path": "core/algorithms/collect_components.cc",
    "content": "\n#include \"algorithms/collect_components.hh\"\n#include \"algorithms/evaluate.hh\"\n\nusing namespace cadabra;\n\n// #define DEBUG 1\n\ncollect_components::collect_components(const Kernel& k, Ex& tr)\n\t: Algorithm(k, tr)\n\t{\n\t}\n\nbool collect_components::can_apply(iterator st)\n\t{\n\tassert(tr.is_valid(st));\n\tif(*st->name==\"\\\\sum\") return true;\n\treturn false;\n\t}\n\nAlgorithm::result_t collect_components::apply(iterator& st)\n\t{\n\tresult_t res=result_t::l_no_action;\n\tevaluate eval(kernel, tr, tr);\n\n\tsibling_iterator s1=tr.begin(st);\n\n#ifdef DEBUG\n\tstd::cerr << \"collect_components::apply: acting on \" << st << std::endl;\n#endif\n\twhile(s1!=tr.end(st)) { // Walk over all terms in the sum, find the first components node.\n\t\tif(*s1->name==\"\\\\components\") { // First term found, now collect all others.\n\t\t\tsibling_iterator s2=s1;//tr.begin(st);\n\t\t\t++s2;\n\t\t\twhile(s2!=tr.end(st)) {\n\t\t\t\tif(*s2->name==\"\\\\components\") {\n#ifdef DEBUG\n\t\t\t\t\tstd::cerr << \"collect_components::apply: merging\" << std::endl;\n#endif\n\t\t\t\t\teval.merge_components(s1,s2);\n\t\t\t\t\ts2=tr.erase(s2);\n\t\t\t\t\tres=result_t::l_applied;\n\t\t\t\t\t}\n\t\t\t\telse ++s2;\n\t\t\t\t}\n\t\t\tbreak; // Exit outer loop; we have found the first components node.\n\t\t\t}\n\t\t++s1;\n\t\t}\n\n\tif(s1!=tr.end(st)) {\n\t\t// Exited the main loop before the end, which means that we have\n\t\t// found at least one components node, stored at s1.\n#ifdef DEBUG\n\t\tstd::cerr << \"collect_components::apply: merged components node now \" << s1 << std::endl;\n#endif\n\t\teval.simplify_components(s1, false);\n\t\tauto comma=tr.end(s1);\n\t\t--comma;\n\t\tif(tr.number_of_children(comma)==0)\n\t\t\tnode_zero(s1);\n\t\t}\n\n\treturn res;\n\t}\n\n"
  },
  {
    "path": "core/algorithms/collect_components.hh",
    "content": "\n#pragma once\n\n#include \"Algorithm.hh\"\n\nnamespace cadabra {\n\n\t/// \\ingroup algorithms\n\t///\n\t/// Collect `\\components` terms inside a sum, merging their substitution rules.\n\n\tclass collect_components : public Algorithm {\n\t\tpublic:\n\t\t\tcollect_components(const Kernel&, Ex&);\n\n\t\t\tvirtual bool     can_apply(iterator) override;\n\t\t\tvirtual result_t apply(iterator&) override;\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/algorithms/collect_factors.cc",
    "content": "\n#include \"Props.hh\"\n#include \"Compare.hh\"\n#include \"Cleanup.hh\"\n#include \"IndexIterator.hh\"\n#include \"algorithms/collect_factors.hh\"\n#include \"algorithms/collect_terms.hh\"\n#include \"properties/Symbol.hh\"\n#include \"properties/Coordinate.hh\"\n\n//#define DEBUG\n\nusing namespace cadabra;\n\ncollect_factors::collect_factors(const Kernel& k, Ex& e)\n\t: Algorithm(k, e)\n\t{\n\t}\n\nbool collect_factors::can_apply(iterator it)\n\t{\n\tif(*it->name==\"\\\\prod\") return true;\n\treturn false;\n\t}\n\n// The hash map is such that all objects which are equal have to sit in the same\n// bin, but objects in the same bin do not necessarily all have to be equal.\nvoid collect_factors::fill_hash_map(iterator it)\n\t{\n\tfactor_hash.clear();\n\tsibling_iterator sib=tr.begin(it);\n\tunsigned int factors=0;\n\twhile(sib!=tr.end(it)) { // iterate over all factors in the product\n\t\tauto chsib=index_iterator::begin(kernel.properties, sib);\n\t\tauto chend=index_iterator::end(kernel.properties, sib);\n\t\tbool dontcollect=false;\n\t\twhile(chsib!=chend) { // iterate over all child nodes of a factor\n\t\t\tconst Symbol     *smb=kernel.properties.get<Symbol>(chsib, true);\n\t\t\tconst Coordinate *coo=kernel.properties.get<Coordinate>(chsib, true);\t\t\t\n\t\t\t// std::cerr << chsib << \": \" << smb << std::endl;\n\t\t\tif((chsib->fl.parent_rel==str_node::p_sub || chsib->fl.parent_rel==str_node::p_super) &&\n\t\t\t      chsib->is_rational()==false && smb==0 && coo==0) {\n\t\t\t\tdontcollect=true;\n\t\t\t\tbreak;\n\t\t\t\t}\n\t\t\t++chsib;\n\t\t\t}\n\t\tif(!dontcollect) {\n\t\t\tif(*sib->name==\"\\\\pow\") {\n\t\t\t\tif(tr.begin(sib)->is_rational()==false) // do not collect exponents of numbers\n\t\t\t\t\tfactor_hash.insert(std::pair<hashval_t, sibling_iterator>(tr.calc_hash(tr.begin(sib)), tr.begin(sib)));\n\t\t\t\t}\n\t\t\telse\n\t\t\t\tfactor_hash.insert(std::pair<hashval_t, sibling_iterator>(tr.calc_hash(sib), sib));\n\t\t\t++factors;\n\t\t\t}\n\t\t++sib;\n\t\t}\n\t}\n\nAlgorithm::result_t collect_factors::apply(iterator& st)\n\t{\n\tassert(tr.is_valid(st));\n\tassert(*st->name==\"\\\\prod\");\n\tresult_t res=result_t::l_no_action;\n\n\tEx_comparator comp(kernel.properties);\n\n\tfill_hash_map(st);\n\tfactor_hash_iterator_t ht=factor_hash.begin();\n\twhile(ht!=factor_hash.end()) {\n\t\thashval_t curr=ht->first;  // hash value of the current set of terms\n\t\tfactor_hash_iterator_t thisbin1=ht, thisbin2;\n\t\twhile(thisbin1!=factor_hash.end() && thisbin1->first==curr) {\n\t\t\tthisbin2=thisbin1;\n\t\t\t++thisbin2;\n\t\t\tEx expsum;\n\t\t\titerator expsumit=expsum.set_head(str_node(\"\\\\sum\"));\n\t\t\t// add the exponent of the first element in this hash bin\n\t\t\tif(*(tr.parent((*thisbin1).second)->name)==\"\\\\pow\") {\n\t\t\t\tsibling_iterator powch=tr.parent((*thisbin1).second).begin();\n\t\t\t\t++powch;\n\t\t\t\titerator newch= expsum.append_child(expsumit, iterator(powch));\n\t\t\t\tnewch->fl.bracket=str_node::b_round;\n\t\t\t\t}\n\t\t\telse {\n\t\t\t\texpsum.append_child(expsumit, str_node(\"1\", str_node::b_round));\n\t\t\t\t}\n\t\t\t// FIXME: If the multiplier of this factor is non-zero, we\n\t\t\t// have (pure number)**(exp). We need to catch this\n\t\t\t// separately.  std::cerr << (*thisbin1).second << std::endl;\n\t\t\t// For now, we have disabled collecting such factors; sympy\n\t\t\t// can do it anyway.\n\t\t\tassert(*((*thisbin1).second->multiplier)==1);\n\t\t\t// find the other, identical factors\n\t\t\twhile(thisbin2!=factor_hash.end() && thisbin2->first==curr) {\n\t\t\t\tif(subtree_exact_equal(&kernel.properties, (*thisbin1).second, (*thisbin2).second)) {\n\t\t\t\t\t// only do something if this factor can be moved to the other one\n\t\t\t\t\titerator objnode1=(*thisbin1).second;\n\t\t\t\t\titerator objnode2=(*thisbin2).second;\n\t\t\t\t\tif(*tr.parent(objnode1)->name==\"\\\\pow\") objnode1=tr.parent(objnode1);\n\t\t\t\t\tif(*tr.parent(objnode2)->name==\"\\\\pow\") objnode2=tr.parent(objnode2);\n\t\t\t\t\tint sign = comp.can_move_adjacent(st, objnode1, objnode2);\n\t\t\t\t\tif(sign!=0) {\n\t\t\t\t\t\t// all clear\n\t\t\t\t\t\tassert(*((*thisbin2).second->multiplier)==1);\n\t\t\t\t\t\tres=result_t::l_applied;\n\t\t\t\t\t\tif(*(tr.parent((*thisbin2).second)->name)==\"\\\\pow\") {\n\t\t\t\t\t\t\tsibling_iterator powch=tr.parent((*thisbin2).second).begin();\n\t\t\t\t\t\t\t++powch;\n\t\t\t\t\t\t\titerator newch=expsum.append_child(expsumit, iterator(powch));\n\t\t\t\t\t\t\tnewch->fl.bracket=str_node::b_round;\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\telse {\n\t\t\t\t\t\t\texpsum.append_child(expsumit, str_node(\"1\", str_node::b_round));\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\tfactor_hash_iterator_t tmp=thisbin2;\n\t\t\t\t\t\t++tmp;\n\t\t\t\t\t\tif(*(tr.parent((*thisbin2).second)->name)==\"\\\\pow\")\n\t\t\t\t\t\t\ttr.erase(tr.parent((*thisbin2).second));\n\t\t\t\t\t\telse\n\t\t\t\t\t\t\ttr.erase((*thisbin2).second);\n\t\t\t\t\t\tfactor_hash.erase(thisbin2);\n\t\t\t\t\t\tthisbin2=tmp;\n\n\t\t\t\t\t\t// Take care of any sign flips.\n\t\t\t\t\t\tmultiply(st->multiplier, sign);\n\t\t\t\t\t\t\n\t\t\t\t\t\tres=result_t::l_applied;\n\t\t\t\t\t\t}\n\t\t\t\t\telse ++thisbin2;\n\t\t\t\t\t}\n\t\t\t\telse ++thisbin2;\n\t\t\t\t}\n\t\t\t// make the modification to the tree\n\t\t\tif(expsum.number_of_children(expsum.begin())>1) {\n\t\t\t\titerator top=expsum.begin();\n\t\t\t\tcleanup_dispatch(kernel,expsum, top);\n\t\t\t\t//\t\t\t\tcleanup_nests_below(expsum, expsum.begin());\n\t\t\t\tif(! (expsum.begin()->is_identity()) ) {\n\t\t\t\t\tcollect_terms ct(kernel, expsum);\n\t\t\t\t\titerator tp=expsum.begin();\n\t\t\t\t\tct.apply(tp);\n\n\t\t\t\t\titerator inserthere=thisbin1->second;\n\t\t\t\t\tif(*(tr.parent(inserthere)->name)==\"\\\\pow\")\n\t\t\t\t\t\tinserthere=tr.parent(inserthere);\n\t\t\t\t\tif(expsum.begin()->is_rational() && (expsum.begin()->is_identity() ||\n\t\t\t\t\t                                     expsum.begin()->is_zero() ) ) {\n\t\t\t\t\t\tif(*(inserthere->name)==\"\\\\pow\") {\n\t\t\t\t\t\t\ttr.flatten(inserthere);\n\t\t\t\t\t\t\tinserthere=tr.erase(inserthere);\n\t\t\t\t\t\t\tsibling_iterator nxt=inserthere;\n\t\t\t\t\t\t\t++nxt;\n\t\t\t\t\t\t\ttr.erase(nxt);\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\tif(expsum.begin()->is_zero()) {\n\t\t\t\t\t\t\trset_t::iterator rem=inserthere->multiplier;\n\t\t\t\t\t\t\tnode_one(inserthere);\n\t\t\t\t\t\t\tinserthere->multiplier=rem;\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\t}\n\t\t\t\t\telse {\n\t\t\t\t\t\tEx repl;\n\t\t\t\t\t\trepl.set_head(str_node(\"\\\\pow\"));\n\t\t\t\t\t\trepl.append_child(repl.begin(), iterator((*thisbin1).second));\n\t\t\t\t\t\trepl.append_child(repl.begin(), expsum.begin());\n\t\t\t\t\t\tif(*(inserthere->name)!=\"\\\\pow\") {\n\t\t\t\t\t\t\tinserthere=(*thisbin1).second;\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\ttr.insert_subtree(inserthere, repl.begin());\n\t\t\t\t\t\ttr.erase(inserthere);\n\t\t\t\t\t\t}\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t//\t\t\telse txtout << \"only one left\" << std::endl;\n\t\t\t++thisbin1;\n\t\t\t}\n\t\tht=thisbin1;\n\t\t}\n\tcleanup_dispatch(kernel, tr, st);\n\treturn res;\n\t}\n\n"
  },
  {
    "path": "core/algorithms/collect_factors.cnb",
    "content": "{\n\t\"cells\" : \n\t[\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\algorithm{collect_factors}{Collect identical factors in a product.}\\n\\nCollect factors in a product that differ only by their exponent. Note\\nthat factors containing sub- or superscripted indices do not get\\ncollected (i.e.~$A_m A^m$ does not get reduced to $(A_m)^2$).\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\algorithm{collect_factors}{Collect identical factors in a product.}\\n\\nCollect factors in a product that differ only by their exponent. Note\\nthat factors containing sub- or superscripted indices do not get\\ncollected (i.e.~$A_m A^m$ does not get reduced to $(A_m)^2$).\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}A A B A B A\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex:=A A B A B A;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}A^{4} B^{2}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"collect_factors(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"Arbitrary powers can be collected this way,\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"Arbitrary powers can be collected this way,\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}X X^{-1} X^{-4}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex:=X X**(-1) X**(-4);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}X^{-4}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"collect_factors(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"The exponent notation can be expanded again \\nusing \\\\algo{expand_power}.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"The exponent notation can be expanded again \\nusing \\\\algo{expand_power}.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}X^{4}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}X X X X\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex:=X**4;\\nexpand_power(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1\n}\n"
  },
  {
    "path": "core/algorithms/collect_factors.hh",
    "content": "\n#pragma once\n\n#include \"Algorithm.hh\"\n\nnamespace cadabra {\n\n\t/// \\ingroup algorithms\n\t///\n\t/// Collect symbolically equal factors in a product.\n\n\tclass collect_factors : public Algorithm {\n\t\tpublic:\n\t\t\tcollect_factors(const Kernel&, Ex&);\n\n\t\t\tvirtual bool     can_apply(iterator);\n\t\t\tvirtual result_t apply(iterator&);\n\t\tprivate:\n\t\t\tvoid fill_hash_map(iterator);\n\n\t\t\ttypedef std::multimap<hashval_t, sibling_iterator> factor_hash_t;\n\t\t\ttypedef factor_hash_t::iterator                    factor_hash_iterator_t;\n\n\t\t\tfactor_hash_t factor_hash;\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/algorithms/collect_terms.cc",
    "content": "#include <algorithm>\n#ifdef HAS_TBB\n#include <execution>\n#endif\n#include \"algorithms/collect_terms.hh\"\n\nusing namespace cadabra;\n\ncollect_terms::collect_terms(const Kernel& k, Ex& tr)\n\t: Algorithm(k, tr)\n\t{\n\t}\n\nbool collect_terms::can_apply(iterator st)\n\t{\n\tassert(tr.is_valid(st));\n\tif(*st->name==\"\\\\sum\") return true;\n\treturn false;\n\t}\n\nvoid collect_terms::fill_hash_map(iterator it)\n\t{\n\tterm_hash.clear();\n#ifdef HAS_TBB\n\tsize_t num = tr.number_of_children(it);\n\tstd::vector<std::pair<hashval_t, sibling_iterator>> hash_pairs(num);\n\tstd::vector<sibling_iterator>                       iterators(num);\n\tsibling_iterator sib=tr.begin(it);\n\tfor(size_t i=0; i<num; ++i) {\n\t\titerators[i]=sib;\n\t\t++sib;\n\t\t}\n\t\n\tstd::transform(std::execution::par_unseq,\n\t\t\t\t\t\titerators.begin(), iterators.end(),\n\t\t\t\t\t\thash_pairs.begin(),\n\t\t\t\t\t\t[this, &iterators, &it](sibling_iterator term_it)\n\t\t\t\t\t\t\t{\n\t\t\t\t\t\t\tauto hv = tr.calc_hash(term_it);\n\t\t\t\t\t\t\treturn std::make_pair(hv, term_it);\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\t);\n\n\tterm_hash = term_hash_t(hash_pairs.begin(), hash_pairs.end());\n#else\n\tsibling_iterator sib=tr.begin(it);\n\tsibling_iterator end=tr.end(it);\n\twhile(sib!=end) {\n\t\tterm_hash.insert(std::pair<hashval_t, sibling_iterator>(tr.calc_hash(sib), sib));\n\t\t++sib;\n\t\t}\n#endif\n\t}\n\nvoid collect_terms::remove_zeroed_terms(sibling_iterator from, sibling_iterator to)\n\t{\n\t// Remove all terms which have zero multiplier.\n\tsibling_iterator one=from;\n\twhile(one!=to) {\n\t\tif(*one->multiplier==0)\n\t\t\tone=tr.erase(one);\n\t\telse if(*one->name==\"\\\\sum\" && *one->multiplier!=1) {\n\t\t\tsibling_iterator oneit=tr.begin(one);\n\t\t\twhile(oneit!=tr.end(one)) {\n\t\t\t\tmultiply(oneit->multiplier, *one->multiplier);\n\t\t\t\t++oneit;\n\t\t\t\t}\n\t\t\tone->multiplier=rat_set.insert(1).first;\n\t\t\t++one;\n\t\t\t}\n\t\telse ++one;\n\t\t}\n\t}\n\nAlgorithm::result_t collect_terms::apply(iterator& st)\n\t{\n\tassert(tr.is_valid(st));\n\tassert(*st->name==\"\\\\sum\");\n\tfill_hash_map(st);\n\tresult_t res=collect_from_hash_map();\n\tremove_zeroed_terms(tr.begin(st), tr.end(st));\n\n\t// If there is only one term left, flatten the tree.\n\tif(tr.number_of_children(st)==1) {\n\t\t// tr.print_recursive_treeform(std::cerr, st);\n\t\ttr.begin(st)->fl.bracket=st->fl.bracket;\n\t\ttr.begin(st)->fl.parent_rel=st->fl.parent_rel;\n\t\ttr.flatten(st);\n\t\tst=tr.erase(st);\n\t\t// tr.print_recursive_treeform(std::cerr, st);\n\t\t// We may have to propagate the multiplier up the tree to make it consistent.\n\t\tpushup_multiplier(st);\n\t\t}\n\telse if(tr.number_of_children(st)==0) {\n\t\t//\t\tzero(st->multiplier);\n\t\tnode_zero(st);\n\t\t}\n\treturn res;\n\t}\n\nAlgorithm::result_t collect_terms::collect_from_hash_map()\n\t{\n\tresult_t res=result_t::l_no_action;\n\tterm_hash_iterator_t ht=term_hash.begin();\n\twhile(ht!=term_hash.end()) {\n\t\thashval_t curr=ht->first;  // hash value of the current set of terms\n\t\tterm_hash_iterator_t thisbin1=ht, thisbin2;\n\t\twhile(thisbin1!=term_hash.end() && thisbin1->first==curr) {\n\t\t\tthisbin2=thisbin1;\n\t\t\t++thisbin2;\n\t\t\twhile(thisbin2!=term_hash.end() && thisbin2->first==curr) {\n\t\t\t\tif(subtree_exact_equal(&kernel.properties, (*thisbin1).second, (*thisbin2).second, -2, true, 0, true)) {\n\t\t\t\t\tres=result_t::l_applied;\n\t\t\t\t\tadd((*thisbin1).second->multiplier, *((*thisbin2).second->multiplier));\n\t\t\t\t\tzero((*thisbin2).second->multiplier);\n\t\t\t\t\tterm_hash_iterator_t tmp=thisbin2;\n\t\t\t\t\t++tmp;\n\t\t\t\t\tterm_hash.erase(thisbin2);\n\t\t\t\t\tthisbin2=tmp;\n\t\t\t\t\t}\n\t\t\t\telse ++thisbin2;\n\t\t\t\t}\n\t\t\t++thisbin1;\n\t\t\t}\n\t\tht=thisbin1;\n\t\t}\n\n\treturn res;\n\t}\n"
  },
  {
    "path": "core/algorithms/collect_terms.cnb",
    "content": "\n{\n\t\"cells\" : \n\t[\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\algorithm{collect_terms}{Collect identical terms in a sum.}\\n\\nCollect terms in a sum that differ only by their numerical\\npre-factor. This is part of the default \\\\verb|post_process| function, so \\ndoes not need to be called by hand.\\n\\nNote that this command only collects terms which are identical, it\\ndoes not collect terms which are different but mathematically\\nequivalent. See \\\\algo{sort_sum} for an example.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\algorithm{collect_terms}{Collect identical terms in a sum.}\\n\\nCollect terms in a sum that differ only by their numerical\\npre-factor. This is part of the default \\\\verb|post_process| function, so \\ndoes not need to be called by hand.\\n\\nNote that this command only collects terms which are identical, it\\ndoes not collect terms which are different but mathematically\\nequivalent. See \\\\algo{sort_sum} for an example.\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1.0\n}\n\n"
  },
  {
    "path": "core/algorithms/collect_terms.hh",
    "content": "\n#pragma once\n\n#include \"Algorithm.hh\"\n\nnamespace cadabra {\n\n\t/// \\ingroup algorithms\n\t///\n\t/// Collect symbolically equal terms in a sum.\n\n\tclass collect_terms : public Algorithm {\n\t\tpublic:\n\t\t\tcollect_terms(const Kernel&, Ex&);\n\n\t\t\tvirtual bool     can_apply(iterator);\n\t\t\tvirtual result_t apply(iterator&);\n\n\t\t\tvoid  fill_hash_map(iterator);\n\t\tprivate:\n\t\t\tresult_t collect_from_hash_map();\n\t\t\tvoid remove_zeroed_terms(sibling_iterator, sibling_iterator);\n\n\t\t\ttypedef std::multimap<hashval_t, sibling_iterator> term_hash_t;\n\t\t\ttypedef term_hash_t::iterator                      term_hash_iterator_t;\n\n\t\t\tterm_hash_t term_hash;\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/algorithms/combine.cc",
    "content": "\n#include \"Cleanup.hh\"\n#include \"Exceptions.hh\"\n#include \"IndexClassifier.hh\"\n#include \"algorithms/combine.hh\"\n#include \"properties/Matrix.hh\"\n\nusing namespace cadabra;\n\ncombine::combine(const Kernel& k, Ex& e, Ex& t)\n\t: Algorithm(k, e), trace_op(t)\n\t{\n\t}\n\nbool combine::can_apply(iterator it)\n\t{\n\tif(*it->name==\"\\\\prod\") return true;\n\treturn false;\n\t}\n\nAlgorithm::result_t combine::apply(iterator& it)\n\t{\n\tsibling_iterator sib=tr.begin(it);\n\tIndexClassifier ic(kernel);\n\tIndexClassifier::index_map_t ind_free, ind_dummy;\n\tstd::vector<Ex::iterator> dummies;\n\twhile(sib!=tr.end(it)) {  // iterate over all factors in the product\n\t\tsibling_iterator ch=tr.begin(sib);\n\t\twhile(ch!=tr.end(sib)) { // iterate over all indices of this factor\n\t\t\t//\t\t\tauto parent=tr.parent(sib);\n\t\t\tif(ch->fl.parent_rel==str_node::p_sub || ch->fl.parent_rel==str_node::p_super) {\n\t\t\t\tic.classify_add_index(ch, ind_free, ind_dummy);\n\t\t\t\t}\n\t\t\t++ch;\n\t\t\t}\n\t\t++sib;\n\t\t}\n\tif(ind_dummy.size()==0) return result_t::l_no_action;\n\n\twhile(ind_dummy.begin()!=ind_dummy.end()) {\n\t\tbool found=false;\n\t\tIndexClassifier::index_map_t::iterator start=ind_dummy.begin(), backup;\n\t\twhile(!found && start!=ind_dummy.end()) {\n\t\t\titerator parent=tr.parent(start->second);\n\t\t\tsibling_iterator ch=tr.begin(parent), last_part;\n\t\t\twhile(ch!=tr.end(parent)) {\n\t\t\t\tauto fnd=ind_dummy.find(Ex(ch));\n\t\t\t\tif(fnd!=ind_dummy.end()) last_part=ch;\n\t\t\t\t++ch;\n\t\t\t\t}\n\t\t\tif(last_part==start->second) {\n\t\t\t\t++last_part;\n\t\t\t\tif(last_part==tr.end(parent)) {\n\t\t\t\t\t// Dummy index with nothing to the right is preferred\n\t\t\t\t\tfound=true;\n\t\t\t\t\t}\n\t\t\t\telse backup=start;\n\t\t\t\t}\n\t\t\tif(!found) ++start;\n\t\t\t}\n\t\t// As a backup, we use a dummy index with only non-dummies to the right\n\t\tif(!found) start=backup;\n\t\tbool paired=true;\n\t\twhile(paired && start!=ind_dummy.end()) {\n\t\t\titerator parent=tr.parent(start->second);\n\t\t\tsibling_iterator ch=tr.begin(parent), last_part;\n\t\t\twhile(ch!=tr.end(parent) && ind_dummy.size()>0) {\n\t\t\t\tauto fnd2=ind_dummy.equal_range(Ex(ch));\n\t\t\t\tauto fnd1=fnd2.first;\n\t\t\t\tif(fnd1->second!=ch) ++fnd1;\n\t\t\t\tif(fnd1->second==ch) {\n\t\t\t\t\tdummies.insert(dummies.end(), ch);\n\t\t\t\t\tind_dummy.erase(fnd1);\n\t\t\t\t\tlast_part=ch;\n\t\t\t\t\t}\n\t\t\t\t++ch;\n\t\t\t\t}\n\t\t\tauto fnd=ind_dummy.find(Ex(last_part));\n\t\t\tif(fnd==ind_dummy.end()) {\n\t\t\t\tlast_part->flip_parent_rel();\n\t\t\t\tfnd=ind_dummy.find(Ex(last_part));\n\t\t\t\tlast_part->flip_parent_rel();\n\t\t\t\t}\n\t\t\tif(fnd==ind_dummy.end()) {\n\t\t\t\t// Contraction ends because we are on a vector\n\t\t\t\t// It could also be a trace if we removed the paired index more than one iteration ago\n\t\t\t\tpaired=false;\n\t\t\t\t}\n\t\t\telse {\n\t\t\t\tstart=fnd;\n\t\t\t\tIndexClassifier::index_map_t::iterator check=ind_dummy.end();\n\t\t\t\titerator parent=tr.parent(start->second);\n\t\t\t\tsibling_iterator ch=tr.begin(parent), first_part;\n\t\t\t\twhile(check==ind_dummy.end()) {\n\t\t\t\t\tfirst_part=ch;\n\t\t\t\t\tcheck=ind_dummy.find(Ex(ch));\n\t\t\t\t\t++ch;\n\t\t\t\t\t}\n\t\t\t\tif(first_part!=start->second) {\n\t\t\t\t\tthrow NotYetImplemented(\"Evaluation requires transposing a matrix.\");\n\t\t\t\t\treturn result_t::l_no_action;\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t}\n\t\t}\n\n\tstd::string trace_start=\"\";\n\tstd::vector<Ex::iterator>::iterator dums1=dummies.begin(), dums2;\n\tdums2=dums1;\n\t++dums2;\n\twhile(dums1!=dummies.end() && dums2!=dummies.end()) {\n\t\t//\t\ttxtout << \"analysing \" << std::endl;\n\t\t//\t\ttxtout << *(dums1->second->name) << std::endl;\n\n\t\tbool isbrack1=false, isbrack2=false;\n\t\tbool ismatorvec1=false, ismatorvec2=false;\n\t\t// These are both to recognize traces\n\t\tbool diffparents=tr.parent(*dums1)!=tr.parent(*dums2);\n\t\tbool consecutive=*(*dums1)->name==*(*dums2)->name;\n\t\tconst Matrix *mat1=kernel.properties.get<Matrix>(tr.parent(*dums1));\n\t\tif(mat1)\n\t\t\tismatorvec1=true;\n\t\telse if(*(tr.parent(*dums1)->name)==\"\\\\indexbracket\") {\n\t\t\tismatorvec1=true;\n\t\t\tisbrack1=true;\n\t\t\t}\n\t\telse if(tr.number_of_children(tr.parent(*dums1))==1)\n\t\t\tismatorvec1=true;\n\t\tconst Matrix *mat2=kernel.properties.get<Matrix>(tr.parent(*dums2));\n\t\tif(mat2)\n\t\t\tismatorvec2=true;\n\t\telse if(*(tr.parent(*dums2)->name)==\"\\\\indexbracket\") {\n\t\t\tismatorvec2=true;\n\t\t\tisbrack2=true;\n\t\t\t}\n\t\telse if(tr.number_of_children(tr.parent(*dums2))==1)\n\t\t\tismatorvec2=true;\n\n\t\tif(ismatorvec1 && ismatorvec2 && diffparents && consecutive) {\n\t\t\t//\t\t\ttxtout << \"gluing \" << *(dums2->second->name) << std::endl;\n\t\t\t// create new indexbracket with product node\n\t\t\titerator outerbrack=tr.insert(tr.parent(*dums1), str_node(\"\\\\indexbracket\"));\n\t\t\titerator brackprod=tr.append_child(outerbrack, str_node(\"\\\\prod\"));\n\t\t\titerator parn1=tr.parent(*dums1);\n\t\t\titerator parn2=tr.parent(*dums2);\n\n\t\t\t// count how many sign changes stand between the two objects\n\t\t\tint sign=1;\n\t\t\tunsigned int hits=0;\n\t\t\tEx_comparator compare(kernel.properties);\n\t\t\tsib=tr.begin(it);\n\t\t\twhile(hits<2) {\n\t\t\t\tif(hits==1 && sib!=parn2) {\n\t\t\t\t\t// pass arguments manually as can_swap() does not check them\n\t\t\t\t\tbool isbrack=*(sib->name)==\"\\\\indexbracket\";\n\t\t\t\t\tif(isbrack && isbrack2) {\n\t\t\t\t\t\tauto es=compare.equal_subtree(tr.begin(parn2), tr.begin(sib));\n\t\t\t\t\t\tsign*=compare.can_swap_components(tr.begin(parn2), tr.begin(sib), es);\n\t\t\t\t\t\t}\n\t\t\t\t\telse if(isbrack && !isbrack2) {\n\t\t\t\t\t\tauto es=compare.equal_subtree(parn2, tr.begin(sib));\n\t\t\t\t\t\tsign*=compare.can_swap_components(parn2, tr.begin(sib), es);\n\t\t\t\t\t\t}\n\t\t\t\t\telse if(!isbrack && isbrack2) {\n\t\t\t\t\t\tauto es=compare.equal_subtree(tr.begin(parn2), sib);\n\t\t\t\t\t\tsign*=compare.can_swap_components(tr.begin(parn2), sib, es);\n\t\t\t\t\t\t}\n\t\t\t\t\telse {\n\t\t\t\t\t\tauto es=compare.equal_subtree(parn2, sib);\n\t\t\t\t\t\tsign*=compare.can_swap_components(parn2, sib, es);\n\t\t\t\t\t\t}\n\t\t\t\t\t}\n\t\t\t\tif(sib==parn1 || sib==parn2) ++hits;\n\t\t\t\t++sib;\n\t\t\t\t}\n\t\t\tif(sign==-1) flip_sign(brackprod->multiplier);\n\n\t\t\t// remove the dummy index from these two objects, and move\n\t\t\t// other (dummy or not) indices to the outer indexbracket.\n\t\t\tsibling_iterator ind1=tr.begin(tr.parent(*dums1));\n\t\t\tsibling_iterator stop1=tr.end(tr.parent(*dums1));\n\t\t\tif(isbrack1)\n\t\t\t\t++ind1;\n\t\t\twhile(ind1!=stop1) {\n\t\t\t\tif(ind1!=*dums1) {\n\t\t\t\t\tsibling_iterator nxt=ind1;\n\t\t\t\t\t++nxt;\n\t\t\t\t\ttr.reparent(outerbrack, ind1, nxt);\n\t\t\t\t\t}\n\t\t\t\t++ind1;\n\t\t\t\t//\t\t\t\tind1=tr.erase(ind1);\n\t\t\t\t}\n\t\t\ttr.erase(*dums1);\n\t\t\tsibling_iterator ind2=tr.begin(tr.parent(*dums2));\n\t\t\tsibling_iterator stop2=tr.end(tr.parent(*dums2));\n\t\t\tif(isbrack2)\n\t\t\t\t++ind2;\n\t\t\twhile(ind2!=stop2) {\n\t\t\t\tif(ind2!=*dums2) {\n\t\t\t\t\tsibling_iterator nxt=ind2;\n\t\t\t\t\t++nxt;\n\t\t\t\t\ttr.reparent(outerbrack, ind2, nxt);\n\t\t\t\t\t}\n\t\t\t\t++ind2;\n\t\t\t\t//\t\t\t\tind2=tr.erase(ind2);\n\t\t\t\t}\n\t\t\ttr.erase(*dums2);\n\n\t\t\t// put both objects inside the indexbracket.\n\t\t\tif(isbrack1) {\n\t\t\t\tsibling_iterator nxt=tr.begin(parn1);\n\t\t\t\t++nxt;\n\t\t\t\t//\t\t\t\ttr.begin(parn1)->fl.bracket=str_node::b_round;\n\t\t\t\ttr.reparent(brackprod, tr.begin(parn1), nxt);\n\t\t\t\tmultiply(brackprod->multiplier, *parn1->multiplier);\n\t\t\t\ttr.erase(parn1);\n\t\t\t\t}\n\t\t\telse {\n\t\t\t\tsibling_iterator nxt=parn1;\n\t\t\t\t++nxt;\n\t\t\t\t//\t\t\t\tparn1->fl.bracket=str_node::b_round;\n\t\t\t\ttr.reparent(brackprod,parn1,nxt);\n\t\t\t\t}\n\t\t\tif(isbrack2) {\n\t\t\t\tsibling_iterator nxt=tr.begin(parn2);\n\t\t\t\t++nxt;\n\t\t\t\t//\t\t\t\ttr.begin(parn2)->fl.bracket=str_node::b_round;\n\t\t\t\ttr.reparent(brackprod, tr.begin(parn2), nxt);\n\t\t\t\tmultiply(brackprod->multiplier, *parn2->multiplier);\n\t\t\t\ttr.erase(parn2);\n\t\t\t\t}\n\t\t\telse {\n\t\t\t\tsibling_iterator nxt=parn2;\n\t\t\t\t++nxt;\n\t\t\t\t//\t\t\t\tparn2->fl.bracket=str_node::b_round;\n\t\t\t\ttr.reparent(brackprod,parn2,nxt);\n\t\t\t\t}\n\t\t\t}\n\t\tif(consecutive) {\n\t\t\t++dums1;\n\t\t\t++dums2;\n\t\t\tif(dums2!=dummies.end() && trace_op.size()>0) {\n\t\t\t\tif(*(*dums2)->name==trace_start) {\n\t\t\t\t\titerator parn=tr.parent(*dums2);\n\t\t\t\t\titerator trace=tr.insert(parn, str_node(trace_op.begin()->name));\n\t\t\t\t\tsibling_iterator nxt=tr.begin(parn);\n\t\t\t\t\t++nxt;\n\t\t\t\t\t++dums1;\n\t\t\t\t\t++dums2;\n\t\t\t\t\ttr.reparent(trace, tr.begin(parn), nxt);\n\t\t\t\t\tmultiply(trace->multiplier, *parn->multiplier);\n\t\t\t\t\ttr.erase(parn);\n\t\t\t\t\ttrace_start=\"\";\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t}\n\t\telse trace_start=*(*dums1)->name;\n\t\t++dums1;\n\t\t++dums2;\n\t\t}\n\n\t//std::cerr << it << std::endl;\n\n\t//\tprodflatten pf(tr, tr.end());\n\t//\tpf.apply_recursive(it, false);\n\n\tcleanup_dispatch(kernel, tr, it);\n\n\treturn result_t::l_applied;\n\t}\n"
  },
  {
    "path": "core/algorithms/combine.cnb",
    "content": "{\n\t\"cells\" : \n\t[\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\algorithm{combine}{Combine two consecutive indexbracket objects}\\n\\nCombine two consecutive objects with indexbrackets and consecutive\\ncontracted indices into one object with an indexbracket. An example\\nwith two contracted matrices:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\algorithm{combine}{Combine two consecutive indexbracket objects}\\n\\nCombine two consecutive objects with indexbrackets and consecutive\\ncontracted indices into one object with an indexbracket. An example\\nwith two contracted matrices:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\left(\\\\Gamma_{r}\\\\right)\\\\,_{\\\\alpha \\\\beta} \\\\left(\\\\Gamma_{s t u}\\\\right)\\\\,_{\\\\beta \\\\gamma}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\left(\\\\Gamma_{r} \\\\Gamma_{s t u}\\\\right)\\\\,_{\\\\alpha \\\\gamma}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex:=(\\\\Gamma_r)_{\\\\alpha\\\\beta} (\\\\Gamma_{s t u})_{\\\\beta\\\\gamma};\\ncombine(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"An example with a matrix and a vector:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"An example with a matrix and a vector:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\left(\\\\Gamma_{r}\\\\right)\\\\,_{\\\\alpha \\\\beta} v_{\\\\beta}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\left(\\\\Gamma_{r} v\\\\right)\\\\,_{\\\\alpha}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex:=(\\\\Gamma_r)_{\\\\alpha\\\\beta} v_{\\\\beta};\\ncombine(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"The inverse of \\\\algo{combine} is \\\\algo{expand}.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"The inverse of \\\\algo{combine} is \\\\algo{expand}.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1\n}\n"
  },
  {
    "path": "core/algorithms/combine.hh",
    "content": "\n#pragma once\n\n#include \"Algorithm.hh\"\n\nnamespace cadabra {\n\n\tclass combine : public Algorithm {\n\t\tpublic:\n\t\t\tcombine(const Kernel&, Ex&, Ex&);\n\n\t\t\tvirtual bool     can_apply(iterator) override;\n\t\t\tvirtual result_t apply(iterator&) override;\n\n\t\tprivate:\n\t\t\ttypedef std::map<nset_t::iterator, iterator> indexlocmap_t;\n\n\t\t\tEx trace_op;\n\t\t\tindexlocmap_t iloc;\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/algorithms/complete.cc",
    "content": "\n#include \"algorithms/complete.hh\"\n#include \"Functional.hh\"\n#include \"properties/Metric.hh\"\n#include \"properties/InverseMetric.hh\"\n#include \"properties/Determinant.hh\"\n#include \"properties/Trace.hh\"\n#include \"SympyCdb.hh\"\n\nusing namespace cadabra;\n\ncomplete::complete(const Kernel& k, Ex& e, Ex& g)\n\t: Algorithm(k, e), goal(g)\n\t{\n\t}\n\nbool complete::can_apply(iterator )\n\t{\n\treturn true;\n\t}\n\nAlgorithm::result_t complete::apply(iterator& )\n\t{\n\tresult_t res=result_t::l_no_action;\n\n\titerator bg=goal.begin();\n\n\tconst InverseMetric *invmetric = kernel.properties.get<InverseMetric>(bg);\n\tif(invmetric) {\n\t\tEx metric(bg);\n\t\tEx::iterator ind1=metric.child(metric.begin(), 0);\n\t\tEx::iterator ind2=metric.child(metric.begin(), 1);\n\t\tind1->flip_parent_rel();\n\t\tind2->flip_parent_rel();\n\n\t\tsympy::invert_matrix(kernel, metric, tr, Ex(bg));\n\t\tres = result_t::l_applied;\n\t\t}\n\tconst Determinant *det = kernel.properties.get<Determinant>(bg);\n\tif(det) {\n\t\tEx metric(det->obj);\n\t\tsympy::determinant(kernel, metric, tr, Ex(bg));\n\t\tres = result_t::l_applied;\n\t\t}\n\tconst Trace *trace = kernel.properties.get<Trace>(bg);\n\tif(trace) {\n\t\tif(trace->obj.size()>0) {\n\t\t\tEx metric(trace->obj);\n\t\t\tsympy::trace(kernel, metric, tr, Ex(bg));\n\t\t\tres = result_t::l_applied;\n\t\t\t}\n\t\t}\n\n\treturn res;\n\t}\n"
  },
  {
    "path": "core/algorithms/complete.cnb",
    "content": "\n{\n\t\"cells\" : \n\t[\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\algorithm{complete}{Complete a set of substitution rules to cover related objects.}\\n\\nComplete a set of substitution rules with additional rules based on the properties of\\nthe objects appearing in the rules. \\n\\nThis can for instance be used to generate rules for the inverse components of the metric\\ngiven the rules for the metric components themselves, as in the example below.\\n\\nNote that the argument itself gets modified (amended) with the additional rules.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\algorithm{complete}{Complete a set of substitution rules to cover related objects.}\\n\\nComplete a set of substitution rules with additional rules based on the properties of\\nthe objects appearing in the rules. \\n\\nThis can for instance be used to generate rules for the inverse components of the metric\\ngiven the rules for the metric components themselves, as in the example below.\\n\\nNote that the argument itself gets modified (amended) with the additional rules.\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"{r,t}::Coordinate.\\n{m,n,p,q}::Indices(values={r,t}).\\ng_{m n}::Metric.\\ng^{m n}::InverseMetric.\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}(g_{t t} = r, g_{t r} = \\\\frac{r^{2}}{a}, g_{r t} = \\\\frac{r^{2}}{a}, g_{r r} = 1)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"rl:={ g_{t t} = r, g_{t r} = r**2/a, g_{r t} = r**2/a, g_{r r} = 1 };\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}(g_{t t} = r, g_{t r} = \\\\frac{r^{2}}{a}, g_{r t} = \\\\frac{r^{2}}{a}, g_{r r} = 1, g^{r r} = 1+\\\\frac{r^{4}}{a^{2} \\\\left(r - \\\\frac{r^{4}}{a^{2}}\\\\right)}, g^{r t} =  - \\\\frac{r^{2}}{a \\\\left(r - \\\\frac{r^{4}}{a^{2}}\\\\right)}, g^{t r} =  - \\\\frac{r^{2}}{a \\\\left(r - \\\\frac{r^{4}}{a^{2}}\\\\right)}, g^{t t} = \\\\frac{1}{r - \\\\frac{r^{4}}{a^{2}}})\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"complete(rl, $g^{m n}$);\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"Note that this uses SymPy behind the scenes to do the scalar algebra and matrix inversion.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"Note that this uses SymPy behind the scenes to do the scalar algebra and matrix inversion.\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1.0\n}\n\n"
  },
  {
    "path": "core/algorithms/complete.hh",
    "content": "\n#pragma once\n\n#include \"Algorithm.hh\"\n\nnamespace cadabra {\n\n\t/// \\ingroup algorithms\n\t///\n\t/// Complete a set of coordinate rules so that they also cover related tensors.\n\t/// At present this only inverts metric rules, but could do more related rules,\n\t/// or expanded to cover symmetry.\n\n\tclass complete : public Algorithm {\n\t\tpublic:\n\t\t\tcomplete(const Kernel&, Ex&, Ex&);\n\n\t\t\tvirtual bool     can_apply(iterator) override;\n\t\t\tvirtual result_t apply(iterator&) override;\n\n\t\tprivate:\n\t\t\tEx goal;\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/algorithms/component.hh",
    "content": "\n#pragma once\n\n#include \"Algorithm.hh\"\n\nnamespace cadabra {\n\n\tclass component : public Algorithm {\n\tpublic:\n\t\tcomponent(const Kernel&, Ex& ex, Ex& rules);\n\n\t\tvirtual bool     can_apply(iterator);\n\t\tvirtual result_t apply(iterator&);\n\t};\n\n}\n"
  },
  {
    "path": "core/algorithms/decompose.cc",
    "content": "\n#include \"algorithms/decompose.hh\"\n#include \"algorithms/collect_terms.hh\"\n#include \"algorithms/rename_dummies.hh\"\n#include \"algorithms/young_project_product.hh\"\n#include \"properties/TableauBase.hh\"\n#include \"Linear.hh\"\n\nusing namespace cadabra;\n\ndecompose::decompose(const Kernel& k, Ex& tr, Ex& b)\n\t: Algorithm(k, tr), basis(b)\n\t{\n\t}\n\nbool decompose::can_apply(iterator it)\n\t{\n\tif(*it->name!=\"\\\\prod\") return false;\n\treturn true;\n\t}\n\nvoid decompose::add_element_to_basis(Ex& projterm, Ex::iterator projtermit)\n\t{\n\t// Add a new column for the new term in the basis\n\tfor(unsigned int ii=0; ii<coefficient_matrix.size(); ++ii)\n\t\tcoefficient_matrix[ii].push_back(0);\n\n\tif(*projtermit->name==\"\\\\sum\") {\n\t\tsibling_iterator moreit=projterm.begin(projtermit);\n\t\twhile(moreit!=projterm.end(projtermit)) {\n\t\t\tmultiplier_t remember_mult=*moreit->multiplier;\n\t\t\tone(moreit->multiplier);\n\t\t\tbool thistermfound=false;\n\t\t\tfor(unsigned int ypi=0; ypi<terms_from_yp.size(); ++ypi) {\n\t\t\t\tif(projterm.equal_subtree(terms_from_yp[ypi].begin(), (iterator)moreit)) {\n\t\t\t\t\tcoefficient_matrix[ypi].back()=remember_mult;\n\t\t\t\t\tthistermfound=true;\n\t\t\t\t\tbreak;\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\tif(!thistermfound) { // new monomial, so add a new row to the coefficient matrix\n\t\t\t\tEx tmp(moreit);\n\t\t\t\t//\t\t\t\ttmp.print_recursive_treeform(txtout, tmp.begin());\n\t\t\t\tterms_from_yp.push_back(tmp);\n\t\t\t\tstd::vector<multiplier_t> crow(coefficient_matrix.size()>0?\n\t\t\t\t                               coefficient_matrix[0].size():1,0);\n\t\t\t\tcrow.back()=remember_mult;\n\t\t\t\tcoefficient_matrix.push_back(crow);\n\t\t\t\t//\t\t\t\ttxtout << \"added new monomial\" << std::endl;\n\t\t\t\t}\n\t\t\t++moreit;\n\t\t\t}\n\t\t}\n\telse {\n\t\tmultiplier_t remember_mult=*projtermit->multiplier;\n\t\tone(projtermit->multiplier);\n\t\tbool thistermfound=false;\n\t\tfor(unsigned int ypi=0; ypi<terms_from_yp.size(); ++ypi) {\n\t\t\tif(projterm.equal_subtree(terms_from_yp[ypi].begin(), projtermit)) {\n\t\t\t\tcoefficient_matrix[ypi].back()=remember_mult;\n\t\t\t\tthistermfound=true;\n\t\t\t\tbreak;\n\t\t\t\t}\n\t\t\t}\n\t\tif(!thistermfound) { // new monomial, so add a new row to the coefficient matrix\n\t\t\tEx tmp(projtermit);\n\t\t\tterms_from_yp.push_back(tmp);\n\t\t\tstd::vector<multiplier_t> crow(coefficient_matrix.size()>0?\n\t\t\t                               coefficient_matrix[0].size():1,0);\n\t\t\tcrow.back()=remember_mult;\n\t\t\tcoefficient_matrix.push_back(crow);\n\t\t\t}\n\t\t}\n\t}\n\nAlgorithm::result_t decompose::apply(iterator& it)\n\t{\n\tbool ypproject=true;\n\n#ifdef DEBUG\n\tstd::cerr << \"Projecting on basis \" << basis.begin() << std::endl;\n#endif\n\n\titerator basisit=basis.begin();\n\tif(! (*basisit->name==\"\\\\comma\")) {\n\t\tsibling_iterator fr=basis.begin();\n\t\tsibling_iterator nd=fr;\n\t\t++nd;\n\t\t// basis should be a list; write it as such even if there's only one element.\n\t\tbasisit->fl.bracket=str_node::b_none;\n\t\tbasisit=tr.wrap(basisit, str_node(\"\\\\comma\"));\n\t\t}\n\n\tEx projbasis;\n\tprojbasis.set_head(str_node(\"\\\\expression\"));\n\tterms_from_yp.clear();\n\tcoefficient_matrix.clear();\n\n\t// Some overlap with code in all_contractions.\n\tbool nontrivial_symmetries_present=false;\n\tsibling_iterator factorit=tr.begin(it);\n\twhile(factorit!=tr.end(it)) { // Do this always, even if ypproject==false, since we need it for rhs.\n\t\tif(tr.number_of_children(factorit)>1) {\n\t\t\tconst TableauBase *tb = kernel.properties.get<TableauBase>(factorit);\n\t\t\tif(tb)\n\t\t\t\tif(!tb->is_simple_symmetry(kernel.properties, tr, it)) {\n\t\t\t\t\tnontrivial_symmetries_present=true;\n\t\t\t\t\tbreak;\n\t\t\t\t\t}\n\t\t\t}\n\t\t++factorit;\n\t\t}\n\n\t// Setup the coefficient matrix.\n\tif(nontrivial_symmetries_present && ypproject) {\n\t\t//debugout << \"Going to project the basis.\" << std::endl;\n\t\t// Need to make a Young-projected basis.\n\t\tsibling_iterator sib=tr.begin(basisit);\n\t\twhile(sib!=tr.end(basisit)) {\n\t\t\t// debugout << \"Next term in the basis.\" << std::endl;\n\t\t\tEx projterm;\n\t\t\tprojterm.set_head(str_node(\"\\\\expression\"));\n\t\t\tprojterm.append_child(projterm.begin(), (iterator)(sib));\n\n#ifdef OLDVERSION\n\t\t\tyoung_project_tensor ypt(projterm, projterm.end());\n\t\t\typt.modulo_monoterm=true;\n\t\t\titerator projtermit=projterm.begin(projterm.begin());\n\t\t\typt.apply_generic(projtermit, true, false, 0);\n\n\t\t\tdistribute dbt(kernel, projterm);\n\t\t\tcanonicalise can(kernel, projterm);\n\t\t\t//\t\t\tcan.method=canonicalise::xperm;\n\t\t\trename_dummies ren(kernel, projterm);\n\t\t\tcollect_terms ct(kernel, projterm);\n\n\t\t\tdbt.apply_generic(projtermit, false);// FIXME: URGENT: should check consistency\n\t\t\tren.apply_recursive(projtermit, false);  // by far the slowest step\n\t\t\tif(*projtermit->name==\"\\\\sum\")\n\t\t\t\tct.apply(projtermit);\n\t\t\tcan.apply_recursive(projtermit, false);\n\t\t\tren.apply_recursive(projtermit, false);\n\t\t\tif(*projtermit->name==\"\\\\sum\")\n\t\t\t\tct.apply(projtermit);\n#else\n\t\t\titerator projtermit=projterm.begin(projterm.begin());\n\t\t\tyoung_project_product ypp(kernel, projterm);\n\t\t\t//\t\t\tsumflatten sf(kernel, projterm);\n\t\t\tcollect_terms ct(kernel, projterm);\n\t\t\trename_dummies ren(kernel, projterm, \"\", \"\");\n\n\t\t\typp.apply_generic(projtermit, true, false, 0);\n\t\t\t//\t\t\tsf.apply_recursive(projtermit, false);\n\t\t\tren.apply_generic(projtermit, true, false, 0);  // by far the slowest step\n\t\t\tif(*projtermit->name==\"\\\\sum\")\n\t\t\t\tct.apply(projtermit);\n\t\t\tsibling_iterator sib2=tr.begin(projtermit);\n\t\t\twhile(sib2!=tr.end(projtermit)) {\n\t\t\t\tsib2->fl.bracket=str_node::b_none;\n\t\t\t\t++sib2;\n\t\t\t\t}\n#endif\n\t\t\t// After young projection, we may get identically zero.\n\t\t\tif(projtermit->is_zero()) {\n\t\t\t\t//\t\t\t\ttxtout << \"An element of the basis is identically zero after Young projection.\" << std::endl;\n\t\t\t\treturn result_t::l_error;\n\t\t\t\t}\n\t\t\tadd_element_to_basis(projterm, projtermit);\n\t\t\t++sib;\n\t\t\t}\n\t\t// debugout << \"Young-projected basis constructed.\" << std::endl;\n\t\t}\n\telse {\n\t\t// Copy the basis straight into the terms_from_yp.\n\t\tassert(*basisit->name==\"\\\\comma\");\n\t\tsibling_iterator sib=tr.begin(basisit);\n\t\twhile(sib!=tr.end(basisit)) {\n\t\t\tEx projterm(sib);\n\t\t\titerator projtermit=projterm.begin();\n\t\t\tsibling_iterator sib2=tr.begin(projtermit);\n\t\t\twhile(sib2!=tr.end(projtermit)) {\n\t\t\t\tsib2->fl.bracket=str_node::b_none;\n\t\t\t\t++sib2;\n\t\t\t\t}\n\t\t\tadd_element_to_basis(projterm, projtermit);\n\t\t\t++sib;\n\t\t\t}\n\t\t// debugout << \"Kept old young-projected basis.\" << std::endl;\n\t\t}\n\n\t// Young project the rhs.\n\tEx rhstree;\n\trhstree.set_head(str_node(\"\\\\expression\"));\n\trhstree.append_child(rhstree.begin(), it);\n\titerator rhsit=rhstree.begin(rhstree.begin());\n\tif(nontrivial_symmetries_present) {\n#ifdef OLDVERSION\n\t\tyoung_project_tensor ypt(rhstree, rhstree.end());\n\t\typt.modulo_monoterm=true;\n\t\typt.apply_generic(rhsit, true, false, 0);\n\t\tif(*rhsit->name==\"\\\\prod\") {\n\t\t\tdistribute dbt(rhstree, rhstree.end());\n\t\t\tcanonicalise can(rhstree, rhstree.end());\n\t\t\trename_dummies ren(rhstree, rhstree.end());\n\t\t\tcollect_terms ct(rhstree, rhstree.end());\n\n\t\t\tdbt.apply(rhsit);\n\t\t\tren.apply_generic(rhsit, true, false, 0);\n\t\t\tif(*rhsit->name==\"\\\\sum\")\n\t\t\t\tct.apply(rhsit);\n\t\t\tcan.apply_generic(rhsit, true, false, 0);\n\t\t\tren.apply_generic(rhsit, true, false, 0);\n\t\t\tif(*rhsit->name==\"\\\\sum\")\n\t\t\t\tct.apply(rhsit);\n\t\t\t}\n#else\n\t\tyoung_project_product ypp(kernel, rhstree);\n\t\t//\t\tsumflatten sf(rhstree, rhstree.end());\n\t\tcollect_terms ct(kernel, rhstree);\n\t\trename_dummies ren(kernel, rhstree, \"\", \"\");\n\n\t\t// debugout << \"young project rhs.\" << std::endl;\n\t\typp.apply_generic(rhsit, true, false, 0);\n\t\t// debugout << \"sumflatten.\" << std::endl;\n\t\t//\t\tsf.apply_recursive(rhsit, false);\n\t\t// debugout << \"rename.\" << std::endl;\n\t\tren.apply_generic(rhsit, true, false, 0);  // by far the slowest step\n\t\t// debugout << \"collect terms.\" << std::endl;\n\t\tct.apply_generic(rhsit, true, false, 0);\n\t\t// debugout << \"rhs projection done.\" << std::endl;\n\n\t\tsibling_iterator sib2=rhstree.begin(rhsit);\n\t\twhile(sib2!=rhstree.end(rhsit)) {\n\t\t\tsib2->fl.bracket=str_node::b_none;\n\t\t\t++sib2;\n\t\t\t}\n#endif\n\t\t}\n\t// debugout << \"Young-projected rhs constructed\" << std::endl;\n\t// rhstree.print_recursive_treeform(debugout, rhstree.begin());\n\n\tstd::vector<multiplier_t> rhs(terms_from_yp.size(),0);\n\tif(*rhsit->name==\"\\\\sum\") {\n\t\t// iterate over all terms\n\t\tsibling_iterator rhssumit=rhstree.begin(rhsit);\n\t\twhile(rhssumit!=rhstree.end(rhsit)) {\n\t\t\tbool found_in_basis=false;\n\t\t\tmultiplier_t rhsmult=*rhssumit->multiplier;\n\t\t\tone(rhssumit->multiplier);\n\t\t\tfor(unsigned int i=0; i<terms_from_yp.size(); ++i) {\n\t\t\t\tif(tr.equal_subtree(terms_from_yp[i].begin(), (iterator)(rhssumit))) {\n\t\t\t\t\trhs[i]=rhsmult;\n\t\t\t\t\tfound_in_basis=true;\n\t\t\t\t\tbreak;\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\tif(!found_in_basis) {\n\t\t\t\t//\t\t\t\ttxtout << \"rhs contains a term not present in the basis\" << std::endl;\n\t\t\t\treturn result_t::l_error;\n\t\t\t\t}\n\t\t\t++rhssumit;\n\t\t\t}\n\t\t}\n\telse {\n\t\t// only one term in the rhs\n\t\tif(rhsit->is_zero()==false) {\n\t\t\tbool found_in_basis=false;\n\t\t\tmultiplier_t rhsmult=*rhsit->multiplier;\n\t\t\tone(rhsit->multiplier);\n\t\t\tfor(unsigned int i=0; i<terms_from_yp.size(); ++i) {\n\t\t\t\tif(tr.equal_subtree(terms_from_yp[i].begin(), rhsit)) {\n\t\t\t\t\trhs[i]=rhsmult;\n\t\t\t\t\tfound_in_basis=true;\n\t\t\t\t\tbreak;\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\tif(!found_in_basis) {\n\t\t\t\t//\t\t\t\t\ttxtout << \"rhs contains a term not present in the basis\" << std::endl;\n\t\t\t\treturn result_t::l_error;\n\t\t\t\t}\n\t\t\t}\n\t\t}\n\n\t// debugout << \"linear problem constructed\" << std::endl;\n\t// for(unsigned int i=0; i<coefficient_matrix.size(); ++i) {\n\t// \tfor(unsigned int j=0; j<coefficient_matrix[i].size(); ++j)\n\t// \t\tdebugout << coefficient_matrix[i][j] << \" \";\n\t// \tdebugout << \" \" << rhs[i] << std::endl;\n\t// \t}\n\t// Now decompose\n\n\tif(rhsit->is_zero()) {\n\t\t// debugout << \"rhs is identically zero\" << std::endl;\n\t\tEx res;\n\t\tres.set_head(str_node(\"\\\\comma\"));\n\t\tfor(unsigned int i=0; i<coefficient_matrix[0].size(); ++i)\n\t\t\tres.append_child(res.begin(), str_node(\"1\"))->multiplier=rat_set.insert(0).first;\n\t\ttr.replace(it, res.begin());\n\t\t}\n\telse {\n\t\t// debugout << \"doing gaussian elimination\" << std::endl;\n\t\tif(linear::gaussian_elimination_inplace(coefficient_matrix, rhs)) {\n\t\t\t// for(unsigned int i=0; i<coefficient_matrix.size(); ++i) {\n\t\t\t// \t\tfor(unsigned int j=0; j<coefficient_matrix[i].size(); ++j)\n\t\t\t// \t\t\t debugout << coefficient_matrix[i][j] << \" \";\n\t\t\t// \t\tdebugout << \" = \" << rhs[i] << std::endl;\n\t\t\t// \t\t}\n\n\t\t\tEx res;\n\t\t\tres.set_head(str_node(\"\\\\comma\"));\n\t\t\tfor(unsigned int i=0; i<coefficient_matrix[0].size(); ++i)\n\t\t\t\tres.append_child(res.begin(), str_node(\"1\"))->multiplier=rat_set.insert(rhs[i]).first;\n\t\t\tit=tr.replace(it, res.begin());\n\t\t\t}\n\t\telse {\n\t\t\t//\t\t\t  txtout << \"decomposing impossible\" << std::endl;\n\t\t\t//\t\ttr.print_recursive_treeform(txtout, it);\n\t\t\treturn result_t::l_error;\n\t\t\t}\n\t\t}\n\n\n\treturn result_t::l_applied;\n\t}\n\n\n"
  },
  {
    "path": "core/algorithms/decompose.cnb",
    "content": "{\n\t\"cells\" : \n\t[\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\algorithm{decompose}{Decompose a tensor monomial on a given basis of monomials.}\\n\\n The basis\\nshould be given in the second argument. All tensor symmetries,\\nincluding those implied by Young tableau Garnir symmetries, are taken\\ninto account. Example,\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\algorithm{decompose}{Decompose a tensor monomial on a given basis of monomials.}\\n\\n The basis\\nshould be given in the second argument. All tensor symmetries,\\nincluding those implied by Young tableau Garnir symmetries, are taken\\ninto account. Example,\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"R_{m n q p} R_{m p n q}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}R_{m n q p} R_{m p n q}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"{m,n,p,q}::Indices(vector).\\n{m,n,p,q}::Integer(0..10).\\nR_{m n p q}::RiemannTensor.\\n\\nex:=R_{m n q p} R_{m p n q};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"{ -  1/2 }\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\left[ - \\\\frac{1}{2}\\\\right]\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"decompose(ex, $R_{m n p q} R_{m n p q}$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"Note that this algorithm does not yet take into account\\ndimension-dependent identities, but it is nevertheless already\\nrequired that the index range is specified.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"Note that this algorithm does not yet take into account\\ndimension-dependent identities, but it is nevertheless already\\nrequired that the index range is specified.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1\n}\n"
  },
  {
    "path": "core/algorithms/decompose.hh",
    "content": "\n#pragma once\n\n#include \"Algorithm.hh\"\n\nnamespace cadabra {\n\n\tclass decompose : public Algorithm {\n\t\tpublic:\n\t\t\tdecompose(const Kernel&, Ex&, Ex&);\n\n\t\t\tvirtual bool     can_apply(iterator) override;\n\t\t\tvirtual result_t apply(iterator&) override;\n\n\t\tprivate:\n\t\t\tEx basis;\n\n\t\t\tvoid add_element_to_basis(Ex&, Ex::iterator);\n\t\t\tstd::vector<Ex>                    terms_from_yp;\n\t\t\tstd::vector<std::vector<multiplier_t> > coefficient_matrix;\n\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/algorithms/decompose_product.cc",
    "content": "\n#include \"Cleanup.hh\"\n#include \"IndexIterator.hh\"\n#include \"Exceptions.hh\"\n#include \"algorithms/decompose_product.hh\"\n#include \"properties/Integer.hh\"\n\nusing namespace cadabra;\n\ndecompose_product::decompose_product(const Kernel& k, Ex&tr)\n\t: Algorithm(k, tr), t1(0), t2(0)\n{\n}\n\nconst Indices *decompose_product::indices_equivalent(iterator it) const\n{\n\tindex_iterator ii=index_iterator::begin(kernel.properties, it);\n\tconst Indices *ret=0, *tmp=0;\n\twhile(ii!=index_iterator::end(kernel.properties, it)) {\n\t\ttmp=kernel.properties.get<Indices>(ii, true);\n\t\tif(tmp==0) return 0;\n\t\tif(ret==0) ret=tmp;\n\t\telse if(ret!=tmp) return 0;\n\t\t++ii;\n\t}\n\treturn ret;\n}\n\nbool decompose_product::can_apply(iterator it)\n{\n\t// Act on products. Find the first object which either has a\n\t// TableauSymmetry or has one vector index only. Then find the next\n\t// indexed object in the product and return true if this is a\n\t// one-indexed or TableauSymmetry object, and if the index types\n\t// of all indices match.\n\n\tif(*it->name==\"\\\\prod\") {\n\t\tsibling_iterator fc=tr.begin(it);\n\t\twhile(fc!=tr.end(it)) {\n\t\t\tt1=kernel.properties.get<TableauBase>(fc);\n\t\t\tif(t1 || number_of_indices(kernel.properties, fc)==1) {\n\t\t\t\tf1=fc;\n\t\t\t\tind1=indices_equivalent(fc);\n\t\t\t\tif(ind1) {\n\t\t\t\t\t++fc;\n\t\t\t\t\tif(fc!=tr.end(it)) {\n\t\t\t\t\t\tt2=kernel.properties.get<TableauBase>(fc);\n\t\t\t\t\t\tif(t2 || number_of_indices(kernel.properties, fc)==1) {\n\t\t\t\t\t\t\tf2=fc;\n\t\t\t\t\t\t\tind2=indices_equivalent(fc);\n\t\t\t\t\t\t\tif(ind2 && ind1==ind2) {\n\t\t\t\t\t\t\t\t// Strip off the parent rel because Integer properties are\n\t\t\t\t\t\t\t\t// declared as {m,n,p}::Integer, not {_m, _n, _p}::Integer.\n\t\t\t\t\t\t\t\tEx index(index_iterator::begin(kernel.properties, fc));\n\t\t\t\t\t\t\t\tindex.begin()->fl.parent_rel=str_node::p_none;\n\t\t\t\t\t\t\t\tconst Integer *itg=\n\t\t\t\t\t\t\t\t   kernel.properties.get<Integer>( index.begin(), true );\n\t\t\t\t\t\t\t\tif(itg) {\n\t\t\t\t\t\t\t\t\tdim=to_long(*itg->difference.begin()->multiplier);\n\t\t\t\t\t\t\t\t\tif(dim>0)\n\t\t\t\t\t\t\t\t\t\treturn true;\n\t\t\t\t\t\t\t\t}\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\t}\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t}\n\t\t\t++fc;\n\t\t}\n\t}\n\treturn false;\n}\n\nvoid decompose_product::fill_asym_ranges(TableauBase::tab_t& tab, int offset,\n      combin::range_vector_t& ranges)\n{\n\t// FIXME: we could also look at all other factors, and see if the index\n\t// _name_ in the slot is contracted to the index name in an antisymmetric\n\t// slot range. But that is more tricky, because index names move, whereas\n\t// slots stay.\n\n\tfor(unsigned int i=0; i<tab.row_size(0); ++i) {\n\t\tTableauBase::tab_t::in_column_iterator ci=tab.begin_column(i);\n\t\tcombin::range_t tmprange;\n\t\twhile(ci!=tab.end_column(i)) {\n\t\t\ttmprange.push_back((*ci)+offset);\n\t\t\t++ci;\n\t\t}\n\t\tif(tmprange.size()>=2)\n\t\t\tranges.push_back(tmprange);\n\t}\n}\n\nAlgorithm::result_t decompose_product::apply(iterator& it)\n{\n\t// Create the tensor product Young tableaux.\n\tsibtab_t  m1,m2;\n\tsibtabs_t prod;\n\tnumtabs_t numprod;\n\n\tunsigned int ioffset1=0, ioffset2=0;\n\n\tif(t1) {\n\t\tif(t1->size(kernel.properties, tr, f1)>1)\n\t\t\tthrow ConsistencyException(\"decompose_product: cannot handle multiple tableau tensors\");\n\t\tt1tab=t1->get_tab(kernel.properties, tr, f1, 0);\n\t\tfor(unsigned int r=0; r<t1tab.number_of_rows(); ++r)\n\t\t\tfor(unsigned int c=0; c<t1tab.row_size(r); ++c) {\n\t\t\t\tindex_iterator tmpii=index_iterator::begin(kernel.properties, f1);\n\t\t\t\ttmpii+=t1tab(r,c);\n\t\t\t\tm1.add_box(r, tmpii);\n\t\t\t}\n\t}\n\telse m1.add_box(0, index_iterator::begin(kernel.properties, f1));\n\n\tif(t2) {\n\t\tif(t2->size(kernel.properties, tr, f2)>1)\n\t\t\tthrow ConsistencyException(\"decompose_product: cannot handle multiple tableau tensors\");\n\t\tt2tab=t2->get_tab(kernel.properties, tr, f2, 0);\n\t\tfor(unsigned int r=0; r<t2tab.number_of_rows(); ++r)\n\t\t\tfor(unsigned int c=0; c<t2tab.row_size(r); ++c) {\n\t\t\t\tindex_iterator tmpii=index_iterator::begin(kernel.properties, f2);\n\t\t\t\ttmpii+=t2tab(r,c);\n\t\t\t\tm2.add_box(r, tmpii);\n\t\t\t}\n\t}\n\telse m2.add_box(0, index_iterator::begin(kernel.properties, f2));\n\n\t// Determine the position of the first index of the two\n\t// factors relative to the product (not to the tensors themselves).\n\tindex_iterator srch=index_iterator::begin(kernel.properties, it);\n\twhile(srch!=index_iterator::end(kernel.properties, it)) {\n\t\tif(iterator(srch)==iterator(index_iterator::begin(kernel.properties, f1)))\n\t\t\tbreak;\n\t\t++ioffset1;\n\t\t++srch;\n\t}\n\tsrch=index_iterator::begin(kernel.properties, it);\n\twhile(srch!=index_iterator::end(kernel.properties, it)) {\n\t\tif(iterator(srch)==iterator(index_iterator::begin(kernel.properties, f2)))\n\t\t\tbreak;\n\t\t++ioffset2;\n\t\t++srch;\n\t}\n\n\t// Determine slot ranges which are anti-symmetric.\n\n\tasym_ranges.clear();\n\tif(t1) fill_asym_ranges(t1tab, ioffset1, asym_ranges);\n\tif(t2) fill_asym_ranges(t2tab, ioffset2, asym_ranges);\n\n\t// Make the tensor product tableaux.\n\n\tyngtab::LR_tensor(m1, m2, dim, prod.get_back_insert_iterator(), true);\n\n\t//std::cerr << \"dim=\" << dim << \", size=\" << prod.storage.size() << std::endl;\n\n\t// The tableaux in 'prod' contain in their boxes iterators to\n\t// the indices in the original expression. We convert these to\n\t// numerical positions so they can be applied to copies of the\n\t// expression as well.\n\n\tsibtabs_t::tableau_container_t::iterator tt=prod.storage.begin();\n\twhile(tt!=prod.storage.end()) {\n\t\tnumtab_t tmptab;\n\t\ttmptab.copy_shape(*tt);\n\t\tsibtab_t::iterator si=tt->begin();\n\t\tnumtab_t::iterator ni=tmptab.begin();\n\t\twhile(si!=tt->end()) {\n\t\t\tindex_iterator fnd=index_iterator::begin(kernel.properties, it);\n\t\t\tunsigned int inum=0;\n\t\t\twhile(fnd!=index_iterator::end(kernel.properties, it)) {\n\t\t\t\tif(iterator(fnd) == (*si)) {\n\t\t\t\t\t*ni=inum;\n\t\t\t\t\tbreak;\n\t\t\t\t}\n\t\t\t\t++inum;\n\t\t\t\t++fnd;\n\t\t\t}\n\t\t\tassert(inum!=number_of_indices(kernel.properties, it));\n\t\t\t++ni;\n\t\t\t++si;\n\t\t}\n\t\tnumprod.storage.push_back(tmptab);\n\t\t++tt;\n\t}\n\n\t// Now create a Young projector sum of terms with the indices\n\t// distributed according to the tensor product tableaux.\n\n\t// \tstd::cout << numprod << std::endl;\n\n\tEx rep;\n\trep.set_head(str_node(\"\\\\tmp\"));  // not \\sum to prevent auto flattening\n\n\tnumtabs_t::tableau_container_t::iterator ntt=numprod.storage.begin();\n\n\twhile(ntt!=numprod.storage.end()) {\n\t\t// TESTINGONLY\n\t\t///\t\t++ntt; ++ntt; ++ntt;\n\n\t\t//\t\ttxtout << \"another tableau\" << std::endl;\n\t\tyoung_project yp(kernel, tr);\n\t\typ.tab=(*ntt);\n\n\t\t//\t\tif(getenv(\"SMART\"))\n\t\typ.asym_ranges=asym_ranges;\n\n\t\t// The asym ranges contain ranges of index locations. What we need\n\t\t// to convert this to is box numbers. This is a value->location\n\t\t// conversion in combinatorics.hh language. This will be done\n\t\t// inside the youngtab.hh routines.\n\n\t\t// Apply the product projector.\n\t\titerator rr=rep.append_child(rep.begin(), it);\n\t\tauto res=yp.can_apply(rr);\n\t\tif(!res)\n\t\t\tthrow InternalError(\"decompose_product: internal error, projector refused to apply, please report a bug.\");\n\t\typ.apply(rr);\n\n\t\t// We cannot use any algorithms which re-order indices, as the\n\t\t// order in yp.sym must match the order in the expression. Also,\n\t\t// we cannot remove terms without removing the corresponding entries\n\t\t// in yp.sym. So for the time being we have decided to put this\n\t\t// simplification in young_project.\n\n\t\t// Now apply the symmetries of the original tableaux (if any).\n\t\t// For each of the permutations in the product projector,\n\t\t// we need to figure out where the indices went which sat on\n\t\t// tensor 1 and 2. This information is stored in the symmetriser\n\t\t// of young_project. These indices then have to be projected using\n\t\t// the tensor projectors.\n\n\n\t\t// TESTINGONLY\n\t\t//\t\ttxtout << \"one ...\" << std::flush;\n\t\tif(t1) project_onto_initial_symmetries(rep, rr, yp, t1, f1, ioffset1, t1tab, false);\n\t\t//\t\ttxtout << \"done\" << std::endl;\n\t\t//\t\ttxtout << \"two ...\" << std::flush;\n\t\tif(t2) project_onto_initial_symmetries(rep, rr, yp, t2, f2, ioffset2, t2tab, true);\n\t\t//\t\ttxtout << \"done\" << std::endl;\n\n\t\t//    TESTINGONLY\n\t\t///\t\tbreak;\n\n\t\t++ntt;\n\t}\n\n\trep.begin()->name=name_set.insert(\"\\\\sum\").first;\n\n\tit=tr.replace(it, rep.begin());\n\n\t// flatten sums\n\t//\ttxtout << \"flattening... \" << std::flush;\n\t//\tsumflatten sf(tr, tr.end());\n\t//\tsf.apply_recursive(it, false);\n\t//\ttxtout << \"done\" << std::endl;\n\n\t//\ttr.print_recursive_treeform(std::cout, it);\n\n\tcleanup_dispatch(kernel, tr, it);\n\n\treturn result_t::l_applied;\n}\n\n\nvoid decompose_product::project_onto_initial_symmetries(Ex& rep, iterator rr, young_project& yp,\n      const TableauBase *, iterator ff,\n      int ioffset, const TableauBase::tab_t& thetab,\n      bool remove_traces)\n{\n\t// Sample: S_{m n} D_{p}{ A_{n q} } with S symmetric and A antisymmetric.\n\t// The tensor product contains one tableau which leads to a symmetriser\n\t// with as first entry 0 3 2 1 4. This means that the 'm' and 'n' index\n\t// names are associated, in the original, to box 0 and 3 respectively.\n\t// Now one of the terms in this symmetriser reads 2 4 0 1 3. In order\n\t// to apply the individual tensor projectors, we read off that the\n\t// 'm' and 'n' indices have now been moved to slot 2 and 1 respectively.\n\t// So we create a [1 1] tableau with numbers 2 and 1 in the boxes,\n\t// and apply this tensor projector to the full product tensor.\n\n\tunsigned int termnum=0;\n\n\t// Run through all terms in this tableau of the tensor product.\n\tsibling_iterator term=rep.begin(rr);\n\twhile(term!=rep.end(rr)) {\n\t\t// Setup the tableau for initial-tensor projection.\n\t\tyoung_project ypinitial(kernel, tr);\n\t\typinitial.tab.copy_shape(thetab);\n\t\tnumtab_t::iterator tabit=ypinitial.tab.begin();\n\t\tnumtab_t::const_iterator origtabit=thetab.begin();\n\n\t\tsibling_iterator nxt=term;\n\t\t++nxt;\n\t\tindex_iterator ii=index_iterator::begin(kernel.properties, ff);\n\t\twhile(ii!=index_iterator::end(kernel.properties, ff)) {\n\t\t\tunsigned int ipos=ioffset + (*origtabit);\n\t\t\tassert(termnum<yp.sym.size());\n\n\t\t\t// Find ipos in the first entry of yp.sym\n\t\t\t// and store the new position in the tableau.\n\t\t\tfor(unsigned int i=0; i<yp.sym[termnum].size(); ++i) {\n\t\t\t\tif(yp.sym[termnum][i]==ipos) {\n\t\t\t\t\t*tabit=yp.sym[0][i];\n\t\t\t\t\t//\t\t\t\t\ttxtout << ipos << \" has moved to \" << yp.sym[0][i] << std::endl;\n\t\t\t\t\tbreak;\n\t\t\t\t}\n\t\t\t}\n\t\t\t++tabit;\n\t\t\t++origtabit;\n\t\t\t++ii;\n\t\t}\n\n\t\t// Now we can finally project.\n\t\typ.remove_traces=remove_traces;\n\n\t\tif(*term->name==\"\\\\sum\") { // apply to all terms in the sum\n\t\t\t// THIS IS NOT CORRECT?! If we turn on asym_ranges  here\n\t\t\t// the result breaks.\n\t\t\t//\t\t\tif(getenv(\"SMART\"))\n\t\t\t//\t\t\t\typinitial.asym_ranges=asym_ranges;\n\t\t\tsibling_iterator trmit=tr.begin(term);\n\t\t\twhile(trmit!=tr.end(term)) {\n\t\t\t\titerator tmp=trmit;\n\t\t\t\tsibling_iterator nxt2=trmit;\n\t\t\t\t++nxt2;\n\n\t\t\t\t// Now apply the projector.\n\t\t\t\tauto res=ypinitial.can_apply(tmp);\n\t\t\t\tif(!res)\n\t\t\t\t\tthrow InternalError(\"project_onto_initial_symmetries: internal error, projector refused to apply, please report a bug.\");\n\t\t\t\typinitial.apply(tmp);\n\t\t\t\ttrmit=nxt2;\n\t\t\t}\n\t\t}\n\t\telse {   // just a single term\n\t\t\t//\t\t\tif(getenv(\"SMART\"))\n\t\t\typinitial.asym_ranges=asym_ranges;\n\t\t\titerator tmp=term;\n\t\t\t[[maybe_unused]] auto res=ypinitial.can_apply(tmp);\n\t\t\tassert(res);\n\t\t\typinitial.apply(tmp);\n\t\t}\n\n\t\t++termnum;\n\t\tterm=nxt;\n\t}\n}\n"
  },
  {
    "path": "core/algorithms/decompose_product.cnb",
    "content": "{\n\t\"cells\" : \n\t[\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\algorithm{decompose_product}{Decompose a product of tensors by using Young projectors.}\\n\\nDecompose a product of tensors by writing it out in terms of\\nirreducible Young tableau representations, discarding the ones which\\nvanish in the indicated dimension, and putting the results back\\ntogether again. This algorithm can thus be used to equate terms which\\nare identical only in certain dimensions.\\n\\nIf there are no dimension-dependent identities playing a role in the\\nproduct, then \\\\algo{decompose_product} returns the original\\nexpression,\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\algorithm{decompose_product}{Decompose a product of tensors by using Young projectors.}\\n\\nDecompose a product of tensors by writing it out in terms of\\nirreducible Young tableau representations, discarding the ones which\\nvanish in the indicated dimension, and putting the results back\\ntogether again. This algorithm can thus be used to equate terms which\\nare identical only in certain dimensions.\\n\\nIf there are no dimension-dependent identities playing a role in the\\nproduct, then \\\\algo{decompose_product} returns the original\\nexpression,\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Indices(position=free) to~}\\\\left\\\\{m, \\\\linebreak[0] n, \\\\linebreak[0] p, \\\\linebreak[0] q\\\\right\\\\}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Integer to~}\\\\left\\\\{m, \\\\linebreak[0] n, \\\\linebreak[0] p, \\\\linebreak[0] q\\\\right\\\\}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property AntiSymmetric to~}\\\\left\\\\{A_{m n p}, \\\\linebreak[0] B_{m n p}\\\\right\\\\}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}A_{m n p} B_{m n q}-A_{m n q} B_{m n p}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"{ m, n, p, q }::Indices(vector);\\n{ m, n, p, q }::Integer(1..4);\\n{ A_{m n p}, B_{m n p} }::AntiSymmetric;\\nex:= A_{m n p} B_{m n q} - A_{m n q} B_{m n p};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}A_{p m n} B_{q m n}-A_{q m n} B_{p m n}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"decompose_product(_)\\ncanonicalise(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"However, in the present example, a Schouten identity makes the\\nexpression vanish identically in three dimensions,\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"However, in the present example, a Schouten identity makes the\\nexpression vanish identically in three dimensions,\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Integer to~}\\\\left\\\\{m, \\\\linebreak[0] n, \\\\linebreak[0] p, \\\\linebreak[0] q\\\\right\\\\}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}A_{m n p} B_{m n q}-A_{m n q} B_{m n p}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}0\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"{ m, n, p, q }::Integer(1..3);\\nex:=A_{m n p} B_{m n q} - A_{m n q} B_{m n p};\\ndecompose_product(ex)\\ncanonicalise(ex);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"Note that \\\\algo{decompose_product} is unfortunately\\ncomputationally expensive, and is therefore not practical for large\\ndimensions.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"Note that \\\\algo{decompose_product} is unfortunately\\ncomputationally expensive, and is therefore not practical for large\\ndimensions.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1\n}\n"
  },
  {
    "path": "core/algorithms/decompose_product.hh",
    "content": "\n#pragma once\n\n#include \"algorithms/young_project.hh\"\n#include \"properties/TableauBase.hh\"\n#include \"properties/Indices.hh\"\n\nnamespace cadabra {\n\n\t/// \\ingroup algorithms\n\t///\n\t/// Decompose a product of tensors by applying Young projectors.\n\n\tclass decompose_product : public Algorithm {\n\t\tpublic:\n\t\t\tdecompose_product(const Kernel&, Ex& tr);\n\n\t\t\tvirtual bool     can_apply(iterator) override;\n\t\t\tvirtual result_t apply(iterator&) override;\n\n\t\tprivate:\n\t\t\ttypedef young_project::name_tab_t  sibtab_t;\n\t\t\ttypedef yngtab::tableaux<sibtab_t> sibtabs_t;\n\t\t\ttypedef young_project::pos_tab_t   numtab_t;\n\t\t\ttypedef yngtab::tableaux<numtab_t> numtabs_t;\n\n\t\t\t/// Test that all indices on the product are equivalent, that is, have\n\t\t\t/// the same Indices property attached to them. Return this property.\n\t\t\tconst Indices *indices_equivalent(iterator it) const;\n\n\t\t\tvoid fill_asym_ranges(TableauBase::tab_t& tab, int offset, combin::range_vector_t&);\n\t\t\tvoid project_onto_initial_symmetries(Ex& rep, iterator rr, young_project& yp,\n\t\t\t                                     const TableauBase *tt, iterator ff,\n\t\t\t                                     int offset, const TableauBase::tab_t& thetab,\n\t\t\t                                     bool remove_traces);\n\n\t\t\titerator               f1, f2;\n\t\t\tconst TableauBase     *t1, *t2;\n\t\t\tTableauBase::tab_t     t1tab, t2tab;\n\t\t\tconst Indices         *ind1, *ind2;\n\t\t\tunsigned int dim;\n\t\t\tyngtab::filled_tableau<iterator> nt1, nt2;\n\n\t\t\tcombin::range_vector_t asym_ranges;\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/algorithms/depprint.tex",
    "content": "\\cdbalgorithm{depprint}{}\n\nDisplay an expression together with all \nproperties of the symbols that appear in this expression. This is a\nvery useful command if you want to extract a result from a long\ncalculation and write it in a separate file for further processing. \n\\begin{screen}{1,2}\n\\Gamma{#}::GammaMatrix.\n{m,n,p,q}::Indices.\n\\Gamma_{m n p};\n@depprint(%);\n\\end{screen}\n~\n\n\\cdbseealgo{print}\n"
  },
  {
    "path": "core/algorithms/distribute.cc",
    "content": "\n#include \"distribute.hh\"\n#include \"Cleanup.hh\"\n#include \"Exceptions.hh\"\n#include \"properties/Distributable.hh\"\n\n#include \"algorithms/flatten_product.hh\"\n#include \"properties/Distributable.hh\"\n\nusing namespace cadabra;\n\ndistribute::distribute(const Kernel& k, Ex& tr)\n\t: Algorithm(k, tr)\n\t{\n\t}\n\nbool distribute::can_apply(iterator st)\n\t{\n\t//\tstd::cout << *st->name << std::endl;\n\tconst Distributable *db=kernel.properties.get<Distributable>(st);\n\tif(!db) {\n\t\treturn false;\n\t\t}\n\n\tsibling_iterator facs=tr.begin(st);\n\twhile(facs!=tr.end(st)) {\n\t\tif(*(*facs).name==\"\\\\sum\" || *(*facs).name==\"\\\\oplus\")\n\t\t\treturn true;\n\t\t//\t\tif(*st->name==\"\\\\indexbracket\" || *st->name==\"\\\\diff\") break; // only first argument is object\n\t\t++facs;\n\t\t}\n\treturn false;\n\t}\n\nAlgorithm::result_t distribute::apply(iterator& prod)\n\t{\n\tEx rep;\n\trep.set_head(str_node(\"\\\\sum\", prod->fl.bracket, prod->fl.parent_rel));\n\tsibling_iterator top=rep.begin();\n\t// add\n\titerator ploc=rep.append_child(top, str_node(prod->name, prod->fl.bracket, prod->fl.parent_rel));\n\t// The multiplier should sit on each term, not on the sum.\n\tploc->multiplier=prod->multiplier;\n\n\t// Examine each child node in turn. If it is a sum, distribute it\n\t// over all previously constructed nodes. Otherwise, add the child\n\t// node as a child to the previously constructed nodes.\n\n\t// \"facs\" iterates over all child nodes of the distributable (top-level) node\n\tsibling_iterator facs=tr.begin(prod);\n\twhile(facs!=tr.end(prod)) {\n\t\tstd::string sumname=*(*facs).name;\n\t\tif(sumname==\"\\\\sum\" || sumname==\"\\\\oplus\") {\n\t\t\tsibling_iterator se=rep.begin(top);\n\t\t\trep.begin()->name=facs->name;\n\t\t\t// \"se\" iterates over all nodes in the replacement \\sum\n\t\t\twhile(se!=rep.end(top)) {\n\t\t\t\tif(interrupted)\n\t\t\t\t\tthrow InterruptionException();\n\n\t\t\t\tEx termrep;\n\t\t\t\ttermrep.set_head(str_node());\n\t\t\t\tsibling_iterator sumch=tr.begin(facs);\n\t\t\t\twhile(sumch!=tr.end(facs)) {\n\t\t\t\t\tif(interrupted)\n\t\t\t\t\t\tthrow InterruptionException();\n\n\t\t\t\t\t// add product \"se\" to termrep.\n\t\t\t\t\tsibling_iterator dup=termrep.append_child(termrep.begin(), str_node()); // dummy\n\t\t\t\t\tdup=termrep.replace(dup, se);\n\t\t\t\t\t// add term from sum as factor to product above.\n\t\t\t\t\tsibling_iterator newfact=termrep.append_child(dup, sumch);\n\t\t\t\t\t// put the multiplier up front\n\t\t\t\t\tmultiply(dup->multiplier,*newfact->multiplier);\n\t\t\t\t\tmultiply(dup->multiplier,*facs->multiplier);\n\t\t\t\t\tone(newfact->multiplier);\n\t\t\t\t\t// make this child inherit the bracket from the sum node\n\t\t\t\t\tnewfact->fl.bracket=facs->fl.bracket;\n\t\t\t\t\t//\t\t\t\t\tnewfact->fl.bracket=str_node::b_none;\n\t\t\t\t\t++sumch;\n\t\t\t\t\t}\n\t\t\t\tsibling_iterator nxt=se;\n\t\t\t\t++nxt;\n\t\t\t\tsibling_iterator sep1=se;\n\t\t\t\t++sep1;\n\t\t\t\tse=rep.move_ontop(se, (sibling_iterator)(termrep.begin()));\n\t\t\t\trep.flatten(se);\n\t\t\t\trep.erase(se);\n\t\t\t\t//\t\t\t\trep.replace(se, sep1, termrep.begin(termrep.begin()), termrep.end(termrep.begin()));\n\t\t\t\tse=nxt;\n\t\t\t\t}\n\t\t\t}\n\t\telse {\n\t\t\tsibling_iterator se=rep.begin(top);\n\t\t\twhile(se!=rep.end(top)) {\n\t\t\t\tif(interrupted)\n\t\t\t\t\tthrow InterruptionException();\n\t\t\t\trep.append_child(se, facs);\n\t\t\t\t++se;\n\t\t\t\t}\n\t\t\t}\n\t\t++facs;\n\t\t}\n\tif(rep.number_of_children(top)==1) { // nothing happened, no sum was present\n\t\t//\t\tprod->fl.mark=0; // handled\n\t\t// std::cerr << \"only one for \" << Ex(prod) << std::endl;\n\t\treturn result_t::l_no_action;\n\t\t}\n\n\t// FIXME: why does this faster move lead to a crash in linear.cdb?\n\titerator ret=tr.move_ontop(prod, (iterator)top);\n\n\t// std::cerr << \"cleaning up at \" << Ex(ret) << std::endl;\n\tauto sib=tr.begin(ret);\n\twhile(sib!=tr.end(ret)) {\n\t\titerator ii=sib;\n\t\t++sib;\n\t\tcleanup_dispatch(kernel, tr, ii);\n\t\t}\n\tcleanup_dispatch(kernel, tr, ret);\n\t// std::cerr << \"cleaned up at \" << Ex(ret) << std::endl;\n\n\n\t// FIXME: if we had a flattened sum, does the apply_recursive now\n\t// go and examine every sum that we have created? Should we better\n\t// return an iterator to the last element in the sum?\n\tprod=ret;\n\treturn result_t::l_applied;\n\t}\n"
  },
  {
    "path": "core/algorithms/distribute.cnb",
    "content": "{\n\t\"cells\" : \n\t[\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\algorithm{distribute}{Distribute factors over sums.}\\n\\nRewrite a product of sums as a sum of products, as in\\n\\\\begin{equation*}\\na\\\\,(b+c) \\\\rightarrow a\\\\,b + a\\\\,c\\\\, .\\n\\\\end{equation*}\\nThis would read\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\algorithm{distribute}{Distribute factors over sums.}\\n\\nRewrite a product of sums as a sum of products, as in\\n\\\\begin{equation*}\\na\\\\,(b+c) \\\\rightarrow a\\\\,b + a\\\\,c\\\\, .\\n\\\\end{equation*}\\nThis would read\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}a \\\\left(b+c\\\\right)\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}a b+a c\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex:=a (b+c);\\ndistribute(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"The algorithm in fact works on all objects which carry\\nthe \\\\prop{Distributable} property, \"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"The algorithm in fact works on all objects which carry\\nthe \\\\prop{Distributable} property, \"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Distributable to~}Op\\\\left(\\\\#\\\\right).\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}Op\\\\left(A+B\\\\right)\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}Op\\\\left(A\\\\right)+Op\\\\left(B\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"Op{#}::Distributable;\\nex:=Op(A+B);\\ndistribute(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"The primary example of a property which inherits\\nthe \\\\prop{Distributable} property\\nis \\\\prop{PartialDerivative}. The \\\\algo{distribute} algorithm\\nthus also automatically writes out partial derivatives of sums as sums\\nof partial derivatives,\\n\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"The primary example of a property which inherits\\nthe \\\\prop{Distributable} property\\nis \\\\prop{PartialDerivative}. The \\\\algo{distribute} algorithm\\nthus also automatically writes out partial derivatives of sums as sums\\nof partial derivatives,\\n\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property PartialDerivative to~}\\\\partial{\\\\#}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\partial_{m}\\\\left(A+B+C\\\\right)\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\partial_{m}{A}+\\\\partial_{m}{B}+\\\\partial_{m}{C}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"\\\\partial{#}::PartialDerivative;\\nex:=\\\\partial_{m}{A + B + C};\\ndistribute(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1\n}\n"
  },
  {
    "path": "core/algorithms/distribute.hh",
    "content": "\n#pragma once\n\n#include \"Algorithm.hh\"\n\nnamespace cadabra {\n\n\t/// \\ingroup algorithms\n\t///\n\t/// Distribute factors over a sum, that is,\n\t/// \\f$ (A+B) C \\rightarrow A C + B C \\f$\n\n\n\tclass distribute : public Algorithm {\n\t\tpublic:\n\t\t\tdistribute(const Kernel&, Ex&);\n\n\t\t\tvirtual bool     can_apply(iterator);\n\t\t\tvirtual result_t apply(iterator&);\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/algorithms/drop_weight.cc",
    "content": "\n#include \"algorithms/drop_weight.hh\"\n#include \"Cleanup.hh\"\n#include \"Props.hh\"\n#include \"properties/Weight.hh\"\n#include \"properties/WeightInherit.hh\"\n\nusing namespace cadabra;\n\ndrop_keep_weight::drop_keep_weight(const Kernel& k, Ex& tr, Ex& a)\n\t: Algorithm(k, tr), arg(a)\n\t{\n\tif(arg.begin()==arg.end())\n\t\tthrow ArgumentException(\"drop_keep_weight: need 'weight=rational' argument.\");\n\n\tif(Ex::number_of_children(arg.begin())!=2)\n\t\tthrow ArgumentException(\"drop_keep_weight: need 'weight=rational' argument.\");\n\n\tif(*(arg.begin()->name)!=\"\\\\equals\")\n\t\tthrow ArgumentException(\"drop_keep_weight: need 'weight=rational' argument.\");\n\t}\n\n\n// This algorithm acts on nodes which have Weight or inherit Weight.\n// It only acts when the parent does _not_ have or inherit weight.\n// This makes sure that we act on sums and products which are not\n// themselves terms or factors in a sum or product.\n\nbool drop_keep_weight::can_apply(iterator st)\n\t{\n\t//std::cerr << \"can act? at \" << st << std::endl;\n\tsibling_iterator argit=arg.begin(arg.begin());\n\tlabel=*argit->name;\n\t++argit;\n\tweight=*argit->multiplier;\n\n\t// std::cerr << \"dk: \" << label << \" = \" << weight << std::endl;\n\n\tconst WeightInherit *gmnpar=0;\n\tconst Weight        *wghpar=0;\n\n\tgmn=kernel.properties.get<WeightInherit>(st, label);\n\twgh=kernel.properties.get<Weight>(st, label);\n\tif(tr.is_head(st)==false) {\n\t\tgmnpar=kernel.properties.get<WeightInherit>(tr.parent(st), label);\n\t\twghpar=kernel.properties.get<Weight>(tr.parent(st), label);\n\t\t}\n\n\t// std::cerr << *st->name << \": \" << gmn << \", \" << wgh << \", \" << gmnpar << \" \" << std::endl;\n\tif(gmn!=0 || wgh!=0) {\n\t\tbool ret = (gmnpar==0 && wghpar==0);\n\t\t// std::cerr << \"can_apply \" << ret << std::endl;\n\t\treturn ret;\n\t\t}\n\n\t// std::cerr << \"cannot apply\" << std::endl;\n\treturn false;\n\t}\n\nAlgorithm::result_t drop_keep_weight::do_apply(iterator& it, bool keepthem)\n\t{\n\tAlgorithm::result_t res=result_t::l_no_action;\n\n\tif(gmn) {\n\t\tif(gmn->combination_type==WeightInherit::multiplicative) {\n\t\t\tif((keepthem==true && weight!=gmn->value(kernel, it, label)) ||\n\t\t\t      (keepthem==false && weight==gmn->value(kernel, it, label))) {\n\t\t\t\tzero(it->multiplier);\n\t\t\t\t}\n\t\t\t}\n\t\telse {\n\t\t\tsibling_iterator sib=tr.begin(it);\n\t\t\twhile(sib!=tr.end(it)) {\n\t\t\t\tif(*sib->name==\"\\\\ldots\") {\n\t\t\t\t\t++sib;\n\t\t\t\t\tcontinue;\n\t\t\t\t\t}\n\n\t\t\t\tconst WeightBase *gnb=kernel.properties.get<WeightBase>(sib, label);\n\t\t\t\tif(gnb) {\n\t\t\t\t\t// std::cerr << \"WeightBase for child \" << Ex(sib) << std::endl;\n\t\t\t\t\tmultiplier_t val;\n\t\t\t\t\tbool no_val=false;\n\t\t\t\t\ttry {\n\t\t\t\t\t\tval=gnb->value(kernel, sib, label);\n\t\t\t\t\t\t// std::cerr << *sib->name << \" has weight \" << val << std::endl;\n\t\t\t\t\t\t}\n\t\t\t\t\tcatch(WeightInherit::WeightException& we) {\n\t\t\t\t\t\t// std::cerr << *sib->name << \" has undeterminable weight \" << std::endl;\n\t\t\t\t\t\t// If we cannot determine the weight of this term because this is a sum of\n\t\t\t\t\t\t// terms with different weights: keep when in @drop, drop when in @keep.\n\t\t\t\t\t\tno_val=true;\n\t\t\t\t\t\t}\n\t\t\t\t\tif( (no_val==false && ( (keepthem==true && weight!=val) || (keepthem==false && weight==val) ) )\n\t\t\t\t\t      || (no_val==true && keepthem==true) ) {\n\t\t\t\t\t\tsib=tr.erase(sib);\n\t\t\t\t\t\t}\n\t\t\t\t\telse ++sib;\n\t\t\t\t\t}\n\t\t\t\telse {\n\t\t\t\t\t// std::cerr << \"NO WeightBase for child \" << Ex(sib) << std::endl;\n\t\t\t\t\tif( (keepthem==true && weight!=0) || (keepthem==false && weight==0) ) {\n\t\t\t\t\t\tsib=tr.erase(sib);\n\t\t\t\t\t\t}\n\t\t\t\t\telse ++sib;\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\tif(tr.number_of_children(it)==0)\n\t\t\t\tzero(it->multiplier);\n\t\t\telse if(tr.number_of_children(it)==1) {\n\t\t\t\ttr.flatten(it);\n\t\t\t\tit=tr.erase(it);\n\t\t\t\t}\n\t\t\tres=result_t::l_applied;\n\t\t\t}\n\t\t}\n\telse {\n\t\tassert(wgh);\n\t\tif((keepthem==true && weight!=wgh->value(kernel, it, label)) ||\n\t\t      (keepthem==false && weight==wgh->value(kernel, it, label))) {\n\t\t\tres = result_t::l_applied;\n\t\t\tzero(it->multiplier);\n\t\t\t}\n\t\t}\n\n\tcleanup_dispatch(kernel, tr, it);\n\n\treturn res;\n\t}\n\ndrop_weight::drop_weight(const Kernel& k, Ex& e, Ex& a)\n\t: drop_keep_weight(k, e, a)\n\t{\n\t}\n\nAlgorithm::result_t drop_weight::apply(iterator& it)\n\t{\n\treturn do_apply(it, false);\n\t}\n\nkeep_weight::keep_weight(const Kernel& k, Ex& e, Ex& a)\n\t: drop_keep_weight(k, e, a)\n\t{\n\t}\n\nAlgorithm::result_t keep_weight::apply(iterator& it)\n\t{\n\treturn do_apply(it, true);\n\t}\n"
  },
  {
    "path": "core/algorithms/drop_weight.cnb",
    "content": "{\n\t\"cells\" : \n\t[\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\algorithm{drop_weight}{Drop terms with given weight}\\n\\nDrop those terms for which a product has the indicated\\nweight. Weights are computed by making use of the \\\\prop{Weight}\\nproperty of symbols. This algorithm does the opposite\\nof \\\\algo{keep_weight}.\\n\\nAs an example, consider the simple case in which we want to drop all\\nterms with 3~fields. This is done using\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\algorithm{drop_weight}{Drop terms with given weight}\\n\\nDrop those terms for which a product has the indicated\\nweight. Weights are computed by making use of the \\\\prop{Weight}\\nproperty of symbols. This algorithm does the opposite\\nof \\\\algo{keep_weight}.\\n\\nAs an example, consider the simple case in which we want to drop all\\nterms with 3~fields. This is done using\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Weight to~}\\\\left[A,~\\\\discretionary{}{}{} B\\\\right].\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}A B B+A A A+A B+B\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"{A,B}::Weight(label=field);\\nex:=A B B + A A A + A B + B;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}A B+B\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"drop_weight(_, $field=3$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"However, you can also do more complicated things by assigning non-unit\\nweights to symbols, as in the example below,\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"However, you can also do more complicated things by assigning non-unit\\nweights to symbols, as in the example below,\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Weight to~}\\\\left[A,~\\\\discretionary{}{}{} B\\\\right].\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Weight to~}C.\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"{A,B}::Weight(label=field);\\nC::Weight(label=field, value=2);\\nex:=A B B + A A A + A B + A C + B:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}A B+B\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"drop_weight(_, $field=3$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"Weights can be ``inherited'' by operators by using\\nthe \\\\prop{WeightInherit} property. Here is an example using\\npartial derivatives,\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"Weights can be ``inherited'' by operators by using\\nthe \\\\prop{WeightInherit} property. Here is an example using\\npartial derivatives,\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Weight to~}\\\\left[\\\\phi,~\\\\discretionary{}{}{} \\\\chi\\\\right].\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property PartialDerivative to~}\\\\partial{\\\\#}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property WeightInherit to~}\\\\partial{\\\\#}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\phi \\\\partial_{0}{\\\\phi}+\\\\partial_{0}{\\\\lambda}+\\\\lambda \\\\partial_{3}{\\\\chi}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"{\\\\phi,\\\\chi}::Weight(label=small, value=1);\\n\\\\partial{#}::PartialDerivative;\\n\\\\partial{#}::WeightInherit(label=all, type=multiplicative);\\nex:=\\\\phi \\\\partial_{0}{\\\\phi} + \\\\partial_{0}{\\\\lambda} + \\\\lambda \\\\partial_{3}{\\\\chi};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\phi \\\\partial_{0}{\\\\phi}+\\\\partial_{0}{\\\\lambda}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"drop_weight(_, $small=1$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1\n}\n"
  },
  {
    "path": "core/algorithms/drop_weight.hh",
    "content": "\n#pragma once\n\n#include \"Algorithm.hh\"\n#include \"properties/WeightInherit.hh\"\n#include \"properties/Weight.hh\"\n#include <string>\n\nnamespace cadabra {\n\n\tclass drop_keep_weight : public Algorithm {\n\t\tpublic:\n\t\t\tdrop_keep_weight(const Kernel&, Ex&, Ex&);\n\n\t\t\tvirtual bool can_apply(iterator) override;\n\t\t\tresult_t     do_apply(iterator&, bool keepthem);\n\n\t\tprotected:\n\t\t\tEx                   arg;\n\t\t\tconst WeightInherit *gmn;\n\t\t\tconst Weight        *wgh;\n\t\t\tstd::string          label;\n\t\t\tmultiplier_t         weight;\n\t\t};\n\n\tclass drop_weight : public drop_keep_weight {\n\t\tpublic:\n\t\t\tdrop_weight(const Kernel&, Ex&, Ex&);\n\n\t\t\tvirtual result_t apply(iterator&) override;\n\t\t};\n\n\tclass keep_weight : public drop_keep_weight {\n\t\tpublic:\n\t\t\tkeep_weight(const Kernel&, Ex&, Ex&);\n\n\t\t\tvirtual result_t apply(iterator&) override;\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/algorithms/dualise_tensor.tex",
    "content": "\\cdbalgorithm{dualise\\_tensor}{}\n\nDualises tensors which have been declared \\subsprop{SelfDual}\n  according to the formula\n\\begin{equation}\nF_{\\mu_{n+1}\\cdots \\mu_{d}}\\;\\; \\rightarrow\\;\\; *F_{\\mu_{n+1}\\cdots \\mu_{d}} = \\frac{1}{n!}\n \\epsilon_{\\mu_{n+1}\\cdots\\mu_d}{}^{\\mu_1\\cdots\\mu_n} F_{\\mu_1\\cdots\n \\mu_n}\\, .\n\\end{equation}\nIn order for this to work the indices on the tensor have to be\ndeclared with \\subsprop{Indices} and their range should have been\nspecified with \\subsprop{Integer}.\n\\begin{screen}{1,2,3,4,5}\n{m,n,p,q,r#}::Indices.\n{m,n,p,q,r#}::Integer(0..5).\nF_{m n p}::SelfDual.\nA_{q} F_{m n p} F_{m n p};\n@dualise_tensor!(%);\n1/36 A_{q} \\epsilon_{m n p r1 r2 r3} F_{r1 r2 r3} \n           \\epsilon_{m n p r4 r5 r6} F_{r4 r5 r6};\n\\end{screen}\nAs indices are by default position-free, all indices on the epsilon\ntensors are generated as lower indices in the example above. Here is a\nmodification which takes index positions into account:\n\\begin{screen}{1,2,3,4,5}\n{m,n,p,q,r#}::Indices(position=fixed).\n{m,n,p,q,r#}::Integer(0..5).\nF_{m n p}::SelfDual.\nF^{m n p}::SelfDual.\nA_{q} F_{m n p} F^{m n p};\n@dualise_tensor!(%);\n1/36 A_{q} \\epsilon_{m n p}^{r1 r2 r3} F_{r1 r2 r3} \n           \\epsilon^{m n p r4 r5 r6} F_{r4 r5 r6};\n\\end{screen}\nProducts of epsilon tensors can be expanded in terms of Kronecker\ndelta symbols with \\subscommand{epsprod2gendelta}.\n\n\\cdbseeprop{SelfDual}\n\\cdbseeprop{Indices}\n\\cdbseeprop{Integer}\n\\cdbseealgo{epsprod2gendelta}\n"
  },
  {
    "path": "core/algorithms/einsteinify.cc",
    "content": "\n#include \"algorithms/einsteinify.hh\"\n#include \"IndexClassifier.hh\"\n\nusing namespace cadabra;\n\neinsteinify::einsteinify(const Kernel& k, Ex& e, Ex& m)\n\t: Algorithm(k, e), metric(m)\n\t{\n\t}\n\nbool einsteinify::can_apply(iterator it)\n\t{\n\tif(*it->name==\"\\\\prod\") return true;\n\treturn false;\n\t}\n\nAlgorithm::result_t einsteinify::apply(iterator& it)\n\t{\n\tresult_t res=result_t::l_no_action;\n\n\tbool insert_metric=false;\n\tif(metric.begin()!=metric.end())\n\t\tif(*metric.begin()->name!=\"\")\n\t\t\tinsert_metric=true;\n\n\tIndexClassifier ic(kernel);\n\tIndexClassifier::index_map_t ind_free, ind_dummy;\n\tic.classify_indices(it, ind_free, ind_dummy);\n\tIndexClassifier::index_map_t::iterator dit=ind_free.begin();\n\tIndexClassifier::index_map_t::iterator prev=ind_free.end();\n\tdit=ind_dummy.begin();\n\tprev=dit;\n\t++dit;\n\twhile(dit!=ind_dummy.end()) {\n\t\tif(tree_exact_equal(&kernel.properties, (*dit).first, (*prev).first)) {\n\t\t\tif(insert_metric) { // put indices down and insert an inverse metric\n\t\t\t\t(*dit).second->fl.parent_rel=str_node::p_sub;\n\t\t\t\t(*prev).second->fl.parent_rel=str_node::p_sub;\n\t\t\t\titerator invmet=tr.append_child(it,str_node(metric.begin()->name));\n\n\t\t\t\t// get a new dummy index\n\t\t\t\tconst Indices *dums=kernel.properties.get<Indices>(dit->second, true);\n\t\t\t\tassert(dums);\n\t\t\t\tEx dum=ic.get_dummy(dums, it);\n\n\t\t\t\t// relink the indices\n\t\t\t\titerator tmpit=tr.append_child(invmet, (*prev).second);\n\t\t\t\ttmpit->fl.bracket=str_node::b_none;\n\t\t\t\ttmpit->fl.parent_rel=str_node::p_super;\n\t\t\t\ttmpit=tr.append_child(invmet, dum.begin());\n\t\t\t\ttmpit->fl.bracket=str_node::b_none;\n\t\t\t\ttmpit->fl.parent_rel=str_node::p_super;\n\t\t\t\ttr.replace_index((*dit).second,dum.begin())->fl.parent_rel=str_node::p_sub;\n\n\t\t\t\tres=result_t::l_applied;\n\t\t\t\t}\n\t\t\telse {   // raise one index\n\t\t\t\tif((*dit).second->fl.parent_rel==(*prev).second->fl.parent_rel) {\n\t\t\t\t\tif((*dit).second->fl.parent_rel==str_node::p_super)\n\t\t\t\t\t\t(*prev).second->fl.parent_rel=str_node::p_sub;\n\t\t\t\t\telse\n\t\t\t\t\t\t(*prev).second->fl.parent_rel=str_node::p_super;\n\t\t\t\t\t}\n\n\t\t\t\tres=result_t::l_applied;\n\t\t\t\t}\n\t\t\t}\n\t\tprev=dit;\n\t\t++dit;\n\t\t}\n\treturn res;\n\t}\n\n"
  },
  {
    "path": "core/algorithms/einsteinify.cnb",
    "content": "{\n\t\"cells\" : \n\t[\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\algorithm{einsteinify}{Raise or lower indices of pairs which are both upper or lower.}\\n\\nIn an expression containing dummy indices at the same position\\n(i.e.~either both subscripts or both superscripts), raise or lower one of the\\nindices.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\algorithm{einsteinify}{Raise or lower indices of pairs which are both upper or lower.}\\n\\nIn an expression containing dummy indices at the same position\\n(i.e.~either both subscripts or both superscripts), raise or lower one of the\\nindices.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"A_{m} A_{m}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}A_{m} A_{m}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"A^{m} A_{m}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}A^{m} A_{m}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex:= A_{m} A_{m};\\neinsteinify(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"A^{m} A^{m}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}A^{m} A^{m}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"A_{m} A^{m}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}A_{m} A^{m}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex:= A^{m} A^{m};\\neinsteinify(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"If an additional argument is given to this algorithm, it instead inserts\\n``inverse metric'' objects, with the name as indicated by the\\nadditional argument.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"If an additional argument is given to this algorithm, it instead inserts\\n``inverse metric'' objects, with the name as indicated by the\\nadditional argument.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"A_{m} A_{m}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}A_{m} A_{m}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"A_{m} A_{n} \\\\eta^{m n}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}A_{m} A_{n} \\\\eta^{m n}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"{m,n}::Indices.\\nex:= A_{m} A_{m};\\neinsteinify(_, $\\\\eta$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"A^{m} A^{m}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}A^{m} A^{m}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"A_{m} A_{n} \\\\eta^{m n}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}A_{m} A_{n} \\\\eta^{m n}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex:= A^{m} A^{m};\\neinsteinify(_, $\\\\eta$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"Note that the second form requires that there are enough dummy indices\\ndefined through the use of \\\\prop{Indices}.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"Note that the second form requires that there are enough dummy indices\\ndefined through the use of \\\\prop{Indices}.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1\n}\n"
  },
  {
    "path": "core/algorithms/einsteinify.hh",
    "content": "\n#pragma once\n\n#include \"Algorithm.hh\"\n\nnamespace cadabra {\n\n\t/// \\ingroup algorithms\n\n\tclass einsteinify : public Algorithm {\n\t\tpublic:\n\t\t\teinsteinify(const Kernel&, Ex&, Ex&);\n\n\t\t\tvirtual bool     can_apply(iterator) override;\n\t\t\tvirtual result_t apply(iterator&) override;\n\t\tprivate:\n\t\t\tEx metric;\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/algorithms/eliminate_kronecker.cc",
    "content": "\n#include \"Cleanup.hh\"\n#include \"algorithms/eliminate_kronecker.hh\"\n#include \"properties/KroneckerDelta.hh\"\n#include \"properties/Integer.hh\"\n\nusing namespace cadabra;\n\neliminate_kronecker::eliminate_kronecker(const Kernel& k, Ex& tr)\n\t: Algorithm(k, tr)\n\t{\n\t}\n\nbool eliminate_kronecker::can_apply(iterator st)\n\t{\n\tif(*st->name!=\"\\\\prod\")\n\t\tif(!is_single_term(st))\n\t\t\treturn false;\n\n\treturn true;\n\t}\n\nAlgorithm::result_t eliminate_kronecker::apply(iterator& st)\n\t{\n\tresult_t ret=result_t::l_no_action;\n\tprod_wrap_single_term(st);\n\tconst nset_t::iterator onept=name_set.insert(\"1\").first;\n\n//\tint looping=0;\n\n\tsibling_iterator it=tr.begin(st);\n\twhile(it!=tr.end(st)) { // Loop over all factors in a product, looking for Kroneckers\n\t\tbool replaced=false;\n\t\t// std::cerr << *it->name << std::endl;\n\t\tconst KroneckerDelta *kr=kernel.properties.get<KroneckerDelta>(it);\n\t\tif(kr && number_of_indices(it)==2) {\n\t\t\t// std::cerr << \"KD \" << Ex(it) << std::endl;\n\t\t\tindex_iterator ii1=begin_index(it);\n\t\t\tindex_iterator ii2=ii1;\n\t\t\t++ii2;\n\t\t\tif(subtree_compare(&kernel.properties, ii1, ii2, 1, false, -2, true)==0) { // a self-contracted Kronecker delta\n\t\t\t\t// std::cerr << \"self-contracted delta with \" << Ex(ii1) << \" = \" << Ex(ii2) << std::endl;\n\t\t\t\tconst Integer *itg1=kernel.properties.get<Integer>(ii1, true);\n\t\t\t\tconst Integer *itg2=kernel.properties.get<Integer>(ii2, true);\n\t\t\t\tif(itg1 && itg2) {\n\t\t\t\t\tif(ii1->is_rational()==false && ii2->is_rational()==false) {\n\t\t\t\t\t\tif(itg1->from.begin()!=itg1->from.end() && itg2->from.begin()!=itg2->from.end()) {\n\t\t\t\t\t\t\tif(itg1->difference.begin()->name==onept) {\n\t\t\t\t\t\t\t\tmultiply(st->multiplier, *itg1->difference.begin()->multiplier);\n\t\t\t\t\t\t\t\tit=tr.erase(it);\n\t\t\t\t\t\t\t\t}\n\t\t\t\t\t\t\telse {\n\t\t\t\t\t\t\t\tit=tr.replace(it, itg1->difference.begin());\n\t\t\t\t\t\t\t\t}\n\t\t\t\t\t\t\tret=result_t::l_applied;\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\telse ++it;\n\t\t\t\t\t\t}\n\t\t\t\t\telse if(ii1->is_rational() && ii2->is_rational()) {\n\t\t\t\t\t\tif(ii1->multiplier==ii2->multiplier) {\n\t\t\t\t\t\t\tit=tr.erase(it);\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\telse {\n\t\t\t\t\t\t\tzero(it->multiplier);\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\t}\n\t\t\t\t\t}\n\t\t\t\telse ++it;\n\t\t\t\t}\n\t\t\telse {\n\t\t\t\tsibling_iterator oi=tr.begin(st);\n//\t\t\t\t++looping;\n\t\t\t\t// iterate over all factors in the product\n\t\t\t\tbool doing1=false;\n\t\t\t\tbool doing2=false;\n\t\t\t\twhile(!replaced && oi!=tr.end(st)) {\n\t\t\t\t\tif(oi!=it) { // this is not the delta node\n\t\t\t\t\t\t// compare delta indices with all indices of this object\n\t\t\t\t\t\tindex_iterator ind=begin_index(oi);\n\t\t\t\t\t\twhile(ind!=end_index(oi)) {\n\t\t\t\t\t\t\tindex_iterator nxt=ind;\n\t\t\t\t\t\t\t++nxt;\n\t\t\t\t\t\t\tif(ii1->is_rational()==false && subtree_compare(&kernel.properties, ind, ii1, 1, false, -2, true)==0 ) {\n\t\t\t\t\t\t\t\tif(! (replaced && doing2) ) {\n\t\t\t\t\t\t\t\t\tmultiplier_t mt=(*ind->multiplier) / (*ii1->multiplier);\n\t\t\t\t\t\t\t\t\titerator rep=tr.replace_index(ind, ii2);\n\t\t\t\t\t\t\t\t\trep->fl.parent_rel=ii2->fl.parent_rel;\n\t\t\t\t\t\t\t\t\tmultiply(rep->multiplier, mt);\n\t\t\t\t\t\t\t\t\treplaced=true;\n\t\t\t\t\t\t\t\t\tdoing1=true;\n\t\t\t\t\t\t\t\t\t}\n\t\t\t\t\t\t\t\t// cannot 'break' here because that would miss cases when the\n\t\t\t\t\t\t\t\t// delta multiplies a sum.\n\t\t\t\t\t\t\t\t}\n\t\t\t\t\t\t\telse if(ii2->is_rational()==false && subtree_compare(&kernel.properties, ind, ii2, 1, false, -2, true)==0) {\n\t\t\t\t\t\t\t\tif(! (replaced && doing1) ) {\n\t\t\t\t\t\t\t\t\tmultiplier_t mt=(*ind->multiplier) / (*ii2->multiplier);\n\t\t\t\t\t\t\t\t\titerator rep=tr.replace_index(ind, ii1);\n\t\t\t\t\t\t\t\t\trep->fl.parent_rel=ii1->fl.parent_rel;\n\t\t\t\t\t\t\t\t\tmultiply(rep->multiplier, mt);\n\t\t\t\t\t\t\t\t\treplaced=true;\n\t\t\t\t\t\t\t\t\tdoing2=true;\n\t\t\t\t\t\t\t\t\t}\n\t\t\t\t\t\t\t\t// no break here either.\n\t\t\t\t\t\t\t\t}\n\t\t\t\t\t\t\tind=nxt;\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\t}\n\t\t\t\t\tif(!replaced)\n\t\t\t\t\t\t++oi;\n\t\t\t\t\t}\n\t\t\t\tif(replaced) {\n\t\t\t\t\tret=result_t::l_applied;\n\t\t\t\t\titerator tmp=oi;\n\t\t\t\t\tcleanup_dispatch(kernel, tr, tmp);\n\t\t\t\t\tit=tr.erase(it);\n\t\t\t\t\t}\n\t\t\t\telse ++it;\n\t\t\t\t}\n\t\t\t}\n\t\telse ++it;\n\t\t}\n\n\t// the product may have reduced to a single factor or even just a constant\n\t//\ttxtout << \"exiting eliminate\" << std::endl;\n\t//\tprod_unwrap_single_term(st);\n\t//\ttxtout << st.node << \" \" << tr.parent(st).node << std::endl;\n\t//\ttxtout << *st->name << \" \" << *(tr.parent(st)->name) << std::endl;\n\tsibling_iterator ff=tr.begin(st);\n\tif(ff==tr.end(st)) {\n\t\tst->name=onept;\n\t\t}\n\telse {\n\t\t++ff;\n\t\tif(ff==tr.end(st)) {\n\t\t\ttr.begin(st)->fl.bracket=st->fl.bracket;\n\t\t\ttr.begin(st)->fl.parent_rel=st->fl.parent_rel;\n\t\t\tmultiply( tr.begin(st)->multiplier, *st->multiplier );\n\t\t\ttr.flatten(st);\n\t\t\tst=tr.erase(st);\n\t\t\t}\n\t\t}\n\tcleanup_dispatch(kernel, tr, st);\n\t//\tcleanup_sums_products(tr, st);\n\t//\ttxtout << \"looped \" << looping << std::endl;\n\n\treturn ret;\n\t}\n"
  },
  {
    "path": "core/algorithms/eliminate_kronecker.cnb",
    "content": "\n{\n\t\"cells\" : \n\t[\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\algorithm{eliminate_kronecker}{Eliminate Kronecker delta symbols.}\\n\\nEliminates Kronecker delta symbols by performing index\\ncontractions. Also replaces contracted Kronecker delta symbols with\\nthe range over which the index runs, if known. \"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\algorithm{eliminate_kronecker}{Eliminate Kronecker delta symbols.}\\n\\nEliminates Kronecker delta symbols by performing index\\ncontractions. Also replaces contracted Kronecker delta symbols with\\nthe range over which the index runs, if known. \"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}A_{m p} \\\\delta_{p q} B_{q n}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}A_{m q} B_{q n}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"\\\\delta_{m n}::KroneckerDelta.\\nex:=A_{m p} \\\\delta_{p q} B_{q n};\\neliminate_kronecker(_);\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"The index range is set as usual with \\\\prop{Integer},\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"The index range is set as usual with \\\\prop{Integer},\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\delta_{p q} \\\\delta_{p q}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}d\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"{m,n,p,q}::Integer(0..d-1).\\n\\\\delta_{m n}::KroneckerDelta.\\nex:=\\\\delta_{p q} \\\\delta_{p q};\\neliminate_kronecker(_);\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"In order to eliminate metric factors (i.e.~to `raise' and 'lower'\\nindices) use the algorithm \\\\algo{eliminate_metric}.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"In order to eliminate metric factors (i.e.~to `raise' and 'lower'\\nindices) use the algorithm \\\\algo{eliminate_metric}.\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1.0\n}\n\n"
  },
  {
    "path": "core/algorithms/eliminate_kronecker.hh",
    "content": "\n#pragma once\n\n#include \"Algorithm.hh\"\n\nnamespace cadabra {\n\n\tclass eliminate_kronecker : public Algorithm {\n\t\tpublic:\n\t\t\teliminate_kronecker(const Kernel&, Ex&);\n\n\t\t\tvirtual bool     can_apply(iterator) override;\n\t\t\tvirtual result_t apply(iterator&) override;\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/algorithms/eliminate_metric.cc",
    "content": "\n#include \"Cleanup.hh\"\n#include \"IndexClassifier.hh\"\n#include \"algorithms/eliminate_metric.hh\"\n#include \"properties/Metric.hh\"\n#include \"properties/InverseMetric.hh\"\n\n//#define DEBUG 1\n\nusing namespace cadabra;\n\neliminate_metric::eliminate_metric(const Kernel& k, Ex& e, Ex& pref, bool redundant)\n\t: eliminate_converter(k, e, pref, redundant)\n\t{\n\t}\n\nbool eliminate_metric::is_conversion_object(iterator fit) const\n\t{\n\tconst Metric        *vb=kernel.properties.get<Metric>(fit);\n\tconst InverseMetric *ivb=kernel.properties.get<InverseMetric>(fit);\n\n\tif(vb || ivb)  return true;\n\telse return false;\n\t}\n\neliminate_converter::eliminate_converter(const Kernel& k, Ex& e, Ex& pref, bool redun)\n\t: Algorithm(k, e), preferred(pref), redundant(redun)\n\t{\n\t}\n\nbool eliminate_converter::can_apply(iterator it)\n\t{\n\tif(*it->name==\"\\\\prod\") return true;\n\treturn false;\n\t}\n\nbool eliminate_converter::handle_one_index(index_iterator ind1, index_iterator ind2, iterator fit, sibling_iterator objs)\n\t{\n\tbool replaced=false;\n\n#ifdef DEBUG\n\tstd::cerr << \"handling \" << ind1 << \", \" << ind2 << \", \" << fit << std::endl;\n#endif\n\t\n\t// For a conversion to be possible, we need one upper and one lower index\n\t// (for position!=free) or two indices (for position=free).\n\n#ifdef DEBUG\n\tstd::cerr << \"dummies: \" << std::endl;\n\tfor(const auto& d: ind_dummy)\n\t\tstd::cerr << d.second << std::endl;\n#endif\n\t\n\tauto locs= ind_dummy.equal_range(Ex(ind1)); \n\tint num1=std::distance(locs.first, locs.second);\n\tEx other(ind1);\n\tother.begin()->flip_parent_rel(); \n\tlocs = ind_dummy.equal_range(other);\n\tint num2=std::distance(locs.first, locs.second);\n\n#ifdef DEBUG\n\tstd::cerr << \"num1 = \" << num1 << \", num2 = \" << num2 << std::endl;\n#endif\n\n\tif(num1==1 && num2==1) {\n\t\twhile(locs.first!=locs.second) {\n\t\t\tif(locs.first->second!=(iterator)ind1) {\n\t\t\t\t// Does this index sit on an object in the \"preferred form\" list?\n\t\t\t\t// (if there is no preferred form, always eliminate)\n\t\t\t\tif(separated_by_derivative(locs.first->second, ind2, fit)==false) {\n\t\t\t\t\tif(objs==preferred.end()) { // no\n#ifdef DEBUG\n\t\t\t\t\t\tstd::cerr << \"Eliminate regardless\" << std::endl;\n#endif\n\t\t\t\t\t\ttr.move_ontop(locs.first->second, iterator(ind2))->fl.parent_rel=ind2->fl.parent_rel;;\n\t\t\t\t\t\tfit=tr.erase(fit);\n\t\t\t\t\t\treplaced=true;\n\t\t\t\t\t\t}\n\t\t\t\t\telse {   // yes\n#ifdef DEBUG\n\t\t\t\t\t\tstd::cerr << \"Index on preferred form tensor\" << std::endl;\n#endif\n\t\t\t\t\t\titerator par=tr.parent(locs.first->second);\n\t\t\t\t\t\tsibling_iterator prefit=tr.begin(objs);\n\t\t\t\t\t\twhile(prefit!=tr.end(objs)) {\n\t\t\t\t\t\t\tif(subtree_equal(&kernel.properties, prefit, par, -1, false)) {\n\t\t\t\t\t\t\t\ttr.move_ontop(locs.first->second, iterator(ind2))->fl.parent_rel=ind2->fl.parent_rel;;\n\t\t\t\t\t\t\t\tfit=tr.erase(fit);\n\t\t\t\t\t\t\t\treplaced=true;\n\t\t\t\t\t\t\t\tbreak;\n\t\t\t\t\t\t\t\t}\n\t\t\t\t\t\t\t++prefit;\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\t}\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\tif(replaced)\n\t\t\t\treturn true;\n\t\t\t++locs.first;\n\t\t\t}\n\t\t}\n\treturn false;\n\t}\n\n\nAlgorithm::result_t eliminate_converter::apply(iterator& it)\n\t{\n\tresult_t res=result_t::l_no_action;\n\n\n\t// Put arguments in canonical form.\n\n\tsibling_iterator objs=preferred.begin();\n\n\tif(objs!=preferred.end())\n\t\tif(*objs->name!=\"\\\\comma\")\n\t\t\tobjs=tr.wrap(objs, str_node(\"\\\\comma\"));\n\n\tind_free.clear();\n\tind_dummy.clear();\n\n\tIndexClassifier ic(kernel);\n\tic.classify_indices(it, ind_free, ind_dummy);\n\n\t// Run over all factors, find metrics, figure out whether they can\n\t// be used to turn the indices on the other tensors to preferred type.\n\n\tsibling_iterator fit=tr.begin(it);\n\twhile(fit!=tr.end(it)) {\n\t\tif(is_conversion_object(fit)) {\n\t\t\tindex_iterator ind1=index_iterator::begin(kernel.properties, fit), ind2=ind1;\n\t\t\t++ind2;\n            \n            if (!redundant || (ind_free.find(Ex(ind1)) == ind_free.end() &&\n                               ind_free.find(Ex(ind2)) == ind_free.end()))  {\n                // 1st index to 2nd index conversion?\n                if(handle_one_index(ind1, ind2, fit, objs)) {\n                    res=result_t::l_applied;\n                    break;\n                    }\n\n                // 2nd index to 1st index conversion?\n                if(handle_one_index(ind2, ind1, fit, objs)) {\n                    res=result_t::l_applied;\n                    break;\n                    }\n                }\n            }\n\n\t\t++fit;\n\t\t}\n\n\tif(res==result_t::l_applied)\n\t\tcleanup_dispatch(kernel, tr, it);\n\n\treturn res;\n\t}\n"
  },
  {
    "path": "core/algorithms/eliminate_metric.cnb",
    "content": "{\n\t\"cell_id\": 12201017813844474228,\n\t\"cells\": [\n\t\t{\n\t\t\t\"cell_id\": 11200548926868858386,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 706940583944905291,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\algorithm{eliminate_metric}{Eliminate metrics by raising or lowering indices.}\\n\\nEliminate metric and inverse metric objects by raising or lowering indices.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\algorithm{eliminate_metric}{Eliminate metrics by raising or lowering indices.}\\n\\nEliminate metric and inverse metric objects by raising or lowering indices.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 9501239282791426272,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 15552618808454340805,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 17909960130070292947,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"g_{m p} g^{p m}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}g_{m p} g^{p m}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 346245979832968625,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 18301710340624209207,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"g^{p}_{p}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}g^{p}\\\\,_{p}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"{m, n, p, q, r}::Indices(vector, position=fixed).\\n{m, n, p, q, r}::Integer(0..9).\\ng_{m n}::Metric.\\ng^{m n}::InverseMetric.\\ng_{m}^{n}::KroneckerDelta.\\ng^{m}_{n}::KroneckerDelta.\\nex:=g_{m p} g^{p m};\\neliminate_metric(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 7815987119515900884,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 692499475391029252,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 12623500600163379539,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"10\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}10\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"eliminate_kronecker(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 11136087069753532813,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 10975080456446455892,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"Related algorithms are \\\\algo{eliminate_kronecker} and \\\\algo{eliminate_vielbein}.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"Related algorithms are \\\\algo{eliminate_kronecker} and \\\\algo{eliminate_vielbein}.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 668070063135773764,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 2955225009111573646,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"It is sometimes useful to eliminate only those metrics which have two\\ndummy indices (so as to avoid changing indices on non-metric factors),\\nas in the following example:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"It is sometimes useful to eliminate only those metrics which have two\\ndummy indices (so as to avoid changing indices on non-metric factors),\\nas in the following example:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 7674476649362588094,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 934843099193461823,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property Indices(position=fixed) attached to~}\\\\left[a, \\\\discretionary{}{}{}b, \\\\discretionary{}{}{}c, \\\\discretionary{}{}{}d, \\\\discretionary{}{}{}e, \\\\discretionary{}{}{}f\\\\right].\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 816358059307477494,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property Metric attached to~}g_{a b}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 2839007278772691664,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property TableauSymmetry attached to~}g^{a b}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 13817763760227715534,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 10707513932396855145,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"X_{a} g^{a b} g_{b c} g^{c d} g_{d e} g^{e f}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}X_{a} g^{a b} g_{b c} g^{c d} g_{d e} g^{e f}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 15694279202429955163,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 16096105714669192847,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"X_{e} g^{e f}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}X_{e} g^{e f}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"{a,b,c,d,e,f}::Indices(position=fixed);\\ng_{a b}::Metric;\\ng^{a b}::InverseMetric;\\nex:=X_{a} g^{a b} g_{b c} g^{c d} g_{d e} g^{e f};\\neliminate_metric(ex, repeat=True, redundant=True);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 10177437379030071371,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 1237014864296849726,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"Without the \\\\verb|redundant=True| option, this would have reduced the \\nexpression to $X^{f}$.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"Without the \\\\verb|redundant=True| option, this would have reduced the \\nexpression to $X^{f}$.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 8153574234349350675,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"\"\n\t\t}\n\t],\n\t\"description\": \"Cadabra JSON notebook format\",\n\t\"version\": 1.0\n}\n"
  },
  {
    "path": "core/algorithms/eliminate_metric.hh",
    "content": "\n#pragma once\n\n#include \"Algorithm.hh\"\n#include \"IndexIterator.hh\"\n\nnamespace cadabra {\n\n\tclass eliminate_converter : public Algorithm {\n\t\tpublic:\n\t\t\teliminate_converter(const Kernel&, Ex&, Ex&, bool);\n\n\t\t\tvirtual bool     can_apply(iterator) override;\n\t\t\tvirtual result_t apply(iterator&) override;\n\n\t\tprotected:\n\t\t\tvirtual bool is_conversion_object(iterator) const=0;\n\n\t\tprivate:\n\t\t\tEx                           preferred;\n\t\t\tIndexClassifier::index_map_t ind_dummy, ind_free;\n\t\t\tbool                         redundant;\n\n\t\t\t/// See if the conversion which turns index 'i1' into index\n\t\t\t/// 'i2' can be applied on the expression, so that it gets a\n\t\t\t/// factor in the expression closer to the 'fit' form.\n\t\t\t/// The two indices 'i1' and 'i2' are objects on the convertor\n\t\t\t/// object, so they need to appear with opposite parent rel\n\t\t\t/// in the expression if they are to be applied (if the index\n\t\t\t/// position type is 'fixed').\n\t\t\tbool handle_one_index(index_iterator i1, index_iterator i2, iterator fit, sibling_iterator objs);\n\t\t};\n\n\n\tclass eliminate_metric : public eliminate_converter {\n\t\tpublic:\n\t\t\teliminate_metric(const Kernel&, Ex&, Ex&, bool);\n\n\t\tprotected:\n\t\t\tvirtual bool is_conversion_object(iterator) const override;\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/algorithms/eliminate_vielbein.cc",
    "content": "\n#include \"IndexClassifier.hh\"\n#include \"algorithms/eliminate_vielbein.hh\"\n#include \"properties/Vielbein.hh\"\n\nusing namespace cadabra;\n\neliminate_vielbein::eliminate_vielbein(const Kernel& k, Ex& e, Ex& pref, bool redundant)\n\t: eliminate_converter(k, e, pref, redundant)\n\t{\n\t}\n\nbool eliminate_vielbein::is_conversion_object(iterator fit) const \n\t{\n\tconst Vielbein        *vb=kernel.properties.get<Vielbein>(fit);\n\tconst InverseVielbein *ivb=kernel.properties.get<InverseVielbein>(fit);\n   \n\tif(vb || ivb)  return true;\n\telse return false;\n\t}\n\n"
  },
  {
    "path": "core/algorithms/eliminate_vielbein.cnb",
    "content": "{\n\t\"cell_id\" : 11106264074822655606,\n\t\"cells\" : \n\t[\n\t\t{\n\t\t\t\"cell_id\" : 7416860080608086163,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 1537526125551451146,\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\algorithm{eliminate_vielbein}{Eliminates vielbein objects.}\\n\\nIndices of one type can be converted to another type by using a vielbein or inverse \\nvielbein object.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\algorithm{eliminate_vielbein}{Eliminates vielbein objects.}\\n\\nIndices of one type can be converted to another type by using a vielbein or inverse \\nvielbein object.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 13229131517806571971,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 9223372036854775809,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\" : 9223372036854775810,\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"H_{m n p} e^{m}_{\\\\mu} e^{p}_{\\\\rho}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}H_{m n p} e^{m}\\\\,_{\\\\mu} e^{p}\\\\,_{\\\\rho}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 9223372036854775811,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\" : 9223372036854775812,\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"H_{\\\\mu n \\\\rho}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}H_{\\\\mu n \\\\rho}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"{ m, n, p }::Indices(flat).\\n{ \\\\mu, \\\\nu, \\\\rho }::Indices(curved).\\ne^{m}_{\\\\mu}::Vielbein.\\nex:= H_{m n p} e^{m}_{\\\\mu} e^{p}_{\\\\rho};\\neliminate_vielbein(_, repeat=True);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 11698189436523020544,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 13335616640459284672,\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"This is similar to \\\\algo{eliminate_metric}.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"This is similar to \\\\algo{eliminate_metric}.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 12210912534254123318,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1\n}\n"
  },
  {
    "path": "core/algorithms/eliminate_vielbein.hh",
    "content": "\n#pragma once\n\n#include \"algorithms/eliminate_metric.hh\"\n\nnamespace cadabra {\n\n\tclass eliminate_vielbein : public eliminate_converter {\n\t\tpublic:\n\t\t\teliminate_vielbein(const Kernel&, Ex&, Ex&, bool);\n\n\t\tprotected:\n\t\t\tvirtual bool is_conversion_object(iterator) const override;\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/algorithms/eliminate_vielbein.tex",
    "content": "\\cdbalgorithm{eliminate\\_vielbein}{}\n\nEliminates vielbein objects.\n\\begin{screen}{1,2,3,4,5}\n{ m, n, p }::Indices(flat).\n{ \\mu, \\nu, \\rho }::Indices(curved).\ne_{m \\mu}::Vielbein.\nH_{m n p} e_{m \\mu};\n@eliminate_vielbein!(%){H_{\\mu\\nu\\rho}};\nH_{\\mu n p};\n\\end{screen}\nOther elimination commands of a similar type are\n\\subscommand{eliminate\\_kr} for Kronecker delta symbols\nand \\subscommand{eliminate\\_metric} for metric and inverse metric objects.\n\n\\cdbseealgo{eliminate_kr}\n\\cdbseealgo{eliminate_metric}\n"
  },
  {
    "path": "core/algorithms/eliminateeps.tex",
    "content": "\\cdbalgorithm{eliminateeps}{}\n\n%{\\bf CONTAINS KNOWN BUGS}\n\nGiven an epsilon tensor and a self-dual tensor contracted with it,\nrewrite the self-dual tensor as epsilon times itself.\n\\begin{screen}{1,2}\nF_{m n p}::SelfDual.\n\\eps_{m n p q r s}::EpsilonTensor.\n\\eps_{m n p q r s} F_{q r s};\n@eliminateeps!(%){F_{m n p}};\n\\end{screen}\nAt a further stage one can then use the\ncommand \\subscommand{epsprod2gendelta} to remove the epsilons\naltogether the arguments contain a list of all tensors for which\nself-duality can be applied). Uses the the tensor with the largest\nnumber of indices in common with the epsilon symbol (can be more than\none, in which case more terms are generated).\n"
  },
  {
    "path": "core/algorithms/epsilon_to_delta.cc",
    "content": "\n#include \"algorithms/epsilon_to_delta.hh\"\n#include \"algorithms/reduce_delta.hh\"\n#include \"properties/EpsilonTensor.hh\"\n#include \"properties/Metric.hh\"\n\nusing namespace cadabra;\n\nepsilon_to_delta::epsilon_to_delta(const Kernel& k, Ex& tr, bool r)\n\t: Algorithm(k, tr), reduce(r)\n\t{\n\t}\n\nbool epsilon_to_delta::can_apply(iterator st)\n\t{\n\tif(*st->name!=\"\\\\prod\")\n\t\treturn false;\n\n\tepsilons.clear();\n\t// Find the two epsilon tensors in the product.\n\tstd::multimap<std::string,Ex::iterator> emap;\n\tsibling_iterator it=tr.begin(st);\n\twhile(it!=tr.end(st)) {\n\t\tconst EpsilonTensor *eps=kernel.properties.get<EpsilonTensor>(it);\n\t\tif(eps) emap.insert(std::pair<std::string,Ex::iterator>(get_index_set_name(begin_index(it)),it));\n\t\t++it;\n\t\t}\n\tsignature=1;\n\tstd::multimap<std::string,Ex::iterator>::iterator eit=emap.begin();\n\twhile(epsilons.size()<2 && eit!=emap.end()) {\n\t\tif(emap.count(eit->first)>1) {\n\t\t\tepsilons.push_back(eit->second);\n\t\t\t++eit;\n\t\t\tepsilons.push_back(eit->second);\n\t\t\tconst EpsilonTensor *eps=kernel.properties.get<EpsilonTensor>(eit->second);\n\t\t\tif(eps->metric.begin()!=eps->metric.end()) {\n\t\t\t\tconst Metric *met=kernel.properties.get<Metric>(eps->metric.begin());\n\t\t\t\tif(met)\n\t\t\t\t\tsignature=met->signature;\n\t\t\t\t}\n\t\t\tif(eps->krdelta.begin()!=eps->krdelta.end())\n\t\t\t\trepdelta=eps->krdelta;\n\t\t\t}\n\t\t++eit;\n\t\t}\n\tif(epsilons.size()<2)\n\t\treturn false;\n\n\tif(repdelta.begin()==repdelta.end())\n\t\treturn false;\n\telse repdelta.erase_children(repdelta.begin());\n\n\treturn true;\n\t}\n\nAlgorithm::result_t epsilon_to_delta::apply(iterator& st)\n\t{\n\tEx       rep(repdelta);\n\titerator delta=rep.begin();\n\n\t// std::cerr << Ex(st) << std::endl;\n\n\tsibling_iterator eps1=tr.begin(epsilons[0]);\n\tsibling_iterator eps2=tr.begin(epsilons[1]);\n\twhile(eps1!=tr.end(epsilons[0])) {\n\t\trep.append_child(delta, *eps1);\n\t\trep.append_child(delta, *eps2);\n\t\t++eps1;\n\t\t++eps2;\n\t\t}\n//\tstd::cerr << \"result: \" << rep.begin() << std::endl;\n\tmultiply(st->multiplier, *epsilons[0]->multiplier);\n\tmultiply(st->multiplier, *epsilons[1]->multiplier);\n\ttr.erase(epsilons[0]);\n\t//\tstd::cerr << tr.number_of_children(epsilons[1]) << std::endl;\n\t//\tstd::cerr << \" -> \" << *st->multiplier << \" * \" << combin::fact(multiplier_t(tr.number_of_children(epsilons[1]))) << std::endl;\n\tmultiply(st->multiplier, combin::fact(mpq_class(tr.number_of_children(epsilons[1]))));\n\t//\tstd::cerr << \"A:\" << *st->multiplier << std::endl;\n\tmultiply(st->multiplier, signature);\n\t//\tstd::cerr << \"B:\" << *st->multiplier << std::endl;\n\n\titerator gend=tr.replace(epsilons[1], rep.begin());\n\t//\tstd::cerr << \"B2:\" << *st->multiplier << std::endl;\n\n\tif(reduce) {\n\t\t//\t\tstd::cerr << \"reducing\" << std::endl;\n\t\treduce_delta rg(kernel, tr);\n\t\tif(rg.can_apply(gend))\n\t\t\trg.apply(gend);\n\t\tif(*gend->multiplier==0) {\n\t\t\tzero(st->multiplier);\n\t\t\treturn result_t::l_applied;\n\t\t\t}\n\t\t}\n\n\tif(*gend->multiplier!=1) {\n\t\t//\t\tstd::cerr << \"B3:\" << *st->multiplier << std::endl;\n\t\t//\t\tstd::cerr << \"B3:\" << *gend->multiplier << std::endl;\n\t\tmultiply(tr.parent(gend)->multiplier, *gend->multiplier);\n\t\tone(gend->multiplier);\n\t\t//\t\tstd::cerr << \"C:\" << *st->multiplier << std::endl;\n\t\t}\n\n\tif(tr.number_of_children(st)==1) {\n\t\tmultiply(tr.begin(st)->multiplier, *st->multiplier);\n\t\ttr.flatten(st);\n\t\tst=tr.erase(st);\n\t\t}\n\n\t//\tstd::cerr << Ex(st) << std::endl;\n\n\treturn result_t::l_applied;\n\t}\n\n"
  },
  {
    "path": "core/algorithms/epsilon_to_delta.cnb",
    "content": "{\n\t\"cell_id\": 222853918104208267,\n\t\"cells\": [\n\t\t{\n\t\t\t\"cell_id\": 6040850254890983940,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 4634821682817089960,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\algorithm{epsilon_to_delta}{Replace a product of two epsilon tensors with a generalised delta}\\n\\nReplace a product of two epsilon tensors with a generalised delta\\naccording to the expression\\n\\\\begin{equation}\\n\\\\epsilon^{r_1\\\\cdots r_{d}} \\\\epsilon_{s_1\\\\cdots s_{d}} =\\n\\\\frac{1}{\\\\sqrt{|g|}}\\\\varepsilon^{r_1 \\\\cdots r_{d}} \\\\sqrt{|g|}\\\\varepsilon_{s_1\\\\cdots s_{d}}\\n= {\\\\rm sign}(g)\\\\, d!\\\\, \\\\delta^{r_1 \\\\cdots r_{d}}_{s_1\\\\cdots s_{d}}\\\\, ,\\n\\\\end{equation}\\nwhere~${\\\\rm sign}(g)$ denotes the signature of the metric~$g$ used to\\nraise/lower the indices (see \\\\prop{EpsilonTensor} for conventions on the\\nepsilon tensor). When the indices are not ocurring up/down as in this\\nexpression, and the index position is not free, metric objects will be\\ngenerated instead.\\n\\nHere is an example:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\algorithm{epsilon_to_delta}{Replace a product of two epsilon tensors with a generalised delta}\\n\\nReplace a product of two epsilon tensors with a generalised delta\\naccording to the expression\\n\\\\begin{equation}\\n\\\\epsilon^{r_1\\\\cdots r_{d}} \\\\epsilon_{s_1\\\\cdots s_{d}} =\\n\\\\frac{1}{\\\\sqrt{|g|}}\\\\varepsilon^{r_1 \\\\cdots r_{d}} \\\\sqrt{|g|}\\\\varepsilon_{s_1\\\\cdots s_{d}}\\n= {\\\\rm sign}(g)\\\\, d!\\\\, \\\\delta^{r_1 \\\\cdots r_{d}}_{s_1\\\\cdots s_{d}}\\\\, ,\\n\\\\end{equation}\\nwhere~${\\\\rm sign}(g)$ denotes the signature of the metric~$g$ used to\\nraise/lower the indices (see \\\\prop{EpsilonTensor} for conventions on the\\nepsilon tensor). When the indices are not ocurring up/down as in this\\nexpression, and the index position is not free, metric objects will be\\ngenerated instead.\\n\\nHere is an example:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 2767356728095795528,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 11241214137464374167,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\epsilon_{a b c} \\\\epsilon_{a b d}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"{a,b,c,d}::Indices.\\n{a,b,c,d}::Integer(1..3).\\n\\\\delta{#}::KroneckerDelta.\\n\\\\epsilon_{a b c}::EpsilonTensor(delta=\\\\delta).\\nex:=\\\\epsilon_{a b c} \\\\epsilon_{a b d};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 17935743127738946687,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 11430802620406115181,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}2\\\\delta_{c d}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"epsilon_to_delta(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 15215213331520901394,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 748503860410381173,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"Remember that if the result is a generalised delta, you can expand it in terms\\nof normal deltas using \\\\algo{expand_delta},\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"Remember that if the result is a generalised delta, you can expand it in terms\\nof normal deltas using \\\\algo{expand_delta},\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 17336055869576702648,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9030028112960476034,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\epsilon_{a b c} \\\\epsilon_{a d e}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 17630286008748119313,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}2\\\\delta_{b d c e}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 8395258090089642276,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\delta_{b d} \\\\delta_{c e}-\\\\delta_{c d} \\\\delta_{b e}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex:=\\\\epsilon_{a b c} \\\\epsilon_{a d e};\\nepsilon_to_delta(_);\\nexpand_delta(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 9743168648695691461,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 18221454557069207811,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"In order for this algorithm to work, you need to make sure that the\\nepsilon symbols in your expression are declared\\nas \\\\prop{EpsilonTensor} \\\\emph{and} that these declarations involve\\na specification of the \\\\verb|delta| and/or \\\\verb|metric| symbols.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"In order for this algorithm to work, you need to make sure that the\\nepsilon symbols in your expression are declared\\nas \\\\prop{EpsilonTensor} \\\\emph{and} that these declarations involve\\na specification of the \\\\verb|delta| and/or \\\\verb|metric| symbols.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 8176311872160163023,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 957392414442768784,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"As you can see from this example, contracted indices inside the\\ngeneralised delta are automatically eliminated, as the\\nalgorithm \\\\algo{reduce_gendelta} is called automatically; if you\\ndo not want this use the optional argument \\\\verb|reduce=False|.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"As you can see from this example, contracted indices inside the\\ngeneralised delta are automatically eliminated, as the\\nalgorithm \\\\algo{reduce_gendelta} is called automatically; if you\\ndo not want this use the optional argument \\\\verb|reduce=False|.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 7584424123443767501,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9606064349568347273,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\epsilon_{a b c} \\\\epsilon_{a b d}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9945886979741973192,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}6\\\\delta_{a a b b c d}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex:=\\\\epsilon_{a b c} \\\\epsilon_{a b d};\\nepsilon_to_delta(_, reduce=False);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 16729448291636328815,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 12273446363140010561,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"Note that the results typically depend on the signature of the\\nspace-time, which can be introduced through the optional \\\\verb|metric|\\nargument of the \\\\prop{EpsilonTensor} property. Compare the two\\nexamples below:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"Note that the results typically depend on the signature of the\\nspace-time, which can be introduced through the optional \\\\verb|metric|\\nargument of the \\\\prop{EpsilonTensor} property. Compare the two\\nexamples below:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 3705264274803310843,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9612433675590522418,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\epsilon_{a b c} \\\\epsilon_{a b c}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"{a,b,c,d}::Indices.\\n{a,b,c,d}::Integer(1..3).\\n\\\\delta{#}::KroneckerDelta.\\n\\\\epsilon_{a b c}::EpsilonTensor(delta=\\\\delta, metric=g_{a b}).\\n\\ng_{a b}::Metric(signature=-1).\\nex:=\\\\epsilon_{a b c} \\\\epsilon_{a b c};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 9533343478392675334,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 10925417497145116574,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}-6\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"epsilon_to_delta(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 637295154036736998,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 16285317753858478265,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\epsilon_{a b c} \\\\epsilon_{a b c}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 15341438585986313279,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}6\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"g_{a b}::Metric(signature=+1).\\nex:=\\\\epsilon_{a b c} \\\\epsilon_{a b c};\\nepsilon_to_delta(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 15369982606590812876,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 6235971706807023652,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"Note that you need to specify the full symbol for the metric,\\nincluding the indices, whereas the \\\\prop{Kronecker} delta argument only\\nrequires the name without the indices (because a contraction can\\ngenerate generalised Kronecker delta symbols with any number of indices).\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"Note that you need to specify the full symbol for the metric,\\nincluding the indices, whereas the \\\\prop{Kronecker} delta argument only\\nrequires the name without the indices (because a contraction can\\ngenerate generalised Kronecker delta symbols with any number of indices).\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 9436220866997150792,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"\"\n\t\t}\n\t],\n\t\"description\": \"Cadabra JSON notebook format\",\n\t\"version\": 1.0\n}\n"
  },
  {
    "path": "core/algorithms/epsilon_to_delta.hh",
    "content": "\n#pragma once\n\n#include \"Algorithm.hh\"\n#include <vector>\n\nnamespace cadabra {\n\n\tclass epsilon_to_delta : public Algorithm {\n\t\tpublic:\n\t\t\tepsilon_to_delta(const Kernel&, Ex&, bool reduce_);\n\n\t\t\tvirtual bool     can_apply(iterator) override;\n\t\t\tvirtual result_t apply(iterator&) override;\n\t\tprivate:\n\t\t\tbool                      reduce;\n\t\t\tstd::vector<Ex::iterator> epsilons;\n\t\t\tint                       signature;\n\t\t\tEx                        repdelta;\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/algorithms/evaluate.cc",
    "content": "\n#include \"Functional.hh\"\n#include \"Cleanup.hh\"\n#include \"Permutations.hh\"\n#include \"MultiIndex.hh\"\n#include \"Exceptions.hh\"\n#include \"algorithms/evaluate.hh\"\n#include \"algorithms/simplify.hh\"\n#include \"algorithms/substitute.hh\"\n#include \"algorithms/collect_terms.hh\"\n#include \"properties/EpsilonTensor.hh\"\n#include \"properties/PartialDerivative.hh\"\n#include \"properties/Coordinate.hh\"\n#include \"properties/DependsBase.hh\"\n#include \"properties/Accent.hh\"\n#include \"DisplayTerminal.hh\"\n#include <functional>\n\n// #define DEBUG 1\n\nusing namespace cadabra;\n\nevaluate::evaluate(const Kernel& k, Ex& tr, const Ex& c, bool rhs, bool simplify)\n\t: Algorithm(k, tr), components(c), only_rhs(rhs), call_sympy(simplify)\n\t{\n\t}\n\nbool evaluate::can_apply(iterator it)\n\t{\n\treturn tr.is_head(it); // only act at top level, we descend ourselves\n\t}\n\nbool evaluate::is_scalar_function(iterator it) const\n\t{\n\tif(*it->name==\"\\\\pow\" || *it->name==\"\\\\exp\" || *it->name==\"\\\\sin\" || *it->name==\"\\\\cos\" ) return true;\n\treturn false;\n\t}\n\nAlgorithm::result_t evaluate::apply(iterator& it)\n\t{\n\tresult_t res=result_t::l_no_action;\n\n\t// The first pass is top-down.\n\n\n\t// The second pass is bottom-up. The general logic of the routines\n\t// this calls is that, instead of looping over all possible index\n\t// value sets, we look straight at the substitution rules, and\n\t// check that these are required for some index values (this is\n\t// where symmetry arguments should come in as well).\n\t//\n\t// The logic in Compare.cc helps us by matching component A_{t r}\n\t// in the rule to an abstract tensor A_{m n} in the expression, storing\n\t// the index name -> index value map.\n\n\titerator rit=it;\n\tif(only_rhs && *it->name==\"\\\\equals\")\n\t\tit = tr.child(rit, 1);\n\t\n\tit = cadabra::do_subtree(tr, it, [&](Ex::iterator walk) -> Ex::iterator {\n#ifdef DEBUG\n\t\tstd::cerr << \"evaluate at \" << walk << std::endl;\n#endif\n\n\t\tif(*(walk->name)==\"\\\\components\") walk = handle_components(walk);\n\t\t// FIXME: currently \\pow is the only function for which we go straight up without\n\t\t// evaluating. For this reason, its children do not get wrapped in a \\components node\n\t\t// in handle_factor. This needs to be extended to other function as well.\n\t\telse if(is_scalar_function(walk))\n\t\t\t{\n\t\t\tunwrap_scalar_in_components_node(walk);   // this is a scalar\n\t\t\treturn walk;\n\t\t\t}\n\t\telse if(is_component(walk)) return walk;\n\t\telse if(*(walk->name)==\"\\\\sum\")   walk = handle_sum(walk);\n\t\telse if(*(walk->name)==\"\\\\prod\" || *(walk->name)==\"\\\\wedge\" || *(walk->name)==\"\\\\frac\")\n\t\t\twalk = handle_prod(walk);\n\t\telse\n\t\t\t{\n\t\t\tconst PartialDerivative *pd = kernel.properties.get<PartialDerivative>(walk);\n\t\t\tif(pd) walk = handle_derivative(walk);\n\t\t\telse {\n\t\t\t\tconst EpsilonTensor *eps = kernel.properties.get<EpsilonTensor>(walk);\n\t\t\t\tif(eps) {\n\t\t\t\t\twalk = handle_epsilon(walk);\n\t\t\t\t\t}\n\t\t\t\telse if(*walk->name!=\"\\\\equals\" && walk->is_index()==false) {\n\t\t\t\t\tif(! (only_rhs && tr.is_head(walk)==false && ( *(tr.parent(walk)->name)==\"\\\\equals\" || *(tr.parent(walk)->name)==\"\\\\arrow\" ) && tr.index(walk)==0) ) {\n\t\t\t\t\t\tIndexClassifier::index_map_t empty;\n\t\t\t\t\t\tsibling_iterator tmp(walk);\n\t\t\t\t\t\twalk = handle_factor(tmp, empty);\n\t\t\t\t\t\t// std::cerr << \"handling factor done\" << std::endl;\n\t\t\t\t\t\t}\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t}\n\t\treturn walk;\n\t\t}\n\t                        );\n\n\t// Final cleanup, e.g. to reduce scalar expressions to proper\n\t// scalars instead of 'components' nodes.\n\n\tif(only_rhs && *rit->name==\"\\\\equals\")\n\t\tit = rit;\n\t\n\tcleanup_dispatch_deep(kernel, tr);\n\n\treturn res;\n\t}\n\nbool evaluate::is_component(iterator it) const\n\t{\n\t// FIXME: The fact that this is called in the main loop above\n\t// prevents any evaluation of tensorial expressions which appear\n\t// inside components. Such things could in principle appear if, in\n\t// an existing components node, a scalar was replaced with an\n\t// object built from a tensor.\n\n\twhile(true) {\n\t\tif(*it->name==\"\\\\components\") {\n\t\t\treturn true;\n\t\t\t}\n\t\tif(tr.is_head(it)==false)\n\t\t\tit=tr.parent(it);\n\t\telse\n\t\t\tbreak;\n\t\t}\n\treturn false;\n\t}\n\nEx::iterator evaluate::handle_components(iterator it)\n\t{\n\t// This just cleans up component nodes. At the moment this means\n\t// taking care of handling dummy pairs.\n\n\tIndexClassifier ic(kernel);\n\tIndexClassifier::index_map_t ind_free, ind_dummy;\n\tic.classify_indices(it, ind_free, ind_dummy);\n\tif(ind_dummy.size()==0) return it;\n\n\t// Wrap in a product, use handle_prod to sort out summation.\n\tit = tr.wrap(it, str_node(\"\\\\prod\"));\n\tit = handle_prod(it);\n\treturn it;\n\t}\n\nEx::iterator evaluate::handle_sum(iterator it)\n\t{\n\t// std::cerr << \"handle sum\" << Ex(it) << std::endl;\n\n\t// pre-scan: remove zero nodes from evaluate having processed\n\t// nodes at lower level, and ensure child nodes are \\component\n\t// nodes.\n\tsibling_iterator sib=tr.begin(it);\n\twhile(sib!=tr.end(it)) {\n\t\tsibling_iterator nxt=sib;\n\t\t++nxt;\n\n\t\tif(*sib->multiplier==0) { // zero terms can be removed\n\t\t\ttr.erase(sib);\n\t\t\t}\n\t\telse if(is_component(sib)==false) {\n\t\t\tIndexClassifier::index_map_t empty;\n\t\t\thandle_factor(sib, empty);\n\t\t\t}\n\n\t\tsib=nxt;\n\t\t}\n\tif(tr.number_of_children(it)==0) {\n\t\tnode_zero(it);\n\t\treturn it;\n\t\t}\n\n\tIndexClassifier::index_map_t full_ind_free, full_ind_dummy;\n\n\t// First find the values that all indices will need to take. We do not loop over\n\t// them, but we need them in order to figure out which patterns in the rule can\n\t// match to patterns in the expression.\n\n\tIndexClassifier ic(kernel);\n\tic.classify_indices(it, full_ind_free, full_ind_dummy);\n\tfor(auto i: full_ind_free) {\n\t\t// std::cerr << \"finding prop for \" << Ex(i.second) << std::endl;\n\t\tconst Indices *prop = kernel.properties.get<Indices>(i.second);\n\t\tif(prop==0) {\n\t\t\tconst Coordinate *crd = kernel.properties.get<Coordinate>(i.second, true);\n\t\t\tif(crd==0)\n\t\t\t\tthrow ArgumentException(\"evaluate: Index \"+*(i.second->name)\n\t\t\t\t                        +\" does not have an Indices property.\");\n\t\t\t}\n\n\t\tif(prop!=0 && prop->values(kernel.properties, i.second).size()==0)\n\t\t\tthrow ArgumentException(\"evaluate: Do not know values of index \"+*(i.second->name)+\".\");\n\t\t}\n\n\t// Iterate over all terms in the sum. These should be of two types: \\component nodes,\n\t// which we do not need to touch anymore, and nodes which have still not been\n\t// evaluated. We send them all to handle_factor, which will return immediately on the\n\t// first node type, and convert the second type to the first.\n\n\tsib=tr.begin(it);\n\twhile(sib!=tr.end(it)) {\n\t\tsibling_iterator nxt=sib;\n\t\t++nxt;\n\t\tif(sib->is_zero())\n\t\t\tsib=tr.erase(sib);\n\t\telse {\n\t\t\thandle_factor(sib, full_ind_free);\n\t\t\tsib=nxt;\n\t\t\t}\n\t\t}\n\n\t// Now all terms in the sum (which has its top node at 'it') are\n\t// \\component nodes. We need to merge these together into a single\n\t// node.\n\n\tauto sib1=tr.begin(it);\n\t//\tmerge_component_children(sib1);\n\tauto sib2=sib1;\n\t++sib2;\n\twhile(sib2!=tr.end(it)) {\n#ifdef DEBUG\n\t\tstd::cerr << \"merging components \" << Ex(sib1) << \" and \" << Ex(sib2) << std::endl;\n#endif\n\t\tmerge_components(sib1, sib2);\n\t\tsib2=tr.erase(sib2);\n\t\t}\n\tcleanup_components(sib1);\n\n\tit=tr.flatten_and_erase(it);\n\n\treturn it;\n\t}\n\nEx::iterator evaluate::handle_factor(sibling_iterator sib, const IndexClassifier::index_map_t& full_ind_free)\n\t{\n#ifdef DEBUG\n\tstd::cerr << \"handle_factor \" << Ex(sib) << std::endl;\n#endif\n\tif(*sib->name==\"\\\\components\") return sib;\n\n\t// If this factor is an accent at the top level, descent further.\n\tconst Accent *acc = kernel.properties.get<Accent>(sib);\n\tif(acc) {\n\t\tauto deeper=tr.begin(sib);\n\t\thandle_factor(deeper, full_ind_free);\n\t\t// Put the accent on each of the components.\n\t\tsibling_iterator cl = tr.end(deeper);\n\t\t--cl;\n\t\tcadabra::do_list(tr, cl, [&](Ex::iterator c) {\n\t\t\tauto towrap = tr.child(c, 1);\n\t\t\ttr.wrap(towrap, *sib);\n\t\t\treturn true;\n\t\t\t});\n\t\t//tr.print_recursive_treeform(std::cerr, sib);\n\t\t// Move the component node up, outside the accent.\n\t\tsib=tr.flatten(sib);\n\t\tsib=tr.erase(sib);\n\t\t//tr.print_recursive_treeform(std::cerr, sib);\n\t\treturn sib;\n\t\t}\n\n\t// We need to know for all indices whether they are free or dummy,\n\t// in particular to handle internal contractions correctly.\n\tIndexClassifier ic(kernel);\n\tIndexClassifier::index_map_t ind_free, ind_dummy;\n\tic.classify_indices(sib, ind_free, ind_dummy);\n\n#ifdef DEBUG\n\tfor(const auto& i: ind_free)\n\t\tstd::cerr << \"free index: \" << i.first;\n#endif\n\t\n\t// Pure scalar nodes need to be wrapped in a \\component node to make life\n\t// easier for the rest of the algorithm.\n\tif(ind_free.size()==0 && ind_dummy.size()==0) {\n\t\tif(!tr.is_head(sib) && *tr.parent(sib)->name!=\"\\\\pow\") {\n\t\t\tsib=wrap_scalar_in_components_node(sib);\n#ifdef DEBUG\n\t\t\tstd::cerr << \"wrapped scalar\" << std::endl;\n#endif\n\t\t\t}\n\t\treturn sib;\n\t\t}\n\t// If the indices are all Coordinates, this is a scalar or tensor\n\t// component, not a tensor.  It then needs simple wrapping just\n\t// like a 'proper' scalar handed above.\n\tif(ind_dummy.size()==0 && ind_free.size()!=0) {\n\t\tbool all_coordinates=true;\n\t\tfor(auto& ind: ind_free) {\n\t\t\tconst Coordinate *crd = kernel.properties.get<Coordinate>(ind.second, true);\n\t\t\tif(!crd && !ind.second->is_integer()) {\n\t\t\t\tall_coordinates=false;\n\t\t\t\tbreak;\n\t\t\t\t}\n\t\t\t}\n\t\tif(all_coordinates) {\n\t\t\tif(!tr.is_head(sib) && *tr.parent(sib)->name!=\"\\\\pow\") {\n\t\t\t\tsib=wrap_scalar_in_components_node(sib);\n#ifdef DEBUG\n\t\t\t\tstd::cerr << \"wrapped scalar with component derivatives\" << std::endl;\n#endif\n\t\t\t\t}\n\t\t\treturn sib;\n\t\t\t}\n\t\t}\n\n\t// Attempt to apply each component substitution rule on this term.\n\tEx repl(\"\\\\components\");\n\t// Add the names of the free indices (if they are truly free, not integers).\n\tfor(auto& ind: ind_free) {\n\t\tif(ind.second->is_integer()==false)\n\t\t\trepl.append_child(repl.begin(), ind.second);\n\t\t}\n\t// If there are no free indices, add an empty first child anyway,\n\t// otherwise we need special cases in various other places.\n\tauto vl = repl.append_child(repl.begin(), str_node(\"\\\\comma\"));\n\tbool has_acted=false;\n\tcadabra::do_list(components, components.begin(), [&](Ex::iterator c) {\n\t\tEx rule(c);\n\t\tEx obj(sib);\n\t\t//\t\t\tstd::cerr << \"attempting rule \" << rule << \" on \" << obj << std::endl;\n\t\t// rule is a single rule, we walk the list.\n\t\tsubstitute subs(kernel, obj, rule);\n\t\tsubs.comparator.set_value_matches_index(true);\n\t\titerator oit=obj.begin();\n\t\tif(subs.can_apply(oit)) {\n\t\t\thas_acted=true;\n\t\t\t// std::cerr << \"can apply\" << std::endl;\n\t\t\tauto el = repl.append_child(vl, str_node(\"\\\\equals\"));\n\t\t\tauto il = repl.append_child(el, str_node(\"\\\\comma\"));\n\t\t\tauto fi = full_ind_free.begin();\n\t\t\t// FIXME: need to do something sensible with indices on the lhs\n\t\t\t// of rules which are not coordinates. You can have A_{m n} as expression,\n\t\t\t// A_{0 0} -> r, A_{i j} -> \\delta_{i j} as rule, but at the moment the\n\t\t\t// second rule does not do the right thing.\n\n\t\t\t// Store all free indices (not the dummies!) in the component node.\n\t\t\t// If we have been passed an empty list of free indices (because the parent\n\t\t\t// node is not a sum node), simply add all free index values in turn.\n\t\t\tif(fi==full_ind_free.end()) {\n\t\t\t\t//\t\t\t\t\tfor(auto& r: subs.comparator.index_value_map) {\n\t\t\t\t//\t\t\t\t\t\trepl.append_child(il, r.second.begin())->fl.parent_rel=str_node::p_none;\n\t\t\t\t//\t\t\t\t\t\t}\n\n\t\t\t\tfi=ind_free.begin();\n\t\t\t\twhile(fi!=ind_free.end()) {\n\t\t\t\t\tfor(auto& r: subs.comparator.index_value_map) {\n\t\t\t\t\t\tif(fi->first == r.first) {\n#ifdef DEBUG\n//\t\t\t\t\t\t\tstd::cerr << \"adding \" << r.second.begin() << std::endl;\n#endif\n\t\t\t\t\t\t\trepl.append_child(il, r.second.begin())->fl.parent_rel=str_node::p_none;\n\t\t\t\t\t\t\tbreak;\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\t}\n\t\t\t\t\tauto fiold(fi);\n\t\t\t\t\twhile(fi!=ind_free.end() && fiold->first==fi->first)\n\t\t\t\t\t\t++fi;\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\telse {\n\t\t\t\twhile(fi!=full_ind_free.end()) {\n\t\t\t\t\tfor(auto& r: subs.comparator.index_value_map) {\n\t\t\t\t\t\tif(fi->first == r.first) {\n#ifdef DEBUG\n//\t\t\t\t\t\t\tstd::cerr << \"adding2 \" << r.second.begin() << std::endl;\n#endif\n\t\t\t\t\t\t\trepl.append_child(il, r.second.begin())->fl.parent_rel=str_node::p_none;\n\t\t\t\t\t\t\tbreak;\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\t}\n\t\t\t\t\tauto fiold(fi);\n\t\t\t\t\twhile(fi!=full_ind_free.end() && fiold->first==fi->first)\n\t\t\t\t\t\t++fi;\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\tsubs.apply(oit);\n\t\t\trepl.append_child(el, obj.begin());\n\n\t\t\treturn true; // Cannot yet abort the do_list loop.\n\t\t\t}\n\t\telse {\n\t\t\t// TRACE: There is no rule which matches this factor. This means that\n\t\t\t// we want to keep all components?\n\t\t\t}\n\t\treturn true;\n\t\t});\n\tif(!has_acted) {\n\t\t// There was not a single rule which matched for this tensor. That's means\n\t\t// that the user wants to keep the entire tensor (all components).\n#ifdef DEBUG\n\t\tstd::cerr << \"No single rule matched \" << Ex(sib) << std::endl;\n#endif\n\t\tsib=dense_factor(sib, ind_free, ind_dummy);\n\t\t}\n\telse {\n\t\tmerge_component_children(repl.begin());\n\n#ifdef DEBUG\n\t\tDisplayTerminal dt(kernel, repl);\n\t\tstd::cerr << \"Result for this factor:\\n\";\n\t\tdt.output(std::cerr);\n\t\tstd::cerr << std::endl;\n#endif\n\t\tsib = tr.move_ontop(iterator(sib), repl.begin());\n\t\t}\n\n\treturn sib;\n\t}\n\nEx::iterator evaluate::dense_factor(iterator it, const IndexClassifier::index_map_t& ind_free,\n\t\t\t\t\t\t\t\t\t\t\t\tconst IndexClassifier::index_map_t& ind_dummy)\n\t{\n\tif(ind_dummy.size()!=0)\n\t\tthrow RuntimeException(\"Cannot yet evaluate this expression.\");\n\n#ifdef DEBUG\n\tstd::cerr << \"dense_factor \" << it << std::endl;\n#endif\n\t\n\t// For each index we need to iterate over all possible values, and generate a\n\t// components node for it. This should be done 'on the fly' eventually, the way\n\t// python treats 'map', but that will require wrapping all access to\n\t// '\\components' in a separate class.\n\n\tIndexClassifier ic(kernel);\n\tIndexClassifier::index_position_map_t ind_pos_free;\n\tic.fill_index_position_map(it, ind_free, ind_pos_free);\n\n\tEx comp(\"\\\\components\");\n\n\tauto fi = ind_free.begin();\n\t//std::cerr << \"dense factor with indices: \";\n\tMultiIndex<Ex> mi;\n\twhile(fi!=ind_free.end()) {\n\t\t// Look up which values this index takes.\n\t\tauto *id = kernel.properties.get<Indices>(fi->second);\n\t\tstd::vector<Ex> values;\n\t\tif(!id || id->values(kernel.properties, fi->second).size()==0) {\n\t\t\t// No index property known, or not known which values the index\n\t\t\t// takes, so keep this index unexpanded.\n\t\t\tauto val=Ex(fi->second);\n\t\t\tval.begin()->fl.parent_rel=str_node::parent_rel_t::p_none;\n\t\t\tvalues.push_back(val);\n\t\t\t}\n\t\telse {\n\t\t\tfor(const auto& ex: id->values(kernel.properties, fi->second))\n\t\t\t\tvalues.push_back(ex);\n\t\t\t}\n\t\tif(fi->second->is_integer()==false)\n\t\t\tcomp.append_child(comp.begin(), fi->first.begin());\n\t\t\n\t\tmi.values.push_back(values);\n\n\t\t++fi;\n\t\t}\n\t\n#ifdef DEBUG\n\tstd::cerr << \"number of indices taking values \" << mi.values.size() << std::endl;\n#endif\n\t\n\tauto comma=comp.append_child(comp.begin(), str_node(\"\\\\comma\"));\n\n\t// For each set of index values...\n\tfor(mi.start(); !mi.end(); ++mi) {\n\t\tauto ivs  = comp.append_child(comma, str_node(\"\\\\equals\"));\n\t\tauto ivsc = comp.append_child(ivs, str_node(\"\\\\comma\"));\n\t\t// ... add the values of the indices\n\t\tauto fi = ind_free.begin();\n\t\tfor(std::size_t i=0; i<mi.values.size(); ++i) {\n\t\t\tif(fi->second->is_integer()==false)\n\t\t\t\tcomp.append_child(ivsc, mi[i].begin());\n\t\t\t++fi;\n\t\t\t}\n\t\t// ... then set the value of the tensor component.\n\t\tauto repfac = comp.append_child(ivs, it);\n\t\tfi = ind_free.begin();\n\t\tsize_t i=0;\n\t\twhile(fi!=ind_free.end()) {\n\t\t\tauto il = begin_index(repfac);\n\t\t\tauto num = ind_pos_free[fi->second];\n\t\t\til += num;\n\t\t\tauto ii = iterator(il);\n\t\t\tauto parent_rel = il->fl.parent_rel;\n\t\t\tcomp.replace(ii, mi[i].begin())->fl.parent_rel=parent_rel;\n\t\t\t++i;\n\t\t\t++fi;\n\t\t\t}\n\t\t}\n\n#ifdef DEBUG\n\tstd::cerr << Ex(it) << \"turning to:\" << std::endl;\n\tstd::cerr << comp << std::endl;\n#endif\n\n\tit=tr.move_ontop(it, comp.begin());\n\n#ifdef DEBUG\n\tstd::cerr << it << std::endl;\n#endif\n\n\treturn it;\n\t}\n\nvoid evaluate::merge_component_children(iterator it)\n\t{\n\t// Scan the entries of a single \\components node for those\n\t// which carry the same index value for the free indices.\n\t// Such things can arise from e.g. A_{m} A_{m n} and the\n\t// rule { A_{r}=3, A_{t}=5, A_{r t}=1, A_{t t}=2 }, which\n\t// leads to two entries for the free index n=t.\n\n\t//\tif(*it->name!=\"\\\\components\")\n\t//\t\tstd::cerr << \"*** \" << *it->name << std::endl;\n\tassert(*it->name==\"\\\\components\");\n\n\tauto comma=tr.end(it);\n\t--comma;\n\n\t//\tif(*comma->name!=\"\\\\comma\")\n\t//\t\tstd::cerr << \"*** \" << *comma->name << std::endl;\n\tassert(*comma->name==\"\\\\comma\");\n\n\tauto cv1=tr.begin(comma);  // equals node\n\twhile(cv1!=tr.end(comma)) {\n\t\tauto iv1=tr.begin(cv1); // index values \\comma\n\t\tauto cv2=cv1;\n\t\t++cv2;\n\t\twhile(cv2!=tr.end(comma)) {\n\t\t\tauto iv2=tr.begin(cv2); // index values \\comma\n\t\t\tif(tr.equal_subtree(iv1, iv2)) {\n\t\t\t\t// std::cerr << \"merging \" << Ex(iv1) << std::endl;\n\t\t\t\tEx::sibling_iterator tv1=iv1; // tensor component value\n\t\t\t\t++tv1;\n\t\t\t\tEx::sibling_iterator tv2=iv2;\n\t\t\t\t++tv2;\n\t\t\t\t// std::cerr << \"need to merge\" << std::endl;\n\t\t\t\tif(*tv1->name!=\"\\\\sum\")\n\t\t\t\t\ttv1=tr.wrap(tv1, str_node(\"\\\\sum\"));\n\t\t\t\ttr.append_child(tv1, tv2);\n\t\t\t\tcv2=tr.erase(cv2);\n\t\t\t\t}\n\t\t\telse ++cv2;\n\t\t\t}\n\t\t++cv1;\n\t\t}\n\t}\n\nvoid evaluate::merge_components(iterator it1, iterator it2)\n\t{\n\t// Merge two component nodes which come from two terms in a sum (so that\n\t// we can be assured that the free indices match; they just may not be\n\t// in the same order).\n\n#ifdef DEBUG\n\tstd::cerr << \"merge_components on \" << Ex(it1) << \" and \" << Ex(it2) << std::endl;\n#endif\n\n\tassert(*it1->name==\"\\\\components\");\n\tassert(*it2->name==\"\\\\components\");\n\tsibling_iterator sib1=tr.end(it1);\n\t--sib1;\n\tsibling_iterator sib2=tr.end(it2);\n\t--sib2;\n\tassert(*sib1->name==\"\\\\comma\");\n\tassert(*sib2->name==\"\\\\comma\");\n\n\t// We cannot directly compare the lhs of the equals nodes of it1\n\t// with the lhs of the equals node of it2, because the index order\n\t// on the two components nodes may be different. We first have to\n\t// ensure that the orders are the same (but only, of course) if we\n\t// have anything to permutate in the first place.\n\n\tif(*tr.begin(it1)->name!=\"\\\\comma\") {\n\t\t// Look at all indices on the two components nodes. Find\n\t\t// the permutation that takes the indices on it2 and brings\n\t\t// them in the order as they are on it1.\n\t\tPerm perm;\n\t\tperm.find(tr.begin(it2), sib2, tr.begin(it1), sib1);\n\n\t\t// For each \\equals node in the it2 comma node, permute\n\t\t// the values so they agree with the index order on it1.\n\t\tcadabra::do_list(tr, sib2, [&](Ex::iterator nd) {\n\t\t\t// nd is an \\equals node.\n\t\t\tassert(*nd->name==\"\\\\equals\");\n\t\t\tauto comma = tr.begin(nd);\n\t\t\tassert(*comma->name==\"\\\\comma\");\n\t\t\tperm.apply(tr.begin(comma), tr.end(comma));\n\t\t\treturn true;\n\t\t\t});\n\n#ifdef DEBUG\n\t\tstd::cerr << \"permutations done\" << std::endl;\n#endif\n\t\t}\n\n\t// Now all index orders match and we can simply compare index value sets.\n\n\tcadabra::do_list(tr, sib2, [&](Ex::iterator it2) {\n\t\tassert(*it2->name==\"\\\\equals\");\n\n\t\tauto lhs2 = tr.begin(it2);\n\t\tauto found = cadabra::find_in_list(tr, sib1, [&](Ex::iterator it1) {\n\n\t\t\tauto lhs1 = tr.begin(it1);\n\t\t\t//std::cerr << \"comparing \" << *lhs1->name << \" with \" << *lhs2->name << std::endl;\n\t\t\tif(tr.equal_subtree(lhs1, lhs2)) {\n\t\t\t\tauto sum1=lhs1;\n\t\t\t\t++sum1;\n\t\t\t\tauto sum2=lhs2;\n\t\t\t\t++sum2;\n\t\t\t\tif(*sum1->name!=\"\\\\sum\")\n\t\t\t\t\tsum1=tr.wrap(sum1, str_node(\"\\\\sum\"));\n\t\t\t\ttr.append_child(sum1, sum2);\n\t\t\t\treturn iterator(sum1);\n\t\t\t\t}\n\n\t\t\treturn tr.end();\n\t\t\t});\n\t\tif(found==tr.end()) {\n\t\t\ttr.append_child(iterator(sib1), it2);\n\t\t\t}\n\t\treturn true;\n\t\t});\n\n\n\tif(call_sympy)\n\t\tsimplify_components(it1, true);\n\t}\n\nvoid evaluate::cleanup_components(iterator it)\n\t{\n\tsibling_iterator sib=tr.end(it);\n\t--sib;\n\n\tcadabra::do_list(tr, sib, [&](Ex::iterator nd) {\n\t\tauto iv=tr.begin(nd);\n\t\t++iv;\n\t\titerator p=iv;\n\t\tcleanup_dispatch(kernel, tr, p);\n\t\treturn true;\n\t\t});\n\t}\n\nEx::iterator evaluate::handle_derivative(iterator it)\n\t{\n#ifdef DEBUG\n\tstd::cerr << \"handle_derivative \" << Ex(it) << std::endl;\n#endif\n\t// Remember the name of the derivative in case we need to put it back later.\n\tnset_t::iterator derivative_name = it->name;\n\t\n\t// In order to figure out which components to keep, we need to do two things:\n\t// expand into components the argument of the derivative, and then\n\t// figure out the dependence of that argument on the various coordinates.\n\t// There may be other orders (for e.g. situations where we want to keep entire\n\t// components unevaluated), but that's for later when we have practical use cases.\n\n\tsibling_iterator sib=tr.begin(it);\n\twhile(sib!=tr.end(it)) {\n\t\tif(sib->is_index()==false) {\n\t\t\tif(is_component(sib)==false) {\n\t\t\t\tIndexClassifier::index_map_t empty;\n\t\t\t\t// This really shouldn't be necessary; the way in which the\n\t\t\t\t// top level 'apply' works, it should have rewritten the argument\n\t\t\t\t// of the derivative into a \\components node already.\n\t\t\t\tsib=handle_factor(sib, empty);\n\t\t\t\t}\n\t\t\tbreak;\n\t\t\t}\n\t\t++sib;\n\t\t}\n\tassert(sib!=tr.end(it));\n\n\t// std::cerr << \"after handle\\n\" << Ex(it) << std::endl;\n\n\tIndexClassifier ic(kernel);\n\tIndexClassifier::index_map_t ind_free, ind_dummy;\n\tic.classify_indices(it, ind_free, ind_dummy);\n\n\t// Flag an error if a partial derivative has an upper index which\n\t// is not position=free: this would require converting the index\n\t// with a metric, and that should be done by the user using\n\t// rewrite_indices.\n\t//\n\t// Also flag an error if there is more than one index type (we do\n\t// not handle those cases yet).\n\n\tauto fu = tr.begin(it);\n\tconst Indices *unique_indices=0;\n\tstd::vector<Ex> index_values;\n\n\twhile(fu!=tr.end(it)) {\n\t\tif(fu->is_index()) {\n\t\t\tconst Indices *ind = kernel.properties.get<Indices>(fu);\n\t\t\tif(ind!=unique_indices) {\n\t\t\t\tif(unique_indices==0) {\n\t\t\t\t\tunique_indices=ind;\n\t\t\t\t\tindex_values = ind->values(kernel.properties, fu);\n\t\t\t\t\t}\n\t\t\t\telse\n\t\t\t\t\tthrow RuntimeException(\"All indices on a single derivative need to be of the same type.\");\n\t\t\t\t}\n\t\t\t\n\t\t\tif(fu->fl.parent_rel==str_node::p_super) {\n\t\t\t\tif(ind && ind->position_type!=Indices::free)\n\t\t\t\t\tthrow RuntimeException(\"All indices on derivatives need to be lowered first.\");\n\t\t\t\t}\n\t\t\t}\n\t\t++fu;\n\t\t}\n\n\t// Figure out the positions of the index values in the components\n\t// node inside the derivative which correspond to values of dummy\n\t// indices (these necessarily have the other dummy on the\n\t// derivative itself).\n\tstd::vector<std::pair<size_t, size_t>> dummy_positions;\n\n\tdecltype(ind_dummy.begin()) dumit[2];\n\tdumit[0] = ind_dummy.begin();\n\twhile(dumit[0]!=ind_dummy.end()) {\n\t\tdumit[1]=dumit[0];\n\t\t++dumit[1];\n\t\tassert(dumit[1]!=ind_dummy.end());\n\n\t\tbool     on_component[2];\n\t\titerator parents[2];\n\t\tfor(int i=0; i<2; ++i) {\n\t\t\tparents[i]=tr.parent(dumit[i]->second);\n\t\t\ton_component[i]=*parents[i]->name==\"\\\\components\";\n\t\t\t}\n\n\t\tif(on_component[0]==false && on_component[1]==true)\n\t\t\tdummy_positions.push_back(std::make_pair(tr.index(dumit[0]->second), tr.index(dumit[1]->second)));\n\t\telse if(on_component[1]==false && on_component[0]==true)\n\t\t\tdummy_positions.push_back(std::make_pair(tr.index(dumit[1]->second), tr.index(dumit[0]->second)));\n\n\t\t++dumit[0];\n\t\t++dumit[0];\n\t\t}\n\n\t// Walk all the index value sets of the \\components node inside the\n\t// \\partial node.  For each, determine the dependencies, and\n\t// generate one element for each dependence.\n\n\tsibling_iterator ivalues = tr.end(sib);\n\t--ivalues;\n\n\tsize_t ni=number_of_direct_indices(it);\n\n\tcadabra::do_list(tr, ivalues, [&](Ex::iterator iv) {\n#ifdef DEBUG\n\t\tstd::cerr << \"====\" << std::endl;\n\t\tstd::cerr << Ex(iv) << std::endl;\n#endif\n\t\t// For each internal dummy set, keep track of the\n\t\t// position in the permutation array where we generate\n\t\t// its value.\n\t\tstd::map<Ex, int, tree_exact_less_for_indexmap_obj> d2p;\n\n\t\tEx_comparator comp(kernel.properties);\n\n\t\tsibling_iterator rhs = tr.begin(iv);\n\t\t++rhs;\n\t\tauto deps=dependencies(rhs);\n\n\t\tif(deps.size()==0) {\n//\t\t\tpm->message(\"No dependencies for \" + *rhs->name);\n\t\t\ttr.erase(iv);\n\t\t\treturn true;\n\t\t\t}\n\n\t\t// If one of the dependencies is '\\partial{#}', replace this will all the\n\t\t// index values that can appear in the derivative.\n\t\tauto dit = deps.begin();\n\t\twhile(dit!=deps.end()) {\n\t\t\tcomp.clear();\n\t\t\tif(*(dit->begin()->name)==\"\\\\partial\") { // FIXME: do a proper full-tree comparison with '\\partial{#}'.\n//\t\t\tif(comp.equal_subtree(\"\\partial{#}\", *dit, Ex_comparator::useprops_t::never, true)==Ex_comparator::match_t::subtree_match) {\n\t\t\t\tdeps.erase(dit);\n\t\t\t\tfor(const auto& ival: index_values)\n\t\t\t\t\tdeps.insert(ival);\n\t\t\t\tbreak;\n\t\t\t\t}\n\t\t\t++dit;\n\t\t\t}\n\n\t\t// If the argument does not depend on anything, all derivatives\n\t\t// would produce zero. Remove this \\equals node from the tree.\n\t\tif(deps.size()==0) {\n\t\t\tpm->message(\"No relevant dependencies for \" + *rhs->name);\n\t\t\ttr.erase(iv);\n\t\t\treturn true;\n\t\t\t}\n\n\t\t// All indices on \\partial can take any of the values of the\n\t\t// dependencies, EXCEPT when the index is a dummy index OR\n\t\t// when the index on the partial is a Coordinate. And of course\n\t\t// we should check that the indices can actually take the\n\t\t// values of the dependencies.\n\t\t//\n\t\t// In the 1st exceptional case, we firstly need to ensure\n\t\t// that both indices in the dummy pair take the same value\n\t\t// (this is done with d2p). Secondly, we need to ensure that\n\t\t// if the second index sits on the argument, we only use the\n\t\t// value of that index as given in the 'iv' list.\n\t\t//\n\t\t// In the 2nd exceptional case, we just need to determine if\n\t\t// the particular derivative does not annihilate the argument.\n\n\t\t// Need all combinations of values, with repetition (multiple\n\t\t// pick) allowed.\n\n\t\tcombin::combinations<Ex> cb;\n\t\tfor(auto& obj: deps) {\n#ifdef DEBUG\n\t\t\tstd::cerr << \"dep \" << obj << std::endl;\n#endif\n\t\t\tif(unique_indices) {\n//\t\t\t\tstd::cerr << \"checking that deps are in values\" << std::endl;\n\t\t\t\tfor(const auto& allowed: index_values) {\n\t\t\t\t\tcomp.clear();\n\t\t\t\t\tif(comp.equal_subtree(allowed.begin(), obj.begin(), Ex_comparator::useprops_t::never, true)<=Ex_comparator::match_t::subtree_match) {\n\t\t\t\t\t\tcb.original.push_back(obj);\n\t\t\t\t\t\tbreak;\n\t\t\t\t\t\t}\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\telse\n\t\t\t\tcb.original.push_back(obj);\n\t\t\t}\n\n\t\tif(cb.original.size()==0) {\n\t\t\t// We may have had dependencies, but none of the index values can take those\n\t\t\t// values. So all is zero.\n\t\t\ttr.erase(iv);\n\t\t\treturn true;\n\t\t\t}\n\n\t\tcb.multiple_pick=true;\n\t\tcb.block_length=1;\n\t\tfor(size_t n=0; n<ni; ++n) {\n\t\t\t// If this child is a coordinate, take it out of the combinatorics\n\t\t\t// of summing over index values (it's a single value).\n\t\t\tif(kernel.properties.get<Coordinate>(tr.child(it, n), true)!=0)\n\t\t\t\tcontinue;\n\n\t\t\tEx iname(tr.child(it,n)); // FIXME: does not handle Accented objects\n\t\t\tif(ind_dummy.find(iname)!=ind_dummy.end()) {\n\t\t\t\t// If this dummy has one leg on the argument of the derivative,\n\t\t\t\t// take it out of the combinatorics, because its value will\n\t\t\t\t// be fixed.\n\t\t\t\tbool out=false;\n\t\t\t\tfor(auto& d: dummy_positions)\n\t\t\t\t\tif(d.first==n) {\n\t\t\t\t\t\tout=true;\n\t\t\t\t\t\tbreak;\n\t\t\t\t\t\t}\n\t\t\t\tif(out) continue;\n\n\t\t\t\tif(d2p.find(iname)!=d2p.end())\n\t\t\t\t\tcontinue;\n\t\t\t\telse {\n\t\t\t\t\td2p[iname]=cb.sublengths.size();\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\tcb.sublengths.push_back(1);\n\t\t\t}\n\t\tif(cb.sublengths.size()>0) // only if not all indices are fixed\n\t\t\tcb.permute();\n\n#ifdef DEBUG\n\t\tstd::cerr << cb.size() << \" permutations of indices\" << std::endl;\n#endif\n\n\t\t// Note: indices on partial may be dummies, in which case the\n\t\t// values cannot be arbitrary. This is a self-contraction,\n\t\t// but cannot be caught by handle_factor because derivatives\n\t\t// do not get handled by patterns directly, they get\n\t\t// constructed by looking at dependencies.\n\n\t\t// For each index value set we constructed for the indices on the\n\t\t// derivative, create an entry in the \\components node.\n\n\t\tfor(unsigned int i=0; i<cb.size() || cb.size()==0; ++i) {\n\t\t\t// 'i' runs over all index combinations.\n#ifdef DEBUG\n\t\t\tstd::cerr << \"Index combination \" << i << std::endl;\n#endif\n\t\t\tEx eqcopy(iv);\n\t\t\tauto lhs=eqcopy.begin(eqcopy.begin());\n\t\t\tassert(*lhs->name==\"\\\\comma\");\n\n\t\t\tif(cb.size()>0) {\n#ifdef DEBUG\n\t\t\t\tstd::cerr << \"Copying values of derivative indices\" << std::endl;\n#endif\n\t\t\t\t// Setup the index values; simply copy from the cb array, but only\n\t\t\t\t// if the indices are not internal dummy.\n\t\t\t\tfor(size_t j=0; j<cb[i].size(); ++j) {\n\t\t\t\t\tauto fd = ind_dummy.find(Ex(tr.child(it, j)));\n\t\t\t\t\tif(fd==ind_dummy.end()) {\n\t\t\t\t\t\teqcopy.append_child(iterator(lhs), cb[i][j].begin() );\n\t\t\t\t\t\t}\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\tauto rhs=lhs;\n\t\t\t++rhs;\n\t\t\tmultiplier_t mult=*rhs->multiplier;\n\t\t\tone(rhs->multiplier);\n\n\t\t\t// Wrap a '\\\\partial' node around the component value, and add the\n\t\t\t// same index values as above to this node.\n\t\t\t// FIXME: use the same derivative as was present in the tree!\n\t\t\trhs=eqcopy.wrap(rhs, str_node(derivative_name)); // \"\\\\partial\"));\n\t\t\tmultiply(rhs->multiplier, mult);\n\t\t\tmultiply(rhs->multiplier, *it->multiplier);\n\t\t\t//\t\t\t\tauto pch=tr.begin(it);\n\t\t\t//\t\t\t\titerator arg=tr.begin(rhs);\n\t\t\tfor(size_t j=0, cb_j=0; j<ni; ++j) {\n#ifdef DEBUG\n\t\t\t\tstd::cerr << j << \" : \";\n#endif\n\t\t\t\tbool done=false;\n\t\t\t\tfor(auto& d: dummy_positions) {\n\t\t\t\t\tif(d.first==j) {\n\t\t\t\t\t\t// This index is forced to a value because it is a dummy of which the partner\n\t\t\t\t\t\t// is fixed by the argument on which the derivative acts.\n#ifdef DEBUG\n\t\t\t\t\t\tstd::cerr << \"fixed\" << std::endl;\n#endif\n\t\t\t\t\t\teqcopy.insert_subtree(rhs.begin(), tr.child(lhs,d.second))->fl.parent_rel=str_node::p_sub;\n\t\t\t\t\t\tdone=true;\n\t\t\t\t\t\tbreak;\n\t\t\t\t\t\t}\n\t\t\t\t\t}\n\t\t\t\t// std::cerr << \"testing index \" << j << \" of \\n\" << Ex(it) << std::endl;\n\t\t\t\tif(kernel.properties.get<Coordinate>(tr.child(it, j), true)!=0) {\n\t\t\t\t\t// std::cerr << \"Coordinate, so need straight copy\" << std::endl;\n\t\t\t\t\teqcopy.insert_subtree(rhs.begin(), tr.child(it,j))->fl.parent_rel=str_node::p_sub;\n\t\t\t\t\tdone=true;\n\t\t\t\t\t}\n\t\t\t\tif(!done) {\n\t\t\t\t\t// If we get here, the index value was not fixed because it is part of an\n\t\t\t\t\t// already fixed dummy pair. And it was not fixed because the index was a\n\t\t\t\t\t// Coordinate. \n\t\t\t\t\tsize_t fromj=cb_j;\n\t\t\t\t\tEx iname(tr.child(it,j));\n\t\t\t\t\tauto fi = d2p.find(iname);\n\t\t\t\t\tif(fi!=d2p.end()) {\n\t\t\t\t\t\tfromj = (*fi).second;\n\t\t\t\t\t\tif(fromj == cb_j)\n\t\t\t\t\t\t\t++cb_j;\n\t\t\t\t\t\t}\n\t\t\t\t\telse {\n\t\t\t\t\t\t++cb_j;\n\t\t\t\t\t\t}\n\t\t\t\t\t// std::cerr << \"cb: \" << i << \", \" << fromj << std::endl;\n\t\t\t\t\teqcopy.insert_subtree(rhs.begin(), cb[i][fromj].begin() )->fl.parent_rel=str_node::p_sub;\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t// std::cerr << \"----\" << std::endl;\n\n\t\t\t// For all dummy pairs which have one index on the\n\t\t\t// \\components node inside the derivative, we need to\n\t\t\t// remove the corresponding value from the components\n\t\t\t// node.\n\t\t\tstd::vector<sibling_iterator> sibs_to_erase;\n\t\t\tfor(auto di: dummy_positions) {\n\t\t\t\tsibs_to_erase.push_back(tr.child(lhs, di.second));\n\t\t\t\t}\n\t\t\tfor(auto se: sibs_to_erase)\n\t\t\t\ttr.erase(se);\n\n\t\t\t// Now move this replacement expression into the tree.\n\n\t\t\t// std::cerr << \"Replacement now \" << std::endl;\n\t\t\t// std::cerr << eqcopy << std::endl;\n\t\t\ttr.move_before(tr.begin(ivalues), eqcopy.begin());\n\n\t\t\tif(cb.size()==0) break;\n\t\t\t}\n\n\t\t// Erase the original \\equals entry (we generated a full replacement above).\n\t\ttr.erase(iv);\n\t\treturn true;\n\t\t});\n\n#ifdef DEBUG\n\tstd::cerr << tr.number_of_children(ivalues) << \" nonzero components in this derivative\" << std::endl;\n#endif\n\tif(tr.number_of_children(ivalues)==0) {\n\t\t// All components of the derivative evaluated to zero because\n\t\t// there were no dependencies. Replace this derivative node with\n\t\t// a zero and return;\n\t\tnode_zero(it);\n\t\treturn it;\n\t\t}\n\n\tone(it->multiplier);\n\n#ifdef DEBUG\n\tstd::cerr << \"now \" << Ex(it) << std::endl;\n#endif\n\n\n\t// Now move the free (but not the internal dummy or Coordinate!)\n\t//\tpartial indices to the components node, and then unwrap the\n\t//\tpartial node.\n\n\tauto pch=tr.begin(it);\n\tfor(size_t n=0; n<ni; ++n) {\n\t\tsibling_iterator nxt=pch;\n\t\t++nxt;\n\t\tif(ind_dummy.find(Ex(pch))!=ind_dummy.end()) {\n\t\t\ttr.erase(pch);\n\t\t\t}\n\t\telse if(kernel.properties.get<Coordinate>(pch, true)!=0) {\n\t\t\ttr.erase(pch);\n\t\t\t}\n\t\telse\n\t\t\ttr.move_before(ivalues, pch);\n\t\tpch=nxt;\n\t\t}\n\n\n\t// Remove indices from the components node which came from the\n\t// argument and which are dummy.\n\tit=tr.flatten_and_erase(it);\n\tauto se = tr.begin(it);\n\twhile(se!=tr.end(it)) {\n\t\tif(ind_dummy.find(Ex(se))!=ind_dummy.end())\n\t\t\tse = tr.erase(se);\n\t\telse\n\t\t\t++se;\n\t\t}\n\n#ifdef DEBUG\n\tstd::cerr << \"after index move \" << Ex(it) << std::endl;\n#endif\n\n\tmerge_component_children(it);\n\n#ifdef DEBUG\n\tstd::cerr << \"after merge \" << Ex(it) << std::endl;\n#endif\n\n\tif(call_sympy)\n\t\tsimplify_components(it, true);\n\t// std::cerr << \"then \" << Ex(it) << std::endl;\n\n\treturn it;\n\t}\n\nEx::iterator evaluate::handle_epsilon(iterator it)\n\t{\n\tEx rep(\"\\\\components\");\n\t// attach indices to components\n\t// figure out the index value ranges\n\t// generate permutations of 'r1 ... rn' and signs\n\t// fill components\n\tauto sib=tr.begin(it);\n\tconst Indices *ind=0;\n\tstd::vector<Ex> values;\n\twhile(sib!=tr.end(it)) {\n\t\tif(!sib->is_integer()) {\n\t\t\trep.append_child(rep.begin(), (iterator)sib);\n\t\t\tconst Indices *ip = kernel.properties.get<Indices>(sib);\n\t\t\tif(ip==0)\n\t\t\t\tthrow ArgumentException(\"No Indices property known for all indices in EpsilonTensor.\");\n\t\t\tif(ind==0)\n\t\t\t\tind=ip;\n\t\t\telse if(ind!=ip)\n\t\t\t\tthrow ArgumentException(\"Indices property not the same for all indices in EpsilonTensor.\");\n\t\t\telse\n\t\t\t\tvalues=ip->values(kernel.properties, sib);\n\t\t\t}\n\t\t\n\t\t++sib;\n\t\t}\n\tauto cvals = rep.append_child(rep.begin(), str_node(\"\\\\comma\"));\n\n\tcombin::combinations<Ex> cb;\n\tif(ind && values.size()==0)\n\t\tthrow ArgumentException(\"No values known for index.\");\n\t\t\n\tfor(auto& val: values)\n\t\tcb.original.push_back(val);\n\n\tcb.multiple_pick=false;\n\tcb.block_length=1;\n\tcb.set_unit_sublengths();\n\tcb.permute();\n\n\tfor(unsigned int i=0; i<cb.size(); ++i) {\n\t\tauto equals = rep.append_child(cvals, str_node(\"\\\\equals\"));\n\t\tauto vcomma = rep.append_child(equals, str_node(\"\\\\comma\"));\n\t\tbool discard=false;\n\t\t\n\t\tauto sib=tr.begin(it);\n\t\tfor(unsigned int j=0; j<cb.original.size(); ++j) {\n\t\t\tif(sib->is_integer()) {\n\t\t\t\tif(cb[i][j].begin()->multiplier != sib->multiplier) {\n\t\t\t\t\tdiscard=true;\n\t\t\t\t\tbreak;\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\telse {\n\t\t\t\trep.append_child(vcomma, cb[i][j].begin());\n\t\t\t\t}\n\t\t\t++sib;\n\t\t\t}\n\t\tif(!discard) {\n\t\t\tauto one = rep.append_child(equals, str_node(\"1\"));\n\t\t\tmultiply(one->multiplier, cb.ordersign(i));\n\t\t\t}\n\t\telse {\n\t\t\trep.erase(equals);\n\t\t\t}\n\t\t//\t\tstd::cerr << std::endl;\n\t\t}\n\n\tit=tr.move_ontop(it, rep.begin());\n\treturn it;\n\t}\n\nvoid evaluate::simplify_components(iterator it, bool run_sympy)\n\t{\n\tassert(*it->name==\"\\\\components\");\n\n\t// Simplify the components of the now single \\component node by\n\t// calling the scalar backend.  We feed it the components\n\t// individually.\n\tsibling_iterator lst = tr.end(it);\n\t--lst;\n\n\tcadabra::collect_terms collect(kernel, tr);\n\tcadabra::simplify simp(kernel, tr);\n\tsimp.set_progress_monitor(pm);\n\n\tcadabra::do_list(tr, lst, [&](Ex::iterator eqs) {\n\t\tassert(*eqs->name==\"\\\\equals\");\n\t\tauto rhs1 = tr.begin(eqs);\n\t\t++rhs1;\n\t\titerator nd=rhs1;\n\t\tif(collect.can_apply(nd))\n\t\t\tcollect.apply(nd);\n\n\t\tif(run_sympy && !nd->is_zero()) {\n\t\t\tScopedProgressGroup group(pm, \"scalar_backend\");\n\t\t\t// std::cerr << \"simplify at \" << Ex(nd) << std::endl;\n\t\t\tsimp.apply_generic(nd, false, false, 0);\n\t\t\t}\n\t\tif(nd->is_zero()) {\n\t\t\t// std::cerr << \"component zero \" << nd << std::endl;\n\t\t\ttr.erase(eqs);\n\t\t\t}\n\t\telse {\n\t\t\t// std::cerr << \"component non-zero \" << nd << std::endl;\n\t\t\t}\n\t\treturn true;\n\t\t});\n\n\t// Note: the 'erase' in the loop above may have left us with a\n\t// \\components node with an empty list of component values. However,\n\t// since all logic expects to find a \\component node, we do NOT yet\n\t// replace this with a scalar zero here.\n\t}\n\nAlgorithm::iterator evaluate::wrap_scalar_in_components_node(iterator sib)\n\t{\n\t// FIXME: would be good if we could write this in a more readable form.\n\tauto eq=tr.wrap(sib, str_node(\"\\\\equals\"));\n\ttr.prepend_child(eq, str_node(\"\\\\comma\"));\n\teq=tr.wrap(eq, str_node(\"\\\\comma\"));\n\tsib=tr.wrap(eq, str_node(\"\\\\components\"));\n\treturn sib;\n\t}\n\nvoid evaluate::unwrap_scalar_in_components_node(iterator it)\n\t{\n\t// To apply to a scalar function: remove all scalars wrapped in\n\t// components nodes and make them normal scalars again.\n\tauto sib=tr.begin(it);\n\twhile(sib!=tr.end(it)) {\n\t\tif(*sib->name==\"\\\\components\") {\n\t\t\titerator tmp=sib;\n\t\t\t::cleanup_components(kernel, tr, tmp);\n\t\t\t}\n\t\t++sib;\n\t\t}\n\t}\n\nEx::iterator evaluate::handle_prod(iterator it)\n\t{\n\t// std::cerr << \"handle_prod \" << Ex(it) << std::endl;\n\n\tstd::string prod_name=*it->name;\n\t\n\t// All factors are either \\component nodes, pure scalar nodes, or nodes which still need replacing.\n\t// The handle_factor function takes care of the latter two.\n\n\tsibling_iterator sib=tr.begin(it);\n\twhile(sib!=tr.end(it)) {\n\t\tsibling_iterator nxt=sib;\n\t\t++nxt;\n\n\t\tif(*sib->multiplier==0) { // zero factors make the entire product zero.\n\t\t\tnode_zero(it);\n\t\t\treturn it;\n\t\t\t}\n\n\t\tif(is_component(sib)==false) {\n\t\t\tIndexClassifier::index_map_t empty;\n\t\t\thandle_factor(sib, empty);\n\t\t\t}\n\n\t\tsib=nxt;\n\t\t}\n\n\t// TRACE: If a factor has not had a rule match, it will be left\n\t// un-evaluated here. So you get\n\t//  X^{a} \\component_{a}( 0=3, 2=-5 )\n\t// and then we fail lower down. What we could do is let\n\t// handle_factor write out such unevaluated expressions to\n\t// component ones. That's somewhat wasteful though.\n\n#ifdef DEBUG\n\tstd::cerr << \"every factor a \\\\components:\\n\" << Ex(it) << std::endl;\n#endif\n\n\t// Now every factor in the product is a \\component node.  The thing\n\t// is effectively a large sparse tensor product. We need to do the\n\t// sums over the dummy indices, turning this into a single\n\t// \\component node.\n\n\tIndexClassifier ic(kernel);\n\tIndexClassifier::index_map_t ind_free, ind_dummy;\n\tic.classify_indices(it, ind_free, ind_dummy);\n\n\tauto di = ind_dummy.begin();\n\t// Since no factor can be a sum anymore, dummy indices always occur in pairs,\n\t// there is no need to account for anything more tricky. Every pair leads\n\t// to a sum.\n\twhile(di!=ind_dummy.end()) {\n\t\tauto di2=di;\n\t\t++di2;\n\t\tint num1 = tr.index(di->second);\n\t\tint num2 = tr.index(di2->second);\n\t\t// std::cerr << *(di->first.begin()->name)\n\t\t// << \" is index \" << num1 << \" in first and index \" << num2 << \" in second node \" << std::endl;\n\n\t\t// three cases:\n\t\t//    two factors, single index in common. Merge is simple.\n\t\t//    two factors, more than one index in common. After merging this turns into:\n\t\t//    single factor, self-contraction\n\n\t\tauto cit1 = tr.parent(di->second);\n\t\tauto cit2 = tr.parent(di2->second);\n\n\t\t// Are the components objects cit1, cit2 on which these indices sit the same one?\n\t\tif(cit1 != cit2) {\n\t\t\t// Walk through all components of the first tensor, and for each check whether\n\t\t\t// any of the components of the second tensor matches the value for this dummy\n\t\t\t// index.\n\t\t\tsibling_iterator sib1=tr.end(cit1);\n\t\t\t--sib1;\n\t\t\tsibling_iterator sib2=tr.end(cit2);\n\t\t\t--sib2;\n\n\t\t\t// Move all indices of the second tensor to be indices of the first.\n\t\t\tsibling_iterator mv=tr.begin(cit2);\n\t\t\twhile(mv!=sib2) {\n\t\t\t\tsibling_iterator nxt=mv;\n\t\t\t\t++nxt;\n\t\t\t\ttr.move_before(sib1, mv);\n\t\t\t\tmv=nxt;\n\t\t\t\t}\n\n\t\t\tcadabra::do_list(tr, sib1, [&](Ex::iterator it1) {\n\t\t\t\tif(*it1->name!=\"\\\\equals\")\n\t\t\t\t\tthrow InternalError(\"evaluate::handle_prod: encountered non-equals node evaluating components.\");\n\n\t\t\t\tauto lhs1 = tr.begin(it1);\n\t\t\t\tauto ivalue1 = tr.begin(lhs1);\n\t\t\t\tivalue1 += num1;\n\t\t\t\tcadabra::do_list(tr, sib2, [&](Ex::iterator it2) {\n\t\t\t\t\tassert(*it2->name==\"\\\\equals\");\n\t\t\t\t\tauto lhs2 = tr.begin(it2);\n\t\t\t\t\tauto ivalue2 = tr.begin(lhs2);\n\t\t\t\t\tivalue2 += num2;\n\n\t\t\t\t\t// Compare the two index values in the two tensors, only continue if\n\t\t\t\t\t// these are the same.\n\t\t\t\t\t// std::cerr << \"comparing value \" << *ivalue1->name << \" with \" << *ivalue2->name << std::endl;\n\t\t\t\t\t// std::cerr << \"                \" << &(*ivalue1) << \" vs \" << &(*ivalue2) << std::endl;\n\t\t\t\t\tif(tr.equal_subtree(ivalue1,ivalue2)) {\n\t\t\t\t\t\t// Create new merged index value set.\n\t\t\t\t\t\tEx ivs(\"\\\\equals\");\n\t\t\t\t\t\tauto ivs_lhs = tr.append_child(ivs.begin(), str_node(\"\\\\comma\"));\n\t\t\t\t\t\tauto ivs_rhs = tr.append_child(ivs.begin(), str_node(prod_name));\n\t\t\t\t\t\tauto ci = tr.begin(lhs1);\n\t\t\t\t\t\tint n=0;\n\t\t\t\t\t\twhile(ci!=tr.end(lhs1)) {\n\t\t\t\t\t\t\tif(n!=num1)\n\t\t\t\t\t\t\t\tivs.append_child(ivs_lhs, iterator(ci));\n\t\t\t\t\t\t\t++ci;\n\t\t\t\t\t\t\t++n;\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\tci = ivs.begin(lhs2);\n\t\t\t\t\t\tn=0;\n\t\t\t\t\t\twhile(ci!=ivs.end(lhs2)) {\n\t\t\t\t\t\t\tif(n!=num2)\n\t\t\t\t\t\t\t\tivs.append_child(ivs_lhs, iterator(ci));\n\t\t\t\t\t\t\t++ci;\n\t\t\t\t\t\t\t++n;\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\tauto rhs1=lhs1;\n\t\t\t\t\t\t++rhs1;\n\t\t\t\t\t\tivs.append_child(ivs_rhs, iterator(rhs1));\n\t\t\t\t\t\tauto rhs2=lhs2;\n\t\t\t\t\t\t++rhs2;\n\t\t\t\t\t\tivs.append_child(ivs_rhs, iterator(rhs2));\n\t\t\t\t\t\t//std::cerr << \"ivs_rhs = \" << Ex(ivs_rhs) << std::endl;\n\t\t\t\t\t\tcleanup_dispatch_deep(kernel, ivs);\n\t\t\t\t\t\t// Insert this new index value set before sib1, so that it will not get used\n\t\t\t\t\t\t// inside the outer loop.\n\t\t\t\t\t\ttr.move_before(it1, ivs.begin());\n\t\t\t\t\t\t}\n\t\t\t\t\treturn true;\n\t\t\t\t\t});\n\t\t\t\t// This index value set can now be erased as all\n\t\t\t\t// possible combinations have been considered.\n\t\t\t\ttr.erase(it1);\n\t\t\t\treturn true;\n\t\t\t\t});\n\t\t\t// Remove the dummy indices from the index set of tensor 1.\n\t\t\ttr.erase(di->second);\n\t\t\ttr.erase(di2->second);\n\t\t\t// Tensor 2 can now be removed from the product as well, as all information is now\n\t\t\t// part of tensor 1.\n\t\t\ttr.erase(cit2);\n\t\t\t}\n\n\t\telse {\n\t\t\t// Components objects cit1 and cit2 are actually the same. We just need to\n\t\t\t// do a single loop now, going over all index value sets and keeping those\n\t\t\t// for which the num1-th and num2-th value are identical.\n\n\t\t\tsibling_iterator sib1=tr.end(cit1);\n\t\t\t--sib1;\n\n\t\t\tcadabra::do_list(tr, sib1, [&](Ex::iterator it1) {\n\t\t\t\tassert(*it1->name==\"\\\\equals\");\n\t\t\t\tauto lhs = tr.begin(it1);\n\t\t\t\tauto ivalue1 = tr.begin(lhs);\n\t\t\t\tauto ivalue2 = ivalue1;\n\t\t\t\tivalue1 += num1;\n\t\t\t\tivalue2 += num2;\n\t\t\t\tif(tr.equal_subtree(ivalue1,ivalue2)) {\n\t\t\t\t\ttr.erase(ivalue1);\n\t\t\t\t\ttr.erase(ivalue2);\n\t\t\t\t\t}\n\t\t\t\telse {\n\t\t\t\t\ttr.erase(it1);\n\t\t\t\t\t}\n\t\t\t\treturn true;\n\t\t\t\t}\n\t\t\t                );\n\t\t\ttr.erase(di->second);\n\t\t\ttr.erase(di2->second);\n\t\t\t}\n\n\t\t++di;\n\t\t++di;\n\t\t}\n\n\t// TRACE: are we still ok here? Looks ok: one component node\n\t// with no indices.\n\t// std::cerr << \"Before doing outer product:\\n\" << Ex(it) << std::endl;\n\n\t// At this stage we have one or more components nodes in the product,\n\t// and we have collected all possible index value combinations.\n\t// We need to do an outer multiplication, merging all index names into\n\t// one, and computing tensor component values for all possible index values.\n\n\tint n=tr.number_of_children(it);\n\t// std::cerr << \"outer product:\\n\" << Ex(it) << std::endl;\n\tif(n>1) {\n\t\t//std::cerr << \"merging\" << std::endl;\n\t\tauto first=tr.begin(it); // component node\n\t\tauto other=first;\n\t\t++other;\n\t\tauto fi=tr.end(first);\n\t\t--fi;\n\t\t// Add the free indices of 'other' to 'first'.\n\t\twhile(other!=tr.end(it)) {\n\t\t\tauto oi=tr.begin(other);\n\t\t\twhile(oi!=tr.end(other)) {\n\t\t\t\tif(oi->is_index()==false)\n\t\t\t\t\tbreak;\n\t\t\t\ttr.insert_subtree(fi, oi);\n\t\t\t\t++oi;\n\t\t\t\t}\n\t\t\t++other;\n\t\t\t}\n\n\t\t// Now do an outer combination of all possible indexvalue/componentvalue\n\t\t// in the various component nodes.\n\t\tauto comma1=tr.end(first);\n\t\t--comma1;\n\t\tother=first;\n\t\t++other;\n\t\twhile(other!=tr.end(it)) {\n\t\t\tEx newcomma(\"\\\\comma\"); // List of index value combinations and associated component values\n\t\t\tauto comma2=tr.end(other);\n\t\t\t--comma2;\n\t\t\tassert(*comma1->name==\"\\\\comma\");\n\t\t\tassert(*comma2->name==\"\\\\comma\");\n\t\t\tauto eq1=tr.begin(comma1);    // The \\equals node\n\t\t\twhile(eq1!=tr.end(comma1)) {\n\t\t\t\tauto eq2=tr.begin(comma2);\n\t\t\t\twhile(eq2!=tr.end(comma2)) {\n\t\t\t\t\t// Collect all index values.\n\t\t\t\t\tauto neq = newcomma.append_child(newcomma.begin(), str_node(\"\\\\equals\"));\n\t\t\t\t\tauto ncm = newcomma.append_child(neq, str_node(\"\\\\comma\")); // List of index values\n\t\t\t\t\tauto iv=tr.begin(tr.begin(eq1));\n\t\t\t\t\twhile(iv!=tr.end(tr.begin(eq1))) {\n\t\t\t\t\t\tnewcomma.append_child(ncm, iterator(iv));\n\t\t\t\t\t\t++iv;\n\t\t\t\t\t\t}\n\t\t\t\t\tiv=tr.begin(tr.begin(eq2));\n\t\t\t\t\twhile(iv!=tr.end(tr.begin(eq2))) {\n\t\t\t\t\t\tnewcomma.append_child(ncm, iterator(iv));\n\t\t\t\t\t\t++iv;\n\t\t\t\t\t\t}\n\t\t\t\t\t// Multiply component values.\n\t\t\t\t\tEx prod(*it->name);\n\t\t\t\t\tiv=tr.end(eq1);\n\t\t\t\t\t--iv;\n\t\t\t\t\tprod.append_child(prod.begin(), iterator(iv));\n\t\t\t\t\tiv=tr.end(eq2);\n\t\t\t\t\t--iv;\n\t\t\t\t\tprod.append_child(prod.begin(), iterator(iv));\n\t\t\t\t\tcleanup_dispatch_deep(kernel, prod);\n\t\t\t\t\tnewcomma.append_child(neq, prod.begin());\n\t\t\t\t\t++eq2;\n\t\t\t\t\t}\n\t\t\t\t++eq1;\n\t\t\t\t}\n\t\t\t// Now replace the original comma1 node with newcomma, and re-iterate if there\n\t\t\t// are further factors in the tensor product.\n\t\t\tcomma1 = tr.move_ontop(iterator(comma1), newcomma.begin());\n\t\t\tother=tr.erase(other);\n\t\t\t}\n\t\t//\t\tstd::cerr << Ex(it) << std::endl;\n\t\t}\n\n\t// At this stage, there should be only one factor in the product, which\n\t// should be a \\components node. We do a cleanup, after which it should be\n\t// at the 'it' node.\n\n\tassert(*it->name==\"\\\\prod\" || *it->name==\"\\\\wedge\" || *it->name==\"\\\\frac\");\n\tassert(tr.number_of_children(it)==1);\n\tassert(*tr.begin(it)->name==\"\\\\components\");\n\ttr.begin(it)->fl.bracket=it->fl.bracket;\n\ttr.begin(it)->fl.parent_rel=it->fl.parent_rel;\n\ttr.begin(it)->multiplier=it->multiplier;\n\ttr.flatten(it);\n\tit=tr.erase(it);\n\tpush_down_multiplier(kernel, tr, it);\n\n\t//\titerator pr=tr.end();\n\t//\tif(tr.is_head(it)==false) {\n\t//\t\tpr=tr.parent(it);\n\t//\t\tstd::cerr << \"Tracing just before merge:\\n \" << Ex(pr) << std::endl;\n\t//\t\t}\n\n\tmerge_component_children(it);\n\n\t//\tif(pr!=tr.end())\n\t//\t\tstd::cerr << \"after component merge:\\n \" << Ex(pr) << std::endl;\n\n\t//\tcleanup_dispatch(kernel, tr, it);\n\t//\tif(pr!=tr.end())\n\t//\t\tstd::cerr << \"And afterwards:\\n \" << Ex(pr) << std::endl;\n\n\tif(*it->name!=\"\\\\components\") {\n\t\t// The result is a scalar. Because we are expected to return\n\t\t// a \\components node, we wrap this scalar again.\n\t\t// std::cerr << \"wrapping scalar\" << std::endl;\n\t\tit=wrap_scalar_in_components_node(it);\n\t\t// std::cerr << Ex(it) << std::endl;\n\t\t}\n\n\t//\telse {\n\t//\t\t// We may have duplicate index value entries; merge them.\n\t//\t\tmerge_component_children(it);\n\t//\t\t}\n\n\t// Use sympy to simplify components.\n\tif(call_sympy)\n\t\tsimplify_components(it, true);\n\t//std::cerr << \"simplified:\\n\" << Ex(it) << std::endl;\n\n\treturn it;\n\t}\n"
  },
  {
    "path": "core/algorithms/evaluate.cnb",
    "content": "{\n\t\"cell_id\": 12848684247103127310,\n\t\"cells\": [\n\t\t{\n\t\t\t\"cell_id\": 568579371302751307,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 2629240782162725687,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\algorithm{evaluate}{Evaluate components of a tensor expression.}\\n\\nGiven an abstract tensor expression and a set of rules for the components of tensors occurring in this\\nexpression, evaluate the components of the full expression. \\n\\nThe minimal information needed for this to work is a declaration of the indices used, and a declaration\\nof the values that those indices use:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\algorithm{evaluate}{Evaluate components of a tensor expression.}\\n\\nGiven an abstract tensor expression and a set of rules for the components of tensors occurring in this\\nexpression, evaluate the components of the full expression. \\n\\nThe minimal information needed for this to work is a declaration of the indices used, and a declaration\\nof the values that those indices use:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 2078015025997043999,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9266946584051970342,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 15728930163650799218,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"A_{n m} B_{m n p} (C_{p s} + D_{s p})\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}A_{n m} B_{m n p} \\\\left(C_{p s}\\\\discretionary{}{}{}+D_{s p}\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"{r,t}::Coordinate.\\n{m,n,p,s}::Indices(values={t,r}).\\nex:= A_{n m} B_{m n p} ( C_{p s} + D_{s p} );\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 17956085546737297170,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 3763835295602699573,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"The list of component values should be given just like the list of rules for the \\\\algo{substitute} algorithm,\\nthat is, as equalities\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"The list of component values should be given just like the list of rules for the \\\\algo{substitute} algorithm,\\nthat is, as equalities\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 11806603033878949925,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 13826571149734596415,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 1251294511456819363,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"{A_{r t} = 3, B_{t r t} = 2, B_{t r r} = 5, C_{t r} = 1, D_{r t} = (r)**2 t, D_{t r} = (t)**2}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\left[A_{r t} = 3, \\\\discretionary{}{}{}B_{t r t} = 2, \\\\discretionary{}{}{}B_{t r r} = 5, \\\\discretionary{}{}{}C_{t r} = 1, \\\\discretionary{}{}{}D_{r t} = {r}^{2} t, \\\\discretionary{}{}{}D_{t r} = {t}^{2}\\\\right]\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"rl:= [ A_{r t} = 3, B_{t r t} = 2, B_{t r r} = 5, C_{t r} = 1, D_{r t} = r**2*t, D_{t r}=t**2 ];\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 18162993330426165363,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 6035873025174353872,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"The \\\\algo{evaluate} algorithm then works out the values of the components of the \\\\verb|ex| expression,\\nwhich will be denoted with a 'box' in its output,\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"The \\\\algo{evaluate} algorithm then works out the values of the components of the \\\\verb|ex| expression,\\nwhich will be denoted with a 'box' in its output,\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 3880092560523380842,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 3635984866168871304,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 17411792686607445405,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\components_{s}({{r} = 6(r)**2 t + 6, {t} = 15(t)**2})\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\square{}_{s}\\\\left\\\\{\\\\begin{aligned}\\\\square{}_{r}& = 6{r}^{2} t\\\\discretionary{}{}{}+6\\\\\\\\[-.5ex]\\n\\\\square{}_{t}& = 15{t}^{2}\\\\\\\\[-.5ex]\\n\\\\end{aligned}\\\\right.\\n\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"evaluate(ex, rl);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 16974789945816146373,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 16655548642815820416,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"Note how the composite tensor of the original expression is now replaced with an 'anonymous tensor' represented by a box (which carries the free indices of the original expression), and all the components of the tensor are listed.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"Note how the composite tensor of the original expression is now replaced with an 'anonymous tensor' represented by a box (which carries the free indices of the original expression), and all the components of the tensor are listed.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 9913249376624945194,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 8032114875278129016,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"If your indices take numerical values, you can also declare them as \\\\prop{Integer}. The \\\\algo{evaluate} algorithm will then figure out the values from there:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"If your indices take numerical values, you can also declare them as \\\\prop{Integer}. The \\\\algo{evaluate} algorithm will then figure out the values from there:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 2761438120839144926,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 4088067589905719785,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 6539583947178836914,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"A_{1} B^{1} + A_{2} B^{2} + A_{3} B^{3}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}A_{1} B^{1}\\\\discretionary{}{}{}+A_{2} B^{2}\\\\discretionary{}{}{}+A_{3} B^{3}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"{i,j}::Indices(space).\\n{i,j}::Integer(1..3).\\nex:= A_{i} B^{i}.\\nevaluate(ex);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 13109713213385796712,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 11136447634481418270,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"If you have more than one list of rules, first join them together using the \\\\algo{join} function before passing them into \\\\algo{evaluate}:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"If you have more than one list of rules, first join them together using the \\\\algo{join} function before passing them into \\\\algo{evaluate}:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 5846925692051611365,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 1404036796615799154,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 18425308353298514846,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"A_{i} B^{i}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}A_{i} B^{i}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 7610436280164036217,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 8189119321700415733,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"{A_{1} = q1, A_{2} = q2}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\left[A_{1} = {q_{1}}, \\\\discretionary{}{}{}A_{2} = {q_{2}}\\\\right]\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 15240812354154612239,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 1966055837491147281,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"{B^{1} = q3, B^{2} = q4}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\left[B^{1} = {q_{3}}, \\\\discretionary{}{}{}B^{2} = {q_{4}}\\\\right]\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 7995301183036670819,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 5565701434140824771,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"q1 q3 + q2 q4\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}{q_{1}} {q_{3}}\\\\discretionary{}{}{}+{q_{2}} {q_{4}}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex:= A_{i} B^{i};\\nrl1:= { A_{1} = q1, A_{2} = q2 };\\nrl2:= { B^{1} = q3, B^{2} = q4 };\\nevaluate(ex, join(rl1, rl2));  \"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 41392486041367439,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 495491244615516088,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"It often happens that you want to evaluate the components of a tensor only on the right-hand side of an equality, for instance when you are trying to build substitution or evaluation rules for subsequent steps. To do this, use the \\\\verb|rhsonly=True| parameter,\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"It often happens that you want to evaluate the components of a tensor only on the right-hand side of an equality, for instance when you are trying to build substitution or evaluation rules for subsequent steps. To do this, use the \\\\verb|rhsonly=True| parameter,\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 6617057626353331254,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 14376512812725812393,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 15216719651059803265,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"T_{m n} = A_{m p} B_{p n}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}T_{m n} = A_{m p} B_{p n}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 13467593821493845773,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 8748930232162884806,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"T_{m n} = \\\\components_{m n}({{r, t} = 3B_{t t}, {r, r} = 3B_{t r}})\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}T_{m n} = \\\\square{}_{m}{}_{n}\\\\left\\\\{\\\\begin{aligned}\\\\square{}_{r}{}_{t}& = 3B_{t t}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{r}& = 3B_{t r}\\\\\\\\[-.5ex]\\n\\\\end{aligned}\\\\right.\\n\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex2:= T_{m n} = A_{m p} B_{p n};\\nevaluate(ex2, rl, rhsonly=True); \"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 12322892869467590884,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"\"\n\t\t}\n\t],\n\t\"description\": \"Cadabra JSON notebook format\",\n\t\"version\": 1.0\n}\n"
  },
  {
    "path": "core/algorithms/evaluate.hh",
    "content": "\n#pragma once\n\n#include \"Compare.hh\"\n#include \"IndexClassifier.hh\"\n\n/// \\ingroup algorithms\n///\n/// Evaluate a tensorial expression to components, performing all\n/// dummy index sums.\n\n/**\n\nSee tests/components.cdb for basic samples.\n\nComponents nodes have the following structure:\n\n  \\components_{a b ... n}({t,t,...r}=value, {t,t,...r}=value, ...)\n\n\n\t\t\t\\verbatim\n\n  \t\t\t\\components\n     _{m}            // index names/types\n     _{n}\n     \t\t\t\\comma          // last child\n         \t\t\t\\equals\n            \t\t\t\\comma   // list of index values\n                \tr\n                \tt\n            [value]  // value of tensor for above values of indices\n         \t\t\t\\equals\n            \t...\n         \t\t\t\\equals\n            \t...\n\n\n  \tex:= A_{m n} ( A_{m n} + B_{m n} );\n  \tcrds:= m -> { t, r, \\phi, \\theta };\n  \tvals:= { A_{t t} -> r, A_{r r} -> r**2, A_{t \\phi} -> t, B_{t t} -> 1 };\n  \tevaluate(ex, crds, vals);\n  \ttst:= r * ( r + 1 ) + r**2 * r**2 + t*t - @(ex);\n\n\t\t\t\\endverbatim\n\nThe algorithm performs\n\tthe following steps.  First, all free and dummy indices are\n\tclassified using members of Algorithm (maybe later?). For all indices, the 'crds'\n\targument to the algorithm is scanned for a\n\n\t\t\t\\verbatim\n\n     \tm -> { a,b,c }\n\n\t\t\t\\endverbatim\n\n\ttype pattern.\n\nDo a dept-first scan until the first sum or product node.\n\n  In a sum node, all terms must have the same index structure, so\n  we can now make a map from the subtree pattern to all possible\n  \tindex values. For each such index value set, lookup if there is a\n  \treplacement pattern, if not replace by zero.  This map can be\n  \treused later for equal sub-expressions (here it is important that\n  \ta normal tensor expression can be used as a pattern immediately,\n  \tthough I would search both on explicit iterator (for things that\n  we have just seen) and on pattern (for things that occur again\n  \tlater in the tree)).\n\n  In a product node, find all dummies and free indices. Create a\n  \tset of all index value sets, e.g.\n\n  \t\t\t\\verbatim\n\n     \t\t\t{m, n, p} ->\n      \t\t\t{ {t, t, t}, {r,t,t}, {t,r,t}, ... }\n\n  \t\t\t\\endverbatim\n\n  For each such index value set, lookup replacement rules.\n\n  KEY: quick way to lookup, for a given set of index values on a\n  (found) pattern/pattern pointed to by iterator, whether and what is the\n  \tvalue of the pattern.\n\n\n*/\n\n#include \"Algorithm.hh\"\n#include \"properties/Indices.hh\"\n\nnamespace cadabra {\n\n\tclass evaluate : public Algorithm {\n\t\tpublic:\n\t\t\tevaluate(const Kernel&, Ex&, const Ex& component_values, bool rhs=false, bool simplify=true);\n\n\t\t\tvirtual bool     can_apply(iterator) override;\n\t\t\tvirtual result_t apply(iterator&) override;\n\n\t\t\t/// Merge the information in two 'components' nodes at the given\n\t\t\t/// iterators, moving all out of the second one into the first\n\t\t\t/// one.\n\t\t\tvoid merge_components(iterator it1, iterator it2);\n\n\t\t\t/// Simplify all components of a 'components' node by\n\t\t\t/// collecting terms and optionally running sympy's simplify\n\t\t\t/// on them. Returns a replacement iterator to the\n\t\t\t/// top. Removes entries for vanishing components.\n\t\t\tvoid simplify_components(iterator, bool run_sympy=true);\n\n\t\tprivate:\n\t\t\tconst Ex& components;\n\t\t\tbool only_rhs, call_sympy;\n\n\t\t\tbool is_component(iterator it) const;\n\t\t\tbool is_scalar_function(iterator it) const;\n\n\t\t\titerator handle_components(iterator it);\n\t\t\titerator handle_sum(iterator it);\n\t\t\titerator handle_prod(iterator it);\n\t\t\titerator handle_derivative(iterator it);\n\t\t\titerator handle_epsilon(iterator it);\n\n\t\t\t/// Replace a single factor with a 'components' ...\n\t\t\t/// The full_ind_free argument can contain a list of indices in the order\n\t\t\t/// in which values should be stored in index value sets.\n\n\t\t\titerator handle_factor(sibling_iterator sib, const IndexClassifier::index_map_t& full_ind_free);\n\n\t\t\t/// Expand a tensor factor into a components node with all components\n\t\t\t/// written out explicitly. Used when there is no sparse rule matching\n\t\t\t/// this factor.\n\t\t\titerator dense_factor(iterator sib, const IndexClassifier::index_map_t& ind_free,\n\t\t\t\t\t\t\t\t\t\t const IndexClassifier::index_map_t& ind_dummy);\n\n\t\t\t/// Merge entries in a single 'components' node when they are for the\n\t\t\t/// same index value(s).\n\t\t\tvoid merge_component_children(iterator it);\n\n\t\t\t/// Cleanup all components in a 'components' node; that is, call the\n\t\t\t/// cleanup_dispatch function on them.\n\t\t\tvoid cleanup_components(iterator it1);\n\n\t\t\t/// Wrap a non-component scalar node in a 'components' node.\n\t\t\titerator wrap_scalar_in_components_node(iterator sib);\n\n\t\t\t/// Inverse of the above.\n\t\t\tvoid     unwrap_scalar_in_components_node(iterator sib);\n\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/algorithms/expand.cc",
    "content": "\n#include \"Cleanup.hh\"\n#include \"Exceptions.hh\"\n#include \"IndexClassifier.hh\"\n#include \"algorithms/expand.hh\"\n#include \"properties/Matrix.hh\"\n\nusing namespace cadabra;\n\nexpand::expand(const Kernel& k, Ex& e)\n\t: Algorithm(k, e)\n\t{\n\t}\n\nindex_iterator expand::nth_implicit_index(Ex::iterator eform, Ex::iterator iform, unsigned int n)\n\t{\n\tunsigned int hits=0;\n\tindex_iterator ch1=begin_index(eform);\n\twhile(ch1!=end_index(eform)) {\n\t\tbool found=false;\n\t\tindex_iterator ch2=begin_index(iform);\n\t\twhile(!found && ch2!=end_index(iform)) {\n\t\t\tif(*ch1->name==*ch2->name) found=true;\n\t\t\t++ch2;\n\t\t\t}\n\t\tif(!found) ++hits;\n\t\tif(hits==n) return ch1;\n\t\t++ch1;\n\t\t}\n\treturn ch1;\n\t}\n\nbool expand::can_apply(iterator it)\n\t{\n\tif(*it->name==\"\\\\indexbracket\")\n\t\tif(*tr.begin(it)->name==\"\\\\prod\") {\n\t\t\t// If we have only one external index, determine whether the first\n\t\t\t// or the last object should be the one with only one index. We\n\t\t\t// do this by checking for the 'Matrix' property on the first and\n\t\t\t// last element.\n\t\t\tcheck_pos=false;\n\t\t\tone_index=(tr.number_of_children(it)==2);\n\t\t\tsibling_iterator prod=tr.begin(it);\n\t\t\tsibling_iterator sib=tr.begin(prod);\n\t\t\tsibling_iterator ind1=prod;\n\t\t\t++ind1;\n\t\t\tsibling_iterator ind2=ind1;\n\t\t\tif(!one_index) ++ind2;\n\t\t\tconst Indices *props=kernel.properties.get<Indices>(ind1, true);\n\t\t\t// For this to stay true, every factor below must come with an\n\t\t\t// index structure. If it is missing even once, we will not be\n\t\t\t// able to guess what the user really meant.\n\t\t\tif(props && props->position_type!=Indices::free) check_pos=true;\n\n\t\t\tmx_first=tr.end();\n\t\t\tmx_last=tr.end();\n\t\t\tii_first=tr.end();\n\t\t\tii_last=tr.end();\n\n\t\t\tunsigned int index_open=0;\n\n\t\t\twhile(sib!=tr.end(prod)) {\n\t\t\t\tint tmp;\n\t\t\t\tauto impi=kernel.properties.get_with_pattern<ImplicitIndex>(sib, tmp, \"\");\n\t\t\t\tif(impi.first) {\n\t\t\t\t\tconst Matrix *mat=kernel.properties.get<Matrix>(sib);\n\t\t\t\t\tif(mat) {\n\t\t\t\t\t\tif(index_open==0) {\n\t\t\t\t\t\t\tmx_first=sib;\n\t\t\t\t\t\t\tindex_open=2;\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\tmx_last=sib;\n\t\t\t\t\t\t// If an explicit form exists, verify that it has\n\t\t\t\t\t\t// exactly two more indices than the implicit one.\n\t\t\t\t\t\tif(impi.first->explicit_form.size()>0) {\n\t\t\t\t\t\t\tEx::iterator eform=impi.first->explicit_form.begin();\n\t\t\t\t\t\t\tEx::iterator iform=impi.second->obj.begin();\n\t\t\t\t\t\t\tif(tr.number_of_children(eform)-tr.number_of_children(iform)!=2) {\n\t\t\t\t\t\t\t\tthrow ConsistencyException(\"Matrices should have two implicit indices.\");\n\t\t\t\t\t\t\t\treturn false;\n\t\t\t\t\t\t\t\t}\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\telse check_pos = false;\n\t\t\t\t\t\t}\n\t\t\t\t\telse {\n\t\t\t\t\t\tif(index_open==0) {\n\t\t\t\t\t\t\tii_first=sib;\n\t\t\t\t\t\t\tmx_first=tr.end();\n\t\t\t\t\t\t\tindex_open=1;\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\telse {\n\t\t\t\t\t\t\tii_last=sib;\n\t\t\t\t\t\t\tmx_last=tr.end();\n\t\t\t\t\t\t\t--index_open;\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\t// If an explicit form exists, verify that it has\n\t\t\t\t\t\t// exactly one more index than the implicit one.\n\t\t\t\t\t\tif(impi.first->explicit_form.size()>0) {\n\t\t\t\t\t\t\tEx::iterator eform=impi.first->explicit_form.begin();\n\t\t\t\t\t\t\tEx::iterator iform=impi.second->obj.begin();\n\t\t\t\t\t\t\tif(tr.number_of_children(eform)-tr.number_of_children(iform)!=1) {\n\t\t\t\t\t\t\t\tthrow ConsistencyException(\"Vectors should have one implicit index.\");\n\t\t\t\t\t\t\t\treturn false;\n\t\t\t\t\t\t\t\t}\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\telse check_pos=false;\n\t\t\t\t\t\t}\n\t\t\t\t\t}\n\t\t\t\t++sib;\n\t\t\t\t}\n\n\t\t\tif(check_pos && mx_first!=tr.end()) {\n\t\t\t\tint tmp;\n\t\t\t\tauto impi=kernel.properties.get_with_pattern<ImplicitIndex>(mx_first, tmp, \"\");\n\t\t\t\tEx::iterator eform=impi.first->explicit_form.begin();\n\t\t\t\tEx::iterator iform=impi.second->obj.begin();\n\t\t\t\tindex_iterator ch1=nth_implicit_index(eform, iform, 1);\n\t\t\t\tif(ch1->fl.parent_rel!=ind1->fl.parent_rel) {\n\t\t\t\t\tthrow ConsistencyException(\"Bracket index structure is not compatible with the factors.\");\n\t\t\t\t\treturn false;\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\tif(check_pos && mx_last!=tr.end()) {\n\t\t\t\tint tmp;\n\t\t\t\tauto impi=kernel.properties.get_with_pattern<ImplicitIndex>(mx_last, tmp, \"\");\n\t\t\t\tEx::iterator eform=impi.first->explicit_form.begin();\n\t\t\t\tEx::iterator iform=impi.second->obj.begin();\n\t\t\t\tindex_iterator ch1=nth_implicit_index(eform, iform, 2);\n\t\t\t\tif(ch1->fl.parent_rel!=ind2->fl.parent_rel) {\n\t\t\t\t\tthrow ConsistencyException(\"Bracket index structure is not compatible with the factors.\");\n\t\t\t\t\treturn false;\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\tif(index_open+1==tr.number_of_children(it)) return true;\n\t\t\t}\n\treturn false;\n\t}\n\nAlgorithm::result_t expand::apply(iterator& it)\n\t{\n\tsibling_iterator prod=tr.begin(it); // the first child of the indexbracket is the product\n\n\t// Figure out the type of the indices to be inserted.\n\tsibling_iterator origind=prod;\n\t++origind;\n\tconst Indices *dums=kernel.properties.get<Indices>(origind, true);\n\tif(!dums)\n\t\tthrow ConsistencyException(\"No information about the index types known.\");\n\n\t// Scan through the factors, adding indexbrackets around any\n\t// objects which already carry indices, and adding new\n\t// dummies when necessary.\n\tIndexClassifier ic(kernel);\n\t\n\tsibling_iterator sib=tr.begin(prod);\n\tEx dum;\n\twhile(sib!=tr.end(prod)) {\n\t\tint tmp;\n\t\tauto impi=kernel.properties.get_with_pattern<ImplicitIndex>(sib, tmp, \"\");\n\t\tsib->fl.bracket=str_node::b_none;\n\t\tif(impi.first) {\n\t\t\tconst Matrix *mat=kernel.properties.get<Matrix>(sib);\n\t\t\tsibling_iterator origobj=sib;\n\n\t\t\tif(tr.number_of_children(sib)>0)\n\t\t\t\tsib=tr.wrap(sib, str_node(\"\\\\indexbracket\"));\n\t\t\tif(dum.size()>0) {\n\t\t\t\titerator tmpit=tr.append_child((iterator)(sib), dum.begin());\n\t\t\t\ttmpit->fl.bracket=str_node::b_none;\n\t\t\t\tif(check_pos) {\n\t\t\t\t\tEx::iterator eform=impi.first->explicit_form.begin();\n\t\t\t\t\tEx::iterator iform=impi.second->obj.begin();\n\t\t\t\t\tindex_iterator ch=nth_implicit_index(eform, iform, 1);\n\t\t\t\t\ttmpit->fl.parent_rel=ch->fl.parent_rel;\n\t\t\t\t\t}\n\t\t\t\telse tmpit->fl.parent_rel=str_node::p_sub;\n\t\t\t\t}\n\n\t\t\tif(mat) { // two-index object\n\t\t\t\tif(origobj==mx_first) { // put in an open index\n\t\t\t\t\ttr.append_child(sib, origind);\n\t\t\t\t\torigind=tr.erase(origind);\n\t\t\t\t\t}\n\t\t\t\tif(origobj==mx_last) {\n\t\t\t\t\ttr.append_child(sib, origind);\n\t\t\t\t\torigind=tr.erase(origind);\n\t\t\t\t\t}\n\t\t\t\telse {\n\t\t\t\t\tdum=ic.get_dummy(dums, sib);\n\t\t\t\t\titerator tmpit=tr.append_child((iterator)(sib), dum.begin());\n\t\t\t\t\ttmpit->fl.bracket=str_node::b_none;\n\t\t\t\t\tif(check_pos) {\n\t\t\t\t\t\tEx::iterator eform=impi.first->explicit_form.begin();\n\t\t\t\t\t\tEx::iterator iform=impi.second->obj.begin();\n\t\t\t\t\t\tindex_iterator ch=nth_implicit_index(eform, iform, 2);\n\t\t\t\t\t\ttmpit->fl.parent_rel=ch->fl.parent_rel;\n\t\t\t\t\t\t}\n\t\t\t\t\telse tmpit->fl.parent_rel=str_node::p_sub;\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\telse {   // one-index object\n\t\t\t\tif(origobj==ii_first) {\n\t\t\t\t\tdum=ic.get_dummy(dums, sib);\n\t\t\t\t\titerator tmpit=tr.append_child((iterator)(sib), dum.begin());\n\t\t\t\t\ttmpit->fl.bracket=str_node::b_none;\n\t\t\t\t\tif(check_pos) {\n\t\t\t\t\t\tEx::iterator eform=impi.first->explicit_form.begin();\n\t\t\t\t\t\tEx::iterator iform=impi.second->obj.begin();\n\t\t\t\t\t\tindex_iterator ch=nth_implicit_index(eform, iform, 1);\n\t\t\t\t\t\ttmpit->fl.parent_rel=ch->fl.parent_rel;\n\t\t\t\t\t\t}\n\t\t\t\t\telse tmpit->fl.parent_rel=str_node::p_sub;\n\t\t\t\t\t}\n\t\t\t\telse dum.clear();\n\t\t\t\t}\n\t\t\t++sib;\n\t\t\t}\n\t\telse ++sib;\n\t\t}\n\n\tit->name=name_set.insert(\"\\\\prod\").first;\n\tcleanup_dispatch(kernel, tr, it);\n\n\treturn result_t::l_applied;\n\t}\n\n"
  },
  {
    "path": "core/algorithms/expand.cnb",
    "content": "{\n\t\"cells\" : \n\t[\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\algorithm{expand}{Write out products of objects with implicit indices.}\\n\\nWrite out products of matrices and vectors inside indexbrackets,\\ninserting new dummy indices for the contraction. This requires that\\nthe objects inside the index bracket are properly declared to\\nhave \\\\prop{Matrix} or \\\\prop{ImplicitIndex} properties.  \\n\\nHere is an example with multiple matrices:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\algorithm{expand}{Write out products of objects with implicit indices.}\\n\\nWrite out products of matrices and vectors inside indexbrackets,\\ninserting new dummy indices for the contraction. This requires that\\nthe objects inside the index bracket are properly declared to\\nhave \\\\prop{Matrix} or \\\\prop{ImplicitIndex} properties.  \\n\\nHere is an example with multiple matrices:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Indices(position=free) to~}\\\\left(a, b, c, d, e\\\\right).\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Matrix to~}\\\\left(A, B, C, D\\\\right).\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\left(A B C D\\\\right)\\\\,_{a b}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"{a,b,c,d,e}::Indices;\\n{A,B,C,D}::Matrix;\\n\\nex:= (A B C D)_{a b};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}A_{a c} B_{c d} C_{d e} D_{e b}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"expand(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"Compare the above to the following example, in which one of the\\nobjects inside the bracket is no longer a matrix:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"Compare the above to the following example, in which one of the\\nobjects inside the bracket is no longer a matrix:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\left(A B Q D\\\\right)\\\\,_{a b}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex:= (A B Q D)_{a b};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}A_{a c} B_{c d} Q D_{d b}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"expand(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"Finally, an example with matrices carrying additional labels, as well\\nas a vector object:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"Finally, an example with matrices carrying additional labels, as well\\nas a vector object:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Indices(position=free) to~}\\\\left(\\\\alpha, \\\\beta\\\\right).\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Matrix to~}\\\\Gamma\\\\left(\\\\#\\\\right).\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property ImplicitIndex to~}v.\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"{\\\\alpha,\\\\beta}::Indices;\\n\\\\Gamma{#}::Matrix;\\nv::ImplicitIndex;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\left(\\\\Gamma_{r} v\\\\right)\\\\,_{\\\\alpha}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex:=(\\\\Gamma_{r} v)_{\\\\alpha};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\left(\\\\Gamma_{r}\\\\right)\\\\,_{\\\\alpha \\\\beta} v_{\\\\beta}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"expand(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1\n}\n"
  },
  {
    "path": "core/algorithms/expand.hh",
    "content": "\n#pragma once\n\n#include \"Algorithm.hh\"\n\nnamespace cadabra {\n\n\tclass expand : public Algorithm {\n\t\tpublic:\n\t\t\texpand(const Kernel&, Ex&);\n\n\t\t\tvirtual bool     can_apply(iterator) override;\n\t\t\tvirtual result_t apply(iterator&) override;\n\n\t\tprivate:\n\t\t\titerator       mx_first, mx_last, ii_first, ii_last;\n\t\t\tbool           one_index, check_pos;\n\t\t\tindex_iterator nth_implicit_index(Ex::iterator eform, Ex::iterator iform, unsigned int n);\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/algorithms/expand_delta.cc",
    "content": "\n#include \"algorithms/expand_delta.hh\"\n#include \"properties/KroneckerDelta.hh\"\n#include \"properties/TableauBase.hh\"\n#include \"Cleanup.hh\"\n\nusing namespace cadabra;\n\n#define ASYM 1\n\nexpand_delta::expand_delta(const Kernel& k, Ex& tr)\n\t: Algorithm(k, tr)\n\t{\n\t}\n\nbool expand_delta::can_apply(iterator st)\n\t{\n\tconst KroneckerDelta *kr=kernel.properties.get<KroneckerDelta>(st);\n\tif(kr)\n\t\tif(tr.number_of_children(st)>2)\n\t\t\treturn true;\n\treturn false;\n\t}\n\nAlgorithm::result_t expand_delta::apply(iterator& st)\n\t{\n\t// std::cerr << \"applying \" << Ex(st) << std::endl;\n\n\tEx rep(\"\\\\sum\");\n\titerator sum=rep.begin();\n\tcombin::combinations<Ex> ci;\n\n#ifdef ASYM\n\t// Determine implicit anti-symmetrisation by looking for anti-symmetric\n\t// tensors in the product (if any). Store these sets in `implicit_sets`.\n\tstd::vector<std::vector<Ex>> implicit_sets;\n\t\n\tif(tr.is_head(st)==false && *(tr.parent(st)->name)==\"\\\\prod\") {\n\t\tsibling_iterator oth=tr.begin(tr.parent(st));\n\t\twhile(oth!=tr.end(tr.parent(st))) {\n\t\t\tif(oth!=st) {\n\t\t\t\tconst TableauBase *tb=kernel.properties.get<TableauBase>(oth);\n\t\t\t\tif(tb) {\n\t\t\t\t\t// std::cerr << \"object \" << oth << \" has symmetry\" << std::endl;\n\t\t\t\t\tfor(unsigned int i=0; i<tb->size(kernel.properties, tr, oth); ++i) {\n\t\t\t\t\t\t// std::cerr << \"object \" << oth << \" tab \" << i << std::endl;\t\t\t\t\t\t\n\t\t\t\t\t\tTableauBase::tab_t tmptab(tb->get_tab(kernel.properties, tr, oth, i));\n\t\t\t\t\t\tfor(unsigned int asset=0; asset<tmptab.row_size(0); ++asset) {\n\t\t\t\t\t\t\tif(tmptab.column_size(asset)>1) {\n\t\t\t\t\t\t\t\t// std::cerr << \"   asym size \" << tmptab.column_size(asset) << std::endl;\n\t\t\t\t\t\t\t\tstd::vector<Ex> iset;\n\t\t\t\t\t\t\t\tfor(unsigned int asel=0; asel<tmptab.column_size(asset); ++asel) {\n\t\t\t\t\t\t\t\t\tint indexnum=tmptab(asel,asset);\n\t\t\t\t\t\t\t\t\tauto oth2=begin_index(oth);\n\t\t\t\t\t\t\t\t\toth2+=indexnum;\n\t\t\t\t\t\t\t\t\tiset.push_back(Ex(oth2));\n\t\t\t\t\t\t\t\t\t}\n\t\t\t\t\t\t\t\tif(iset.size()>1)\n\t\t\t\t\t\t\t\t\timplicit_sets.push_back(iset);\n\t\t\t\t\t\t\t\t}\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\t}\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t++oth;\n\t\t\t}\n\t\t}\n#endif\n\t// std::cerr << implicit_sets.size() << std::endl;\n\t// for(const auto& implicit_set: implicit_sets) {\n\t// \tfor(const auto& implicit_index: implicit_set) {\n\t// \t\tstd::cerr << *implicit_index.begin()->name << \"  \";\n\t// \t\t}\n\t// \tstd::cerr << std::endl;\n\t// \t}\n\n\n\t// Determine the overlap factors. For each index set\n\t// which is to be kept implicitly anti-symmetrised, we need\n\t// to determine how many of those indices actually sit on\n\t// the Kronecker delta. E.g. \\delta^a_m^b_n A_{m n p} will\n\t// have an implicit set [m,n,p], but there are only two\n\t// indices overlapping, so the reduction in number of terms\n\t// is 2, not 6.\n\tmultiplier_t divfactor1=1, divfactor2=1;\n\n#ifdef ASYM\n\tEx_comparator comp(kernel.properties);\n\tfor(const auto& implicit_set: implicit_sets) {\n\t\tunsigned int overlap1=0, overlap2=0;\n\t\tfor(const auto& implicit_index: implicit_set) {\n\t\t\tsibling_iterator ind=tr.begin(st);\n\t\t\tfor(unsigned int pairnum=0; pairnum<tr.number_of_children(st); pairnum+=2) {\n\t\t\t\t// std::cerr << \"does \" << ind << \" match \" << implicit_index.begin() << std::endl;\n\t\t\t\tcomp.clear();\n\t\t\t\tauto m1=comp.equal_subtree(ind, implicit_index.begin(), Ex_comparator::useprops_t::never, true);\n\t\t\t\t// std::cerr << static_cast<int>(m1) << std::endl;\n\t\t\t\tif(m1<=Ex_comparator::match_t::subtree_match) ++overlap1;\n\t\t\t\t++ind;\n\t\t\t\tcomp.clear();\t\t\t\t\n\t\t\t\tauto m2=comp.equal_subtree(ind, implicit_index.begin(), Ex_comparator::useprops_t::never, true);\n\t\t\t\tif(m2<=Ex_comparator::match_t::subtree_match) ++overlap2;\n\t\t\t\t++ind;\n\t\t\t\t}\n\t\t\t}\n\t\tdivfactor1*=combin::fact(overlap1);\n\t\tdivfactor2*=combin::fact(overlap2);\n\t\t}\n#endif\n\n\t// std::cerr << divfactor1 << \", \" << divfactor2 << std::endl;\n\t\n\tbool permute_second_set=(divfactor2>divfactor1);\n\n\t// Construct the original permutation.\n\tsibling_iterator ind=tr.begin(st);\n\tfor(unsigned int pairnum=0; pairnum<tr.number_of_children(st); pairnum+=2) {\n\t\tif(permute_second_set)\n\t\t\t++ind;\n\t\tif(std::find(ci.original.begin(), ci.original.end(), Ex(ind))!=ci.original.end()) {\n\t\t\tzero(st->multiplier);\n\t\t\tcleanup_dispatch(kernel, tr, st);\n\t\t\treturn result_t::l_applied;\n\t\t\t}\n\t\tci.original.push_back(Ex(ind));\n\t\t++ind;\n\t\tif(!permute_second_set)\n\t\t\t++ind;\n\t\tci.sublengths.push_back(1);\n\t\t}\n\n#ifdef ASYM\n\t// Now construct the output asym ranges. \n\tfor(const auto& implicit_set: implicit_sets) {\n\t\tcombin::range_t asymrange1;\n\t\tfor(const auto& implicit_index: implicit_set) {\n\t\t\tfor(unsigned int i1=0; i1<ci.original.size(); ++i1) {\n\t\t\t\tcomp.clear();\t\t\t\t\n\t\t\t\tauto m = comp.equal_subtree(ci.original[i1].begin(), implicit_index.begin(), Ex_comparator::useprops_t::never, true);\n\t\t\t\tif(m<=Ex_comparator::match_t::subtree_match) {\n\t\t\t\t\t// std::cerr << \"add to asymrange: \" << i1 << std::endl;\n\t\t\t\t\tasymrange1.push_back(i1);\n\t\t\t\t\tbreak;\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t}\n\t\tci.input_asym.push_back(asymrange1);\n\t\t}\n#endif\n\t\n\t// Now generate all the permutations of the indices.\n\tci.permute();\n\t// std::cerr << \"number of permutations: \" << ci.size() << std::endl;\n\n\t// For each permutation, add a product of deltas with two indices.\n\tfor(unsigned int permnum=0; permnum<ci.size(); ++permnum) {\n// FIXME: replace with progress indicator\n//\t\tif(permnum%10000==0)\n//\t\t\tstd::cerr << \"permutation \" << permnum << std::endl;\n\t\titerator prod=tr.append_child(sum, str_node(\"\\\\prod\"));\n\t\tint sgn=combin::ordersign(ci[permnum].begin(), ci[permnum].end(),\n\t\t                          ci.original.begin(), ci.original.end());\n\t\tmultiplier_t mult=multiplier_t(ci.multiplier(permnum))/multiplier_t(combin::fact((unsigned long)ci.original.size()))*sgn;\n\t\t//\t\tstd::cerr << \"multipliers: \" << mult << \" = \" << ci.multiplier(permnum)\n\t\t//\t\t\t\t\t << \" / \" << combin::fact(ci.original.size()) << \" * \" << sgn << std::endl;\n\t\tmultiply(prod->multiplier, mult);\n\t\tmultiply(prod->multiplier, *st->multiplier);\n\t\tsibling_iterator ind=tr.begin(st);\n\t\tfor(unsigned int pairnum=0; pairnum<ci.original.size(); ++pairnum) {\n\t\t\titerator delta=tr.append_child(prod, str_node(st->name));//\"\\\\delta\"));\n\t\t\tif(permute_second_set)\n\t\t\t\ttr.append_child(delta, (iterator)(ind));\n\t\t\ttr.append_child(delta, ci[permnum][pairnum].begin());\n\t\t\t++ind;\n\t\t\tif(!permute_second_set)\n\t\t\t\ttr.append_child(delta, (iterator)(ind));\n\t\t\t++ind;\n\t\t\t}\n\t\t}\n//\tstd::cerr << \"flatten\" << std::endl;\n\n\tif(rep.number_of_children(sum)==1) { // flatten \\sum node if there was only one term\n\t\trep.flatten(sum);\n\t\trep.erase(sum);\n\t\t}\n\tst=tr.replace(st, rep.begin());\n\n//\tstd::cerr << \"cleanup\" << std::endl;\n\tcleanup_dispatch(kernel, tr, st);\n//\tstd::cerr << \"done\" << std::endl;\n\n\t// After the return, we need to indicate that no new dummies were\n\t// introduced, otherwise we go into rename_replacement_dummies,\n\t// which can be extremely time-consuming.\n//\tstd::cerr << \"####### returning new value \" << std::endl;\n\t\n\treturn result_t::l_applied_no_new_dummies;\n\t}\n\n"
  },
  {
    "path": "core/algorithms/expand_delta.cnb",
    "content": "{\n\t\"cells\" : \n\t[\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\algorithm{expand_delta}{Expand generalised Kronecker delta symbols}\\n\\nIn Cadabra the \\\\prop{KroneckerDelta} property indicates a generalised Kronecker\\ndelta symbol. In order to expand it into standard two-index Kronecker deltas, use\\n\\\\algo{expand_delta}, as in the example below.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\algorithm{expand_delta}{Expand generalised Kronecker delta symbols}\\n\\nIn Cadabra the \\\\prop{KroneckerDelta} property indicates a generalised Kronecker\\ndelta symbol. In order to expand it into standard two-index Kronecker deltas, use\\n\\\\algo{expand_delta}, as in the example below.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property KroneckerDelta to~}\\\\delta\\\\left(\\\\#\\\\right).\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"\\\\delta{#}::KroneckerDelta;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\delta^{a}\\\\,_{b}\\\\,^{c}\\\\,_{d}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex:=\\\\delta^{a}_{b}^{c}_{d};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\frac{1}{2}\\\\delta^{a}\\\\,_{b} \\\\delta^{c}\\\\,_{d} - \\\\frac{1}{2}\\\\delta^{c}\\\\,_{b} \\\\delta^{a}\\\\,_{d}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"expand_delta(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\delta^{a}\\\\,_{m}\\\\,^{l}\\\\,_{n} \\\\delta_{a}\\\\,^{c}\\\\,_{b}\\\\,^{d}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex:=\\\\delta^{a}_{m}^{l}_{n} \\\\delta_{a}^{c}_{b}^{d};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\left(\\\\frac{1}{2}\\\\delta^{a}\\\\,_{m} \\\\delta^{l}\\\\,_{n} - \\\\frac{1}{2}\\\\delta^{l}\\\\,_{m} \\\\delta^{a}\\\\,_{n}\\\\right) \\\\left(\\\\frac{1}{2}\\\\delta_{a}\\\\,^{c} \\\\delta_{b}\\\\,^{d} - \\\\frac{1}{2}\\\\delta_{b}\\\\,^{c} \\\\delta_{a}\\\\,^{d}\\\\right)\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\frac{1}{4}\\\\delta^{a}\\\\,_{m} \\\\delta^{l}\\\\,_{n} \\\\delta_{a}\\\\,^{c} \\\\delta_{b}\\\\,^{d} - \\\\frac{1}{4}\\\\delta^{a}\\\\,_{m} \\\\delta^{l}\\\\,_{n} \\\\delta_{b}\\\\,^{c} \\\\delta_{a}\\\\,^{d} - \\\\frac{1}{4}\\\\delta^{l}\\\\,_{m} \\\\delta^{a}\\\\,_{n} \\\\delta_{a}\\\\,^{c} \\\\delta_{b}\\\\,^{d}+\\\\frac{1}{4}\\\\delta^{l}\\\\,_{m} \\\\delta^{a}\\\\,_{n} \\\\delta_{b}\\\\,^{c} \\\\delta_{a}\\\\,^{d}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\frac{1}{4}\\\\delta^{l}\\\\,_{n} \\\\delta_{m}\\\\,^{c} \\\\delta_{b}\\\\,^{d} - \\\\frac{1}{4}\\\\delta^{l}\\\\,_{n} \\\\delta_{b}\\\\,^{c} \\\\delta_{m}\\\\,^{d} - \\\\frac{1}{4}\\\\delta^{l}\\\\,_{m} \\\\delta_{n}\\\\,^{c} \\\\delta_{b}\\\\,^{d}+\\\\frac{1}{4}\\\\delta^{l}\\\\,_{m} \\\\delta_{b}\\\\,^{c} \\\\delta_{n}\\\\,^{d}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\frac{1}{4}\\\\delta_{b}\\\\,^{d} \\\\delta^{c}\\\\,_{m} \\\\delta^{l}\\\\,_{n} - \\\\frac{1}{4}\\\\delta_{b}\\\\,^{c} \\\\delta^{d}\\\\,_{m} \\\\delta^{l}\\\\,_{n} - \\\\frac{1}{4}\\\\delta_{b}\\\\,^{d} \\\\delta^{c}\\\\,_{n} \\\\delta^{l}\\\\,_{m}+\\\\frac{1}{4}\\\\delta_{b}\\\\,^{c} \\\\delta^{d}\\\\,_{n} \\\\delta^{l}\\\\,_{m}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"expand_delta(_);\\ndistribute(_);\\neliminate_kronecker(_);\\ncanonicalise(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"Note that it is in principle possible to get a result similar to the expanded form by using the \\nYoung projector and then canonicalising, but this is more expensive:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"Note that it is in principle possible to get a result similar to the expanded form by using the \\nYoung projector and then canonicalising, but this is more expensive:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\delta^{a}\\\\,_{b}\\\\,^{c}\\\\,_{d}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex:=\\\\delta^{a}_{b}^{c}_{d};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\delta^{a}\\\\,_{b}\\\\,^{c}\\\\,_{d}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"young_project_tensor(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1\n}\n"
  },
  {
    "path": "core/algorithms/expand_delta.hh",
    "content": "\n#pragma once\n\n#include \"Algorithm.hh\"\n\nnamespace cadabra {\n\n\tclass expand_delta : public Algorithm {\n\t\tpublic:\n\t\t\texpand_delta(const Kernel&, Ex&);\n\n\t\t\tvirtual bool     can_apply(iterator) override;\n\t\t\tvirtual result_t apply(iterator&) override;\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/algorithms/expand_diracbar.cc",
    "content": "\n#include \"Cleanup.hh\"\n#include \"algorithms/expand_diracbar.hh\"\n#include \"properties/DiracBar.hh\"\n#include \"properties/Spinor.hh\"\n#include \"properties/GammaMatrix.hh\"\n\nusing namespace cadabra;\n\nexpand_diracbar::expand_diracbar(const Kernel& k, Ex& e)\n\t: Algorithm(k, e)\n\t{\n\t}\n\nbool expand_diracbar::can_apply(iterator it)\n\t{\n\tconst DiracBar *db=kernel.properties.get<DiracBar>(it);\n\tif(db) {\n\t\tif(*tr.begin(it)->name==\"\\\\prod\") {\n\t\t\tsibling_iterator ch=tr.begin(tr.begin(it));\n\t\t\tconst GammaMatrix *gam=kernel.properties.get<GammaMatrix>(ch);\n\t\t\tif(gam) {\n\t\t\t\t++ch;\n\t\t\t\tconst Spinor *sp=kernel.properties.get<Spinor>(ch);\n\t\t\t\tif(sp && ++ch==tr.end(tr.begin(it))) return true;\n\t\t\t\t}\n\t\t\t}\n\t\t}\n\treturn false;\n\t}\n\nAlgorithm::result_t expand_diracbar::apply(iterator& it)\n\t{\n\t// \\bar{\\prod{\\gamma_{a b} \\epsilon}} -> \\prod{\\bar{\\epsilon} \\gamma_{a b}}\n\n\tsibling_iterator prodnode=tr.begin(it);\n\tsibling_iterator gamnode =tr.begin(prodnode);\n\tsibling_iterator spinnode=gamnode;\n\t++spinnode;\n\n\titerator newprod=tr.wrap(it, str_node(\"\\\\prod\"));\n\tmultiply(newprod->multiplier, *prodnode->multiplier);\n\tmultiply(newprod->multiplier, *it->multiplier);\n\tone(prodnode->multiplier);\n\tone(it->multiplier);\n\ttr.move_after(it, (iterator)gamnode);\n\ttr.flatten(prodnode);\n\ttr.erase(prodnode);\n\n\t// n + (n-1) + .. 1 = 1/2 n (n+1) signs, of which the first 'n' are Minkowski.\n\n\tunsigned int n=tr.number_of_children(gamnode);\n\tif(n*(n+1)/2 % 2 != 0)\n\t\tflip_sign(newprod->multiplier);\n\n\tit=newprod;\n\tcleanup_dispatch(kernel, tr, it);\n\n\treturn result_t::l_applied;\n\t}\n"
  },
  {
    "path": "core/algorithms/expand_diracbar.cnb",
    "content": "\n{\n\t\"cells\" : \n\t[\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\algorithm{expand_diracbar}{Simplify the Dirac bar of a composite object.}\\n\\nRewrite the Dirac conjugate of a product of spinors and gamma matrices\\nas a product of Dirac and hermitean conjugates. This uses\\n\\\\begin{equation} \\n\\\\bar\\\\psi = i \\\\psi^\\\\dagger\\\\Gamma^0\\\\,,\\n\\\\end{equation}\\ntogether with \\n\\\\begin{equation}\\n\\\\Gamma_m^{\\\\dagger} = \\\\Gamma_0\\\\Gamma_m\\\\Gamma_0 \\\\,.\\n\\\\end{equation}\\nFor example,\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\algorithm{expand_diracbar}{Simplify the Dirac bar of a composite object.}\\n\\nRewrite the Dirac conjugate of a product of spinors and gamma matrices\\nas a product of Dirac and hermitean conjugates. This uses\\n\\\\begin{equation} \\n\\\\bar\\\\psi = i \\\\psi^\\\\dagger\\\\Gamma^0\\\\,,\\n\\\\end{equation}\\ntogether with \\n\\\\begin{equation}\\n\\\\Gamma_m^{\\\\dagger} = \\\\Gamma_0\\\\Gamma_m\\\\Gamma_0 \\\\,.\\n\\\\end{equation}\\nFor example,\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\bar{\\\\Gamma^{m n p} \\\\psi}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"\\\\bar{#}::DiracBar.\\n\\\\psi::Spinor(dimension=10).\\n\\\\Gamma{#}::GammaMatrix.\\nex:=\\\\bar{\\\\Gamma^{m n p} \\\\psi};\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\bar{\\\\psi} \\\\Gamma^{m n p}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"expand_diracbar(_);\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1.0\n}\n\n"
  },
  {
    "path": "core/algorithms/expand_diracbar.hh",
    "content": "\n#pragma once\n\n#include \"Algorithm.hh\"\n\nnamespace cadabra {\n\n\tclass expand_diracbar : public Algorithm {\n\t\tpublic:\n\t\t\texpand_diracbar(const Kernel&, Ex&);\n\n\t\t\tvirtual bool     can_apply(iterator) override;\n\t\t\tvirtual result_t apply(iterator&) override;\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/algorithms/expand_dummies.cc",
    "content": "#include <vector>\n#include \"properties/Coordinate.hh\"\n#include \"algorithms/expand_dummies.hh\"\n#include \"Cleanup.hh\"\n#include \"Compare.hh\"\n#include \"IndexClassifier.hh\"\n#include \"IndexIterator.hh\"\n#include \"Functional.hh\"\n#include \"substitute.hh\"\n\nusing namespace cadabra;\n\nexpand_dummies::expand_dummies(const Kernel& kernel, Ex& ex, const Ex* components, bool zero_missing_components)\n\t: Algorithm(kernel, ex)\n\t, comp(kernel.properties)\n\t, components(components)\n\t, zero_missing_components(zero_missing_components)\n\t{\n\tenumerate_patterns();\n\t}\n\nvoid expand_dummies::enumerate_patterns()\n{\n\t// If components is provided create a list of patterns which are inside\n\t// the components \n\tif (components != nullptr) {\n\t\tdo_list(*components, components->begin(), [this] (Ex::iterator c) {\n\t\t\tchar idx_placeholder = 'A';\n\t\t\tEx pattern(c.begin());\n\t\t\tauto beg = index_iterator::begin(kernel.properties, pattern.begin());\n\t\t\tauto end = index_iterator::end(kernel.properties, pattern.begin());\n\t\t\twhile (beg != end) {\n\t\t\t\tauto pr = beg->fl.parent_rel;\n\t\t\t\tauto repl = pattern.replace(beg, str_node(std::string(1, idx_placeholder++) + \"?\"));\n\t\t\t\trepl->fl.parent_rel = pr;\n\t\t\t\tbeg.walk = repl;\n\t\t\t\tbeg.node = repl.node;\n\t\t\t\t++beg;\n\t\t\t\t}\n\n\t\t\tbool found = false;\n\t\t\tfor (const auto& other : component_patterns) {\n\t\t\t\tcomp.clear();\n\t\t\t\tif (comp.equal_subtree(pattern.begin(), other.begin()) == Ex_comparator::match_t::subtree_match) {\n\t\t\t\t\tfound = true;\n\t\t\t\t\tbreak;\n\t\t\t\t}\n\t\t\t}\n\t\t\tif (!found)\n\t\t\t\tcomponent_patterns.push_back(pattern);\n\t\t\treturn true;\n\t\t\t});\n\t\t}\n}\n\nbool expand_dummies::can_apply(iterator it)\n\t{\n\tif (*it->name == \"\\\\sum\" || *it->name == \"\\\\equals\")\n\t\treturn false;\n\n\t// Require a node which has dummy indices with values attached\n\tstd::vector<Ex::iterator> candidates;\n\tauto beg = index_iterator::begin(kernel.properties, it);\n\tauto end = index_iterator::end(kernel.properties, it);\n\twhile (beg != end) {\n\t\tauto prop = kernel.properties.get<Indices>(beg);\n\t\tif(prop) {\n\t\t\tconst auto& index_values = prop->values(kernel.properties, beg);\n\t\t\tif(!index_values.empty()) {\n\t\t\t\tfor (const auto& candidate : candidates) {\n\t\t\t\t\tcomp.clear();\n\t\t\t\t\tauto res = comp.equal_subtree(candidate, beg, Ex_comparator::useprops_t::always, true);\n\t\t\t\t\tif (res == Ex_comparator::match_t::subtree_match)\n\t\t\t\t\t\treturn true;\n\t\t\t\t\t}\n\t\t\t\tcandidates.push_back(beg);\n\t\t\t\t}\n\t\t\t}\n\t\t++beg;\n\t\t}\n\t return false;\n\t }\n\nAlgorithm::result_t expand_dummies::apply(iterator& it)\n\t{\n\t// Create a new expression which we will modify and a sum node which will\n\t// replace it\n\tEx pat(it), sum(\"\\\\sum\");\n\tstd::vector<std::vector<iterator>> dummies;\n\tstd::vector<const std::vector<Ex>*> values;\n\n\tIndexClassifier ic(kernel);\n\tIndexClassifier::index_map_t full_ind_free, full_ind_dummy;\n\tic.classify_indices(pat.begin(), full_ind_free, full_ind_dummy);\n\tfor (const auto& kv : full_ind_dummy) {\n\t\tauto pos = std::find_if(dummies.begin(), dummies.end(),\n\t\t\t\t\t\t\t\t\t\t[this, kv](const std::vector<iterator>& lhs) {\n\t\t\t\t\t\t\t\t\t\tcomp.clear();\n\t\t\t\t\t\t\t\t\t\tauto res = comp.equal_subtree(lhs[0], kv.second, Ex_comparator::useprops_t::always, true);\n\t\t\t\t\t\t\t\t\t\treturn res == Ex_comparator::match_t::subtree_match;\n\t\t\t\t\t\t\t\t\t\t});\n\t\tif(pos == dummies.end()) {\n\t\t\tauto prop = kernel.properties.get<Indices>(kv.first.begin(), true);\n\t\t\tif (prop) {\n\t\t\t\tconst auto& index_values = prop->values(kernel.properties, kv.first.begin());\n\t\t\t\tif(!index_values.empty()) {\n\t\t\t\t\tdummies.emplace_back(1, kv.second);\n\t\t\t\t\tvalues.push_back(&(index_values));\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t}\n\t\telse {\n\t\t\tpos->push_back(kv.second);\n\t\t\t}\n\t\t}\n\n\t// Set up 'positions' to hold iterators into the corresponding elements of the\n\t// 'values' vector, we will loop through all possible combinations\n\tstd::vector<std::vector<Ex>::const_iterator> positions;\n\tfor (const auto& vec : values)\n\t\tpositions.push_back(vec->begin());\n\n\tdo {\n\t\t// Rewrite each dummy pair with the coordinate pointed to by the\n\t\t// positions vector and append to the sum\n\t\tfor (size_t i = 0; i < dummies.size(); ++i) {\n\t\t\tfor (iterator& dummy : dummies[i])\n\t\t\t\tdummy = pat.replace_index(dummy, positions[i]->begin(), true);\n\t\t}\n\n\t\tauto term = sum.append_child(sum.begin(), pat.begin());\n\t\tfill_components(term);\n\n\t\t// Increment the positions vector\n\t\tfor (size_t i = 0; i < positions.size(); ++i) {\n\t\t\t++positions[i];\n\t\t\tif (positions[i] != values[i]->end())\n\t\t\t\tbreak;\n\t\t\telse if (i != positions.size() - 1)\n\t\t\t\tpositions[i] = values[i]->begin();\n\t\t\t}\n\t\t} while (positions.back() != values.back()->end());\n\t \n\t// Replace the node with the new sum\n\tit = tr.replace(it, sum.begin());\n\n\treturn result_t::l_applied;\n\t}\n\nvoid expand_dummies::fill_components(Ex::iterator it)\n\t{\n\tif (components == nullptr)\n\t\treturn;\n\n\tEx::post_order_iterator walk = it, last = it;\n\twalk.descend_all();\n\t++last;\n\n\tdo {\n\t\tauto next = walk;\n\t\t++next;\n\n\t\t// Try to match a pattern against the current node\n\t\tfor (const auto& pattern : component_patterns) {\n\t\t\tcomp.clear();\n\t\t\tauto res = comp.equal_subtree(pattern.begin(), walk);\n\t\t\tif ((res != Ex_comparator::match_t::subtree_match) &&\n\t\t\t\t (res != Ex_comparator::match_t::match_index_greater) &&\n\t\t\t\t (res != Ex_comparator::match_t::match_index_less))\n\t\t\t\tcontinue;\n\n\t\t\t// Ensure all indices are coordinates\n\t\t\tauto ibeg = index_iterator::begin(kernel.properties, walk);\n\t\t\tauto iend = index_iterator::end(kernel.properties, walk);\n\t\t\twhile (ibeg != iend) {\n\t\t\t\tif (kernel.properties.get<Coordinate>(ibeg, true) == nullptr)\n\t\t\t\t\tbreak;\n\t\t\t\t++ibeg;\n\t\t\t\t}\n\t\t\tif (ibeg != iend)\n\t\t\t\tcontinue;\n\n\t\t\t// Find the matching term in components\n\t\t\tbool replaced = false;\n\t\t\tauto head = components->begin();\n\t\t\tif (*head->name == \"\\\\comma\") {\n\t\t\t\tfor (Ex::sibling_iterator cbeg = head.begin(), cend = head.end(); cbeg != cend; ++cbeg) {\n\t\t\t\t\tEx::sibling_iterator term = cbeg.begin();\n\t\t\t\t\tcomp.clear();\n\t\t\t\t\tif (comp.equal_subtree(term, walk) == Ex_comparator::match_t::subtree_match) {\n\t\t\t\t\t\t++term;\n\t\t\t\t\t\tif (walk == it)\n\t\t\t\t\t\t\tit = tr.replace(walk, term);\n\t\t\t\t\t\telse\n\t\t\t\t\t\t\ttr.replace(walk, term);\n\t\t\t\t\t\treplaced = true;\n\t\t\t\t\t\tbreak;\n\t\t\t\t\t\t}\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\telse {\n\t\t\t\tauto term = head.begin();\n\t\t\t\tcomp.clear();\n\t\t\t\tif (comp.equal_subtree(walk, term) == Ex_comparator::match_t::subtree_match) {\n\t\t\t\t\t++term;\n\t\t\t\t\tif (walk == it)\n\t\t\t\t\t\tit = tr.replace(walk, term);\n\t\t\t\t\telse\n\t\t\t\t\t\ttr.replace(walk, term);\n\t\t\t\t\treplaced = true;\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\tif (!replaced && zero_missing_components) {\n\t\t\t\t// No rule found, term is 0\n\t\t\t\ttr.erase(it);\n\t\t\t\treturn;\n\t\t\t\t}\n\t\t\tbreak;\n\t\t\t}\n\t\twalk = next;\n\t\t} while (walk != last);\n\n\t\tcleanup_dispatch(kernel, tr, it);\n\t}\n"
  },
  {
    "path": "core/algorithms/expand_dummies.cnb",
    "content": "{\n\t\"cell_id\": 2562151665405295138,\n\t\"cells\": [\n\t\t{\n\t\t\t\"cell_id\": 12143407317319097504,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 16138737595395674485,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\algorithm{expand_dummies}{Expand contracted dummy index pairs}\\n\\nExpand contracted dummy index as a sum over coordinate values optionally taking a list of component values to be\\napplied. The behaviour is similar to \\\\verb|evaluate| but free indices are not split into components.\\n\\nThe minimal information needed for this to work is a declaration of the indices used, and a declaration\\nof the values that those indices use:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\algorithm{expand_dummies}{Expand contracted dummy index pairs}\\n\\nExpand contracted dummy index as a sum over coordinate values optionally taking a list of component values to be\\napplied. The behaviour is similar to \\\\verb|evaluate| but free indices are not split into components.\\n\\nThe minimal information needed for this to work is a declaration of the indices used, and a declaration\\nof the values that those indices use:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 2017365017951042585,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 1505606892611914647,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 17475896370694076262,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"x_{\\\\mu} g_{\\\\rho \\\\lambda} k^{\\\\rho} k^{\\\\lambda}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}x_{\\\\mu} g_{\\\\rho \\\\lambda} k^{\\\\rho} k^{\\\\lambda}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"{r,t}::Coordinate.\\n{\\\\mu, \\\\rho, \\\\lambda}::Indices(values={t,r}).\\nex:= x_{\\\\mu} g_{\\\\rho \\\\lambda} k^{\\\\rho} k^{\\\\lambda};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 17703473076253312356,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 14504720855055869363,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"The list of component values should be given just like the list of rules for the \\\\algo{substitute} algorithm,\\nthat is, as equalities. If values are defined for some components of an object, then any missing components are assumed\\nto be 0.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"The list of component values should be given just like the list of rules for the \\\\algo{substitute} algorithm,\\nthat is, as equalities. If values are defined for some components of an object, then any missing components are assumed\\nto be 0.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 8925692542070146850,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9153063957121711585,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 1067579206710593719,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"{g_{t t} = -1, g_{r r} = 1, k^{t} = t, k^{r} = 1}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\left[g_{t t} = -1,~\\\\discretionary{}{}{} g_{r r} = 1,~\\\\discretionary{}{}{} k^{t} = t,~\\\\discretionary{}{}{} k^{r} = 1\\\\right]\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 18071988885446484485,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 10822680472589489966,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"-x_{\\\\mu} t t + x_{\\\\mu}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}-x_{\\\\mu} t t+x_{\\\\mu}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"rl:= [ g_{t t} = -1, g_{r r} = 1, k^{t} = t, k^{r} = 1];\\nexpand_dummies(ex, rl);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 3025834967703068036,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 13099037626349655268,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"If no components are given it returns the full expanded sum over coordinates:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"If no components are given it returns the full expanded sum over coordinates:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 17352955123336242996,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 881369153435038127,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 9663947892634825925,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"r_{\\\\mu} g_{t t} k^{t} k^{t} + r_{\\\\mu} g_{t r} k^{t} k^{r} + r_{\\\\mu} g_{r t} k^{r} k^{t} + r_{\\\\mu} g_{r r} k^{r} k^{r}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}r_{\\\\mu} g_{t t} k^{t} k^{t}+r_{\\\\mu} g_{t r} k^{t} k^{r}+r_{\\\\mu} g_{r t} k^{r} k^{t}+r_{\\\\mu} g_{r r} k^{r} k^{r}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex:= r_{\\\\mu} g_{\\\\rho \\\\lambda} k^{\\\\rho} k^{\\\\lambda}.\\nexpand_dummies(ex);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 5160058283724869326,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"\"\n\t\t}\n\t],\n\t\"description\": \"Cadabra JSON notebook format\",\n\t\"version\": 1.0\n}\n"
  },
  {
    "path": "core/algorithms/expand_dummies.hh",
    "content": "\n#pragma once\n\n#include <set>\n#include \"Algorithm.hh\"\n\nnamespace cadabra {\n\n\tclass expand_dummies : public Algorithm {\n\t\tpublic:\n\t\t\texpand_dummies(const Kernel& kernel, Ex& ex, const Ex* components = nullptr, bool zero_missing_components = true);\n\n\t\t\tvirtual bool can_apply(iterator) override;\n\t\t\tvirtual result_t apply(iterator&) override;\n\n\t\tprivate:\n\t\t\tvoid enumerate_patterns();\n\t\t\tvoid fill_components(Ex::iterator it);\n\n\t\t\tEx_comparator comp;\n\t\t\tconst Ex* components;\n\t\t\tstd::vector<Ex> component_patterns;\n\t\t\tbool zero_missing_components;\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/algorithms/expand_power.cc",
    "content": "\n#include \"Cleanup.hh\"\n#include \"algorithms/expand_power.hh\"\n\nusing namespace cadabra;\n\nexpand_power::expand_power(const Kernel& k, Ex& e)\n\t: Algorithm(k, e)\n\t{\n\t}\n\nbool expand_power::can_apply(iterator it)\n\t{\n\tif(*it->name==\"\\\\pow\") {\n\t\tsibling_iterator exponent=tr.begin(it);\n\t\t++exponent;\n\t\tif(exponent->is_integer())\n\t\t\treturn true;\n\t\t}\n\treturn false;\n\t}\n\nAlgorithm::result_t expand_power::apply(iterator& it)\n\t{\n\titerator argument=tr.begin(it);\n\tsibling_iterator exponent=tr.begin(it);\n\t++exponent;\n\n\tint num=to_long(*exponent->multiplier);\n//\tif(num<1)\n//\t\treturn result_t::l_no_action;\n\n\tif(num==-1 && *argument->name!=\"\\\\prod\")\n\t\treturn result_t::l_no_action;\n\n\tif(num==0) {\n\t\tnode_one(it);\n\t\treturn result_t::l_applied;\n\t\t}\n\t\n\titerator prodn=tr.insert(argument,str_node(\"\\\\prod\"));\n\n\t// If the current \\pow is inside a sum, do not discard the bracket\n\t// type on \\pow but copy it onto each generated \\prod element.\n\tif(tr.is_head(it)==false && *tr.parent(it)->name==\"\\\\sum\")\n\t\tprodn->fl.bracket=it->fl.bracket;\n\n\t// Two cases:\n\t//    (a b c)**2 -> a b c a b c;\n\t//    (a b c)**(-2) -> a**(-1) b**(-1) c**(-1) a**(-1) b**(-1) c**(-1)\n\t// So we treat the latter as the former, and then at the end\n\t// just wrap all factors in a \\pow{...}{-1}.\n\t\n\tsibling_iterator beg=argument;\n\tsibling_iterator nd=beg;\n\t++nd;\n\targument=tr.reparent(prodn, beg, nd);\n\ttr.erase(exponent);\n\ttr.flatten(it);\n\tmultiply(prodn->multiplier, *it->multiplier);\n\tit=tr.erase(it);\n\t\n\t// Now duplicate the factor abs(num)-1 times.\n\tmultiplier_t tot=*argument->multiplier;\n\tfor(int i=0; i<std::abs(num)-1; ++i) {\n\t\titerator tmp=tr.append_child(prodn);\n\t\ttot *= *argument->multiplier;\n\t\titerator ins=tr.replace(tmp, argument);\n\t\tone(ins->multiplier);\n\t\trename_replacement_dummies(ins);\n\t\t}\n\tone(argument->multiplier);\n\tif(num<1)\n\t\tdivide(prodn->multiplier, tot);\n\telse\n\t\tmultiply(prodn->multiplier, tot);\n\n\n\t// If the argument of the original \\pow{...}{...} was a \\prod,\n\t// then we now have a nested product.\n\tcleanup_dispatch(kernel, tr, it);\n\n\tif(num<1) {\n\t\tif(*it->name==\"\\\\prod\") {\n\t\t\tsibling_iterator sib = tr.begin(it);\n\t\t\twhile(sib!=tr.end(it)) {\n\t\t\t\tauto nxt=sib;\n\t\t\t\t++nxt;\n\t\t\t\tauto newpow = tr.wrap(sib, str_node(\"\\\\pow\"));\n\t\t\t\ttr.append_child(newpow, str_node(\"1\"))->multiplier = rat_set.insert(-1).first;\n\t\t\t\tsib=nxt;\n\t\t\t\t}\n\t\t\t}\n\t\telse {\n\t\t\tauto newpow = tr.wrap(it, str_node(\"\\\\pow\"));\n\t\t\ttr.append_child(newpow, str_node(\"1\"))->multiplier = rat_set.insert(-1).first;\n\t\t\t}\n\t\t}\n\n\n\treturn result_t::l_applied;\n\t}\n"
  },
  {
    "path": "core/algorithms/expand_power.cnb",
    "content": "{\n\t\"cells\" : \n\t[\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\algorithm{expand_power}{Expand powers into repeated products}\\n\\nExpand powers into repeated products, i.e.~do the opposite\\nof \\\\algo{collect_factors}. For example,\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\algorithm{expand_power}{Expand powers into repeated products}\\n\\nExpand powers into repeated products, i.e.~do the opposite\\nof \\\\algo{collect_factors}. For example,\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\left(A B\\\\right)^{3}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex:=(A B)**3;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}A B A B A B\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"expand_power(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}A A A B B B\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"sort_product(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}A^{3} B^{3}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"collect_factors(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"This command automatically takes care of index relabelling when\\nnecessary, as in the following example\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"This command automatically takes care of index relabelling when\\nnecessary, as in the following example\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\left(A_{m} B_{m}\\\\right)^{3}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"{m,n,p,q,r}::Indices(vector).\\nex:= (A_m B_m)**3;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}A_{m} B_{m} A_{n} B_{n} A_{p} B_{p}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"expand_power(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1\n}\n"
  },
  {
    "path": "core/algorithms/expand_power.hh",
    "content": "\n#pragma once\n\n#include \"Algorithm.hh\"\n\nnamespace cadabra {\n\n\tclass expand_power : public Algorithm {\n\t\tpublic:\n\t\t\texpand_power(const Kernel&, Ex&);\n\n\t\t\tvirtual bool     can_apply(iterator) override;\n\t\t\tvirtual result_t apply(iterator&) override;\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/algorithms/expand_product_shorthand.tex",
    "content": "\\cdbalgorithm{expand\\_product\\_shorthand}{}\n\nReverse of the \\subscommand{product\\_shorthand} algorithm. In addition\nto the two tensor names, it takes a number denoting the total number\nof indices.\n\\begin{screen}{1,2,3,5}\nF_{m n p q}::Symmetric.\nG_{m n p q}::Symmetric.\n@product_shorthand![ F_{a b c d} G_{a b d f} ]{F}{G};\nF_{c} G_{f};\n@expand_product_shorthand!(%){F}{G}{4};\nF_{c a b d} G_{f a b d};\n\\end{screen}\nNote that writing a product as a shorthand and then expanding again\nmay re-order the indices, as in the example above.\n\n\\cdbseealgo{product_shorthand}\n\\cdbseeprop{Symmetric}\n\\cdbseeprop{AntiSymmetric}\n"
  },
  {
    "path": "core/algorithms/explicit_indices.cc",
    "content": "\n#include \"explicit_indices.hh\"\n\n#include \"Cleanup.hh\"\n#include \"Exceptions.hh\"\n#include \"algorithms/substitute.hh\"\n#include \"properties/ImplicitIndex.hh\"\n#include \"properties/PartialDerivative.hh\"\n#include \"properties/Trace.hh\"\n\nusing namespace cadabra;\n\nexplicit_indices::explicit_indices(const Kernel& k, Ex& tr)\n\t: Algorithm(k, tr)\n\t{\n\t}\n\nbool explicit_indices::can_apply(iterator st)\n\t{\n\t// Work on equals nodes, or single terms (not terms in a sum) or\n\t// sums, provided the latter are not lhs or rhs of an equals node.\n\t// All this because when we generate free indices, we need to\n\t// ensure that all terms and all sides of an equals node use the\n\t// same index names.\n\n\tif(*st->name==\"\\\\equals\" || *st->name==\"\\\\arrow\") {\n\t\tsibling_iterator lhs=tr.begin(st);\n\t\tif(can_apply(lhs)) {\n\t\t\t++lhs;\n\t\t\tif(can_apply(lhs))\n\t\t\t\treturn true;\n\t\t\t}\n\t\treturn false;\n\t\t}\n\tauto trace = kernel.properties.get<Trace>(st);\n\tif(trace)   return true;\n\tif(is_termlike(st) || *st->name==\"\\\\sum\") {\n\t\tif(tr.is_head(st)) return         true;\n\t\tif(*tr.parent(st)->name==\"\\\\sum\") return false;\n\t\tif(*tr.parent(st)->name==\"\\\\equals\" || *tr.parent(st)->name==\"\\\\arrow\") return false;\n\t\tauto ptrace = kernel.properties.get<Trace>(tr.parent(st));\n\t\tif(ptrace) return false;\n\t\tauto pderiv = kernel.properties.get<PartialDerivative>(tr.parent(st));\n\t\tif(pderiv) return false;\n\t\treturn true;\n\t\t}\n\n\treturn false;\n\t}\n\nAlgorithm::result_t explicit_indices::apply(iterator& it)\n\t{\n\tresult_t res=result_t::l_no_action;\n\n\tif(*it->name==\"\\\\equals\" || *it->name==\"\\\\arrow\") {\n\t\t// FIXME: collect existing indices on both sides to avoid\n\t\t// adding new free indices which are already in use on the\n\t\t// other side.\n\n\t\t// Do the lhs, keep track of free indices added there.\n\t\titerator ch=tr.begin(it);\n\t\tauto lhs_res = apply(ch);\n\n\t\t// Then do the rhs, feeding it the free indices just generated.\n\t\t++ch;\n\t\tauto rhs_res = apply(ch);\n\n\t\tif(lhs_res==result_t::l_applied || rhs_res==result_t::l_applied)\n\t\t\treturn result_t::l_applied;\n\t\treturn result_t::l_no_action;\n\t\t}\n\n\t// All non-equality and non-rule cases follow.\n\tauto trace = kernel.properties.get<Trace>(it);\n\titerator parit=it;\n\tif(trace) {\n\t\t// Handle the argument, then at the end, close the index loop\n\t\t// and remove the trace operator.\n\t\titerator arg=tr.begin(it);\n\t\tif(! (*arg->name==\"\\\\sum\" || is_termlike(arg)))\n\t\t\treturn res;\n\t\tit=arg;\n\t\t}\n\n\t// Ensure that we are always working on a sum, even\n\t// if there is only one term.\n\tif(is_termlike(it))\n\t\tforce_node_wrap(it, \"\\\\sum\");\n\n\t// Classify all free and dummy indices already present. Any new\n\t// indices cannot be taken from these.\n//\tstd::cerr << \"acting at \" << it << std::endl;\n\t\n\tind_free_sum.clear();\n\tind_dummy_sum.clear();\n\tIndexClassifier ic(kernel);\n\tic.classify_indices(it, ind_free_sum, ind_dummy_sum);\n\n\tsibling_iterator term=tr.begin(it);\n\twhile(term!=tr.end(it)) {\n\t\tsibling_iterator nxt=term;\n\t\t++nxt;\n\n\t\titerator tmp=term;\n\t\tprod_wrap_single_term(tmp);\n\t\tterm=tmp;\n\n\t\t// For each index set, keep track of the last used index in\n\t\t// building the explicit index line.\n\t\tadded_this_term.clear();\n\t\tindex_lines.clear();\n\t\tfirst_index.clear();\n\t\tlast_index.clear();\n\n\t\tsibling_iterator factor=tr.begin(term);\n\t\twhile(factor!=tr.end(term)) {\n\t\t\tconst PartialDerivative *pd = kernel.properties.get<PartialDerivative>(factor);\n\t\t\tif(pd) {\n\t\t\t\tsibling_iterator args=tr.begin(factor);\n\t\t\t\twhile(args!=tr.end(factor)) {\n\t\t\t\t\tif(args->fl.parent_rel==str_node::p_none) {\n\t\t\t\t\t\tres=result_t::l_applied;\n\t\t\t\t\t\thandle_factor(args, trace!=0);\n\t\t\t\t\t\tbreak;\n\t\t\t\t\t\t}\n\t\t\t\t\t++args;\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\telse {\n\t\t\t\tres=result_t::l_applied;\t\t\t\t\n\t\t\t\thandle_factor(factor, trace!=0);\n\t\t\t\t}\n\t\t\t++factor;\n\t\t\t}\n\t\t// If this term is a trace, make indices equal\n\t\tif(trace) {\n\t\t\tfor(auto& li: last_index) {\n\t\t\t\ttr.replace_index(li.second, first_index[li.first], true);\n\t\t\t\t}\n\t\t\t}\n\n\n\t\ttmp=term;\n\t\tprod_unwrap_single_term(tmp);\n\n\t\t//\t\tstd::cerr << \"after unwrap\" << tmp << std::endl;\n\n\t\tterm=nxt;\n\t\t}\n\n\tif(trace) {\n\t\tit=parit;\n\t\tit = tr.flatten_and_erase(it);\n\t\t}\n\tif(*it->name==\"\\\\sum\" && tr.number_of_children(it)==1)\n\t\tit = tr.flatten_and_erase(it);\n\t// It looks like we will have trouble if we also flatten the\n\t// \\prod node, becuase then rename_dummies will only act on\n\t// the first factor we introduced, and fail to rename\n\t// properly.\n//\tcleanup_dispatch(kernel, tr, it);\n\n//\tstd::cerr << \"after explicit_indicex: \" << tr.begin() << std::endl;\n//\tstd::cerr << \"and it is now \" << it << std::endl;\n\t\n\treturn res;\n\t}\n\nvoid explicit_indices::handle_factor(sibling_iterator& factor, bool )\n\t{\n\tint tmp;\n\tauto ii = kernel.properties.get_with_pattern<ImplicitIndex>(factor, tmp, \"\");\n\tif(ii.first) {\n\t\t// Determine indices on this factor. Use a copy because we\n\t\t// need this object later.\n\t\tEx orig(factor);\n\t\tIndexClassifier ic(kernel);\n\t\tIndexClassifier::index_map_t factor_ind_free, factor_ind_dummy;\n\t\tic.classify_indices(orig.begin(), factor_ind_free, factor_ind_dummy);\n\n\t\t// Substitute explcit replacement and rename the indices\n\t\t// already present on the implicit factor.\n\t\tEx replacement(\"\\\\arrow\");\n\t\treplacement.append_child(replacement.begin(), ii.second->obj.begin());\n\t\treplacement.append_child(replacement.begin(), ii.first->explicit_form.begin());\n\t\tsubstitute subs(kernel, tr, replacement);\n\t\titerator factor_tmp=factor;\n\t\tif(subs.can_apply(factor_tmp))\n\t\t\tsubs.apply(factor_tmp);\n\t\telse\n\t\t\tthrow InternalError(\"Internal inconsistency encountered, aborting.\");\n\t\tfactor=factor_tmp;\n\n\t\t// Determine indices on the replacement.\n\t\tIndexClassifier::index_map_t repl_ind_free, repl_ind_dummy;\n\t\tic.classify_indices(factor, repl_ind_free, repl_ind_dummy);\n\n\t\t// Which indices have been added?\n\t\tIndexClassifier::index_map_t ind_same;\n\t\tic.determine_intersection(factor_ind_free, repl_ind_free, ind_same, true);\n\n\t\t// Keep track of indices already added in this factor, to avoid making\n\t\t// an index trace on a single factor.\n\t\tstd::map<const Indices *, Ex::iterator> index_lines_factor;\n\n\t\t// Go through indices in order of appearance, determine if they have\n\t\t// been added, and rename. Note: indices do not appear in order in the\n\t\t// index maps above.\n\t\tauto iit=index_iterator::begin(kernel.properties, factor);\n\t\twhile(iit!=index_iterator::end(kernel.properties, factor)) {\n\t\t\tauto search=repl_ind_free.begin();\n\t\t\tbool found=false;\n\t\t\twhile(search!=repl_ind_free.end()) {\n\t\t\t\tif(search->second == (iterator)iit) {\n\t\t\t\t\tfound=true;\n\t\t\t\t\tbreak;\n\t\t\t\t\t}\n\t\t\t\t++search;\n\t\t\t\t}\n\t\t\t++iit; // Update now, we may be replacing this index.\n\t\t\tif(found) {\n\t\t\t\t// This index was added.\n\t\t\t\tconst Indices *ip = kernel.properties.get<Indices>(search->second);\n\t\t\t\tif(!ip)\n\t\t\t\t\tthrow InternalError(\"Do not have Indices property for all implicit indices.\");\n\n\t\t\t\t// Determine if we have an 'active' index line for\n\t\t\t\t// this index type.\n\t\t\t\tauto line        = index_lines.find(ip);\n\t\t\t\tauto line_factor = index_lines_factor.find(ip);\n\t\t\t\tif(line==index_lines.end() || line_factor!=index_lines_factor.end()) {\n\t\t\t\t\t// No active line. Get a new free index.\n\t\t\t\t\tauto di = ic.get_dummy(ip, &ind_free_sum, &ind_dummy_sum, &added_this_term);\n\t\t\t\t\tauto loc = tr.replace_index(search->second, di.begin(), true);\n\t\t\t\t\tadded_this_term.insert(IndexClassifier::index_map_t::value_type(di, loc));\n\t\t\t\t\tindex_lines[ip]=loc;\n\t\t\t\t\tindex_lines_factor[ip]=loc;\n\t\t\t\t\tlast_index[ip]=loc;\n\t\t\t\t\tauto first = first_index.find(ip);\n\t\t\t\t\tif(first==first_index.end()) {\n\t\t\t\t\t\tfirst_index[ip]=loc;\n\t\t\t\t\t\t}\n\t\t\t\t\t}\n\t\t\t\telse {\n\t\t\t\t\t// Use the active line index, then unset the active line.\n\t\t\t\t\ttr.replace_index(search->second, line->second, true);\n\t\t\t\t\tindex_lines.erase(line);\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t}\n\t\t}\n\t}\n"
  },
  {
    "path": "core/algorithms/explicit_indices.cnb",
    "content": "{\n\t\"cells\" : \n\t[\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\algorithm{explicit_indices}{Make indices explicit on an expression with implicit indices.}\\n\\nIn Cadabra you can write expressions which are understood to have indices suppressed, in order\\nto get a cleaner notation. This is often used for vector/matrix notation, or when dealing\\nwith spinors. In order to inform Cadabra about these implicit indices, you use the\\n\\\\prop{ImplicitIndex} property (which is also necessary to prevent Cadabra from moving\\nthese objects through each other when sorting products into canonical form). \\nThe \\\\algo{explicit_indices} algorithm can then make these  indices explicit, which can \\nsometimes make them easier to work with, for example when doing substitutions.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\algorithm{explicit_indices}{Make indices explicit on an expression with implicit indices.}\\n\\nIn Cadabra you can write expressions which are understood to have indices suppressed, in order\\nto get a cleaner notation. This is often used for vector/matrix notation, or when dealing\\nwith spinors. In order to inform Cadabra about these implicit indices, you use the\\n\\\\prop{ImplicitIndex} property (which is also necessary to prevent Cadabra from moving\\nthese objects through each other when sorting products into canonical form). \\nThe \\\\algo{explicit_indices} algorithm can then make these  indices explicit, which can \\nsometimes make them easier to work with, for example when doing substitutions.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"In the following example we define two sets of indices, and several objects which are assumed\\nto have implicit indices.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"In the following example we define two sets of indices, and several objects which are assumed\\nto have implicit indices.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Indices(position=fixed) to~}\\\\left[m,~\\\\discretionary{}{}{} n,~\\\\discretionary{}{}{} p\\\\right].\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Indices(position=fixed) to~}\\\\left[a,~\\\\discretionary{}{}{} b,~\\\\discretionary{}{}{} c,~\\\\discretionary{}{}{} d,~\\\\discretionary{}{}{} e,~\\\\discretionary{}{}{} f,~\\\\discretionary{}{}{} g,~\\\\discretionary{}{}{} h\\\\right].\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property ImplicitIndex to~}\\\\sigma^{p}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property ImplicitIndex to~}\\\\psi.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property ImplicitIndex to~}\\\\chi.\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"{m,n,p}::Indices(spacetime, position=fixed);\\n{a,b,c,d,e,f,g,h}::Indices(spinor, position=fixed);\\n\\\\sigma^{p}::ImplicitIndex(\\\\sigma^{p a}_{b});\\n\\\\psi::ImplicitIndex(\\\\psi_{a});\\n\\\\chi::ImplicitIndex(\\\\chi^{a});\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"The following is a valid expression for a spinor bilinear,\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"The following is a valid expression for a spinor bilinear,\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"\\\\psi \\\\sigma^{m} \\\\sigma^{n} \\\\chi\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\psi \\\\sigma^{m} \\\\sigma^{n} \\\\chi\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex:= \\\\psi \\\\sigma^{m} \\\\sigma^{n} \\\\chi;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"We can now make the indices explicit using\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"We can now make the indices explicit using\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"\\\\psi_{a} \\\\sigma^{m a}_{b} \\\\sigma^{n b}_{c} \\\\chi^{c}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\psi_{a} \\\\sigma^{m a}\\\\,_{b} \\\\sigma^{n b}\\\\,_{c} \\\\chi^{c}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"explicit_indices(ex);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"This also works when there are trace operators, as is illustrated in the following \\nexample.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"This also works when there are trace operators, as is illustrated in the following \\nexample.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Trace to~}{\\\\rm Tr}\\\\left(\\\\#\\\\right).\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"Tr(\\\\sigma^{m} \\\\sigma^{n} + \\\\sigma^{n} \\\\sigma^{m})\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}{\\\\rm Tr}\\\\left(\\\\sigma^{m} \\\\sigma^{n}+\\\\sigma^{n} \\\\sigma^{m}\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"Tr{#}::LaTeXForm(\\\"{\\\\rm Tr}\\\").\\nTr{#}::Trace(indices=spinor);\\nex:= Tr(\\\\sigma^{m} \\\\sigma^{n} + \\\\sigma^{n} \\\\sigma^{m});\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"\\\\sigma^{m a}_{b} \\\\sigma^{n b}_{a} + \\\\sigma^{n a}_{b} \\\\sigma^{m b}_{a}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\sigma^{m a}\\\\,_{b} \\\\sigma^{n b}\\\\,_{a}+\\\\sigma^{n a}\\\\,_{b} \\\\sigma^{m b}\\\\,_{a}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"explicit_indices(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1\n}\n"
  },
  {
    "path": "core/algorithms/explicit_indices.hh",
    "content": "\n#pragma once\n\n#include \"Algorithm.hh\"\n#include \"IndexClassifier.hh\"\n\nnamespace cadabra {\n\n\tclass explicit_indices : public Algorithm {\n\t\tpublic:\n\t\t\texplicit_indices(const Kernel&, Ex&);\n\n\t\t\tvirtual bool     can_apply(iterator);\n\t\t\tvirtual result_t apply(iterator&);\n\n\t\tprivate:\n\t\t\tIndexClassifier::index_map_t            ind_free_sum, ind_dummy_sum;\n\t\t\tIndexClassifier::index_map_t            added_this_term;\n\t\t\tstd::map<const Indices *, Ex::iterator> index_lines, first_index, last_index;         // for the current term\n\n\t\t\tvoid handle_factor(sibling_iterator& factor, bool trace_it);\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/algorithms/factor_in.cc",
    "content": "\n#include \"Functional.hh\"\n#include \"algorithms/factor_in.hh\"\n#include <boost/functional/hash.hpp>\n\n#define DBG_MACRO_NO_WARNING \n#define DBG_MACRO_DISABLE \n#include \"dbg.h\"\n\nusing namespace cadabra;\n\nfactor_in::factor_in(const Kernel& k, Ex& tr, Ex& factors_)\n\t: Algorithm(k, tr), factors(factors_)\n\t{\n\t}\n\nbool factor_in::can_apply(iterator st)\n\t{\n\tfactnodes.clear();\n\tassert(tr.is_valid(st));\n\tif(*st->name==\"\\\\sum\") {\n\t\tcadabra::do_list(factors, factors.begin(), [&](Ex::iterator f) {\n\t\t\tfactnodes.insert(Ex(f));\n\t\t\treturn true;\n\t\t\t});\n\t\treturn true;\n\t\t}\n\telse return false;\n\t}\n\nhashval_t factor_in::calc_restricted_hash(iterator it) const\n\t{\n\tif(*it->name!=\"\\\\prod\") return tr.calc_hash(it);\n\n\thashval_t ret=0;\n//\tboost::hash_combine(ret, *it->name);\n\n\tauto sib=tr.begin(it);\n\tbool first=true;\n\twhile(sib!=tr.end(it)) { // see storage.cc for the original calc_hash\n\t\tif(factnodes.count(Ex(sib))==0) {\n\t\t\tif(first) {\n\t\t\t\t// ensure that if there is only one factor, the hash equals tr.calc_hash\n\t\t\t\t// on that single factor.\n\t\t\t\tfirst=false;\n\t\t\t\tret=tr.calc_hash(sib);\n\t\t\t\t}\n\t\t\telse \n\t\t\t\tboost::hash_combine(ret, tr.calc_hash(sib));\n\t\t\t}\n\t\t++sib;\n\t\t}\n\treturn ret;\n\t}\n\nvoid factor_in::fill_hash_map(iterator it)\n\t{\n\tterm_hash.clear();\n\tsibling_iterator sib=tr.begin(it);\n\tunsigned int terms=0;\n\twhile(sib!=tr.end(it)) {\n\t\tdbg( sib );\n\t\tdbg( calc_restricted_hash(sib) );\n\t\tterm_hash.insert(std::pair<hashval_t, sibling_iterator>(calc_restricted_hash(sib), sib));\n\t\t++terms;\n\t\t++sib;\n\t\t}\n\t}\n\nbool factor_in::compare_prod_nonprod(iterator prod, iterator nonprod) const\n\t{\n\tassert(*(prod->name)==\"\\\\prod\");\n\tassert(*(nonprod->name)!=\"\\\\prod\");\n\tsibling_iterator it=tr.begin(prod);\n\tbool found=false;\n\twhile(it!=tr.end(prod)) {\n\t\tif(factnodes.count(Ex(it))==0) {\n\t\t\tif(nonprod->name==it->name) { // FIXME: subtree_equal\n\t\t\t\tif(found) return false; // already found\n\t\t\t\telse found=true;\n\t\t\t\t}\n\t\t\telse return false;\n\t\t\t}\n\t\t++it;\n\t\t}\n\tif(found || (!found && factnodes.count(Ex(nonprod))!=0)) return true;\n\treturn false;\n\t}\n\nbool factor_in::compare_restricted(iterator one, iterator two) const\n\t{\n\tif(one->name==two->name) {\n\t\tif(*one->name==\"\\\\prod\") {\n\t\t\tsibling_iterator it1=tr.begin(one), it2=tr.begin(two);\n\t\t\twhile(it1!=tr.end(one) && it2!=tr.end(two)) {\n\t\t\t\tif(factnodes.count(Ex(it1))!=0) {\n\t\t\t\t\t++it1;\n\t\t\t\t\tcontinue;\n\t\t\t\t\t}\n\t\t\t\tif(factnodes.count(Ex(it2))!=0) {\n\t\t\t\t\t++it2;\n\t\t\t\t\tcontinue;\n\t\t\t\t\t}\n\t\t\t\titerator nxt=it1;\n\t\t\t\tnxt.skip_children();\n\t\t\t\t++nxt;\n\t\t\t\tif(!tr.equal(tr.begin(it1), sibling_iterator(nxt), tr.begin(it2)))\n\t\t\t\t\treturn false;\n\t\t\t\t++it1;\n\t\t\t\t++it2;\n\t\t\t\t}\n\t\t\t}\n\t\t}\n\telse {\n\t\tif(*one->name==\"\\\\prod\" && *two->name!=\"\\\\prod\")\n\t\t\treturn compare_prod_nonprod(one,two);\n\t\telse if(*one->name!=\"\\\\prod\" && *two->name==\"\\\\prod\")\n\t\t\treturn compare_prod_nonprod(two,one);\n\t\t}\n\treturn true;\n\t}\n\nAlgorithm::result_t factor_in::apply(iterator& it)\n\t{\n\tresult_t ret=result_t::l_no_action;\n\tfill_hash_map(it);\n\n\tterm_hash_iterator_t ht=term_hash.begin();\n\twhile(ht!=term_hash.end()) { // loop over hash bins\n\t\thashval_t curr=ht->first;\n\t\tterm_hash_iterator_t thisbin1=ht, thisbin2=ht;\n\t\t++thisbin2;\n\t\tif(thisbin2==term_hash.end() || thisbin2->first!=thisbin1->first) { // only one term in this bin\n\t\t\t++ht;\n\t\t\tcontinue;\n\t\t\t}\n\n\t\t// extract the prefactor of every term in this bin.\n\t\tstd::map<iterator, Ex, Ex::iterator_base_less> prefactors;\n\t\twhile(thisbin1!=term_hash.end() && thisbin1->first==curr) {\n\t\t\tEx prefac;\n\t\t\t//\t\t\ttxtout << \"doing one\" << std::endl;\n\t\t\tprefac.set_head(str_node(\"\\\\sum\"));\n\t\t\tif(*(thisbin1->second->name)==\"\\\\prod\") { // search for all to-be-factored-out factors\n\t\t\t\titerator prefacprod=prefac.append_child(prefac.begin(), str_node(\"\\\\prod\"));\n\t\t\t\tsibling_iterator ps=tr.begin(thisbin1->second);\n\t\t\t\twhile(ps!=tr.end(thisbin1->second)) {\n\t\t\t\t\tif(factnodes.count(Ex(ps))!=0) {\n\t\t\t\t\t\tprefac.append_child(prefacprod, (iterator)(ps));\n\t\t\t\t\t\t}\n\t\t\t\t\t++ps;\n\t\t\t\t\t}\n\t\t\t\tprefacprod->multiplier=thisbin1->second->multiplier;\n\t\t\t\tswitch(prefac.number_of_children(prefacprod)) {\n\t\t\t\t\tcase 0:\n\t\t\t\t\t\tprefacprod->name=name_set.insert(\"1\").first;\n\t\t\t\t\t\tbreak;\n\t\t\t\t\tcase 1:\n\t\t\t\t\t\tmultiply(prefac.begin(prefacprod)->multiplier, *(prefacprod->multiplier));\n\t\t\t\t\t\tprefac.flatten(prefacprod);\n\t\t\t\t\t\tprefacprod=prefac.erase(prefacprod);\n\t\t\t\t\t\tbreak;\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\telse {   // just insert the constant\n\t\t\t\tstr_node pf(\"1\");\n\t\t\t\tpf.multiplier=thisbin1->second->multiplier;\n\t\t\t\tprefac.append_child(prefac.begin(), pf);\n\t\t\t\t}\n\t\t\tprefactors[thisbin1->second]=prefac;\n\t\t\t++thisbin1;\n\t\t\t}\n\n\t\t// add up prefactors for terms which differ only by the prefactor\n\t\tthisbin1=ht;\n\t\twhile(thisbin1!=term_hash.end() && thisbin1->first==curr) {\n\t\t\tthisbin2=thisbin1;\n\t\t\t++thisbin2;\n\t\t\twhile(thisbin2!=term_hash.end() && thisbin2->first==curr) {\n\t\t\t\tif(compare_restricted(thisbin1->second, thisbin2->second)) {\n\t\t\t\t\tret=result_t::l_applied;\n\t\t\t\t\t//\t\t\t\t\ttxtout << \"found match\" << std::endl;\n\t\t\t\t\tassert(prefactors.count(thisbin1->second)>0);\n\t\t\t\t\tassert(prefactors.count(thisbin2->second)>0);\n\t\t\t\t\titerator sumhead1=prefactors[thisbin1->second].begin();\n\t\t\t\t\titerator sumhead2=prefactors[thisbin2->second].begin();\n\t\t\t\t\ttr.reparent(sumhead1,tr.begin(sumhead2),tr.end(sumhead2));\n\t\t\t\t\t//\t\t\t\t\ttxtout << \"reparented\" << std::endl;\n\t\t\t\t\tzero((*thisbin2).second->multiplier);\n\t\t\t\t\tprefactors.erase(thisbin2->second);\n\t\t\t\t\tterm_hash_iterator_t tmp=thisbin2;\n\t\t\t\t\t++tmp;\n\t\t\t\t\tterm_hash.erase(thisbin2);\n\t\t\t\t\tthisbin2=tmp;\n\t\t\t\t\t}\n\t\t\t\telse ++thisbin2;\n\t\t\t\t}\n\t\t\t++thisbin1;\n\t\t\t}\n\t\t// remove old prefactors and add prefactor sums\n\t\tstd::map<iterator, Ex, Ex::iterator_base_less>::iterator prefit=prefactors.begin();\n\t\twhile(prefit!=prefactors.end()) {\n\t\t\tif(tr.number_of_children(prefit->second.begin())>1) { // only do this if there really is more than just one term\n\t\t\t\tsibling_iterator facit=tr.begin(prefit->first);\n\t\t\t\twhile(facit!=tr.end(prefit->first)) {\n\t\t\t\t\tif(factnodes.count(Ex(facit))>0)\n\t\t\t\t\t\tfacit=tr.erase(facit);\n\t\t\t\t\telse\n\t\t\t\t\t\t++facit;\n\t\t\t\t\t}\n\t\t\t\titerator inserthere=prefit->first.begin();\n\t\t\t\tif(*(prefit->first->name)!=\"\\\\prod\") {\n\t\t\t\t\titerator prodnode=tr.insert(prefit->first, str_node(\"\\\\prod\"));\n\t\t\t\t\tone(prefit->first->multiplier);\n\t\t\t\t\ttr.append_child(prodnode, prefit->first); // FIXME: we need a 'move'\n\t\t\t\t\ttr.erase(prefit->first);\n\t\t\t\t\tinserthere=tr.begin(prodnode);\n\t\t\t\t\t}\n\t\t\t\telse one(prefit->first->multiplier);\n\t\t\t\ttr.insert_subtree(inserthere, (*prefit).second.begin());\n\t\t\t\t}\n\t\t\t++prefit;\n\t\t\t}\n\n\n\t\tht=thisbin1;\n\t\t}\n\n\t// Remove all terms which have zero multiplier.\n\t// Remove all terms which are empty `\\prod` nodes.\n\t// Distribute sum multipliers over terms.\n//\tdbg( it );\n\tsibling_iterator one=tr.begin(it);\n\twhile(one!=tr.end(it)) {\n//\t\tdbg( one );\n\t\tif(*one->multiplier==0)\n\t\t\tone=tr.erase(one);\n\t\telse if(*one->name==\"\\\\prod\" && tr.number_of_children(one)==0) {\n\t\t\tone=tr.erase(one);\n\t\t\t}\n\t\telse if(*one->name==\"\\\\sum\" && *one->multiplier!=1) {\n\t\t\tsibling_iterator oneit=tr.begin(one);\n\t\t\twhile(oneit!=tr.end(one)) {\n\t\t\t\tmultiply(oneit->multiplier, *one->multiplier);\n\t\t\t\t++oneit;\n\t\t\t\t}\n\t\t\tone->multiplier=rat_set.insert(1).first;\n\t\t\t++one;\n\t\t\t}\n\t\telse ++one;\n\t\t}\n\n\t// If there is only one term in the sum left, flatten the tree.\n\tif(tr.number_of_children(it)==1) {\n\t\ttr.begin(it)->fl.bracket=it->fl.bracket;\n\t\ttr.begin(it)->fl.parent_rel=it->fl.parent_rel;\n\t\ttr.flatten(it);\n\t\tit=tr.erase(it);\n\t\t}\n\telse if(tr.number_of_children(it)==0) {\n\t\tit->multiplier=rat_set.insert(0).first;\n\t\t}\n\n\n\treturn ret;\n\t}\n\n\n"
  },
  {
    "path": "core/algorithms/factor_in.cnb",
    "content": "\n{\n\t\"cells\" : \n\t[\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\algorithm{factor_in}{Collect terms in a sum that differ only by given pre-factors.}\\n\\nGiven a list of symbols, this algorithm collects terms in a sum that\\nonly differ by pre-factors consisting of these given symbols. As an\\nexample,\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\algorithm{factor_in}{Collect terms in a sum that differ only by given pre-factors.}\\n\\nGiven a list of symbols, this algorithm collects terms in a sum that\\nonly differ by pre-factors consisting of these given symbols. As an\\nexample,\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}a b+a c+a d\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex:=a b + a c + a d;\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\left(b+c\\\\right) a+a d\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"factor_in(_, $b,c$);\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"The name is perhaps most easily understood by thinking of it as a\\ncomplement to \\\\algo{factor_out}. Or in case you are familiar with\\nFORM, \\\\algo{factor_in} is like its \\\\verb|antibracket| statement.\\n\\nThe algorithm of course also works with indexed objects, as in\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"The name is perhaps most easily understood by thinking of it as a\\ncomplement to \\\\algo{factor_out}. Or in case you are familiar with\\nFORM, \\\\algo{factor_in} is like its \\\\verb|antibracket| statement.\\n\\nThe algorithm of course also works with indexed objects, as in\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}A_{m} B_{m}+C_{m} A_{m}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}A_{m} B_{m}+C_{m} A_{m}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex:=A_{m} B_{m} + C_{m} A_{m};\\nfactor_in(_, $B_{n}, C_{n}$);\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"(not yet finished)\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"(not yet finished)\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1.0\n}\n\n"
  },
  {
    "path": "core/algorithms/factor_in.hh",
    "content": "\n#pragma once\n\n#include \"Algorithm.hh\"\n\nnamespace cadabra {\n\n\t/// \\ingroup algorithms\n\n\tclass factor_in : public Algorithm {\n\t\tpublic:\n\t\t\tfactor_in(const Kernel&, Ex&, Ex&);\n\n\t\t\tvirtual bool     can_apply(iterator) override;\n\t\t\tvirtual result_t apply(iterator&) override;\n\n\t\tprotected:\n\t\t\tEx& factors;\n\t\t\tstd::set<Ex, tree_exact_less_for_indexmap_obj> factnodes; // objects to be taken in brackets;\n\t\t\t// FIXME: use patterns\n\t\t\tbool      compare_restricted(iterator one, iterator two) const;\n\t\t\tbool      compare_prod_nonprod(iterator prod, iterator nonprod) const;\n\n\t\t\t// Calculate the hash value excluding factors given in the argument list\n\t\t\thashval_t calc_restricted_hash(iterator it) const;\n\t\t\tvoid      fill_hash_map(iterator);\n\n\t\t\ttypedef std::multimap<hashval_t, Ex::sibling_iterator> term_hash_t;\n\t\t\ttypedef term_hash_t::iterator                          term_hash_iterator_t;\n\n\t\t\tterm_hash_t term_hash;\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/algorithms/factor_out.cc",
    "content": "\n#include \"Cleanup.hh\"\n#include \"Functional.hh\"\n#include \"algorithms/factor_out.hh\"\n#include \"algorithms/sort_product.hh\"\n\n//#define DEBUG __FILE__\n#include \"Debug.hh\"\n\nusing namespace cadabra;\n\nfactor_out::factor_out(const Kernel& k, Ex& e, Ex& args, bool right)\n\t: Algorithm(k, e), to_right(right)\n\t{\n\tcadabra::do_list(args, args.begin(), [&](Ex::iterator arg) {\n\t\tto_factor_out.push_back(Ex(arg));\n\t\treturn true;\n\t\t}\n\t                );\n\t}\n\n/// Check if the expression is a sum with more than one term\nbool factor_out::can_apply(iterator st)\n\t{\n\tif(*st->name==\"\\\\sum\")  return true;\n\treturn false;\n\t}\n\nAlgorithm::result_t factor_out::apply(iterator& it)\n\t{\n\tresult_t result=result_t::l_no_action;\n\n\t// For every term in the sum, we look at the factors in the product\n\t// (or at the single object if there is no product). If this factor\n\t// needs to be factored out, we determine if it can be moved all the\n\t// way to the left of the expression. If so, move the object to\n\t// a 'factored_out' temporary, and take out of the tree. Rinse/repeat.\n\t// What's left at the end is two objects: the stuff factored out,\n\t// and the rest. Look up if we already have 'the stuff factored out'.\n\t// If not, create new. If so, add this term.\n\n\tEx_comparator comparator(kernel.properties);\n\n\t// `new_term_t` holds the factored-out factors, and a sum of terms\n\t// which multiply that. \n\ttypedef std::pair<Ex, std::vector<Ex> > new_term_t;\n\tstd::vector<new_term_t> new_terms;\n\n\tauto term=tr.begin(it);\n\twhile(term!=tr.end(it)) {\n\t\tauto next_term=term;\n\t\t++next_term;\n\n\t\titerator prod=term;\n\t\tprod_wrap_single_term(prod);\n\n\t\tEx collector(\"\\\\prod\"); // collect all factors that we have taken out\n\n\t\t// Insert a dummy symbol at the very front or back.\n\t\t// FIXME: there is now a 'can_move_to_front', use that.\n\t\titerator dummy;\n\t\tif(to_right) dummy = tr.append_child(prod, str_node(\"dummy\"));\n\t\telse         dummy = tr.prepend_child(prod, str_node(\"dummy\"));\n\n\t\t// Look at all factors in turn and determine if they should be taken out.\n\t\tif(to_right) {\n\t\t\tauto fac=tr.end(prod);\n\t\t\tauto next=fac;\n\t\t\t--next;\n\t\t\tdo {\n\t\t\t\tfac=next;\n\t\t\t\t--next;\n\t\t\t\tfor(size_t i=0; i<to_factor_out.size(); ++i) {\n\t\t\t\t\tauto match=comparator.equal_subtree(fac, to_factor_out[i].begin());\n\t\t\t\t\tif(match==Ex_comparator::match_t::subtree_match) {\n\t\t\t\t\t\tint sign=comparator.can_move_adjacent(prod, dummy, fac, false);\n\t\t\t\t\t\tif(sign!=0) {\n\t\t\t\t\t\t\tcollector.append_child(collector.begin(), iterator(fac));\n\t\t\t\t\t\t\tmultiply(prod->multiplier, sign);\n\t\t\t\t\t\t\tnext=tr.erase(fac);\n\t\t\t\t\t\t\tresult=result_t::l_applied;\n\t\t\t\t\t\t\tbreak;\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\t}\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\twhile(fac!=tr.begin(prod));\n\t\t\t}\n\t\telse {\n\t\t\tauto fac=tr.begin(prod);\n\t\t\twhile(fac!=tr.end(prod)) {\n\t\t\t\tauto next=fac;\n\t\t\t\t++next;\n\t\t\t\tfor(size_t i=0; i<to_factor_out.size(); ++i) {\n\t\t\t\t\tauto match=comparator.equal_subtree(fac, to_factor_out[i].begin());\n\t\t\t\t\tif(match==Ex_comparator::match_t::subtree_match) {\n\t\t\t\t\t\tint sign=comparator.can_move_adjacent(prod, dummy, fac, true);\n\t\t\t\t\t\tif(sign!=0) {\n\t\t\t\t\t\t\tcollector.append_child(collector.begin(), iterator(fac));\n\t\t\t\t\t\t\tmultiply(prod->multiplier, sign);\n\t\t\t\t\t\t\tnext=tr.erase(fac);\n\t\t\t\t\t\t\tresult=result_t::l_applied;\n\t\t\t\t\t\t\tbreak;\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\t}\n\t\t\t\t\t}\n\t\t\t\tfac=next;\n\t\t\t\t}\n\t\t\t}\n\n\t\ttr.erase(dummy);\n\t\tif(tr.number_of_children(prod)==0)\n\t\t\ttr.append_child(prod, str_node(\"1\"));\n\n\t\tDEBUGLN( std::cerr << \"product after factoring out \" << Ex(prod) << std::endl; );\n\n\t\tif(collector.number_of_children(collector.begin())!=0) {\n\t\t\t// The stuff factored out of this term is in 'collector'. See\n\t\t\t// if we have factored out that thing before for a different\n\t\t\t// term. Because we may not always have collected factors in\n\t\t\t// the same order (the original expression may not have had\n\t\t\t// its product sorted), we first sort the collector product.\n\n\t\t\tsort_product sp(kernel, collector);\n\t\t\tsp.dont_cleanup(); // otherwise single-factor products will get stripped of the \\prod wrapper.\n\t\t\tauto coltop=collector.begin();\n\t\t\tif(sp.can_apply(coltop)) {\n\t\t\t\tsp.apply(coltop);\n\t\t\t\t}\n\t\t\tmultiply(prod->multiplier, *coltop->multiplier);\n\t\t\tone(coltop->multiplier);\n\n\t\t\tDEBUGLN( std::cerr << \"collector for this term \" << collector << std::endl; );\n\t\t\t\n\t\t\t// Scan through the things factored out so far.\n\t\t\tbool found=false;\n\t\t\tfor(auto& nt: new_terms) {\n\t\t\t\tif(nt.first==collector) { // have that factored out already, add the other factors\n\t\t\t\t\tnt.second.push_back(Ex(prod));\n\t\t\t\t\tfound=true;\n\t\t\t\t\tbreak;\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t// We hadn't factored this bit out before, make a new term.\n\t\t\tif(!found) {\n\t\t\t\tDEBUGLN( std::cerr << \"found new term \" << prod << std::endl; );\n\t\t\t\tstd::vector<Ex> v;\n\t\t\t\tv.push_back(Ex(prod));\n\t\t\t\tnew_term_t nt(collector, v);\n\t\t\t\tnew_terms.push_back(nt);\n\t\t\t\t}\n\n\t\t\t// All info is now in new_terms; can remove the original.\n\t\t\ttr.erase(prod);\n\t\t\t}\n\t\telse {\n\t\t\tprod_unwrap_single_term(prod);\n\t\t\t}\n\t\tterm=next_term;\n\t\t}\n\n\t// Everything has been collected now into new_terms. Expand those out\n\t// into a proper sum of products.\n\n\tfor(auto& nt: new_terms) {\n\t\tauto prod = tr.append_child(it, nt.first.begin());\n\t\tif(nt.second.size()==1) { // factored, but only one term found.\n\t\t\tauto top = nt.second[0].begin(); // prod node\n\t\t\tif(to_right) {\n\t\t\t\tauto ins = tr.end(top);\n\t\t\t\t--ins;\n\t\t\t\twhile(tr.is_valid(ins)) {\n\t\t\t\t\ttr.prepend_child(prod, iterator(ins));\n\t\t\t\t\t--ins;\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\telse {\n\t\t\t\tauto ins = tr.begin(top);\n\t\t\t\twhile(ins!=tr.end(top)) {\n\t\t\t\t\ttr.append_child(prod, iterator(ins));\n\t\t\t\t\t++ins;\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\tmultiply(prod->multiplier, *(nt.second[0].begin()->multiplier));\n\t\t\t// FIXME: append_children has a BUG! Messes up the tree. But it is needed to\n\t\t\t// handle terms where the sub-factor is not a simple element.\n\t\t\t//\t\t\ttr.append_children(prod, nt.second[0].begin(top), nt.second[0].end(top));\n\n\t\t\tcleanup_dispatch(kernel, tr, prod);\n\t\t\t}\n\t\telse {\n\t\t\titerator sum;\n\t\t\tif(to_right)\n\t\t\t\tsum = tr.prepend_child(prod, str_node(\"\\\\sum\"));\n\t\t\telse\n\t\t\t\tsum = tr.append_child(prod, str_node(\"\\\\sum\"));\n\t\t\tfor(auto& term: nt.second) {\n\t\t\t\tauto tmp = tr.append_child(sum, term.begin());\n\t\t\t\tcleanup_dispatch(kernel, tr, tmp);\n\t\t\t\t}\n\t\t\tcleanup_dispatch(kernel, tr, sum);\n\t\t\t}\n\t\t}\n\n\t// std::cerr << \"end of factor_out: \\n\" << Ex(it) << std::endl;\n\n\treturn result;\n\t}\n\n"
  },
  {
    "path": "core/algorithms/factor_out.cnb",
    "content": "{\n\t\"cell_id\": 16631768661980820700,\n\t\"cells\": [\n\t\t{\n\t\t\t\"cell_id\": 15110587217203656507,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 2442514580917179909,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\algorithm{factor_out}{Isolate common factors in a sum of products}\\n\\nGiven a list of symbols, this algorithm tries to factor those symbols\\nout of terms. As an example,\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\algorithm{factor_out}{Isolate common factors in a sum of products}\\n\\nGiven a list of symbols, this algorithm tries to factor those symbols\\nout of terms. As an example,\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 5326350575773906895,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 12393491783316939441,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 7753338784577544398,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"a b + 3a c e + a d\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}a b\\\\discretionary{}{}{}+3\\\\,a c e\\\\discretionary{}{}{}+a d\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex:= a b + 3 a c e + a d;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 8526452968883721051,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 14695698502576205301,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 4442340611833814025,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"a (b + 3c e + d)\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}a \\\\left(b\\\\discretionary{}{}{}+3\\\\,c e\\\\discretionary{}{}{}+d\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"factor_out(_, $a$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 8168015960473753308,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 6969777224887872393,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"If you have non-commuting objects and want to factor out to the right, use the \\\\verb|right=True| option, as in\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"If you have non-commuting objects and want to factor out to the right, use the \\\\verb|right=True| option, as in\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 4328956871078085908,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 17779677811794871151,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property NonCommuting attached to~}\\\\left[A, \\\\discretionary{}{}{}B, \\\\discretionary{}{}{}C, \\\\discretionary{}{}{}D\\\\right].\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 7428455874108183042,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 2681337086457739526,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"A B C D + 2B A C D\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}A B C D\\\\discretionary{}{}{}+2\\\\,B A C D\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 11623263169543829254,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 2686784791333189033,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"(A B C + 2B A C) D\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\left(A B C\\\\discretionary{}{}{}+2\\\\,B A C\\\\right) D\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"{A,B,C,D}::NonCommuting;\\nex:= A B C D + 2 B A C D;\\nfactor_out(ex, $D$, right=True);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 1035209040436501181,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 11849596451828232828,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"In case you are familiar with FORM, \\\\algo{factor_out} is like its \\\\verb|bracket| statement. \\nIf you add more factors to factor out, it works as in the following example.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"In case you are familiar with FORM, \\\\algo{factor_out} is like its \\\\verb|bracket| statement. \\nIf you add more factors to factor out, it works as in the following example.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 4287461539531373554,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 7584698066549537904,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 1522186259200143136,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"a b + a c e + a c + c e + c d + a d\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}a b\\\\discretionary{}{}{}+a c e\\\\discretionary{}{}{}+a c\\\\discretionary{}{}{}+c e\\\\discretionary{}{}{}+c d\\\\discretionary{}{}{}+a d\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex:= a b + a c e + a c + c e + c d + a d;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 3486320937648814737,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 1301258625577700972,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 6006025610129981929,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"a (b + d) + a c (e + 1) + c (e + d)\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}a \\\\left(b\\\\discretionary{}{}{}+d\\\\right)\\\\discretionary{}{}{}+a c \\\\left(e\\\\discretionary{}{}{}+1\\\\right)\\\\discretionary{}{}{}+c \\\\left(e\\\\discretionary{}{}{}+d\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"factor_out(_, $a, c$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 15121932675043815974,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 16608972969483160360,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"That is, separate terms will be generated for terms which differ by\\npowers of the factors to be factored out.\\n\\nThe algorithm of course also works with indexed objects, as in\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"That is, separate terms will be generated for terms which differ by\\npowers of the factors to be factored out.\\n\\nThe algorithm of course also works with indexed objects, as in\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 3932854604912589951,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 6388461315274603657,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 9194744312555876804,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"A_{m} B_{m} + C_{m} A_{m}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}A_{m} B_{m}\\\\discretionary{}{}{}+C_{m} A_{m}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex:= A_{m} B_{m} + C_{m} A_{m};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 7492206986106571139,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 5561508064053721308,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 4353108678157183737,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"A_{m} (B_{m} + C_{m})\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}A_{m} \\\\left(B_{m}\\\\discretionary{}{}{}+C_{m}\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"factor_out(_, $A_{m}$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 7869881142525470487,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"\"\n\t\t}\n\t],\n\t\"description\": \"Cadabra JSON notebook format\",\n\t\"flags\": {\n\t\t\"hide_input_cells\": false\n\t},\n\t\"version\": 1.0\n}\n"
  },
  {
    "path": "core/algorithms/factor_out.hh",
    "content": "\n#pragma once\n\n#include \"Algorithm.hh\"\n\nnamespace cadabra {\n\n\t/// \\ingroup algorithms\n\n\tclass factor_out : public Algorithm {\n\t\tpublic:\n\t\t\tfactor_out(const Kernel&, Ex&, Ex&, bool right);\n\n\t\t\tvirtual bool     can_apply(iterator) override;\n\t\t\tvirtual result_t apply(iterator&) override;\n\n\t\tprivate:\n\t\t\tbool                       to_right;\n\n\t\t\ttypedef std::vector<Ex>    to_factor_out_t;\n\t\t\tto_factor_out_t            to_factor_out;\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/algorithms/fierz.cc",
    "content": "\n#include \"Cleanup.hh\"\n#include \"Exceptions.hh\"\n#include \"IndexClassifier.hh\"\n\n#include \"algorithms/fierz.hh\"\n\n#include \"properties/GammaMatrix.hh\"\n#include \"properties/Integer.hh\"\n#include \"properties/DiracBar.hh\"\n\nusing namespace cadabra;\n\n// #define DEBUG(ln) ln\n#define DEBUG(ln)\n\nfierz::fierz(const Kernel& k, Ex& e, Ex& args)\n\t: Algorithm(k, e), spinor_list(Ex(args.begin()))\n\t{\n\tif(*(spinor_list.begin()->name)!=\"\\\\comma\")\n\t\tthrow ArgumentException(\"fierz: need a list of spinors\");\n\n\tif(tr.number_of_children(spinor_list.begin())!=4)\n\t\tthrow ArgumentException(\"fierz: need a list of 4 spinors.\");\n\t}\n\nbool fierz::can_apply(iterator it)\n\t{\n\tif(*it->name!=\"\\\\prod\") return false;\n\n\t// Find a Dirac bar, and then continue inside the product\n\t// to find the gamma matrix, fermion and second fermi bilinear.\n\n\tsibling_iterator sib=tr.begin(it);\n\tconst Integer *indit=0;\n\twhile(sib!=tr.end(it)) {\n\t\tconst DiracBar *db=kernel.properties.get<DiracBar>(sib);\n\t\tif(db) {\n\t\t\tDEBUG( std::cerr << \"found db\" << sib << std::endl; );\n\t\t\tspin1=sib;\n\t\t\tprop1=kernel.properties.get<Spinor>(spin1);\n\t\t\tsibling_iterator ch=sib;\n\t\t\tconst GammaMatrix *gmnxt=0;\n\t\t\tconst Spinor      *spnxt=0;\n\t\t\t// Skip to next spinor-index carrying object\n\t\t\tdo {\n\t\t\t\t++ch;\n\t\t\t\tif(ch==tr.end(it)) break;\n\t\t\t\tgmnxt=kernel.properties.get<GammaMatrix>(ch);\n\t\t\t\tspnxt=kernel.properties.get<Spinor>(ch);\n\t\t\t\t}\n\t\t\twhile(gmnxt==0 && spnxt==0);\n\t\t\tif(gmnxt) {\n\t\t\t\tDEBUG( std::cerr << \"found gamma \" << ch << std::endl; );\n\t\t\t\t// FIXME: should also work when there is a unit matrix in between.\n\t\t\t\tindit=kernel.properties.get<Integer>(ch.begin(), true);\n\t\t\t\tindprop=kernel.properties.get<Indices>(ch.begin(), true);\n\t\t\t\tif(!indit || !indprop) return false;\n\t\t\t\tdim=to_long(*indit->difference.begin()->multiplier);\n\t\t\t\tif(dim==1)\n\t\t\t\t\treturn false;\n\n\t\t\t\tgam1=ch;\n\t\t\t\t// Skip to next spinor-index carrying object\n\t\t\t\tdo {\n\t\t\t\t\t++ch;\n\t\t\t\t\tif(ch==tr.end(it)) break;\n\t\t\t\t\tspnxt=kernel.properties.get<Spinor>(ch);\n\t\t\t\t\tgmnxt=kernel.properties.get<GammaMatrix>(ch);\n\t\t\t\t\t}\n\t\t\t\twhile(gmnxt==0 && spnxt==0);\n\t\t\t\tprop2=spnxt;\n\t\t\t\tif(prop2) { // one fermi bilinear found.\n\t\t\t\t\tDEBUG( std::cerr << \"found spin2 \" << Ex(ch) << std::endl; );\n\t\t\t\t\tspin2=ch;\n\t\t\t\t\t// Skip to next spinor-index carrying object\n\t\t\t\t\tdo {\n\t\t\t\t\t\t++ch;\n\t\t\t\t\t\tif(ch==tr.end(it)) break;\n\t\t\t\t\t\tspnxt=kernel.properties.get<Spinor>(ch);\n\t\t\t\t\t\tgmnxt=kernel.properties.get<GammaMatrix>(ch);\n\t\t\t\t\t\t}\n\t\t\t\t\twhile(gmnxt==0 && spnxt==0);\n\t\t\t\t\tdb=kernel.properties.get<DiracBar>(ch);\n\t\t\t\t\tif(db) {\n\t\t\t\t\t\tDEBUG( std::cerr << \"found db2\" << std::endl; );\n\t\t\t\t\t\tspin3=ch;\n\t\t\t\t\t\tprop3=spnxt;\n\t\t\t\t\t\t// Skip to next spinor-index carrying object\n\t\t\t\t\t\tdo {\n\t\t\t\t\t\t\t++ch;\n\t\t\t\t\t\t\tif(ch==tr.end(it)) break;\n\t\t\t\t\t\t\tspnxt=kernel.properties.get<Spinor>(ch);\n\t\t\t\t\t\t\tgmnxt=kernel.properties.get<GammaMatrix>(ch);\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\twhile(gmnxt==0 && spnxt==0);\n\t\t\t\t\t\tif(gmnxt) {\n\t\t\t\t\t\t\tgam2=ch;\n\t\t\t\t\t\t\tDEBUG( std::cerr << \"found gam2: \" << gam2 << std::endl; );\n\t\t\t\t\t\t\t// Skip to next spinor-index carrying object\n\t\t\t\t\t\t\tdo {\n\t\t\t\t\t\t\t\t++ch;\n\t\t\t\t\t\t\t\tif(ch==tr.end(it)) break;\n\t\t\t\t\t\t\t\tspnxt=kernel.properties.get<Spinor>(ch);\n\t\t\t\t\t\t\t\tgmnxt=kernel.properties.get<GammaMatrix>(ch);\n\t\t\t\t\t\t\t\t}\n\t\t\t\t\t\t\twhile(gmnxt==0 && spnxt==0);\n\t\t\t\t\t\t\tprop4=spnxt;\n\t\t\t\t\t\t\tif(prop4) {\n\t\t\t\t\t\t\t\tDEBUG( std::cerr << \"found spin4\" << std::endl; );\n\t\t\t\t\t\t\t\tspin4=ch;\n\t\t\t\t\t\t\t\treturn true;\n\t\t\t\t\t\t\t\t}\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\t}\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t}\n\t\t++sib;\n\t\t}\n\treturn false;\n\t}\n\nAlgorithm::result_t fierz::apply(iterator& it)\n\t{\n\tsibling_iterator spt=spinor_list.begin(spinor_list.begin());\n\n\t// Catch terms with spinors in the right order.\n\tif(subtree_equal(&kernel.properties, tr.begin(spin1), spt)) {\n\t\t++spt;\n\t\tif(subtree_equal(&kernel.properties, spin2, spt)) {\n\t\t\t++spt;\n\t\t\tif(subtree_equal(&kernel.properties, tr.begin(spin3), spt)) {\n\t\t\t\t++spt;\n\t\t\t\tif(subtree_equal(&kernel.properties, spin4, spt)) {\n\t\t\t\t\tDEBUG( std::cerr << \"Found term with spinors in correct order already\" << std::endl; );\n\t\t\t\t\treturn result_t::l_no_action;\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t}\n\t\t}\n\n\t// Catch terms with right spinors but wrong order.\n\tbool doit=false;\n\tspt=spinor_list.begin(spinor_list.begin());\n\tif(subtree_equal(&kernel.properties, tr.begin(spin1), spt)) {\n\t\t++spt;\n\t\tif(subtree_equal(&kernel.properties, spin4, spt)) {\n\t\t\t++spt;\n\t\t\tif(subtree_equal(&kernel.properties, tr.begin(spin3), spt)) {\n\t\t\t\t++spt;\n\t\t\t\tif(subtree_equal(&kernel.properties, spin2, spt)) {\n\t\t\t\t\tDEBUG( std::cerr << \"Found term with spinors wrong order\" << std::endl; );\n\t\t\t\t\tdoit=true;\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t}\n\t\t}\n\tif(!doit) {\n\t\tDEBUG( std::cerr << \"Spinors in this factor do not match algorithm list.\" << std::endl; );\n\t\treturn result_t::l_no_action;\n\t\t}\n\n\t//\ttxtout << \"going to Fierz\" << std::endl;\n\n\tEx rep(\"\\\\sum\");\n\n\tIndexClassifier ic(kernel);\n\tIndexClassifier::index_map_t ind_free, ind_dummy;\n\tic.classify_indices(it, ind_free, ind_dummy);\n\tspinordim=(1 << dim/2);\n\tint maxind=dim;\n\tif(prop1->weyl || dim%2==1)\n\t\tmaxind/=2;\n\n\tfor(int i=0; i<=maxind; ++i) {\n\t\tDEBUG( std::cerr << i << \" of \" << maxind << std::endl; );\n\n\t\t// Make a copy of this term, moving the gamma matrices into the\n\t\t// first factor and inserting projector gamma matrices as well.\n\t\tEx cpyterm(\"\\\\prod\");\n\t\tcpyterm.begin()->multiplier=it->multiplier;\n\t\tmultiply(cpyterm.begin()->multiplier, multiplier_t(-1)/multiplier_t(spinordim));\n\t\tif(i>0)\n\t\t\tmultiply(cpyterm.begin()->multiplier, multiplier_t(1)/multiplier_t(combin::fact<int>(i)));\n\t\tsibling_iterator cpit=tr.begin(it);\n\n\t\t// Copy and put the gammas and projector gammas in the right spot.\n\t\titerator locgam1,  locgam2;  // locations of the projector gammas\n\t\twhile(cpit!=tr.end(it)) {\n\t\t\titerator tmpit;\n\t\t\tif(cpit==spin2)\n\t\t\t\ttmpit=cpyterm.append_child(cpyterm.begin(), spin4);\n\t\t\telse if(cpit==spin4)\n\t\t\t\ttmpit=cpyterm.append_child(cpyterm.begin(), spin2);\n\t\t\telse tmpit=cpyterm.append_child(cpyterm.begin(), (iterator)cpit);\n\n\t\t\tif(cpit==gam1) {\n\t\t\t\tif(i>0) {\n\t\t\t\t\tlocgam1=cpyterm.append_child(cpyterm.begin(), gam1);\n\t\t\t\t\tcpyterm.erase_children(locgam1);\n\t\t\t\t\t}\n\t\t\t\tcpyterm.append_child(cpyterm.begin(), gam2);\n\t\t\t\t}\n\t\t\tif(cpit==gam2) {\n\t\t\t\tlocgam2=tmpit;\n\t\t\t\tif(i==0) cpyterm.erase(locgam2);\n\t\t\t\telse \t\tcpyterm.erase_children(locgam2);\n\t\t\t\tif(i>0) {\n\t\t\t\t\tDEBUG( std::cerr << \"New gamma reads \" << Ex(locgam2) << std::endl; );\n\t\t\t\t\t}\n\t\t\t\t}\n\n\t\t\t++cpit;\n\t\t\t}\n\n\t\t// Insert the indices on the projector gammas.\n\t\tIndexClassifier::index_map_t ind_added;\n\t\tfor(int j=1; j<=i; ++j) {\n\t\t\tEx newdum=ic.get_dummy(indprop, &ind_free, &ind_dummy, &ind_added);\n\t\t\titerator loc1=cpyterm.append_child(locgam1, newdum.begin());\n\t\t\tind_added.insert(IndexClassifier::index_map_t::value_type(newdum, loc1));\n\t\t\tloc1->fl.parent_rel=str_node::p_super;\n\t\t\t// Add the indices in opposite order in the second gamma matrix\n\t\t\t//\t\t\tstd::cerr << \"inserting \" << newdum << \" at \" << Ex(locgam2) << std::endl;\n\t\t\titerator loc2=cpyterm.prepend_child(locgam2, newdum.begin());\n\t\t\tif(indprop->position_type==Indices::free)\n\t\t\t\tloc1->fl.parent_rel=str_node::p_super;\n\t\t\telse\n\t\t\t\tloc2->fl.parent_rel=str_node::p_sub;\n\t\t\t}\n\n\t\t//\t\tstd::cerr << cpyterm << std::endl;\n\t\trep.append_child(rep.begin(), cpyterm.begin());\n\t\t}\n\n\t//\tstd::cerr << rep << std::endl;\n\n\tit=tr.replace(it, rep.begin());\n\tcleanup_dispatch(kernel, tr, it);\n\n\treturn result_t::l_applied;\n\t}\n"
  },
  {
    "path": "core/algorithms/fierz.cnb",
    "content": "{\n\t\"cells\" : \n\t[\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\algorithm{fierz}{Perform a Fierz transformation on a product of four spinors}\\n\\nChange the order of the spinors in a four-spinor expression using a Fierz\\ntransformation. This relies on the generic fact that Dirac gamma matrices satisfy\\nthe completeness relation\\n\\\\begin{equation*}\\n\\\\sum_{a} \\\\left(\\\\Gamma_{a}\\\\right)_{ij} \\\\left(\\\\Gamma^{a}\\\\right)_{kl} \\n = \\\\delta_{il} \\\\delta_{jk}\\\\,.\\n\\\\end{equation*}\\nThe following example explains the typical usage pattern.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\algorithm{fierz}{Perform a Fierz transformation on a product of four spinors}\\n\\nChange the order of the spinors in a four-spinor expression using a Fierz\\ntransformation. This relies on the generic fact that Dirac gamma matrices satisfy\\nthe completeness relation\\n\\\\begin{equation*}\\n\\\\sum_{a} \\\\left(\\\\Gamma_{a}\\\\right)_{ij} \\\\left(\\\\Gamma^{a}\\\\right)_{kl} \\n = \\\\delta_{il} \\\\delta_{jk}\\\\,.\\n\\\\end{equation*}\\nThe following example explains the typical usage pattern.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Indices(position=free) to~}\\\\left(m, \\\\linebreak[0] n, \\\\linebreak[0] p, \\\\linebreak[0] q, \\\\linebreak[0] r, \\\\linebreak[0] s\\\\right).\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Integer to~}\\\\left(m, \\\\linebreak[0] n, \\\\linebreak[0] p, \\\\linebreak[0] q, \\\\linebreak[0] r, \\\\linebreak[0] s\\\\right).\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property GammaMatrix to~}\\\\Gamma\\\\left(\\\\#\\\\right).\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property DiracBar to~}\\\\bar{\\\\#}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Spinor to~}\\\\left(\\\\theta, \\\\linebreak[0] \\\\lambda, \\\\linebreak[0] \\\\psi, \\\\linebreak[0] \\\\chi\\\\right).\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\bar{\\\\theta} \\\\Gamma_{m} \\\\chi \\\\bar{\\\\psi} \\\\Gamma^{m} \\\\lambda\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"{m,n,p,q,r,s}::Indices;\\n{m,n,p,q,r,s}::Integer(0..3);\\n\\\\Gamma{#}::GammaMatrix;\\n\\\\bar{#}::DiracBar;\\n{\\\\theta, \\\\lambda, \\\\psi, \\\\chi}::Spinor;\\nex:=\\\\bar{\\\\theta} \\\\Gamma_{m} \\\\chi \\\\bar{\\\\psi} \\\\Gamma^{m} \\\\lambda;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{} - \\\\frac{1}{4}\\\\bar{\\\\theta} \\\\Gamma_{m} \\\\Gamma^{m} \\\\lambda \\\\bar{\\\\psi} \\\\chi - \\\\frac{1}{4}\\\\bar{\\\\theta} \\\\Gamma_{m} \\\\Gamma_{n} \\\\Gamma^{m} \\\\lambda \\\\bar{\\\\psi} \\\\Gamma_{n} \\\\chi - \\\\frac{1}{8}\\\\bar{\\\\theta} \\\\Gamma_{m} \\\\Gamma_{n p} \\\\Gamma^{m} \\\\lambda \\\\bar{\\\\psi} \\\\Gamma_{p n} \\\\chi\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"fierz(_, $\\\\theta, \\\\lambda, \\\\psi, \\\\chi$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"The argument to \\\\algo{fierz} is the required order of the\\nfermions; note that this algorithm does not flip around Majorana\\nspinors and \\\\algo{sort_spinors} should be used for that.  Also\\nnote that it is important to define not only the symbols representing\\nthe spinors, Dirac bar and gamma matrices, but also the range of the\\nindices.\\n\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"The argument to \\\\algo{fierz} is the required order of the\\nfermions; note that this algorithm does not flip around Majorana\\nspinors and \\\\algo{sort_spinors} should be used for that.  Also\\nnote that it is important to define not only the symbols representing\\nthe spinors, Dirac bar and gamma matrices, but also the range of the\\nindices.\\n\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1\n}\n"
  },
  {
    "path": "core/algorithms/fierz.hh",
    "content": "\n#pragma once\n\n#include \"Algorithm.hh\"\n#include \"properties/Indices.hh\"\n#include \"properties/Spinor.hh\"\n\nnamespace cadabra {\n\n\tclass fierz : public Algorithm {\n\t\tpublic:\n\t\t\tfierz(const Kernel&, Ex&, Ex&);\n\n\t\t\tvirtual bool     can_apply(iterator) override;\n\t\t\tvirtual result_t apply(iterator&) override;\n\n\t\tprivate:\n\t\t\tEx              spinor_list;\n\n\t\t\titerator        spin1, spin2, spin3, spin4;\n\t\t\tconst Spinor   *prop1,*prop2,*prop3,*prop4;\n\t\t\titerator        gam1, gam2;\n\t\t\tint             dim, spinordim;\n\t\t\tconst Indices  *indprop;\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/algorithms/first_order_form.cc",
    "content": "\n#include \"algorithms/first_order_form.hh\"\n#include \"Algorithm.hh\"\n#include \"Compare.hh\"\n#include \"Equals.hh\"\n#include \"Sum.hh\"\n#include \"Exceptions.hh\"\n#include \"Functional.hh\"\n#include \"properties/PartialDerivative.hh\"\n\n// #define DEBUG __FILE__\n#include \"Debug.hh\"\n\nusing namespace cadabra;\n\nfirst_order_form::first_order_form(const Kernel &k, Ex &tr, Ex& funcs)\n\t: Algorithm(k, tr)\n\t, functions(funcs)\n\t{\n\t}\n\nbool first_order_form::can_apply(iterator it)\n\t{\n\t// FIXME: move some of the checks in `apply` here.\n\t// determine that this is a set of ODEs or a single ODE\n\t// determine that each is an equality\n\t// determine that the highest-order derivatives appear linearly\n  \n\treturn *it->name==\"\\\\comma\";\n\t}\n\n//\tList odes(tr);\n//\tfor(auto& ode: odes) {\n//\t\t}\n//\n//\tList funs(functions);\n//\tfor(auto& fun: funs) {\n//\t\tauto deps = kernel.properties.get<Depends>(fun.begin());\n//\t\t}\n\n\nAlgorithm::result_t first_order_form::apply(iterator& it)\n\t{\n\t// If we have a single ODE, convert to a list with one ODE in it.\n\tmake_list(tr);\n\n\t// Ensure that each ODE is an equality. Move all terms to the lhs.\n\tdo_list(tr, tr.begin(),\n\t\t\t  [this](iterator ode)\n\t\t\t\t  {\n\t\t\t\t  visit::Equals eq(kernel, tr, ode);\n\t\t\t\t  eq.move_all_to_lhs();\n\t\t\t\t  return true;\n\t\t\t\t  }\n\t\t\t  );\n\t\n\t// If we have a single function, convert to a list with one function in it.\n\tmake_list(functions);\n\n\t// Determine the independent variable.\n\ttree_exact_less_obj comp(&kernel.properties);\n\tstd::set<Ex, tree_exact_less_obj> all_deps(comp);\n\tdo_list(functions, functions.begin(),\n\t\t\t  [this, &all_deps](Ex::iterator fun)\n\t\t\t\t  {\n\t\t\t\t  auto deps = dependencies(fun, false);\n\t\t\t\t  all_deps.insert(deps.begin(), deps.end());\n\t\t\t\t  return true;\n\t\t\t\t  }\n\t\t\t  );\n\tif(all_deps.size()!=1) {\n\t\tDEBUGLN( for(auto var: all_deps) std::cerr << \"first_order_form: dep \" << var << std::endl; );\n\t\tthrow std::logic_error(\"first_order_form: more than one dependent variable present\");\n\t\t}\n\tDEBUGLN( std::cerr << \"first_order_form: found dependent variable \" << *all_deps.begin() << std::endl; );\n\n\t// Walk all nodes in the ODEs, and determine the location of the\n\t// functions and their derivative orders. The goal later will be to\n\t// write this as a linear system in which the highest-order\n\t// derivatives for each variable are the 'independents'. We then\n\t// solve for those to get the ODEs in canonical form.\n\tdo_list(tr, it,\n\t\t\t  // One ODE at a time.\n\t\t\t  [this](Ex::iterator ode)\n\t\t\t\t  {\n\t\t\t\t  DEBUGLN( std::cerr << \"process ODE \" << ode << std::endl; );\n\t\t\t\t  visit::Equals equals(kernel, tr, ode);\n\t\t\t\t  visit::Sum    sum(kernel, tr, equals.lhs());\n\t\t\t\t  \n\t\t\t\t  // For each function, figure out where it appears in this ODE\n\t\t\t\t  std::map<Ex::iterator, std::vector<std::pair<Ex::iterator, int>> > appearances;\n\n\t\t\t\t  do_list(functions, functions.begin(),\n\t\t\t\t\t\t\t [this, &appearances, &sum](Ex::iterator fun)\n\t\t\t\t\t\t\t\t {\n\t\t\t\t\t\t\t\t auto fun_locs = sum.find_terms_containing(fun);\n\t\t\t\t\t\t\t\t std::vector<std::pair<Ex::iterator, int>> this_fun_appearances;\n\t\t\t\t\t\t\t\t for(auto fun_loc: fun_locs) {\n\t\t\t\t\t\t\t\t\t Ex::iterator walk=fun_loc;\n\t\t\t\t\t\t\t\t\t int order=0;\n\t\t\t\t\t\t\t\t\t do {\n\t\t\t\t\t\t\t\t\t\t walk = tr.parent(walk);\n\t\t\t\t\t\t\t\t\t\t const auto *pd = kernel.properties.get<PartialDerivative>(walk);\n\t\t\t\t\t\t\t\t\t\t if(pd) {\n\t\t\t\t\t\t\t\t\t\t\t ++order;\n\t\t\t\t\t\t\t\t\t\t\t DEBUGLN( std::cerr << \"     derivative!\" << std::endl; );\n\t\t\t\t\t\t\t\t\t\t\t }\n\t\t\t\t\t\t\t\t\t\t else break;\n\t\t\t\t\t\t\t\t\t\t } while(walk != sum.node());\n\t\t\t\t\t\t\t\t\t this_fun_appearances.push_back(std::make_pair(fun_loc, order));\n\t\t\t\t\t\t\t\t\t }\n\t\t\t\t\t\t\t\t appearances[fun] = this_fun_appearances;\n\t\t\t\t\t\t\t\t return true;\n\t\t\t\t\t\t\t\t }\n\t\t\t\t\t\t\t );\n\n\t\t\t\t  // All functions scanned for this ODE.\n\t\t\t\t  for(auto& fun: appearances) {\n\t\t\t\t\t  for(auto& pr: fun.second) {\n\t\t\t\t\t\t  std::cerr << \"function \" << fun.first << \" order \" << pr.second << std::endl;\n\t\t\t\t\t\t  }\n\t\t\t\t\t  }\n\n\t\t\t  return true;\n\t\t\t  }\n\t\t  );\n\n\t// Move all terms except the highest-order derivative term to the\n\t// rhs of every ODE. If this term is not linear in that highest-derivative\n\t// term, throw an exception.\n\t\n\t\n\t// We now know the location of the highest order derivatives of each function.\n\t// Treat these as independent variables and construct a linear system so that\n\t// we can solve for these independent variables.\n\n\t//LinearExSystem ...;\n\t\n\t// \n\treturn result_t::l_no_action;\n\t}\n\n        \n"
  },
  {
    "path": "core/algorithms/first_order_form.hh",
    "content": "\n#pragma once\n\n#include \"Algorithm.hh\"\n\nnamespace cadabra {\n\n\t/// \\ingroup algorithms\n\t///\n\t/// Transform a (system of) higher order ODEs to first order, and ensure that\n\t/// the derivatives are on the lhs with all the other terms on the rhs.\n\n\tclass first_order_form : public Algorithm {\n\t\tpublic:\n\t\t\tfirst_order_form(const Kernel&, Ex& odes, Ex& funcs);\n\n\t\t\tvirtual bool     can_apply(iterator);\n\t\t\tvirtual result_t apply(iterator&);\n\n\t\tprivate:\n\t\t\tEx functions;\n\n\t\t\t// Location at which the above functions appear...\n\t\t\tstd::vector<Ex::iterator> locations;\n\t\t\t// ... and the order of the derivative on these functions.\n\t\t\tstd::vector<int>          orders;\n\t};\n\t\n}\n"
  },
  {
    "path": "core/algorithms/flatten_product.cc",
    "content": "\n#include \"algorithms/flatten_product.hh\"\n#include \"properties/PartialDerivative.hh\"\n\nusing namespace cadabra;\n\n\nflatten_product::flatten_product(const Kernel& k, Ex& tr)\n\t: Algorithm(k, tr), make_consistent_only(false), is_diff(false)\n\t{\n\t}\n\nbool flatten_product::can_apply(iterator it)\n\t{\n\tis_diff=false;\n\tif(*it->name!=\"\\\\prod\")\n\t\treturn false;\n\n\t// FIXME: acting on PartialDerivative has been disabled because\n\t// it really does not make sense anymore.\n\t//\t\t if(properties::get<PartialDerivative>(it)==0)\n\t//\t\t\t  return false;\n\t//\t\t else is_diff=true;\n\n\tif(!is_diff && tr.number_of_children(it)==1) return true;\n\tsibling_iterator facs=tr.begin(it);\n\twhile(facs!=tr.end(it)) {\n\t\tconst PartialDerivative *pd=kernel.properties.get<PartialDerivative>(facs);\n\t\tif((is_diff && pd) || (!is_diff && *facs->name==\"\\\\prod\"))\n\t\t\treturn true;\n\t\tif(is_diff) break;\n\t\t++facs;\n\t\t}\n\treturn false;\n\t}\n\nAlgorithm::result_t flatten_product::apply(iterator& it)\n\t{\n\t//\tdebugout << \"acting with flatten_product at \" << *it->name << std::endl;\n\tif(!is_diff && tr.number_of_children(it)==1) {\n\t\ttr.begin(it)->fl.bracket = it->fl.bracket;\n\t\tmultiply(tr.begin(it)->multiplier, *it->multiplier);\n\t\ttr.flatten(it);\n\t\tit=tr.erase(it);\n\t\tpushup_multiplier(it);\n\t\treturn result_t::l_applied;\n\t\t}\n\n\tresult_t ret=result_t::l_no_action;\n\tsibling_iterator facs=tr.begin(it);\n\tstr_node::bracket_t btype=facs->fl.bracket;\n\twhile(facs!=tr.end(it)) {\n\t\tconst PartialDerivative *pd=kernel.properties.get<PartialDerivative>(facs);\n\t\tif((is_diff && pd) || (!is_diff && *facs->name==\"\\\\prod\")) {\n\t\t\tstr_node::bracket_t cbtype=tr.begin(facs)->fl.bracket;\n\t\t\tif(!make_consistent_only || cbtype==str_node::b_none || cbtype==str_node::b_no) {\n\t\t\t\tsibling_iterator prodch=tr.begin(facs);\n\t\t\t\twhile(prodch!=tr.end(facs)) {\n\t\t\t\t\tprodch->fl.bracket=btype;\n\t\t\t\t\t++prodch;\n\t\t\t\t\t}\n\t\t\t\tsibling_iterator tmp=facs;\n\t\t\t\t++tmp;\n\t\t\t\ttr.flatten(facs);\n\t\t\t\tmultiply(it->multiplier,*facs->multiplier);\n\t\t\t\ttr.erase(facs);\n\t\t\t\tpushup_multiplier(it);\n\t\t\t\tfacs=tmp;\n\t\t\t\tret=result_t::l_applied;\n\t\t\t\t}\n\t\t\telse ++facs;\n\t\t\t}\n\t\telse ++facs;\n\t\tif(is_diff) break;\n\t\t}\n\treturn ret;\n\t}\n"
  },
  {
    "path": "core/algorithms/flatten_product.hh",
    "content": "\n#pragma once\n\n#include \"Algorithm.hh\"\n\nnamespace cadabra {\n\n\tclass flatten_product : public Algorithm {\n\t\tpublic:\n\t\t\tflatten_product(const Kernel&, Ex&);\n\n\t\t\tvirtual bool     can_apply(iterator);\n\t\t\tvirtual result_t apply(iterator&);\n\n\t\t\tbool make_consistent_only, is_diff;\n\t\t};\n\t}\n\n"
  },
  {
    "path": "core/algorithms/flatten_sum.cc",
    "content": "\n#include \"algorithms/flatten_sum.hh\"\n\nusing namespace cadabra;\n\nflatten_sum::flatten_sum(const Kernel& k, Ex& tr)\n\t: Algorithm(k, tr), make_consistent_only(false)\n\t{\n\t}\n\nbool flatten_sum::can_apply(iterator it)\n\t{\n\tif(*it->name!=\"\\\\sum\") return false;\n\tif(tr.number_of_children(it)==1 || tr.number_of_children(it)==0) return true;\n\tsibling_iterator facs=tr.begin(it);\n\twhile(facs!=tr.end(it)) {\n\t\tif(*(*facs).name==\"\\\\sum\")\n\t\t\treturn true;\n\t\t++facs;\n\t\t}\n\treturn false;\n\t}\n\nAlgorithm::result_t flatten_sum::apply(iterator &it)\n\t{\n\tresult_t ret=result_t::l_no_action;\n\n\tassert(*it->name==\"\\\\sum\");\n\n\tlong num=tr.number_of_children(it);\n\tif(num==1 && ! tr.begin(it)->is_range_wildcard() ) {\n\t\tmultiply(tr.begin(it)->multiplier, *it->multiplier);\n\t\ttr.flatten(it);\n\t\tit=tr.erase(it);\n\t\tret=result_t::l_applied;\n\t\t}\n\telse if(num==0) {\n\t\tnode_zero(it);\n\t\tret=result_t::l_applied;\n\t\t}\n\telse {\n\t\tsibling_iterator facs=tr.begin(it);\n\t\tstr_node::bracket_t btype_par=facs->fl.bracket;\n\t\twhile(facs!=tr.end(it)) {\n\t\t\tif(facs->fl.bracket!=str_node::b_none)\n\t\t\t\tbtype_par=facs->fl.bracket;\n\t\t\t++facs;\n\t\t\t}\n\t\tfacs=tr.begin(it);\n\t\twhile(facs!=tr.end(it)) {\n\t\t\tif(*facs->name==\"\\\\sum\") {\n\t\t\t\tsibling_iterator terms=tr.begin(facs);\n\t\t\t\tstr_node::bracket_t btype=terms->fl.bracket;\n\t\t\t\tif(!make_consistent_only || btype==str_node::b_none || btype==str_node::b_no) {\n\t\t\t\t\tret=result_t::l_applied;\n\t\t\t\t\tsibling_iterator tmp=facs;\n\t\t\t\t\t++tmp;\n\t\t\t\t\twhile(terms!=tr.end(facs)) {\n\t\t\t\t\t\tmultiply(terms->multiplier,*facs->multiplier);\n\t\t\t\t\t\tterms->fl.bracket=btype_par;\n\t\t\t\t\t\t//\t\t\t\t\t\tif(terms->fl.bracket==str_node::b_none)\n\t\t\t\t\t\t//\t\t\t\t\t\t\tterms->fl.bracket=facs->fl.bracket;\n\t\t\t\t\t\t++terms;\n\t\t\t\t\t\t}\n\t\t\t\t\ttr.flatten(facs);\n\t\t\t\t\ttr.erase(facs);\n\t\t\t\t\tfacs=tmp;\n\t\t\t\t\t}\n\t\t\t\telse ++facs;\n\t\t\t\t}\n\t\t\telse ++facs;\n\t\t\t}\n\t\t}\n\treturn ret;\n\t}\n"
  },
  {
    "path": "core/algorithms/flatten_sum.hh",
    "content": "#pragma once\n\n#include \"Algorithm.hh\"\n\nnamespace cadabra {\n\n\tclass flatten_sum : public Algorithm {\n\t\tpublic:\n\t\t\tflatten_sum(const Kernel&, Ex&);\n\n\t\t\tvirtual bool     can_apply(iterator);\n\t\t\tvirtual result_t apply(iterator&);\n\n\t\t\tbool make_consistent_only;\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/algorithms/impose_asym.tex",
    "content": "\\cdbalgorithm{impose\\_asym}{}\n\nImpose anti-symmetry in\nexternal indices, that is, remove terms in the expression which have\nanti-symmetry imposed on more than one index sitting on a symmetric\nobject.\n"
  },
  {
    "path": "core/algorithms/impose_bianchi.tex",
    "content": "\\cdbalgorithm{impose\\_bianchi}{}\n\nRemoves terms which are proportional to the (Garnir generalised)\nBianchi identity. It removes all products for which a set of indices\nin Garnir hook form is contracted with an anti-symmetric set. Here is\na simple example with a Riemann tensor,\n\\begin{screen}{1,2,3,4}\nA^{m n p}::AntiSymmetric.\nR_{m n p q}::RiemannTensor.\nR_{m n p q} A^{m n p};\n@impose_bianchi!(%);\n0;\n\\end{screen}\nHere is a more complicated one using a \\subsprop{TableauSymmetry}\nproperty,\n\\begin{screen}{1,2,3,4}\n\\epsilon^{m n p q}::EpsilonTensor.\nB_{m n p}::TableauSymmetry(shape={2,1}, indices={0,1,2}).\n\\epsilon^{m n p q} B_{m n p};\n@impose_bianchi!(%);\n0;\n\\end{screen}\nAn alternative way to obtain the same result is to project each tensor\nusing the generic \\subscommand{young\\_project\\_tensor} algorithm, and\nthen use \\subscommand{distribute} followed by \\subscommand{canonicalise}, but that\ngenerically takes much more time.\n\n\\cdbseeprop{RiemannTensor}\n\\cdbseeprop{TableauSymmetry}\n\\cdbseealgo{young_project_tensor}\n\\cdbseealgo{canonicalise}\n"
  },
  {
    "path": "core/algorithms/index_rename.tex",
    "content": "\\cdbalgorithm{index\\_rename}{}\n\nReplace index names. This should preferably be avoided, but can\nincidentally come in useful to relabel a large set of numbered indices\nin one go, as the following example shows.\n\\begin{screen}{1,2}\n{m#,n#}::Indices(spacetime).\nA_{m1 m2 m3} B_{m4 m2};\n@index_rename!(%){m}{n}{true};\nA_{n1 m2 n3} B_{n4 m2};\n\\end{screen}\nThe {\\tt true} argument to the algorithm indicates that numbered\nindices starting with the given index name should be relabelled too.\n\nGenerically, it is a better practise to avoid renaming indices\naltogether, and try to set up calculations such that they do not\ndepend on the names of indices.\n\n\\cdbseealgo{substitute}\n\n"
  },
  {
    "path": "core/algorithms/indexlist.tex",
    "content": "\\cdbalgorithm{indexlist}{}\n\nDisplays a\nlist of all indices in an expression, together with their type\n(dummy or free).\n"
  },
  {
    "path": "core/algorithms/indexsort.cc",
    "content": "\n#include \"IndexIterator.hh\"\n#include \"properties/TableauSymmetry.hh\"\n#include \"algorithms/indexsort.hh\"\n\nusing namespace cadabra;\n\nindexsort::indexsort(const Kernel& k, Ex& tr)\n\t: Algorithm(k, tr), tb(0)\n\t{\n\t}\n\nbool indexsort::can_apply(iterator st)\n\t{\n\tif(number_of_indices(kernel.properties, st)<2) return false;\n\ttb=kernel.properties.get<TableauBase>(st);\n\tif(tb) return true;\n\treturn false;\n\t}\n\nindexsort::less_indexed_treenode::less_indexed_treenode(const Kernel& k, Ex&, iterator i)\n\t: kernel(k), it(i)\n\t{\n\t}\n\nbool indexsort::less_indexed_treenode::operator()(unsigned int i1, unsigned int i2) const\n\t{\n\treturn subtree_exact_less(&kernel.properties,\n\t                          index_iterator::begin(kernel.properties, it, i1),\n\t                          index_iterator::begin(kernel.properties, it,i2) );\n\t}\n\nAlgorithm::result_t indexsort::apply(iterator& st)\n\t{\n\t//\ttxtout << \"indexsort acting on \" << *st->name << std::endl;\n\t//\ttxtout << properties::get<TableauBase>(st) << std::endl;\n\n\tresult_t res=result_t::l_no_action;\n\tEx backup(st);\n\n\tfor(unsigned int i=0; i<tb->size(kernel.properties, tr, st); ++i) {\n\t\tTableauSymmetry::tab_t tmptab(tb->get_tab(kernel.properties, tr, st, i));\n\t\tTableauSymmetry::tab_t origtab(tmptab);\n\t\tless_indexed_treenode comp(kernel,tr,st);\n\t\ttmptab.canonicalise(comp, false); // KP: why is this here? tb->only_column_exchange());\n\t\tTableauSymmetry::tab_t::iterator it1=origtab.begin();\n\t\tTableauSymmetry::tab_t::iterator it2=tmptab.begin();\n\t\twhile(it2!=tmptab.end()) {\n\t\t\tif(*it1!=*it2) {\n\t\t\t\ttr.replace_index(index_iterator::begin(kernel.properties,st,*it1),\n\t\t\t\t                 index_iterator::begin(kernel.properties,backup.begin(),*it2) );\n\t\t\t\t//\t\t\t\ttr.tensor_index(st,*it1)->multiplier=backup.tensor_index(backup.begin(),*it2)->multiplier;\n\t\t\t\tres = result_t::l_applied;\n\t\t\t\t}\n\t\t\t++it1;\n\t\t\t++it2;\n\t\t\t}\n\t\tif(*(tr.parent(st)->name)==\"\\\\prod\") {\n\t\t\tmultiply(tr.parent(st)->multiplier, multiplier_t(tmptab.multiplicity*origtab.multiplicity));\n\t\t\tpushup_multiplier(tr.parent(st));\n\t\t\t}\n\t\telse {\n\t\t\tmultiply(st->multiplier, multiplier_t(tmptab.multiplicity*origtab.multiplicity));\n\t\t\tpushup_multiplier(st);\n\t\t\t}\n\t\t}\n\treturn res;\n\t}\n\n"
  },
  {
    "path": "core/algorithms/indexsort.hh",
    "content": "#pragma once\n\n#include \"Algorithm.hh\"\n#include \"properties/TableauBase.hh\"\n\nnamespace cadabra {\n\n\tclass indexsort : public Algorithm {\n\t\tpublic:\n\t\t\tindexsort(const Kernel&, Ex&);\n\n\t\t\tvirtual bool     can_apply(iterator);\n\t\t\tvirtual result_t apply(iterator&);\n\n\t\t\tclass less_indexed_treenode {\n\t\t\t\tpublic:\n\t\t\t\t\tless_indexed_treenode(const Kernel&, Ex&, iterator it);\n\t\t\t\t\tbool operator()(unsigned int, unsigned int) const;\n\t\t\t\tprivate:\n\t\t\t\t\tconst Kernel&           kernel;\n\t\t\t\t\t//\t\t\t\t\tEx&          tr;\n\t\t\t\t\tEx::iterator it;\n\t\t\t\t};\n\t\tprivate:\n\t\t\tconst TableauBase     *tb;\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/algorithms/indexsort.tex",
    "content": "\\cdbalgorithm{indexsort}{}\n\nLexographically sorts indices of all tensors according to their Young\ntableau symmetries. This works in simple symmetric or anti-symmetric\ncases as expected:\n\\begin{screen}{1,2}\nA_{m n}::AntiSymmetric.\nA_{n m};\n@indexsort!(%);\n(-1) A_{m n};\n\\end{screen}\nIt also sorts index groups in tensors with row exchange\nsymmetries, such as the Riemann tensor,\n\\begin{screen}{1,2}\nR_{a b c d}::RiemannTensor.\nR_{d c a b};\n@indexsort!(%);\n(-1) R_{a b c d};\n\\end{screen}\nFor more complicated canonicalisation algorithms,\nsee \\subscommand{canonicalise} as well as \\subscommand{reduce}.\n\n\\cdbseealgo{canonicalise}\n\\cdbseealgo{reduce}\n\\cdbseeprop{AntiSymmetric}\n\\cdbseeprop{TableauSymmetry}\n"
  },
  {
    "path": "core/algorithms/inner.tex",
    "content": "\\cdbalgorithm{inner}{}\n\nConstruct an inner product between two\n  lists appearing in a list,\n\\begin{screen}{1,2,4}\nlst1:= {a_m, b_m ,c_m ,d_m ,e_m }:\nlst2:= @range[{1, @length[@(lst1)]}];\n\\{ 1,2,3,4,5 \\};\n@inner[ { @(lst1), @(lst2) } ];\na_m + 2 b_m + 3 c_m + 4 d_m + 5 e_m;\n\\end{screen}\nIn order to generate a list of the sum of elements,\nuse \\subscommand{list\\_sum} instead.\n\n\\cdbseealgo{list_sum}\n\\cdbseealgo{length}\n\\cdbseealgo{range}\n"
  },
  {
    "path": "core/algorithms/integrate_by_parts.cc",
    "content": "\n#include <iterator>\n#include \"algorithms/integrate_by_parts.hh\"\n#include \"properties/Derivative.hh\"\n#include \"Cleanup.hh\"\n#include \"Exceptions.hh\"\n\nusing namespace cadabra;\n\nintegrate_by_parts::integrate_by_parts(const Kernel& k, Ex& tr, Ex& af)\n\t: Algorithm(k, tr), away_from(af)\n\t{\n\t}\n\nbool integrate_by_parts::can_apply(iterator st)\n\t{\n\tif(*st->name==\"\\\\int\") return true;\n\treturn false;\n\t}\n\nAlgorithm::result_t integrate_by_parts::apply(iterator& it)\n\t{\n\tresult_t ret=result_t::l_no_action;\n\n\tauto sib=tr.begin(it);\n\twhile(sib!=tr.end(it)) {\n\t\tif(sib->fl.parent_rel==str_node::p_none) {\n\t\t\t// Have found the integrand.\n\t\t\tif(*sib->name==\"\\\\sum\") {\n\t\t\t\tauto term=tr.begin(sib);\n\t\t\t\twhile(term!=tr.end(sib)) {\n\t\t\t\t\titerator ti(term);\n\t\t\t\t\t++term;\n\t\t\t\t\tauto res=handle_term(it, ti);\n\t\t\t\t\tif(res==result_t::l_applied) {\n\t\t\t\t\t\tret=res;\n\t\t\t\t\t\tcleanup_dispatch(kernel, tr, ti);\n\t\t\t\t\t\t}\n\t\t\t\t\t}\n\t\t\t\t// Cleanup nested sums\n\t\t\t\titerator tmp(sib);\n\t\t\t\tcleanup_dispatch(kernel, tr, tmp);\n\t\t\t\t}\n\t\t\telse {\n\t\t\t\titerator ti(sib);\n\t\t\t\tret=handle_term(it, ti);\n\t\t\t\tif(ret==result_t::l_applied)\n\t\t\t\t\tcleanup_dispatch(kernel, tr, ti);\n\t\t\t\t}\n\t\t\tbreak;\n\t\t\t}\n\t\t++sib;\n\t\t}\n\n\tcleanup_dispatch(kernel, tr, it);\n\treturn ret;\n\t}\n\nbool integrate_by_parts::int_and_derivative_related(iterator, iterator) const\n\t{\n\treturn true;\n\t}\n\nbool integrate_by_parts::derivative_acting_on_arg(iterator der_it) const\n\t{\n\tsibling_iterator arg=tr.begin(der_it);\n\twhile(arg->is_index())\n\t\t++arg;\n\n\tEx_comparator comp(kernel.properties);\n\tauto top=away_from.begin();\n\tif( is_in( comp.equal_subtree(top, arg), {\n\tEx_comparator::match_t::subtree_match,\n\tEx_comparator::match_t::match_index_less,\n\tEx_comparator::match_t::match_index_greater\n\t} ) ) return true;\n\treturn false;\n\t}\n\nvoid integrate_by_parts::split_off_single_derivative(iterator, iterator der_it)\n\t{\n\tauto ni=number_of_direct_indices(der_it);\n\tif(ni==0 || ni==1) return;\n\n\tsibling_iterator sib=tr.begin(der_it);\n\t++sib;\n\tsibling_iterator arg=sib;\n\twhile(arg!=tr.end(der_it) && arg->is_index())\n\t\t++arg;\n\tif(arg==tr.end(der_it))\n\t\tthrow ConsistencyException(\"Derivative without argument encountered\");\n\tauto wrap=tr.wrap(arg, str_node(der_it->name));\n\twhile(sib!=wrap) {\n\t\tauto nxt=sib;\n\t\t++nxt;\n\t\ttr.move_before(tr.begin(wrap), sib);\n\t\tsib=nxt;\n\t\t}\n\t}\n\nAlgorithm::result_t integrate_by_parts::handle_term(iterator int_it, iterator& it)\n\t{\n\t// Either this is a Derivative node, in which case it is a total derivative.\n\t// Or this is a product, in which case we need to scan factors for a Derivative\n\t// and figure out whether it contains the searched-for expression.\n\n\tif(*it->name==\"\\\\ldots\") return result_t::l_no_action;\n\n\tconst Derivative *dtop=kernel.properties.get<Derivative>(it);\n\tif(dtop) {\n\t\tif(int_and_derivative_related(int_it, it)) {\n\t\t\tzero(it->multiplier);\n\t\t\treturn result_t::l_applied;\n\t\t\t}\n\t\t}\n\n\tprod_wrap_single_term(it);\n\n\tassert(*it->name==\"\\\\prod\");\n\tauto fac=tr.begin(it);\n\tint pos=0;\n\twhile(fac!=tr.end(it)) {\n\t\tconst Derivative *der=kernel.properties.get<Derivative>(fac);\n\t\tif(der) {\n\t\t\t// If this is a multiple partial derivative, we split off the\n\t\t\t// outermost derivative and then look at the remaining argument.\n\t\t\tsplit_off_single_derivative(int_it, fac);\n//\t\t\tstd::cerr << \"after split-off:\" << int_it << std::endl;\n//\t\t\tstd::cerr << \" c1: \" << int_and_derivative_related(int_it, fac) << std::endl;\n//\t\t\tstd::cerr << \" c2: \" << derivative_acting_on_arg(fac) << std::endl;\n\t\t\tif(int_and_derivative_related(int_it, fac) && derivative_acting_on_arg(fac) ) {\n\t\t\t\t// Generate one term with the derivative acting on all\n\t\t\t\t// factors which come before the derivative node (if\n\t\t\t\t// present).  Generate another one for those factors\n\t\t\t\t// coming after the derivative (if present).\n\n\t\t\t\t// FIXME: this does not yet take anti-commutativity of the\n\t\t\t\t// derivative itself into account.\n\n\t\t\t\tif(fac==tr.begin(it) || std::next(fac)==tr.end(it)) {\n\t\t\t\t\t// Derivative is first or last factor in product; generate one term only.\n\t\t\t\t\t// Note: total derivatives have already been handled!\n\n\t\t\t\t\tsibling_iterator from, to;\n\t\t\t\t\tif(fac==tr.begin(it)) {\n\t\t\t\t\t\tfrom=fac;\n\t\t\t\t\t\t++from;\n\t\t\t\t\t\tto=tr.end(it);\n\t\t\t\t\t\t}\n\t\t\t\t\telse {\n\t\t\t\t\t\tfrom=tr.begin(it);\n\t\t\t\t\t\tto=fac;\n\t\t\t\t\t\t}\n\t\t\t\t\tif(std::next(from)!=to)\n\t\t\t\t\t\tfrom = tr.wrap(from, to, str_node(\"\\\\prod\"));\n\n\t\t\t\t\t// Find the argument of the derivative. Needs to handle derivatives with\n\t\t\t\t\t// a single index, and derivatives with no index at all.\n\t\t\t\t\tauto der_arg = tr.begin(fac);\n\t\t\t\t\tif(der_arg==tr.end(fac))\n\t\t\t\t\t\tthrow ConsistencyException(\"integrate_by_parts: Derivative without argument encountered.\");\n\n\t\t\t\t\tif(der_arg->is_index()) {\n\t\t\t\t\t\t++der_arg;\n\t\t\t\t\t\t// This _has_ to be the argument because we have peeled off a single derivative.\n\t\t\t\t\t\tif(der_arg==tr.end(fac))\n\t\t\t\t\t\t\tthrow ConsistencyException(\"integrate_by_parts: Derivative without argument encountered.\");\n\t\t\t\t\t\t}\n\t\t\t\t\t\n\t\t\t\t\ttr.swap(der_arg, from);\n\t\t\t\t\ttr.swap(fac, der_arg);\n\t\t\t\t\tmultiply(it->multiplier, -1);\n\t\t\t\t\titerator tmp(fac);\n\t\t\t\t\tcleanup_dispatch(kernel, tr, tmp);\n\t\t\t\t\treturn result_t::l_applied;\n\t\t\t\t\t}\n\t\t\t\telse {\n\t\t\t\t\t// Two terms needed.\n\t\t\t\t\tEx sum(\"\\\\sum\");\n\t\t\t\t\tauto t1prod = sum.append_child(sum.begin(), it);\n\t\t\t\t\tauto t2prod = sum.append_child(sum.begin(), it);\n\n\t\t\t\t\t// First term.\n\t\t\t\t\tsibling_iterator from=sum.begin(t1prod);\n\t\t\t\t\tsibling_iterator to  =from;\n\t\t\t\t\tto+=pos;\n\t\t\t\t\tif(std::next(from)!=to)\n\t\t\t\t\t\tfrom = tr.wrap(from, to, str_node(\"\\\\prod\"));\n\n\t\t\t\t\tauto der_arg = tr.begin(to);\n\t\t\t\t\twhile(der_arg->is_index() && der_arg!=tr.end(to))\n\t\t\t\t\t\t++der_arg;\n\n\t\t\t\t\tif(der_arg==tr.end(to))\n\t\t\t\t\t\tthrow ConsistencyException(\"integrate_by_parts: Derivative without argument encountered.\");\n\n\t\t\t\t\ttr.swap(der_arg, from);\n\t\t\t\t\ttr.swap(to, der_arg);\n\t\t\t\t\tmultiply(t1prod->multiplier, -1);\n\t\t\t\t\titerator tmp(to);\n\t\t\t\t\tcleanup_dispatch(kernel, tr, tmp);\n\n\t\t\t\t\t// Second term.\n\t\t\t\t\tfrom=sum.begin(t2prod);\n\t\t\t\t\tfrom+=pos;\n\t\t\t\t\tauto der=from;\n\t\t\t\t\t++from;\n\t\t\t\t\tto  =sum.end(t2prod);\n\t\t\t\t\tif(std::next(from)!=to)\n\t\t\t\t\t\tfrom = tr.wrap(from, to, str_node(\"\\\\prod\"));\n\n\t\t\t\t\tder_arg = tr.begin(der);\n\t\t\t\t\twhile(der_arg->is_index() && der_arg!=tr.end(der))\n\t\t\t\t\t\t++der_arg;\n\n\t\t\t\t\tif(der_arg==tr.end(der))\n\t\t\t\t\t\tthrow ConsistencyException(\"integrate_by_parts: Derivative without argument encountered.\");\n\n\t\t\t\t\ttr.swap(der_arg, from);\n\t\t\t\t\ttr.swap(der, der_arg);\n\t\t\t\t\tmultiply(t2prod->multiplier, -1);\n\t\t\t\t\ttmp=der;\n\t\t\t\t\tcleanup_dispatch(kernel, tr, tmp);\n\n\t\t\t\t\t// Replace the original with the sum.\n\t\t\t\t\tit=tr.move_ontop(it, sum.begin());\n\n\t\t\t\t\treturn result_t::l_applied;\n\t\t\t\t\t}\n\n\t\t\t\t//\t\t\t\tfor(auto& pat: kernel.properties.pats) {\n\t\t\t\t//\t\t\t\t\tif(pat.first->name()==\"Coordinate\") {\n\t\t\t\t//\t\t\t\t\t\tstd::cerr << pat.second->obj << std::endl;\n\t\t\t\t//\t\t\t\t\t\t}\n\t\t\t\t//\t\t\t\t\t}\n\t\t\t\t}\n\t\t\telse {\n\t\t\t\t// Undo the split-off.\n\t\t\t\titerator tmp=fac;\n\t\t\t\tcleanup_dispatch(kernel, tr, tmp);\n\t\t\t\t}\n\t\t\t}\n\t\t++fac;\n\t\t++pos;\n\t\t}\n\n\treturn result_t::l_no_action;\n\t}\n\nEx integrate_by_parts::wrap(iterator, sibling_iterator, sibling_iterator ) const\n\t{\n\treturn Ex(\"\");\n\t}\n"
  },
  {
    "path": "core/algorithms/integrate_by_parts.cnb",
    "content": "{\n\t\"cells\" : \n\t[\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\algorithm{integrate_by_parts}{Integrate by parts away from the indicated expression}\\n\\nIntegrate by parts. This requires an expression with an\\nobject carrying a \\\\prop{Derivative} property. The algorithm should be given\\nan expression that any derivatives should be integrated away from. An example \\nmakes this more clear:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\algorithm{integrate_by_parts}{Integrate by parts away from the indicated expression}\\n\\nIntegrate by parts. This requires an expression with an\\nobject carrying a \\\\prop{Derivative} property. The algorithm should be given\\nan expression that any derivatives should be integrated away from. An example \\nmakes this more clear:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property PartialDerivative to~}\\\\partial{\\\\#}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\int{}\\\\partial_{m}{A} B C D\\\\, {\\\\rm d}x\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"\\\\partial{#}::PartialDerivative;\\nex:= \\\\int{ \\\\partial_{m}{ A } B C D }{x};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}-\\\\int{}A \\\\partial_{m}\\\\left(B C D\\\\right)\\\\, {\\\\rm d}x\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"integrate_by_parts(_, $A$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}-\\\\int{}A \\\\left(\\\\partial_{m}{B} C D+B \\\\partial_{m}{C} D+B C \\\\partial_{m}{D}\\\\right)\\\\, {\\\\rm d}x\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"product_rule(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}-\\\\int{}\\\\left(A \\\\partial_{m}{B} C D+A B \\\\partial_{m}{C} D+A B C \\\\partial_{m}{D}\\\\right)\\\\, {\\\\rm d}x\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"distribute(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"Note that \\\\algo{integrate_by_parts} only does the formal manipulation of moving the \\nderivative around. If you want to discard derivatives of objects which are constant,\\nyou need to use the \\\\prop{Depends} property to indicate on which coordinates or derivatives \\nobjects depend, and the \\\\algo{unwrap} algorithm to eliminate derivatives of constants, \\nas in the following lines.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"Note that \\\\algo{integrate_by_parts} only does the formal manipulation of moving the \\nderivative around. If you want to discard derivatives of objects which are constant,\\nyou need to use the \\\\prop{Depends} property to indicate on which coordinates or derivatives \\nobjects depend, and the \\\\algo{unwrap} algorithm to eliminate derivatives of constants, \\nas in the following lines.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Depends to~}\\\\left(B, \\\\linebreak[0] D\\\\right).\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"{B,D}::Depends(\\\\partial);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}-\\\\int{}\\\\left(A \\\\partial_{m}{B} C D+A B C \\\\partial_{m}{D}\\\\right)\\\\, {\\\\rm d}x\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"unwrap(ex);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1\n}\n"
  },
  {
    "path": "core/algorithms/integrate_by_parts.hh",
    "content": "\n\n#pragma once\n\n#include \"Algorithm.hh\"\n\nnamespace cadabra {\n\n\t/// \\ingroup algorithms\n\t///\n\t/// Integrate by parts away from the indicated derivative object.\n\n\n\tclass integrate_by_parts : public Algorithm {\n\t\tpublic:\n\t\t\tintegrate_by_parts(const Kernel&, Ex&, Ex&);\n\n\t\t\tvirtual bool     can_apply(iterator) override;\n\t\t\tvirtual result_t apply(iterator&) override;\n\n\t\tprivate:\n\t\t\t// Integrate by parts on a single term in the integrand. First\n\t\t\t// argument points to the integral, second to a term in the\n\t\t\t// integrand.\n\t\t\tresult_t handle_term(iterator, iterator&);\n\n\t\t\t// Are the given integral and derivative inverses of each-other?\n\t\t\tbool int_and_derivative_related(iterator int_it, iterator der_it) const;\n\n\t\t\t// Split one derivative from a multiple derivative.\n\t\t\tvoid split_off_single_derivative(iterator int_it, iterator der_it);\n\n\t\t\t// Wrap the indicated range of factor nodes inside the product node in\n\t\t\t// the derivative.\n\t\t\tEx wrap(iterator, sibling_iterator, sibling_iterator) const;\n\n\t\t\t// Determine whether the indicated derivative acts on the 'away_from'\n\t\t\t// expression.\n\t\t\tbool derivative_acting_on_arg(iterator der_it) const;\n\n\t\t\t// Expression to move derivative away from.\n\t\t\tEx away_from;\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/algorithms/join_gamma.cc",
    "content": "\n#include \"Storage.hh\"\n#include \"algorithms/join_gamma.hh\"\n#include \"Exceptions.hh\"\n#include \"Cleanup.hh\"\n#include \"properties/Integer.hh\"\n\nusing namespace cadabra;\n\njoin_gamma::join_gamma(const Kernel& kernel, Ex& tr_, bool e, bool g)\n\t: Algorithm(kernel, tr_), expand(e), use_generalised_delta_(g)\n\t{\n\t}\n\nvoid join_gamma::regroup_indices_(sibling_iterator gam1, sibling_iterator gam2,\n                                  unsigned int i, std::vector<Ex>& r1, std::vector<Ex>& r2)\n\t{\n\tunsigned int num1=tr.number_of_children(gam1);\n\n\tunsigned int len1=0;\n\tunsigned int len2=0;\n\tsibling_iterator g1=tr.begin(gam1);\n\twhile(len1<num1-i) {\n\t\tr1.push_back(Ex(g1));\n\t\t++g1;\n\t\t++len1;\n\t\t}\n\tsibling_iterator g2=tr.begin(gam2);\n\twhile(g2!=tr.end(gam2)) {\n\t\tif(len2>=i)\n\t\t\tr2.push_back(Ex(g2));\n\t\t++g2;\n\t\t++len2;\n\t\t}\n\tif(i>0) {\n\t\tg2=tr.begin(gam2);\n\t\tg1=tr.end(gam1);\n\t\t--g1;\n\t\tlen1=0;\n\t\tfor(len1=0; len1<i; ++len1) {\n\t\t\tr1.push_back(Ex(g1));\n\t\t\tr2.push_back(Ex(g2));\n\t\t\t--g1;\n\t\t\t++g2;\n\t\t\t}\n\t\t}\n\t}\n\nvoid join_gamma::append_prod_(const std::vector<Ex>& r1, const std::vector<Ex>& r2,\n                              unsigned int num1, unsigned int num2, unsigned int i, multiplier_t mult,\n                              Ex& rep, iterator loc)\n\t{\n\tEx::iterator gamma;\n\n\tbool hasgamma     =(num1-i>0 || num2-i>0);\n\tbool hasdelta     =(i>0);\n\tbool hasmoredeltas=(i>1 && !use_generalised_delta_);\n\n\tstr_node::bracket_t subsbr=gamma_bracket_;\n\tif((hasgamma && hasdelta) || hasmoredeltas) {\n\t\tloc=rep.append_child(loc, str_node(\"\\\\prod\", gamma_bracket_, (*loc).fl.parent_rel));\n\t\tloc->multiplier=rat_set.insert(mult).first;\n\t\tsubsbr=str_node::b_none;\n\t\t}\n\n\tif(num1-i>0 || num2-i>0) {\n\t\tgamma=rep.append_child(loc, str_node(*gamma_name_->name, subsbr));\n\t\tfor(unsigned int j=0; j<num1-i; ++j)\n\t\t\trep.append_child(gamma, r1[j].begin());\n\t\tfor(unsigned int j=0; j<num2-i; ++j)\n\t\t\trep.append_child(gamma, r2[j].begin()); //str_node(*r2[j].name, str_node::b_none, r2[j].fl.parent_rel));\n\t\tif(!hasdelta)\n\t\t\tgamma->multiplier=rat_set.insert(mult).first;\n\t\t}\n\n\tEx::iterator delt;\n\tif(use_generalised_delta_ && i>0) {\n\t\tif(gm1->metric.size()==0)\n\t\t\tthrow ConsistencyException(\"The gamma matrix property does not contain metric information.\");\n\n\t\tdelt=rep.append_child(loc, gm1->metric.begin());\n\t\tdelt->fl.bracket=subsbr;\n\t\ttr.erase_children(delt);\n\t\tif(!hasgamma)\n\t\t\tdelt->multiplier=rat_set.insert(mult).first;\n\t\t}\n\n\tfor(unsigned int j=0; j<i; ++j) {\n\t\tif(!use_generalised_delta_) {\n\t\t\tif(gm1->metric.size()==0)\n\t\t\t\tthrow ConsistencyException(\"The gamma matrix property does not contain metric information.\");\n\n\t\t\tdelt=rep.append_child(loc, gm1->metric.begin());\n\t\t\tdelt->fl.bracket=subsbr;\n\t\t\ttr.erase_children(delt);\n\t\t\t}\n\n\t\tif(tree_exact_less(&kernel.properties, r1[j+num1-i], r2[j+num2-i]) || use_generalised_delta_) {\n\t\t\trep.append_child(delt, r1[j+num1-i].begin());\n\t\t\trep.append_child(delt, r2[j+num2-i].begin());\n\t\t\t}\n\t\telse {\n\t\t\trep.append_child(delt, r2[j+num2-i].begin());\n\t\t\trep.append_child(delt, r1[j+num1-i].begin());\n\t\t\t}\n\t\t}\n\t}\n\nbool join_gamma::can_apply(iterator st)\n\t{\n\tif(*st->name==\"\\\\prod\") {\n\t\tsibling_iterator fc=tr.begin(st);\n\t\twhile(fc!=tr.end(st)) {\n\t\t\tgm1=kernel.properties.get<GammaMatrix>(fc);\n\t\t\tif(gm1) {\n\t\t\t\tstd::string target=get_index_set_name(begin_index(fc));\n\t\t\t\t++fc;\n\t\t\t\tif(fc!=tr.end(st)) {\n\t\t\t\t\tgm2=kernel.properties.get<GammaMatrix>(fc);\n\t\t\t\t\tif(gm2) {\n\t\t\t\t\t\tif(target==get_index_set_name(begin_index(fc))) {\n\t\t\t\t\t\t\tonly_expand.clear();\n\t\t\t\t\t\t\t// FIXME: handle only expansion into single term\n\t\t\t\t\t\t\t//\t\t\t\t\t\t\telse if(it->is_rational()) {\n\t\t\t\t\t\t\t//\t\t\t\t\t\t\t\tonly_expand.push_back(to_long(*it->multiplier));\n\t\t\t\t\t\t\treturn true;\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\telse --fc;\n\t\t\t\t\t\t}\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t++fc;\n\t\t\t}\n\t\t}\n\treturn false;\n\t}\n\nAlgorithm::result_t join_gamma::apply(iterator& st)\n\t{\n\tassert(*st->name==\"\\\\prod\");\n\tsibling_iterator gam1=tr.begin(st);\n\tsibling_iterator gam2;\n\twhile(gam1!=tr.end(st)) {\n\t\tconst GammaMatrix *gm1=kernel.properties.get<GammaMatrix>(gam1);\n\t\tif(gm1) {\n\t\t\tgamma_name_=gam1;\n\t\t\tgam2=gam1;\n\t\t\t++gam2;\n\t\t\tif(gam2!=tr.end(st)) {\n\t\t\t\tconst GammaMatrix *gm2=kernel.properties.get<GammaMatrix>(gam2);\n\t\t\t\tif(gm2)\n\t\t\t\t\tbreak;\n\t\t\t\t}\n\t\t\t}\n\t\t++gam1;\n\t\t}\n\tif(gam1==tr.end(st)) {\n\t\tst=tr.end();\n\t\treturn result_t::l_error;\n\t\t}\n\n\tgamma_bracket_=gam2->fl.bracket;\n\n\tEx rep;\n\tsibling_iterator top=rep.set_head(str_node(\"\\\\sum\"));\n\n\t// Figure out the dimension of the gamma matrix.\n\tbool bad_index=false;\n\tlong number_of_dimensions=-1; // i.e. not known.\n\tindex_iterator firstind=begin_index(gam1);\n\tstd::vector<str_node> seen_indices;\n\twhile(firstind!=end_index(gam1)) {  // select the maximum value; FIXME: be more refined...\n\t\tconst Integer *ipr=kernel.properties.get<Integer>(firstind, true);\n\t\tif(std::find(seen_indices.begin(), seen_indices.end(), *firstind)!=seen_indices.end()) {\n\t\t\tzero(st->multiplier);\n\t\t\tcleanup_dispatch(kernel, tr, st);\n\t\t\treturn result_t::l_applied;\n\t\t\t}\n\t\tseen_indices.push_back(*firstind);\n\t\tif(ipr && !bad_index) {\n\t\t\tif(ipr->difference.begin()->is_integer()) {\n\t\t\t\tnumber_of_dimensions=std::max(number_of_dimensions, to_long(*ipr->difference.begin()->multiplier));\n\t\t\t\t}\n\t\t\t}\n\t\telse {\n\t\t\tnumber_of_dimensions=-1;\n\t\t\tbad_index=true;\n\t\t\t}\n\t\t++firstind;\n\t\t}\n\tfirstind=begin_index(gam2);\n\tseen_indices.clear();\n\twhile(firstind!=end_index(gam2)) {  // select the maximum value; FIXME: be more refined...\n\t\tconst Integer *ipr=kernel.properties.get<Integer>(firstind, true);\n\t\tif(std::find(seen_indices.begin(), seen_indices.end(), *firstind)!=seen_indices.end()) {\n\t\t\tzero(st->multiplier);\n\t\t\tcleanup_dispatch(kernel, tr, st);\n\t\t\treturn result_t::l_applied;\n\t\t\t}\n\t\tseen_indices.push_back(*firstind);\n\t\tif(ipr && !bad_index) {\n\t\t\tif(ipr->difference.begin()->is_integer()) {\n\t\t\t\tnumber_of_dimensions=std::max(number_of_dimensions, to_long(*ipr->difference.begin()->multiplier));\n\t\t\t\t}\n\t\t\t}\n\t\telse {\n\t\t\tnumber_of_dimensions=-1;\n\t\t\tbad_index=true;\n\t\t\t}\n\t\t++firstind;\n\t\t}\n\n\t// iterators over the two index ranges\n\tunsigned int num1=tr.number_of_children(gam1);\n\tunsigned int num2=tr.number_of_children(gam2);\n\tfor(unsigned int i=0; i<=std::min(num1, num2); ++i) {\n\t\t// Ignore gammas with more than 'd' indices.\n\t\tif(number_of_dimensions>0) {\n\t\t\tif(num1+num2 > number_of_dimensions+2*i) {\n\t\t\t\tcontinue;\n\t\t\t\t}\n\t\t\t}\n\n\t\tif(only_expand.size()!=0) {\n\t\t\tif(std::find(only_expand.begin(), only_expand.end(), (int)(num1+num2-2*i))==only_expand.end())\n\t\t\t\t//\t\t\tif((int)(num1+num2-2*i)!=only_expand)\n\t\t\t\tcontinue;\n\t\t\t}\n\n\t\tstd::vector<Ex> r1, r2;\n\t\tregroup_indices_(gam1, gam2, i, r1, r2);\n\n\t\tmultiplier_t mult=multiplier_t( (combin::fact(mpz_class(num1))*combin::fact(mpz_class(num2))), \n\t\t\t\t\t\t\t\t\t\t\t\t  (combin::fact(mpz_class(num1-i))*combin::fact(mpz_class(num2-i))*combin::fact(mpz_class(i))) );\n\n\t\t//\t\tdebugout << \"join: contracting \" << i << \" indices...\" << std::endl;\n\t\tif(!expand) {\n\t\t\tappend_prod_(r1, r2, num1, num2, i, mult, rep, top);\n\t\t\t}\n\t\telse {\n\t\t\tcombin::combinations<Ex> c1(r1);\n\t\t\tcombin::combinations<Ex> c2(r2);\n\t\t\tif(num1-i>0)\n\t\t\t\tc1.sublengths.push_back(num1-i);\n\t\t\tif(num2-i>0)\n\t\t\t\tc2.sublengths.push_back(num2-i);\n\t\t\tif(use_generalised_delta_ && i>0)\n\t\t\t\tc1.sublengths.push_back(i);\n\t\t\telse {\n\t\t\t\tfor(unsigned int k=0; k<i; ++k)\n\t\t\t\t\tc1.sublengths.push_back(1); // the individual \\deltas, antisymmetrise 'first' group\n\t\t\t\t}\n\t\t\tif(i>0)\n\t\t\t\tc2.sublengths.push_back(i); // the individual \\deltas, do not antisymmetrise again.\n\n\t\t\t// Collect information about which indices to write in implicit antisymmetric form.\n\t\t\t// FIXME: this should move into combinatorics.hh\n\t\t\t//\t\t\titerator it=args_begin();\n\t\t\t//\t\t\twhile(it!=args_end()) {\n\t\t\t//\t\t\t\tif(*it->name==\"\\\\comma\") {\n\t\t\t//\t\t\t\t\tsibling_iterator cst=tr.begin(it);\n\t\t\t//\t\t\t\t\tcombin::range_t asymrange1, asymrange2;\n\t\t\t//\t\t\t\t\twhile(cst!=tr.end(it)) {\n\t\t\t//\t\t\t\t\t\tfor(unsigned int i1=0; i1<r1.size(); ++i1) {\n\t\t\t//\t\t\t\t\t\t\tif(subtree_exact_equal(&kernel.properties, r1[i1].begin(), cst, 0)) {\n\t\t\t//\t\t\t\t\t\t\t\tasymrange1.push_back(i1);\n\t\t\t//\t\t\t\t\t\t\t\tbreak;\n\t\t\t//\t\t\t\t\t\t\t\t}\n\t\t\t//\t\t\t\t\t\t\t}\n\t\t\t//\t\t\t\t\t\tfor(unsigned int i2=0; i2<r2.size(); ++i2) {\n\t\t\t//\t\t\t\t\t\t\tif(subtree_exact_equal(&kernel.properties, r2[i2].begin(), cst, 0)) {\n\t\t\t//\t\t\t\t\t\t\t\tasymrange2.push_back(i2);\n\t\t\t//\t\t\t\t\t\t\t\tbreak;\n\t\t\t//\t\t\t\t\t\t\t\t}\n\t\t\t//\t\t\t\t\t\t\t}\n\t\t\t//\t\t\t\t\t\t++cst;\n\t\t\t//\t\t\t\t\t\t}\n\t\t\t//\t\t\t\t\tc1.input_asym.push_back(asymrange1);\n\t\t\t//\t\t\t\t\tc2.input_asym.push_back(asymrange2);\n\t\t\t//\t\t\t\t\t}\n\t\t\t//\t\t\t\t++it;\n\t\t\t//\t\t\t\t}\n\n\t\t\tc1.permute();\n\t\t\tc2.permute();\n\n\t\t\tfor(unsigned int k=0; k<c1.size(); ++k) {\n\t\t\t\tfor(unsigned int l=0; l<c2.size(); ++l) {\n\t\t\t\t\tif(interrupted) {\n\t\t\t\t\t\t// FIXME: handle interrupts gracefully.\n\t\t\t\t\t\t//\t\t\t\t\t\ttxtout << \"join interrupted while producing GammaMatrix[\" << num1+num2-2*i\n\t\t\t\t\t\t//\t\t\t\t\t\t\t\t << \"] terms.\" << std::endl;\n\t\t\t\t\t\tinterrupted=false;\n\t\t\t\t\t\tst=tr.end();\n\t\t\t\t\t\treturn result_t::l_error;\n\t\t\t\t\t\t}\n\n\t\t\t\t\tint sgn=\n\t\t\t\t\t   combin::ordersign(c1[k].begin(), c1[k].end(), r1.begin(), r1.end())\n\t\t\t\t\t   *combin::ordersign(c2[l].begin(), c2[l].end(), r2.begin(), r2.end());\n\t\t\t\t\tmultiplier_t mul=1;\n\t\t\t\t\tif(use_generalised_delta_)\n\t\t\t\t\t\tmul=combin::fact(i);\n\n\t\t\t\t\tappend_prod_(c1[k], c2[l], num1, num2, i,\n\t\t\t\t\t             multiplier_t(c1.multiplier(k))*multiplier_t(c2.multiplier(l))*sgn*mul, rep, top);\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t}\n\t\t}\n\n\t// Finally, replace the old product by the new sum of products.\n\tif(rep.number_of_children(rep.begin())==0) {\n\t\tmultiply(st->multiplier,0);\n\t\treturn result_t::l_applied;\n\t\t}\n\telse if(rep.number_of_children(rep.begin())==1) {\n\t\trep.flatten(rep.begin());\n\t\trep.erase(rep.begin());\n\t\t}\n\n\tif(tr.number_of_children(st)>2) { // erase one gamma, replace the other one\n\t\tmultiply(rep.begin()->multiplier, *gam1->multiplier);\n\t\tmultiply(rep.begin()->multiplier, *gam2->multiplier);\n\t\ttr.replace(tr.erase(gam1), rep.begin());\n\t\t}\n\telse {\n\t\tmultiply(rep.begin()->multiplier, *st->multiplier);\n\t\tst = tr.replace(st, rep.begin());\n\t\t}\n\n\tcleanup_dispatch(kernel, tr, st);\n\t//   cleanup_expression(tr, st);\n\t//   cleanup_nests(tr, st);\n\treturn result_t::l_applied;\n\t}\n\n"
  },
  {
    "path": "core/algorithms/join_gamma.cnb",
    "content": "{\n\t\"cell_id\": 4331041475102962477,\n\t\"cells\": [\n\t\t{\n\t\t\t\"cell_id\": 9724265789201400066,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9710205063486850115,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\algorithm{join_gamma}{Work out the product of two generalised Dirac gamma matrices.}\\n\\nJoin two fully anti-symmetrised gamma matrix products according to the\\nexpression\\n\\\\begin{equation}\\n   \\\\Gamma^{b_{1}\\\\dots b_{n}}\\\\Gamma_{a_{1}\\\\dots a_{m}} =\\n      \\\\sum_{p=0}^{\\\\text{min}(n,m)}\\\\ \\\\frac{n! m!}{(n-p)! (m-p)! p!}\\n         \\\\Gamma^{[b_{1}\\\\ldots b_{n-p}}{}_{[a_{p+1}\\\\ldots a_{m}}\\n         \\\\eta^{b_{n-p+1}\\\\ldots b_{n}]}{}_{a_{1}\\\\ldots a_{m-p}]} \\\\, .\\n\\\\end{equation}\\nThis is the opposite of \\\\algo{split_gamma}.\\n\\nWithout further arguments, the anti-symmetrisations will be worked out\\nexplicitly (changed from v1). The setting the flag ``{\\\\tt expand}'' to\\nfalse instead keeps them implicit. Compare\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\algorithm{join_gamma}{Work out the product of two generalised Dirac gamma matrices.}\\n\\nJoin two fully anti-symmetrised gamma matrix products according to the\\nexpression\\n\\\\begin{equation}\\n   \\\\Gamma^{b_{1}\\\\dots b_{n}}\\\\Gamma_{a_{1}\\\\dots a_{m}} =\\n      \\\\sum_{p=0}^{\\\\text{min}(n,m)}\\\\ \\\\frac{n! m!}{(n-p)! (m-p)! p!}\\n         \\\\Gamma^{[b_{1}\\\\ldots b_{n-p}}{}_{[a_{p+1}\\\\ldots a_{m}}\\n         \\\\eta^{b_{n-p+1}\\\\ldots b_{n}]}{}_{a_{1}\\\\ldots a_{m-p}]} \\\\, .\\n\\\\end{equation}\\nThis is the opposite of \\\\algo{split_gamma}.\\n\\nWithout further arguments, the anti-symmetrisations will be worked out\\nexplicitly (changed from v1). The setting the flag ``{\\\\tt expand}'' to\\nfalse instead keeps them implicit. Compare\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 2947240613828784017,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 17300951477357957419,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 4472257405767180424,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\Gamma_{m n} \\\\Gamma_{p}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\Gamma_{m n} \\\\Gamma_{p}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 5629509010473670416,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 5284856236849942701,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\Gamma_{m n p} + 2\\\\Gamma_{m} g_{n p}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\Gamma_{m n p}+2\\\\Gamma_{m} g_{n p}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"\\\\Gamma{#}::GammaMatrix(metric=g).\\nex:= \\\\Gamma_{m n} \\\\Gamma_{p};\\njoin_gamma(ex, expand=False);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 12124424772252241647,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 10410932945721111027,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"with\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"with\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 15611766653738663169,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 3478877256762712012,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 8525122839191917179,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\Gamma_{m n} \\\\Gamma_{p}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\Gamma_{m n} \\\\Gamma_{p}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 10982516367231400775,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 4718554144418310653,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\Gamma_{m n p} + \\\\Gamma_{m} g_{n p}-\\\\Gamma_{n} g_{m p}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\Gamma_{m n p}+\\\\Gamma_{m} g_{n p}-\\\\Gamma_{n} g_{m p}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"\\\\Gamma{#}::GammaMatrix(metric=g).\\nex:= \\\\Gamma_{m n} \\\\Gamma_{p};\\njoin_gamma(ex, expand=True);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 9430663871766692927,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 17614251815043467495,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"Note that the gamma matrices need to have a metric associated to them\\nin order for this algorithm to work.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"Note that the gamma matrices need to have a metric associated to them\\nin order for this algorithm to work.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 16437583614585627386,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 5501818122039199499,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"In order to reduce the number of terms somewhat, one can instruct the algorithm\\nto make use of generalised Kronecker delta symbols in the result;\\nthese symbols are defined as\\n\\\\begin{equation}\\n\\\\delta^{r_1}{}_{s_1}{}^{r_2}{}_{s_2}\\\\cdots{}^{r_n}{}_{s_n}\\n= \\\\delta^{[r_1}{}_{s_1}\\\\delta^{r_2}{}_{s_2}\\\\cdots {}^{r_n]}{}_{s_n}\\\\, .\\n\\\\end{equation}\\nAnti-symmetrisation is implied in the set of even-numbered\\nindices. The use of these symbols is triggered by the \\\\verb|use_gendelta| option,\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"In order to reduce the number of terms somewhat, one can instruct the algorithm\\nto make use of generalised Kronecker delta symbols in the result;\\nthese symbols are defined as\\n\\\\begin{equation}\\n\\\\delta^{r_1}{}_{s_1}{}^{r_2}{}_{s_2}\\\\cdots{}^{r_n}{}_{s_n}\\n= \\\\delta^{[r_1}{}_{s_1}\\\\delta^{r_2}{}_{s_2}\\\\cdots {}^{r_n]}{}_{s_n}\\\\, .\\n\\\\end{equation}\\nAnti-symmetrisation is implied in the set of even-numbered\\nindices. The use of these symbols is triggered by the \\\\verb|use_gendelta| option,\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 7789778040065469689,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 7408405214600871734,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 2331280886798738445,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\Gamma_{m n} \\\\Gamma^{p q}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\Gamma_{m n} \\\\Gamma^{p q}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 14412138631638015690,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 12818109545470385155,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\Gamma_{m n}^{p q} + \\\\Gamma_{m}^{q} \\\\delta_{n}^{p}-\\\\Gamma_{m}^{p} \\\\delta_{n}^{q}-\\\\Gamma_{n}^{q} \\\\delta_{m}^{p} + \\\\Gamma_{n}^{p} \\\\delta_{m}^{q} + 2\\\\delta_{n}^{p}_{m}^{q}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\Gamma_{m n}\\\\,^{p q}+\\\\Gamma_{m}\\\\,^{q} \\\\delta_{n}\\\\,^{p}-\\\\Gamma_{m}\\\\,^{p} \\\\delta_{n}\\\\,^{q}-\\\\Gamma_{n}\\\\,^{q} \\\\delta_{m}\\\\,^{p}+\\\\Gamma_{n}\\\\,^{p} \\\\delta_{m}\\\\,^{q}+2\\\\delta_{n}\\\\,^{p}\\\\,_{m}\\\\,^{q}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"{m,n,p,q}::Indices(position=fixed).\\n\\\\Gamma{#}::GammaMatrix(metric=\\\\delta).\\nex:=\\\\Gamma_{m n} \\\\Gamma^{p q};\\njoin_gamma(_, use_gendelta=True);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 17814295563262518594,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"\"\n\t\t}\n\t],\n\t\"description\": \"Cadabra JSON notebook format\",\n\t\"version\": 1.0\n}\n"
  },
  {
    "path": "core/algorithms/join_gamma.hh",
    "content": "#pragma once\n\n#include \"Algorithm.hh\"\n#include \"properties/GammaMatrix.hh\"\n\nnamespace cadabra {\n\n\tclass join_gamma : public Algorithm {\n\t\tpublic:\n\t\t\tjoin_gamma(const Kernel&, Ex&, bool expand, bool use_gendelta);\n\n\t\t\tvirtual bool     can_apply(iterator);\n\t\t\tvirtual result_t apply(iterator&);\n\n\t\t\tbool expand;\n\t\t\tstd::vector<int>     only_expand;\n\t\t\tconst GammaMatrix   *gm1, *gm2;\n\t\tprivate:\n\t\t\tvoid regroup_indices_(sibling_iterator, sibling_iterator, unsigned int,\n\t\t\t                      std::vector<Ex>&, std::vector<Ex>& );\n\t\t\tvoid append_prod_(const std::vector<Ex>& r1, const std::vector<Ex>& r2,\n\t\t\t                  unsigned int num1, unsigned int num2, unsigned int i, multiplier_t mult,\n\t\t\t                  Ex& rep, iterator loc);\n\n\t\t\tbool                use_generalised_delta_;\n\t\t\tEx::iterator   gamma_name_;\n\t\t\tstr_node::bracket_t gamma_bracket_;\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/algorithms/keep_terms.cc",
    "content": "\n#include \"Cleanup.hh\"\n#include \"algorithms/keep_terms.hh\"\n\nusing namespace cadabra;\n\nkeep_terms::keep_terms(const Kernel& k, Ex& tr, std::vector<int> terms)\n\t: Algorithm(k, tr), terms_(terms)\n\t{\n\t}\n\nbool keep_terms::can_apply(iterator it)\n\t{\n\tif(*it->name!=\"\\\\sum\") return false;\n\treturn true;\n\t}\n\nAlgorithm::result_t keep_terms::apply(iterator& it)\n\t{\n\tresult_t res=result_t::l_no_action;\n\n\tint count=0;\n\tsibling_iterator walk=tr.begin(it);\n\twhile(walk!=tr.end(it)) {\n\t\tif(std::find(terms_.begin(), terms_.end(), count)==terms_.end()) {\n\t\t\tnode_zero(walk);\n\t\t\tres=result_t::l_applied;\n\t\t\t}\n\t\t++count;\n\t\t++walk;\n\t\t}\n\n\tcleanup_dispatch(kernel, tr, it);\n\n\treturn res;\n\t}\n\n"
  },
  {
    "path": "core/algorithms/keep_terms.hh",
    "content": "\n#pragma once\n\n#include \"Algorithm.hh\"\n\nnamespace cadabra {\n\n\tclass keep_terms : public Algorithm {\n\t\tpublic:\n\t\t\tkeep_terms(const Kernel&, Ex&, std::vector<int> terms);\n\n\t\t\tvirtual bool     can_apply(iterator);\n\t\t\tvirtual result_t apply(iterator&);\n\n\t\tprivate:\n\t\t\tstd::vector<int> terms_;\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/algorithms/keep_terms.tex",
    "content": "\\cdbalgorithm{keep\\_terms}{\\it terms=[{\\sf list of term numbers}]}\n\nKeep the terms indicated by the list, dropping all others.\n\\begin{screen}{1,2,3}\nex:= A + B + C + D + E + F;\nkeep_terms(_, [2,4])\nC + E\n\\end{screen}\nNote that counting starts from zero.\n\n\\cdbseealgo{keep_weight}\n\\cdbseealgo{take_match}\n"
  },
  {
    "path": "core/algorithms/keep_weight.cnb",
    "content": "{\n\t\"cells\" : \n\t[\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\algorithm{keep_weight}{Keep terms with indicated weight}\\n\\nKeep only those terms for which a product has the indicated\\nweight. Weights are computed by making use of the \\\\prop{Weight}\\nproperty of symbols. This algorithm does the opposite\\nof \\\\algo{drop_weight}.\\n\\nAs an example, consider the simple case in which we want to keep all\\nterms with 3~fields. This is done using\\n\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\algorithm{keep_weight}{Keep terms with indicated weight}\\n\\nKeep only those terms for which a product has the indicated\\nweight. Weights are computed by making use of the \\\\prop{Weight}\\nproperty of symbols. This algorithm does the opposite\\nof \\\\algo{drop_weight}.\\n\\nAs an example, consider the simple case in which we want to keep all\\nterms with 3~fields. This is done using\\n\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Weight to~}\\\\left[A,~\\\\discretionary{}{}{} B\\\\right].\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}A B B+A A A+A B+B\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}A B B+A A A\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"{A,B}::Weight(label=field);\\nex:=A B B + A A A + A B + B;\\nkeep_weight(_, $field=3$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"However, you can also do more complicated things by assigning non-unit\\nweights to symbols, as in the example below,\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"However, you can also do more complicated things by assigning non-unit\\nweights to symbols, as in the example below,\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Weight to~}\\\\left[A,~\\\\discretionary{}{}{} B\\\\right].\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Weight to~}C.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}A B B+A A A+A B+A C+B\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"{A,B}::Weight(label=field);\\nC::Weight(label=field, value=2);\\nex:= A B B + A A A + A B + A C + B;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}A B B+A A A+A C\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"keep_weight(_, $field=3$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"Weights also apply to tensorial expressions. Consider e.g.~a situation\\nin which we have a polynomial of the type\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"Weights also apply to tensorial expressions. Consider e.g.~a situation\\nin which we have a polynomial of the type\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}c^{a}+c^{a}\\\\,_{b} x^{b}+c^{a}\\\\,_{b c} x^{b} x^{c}+c^{a}\\\\,_{b c d} x^{b} x^{c} x^{d}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex:=c^{a} + c^{a}_{b} x^{b} + c^{a}_{b c} x^{b} x^{c} + c^{a}_{b c d} x^{b} x^{c} x^{d};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"and we want to keep only the quadratic term. This can be done using\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"and we want to keep only the quadratic term. This can be done using\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Weight to~}x^{a}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Weight to~}c^{\\\\#}.\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"x^{a}::Weight(label=crd, value=1);\\nc^{#}::Weight(label=crd, value=0);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}c^{a}\\\\,_{b c} x^{b} x^{c}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"keep_weight(ex, $crd=2$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"Weights can be ``inherited'' by operators by using\\nthe \\\\prop{WeightInherit} property. Here is an example using\\npartial derivatives,\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"Weights can be ``inherited'' by operators by using\\nthe \\\\prop{WeightInherit} property. Here is an example using\\npartial derivatives,\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Weight to~}\\\\left[\\\\phi,~\\\\discretionary{}{}{} \\\\chi\\\\right].\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property PartialDerivative to~}\\\\partial{\\\\#}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property WeightInherit to~}\\\\partial{\\\\#}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\phi \\\\partial_{0}{\\\\phi}+\\\\partial_{0}{\\\\lambda}+\\\\lambda \\\\partial_{3}{\\\\chi}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\lambda \\\\partial_{3}{\\\\chi}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"{\\\\phi,\\\\chi}::Weight(label=small, value=1);\\n\\\\partial{#}::PartialDerivative;\\n\\\\partial{#}::WeightInherit(label=all, type=multiplicative);\\nex:=\\\\phi \\\\partial_{0}{\\\\phi} + \\\\partial_{0}{\\\\lambda} + \\\\lambda \\\\partial_{3}{\\\\chi};\\nkeep_weight(_, $small=1$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"If you want to use weights for dimension counting, in which operators\\ncan also carry a dimension themselves (e.g.~derivatives), then use the\\n\\\\verb|self| attribute,\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"If you want to use weights for dimension counting, in which operators\\ncan also carry a dimension themselves (e.g.~derivatives), then use the\\n\\\\verb|self| attribute,\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"reset();\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Weight to~}\\\\left[\\\\phi,~\\\\discretionary{}{}{} \\\\chi\\\\right].\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Coordinate to~}x.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property PartialDerivative to~}\\\\partial{\\\\#}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property WeightInherit to~}\\\\partial{\\\\#}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\phi \\\\partial_{x}{\\\\phi}+\\\\phi \\\\chi+\\\\partial_{x}\\\\left(\\\\phi {\\\\chi}^{2}\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"{\\\\phi,\\\\chi}::Weight(label=length, value=1);\\n\\nx::Coordinate;\\n\\\\partial{#}::PartialDerivative;\\n\\\\partial{#}::WeightInherit(label=length, type=multiplicative, self=-1);\\n\\nex:=\\\\phi \\\\partial_{x}{\\\\phi} + \\\\phi\\\\chi + \\\\partial_{x}{ \\\\phi \\\\chi**2 };\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\phi \\\\partial_{x}{\\\\phi}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"keep_weight(_, $length=1$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1\n}\n"
  },
  {
    "path": "core/algorithms/list_sum.tex",
    "content": "\\cdbalgorithm{list\\_sum}{}\n\nIn an expression containing sums of identical-length lists, create one\nnew list constructed by adding the elements at the same position in\neach list. Example,\n\\begin{screen}{1,2,3}\n{a, b, 7 c + q, d, e} - {-f, g, h, i, j}:\n@list_sum!(%):\n@sumflatten!(%);\n\\{ a + f, b - g, 7c + q - h, d - i, e - j \\};\n\\end{screen}\nTo generate a list of the products of the elements,\nuse \\subscommand{inner} instead.\n\n\\cdbseealgo{inner}\n\\cdbseealgo{range}\n"
  },
  {
    "path": "core/algorithms/listflatten.tex",
    "content": "\\cdbalgorithm{listflatten}{}\n\nTurns nested lists into one list, as in\n\\begin{equation}\n\\{ a, b, \\{ c, d \\} \\} \\rightarrow \\{ a, b, c, d \\}\\,.\n\\end{equation}\nIn terms of code this reads\n\\begin{screen}{1,2}\n{a,b,{c,d}};\n@listflatten!(%);\n\\{ a,b,c,d \\};\n\\end{screen}\n~\n\n\\cdbseealgo{prodflatten}\n\\cdbseealgo{listflatten}\n\\cdbseealgo{distribute}\n"
  },
  {
    "path": "core/algorithms/lower_free_indices.cc",
    "content": "\n#include \"lower_free_indices.hh\"\n\nusing namespace cadabra;\n\nlower_free_indices::lower_free_indices(const Kernel& k, Ex& tr, bool lower_)\n\t: Algorithm(k, tr), lower(lower_)\n\t{\n\t}\n\nbool lower_free_indices::can_apply(iterator )\n\t{\n\treturn true;\n\t}\n\nAlgorithm::result_t lower_free_indices::apply(iterator& it)\n\t{\n\tauto res = result_t::l_no_action;\n\n\tauto sib=tr.begin(it);\n\twhile(sib!=tr.end(it)) {\n\t\tif(sib->fl.parent_rel==(lower?str_node::p_super:str_node::p_sub)) {\n\t\t\tauto indices = kernel.properties.get<Indices>(sib, true);\n\t\t\tif(indices && indices->position_type==Indices::position_t::free) {\n\t\t\t\tsib->fl.parent_rel=(lower?str_node::p_sub:str_node::p_super);\n\t\t\t\tres=result_t::l_applied;\n\t\t\t\t}\n\t\t\t}\n\t\t++sib;\n\t\t}\n\n\treturn res;\n\t}\n"
  },
  {
    "path": "core/algorithms/lower_free_indices.cnb",
    "content": "{\n\t\"cells\" : \n\t[\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\algorithm{lower_free_indices}{Make all free indices in an expression subscripts.}\\n\\nFree indicies (indices declared with the \\\\verb|Indices(position=free)| property) can appear as subscripts or superscripts,\\nbut sometimes it is useful to move them all into the same position. \"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\algorithm{lower_free_indices}{Make all free indices in an expression subscripts.}\\n\\nFree indicies (indices declared with the \\\\verb|Indices(position=free)| property) can appear as subscripts or superscripts,\\nbut sometimes it is useful to move them all into the same position. \"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Indices(position=free) to~}\\\\left[a,~\\\\discretionary{}{}{} b,~\\\\discretionary{}{}{} c\\\\right].\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Indices(position=fixed) to~}\\\\left[m,~\\\\discretionary{}{}{} n,~\\\\discretionary{}{}{} p\\\\right].\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"A_{a b m} B^{a b m}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}A_{a b m} B^{a b m}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"{a,b,c}::Indices(name=A, position=free);\\n{m,n,p}::Indices(name=B, position=fixed);\\nex:=A_{a b m} B^{a b m};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"A_{a b m} B_{a b}^{m}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}A_{a b m} B_{a b}\\\\,^{m}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"lower_free_indices(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"The opposite of this is \\\\algo{raise_free_indices}, which moves all indices to be superscripts.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"The opposite of this is \\\\algo{raise_free_indices}, which moves all indices to be superscripts.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1\n}\n"
  },
  {
    "path": "core/algorithms/lower_free_indices.hh",
    "content": "\n#pragma once\n\n#include \"Algorithm.hh\"\n\nnamespace cadabra {\n\n\tclass lower_free_indices : public Algorithm {\n\t\tpublic:\n\t\t\tlower_free_indices(const Kernel&, Ex&, bool lower);\n\n\t\t\tvirtual bool     can_apply(iterator) override;\n\t\t\tvirtual result_t apply(iterator&) override;\n\n\t\tprivate:\n\t\t\tbool lower;\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/algorithms/lr_tensor.cc",
    "content": "\n#include \"Cleanup.hh\"\n#include \"algorithms/lr_tensor.hh\"\n#include \"properties/Tableau.hh\"\n#include \"properties/FilledTableau.hh\"\n\nusing namespace cadabra;\n\nlr_tensor::lr_tensor(const Kernel& k, Ex& tr)\n\t: tab_basics(k, tr)\n\t{\n\t}\n\nbool lr_tensor::can_apply(iterator it)\n\t{\n\tif(*it->name==\"\\\\prod\") {\n\t\tsibling_iterator sib=tr.begin(it);\n\t\ttab1=tr.end(it);\n\t\ttab2=tr.end(it);\n\t\twhile(sib!=tr.end(it)) {\n\t\t\tif(kernel.properties.get<Tableau>(sib)) {\n\t\t\t\t// FIXME: test that tab2 has the same dimension!\n\t\t\t\tif(tab1==tr.end(it))\n\t\t\t\t\ttab1=sib;\n\t\t\t\telse {\n\t\t\t\t\ttab2=sib;\n\t\t\t\t\tbreak;\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t++sib;\n\t\t\t}\n\t\tif(tab2!=tr.end(it)) return true;\n\n\t\tsib=tr.begin(it);\n\t\ttab1=tr.end(it);\n\t\ttab2=tr.end(it);\n\t\twhile(sib!=tr.end(it)) {\n\t\t\tif(kernel.properties.get<FilledTableau>(sib)) {\n\t\t\t\tif(tab1==tr.end(it))\n\t\t\t\t\ttab1=sib;\n\t\t\t\telse {\n\t\t\t\t\ttab2=sib;\n\t\t\t\t\tbreak;\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t++sib;\n\t\t\t}\n\t\tif(tab2!=tr.end(it)) return true;\n\t\t}\n\treturn false;\n\t}\n\nAlgorithm::result_t lr_tensor::apply(iterator& it)\n\t{\n\tconst Tableau       *t1=kernel.properties.get<Tableau>(tab1);\n\tconst FilledTableau *f1=kernel.properties.get<FilledTableau>(tab1);\n\t\n\tif(t1) do_tableau(it, t1->dimension);\n\telse   do_filledtableau(it, f1->dimension);\n\n\treturn result_t::l_applied;\n\t}\n\n// The format is \\ftab{a,b,c}{d,e}{f}.\n//\nvoid lr_tensor::do_filledtableau(iterator& it, int dimension)\n\t{\n\tbool even_only=false;\n\tbool singlet_rules=false;\n\n\t// FIXME: put arguments back\n\t//\tif(has_argument(\"EvenOnly\"))\n\t//\t\t even_only=true;\n\t//\tif(has_argument(\"SingletRules\"))\n\t//\t\t singlet_rules=true;\n\n\tuinttab_t one, two;\n\n\t// For efficiency we store integers in the tableaux, not the actual\n\t// Ex objects.\n\tuinttabs_t prod;\n\n\tnum_to_it.clear();\n\ttree_to_numerical_tab(tab1, one);\n\ttree_to_numerical_tab(tab2, two);\n\n\tyngtab::LR_tensor(one,two,dimension,prod.get_back_insert_iterator());\n\n\tEx rep;\n\titerator top=rep.set_head(str_node(\"\\\\sum\"));\n\n\tif(singlet_rules) tabs_to_singlet_rules(prod, top);\n\telse              tabs_to_tree(prod, top, tab1, even_only);\n\n\tsibling_iterator sib=rep.begin(top);\n\twhile(sib!=rep.end(top)) {\n\t\tsib->fl.bracket=str_node::b_round;\n\t\t++sib;\n\t\t}\n\n\ttr.replace(tab1, rep.begin());\n\ttr.erase(tab2);\n\tcleanup_dispatch(kernel, tr, it);\n\t}\n\nvoid lr_tensor::do_tableau(iterator& it, int dimension)\n\t{\n\tbool even_only=false;\n\t// FIXME: put arguments back in\n\t//\tif(has_argument(\"EvenOnly\"))\n\t//\t\t even_only=true;\n\n\tyngtab::tableau one, two;\n\tyngtab::tableaux<yngtab::tableau> prod;\n\n\tsibling_iterator sib=tr.begin(tab1);\n\twhile(sib!=tr.end(tab1)) {\n\t\tone.add_row(to_long(*sib->multiplier));\n\t\t++sib;\n\t\t}\n\tsib=tr.begin(tab2);\n\twhile(sib!=tr.end(tab2)) {\n\t\ttwo.add_row(to_long(*sib->multiplier));\n\t\t++sib;\n\t\t}\n\tyngtab::LR_tensor(one,two,dimension,prod.get_back_insert_iterator());\n\n\tEx rep;\n\titerator top=rep.set_head(str_node(\"\\\\sum\"));\n\titerator tt;\n\tyngtab::tableaux<yngtab::tableau>::tableau_container_t::iterator tabit=prod.storage.begin();\n\twhile(tabit!=prod.storage.end()) {\n\t\t// Keep only the diagrams which lead to a singlet if requested.\n\t\tif(even_only)\n\t\t\tfor(unsigned int r=0; r<(*tabit).number_of_rows(); ++r)\n\t\t\t\tif((*tabit).row_size(r)%2!=0)\n\t\t\t\t\tgoto next_tab;\n\n\t\ttt=tr.append_child(top, str_node(tab1->name));\n\t\tmultiply(tt->multiplier, tabit->multiplicity);\n\t\tfor(unsigned int r=0; r<(*tabit).number_of_rows(); ++r)\n\t\t\tmultiply(tr.append_child(tt, str_node(\"1\"))->multiplier, (*tabit).row_size(r));\n\nnext_tab:\n\t\t++tabit;\n\t\t}\n\n\ttr.replace(tab1, rep.begin());\n\ttr.erase(tab2);\n\tcleanup_dispatch(kernel, tr, it);\n\t}\n\n\n\n"
  },
  {
    "path": "core/algorithms/lr_tensor.cnb",
    "content": "{\n\t\"cell_id\" : 3529167709221557556,\n\t\"cells\" : \n\t[\n\t\t{\n\t\t\t\"cell_id\" : 13034055670763138185,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 1827403652131020063,\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\algorithm{lr_tensor}{Compute the tensor product of two Young tableaux}\\n\\nCompute the tensor product of two tableaux or filled tableaux. The\\nalgorithm acts on objects which have the \\\\prop{Tableau}\\nor \\\\prop{FilledTableau} property, through which it is possible to\\nset the dimension. The standard Littlewoord-Richardson algorithm is\\nused to construct the tableaux in the tensor product. An example\\nwith \\\\prop{Tableau} objects is given below.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\algorithm{lr_tensor}{Compute the tensor product of two Young tableaux}\\n\\nCompute the tensor product of two tableaux or filled tableaux. The\\nalgorithm acts on objects which have the \\\\prop{Tableau}\\nor \\\\prop{FilledTableau} property, through which it is possible to\\nset the dimension. The standard Littlewoord-Richardson algorithm is\\nused to construct the tableaux in the tensor product. An example\\nwith \\\\prop{Tableau} objects is given below.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 16444213282225630456,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 7013982910635865128,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\" : 6896144092362820956,\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"\\\\tableau(2 , 2) \\\\tableau(2 , 2 , 1)\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\ydiagram{2,2} \\\\otimes \\\\ydiagram{2,2,1}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 18383779963759909769,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\" : 6438556487849008423,\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"\\\\tableau(4 , 4 , 1) + \\\\tableau(4 , 3 , 2) + \\\\tableau(4 , 3 , 1 , 1) + \\\\tableau(4 , 2 , 2 , 1) + \\\\tableau(3 , 3 , 2 , 1) + \\\\tableau(3 , 3 , 1 , 1 , 1) + \\\\tableau(3 , 2 , 2 , 2) + \\\\tableau(3 , 2 , 2 , 1 , 1) + \\\\tableau(2 , 2 , 2 , 2 , 1)\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\ydiagram{4,4,1} \\\\oplus \\\\ydiagram{4,3,2} \\\\oplus \\\\ydiagram{4,3,1,1} \\\\oplus \\\\ydiagram{4,2,2,1} \\\\oplus \\\\ydiagram{3,3,2,1} \\\\oplus \\\\ydiagram{3,3,1,1,1} \\\\oplus \\\\ydiagram{3,2,2,2} \\\\oplus \\\\ydiagram{3,2,2,1,1} \\\\oplus \\\\ydiagram{2,2,2,2,1}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"\\\\tableau{#}::Tableau(dimension=10).\\nex:=\\\\tableau{2}{2} \\\\tableau{2}{2}{1};\\nlr_tensor(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 8976033163574012771,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 5151218776706305939,\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"The same example, but now with \\\\prop{FilledTableau} objects, is\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"The same example, but now with \\\\prop{FilledTableau} objects, is\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 9523266717767366903,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 11355820928989299880,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\" : 216113284021982139,\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"\\\\ftableau({0, 0} , {1, 1}) \\\\ftableau({a, a} , {b, b})\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\ytableaushort{{0}{0},{1}{1}} \\\\otimes \\\\ytableaushort{{a}{a},{b}{b}}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"\\\\ftableau{#}::FilledTableau(dimension=10).\\nex:=\\\\ftableau{0,0}{1,1} \\\\ftableau{a,a}{b,b};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 5195300418742761648,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 5296348393282597622,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\" : 172526134674294674,\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"\\\\ftableau({0, 0, a, a} , {1, 1, b, b}) + \\\\ftableau({0, 0, a, a} , {1, 1, b} , b) + \\\\ftableau({0, 0, a, a} , {1, 1} , {b, b}) + \\\\ftableau({0, 0, a} , {1, 1, b} , a , b) + \\\\ftableau({0, 0, a} , {1, 1} , {a, b} , b) + \\\\ftableau({0, 0} , {1, 1} , {a, a} , {b, b})\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\ytableaushort{{0}{0}{a}{a},{1}{1}{b}{b}} \\\\oplus \\\\ytableaushort{{0}{0}{a}{a},{1}{1}{b},{b}} \\\\oplus \\\\ytableaushort{{0}{0}{a}{a},{1}{1},{b}{b}} \\\\oplus \\\\ytableaushort{{0}{0}{a},{1}{1}{b},{a},{b}} \\\\oplus \\\\ytableaushort{{0}{0}{a},{1}{1},{a}{b},{b}} \\\\oplus \\\\ytableaushort{{0}{0},{1}{1},{a}{a},{b}{b}}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"lr_tensor(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 5845876384223724695,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 11331787825651452460,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\" : 16271400071290618863,\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"\\\\ftableau(1) \\\\ftableau(2) \\\\ftableau(3) \\\\ftableau(4)\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\ytableaushort{{1}} \\\\otimes \\\\ytableaushort{{2}} \\\\otimes \\\\ytableaushort{{3}} \\\\otimes \\\\ytableaushort{{4}}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex:=\\\\ftableau{1} \\\\ftableau{2} \\\\ftableau{3} \\\\ftableau{4};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 2051960691195043819,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 131905216012038794,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\" : 14250555613362516514,\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"\\\\ftableau({1, 2, 3, 4}) + \\\\ftableau({1, 2, 3} , 4) + \\\\ftableau({1, 2, 4} , 3) + \\\\ftableau({1, 2} , {3, 4}) + \\\\ftableau({1, 2} , 3 , 4) + \\\\ftableau({1, 3, 4} , 2) + \\\\ftableau({1, 3} , {2, 4}) + \\\\ftableau({1, 3} , 2 , 4) + \\\\ftableau({1, 4} , 2 , 3) + \\\\ftableau(1 , 2 , 3 , 4)\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\ytableaushort{{1}{2}{3}{4}} \\\\oplus \\\\ytableaushort{{1}{2}{3},{4}} \\\\oplus \\\\ytableaushort{{1}{2}{4},{3}} \\\\oplus \\\\ytableaushort{{1}{2},{3}{4}} \\\\oplus \\\\ytableaushort{{1}{2},{3},{4}} \\\\oplus \\\\ytableaushort{{1}{3}{4},{2}} \\\\oplus \\\\ytableaushort{{1}{3},{2}{4}} \\\\oplus \\\\ytableaushort{{1}{3},{2},{4}} \\\\oplus \\\\ytableaushort{{1}{4},{2},{3}} \\\\oplus \\\\ytableaushort{{1},{2},{3},{4}}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"converge(ex):\\n   lr_tensor(_)\\n   distribute(_)\\n;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 12366589379348825691,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1\n}\n"
  },
  {
    "path": "core/algorithms/lr_tensor.hh",
    "content": "#pragma once\n\n#include \"Algorithm.hh\"\n#include \"algorithms/tab_basics.hh\"\n\nnamespace cadabra {\n\n\tclass lr_tensor : public tab_basics {\n\t\tpublic:\n\t\t\tlr_tensor(const Kernel&, Ex&);\n\n\t\t\tvirtual bool     can_apply(iterator) override;\n\t\t\tvirtual result_t apply(iterator&) override;\n\n\t\t\tsibling_iterator tab1, tab2;\n\n\t\tprivate:\n\t\t\tvoid do_tableau(iterator&, int dimension);\n\t\t\tvoid do_filledtableau(iterator&, int dimension);\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/algorithms/lsolve.tex",
    "content": "\\cdbalgorithm{lsolve}{}\n\nSolve a system of linear equations over integers. Example,\n\\begin{screen}{1,2}\n{ a0+2*a2 + a3= 3, -a0 - a2 + a3= - (8/3) , a3 = 3};\n@lsolve(%){a0,a2,a3};\n{a0 = 34/3, a2 = (-17/3), a3 = 3};\n\\end{screen}\nUnderdetermined and inconsistent systems are handled as expected:\neither some coefficients are left unfixed or the system is returned\nand an error message is printed.\n\n\\cdbseealgo{decompose}\n"
  },
  {
    "path": "core/algorithms/map_mma.cc",
    "content": "\n#include \"algorithms/map_mma.hh\"\n#include \"MMACdb.hh\"\n#include \"properties/Coordinate.hh\"\n#include \"properties/Symbol.hh\"\n#include \"SympyCdb.hh\"\n\nusing namespace cadabra;\n\n//#define DEBUG 1\n\nmap_mma::map_mma(const Kernel& k, Ex& tr, const std::string& head)\n\t: Algorithm(k, tr), head_(head)\n\t{\n\t}\n\nbool map_mma::can_apply(iterator st)\n\t{\n\t// For \\components nodes we need to map at the level of the individual\n\t// component values, not the top \\components node.\n\tif(*st->name==\"\\\\components\") return false;\n\tif(*st->name==\"\\\\equals\") return false;\n\tif(*st->name==\"\\\\comma\") return false;\n\n\tleft.clear();\n\tindex_factors.clear();\n\tindex_map_t ind_free, ind_dummy;\n\tclassify_indices(st, ind_free, ind_dummy);\n\n\tbool still_ok=true;\n\n\t// Determine if any of the free indices are harmless (Coordinates or Symbols).\n\tfor(auto& ind: ind_free) {\n\t\tconst Coordinate *cdn=kernel.properties.get<Coordinate>(ind.second, true);\n\t\tconst Symbol     *smb=kernel.properties.get<Symbol>(ind.second, true);\n\t\tif(cdn==0 && smb==0) {\n\t\t\tstill_ok=false;\n\t\t\tbreak;\n\t\t\t}\n\t\t}\n\n\tif(still_ok && ind_dummy.size()==0) return true;\n\n\t// In a product, it is still possible that there is a sub-product which\n\t// contains no indices.\n\tif(*st->name==\"\\\\prod\") {\n\t\t// Find the factors in the product which have a proper index on them. Do this by\n\t\t// starting at the index, and if it is not coordinate or symbol, then go up until we\n\t\t// reach the first child level of the product.\n\t\tfor(auto& ind: ind_free) {\n\t\t\tconst Coordinate *cdn=kernel.properties.get<Coordinate>(ind.second, true);\n\t\t\tconst Symbol     *smb=kernel.properties.get<Symbol>(ind.second, true);\n\t\t\tif(cdn==0 && smb==0) {\n\t\t\t\tauto fac=tr.parent(ind.second);\n\t\t\t\twhile(tr.parent(fac)!=iterator(st))\n\t\t\t\t\tfac=tr.parent(fac);\n\t\t\t\tindex_factors.insert(fac);\n\t\t\t\t}\n\t\t\t}\n\t\tfor(auto& ind: ind_dummy) {\n\t\t\tconst Coordinate *cdn=kernel.properties.get<Coordinate>(ind.second, true);\n\t\t\tconst Symbol     *smb=kernel.properties.get<Symbol>(ind.second, true);\n\t\t\tif(cdn==0 && smb==0) {\n\t\t\t\tauto fac=tr.parent(ind.second);\n\t\t\t\twhile(tr.parent(fac)!=iterator(st))\n\t\t\t\t\tfac=tr.parent(fac);\n\t\t\t\tindex_factors.insert(fac);\n\t\t\t\t}\n\t\t\t}\n\t\tsibling_iterator sib=tr.begin(st);\n\t\twhile(sib!=tr.end(st)) {\n\t\t\tif(index_factors.find(iterator(sib))==index_factors.end())\n\t\t\t\tleft.push_back(sib);\n\t\t\t++sib;\n\t\t\t}\n\t\treturn left.size()>0;\n\t\t}\n\n\treturn false;\n\t}\n\nAlgorithm::result_t map_mma::apply(iterator& it)\n\t{\n#ifdef DEBUG\n\tstd::cerr << \"map_mma on \" << Ex(it) << std::endl;\n#endif\n\n\tstd::vector<std::string> wrap, args;\n\tif(head_.size()>0)\n\t\twrap.push_back(head_);\n\n\tif(left.size()>0) {\n\t\tEx prod(\"\\\\prod\");\n\t\tfor(auto& fac: left)\n\t\t\tprod.append_child(prod.begin(), fac);\n\t\tauto top=prod.begin();\n\t\t// std::cerr << \"Feeding to sympy \" << prod << std::endl;\n\t\tMMA::apply_mma(kernel, prod, top, wrap, args, \"\");\n\t\t// Now remove the non-index carrying factors and replace with\n\t\t// the factors of 'prod' just simplified.\n\t\ttr.insert_subtree(*left.begin(), top);\n\t\t// std::cerr << \"Before erasing \" << Ex(it) << std::endl;\n\t\tfor(auto& kl: left)\n\t\t\ttr.erase(kl);\n\t\t// std::cerr << \"After erasing \" << Ex(it) << std::endl;\n\n\t\treturn result_t::l_applied;\n\t\t}\n\telse {\n\t\tMMA::apply_mma(kernel, tr, it, wrap, args, \"\");\n\t\tit.skip_children();\n\t\treturn result_t::l_applied;\n\t\t}\n\t}\n"
  },
  {
    "path": "core/algorithms/map_mma.hh",
    "content": "\n#pragma once\n\n#include \"Algorithm.hh\"\n\nnamespace cadabra {\n\n\t/// \\ingroup algorithms\n\t///\n\t/// Functionality to act with Mathematica on all scalar parts of an\n\t/// expression, and keep the result in-place. This is a higher-level\n\t/// thing than 'mma::apply' in the MMACdb.cc module.\n\n\tclass map_mma : public Algorithm {\n\t\tpublic:\n\t\t\tmap_mma(const Kernel&, Ex&, const std::string& head);\n\n\t\t\tvirtual bool     can_apply(iterator);\n\t\t\tvirtual result_t apply(iterator&);\n\n\t\tprivate:\n\t\t\tstd::string               head_;\n\t\t\tstd::vector<Ex::iterator> left;\n\t\t\tstd::set<Ex::iterator>    index_factors;\n\t\t};\n\n\t}\n\n"
  },
  {
    "path": "core/algorithms/map_sympy.cc",
    "content": "\n#include \"algorithms/map_sympy.hh\"\n#include \"properties/Coordinate.hh\"\n#include \"properties/Symbol.hh\"\n#include \"SympyCdb.hh\"\n#include \"IndexClassifier.hh\"\n\nusing namespace cadabra;\n\n//#define DEBUG 1\n\nmap_sympy::map_sympy(const Kernel& k, Ex& tr, const std::string& head, std::vector<std::string> args=std::vector<std::string>() )\n\t: Algorithm(k, tr), head_(head), args_(args)\n\t{\n\t}\n\nbool map_sympy::can_apply(iterator st)\n\t{\n\t// For \\components nodes we need to map at the level of the individual\n\t// component values, not the top \\components node.\n\tif(*st->name==\"\\\\components\") return false;\n\tif(*st->name==\"\\\\equals\") return false;\n\tif(*st->name==\"\\\\comma\") return false;\n\tif(*st->name==\"\\\\arrow\") return false;\n\n\tleft.clear();\n\tindex_factors.clear();\n\tIndexClassifier ic(kernel);\n\tIndexClassifier::index_map_t ind_free, ind_dummy;\n\tic.classify_indices(st, ind_free, ind_dummy);\n\n\tbool still_ok=true;\n\n\t// Determine if any of the free indices are harmless (Coordinates or Symbols).\n\tfor(auto& ind: ind_free) {\n\t\tconst Coordinate *cdn=kernel.properties.get<Coordinate>(ind.second, true);\n\t\tconst Symbol     *smb=kernel.properties.get<Symbol>(ind.second, true);\n\t\tif(cdn==0 && smb==0) {\n\t\t\tstill_ok=false;\n\t\t\tbreak;\n\t\t\t}\n\t\t}\n\n\tif(still_ok && ind_dummy.size()==0) return true;\n\n\t// In a product, it is still possible that there is a sub-product which\n\t// contains no indices.\n\tif(*st->name==\"\\\\prod\") {\n\t\t// Find the factors in the product which have a proper index on them. Do this by\n\t\t// starting at the index, and if it is not coordinate or symbol, then go up until we\n\t\t// reach the first child level of the product.\n\t\tfor(auto& ind: ind_free) {\n\t\t\tconst Coordinate *cdn=kernel.properties.get<Coordinate>(ind.second, true);\n\t\t\tconst Symbol     *smb=kernel.properties.get<Symbol>(ind.second, true);\n\t\t\tif(cdn==0 && smb==0) {\n\t\t\t\tauto fac=tr.parent(ind.second);\n\t\t\t\twhile(tr.parent(fac)!=iterator(st))\n\t\t\t\t\tfac=tr.parent(fac);\n\t\t\t\tindex_factors.insert(fac);\n\t\t\t\t}\n\t\t\t}\n\t\tfor(auto& ind: ind_dummy) {\n\t\t\tconst Coordinate *cdn=kernel.properties.get<Coordinate>(ind.second, true);\n\t\t\tconst Symbol     *smb=kernel.properties.get<Symbol>(ind.second, true);\n\t\t\tif(cdn==0 && smb==0) {\n\t\t\t\tauto fac=tr.parent(ind.second);\n\t\t\t\twhile(tr.parent(fac)!=iterator(st))\n\t\t\t\t\tfac=tr.parent(fac);\n\t\t\t\tindex_factors.insert(fac);\n\t\t\t\t}\n\t\t\t}\n\t\tsibling_iterator sib=tr.begin(st);\n\t\twhile(sib!=tr.end(st)) {\n\t\t\tif(index_factors.find(iterator(sib))==index_factors.end())\n\t\t\t\tleft.push_back(sib);\n\t\t\t++sib;\n\t\t\t}\n\t\treturn left.size()>0;\n\t\t}\n\n\treturn false;\n\t}\n\nAlgorithm::result_t map_sympy::apply(iterator& it)\n\t{\n#ifdef DEBUG\n\tstd::cerr << \"map_sympy on \" << Ex(it) << std::endl;\n#endif\n\n\tstd::vector<std::string> wrap;\n\twrap.push_back(head_);\n\n\tif(left.size()>0) {\n\t\tEx prod(\"\\\\prod\");\n\t\tfor(auto& fac: left)\n\t\t\tprod.append_child(prod.begin(), fac);\n\t\tauto top=prod.begin();\n\t\t// std::cerr << \"Feeding to sympy \" << prod << std::endl;\n\t\tsympy::apply(kernel, prod, top, wrap, args_, \"\");\n\t\t// Now remove the non-index carrying factors and replace with\n\t\t// the factors of 'prod' just simplified.\n\t\ttr.insert_subtree(*left.begin(), top);\n\t\t// std::cerr << \"Before erasing \" << Ex(it) << std::endl;\n\t\tfor(auto& kl: left)\n\t\t\ttr.erase(kl);\n\t\t// std::cerr << \"After erasing \" << Ex(it) << std::endl;\n\n\t\treturn result_t::l_applied;\n\t\t}\n\telse {\n\t\tsympy::apply(kernel, tr, it, wrap, args_, \"\");\n\t\tit.skip_children();\n\t\treturn result_t::l_applied;\n\t\t}\n\t}\n"
  },
  {
    "path": "core/algorithms/map_sympy.cnb",
    "content": "{\n\t\"cells\" : \n\t[\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\algorithm{map_sympy}{Map Sympy algorithms to Cadabra expressions}\\n\\nCadabra expressions are typically tensor expressions, which you cannot feed directly\\ninto Sympy. With the \\\\algo{map_sympy} function you can recursively apply Sympy algorithms\\nto the scalar parts of Cadabra expressions.\\n\\nThe simplest example is when you have a scalar expression in Cadabra, for instance\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\algorithm{map_sympy}{Map Sympy algorithms to Cadabra expressions}\\n\\nCadabra expressions are typically tensor expressions, which you cannot feed directly\\ninto Sympy. With the \\\\algo{map_sympy} function you can recursively apply Sympy algorithms\\nto the scalar parts of Cadabra expressions.\\n\\nThe simplest example is when you have a scalar expression in Cadabra, for instance\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\int \\\\sin{x}\\\\,\\\\,{\\\\rm d}x\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex:= \\\\int{\\\\sin(x)}{x};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}-\\\\cos{x}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"map_sympy(ex);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"The inert Cadabra expression gets evaluated by Sympy and then stored again in the `ex` object,\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"The inert Cadabra expression gets evaluated by Sympy and then stored again in the `ex` object,\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}-\\\\cos{x}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"In more complicated cases you may have a tensorial expression which you would like to \\nsimplify using Sympy, for instance\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"In more complicated cases you may have a tensorial expression which you would like to \\nsimplify using Sympy, for instance\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\left({\\\\left(\\\\sin{x}\\\\right)}^{2}+{\\\\left(\\\\cos{x}\\\\right)}^{2}\\\\right) A_{m}-A_{m}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex:= (\\\\sin(x)**2 + \\\\cos(x)**2) A_{m} - A_{m};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}0\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"map_sympy(ex, \\\"simplify\\\");\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1\n}\n"
  },
  {
    "path": "core/algorithms/map_sympy.hh",
    "content": "\n#pragma once\n\n#include \"Algorithm.hh\"\n\nnamespace cadabra {\n\n\t/// \\ingroup algorithms\n\t///\n\t/// Functionality to act with Sympy on all scalar parts of an expression, and\n\t/// keep the result in-place. This is a higher-level thing than\n\t/// 'sympy::apply' in the SympyCdb.cc module.\n\n\tclass map_sympy : public Algorithm {\n\t\tpublic:\n\t\t\tmap_sympy(const Kernel&, Ex&, const std::string& head, std::vector<std::string> args);\n\n\t\t\tvirtual bool     can_apply(iterator);\n\t\t\tvirtual result_t apply(iterator&);\n\n\t\tprivate:\n\t\t\tstd::string               head_;\n\t\t\tstd::vector<std::string>  args_;\n\t\t\tstd::vector<Ex::iterator> left;\n\t\t\tstd::set<Ex::iterator>    index_factors;\n\t\t};\n\n\t}\n\n"
  },
  {
    "path": "core/algorithms/meld.cc",
    "content": "\n#include <vector>\n#include <set>\n#include <numeric>\n\n#include \"Cleanup.hh\"\n#include \"DisplayTerminal.hh\"\n#include \"Functional.hh\"\n#include \"Linear.hh\"\n#include \"Exceptions.hh\"\n\n#include \"algorithms/meld.hh\"\n\n#include \"properties/Coordinate.hh\"\n#include \"properties/Derivative.hh\"\n#include \"properties/Diagonal.hh\"\n#include \"properties/ImplicitIndex.hh\"\n#include \"properties/RiemannTensor.hh\"\n#include \"properties/PartialDerivative.hh\"\n#include \"properties/Symbol.hh\"\n#include \"properties/Trace.hh\"\n#include \"properties/Traceless.hh\"\n#include \"properties/TableauBase.hh\"\n#include \"properties/SelfNonCommuting.hh\"\n#include \"properties/NonCommuting.hh\"\n\n// #define DEBUG __FILE__\n#include \"Debug.hh\"\n\nusing namespace cadabra;\n\nmeld::meld(const Kernel& kernel, Ex& ex, bool project_as_sum)\n\t: Algorithm(kernel, ex)\n\t, index_map(kernel)\n\t, project_as_sum(project_as_sum)\n\t{\n\t}\n\nmeld::~meld()\n\t{\n\t}\n\nbool meld::can_apply(iterator it)\n\t{\n\treturn\n\t\tcan_apply_diagonals(it) ||\n\t\tcan_apply_traceless(it) ||\n\t\tcan_apply_cycle_traces(it) ||\n\t\tcan_apply_tableaux(it);\n\t}\n\nmeld::result_t meld::apply(iterator& it)\n\t{\n\tresult_t res = result_t::l_no_action;\n\n\tif (can_apply_diagonals(it) && apply_diagonals(it)) {\n\t\tres = result_t::l_applied;\n\t\tcleanup_dispatch(kernel, tr, it);\n#ifdef DEBUG\n\t\tstd::cerr << \"meld::can_apply: diagonals,\" << it << std::endl;\n#endif\n\t\t}\n\tif (can_apply_traceless(it) && apply_traceless(it)) {\n\t\tres = result_t::l_applied;\n\t\tcleanup_dispatch(kernel, tr, it);\n#ifdef DEBUG\n\t\tstd::cerr << \"meld::can_apply: traceless,\" << it << std::endl;\n#endif\n\t\t}\n\tif (can_apply_cycle_traces(it) && apply_cycle_traces(it)) {\n\t\tres = result_t::l_applied;\n\t\tcleanup_dispatch(kernel, tr, it);\n#ifdef DEBUG\n\t\tstd::cerr << \"meld::can_apply: cycle,\" << it << std::endl;\n#endif\n\t\t}\n\t//if (can_apply_side_relations(it) && apply_side_relations(it)) {\n\t//\tres = result_t::l_applied;\n\t//\tcleanup_dispatch(kernel, tr, it);\n\t//}\n\tif (can_apply_tableaux(it) && apply_tableaux(it)) {\n\t\tres = result_t::l_applied;\n#ifdef DEBUG\n\t\tstd::cerr << \"meld::can_apply: tableaux before cleanup,\" << it << std::endl;\n#endif\n\t\tcleanup_dispatch(kernel, tr, it);\n#ifdef DEBUG\n\t\tstd::cerr << \"meld::can_apply: tableaux,\" << it << std::endl;\n#endif\n\t\t}\n\n\treturn res;\n\t}\n\n\n// *_diagonals\n// Remove Diagonal objects with numerical indices which are not all the same.\n\nbool meld::can_apply_diagonals(iterator it)\n\t{\n\tauto diagonal = kernel.properties.get<Diagonal>(it);\n\treturn diagonal != nullptr;\n\t}\n\nbool meld::apply_diagonals(iterator it)\n\t{\n\t\n\tassert(kernel.properties.get<Diagonal>(it) != nullptr);\n\tindex_iterator indit = begin_index(it);\n\tif (indit->is_rational()) {\n\t\tindex_iterator indit2 = indit;\n\t\t++indit2;\n\t\twhile (indit2 != end_index(it)) {\n\t\t\tif (indit2->is_rational() == false)\n\t\t\t\tbreak;\n\t\t\tif (indit2->multiplier != indit->multiplier) {\n\t\t\t\tzero(it->multiplier);\n\t\t\t\treturn true;\n\t\t\t\t}\n\t\t\t++indit2;\n\t\t\t}\n\t\t}\n\treturn false;\n\t}\n\n\n// *_traceless\n// // Remove any traces of traceless tensors.\n\nbool meld::can_apply_traceless(iterator it)\n\t{\n\tauto traceless = kernel.properties.get<Traceless>(it);\n\treturn traceless != nullptr;\n\t}\n\nbool meld::apply_traceless(iterator it)\n\t{\n\tconst Traceless* trl = kernel.properties.get<Traceless>(it);\n\tunsigned int ihits = 0;\n\ttree_exact_less_mod_prel_obj comp(&kernel.properties);\n\tstd::set<Ex, tree_exact_less_mod_prel_obj> countmap(comp);\n\tindex_iterator indit = begin_index(it);\n\twhile (indit != end_index(it)) {\n\t\tbool incremented_now = false;\n\t\tauto ind = kernel.properties.get<Indices>(indit, true);\n\t\tif (ind) {\n\t\t\t// The indexs need to be in the set for which the object is\n\t\t\t// traceless (if specified, otherwise accept all).\n\t\t\tif (trl->index_set_names.find(ind->set_name) != trl->index_set_names.end() || trl->index_set_names.size() == 0) {\n\t\t\t\tincremented_now = true;\n\t\t\t\t++ihits;\n\t\t\t\t}\n\t\t\t}\n\t\telse incremented_now = true;\n\t\t// Having no name is treated as having the right name\n\t\tif (countmap.find(Ex(indit)) == countmap.end()) {\n\t\t\tcountmap.insert(Ex(indit));\n\t\t\t}\n\t\telse if (incremented_now) {\n\t\t\tzero(it->multiplier);\n\t\t\treturn true;\n\t\t\t}\n\t\t++indit;\n\t\t}\n\titerator parent = it;\n\tif (tr.number_of_children(it) == 1 && !tr.is_head(it)) parent = tr.parent(it);\n\tconst Trace* trace = kernel.properties.get<Trace>(parent);\n\tif (trace) {\n\t\tint tmp;\n\t\tauto impi = kernel.properties.get_with_pattern<ImplicitIndex>(it, tmp, \"\");\n\t\tif (impi.first->explicit_form.size() > 0) {\n\t\t\t// Does the explicit form have two more indices of the right type?\n\t\t\tEx::iterator eform = impi.first->explicit_form.begin();\n\t\t\tunsigned int ehits = 0;\n\t\t\tindit = begin_index(eform);\n\t\t\twhile (indit != end_index(eform)) {\n\t\t\t\tauto ind = kernel.properties.get<Indices>(indit, true);\n\t\t\t\tif (trl->index_set_names.find(ind->set_name) != trl->index_set_names.end() && ind->set_name == trace->index_set_name) ++ehits;\n\t\t\t\tif (ehits - ihits > 1) {\n\t\t\t\t\tzero(it->multiplier);\n\t\t\t\t\treturn true;\n\t\t\t\t\t}\n\t\t\t\t++indit;\n\t\t\t\t}\n\t\t\t}\n\t\t}\n\treturn false;\n\t}\n\n\n// *_tableaux\n\nbool meld::can_apply_tableaux(iterator it)\n\t{\n\t// This node can be a sum, but the rest of the tree must be strictly monomial. Also\n\t// helps if there is an index lying around somewhere\n\tbool found_index = false;\n\tfor (Ex::iterator beg = it.begin(), end = it.end(); beg != end; ++beg) {\n\t\tif (*beg->name == \"\\\\sum\" || *beg->name == \"\\\\equals\" || *beg->name == \"\\\\comma\")\n\t\t\treturn false;\n\t\tif (beg->is_index()) {\n\t\t\tfound_index = true;\n\t\t\tbeg.skip_children();\n\t\t\t}\n\t\t}\n\n\treturn found_index;\n\t}\n\nbool meld::apply_tableaux(iterator it)\n\t{\n\tif (*it->name == \"\\\\equals\") {\n\t\tbool res = false;\n\t\tEx::sibling_iterator side = it.begin();\n\t\tres |= apply_tableaux(side);\n\t\t++side;\n\t\tres |= apply_tableaux(side);\n\t\treturn res;\n\t\t}\n\n#ifdef DEBUG\n\tstd::cerr << \"Applying tableau for node \" << *it->name << std::endl;\n#endif\n\t\n\tusing namespace boost::numeric::ublas;\n\tusing matrix_type = matrix<mpq_class>;\n\tusing vector_type = vector<mpq_class>;\n\n\tbool applied = false;\n\n\t// Collect terms which have a matching structure (modulo index positions) into groups\n\tstd::vector<std::vector<ProjectedTerm>> patterns;\n\tfor (const auto& term : split_it(it, \"\\\\sum\")) {\n\t\tProjectedTerm projected_term(kernel, index_map, tr, term);\n#ifdef DEBUG\n\t\tstd::cout << \"meld::apply_tableaux: projected = \\n\";\n\t\tfor(const auto& m: projected_term.ident)\n\t\t\tstd::cout << m << \" \";\n\t\tstd::cout << std::endl;\n#endif\n\t\tif (projected_term.ident.size() == 0)\n\t\t\tcontinue;\n\t\tbool found = false;\n\t\tfor (auto& pattern : patterns) {\n\t\t\tif (pattern[0].compare(kernel, projected_term)) {\n\t\t\t\tfound = true;\n\t\t\t\tpattern.push_back(projected_term);\n\t\t\t\tbreak;\n\t\t\t\t}\n\t\t\t}\n\t\tif (!found)\n\t\t\tpatterns.emplace_back(1, std::move(projected_term));\n\t\t}\n\n\t// Apply to each pattern group in turn\n\tfor (auto& terms : patterns) {\n\t\tScopedProgressGroup group(pm,\n\t\t\t\t\t\t\t\t\t\t  \"Melding terms of form \" + ex_to_string<DisplayTerminal>(kernel, terms[0].tensor),\n\t\t\t\t\t\t\t\t\t\t  terms.size());\n\n\t\t// Initialize the linear solver; 'coeffs' is a square matrix of YP coefficients which grows\n\t\t// every time we encounter a linearly-independent term. 'mapping' is a map between matrix\n\t\t// rows and YP terms. 'adjforms' is a list of the complete decompositions (one for each column\n\t\t// in 'coeffs') which we need to keep to ensure the solution we get by solving for 'coeffs', which\n\t\t// does not contain the coefficients for every term in the YP, is an actual solution \n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t  linear::Solver<mpq_class> solver;\n\t\tmatrix_type coeffs;\n\t\tstd::vector<Adjform> mapping;\n\n\t\t// Calculate the symmetrizers for this pattern group. If we are symmetrizing as a sum, then each\n\t\t// new term in the sum is marked by the 'independent' flag being set\n\t\tauto tabs = collect_tableaux(terms[0].tensor);\n\t\tstd::vector<symmetrizer_t> symmetrizers;\n\t\tbool is_zero = collect_symmetries(tabs, symmetrizers);\n\n\t\tif (is_zero) {\n#ifdef DEBUG\n\t\t\tstd::cout << \"term is identically zero\" << std::endl;\n#endif\n\t\t\t// The term is identically zero due to its tableaux, delete all and move\n\t\t\t// onto next pattern\n\t\t\tfor (auto& term : terms) {\n\t\t\t\tnode_zero(term.it);\n\t\t\t\tapplied = true;\n\t\t\t\t}\n\t\t\tcontinue;\n\t\t\t}\n\n\t\t// Go through all terms in this pattern group one at a time\n\t\tfor (size_t term_idx = 0; term_idx < terms.size(); ++term_idx) {\n\t\t\tgroup.progress();\n\t\t\tauto& term = terms[term_idx];\n\t\t\tsymmetrize(term, symmetrizers);\n\n\t\t\tif (term.projection.empty()) {\n#ifdef DEBUG\n\t\t\t\tstd::cout << \"term is identically zero after projection\" << std::endl;\n#endif\n\t\t\t\t// Empty adjform means that the term is identically equal to 0\n\t\t\t\tnode_zero(term.it);\n\t\t\t\tterms.erase(terms.begin() + term_idx);\n\t\t\t\t--term_idx;\n\t\t\t\tapplied = true;\n\t\t\t\t}\n\t\t\telse {\n\t\t\t\t// We need to try and express the current YP as a linear combination of previous YPs\n\t\t\t\t// by solving \"coeffs * x = y\"\n\t\t\t\tvector_type x, y;\n\t\t\t\tbool has_solution = false;\n\n\t\t\t\tif (coeffs.size1() > 0) {\n\t\t\t\t\ty.resize(coeffs.size1());\n\t\t\t\t\tfor (size_t i = 0; i < mapping.size(); ++i)\n\t\t\t\t\t\ty(i) = term.projection.get(mapping[i]);\n\t\t\t\t\tx = solver.solve(y);\n\t\t\t\t\thas_solution = true;\n\n\t\t\t\t\t// x is guaranteed to be a solution as the 'coeffs' matrix is square and the columns\n\t\t\t\t\t// are linearly dependent. To check whether it is actually a solution, go back over\n\t\t\t\t\t// all the adjforms and ensure that the equation holds for each term\n\t\t\t\t\t// To do this we keep track of iterators into each YP we have calculated. Different YPs\n\t\t\t\t\t// will contain different terms (as they are a sparse storage), but as they are\n\t\t\t\t\t// held in a std::map the terms are already sorted, so when constructing the vector\n\t\t\t\t\t// which holds iterators into each YP we find which one has the smallest term.\n\t\t\t\t\t// Then starting with this term we go through each iterator; if it points to this term\n\t\t\t\t\t// then we accumulate the value * x[i] and increment the iterator, otherwise we skip\n\t\t\t\t\t// over it. If the YP we just calculated contains this term then we check to make sure\n\t\t\t\t\t// the value in the right hand equals this total, otherwise we check to make sure the total\n\t\t\t\t\t// was 0. If we find a mismatch we set has_solution to false, otherwise we continue doing\n\t\t\t\t\t// this until all the iterators have expired\n\n\t\t\t\t\tstd::vector<ProjectedAdjform::const_iterator> lhs_its;\n\t\t\t\t\tProjectedAdjform::const_iterator rhs_it = term.projection.begin();\n\t\t\t\t\tAdjform cur_term = rhs_it->first;\n\n\t\t\t\t\t// Populate the lhs_its vector and find the first (i.e. smallest) term\n\t\t\t\t\tfor (size_t i = 0; i < term_idx; ++i) {\n\t\t\t\t\t\tauto it = terms[i].projection.begin();\n\t\t\t\t\t\tif (it->first < cur_term)\n\t\t\t\t\t\t\tcur_term = it->first;\n\t\t\t\t\t\tlhs_its.push_back(it);\n\t\t\t\t\t\t}\n\n\t\t\t\t\t// Keep on iterating while there are unexpired iterators\n\t\t\t\t\tsize_t n_finished = 0;\n\t\t\t\t\twhile (n_finished < lhs_its.size()) {\n\t\t\t\t\t\t// Calculate the sum on the left hand side. We simultaneously calculate the\n\t\t\t\t\t\t// next term which we will examine by checking every time we increment an\n\t\t\t\t\t\t// iterator if it is smaller than next_term (which we initialize to be the\n\t\t\t\t\t\t// largest possible)\n\t\t\t\t\t\tAdjform next_term;\n\t\t\t\t\t\tnext_term.push_coordinate(std::numeric_limits<Adjform::value_type>::max());\n\t\t\t\t\t\tmpq_class sum = 0;\n\t\t\t\t\t\tfor (size_t i = 0; i < term_idx; ++i) {\n\t\t\t\t\t\t\tif (lhs_its[i] != terms[i].projection.end() && lhs_its[i]->first == cur_term) {\n\t\t\t\t\t\t\t\tsum += x(i) * lhs_its[i]->second;\n\t\t\t\t\t\t\t\t++lhs_its[i];\n\t\t\t\t\t\t\t\tif (lhs_its[i] == terms[i].projection.end())\n\t\t\t\t\t\t\t\t\t++n_finished;\n\t\t\t\t\t\t\t\t}\n\t\t\t\t\t\t\tif (lhs_its[i] != terms[i].projection.end() && lhs_its[i]->first < next_term)\n\t\t\t\t\t\t\t\tnext_term = lhs_its[i]->first;\n\t\t\t\t\t\t\t}\n\n\t\t\t\t\t\t// Calculate the sum on the right hand side \n\t\t\t\t\t\t\t\tmpq_class rhs_sum;\n\t\t\t\t\t\tif (rhs_it == term.projection.end() || rhs_it->first != cur_term) {\n\t\t\t\t\t\t\trhs_sum = 0;\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\telse {\n\t\t\t\t\t\t\trhs_sum = rhs_it->second;\n\t\t\t\t\t\t\t++rhs_it;\n\t\t\t\t\t\t\t}\n\n\t\t\t\t\t\t// Early return if there is a mismatch\n\t\t\t\t\t\tif (sum != rhs_sum) {\n\t\t\t\t\t\t\thas_solution = false;\n\t\t\t\t\t\t\tbreak;\n\t\t\t\t\t\t\t}\n\n\t\t\t\t\t\t// See if next smallest term is from the YP we just calculated\n\t\t\t\t\t\tif (rhs_it != term.projection.end() && rhs_it->first < next_term)\n\t\t\t\t\t\t\tnext_term = rhs_it->first;\n\t\t\t\t\t\tcur_term = next_term;\n\t\t\t\t\t\t}\n\n\t\t\t\t\t// If all the LHS iterators have expired, but there are still non-zero terms\n\t\t\t\t\t// on the RHS (i.e. the iterator isn't expired) then this is a mismatch\n\t\t\t\t\tif (rhs_it != term.projection.end())\n\t\t\t\t\t\thas_solution = false;\n\t\t\t\t\t}\n\n\t\t\t\tif (has_solution) {\n\t\t\t\t\t// If there is a solution, we add contributions from the current term to the\n\t\t\t\t\t// scalar parts of all the other terms and set their 'changed' flag to true.\n\t\t\t\t\t// Then zero and erase the current node; this is the only change to the actual\n\t\t\t\t\t// tree we make right now, we will make the changes to the other nodes once we\n\t\t\t\t\t// have accumulated all the contributions\n\t\t\t\t\tfor (size_t i = 0; i < term_idx; ++i) {\n\t\t\t\t\t\tif (x(i) != 0) {\n\t\t\t\t\t\t\tterms[i].changed = true;\n\t\t\t\t\t\t\tEx::iterator scalar_head = term.scalar.begin();\n\t\t\t\t\t\t\tfor (Ex::sibling_iterator beg = scalar_head.begin(), end = scalar_head.end(); beg != end; ++beg) {\n\t\t\t\t\t\t\t\tauto new_term = terms[i].scalar.append_child(terms[i].scalar.begin(), (Ex::iterator)beg);\n\t\t\t\t\t\t\t\tmultiply(new_term->multiplier, multiplier_t(x(i)) * (*scalar_head->multiplier));\n\t\t\t\t\t\t\t\t}\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\t}\n\t\t\t\t\tapplied = true;\n\t\t\t\t\tnode_zero(term.it);\n\t\t\t\t\tterms.erase(terms.begin() + term_idx);\n\t\t\t\t\t--term_idx;\n\t\t\t\t\t}\n\t\t\t\telse {\n\t\t\t\t\t// Expand the dimensions of the matrix by 1\n\t\t\t\t\tcoeffs.resize(coeffs.size1() + 1, coeffs.size2() + 1);\n\n\t\t\t\t\t// Find a representative term for the YP we just calculated to add to the matrix, i.e.\n\t\t\t\t\t// a term which isn't already in the 'mapping'. Once we find one, we fill in the bottom\n\t\t\t\t\t// row (the coefficient this term has in the previously calculated YPs), the right\n\t\t\t\t\t// hand column (the coefficient in of each term in 'mapping' in the YP we just\n\t\t\t\t\t// calculated) and the bottom right element (the representative term in the new YP).\n\t\t\t\t\tbool found = false;\n\t\t\t\t\tfor (const auto& kv : term.projection) {\n\t\t\t\t\t\tauto pos = std::find(mapping.begin(), mapping.end(), kv.first);\n\t\t\t\t\t\tif (pos == mapping.end()) {\n\t\t\t\t\t\t\t// Fill in bottom row\n\t\t\t\t\t\t\tfor (size_t i = 0; i < term_idx; ++i)\n\t\t\t\t\t\t\t\tcoeffs(coeffs.size1() - 1, i) = terms[i].projection.get(kv.first);\n\t\t\t\t\t\t\t// Fill in the righthand column\n\t\t\t\t\t\t\tfor (size_t i = 0; i < mapping.size(); ++i)\n\t\t\t\t\t\t\t\tcoeffs(i, coeffs.size2() - 1) = term.projection.get(mapping[i]);\n\t\t\t\t\t\t\t// Fill in the bottom right element\n\t\t\t\t\t\t\tcoeffs(coeffs.size1() - 1, coeffs.size2() - 1) = term.projection.get(kv.first);\n\t\t\t\t\t\t\tif (solver.factorize(coeffs)) {\n\t\t\t\t\t\t\t\tmapping.push_back(kv.first);\n\t\t\t\t\t\t\t\tfound = true;\n\t\t\t\t\t\t\t\tbreak;\n\t\t\t\t\t\t\t\t}\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\t}\n\n\t\t\t\t\t// Shouldn't ever happen...if this error does get thrown then probably need a new way\n\t\t\t\t\t// to calculate the representative terms\n\t\t\t\t\tif (!found)\n\t\t\t\t\t\tthrow std::runtime_error(\"Could not find a suitable element to add to the matrix\");\n\t\t\t\t\t} // if (has_solution) {} else {}\n\t\t\t\t} // if (term.projection.empty()) {} else {}\n\t\t\t} //for (size_t term_idx = 0; term_idx < terms.size(); ++term_idx)\n\n\t\t// Replace any nodes which have the 'changed' flag\n\t\tfor (auto& term : terms) {\n\t\t\tif (term.changed) {\n\t\t\t\t// Replace the node with a product of the scalar and tensor parts, then cleanup\n\t\t\t\ttr.erase_children(term.it);\n\t\t\t\tterm.it = tr.replace(term.it, str_node(\"\\\\prod\"));\n\t\t\t\ttr.append_child(term.it, term.scalar.begin());\n\t\t\t\ttr.append_child(term.it, term.tensor.begin());\n\t\t\t\tcleanup_dispatch(kernel, tr, term.it);\n\t\t\t\t}\n\t\t\t}\n\t\t} // for (auto& terms : patterns)\n\n\treturn applied;\n\t}\n\nbool it_is_scalar(const Kernel& kernel, Ex::iterator it)\n\t{\n\tbool is_scalar = true;\n\titer_indices term_indices(kernel.properties, it);\n\t// size_t n_indices = term_indices.size();\n\tfor (const auto& idx : term_indices) {\n\t\tauto symb = kernel.properties.get<Symbol>(idx, true);\n\t\tauto coord = kernel.properties.get<Coordinate>(idx, true);\n\t\tbool is_index = !(symb || coord || idx->is_integer());\n\t\tif (is_index) {\n\t\t\tis_scalar = false;\n\t\t\tbreak;\n\t\t\t}\n\t\t}\n\treturn is_scalar;\n\t}\n\nmeld::ProjectedTerm::ProjectedTerm(const Kernel& kernel, IndexMap& index_map, Ex& ex, Ex::iterator it)\n\t: scalar(\"\\\\sum\")\n\t, tensor(\"\\\\prod\")\n\t, it(it)\n\t, changed(false)\n\t{\n\t// Split the term up into a scalar part and a tensor part. The scalar part always starts\n\t// with a \\\\sum node, as contributions will be added to it during the melding process,\n\t// so we start by adding a \\\\prod node which will collect the scalar factors.\n\tauto scalar_head = scalar.append_child(scalar.begin(), str_node(\"\\\\prod\"));\n\n\t// If the object is not a product, then it either a single scalar object or a single\n\t// tensor object; detect which it is and move onto the appropriate part.\n\tif (*it->name != \"\\\\prod\") {\n\t\tbool is_scalar = it_is_scalar(kernel, it);\n\t\tif (!is_scalar) {\n\t\t\tauto term = tensor.append_child(tensor.begin(), it);\n\t\t\tauto factor = scalar.append_child(scalar_head, str_node(\"1\"));\n\t\t\tmultiply(factor->multiplier, *it->multiplier);\n\t\t\tone(term->multiplier);\n\t\t\t}\n\t\t}\n\telse {\n\t\t// Object is a product of multiple terms.\n\t\t// Loop through all terms in the product. If they have indices, then see if they\n\t\t// can commute through the tensor bits in front of it to join other scalar terms\n\t\t// out the front. Otherwise it will have to stay in the the tensor part of the\n\t\t// expression\n\t\tEx_comparator comp(kernel.properties);\n\t\t// Position of the last scalar value in the expression. Start this off with a\n\t\t// sentinel \"null iterator\" so that we know we haven't met any scalar terms yet\n\t\tEx::iterator last_scalar(0);\n\t\tfor (Ex::sibling_iterator beg = it.begin(), end = it.end(); beg != end; ++beg) {\n\t\t\t// Determine if it is scalar or tensor. We decide this by assuming it is a\n\t\t\t// scalar, and then iterating through its indices checking for one which isn't\n\t\t\t// a coordinate, symbol or integer. If we find a 'real' index, we know that it\n\t\t\t// is a tensor and can stop checking the indices.\n\t\t\tbool is_scalar = it_is_scalar(kernel, beg);\n\t\t\t// If it is a scalar term, then attempt to commute it through the expression\n\t\t\t// to join the rest of the scalar terms. If it can't commute through, then\n\t\t\t// mark it as a tensor --- this ensures that it won't get moved anywhere.\n\t\t\tif (is_scalar) {\n\t\t\t\tif (last_scalar == Ex::iterator(0))\n\t\t\t\t\tis_scalar = comp.can_move_to_front(ex, it, beg);\n\t\t\t\telse\n\t\t\t\t\tis_scalar = comp.can_move_adjacent(it, last_scalar, beg);\n\t\t\t\t}\n\n\t\t\t// Move scalar terms onto the scalar node, and tensor (including non-\n\t\t\t// commuting tensors) onto the tensor node\n\t\t\tif (is_scalar) {\n\t\t\t\tauto term = scalar.append_child(scalar_head, (Ex::iterator)beg);\n\t\t\t\tlast_scalar = beg;\n\t\t\t\t}\n\t\t\telse {\n\t\t\t\ttensor.append_child(tensor.begin(), (Ex::iterator)beg);\n\t\t\t\t}\n\t\t\t}\n\n\t\t// If we had no scalar components, then create a numeric constant to\n\t\t// hold the overall factor\n\t\tif (scalar_head.number_of_children() == 0)\n\t\t\tauto term = scalar.append_child(scalar_head, str_node(\"1\"));\n\t\t// Copy the overall numeric factor onto the scalar component\n\t\tmultiply(scalar_head->multiplier, *it->multiplier);\n\t\t}\n\n\t// Flatten/cleanup the expressions\n\tEx::iterator tensor_head = tensor.begin();\n\tcleanup_dispatch(kernel, scalar, scalar_head);\n\tcleanup_dispatch(kernel, tensor, tensor_head);\n\n\t// Calculate the index structure of the tensor part.\n\tauto ibeg = index_iterator::begin(kernel.properties, tensor.begin());\n\tauto iend = index_iterator::end(kernel.properties, tensor.begin());\n\tident = Adjform(ibeg, iend, index_map, kernel);\n\t}\n\n// Return 'true' if the tensor parts are identical up to index structure.\nbool meld::ProjectedTerm::compare(const Kernel& kernel, const ProjectedTerm& other)\n\t{\n\tauto head1 = tensor.begin(), head2 = other.tensor.begin();\n\tif (head1->name != head2->name)\n\t\treturn false;\n\n\tauto separated_by_derivative = [&kernel](const Ex& ex, Ex::iterator a, Ex::iterator b) {\n\t\t// Climb the tree until we meet, returning true if we find a derivative along the way\n\t\tEx::iterator lca = ex.lowest_common_ancestor(a, b);\n\t\twhile (a != lca || b != lca) {\n\t\t\t// Check for partial derivative\n\t\t\tif (kernel.properties.get<Derivative>(a))\n\t\t\t\treturn true;\n\t\t\tif (kernel.properties.get<Derivative>(b))\n\t\t\t\treturn true;\n\t\t\t// Move nodes up a level\n\t\t\tif (a != lca)\n\t\t\t\ta = ex.parent(a);\n\t\t\tif (b != lca)\n\t\t\t\tb = ex.parent(b);\n\t\t\t}\n\t\treturn false;\n\t\t};\n\n\tstd::set<Ex::iterator> dummies1, dummies2;\n\tEx_comparator comp(kernel.properties);\n\n\tEx::iterator beg1 = head1.begin(), end1 = head1.end();\n\tEx::iterator beg2 = head2.begin(), end2 = head2.end();\n\tfor (; beg1 != end1 && beg2 != end2; ++beg1, ++beg2) {\n\t\tauto match = comp.equal_subtree(beg1, beg2);\n\t\tif (match == Ex_comparator::match_t::subtree_match) {\n\t\t\t// Whole subtree is a match, skip children and continue\n\t\t\tbeg1.skip_children();\n\t\t\tbeg2.skip_children();\n\t\t\tcontinue;\n\t\t\t}\n\t\tif (beg1->name == beg2->name && beg1->fl.parent_rel == beg2->fl.parent_rel) {\n\t\t\t// Nodes are the same, continue but don't skip children\n\t\t\tcontinue;\n\t\t\t}\n\n\t\t// No match is ok if the index structure is the same. Let's check that they\n\t\t// are both indices\n\t\tif (!beg1->is_index() || !beg2->is_index())\n\t\t\treturn false;\n\n\t\t// We will not need to dig further into the tree if these match\n\t\tbeg1.skip_children();\n\t\tbeg2.skip_children();\n\n\t\t// We begin by checking if they are coordinates,\n\t\t// symbols or integers in which case they must match exactly\n\t\tbool int1 = beg1->is_integer();\n\t\tbool int2 = beg2->is_integer();\n\t\tbool coord1 = kernel.properties.get<Coordinate>(beg1, true);\n\t\tbool coord2 = kernel.properties.get<Coordinate>(beg2, true);\n\t\tbool sym1 = kernel.properties.get<Symbol>(beg1, true);\n\t\tbool sym2 = kernel.properties.get<Symbol>(beg2, true);\n\n\t\tif ((int1 && int2) || (coord1 && coord2) || (sym1 && sym2))\n\t\t\treturn true;\n\t\tif ((int1 != int2) || (coord1 != coord2) || (sym1 != sym2))\n\t\t\treturn false;\n\n\t\t// Okay, we will treat these as indices of some sort now. First we check for\n\t\t// Indices property to check the sets\n\t\tauto iprop1 = kernel.properties.get<Indices>(beg1);\n\t\tauto iprop2 = kernel.properties.get<Indices>(beg2);\n\n\t\t// If neither is in a set then they are both free and that is fine\n\t\tif (!iprop1 && !iprop2)\n\t\t\tcontinue;\n\n\t\t// If one is a set but the other isn't then its a mismatch\n\t\tif ((bool)iprop1 != (bool)iprop2)\n\t\t\treturn false;\n\n\t\t// If they are both in sets but they're different sets then its a mismatch\n\t\tif (iprop1->set_name != iprop2->set_name)\n\t\t\treturn false;\n\n\t\t// Ok - they're both in the same set. If they are at the same height then that\n\t\t// is fine\n\t\tif (beg1->fl.parent_rel == beg2->fl.parent_rel)\n\t\t\tcontinue;\n\n\t\t// They are at different heights. If they're free then thats fine\n\t\tif (iprop1->position_type == Indices::position_t::free)\n\t\t\tcontinue;\n\n\t\t// If they are independent then thats a mismatch\n\t\tif (iprop1->position_type == Indices::position_t::independent)\n\t\t\treturn false;\n\n\t\t// Fixed is okay if they are in a dummy pair which isn't separated by a derivative\n\t\tif (iprop1->position_type == Indices::position_t::fixed) {\n\t\t\tbool beg1isdummy = false, beg2isdummy = false;\n\t\t\tif (dummies1.find(beg1) != dummies1.end()) {\n\t\t\t\tbeg1isdummy = true;\n\t\t\t\tdummies1.erase(dummies1.find(beg1));\n\t\t\t\t}\n\t\t\tif (dummies2.find(beg2) != dummies2.end()) {\n\t\t\t\tbeg2isdummy = true;\n\t\t\t\tdummies2.erase(dummies2.find(beg2));\n\t\t\t\t}\n\t\t\t// Secondly we iterate through the rest of the tree to check for a match\n\t\t\tif (!beg1isdummy) {\n\t\t\t\tEx::iterator search = beg1;\n\t\t\t\tsearch.skip_children();\n\t\t\t\t++search;\n\t\t\t\twhile (search != end1) {\n\t\t\t\t\tcomp.clear();\n\t\t\t\t\tif (comp.equal_subtree(beg1, search, Ex_comparator::useprops_t::never, true) == Ex_comparator::match_t::subtree_match) {\n\t\t\t\t\t\t// Found dummy, first we check whether it is separated by a derivative\n\t\t\t\t\t\tif (!separated_by_derivative(tensor, beg1, search)) {\n\t\t\t\t\t\t\t// Valid dummy, add this iterator to dummies so we can find it later\n\t\t\t\t\t\t\tdummies1.insert(search);\n\t\t\t\t\t\t\tbeg1isdummy = true;\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\t}\n\t\t\t\t\tif (search->is_index())\n\t\t\t\t\t\tsearch.skip_children();\n\t\t\t\t\t++search;\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\tif (!beg2isdummy) {\n\t\t\t\tEx::iterator search = beg2;\n\t\t\t\tsearch.skip_children();\n\t\t\t\t++search;\n\t\t\t\twhile (search != end2) {\n\t\t\t\t\tif (comp.equal_subtree(beg2, search) == Ex_comparator::match_t::subtree_match) {\n\t\t\t\t\t\t// Found dummy, first we check whether it is separated by a derivative\n\t\t\t\t\t\tEx::iterator tmp;\n\t\t\t\t\t\tif (!separated_by_derivative(other.tensor, beg2, search)) {\n\t\t\t\t\t\t\t// Valid dummy, add this iterator to dummies so we can find it later\n\t\t\t\t\t\t\tdummies2.insert(search);\n\t\t\t\t\t\t\tbeg2isdummy = true;\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\t}\n\t\t\t\t\tif (search->is_index())\n\t\t\t\t\t\tsearch.skip_children();\n\t\t\t\t\t++search;\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t// In case we've forgotten what we were meant to be doing here; the two indices have different\n\t\t\t// heights but this is ok if they are both in valid dummy pairs; so we return false if that\n\t\t\t// is not the case\n\t\t\tif (!beg1isdummy || !beg2isdummy)\n\t\t\t\treturn false;\n\t\t\t}\n\t\t}\n\n\t// One of the iterators has expired, check that both have\n\treturn beg1 == end1 && beg2 == end2;\n\t}\n\nstd::vector<meld::tab_t> meld::collect_tableaux(Ex& ex) const\n\t{\n\tstd::vector<tab_t> tabs;\n\tsize_t total_indices = 0;\n\tfor (const auto& term : split_it(ex.begin(), \"\\\\prod\")) {\n\t\tauto tb = kernel.properties.get<TableauBase>(term);\n\t\tif (tb) {\n\t\t\tif (project_as_sum && !tabs.empty()) \n\t\t\t\tthrow std::runtime_error(\"meld cannot project_as_sum the product of tensors with non-trivial tableau shapes\");\n\n\t\t\tsize_t n_tabs = tb->size(kernel.properties, ex, term);\n\t\t\tfor (size_t i = 0; i < n_tabs; ++i) {\n\t\t\t\tauto tab = tb->get_tab(kernel.properties, ex, term, i);\n\t\t\t\tfor (auto& cell : tab)\n\t\t\t\t\tcell += total_indices;\n\t\t\t\ttabs.push_back(std::move(tab));\n\t\t\t\t}\n\n\t\t\t// Are we a derivative of a Riemann tensor?\n\t\t\tif (n_tabs == 1) {\n\t\t\t\tEx::iterator child = term;\n\t\t\t\tsize_t depth = 0;\n\t\t\t\twhile (kernel.properties.get<Derivative>(child)) {\n\t\t\t\t\tchild = child.begin();\n\t\t\t\t\t++child;\n\t\t\t\t\t++depth;\n\t\t\t\t\t}\n\t\t\t\tif (kernel.properties.get<RiemannTensor>(child)) {\n\t\t\t\t\tDEBUGLN( std::cerr << \"collect_tableaux: this is a derivative of a Riemann.\" << std::endl; );\n\t\t\t\t\t// Append indices to top row of Riemann tableau\n\t\t\t\t\tfor (size_t k = 0; k < depth; ++k) {\n\t\t\t\t\t\ttabs.back().add_box(0, total_indices + k);\n\t\t\t\t\t\t}\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t}\n\t\titer_indices indices(kernel.properties, term);\n\t\ttotal_indices += indices.size();\n\t\t}\n\n\treturn tabs;\n\t}\n\nbool meld::collect_symmetries(const std::vector<tab_t>& tabs, std::vector<symmetrizer_t>& symmetrizers) const\n\t{\n\tif (project_as_sum)\n\t\treturn collect_symmetries_as_sum(tabs, symmetrizers);\n\telse\n\t\treturn collect_symmetries_as_product(tabs, symmetrizers);\n\t}\n\nbool meld::collect_symmetries_as_product(const std::vector<tab_t>& tabs, std::vector<symmetrizer_t>& symmetrizers) const\n\t{\n\t// We collect all the symmetrizers and antisymmerizers into a list\n\t// to end up with e.g.\n\t//   S(01) A(02) S(34) A(57) A(68) S(56) S(78)\n\t// We then apply operations to this list by commuting symmetrizers\n\t// through each other and collecting any symmetrizers which\n\t// cancel each other\n\n\tfor (const auto& tab : tabs) {\n\t\tfor (size_t col = 0; col < tab.row_size(0); ++col) {\n\t\t\tif (tab.column_size(col) > 1) {\n\t\t\t\tsymmetrizer_t sym(true, true);\n\t\t\t\tsym.indices.assign(tab.begin_column(col), tab.end_column(col));\n\t\t\t\tstd::sort(sym.indices.begin(), sym.indices.end());\n\t\t\t\tsymmetrizers.push_back(std::move(sym));\n\t\t\t\t}\n\t\t\t}\n\t\tfor (size_t row = 0; row < tab.number_of_rows(); ++row) {\n\t\t\tif (tab.row_size(row) > 1) {\n\t\t\t\tsymmetrizer_t sym(false, true);\n\t\t\t\tsym.indices.assign(tab.begin_row(row), tab.end_row(row));\n\t\t\t\tstd::sort(sym.indices.begin(), sym.indices.end());\n\t\t\t\tsymmetrizers.push_back(std::move(sym));\n\t\t\t\t}\n\t\t\t}\n\t\t}\n\n\t// For each symmetrizer i, try and commute it though the symmetrizers to the right and left\n\t// of it to try and find simplifications\n\tfor (size_t i = 0; i < symmetrizers.size(); ++i) {\n\t\tauto& lhs = symmetrizers[i].indices;\n\t\t// Commute right\n\t\tfor (size_t j = i + 1; j < symmetrizers.size(); ++j) {\n\t\t\t// Calculate intersection and union of the two terms\n\t\t\tauto& rhs = symmetrizers[j].indices;\n\t\t\tstd::vector<size_t> uni, inter;\n\t\t\tstd::set_union(lhs.begin(), lhs.end(), rhs.begin(), rhs.end(), std::back_inserter(uni));\n\t\t\tstd::set_intersection(lhs.begin(), lhs.end(), rhs.begin(), rhs.end(), std::back_inserter(inter));\n\t\t\tbool can_commute = inter.empty();\n\n\t\t\tif (symmetrizers[i].antisymmetric == symmetrizers[j].antisymmetric) {\n\t\t\t\t// Both symmetric/antisymmetric: can be combined if one is a subset of the other.\n\t\t\t\tif (lhs == uni || rhs == uni) {\n\t\t\t\t\tlhs = uni;\n\t\t\t\t\tsymmetrizers.erase(symmetrizers.begin() + j);\n\t\t\t\t\t--j;\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\telse {\n\t\t\t\t// One is symmetric and the other antisymmetric: if they overlap by more than one index\n\t\t\t\t// then the whole projection is identically zero\n\t\t\t\tif (inter.size() > 1) {\n\t\t\t\t\treturn true;\n\t\t\t\t\t}\n\t\t\t\t}\n\n\t\t\t// If these two terms do not commute then move lhs on\n\t\t\tif (!can_commute) {\n\t\t\t\tsymmetrizers[i].independent = false;\n\t\t\t\tbreak;\n\t\t\t\t}\n\t\t\t}\n\n\t\t// Commute left\n\t\tfor (size_t j = i - 1; j != (size_t)-1; --j) {\n\t\t\t// Calculate intersection and union of the two terms\n\t\t\tauto& rhs = symmetrizers[j].indices;\n\t\t\tstd::vector<size_t> uni, inter;\n\t\t\tstd::set_union(lhs.begin(), lhs.end(), rhs.begin(), rhs.end(), std::back_inserter(uni));\n\t\t\tstd::set_intersection(lhs.begin(), lhs.end(), rhs.begin(), rhs.end(), std::back_inserter(inter));\n\t\t\tbool can_commute = inter.empty();\n\n\t\t\tif (symmetrizers[i].antisymmetric == symmetrizers[j].antisymmetric) {\n\t\t\t\t// Both symmetric/antisymmetric: can be combined if one is a subset of the other.\n\t\t\t\tif (lhs == uni || rhs == uni) {\n\t\t\t\t\tlhs = uni;\n\t\t\t\t\tsymmetrizers.erase(symmetrizers.begin() + j);\n\t\t\t\t\t++j;\n\t\t\t\t\t--i;\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\telse {\n\t\t\t\t// One is symmetric and the other antisymmetric: if they overlap by more than one index\n\t\t\t\t// then the whole projection is identically zero\n\t\t\t\tif (inter.size() > 1) {\n\t\t\t\t\treturn true;\n\t\t\t\t\t}\n\t\t\t\t}\n\n\t\t\t// If these two terms do not commute then move lhs on\n\t\t\tif (!can_commute) {\n\t\t\t\tsymmetrizers[i].independent = false;\n\t\t\t\tbreak;\n\t\t\t\t}\n\t\t\t}\n\t\t}\n\n\treturn false;\n\t}\n\n\nbool meld::collect_symmetries_as_sum(const std::vector<tab_t>& tabs, std::vector<symmetrizer_t>& symmetrizers) const\n\t{\n\tauto reduce_tab = [](tab_t tab) {\n\t\t// Get the row with the biggest element\n\t\tsize_t n_cells = 0;\n\t\tsize_t greatest_row = 0;\n\t\tint greatest_elem = -1;\n\t\tfor (size_t row = 0; row < tab.number_of_rows(); ++row) {\n\t\t\tn_cells += tab.row_size(row);\n\t\t\tint back = (int)tab(row, tab.row_size(row) - 1);\n\t\t\tif (back > greatest_elem) {\n\t\t\t\tgreatest_elem = back;\n\t\t\t\tgreatest_row = row;\n\t\t\t\t}\n\t\t\t}\n\n\t\ttab.remove_box(greatest_row);\n\t\treturn tab;\n\t\t};\n\n\tauto is_trivial = [](const tab_t& tab) {\n\t\treturn std::distance(tab.begin(), tab.end()) <= 2;\n\t\t};\n\n\tstd::vector<mpz_class> norms;\n\tfor (const auto& tab : tabs) {\n\t\t// Check tableau is row-standard\n\t\tfor (size_t row = 0; row < tab.number_of_rows(); ++row) {\n\t\t\tint prev = -1;\n\t\t\tfor (auto beg = tab.begin_row(row), end = tab.end_row(row); beg != end; ++beg) {\n\t\t\t\tint next = *beg;\n\t\t\t\tif (next < prev)\n\t\t\t\t\tthrow ConsistencyException(\"Trying to symmetrize non-standard tableau as sum\");\n\t\t\t\tprev = next;\n\t\t\t\t}\n\t\t\t}\n\t\t// Check tableau is column-standard\n\t\tfor (size_t col = 0; col < tab.row_size(0); ++col) {\n\t\t\tint prev = -1;\n\t\t\tfor (auto beg = tab.begin_column(col), end = tab.end_column(col); beg != end; ++beg) {\n\t\t\t\tint next = *beg;\n\t\t\t\tif (next < prev)\n\t\t\t\t\tthrow ConsistencyException(\"Trying to symmetrize non-standard tableau as sum\");\n\t\t\t\tprev = next;\n\t\t\t\t}\n\t\t\t}\n\n\t\t// Create the hermitian product as described in Theorem 6 of arXiv:1307.6147\n\t\t// We start by creating a list 'hermprod' containing the original tableau\n\t\t// and a second list 'is_decomposed' which contains a flag for whether the ith term\n\t\t// in hermprod has been decomposed. We then iterate through all the elements of hermprod\n\t\t// applying Y_n -> P_{n-1} Y_n P_{n-1} until no P's are left in the list.\n\t\tstd::vector<tab_t> hermprod(1, tab);\n\t\tstd::vector<bool> is_decomposed(1, is_trivial(tab));\n\t\tfor (int i = 0; i < (int)hermprod.size(); ++i) {\n\t\t\tif (!is_decomposed[i]) {\n\t\t\t\t// Sandwich hermprod[i] between reduced\n\t\t\t\tis_decomposed[i] = true;\n\t\t\t\tauto reduced = reduce_tab(hermprod[i]);\n\t\t\t\tauto triv = is_trivial(reduced);\n\t\t\t\thermprod.insert(hermprod.begin() + i + 1, reduced);\n\t\t\t\tis_decomposed.insert(is_decomposed.begin() + i + 1, triv);\n\t\t\t\thermprod.insert(hermprod.begin() + i, reduced);\n\t\t\t\tis_decomposed.insert(is_decomposed.begin() + i, triv);\n\t\t\t\t--i;\n\t\t\t\t}\n\t\t\t}\n\n\t\t// Collect the symmetrizers. We begin with an object which has\n\t\t// independent=true and indices contains one element, which is the normalisation\n\t\t// of the overall product. We don't actually fill in the normalisation now, as we will first\n\t\t// divide out by the GCD so we wont run the risk of overflowing int\n\t\tsymmetrizers.emplace_back(false, true);\n\t\tmpz_class norm = 1;\n\t\tfor (const auto& herm : hermprod) {\n\t\t\tnorm *= herm.hook_length_prod();\n\t\t\tfor (size_t col = 0; col < herm.row_size(0); ++col) {\n\t\t\t\tif (herm.column_size(col) > 1) {\n\t\t\t\t\tsymmetrizer_t sym(true, false);\n\t\t\t\t\tsym.indices.assign(herm.begin_column(col), herm.end_column(col));\n\t\t\t\t\tstd::sort(sym.indices.begin(), sym.indices.end());\n\t\t\t\t\tsymmetrizers.push_back(std::move(sym));\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\tfor (size_t row = 0; row < herm.number_of_rows(); ++row) {\n\t\t\t\tif (herm.row_size(row) > 1) {\n\t\t\t\t\tsymmetrizer_t sym(false, false);\n\t\t\t\t\tsym.indices.assign(herm.begin_row(row), herm.end_row(row));\n\t\t\t\t\tstd::sort(sym.indices.begin(), sym.indices.end());\n\t\t\t\t\tsymmetrizers.push_back(std::move(sym));\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t}\n\t\tnorms.push_back(norm);\n\n\t\t}\n\n\t// Get the GCD of the norms\n\tmpz_class gcd = 1;\n\tif (norms.size() > 1) {\n\t\tmpz_gcd(gcd.get_mpz_t(), norms[0].get_mpz_t(), norms[1].get_mpz_t());\n\t\tfor (size_t i = 2; i < norms.size(); ++i)\n\t\t\tmpz_gcd(gcd.get_mpz_t(), gcd.get_mpz_t(), norms[i].get_mpz_t());\n\t\t}\n\n\tsize_t pos = 0;\n\tfor (auto& symmetrizer : symmetrizers) {\n\t\tif (symmetrizer.independent) {\n\t\t\tmpz_class norm = norms[pos] / gcd;\n\t\t\tsymmetrizer.indices.push_back(norm.get_si());\n\t\t\t++pos;\n\t\t\t}\n\t\t}\n\n\treturn false;\n\t}\n\nvoid meld::symmetrize(ProjectedTerm& projterm, const std::vector<symmetrizer_t>& symmetrizers)\n\t{\n\tif (project_as_sum)\n\t\treturn symmetrize_as_sum(projterm, symmetrizers);\n\telse\n\t\treturn symmetrize_as_product(projterm, symmetrizers);\n\t}\n\nvoid meld::symmetrize_as_product(ProjectedTerm& projterm, const std::vector<symmetrizer_t>& symmetrizers)\n\t{\n\tAdjform seed = projterm.ident;\n\tint seed_value = 1;\n\n\tif (seed.empty())\n\t\tthrow std::runtime_error(\"symmetrize_as_product received term with no indices\");\n\n\t// Keep track of which symmetrizers we have applied. Note: do not mistake this for us applying\n\t// the symmetrizers out-of-order: we will first apply the 'independent' symmetrizers which\n\t// commute with every other symmetrizer so really this is an alternative to reordering the\n\t// elements in the 'symmetrizers' vector by commuting elements through each other\n\tstd::vector<bool> applied(symmetrizers.size(), false);\n\n\t// Calculate the independent symmetrizers (those which have no overlap with any other symmetrizer).\n\t// This means that it needs the 'independent' flag AND no dummy indices. Then use these to sort the\n\t// independent indices in seed and possibly pick up a factor of -1.\n\tfor (size_t i = 0; i < symmetrizers.size(); ++i) {\n\t\tbool independent =\n\t\t\tsymmetrizers[i].independent &&\n\t\t\tstd::all_of(symmetrizers[i].indices.begin(), symmetrizers[i].indices.end(),\n\t\t\t\t\t\t\t[seed](size_t i) { return seed[i] < 0; });\n#ifdef DEBUG\n\t\tstd::cerr << \"meld::symmetrize_as_product: symmetriser \" << i << \" independent \" << independent << std::endl;\n#endif\n\t\tif (independent) {\n\t\t\tAdjform indices;\n\t\t\tfor (const auto& index : symmetrizers[i].indices)\n\t\t\t\tindices.push_coordinate(seed[index]); // push_coordinate is more efficient if we know there are no dummy indices\n\t\t\tstd::vector<Adjform::value_type> sorted_indices(indices.begin(), indices.end());\n\t\t\tstd::sort(sorted_indices.begin(), sorted_indices.end());\n\t\t\tfor (size_t j = 0; j < (size_t)indices.size(); ++j) {\n\t\t\t\tauto idx1 = indices[j];\n\t\t\t\tauto idx2 = sorted_indices[j];\n\t\t\t\tif (idx1 != idx2) {\n\t\t\t\t\tif (symmetrizers[i].antisymmetric)\n\t\t\t\t\t\tseed_value *= -1;\n\t\t\t\t\tauto pos1 = seed.index_of(idx1);\n\t\t\t\t\tauto pos2 = seed.index_of(idx2);\n\t\t\t\t\tseed.swap(pos1, pos2);\n\t\t\t\t\tindices.swap(j, indices.index_of(idx2));\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\tapplied[i] = true;\n\t\t\t}\n\t\t}\n\n\t// Shared-dummy optimization: see if the symmetrizer at the front has cancellations (a la\n\t// logic in symmetrize_as_product) taking into account dummy positions. We can only do this\n\t// with the front of the symmetrisers as after this the dummies will be mixed up. We rewrite\n\t// the symmetrizers replacing index positions with their dummy equivalents if this points to\n\t// a lower slot and then look for cancellations.\n\n\t// Find first two unapplied terms\n\tauto first_not_applied = std::find(applied.begin(), applied.end(), false);\n\tauto second_not_applied = first_not_applied == applied.end()\n\t\t? applied.end()\n\t\t: std::find(first_not_applied + 1, applied.end(), false);\n\n\tif (second_not_applied != applied.end()) {\n\t\tauto remove_dummies = [seed](Adjform::value_type idx) { return (seed[idx] < idx && seed[idx] >= 0) ? (size_t)seed[idx] : idx; };\n\n\t\t// Remove dummies from first term\n\t\tsize_t first_idx = std::distance(applied.begin(), first_not_applied);\n\t\tconst auto& first = symmetrizers[first_idx];\n\t\tstd::vector<size_t> first_nd(first.indices.size());\n\t\tstd::transform(first.indices.begin(), first.indices.end(), first_nd.begin(), remove_dummies);\n\t\tstd::sort(first_nd.begin(), first_nd.end());\n\n\t\t// Remove dummies from second term\n\t\tsize_t second_idx = std::distance(applied.begin(), second_not_applied);\n\t\tconst auto& second = symmetrizers[second_idx];\n\t\tstd::vector<size_t>second_nd(second.indices.size());\n\t\tstd::transform(second.indices.begin(), second.indices.end(), second_nd.begin(), remove_dummies);\n\t\tstd::sort(second_nd.begin(), second_nd.end());\n\n\t\t// Get intersection and union\n\t\tstd::vector<size_t> uni, inter;\n\t\tstd::set_union(first_nd.begin(), first_nd.end(), second_nd.begin(), second_nd.end(), std::back_inserter(uni));\n\t\tstd::set_intersection(first_nd.begin(), first_nd.end(), second_nd.begin(), second_nd.end(), std::back_inserter(inter));\n\t\tif (first.antisymmetric == second.antisymmetric) {\n\t\t\t// Both symmetric/antisymmetric: can be combined if one is a subset of the other.\n\t\t\tif (first_nd == uni || second_nd == uni) {\n\t\t\t\tif (first_nd.size() < second_nd.size())\n\t\t\t\t\t*first_not_applied = true;\n\t\t\t\telse\n\t\t\t\t\t*second_not_applied = true;\n\t\t\t\t}\n\t\t\t}\n\t\telse {\n\t\t\t// One is symmetric and the other antisymmetric: if they overlap by more than one index\n\t\t\t// then the whole projection is identically zero\n\t\t\tif (inter.size() > 1) {\n#ifdef DEBUG\n\t\t\t\tfor(const auto& aa: inter)\n\t\t\t\t\tstd::cerr << aa << std::endl;\n\t\t\t\tstd::cerr << \"meld::symmetrize_as_product: overlapping symmetric/anti-symmetric symmetriser\" << std::endl;\n#endif\n\t\t\t\t// FIXME: the logic here is incorrect.\n//\t\t\t\treturn;\n\t\t\t\t}\n\t\t\t}\n\t\t}\n\n\t// Seed the symmetrized expression\n\tprojterm.projection.add(seed, seed_value);\n\n\t// Go over the rest of the symmetrizers and apply them as normal\n\tfor (size_t i = 0; i < symmetrizers.size(); ++i) {\n\t\tif (!applied[i]) {\n\t\t\tprojterm.projection.apply_young_symmetry(symmetrizers[i].indices, symmetrizers[i].antisymmetric);\n\t\t\t}\n\t\t}\n\n\t// Symmetrize in identical tensors and we're done!\n\tsymmetrize_idents(projterm);\n\t}\n\nvoid meld::symmetrize_as_sum(ProjectedTerm& projterm, const std::vector<symmetrizer_t>& symmetrizers)\n\t{\n\tProjectedAdjform cur;\n\tAdjform seed = projterm.ident;\n\n\t// Get the product of all normalizations\n\tProjectedAdjform::integer_type overall_norm = 1;\n\tfor (size_t i = 0; i < symmetrizers.size(); ++i) {\n\t\tif (symmetrizers[i].independent)\n\t\t\toverall_norm *= symmetrizers[i].indices[0];\n\t\t}\n\n\tfor (size_t i = 0; i < symmetrizers.size(); ++i) {\n\t\tif (symmetrizers[i].independent) {\n\t\t\t// The independent flag here tells us that this just contains the normalisation\n\t\t\t// for the following product of symmetrizers. To keep things integer, we multiply by\n\t\t\t// the overall normalisation and then divide by the normalization for this group\n\t\t\tprojterm.projection += cur;\n\t\t\tcur.clear();\n\t\t\tcur.set(seed, overall_norm / symmetrizers[i].indices[0]);\n\t\t\t}\n\t\telse {\n\t\t\tcur.apply_young_symmetry(symmetrizers[i].indices, symmetrizers[i].antisymmetric);\n\t\t\t}\n\t\t}\n\tprojterm.projection += cur;\n\n\tsymmetrize_idents(projterm);\n\t}\n\n// Store information about how to symmetrize in identical tensors\nstruct Ident {\n\t\tIdent() : n_indices(0) {}\n\t\tsize_t n_indices;\n\t\tstd::vector<Ex::iterator> its;\n\t\tstd::vector<size_t> positions;\n\n\t\tstd::vector<std::vector<int>> generate_commutation_matrix(const Kernel& kernel) const\n\t\t\t{\n\t\t\tEx_comparator comp(kernel.properties);\n\t\t\tstd::vector<std::vector<int>> cm(its.size(), std::vector<int>(its.size()));\n\t\t\tfor (size_t i = 0; i < its.size(); ++i) {\n\t\t\t\tfor (size_t j = 0; j < its.size(); ++j) {\n\t\t\t\t\tif (i == j)\n\t\t\t\t\t\tcontinue;\n\t\t\t\t\tcm[i][j] = comp.can_move_adjacent(Ex::parent(its[i]), its[i], its[j]) * comp.can_swap(its[i], its[j], Ex_comparator::match_t::subtree_match);\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\treturn cm;\n\t\t\t}\n};\n\nvoid meld::symmetrize_idents(ProjectedTerm& projterm)\n\t{\n\t// Symmetrize in identical tensors\n\tauto prod = projterm.tensor.begin();\n\tif (*prod->name != \"\\\\prod\")\n\t\treturn;\n\n\t// Map holding hash of tensor -> { number of indices, {pos1, pos2, ...} }\n\tstd::map<nset_t::iterator, Ident, nset_it_less> idents;\n\tsize_t pos = 0;\n\tfor (Ex::sibling_iterator beg = prod.begin(), end = prod.end(); beg != end; ++beg) {\n\t\tauto elem = idents.insert({ beg->name, {} });\n\t\tauto& ident = elem.first->second;\n\t\tif (elem.second) {\n\t\t\t// Insertion took place, count indices\n\t\t\titer_indices indices(kernel.properties, beg);\n\t\t\tident.n_indices = indices.size();\n\t\t\t}\n\t\tident.its.push_back(beg);\n\t\tident.positions.push_back(pos);\n\t\tpos += ident.n_indices;\n\t\t}\n\tfor (const auto& ident : idents) {\n\t\tif (ident.second.positions.size() != 1) {\n\t\t\tprojterm.projection.apply_ident_symmetry(\n\t\t\t\tident.second.positions, ident.second.n_indices,\n\t\t\t\tident.second.generate_commutation_matrix(kernel));\n\t\t\t}\n\t\t}\n\t}\n\n\n// Trace routines\n\nbool meld::can_apply_cycle_traces(iterator it)\n\t{\n\tauto trace = kernel.properties.get<Trace>(it);\n\treturn trace && *it.begin()->name == \"\\\\sum\";\n\t}\n\nstruct CycledTerm\n{\n\t\tCycledTerm(Ex::iterator it, IndexMap& index_map, const Kernel& kernel)\n\t\t\t: commuting(\"\\\\sum\")\n\t\t\t, noncommuting(\"\\\\prod\")\n\t\t\t, it(it)\n\t\t\t, n_terms(0)\n\t\t\t, changed(false)\n\t\t\t{\n\n\t\t\tif (*it->name != \"\\\\prod\") {\n\t\t\t\t// A single term has nothing to commute with, so commutes by default\n\t\t\t\tauto term = commuting.append_child(commuting.begin(), it);\n\t\t\t\t}\n\t\t\telse {\n\t\t\t\t// The 'commuting' ex is a sum node, the first child of which is a product node representing\n\t\t\t\t// the commuting terms of 'it' (including the numeric prefactor of it).\n\t\t\t\t// If we compare against other CycledTerms and find a match, then\n\t\t\t\t// we merge the two sum nodes of the commuting term together and set the changed flag to true.\n\t\t\t\tauto commuting_head = commuting.append_child(commuting.begin(), str_node(\"\\\\prod\"));\n\t\t\t\tmultiply(commuting_head->multiplier, *it->multiplier);\n\n\t\t\t\t// Iterate through all terms in the product to see the they are commuting or noncommuting\n\t\t\t\tfor (Ex::sibling_iterator beg = it.begin(), end = it.end(); beg != end; ++beg) {\n\t\t\t\t\tauto nc = kernel.properties.get<NonCommuting>(beg);\n\t\t\t\t\tauto snc = kernel.properties.get<SelfNonCommuting>(beg);\n\t\t\t\t\tif (nc || snc) {\n\t\t\t\t\t\t// Non-commuting term: append it to the noncommuting Ex, increment the total number of\n\t\t\t\t\t\t// terms counter and then loop through its indices appending them to the Adjform we hold\n\t\t\t\t\t\t// We also count the number of indices each term has and add this information to the\n\t\t\t\t\t\t// 'index_groups' member so that cycle() knows how many times to cycle the Adjform\n\t\t\t\t\t\tauto term = noncommuting.append_child(noncommuting.begin(), (Ex::iterator)beg);\n\t\t\t\t\t\t++n_terms;\n\t\t\t\t\t\tsize_t n_indices = 0;\n\t\t\t\t\t\tfor (auto& index : iter_indices(kernel.properties, term)) {\n\t\t\t\t\t\t\tindices.push(index, index_map, kernel);\n\t\t\t\t\t\t\t++n_indices;\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\tindex_groups.push_back(n_indices);\n\t\t\t\t\t\t}\n\t\t\t\t\telse {\n\t\t\t\t\t\tauto term = commuting.append_child(commuting_head, (Ex::iterator)beg);\n\t\t\t\t\t\t}\n\t\t\t\t\t}\n\t\t\t\tcleanup_dispatch(kernel, commuting, commuting_head);\n\t\t\t\t}\n\t\t\t}\n\n\t\tvoid cycle(const Kernel& kernel)\n\t\t\t{\n\t\t\t// Rotate noncommuting\n\t\t\tEx::iterator head = noncommuting.begin();\n\t\t\tEx::sibling_iterator first = head.begin(), last = head.end();\n\t\t\t--last;\n\t\t\tnoncommuting.move_before(first, last);\n\t\t\t// Rotate indices\n\t\t\tif (index_groups.size() > 1) {\n\t\t\t\tindices.rotate(index_groups.back());\n\t\t\t\tstd::rotate(index_groups.begin(), index_groups.end() - 1, index_groups.end());\n\t\t\t\t}\n\t\t\t}\n\n\t\tbool compare(const Kernel& kernel, const CycledTerm& other)\n\t\t\t{\n\t\t\tif (indices != other.indices)\n\t\t\t\treturn false;\n\n\t\t\tEx_comparator comp(kernel.properties);\n\t\t\tauto res = comp.equal_subtree(noncommuting.begin(), other.noncommuting.begin());\n\t\t\treturn res == Ex_comparator::match_t::subtree_match ||\n\t\t\t\tres == Ex_comparator::match_t::match_index_less ||\n\t\t\t\tres == Ex_comparator::match_t::match_index_greater;\n\t\t\t}\n\n\t\tEx commuting, noncommuting; // Commuting and non-commuting parts of the expression\n\t\tAdjform indices; // Index structure of the groups\n\t\tstd::vector<size_t> index_groups; // Number of indices in each 'noncommuting' term\n\t\tEx::iterator it; // The iterator this object is constructed from\n\t\tsize_t n_terms; // Number of non-commuting terms\n\t\tbool changed; // Flag to be set if the commuting part of this object is modified but 'it' is not updated\n};\n\nbool meld::apply_cycle_traces(iterator it)\n\t{\n\tassert(*it.begin()->name == \"\\\\sum\");\n\tbool applied = false;\n\tstd::vector<CycledTerm> terms;\n\tfor (const auto& term : split_it(it.begin(), \"\\\\sum\"))\n\t\tterms.emplace_back(term, index_map, kernel);\n\tfor (size_t i = 0; i < terms.size(); ++i) {\n\t\tfor (size_t j = i + 1; j < terms.size(); ++j) {\n\t\t\tif (terms[i].n_terms != terms[j].n_terms)\n\t\t\t\tcontinue;\n\t\t\tfor (size_t k = 0; k <= terms[j].n_terms; ++k) {\n\t\t\t\tif (terms[i].compare(kernel, terms[j])) {\n\t\t\t\t\tEx::iterator head = terms[j].commuting.begin();\n\t\t\t\t\tfor (Ex::sibling_iterator beg = head.begin(), end = head.end(); beg != end; ++beg)\n\t\t\t\t\t\tterms[i].commuting.append_child(terms[i].commuting.begin(), (Ex::iterator)beg);\n\t\t\t\t\tnode_zero(terms[j].it);\n\t\t\t\t\tapplied = true;\n\t\t\t\t\tterms[i].changed = true;\n\t\t\t\t\tterms.erase(terms.begin() + j);\n\t\t\t\t\t--j;\n\t\t\t\t\tbreak;\n\t\t\t\t\t}\n\t\t\t\tterms[j].cycle(kernel);\n\t\t\t\t}\n\t\t\t}\n\t\t}\n\tfor (const auto& term : terms) {\n\t\tif (term.changed) {\n\t\t\ttr.erase_children(term.it);\n\t\t\tit = tr.replace(term.it, str_node(\"\\\\prod\"));\n\t\t\ttr.append_child(it, term.commuting.begin());\n\t\t\ttr.append_child(it, term.noncommuting.begin());\n\t\t\tcleanup_dispatch(kernel, tr, it);\n\t\t\t}\n\t\t}\n\treturn applied;\n\t}\n\n//bool meld::can_apply_side_relations(iterator it)\n//{\n//\treturn *it->name == \"\\\\sum\";\n//}\n//\n//\n//std::vector<Ex> collect_bases(Ex::iterator it)\n//{\n//\tassert(*it->name == \"\\\\equals\");\n//\tstd::vector<Ex> terms;\n//\n//\t// Get terms on left hand side\n//\tEx::sibling_iterator side = it.begin();\n//\tfor (const auto& term : split_sum(side)) {\n//\t\tterms.push_back(term);\n//\t}\n//\n//\t// Get terms on right hand side\n//\t++side;\n//\tfor (const auto& term : split_sum(side)) {\n//\t\tterms.push_back(term);\n//\t\tmultiply(terms.back().begin()->multiplier, -1);\n//\t}\n//\n//\tstd::vector<Ex> bases;\n//\tfor (size_t i = 0; i < terms.size(); ++i) {\n//\t\tEx basis(\"\\\\equals\");\n//\t\tbasis.append_child(basis.begin(), terms[i].begin());\n//\t\tEx sum(\"\\\\sum\");\n//\t\tmultiply(sum.begin()->multiplier, mpq_class(1, 2));\n//\t\tfor (size_t j = 0; j < terms.size(); ++j)\n//\t\t\tsum.append_child(sum.begin(), terms[j].begin());\n//\t\tbasis.append_child(basis.begin(), sum.begin());\n//\t\tbases.push_back(basis);\n//\t}\n//\n//\treturn bases;\n//}\n//\n//bool meld::apply_side_relations(iterator it)\n//{\n//\treturn false;\n//\tassert(*it->name == \"\\\\sum\");\n//\n//\tstd::vector<Ex> bases;\n//\tif (*side_relations.begin()->name == \"\\\\comma\") {\n//\t\tauto top = side_relations.begin();\n//\t\tfor (Ex::sibling_iterator beg = top.begin(), end = top.end(); beg != end; ++beg) {\n//\t\t\tauto subbases = collect_bases(beg);\n//\t\t\tbases.insert(bases.end(), subbases.begin(), subbases.end());\n//\t\t}\n//\t}\n//\telse if (*side_relations.begin()->name == \"\\\\equals\") {\n//\t\tbases = collect_bases(side_relations.begin());\n//\t}\n//\telse {\n//\t\tthrow std::runtime_error(\"meld: side_relations is not a relation or comma separated list of relations\");\n//\t}\n//\n//\t// Iterate through all terms in 'it' calculating their projections in terms of side relations\n//\tstd::vector<std::tuple<Ex::iterator>> projected_terms;\n//\tfor (const auto& term : split_sum(it)) {\n//\t\t// Loop through the bases to find a match\n//\t\tfor (const auto& basis : bases) {\n//\t\t\tauto lhs = basis.begin().begin(); \n//\t\t\tif (*lhs->name == \"\\\\prod\") {\n//\t\t\t\t// If term is not a product then it can't match\n//\t\t\t\tif (*term->name != \"\\\\prod\")\n//\t\t\t\t\tcontinue;\n//\t\t\t\t// If it is a product, then iterate through the terms hoping to find a range of\n//\t\t\t\t// terms which matches 'basis'\n//\t\t\t\tauto curterm = lhs.begin();\n//\t\t\t\tEx::iterator matchpos = term.end();\n//\t\t\t\tfor (Ex::sibling_iterator beg = term.begin(), end = term.end(); beg != end; ++beg) {\n//\t\t\t\t\tif (similar_form(curterm, beg)) {\n//\t\t\t\t\t\t++curterm;\n//\t\t\t\t\t\tif (curterm == lhs.end()) {\n//\t\t\t\t\t\t\tauto next = beg;\n//\t\t\t\t\t\t\t++next;\n//\t\t\t\t\t\t\tif (next == end) {\n//\t\t\t\t\t\t\t\tmatchpos = beg;\n//\t\t\t\t\t\t\t\tbreak;\n//\t\t\t\t\t\t\t}\n//\t\t\t\t\t\t}\n//\t\t\t\t\t}\n//\t\t\t\t\telse {\n//\t\t\t\t\t\tcurterm = lhs.begin();\n//\t\t\t\t\t}\n//\t\t\t\t}\n//\t\t\t\tif (matchpos != term.end()) {\n//\t\t\t\t\t// Found a matching basis term\n//\t\t\t\t\tEx prefactor(\"\\\\prod\"), base(\"\\\\prod\");\n//\t\t\t\t\tmultiply(prefactor.begin()->multiplier, *term->multiplier);\n//\t\t\t\t\tEx* on = &prefactor;\n//\t\t\t\t\tfor (Ex::sibling_iterator beg = term.begin(), end = term.end(); beg != end; ++beg) {\n//\t\t\t\t\t\tif (curterm == beg)\n//\t\t\t\t\t\t\ton = &base;\n//\t\t\t\t\t\ton->append_child(beg);\n//\t\t\t\t\t}\n//\t\t\t\t\tstd::map<std::pair<Ex::iterator, Adjform>, mpq_class> projection;\n//\t\t\t\t\t++lhs;\n//\t\t\t\t\tfor (const auto& projterm : split_sum(lhs))\n//\t\t\t\t\t\tprojection[{projterm, Adjform(projterm, index_map, kernel)}] = 1;\n//\t\t\t\t}\n//\t\t\t}\n//\t\t}\n//\t}\n// }\n"
  },
  {
    "path": "core/algorithms/meld.cnb",
    "content": "{\n\t\"cell_id\" : 3662228307020711861,\n\t\"cells\" : \n\t[\n\t\t{\n\t\t\t\"cell_id\" : 12813496339189008854,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 15852928793838010821,\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\algorithm{meld}{Combine terms when allowed by symmetries.}\\n\\nIn a sum of terms, combine terms using mono-term and multi-term symmetries such that\\nthe expression does not use an overcomplete basis. The \\\\algo{meld} algorithm does \\\\emph{not}\\nrewrite the expression to a canonical form, but it instead combines terms such that no terms\\nremain which are a linear combination of the other terms. It can hence be used to prove equivalency of\\nexpressions under both mono-term and multi-term symmetries.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\algorithm{meld}{Combine terms when allowed by symmetries.}\\n\\nIn a sum of terms, combine terms using mono-term and multi-term symmetries such that\\nthe expression does not use an overcomplete basis. The \\\\algo{meld} algorithm does \\\\emph{not}\\nrewrite the expression to a canonical form, but it instead combines terms such that no terms\\nremain which are a linear combination of the other terms. It can hence be used to prove equivalency of\\nexpressions under both mono-term and multi-term symmetries.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 10430932811586932061,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 13010077731798931907,\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"A typical use cases where \\\\algo{meld} is preferable over e.g.~\\\\algo{canonicalise} is when \\nthe expression contains tensors with multi-term symmetries:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"A typical use cases where \\\\algo{meld} is preferable over e.g.~\\\\algo{canonicalise} is when \\nthe expression contains tensors with multi-term symmetries:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 323968739795205784,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 8988964609217598141,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property TableauSymmetry to~}R_{a b c d}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 1065448456801871039,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\" : 13154882953131082344,\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"R_{a b c d} R_{a b c d} + R_{a b c d} R_{a c b d}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}R_{a b c d} R_{a b c d}+R_{a b c d} R_{a c b d}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 36583085602117144,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\" : 4631733436145613510,\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \" 3/2 R_{a b c d} R_{a b c d}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\frac{3}{2}R_{a b c d} R_{a b c d}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"R_{a b c d}::RiemannTensor;\\nex:=R_{a b c d}R_{a b c d} + R_{a b c d}R_{a c b d};\\nmeld(ex);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 15791155294640585690,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 549755148636681523,\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"What has happened here is that the algorithm figured out that the first term is \\nexpressible in terms of the second, and has combined the two. If you write the\\nterms in the opposite order, \\\\algo{meld} still combines them, but now in the form\\nof the other term:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"What has happened here is that the algorithm figured out that the first term is \\nexpressible in terms of the second, and has combined the two. If you write the\\nterms in the opposite order, \\\\algo{meld} still combines them, but now in the form\\nof the other term:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 9029450935143328467,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 12220530943791649783,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\" : 18413295438109622151,\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"R_{a b c d} R_{a c b d} + R_{a b c d} R_{a b c d}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}R_{a b c d} R_{a c b d}+R_{a b c d} R_{a b c d}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 3165521023551330747,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\" : 9944219571662242538,\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"3R_{a b c d} R_{a c b d}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}3R_{a b c d} R_{a c b d}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex:=R_{a b c d}R_{a c b d}+ R_{a b c d}R_{a b c d};\\nmeld(ex);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 1216084673125169191,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 6488164179292980876,\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"So \\\\algo{meld} does not canonicalise, but rather writes the expression such that there\\nremain no linear dependencies between terms.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"So \\\\algo{meld} does not canonicalise, but rather writes the expression such that there\\nremain no linear dependencies between terms.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 4207227977087905811,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 16224843818528585899,\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"This algorithm can of course be used for simpler situations, e.g.~one which uses\\nmono-term symmetries only:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"This algorithm can of course be used for simpler situations, e.g.~one which uses\\nmono-term symmetries only:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 4713573064776445830,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 12868928690304720995,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property AntiSymmetric to~}A_{m n}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 6839470590631291578,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\" : 16338866573341407972,\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"A_{m n}-A_{n m}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}A_{m n}-A_{n m}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 11737426428168493788,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\" : 17438531506218084942,\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"2A_{m n}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}2A_{m n}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"A_{m n}::AntiSymmetric;\\nex:=A_{m n} - A_{n m};\\nmeld(ex);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 6514381677355245703,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 11668151019223862308,\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"The \\\\algo{meld} algorithm can also be used as a quick way to collect terms which only differ by dummy index\\nrelabelling (even when there are no symmetries present), e.g.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"The \\\\algo{meld} algorithm can also be used as a quick way to collect terms which only differ by dummy index\\nrelabelling (even when there are no symmetries present), e.g.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 14013980821582684444,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 5390606172301622082,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\" : 15488886801634223375,\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"Q_{m n} R^{m n} + R^{p q} Q_{p q}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}Q_{m n} R^{m n}+R^{p q} Q_{p q}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex:=Q_{m n} R^{m n} + R^{p q} Q_{p q};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 1656392514422199773,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 7063320059612004650,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\" : 3548296417909860369,\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"2Q_{m n} R^{m n}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}2Q_{m n} R^{m n}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"meld(ex);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 11870955447027965657,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 8936521076228235993,\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"The algorithm also handles cyclic symmetries of traces:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"The algorithm also handles cyclic symmetries of traces:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 406611350630800730,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 6605104543728451938,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\" : 1701022937828344821,\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"tr(u^{\\\\mu} u^{\\\\mu} u^{\\\\nu} u^{\\\\nu})-tr(u^{\\\\mu} u^{\\\\nu} u^{\\\\nu} u^{\\\\mu})\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}tr\\\\left(u^{\\\\mu} u^{\\\\mu} u^{\\\\nu} u^{\\\\nu}\\\\right)-tr\\\\left(u^{\\\\mu} u^{\\\\nu} u^{\\\\nu} u^{\\\\mu}\\\\right)\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 14496227590260612013,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\" : 2255656535567173132,\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"0\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}0\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"{\\\\mu,\\\\nu}::Indices(vector).\\nu^{\\\\mu}::ImplicitIndex.\\nu^{\\\\mu}::SelfNonCommuting.\\ntr{#}::Trace.\\nex := tr{u^{\\\\mu} u^{\\\\mu} u^{\\\\nu} u^{\\\\nu}} - \\n      tr{u^{\\\\mu} u^{\\\\nu} u^{\\\\nu} u^{\\\\mu}};\\nmeld(ex);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 130835195174808300,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1\n}\n"
  },
  {
    "path": "core/algorithms/meld.hh",
    "content": "#pragma once\n\n#include <memory>\n#include <array>\n#include \"Algorithm.hh\"\n#include \"Adjform.hh\"\n#include \"properties/TableauBase.hh\"\n\nnamespace cadabra {\n\n\tclass meld : public Algorithm\n\t\t{\n\t\tpublic:\n\t\t\tmeld(const Kernel& kernel, Ex& ex, bool project_as_sum = false);\n\t\t\tvirtual ~meld();\n\n\t\t\tvirtual bool can_apply(iterator it) override;\n\t\t\tvirtual result_t apply(iterator& it) override;\n\n\t\tprivate:\n\t\t\tusing tab_t = cadabra::TableauBase::tab_t;\n\n\t\t\tstruct ProjectedTerm {\n\t\t\t\tProjectedTerm(const Kernel& kernel, IndexMap& index_map, Ex& ex, Ex::iterator it);\n\t\t\t\t// Return 'true' if the tensor parts are identical up to index structure\n\t\t\t\tbool compare(const Kernel& kernel, const ProjectedTerm& other);\n\n\t\t\t\tEx scalar, tensor;\n\t\t\t\tProjectedAdjform projection;\n\t\t\t\tAdjform ident;\n\t\t\t\tEx::iterator it;\n\t\t\t\tbool changed;\n\t\t\t};\n\n\t\t\tstruct symmetrizer_t {\n\t\t\t\tsymmetrizer_t(bool antisymmetric, bool independent) : antisymmetric(antisymmetric), independent(independent) {}\n\t\t\t\tstd::vector<size_t> indices;\n\t\t\t\tbool antisymmetric, independent;\n\t\t\t};\n\n\t\t\t// Return the tableaux associated with the expression, offsetting\n\t\t\t// cells with how many indices *deep* it is \n\t\t\tstd::vector<tab_t> collect_tableaux(Ex& ex) const;\n\n\t\t\t// Collects all the columns and rows of the tableaux starting at node 'it' and combines\n\t\t\t// similar columns where possible. Returns 'true' if the symmetrizers mean the term is\n\t\t\t// identically 0\n\t\t\tbool collect_symmetries(const std::vector<tab_t>& tabs, std::vector<symmetrizer_t>& symmetrizers) const;\n\t\t\tbool collect_symmetries_as_product(const std::vector<tab_t>& tabs, std::vector<symmetrizer_t>& symmetrizers) const;\n\t\t\tbool collect_symmetries_as_sum(const std::vector<tab_t>& tabs, std::vector<symmetrizer_t>& symmetrizers) const;\n\n\t\t\tvoid symmetrize(ProjectedTerm& adj, const std::vector<symmetrizer_t>& symmetries);\n\t\t\tvoid symmetrize_as_product(ProjectedTerm& adj, const std::vector<symmetrizer_t>& symmetrizers);\n\t\t\tvoid symmetrize_as_sum(ProjectedTerm& adj, const std::vector<symmetrizer_t>& symmetries);\n\t\t\tvoid symmetrize_idents(ProjectedTerm& sym);\n\n\t\t\t// Remove non-diagonal terms of diagonal objects\n\t\t\tbool can_apply_diagonals(iterator it);\n\t\t\tbool apply_diagonals(iterator it);\n\n\t\t\t// Remove terms which contain contractions of traceless objects\n\t\t\tbool can_apply_traceless(iterator it);\n\t\t\tbool apply_traceless(iterator it);\n\n\t\t\t// Apply the symmetry Tr(ABC) = Tr(BCA) = Tr(CAB)\n\t\t\tbool can_apply_cycle_traces(iterator it);\n\t\t\tbool apply_cycle_traces(iterator it);\n\n\t\t\t// Compare Young projections of each term for symmetry\n\t\t\tbool can_apply_tableaux(iterator it);\n\t\t\tbool apply_tableaux(iterator it);\n\n\t\t\t//bool can_apply_side_relations(iterator it);\n\t\t\t//bool apply_side_relations(iterator it);\n\t\t\t//Ex side_relations;\n\n\t\t\tIndexMap index_map;\n\t\t\tbool project_as_sum;\n\t\t};\n\n}\n"
  },
  {
    "path": "core/algorithms/ndsolve.cnb",
    "content": "{\n\t\"cell_id\": 4159629932159188174,\n\t\"cells\": [\n\t\t{\n\t\t\t\"cell_id\": 11219555704534006485,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 8969349706567807986,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\algorithm{ndsolve}{Numerically solve ordinary differential equations}\\n\\nThe \\\\algo{ndsolve} function determines numerical solutions to ordinary differential equations. These should be provided in the form of a system of first order equations. The result is one or more interpolating functions, which can be plotted or evaluated.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\algorithm{ndsolve}{Numerically solve ordinary differential equations}\\n\\nThe \\\\algo{ndsolve} function determines numerical solutions to ordinary differential equations. These should be provided in the form of a system of first order equations. The result is one or more interpolating functions, which can be plotted or evaluated.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 2031683651874267390,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 8182632709474581575,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"In order to use \\\\algo{ndsolve}, one has to set up the dependent and independent variables, and also determine how one wants to write the derivatives. So the starting point is something similar to:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"In order to use \\\\algo{ndsolve}, one has to set up the dependent and independent variables, and also determine how one wants to write the derivatives. So the starting point is something similar to:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 3378058555525685856,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 16454169886491317342,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property Coordinate attached to~}x.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 2546539306288634200,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property Derivative attached to~}\\\\backslash\\\\texttt{dot}\\\\{\\\\#\\\\}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 2994116835118515531,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property Depends attached to~}y.\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"x::Coordinate;\\n\\\\dot{#}::Derivative(x);\\ny::Depends(x);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 15660980455924652948,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 15635936478455511718,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"The differential equation we want to solve is entered as an equation with the derivative on the left-hand side.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"The differential equation we want to solve is entered as an equation with the derivative on the left-hand side.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 17719828191640014056,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 7840500627894877419,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 12065436743873785622,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\dot(y) = y \\\\cos(x + y)\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\dot{y} = y \\\\cos\\\\left(x\\\\discretionary{}{}{}+y\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"eq1 := \\\\dot{y} = y \\\\cos(x + y);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 14465595702660739862,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 10821151553991852316,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"This can now be solved with \\\\algo{ndsolve}, by passing it the differential equation, the initial conditions (one in our case, for $y$) and the range of the independent variable $x$,\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"This can now be solved with \\\\algo{ndsolve}, by passing it the differential equation, the initial conditions (one in our case, for $y$) and the range of the independent variable $x$,\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 14773701118463138445,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 3951865395403951012,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 15414984127114973431,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"{y =  (NInterpolatingFunction)}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\left[y = \\\\square{}\\n(x)\\\\right]\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"sol1 = ndsolve(eq1, {$y$: 1}, ($x$, 0, 30));\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 5256175863245383797,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 1791026440551467646,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"The result above is an equation for $y$ in terms of an anonymous function (the 'box'), which can be used directly in the \\\\algo{plot} function (anonymous functions are similar to Mathematica's \\\\verb|InterpolatingFunction|).\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"The result above is an equation for $y$ in terms of an anonymous function (the 'box'), which can be used directly in the \\\\algo{plot} function (anonymous functions are similar to Mathematica's \\\\verb|InterpolatingFunction|).\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 18264659085209943245,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 14916881075920151773,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"image_svg\",\n\t\t\t\t\t\"source\": \"<?xml version="1.0" encoding="utf-8" standalone="no"?>
<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
  "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="460.8pt" height="345.6pt" viewBox="0 0 460.8 345.6" xmlns="http://www.w3.org/2000/svg" version="1.1">
 <metadata>
  <rdf:RDF xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:cc="http://creativecommons.org/ns#" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
   <cc:Work>
    <dc:type rdf:resource="http://purl.org/dc/dcmitype/StillImage"/>
    <dc:date>2025-05-28T22:03:47.647704</dc:date>
    <dc:format>image/svg+xml</dc:format>
    <dc:creator>
     <cc:Agent>
      <dc:title>Matplotlib v3.6.3, https://matplotlib.org/</dc:title>
     </cc:Agent>
    </dc:creator>
   </cc:Work>
  </rdf:RDF>
 </metadata>
 <defs>
  <style type="text/css">*{stroke-linejoin: round; stroke-linecap: butt}</style>
 </defs>
 <g id="figure_1">
  <g id="patch_1">
   <path d="M 0 345.6 
L 460.8 345.6 
L 460.8 0 
L 0 0 
z
" style="fill: #ffffff"/>
  </g>
  <g id="axes_1">
   <g id="patch_2">
    <path d="M 57.6 307.584 
L 414.72 307.584 
L 414.72 41.472 
L 57.6 41.472 
z
" style="fill: #ffffff"/>
   </g>
   <g id="matplotlib.axis_1">
    <g id="xtick_1">
     <g id="line2d_1">
      <defs>
       <path id="m2fb4b6f6ee" d="M 0 0 
L 0 3.5 
" style="stroke: #000000; stroke-width: 0.8"/>
      </defs>
      <g>
       <use xlink:href="#m2fb4b6f6ee" x="73.832727" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_1">
      <!-- 0 -->
      <g transform="translate(70.651477 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-30" d="M 2034 4250 
Q 1547 4250 1301 3770 
Q 1056 3291 1056 2328 
Q 1056 1369 1301 889 
Q 1547 409 2034 409 
Q 2525 409 2770 889 
Q 3016 1369 3016 2328 
Q 3016 3291 2770 3770 
Q 2525 4250 2034 4250 
z
M 2034 4750 
Q 2819 4750 3233 4129 
Q 3647 3509 3647 2328 
Q 3647 1150 3233 529 
Q 2819 -91 2034 -91 
Q 1250 -91 836 529 
Q 422 1150 422 2328 
Q 422 3509 836 4129 
Q 1250 4750 2034 4750 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-30"/>
      </g>
     </g>
    </g>
    <g id="xtick_2">
     <g id="line2d_2">
      <g>
       <use xlink:href="#m2fb4b6f6ee" x="127.941818" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_2">
      <!-- 5 -->
      <g transform="translate(124.760568 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-35" d="M 691 4666 
L 3169 4666 
L 3169 4134 
L 1269 4134 
L 1269 2991 
Q 1406 3038 1543 3061 
Q 1681 3084 1819 3084 
Q 2600 3084 3056 2656 
Q 3513 2228 3513 1497 
Q 3513 744 3044 326 
Q 2575 -91 1722 -91 
Q 1428 -91 1123 -41 
Q 819 9 494 109 
L 494 744 
Q 775 591 1075 516 
Q 1375 441 1709 441 
Q 2250 441 2565 725 
Q 2881 1009 2881 1497 
Q 2881 1984 2565 2268 
Q 2250 2553 1709 2553 
Q 1456 2553 1204 2497 
Q 953 2441 691 2322 
L 691 4666 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-35"/>
      </g>
     </g>
    </g>
    <g id="xtick_3">
     <g id="line2d_3">
      <g>
       <use xlink:href="#m2fb4b6f6ee" x="182.050909" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_3">
      <!-- 10 -->
      <g transform="translate(175.688409 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-31" d="M 794 531 
L 1825 531 
L 1825 4091 
L 703 3866 
L 703 4441 
L 1819 4666 
L 2450 4666 
L 2450 531 
L 3481 531 
L 3481 0 
L 794 0 
L 794 531 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-31"/>
       <use xlink:href="#DejaVuSans-30" x="63.623047"/>
      </g>
     </g>
    </g>
    <g id="xtick_4">
     <g id="line2d_4">
      <g>
       <use xlink:href="#m2fb4b6f6ee" x="236.16" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_4">
      <!-- 15 -->
      <g transform="translate(229.7975 322.182437) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-31"/>
       <use xlink:href="#DejaVuSans-35" x="63.623047"/>
      </g>
     </g>
    </g>
    <g id="xtick_5">
     <g id="line2d_5">
      <g>
       <use xlink:href="#m2fb4b6f6ee" x="290.269091" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_5">
      <!-- 20 -->
      <g transform="translate(283.906591 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-32" d="M 1228 531 
L 3431 531 
L 3431 0 
L 469 0 
L 469 531 
Q 828 903 1448 1529 
Q 2069 2156 2228 2338 
Q 2531 2678 2651 2914 
Q 2772 3150 2772 3378 
Q 2772 3750 2511 3984 
Q 2250 4219 1831 4219 
Q 1534 4219 1204 4116 
Q 875 4013 500 3803 
L 500 4441 
Q 881 4594 1212 4672 
Q 1544 4750 1819 4750 
Q 2544 4750 2975 4387 
Q 3406 4025 3406 3419 
Q 3406 3131 3298 2873 
Q 3191 2616 2906 2266 
Q 2828 2175 2409 1742 
Q 1991 1309 1228 531 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-32"/>
       <use xlink:href="#DejaVuSans-30" x="63.623047"/>
      </g>
     </g>
    </g>
    <g id="xtick_6">
     <g id="line2d_6">
      <g>
       <use xlink:href="#m2fb4b6f6ee" x="344.378182" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_6">
      <!-- 25 -->
      <g transform="translate(338.015682 322.182437) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-32"/>
       <use xlink:href="#DejaVuSans-35" x="63.623047"/>
      </g>
     </g>
    </g>
    <g id="xtick_7">
     <g id="line2d_7">
      <g>
       <use xlink:href="#m2fb4b6f6ee" x="398.487273" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_7">
      <!-- 30 -->
      <g transform="translate(392.124773 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-33" d="M 2597 2516 
Q 3050 2419 3304 2112 
Q 3559 1806 3559 1356 
Q 3559 666 3084 287 
Q 2609 -91 1734 -91 
Q 1441 -91 1130 -33 
Q 819 25 488 141 
L 488 750 
Q 750 597 1062 519 
Q 1375 441 1716 441 
Q 2309 441 2620 675 
Q 2931 909 2931 1356 
Q 2931 1769 2642 2001 
Q 2353 2234 1838 2234 
L 1294 2234 
L 1294 2753 
L 1863 2753 
Q 2328 2753 2575 2939 
Q 2822 3125 2822 3475 
Q 2822 3834 2567 4026 
Q 2313 4219 1838 4219 
Q 1578 4219 1281 4162 
Q 984 4106 628 3988 
L 628 4550 
Q 988 4650 1302 4700 
Q 1616 4750 1894 4750 
Q 2613 4750 3031 4423 
Q 3450 4097 3450 3541 
Q 3450 3153 3228 2886 
Q 3006 2619 2597 2516 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-33"/>
       <use xlink:href="#DejaVuSans-30" x="63.623047"/>
      </g>
     </g>
    </g>
   </g>
   <g id="matplotlib.axis_2">
    <g id="ytick_1">
     <g id="line2d_8">
      <defs>
       <path id="m9d0f3efb5b" d="M 0 0 
L -3.5 0 
" style="stroke: #000000; stroke-width: 0.8"/>
      </defs>
      <g>
       <use xlink:href="#m9d0f3efb5b" x="57.6" y="299.782542" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_8">
      <!-- 0.0 -->
      <g transform="translate(34.696875 303.581761) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-2e" d="M 684 794 
L 1344 794 
L 1344 0 
L 684 0 
L 684 794 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-30"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-30" x="95.410156"/>
      </g>
     </g>
    </g>
    <g id="ytick_2">
     <g id="line2d_9">
      <g>
       <use xlink:href="#m9d0f3efb5b" x="57.6" y="255.282804" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_9">
      <!-- 0.2 -->
      <g transform="translate(34.696875 259.082023) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-30"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-32" x="95.410156"/>
      </g>
     </g>
    </g>
    <g id="ytick_3">
     <g id="line2d_10">
      <g>
       <use xlink:href="#m9d0f3efb5b" x="57.6" y="210.783065" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_10">
      <!-- 0.4 -->
      <g transform="translate(34.696875 214.582284) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-34" d="M 2419 4116 
L 825 1625 
L 2419 1625 
L 2419 4116 
z
M 2253 4666 
L 3047 4666 
L 3047 1625 
L 3713 1625 
L 3713 1100 
L 3047 1100 
L 3047 0 
L 2419 0 
L 2419 1100 
L 313 1100 
L 313 1709 
L 2253 4666 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-30"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-34" x="95.410156"/>
      </g>
     </g>
    </g>
    <g id="ytick_4">
     <g id="line2d_11">
      <g>
       <use xlink:href="#m9d0f3efb5b" x="57.6" y="166.283327" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_11">
      <!-- 0.6 -->
      <g transform="translate(34.696875 170.082545) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-36" d="M 2113 2584 
Q 1688 2584 1439 2293 
Q 1191 2003 1191 1497 
Q 1191 994 1439 701 
Q 1688 409 2113 409 
Q 2538 409 2786 701 
Q 3034 994 3034 1497 
Q 3034 2003 2786 2293 
Q 2538 2584 2113 2584 
z
M 3366 4563 
L 3366 3988 
Q 3128 4100 2886 4159 
Q 2644 4219 2406 4219 
Q 1781 4219 1451 3797 
Q 1122 3375 1075 2522 
Q 1259 2794 1537 2939 
Q 1816 3084 2150 3084 
Q 2853 3084 3261 2657 
Q 3669 2231 3669 1497 
Q 3669 778 3244 343 
Q 2819 -91 2113 -91 
Q 1303 -91 875 529 
Q 447 1150 447 2328 
Q 447 3434 972 4092 
Q 1497 4750 2381 4750 
Q 2619 4750 2861 4703 
Q 3103 4656 3366 4563 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-30"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-36" x="95.410156"/>
      </g>
     </g>
    </g>
    <g id="ytick_5">
     <g id="line2d_12">
      <g>
       <use xlink:href="#m9d0f3efb5b" x="57.6" y="121.783588" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_12">
      <!-- 0.8 -->
      <g transform="translate(34.696875 125.582807) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-38" d="M 2034 2216 
Q 1584 2216 1326 1975 
Q 1069 1734 1069 1313 
Q 1069 891 1326 650 
Q 1584 409 2034 409 
Q 2484 409 2743 651 
Q 3003 894 3003 1313 
Q 3003 1734 2745 1975 
Q 2488 2216 2034 2216 
z
M 1403 2484 
Q 997 2584 770 2862 
Q 544 3141 544 3541 
Q 544 4100 942 4425 
Q 1341 4750 2034 4750 
Q 2731 4750 3128 4425 
Q 3525 4100 3525 3541 
Q 3525 3141 3298 2862 
Q 3072 2584 2669 2484 
Q 3125 2378 3379 2068 
Q 3634 1759 3634 1313 
Q 3634 634 3220 271 
Q 2806 -91 2034 -91 
Q 1263 -91 848 271 
Q 434 634 434 1313 
Q 434 1759 690 2068 
Q 947 2378 1403 2484 
z
M 1172 3481 
Q 1172 3119 1398 2916 
Q 1625 2713 2034 2713 
Q 2441 2713 2670 2916 
Q 2900 3119 2900 3481 
Q 2900 3844 2670 4047 
Q 2441 4250 2034 4250 
Q 1625 4250 1398 4047 
Q 1172 3844 1172 3481 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-30"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-38" x="95.410156"/>
      </g>
     </g>
    </g>
    <g id="ytick_6">
     <g id="line2d_13">
      <g>
       <use xlink:href="#m9d0f3efb5b" x="57.6" y="77.28385" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_13">
      <!-- 1.0 -->
      <g transform="translate(34.696875 81.083068) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-31"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-30" x="95.410156"/>
      </g>
     </g>
    </g>
   </g>
   <g id="line2d_14">
    <path d="M 73.832727 77.28385 
L 77.112066 53.568 
L 80.391405 54.201931 
L 83.670744 71.539878 
L 86.950083 99.979165 
L 90.229421 131.98719 
L 93.50876 163.702566 
L 96.788099 193.563898 
L 100.067438 218.612505 
L 103.346777 238.696564 
L 106.626116 254.362784 
L 109.905455 265.995576 
L 113.184793 274.147541 
L 116.464132 279.373591 
L 119.743471 281.900971 
L 123.02281 283.238226 
L 126.302149 283.213792 
L 129.581488 280.60743 
L 132.860826 277.454265 
L 136.140165 271.026899 
L 139.419504 260.951224 
L 142.698843 247.516209 
L 145.978182 232.543557 
L 149.257521 218.386469 
L 152.53686 210.556269 
L 155.816198 209.714958 
L 159.095537 215.747187 
L 162.374876 227.629413 
L 165.654215 241.321489 
L 168.933554 254.30206 
L 172.212893 265.102326 
L 175.492231 274.579091 
L 178.77157 280.521506 
L 182.050909 285.081589 
L 185.330248 288.176905 
L 188.609587 289.463522 
L 191.888926 290.129271 
L 195.168264 289.884354 
L 198.447603 288.131982 
L 201.726942 285.973132 
L 205.006281 281.970515 
L 208.28562 275.733246 
L 211.564959 268.043189 
L 214.844298 258.303442 
L 218.123636 249.772027 
L 221.402975 242.9954 
L 224.682314 241.938542 
L 227.961653 245.345639 
L 231.240992 252.124872 
L 234.520331 260.802438 
L 237.799669 269.596092 
L 241.079008 276.862551 
L 244.358347 282.648462 
L 247.637686 287.049304 
L 250.917025 289.771522 
L 254.196364 291.889955 
L 257.475702 292.58532 
L 260.755041 292.956002 
L 264.03438 292.540264 
L 267.313719 291.350918 
L 270.593058 289.569139 
L 273.872397 286.286842 
L 277.151736 281.638386 
L 280.431074 275.806018 
L 283.710413 268.757033 
L 286.989752 262.281645 
L 290.269091 257.70076 
L 293.54843 256.801105 
L 296.827769 259.813192 
L 300.107107 264.854384 
L 303.386446 271.377221 
L 306.665785 277.957105 
L 309.945124 283.225099 
L 313.224463 287.35944 
L 316.503802 290.470227 
L 319.78314 292.52915 
L 323.062479 293.793572 
L 326.341818 294.323805 
L 329.621157 294.417243 
L 332.900496 294.060983 
L 336.179835 292.908907 
L 339.459174 291.444656 
L 342.738512 288.574925 
L 346.017851 284.68186 
L 349.29719 279.903872 
L 352.576529 274.380864 
L 355.855868 269.287131 
L 359.135207 266.166165 
L 362.414545 265.778005 
L 365.693884 268.533401 
L 368.973223 272.728053 
L 372.252562 278.033718 
L 375.531901 283.117237 
L 378.81124 287.133494 
L 382.090579 290.530544 
L 385.369917 292.588033 
L 388.649256 294.188326 
L 391.928595 295.11133 
L 395.207934 295.356552 
L 398.487273 295.488 
" clip-path="url(#p8c442c6fe2)" style="fill: none; stroke: #1f77b4; stroke-width: 1.5; stroke-linecap: square"/>
   </g>
   <g id="patch_3">
    <path d="M 57.6 307.584 
L 57.6 41.472 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
   <g id="patch_4">
    <path d="M 414.72 307.584 
L 414.72 41.472 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
   <g id="patch_5">
    <path d="M 57.6 307.584 
L 414.72 307.584 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
   <g id="patch_6">
    <path d="M 57.6 41.472 
L 414.72 41.472 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
   <g id="legend_1">
    <g id="patch_7">
     <path d="M 370.72 64.170437 
L 407.72 64.170437 
Q 409.72 64.170437 409.72 62.170437 
L 409.72 48.472 
Q 409.72 46.472 407.72 46.472 
L 370.72 46.472 
Q 368.72 46.472 368.72 48.472 
L 368.72 62.170437 
Q 368.72 64.170437 370.72 64.170437 
z
" style="fill: #ffffff; opacity: 0.8; stroke: #cccccc; stroke-linejoin: miter"/>
    </g>
    <g id="line2d_15">
     <path d="M 372.72 54.570437 
L 382.72 54.570437 
L 392.72 54.570437 
" style="fill: none; stroke: #1f77b4; stroke-width: 1.5; stroke-linecap: square"/>
    </g>
    <g id="text_14">
     <!-- $y$ -->
     <g transform="translate(400.72 58.070437) scale(0.1 -0.1)">
      <defs>
       <path id="Cmmi10-79" d="M 538 -916 
Q 672 -1147 1006 -1147 
Q 1309 -1147 1531 -934 
Q 1753 -722 1889 -420 
Q 2025 -119 2100 197 
Q 1816 -72 1484 -72 
Q 1231 -72 1053 15 
Q 875 103 776 276 
Q 678 450 678 697 
Q 678 906 734 1126 
Q 791 1347 892 1617 
Q 994 1888 1069 2088 
Q 1153 2322 1153 2472 
Q 1153 2663 1013 2663 
Q 759 2663 595 2402 
Q 431 2141 353 1819 
Q 341 1778 300 1778 
L 225 1778 
Q 172 1778 172 1838 
L 172 1856 
Q 275 2238 487 2533 
Q 700 2828 1025 2828 
Q 1253 2828 1411 2678 
Q 1569 2528 1569 2297 
Q 1569 2178 1516 2047 
Q 1488 1969 1388 1706 
Q 1288 1444 1234 1272 
Q 1181 1100 1147 934 
Q 1113 769 1113 603 
Q 1113 391 1203 244 
Q 1294 97 1491 97 
Q 1888 97 2203 581 
L 2688 2553 
Q 2709 2638 2787 2698 
Q 2866 2759 2956 2759 
Q 3034 2759 3092 2709 
Q 3150 2659 3150 2578 
Q 3150 2541 3144 2528 
L 2509 -19 
Q 2425 -347 2200 -647 
Q 1975 -947 1658 -1130 
Q 1341 -1313 997 -1313 
Q 831 -1313 668 -1248 
Q 506 -1184 406 -1056 
Q 306 -928 306 -756 
Q 306 -581 409 -453 
Q 513 -325 684 -325 
Q 788 -325 858 -389 
Q 928 -453 928 -556 
Q 928 -703 818 -812 
Q 709 -922 563 -922 
Q 556 -919 550 -917 
Q 544 -916 538 -916 
z
" transform="scale(0.015625)"/>
      </defs>
      <use xlink:href="#Cmmi10-79" transform="translate(0 0.8125)"/>
     </g>
    </g>
   </g>
  </g>
 </g>
 <defs>
  <clipPath id="p8c442c6fe2">
   <rect x="57.6" y="41.472" width="357.12" height="266.112"/>
  </clipPath>
 </defs>
</svg>
\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"from cdb.graphics.plot import *\\nplot(sol1, {$x$: (0,30)} );\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 2092794637457731817,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 15128024325732434531,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"The logic is similar for systems of ODEs. Declare the dependent coordinate, the functions to solve for, and the differential equation:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"The logic is similar for systems of ODEs. Declare the dependent coordinate, the functions to solve for, and the differential equation:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 6653894977252875634,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"t::Coordinate.\\n{x, y}::Depends(1t).\\n\\\\dot{#}::Derivative(t).\\nx:=x.\\ny:=y.\\nt:=t.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 5605800596123671638,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 10005016116980070347,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 3938986142103128901,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"{\\\\dot(x) = -y-(x)**2, \\\\dot(y) = 2x-(y)**3}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\left[\\\\dot{x} = -\\\\,y\\\\discretionary{}{}{}-\\\\,{x}^{2\\\\,}, \\\\discretionary{}{}{}\\\\dot{y} = 2\\\\,x\\\\discretionary{}{}{}-\\\\,{y}^{3\\\\,}\\\\right]\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"eq3 := [ \\\\dot{x} = -y - x**2, \\\\dot{y} = 2 x - y**3 ];\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 6206407786016539210,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 13493237994077552543,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"Then solve using \\\\algo{ndsolve}. This now returns a set of equations, one for each function that it has solved for, in terms of two anonymous functions.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"Then solve using \\\\algo{ndsolve}. This now returns a set of equations, one for each function that it has solved for, in terms of two anonymous functions.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 2309181205671768014,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 75368401574407836,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 9330809909018693897,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"{x =  (NInterpolatingFunction), y =  (NInterpolatingFunction)}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\left[x = \\\\square{}\\n(t), \\\\discretionary{}{}{}y = \\\\square{}\\n(t)\\\\right]\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"res3 = ndsolve(eq3, {x: 1, y: 1}, (t, 0, 20));\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 14565517351895850011,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 1118775784614114176,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"image_svg\",\n\t\t\t\t\t\"source\": \"<?xml version="1.0" encoding="utf-8" standalone="no"?>
<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
  "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="460.8pt" height="345.6pt" viewBox="0 0 460.8 345.6" xmlns="http://www.w3.org/2000/svg" version="1.1">
 <metadata>
  <rdf:RDF xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:cc="http://creativecommons.org/ns#" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
   <cc:Work>
    <dc:type rdf:resource="http://purl.org/dc/dcmitype/StillImage"/>
    <dc:date>2025-05-28T22:03:49.662495</dc:date>
    <dc:format>image/svg+xml</dc:format>
    <dc:creator>
     <cc:Agent>
      <dc:title>Matplotlib v3.6.3, https://matplotlib.org/</dc:title>
     </cc:Agent>
    </dc:creator>
   </cc:Work>
  </rdf:RDF>
 </metadata>
 <defs>
  <style type="text/css">*{stroke-linejoin: round; stroke-linecap: butt}</style>
 </defs>
 <g id="figure_1">
  <g id="patch_1">
   <path d="M 0 345.6 
L 460.8 345.6 
L 460.8 0 
L 0 0 
z
" style="fill: #ffffff"/>
  </g>
  <g id="axes_1">
   <g id="patch_2">
    <path d="M 57.6 307.584 
L 414.72 307.584 
L 414.72 41.472 
L 57.6 41.472 
z
" style="fill: #ffffff"/>
   </g>
   <g id="matplotlib.axis_1">
    <g id="xtick_1">
     <g id="line2d_1">
      <defs>
       <path id="m96cef4e612" d="M 0 0 
L 0 3.5 
" style="stroke: #000000; stroke-width: 0.8"/>
      </defs>
      <g>
       <use xlink:href="#m96cef4e612" x="73.832727" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_1">
      <!-- 0.0 -->
      <g transform="translate(65.881165 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-30" d="M 2034 4250 
Q 1547 4250 1301 3770 
Q 1056 3291 1056 2328 
Q 1056 1369 1301 889 
Q 1547 409 2034 409 
Q 2525 409 2770 889 
Q 3016 1369 3016 2328 
Q 3016 3291 2770 3770 
Q 2525 4250 2034 4250 
z
M 2034 4750 
Q 2819 4750 3233 4129 
Q 3647 3509 3647 2328 
Q 3647 1150 3233 529 
Q 2819 -91 2034 -91 
Q 1250 -91 836 529 
Q 422 1150 422 2328 
Q 422 3509 836 4129 
Q 1250 4750 2034 4750 
z
" transform="scale(0.015625)"/>
        <path id="DejaVuSans-2e" d="M 684 794 
L 1344 794 
L 1344 0 
L 684 0 
L 684 794 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-30"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-30" x="95.410156"/>
      </g>
     </g>
    </g>
    <g id="xtick_2">
     <g id="line2d_2">
      <g>
       <use xlink:href="#m96cef4e612" x="114.414545" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_2">
      <!-- 2.5 -->
      <g transform="translate(106.462983 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-32" d="M 1228 531 
L 3431 531 
L 3431 0 
L 469 0 
L 469 531 
Q 828 903 1448 1529 
Q 2069 2156 2228 2338 
Q 2531 2678 2651 2914 
Q 2772 3150 2772 3378 
Q 2772 3750 2511 3984 
Q 2250 4219 1831 4219 
Q 1534 4219 1204 4116 
Q 875 4013 500 3803 
L 500 4441 
Q 881 4594 1212 4672 
Q 1544 4750 1819 4750 
Q 2544 4750 2975 4387 
Q 3406 4025 3406 3419 
Q 3406 3131 3298 2873 
Q 3191 2616 2906 2266 
Q 2828 2175 2409 1742 
Q 1991 1309 1228 531 
z
" transform="scale(0.015625)"/>
        <path id="DejaVuSans-35" d="M 691 4666 
L 3169 4666 
L 3169 4134 
L 1269 4134 
L 1269 2991 
Q 1406 3038 1543 3061 
Q 1681 3084 1819 3084 
Q 2600 3084 3056 2656 
Q 3513 2228 3513 1497 
Q 3513 744 3044 326 
Q 2575 -91 1722 -91 
Q 1428 -91 1123 -41 
Q 819 9 494 109 
L 494 744 
Q 775 591 1075 516 
Q 1375 441 1709 441 
Q 2250 441 2565 725 
Q 2881 1009 2881 1497 
Q 2881 1984 2565 2268 
Q 2250 2553 1709 2553 
Q 1456 2553 1204 2497 
Q 953 2441 691 2322 
L 691 4666 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-32"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-35" x="95.410156"/>
      </g>
     </g>
    </g>
    <g id="xtick_3">
     <g id="line2d_3">
      <g>
       <use xlink:href="#m96cef4e612" x="154.996364" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_3">
      <!-- 5.0 -->
      <g transform="translate(147.044801 322.182437) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-35"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-30" x="95.410156"/>
      </g>
     </g>
    </g>
    <g id="xtick_4">
     <g id="line2d_4">
      <g>
       <use xlink:href="#m96cef4e612" x="195.578182" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_4">
      <!-- 7.5 -->
      <g transform="translate(187.626619 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-37" d="M 525 4666 
L 3525 4666 
L 3525 4397 
L 1831 0 
L 1172 0 
L 2766 4134 
L 525 4134 
L 525 4666 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-37"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-35" x="95.410156"/>
      </g>
     </g>
    </g>
    <g id="xtick_5">
     <g id="line2d_5">
      <g>
       <use xlink:href="#m96cef4e612" x="236.16" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_5">
      <!-- 10.0 -->
      <g transform="translate(225.027188 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-31" d="M 794 531 
L 1825 531 
L 1825 4091 
L 703 3866 
L 703 4441 
L 1819 4666 
L 2450 4666 
L 2450 531 
L 3481 531 
L 3481 0 
L 794 0 
L 794 531 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-31"/>
       <use xlink:href="#DejaVuSans-30" x="63.623047"/>
       <use xlink:href="#DejaVuSans-2e" x="127.246094"/>
       <use xlink:href="#DejaVuSans-30" x="159.033203"/>
      </g>
     </g>
    </g>
    <g id="xtick_6">
     <g id="line2d_6">
      <g>
       <use xlink:href="#m96cef4e612" x="276.741818" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_6">
      <!-- 12.5 -->
      <g transform="translate(265.609006 322.182437) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-31"/>
       <use xlink:href="#DejaVuSans-32" x="63.623047"/>
       <use xlink:href="#DejaVuSans-2e" x="127.246094"/>
       <use xlink:href="#DejaVuSans-35" x="159.033203"/>
      </g>
     </g>
    </g>
    <g id="xtick_7">
     <g id="line2d_7">
      <g>
       <use xlink:href="#m96cef4e612" x="317.323636" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_7">
      <!-- 15.0 -->
      <g transform="translate(306.190824 322.182437) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-31"/>
       <use xlink:href="#DejaVuSans-35" x="63.623047"/>
       <use xlink:href="#DejaVuSans-2e" x="127.246094"/>
       <use xlink:href="#DejaVuSans-30" x="159.033203"/>
      </g>
     </g>
    </g>
    <g id="xtick_8">
     <g id="line2d_8">
      <g>
       <use xlink:href="#m96cef4e612" x="357.905455" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_8">
      <!-- 17.5 -->
      <g transform="translate(346.772642 322.182437) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-31"/>
       <use xlink:href="#DejaVuSans-37" x="63.623047"/>
       <use xlink:href="#DejaVuSans-2e" x="127.246094"/>
       <use xlink:href="#DejaVuSans-35" x="159.033203"/>
      </g>
     </g>
    </g>
    <g id="xtick_9">
     <g id="line2d_9">
      <g>
       <use xlink:href="#m96cef4e612" x="398.487273" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_9">
      <!-- 20.0 -->
      <g transform="translate(387.35446 322.182437) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-32"/>
       <use xlink:href="#DejaVuSans-30" x="63.623047"/>
       <use xlink:href="#DejaVuSans-2e" x="127.246094"/>
       <use xlink:href="#DejaVuSans-30" x="159.033203"/>
      </g>
     </g>
    </g>
   </g>
   <g id="matplotlib.axis_2">
    <g id="ytick_1">
     <g id="line2d_10">
      <defs>
       <path id="md409c7bddb" d="M 0 0 
L -3.5 0 
" style="stroke: #000000; stroke-width: 0.8"/>
      </defs>
      <g>
       <use xlink:href="#md409c7bddb" x="57.6" y="306.042167" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_10">
      <!-- −1.00 -->
      <g transform="translate(19.954687 309.841386) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-2212" d="M 678 2272 
L 4684 2272 
L 4684 1741 
L 678 1741 
L 678 2272 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-2212"/>
       <use xlink:href="#DejaVuSans-31" x="83.789062"/>
       <use xlink:href="#DejaVuSans-2e" x="147.412109"/>
       <use xlink:href="#DejaVuSans-30" x="179.199219"/>
       <use xlink:href="#DejaVuSans-30" x="242.822266"/>
      </g>
     </g>
    </g>
    <g id="ytick_2">
     <g id="line2d_11">
      <g>
       <use xlink:href="#md409c7bddb" x="57.6" y="275.781733" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_11">
      <!-- −0.75 -->
      <g transform="translate(19.954687 279.580952) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-2212"/>
       <use xlink:href="#DejaVuSans-30" x="83.789062"/>
       <use xlink:href="#DejaVuSans-2e" x="147.412109"/>
       <use xlink:href="#DejaVuSans-37" x="179.199219"/>
       <use xlink:href="#DejaVuSans-35" x="242.822266"/>
      </g>
     </g>
    </g>
    <g id="ytick_3">
     <g id="line2d_12">
      <g>
       <use xlink:href="#md409c7bddb" x="57.6" y="245.5213" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_12">
      <!-- −0.50 -->
      <g transform="translate(19.954687 249.320519) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-2212"/>
       <use xlink:href="#DejaVuSans-30" x="83.789062"/>
       <use xlink:href="#DejaVuSans-2e" x="147.412109"/>
       <use xlink:href="#DejaVuSans-35" x="179.199219"/>
       <use xlink:href="#DejaVuSans-30" x="242.822266"/>
      </g>
     </g>
    </g>
    <g id="ytick_4">
     <g id="line2d_13">
      <g>
       <use xlink:href="#md409c7bddb" x="57.6" y="215.260866" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_13">
      <!-- −0.25 -->
      <g transform="translate(19.954687 219.060085) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-2212"/>
       <use xlink:href="#DejaVuSans-30" x="83.789062"/>
       <use xlink:href="#DejaVuSans-2e" x="147.412109"/>
       <use xlink:href="#DejaVuSans-32" x="179.199219"/>
       <use xlink:href="#DejaVuSans-35" x="242.822266"/>
      </g>
     </g>
    </g>
    <g id="ytick_5">
     <g id="line2d_14">
      <g>
       <use xlink:href="#md409c7bddb" x="57.6" y="185.000433" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_14">
      <!-- 0.00 -->
      <g transform="translate(28.334375 188.799651) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-30"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-30" x="95.410156"/>
       <use xlink:href="#DejaVuSans-30" x="159.033203"/>
      </g>
     </g>
    </g>
    <g id="ytick_6">
     <g id="line2d_15">
      <g>
       <use xlink:href="#md409c7bddb" x="57.6" y="154.739999" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_15">
      <!-- 0.25 -->
      <g transform="translate(28.334375 158.539218) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-30"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-32" x="95.410156"/>
       <use xlink:href="#DejaVuSans-35" x="159.033203"/>
      </g>
     </g>
    </g>
    <g id="ytick_7">
     <g id="line2d_16">
      <g>
       <use xlink:href="#md409c7bddb" x="57.6" y="124.479565" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_16">
      <!-- 0.50 -->
      <g transform="translate(28.334375 128.278784) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-30"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-35" x="95.410156"/>
       <use xlink:href="#DejaVuSans-30" x="159.033203"/>
      </g>
     </g>
    </g>
    <g id="ytick_8">
     <g id="line2d_17">
      <g>
       <use xlink:href="#md409c7bddb" x="57.6" y="94.219132" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_17">
      <!-- 0.75 -->
      <g transform="translate(28.334375 98.01835) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-30"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-37" x="95.410156"/>
       <use xlink:href="#DejaVuSans-35" x="159.033203"/>
      </g>
     </g>
    </g>
    <g id="ytick_9">
     <g id="line2d_18">
      <g>
       <use xlink:href="#md409c7bddb" x="57.6" y="63.958698" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_18">
      <!-- 1.00 -->
      <g transform="translate(28.334375 67.757917) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-31"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-30" x="95.410156"/>
       <use xlink:href="#DejaVuSans-30" x="159.033203"/>
      </g>
     </g>
    </g>
   </g>
   <g id="line2d_19">
    <path d="M 73.832727 63.958698 
L 77.112066 106.258835 
L 80.391405 139.004963 
L 83.670744 165.179073 
L 86.950083 187.284576 
L 90.229421 206.43701 
L 93.50876 223.384461 
L 96.788099 238.250494 
L 100.067438 251.024695 
L 103.346777 260.781827 
L 106.626116 266.269229 
L 109.905455 266.113122 
L 113.184793 259.519525 
L 116.464132 247.100241 
L 119.743471 229.940951 
L 123.02281 210.1211 
L 126.302149 189.790237 
L 129.581488 171.45272 
L 132.860826 156.679112 
L 136.140165 146.292285 
L 139.419504 140.447521 
L 142.698843 138.843441 
L 145.978182 141.028111 
L 149.257521 146.262025 
L 152.53686 153.663829 
L 155.816198 162.715656 
L 159.095537 172.655389 
L 162.374876 182.868847 
L 165.654215 192.839373 
L 168.933554 202.104342 
L 172.212893 210.255951 
L 175.492231 216.882218 
L 178.77157 221.491243 
L 182.050909 223.567456 
L 185.330248 222.628761 
L 188.609587 218.47354 
L 191.888926 210.87436 
L 195.168264 200.765789 
L 198.447603 189.5327 
L 201.726942 178.235792 
L 205.006281 168.164209 
L 208.28562 160.226709 
L 211.564959 154.977406 
L 214.844298 152.587897 
L 218.123636 152.943326 
L 221.402975 155.780657 
L 224.682314 160.590186 
L 227.961653 166.832757 
L 231.240992 174.08224 
L 234.520331 181.87221 
L 237.799669 189.685096 
L 241.079008 197.029662 
L 244.358347 203.544608 
L 247.637686 208.866745 
L 250.917025 212.629742 
L 254.196364 214.477517 
L 257.475702 214.091776 
L 260.755041 210.895998 
L 264.03438 205.287221 
L 267.313719 197.869054 
L 270.593058 189.360838 
L 273.872397 180.605055 
L 277.151736 172.319975 
L 280.431074 165.637673 
L 283.710413 160.922699 
L 286.989752 158.466253 
L 290.269091 158.337628 
L 293.54843 160.302676 
L 296.827769 164.082991 
L 300.107107 169.207673 
L 303.386446 175.190271 
L 306.665785 181.669869 
L 309.945124 188.284 
L 313.224463 194.68598 
L 316.503802 200.328031 
L 319.78314 204.889207 
L 323.062479 208.089583 
L 326.341818 209.654462 
L 329.621157 209.363104 
L 332.900496 207.074674 
L 336.179835 202.473919 
L 339.459174 196.279473 
L 342.738512 189.168699 
L 346.017851 181.789332 
L 349.29719 174.798193 
L 352.576529 168.800008 
L 355.855868 164.521801 
L 359.135207 162.24899 
L 362.414545 161.915947 
L 365.693884 163.395304 
L 368.973223 166.475551 
L 372.252562 170.793073 
L 375.531901 175.944505 
L 378.81124 181.636327 
L 382.090579 187.538529 
L 385.369917 193.163089 
L 388.649256 198.179804 
L 391.928595 202.31367 
L 395.207934 205.302407 
L 398.487273 206.982564 
" clip-path="url(#peaedfb376f)" style="fill: none; stroke: #1f77b4; stroke-width: 1.5; stroke-linecap: square"/>
   </g>
   <g id="line2d_20">
    <path d="M 73.832727 63.958698 
L 77.112066 53.568 
L 80.391405 58.73271 
L 83.670744 70.178082 
L 86.950083 84.260457 
L 90.229421 100.314086 
L 93.50876 118.515269 
L 96.788099 139.72343 
L 100.067438 164.424776 
L 103.346777 193.261762 
L 106.626116 224.89336 
L 109.905455 255.053209 
L 113.184793 278.330741 
L 116.464132 291.809466 
L 119.743471 295.488 
L 123.02281 291.946796 
L 126.302149 283.068828 
L 129.581488 270.288172 
L 132.860826 254.975173 
L 136.140165 237.849187 
L 139.419504 219.544181 
L 142.698843 200.75298 
L 145.978182 182.407639 
L 149.257521 165.747009 
L 152.53686 151.766989 
L 155.816198 141.736483 
L 159.095537 136.120874 
L 162.374876 134.901923 
L 165.654215 137.695432 
L 168.933554 144.051596 
L 172.212893 153.408265 
L 175.492231 165.29451 
L 178.77157 179.224211 
L 182.050909 194.449565 
L 185.330248 209.837205 
L 188.609587 223.941497 
L 191.888926 234.718273 
L 195.168264 240.744217 
L 198.447603 242.152773 
L 201.726942 239.501023 
L 205.006281 232.729593 
L 208.28562 223.081569 
L 211.564959 211.38885 
L 214.844298 198.523595 
L 218.123636 185.388748 
L 221.402975 172.980019 
L 224.682314 162.252811 
L 227.961653 153.849975 
L 231.240992 148.340581 
L 234.520331 146.000695 
L 237.799669 147.320733 
L 241.079008 151.520134 
L 244.358347 158.206396 
L 247.637686 167.010407 
L 250.917025 177.48396 
L 254.196364 189.055772 
L 257.475702 200.984041 
L 260.755041 211.988727 
L 264.03438 220.77224 
L 267.313719 226.559382 
L 270.593058 228.854817 
L 273.872397 227.861267 
L 277.151736 223.735183 
L 280.431074 216.567317 
L 283.710413 207.45156 
L 286.989752 197.079516 
L 290.269091 186.245886 
L 293.54843 175.816928 
L 296.827769 166.673066 
L 300.107107 159.538095 
L 303.386446 154.727642 
L 306.665785 152.460308 
L 309.945124 152.78536 
L 313.224463 155.611312 
L 316.503802 161.126646 
L 319.78314 168.527223 
L 323.062479 177.326349 
L 326.341818 187.013439 
L 329.621157 196.968165 
L 332.900496 206.460265 
L 336.179835 214.182997 
L 339.459174 219.384133 
L 342.738512 221.794706 
L 346.017851 221.332198 
L 349.29719 218.136451 
L 352.576529 212.540347 
L 355.855868 204.894533 
L 359.135207 195.999423 
L 362.414545 186.658461 
L 365.693884 177.587844 
L 368.973223 169.519541 
L 372.252562 163.067685 
L 375.531901 158.51237 
L 378.81124 156.123548 
L 382.090579 156.122719 
L 385.369917 158.826579 
L 388.649256 163.463149 
L 391.928595 169.757362 
L 395.207934 177.373276 
L 398.487273 185.910096 
" clip-path="url(#peaedfb376f)" style="fill: none; stroke: #ff7f0e; stroke-width: 1.5; stroke-linecap: square"/>
   </g>
   <g id="patch_3">
    <path d="M 57.6 307.584 
L 57.6 41.472 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
   <g id="patch_4">
    <path d="M 414.72 307.584 
L 414.72 41.472 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
   <g id="patch_5">
    <path d="M 57.6 307.584 
L 414.72 307.584 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
   <g id="patch_6">
    <path d="M 57.6 41.472 
L 414.72 41.472 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
   <g id="legend_1">
    <g id="patch_7">
     <path d="M 369.92 78.848563 
L 407.72 78.848563 
Q 409.72 78.848563 409.72 76.848563 
L 409.72 48.472 
Q 409.72 46.472 407.72 46.472 
L 369.92 46.472 
Q 367.92 46.472 367.92 48.472 
L 367.92 76.848563 
Q 367.92 78.848563 369.92 78.848563 
z
" style="fill: #ffffff; opacity: 0.8; stroke: #cccccc; stroke-linejoin: miter"/>
    </g>
    <g id="line2d_21">
     <path d="M 371.92 54.570438 
L 381.92 54.570438 
L 391.92 54.570438 
" style="fill: none; stroke: #1f77b4; stroke-width: 1.5; stroke-linecap: square"/>
    </g>
    <g id="text_19">
     <!-- $x$ -->
     <g transform="translate(399.92 58.070438) scale(0.1 -0.1)">
      <defs>
       <path id="Cmmi10-78" d="M 500 184 
Q 613 97 819 97 
Q 1019 97 1172 289 
Q 1325 481 1381 709 
L 1672 1844 
Q 1741 2153 1741 2266 
Q 1741 2425 1652 2544 
Q 1563 2663 1403 2663 
Q 1200 2663 1022 2536 
Q 844 2409 722 2214 
Q 600 2019 550 1819 
Q 538 1778 500 1778 
L 422 1778 
Q 372 1778 372 1838 
L 372 1856 
Q 434 2094 584 2320 
Q 734 2547 951 2687 
Q 1169 2828 1416 2828 
Q 1650 2828 1839 2703 
Q 2028 2578 2106 2363 
Q 2216 2559 2386 2693 
Q 2556 2828 2759 2828 
Q 2897 2828 3040 2779 
Q 3184 2731 3275 2631 
Q 3366 2531 3366 2381 
Q 3366 2219 3261 2101 
Q 3156 1984 2994 1984 
Q 2891 1984 2822 2050 
Q 2753 2116 2753 2216 
Q 2753 2350 2845 2451 
Q 2938 2553 3066 2572 
Q 2950 2663 2747 2663 
Q 2541 2663 2389 2472 
Q 2238 2281 2175 2047 
L 1894 916 
Q 1825 659 1825 494 
Q 1825 331 1917 214 
Q 2009 97 2163 97 
Q 2463 97 2698 361 
Q 2934 625 3009 941 
Q 3022 978 3059 978 
L 3138 978 
Q 3163 978 3178 961 
Q 3194 944 3194 922 
Q 3194 916 3188 903 
Q 3097 522 2806 225 
Q 2516 -72 2150 -72 
Q 1916 -72 1727 54 
Q 1538 181 1459 397 
Q 1359 209 1182 68 
Q 1006 -72 806 -72 
Q 669 -72 523 -23 
Q 378 25 287 125 
Q 197 225 197 378 
Q 197 528 301 651 
Q 406 775 563 775 
Q 669 775 741 711 
Q 813 647 813 544 
Q 813 409 723 309 
Q 634 209 500 184 
z
" transform="scale(0.015625)"/>
      </defs>
      <use xlink:href="#Cmmi10-78" transform="translate(0 0.8125)"/>
     </g>
    </g>
    <g id="line2d_22">
     <path d="M 371.92 69.248563 
L 381.92 69.248563 
L 391.92 69.248563 
" style="fill: none; stroke: #ff7f0e; stroke-width: 1.5; stroke-linecap: square"/>
    </g>
    <g id="text_20">
     <!-- $y$ -->
     <g transform="translate(399.92 72.748563) scale(0.1 -0.1)">
      <defs>
       <path id="Cmmi10-79" d="M 538 -916 
Q 672 -1147 1006 -1147 
Q 1309 -1147 1531 -934 
Q 1753 -722 1889 -420 
Q 2025 -119 2100 197 
Q 1816 -72 1484 -72 
Q 1231 -72 1053 15 
Q 875 103 776 276 
Q 678 450 678 697 
Q 678 906 734 1126 
Q 791 1347 892 1617 
Q 994 1888 1069 2088 
Q 1153 2322 1153 2472 
Q 1153 2663 1013 2663 
Q 759 2663 595 2402 
Q 431 2141 353 1819 
Q 341 1778 300 1778 
L 225 1778 
Q 172 1778 172 1838 
L 172 1856 
Q 275 2238 487 2533 
Q 700 2828 1025 2828 
Q 1253 2828 1411 2678 
Q 1569 2528 1569 2297 
Q 1569 2178 1516 2047 
Q 1488 1969 1388 1706 
Q 1288 1444 1234 1272 
Q 1181 1100 1147 934 
Q 1113 769 1113 603 
Q 1113 391 1203 244 
Q 1294 97 1491 97 
Q 1888 97 2203 581 
L 2688 2553 
Q 2709 2638 2787 2698 
Q 2866 2759 2956 2759 
Q 3034 2759 3092 2709 
Q 3150 2659 3150 2578 
Q 3150 2541 3144 2528 
L 2509 -19 
Q 2425 -347 2200 -647 
Q 1975 -947 1658 -1130 
Q 1341 -1313 997 -1313 
Q 831 -1313 668 -1248 
Q 506 -1184 406 -1056 
Q 306 -928 306 -756 
Q 306 -581 409 -453 
Q 513 -325 684 -325 
Q 788 -325 858 -389 
Q 928 -453 928 -556 
Q 928 -703 818 -812 
Q 709 -922 563 -922 
Q 556 -919 550 -917 
Q 544 -916 538 -916 
z
" transform="scale(0.015625)"/>
      </defs>
      <use xlink:href="#Cmmi10-79" transform="translate(0 0.8125)"/>
     </g>
    </g>
   </g>
  </g>
 </g>
 <defs>
  <clipPath id="peaedfb376f">
   <rect x="57.6" y="41.472" width="357.12" height="266.112"/>
  </clipPath>
 </defs>
</svg>
\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"plot(res3, {$t$: (0,20)});\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 14755585189165933949,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"\"\n\t\t}\n\t],\n\t\"description\": \"Cadabra JSON notebook format\",\n\t\"flags\": {\n\t\t\"hide_input_cells\": false\n\t},\n\t\"version\": 1.0\n}\n"
  },
  {
    "path": "core/algorithms/nevaluate.cc",
    "content": "#include \"nevaluate.hh\"\n#include \"NEvaluator.hh\"\n\nusing namespace cadabra;\n\nnevaluate::nevaluate(const Kernel& k, Ex& tr, NEvaluator& ev)\n\t: Algorithm(k, tr), evaluator(ev)\n\t{\n\t}\n\nbool nevaluate::can_apply(iterator it)\n\t{\n\treturn true;\n\t}\n\nAlgorithm::result_t nevaluate::apply(iterator& it)\n\t{\n\t// Evaluate and store the result in the tree.\n\tstd::cerr << \"About to call evaluator.evaluate()\" << std::endl;\n\tauto result = evaluator.evaluate();\n\tstd::cerr << \"evaluate() returned successfully\" << std::endl;\n\tit->content = std::make_shared<NTensor>( result );\n\tstd::cerr << \"NTensor created\" << std::endl;\n\tnode_one(it);\n\t\n\treturn result_t::l_applied;\n\t}\n"
  },
  {
    "path": "core/algorithms/nevaluate.cnb",
    "content": "{\n\t\"cell_id\": 7056241270934378170,\n\t\"cells\": [\n\t\t{\n\t\t\t\"cell_id\": 6442002833303548429,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 14156260080777624593,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\algorithm{nevaluate}{Numerically evaluate an expression.}\\n\\nGiven a scalar expression of one or more variables, evaluate it for a range of values \\nof those variables. This algorithm accepts a Cadabra expression and one or more numpy arrays\\ncontaining the values of the variables, in the form of a dictionary. A simple example with \\nan expression of one variable:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\algorithm{nevaluate}{Numerically evaluate an expression.}\\n\\nGiven a scalar expression of one or more variables, evaluate it for a range of values \\nof those variables. This algorithm accepts a Cadabra expression and one or more numpy arrays\\ncontaining the values of the variables, in the form of a dictionary. A simple example with \\nan expression of one variable:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 7717361411841115229,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 16317621934812508465,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 3643042606220920068,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\cos(x) \\\\exp( -  1/4 (x)**2)\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\cos{x} \\\\exp\\\\left( - \\\\frac{1}{4}{x}^{2}\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex:= \\\\cos(x) \\\\exp(-x**2/4);\\n\\nimport numpy as np\\n\\nxv = np.linspace(0, 3, 100)\\nz = np.array( nevaluate(ex, {$x$: xv} ) )\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 9285492536561123852,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9668872934801381964,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"verbatim\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}[1.         0.99931146 0.99724785 0.99381515 0.98902334 0.98288631\\n 0.97542182 0.96665142 0.95660038 0.94529757]\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"z[0:10];\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 5511376990109163867,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 3830134294778153283,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"The \\\\algo{nevaluate} function thus takes as its second argument a Python\\ndictionary which maps each variable in the expression to a list of values.\\n\\nFor expressions of multiple variables, the logic is the same: just list all \\nthe variables in the dictionary, as in the example below.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"The \\\\algo{nevaluate} function thus takes as its second argument a Python\\ndictionary which maps each variable in the expression to a list of values.\\n\\nFor expressions of multiple variables, the logic is the same: just list all \\nthe variables in the dictionary, as in the example below.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 2992782121045095320,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 3251060037967502714,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 6149534026651365282,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\cos(x) \\\\sin(y)\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\cos{x} \\\\sin{y}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex:= \\\\cos(x) \\\\sin(y);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 13003303353493457346,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"xv = np.linspace(0,   np.pi, 100)\\nyv = np.linspace(0, np.pi, 100)\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 14177849469379369091,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"z = np.array( nevaluate(ex, {$x$: xv, $y$: yv}) )\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 10078872525967387623,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 26823108033460839,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"verbatim\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}0.3106205340965772\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"z[3,10];\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 10368637782920619472,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"\"\n\t\t}\n\t],\n\t\"description\": \"Cadabra JSON notebook format\",\n\t\"version\": 1.0\n}\n"
  },
  {
    "path": "core/algorithms/nevaluate.hh",
    "content": "\n#pragma once\n\n#include \"Algorithm.hh\"\n#include \"NTensor.hh\"\n#include \"NEvaluator.hh\"\n#include <pybind11/stl.h>\n\nnamespace cadabra {\n\n\tclass nevaluate : public Algorithm {\n\t\tpublic:\n\t\t\tnevaluate(const Kernel&, Ex&, NEvaluator&);\n\n\t\t\tvirtual bool     can_apply(iterator) override;\n\t\t\tvirtual result_t apply(iterator&) override;\n\n\t\tprivate:\n\t\t\tconst std::vector<std::pair<Ex, NTensor>> values;\n\t\t\tNEvaluator& evaluator;\n\t};\n\n}\n"
  },
  {
    "path": "core/algorithms/nval.cc",
    "content": "#include \"nval.hh\"\n#include \"NEvaluator.hh\"\n#include \"NIntegrator.hh\"\n#include \"Cleanup.hh\"\n\nusing namespace cadabra;\n\nnval::nval(const Kernel& k, Ex& tr, NEvaluator& ev)\n\t: Algorithm(k, tr), evaluator(ev)\n\t{\n\t}\n\nbool nval::can_apply(iterator it)\n\t{\n\tif(*it->name==\"\\\\int\") return true;\n\treturn false;\n\t}\n\nAlgorithm::result_t nval::apply(iterator& it)\n\t{\n\tif(*it->name==\"\\\\int\") {\n\t\tsibling_iterator arg=tr.begin(it);\n\t\tEx igrand(arg);\n\t\tEx range(++arg);\n\n\t\t// std::cerr << range << \" is the range\" << std::endl;\n\t\t\n\t\tsibling_iterator r=tr.begin(range.begin());\n\t\tEx ivar(r);\n\t\t// The integration range can be symbolic, so we need to first evaluate that\n\t\tevaluator.set_function(++r);\n\t\tauto nt_from = evaluator.evaluate();\n\t\tevaluator.set_function(++r);\n\t\tauto nt_to   = evaluator.evaluate();\n\t\t// std::cerr << nt_from.shape.size() << \", \" << nt_to.shape.size() << std::endl;\n\t\t// std::cerr << nt_to.shape[0] << std::endl;\n\t\t// std::cerr << nt_to << std::endl;\n\t\tif(nt_from.shape.size()!=1 || nt_from.shape[0]!=1)\n\t\t\tthrow ArgumentException(\"Lower integration limit is not a scalar.\");\n\t\tif(nt_to.shape.size()!=1 || nt_to.shape[0]!=1)\n\t\t\tthrow ArgumentException(\"Upper integration limit is not a scalar.\");\n\n\t\tif(!nt_from.is_real())\n\t\t\tthrow ArgumentException(\"Lower integration limit not real.\");\n\t\tif(!nt_to.is_real())\n\t\t\tthrow ArgumentException(\"Lower integration limit not real.\");\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t// Setup the integrator.\n\t\tNIntegrator ig(igrand.begin());\n\t\tig.evaluator = evaluator;\n\t\tig.evaluator.set_function(igrand.begin());\n\n\t\t// std::cerr << ivar << \" is the ivar \" << from << \" - \" << to << std::endl;\n\t\tig.set_range(ivar, nt_from.at().real(), nt_to.at().real());\n\t\tauto nt = std::make_shared<NTensor>( ig.integrate() );\n\t\tauto mult = *it->multiplier;\n\t\tnode_one(it);\n\t\t\n\t\t(*nt) *= to_double(mult);\n\t\tit->content = nt;\n\n\t\tcleanup_dispatch(kernel, tr, it);\n\t\t}\n\t\n\treturn result_t::l_applied;\n\t}\n"
  },
  {
    "path": "core/algorithms/nval.cnb",
    "content": "{\n\t\"cell_id\": 3727501436159002512,\n\t\"cells\": [\n\t\t{\n\t\t\t\"cell_id\": 4784819847101530838,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 17824719808299684344,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\algorithm{nval}{Numerically evaluate expressions}\\n\\\\available{2.5.12}\\n\\nBy default Cadabra does not evaluate integrals, neither symbolically nor numerically. If you want to replace an integral with its numerical value, use \\\\algo{nval} (for symbolic evaluation, consult \\\\algo{integrate} instead).\\n\\nThis function will in future versions be extended to handle other numerical evaluations (e.g.~sums) as well.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\algorithm{nval}{Numerically evaluate expressions}\\n\\\\available{2.5.12}\\n\\nBy default Cadabra does not evaluate integrals, neither symbolically nor numerically. If you want to replace an integral with its numerical value, use \\\\algo{nval} (for symbolic evaluation, consult \\\\algo{integrate} instead).\\n\\nThis function will in future versions be extended to handle other numerical evaluations (e.g.~sums) as well.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 16885271034272663252,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 15341348911764094688,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"The example below shows the basic usage of \\\\algo{nval}:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"The example below shows the basic usage of \\\\algo{nval}:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 8200378717852774649,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 16316296686794774834,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 16571987704878116452,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\int{\\\\sin(x) (x + 3)**( -  1/2 )}{{x, 0, 1}}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\int_{0\\\\,}^{1} \\\\sin{x} {\\\\left(x\\\\discretionary{}{}{}+3\\\\,\\\\right)}^{ - \\\\frac{1}{2}\\\\,}\\\\,\\\\,{\\\\rm d}x\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex:= \\\\int{ \\\\sin(x)/\\\\sqrt{x+3} }{x, 0, 1};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 3175130663067913368,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 6741586603258412245,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 504619274123144884,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"0.240842\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}0.240842\\\\,\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"nval(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 13713495055462043320,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 7469151042879232966,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"Note how this has change the original expression:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"Note how this has change the original expression:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 10057106055578097114,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 17337315644736004785,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 10521423291990612155,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"0.240842\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}0.240842\\\\,\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 5301092461037266292,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 17975472720885149527,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"You can pass an optional dict of values for parameters in the expression. The values passed here must be numerical (so if you want to use e.g.~$\\\\pi$, use \\\\verb|np.pi| for now). In the following example we have an integral which depends on a parameter~$a$,\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"You can pass an optional dict of values for parameters in the expression. The values passed here must be numerical (so if you want to use e.g.~$\\\\pi$, use \\\\verb|np.pi| for now). In the following example we have an integral which depends on a parameter~$a$,\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 18339386030332043574,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 1119752775661119862,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 2641388767671269607,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\int{\\\\sin(x)}{{x, 0, a}}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\int_{0\\\\,}^{a} \\\\sin{x}\\\\,\\\\,{\\\\rm d}x\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex:= \\\\int{ \\\\sin(x) }{x, 0, a};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 713608360128686673,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 14912885148494620121,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"We can evaluate this for $a=2$ by passing that value into \\\\algo{nval},\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"We can evaluate this for $a=2$ by passing that value into \\\\algo{nval},\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 8813303992966376073,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 8858560042190640155,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 6933617649108786327,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"1.41615\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}1.41615\\\\,\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"nval(ex, {$a$: 2} );\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 15591246746432587564,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 5762584324112817536,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"If you want to evaluate only a certain part of your expression numerically, first zoom in to that part before you call \\\\algo{nval}. In the example below, we initially want to evaluate the integral containing the sine, but not the one containing the cosine.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"If you want to evaluate only a certain part of your expression numerically, first zoom in to that part before you call \\\\algo{nval}. In the example below, we initially want to evaluate the integral containing the sine, but not the one containing the cosine.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 17377712600830363840,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 13904124956940548149,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 13377100612769348594,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\int{\\\\sin(x)}{{x, 0, \\\\pi}} + \\\\int{(\\\\cos(x))**2}{{x, 0, \\\\pi}}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\int_{0\\\\,}^{\\\\pi} \\\\sin{x}\\\\,\\\\,{\\\\rm d}x\\\\discretionary{}{}{}+\\\\int_{0\\\\,}^{\\\\pi} {\\\\left(\\\\cos{x}\\\\right)}^{2\\\\,}\\\\,\\\\,{\\\\rm d}x\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex:= \\\\int{\\\\sin(x)}{x,0,\\\\pi} + \\\\int{\\\\cos(x)**2}{x,0,\\\\pi};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 9069530760613241717,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 10398718852102296679,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 17464744525266734230,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\int{\\\\sin(x)}{{x, 0, \\\\pi}} +  ... \"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\int_{0\\\\,}^{\\\\pi} \\\\sin{x}\\\\,\\\\,{\\\\rm d}x\\\\discretionary{}{}{}+ \\\\ldots \\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"zoom(_, $\\\\int{\\\\sin{A??}}{B??}$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 1671145987561998956,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 6746369443998143815,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 16743511995547134131,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"2 +  ... \"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}2\\\\,\\\\discretionary{}{}{}+ \\\\ldots \\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"nval(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 5095242746938654645,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 5311055194625327416,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 1630048626783410932,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"2 + \\\\int{(\\\\cos(x))**2}{{x, 0, \\\\pi}}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}2\\\\,\\\\discretionary{}{}{}+\\\\int_{0\\\\,}^{\\\\pi} {\\\\left(\\\\cos{x}\\\\right)}^{2\\\\,}\\\\,\\\\,{\\\\rm d}x\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"unzoom(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 6655203699757759082,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 10790235354729473770,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"If you now still want to evaluate the cosine integral too, you can call \\\\algo{nval} on the full, unzoomed expression,\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"If you now still want to evaluate the cosine integral too, you can call \\\\algo{nval} on the full, unzoomed expression,\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 12818430237452113697,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 11816992663016848683,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 3142977150515540002,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"3.5708\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}3.5708\\\\,\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"nval(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 7062595186920898441,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"source\": \"While the integration variable has to be real, \\\\algo{nval} function can deal with complex-valued integrands\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 7160907691233309035,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 11929487896157463962,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property ImaginaryI attached to~}i.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 5381501152817545418,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 7245863370580040533,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"A \\\\int{\\\\exp(i x)}{{x, 0, \\\\pi}}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}A \\\\int_{0\\\\,}^{\\\\pi} \\\\exp\\\\left(i x\\\\right)\\\\,\\\\,{\\\\rm d}x\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 2339098002887347228,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 2328464668007335859,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"A [1.1847e-16 + 2i]\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}A (1.1847 \\\\times 10^{-16} + 2i)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"i::ImaginaryI;\\nex:= A \\\\int{ \\\\exp{i x} }{x, 0, \\\\pi};\\nnval(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 2494128600755150446,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 14128870615555357155,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"Under the hood, the numerical integration method used is Gauss-Kronrod, which does not (yet) deal with infinite or semi-infinite integration ranges. \"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"Under the hood, the numerical integration method used is Gauss-Kronrod, which does not (yet) deal with infinite or semi-infinite integration ranges. \"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 2642172041483479399,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"\"\n\t\t}\n\t],\n\t\"description\": \"Cadabra JSON notebook format\",\n\t\"flags\": {\n\t\t\"hide_input_cells\": false\n\t},\n\t\"version\": 1.0\n}\n"
  },
  {
    "path": "core/algorithms/nval.hh",
    "content": "\n#pragma once\n\n#include \"Algorithm.hh\"\n#include \"NTensor.hh\"\n#include \"NEvaluator.hh\"\n#include <pybind11/stl.h>\n\nnamespace cadabra {\n\n\tclass nval : public Algorithm {\n\t\tpublic:\n\t\t\tnval(const Kernel&, Ex&, NEvaluator&);\n\n\t\t\tvirtual bool     can_apply(iterator) override;\n\t\t\tvirtual result_t apply(iterator&) override;\n\n\t\tprivate:\n\t\t\tconst std::vector<std::pair<Ex, NTensor>> values;\n\t\t\tNEvaluator& evaluator;\n\t};\n\n}\n"
  },
  {
    "path": "core/algorithms/order.cc",
    "content": "\n#include \"algorithms/order.hh\"\n#include \"Combinatorics.hh\"\n\nusing namespace cadabra;\n\norder::order(const Kernel& k, Ex& tr, Ex& objs, bool ac)\n\t: Algorithm(k, tr), objects(objs), anticomm(ac)\n\t{\n\t}\n\nbool order::can_apply(iterator st)\n\t{\n\tif(*(st->name)!=\"\\\\prod\")\n\t\treturn(is_single_term(st));\n\treturn true;\n\t}\n\nAlgorithm::result_t order::apply(iterator& st)\n\t{\n\tresult_t res=result_t::l_no_action;\n\n\tprod_wrap_single_term(st);\n\n\tstd::vector<unsigned int> locs;\n\tif(locate_object_set(objects, tr.begin(st), tr.end(st), locs)) {\n\n\t\tif(!(std::is_sorted(locs.begin(), locs.end()))) {\n\t\t\tres=result_t::l_applied;\n\n\t\t\tstd::vector<unsigned int> ordered(locs);\n\t\t\tstd::sort(ordered.begin(), ordered.end());\n\t\t\tif(anticomm) {\n\t\t\t\tint osign=combin::ordersign(ordered.begin(), ordered.end(), locs.begin(), locs.end());\n\t\t\t\tif(osign!=1) {\n\t\t\t\t\tmultiply(st->multiplier, osign);\n\t\t\t\t\t}\n\t\t\t\t}\n\n\t\t\t// \\comma{A}{B}}\n\t\t\tsibling_iterator orig_st=objects.begin(objects.begin());\n\n\t\t\tfor(unsigned int i=0; i<ordered.size(); ++i) {\n\t\t\t\titerator dest_st=tr.begin(st);\n\t\t\t\tfor(unsigned int k=0; k<ordered[i]; ++k)\n\t\t\t\t\t++dest_st;\n\t\t\t\tif((*orig_st->name).size()==0)\n\t\t\t\t\ttr.replace(dest_st, tr.begin(orig_st));\n\t\t\t\telse\n\t\t\t\t\ttr.replace(dest_st, orig_st);\n\n\t\t\t\t++orig_st;\n\t\t\t\t}\n\n\t\t\tres=result_t::l_applied;\n\t\t\t}\n\t\t}\n\tprod_unwrap_single_term(st);\n\n\treturn res;\n\t}\n\n"
  },
  {
    "path": "core/algorithms/order.hh",
    "content": "\n#pragma once\n\n#include \"Algorithm.hh\"\n\nnamespace cadabra {\n\n\tclass order : virtual public Algorithm {\n\t\tpublic:\n\t\t\torder(const Kernel&, Ex&, Ex& objs, bool ac);\n\n\t\t\tvirtual bool     can_apply(iterator) override;\n\t\t\tvirtual result_t apply(iterator&) override;\n\n\t\tprotected:\n\t\t\tEx objects;\n\t\t\tbool    anticomm;\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/algorithms/order.tex",
    "content": "\\cdbalgorithm{acanonicalorder}{}\n\nOrders the indicated objects in the expression in canonical order,\ntaking care of permutation signs. On a simple product of objects it\nworks as a partial product sort for anti-commuting objects,\n\\begin{screen}{1,2}\nC B E D F A ;\n@acanonicalorder!(%)(A, B, E, F);\n(-1) C A B D E F;\n\\end{screen}\nIt can, however, also be used to sort indices. Thereby, it facilitates\nimposing index symmetry on a tensor with open indices, as the\nfollowing example illustrates.\n\\begin{screen}{1,2}\nA^{m n p} B^{q r} + A^{q m} B^{n p r};\n@acanonicalorder!(%)( ^{m}, ^{n}, ^{p}, ^{r}, ^{q} );\n- A^{m n p} B^{r q} + A^{m n} B^{p r q};\n\\end{screen}\nA similar type of canonical ordering but without the permutation signs\nis provided for by \\subscommand{canonicalorder}.\n~\n\n\\cdbseealgo{canonicalorder}\n\\cdbseealgo{prodsort}\n\\cdbseealgo{canonicalise}\n"
  },
  {
    "path": "core/algorithms/permute.tex",
    "content": "\\cdbalgorithm{permute}{}\n\nGeneric algorithm to generate permutations and combinations of\nelements in a list. It takes several arguments depending on the type\nof permutations which one wishes to generate.\n\nThe simplest permutations are generated by stating whether items can\nbe taken from the original set more than once (multiple-pick or\nsingle-pick), and stating the length of the permutation sets to be\ngenerated. An example with single-pick is\n\\begin{screen}{1,2}\n{a,b,c,d};\n@permute!(%){false}{3};\n{{a, b, c}, {a, b, d}, {a, c, d}, {b, c, d}};\n\\end{screen}\nwhile an example with multiple-pick is\n\\begin{screen}{1,2}\n{a,b,c,d};\n@permute!(%){true}{2};\n{{a, a}, {a, b}, {a, c}, {a, d}, {b, b}, {b, c},\n                         {b, d}, {c, c}, {c, d}, {d, d}};\n\\end{screen}\nThe length parameter is in fact fixing the length of the subsets in\nthe result for which the order of the elements does not\nmatter. Therefore, \n\\begin{screen}{1,2}\n{a,b,c};\n@permute!(%){false}{1,1};\n{{a, b}, {a, c}, {b, a}, {b, c}, {c, a}, {c, b}};\n\\end{screen}\nFinally, it is also possible to generate all permutations with a given\nmaximal length,\n\\begin{screen}{1,2}\n{a,b,c};\n@permute!(%){false}{<3};\n{{a}, {b}, {c}, {a, b}, {a, c}, {b, c}};\n\\end{screen}\n\nMore complicated permutations can be generated by assigning weights to\nthe objects in the original list. Here is an example in which~$a,b,c$\nhave weights~$2,1,0$ respectively, and lists of length~3 are generated\nfor which the total weight is~4.\n\\begin{screen}{1,2}\n{a,b,c};\n@permute!(%){true}{3}{2,1,0}{4};\n{{a, a, c}, {a, b, b}};\n\\end{screen}\nObjects can be assigned more than one type of weight by simply\nrepeating the two arguments associated to weights. For instance, if we\nin addition introduce another weight type, under which~$a,b,c$ have\nweight~$0,1,0$ respectively, and also impose that this weight should\nadd up to~$2$, we get\n\\begin{screen}{1,2}\n{a,b,c};\n@permute!(%){true}{3}{2,1,0}{4}{0,1,0}{2};\n{{a, b, b}};\n\\end{screen}\nThis functionality is useful when constructing field polynomials\nrestricted to certain length dimension or Grassmann number.\n\n\\cdbseealgo{range}\n"
  },
  {
    "path": "core/algorithms/product_rule.cc",
    "content": "\n#include \"Compare.hh\"\n#include \"Cleanup.hh\"\n#include \"Exceptions.hh\"\n#include \"algorithms/product_rule.hh\"\n#include \"properties/Derivative.hh\"\n#include \"properties/DerivativeOp.hh\"\n#include \"properties/DifferentialForm.hh\"\n\nusing namespace cadabra;\n\n// #define DEBUG 1\n\nproduct_rule::product_rule(const Kernel& k, Ex& tr)\n\t: Algorithm(k, tr), number_of_indices(0)\n\t{\n\t}\n\n//\n//  A(b*c*d)     -> A(b)*c*d + b*A(c)*d + b*c*A(d)\n//  A(b*c)(e*f) 1-> A(b)(e*f)*c + b*A(c)(e*f)\n//  A(b*c)(e*f) 2-> A(b*c)(e)*f + e*A(b*c)(f)\n\nbool product_rule::can_apply(iterator it)\n\t{\n\tconst Derivative *der=kernel.properties.get<Derivative>(it);\n\tif(der || *it->name==\"\\\\cdbDerivative\") {\n\t\tprodnode=tr.end();\n\t\tnumber_of_indices=0;\n\t\tif(tr.number_of_children(it)>0) {\n\t\t\tsibling_iterator ch=tr.begin(it);\n\t\t\twhile(ch!=tr.end(it)) {\n\t\t\t\tif(prodnode==tr.end() && ( *ch->name==\"\\\\prod\" || *ch->name==\"\\\\pow\" || *ch->name==\"\\\\wedge\" ) )\n\t\t\t\t\tprodnode=ch; // prodnode contains the first product node, there may be more\n\t\t\t\telse {\n\t\t\t\t\tif(ch->is_index()) ++number_of_indices;\n\t\t\t\t\t}\n\t\t\t\t++ch;\n\t\t\t\t}\n\t\t\tif(prodnode!=tr.end()) return true;\n\t\t\t}\n\t\t}\n\telse {\n\t\tconst DerivativeOp *derop=kernel.properties.get<DerivativeOp>(it);\n\t\tif(derop) return true;\n\t\t}\n\n\treturn false;\n\t}\n\nAlgorithm::result_t product_rule::apply(iterator& it)\n\t{\n#ifdef DEBUG\n\tstd::cerr << \"product_rule::apply: at \" << it << std::endl;\n#endif\n\tEx rep; // the subtree storing the result\n\titerator sm; // the sum node inside 'rep'\n\n\t// If we are distributing a multiple derivative, take out all\n\t// indices except the last one, and wrap things in a new derivative\n\t// node which has these indices as child nodes.\n\tbool indices_at_front=true;\n\tif(number_of_indices>1) {\n\t\trep.set_head(str_node(it->name));\n\t\tsm=rep.append_child(rep.begin(),str_node(\"\\\\sum\"));\n\t\tsibling_iterator sib=tr.begin(it);\n\t\tif(sib->is_index()==false)\n\t\t\tindices_at_front=false;\n\t\tint todo=number_of_indices-1;\n\t\twhile(todo>0) { // Move all indices except the last one away.\n\t\t\tif(sib->is_index()) {\n\t\t\t\t--todo;\n\t\t\t\tsibling_iterator nxt=sib;\n\t\t\t\t++nxt;\n\t\t\t\tif(indices_at_front) rep.move_before(sm, (iterator)sib);\n\t\t\t\telse                 rep.move_after(sm, (iterator)sib);\n\t\t\t\tsib=nxt;\n\t\t\t\t}\n\t\t\telse ++sib;\n\t\t\tif(sib==tr.end(it))\n\t\t\t\tthrow ConsistencyException(\"product_rule: Error isolating derivative indices.\");\n\t\t\t}\n\t\t}\n\telse {\n\t\tsm=rep.set_head(str_node(\"\\\\sum\"));\n\t\tif(tr.begin(it)->is_index()==false)\n\t\t\tindices_at_front=false;\n\t\t}\n\n\n\t// Two cases to handle now: D(A**n) -> n D(A**(n-1)) and\n\t//                          D(A*B)  -> D(A)*B + A*D(B)\n\t// both suitably generalised to anti-commuting derivatives.\n\n\titerator rename_dummies_at = tr.end();\n\n\tif(*prodnode->name==\"\\\\pow\") {\n\t\t// FIXME: the code below assumes that the derivative acts on the first\n\t\t// child of \\pow only, so \\partial_{x}{x^n} is done correctly, but\n\t\t// \\partial_{x}{e^x} becomes x e^{x-1} \\partial_{x}{e} which is wrong.\n\n\t\tsibling_iterator ar=tr.begin(prodnode);\n\t\tsibling_iterator pw=ar;\n\t\t++pw;\n\t\tsm->name=name_set.insert(\"\\\\prod\").first;\n\t\tif(pw->is_integer())\n\t\t\tmultiply(sm->multiplier, *pw->multiplier);\n\t\telse rep.append_child(sm, (iterator)pw);\n\n\t\t// \\partial(A**n)\n\t\titerator pref=rep.append_child(sm, iterator(prodnode));  // add A**n\n\t\titerator theD=rep.append_child(sm, it);                  // add \\partial_{m}(A**n)\n\t\trename_dummies_at=theD;\n\t\tsibling_iterator repch=tr.begin(theD);                   // convert to \\partial_{m}(A)\n\t\twhile(*repch->name!=\"\\\\pow\")\n\t\t\t++repch;\n\t\tsibling_iterator pw2=tr.begin(repch);\n\t\trep.move_before(repch, pw2);\n\t\t//\t\t txtout << \"after rep.move_before\" << std::endl;\n\t\t//\t\t tr.print_recursive_treeform(txtout, rep.begin());\n\t\trep.erase(repch);\n\n\t\t//\t\t txtout << \"after rep.erase\" << std::endl;\n\t\t//\t\t tr.print_recursive_treeform(txtout, rep.begin());\n\n\t\tif(pw->is_integer()) {                                   // A**n -> A**(n-1)\n\t\t\tif(*pw->multiplier==2) {\n\t\t\t\titerator nn=rep.move_after(pref, iterator(tr.begin(pref)));\n\t\t\t\tmultiply(nn->multiplier, *pref->multiplier);\n\t\t\t\trep.erase(pref);\n\t\t\t\t}\n\t\t\telse {\n\t\t\t\tpw2=tr.begin(pref);\n\t\t\t\t++pw2;\n\t\t\t\tadd(pw2->multiplier, -1);\n\t\t\t\t}\n\t\t\t//\t\t\t  txtout << \"after all done \" << std::endl;\n\t\t\t//\t\t\t  tr.print_recursive_treeform(txtout, rep.begin());\n\t\t\t}\n\t\telse {\n\t\t\tpw2=tr.begin(pref);\n\t\t\t++pw2;\n\t\t\tif(*pw2->name==\"\\\\sum\") {\n\t\t\t\titerator tmp=rep.append_child(pw2, str_node(\"1\"));\n\t\t\t\ttmp->fl.bracket=rep.begin(pw2)->fl.bracket;\n\t\t\t\tmultiply(tmp->multiplier, -1);\n\t\t\t\t}\n\t\t\telse {\n\t\t\t\titerator sumn=rep.wrap(pw2, str_node(\"\\\\sum\"));\n\t\t\t\titerator tmp=rep.append_child(sumn, str_node(\"1\"));\n\t\t\t\tmultiply(tmp->multiplier, -1);\n\t\t\t\t}\n\t\t\t}\n\n\t\titerator top=rep.begin();\n\t\tcleanup_dispatch(kernel, tr, top);\n\t\t}\n\telse {\n\t\t// replace the '\\diff' with a '\\sum' of diffs.\n\t\tunsigned int num=0;\n\t\tsibling_iterator chl=tr.begin(prodnode); // pointer to current factor in the product\n\t\tint sign=1; // keep track of a sign for anti-commuting derivatives\n\n\t\t// In order to figure out whether a derivative is anti-commuting with\n\t\t// a given object in the product on which it acts, we need to consider\n\t\t// a number of cases:\n\t\t//\n\t\t//    D_{a}{\\theta^{b}}                    with \\theta^{a} Coordinate & SelfAntiCommuting\n\t\t//    D_{\\theta^{a}}{\\theta^{b}}           with \\theta^{a} Coordinate and a,b,c AntiCommuting\n\t\t//    D_{a}{D_{b}{G}}                      handled by making indices AntiCommuting.\n\t\t//    D_{a}{D_{\\dot{b}}{G}}                handled by making indices AntiCommuting.\n\t\t//    D_{a}{T^{a b}}                       handled by making indices AntiCommuting.\n\t\t//    D_{a}{\\theta}                        with \\theta having an ImplicitIndex of type 'a'\n\t\t//    D{ A B }                             not yet handled (problem is to give scalar anti-commutativity\n\t\t//                                            property to D, A, B).\n\n\t\tEx_comparator comp(kernel.properties);\n\n\t\twhile(chl!=tr.end(prodnode)) { // iterate over all factors in the product\n\t\t\t// Add the whole product node to the replacement sum.\n\t\t\titerator dummy=rep.append_child(sm);\n\t\t\tdummy=rep.replace(dummy, prodnode);\n//\t\t\tif(tr.is_head(it))\n\t\t\t\tdummy->fl.bracket=str_node::b_none;\n//\t\t\telse dummy->fl.bracket=str_node::b_round;\n\n\t\t\tsibling_iterator wrap=rep.begin(dummy);\n\t\t\t// Go to the 'num'th factor in the product.\n\t\t\twrap+=num;\n\t\t\t// Replace this num'th factor with the original expression.\n\t\t\t// We will then remove all that has to be removed.\n\t\t\titerator theD=rep.insert_subtree(wrap, it);  // iterator to the Derivative node\n\t\t\ttheD->fl.bracket=wrap->fl.bracket;\n\t\t\t// Go to the 'prod' child of the \\diff.\n\t\t\tsibling_iterator repch=tr.begin(theD);\n\t\t\twhile(*repch->name!=\"\\\\prod\" && *repch->name!=\"\\\\wedge\") {\n\t\t\t\t++repch;\n\t\t\t\tif(repch==tr.end(theD))\n\t\t\t\t\tthrow InternalError(\"Inconsistent intermediate expression in product_rule()\");\n\t\t\t\t}\n\t\t\t// Replace this 'prod' child with 'just' the factor to be replaced, i.e.\n\t\t\t// remove all the other factors which have been taken out of the derivative.\n\t\t\twrap->fl.bracket=prodnode->fl.bracket;\n\t\t\trepch=tr.replace(repch,wrap);\n\t\t\t// Erase the factor which we replaced with the \\diff.\n\t\t\ttr.erase(wrap);\n\n\t\t\t// Handle signs for anti-commuting derivatives.\n\t\t\tmultiply(dummy->multiplier, sign);\n\t\t\t// Update the sign. First create an Ex containing the derivative _without_\n\t\t\t// the object on which it acts.\n\t\t\tEx emptyD(theD);\n\t\t\tsibling_iterator theDargs=emptyD.begin(emptyD.begin());\n\t\t\twhile(theDargs!=emptyD.end(emptyD.begin())) {\n\t\t\t\tif(theDargs->is_index()==false)\n\t\t\t\t\ttheDargs=tr.erase(theDargs);\n\t\t\t\telse ++theDargs;\n\t\t\t\t}\n\n\t\t\tauto stc=comp.equal_subtree(emptyD.begin(), repch);\n\t\t\t//\t\t\t  txtout << \"trying to move \" << *emptyD.begin()->name << \" through \" << *repch->name\n\t\t\t//\t\t\t\t\t\t<< \" \" << stc << std::endl;\n\t\t\tint ret=comp.can_swap(emptyD.begin(), repch, stc);\n\t\t\t//\t\t\t  txtout << ret << std::endl;\n\t\t\tif(ret==0) {\n\t\t\t\t// This happens when a derivative acts on a product of ImplicitIndices\n\t\t\t\t// objects. That's not going to be an anti-commuting derivative, so set\n\t\t\t\t// the sign to 1.\n\t\t\t\tret=1;\n\t\t\t\t// return result_t::l_no_action;\n\t\t\t\t}\n\t\t\tsign*=ret;\n\n\t\t\t// Because 'd' already reports itself to have differential form degree one,\n\t\t\t// and can_swap takes that into account when computing the swap behaviour of\n\t\t\t// 'd' and another form, we do not need to do anything separately for the\n\t\t\t// exterior derivative.\n\n\t\t\t// Avoid \\partial_{a}{\\partial_{b} ...} constructions in\n\t\t\t// case this child is a \\partial-like too.\n\t\t\t//\t\t\t  iterator repchi=repch;\n\n\t\t\t// The 'dummy' iterator points to the \\prod node.\n\t\t\tcleanup_dispatch(kernel, tr, theD);\n\t\t\tcleanup_dispatch(kernel, tr, dummy);\n\n\t\t\t++chl;\n\t\t\t++num;\n\t\t\t}\n\t\t}\n\t//\tit=tr.replace(it,rep.begin());\n\tit=tr.move_ontop(it, rep.begin());\n\n#ifdef DEBUG\n\tstd::cerr << \"product_rule: \" << it << std::endl;\n#endif\n\t\n\tif(rename_dummies_at!=tr.end()) {\n\t\t//\t\tstd::cerr << \"...\\n\";\n\t\t//\t\tstd::cerr << Ex(rename_dummies_at) << std::endl;\n\t\t//\t\tstd::cerr << \"---\\n\";\n\t\t//\t\tstd::cerr << Ex(it) << std::endl;\n\t\t//\t\tstd::cerr << \"===\\n\";\n\t\trename_replacement_dummies(rename_dummies_at, false);\n\t\t}\n\t//\tcleanup_expression(tr, it);\n\t//\tcleanup_nests_below(tr, it);\n\treturn result_t::l_applied;\n\t}\n"
  },
  {
    "path": "core/algorithms/product_rule.cnb",
    "content": "{\n\t\"cells\" : \n\t[\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\algorithm{product_rule}{Apply the Leibnitz rule to a derivative of a product}\\n\\nApply the product rule or ``Leibnitz\\n  identity'' to an object which has the \\\\prop{Derivative} property, i.e.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\algorithm{product_rule}{Apply the Leibnitz rule to a derivative of a product}\\n\\nApply the product rule or ``Leibnitz\\n  identity'' to an object which has the \\\\prop{Derivative} property, i.e.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Derivative to~}D{\\\\#}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}D\\\\left(f g\\\\right)\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}D{f} g+f D{g}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"D{#}::Derivative;\\nex:=D(f g);\\nproduct_rule(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"This of course also works for derivatives which explicitly mention\\nindices or components, as well as for multiple derivatives, as in the example below.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"This of course also works for derivatives which explicitly mention\\nindices or components, as well as for multiple derivatives, as in the example below.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}D_{m n}\\\\left(f g\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"D{#}::Derivative.\\nex:=D_{m n}(f g);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}D_{m}\\\\left(D_{n}{f} g+f D_{n}{g}\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"product_rule(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}D_{m}\\\\left(D_{n}{f} g\\\\right)+D_{m}\\\\left(f D_{n}{g}\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"distribute(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}D_{m}{D_{n}{f}} g+D_{n}{f} D_{m}{g}+D_{m}{f} D_{n}{g}+f D_{m}{D_{n}{g}}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"product_rule(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1\n}\n"
  },
  {
    "path": "core/algorithms/product_rule.hh",
    "content": "#pragma once\n\n#include \"Algorithm.hh\"\n\nnamespace cadabra {\n\n\tclass product_rule : public Algorithm {\n\t\tpublic:\n\t\t\tproduct_rule(const Kernel&, Ex&);\n\n\t\t\tvirtual bool     can_apply(iterator) override;\n\t\t\tvirtual result_t apply(iterator&) override;\n\n\t\t\tsibling_iterator prodnode;\n\t\t\tunsigned int     number_of_indices;\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/algorithms/product_shorthand.tex",
    "content": "\\cdbalgorithm{product\\_shorthand}{}\n\nRewrites the product of two fully symmetric or anti-symmetric tensors\nin a compact form by removing the contracting dummy indices.\n\\begin{screen}{1,2,3}\nF_{m n p q}::Symmetric.\nG_{m n p q}::Symmetric.\n@product_shorthand![ F_{a b c d} G_{a b d f} ]{F}{G};\nF_{c} G_{f};\n\\end{screen}\nThe two arguments denote the tensors to which the algorithm should\napply. Expanding the product again in terms of the full tensors can be\ndone with the algorithm \\subscommand{expand\\_product\\_shorthand}.\n\n\\cdbseealgo{expand_product_shorthand}\n\\cdbseeprop{Symmetric}\n\\cdbseeprop{AntiSymmetric}\n\n"
  },
  {
    "path": "core/algorithms/projweyl.tex",
    "content": "\\cdbalgorithm{projweyl}{}\n\nProjects an expression onto Weyl spinors of positive chirality (this\nalgorithm only works in even dimensions). On such a subspace, we have\n\\begin{equation}\n\\label{e:g10toeps}\n\\Gamma^{r_1 \\cdots r_{d}}\\Big|_{\\text{Weyl}} = \\frac{1}{\\sqrt{-g}}\\epsilon^{r_1\\cdots\nr_{d}}\n\\, ,\\quad \\epsilon^{0\\cdots (d-1)} = +1\\, ,\n\\end{equation}\nand therefore all gamma matrices with more than $d/2$ indices can be\nconverted to their ``dual'' gamma matrices. By repeated contraction\nof~\\eqref{e:g10toeps} with gamma matrices on the left one deduces that\n\\begin{equation}\n\\Gamma^{r_1\\cdots r_n}\\Big|_{\\text{Weyl}} = \\frac{1}{\\sqrt{-g}} \\frac{(-1)^{\\frac{1}{2}n(n+1)+1}}{(d-n)!}\n\\Gamma_{s_1\\cdots s_{d-n}}\\Big|_{\\text{Weyl}} \\epsilon^{s_1\\cdots s_{d-n} r_1\\cdots r_n}\\, .\n\\end{equation}\nHere is an example:\n\\begin{screen}{1,2}\n{m,n,p,q,r,s,t}::Indices.\n{m,n,p,q,r,s,t}::Integer(0..5).\n\\Gamma{#}::GammaMatrix.\n\\Gamma_{m n p q};\n@projweyl!(%);\n\\end{screen}\n\n\\cdbseeprop{GammaMatrix}\n\\cdbseealgo{join}\n"
  },
  {
    "path": "core/algorithms/properties.tex",
    "content": "\\cdbalgorithm{properties}{}\n\nDisplay a list of all available properties.\n\\begin{screen}{1}\n@properties;\n::Accent\n::AntiCommuting\n::AntiSelfDual\n...\n\\end{screen}\nThis list is also available in the graphical notebook interface from\nthe Help menu.\n\n\\cdbseealgo{algorithms}\n\\cdbseealgo{timing}\n"
  },
  {
    "path": "core/algorithms/proplist.tex",
    "content": "\\cdbalgorithm{properties}{}\n\nShow all properties and the patterns to which they are\nassociated. Note that this includes all default properties for objects\nlike {\\tt $\\backslash prod$}.\n\\begin{screen}{1,2}\n{A,B}::AntiCommuting.\nA_{m n}::Symmetric.\n@proplist;\n\\sum{#}::CommutingAsSum\n\\prod{#}::IndexInherit\n\\prod{#}::Distributable\n...\n{A, B}::AntiCommuting\nA_{m n}::Symmetric\n\\end{screen}\nA list of all available properties (not necessarily attached to any\nobject) is instead obtained using \\subscommand{properties}.\n\n\\cdbseealgo{properties}\n\n\n"
  },
  {
    "path": "core/algorithms/raise_free_indices.cnb",
    "content": "{\n\t\"cells\" : \n\t[\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\algorithm{raise_free_indices}{Make all free indices in an expression superscripts.}\\n\\nFree indicies (indices declared with the \\\\verb|Indices(position=free)| property) can appear as subscripts or superscripts,\\nbut sometimes it is useful to move them all into the same position. \"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\algorithm{raise_free_indices}{Make all free indices in an expression superscripts.}\\n\\nFree indicies (indices declared with the \\\\verb|Indices(position=free)| property) can appear as subscripts or superscripts,\\nbut sometimes it is useful to move them all into the same position. \"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Indices(position=free) to~}\\\\left[a,~\\\\discretionary{}{}{} b,~\\\\discretionary{}{}{} c\\\\right].\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Indices(position=fixed) to~}\\\\left[m,~\\\\discretionary{}{}{} n,~\\\\discretionary{}{}{} p\\\\right].\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"A_{a b m} B^{a b m}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}A_{a b m} B^{a b m}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"{a,b,c}::Indices(name=A, position=free);\\n{m,n,p}::Indices(name=B, position=fixed);\\nex:=A_{a b m} B^{a b m};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"A^{a b}_{m} B^{a b m}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}A^{a b}\\\\,_{m} B^{a b m}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"raise_free_indices(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"The opposite of this is \\\\algo{lower_free_indices}, which moves all free indices to be subscripts.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"The opposite of this is \\\\algo{lower_free_indices}, which moves all free indices to be subscripts.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1\n}\n"
  },
  {
    "path": "core/algorithms/range.tex",
    "content": "\\cdbalgorithm{range}{}\n\nReplaces a two-element list of integers\n  with the elements in the range,\n\\begin{screen}{1,2,4}\n{-3,2};\n@range(%);\n\\{ -3,-2,-1,0,1,2 \\}\n@range[{1,3}];\n\\{ 1,2,3 \\}\n\\end{screen}\nWhen the list has three elements, the algorithm generates a list\nconsisting of a number of copies of the third element of the given\nlist,\n\\begin{screen}{1}\n@range[{1,3,c}];\n{c,c,c};\n\\end{screen}\nWhen the list contains four elements, the first one is used as a\ncounter, and can appear in the fourth element to generate different\nlist elements,\n\\begin{screen}{1}\n@range[{i, 1, 5, c_{i} }];\n{ c_1, c_2, c_3, c_4, c_5 };\n\\end{screen}\n~\n\n\\cdbseealgo{inner}\n\\cdbseealgo{length}\n\\cdbseealgo{coefficients}\n"
  },
  {
    "path": "core/algorithms/reduce.tex",
    "content": "\\cdbalgorithm{reduce}{}\n\n{\\bf NOT YET FUNCTIONAL}\n\\bigskip\n\nReduce a sum of tensor monomials of the same type, taking into account\nmono-term as well as multi-term symmetries. This does not aim for a\ncanonical form, but rather for a form in which no monomials occur\nwhich can be expressed (using mono- and multi-term symmetries) as a\nlinear combination of other monomials appearing in the sum. An example\nmakes this more clear:\n\\begin{screen}{0,1}\n{m,n,p,q}::Indices(vector).\n{m,n,p,q}::Integer(0..10).\nR_{m n p q}::RiemannTensor.\n\nR_{m n q p} R_{m n p q} + R_{m p n q} R_{m n p q};\n@reduce!(%);\n\\end{screen}\n~\n"
  },
  {
    "path": "core/algorithms/reduce_delta.cc",
    "content": "\n#include \"Exceptions.hh\"\n#include \"algorithms/reduce_delta.hh\"\n#include \"properties/Integer.hh\"\n#include \"properties/KroneckerDelta.hh\"\n\nusing namespace cadabra;\n\nreduce_delta::reduce_delta(const Kernel& k, Ex& e)\n\t: Algorithm(k, e)\n\t{\n\t}\n\nbool reduce_delta::can_apply(iterator st)\n\t{\n\tconst KroneckerDelta *kr=kernel.properties.get<KroneckerDelta>(st);\n\tif(kr) {\n\t\tif(tr.number_of_children(st)>2)\n\t\t\treturn true;\n\t\t}\n\treturn false;\n\t}\n\nAlgorithm::result_t reduce_delta::apply(iterator& st)\n\t{\n\tresult_t res=result_t::l_no_action;\n\n\tint num=0;\n\twhile(one_step_(st)) {\n\t\t++num;\n\t\tres=result_t::l_applied;\n\t\tif(tr.number_of_children(st)==0) {\n\t\t\tst->name=name_set.insert(\"1\").first;\n\t\t\tbreak;\n\t\t\t}\n\t\t};\n\treturn res;\n\t}\n\nbool reduce_delta::one_step_(sibling_iterator dl)\n\t{\n\tsibling_iterator up=tr.begin(dl), dn;\n\tint flip=999, masterflip=1;\n\twhile(up!=tr.end(dl)) {\n\t\tflip=masterflip;\n\t\tdn=tr.begin(dl);\n\t\t++dn;\n\t\twhile(dn!=tr.end(dl)) {\n\t\t\tif(up->name==dn->name) {\n\t\t\t\tif(!up->is_rational()) {\n\t\t\t\t\tgoto found;\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t++dn;\n\t\t\t++dn;\n\t\t\tflip=-flip;\n\t\t\t}\n\t\t++up;\n\t\t++up;\n\t\tmasterflip=-masterflip;\n\t\t}\n\treturn false;\nfound:\n\t//\tstd::cerr << \"reduce_delta: eliminating \" << *up->name << \" contraction.\" << std::endl;\n\t//\t{unsigned int num=1;\n\t//\ttr.print_recursive_treeform(debugout, dl, num) << std::endl;}\n\t// FIXME: use properties for the dimension!\n\t//\ttxtout << *dl->multiplier << std::endl;\n\tconst Integer *itg=kernel.properties.get<Integer>(up, true);\n\tint dim;\n\tif(itg) {\n\t\tconst nset_t::iterator onept=name_set.insert(\"1\").first;\n\t\tif(itg->difference.begin()->name==onept)\n\t\t\tdim=to_long(*itg->difference.begin()->multiplier);\n\t\telse\n\t\t\tthrow ConsistencyException(\"Summation range for index is not an integer.\");\n\t\t}\n\telse throw ConsistencyException(\"No dimension known for summation index \"+*up->name+\".\");\n\n\tint mult=flip*(dim-tr.number_of_children(dl)/2+1);\n\tmultiply(dl->multiplier, (multiplier_t)(mult));\n\tmultiply(dl->multiplier, multiplier_t(2)/((multiplier_t)(tr.number_of_children(dl))));\n\t//\ttxtout << \"flip =\" << flip << std::endl;\n\n\t// remove the indices\n\tsibling_iterator up2=up;\n\t++up2;\n\t++up2;\n\twhile(up2!=tr.end(dl)) {\n\t\tup->name=up2->name;\n\t\tup->multiplier=up2->multiplier;\n\t\t++up;\n\t\t++up;\n\t\t++up2;\n\t\t++up2;\n\t\t}\n\tsibling_iterator dn2=dn;\n\t++dn2;\n\t++dn2;\n\twhile(dn2!=tr.end(dl)) {\n\t\tdn->name=dn2->name;\n\t\tdn->multiplier=dn2->multiplier;\n\t\t++dn;\n\t\t++dn;\n\t\t++dn2;\n\t\t++dn2;\n\t\t}\n\tsibling_iterator lst=tr.end(dl);\n\t--lst;\n\t--lst;\n\tlst=tr.erase(lst);\n\ttr.erase(lst);\n\n\t//\t{unsigned int num=1;\n\t//\ttr.print_recursive_treeform(debugout, dl, num) << std::endl;}\n\n\treturn true;\n\t}\n"
  },
  {
    "path": "core/algorithms/reduce_delta.cnb",
    "content": "{\n\t\"cells\" : \n\t[\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\algorithm{reduce_delta}{Simplify a self-contracted generalised delta.}\\n\\nReduce a self-contracted generalised Kronecker delta symbol to a simpler\\nexpression without self-contractions, according to\\n\\\\begin{equation}\\nn! \\\\, \\\\delta^{a_1\\\\cdots a_n}_{b_1\\\\cdots b_n}\\\\, \\\\delta^{b_1}_{a_1}\\n\\\\cdots \\\\delta^{b_m}_{a_m} = \\n\\\\Big[\\\\prod_{i=1}^m \\\\big( d-(n-i) \\\\big) \\\\Big]\\n\\\\, (n-m)!\\\\, \\\\delta^{a_{m+1}\\\\cdots a_n}_{b_{m+1}\\\\cdots b_n}\\\\, .\\n\\\\end{equation}\\nHere is an example:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\algorithm{reduce_delta}{Simplify a self-contracted generalised delta.}\\n\\nReduce a self-contracted generalised Kronecker delta symbol to a simpler\\nexpression without self-contractions, according to\\n\\\\begin{equation}\\nn! \\\\, \\\\delta^{a_1\\\\cdots a_n}_{b_1\\\\cdots b_n}\\\\, \\\\delta^{b_1}_{a_1}\\n\\\\cdots \\\\delta^{b_m}_{a_m} = \\n\\\\Big[\\\\prod_{i=1}^m \\\\big( d-(n-i) \\\\big) \\\\Big]\\n\\\\, (n-m)!\\\\, \\\\delta^{a_{m+1}\\\\cdots a_n}_{b_{m+1}\\\\cdots b_n}\\\\, .\\n\\\\end{equation}\\nHere is an example:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property KroneckerDelta to~}\\\\delta\\\\left(\\\\#\\\\right).\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Integer to~}\\\\left(m, n, q\\\\right).\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\delta_{m}\\\\,^{n}\\\\,_{n}\\\\,^{q}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"\\\\delta{#}::KroneckerDelta;\\n{m,n,q}::Integer(0..3);\\nex:=\\\\delta_{m}^{n}_{n}^{q};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{} - \\\\frac{3}{2}\\\\delta_{m}\\\\,^{q}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"reduce_delta(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"Note that this requires that the indices on the Kronecker\\ndelta symbol also carry an \\\\prop{Integer} property to specify\\ntheir range.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"Note that this requires that the indices on the Kronecker\\ndelta symbol also carry an \\\\prop{Integer} property to specify\\ntheir range.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1\n}\n"
  },
  {
    "path": "core/algorithms/reduce_delta.hh",
    "content": "\n#pragma once\n\n#include \"Algorithm.hh\"\n\nnamespace cadabra {\n\n\tclass reduce_delta : public Algorithm {\n\t\tpublic:\n\t\t\treduce_delta(const Kernel&, Ex&);\n\n\t\t\tvirtual bool     can_apply(iterator) override;\n\t\t\tvirtual result_t apply(iterator&) override;\n\n\t\tprivate:\n\t\t\tbool one_step_(sibling_iterator);\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/algorithms/remove_indexbracket.tex",
    "content": "\\cdbalgorithm{remove\\_indexbracket}{}\n\nWhen a single symbol-with-indices is entered as\n\\begin{screen}{1}\n(A)_{\\mu\\nu};\n\\end{screen}\nit gets wrapped in an \\texcommand{indexbracket} node. In order to\nremove this node again, and produce\n\\begin{screen}{1}\nA_{\\mu\\nu}\n\\end{screen}\nagain, use \\subscommand{remove\\_indexbracket}. \n\\begin{screen}{1,2}\n(A)_{\\mu\\nu};\n@remove_indexbracket!(%);\nA_{\\mu\\nu};\n\\end{screen}\n\nThis algorithm is also useful after the \\subscommand{distribute}\ncommand has\nbeen called on an\n\\texcommand{indexbracket} node which contained a sum; the\n\\subscommand{remove\\_indexbracket} will then remove the superfluous\nbrackets around the single symbols.\n\n\\cdbseealgo{distribute}\n"
  },
  {
    "path": "core/algorithms/remove_weyl_traces.tex",
    "content": "\\cdbalgorithm{remove\\_weyl\\_traces}{}\n\nRemoves terms containing\nthe trace of a Weyl tensor, i.e.~a Weyl tensor with two indices\ncontracted.\n"
  },
  {
    "path": "core/algorithms/rename_dummies.cc",
    "content": "\n#include \"algorithms/rename_dummies.hh\"\n#include \"properties/Indices.hh\"\n#include \"Exceptions.hh\"\n#include \"IndexClassifier.hh\"\n\nusing namespace cadabra;\n\nrename_dummies::rename_dummies(const Kernel& k, Ex& tr, std::string d1, std::string d2)\n\t: Algorithm(k, tr), dset1(d1), dset2(d2)\n\t{\n\t}\n\nbool rename_dummies::can_apply(iterator st)\n\t{\n\t//\tstd::cerr << \"---\" << std::endl << Ex(st);\n\n\tif(*st->name==\"\\\\equals\") {\n\t\t// special case: rename all free indices on lhs and rhs.\n\t\t// FIXME: add flag to class to disable this when called as rename_dummies.\n\t\treturn true;\n\t\t}\n\n\tif(*st->name!=\"\\\\prod\") // && *st->name!=\"\\\\sum\")\n\t\tif(!is_single_term(st))\n\t\t\treturn false;\n\n\t//\tif(*st->name==\"\\\\prod\" && tr.is_head(st)==false && *(tr.parent(st)->name)==\"\\\\sum\") return false;\n\treturn true;\n\t}\n\nAlgorithm::result_t rename_dummies::apply(iterator& st)\n\t{\n\tresult_t res=result_t::l_no_action;\n\n\t//\tif(*st->name==\"\\\\equals\") {\n\t//\n\t//\t\t}\n\n\t//\tstd::cerr << Ex(st);\n\tprod_wrap_single_term(st);\n\t//\tstd::cerr << Ex(st);\n\n\t// First do a normal classify_indices both downwards and upwards.\n\t//\n\tIndexClassifier ic(kernel);\n\tIndexClassifier::index_map_t ind_free, ind_dummy, ind_free_up, ind_dummy_up;\n\tic.classify_indices(st, ind_free, ind_dummy);\n\tic.classify_indices_up(st, ind_free_up, ind_dummy_up);\n\n\t//\tprint_classify_indices(std::cerr, st);\n\n\t// Run through all indices once more, in order. If an index\n\t// occurs in the ind_dummy set, and there is no entry in repmap,\n\t// find the index type and get a new dummy. If the index already\n\t// occurs in repmap, reuse the new dummy stored there.\n\t//\n\ttypedef std::map<Ex, Ex, tree_exact_less_for_indexmap_obj> repmap_t;\n\trepmap_t    repmap;\n\tIndexClassifier::index_map_t added_dummies;\n\n\t// If a target set is provided, move any dummies from this set in ind_dummy\n\t// to added_dummies to prevent them from being reused\n\tif (dset2 != \"\") {\n\t\tfor (const auto& idx : ind_dummy) {\n\t\t\tconst Indices* idxset = kernel.properties.get<Indices>(idx.second, true);\n\t\t\tif (idxset->set_name == dset2)\n\t\t\t\tadded_dummies.insert(idx);\n\t\t\t}\n\t\t}\n\n\t// Store all indices in a map sorted by the name of the parent.\n\t// FIXME: this is not sufficient, you really need to determine which\n\t// are common factors in all terms in a sum, and then collect those\n\t// to the front of the renaming queue.\n\tstd::multimap<nset_t::iterator, index_iterator, nset_it_less> parent_sorted_indices;\n\tauto ii = begin_index(st);\n\twhile(ii!=end_index(st)) {\n\t\tparent_sorted_indices.insert(std::make_pair(tr.parent(iterator(ii))->name, ii));\n\t\t++ii;\n\t\t}\n\n\t// If target set is specified, find a handle to the Indices property\n\t// with this name.\n\tconst Indices *ind2=0;\n\tif(dset2!=\"\") {\n\t\tauto f2=kernel.properties.pats.begin();\n\t\twhile(f2!=kernel.properties.pats.end()) {\n\t\t\tind2 = dynamic_cast<const Indices *>(f2->first);\n\t\t\tif(ind2) {\n\t\t\t\tif(ind2->set_name==dset2)\n\t\t\t\t\tbreak;\n\t\t\t\telse ind2=0;\n\t\t\t\t}\n\t\t\t++f2;\n\t\t\t}\n\t\tif(ind2==0)\n\t\t\tthrow ConsistencyException(\"No index set with name `\"+dset2+\"' known.\");\n\t\t}\n\n\tauto iim=parent_sorted_indices.begin();\n\twhile(iim!=parent_sorted_indices.end()) {\n\t\tii = iim->second;\n\t\tif(ind_dummy.find(Ex(ii))!=ind_dummy.end()) {\n\t\t\t// std::cerr << Ex(ii) << \" is dummy \" << std::endl;\n\t\t\trepmap_t::iterator rmi=repmap.find(Ex(ii));\n\t\t\tif(rmi==repmap.end()) {\n\t\t\t\tEx other_parent_rel(ii);\n\t\t\t\tif(other_parent_rel.begin()->fl.parent_rel==str_node::p_super)\n\t\t\t\t\tother_parent_rel.begin()->fl.parent_rel=str_node::p_sub;\n\t\t\t\telse\n\t\t\t\t\tother_parent_rel.begin()->fl.parent_rel=str_node::p_super;\n\t\t\t\trmi=repmap.find(other_parent_rel);\n\t\t\t\t}\n\t\t\tif(rmi==repmap.end()) {\n\t\t\t\tconst Indices *dums=kernel.properties.get<Indices>(ii, true);\n\t\t\t\tif(!dums)\n\t\t\t\t\tthrow ConsistencyException(\"No index set for index \"+*ii->name+\" known.\");\n\n\t\t\t\t// only rename dummies from dset1.\n\t\t\t\tif(dset1==\"\" || dums->set_name==dset1) {\n\t\t\t\t\tif(dset2!=\"\") dums=ind2; // replace with dummies from set 2\n\n\t\t\t\t\tEx relabel=ic.get_dummy(dums, &ind_free, &ind_free_up, &ind_dummy_up, &added_dummies);\n\t\t\t\t\trepmap.insert(repmap_t::value_type(Ex(ii),relabel));\n\t\t\t\t\tadded_dummies.insert(IndexClassifier::index_map_t::value_type(relabel, ii));\n\t\t\t\t\tif(subtree_compare(&kernel.properties, ii, relabel.begin())!=0) {\n\t\t\t\t\t\tres=result_t::l_applied;\n\t\t\t\t\t\ttr.replace_index(ii, relabel.begin(), true);\n\t\t\t\t\t\t}\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\telse {\n\t\t\t\t// std::cerr << \"already encountered => \" << rmi->second << std::endl;\n\t\t\t\t//\t\t\t\tindex_iterator tmp(ii);\n\t\t\t\t//\t\t\t\t++tmp;\n\t\t\t\ttr.replace_index(ii, (*rmi).second.begin(), true);\n\t\t\t\t//\t\t\t\tii=tmp;\n\t\t\t\t}\n\t\t\t}\n\t\t++iim;\n\t\t}\n\n\t// Now rename free indices.\n\n\t//\tif(*st->name==\"\\\\equals\") {\n\t//\t\tauto fit = ind_free.begin();\n\t//\t\twhile(fit!=ind_free.end()) {\n\t//\t\t\tstd::cerr << \"renaming \" << fit->first << std::endl;\n\t//\t\t\tEx relabel=get_dummy(dums, &ind_free, &ind_free_up, &ind_dummy_up, &added_dummies);\n\t//\t\t\t++fit;\n\t//\t\t\t}\n\t//\t\tstd::cerr << \"----\" << std::endl;\n\t//\t\t}\n\n\t//\tstd::cerr << Ex(st);\n\tprod_unwrap_single_term(st);\n\t//\tstd::cerr << Ex(st);\n\n\treturn res;\n\t}\n"
  },
  {
    "path": "core/algorithms/rename_dummies.cnb",
    "content": "{\n\t\"cells\" : \n\t[\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\algorithm{rename_dummies}{Rename dummy indices, within a set or from one set to another.}\\n\\nRename the dummy indices in an expression. This can be necessary in\\norder to make various terms in a sum use the same names for the\\nindices, so that they can be collected.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\algorithm{rename_dummies}{Rename dummy indices, within a set or from one set to another.}\\n\\nRename the dummy indices in an expression. This can be necessary in\\norder to make various terms in a sum use the same names for the\\nindices, so that they can be collected.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Indices(position=free) to~}\\\\left(m, \\\\linebreak[0] n, \\\\linebreak[0] p, \\\\linebreak[0] q, \\\\linebreak[0] r, \\\\linebreak[0] s\\\\right).\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}A_{m n} B_{m n}-A_{p q} B_{p q}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"{m,n,p,q,r,s}::Indices(vector);\\nex:=A_{m n} B_{m n} - A_{p q} B_{p q};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"Using \\\\algo{canonicalise} does nothing here, \"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"Using \\\\algo{canonicalise} does nothing here, \"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}A_{m n} B_{m n}-A_{p q} B_{p q}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"canonicalise(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"However, renaming indices does the trick,\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"However, renaming indices does the trick,\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}0\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"rename_dummies(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"Note that the indices need to have been declared as being part of an\\nindex list, using the \\\\prop{Indices} property.\\n\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"Note that the indices need to have been declared as being part of an\\nindex list, using the \\\\prop{Indices} property.\\n\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"The algorithm can also be used to rename dummies from one set to another one, e.g. to change index conventions\\n(this is used in many of Cadabra's packages). Here is an example.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"The algorithm can also be used to rename dummies from one set to another one, e.g. to change index conventions\\n(this is used in many of Cadabra's packages). Here is an example.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Indices(position=free) to~}\\\\left[m,~\\\\discretionary{}{}{} n,~\\\\discretionary{}{}{} p,~\\\\discretionary{}{}{} q\\\\right].\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Indices(position=free) to~}\\\\left[a,~\\\\discretionary{}{}{} b,~\\\\discretionary{}{}{} c,~\\\\discretionary{}{}{} d\\\\right].\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}A_{m} A^{m}+B_{m} C^{m}+A_{n} A^{n}+Q_{c d} R^{d c}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"{m,n,p,q}::Indices(\\\"one\\\");\\n{a,b,c,d}::Indices(\\\"two\\\");\\nex:= A_{m} A^{m} + B_{m} C^{m} + A_{n} A^{n} + Q_{c d} R^{d c};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"The above expression has indices in two different sets. We now rename the first set to the second,\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"The above expression has indices in two different sets. We now rename the first set to the second,\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}2A_{a} A^{a}+B_{a} C^{a}+Q_{c d} R^{d c}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"rename_dummies(_, \\\"one\\\", \\\"two\\\");\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1\n}\n"
  },
  {
    "path": "core/algorithms/rename_dummies.hh",
    "content": "\n#pragma once\n\n#include \"Algorithm.hh\"\n\nnamespace cadabra {\n\n\tclass rename_dummies : public Algorithm {\n\t\tpublic:\n\t\t\trename_dummies(const Kernel&, Ex&, std::string, std::string);\n\n\t\t\tvirtual bool     can_apply(iterator);\n\t\t\tvirtual result_t apply(iterator&);\n\n\t\tprivate:\n\t\t\tstd::string dset1, dset2;\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/algorithms/replace_match.cc",
    "content": "\n#include \"Cleanup.hh\"\n#include \"algorithms/replace_match.hh\"\n#include \"algorithms/substitute.hh\"\n\nusing namespace cadabra;\n\nreplace_match::replace_match(const Kernel& k, Ex& e)\n\t: Algorithm(k, e)\n\t{\n\t}\n\nbool replace_match::can_apply(iterator)\n\t{\n\tif(tr.history_size()>0) return true;\n\treturn false;\n\t}\n\nAlgorithm::result_t replace_match::apply(iterator& it)\n\t{\n\t// Preserve the expression before popping. After this, the 'tr' is\n\t// the original expression from before 'take_match'.\n\tEx current(tr);\n\tauto to_keep=tr.pop_history();\n\tif(to_keep.size()==0) {\n\t\treturn result_t::l_applied;\n\t\t}\n\n\t// Remove the terms which we will replace, by converting\n\t// the 'to_keep' paths above to iterators, then removing.\n\titerator sum_node = tr.parent(tr.iterator_from_path(to_keep[0], tr.begin()));\n\tstd::vector<iterator> to_erase;\n\tfor(const auto& p: to_keep)\n\t\tto_erase.push_back( tr.iterator_from_path(p, tr.begin()) );\n\tfor(auto& erase: to_erase)\n\t\ttr.erase(erase);\n\n\t// If the replacement is zero, there is nothing to substitute.\n\tif(!current.begin()->is_zero()) {\n\n\t\t// We already have an iterator to the sum node in the now-current\n\t\t// expression (sum_node). We also need one to the sum node in the\n\t\t// replacement sum.\n\t\titerator replacement_sum_node = current.iterator_from_path(tr.path_from_iterator(sum_node, tr.begin()), current.begin());\n\n\t\t// If the original sum has disappeared (because subsequent manipulations\n\t\t// made all but one terms vanish), wrap it again in a sum.\n\t\tif(*replacement_sum_node->name!=\"\\\\sum\")\n\t\t\treplacement_sum_node = current.wrap(replacement_sum_node, str_node(\"\\\\sum\"));\n\n\t\t// If we are inside an integral, determine the \\int multiplier in the original\n\t\t// and in the replacement.\n\t\tmultiplier_t rescale=1;\n\t\tif(!tr.is_head(it) && *tr.parent(it)->name==\"\\\\int\") {\n\t\t\tmultiplier_t orig_mult = *tr.parent(it)->multiplier;\n\t\t\tmultiplier_t repl_mult = *current.parent(replacement_sum_node)->multiplier;\n\t\t\trescale = repl_mult/orig_mult;\n\t\t\t}\n\n\t\tsibling_iterator repit=current.begin(replacement_sum_node);\n\t\twhile(repit!=current.end(replacement_sum_node)) {\n\t\t\tmultiply( tr.append_child(sum_node, iterator(repit))->multiplier, rescale);\n\t\t\t++repit;\n\t\t\t}\n\t\t}\n\n\tcleanup_dispatch(kernel, tr, it);\n\treturn result_t::l_applied;\n\t}\n\n"
  },
  {
    "path": "core/algorithms/replace_match.cnb",
    "content": "{\n\t\"cells\" : \n\t[\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\algorithm{replace_match}{Put the result of a sub-computation back into the original expression}\\n\\nThis algorithm is the partner of \\\\algo{take_match}; see the documentation of that algorithm for\\nfurther details.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\algorithm{replace_match}{Put the result of a sub-computation back into the original expression}\\n\\nThis algorithm is the partner of \\\\algo{take_match}; see the documentation of that algorithm for\\nfurther details.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1\n}\n"
  },
  {
    "path": "core/algorithms/replace_match.hh",
    "content": "\n#pragma once\n\n#include \"Algorithm.hh\"\n\nnamespace cadabra {\n\n\tclass replace_match : public Algorithm {\n\t\tpublic:\n\t\t\treplace_match(const Kernel&, Ex&);\n\n\t\t\tvirtual bool     can_apply(iterator) override;\n\t\t\tvirtual result_t apply(iterator&) override;\n\t\t};\n\n\t}\n\n"
  },
  {
    "path": "core/algorithms/rewrite_indices.cc",
    "content": "\n#include \"Cleanup.hh\"\n#include \"Exceptions.hh\"\n#include \"IndexClassifier.hh\"\n#include \"algorithms/rewrite_indices.hh\"\n#include \"properties/Derivative.hh\"\n#include \"properties/Indices.hh\"\n\nusing namespace cadabra;\n\nrewrite_indices::rewrite_indices(const Kernel& k, Ex& e, Ex& pref, Ex& conv)\n\t: Algorithm(k, e), preferred(pref), converters(conv)\n\t{\n\tauto c=converters.begin();\n\tif(*c->name!=\"\\\\comma\")\n\t\tconverters.wrap(c, str_node(\"\\\\comma\"));\n\n\tauto p=preferred.begin();\n\tif(*p->name!=\"\\\\comma\")\n\t\tpreferred.wrap(p, str_node(\"\\\\comma\"));\n\t}\n\nbool rewrite_indices::can_apply(iterator it)\n\t{\n\tis_derivative_argument=false;\n\tif(*it->name==\"\\\\prod\" || is_single_term(it))\n\t\treturn true;\n\n\tif(tr.is_head(it)==false) { // FIXME: should eventually go into prod_wrap_single_term\n\t\tconst Derivative *der=kernel.properties.get<Derivative>(tr.parent(it));\n\t\tif(der) {\n\t\t\tif(it->fl.parent_rel==str_node::p_none) {\n\t\t\t\tis_derivative_argument=true;\n\t\t\t\treturn true;\n\t\t\t\t}\n\t\t\t}\n\t\t}\n\n\treturn false;\n\t}\n\nAlgorithm::result_t rewrite_indices::apply(iterator& it)\n\t{\n\t// std::cerr << \"apply at \" << Ex(it) << std::endl;\n\n\tresult_t res=result_t::l_no_action;\n\n\tif(is_derivative_argument) force_node_wrap(it, \"\\\\prod\");\n\telse                       prod_wrap_single_term(it);\n\n\tIndexClassifier ic(kernel);\n\tIndexClassifier::index_map_t ind_free, ind_dummy;\n\tic.classify_indices(it, ind_free, ind_dummy);\n\n\t// Put arguments in canonical form.\n\n\tsibling_iterator objs=preferred.begin();\n\tsibling_iterator vielb=converters.begin().begin();\n\n\t// Determine which conversion types are possible by determining\n\t// the index sets in which the two indices of the converter sit.\n\t// itype1 and itype2 are the index types of the 1st and 2nd index of the\n\t// converter (i.e. vielbein or metric).\n\n\tsibling_iterator vbind=tr.begin(vielb);\n\tconst Indices *itype1=kernel.properties.get<Indices>(vbind, true);\n\tstr_node::parent_rel_t pr1=vbind->fl.parent_rel;\n\t++vbind;\n\tconst Indices *itype2=kernel.properties.get<Indices>(vbind, true);\n\tstr_node::parent_rel_t pr2=vbind->fl.parent_rel;\n\n\t// FIXME: should we even continue if one of itype1 or itype2 is 0?\n\n\t// std::cerr << \"can convert between \" << itype1->set_name << \" and \" << itype2->set_name << std::endl;\n\n\t// Since this algorithm works both on dummy indices and on free\n\t// ones, we merge the two.\n\n\tind_dummy.insert(ind_free.begin(), ind_free.end());\n\n\t// Go through all indices, determine on which object they sit,\n\t// and see if that object appears in the list of preferred-form\n\t// objects. If so, take appropriate action.\n\t// FIXME: this attempts to convert every object as many times as\n\t// there are indices on the object!!!\n\n\t// 'dit' is the index under consideration for a rewrite.\n\tIndexClassifier::index_map_t::const_iterator dit=ind_dummy.begin();\n\twhile(dit!=ind_dummy.end()) {\n\t\t//std::cerr << \"** considering index \" << Ex(dit->second) << std::endl;\n\t\tsibling_iterator par=tr.parent(dit->second);\n\t\tfor(sibling_iterator prefit=tr.begin(objs); prefit!=tr.end(objs); ++prefit) {\n\t\t\t// std::cerr << \"one \" << Ex(par) << \", \" << Ex(prefit) << std::endl;\n\n\t\t\t// We want to determine whether the 'par' object is the same\n\t\t\t// as the 'prefit' object, but the index types are different\n\t\t\t// on the 'prefit' object, or the index positions are\n\t\t\t// different. So we need to compare these two without using\n\t\t\t// index properties, so that we get a comparison strictly\n\t\t\t// based on alpha info.\n\n\t\t\tEx_comparator comp(kernel.properties);\n\t\t\tEx_comparator::match_t fnd = comp.equal_subtree(par, prefit, Ex_comparator::useprops_t::never);\n\n\t\t\tif(is_in(fnd, { Ex_comparator::match_t::subtree_match,\n\t\t\t                Ex_comparator::match_t::match_index_less,\n\t\t\t                Ex_comparator::match_t::match_index_greater,\n\t\t\t                Ex_comparator::match_t::no_match_indexpos_less,\n\t\t\t                Ex_comparator::match_t::no_match_indexpos_greater\n\t\t\t              \t})) {\n\t\t\t\t//std::cerr << \"found \" << *par->name << std::endl;\n\n\t\t\t\t// Determine whether the indices are of preferred type or not.\n\t\t\t\tint num=std::distance(tr.begin(par), (sibling_iterator)dit->second);\n\t\t\t\tconst Indices *origtype=kernel.properties.get<Indices>(dit->second, true);\n\t\t\t\tif(!origtype)\n\t\t\t\t\tthrow ArgumentException(\"Need to know about the index type of index \"+*dit->second->name+\".\");\n\n\t\t\t\t// 'walk' is the index on the preferred form of the tensor, corresponding\n\t\t\t\t// to the index on the original tensor which is currently under consideration\n\t\t\t\t// for change. We need to preserve the parent rel of this index on the preferred form.\n\t\t\t\tsibling_iterator walk=begin_index(prefit);\n\t\t\t\twhile(num-- > 0)\n\t\t\t\t\t++walk;\n\n\t\t\t\tconst Indices *newtype=kernel.properties.get<Indices>(walk, true);\n\t\t\t\tif(!newtype)\n\t\t\t\t\tthrow ArgumentException(\"Need to know about the index type of index \"+*walk->name+\".\");\n\n\t\t\t\tif(newtype->set_name == origtype->set_name) {\n\t\t\t\t\t// Index already has preferred type.\n\t\t\t\t\tif(origtype->position_type==Indices::free || walk->fl.parent_rel==dit->second->fl.parent_rel) {\n\t\t\t\t\t\t// Position is also already fine.\n\t\t\t\t\t\t//std::cerr << \"index position already fine\" << std::endl;\n\t\t\t\t\t\tcontinue; // already fine, no need for conversion\n\t\t\t\t\t\t}\n\t\t\t\t\telse {\n\t\t\t\t\t\t//std::cerr << \"index position wrong\" << std::endl;\n\t\t\t\t\t\t}\n\t\t\t\t\t}\n\n\t\t\t\t//std::cerr << \"need to convert from \" << origtype->set_name << \" to \" << newtype->set_name << std::endl;\n\n\t\t\t\tEx repvb(vielb);\n\t\t\t\tsibling_iterator vbi1=repvb.begin(repvb.begin());\n\t\t\t\tsibling_iterator vbi2=vbi1;\n\t\t\t\t++vbi2;\n\n\t\t\t\t// Set the indices on the vielbein/converter which we are going to insert.\n\t\t\t\tif(origtype->set_name == itype1->set_name && newtype->set_name == itype2->set_name) {\n\t\t\t\t\tif( itype1->position_type==Indices::free || dit->second->fl.parent_rel == pr1 ) {\n\t\t\t\t\t\tif( itype2->position_type==Indices::free || walk->fl.parent_rel != pr2 ) {\n\t\t\t\t\t\t\ttr.replace_index(vbi1, dit->second);\n\t\t\t\t\t\t\tEx nd=ic.get_dummy(itype2, par);\n\t\t\t\t\t\t\tauto nl = tr.replace_index(dit->second, nd.begin(), true);\n\t\t\t\t\t\t\tauto vielbein_index = tr.replace_index(vbi2, nd.begin());\n\t\t\t\t\t\t\tnl->fl.parent_rel=walk->fl.parent_rel;\n\t\t\t\t\t\t\tvielbein_index->fl.parent_rel=walk->fl.parent_rel;\n\t\t\t\t\t\t\tvielbein_index->flip_parent_rel();\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\telse continue;\n\t\t\t\t\t\t}\n\t\t\t\t\telse continue;\n\t\t\t\t\t}\n\t\t\t\telse if(origtype->set_name == itype2->set_name && newtype->set_name == itype1->set_name) {\n\t\t\t\t\tif( itype2->position_type==Indices::free || dit->second->fl.parent_rel == pr2 ) {\n\t\t\t\t\t\tif( itype1->position_type==Indices::free || walk->fl.parent_rel != pr1 ) {\n\t\t\t\t\t\t\ttr.replace_index(vbi2, dit->second);\n\t\t\t\t\t\t\tEx nd=ic.get_dummy(itype1, par);\n\t\t\t\t\t\t\tauto nl=tr.replace_index(dit->second,nd.begin());\n\t\t\t\t\t\t\tauto vielbein_index = tr.replace_index(vbi1,nd.begin());\n\t\t\t\t\t\t\tnl->fl.parent_rel=walk->fl.parent_rel;\n\t\t\t\t\t\t\tvielbein_index->fl.parent_rel=walk->fl.parent_rel;\n\t\t\t\t\t\t\tvielbein_index->flip_parent_rel();\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\telse continue;\n\t\t\t\t\t\t}\n\t\t\t\t\telse continue;\n\t\t\t\t\t}\n\t\t\t\telse {\n\t\t\t\t\t// std::cerr << \"Uh, cannot convert?\" << std::endl;\n\t\t\t\t\tcontinue; // next index\n\t\t\t\t\t}\n\n\t\t\t\t// Insert the conversion object.\n\t\t\t\titerator vbit;\n\t\t\t\tif(*tr.parent(par)->name==\"\\\\sum\") { // need to wrap inside a product\n\t\t\t\t\titerator prod=tr.wrap(par, str_node(\"\\\\prod\"));\n\t\t\t\t\tprod->fl.bracket=par->fl.bracket;\n\t\t\t\t\tpar->fl.bracket=str_node::b_none;\n\t\t\t\t\tvbit=tr.append_child(prod, repvb.begin());\n\t\t\t\t\tres=result_t::l_applied;\n\t\t\t\t\t}\n\t\t\t\telse {\n\t\t\t\t\tassert(*tr.parent(par)->name==\"\\\\prod\");\n\t\t\t\t\tvbit=tr.append_child((iterator)tr.parent(par), repvb.begin());\n\t\t\t\t\tvbit->fl.bracket=par->fl.bracket;\n\t\t\t\t\tres=result_t::l_applied;\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t}\n\t\t++dit;\n\t\t}\n\n\tprod_unwrap_single_term(it);\n\n\treturn res;\n\t}\n"
  },
  {
    "path": "core/algorithms/rewrite_indices.cnb",
    "content": "{\n\t\"cells\" : \n\t[\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\algorithm{rewrite_indices}{Rewrite indices by contracting with vielbein or metric.}\\n\\nRewrite indices on an object by contracting it with a second object\\nwhich contains indices of both the old and the new type (a vielbein,\\nin other words, or a metric). A vielbein example is\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\algorithm{rewrite_indices}{Rewrite indices by contracting with vielbein or metric.}\\n\\nRewrite indices on an object by contracting it with a second object\\nwhich contains indices of both the old and the new type (a vielbein,\\nin other words, or a metric). A vielbein example is\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}T_{m n p}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}T_{\\\\mu \\\\nu \\\\rho} e^{\\\\mu}\\\\,_{m} e^{\\\\nu}\\\\,_{n} e^{\\\\rho}\\\\,_{p}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"{m,n,p}::Indices(flat).\\n{\\\\mu,\\\\nu,\\\\rho}::Indices(curved).\\nex:=T_{m n p};\\nrewrite_indices(_, $T_{\\\\mu\\\\nu\\\\rho}$, $e_{\\\\mu}^{n}$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"If you want to raise or lower an index with a metric, this can also be\\ndone with as an index rewriting command, as the following example shows:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"If you want to raise or lower an index with a metric, this can also be\\ndone with as an index rewriting command, as the following example shows:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}H_{\\\\mu \\\\nu \\\\rho}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}H^{\\\\sigma \\\\lambda \\\\kappa} g_{\\\\mu \\\\sigma} g_{\\\\nu \\\\lambda} g_{\\\\rho \\\\kappa}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"{\\\\mu,\\\\nu,\\\\rho,\\\\sigma,\\\\lambda,\\\\kappa}::Indices(curved, position=fixed).\\nex:=H_{\\\\mu \\\\nu \\\\rho};\\nrewrite_indices(_, $H^{\\\\mu \\\\nu \\\\rho}$, $g_{\\\\mu \\\\nu}$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"As these examples show, the desired form of the tensor should be given\\nas the first argument, and the conversion object (metric, vielbein) as\\nthe second object. \"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"As these examples show, the desired form of the tensor should be given\\nas the first argument, and the conversion object (metric, vielbein) as\\nthe second object. \"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1\n}\n"
  },
  {
    "path": "core/algorithms/rewrite_indices.hh",
    "content": "\n#pragma once\n\n#include \"Algorithm.hh\"\n\nnamespace cadabra {\n\n\tclass rewrite_indices : public Algorithm {\n\t\tpublic:\n\t\t\trewrite_indices(const Kernel&, Ex&, Ex&, Ex&);\n\n\t\t\tvirtual bool     can_apply(iterator) override;\n\t\t\tvirtual result_t apply(iterator&) override;\n\n\t\tprivate:\n\t\t\tEx          preferred, converters;\n\t\t\tbool        is_derivative_argument;\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/algorithms/simplify.cc",
    "content": "\n#include \"Config.hh\"\n#include \"simplify.hh\"\n#include \"Cleanup.hh\"\n#include \"IndexClassifier.hh\"\n#include \"properties/Coordinate.hh\"\n#include \"properties/Symbol.hh\"\n#include \"SympyCdb.hh\"\n#ifdef MATHEMATICA_FOUND\n#include \"MMACdb.hh\"\n#endif\n\nusing namespace cadabra;\n\nsimplify::simplify(const Kernel& k, Ex& tr)\n\t: Algorithm(k, tr)\n\t{\n\t}\n\nbool simplify::can_apply(iterator st)\n\t{\n\t// For \\components nodes we need to map at the level of the individual\n\t// component values, not the top \\components node.\n\tif(*st->name==\"\\\\components\") return false;\n\tif(*st->name==\"\\\\equals\") return false;\n\tif(*st->name==\"\\\\comma\") return false;\n\tif(*st->name==\"\\\\wedge\") return false;\n\n\t// If this is a sum, determine if there are any wedge products (we\n\t// do not pass enough info to sympy yet to enable it to simplify these).\n\n\tif(*st->name==\"\\\\sum\") {\n\t\tfor(sibling_iterator sib=tr.begin(st), end=tr.end(st); sib!=end; ++sib)\n\t\t\tif(*sib->name==\"\\\\wedge\")\n\t\t\t\treturn false;\n\t\t}\n\n\t// Check that any occuring indices are 'harmless', in the sense that\n\t// sympy knows how to handle them.\n\t\n\tleft.clear();\n\tindex_factors.clear();\n\tIndexClassifier ic(kernel);\n\tIndexClassifier::index_map_t ind_free, ind_dummy;\n\tic.classify_indices(st, ind_free, ind_dummy);\n//\tprint_classify_indices(std::cerr, st);\n\n\tbool still_ok=true;\n\n\t// Determine if any of the free indices are harmless (Coordinates or Symbols).\n\tfor(auto& ind: ind_free) {\n\t\tconst Coordinate *cdn=kernel.properties.get<Coordinate>(ind.second, true);\n\t\tconst Symbol     *smb=kernel.properties.get<Symbol>(ind.second, true);\n\t\tif(cdn==0 && smb==0) {\n\t\t\tstill_ok=false;\n\t\t\tbreak;\n\t\t\t}\n\t\t}\n\n\tif(still_ok && ind_dummy.size()==0) return true;\n\n\t// In a product, it is still possible that there is a sub-product which\n\t// contains no indices.\n\tif(*st->name==\"\\\\prod\") {\n\t\t// Find the factors in the product which have a proper index on them. Do this by\n\t\t// starting at the index, and if it is not coordinate or symbol, then go up until we\n\t\t// reach the first child level of the product.\n\t\tfor(auto& ind: ind_free) {\n\t\t\tconst Coordinate *cdn=kernel.properties.get<Coordinate>(ind.second, true);\n\t\t\tconst Symbol     *smb=kernel.properties.get<Symbol>(ind.second, true);\n\t\t\tif(cdn==0 && smb==0) {\n\t\t\t\tauto fac=tr.parent(ind.second);\n\t\t\t\twhile(tr.parent(fac)!=iterator(st))\n\t\t\t\t\tfac=tr.parent(fac);\n\t\t\t\tindex_factors.insert(fac);\n\t\t\t\t}\n\t\t\t}\n\t\tfor(auto& ind: ind_dummy) {\n\t\t\tconst Coordinate *cdn=kernel.properties.get<Coordinate>(ind.second, true);\n\t\t\tconst Symbol     *smb=kernel.properties.get<Symbol>(ind.second, true);\n\t\t\tif(cdn==0 && smb==0) {\n\t\t\t\tauto fac=tr.parent(ind.second);\n\t\t\t\twhile(tr.parent(fac)!=iterator(st))\n\t\t\t\t\tfac=tr.parent(fac);\n\t\t\t\tindex_factors.insert(fac);\n\t\t\t\t}\n\t\t\t}\n\t\tsibling_iterator sib=tr.begin(st);\n\t\twhile(sib!=tr.end(st)) {\n\t\t\tif(index_factors.find(iterator(sib))==index_factors.end())\n\t\t\t\tleft.push_back(sib);\n\t\t\t++sib;\n\t\t\t}\n\t\treturn left.size()>0;\n\t\t}\n\n\treturn false;\n\t}\n\nAlgorithm::result_t simplify::apply(iterator& it)\n\t{\n\tstd::vector<std::string> wrap;\n\tstd::vector<std::string> args_;\n\n\tif(left.size()>0) {\n\t\tEx prod(\"\\\\prod\");\n\t\tfor(auto& fac: left)\n\t\t\tprod.append_child(prod.begin(), fac);\n\t\tauto top=prod.begin();\n\t\t// std::cerr << \"Feeding to sympy \" << prod << std::endl;\n\t\tswitch(kernel.scalar_backend) {\n\t\t\tcase Kernel::scalar_backend_t::sympy:\n\t\t\t\twrap.push_back(\"simplify\");\n\t\t\t\t\t{\n\t\t\t\t\tScopedProgressGroup group(pm, \"sympy\");\n\t\t\t\t\tsympy::apply(kernel, prod, top, wrap, args_, \"\");\n\t\t\t\t\t}\n\t\t\t\tbreak;\n\t\t\tcase Kernel::scalar_backend_t::mathematica:\n#ifdef MATHEMATICA_FOUND\n\t\t\t\twrap.push_back(\"FullSimplify\");\n\t\t\t\t//\t\t\t\targs_.push_back(\"Trig -> False\");\n\t\t\t\t{\n\t\t\t\t\tScopedProgressGroup(pm, \"mathematica\");\n\t\t\t\t\tMMA::apply_mma(kernel, prod, top, wrap, args_, \"\");\n\t\t\t\t}\n#endif\n\t\t\t\tbreak;\n\t\t\t}\n\t\t// Now remove the non-index carrying factors and replace with\n\t\t// the factors of 'prod' just simplified.\n\t\ttr.insert_subtree(*left.begin(), top);\n\t\t// std::cerr << \"Before erasing \" << Ex(it) << std::endl;\n\t\tfor(auto& kl: left)\n\t\t\ttr.erase(kl);\n\t\t// std::cerr << \"After erasing \" << Ex(it) << std::endl;\n\n\t\treturn result_t::l_applied;\n\t\t}\n\telse {\n\t\tswitch(kernel.scalar_backend) {\n\t\t\tcase Kernel::scalar_backend_t::sympy:\n\t\t\t\twrap.push_back(\"simplify\");\n\t\t\t\tif(pm) pm->group(\"sympy\");\n\t\t\t\tsympy::apply(kernel, tr, it, wrap, args_, \"\");\n\t\t\t\tif(pm) pm->group();\n\t\t\t\tbreak;\n\t\t\tcase Kernel::scalar_backend_t::mathematica:\n#ifdef MATHEMATICA_FOUND\n\t\t\t\twrap.push_back(\"FullSimplify\");\n\t\t\t\t//\t\t\t\targs_.push_back(\"Trig -> False\");\n\t\t\t\tif(pm) pm->group(\"mathematica\");\n\t\t\t\tMMA::apply_mma(kernel, tr, it, wrap, args_, \"\");\n\t\t\t\tif(pm) pm->group();\n#endif\n\t\t\t\tbreak;\n\t\t\t}\n\t\tit.skip_children();\n\t\treturn result_t::l_applied;\n\t\t}\n\t}\n"
  },
  {
    "path": "core/algorithms/simplify.cnb",
    "content": "{\n\t\"cells\" : \n\t[\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\algorithm{simplify}{Simplify the scalar part of an expression.}\\n\\nWhen expressions (or sub-expressions) involve scalars, simplification of such expressions can be\\n`outsourced' to an external scalar computer algebra system, at present either Sympy or Mathematica.\\nThe \\\\algo{simplify} algorithm finds all scalar sub-expressions and runs the simplification algorithm\\nof one of these systems on them.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\algorithm{simplify}{Simplify the scalar part of an expression.}\\n\\nWhen expressions (or sub-expressions) involve scalars, simplification of such expressions can be\\n`outsourced' to an external scalar computer algebra system, at present either Sympy or Mathematica.\\nThe \\\\algo{simplify} algorithm finds all scalar sub-expressions and runs the simplification algorithm\\nof one of these systems on them.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"((\\\\sin(x))**2 + (\\\\cos(x))**2) A_{m}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\left({\\\\left(\\\\sin{x}\\\\right)}^{2}+{\\\\left(\\\\cos{x}\\\\right)}^{2}\\\\right) A_{m}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex:= (\\\\sin{x}**2 + \\\\cos{x}**2) A_{m};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"A_{m}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}A_{m}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"simplify(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"By default it will use the Sympy backend, but if you have compiled Cadabra on a system which has Mathematica installed, \\nyou can also switch it to use Mathematica instead, by using\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"By default it will use the Sympy backend, but if you have compiled Cadabra on a system which has Mathematica installed, \\nyou can also switch it to use Mathematica instead, by using\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"kernel(scalar_backend=\\\"mathematica\\\")\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1\n}\n"
  },
  {
    "path": "core/algorithms/simplify.hh",
    "content": "\n#pragma once\n\n#include \"Algorithm.hh\"\n\nnamespace cadabra {\n\n\t/// \\ingroup algorithms\n\t///\n\t/// General purpose brute force scalar simplification algorithm.\n\t/// Can be switched to use different scalar backends and thus\n\t/// acts as a uniform front-end for different scalar CAS simplify\n\t/// algorithms.\n\n\tclass simplify : public Algorithm {\n\t\tpublic:\n\t\t\tsimplify(const Kernel&, Ex&);\n\n\t\t\tvirtual bool     can_apply(iterator);\n\t\t\tvirtual result_t apply(iterator&);\n\n\t\tprivate:\n\t\t\tstd::vector<Ex::iterator> left;\n\t\t\tstd::set<Ex::iterator>    index_factors;\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/algorithms/slot_asym.cnb",
    "content": "{\n\t\"cell_id\": 15939251759909380531,\n\t\"cells\": [\n\t\t{\n\t\t\t\"cell_id\": 9909884154184314133,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 11121169234497922857,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\algorithm{slot_asym}{Anti-symmetrise or symmetrise an expression in indicated index slots}\\n\\nAnti-symmetrise or symmetrise (depending on the \\\\verb|antisymmetric| flag) a product or tensor in the indicated indices,\\nwhere the indices are given as slot positions. This complements the \\\\algo{asym} algorithm, which instead takes the\\nindex names over which to (anti-)symmetrise.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\algorithm{slot_asym}{Anti-symmetrise or symmetrise an expression in indicated index slots}\\n\\nAnti-symmetrise or symmetrise (depending on the \\\\verb|antisymmetric| flag) a product or tensor in the indicated indices,\\nwhere the indices are given as slot positions. This complements the \\\\algo{asym} algorithm, which instead takes the\\nindex names over which to (anti-)symmetrise.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 1631820596417225138,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 7595867900720961056,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 13265193798604235312,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"A_{m n} B_{p q}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}A_{m n} B_{p q}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex:=A_{m n} B_{p q};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 15329301797986921853,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 6618699822479866787,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 4925730957034195862,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \" 1/2 A_{m n} B_{p q} -  1/2 A_{m p} B_{n q}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\frac{1}{2}A_{m n} B_{p q} - \\\\frac{1}{2}A_{m p} B_{n q}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"slot_asym(_, [1,2]);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 2136548790978716924,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9595072634954805885,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"If you want to \\\\emph{symmetrise} in the indicated objects instead, use the \\\\verb|antisymmetric=False| flag:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"If you want to \\\\emph{symmetrise} in the indicated objects instead, use the \\\\verb|antisymmetric=False| flag:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 341154554226938963,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 10010981841376155594,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 1454030977596719820,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"A_{m n} B_{p q}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}A_{m n} B_{p q}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 13362812056189562810,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 6588625381382353233,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \" 1/2 A_{m n} B_{p q} +  1/2 A_{m p} B_{n q}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\frac{1}{2}A_{m n} B_{p q}+\\\\frac{1}{2}A_{m p} B_{n q}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex:=A_{m n} B_{p q};\\nslot_asym(_, [1,2], antisymmetric=False);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 5279739485549689433,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"\"\n\t\t}\n\t],\n\t\"description\": \"Cadabra JSON notebook format\",\n\t\"version\": 1.0\n}\n"
  },
  {
    "path": "core/algorithms/sort_product.cc",
    "content": "\n#include \"Cleanup.hh\"\n#include \"IndexClassifier.hh\"\n#include \"algorithms/sort_product.hh\"\n#include \"properties/Trace.hh\"\n\nusing namespace cadabra;\n\n// #define DEBUG 1\n\nsort_product::sort_product(const Kernel&k, Ex& tr)\n\t: Algorithm(k, tr), cleanup(true)\n\t{\n\t//\tif(has_argument(\"IgnoreNumbers\")) {\n\t//\t\ttxtout << \"ignoring numbers\" << std::endl;\n\t//\t\tignore_numbers_=true;\n\t//\t\t}\n\t}\n\nvoid sort_product::dont_cleanup()\n\t{\n\tcleanup=false;\n\t}\n\nbool sort_product::can_apply(iterator st)\n\t{\n\tif(*st->name==\"\\\\prod\" || *st->name==\"\\\\inner\" || *st->name==\"\\\\wedge\") {\n\t\t// ensure that there are no factors with object or name wildcards, as we\n\t\t// cannot know what they would match to (in general, sort_product does\n\t\t// not make much sense acting on patterns).\n\n\t\tsibling_iterator sib=tr.begin(st);\n\t\twhile(sib!=tr.end(st)) {\n\t\t\tif(sib->is_name_wildcard() || sib->is_object_wildcard())\n\t\t\t\treturn false;\n\t\t\t++sib;\n\t\t\t}\n\t\treturn true;\n\t\t}\n\telse return false;\n\t}\n\nAlgorithm::result_t sort_product::apply(iterator& st)\n\t{\n\t// This could have been done using STL's sort, but then you have to worry\n\t// about using stable_sort, and then the tree.sort() doesn't do that,\n\t// and anyhow you would perhaps want exceptions. Let's just use a bubble\n\t// sort since how many times do we have more than 100 items in a product?\n\n\tresult_t ret=result_t::l_no_action;\n\n\tEx::sibling_iterator one, two;\n\tEx_comparator compare(kernel.properties);\n\tcompare.set_value_matches_index(true);\n\n\t//\tstd::cerr << \"sorting\\n\" << Ex(st) << std::endl;\n\t//\tstd::cout << \"entering sort\" << std::endl;\n\t//\ttr.print_recursive_treeform(std::cout, st);\n\n\tunsigned int num=tr.number_of_children(st);\n\tfor(unsigned int i=1; i<num; ++i) {\n\t\tone=tr.begin(st);\n\t\ttwo=one;\n\t\t++two;\n\t\t//\t\tfor(unsigned int j=i+1; j<=num; ++j) { // this loops too many times, no?\n\t\twhile(two!=tr.end(st)) {\n\t\t\tcompare.clear();\n\t\t\tauto es = compare.equal_subtree(one, two);\n\t\t\tif(compare.should_swap(one, es)) {\n#ifdef DEBUG\n\t\t\t\tstd::cerr << \"should swap \" << *(one->name) << \" with \" << *(two->name) << std::endl;\n#endif\n\t\t\t\tint canswap=compare.can_swap(one, two, es);\n#ifdef DEBUG\n\t\t\t\tstd::cerr << \"can swap? \" << *(one->name) << \" with \" << *(two->name) << std::endl;\n#endif\n\t\t\t\tif(canswap!=0) {\n\t\t\t\t\t// std::cerr << \"swapping \" << Ex(one) << \" with \" << Ex(two) << std::endl;\n\t\t\t\t\ttr.swap(one);\n\t\t\t\t\tstd::swap(one,two);  // put the iterators back in order\n\t\t\t\t\tif(canswap==-1) {\n\t\t\t\t\t\t//\t\t\t\t\t\tstd::cout << \"MINUS\" << std::endl;\n\t\t\t\t\t\tflip_sign(st->multiplier);\n\t\t\t\t\t\t}\n\t\t\t\t\tret=result_t::l_applied;\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t++one;\n\t\t\t++two;\n\t\t\t}\n\t\t}\n\n\tif(ret==result_t::l_no_action) {\n\t\tbool found=false;\n\t\tbool ascend=true;\n\t\titerator parn=st;\n\t\t// It is fine to cycle when we have a sum of a sum inside a trace\n\t\twhile(ascend && !tr.is_head(parn)) {\n\t\t\tparn=tr.parent(parn);\n\t\t\tconst Trace *trace=kernel.properties.get<Trace>(parn);\n\t\t\tif(trace) {\n\t\t\t\tascend=false;\n\t\t\t\tfound=true;\n\t\t\t\t}\n\t\t\telse if(*parn->name==\"\\\\indexbracket\") {\n\t\t\t\tascend=false;\n\t\t\t\tif(number_of_indices(parn)==2) {\n\t\t\t\t\tindex_iterator first=begin_index(parn);\n\t\t\t\t\tindex_iterator last=first;\n\t\t\t\t\t++last;\n\t\t\t\t\tif(*first->name==*last->name) found=true;\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\telse if(*parn->name!=\"\\\\sum\") {\n\t\t\t\tascend=false;\n\t\t\t\t}\n\t\t\t}\n\t\tif(found) {\n\t\t\t// Construct all cyclic orderings\n\t\t\tstd::vector<std::vector<Ex::sibling_iterator>> candidates;\n\t\t\tone=tr.begin(st);\n\t\t\twhile(one!=tr.end(st)) {\n\t\t\t\ttwo=one;\n\t\t\t\t++two;\n\t\t\t\tif(two==tr.end(st)) two=tr.begin(st);\n\t\t\t\tstd::vector<Ex::sibling_iterator> candidate(1, one);\n\t\t\t\twhile(two!=one) {\n\t\t\t\t\tcandidate.push_back(two);\n\t\t\t\t\t++two;\n\t\t\t\t\tif(two==tr.end(st)) two=tr.begin(st);\n\t\t\t\t\t}\n\t\t\t\tcandidates.push_back(candidate);\n\t\t\t\t++one;\n\t\t\t\t}\n\t\t\t// Narrow them down by comparing first digit, then second digit, ...\n\t\t\tunsigned int digit=1;\n\t\t\tIndexClassifier ic(kernel);\n\t\t\tIndexClassifier::index_map_t ind_free, ind_dummy;\n\t\t\twhile(candidates.size()>1 && digit<=num) {\n\t\t\t\tstd::vector<std::vector<Ex::sibling_iterator>>::iterator candidate=candidates.begin();\n\t\t\t\tone=candidate->at(digit-1);\n\t\t\t\t++candidate;\n\t\t\t\twhile(candidate!=candidates.end()) {\n\t\t\t\t\ttwo=candidate->at(digit-1);\n\t\t\t\t\tcompare.clear();\n\t\t\t\t\tint dir=0;\n\t\t\t\t\tauto es=compare.equal_subtree(one, two);\n\t\t\t\t\tif(es==Ex_comparator::match_t::no_match_greater) dir=1;\n\t\t\t\t\telse if(es==Ex_comparator::match_t::no_match_less) dir=-1;\n\t\t\t\t\telse {\n\t\t\t\t\t\tunsigned int free1=0;\n\t\t\t\t\t\tunsigned int free2=0;\n\t\t\t\t\t\tstd::string free1_names=\"\";\n\t\t\t\t\t\tstd::string free2_names=\"\";\n\t\t\t\t\t\tif(ind_free.size()==0 && ind_dummy.size()==0) ic.classify_indices(st, ind_free, ind_dummy);\n\t\t\t\t\t\tindex_iterator ch=begin_index(one);\n\t\t\t\t\t\twhile(ch!=end_index(one)) {\n\t\t\t\t\t\t\tauto fnd=ind_free.find(Ex(ch));\n\t\t\t\t\t\t\tif(fnd!=ind_free.end()) {\n\t\t\t\t\t\t\t\tfree1_names+=*ch->name;\n\t\t\t\t\t\t\t\t++free1;\n\t\t\t\t\t\t\t\t}\n\t\t\t\t\t\t\t++ch;\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\tch=begin_index(two);\n\t\t\t\t\t\twhile(ch!=end_index(two)) {\n\t\t\t\t\t\t\tauto fnd=ind_free.find(Ex(ch));\n\t\t\t\t\t\t\tif(fnd!=ind_free.end()) {\n\t\t\t\t\t\t\t\tfree2_names+=*ch->name;\n\t\t\t\t\t\t\t\t++free2;\n\t\t\t\t\t\t\t\t}\n\t\t\t\t\t\t\t++ch;\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\tif(free1>free2) dir=1;\n\t\t\t\t\t\telse if(free1<free2) dir=-1;\n\t\t\t\t\t\telse if(free1_names>free2_names) dir=1;\n\t\t\t\t\t\telse if(free1_names<free2_names) dir=-1;\n\t\t\t\t\t\t}\n\t\t\t\t\tif(dir==1) {\n\t\t\t\t\t\tcandidate=candidates.erase(candidates.begin(), candidate);\n\t\t\t\t\t\tone=candidate->at(digit-1);\n\t\t\t\t\t\t++candidate;\n\t\t\t\t\t\t}\n\t\t\t\t\telse if(dir==-1) {\n\t\t\t\t\t\tcandidate=candidates.erase(candidate);\n\t\t\t\t\t\t}\n\t\t\t\t\telse ++candidate;\n\t\t\t\t\t}\n\t\t\t\t++digit;\n\t\t\t\t}\n\t\t\t// Use the first ordering but keep track of signs this time\n\t\t\tEx::sibling_iterator front=candidates.at(0).at(0);\n\t\t\tif(front!=tr.begin(st)) {\n\t\t\t\twhile(tr.begin(st)!=front) {\n\t\t\t\t\tone=tr.begin(st);\n\t\t\t\t\ttwo=one;\n\t\t\t\t\t++two;\n\t\t\t\t\twhile(two!=tr.end(st)) {\n\t\t\t\t\t\tcompare.clear();\n\t\t\t\t\t\tauto es=compare.equal_subtree(one, two);\n\t\t\t\t\t\tint sign=compare.can_swap_components(one, two, es);\n\t\t\t\t\t\tif(sign==-1) flip_sign(st->multiplier);\n\t\t\t\t\t\ttr.swap(one);\n\t\t\t\t\t\t++two;\n\t\t\t\t\t\t++two;\n\t\t\t\t\t\t}\n\t\t\t\t\t}\n\t\t\t\tret=result_t::l_applied;\n\t\t\t\t}\n\t\t\t}\n\t\t}\n\n\tif(cleanup)\n\t\tcleanup_dispatch(kernel, tr, st);\n\n\treturn ret;\n\t}\n"
  },
  {
    "path": "core/algorithms/sort_product.cnb",
    "content": "{\n\t\"cells\" : \n\t[\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\algorithm{sort_product}{Sort factors in a product}\\n\\nSort factors in a product, taking into account\\nany \\\\prop{SortOrder} properties. Also takes into account\\ncommutativity properties, such as \\\\prop{SelfCommuting}. If no sort\\norder is given, it first does a lexographical sort based on the name\\nof the factor, and if two names are identical, does a sort based on\\nthe number of children and (if this number is equal) a lexographical\\ncomparison of the names of the children. Symbols starting with a backslash\\n(greek letters etc.) get sorted to the right of roman letters.\\n\\nThe simplest sort is illustrated below,\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\algorithm{sort_product}{Sort factors in a product}\\n\\nSort factors in a product, taking into account\\nany \\\\prop{SortOrder} properties. Also takes into account\\ncommutativity properties, such as \\\\prop{SelfCommuting}. If no sort\\norder is given, it first does a lexographical sort based on the name\\nof the factor, and if two names are identical, does a sort based on\\nthe number of children and (if this number is equal) a lexographical\\ncomparison of the names of the children. Symbols starting with a backslash\\n(greek letters etc.) get sorted to the right of roman letters.\\n\\nThe simplest sort is illustrated below,\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}C B A D\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}A B C D\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex := C B A D;\\nsort_product(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"We can declare the objects to be anti-commuting, which then leads to\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"We can declare the objects to be anti-commuting, which then leads to\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}C B A D\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}-A B C D\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"{A, B, C, D}::AntiCommuting.\\nex := C B A D;\\nsort_product(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"For indexed objects, the anti-commutativity of components is indicated\\nusing the \\\\prop{SelfAntiCommuting} property,\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"For indexed objects, the anti-commutativity of components is indicated\\nusing the \\\\prop{SelfAntiCommuting} property,\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\psi_{n} \\\\psi_{m} \\\\psi_{p}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}-\\\\psi_{m} \\\\psi_{n} \\\\psi_{p}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"\\\\psi_{m}::SelfAntiCommuting.\\nex := \\\\psi_{n} \\\\psi_{m} \\\\psi_{p};\\nsort_product(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"Finally, the lexographical sort order can be overridden by using\\nthe \\\\prop{SortOrder} property,\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"Finally, the lexographical sort order can be overridden by using\\nthe \\\\prop{SortOrder} property,\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}C B A D\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}-D C B A\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"{D, C, B, A}::SortOrder.\\n{A, B, C, D}::AntiCommuting.\\nex := C B A D;\\nsort_product(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1\n}\n"
  },
  {
    "path": "core/algorithms/sort_product.hh",
    "content": "\n#pragma once\n\n#include \"Algorithm.hh\"\n\nnamespace cadabra {\n\n\tclass sort_product : public Algorithm {\n\t\tpublic:\n\t\t\tsort_product(const Kernel&, Ex&);\n\n\t\t\tvirtual bool     can_apply(iterator);\n\t\t\tvirtual result_t apply(iterator&);\n\n\t\t\tvoid dont_cleanup();\n\n\t\tprivate:\n\t\t\t//\t\t\tbool ignore_numbers_;\n\t\t\tbool cleanup;\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/algorithms/sort_spinors.cc",
    "content": "\n#include \"Exceptions.hh\"\n#include \"algorithms/sort_spinors.hh\"\n#include \"properties/GammaMatrix.hh\"\n#include \"properties/Spinor.hh\"\n#include \"properties/DiracBar.hh\"\n#include \"properties/SortOrder.hh\"\n\nusing namespace cadabra;\n\nsort_spinors::sort_spinors(const Kernel& k, Ex& e)\n\t: Algorithm(k, e)\n\t{\n\t}\n\nbool sort_spinors::can_apply(iterator it)\n\t{\n\tconst Spinor   *sp1=kernel.properties.get<Spinor>(it);\n\tconst DiracBar *db1=kernel.properties.get<DiracBar>(it);\n\n\t// Only act if the node is a Dirac conjugate Majorana spinor.\n\tif(! (sp1 && sp1->majorana && db1)) return false;\n\n\t// Only act if we are inside a product.\n\tif(tr.is_head(it)) return false;\n\t\n\tauto par=tr.parent(it);\n\tif(*par->name!=\"\\\\prod\")\n\t\treturn false;\n\n\tone=it;\n\tgammamat=tr.end();\n\ttwo=tr.end();\n\n\tsibling_iterator sib=it;\n\t++sib;\n\twhile(sib!=tr.end(par)) {\n\t\tconst Spinor      *spinor=kernel.properties.get<Spinor>(sib);\n\t\tconst GammaMatrix *gamma =kernel.properties.get<GammaMatrix>(sib);\n\n\t\tif(spinor) {\n\t\t\tif(!spinor->majorana)\n\t\t\t\tthrow ArgumentException(\"sort_spinors: second spinor not Majorana.\");\n\t\t\ttwo=sib;\n\t\t\treturn true;\n\t\t\t}\n\t\tif(gamma) {\n\t\t\tif(gammamat!=tr.end())\n\t\t\t\tthrow ArgumentException(\"sort_spinors: need to join_gamma first.\");\n\t\t\tgammamat=sib;\n\t\t\t}\n\t\t++sib;\n\t\t}\n\treturn false;\n\t}\n\nAlgorithm::result_t sort_spinors::apply(iterator& )\n\t{\n\tint num1, num2;\n\tconst SortOrder     *so1=kernel.properties.get<SortOrder>(one,num1);\n\tconst SortOrder     *so2=kernel.properties.get<SortOrder>(two,num2);\n\n\tif(so1!=0 && so1==so2) {\n\t\tif(num1>num2) {\n\t\t\tint numind=0;\n\t\t\tif(gammamat!=tr.end())\n\t\t\t\tnumind=number_of_indices(gammamat);\n\t\t\tint sign=1;\n\t\t\tif(((numind*(numind+1))/2)%2 == 0)\n\t\t\t\tsign*=-1;\n\n\t\t\t// Are we dealing with commuting or anti-commuting spinors?\n\t\t\tEx_comparator comp(kernel.properties);\n\t\t\tauto cmp = comp.equal_subtree(one, two);//\t\t\tauto cmp=subtree_compare(&kernel.properties, one, two);\n\t\t\tint ordersign=comp.can_swap(one, two, cmp, true /* ignore implicit indices */);\n\t\t\tsign*=ordersign;\n\n\t\t\t// Now flip the symbols and the sign, if necessary.\n\t\t\tsibling_iterator tru1=tr.begin(one);\n\t\t\ttr.swap(tru1, two);\n\t\t\tif(sign==-1) {\n\t\t\t\tflip_sign(one->multiplier);\n\t\t\t\tpushup_multiplier(one);\n\t\t\t\t}\n\t\t\treturn result_t::l_applied;\n\t\t\t}\n\t\telse return result_t::l_no_action;\n\t\t}\n\telse return result_t::l_no_action;\n\t}\n\n"
  },
  {
    "path": "core/algorithms/sort_spinors.cnb",
    "content": "{\n\t\"cells\" : \n\t[\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\algorithm{sort_spinors}{Sort Majorana spinor bilinears}\\n\\nSorts Majorana spinor bilinears using the Majorana flip property,\\nwhich for anti-commuting spinors takes the form\\n\\\\begin{equation}\\n\\\\bar\\\\psi_1 \\\\Gamma_{r_1\\\\cdots r_n}\\\\psi_2 = \\n  \\\\alpha \\\\beta^n (-)^{\\\\frac{1}{2}n(n-1)}\\\\, \\\\bar\\\\psi_1\\n  \\\\Gamma_{r_1\\\\cdots r_n}\\\\psi_2\\\\, .\\n\\\\end{equation}\\nHere $\\\\alpha$ and $\\\\beta$ determine the properties of the charge\\nconjugation matrix,\\n\\\\begin{equation}\\n{\\\\cal C}^T = \\\\alpha {\\\\cal C}\\\\,,\\\\quad\\n{\\\\cal C}\\\\Gamma_r {\\\\cal C}^{-1} = \\\\beta \\\\Gamma_r^T\\\\, .\\n\\\\end{equation}\\nHere is an example.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\algorithm{sort_spinors}{Sort Majorana spinor bilinears}\\n\\nSorts Majorana spinor bilinears using the Majorana flip property,\\nwhich for anti-commuting spinors takes the form\\n\\\\begin{equation}\\n\\\\bar\\\\psi_1 \\\\Gamma_{r_1\\\\cdots r_n}\\\\psi_2 = \\n  \\\\alpha \\\\beta^n (-)^{\\\\frac{1}{2}n(n-1)}\\\\, \\\\bar\\\\psi_1\\n  \\\\Gamma_{r_1\\\\cdots r_n}\\\\psi_2\\\\, .\\n\\\\end{equation}\\nHere $\\\\alpha$ and $\\\\beta$ determine the properties of the charge\\nconjugation matrix,\\n\\\\begin{equation}\\n{\\\\cal C}^T = \\\\alpha {\\\\cal C}\\\\,,\\\\quad\\n{\\\\cal C}\\\\Gamma_r {\\\\cal C}^{-1} = \\\\beta \\\\Gamma_r^T\\\\, .\\n\\\\end{equation}\\nHere is an example.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\bar{\\\\chi} \\\\Gamma_{m n} \\\\psi\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"{\\\\chi, \\\\psi, \\\\psi_{m}}::Spinor(dimension=10, type=MajoranaWeyl).\\n{\\\\chi, \\\\psi, \\\\psi_{m}}::AntiCommuting.\\n\\\\bar{#}::DiracBar.\\n\\\\Gamma{#}::GammaMatrix.\\n{\\\\psi_{m}, \\\\psi, \\\\chi}::SortOrder.\\nex:=\\\\bar{\\\\chi} \\\\Gamma_{m n} \\\\psi;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}-\\\\bar{\\\\psi} \\\\Gamma_{m n} \\\\chi\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"sort_spinors(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1\n}\n"
  },
  {
    "path": "core/algorithms/sort_spinors.hh",
    "content": "\n#pragma once\n\n#include \"Algorithm.hh\"\n\nnamespace cadabra {\n\n\tclass sort_spinors : public Algorithm {\n\t\tpublic:\n\t\t\tsort_spinors(const Kernel&, Ex&);\n\n\t\t\tvirtual bool     can_apply(iterator) override;\n\t\t\tvirtual result_t apply(iterator&) override;\n\n\t\t\tsibling_iterator one, gammamat, two;\n\t\t};\n\n\t}\n\n\n"
  },
  {
    "path": "core/algorithms/sort_sum.cc",
    "content": "\n#include \"properties/SortOrder.hh\"\n#include \"algorithms/sort_sum.hh\"\n\nusing namespace cadabra;\n\nsort_sum::sort_sum(const Kernel& k, Ex& e)\n\t: Algorithm(k, e)\n\t{\n\t}\n\nbool sort_sum::can_apply(iterator st)\n\t{\n\tif(*st->name==\"\\\\sum\") return true;\n\telse return false;\n\t}\n\nAlgorithm::result_t sort_sum::apply(iterator& st)\n\t{\n\t// This bubble sort is of course a disaster, but it'll have to do for now.\n\n\tresult_t ret=result_t::l_no_action;\n\tsibling_iterator one, two;\n\tunsigned int num=tr.number_of_children(st);\n\tfor(unsigned int i=1; i<num; ++i) {\n\t\tone=tr.begin(st);\n\t\ttwo=one;\n\t\t++two;\n\t\tfor(unsigned int j=i+1; j<=num; ++j) { // this loops too many times, no?\n\t\t\tint es=subtree_compare(&kernel.properties, one, two, -2, true, 0, true);\n\t\t\tif(should_swap(one, es)) {\n\t\t\t\ttr.swap(one);\n\t\t\t\tstd::swap(one,two);  // put the iterators back in order\n\t\t\t\tret=result_t::l_applied;\n\t\t\t\t}\n\t\t\t++one;\n\t\t\t++two;\n\t\t\t}\n\t\t}\n\n\treturn ret;\n\t}\n\nbool sort_sum::should_swap(iterator obj, int subtree_comparison) const\n\t{\n\tsibling_iterator one=obj, two=obj;\n\t++two;\n\n\t// Find a SortOrder property which contains both one and two.\n\tint num1, num2;\n\tconst SortOrder *so1=kernel.properties.get<SortOrder>(one,num1);\n\tconst SortOrder *so2=kernel.properties.get<SortOrder>(two,num2);\n\n\tif(so1==0 || so2==0) { // No sort order known\n\t\tif(subtree_comparison<0) return true;\n\t\treturn false;\n\t\t}\n\telse if(abs(subtree_comparison)<=1) {   // Identical up to index names\n\t\tif(subtree_comparison==-1) return true;\n\t\treturn false;\n\t\t}\n\telse {\n\t\tif(so1==so2) {\n\t\t\tif(num1>num2) return true;\n\t\t\treturn false;\n\t\t\t}\n\t\t}\n\n\treturn false;\n\t}\n\n"
  },
  {
    "path": "core/algorithms/sort_sum.cnb",
    "content": "{\n\t\"cells\" : \n\t[\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\algorithm{sort_sum}{Sort terms in a sum.}\\n\\nSort terms in a sum, taking into account any \\\\prop{SortOrder}\\nproperties, or else sorting lexographically. \"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\algorithm{sort_sum}{Sort terms in a sum.}\\n\\nSort terms in a sum, taking into account any \\\\prop{SortOrder}\\nproperties, or else sorting lexographically. \"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}E+D+A+C+B\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex:=E+D+A+C+B;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}A+B+C+D+E\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"sort_sum(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"This is often useful in case sums appear as exponents; in this case it\\nis necessary to first sort the sums before terms can be collected, as\\nthe following example shows.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"This is often useful in case sums appear as exponents; in this case it\\nis necessary to first sort the sums before terms can be collected, as\\nthe following example shows.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}a^{\\\\left(-1+d\\\\right)}-a^{\\\\left(d-1\\\\right)}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex:=a**(-1+d) - a**(d-1);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}0\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"sort_sum(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1\n}\n"
  },
  {
    "path": "core/algorithms/sort_sum.hh",
    "content": "\n#pragma once\n\n#include \"Algorithm.hh\"\n\nnamespace cadabra {\n\n\tclass sort_sum : public Algorithm {\n\t\tpublic:\n\t\t\tsort_sum(const Kernel&, Ex&);\n\n\t\t\tvirtual bool     can_apply(iterator) override;\n\t\t\tvirtual result_t apply(iterator&) override;\n\n\t\tprivate:\n\t\t\tbool should_swap(iterator obj, int subtree_comparison) const;\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/algorithms/split.cc",
    "content": "\n#include \"split.hh\"\n\nusing namespace cadabra;\n\nsplit::split(const Kernel& k, Ex& tr)\n\t: Algorithm(k, tr)\n\t{\n\t}\n\nbool split::can_apply(iterator st)\n\t{\n\treturn true;\n\t}\n\nAlgorithm::result_t split::apply(iterator& sum)\n\t{\n\tsibling_iterator sib=tr.begin(sum);\n\twhile(sib!=tr.end(sum)) {\n\t\tEx rep;\n\t\t++sib;\n\t\t}\n\n\treturn result_t::l_applied;\n\t}\n"
  },
  {
    "path": "core/algorithms/split.hh",
    "content": "\n#pragma once\n\n#include \"Algorithm.hh\"\n\nnamespace cadabra {\n\n\t/// \\ingroup algorithms\n\t///\n\t/// Split an expression into terms or factors.\n\n\n\tclass split : public Algorithm {\n\tpublic:\n\t\tsplit(const Kernel&, Ex&);\n\n\t\tvirtual bool     can_apply(iterator);\n\t\tvirtual result_t apply(iterator&);\n\t};\n\n}\n"
  },
  {
    "path": "core/algorithms/split_gamma.cc",
    "content": "\n#include \"Cleanup.hh\"\n#include \"algorithms/split_gamma.hh\"\n#include \"algorithms/join_gamma.hh\"\n\nusing namespace cadabra;\n\nsplit_gamma::split_gamma(const Kernel& k, Ex& e, bool ob)\n\t: Algorithm(k, e), on_back(ob)\n\t{\n\t}\n\nbool split_gamma::can_apply(iterator it)\n\t{\n\tif(kernel.properties.get<GammaMatrix>(it))\n\t\tif(tr.number_of_children(it)>1) {\n\t\t\treturn true;\n\t\t\t}\n\treturn false;\n\t}\n\nAlgorithm::result_t split_gamma::apply(iterator& it)\n\t{\n\t// Make a new expression which is the 'join' of the result which we want.\n\tEx work;\n\twork.set_head(str_node(\"\\\\expression\"));\n\titerator prodnode=work.append_child(work.begin(), str_node(\"\\\\prod\"));\n\titerator firstgam, secondgam;\n\tif(on_back) {\n\t\tfirstgam =work.append_child(prodnode, it);\n\t\tsecondgam=work.append_child(prodnode, *it);\n\t\t}\n\telse {\n\t\tsecondgam=work.append_child(prodnode, *it);\n\t\tfirstgam =work.append_child(prodnode, it);\n\t\t}\n\tsibling_iterator specind;\n\tif(on_back) {\n\t\tspecind=work.end(firstgam);\n\t\t--specind;\n\t\t}\n\telse specind=work.begin(firstgam);\n\twork.append_child(secondgam, (iterator)(specind));\n\twork.erase(specind);\n\n\tjoin_gamma jn(kernel, tr, true, true);\n\tconst GammaMatrix *gm1=kernel.properties.get<GammaMatrix>(it);\n\tjn.gm1=gm1;\n\tjn.apply(prodnode);\n\n\t// Replace maximally-antisymmetric gamma with the product\n\t// in which one gamma is back-split.\n\titerator maxgam=work.begin(prodnode);\n\tif(on_back) {\n\t\tspecind=work.end(maxgam);\n\t\t--specind;\n\t\t}\n\telse specind=work.begin(maxgam);\n\titerator newprod=work.insert(maxgam, str_node(\"\\\\prod\"));\n\tsibling_iterator fr=maxgam, to=fr;\n\t++to;\n\tmaxgam=work.reparent(newprod, fr, to);\n\titerator splitgam;\n\tif(on_back) splitgam=work.append_child(newprod, *maxgam);\n\telse        splitgam=work.insert(maxgam, *maxgam);\n\twork.append_child(splitgam,(iterator)(specind));\n\twork.erase(specind);\n\n\t// Flip signs on all other terms.\n\tsibling_iterator other=work.begin(prodnode);\n\t++other;\n\twhile(other!=work.end(prodnode)) {\n\t\tflip_sign(other->multiplier);\n\t\t++other;\n\t\t}\n\tit=tr.replace(it, prodnode);\n\n\tcleanup_dispatch(kernel, tr, it);\n\treturn result_t::l_applied;\n\t}\n\n"
  },
  {
    "path": "core/algorithms/split_gamma.cnb",
    "content": "{\n\t\"cells\" : \n\t[\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\algorithm{split_gamma}{Split a Dirac gamma matrix off a generalised product of gamma matrices.}\\n\\nGiven a generalised product of Dirac gamma matrices, rewrite it as a product with an \\nexplicit single gamma matrix. This is the inverse of the \\\\algo{join_gamma} algorithm.\\nAn example:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\algorithm{split_gamma}{Split a Dirac gamma matrix off a generalised product of gamma matrices.}\\n\\nGiven a generalised product of Dirac gamma matrices, rewrite it as a product with an \\nexplicit single gamma matrix. This is the inverse of the \\\\algo{join_gamma} algorithm.\\nAn example:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property GammaMatrix to~}\\\\Gamma\\\\left(\\\\#\\\\right).\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\Gamma^{m n p}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"\\\\Gamma{#}::GammaMatrix(metric=\\\\eta);\\nex:=\\\\Gamma^{m n p};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\Gamma^{m} \\\\Gamma^{n p}-\\\\Gamma^{p} \\\\eta^{m n}+\\\\Gamma^{n} \\\\eta^{m p}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"split_gamma(_, on_back=False);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1\n}\n"
  },
  {
    "path": "core/algorithms/split_gamma.hh",
    "content": "\n#pragma once\n\n#include \"Algorithm.hh\"\n#include \"properties/GammaMatrix.hh\"\n\nnamespace cadabra {\n\n\tclass split_gamma : public Algorithm {\n\t\tpublic:\n\t\t\tsplit_gamma(const Kernel&, Ex&, bool on_back);\n\n\t\t\tvirtual bool     can_apply(iterator) override;\n\t\t\tvirtual result_t apply(iterator&) override;\n\n\t\t\tbool on_back;\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/algorithms/split_index.cc",
    "content": "\n#include \"Exceptions.hh\"\n#include \"IndexClassifier.hh\"\n#include \"algorithms/split_index.hh\"\n\n// #define DEBUG 1\n\nusing namespace cadabra;\n\nsplit_index::split_index(const Kernel& k, Ex& tr, Ex& triple)\n\t: Algorithm(k, tr), part1_class(0), part2_class(0),\n\t  part1_coord(0), part2_coord(0), part1_is_number(false), part2_is_number(false)\n\t{\n\titerator top=triple.begin();\n\tif(*(top->name)!=\"\\\\comma\") {\n\t\tstd::cout << \"not comma\" << std::endl;\n\t\tthrow ArgumentException(\"split_index: Need a list of three index names.\");\n\t\t}\n\telse if(triple.number_of_children(top)!=3) {\n\t\tstd::cout << \"not 3\" << std::endl;\n\t\tthrow ArgumentException(\"split_index: Need a list of three (no more, no less) index names.\");\n\t\t}\n\n\tsibling_iterator iname=triple.begin(top);\n\tfull_class=kernel.properties.get<Indices>(iname, true);\n\t++iname;\n\tif(iname->is_integer()) {\n\t\tpart1_is_number=true;\n\t\tnum1=to_long(*(iname->multiplier));\n\t\t}\n\telse {\n\t\tpart1_class=kernel.properties.get<Indices>(iname, true);\n\t\tpart1_coord=kernel.properties.get<Coordinate>(iname, true);\n\t\tif(part1_coord) part1_coord_node=iname;\n\t\t}\n\t++iname;\n\tif(iname->is_integer()) {\n\t\tpart2_is_number=true;\n\t\tnum2=to_long(*(iname->multiplier));\n\t\t}\n\telse {\n\t\tpart2_class=kernel.properties.get<Indices>(iname, true);\n\t\tpart2_coord=kernel.properties.get<Coordinate>(iname, true);\n\t\tif(part2_coord) part2_coord_node=iname;\n\t\t}\n\tif(full_class && (part1_is_number || part1_class || part1_coord) && (part2_is_number || part2_class || part2_coord) )\n\t\treturn;\n\n\tthrow ArgumentException(\"split_index: The index types of (some of) these indices are not known.\");\n\t}\n\nbool split_index::can_apply(iterator it)\n\t{\n\tif((tr.is_head(it) && (*it->name!=\"\\\\equals\" && *it->name!=\"\\\\sum\"))) return true;\n\tif(!tr.is_head(it)) {\n\t\tif((*tr.parent(it)->name==\"\\\\equals\" && *it->name!=\"\\\\sum\") ||\n\t\t      (*tr.parent(it)->name==\"\\\\sum\") )\n\t\t\treturn true;\n\t\t}\n\n\treturn false;\n\n\t// This does not work well:\n\t//\t  return is_termlike(it);\n\t// The problem is that split_index has a very restricted applicability,\n\t// which is less than on what the core thinks is 'term-like'. Hence\n\t// the hard-coded logic above.\n\t}\n\nAlgorithm::result_t split_index::apply(iterator& it)\n\t{\n\tresult_t ret=result_t::l_no_action;\n\n\tEx rep;\n\trep.set_head(str_node(\"\\\\sum\"));\n\tEx workcopy(it); // so we can make changes without spoiling the big tree\n\t//\tassert(*it->multiplier==1); // see if this made a difference\n\n#ifdef DEBUG\n\tstd::cerr << \"split index acting at \" << it << std::endl;\n#endif\n\n\t// we only replace summed indices, so first find them.\n\tIndexClassifier ic(kernel);\n\tIndexClassifier::index_map_t ind_free, ind_dummy;\n\tic.classify_indices(workcopy.begin(), ind_free, ind_dummy);\n\t//\ttxtout << \"indices classified\" << std::endl;\n\n\tIndexClassifier::index_map_t::iterator prs=ind_dummy.begin();\n\twhile(prs!=ind_dummy.end()) {\n\t\tconst Indices *tcl=kernel.properties.get<Indices>((*prs).second, true);\n\t\tif(tcl) {\n\t\t\tif((*tcl).set_name==(*full_class).set_name) {\n\t\t\t\tEx dum1,dum2;\n\t\t\t\tif(!part1_is_number && !part1_coord)\n\t\t\t\t\tdum1=ic.get_dummy(part1_class, it);\n\t\t\t\tIndexClassifier::index_map_t::iterator current=prs;\n\t\t\t\twhile(current!=ind_dummy.end() && tree_exact_equal(&kernel.properties, (*prs).first,(*current).first,true)) {\n\t\t\t\t\tif(part1_is_number) {\n\t\t\t\t\t\tnode_integer(current->second, num1);\n\t\t\t\t\t\t//\t\t\t\t\t\t(*prs).second->name=name_set.insert(to_string(num1)).first;\n\t\t\t\t\t\t}\n\t\t\t\t\telse if(part1_coord) {\n\t\t\t\t\t\t(*current).second=tr.replace_index((*current).second, part1_coord_node, true);\n\t\t\t\t\t\t}\n\t\t\t\t\telse {\n\t\t\t\t\t\t//\t\t\t\t\t\ttxtout << \"going to replace\" << std::endl;\n\t\t\t\t\t\t(*current).second=tr.replace_index((*current).second, dum1.begin(), true);\n\t\t\t\t\t\t//\t\t\t\t\t\ttxtout << \"replaced\" << std::endl;\n\t\t\t\t\t\t}\n\t\t\t\t\t// Important: restoring (*prs).second in the line above.\n\t\t\t\t\t++current;\n\t\t\t\t\t}\n\t\t\t\trep.append_child(rep.begin(), workcopy.begin());\n\t\t\t\tcurrent=prs;\n\t\t\t\tif(!part2_is_number && !part2_coord)\n\t\t\t\t\tdum2=ic.get_dummy(part2_class, it);\n\t\t\t\twhile(current!=ind_dummy.end() && tree_exact_equal(&kernel.properties, (*prs).first,(*current).first,true)) {\n\t\t\t\t\tif(part2_is_number) {\n\t\t\t\t\t\tnode_integer(current->second, num2);\n\t\t\t\t\t\t//\t\t\t\t\t\t(*prs).second->name=name_set.insert(to_string(num2)).first;\n\t\t\t\t\t\t}\n\t\t\t\t\telse if(part2_coord) {\n\t\t\t\t\t\t(*current).second=tr.replace_index((*current).second, part2_coord_node, true);\n\t\t\t\t\t\t}\n\t\t\t\t\telse tr.replace_index((*current).second,dum2.begin(), true);\n\t\t\t\t\t++current;\n\t\t\t\t\t}\n\t\t\t\trep.append_child(rep.begin(), workcopy.begin());\n\t\t\t\t// Do not copy the multiplier; it has already been copied by cloning the original into workcopy.\n\t\t\t\t//\trep.begin()->multiplier=it->multiplier;\n\t\t\t\t//\t\t\t\ttxtout << \"cleaning up\" << std::endl;\n\t\t\t\t//\t\t\t\trep.print_recursive_treeform(txtout, rep.begin());\n\t\t\t\tit=tr.replace(it, rep.begin());\n\n\t\t\t\t// FIXME: need to cleanup nests\n\n\t\t\t\t//\t\t\t\tcleanup_nests(tr, it);\n\n\t\t\t\tret=result_t::l_applied;\n\t\t\t\tbreak;\n\t\t\t\t}\n\t\t\t}\n\t\t// skip other occurrances of this index\n\t\tIndexClassifier::index_map_t::iterator current=prs;\n\t\twhile(prs!=ind_dummy.end() && tree_exact_equal(&kernel.properties, (*prs).first,(*current).first,false))\n\t\t\t++prs;\n\t\t}\n\n\treturn ret;\n\t}\n"
  },
  {
    "path": "core/algorithms/split_index.cnb",
    "content": "{\n\t\"cells\" : \n\t[\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\algorithm{split_index}{Split the range of an index into two subsets}\\n\\nReplace a sum by a sum-of-sums, abstractly. Concretely, replaces all\\nindex contractions of a given type by a sum of two terms, each with\\nindices of a different type. Useful for Kaluza-Klein reductions and\\nthe like. An example makes this more clear:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\algorithm{split_index}{Split the range of an index into two subsets}\\n\\nReplace a sum by a sum-of-sums, abstractly. Concretely, replaces all\\nindex contractions of a given type by a sum of two terms, each with\\nindices of a different type. Useful for Kaluza-Klein reductions and\\nthe like. An example makes this more clear:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"{M,N,P,Q,R}::Indices(full).\\n{m,n,p,q,r}::Indices(space1).\\n{a,b,c,d,e}::Indices(space2).\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}A_{M p} B_{M p}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}A_{m p} B_{m p}+A_{a p} B_{a p}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex:=A_{M p} B_{M p};\\nsplit_index(_, $M,m,a$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}A_{M p} B_{M p}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}A_{m p} B_{m p}+A_{4 p} B_{4 p}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex:=A_{M p} B_{M p};\\nsplit_index(_, $M,m,4$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"Note that the two index types into which the original indices should be\\nsplit can be either symbolic (as in the first case above) or numeric\\n(as in the second case).\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"Note that the two index types into which the original indices should be\\nsplit can be either symbolic (as in the first case above) or numeric\\n(as in the second case).\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1\n}\n"
  },
  {
    "path": "core/algorithms/split_index.hh",
    "content": "\n#pragma once\n\n#include \"Algorithm.hh\"\n#include \"properties/Indices.hh\"\n#include \"properties/Coordinate.hh\"\n\nnamespace cadabra {\n\n\tclass split_index : public Algorithm {\n\t\tpublic:\n\t\t\tsplit_index(const Kernel&, Ex&, Ex&);\n\n\t\t\tvirtual bool     can_apply(iterator);\n\t\t\tvirtual result_t apply(iterator&);\n\n\t\tprivate:\n\t\t\tconst Indices *full_class, *part1_class, *part2_class;\n\t\t\tconst Coordinate *part1_coord, *part2_coord;\n\t\t\tbool     part1_is_number, part2_is_number;\n\t\t\tlong     num1, num2;\n\n\t\t\titerator part1_coord_node, part2_coord_node;\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/algorithms/substitute.cc",
    "content": "\n#include <sstream>\n#include \"Cleanup.hh\"\n#include \"Exceptions.hh\"\n#include \"Functional.hh\"\n#include \"IndexClassifier.hh\"\n#include \"algorithms/substitute.hh\"\n#include \"properties/Indices.hh\"\n\n#define DBG_MACRO_NO_WARNING \n#define DBG_MACRO_DISABLE\n#include \"dbg.h\"\n\n// #define DEBUG \"substitute.cc\"\n#include \"Debug.hh\"\n\n\nusing namespace cadabra;\n\nsubstitute::Rules substitute::replacement_rules = substitute::Rules();\nsize_t substitute::cache_hits   = 0;\nsize_t substitute::cache_misses = 0;\n\nsubstitute::substitute(const Kernel& k, Ex& tr, Ex& args_, bool partial)\n\t: Algorithm(k, tr), comparator(k.properties), args(args_), sort_product_(k, tr), partial(partial)\n\t{\n\tif(args.is_empty()) \n\t\tthrow ArgumentException(\"substitute: Replacement rule is an empty expression.\");\n\n\t// Stopwatch sw;\n\t// sw.start();\n\n\t// Check if args are present in global_rules\n\t// bool skipchecks = k.replacement_rules->is_present(args);\n\tbool skipchecks = replacement_rules.is_present(args);\n\tif(skipchecks) ++cache_hits;\n\telse           ++cache_misses;\n\n\t// std::cerr << cache_hits << \" vs \" << cache_misses << std::endl;\n\t\n\t// skip if args have already been checked\n\tif (!skipchecks) {\n\t\tcadabra::do_list(args, args.begin(), [&](Ex::iterator arrow) {\n\t\t\t//args.print_recursive_treeform(std::cerr, arrow);\n\t\t\tif(*arrow->name!=\"\\\\arrow\" && *arrow->name!=\"\\\\equals\")\n\t\t\t\tthrow ArgumentException(\"substitute: Argument is neither a replacement rule nor an equality.\");\n\n\t\t\tsibling_iterator lhs=args.begin(arrow);\n\t\t\tsibling_iterator rhs=lhs;\n\t\t\trhs.skip_children();\n\t\t\t++rhs;\n\n\t\t\tif(*lhs->name==\"\") { // replacing a sub or superscript\n\t\t\t\tlhs=tr.flatten_and_erase(lhs);\n\t\t\t\t}\n\t\t\tif(*rhs->name==\"\") { // replacing with a sub or superscript\n\t\t\t\trhs=tr.flatten_and_erase(rhs);\n\t\t\t\t}\n\n\t\t\ttry {\n\t\t\t\tif(*lhs->multiplier!=1) {\n\t\t\t\t\tthrow ArgumentException(\"substitute: No numerical pre-factors allowed on lhs of replacement rule.\");\n\t\t\t\t\t}\n\t\t\t\t// test validity of lhs and rhs\n\t\t\t\titerator lhsit=lhs, stopit=lhs;\n\t\t\t\tstopit.skip_children();\n\t\t\t\t++stopit;\n\t\t\t\twhile(lhsit!=stopit) {\n\t\t\t\t\tif(lhsit->is_object_wildcard()) {\n\t\t\t\t\t\tif(tr.number_of_children(lhsit)>0) {\n\t\t\t\t\t\t\tthrow ArgumentException(\"substitute: Object wildcards cannot have child nodes.\");\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\t}\n\t\t\t\t\t++lhsit;\n\t\t\t\t\t}\n\t\t\t\tlhsit=rhs;\n\t\t\t\tstopit=rhs;\n\t\t\t\tstopit.skip_children();\n\t\t\t\t++stopit;\n\t\t\t\twhile(lhsit!=stopit) {\n\t\t\t\t\tif(lhsit->is_object_wildcard()) {\n\t\t\t\t\t\tif(tr.number_of_children(lhsit)>0) {\n\t\t\t\t\t\t\tthrow ArgumentException(\"substitute: Object wildcards cannot have child nodes.\");\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\t}\n\t\t\t\t\t++lhsit;\n\t\t\t\t\t}\n\n\t\t\t\t// check whether there are dummies.\n\t\t\t\tIndexClassifier ic(kernel);\n\t\t\t\tIndexClassifier::index_map_t ind_free, ind_dummy;\n\t\t\t\tic.classify_indices(lhs, ind_free, ind_dummy);\n\t\t\t\tlhs_contains_dummies[arrow]= ind_dummy.size()>0;\n\t\t\t\tind_free.clear();\n\t\t\t\tind_dummy.clear();\n\t\t\t\tif(rhs!=tr.end()) {\n\t\t\t\t\tic.classify_indices(rhs, ind_free, ind_dummy);\n\t\t\t\t\trhs_contains_dummies[arrow]=ind_dummy.size()>0;\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\tcatch(std::exception& er) {\n\t\t\t\tthrow ArgumentException(std::string(\"substitute: Index error in replacement rule. \")+er.what());\n\t\t\t\t}\n\t\t\treturn true;\n\t\t\t});\n\t\treplacement_rules.store(args, lhs_contains_dummies, rhs_contains_dummies);\n\t\t}\n\telse {\n\t\treplacement_rules.retrieve(args, lhs_contains_dummies, rhs_contains_dummies);\n\t\t}\n\n\t// sw.stop();\n\t// std::cerr << \"preparation took \" << sw << std::endl;\n\t}\n\nbool substitute::can_apply(iterator st)\n\t{\n\t// std::cerr << \"attempting to match at \" << st << std::endl;\n\n\tEx::iterator found = cadabra::find_in_list(args, args.begin(), [&](Ex::iterator arrow) {\n\t\tcomparator.clear();\n\t\titerator lhs=tr.begin(arrow);\n\t\tif(*lhs->name==\"\\\\conditional\") {\n\t\t\tlhs=tr.begin(lhs);\n\t\t\tconditions=lhs;\n\t\t\tconditions.skip_children();\n\t\t\t++conditions;\n\t\t\t}\n\t\telse conditions=tr.end();\n\n\t\tif(lhs->name!=st->name && !lhs->is_object_wildcard() && !lhs->is_name_wildcard() && lhs->name->size()>0)\n\t\t\treturn args.end();\n\n\t\tEx_comparator::match_t ret;\n\t\tcomparator.lhs_contains_dummies=lhs_contains_dummies[arrow];\n\t\t// std::cerr << \"lhs_contains_dummies \" << comparator.lhs_contains_dummies << std::endl;\n\n\t\t//\tHERE: we need to have one entry point for matching, which dispatches depending\n\t\t// on whether we have a normal node, a product, a sum or a sibling range with\n\t\t// sibling wildcards. We also need a simple notation (and an exception at top\n\t\t// level for plus and prod).\n\t\t//\n\t\t//\t> ex:=A+B+C+D;\n\t\t// A + B + C + D\n\t\t// > substitute(_, $B+C -> Q$)\n\n\t\tif(*lhs->name==\"\\\\prod\")     ret=comparator.match_subproduct(tr, lhs, tr.begin(lhs), st, conditions);\n\t\telse if(*lhs->name==\"\\\\sum\") ret=comparator.match_subsum(tr, lhs, tr.begin(lhs), st, conditions);\n\t\telse {\n\t\t\tDEBUGLN( std::cerr << \"substitute::can_apply: testing \" << lhs << \" against \" << st << std::endl; );\n\t\t\tret=comparator.match_subtree(tr, lhs, st, conditions);\n\t\t\t}\n\n\t\tif(ret == Ex_comparator::match_t::subtree_match ||\n\t\t\tret == Ex_comparator::match_t::match_index_less ||\n\t\t\tret == Ex_comparator::match_t::match_index_greater) {\n\t\t\tuse_rule=arrow;\n\n\t\t\t// If we are not matching a partial sum or partial product, need to check that all\n\t\t\t// terms or factors are accounted for.\n\t\t\tif(!partial) {\n\t\t\t\tif(*lhs->name==\"\\\\prod\") {\n\t\t\t\t\tif(*st->name!=\"\\\\prod\")\n\t\t\t\t\t\treturn args.end();\n\t\t\t\t\t\n\t\t\t\t\tDEBUGLN(std::cerr << \"substitute::can_apply: partial=false, so \" \n\t\t\t\t\t\t\t  << comparator.factor_locations.size()\n\t\t\t\t\t\t\t  << \" has to equal \"\n\t\t\t\t\t\t\t  << tr.number_of_children(st) << std::endl;)\n\t\t\t\t\tif(comparator.factor_locations.size()!=tr.number_of_children(st))\n\t\t\t\t\t\treturn args.end();\n\t\t\t\t\t}\n\t\t\t\telse {\n\t\t\t\t\t// If lhs is not a product, then we need to check that the node in the\n\t\t\t\t\t// expression we act on does not sit inside a product (and hence has\n\t\t\t\t\t// more factors).\n\t\t\t\t\tif(tr.is_head(st) || (*tr.parent(st)->name)!=\"\\\\prod\")\n\t\t\t\t\t\treturn arrow;\n\t\t\t\t\telse\n\t\t\t\t\t\treturn args.end();\n\t\t\t\t\t}\n\t\t\t\t}\n\n\t\t\treturn arrow;\n\t\t\t}\n\n\t\treturn args.end();\n\t\t});\n\t//\tif(found!=args.end())\n\t//\t\tstd::cerr << \"rule working: \" << Ex(found) << std::endl;\n\t//\telse\n\t//\t\tstd::cerr << \"rule not working, going to return \" << (found!=args.end()) << std::endl;\n\n\treturn found!=args.end();\n\t}\n\nAlgorithm::result_t substitute::apply(iterator& st)\n\t{\n\tDEBUGLN( std::cerr << \"substitute::apply at \" << Ex(st) << std::endl; )\n\n//\tdbg(comparator.replacement_map);\n//\tfor(auto& rule: comparator.replacement_map)\n//\t\tstd::cerr << \"* \" << rule.first << \" -> \" << rule.second << std::endl;\n\n\tsibling_iterator arrow=use_rule;\n\titerator lhs=tr.begin(arrow);\n\titerator rhs=lhs;\n\trhs.skip_children();\n\t++rhs;\n\tif(*lhs->name==\"\\\\conditional\")\n\t\tlhs=tr.begin(lhs);\n\n\t// We construct a new tree 'repl' which is a copy of the rhs of the\n\t// replacement rule, and then replace nodes and subtrees in there\n\t// based on how the pattern matching went.\n\tEx repl(rhs);\n\tIndexClassifier ic(kernel);\n\tIndexClassifier::index_map_t ind_free, ind_dummy, ind_forced;\n\n\tif(rhs_contains_dummies[use_rule]) {\n\t\tic.classify_indices(repl.begin(), ind_free, ind_dummy);\n\t\t//std::cerr << \"rhs contains dummies \" << ind_dummy.size() << std::endl;\n\t\t}\n\telse {\n\t\t//std::cerr << \"rhs does not contain dummies\" << std::endl;\n\t\t}\n\n\t// Stage 1: Replace all patterns on the rhs of the rule with the\n\t// objects they matched.\n\t\n\t// Keep track of all indices which _have_ to stay what they are, in ind_forced.\n\t// Keep track of insertion points of subtrees.\n\t// NOTE: this does not yet insert the replacement into the main tree!\n\n\titerator it=repl.begin();\n\tEx_comparator::replacement_map_t::iterator loc;\n\tEx_comparator::subtree_replacement_map_t::iterator sloc;\n\tstd::vector<iterator> subtree_insertion_points;\n\twhile(it!=repl.end()) {\n\t\tbool is_stripped=false;\n\n\t\t// For some reason 'a?' is not found!?! Well, that's presumably because _{a?} does not\n\t\t// match ^{a?}. (though this does match when we write 'i' instead of a?.\n\n\t\tloc=comparator.replacement_map.find(Ex(it));\n\t\tif(loc==comparator.replacement_map.end() && it->is_name_wildcard() && tr.number_of_children(it)!=0) {\n\t\t\tEx tmp(it);\n\t\t\ttmp.erase_children(tmp.begin());\n\t\t\tloc=comparator.replacement_map.find(tmp);\n\t\t\tis_stripped=true;\n\t\t\t}\n\n\t\t//std::cerr << \"consider element of repl \" << Ex(it) << std::endl;\n\n\t\tif(loc!=comparator.replacement_map.end()) { // name wildcards\n\t\t\tDEBUGLN( std::cerr << \"wildcard replaced: \" << loc->first << \" -> \" << loc->second << std::endl; )\n\n\t\t\t// When a replacement is made here, and the index is actually\n\t\t\t// a dummy in the replacement, we screw up the ind_dummy\n\t\t\t// map. Then, at the next step, when conflicting dummies are\n\t\t\t// relabelled, things go wrong.  Solution: in this case, the\n\t\t\t// index under consideration should be taken out of ind_dummy.\n\t\t\t// This is easy, because we can just throw out all indices\n\t\t\t// with the original name.\n\n\t\t\tind_dummy.erase(Ex(it));\n\n\t\t\tstr_node::bracket_t remember_br=it->fl.bracket;\n\t\t\tif(is_stripped || (it->is_name_wildcard() && !it->is_index()) ) {\n\t\t\t\t// a?_{i j k} type patterns should only replace the head\n\t\t\t\t// TODO: should we replace brackets here too?\n\t\t\t\tDEBUGLN( std::cerr << \"stripped replacing \" << it\n\t\t\t\t\t\t\t<< \" with \" << (*loc).second.begin() << \" * \" << *it->multiplier << std::endl; );\n\t\t\t\tit->name=(*loc).second.begin()->name;\n\t\t\t\t// See the comment below about multipliers.\n\t\t\t\tmultiply(it->multiplier, *(*loc).second.begin()->multiplier);\n\t\t\t\tit->fl=(*loc).second.begin()->fl;\n\t\t\t\t}\n\t\t\telse {\n\t\t\t\t// Consider \"A? -> 3 A?\". If \"A?\" matches \"2 C\", then the replacement\n\t\t\t\t// map will contain \"A? mapsto 2 C\". The rhs of the rule contains\n\t\t\t\t// \"3 A?\" which should be changed to \"3*2 C\". After that, this \"6 C\"\n\t\t\t\t// will get inserted into the tree in Stage 2 below.\n\t\t\t\tmultiplier_t mt=*it->multiplier;\n\t\t\t\tDEBUGLN( std::cerr << \"replacing \" << it\n\t\t\t\t\t\t\t<< \" with \" << (*loc).second.begin() << \" * \" << mt << std::endl; );\n\t\t\t\tit=tr.replace_index(it, (*loc).second.begin()); //, true);\n\t\t\t\tmultiply(it->multiplier, mt);\n\t\t\t\t}\n\t\t\tit->fl.bracket=remember_br;\n\t\t\tif(rhs_contains_dummies[use_rule])\n\t\t\t\tind_forced.insert(IndexClassifier::index_map_t::value_type(Ex(it), it));\n\t\t\t++it;\n\n\t\t\t}\n\t\telse if( (sloc=comparator.subtree_replacement_map.find(it->name))\n\t\t         !=comparator.subtree_replacement_map.end()) { // object wildcards\n\t\t\t//std::cerr << \"srule : \" << Ex(it) << std::endl;\n\t\t\tmultiplier_t tmpmult=*it->multiplier; // remember target multiplier\n\t\t\titerator tmp= tr.insert_subtree(it, (*sloc).second);\n\n\t\t\tDEBUGLN( std::cerr << \"subtree replaced: \" << repl << std::endl; );\n\t\t\t\n\t\t\ttmp->fl.bracket=it->fl.bracket;\n\t\t\ttmp->fl.parent_rel=it->fl.parent_rel; // ok?\n\t\t\tit=tr.erase(it);\n\t\t\tmultiply(tmp->multiplier, tmpmult);\n\t\t\t\n\t\t\tDEBUGLN( std::cerr << \"subtree replaced 2: \" << repl << std::endl; );\n\n\t\t\tsubtree_insertion_points.push_back(tmp);\n\t\t\tIndexClassifier::index_map_t ind_subtree_free, ind_subtree_dummy;\n\t\t\t// FIXME: as in the name wildcard case above, we only need these\n\t\t\t// next three lines if there are wildcards in the rhs.\n\t\t\tic.classify_indices(tmp, ind_subtree_free, ind_subtree_dummy);\n\t\t\tind_forced.insert(ind_subtree_free.begin(), ind_subtree_free.end());\n\t\t\tind_forced.insert(ind_subtree_dummy.begin(), ind_subtree_dummy.end());\n\t\t\t}\n\t\telse ++it;\n\t\t}\n\n\t// If the replacement contains dummies, avoid clashes introduced when\n\t// free indices in the replacement (induced from the original expression)\n\t// take values already used for the dummies.\n\t//\n\t// Note: the dummies which clash with other factors in a product are\n\t// not replaced here, but rather in the next step.\n\t// std::cerr << ind_dummy.size() << std::endl;\n\tif(ind_dummy.size()>0) {\n\n\t\tDEBUGLN( std::cerr << \"avoid dummy clashes\" << std::endl; );\n\n\t\tIndexClassifier::index_map_t must_be_empty;\n\t\tic.determine_intersection(ind_forced, ind_dummy, must_be_empty);\n\t\tIndexClassifier::index_map_t::iterator indit=must_be_empty.begin();\n\t\tIndexClassifier::index_map_t added_dummies;\n\t\t// std::cerr << must_be_empty.size() << \" dummies have to be relabelled\" << std::endl;\n\t\twhile(indit!=must_be_empty.end()) {\n\t\t\tEx the_key=indit->first;\n\t\t\tconst Indices *dums=kernel.properties.get<Indices>(indit->second, true);\n\t\t\tif(dums==0) {\n\t\t\t\tstd::ostringstream str;\n\t\t\t\tstr << \"Need to know an index set for \" << Ex(*indit->second) << \".\";\n\t\t\t\tthrow ConsistencyException(str.str());\n\t\t\t\t}\n\t\t\tEx relabel=ic.get_dummy(dums, &ind_dummy, &ind_forced, &added_dummies);\n\t\t\tadded_dummies.insert(IndexClassifier::index_map_t::value_type(relabel,(*indit).second));\n\t\t\tdo {\n\t\t\t\t// std::cerr << \"replace index \" << *(indit->second->name) << \" with \" << *(relabel.begin()->name) << std::endl;\n\t\t\t\ttr.replace_index(indit->second,relabel.begin(), true);\n\t\t\t\t++indit;\n\t\t\t\t//\t\t\t\ttxtout << *(indit->first.begin()->name) << \" vs \" << *(the_key.begin()->name) << std::endl;\n\t\t\t\t}\n\t\t\twhile(indit!=must_be_empty.end() && tree_exact_equal(&kernel.properties, indit->first,the_key,-1));\n\t\t\t}\n\t\t}\n\n\t// After all replacements have been done, we need to cleanup the\n\t// replacement tree.\n\n\tDEBUGLN( std::cerr << \"replacement before cleanup:\\n\" << repl << std::endl; );\n\t\n\tcleanup_dispatch_deep(kernel, repl);\n\n\tDEBUGLN( std::cerr << \"after cleanup:\\n\" << repl << std::endl; );\n\n\n\t// Stage 2: Now we can insert the right-hand side of the rule into\n\t// the original tree.\n\n\trepl.begin()->fl.bracket=st->fl.bracket;\n\tbool rename_replacement_dummies_called=false;\n\n\t// Now we do the actual replacement, putting the \"repl\" in the tree.\n\t// If the to-be-replaced object sits in a product, we have to relabel all\n\t// dummy indices in the replacement which clash with indices in other factors\n\t// in the product.\n\tif(*lhs->name==\"\\\\prod\") {\n\t\tfor(unsigned int i=1; i<comparator.factor_locations.size(); ++i)\n\t\t\ttr.erase(comparator.factor_locations[i]);\n\n\t\t// no need to keep repl\n\t\titerator newtr=tr.move_ontop(iterator(comparator.factor_locations[0]),repl.begin());\n\t\tmultiply(st->multiplier, *newtr->multiplier);\n\t\tone(newtr->multiplier);\n\t\tif(ind_dummy.size()>0) {\n\t\t\trename_replacement_dummies(newtr); // do NOW, otherwise the replacement cannot be isolated anymore\n\t\t\trename_replacement_dummies_called=true;\n\t\t\t}\n\t\tif(*rhs->name==\"\\\\prod\" && *newtr->name==\"\\\\prod\") {\n\t\t\ttr.flatten(newtr);\n\t\t\ttr.erase(newtr);\n\t\t\t}\n\t\tif(tr.number_of_children(st)==1) {\n\t\t\tmultiply(tr.begin(st)->multiplier, *st->multiplier);\n\t\t\ttr.flatten(st);\n\t\t\tst=tr.erase(st);\n\t\t\t}\n\t\t}\n\telse if(*lhs->name==\"\\\\sum\") {\n\t\tfor(unsigned int i=1; i<comparator.factor_locations.size(); ++i)\n\t\t\ttr.erase(comparator.factor_locations[i]);\n\n\t\tdivide(repl.begin()->multiplier, comparator.term_ratio);\n\n\t\t// no need to keep repl\n\t\titerator newtr=tr.move_ontop(iterator(comparator.factor_locations[0]),repl.begin());\n\t\t//\t\tmultiply(st->multiplier, *newtr->multiplier);\n\t\t//\t\tone(newtr->multiplier);\n\t\tif(ind_dummy.size()>0) {\n\t\t\trename_replacement_dummies(newtr); // do NOW, otherwise the replacement cannot be isolated anymore\n\t\t\trename_replacement_dummies_called=true;\n\t\t\t}\n\n\t\t}\n\telse {\n\t\tDEBUGLN( std::cerr << \"move \" << repl << \" on top of \" << st << std::endl; );\n\n\t\tif(!lhs->is_name_wildcard()\n\t\t\t&& !lhs->is_range_wildcard()\n\t\t\t&& !lhs->is_siblings_wildcard()\n\t\t\t&& !lhs->is_autodeclare_wildcard()\n\t\t\t&& !lhs->is_object_wildcard())\n\t\t\tmultiply(repl.begin()->multiplier, *st->multiplier);\n\t\t\n\t\tauto keep_parent_rel=st->fl.parent_rel;\n\t\tst=tr.move_ontop(st, repl.begin()); // no need to keep the original repl tree\n\t\tst->fl.parent_rel=keep_parent_rel;\n\t\t}\n\n\tif(ind_dummy.size()>0 && !rename_replacement_dummies_called)\n\t\trename_replacement_dummies(st);\n\n\t// The replacement is done now.  What is left is to take into\n\t// account any signs caused by moving factors through each other\n\tint totsign=1;\n\tfor(unsigned int i=0; i<comparator.factor_moving_signs.size(); ++i) {\n\t\ttotsign*=comparator.factor_moving_signs[i];\n\t\tdbg(i);\n\t\tdbg(comparator.factor_moving_signs[i]);\n\t\t}\n\tmultiply(st->multiplier, totsign);\n\n\t//\t// Get rid of numerical '1' factors inside products (this will not clean up\n\t//\t// '1's from a 'q -> 1' type replacement, since in this case 'st' points to the 'q'\n\t//   // node and we are not allowed to touch the tree above the entry point; these\n\t//\t// things are taken care of by the algorithm class itself).\n\t//\t// FIXME: still needed?\n\t//\tcleanup_dispatch(kernel, tr, st);\n\n\tDEBUGLN( std::cerr << tr << std::endl; );\n\n\tdbg(tr.begin());\n\tdbg(subtree_insertion_points.size());\n\n\t// Cleanup nests on all insertion points and on the top node.\n//\tfor(unsigned int i=0; i<subtree_insertion_points.size(); ++i) {\n//\t\titerator ip=subtree_insertion_points[i];\n//\t\t//std::cerr << *ip->name << std::endl;\n//\t\tcleanup_dispatch(kernel, tr, ip);\n//\t\t}\n//\n\tcleanup_dispatch(kernel, tr, st);\n\n\tdbg(\"complete\");\n\n\treturn result_t::l_applied;\n\t}\n\n\nsize_t substitute::cache_size()\n\t{\n\treturn replacement_rules.size();\n\t}\n\nvoid substitute::Rules::store(Ex& rules,\n\t\t\t\t\t\t\t\tstd::map<iterator, bool>& lhs_contains_dummies,\n\t\t\t\t\t\t\t\tstd::map<iterator, bool>& rhs_contains_dummies)\n\t{\n\ttry {\n\t\t// if number of stored rules has grown large, clean them up.\n\t\tif (properties.size() >= cleanup_threshold) {\n\t\t\tcleanup();\n\t\t\t}\n\t\t// If that didn't fix it, double the cleanup_threshold up to max_size\n\t\tif (cleanup_threshold != max_size && properties.size() >= cleanup_threshold) {\n\t\t\tif (cleanup_threshold * 2 < max_size) {\n\t\t\t\tcleanup_threshold *= 2;\n\t\t\t\t} \n\t\t\telse {\n\t\t\t\tcleanup_threshold = max_size;\n\t\t\t\t}\n\t\t\t}\n\n\t\tstd::weak_ptr<Ex> rules_ptr = rules.shared_from_this();\n\t\t// properties[rules_ptr] = { lhs_contains_dummies, rhs_contains_dummies };'\n\t\tproperties.insert(rules_ptr, { lhs_contains_dummies, rhs_contains_dummies });\n\t\t// Mark this expression as cached; any change will remove that state\n\t\t// and ensure that we do not use the cached expression later.\n\t\trules.update_state(result_t::l_cached);\n\t\t}\n\tcatch(const std::bad_weak_ptr& error) {\n\t\treturn;\n\t\t}\n\t}\n\nvoid substitute::Rules::retrieve(Ex& rules,\n\t\t\t\t\t\t\t\tstd::map<iterator, bool>& lhs_contains_dummies,\n\t\t\t\t\t\t\t\tstd::map<iterator, bool>& rhs_contains_dummies) const\n\t{\n\t// Rules::present is assumed to have been called to check that the rules are valid\n\tstd::weak_ptr<Ex> rules_ptr = rules.shared_from_this();\n\tlhs_contains_dummies = properties.at(rules_ptr).first;\n\trhs_contains_dummies = properties.at(rules_ptr).second;\n\t}\n\n\nbool substitute::Rules::is_present(Ex& rules) const\n\t{\n\t// Look to see if the rules are present in the map\n\t\n\ttry {\n\t\tstd::weak_ptr<Ex> rules_ptr = rules.shared_from_this();\n\t\tauto rule_it = properties.find(rules_ptr);\n\t\tbool rule_found = (rule_it != properties.end());\n\t\tif (!rule_found) return false;\n\t\t\n\t\t// rules should have l_cached set\n\t\tbool rule_unchanged = (rules.state() == result_t::l_cached);\n\t\t\n\t\t// If rule has been changed, erase it.\n\t\tif (!rule_unchanged) {\n\t\t\tproperties.erase(rule_it);\n\t\t\treturn false;\n\t\t\t} \n\t\telse {\n\t\t\treturn true;\n\t\t\t}\n\t\t}\n\tcatch(const std::bad_weak_ptr& error) {\n\t\treturn false;\n\t\t}\n\t}\n\nsize_t substitute::Rules::size() const\n\t{\n\treturn properties.size();\n\t}\n\nvoid substitute::Rules::cleanup()\n\t{\n\t// Erase rules that are pointing to garbage-collected Ex expressions\n\t// or rules that have possibly been changed.\n\tfor (auto it = properties.begin(); it != properties.end(); ) {\n\t\tif (it->first.expired()) {\n\t\t\tit = properties.erase(it);\n\t\t\t} \n\t\telse if (it->first.lock()->state() != result_t::l_cached) {\n\t\t\tit = properties.erase(it);\n\t\t\t}\n\t\telse {\n\t\t\t++it;\n\t\t\t}\n\t\t}\n\t}\n"
  },
  {
    "path": "core/algorithms/substitute.cnb",
    "content": "{\n\t\"cells\" : \n\t[\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\algorithm{substitute}{Generic substitution algorithm.}\\n\\n Generic substitution algorithm.\\nTakes a rule or a set of rules according to which an expression\\nshould be modified. If more than one rule is given, it tries each rule\\nin turn, until the first working one is encountered, after which it\\ncontinues with the next node.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\algorithm{substitute}{Generic substitution algorithm.}\\n\\n Generic substitution algorithm.\\nTakes a rule or a set of rules according to which an expression\\nshould be modified. If more than one rule is given, it tries each rule\\nin turn, until the first working one is encountered, after which it\\ncontinues with the next node.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}G_{\\\\mu \\\\nu \\\\rho}+F_{\\\\mu \\\\nu \\\\rho}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}G_{\\\\mu \\\\nu \\\\rho}+A_{\\\\mu \\\\nu} B_{\\\\rho}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex:=G_{\\\\mu \\\\nu \\\\rho} + F_{\\\\mu \\\\nu \\\\rho};\\nsubstitute(_,  $F_{\\\\mu \\\\nu \\\\rho} -> A_{\\\\mu \\\\nu} B_{\\\\rho}$ );\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}A_{\\\\mu \\\\nu} B_{\\\\nu \\\\rho} C_{\\\\rho \\\\sigma}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}D_{\\\\mu \\\\sigma} B_{\\\\nu \\\\rho}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex:= A_{\\\\mu \\\\nu} B_{\\\\nu \\\\rho} C_{\\\\rho \\\\sigma};\\nsubstitute(_, $A_{m n} C_{p q} -> D_{m q}$ );\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"This command takes full care of dummy index relabelling, as the\\nfollowing example shows:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"This command takes full care of dummy index relabelling, as the\\nfollowing example shows:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}a_{m} b_{n}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"{m,n,q,r,s,t,u}::Indices(vector).\\nex:= a_{m} b_{n};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}c_{q r} d_{q r m} b_{n}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"substitute(_, $a_{q} -> c_{m n} d_{m n q}$ );\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"By postfixing a name with a question mark, it becomes a pattern. You do not need this for indices (as the examples\\nabove show) but it is necessary for other types of function arguments.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"By postfixing a name with a question mark, it becomes a pattern. You do not need this for indices (as the examples\\nabove show) but it is necessary for other types of function arguments.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\sin{x}^{2}+3+\\\\cos{x}^{2}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}4\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex:= \\\\sin{ x }**2 + 3 + \\\\cos{ x }**2;\\nsubstitute(ex, $\\\\sin{A?}**2 + \\\\cos{A?}**2 = 1$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"Substitute can match sub-products and sub-sums, and you do not have to specify terms or factors in the order in which they appear,\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"Substitute can match sub-products and sub-sums, and you do not have to specify terms or factors in the order in which they appear,\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"A + B + C + D\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}A+B+C+D\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"Q + B + D\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}Q+B+D\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex:= A + B + C + D;\\nsubstitute(_, $A+C=Q$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"A B C D\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}A B C D\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"A Q C\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}A Q C\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex:= A B C D;\\nsubstitute(_, $B D = Q$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"However, you can request that the match is for the full sum or product, \"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"However, you can request that the match is for the full sum or product, \"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"A B C D + A B C D E F\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}A B C D+A B C D E F\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"1 + A B C D E F\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}1+A B C D E F\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex:= A B C D  + A B C D E F;\\nsubstitute(_, $A B C D = 1$, partial=False);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"It will respect non-commuting objects and will not match if that would require moving non-commuting objects through each other,\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"It will respect non-commuting objects and will not match if that would require moving non-commuting objects through each other,\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property NonCommuting to~}\\\\left[Q,~\\\\discretionary{}{}{} R,~\\\\discretionary{}{}{} S,~\\\\discretionary{}{}{} T\\\\right].\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"Q R S T\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}Q R S T\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"Q R S T\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}Q R S T\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"{Q,R,S,T}::NonCommuting;\\nex:= Q R S T;\\nsubstitute(_, $S Q = 1$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1\n}\n"
  },
  {
    "path": "core/algorithms/substitute.hh",
    "content": "\n#pragma once\n\n#include \"Algorithm.hh\"\n#include \"algorithms/sort_product.hh\"\n#include \"lru_cache.hh\"\n\nnamespace cadabra {\n\n\t/// \\ingroup algorithms\n\t///\n\t/// Generic substitution algorithm.\n\n\tclass substitute : public Algorithm {\n\t\tpublic:\n\t\t\tsubstitute(const Kernel&, Ex& tr, Ex& args, bool partial=true);\n\n\t\t\t/// Match the lhs of the replacement rule to the subtree 'st' under consideration.\n\t\t\t/// This will fill the replacement_map giving a map from objects appearing in the\n\t\t\t/// _rule_ to what they matched to.\n\t\t\t///\n\t\t\t/// For F_{m n} -> G_{m n}, position-free indices and the\n\t\t\t/// expression F^{m n}, we would get a replacement map\n\t\t\t///\n\t\t\t///      _m  -> ^m\n\t\t\t///      _n  -> ^n\n\t\t\t///\n\t\t\t/// (Note how it is important that despite these indices being position-free,\n\t\t\t/// the rules in the replacement map do not ignore sub/superscript information).\n\t\t\t/// In the apply member, we then replace all of 'st' with the rhs of the rule,\n\t\t\t/// and scan through the rule (with a basic replacement_map.find based on\n\t\t\t/// simple tree comparison logic, not pattern matching) for replacements to be made.\n\n\t\t\tvirtual bool     can_apply(iterator st);\n\n\t\t\tvirtual result_t apply(iterator&);\n\n\t\t\tEx_comparator comparator;\n\n\t\t\t/// Return the number of substitution rules which have been\n\t\t\t/// pre-processed and sit in the cache.\n\t\t\tstatic size_t cache_size();\n\n\t\tprivate:\n\t\t\tEx&     args;\n\n\t\t\titerator      use_rule;\n\t\t\titerator      conditions;\n\n\t\t\tstd::map<iterator, bool> lhs_contains_dummies, rhs_contains_dummies;\n\n\t\t\t// For object swap testing routines:\n\t\t\tsort_product    sort_product_;\n\t\t\tbool            partial;\n\t\t\t\n\t\t\t// Rules is a class for caching properties of substitution\n\t\t\t// rules to avoid processing them in subsequent calls.\n\n\t\t\tclass Rules {\n\n\t\t\t\tpublic:\n\t\t\t\t\tRules(size_t max_size_=1000, size_t cleanup_threshold_=100) \n\t\t\t\t\t\t: properties(max_size_), max_size(max_size_), cleanup_threshold(cleanup_threshold_) {}\n\n\t\t\t\t\t// Associate rule properties with a specific object\n\t\t\t\t\tvoid store(Ex& rules,\n\t\t\t\t\t\t\t\t  std::map<iterator, bool>& lhs_contains_dummies,\n\t\t\t\t\t\t\t\t  std::map<iterator, bool>& rhs_contains_dummies);\n\t\t\t\t\t\n\t\t\t\t\t// Check if rules are present\n\t\t\t\t\tbool is_present(Ex& rules) const;\n\t\t\t\t\t\n\t\t\t\t\t// Retrieve properties from rules\n\t\t\t\t\tvoid retrieve(Ex& rules,\n\t\t\t\t\t\t\t\t\t  std::map<iterator, bool>& lhs_contains_dummies,\n\t\t\t\t\t\t\t\t\t  std::map<iterator, bool>& rhs_contains_dummies) const;\n\t\t\t\t\t\n\t\t\t\t\t// Count number of rules\n\t\t\t\t\tsize_t size() const;\n\t\t\t\t\t\n\t\t\t\t\t// Eliminate rules that are expired\n\t\t\t\t\tvoid cleanup();\n\n\t\t\t\tprivate:\n\t\t\t\t\t// Map storing weak pointers to `Ex` and pairs of lhs/rhs maps as values\n\t\t\t\t\tmutable LRUcache<std::weak_ptr<Ex>, \n\t\t\t\t\t\t\t\t\t\tstd::pair< std::map<iterator, bool>, std::map<iterator, bool> >,\n\t\t\t\t\t\t\t\t\t\tstd::owner_less<std::weak_ptr<Ex>>\n\t\t\t\t\t\t\t\t\t\t> properties;\n\t\t\t\t\t// Max size of the rules list\n\t\t\t\t\tsize_t max_size;\n\t\t\t\t\t// Initial size threshold to trigger cleanup_rules\n\t\t\t\t\tsize_t cleanup_threshold;\n\n\n\t\t\t\t};\n\n\t\t\t// Shared instance of all replacement rules.\n\t\t\tstatic Rules    replacement_rules;\n\t\t\tstatic size_t   cache_hits, cache_misses;\n\t\t\t\n\t};\n\n\n\t}\n\n\n"
  },
  {
    "path": "core/algorithms/sumflatten.tex",
    "content": "\\cdbalgorithm{sumflatten}{}\n\nRemoves brackets in a sum, that is, makes changes of the type\n\\begin{equation}\na+(b+c) \\rightarrow a+b+c\\, .\n\\end{equation}\nIn terms of code this reads\n\\begin{screen}{1,2}\na + (b + c);\n@sumflatten!(%);\na + b + c;\n\\end{screen}\nThe above is sometimes required because it is possible to write and\nkeep nested sums with brackets, like in the example above, in order to\nimprove readability of expressions.  \n\n\\cdbseealgo{prodflatten}\n\\cdbseealgo{listflatten}\n\\cdbseealgo{distribute}\n"
  },
  {
    "path": "core/algorithms/sym.cc",
    "content": "\n#include \"Exceptions.hh\"\n#include \"algorithms/sym.hh\"\n\nusing namespace cadabra;\n\n// #define DEBUG 1\n\nsym::sym(const Kernel& k, Ex& tr, const std::vector<unsigned int>& slots, bool s)\n\t: Algorithm(k, tr), sign(s), slotloc(slots)\n\t{\n#ifdef DEBUG\n\tstd::cerr << \"sym::sym: initialised with slot positions.\" << std::endl;\n#endif\n\t}\n\nsym::sym(const Kernel& k, Ex& tr, Ex& objs, bool s)\n\t: Algorithm(k, tr), objects(objs), sign(s)\n\t{\n\tif(objects.size()==0)\n\t\tthrow ArgumentException(\"sym/asym: need a list of objects over which to (anti)symmetrise.\");\n\t}\n\nbool sym::can_apply(iterator it)\n\t{\n\tif(*it->name!=\"\\\\prod\")\n\t\tif(!is_single_term(it))\n\t\t\treturn false;\n\n\tprod_wrap_single_term(it);\n\tbool located=false;\n\tif(objects.size()>0) {\n#ifdef DEBUG\n\t\tstd::cerr << \"sym::can_apply: finding objects\" << std::endl;\n#endif\n\t\targloc_2_treeloc.clear();\n\t\tlocated=locate_object_set(objects, tr.begin(it), tr.end(it), argloc_2_treeloc);\n\t\t}\n\telse {\n#ifdef DEBUG\n\t\tstd::cerr << \"sym::can_apply: collecting objects\" << std::endl;\n#endif\n\t\tobjects.set_head(str_node(\"\\\\comma\"));\n\t\targloc_2_treeloc.clear();\n\t\targloc_2_treeloc.resize(slotloc.size(), 0);\n\t\tfor(size_t i=0; i<slotloc.size(); ++i) {\n\t\t\tauto ind=begin_index(it);\n\t\t\tind+=slotloc[i];\n\t\t\tif(tr.is_valid(ind)==false) {\n\t\t\t\tthrow ArgumentException(\"Expression does not have at least \"+std::to_string(slotloc[i]+1)+\" indices.\");\n\t\t\t\t}\n#ifdef DEBUG\n\t\t\tstd::cerr << \"sym::can_apply: adding \" << ind << std::endl;\n#endif\n\t\t\tobjects.append_child(objects.begin(), Ex::iterator(ind));\n\n\t\t\t// Convert the index-index to iterator-index (the former says how many times\n\t\t\t// an IndexIterator should be incremented, the latter says how many times a\n\t\t\t// generic Iterator should be incremented).\n\t\t\titerator steps=tr.begin(it);\n\t\t\twhile(steps!=iterator(ind)) {\n\t\t\t\t++steps;\n\t\t\t\t++argloc_2_treeloc[i];\n\t\t\t\t}\n\t\t\t}\n\t\tlocated=true;\n\t\t}\n\tprod_unwrap_single_term(it);\n#ifdef DEBUG\n\tstd::cerr << \"sym::can_apply: ready to go: \" << located << std::endl;\n#endif\n\treturn located;\n\t}\n\nAlgorithm::result_t sym::apply(iterator& it)\n\t{\n#ifdef DEBUG\n\tstd::cerr << \"sym::apply: running\" << std::endl;\n#endif\n\n\tprod_wrap_single_term(it);\n\tresult_t res=doit(it,sign);\n\t//\tif(res==result_t::l_applied)\n\t//\t\tit=tr.parent(st);\n\n\t//IS DOIT not doing that right?\n\n\treturn res;\n\t}\n\nAlgorithm::result_t sym::doit(iterator& it, bool sign)\n\t{\n\tassert(*it->name==\"\\\\prod\");\n\n#ifdef DEBUG\n\tstd::cerr << \"sym::doit: \" << objects << std::endl;\n#endif\n\t\n\t// Setup combinations class. First construct original and block length.\n\tsibling_iterator fst=objects.begin(objects.begin());\n\tsibling_iterator fnd=objects.end(objects.begin());\n\traw_ints.clear();\n\traw_ints.block_length=0;\n\n\tfor(unsigned int i=0; i<argloc_2_treeloc.size(); ++i)\n\t\traw_ints.original.push_back(i);\n\twhile(fst!=fnd) {\n#ifdef DEBUG\n\t\tstd::cerr << \"sym::doit: object \" << *fst->name\t<< std::endl;\n#endif\n\t\tif(*(fst->name)==\"\\\\comma\") {\n\t\t\tif(raw_ints.block_length==0) raw_ints.block_length=tr.number_of_children(fst);\n\t\t\telse                         assert(raw_ints.block_length==tr.number_of_children(fst));\n\t\t\t}\n\t\telse if(fst->name->size()>0 || (fst->name->size()==0 && tr.number_of_children(fst)==1)) {\n\t\t\tif(raw_ints.block_length==0) raw_ints.block_length=1;\n\t\t\telse                         assert(raw_ints.block_length==1);\n\t\t\t}\n\t\t++fst;\n\t\t}\n\tlong start_=-1, end_=-1;\n\n\n\t// FIXME: what was this v1 feature supposed to do?\n\t//\n\t//\tsibling_iterator other_args=args_begin();\n\t//\t++other_args;\n\t//\twhile(other_args!=args_end()) {\n\t//\t\tif(*(other_args->name)==\"\\\\setoption\") {\n\t//\t\t\tif(*tr.child(other_args,0)->name==\"Start\")\n\t//\t\t\t\tstart_=to_long(*tr.child(other_args,1)->multiplier);\n\t//\t\t\telse if(*tr.child(other_args,0)->name==\"End\")\n\t//\t\t\t\tend_=to_long(*tr.child(other_args,1)->multiplier);\n\t//\t\t\t}\n\t//\t\t++other_args;\n\t//\t\t}\n\n\traw_ints.set_unit_sublengths();\n\t// Sort within the blocks, if any\n\tif(raw_ints.block_length!=1) {\n\t\tstd::vector<unsigned int>::iterator fr=argloc_2_treeloc.begin();\n\t\tstd::vector<unsigned int>::iterator to=argloc_2_treeloc.begin();\n\t\tto+=raw_ints.block_length;\n\t\tfor(unsigned int i=0; i<raw_ints.original.size()/raw_ints.block_length; ++i) {\n\t\t\tstd::sort(fr, to);\n\t\t\tfr+=raw_ints.block_length;\n\t\t\tto+=raw_ints.block_length;\n\t\t\t}\n\t\t}\n\t//\ttxtout << raw_ints.original.size() << \" original size\" << std::endl;\n\t//\ttxtout << raw_ints.block_length << \" block length\" << std::endl;\n\n\t// Add output asym ranges.\n\t// FIXME: v2: this is probably not very useful for the average user.\n\t//\tif(number_of_args()>1) {\n\t//\t\tsibling_iterator ai=args_begin();\n\t//\t\t++ai;\n\t//\t\twhile(ai!=args_end()) {\n\t//\t\t\tif(*ai->name==\"\\\\comma\") {\n\t//\t\t\t\tsibling_iterator cst=tr.begin(ai);\n\t//\t\t\t\tcombin::range_t asymrange;\n\t//\t\t\t\twhile(cst!=tr.end(ai)) {\n\t//\t\t\t\t\tasymrange.push_back(to_long(*cst->multiplier));\n\t//\t\t\t\t\t++cst;\n\t//\t\t\t\t\t}\n\t//\t\t\t\traw_ints.input_asym.push_back(asymrange);\n\t//\t\t\t\t}\n\t//\t\t\t++ai;\n\t//\t\t\t}\n\t//\t\t}\n\n\traw_ints.permute(start_, end_);\n\n#ifdef DEBUG\n\tstd::cerr << \"Computed all permutations: \" << raw_ints.size() << std::endl;\n#endif\n\n\t// Build replacement tree.\n\tEx rep;\n\tsibling_iterator top=rep.set_head(str_node(\"\\\\sum\"));\n\tsibling_iterator dummy=rep.append_child(top, str_node(\"dummy\"));\n\n\tfor(unsigned int i=0; i<raw_ints.size(); ++i) {\n\t\tEx copytree(it);// CORRECT?\n\t\tcopytree.begin()->fl.bracket=str_node::b_none;\n\t\tcopytree.begin()->fl.parent_rel=str_node::p_none;\n\n\t\tstd::map<iterator, iterator, Ex::iterator_base_less> replacement_map;\n\n\t\tfor(unsigned int j=0; j<raw_ints[i].size(); ++j) {\n\t\t\titerator repl=copytree.begin(), orig=it; // CORRECT?\n\t\t\t++repl;\n\t\t\t++orig;\n\t\t\tfor(unsigned int k=0; k<argloc_2_treeloc[raw_ints[i][j]]; ++k)\n\t\t\t\t++orig;\n\t\t\tfor(unsigned int k=0; k<argloc_2_treeloc[raw_ints.original[j]]; ++k)\n\t\t\t\t++repl;\n\n\t\t\t// We cannot just replace here, because then walking along the tree\n\t\t\t// in the next step may no longer work (we may be swapping objects\n\t\t\t// with different numbers of indices, as in\n\t\t\t//\n\t\t\t//   A_{a b} B_{c};\n\t\t\t//   @sym!(%){A_{a b}, B_{c}};\n\t\t\t//\n\t\t\t// so we store iterators first.\n\n\t\t\tif((*orig->name).size()==0)\n\t\t\t\treplacement_map[repl]=tr.begin(orig);\n\t\t\telse\n\t\t\t\treplacement_map[repl]=orig;\n\t\t\t}\n\n\t\t// All replacement rules now figured out, let's do them.\n\t\tstd::map<iterator, iterator>::iterator rit=replacement_map.begin();\n\t\twhile(rit!=replacement_map.end()) {\n\t\t\tstr_node::bracket_t cbr=rit->first->fl.bracket;\n\t\t\titerator repl=copytree.replace(rit->first, rit->second);\n\t\t\t// FIXME: think about whether this is what we want: the bracket\n\t\t\t// type 'stays', while the parent rel is moved together with the\n\t\t\t// index. A(x)*Z[y] -> A(y)*Z[x] ,\n\t\t\t//        A^m_n     -> A_n^m .\n\t\t\trepl->fl.bracket=cbr;\n\t\t\t++rit;\n\t\t\t}\n\n\t\t// Some final multiplier stuff and cleanup\n\n\t\tdivide(copytree.begin()->multiplier, multiplier_t(raw_ints.total_permutations()));\n\t\t//\t\tmultiply(copytree.begin()->multiplier, *st->multiplier);\n\t\tif(sign)\n\t\t\tmultiply(copytree.begin()->multiplier, raw_ints.ordersign(i));\n\n\t\titerator tmp=copytree.begin();\n\t\tprod_unwrap_single_term(tmp);\n\t\trep.insert_subtree(dummy, copytree.begin());\n#ifdef DEBUG\n\t\tif(i%1000==0)\n\t\t\tstd::cerr << i << std::endl;\n#endif\n\t\t}\n\trep.erase(dummy);\n\n\t// show replacement tree\n\t//\ttxtout << \"replacement : \" << std::endl;\n\t//\teo.print_infix(rep.begin());\n\t//\ttxtout << std::endl;\n\n\tit=tr.replace(it, rep.begin());\n\t//\tif(*(tr.parent(reploc)->name)==\"\\\\sum\") {\n\t//\t\ttr.flatten(reploc);\n\t//\t\treploc=tr.erase(reploc);\n\t//\t\t}\n\treturn result_t::l_applied;\n\t}\n"
  },
  {
    "path": "core/algorithms/sym.hh",
    "content": "#pragma once\n\n#include \"Algorithm.hh\"\n#include <vector>\n#include \"Combinatorics.hh\"\n\nnamespace cadabra {\n\n\tclass sym : virtual public Algorithm {\n\t\tpublic:\n\t\t\tsym(const Kernel&, Ex&, Ex&, bool sign);\n\t\t\tsym(const Kernel&, Ex&, const std::vector<unsigned int>&, bool sign);\n\n\t\t\tvirtual bool     can_apply(iterator) override;\n\t\t\tvirtual result_t apply(iterator& it) override;\n\n\t\tprotected:\n\t\t\tEx objects;\n\t\t\tbool    sign;\n\n\t\t\tstd::vector<unsigned int>  slotloc;\n\t\t\tstd::vector<unsigned int>  argloc_2_treeloc;\n\t\t\tcombin::combinations<unsigned int> raw_ints;\n\n\t\t\tresult_t doit(iterator&, bool);\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/algorithms/sym.tex",
    "content": "\\cdbalgorithm{sym}{}\n\nSymmetrise a product or tensor in the indicated objects. This works\nboth with normal objects, as in\n\\begin{screen}{1,2}\nA B C;\n@sym!(%){A,B,C};\n1/6 A B C + 1/6 A C B + 1/6 B A C \n              + 1/6 B C A + 1/6 C A B + 1/6 C B A;\n\\end{screen}\nas well as with indices. When used with indices, remember to also\nindicate whether you want to symmetrise upper or lower indices, as in\nthe example below.\n\\begin{screen}{1,2}\nA_{m n} B_{p};\n@sym!(%){ _{m}, _{n}, _{p} };\n1/6 A_{m n} B_{p} + 1/6 A_{m p} B_{n} + 1/6 A_{n m} B_{p}\n   + 1/6 A_{n p} B_{m} + 1/6 A_{p m} B_{n} + 1/6 A_{p n} B_{m};\n\\end{screen}\nAnti-symmetrisation (i.e.~introducing a sign depending on the\npermutation of each term) is handled by the \\subscommand{asym}\nalgorithm.  \n\n\\cdbseealgo{asym}\n\\cdbseealgo{young_project}\n\\cdbseealgo{young_project_tensor}\n"
  },
  {
    "path": "core/algorithms/tab_basics.cc",
    "content": "\n#include \"algorithms/tab_basics.hh\"\n\nusing namespace cadabra;\n\ntab_basics::tab_basics(const Kernel& k, Ex& tr)\n\t: Algorithm(k, tr)\n\t{\n\t}\n\nunsigned int tab_basics::find_obj(const Ex& other)\n\t{\n\tfor(unsigned int i=0; i<num_to_it.size(); ++i) {\n\t\tif(tree_exact_equal(&kernel.properties, Ex(num_to_it[i]), other))\n\t\t\treturn i;\n\t\t}\n\tthrow std::logic_error(\"internal error in tab_basics::find_obj\");\n\t}\n\nvoid tab_basics::tree_to_numerical_tab(iterator tab1, uinttab_t& one)\n\t{\n\tunsigned int prevsize=num_to_it.size();\n\n\t// First determine the sort order of the children of tab1.\n\tsibling_iterator sib=tr.begin(tab1);\n\twhile(sib!=tr.end(tab1)) {\n\t\tif(*sib->name==\"\\\\comma\") {\n\t\t\tsibling_iterator sib2=tr.begin(sib);\n\t\t\twhile(sib2!=tr.end(sib)) {\n\t\t\t\tnum_to_it.push_back(sib2);\n\t\t\t\t++sib2;\n\t\t\t\t}\n\t\t\t}\n\t\telse {\n\t\t\tnum_to_it.push_back(sib);\n\t\t\t}\n\t\t++sib;\n\t\t}\n\n\ttree_exact_less_obj cmp(&kernel.properties);\n\tstd::vector<Ex::iterator>::iterator startit=num_to_it.begin();\n\tstartit+=prevsize;\n\tstd::sort(startit, num_to_it.end(), cmp);\n\n\t// Now fill the uinttab.\n\tsib=tr.begin(tab1);\n\tunsigned int currow=0;\n\twhile(sib!=tr.end(tab1)) {\n\t\tif(*sib->name==\"\\\\comma\") {\n\t\t\tsibling_iterator sib2=tr.begin(sib);\n\t\t\twhile(sib2!=tr.end(sib)) {\n\t\t\t\tone.add_box(currow, find_obj(Ex(sib2)) );\n\t\t\t\t++sib2;\n\t\t\t\t}\n\t\t\t}\n\t\telse {\n\t\t\tone.add_box(currow, find_obj(Ex(sib)) );\n\t\t\t}\n\t\t++sib;\n\t\t++currow;\n\t\t}\n\t}\n\nvoid tab_basics::tabs_to_singlet_rules(uinttabs_t& tabs, iterator top)\n\t{\n\tuinttabs_t::tableau_container_t::iterator tabit=tabs.storage.begin();\n\n\twhile(tabit!=tabs.storage.end()) {\n\t\t// Keep only the diagrams which lead to a singlet.\n\t\titerator tprod;\n\t\tfor(unsigned int r=0; r<(*tabit).number_of_rows(); ++r)\n\t\t\tif((*tabit).row_size(r)%2!=0)\n\t\t\t\tgoto next_tab;\n\n\t\ttprod=tr.append_child(top, str_node(\"\\\\prod\"));\n\t\tfor(unsigned int r=0; r<(*tabit).number_of_rows(); ++r) {\n\t\t\tfor(unsigned int c=0; c<(*tabit).row_size(r); ++c) {\n\t\t\t\titerator tt=tr.append_child(tprod, str_node(\"\\\\delta\"));\n\t\t\t\ttr.append_child(tt, num_to_it[(*tabit)(r,c++)]);\n\t\t\t\ttr.append_child(tt, num_to_it[(*tabit)(r,c)]);\n\t\t\t\t}\n\t\t\t}\n\nnext_tab:\n\t\t++tabit;\n\t\t}\n\t}\n\n\nvoid tab_basics::tabs_to_tree(uinttabs_t& tabs, iterator top, iterator tabpat, bool even_only)\n\t{\n\tuinttabs_t::tableau_container_t::iterator tabit=tabs.storage.begin();\n\n\twhile(tabit!=tabs.storage.end()) {\n\t\t// Keep only the diagrams which lead to a singlet if requested.\n\t\titerator tt;\n\t\tif(even_only)\n\t\t\tfor(unsigned int r=0; r<(*tabit).number_of_rows(); ++r)\n\t\t\t\tif((*tabit).row_size(r)%2!=0)\n\t\t\t\t\tgoto next_tab;\n\n\t\ttt=tr.append_child(top, str_node(tabpat->name));\n\t\tmultiply(tt->multiplier, tabit->multiplicity);\n\t\tfor(unsigned int r=0; r<(*tabit).number_of_rows(); ++r) {\n\t\t\tunsigned int rs=(*tabit).row_size(r);\n\t\t\tif(rs==1)\n\t\t\t\ttr.append_child(tt, num_to_it[(*tabit)(r,0)]);\n\t\t\telse {\n\t\t\t\titerator tmp=tr.append_child(tt, str_node(\"\\\\comma\"));\n\t\t\t\tfor(unsigned int c=0; c<rs; ++c)\n\t\t\t\t\ttr.append_child(tmp, num_to_it[(*tabit)(r,c)]);\n\t\t\t\t}\n\t\t\t}\n\nnext_tab:\n\t\t++tabit;\n\t\t}\n\t}\n\n"
  },
  {
    "path": "core/algorithms/tab_basics.hh",
    "content": "#pragma once\n\n#include \"Algorithm.hh\"\n#include \"YoungTab.hh\"\n\nnamespace cadabra {\n\n\tclass tab_basics : public Algorithm {\n\t\tpublic:\n\t\t\ttab_basics(const Kernel&, Ex&);\n\n\t\t\ttypedef yngtab::filled_tableau<unsigned int> uinttab_t;\n\t\t\ttypedef yngtab::tableaux<uinttab_t>          uinttabs_t;\n\n\t\t\t/// Convert an Ex to a numerical Young tableau, using num_to_it below.\n\t\t\tvoid tree_to_numerical_tab(iterator, uinttab_t& );\n\t\t\tunsigned int find_obj(const Ex& other);\n\n\t\t\t/// The inverse, converting tableaux to Ex objects attached as children of the iterator.\n\t\t\tvoid tabs_to_tree(uinttabs_t&, iterator, iterator, bool even_only);\n\t\t\tvoid tabs_to_singlet_rules(uinttabs_t&, iterator);\n\n\t\t\tstd::vector<Ex::iterator> num_to_it;\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/algorithms/tab_dimension.cc",
    "content": "\n#include \"Cleanup.hh\"\n#include \"algorithms/tab_dimension.hh\"\n\nusing namespace cadabra;\n\ntabdimension::tabdimension(const Kernel& k, Ex& ex)\n\t: Algorithm(k, ex)\n\t{\n\t}\n\nbool tabdimension::can_apply(iterator it)\n\t{\n\tdimension=-1;\n\n\ttab=kernel.properties.get<Tableau>(it);\n\tif(tab) {\n\t\tdimension=tab->dimension;\n\t\tif(dimension>0)\n\t\t\treturn true;\n\t\t}\n\n\tftab=kernel.properties.get<FilledTableau>(it);\n\tif(ftab) {\n\t\tdimension=ftab->dimension;\n\t\t// std::cerr << \"dimension \" << dimension << std::endl;\n\t\tif(dimension>0)\n\t\t\treturn true;\n\t\t}\n\n\treturn false;\n\t}\n\nAlgorithm::result_t tabdimension::apply(iterator& it)\n\t{\n\t// std::cerr << \"applying at \" << it << std::endl;\n\tif(ftab) {\n\t\tyngtab::filled_tableau<Ex> one;\n\n\t\tsibling_iterator sib=tr.begin(it);\n\t\tunsigned int currow=0;\n\t\twhile(sib!=tr.end(it)) {\n\t\t\tif(*sib->name==\"\\\\comma\") {\n\t\t\t\tsibling_iterator sib2=tr.begin(sib);\n\t\t\t\twhile(sib2!=tr.end(sib)) {\n\t\t\t\t\tone.add_box(currow, Ex(sib2));\n\t\t\t\t\t++sib2;\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\telse one.add_box(currow, Ex(sib));\n\t\t\t++sib;\n\t\t\t++currow;\n\t\t\t}\n\t\tauto tmp=it->multiplier;\n\t\tnode_one(it);\n\t\tit->multiplier=tmp;\n\t\tmultiply(it->multiplier, one.dimension(dimension));\n\t\t}\n\telse {\n\t\tyngtab::tableau one;\n\t\tsibling_iterator sib=tr.begin(it);\n\t\twhile(sib!=tr.end(it)) {\n\t\t\tone.add_row(to_long(*sib->multiplier));\n\t\t\t++sib;\n\t\t\t}\n\t\tauto tmp=it->multiplier;\n\t\tnode_one(it);\n\t\tit->multiplier=tmp;\n\t\tmultiply(it->multiplier, one.dimension(dimension));\n\t\t}\n\tcleanup_dispatch(kernel, tr, it);\n\treturn result_t::l_applied;\n\t}\n\n"
  },
  {
    "path": "core/algorithms/tab_dimension.hh",
    "content": "#pragma once\n\n#include \"Algorithm.hh\"\n#include \"YoungTab.hh\"\n#include \"properties/Tableau.hh\"\n#include \"properties/FilledTableau.hh\"\n\nnamespace cadabra {\n\n\tclass tabdimension : public Algorithm {\n\t\tpublic:\n\t\t\ttabdimension(const Kernel&, Ex&);\n\n\t\t\tvirtual bool     can_apply(iterator);\n\t\t\tvirtual result_t apply(iterator&);\n\n\t\t\tconst Tableau *tab;\n\t\t\tconst FilledTableau *ftab;\n\t\t\tint dimension;\n\t\t};\n\n\n\n\t}\n"
  },
  {
    "path": "core/algorithms/tabcanonicalise.tex",
    "content": "\\cdbalgorithm{tabcanonicalise}{}\n\nCanonicalise a tableau, that is, sort equal-length columns and sort\nboxes within columns. This algorithm acts on objects with\nthe \\subsprop{FilledTableau} property.\n\\begin{screen}{1,2,3}\n\\tableau{#}::FilledTableau.\n\\tableau{b,d}{c,a};\n@tabcanonicalise!(%);\n-\\tableau{a,b}{d,c};\n\\end{screen}\nThis algorithm only uses mono-term symmetries of Young tableaux,\ni.e.~symmetries which relate the given tableau to one other\ntableau. Garnir symmetries (generalised Bianchi and Ricci identities)\nare not handled by \\subscommand{tabcanonicalise} but require the use\nof \\subscommand{tabstandardform}.\n\n\\cdbseeprop{FilledTableau}\n\\cdbseealgo{tabstandardform}\n"
  },
  {
    "path": "core/algorithms/tabdimension.tex",
    "content": "\\cdbalgorithm{tabdimension}{}\n\nCompute the dimension of the representation corresponding to a tableau\nor filled tableau. This algorithm acts on objects with\nthe \\subsprop{Tableau} or \\subsprop{FilledTableau} property, which\nshould have the {\\tt dimension} argument set.\n\\begin{screen}{1,2,3,5,6,7}\n\\tableau{#}::Tableau(dimension=10).\n\\tableau{2}{2};\n@tabdimension!(%);\n825;\n\\tableau{#}::Tableau(dimension=8).\n\\tableau{2}{2};\n@tabdimension!(%);\n336;\n\\end{screen}\nThe computation uses the standard hook rule.\n\n\\cdbseeprop{Tableau}\n\\cdbseeprop{FilledTableau}\n\\cdbseealgo{tabdimension}\n\\cdbseealgo{decompose_product}\n\\cdbseealgo{tabcanonicalise}\n"
  },
  {
    "path": "core/algorithms/tabstandardform.tex",
    "content": "\\cdbalgorithm{tabstandardform}{}\n\nBring a filled Young tableau to standard form, that is, to a form in\nwhich two horizontally adjacent boxes appear in sorted form. This\nrequires the use of Garnir symmetries and generically produces a sum\nof tableaux. This algorithm acts on objects with\nthe \\subsprop{FilledTableau} property.\n\\begin{screen}{1,2,3}\n\\tableau{#}::FilledTableau.\n\\tableau{b,d}{c,a};\n@tabstandardform!(%);\n\\tableau{a,c}{b,d} - \\tableau{a,b}{c,d};\n\\end{screen}\nIn the graphical interface this displays as\n\\begin{equation}\n\\ftableau{{a}{c},{b}{d}} - \\ftableau{{a}{b},{c}{d}};\n\\end{equation}\n\n\\cdbseeprop{FilledTableau}\n\\cdbseealgo{tabcanonicalise}\n"
  },
  {
    "path": "core/algorithms/take_match.cc",
    "content": "\n#include \"algorithms/take_match.hh\"\n#include \"algorithms/substitute.hh\"\n#include \"Cleanup.hh\"\n\nusing namespace cadabra;\n\ntake_match::take_match(const Kernel& k, Ex& e, Ex& rules_)\n\t: Algorithm(k, e), rules(rules_)\n\t{\n\t// Create a proper substitution rule out of the pattern (otherwise\n\t// substitute will not swallow it).\n\tauto wrap = rules.wrap(rules.begin(), str_node(\"\\\\arrow\"));\n\trules.append_child(wrap, str_node(\"dummy\"));\n\t}\n\nbool take_match::can_apply(iterator it)\n\t{\n\t// Apply only on terms in a top-level sum (NO LONGER: or elements of a top-level list),\n\t// or on terms inside an integral.\n\t// The second condition can be relaxed in the future to cover other\n\t// operators which distribute over sums; for now let's be conservative.\n\t// Note that any changes here need corresponding changes in replace_match.\n\n\tif(*it->name==\"\\\\sum\") {\n\t\tif(tr.is_head(it) ||\n\t\t      *tr.parent(it)->name==\"\\\\int\" ||\n\t\t      *tr.parent(it)->name==\"\\\\equals\") {\n\n\t\t\tto_keep.clear();\n\t\t\tto_erase.clear();\n\n\t\t\tsubstitute subs(kernel, tr, rules);\n\t\t\tsibling_iterator sib=tr.begin(it);\n\t\t\twhile(sib!=tr.end(it)) {\n\t\t\t\tif(subs.can_apply(sib)==false)\n\t\t\t\t\tto_erase.push_back(sib);\n\t\t\t\telse\n\t\t\t\t\tto_keep.push_back(tr.path_from_iterator(sib, tr.begin()));\n\t\t\t\t++sib;\n\t\t\t\t}\n\n\t\t\t// If there is no match whatsoever we cannot apply here.\n\t\t\tif(to_keep.size()==0) return false;\n\t\t\treturn true;\n\t\t\t}\n\t\t}\n\treturn false;\n\t}\n\nAlgorithm::result_t take_match::apply(iterator& it)\n\t{\n\t// Push a copy of the expression onto the history stack. The\n\t// 'to_keep' is a reference to the paths vector on the associated\n\t// stack.\n\tauto itpath = tr.path_from_iterator(it, tr.begin());\n\ttr.push_history(to_keep);\n\n\t// Now erase what we do not want anymore, the cleanup\n\tfor(auto& s: to_erase)\n\t\ttr.erase(s);\n\tcleanup_dispatch(kernel, tr, it);\n\n\treturn result_t::l_applied;\n\t}\n"
  },
  {
    "path": "core/algorithms/take_match.cnb",
    "content": "{\n\t\"cells\" : \n\t[\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\algorithm{take_match}{Select a subset of terms in a sum for further computations.}\\n\\nThe \\\\algo{take_match} and \\\\algo{replace_match} algorithms enable you to temporarily work\\nonly on a part of an expression. You select the terms that you want to work on with\\n\\\\algo{take_match}. When you are done, put the result back into the larger expression \\nwith \\\\algo{replace_match}.\\n\\nA simple example shows how this works:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\algorithm{take_match}{Select a subset of terms in a sum for further computations.}\\n\\nThe \\\\algo{take_match} and \\\\algo{replace_match} algorithms enable you to temporarily work\\nonly on a part of an expression. You select the terms that you want to work on with\\n\\\\algo{take_match}. When you are done, put the result back into the larger expression \\nwith \\\\algo{replace_match}.\\n\\nA simple example shows how this works:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}A C+B D G+C D A\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex:=A C + B D G + C D A;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}B D G+C D A\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"take_match(_, $D Q??$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}B D G+Q D A\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"substitute(_, $C -> Q$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}A C+B D G+Q D A\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"replace_match(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"As you can see here, the replacement $C\\\\rightarrow Q$ was only done on the 2nd and 3rd term\\nof the original expression, to which we restricted all manipulations using the \\\\algo{take_match}\\ncommand.\\n\\nThis of course also works with more complicated, tensorial expressions, as the example below shows.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"As you can see here, the replacement $C\\\\rightarrow Q$ was only done on the 2nd and 3rd term\\nof the original expression, to which we restricted all manipulations using the \\\\algo{take_match}\\ncommand.\\n\\nThis of course also works with more complicated, tensorial expressions, as the example below shows.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}A_{m n} \\\\chi B^{m}\\\\,_{p}+\\\\psi A_{n p}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex:= A_{m n} \\\\chi B^{m}_{p} + \\\\psi A_{n p};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}A_{m n} \\\\chi B^{m}\\\\,_{p}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"take_match(_, $\\\\chi Q??$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}C_{m n} \\\\chi B^{m}\\\\,_{p}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"substitute(_, $A_{m n} -> C_{m n}$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}C_{m n} \\\\chi B^{m}\\\\,_{p}+\\\\psi A_{n p}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"replace_match(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"When you are working on a part of an expression, you can restrict attention further by applying\\n\\\\algo{take_match} again. The \\\\algo{replace_match} then puts sub-expressions back into the larger expression in \\nreverse order:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"When you are working on a part of an expression, you can restrict attention further by applying\\n\\\\algo{take_match} again. The \\\\algo{replace_match} then puts sub-expressions back into the larger expression in \\nreverse order:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}A B+C B+C D B\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex:=A B + C B + C D B;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}C B+C D B\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"take_match(_, $C Q??$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}Q B+Q D B\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"substitute(_, $C -> Q$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}Q D B\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"take_match(_, $D Q??$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}Q D R\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"substitute(_, $B -> R$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}Q B\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"replace_match(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}A B+Q B\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"replace_match(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1\n}\n"
  },
  {
    "path": "core/algorithms/take_match.hh",
    "content": "\n#pragma once\n\n#include \"Algorithm.hh\"\n\nnamespace cadabra {\n\n\tclass take_match : public Algorithm {\n\t\tpublic:\n\t\t\ttake_match(const Kernel& k, Ex& e, Ex& r);\n\n\t\t\tvirtual bool     can_apply(iterator) override;\n\t\t\tvirtual result_t apply(iterator&) override;\n\n\t\tprivate:\n\t\t\tEx& rules;\n\n\t\t\tstd::vector<sibling_iterator> to_erase;\n\t\t\tstd::vector<Ex::path_t>       to_keep;\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/algorithms/tree.tex",
    "content": "\\cdbalgorithm{tree}{}\n\nDisplay the internal tree form of a given\nexpression. Can be used on a single expression or on an entire tree:\n\\begin{screen}{1,2,3,10}\nA_{m n}:\nB_{m n}:\n@tree(1);\n(1): \\history  (0)\n  1:{\\expression}  (1)\n  2:  {A}  (2)\n  3:    _{m}  (3)\n  4:    _{n}  (3)\n  5:  \\asymimplicit  (2)\n@tree;\n(1): {\\expression}  (1)\n  1:  {A}  (2)\n  2:    _{m}  (3)\n  3:    _{n}  (3)\n  4:  \\asymimplicit  (2)\n\n(2): {\\expression}  (1)\n  1:  {B}  (2)\n  2:    _{m}  (3)\n  3:    _{n}  (3)\n  4:  \\asymimplicit  (2)\n\\end{screen}\nMost expressions lead to extremely lengthy output, so it is useful to\nredirect it to a file using output redirection.\n\n"
  },
  {
    "path": "core/algorithms/unique_indices.tex",
    "content": "\\cdbalgorithm{unique\\_indices}{}\n\nMake all open indices in a product of tensors unique, taking into\naccount index set declarations.\n\\begin{screen}{1,2}\n{m,n,p#}::Indices.\n{ A_{m n}, B_{m n},  C_{m n} };\n@unique_indices!(%);\n\\end{screen}\n"
  },
  {
    "path": "core/algorithms/untrace.cc",
    "content": "\n#include \"untrace.hh\"\n#include \"Cleanup.hh\"\n\n#include \"properties/ImplicitIndex.hh\"\n#include \"properties/Trace.hh\"\n\nusing namespace cadabra;\n\nuntrace::untrace(const Kernel& k, Ex& tr)\n\t: Algorithm(k, tr)\n\t{\n\t}\n\nbool untrace::can_apply(iterator st)\n\t{\n\tconst Trace *trace = kernel.properties.get<Trace>(st);\n\tif(trace) {\n\t\tauto sib=tr.begin(st);\n\t\tif(sib==tr.end(st))      return false;\n\t\tif(*sib->name==\"\\\\prod\") return true;\n\t\tif(is_single_term(sib))  return true;\n\t\t}\n\treturn false;\n\t}\n\nAlgorithm::result_t untrace::apply(iterator& trloc)\n\t{\n\tauto res=result_t::l_no_action;\n\tconst Trace *trace = kernel.properties.get<Trace>(trloc);\n\n\t// We cannot touch any nodes above `trloc`, so\n\t// we will wrap the trace node in a product and\n\t// then let cleanup take care of unwrapping\n\t// that product.\n\titerator moveprod=trloc;\n\tforce_node_wrap(moveprod, \"\\\\prod\");\n\n\t// ensure the argument is a product\n\titerator prodloc=tr.begin(trloc);\n\tprod_wrap_single_term(prodloc);\n\n\t// scan arguments of trace\n\tsibling_iterator st=tr.begin(prodloc);\n\twhile(st!=tr.end(prodloc)) {\n\t\tsibling_iterator nxt=st;\n\t\t++nxt;\n\n\t\tbool move_out=true;\n\n\t\tauto imp = kernel.properties.get<ImplicitIndex>(st);\n\t\tif(imp) {\n\t\t\t// std::cerr << st << \" has implicit index\" << std::endl;\n\t\t\tif(imp->explicit_form.size()==0) move_out=false;\n\t\t\telse {\n\t\t\t\titerator eb=imp->explicit_form.begin();\n\t\t\t\tindex_iterator ii=index_iterator::begin(kernel.properties, eb);\n\t\t\t\twhile(ii!=index_iterator::end(kernel.properties, eb)) {\n\t\t\t\t\tauto ind=kernel.properties.get<Indices>(ii, true);\n\t\t\t\t\tif(ind) {\n\t\t\t\t\t\t// std::cerr << \"seen set name \" << ind->set_name << std::endl;\n\t\t\t\t\t\tif(ind->set_name==trace->index_set_name) {\n\t\t\t\t\t\t\tmove_out=false;\n\t\t\t\t\t\t\tbreak;\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\t}\n\t\t\t\t\telse {\n\t\t\t\t\t\t// no Indices property known, better be safe.\n\t\t\t\t\t\tmove_out=false;\n\t\t\t\t\t\tbreak;\n\t\t\t\t\t\t}\n\t\t\t\t\t++ii;\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t}\n\n\t\tif(move_out) {\n\t\t\tres=result_t::l_applied;\n\t\t\tint sign=1;\n\t\t\tsibling_iterator st2=tr.begin(prodloc);\n\t\t\tEx_comparator compare(kernel.properties);\n\t\t\twhile(st2!=st) {\n\t\t\t\tauto es=compare.equal_subtree(st, st2);\n\t\t\t\tsign*=compare.can_swap_components(st, st2, es);\n\t\t\t\t++st2;\n\t\t\t\t}\n\t\t\ttr.move_before(trloc, st);\n\t\t\tmultiply(trloc->multiplier, sign);\n\t\t\t}\n\n\t\tst=nxt;\n\t\t}\n\n\t// Trace of empty product should become trace of 1.\n\tif(tr.number_of_children(prodloc)==0)\n\t\tnode_one(prodloc);\n\n\ttrloc = moveprod;\n\n//\tstd::cerr << trloc << std::endl;\n\tcleanup_dispatch(kernel, tr, trloc);\n\t\n\treturn res;\n\t}\n"
  },
  {
    "path": "core/algorithms/untrace.cnb",
    "content": "{\n\t\"cell_id\": 17473324490989807474,\n\t\"cells\": [\n\t\t{\n\t\t\t\"cell_id\": 17620023483363172328,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 7700461705362123739,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\algorithm{untrace}{Take objects out of traces}\\n\\nWhen a trace contains objects which do not carry any implicit indices on which the \\ntrace acts, the \\\\algo{untrace} algorithm can be used to take them out of the\\ntrace. This is similar to the way in which \\\\algo{unwrap} takes objects out of\\nderivatives when they do not depend on the object with respect to which the derivative \\nis taken.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\algorithm{untrace}{Take objects out of traces}\\n\\nWhen a trace contains objects which do not carry any implicit indices on which the \\ntrace acts, the \\\\algo{untrace} algorithm can be used to take them out of the\\ntrace. This is similar to the way in which \\\\algo{unwrap} takes objects out of\\nderivatives when they do not depend on the object with respect to which the derivative \\nis taken.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 12842358434533101410,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 14029965045660066717,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"Unless you declare objects to have a \\\\prop{ImplicitIndex} property, they will be taken out. The minimal example does not specify these indices, e.g.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"Unless you declare objects to have a \\\\prop{ImplicitIndex} property, they will be taken out. The minimal example does not specify these indices, e.g.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 9535091562390105121,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 12470129597878327812,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 14929967836227092198,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"tr(q A B)\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}tr\\\\left(q A B\\\\right)\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 14602620579978943179,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 1773090927971160558,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"q tr(A B)\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}q tr\\\\left(A B\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"{A,B}::ImplicitIndex.\\ntr{#}::Trace.\\nex:= tr( q A B );\\nuntrace(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 599709734600671488,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 6801199231042999205,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"In the declaration of a trace, it is possible to indicate over which indices the trace is being taken.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"In the declaration of a trace, it is possible to indicate over which indices the trace is being taken.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 14632792720123745310,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"{a,b,c}::Indices(spinor).\\n{m,n,p}::Indices(vector).\\nC::ImplicitIndex(C_{a b}).\\nD::ImplicitIndex(D_{a b}).\\nE::ImplicitIndex(E^{m n}).\\nTr{#}::Trace(indices=spinor).\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 14282261514648391593,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 1628602802577310529,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 3495019957146126718,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"Tr(C D E)\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}Tr\\\\left(C D E\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex:= Tr( C D E );\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 7947298485656223155,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 17084545913981834117,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 2107438105775406723,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"E Tr(C D)\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}E Tr\\\\left(C D\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"untrace(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 13091146635063293823,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 17938807333085018593,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"Note how, even though $E$ has implicit indices, it has been moved out of the trace, as the\\nlatter is declared to be a trace over spinor indices, not vector indices.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"Note how, even though $E$ has implicit indices, it has been moved out of the trace, as the\\nlatter is declared to be a trace over spinor indices, not vector indices.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 13319255015209183503,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"\"\n\t\t}\n\t],\n\t\"description\": \"Cadabra JSON notebook format\",\n\t\"version\": 1.0\n}\n"
  },
  {
    "path": "core/algorithms/untrace.hh",
    "content": "\n#pragma once\n\n#include \"Algorithm.hh\"\n\nnamespace cadabra {\n\n\tclass untrace : public Algorithm {\n\t\tpublic:\n\t\t\tuntrace(const Kernel&, Ex&);\n\n\t\t\tvirtual bool     can_apply(iterator) override;\n\t\t\tvirtual result_t apply(iterator&) override;\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/algorithms/unwrap.cc",
    "content": "\n#include \"Compare.hh\"\n#include \"Cleanup.hh\"\n#include \"algorithms/unwrap.hh\"\n#include \"properties/Derivative.hh\"\n#include \"properties/Accent.hh\"\n#include \"properties/DiracBar.hh\"\n#include \"properties/Spinor.hh\"\n#include \"properties/DifferentialForm.hh\"\n#include \"properties/GammaMatrix.hh\"\n#include \"properties/DependsBase.hh\"\n//#include \"algorithms/prodcollectnum.hh\"\n\n// #define DEBUG 1\n\nusing namespace cadabra;\n\nunwrap::unwrap(const Kernel& k, Ex& tr, Ex& w)\n\t: Algorithm(k, tr)\n\t{\n\tif(w.begin()!=w.end()) {\n\t\tif(*w.begin()->name!=\"\\\\comma\")\n\t\t\twrappers.push_back(w);\n\t\telse {\n\t\t\tauto sib=w.begin(w.begin());\n\t\t\twhile(sib!=w.end(w.begin())) {\n\t\t\t\twrappers.push_back(Ex(sib));\n\t\t\t\t++sib;\n\t\t\t\t}\n\t\t\t}\n\t\t}\n\t}\n\nbool unwrap::can_apply(iterator it)\n\t{\n\tconst Derivative *der=kernel.properties.get<Derivative>(it);\n\tconst Accent     *acc=kernel.properties.get<Accent>(it);\n\tif(der || acc) {\n\t\tEx_comparator comp(kernel.properties);\n\t\tif(wrappers.size()>0) {\n\t\t\tbool found=false;\n\t\t\tfor(auto&w : wrappers) {\n#ifdef DEBUG\n\t\t\t\tstd::cerr << \"comparing \" << w << \" to \" << Ex(it) << std::endl;\n#endif\n\t\t\t\tif(comp.equal_subtree(w.begin(), it)==Ex_comparator::match_t::subtree_match) {\n#ifdef DEBUG\n\t\t\t\t\tstd::cerr << \"yes\" << std::endl;\n#endif\n\t\t\t\t\tfound=true;\n\t\t\t\t\tbreak;\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\tif(!found) return false;\n\t\t\t}\n\t\treturn true;\n\t\t}\n\n\tif(*it->name==\"\\\\wedge\") return true;\n\n\treturn false;\n\t}\n\nAlgorithm::result_t unwrap::apply_on_wedge(iterator& it)\n\t{\n\tresult_t res=result_t::l_no_action;\n\n\tauto prodwrap = tr.wrap(it, str_node(\"\\\\prod\"));\n\t\n\tsibling_iterator sib=tr.begin(it);\n\twhile(sib!=tr.end(it)) {\n\t\tif(*sib->name==\"\\\\prod\") {\n\t\t\tsibling_iterator fac=tr.begin(sib);\n\t\t\twhile(fac!=tr.end(sib)) {\n\t\t\t\tconst DifferentialFormBase *diff = kernel.properties.get<DifferentialFormBase>(fac);\n\t\t\t\tsibling_iterator nxt=fac;\n\t\t\t\t++nxt;\n\t\t\t\tif(diff==0 || diff->degree(kernel.properties, fac).begin()->is_zero() ) {\n\t\t\t\t\t// Figure out the sign. First move to front of existing\n\t\t\t\t\t// simple product. Then move through all other factors\n\t\t\t\t\t// in the wedge product.\n\t\t\t\t\tEx_comparator comp(kernel.properties);\n\t\t\t\t\tint sign=comp.can_move_to_front(tr, sib, fac);\n\t\t\t\t\tif(sign!=0) {\n\t\t\t\t\t\tsibling_iterator prevwedfac=sib;\n\t\t\t\t\t\tif(prevwedfac!=tr.begin(it)) {\n\t\t\t\t\t\t\tdo {\n\t\t\t\t\t\t\t\t--prevwedfac;\n\t\t\t\t\t\t\t\tauto stc=comp.equal_subtree(prevwedfac, fac);\n\t\t\t\t\t\t\t\tsign*=comp.can_swap(prevwedfac, fac, stc);\n\t\t\t\t\t\t\t\t} while(prevwedfac!=tr.begin(it));\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\tif(sign!=0) {\n\t\t\t\t\t\t\ttr.move_before(it, fac);\n\t\t\t\t\t\t\tmultiply(prodwrap->multiplier, sign);\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\t}\n\t\t\t\t\t}\n\t\t\t\tfac=nxt;\n\t\t\t\t}\n\t\t\t}\n\t\tsibling_iterator nxt=sib;\n\t\t++nxt;\n\t\titerator tmp=sib;\n\t\tcleanup_dispatch(kernel, tr, tmp);\n\t\tsib=nxt;\n\t\t}\n\tcleanup_dispatch(kernel, tr, prodwrap);\t\n\t\n\treturn res;\n\t}\n\n// \\del{a*f*A*b*C*d*e} -> a*f*\\del{A*b*C}*d*e\n//\n// locate first dependent factor\n// locate first following independent factor\n// ...\n//\n// Should also work for brackets, like\n//\n//    \\poisson( A )( B ) -> 0\n//\n// if either A or B has vanishing poisson bracket, and\n//\n//    \\poisson( N1 D1 )( N2 D2 ) -> N1 N2 \\poisson( D1 )( D2 ).\n//\n// So all \"derivatives\"\n\nAlgorithm::result_t unwrap::apply(iterator& it)\n\t{\n#ifdef DEBUG\n\tstd::cerr << \"Applying unwrap at \" << Ex(it) << std::endl;\n#endif\n\n\tif(*it->name==\"\\\\wedge\")\n\t\treturn apply_on_wedge(it);\n\t\n\tresult_t res = result_t::l_no_action;\n\n\tbool is_accent=kernel.properties.get<Accent>(it);\n\tbool is_diracbar=kernel.properties.get<DiracBar>(it);\n\n\t// Wrap the 'derivative' in a product node so we can take\n\t// child nodes out and stuff them inside the product.\n\n\titerator old_it=it;\n\tit=tr.wrap(it, str_node(\"\\\\prod\"));\n\n\tbool all_arguments_moved_out=true;\n\tsibling_iterator acton=tr.begin(old_it);\n\twhile(acton!=tr.end(old_it)) {\n\t\t// Only look at child nodes which are not indices.\n\t\tif(acton->is_index()==false) {\n\t\t\tsibling_iterator derarg=acton;\n\t\t\t++acton; // don't use this anymore this loop\n\n\t\t\tif(*derarg->name==\"\\\\sum\") {\n\t\t\t\tall_arguments_moved_out=false;\n\t\t\t\tcontinue; // FIXME: Don't know how to handle this yet.\n\t\t\t\t}\n\n#ifdef DEBUG\n\t\t\tstd::cerr << \"doing \" << *derarg->name << std::endl;\n#endif\n\n\t\t\t// If the argument of the derivative is not a product, make\n\t\t\t// into one, so we can handle everything using the same code.\n\t\t\tif(*derarg->name!=\"\\\\prod\")\n\t\t\t\tderarg=tr.wrap(derarg, str_node(\"\\\\prod\"));\n\n\t\t\t// Iterate over all arguments of the product sitting inside\n\t\t\t// the derivative (but see the comment above).\n\t\t\tsibling_iterator factor=tr.begin(derarg);\n\t\t\twhile(factor!=tr.end(derarg)) {\n\t\t\t\t// std::cerr << \"checking \" << Ex(factor) << std::endl;\n\n\t\t\t\tsibling_iterator nxt=factor;\n\t\t\t\t++nxt;\n\t\t\t\tbool move_out=true;\n\n\t\t\t\t// An object pattern like 'A??' should always be assumed to have\n\t\t\t\t// dependence, because we don't yet know what it will match.\n\t\t\t\tif(move_out) {\n\t\t\t\t\tif(factor->is_name_wildcard() || factor->is_object_wildcard())\n\t\t\t\t\t\tmove_out=false;\n\t\t\t\t\t}\n\n\t\t\t\tif(move_out) {\n\t\t\t\t\tif(is_diracbar)\n\t\t\t\t\t\tif(kernel.properties.get<Spinor>(factor) || kernel.properties.get<GammaMatrix>(factor))\n\t\t\t\t\t\t\tmove_out=false;\n\t\t\t\t\t}\n\n\t\t\t\t// Then figure out whether there is implicit dependence on the operator.\n\t\t\t\t// or on the coordinate.\n\t\t\t\tif(move_out) {\n\t\t\t\t\tconst DependsBase *dep=kernel.properties.get<DependsBase>(factor);\n\t\t\t\t\tif(dep!=0) {\n#ifdef DEBUG\n\t\t\t\t\t\tstd::cerr << *factor->name << \" acted on by \" << *old_it->name << \"; depends\" << std::endl;\n#endif\n\t\t\t\t\t\tauto derivative=kernel.properties.get<Derivative>(old_it);\n\t\t\t\t\t\tEx deps=dep->dependencies(kernel, factor /* it */);\n\t\t\t\t\t\tsibling_iterator depobjs=deps.begin(deps.begin());\n\t\t\t\t\t\twhile(depobjs!=deps.end(deps.begin())) {\n#ifdef DEBUG\n\t\t\t\t\t\t\tstd::cerr << \"?\" << *old_it->name << \" == \" << *depobjs->name << std::endl;\n#endif\n\t\t\t\t\t\t\t// FIXME: need to compare more than the name\n\t\t\t\t\t\t\tif(old_it->name == depobjs->name) {\n\t\t\t\t\t\t\t\tmove_out=false;\n\t\t\t\t\t\t\t\tbreak;\n\t\t\t\t\t\t\t\t}\n\t\t\t\t\t\t\telse if(derivative && derivative->with_respect_to.size()>0 && derivative->with_respect_to.begin()->name==depobjs->name) {\n\t\t\t\t\t\t\t\tmove_out=false;\n\t\t\t\t\t\t\t\tbreak;\n\t\t\t\t\t\t\t\t}\n\t\t\t\t\t\t\telse {\n\t\t\t\t\t\t\t\t// compare all indices\n#ifdef DEBUG\n\t\t\t\t\t\t\t\tstd::cerr << \"comparing indices\" << std::endl;\n#endif\n\t\t\t\t\t\t\t\tsibling_iterator indit=tr.begin(old_it);\n\t\t\t\t\t\t\t\twhile(indit!=tr.end(old_it)) {\n\t\t\t\t\t\t\t\t\tif(indit->is_index()) {\n#ifdef DEBUG\n\t\t\t\t\t\t\t\t\t\tstd::cerr << \"compare \" << *indit->name << \" to \" << *depobjs->name << std::endl;\n#endif\n\t\t\t\t\t\t\t\t\t\tif(subtree_compare(&kernel.properties, indit, depobjs, 0, false, 0, false)==0) {\n#ifdef DEBUG\n\t\t\t\t\t\t\t\t\t\t\tstd::cerr << \"not moving out\" << std::endl;\n#endif\n\t\t\t\t\t\t\t\t\t\t\tmove_out=false;\n\t\t\t\t\t\t\t\t\t\t\tbreak;\n\t\t\t\t\t\t\t\t\t\t\t}\n\t\t\t\t\t\t\t\t\t\t}\n\t\t\t\t\t\t\t\t\t++indit;\n\t\t\t\t\t\t\t\t\t}\n\t\t\t\t\t\t\t\tif(!move_out) break;\n\t\t\t\t\t\t\t\t}\n\t\t\t\t\t\t\t++depobjs;\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\t}\n\t\t\t\t\t}\n\n\t\t\t\t// Finally, there may also be explicit dependence.\n\t\t\t\tif(move_out) {\n\t\t\t\t\t// FIXME: This certainly does not handle Y(a,b) correctly\n\t\t\t\t\tsibling_iterator chldit=tr.begin(factor);\n\t\t\t\t\twhile(chldit!=tr.end(factor)) {\n\t\t\t\t\t\tif(chldit->is_index()==false) {\n\t\t\t\t\t\t\tsibling_iterator indit=tr.begin(old_it);\n\t\t\t\t\t\t\twhile(indit!=tr.end(old_it)) {\n\t\t\t\t\t\t\t\tif(subtree_exact_equal(&kernel.properties, chldit, indit, 0)) {\n\t\t\t\t\t\t\t\t\tmove_out=false;\n\t\t\t\t\t\t\t\t\tbreak;\n\t\t\t\t\t\t\t\t\t}\n\t\t\t\t\t\t\t\t++indit;\n\t\t\t\t\t\t\t\t}\n\t\t\t\t\t\t\tif(!move_out) break;\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\t++chldit;\n\t\t\t\t\t\t}\n\t\t\t\t\t}\n\n\t\t\t\t// If no dependence found, move this child out of the derivative.\n\t\t\t\tif(move_out) {\n\t\t\t\t\t// FIXME: Does does not look at the commutativity\n\t\t\t\t\t// property of the index/indices wrt. which the\n\t\t\t\t\t// derivative is taken.\n\t\t\t\t\tint sign=1;\n\t\t\t\t\tif(factor!=tr.begin(derarg)) {\n\t\t\t\t\t\tEx_comparator compare(kernel.properties);\n\t\t\t\t\t\tsign=compare.can_move_to_front(tr, derarg, factor); //, Ex_comparator::match_t::no_match_less);\n\t\t\t\t\t\t}\n\t\t\t\t\tif(sign!=0) {\n\t\t\t\t\t\t// If the sign *is* zero, it means that we are trying to move a factor\n\t\t\t\t\t\t// through another one, but do not know how to do that. In that case,\n\t\t\t\t\t\t// you cannot move the factor out.\n\t\t\t\t\t\tres=result_t::l_applied;\n\t\t\t\t\t\ttr.move_before(old_it, factor);\n\t\t\t\t\t\tmultiply(it->multiplier, sign);\n\t\t\t\t\t\t}\n\t\t\t\t\t}\n\n\t\t\t\tfactor=nxt;\n\t\t\t\t}\n\n\t\t\t// std::cerr << \"after step \" << Ex(it) << std::endl;\n\n\t\t\t// All factors in this argument have been handled now, let's see what's left.\n\t\t\tunsigned int derarg_num_chldr=tr.number_of_children(derarg);\n\t\t\tif(derarg_num_chldr==0) {\n\t\t\t\t// Empty accents should simply be ignored, but empty derivatives vanish.\n\t\t\t\tif(!is_accent) {\n\t\t\t\t\tzero(it->multiplier);\n\t\t\t\t\tbreak; // we can stop now, the entire expression is zero.\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\telse {\n\t\t\t\tall_arguments_moved_out=false;\n\t\t\t\tif(derarg_num_chldr==1) {\n\t\t\t\t\tderarg=tr.flatten_and_erase(derarg);\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t}\n\t\telse ++acton;\n\t\t}\n\n\n\t// All non-index arguments have now been handled.\n\tif(all_arguments_moved_out && is_accent) {\n\t\tzero(it->multiplier);\n\t\t}\n\telse if(*it->multiplier!=0) {\n\t\tif(tr.number_of_children(it)==1) { // nothing was moved out\n\t\t\ttr.flatten(it);\n\t\t\tit=tr.erase(it);\n\t\t\t}\n\t\telse {\n\t\t\t// Moving factors around has potentially led to a top-level product\n\t\t\t// which contains children with non-unit multiplier.\n\t\t\tcleanup_dispatch(kernel, tr, it);\n\n\t\t\t// If the derivative acts on another derivative, we need\n\t\t\t// to un-nest the argument of the outer (and this situation\n\t\t\t// can only happen if there is only one non-index child node)\n\t\t\titerator itarg=tr.begin(it);\n\t\t\twhile(itarg->is_index())\n\t\t\t\t++itarg;\n\n\t\t\tcleanup_dispatch(kernel, tr, itarg);\n\t\t\t}\n\t\t}\n\tcleanup_dispatch(kernel, tr, it);\n\t\n//\tstd::cerr << \"unwrap done \" << it << std::endl;\n\n\treturn res;\n\t}\n"
  },
  {
    "path": "core/algorithms/unwrap.cnb",
    "content": "{\n\t\"cell_id\": 16367551995434684411,\n\t\"cells\": [\n\t\t{\n\t\t\t\"cell_id\": 14504029108633095928,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 8055144346042432708,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\algorithm{unwrap}{Move objects out of derivatives, accents or exterior products.}\\n\\nMove objects out of \\\\prop{Derivative}s, \\\\prop{Accent}s or exterior (wedge) products when\\nthey do not depend on these operators.  The most basic example is Accents, which\\nwill get removed from objects which do not depend on them, as\\nin the following example:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\algorithm{unwrap}{Move objects out of derivatives, accents or exterior products.}\\n\\nMove objects out of \\\\prop{Derivative}s, \\\\prop{Accent}s or exterior (wedge) products when\\nthey do not depend on these operators.  The most basic example is Accents, which\\nwill get removed from objects which do not depend on them, as\\nin the following example:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 14249786823637233933,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9223372036854775816,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Attached property Accent to~}\\\\widehat{\\\\#}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9223372036854775817,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Attached property Distributable to~}\\\\widehat{\\\\#}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9223372036854775818,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Attached property Depends to~}B.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9223372036854775819,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 9223372036854775820,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\hat{A + B + C}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\widehat{A+B+C}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"\\\\hat{#}::Accent;\\n\\\\hat{#}::Distributable;\\nB::Depends(\\\\hat);\\n\\nex:=\\\\hat{A+B+C};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 8019439534319867171,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9223372036854775822,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 9223372036854775823,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\hat{A} + \\\\hat{B} + \\\\hat{C}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\widehat{A}+\\\\widehat{B}+\\\\widehat{C}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"distribute(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 16433109665923551967,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9223372036854775825,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 9223372036854775826,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\hat{B}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\widehat{B}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"unwrap(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 15581052402337717386,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 13385333830224401826,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"Derivatives will be set to zero if an object inside does not depend on\\nit. All objects which are annihilated by the derivative operator are\\nmoved to the front (taking into account anti-commutativity if necessary),\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"Derivatives will be set to zero if an object inside does not depend on\\nit. All objects which are annihilated by the derivative operator are\\nmoved to the front (taking into account anti-commutativity if necessary),\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 5108931698136803462,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9223372036854775832,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Attached property PartialDerivative to~}\\\\partial{\\\\#}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9223372036854775833,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Attached property AntiCommuting to~}\\\\left[A,~\\\\discretionary{}{}{} B,~\\\\discretionary{}{}{} C,~\\\\discretionary{}{}{} D\\\\right].\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9223372036854775834,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Attached property Coordinate to~}x.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9223372036854775835,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Attached property Depends to~}\\\\left[B,~\\\\discretionary{}{}{} D\\\\right].\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"\\\\partial{#}::PartialDerivative;\\n{A,B,C,D}::AntiCommuting;\\nx::Coordinate;\\n{B,D}::Depends(\\\\partial{#});\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 8096057681359605817,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9223372036854775837,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 9223372036854775838,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\partial_{x}(A B C D)\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\partial_{x}\\\\left(A B C D\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex:=\\\\partial_{x}{A B C D};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 406841013989955329,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9223372036854775840,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 9223372036854775841,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"-A C \\\\partial_{x}(B D)\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}-A C \\\\partial_{x}\\\\left(B D\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"unwrap(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 13736871175375612419,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 8242814143146979662,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"Note that a product remains inside the derivative; to expand that\\nuse \\\\algo{product_rule}. Here is another example:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"Note that a product remains inside the derivative; to expand that\\nuse \\\\algo{product_rule}. Here is another example:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 729755081056442813,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9223372036854775845,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Attached property Derivative to~}\\\\partial{\\\\#}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9223372036854775846,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Attached property Depends to~}X.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9223372036854775847,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 9223372036854775848,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\del(X Y Z)\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\partial\\\\left(X Y Z\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"\\\\del{#}::LaTeXForm(\\\"\\\\partial\\\").\\n\\\\del{#}::Derivative;\\nX::Depends(\\\\del{#});\\nex:=\\\\del{X*Y*Z};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 5187664421558439268,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9223372036854775850,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 9223372036854775851,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\del(X) Y Z + X \\\\del(Y) Z + X Y \\\\del(Z)\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\partial{X} Y Z+X \\\\partial{Y} Z+X Y \\\\partial{Z}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"product_rule(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 654130972420458309,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9223372036854775853,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 9223372036854775854,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\del(X) Y Z\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\partial{X} Y Z\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"unwrap(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 6389123235373527656,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 4815211910380063113,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"Note that all objects are by default constants for the action of\\n\\\\prop{Derivative} operators. If you want objects to stay inside\\nderivative operators you have to explicitly declare that they depend\\non the derivative operator or on the coordinate with respect to which\\nyou take a derivative.\\n\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"Note that all objects are by default constants for the action of\\n\\\\prop{Derivative} operators. If you want objects to stay inside\\nderivative operators you have to explicitly declare that they depend\\non the derivative operator or on the coordinate with respect to which\\nyou take a derivative.\\n\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 10338581126428217968,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 5287169212014684320,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"The final case where \\\\algo{unwrap} acts is when exterior products contain factors which are\\nscalars (or forms of degree zero). The following example shows this.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"The final case where \\\\algo{unwrap} acts is when exterior products contain factors which are\\nscalars (or forms of degree zero). The following example shows this.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 9979798330945148543,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9223372036854775809,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Attached property AntiCommuting to~}\\\\left[V,~\\\\discretionary{}{}{} g\\\\right].\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9223372036854775810,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 9223372036854775811,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"f V ^ W g\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\left(f V\\\\right)\\\\wedge \\\\left(W g\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"{f,g}::DifferentialForm(degree=0).\\n{V, W}::DifferentialForm(degree=1).\\n{V,g}::AntiCommuting;\\nfoo := f V ^ W g;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 3962568245785140347,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9223372036854775813,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 9223372036854775814,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"-f g V ^ W\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}-f g V\\\\wedge W\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"unwrap(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 10446126163656098854,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 5660117810038829021,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"As this example shows, \\\\algo{unwrap} takes into account commutativity properties (hence the sign flip).\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"As this example shows, \\\\algo{unwrap} takes into account commutativity properties (hence the sign flip).\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 16216585032253051571,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"\"\n\t\t}\n\t],\n\t\"description\": \"Cadabra JSON notebook format\",\n\t\"version\": 1.0\n}\n"
  },
  {
    "path": "core/algorithms/unwrap.hh",
    "content": "#pragma once\n\n#include \"Algorithm.hh\"\n\nnamespace cadabra {\n\n\tclass unwrap : public Algorithm {\n\t\tpublic:\n\t\t\tunwrap(const Kernel&, Ex&, Ex&);\n\n\t\t\tvirtual bool     can_apply(iterator) override;\n\t\t\tvirtual result_t apply(iterator&) override;\n\n\t\t\tstd::vector<Ex> wrappers;\n\n\t\tprivate:\n\t\t\tresult_t apply_on_wedge(iterator&);\n\t\t\t\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/algorithms/unzoom.cc",
    "content": "\n#include \"Cleanup.hh\"\n#include \"algorithms/unzoom.hh\"\n#include \"algorithms/substitute.hh\"\n\nusing namespace cadabra;\n\nunzoom::unzoom(const Kernel& k, Ex& e)\n\t: Algorithm(k, e)\n\t{\n\ttraverse_ldots=true;\n\t}\n\nbool unzoom::can_apply(iterator it)\n\t{\n\tif(*it->name==\"\\\\ldots\")  return true;\n\treturn false;\n\t}\n\nAlgorithm::result_t unzoom::apply(iterator& it)\n\t{\n\tit=tr.flatten_and_erase(it);\n\treturn result_t::l_applied;\n\t}\n\n"
  },
  {
    "path": "core/algorithms/unzoom.hh",
    "content": "\n#pragma once\n\n#include \"Algorithm.hh\"\n\nnamespace cadabra {\n\n\tclass unzoom : public Algorithm {\n\t\tpublic:\n\t\t\tunzoom(const Kernel&, Ex&);\n\n\t\t\tvirtual bool     can_apply(iterator) override;\n\t\t\tvirtual result_t apply(iterator&) override;\n\t\t};\n\n\t}\n\n"
  },
  {
    "path": "core/algorithms/vary.cc",
    "content": "\n#include \"Cleanup.hh\"\n#include \"Exceptions.hh\"\n#include \"algorithms/vary.hh\"\n#include \"algorithms/substitute.hh\"\n#include \"algorithms/product_rule.hh\"\n#include \"properties/Derivative.hh\"\n#include \"properties/Accent.hh\"\n\nusing namespace cadabra;\n\n// #define DEBUG 1\n\nvary::vary(const Kernel& k, Ex& tr, Ex& args_)\n\t: Algorithm(k, tr), args(args_)\n\t{\n\t}\n\nbool vary::can_apply(iterator it)\n\t{\n\tif(it->is_zero()) return false;\n\t\n\tif(*it->name==\"\\\\prod\") return true;\n\tif(*it->name==\"\\\\commutator\") return true;\n\tif(*it->name==\"\\\\anticommutator\") return true;\n\tif(*it->name==\"\\\\sum\") return true;\n\tif(*it->name==\"\\\\pow\") return true;\n\tif(*it->name==\"\\\\int\") return true;\n\tif(*it->name==\"\\\\equals\") return false;\n\tif(is_single_term(it)) return true;\n\tif(is_nonprod_factor_in_prod(it)) return true;\n\tconst Derivative *der = kernel.properties.get<Derivative>(it);\n\tif(der) return true;\n\tconst Accent *acc = kernel.properties.get<Accent>(it);\n\tif(acc) return true;\n\n\tif(!tr.is_head(it)) {\n\t\tder = kernel.properties.get<Derivative>(tr.parent(it));\n\t\tif(der) return true;\n\t\tacc = kernel.properties.get<Accent>(tr.parent(it));\n\t\tif(acc) return true;\n\t\t}\n\treturn false;\n\t}\n\n/*\n\nD(A) C + D(A);\n@vary(%)(\n\n\n*/\n\nAlgorithm::result_t vary::apply(iterator& it)\n\t{\n\tresult_t res=result_t::l_no_action;\n\n\tif(*it->name==\"\\\\prod\" || *it->name==\"\\\\commutator\" || *it->name==\"\\\\anticommutator\") {\n\t\tEx result;\n\t\tresult.set_head(str_node(\"\\\\sum\"));\n\t\titerator newsum=result.begin();\n\n\t\t// Iterate over all factors, attempting a substitute. If this\n\t\t// succeeds, copy the term to the \"result\" tree. Then restore the\n\t\t// original. We have to do the substitute on the original tree so\n\t\t// that index relabelling takes into account the rest of the tree.\n\n\t\tEx prodcopy(it); // keep a copy to restore after each substitute\n\n\t\tvary varyfac(kernel, tr, args);\n\t\tint pos=0;\n\t\tfor(;;) {\n\t\t\tsibling_iterator fcit=tr.begin(it);\n\t\t\tfcit+=pos;\n\t\t\tif(fcit==tr.end(it)) break;\n\n\t\t\titerator fcit2(fcit);\n\t\t\tif(varyfac.can_apply(fcit2)) {\n\t\t\t\tresult_t res = varyfac.apply(fcit2);\n\t\t\t\tif(fcit2->is_zero()==false && res==result_t::l_applied) {\n\t\t\t\t\tauto toclean = result.append_child(newsum, it);\n\t\t\t\t\t// the varied factor itself cannot get rid of nested\n\t\t\t\t\t// products, that's for us to do at the top level prod.\n\t\t\t\t\tcleanup_dispatch(kernel, tr, toclean);\n\t\t\t\t\t// std::cerr << toclean << std::endl;\n\t\t\t\t\t}\n\n\t\t\t\t// restore original\n\t\t\t\tit=tr.replace(it, prodcopy.begin());\n\t\t\t\t}\n\t\t\t++pos;\n\t\t\t}\n\t\tif(tr.number_of_children(newsum)>0) {\n\t\t\tit=tr.move_ontop(it, newsum);\n\t\t\t}\n\t\telse {   // varying any of the factors produces nothing, variation is zero\n\t\t\tzero(it->multiplier);\n\t\t\t}\n//\t\tstd::cerr << it << std::endl;\n\t\tcleanup_dispatch(kernel, tr, it);\n//\t\tstd::cerr << it << std::endl;\t\t\n\t\tres=result_t::l_applied;\n\t\treturn res;\n\t\t}\n\n\tconst Derivative *der = kernel.properties.get<Derivative>(it);\n\tconst Accent     *acc = kernel.properties.get<Accent>(it);\n\tif(der || acc) {\n\t\tvary vry(kernel, tr, args);\n\n\t\tsibling_iterator sib=tr.begin(it);\n\t\tbool has_applied=false;\n\t\twhile(sib!=tr.end(it)) {\n\t\t\titerator app=sib;\n\t\t\t++sib;\n\t\t\tif(app->is_index()) continue;\n\t\t\tif(vry.can_apply(app)) {\n\t\t\t\tif(vry.apply(app)==result_t::l_applied) {\n\t\t\t\t\thas_applied=true;\n\t\t\t\t\tres=result_t::l_applied;\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t}\n\n\t\t// If no variation took place, set to zero if we are termlike.\n\t\tif(!has_applied && is_termlike(it)) {\n\t\t\tzero(it->multiplier);\n\t\t\treturn result_t::l_applied;\n\t\t\t}\n\n\t\treturn res;\n\t\t}\n\n\tif(*it->name==\"\\\\sum\") { // call vary on every term\n\t\tvary vry(kernel, tr, args);\n\n\t\tsibling_iterator sib=tr.begin(it);\n\t\twhile(sib!=tr.end(it)) {\n\t\t\titerator app=sib;\n\t\t\t++sib;\n\t\t\tif(vry.can_apply(app)) {\n\t\t\t\tres = vry.apply(app);\n\t\t\t\t}\n\t\t\telse {\n\t\t\t\t// remove this term\n\t\t\t\tres=result_t::l_applied;\n\t\t\t\tnode_zero(app);\n\t\t\t\t}\n\t\t\t}\n\n\t\tcleanup_dispatch(kernel, tr, it);\n\t\treturn res;\n\t\t}\n\n\tif(*it->name==\"\\\\int\") { // call vary on first argument\n\t\tvary vry(kernel, tr, args);\n\n\t\titerator sib=tr.begin(it);\n\t\tif(vry.can_apply(sib))\n\t\t\tres=vry.apply(sib);\n\t\treturn res;\n\t\t}\n\n\tif(*it->name==\"\\\\pow\") {\n\t\tEx backup(it);\n\t\t// Wrap the power in a \\cdbDerivative and then call @prodrule.\n\t\tit=tr.wrap(it, str_node(\"\\\\cdbDerivative\"));\n\t\tproduct_rule pr(kernel, tr);\n\t\tpr.can_apply(it);\n\t\tpr.apply(it);\n\t\t// Find the '\\cdbDerivative node again'.\n\t\tsibling_iterator sib=tr.begin(it);\n\t\tres=result_t::l_no_action;\n\t\twhile(sib!=tr.end(it)) {\n\t\t\tif(*sib->name==\"\\\\cdbDerivative\") {\n\t\t\t\ttr.flatten(sib);\n\t\t\t\tsib=tr.erase(sib);\n\t\t\t\tvary vry(kernel, tr, args);\n\t\t\t\titerator app=sib;\n\t\t\t\tif(vry.can_apply(app)) {\n\t\t\t\t\tres=vry.apply(app);\n\t\t\t\t\t}\n\t\t\t\tbreak;\n\t\t\t\t}\n\t\t\t++sib;\n\t\t\t}\n\t\tif(res!=result_t::l_applied) {\n\t\t\t// restore original\n\t\t\tit=tr.replace(it, backup.begin());\n\t\t\t}\n\t\treturn res;\n\t\t}\n\n\tif(tr.is_head(it)==false) {\n\t\tder = kernel.properties.get<Derivative>(tr.parent(it));\n\t\tacc = kernel.properties.get<Accent>(tr.parent(it));\n\n\t\tif(der || acc || is_single_term(it)) { // easy: just vary this term by substitution\n\t\t\t// std::cerr << \"single term \" << *it->name << std::endl;\n\t\t\tsubstitute subs(kernel, tr, args);\n\t\t\tif(subs.can_apply(it)) {\n\t\t\t\tif(subs.apply(it)==result_t::l_applied) {\n\t\t\t\t\treturn result_t::l_applied;\n\t\t\t\t\t}\n\t\t\t\t}\n\n\t\t\tif(is_termlike(it)) {\n\t\t\t\tzero(it->multiplier);\n\t\t\t\treturn result_t::l_applied;\n\t\t\t\t}\n\t\t\treturn result_t::l_no_action;\n\t\t\t}\n\t\t}\n\n\tif(is_nonprod_factor_in_prod(it)) {\n\t\tsubstitute subs(kernel, tr, args);\n\t\tif(subs.can_apply(it)) {\n\t\t\tif(subs.apply(it)==result_t::l_applied) {\n\t\t\t\treturn result_t::l_applied;\n\t\t\t\t}\n\t\t\t}\n\n\t\tif(is_termlike(it)) {\n\t\t\tzero(it->multiplier);\n\t\t\treturn result_t::l_applied;\n\t\t\t}\n\t\treturn result_t::l_no_action;\n\t\t}\n\n\t// If we get here, we are talking about a single term, e.g.\n\t// ex:= x_{m};\n\n\tif(is_single_term(it)) {\n\t\tsubstitute subs(kernel, tr, args);\n\t\tif(subs.can_apply(it)) {\n\t\t\tif(subs.apply(it)==result_t::l_applied) {\n\t\t\t\treturn result_t::l_applied;\n\t\t\t\t}\n\t\t\t}\n\t\t}\n\n\t// If we get here we have a single term for which we do not know\n\t// (yet) how to take a variational derivative. For instance some\n\t// unknown function f(a) varied wrt. a. This should spit out\n\t// \\delta{f(a)}{\\delta{a}}\\delta{a} or something like that.\n\n\tthrow RuntimeException(\"Do not yet know how to vary that expression.\");\n\t//\tstd::cerr << \"No idea how to vary single term \" << Ex(it) << std::endl;\n\n\treturn res;\n\t}\n\n"
  },
  {
    "path": "core/algorithms/vary.cnb",
    "content": "{\n\t\"cells\" : \n\t[\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\algorithm{vary}{Generic variation algorithm for functional derivatives.}\\n\\nGeneric variation command.  Takes a rule or a set of rules\\naccording to which the terms in a sum should be varied. In every term,\\napply the rule once to every factor.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\algorithm{vary}{Generic variation algorithm for functional derivatives.}\\n\\nGeneric variation command.  Takes a rule or a set of rules\\naccording to which the terms in a sum should be varied. In every term,\\napply the rule once to every factor.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}A B%\\n+A C\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\epsilon D B%\\n+A \\\\epsilon C%\\n+\\\\epsilon D C%\\n+A \\\\left(\\\\epsilon A%\\n-\\\\epsilon B\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex:= A B + A C;\\n\\nvary(_, $A -> \\\\epsilon D, B -> \\\\epsilon C, C -> \\\\epsilon A - \\\\epsilon B$ );\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"It also works when acting on powers, in which case it will use the\\nproduct rule to expand them.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"It also works when acting on powers, in which case it will use the\\nproduct rule to expand them.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}A^{3}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}3A^{2} \\\\delta\\\\left(A\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex:= A**3;\\nvary(_, $A -> \\\\delta{A}$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"This algorithm is thus mostly intended for variational derivatives.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"This algorithm is thus mostly intended for variational derivatives.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property PartialDerivative to~}\\\\partial{\\\\#}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}-\\\\int{}\\\\left(\\\\partial_{\\\\mu}{\\\\phi} \\\\partial^{\\\\mu}{\\\\phi}%\\n+m^{2} \\\\phi^{2}\\\\right)\\\\, {\\\\rm d}x\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"\\\\partial{#}::PartialDerivative;\\nex:= -\\\\int{\\\\partial_{\\\\mu}{\\\\phi} \\\\partial^{\\\\mu}{\\\\phi} + m**2 \\\\phi**2}{x};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}-\\\\int{}\\\\left(\\\\partial_{\\\\mu}{\\\\delta\\\\left(\\\\phi\\\\right)} \\\\partial^{\\\\mu}{\\\\phi}%\\n+\\\\partial_{\\\\mu}{\\\\phi} \\\\partial^{\\\\mu}{\\\\delta\\\\left(\\\\phi\\\\right)}%\\n+2m^{2} \\\\phi \\\\delta\\\\left(\\\\phi\\\\right)\\\\right)\\\\, {\\\\rm d}x\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"vary(ex, $\\\\phi -> \\\\delta{\\\\phi}$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}-\\\\int{}\\\\left(-\\\\delta\\\\left(\\\\phi\\\\right) \\\\partial_{\\\\mu}\\\\,^{\\\\mu}{\\\\phi}%\\n-\\\\partial^{\\\\mu}\\\\,_{\\\\mu}{\\\\phi} \\\\delta\\\\left(\\\\phi\\\\right)%\\n+2m^{2} \\\\phi \\\\delta\\\\left(\\\\phi\\\\right)\\\\right)\\\\, {\\\\rm d}x\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"integrate_by_parts(ex, $\\\\delta{\\\\phi}$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}-\\\\int{}\\\\left(-2\\\\delta\\\\left(\\\\phi\\\\right) \\\\partial^{\\\\mu}\\\\,_{\\\\mu}{\\\\phi}%\\n+2\\\\delta\\\\left(\\\\phi\\\\right) \\\\phi m^{2}\\\\right)\\\\, {\\\\rm d}x\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"canonicalise(_)\\nsort_product(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}-\\\\int{}\\\\delta\\\\left(\\\\phi\\\\right) \\\\left(-2\\\\partial^{\\\\mu}\\\\,_{\\\\mu}{\\\\phi}%\\n+2\\\\phi m^{2}\\\\right)\\\\, {\\\\rm d}x\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"factor_out(_, $\\\\delta{\\\\phi}$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1\n}\n"
  },
  {
    "path": "core/algorithms/vary.hh",
    "content": "\n#pragma once\n\n#include \"Algorithm.hh\"\n#include \"algorithms/sort_product.hh\"\n\nnamespace cadabra {\n\n\t/// \\ingroup algorithms\n\t///\n\t/// Generic variational derivative algorithm.\n\n\tclass vary : public Algorithm {\n\t\tpublic:\n\t\t\tvary(const Kernel&, Ex& tr, Ex& args);\n\n\t\t\tvirtual bool     can_apply(iterator st) override;\n\t\t\tvirtual result_t apply(iterator&) override;\n\n\t\tprivate:\n\t\t\tEx&        args;\n\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/algorithms/weyl_index_order.tex",
    "content": "\\cdbalgorithm{weyl\\_index\\_order}{}\n\nSorts the indices on a \\deprecated \nRiemann or Weyl tensor by first applying anti-symmetry in each pair,\nand subsequently sorting the pairs by using symmetry under pair\nexchange. This alphabetical sorting can be prohibited by giving a\nlist of indices which is preferred to be in the first pair.\n\\begin{screen}{1,2,4}\nR_{s2 s1 s3 r1};\n@weyl_index_order(%){s1};\nR_{s1 s2 r1 s3}\n@weyl_index_order(%);\nR_{r1 s3 s1 s2}\n\\end{screen}\n~\n"
  },
  {
    "path": "core/algorithms/young_project.cc",
    "content": "\n#include \"IndexIterator.hh\"\n#include \"algorithms/young_project.hh\"\n\nusing namespace cadabra;\n\nyoung_project::young_project(const Kernel& k, Ex& tr)\n\t: Algorithm(k,tr), remove_traces(false)\n\t{\n\t// For internal use in which one fills the young tableau structures directly.\n\t}\n\nyoung_project::young_project(const Kernel& k, Ex& tr,\n                             const std::vector<int>& shape,\n                             const std::vector<int>& indices)\n\t: Algorithm(k,tr), remove_traces(false)\n\t{\n\tint count=0;\n\tfor(unsigned int row=0; row<shape.size(); ++row) {\n\t\tfor(int col=0; col<shape[row]; ++col) {\n\t\t\ttab.add_box(row, indices[count]);\n\t\t\t++count;\n\t\t\t}\n\t\t}\n\t}\n\nbool young_project::can_apply(iterator it)\n\t{\n\tif(*it->name!=\"\\\\prod\") {\n\t\tif(!is_single_term(it)) {\n\t\t\treturn false;\n\t\t\t}\n\t\t}\n\n\tprod_wrap_single_term(it);\n\tif(nametab.number_of_rows()>0) { // have to convert names to numbers\n\t\ttab.copy_shape(nametab);\n\t\tpos_tab_t::iterator pi=tab.begin();\n\t\tname_tab_t::iterator ni=nametab.begin();\n\t\twhile(ni!=nametab.end()) {\n\t\t\tindex_iterator ii=index_iterator::begin(kernel.properties, it);\n\t\t\tunsigned int indexnum=0;\n\t\t\twhile(ii!=index_iterator::end(kernel.properties, it)) {\n\t\t\t\tif(subtree_exact_equal(&kernel.properties, ii, *ni)) {\n\t\t\t\t\t*pi=indexnum;\n\t\t\t\t\tbreak;\n\t\t\t\t\t}\n\t\t\t\t++indexnum;\n\t\t\t\t++ii;\n\t\t\t\t}\n\t\t\tif(indexnum==number_of_indices(kernel.properties, it)) {\n\t\t\t\tprod_unwrap_single_term(it);\n\t\t\t\treturn false; // cannot find indicated index in expression\n\t\t\t\t}\n\t\t\t++pi;\n\t\t\t++ni;\n\t\t\t}\n\t\t}\n\n\tprod_unwrap_single_term(it);\n\treturn true;\n\t}\n\nEx::iterator young_project::nth_index_node(iterator it, unsigned int num)\n\t{\n\tEx::fixed_depth_iterator indname=tr.begin_fixed(it, 2);\n\tindname+=num;\n\treturn indname;\n\t}\n\nAlgorithm::result_t young_project::apply(iterator& it)\n\t{\n\tprod_wrap_single_term(it);\n\tsym.clear();\n\n\tif(asym_ranges.size()>0) {\n\t\t// Convert index locations to box numbers.\n\t\tcombin::range_vector_t sublengths_scattered;\n\t\t//\t\ttxtout << \"asym_ranges: \";\n\t\tfor(unsigned int i=0; i<asym_ranges.size(); ++i) {\n\t\t\tcombin::range_t newr;\n\t\t\tfor(unsigned int j=0; j<asym_ranges[i].size(); ++j) {\n\t\t\t\t// Search asym_ranges[i][j]\n\t\t\t\tint offs=0;\n\t\t\t\tpos_tab_t::iterator tt=tab.begin();\n\t\t\t\twhile(tt!=tab.end()) {\n\t\t\t\t\tif((*tt)==asym_ranges[i][j]) {\n\t\t\t\t\t\tnewr.push_back(offs);\n\t\t\t\t\t\t//\t\t\t\t\t\ttxtout << asym_ranges[i][j] << \" \";\n\t\t\t\t\t\tbreak;\n\t\t\t\t\t\t}\n\t\t\t\t\t++tt;\n\t\t\t\t\t++offs;\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\tsublengths_scattered.push_back(newr);\n\t\t\t//\t\t\ttxtout << std::endl;\n\t\t\t}\n\t\ttab.projector(sym, sublengths_scattered);\n\t\t}\n\telse tab.projector(sym);\n\n\t// FIXME: We can also compress the result by sorting all\n\t// locations which belong to the same asym set. This could actually\n\t// be done in combinatorics already.\n\n\tEx rep;\n\trep.set_head(str_node(\"\\\\sum\"));\n\tfor(unsigned int i=0; i<sym.size(); ++i) {\n\t\t// Generate the term.\n\t\tEx repfac(it);\n\t\tfor(unsigned int j=0; j<sym[i].size(); ++j) {\n\t\t\tindex_iterator src_fd=index_iterator::begin(kernel.properties, it);\n\t\t\tindex_iterator dst_fd=index_iterator::begin(kernel.properties, repfac.begin());\n\t\t\tsrc_fd+=sym[i][j];        // take the index at location sym[i][j]\n\t\t\tdst_fd+=sym.original[j];  // and store it in location sym.original[j]\n\t\t\ttr.replace_index(dst_fd, src_fd);\n\t\t\t}\n\t\t// Remove traces of antisymmetric objects. This can really\n\t\t// only be done here, since combinatorics.hh does not know\n\t\t// about index values, only about index locations. Note: we also\n\t\t// have to remove the entry in sym.original & sym.multiplicity if\n\t\t// we decide that a term vanishes.\n\t\t// IMPORTANT: if there are still permutations by value to be\n\t\t// done afterwards, do not use this!\n\t\tif(remove_traces) {\n\t\t\tfor(unsigned int k=0; k<asym_ranges.size(); ++k) {\n\t\t\t\tfor(unsigned int kk=0; kk<asym_ranges[k].size(); ++kk) {\n\t\t\t\t\tindex_iterator it1=index_iterator::begin(kernel.properties, repfac.begin());\n\t\t\t\t\tit1+=asym_ranges[k][kk];\n\t\t\t\t\tfor(unsigned int kkk=kk+1; kkk<asym_ranges[k].size(); ++kkk) {\n\t\t\t\t\t\tindex_iterator it2=index_iterator::begin(kernel.properties, repfac.begin());\n\t\t\t\t\t\tit2+=asym_ranges[k][kkk];\n\t\t\t\t\t\tif(subtree_exact_equal(&kernel.properties, it1,it2)) {\n\t\t\t\t\t\t\tsym.set_multiplicity(i,0);\n\t\t\t\t\t\t\tgoto traceterm;\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\t}\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t}\n\n\t\t\t{\n\t\t\tmultiply(repfac.begin()->multiplier, sym.signature(i));\n\t\t\tmultiply(repfac.begin()->multiplier, tab.projector_normalisation());\n\t\t\titerator repfactop=repfac.begin();\n\t\t\tprod_unwrap_single_term(repfactop);\n\t\t\trep.append_child(rep.begin(), repfac.begin());\n\t\t\t}\n\ntraceterm:\n\t\t;\n\t\t}\n\tit=tr.replace(it,rep.begin());\n\n\tsym.remove_multiplicity_zero();\n\n\treturn result_t::l_applied;\n\t}\n"
  },
  {
    "path": "core/algorithms/young_project.hh",
    "content": "\n#pragma once\n\n#include \"Algorithm.hh\"\n#include \"YoungTab.hh\"\n\nnamespace cadabra {\n\n\tclass young_project : public Algorithm {\n\t\tpublic:\n\t\t\tyoung_project(const Kernel&, Ex&);\n\t\t\tyoung_project(const Kernel&, Ex&, const std::vector<int>& shape, const std::vector<int>& indices);\n\n\t\t\tvirtual bool     can_apply(iterator);\n\t\t\tvirtual result_t apply(iterator&);\n\n\t\t\t// Boxes represent tensor slots, the values in them\n\t\t\t// give the location in the tensor.\n\t\t\ttypedef yngtab::filled_tableau<unsigned int> pos_tab_t;\n\t\t\ttypedef yngtab::filled_tableau<iterator>     name_tab_t;\n\t\t\tpos_tab_t  tab;\n\t\t\tname_tab_t nametab;\n\t\t\tcombin::symmetriser<unsigned int> sym;\n\n\t\t\t// Implicit antisymmetry; used by tableaux.cc only so far. These\n\t\t\t// store index locations, so these are \"values\" from the\n\t\t\t// combinatorics.hh point of view.\n\t\t\tcombin::combinations<unsigned int>::permuted_sets_t asym_ranges;\n\t\t\tbool remove_traces;\n\n\t\tprivate:\n\t\t\titerator nth_index_node(iterator, unsigned int);\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/algorithms/young_project.tex",
    "content": "\\cdbalgorithm{young\\_project}{shape,indices}\n\nProject the indicated expression onto a Young tableau \nrepresentation. This includes the normalisation factor, such that\napplying the operation twice does not change the result anymore. \nFor example,\n\\begin{screen}{1,2,5,6}\nex:= A_{m n} B_{p}:\nyoung_project(_, shape=[2,1], indices=[0,1,2])\n  1/3 A_{m n} B_{p} + 1/3 A_{n m} B_{p} \n- 1/3 A_{p n} B_{m} - 1/3 A_{n p} B_{m};\nyoung_project(_, shape=[2,1], indices=[0,1,2])\n  1/3 A_{m n} B_{p} + 1/3 A_{n m} B_{p} \n- 1/3 A_{p n} B_{m} - 1/3 A_{n p} B_{m};\n\\end{screen}\nThe first argument gives the tableau shape, while the second argument\ngives the index position associated to each box in the Young tableau\n(similar to the way in which the \\subsprop{TableauSymmetry} property\nworks; note that this algorithm does not require the tensors to have\nany specific symmetries).  The index positions given in the second\nargument count from zero.\n\n\\cdbseealgo{young_project_tensor}\n\\cdbseealgo{young_project_product}\n\\cdbseeprop{TableauSymmetry}\n\n\n"
  },
  {
    "path": "core/algorithms/young_project_product.cc",
    "content": "\n#include \"Cleanup.hh\"\n#include \"algorithms/young_project_product.hh\"\n#include \"algorithms/young_project_tensor.hh\"\n#include \"algorithms/distribute.hh\"\n#include \"algorithms/collect_terms.hh\"\n#include \"algorithms/canonicalise.hh\"\n\nusing namespace cadabra;\n\nyoung_project_product::young_project_product(const Kernel& k, Ex& tr)\n\t: Algorithm(k, tr)\n\t{\n\t}\n\nbool young_project_product::can_apply(iterator it)\n\t{\n\tif(*it->name==\"\\\\prod\") return true;\n\treturn false;\n\t}\n\nAlgorithm::result_t young_project_product::apply(iterator& it)\n\t{\n\tresult_t res=result_t::l_no_action;\n\n\tEx rep;\n\titerator topsum = rep.set_head(str_node(\"\\\\sum\"));\n\n\tsibling_iterator sib=tr.begin(it);\n\tbool first=true;\n\twhile(sib!=tr.end(it)) {\n\t\tyoung_project_tensor ypt(kernel, tr, true);\n\t\tsibling_iterator nxt=sib;\n\t\t++nxt;\n\t\tif(ypt.can_apply(sib)) {\n\t\t\typt.modulo_monoterm=true;\n\t\t\titerator ii(sib);\n\t\t\typt.apply(ii);\n\t\t\tif(*ii->name!=\"\\\\sum\")\n\t\t\t\tii=tr.wrap(ii, str_node(\"\\\\sum\"));\n\n\t\t\tres=result_t::l_applied;\n\t\t\tif(first) {\n\t\t\t\t// Add a new \\prod node to rep for each term in the projected factor.\n\t\t\t\tfirst=false;\n\t\t\t\tsibling_iterator trm=tr.begin(ii);\n\t\t\t\twhile(trm!=tr.end(ii)) {\n\t\t\t\t\titerator prod=rep.append_child(topsum, str_node(\"\\\\prod\"));\n\t\t\t\t\tprod->fl.bracket=str_node::b_round;\n\t\t\t\t\tprod->multiplier=it->multiplier;\n\t\t\t\t\trep.append_child(prod, iterator(trm));\n\t\t\t\t\t++trm;\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\telse {\n\t\t\t\t// Distribute this projected factor over all existing terms in rep,\n\t\t\t\tsibling_iterator trm=rep.begin(topsum);\n\t\t\t\twhile(trm!=rep.end(topsum)) {\n\t\t\t\t\t//\t\t\t\t\t\t iterator tmp=trm;\n\t\t\t\t\tsibling_iterator nxttrm=trm;\n\t\t\t\t\t++nxttrm;\n\n\t\t\t\t\t// Copy this term out of the sum and append projected factor.\n\t\t\t\t\tEx work(trm);\n\t\t\t\t\titerator workit=work.begin();\n\t\t\t\t\titerator put=rep.append_child(work.begin(), str_node());\n\t\t\t\t\tif(tr.number_of_children(ii)==1)\n\t\t\t\t\t\trep.replace(put, tr.begin(ii));\n\t\t\t\t\telse {\n\t\t\t\t\t\trep.replace(put, ii);\n\n\t\t\t\t\t\t// Distribute the product.\n\t\t\t\t\t\tdistribute   dis(kernel, work);\n\t\t\t\t\t\tif(dis.can_apply(workit))\n\t\t\t\t\t\t\tdis.apply(workit);\n\t\t\t\t\t\t}\n\t\t\t\t\t//\t\t\t\t\t\t txtout << \"GOOD?\" << std::endl;\n\t\t\t\t\t//\t\t\t\t\t\t work.print_recursive_treeform(txtout, work.begin());\n\n\t\t\t\t\t// Canonicalise all new products.\n\t\t\t\t\tcanonicalise can(kernel, work);\n\t\t\t\t\t//\t\t\t\t\t\t txtout << *workit->name << \" \" << *put->name << std::endl;\n\t\t\t\t\tcan.apply_generic(workit, true, false, 0);\n\t\t\t\t\tif(*work.begin()->multiplier!=0) {\n\t\t\t\t\t\t// The upcoming move wants to see a sum, even if there is only one term\n\t\t\t\t\t\tif(*work.begin()->name!=\"\\\\sum\")\n\t\t\t\t\t\t\twork.wrap(work.begin(), str_node(\"\\\\sum\"));\n\n\t\t\t\t\t\t// Move back to the original tree.\n\t\t\t\t\t\tsibling_iterator cpyit=work.begin(work.begin());\n\t\t\t\t\t\twhile(cpyit!=work.end(work.begin())) {\n\t\t\t\t\t\t\tsibling_iterator cpyitnxt=cpyit;\n\t\t\t\t\t\t\t++cpyitnxt;\n\t\t\t\t\t\t\trep.move_before(trm, cpyit);\n\t\t\t\t\t\t\tcpyit=cpyitnxt;\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\t}\n\t\t\t\t\trep.erase(trm);\n\n\t\t\t\t\ttrm=nxttrm;\n\t\t\t\t\t}\n\t\t\t\tcollect_terms coll(kernel, rep);\n\t\t\t\tif(coll.can_apply(topsum))\n\t\t\t\t\tcoll.apply(topsum);\n\n\t\t\t\t// If collect terms removed the sum because there was only\n\t\t\t\t// one term (or zero) left, put it back in.\n\t\t\t\tif(*topsum->name!=\"\\\\sum\")\n\t\t\t\t\ttopsum=tr.wrap(topsum, str_node(\"\\\\sum\"));\n\t\t\t\t}\n\t\t\t}\n\t\telse {\n\t\t\tif(first) {\n\t\t\t\tfirst=false;\n\t\t\t\titerator prod=rep.append_child(topsum, str_node(\"\\\\prod\"));\n\t\t\t\tprod->fl.bracket=str_node::b_round;\n\t\t\t\tprod->multiplier=it->multiplier;\n\t\t\t\trep.append_child(prod, iterator(sib));\n\t\t\t\t}\n\t\t\telse {\n\t\t\t\t// just multiply all terms with this factor\n\t\t\t\tsibling_iterator trm=rep.begin(topsum);\n\t\t\t\twhile(trm!=rep.end(topsum)) {\n\t\t\t\t\titerator put=rep.append_child(trm,str_node());\n\t\t\t\t\ttr.replace(put, iterator(sib));\n\t\t\t\t\t++trm;\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t}\n\t\t//\t\t rep.print_recursive_treeform(debugout, rep.begin());\n\t\tsib=nxt;\n\t\t}\n\n\tif(res==result_t::l_applied) {\n\t\tit=tr.replace(it, rep.begin());\n\t\t// FIXME: this canonicalise should really not be necessary\n\t\t//\t\t txtout << \"WHOOAAH \" << *it->name << std::endl;\n\t\t//\t\t tr.print_recursive_treeform(txtout, it);\n\t\t//\t\t canonicalise can(tr, tr.end());\n\t\t//\t\t can.apply_recursive(it, false);\n\n\t\tcleanup_dispatch(kernel, tr, it);\n\t\t}\n\n\treturn res;\n\t}\n"
  },
  {
    "path": "core/algorithms/young_project_product.cnb",
    "content": "{\n\t\"cells\" : \n\t[\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\algorithm{young_project_product}{Project all tensors in a product with their Young tableau projector.}\\n\\nProject all tensors in a product with their Young tableau\\nprojector. Each factor is projected in turn, after which the product\\nis distributed and then canonicalised. This is often faster and more\\nmemory-efficient than first projecting every factor and then\\ndistributing.\\n\\nYoung projection can be used to find equalities between tensor\\npolynomials which are due to multi-term symmetries, such as the Ricci\\nidentity in the example below.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\algorithm{young_project_product}{Project all tensors in a product with their Young tableau projector.}\\n\\nProject all tensors in a product with their Young tableau\\nprojector. Each factor is projected in turn, after which the product\\nis distributed and then canonicalised. This is often faster and more\\nmemory-efficient than first projecting every factor and then\\ndistributing.\\n\\nYoung projection can be used to find equalities between tensor\\npolynomials which are due to multi-term symmetries, such as the Ricci\\nidentity in the example below.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}2R_{a b c d} R_{a c b d}-R_{a b c d} R_{a b c d}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"{a,b,c,d}::Indices.\\nR_{a b c d}::RiemannTensor.\\n\\nex:=2 R_{a b c d} R_{a c b d} - R_{a b c d} R_{a b c d};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}0\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"young_project_product(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1\n}\n"
  },
  {
    "path": "core/algorithms/young_project_product.hh",
    "content": "\n#pragma once\n\n#include \"Algorithm.hh\"\n\nnamespace cadabra {\n\n\tclass young_project_product : public Algorithm {\n\t\tpublic:\n\t\t\tyoung_project_product(const Kernel&, Ex&);\n\n\t\t\tvirtual bool     can_apply(iterator) override;\n\t\t\tvirtual result_t apply(iterator&) override;\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/algorithms/young_project_tensor.cc",
    "content": "\n#include \"IndexIterator.hh\"\n#include \"Exceptions.hh\"\n#include \"Cleanup.hh\"\n#include \"IndexClassifier.hh\"\n#include \"properties/Indices.hh\"\n#include \"properties/Integer.hh\"\n#include \"algorithms/young_project_tensor.hh\"\n#include \"algorithms/collect_terms.hh\"\n#include \"algorithms/indexsort.hh\"\n\nusing namespace cadabra;\n\nyoung_project_tensor::young_project_tensor(const Kernel& k, Ex& tr, bool modmono)\n\t: Algorithm(k, tr), modulo_monoterm(modmono)\n\t{\n\t}\n\nbool young_project_tensor::can_apply(iterator it)\n\t{\n\tif(*it->name==\"\\\\prod\") return false;\n\t\n\ttb=kernel.properties.get<TableauBase>(it);\n\tif(tb) {\n\t\tif(tb->size(kernel.properties, tr, it)>0)\n\t\t\treturn true;\n\t\t}\n\treturn false;\n\t}\n\nAlgorithm::result_t young_project_tensor::apply(iterator& it)\n\t{\n\t//\tstd::cout << \"at \" << *it->name << std::endl;\n\tassert(tb);\n\t//\ttxtout << typeid(*tb).name() << std::endl;\n\t// FIXME: handle cases with multiple tabs.\n\tTableauBase::tab_t tab=tb->get_tab(kernel.properties, tr, it, 0);\n\tif(tab.number_of_rows()==0)\n\t\treturn result_t::l_no_action;\n\t//\ttxtout << tab << std::endl;\n\n\tif(modulo_monoterm) {\n\t\tif(tab.number_of_rows()==1) // Nothing happends with fully symmetric tensors modulo monoterm.\n\t\t\treturn result_t::l_no_action;\n\t\tif(tab.row_size(0)==1 && tab.selfdual_column==0) // Ditto for fully anti-symmetric tensors & modmono.\n\t\t\treturn result_t::l_no_action;\n\t\t}\n\n\t// For non-trivial tableau shapes, apply the Young projector.\n\tEx rep;\n\trep.set_head(str_node(\"\\\\sum\"));\n\tif(tab.row_size(0)>0) {\n\t\tsym.clear();\n\t\ttab.projector(sym); //, modulo_monoterm);\n\n\t\t//\t\ttxtout << sym.size() << std::endl;\n\t\tfor(unsigned int i=0; i<sym.size(); ++i) {\n\t\t\tEx repfac(it);\n\t\t\tfor(unsigned int j=0; j<sym[i].size(); ++j) {\n\t\t\t\tindex_iterator src_fd=index_iterator::begin(kernel.properties, it);\n\t\t\t\tindex_iterator dst_fd=index_iterator::begin(kernel.properties, repfac.begin());\n\t\t\t\t//\t\t\ttxtout << sym[i][j] << \" \" << sym.original[j] << std::endl;\n\t\t\t\tsrc_fd+=sym[i][j];\n\t\t\t\tdst_fd+=sym.original[j];\n\t\t\t\t//\t\t\ttxtout << *src_fd->name  << std::endl;\n\t\t\t\t//\t\t\ttxtout << *dst_fd->name  << std::endl;\n\t\t\t\tdst_fd->name=src_fd->name;\n\t\t\t\t}\n\t\t\tmultiply(repfac.begin()->multiplier, sym.signature(i));\n\t\t\tmultiply(repfac.begin()->multiplier, tb->get_tab(kernel.properties, tr, it, 0).projector_normalisation());\n\t\t\titerator newtensor=rep.append_child(rep.begin(), repfac.begin());\n\t\t\tif(modulo_monoterm) { // still necessary for column exchange\n\t\t\t\tindexsort isort(kernel, rep);\n\t\t\t\t[[maybe_unused]] auto res=isort.can_apply(newtensor); // to set tb\n\t\t\t\tassert(res);\n\t\t\t\tisort.apply(newtensor);\n\t\t\t\t}\n\t\t\t}\n\t\tcollect_terms cterms(kernel, rep);\n\t\titerator rephead=rep.begin();\n\t\tcterms.apply(rephead);\n\t\t}\n\telse {\n\t\trep.append_child(rep.begin(), it);\n\t\t}\n\n\t// If there is a selfdual or anti-selfdual component, we need to add a term\n\t// for each generated term, which contains an epsilon. In the generated term,\n\t// find the positions of the indices which originally sat on the selfdual tensor,\n\t// then replace these with dummies which are repeated on the epsilon tensor.\n\n\t//\tWe should do all of this _here_, not before the Young projector, because we\n\t// want to avoid using indexsort.\n\n\tif(tab.selfdual_column!=0) {\n\t\t// Classify indices so we can insert dummies.\n\t\tIndexClassifier ic(kernel);\n\t\tIndexClassifier::index_map_t one, two, three, four, added_dummies;\n\t\tic.classify_indices_up(it, one, two);\n\t\tic.classify_indices(it, three, four);\n\n\t\t// Figure out the properties of the indices for which we want dummy partners.\n\t\tindex_iterator iit=index_iterator::begin(kernel.properties, it);\n\t\tiit+=tab(0,abs(tab.selfdual_column)-1);\n\t\tconst Integer *itg=kernel.properties.get<Integer>(iit, true);\n\t\tconst Indices *ind=kernel.properties.get<Indices>(iit, true);\n\t\tif(itg==0)\n\t\t\tthrow ConsistencyException(\"young_project_tensor: Need to know the range of the indices.\");\n\t\tif(ind==0)\n\t\t\tthrow ConsistencyException(\"young_project_tensor: Need to have a set of dummy indices.\");\n\n\t\t// Step through all generated terms and give each one an epsilon partner term.\n\t\tsibling_iterator tt=rep.begin(rep.begin());\n\t\twhile(tt!=rep.end(rep.begin())) {\n\t\t\tEx repfac(tt);\n\t\t\titerator prodit=repfac.wrap(repfac.begin(), str_node(\"\\\\prod\"));\n\t\t\titerator tensit=repfac.begin(prodit);\n\t\t\t// FIXME: take care of Euclidean signature cases.\n\t\t\t//\t\t\trepfac.insert(repfac.begin(prodit), str_node(\"I\"));\n\t\t\titerator epsit =repfac.append_child(prodit, str_node(\"\\\\epsilon\"));\n\n\t\t\t// Normalise the epsilon term appropriately.\n\t\t\tmultiply(prodit->multiplier,\n\t\t\t         multiplier_t(1)/combin::factorial(to_long(*(itg->difference.begin()->multiplier)/2)));\n\t\t\tif(tab.selfdual_column<0)\n\t\t\t\tflip_sign(prodit->multiplier);\n\n\t\t\t// Move the free indices to the epsilon factor.\n\t\t\tfor(unsigned int row=0; row<tab.column_size(abs(tab.selfdual_column)-1); ++row) {\n\t\t\t\t// Find index of original in newly generated term (all indices are different,\n\t\t\t\t// so this works).\n\t\t\t\tiit=index_iterator::begin(kernel.properties, tensit);\n\t\t\t\tindex_iterator iit_orig=index_iterator::begin(kernel.properties, it);\n\t\t\t\tiit_orig+=tab(row, abs(tab.selfdual_column)-1);\n\t\t\t\twhile(subtree_exact_equal(&kernel.properties, iit, iit_orig)==false)\n\t\t\t\t\t++iit;\n\n\t\t\t\tEx dum=ic.get_dummy(ind, &one, &two, &three, &four, &added_dummies);\n\t\t\t\trepfac.append_child(epsit, iterator(iit)); // move index to eps\n\t\t\t\titerator repind=rep.replace_index(iterator(iit), dum.begin()); // replace index on tens\n\t\t\t\tadded_dummies.insert(IndexClassifier::index_map_t::value_type(dum, repind));\n\t\t\t\t}\n\t\t\t// Now insert the new dummies in the epsilon.\n\t\t\tIndexClassifier::index_map_t::iterator adi=added_dummies.begin();\n\t\t\twhile(adi!=added_dummies.end()) {\n\t\t\t\titerator ni=repfac.append_child(epsit, adi->first.begin());\n\t\t\t\tni->fl.parent_rel=str_node::p_sub;\n\t\t\t\t++adi;\n\t\t\t\t}\n\t\t\tadded_dummies.clear();\n\n\t\t\t++tt;\n\t\t\trep.insert_subtree(tt, repfac.begin());\n\t\t\t}\n\t\t}\n\n\t// Final cleanup\n\tit=tr.replace(it,rep.begin());\n\n\tcleanup_dispatch(kernel, tr, it);\n\treturn result_t::l_applied;\n\t}\n"
  },
  {
    "path": "core/algorithms/young_project_tensor.cnb",
    "content": "\n{\n\t\"cells\" : \n\t[\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\algorithm{young_project_tensor}{Project tensors with their Young projector.}\\n\\nProject tensors with their Young projection operator. This works for\\nsimple symmetric or anti-symmetric objects, as in\\n\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\algorithm{young_project_tensor}{Project tensors with their Young projector.}\\n\\nProject tensors with their Young projection operator. This works for\\nsimple symmetric or anti-symmetric objects, as in\\n\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}A_{m n} A_{m p}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"A_{m n}::Symmetric.\\nex:= A_{m n} A_{m p};\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\left(\\\\frac{1}{2}A_{m n}+\\\\frac{1}{2}A_{n m}\\\\right) \\\\left(\\\\frac{1}{2}A_{m p}+\\\\frac{1}{2}A_{p m}\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"young_project_tensor(_);\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"but more generically works for any tensor which has\\na \\\\prop{TableauSymmetry} property attached to it. \"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"but more generically works for any tensor which has\\na \\\\prop{TableauSymmetry} property attached to it. \"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}A_{m n p}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"A_{m n p}::TableauSymmetry(shape={2,1}, indices={0,2,1}).\\nex:= A_{m n p};\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\frac{1}{3}A_{m n p}+\\\\frac{1}{3}A_{p n m} - \\\\frac{1}{3}A_{n m p} - \\\\frac{1}{3}A_{p m n}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"young_project_tensor(_);\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"When the parameters \\\\verb|modulo_monoterm| is set to \\\\verb|True|, the resulting\\nexpression will be simplified using the monoterm symmetries of the\\ntensor,\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"When the parameters \\\\verb|modulo_monoterm| is set to \\\\verb|True|, the resulting\\nexpression will be simplified using the monoterm symmetries of the\\ntensor,\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}A_{m n p}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"A_{m n p}::TableauSymmetry(shape={2,1}, indices={0,2,1}).\\nex:= A_{m n p};\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\frac{2}{3}A_{m n p} - \\\\frac{1}{3}A_{n p m}+\\\\frac{1}{3}A_{m p n}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"young_project_tensor(_, modulo_monoterm=True);\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"(in this example, the tensor is anti-symmetric in the indices~0 and 1,\\nhence the simplification compared to the previous example).\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"(in this example, the tensor is anti-symmetric in the indices~0 and 1,\\nhence the simplification compared to the previous example).\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1.0\n}\n\n"
  },
  {
    "path": "core/algorithms/young_project_tensor.hh",
    "content": "\n#pragma once\n\n#include \"Algorithm.hh\"\n#include \"properties/TableauBase.hh\"\n\nnamespace cadabra {\n\n\tclass young_project_tensor : public Algorithm {\n\t\tpublic:\n\t\t\tyoung_project_tensor(const Kernel&, Ex&, bool);\n\n\t\t\tvirtual bool     can_apply(iterator);\n\t\t\tvirtual result_t apply(iterator&);\n\n\t\t\tbool modulo_monoterm;\n\t\t\tcombin::symmetriser<unsigned int> sym;\n\t\tprivate:\n\t\t\tconst TableauBase     *tb;\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/algorithms/zoom.cc",
    "content": "\n#include \"algorithms/zoom.hh\"\n#include \"algorithms/substitute.hh\"\n#include \"Functional.hh\"\n#include \"Cleanup.hh\"\n\nusing namespace cadabra;\n\nzoom::zoom(const Kernel& k, Ex& e, Ex& rules_, bool partial)\n\t: Algorithm(k, e), rules(rules_), partial(partial)\n\t{\n\t// Convert rules into a list (if it isn't already)\n\trules = cadabra::make_list(rules);\n\n\t// Create a proper substitution rule out of the patterns (otherwise\n\t// substitute will not swallow them).\n\tcadabra::do_list(rules, rules.begin(), [&](Ex::iterator it) {\n\t\tif(*it->name!=\"\\\\arrow\") {\n\t\t\tauto wrap = rules.wrap(it, str_node(\"\\\\arrow\"));\n\t\t\trules.append_child(wrap, str_node(\"dummy\"));\n\t\t\t}\n\t\treturn true;\n\t\t});\n\n\t// Create a proper substitution rule out of the pattern (otherwise\n\t// substitute will not swallow it).\n\t// auto wrap = rules.wrap(rules.begin(), str_node(\"\\\\arrow\"));\n\t// rules.append_child(wrap, str_node(\"dummy\"));\n\t}\n\nbool zoom::can_apply(iterator it)\n\t{\n\t// Apply only on terms in a top-level sum (NO LONGER: or elements of a top-level list),\n\t// or on terms inside an integral.\n\t// The second condition can be relaxed in the future to cover other\n\t// operators which distribute over sums; for now let's be conservative.\n\t// Note that any changes here need corresponding changes in replace_match.\n\n\tif(*it->name==\"\\\\sum\") {\n\t\tif(tr.is_head(it) ||\n\t\t      *tr.parent(it)->name==\"\\\\int\" ||\n\t\t      *tr.parent(it)->name==\"\\\\equals\") {\n\n\t\t\treturn true;\n\t\t\t}\n\t\t}\n\tif(*it->name==\"\\\\ldots\")\n\t\treturn true;\n\t\n\treturn false;\n\t}\n\nAlgorithm::result_t zoom::apply(iterator& it)\n\t{\n\tresult_t res=result_t::l_no_action;\n\n\tif(*it->name==\"\\\\ldots\") {\n\t\t// Simply wrap in another ldots node.\n\t\tsibling_iterator sib=it, nxt=it;\n\t\t++nxt;\n\t\tauto ldots = tr.insert(sib, str_node(\"\\\\ldots\"));\n\t\ttr.reparent(ldots, sib, nxt);\n\t\treturn res;\n\t\t}\n\t\n   // Wrap all things which we want to remove from view in an\n\t// \\ldots node.\n\n\tsubstitute subs(kernel, tr, rules, partial);\n\tsibling_iterator sib=tr.begin(it);\n\tbool hiding=false;\n\tsibling_iterator current_ldots=tr.end(it);\n\twhile(sib!=tr.end(it)) {\n\t\tif(subs.can_apply(sib)==false) {\n\t\t\t// Hide this term/factor.\n\t\t\tres=result_t::l_applied;\n\t\t\tauto nxt=sib;\n\t\t\t++nxt;\n\t\t\tif(!hiding) {\n\t\t\t\tcurrent_ldots=tr.insert(sib, str_node(\"\\\\ldots\"));\n\t\t\t\thiding=true;\n\t\t\t\t}\n\t\t\telse {\n\t\t\t\tif(*current_ldots->name!=\"\\\\sum\") // wrap single term in new sum node.\n\t\t\t\t\tcurrent_ldots=tr.wrap(tr.begin(current_ldots), str_node(\"\\\\sum\"));\n\t\t\t\t}\n\t\t\ttr.reparent(current_ldots, sib, nxt);\n\t\t\tsib=nxt;\n\t\t\t}\n\t\telse {\n\t\t\t// Keep this term/factor visible.\n\t\t\thiding=false;\n\t\t\t++sib;\n\t\t\t}\n\t\t}\n\n\tcleanup_dispatch(kernel, tr, it);\n\n\treturn res;\n\t}\n"
  },
  {
    "path": "core/algorithms/zoom.cnb",
    "content": "{\n\t\"cell_id\": 12388625031739274582,\n\t\"cells\": [\n\t\t{\n\t\t\t\"cell_id\": 9790434250152926668,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 15712383533467766647,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\algorithm{zoom}{Only show selected terms in a sum, and restrict subsequent algorithms to these terms.}\\n\\nOften you want manipulations to only apply to a selected subset of terms in a large sum. The \\\\algo{zoom} \\nalgorithm makes only certain terms visible, representing the remaining terms with dots. Any subsequent \\nalgorithms will only act on these visible terms.\\n\\nHere is an expression with 5 terms,\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\algorithm{zoom}{Only show selected terms in a sum, and restrict subsequent algorithms to these terms.}\\n\\nOften you want manipulations to only apply to a selected subset of terms in a large sum. The \\\\algo{zoom} \\nalgorithm makes only certain terms visible, representing the remaining terms with dots. Any subsequent \\nalgorithms will only act on these visible terms.\\n\\nHere is an expression with 5 terms,\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 18249221998629101273,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 832102351445041075,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 9949232075425525555,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\int{A_{m n} + B_{m n} C + D_{m} F_{n} C + T_{m n} + B_{m n} R}{x}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\int \\\\left(A_{m n}+B_{m n} C+D_{m} F_{n} C+T_{m n}+B_{m n} R\\\\right)\\\\,\\\\,{\\\\rm d}x\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex:=\\\\int{ A_{m n} + B_{m n} C + D_{m} F_{n} C  + T_{m n} + B_{m n} R}{x};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 13659065226182250481,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 7824220655507828023,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"In order to restrict attention only to the terms containing a $B_{m n}$ factor, we use\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"In order to restrict attention only to the terms containing a $B_{m n}$ factor, we use\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 1689356463027717950,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 12771084065845159432,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 9274589530037907797,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\int{ ...  + B_{m n} C +  ...  + B_{m n} R}{x}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\int \\\\left( \\\\ldots +B_{m n} C+ \\\\ldots +B_{m n} R\\\\right)\\\\,\\\\,{\\\\rm d}x\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"zoom(_, $B_{m n} Q??$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 15624721342745846134,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 17410332808818929102,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"Subsequent algorithms only work on the visible terms above, not on the terms hidden inside the dots,\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"Subsequent algorithms only work on the visible terms above, not on the terms hidden inside the dots,\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 10129922943028457003,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 18342956436361625444,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 16005847141097910160,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\int{ ...  + B_{m n} Q +  ...  + B_{m n} R}{x}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\int \\\\left( \\\\ldots +B_{m n} Q+ \\\\ldots +B_{m n} R\\\\right)\\\\,\\\\,{\\\\rm d}x\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"substitute(_, $C->Q$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 3698624047896256704,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 1364384404771354882,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"To make the hidden terms visible again, use \\\\algo{unzoom}, and note that the third term below has remained unaffected\\nby the substitution above,\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"To make the hidden terms visible again, use \\\\algo{unzoom}, and note that the third term below has remained unaffected\\nby the substitution above,\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 12305737181127973918,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 14182150800835876859,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 15817951198748811538,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\int{A_{m n} + B_{m n} Q + D_{m} F_{n} C + T_{m n} + B_{m n} R}{x}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\int \\\\left(A_{m n}+B_{m n} Q+D_{m} F_{n} C+T_{m n}+B_{m n} R\\\\right)\\\\,\\\\,{\\\\rm d}x\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"unzoom(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 16646151267176514516,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 15699559416768481923,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"The \\\\algo{zoom}/\\\\algo{unzoom} combination is somewhat similar to the old deprecated \\\\algo{take_match}/\\\\algo{replace_match}\\nalgorithms, but makes it more clear that terms have been suppressed.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"The \\\\algo{zoom}/\\\\algo{unzoom} combination is somewhat similar to the old deprecated \\\\algo{take_match}/\\\\algo{replace_match}\\nalgorithms, but makes it more clear that terms have been suppressed.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 7109914892061753876,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 13381205589170017357,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"It is possible to give \\\\algo{zoom} a list of patterns, in which case each term that is kept \\nmust match at least one of these patterns. See the examples below.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"It is possible to give \\\\algo{zoom} a list of patterns, in which case each term that is kept \\nmust match at least one of these patterns. See the examples below.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 8311727161713613771,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 12630693352689133903,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 4332350231412736633,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"x A1 + (x)**2 A2 + y A3 + (y)**2 A4\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}x {A_{1}}+{x}^{2} {A_{2}}+y {A_{3}}+{y}^{2} {A_{4}}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex:= x A1 + x**2 A2 + y A3 + y**2 A4;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 3583791065499312572,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 13249471701688341117,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 3109806130242165243,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"x A1 +  ...  + y A3 +  ... \"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}x {A_{1}}+ \\\\ldots +y {A_{3}}+ \\\\ldots \\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"zoom(ex, ${x A??, y A??}$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 13696329711587056329,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 17285963096983226809,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 4422541137627824015,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"x A1 + (x)**2 A2 + y A3 + (y)**2 A4\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}x {A_{1}}+{x}^{2} {A_{2}}+y {A_{3}}+{y}^{2} {A_{4}}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"unzoom(ex);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 4724132867443574503,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 7359062134225205211,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 7673380454616900479,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"x A1 + (x)**2 A2 +  ... \"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}x {A_{1}}+{x}^{2} {A_{2}}+ \\\\ldots \\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"zoom(ex, ${x A??, x**2 A??}$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 6103038216337334699,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"\"\n\t\t}\n\t],\n\t\"description\": \"Cadabra JSON notebook format\",\n\t\"version\": 1.0\n}\n"
  },
  {
    "path": "core/algorithms/zoom.hh",
    "content": "\n#pragma once\n\n#include \"Algorithm.hh\"\n\nnamespace cadabra {\n\n\tclass zoom : public Algorithm {\n\t\tpublic:\n\t\t\tzoom(const Kernel& k, Ex& e, Ex& r, bool partial = true);\n\n\t\t\tvirtual bool     can_apply(iterator) override;\n\t\t\tvirtual result_t apply(iterator&) override;\n\n\t\tprivate:\n\t\t\tEx rules;\n\n\t\t\tstd::vector<sibling_iterator> to_erase;\n\t\t\tstd::vector<Ex::path_t>       to_keep;\n\n\t\t\tbool partial;\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/cadabra2-cli.cc",
    "content": "#include <iostream>\n#include <sstream>\n#include <linenoise.hpp>\n#ifndef _WIN32\n#include <sys/types.h>\n#include <pwd.h>\n#endif\n#ifdef _WIN32\n#include <Windows.h>\n#include <glibmm/miscutils.h>\n#endif\n#include <internal/string_tools.h>\n#include \"cadabra2-cli.hh\"\n#include \"CdbPython.hh\"\n#include \"Config.hh\"\n#include \"Exceptions.hh\"\n#include \"Config.hh\"\n#include \"pythoncdb/py_helpers.hh\"\n\n#include <boost/dll.hpp>\n#include <locale>\n#include <codecvt>\n\nusing namespace linenoise;\nnamespace py = pybind11;\n\n#define DATA_BEGIN   ((char) 2)\n#define DATA_END     ((char) 5)\n#define DATA_COMMAND ((char) 16)\n#define DATA_ESCAPE  ((char) 27)\n\nstd::string replace_all(std::string const& original, std::string const& from, std::string const& to )\n\t{\n\tstd::string results;\n\tstd::string::const_iterator end = original.end();\n\tstd::string::const_iterator current = original.begin();\n\tstd::string::const_iterator next = std::search( current, end, from.begin(), from.end() );\n\twhile ( next != end ) {\n\t\tresults.append( current, next );\n\t\tresults.append( to );\n\t\tcurrent = next + from.size();\n\t\tnext = std::search( current, end, from.begin(), from.end() );\n\t\t}\n\tresults.append( current, next );\n\treturn results;\n\t}\n\nShell::CatchOutput::CatchOutput()\n\t{\n\t}\n\nShell::CatchOutput::CatchOutput(const CatchOutput&)\n\t{\n\t}\n\nvoid Shell::CatchOutput::write(const std::string& str)\n\t{\n\t// std::cerr << \"Python wrote: \" << str << std::endl;\n\tcollect+=str;\n\t}\n\nvoid Shell::CatchOutput::clear()\n\t{\n\t// std::cerr << \"Python clear\" << std::endl;\n\tcollect=\"\";\n\t}\n\nvoid Shell::CatchOutput::flush()\n\t{\n\t}\n\nstd::string Shell::CatchOutput::str() const\n\t{\n\treturn collect;\n\t}\n\nShell::Shell(Flags flags)\n\t: globals(py::reinterpret_steal<py::dict>(nullptr))\n\t, flags(flags)\n\t{\n\tbool no_colour = flags & Flags::NoColour;\n\tcolour_error   = no_colour ? \"\" : \"\\033[31m\";\n\tcolour_warning = no_colour ? \"\" : \"\\033[33m\";\n\tcolour_info    = no_colour ? \"\" : \"\\033[36m\";\n\tcolour_success = no_colour ? \"\" : \"\\033[32m\";\n\tcolour_reset   = no_colour ? \"\" : \"\\033[0m\";\n\tcolour_bold    = no_colour ? \"\" : \"\\033[1m\";\n\n\tif (!(flags & Flags::NoReadline)) {\n\t\tset_histfile();\n\t\tLoadHistory(histfile.c_str());\n\t\tSetMultiLine(true);\n\t\t}\n\n\tsite_path = cadabra::install_prefix_of_module();\n\tglobals = py::globals();\n\tif (!globals) {\n\t\tthrow std::runtime_error(\"Could not fetch globals\");\n\t\t}\n\tsys = py::module::import(\"sys\");\n\tmain_module = pybind11::module::import(\"__main__\");\n\tmain_namespace = main_module.attr(\"__dict__\");\n\n\t// // Get sys module and append site path\n\t// py::list py_path = sys.attr(\"path\");\n\t// py_path.append(site_path);\n\tpy_stdout = sys.attr(\"stdout\");\n\tpy_stderr = sys.attr(\"stderr\");\n\t}\n\nShell::~Shell()\n\t{\n\tif (!(flags & Flags::NoReadline))\n\t\tSaveHistory(histfile.c_str());\n\t}\n\nvoid Shell::open_texmacs_logfile()\n\t{\n//\tlogf.open(\"cdb.log\");\n\t\n//\t// Get the file descriptor (so we can propagate it to the python side).\n//\tint fd=-1;\n//\t\n//#if defined(__unix__) || defined(__APPLE__)\n//\tFILE* file = (FILE*)(*((class std::basic_filebuf<char>*)fs.rdbuf())).\n//\t\t__get_file().file();\n//\tfd = fileno(file);\n//#elif defined(_WIN32)\n//\tfd = _fileno(((class std::basic_filebuf<char>*)fs.rdbuf())->_M_file.file());\n//#else\n//\tthrow std::runtime_error(\"cadabra2-cli: TeXmacs not supported on this platform\");\n//#endif\n//\n//\t// Make this log file available to python.\n//\tpy::module io = py::module::import(\"io\");\n//\tpy::object py_file = io.attr(\"open\")(fd, \"w\");\n//\tglobals[\"server\"].attr(\"logf\") = py_file;\n\t}\n\nvoid Shell::interact_texmacs()\n\t{\n\topen_texmacs_logfile();\n\t\n\t// Run cadabra2_defaults.py\n\ttry {\n\t\texecute_file(site_path + \"/cadabra2_defaults.py\", false);\n\t\t}\n\tcatch (const ExitRequest& err) {\n\t\tthrow ExitRequest(\"Error encountered while initializing the interpreter\");\n\t\t}\n\tstd::string stdOutErr =\n\t   \"import sys\\n\"\n\n\t   \"from cadabra2_cli import CatchOutput\\n\"\n\t   \"def setup_catch(cO, cE, sE):\\n\"\n\t   \"   global server\\n\"\n\t   \"   sys.stdout=cO\\n\"\n\t   \"   sys.stderr=cE\\n\";\n\texecute(stdOutErr);\n\n\t// Setup the C++ output catching objects and setup the Python side to\n\t// use these as stdout and stderr streams.\n\n\tpybind11::object setup_catch = main_module.attr(\"setup_catch\");\n\tsetup_catch(std::ref(catchOut), std::ref(catchErr), std::ref(*this));\n\n\tstd::cout << DATA_BEGIN << \"prompt#> \" << DATA_END;\n\tstd::cout << DATA_BEGIN << \"verbatim:\";\n\tshow_banner();\n\tstd::cout << DATA_END;\n\tstd::cout.flush();\n\n\tglobals[\"server\"].attr(\"texmacs\")=true;\n\n\tstd::string line;\n\tbool first=true;\n\n\twhile(true) {\n\t\tcollect.clear();\n\t\tif(!first) {\n\t\t\tif( globals[\"server\"].attr(\"output_sent\").cast<bool>()==false ) \n\t\t\t\tstd::cout << DATA_BEGIN << \"verbatim:\" << DATA_END << std::flush;\n\t\t\telse\n\t\t\t\tglobals[\"server\"].attr(\"output_sent\")=false;\n\t\t\t}\n\t\telse first=false;\n\t\t\n\t\twhile(std::getline(std::cin, line)) {\n\t\t\tif(line==\"<EOF>\")\n\t\t\t\tbreak;\n\t\t\tcollect += line+\"\\n\";\n\t\t\t}\n\t\tlogf << \"received block for execution: |\" << collect << \"|\" << std::endl;\n\t\tlogf.flush();\n\t\tstd::cout << DATA_BEGIN << \"verbatim:\" << std::flush;\n\t\ttry {\n\t\t\tbool display = !(flags & Flags::IgnoreSemicolons);\n\t\t\tstd::string error;\n\t\t\tstd::string code = cadabra::cdb2python_string(collect, display, error);\n\t\t\texecute(code);\n\t\t\tstd::string stdout_result = catchOut.str();\n\t\t\tcatchOut.clear();\n\t\t\tif(stdout_result.size()>0)\n\t\t\t\tstd::cout << DATA_BEGIN << \"verbatim:\" << stdout_result << DATA_END << std::flush;\n\t\t\t\n\t\t\tstd::cout << DATA_END << std::flush;\n\t\t\t}\n\t\tcatch (py::error_already_set& err) {\n\t\t\tstd::cout << DATA_END << std::flush;\n\t\t\tlogf << \"error: \" << err.what() << std::endl;\n\t\t\tlogf.flush();\n\t\t\thandle_error(err);\n\t\t\t}\n\t\t}\t\t\n\t}\n\nvoid Shell::show_banner() const\n\t{\n\tstd::cout << colour_bold + std::string(\"Cadabra \") + std::string(CADABRA_VERSION_FULL) + colour_reset\n\t\t\t\t << \" (build \" + std::string(CADABRA_VERSION_BUILD) + \" dated \"\n\t\t\t\t << std::string(CADABRA_VERSION_DATE) + \")\" << std::endl;\n\tstd::cout << \"Copyright (C) \" COPYRIGHT_YEARS \"  Kasper Peeters <info@cadabra.science>\" << std::endl;\n\tstd::cout << \"Info at https://cadabra.science/\" << std::endl;\n\tstd::cout << \"Available under the terms of the GNU GPL v3.\" << std::endl;\n\tstd::cout << \"Using SymPy version \" + str(evaluate(\"sympy.__version__\"))+\".\" << std::endl;\n\t}\n\nvoid Shell::interact()\n\t{\n\t// Run cadabra2_defaults.py\n\ttry {\n\t\texecute_file(site_path + \"/cadabra2_defaults.py\", false);\n\t\t}\n\tcatch (const ExitRequest& err) {\n\t\tthrow ExitRequest(\"Error encountered while initializing the interpreter\");\n\t\t}\n\n\t// Print startup info banner\n\tif (!(flags & Flags::NoBanner)) \n\t\tshow_banner();\n\n\t// Line input function (either use plain std::cin or Readline).\n\tstd::function<bool(const std::string&, std::string&)> get_input;\n\tif (flags & Flags::NoReadline)\n\t\tget_input = [](const std::string& prompt, std::string& line) {\n\t\t\tstd::cout << prompt << std::flush;\n\t\t\tstd::getline(std::cin, line);\n\t\t\tif (std::cin.eof()) {\n\t\t\t\tstd::cin.clear();\n\t\t\t\treturn true;\n\t\t\t\t}\n\t\t\telse {\n\t\t\t\treturn false;\n\t\t\t\t}\n\t\t\t};\n\telse {\n\t\tget_input = [](const std::string& prompt, std::string& line) {\n\t\t\treturn Readline(prompt.c_str(), line);\n\t\t\t};\n\t\t}\n\n\tstd::string curline;\n\twhile (true) {\n\t\tusing namespace std::placeholders;\n\t\tif (!(flags & Flags::NoReadline))\n\t\t\tSetCompletionCallback(std::bind(&Shell::set_completion_callback, this, _1, _2));\n\n\t\t\n\t\tif (collect.empty()) {\n\t\t\tcurline.clear();\n\t\t\tif (get_input(get_ps1(), curline)) {\n\t\t\t\tPyErr_SetNone(PyExc_KeyboardInterrupt);\n\t\t\t\thandle_error();\n\t\t\t\t}\n\t\t\ttry {\n\t\t\t\tprocess_ps1(curline);\n\t\t\t\t}\n\t\t\tcatch (py::error_already_set& err) {\n\t\t\t\thandle_error(err);\n\t\t\t\t}\n\t\t\t}\n\t\telse {\n\t\t\tif (get_input(get_ps2(), curline)) {\n\t\t\t\tPyErr_SetNone(PyExc_KeyboardInterrupt);\n\t\t\t\thandle_error();\n\t\t\t\t}\n\t\t\ttry {\n\t\t\t\tprocess_ps2(curline);\n\t\t\t\t}\n\t\t\tcatch (py::error_already_set& err) {\n\t\t\t\thandle_error();\n\t\t\t\t}\n\t\t\t}\n\n\t\tif (!(flags & Flags::NoReadline))\n\t\t\tAddHistory(curline.c_str());\n\t\t}\n\t}\n\npybind11::object Shell::evaluate(const std::string& code, const std::string& filename) const\n\t{\n\tauto co = py::reinterpret_steal<py::object>(\n\t\tPy_CompileString(code.c_str(), filename.c_str(), Py_eval_input));\n\tif (!co)\n\t\tthrow py::error_already_set();\n\n\tauto res = py::reinterpret_steal<py::object>(PyEval_EvalCode(co.ptr(), globals.ptr(), globals.ptr()));\n\tif (!res)\n\t\tthrow py::error_already_set();\n\treturn res;\n\t}\n\nvoid Shell::execute(const std::string& code, const std::string& filename)\n\t{\n\tauto co = py::reinterpret_steal<py::object>(\n\t\tPy_CompileString(code.c_str(), filename.c_str(), Py_file_input));\n\tif (!co)\n\t\tthrow py::error_already_set();\n\n\tauto res = py::reinterpret_steal<py::object>(PyEval_EvalCode(co.ptr(), globals.ptr(), globals.ptr()));\n\tif (!res)\n\t\tthrow py::error_already_set();\n\t}\n\nvoid Shell::execute_file(const std::string& filename, bool preprocess)\n\t{\n\tboost::filesystem::path abs_path = boost::filesystem::absolute(filename);\n\tstd::string abs_path_str = abs_path.parent_path().string();\n\tpy::list py_path = sys.attr(\"path\");\n\tpy_path.append(abs_path_str);\n\t\n\tbool display = !(flags & Flags::IgnoreSemicolons);\n\tstd::string code;\n\tstd::ifstream ifs(filename);\n\tif (!ifs.is_open()) {\n\t\tstd::string message = \"Could not open file \" + filename;\n\t\tPyErr_SetString(PyExc_FileNotFoundError, message.c_str());\n\t\thandle_error();\n\t\tthrow ExitRequest(\"Script ended execution due to an uncaught exception\");\n\t\t}\n\telse {\n\t\tstd::stringstream buffer;\n\t\tbuffer << ifs.rdbuf();\n\t\tcode = buffer.str();\n\t\t}\n\tif (preprocess) {\n\t\t// FIXME: this duplicates code in Server.cc; separate out so we always stay consistent.\n\t\tauto python_path = cadabra::install_prefix_of_module();\n\t\tstd::string startup =\n\t\t\t\"f=open(r'\" + python_path + \"/cadabra2_defaults.py'); \"\n\t\t\t\"code=compile(f.read(), 'cadabra2_defaults.py', 'exec'); \"\n\t\t\t\"exec(code); f.close() \";\n\t\tpy::exec(startup, main_namespace);\n\n\t\tstd::string error;\n//\t\tcode = \"import cadabra2\\nfrom cadabra2 import *\\nfrom cadabra2_defaults import *\\n\\n\" + cadabra::cdb2python_string(code, display, error);\n\t\tcode = cadabra::cdb2python_string(code, display, error);\n\t\t}\n\n\ttry {\n\t\tpy::exec(code, main_namespace); // globals, globals);\n\t\t}\n\tcatch (py::error_already_set& err) {\n\t\thandle_error(err);\n\t\tthrow ExitRequest(\"Script ended execution due to an uncaught exception.\");\n\t\t}\n\t}\n\nvoid Shell::interact_file(const std::string& filename, bool preprocess)\n\t{\n\tstd::ifstream ifs(filename);\n\tif (!ifs.is_open())\n\t\tthrow ExitRequest(\"Could not open file \" + filename);\n\n\ttry {\n\t\texecute(\n\t\t\t\"import cadabra2\\n\"\n\t\t\t\"from cadabra2 import *\\n\"\n\t\t\t\"from cadabra2_defaults import *\\n\"\n\t\t\t\"__cdbkernel__ = cadabra2.__cdbkernel__\");\n\t\t}\n\tcatch (py::error_already_set& err) {\n\t\thandle_error(err);\n\t\tthrow ExitRequest(\"Error occurred during script initialization\");\n\t\t}\n\n\tstd::string curline;\n\twhile (std::getline(ifs, curline)) {\n\t\t// Continuation line handling.\n\t\tif (!collect.empty() && curline.find_first_not_of(\" \\t\") == 0) {\n\t\t\ttry {\n\t\t\t\tprocess_ps2(\"\");\n\t\t\t\t}\n\t\t\tcatch (py::error_already_set& err) {\n\t\t\t\thandle_error();\n\t\t\t\tthrow ExitRequest(\"Script ended execution due to an uncaught exception\");\n\t\t\t\t}\n\t\t\t}\n\n\t\t// We don't yet have input for this 'cell'.\n\t\tif (collect.empty()) {\n\t\t\twrite_stdout(get_ps1() + curline, \"\", true);\n\t\t\ttry {\n\t\t\t\tprocess_ps1(curline);\n\t\t\t\t}\n\t\t\tcatch (py::error_already_set& err) {\n\t\t\t\thandle_error();\n\t\t\t\tthrow ExitRequest(\"Script ended execution due to an uncaught exception\");\n\t\t\t\t}\n\t\t\t}\n\t\telse {\n\t\t\twrite_stdout(get_ps2() + curline);\n\t\t\ttry {\n\t\t\t\tprocess_ps2(curline);\n\t\t\t\t}\n\t\t\tcatch (py::error_already_set& err) {\n\t\t\t\thandle_error();\n\t\t\t\tthrow ExitRequest(\"Script ended execution due to an uncaught exception\");\n\t\t\t\t}\n\t\t\t}\n\t\t}\n\n\tif (!collect.empty()) {\n\t\ttry {\n\t\t\tprocess_ps2(\"\");\n\t\t\t}\n\t\tcatch (py::error_already_set& err) {\n\t\t\thandle_error();\n\t\t\tthrow ExitRequest(\"Script ended execution due to an uncaught exception\");\n\t\t\t}\n\t\t}\n\t}\n\nvoid Shell::write_stdout(const std::string& text, const std::string& end, bool flush)\n\t{\n\ttry {\n\t\tpy_stdout.attr(\"write\")(text + end);\n\t\tif (flush)\n\t\t\tpy_stdout.attr(\"flush\")();\n\t\t}\n\tcatch (py::error_already_set& err) {\n\t\tstd::cerr << err.what() << '\\n';\n\t\t}\n\t}\n\nvoid Shell::write_stderr(const std::string& text, const std::string& end, bool flush)\n\t{\n\ttry {\n\t\tpy_stderr.attr(\"write\")(text + end);\n\t\tif (flush)\n\t\t\tpy_stderr.attr(\"flush\")();\n\t\t}\n\tcatch (py::error_already_set& err) {\n\t\tstd::cerr << err.what() << '\\n';\n\t\t}\n\t}\n\nvoid Shell::set_histfile()\n\t{\n\tstd::string homedir = \"~\";\n#ifdef _WIN32\n\tconst char* userprofile = getenv(\"USERPROFILE\");\n\tif (userprofile) {\n\t\thomedir = userprofile;\n\t\t}\n\telse {\n\t\tconst char* homedrive = getenv(\"HOMEDRIVE\");\n\t\tconst char* homepath = getenv(\"HOMEPATH\");\n\t\tif (homedrive && homepath) {\n\t\t\thomedir = homedrive;\n\t\t\thomedir += homepath;\n\t\t\t}\n\t\t}\n#else\n\tconst char* home = getenv(\"HOME\");\n\tif (home) {\n\t\thomedir = home;\n\t\t}\n\telse {\n\t\tauto pw = getpwuid(getuid());\n\t\tif (pw) {\n\t\t\thomedir = pw->pw_dir;\n\t\t\t}\n\t\t}\n#endif\n\n\tif (homedir.back() == '/' || homedir.back() == '\\\\')\n\t\thistfile = homedir + \".cadabra2_history\";\n\telse\n\t\thistfile = homedir + \"/.cadabra2_history\";\n\t}\n\nstd::string Shell::str(const py::handle& obj) const\n\t{\n\treturn py::str(obj); //.str().cast<std::string>();\n\t}\n\nstd::string Shell::repr(const py::handle& obj)\n\t{\n\tauto uni = py::reinterpret_steal<py::object>(PyObject_Repr(obj.ptr()));\n\tif (!uni) {\n\t\thandle_error();\n\t\treturn \"\";\n\t\t}\n\treturn str(uni);\n\t}\n\nstd::string Shell::sanitize(std::string s)\n\t{\n   replace_all(s, \"\\\\\", \"\\\\\\\\\");\n\treturn s;\n\t}\n\nvoid Shell::process_ps1(const std::string& line)\n\t{\n\t// Convert cadabra to python\n\tbool display = !(flags & Flags::IgnoreSemicolons);\n\n\t// In contrast to notebook cell processing, what we do here is\n\t// simpler. We just convert this first line. If it is complete\n\t// python code, we can execute it. If not, we just take this\n\t// line together with future lines until an empty line is\n\t// input, and then we convert & execute the whole block.\n\t// So we don't really do anything with ConvertData nor with\n\t// the result of `convert_line`.\n\tcadabra::ConvertData cv;\n\n\t// `converge` lines are *never* complete by themselves\n\tif(line.find(\"converge(\")!=std::string::npos) {\n\t\tcollect = line + \"\\n\";\n\t\treturn;\n\t\t}\n\t\n\tstd::pair<std::string, std::string> res = cadabra::convert_line(line, cv, display);\n\tconst std::string& output = res.second;\n\tif(output == \"::empty\") {\n\t\t// Cadabra continuation line, add the unprocessed line to collect\n\t\tcollect = line + \"\\n\";\n\t\treturn;\n\t\t}\n\n\tstd::string error;\n\tint status = cadabra::is_python_code_complete(output, error);\n\t// std::cerr << \"code=\" << status << \", \" << res.second << std::endl;\n\tswitch(status) {\n\t\tcase 0: // incomplete\n\t\t\t// std::cerr << \"seting collect to\\n|\" << res.first + res.second << \"|\" << std::endl;\n\t\t\tcollect = res.first + res.second + \"\\n\";\n\t\t\tbreak;\n\t\tcase 1: { // complete\n\t\t\tstd::string tmp = res.first + res.second;\n\t\t\tcollect.clear();\n\t\t\tif(tmp.size()>0) {\n\t\t\t\t// std::cerr << \"executing ps1\\n|\" << tmp << \"|\" << std::endl;\n\t\t\t\texecute(tmp);\n\t\t\t\t}\n\t\t\tbreak;\n\t\t\t}\n\t\tcase -1: // indentation error\n\t\t\tcollect.clear();\n\t\t\tthrow ParseException(error);\n\t\tcase -2: // syntax error\n\t\t\tcollect.clear();\n\t\t\tthrow ParseException(error);\n\t\tdefault:\n\t\t\tthrow InternalError(\"Code completion check returned invalid response.\");\n\t\t}\n\t}\n\nvoid Shell::process_ps2(const std::string& line)\n\t{\n\tstd::string code;\n\t\n\tif(line[0]!=DATA_END) {\n\t\tif(!line.empty()) {\n\t\t\t// std::cerr << \"received another line\" << std::endl;\n\t\t\tcollect += line + \"\\n\";\n\t\t\treturn;\n\t\t\t}\n\t\t\n\t\tbool display = !(flags & Flags::IgnoreSemicolons);\n\t\tstd::string error;\n\t\tcode = cadabra::cdb2python_string(collect, display, error);\n\t\tcollect.clear();\n\t\t}\n\telse {\n\t\tcode=collect;\n\t\t// std::cerr << \"received |\" << code << \"|\" << std::endl;\n\t\t}\n\t// std::cerr << \"executing ps2\\n|\" << code << \"|\" << std::endl;\n\texecute(code);\n\t}\n\nvoid Shell::set_completion_callback(const char* buffer, std::vector<std::string>& completions)\n\t{\n\tint len = strlen(buffer);\n\tif (len == 0 || !isalnum(buffer[len - 1]))\n\t\treturn;\n\tint pos = len - 1;\n\twhile (pos > 0) {\n\t\tif (!isalnum(buffer[pos - 1]))\n\t\t\tbreak;\n\t\t--pos;\n\t\t}\n\n\tstd::string partial(buffer + pos, len - pos);\n\tfor (const auto& item : globals) {\n\t\tauto key = str(item.first);\n\t\tif (key.rfind(partial, 0) == 0)\n\t\t\tcompletions.push_back(buffer + key.substr(partial.size()));\n\t\t}\n\t}\n\nstd::string Shell::get_ps1()\n\t{\n\tif( flags & Flags::TeXmacs ) {\n\t\treturn \"\";\n\t\t}\n\t\n\tif(py::hasattr(sys, \"ps1\")==false)\n\t\tsys.attr(\"ps1\") = \"> \";\n\tauto ps1 = sys.attr(\"ps1\");\n\treturn str(ps1);\n\t}\n\nstd::string Shell::get_ps2()\n\t{\n\tif( flags & Flags::TeXmacs )\n\t\treturn \"\";\n\n\tif(pybind11::hasattr(sys, \"ps2\")==false)\n\t\tsys.attr(\"ps2\") = \". \";\n\tauto ps2 = sys.attr(\"ps2\");\n\treturn str(ps2);\n\t}\n\nvoid Shell::handle_error()\n\t{\n\tcollect.clear();\n\tif (PyErr_Occurred()) {\n\t\tpy::error_already_set err;\n\t\thandle_error(err);\n\t\t}\n\t}\n\nvoid Shell::handle_error(py::error_already_set& err)\n\t{\n\tif(err.matches(PyExc_SystemExit)) {\n\t\tauto value = err.value();\n\t\tif(PyExceptionInstance_Check(value.ptr())) {\n\t\t\tpy::object code = py::reinterpret_borrow<py::object>(value.ptr()).attr(\"code\");\n\t\t\tif (code) {\n\t\t\t\tvalue = py::reinterpret_borrow<py::object>(code);\n\t\t\t\t}\n\t\t\t}\n\t\tif (!value || value.is_none()) {\n\t\t\tthrow ExitRequest{};\n\t\t\t}\n\t\telse if(PyLong_Check(value.ptr())) {\n\t\t\tthrow ExitRequest{ static_cast<int>(PyLong_AsLong(value.ptr())) };\n\t\t\t}\n\t\telse {\n\t\t\tthrow ExitRequest{ str(value) };\n\t\t\t}\n\t\t}\n\telse {\n\t\tlogf << \"sending error message\" << std::endl;\n\t\tif(flags & Flags::TeXmacs) {\n\t\t\tstd::cout << DATA_BEGIN << \"verbatim:\" << err.what() << DATA_END;\n\t\t\tstd::cout.flush();\n\t\t\tglobals[\"server\"].attr(\"output_sent\")=true;\n\t\t\t}\n\t\telse {\n\t\t\terr.restore(); // restore the exception so that python sees it again\n\t\t\tPySys_WriteStderr(\"%.1000s\", colour_error);\n\t\t\tPyErr_Print();\n\t\t\twrite_stderr(colour_reset, \"\", true);\n\t\t\t}\n\t\t}\n\n\tcollect.clear();\n\t}\n\nExitRequest::ExitRequest()\n\t: code(0) {}\n\nExitRequest::ExitRequest(int code)\n\t: code(code) {}\n\nExitRequest::ExitRequest(const std::string& message)\n\t: code(1), message(message) {}\n\nconst char* ExitRequest::what() const noexcept\n\t{\n\treturn message.c_str();\n\t}\n\nShell::Flags& operator |= (Shell::Flags& lhs, Shell::Flags rhs)\n\t{\n\tlhs = static_cast<Shell::Flags>(\n\t\tstatic_cast<unsigned int>(lhs) | static_cast<unsigned int>(rhs)\n\t\t\t\t\t\t\t\t\t\t\t  );\n\treturn lhs;\n\t}\n\nShell::Flags operator | (Shell::Flags lhs, Shell::Flags rhs)\n\t{\n\treturn lhs |= rhs;\n\t}\n\nbool operator & (Shell::Flags lhs, Shell::Flags rhs)\n\t{\n\treturn static_cast<bool>(\n\t\tstatic_cast<unsigned int>(lhs) & static_cast<unsigned int>(rhs)\n\t\t\t\t\t\t\t\t\t );\n\t}\n\nvoid help()\n\t{\n\tstd::cout <<\n\t\t\"cadabra2-cli: command line interface to cadabra2\\n\"\n\t\t\"Usage: cadabra2-cli [OPTIONS] [script1 [script2 [...]]\\n\"\n\t\t\"  -h      --help                Display this help message and exit\\n\"\n\t\t\"  -v      --version             Display the version number and exit\\n\"\n\t\t\"  -i      --interactive         Force interactive mode even if scripts are\\n\"\n\t\t\"                                provided (will be started in the same Python\\n\"\n\t\t\"                                context as the last script)\\n\"\n\t\t\"  -l      --linebyline          Run scripts as though the input to an\\n\"\n\t\t\"                                interactive session\\n\"\n\t\t\"  -f      --fatal               When a SystemExit exception is raised, do not\\n\"\n\t\t\"                                continue to execute any more scripts\\n\"\n\t\t\"  -q      --quiet               Do not display startup banner\\n\"\n\t\t\"  -n      --ignore-semicolons   Do not replace semicolons with calls to\\n\"\n\t\t\"                                display(...)\\n\"\n\t\t\"  -r      --noreadline          Do not use readline libraries for input\\n\"\n\t\t\"  -w      --nocolor             Do not colourize output\\n\"\n\t\t\"          --nocolour\\n\"\n\t\t\"  -V      --verbose             Print extra debugging information\" << std::endl;\n\t}\n\nvoid version()\n\t{\n\tstd::cout << CADABRA_VERSION_FULL << ' ' << CADABRA_VERSION_BUILD << '\\n';\n\t}\n\nint main(int argc, char* argv[])\n\t{\n   // Collect arguments\n\tstd::vector<std::string> opts, scripts;\n\tbool accept_opts = true;\n\tfor (int i = 1; i < argc; ++i) {\n\t\tchar* arg = argv[i];\n\t\tint len = strlen(arg);\n\t\tif (len == 0)\n\t\t\tcontinue;\n\t\tif(accept_opts) {\n\t\t\tif (arg[0] == '-') {\n\t\t\t\tif (len == 1) {\n\t\t\t\t\taccept_opts = false;\n\t\t\t\t\t}\n\t\t\t\telse if (arg[1] == '-') {\n\t\t\t\t\topts.emplace_back(arg + 2);\n\t\t\t\t\t}\n\t\t\t\telse {\n\t\t\t\t\tfor (int j = 1; j < len; ++j)\n\t\t\t\t\t\topts.emplace_back(1, arg[j]);\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\telse {\n\t\t\t\tscripts.emplace_back(arg);\n\t\t\t\t}\n\t\t\t}\n\t\telse {\n\t\t\tscripts.emplace_back(arg);\n\t\t\t}\n\t\t}\n\n\tShell::Flags flags = Shell::Flags::None;\n\tbool force_interactive = false;\n\tbool line_by_line = false;\n\tbool fatal = false;\n\tbool verbose = false;\n\n\tfor (const auto& opt : opts) {\n\t\tif (opt == \"i\" || opt == \"interactive\") {\n\t\t\tforce_interactive = true;\n\t\t\t}\n\t\telse if (opt == \"l\" || opt == \"linebyline\") {\n\t\t\tline_by_line = true;\n\t\t\t}\n\t\telse if (opt == \"f\" || opt == \"fatal\") {\n\t\t\tfatal = true;\n\t\t\t}\n\t\telse if (opt == \"q\" || opt == \"quiet\") {\n\t\t\tflags |= Shell::Flags::NoBanner;\n\t\t\t}\n\t\telse if (opt == \"n\" || opt == \"ignore-semicolons\") {\n\t\t\tflags |= Shell::Flags::IgnoreSemicolons;\n\t\t\t}\n\t\telse if (opt == \"h\" || opt == \"help\") {\n\t\t\thelp();\n\t\t\treturn 0;\n\t\t\t}\n\t\telse if (opt == \"v\" || opt == \"version\") {\n\t\t\tversion();\n\t\t\treturn 0;\n\t\t\t}\n\t\telse if (opt == \"V\" || opt == \"verbose\") {\n\t\t\tverbose = true;\n\t\t\t}\n\t\telse if (opt == \"w\" || opt == \"nocolour\" || opt == \"nocolor\") {\n\t\t\tflags |= Shell::Flags::NoColour;\n\t\t\t}\n\t\telse if (opt == \"r\" || opt == \"noreadline\") {\n\t\t\tflags |= Shell::Flags::NoReadline;\n\t\t\t}\n\t\telse if (opt == \"t\" || opt == \"texmacs\") {\n\t\t\tflags |= Shell::Flags::TeXmacs;\n\t\t\tflags |= Shell::Flags::NoReadline;\n\t\t\tflags |= Shell::Flags::NoColour;\n\t\t\t}\n\t\telse {\n\t\t\tstd::cerr << \"Unrecognised option \\\"\" << opt << \"\\\"\\n\";\n\t\t\thelp();\n\t\t\treturn 1;\n\t\t\t}\n\t\t}\n\n\tif (!scripts.empty())\n\t\tflags |= Shell::Flags::NoBanner;\n\n\tShell shell(flags);\n\tint last_exit_code = 0;\n\n\tfor (const auto& script : scripts) {\n\t\ttry {\n\t\t\tif (line_by_line)\n\t\t\t\tshell.interact_file(script, true);\n\t\t\telse\n\t\t\t\tshell.execute_file(script, true);\n\t\t\tlast_exit_code = 0;\n\t\t\t}\n\t\tcatch (const ExitRequest& err) {\n\t\t\tif (err.code != 0) {\n\t\t\t\tif (!err.message.empty())\n\t\t\t\t\tshell.write_stderr(err.message, \"\\n\", true);\n\t\t\t\tlast_exit_code = err.code;\n\t\t\t\t}\n\t\t\tif (verbose)\n\t\t\t\tshell.write_stderr(\"Script exited with code \" + std::to_string(err.code), \"\\n\", true);\n\t\t\tif (fatal)\n\t\t\t\treturn err.code;\n\t\t\t}\n\t\t}\n\tif (scripts.empty() || force_interactive) {\n\t\ttry {\n\t\t\tif(flags & Shell::Flags::TeXmacs) shell.interact_texmacs();\n\t\t\telse                              shell.interact();\n\t\t\t}\n\t\tcatch (const std::logic_error& err) {\n\t\t\tshell.write_stderr(\"\\nTerminated by user interrupt.\\n\");\n\t\t\treturn 0;\n\t\t\t}\n\t\tcatch (const ExitRequest& err) {\n\t\t\tif (err.code != 0) {\n\t\t\t\tif (!err.message.empty())\n\t\t\t\t\tshell.write_stderr(err.message, \"\\n\", true);\n\t\t\t\tlast_exit_code = err.code;\n\t\t\t\t}\n\t\t\tif (verbose)\n\t\t\t\tshell.write_stderr(\"Exited with code \" + std::to_string(err.code), \"\\n\", true);\n\t\t\treturn err.code;\n\t\t\t}\n\t\t}\n\n\treturn last_exit_code;\n\t}\n\nPYBIND11_EMBEDDED_MODULE(cadabra2_cli, m)\n\t{\n\t//   auto cadabra_module = pybind11::module::import(\"cadabra2\");\n\n\tpybind11::class_<Shell::CatchOutput>(m, \"CatchOutput\")\n\t.def(\"write\", &Shell::CatchOutput::write)\n\t.def(\"clear\", &Shell::CatchOutput::clear)\n\t.def(\"flush\", &Shell::CatchOutput::flush)\t\t\n\t;\n\n\tpybind11::class_<Shell>(m, \"Shell\");\n\t}\n"
  },
  {
    "path": "core/cadabra2-cli.hh",
    "content": "#include <string>\n#include <memory>\n#include <fstream>\n\n// Work around MSVC linking problem\n#ifdef _DEBUG\n#define CADABRA_CLI_DEBUG_MARKER\n#undef _DEBUG\n#endif\n//#include <Python.h>\n#include <pybind11/pybind11.h>\n#include <pybind11/embed.h>\n#ifdef CADABRA_CLI_DEBUG_MARKER\n#define _DEBUG\n#undef CADABRA_CLI_DEBUG_MARKER\n#endif\n\nclass Shell : public pybind11::scoped_interpreter {\n\tpublic:\n\t\tenum class Flags : unsigned int {\n\t\t\tNone             = 0x00,\n\t\t\tNoBanner         = 0x01,\n\t\t\tIgnoreSemicolons = 0x02,\n\t\t\tNoColour         = 0x04,\n\t\t\tNoReadline       = 0x08,\n\t\t\tTeXmacs          = 0x10\n\t\t};\n\t\t\n\t\tShell(Flags flags);\n\t\t~Shell();\n\t\t\n\t\tvoid start();\n\t\tvoid interact();\n\t\tvoid interact_texmacs();\n\t\tpybind11::object evaluate(const std::string& code, const std::string& filename = \"<stdin>\") const;\n\t\tvoid execute(const std::string& code, const std::string& filename = \"<stdin>\");\n\t\tvoid execute_file(const std::string& filename, bool preprocess = true);\n\t\tvoid interact_file(const std::string& filename, bool preprocess = true);\n\n\t\tvoid show_banner() const;\n\t\tvoid write_stdout(const std::string& text, const std::string& end = \"\\n\", bool flush = false);\n\t\tvoid write_stderr(const std::string& text, const std::string& end = \"\\n\", bool flush = false);\n\t\t\n\t\tclass CatchOutput {\n\t\t\tpublic:\n\t\t\t\tCatchOutput();\n\t\t\t\tCatchOutput(const CatchOutput&);\n\n\t\t\t\tvoid        write(const std::string& txt);\n\t\t\t\tvoid        clear();\n\t\t\t\tvoid        flush();\n\t\t\t\tstd::string str() const;\n\t\t\tprivate:\n\t\t\t\tstd::string collect;\n\t\t\t};\n\n\t\tCatchOutput catchOut, catchErr;\n\n\tprivate:\n\t\tvoid set_histfile();\n\t\tstd::string histfile;\n\t\tstd::string site_path;\n\t\tstd::ofstream logf;\n\n\t\tstd::string str(const pybind11::handle& obj) const;\n\t\tstd::string repr(const pybind11::handle& obj);\n\t\tstd::string sanitize(std::string s);\n\n\t\tvoid process_ps1(const std::string& line);\n\t\tvoid process_ps2(const std::string& line);\n\t\tvoid set_completion_callback(const char* buffer, std::vector<std::string>& completions);\n\n\t\tstd::string get_ps1();\n\t\tstd::string get_ps2();\n\n\t\tvoid handle_error();\n\t\tvoid handle_error(pybind11::error_already_set& err);\n\n\t\tvoid open_texmacs_logfile();\n\t\t\n\t\t// These mimic what we do in Server.cc\n\t\tpybind11::module             main_module;\n\t\tpybind11::object             main_namespace;\n\t\t// FIXME: Do we need globals?\n\t\tpybind11::dict   globals;\n\t\tpybind11::object sys;\n\t\tpybind11::object py_stdout, py_stderr;\n\t\tstd::string      collect;\n\n\t\tconst char* colour_error;\n\t\tconst char* colour_warning;\n\t\tconst char* colour_info;\n\t\tconst char* colour_success;\n\t\tconst char* colour_reset;\n\t\tconst char* colour_bold;\n\t\tFlags flags;\n};\n\nclass ExitRequest : public std::exception {\n\tpublic:\n\t\tExitRequest();\n\t\tExitRequest(int code);\n\t\tExitRequest(const std::string& message);\n\n\t\tvirtual const char* what() const noexcept override;\n\n\t\tint code;\n\t\tstd::string message;\n};\n\n\nShell::Flags& operator |= (Shell::Flags& lhs, Shell::Flags rhs);\nShell::Flags operator | (Shell::Flags lhs, Shell::Flags rhs);\nbool operator & (Shell::Flags lhs, Shell::Flags rhs);\n"
  },
  {
    "path": "core/cadabra2.in",
    "content": "#!${Python_CDB_EXECUTABLE}\n#\n# \\ingroup pythoncore\n#\n# \\file \n# Command line interpreter for Cadabra, written in Python.\n#\n#     cadabra2 [-d] [filename]\n#\n# Running with the '-d' flag runs cadabra under gdb, so that\n# one can generate back traces etc.\n\nimport sys\nimport site\nfrom code import InteractiveConsole\nimport code\nimport re\nimport readline\nimport rlcompleter\nimport os\n\n# Make sure we can find the cadabra2 python module; is always\n# installed in PYTHON_SITE_PATH. DEPRECATED and no longer necessary.\n# install_prefix=os.path.realpath(sys.argv[0])\n# install_prefix=install_prefix.replace(os.sep+'bin'+os.sep+'cadabra2', os.sep+'${PYTHON_SITE_PATH}')\n# print(\"Module path \", install_prefix)\n# sys.path.append(install_prefix)\n\nfrom cadabra2 import *\n\nclass FileCacher:\n    \"Cache the stdout text so we can analyze it before returning it\"\n    def __init__(self): self.reset()\n    def reset(self): self.out = []\n    def write(self,line): self.out.append(line)\n    def flush(self):\n#        output = '\\n'.join(self.out)\n        output=self.out\n        self.reset()\n        return output\n\ndef findDefaults():\n    for d in sys.path:\n        filepath = os.path.join(d, \"cadabra2_defaults.py\")\n        if os.path.isfile(filepath):\n            return filepath\n    return None\n    \nclass Shell(InteractiveConsole):\n    \"Wrapper around Python that can filter input/output to the shell\"\n    def __init__(self):\n        self.stdout = sys.stdout\n        self.cache = FileCacher()\n        # Variables to keep track of multi-line parsing info.\n        self.convert_data = ConvertData()\n        InteractiveConsole.__init__(self)\n        return\n\n    # If the object to be displayed is an Ex (add Property), print it\n    # using the human-readable str (FIXME: add other printers). If not,\n    # pass it on to the previously existing display hook.\n    def _displayhook(self, arg):\n        if isinstance(arg, Ex):\n            pass\n            #print(str(arg))\n        elif isinstance(arg, Property):\n            pass\n            #print(str(arg))\n        else:\n            self.remember_display_hook(arg)\n\n            \n    # Setup hooks for pretty printing.\n    def set_display(self):\n        self.remember_display_hook = sys.displayhook\n        sys.displayhook = self._displayhook\n\n    def unset_display(self):\n        sys.displayhook = self.remember_display_hook\n\n\n    def get_output(self): sys.stdout = self.cache\n    def return_output(self): sys.stdout = self.stdout\n\n    def push(self, line):\n\n        # line = self.preprocess(line, True)\n        prefix, line = convert_line(line, self.convert_data, True)\n        if self.convert_data.lhs == \"\":\n            # print('executing: ')\n            # print(line) # line is generically multiple lines\n\n            # Now feed the pre-parsed input to Python.\n            self.get_output()\n            sys.ps1='> '\n            ret=\"\"\n            line+=\"\\n\" # InteractiveConsole needs a terminating newline\n            for single in line.splitlines():\n               ret=InteractiveConsole.push(self, single)\n            self.return_output()\n            output = self.cache.flush()\n            for line in output:\n                sys.stdout.write(line)\n\n            return ret\n        else:\n            # Preprocessing has detected an unfinished Cadabra line;\n            # switch the prompt to indicate Cadabra continuation, and\n            # do not feed the line to Python yet.\n            sys.ps1='| '\n            return \"\"\n\nif __name__ == '__main__':\n    sh = Shell()\n    sys.ps1='> '\n    sys.ps2='. '\n    readline.set_completer(rlcompleter.Completer(locals()).complete)\n    readline.parse_and_bind(\"tab: complete\")\n\n    if len(sys.argv)>1:\n        if '-d' in sys.argv:\n            #rs = \"lldb -ex r --args ${Python_EXECUTABLE} \"+sys.argv[0];\n            rs = \"gdb -q -ex r --args ${Python_EXECUTABLE} \"+sys.argv[0];\n            for a in sys.argv[1:]:\n                if a!='-d':\n                    rs += \" \"+a\n            #print('executing '+rs)\n            os.system(rs)\n        else:\n            with open(findDefaults()) as f:\n                code = compile(f.read(), \"cadabra2_defaults.py\", 'exec')\n                exec(code)\n\n            sh2 = InteractiveConsole()\n            with open(sys.argv[1]) as f:\n                collect=\"\"\n                for line in f:\n                    line=line.rstrip()\n                    prefix, res = convert_line(line, sh.convert_data, True)\n                    if res!=\"::empty\":\n                       collect += res+\"\\n\"\t\t    \n                # print(\"----\\n\"+collect+\"----\\n\")\n                cmp = compile(collect, sys.argv[1], 'exec')\n                exec(cmp)\n                # would be nice to be able to continue from here on the command line, but that requires\n                # pulling in the right locals/globals\n    else:\n        defaults_loc = findDefaults()\n        sh.runsource(\"import os; import sys; print('Cadabra @CADABRA_VERSION_SEM@ (build @CADABRA_VERSION_BUILD@ dated @CADABRA_VERSION_DATE@)'); print ('Copyright (C) @COPYRIGHT_YEARS@  Kasper Peeters <info@cadabra.science>'); f=open('\"+defaults_loc+\"'); code=compile(f.read(), 'cadabra2_defaults.py', 'exec'); exec(code); f.close(); print('Using SymPy version '+sympy.__version__);\")\n        sh.interact(banner='Info at https://cadabra.science/\\nAvailable under the terms of the GNU General Public License v3\\n')\n"
  },
  {
    "path": "core/cadabra2_defaults.py.in",
    "content": "##\n# \\file    cadabra2_defaults.py\n# \\ingroup pythoncore\n# Cadabra2 pure Python functionality.\n#\n# This is a pure-python initialisation script to set the  path to\n# sympy and setup printing of Cadabra expressions.  This script is\n# called both by the command line interface 'cadabra2' as well as by\n# the GUI backend server 'cadabra-server'.\n\nimport sys\nimport cadabra2\nfrom cadabra2 import *\nfrom importlib.machinery import PathFinder, ModuleSpec, SourceFileLoader\nfrom importlib.abc import MetaPathFinder\nfrom cdb_appdirs import user_config_dir, user_data_dir\nfrom pathlib import Path\nimport datetime\nimport atexit\nimport rlcompleter\n\n__cdbkernel__=cadabra2.__cdbkernel__\n__cdbkernel__.completer=rlcompleter.Completer()\n\nimport os\nos.environ.setdefault('PATH', '')\n\nPY3 = sys.version_info[0] == 3\nif PY3:\n   unicode = str\n\nif \"@ENABLE_JUPYTER@\" == \"OFF\":\n   discr = \"\\\\discretionary{}{}{} \"\nelse:\n   discr = \"\"\n   \nclass PackageCompiler(MetaPathFinder):\n        @classmethod\n        def find_module(cls, fullname, path):\n                return find_spec(fullname, path, None)\n\n        @classmethod\n        def find_spec(cls, fullname, path, target=None):\n                #log_(\"Finding {}, path=[{}]\".format(fullname, ', '.join(f'\"{p}\"' for p in path) if path is not None else \"\"))\n                # Top-level import if path=None\n                if path is None or path == \"\":\n                        path = sys.path\n                # Get unqualified package name\n                if '.' in fullname:\n                        parents = fullname.split('.')\n                        name = parents.pop()\n                else:\n                        name = fullname\n                        parents = []\n                # Go through path and try to find a notebook.\n                for entry in path:\n                   have_cnb = os.path.isfile(os.path.join(entry, name + \".cnb\"))\n                   have_cdb = os.path.isfile(os.path.join(entry, name + \".cdb\"))\n                   have_ipynb = os.path.isfile(os.path.join(entry, name + \".ipynb\"))\n                   if have_cnb or have_cdb or have_ipynb:\n                       # Prepend the folder to the `parents`, so that two identically named\n                       # notebooks in different folders will not map to the same cached/converted file.\n                       path_parts = list( Path(entry).resolve().parts[1:] )\n                       parents = path_parts + parents\n                      \n                       # Notebook was found. Create a version of it in the temporary directory, then\n                       # return a ModuleSpec object to allow Python to load that file\n                       pkg_path = os.path.join(user_config_dir(), \"cadabra_packages\", *parents)\n                       # Create the path if it doesn't exist\n                       if not os.path.exists(pkg_path):\n                               os.makedirs(pkg_path)\n                       if have_cnb:                                             \n                          compile_package__(os.path.join(entry, name + \".cnb\"), os.path.join(pkg_path, name + \".py\"))\n                       elif have_cdb:                                             \n                          compile_package__(os.path.join(entry, name + \".cdb\"), os.path.join(pkg_path, name + \".py\"))\n                       else:                                             \n                          compile_package__(os.path.join(entry, name + \".ipynb\"), os.path.join(pkg_path, name + \".py\"))\n                       return ModuleSpec(\n                                        fullname, \n                                        SourceFileLoader(fullname, os.path.join(pkg_path, name + \".py\")), \n                                        origin=os.path.join(pkg_path, name + \".py\"))\n                \n                # Return none if no notebook was found\n                return None\n\n# Prepend to sys.meta_path, so that all imports will first be checked in\n# case they are notebooks that need compiling\nsys.meta_path.insert(0, PackageCompiler)\n\n# Add current directory to Python module import path.\nsys.path.append(\".\")\n\n#sys.path.insert(0,'/home/kasper/Development/git.others/sympy') \n\n# Attempt to import sympy; if not, setup logic so that the\n# shell does not fail later.\n\ntry:\n    import sympy\nexcept:\n    class Sympy:\n        \"\"\"!@brief Stub object for when Sympy itself is not available.\n        \n        @long When Sympy is not available, this object contains some basic\n        functionality to prevent things from breaking elsewhere.\n        \"\"\"\n        __version__=\"unavailable\"\n\n    sympy = Sympy()\n\nif sympy.__version__ != \"unavailable\":\n    from sympy import symbols\n    from sympy import latex\n    from sympy import Matrix as sMatrix\n\n\ndef detect_terminal():\n    \"\"\"Detect which terminal emulator is being used.\"\"\"\n    term = os.environ.get('TERM', '').lower()\n    term_program = os.environ.get('TERM_PROGRAM', '').lower()\n    \n    if 'kitty' in term:\n        return 'kitty'\n    elif 'iterm' in term_program:\n        return 'iterm2'\n    else:\n        return 'unknown'      \n\ndef kitty_serialize_gr_command(**cmd):\n    payload = cmd.pop('payload', None)\n    cmd = ','.join(f'{k}={v}' for k, v in cmd.items())\n    ans = []\n    w = ans.append\n    w(b'\\033_G'), w(cmd.encode('ascii'))\n    if payload:\n        w(b';')\n        w(payload)\n    w(b'\\033\\\\')\n    return b''.join(ans)\n\ndef kitty_write_chunked(**cmd):\n    data = base64.standard_b64encode(cmd.pop('data'))\n    while data:\n        chunk, data = data[:4096], data[4096:]\n        m = 1 if data else 0\n        sys.stdout.buffer.write(kitty_serialize_gr_command(payload=chunk, m=m, **cmd))\n        sys.stdout.flush()\n        cmd.clear()\n    print('')\n        \n# Whether running in command-line mode or as client-server, there always\n# needs to be a Server object known as 'server' through which interaction\n# with the display routines is handled. The 'display' function will\n# call the 'server.send' method.\n\nif 'server' in globals():\n    mopen=\"\\\\begin{dmath*}{}\";\n    mclose=\"\\\\end{dmath*}\";\nelse:\n    mopen=''\n    mclose=''\n    class Server:\n        \"\"\"!@brief Object to handle advanced display in a UI-independent way.\n\n        @long Cadabra makes available to Python a Server object, which\n        contains functions to send output to the user. When running\n        from the command line this simply prints to the screen, but it\n        can talk to a remote client to display images and maths.\n        \"\"\"\n\n        def __init__(self):\n            self.texmacs = False\n            # self.logf    = open(\"cdb_out.log\", \"w\")\n            self.DATA_START = chr(2)\n            self.DATA_END   = chr(5)\n            self.output_sent = False\n        \n        def send(self, data, typestr, parent_id, cell_id, last_in_sequence):\n            \"\"\" Send a message to the client; 'typestr' indicates the cell type,\n            'parent_id', if non-null, indicates the serial number of the parent\n            cell. If 'cell_id' is not 0, put the output in the cell with that id.\n            \"\"\"\n            if self.texmacs and typestr=='input_form':\n               return 0\n            if self.texmacs:\n               if typestr==\"image_ps\":\n                  self.output_sent=True\n                  print(self.DATA_START, end='')\n                  print(r\"ps:\", end='')\n                  #print(base64.b64decode(data), file=self.logf, flush=True)\n                  print(base64.b64decode(data).decode('utf-8'), end='')\n                  print(self.DATA_END, flush=True)\n               elif typestr=='latex_view':\n                  self.output_sent=True\n                  print(self.DATA_START, end='')\n                  print(r\"latex:\\begin{equation*}\", end='')\n                  data = data.replace(r\"\\discretionary{}{}{}\", \"\")\n                  # print(data, file=self.logf, flush=True)\n                  print(data, end='')\n                  print(r\"\\end{equation*}\", end='')\n                  print(self.DATA_END, flush=True)\n               else:\n                  self.output_sent=True\n                  print(self.DATA_START, end='')\n                  print(r\"verbatim:\", end='')\n                  print(data, end='')\n                  print(self.DATA_END, flush=True)\n            else:\n               if typestr==\"image_png\":\n                  term = detect_terminal()\n                  if term==\"kitty\":\n                     kitty_write_chunked(a='T', f=100, data=base64.b64decode(data))\n                  elif term==\"iterm2\":\n                     payload = f\"\\033]1337;File=inline=1;size={len(data)}:{data.decode('utf-8')}\\007\"\n                     sys.stdout.write(payload)\n                     sys.stdout.flush()\n                     print('', flush=True)\n                  else:\n                     print(\"<image>\")\n               else:\n                  print(data)\n            return 0\n\n        def architecture(self):\n            return \"terminal\"\n\n        def test(self):\n            print(\"hello there!\")\n\n        def handles(self, otype):\n            if self.texmacs:\n               if otype==\"image_ps\" or otype==\"latex_view\" or otype==\"verbatim\" or otype==\"plain\":\n                  return True\n            elif otype==\"plain\" or otype==\"verbatim\":\n                return True\n            elif otype==\"image_png\":\n                return True\n            else:\n                return False\n\n        def totals(self):\n            return __cdb_progress_monitor__.totals()\n            \n    server = Server()\n\n# Import matplotlib and setup functions to prepare its output\n# for sending as base64 to the client. Example use:\n#\n#   import matplotlib.pyplot as plt\n#   p = plt.plot([1,2,3],[1,2,5],'-o')\n#   display(p[0])\n#\n\nhave_matplotlib=True\ntry:\n    import matplotlib\n    import matplotlib.artist\n    import matplotlib.figure\n    matplotlib.use('Agg')\nexcept ImportError:\n    have_matplotlib=False\n\nhave_plotly=True\ntry:\n    import plotly.graph_objs._figure \nexcept ImportError:\n    have_plotly=False\n\n    \ndef save_history(history_path):\n    try:\n        readline.write_history_file(history_path)\n    except:\n        pass\n\ntry:\n    import readline\n    if not hasattr(readline, 'redisplay'):\n      readline.redisplay = lambda: None\n    history_path = os.path.join(user_data_dir(), \"cadabra_history\")\n    if os.path.exists(history_path):\n        readline.read_history_file(history_path)\n        readline.set_history_length(1000)\n    atexit.register(save_history, history_path)\nexcept:\n    pass\n\nimport io\nimport base64\n\n## @brief Generic display function which handles local as well as remote clients.\n#\n# The 'display' function is a replacement for 'str', in the sense that\n# it will generate human-readable output. However, in contrast to\n# 'str', it knows about what the front-end ('server') can display, and\n# will adapt the output to that. For instance, if\n# server.handles('latex_view') is true, it will generate LaTeX output,\n# while it will generate just plain text otherwise.\n# \n# Once it has figured out which display is accepted by 'server', it\n# will call server.send() with data depending on the object type it is\n# being fed. Data types the server object can support are:\n# \n# - \"latex_view\": text-mode LaTeX string.\n# - \"image_png\":  base64 encoded png image.\n# - \"image_svg\":  svg image.\n# - \"image_ps\":   ps image\n# - \"verbatim\":   ascii string to be displayed verbatim.\n\ndef display(obj, cell_id=0, delay_send=False):\n    \"\"\"\n    Generalised 'print' function which knows how to display objects in the \n    best possible way on the used interface, be it a console or graphical\n    notebook. In particular, it knows how to display Cadabra expressions\n    in typeset form whenever LaTeX functionality is available. Can also be\n    used to display matplotlib plots.\n\n    When using a Cadabra front-end (command line or notebook), an expression\n    with a trailing semi-colon ';' will automatically be wrapped in a \n    'display' function call so that the expression is displayed immediately.\n    \"\"\"\n\n    if cell_id==None:\n       cell_id = 0\n       \n    if type(obj)==list and len(obj)>0 and (isinstance(obj[0], matplotlib.figure.Figure) or isinstance(obj[0], matplotlib.figure.Artist)):\n       # matplotlib has the annoying habit of returning plots as lists of figures.\n       # print(\"list of figures\", file=sys.stderr)\n       return display(obj[0], cell_id, delay_send)\n    \n    if 'matplotlib' in sys.modules and isinstance(obj, matplotlib.figure.Figure):\n        if server.handles('image_svg'):\n            imgstring = io.BytesIO()\n            obj.savefig(imgstring,format='svg')\n            imgstring.seek(0)\n            b64 = base64.b64encode(imgstring.getvalue())\n            return server.send(b64, \"image_svg\", 0, cell_id, False)\n        elif server.handles('image_ps'):\n            imgstring = io.BytesIO()\n            obj.savefig(imgstring,format='eps', bbox_inches='tight', pad_inches=0.1)\n            imgstring.seek(0)\n            b64 = base64.b64encode(imgstring.getvalue())\n            return server.send(b64, \"image_ps\", 0, cell_id, False)\n        elif server.handles('image_png'):\n            imgstring = io.BytesIO()\n            obj.savefig(imgstring,format='png')\n            imgstring.seek(0)\n            b64 = base64.b64encode(imgstring.getvalue())\n            return server.send(b64, \"image_png\", 0, cell_id, False)\n        else:\n            return None\n\n    elif 'matplotlib' in sys.modules and isinstance(obj, matplotlib.artist.Artist):\n        if server.handles('image_svg'):\n            f = obj.get_figure()\n            imgstring = io.BytesIO()\n            f.savefig(imgstring,format='svg')\n            imgstring.seek(0)\n            b64 = base64.b64encode(imgstring.getvalue())\n            return server.send(b64, \"image_svg\", 0, cell_id, False)\n        elif server.handles('image_ps'):\n            f = obj.get_figure()\n            imgstring = io.BytesIO()\n            f.savefig(imgstring,format='ps')\n            imgstring.seek(0)\n            b64 = base64.b64encode(imgstring.getvalue())\n            return server.send(b64, \"image_svg\", 0, cell_id, False)\n        elif server.handles('image_png'):\n            f = obj.get_figure()\n            imgstring = io.BytesIO()\n            f.savefig(imgstring,format='png')\n            imgstring.seek(0)\n            b64 = base64.b64encode(imgstring.getvalue())\n            return server.send(b64, \"image_png\", 0, cell_id, False)\n        else:\n            return None\n\n    elif have_plotly and isinstance(obj, plotly.graph_objs._figure.Figure):\n        imgstring = obj.to_image(format=\"svg\")\n        b64 = base64.b64encode(imgstring)\n        return server.send(b64, \"image_svg\", 0, cell_id, False)\n     \n    elif hasattr(obj,'_backend'):\n        # print(\"figure 3\", file=sys.stderr)\n        if hasattr(obj._backend,'fig'):\n            f = obj._backend.fig\n            imgstring = io.BytesIO()\n            f.savefig(imgstring,format='svg')\n            imgstring.seek(0)\n            b64 = base64.b64encode(imgstring.getvalue())\n            return server.send(b64, \"image_svg\", 0, cell_id, False)\n\n    elif 'vtk' in sys.modules and isinstance(obj, vtk.vtkRenderer):\n        # Vtk renderer, see http://nbviewer.ipython.org/urls/bitbucket.org/somada141/pyscience/raw/master/20140917_RayTracing/Material/PythonRayTracingEarthSun.ipynb\n        pass\n                    \n#    elif isinstance(obj, numpy.ndarray):\n#        server.send(\"\\\\begin{dmath*}{}\"+str(obj.to_list())+\"\\\\end{dmath*}\", \"latex\")\n\n    elif isinstance(obj, Ex):\n        if server.handles('latex_view'):\n            if delay_send:\n                return obj._latex_()\n            else:\n                ret = mopen+obj._latex_()+mclose\n                id=server.send(ret, \"latex_view\", 0, cell_id, False)\n                # print(id)\n                # Make a child cell of the above with input form content.\n                cell_id = server.send(obj.input_form(), \"input_form\", id, cell_id, False)\n                return cell_id\n        else:\n            server.send(unicode(obj), \"plain\", 0, cell_id, False)\n\n    elif isinstance(obj, ExNode):\n        if server.handles('latex_view'):\n            if delay_send:\n                return obj._latex_()\n            else:\n                ret = mopen+obj._latex_()+mclose\n                id=server.send(ret, \"latex_view\", 0, cell_id, False)\n                # print(id)\n                # Make a child cell of the above with input form content.\n                cell_id = server.send(obj.input_form(), \"input_form\", id, cell_id, False)\n                return cell_id\n        else:\n            server.send(unicode(obj), \"plain\", 0, cell_id, False)\n            return None\n\n    elif isinstance(obj, LaTeXString):\n        if server.handles('latex_view'):\n            ret = mopen+obj._latex_()+mclose\n            if delay_send:\n                return ret\n            else:\n                cell_id = server.send(ret , \"latex_view\", 0, cell_id, False)\n                return cell_id\n        else:\n            server.send(unicode(obj), \"plain\", 0, cell_id, False)\n            return None\n            \n    elif isinstance(obj, Property):\n        if server.handles('latex_view'):\n            ret = mopen+obj._latex_()+mclose\n            if delay_send:\n                return ret\n            else:\n                return server.send(ret , \"latex_view\", 0, cell_id, False)\n                # Not yet available.\n                # server.send(obj.input_form(), \"input_form\", 0, False)\n        else:\n            server.send(unicode(obj), \"plain\", 0, cell_id, False)\n            return None\n            \n    elif type(obj)==list:\n        if server.handles('latex_view'):\n           # print(f\"list {obj}\", file=sys.stderr)\n           atleast_one_unstolen=False\n           cdb_out=\"$\\\\big[$\"\n           first=True\n           for elm in obj:\n               if first==False:\n                   cdb_out+=\",\"+discr\n               else:\n                   first=False\n               nxt = display(elm, cell_id, delay_send=True)\n               if nxt != None:\n                  cdb_out+= \"$\"+str(display(elm, cell_id=cell_id, delay_send=True))+\"$\"\n                  atleast_one_unstolen=True\n           cdb_out+=\"$\\\\big]$\";\n           if delay_send:\n              return cdb_out\n           if atleast_one_unstolen:\n              return server.send(cdb_out, \"latex_view\", 0, cell_id, False)\n        else:\n           cdb_out = \"[\"\n           first=True           \n           for elm in obj:\n               if not first:\n                   cdb_out+=\", \"\n               else:\n                   first=False                  \n               cdb_out += str(elm)\n           cdb_out += \"]\"\n           server.send(unicode(cdb_out), \"plain\", 0, cell_id, False)\n           return None\n           # FIXME: send input_form version.\n\n    elif type(obj)==dict:\n        if server.handles('latex_view'):\n           cdb_out = \"\\\\left\\\\{\\\\displaystyle{}\";\n           first = True\n           for key in obj:\n              if first==False:\n                 cdb_out += \",\\\\hspace{.5em}\";\n              else:\n                 first = False;\n              if type(key)==str:\n                 cdb_out += \"\\\\text{'}\"\n              cdb_out += display(key, cell_id, delay_send=True)\n              if type(key)==str:\n                 cdb_out += \"\\\\text{'}\"\n              cdb_out += \":\\\\,\"\n              cdb_out += display(obj[key], cell_id, delay_send=True)\n           cdb_out += \"\\\\right\\\\}\"\n           if delay_send:\n              return cdb_out;\n           else:\n              return server.send(cdb_out, \"latex_view\", 0, cell_id, False)\n        else:\n           server.send(str(obj), \"plain\", 0, cell_id, False)\n           return None\n           \n    elif hasattr(obj, \"__send_to_server__\"):\n        obj.__send_to_server__(server)\n           \n    elif hasattr(obj, \"__module__\") and hasattr(obj.__module__, \"find\") and obj.__module__.find(\"sympy\")!=-1:\n        if delay_send:\n           return latex(obj)\n        else:\n           if server.handles('latex_view'):\n               return server.send(\"\\\\begin{dmath*}{}\"+latex(obj)+\"\\\\end{dmath*}\", \"latex_view\", 0, cell_id, False)\n           else:\n               server.send(latex(obj), \"plain\", 0, cell_id, False)\n               return None\n        \n    else:\n        # Failing all else, just dump a str representation to the notebook, asking\n        # it to display this verbatim.\n        # server.send(\"\\\\begin{dmath*}{}\"+str(obj)+\"\\\\end{dmath*}\", \"latex\")\n        if delay_send:\n            if server.handles('latex_view'):\n               return \"\\\\verb|\"+str(obj)+\"|\"\n            else:\n               return str(obj)\n        else:\n            if server.handles('latex_view'):\n               return server.send(unicode(obj), \"verbatim\", 0, cell_id, False)\n            else:\n               server.send(unicode(obj), \"plain\", 0, cell_id, False)\n               return None\n    \n__cdbkernel__.server=server\n__cdbkernel__.display=display\n\nclass Console(object):\n        \"\"\"\n        The interactive console works in the same Python context as \n        the notebook cells to allow evaluation of expressions for \n        debugging/logging purposes\n        \"\"\"\n        def log(self, *objs):\n            \"\"\"Sends a string representation of objs to the console\"\"\"\n            if server.architecture() == \"terminal\":\n                print(*objs)\n            elif server.architecture() == \"client-server\":\n                server.send(\" \".join(str(obj) for obj in objs), \"csl_out\", 0, cell_id, False)\n\n        def clear(self):\n            \"\"\"Clears the output of the console window\"\"\"\n            if server.architecture() == \"client-server\":\n                server.send(\"\", \"csl_clear\", 0, cell_id, False)\n\n        def warn(self, msg):\n            if server.architecture() == \"terminal\":\n                print(\"Warning: \" + msg)\n            elif server.architecture() == \"client-server\":\n                server.send(msg, \"csl_warn\", 0, cell_id, False)\n\nconsole = Console()\n__cdbkernel__.configure_warnings(callback=console.warn)\n    \n# Set display hooks to catch certain objects and print them\n# differently. Should probably eventually be done cleaner.\n\ndef _displayhook(arg):\n    global remember_display_hook\n    if isinstance(arg, Ex):\n        print(unicode(arg))\n    elif isinstance(arg, Property):\n        print(unicode(arg))\n    else:\n        remember_display_hook(arg)\n\nremember_display_hook = sys.displayhook\nsys.displayhook = _displayhook\n\n# Default post-processing algorithms. These are not pre-processed\n# so need to have the '__cdbkernel__' argument.\n\ndef post_process(__cdbkernel__, ex):\n    collect_terms(ex)\n\n"
  },
  {
    "path": "core/cadabra2cadabra.cc",
    "content": "#include <fstream>\n#include <iostream>\n#include \"DataCell.hh\"\n\nint main(int argc, char **argv)\n\t{\n\tif(argc<3) {\n\t\tstd::cerr << \"Usage: cadabra2cadabra [cadabra notebook] [cadabra/python output]\\n\\n\";\n\t\tstd::cerr << \"Convert a Cadabra v2 notebook to an standalone Cadabra/Python file.\\n\"\n\t\t          << \"If the output file name is not given, output goes to standard out.\\n\";\n\t\treturn -1;\n\t\t}\n\n\tstd::string cdb_file, py_file;\n\tint n=1;\n\twhile(n<argc) {\n\t\tif(cdb_file==\"\")\n\t\t\tcdb_file=argv[n];\n\t\telse\n\t\t\tpy_file=argv[n];\n\t\t++n;\n\t\t}\n\n\t//\tauto from=cdb_file.find_last_of(\"/\");\n\t//\t++from;\n\t//\tauto to  =cdb_file.find_last_of(\".\");\n\t//\tstd::string t=cdb_file.substr(from, to-from);\n\t//\tt[0]=toupper(t[0]);\n\t//\tstd::string title=\"Cadabra manual: \"+t;\n\n\tstd::ifstream file(cdb_file);\n\tstd::string content, line;\n\twhile(std::getline(file, line))\n\t\tcontent+=line;\n\n\tcadabra::DTree doc;\n\tJSON_deserialise(content, doc);\n\tstd::string pycode = export_as_python(doc);\n\n\tif(py_file!=\"\") {\n\t\tstd::ofstream pyfile(py_file);\n\t\tpyfile << pycode;\n\t\t}\n\telse {\n\t\tstd::cout << pycode;\n\t\t}\n\n\treturn 0;\n\t}\n"
  },
  {
    "path": "core/cadabra2ipynb.cc",
    "content": "\n// Convert a Cadabra .cnb notebook to a Jupyter notebook. input file to pure Python .py, by doing the\n// pre-processing stage.\n\n#include <iostream>\n#include <CdbPython.hh>\n#include <fstream>\n#include \"nlohmann/json.hpp\"\n#include \"DataCell.hh\"\n\nint main(int argc, char **argv)\n\t{\n\tif(argc<2) {\n\t\tstd::cerr << \"Usage: cadabra2ipynb [cadabra notebook] [jupyter notebook]\\n\\n\";\n\t\tstd::cerr << \"Convert a Cadabra notebook to a Jupyter notebook.\\n\"\n\t\t          << \"If the Jupyter notebook name is not given, output goes to standard out.\\n\";\n\t\treturn -1;\n\t\t}\n\n\tstd::string cdb_file, python_file;\n\tint n=1;\n\twhile(n<argc) {\n\t\tif(cdb_file==\"\")\n\t\t\tcdb_file=argv[n];\n\t\telse\n\t\t\tpython_file=argv[n];\n\t\t++n;\n\t\t}\n\n\tauto from=cdb_file.find_last_of(\"/\");\n\t++from;\n\tauto to  =cdb_file.find_last_of(\".\");\n\tstd::string t=cdb_file.substr(from, to-from);\n\tt[0]=toupper(t[0]);\n\tstd::string title=\"Cadabra manual: \"+t;\n\n\tstd::ifstream file(cdb_file);\n\tif(!file.is_open()) {\n\t\tstd::cerr << \"cadabra2ipynb: failed to open \" << cdb_file << std::endl;\n\t\treturn -1;\n\t\t}\n\tnlohmann::json content;\n\tfile >> content;\n\n\tauto python = cadabra::cnb2ipynb(content);\n\n\tif(python_file!=\"\") {\n\t\tstd::ofstream pythonfile(python_file);\n\t\tpythonfile << python.dump(3);\n\t\t}\n\telse {\n\t\tstd::cout << python.dump(3);\n\t\t}\n\n\treturn 0;\n\t}\n"
  },
  {
    "path": "core/cadabra2python.cc",
    "content": "\n// Convert a Cadabra .cdb input file to pure Python .py, by doing the\n// pre-processing stage.\n\n#include <iostream>\n#include <CdbPython.hh>\n#include <fstream>\n#include <pybind11/pybind11.h>\n#include <pybind11/embed.h>\n\nint main(int argc, char **argv)\n\t{\n\tif(argc<2) {\n\t\tstd::cerr << \"Usage: cadabra2python [cadabra file] [python file]\\n\\n\";\n\t\tstd::cerr << \"Convert a Cadabra v2 input file or notebook to a pure Python file.\\n\"\n\t\t          << \"If the Python file name is not given, output goes to standard out.\\n\";\n\t\treturn -1;\n\t\t}\n\n\tstd::string cdb_file, python_file;\n\tint n=1;\n\twhile(n<argc) {\n\t\tif(cdb_file==\"\")\n\t\t\tcdb_file=argv[n];\n\t\telse\n\t\t\tpython_file=argv[n];\n\t\t++n;\n\t\t}\n\n\tauto from=cdb_file.find_last_of(\"/\");\n\t++from;\n\tauto to  =cdb_file.find_last_of(\".\");\n\tstd::string t=cdb_file.substr(from, to-from);\n\tt[0]=toupper(t[0]);\n\tstd::string title=\"Cadabra manual: \"+t;\n\n\tstd::ifstream file(cdb_file);\n\tif(!file.is_open()) {\n\t\tstd::cerr << \"cadabra2python: failed to open \" << cdb_file << std::endl;\n\t\treturn -1;\n\t\t}\n\tstd::string content, line;\n\twhile(std::getline(file, line))\n\t\tcontent+=line+\"\\n\";\n\n\tstd::string error;\n\t// Because cdb2python_string now runs some python code to\n\t// parse the input (and imports `codeop` for that), we need\n\t// to make sure that pybind11 is initialised.\n\tpybind11::scoped_interpreter guard{}; \n\tauto python = cadabra::cdb2python_string(content, true, error);\n\n\tif(python_file!=\"\") {\n\t\tstd::ofstream pythonfile(python_file);\n\t\tpythonfile << python;\n\t\t}\n\telse {\n\t\tstd::cout << python;\n\t\t}\n\n\treturn 0;\n\t}\n"
  },
  {
    "path": "core/cdb-nbtool.cc",
    "content": "#include <internal/difflib.h>\n#include <internal/string_tools.h>\n#include <internal/uuid.h>\n#include <iostream>\n#include <iomanip>\n#include <fstream>\n\n#ifdef _MSC_VER\n#include <Windows.h>\n#endif\n\n#include \"process.hpp\"\n#include \"nlohmann/json.hpp\"\n\n// Global colour constants\n\nconst char* colour_insert = \"\\033[32m\";\nconst char* colour_delete = \"\\033[31m\";\nconst char* colour_insert_bg = \"\\033[42m\";\nconst char* colour_delete_bg = \"\\033[41m\";\nconst char* colour_info = \"\\033[36m\";\nconst char* colour_modified = \"\\033[33m\";\nconst char* colour_reset = \"\\033[0m\";\n\nvoid strip_newline(std::string& s)\n{\n\twhile (!s.empty() && (s.back() == '\\n' || s.back() == '\\r'))\n\t\ts.pop_back();\n}\n\n// Run git commands\n\nstd::string git_path;\n\nstd::string run_command(std::string command)\n{\n\tusing namespace TinyProcessLib;\n\n\tstd::string sout;\n\tstd::string serr;\n\tProcess proc(command, \"\",\n\t\t[&sout](const char* bytes, size_t n) {\n\t\t\tsout += std::string(bytes, n);\n\t\t},\n\t\t[&serr](const char* bytes, size_t n) {\n\t\t\tserr += std::string(bytes, n);\n\t\t}\n\t\t);\n\tif (proc.get_exit_status())\n\t\tthrow std::runtime_error(serr);\n\treturn sout;\n}\n\nstd::string run_git_command(std::string command)\n{\n\tif (git_path.empty()) {\n#ifdef _MSC_VER\n\t\tLPSTR lpFilePart;\n\t\tchar filename[MAX_PATH];\n\t\tif (!SearchPath(NULL, \"git\", \".exe\", MAX_PATH, filename, &lpFilePart)) {\n\t\t\tstd::cerr << \"Could not find git executable\\n\";\n\t\t\texit(1);\n\t\t}\n\t\tgit_path = std::string(\"\\\"\") + filename + std::string(\"\\\"\");\n#else\n\t\tstd::string temp;\n\t\tTinyProcessLib::Process proc(\"/usr/bin/which git\", \"\", [&temp](const char* bytes, size_t n) {\n\t\t\ttemp += std::string(bytes, n);\n\t\t\t}\n\t\t);\n\t\tif (proc.get_exit_status()) {\n\t\t\tstd::cerr << \"Could not find git executable in path\\n\";\n\t\t\texit(1);\n\t\t}\n\t\ttrim(temp);\n\t\tstrip_newline(temp);\n\t\tgit_path = temp;\n#endif\n\t}\n\treturn run_command(git_path + \" \" + command);\n}\n\n\n// Diffing tools\n\nusing Cells = std::pair<std::vector<std::string>, std::vector<std::string>>;\n\nstd::string diff_substr(const std::string& s, size_t i1, size_t i2, difflib::tag_t tag)\n{\n\tusing namespace difflib;\n\tauto substr = s.substr(i1, i2 - i1);\n\n\tif (tag == tag_t::t_delete) {\n\t\treplace_all(substr, \" \", colour_delete_bg + std::string(\" \") + std::string(colour_reset) + colour_delete);\n\t\treplace_all(substr, \"\\t\", colour_delete_bg + std::string(\" \") + std::string(colour_reset) + colour_delete);\n\t\treturn colour_delete + substr;\n\t}\n\telse if (tag == tag_t::t_insert) {\n\t\treplace_all(substr, \" \", colour_insert_bg + std::string(\" \") + std::string(colour_reset) + colour_insert);\n\t\treplace_all(substr, \"\\t\", colour_insert_bg + std::string(\" \\b\\t\") + std::string(colour_reset) + colour_insert);\n\t\treturn colour_insert + substr;\n\t}\n\telse {\n\t\treturn colour_reset + substr;\n\t}\n}\n\nvoid compare_cell(const std::string& a_, const std::string& b_, const std::string& id)\n{\n\tauto a = string_to_vec(a_);\n\tauto b = string_to_vec(b_);\n\tstd::for_each(a.begin(), a.end(), strip_newline);\n\tstd::for_each(b.begin(), b.end(), strip_newline);\n\n\tif (a_.empty() && !b_.empty()) {\n\t\t// Insert only\n\t\tstd::cout << colour_info << \"## Inserted cell \" << id << \"\\n\";\n\t\tfor (const auto& line : b)\n\t\t\tstd::cout << colour_insert << \"+  \" << line << '\\n';\n\t\tstd::cout << colour_reset << '\\n';\n\t}\n\telse if (b_.empty() && !a_.empty()) {\n\t\t// Delete only\n\t\tstd::cout << colour_info << \"## Deleted cell \" << id << \"\\n\";\n\t\tfor (const auto& line : a)\n\t\t\tstd::cout << colour_delete << \"-  \" << line << '\\n';\n\t\tstd::cout << colour_reset << '\\n';\n\t}\n\telse {\n\t\t// Compare both\n\t\tusing namespace difflib;\n\t\tDiffer<std::string> d;\n\t\tauto deltas = d.get_deltas(a, b);\n\n\t\tbool changed = std::any_of(deltas.begin(), deltas.end(), [](const Delta<std::string>& d) { return d.tag != tag_t::t_equal; });\n\t\tif (!changed)\n\t\t\treturn;\n\n\t\tstd::cout << colour_info << \"## Modified cell \" << id << '\\n';\n\t\tsize_t next;\n\t\tfor (size_t i = 0; i < deltas.size(); ++i) {\n\t\t\tauto delta = deltas[i];\n\t\t\tswitch (delta.tag) {\n\t\t\tcase tag_t::t_delete:\n\t\t\t\tstd::cout << colour_delete << \"-  \" << delta.a << '\\n';\n\t\t\t\tbreak;\n\t\t\tcase tag_t::t_insert:\n\t\t\t\tstd::cout << colour_insert << \"+  \" << delta.b << '\\n';\n\t\t\t\tbreak;\n\t\t\tcase tag_t::t_equal:\n\t\t\t\t// Find next line which isnt equal\n\t\t\t\tnext = deltas.size();\n\t\t\t\tfor (size_t j = i + 1; j < deltas.size(); ++j) {\n\t\t\t\t\tif (deltas[j].tag != tag_t::t_equal) {\n\t\t\t\t\t\tnext = j;\n\t\t\t\t\t\tbreak;\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t\t// If there is a gap of more than two lines, replace it with ellipsis\n\t\t\t\tif (next - i > 3) {\n\t\t\t\t\tif (i == 0) {\n\t\t\t\t\t\tstd::cout\n\t\t\t\t\t\t\t<< colour_info << \".  (skipping \" << (next - i - 1) << \" lines)\\n\"\n\t\t\t\t\t\t\t<< colour_reset << \"=  \" << deltas[next - 1].a << '\\n';\n\t\t\t\t\t}\n\t\t\t\t\telse {\n\t\t\t\t\t\tstd::cout\n\t\t\t\t\t\t\t<< colour_reset << \"=  \" << deltas[i].a << '\\n'\n\t\t\t\t\t\t\t<< colour_info << \".  (skipping \" << (next - i - 2) << \" lines)\\n\"\n\t\t\t\t\t\t\t<< colour_reset << \"=  \" << deltas[next - 1].a << '\\n';\n\t\t\t\t\t}\n\t\t\t\t\ti = next - 1;\n\t\t\t\t}\n\t\t\t\telse {\n\t\t\t\t\tstd::cout << colour_reset << \"=  \" << delta.a << '\\n';\n\t\t\t\t}\n\t\t\t\tbreak;\n\t\t\tcase tag_t::t_replace:\n\t\t\t\tstd::cout << colour_modified << \"*  \";\n\t\t\t\tfor (const auto& opcode : delta.opcodes) {\n\t\t\t\t\tswitch (opcode.tag) {\n\t\t\t\t\tcase tag_t::t_delete:\n\t\t\t\t\t\tstd::cout << diff_substr(delta.a, opcode.i1, opcode.i2, tag_t::t_delete);\n\t\t\t\t\t\tbreak;\n\t\t\t\t\tcase tag_t::t_insert:\n\t\t\t\t\t\tstd::cout << diff_substr(delta.b, opcode.j1, opcode.j2, tag_t::t_insert);\n\t\t\t\t\t\tbreak;\n\t\t\t\t\tcase tag_t::t_replace:\n\t\t\t\t\t\tstd::cout << diff_substr(delta.a, opcode.i1, opcode.i2, tag_t::t_delete);\n\t\t\t\t\t\tstd::cout << diff_substr(delta.b, opcode.j1, opcode.j2, tag_t::t_insert);\n\t\t\t\t\t\tbreak;\n\t\t\t\t\tcase tag_t::t_equal:\n\t\t\t\t\t\tstd::cout << diff_substr(delta.a, opcode.i1, opcode.i2, tag_t::t_equal);\n\t\t\t\t\t\tbreak;\n\t\t\t\t\tdefault:\n\t\t\t\t\t\tthrow std::runtime_error(\"Unexpected tag encountered in differ\");\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t\tstd::cout << '\\n';\n\t\t\t\tbreak;\n\t\t\tdefault:\n\t\t\t\tthrow std::runtime_error(\"Unexpected tag encountered in differ\");\n\t\t\t}\n\t\t}\n\t}\n\tstd::cout << colour_reset << \"\\n\\n\";\n}\n\nCells cnb_to_cells(std::istream& stream)\n{\n\tCells ret;\n\tif (stream.eof())\n\t\treturn ret;\n\ttry {\n\t\tnlohmann::json nb;\n\t\tstream >> nb;\n\t\tnb = nb[\"cells\"];\n\t\tfor (auto it = nb.begin(); it != nb.end(); ++it) {\n\t\t\tif (!it->contains(\"cell_id\")) {\n\t\t\t\tstd::cerr << \"Notebook version is too old for diff tool, please update by resaving the notebook\\n\";\n\t\t\t\texit(1);\n\t\t\t}\n\t\t\tret.first.push_back(std::to_string((*it)[\"cell_id\"].get<uint64_t>()));\n\t\t\tret.second.push_back((*it)[\"source\"].get<std::string>());\n\t\t}\n\t}\n\tcatch (nlohmann::json::exception& e) {\n\t\tthrow std::runtime_error(\"Not a valid Cadabra notebook.\");\n\t}\n\treturn ret;\n}\n\nvoid cnb_diff(std::istream& a, std::istream& b)\n{\n\tusing namespace difflib;\n\n\tauto lhs_cells = cnb_to_cells(a);\n\tauto rhs_cells = cnb_to_cells(b);\n\n\tDiffer<std::string> d(nullptr, nullptr, 1.);\n\tfor (const auto& delta : d.get_deltas(lhs_cells.first, rhs_cells.first)) {\n\t\tif (delta.tag == tag_t::t_insert) {\n\t\t\tauto pos = std::find(rhs_cells.first.begin(), rhs_cells.first.end(), delta.b);\n\t\t\tcompare_cell(\"\", rhs_cells.second[std::distance(rhs_cells.first.begin(), pos)], delta.b);\n\t\t}\n\t\telse if (delta.tag == tag_t::t_delete) {\n\t\t\tauto pos = std::find(lhs_cells.first.begin(), lhs_cells.first.end(), delta.a);\n\t\t\tcompare_cell(lhs_cells.second[std::distance(lhs_cells.first.begin(), pos)], \"\", delta.a);\n\t\t}\n\t\telse {\n\t\t\tauto pos_a = std::find(lhs_cells.first.begin(), lhs_cells.first.end(), delta.a);\n\t\t\tauto pos_b = std::find(rhs_cells.first.begin(), rhs_cells.first.end(), delta.a);\n\t\t\tcompare_cell(lhs_cells.second[std::distance(lhs_cells.first.begin(), pos_a)], rhs_cells.second[std::distance(rhs_cells.first.begin(), pos_b)], delta.a);\n\t\t}\n\t}\n}\n\n\n// View functions\nstd::vector<std::string> split_to_maxlength(std::string s, int maxlength)\n{\n\tstd::vector<std::string> res;\n\twhile ((int)s.size() > maxlength) {\n\t\tres.push_back(s.substr(0, maxlength));\n\t\ts = \"  \" + s.substr(maxlength);\n\t}\n\tres.push_back(s);\n\treturn res;\n}\n\n// Commands \n\nvoid help()\n{\n\tstd::cout\n\t\t<< \"cdb-nbtool: Command line tools for working with Cadabra notebooks. It is recommended to\\n\"\n\t\t<< \"pass the output of these tools to a program like `less` or `more` for better viewing.\\n\"\n\t\t<< \"  -- cdb-nbtool view <file>\\n\"\n\t\t<< \"       View a notebook in the console\\n\"\n\t\t<< \"  -- cdb-nbtool diff <file1> <file2>\\n\"\n\t\t<< \"       Compute differences between two Cadabra notebooks in a CLI friendly way\\n\"\n\t\t<< \"  -- cdb-nbtool gitdiff\\n\"\n\t\t<< \"       Specialised version of the diff tool to integrate with git. To setup git to\\n\"\n\t\t<< \"       use this tool with .cnb files, edit your .gitconfig file by adding the two lines:\\n\"\n\t\t<< \"         |  [diff \\\"cadabranotebook\\\"]\\n\"\n\t\t<< \"         |      command = cdb-nbtool gitdiff\\n\"\n\t\t<< \"       and add the following line to your .gitattributes file:\\n\"\n\t\t<< \"         |  *.cnb diff=cadabranotebook\\n\"\n\t\t<< \"  -- cdb-nbtool merge <file1> <file2>\\n\"\n\t\t<< \"       Interactively merge changes from <file1> into <file2>\\n\"\n\t\t<< \"  -- cdb-nbtool gitmerge\\n\"\n\t\t<< \"       Specialised version of the merge tool to integrate with git. To setup git to\\n\"\n\t\t<< \"       use this tool with .cnb files, edit your .gitconfig file by adding the two lines:\\n\"\n\t\t<< \"         |  [merge \\\"cadabranotebook\\\"]\\n\"\n\t\t<< \"         |    command = cdb-nbtool gitmerge\\n\"\n\t\t<< \"       and add the following line to your .gitattributes file:\\n\"\n\t\t<< \"         |  *.cnb merge=cadabranotebook\\n\"\n\t\t<< \"  -- cdb-nbtool clean <file>\\n\"\n\t\t<< \"       Ensures that all input cells are visible and deletes all output cells. This can fix\\n\"\n\t\t<< \"       problems with corrupt notebooks. The original notebook is saved as <file>~\\n\";\n}\n\nvoid view(const char* fname)\n{\n\tstd::ifstream f(fname);\n\tif (!f.is_open()) {\n\t\tstd::cerr << \"Could not open notebook \" << fname << '\\n';\n\t\texit(1);\n\t}\n\tnlohmann::json nb;\n\tf >> nb;\n\tnb = nb[\"cells\"];\n\n\t// Get terminal width for drawing cell boxes\n\tint width;\n\ttry {\n\t\twidth = stoi(run_command(\"tput cols\")) - 1;\n\t}\n\tcatch (std::runtime_error& e) {\n\t\twidth = 100;\n\t}\n\n\t// Loop through all cells\n\tint cell_num = 1;\n\tfor (auto it = nb.begin(); it != nb.end(); ++it) {\n\t\t// Top banner with logical cell number\n\t\tstd::string cell_num_str = std::to_string(cell_num);\n\t\t++cell_num;\n\t\tstd::cout << \"┌─Cell \" << cell_num_str << \" (\";\n\t\tstd::string cell_type = (*it)[\"cell_type\"].get<std::string>();\n\t\tint cell_type_len;\n\t\tif (cell_type == \"latex\") {\n\t\t\tstd::cout << \"LaTeX\";\n\t\t\tcell_type_len = 5;\n\t\t}\n\t\telse if (cell_type == \"input\") {\n\t\t\tstd::cout << \"Python\";\n\t\t\tcell_type_len = 6;\n\t\t}\n\t\telse {\n\t\t\tstd::cout << cell_type;\n\t\t\tcell_type_len = cell_type.size();\n\t\t}\n\t\tstd::cout << \")\";\n\t\tfor (int i = 0; i < width - (int)cell_num_str.size() - cell_type_len - 11; ++i)\n\t\t\tstd::cout << \"─\";\n\t\tstd::cout << \"┐\\n\";\n\n\t\t// Cell source\n\t\tstd::string source = (*it)[\"source\"].get<std::string>();\n\t\t// Need to temporarily escape things like the \\t in \\theta because this is a\n\t\t// really bad way of doing this\n\t\treplace_all(source, \"\\t\", \"    \");\n\n\t\tint line_num = 1;\n\t\tfor (auto line : string_to_vec(source)) {\n\t\t\tstrip_newline(line);\n\t\t\tint maxlength = width - 8;\n\t\t\tauto sublines = split_to_maxlength(line, width - 8);\n\t\t\tif (sublines.empty())\n\t\t\t\tbreak;\n\t\t\tstd::cout\n\t\t\t\t<< \"│\" << std::right << std::setw(3) << line_num\n\t\t\t\t<< \"┆ \" << std::left << std::setw(maxlength) << sublines[0] << \" │\\n\";\n\t\t\t++line_num;\n\t\t\tfor (size_t i = 1; i < sublines.size(); ++i) {\n\t\t\t\tstd::cout << \"│   \" << \"┆ \" << std::left << std::setw(maxlength) << sublines[i] << \" │\\n\";\n\t\t\t}\n\t\t}\n\n\t\t// Cell outputs\n\t\tif (cell_type == \"input\" && it->contains(\"cells\")) {\n\t\t\tauto cells = (*it)[\"cells\"];\n\t\t\tfor (auto ot = cells.begin(); ot != cells.end(); ++ot) {\n\t\t\t\t// Divider\n\t\t\t\tstd::cout << \"├\";\n\t\t\t\tfor (int i = 0; i < width - 2; ++i)\n\t\t\t\t\tstd::cout << \"─\";\n\t\t\t\tstd::cout << \"┤\\n\";\n\t\t\t\tstd::string output_type = (*ot)[\"cell_type\"];\n\t\t\t\t// Sanitize output\n\t\t\t\tstd::string output_str;\n\t\t\t\tif (output_type == \"latex_view\") {\n\t\t\t\t\toutput_str = (*ot)[\"source\"];\n\t\t\t\t\treplace_all(output_str, \"\\\\\\\\\", \"\\\\\");\n\t\t\t\t\treplace_all(output_str, \"\\\\begin{dmath*}\", \"\");\n\t\t\t\t\treplace_all(output_str, \"\\\\end{dmath*}\", \"\");\n\t\t\t\t\treplace_all(output_str, \"\\\\left\", \"\");\n\t\t\t\t\treplace_all(output_str, \"\\\\right\", \"\");\n\t\t\t\t}\n\t\t\t\telse if (output_type == \"verbatim\" || output_type == \"output\") {\n\t\t\t\t\toutput_str = (*ot)[\"source\"];\n\t\t\t\t\treplace_all(output_str, \"\\\\\\\\\", \"\\\\\");\n\t\t\t\t\treplace_all(output_str, \"\\\\begin{verbatim}\", \"\");\n\t\t\t\t\treplace_all(output_str, \"\\\\end{verbatim}\", \"\");\n\t\t\t\t}\n\t\t\t\telse {\n\t\t\t\t\toutput_str = \"[output cell of type \" + output_type + \"]\";\n\t\t\t\t}\n\t\t\t\t// Print output\n\t\t\t\tfor (auto line : string_to_vec(output_str)) {\n\t\t\t\t\tstrip_newline(line);\n\t\t\t\t\tfor (auto subline : split_to_maxlength(line, width - 4)) {\n\t\t\t\t\t\tstd::cout << \"│ \" << std::left << std::setw(width - 4) << subline << \" │\\n\";\n\t\t\t\t\t}\n\t\t\t\t}\n\n\t\t\t}\n\t\t}\n\n\t\t// Finish off bottom of box\n\t\tstd::cout << \"└\";\n\t\tfor (int i = 0; i < width - 2; ++i)\n\t\t\tstd::cout << \"─\";\n\t\tstd::cout << \"┘\\n\\n\";\n\t}\n}\n\nvoid diff(const char* a, const char* b)\n{\n\tstd::ifstream af(a);\n\tstd::ifstream bf(b);\n\tif (!af.is_open()) {\n\t\tstd::cerr << \"Could not open file \" << a << '\\n';\n\t\texit(1);\n\t}\n\tif (!bf.is_open()) {\n\t\tstd::cerr << \"Could not open file \" << b << '\\n';\n\t\texit(1);\n\t}\n\tstd::cout << \"--- \" << a << \"\\n+++ \" << b << \"\\n\\n\";\n\tcnb_diff(af, bf);\n}\n\nvoid gitdiff(const char* a, const char* b, const char* relpath)\n{\n\tstd::ifstream af(a);\n\tstd::ifstream bf(b);\n\n\tstd::cout << \"--- a/\" << relpath;\n\tif (!af.is_open()) {\n\t\tstd::cout << \" [does not exist]\";\n\t\taf.setstate(std::ios::eofbit);\n\t}\n\tstd::cout << \"\\n+++ b/\" << relpath;\n\tif (!bf.is_open()) {\n\t\tstd::cout << \" [does not exist]\";\n\t\tbf.setstate(std::ios::eofbit);\n\t}\n\tstd::cout << \"\\n\\n\";\n\tcnb_diff(af, bf);\n}\n\nvoid clean(const char* a)\n{\n\tstd::ifstream ifs(a);\n\tif (!ifs.is_open()) {\n\t\tstd::cerr << \"Could not open file \" << a << \"\\n\";\n\t\texit(1);\n\t}\n\n\t// Copy the file to a~\n\t{\n\t\tstd::ofstream ofs(std::string(a) + \"~\");\n\t\tif (!ofs.is_open()) {\n\t\t\tstd::cerr << \"Could not create backup at \" << a << \"~\\n\";\n\t\t\texit(1);\n\t\t}\n\t\tofs << ifs.rdbuf();\n\t}\n\n\t// Return to beginning of file and read as JSON\n\tifs.clear();\n\tifs.seekg(0);\n\tnlohmann::json nb;\n\tifs >> nb;\n\n\t// Clean cells\n\tauto& cell_list = nb[\"cells\"];\n\tfor (auto it = cell_list.begin(), end = cell_list.end(); it != end; ++it) {\n\t\tif (it->contains(\"cells\"))\n\t\t\tit->erase(\"cells\");\n\t\tif (it->value(\"cell_type\", \"\") == \"latex\") {\n\t\t\t(*it)[\"hidden\"] = false;\n\t\t\tstd::map<std::string, nlohmann::json> output_cell;\n\t\t\toutput_cell[\"cell_id\"] = cadabra::generate_uuid<uint64_t>();\n\t\t\toutput_cell[\"cell_origin\"] = \"client\";\n\t\t\toutput_cell[\"cell_type\"] = \"latex_view\";\n\t\t\toutput_cell[\"source\"] = \"~\";\n\t\t\t(*it)[\"cells\"] = std::vector<nlohmann::json>(1, output_cell);\n\t\t}\n\t}\n\n\t// Write file\n\tifs.close();\n\tstd::ofstream ofs(a);\n\tif (!ofs.is_open()) {\n\t\tstd::cerr << \"Could not open \" << a << \" for writing\\n\";\n\t\texit(1);\n\t}\n\tofs << std::setw(4) << nb << '\\n';\n}\n\nint run(int argc, char** argv)\n{\n#if _MSC_VER\n\tSetConsoleCP(CP_UTF8);\n#endif\n\n\tif (argc < 2 || strcmp(argv[1], \"-h\") == 0 || strcmp(argv[1], \"--help\") == 0) {\n\t\thelp();\n\t\treturn 0;\n\t}\n\telse if (strcmp(argv[1], \"view\") == 0) {\n\t\tif (argc != 3) {\n\t\t\tstd::cerr << \"Wrong number of arguments passed to view, 1 filename expected\\n\";\n\t\t\treturn 1;\n\t\t}\n\t\ttry {\n\t\t\tview(argv[2]);\n\t\t}\n\t\tcatch (nlohmann::json::exception& e) {\n\t\t\tthrow std::runtime_error(\"Not a valid Cadabra notebook.\");\n\t\t}\n\t}\n\telse if (strcmp(argv[1], \"diff\") == 0) {\n\t\tif (argc != 4) {\n\t\t\tstd::cerr << \"Wrong number of arguments passed to diff, 2 filenames expected\\n\";\n\t\t\treturn 1;\n\t\t}\n\t\tdiff(argv[2], argv[3]);\n\t}\n\telse if (strcmp(argv[1], \"gitdiff\") == 0) {\n\t\tif (argc != 9) {\n\t\t\tstd::cerr << \"Wrong number of arguments passed to gitdiff, if you are trying to diff manually use the 'diff' command\\n\";\n\t\t\treturn 1;\n\t\t}\n\t\tstd::string repo_base = trim(run_git_command(\"rev-parse --show-toplevel\")) + \"/\";\n\t\tstd::string filename = repo_base + argv[2];\n\t\tgitdiff(argv[3], filename.c_str(), argv[2]);\n\t}\n\telse if (strcmp(argv[1], \"merge\") == 0) {\n\t\tstd::cerr << \"Sorry, not yet implemented!\\n\";\n\t}\n\telse if (strcmp(argv[1], \"gitmerge\") == 0) {\n\t\tstd::cerr << \"Sorry, not yet implemented!\\n\";\n\t}\n\telse if (strcmp(argv[1], \"clean\") == 0) {\n\t\tif (argc != 3) {\n\t\t\tstd::cerr << \"Wrong number of arguments passed to clean, expected 1 filename\\n\";\n\t\t\texit(1);\n\t\t}\n\t\tclean(argv[2]);\n\t}\n\telse {\n\t\tstd::cerr << \"Unrecognised option \" << argv[1] << '\\n';\n\t\thelp();\n\t\treturn 1;\n\t}\n\n\treturn 0;\n}\n\nint main(int argc, char** argv)\n{\n\ttry {\n\t\treturn run(argc, argv);\n\t}\n\tcatch (std::exception& e) {\n\t\tstd::cerr << \"cdb-nbtool failed with error: \" << e.what() << '\\n';\n\t\treturn 1;\n\t}\n}\n"
  },
  {
    "path": "core/echokernel.py",
    "content": "from ipykernel.kernelbase import Kernel\n\nclass EchoKernel(Kernel):\n    implementation_version = '1.0'\n    language = 'no-op'\n    language_version = '0.1'\n    language_info = {'mimetype': 'text/plain'}\n    banner = \"Echo kernel - as useful as a parrot\"\n    implementation = 'Echo'\n\n    def do_execute(self, code, silent, store_history=True, user_expressions=None, allow_stdin=False):\n        if not silent:\n            stream_content = {'name': 'stdout', 'text': code}\n            self.send_response(self.iopub_socket, 'stream', stream_content)\n\n        return {'status': 'ok',\n                # The base class increments the execution count\n                'execution_count': self.execution_count,\n                'payload': [],\n                'user_expressions': {},\n            }\n\nif __name__ == '__main__':\n    from ipykernel.kernelapp import IPKernelApp\n    IPKernelApp.launch_instance(kernel_class=EchoKernel)\n\n\n"
  },
  {
    "path": "core/lru_cache.hh",
    "content": "//\tSTL-like templated LRU cache.\n//\n// Copyright (C) 2024 Daniel Butter <dbutter@gmail.com>\n// Distributed under the MIT license.\n//\n\n/** \\mainpage lru_cache.hh\n    \\author   Daniel Butter\n    \\version  1.00\n    \\date     2024-11-15\n    \\see      http://github.com/dpbutter/lru_cache.hh/\n\n*/\n\n\n#ifndef lru_cache_hh_\n#define lru_cache_hh_\n\n#include <map>\n#include <list>\n#include <stdexcept>\n#include <iterator>\n\ntemplate <typename Key, typename Value, typename Compare = std::less<Key>>\nclass LRUcache {\npublic:\n    using value_type = std::pair<Key, Value>;\n    using List = std::list<value_type>;\n    using iterator = typename List::iterator;\n    using const_iterator = typename List::const_iterator;\n    using size_type = size_t;\n\n\n    LRUcache(size_t capacity) : max_size(capacity) {}\n\n    // Touches a list iterator, moving it to the top\n    void touch(iterator& it) { \n        if (it != cache_list.begin()) {\n            cache_list.splice(cache_list.begin(), cache_list, it);\n        }\n    }\n\n    // Access an item by key (possibly touching it)\n    Value& at(const Key& key, bool touching = true) {\n        auto lookup_it = cache_lookup.find(key);\n        if (lookup_it == cache_lookup.end()) {\n            throw std::out_of_range(\"Key not found\");\n        }\n        if (touching) {\n            touch(lookup_it->second);\n        }\n        return lookup_it->second->second;\n    }\n\n    // Insert or update an item (always touches)\n    void insert(const Key& key, const Value& value) {\n        auto lookup_it = cache_lookup.find(key);\n        if (lookup_it != cache_lookup.end()) {\n            touch(lookup_it->second);\n            lookup_it->second->second = value;\n        } else {\n            cache_list.emplace_front(key, value);\n            cache_lookup[key] = cache_list.begin();\n            while (cache_list.size() > max_size) {\n                evict();\n            }\n        }\n    }\n\n    // Access an item (or create it) using operator[] (always touches)\n    Value& operator[](const Key& key) {\n        auto lookup_it = cache_lookup.find(key);\n        if (lookup_it != cache_lookup.end()) {\n            // If found, move it to the front of the list (LRU behavior)\n            touch(lookup_it->second);\n            return lookup_it->second->second;\n        } else {\n            // Create new entry, inserting at the front of the list\n            cache_list.emplace_front(key, Value());\n            iterator new_iter = cache_list.begin();\n            cache_lookup[key] = new_iter;\n            while (cache_list.size() > max_size) {\n                evict();\n            }\n            return new_iter->second;\n        }\n    }\n\n    // Find a key (possibly touching it)\n    iterator find(const Key& key, bool touching = true) {\n        auto lookup_it = cache_lookup.find(key);\n        if (lookup_it == cache_lookup.end()) {\n            return cache_list.end();  // Key not found\n        }\n        if (touching) {\n            touch(lookup_it->second);\n        }\n        return lookup_it->second;\n    }\n\n    // Check if a key exists (possibly touching it)\n    bool contains(const Key& key, bool touching = true) {\n        return find(key, touching) != end();\n    }\n\n    // Remove an item by key\n    size_t erase(const Key& key) {\n        auto lookup_it = cache_lookup.find(key);\n        if (lookup_it != cache_lookup.end()) {\n            cache_list.erase(lookup_it->second);\n            cache_lookup.erase(lookup_it);\n            return 1;\n        }\n        return 0;\n    }\n\n    // Remove an item by iterator\n    iterator erase(const_iterator& it) {\n        cache_lookup.erase(it->first);\n        return cache_list.erase(it);\n    }\n    iterator erase(iterator& it) {\n        cache_lookup.erase(it->first);\n        return cache_list.erase(it);\n    }\n\n\n    // Clear the cache\n    void clear() {\n        cache_list.clear();\n        cache_lookup.clear();\n    }\n\n    // Check if the cache is empty\n    bool empty() const {\n        return cache_list.empty();\n    }\n\n    // Get the current size of the cache\n    size_t size() const {\n        assert(cache_list.size() == cache_lookup.size());\n        return cache_list.size();\n    }\n\n    // Resize the cache\n    void resize(size_t new_size) {\n        max_size = new_size;\n        while (cache_list.size() > max_size) {\n            evict();\n        }\n    }\n\n    // Iterators\n    iterator begin() { return cache_list.begin(); }\n    iterator end() { return cache_list.end(); }\n\n\nprivate:\n\n    List cache_list;  \t\t\t\t\t\t\t        // Doubly linked list of key-value pairs\n    std::map<Key, iterator, Compare> cache_lookup;      // Map to locate list nodes\n    size_t max_size;\n\n    void evict() {\n        auto lru = cache_list.back().first;\n        cache_lookup.erase(lru);\n        cache_list.pop_back();\n    }\n};\n\n\n#endif\n"
  },
  {
    "path": "core/modules/Lie.cc",
    "content": "unsigned int exchange::possible_singlets(exptree& tr, exptree::iterator it)\n\t{\n\tstd::vector<identical_tensors_t> idts;\n\tcollect_identical_tensors(tr, it, idts);\n\n\tif(idts.size()==0) return 1; // no indices, so this is a singlet already\n\n\tLiE::LiE_t lie;\n\t// Figure out the algebra from one of the indices.\n\texptree::index_iterator indit=tr.begin_index(idts[0].tensors[0]);\n\tconst numerical::Integer *iprop=properties::get<numerical::Integer>(indit, true);\n\tif(!iprop)\n\t\tthrow consistency_error(\"Need to know about the range of the \" + *indit->name + \" index.\");\n\n\t//\tiprop->difference.print_recursive_treeform(txtout, iprop->difference.begin());\n\tunsigned int dims=to_long(*iprop->difference.begin()->multiplier);\n\t//\tstd::cout << \"*** \" << dims << std::endl;\n\tif(dims%2==0)\n\t\tlie.algebra_type=LiE::LiE_t::alg_D;\n\telse\n\t\tlie.algebra_type=LiE::LiE_t::alg_B;\n\tlie.algebra_dim=dims/2;\n\n\tlie.start();\n\n\t// Find the representation for each group of tensors, taking into\n\t// account their exchange symmetries.\n\tstd::vector<LiE::LiE_t::reps_t> groupreps;\n\n\tfor(unsigned int i=0; i<idts.size(); ++i) {\n\t\tLiE::LiE_t::reps_t single_tensor_rep;\n\t\tif(idts[i].number_of_indices>1) {\n\t\t\tassert(idts[i].tab); // Every tensor with 2+ indices needs a TableauSymmetry.\n\t\t\tTableauBase::tab_t thetab=idts[i].tab->get_tab(tr, idts[i].tensors[0], 0);\n\n\t\t\tstd::vector<unsigned int> topleth;\n\t\t\tfor(unsigned int rws=0; rws<thetab.number_of_rows(); ++rws)\n\t\t\t\ttopleth.push_back(thetab.row_size(rws));\n\t\t\tlie.plethysm(topleth, single_tensor_rep, idts[i].traceless!=0,\n\t\t\t             (thetab.selfdual_column==0)?0:thetab.selfdual_column/abs(thetab.selfdual_column));\n\t\t\t}\n\t\telse {   // vector representation\n\t\t\tLiE::LiE_t::rep_t tmp;\n\t\t\ttmp.weight.resize(lie.algebra_dim,0);\n\t\t\ttmp.weight[0]=1;\n\t\t\tif(lie.algebra_type==LiE::LiE_t::alg_D && lie.algebra_dim==2)\n\t\t\t\ttmp.weight[1]=1;\n\t\t\t//\t\t\ttxtout << tmp.weight[1] << std::endl;\n\t\t\tsingle_tensor_rep.push_back(tmp);\n\t\t\t}\n\t\t// If it's a spinor, still tensor with a spinor rep.\n\t\tif(idts[i].spino) {\n\t\t\tLiE::LiE_t::reps_t vectorpart=single_tensor_rep;\n\t\t\tLiE::LiE_t::reps_t spinorpart;\n\t\t\tLiE::LiE_t::rep_t spinorrep;\n\t\t\tspinorrep.weight.resize(lie.algebra_dim,0);\n\t\t\tspinorrep.weight[lie.algebra_dim-1]=1;\n\t\t\tspinorpart.push_back(spinorrep);\n\t\t\tlie.tensor(vectorpart, spinorpart, single_tensor_rep);\n\t\t\tif(idts[i].gammatraceless)\n\t\t\t\tlie.keep_largest_dim(single_tensor_rep);\n\t\t\t}\n\n\t\tif(idts[i].tensors.size()==1) { // we're done\n\t\t\tgroupreps.push_back(single_tensor_rep);\n\t\t\t}\n\t\telse {\n\t\t\tLiE::LiE_t::reps_t multi_tensor_rep;\n\t\t\tint sign=idts[i].extra_sign + (idts[i].spino!=0);\n\t\t\tif(idts[i].comm && idts[i].comm->sign()==-1)\n\t\t\t\t++sign;\n\t\t\tlie.alt_sym_tensor(idts[i].tensors.size(), single_tensor_rep, multi_tensor_rep, sign%2==0);\n\t\t\tgroupreps.push_back(multi_tensor_rep);\n\t\t\t}\n\t\t}\n\n\t// Now tensor the whole lot together.\n\tLiE::LiE_t::reps_t result=groupreps[0], tmpstore;\n\n\tfor(unsigned int i=0; i<groupreps.size()-1; ++i) {\n\t\tlie.tensor(result, groupreps[i+1], tmpstore);\n\t\tresult=tmpstore;\n\t\t}\n\tunsigned int retval=lie.multiplicity_of_singlet(result);\n\tlie.stop();\n\n\treturn retval;\n\t}\n"
  },
  {
    "path": "core/modules/xperm_new.cc",
    "content": "/*********************************************************************\n*********************************************************************\n*********************************************************************\n*\n*  xperm.c\n*\n* \t(C) Jose M. Martin-Garcia 2003-2008.\n*      jmm@iem.cfmac.csic.es, IEM, CSIC, Madrid, Spain.\n*\n*\tThis is free software, distributed under the GNU GPL license.\n*      See http://metric.iem.csic.es/Martin-Garcia/xAct/\n*\n*  These are a collection of C-functions that find Strong Generating\n*  Sets, Coset representatives and Double-coset representatives.\n*  The algorithms are based on Butler and Portugal et al.\n*\n*  xperm can be used standalone or from the Mathematica package xPerm.\n*\n*  20 June - 5 July 2003. Main development.\n*   3 September 2004. Eliminated MAX variables.\n*   9 November 2005. Corrected treatment of SGS of group D.\n*   6 May 2006. All arrays declared dynamically to avoid stack limits.\n*     Thanks to Kasper Peeters for spotting and correcting this.\n*  25-28 June 2007. Large extension to included multiple dummysets and\n*     repeatedsets.\n*   2015. Eliminate nested functions. Kasper Peeters.\n*\n*  Main ideas:\n*      - Permutations are represented using Images notation.\n*      - Generating sets with m n-permutations are stored as lists of\n*\t  length m*n.\n*\t- #define VERBOSE_* to turn on log output.               *PPC*\n*\n*  Comments:\n*\t- Permutations are assumed to have degree n>0.\n*\t- Lists can have length 0 or positive.\n*\n*  This is ISO C99, not ANSI-C. There are some gcc extensions:\n*\t- ISO C forbids nested functions\n*\t- ISO C89 forbids mixed declarations and code\n*\t- ISO C90 does not support `long long'\n*\t- ISO C90 forbids variable-size arrays\n*\n*********************************************************************\n*********************************************************************\n*********************************************************************/\n\n/* KP */\n#include <stdio.h>\n#include <stdlib.h>\n#include <string.h>\n#include <vector>\n#include \"xperm_new.h\"\n#include <iostream>\n\n/*********************************************************************\n*                             PROTOTYPES                            *\n*********************************************************************/\n\n/* Output */\nvoid print_perm(int *p, int n, int nl);\nvoid print_array_perm(int *perms, int m, int n, int nl);\nvoid print_list(int *list, int n, int nl);\nvoid print_array(int *array, int m, int n, int nl);\n\n/* Lists */\nint equal_list(int *list1, int *list2, int n);\nvoid copy_list(int *list1, int *list2, int n);\nint position(int i, int *list, int n);\nint position_list(int *matrix, int m, int *row, int n);\nvoid zeros(int *list, int n);\nvoid range(int *list, int n);\nvoid complement(int *all, int al, int *part, int pl, int n,\n                int *com, int *cl);\nvoid sort(int *list, int *slist, int l);\nvoid sortB(int *list, int *slist, int l, int *B, int Bl);\nint minim(int *list, int n);\nint maxim(int *list, int n);\nvoid intersection(int *list1, int l1, int *list2, int l2, int *list,\n                  int *l);\n\n/* Permutations */\nint isid(int *list, int n );\nvoid product(int *p1, int *p2, int *p, int n);\nvoid inverse(int *p, int *ip, int n);\nint onpoints(int point, int *p, int n);\nvoid stable_points(int *p, int n, int *list, int *m);\nint first_nonstable_point(int *p, int n);\nvoid nonstable_points(int *list1, int l1, int *GS, int m, int n,\n                      int *list2, int *l2);\nvoid stabilizer(int *points, int k, int *GS, int m, int n, int *subGS,\n                int *mm);\nvoid one_orbit(int point, int *GS, int m, int n, int *orbit, int *ol);\nvoid all_orbits(int *GS, int m, int n, int *orbits);\nvoid schreier_vector(int point, int *GS, int m, int n, int *nu, int *w);\nvoid trace_schreier(int point, int *nu, int *w, int *perm, int n);\n\n/* Algorithms */\nlong long int order_of_group(int *base, int bl, int *GS, int m, int n);\nint perm_member(int *p, int *base, int bl, int *GS, int m, int n);\nvoid schreier_sims_step(int *base, int bl, int *GS, int m, int n, int i,\n                        int *T, int mm, int *newbase, int *nbl, int **newGS, int *nm,\n                        int *num);\nvoid schreier_sims(int *base, int bl, int *GS, int m, int n,\n                   int *newbase, int *nbl, int **newGS, int *nm, int *num);\nvoid coset_rep(int *p, int n, int *base, int bl, int *GS, int *m,\n               int *freeps, int fl, int *cr);\nvoid SGSD(int *vds, int vdsl, int *dummies, int dl, int *mQ,\n          int *vrs, int vrsl, int *repes, int rl, int n,\n          int firstd, int *KD, int *KDl, int *bD, int *bDl);\nvoid double_coset_rep(int *g, int n, int *base, int bl, int *GS, int m,\n                      int *vds, int vdsl, int *dummies, int dl, int *mQ,\n                      int *vrs, int vrsl, int *repes, int rl, int *dcr);\nvoid canonical_perm(int *perm,\n                    int SGSQ, int *base, int bl, int *GS, int m, int n,\n                    int *freeps, int fl, int *dummyps, int dl, int ob, int metricQ,\n                    int *cperm);\nvoid canonical_perm_ext(int *perm, int n,\n                        int SGSQ, int *base, int bl, int *GS, int m,\n                        int *frees, int fl,\n                        int *vds, int vdsl, int *dummies, int dl, int *mQ,\n                        int *vrs, int vrsl, int *repes, int rl,\n                        int *cperm);\n\n\n/*********************************************************************\n*                         PRINTING FUNCTIONS                        *\n*********************************************************************/\n\n/**********************************************************************/\n\n/* print_perm. JMM, 22 June 2003\n*\n* This function prints a permutation p of degree n. If nl=1(0) adds\n* (does not) a newline. */\n\nvoid print_perm(int *p, int n, int nl)\n\t{\n\tint i;\n\tif (isid(p,n)) printf(\"id\");\n\telse {\n\t\tprintf(\"(\");\n\t\tprintf(\"%d\", p[0]);          /* No comma */\n\t\tfor (i=1; i<n; i++) {\n\t\t\tprintf(\",%d\", p[i]); /* Comma separated */\n\t\t\t}\n\t\tprintf(\")\");\n\t\t}\n\tif (nl) printf(\"\\n\");\n\t}\n\n/**********************************************************************/\n\n/* print_array_perm. JMM, 22 June 2003\n*\n* This function prints an array of m n-permutations.\n* If nl=1 (0) adds (does not) a newline after each row.\n* There are no commas between permutations. */\n\nvoid print_array_perm(int *perms, int m, int n, int nl)\n\t{\n\tint j;\n\tprintf(\"{\");\n\tif (nl) printf(\"\\n\");\n\tfor(j=0; j<m; j++) {\n\t\tprintf(\" \");\n\t\tprint_perm(perms+j*n, n, nl);\n\t\t}\n\tif (nl) printf(\"}\\n\");\n\telse printf(\" }\\n\");\n\t}\n\n/**********************************************************************/\n\n/* print_list. JMM, 22 June 2003\n*\n* This function prints a list of length n in curly brackets.\n* If nl=1 (0) it adds (does not) a newline. */\n\nvoid print_list(int *list, int n, int nl)\n\t{\n\tint i;\n\tprintf(\"{\");\n\tif (n>0) printf(\"%d\", list[0]);            /* No comma */\n\tfor (i=1; i<n; i++) printf(\",%d\", list[i]);/* Comma separated */\n\tprintf(\"}\");\n\tif (nl) printf(\"\\n\");\n\t}\n\n/**********************************************************************/\n\n/* print_array. JMM, 22 June 2003\n*\n* This function prints an array of dimensions m x n in curly brackets.\n* If nl=1 (0) adds (does not) a newline after each row.\n* There are no commas between lists. */\n\nvoid print_array(int *array, int m, int n, int nl)\n\t{\n\tint j;\n\tprintf(\"{\");\n\tif(nl) printf(\"\\n\");\n\tfor(j=0; j<m; j++) {\n\t\tprintf(\" \");\n\t\tprint_list(array+j*n, n, nl);\n\t\t}\n\tif (!nl) printf(\" \");\n\tprintf(\"}\\n\");\n\t}\n\n/**********************************************************************/\n\n\n/*********************************************************************\n*                          GENERIC FUNCTIONS                        *\n*********************************************************************/\n\n/**********************************************************************/\n\n/* equal_list. JMM, 27 June 2003\n*\n* Checks that list1 and list2 (both with length n) are equal.\n* If n=0 the result is 1.\n*/\n\n/* Old code\nint equal_list(int *list1, int *list2, int n) {\n\twhile(n--) { * Run from n-1 to 0 *\n\tif(*(list1+n) != *(list2+n)) return(0); * different *\n\t\t\t}\n\treturn(1); * equal *\n\t\t\t}\n*/\n\n/* KP, 7 May 2006 */\nint equal_list(int *list1, int *list2, int n)\n\t{\n\tif (n==0) return 1;\n\tif (memcmp(list1, list2, n*sizeof(int))==0) return 1;\n\telse return 0;\n\t}\n\n/**********************************************************************/\n\n/* copy_list. JMM, 27 June 2003\n*\n* Copies first n elements of list1 onto list2. If n=0 nothing is done.\n*/\n\n/* Old code\nvoid copy_list(int *list1, int *list2, int n) {\n\twhile(n--) *(list2+n) = *(list1+n);\n\t\t\t}\n*/\n\n/* KP, 7 May 2006 */\n/* KP, 26 Nov 2007: memcpy changed to memmove */\nvoid copy_list(int *list1, int *list2, int n)\n\t{\n\tif (n==0) return;\n\tmemmove(list2, list1, n*sizeof(int));\n\t}\n\n/**********************************************************************/\n\n/* position. JMM, 20 June 2003\n*\n* This function finds the position of the integer i in list (length n),\n* counting from 1 to n, or else gives 0 if i is not in list. Note that\n* it starts from the end so that if i appears several times in list it\n* will only find the last one. If n=0 the result is 0.\n*\n* More than 60% of time in the Schreier-Sims algorithm is spent here!\n*\n* Note: it is not possible to use  memchr  because it only works with\n* characters (integers up to 255).\n*/\n\nint position(int i, int *list, int n)\n\t{\n\twhile(n--) {\n\t\tif (*(list+n) == i) return(n+1);\n\t\t}\n\treturn(0);\n\t}\n\n/**********************************************************************/\n\n/* position_list. JMM, 28 June 2003\n*\n* This function gives the position of list row (length n) in the\n* matrix of dimensions m, n. If row is not present in matrix, 0\n* is returned.\n*/\n\nint position_list(int *matrix, int m, int *row, int n)\n\t{\n\twhile(m--) {\n\t\tif(equal_list(matrix+m*n, row, n)) return(m+1);\n\t\t}\n\treturn(0);\n\t}\n\n/**********************************************************************/\n\n/* zeros, range. JMM, 22 June 2003\n*\n* These functions generate lists of n zeros or the range 1...n,\n* respectively, storing the result in list.\n*/\n\n/* Old code\nvoid zeros(int *list, int n) {\n\twhile(n--) *(list+n) = 0;\n\t\t\t}\n*/\n\n/* KP, 7 May 2006 */\nvoid zeros(int *list, int n)\n\t{\n\tif (n==0) return;\n\tmemset(list, 0, n*sizeof(int));\n\t}\n\nvoid range(int *list, int n)\n\t{\n\twhile(n--) *(list+n) = n+1;\n\t}\n\n/**********************************************************************/\n\n/* complement. JMM, 28 June 2003\n*\n* This function gives all sublists of length n in list all (length al)\n* that are not members of list part (length pl), storing the result\n* in list com (length cl).\n* We assume that enough space (typically al n-lists) has been already\n* allocated for com.\n*/\n\nvoid complement(int *all, int al, int *part, int pl, int n,\n                int *com, int *cl)\n\t{\n\tint i;\n\t*cl = 0;\n\tfor(i=0; i<al; i++) {\n\t\tif (!position_list(part, pl, all+i*n, n)) {\n\t\t\tcopy_list(all+i*n, com+(*cl)*n, n);\n\t\t\t(*cl)++;\n\t\t\t}\n\t\t}\n\t}\n\n/**********************************************************************/\n\n/* sort. JMM, 30 June 2003\n*\n* Sorts list (length l) storing the result in slist (length l, too).\n* There are l*(l-1)/2 element comparisons. This could be improved.\n*/\n\nvoid sort(int *list, int *slist, int l)\n\t{\n\n\tint i,j;\n\tint tmp, mini; /* mini is a position, not an element of list */\n\n#ifdef VERBOSE_LISTS\t\t\t\t\t\t/*PPC*/\n\tprintf(\"sort: Sorting list \");\n\tprint_list(list, l, 1);\t/*PPC*/\n#endif\t\t\t\t\t\t\t\t/*PPC*/\n\tcopy_list(list, slist, l);\n\tfor (i=0; i<l-1; i++) {\n\t\t/* Assume points at positions 0...i-1 are already sorted */\n\t\t/* Compare point at position i with points to the right */\n\t\tmini = i;\n\t\tfor(j=i+1; j<l; j++) {\n\t\t\tif ( slist[j] < slist[mini] ) mini = j;\n\t\t\t}\n\t\t/* Swap points i and mini */\n\t\ttmp = slist[i];\n\t\tslist[i] = slist[mini];\n\t\tslist[mini] = tmp;\n\t\t}\n#ifdef VERBOSE_LISTS\t\t\t\t\t\t/*PPC*/\n\tprintf(\"sort: with result \");\n\tprint_list(slist, l, 1);\t/*PPC*/\n#endif\t\t\t\t\t\t\t\t/*PPC*/\n\t}\n\n/* sortB. JMM, 30 June 2003\n*\n* Sorts list (length l) according to the order given by B (length Bl),\n* storing the result in slist (length l, too). Elements not in B\n* are pushed to the end, and sorted using sort.\n*/\n\nvoid sortB(int *list, int *slist, int l, int *B, int Bl)\n\t{\n\n\tint sl;\n\tint *tmp=  (int*)malloc(l*sizeof(int)), tmpl;\n\tint *stmp= (int*)malloc(l*sizeof(int));\n\n#ifdef VERBOSE_LISTS\t\t\t\t\t\t/*PPC*/\n\tprintf(\"sortB: Sorting list \");\n\tprint_list(list, l, 1);\t/*PPC*/\n\tprintf(\"sortB: using base \");\n\tprint_list(B, Bl, 1);\t/*PPC*/\n#endif\t\t\t\t\t\t\t\t/*PPC*/\n\t/* Elements of list in B, keeping order of B, moved to slist */\n\tintersection(B, Bl, list, l, slist, &sl);\n\t/* Other elements of list are appended to slist */\n\tcomplement(list, l, B, Bl, 1, tmp, &tmpl);\n\t/* Check that tmpl+sl==l */\n\tif(tmpl+sl != l) printf(\"Error in sortB\\n\");\n\t/* Sort the latter integers using sort */\n\tsort(tmp, stmp, tmpl);\n\tcopy_list(stmp, slist+sl, tmpl);\n#ifdef VERBOSE_LISTS\t\t\t\t\t\t/*PPC*/\n\tprintf(\"sortB: with result \");\n\tprint_list(slist, l, 1);\t/*PPC*/\n#endif\t\t\t\t\t\t\t\t/*PPC*/\n\t/* Free allocated memory */\n\tfree(tmp);\n\tfree(stmp);\n\n\t}\n\n/**********************************************************************/\n\n/* minim, maxim. JMM, 2 July 2003\n*\n* These functions find the minimum and maximum elements of a given\n* list of length n, using normal integer ordering. Names min, max are\n* reserved.\n*/\n\nint minim(int *list, int n)\n\t{\n\n\tint m=list[n-1];\n\n\twhile(n--) {\n\t\tif (list[n]<m) m=list[n];\n\t\t}\n\treturn(m);\n\n\t}\n\nint maxim(int *list, int n)\n\t{\n\n\tint m=list[n-1];\n\n\twhile(n--) {\n\t\tif (list[n]>m) m=list[n];\n\t\t}\n\treturn(m);\n\n\t}\n\n/**********************************************************************/\n\n/* intersection. JMM, 3 July 2003\n*\n* This function returns in list (length l) the intersection of the\n* elements of lists list1 (length l1) and list2 (length l2). Note that\n* we return unique (that is, non-repeated) elements. Returned elements\n* keep the original order in list1.\n* We assume that enough space (typical l1 or l2 integers) has been\n* already allocated for list.\n*/\n\nvoid intersection(int *list1, int l1, int *list2, int l2, int *list,\n                  int *l)\n\t{\n\n\tint i, j, a;\n\n\t*l = 0;\n\tfor(i=0; i<l1; i++) { /* Range over elements of list1 */\n\t\ta = list1[i];\n\t\tfor(j=0; j<l2; j++) { /* Range over elements of list2 */\n\t\t\t/* a is in list2 and not yet in list, append */\n\t\t\tif ((list2[j] == a) && (!position(a, list, *l)))\n\t\t\t\tlist[(*l)++] = a;\n\t\t\t}\n\t\t}\n\n\t}\n\n/**********************************************************************/\n\n\n/*********************************************************************\n*                        PERMUTATIONS FUNCTIONS                     *\n*********************************************************************/\n\n/**********************************************************************/\n\n/* isid. JMM, 20 June 2003\n*\n* This function detects whether the n-permutation p is the identity\n* (returning 1) or not (returning 0). */\n\nint isid(int *p, int n )\n\t{\n\n\twhile(n--) {\n\t\tif (*(p+n)!=n+1) return(0); /* Not the identity */\n\t\t}\n\treturn(1); /* Identity */\n\n\t}\n\n/**********************************************************************/\n\n/* product. JMM, 20 June 2003\n*\n* Product of n-permutations p1 and p2 (from left to right) storing the\n* result in the n-permutation p. Note that the points of the\n* permutations go from 1 to n, while we want to add from 0 to n-1 to\n* the pointer p2. That's why we need to add -1.\n* This function is highly efficient, but rather criptic. */\n\nvoid product(int *p1, int *p2, int *p, int n)\n\t{\n\n\twhile(n--) *(p++) = *(p2-1+*(p1++));\n\n\t/* Example:\n\t* Suppose we have p1=(3,2,1) and p2=(3,1,2) of degree n=3.\n\t* The following operations take place, in this order:\n\t*   n=3, n--\n\t*   *(p1++)=3\n\t*   *(p2-1+3)=*(p2+2)=2\n\t*   *(p++)=2  Computed first element of p\n\t*   n=2, n--\n\t*   *(p1++)=2\n\t*   *(p2-1+2)=*(p2+1)=1\n\t*   *(p++)=1  Computed second element of p\n\t*   n=1, n--\n\t*   *(p1++)=1\n\t*   *(p2-1+1)=*(p2)=3\n\t*   *(p++)=3  Computed third element of p\n\t*   n=0, END\n\t* Therefore the final permutation returned is p=(2,1,3).\n\t*/\n\n\t}\n\n/* Taken out KP */\n/* TAB1 is an element of S; TAB2 is an element of D */\nvoid F2(int *TAB1, int *g, int *TAB2, int *sgd, int n)\n\t{\n\tint *tmp= (int*)malloc(n*sizeof(int));\n\n\tproduct(TAB1, g, tmp, n);\n\tproduct(tmp, TAB2, sgd, n);\n\n\tfree(tmp);\n\t} /* End of function F2 */\n\n/**********************************************************************/\n\n/* inverse. JMM, 20 June 2003\n*\n* Inverse of the n-permutation p, storing the result in the\n* n-permutation ip. Again we need to add -1 to the pointer ip.\n* Conversely, note that we need to add +1 to n because n ranges from\n* 0 to n-1 in the while loop. */\n\nvoid inverse(int *p, int *ip, int n)\n\t{\n\n\twhile(n--) *(ip-1+*(p+n)) = n+1 ;\n\n\t}\n\n/**********************************************************************/\n\n/* onpoints. JMM, 20 June 2003\n*\n* Image of point under the n-permutation p. If point is larger than\n* the degree n we return point. */\n\nint onpoints(int point, int *p, int n)\n\t{\n\n\tif (point <= n) return(*(p-1+point));\n\telse return(point);\n\n\t}\n\n/**********************************************************************/\n\n/* stable_points. JMM, 20 June 2003\n*\n* This function finds the points which remain stable under the\n* n-permutation p, storing the result in list of length m (<=n).\n* With n=0 we get an empty list (m=0).\n* We assume that enough space (typically n integers) has been already\n* allocated for list.\n*/\n\nvoid stable_points(int *p, int n, int *list, int *m)\n\t{\n\n\tint i;\n\n\t*m = 0;\n\tfor(i=1; i<=n; i++) {\n\t\tif ( onpoints(i, p, n) == i ) list[(*m)++] = i;\n\t\t}\n\n\t}\n\n/**********************************************************************/\n\n/* first_nonstable_point. JMM, 30 June 2003\n*\n* This function gives the smallest moved point by the permutation p.\n* If no point is moved the result is 0. If n=0 the result is 0.\n* This is a restricted form of stable_points.\n*/\n\nint first_nonstable_point(int *p, int n)\n\t{\n\n\tint i;\n\n\tfor(i=1; i<=n; i++) {\n\t\tif (onpoints(i, p, n) != i) return(i);\n\t\t}\n\treturn(0);\n\t}\n\n/**********************************************************************/\n\n/* nonstable_points. JMM, 30 June 2003\n*\n* This function gives a set of points (list2, length l2) such that\n* none of the permutations in GS fixes them all. The first l1 points\n* of list2 will be those of list1, even if they are all stable under\n* GS. If m=0 the resulting list2 is just list1.\n* We assume that enough space (typically n integers) has been already\n* allocated for list2.\n*/\n\nvoid nonstable_points(int *list1, int l1, int *GS, int m, int n,\n                      int *list2, int *l2)\n\t{\n\n\tint i, j;\n\n\tcopy_list(list1, list2, l1);\n\t*l2 = l1; /* Initialize list2 */\n\tfor(j=0; j<m; j++) { /* Range over permutations of GS */\n\t\tint stable=1;\n\t\tfor(i=0; i<*l2; i++) {\n\t\t\tif (onpoints(list2[i], GS+j*n, n) != list2[i]) {\n\t\t\t\tstable=0;\n\t\t\t\tbreak;\n\t\t\t\t}\n\t\t\t}\n\t\t/* If all points already in list2 are stable under the\n\t\t\tpermutation, append the smallest nonstable point */\n\t\tif (stable) {\n\t\t\tlist2[*l2] = first_nonstable_point(GS+j*n, n);\n\t\t\t(*l2)++;\n\t\t\t}\n\t\t}\n\t}\n\n/**********************************************************************/\n\n/* stabilizer. JMM, 22 June 2003\n*\n* This function finds the permutations that stabilize the set of k\n* points among the GeneratingSet GS with m n-permutations. With m=0\n* we return an empty subset (mm=0). Recall that the stabilizer of a\n* generating set of a group is not, in general, a generating set for\n* the corresponding stabilizer of that group.\n* We assume that enough space (typically m*n integers) has been already\n* allocated for subGS.\n*/\n\nvoid stabilizer(int *points, int k, int *GS, int m, int n,\n                int *subGS, int *mm)\n\t{\n\n\tint i, j;\n\tint stable;\n\n\t*mm=0;\n\tfor(j=0; j<m; j++) {\n\t\tstable=1;\n\t\tfor(i=0; i<k; i++) {\n\t\t\tif (onpoints(points[i],GS+n*j,n) != points[i]) {\n\t\t\t\tstable = 0;\n\t\t\t\tbreak;\n\t\t\t\t}\n\t\t\t}\n\t\tif (stable) {\n\t\t\tcopy_list(GS+n*j, subGS+(*mm)*n, n);\n\t\t\t++(*mm);\n\t\t\t}\n\t\t}\n\n\t}\n\n/**********************************************************************/\n\n/* one_orbit. JMM, 22 June 2003\n*\n* Orbit of a given point under a GeneratingSet GS with m\n* n-permutations. The result is stored in orbit (length ol).\n* With m=0 the orbit is just {point}.\n* We assume that enough space (typically n integers) has been already\n* allocated for orbit.\n*/\n\nvoid one_orbit(int point, int *GS, int m, int n, int *orbit, int *ol)\n\t{\n\n\tint np=0;  /* Index of current element in the orbit */\n\tint gamma; /* Current element in the orbit */\n\tint mp;    /* Index of current permutation in GS */\n\tint newgamma;\n\n\torbit[0] = point;\n\t*ol = 1;\n\twhile(np < *ol) {\n\t\tgamma = orbit[np];\n\t\tfor(mp=0; mp<m; mp++) {\n\t\t\tnewgamma = onpoints(gamma, GS+mp*n, n);\n\t\t\tif (!position(newgamma, orbit, *ol))\n\t\t\t\torbit[(*ol)++] = newgamma;\n\t\t\t}\n\t\tnp++;\n\t\t}\n\n\t}\n\n/**********************************************************************/\n\n/* all_orbits. JMM, 1 July 2003\n*\n* This function returns all orbits of the generating set GS (with\n* m n-permutations). Note that we use a very special notation: the\n* result is a vector orbits of length n such that all points marked\n* with 1 belong to the same orbit; all points marked with 2 belong to\n* another orbit, and so on. With m=0 we return the list {1,2,...,n}.\n*/\n\nvoid all_orbits(int *GS, int m, int n, int *orbits)\n\t{\n\n\tint i, j;                                   /* Counters */\n\tint *orbit= (int*)malloc(n*sizeof(int)), ol;/* Computed orbit */\n\tint orbit_index=1;                                   /* Orbit index */\n\n\t/* Initialize orbits */\n\tmemset(orbits, 0, n*sizeof(int));\n\n\t/* Compute orbits */\n\tfor (i=1; i<=n; i++) { /* Points */\n\t\tif(orbits[i-1]==0) { /* New orbit condition */\n\t\t\t/* Compute new orbit */\n\t\t\tone_orbit(i, GS, m, n, orbit, &ol);\n\t\t\t/* Mark points of new orbit with index or */\n\t\t\tfor (j=0; j<ol; j++) orbits[orbit[j]-1] = orbit_index;\n\t\t\t/* Increment index for next orbit */\n\t\t\torbit_index++;\n\t\t\t}\n\t\t}\n\n\t/* Free allocated memory */\n\tfree(orbit);\n\n\t}\n\n/**********************************************************************/\n\n/* one_schreier_orbit. JMM, 22 June 2003\n*\n* Orbit of point under the GeneratingSet GS with m n-permutations.\n* The result is stored in orbit and the vectors nu of permutations and\n* w of backward points. If init=1 both nu and w are reset to 0.\n*\n* Note: the profiler shows that roughly half of the time in this\n* function is spent in the subroutine `position'.\n*/\n\nvoid one_schreier_orbit(int point, int *GS, int m, int n,\n                        int *orbit, int *ol, int *nu, int *w, int init)\n\t{\n\n\tint np;    /* Index of current element in the orbit */\n\tint gamma; /* Current element in the orbit */\n\tint mp;    /* Index of current permutation in GS */\n\tint *perm= (int*)malloc(n*sizeof(int));\n\tint newgamma;\n\n\t/* Initialize schreier with zeros if required */\n\tmemset(orbit, 0, n*sizeof(int));\n\tif (init) {\n\t\tmemset(nu, 0, n*n*sizeof(int));\n\t\tmemset(w, 0, n*sizeof(int));\n\t\t}\n\t/* First element of orbit. There is no backward pointer */\n\torbit[0] = point;\n\t*ol = 1;\n\t/* Other elements of orbit */\n\tnp = 0;\n\twhile(np < *ol) {\n\t\tgamma = orbit[np];\n\t\tfor(mp=0; mp<m; mp++) {\n\t\t\tcopy_list(GS+mp*n, perm, n);\n\t\t\tnewgamma = onpoints(gamma, perm, n);\n\t\t\tif (position(newgamma, orbit, *ol));\n\t\t\telse {\n\t\t\t\t/* Append to orbit */\n\t\t\t\torbit[(*ol)++] = newgamma;\n\t\t\t\t/* Perm moving gamma to newgamma */\n\t\t\t\tcopy_list(perm, nu+(newgamma-1)*n, n);\n\t\t\t\t/* Gamma backward pointer of newgamma */\n\t\t\t\t*(w+newgamma-1) = gamma;\n\t\t\t\t}\n\t\t\t}\n\t\tnp++;\n\t\t}\n\t/* Free allocated memory */\n\tfree(perm);\n\n\t}\n\n/**********************************************************************/\n\n/* schreier_vector. JMM, 22 June 2003\n*\n* All orbits of a given GeneratingSet GS with m n-permutations, with\n* combined vectors of backward permutations and pointers. Note that we\n* do not return the orbits information, though it can be reconstructed\n* from w and nu.\n*/\n\nvoid schreier_vector(int point, int *GS, int m, int n, int *nu, int *w)\n\t{\n\n\tint i;    /* Point counter (from 1 to n) */\n\tint *orbit=      (int*)malloc(n*sizeof(int));\n\tint *usedpoints= (int*)malloc(n*sizeof(int));\n\tint j=0;  /* Counter of used points */\n\tint ol;\n\n\t/* First orbit */\n\tone_schreier_orbit(point, GS, m, n, orbit, &ol, nu, w, 1);\n\twhile(ol--) usedpoints[j++] = orbit[ol];\n\t/* Other orbits */\n\tfor(i=1; i<=n; i++) {\n\t\tif (!position(i, usedpoints, j)) {\n\t\t\tone_schreier_orbit(i, GS, m, n, orbit, &ol, nu, w, 0);\n\t\t\twhile(ol--) usedpoints[j++] = orbit[ol];\n\t\t\t}\n\t\t}\n\t/* Free allocated memory */\n\tfree(orbit);\n\tfree(usedpoints);\n\n\t}\n\n/**********************************************************************/\n\n/* trace_schreier. JMM, 22 June 2003\n*\n* This function traces the Schreier vector (orbits, nu, w) with the\n* point given, returning in perm a permutation wich moves the first\n* point of the corresponding orbit to point.\n*/\n\nvoid trace_schreier(int point, int *nu, int *w, int *perm, int n)\n\t{\n\n\tint i;\n\tint found=0;\n\tint *newperm= (int*)malloc(n*sizeof(int));\n\n\tfor(i=0; i<n; i++) {\n\t\tif (*(w+point-1) == 0) {\n\t\t\trange(perm, n);\n\t\t\tfound=1;\n\t\t\tbreak;\n\t\t\t}\n\t\t}\n\tif (!found) {\n\t\ttrace_schreier(*(w+point-1), nu, w, newperm, n);\n\t\tproduct(newperm, nu+(point-1)*n, perm, n);\n\t\t}\n\tfree(newperm);\n\n\t}\n\n/**********************************************************************/\n\n/* order_of_group. JMM, 27 June 2003\n*\n* This function calculates the order of the group generated by the SGS\n* given by base (with bl points) and GS (with m n-permutations).\n*\n* JMM, 12 March 2006: changed type to long long int (8 bytes).\n* This allows numbers up to ~ 10^19.\n*/\n\nlong long int order_of_group(int *base, int bl, int *GS, int m, int n)\n\t{\n\n\tif (m==0) return(1);\n\telse {\n\t\tint *stab=  (int*)malloc(m*n*sizeof(int)), sl;\n\t\tint *orbit= (int*)malloc(  n*sizeof(int)), ol;\n\t\tone_orbit(base[0], GS, m, n, orbit, &ol);\n\t\tstabilizer(base, 1, GS, m, n, stab, &sl);\n\t\tlong long int ret=ol* order_of_group(base+1,bl-1,stab,sl,n);\n\t\tfree(stab);\n\t\tfree(orbit);\n\t\treturn ret;\n\t\t}\n\t}\n\n/**********************************************************************/\n\n/* perm_member. JMM, 27 June 2003\n*\n* Checks whether permutation p belongs (returns 1) or not (returns 0)\n* to the group generated by the SGS given by base (length bl) and GS\n* (m n-permutations). If bl=0 or m=0 the result is  isid(p, n) .\n*\n* JMM, 26 June 2007: modified behaviour of m==0. It gave ret=1 before.\n*/\n\nint perm_member(int *p, int *base, int bl, int *GS, int m, int n)\n\t{\n\n\tif (bl==0 || m==0) return( isid(p, n) );\n\telse {\n\t\tint *pp=    (int*)malloc(  n*sizeof(int));\n\t\tint *ip=    (int*)malloc(  n*sizeof(int));\n\t\tint *orbit= (int*)malloc(  n*sizeof(int)), ol;\n\t\tint *w=     (int*)malloc(  n*sizeof(int));\n\t\tint *nu=    (int*)malloc(n*n*sizeof(int));\n\t\tint *stab=  (int*)malloc(m*n*sizeof(int)), sl;\n\t\tint point, ret;\n\n\t\tone_schreier_orbit(base[0], GS,m,n, orbit,&ol, nu,w, 1);\n\t\tpoint = onpoints(base[0], p, n);\n\t\tif (position(point, orbit, ol)) {\n\t\t\ttrace_schreier(point, nu, w, pp, n);\n\t\t\tinverse(pp, ip, n);\n\t\t\tproduct(p, ip, pp, n);\n\t\t\tstabilizer(base, 1, GS, m, n, stab, &sl);\n\t\t\tret = perm_member(pp, base+1, bl-1, stab,sl,n);\n\t\t\t}\n\t\telse ret = 0;\n\n\t\tfree(pp);\n\t\tfree(ip);\n\t\tfree(orbit);\n\t\tfree(w);\n\t\tfree(nu);\n\t\tfree(stab);\n\n\t\treturn(ret);\n\t\t}\n\n\t}\n\n/**********************************************************************/\n\n/* schreier_sims. JMM, 28-30 June 2003\n*\n* This function computes a Strong Generating Set for the group of\n* permutations generated by GS (with m n-permutations). It is\n* possible to give the first bl (possibly 0) elements of the base,\n* and the code computes all the others. There are possibly (and\n* probably) redundant points in the final base. n=0 is not consistent\n* here.\n* We assume that enough space (at least, and typically, m*n integers)\n* has been already allocated for newGS. We also assume that newGS can\n* be reallocated. That's why we do not send a pointer, but a pointer\n* to that pointer. That is, it needs to be reallocated in a different\n* subroutine, and that cannot be done with a normal pointer!\n*/\n\nvoid schreier_sims(int *base, int bl, int *GS, int m, int n,\n                   int *newbase, int *nbl, int **newGS, int *nm, int *num)\n\t{\n\n#ifdef VERBOSE_SCHREIER\t\t\t\t\t\t/*PPC*/\n\tprintf(\"******** SCHREIER-SIMS ALGORITHM ********\\n\");\t/*PPC*/\n#endif\t\t\t\t\t\t\t\t/*PPC*/\n\t/* Note the cycle: base -> newbase -> base2 -> newbase -> ... */\n\n\t/* Copy base into newbase, adding more points if needed */\n\tnonstable_points(base, bl, GS, m, n, newbase, nbl);\n#ifdef VERBOSE_SCHREIER\t\t\t\t\t\t/*PPC*/\n\tprintf(\"Original base:\");\n\tprint_list(base, bl, 1);\t/*PPC*/\n\tprintf(\"New base:\");\n\tprint_list(newbase, *nbl, 1);\t/*PPC*/\n#endif\t\t\t\t\t\t\t\t/*PPC*/\n\t/* Initialize newGS=GS */\n\tcopy_list(GS, *newGS, m*n);\n\t*nm = m;\n\tif (*nbl==0) { /* Problem. Return input sets  */\n\t\tcopy_list(base, newbase, bl);\n\t\t*nbl = bl;\n\t\treturn;\n\t\t}\n\n\t/* Allocate memory for intermediate SGS and stabilizer */\n\tint i;                                         /* Base index */\n\tint *base2= (int*)malloc(  n*sizeof(int)), bl2;/* Interm base */\n\tint *GS2=   (int*)malloc(m*n*sizeof(int)), m2; /* Interm GS */\n\tint *stab=  (int*)malloc(m*n*sizeof(int)), mm; /* Stabilizer */\n\n\t/* Main loop */\n\tm2 = *nm; /* Initially GS2 will be just newGS */\n\tfor(i=(*nbl); i>0; i--) {\n#ifdef VERBOSE_SCHREIER\t\t\t\t\t\t/*PPC*/\n\t\tprintf(\"\\nComputing SGS for H^(%d)\\n\", i-1);\t\t/*PPC*/\n#endif\t\t\t\t\t\t\t\t/*PPC*/\n\t\tif (*nm > m2) { /* Reallocate GS2 and stab */\n\t\t\tGS2 =  (int*)realloc(GS2,  (*nm)*n*sizeof(int));\n\t\t\tstab = (int*)realloc(stab, (*nm)*n*sizeof(int));\n\t\t\t}\n\t\t/* Copy newbase into base2 */\n\t\tcopy_list(newbase, base2, *nbl);\n\t\tbl2=*nbl;\n\t\tcopy_list(*newGS, GS2, (*nm)*n);\n\t\tm2=*nm;\n\t\t/* Compute newbase from base2 */\n\t\tstabilizer(base2, i-1, GS2, m2, n, stab, &mm);\n\t\tschreier_sims_step(base2, bl2, GS2, m2, n, i,\n\t\t                   stab, mm, newbase, nbl, newGS, nm, num);\n\t\t}\n\n\t/* Free allocated memory */\n\tfree(base2);\n\tfree(GS2);\n\tfree(stab);\n\n#ifdef VERBOSE_SCHREIER\t\t\t\t\t\t/*PPC*/\n\tprintf(\"************ END OF ALGORITHM ***********\\n\");\t/*PPC*/\n#endif\t\t\t\t\t\t\t\t/*PPC*/\n\t}\n\n/* Intermediate function for schreier_sims.\n*\n* Assuming that S^(i-1) is a GenSet for H^(i-1) and that [B, S^(i)]\n* are a StrongGenSet for H^(i), find a StrongGenSet for H^(i-1).\n* T is the set of additional generators in S^(i-1) since the previous\n* call to the procedure with the present value of i. Assume that a\n* StrongGenSet of < S^(i-1) - T > (the previous value of H^(i-1)) is\n* included in B and S. The present value of nu^(i-1) must be an\n* extension of the previous value.\n*\n* base (length bl): tentative base for the whole group\n* GS (m n-permutations): tentative StrongGenSet for the whole group\n* i: current order in the hierarchy of stabilizers\n*\n* Sizes on input:\n*\ti <= bl <= n   Not changed\n*      mm <= m        Not changed\n*      nbl = bl       nbl will increase\n*      nm = m         nm will increase\n*/\n\nvoid schreier_sims_step(int *base, int bl, int *GS, int m, int n,\n                        int i, int *T, int mm,\n                        int *newbase, int *nbl, int **newGS, int *nm, int *num)\n\t{\n\n\t/* Declarations */\n\t/* Counters */\n\tint c, j=0, jj, level;\n\t/* Intermediate permutations */\n\tint *p=   (int*)malloc(n*sizeof(int));\n\tint *ip=  (int*)malloc(n*sizeof(int));\n\tint *pp=  (int*)malloc(n*sizeof(int));\n\tint *ppp= (int*)malloc(n*sizeof(int));\n\t/* Stabilizer of base[1...i-1] */\n\tint *Si= (int*)malloc(m*n*sizeof(int)), Sil;\n\t/* Old stabilizer. Here we could use mm*n rather than m*n */\n\tint *oldSi= (int *)malloc(m*n*sizeof(int)), oldSil;\n\t/* Orbit of base[i] */\n\tint *Deltai= (int*)malloc(  n*sizeof(int)), Deltail;\n\tint *w=      (int*)malloc(  n*sizeof(int));\n\tint *nu=     (int*)malloc(n*n*sizeof(int));\n\t/* Old orbit */\n\tint *oldDeltai= (int*)malloc(  n*sizeof(int)), oldDeltail;\n\tint *oldw=      (int*)malloc(  n*sizeof(int));\n\tint *oldnu=     (int*)malloc(n*n*sizeof(int));\n\t/* Generators to check */\n\tint *genset= (int*)malloc(m*n*sizeof(int)), gensetl;\n\t/* Loops */\n\tint gamma, gn, sn;\n\tint *s= (int*)malloc(n*sizeof(int));\n\tint *g= (int*)malloc(n*sizeof(int));\n\t/* Stabilizer */\n\tint *stab =  (int*)malloc(m*n*sizeof(int)), stabl;\n\tint *stabps= (int*)malloc(  n*sizeof(int)), stabpsl;\n\n#ifdef VERBOSE_SCHREIER\t\t\t\t\t\t/*PPC*/\n\tprintf(\"******** schreier_sims_step ********\\n\");\t/*PPC*/\n\tprintf(\"base:\");\n\tprint_list(base, bl, 1);\t\t/*PPC*/\n\tprintf(\"GS (%d perms of degree %d):\", m, n);\t\t/*PPC*/\n\tprint_array_perm(GS, m, n, 1);\t\t\t\t/*PPC*/\n#endif\t\t\t\t\t\t\t\t/*PPC*/\n\t/* Initialize newbase=base and newGS=GS (and their lengths) */\n\t/* They are already equal on input. Always true? */\n\tcopy_list(base, newbase, bl);\n\t*nbl = bl;\n\tcopy_list(GS, *newGS, m*n);\n\t*nm = m;\n\t/* Original generating sets. We get Sil<=m and oldSil<=mm */\n\tstabilizer(base, i-1, GS, m, n, Si, &Sil);\n#ifdef VERBOSE_SCHREIER\t\t\t\t\t\t/*PPC*/\n\tprintf(\"Stabilizer of first %d points of base \", i-1);\t/*PPC*/\n\tprint_list(base, i-1, 0);\n\tprintf(\" :\\n\");\t\t/*PPC*/\n\tprint_array_perm(Si, Sil, n, 1);\t\t\t/*PPC*/\n#endif\t\t\t\t\t\t\t\t/*PPC*/\n\tcomplement(Si, Sil, T, mm, n, oldSi, &oldSil);\n#ifdef VERBOSE_SCHREIER\t\t\t\t\t\t/*PPC*/\n\tprintf(\"Previous stabilizer of %d points:\\n\", i-1);\t/*PPC*/\n\tprint_array_perm(oldSi, oldSil, n, 1);\t\t\t/*PPC*/\n#endif\t\t\t\t\t\t\t\t/*PPC*/\n\t/* Basic orbits */\n\tone_schreier_orbit(base[i-1], Si, Sil, n,\n\t                   Deltai, &Deltail, nu, w, 1);\n\tone_schreier_orbit(base[i-1], oldSi, oldSil, n,\n\t                   oldDeltai, &oldDeltail, oldnu, oldw, 1);\n\t/* Check that Deltai is an extension of oldDeltai */\n\tfor(c=0; c<n; c++) {\n\t\tif(w[c]!=oldw[c] && oldw[c]!=0) {\n#ifdef VERBOSE_SCHREIER\t\t\t\t\t\t/*PPC*/\n\t\t\tprintf(\"Deltai[%d] modified to match oldDeltai\\n\", c);  /*PPC*/\n#endif\t\t\t\t\t\t\t\t/*PPC*/\n\t\t\tcopy_list(oldnu+c*n, nu+c*n, n);\n\t\t\tw[c] = oldw[c];\n\t\t\t}\n\t\t}\n#ifdef VERBOSE_SCHREIER\t\t\t\t\t\t/*PPC*/\n\tprintf(\"Orbit: \");\n\tprint_list(Deltai, Deltail, 1);\t/*PPC*/\n#endif\t\t\t\t\t\t\t\t/*PPC*/\n\n\t/* Loop gn over elements gamma of basic orbit */\n\tfor(gn=0; gn<Deltail; gn++) {\n\n\t\tgamma = Deltai[gn];\n\n#ifdef VERBOSE_SCHREIER\t\t\t\t\t\t/*PPC*/\n\t\tprintf(\"  gamma=%d\\n\", gamma);\t\t\t\t/*PPC*/\n#endif\t\t\t\t\t\t\t\t/*PPC*/\n\t\t/* In both cases here we get gensetl<=m */\n\t\tif (position(gamma, oldDeltai, oldDeltail)) {\n\t\t\tcopy_list(T, genset, mm*n);\n\t\t\tgensetl=mm;\n\t\t\t}\n\t\telse {\n\t\t\tcopy_list(Si, genset, Sil*n);\n\t\t\tgensetl=Sil;\n\t\t\t}\n\n\t\t/* Loop sn over generators s in genset */\n\t\tfor (sn=0; sn<gensetl; sn++) {\n\n\t\t\tcopy_list(genset+sn*n, s, n);\n\t\t\t(*num)++;\n\n\t\t\t/* Compute Schreier generator */\n\t\t\ttrace_schreier(gamma, nu,w, p,n);\n\t\t\ttrace_schreier(onpoints(gamma,s,n), nu,w, pp,n);\n\t\t\tinverse(pp, ip, n);\n\t\t\tproduct(p, s, ppp, n);\n\t\t\tproduct(ppp, ip, g, n);\n#ifdef VERBOSE_SCHREIER\t\t\t\t\t\t/*PPC*/\n\t\t\tprintf(\"    g(%d)=\", *num);\n\t\t\tprint_perm(g, n, 1);\t/*PPC*/\n#endif\t\t\t\t\t\t\t\t/*PPC*/\n\n\t\t\t/* Compute stabilizer. Reallocate to maximum size */\n\t\t\tstab = (int*)realloc(stab, (*nm)*n*sizeof(int));\n\t\t\tstabilizer(newbase, i, *newGS, *nm, n, stab, &stabl);\n\t\t\t/* If g is not in subgroup H^(i) */\n\t\t\tif(!isid(g, n)) {\n\t\t\t\tif ((stabl==0)||(!perm_member(g, newbase+i,*nbl-i, stab,stabl, n))) {\n#ifdef VERBOSE_SCHREIER\t\t\t\t\t\t/*PPC*/\n\t\t\t\t\tprintf(\"      g not in H^(%d)\\n\", i);\t\t\t/*PPC*/\n#endif\t\t\t\t\t\t\t\t/*PPC*/\n\t\t\t\t\t/* Enlarge newGS. We need reallocation */\n\t\t\t\t\t*newGS = (int*)realloc(*newGS, ((*nm)+1)*n*sizeof(int));\n\t\t\t\t\tcopy_list(g, (*newGS)+(*nm)*n, n);\n\t\t\t\t\t(*nm)++;\n\t\t\t\t\t/* Extend newbase if needed, so that no strong\n\t\t\t\t\t* generator fixes all base points. */\n\t\t\t\t\tstable_points(g, n, stabps, &stabpsl);\n#ifdef VERBOSE_SCHREIER\t\t\t\t\t\t/*PPC*/\n\t\t\t\t\tprintf(\"      Stable under g: \"); \t\t\t/*PPC*/\n\t\t\t\t\tprint_list(stabps, stabpsl, 1);\t\t\t\t/*PPC*/\n#endif\t\t\t\t\t\t\t\t/*PPC*/\n\t\t\t\t\t/* If g moves a point of newbase then set j */\n\t\t\t\t\tfor(jj=0; jj<*nbl; jj++) {\n\t\t\t\t\t\tif(!position(newbase[jj], stabps, stabpsl)) {\n\t\t\t\t\t\t\tj = jj+1;\n#ifdef VERBOSE_SCHREIER\t\t\t\t\t\t/*PPC*/\n\t\t\t\t\t\t\tprintf(\"      g moves %d in newbase\\n\", newbase[jj]);\t/*PPC*/\n#endif\t\t\t\t\t\t\t\t/*PPC*/\n\t\t\t\t\t\t\tbreak;\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\t/* else choose a new point */\n\t\t\t\t\t\tj = *nbl+1;\n\t\t\t\t\t\t}\n\t\t\t\t\tif (j == *nbl+1) {\n\t\t\t\t\t\tfor(jj=1; jj<=n; jj++) {\n\t\t\t\t\t\t\tif(!position(jj, stabps, stabpsl) &&\n\t\t\t\t\t\t\t      !position(jj, newbase, *nbl)) {\n\t\t\t\t\t\t\t\tnewbase[*nbl]=jj;\n\t\t\t\t\t\t\t\t(*nbl)++;\n#ifdef VERBOSE_SCHREIER\t\t\t\t\t\t/*PPC*/\n\t\t\t\t\t\t\t\tprintf(\"      Point %d added to newbase\\n\", jj);\t/*PPC*/\n#endif\t\t\t\t\t\t\t\t/*PPC*/\n\t\t\t\t\t\t\t\tbreak;\n\t\t\t\t\t\t\t\t}\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\t}\n\t\t\t\t\t/* Ensure we still have a base and SGS for\n\t\t\t\t\t* H^(i+1) */\n\t\t\t\t\tfor(level=j; level>i; level--) {\n#ifdef VERBOSE_SCHREIER\t\t\t\t\t\t/*PPC*/\n\t\t\t\t\t\tprintf(\"\\nEnsuring H^(%d) at level %d\\n\", i+1, level);\t/*PPC*/\n#endif\t\t\t\t\t\t\t\t/*PPC*/\n\t\t\t\t\t\tschreier_sims_step(newbase,*nbl,*newGS,*nm, n,\n\t\t\t\t\t\t                   level, g, 1,\n\t\t\t\t\t\t                   newbase,nbl,newGS,nm,num);\n\t\t\t\t\t\t}\n#ifdef VERBOSE_SCHREIER\t\t\t\t\t\t/*PPC*/\n\t\t\t\t\tprintf(\"***** Finished check of H(%d) ******\\n\\n\", i+1);/*PPC*/\n#endif\t\t\t\t\t\t\t\t/*PPC*/\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t}\n\t\t}\n\n\t/* Free allocated memory */\n\tfree(p);\n\tfree(ip);\n\tfree(pp);\n\tfree(ppp);\n\tfree(Si);\n\tfree(oldSi);\n\tfree(Deltai);\n\tfree(w);\n\tfree(nu);\n\tfree(oldDeltai);\n\tfree(oldw);\n\tfree(oldnu);\n\tfree(genset);\n\tfree(s);\n\tfree(g);\n\tfree(stab);\n\tfree(stabps);\n\n\t}\n\n/**********************************************************************\n*\n* Notations and comments:\n*  - In xTensor, a permutation g corresponding to a given tensor\n*    configuration is understood as acting on index-numbers giving\n*    tensor-slot numbers. That is, p = i^g (which is p= onpoints(i, g))\n*    means that i is the index at slot p in the configuration g.\n*    Equivalently, i = p^ig, where ig is the inverse of g.\n*  - That convention is precisely the opposite to the one chosen by\n*    Renato. Everything here and in xPerm follow Renato's convention.\n*    There are two InversePerm actions in ToCanonicalOne in xTensor to\n*    perform the change of notation. Here canonical_perm also has two\n*    inverse  actions for backwards compatibility.\n*  - The base of a SGS for the group S represents an ordering of the\n*    slots of the tensor. Changing the base can be understood as a\n*    change of priorities for index canonicalization.\n*/\n\n/**********************************************************************/\n\n/* coset_rep. JMM, 30 June 2003\n*\n* This algorithm is encoded from Renato Portugal et al.\n*\n* This function gives a canonical representant of a n-permutation p\n* in the group described by a SGS (pair base,GS) and the result is\n* stored in cr. In other words, it gives the canonical representant\n* of the right coset S.p. The free slots are different at return time.\n*/\n\nvoid coset_rep(int *p, int n,\n               int *base, int bl, int *GS, int *m,\n               int *freeps, int fl,\n               int *cr)\n\t{\n\n#ifdef VERBOSE_COSET\t\t\t\t\t\t/*PPC*/\n\tprintf(\"***** RIGHT-COSET-REP ALGORITHM ****\\n\");\t/*PPC*/\n\tprintf(\"Permutation \");\n\tprint_perm(p, n, 1);\t\t/*PPC*/\n\tprintf(\"Base: \");\n\tprint_list(base, bl, 1);\t\t/*PPC*/\n#endif\t\t\t\t\t\t\t\t/*PPC*/\n\t/* Trivial case without symmetries */\n\tif (*m==0) {\n\t\tcopy_list(p, cr, n);\n\t\treturn;\n\t\t}\n\t/* else */\n\n\tint i, j, k, b, pp;\n\tint *deltap=       (int*)malloc(  n*sizeof(int)), deltapl;\n\tint *deltapsorted= (int*)malloc(  n*sizeof(int));\n\tint *om=           (int*)malloc(  n*sizeof(int));\n\tint *PERM=         (int*)malloc(  n*sizeof(int));\n\tint *perm2=        (int*)malloc(  n*sizeof(int));\n\tint *orbit=        (int*)malloc(  n*sizeof(int)), ol;\n\tint *orbit1=       (int*)malloc(  n*sizeof(int)), o1l;\n\tint *w=            (int*)malloc(  n*sizeof(int));\n\tint *nu=           (int*)malloc(n*n*sizeof(int));\n\tint *genset=       (int*)malloc(*m*n*sizeof(int)), gensetl;\n\tint *stab=         (int*)malloc(*m*n*sizeof(int)), mm;\n\n\t/* Copy p to PERM and GS to genset, to avoid side effects. */\n\tcopy_list(p, PERM, n);\n\tcopy_list(GS, genset, *m*n);\n\tgensetl=*m;\n\n\t/* Loop over elements of base */\n\tfor(i=0; i<bl; i++) {\n\t\tb = base[i]; /* Slot to analyze */\n\t\tone_schreier_orbit(b, genset, gensetl, n,\n\t\t                   orbit, &ol, nu, w, 1);\n#ifdef VERBOSE_COSET\t\t\t\t\t\t/*PPC*/\n\t\tprintf(\"\\nAnalyzing slot %d\\n\", b);\t\t\t/*PPC*/\n\t\tprintf(\"orbit: \");\n\t\tprint_list(orbit, ol, 1);\t\t/*PPC*/\n\t\tprintf(\"freeps: \");\n\t\tprint_list(freeps, fl, 1);\t\t/*PPC*/\n#endif\t\t\t\t\t\t\t\t/*PPC*/\n\t\tintersection(orbit, ol, freeps, fl, orbit1, &o1l);\n#ifdef VERBOSE_COSET\t\t\t\t\t\t/*PPC*/\n\t\tprintf(\"Free slots that can go to that slot: \");\t/*PPC*/\n\t\tprint_list(orbit1, o1l, 1);\t\t\t\t/*PPC*/\n#endif\t\t\t\t\t\t\t\t/*PPC*/\n\t\tif (o1l==0) continue; /* Slot with no symmetries */\n\t\t/* else */\n\t\tfor(j=0; j<o1l; j++) {\n\t\t\tdeltap[j] = onpoints(orbit1[j], PERM, n);\n\t\t\t}\n\t\tdeltapl=o1l;\n#ifdef VERBOSE_COSET\t\t\t\t\t\t/*PPC*/\n\t\tprintf(\"At those slots we resp. find indices deltap: \");/*PPC*/\n\t\tprint_list(deltap, deltapl, 1);\t\t\t/*PPC*/\n#endif\t\t\t\t\t\t\t\t/*PPC*/\n\t\tsortB(deltap, deltapsorted, deltapl, base, bl);\n\t\tk = position(deltapsorted[0], deltap, deltapl);\n#ifdef VERBOSE_COSET\t\t\t\t\t\t/*PPC*/\n\t\tprintf(\"Least index: %d, at position k: %d of deltap\\n\",/*PPC*/\n\t\t       deltap[k-1], k);\t\t\t/*PPC*/\n#endif\t\t\t\t\t\t\t\t/*PPC*/\n\t\tpp = orbit1[k-1];\n#ifdef VERBOSE_COSET\t\t\t\t\t\t/*PPC*/\n\t\tprintf(\"That index is at tensor slot pp: %d\\n\", pp);\t/*PPC*/\n#endif\t\t\t\t\t\t\t\t/*PPC*/\n\t\t/* Compute permutation om such that b^om = pp */\n\t\ttrace_schreier(pp, nu, w, om, n);\n#ifdef VERBOSE_COSET\t\t\t\t\t\t/*PPC*/\n\t\tprintf(\"We can move slot %d to slot %d with perm om:\",\t/*PPC*/\n\t\t       pp, b);\t\t\t\t\t/*PPC*/\n\t\tprint_perm(om, n, 0);\n\t\tprintf(\" in S\\n\");\t/*PPC*/\n#endif\t\t\t\t\t\t\t\t/*PPC*/\n\t\tproduct(om, PERM, perm2, n);\n#ifdef VERBOSE_COSET\t\t\t\t\t\t/*PPC*/\n\t\tprintf(\"New list of indices: \");\t\t\t/*PPC*/\n\t\tprint_perm(perm2, n, 1);\t\t\t/*PPC*/\n#endif\t\t\t\t\t\t\t\t/*PPC*/\n\t\tcopy_list(perm2, PERM, n);\n\t\t/* New positions of free indices */\n\t\tinverse(om, perm2, n);\n\t\tfor(j=0; j<fl; j++) {\n\t\t\tfreeps[j] = onpoints(freeps[j], perm2, n);\n\t\t\t}\n#ifdef VERBOSE_COSET\t\t\t\t\t\t/*PPC*/\n\t\tprintf(\"Removing those perms that move slot %d\\n\", b);\t/*PPC*/\n#endif\t\t\t\t\t\t\t\t/*PPC*/\n\t\t/* Note that we do not change base to have i as first\n\t\t\tmember of base. This is not general, but I think\n\t\there it is valid due to the nature of our problem */\n\t\tstabilizer(base+i, 1, genset, gensetl, n, stab, &mm);\n\t\tcopy_list(stab, genset, mm*n);\n\t\tgensetl=mm;\n\t\t}\n\t/* Move to result */\n\tcopy_list(PERM, cr, n);\n\t/* Return new SGS */\n\tcopy_list(genset, GS, gensetl*n);\n\t*m=gensetl;\n#ifdef VERBOSE_COSET\t\t\t\t\t\t/*PPC*/\n\tprintf(\"************ END OF ALGORITHM ***********\\n\");\t/*PPC*/\n#endif\t\t\t\t\t\t\t\t/*PPC*/\n\n\t/* Free allocated memory */\n\tfree(deltap);\n\tfree(deltapsorted);\n\tfree(om);\n\tfree(PERM);\n\tfree(perm2);\n\tfree(orbit);\n\tfree(orbit1);\n\tfree(w);\n\tfree(nu);\n\tfree(genset);\n\tfree(stab);\n\n\t}\n\n/**********************************************************************/\n\n/* SGSD. JMM, 26 June 2007\n*\n* We construct a number of functions that generate the strong\n* generating set for a given list of (multiple) dummysets (all pairs\n* of dummies of a vbundle) and repeatedsets (the positions of repeated\n* indices, like components or directions). The main function is SGSD,\n* but there are other elementary operations: SGSofdummyset,\n* SGSofrepeatedset, movedummyset, moverepeatedset.\n* We introduce another funny name here: drummy: either a dummy or a\n* repeated index.\n*/\n\n/* SGS for a dummyset. List dummies not modified */\nvoid SGSofdummyset(int *dummies, int dl, int sym, int n,\n                   int *KD, int *KDl, int *bD, int *bDl)\n\t{\n\n\tif (dl==0) {\n\t\t*KDl=0;\n\t\t*bDl=0;\n\t\treturn;\n\t\t} /* else */\n\n\t/* Number of pairs of dummies: dpl */\n\tint dpl = dl/2;\n\tint *range_perm = (int*)malloc(    n*sizeof(int));\n\tint *KD1 =        (int*)malloc(dpl*n*sizeof(int));\n\tint *KD2 =        (int*)malloc(dpl*n*sizeof(int));\n\tint i;\n\n\trange(range_perm, n);\n\t/* KD1: exchange indices. Ex: Cycles[{1,3},{2,4}]\n\t     There are always dpl-1 permutations */\n\tfor (i=0; i<dpl-1; i++) {\n\t\t/* Copy the identity */\n\t\tcopy_list(range_perm, KD1+i*n, n);\n\t\t/* Swap elements of consecutive pairs */\n\t\tKD1[ i*n+dummies[2*i  ]-1 ] = dummies[2*i+2];\n\t\tKD1[ i*n+dummies[2*i+2]-1 ] = dummies[2*i  ];\n\t\tKD1[ i*n+dummies[2*i+1]-1 ] = dummies[2*i+3];\n\t\tKD1[ i*n+dummies[2*i+3]-1 ] = dummies[2*i+1];\n\t\t}\n\t/* KD2: exchange indices of the same pair.\n\t     If sym!=0 there are dpl permutations */\n\tif (sym == 1) { /* Symmetric metric */\n\t\tfor (i=0; i<dpl; i++) {\n\t\t\t/* Copy the identity */\n\t\t\tcopy_list(range_perm, KD2+i*n, n);\n\t\t\t/* Swap elements of pair */\n\t\t\tKD2[i*n+dummies[2*i]-1] = dummies[2*i+1];\n\t\t\tKD2[i*n+dummies[2*i+1]-1] = dummies[2*i];\n\t\t\t/* Keep positive sign */\n\t\t\t}\n\t\t*KDl = 2*dpl-1;\n\t\t}\n\telse if (sym == -1) {\n\t\tfor (i=0; i<dpl; i++) {\n\t\t\t/* Copy the identity */\n\t\t\tcopy_list(range_perm, KD2+i*n, n);\n\t\t\t/* Swap elements of pair */\n\t\t\tKD2[i*n+dummies[2*i]-1] = dummies[2*i+1];\n\t\t\tKD2[i*n+dummies[2*i+1]-1] = dummies[2*i];\n\t\t\t/* Set negative sign */\n\t\t\tKD2[i*n+n-2] = n;\n\t\t\tKD2[i*n+n-1] = n-1;\n\t\t\t}\n\t\t*KDl = 2*dpl-1;\n\t\t}\n\telse if (sym == 0) {\n\t\t/* Do nothing */\n\t\t*KDl = dpl-1;\n\t\t}\n\telse {\n\t\t/* Unknown value of sym */\n\t\t}\n\t/* KD */\n\tcopy_list(KD1, KD, (dpl-1)*n);\n\tif (sym!=0) copy_list(KD2, KD+(dpl-1)*n, dpl*n);\n\t/* base of group D */\n\tfor (i=0; i<dpl; i++) {\n\t\tbD[i] = dummies[2*i];\n\t\t}\n\t*bDl=dpl;\n#ifdef VERBOSE_DOUBLE\t\t\t\t\t\t/*PPC*/\n\tprintf(\"KD: \");\n\tprint_array_perm(KD, *KDl, n, 1);\t/*PPC*/\n\tprintf(\"bD: \");\n\tprint_list(bD, *bDl, 1);\t\t/*PPC*/\n#endif\t\t\t\t\t\t\t\t/*PPC*/\n\tfree(range_perm);\n\tfree(KD1);\n\tfree(KD2);\n\t}\n\n/* SGS for a repeatedset. List repes not modified */\nvoid SGSofrepeatedset(int *repes, int rl, int n,\n                      int *KD, int *KDl, int *bD, int *bDl)\n\t{\n\n#ifdef VERBOSE_DOUBLE\t\t\t\t\t\t/*PPC*/\n\tprintf(\"From SGSofrepeatedset:\\n\");\t\t\t/*PPC*/\n\tprintf(\"repes: \");\n\tprint_list(repes, rl, 1);\n#endif\t\t\t\t\t\t\t\t/*PPC*/\n\tif (rl==0) {\n\t\t*KDl=0;\n\t\t*bDl=0;\n\t\treturn;\n\t\t} /* else */\n\n\tint *range_perm = (int*)malloc(    n*sizeof(int));\n\tint i;\n\n\trange(range_perm, n);\n\tfor (i=0; i<rl-1; i++) {\n\t\t/* Copy the identity */\n\t\tcopy_list(range_perm, KD+i*n, n);\n\t\t/* Swap elements of pair */\n\t\tKD[i*n+repes[i]-1] = repes[i+1];\n\t\tKD[i*n+repes[i+1]-1] = repes[i];\n\t\t/* Keep positive sign */\n\t\t}\n\t*KDl = rl-1;\n\tcopy_list(repes, bD, rl-1);\n\t*bDl = rl-1;\n#ifdef VERBOSE_DOUBLE\t\t\t\t\t\t/*PPC*/\n\tprintf(\"KD: \");\n\tprint_array_perm(KD, *KDl, n, 1);\t/*PPC*/\n\tprintf(\"bD: \");\n\tprint_list(bD, *bDl, 1);\t\t/*PPC*/\n#endif\t\t\t\t\t\t\t\t/*PPC*/\n\tfree(range_perm);\n\t}\n\n/* Move index in a dummyset. List dummies reordered */\nvoid movedummyset(int firstd, int *dummies, int dl, int)\n\t{\n\n\t/* Find position of dummy and relative\n\t\tposition of its pair */\n#ifdef VERBOSE_DOUBLE\t\t\t\t\t\t/*PPC*/\n\tprintf(\"Rearrange dummies for %d. dummies: \", firstd);\t/*PPC*/\n\tprint_list(dummies, dl, 1);\t\t\t\t/*PPC*/\n#endif\t\t\t\t\t\t\t\t/*PPC*/\n\tint pos, j;\n\tpos = position(firstd, dummies, dl)-1;\n\tif (pos==-1) { /* firstd not in dummies */\n\t\t/* Do nothing */\n\t\t}\n\telse {\n\t\tint tmp;\n\t\t/* Swap all pairs if firstd found as second */\n\t\tif (pos%2==0) {\n\t\t\t/* 1st member: Do nothing */\n\t\t\t}\n\t\telse {\n\t\t\tpos=pos-1;\n\t\t\t/* 2nd member: Swap all pairs */\n\t\t\tfor (j=0; j<dl/2; j++) {\n\t\t\t\ttmp= dummies[2*j];\n\t\t\t\tdummies[2*j]=dummies[2*j+1];\n\t\t\t\tdummies[2*j+1]=tmp;\n\t\t\t\t}\n\t\t\t}\n\t\t/* Exchange position of pair with first pair */\n\t\tif (pos==0) {\n\t\t\t/* 1st pair: Do nothing */\n\t\t\t}\n\t\telse {\n\t\t\t/* Exchange two pairs of dummies */\n\t\t\ttmp=dummies[0];\n\t\t\tdummies[0]=firstd;\n\t\t\tdummies[pos]=tmp;\n\t\t\ttmp=dummies[1];\n\t\t\tdummies[1]=dummies[pos+1];\n\t\t\tdummies[pos+1]=tmp;\n\t\t\t}\n\t\t}\n#ifdef VERBOSE_DOUBLE\t\t\t\t\t\t/*PPC*/\n\tprintf(\"Now dummies: \");                        \t/*PPC*/\n\tprint_list(dummies, dl, 1);\t\t\t\t/*PPC*/\n#endif\t\t\t\t\t\t\t\t/*PPC*/\n\t}\n\n/* Move index in a repeated set. List repes reordered */\nvoid moverepeatedset(int firstd, int *repes, int rl)\n\t{\n\n\t/* Find position of dummy and relative\n\t\tposition of its pair */\n#ifdef VERBOSE_DOUBLE\t\t\t\t\t\t/*PPC*/\n\tprintf(\"Rearrange dummies for %d. repes: \", firstd);\t/*PPC*/\n\tprint_list(repes, rl, 1);\t\t\t\t/*PPC*/\n#endif\t\t\t\t\t\t\t\t/*PPC*/\n\tint pos;\n\tpos = position(firstd, repes, rl)-1;\n\tif (pos==-1) { /* firstd not in repes */\n\t\t/* Do nothing */\n\t\t}\n\telse {\n\t\tif (pos==0) {\n\t\t\t/* 1st index: Do nothing */\n\t\t\t}\n\t\telse {\n\t\t\t/* Exchange two positions */\n\t\t\trepes[pos] = repes[0];\n\t\t\trepes[0] = firstd;\n\t\t\t}\n\t\t}\n#ifdef VERBOSE_DOUBLE\t\t\t\t\t\t/*PPC*/\n\tprintf(\"Now repes: \");\t                        \t/*PPC*/\n\tprint_list(repes, rl, 1);\t\t\t\t/*PPC*/\n#endif\t\t\t\t\t\t\t\t/*PPC*/\n\t}\n\n/* Remove a first-pair from dummies */\nvoid dropdummyset(int firstd,\n                  int *vds, int vdsl, int *dummies, int *dl)\n\t{\n\n\tint i, j, itotal=0;\n\n\tfor (i=0; i<vdsl; i++) {\n\t\tif (dummies[itotal]==firstd && vds[i]!=0) {\n\t\t\tfor (j=itotal; j<*dl-2; j++) {\n\t\t\t\tdummies[j] = dummies[j+2];\n\t\t\t\t}\n\t\t\tvds[i] = vds[i]-2;\n\t\t\t*dl = *dl - 2;\n\t\t\treturn;\n\t\t\t}\n\t\titotal = itotal + vds[i];\n\t\t}\n\t}\n\n/* Remove a first-point from repes */\nvoid droprepeatedset(int firstd,\n                     int *vrs, int vrsl, int *repes, int *rl)\n\t{\n\n\tint i, j, itotal=0;\n\n\tfor (i=0; i<vrsl; i++) {\n\t\tif (repes[itotal]==firstd && vrs[i]!=0) {\n\t\t\tfor (j=itotal; j<*rl; j++) {\n\t\t\t\trepes[j] = repes[j+1];\n\t\t\t\t}\n\t\t\tvrs[i] = vrs[i]-1;\n\t\t\t*rl = *rl - 1;\n\t\t\treturn;\n\t\t\t}\n\t\titotal = itotal + vrs[i];\n\t\t}\n\t}\n\n/* SGSD for a given list of dummies and repes */\nvoid SGSD(int *vds, int vdsl, int *dummies, int dl, int *mQ,\n          int *vrs, int vrsl, int *repes, int rl, int n,\n          int firstd, int *KD, int *KDl, int *bD, int *bDl)\n\t{\n\n\tif (dl==0 && rl==0) {\n\t\t*KDl=0;\n\t\t*bDl=0;\n\t\treturn;\n\t\t} /* else */\n\n\tint *tmp, tmpl;\n\tint *tmpGS   = (int*)malloc(n*n*sizeof(int)), tmpGSl;\n\tint *tmpbase = (int*)malloc(  n*sizeof(int)), tmpbasel;\n\tint i, itotal;\n\n\t/* Loop over all dummysets */\n\titotal = 0;\n\t*KDl = 0;\n\t*bDl = 0;\n\tfor (i=0; i<vdsl; i++) {\n\t\ttmpl = vds[i];\n\t\ttmp = dummies + itotal;\n\t\tmovedummyset(firstd, tmp, tmpl, mQ[i]);\n\t\titotal = itotal + tmpl;\n\t\tSGSofdummyset(tmp, tmpl, mQ[i], n,\n\t\t              tmpGS, &tmpGSl, tmpbase, &tmpbasel);\n\t\tcopy_list(tmpGS, KD+(*KDl)*n, tmpGSl*n);\n\t\t*KDl = *KDl + tmpGSl;\n\t\tcopy_list(tmpbase, bD+ *bDl, tmpbasel);\n\t\t*bDl = *bDl + tmpbasel;\n\t\t}\n\n\t/* Loop over all repeatedsets */\n\titotal=0;\n\tfor (i=0; i<vrsl; i++) {\n\t\ttmpl = vrs[i];\n\t\ttmp = repes + itotal;\n\t\tmoverepeatedset(firstd, tmp, tmpl);\n\t\titotal = itotal + tmpl;\n\t\tSGSofrepeatedset(tmp, tmpl, n,\n\t\t                 tmpGS, &tmpGSl, tmpbase, &tmpbasel);\n\t\tcopy_list(tmpGS, KD+(*KDl)*n, tmpGSl*n);\n\t\t*KDl = *KDl + tmpGSl;\n\t\tcopy_list(tmpbase, bD+ *bDl, tmpbasel);\n\t\t*bDl = *bDl + tmpbasel;\n\t\t}\n\n\tfree(tmpGS);\n\tfree(tmpbase);\n\n#ifdef VERBOSE_DOUBLE\n\tprintf(\"base of D:\");\n\tprint_list(bD, *bDl, 1);\t\t/*PPC*/\n\tprintf(\"GS of D (%d perms of degree %d):\", *KDl, n);\t/*PPC*/\n\tprint_array_perm(KD, *KDl, n, 1);\t\t\t/*PPC*/\n#endif\t\t\t\t\t\t\t\t/*PPC*/\n\t}\n\n/**********************************************************************/\n\n/* double_coset_rep. JMM, 1-5 July 2003.\n* JMM, 9 November 2005. Corrected treatment of SGS of group D.\n* JMM, 26 June 2007. Large extension to consider several dummysets and\n*      several repeatedsets.\n*\n* This algorithm is encoded from Renato Portugal et al, with the\n* extensions to repeatedsets.\n*\n* This function gives a canonical representant for the n-permutation g\n* in the double coset S.g.D given by the groups S, described by a SGS\n* (pair base, GS) and the group D, described by the direct product of\n* the pair symmetric dpl pairs of dummies and the S_k groups of k\n* repeated indices. Each dummyset has a metric_symmetry sign: if mQ=1\n* the metric is symmetric. If mQ=-1 the metric is antisymmetric\n* (spinor calculus). If mQ=0 there is no metric.\n* Note that n = dl + dr. The result is stored in dcr.\n*/\n\nclass alphastruct {\n\tpublic:\n\t\talphastruct();\n\t\talphastruct(const alphastruct&);\n\t\t~alphastruct();\n\n\t\tvoid init(int n);\n\n\t\tint *L; \t/* We assume that elements of L cannot\n\t\t\t\t\t\tbe repeated. I only have experimental\n\t\t\t\t\t\t\tevidence for this */\n\t\tint Ll;\n\t\tint *s;\n\t\tint *d;\n\t\tint *o;\n\n\t\tint nn;\n\t};\n\nalphastruct::alphastruct()\n\t: L(0), Ll(0), s(0), d(0), o(0), nn(0)\n\t{\n\t}\n\nalphastruct::alphastruct(const alphastruct& other)\n\t{\n\tinit(other.nn);\n\tfor(int i=0; i<nn; ++i) {\n\t\tL[i]=other.L[i];\n\t\ts[i]=other.s[i];\n\t\td[i]=other.d[i];\n\t\to[i]=other.o[i];\n\t\t}\n\tLl=other.Ll;\n\t}\n\n\nvoid alphastruct::init(int n)\n\t{\n\tL = new int[n];\n\ts = new int[n];\n\td = new int[n];\n\to = new int[n];\n\tnn=n;\n\t}\n\nalphastruct::~alphastruct()\n\t{\n\tif(L) delete [] L;\n\tif(s) delete [] s;\n\tif(d) delete [] d;\n\tif(o) delete [] o;\n\tnn=0;\n\t}\n\n\nvoid TAB(std::vector<alphastruct>& ALPHA, int *L, int Ll, int *s1, int *d1, int n)\n\t{\n\tint i;\n\tint l=0;\n\n\t/* Search ALPHA for the l corresponding to L */\n\t//\tstd::cout << ALPHA.size() << \", \" << Ll << std::endl;\n\tfor (i=0; i<Ll; i++) l=ALPHA[l].o[L[i]-1];\n\t/* Copy permutations of element l */\n\tcopy_list(ALPHA[l].s, s1, n);\n\tcopy_list(ALPHA[l].d, d1, n);\n\t}\n\nvoid F1(std::vector<alphastruct>& ALPHA, int *L, int Ll, int *g, int *list, int *listl, int n, int Deltabl, int *Deltab, int *DeltaD)\n\t{\n\tint c, c1, c2;\n\tint *sgd=  (int*)malloc(n*sizeof(int));\n\tint *TAB1= (int*)malloc(n*sizeof(int));\n\tint *TAB2= (int*)malloc(n*sizeof(int));\n\tint *tmp=  (int*)malloc(n*sizeof(int));\n\n\tTAB(ALPHA, L, Ll, TAB1, TAB2, n);\n\n\t/* Compute s.g.d */\n\tF2(TAB1, g, TAB2, sgd, n);\n#ifdef VERBOSE_DOUBLE\t\t\t\t\t\t/*PPC*/\n\tprintf(\"With L=\");\n\tprint_list(L, Ll, 0);\t\t/*PPC*/\n\tprintf(\" we get sgd: \");\n\tprint_perm(sgd, n, 1);\t\t/*PPC*/\n#endif\t\t\t\t\t\t\t\t/*PPC*/\n\t/* Images of Deltab under sgd. Note that tmp has length\n\tDeltabl */\n\tfor (c=0; c<Deltabl; c++)\n\t\ttmp[c] = onpoints(Deltab[c], sgd, n);\n#ifdef VERBOSE_DOUBLE\t\t\t\t\t\t/*PPC*/\n\tprintf(\" which maps slots in Deltab to indices list: \");/*PPC*/\n\tprint_list(tmp, Deltabl, 1);\t\t\t/*PPC*/\n#endif\t\t\t\t\t\t\t\t/*PPC*/\n\t/* Orbits of DeltaD containing the points in tmp */\n\tint oi;\n\tfor (c1=0; c1<Deltabl; c1++) {\n\t\toi = DeltaD[tmp[c1]-1];\n\t\tif(oi) {\n\t\t\tfor(c2=0; c2<n; c2++) {\n\t\t\t\tif ((DeltaD[c2]==oi) &&\n\t\t\t\t      (!position(c2+1, list, *listl)))\n\t\t\t\t\tlist[(*listl)++] = c2+1;\n\t\t\t\t}\n\t\t\t}\n\t\t}\n#ifdef VERBOSE_DOUBLE\t\t\t\t\t\t/*PPC*/\n\tprintf(\" whose points belong to orbits \");\t\t/*PPC*/\n\tprint_list(list, *listl, 1);\t\t\t\t/*PPC*/\n#endif\t\t\t\t\t\t\t\t/*PPC*/\n\tfree(sgd);\n\tfree(TAB1);\n\tfree(TAB2);\n\tfree(tmp);\n\t}\n\n\n/* Consistency check */\nint consistency(int *array, int m, int n)\n\t{\n\tint *arrayp= (int*)malloc(m*n*sizeof(int)), arraypl;\n\tint *arrayn= (int*)malloc(m*n*sizeof(int)), arraynl;\n\tint i, ip, in, ret;\n\n#ifdef VERBOSE_DOUBLE\t\t\t\t\t\t/*PPC*/\n\tprintf(\"Checking consistency in m:%d, n:%d\\n\", m, n);\t/*PPC*/\n\tprint_array_perm(array, m, n, 1);\t\t\t/*PPC*/\n#endif\t\t\t\t\t\t\t\t/*PPC*/\n\n\t/* Detect sign of permutation */\n\tarraypl=0;\n\tarraynl=0;\n\tfor(i=0; i<m; i++) {\n\t\tif (array[i*n+n-2]<array[i*n+n-1]) /* Positive */\n\t\t\tcopy_list(array+i*n, arrayp+(arraypl++)*n, n);\n\t\telse                               /* Negative */\n\t\t\tcopy_list(array+i*n, arrayn+(arraynl++)*n, n);\n\t\t}\n#ifdef VERBOSE_DOUBLE\t\t\t\t\t\t/*PPC*/\n\tprintf(\"Found positive perms: %d\\n\", arraypl);\t\t/*PPC*/\n\tprintf(\"Found negative perms: %d\\n\", arraynl);\t\t/*PPC*/\n#endif\t\t\t\t\t\t\t\t/*PPC*/\n\t/* Here there are arraynl*arraypl comparisons. This\n\t\tshould be improved with a better intersection\n\talgorithm which sorts the lists in advance */\n\tret = 1; /* True */\n\tfor (in=0; in<arraynl; in++) {\n\t\tfor (ip=0; ip<arraypl; ip++) {\n\t\t\tif (equal_list(arrayp+ip*n, arrayn+in*n, n-2)) {\n\t\t\t\tret = 0; /* False */\n\t\t\t\tbreak;\n\t\t\t\t}\n\t\t\t}\n\t\t}\n#ifdef VERBOSE_DOUBLE\t\t\t\t\t\t/*PPC*/\n\tif (ret) printf(\"Found no problem in check\\n\");\t\t/*PPC*/\n\telse printf(\"Found perm with two signs.\\n\");\t\t/*PPC*/\n#endif\t\t\t\t\t\t\t\t/*PPC*/\n\tfree(arrayp);\n\tfree(arrayn);\n\treturn(ret);\n\t}\n\n\nvoid double_coset_rep(int *g, int n, int *base, int bl, int *GS, int m,\n                      int *vds, int vdsl, int *dummies, int dl, int *mQ,\n                      int *vrs, int vrsl, int *repes, int rl, int *dcr)\n\t{\n\n\tint i, j, l, jj, kk, c;         /* Counters */\n\tint result;\n\t/* Inverse of permutation g */\n\tint *ig=            (int*)malloc(  n*sizeof(int));\n\t/* All drummies, both the pair-dummies and the repes */\n\tint *drummies=      (int*)malloc(  n*sizeof(int)), dril;\n\t/* The initial slots of all those dummies */\n\tint *drummyslots=   (int*)malloc(  n*sizeof(int));\n\t/* Temporary space for sorting */\n\tint *drummytmp=     (int*)malloc(  n*sizeof(int)), drummytmpl;\n\tint *drummytmp2=    (int*)malloc(  n*sizeof(int));\n\t/* Bases for group S */\n\tint *bS=            (int*)malloc(  n*sizeof(int)), bSl;\n\tint *bSsort=        (int*)malloc(  n*sizeof(int));\n\t/* gs for group S. It cannot be larger than GS */\n\tint *KS=            (int*)malloc(m*n*sizeof(int)), KSl;\n\t/* gs for group D. The number dl+dr is an upper bound */\n\tint *KD=            (int*)malloc(n*n*sizeof(int)), KDl;\n\tint *bD=            (int*)malloc(  n*sizeof(int)), bDl;\n\tint *nu=            (int*)malloc(n*n*sizeof(int));\n\tint *w=             (int*)malloc(  n*sizeof(int));\n\tint *Deltab=        (int*)malloc(  n*sizeof(int)), Deltabl;\n\tint *DeltaD=        (int*)malloc(  n*sizeof(int));\n\tint *IMAGES=        (int*)malloc(  n*sizeof(int)), IMAGESl;\n\tint *IMAGESsorted=  (int*)malloc(  n*sizeof(int));\n\tint *p=             (int*)malloc(  n*sizeof(int));\n\tint *nuD=           (int*)malloc(n*n*sizeof(int));\n\tint *wD=            (int*)malloc(  n*sizeof(int));\n\tint *Deltap=        (int*)malloc(  n*sizeof(int)), Deltapl;\n\tint *NEXT=          (int*)malloc(  n*sizeof(int)), NEXTl;\n\tint *L=             (int*)malloc(  n*sizeof(int)), Ll;\n\tint *L1=            (int*)malloc(  n*sizeof(int)), L1l;\n\tint *s=             (int*)malloc(  n*sizeof(int));\n\tint *d=             (int*)malloc(  n*sizeof(int));\n\tint *list1=         (int*)malloc(  n*sizeof(int)), list1l;\n\tint *list2=         (int*)malloc(  n*sizeof(int)), list2l;\n\tint *perm1=         (int*)malloc(  n*sizeof(int));\n\tint *perm2=         (int*)malloc(  n*sizeof(int));\n\tint *perm3=         (int*)malloc(  n*sizeof(int));\n\tint *s1=            (int*)malloc(  n*sizeof(int));\n\tint *d1=            (int*)malloc(  n*sizeof(int));\n\n\n\t/* We use Renato's notation, with g mapping slots to indices */\n\n\t/**************************************************************\n\t*                       DEFINITIONS\n\t**************************************************************/\n\n\t/* Given a list L={i1, ..., il} the function TAB must return\n\ta pair (s1, d1) corresponding to L. The whole collection of\n\t\tlists L and their pairs is stored in the array ALPHA of\n\t\tstructures alphastruct. Each L in ALPHA is actually\n\tidentified by its position l in the array. The structure\n\tfor a given L contains a list of values of l corresponding\n\tto the n possible extensions of L.\n\t*/\n\n\t/* Define ALPHA and TAB */\n\n\tint ALPHAl;\n\tint *ALPHAstep= (int*)malloc(n*sizeof(int));\n\n\t/* Initialize ALPHA to {} and TAB to {id, id} */\n\tALPHAl= 1;\n\tstd::vector<alphastruct> ALPHA(1);\n\t//\talphastruct *ALPHA= new alphastruct[1]; //(struct alphastruct*)malloc(sizeof(struct alphastruct));\n\tALPHA[0].init(n);\n\tALPHA[0].Ll=0;\n\tLl=0; // ?\n\trange(ALPHA[0].s, n);\n\trange(ALPHA[0].d, n);\n\tALPHAstep[0]=0;\n\tALPHAstep[1]=1;\n\n\n\t/**************************************************************\n\t*               CONSTRUCTION OF BASES\n\t**************************************************************/\n\n\t/* Join all drummies */\n\tcopy_list(dummies, drummies, dl);\n\tcopy_list(repes, drummies+dl, rl);\n\tdril = dl + rl;\n\n\t/* Slots of all those drummies */\n\tinverse(g, ig, n);\n\tfor (i=0; i<dril; i++) {\n\t\tdrummyslots[i] = onpoints(drummies[i], ig, n);\n\t\t}\n\n\t/* Initialize KS */\n\tcopy_list(GS, KS, m*n);\n\tKSl=m;\n\n\t/* Extend base to bS to cover all positions of drummies.\n\t* We assume that in the intersection we get bS=base really.\n\t* We sort the missing drummies, but not the given base  */\n\tintersection(base, bl, drummyslots, dril, bS, &bSl);\n\tcomplement(drummyslots,dril, base,bl, 1, drummytmp,&drummytmpl);\n\tsort(drummytmp, drummytmp2, drummytmpl);\n\tcopy_list(drummytmp2, bS+bSl, drummytmpl);\n\tbSl = bSl + drummytmpl;\n#ifdef VERBOSE_DOUBLE\t\t\t\t\t\t/*PPC*/\n\tprintf(\"All drummies: drummies: \");\t\t\t/*PPC*/\n\tprint_list(drummies, dril, 1);\t\t\t\t/*PPC*/\n\tprintf(\"Their slots: drummyslots: \");\t\t\t/*PPC*/\n\tprint_list(drummyslots, dril, 1);\t\t\t/*PPC*/\n\tprintf(\"base: \");\t\t\t\t\t/*PPC*/\n\tprint_list(base, bl, 1);\t\t\t\t/*PPC*/\n\tprintf(\"Complement: drummytmp: \");\t\t\t/*PPC*/\n\tprint_list(drummytmp, drummytmpl, 1);\t\t\t/*PPC*/\n\tprintf(\"Sort them: drummytmp2: \");\t\t\t/*PPC*/\n\tprint_list(drummytmp2, drummytmpl, 1);\t\t\t/*PPC*/\n\tprintf(\"base extended to bS: \");\t\t\t/*PPC*/\n\tprint_list(bS, bSl, 1);\t\t\t\t\t/*PPC*/\n#endif\t\t\t\t\t\t\t\t/*PPC*/\n\t/* Generate associated base for sorting names of dummies */\n\t/* We choose a particular form of bSsort for aesthetics */\n\tsort(drummies,drummytmp2,dril);\n\tsort(bS, drummytmp, bSl);\n\tfor (i=0; i<bSl; i++) {\n\t\tbSsort[i]=drummytmp2[position(bS[i],drummytmp,bSl)-1];\n\t\t}\n\n#ifdef VERBOSE_DOUBLE\t\t\t\t\t\t/*PPC*/\n\tprintf(\"drummies: \");\t\t\t\t\t/*PPC*/\n\tprint_list(drummies, dril, 1);\t\t\t\t/*PPC*/\n\tprintf(\"Base of SGSS: bS: \");\t\t\t\t/*PPC*/\n\tprint_list(bS, bSl, 1);\t\t\t\t\t/*PPC*/\n\tprintf(\"Sorted slots: \");\t\t\t\t/*PPC*/\n\tprint_list(drummytmp2, bSl, 1);\t\t\t\t/*PPC*/\n\tprintf(\"Sorted base bS: \");\t\t\t\t/*PPC*/\n\tprint_list(drummytmp, bSl, 1);\t\t\t\t/*PPC*/\n\tprintf(\"Base for sorting: bSsort: \");\t\t\t/*PPC*/\n\tprint_list(bSsort, bSl, 1);\t\t\t\t/*PPC*/\n#endif\t\t\t\t\t\t\t\t/*PPC*/\n\n\n\t/*******************/\n\t/**** Main loop ****/\n\t/*******************/\n\n\t/* Note we use i=1..bSl instead of the usual i=0 ..(bSl-1) */\n\tfor (i=1; i<=bSl; i++) {\n\t\tint b=bS[i-1];\n\n#ifdef VERBOSE_DOUBLE\t\t\t\t\t\t/*PPC*/\n\t\tprintf(\"\\n************** Loop i=%d *************\\n\", i);/*PPC*/\n\t\tprintf(\"Analyzing slot bS[%d]=%d of tensor\\n\", i-1, b);\t/*PPC*/\n#endif\t\t\t\t\t\t\t\t/*PPC*/\n\t\t/* Schreier vector of S */\n\t\tschreier_vector(b, KS, KSl, n, nu, w);\n\t\tone_orbit(b, KS, KSl, n, Deltab, &Deltabl);\n#ifdef VERBOSE_DOUBLE\t\t\t\t\t\t/*PPC*/\n\t\tprintf(\"Under S, slot %d go to slots Deltab: \",b);\t/*PPC*/\n\t\tprint_list(Deltab, Deltabl, 1);\t\t\t\t/*PPC*/\n#endif\t\t\t\t\t\t\t\t/*PPC*/\n\t\t/* Compute SGS for group D. Do not rearrange drummies */\n\t\tSGSD(vds, vdsl, dummies, dl, mQ,\n\t\t     vrs, vrsl, repes, rl, n,\n\t\t     0, KD, &KDl, bD, &bDl);\n\t\t/* Orbits of D */\n\t\tall_orbits(KD, KDl, n, DeltaD);\n#ifdef VERBOSE_DOUBLE\t\t\t\t\t\t/*PPC*/\n\t\tprintf(\"Orbits of indices: DeltaD: \");\t\t\t/*PPC*/\n\t\tprint_list(DeltaD, n, 1);\t\t\t\t/*PPC*/\n#endif\t\t\t\t\t\t\t\t/*PPC*/\n\t\t/* Images of b under elements of S.g.D.\n\t\tDeltab and DeltaD are used by F1 */\n\t\tIMAGESl=0;\n\t\tfor (c=ALPHAstep[i-1]; c<ALPHAstep[i]; c++)\n\t\t\tF1(ALPHA, ALPHA[c].L, ALPHA[c].Ll, g, IMAGES, &IMAGESl, n, Deltabl, Deltab, DeltaD);\n#ifdef VERBOSE_DOUBLE\t\t\t\t\t\t/*PPC*/\n\t\tprintf(\"At slot %d we can have indices IMAGES: \", b);\t/*PPC*/\n\t\tprint_list(IMAGES, IMAGESl, 1);\t\t\t\t/*PPC*/\n\t\tprintf(\"IMAGESl: %d\\n\", IMAGESl);\t\t\t/*PPC*/\n#endif\t\t\t\t\t\t\t\t/*PPC*/\n\t\t/* If there are no images we have finished */\n\t\tif(IMAGESl==0) continue;\n\n\t\t/* Find minimum index */\n\t\tsortB(IMAGES, IMAGESsorted, IMAGESl, bSsort, bSl);\n\t\tp[i-1] = IMAGESsorted[0];\n#ifdef VERBOSE_DOUBLE\t\t\t\t\t\t/*PPC*/\n\t\tprintf(\"The least of them is p[i-1]=%d\\n\", p[i-1]);\t/*PPC*/\n#endif\t\t\t\t\t\t\t\t/*PPC*/\n\t\t/* Recompute SGS of D */\n\t\tif (dl>0 || rl>0) {\n\t\t\tSGSD(vds, vdsl, dummies, dl, mQ,\n\t\t\t     vrs, vrsl, repes, rl, n,\n\t\t\t     p[i-1], KD, &KDl, bD, &bDl);\n\t\t\t}\n\t\telse {   /* Do nothing */\n#ifdef VERBOSE_DOUBLE\t\t\t\t\t\t/*PPC*/\n\t\t\tprintf(\"Rearrangement of base of D not required.\\n\");\t/*PPC*/\n#endif\t\t\t\t\t\t\t\t/*PPC*/\n\t\t\t}\n\t\t/* Schreier vector of D */\n\t\tschreier_vector(p[i-1], KD, KDl, n, nuD, wD);\n\t\t/* Orbit of p[i-1] under D */\n\t\tone_orbit(p[i-1], KD, KDl, n, Deltap, &Deltapl);\n#ifdef VERBOSE_DOUBLE\t\t\t\t\t\t/*PPC*/\n\t\tprintf(\"The orbit of index %d is Deltap: \", p[i-1]);\t/*PPC*/\n\t\tprint_list(Deltap, Deltapl, 1);\t\t\t\t/*PPC*/\n\t\tprintf(\"Looking for digs moving index %d to slot %d\\n\",\t/*PPC*/\n\t\t       p[i-1], b);\t\t\t\t\t/*PPC*/\n#endif\t\t\t\t\t\t\t\t/*PPC*/\n\t\t/* Calculate ALPHA and TAB */\n\t\tALPHAstep[i+1]=ALPHAstep[i];\n\t\tfor(l=ALPHAstep[i-1]; l<ALPHAstep[i]; l++) {\n#ifdef VERBOSE_DOUBLE\t\t\t\t\t\t/*PPC*/\n\t\t\tprintf(\"Loop with l=%d\\n\", l);\t\t\t\t/*PPC*/\n#endif\t\t\t\t\t\t\t\t/*PPC*/\n\t\t\tLl=ALPHA[l].Ll;\n\t\t\tcopy_list(ALPHA[l].L, L, Ll);\n#ifdef VERBOSE_DOUBLE\t\t\t\t\t\t/*PPC*/\n\t\t\tprintf(\"L: \");\n\t\t\tprint_list(L, Ll, 1);\t\t\t/*PPC*/\n#endif\t\t\t\t\t\t\t\t/*PPC*/\n\t\t\tcopy_list(ALPHA[l].s, s, n);\n\t\t\tcopy_list(ALPHA[l].d, d, n);\n#ifdef VERBOSE_DOUBLE\t\t\t\t\t\t/*PPC*/\n\t\t\tprintf(\"TAB[L]={\");\t\t\t\t\t/*PPC*/\n\t\t\tprint_perm(s, n, 0);\t\t\t\t\t/*PPC*/\n\t\t\tprintf(\", \");\t\t\t\t\t\t/*PPC*/\n\t\t\tprint_perm(d, n, 0);\t\t\t\t\t/*PPC*/\n\t\t\tprintf(\"}\\n\");\t\t\t\t\t\t/*PPC*/\n#endif\t\t\t\t\t\t\t\t/*PPC*/\n\t\t\tlist1l=Deltabl;\n\t\t\tfor (c=0; c<list1l; c++)\n\t\t\t\tlist1[c]=onpoints(Deltab[c], s, n);\n\t\t\tproduct(g, d, perm1, n);\n\t\t\tinverse(perm1, perm2, n);\n\t\t\tlist2l=Deltapl;\n\t\t\tfor (c=0; c<list2l; c++)\n\t\t\t\tlist2[c]=onpoints(Deltap[c], perm2, n);\n#ifdef VERBOSE_DOUBLE\t\t\t\t\t\t/*PPC*/\n\t\t\tprintf(\"NEXT: intersection of sets of slots \");\t\t/*PPC*/\n\t\t\tprint_list(list1, list1l, 0);\n\t\t\tprintf(\" and \");\t\t/*PPC*/\n\t\t\tprint_list(list2, list2l, 1);\t\t\t\t/*PPC*/\n#endif\t\t\t\t\t\t\t\t/*PPC*/\n\t\t\tintersection(list1, list1l, list2, list2l,\n\t\t\t             NEXT, &NEXTl);\n#ifdef VERBOSE_DOUBLE\t\t\t\t\t\t/*PPC*/\n\t\t\tprintf(\"Intermediate slots NEXT: \");\t\t\t/*PPC*/\n\t\t\tprint_list(NEXT, NEXTl, 1);\t\t\t\t/*PPC*/\n#endif\t\t\t\t\t\t\t\t/*PPC*/\n\n\t\t\tfor(jj=0; jj<NEXTl; jj++) {\n\t\t\t\tj = NEXT[jj];\n\t\t\t\tinverse(s, perm1, n);\n\t\t\t\ttrace_schreier(onpoints(j,perm1,n), nu,w, perm2,n);\n\t\t\t\tproduct(perm2, s, s1, n);\n#ifdef VERBOSE_DOUBLE\t\t\t\t\t\t/*PPC*/\n\t\t\t\tprintf(\"From slot %d to interm. slot %d use s1: \",\t/*PPC*/\n\t\t\t\t       b, j);\n\t\t\t\tprint_perm(s1, n, 1);\t\t\t/*PPC*/\n#endif\t\t\t\t\t\t\t\t/*PPC*/\n\t\t\t\tproduct(g, d, perm2, n);\n\t\t\t\ttrace_schreier(onpoints(j,perm2,n),nuD,wD,perm3,n);\n\t\t\t\tinverse(perm3, perm1, n);\n\t\t\t\tproduct(d, perm1, d1, n);\n\t\t\t\tcopy_list(L, L1, Ll);\n\t\t\t\tL1l=Ll;\n\t\t\t\tL1[L1l++] = j;\n#ifdef VERBOSE_DOUBLE\t\t\t\t\t\t/*PPC*/\n\t\t\t\tprintf(\"d1: \");\n\t\t\t\tprint_perm(d1, n, 1);\t\t\t/*PPC*/\n\t\t\t\tprintf(\"L1: \");\n\t\t\t\tprint_list(L1, L1l, 1);\t\t\t/*PPC*/\n#endif\t\t\t\t\t\t\t\t/*PPC*/\n\n\t\t\t\tkk=ALPHAstep[i+1];\n\t\t\t\tALPHA[l].o[j-1] = kk;\n\t\t\t\tALPHAl++;\n\t\t\t\tALPHAstep[i+1]++;\n\t\t\t\t//\t\t\t\tstd::cout << \"resizing \" << ALPHAl << std::endl;\n\t\t\t\t//\t\t\t\tALPHA = (struct alphastruct*)realloc(ALPHA, ALPHAl* sizeof(struct alphastruct));\n\t\t\t\tALPHA.resize(ALPHAl);\n\t\t\t\tALPHA.back().init(n);\n\t\t\t\tcopy_list(L1, ALPHA[kk].L, L1l);\n\t\t\t\tALPHA[kk].Ll = L1l;\n\t\t\t\tcopy_list(s1, ALPHA[kk].s, n);\n\t\t\t\tcopy_list(d1, ALPHA[kk].d, n);\n\n\t\t\t\tF2(s1, g, d1, perm1, n);\n#ifdef VERBOSE_DOUBLE\t\t\t\t\t\t/*PPC*/\n\t\t\t\tprintf(\"This gives the new index configuration: \");\t/*PPC*/\n\t\t\t\tinverse(perm1, perm2, n);\t\t\t\t/*PPC*/\n\t\t\t\tprint_perm(perm2, n, 1);\t\t\t\t/*PPC*/\n\t\t\t\tfor(ii=0; ii<i; ii++) {\t\t\t\t\t/*PPC*/\n\t\t\t\t\tproduct(s1, g, perm2, n);\t\t\t/*PPC*/\n\t\t\t\t\tproduct(perm2, d1, perm3, n);\t\t\t/*PPC*/\n\t\t\t\t\tprintf(\"Checking slot %d with point %d: \",\t/*PPC*/\n\t\t\t\t\t       bS[ii], p[ii]);\t\t\t\t/*PPC*/\n\t\t\t\t\tif(onpoints(bS[ii], perm3, n)==p[ii])\t\t/*PPC*/\n\t\t\t\t\t\tprintf(\"True\\n\");\t\t\t/*PPC*/\n\t\t\t\t\telse printf(\"*************FALSE************\\n\");/*PPC*/\n\t\t\t\t\t}\t\t\t\t\t\t\t/*PPC*/\n#endif\t\t\t\t\t\t\t\t/*PPC*/\n\t\t\t\t}\n\t\t\t}\n\t\t\t{\n\t\t\t/* Verify if there are 2 equal permutations\n\t\t\tof opposite sign in SgD */\n\t\t\tint *array= (int*)malloc(n*(ALPHAstep[i+1]-ALPHAstep[i])\n\t\t\t                         *sizeof(int));\n\t\t\tint arrayl= 0;\n#ifdef VERBOSE_DOUBLE\t\t\t\t\t\t/*PPC*/\n\t\t\tprintf(\"Astep[i-1]=%d, Astep[i]=%d, Astep[i+1]=%d\\n\",\t/*PPC*/\n\t\t\t       ALPHAstep[i-1], ALPHAstep[i], ALPHAstep[i+1]);\t/*PPC*/\n#endif \t\t\t\t\t\t\t\t/*PPC*/\n\t\t\tfor(l=ALPHAstep[i]; l<ALPHAstep[i+1]; l++) {\n\t\t\t\tF2(ALPHA[l].s, g, ALPHA[l].d, perm1, n);\n\t\t\t\tcopy_list(perm1, array+(arrayl++)*n, n);\n\t\t\t\t}\n#ifdef VERBOSE_DOUBLE\t\t\t\t\t\t/*PPC*/\n\t\t\tprintf(\"Perform check.\\n\");\t\t\t\t/*PPC*/\n#endif\t\t\t\t\t\t\t\t/*PPC*/\n\t\t\tresult= consistency(array, arrayl, n);\n#ifdef VERBOSE_DOUBLE\t\t\t\t\t\t/*PPC*/\n\t\t\tprintf(\"Result of check: %d\\n\", result);\t\t/*PPC*/\n#endif\t\t\t\t\t\t\t\t/*PPC*/\n\t\t\tfree(array);\n\t\t\tif (!result) break;\n\t\t\t}\n\t\t/* Find the stabilizers S^(i+1) and D^(i+1) */\n\t\tstabilizer(&bS[i-1], 1, KS, KSl, n, KS, &KSl);\n\t\tdropdummyset(p[i-1], vds, vdsl, dummies, &dl);\n\t\tdroprepeatedset(p[i-1], vrs, vrsl, repes, &rl);\n#ifdef VERBOSE_DOUBLE\t\t\t\t\t\t/*PPC*/\n\t\tprintf(\"Remove perms of KS moving slot %d\\n\", b);\t/*PPC*/\n\t\tprintf(\"Remove perms of KD moving index %d\\n\", p[i-1]);\t/*PPC*/\n#endif\t\t\t\t\t\t\t\t/*PPC*/\n\n\t\t} /* End of main loop */\n\n\t/* Result */\n\tif (result==0) {\n\t\tzeros(perm1, n);\n\t\t}\n\telse {\n\t\tl=ALPHAstep[i-1];\n\t\tF2(ALPHA[l].s, g, ALPHA[l].d, perm1, n);\n\t\t}\n\tcopy_list(perm1, dcr, n);\n\n\t/* Free allocated memory */\n\t//\tfree(ALPHA);\n\tfree(ALPHAstep);\n\tfree(ig);\n\tfree(drummies);\n\tfree(drummyslots);\n\tfree(drummytmp);\n\tfree(drummytmp2);\n\tfree(bS);\n\tfree(bSsort);\n\tfree(KS);\n\tfree(KD);\n\tfree(bD);\n\tfree(nu);\n\tfree(w);\n\tfree(Deltab);\n\tfree(DeltaD);\n\tfree(IMAGES);\n\tfree(IMAGESsorted);\n\tfree(p);\n\tfree(nuD);\n\tfree(wD);\n\tfree(Deltap);\n\tfree(NEXT);\n\tfree(L);\n\tfree(L1);\n\tfree(s);\n\tfree(d);\n\tfree(list1);\n\tfree(list2);\n\tfree(perm1);\n\tfree(perm2);\n\tfree(perm3);\n\tfree(s1);\n\tfree(d1);\n\t}\n\n/**********************************************************************/\n\n/* canonical_perm. JMM, 5 July 2003\n*\n* JMM, 26 June 2007. Function extended. The old function is kept\n*      as a call to the new function for backwards compatibility.\n*\n* The \"dummy\" group D is given through the list dummyps of dpl pairs\n* of (initial) slots of dummies. The list freeps (length fl) contains\n* the slots of the free indices. Clearly 2*dpl+fl+2=n.\n* See notes for canonical_perm_ext.\n* Parameter ob is now useless. Kept for backwards compatibility.\n*/\n\nvoid canonical_perm(int *PERM,\n                    int SGSQ, int *base, int bl, int *GS, int m, int n,\n                    int *freeps, int fl, int *dummyps, int dpl, int, int metricQ,\n                    int *CPERM)\n\t{\n\n\tint i;\n\tint vds;\n\tint mQ;\n\tint *repes= NULL;\n\tint *vrs= NULL;\n\tint *PERM1=   (int*)malloc(n    *sizeof(int));\n\tint *PERM2=   (int*)malloc(n    *sizeof(int));\n\tint *frees=   (int*)malloc(fl   *sizeof(int));\n\tint *dummies= (int*)malloc(2*dpl*sizeof(int));\n\n\t/* Construct \"vectors\" vds and mQ */\n\tvds = 2*dpl;\n\tmQ = metricQ;\n\n\t/* !!!!!!!! Change to Renato's notation !!!!!!!! */\n\tinverse(PERM, PERM1, n);\n\tfor (i=0; i<fl; i++) {\n\t\tfrees[i] = onpoints(freeps[i], PERM1, n);\n\t\t}\n\tfor (i=0; i<2*dpl; i++) {\n\t\tdummies[i] = onpoints(dummyps[i], PERM1, n);\n\t\t}\n\n\t/* Call new, extended function */\n\tcanonical_perm_ext(PERM1, n, SGSQ, base, bl, GS, m,\n\t                   frees, fl, &vds, 1, dummies, 2*dpl, &mQ,\n\t                   vrs, 0, repes, 0,\n\t                   PERM2);\n\n\t/* !!!!!!!! Change back to our notation !!!!!!!! */\n\tif (PERM2[0] != 0) inverse(PERM2, CPERM, n);\n\telse copy_list(PERM2, CPERM, n);\n\n\t/* Free allocated space */\n\tfree(PERM1);\n\tfree(PERM2);\n\tfree(frees);\n\tfree(dummies);\n\t}\n\n/**********************************************************************/\n\n/* canonical_perm_ext. JMM, 26 June 2007\n*\n* This function finds a canonical representant of the permutation PERM\n* in the double_coset with group S (slot symmetries) and group D\n* (dummy index or repeated index symmetries).\n*\n* There are two steps: first S, then S and D. The \"slot\" group S is\n* given through the generating set GS (with m n-permutations), that\n* can be a SGS (then SGSQ must be 1) or not (then SGSQ must be 0).\n* In the former case base (length bl) contains the associated base;\n* in the latter case a SGS will be constructed using the Schreier_Sims\n* algorithm using the points in base as the first points for the base.\n* The algorithm first calls coset_rep with PERM and the free indices\n* converting PERM into PERM1. The SGS is then stabilized with respect\n* to those points. Then the double_coset_rep algorithm is called with\n* PERM1 returning PERM2, which is finally copied to CPERM.\n*\n* The \"drummy\" group D is given through the specification of so-called\n* dummysets and repeatedsets. A dummyset is a collection of pairs of\n* indices (first the up-index, then the down-index) and a symmetry\n* switch saying if there is a symmetric metric (switch 1), an\n* antisymmetric metric (-1) or no metric at all (0). A repeated set\n* is simply a list of the names of repeated indices. Both dummies and\n* repes are collectively called drummies. Note that dummysets and\n* repeatedsets contain **names** (i.e. positions in the canonical\n* configuration) in the initial configuration.\n*\n* The result is stored in the permutation CPERM.\n* Note that we input a pointer to GS, and not a pointer to a pointer\n* because there is no need to return a modified GS.\n*\n* This is probably the most important function of this code, and hence\n* it is worth to explain the meaning of the input fields:\n*      PERM: pointer to permutation (Images notation) to canonicalize\n*      n:    degree of perm (length of list of images)\n*      SGSQ: switch. 1 if we supply a SGS, 0 if we only give a GS\n*      base: sorted list of points for the SGS. Start of base if SGSQ=0\n*      bl:   length of base\n*      GS:   pointer to the list of permutations forming the GS\n*      m:    number of permutations in the GS\n*      freeps: list of initial names of free indices\n*      fl:   length of list freeps\n*      vds:  list of lengths of dummysets\n*      vdsl: length of vds (number of dummysets)\n*      dummies: list with pairs of names dummies\n*      dl:   length of list dummies (sum of elements of vdsl)\n*      mQ:   list (of length vdsl) with symmetry signs\n*      vrs:  list of lengths of repeatedsets\n*      vrsl: length of rds (number of repeatedsets)\n*      repes: list with repeated indices\n*      rl:   length of list repes (sum of elements of vrsl)\n*      CPERM: pointer to return the canonicalized permutation\n*/\n\nvoid canonical_perm_ext(int *PERM, int n,\n                        int SGSQ, int *base, int bl, int *GS, int m,\n                        int *frees, int fl,\n                        int *vds, int vdsl, int *dummies, int dl, int *mQ,\n                        int *vrs, int vrsl, int *repes, int rl,\n                        int *CPERM)\n\t{\n\n\tint i;\n\tint *freeps=    (int*)malloc(fl*sizeof(int));\n\tint *PERM1=     (int*)malloc(n *sizeof(int));\n\tint *PERM2=     (int*)malloc(n *sizeof(int));\n\tint *newbase=   (int*)malloc(n *sizeof(int)), newbl;\n\tint **newGS = NULL;\n\tint *pointer;\n\tint newm;\n\tint *tmpbase=   (int*)malloc(n *sizeof(int)), tmpbl;\n\tint num=0;\n\n\tpointer= (int*)malloc(m*n*sizeof(int));\n\tnewGS= &pointer;\n\n#ifdef VERBOSE_CANON\t\t\t\t\t\t/*PPC*/\n\tprintf(\"can: input base: \");\t\t\t\t/*PPC*/\n\tprint_list(base, bl, 1);\t\t\t\t/*PPC*/\n#endif\t\t\t\t\t\t\t\t/*PPC*/\n\n\tif (!SGSQ) { /* Compute a Strong Generating Set */\n\t\tnonstable_points(base, bl, GS, m, n,\n\t\t                 tmpbase, &tmpbl);\n\t\tschreier_sims(tmpbase, tmpbl, GS, m, n,\n\t\t              newbase, &newbl, newGS, &newm, &num);\n\t\t}\n\telse {\n\t\tcopy_list(base, newbase, bl);\n\t\tnewbl=bl;\n\t\tcopy_list(GS, *newGS, m*n);\n\t\tnewm=m;\n\t\t}\n\n#ifdef VERBOSE_CANON\t\t\t\t\t\t/*PPC*/\n\tprintf(\"can: SGS computed.\\n\");\t\t\t\t/*PPC*/\n\tprintf(\"can: newbase: \");\t\t\t\t/*PPC*/\n\tprint_list(newbase, newbl, 1);\t\t\t\t/*PPC*/\n#endif\t\t\t\t\t\t\t\t/*PPC*/\n\n\t/* Compute slots of free indices */\n\tinverse(PERM, PERM1, n);\n\tfor (i=0; i<fl; i++) {\n\t\tfreeps[i] = onpoints(frees[i], PERM1, n);\n\t\t}\n\t/* Call coset_rep algorithm. Result in PERM1 */\n\tcoset_rep(PERM, n, newbase, newbl, *newGS, &newm,\n\t          freeps, fl, PERM1);\n#ifdef VERBOSE_CANON\t\t\t\t\t\t/*PPC*/\n\tprintf(\"can: Canonical perm after coset algorithm: \");\t/*PPC*/\n\tprint_perm(PERM1, n, 1);\t\t\t\t/*PPC*/\n\tprintf(\"New positions of free indices: \");\t\t/*PPC*/\n\tprint_list(freeps, fl, 1);\t\t\t\t/*PPC*/\n#endif\t\t\t\t\t\t\t\t/*PPC*/\n\n\tif (dl+rl==0) { /* No drummy indices */\n\t\tcopy_list(PERM1, CPERM, n);\n\t\t}\n\telse {\n\n\t\tcomplement(newbase, newbl, freeps, fl, 1, tmpbase, &tmpbl);\n\t\tcopy_list(tmpbase, newbase, tmpbl);\n\t\tnewbl=tmpbl;\n\t\tstabilizer(freeps, fl, *newGS, newm, n, *newGS, &newm);\n#ifdef VERBOSE_CANON\t\t\t\t\t\t/*PPC*/\n\t\tprintf(\"can: newbase after fixing: \");\t\t\t/*PPC*/\n\t\tprint_list(newbase, newbl, 1);\t\t\t\t/*PPC*/\n\t\tprintf(\"can: newGS after fixing: \");\t\t\t/*PPC*/\n\t\tprint_array_perm(*newGS, newm, n, 1);\t\t\t/*PPC*/\n#endif\t\t\t\t\t\t\t\t/*PPC*/\n\n\t\t/* Apply dummy-indices algorithm. Result in PERM2 */\n#ifdef VERBOSE_CANON\t\t\t\t\t\t/*PPC*/\n\t\tprintf(\"can: Starting double_coset algorithm.\\n\");\t/*PPC*/\n#endif\t\t\t\t\t\t\t\t/*PPC*/\n\t\tdouble_coset_rep(PERM1, n, newbase, newbl, *newGS, newm,\n\t\t                 vds, vdsl, dummies, dl, mQ,\n\t\t                 vrs, vrsl, repes, rl, PERM2);\n#ifdef VERBOSE_CANON\t\t\t\t\t\t/*PPC*/\n\t\tprintf(\"can: Finished double_coset algorithm.\\n\");\t/*PPC*/\n#endif\t\t\t\t\t\t\t\t/*PPC*/\n\n\t\t/* Copy to result */\n\t\tcopy_list(PERM2, CPERM, n);\n\n\t\t}\n\n\t/* Free allocated memory */\n\tfree(freeps);\n\tfree(PERM1);\n\tfree(PERM2);\n\tfree(newbase);\n\tfree(tmpbase);\n\tfree(*newGS);\n\n#ifdef VERBOSE_CANON\t\t\t\t\t\t/*PPC*/\n\tprintf(\"************ END OF ALGORITHM ***********\\n\");\t/*PPC*/\n#endif\t\t\t\t\t\t\t\t/*PPC*/\n\t}\n"
  },
  {
    "path": "core/modules/xperm_new.h",
    "content": "/* \n\n\tCadabra: a field-theory motivated computer algebra system.\n\tCopyright (C) 2001-2009  Kasper Peeters <kasper.peeters@aei.mpg.de>\n\n   This program is free software: you can redistribute it and/or\n   modify it under the terms of the GNU General Public License as\n   published by the Free Software Foundation, either version 3 of the\n   License, or (at your option) any later version.\n\n   This program is distributed in the hope that it will be useful,\n   but WITHOUT ANY WARRANTY; without even the implied warranty of\n   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU\n   General Public License for more details.\n\n   You should have received a copy of the GNU General Public License\n   along with this program.  If not, see <http://www.gnu.org/licenses/>.\n \n*/\n\n#ifndef xperm_h_\n#define xperm_h_\n\nvoid canonical_perm(int *perm,\n\tint SGSQ, int *base, int bl, int *GS, int m, int n,\n\tint *freeps, int fl, int *dummyps, int dl, int ob, int metricQ,\n\tint *cperm);\n\nvoid canonical_perm_ext(int *perm, int n,\n\tint SGSQ, int *base, int bl, int *GS, int m,\n\tint *frees, int fl,\n        int *vds, int vdsl, int *dummies, int dl, int *mQ,\n        int *vrs, int vrsl, int *repes, int rl,\n\tint *cperm);\n\nvoid inverse(int *p, int *ip, int n);\nint onpoints(int point, int *p, int n);\nvoid copy_list(int *list1, int *list2, int n);\n\n\n#endif\n"
  },
  {
    "path": "core/packages/CMakeLists.txt",
    "content": "cmake_minimum_required(VERSION ${CADABRA_CMAKE_VERSION}) \nproject(Cadabra)\n\n\n#---------------------------------------------------------------------------\n# Preamble.\n#---------------------------------------------------------------------------\n\nprint_header(\"Configuring packages\")\n\nset(PYTHON_CDB_PACKAGE_PATH    ${PYTHON_SITE_PATH}/cdb)\nset(SOURCE_PACKAGEDIR          ${CMAKE_SOURCE_DIR}/core/packages/cdb)\nset(PACKAGEDIR                 ${CMAKE_BINARY_DIR}/core/packages/cdb)\n\n#---------------------------------------------------------------------------\n# Enumerate packages\n#---------------------------------------------------------------------------\n\nset(PACKAGES\n  core/component\n  core/manip\n  core/solve\n  core/trace\n  interact/slider\n  numeric/integrate\n  numeric/evaluate\n  graphics/plot\n  utils/node\n  utils/indices\n  utils/develop\n  utils/tableau\n  sympy/solvers\n  sympy/calculus\n  gauge_theory/instantons\n  relativity/abstract\n  relativity/schwarzschild\n  )\n\nset(PURE_PYTHON_PACKAGES\n  main.py\n  remote/__init__.py\n  remote/speech.py\n  remote/highlight.py\n  remote/record.py\n)\n\nif(WIN32)\n  set(COMPILED_PACKAGES\n  )\nelse()\n  set(COMPILED_PACKAGES\n    core/_component.cc\n    utils/_algorithm.cc\n  )\nendif()\n\n#---------------------------------------------------------------------------\n# Install packages\n#---------------------------------------------------------------------------\n\nforeach(PACKAGE ${PACKAGES})\n  get_filename_component(PINSTALL ${PACKAGE} DIRECTORY)\n  install(\n    FILES \n      \"${SOURCE_PACKAGEDIR}/${PACKAGE}.cnb\" \n    DESTINATION \n      ${PYTHON_CDB_PACKAGE_PATH}/${PINSTALL}\n  )\nendforeach()\n\nforeach(PACKAGE ${PURE_PYTHON_PACKAGES})\n  get_filename_component(PINSTALL ${PACKAGE} DIRECTORY)\n  install(\n    FILES\n    \"${SOURCE_PACKAGEDIR}/${PACKAGE}\"\n    DESTINATION \n    \"${PYTHON_CDB_PACKAGE_PATH}/${PINSTALL}\"\n  )\nendforeach()\n\n# Also add main.py to the build folder.\nadd_custom_target(\n  copy-main ALL\n  COMMAND ${CMAKE_COMMAND} -E copy\n  \"${SOURCE_PACKAGEDIR}/main.py\"\n  \"${CMAKE_CURRENT_BINARY_DIR}/cdb/main.py\"\n)\n\n\nfind_package(GMPXX REQUIRED STATIC)\n\nforeach(PACKAGE ${COMPILED_PACKAGES})\n  SET(CMAKE_SKIP_BUILD_RPATH FALSE)\n  SET(CMAKE_BUILD_WITH_INSTALL_RPATH TRUE)\n  get_filename_component(PINSTALL ${PACKAGE} DIRECTORY)\n  get_filename_component(PNAME ${PACKAGE} NAME_WE)\n  pybind11_add_module(${PNAME} SHARED ${SOURCE_PACKAGEDIR}/${PACKAGE})\n  message(STATUS \"Storing algorithm C++ module as ${PINSTALL}\")\n  set_target_properties(${PNAME} PROPERTIES RUNTIME_OUTPUT_DIRECTORY \"${CMAKE_CURRENT_BINARY_DIR}/cdb/${PINSTALL}\")\n  set_target_properties(${PNAME} PROPERTIES LIBRARY_OUTPUT_DIRECTORY \"${CMAKE_CURRENT_BINARY_DIR}/cdb/${PINSTALL}\")\n  set_target_properties(${PNAME} PROPERTIES SUFFIX \".${Python_MOD_SUFFIX}\")\n  set_target_properties(${PNAME} PROPERTIES INSTALL_RPATH \"$ORIGIN/../../:$ORIGIN/../../../../\")\n  \n  target_link_libraries(${PNAME} PUBLIC cadabra2 ${GMPXX_LIBRARIES} ${GMP_LIBRARIES})\n  target_include_directories(${PNAME} PUBLIC ${CADABRA_CORE_DIR})\n\n  if(IPO_SUPPORTED)\n    message(STATUS \"IPO / LTO for ${PNAME} enabled\")     \n    set_property(TARGET ${PNAME} PROPERTY INTERPROCEDURAL_OPTIMIZATION TRUE)\n    set_target_properties(${PNAME} PROPERTIES COMPILE_FLAGS \"-flto=auto\")\n    set_target_properties(${PNAME} PROPERTIES LINK_FLAGS \"-flto=auto\")  \n  endif()\n  \n  install(TARGETS ${PNAME} DESTINATION ${PYTHON_CDB_PACKAGE_PATH}/${PINSTALL})\nendforeach()\n\ninstall(\n  DIRECTORY DESTINATION \n    ${PYTHON_CDB_PACKAGE_PATH} \n  DIRECTORY_PERMISSIONS \n  OWNER_READ \n  OWNER_WRITE \n  OWNER_EXECUTE\n  GROUP_READ \n  GROUP_EXECUTE\n  WORLD_READ \n  WORLD_EXECUTE\n)\n"
  },
  {
    "path": "core/packages/cdb/core/_component.cc",
    "content": "#include <pybind11/pybind11.h>\n#include \"pythoncdb/py_ex.hh\"\n#include \"pythoncdb/py_kernel.hh\"\n\n#include \"Exceptions.hh\"\n#include \"properties/Coordinate.hh\"\n#include \"properties/IndexInherit.hh\"\n#include \"properties/Symbol.hh\"\n\nusing namespace cadabra;\nnamespace py = pybind11;\n\nstd::vector<Ex> get_free_indices(const Kernel& kernel, Ex::iterator it)\n{\n\twhile (*it->name == \"\\\\sum\" || *it->name == \"\\\\equals\") {\n\t\tbool found_term = false;\n\t\tfor (Ex::sibling_iterator beg = it.begin(), end = it.end(); beg != end; ++beg) {\n\t\t\tif (*beg->name != \"1\") {\n\t\t\t\tfound_term = true;\n\t\t\t\tit = beg;\n\t\t\t\tbreak;\n\t\t\t}\n\t\t}\n\t\tif (!found_term)\n\t\t\treturn {};\n\t}\n\n\tstd::vector<Ex> indices;\n\tbool inherits_indices = kernel.properties.get<IndexInherit>(it);\n\tfor (Ex::sibling_iterator beg = it.begin(), end = it.end(); beg != end; ++beg) {\n\t\tif (beg->is_index()) {\n\t\t\tauto symbol = kernel.properties.get<Symbol>(beg, true);\n\t\t\tauto coord = kernel.properties.get<Coordinate>(beg, true);\n\t\t\tif (!(symbol || coord || beg->is_integer())) {\n\t\t\t\tEx idx(beg);\n\t\t\t\tidx.begin()->fl.parent_rel = str_node::parent_rel_t::p_sub;\n\t\t\t\tauto pos = std::find(indices.begin(), indices.end(), idx);\n\t\t\t\tif (pos == indices.end())\n\t\t\t\t\tindices.push_back(idx);\n\t\t\t\telse\n\t\t\t\t\tindices.erase(pos);\n\t\t\t}\n\t\t}\n\t\telse if (inherits_indices) {\n\t\t\tauto new_indices = get_free_indices(kernel, beg);\n\t\t\tfor (const auto& idx : new_indices) {\n\t\t\t\tauto pos = std::find(indices.begin(), indices.end(), idx);\n\t\t\t\tif (pos == indices.end())\n\t\t\t\t\tindices.push_back(idx);\n\t\t\t\telse\n\t\t\t\t\tindices.erase(pos);\n\t\t\t}\n\t\t}\n\t}\n\n\treturn indices;\n}\n\nEx_ptr get_component(Ex_ptr ex, Ex_ptr components)\n{\n\tKernel& kernel = *get_kernel_from_scope();\n\tEx_comparator comp(kernel.properties);\n\n\tEx_ptr res = std::make_shared<Ex>(*ex);\n\n\t// Ensure components is a comma node\n\tif (*components->begin()->name != \"\\\\comma\") {\n\t\tEx_ptr new_components = std::make_shared<Ex>(\"\\\\comma\");\n\t\tnew_components->append_child(new_components->begin(), components->begin());\n\t\tcomponents = new_components;\n\t}\n\n\t// Resolve free indices\n\tauto free_indices = get_free_indices(kernel, res->begin());\n\tif (free_indices.empty())\n\t\treturn res;\n\n\t// Match free indices to coordinates\n\tEx::sibling_iterator curcomp = components->begin().begin(), endcomp = components->begin().end();\n\tstd::map<Ex, Ex::iterator> idx_to_coord;\n\tfor (const auto& free_index : free_indices) {\n\t\tif (curcomp == endcomp)\n\t\t\tthrow ArgumentException(\"get_component: number of components does not match number of free indices\");\n\t\tidx_to_coord[free_index] = curcomp;\n\t\t++curcomp;\n\t}\n\n\t// Resolve component nodes\n\tfor (Ex::iterator beg = res->begin(), end = res->end(); beg != end; ++beg) {\n\t\tif (*beg->name == \"\\\\components\") {\n\t\t\tEx::sibling_iterator comma = beg.begin();\n\t\t\tEx comp(\"\\\\comma\");\n\t\t\twhile (*comma->name != \"\\\\comma\") {\n\t\t\t\tfor (const auto& elem : idx_to_coord) {\n\t\t\t\t\tif (subtree_equal(&kernel.properties, comma, elem.first.begin(), -1)) {\n\t\t\t\t\t\tcomp.append_child(comp.begin(), elem.second);\n\t\t\t\t\t\tbreak;\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t\t++comma;\n\t\t\t}\n\t\t\tbool found = false;\n\t\t\tfor (Ex::sibling_iterator compbeg = comma.begin(), compend = comma.end(); compbeg != compend; ++compbeg) {\n\t\t\t\tEx::sibling_iterator side = compbeg.begin();\n\t\t\t\tif (subtree_equal(&kernel.properties, side, comp.begin(), -1)) {\n\t\t\t\t\t++side;\n\t\t\t\t\tEx tmp(side);\n\t\t\t\t\tbeg = res->replace(beg, tmp.begin());\n\t\t\t\t\tfound = true;\n\t\t\t\t\tbreak;\n\t\t\t\t}\n\t\t\t}\n\t\t\tif (!found) {\n\t\t\t\tbeg = res->replace(beg, str_node(\"1\"));\n\t\t\t\tmultiply(beg->multiplier, 0);\n\t\t\t}\n\t\t}\n\t}\n\n\tEx::post_order_iterator walk = res->begin(), last = res->begin();\n\twalk.descend_all();\n\t++last;\n\n\tdo {\n\t\tauto next = walk;\n\t\t++next;\n\n\t\tif (walk->is_index()) {\n\t\t\tfor (const auto& elem : idx_to_coord) {\n\t\t\t\tif (subtree_equal(&kernel.properties, walk, elem.first.begin(), -1)) {\n\t\t\t\t\tres->replace_index(walk, elem.second, true);\n\t\t\t\t\tbreak;\n\t\t\t\t}\n\t\t\t}\n\t\t}\n\n\t\twalk = next;\n\t} while (walk != last);\n\n\treturn res;\n}\n\n\nPYBIND11_MODULE(_component, m)\n{\n\tm.def(\"get_component\", get_component);\n}\n"
  },
  {
    "path": "core/packages/cdb/core/component.cnb",
    "content": "{\n\t\"cell_id\": 8176786609067457502,\n\t\"cells\": [\n\t\t{\n\t\t\t\"cell_id\": 11457506631850813640,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 10008607845695988739,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\package{cdb.core.component}{Simple access to component expressions}\\n\\nThis package contains helper functions to access components of tensors, as they are computed by e.g.~\\\\algo{evaluate}.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\package{cdb.core.component}{Simple access to component expressions}\\n\\nThis package contains helper functions to access components of tensors, as they are computed by e.g.~\\\\algo{evaluate}.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 6181105877766386294,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"from cdb.utils.node import n_children\\nfrom cdb.core.manip import get_lhs, get_rhs\\nfrom cdb.utils.indices import get_free_indices\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 11505235534497815577,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9280419895947204080,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\algorithm{get_component(ex: Ex, component: Ex) -> Ex}{Extract a single component from an expression.}\\n\\nGets a component of an expression including those from an \\\\algo{evaluate} command. \\nThe \\\\verb|component| argument for vector-like objects should be e.g.~\\\\verb|$t$|,\\nand for higher-rank tensors like e.g.~\\\\verb|$x, t$|.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\algorithm{get_component(ex: Ex, component: Ex) -> Ex}{Extract a single component from an expression.}\\n\\nGets a component of an expression including those from an \\\\algo{evaluate} command. \\nThe \\\\verb|component| argument for vector-like objects should be e.g.~\\\\verb|$t$|,\\nand for higher-rank tensors like e.g.~\\\\verb|$x, t$|.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 2743671539812446348,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"from cdb.core._component import get_component\\n\\n#def get_component(ex, components):\\n#\\t\\\"\\\"\\\"Gets a particular component of an expression\\\"\\\"\\\"\\n#\\t# Work on a copy of ex\\n#\\tex = ex.top().ex()\\n#\\n#\\t# Replace all free indices with the components\\n#\\tfree_indices = get_free_indices(ex.top())\\n#\\tif components.top().name != r\\\"\\\\comma\\\":\\n#\\t\\ttmp = Ex(r'\\\\comma')\\n#\\t\\ttmp.top().append_child(components.top())\\n#\\t\\tcomponents = tmp\\n#\\tassert len(free_indices) == n_children(components.top()), f\\\"Expression contains {len(free_indices)} free indices, but {n_children(components.top())} components supplied\\\"\\n#\\tfor index, component in zip(free_indices, components.top().children()):\\n#\\t\\tnode = next(ex[index.top().name], None)\\n#\\t\\tchanged = True\\n#\\t\\twhile changed:\\n#\\t\\t\\tfor node in ex[index.top().name]:\\n#\\t\\t\\t\\tif node.parent_rel == parent_rel_t.super or node.parent_rel == parent_rel_t.sub:\\n#\\t\\t\\t\\t\\tpr = node.parent_rel\\n#\\t\\t\\t\\t\\tnode.replace(component.ex())\\n#\\t\\t\\t\\t\\tnode.parent_rel = pr\\n#\\t\\t\\t\\t\\tbreak\\n#\\t\\t\\telse:\\n#\\t\\t\\t\\tchanged = False\\n#\\n#\\t# Replace all component nodes with the particular component we are looking for\\n#\\tfor node in ex[r'\\\\components']:\\n#\\t\\t# Sift through \\\\equals nodes finding the one with the right components\\n#\\t\\tfor candidate in node[r'\\\\equals']:\\n#\\t\\t\\targ = get_lhs(candidate)\\n#\\t\\t\\tif arg == components:\\n#\\t\\t\\t\\tnode = node.replace(get_rhs(candidate))\\n#\\t\\t\\t\\tbreak\\n#\\t\\telse:\\n#\\t\\t\\tnode = node.replace($0$)\\n#\\n#\\t# The components paramater needs to have a head '\\\\comma' node\\n#\\t# so let's quickly make sure that's true.\\n#\\tif components.head() != r'\\\\comma':\\n#\\t\\tbit = $@(components)$\\n#\\t\\tcomponents.top().name = r'\\\\comma'\\n#\\t\\tcomponents.top().append_child(bit)\\n#\\n#\\treturn ex\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 3091027410461552154,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 10702135062815239023,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property Coordinate attached to~}\\\\left[t,~\\\\discretionary{}{}{} x\\\\right].\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 7913033517866597731,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property Indices(position=free) attached to~}\\\\left[i,~\\\\discretionary{}{}{} j\\\\right].\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 7270033254803685303,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 12003858549170534122,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"b_{i} = a_{i}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}b_{i} = a_{i}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 6142898072093974525,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 16609044361570361619,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"b_{i} = \\\\components_{i}({{t} = 1, {x} = 2})\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}b_{i} = \\\\square{}_{i}\\\\left\\\\{\\\\begin{aligned}\\\\square{}_{t}& = 1\\\\\\\\[-.5ex]\\n\\\\square{}_{x}& = 2\\\\\\\\[-.5ex]\\n\\\\end{aligned}\\\\right.\\n\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 15779107546857997208,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 2447125086089804696,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"b_{x} = 2\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}b_{x} = 2\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"ignore_on_import\": true,\n\t\t\t\"source\": \"{t,x}::Coordinate;\\n{i,j}::Indices(values={t,x});\\nex:= b_{i} = a_{i};\\nevaluate(ex, $a_{t}=1, a_{x}=2$, rhsonly=True);\\nget_component(ex, $x$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 5679090421226085066,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 5006167440808421109,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 18189614503928553251,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"0 = 6(\\\\Phi)**1 a2 k_{\\\\nu} k_{\\\\mu}-(\\\\Phi)**1 b2 \\\\eta^{\\\\sigma \\\\rho} \\\\partial_{\\\\rho}(z) \\\\omega (c)**(-1) B_{\\\\nu \\\\sigma} k_{\\\\mu}-2(\\\\Phi)**1 a2 k_{\\\\mu} k_{\\\\nu} + (\\\\Phi)**1 b2 \\\\partial_{\\\\sigma}(z) \\\\omega (c)**(-1) B_{\\\\nu \\\\mu} k_{\\\\rho} \\\\eta^{\\\\sigma \\\\rho} + (\\\\Phi)**1 b2 \\\\eta^{\\\\sigma \\\\rho} \\\\partial_{\\\\rho}(z) \\\\omega (c)**(-1) B_{\\\\nu \\\\mu} k_{\\\\sigma}-(\\\\Phi)**1 b2 \\\\partial_{\\\\alpha}(z) \\\\omega (c)**(-1) B_{\\\\rho \\\\mu} k_{\\\\nu} \\\\eta^{\\\\alpha \\\\rho} -  1/2 A_{\\\\rho \\\\sigma} k_{\\\\nu} A_{\\\\beta \\\\alpha} k_{\\\\mu} \\\\eta^{\\\\beta \\\\rho} \\\\eta^{\\\\sigma \\\\alpha} -  1/2 A_{\\\\rho \\\\sigma} A_{\\\\beta \\\\alpha} k_{\\\\nu} k_{\\\\mu} \\\\eta^{\\\\beta \\\\rho} \\\\eta^{\\\\sigma \\\\alpha} +  1/4 A_{\\\\alpha \\\\beta} k_{\\\\nu} A_{\\\\sigma \\\\rho} k_{\\\\mu} \\\\eta^{\\\\beta \\\\sigma} \\\\eta^{\\\\rho \\\\alpha}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}0 = 6{\\\\Phi}^{1} {a_{2}} k_{\\\\nu} k_{\\\\mu}-{\\\\Phi}^{1} {b_{2}} \\\\eta^{\\\\sigma \\\\rho} \\\\partial_{\\\\rho}\\\\left(z\\\\right) \\\\omega {c}^{-1} B_{\\\\nu \\\\sigma} k_{\\\\mu}-2{\\\\Phi}^{1} {a_{2}} k_{\\\\mu} k_{\\\\nu}+{\\\\Phi}^{1} {b_{2}} \\\\partial_{\\\\sigma}\\\\left(z\\\\right) \\\\omega {c}^{-1} B_{\\\\nu \\\\mu} k_{\\\\rho} \\\\eta^{\\\\sigma \\\\rho}+{\\\\Phi}^{1} {b_{2}} \\\\eta^{\\\\sigma \\\\rho} \\\\partial_{\\\\rho}\\\\left(z\\\\right) \\\\omega {c}^{-1} B_{\\\\nu \\\\mu} k_{\\\\sigma}-{\\\\Phi}^{1} {b_{2}} \\\\partial_{\\\\alpha}\\\\left(z\\\\right) \\\\omega {c}^{-1} B_{\\\\rho \\\\mu} k_{\\\\nu} \\\\eta^{\\\\alpha \\\\rho} - \\\\frac{1}{2}A_{\\\\rho \\\\sigma} k_{\\\\nu} A_{\\\\beta \\\\alpha} k_{\\\\mu} \\\\eta^{\\\\beta \\\\rho} \\\\eta^{\\\\sigma \\\\alpha} - \\\\frac{1}{2}A_{\\\\rho \\\\sigma} A_{\\\\beta \\\\alpha} k_{\\\\nu} k_{\\\\mu} \\\\eta^{\\\\beta \\\\rho} \\\\eta^{\\\\sigma \\\\alpha}+\\\\frac{1}{4}A_{\\\\alpha \\\\beta} k_{\\\\nu} A_{\\\\sigma \\\\rho} k_{\\\\mu} \\\\eta^{\\\\beta \\\\sigma} \\\\eta^{\\\\rho \\\\alpha}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 13426140165273122169,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 7820754601545462471,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"0 = 6(\\\\Phi)**1 a2 k_{t} k_{t}-(\\\\Phi)**1 b2 \\\\eta^{\\\\sigma \\\\rho} \\\\partial_{\\\\rho}(z) \\\\omega (c)**(-1) B_{t \\\\sigma} k_{t}-2(\\\\Phi)**1 a2 k_{t} k_{t} + (\\\\Phi)**1 b2 \\\\partial_{\\\\sigma}(z) \\\\omega (c)**(-1) B_{t t} k_{\\\\rho} \\\\eta^{\\\\sigma \\\\rho} + (\\\\Phi)**1 b2 \\\\eta^{\\\\sigma \\\\rho} \\\\partial_{\\\\rho}(z) \\\\omega (c)**(-1) B_{t t} k_{\\\\sigma}-(\\\\Phi)**1 b2 \\\\partial_{\\\\alpha}(z) \\\\omega (c)**(-1) B_{\\\\rho t} k_{t} \\\\eta^{\\\\alpha \\\\rho} -  1/2 A_{\\\\rho \\\\sigma} k_{t} A_{\\\\beta \\\\alpha} k_{t} \\\\eta^{\\\\beta \\\\rho} \\\\eta^{\\\\sigma \\\\alpha} -  1/2 A_{\\\\rho \\\\sigma} A_{\\\\beta \\\\alpha} k_{t} k_{t} \\\\eta^{\\\\beta \\\\rho} \\\\eta^{\\\\sigma \\\\alpha} +  1/4 A_{\\\\alpha \\\\beta} k_{t} A_{\\\\sigma \\\\rho} k_{t} \\\\eta^{\\\\beta \\\\sigma} \\\\eta^{\\\\rho \\\\alpha}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}0 = 6{\\\\Phi}^{1} {a_{2}} k_{t} k_{t}-{\\\\Phi}^{1} {b_{2}} \\\\eta^{\\\\sigma \\\\rho} \\\\partial_{\\\\rho}\\\\left(z\\\\right) \\\\omega {c}^{-1} B_{t \\\\sigma} k_{t}-2{\\\\Phi}^{1} {a_{2}} k_{t} k_{t}+{\\\\Phi}^{1} {b_{2}} \\\\partial_{\\\\sigma}\\\\left(z\\\\right) \\\\omega {c}^{-1} B_{t t} k_{\\\\rho} \\\\eta^{\\\\sigma \\\\rho}+{\\\\Phi}^{1} {b_{2}} \\\\eta^{\\\\sigma \\\\rho} \\\\partial_{\\\\rho}\\\\left(z\\\\right) \\\\omega {c}^{-1} B_{t t} k_{\\\\sigma}-{\\\\Phi}^{1} {b_{2}} \\\\partial_{\\\\alpha}\\\\left(z\\\\right) \\\\omega {c}^{-1} B_{\\\\rho t} k_{t} \\\\eta^{\\\\alpha \\\\rho} - \\\\frac{1}{2}A_{\\\\rho \\\\sigma} k_{t} A_{\\\\beta \\\\alpha} k_{t} \\\\eta^{\\\\beta \\\\rho} \\\\eta^{\\\\sigma \\\\alpha} - \\\\frac{1}{2}A_{\\\\rho \\\\sigma} A_{\\\\beta \\\\alpha} k_{t} k_{t} \\\\eta^{\\\\beta \\\\rho} \\\\eta^{\\\\sigma \\\\alpha}+\\\\frac{1}{4}A_{\\\\alpha \\\\beta} k_{t} A_{\\\\sigma \\\\rho} k_{t} \\\\eta^{\\\\beta \\\\sigma} \\\\eta^{\\\\rho \\\\alpha}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"ignore_on_import\": true,\n\t\t\t\"source\": \"ex := 0 = \\n\\t6(\\\\Phi)**1 a2 k_{\\\\nu} k_{\\\\mu}-\\n\\t(\\\\Phi)**1 b2 \\\\eta^{\\\\sigma \\\\rho} \\\\partial_{\\\\rho}(z) \\\\omega (c)**(-1) B_{\\\\nu \\\\sigma} k_{\\\\mu}-\\n\\t2(\\\\Phi)**1 a2 k_{\\\\mu} k_{\\\\nu} + \\n\\t(\\\\Phi)**1 b2 \\\\partial_{\\\\sigma}(z) \\\\omega (c)**(-1) B_{\\\\nu \\\\mu} k_{\\\\rho} \\\\eta^{\\\\sigma \\\\rho} + \\n\\t(\\\\Phi)**1 b2 \\\\eta^{\\\\sigma \\\\rho} \\\\partial_{\\\\rho}(z) \\\\omega (c)**(-1) B_{\\\\nu \\\\mu} k_{\\\\sigma}-\\n\\t(\\\\Phi)**1 b2 \\\\partial_{\\\\alpha}(z) \\\\omega (c)**(-1) B_{\\\\rho \\\\mu} k_{\\\\nu} \\\\eta^{\\\\alpha \\\\rho} -  \\n\\t1/2 A_{\\\\rho \\\\sigma} k_{\\\\nu} A_{\\\\beta \\\\alpha} k_{\\\\mu} \\\\eta^{\\\\beta \\\\rho} \\\\eta^{\\\\sigma \\\\alpha} -  \\n\\t1/2 A_{\\\\rho \\\\sigma} A_{\\\\beta \\\\alpha} k_{\\\\nu} k_{\\\\mu} \\\\eta^{\\\\beta \\\\rho} \\\\eta^{\\\\sigma \\\\alpha} +  \\n\\t1/4 A_{\\\\alpha \\\\beta} k_{\\\\nu} A_{\\\\sigma \\\\rho} k_{\\\\mu} \\\\eta^{\\\\beta \\\\sigma} \\\\eta^{\\\\rho \\\\alpha};\\nget_component(ex, $t, t$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 16409402158754707338,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 5333473821107834285,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\algorithm{remove_zero_components(ex: Ex) -> Ex}{Remove all components of an expression that are equal to zero.}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\algorithm{remove_zero_components(ex: Ex) -> Ex}{Remove all components of an expression that are equal to zero.}\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 9384605071867656007,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"def remove_zero_components(ex):\\n\\t\\\"\\\"\\\"Removes all components of an expression that are equal to 0\\\"\\\"\\\"\\n\\tfor node in ex[r'\\\\equals']:\\n\\t\\tif get_lhs(node).head() == r'\\\\comma':\\n\\t\\t\\tif get_rhs(node).top().multiplier == 0:\\n\\t\\t\\t\\tnode.erase()\\n\\treturn ex\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 16820310678693438548,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 4375173011433589475,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 2725614521603779721,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"a_{i} a_{j}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}a_{i} a_{j}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 15596320799981300764,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 17539437833194849023,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\components_{i j}({{x, x} = (k)**2, {x, y} = k l, {x, z} = 0, {y, x} = k l, {y, y} = (l)**2, {y, z} = l m, {z, x} = 0, {z, y} = l m, {z, z} = (m)**2})\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\square{}_{i}{}_{j}\\\\left\\\\{\\\\begin{aligned}\\\\square{}_{x}{}_{x}& = {k}^{2}\\\\\\\\[-.5ex]\\n\\\\square{}_{x}{}_{y}& = k l\\\\\\\\[-.5ex]\\n\\\\square{}_{x}{}_{z}& = 0\\\\\\\\[-.5ex]\\n\\\\square{}_{y}{}_{x}& = k l\\\\\\\\[-.5ex]\\n\\\\square{}_{y}{}_{y}& = {l}^{2}\\\\\\\\[-.5ex]\\n\\\\square{}_{y}{}_{z}& = l m\\\\\\\\[-.5ex]\\n\\\\square{}_{z}{}_{x}& = 0\\\\\\\\[-.5ex]\\n\\\\square{}_{z}{}_{y}& = l m\\\\\\\\[-.5ex]\\n\\\\square{}_{z}{}_{z}& = {m}^{2}\\\\\\\\[-.5ex]\\n\\\\end{aligned}\\\\right.\\n\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9710818811944152525,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 11681310114441799183,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\components_{i j}({{x, x} = (k)**2, {x, y} = k l, {y, x} = k l, {y, y} = (l)**2, {y, z} = l m, {z, y} = l m, {z, z} = (m)**2})\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\square{}_{i}{}_{j}\\\\left\\\\{\\\\begin{aligned}\\\\square{}_{x}{}_{x}& = {k}^{2}\\\\\\\\[-.5ex]\\n\\\\square{}_{x}{}_{y}& = k l\\\\\\\\[-.5ex]\\n\\\\square{}_{y}{}_{x}& = k l\\\\\\\\[-.5ex]\\n\\\\square{}_{y}{}_{y}& = {l}^{2}\\\\\\\\[-.5ex]\\n\\\\square{}_{y}{}_{z}& = l m\\\\\\\\[-.5ex]\\n\\\\square{}_{z}{}_{y}& = l m\\\\\\\\[-.5ex]\\n\\\\square{}_{z}{}_{z}& = {m}^{2}\\\\\\\\[-.5ex]\\n\\\\end{aligned}\\\\right.\\n\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"ignore_on_import\": true,\n\t\t\t\"source\": \"{x, y, z}::Coordinate.\\n{i, j}::Indices(values={x, y, z}, position=fixed).\\nex := a_{i}a_{j};\\nevaluate(ex, $a_{x} = k, a_{y} = l, a_{z} = m$)\\nsubstitute(ex, $k m -> 0$);\\nremove_zero_components(ex);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 2548545959295068830,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 13138241579944557857,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\algorithm{components_to_subrule(ex: Ex) -> Ex}{Turn a component expression into a set of substitution rules}\\n\\nThe \\\\algo{evaluate} algorithm evaluates the component values of a tensor expression, and returns this in the form of an anonymous tensor component expression. This function turns such an expression into a set of substitution rules.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\algorithm{components_to_subrule(ex: Ex) -> Ex}{Turn a component expression into a set of substitution rules}\\n\\nThe \\\\algo{evaluate} algorithm evaluates the component values of a tensor expression, and returns this in the form of an anonymous tensor component expression. This function turns such an expression into a set of substitution rules.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 3321195237657858341,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"def components_to_subrule(ex):\\n\\tassert ex.top().name == r\\\"\\\\equals\\\", \\\"components_to_subrules requires an equation type expression\\\"\\n\\tres = Ex(r\\\"\\\\comma\\\")\\n\\n\\tcomponents = ex[1]\\n\\tindices = [index.name for index in components.top().indices()]\\n\\tfor rule in components[r\\\"\\\\equals\\\"]:\\n\\t\\tcoordinates = [index.name for index in get_lhs(rule).top().args()]\\n\\t\\t# Replace indices of lhs with component coordinates\\n\\t\\tpat = ex[0]\\n\\t\\tfor index, coordinate in zip(indices, coordinates):\\n\\t\\t\\tfor node in pat[index]:\\n\\t\\t\\t\\t# Ensure we've hit an index\\n\\t\\t\\t\\tif node.parent_rel == parent_rel_t.super or node.parent_rel == parent_rel_t.sub:\\n\\t\\t\\t\\t\\tnode.name = coordinate\\n\\t\\t\\t\\t\\tbreak\\n\\t\\t\\telse:\\n\\t\\t\\t\\traise RuntimeError(\\\"could not find index for coordinate substitution\\\")\\n\\t\\tfilledrule = Ex(r\\\"\\\\arrow\\\")\\n\\t\\tfilledrule.top().append_child(pat)\\n\\t\\tfilledrule.top().append_child(get_rhs(rule))\\n\\t\\tres.top().append_child(filledrule)\\n\\treturn res\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 3334462144877032844,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 7640103236893243329,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 2627810145891272135,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"b_{i j} = a_{i} a_{j}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}b_{i j} = a_{i} a_{j}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 7085476904939279437,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 14912669988470921544,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"b_{i j} = \\\\components_{i j}({{x, x} = (k)**2, {x, y} = k l, {x, z} = k m, {y, x} = k l, {y, y} = (l)**2, {y, z} = l m, {z, x} = k m, {z, y} = l m, {z, z} = (m)**2})\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}b_{i j} = \\\\square{}_{i}{}_{j}\\\\left\\\\{\\\\begin{aligned}\\\\square{}_{x}{}_{x}& = {k}^{2}\\\\\\\\[-.5ex]\\n\\\\square{}_{x}{}_{y}& = k l\\\\\\\\[-.5ex]\\n\\\\square{}_{x}{}_{z}& = k m\\\\\\\\[-.5ex]\\n\\\\square{}_{y}{}_{x}& = k l\\\\\\\\[-.5ex]\\n\\\\square{}_{y}{}_{y}& = {l}^{2}\\\\\\\\[-.5ex]\\n\\\\square{}_{y}{}_{z}& = l m\\\\\\\\[-.5ex]\\n\\\\square{}_{z}{}_{x}& = k m\\\\\\\\[-.5ex]\\n\\\\square{}_{z}{}_{y}& = l m\\\\\\\\[-.5ex]\\n\\\\square{}_{z}{}_{z}& = {m}^{2}\\\\\\\\[-.5ex]\\n\\\\end{aligned}\\\\right.\\n\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 15806421466316692092,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 17702748017509995526,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"{b_{x x} -> (k)**2, b_{x y} -> k l, b_{x z} -> k m, b_{y x} -> k l, b_{y y} -> (l)**2, b_{y z} -> l m, b_{z x} -> k m, b_{z y} -> l m, b_{z z} -> (m)**2}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\left[b_{x x} \\\\rightarrow {k}^{2},~\\\\discretionary{}{}{} b_{x y} \\\\rightarrow k l,~\\\\discretionary{}{}{} b_{x z} \\\\rightarrow k m,~\\\\discretionary{}{}{} b_{y x} \\\\rightarrow k l,~\\\\discretionary{}{}{} b_{y y} \\\\rightarrow {l}^{2},~\\\\discretionary{}{}{} b_{y z} \\\\rightarrow l m,~\\\\discretionary{}{}{} b_{z x} \\\\rightarrow k m,~\\\\discretionary{}{}{} b_{z y} \\\\rightarrow l m,~\\\\discretionary{}{}{} b_{z z} \\\\rightarrow {m}^{2}\\\\right]\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"ignore_on_import\": true,\n\t\t\t\"source\": \"{x, y, z}::Coordinate.\\n{i, j}::Indices(values={x, y, z}, position=fixed).\\nex := b_{i j} = a_{i}a_{j};\\nevaluate(ex, $a_{x} = k, a_{y} = l, a_{z} = m$, rhsonly=True);\\n# substitute(ex, $k m -> 0$);\\ncomponents_to_subrule(ex);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 616193830461043874,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"\"\n\t\t}\n\t],\n\t\"description\": \"Cadabra JSON notebook format\",\n\t\"flags\": {\n\t\t\"hide_input_cells\": false\n\t},\n\t\"version\": 1.0\n}\n"
  },
  {
    "path": "core/packages/cdb/core/manip.cnb",
    "content": "{\n\t\"cell_id\": 15268771084326197047,\n\t\"cells\": [\n\t\t{\n\t\t\t\"cell_id\": 17635366168350014876,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 7159893924636242532,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\package{cdb.core.manip}{Manipulating equations, inequalities and similar expressions}\\n\\nThis package contains various helper functions to manipulate expressions in elementary ways, e.g.~moving terms\\naround or multiplying sides of an expression by a factor. In order to use this package, import it with the standard\\nPython import statement: if you do \\\\verb|import cdb.core.manip as manip| then e.g.~the \\\\verb|isolate| function is available as\\n\\\\verb|manip.isolate|.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\package{cdb.core.manip}{Manipulating equations, inequalities and similar expressions}\\n\\nThis package contains various helper functions to manipulate expressions in elementary ways, e.g.~moving terms\\naround or multiplying sides of an expression by a factor. In order to use this package, import it with the standard\\nPython import statement: if you do \\\\verb|import cdb.core.manip as manip| then e.g.~the \\\\verb|isolate| function is available as\\n\\\\verb|manip.isolate|.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 219606435123158463,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"from cdb.utils.node import nth_arg, n_args\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 7835392520042021345,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 3764403960157589060,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\algorithm{eq_to_subrule(ex: Ex) -> Ex}{Create substitution rule from an equation.}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\algorithm{eq_to_subrule(ex: Ex) -> Ex}{Create substitution rule from an equation.}\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 9954784203102623338,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"def eq_to_subrule(ex):\\n\\t\\\"\\\"\\\"Turns $a = b$ into $b -> a$\\\"\\\"\\\"\\n\\tif ex.head() != r'\\\\equals':\\n\\t\\traise Exception(\\\"eq_to_subrule called on expression which is not an equation\\\")\\n\\tif n_args(ex.top()) != 2:\\n\\t\\traise Exception(\\\"eq_to_subrule called on expression whose top node contains {} arguments, 2 required\\\".format(n_args(ex.top())))\\n\\n\\t# Get the lhs and rhs\\n\\tfor i, arg in enumerate(ex.top().args()):\\n\\t\\tif i == 0:\\n\\t\\t\\tlhs = $@(arg)$\\n\\t\\telif i == 1:\\n\\t\\t\\trhs = $@(arg)$\\n\\n\\t# Substitute them into a subrule\\n\\treturn $@(rhs) -> @(lhs)$\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 9634307933222533368,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 6645472134591897231,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"Creates a substitution rule from an equation \\\\verb|Ex|.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"Creates a substitution rule from an equation \\\\verb|Ex|.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 9556965808134248954,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 1231767427432608563,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 2956203403061753577,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"b + c + d -> a\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}b+c+d \\\\rightarrow a\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"ignore_on_import\": true,\n\t\t\t\"source\": \"eq_to_subrule($a = b + c + d$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 7756973939992329781,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 12564986469045592293,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\algorithm{multiply_through(ex: Ex, factor: Ex, auto_distribute=False) -> Ex}{Multiply all terms by the same factor.}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\algorithm{multiply_through(ex: Ex, factor: Ex, auto_distribute=False) -> Ex}{Multiply all terms by the same factor.}\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 1501528717858725061,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"def multiply_through(ex, factor, auto_distribute = False):\\n\\t\\\"\\\"\\\"Multiplies all terms in ex by factor\\\"\\\"\\\"\\n\\tfor arg in ex.top().args():\\n\\t\\targ.replace($@(factor) @(arg)$)\\n\\tif auto_distribute:\\n\\t\\tdistribute(ex)\\n\\treturn ex\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 6901152875545504437,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 3831153165854597002,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"Multiplies all terms in \\\\verb|ex| by \\\\verb|factor|. If \\\\verb|auto_distribute| is \\\\verb|True|, distribute is called on the resulting expression.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"Multiplies all terms in \\\\verb|ex| by \\\\verb|factor|. If \\\\verb|auto_distribute| is \\\\verb|True|, distribute is called on the resulting expression.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 9575833646660580740,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 2887283422742923798,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 5607098118281175915,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"k (a + b) < k c\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}k \\\\left(a+b\\\\right) < k c\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"ignore_on_import\": true,\n\t\t\t\"source\": \"multiply_through($a+b < c$, $k$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 3396515398006428816,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 3396515398006428816,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\algorithm{add_through(ex: Ex, factor: Ex) -> Ex}{Add a factor to both sides of an equation.}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\algorithm{add_through(ex: Ex, factor: Ex) -> Ex}{Add a factor to both sides of an equation.}\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 544175776537438149,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"def add_through(ex, factor):\\n\\t\\\"\\\"\\\"Adds a factor to both sides of ex\\\"\\\"\\\"\\n\\tfor arg in ex.top().args():\\n\\t\\targ.replace($@(arg) + @(factor)$)\\n\\treturn ex\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 16915415318035386515,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9720663929603140956,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 10454479142087391198,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"A_{\\\\mu} B_{\\\\nu} + D_{\\\\mu \\\\nu} = C_{\\\\mu \\\\nu} + D_{\\\\mu \\\\nu}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}A_{\\\\mu} B_{\\\\nu}+D_{\\\\mu \\\\nu} = C_{\\\\mu \\\\nu}+D_{\\\\mu \\\\nu}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"ignore_on_import\": true,\n\t\t\t\"source\": \"add_through($A_{\\\\mu}B_{\\\\nu} = C_{\\\\mu \\\\nu}$, $D_{\\\\mu \\\\nu}$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 13652224870070875183,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 18204803698960052673,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\algorithm{apply_through(ex: Ex, op: Ex) -> Ex}{Apply an operator through both sides of an equation.}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\algorithm{apply_through(ex: Ex, op: Ex) -> Ex}{Apply an operator through both sides of an equation.}\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 7129671199504928557,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"def apply_through(ex, op):\\n\\tfor child in ex.top().children():\\n\\t\\tapp := @(op);\\n\\t\\tfor node in app[\\\"#\\\"]:\\n\\t\\t\\tnode.replace($@(child)$)\\n\\t\\tchild.replace($@(app)$)\\n\\treturn ex\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 1222096101185570042,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 17643016095692415648,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 17377967479870284885,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\partial(\\\\partial(x_{\\\\mu})) = \\\\partial(0)\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\partial\\\\left(\\\\partial\\\\left(x_{\\\\mu}\\\\right)\\\\right) = \\\\partial\\\\left(0\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"ignore_on_import\": true,\n\t\t\t\"source\": \"apply_through($\\\\partial{x_{\\\\mu}} = 0$, $\\\\partial{#}$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 3411326601020319930,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 2419666349840739992,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\algorithm{get_lhs(ex: Ex) -> Ex}{Return left-hand side of an expression}\\n\\nReturns the left hand side of an equation, inequality or expression whose top node contains two children. \"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\algorithm{get_lhs(ex: Ex) -> Ex}{Return left-hand side of an expression}\\n\\nReturns the left hand side of an equation, inequality or expression whose top node contains two children. \"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 5307119722135943631,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"def get_lhs(ex):\\n\\t\\\"\\\"\\\"Returns the left hand side of an equation, inequality, or expression whose top node contains two arguments\\\"\\\"\\\"\\n\\tif isinstance(ex, Ex):\\n\\t\\tex = ex.top()\\n\\tif n_args(ex) != 2:\\n\\t\\traise Exception(\\\"get_lhs called on expression whose top node contains {} arguments, 2 required\\\".format(n_args(ex)))\\n\\treturn nth_arg(ex, 0).ex()\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 5233847834690152710,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 3168203333233232823,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 8343678120098024622,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"a\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}a\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"ignore_on_import\": true,\n\t\t\t\"source\": \"get_lhs($a=b$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 9795365978364924824,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 14660442160948713050,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\algorithm{get_rhs(ex: Ex) -> Ex}{Return right-hand side of an expression}\\n\\nReturns the right-hand side of an equation, inequality or expression whose top node contains two children. \"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\algorithm{get_rhs(ex: Ex) -> Ex}{Return right-hand side of an expression}\\n\\nReturns the right-hand side of an equation, inequality or expression whose top node contains two children. \"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 11895343331560033174,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"def get_rhs(ex):\\n\\t\\\"\\\"\\\"Returns the right hand side of an equation, inequality, or expression whose top node contains two arguments\\\"\\\"\\\"\\n\\tif isinstance(ex, Ex):\\n\\t\\tex = ex.top()\\n\\tif n_args(ex) != 2:\\n\\t\\traise Exception(\\\"get_rhs called on expression whose top node contains {} arguments, 2 required\\\".format(n_args(ex)))\\n\\treturn nth_arg(ex, 1).ex()\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 8733667829887500319,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 11709535240682201585,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 13877803436156210079,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"b\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}b\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"ignore_on_import\": true,\n\t\t\t\"source\": \"get_rhs($a=b$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 11158988917891525944,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 5905171491089882952,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\algorithm{swap_sides(ex: Ex) -> Ex}{Swap the left and right-hand sides of an expression.}\\n\\n\\tSwaps the two sides of an equation, inequality or expression whose top node contains two children. Inequalities will flip as appropriate. \\n\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\algorithm{swap_sides(ex: Ex) -> Ex}{Swap the left and right-hand sides of an expression.}\\n\\n\\tSwaps the two sides of an equation, inequality or expression whose top node contains two children. Inequalities will flip as appropriate. \\n\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 8794265449613865573,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"def swap_sides(ex):\\n\\t\\\"\\\"\\\"Swaps the left and right hand sides of an equation, inequality or expression whose top node contains two arguments\\\"\\\"\\\"\\n\\tif n_args(ex.top()) != 2:\\n\\t\\traise Exception(\\\"swap_sides called on expression whose top node contains {} arguments, 2 required\\\".format(n_args(ex.top())))\\n\\n\\t# Get the lhs and rhs\\n\\tlhs = get_lhs(ex)\\n\\trhs = get_rhs(ex)\\n\\n\\t# Iterate through both sides of the equation and perform substitution\\n\\tfor i, arg in enumerate(ex.top().args()):\\n\\t\\tif i == 0:\\n\\t\\t\\targ.replace(rhs)\\n\\t\\tif i == 1:\\n\\t\\t\\targ.replace(lhs)\\n\\n\\t# Swap inequalities\\n\\tif ex.head() == r'\\\\less':\\n\\t\\tex.top().name = r'\\\\greater'\\n\\telif ex.head() == r'\\\\greater':\\n\\t\\tex.top().name = r'\\\\less'\\n\\n\\treturn ex\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 8255195960622299062,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 14853923507974116134,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\algorithm{get_factor(node: ExNode, term: Ex) -> Ex}{Get all multiplicative factors of term in node}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\algorithm{get_factor(node: ExNode, term: Ex) -> Ex}{Get all multiplicative factors of term in node}\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 12899144978785485126,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"def get_factor(node, term):\\n\\t\\\"\\\"\\\"If node is a product containing term, then return node without term. Otherwise, return None\\\"\\\"\\\"\\n\\tif term.matches(node):\\n\\t\\treturn substitute($@(node)$, $@(term) -> 1$)\\n\\n\\tif node.name == r'\\\\prod':\\n\\t\\tret = $@(node)$\\n\\t\\tfor elem in ret.top().children():\\n\\t\\t\\tif term.matches(elem):\\n\\t\\t\\t\\tfactor = elem.multiplier\\n\\t\\t\\t\\telem.erase()\\n\\t\\t\\t\\tret.top().multiplier *= factor\\n\\t\\t\\t\\treturn ret\\n\\n\\treturn None\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 6640730744419052590,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 2447757695444069929,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 11353889507680660796,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \" 3/2 \"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\frac{3}{2}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"ignore_on_import\": true,\n\t\t\t\"source\": \"get_factor($3/2 R$.top(), $R$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 16431542648255979031,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 30848241778554462,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\algorithm{get_basis_component(ex: Ex, basis: Ex) -> Ex}{Returns the multiplicative coefficients of \\\\texttt{basis} in \\\\texttt{ex}}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"\\\\algorithm{get_basis_component(ex: Ex, basis: Ex) -> Ex}{Returns the multiplicative coefficients of \\\\texttt{basis} in \\\\texttt{ex}}\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 13837484073210088531,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"def get_basis_component(ex, basis):\\n\\tcoeff = take_match($@(ex)$, $@(basis) Q??$)\\n\\tsubstitute(coeff, $@(basis) -> 1$)\\n\\tif ex == coeff:\\n\\t\\treturn $0$\\n\\telse:\\n\\t\\treturn $@(coeff)$\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 9594057414621049635,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 16102671816984278626,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 16215812578025033456,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"A_{\\\\mu \\\\nu} \\\\exp(i k_{\\\\mu} x^{\\\\mu}) + B_{\\\\mu \\\\nu} \\\\exp(-i k_{\\\\mu} x^{\\\\mu})\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}A_{\\\\mu \\\\nu} \\\\exp\\\\left(i k_{\\\\mu} x^{\\\\mu}\\\\right)+B_{\\\\mu \\\\nu} \\\\exp\\\\left(-i k_{\\\\mu} x^{\\\\mu}\\\\right)\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 3121979421771299112,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 5653504327284017440,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"B_{\\\\mu \\\\nu}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}B_{\\\\mu \\\\nu}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 724265581768911366,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 17952817033461765105,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\exp(i k_{\\\\mu} x^{\\\\mu})\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\exp\\\\left(i k_{\\\\mu} x^{\\\\mu}\\\\right)\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 11823143836272174168,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 2203812047172188274,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"A_{\\\\mu \\\\nu} \\\\exp(i x^{\\\\mu}) + B_{\\\\mu \\\\nu} \\\\exp(-i x^{\\\\mu})\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}A_{\\\\mu \\\\nu} \\\\exp\\\\left(i x^{\\\\mu}\\\\right)+B_{\\\\mu \\\\nu} \\\\exp\\\\left(-i x^{\\\\mu}\\\\right)\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 2563792950653075125,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 2527418973058329912,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"0\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}0\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"ignore_on_import\": true,\n\t\t\t\"source\": \"test := A_{\\\\mu\\\\nu} \\\\exp(i*k_\\\\mu*x^{\\\\mu})+B_{\\\\mu\\\\nu} \\\\exp(-i*k_\\\\mu*x^{\\\\mu});\\nget_basis_component(test, $\\\\exp(-i*k_\\\\mu*x^{\\\\mu})$);\\nget_basis_component(test, $A_{\\\\mu\\\\nu}$);\\nget_basis_component(test, $k_{\\\\mu}$);\\nget_basis_component(test, $C_{\\\\mu\\\\nu}$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 560186604802672427,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 4386267152773659670,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\algorithm{to_rhs(ex: Ex, *parts: Ex..., match_type: str = \\\"all\\\") -> Ex}{Move the indicated term of the expression to the right-hand side.}\\n\\n\\tIf \\\\verb|ex| is an equation or inequality which contains \\\\verb|part| on its left hand side, then moves all \\\\verb|parts| to the right hand side. \\n\\t\\\\verb|match_type| can be either \\\\verb|all| which will move all terms which contain each part as a factor, \\\\verb|numeric| which will move terms up to a numeric prefactor or \\n     \\\\verb|exact| which will only move the term if the subtree matches exactly.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\algorithm{to_rhs(ex: Ex, *parts: Ex..., match_type: str = \\\"all\\\") -> Ex}{Move the indicated term of the expression to the right-hand side.}\\n\\n\\tIf \\\\verb|ex| is an equation or inequality which contains \\\\verb|part| on its left hand side, then moves all \\\\verb|parts| to the right hand side. \\n\\t\\\\verb|match_type| can be either \\\\verb|all| which will move all terms which contain each part as a factor, \\\\verb|numeric| which will move terms up to a numeric prefactor or \\n     \\\\verb|exact| which will only move the term if the subtree matches exactly.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 2183163939635232499,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"def to_rhs(ex, *parts, match_type = \\\"all\\\"):\\n\\t\\\"\\\"\\\"Moves part from the left to the right hand side of an equation or inequality\\\"\\\"\\\"\\n\\n\\tassert(ex.top().name in [r'\\\\equals', r'\\\\less', r'\\\\greater'])\\n\\tassert(n_args(ex.top()) == 2)\\n\\n\\tif match_type == \\\"exact\\\":\\n\\t\\tcomp = lambda ex, node: ex == $@(node)$\\n\\telif match_type == \\\"numeric\\\":\\n\\t\\tcomp = lambda ex, node: ex.matches(node)\\n\\telif match_type == \\\"all\\\":\\n\\t\\tcomp = lambda ex, node: get_factor(node, ex) is not None\\n\\n\\tlhs = nth_arg(ex.top(), 0)\\n\\trhs = nth_arg(ex.top(), 1)\\n\\n\\tif len(parts) == 0:\\n\\t\\tterms = $@(rhs) - @(lhs)$\\n\\t\\tlhs.replace($0$)\\n\\t\\trhs.replace(terms)\\n\\telse:\\n\\t\\tfor part in parts:\\n\\t\\t\\tterms = $@(rhs)$\\n\\t\\t\\tif comp(part, lhs):\\n\\t\\t\\t\\tterms -= lhs\\n\\t\\t\\t\\tlhs.replace($0$)\\n\\t\\t\\telif lhs.name == r'\\\\sum':\\n\\t\\t\\t\\tfor i in reversed(range(n_args(lhs))):\\n\\t\\t\\t\\t\\tnode = nth_arg(lhs, i)\\n\\t\\t\\t\\t\\tif comp(part, node):\\n\\t\\t\\t\\t\\t\\tterms -= node\\n\\t\\t\\t\\t\\t\\tif n_args(lhs) == 1:\\n\\t\\t\\t\\t\\t\\t\\tnode.replace($0$)\\n\\t\\t\\t\\t\\t\\telse:\\n\\t\\t\\t\\t\\t\\t\\tnode.erase()\\n\\t\\t\\trhs.replace(terms)\\n\\n\\treturn ex\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 11883098882754637540,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 13131403568144277521,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 9493999741510812343,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"0 = c + d-2a-b-j b-k b\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}0 = c+d-2a-b-j b-k b\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"ignore_on_import\": true,\n\t\t\t\"source\": \"to_rhs($2a+b+j*b+k*b = c+d$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 9319840788300028258,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 15999046563881551767,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 17760236547502669845,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"-\\\\partial_{\\\\alpha}(b_{\\\\beta})-\\\\partial_{\\\\beta}(a_{\\\\alpha}) = 0\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}-\\\\partial_{\\\\alpha}{b_{\\\\beta}}-\\\\partial_{\\\\beta}{a_{\\\\alpha}} = 0\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"ignore_on_import\": true,\n\t\t\t\"source\": \"\\\\partial{#}::Derivative.\\nto_rhs($-\\\\partial_{\\\\alpha}{b_{\\\\beta}} - \\\\partial_{\\\\beta}{a_{\\\\alpha}} = 0$, $\\\\partial_{\\\\alpha}{b_{\\\\beta}}$, match_type=\\\"exact\\\");\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 831589588542616074,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 5886747838826691399,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\algorithm{to_lhs(ex: Ex, *parts: Ex..., match_type: str = \\\"all\\\") -> Ex}{Move the indicated term of the expression to the left-hand side.}\\n\\nComplement of \\\\algo{to_rhs}.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\algorithm{to_lhs(ex: Ex, *parts: Ex..., match_type: str = \\\"all\\\") -> Ex}{Move the indicated term of the expression to the left-hand side.}\\n\\nComplement of \\\\algo{to_rhs}.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 5674786013392212620,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"def to_lhs(ex, *parts, match_type=\\\"all\\\"):\\n\\t\\\"\\\"\\\"Moves part from the right to the left hand side of an equation or inequality\\\"\\\"\\\"\\n\\t# to_lhs is the same as to_rhs called on an equation with the sides swapped ;)\\n\\tswap_sides(ex)\\n\\tto_rhs(ex, *parts, match_type=match_type)\\n\\tswap_sides(ex)\\t\\n\\treturn ex\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 4956212081149797277,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 15571824009976413118,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\algorithm{isolate()}{Isolates a term on the left hand side of an equation or inequality}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\algorithm{isolate()}{Isolates a term on the left hand side of an equation or inequality}\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 15010735023331358315,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"def isolate(ex, term, divide_through = True):\\n\\t\\\"\\\"\\\"Isolates a term on the left hand side of an equation or inequality\\\"\\\"\\\"\\n\\tassert(ex.top().name in [r'\\\\equals', r'\\\\less', r'\\\\greater'])\\n\\tassert(n_args(ex.top()) == 2)\\n\\n\\t# Move everything to the rhs\\n\\tto_rhs(ex)\\n\\tlhs = nth_arg(ex.top(), 0)\\n\\trhs = nth_arg(ex.top(), 1)\\n\\n\\t# Gather all terms containing the isolating term\\n\\tfactors = $0$\\n\\tif get_factor(rhs, term) is not None:\\n\\t\\tfactors -= get_factor(rhs, term)\\n\\t\\trhs.replace($0$)\\n\\telif rhs.name == r'\\\\sum':\\n\\t\\tfor i in reversed(range(n_args(rhs))):\\n\\t\\t\\tnode = nth_arg(rhs, i)\\n\\t\\t\\tfactor = get_factor(node, term)\\n\\t\\t\\tif factor is not None:\\n\\t\\t\\t\\tfactors -= factor\\n\\t\\t\\t\\tif n_args(rhs) == 1:\\n\\t\\t\\t\\t\\tnode.replace($0$)\\n\\t\\t\\t\\telse:\\n\\t\\t\\t\\t\\tnode.erase()\\n\\t# Move the isolated term over to the left hand side\\n\\tif divide_through:\\n\\t\\tlhs.replace($@(term)$)\\n\\t\\trhs.replace($\\\\frac{@(rhs)}{@(factors)}$)\\n\\telse:\\n\\t\\tlhs.replace($@(term) @(factors)$)\\n\\treturn ex\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 1368746495472243320,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 2873619635301860056,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 13925632780223323022,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"2a +  1/2 a k-b = c a + b k + a-4\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}2a+\\\\frac{1}{2}a k-b = c a+b k+a-4\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 3371428283246160850,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 11163140055737119195,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"a = (b k-4 + b) (1-c)**(-1)\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}a = \\\\left(b k-4+b\\\\right) {\\\\left(1-c\\\\right)}^{-1}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 18420991104162350602,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 990642930475677695,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \" -  3/2 R + 5\\\\Lambda = T \\\\kappa\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{} - \\\\frac{3}{2}R+5\\\\Lambda = T \\\\kappa\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 14637382425423859095,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 17517195226234096204,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"R =  -  2/3 T \\\\kappa +  10/3 \\\\Lambda\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}R =  - \\\\frac{2}{3}T \\\\kappa+\\\\frac{10}{3}\\\\Lambda\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"ignore_on_import\": true,\n\t\t\t\"source\": \"ex := 2a + 1/2 a * k - b = c * a + b * k + a - 4;\\nisolate(ex, $a$, True);\\nex2 := -3/2 R + 5\\\\Lambda = T\\\\kappa;\\nisolate(ex2, $R$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 772577804236751633,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"\"\n\t\t}\n\t],\n\t\"description\": \"Cadabra JSON notebook format\",\n\t\"version\": 1.0\n}\n"
  },
  {
    "path": "core/packages/cdb/core/solve.cnb",
    "content": "{\n\t\"cells\" : \n\t[\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1\n}\n"
  },
  {
    "path": "core/packages/cdb/core/trace.cnb",
    "content": "{\n\t\"cell_id\": 4804704193557178778,\n\t\"cells\": [\n\t\t{\n\t\t\t\"cell_id\": 8047503705196211138,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 10083330039593489527,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\package{cdb.core.trace}{Manipulating Trace objects}\\n\\nThis package defines functionality for manipulating nodes and expressions which define the \\\\verb|Trace| property\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\package{cdb.core.trace}{Manipulating Trace objects}\\n\\nThis package defines functionality for manipulating nodes and expressions which define the \\\\verb|Trace| property\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 17733580437840025116,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"from cdb.utils.node import n_indices, nth_child, empty_sum\\nfrom cdb.utils.develop import inherit_kernel\\nfrom collections import defaultdict\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 8325441738150275359,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 8330453056931653295,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\algorithm{combine_traces(ex: Ex) -> Ex}{Combine separate trace nodes into one sum.}\\n\\nThis will only move nodes which it classifies as safe to do this on, checking that no objects which are non-scalar will be pulled inside the new trace node. If multiple nodes\\nwith different names, but the Trace property defined, are found then they will be combined separately.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\algorithm{combine_traces(ex: Ex) -> Ex}{Combine separate trace nodes into one sum.}\\n\\nThis will only move nodes which it classifies as safe to do this on, checking that no objects which are non-scalar will be pulled inside the new trace node. If multiple nodes\\nwith different names, but the Trace property defined, are found then they will be combined separately.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 12226727171243122299,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"def combine_traces(ex):\\n\\t__cdbkernel__ = inherit_kernel()\\n\\tdef recurse(node):\\n\\t\\tnonlocal __cdbkernel__\\n\\t\\tif node.name == \\\"\\\\\\\\sum\\\":\\n\\t\\t\\t# Enumerate all trace terms\\n\\t\\t\\tnodes = defaultdict(list)\\n\\t\\t\\tfor i, child in enumerate(node.children()):\\n\\t\\t\\t\\tif child.name == \\\"\\\\\\\\prod\\\":\\n\\t\\t\\t\\t\\t# Only allow Trace nodes with scalars outside\\n\\t\\t\\t\\t\\tcan_move = False\\n\\t\\t\\t\\t\\tname = \\\"\\\"\\n\\t\\t\\t\\t\\tfor obj in child.children():\\n\\t\\t\\t\\t\\t\\tif Trace.get(obj) is not None:\\n\\t\\t\\t\\t\\t\\t\\tif can_move: # Already hit a Trace node, can't move\\n\\t\\t\\t\\t\\t\\t\\t\\tbreak\\n\\t\\t\\t\\t\\t\\t\\tname = obj.name\\n\\t\\t\\t\\t\\t\\t\\tcan_move = True\\n\\t\\t\\t\\t\\t\\telif n_indices(obj) != 0 or ImplicitIndex.get(obj) is not None:\\n\\t\\t\\t\\t\\t\\t\\tcan_move = False\\n\\t\\t\\t\\t\\t\\t\\tbreak\\n\\t\\t\\t\\t\\tif can_move:\\n\\t\\t\\t\\t\\t\\tnodes[obj.name].append(i)\\n\\t\\t\\t\\telif Trace.get(child) is not None:\\n\\t\\t\\t\\t\\tnodes[child.name].append(i)\\n\\n\\t\\t\\t# Combine traces\\n\\t\\t\\tfor t in nodes:\\n\\t\\t\\t\\tnew_node = node.append_child(Ex(t + \\\"{}\\\")).append_child(empty_sum())\\n\\t\\t\\t\\tfor i, child in enumerate(node.children()):\\n\\t\\t\\t\\t\\tif i in nodes[t]:\\n\\t\\t\\t\\t\\t\\tnew_term = new_node.append_child(child)\\n\\t\\t\\t\\t\\t\\t# Remove the existing Trace\\n\\t\\t\\t\\t\\t\\tif new_term.name == \\\"\\\\\\\\prod\\\":\\n\\t\\t\\t\\t\\t\\t\\tfor obj in new_term.children():\\n\\t\\t\\t\\t\\t\\t\\t\\tif Trace.get(obj) is not None:\\n\\t\\t\\t\\t\\t\\t\\t\\t\\tr = nth_child(obj, 0)\\n\\t\\t\\t\\t\\t\\t\\t\\t\\tr := @(r):\\n\\t\\t\\t\\t\\t\\t\\t\\t\\tr *= Ex(obj.multiplier)\\n\\t\\t\\t\\t\\t\\t\\t\\t\\tobj = obj.replace(r)\\n\\t\\t\\t\\t\\t\\telif Trace.get(new_term) is not None:\\n\\t\\t\\t\\t\\t\\t\\tr = nth_child(new_term, 0)\\n\\t\\t\\t\\t\\t\\t\\tr := @(r):\\n\\t\\t\\t\\t\\t\\t\\tr *= Ex(new_term.multiplier)\\n\\t\\t\\t\\t\\t\\t\\tnew_term = new_term.replace(r)\\n\\n\\t\\t\\t# Remove old terms\\n\\t\\t\\tindices = list(i for t in nodes for i in nodes[t])\\n\\t\\t\\tfor i, child in enumerate(node.children()):\\n\\t\\t\\t\\tif i in indices:\\n\\t\\t\\t\\t\\tchild.erase()\\n\\t\\t\\t\\n\\t\\telse:\\n\\t\\t\\t# Go deeper\\n\\t\\t\\tfor child in node.children():\\n\\t\\t\\t\\trecurse(child)\\n\\trecurse(ex.top())\\n\\tex.cleanup()\\n\\treturn ex\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 1491461674503604418,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 1302745897165290177,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"output\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}Test 1 passed\\n\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"ignore_on_import\": true,\n\t\t\t\"source\": \"def test01():\\n\\t__cdbkernel__ = create_scope()\\n\\tTr{#}::Trace.\\n\\t{A, B, C, D}::NonCommuting.\\n\\tex := Tr{A B C D + C D A B + B C D A} - 2 * Tr{3 * D A B C}:\\n\\tcombine_traces(ex)\\n\\tassert ex == $Tr{A B C D + C D A B + B C D A - 6 D A B C}$\\n\\tprint(\\\"Test 1 passed\\\")\\ntest01()\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 2285946178549455777,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"\"\n\t\t}\n\t],\n\t\"description\": \"Cadabra JSON notebook format\",\n\t\"version\": 1.0\n}\n"
  },
  {
    "path": "core/packages/cdb/gauge_theory/instantons.cnb",
    "content": "{\n\t\"cell_id\": 1093201800894685878,\n\t\"cells\": [\n\t\t{\n\t\t\t\"cell_id\": 9551562792113345335,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 10193244651179153720,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"This is work-in-progress.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"This is work-in-progress.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 13378244708702775521,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"{i,j,k,l,m,n,q}::Indices(space).\\n{i,j,k,l,m,n,q}::Integer(1..4).\\n{a,b,c,d,e,f,g}::Indices(group).\\n{a,b,c,d,e,f,g}::Integer(1..3).\\n\\\\epsilon^{a b c}::EpsilonTensor.\\n\\\\epsilon_{i j k l}::EpsilonTensor.\\n\\\\delta_{i j}::KroneckerDelta.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 14244909242721652665,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"def thooft_symbols():\\n   \\\\eta^{a}_{i j}::TableauSymmetry(shape={1,1}, indices={1,2}).\\n   rl := { \\\\eta^{a}_{i j} \\\\eta^{a}_{k l} -> \\\\delta_{i k} \\\\delta_{j l} - \\\\delta_{i l} \\\\delta_{k j} + \\\\epsilon_{i j k l}, \\n           \\\\epsilon^{a b c} \\\\eta^{b}_{i k} \\\\eta^{c}_{j l} -> -\\\\delta_{i j} \\\\eta^{a}_{k l} - \\\\delta_{k l} \\\\eta^{a}_{i j} \\n               + \\\\delta_{i l} \\\\eta^{a}_{k j} + \\\\delta_{k j} \\\\eta^{a}_{i l},\\n           \\\\eta^{a}_{i k} \\\\eta^{b}_{k j} -> -\\\\delta^{a b} \\\\delta_{i j} + \\\\epsilon^{a b c} \\\\eta^{c}_{i j}, \\n           \\\\epsilon_{i j l k} \\\\eta^{a}_{l m} -> - \\\\delta_{i m} \\\\eta^{a}_{j k} - \\\\delta_{j m} \\\\eta^{a}_{k i} - \\\\delta_{k m} \\\\eta^{a}_{i j},\\n           \\\\epsilon_{i j k l} \\\\eta^{a}_{k l} -> - 2 \\\\eta^{a}_{i j} \\n         }:\\n   return rl\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 12233334157585209624,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 5794629913266740770,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 16176927491324925232,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\eta^{a}_{i j} \\\\eta^{a}_{k l}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\eta^{a}\\\\,_{i j} \\\\eta^{a}\\\\,_{k l}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 8908317684532789837,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 5106167770278682541,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"{\\\\eta^{a}_{i j} \\\\eta^{a}_{k l} -> \\\\delta_{i k} \\\\delta_{j l}-\\\\delta_{i l} \\\\delta_{k j} + \\\\epsilon_{i j k l}, \\\\epsilon^{a b c} \\\\eta^{b}_{i k} \\\\eta^{c}_{j l} -> -\\\\delta_{i j} \\\\eta^{a}_{k l}-\\\\delta_{k l} \\\\eta^{a}_{i j} + \\\\delta_{i l} \\\\eta^{a}_{k j} + \\\\delta_{k j} \\\\eta^{a}_{i l}, \\\\eta^{a}_{i k} \\\\eta^{b}_{k j} -> -\\\\delta^{a b} \\\\delta_{i j} + \\\\epsilon^{a b c} \\\\eta^{c}_{i j}, \\\\epsilon_{i j l k} \\\\eta^{a}_{l m} -> -\\\\delta_{i m} \\\\eta^{a}_{j k}-\\\\delta_{j m} \\\\eta^{a}_{k i}-\\\\delta_{k m} \\\\eta^{a}_{i j}, \\\\epsilon_{i j k l} \\\\eta^{a}_{k l} -> -2\\\\eta^{a}_{i j}}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\left[\\\\eta^{a}\\\\,_{i j} \\\\eta^{a}\\\\,_{k l} \\\\rightarrow \\\\delta_{i k} \\\\delta_{j l}-\\\\delta_{i l} \\\\delta_{k j}+\\\\epsilon_{i j k l},~\\\\discretionary{}{}{} \\\\epsilon^{a b c} \\\\eta^{b}\\\\,_{i k} \\\\eta^{c}\\\\,_{j l} \\\\rightarrow -\\\\delta_{i j} \\\\eta^{a}\\\\,_{k l}-\\\\delta_{k l} \\\\eta^{a}\\\\,_{i j}+\\\\delta_{i l} \\\\eta^{a}\\\\,_{k j}+\\\\delta_{k j} \\\\eta^{a}\\\\,_{i l},~\\\\discretionary{}{}{} \\\\eta^{a}\\\\,_{i k} \\\\eta^{b}\\\\,_{k j} \\\\rightarrow -\\\\delta^{a b} \\\\delta_{i j}+\\\\epsilon^{a b c} \\\\eta^{c}\\\\,_{i j},~\\\\discretionary{}{}{} \\\\epsilon_{i j l k} \\\\eta^{a}\\\\,_{l m} \\\\rightarrow -\\\\delta_{i m} \\\\eta^{a}\\\\,_{j k}-\\\\delta_{j m} \\\\eta^{a}\\\\,_{k i}-\\\\delta_{k m} \\\\eta^{a}\\\\,_{i j},~\\\\discretionary{}{}{} \\\\epsilon_{i j k l} \\\\eta^{a}\\\\,_{k l} \\\\rightarrow -2\\\\eta^{a}\\\\,_{i j}\\\\right]\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 1907482009801816494,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 7793857489603711042,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\delta_{i k} \\\\delta_{j l}-\\\\delta_{i l} \\\\delta_{k j} + \\\\epsilon_{i j k l}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\delta_{i k} \\\\delta_{j l}-\\\\delta_{i l} \\\\delta_{k j}+\\\\epsilon_{i j k l}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"ignore_on_import\": true,\n\t\t\t\"source\": \"ex:=\\\\eta^{a}_{i j} \\\\eta^{a}_{k l};\\nsubstitute(ex, thooft_symbols());\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 18158312902258495406,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"\"\n\t\t}\n\t],\n\t\"description\": \"Cadabra JSON notebook format\",\n\t\"version\": 1.0\n}\n"
  },
  {
    "path": "core/packages/cdb/graphics/plot.cnb",
    "content": "{\n\t\"cell_id\": 5758669193656196492,\n\t\"cells\": [\n\t\t{\n\t\t\t\"cell_id\": 10933180705315449745,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 6243630859011953106,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\package{cdb.graphics.plot}{Plotting of functions}\\nFunctionality to make plots of functions. Currently supports two backends, matplotlib and plotly.\\nSelect which one of these you want by using the \\\\verb|set_plot_backend| function with argument\\n\\\\verb|Backend.MATPLOTLIB| (default) or \\\\verb|Backend.PLOTLY|.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\package{cdb.graphics.plot}{Plotting of functions}\\nFunctionality to make plots of functions. Currently supports two backends, matplotlib and plotly.\\nSelect which one of these you want by using the \\\\verb|set_plot_backend| function with argument\\n\\\\verb|Backend.MATPLOTLIB| (default) or \\\\verb|Backend.PLOTLY|.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 2557258518313563186,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"import numpy as np\\nimport enum\\nimport sys\\n\\nclass Backend(enum.Enum):\\n    MATPLOTLIB = \\\"matplotlib\\\"\\n    PLOTLY = \\\"plotly\\\"\\n\\n_backend = Backend.MATPLOTLIB\\n\\ndef set_plot_backend(backend: Backend):\\n    global _backend\\n    _backend = backend\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 13829488039530744102,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 4476840713489814492,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\algorithm{plot(ex: Ex, range: tuple, grid: bool, xlabel: str, ylabel: str, title: str, samples: int) -> plot}{Plot a function of one variable given the range.}\\n\\nThe function should be a Cadabra expression (so written using dollar symbols if it is constructed inline). The range is a tuple or list with three elements: the symbol which is the dependent variable as a Cadabra expression, the starting value and the end value. If the function to plot is an interpolating function, the range can be inferred automatically. Additional options like labels and grid can be specified.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\algorithm{plot(ex: Ex, range: tuple, grid: bool, xlabel: str, ylabel: str, title: str, samples: int) -> plot}{Plot a function of one variable given the range.}\\n\\nThe function should be a Cadabra expression (so written using dollar symbols if it is constructed inline). The range is a tuple or list with three elements: the symbol which is the dependent variable as a Cadabra expression, the starting value and the end value. If the function to plot is an interpolating function, the range can be inferred automatically. Additional options like labels and grid can be specified.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 5493679695024414274,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"def exlist_to_list(fn):\\n   \\\"\\\"\\\" Convert a cadabra list to a python list, and ensure that single items sit in lists too. \\\"\\\"\\\"\\n   if isinstance(fn, Ex):\\n      if fn.top().name==r\\\"\\\\comma\\\":\\n         tmp = []\\n         for t in fn.top().args():\\n             tmp.append(t.ex())\\n      else:\\n         tmp = [fn]\\n   else:\\n      tmp = fn\\n   return tmp\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 15037727445318550071,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"def handle_equations(fn, default_label, legend):\\n   \\\"\\\"\\\" If the functions are equations, extract rhs as the function. Also return\\n       the lhs as labels, and a bool indicating whether or not a legend is required.\\\"\\\"\\\"\\n   tmp=[]\\n   labels=[]\\n   need_legend=False\\n   for f in fn:\\n      if f.top().name == r\\\"\\\\equals\\\":\\n         tmp.append(rhs(f))\\n         labels.append(\\\"$\\\"+str(lhs(f))+\\\"$\\\")\\n         need_legend=True\\n      else:\\n         tmp.append(f)\\n         labels.append(default_label)\\n   if legend != None:\\n      labels=legend\\n      need_legend=True\\n   return (tmp, labels, need_legend)\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 8859335912767278792,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"def plot(fn, range_={}, samples=1000, grid=None, xlabel=None, ylabel=None, title=None, \\n         xrange=[], yrange=[], fig=None, label=\\\"_\\\", legend=None, color=None, aspect=None):\\n\\n   if range_ == {}:\\n      range_ = function_domain(fn)\\n   if range_ == {}:\\n      raise Exception(\\\"cdb.graphics.plot.plot: No plot range set, and none could be deduced.\\\")\\n   \\n   fn                      = exlist_to_list(fn)\\n   fn, labels, need_legend = handle_equations(fn, label, legend)\\n\\n   if isinstance(range_, dict):\\n      fvc = list(map(lambda arg: nevaluate(arg, range_), fn))\\n      r = np.array(nrange(range_)[1])\\n   else:\\n      xvar = range_[0]\\n      xstart = range_[1]\\n      xend = range_[2]\\n      r = np.linspace(xstart, xend, samples)\\n      fvc = list(map(lambda arg: nevaluate(arg, {xvar: r}), fn))\\n   \\n   if not all( vals.is_real() for vals in fvc ):\\n      raise Exception(\\\"cdb.graphics.plot.plot: Values not all real.\\\")\\n   fv = list(map(lambda arg: np.array(arg), fvc))   \\n   \\n   if color == None:\\n      import matplotlib.pyplot as plt\\n      cycler = plt.rcParams['axes.prop_cycle']\\n      color = [c['color'] for c in cycler]\\n   if isinstance(color, list)==False:\\n      color = [color]\\n   if len(color) < len(fn):\\n      color = color * int( (len(fn)/len(color)+1) )\\n   if _backend==Backend.MATPLOTLIB:\\n      import matplotlib.pyplot as plt\\n      newplot=False\\n      if fig==None:\\n         fig = plt.figure()\\n         fig.add_subplot(1,1,1)\\n         newplot=True\\n      ax = fig.axes[0]\\n      if aspect:\\n         ax.set_aspect(aspect)\\n      if grid!=None:\\n         ax.grid(visible=grid)\\n      for line in ax.get_lines():\\n         for i in range(len(labels)):\\n            if line.get_label() == labels[i]:\\n               line.remove()\\n               break\\n\\n      for i in range(len(fv)):\\n         ax.plot(r, fv[i], color=color[i], label=labels[i])\\n\\n      plt.rcParams['mathtext.fontset'] = 'cm'\\n      if need_legend:\\n         ax.legend()\\n      if title:\\n         fig.suptitle(title, fontsize=18, fontfamily=\\\"cmr10\\\", y=0.96)\\n      if xlabel:\\n         ax.set_xlabel(xlabel, fontsize=16, fontname=\\\"cmr10\\\")\\n      if ylabel:\\n         ax.set_ylabel(ylabel, fontsize=16, fontname=\\\"cmr10\\\")\\n      if len(xrange)==2:\\n         ax.set(xlim=xrange)\\n      if len(yrange)==2:\\n         ax.set(ylim=yrange)\\n      return fig\\n   if _backend==Backend.PLOTLY:\\n      import plotly.express as px\\n      return px.line(x=r, y=fv, title=title, labels = {\\\"x\\\": xlabel, \\\"y\\\": ylabel})\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 17159631298674128296,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"ignore_on_import\": true,\n\t\t\t\"source\": \"from matplotlib import font_manager\\nsorted(font_manager.get_font_names())\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 8913425743399961136,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 18428450946024177796,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"image_svg\",\n\t\t\t\t\t\"source\": \"<?xml version="1.0" encoding="utf-8" standalone="no"?>
<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
  "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="460.8pt" height="345.6pt" viewBox="0 0 460.8 345.6" xmlns="http://www.w3.org/2000/svg" version="1.1">
 <metadata>
  <rdf:RDF xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:cc="http://creativecommons.org/ns#" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
   <cc:Work>
    <dc:type rdf:resource="http://purl.org/dc/dcmitype/StillImage"/>
    <dc:date>2025-03-30T13:19:59.103614</dc:date>
    <dc:format>image/svg+xml</dc:format>
    <dc:creator>
     <cc:Agent>
      <dc:title>Matplotlib v3.6.3, https://matplotlib.org/</dc:title>
     </cc:Agent>
    </dc:creator>
   </cc:Work>
  </rdf:RDF>
 </metadata>
 <defs>
  <style type="text/css">*{stroke-linejoin: round; stroke-linecap: butt}</style>
 </defs>
 <g id="figure_1">
  <g id="patch_1">
   <path d="M 0 345.6 
L 460.8 345.6 
L 460.8 0 
L 0 0 
z
" style="fill: #ffffff"/>
  </g>
  <g id="axes_1">
   <g id="patch_2">
    <path d="M 57.6 307.584 
L 414.72 307.584 
L 414.72 41.472 
L 57.6 41.472 
z
" style="fill: #ffffff"/>
   </g>
   <g id="matplotlib.axis_1">
    <g id="xtick_1">
     <g id="line2d_1">
      <path d="M 73.832727 307.584 
L 73.832727 41.472 
" clip-path="url(#p4a4d8e2eef)" style="fill: none; stroke: #b0b0b0; stroke-width: 0.8; stroke-linecap: square"/>
     </g>
     <g id="line2d_2">
      <defs>
       <path id="mdc2232257c" d="M 0 0 
L 0 3.5 
" style="stroke: #000000; stroke-width: 0.8"/>
      </defs>
      <g>
       <use xlink:href="#mdc2232257c" x="73.832727" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_1">
      <!-- 0 -->
      <g transform="translate(70.651477 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-30" d="M 2034 4250 
Q 1547 4250 1301 3770 
Q 1056 3291 1056 2328 
Q 1056 1369 1301 889 
Q 1547 409 2034 409 
Q 2525 409 2770 889 
Q 3016 1369 3016 2328 
Q 3016 3291 2770 3770 
Q 2525 4250 2034 4250 
z
M 2034 4750 
Q 2819 4750 3233 4129 
Q 3647 3509 3647 2328 
Q 3647 1150 3233 529 
Q 2819 -91 2034 -91 
Q 1250 -91 836 529 
Q 422 1150 422 2328 
Q 422 3509 836 4129 
Q 1250 4750 2034 4750 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-30"/>
      </g>
     </g>
    </g>
    <g id="xtick_2">
     <g id="line2d_3">
      <path d="M 138.763636 307.584 
L 138.763636 41.472 
" clip-path="url(#p4a4d8e2eef)" style="fill: none; stroke: #b0b0b0; stroke-width: 0.8; stroke-linecap: square"/>
     </g>
     <g id="line2d_4">
      <g>
       <use xlink:href="#mdc2232257c" x="138.763636" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_2">
      <!-- 2 -->
      <g transform="translate(135.582386 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-32" d="M 1228 531 
L 3431 531 
L 3431 0 
L 469 0 
L 469 531 
Q 828 903 1448 1529 
Q 2069 2156 2228 2338 
Q 2531 2678 2651 2914 
Q 2772 3150 2772 3378 
Q 2772 3750 2511 3984 
Q 2250 4219 1831 4219 
Q 1534 4219 1204 4116 
Q 875 4013 500 3803 
L 500 4441 
Q 881 4594 1212 4672 
Q 1544 4750 1819 4750 
Q 2544 4750 2975 4387 
Q 3406 4025 3406 3419 
Q 3406 3131 3298 2873 
Q 3191 2616 2906 2266 
Q 2828 2175 2409 1742 
Q 1991 1309 1228 531 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-32"/>
      </g>
     </g>
    </g>
    <g id="xtick_3">
     <g id="line2d_5">
      <path d="M 203.694545 307.584 
L 203.694545 41.472 
" clip-path="url(#p4a4d8e2eef)" style="fill: none; stroke: #b0b0b0; stroke-width: 0.8; stroke-linecap: square"/>
     </g>
     <g id="line2d_6">
      <g>
       <use xlink:href="#mdc2232257c" x="203.694545" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_3">
      <!-- 4 -->
      <g transform="translate(200.513295 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-34" d="M 2419 4116 
L 825 1625 
L 2419 1625 
L 2419 4116 
z
M 2253 4666 
L 3047 4666 
L 3047 1625 
L 3713 1625 
L 3713 1100 
L 3047 1100 
L 3047 0 
L 2419 0 
L 2419 1100 
L 313 1100 
L 313 1709 
L 2253 4666 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-34"/>
      </g>
     </g>
    </g>
    <g id="xtick_4">
     <g id="line2d_7">
      <path d="M 268.625455 307.584 
L 268.625455 41.472 
" clip-path="url(#p4a4d8e2eef)" style="fill: none; stroke: #b0b0b0; stroke-width: 0.8; stroke-linecap: square"/>
     </g>
     <g id="line2d_8">
      <g>
       <use xlink:href="#mdc2232257c" x="268.625455" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_4">
      <!-- 6 -->
      <g transform="translate(265.444205 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-36" d="M 2113 2584 
Q 1688 2584 1439 2293 
Q 1191 2003 1191 1497 
Q 1191 994 1439 701 
Q 1688 409 2113 409 
Q 2538 409 2786 701 
Q 3034 994 3034 1497 
Q 3034 2003 2786 2293 
Q 2538 2584 2113 2584 
z
M 3366 4563 
L 3366 3988 
Q 3128 4100 2886 4159 
Q 2644 4219 2406 4219 
Q 1781 4219 1451 3797 
Q 1122 3375 1075 2522 
Q 1259 2794 1537 2939 
Q 1816 3084 2150 3084 
Q 2853 3084 3261 2657 
Q 3669 2231 3669 1497 
Q 3669 778 3244 343 
Q 2819 -91 2113 -91 
Q 1303 -91 875 529 
Q 447 1150 447 2328 
Q 447 3434 972 4092 
Q 1497 4750 2381 4750 
Q 2619 4750 2861 4703 
Q 3103 4656 3366 4563 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-36"/>
      </g>
     </g>
    </g>
    <g id="xtick_5">
     <g id="line2d_9">
      <path d="M 333.556364 307.584 
L 333.556364 41.472 
" clip-path="url(#p4a4d8e2eef)" style="fill: none; stroke: #b0b0b0; stroke-width: 0.8; stroke-linecap: square"/>
     </g>
     <g id="line2d_10">
      <g>
       <use xlink:href="#mdc2232257c" x="333.556364" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_5">
      <!-- 8 -->
      <g transform="translate(330.375114 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-38" d="M 2034 2216 
Q 1584 2216 1326 1975 
Q 1069 1734 1069 1313 
Q 1069 891 1326 650 
Q 1584 409 2034 409 
Q 2484 409 2743 651 
Q 3003 894 3003 1313 
Q 3003 1734 2745 1975 
Q 2488 2216 2034 2216 
z
M 1403 2484 
Q 997 2584 770 2862 
Q 544 3141 544 3541 
Q 544 4100 942 4425 
Q 1341 4750 2034 4750 
Q 2731 4750 3128 4425 
Q 3525 4100 3525 3541 
Q 3525 3141 3298 2862 
Q 3072 2584 2669 2484 
Q 3125 2378 3379 2068 
Q 3634 1759 3634 1313 
Q 3634 634 3220 271 
Q 2806 -91 2034 -91 
Q 1263 -91 848 271 
Q 434 634 434 1313 
Q 434 1759 690 2068 
Q 947 2378 1403 2484 
z
M 1172 3481 
Q 1172 3119 1398 2916 
Q 1625 2713 2034 2713 
Q 2441 2713 2670 2916 
Q 2900 3119 2900 3481 
Q 2900 3844 2670 4047 
Q 2441 4250 2034 4250 
Q 1625 4250 1398 4047 
Q 1172 3844 1172 3481 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-38"/>
      </g>
     </g>
    </g>
    <g id="xtick_6">
     <g id="line2d_11">
      <path d="M 398.487273 307.584 
L 398.487273 41.472 
" clip-path="url(#p4a4d8e2eef)" style="fill: none; stroke: #b0b0b0; stroke-width: 0.8; stroke-linecap: square"/>
     </g>
     <g id="line2d_12">
      <g>
       <use xlink:href="#mdc2232257c" x="398.487273" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_6">
      <!-- 10 -->
      <g transform="translate(392.124773 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-31" d="M 794 531 
L 1825 531 
L 1825 4091 
L 703 3866 
L 703 4441 
L 1819 4666 
L 2450 4666 
L 2450 531 
L 3481 531 
L 3481 0 
L 794 0 
L 794 531 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-31"/>
       <use xlink:href="#DejaVuSans-30" x="63.623047"/>
      </g>
     </g>
    </g>
    <g id="text_7">
     <!-- x-axis -->
     <g transform="translate(215.69875 339.364625) scale(0.16 -0.16)">
      <defs>
       <path id="Cmr10-78" d="M 78 0 
L 78 225 
Q 322 225 537 320 
Q 753 416 903 603 
L 1484 1344 
L 728 2328 
Q 616 2469 483 2501 
Q 350 2534 109 2534 
L 109 2759 
L 1441 2759 
L 1441 2534 
Q 1356 2534 1282 2496 
Q 1209 2459 1209 2388 
Q 1209 2363 1228 2328 
L 1741 1663 
L 2125 2156 
Q 2203 2250 2203 2344 
Q 2203 2422 2151 2478 
Q 2100 2534 2016 2534 
L 2016 2759 
L 3194 2759 
L 3194 2534 
Q 2947 2534 2730 2439 
Q 2513 2344 2363 2156 
L 1856 1509 
L 2675 428 
Q 2797 288 2928 256 
Q 3059 225 3303 225 
L 3303 0 
L 1972 0 
L 1972 225 
Q 2050 225 2122 262 
Q 2194 300 2194 372 
Q 2194 400 2175 428 
L 1600 1191 
L 1141 603 
Q 1069 522 1069 416 
Q 1069 338 1122 281 
Q 1175 225 1247 225 
L 1247 0 
L 78 0 
z
" transform="scale(0.015625)"/>
       <path id="Cmr10-2d" d="M 72 1184 
L 72 1581 
L 1766 1581 
L 1766 1184 
L 72 1184 
z
" transform="scale(0.015625)"/>
       <path id="Cmr10-61" d="M 256 628 
Q 256 1009 556 1248 
Q 856 1488 1276 1586 
Q 1697 1684 2075 1684 
L 2075 1947 
Q 2075 2131 1994 2304 
Q 1913 2478 1759 2589 
Q 1606 2700 1422 2700 
Q 997 2700 775 2509 
Q 897 2509 976 2417 
Q 1056 2325 1056 2203 
Q 1056 2075 965 1984 
Q 875 1894 750 1894 
Q 622 1894 531 1984 
Q 441 2075 441 2203 
Q 441 2541 747 2705 
Q 1053 2869 1422 2869 
Q 1681 2869 1943 2758 
Q 2206 2647 2373 2440 
Q 2541 2234 2541 1959 
L 2541 519 
Q 2541 394 2594 289 
Q 2647 184 2759 184 
Q 2866 184 2917 290 
Q 2969 397 2969 519 
L 2969 928 
L 3156 928 
L 3156 519 
Q 3156 375 3081 245 
Q 3006 116 2879 39 
Q 2753 -38 2606 -38 
Q 2419 -38 2283 107 
Q 2147 253 2131 453 
Q 2013 213 1781 70 
Q 1550 -72 1288 -72 
Q 1044 -72 808 0 
Q 572 72 414 226 
Q 256 381 256 628 
z
M 775 628 
Q 775 403 940 250 
Q 1106 97 1331 97 
Q 1538 97 1706 200 
Q 1875 303 1975 481 
Q 2075 659 2075 856 
L 2075 1522 
Q 1784 1522 1479 1426 
Q 1175 1331 975 1128 
Q 775 925 775 628 
z
" transform="scale(0.015625)"/>
       <path id="Cmr10-69" d="M 197 0 
L 197 225 
Q 416 225 556 259 
Q 697 294 697 428 
L 697 2175 
Q 697 2422 601 2478 
Q 506 2534 225 2534 
L 225 2759 
L 1147 2828 
L 1147 428 
Q 1147 294 1269 259 
Q 1391 225 1594 225 
L 1594 0 
L 197 0 
z
M 469 3928 
Q 469 4069 575 4175 
Q 681 4281 819 4281 
Q 909 4281 993 4234 
Q 1078 4188 1125 4103 
Q 1172 4019 1172 3928 
Q 1172 3791 1065 3684 
Q 959 3578 819 3578 
Q 681 3578 575 3684 
Q 469 3791 469 3928 
z
" transform="scale(0.015625)"/>
       <path id="Cmr10-73" d="M 213 -19 
L 213 1025 
Q 213 1075 269 1075 
L 347 1075 
Q 384 1075 397 1025 
Q 575 97 1259 97 
Q 1563 97 1767 234 
Q 1972 372 1972 659 
Q 1972 866 1812 1011 
Q 1653 1156 1434 1209 
L 1006 1294 
Q 791 1341 614 1437 
Q 438 1534 325 1695 
Q 213 1856 213 2069 
Q 213 2350 361 2529 
Q 509 2709 746 2789 
Q 984 2869 1259 2869 
Q 1588 2869 1831 2694 
L 2016 2853 
Q 2016 2869 2047 2869 
L 2094 2869 
Q 2113 2869 2128 2851 
Q 2144 2834 2144 2816 
L 2144 1978 
Q 2144 1919 2094 1919 
L 2016 1919 
Q 1959 1919 1959 1978 
Q 1959 2313 1773 2516 
Q 1588 2719 1253 2719 
Q 966 2719 755 2612 
Q 544 2506 544 2247 
Q 544 2069 695 1955 
Q 847 1841 1050 1791 
L 1484 1709 
Q 1703 1659 1892 1540 
Q 2081 1422 2192 1240 
Q 2303 1059 2303 831 
Q 2303 600 2223 429 
Q 2144 259 2001 146 
Q 1859 34 1665 -19 
Q 1472 -72 1259 -72 
Q 859 -72 575 197 
L 341 -56 
Q 341 -72 306 -72 
L 269 -72 
Q 213 -72 213 -19 
z
" transform="scale(0.015625)"/>
      </defs>
      <use xlink:href="#Cmr10-78"/>
      <use xlink:href="#Cmr10-2d" x="52.685547"/>
      <use xlink:href="#Cmr10-61" x="85.986328"/>
      <use xlink:href="#Cmr10-78" x="135.986328"/>
      <use xlink:href="#Cmr10-69" x="188.671875"/>
      <use xlink:href="#Cmr10-73" x="216.357422"/>
     </g>
    </g>
   </g>
   <g id="matplotlib.axis_2">
    <g id="ytick_1">
     <g id="line2d_13">
      <path d="M 57.6 307.584 
L 414.72 307.584 
" clip-path="url(#p4a4d8e2eef)" style="fill: none; stroke: #b0b0b0; stroke-width: 0.8; stroke-linecap: square"/>
     </g>
     <g id="line2d_14">
      <defs>
       <path id="m01b422698f" d="M 0 0 
L -3.5 0 
" style="stroke: #000000; stroke-width: 0.8"/>
      </defs>
      <g>
       <use xlink:href="#m01b422698f" x="57.6" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_8">
      <!-- −1.00 -->
      <g transform="translate(19.954687 311.383219) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-2212" d="M 678 2272 
L 4684 2272 
L 4684 1741 
L 678 1741 
L 678 2272 
z
" transform="scale(0.015625)"/>
        <path id="DejaVuSans-2e" d="M 684 794 
L 1344 794 
L 1344 0 
L 684 0 
L 684 794 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-2212"/>
       <use xlink:href="#DejaVuSans-31" x="83.789062"/>
       <use xlink:href="#DejaVuSans-2e" x="147.412109"/>
       <use xlink:href="#DejaVuSans-30" x="179.199219"/>
       <use xlink:href="#DejaVuSans-30" x="242.822266"/>
      </g>
     </g>
    </g>
    <g id="ytick_2">
     <g id="line2d_15">
      <path d="M 57.6 274.32 
L 414.72 274.32 
" clip-path="url(#p4a4d8e2eef)" style="fill: none; stroke: #b0b0b0; stroke-width: 0.8; stroke-linecap: square"/>
     </g>
     <g id="line2d_16">
      <g>
       <use xlink:href="#m01b422698f" x="57.6" y="274.32" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_9">
      <!-- −0.75 -->
      <g transform="translate(19.954687 278.119219) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-37" d="M 525 4666 
L 3525 4666 
L 3525 4397 
L 1831 0 
L 1172 0 
L 2766 4134 
L 525 4134 
L 525 4666 
z
" transform="scale(0.015625)"/>
        <path id="DejaVuSans-35" d="M 691 4666 
L 3169 4666 
L 3169 4134 
L 1269 4134 
L 1269 2991 
Q 1406 3038 1543 3061 
Q 1681 3084 1819 3084 
Q 2600 3084 3056 2656 
Q 3513 2228 3513 1497 
Q 3513 744 3044 326 
Q 2575 -91 1722 -91 
Q 1428 -91 1123 -41 
Q 819 9 494 109 
L 494 744 
Q 775 591 1075 516 
Q 1375 441 1709 441 
Q 2250 441 2565 725 
Q 2881 1009 2881 1497 
Q 2881 1984 2565 2268 
Q 2250 2553 1709 2553 
Q 1456 2553 1204 2497 
Q 953 2441 691 2322 
L 691 4666 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-2212"/>
       <use xlink:href="#DejaVuSans-30" x="83.789062"/>
       <use xlink:href="#DejaVuSans-2e" x="147.412109"/>
       <use xlink:href="#DejaVuSans-37" x="179.199219"/>
       <use xlink:href="#DejaVuSans-35" x="242.822266"/>
      </g>
     </g>
    </g>
    <g id="ytick_3">
     <g id="line2d_17">
      <path d="M 57.6 241.056 
L 414.72 241.056 
" clip-path="url(#p4a4d8e2eef)" style="fill: none; stroke: #b0b0b0; stroke-width: 0.8; stroke-linecap: square"/>
     </g>
     <g id="line2d_18">
      <g>
       <use xlink:href="#m01b422698f" x="57.6" y="241.056" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_10">
      <!-- −0.50 -->
      <g transform="translate(19.954687 244.855219) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-2212"/>
       <use xlink:href="#DejaVuSans-30" x="83.789062"/>
       <use xlink:href="#DejaVuSans-2e" x="147.412109"/>
       <use xlink:href="#DejaVuSans-35" x="179.199219"/>
       <use xlink:href="#DejaVuSans-30" x="242.822266"/>
      </g>
     </g>
    </g>
    <g id="ytick_4">
     <g id="line2d_19">
      <path d="M 57.6 207.792 
L 414.72 207.792 
" clip-path="url(#p4a4d8e2eef)" style="fill: none; stroke: #b0b0b0; stroke-width: 0.8; stroke-linecap: square"/>
     </g>
     <g id="line2d_20">
      <g>
       <use xlink:href="#m01b422698f" x="57.6" y="207.792" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_11">
      <!-- −0.25 -->
      <g transform="translate(19.954687 211.591219) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-2212"/>
       <use xlink:href="#DejaVuSans-30" x="83.789062"/>
       <use xlink:href="#DejaVuSans-2e" x="147.412109"/>
       <use xlink:href="#DejaVuSans-32" x="179.199219"/>
       <use xlink:href="#DejaVuSans-35" x="242.822266"/>
      </g>
     </g>
    </g>
    <g id="ytick_5">
     <g id="line2d_21">
      <path d="M 57.6 174.528 
L 414.72 174.528 
" clip-path="url(#p4a4d8e2eef)" style="fill: none; stroke: #b0b0b0; stroke-width: 0.8; stroke-linecap: square"/>
     </g>
     <g id="line2d_22">
      <g>
       <use xlink:href="#m01b422698f" x="57.6" y="174.528" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_12">
      <!-- 0.00 -->
      <g transform="translate(28.334375 178.327219) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-30"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-30" x="95.410156"/>
       <use xlink:href="#DejaVuSans-30" x="159.033203"/>
      </g>
     </g>
    </g>
    <g id="ytick_6">
     <g id="line2d_23">
      <path d="M 57.6 141.264 
L 414.72 141.264 
" clip-path="url(#p4a4d8e2eef)" style="fill: none; stroke: #b0b0b0; stroke-width: 0.8; stroke-linecap: square"/>
     </g>
     <g id="line2d_24">
      <g>
       <use xlink:href="#m01b422698f" x="57.6" y="141.264" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_13">
      <!-- 0.25 -->
      <g transform="translate(28.334375 145.063219) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-30"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-32" x="95.410156"/>
       <use xlink:href="#DejaVuSans-35" x="159.033203"/>
      </g>
     </g>
    </g>
    <g id="ytick_7">
     <g id="line2d_25">
      <path d="M 57.6 108 
L 414.72 108 
" clip-path="url(#p4a4d8e2eef)" style="fill: none; stroke: #b0b0b0; stroke-width: 0.8; stroke-linecap: square"/>
     </g>
     <g id="line2d_26">
      <g>
       <use xlink:href="#m01b422698f" x="57.6" y="108" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_14">
      <!-- 0.50 -->
      <g transform="translate(28.334375 111.799219) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-30"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-35" x="95.410156"/>
       <use xlink:href="#DejaVuSans-30" x="159.033203"/>
      </g>
     </g>
    </g>
    <g id="ytick_8">
     <g id="line2d_27">
      <path d="M 57.6 74.736 
L 414.72 74.736 
" clip-path="url(#p4a4d8e2eef)" style="fill: none; stroke: #b0b0b0; stroke-width: 0.8; stroke-linecap: square"/>
     </g>
     <g id="line2d_28">
      <g>
       <use xlink:href="#m01b422698f" x="57.6" y="74.736" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_15">
      <!-- 0.75 -->
      <g transform="translate(28.334375 78.535219) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-30"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-37" x="95.410156"/>
       <use xlink:href="#DejaVuSans-35" x="159.033203"/>
      </g>
     </g>
    </g>
    <g id="ytick_9">
     <g id="line2d_29">
      <path d="M 57.6 41.472 
L 414.72 41.472 
" clip-path="url(#p4a4d8e2eef)" style="fill: none; stroke: #b0b0b0; stroke-width: 0.8; stroke-linecap: square"/>
     </g>
     <g id="line2d_30">
      <g>
       <use xlink:href="#m01b422698f" x="57.6" y="41.472" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_16">
      <!-- 1.00 -->
      <g transform="translate(28.334375 45.271219) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-31"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-30" x="95.410156"/>
       <use xlink:href="#DejaVuSans-30" x="159.033203"/>
      </g>
     </g>
    </g>
    <g id="text_17">
     <!-- function value -->
     <g transform="translate(12.852187 224.2505) rotate(-90) scale(0.16 -0.16)">
      <defs>
       <path id="Cmr10-66" d="M 206 0 
L 206 225 
Q 422 225 562 259 
Q 703 294 703 428 
L 703 2534 
L 213 2534 
L 213 2759 
L 703 2759 
L 703 3525 
Q 703 3731 789 3911 
Q 875 4091 1020 4225 
Q 1166 4359 1355 4436 
Q 1544 4513 1747 4513 
Q 1963 4513 2136 4384 
Q 2309 4256 2309 4044 
Q 2309 3922 2226 3839 
Q 2144 3756 2022 3756 
Q 1900 3756 1814 3839 
Q 1728 3922 1728 4044 
Q 1728 4244 1900 4313 
Q 1797 4347 1716 4347 
Q 1528 4347 1395 4214 
Q 1263 4081 1197 3890 
Q 1131 3700 1131 3513 
L 1131 2759 
L 1869 2759 
L 1869 2534 
L 1153 2534 
L 1153 428 
Q 1153 297 1340 261 
Q 1528 225 1772 225 
L 1772 0 
L 206 0 
z
" transform="scale(0.015625)"/>
       <path id="Cmr10-75" d="M 691 763 
L 691 2175 
Q 691 2347 639 2423 
Q 588 2500 491 2517 
Q 394 2534 191 2534 
L 191 2759 
L 1159 2828 
L 1159 763 
Q 1159 513 1195 373 
Q 1231 234 1348 165 
Q 1466 97 1722 97 
Q 2066 97 2269 384 
Q 2472 672 2472 1038 
L 2472 2175 
Q 2472 2347 2419 2423 
Q 2366 2500 2270 2517 
Q 2175 2534 1972 2534 
L 1972 2759 
L 2938 2828 
L 2938 581 
Q 2938 413 2989 336 
Q 3041 259 3137 242 
Q 3234 225 3438 225 
L 3438 0 
L 2491 -72 
L 2491 469 
Q 2372 228 2159 78 
Q 1947 -72 1691 -72 
Q 1231 -72 961 123 
Q 691 319 691 763 
z
" transform="scale(0.015625)"/>
       <path id="Cmr10-6e" d="M 191 0 
L 191 225 
Q 409 225 550 259 
Q 691 294 691 428 
L 691 2175 
Q 691 2347 639 2423 
Q 588 2500 491 2517 
Q 394 2534 191 2534 
L 191 2759 
L 1119 2828 
L 1119 2203 
Q 1247 2478 1498 2653 
Q 1750 2828 2047 2828 
Q 2491 2828 2714 2615 
Q 2938 2403 2938 1966 
L 2938 428 
Q 2938 294 3078 259 
Q 3219 225 3438 225 
L 3438 0 
L 1972 0 
L 1972 225 
Q 2191 225 2331 259 
Q 2472 294 2472 428 
L 2472 1947 
Q 2472 2259 2381 2461 
Q 2291 2663 2009 2663 
Q 1638 2663 1398 2366 
Q 1159 2069 1159 1691 
L 1159 428 
Q 1159 294 1300 259 
Q 1441 225 1656 225 
L 1656 0 
L 191 0 
z
" transform="scale(0.015625)"/>
       <path id="Cmr10-63" d="M 1594 -72 
Q 1206 -72 890 129 
Q 575 331 394 667 
Q 213 1003 213 1381 
Q 213 1759 392 2106 
Q 572 2453 889 2661 
Q 1206 2869 1594 2869 
Q 1969 2869 2276 2722 
Q 2584 2575 2584 2241 
Q 2584 2116 2495 2023 
Q 2406 1931 2278 1931 
Q 2150 1931 2061 2023 
Q 1972 2116 1972 2241 
Q 1972 2353 2044 2436 
Q 2116 2519 2222 2541 
Q 2000 2681 1600 2681 
Q 1294 2681 1106 2478 
Q 919 2275 844 1975 
Q 769 1675 769 1381 
Q 769 1072 861 783 
Q 953 494 1158 305 
Q 1363 116 1672 116 
Q 1975 116 2187 302 
Q 2400 488 2478 788 
Q 2478 825 2528 825 
L 2606 825 
Q 2625 825 2640 808 
Q 2656 791 2656 769 
L 2656 750 
Q 2559 372 2271 150 
Q 1984 -72 1594 -72 
z
" transform="scale(0.015625)"/>
       <path id="Cmr10-74" d="M 653 769 
L 653 2534 
L 122 2534 
L 122 2700 
Q 541 2700 737 3090 
Q 934 3481 934 3938 
L 1119 3938 
L 1119 2759 
L 2022 2759 
L 2022 2534 
L 1119 2534 
L 1119 781 
Q 1119 516 1208 316 
Q 1297 116 1528 116 
Q 1747 116 1844 327 
Q 1941 538 1941 781 
L 1941 1159 
L 2125 1159 
L 2125 769 
Q 2125 569 2051 373 
Q 1978 178 1834 53 
Q 1691 -72 1484 -72 
Q 1100 -72 876 158 
Q 653 388 653 769 
z
" transform="scale(0.015625)"/>
       <path id="Cmr10-6f" d="M 1600 -72 
Q 1216 -72 887 123 
Q 559 319 368 647 
Q 178 975 178 1363 
Q 178 1656 283 1928 
Q 388 2200 583 2414 
Q 778 2628 1037 2748 
Q 1297 2869 1600 2869 
Q 1994 2869 2317 2661 
Q 2641 2453 2828 2104 
Q 3016 1756 3016 1363 
Q 3016 978 2825 648 
Q 2634 319 2307 123 
Q 1981 -72 1600 -72 
z
M 1600 116 
Q 2113 116 2284 487 
Q 2456 859 2456 1434 
Q 2456 1756 2422 1967 
Q 2388 2178 2272 2350 
Q 2200 2456 2089 2536 
Q 1978 2616 1854 2658 
Q 1731 2700 1600 2700 
Q 1400 2700 1220 2609 
Q 1041 2519 922 2350 
Q 803 2169 770 1951 
Q 738 1734 738 1434 
Q 738 1075 800 789 
Q 863 503 1052 309 
Q 1241 116 1600 116 
z
" transform="scale(0.015625)"/>
       <path id="Cmr10-20" transform="scale(0.015625)"/>
       <path id="Cmr10-76" d="M 1563 0 
L 628 2350 
Q 569 2469 445 2501 
Q 322 2534 122 2534 
L 122 2759 
L 1466 2759 
L 1466 2534 
Q 1106 2534 1106 2381 
Q 1106 2356 1113 2344 
L 1831 538 
L 2478 2169 
Q 2497 2219 2497 2272 
Q 2497 2394 2405 2464 
Q 2313 2534 2188 2534 
L 2188 2759 
L 3250 2759 
L 3250 2534 
Q 3053 2534 2904 2443 
Q 2756 2353 2675 2175 
L 1813 0 
Q 1788 -72 1709 -72 
L 1663 -72 
Q 1584 -72 1563 0 
z
" transform="scale(0.015625)"/>
       <path id="Cmr10-6c" d="M 197 0 
L 197 225 
Q 416 225 556 259 
Q 697 294 697 428 
L 697 3788 
Q 697 3959 645 4036 
Q 594 4113 497 4130 
Q 400 4147 197 4147 
L 197 4372 
L 1147 4441 
L 1147 428 
Q 1147 294 1287 259 
Q 1428 225 1644 225 
L 1644 0 
L 197 0 
z
" transform="scale(0.015625)"/>
       <path id="Cmr10-65" d="M 1594 -72 
Q 1203 -72 876 133 
Q 550 338 364 680 
Q 178 1022 178 1403 
Q 178 1778 348 2115 
Q 519 2453 823 2661 
Q 1128 2869 1503 2869 
Q 1797 2869 2014 2770 
Q 2231 2672 2372 2497 
Q 2513 2322 2584 2084 
Q 2656 1847 2656 1563 
Q 2656 1478 2591 1478 
L 738 1478 
L 738 1409 
Q 738 878 952 497 
Q 1166 116 1650 116 
Q 1847 116 2014 203 
Q 2181 291 2304 447 
Q 2428 603 2472 781 
Q 2478 803 2495 820 
Q 2513 838 2534 838 
L 2591 838 
Q 2656 838 2656 756 
Q 2566 394 2266 161 
Q 1966 -72 1594 -72 
z
M 744 1638 
L 2203 1638 
Q 2203 1878 2136 2125 
Q 2069 2372 1912 2536 
Q 1756 2700 1503 2700 
Q 1141 2700 942 2361 
Q 744 2022 744 1638 
z
" transform="scale(0.015625)"/>
      </defs>
      <use xlink:href="#Cmr10-66"/>
      <use xlink:href="#Cmr10-75" x="30.517578"/>
      <use xlink:href="#Cmr10-6e" x="86.035156"/>
      <use xlink:href="#Cmr10-63" x="141.552734"/>
      <use xlink:href="#Cmr10-74" x="185.9375"/>
      <use xlink:href="#Cmr10-69" x="224.755859"/>
      <use xlink:href="#Cmr10-6f" x="252.441406"/>
      <use xlink:href="#Cmr10-6e" x="302.441406"/>
      <use xlink:href="#Cmr10-20" x="357.958984"/>
      <use xlink:href="#Cmr10-76" x="391.259766"/>
      <use xlink:href="#Cmr10-61" x="443.945312"/>
      <use xlink:href="#Cmr10-6c" x="493.945312"/>
      <use xlink:href="#Cmr10-75" x="521.630859"/>
      <use xlink:href="#Cmr10-65" x="577.148438"/>
     </g>
    </g>
   </g>
   <g id="line2d_31">
    <path d="M 73.832727 41.472 
L 74.807666 41.555976 
L 76.107584 41.928778 
L 77.407502 42.598085 
L 78.70742 43.560928 
L 80.007338 44.813047 
L 81.307256 46.348911 
L 82.932154 48.657341 
L 84.557052 51.382657 
L 86.181949 54.506291 
L 88.131826 58.750495 
L 90.406683 64.333417 
L 92.68154 70.526918 
L 95.281376 78.250915 
L 98.531171 88.687987 
L 102.430925 102.015065 
L 115.755086 148.229974 
L 119.004881 158.407429 
L 121.929697 166.87655 
L 124.529533 173.773514 
L 127.129369 180.022126 
L 129.404226 184.928681 
L 131.679083 189.295437 
L 133.62896 192.603382 
L 135.578837 195.510041 
L 137.528714 198.019857 
L 139.478591 200.14101 
L 141.428468 201.88508 
L 143.053366 203.060889 
L 144.678264 203.994833 
L 146.303161 204.697926 
L 147.928059 205.182152 
L 149.552957 205.460297 
L 151.177854 205.545796 
L 153.127731 205.413736 
L 155.077609 205.049026 
L 157.027486 204.476705 
L 159.302342 203.580013 
L 161.902179 202.301244 
L 164.826994 200.606401 
L 168.401769 198.273177 
L 174.2514 194.140136 
L 181.72593 188.899826 
L 186.275643 185.988816 
L 190.175397 183.747505 
L 194.075152 181.772234 
L 197.649926 180.204855 
L 201.224701 178.867756 
L 205.124455 177.659062 
L 209.02421 176.690023 
L 213.248943 175.879513 
L 217.798657 175.243138 
L 222.998329 174.75737 
L 228.847961 174.441186 
L 236.32249 174.271967 
L 247.371794 174.268452 
L 305.543129 174.524711 
L 398.487273 174.528 
L 398.487273 174.528 
" clip-path="url(#p4a4d8e2eef)" style="fill: none; stroke: #008000; stroke-width: 1.5; stroke-linecap: square"/>
   </g>
   <g id="patch_3">
    <path d="M 57.6 307.584 
L 57.6 41.472 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
   <g id="patch_4">
    <path d="M 414.72 307.584 
L 414.72 41.472 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
   <g id="patch_5">
    <path d="M 57.6 307.584 
L 414.72 307.584 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
   <g id="patch_6">
    <path d="M 57.6 41.472 
L 414.72 41.472 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
   <g id="legend_1">
    <g id="patch_7">
     <path d="M 357.32 64.570437 
L 407.72 64.570437 
Q 409.72 64.570437 409.72 62.570437 
L 409.72 48.472 
Q 409.72 46.472 407.72 46.472 
L 357.32 46.472 
Q 355.32 46.472 355.32 48.472 
L 355.32 62.570437 
Q 355.32 64.570437 357.32 64.570437 
z
" style="fill: #ffffff; opacity: 0.8; stroke: #cccccc; stroke-linejoin: miter"/>
    </g>
    <g id="line2d_32">
     <path d="M 359.32 54.570437 
L 369.32 54.570437 
L 379.32 54.570437 
" style="fill: none; stroke: #008000; stroke-width: 1.5; stroke-linecap: square"/>
    </g>
    <g id="text_18">
     <!-- $f(x)$ -->
     <g transform="translate(387.32 58.070437) scale(0.1 -0.1)">
      <defs>
       <path id="Cmmi10-66" d="M 622 -1056 
Q 741 -1147 909 -1147 
Q 1138 -1147 1281 -641 
Q 1341 -397 1606 966 
L 1900 2534 
L 1350 2534 
Q 1288 2534 1288 2619 
Q 1313 2759 1369 2759 
L 1941 2759 
L 2016 3175 
Q 2053 3369 2084 3508 
Q 2116 3647 2152 3765 
Q 2188 3884 2259 4031 
Q 2369 4241 2555 4377 
Q 2741 4513 2956 4513 
Q 3097 4513 3230 4461 
Q 3363 4409 3447 4306 
Q 3531 4203 3531 4063 
Q 3531 3900 3423 3779 
Q 3316 3659 3163 3659 
Q 3059 3659 2986 3723 
Q 2913 3788 2913 3891 
Q 2913 4031 3008 4136 
Q 3103 4241 3244 4256 
Q 3125 4347 2950 4347 
Q 2853 4347 2767 4256 
Q 2681 4166 2656 4063 
Q 2616 3900 2478 3181 
L 2400 2759 
L 3059 2759 
Q 3122 2759 3122 2675 
Q 3119 2659 3109 2620 
Q 3100 2581 3083 2557 
Q 3066 2534 3041 2534 
L 2356 2534 
L 2059 972 
Q 2003 631 1929 279 
Q 1856 -72 1723 -442 
Q 1591 -813 1384 -1063 
Q 1178 -1313 897 -1313 
Q 681 -1313 511 -1189 
Q 341 -1066 341 -863 
Q 341 -700 445 -579 
Q 550 -459 709 -459 
Q 816 -459 887 -523 
Q 959 -588 959 -691 
Q 959 -828 857 -942 
Q 756 -1056 622 -1056 
z
" transform="scale(0.015625)"/>
       <path id="Cmr10-28" d="M 1984 -1588 
Q 1628 -1306 1370 -942 
Q 1113 -578 948 -165 
Q 784 247 703 697 
Q 622 1147 622 1600 
Q 622 2059 703 2509 
Q 784 2959 951 3375 
Q 1119 3791 1378 4153 
Q 1638 4516 1984 4788 
Q 1984 4800 2016 4800 
L 2075 4800 
Q 2094 4800 2109 4783 
Q 2125 4766 2125 4744 
Q 2125 4716 2113 4703 
Q 1800 4397 1592 4047 
Q 1384 3697 1257 3301 
Q 1131 2906 1075 2482 
Q 1019 2059 1019 1600 
Q 1019 -434 2106 -1491 
Q 2125 -1509 2125 -1544 
Q 2125 -1559 2108 -1579 
Q 2091 -1600 2075 -1600 
L 2016 -1600 
Q 1984 -1600 1984 -1588 
z
" transform="scale(0.015625)"/>
       <path id="Cmmi10-78" d="M 500 184 
Q 613 97 819 97 
Q 1019 97 1172 289 
Q 1325 481 1381 709 
L 1672 1844 
Q 1741 2153 1741 2266 
Q 1741 2425 1652 2544 
Q 1563 2663 1403 2663 
Q 1200 2663 1022 2536 
Q 844 2409 722 2214 
Q 600 2019 550 1819 
Q 538 1778 500 1778 
L 422 1778 
Q 372 1778 372 1838 
L 372 1856 
Q 434 2094 584 2320 
Q 734 2547 951 2687 
Q 1169 2828 1416 2828 
Q 1650 2828 1839 2703 
Q 2028 2578 2106 2363 
Q 2216 2559 2386 2693 
Q 2556 2828 2759 2828 
Q 2897 2828 3040 2779 
Q 3184 2731 3275 2631 
Q 3366 2531 3366 2381 
Q 3366 2219 3261 2101 
Q 3156 1984 2994 1984 
Q 2891 1984 2822 2050 
Q 2753 2116 2753 2216 
Q 2753 2350 2845 2451 
Q 2938 2553 3066 2572 
Q 2950 2663 2747 2663 
Q 2541 2663 2389 2472 
Q 2238 2281 2175 2047 
L 1894 916 
Q 1825 659 1825 494 
Q 1825 331 1917 214 
Q 2009 97 2163 97 
Q 2463 97 2698 361 
Q 2934 625 3009 941 
Q 3022 978 3059 978 
L 3138 978 
Q 3163 978 3178 961 
Q 3194 944 3194 922 
Q 3194 916 3188 903 
Q 3097 522 2806 225 
Q 2516 -72 2150 -72 
Q 1916 -72 1727 54 
Q 1538 181 1459 397 
Q 1359 209 1182 68 
Q 1006 -72 806 -72 
Q 669 -72 523 -23 
Q 378 25 287 125 
Q 197 225 197 378 
Q 197 528 301 651 
Q 406 775 563 775 
Q 669 775 741 711 
Q 813 647 813 544 
Q 813 409 723 309 
Q 634 209 500 184 
z
" transform="scale(0.015625)"/>
       <path id="Cmr10-29" d="M 416 -1600 
Q 359 -1600 359 -1544 
Q 359 -1516 372 -1503 
Q 1466 -434 1466 1600 
Q 1466 3634 384 4691 
Q 359 4706 359 4744 
Q 359 4766 376 4783 
Q 394 4800 416 4800 
L 475 4800 
Q 494 4800 506 4788 
Q 966 4425 1272 3906 
Q 1578 3388 1720 2800 
Q 1863 2213 1863 1600 
Q 1863 1147 1786 708 
Q 1709 269 1542 -157 
Q 1375 -584 1119 -945 
Q 863 -1306 506 -1588 
Q 494 -1600 475 -1600 
L 416 -1600 
z
" transform="scale(0.015625)"/>
      </defs>
      <use xlink:href="#Cmmi10-66"/>
      <use xlink:href="#Cmr10-28" transform="translate(48.876953 0)"/>
      <use xlink:href="#Cmmi10-78" transform="translate(87.695312 0)"/>
      <use xlink:href="#Cmr10-29" transform="translate(144.775391 0)"/>
     </g>
    </g>
   </g>
  </g>
  <g id="text_19">
   <!-- Sample plot -->
   <g transform="translate(183.445312 26.516813) scale(0.18 -0.18)">
    <defs>
     <path id="Cmr10-53" d="M 359 -91 
L 359 1403 
Q 359 1453 416 1453 
L 494 1453 
Q 513 1453 528 1437 
Q 544 1422 544 1403 
Q 544 775 933 429 
Q 1322 84 1953 84 
Q 2175 84 2362 212 
Q 2550 341 2654 548 
Q 2759 756 2759 978 
Q 2759 1172 2681 1355 
Q 2603 1538 2456 1672 
Q 2309 1806 2125 1850 
L 1294 2053 
Q 881 2163 620 2502 
Q 359 2841 359 3263 
Q 359 3594 528 3884 
Q 697 4175 983 4344 
Q 1269 4513 1600 4513 
Q 2241 4513 2619 4078 
L 2881 4494 
Q 2900 4513 2925 4513 
L 2969 4513 
Q 2988 4513 3005 4498 
Q 3022 4484 3022 4459 
L 3022 2975 
Q 3022 2919 2969 2919 
L 2894 2919 
Q 2834 2919 2834 2975 
Q 2834 3138 2779 3331 
Q 2725 3525 2628 3703 
Q 2531 3881 2419 3994 
Q 2109 4306 1600 4306 
Q 1381 4306 1197 4195 
Q 1013 4084 903 3893 
Q 794 3703 794 3494 
Q 794 3219 964 2995 
Q 1134 2772 1409 2700 
L 2241 2497 
Q 2447 2447 2630 2317 
Q 2813 2188 2934 2016 
Q 3056 1844 3125 1633 
Q 3194 1422 3194 1197 
Q 3194 850 3034 542 
Q 2875 234 2586 46 
Q 2297 -141 1953 -141 
Q 1741 -141 1519 -94 
Q 1297 -47 1109 50 
Q 922 147 769 300 
L 500 -122 
Q 481 -141 453 -141 
L 416 -141 
Q 359 -141 359 -91 
z
" transform="scale(0.015625)"/>
     <path id="Cmr10-6d" d="M 191 0 
L 191 225 
Q 409 225 550 259 
Q 691 294 691 428 
L 691 2175 
Q 691 2347 639 2423 
Q 588 2500 491 2517 
Q 394 2534 191 2534 
L 191 2759 
L 1119 2828 
L 1119 2203 
Q 1247 2478 1498 2653 
Q 1750 2828 2047 2828 
Q 2784 2828 2913 2228 
Q 3041 2497 3287 2662 
Q 3534 2828 3828 2828 
Q 4119 2828 4317 2734 
Q 4516 2641 4616 2448 
Q 4716 2256 4716 1966 
L 4716 428 
Q 4716 294 4858 259 
Q 5000 225 5216 225 
L 5216 0 
L 3750 0 
L 3750 225 
Q 3969 225 4109 259 
Q 4250 294 4250 428 
L 4250 1947 
Q 4250 2269 4159 2466 
Q 4069 2663 3788 2663 
Q 3419 2663 3178 2366 
Q 2938 2069 2938 1691 
L 2938 428 
Q 2938 294 3078 259 
Q 3219 225 3438 225 
L 3438 0 
L 1972 0 
L 1972 225 
Q 2191 225 2331 259 
Q 2472 294 2472 428 
L 2472 1947 
Q 2472 2259 2381 2461 
Q 2291 2663 2009 2663 
Q 1638 2663 1398 2366 
Q 1159 2069 1159 1691 
L 1159 428 
Q 1159 294 1300 259 
Q 1441 225 1656 225 
L 1656 0 
L 191 0 
z
" transform="scale(0.015625)"/>
     <path id="Cmr10-70" d="M 166 -1241 
L 166 -1019 
Q 384 -1019 525 -981 
Q 666 -944 666 -813 
L 666 2272 
Q 666 2447 541 2490 
Q 416 2534 166 2534 
L 166 2759 
L 1113 2828 
L 1113 2431 
Q 1288 2625 1520 2726 
Q 1753 2828 2016 2828 
Q 2394 2828 2697 2623 
Q 3000 2419 3170 2086 
Q 3341 1753 3341 1381 
Q 3341 994 3152 659 
Q 2963 325 2636 126 
Q 2309 -72 1919 -72 
Q 1453 -72 1131 306 
L 1131 -813 
Q 1131 -944 1273 -981 
Q 1416 -1019 1631 -1019 
L 1631 -1241 
L 166 -1241 
z
M 1131 622 
Q 1244 394 1444 245 
Q 1644 97 1881 97 
Q 2103 97 2273 215 
Q 2444 334 2559 534 
Q 2675 734 2729 954 
Q 2784 1175 2784 1381 
Q 2784 1638 2692 1936 
Q 2600 2234 2411 2439 
Q 2222 2644 1953 2644 
Q 1694 2644 1476 2511 
Q 1259 2378 1131 2150 
L 1131 622 
z
" transform="scale(0.015625)"/>
    </defs>
    <use xlink:href="#Cmr10-53"/>
    <use xlink:href="#Cmr10-61" x="55.517578"/>
    <use xlink:href="#Cmr10-6d" x="105.517578"/>
    <use xlink:href="#Cmr10-70" x="188.818359"/>
    <use xlink:href="#Cmr10-6c" x="244.335938"/>
    <use xlink:href="#Cmr10-65" x="272.021484"/>
    <use xlink:href="#Cmr10-20" x="316.40625"/>
    <use xlink:href="#Cmr10-70" x="349.707031"/>
    <use xlink:href="#Cmr10-6c" x="405.224609"/>
    <use xlink:href="#Cmr10-6f" x="432.910156"/>
    <use xlink:href="#Cmr10-74" x="482.910156"/>
   </g>
  </g>
 </g>
 <defs>
  <clipPath id="p4a4d8e2eef">
   <rect x="57.6" y="41.472" width="357.12" height="266.112"/>
  </clipPath>
 </defs>
</svg>
\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"ignore_on_import\": true,\n\t\t\t\"source\": \"set_plot_backend(Backend.MATPLOTLIB)\\nf = plot($f(x)=\\\\cos(x)*\\\\exp(-x**2/5)$, ($x$, 0, 10), \\n         grid=True, xlabel=\\\"x-axis\\\", ylabel=\\\"function value\\\", title=\\\"Sample plot\\\", yrange=[-1,1], color=\\\"green\\\");\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 14481851293247292909,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 4836078092906293774,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"image_svg\",\n\t\t\t\t\t\"source\": \"<?xml version="1.0" encoding="utf-8" standalone="no"?>
<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
  "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="460.8pt" height="345.6pt" viewBox="0 0 460.8 345.6" xmlns="http://www.w3.org/2000/svg" version="1.1">
 <metadata>
  <rdf:RDF xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:cc="http://creativecommons.org/ns#" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
   <cc:Work>
    <dc:type rdf:resource="http://purl.org/dc/dcmitype/StillImage"/>
    <dc:date>2025-03-30T13:19:59.587486</dc:date>
    <dc:format>image/svg+xml</dc:format>
    <dc:creator>
     <cc:Agent>
      <dc:title>Matplotlib v3.6.3, https://matplotlib.org/</dc:title>
     </cc:Agent>
    </dc:creator>
   </cc:Work>
  </rdf:RDF>
 </metadata>
 <defs>
  <style type="text/css">*{stroke-linejoin: round; stroke-linecap: butt}</style>
 </defs>
 <g id="figure_1">
  <g id="patch_1">
   <path d="M 0 345.6 
L 460.8 345.6 
L 460.8 0 
L 0 0 
z
" style="fill: #ffffff"/>
  </g>
  <g id="axes_1">
   <g id="patch_2">
    <path d="M 57.6 307.584 
L 414.72 307.584 
L 414.72 41.472 
L 57.6 41.472 
z
" style="fill: #ffffff"/>
   </g>
   <g id="matplotlib.axis_1">
    <g id="xtick_1">
     <g id="line2d_1">
      <path d="M 73.832727 307.584 
L 73.832727 41.472 
" clip-path="url(#p1cadc425d4)" style="fill: none; stroke: #b0b0b0; stroke-width: 0.8; stroke-linecap: square"/>
     </g>
     <g id="line2d_2">
      <defs>
       <path id="mefd99b1c57" d="M 0 0 
L 0 3.5 
" style="stroke: #000000; stroke-width: 0.8"/>
      </defs>
      <g>
       <use xlink:href="#mefd99b1c57" x="73.832727" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_1">
      <!-- 0 -->
      <g transform="translate(70.651477 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-30" d="M 2034 4250 
Q 1547 4250 1301 3770 
Q 1056 3291 1056 2328 
Q 1056 1369 1301 889 
Q 1547 409 2034 409 
Q 2525 409 2770 889 
Q 3016 1369 3016 2328 
Q 3016 3291 2770 3770 
Q 2525 4250 2034 4250 
z
M 2034 4750 
Q 2819 4750 3233 4129 
Q 3647 3509 3647 2328 
Q 3647 1150 3233 529 
Q 2819 -91 2034 -91 
Q 1250 -91 836 529 
Q 422 1150 422 2328 
Q 422 3509 836 4129 
Q 1250 4750 2034 4750 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-30"/>
      </g>
     </g>
    </g>
    <g id="xtick_2">
     <g id="line2d_3">
      <path d="M 138.763636 307.584 
L 138.763636 41.472 
" clip-path="url(#p1cadc425d4)" style="fill: none; stroke: #b0b0b0; stroke-width: 0.8; stroke-linecap: square"/>
     </g>
     <g id="line2d_4">
      <g>
       <use xlink:href="#mefd99b1c57" x="138.763636" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_2">
      <!-- 2 -->
      <g transform="translate(135.582386 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-32" d="M 1228 531 
L 3431 531 
L 3431 0 
L 469 0 
L 469 531 
Q 828 903 1448 1529 
Q 2069 2156 2228 2338 
Q 2531 2678 2651 2914 
Q 2772 3150 2772 3378 
Q 2772 3750 2511 3984 
Q 2250 4219 1831 4219 
Q 1534 4219 1204 4116 
Q 875 4013 500 3803 
L 500 4441 
Q 881 4594 1212 4672 
Q 1544 4750 1819 4750 
Q 2544 4750 2975 4387 
Q 3406 4025 3406 3419 
Q 3406 3131 3298 2873 
Q 3191 2616 2906 2266 
Q 2828 2175 2409 1742 
Q 1991 1309 1228 531 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-32"/>
      </g>
     </g>
    </g>
    <g id="xtick_3">
     <g id="line2d_5">
      <path d="M 203.694545 307.584 
L 203.694545 41.472 
" clip-path="url(#p1cadc425d4)" style="fill: none; stroke: #b0b0b0; stroke-width: 0.8; stroke-linecap: square"/>
     </g>
     <g id="line2d_6">
      <g>
       <use xlink:href="#mefd99b1c57" x="203.694545" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_3">
      <!-- 4 -->
      <g transform="translate(200.513295 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-34" d="M 2419 4116 
L 825 1625 
L 2419 1625 
L 2419 4116 
z
M 2253 4666 
L 3047 4666 
L 3047 1625 
L 3713 1625 
L 3713 1100 
L 3047 1100 
L 3047 0 
L 2419 0 
L 2419 1100 
L 313 1100 
L 313 1709 
L 2253 4666 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-34"/>
      </g>
     </g>
    </g>
    <g id="xtick_4">
     <g id="line2d_7">
      <path d="M 268.625455 307.584 
L 268.625455 41.472 
" clip-path="url(#p1cadc425d4)" style="fill: none; stroke: #b0b0b0; stroke-width: 0.8; stroke-linecap: square"/>
     </g>
     <g id="line2d_8">
      <g>
       <use xlink:href="#mefd99b1c57" x="268.625455" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_4">
      <!-- 6 -->
      <g transform="translate(265.444205 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-36" d="M 2113 2584 
Q 1688 2584 1439 2293 
Q 1191 2003 1191 1497 
Q 1191 994 1439 701 
Q 1688 409 2113 409 
Q 2538 409 2786 701 
Q 3034 994 3034 1497 
Q 3034 2003 2786 2293 
Q 2538 2584 2113 2584 
z
M 3366 4563 
L 3366 3988 
Q 3128 4100 2886 4159 
Q 2644 4219 2406 4219 
Q 1781 4219 1451 3797 
Q 1122 3375 1075 2522 
Q 1259 2794 1537 2939 
Q 1816 3084 2150 3084 
Q 2853 3084 3261 2657 
Q 3669 2231 3669 1497 
Q 3669 778 3244 343 
Q 2819 -91 2113 -91 
Q 1303 -91 875 529 
Q 447 1150 447 2328 
Q 447 3434 972 4092 
Q 1497 4750 2381 4750 
Q 2619 4750 2861 4703 
Q 3103 4656 3366 4563 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-36"/>
      </g>
     </g>
    </g>
    <g id="xtick_5">
     <g id="line2d_9">
      <path d="M 333.556364 307.584 
L 333.556364 41.472 
" clip-path="url(#p1cadc425d4)" style="fill: none; stroke: #b0b0b0; stroke-width: 0.8; stroke-linecap: square"/>
     </g>
     <g id="line2d_10">
      <g>
       <use xlink:href="#mefd99b1c57" x="333.556364" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_5">
      <!-- 8 -->
      <g transform="translate(330.375114 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-38" d="M 2034 2216 
Q 1584 2216 1326 1975 
Q 1069 1734 1069 1313 
Q 1069 891 1326 650 
Q 1584 409 2034 409 
Q 2484 409 2743 651 
Q 3003 894 3003 1313 
Q 3003 1734 2745 1975 
Q 2488 2216 2034 2216 
z
M 1403 2484 
Q 997 2584 770 2862 
Q 544 3141 544 3541 
Q 544 4100 942 4425 
Q 1341 4750 2034 4750 
Q 2731 4750 3128 4425 
Q 3525 4100 3525 3541 
Q 3525 3141 3298 2862 
Q 3072 2584 2669 2484 
Q 3125 2378 3379 2068 
Q 3634 1759 3634 1313 
Q 3634 634 3220 271 
Q 2806 -91 2034 -91 
Q 1263 -91 848 271 
Q 434 634 434 1313 
Q 434 1759 690 2068 
Q 947 2378 1403 2484 
z
M 1172 3481 
Q 1172 3119 1398 2916 
Q 1625 2713 2034 2713 
Q 2441 2713 2670 2916 
Q 2900 3119 2900 3481 
Q 2900 3844 2670 4047 
Q 2441 4250 2034 4250 
Q 1625 4250 1398 4047 
Q 1172 3844 1172 3481 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-38"/>
      </g>
     </g>
    </g>
    <g id="xtick_6">
     <g id="line2d_11">
      <path d="M 398.487273 307.584 
L 398.487273 41.472 
" clip-path="url(#p1cadc425d4)" style="fill: none; stroke: #b0b0b0; stroke-width: 0.8; stroke-linecap: square"/>
     </g>
     <g id="line2d_12">
      <g>
       <use xlink:href="#mefd99b1c57" x="398.487273" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_6">
      <!-- 10 -->
      <g transform="translate(392.124773 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-31" d="M 794 531 
L 1825 531 
L 1825 4091 
L 703 3866 
L 703 4441 
L 1819 4666 
L 2450 4666 
L 2450 531 
L 3481 531 
L 3481 0 
L 794 0 
L 794 531 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-31"/>
       <use xlink:href="#DejaVuSans-30" x="63.623047"/>
      </g>
     </g>
    </g>
    <g id="text_7">
     <!-- x-axis -->
     <g transform="translate(215.69875 339.364625) scale(0.16 -0.16)">
      <defs>
       <path id="Cmr10-78" d="M 78 0 
L 78 225 
Q 322 225 537 320 
Q 753 416 903 603 
L 1484 1344 
L 728 2328 
Q 616 2469 483 2501 
Q 350 2534 109 2534 
L 109 2759 
L 1441 2759 
L 1441 2534 
Q 1356 2534 1282 2496 
Q 1209 2459 1209 2388 
Q 1209 2363 1228 2328 
L 1741 1663 
L 2125 2156 
Q 2203 2250 2203 2344 
Q 2203 2422 2151 2478 
Q 2100 2534 2016 2534 
L 2016 2759 
L 3194 2759 
L 3194 2534 
Q 2947 2534 2730 2439 
Q 2513 2344 2363 2156 
L 1856 1509 
L 2675 428 
Q 2797 288 2928 256 
Q 3059 225 3303 225 
L 3303 0 
L 1972 0 
L 1972 225 
Q 2050 225 2122 262 
Q 2194 300 2194 372 
Q 2194 400 2175 428 
L 1600 1191 
L 1141 603 
Q 1069 522 1069 416 
Q 1069 338 1122 281 
Q 1175 225 1247 225 
L 1247 0 
L 78 0 
z
" transform="scale(0.015625)"/>
       <path id="Cmr10-2d" d="M 72 1184 
L 72 1581 
L 1766 1581 
L 1766 1184 
L 72 1184 
z
" transform="scale(0.015625)"/>
       <path id="Cmr10-61" d="M 256 628 
Q 256 1009 556 1248 
Q 856 1488 1276 1586 
Q 1697 1684 2075 1684 
L 2075 1947 
Q 2075 2131 1994 2304 
Q 1913 2478 1759 2589 
Q 1606 2700 1422 2700 
Q 997 2700 775 2509 
Q 897 2509 976 2417 
Q 1056 2325 1056 2203 
Q 1056 2075 965 1984 
Q 875 1894 750 1894 
Q 622 1894 531 1984 
Q 441 2075 441 2203 
Q 441 2541 747 2705 
Q 1053 2869 1422 2869 
Q 1681 2869 1943 2758 
Q 2206 2647 2373 2440 
Q 2541 2234 2541 1959 
L 2541 519 
Q 2541 394 2594 289 
Q 2647 184 2759 184 
Q 2866 184 2917 290 
Q 2969 397 2969 519 
L 2969 928 
L 3156 928 
L 3156 519 
Q 3156 375 3081 245 
Q 3006 116 2879 39 
Q 2753 -38 2606 -38 
Q 2419 -38 2283 107 
Q 2147 253 2131 453 
Q 2013 213 1781 70 
Q 1550 -72 1288 -72 
Q 1044 -72 808 0 
Q 572 72 414 226 
Q 256 381 256 628 
z
M 775 628 
Q 775 403 940 250 
Q 1106 97 1331 97 
Q 1538 97 1706 200 
Q 1875 303 1975 481 
Q 2075 659 2075 856 
L 2075 1522 
Q 1784 1522 1479 1426 
Q 1175 1331 975 1128 
Q 775 925 775 628 
z
" transform="scale(0.015625)"/>
       <path id="Cmr10-69" d="M 197 0 
L 197 225 
Q 416 225 556 259 
Q 697 294 697 428 
L 697 2175 
Q 697 2422 601 2478 
Q 506 2534 225 2534 
L 225 2759 
L 1147 2828 
L 1147 428 
Q 1147 294 1269 259 
Q 1391 225 1594 225 
L 1594 0 
L 197 0 
z
M 469 3928 
Q 469 4069 575 4175 
Q 681 4281 819 4281 
Q 909 4281 993 4234 
Q 1078 4188 1125 4103 
Q 1172 4019 1172 3928 
Q 1172 3791 1065 3684 
Q 959 3578 819 3578 
Q 681 3578 575 3684 
Q 469 3791 469 3928 
z
" transform="scale(0.015625)"/>
       <path id="Cmr10-73" d="M 213 -19 
L 213 1025 
Q 213 1075 269 1075 
L 347 1075 
Q 384 1075 397 1025 
Q 575 97 1259 97 
Q 1563 97 1767 234 
Q 1972 372 1972 659 
Q 1972 866 1812 1011 
Q 1653 1156 1434 1209 
L 1006 1294 
Q 791 1341 614 1437 
Q 438 1534 325 1695 
Q 213 1856 213 2069 
Q 213 2350 361 2529 
Q 509 2709 746 2789 
Q 984 2869 1259 2869 
Q 1588 2869 1831 2694 
L 2016 2853 
Q 2016 2869 2047 2869 
L 2094 2869 
Q 2113 2869 2128 2851 
Q 2144 2834 2144 2816 
L 2144 1978 
Q 2144 1919 2094 1919 
L 2016 1919 
Q 1959 1919 1959 1978 
Q 1959 2313 1773 2516 
Q 1588 2719 1253 2719 
Q 966 2719 755 2612 
Q 544 2506 544 2247 
Q 544 2069 695 1955 
Q 847 1841 1050 1791 
L 1484 1709 
Q 1703 1659 1892 1540 
Q 2081 1422 2192 1240 
Q 2303 1059 2303 831 
Q 2303 600 2223 429 
Q 2144 259 2001 146 
Q 1859 34 1665 -19 
Q 1472 -72 1259 -72 
Q 859 -72 575 197 
L 341 -56 
Q 341 -72 306 -72 
L 269 -72 
Q 213 -72 213 -19 
z
" transform="scale(0.015625)"/>
      </defs>
      <use xlink:href="#Cmr10-78"/>
      <use xlink:href="#Cmr10-2d" x="52.685547"/>
      <use xlink:href="#Cmr10-61" x="85.986328"/>
      <use xlink:href="#Cmr10-78" x="135.986328"/>
      <use xlink:href="#Cmr10-69" x="188.671875"/>
      <use xlink:href="#Cmr10-73" x="216.357422"/>
     </g>
    </g>
   </g>
   <g id="matplotlib.axis_2">
    <g id="ytick_1">
     <g id="line2d_13">
      <path d="M 57.6 307.584 
L 414.72 307.584 
" clip-path="url(#p1cadc425d4)" style="fill: none; stroke: #b0b0b0; stroke-width: 0.8; stroke-linecap: square"/>
     </g>
     <g id="line2d_14">
      <defs>
       <path id="me442b8523c" d="M 0 0 
L -3.5 0 
" style="stroke: #000000; stroke-width: 0.8"/>
      </defs>
      <g>
       <use xlink:href="#me442b8523c" x="57.6" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_8">
      <!-- −1.00 -->
      <g transform="translate(19.954687 311.383219) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-2212" d="M 678 2272 
L 4684 2272 
L 4684 1741 
L 678 1741 
L 678 2272 
z
" transform="scale(0.015625)"/>
        <path id="DejaVuSans-2e" d="M 684 794 
L 1344 794 
L 1344 0 
L 684 0 
L 684 794 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-2212"/>
       <use xlink:href="#DejaVuSans-31" x="83.789062"/>
       <use xlink:href="#DejaVuSans-2e" x="147.412109"/>
       <use xlink:href="#DejaVuSans-30" x="179.199219"/>
       <use xlink:href="#DejaVuSans-30" x="242.822266"/>
      </g>
     </g>
    </g>
    <g id="ytick_2">
     <g id="line2d_15">
      <path d="M 57.6 274.32 
L 414.72 274.32 
" clip-path="url(#p1cadc425d4)" style="fill: none; stroke: #b0b0b0; stroke-width: 0.8; stroke-linecap: square"/>
     </g>
     <g id="line2d_16">
      <g>
       <use xlink:href="#me442b8523c" x="57.6" y="274.32" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_9">
      <!-- −0.75 -->
      <g transform="translate(19.954687 278.119219) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-37" d="M 525 4666 
L 3525 4666 
L 3525 4397 
L 1831 0 
L 1172 0 
L 2766 4134 
L 525 4134 
L 525 4666 
z
" transform="scale(0.015625)"/>
        <path id="DejaVuSans-35" d="M 691 4666 
L 3169 4666 
L 3169 4134 
L 1269 4134 
L 1269 2991 
Q 1406 3038 1543 3061 
Q 1681 3084 1819 3084 
Q 2600 3084 3056 2656 
Q 3513 2228 3513 1497 
Q 3513 744 3044 326 
Q 2575 -91 1722 -91 
Q 1428 -91 1123 -41 
Q 819 9 494 109 
L 494 744 
Q 775 591 1075 516 
Q 1375 441 1709 441 
Q 2250 441 2565 725 
Q 2881 1009 2881 1497 
Q 2881 1984 2565 2268 
Q 2250 2553 1709 2553 
Q 1456 2553 1204 2497 
Q 953 2441 691 2322 
L 691 4666 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-2212"/>
       <use xlink:href="#DejaVuSans-30" x="83.789062"/>
       <use xlink:href="#DejaVuSans-2e" x="147.412109"/>
       <use xlink:href="#DejaVuSans-37" x="179.199219"/>
       <use xlink:href="#DejaVuSans-35" x="242.822266"/>
      </g>
     </g>
    </g>
    <g id="ytick_3">
     <g id="line2d_17">
      <path d="M 57.6 241.056 
L 414.72 241.056 
" clip-path="url(#p1cadc425d4)" style="fill: none; stroke: #b0b0b0; stroke-width: 0.8; stroke-linecap: square"/>
     </g>
     <g id="line2d_18">
      <g>
       <use xlink:href="#me442b8523c" x="57.6" y="241.056" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_10">
      <!-- −0.50 -->
      <g transform="translate(19.954687 244.855219) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-2212"/>
       <use xlink:href="#DejaVuSans-30" x="83.789062"/>
       <use xlink:href="#DejaVuSans-2e" x="147.412109"/>
       <use xlink:href="#DejaVuSans-35" x="179.199219"/>
       <use xlink:href="#DejaVuSans-30" x="242.822266"/>
      </g>
     </g>
    </g>
    <g id="ytick_4">
     <g id="line2d_19">
      <path d="M 57.6 207.792 
L 414.72 207.792 
" clip-path="url(#p1cadc425d4)" style="fill: none; stroke: #b0b0b0; stroke-width: 0.8; stroke-linecap: square"/>
     </g>
     <g id="line2d_20">
      <g>
       <use xlink:href="#me442b8523c" x="57.6" y="207.792" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_11">
      <!-- −0.25 -->
      <g transform="translate(19.954687 211.591219) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-2212"/>
       <use xlink:href="#DejaVuSans-30" x="83.789062"/>
       <use xlink:href="#DejaVuSans-2e" x="147.412109"/>
       <use xlink:href="#DejaVuSans-32" x="179.199219"/>
       <use xlink:href="#DejaVuSans-35" x="242.822266"/>
      </g>
     </g>
    </g>
    <g id="ytick_5">
     <g id="line2d_21">
      <path d="M 57.6 174.528 
L 414.72 174.528 
" clip-path="url(#p1cadc425d4)" style="fill: none; stroke: #b0b0b0; stroke-width: 0.8; stroke-linecap: square"/>
     </g>
     <g id="line2d_22">
      <g>
       <use xlink:href="#me442b8523c" x="57.6" y="174.528" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_12">
      <!-- 0.00 -->
      <g transform="translate(28.334375 178.327219) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-30"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-30" x="95.410156"/>
       <use xlink:href="#DejaVuSans-30" x="159.033203"/>
      </g>
     </g>
    </g>
    <g id="ytick_6">
     <g id="line2d_23">
      <path d="M 57.6 141.264 
L 414.72 141.264 
" clip-path="url(#p1cadc425d4)" style="fill: none; stroke: #b0b0b0; stroke-width: 0.8; stroke-linecap: square"/>
     </g>
     <g id="line2d_24">
      <g>
       <use xlink:href="#me442b8523c" x="57.6" y="141.264" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_13">
      <!-- 0.25 -->
      <g transform="translate(28.334375 145.063219) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-30"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-32" x="95.410156"/>
       <use xlink:href="#DejaVuSans-35" x="159.033203"/>
      </g>
     </g>
    </g>
    <g id="ytick_7">
     <g id="line2d_25">
      <path d="M 57.6 108 
L 414.72 108 
" clip-path="url(#p1cadc425d4)" style="fill: none; stroke: #b0b0b0; stroke-width: 0.8; stroke-linecap: square"/>
     </g>
     <g id="line2d_26">
      <g>
       <use xlink:href="#me442b8523c" x="57.6" y="108" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_14">
      <!-- 0.50 -->
      <g transform="translate(28.334375 111.799219) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-30"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-35" x="95.410156"/>
       <use xlink:href="#DejaVuSans-30" x="159.033203"/>
      </g>
     </g>
    </g>
    <g id="ytick_8">
     <g id="line2d_27">
      <path d="M 57.6 74.736 
L 414.72 74.736 
" clip-path="url(#p1cadc425d4)" style="fill: none; stroke: #b0b0b0; stroke-width: 0.8; stroke-linecap: square"/>
     </g>
     <g id="line2d_28">
      <g>
       <use xlink:href="#me442b8523c" x="57.6" y="74.736" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_15">
      <!-- 0.75 -->
      <g transform="translate(28.334375 78.535219) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-30"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-37" x="95.410156"/>
       <use xlink:href="#DejaVuSans-35" x="159.033203"/>
      </g>
     </g>
    </g>
    <g id="ytick_9">
     <g id="line2d_29">
      <path d="M 57.6 41.472 
L 414.72 41.472 
" clip-path="url(#p1cadc425d4)" style="fill: none; stroke: #b0b0b0; stroke-width: 0.8; stroke-linecap: square"/>
     </g>
     <g id="line2d_30">
      <g>
       <use xlink:href="#me442b8523c" x="57.6" y="41.472" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_16">
      <!-- 1.00 -->
      <g transform="translate(28.334375 45.271219) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-31"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-30" x="95.410156"/>
       <use xlink:href="#DejaVuSans-30" x="159.033203"/>
      </g>
     </g>
    </g>
    <g id="text_17">
     <!-- function value -->
     <g transform="translate(12.852187 224.2505) rotate(-90) scale(0.16 -0.16)">
      <defs>
       <path id="Cmr10-66" d="M 206 0 
L 206 225 
Q 422 225 562 259 
Q 703 294 703 428 
L 703 2534 
L 213 2534 
L 213 2759 
L 703 2759 
L 703 3525 
Q 703 3731 789 3911 
Q 875 4091 1020 4225 
Q 1166 4359 1355 4436 
Q 1544 4513 1747 4513 
Q 1963 4513 2136 4384 
Q 2309 4256 2309 4044 
Q 2309 3922 2226 3839 
Q 2144 3756 2022 3756 
Q 1900 3756 1814 3839 
Q 1728 3922 1728 4044 
Q 1728 4244 1900 4313 
Q 1797 4347 1716 4347 
Q 1528 4347 1395 4214 
Q 1263 4081 1197 3890 
Q 1131 3700 1131 3513 
L 1131 2759 
L 1869 2759 
L 1869 2534 
L 1153 2534 
L 1153 428 
Q 1153 297 1340 261 
Q 1528 225 1772 225 
L 1772 0 
L 206 0 
z
" transform="scale(0.015625)"/>
       <path id="Cmr10-75" d="M 691 763 
L 691 2175 
Q 691 2347 639 2423 
Q 588 2500 491 2517 
Q 394 2534 191 2534 
L 191 2759 
L 1159 2828 
L 1159 763 
Q 1159 513 1195 373 
Q 1231 234 1348 165 
Q 1466 97 1722 97 
Q 2066 97 2269 384 
Q 2472 672 2472 1038 
L 2472 2175 
Q 2472 2347 2419 2423 
Q 2366 2500 2270 2517 
Q 2175 2534 1972 2534 
L 1972 2759 
L 2938 2828 
L 2938 581 
Q 2938 413 2989 336 
Q 3041 259 3137 242 
Q 3234 225 3438 225 
L 3438 0 
L 2491 -72 
L 2491 469 
Q 2372 228 2159 78 
Q 1947 -72 1691 -72 
Q 1231 -72 961 123 
Q 691 319 691 763 
z
" transform="scale(0.015625)"/>
       <path id="Cmr10-6e" d="M 191 0 
L 191 225 
Q 409 225 550 259 
Q 691 294 691 428 
L 691 2175 
Q 691 2347 639 2423 
Q 588 2500 491 2517 
Q 394 2534 191 2534 
L 191 2759 
L 1119 2828 
L 1119 2203 
Q 1247 2478 1498 2653 
Q 1750 2828 2047 2828 
Q 2491 2828 2714 2615 
Q 2938 2403 2938 1966 
L 2938 428 
Q 2938 294 3078 259 
Q 3219 225 3438 225 
L 3438 0 
L 1972 0 
L 1972 225 
Q 2191 225 2331 259 
Q 2472 294 2472 428 
L 2472 1947 
Q 2472 2259 2381 2461 
Q 2291 2663 2009 2663 
Q 1638 2663 1398 2366 
Q 1159 2069 1159 1691 
L 1159 428 
Q 1159 294 1300 259 
Q 1441 225 1656 225 
L 1656 0 
L 191 0 
z
" transform="scale(0.015625)"/>
       <path id="Cmr10-63" d="M 1594 -72 
Q 1206 -72 890 129 
Q 575 331 394 667 
Q 213 1003 213 1381 
Q 213 1759 392 2106 
Q 572 2453 889 2661 
Q 1206 2869 1594 2869 
Q 1969 2869 2276 2722 
Q 2584 2575 2584 2241 
Q 2584 2116 2495 2023 
Q 2406 1931 2278 1931 
Q 2150 1931 2061 2023 
Q 1972 2116 1972 2241 
Q 1972 2353 2044 2436 
Q 2116 2519 2222 2541 
Q 2000 2681 1600 2681 
Q 1294 2681 1106 2478 
Q 919 2275 844 1975 
Q 769 1675 769 1381 
Q 769 1072 861 783 
Q 953 494 1158 305 
Q 1363 116 1672 116 
Q 1975 116 2187 302 
Q 2400 488 2478 788 
Q 2478 825 2528 825 
L 2606 825 
Q 2625 825 2640 808 
Q 2656 791 2656 769 
L 2656 750 
Q 2559 372 2271 150 
Q 1984 -72 1594 -72 
z
" transform="scale(0.015625)"/>
       <path id="Cmr10-74" d="M 653 769 
L 653 2534 
L 122 2534 
L 122 2700 
Q 541 2700 737 3090 
Q 934 3481 934 3938 
L 1119 3938 
L 1119 2759 
L 2022 2759 
L 2022 2534 
L 1119 2534 
L 1119 781 
Q 1119 516 1208 316 
Q 1297 116 1528 116 
Q 1747 116 1844 327 
Q 1941 538 1941 781 
L 1941 1159 
L 2125 1159 
L 2125 769 
Q 2125 569 2051 373 
Q 1978 178 1834 53 
Q 1691 -72 1484 -72 
Q 1100 -72 876 158 
Q 653 388 653 769 
z
" transform="scale(0.015625)"/>
       <path id="Cmr10-6f" d="M 1600 -72 
Q 1216 -72 887 123 
Q 559 319 368 647 
Q 178 975 178 1363 
Q 178 1656 283 1928 
Q 388 2200 583 2414 
Q 778 2628 1037 2748 
Q 1297 2869 1600 2869 
Q 1994 2869 2317 2661 
Q 2641 2453 2828 2104 
Q 3016 1756 3016 1363 
Q 3016 978 2825 648 
Q 2634 319 2307 123 
Q 1981 -72 1600 -72 
z
M 1600 116 
Q 2113 116 2284 487 
Q 2456 859 2456 1434 
Q 2456 1756 2422 1967 
Q 2388 2178 2272 2350 
Q 2200 2456 2089 2536 
Q 1978 2616 1854 2658 
Q 1731 2700 1600 2700 
Q 1400 2700 1220 2609 
Q 1041 2519 922 2350 
Q 803 2169 770 1951 
Q 738 1734 738 1434 
Q 738 1075 800 789 
Q 863 503 1052 309 
Q 1241 116 1600 116 
z
" transform="scale(0.015625)"/>
       <path id="Cmr10-20" transform="scale(0.015625)"/>
       <path id="Cmr10-76" d="M 1563 0 
L 628 2350 
Q 569 2469 445 2501 
Q 322 2534 122 2534 
L 122 2759 
L 1466 2759 
L 1466 2534 
Q 1106 2534 1106 2381 
Q 1106 2356 1113 2344 
L 1831 538 
L 2478 2169 
Q 2497 2219 2497 2272 
Q 2497 2394 2405 2464 
Q 2313 2534 2188 2534 
L 2188 2759 
L 3250 2759 
L 3250 2534 
Q 3053 2534 2904 2443 
Q 2756 2353 2675 2175 
L 1813 0 
Q 1788 -72 1709 -72 
L 1663 -72 
Q 1584 -72 1563 0 
z
" transform="scale(0.015625)"/>
       <path id="Cmr10-6c" d="M 197 0 
L 197 225 
Q 416 225 556 259 
Q 697 294 697 428 
L 697 3788 
Q 697 3959 645 4036 
Q 594 4113 497 4130 
Q 400 4147 197 4147 
L 197 4372 
L 1147 4441 
L 1147 428 
Q 1147 294 1287 259 
Q 1428 225 1644 225 
L 1644 0 
L 197 0 
z
" transform="scale(0.015625)"/>
       <path id="Cmr10-65" d="M 1594 -72 
Q 1203 -72 876 133 
Q 550 338 364 680 
Q 178 1022 178 1403 
Q 178 1778 348 2115 
Q 519 2453 823 2661 
Q 1128 2869 1503 2869 
Q 1797 2869 2014 2770 
Q 2231 2672 2372 2497 
Q 2513 2322 2584 2084 
Q 2656 1847 2656 1563 
Q 2656 1478 2591 1478 
L 738 1478 
L 738 1409 
Q 738 878 952 497 
Q 1166 116 1650 116 
Q 1847 116 2014 203 
Q 2181 291 2304 447 
Q 2428 603 2472 781 
Q 2478 803 2495 820 
Q 2513 838 2534 838 
L 2591 838 
Q 2656 838 2656 756 
Q 2566 394 2266 161 
Q 1966 -72 1594 -72 
z
M 744 1638 
L 2203 1638 
Q 2203 1878 2136 2125 
Q 2069 2372 1912 2536 
Q 1756 2700 1503 2700 
Q 1141 2700 942 2361 
Q 744 2022 744 1638 
z
" transform="scale(0.015625)"/>
      </defs>
      <use xlink:href="#Cmr10-66"/>
      <use xlink:href="#Cmr10-75" x="30.517578"/>
      <use xlink:href="#Cmr10-6e" x="86.035156"/>
      <use xlink:href="#Cmr10-63" x="141.552734"/>
      <use xlink:href="#Cmr10-74" x="185.9375"/>
      <use xlink:href="#Cmr10-69" x="224.755859"/>
      <use xlink:href="#Cmr10-6f" x="252.441406"/>
      <use xlink:href="#Cmr10-6e" x="302.441406"/>
      <use xlink:href="#Cmr10-20" x="357.958984"/>
      <use xlink:href="#Cmr10-76" x="391.259766"/>
      <use xlink:href="#Cmr10-61" x="443.945312"/>
      <use xlink:href="#Cmr10-6c" x="493.945312"/>
      <use xlink:href="#Cmr10-75" x="521.630859"/>
      <use xlink:href="#Cmr10-65" x="577.148438"/>
     </g>
    </g>
   </g>
   <g id="line2d_31">
    <path d="M 73.832727 41.472 
L 74.807666 41.555976 
L 76.107584 41.928778 
L 77.407502 42.598085 
L 78.70742 43.560928 
L 80.007338 44.813047 
L 81.307256 46.348911 
L 82.932154 48.657341 
L 84.557052 51.382657 
L 86.181949 54.506291 
L 88.131826 58.750495 
L 90.406683 64.333417 
L 92.68154 70.526918 
L 95.281376 78.250915 
L 98.531171 88.687987 
L 102.430925 102.015065 
L 115.755086 148.229974 
L 119.004881 158.407429 
L 121.929697 166.87655 
L 124.529533 173.773514 
L 127.129369 180.022126 
L 129.404226 184.928681 
L 131.679083 189.295437 
L 133.62896 192.603382 
L 135.578837 195.510041 
L 137.528714 198.019857 
L 139.478591 200.14101 
L 141.428468 201.88508 
L 143.053366 203.060889 
L 144.678264 203.994833 
L 146.303161 204.697926 
L 147.928059 205.182152 
L 149.552957 205.460297 
L 151.177854 205.545796 
L 153.127731 205.413736 
L 155.077609 205.049026 
L 157.027486 204.476705 
L 159.302342 203.580013 
L 161.902179 202.301244 
L 164.826994 200.606401 
L 168.401769 198.273177 
L 174.2514 194.140136 
L 181.72593 188.899826 
L 186.275643 185.988816 
L 190.175397 183.747505 
L 194.075152 181.772234 
L 197.649926 180.204855 
L 201.224701 178.867756 
L 205.124455 177.659062 
L 209.02421 176.690023 
L 213.248943 175.879513 
L 217.798657 175.243138 
L 222.998329 174.75737 
L 228.847961 174.441186 
L 236.32249 174.271967 
L 247.371794 174.268452 
L 305.543129 174.524711 
L 398.487273 174.528 
L 398.487273 174.528 
" clip-path="url(#p1cadc425d4)" style="fill: none; stroke: #008000; stroke-width: 1.5; stroke-linecap: square"/>
   </g>
   <g id="line2d_32">
    <path d="M 73.832727 174.528 
L 82.607174 139.003125 
L 87.481867 120.221952 
L 91.381622 106.057443 
L 94.956396 93.935415 
L 97.881212 84.737189 
L 100.806028 76.267232 
L 103.405864 69.405447 
L 105.680721 63.952689 
L 107.955577 59.042614 
L 110.230434 54.699319 
L 112.180311 51.443841 
L 114.130188 48.63222 
L 115.755086 46.635623 
L 117.379984 44.959331 
L 119.004881 43.607542 
L 120.629779 42.583641 
L 121.929697 42.002351 
L 123.229615 41.633498 
L 124.529533 41.477674 
L 125.829451 41.535128 
L 127.129369 41.805768 
L 128.429287 42.289161 
L 129.729206 42.984532 
L 131.354103 44.150109 
L 132.979001 45.642214 
L 134.603898 47.457113 
L 136.228796 49.590258 
L 138.178673 52.562542 
L 140.12855 55.974648 
L 142.078428 59.814272 
L 144.353284 64.815614 
L 146.628141 70.355403 
L 149.227977 77.310921 
L 151.827813 84.889541 
L 154.752629 94.099664 
L 158.002424 105.094789 
L 161.577199 117.987864 
L 165.801933 134.095297 
L 171.326585 156.146789 
L 187.250581 220.390113 
L 191.475315 236.210058 
L 195.05009 248.791724 
L 198.299885 259.452866 
L 201.224701 268.32381 
L 203.824537 275.572538 
L 206.424373 282.173632 
L 208.69923 287.384958 
L 210.974087 292.042405 
L 212.923964 295.576257 
L 214.873841 298.673593 
L 216.823718 301.323244 
L 218.448616 303.182362 
L 220.073514 304.719268 
L 221.698411 305.930112 
L 222.998329 306.661956 
L 224.298247 307.181992 
L 225.598165 307.489384 
L 226.898084 307.58364 
L 228.198002 307.464609 
L 229.49792 307.132483 
L 230.797838 306.587792 
L 232.097756 305.831411 
L 233.722654 304.590124 
L 235.347551 303.023098 
L 236.972449 301.134259 
L 238.597346 298.928336 
L 240.547224 295.870512 
L 242.497101 292.375111 
L 244.446978 288.454739 
L 246.721835 283.362798 
L 248.996691 277.736718 
L 251.596527 270.688397 
L 254.196364 263.023747 
L 257.121179 253.72562 
L 260.370975 242.644449 
L 263.945749 229.671979 
L 268.170483 213.492579 
L 273.695135 191.384571 
L 288.644193 130.980464 
L 292.868927 115.033803 
L 296.443702 102.315916 
L 299.693497 91.509324 
L 302.618313 82.491112 
L 305.543129 74.219387 
L 308.142965 67.547805 
L 310.417821 62.271286 
L 312.692678 57.545701 
L 314.642555 53.951355 
L 316.592432 50.791823 
L 318.54231 48.078499 
L 320.167207 46.165358 
L 321.792105 44.573699 
L 323.417002 43.307508 
L 325.0419 42.369957 
L 326.341818 41.858143 
L 327.641736 41.558997 
L 328.941654 41.473 
L 330.241572 41.600288 
L 331.541491 41.940658 
L 332.841409 42.493564 
L 334.141327 43.258121 
L 335.766224 44.50955 
L 337.391122 46.086608 
L 339.01602 47.985345 
L 340.640917 50.201007 
L 342.590794 53.270273 
L 344.540672 56.77681 
L 346.490549 60.707972 
L 348.765405 65.812012 
L 351.040262 71.449609 
L 353.640098 78.510305 
L 356.564914 87.186791 
L 359.48973 96.57168 
L 362.739525 107.737416 
L 366.639279 122.008642 
L 371.188993 139.599946 
L 377.363604 164.501285 
L 389.387846 213.205267 
L 393.937559 230.609064 
L 397.837314 244.663812 
L 398.487273 246.913273 
L 398.487273 246.913273 
" clip-path="url(#p1cadc425d4)" style="fill: none; stroke: #ff0000; stroke-width: 1.5; stroke-linecap: square"/>
   </g>
   <g id="patch_3">
    <path d="M 57.6 307.584 
L 57.6 41.472 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
   <g id="patch_4">
    <path d="M 414.72 307.584 
L 414.72 41.472 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
   <g id="patch_5">
    <path d="M 57.6 307.584 
L 414.72 307.584 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
   <g id="patch_6">
    <path d="M 57.6 41.472 
L 414.72 41.472 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
   <g id="legend_1">
    <g id="patch_7">
     <path d="M 357.32 64.570437 
L 407.72 64.570437 
Q 409.72 64.570437 409.72 62.570437 
L 409.72 48.472 
Q 409.72 46.472 407.72 46.472 
L 357.32 46.472 
Q 355.32 46.472 355.32 48.472 
L 355.32 62.570437 
Q 355.32 64.570437 357.32 64.570437 
z
" style="fill: #ffffff; opacity: 0.8; stroke: #cccccc; stroke-linejoin: miter"/>
    </g>
    <g id="line2d_33">
     <path d="M 359.32 54.570437 
L 369.32 54.570437 
L 379.32 54.570437 
" style="fill: none; stroke: #008000; stroke-width: 1.5; stroke-linecap: square"/>
    </g>
    <g id="text_18">
     <!-- $f(x)$ -->
     <g transform="translate(387.32 58.070437) scale(0.1 -0.1)">
      <defs>
       <path id="Cmmi10-66" d="M 622 -1056 
Q 741 -1147 909 -1147 
Q 1138 -1147 1281 -641 
Q 1341 -397 1606 966 
L 1900 2534 
L 1350 2534 
Q 1288 2534 1288 2619 
Q 1313 2759 1369 2759 
L 1941 2759 
L 2016 3175 
Q 2053 3369 2084 3508 
Q 2116 3647 2152 3765 
Q 2188 3884 2259 4031 
Q 2369 4241 2555 4377 
Q 2741 4513 2956 4513 
Q 3097 4513 3230 4461 
Q 3363 4409 3447 4306 
Q 3531 4203 3531 4063 
Q 3531 3900 3423 3779 
Q 3316 3659 3163 3659 
Q 3059 3659 2986 3723 
Q 2913 3788 2913 3891 
Q 2913 4031 3008 4136 
Q 3103 4241 3244 4256 
Q 3125 4347 2950 4347 
Q 2853 4347 2767 4256 
Q 2681 4166 2656 4063 
Q 2616 3900 2478 3181 
L 2400 2759 
L 3059 2759 
Q 3122 2759 3122 2675 
Q 3119 2659 3109 2620 
Q 3100 2581 3083 2557 
Q 3066 2534 3041 2534 
L 2356 2534 
L 2059 972 
Q 2003 631 1929 279 
Q 1856 -72 1723 -442 
Q 1591 -813 1384 -1063 
Q 1178 -1313 897 -1313 
Q 681 -1313 511 -1189 
Q 341 -1066 341 -863 
Q 341 -700 445 -579 
Q 550 -459 709 -459 
Q 816 -459 887 -523 
Q 959 -588 959 -691 
Q 959 -828 857 -942 
Q 756 -1056 622 -1056 
z
" transform="scale(0.015625)"/>
       <path id="Cmr10-28" d="M 1984 -1588 
Q 1628 -1306 1370 -942 
Q 1113 -578 948 -165 
Q 784 247 703 697 
Q 622 1147 622 1600 
Q 622 2059 703 2509 
Q 784 2959 951 3375 
Q 1119 3791 1378 4153 
Q 1638 4516 1984 4788 
Q 1984 4800 2016 4800 
L 2075 4800 
Q 2094 4800 2109 4783 
Q 2125 4766 2125 4744 
Q 2125 4716 2113 4703 
Q 1800 4397 1592 4047 
Q 1384 3697 1257 3301 
Q 1131 2906 1075 2482 
Q 1019 2059 1019 1600 
Q 1019 -434 2106 -1491 
Q 2125 -1509 2125 -1544 
Q 2125 -1559 2108 -1579 
Q 2091 -1600 2075 -1600 
L 2016 -1600 
Q 1984 -1600 1984 -1588 
z
" transform="scale(0.015625)"/>
       <path id="Cmmi10-78" d="M 500 184 
Q 613 97 819 97 
Q 1019 97 1172 289 
Q 1325 481 1381 709 
L 1672 1844 
Q 1741 2153 1741 2266 
Q 1741 2425 1652 2544 
Q 1563 2663 1403 2663 
Q 1200 2663 1022 2536 
Q 844 2409 722 2214 
Q 600 2019 550 1819 
Q 538 1778 500 1778 
L 422 1778 
Q 372 1778 372 1838 
L 372 1856 
Q 434 2094 584 2320 
Q 734 2547 951 2687 
Q 1169 2828 1416 2828 
Q 1650 2828 1839 2703 
Q 2028 2578 2106 2363 
Q 2216 2559 2386 2693 
Q 2556 2828 2759 2828 
Q 2897 2828 3040 2779 
Q 3184 2731 3275 2631 
Q 3366 2531 3366 2381 
Q 3366 2219 3261 2101 
Q 3156 1984 2994 1984 
Q 2891 1984 2822 2050 
Q 2753 2116 2753 2216 
Q 2753 2350 2845 2451 
Q 2938 2553 3066 2572 
Q 2950 2663 2747 2663 
Q 2541 2663 2389 2472 
Q 2238 2281 2175 2047 
L 1894 916 
Q 1825 659 1825 494 
Q 1825 331 1917 214 
Q 2009 97 2163 97 
Q 2463 97 2698 361 
Q 2934 625 3009 941 
Q 3022 978 3059 978 
L 3138 978 
Q 3163 978 3178 961 
Q 3194 944 3194 922 
Q 3194 916 3188 903 
Q 3097 522 2806 225 
Q 2516 -72 2150 -72 
Q 1916 -72 1727 54 
Q 1538 181 1459 397 
Q 1359 209 1182 68 
Q 1006 -72 806 -72 
Q 669 -72 523 -23 
Q 378 25 287 125 
Q 197 225 197 378 
Q 197 528 301 651 
Q 406 775 563 775 
Q 669 775 741 711 
Q 813 647 813 544 
Q 813 409 723 309 
Q 634 209 500 184 
z
" transform="scale(0.015625)"/>
       <path id="Cmr10-29" d="M 416 -1600 
Q 359 -1600 359 -1544 
Q 359 -1516 372 -1503 
Q 1466 -434 1466 1600 
Q 1466 3634 384 4691 
Q 359 4706 359 4744 
Q 359 4766 376 4783 
Q 394 4800 416 4800 
L 475 4800 
Q 494 4800 506 4788 
Q 966 4425 1272 3906 
Q 1578 3388 1720 2800 
Q 1863 2213 1863 1600 
Q 1863 1147 1786 708 
Q 1709 269 1542 -157 
Q 1375 -584 1119 -945 
Q 863 -1306 506 -1588 
Q 494 -1600 475 -1600 
L 416 -1600 
z
" transform="scale(0.015625)"/>
      </defs>
      <use xlink:href="#Cmmi10-66"/>
      <use xlink:href="#Cmr10-28" transform="translate(48.876953 0)"/>
      <use xlink:href="#Cmmi10-78" transform="translate(87.695312 0)"/>
      <use xlink:href="#Cmr10-29" transform="translate(144.775391 0)"/>
     </g>
    </g>
   </g>
  </g>
  <g id="text_19">
   <!-- Sample plot -->
   <g transform="translate(183.445312 26.516813) scale(0.18 -0.18)">
    <defs>
     <path id="Cmr10-53" d="M 359 -91 
L 359 1403 
Q 359 1453 416 1453 
L 494 1453 
Q 513 1453 528 1437 
Q 544 1422 544 1403 
Q 544 775 933 429 
Q 1322 84 1953 84 
Q 2175 84 2362 212 
Q 2550 341 2654 548 
Q 2759 756 2759 978 
Q 2759 1172 2681 1355 
Q 2603 1538 2456 1672 
Q 2309 1806 2125 1850 
L 1294 2053 
Q 881 2163 620 2502 
Q 359 2841 359 3263 
Q 359 3594 528 3884 
Q 697 4175 983 4344 
Q 1269 4513 1600 4513 
Q 2241 4513 2619 4078 
L 2881 4494 
Q 2900 4513 2925 4513 
L 2969 4513 
Q 2988 4513 3005 4498 
Q 3022 4484 3022 4459 
L 3022 2975 
Q 3022 2919 2969 2919 
L 2894 2919 
Q 2834 2919 2834 2975 
Q 2834 3138 2779 3331 
Q 2725 3525 2628 3703 
Q 2531 3881 2419 3994 
Q 2109 4306 1600 4306 
Q 1381 4306 1197 4195 
Q 1013 4084 903 3893 
Q 794 3703 794 3494 
Q 794 3219 964 2995 
Q 1134 2772 1409 2700 
L 2241 2497 
Q 2447 2447 2630 2317 
Q 2813 2188 2934 2016 
Q 3056 1844 3125 1633 
Q 3194 1422 3194 1197 
Q 3194 850 3034 542 
Q 2875 234 2586 46 
Q 2297 -141 1953 -141 
Q 1741 -141 1519 -94 
Q 1297 -47 1109 50 
Q 922 147 769 300 
L 500 -122 
Q 481 -141 453 -141 
L 416 -141 
Q 359 -141 359 -91 
z
" transform="scale(0.015625)"/>
     <path id="Cmr10-6d" d="M 191 0 
L 191 225 
Q 409 225 550 259 
Q 691 294 691 428 
L 691 2175 
Q 691 2347 639 2423 
Q 588 2500 491 2517 
Q 394 2534 191 2534 
L 191 2759 
L 1119 2828 
L 1119 2203 
Q 1247 2478 1498 2653 
Q 1750 2828 2047 2828 
Q 2784 2828 2913 2228 
Q 3041 2497 3287 2662 
Q 3534 2828 3828 2828 
Q 4119 2828 4317 2734 
Q 4516 2641 4616 2448 
Q 4716 2256 4716 1966 
L 4716 428 
Q 4716 294 4858 259 
Q 5000 225 5216 225 
L 5216 0 
L 3750 0 
L 3750 225 
Q 3969 225 4109 259 
Q 4250 294 4250 428 
L 4250 1947 
Q 4250 2269 4159 2466 
Q 4069 2663 3788 2663 
Q 3419 2663 3178 2366 
Q 2938 2069 2938 1691 
L 2938 428 
Q 2938 294 3078 259 
Q 3219 225 3438 225 
L 3438 0 
L 1972 0 
L 1972 225 
Q 2191 225 2331 259 
Q 2472 294 2472 428 
L 2472 1947 
Q 2472 2259 2381 2461 
Q 2291 2663 2009 2663 
Q 1638 2663 1398 2366 
Q 1159 2069 1159 1691 
L 1159 428 
Q 1159 294 1300 259 
Q 1441 225 1656 225 
L 1656 0 
L 191 0 
z
" transform="scale(0.015625)"/>
     <path id="Cmr10-70" d="M 166 -1241 
L 166 -1019 
Q 384 -1019 525 -981 
Q 666 -944 666 -813 
L 666 2272 
Q 666 2447 541 2490 
Q 416 2534 166 2534 
L 166 2759 
L 1113 2828 
L 1113 2431 
Q 1288 2625 1520 2726 
Q 1753 2828 2016 2828 
Q 2394 2828 2697 2623 
Q 3000 2419 3170 2086 
Q 3341 1753 3341 1381 
Q 3341 994 3152 659 
Q 2963 325 2636 126 
Q 2309 -72 1919 -72 
Q 1453 -72 1131 306 
L 1131 -813 
Q 1131 -944 1273 -981 
Q 1416 -1019 1631 -1019 
L 1631 -1241 
L 166 -1241 
z
M 1131 622 
Q 1244 394 1444 245 
Q 1644 97 1881 97 
Q 2103 97 2273 215 
Q 2444 334 2559 534 
Q 2675 734 2729 954 
Q 2784 1175 2784 1381 
Q 2784 1638 2692 1936 
Q 2600 2234 2411 2439 
Q 2222 2644 1953 2644 
Q 1694 2644 1476 2511 
Q 1259 2378 1131 2150 
L 1131 622 
z
" transform="scale(0.015625)"/>
    </defs>
    <use xlink:href="#Cmr10-53"/>
    <use xlink:href="#Cmr10-61" x="55.517578"/>
    <use xlink:href="#Cmr10-6d" x="105.517578"/>
    <use xlink:href="#Cmr10-70" x="188.818359"/>
    <use xlink:href="#Cmr10-6c" x="244.335938"/>
    <use xlink:href="#Cmr10-65" x="272.021484"/>
    <use xlink:href="#Cmr10-20" x="316.40625"/>
    <use xlink:href="#Cmr10-70" x="349.707031"/>
    <use xlink:href="#Cmr10-6c" x="405.224609"/>
    <use xlink:href="#Cmr10-6f" x="432.910156"/>
    <use xlink:href="#Cmr10-74" x="482.910156"/>
   </g>
  </g>
 </g>
 <defs>
  <clipPath id="p1cadc425d4">
   <rect x="57.6" y="41.472" width="357.12" height="266.112"/>
  </clipPath>
 </defs>
</svg>
\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"ignore_on_import\": true,\n\t\t\t\"source\": \"plot($\\\\sin(x)$, ($x$, 0, 10), fig=f, color=\\\"red\\\", label=\\\"red\\\");\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 15831073682575658032,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 12135673050887537409,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"image_svg\",\n\t\t\t\t\t\"source\": \"<?xml version="1.0" encoding="utf-8" standalone="no"?>
<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
  "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="460.8pt" height="345.6pt" viewBox="0 0 460.8 345.6" xmlns="http://www.w3.org/2000/svg" version="1.1">
 <metadata>
  <rdf:RDF xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:cc="http://creativecommons.org/ns#" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
   <cc:Work>
    <dc:type rdf:resource="http://purl.org/dc/dcmitype/StillImage"/>
    <dc:date>2025-03-30T13:20:00.208329</dc:date>
    <dc:format>image/svg+xml</dc:format>
    <dc:creator>
     <cc:Agent>
      <dc:title>Matplotlib v3.6.3, https://matplotlib.org/</dc:title>
     </cc:Agent>
    </dc:creator>
   </cc:Work>
  </rdf:RDF>
 </metadata>
 <defs>
  <style type="text/css">*{stroke-linejoin: round; stroke-linecap: butt}</style>
 </defs>
 <g id="figure_1">
  <g id="patch_1">
   <path d="M 0 345.6 
L 460.8 345.6 
L 460.8 0 
L 0 0 
z
" style="fill: #ffffff"/>
  </g>
  <g id="axes_1">
   <g id="patch_2">
    <path d="M 57.6 307.584 
L 414.72 307.584 
L 414.72 41.472 
L 57.6 41.472 
z
" style="fill: #ffffff"/>
   </g>
   <g id="matplotlib.axis_1">
    <g id="xtick_1">
     <g id="line2d_1">
      <path d="M 73.832727 307.584 
L 73.832727 41.472 
" clip-path="url(#p435b9db52d)" style="fill: none; stroke: #b0b0b0; stroke-width: 0.8; stroke-linecap: square"/>
     </g>
     <g id="line2d_2">
      <defs>
       <path id="m607d2edc4f" d="M 0 0 
L 0 3.5 
" style="stroke: #000000; stroke-width: 0.8"/>
      </defs>
      <g>
       <use xlink:href="#m607d2edc4f" x="73.832727" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_1">
      <!-- 0 -->
      <g transform="translate(70.651477 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-30" d="M 2034 4250 
Q 1547 4250 1301 3770 
Q 1056 3291 1056 2328 
Q 1056 1369 1301 889 
Q 1547 409 2034 409 
Q 2525 409 2770 889 
Q 3016 1369 3016 2328 
Q 3016 3291 2770 3770 
Q 2525 4250 2034 4250 
z
M 2034 4750 
Q 2819 4750 3233 4129 
Q 3647 3509 3647 2328 
Q 3647 1150 3233 529 
Q 2819 -91 2034 -91 
Q 1250 -91 836 529 
Q 422 1150 422 2328 
Q 422 3509 836 4129 
Q 1250 4750 2034 4750 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-30"/>
      </g>
     </g>
    </g>
    <g id="xtick_2">
     <g id="line2d_3">
      <path d="M 138.763636 307.584 
L 138.763636 41.472 
" clip-path="url(#p435b9db52d)" style="fill: none; stroke: #b0b0b0; stroke-width: 0.8; stroke-linecap: square"/>
     </g>
     <g id="line2d_4">
      <g>
       <use xlink:href="#m607d2edc4f" x="138.763636" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_2">
      <!-- 2 -->
      <g transform="translate(135.582386 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-32" d="M 1228 531 
L 3431 531 
L 3431 0 
L 469 0 
L 469 531 
Q 828 903 1448 1529 
Q 2069 2156 2228 2338 
Q 2531 2678 2651 2914 
Q 2772 3150 2772 3378 
Q 2772 3750 2511 3984 
Q 2250 4219 1831 4219 
Q 1534 4219 1204 4116 
Q 875 4013 500 3803 
L 500 4441 
Q 881 4594 1212 4672 
Q 1544 4750 1819 4750 
Q 2544 4750 2975 4387 
Q 3406 4025 3406 3419 
Q 3406 3131 3298 2873 
Q 3191 2616 2906 2266 
Q 2828 2175 2409 1742 
Q 1991 1309 1228 531 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-32"/>
      </g>
     </g>
    </g>
    <g id="xtick_3">
     <g id="line2d_5">
      <path d="M 203.694545 307.584 
L 203.694545 41.472 
" clip-path="url(#p435b9db52d)" style="fill: none; stroke: #b0b0b0; stroke-width: 0.8; stroke-linecap: square"/>
     </g>
     <g id="line2d_6">
      <g>
       <use xlink:href="#m607d2edc4f" x="203.694545" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_3">
      <!-- 4 -->
      <g transform="translate(200.513295 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-34" d="M 2419 4116 
L 825 1625 
L 2419 1625 
L 2419 4116 
z
M 2253 4666 
L 3047 4666 
L 3047 1625 
L 3713 1625 
L 3713 1100 
L 3047 1100 
L 3047 0 
L 2419 0 
L 2419 1100 
L 313 1100 
L 313 1709 
L 2253 4666 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-34"/>
      </g>
     </g>
    </g>
    <g id="xtick_4">
     <g id="line2d_7">
      <path d="M 268.625455 307.584 
L 268.625455 41.472 
" clip-path="url(#p435b9db52d)" style="fill: none; stroke: #b0b0b0; stroke-width: 0.8; stroke-linecap: square"/>
     </g>
     <g id="line2d_8">
      <g>
       <use xlink:href="#m607d2edc4f" x="268.625455" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_4">
      <!-- 6 -->
      <g transform="translate(265.444205 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-36" d="M 2113 2584 
Q 1688 2584 1439 2293 
Q 1191 2003 1191 1497 
Q 1191 994 1439 701 
Q 1688 409 2113 409 
Q 2538 409 2786 701 
Q 3034 994 3034 1497 
Q 3034 2003 2786 2293 
Q 2538 2584 2113 2584 
z
M 3366 4563 
L 3366 3988 
Q 3128 4100 2886 4159 
Q 2644 4219 2406 4219 
Q 1781 4219 1451 3797 
Q 1122 3375 1075 2522 
Q 1259 2794 1537 2939 
Q 1816 3084 2150 3084 
Q 2853 3084 3261 2657 
Q 3669 2231 3669 1497 
Q 3669 778 3244 343 
Q 2819 -91 2113 -91 
Q 1303 -91 875 529 
Q 447 1150 447 2328 
Q 447 3434 972 4092 
Q 1497 4750 2381 4750 
Q 2619 4750 2861 4703 
Q 3103 4656 3366 4563 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-36"/>
      </g>
     </g>
    </g>
    <g id="xtick_5">
     <g id="line2d_9">
      <path d="M 333.556364 307.584 
L 333.556364 41.472 
" clip-path="url(#p435b9db52d)" style="fill: none; stroke: #b0b0b0; stroke-width: 0.8; stroke-linecap: square"/>
     </g>
     <g id="line2d_10">
      <g>
       <use xlink:href="#m607d2edc4f" x="333.556364" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_5">
      <!-- 8 -->
      <g transform="translate(330.375114 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-38" d="M 2034 2216 
Q 1584 2216 1326 1975 
Q 1069 1734 1069 1313 
Q 1069 891 1326 650 
Q 1584 409 2034 409 
Q 2484 409 2743 651 
Q 3003 894 3003 1313 
Q 3003 1734 2745 1975 
Q 2488 2216 2034 2216 
z
M 1403 2484 
Q 997 2584 770 2862 
Q 544 3141 544 3541 
Q 544 4100 942 4425 
Q 1341 4750 2034 4750 
Q 2731 4750 3128 4425 
Q 3525 4100 3525 3541 
Q 3525 3141 3298 2862 
Q 3072 2584 2669 2484 
Q 3125 2378 3379 2068 
Q 3634 1759 3634 1313 
Q 3634 634 3220 271 
Q 2806 -91 2034 -91 
Q 1263 -91 848 271 
Q 434 634 434 1313 
Q 434 1759 690 2068 
Q 947 2378 1403 2484 
z
M 1172 3481 
Q 1172 3119 1398 2916 
Q 1625 2713 2034 2713 
Q 2441 2713 2670 2916 
Q 2900 3119 2900 3481 
Q 2900 3844 2670 4047 
Q 2441 4250 2034 4250 
Q 1625 4250 1398 4047 
Q 1172 3844 1172 3481 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-38"/>
      </g>
     </g>
    </g>
    <g id="xtick_6">
     <g id="line2d_11">
      <path d="M 398.487273 307.584 
L 398.487273 41.472 
" clip-path="url(#p435b9db52d)" style="fill: none; stroke: #b0b0b0; stroke-width: 0.8; stroke-linecap: square"/>
     </g>
     <g id="line2d_12">
      <g>
       <use xlink:href="#m607d2edc4f" x="398.487273" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_6">
      <!-- 10 -->
      <g transform="translate(392.124773 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-31" d="M 794 531 
L 1825 531 
L 1825 4091 
L 703 3866 
L 703 4441 
L 1819 4666 
L 2450 4666 
L 2450 531 
L 3481 531 
L 3481 0 
L 794 0 
L 794 531 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-31"/>
       <use xlink:href="#DejaVuSans-30" x="63.623047"/>
      </g>
     </g>
    </g>
    <g id="text_7">
     <!-- x-axis -->
     <g transform="translate(215.69875 339.364625) scale(0.16 -0.16)">
      <defs>
       <path id="Cmr10-78" d="M 78 0 
L 78 225 
Q 322 225 537 320 
Q 753 416 903 603 
L 1484 1344 
L 728 2328 
Q 616 2469 483 2501 
Q 350 2534 109 2534 
L 109 2759 
L 1441 2759 
L 1441 2534 
Q 1356 2534 1282 2496 
Q 1209 2459 1209 2388 
Q 1209 2363 1228 2328 
L 1741 1663 
L 2125 2156 
Q 2203 2250 2203 2344 
Q 2203 2422 2151 2478 
Q 2100 2534 2016 2534 
L 2016 2759 
L 3194 2759 
L 3194 2534 
Q 2947 2534 2730 2439 
Q 2513 2344 2363 2156 
L 1856 1509 
L 2675 428 
Q 2797 288 2928 256 
Q 3059 225 3303 225 
L 3303 0 
L 1972 0 
L 1972 225 
Q 2050 225 2122 262 
Q 2194 300 2194 372 
Q 2194 400 2175 428 
L 1600 1191 
L 1141 603 
Q 1069 522 1069 416 
Q 1069 338 1122 281 
Q 1175 225 1247 225 
L 1247 0 
L 78 0 
z
" transform="scale(0.015625)"/>
       <path id="Cmr10-2d" d="M 72 1184 
L 72 1581 
L 1766 1581 
L 1766 1184 
L 72 1184 
z
" transform="scale(0.015625)"/>
       <path id="Cmr10-61" d="M 256 628 
Q 256 1009 556 1248 
Q 856 1488 1276 1586 
Q 1697 1684 2075 1684 
L 2075 1947 
Q 2075 2131 1994 2304 
Q 1913 2478 1759 2589 
Q 1606 2700 1422 2700 
Q 997 2700 775 2509 
Q 897 2509 976 2417 
Q 1056 2325 1056 2203 
Q 1056 2075 965 1984 
Q 875 1894 750 1894 
Q 622 1894 531 1984 
Q 441 2075 441 2203 
Q 441 2541 747 2705 
Q 1053 2869 1422 2869 
Q 1681 2869 1943 2758 
Q 2206 2647 2373 2440 
Q 2541 2234 2541 1959 
L 2541 519 
Q 2541 394 2594 289 
Q 2647 184 2759 184 
Q 2866 184 2917 290 
Q 2969 397 2969 519 
L 2969 928 
L 3156 928 
L 3156 519 
Q 3156 375 3081 245 
Q 3006 116 2879 39 
Q 2753 -38 2606 -38 
Q 2419 -38 2283 107 
Q 2147 253 2131 453 
Q 2013 213 1781 70 
Q 1550 -72 1288 -72 
Q 1044 -72 808 0 
Q 572 72 414 226 
Q 256 381 256 628 
z
M 775 628 
Q 775 403 940 250 
Q 1106 97 1331 97 
Q 1538 97 1706 200 
Q 1875 303 1975 481 
Q 2075 659 2075 856 
L 2075 1522 
Q 1784 1522 1479 1426 
Q 1175 1331 975 1128 
Q 775 925 775 628 
z
" transform="scale(0.015625)"/>
       <path id="Cmr10-69" d="M 197 0 
L 197 225 
Q 416 225 556 259 
Q 697 294 697 428 
L 697 2175 
Q 697 2422 601 2478 
Q 506 2534 225 2534 
L 225 2759 
L 1147 2828 
L 1147 428 
Q 1147 294 1269 259 
Q 1391 225 1594 225 
L 1594 0 
L 197 0 
z
M 469 3928 
Q 469 4069 575 4175 
Q 681 4281 819 4281 
Q 909 4281 993 4234 
Q 1078 4188 1125 4103 
Q 1172 4019 1172 3928 
Q 1172 3791 1065 3684 
Q 959 3578 819 3578 
Q 681 3578 575 3684 
Q 469 3791 469 3928 
z
" transform="scale(0.015625)"/>
       <path id="Cmr10-73" d="M 213 -19 
L 213 1025 
Q 213 1075 269 1075 
L 347 1075 
Q 384 1075 397 1025 
Q 575 97 1259 97 
Q 1563 97 1767 234 
Q 1972 372 1972 659 
Q 1972 866 1812 1011 
Q 1653 1156 1434 1209 
L 1006 1294 
Q 791 1341 614 1437 
Q 438 1534 325 1695 
Q 213 1856 213 2069 
Q 213 2350 361 2529 
Q 509 2709 746 2789 
Q 984 2869 1259 2869 
Q 1588 2869 1831 2694 
L 2016 2853 
Q 2016 2869 2047 2869 
L 2094 2869 
Q 2113 2869 2128 2851 
Q 2144 2834 2144 2816 
L 2144 1978 
Q 2144 1919 2094 1919 
L 2016 1919 
Q 1959 1919 1959 1978 
Q 1959 2313 1773 2516 
Q 1588 2719 1253 2719 
Q 966 2719 755 2612 
Q 544 2506 544 2247 
Q 544 2069 695 1955 
Q 847 1841 1050 1791 
L 1484 1709 
Q 1703 1659 1892 1540 
Q 2081 1422 2192 1240 
Q 2303 1059 2303 831 
Q 2303 600 2223 429 
Q 2144 259 2001 146 
Q 1859 34 1665 -19 
Q 1472 -72 1259 -72 
Q 859 -72 575 197 
L 341 -56 
Q 341 -72 306 -72 
L 269 -72 
Q 213 -72 213 -19 
z
" transform="scale(0.015625)"/>
      </defs>
      <use xlink:href="#Cmr10-78"/>
      <use xlink:href="#Cmr10-2d" x="52.685547"/>
      <use xlink:href="#Cmr10-61" x="85.986328"/>
      <use xlink:href="#Cmr10-78" x="135.986328"/>
      <use xlink:href="#Cmr10-69" x="188.671875"/>
      <use xlink:href="#Cmr10-73" x="216.357422"/>
     </g>
    </g>
   </g>
   <g id="matplotlib.axis_2">
    <g id="ytick_1">
     <g id="line2d_13">
      <path d="M 57.6 307.584 
L 414.72 307.584 
" clip-path="url(#p435b9db52d)" style="fill: none; stroke: #b0b0b0; stroke-width: 0.8; stroke-linecap: square"/>
     </g>
     <g id="line2d_14">
      <defs>
       <path id="md6572bf1e8" d="M 0 0 
L -3.5 0 
" style="stroke: #000000; stroke-width: 0.8"/>
      </defs>
      <g>
       <use xlink:href="#md6572bf1e8" x="57.6" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_8">
      <!-- −1.00 -->
      <g transform="translate(19.954687 311.383219) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-2212" d="M 678 2272 
L 4684 2272 
L 4684 1741 
L 678 1741 
L 678 2272 
z
" transform="scale(0.015625)"/>
        <path id="DejaVuSans-2e" d="M 684 794 
L 1344 794 
L 1344 0 
L 684 0 
L 684 794 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-2212"/>
       <use xlink:href="#DejaVuSans-31" x="83.789062"/>
       <use xlink:href="#DejaVuSans-2e" x="147.412109"/>
       <use xlink:href="#DejaVuSans-30" x="179.199219"/>
       <use xlink:href="#DejaVuSans-30" x="242.822266"/>
      </g>
     </g>
    </g>
    <g id="ytick_2">
     <g id="line2d_15">
      <path d="M 57.6 274.32 
L 414.72 274.32 
" clip-path="url(#p435b9db52d)" style="fill: none; stroke: #b0b0b0; stroke-width: 0.8; stroke-linecap: square"/>
     </g>
     <g id="line2d_16">
      <g>
       <use xlink:href="#md6572bf1e8" x="57.6" y="274.32" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_9">
      <!-- −0.75 -->
      <g transform="translate(19.954687 278.119219) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-37" d="M 525 4666 
L 3525 4666 
L 3525 4397 
L 1831 0 
L 1172 0 
L 2766 4134 
L 525 4134 
L 525 4666 
z
" transform="scale(0.015625)"/>
        <path id="DejaVuSans-35" d="M 691 4666 
L 3169 4666 
L 3169 4134 
L 1269 4134 
L 1269 2991 
Q 1406 3038 1543 3061 
Q 1681 3084 1819 3084 
Q 2600 3084 3056 2656 
Q 3513 2228 3513 1497 
Q 3513 744 3044 326 
Q 2575 -91 1722 -91 
Q 1428 -91 1123 -41 
Q 819 9 494 109 
L 494 744 
Q 775 591 1075 516 
Q 1375 441 1709 441 
Q 2250 441 2565 725 
Q 2881 1009 2881 1497 
Q 2881 1984 2565 2268 
Q 2250 2553 1709 2553 
Q 1456 2553 1204 2497 
Q 953 2441 691 2322 
L 691 4666 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-2212"/>
       <use xlink:href="#DejaVuSans-30" x="83.789062"/>
       <use xlink:href="#DejaVuSans-2e" x="147.412109"/>
       <use xlink:href="#DejaVuSans-37" x="179.199219"/>
       <use xlink:href="#DejaVuSans-35" x="242.822266"/>
      </g>
     </g>
    </g>
    <g id="ytick_3">
     <g id="line2d_17">
      <path d="M 57.6 241.056 
L 414.72 241.056 
" clip-path="url(#p435b9db52d)" style="fill: none; stroke: #b0b0b0; stroke-width: 0.8; stroke-linecap: square"/>
     </g>
     <g id="line2d_18">
      <g>
       <use xlink:href="#md6572bf1e8" x="57.6" y="241.056" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_10">
      <!-- −0.50 -->
      <g transform="translate(19.954687 244.855219) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-2212"/>
       <use xlink:href="#DejaVuSans-30" x="83.789062"/>
       <use xlink:href="#DejaVuSans-2e" x="147.412109"/>
       <use xlink:href="#DejaVuSans-35" x="179.199219"/>
       <use xlink:href="#DejaVuSans-30" x="242.822266"/>
      </g>
     </g>
    </g>
    <g id="ytick_4">
     <g id="line2d_19">
      <path d="M 57.6 207.792 
L 414.72 207.792 
" clip-path="url(#p435b9db52d)" style="fill: none; stroke: #b0b0b0; stroke-width: 0.8; stroke-linecap: square"/>
     </g>
     <g id="line2d_20">
      <g>
       <use xlink:href="#md6572bf1e8" x="57.6" y="207.792" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_11">
      <!-- −0.25 -->
      <g transform="translate(19.954687 211.591219) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-2212"/>
       <use xlink:href="#DejaVuSans-30" x="83.789062"/>
       <use xlink:href="#DejaVuSans-2e" x="147.412109"/>
       <use xlink:href="#DejaVuSans-32" x="179.199219"/>
       <use xlink:href="#DejaVuSans-35" x="242.822266"/>
      </g>
     </g>
    </g>
    <g id="ytick_5">
     <g id="line2d_21">
      <path d="M 57.6 174.528 
L 414.72 174.528 
" clip-path="url(#p435b9db52d)" style="fill: none; stroke: #b0b0b0; stroke-width: 0.8; stroke-linecap: square"/>
     </g>
     <g id="line2d_22">
      <g>
       <use xlink:href="#md6572bf1e8" x="57.6" y="174.528" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_12">
      <!-- 0.00 -->
      <g transform="translate(28.334375 178.327219) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-30"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-30" x="95.410156"/>
       <use xlink:href="#DejaVuSans-30" x="159.033203"/>
      </g>
     </g>
    </g>
    <g id="ytick_6">
     <g id="line2d_23">
      <path d="M 57.6 141.264 
L 414.72 141.264 
" clip-path="url(#p435b9db52d)" style="fill: none; stroke: #b0b0b0; stroke-width: 0.8; stroke-linecap: square"/>
     </g>
     <g id="line2d_24">
      <g>
       <use xlink:href="#md6572bf1e8" x="57.6" y="141.264" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_13">
      <!-- 0.25 -->
      <g transform="translate(28.334375 145.063219) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-30"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-32" x="95.410156"/>
       <use xlink:href="#DejaVuSans-35" x="159.033203"/>
      </g>
     </g>
    </g>
    <g id="ytick_7">
     <g id="line2d_25">
      <path d="M 57.6 108 
L 414.72 108 
" clip-path="url(#p435b9db52d)" style="fill: none; stroke: #b0b0b0; stroke-width: 0.8; stroke-linecap: square"/>
     </g>
     <g id="line2d_26">
      <g>
       <use xlink:href="#md6572bf1e8" x="57.6" y="108" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_14">
      <!-- 0.50 -->
      <g transform="translate(28.334375 111.799219) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-30"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-35" x="95.410156"/>
       <use xlink:href="#DejaVuSans-30" x="159.033203"/>
      </g>
     </g>
    </g>
    <g id="ytick_8">
     <g id="line2d_27">
      <path d="M 57.6 74.736 
L 414.72 74.736 
" clip-path="url(#p435b9db52d)" style="fill: none; stroke: #b0b0b0; stroke-width: 0.8; stroke-linecap: square"/>
     </g>
     <g id="line2d_28">
      <g>
       <use xlink:href="#md6572bf1e8" x="57.6" y="74.736" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_15">
      <!-- 0.75 -->
      <g transform="translate(28.334375 78.535219) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-30"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-37" x="95.410156"/>
       <use xlink:href="#DejaVuSans-35" x="159.033203"/>
      </g>
     </g>
    </g>
    <g id="ytick_9">
     <g id="line2d_29">
      <path d="M 57.6 41.472 
L 414.72 41.472 
" clip-path="url(#p435b9db52d)" style="fill: none; stroke: #b0b0b0; stroke-width: 0.8; stroke-linecap: square"/>
     </g>
     <g id="line2d_30">
      <g>
       <use xlink:href="#md6572bf1e8" x="57.6" y="41.472" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_16">
      <!-- 1.00 -->
      <g transform="translate(28.334375 45.271219) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-31"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-30" x="95.410156"/>
       <use xlink:href="#DejaVuSans-30" x="159.033203"/>
      </g>
     </g>
    </g>
    <g id="text_17">
     <!-- function value -->
     <g transform="translate(12.852187 224.2505) rotate(-90) scale(0.16 -0.16)">
      <defs>
       <path id="Cmr10-66" d="M 206 0 
L 206 225 
Q 422 225 562 259 
Q 703 294 703 428 
L 703 2534 
L 213 2534 
L 213 2759 
L 703 2759 
L 703 3525 
Q 703 3731 789 3911 
Q 875 4091 1020 4225 
Q 1166 4359 1355 4436 
Q 1544 4513 1747 4513 
Q 1963 4513 2136 4384 
Q 2309 4256 2309 4044 
Q 2309 3922 2226 3839 
Q 2144 3756 2022 3756 
Q 1900 3756 1814 3839 
Q 1728 3922 1728 4044 
Q 1728 4244 1900 4313 
Q 1797 4347 1716 4347 
Q 1528 4347 1395 4214 
Q 1263 4081 1197 3890 
Q 1131 3700 1131 3513 
L 1131 2759 
L 1869 2759 
L 1869 2534 
L 1153 2534 
L 1153 428 
Q 1153 297 1340 261 
Q 1528 225 1772 225 
L 1772 0 
L 206 0 
z
" transform="scale(0.015625)"/>
       <path id="Cmr10-75" d="M 691 763 
L 691 2175 
Q 691 2347 639 2423 
Q 588 2500 491 2517 
Q 394 2534 191 2534 
L 191 2759 
L 1159 2828 
L 1159 763 
Q 1159 513 1195 373 
Q 1231 234 1348 165 
Q 1466 97 1722 97 
Q 2066 97 2269 384 
Q 2472 672 2472 1038 
L 2472 2175 
Q 2472 2347 2419 2423 
Q 2366 2500 2270 2517 
Q 2175 2534 1972 2534 
L 1972 2759 
L 2938 2828 
L 2938 581 
Q 2938 413 2989 336 
Q 3041 259 3137 242 
Q 3234 225 3438 225 
L 3438 0 
L 2491 -72 
L 2491 469 
Q 2372 228 2159 78 
Q 1947 -72 1691 -72 
Q 1231 -72 961 123 
Q 691 319 691 763 
z
" transform="scale(0.015625)"/>
       <path id="Cmr10-6e" d="M 191 0 
L 191 225 
Q 409 225 550 259 
Q 691 294 691 428 
L 691 2175 
Q 691 2347 639 2423 
Q 588 2500 491 2517 
Q 394 2534 191 2534 
L 191 2759 
L 1119 2828 
L 1119 2203 
Q 1247 2478 1498 2653 
Q 1750 2828 2047 2828 
Q 2491 2828 2714 2615 
Q 2938 2403 2938 1966 
L 2938 428 
Q 2938 294 3078 259 
Q 3219 225 3438 225 
L 3438 0 
L 1972 0 
L 1972 225 
Q 2191 225 2331 259 
Q 2472 294 2472 428 
L 2472 1947 
Q 2472 2259 2381 2461 
Q 2291 2663 2009 2663 
Q 1638 2663 1398 2366 
Q 1159 2069 1159 1691 
L 1159 428 
Q 1159 294 1300 259 
Q 1441 225 1656 225 
L 1656 0 
L 191 0 
z
" transform="scale(0.015625)"/>
       <path id="Cmr10-63" d="M 1594 -72 
Q 1206 -72 890 129 
Q 575 331 394 667 
Q 213 1003 213 1381 
Q 213 1759 392 2106 
Q 572 2453 889 2661 
Q 1206 2869 1594 2869 
Q 1969 2869 2276 2722 
Q 2584 2575 2584 2241 
Q 2584 2116 2495 2023 
Q 2406 1931 2278 1931 
Q 2150 1931 2061 2023 
Q 1972 2116 1972 2241 
Q 1972 2353 2044 2436 
Q 2116 2519 2222 2541 
Q 2000 2681 1600 2681 
Q 1294 2681 1106 2478 
Q 919 2275 844 1975 
Q 769 1675 769 1381 
Q 769 1072 861 783 
Q 953 494 1158 305 
Q 1363 116 1672 116 
Q 1975 116 2187 302 
Q 2400 488 2478 788 
Q 2478 825 2528 825 
L 2606 825 
Q 2625 825 2640 808 
Q 2656 791 2656 769 
L 2656 750 
Q 2559 372 2271 150 
Q 1984 -72 1594 -72 
z
" transform="scale(0.015625)"/>
       <path id="Cmr10-74" d="M 653 769 
L 653 2534 
L 122 2534 
L 122 2700 
Q 541 2700 737 3090 
Q 934 3481 934 3938 
L 1119 3938 
L 1119 2759 
L 2022 2759 
L 2022 2534 
L 1119 2534 
L 1119 781 
Q 1119 516 1208 316 
Q 1297 116 1528 116 
Q 1747 116 1844 327 
Q 1941 538 1941 781 
L 1941 1159 
L 2125 1159 
L 2125 769 
Q 2125 569 2051 373 
Q 1978 178 1834 53 
Q 1691 -72 1484 -72 
Q 1100 -72 876 158 
Q 653 388 653 769 
z
" transform="scale(0.015625)"/>
       <path id="Cmr10-6f" d="M 1600 -72 
Q 1216 -72 887 123 
Q 559 319 368 647 
Q 178 975 178 1363 
Q 178 1656 283 1928 
Q 388 2200 583 2414 
Q 778 2628 1037 2748 
Q 1297 2869 1600 2869 
Q 1994 2869 2317 2661 
Q 2641 2453 2828 2104 
Q 3016 1756 3016 1363 
Q 3016 978 2825 648 
Q 2634 319 2307 123 
Q 1981 -72 1600 -72 
z
M 1600 116 
Q 2113 116 2284 487 
Q 2456 859 2456 1434 
Q 2456 1756 2422 1967 
Q 2388 2178 2272 2350 
Q 2200 2456 2089 2536 
Q 1978 2616 1854 2658 
Q 1731 2700 1600 2700 
Q 1400 2700 1220 2609 
Q 1041 2519 922 2350 
Q 803 2169 770 1951 
Q 738 1734 738 1434 
Q 738 1075 800 789 
Q 863 503 1052 309 
Q 1241 116 1600 116 
z
" transform="scale(0.015625)"/>
       <path id="Cmr10-20" transform="scale(0.015625)"/>
       <path id="Cmr10-76" d="M 1563 0 
L 628 2350 
Q 569 2469 445 2501 
Q 322 2534 122 2534 
L 122 2759 
L 1466 2759 
L 1466 2534 
Q 1106 2534 1106 2381 
Q 1106 2356 1113 2344 
L 1831 538 
L 2478 2169 
Q 2497 2219 2497 2272 
Q 2497 2394 2405 2464 
Q 2313 2534 2188 2534 
L 2188 2759 
L 3250 2759 
L 3250 2534 
Q 3053 2534 2904 2443 
Q 2756 2353 2675 2175 
L 1813 0 
Q 1788 -72 1709 -72 
L 1663 -72 
Q 1584 -72 1563 0 
z
" transform="scale(0.015625)"/>
       <path id="Cmr10-6c" d="M 197 0 
L 197 225 
Q 416 225 556 259 
Q 697 294 697 428 
L 697 3788 
Q 697 3959 645 4036 
Q 594 4113 497 4130 
Q 400 4147 197 4147 
L 197 4372 
L 1147 4441 
L 1147 428 
Q 1147 294 1287 259 
Q 1428 225 1644 225 
L 1644 0 
L 197 0 
z
" transform="scale(0.015625)"/>
       <path id="Cmr10-65" d="M 1594 -72 
Q 1203 -72 876 133 
Q 550 338 364 680 
Q 178 1022 178 1403 
Q 178 1778 348 2115 
Q 519 2453 823 2661 
Q 1128 2869 1503 2869 
Q 1797 2869 2014 2770 
Q 2231 2672 2372 2497 
Q 2513 2322 2584 2084 
Q 2656 1847 2656 1563 
Q 2656 1478 2591 1478 
L 738 1478 
L 738 1409 
Q 738 878 952 497 
Q 1166 116 1650 116 
Q 1847 116 2014 203 
Q 2181 291 2304 447 
Q 2428 603 2472 781 
Q 2478 803 2495 820 
Q 2513 838 2534 838 
L 2591 838 
Q 2656 838 2656 756 
Q 2566 394 2266 161 
Q 1966 -72 1594 -72 
z
M 744 1638 
L 2203 1638 
Q 2203 1878 2136 2125 
Q 2069 2372 1912 2536 
Q 1756 2700 1503 2700 
Q 1141 2700 942 2361 
Q 744 2022 744 1638 
z
" transform="scale(0.015625)"/>
      </defs>
      <use xlink:href="#Cmr10-66"/>
      <use xlink:href="#Cmr10-75" x="30.517578"/>
      <use xlink:href="#Cmr10-6e" x="86.035156"/>
      <use xlink:href="#Cmr10-63" x="141.552734"/>
      <use xlink:href="#Cmr10-74" x="185.9375"/>
      <use xlink:href="#Cmr10-69" x="224.755859"/>
      <use xlink:href="#Cmr10-6f" x="252.441406"/>
      <use xlink:href="#Cmr10-6e" x="302.441406"/>
      <use xlink:href="#Cmr10-20" x="357.958984"/>
      <use xlink:href="#Cmr10-76" x="391.259766"/>
      <use xlink:href="#Cmr10-61" x="443.945312"/>
      <use xlink:href="#Cmr10-6c" x="493.945312"/>
      <use xlink:href="#Cmr10-75" x="521.630859"/>
      <use xlink:href="#Cmr10-65" x="577.148438"/>
     </g>
    </g>
   </g>
   <g id="line2d_31">
    <path d="M 73.832727 41.472 
L 74.807666 41.555976 
L 76.107584 41.928778 
L 77.407502 42.598085 
L 78.70742 43.560928 
L 80.007338 44.813047 
L 81.307256 46.348911 
L 82.932154 48.657341 
L 84.557052 51.382657 
L 86.181949 54.506291 
L 88.131826 58.750495 
L 90.406683 64.333417 
L 92.68154 70.526918 
L 95.281376 78.250915 
L 98.531171 88.687987 
L 102.430925 102.015065 
L 115.755086 148.229974 
L 119.004881 158.407429 
L 121.929697 166.87655 
L 124.529533 173.773514 
L 127.129369 180.022126 
L 129.404226 184.928681 
L 131.679083 189.295437 
L 133.62896 192.603382 
L 135.578837 195.510041 
L 137.528714 198.019857 
L 139.478591 200.14101 
L 141.428468 201.88508 
L 143.053366 203.060889 
L 144.678264 203.994833 
L 146.303161 204.697926 
L 147.928059 205.182152 
L 149.552957 205.460297 
L 151.177854 205.545796 
L 153.127731 205.413736 
L 155.077609 205.049026 
L 157.027486 204.476705 
L 159.302342 203.580013 
L 161.902179 202.301244 
L 164.826994 200.606401 
L 168.401769 198.273177 
L 174.2514 194.140136 
L 181.72593 188.899826 
L 186.275643 185.988816 
L 190.175397 183.747505 
L 194.075152 181.772234 
L 197.649926 180.204855 
L 201.224701 178.867756 
L 205.124455 177.659062 
L 209.02421 176.690023 
L 213.248943 175.879513 
L 217.798657 175.243138 
L 222.998329 174.75737 
L 228.847961 174.441186 
L 236.32249 174.271967 
L 247.371794 174.268452 
L 305.543129 174.524711 
L 398.487273 174.528 
L 398.487273 174.528 
" clip-path="url(#p435b9db52d)" style="fill: none; stroke: #008000; stroke-width: 1.5; stroke-linecap: square"/>
   </g>
   <g id="line2d_32">
    <path d="M 73.832727 41.472 
L 76.757543 52.934927 
L 79.682359 63.41031 
L 82.607174 72.983226 
L 85.53199 81.731425 
L 88.456806 89.725956 
L 91.381622 97.03175 
L 94.306437 103.708141 
L 97.231253 109.809353 
L 100.156069 115.384938 
L 103.080885 120.480181 
L 106.0057 125.136463 
L 108.930516 129.3916 
L 111.855332 133.280153 
L 114.780147 136.833702 
L 118.029943 140.424203 
L 121.279738 143.672697 
L 124.529533 146.611762 
L 127.779328 149.270872 
L 131.354103 151.904293 
L 134.928878 154.263143 
L 138.828632 156.556843 
L 142.728387 158.590928 
L 146.95312 160.535551 
L 151.177854 162.242893 
L 155.727568 163.849338 
L 160.60226 165.33817 
L 165.801933 166.698198 
L 171.651564 167.989178 
L 177.826175 169.121689 
L 184.650745 170.146651 
L 192.450254 171.082337 
L 201.224701 171.898362 
L 211.299066 172.599898 
L 222.998329 173.183294 
L 237.297428 173.662342 
L 255.171302 174.028833 
L 279.544767 174.292387 
L 317.242391 174.454224 
L 395.887437 174.521456 
L 398.487273 174.521959 
L 398.487273 174.521959 
" clip-path="url(#p435b9db52d)" style="fill: none; stroke: #1f77b4; stroke-width: 1.5; stroke-linecap: square"/>
   </g>
   <g id="patch_3">
    <path d="M 57.6 307.584 
L 57.6 41.472 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
   <g id="patch_4">
    <path d="M 414.72 307.584 
L 414.72 41.472 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
   <g id="patch_5">
    <path d="M 57.6 307.584 
L 414.72 307.584 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
   <g id="patch_6">
    <path d="M 57.6 41.472 
L 414.72 41.472 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
   <g id="legend_1">
    <g id="patch_7">
     <path d="M 357.32 64.570437 
L 407.72 64.570437 
Q 409.72 64.570437 409.72 62.570437 
L 409.72 48.472 
Q 409.72 46.472 407.72 46.472 
L 357.32 46.472 
Q 355.32 46.472 355.32 48.472 
L 355.32 62.570437 
Q 355.32 64.570437 357.32 64.570437 
z
" style="fill: #ffffff; opacity: 0.8; stroke: #cccccc; stroke-linejoin: miter"/>
    </g>
    <g id="line2d_33">
     <path d="M 359.32 54.570437 
L 369.32 54.570437 
L 379.32 54.570437 
" style="fill: none; stroke: #008000; stroke-width: 1.5; stroke-linecap: square"/>
    </g>
    <g id="text_18">
     <!-- $f(x)$ -->
     <g transform="translate(387.32 58.070437) scale(0.1 -0.1)">
      <defs>
       <path id="Cmmi10-66" d="M 622 -1056 
Q 741 -1147 909 -1147 
Q 1138 -1147 1281 -641 
Q 1341 -397 1606 966 
L 1900 2534 
L 1350 2534 
Q 1288 2534 1288 2619 
Q 1313 2759 1369 2759 
L 1941 2759 
L 2016 3175 
Q 2053 3369 2084 3508 
Q 2116 3647 2152 3765 
Q 2188 3884 2259 4031 
Q 2369 4241 2555 4377 
Q 2741 4513 2956 4513 
Q 3097 4513 3230 4461 
Q 3363 4409 3447 4306 
Q 3531 4203 3531 4063 
Q 3531 3900 3423 3779 
Q 3316 3659 3163 3659 
Q 3059 3659 2986 3723 
Q 2913 3788 2913 3891 
Q 2913 4031 3008 4136 
Q 3103 4241 3244 4256 
Q 3125 4347 2950 4347 
Q 2853 4347 2767 4256 
Q 2681 4166 2656 4063 
Q 2616 3900 2478 3181 
L 2400 2759 
L 3059 2759 
Q 3122 2759 3122 2675 
Q 3119 2659 3109 2620 
Q 3100 2581 3083 2557 
Q 3066 2534 3041 2534 
L 2356 2534 
L 2059 972 
Q 2003 631 1929 279 
Q 1856 -72 1723 -442 
Q 1591 -813 1384 -1063 
Q 1178 -1313 897 -1313 
Q 681 -1313 511 -1189 
Q 341 -1066 341 -863 
Q 341 -700 445 -579 
Q 550 -459 709 -459 
Q 816 -459 887 -523 
Q 959 -588 959 -691 
Q 959 -828 857 -942 
Q 756 -1056 622 -1056 
z
" transform="scale(0.015625)"/>
       <path id="Cmr10-28" d="M 1984 -1588 
Q 1628 -1306 1370 -942 
Q 1113 -578 948 -165 
Q 784 247 703 697 
Q 622 1147 622 1600 
Q 622 2059 703 2509 
Q 784 2959 951 3375 
Q 1119 3791 1378 4153 
Q 1638 4516 1984 4788 
Q 1984 4800 2016 4800 
L 2075 4800 
Q 2094 4800 2109 4783 
Q 2125 4766 2125 4744 
Q 2125 4716 2113 4703 
Q 1800 4397 1592 4047 
Q 1384 3697 1257 3301 
Q 1131 2906 1075 2482 
Q 1019 2059 1019 1600 
Q 1019 -434 2106 -1491 
Q 2125 -1509 2125 -1544 
Q 2125 -1559 2108 -1579 
Q 2091 -1600 2075 -1600 
L 2016 -1600 
Q 1984 -1600 1984 -1588 
z
" transform="scale(0.015625)"/>
       <path id="Cmmi10-78" d="M 500 184 
Q 613 97 819 97 
Q 1019 97 1172 289 
Q 1325 481 1381 709 
L 1672 1844 
Q 1741 2153 1741 2266 
Q 1741 2425 1652 2544 
Q 1563 2663 1403 2663 
Q 1200 2663 1022 2536 
Q 844 2409 722 2214 
Q 600 2019 550 1819 
Q 538 1778 500 1778 
L 422 1778 
Q 372 1778 372 1838 
L 372 1856 
Q 434 2094 584 2320 
Q 734 2547 951 2687 
Q 1169 2828 1416 2828 
Q 1650 2828 1839 2703 
Q 2028 2578 2106 2363 
Q 2216 2559 2386 2693 
Q 2556 2828 2759 2828 
Q 2897 2828 3040 2779 
Q 3184 2731 3275 2631 
Q 3366 2531 3366 2381 
Q 3366 2219 3261 2101 
Q 3156 1984 2994 1984 
Q 2891 1984 2822 2050 
Q 2753 2116 2753 2216 
Q 2753 2350 2845 2451 
Q 2938 2553 3066 2572 
Q 2950 2663 2747 2663 
Q 2541 2663 2389 2472 
Q 2238 2281 2175 2047 
L 1894 916 
Q 1825 659 1825 494 
Q 1825 331 1917 214 
Q 2009 97 2163 97 
Q 2463 97 2698 361 
Q 2934 625 3009 941 
Q 3022 978 3059 978 
L 3138 978 
Q 3163 978 3178 961 
Q 3194 944 3194 922 
Q 3194 916 3188 903 
Q 3097 522 2806 225 
Q 2516 -72 2150 -72 
Q 1916 -72 1727 54 
Q 1538 181 1459 397 
Q 1359 209 1182 68 
Q 1006 -72 806 -72 
Q 669 -72 523 -23 
Q 378 25 287 125 
Q 197 225 197 378 
Q 197 528 301 651 
Q 406 775 563 775 
Q 669 775 741 711 
Q 813 647 813 544 
Q 813 409 723 309 
Q 634 209 500 184 
z
" transform="scale(0.015625)"/>
       <path id="Cmr10-29" d="M 416 -1600 
Q 359 -1600 359 -1544 
Q 359 -1516 372 -1503 
Q 1466 -434 1466 1600 
Q 1466 3634 384 4691 
Q 359 4706 359 4744 
Q 359 4766 376 4783 
Q 394 4800 416 4800 
L 475 4800 
Q 494 4800 506 4788 
Q 966 4425 1272 3906 
Q 1578 3388 1720 2800 
Q 1863 2213 1863 1600 
Q 1863 1147 1786 708 
Q 1709 269 1542 -157 
Q 1375 -584 1119 -945 
Q 863 -1306 506 -1588 
Q 494 -1600 475 -1600 
L 416 -1600 
z
" transform="scale(0.015625)"/>
      </defs>
      <use xlink:href="#Cmmi10-66"/>
      <use xlink:href="#Cmr10-28" transform="translate(48.876953 0)"/>
      <use xlink:href="#Cmmi10-78" transform="translate(87.695312 0)"/>
      <use xlink:href="#Cmr10-29" transform="translate(144.775391 0)"/>
     </g>
    </g>
   </g>
  </g>
  <g id="text_19">
   <!-- Sample plot -->
   <g transform="translate(183.445312 26.516813) scale(0.18 -0.18)">
    <defs>
     <path id="Cmr10-53" d="M 359 -91 
L 359 1403 
Q 359 1453 416 1453 
L 494 1453 
Q 513 1453 528 1437 
Q 544 1422 544 1403 
Q 544 775 933 429 
Q 1322 84 1953 84 
Q 2175 84 2362 212 
Q 2550 341 2654 548 
Q 2759 756 2759 978 
Q 2759 1172 2681 1355 
Q 2603 1538 2456 1672 
Q 2309 1806 2125 1850 
L 1294 2053 
Q 881 2163 620 2502 
Q 359 2841 359 3263 
Q 359 3594 528 3884 
Q 697 4175 983 4344 
Q 1269 4513 1600 4513 
Q 2241 4513 2619 4078 
L 2881 4494 
Q 2900 4513 2925 4513 
L 2969 4513 
Q 2988 4513 3005 4498 
Q 3022 4484 3022 4459 
L 3022 2975 
Q 3022 2919 2969 2919 
L 2894 2919 
Q 2834 2919 2834 2975 
Q 2834 3138 2779 3331 
Q 2725 3525 2628 3703 
Q 2531 3881 2419 3994 
Q 2109 4306 1600 4306 
Q 1381 4306 1197 4195 
Q 1013 4084 903 3893 
Q 794 3703 794 3494 
Q 794 3219 964 2995 
Q 1134 2772 1409 2700 
L 2241 2497 
Q 2447 2447 2630 2317 
Q 2813 2188 2934 2016 
Q 3056 1844 3125 1633 
Q 3194 1422 3194 1197 
Q 3194 850 3034 542 
Q 2875 234 2586 46 
Q 2297 -141 1953 -141 
Q 1741 -141 1519 -94 
Q 1297 -47 1109 50 
Q 922 147 769 300 
L 500 -122 
Q 481 -141 453 -141 
L 416 -141 
Q 359 -141 359 -91 
z
" transform="scale(0.015625)"/>
     <path id="Cmr10-6d" d="M 191 0 
L 191 225 
Q 409 225 550 259 
Q 691 294 691 428 
L 691 2175 
Q 691 2347 639 2423 
Q 588 2500 491 2517 
Q 394 2534 191 2534 
L 191 2759 
L 1119 2828 
L 1119 2203 
Q 1247 2478 1498 2653 
Q 1750 2828 2047 2828 
Q 2784 2828 2913 2228 
Q 3041 2497 3287 2662 
Q 3534 2828 3828 2828 
Q 4119 2828 4317 2734 
Q 4516 2641 4616 2448 
Q 4716 2256 4716 1966 
L 4716 428 
Q 4716 294 4858 259 
Q 5000 225 5216 225 
L 5216 0 
L 3750 0 
L 3750 225 
Q 3969 225 4109 259 
Q 4250 294 4250 428 
L 4250 1947 
Q 4250 2269 4159 2466 
Q 4069 2663 3788 2663 
Q 3419 2663 3178 2366 
Q 2938 2069 2938 1691 
L 2938 428 
Q 2938 294 3078 259 
Q 3219 225 3438 225 
L 3438 0 
L 1972 0 
L 1972 225 
Q 2191 225 2331 259 
Q 2472 294 2472 428 
L 2472 1947 
Q 2472 2259 2381 2461 
Q 2291 2663 2009 2663 
Q 1638 2663 1398 2366 
Q 1159 2069 1159 1691 
L 1159 428 
Q 1159 294 1300 259 
Q 1441 225 1656 225 
L 1656 0 
L 191 0 
z
" transform="scale(0.015625)"/>
     <path id="Cmr10-70" d="M 166 -1241 
L 166 -1019 
Q 384 -1019 525 -981 
Q 666 -944 666 -813 
L 666 2272 
Q 666 2447 541 2490 
Q 416 2534 166 2534 
L 166 2759 
L 1113 2828 
L 1113 2431 
Q 1288 2625 1520 2726 
Q 1753 2828 2016 2828 
Q 2394 2828 2697 2623 
Q 3000 2419 3170 2086 
Q 3341 1753 3341 1381 
Q 3341 994 3152 659 
Q 2963 325 2636 126 
Q 2309 -72 1919 -72 
Q 1453 -72 1131 306 
L 1131 -813 
Q 1131 -944 1273 -981 
Q 1416 -1019 1631 -1019 
L 1631 -1241 
L 166 -1241 
z
M 1131 622 
Q 1244 394 1444 245 
Q 1644 97 1881 97 
Q 2103 97 2273 215 
Q 2444 334 2559 534 
Q 2675 734 2729 954 
Q 2784 1175 2784 1381 
Q 2784 1638 2692 1936 
Q 2600 2234 2411 2439 
Q 2222 2644 1953 2644 
Q 1694 2644 1476 2511 
Q 1259 2378 1131 2150 
L 1131 622 
z
" transform="scale(0.015625)"/>
    </defs>
    <use xlink:href="#Cmr10-53"/>
    <use xlink:href="#Cmr10-61" x="55.517578"/>
    <use xlink:href="#Cmr10-6d" x="105.517578"/>
    <use xlink:href="#Cmr10-70" x="188.818359"/>
    <use xlink:href="#Cmr10-6c" x="244.335938"/>
    <use xlink:href="#Cmr10-65" x="272.021484"/>
    <use xlink:href="#Cmr10-20" x="316.40625"/>
    <use xlink:href="#Cmr10-70" x="349.707031"/>
    <use xlink:href="#Cmr10-6c" x="405.224609"/>
    <use xlink:href="#Cmr10-6f" x="432.910156"/>
    <use xlink:href="#Cmr10-74" x="482.910156"/>
   </g>
  </g>
 </g>
 <defs>
  <clipPath id="p435b9db52d">
   <rect x="57.6" y="41.472" width="357.12" height="266.112"/>
  </clipPath>
 </defs>
</svg>
\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"ignore_on_import\": true,\n\t\t\t\"source\": \"plot($\\\\exp(-x)$, ($x$, 0, 10), fig=f, label=\\\"red\\\");\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 14025577843904916616,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"ignore_on_import\": true,\n\t\t\t\"source\": \"#set_plot_backend(Backend.PLOTLY)\\n#plot($\\\\cos(x)*\\\\exp(-x**2/5)$, ($x$, 0, 10), grid=True, xlabel=\\\"x-axis\\\", ylabel=\\\"y-axis\\\", title=\\\"Sample plot\\\");\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 13839647066874094386,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 6573578691714100778,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\algorithm{parametric_plot(fnx: Ex, fny: Ex, range: tuple, grid: bool, xlabel: str, ylabel: str, title: str, samples: int) -> plot}{Plot pairs of functions against each other.}\\n\\nThe functions \\\\verb|fnx| and \\\\verb|fny| should be single functions or lists of functions, determining the $x$ and $y$ values. The range is a tuple or list with three elements: the symbol which is the \\ndependent variable as a Cadabra expression, the starting value and the end value. You can specify\\nthe number of samples with the optional parameter.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\algorithm{parametric_plot(fnx: Ex, fny: Ex, range: tuple, grid: bool, xlabel: str, ylabel: str, title: str, samples: int) -> plot}{Plot pairs of functions against each other.}\\n\\nThe functions \\\\verb|fnx| and \\\\verb|fny| should be single functions or lists of functions, determining the $x$ and $y$ values. The range is a tuple or list with three elements: the symbol which is the \\ndependent variable as a Cadabra expression, the starting value and the end value. You can specify\\nthe number of samples with the optional parameter.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 13673066928362633891,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"def parametric_plot(fnx, fny, range_={}, samples=1000, grid=False, xlabel=None, ylabel=None, title=None, \\n                    xrange=[], yrange=[], fig=None, label=\\\"default_label\\\", legend=None, color=None, aspect=None):\\n   \\n   if range_ == {}:\\n      range_ = function_domain(fnx)\\n   if range_ == {}:\\n      range_ = function_domain(fny)\\n   if range_ == {}:\\n      raise Exception(\\\"cdb.graphics.plot.parametric_plot: No plot range set, and none could be deduced.\\\")\\n\\n   fnx = exlist_to_list(fnx)\\n   fny = exlist_to_list(fny)\\n   fnx, _, _, = handle_equations(fnx, label, legend)\\n   fny, _, _, = handle_equations(fny, label, legend)\\n\\n   # Colours.\\n   if color == None:\\n      import matplotlib.pyplot as plt\\n      cycler = plt.rcParams['axes.prop_cycle']\\n      color = [c['color'] for c in cycler]\\n   if isinstance(color, list)==False:\\n      color = [color]\\n   if len(color) < len(fnx):\\n      color = color * int( (len(fn)/len(color)+1) )\\n\\n   if isinstance(range_, dict):\\n      fvx = list(map(lambda arg: np.array(nevaluate(arg, range_)), fnx))\\n      fvy = list(map(lambda arg: np.array(nevaluate(arg, range_)), fny))\\n      r = np.array(nrange(range_)[1])\\n   else:\\n      xvar = range_[0]\\n      xstart = range_[1]\\n      xend = range_[2]\\n      r = np.linspace(xstart, xend, samples)\\n      fvx = list(map(lambda arg: np.array(nevaluate(arg, {range_[0]: r})), fnx))\\n      fvy = list(map(lambda arg: np.array(nevaluate(arg, {range_[0]: r})), fny))\\n\\n   if True:\\n      import matplotlib.pyplot as plt\\n      newplot=False\\n      if fig==None:\\n         fig = plt.figure()\\n         fig.add_subplot(1,1,1)\\n         newplot=True\\n      ax = fig.axes[0]\\n      if aspect:\\n         ax.set_aspect(aspect)\\n      if grid!=None:\\n         ax.grid(visible=grid)\\n      for line in ax.get_lines():\\n         if line.get_label() == label:\\n            line.remove()\\n            break\\n\\n      for i in range(len(fvx)):\\n         ax.plot(fvx[i], fvy[i], color=color[i], label=label)\\n\\n      if title:\\n         fig.suptitle(title, fontsize=18, fontfamily=\\\"cmr10\\\", y=0.96)\\n      if xlabel:\\n         ax.set_xlabel(xlabel, fontsize=16, fontname=\\\"cmr10\\\")\\n      if ylabel:\\n         ax.set_ylabel(ylabel, fontsize=16, fontname=\\\"cmr10\\\")\\n      if len(xrange)==2:\\n         ax.set(xlim=xrange)\\n      if len(yrange)==2:\\n         ax.set(ylim=yrange)\\n      return fig\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 11295583760114920559,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 14650780130349334767,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"image_svg\",\n\t\t\t\t\t\"source\": \"<?xml version="1.0" encoding="utf-8" standalone="no"?>
<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
  "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="460.8pt" height="345.6pt" viewBox="0 0 460.8 345.6" xmlns="http://www.w3.org/2000/svg" version="1.1">
 <metadata>
  <rdf:RDF xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:cc="http://creativecommons.org/ns#" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
   <cc:Work>
    <dc:type rdf:resource="http://purl.org/dc/dcmitype/StillImage"/>
    <dc:date>2025-03-30T14:01:10.886905</dc:date>
    <dc:format>image/svg+xml</dc:format>
    <dc:creator>
     <cc:Agent>
      <dc:title>Matplotlib v3.6.3, https://matplotlib.org/</dc:title>
     </cc:Agent>
    </dc:creator>
   </cc:Work>
  </rdf:RDF>
 </metadata>
 <defs>
  <style type="text/css">*{stroke-linejoin: round; stroke-linecap: butt}</style>
 </defs>
 <g id="figure_1">
  <g id="patch_1">
   <path d="M 0 345.6 
L 460.8 345.6 
L 460.8 0 
L 0 0 
z
" style="fill: #ffffff"/>
  </g>
  <g id="axes_1">
   <g id="patch_2">
    <path d="M 103.10412 307.584 
L 369.21588 307.584 
L 369.21588 41.472 
L 103.10412 41.472 
z
" style="fill: #ffffff"/>
   </g>
   <g id="matplotlib.axis_1">
    <g id="xtick_1">
     <g id="line2d_1">
      <defs>
       <path id="mfed016fa84" d="M 0 0 
L 0 3.5 
" style="stroke: #000000; stroke-width: 0.8"/>
      </defs>
      <g>
       <use xlink:href="#mfed016fa84" x="115.199782" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_1">
      <!-- −1.0 -->
      <g transform="translate(103.058376 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-2212" d="M 678 2272 
L 4684 2272 
L 4684 1741 
L 678 1741 
L 678 2272 
z
" transform="scale(0.015625)"/>
        <path id="DejaVuSans-31" d="M 794 531 
L 1825 531 
L 1825 4091 
L 703 3866 
L 703 4441 
L 1819 4666 
L 2450 4666 
L 2450 531 
L 3481 531 
L 3481 0 
L 794 0 
L 794 531 
z
" transform="scale(0.015625)"/>
        <path id="DejaVuSans-2e" d="M 684 794 
L 1344 794 
L 1344 0 
L 684 0 
L 684 794 
z
" transform="scale(0.015625)"/>
        <path id="DejaVuSans-30" d="M 2034 4250 
Q 1547 4250 1301 3770 
Q 1056 3291 1056 2328 
Q 1056 1369 1301 889 
Q 1547 409 2034 409 
Q 2525 409 2770 889 
Q 3016 1369 3016 2328 
Q 3016 3291 2770 3770 
Q 2525 4250 2034 4250 
z
M 2034 4750 
Q 2819 4750 3233 4129 
Q 3647 3509 3647 2328 
Q 3647 1150 3233 529 
Q 2819 -91 2034 -91 
Q 1250 -91 836 529 
Q 422 1150 422 2328 
Q 422 3509 836 4129 
Q 1250 4750 2034 4750 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-2212"/>
       <use xlink:href="#DejaVuSans-31" x="83.789062"/>
       <use xlink:href="#DejaVuSans-2e" x="147.412109"/>
       <use xlink:href="#DejaVuSans-30" x="179.199219"/>
      </g>
     </g>
    </g>
    <g id="xtick_2">
     <g id="line2d_2">
      <g>
       <use xlink:href="#mfed016fa84" x="175.679818" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_2">
      <!-- −0.5 -->
      <g transform="translate(163.538412 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-35" d="M 691 4666 
L 3169 4666 
L 3169 4134 
L 1269 4134 
L 1269 2991 
Q 1406 3038 1543 3061 
Q 1681 3084 1819 3084 
Q 2600 3084 3056 2656 
Q 3513 2228 3513 1497 
Q 3513 744 3044 326 
Q 2575 -91 1722 -91 
Q 1428 -91 1123 -41 
Q 819 9 494 109 
L 494 744 
Q 775 591 1075 516 
Q 1375 441 1709 441 
Q 2250 441 2565 725 
Q 2881 1009 2881 1497 
Q 2881 1984 2565 2268 
Q 2250 2553 1709 2553 
Q 1456 2553 1204 2497 
Q 953 2441 691 2322 
L 691 4666 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-2212"/>
       <use xlink:href="#DejaVuSans-30" x="83.789062"/>
       <use xlink:href="#DejaVuSans-2e" x="147.412109"/>
       <use xlink:href="#DejaVuSans-35" x="179.199219"/>
      </g>
     </g>
    </g>
    <g id="xtick_3">
     <g id="line2d_3">
      <g>
       <use xlink:href="#mfed016fa84" x="236.159855" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_3">
      <!-- 0.0 -->
      <g transform="translate(228.208292 322.182437) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-30"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-30" x="95.410156"/>
      </g>
     </g>
    </g>
    <g id="xtick_4">
     <g id="line2d_4">
      <g>
       <use xlink:href="#mfed016fa84" x="296.639891" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_4">
      <!-- 0.5 -->
      <g transform="translate(288.688328 322.182437) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-30"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-35" x="95.410156"/>
      </g>
     </g>
    </g>
    <g id="xtick_5">
     <g id="line2d_5">
      <g>
       <use xlink:href="#mfed016fa84" x="357.119927" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_5">
      <!-- 1.0 -->
      <g transform="translate(349.168365 322.182437) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-31"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-30" x="95.410156"/>
      </g>
     </g>
    </g>
   </g>
   <g id="matplotlib.axis_2">
    <g id="ytick_1">
     <g id="line2d_6">
      <defs>
       <path id="mfdcc889a72" d="M 0 0 
L -3.5 0 
" style="stroke: #000000; stroke-width: 0.8"/>
      </defs>
      <g>
       <use xlink:href="#mfdcc889a72" x="103.10412" y="295.488145" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_6">
      <!-- −1.00 -->
      <g transform="translate(65.458807 299.287364) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-2212"/>
       <use xlink:href="#DejaVuSans-31" x="83.789062"/>
       <use xlink:href="#DejaVuSans-2e" x="147.412109"/>
       <use xlink:href="#DejaVuSans-30" x="179.199219"/>
       <use xlink:href="#DejaVuSans-30" x="242.822266"/>
      </g>
     </g>
    </g>
    <g id="ytick_2">
     <g id="line2d_7">
      <g>
       <use xlink:href="#mfdcc889a72" x="103.10412" y="265.248127" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_7">
      <!-- −0.75 -->
      <g transform="translate(65.458807 269.047346) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-37" d="M 525 4666 
L 3525 4666 
L 3525 4397 
L 1831 0 
L 1172 0 
L 2766 4134 
L 525 4134 
L 525 4666 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-2212"/>
       <use xlink:href="#DejaVuSans-30" x="83.789062"/>
       <use xlink:href="#DejaVuSans-2e" x="147.412109"/>
       <use xlink:href="#DejaVuSans-37" x="179.199219"/>
       <use xlink:href="#DejaVuSans-35" x="242.822266"/>
      </g>
     </g>
    </g>
    <g id="ytick_3">
     <g id="line2d_8">
      <g>
       <use xlink:href="#mfdcc889a72" x="103.10412" y="235.008109" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_8">
      <!-- −0.50 -->
      <g transform="translate(65.458807 238.807328) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-2212"/>
       <use xlink:href="#DejaVuSans-30" x="83.789062"/>
       <use xlink:href="#DejaVuSans-2e" x="147.412109"/>
       <use xlink:href="#DejaVuSans-35" x="179.199219"/>
       <use xlink:href="#DejaVuSans-30" x="242.822266"/>
      </g>
     </g>
    </g>
    <g id="ytick_4">
     <g id="line2d_9">
      <g>
       <use xlink:href="#mfdcc889a72" x="103.10412" y="204.768091" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_9">
      <!-- −0.25 -->
      <g transform="translate(65.458807 208.56731) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-32" d="M 1228 531 
L 3431 531 
L 3431 0 
L 469 0 
L 469 531 
Q 828 903 1448 1529 
Q 2069 2156 2228 2338 
Q 2531 2678 2651 2914 
Q 2772 3150 2772 3378 
Q 2772 3750 2511 3984 
Q 2250 4219 1831 4219 
Q 1534 4219 1204 4116 
Q 875 4013 500 3803 
L 500 4441 
Q 881 4594 1212 4672 
Q 1544 4750 1819 4750 
Q 2544 4750 2975 4387 
Q 3406 4025 3406 3419 
Q 3406 3131 3298 2873 
Q 3191 2616 2906 2266 
Q 2828 2175 2409 1742 
Q 1991 1309 1228 531 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-2212"/>
       <use xlink:href="#DejaVuSans-30" x="83.789062"/>
       <use xlink:href="#DejaVuSans-2e" x="147.412109"/>
       <use xlink:href="#DejaVuSans-32" x="179.199219"/>
       <use xlink:href="#DejaVuSans-35" x="242.822266"/>
      </g>
     </g>
    </g>
    <g id="ytick_5">
     <g id="line2d_10">
      <g>
       <use xlink:href="#mfdcc889a72" x="103.10412" y="174.528073" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_10">
      <!-- 0.00 -->
      <g transform="translate(73.838495 178.327291) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-30"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-30" x="95.410156"/>
       <use xlink:href="#DejaVuSans-30" x="159.033203"/>
      </g>
     </g>
    </g>
    <g id="ytick_6">
     <g id="line2d_11">
      <g>
       <use xlink:href="#mfdcc889a72" x="103.10412" y="144.288055" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_11">
      <!-- 0.25 -->
      <g transform="translate(73.838495 148.087273) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-30"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-32" x="95.410156"/>
       <use xlink:href="#DejaVuSans-35" x="159.033203"/>
      </g>
     </g>
    </g>
    <g id="ytick_7">
     <g id="line2d_12">
      <g>
       <use xlink:href="#mfdcc889a72" x="103.10412" y="114.048036" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_12">
      <!-- 0.50 -->
      <g transform="translate(73.838495 117.847255) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-30"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-35" x="95.410156"/>
       <use xlink:href="#DejaVuSans-30" x="159.033203"/>
      </g>
     </g>
    </g>
    <g id="ytick_8">
     <g id="line2d_13">
      <g>
       <use xlink:href="#mfdcc889a72" x="103.10412" y="83.808018" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_13">
      <!-- 0.75 -->
      <g transform="translate(73.838495 87.607237) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-30"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-37" x="95.410156"/>
       <use xlink:href="#DejaVuSans-35" x="159.033203"/>
      </g>
     </g>
    </g>
    <g id="ytick_9">
     <g id="line2d_14">
      <g>
       <use xlink:href="#mfdcc889a72" x="103.10412" y="53.568" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_14">
      <!-- 1.00 -->
      <g transform="translate(73.838495 57.367219) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-31"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-30" x="95.410156"/>
       <use xlink:href="#DejaVuSans-30" x="159.033203"/>
      </g>
     </g>
    </g>
   </g>
   <g id="line2d_15">
    <path d="M 236.159855 53.568 
L 241.480865 53.685092 
L 246.791573 54.03614 
L 252.081698 54.620466 
L 257.340997 55.436938 
L 262.559289 56.483975 
L 267.72647 57.75955 
L 272.832538 59.261193 
L 277.867605 60.985998 
L 282.821925 62.930625 
L 287.685905 65.091309 
L 292.450129 67.463867 
L 297.105372 70.043705 
L 301.642622 72.825829 
L 306.053096 75.804853 
L 310.328253 78.975009 
L 314.459817 82.33016 
L 318.439789 85.863809 
L 322.260464 89.569116 
L 325.914445 93.438907 
L 329.394657 97.46569 
L 332.694363 101.641669 
L 335.807174 105.958758 
L 338.727064 110.408601 
L 341.44838 114.982581 
L 343.965853 119.671844 
L 346.27461 124.467311 
L 348.37018 129.359697 
L 350.248506 134.339531 
L 351.905952 139.397172 
L 353.339309 144.522827 
L 354.545801 149.706574 
L 355.523094 154.938377 
L 356.269295 160.208105 
L 356.782959 165.505558 
L 357.063093 170.820479 
L 357.109152 176.142578 
L 356.921049 181.461551 
L 356.499147 186.7671 
L 355.844264 192.048955 
L 354.957667 197.296888 
L 353.841073 202.50074 
L 352.496643 207.650435 
L 350.92698 212.736005 
L 349.135124 217.747602 
L 347.124543 222.675525 
L 344.89913 227.510232 
L 342.463193 232.242363 
L 339.821449 236.862758 
L 336.979012 241.36247 
L 333.941385 245.732788 
L 330.714449 249.965251 
L 327.304452 254.051664 
L 323.717995 257.984117 
L 319.962022 261.754995 
L 316.043804 265.356999 
L 311.970928 268.783154 
L 307.751279 272.026827 
L 303.393026 275.081739 
L 298.904607 277.941975 
L 294.294712 280.601998 
L 289.572265 283.056657 
L 284.746409 285.301201 
L 279.826488 287.331283 
L 274.822027 289.142974 
L 269.742714 290.732766 
L 264.598383 292.097581 
L 259.398995 293.234777 
L 254.154614 294.142151 
L 248.875395 294.817948 
L 243.571558 295.26086 
L 238.253372 295.470027 
L 232.931132 295.445046 
L 227.615144 295.185966 
L 222.315698 294.693286 
L 217.043055 293.967962 
L 211.807423 293.011398 
L 206.618939 291.825445 
L 201.487647 290.412399 
L 196.423481 288.774997 
L 191.436247 286.916409 
L 186.535599 284.840232 
L 181.731026 282.550486 
L 177.03183 280.051605 
L 172.447107 277.348426 
L 167.985735 274.446182 
L 163.656351 271.350493 
L 159.467337 268.067353 
L 155.426802 264.603116 
L 151.54257 260.96449 
L 147.82216 257.15852 
L 144.272775 253.192574 
L 140.901288 249.074331 
L 137.714225 244.811763 
L 134.717756 240.413123 
L 131.917684 235.886927 
L 129.319428 231.241938 
L 126.92802 226.487148 
L 124.748089 221.631764 
L 122.783856 216.685184 
L 121.039123 211.656988 
L 119.517268 206.556908 
L 118.221239 201.394819 
L 117.153543 196.180714 
L 116.316248 190.92469 
L 115.710975 185.636921 
L 115.338896 180.327645 
L 115.200731 175.00714 
L 115.296747 169.685708 
L 115.62676 164.373651 
L 116.190129 159.081254 
L 116.985765 153.818762 
L 118.012126 148.596364 
L 119.267227 143.424171 
L 120.748636 138.312196 
L 122.453485 133.270337 
L 124.378475 128.308355 
L 126.519878 123.435855 
L 128.873548 118.662272 
L 131.434929 113.996848 
L 134.199062 109.448614 
L 137.160594 105.026377 
L 140.313794 100.738698 
L 143.652555 96.593878 
L 147.170414 92.599942 
L 150.860559 88.764622 
L 154.715848 85.095344 
L 158.728816 81.59921 
L 162.891693 78.282991 
L 167.196421 75.153106 
L 171.634664 72.215615 
L 176.19783 69.476205 
L 180.877086 66.94018 
L 185.663371 64.612449 
L 190.54742 62.497519 
L 195.519775 60.599485 
L 200.570812 58.922021 
L 205.690751 57.468375 
L 210.869678 56.241361 
L 216.097569 55.243355 
L 221.364301 54.476289 
L 226.659678 53.941648 
L 231.973448 53.640467 
L 235.77456 53.568614 
L 235.77456 53.568614 
" clip-path="url(#p2041aac349)" style="fill: none; stroke: #1f77b4; stroke-width: 1.5; stroke-linecap: square"/>
   </g>
   <g id="patch_3">
    <path d="M 103.10412 307.584 
L 103.10412 41.472 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
   <g id="patch_4">
    <path d="M 369.21588 307.584 
L 369.21588 41.472 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
   <g id="patch_5">
    <path d="M 103.10412 307.584 
L 369.21588 307.584 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
   <g id="patch_6">
    <path d="M 103.10412 41.472 
L 369.21588 41.472 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
  </g>
 </g>
 <defs>
  <clipPath id="p2041aac349">
   <rect x="103.10412" y="41.472" width="266.11176" height="266.112"/>
  </clipPath>
 </defs>
</svg>
\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"ignore_on_import\": true,\n\t\t\t\"source\": \"#set_plot_backend(Backend.MATPLOTLIB)\\nfig = parametric_plot($x=\\\\sin(x)$, $y=\\\\cos(x)$, ($x$,0,6.28), aspect='equal');\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 17256249505069699125,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 4091782214796069523,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\algorithm{plot3d(ex: Ex, range1: tuple, range2: tuple, samples: (int,int)) -> plot}{Plot a function of two variables given their ranges.}\\n\\nThe function should be a Cadabra expression (so written using dollar symbols if it is constructed \\ninline). The ranges is are tuples with three elements each: the symbol which is the \\ndependent variable as a Cadabra expression, the starting value and the end value. You can specify the\\nnumber of samples with the optional parameter.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\algorithm{plot3d(ex: Ex, range1: tuple, range2: tuple, samples: (int,int)) -> plot}{Plot a function of two variables given their ranges.}\\n\\nThe function should be a Cadabra expression (so written using dollar symbols if it is constructed \\ninline). The ranges is are tuples with three elements each: the symbol which is the \\ndependent variable as a Cadabra expression, the starting value and the end value. You can specify the\\nnumber of samples with the optional parameter.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 1072622800111302942,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"def plot3d(fn, range1, range2, samples=(100,100)):\\n   r1 = np.linspace(range1[1], range2[2], samples[0])\\n   r2 = np.linspace(range2[1], range2[2], samples[1])\\n   z = np.array( nevaluate(fn, {range1[0]: r1, range2[0]: r2} ) )\\n   XV, YV = np.meshgrid(r1, r2)\\n   if _backend==Backend.MATPLOTLIB:\\n      import matplotlib.pyplot as plt\\n      plt.clf()\\n      ax = plt.axes(projection='3d')\\n      plt.figure().subplots_adjust(top=1, bottom=0, left=0, right=1, wspace=0)\\n      ret = ax.plot_surface(XV, YV, z, rstride=1, cstride=1, cmap='terrain', edgecolor=None)\\n      return ret \\n   if _backend==Backend.PLOTLY:\\n      import plotly.graph_objects as go\\n      fig = go.Figure(data=[go.Surface(z=z, x=r1, y=r2)])\\n      return fig\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 6753832780309258849,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 7595903134064056914,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"image_svg\",\n\t\t\t\t\t\"source\": \"<svg class="main-svg" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" width="700" height="500" style="" viewBox="0 0 700 500"><rect x="0" y="0" width="700" height="500" style="fill: rgb(255, 255, 255); fill-opacity: 1;"/><defs id="defs-919ddb"><g class="clips"/><g class="gradients"><linearGradient x1="0" x2="0" y1="1" y2="0" id="g919ddb-cb50446a"><stop offset="0%" stop-color="rgb(13, 8, 135)" stop-opacity="1"/><stop offset="11.111111%" stop-color="rgb(70, 3, 159)" stop-opacity="1"/><stop offset="22.222222%" stop-color="rgb(114, 1, 168)" stop-opacity="1"/><stop offset="33.333333%" stop-color="rgb(156, 23, 158)" stop-opacity="1"/><stop offset="44.444444%" stop-color="rgb(189, 55, 134)" stop-opacity="1"/><stop offset="55.555556%" stop-color="rgb(216, 87, 107)" stop-opacity="1"/><stop offset="66.666667%" stop-color="rgb(237, 121, 83)" stop-opacity="1"/><stop offset="77.777778%" stop-color="rgb(251, 159, 58)" stop-opacity="1"/><stop offset="88.888889%" stop-color="rgb(253, 202, 38)" stop-opacity="1"/><stop offset="100%" stop-color="rgb(240, 249, 33)" stop-opacity="1"/></linearGradient></g><g class="patterns"/></defs><g class="bglayer"/><g class="layer-below"><g class="imagelayer"/><g class="shapelayer"/></g><g class="cartesianlayer"/><g class="polarlayer"/><g class="smithlayer"/><g class="ternarylayer"/><g class="geolayer"/><g class="funnelarealayer"/><g class="pielayer"/><g class="iciclelayer"/><g class="treemaplayer"/><g class="sunburstlayer"/><g class="glimages"><image xmlns="http://www.w3.org/2000/svg" xlink:href="data:image/png;base64,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" x="80" y="100" width="524" height="320" preserveAspectRatio="none"/></g><defs id="topdefs-919ddb"><g class="clips"/></defs><g class="layer-above"><g class="imagelayer"/><g class="shapelayer"/></g><g class="infolayer"><g class="cb50446a colorbar" transform="translate(80,100)"><rect class="cbbg" x="534" y="0" width="73.9375" height="320" style="fill: rgb(0, 0, 0); fill-opacity: 0; stroke: rgb(68, 68, 68); stroke-opacity: 1; stroke-width: 0;"/><g class="cbfills" transform="translate(0,10)"><rect class="cbfill gradient_filled" style="fill: url('#g919ddb-cb50446a');" x="544" y="0" width="30" height="300"/></g><g class="cblines" transform="translate(0,10)"/><g class="cbaxis crisp" transform="translate(0,-100)"><g class="ycb50446atick"><text text-anchor="start" x="576.9" y="4.199999999999999" transform="translate(0,410.01)" style="font-family: 'Open Sans', verdana, arial, sans-serif; font-size: 12px; fill: rgb(42, 63, 95); fill-opacity: 1; white-space: pre; opacity: 1;">−1</text></g><g class="ycb50446atick"><text text-anchor="start" x="576.9" y="4.199999999999999" style="font-family: 'Open Sans', verdana, arial, sans-serif; font-size: 12px; fill: rgb(42, 63, 95); fill-opacity: 1; white-space: pre; opacity: 1;" transform="translate(0,335.01)">−0.5</text></g><g class="ycb50446atick"><text text-anchor="start" x="576.9" y="4.199999999999999" style="font-family: 'Open Sans', verdana, arial, sans-serif; font-size: 12px; fill: rgb(42, 63, 95); fill-opacity: 1; white-space: pre; opacity: 1;" transform="translate(0,260)">0</text></g><g class="ycb50446atick"><text text-anchor="start" x="576.9" y="4.199999999999999" style="font-family: 'Open Sans', verdana, arial, sans-serif; font-size: 12px; fill: rgb(42, 63, 95); fill-opacity: 1; white-space: pre; opacity: 1;" transform="translate(0,185)">0.5</text></g><g class="ycb50446atick"><text text-anchor="start" x="576.9" y="4.199999999999999" style="font-family: 'Open Sans', verdana, arial, sans-serif; font-size: 12px; fill: rgb(42, 63, 95); fill-opacity: 1; white-space: pre; opacity: 1;" transform="translate(0,110)">1</text></g></g><g class="cbtitleunshift" transform="translate(-80,-100)"><g class="cbtitle"/></g><rect class="cboutline" x="544" y="10" width="30" height="300" style="stroke: rgb(68, 68, 68); stroke-opacity: 1; fill: none; stroke-width: 0;"/></g><g class="g-gtitle"/></g></svg>\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"ignore_on_import\": true,\n\t\t\t\"source\": \"plot3d( $\\\\sin(x)\\\\cos(y)$, ($x$, 0, 12), ($y$, 0, 12));\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 10075567838808318563,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"\"\n\t\t}\n\t],\n\t\"description\": \"Cadabra JSON notebook format\",\n\t\"flags\": {\n\t\t\"hide_input_cells\": false\n\t},\n\t\"version\": 1.0\n}\n"
  },
  {
    "path": "core/packages/cdb/interact/slider.cnb",
    "content": "{\n\t\"cell_id\": 16200933986566133880,\n\t\"cells\": [\n\t\t{\n\t\t\t\"cell_id\": 2740829623175894998,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"import json\\nclass Slider():\\n   \\\"\\\"\\\"\\n   Create a slider in the notebook interface, which can be used to \\n   update the indicated variable dynamically.\\n   \\\"\\\"\\\"\\n   def __init__(self, name, value=0, min_value=0, max_value=1, step_size=0.1):\\n      self.params = {\\n\\t      \\\"value\\\": value,\\n\\t      \\\"variable\\\": name,\\n\\t      \\\"min_value\\\": min_value,\\n\\t      \\\"max_value\\\": max_value,\\n         \\\"step_size\\\": step_size\\n      }\\n      \\n   def __send_to_server__(self, server):\\n      server.send(json.dumps(self.params), \\\"slider\\\", 0, 0, False)\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 16643530752732994278,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"def slider(name, value=0, min_value=0, max_value=1, step_size=0.1):\\n   \\\"\\\"\\\"\\n   Create a slider object, which can be used to \\n   update the indicated variable dynamically.\\n   \\\"\\\"\\\"\\n   globals()[name] = value\\n   return Slider(name, value, min_value, max_value, step_size)\\n\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 11001462995080903250,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"\"\n\t\t}\n\t],\n\t\"description\": \"Cadabra JSON notebook format\",\n\t\"version\": 1.0\n}\n"
  },
  {
    "path": "core/packages/cdb/main.py",
    "content": "# Empty just so we can find the location of the packages.\n"
  },
  {
    "path": "core/packages/cdb/numeric/evaluate.cnb",
    "content": "{\n\t\"cell_id\": 4999409792745105779,\n\t\"cells\": [\n\t\t{\n\t\t\t\"cell_id\": 7373466807312405365,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 10413878374203257041,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\package{cdb.numeric.evaluate}{Numeric evaluation of Cadabra expressions}\\nFunctions for evaluating Cadabra expressions given floating point values for variables \"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\package{cdb.numeric.evaluate}{Numeric evaluation of Cadabra expressions}\\nFunctions for evaluating Cadabra expressions given floating point values for variables \"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 11376245561910922914,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 16105197977829845906,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\algorithm{evalf(ex: Ex, values: Ex|dict) -> float}{Evaluate an expression to a floating point number}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\algorithm{evalf(ex: Ex, values: Ex|dict) -> float}{Evaluate an expression to a floating point number}\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 13823390372129062478,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"def evalf(ex, values):\\n\\ts = SympyBridge(ex).to_sympy()\\n\\tsubs = _create_sublist(values)\\n\\treturn s.evalf(subs=subs)\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 13489163334655936980,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 17250236824289587380,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}9.0\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 12232332659023869728,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}1.28\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"ignore_on_import\": true,\n\t\t\t\"source\": \"evalf($x**2$, { \\\"x\\\": 3.0 });\\nevalf($a + b + c$, $a->1, b->0.5, c->-0.22$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 307928729963218244,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 14397007498469288962,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\algorithm{lambdify(ex: Ex, parameters: Ex|Iterable[Ex], constants: Ex|dict) -> Function}{Create a Python function which evaluates\\nan expression with the given parameters}\\nIf provided, any substitution rules in \\\\verb|constants| are applied before the function is `lambdified'.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\algorithm{lambdify(ex: Ex, parameters: Ex|Iterable[Ex], constants: Ex|dict) -> Function}{Create a Python function which evaluates\\nan expression with the given parameters}\\nIf provided, any substitution rules in \\\\verb|constants| are applied before the function is `lambdified'.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 7689315691730539427,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"def lambdify(ex, parameters, constants=None):\\n\\tex = ex.top().ex()\\n\\tsb = SympyBridge(ex)\\n\\tif constants is not None:\\n\\t\\tsubs = _create_sublist(constants)\\n\\t\\tsubbed = sb.to_sympy().subs(subs)\\n\\t\\tsb.from_sympy(str(subbed))\\n\\tif isinstance(parameters, Ex):\\n\\t\\tparams = _create_symbol(parameters)\\n\\telse:\\n\\t\\tparams = [_create_symbol(param) for param in parameters]\\n\\treturn sympy.lambdify(params, sb.to_sympy())\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 3590404544007582222,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 16265883368783821044,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"verbatim\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}5.0\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"ignore_on_import\": true,\n\t\t\t\"source\": \"l = lambdify($\\\\sqrt(x**2 + y**2)$, $x, y$)\\nl(3, 4);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 12041517788363212463,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9416580652087427055,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"verbatim\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}0.0\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"ignore_on_import\": true,\n\t\t\t\"source\": \"k = lambdify($A x**2 + B x + C$, $x$, $A -> 1, B-> 0, C -> -4$)\\nk(2);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 12041068264923901971,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 3298245029619223396,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"def _create_symbol(symbol):\\n\\tif isinstance(symbol, str):\\n\\t\\treturn sympy.symbols(symbol)\\n\\telif isinstance(symbol, Ex):\\n\\t\\tif symbol.head() == r\\\"\\\\comma\\\":\\n\\t\\t\\treturn [sympy.symbols(s.ex().sympy_form()) for s in symbol.top().children()]\\n\\t\\telse:\\n\\t\\t\\treturn sympy.symbols(symbol.sympy_form())\\n\\telse:\\n\\t\\traise ValueError(\\\"_create_symbol: expected symbol to be str or Ex\\\")\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 9467217440484724795,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 8626601393501616912,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}Raux\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9843579008991660363,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"{}$\\\\big[$$r$,\\\\discretionary{}{}{} $R$,\\\\discretionary{}{}{} $Raux$$\\\\big]$\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"ignore_on_import\": true,\n\t\t\t\"source\": \"_create_symbol($Raux$);\\n_create_symbol($r, R, Raux$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 5592064898772723427,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"def _create_sublist(values):\\n\\tsubs = {}\\n\\tif isinstance(values, dict):\\n\\t\\tfor key, value in values.items():\\n\\t\\t\\tsubs[_create_symbol(key)] = value\\n\\telif isinstance(values, Ex):\\n\\t\\tif values.head() == r\\\"\\\\comma\\\":\\n\\t\\t\\tfor keyval in values.top().children():\\n\\t\\t\\t\\ttmp = keyval.ex()\\n\\t\\t\\t\\tsubs[sympy.symbols(tmp[0].sympy_form())] = SympyBridge(tmp[1]).to_sympy().evalf()\\n\\t\\telse:\\n\\t\\t\\tsubs[sympy.symbols(values[0].sympy_form())] = SympyBridge(values[1]).to_sympy().evalf()\\n\\telse:\\n\\t\\traise ValueError(\\\"_create_sublist: expected values to be of type Ex or dict\\\")\\n\\treturn subs\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 13578069033175043843,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 13766539726338208847,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"verbatim\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}{x: 2.00000000000000, y: 4.00000000000000}\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"ignore_on_import\": true,\n\t\t\t\"source\": \"_create_sublist($x=2, y=4$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 10532033700422622820,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"\"\n\t\t}\n\t],\n\t\"description\": \"Cadabra JSON notebook format\",\n\t\"version\": 1.0\n}\n"
  },
  {
    "path": "core/packages/cdb/numeric/integrate.cnb",
    "content": "{\n\t\"cell_id\": 10135449329227921550,\n\t\"cells\": [\n\t\t{\n\t\t\t\"cell_id\": 3989415718163890231,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 3791214211892782773,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\package{cdb.numeric.integrate}{Functions for numeric integration and numeric solutions to differential equations}\\n\\nA collection of wrappers for some of the numeric functionality of the scipy library in order to accept cadabra Ex objects\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\package{cdb.numeric.integrate}{Functions for numeric integration and numeric solutions to differential equations}\\n\\nA collection of wrappers for some of the numeric functionality of the scipy library in order to accept cadabra Ex objects\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 8362589260562156834,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"import numpy\\nfrom scipy.integrate import odeint\\nfrom cdb.numeric.evaluate import lambdify, _create_sublist\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 6052509396776782195,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 11317838269335231990,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\algorithm{integrate_ode(eqns: Ex|Iterable[Ex], variables: Ex|Iterable[Ex], initial_values: List[float], \\nendpoint: float, delta: float, constants: Ex|dict) -> List}{Numerically integrate a system of ODEs over a range of values}\\n\\\\begin{description}\\n\\\\item \\\\verb|eqns| \\\\\\\\\\n\\tList of expressions representing first order derivatives with respect to a common variable. The expression\\n\\tshould not contain the derivative, so e.g. use $x - \\\\frac{1}{2}xy$ instead of $\\\\partial_{t}{x} = x - \\\\frac{1}{2}xy$.\\n\\tCan be a comma-separated in an Ex object, or any iterable of Ex objects.\\n\\\\item \\\\verb|variables| \\\\\\\\\\n\\tList of variables, starting with the derivative variable and then each variable in the order that its derivative appears\\n\\tin \\\\verb|eqns|, so $(\\\\frac{dx}{dt}, \\\\frac{dy}{dt}, \\\\frac{dz}{dt})$ would have variables $(t, x, y, z)$\\n\\\\item \\\\verb|initial_values| \\\\\\\\\\n\\tThe initial values of each variable in \\\\verb|variables| as a floating point number\\n\\\\item \\\\verb|endpoint| \\\\\\\\\\n\\tThe value of the derivative variable at which to finish\\n\\\\item \\\\verb|delta| \\\\\\\\\\n\\tThe amount to increase the derivative variable at each iteration\\n\\\\item \\\\verb|constants| \\\\\\\\\\n\\tEx or dictionary object with a list of substitutions of constants to be performed before the numeric integration\\n\\\\end{description}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\algorithm{integrate_ode(eqns: Ex|Iterable[Ex], variables: Ex|Iterable[Ex], initial_values: List[float], \\nendpoint: float, delta: float, constants: Ex|dict) -> List}{Numerically integrate a system of ODEs over a range of values}\\n\\\\begin{description}\\n\\\\item \\\\verb|eqns| \\\\\\\\\\n\\tList of expressions representing first order derivatives with respect to a common variable. The expression\\n\\tshould not contain the derivative, so e.g. use $x - \\\\frac{1}{2}xy$ instead of $\\\\partial_{t}{x} = x - \\\\frac{1}{2}xy$.\\n\\tCan be a comma-separated in an Ex object, or any iterable of Ex objects.\\n\\\\item \\\\verb|variables| \\\\\\\\\\n\\tList of variables, starting with the derivative variable and then each variable in the order that its derivative appears\\n\\tin \\\\verb|eqns|, so $(\\\\frac{dx}{dt}, \\\\frac{dy}{dt}, \\\\frac{dz}{dt})$ would have variables $(t, x, y, z)$\\n\\\\item \\\\verb|initial_values| \\\\\\\\\\n\\tThe initial values of each variable in \\\\verb|variables| as a floating point number\\n\\\\item \\\\verb|endpoint| \\\\\\\\\\n\\tThe value of the derivative variable at which to finish\\n\\\\item \\\\verb|delta| \\\\\\\\\\n\\tThe amount to increase the derivative variable at each iteration\\n\\\\item \\\\verb|constants| \\\\\\\\\\n\\tEx or dictionary object with a list of substitutions of constants to be performed before the numeric integration\\n\\\\end{description}\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 17270037226329397630,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"def integrate_ode(eqns, variables, initial_values, endpoint, step=None, constants=None):\\n\\t# Collect list of equations and lambdify them\\n\\tif isinstance(eqns, Ex):\\n\\t\\tif eqns.head() == r\\\"\\\\comma\\\":\\n\\t\\t\\tfuncs = [lambdify(eqn.ex(), variables, constants) for eqn in eqns.top().children()]\\n\\t\\telse:\\n\\t\\t\\tfuncs = [lambdify(eqns, variables, constants)]\\n\\telse:\\n\\t\\tfuncs = [lambdify(eqn, variables, constants) for eqn in eqns]\\n\\t\\n\\t# Master function\\n\\tf = lambda xs, t, params: [func(t, *xs) for func in funcs]\\n\\n\\t# Integration range\\n\\tnpoints = 1000 if step is None else int((1 + endpoint - initial_values[0]) / step)\\n\\tpoints = numpy.linspace(initial_values[0], endpoint, npoints)\\n\\n\\t# Rebroadcast so that each return list corresponds to a variable\\n\\tsol = odeint(f, initial_values[1:], points, ((),))\\n\\treturn [points] + [sol[:,i] for i in range(len(variables)-1)]\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 12331971389017128553,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"ignore_on_import\": true,\n\t\t\t\"source\": \"{t}::Coordinate.\\ndx := x-A*x*y.\\ndy := -B*y + C*x*y.\\n#sols = integrate_ode((dx, dy), $t, x, y$, (0, 1, 1), 10, 0.001, $A->1/2, B->3/4, C->1/4$)\\nsols = integrate_ode($@(dx), @(dy)$, $t, x, y$, (0, 1, 1), 10, 0.001, {\\\"A\\\": 0.5, \\\"B\\\": 3/4, \\\"C\\\": 0.25})\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 10058019511408460871,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 18371720257697375934,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"image_png\",\n\t\t\t\t\t\"source\": \"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\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"ignore_on_import\": true,\n\t\t\t\"source\": \"import matplotlib.pyplot as plt\\nfig, axes = plt.subplots(2,1)\\naxes[0].plot(sols[0], sols[1])\\naxes[0].plot(sols[0], sols[2])\\naxes[1].plot(sols[1], sols[2])\\nfig;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 4262269971924348028,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 1287486217584996925,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 6643470899229452613,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"Raux\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}R_{aux}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 17755464265255366914,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 8501208413624250549,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"-(4(M)**2 Raux + 2(r)**2 Raux + 2(laux R-3r Raux) M + ((\\\\omega)**2 (r)**3-laux r) R) (4(M)**2 r-4M (r)**2 + (r)**3)**(-1)\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}-\\\\left(4{M}^{2} R_{aux}+2{r}^{2} R_{aux}+2\\\\left(\\\\lambda_{aux} R-3r R_{aux}\\\\right) M+\\\\left({\\\\omega}^{2} {r}^{3}-\\\\lambda_{aux} r\\\\right) R\\\\right) {\\\\left(4{M}^{2} r-4M {r}^{2}+{r}^{3}\\\\right)}^{-1}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"ignore_on_import\": true,\n\t\t\t\"source\": \"Raux::LaTeXForm(\\\"R_{aux}\\\")\\nlaux::LaTeXForm(\\\"\\\\lambda_{aux}\\\")\\ndR := Raux;\\ndRaux := -(4* M**2* Raux + 2* r**2* Raux + 2*( laux * R - 3* r * Raux ) * M + (\\n\\t\\\\omega**2* r**3 - laux * r ) * R ) /(4* M**2* r - 4* M * r**2 + r**3);\\nsols = integrate_ode((dR, dRaux), $r, R, Raux$, (0.3, 1, 0.5), 100, 0.01, $M->0.1, \\\\omega->0.2, k->2, laux->2$)\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 15414656810465219608,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 13895594005555715725,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"image_png\",\n\t\t\t\t\t\"source\": \"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\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"fig, axes = plt.subplots(2,1)\\naxes[0].plot(sols[0], sols[1])\\nfig;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 7751065038176589856,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 14974314265954450945,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"\"\n\t\t}\n\t],\n\t\"description\": \"Cadabra JSON notebook format\",\n\t\"version\": 1.0\n}\n"
  },
  {
    "path": "core/packages/cdb/relativity/__init__.cdb",
    "content": "\n\"\"\"\n   General relativity package for Cadabra.\n   NOTE: this is a proof of concept, not something that is finished in any sense.\n\"\"\"\n\nimport cadabra2\n\n__cdbkernel__ = cadabra2.__cdbkernel__\nserver        = __cdbkernel__.server\ndisplay       = __cdbkernel__.display\n\n#import cadabra2\nfrom cadabra2 import *\n\nsetup_done=False\n\ndef setup():\n    global setup_done\n    if setup_done==False:\n        {\\mu,\\nu,\\rho,\\sigma,\\kappa,\\gamma,\\lambda}::Indices(spacetime, position=fixed);\n        \\partial{#}::PartialDerivative.\n        setup_done=True\n\ndef riemann_from_christoffel(R=$R$, c=$\\Gamma$):\n    \"\"\" Return the Riemann tensor expressed in terms of Christoffel symbols. \"\"\"\n    setup()\n            # FIXME: need to create_scope_from_global, then\n            # create new index declaration in there, with e.g. name \"cdb.relativity.spacetime\".\n            # Then generate the equation using the symbol (need 'head'!) passed in\n            # as R and c. Then find name of index set on those function arguments\n            # and finally do a rename_dummies/indices.\n    ex:= @(R)^{\\rho}_{\\sigma\\mu\\nu} =\n          \\partial_{\\mu}{@(c)^{\\rho}_{\\nu\\sigma}}\n         -\\partial_{\\nu}{@(c)^{\\rho}_{\\mu\\sigma}}\n         + @(c)^{\\rho}_{\\mu\\lambda} @(c)^{\\lambda}_{\\nu\\sigma}\n         - @(c)^{\\rho}_{\\nu\\lambda} @(c)^{\\lambda}_{\\mu\\sigma}.\n    return ex\n\ndef christoffel_from_metric(c=Ex(r'\\Gamma'), g=Ex(r'g')):\n    setup()\n    ex:= @(c)^{\\lambda}_{\\mu\\nu} = 1/2 g^{\\lambda\\kappa} ( \\partial_{\\mu}{ g_{\\kappa\\nu} }\n                                                           + \\partial_{\\nu}{ g_{\\kappa\\mu} } - \\partial_{\\kappa}{ g_{\\mu\\nu} } ).\n    return ex\n\ndef expand_covariant_derivative():\n    setup()\n    ex = Ex(r'\\nabla_{\\mu}{A?^{\\nu}} = \\partial_{\\mu}{A?^{\\nu}} + \\Gamma^{\\nu}_{\\mu\\rho} A?^{\\rho}')\n    return ex\n\ndef riemann_to_ricci(ex):\n    \"\"\" Convert contractions of Riemann tensors to Ricci tensors or scalars. \"\"\"\n\n    rl1:= R^{a?}_{b? a? c?}     =  R_{b? c?}, R^{a?}_{b? c? a?}     = -R_{b? c?}.\n    rl2:= R_{a?}_{b?}^{a?}_{c?} =  R_{b? c?}, R_{a?}_{b? c?}^{a?}   = -R_{b? c?}.\n    rl3:= R_{b?}^{a?}_{c? a?}   =  R_{b? c?}, R_{b?}^{a?}_{a? c?}   = -R_{b? c?}.\n    rl4:= R_{b?}_{a?}^{c? a?}   =  R_{b?}^{c?}.\n    rl5:= R^{a?}_{a?} = R, R_{a?}^{a?} = R.\n\n    substitute(ex, rl1+rl2+rl3+rl4+rl5, repeat=True)\n\n    return ex\n"
  },
  {
    "path": "core/packages/cdb/relativity/abstract.cnb",
    "content": "{\n\t\"cell_id\" : 153469803931434802,\n\t\"cells\" : \n\t[\n\t\t{\n\t\t\t\"cell_id\" : 3324461703110413508,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 14419213666533296135,\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\package{cdb.relativity.abstract}{Core general relativity package, mainly a library of various standard expressions.}\\n\\nImporting this library will make \\\\verb|\\\\partial| a partial derivative and will also declare the\\ngreek indices to be space-time indices.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\package{cdb.relativity.abstract}{Core general relativity package, mainly a library of various standard expressions.}\\n\\nImporting this library will make \\\\verb|\\\\partial| a partial derivative and will also declare the\\ngreek indices to be space-time indices.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 12613540530229412949,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 7383066680787787249,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property PartialDerivative to~}\\\\partial{\\\\#}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 13136258987904215825,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Indices(position=fixed) to~}\\\\left[\\\\mu,~\\\\discretionary{}{}{} \\\\nu,~\\\\discretionary{}{}{} \\\\rho,~\\\\discretionary{}{}{} \\\\sigma,~\\\\discretionary{}{}{} \\\\kappa,~\\\\discretionary{}{}{} \\\\gamma,~\\\\discretionary{}{}{} \\\\lambda\\\\right].\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"\\\\partial{#}::PartialDerivative;\\n{\\\\mu,\\\\nu,\\\\rho,\\\\sigma,\\\\kappa,\\\\gamma,\\\\lambda}::Indices(spacetime, position=fixed);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 11955494087904535027,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 15119378517043388215,\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\algorithm{riemann_from_christoffel(R: Ex, c: Ex) -> Ex}{Generates an equality which determines the Riemann tensor in terms of the Christoffel symbols.}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\algorithm{riemann_from_christoffel(R: Ex, c: Ex) -> Ex}{Generates an equality which determines the Riemann tensor in terms of the Christoffel symbols.}\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 14094191732391016476,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"def riemann_from_christoffel(R=$R$, c=$\\\\Gamma$):\\n    ex:= @(R)^{\\\\rho}_{\\\\sigma\\\\mu\\\\nu} = \\\\partial_{\\\\mu}{@(c)^{\\\\rho}_{\\\\nu\\\\sigma}} \\n                                     -\\\\partial_{\\\\nu}{@(c)^{\\\\rho}_{\\\\mu\\\\sigma}} \\n                                     + @(c)^{\\\\rho}_{\\\\mu\\\\lambda} @(c)^{\\\\lambda}_{\\\\nu\\\\sigma} \\n                                     - @(c)^{\\\\rho}_{\\\\nu\\\\lambda} @(c)^{\\\\lambda}_{\\\\mu\\\\sigma}:\\n    return ex\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 17711059759552177114,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 2943028165866679465,\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\algorithm{christoffel_from_metric(c: Ex, g: Ex) -> Ex}{Generates an equality which determines the Christoffel symbols in terms of the metric.}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\algorithm{christoffel_from_metric(c: Ex, g: Ex) -> Ex}{Generates an equality which determines the Christoffel symbols in terms of the metric.}\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 16328687583199300518,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"def christoffel_from_metric(c=$\\\\Gamma$, g=$g$):\\n    ex:= @(c)^{\\\\lambda}_{\\\\mu\\\\nu} = 1/2 g^{\\\\lambda\\\\kappa} ( \\\\partial_{\\\\mu}{ g_{\\\\kappa\\\\nu} }\\n                                                           + \\\\partial_{\\\\nu}{ g_{\\\\kappa\\\\mu} } - \\\\partial_{\\\\kappa}{ g_{\\\\mu\\\\nu} } ).\\n    return ex\\n\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 17531443358799556997,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 16528097175233509746,\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\algorithm{riemann_to_ricci}{Convert contractions of Riemann tensors to Ricci tensors or scalars.}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\algorithm{riemann_to_ricci}{Convert contractions of Riemann tensors to Ricci tensors or scalars.}\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 6890929525873944922,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"def riemann_to_ricci(ex, R=$R$):\\n    rl1:= @(R)^{a?}_{b? a? c?}     =  @(R)_{b? c?}, @(R)^{a?}_{b? c? a?}     = -@(R)_{b? c?}.\\n    rl2:= @(R)_{a?}_{b?}^{a?}_{c?} =  @(R)_{b? c?}, @(R)_{a?}_{b? c?}^{a?}   = -@(R)_{b? c?}.\\n    rl3:= @(R)_{b?}^{a?}_{c? a?}   =  @(R)_{b? c?}, @(R)_{b?}^{a?}_{a? c?}   = -@(R)_{b? c?}.\\n    rl4:= @(R)_{b?}_{a?}^{c? a?}   =  @(R)_{b?}^{c?}.\\n    rl5:= @(R)^{a?}_{a?} = @(R), @(R)_{a?}^{a?} = @(R).\\n    rl6:= @(R)^{a?}_{a? b? c?} = 0.\\n\\n    substitute(ex, rl1+rl2+rl3+rl4+rl5, repeat=True)\\n    return ex\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 3773496488914727547,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 9254795296086812746,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\" : 9775705670236367127,\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"R^{a}_{b c a}-R^{a}_{b a c}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}R^{a}\\\\,_{b c a}-R^{a}\\\\,_{b a c}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"ignore_on_import\" : true,\n\t\t\t\"source\" : \"ex:= R^{a}_{b c a} - R^{a}_{b a c};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 2143829647108705411,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 11401984921286068745,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\" : 16470249316118331173,\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"-2R_{b c}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}-2R_{b c}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"ignore_on_import\" : true,\n\t\t\t\"source\" : \"riemann_to_ricci(ex);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 8133262252432645091,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1\n}\n"
  },
  {
    "path": "core/packages/cdb/relativity/schwarzschild.cnb",
    "content": "{\n\t\"cell_id\": 11589016112009228246,\n\t\"cells\": [\n\t\t{\n\t\t\t\"cell_id\": 5431623313440051550,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 14868548388294414250,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"Data for the Schwarzschild spacetime in four dimensions in Schwarzschild coordinates.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"Data for the Schwarzschild spacetime in four dimensions in Schwarzschild coordinates.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 14184770737784996463,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"class SpaceTime:\\n    indices      = Ex(\\\"\\\")\\n    metric       = Ex(\\\"\\\")\\n    coordinates  = Ex(\\\"\\\")\\n    metric_rules = Ex(\\\"\\\")\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 17548331014027880039,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"def spacetime():\\n    c = SpaceTime()\\n    c.indices      := {\\\\mu,\\\\nu,\\\\rho,\\\\sigma,\\\\kappa}.\\n    c.metric       := g_{\\\\mu\\\\nu}.\\n    c.coordinates  := {t, r, \\\\phi, \\\\theta}.\\n    c.metric_rules := { g_{t t} = -(1-2 M/r), \\n             g_{r r} = 1/(1-2 M/r), \\n             g_{\\\\theta \\\\theta} = r**2,\\n             g_{\\\\phi \\\\phi} = r**2 \\\\sin(\\\\theta)**2 \\n           }.\\n    return c\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 4644968870827311775,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 3268253734647884419,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property Coordinate attached to~}\\\\left[t, \\\\discretionary{}{}{}r, \\\\discretionary{}{}{}\\\\phi, \\\\discretionary{}{}{}\\\\theta\\\\right].\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"Coordinate(spacetime().coordinates);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 8155200362414200036,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9902468695318796294,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property Indices(position=fixed, values=\\\\{{t}\\n, {r}\\n, {\\\\phi}\\n, {\\\\theta}\\n\\\\}) attached to~}\\\\left[\\\\mu, \\\\discretionary{}{}{}\\\\nu, \\\\discretionary{}{}{}\\\\rho, \\\\discretionary{}{}{}\\\\sigma, \\\\discretionary{}{}{}\\\\kappa\\\\right].\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"Indices(spacetime().indices, Ex(\\\"position=fixed, values=\\\"+str(spacetime().coordinates)));\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 3405752486651042519,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 1504370637397744113,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property Metric attached to~}g_{\\\\mu \\\\nu}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 13144844234706853495,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property TableauSymmetry attached to~}g^{\\\\mu \\\\nu}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 1955619426774429646,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property PartialDerivative attached to~}\\\\backslash\\\\texttt{partial}\\\\{\\\\#\\\\}.\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"g_{\\\\mu\\\\nu}::Metric;\\ng^{\\\\mu\\\\nu}::InverseMetric;\\n\\\\partial{#}::PartialDerivative;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 4097485587392404069,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 3660335434785809237,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 12505541162642258272,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"{g_{t t} = -1 + 2M (r)**(-1), g_{r r} = (1-2M (r)**(-1))**(-1), g_{\\\\theta \\\\theta} = (r)**2, g_{\\\\phi \\\\phi} = (r)**2 (\\\\sin(\\\\theta))**2}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\left[g_{t t} = -1\\\\discretionary{}{}{}+2M {r}^{-1}, \\\\discretionary{}{}{}g_{r r} = {\\\\left(1\\\\discretionary{}{}{}-2M {r}^{-1}\\\\right)}^{-1}, \\\\discretionary{}{}{}g_{\\\\theta \\\\theta} = {r}^{2}, \\\\discretionary{}{}{}g_{\\\\phi \\\\phi} = {r}^{2} {\\\\left(\\\\sin{\\\\theta}\\\\right)}^{2}\\\\right]\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 7655172605122154351,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 6557964990441727655,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"{g_{t t} = -1 + 2M (r)**(-1), g_{r r} = (1-2M (r)**(-1))**(-1), g_{\\\\theta \\\\theta} = (r)**2, g_{\\\\phi \\\\phi} = (r)**2 (\\\\sin(\\\\theta))**2, g^{t t} = (2M (r)**(-1)-1)**(-1), g^{r r} = -2M (r)**(-1) + 1, g^{\\\\phi \\\\phi} = ((r)**2 (\\\\sin(\\\\theta))**2)**(-1), g^{\\\\theta \\\\theta} = (r)**(-2)}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\left[g_{t t} = -1\\\\discretionary{}{}{}+2M {r}^{-1}, \\\\discretionary{}{}{}g_{r r} = {\\\\left(1\\\\discretionary{}{}{}-2M {r}^{-1}\\\\right)}^{-1}, \\\\discretionary{}{}{}g_{\\\\theta \\\\theta} = {r}^{2}, \\\\discretionary{}{}{}g_{\\\\phi \\\\phi} = {r}^{2} {\\\\left(\\\\sin{\\\\theta}\\\\right)}^{2}, \\\\discretionary{}{}{}g^{t t} = {\\\\left(2M {r}^{-1}\\\\discretionary{}{}{}-1\\\\right)}^{-1}, \\\\discretionary{}{}{}g^{r r} = -2M {r}^{-1}\\\\discretionary{}{}{}+1, \\\\discretionary{}{}{}g^{\\\\phi \\\\phi} = {\\\\left({r}^{2} {\\\\left(\\\\sin{\\\\theta}\\\\right)}^{2}\\\\right)}^{-1}, \\\\discretionary{}{}{}g^{\\\\theta \\\\theta} = {r}^{-2}\\\\right]\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"r = spacetime().metric_rules;\\ncomplete(r, $g^{\\\\mu\\\\nu}$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 15610912201130190902,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"def christoffels():\\n   c:= \\\\Gamma^{\\\\mu}_{\\\\nu\\\\rho} = 1/2 g^{\\\\mu\\\\kappa} (\\\\partial_{\\\\nu}{g_{\\\\rho\\\\kappa}}\\n                                                   + \\\\partial_{\\\\rho}{g_{\\\\nu\\\\kappa}} - \\\\partial_{\\\\kappa}{g_{\\\\nu\\\\rho}}).\\n   return c;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 591433388179556682,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"def geodesic():\\n   \\\\tau::Coordinate.\\n   x^\\\\mu::Depends(\\\\tau).\\n   gd:= \\\\partial_{\\\\tau\\\\tau}{x^\\\\mu} + \\\\Gamma^{\\\\mu}_{\\\\nu\\\\rho} \\\\partial_{\\\\tau}{x^{\\\\nu}} \\\\partial_{\\\\tau}{x^{\\\\rho}};\\n   return gd;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 16605355540986002381,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 15593847089693141832,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 7891886689801112735,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\Gamma^{\\\\mu}_{\\\\nu \\\\rho} =  1/2 g^{\\\\mu \\\\kappa} (\\\\partial_{\\\\nu}(g_{\\\\rho \\\\kappa}) + \\\\partial_{\\\\rho}(g_{\\\\nu \\\\kappa})-\\\\partial_{\\\\kappa}(g_{\\\\nu \\\\rho}))\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\Gamma^{\\\\mu}\\\\,_{\\\\nu \\\\rho} = \\\\frac{1}{2}g^{\\\\mu \\\\kappa} \\\\left(\\\\partial_{\\\\nu}{g_{\\\\rho \\\\kappa}}\\\\discretionary{}{}{}+\\\\partial_{\\\\rho}{g_{\\\\nu \\\\kappa}}\\\\discretionary{}{}{}-\\\\partial_{\\\\kappa}{g_{\\\\nu \\\\rho}}\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"christoffels();\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 15669302293362150534,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 17662224927914126837,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 13649705606144919420,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\Gamma^{\\\\mu}_{\\\\nu \\\\rho} = \\\\components_{\\\\rho \\\\nu}^{\\\\mu}({{\\\\phi, r, \\\\phi} = (r)**(-1), {\\\\phi, \\\\theta, \\\\phi} = (\\\\tan(\\\\theta))**(-1), {\\\\theta, r, \\\\theta} = (r)**(-1), {r, r, r} = M (r (2M-r))**(-1), {t, r, t} = M (r (-2M + r))**(-1), {r, \\\\phi, \\\\phi} = (r)**(-1), {\\\\theta, \\\\phi, \\\\phi} = (\\\\tan(\\\\theta))**(-1), {r, \\\\theta, \\\\theta} = (r)**(-1), {r, t, t} = M (r (-2M + r))**(-1), {\\\\phi, \\\\phi, r} = (2M-r) (\\\\sin(\\\\theta))**2, {\\\\phi, \\\\phi, \\\\theta} =  -  1/2 \\\\sin(2\\\\theta), {\\\\theta, \\\\theta, r} = 2M-r, {t, t, r} = M (-2M + r) (r)**(-3)})\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\Gamma^{\\\\mu}\\\\,_{\\\\nu \\\\rho} = \\\\square{}_{\\\\rho}{}_{\\\\nu}{}^{\\\\mu}\\\\left\\\\{\\\\begin{aligned}\\\\square{}_{\\\\phi}{}_{r}{}^{\\\\phi}& = {r}^{-1}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{\\\\theta}{}^{\\\\phi}& = {\\\\left(\\\\tan{\\\\theta}\\\\right)}^{-1}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{r}{}^{\\\\theta}& = {r}^{-1}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{r}{}^{r}& = M {\\\\left(r \\\\left(2M\\\\discretionary{}{}{}-r\\\\right)\\\\right)}^{-1}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}_{r}{}^{t}& = M {\\\\left(r \\\\left(-2M\\\\discretionary{}{}{}+r\\\\right)\\\\right)}^{-1}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{\\\\phi}{}^{\\\\phi}& = {r}^{-1}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{\\\\phi}{}^{\\\\phi}& = {\\\\left(\\\\tan{\\\\theta}\\\\right)}^{-1}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{\\\\theta}{}^{\\\\theta}& = {r}^{-1}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{t}{}^{t}& = M {\\\\left(r \\\\left(-2M\\\\discretionary{}{}{}+r\\\\right)\\\\right)}^{-1}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{\\\\phi}{}^{r}& = \\\\left(2M\\\\discretionary{}{}{}-r\\\\right) {\\\\left(\\\\sin{\\\\theta}\\\\right)}^{2}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{\\\\phi}{}^{\\\\theta}& =  - \\\\frac{1}{2}\\\\sin\\\\left(2\\\\theta\\\\right)\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{\\\\theta}{}^{r}& = 2M\\\\discretionary{}{}{}-r\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}_{t}{}^{r}& = M \\\\left(-2M\\\\discretionary{}{}{}+r\\\\right) {r}^{-3}\\\\\\\\[-.5ex]\\n\\\\end{aligned}\\\\right.\\n\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"q=evaluate(christoffels(), r, rhsonly=True);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 10260134696379332997,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 13829258555824241257,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 12187347823820369030,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\partial_{\\\\tau \\\\tau}(x^{\\\\mu}) + \\\\Gamma^{\\\\mu}_{\\\\nu \\\\rho} \\\\partial_{\\\\tau}(x^{\\\\nu}) \\\\partial_{\\\\tau}(x^{\\\\rho})\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\partial_{\\\\tau \\\\tau}{x^{\\\\mu}}\\\\discretionary{}{}{}+\\\\Gamma^{\\\\mu}\\\\,_{\\\\nu \\\\rho} \\\\partial_{\\\\tau}{x^{\\\\nu}} \\\\partial_{\\\\tau}{x^{\\\\rho}}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"g=geodesic();\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 10933720102375644496,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 8157876752454947899,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 6224718788724496171,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\partial_{\\\\tau \\\\tau}(x^{\\\\mu}) + \\\\components_{\\\\rho \\\\nu}^{\\\\mu}({{\\\\phi, r, \\\\phi} = (r)**(-1), {\\\\phi, \\\\theta, \\\\phi} = (\\\\tan(\\\\theta))**(-1), {\\\\theta, r, \\\\theta} = (r)**(-1), {r, r, r} = M (r (2M-r))**(-1), {t, r, t} = M (r (-2M + r))**(-1), {r, \\\\phi, \\\\phi} = (r)**(-1), {\\\\theta, \\\\phi, \\\\phi} = (\\\\tan(\\\\theta))**(-1), {r, \\\\theta, \\\\theta} = (r)**(-1), {r, t, t} = M (r (-2M + r))**(-1), {\\\\phi, \\\\phi, r} = (2M-r) (\\\\sin(\\\\theta))**2, {\\\\phi, \\\\phi, \\\\theta} =  -  1/2 \\\\sin(2\\\\theta), {\\\\theta, \\\\theta, r} = 2M-r, {t, t, r} = M (-2M + r) (r)**(-3)}) \\\\partial_{\\\\tau}(x^{\\\\nu}) \\\\partial_{\\\\tau}(x^{\\\\rho})\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\partial_{\\\\tau \\\\tau}{x^{\\\\mu}}\\\\discretionary{}{}{}+\\\\square{}_{\\\\rho}{}_{\\\\nu}{}^{\\\\mu}\\\\left\\\\{\\\\begin{aligned}\\\\square{}_{\\\\phi}{}_{r}{}^{\\\\phi}& = {r}^{-1}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{\\\\theta}{}^{\\\\phi}& = {\\\\left(\\\\tan{\\\\theta}\\\\right)}^{-1}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{r}{}^{\\\\theta}& = {r}^{-1}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{r}{}^{r}& = M {\\\\left(r \\\\left(2M\\\\discretionary{}{}{}-r\\\\right)\\\\right)}^{-1}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}_{r}{}^{t}& = M {\\\\left(r \\\\left(-2M\\\\discretionary{}{}{}+r\\\\right)\\\\right)}^{-1}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{\\\\phi}{}^{\\\\phi}& = {r}^{-1}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{\\\\phi}{}^{\\\\phi}& = {\\\\left(\\\\tan{\\\\theta}\\\\right)}^{-1}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{\\\\theta}{}^{\\\\theta}& = {r}^{-1}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{t}{}^{t}& = M {\\\\left(r \\\\left(-2M\\\\discretionary{}{}{}+r\\\\right)\\\\right)}^{-1}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{\\\\phi}{}^{r}& = \\\\left(2M\\\\discretionary{}{}{}-r\\\\right) {\\\\left(\\\\sin{\\\\theta}\\\\right)}^{2}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{\\\\phi}{}^{\\\\theta}& =  - \\\\frac{1}{2}\\\\sin\\\\left(2\\\\theta\\\\right)\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{\\\\theta}{}^{r}& = 2M\\\\discretionary{}{}{}-r\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}_{t}{}^{r}& = M \\\\left(-2M\\\\discretionary{}{}{}+r\\\\right) {r}^{-3}\\\\\\\\[-.5ex]\\n\\\\end{aligned}\\\\right.\\n \\\\partial_{\\\\tau}{x^{\\\\nu}} \\\\partial_{\\\\tau}{x^{\\\\rho}}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"substitute(g, q);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 10461999179990682474,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 15969941059281404733,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 8821203194508076381,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\components^{\\\\mu}({{\\\\theta} =  -  1/2 \\\\sin(2\\\\theta) (\\\\partial_{\\\\tau}(x^{\\\\phi}))**2 + \\\\partial_{\\\\tau \\\\tau}(x^{\\\\theta}) + 2\\\\partial_{\\\\tau}(x^{r}) \\\\partial_{\\\\tau}(x^{\\\\theta}) (r)**(-1), {\\\\phi} = \\\\partial_{\\\\tau \\\\tau}(x^{\\\\phi}) + 2\\\\partial_{\\\\tau}(x^{\\\\phi}) \\\\partial_{\\\\tau}(x^{\\\\theta}) (\\\\tan(\\\\theta))**(-1) + 2\\\\partial_{\\\\tau}(x^{\\\\phi}) \\\\partial_{\\\\tau}(x^{r}) (r)**(-1), {r} = (M (r)**2 (\\\\partial_{\\\\tau}(x^{r}))**2-M (2M-r)**2 (\\\\partial_{\\\\tau}(x^{t}))**2 + (r)**3 (2M-r)**2 ((\\\\sin(\\\\theta))**2 (\\\\partial_{\\\\tau}(x^{\\\\phi}))**2 + (\\\\partial_{\\\\tau}(x^{\\\\theta}))**2) + (r)**3 (2M-r) \\\\partial_{\\\\tau \\\\tau}(x^{r})) ((r)**3 (2M-r))**(-1), {t} = (-2M \\\\partial_{\\\\tau}(x^{r}) \\\\partial_{\\\\tau}(x^{t}) + r (2M-r) \\\\partial_{\\\\tau \\\\tau}(x^{t})) (r (2M-r))**(-1)})\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\square{}^{\\\\mu}\\\\left\\\\{\\\\begin{aligned}\\\\square{}^{\\\\theta}& =  - \\\\frac{1}{2}\\\\sin\\\\left(2\\\\theta\\\\right) {\\\\left(\\\\partial_{\\\\tau}{x^{\\\\phi}}\\\\right)}^{2}\\\\discretionary{}{}{}+\\\\partial_{\\\\tau \\\\tau}{x^{\\\\theta}}\\\\discretionary{}{}{}+2\\\\partial_{\\\\tau}{x^{r}} \\\\partial_{\\\\tau}{x^{\\\\theta}} {r}^{-1}\\\\\\\\[-.5ex]\\n\\\\square{}^{\\\\phi}& = \\\\partial_{\\\\tau \\\\tau}{x^{\\\\phi}}\\\\discretionary{}{}{}+2\\\\partial_{\\\\tau}{x^{\\\\phi}} \\\\partial_{\\\\tau}{x^{\\\\theta}} {\\\\left(\\\\tan{\\\\theta}\\\\right)}^{-1}\\\\discretionary{}{}{}+2\\\\partial_{\\\\tau}{x^{\\\\phi}} \\\\partial_{\\\\tau}{x^{r}} {r}^{-1}\\\\\\\\[-.5ex]\\n\\\\square{}^{r}& = \\\\left(M {r}^{2} {\\\\left(\\\\partial_{\\\\tau}{x^{r}}\\\\right)}^{2}\\\\discretionary{}{}{}-M {\\\\left(2M\\\\discretionary{}{}{}-r\\\\right)}^{2} {\\\\left(\\\\partial_{\\\\tau}{x^{t}}\\\\right)}^{2}\\\\discretionary{}{}{}+{r}^{3} {\\\\left(2M\\\\discretionary{}{}{}-r\\\\right)}^{2} \\\\left({\\\\left(\\\\sin{\\\\theta}\\\\right)}^{2} {\\\\left(\\\\partial_{\\\\tau}{x^{\\\\phi}}\\\\right)}^{2}\\\\discretionary{}{}{}+{\\\\left(\\\\partial_{\\\\tau}{x^{\\\\theta}}\\\\right)}^{2}\\\\right)\\\\discretionary{}{}{}+{r}^{3} \\\\left(2M\\\\discretionary{}{}{}-r\\\\right) \\\\partial_{\\\\tau \\\\tau}{x^{r}}\\\\right) {\\\\left({r}^{3} \\\\left(2M\\\\discretionary{}{}{}-r\\\\right)\\\\right)}^{-1}\\\\\\\\[-.5ex]\\n\\\\square{}^{t}& = \\\\left(-2M \\\\partial_{\\\\tau}{x^{r}} \\\\partial_{\\\\tau}{x^{t}}\\\\discretionary{}{}{}+r \\\\left(2M\\\\discretionary{}{}{}-r\\\\right) \\\\partial_{\\\\tau \\\\tau}{x^{t}}\\\\right) {\\\\left(r \\\\left(2M\\\\discretionary{}{}{}-r\\\\right)\\\\right)}^{-1}\\\\\\\\[-.5ex]\\n\\\\end{aligned}\\\\right.\\n\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"evaluate(g);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 2631434789632886585,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 12617961520759459540,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 10694658628125813077,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\components^{\\\\mu}({{\\\\theta} =  -  1/2 \\\\sin(2\\\\theta) (\\\\partial_{\\\\tau}(x^{\\\\phi}))**2 +  1/2 \\\\partial_{\\\\tau \\\\tau}(\\\\pi) + \\\\partial_{\\\\tau}(x^{r}) \\\\partial_{\\\\tau}(\\\\pi) (r)**(-1), {\\\\phi} = \\\\partial_{\\\\tau \\\\tau}(x^{\\\\phi}) + \\\\partial_{\\\\tau}(x^{\\\\phi}) \\\\partial_{\\\\tau}(\\\\pi) (\\\\tan(\\\\theta))**(-1) + 2\\\\partial_{\\\\tau}(x^{\\\\phi}) \\\\partial_{\\\\tau}(x^{r}) (r)**(-1), {r} = (M (r)**2 (\\\\partial_{\\\\tau}(x^{r}))**2-M (2M-r)**2 (\\\\partial_{\\\\tau}(x^{t}))**2 + (r)**3 (2M-r)**2 ((\\\\sin(\\\\theta))**2 (\\\\partial_{\\\\tau}(x^{\\\\phi}))**2 +  1/4 (\\\\partial_{\\\\tau}(\\\\pi))**2) + (r)**3 (2M-r) \\\\partial_{\\\\tau \\\\tau}(x^{r})) ((r)**3 (2M-r))**(-1), {t} = (-2M \\\\partial_{\\\\tau}(x^{r}) \\\\partial_{\\\\tau}(x^{t}) + r (2M-r) \\\\partial_{\\\\tau \\\\tau}(x^{t})) (r (2M-r))**(-1)})\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\square{}^{\\\\mu}\\\\left\\\\{\\\\begin{aligned}\\\\square{}^{\\\\theta}& =  - \\\\frac{1}{2}\\\\sin\\\\left(2\\\\theta\\\\right) {\\\\left(\\\\partial_{\\\\tau}{x^{\\\\phi}}\\\\right)}^{2}\\\\discretionary{}{}{}+\\\\frac{1}{2}\\\\partial_{\\\\tau \\\\tau}{\\\\pi}\\\\discretionary{}{}{}+\\\\partial_{\\\\tau}{x^{r}} \\\\partial_{\\\\tau}{\\\\pi} {r}^{-1}\\\\\\\\[-.5ex]\\n\\\\square{}^{\\\\phi}& = \\\\partial_{\\\\tau \\\\tau}{x^{\\\\phi}}\\\\discretionary{}{}{}+\\\\partial_{\\\\tau}{x^{\\\\phi}} \\\\partial_{\\\\tau}{\\\\pi} {\\\\left(\\\\tan{\\\\theta}\\\\right)}^{-1}\\\\discretionary{}{}{}+2\\\\partial_{\\\\tau}{x^{\\\\phi}} \\\\partial_{\\\\tau}{x^{r}} {r}^{-1}\\\\\\\\[-.5ex]\\n\\\\square{}^{r}& = \\\\left(M {r}^{2} {\\\\left(\\\\partial_{\\\\tau}{x^{r}}\\\\right)}^{2}\\\\discretionary{}{}{}-M {\\\\left(2M\\\\discretionary{}{}{}-r\\\\right)}^{2} {\\\\left(\\\\partial_{\\\\tau}{x^{t}}\\\\right)}^{2}\\\\discretionary{}{}{}+{r}^{3} {\\\\left(2M\\\\discretionary{}{}{}-r\\\\right)}^{2} \\\\left({\\\\left(\\\\sin{\\\\theta}\\\\right)}^{2} {\\\\left(\\\\partial_{\\\\tau}{x^{\\\\phi}}\\\\right)}^{2}\\\\discretionary{}{}{}+\\\\frac{1}{4}{\\\\left(\\\\partial_{\\\\tau}{\\\\pi}\\\\right)}^{2}\\\\right)\\\\discretionary{}{}{}+{r}^{3} \\\\left(2M\\\\discretionary{}{}{}-r\\\\right) \\\\partial_{\\\\tau \\\\tau}{x^{r}}\\\\right) {\\\\left({r}^{3} \\\\left(2M\\\\discretionary{}{}{}-r\\\\right)\\\\right)}^{-1}\\\\\\\\[-.5ex]\\n\\\\square{}^{t}& = \\\\left(-2M \\\\partial_{\\\\tau}{x^{r}} \\\\partial_{\\\\tau}{x^{t}}\\\\discretionary{}{}{}+r \\\\left(2M\\\\discretionary{}{}{}-r\\\\right) \\\\partial_{\\\\tau \\\\tau}{x^{t}}\\\\right) {\\\\left(r \\\\left(2M\\\\discretionary{}{}{}-r\\\\right)\\\\right)}^{-1}\\\\\\\\[-.5ex]\\n\\\\end{aligned}\\\\right.\\n\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"substitute(g, $x^\\\\theta=\\\\pi/2$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 4159579976835826498,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 8408118218291458194,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 16154116095790560403,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\components^{\\\\mu}({{\\\\theta} =  -  1/2 \\\\sin(2\\\\theta) (\\\\partial_{\\\\tau}(x^{\\\\phi}))**2, {\\\\phi} = \\\\partial_{\\\\tau \\\\tau}(x^{\\\\phi}) + 2\\\\partial_{\\\\tau}(x^{\\\\phi}) \\\\partial_{\\\\tau}(x^{r}) (r)**(-1), {r} = (M (r)**2 (\\\\partial_{\\\\tau}(x^{r}))**2-M (2M-r)**2 (\\\\partial_{\\\\tau}(x^{t}))**2 + (r)**3 (2M-r)**2 (\\\\sin(\\\\theta))**2 (\\\\partial_{\\\\tau}(x^{\\\\phi}))**2 + (r)**3 (2M-r) \\\\partial_{\\\\tau \\\\tau}(x^{r})) ((r)**3 (2M-r))**(-1), {t} = (-2M \\\\partial_{\\\\tau}(x^{r}) \\\\partial_{\\\\tau}(x^{t}) + r (2M-r) \\\\partial_{\\\\tau \\\\tau}(x^{t})) (r (2M-r))**(-1)})\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\square{}^{\\\\mu}\\\\left\\\\{\\\\begin{aligned}\\\\square{}^{\\\\theta}& =  - \\\\frac{1}{2}\\\\sin\\\\left(2\\\\theta\\\\right) {\\\\left(\\\\partial_{\\\\tau}{x^{\\\\phi}}\\\\right)}^{2}\\\\\\\\[-.5ex]\\n\\\\square{}^{\\\\phi}& = \\\\partial_{\\\\tau \\\\tau}{x^{\\\\phi}}\\\\discretionary{}{}{}+2\\\\partial_{\\\\tau}{x^{\\\\phi}} \\\\partial_{\\\\tau}{x^{r}} {r}^{-1}\\\\\\\\[-.5ex]\\n\\\\square{}^{r}& = \\\\left(M {r}^{2} {\\\\left(\\\\partial_{\\\\tau}{x^{r}}\\\\right)}^{2}\\\\discretionary{}{}{}-M {\\\\left(2M\\\\discretionary{}{}{}-r\\\\right)}^{2} {\\\\left(\\\\partial_{\\\\tau}{x^{t}}\\\\right)}^{2}\\\\discretionary{}{}{}+{r}^{3} {\\\\left(2M\\\\discretionary{}{}{}-r\\\\right)}^{2} {\\\\left(\\\\sin{\\\\theta}\\\\right)}^{2} {\\\\left(\\\\partial_{\\\\tau}{x^{\\\\phi}}\\\\right)}^{2}\\\\discretionary{}{}{}+{r}^{3} \\\\left(2M\\\\discretionary{}{}{}-r\\\\right) \\\\partial_{\\\\tau \\\\tau}{x^{r}}\\\\right) {\\\\left({r}^{3} \\\\left(2M\\\\discretionary{}{}{}-r\\\\right)\\\\right)}^{-1}\\\\\\\\[-.5ex]\\n\\\\square{}^{t}& = \\\\left(-2M \\\\partial_{\\\\tau}{x^{r}} \\\\partial_{\\\\tau}{x^{t}}\\\\discretionary{}{}{}+r \\\\left(2M\\\\discretionary{}{}{}-r\\\\right) \\\\partial_{\\\\tau \\\\tau}{x^{t}}\\\\right) {\\\\left(r \\\\left(2M\\\\discretionary{}{}{}-r\\\\right)\\\\right)}^{-1}\\\\\\\\[-.5ex]\\n\\\\end{aligned}\\\\right.\\n\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"unwrap(g);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 2119769314929757895,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"gn:=@(g).\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 8852027245216028416,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 13419103005502537788,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 13032143019866061980,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\components^{\\\\mu}({{ 1/2 \\\\pi} =  -  1/2 \\\\sin(\\\\pi) (\\\\partial_{\\\\tau}(x^{\\\\phi}))**2, {\\\\phi} = \\\\partial_{\\\\tau \\\\tau}(x^{\\\\phi}) + 2\\\\partial_{\\\\tau}(x^{\\\\phi}) \\\\partial_{\\\\tau}(x^{r}) (r)**(-1), {r} = (M (r)**2 (\\\\partial_{\\\\tau}(x^{r}))**2-M (2M-r)**2 (\\\\partial_{\\\\tau}(x^{t}))**2 + (r)**3 (2M-r)**2 (\\\\sin( 1/2 \\\\pi))**2 (\\\\partial_{\\\\tau}(x^{\\\\phi}))**2 + (r)**3 (2M-r) \\\\partial_{\\\\tau \\\\tau}(x^{r})) ((r)**3 (2M-r))**(-1), {t} = (-2M \\\\partial_{\\\\tau}(x^{r}) \\\\partial_{\\\\tau}(x^{t}) + r (2M-r) \\\\partial_{\\\\tau \\\\tau}(x^{t})) (r (2M-r))**(-1)})\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\square{}^{\\\\mu}\\\\left\\\\{\\\\begin{aligned}\\\\square{}^{\\\\frac{1}{2}\\\\pi}& =  - \\\\frac{1}{2}\\\\sin{\\\\pi} {\\\\left(\\\\partial_{\\\\tau}{x^{\\\\phi}}\\\\right)}^{2}\\\\\\\\[-.5ex]\\n\\\\square{}^{\\\\phi}& = \\\\partial_{\\\\tau \\\\tau}{x^{\\\\phi}}\\\\discretionary{}{}{}+2\\\\partial_{\\\\tau}{x^{\\\\phi}} \\\\partial_{\\\\tau}{x^{r}} {r}^{-1}\\\\\\\\[-.5ex]\\n\\\\square{}^{r}& = \\\\left(M {r}^{2} {\\\\left(\\\\partial_{\\\\tau}{x^{r}}\\\\right)}^{2}\\\\discretionary{}{}{}-M {\\\\left(2M\\\\discretionary{}{}{}-r\\\\right)}^{2} {\\\\left(\\\\partial_{\\\\tau}{x^{t}}\\\\right)}^{2}\\\\discretionary{}{}{}+{r}^{3} {\\\\left(2M\\\\discretionary{}{}{}-r\\\\right)}^{2} {\\\\sin\\\\left(\\\\frac{1}{2}\\\\pi\\\\right)}^{2} {\\\\left(\\\\partial_{\\\\tau}{x^{\\\\phi}}\\\\right)}^{2}\\\\discretionary{}{}{}+{r}^{3} \\\\left(2M\\\\discretionary{}{}{}-r\\\\right) \\\\partial_{\\\\tau \\\\tau}{x^{r}}\\\\right) {\\\\left({r}^{3} \\\\left(2M\\\\discretionary{}{}{}-r\\\\right)\\\\right)}^{-1}\\\\\\\\[-.5ex]\\n\\\\square{}^{t}& = \\\\left(-2M \\\\partial_{\\\\tau}{x^{r}} \\\\partial_{\\\\tau}{x^{t}}\\\\discretionary{}{}{}+r \\\\left(2M\\\\discretionary{}{}{}-r\\\\right) \\\\partial_{\\\\tau \\\\tau}{x^{t}}\\\\right) {\\\\left(r \\\\left(2M\\\\discretionary{}{}{}-r\\\\right)\\\\right)}^{-1}\\\\\\\\[-.5ex]\\n\\\\end{aligned}\\\\right.\\n\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"substitute(gn, $\\\\theta=\\\\pi/2$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 14536697356937499824,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 3832125110698168679,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 1130372328554165006,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\components^{\\\\mu}({{ 1/2 \\\\pi} =  -  1/2 \\\\sin(\\\\pi) (\\\\partial_{\\\\tau}(x^{\\\\phi}))**2, {\\\\phi} = \\\\partial_{\\\\tau \\\\tau}(x^{\\\\phi}) + 2\\\\partial_{\\\\tau}(x^{\\\\phi}) \\\\partial_{\\\\tau}(x^{r}) (r)**(-1), {r} = (M (r)**2 (\\\\partial_{\\\\tau}(x^{r}))**2-M (2M-r)**2 (\\\\partial_{\\\\tau}(x^{t}))**2 + (r)**3 (2M-r)**2 (\\\\partial_{\\\\tau}(x^{\\\\phi}))**2 + (r)**3 (2M-r) \\\\partial_{\\\\tau \\\\tau}(x^{r})) ((r)**3 (2M-r))**(-1), {t} = (-2M \\\\partial_{\\\\tau}(x^{r}) \\\\partial_{\\\\tau}(x^{t}) + r (2M-r) \\\\partial_{\\\\tau \\\\tau}(x^{t})) (r (2M-r))**(-1)})\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\square{}^{\\\\mu}\\\\left\\\\{\\\\begin{aligned}\\\\square{}^{\\\\frac{1}{2}\\\\pi}& =  - \\\\frac{1}{2}\\\\sin{\\\\pi} {\\\\left(\\\\partial_{\\\\tau}{x^{\\\\phi}}\\\\right)}^{2}\\\\\\\\[-.5ex]\\n\\\\square{}^{\\\\phi}& = \\\\partial_{\\\\tau \\\\tau}{x^{\\\\phi}}\\\\discretionary{}{}{}+2\\\\partial_{\\\\tau}{x^{\\\\phi}} \\\\partial_{\\\\tau}{x^{r}} {r}^{-1}\\\\\\\\[-.5ex]\\n\\\\square{}^{r}& = \\\\left(M {r}^{2} {\\\\left(\\\\partial_{\\\\tau}{x^{r}}\\\\right)}^{2}\\\\discretionary{}{}{}-M {\\\\left(2M\\\\discretionary{}{}{}-r\\\\right)}^{2} {\\\\left(\\\\partial_{\\\\tau}{x^{t}}\\\\right)}^{2}\\\\discretionary{}{}{}+{r}^{3} {\\\\left(2M\\\\discretionary{}{}{}-r\\\\right)}^{2} {\\\\left(\\\\partial_{\\\\tau}{x^{\\\\phi}}\\\\right)}^{2}\\\\discretionary{}{}{}+{r}^{3} \\\\left(2M\\\\discretionary{}{}{}-r\\\\right) \\\\partial_{\\\\tau \\\\tau}{x^{r}}\\\\right) {\\\\left({r}^{3} \\\\left(2M\\\\discretionary{}{}{}-r\\\\right)\\\\right)}^{-1}\\\\\\\\[-.5ex]\\n\\\\square{}^{t}& = \\\\left(-2M \\\\partial_{\\\\tau}{x^{r}} \\\\partial_{\\\\tau}{x^{t}}\\\\discretionary{}{}{}+r \\\\left(2M\\\\discretionary{}{}{}-r\\\\right) \\\\partial_{\\\\tau \\\\tau}{x^{t}}\\\\right) {\\\\left(r \\\\left(2M\\\\discretionary{}{}{}-r\\\\right)\\\\right)}^{-1}\\\\\\\\[-.5ex]\\n\\\\end{aligned}\\\\right.\\n\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"substitute(gn, $\\\\sin\\\\pi=0, \\\\sin(\\\\pi/2)=1$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 1001501096333441621,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 12564307241139471620,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 17322407036073179915,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\components^{\\\\mu}({{ 1/2 \\\\pi} =  -  1/2 \\\\sin(\\\\pi) (\\\\partial_{\\\\tau}(x^{\\\\phi}))**2, {\\\\phi} = \\\\partial_{\\\\tau \\\\tau}(x^{\\\\phi}) + 2\\\\partial_{\\\\tau}(x^{\\\\phi}) \\\\partial_{\\\\tau}(x^{r}) (r)**(-1), {r} = (M (r)**2 (\\\\partial_{\\\\tau}(x^{r}))**2-M (2M-r)**2 + (r)**3 (2M-r)**2 (\\\\partial_{\\\\tau}(x^{\\\\phi}))**2 + (r)**3 (2M-r) \\\\partial_{\\\\tau \\\\tau}(x^{r})) ((r)**3 (2M-r))**(-1), {t} = (-2M \\\\partial_{\\\\tau}(x^{r}) + r (2M-r) \\\\partial_{\\\\tau \\\\tau}(x^{t})) (r (2M-r))**(-1)})\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\square{}^{\\\\mu}\\\\left\\\\{\\\\begin{aligned}\\\\square{}^{\\\\frac{1}{2}\\\\pi}& =  - \\\\frac{1}{2}\\\\sin{\\\\pi} {\\\\left(\\\\partial_{\\\\tau}{x^{\\\\phi}}\\\\right)}^{2}\\\\\\\\[-.5ex]\\n\\\\square{}^{\\\\phi}& = \\\\partial_{\\\\tau \\\\tau}{x^{\\\\phi}}\\\\discretionary{}{}{}+2\\\\partial_{\\\\tau}{x^{\\\\phi}} \\\\partial_{\\\\tau}{x^{r}} {r}^{-1}\\\\\\\\[-.5ex]\\n\\\\square{}^{r}& = \\\\left(M {r}^{2} {\\\\left(\\\\partial_{\\\\tau}{x^{r}}\\\\right)}^{2}\\\\discretionary{}{}{}-M {\\\\left(2M\\\\discretionary{}{}{}-r\\\\right)}^{2}\\\\discretionary{}{}{}+{r}^{3} {\\\\left(2M\\\\discretionary{}{}{}-r\\\\right)}^{2} {\\\\left(\\\\partial_{\\\\tau}{x^{\\\\phi}}\\\\right)}^{2}\\\\discretionary{}{}{}+{r}^{3} \\\\left(2M\\\\discretionary{}{}{}-r\\\\right) \\\\partial_{\\\\tau \\\\tau}{x^{r}}\\\\right) {\\\\left({r}^{3} \\\\left(2M\\\\discretionary{}{}{}-r\\\\right)\\\\right)}^{-1}\\\\\\\\[-.5ex]\\n\\\\square{}^{t}& = \\\\left(-2M \\\\partial_{\\\\tau}{x^{r}}\\\\discretionary{}{}{}+r \\\\left(2M\\\\discretionary{}{}{}-r\\\\right) \\\\partial_{\\\\tau \\\\tau}{x^{t}}\\\\right) {\\\\left(r \\\\left(2M\\\\discretionary{}{}{}-r\\\\right)\\\\right)}^{-1}\\\\\\\\[-.5ex]\\n\\\\end{aligned}\\\\right.\\n\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"substitute(gn, $\\\\partial_{\\\\tau}{x^t}=1$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 6946023956310198656,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 11734860790536619624,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"Now fix $\\\\dot{r}$ and $\\\\dot{\\\\phi}$ (with $\\\\dot{\\\\theta}=0$), and solve for $\\\\dot{t}$ from $\\\\dot{x}^\\\\mu \\\\dot{x}_\\\\mu = 0$ for lightlike geodesics. Use this as initial conditions together with $t=\\\\phi=0$ and $r=r_0$.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"Now fix $\\\\dot{r}$ and $\\\\dot{\\\\phi}$ (with $\\\\dot{\\\\theta}=0$), and solve for $\\\\dot{t}$ from $\\\\dot{x}^\\\\mu \\\\dot{x}_\\\\mu = 0$ for lightlike geodesics. Use this as initial conditions together with $t=\\\\phi=0$ and $r=r_0$.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 1864741910303041367,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"\"\n\t\t}\n\t],\n\t\"description\": \"Cadabra JSON notebook format\",\n\t\"version\": 1.0\n}\n"
  },
  {
    "path": "core/packages/cdb/remote/__init__.py",
    "content": "#!/usr/bin/env python3\n\nimport json\nimport sys\nimport subprocess\nimport websocket\nimport threading\nimport time\n\nclass CadabraRemoteException(Exception):\n    def __init__(self, msg):\n        pass\n        \nclass CadabraRemote:\n    def __init__(self):\n        self.url = \"\"\n        self.process = None\n        self.ws = None\n        self.ws_thread = None\n        self.serial = 99\n        self.condition = threading.Condition()\n        self.open_condition = threading.Condition()\n        self.close_condition = threading.Condition()\n        self.name = \"cadabra2-gtk\"\n        self.received_msg = {} # FIXME: need to keep a stack of messages?\n\n    def start(self, extra_args=[]):\n        args = [self.name]\n        args.extend(extra_args)\n        self.process = subprocess.Popen(args, stdout=subprocess.PIPE, stderr=subprocess.PIPE, text=True)\n        try:\n            info = self.process.stderr.readline()\n            while not info:\n                time.sleep(0.1)\n                info = self.process.stderr.readline()\n            print(f\"Socket at {info}\")\n            self.url = info[16:-1]\n            print(f\"URL {self.url}\")\n            self.connect()\n            with self.open_condition:\n                self.open_condition.wait()\n                print(\"Notebook up and communicating ***\")\n        except Exception as ex:\n            raise CadabraRemoteException(f\"Failed to start cadabra2-gtk: {ex}\")\n\n    def connect(self):\n        print(\"Starting thread...\")\n        self.ws_thread = threading.Thread(target=self.ws_run)\n        self.ws_thread.daemon = True\n        self.ws_thread.start()\n\n    def ws_run(self):\n        print(\"Thread started\")\n        print(f\"Connecting to control socket {self.url}...\")\n        # websocket.enableTrace(True)\n        self.ws = websocket.WebSocketApp(self.url,\n                                         on_open = self.on_open,\n                                         on_message = self.on_message,\n                                         on_error = self.on_error,\n                                         on_close = self.on_close)\n        # self.ws.on_open = self.on_open\n        print(\"Websocket handler going into main loop\")\n        self.ws.run_forever()\n        print(\"Websocket handler exited\")\n        with self.close_condition:\n            self.close_condition.notify()\n        \n    def on_message(self, ws, message):\n        try:\n            with self.condition:\n                self.received_msg = json.loads(message)\n                print(f\"Received completion message {self.received_msg}\")\n                self.condition.notify()\n        except Exception as ex:\n            print(f\"Cannot parse message {message}: {ex}\")\n\n    def on_open(self, ws):\n        print(\"Connection open.\")\n        with self.open_condition:\n            self.open_condition.notify()\n\n    def on_close(self, ws, v1, v2):\n        print(f\"Connection closed: {v1}, {v2}\")\n        # remaining_stdout = self.process.stdout.read()\n        # remaining_stderr = self.process.stderr.read()\n        # print(remaining_stdout)\n        # print(remaining_stderr)\n\n    def on_error(self, ws, message):\n        print(f\"Connection error {message}.\")\n        # remaining_stdout = self.process.stdout.read()\n        # remaining_stderr = self.process.stderr.read()\n        # print(remaining_stdout)\n        # print(remaining_stderr)\n            \n    def open(self, notebook, wait=True):\n        self.serial += 1\n        msg = { \"action\":   \"open\",\n                \"notebook\": notebook,\n                \"serial\":   self.serial\n               }\n        print(\"Loading notebook\")\n        self.ws.send( json.dumps(msg) )\n        if wait:\n            with self.condition:\n                self.condition.wait()\n\n    def run_all_cells(self, wait=True):\n        self.serial += 1\n        msg = { \"action\":   \"run_all_cells\",\n                \"serial\":   self.serial\n               }\n        try:\n            print(\"Running cells\")\n            self.ws.send( json.dumps(msg) )\n            if wait:\n                with self.condition:\n                    self.condition.wait()\n        except:\n            raise CadabraRemoteException(\"Connection to Cadabra notebook not open.\")\n\n    def run_cell(self, cell_id, wait=True):\n        self.serial += 1\n        msg = { \"action\":   \"run_cell\",\n                \"cell_id\":  cell_id,\n                \"serial\":   self.serial\n               }\n        try:\n            print(f\"Running cell {cell_id}\")\n            self.ws.send( json.dumps(msg) )\n            if wait:\n                with self.condition:\n                    self.condition.wait()\n        except:\n            raise CadabraRemoteException(\"Connection to Cadabra notebook not open.\")\n\n    def add_cell(self, content, cell_id=0, wait=True):\n        \"\"\" Add a cell to the notebook. If `cell_id` is non-zero,\n        and a cell with that id already exists, just update the content.\"\"\"\n        self.serial += 1\n        msg = { \"action\":   \"add_cell\",\n                \"cell_id\":  cell_id,\n                \"serial\":   self.serial,\n                \"content\":  content\n               }\n        self.ws.send( json.dumps(msg) )\n        if wait:\n            with self.condition:\n                self.condition.wait()\n            return self.received_msg[\"cell_id\"]\n        return 0\n\n    def insert_text(self, content, cell_id=0, wait=True):\n        \"\"\" Add a text to the given cell. \"\"\"\n        self.serial += 1\n        msg = { \"action\":   \"insert_text\",\n                \"cell_id\":  cell_id,\n                \"serial\":   self.serial,\n                \"content\":  content\n               }\n        self.ws.send( json.dumps(msg) )\n        if wait:\n            with self.condition:\n                self.condition.wait()\n            return self.received_msg[\"cell_id\"]\n        return 0\n\n    def wait(self):\n        with self.close_condition:\n            try:\n                self.close_condition.wait()\n                if self.process:\n                    self.process.terminate()\n            except KeyboardInterrupt:\n                if self.process:\n                    self.process.terminate()\n                \n\nif __name__==\"__main__\":\n    # This is for testing only; see for more extensive\n    # usage of this module the scripts in the \"tutorials\"\n    # folder of the Cadabra repository.\n    cdb = CadabraRemote()\n    cdb.start()\n    cdb.open(\"../examples/schwarzschild.cnb\")\n    time.sleep(1)\n    print(\"Notebook loaded\")\n    cdb.run_all_cells()\n    print(\"Cells ran\")\n    print(\"Press ctrl-c to terminate\")\n    cdb.wait()\n            \n"
  },
  {
    "path": "core/packages/cdb/remote/highlight.py",
    "content": "from gi.repository import Gio, GLib\nimport gi\ngi.require_version('Gtk', '3.0')\nfrom gi.repository import Gtk, Gdk\nimport dbus\nfrom dbus.mainloop.glib import DBusGMainLoop\nimport pyatspi\nimport cairo\nimport sys\nfrom threading import Thread\nimport time\nimport math\nimport textwrap\n\nclass WidgetHighlighter:\n    def __init__(self, window_name):\n        self.window = None\n        self.window_name = window_name\n        self.current_highlight = None\n        self.subtitle_window = None\n        self.subtitle_x = 0\n        self.subtitle_y = 0\n        self.subtitle_bottom = 20\n        self.subtitle_large = False\n        self.label = None\n        self.loop = None\n        self.target_window = self.find_window(self.window_name)\n\n    def create_highlight_window(self, x, y, width, height):\n        # from gi.repository import Gtk, Gdk\n        \n        if self.current_highlight:\n            self.remove_highlight()\n            \n        win = Gtk.Window(type=Gtk.WindowType.POPUP)\n        win.set_app_paintable(True)\n        win.set_visual(win.get_screen().get_rgba_visual())\n        print(x,y,width,height)\n        win.resize(width + 4, height + 4)\n        win.move(x - 2, y - 2)\n        \n        win.connect('draw', self.draw_highlight)\n        win.show_all()\n        self.current_highlight = win\n        \n    def draw_highlight(self, widget, cr):\n        cr.set_operator(cairo.OPERATOR_SOURCE)\n        cr.set_source_rgba(1.0, 0.6, 0.0, 0.3)  # Semi-transparent orange\n        cr.paint()\n        cr.set_source_rgba(1.0, 0.6, 0.0, 0.8)  # Solid orange border\n        cr.set_line_width(2)\n        cr.rectangle(1, 1, widget.get_allocated_width() - 2,\n                    widget.get_allocated_height() - 2)\n        cr.stroke()\n        return False\n\n    def remove_highlight(self):\n        if self.current_highlight:\n            self.current_highlight.destroy()\n            self.current_highlight = None\n\n    def find_button_by_label(self, app_name, button_label):\n        desktop = pyatspi.Registry.getDesktop(0)\n        for app in desktop:\n            if app and app_name.lower() in app.name.lower():\n                for window in app:\n                    button = self._find_button_recursive(window, button_label)\n                    if button:\n                        return button\n        return None\n    \n    def _find_button_recursive(self, obj, label):\n        if not obj.getRole() == pyatspi.ROLE_MENU_ITEM:\n            if label.lower() in obj.name.lower():\n                return obj\n                \n        for child in obj:\n            result = self._find_button_recursive(child, label)\n            if result:\n                return result\n        return None\n    \n    def highlight_button(self, button):\n        if not button:\n            return\n            \n        component = button.queryComponent()\n        print(component)\n        x, y = component.getPosition(pyatspi.DESKTOP_COORDS)\n        w, h = component.getSize()\n        # print(x,y,w,h)\n        \n        # Create highlight overlay\n        self.create_highlight_window(x, y, w, h)\n        \n        # Start GTK main loop in a separate thread\n        if not self.loop:\n            self.loop = GLib.MainLoop()\n            thread = Thread(target=self._run_loop)\n            thread.daemon = True\n            thread.start()\n\n    def _run_loop(self):\n        self.loop.run()\n\n    def find_window(self, name):\n        desktop = pyatspi.Registry.getDesktop(0)\n        self.target_window = None\n        for app in desktop:\n            if app:\n                for window in app:\n                    if self.window_name.lower() in window.name.lower():\n                        return window\n\n        raise Exception(\"Window \"+self.window_name+\" not found\")\n        \n    def subtitle(self, text, large=False):\n        \"\"\"Display a subtitle at the bottom of the specified window.\n        If window_name is None, places it at bottom of screen.\"\"\"\n        if self.subtitle_window:\n            self.remove_subtitle()\n        self.subtitle_large = large\n            \n        # Create subtitle window\n        win = Gtk.Window(type=Gtk.WindowType.POPUP)\n        self.subtitle_window = win\n        win.set_app_paintable(True)\n        win.set_visual(win.get_screen().get_rgba_visual())\n        win.set_type_hint(Gdk.WindowTypeHint.POPUP_MENU)\n        win.set_name(\"subtitle-window\")  # Give the window a name for CSS\n        \n        # Create label with text\n        self.label = Gtk.Label()\n        self.label.set_text(\"\\n\".join(textwrap.wrap(text)))\n        self.label.set_name(\"subtitle\")\n        \n        # Style the label\n        css_provider = Gtk.CssProvider()\n        if large:\n            css_provider.load_from_data(b\"\"\"\n                #subtitle-window {\n                    border-radius: 5px;\n                }\n                #subtitle {\n                    padding: 10px 40px;\n                    font-size: 90px;\n                    color: black;\n                }\n            \"\"\")\n        else:\n            css_provider.load_from_data(b\"\"\"\n                #subtitle-window {\n                    border-radius: 5px;\n                }\n                #subtitle {\n                    padding: 10px 20px;\n                    font-size: 45px;\n                    color: black;\n                }\n            \"\"\")\n\n        context = self.label.get_style_context()\n        context.add_provider(css_provider, \n                           Gtk.STYLE_PROVIDER_PRIORITY_APPLICATION)\n\n        win.add(self.label)\n        win.connect('draw', self.draw_subtitle)\n        win.show_all()\n        self.startloop()\n\n    def startloop(self):\n        # Start GTK main loop if not already running\n        if not self.loop:\n            self.loop = GLib.MainLoop()\n            thread = Thread(target=self._run_loop)\n            thread.daemon = True\n            thread.start()\n\n    def draw_subtitle(self, widget, cr):\n        # Size and position the window\n        monitor = Gdk.Display.get_default().get_primary_monitor()\n        geometry = monitor.get_geometry()\n\n        # Get natural size of label\n        label_width, label_height = self.label.get_preferred_size()[1].width, \\\n            self.label.get_preferred_size()[1].height\n        # print(\"LABEL:\", label_width, label_height)\n        \n        component = self.target_window.queryComponent()\n        wx, wy = component.getPosition(pyatspi.WINDOW_COORDS)\n        ww, wh = component.getSize()\n        self.subtitle_x = wx + (ww - label_width) // 2 \n        self.subtitle_y = wy + wh - label_height - self.subtitle_bottom\n        # print(wx, wy, ww, wh, label_width, label_height, self.subtitle_x, self.subtitle_y)\n        \n        self.subtitle_window.move(self.subtitle_x, self.subtitle_y)\n        self.draw_subtitle_background(widget, cr) #connect('draw', self.draw_subtitle_background)\n        \n    \n    def draw_subtitle_background(self, widget, cr):\n        cr.set_operator(cairo.OPERATOR_SOURCE)\n        gl=0.9\n        cr.set_source_rgba(gl, gl, gl, 0.6)  # 0=transparent, 1=opaque\n        \n        # Get the window dimensions\n        width = widget.get_allocated_width()\n        height = widget.get_allocated_height()\n        \n        # Set the radius for rounded corners\n        radius = 12\n        \n        # Create rounded rectangle path\n        cr.new_path()\n        \n        # Top left corner\n        cr.arc(radius, radius, radius, 180 * (math.pi/180), 270 * (math.pi/180))\n        # Top right corner\n        cr.arc(width - radius, radius, radius, -90 * (math.pi/180), 0)\n        # Bottom right corner\n        cr.arc(width - radius, height - radius, radius, 0, 90 * (math.pi/180))\n        # Bottom left corner\n        cr.arc(radius, height - radius, radius, 90 * (math.pi/180), 180 * (math.pi/180))\n        cr.close_path()\n        cr.fill()\n\n        if self.subtitle_large:\n            radius = 18\n            # Marker left #209020;\n            cr.set_source_rgba(0.125, 0.565, 0.125, 1)  # 0=transparent, 1=opaque\n            cr.new_path()\n            # Top left corner\n            cr.arc(radius, radius, radius, 180 * (math.pi/180), 270 * (math.pi/180))\n            # Bottom left corner\n            cr.arc(radius, height - radius, radius, 90 * (math.pi/180), 180 * (math.pi/180))\n            cr.close_path()\n            cr.fill()\n        \n        return False\n    \n    def remove_subtitle(self):\n        \"\"\"Remove the subtitle window if it exists\"\"\"\n        if self.subtitle_window:\n            self.subtitle_window.destroy()\n            self.subtitle_window = None\n\n    def remove_all(self):\n        \"\"\"Remove both highlight and subtitle windows\"\"\"\n        self.remove_highlight()\n        self.remove_subtitle()\n\nhighlighter = None\n\ndef init_highlight(title=\"Cadabra\"):\n    global highlighter\n    if highlighter == None:\n        highlighter = WidgetHighlighter(title)\n    \n\ndef mark(label=\"\"):\n    global highlighter\n\n    if label==\"\":\n        highlighter.remove_highlight()\n    else:\n        obj = highlighter.find_button_by_label(\"cadabra2-gtk\", label)\n        if obj:\n            print(\"FOUND\", obj)\n            highlighter.highlight_button(obj)\n\ndef subtitle(txt=\"\", large=False, bottom=20):\n    global highlighter\n\n    highlighter.subtitle_bottom = bottom\n    if txt==\"\":\n        highlighter.remove_subtitle()\n    else:\n        highlighter.subtitle(txt, large)\n\nDBusGMainLoop(set_as_default=True)\n        \nif __name__ == \"__main__\":\n    main()\n"
  },
  {
    "path": "core/packages/cdb/remote/record.py",
    "content": "#import obspython as obs\nfrom obswebsocket import obsws, requests\nimport subprocess\nimport json\nimport time\nimport re\n\ndef get_window_geometry(window_name):\n    \"\"\"Get window position and size using xdotool\"\"\"\n    try:\n        # Get window ID\n        cmd = f\"xdotool search --name '{window_name}'\"\n        window_id = subprocess.check_output(cmd, shell=True).decode().strip()\n        # print(window_id)\n        \n        # Get window geometry\n        cmd = f\"xwininfo -id {window_id}\"\n        wininfo_output = subprocess.check_output(cmd, shell=True).decode()\n        \n        # Parse xwininfo output using regex\n        x_match = re.search(r'Absolute upper-left X:\\s+(\\d+)', wininfo_output)\n        y_match = re.search(r'Absolute upper-left Y:\\s+(\\d+)', wininfo_output)\n        width_match = re.search(r'Width:\\s+(\\d+)', wininfo_output)\n        height_match = re.search(r'Height:\\s+(\\d+)', wininfo_output)\n\n        # Get screen geometry\n        cmd = f\"xdotool getdisplaygeometry\"\n        screen_geometry = subprocess.check_output(cmd, shell=True).decode().strip()\n        # print(screen_geometry)\n            \n        sw, sh = screen_geometry.split(' ')\n            \n        return {\n            'x': int(x_match.group(1)),\n            'y': int(y_match.group(1)),\n            'width': int(width_match.group(1)),\n            'height': int(height_match.group(1)),\n            'screen_width':  int(sw),\n            'screen_height': int(sh)\n        }\n    except Exception as e:\n        print(f\"Error getting window geometry: {e}\")\n        return None\n\nws = None    \n    \ndef setup_region_capture(window_name, password):\n    global ws\n    # Connect to OBS WebSocket\n    ws = obsws(\"localhost\", 4455, password)\n    ws.connect()\n    \n    try:\n        # Get window geometry to determine capture region\n        geometry = get_window_geometry(window_name)\n        if not geometry:\n            raise Exception(\"Could not get window geometry\")\n        \n        # Add some padding to ensure we capture overlapping windows\n        # padding = 10  # adjust as needed\n        # geometry['x'] = max(0, geometry['x'] - padding)\n        # geometry['y'] = max(0, geometry['y'] - padding)\n        # geometry['width'] += 2 * padding\n        # geometry['height'] += 2 * padding\n        \n        # Create a scene if it doesn't exist\n        scene_name = \"Cadabra Recording\"\n        ws.call(requests.CreateScene(sceneName=scene_name))\n        \n        # Create display capture source with region\n        source_settings = {\n            \"display\": 0,  # Primary display\n            \"cursor\": True\n        }\n        source_name = \"Cadabra Window\"\n        \n        ws.call(requests.CreateInput(\n            sceneName=scene_name,\n            inputName=source_name,\n            inputKind=\"xshm_input\",  # Use monitor capture instead of window capture\n            settings=source_settings\n        ))\n        ws.call(requests.CreateInput(\n            sceneName=scene_name,\n            inputName=\"Audio Capture\",\n            inputKind=\"pulse_output_capture\"\n        ))\n        time.sleep(1)\n        \n        crop_settings = {\n            \"cut_left\":   geometry['x'],\n            \"cut_top\":    geometry['y'],\n            \"cut_right\":  geometry['screen_width'] - (geometry['x']+geometry['width']),\n            \"cut_bot\":    geometry['screen_height']- (geometry['y']+geometry['height'])\n        }\n        \n        ws.call(requests.SetInputSettings(\n            inputName=source_name,\n            inputSettings=crop_settings\n        ))\n\n        # Turn off microphone. FIXME: not working\n        ws.call(requests.SetInputSettings(\n            inputName=\"Mic/Aux\",\n            inputSettings={ \"muted\": True }\n        ))\n        \n        # Set as current scene\n        ws.call(requests.SetCurrentProgramScene(sceneName=scene_name))\n        \n        # print(f\"Capture region: {json.dumps(geometry, indent=2)}\")\n        \n    except Exception as e:\n        print(f\"Error: {e}\")\n#     finally:\n#         ws.disconnect()\n\ndef start_record():\n    global ws\n    ws.call(requests.StartRecord())\n        \ndef stop_record():\n    global ws\n    ws.call(requests.StopRecord())\n        \n        \nif __name__ == \"__main__\":\n    # Replace with your GTK window name\n    gtk_window_name = \"Your Window Name\"\n    setup_region_capture(gtk_window_name, sys.argv[1])\n"
  },
  {
    "path": "core/packages/cdb/remote/speech.py",
    "content": "\nimport io\nimport wave\nimport time\nimport tempfile\nimport cdb.remote.highlight\nimport openai\nimport subprocess\nimport time\n\ninitialised=False\nmodel    = None\nwarping  = False\nclient   = None\nsay_proc = None\nsay_num  = 0\n\ndef init(url=\"http://localhost:8880/v1\"):\n    global client\n    client=openai.OpenAI(base_url=url, api_key=\"not-needed\")\n\ndef warp(w=True):\n    global warping\n    warping=w\n\ndef tts(txt, fname):\n    # print(f\"calling api for {txt}...\")\n    with client.audio.speech.with_streaming_response.create(\n            model=\"kokoro\",\n            speed=1.1,\n            voice=\"bm_fable\", #single or multiple voicepack combo\n            input=txt\n    ) as response:\n        response.stream_to_file(fname)\n        \ndef say_async(fname, delay):\n    global say_proc\n    # print(f\"playing...\")\n    say_proc = subprocess.Popen([\"bash\", \"-c\", f\"sleep {delay} && mpv {fname}\"],\n                                stdout=subprocess.PIPE,\n                                stderr=subprocess.PIPE)\n\ndef say(text, subtitle=True, subtext=\"\", delay=0, block=False, bottom=20):\n    \"\"\"\n    Say a text. This will do the text-to-speech, then play the audio\n    async. So it returns immediately after the playing starts.\n    The async task will play silence for the indicated delay first.\n\n    If another text is still being spoken, this function always\n    blocks until that previous text is finished.\n    \"\"\"\n    global model, warping, say_num, say_proc\n    \n    if client == None:\n        init()\n\n    if not warping:\n        say_num += 1\n        fname = f\"/tmp/output_{say_num}.mp3\"\n        tts(text, fname)\n        if say_proc != None:\n            say_proc.wait()\n        say_async(fname, delay)\n       \n    if subtitle:\n        if subtext!=\"\":\n            cdb.remote.highlight.subtitle(subtext, bottom=bottom)\n        else:\n            cdb.remote.highlight.subtitle(text, bottom=bottom)\n\n    if block:\n        say_proc.wait()\n        \n#    if subtitle:\n#        cdb.remote.highlight.subtitle()\n\nif __name__ == \"__main__\":\n    say(\"Hello!\", subtitle=False)\n    say(\"We are going to have some fun with this.\", subtitle=False)\n    say_proc.wait()\n    \n"
  },
  {
    "path": "core/packages/cdb/sympy/calculus.cnb",
    "content": "{\n\t\"cell_id\": 6806321452497212969,\n\t\"cells\": [\n\t\t{\n\t\t\t\"cell_id\": 1025456808033925757,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 15168816901646088639,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\package{cdb.sympy.calculus}{Use SymPy calculus functionality on Cadabra expressions.}\\n\\nA lot of functionality in SymPy can be used on Cadabra expressions, but in order to correctly\\nconvert from and to the SymPy expression form, we need a bridge. This package contains such\\nbridging fuctions, which will ensure that e.g. tensor indices are handled correctly when\\nfed through SymPy's scalar algebra algorithms.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\package{cdb.sympy.calculus}{Use SymPy calculus functionality on Cadabra expressions.}\\n\\nA lot of functionality in SymPy can be used on Cadabra expressions, but in order to correctly\\nconvert from and to the SymPy expression form, we need a bridge. This package contains such\\nbridging fuctions, which will ensure that e.g. tensor indices are handled correctly when\\nfed through SymPy's scalar algebra algorithms.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 13465434077161054101,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 11839947054515140372,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\algorithm{diff}{Differentiate an expression with respect to one or more variables.}\\n\\nThis function mimics the SymPy \\\\verb|diff| function, except that all expressions need\\nto be Cadabra expressions. The function takes an expression and an arbitrary number\\nof variables with respect to which to differentiate it.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\algorithm{diff}{Differentiate an expression with respect to one or more variables.}\\n\\nThis function mimics the SymPy \\\\verb|diff| function, except that all expressions need\\nto be Cadabra expressions. The function takes an expression and an arbitrary number\\nof variables with respect to which to differentiate it.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 3804610120254550473,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"def diff(ex, *args):\\n   ret = $@(ex)$\\n   sb = SympyBridge(ret)\\n   dvars = []\\n   for arg in args:\\n       sbtmp = SympyBridge(arg)\\n       dvars.append( sbtmp.to_sympy() )\\n   sb.from_sympy( sympy.diff( sb.to_sympy(), *dvars ) )\\n   return ret\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 12308609622224851480,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 13996360633394007671,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"A typical example, differentiating with respect to a single variable:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"A typical example, differentiating with respect to a single variable:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 1389897799554975903,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 10741333136404033680,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 10741176021733363837,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\cos(x) A_{\\\\mu}(x) + \\\\sin(x) \\\\partial_{x}(A_{\\\\mu}(x))\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\cos{x} A_{\\\\mu}\\\\left(x\\\\right)\\\\discretionary{}{}{}+\\\\sin{x} \\\\partial_{x}\\\\left(A_{\\\\mu}\\\\left(x\\\\right)\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"ignore_on_import\": true,\n\t\t\t\"source\": \"diff($\\\\sin(x) A_{\\\\mu}(x)$, $x$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 549591636986061462,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 15761683789547886217,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 16581721455931262993,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"-\\\\sin(y) \\\\cos(x)\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}-\\\\,\\\\sin{y} \\\\cos{x}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"ignore_on_import\": true,\n\t\t\t\"source\": \"diff($\\\\sin(x)\\\\cos(y)$, $x$, $y$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 6234003092100779795,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 10150353556520051186,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\algorithm{integrate}{Integrate a definite or indefinite integral.}\\n\\nThis function mimics the SymPy \\\\verb|integrate| function, except that all\\nmathematical expressions need to be Cadabra expressions. Indefinite integration\\nis done by passing an argument which is just an expression, while definite\\nintegration is done by passing a tuple consisting of the integration variable,\\nthe starting point and the end point.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\algorithm{integrate}{Integrate a definite or indefinite integral.}\\n\\nThis function mimics the SymPy \\\\verb|integrate| function, except that all\\nmathematical expressions need to be Cadabra expressions. Indefinite integration\\nis done by passing an argument which is just an expression, while definite\\nintegration is done by passing a tuple consisting of the integration variable,\\nthe starting point and the end point.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 15467993639628642890,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"def integrate(ex1, *args):\\n   ret = ex1.copy()\\n   sb = SympyBridge(ret)\\n   iranges = []\\n   for arg in args:\\n      if isinstance(arg, tuple):\\n          # print(arg)\\n          tmp0 = SympyBridge(arg[0]).to_sympy()\\n          tmp1 = SympyBridge(arg[1]).to_sympy() if isinstance(arg[1], Ex) else arg[1]\\n          tmp2 = SympyBridge(arg[2]).to_sympy() if isinstance(arg[2], Ex) else arg[2]\\n          tpl = ( tmp0, tmp1, tmp2 )\\n          iranges.append(tpl)\\n      else:\\n         tmp = SympyBridge(arg).to_sympy()\\n         iranges.append( tmp )\\n      \\n   # print(sb.to_sympy())\\n   # print(iranges)\\n   sb.from_sympy( sympy.integrate( sb.to_sympy(), *iranges) )\\n   return ret\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 3801120048138997797,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 13060402605556641930,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"The following is an example of a definite integration:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"The following is an example of a definite integration:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 14525293143474443676,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 3923950039630300427,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 17106994130473408151,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \" 9/2 \"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\frac{9}{2}\\\\,\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"ignore_on_import\": true,\n\t\t\t\"source\": \"integrate($x**2 y$, ($x$, 0, 3), ($y$, 0, 1) );\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 2354178610469859185,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 17727729829154494875,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"Here is an indefinite integration:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"Here is an indefinite integration:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 2273072162227922772,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 400193765716168062,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 11825667400944765124,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \" 1/3 (x)**3 y\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\frac{1}{3}\\\\,{x}^{3\\\\,} y\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"ignore_on_import\": true,\n\t\t\t\"source\": \"integrate($x**2$, $x$, $y$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 14437617558705092816,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9935958107203452733,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"Mixed versions are also possible:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"Mixed versions are also possible:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 6556436360376410122,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 13729551692473219465,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 1123541809795391727,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \" 1/4 (y)**2\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\frac{1}{4}\\\\,{y}^{2\\\\,}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"ignore_on_import\": true,\n\t\t\t\"source\": \"integrate($x y$, ($x$, 0, 1), $y$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 15496749977354253222,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 11565454487843639642,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\algorithm{limit}{Take the limit of an expression.}\\n\\nThis function mimics the SymPy \\\\verb|limit| function, except that all\\nmathematical expressions need to be Cadabra expressions.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\algorithm{limit}{Take the limit of an expression.}\\n\\nThis function mimics the SymPy \\\\verb|limit| function, except that all\\nmathematical expressions need to be Cadabra expressions.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 14261374590043911759,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"def limit(ex, v, loc, *args):\\n   ret = $@(ex)$\\n   sbex  = SympyBridge(ret)\\n   sbvar = SympyBridge(v).to_sympy()\\n   sbloc = SympyBridge(loc).to_sympy() if isinstance(loc, Ex) else loc\\n   sbex.from_sympy( sympy.limit( sbex.to_sympy(), sbvar, sbloc ) )\\n   return ret\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 15671206733202710229,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 3270259090712891077,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 9414493474589972675,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"1\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}1\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"ignore_on_import\": true,\n\t\t\t\"source\": \"limit($\\\\sin(x)/x$, $x$, 0);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 4403018984250840411,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 11512538112824887976,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\algorithm{series}{Construct a Taylor series.}\\n\\nThis function mimics the SymPy \\\\verb|series| function, except that all\\nmathematical expressions need to be Cadabra expressions.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\algorithm{series}{Construct a Taylor series.}\\n\\nThis function mimics the SymPy \\\\verb|series| function, except that all\\nmathematical expressions need to be Cadabra expressions.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 1152336426546868041,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"def series(ex, v, loc, order_, *args):\\n   ret = $@(ex)$\\n   sbex  = SympyBridge(ret)\\n   sbvar = SympyBridge(v).to_sympy()\\n   sbloc = SympyBridge(loc).to_sympy() if isinstance(loc, Ex) else loc\\n   tmp = sympy.series( sbex.to_sympy(), sbvar, sbloc, order_ )\\n   #tmp = tmp.replace(\\\"O(\\\", r\\\"\\\\bigO(\\\")\\n   sbex.from_sympy( tmp )\\n   return ret\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 796023660136979964,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 16012079193316282695,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 1666930631384807356,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"1 -  1/6 (x)**2 +  1/120 (x)**4 -  1/5040 (x)**6 + \\\\bigO((x)**8)\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}1\\\\discretionary{}{}{} - \\\\frac{1}{6}\\\\,{x}^{2\\\\,}\\\\discretionary{}{}{}+\\\\frac{1}{120}\\\\,{x}^{4\\\\,}\\\\discretionary{}{}{} - \\\\frac{1}{5040}\\\\,{x}^{6\\\\,}\\\\discretionary{}{}{}+\\\\bigO\\\\left({x}^{8\\\\,}\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"ignore_on_import\": true,\n\t\t\t\"source\": \"q=series($\\\\sin(x)/x$, $x$, 0, 8);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 12877610158835516880,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 16429600809897384787,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 4370193819508955020,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"1 -  1/6 (x)**2 +  1/120 (x)**4 -  1/5040 (x)**6\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}1\\\\discretionary{}{}{} - \\\\frac{1}{6}\\\\,{x}^{2\\\\,}\\\\discretionary{}{}{}+\\\\frac{1}{120}\\\\,{x}^{4\\\\,}\\\\discretionary{}{}{} - \\\\frac{1}{5040}\\\\,{x}^{6\\\\,}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"ignore_on_import\": true,\n\t\t\t\"source\": \"substitute(q, $\\\\bigO(A??) ->0$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 6061726248509003999,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 3476155041445637448,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 83988254890014517,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \" 1/2 2**( 1/2 ) -  1/2 (x -  1/4 \\\\pi) 2**( 1/2 ) + \\\\bigO((x -  1/4 \\\\pi)**2)\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\frac{1}{2}\\\\,\\\\sqrt{2\\\\,}\\\\discretionary{}{}{} - \\\\frac{1}{2}\\\\,\\\\left(x\\\\discretionary{}{}{} - \\\\frac{1}{4}\\\\,\\\\pi\\\\right) \\\\sqrt{2\\\\,}\\\\discretionary{}{}{}+\\\\bigO\\\\left({\\\\left(x\\\\discretionary{}{}{} - \\\\frac{1}{4}\\\\,\\\\pi\\\\right)}^{2\\\\,}\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"ignore_on_import\": true,\n\t\t\t\"source\": \"series($\\\\cos(x)$, $x$, $\\\\pi/4$, 2);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 16349293761953373413,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 10700541688820127695,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\algorithm{factor}{Factorise an expression}\\n\\nThis function mimics the SymPy \\\\verb|factor| function, except that the argument has to be a Cadabra expression.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\algorithm{factor}{Factorise an expression}\\n\\nThis function mimics the SymPy \\\\verb|factor| function, except that the argument has to be a Cadabra expression.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 17538488045608728761,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"def factor(ex):\\n   ret = $@(ex)$\\n   sbex  = SympyBridge(ret)\\n   tmp = sympy.factor( sbex.to_sympy() )\\n   sbex.from_sympy( tmp )\\n   return ret\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 7561547917241467470,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 5406323791023273832,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 1855448709790499107,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"(x + 1) x\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\left(x\\\\discretionary{}{}{}+1\\\\right) x\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"ignore_on_import\": true,\n\t\t\t\"source\": \"ex = factor($ x**2 + x $);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 16786632068897082656,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"\"\n\t\t}\n\t],\n\t\"description\": \"Cadabra JSON notebook format\",\n\t\"flags\": {\n\t\t\"hide_input_cells\": false\n\t},\n\t\"version\": 1.0\n}\n"
  },
  {
    "path": "core/packages/cdb/sympy/solvers.cnb",
    "content": "{\n\t\"cell_id\": 10165666682519261461,\n\t\"cells\": [\n\t\t{\n\t\t\t\"cell_id\": 15790243487325388783,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 117344227491248367,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\package{cdb.sympy.solvers}{Access to Sympy solver functions.}\\n\\nThese are simple wrappers to make Sympy solvers available from Cadabra, using\\nCadabra expressions. There are some differences in the input and output of these\\nfunctions with respect to Sympy, mainly to make things more consistent.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\package{cdb.sympy.solvers}{Access to Sympy solver functions.}\\n\\nThese are simple wrappers to make Sympy solvers available from Cadabra, using\\nCadabra expressions. There are some differences in the input and output of these\\nfunctions with respect to Sympy, mainly to make things more consistent.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 18194547037908567614,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 11537546742094706282,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\algorithm{dsolve(Ex: equation(s), Ex: function(s)) -> Ex}{Solve (system of) ordinary differential equation(s).}\\n\\nGiven a single differential equation or a system of differential equations, return the solution. The second argument\\nis optional; if not given, \\\\algo{dsolve} will try to figure out the unknown(s). Functions can\\nhave implicit dependence on the independent variable, as in the example below, where $f$ depends on $x$\\nbut that dependence is not spelled out again explicitly in the equation.\\n\\nNote that since this is backed by \\\\verb|sympy.dsolve|, and the latter is rather buggy for systems\\nof differential equations, do not expect miracles in that case.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\algorithm{dsolve(Ex: equation(s), Ex: function(s)) -> Ex}{Solve (system of) ordinary differential equation(s).}\\n\\nGiven a single differential equation or a system of differential equations, return the solution. The second argument\\nis optional; if not given, \\\\algo{dsolve} will try to figure out the unknown(s). Functions can\\nhave implicit dependence on the independent variable, as in the example below, where $f$ depends on $x$\\nbut that dependence is not spelled out again explicitly in the equation.\\n\\nNote that since this is backed by \\\\verb|sympy.dsolve|, and the latter is rather buggy for systems\\nof differential equations, do not expect miracles in that case.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 8589228160107610297,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"import sympy\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 11180798987284830538,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"def dsolve(ex, obj=None):\\n   # FIXME: If ex is a list, convert to an Ex when it is pulled\\n   # into an expression like below!\\n   ret = $@(ex)$\\n   sb = SympyBridge(ret)\\n   if obj is None:\\n      sb.from_sympy( sympy.dsolve( sb.to_sympy() ) )\\n   else:\\n      sbo = SympyBridge(obj)\\n      sb.from_sympy( sympy.dsolve( sb.to_sympy(), sbo.to_sympy() ) )\\n   return ret\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 497397197071890198,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 11971036040051999520,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property Coordinate attached to~}x.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 5099464181795568820,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property Depends attached to~}\\\\left[f, \\\\discretionary{}{}{}g\\\\right].\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 2854117650171105912,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property PartialDerivative attached to~}\\\\backslash\\\\texttt{partial}\\\\{\\\\#\\\\}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 13636765245901389818,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 8535022108651334760,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\partial_{x x}(f) + \\\\partial_{x}(f) = \\\\sin(x)\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\partial_{x x}{f}\\\\discretionary{}{}{}+\\\\partial_{x}{f} = \\\\sin{x}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 17317240651681688211,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 5271676865441383344,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"f = C1 + \\\\exp(-x) C2 -  1/2 \\\\sin(x) -  1/2 \\\\cos(x)\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}f = {C_{1}}\\\\discretionary{}{}{}+\\\\exp\\\\left(-\\\\,x\\\\right) {C_{2}}\\\\discretionary{}{}{} - \\\\frac{1}{2}\\\\,\\\\sin{x}\\\\discretionary{}{}{} - \\\\frac{1}{2}\\\\,\\\\cos{x}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"ignore_on_import\": true,\n\t\t\t\"source\": \"x::Coordinate;\\n{f,g}::Depends(x);\\n\\\\partial{#}::PartialDerivative;\\nex:= \\\\partial_{x x}{f} + \\\\partial_{x}{f} = \\\\sin(x);\\nsol=dsolve(ex, $f$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 4985987136595864320,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 4568106667759646646,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 13426020657821151832,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\partial_{x x}((C1 + \\\\exp(-x) C2 -  1/2 \\\\sin(x) -  1/2 \\\\cos(x))) + \\\\partial_{x}((C1 + \\\\exp(-x) C2 -  1/2 \\\\sin(x) -  1/2 \\\\cos(x))) = \\\\sin(x)\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\partial_{x x}\\\\left({C_{1}}\\\\discretionary{}{}{}+\\\\exp\\\\left(-\\\\,x\\\\right) {C_{2}}\\\\discretionary{}{}{} - \\\\frac{1}{2}\\\\,\\\\sin{x}\\\\discretionary{}{}{} - \\\\frac{1}{2}\\\\,\\\\cos{x}\\\\right)\\\\discretionary{}{}{}+\\\\partial_{x}\\\\left({C_{1}}\\\\discretionary{}{}{}+\\\\exp\\\\left(-\\\\,x\\\\right) {C_{2}}\\\\discretionary{}{}{} - \\\\frac{1}{2}\\\\,\\\\sin{x}\\\\discretionary{}{}{} - \\\\frac{1}{2}\\\\,\\\\cos{x}\\\\right) = \\\\sin{x}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"ignore_on_import\": true,\n\t\t\t\"source\": \"substitute(ex, sol);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 6058106723051096452,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 17422987312986399839,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 14317938847461642013,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\sin(x) = \\\\sin(x)\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\sin{x} = \\\\sin{x}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"ignore_on_import\": true,\n\t\t\t\"source\": \"map_sympy(ex, \\\"simplify\\\");\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 9955417298432415316,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 4251291386534782263,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 18082648744036411038,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"{\\\\partial_{x}(f) = f g \\\\sin(x), \\\\partial_{x}(g) = (g)**2 \\\\sin(x)}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\left[\\\\partial_{x}{f} = f g \\\\sin{x}, \\\\discretionary{}{}{}\\\\partial_{x}{g} = {g}^{2\\\\,} \\\\sin{x}\\\\right]\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"ignore_on_import\": true,\n\t\t\t\"source\": \"st:= { \\\\partial_{x}{f} = f g \\\\sin(x), \\\\partial_{x}{g} = g**2 \\\\sin(x) };\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 17502079193295596278,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 8586148297137285798,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 18203959768896801723,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"{f = -\\\\exp(C1) (\\\\exp(C1) C2-\\\\cos(x))**(-1), g = -(C1-\\\\cos(x))**(-1)}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\left[f = -\\\\,\\\\exp\\\\left({C_{1}}\\\\right) {\\\\left(\\\\exp\\\\left({C_{1}}\\\\right) {C_{2}}\\\\discretionary{}{}{}-\\\\,\\\\cos{x}\\\\right)}^{-\\\\,1}, \\\\discretionary{}{}{}g = -\\\\,{\\\\left({C_{1}}\\\\discretionary{}{}{}-\\\\,\\\\cos{x}\\\\right)}^{-\\\\,1}\\\\right]\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"ignore_on_import\": true,\n\t\t\t\"source\": \"dsolve(st);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 11970634058257249996,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 10103860588900185699,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\algorithm{linsolve(Ex: equations, Ex: objects) -> Ex}{Solve a linear system for unknowns.}\\n\\nGiven an expression containing one or more linear equations, and an second expression containing\\nthe variables to solve for, determine the solutions. Returns list with one element, which is a\\nlist of substitution rules for the variables that have been solved for (the output is a nested\\nlist to ensure that it is similar to the output of \\\\algo{nonlinsolve}, which can return more than one solution set).\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\algorithm{linsolve(Ex: equations, Ex: objects) -> Ex}{Solve a linear system for unknowns.}\\n\\nGiven an expression containing one or more linear equations, and an second expression containing\\nthe variables to solve for, determine the solutions. Returns list with one element, which is a\\nlist of substitution rules for the variables that have been solved for (the output is a nested\\nlist to ensure that it is similar to the output of \\\\algo{nonlinsolve}, which can return more than one solution set).\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 17888835071658719091,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"def linsolve(exs, objs):\\n   ret = $@(exs)$\\n   obl = $@(objs)$\\n   if ret.head()!=r\\\"\\\\comma\\\":\\n      ret = $\\\\comma{ @(ret) }$\\n   if obl.head()!=r\\\"\\\\comma\\\":\\n      obl = $\\\\comma{ @(obl) }$\\n   sb = SympyBridge(ret)\\n   sb.from_sympy( sympy.linsolve( sb.to_sympy(), obl._sympy_()) )\\n   ret;\\n   nret = $\\\\comma{}$\\n   for i in range(len(ret[0])):\\n      tmpv=obl[i]\\n      tmps=ret[0][i]\\n      nret.top().append_child($ @(tmpv) -> @(tmps) $)\\n   ret=$ \\\\comma{ @(nret) }$\\n   return ret\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 3825114940942753284,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 13367518239337213466,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 17081387208087638311,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"x + a = 0\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}x\\\\discretionary{}{}{}+a = 0\\\\,\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 7109351760917556632,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 1720716397702529034,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"{{-a}}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\left[\\\\left[-\\\\,a\\\\right]\\\\right]\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 12396475032184992506,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 14731485227261171027,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"{{x -> -a}}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\left[\\\\left[x \\\\rightarrow -\\\\,a\\\\right]\\\\right]\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"ignore_on_import\": true,\n\t\t\t\"source\": \"ex:=  x + a = 0;\\nsol=linsolve(ex, $x$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 6176825001521917917,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 198037658084628295,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 16575753805642399862,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"0 = 0\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}0\\\\, = 0\\\\,\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"ignore_on_import\": true,\n\t\t\t\"source\": \"substitute(ex, sol[0]);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 9426120572392451421,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 3818775303993614347,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 5337358205483137739,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"{x + 1 = 0, y +  4/3 x + 2a = 0}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\left[x\\\\discretionary{}{}{}+1 = 0\\\\,, \\\\discretionary{}{}{}y\\\\discretionary{}{}{}+\\\\frac{4}{3}\\\\,x\\\\discretionary{}{}{}+2\\\\,a = 0\\\\,\\\\right]\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 11902778502025647670,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 17095935178189177560,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"{{-1,  4/3 -2a}}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\left[\\\\left[-\\\\,1, \\\\discretionary{}{}{}\\\\frac{4}{3}\\\\,\\\\discretionary{}{}{}-2\\\\,a\\\\right]\\\\right]\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 1794082835830977518,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 16164563890887887189,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"{{x -> -1, y ->  4/3 -2a}}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\left[\\\\left[x \\\\rightarrow -\\\\,1, \\\\discretionary{}{}{}y \\\\rightarrow \\\\frac{4}{3}\\\\,\\\\discretionary{}{}{}-2\\\\,a\\\\right]\\\\right]\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"ignore_on_import\": true,\n\t\t\t\"source\": \"ex:= x + 1 = 0, y + 4/3 x + 2 a = 0;\\nsol=linsolve(ex, $x,y$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 16125223527973836266,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 1172967512044477501,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 4244812262178743007,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"{0 = 0, 0 = 0}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\left[0\\\\, = 0\\\\,, \\\\discretionary{}{}{}0\\\\, = 0\\\\,\\\\right]\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"ignore_on_import\": true,\n\t\t\t\"source\": \"substitute(ex, sol[0]);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 7353939443993816784,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9953383820951286777,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 15642781551709841683,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"x A_{m} C^{m} + b D_{n p} G^{n p} = 0\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}x A_{m} C^{m}\\\\discretionary{}{}{}+b D_{n p} G^{n p} = 0\\\\,\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 12738663009888911183,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 12794083091240205511,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"{{-G^{n p} D_{n p} (C^{m})**(-1) (A_{m})**(-1) b}}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\left[\\\\left[-\\\\,G^{n p} D_{n p} {C^{m}}^{-\\\\,1} {A_{m}}^{-\\\\,1} b\\\\right]\\\\right]\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 2973711497616083395,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"error\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}RuntimeError: Power with free indices not allowed.\\n\\nAt:\\n  <string>(17): linsolve\\n  Notebook Cell (Line 4): _ = linsolve(ex, Ex('x', False))\\n\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"ignore_on_import\": true,\n\t\t\t\"source\": \"ex:= x A_{m} C^{m} + b D_{n p} G^{n p} = 0;\\nlinsolve(ex, $x$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 10231998506255394040,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 5465144330139214481,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 13932574290516155813,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"x A_{m} C^{m} + b D_{n p} G^{n p} = 0\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}x A_{m} C^{m}+b D_{n p} G^{n p} = 0\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 4663387022186441696,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 13913668299812041980,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"{{x -> -b D_{n p} G^{n p} (A_{m} C^{m})**(-1)}}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\left[\\\\left[x \\\\rightarrow -b D_{n p} G^{n p} {\\\\left(A_{m} C^{m}\\\\right)}^{-1}\\\\right]\\\\right]\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"ignore_on_import\": true,\n\t\t\t\"source\": \"ex:= x A_{m} C^{m} + b D_{n p} G^{n p} = 0;\\nlinsolve(ex, $x$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 15662243220303454349,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 17001975289188242795,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\algorithm{nonlinsolve}{Solve a system of non-linear equations.}\\n\\nGiven an expression containing one or more linear equations, and an second expression containing\\nthe variables to solve for, determine the solutions. Returns a substitution rule or a list of\\nsubstitution rules for the variables that have been solved for.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\algorithm{nonlinsolve}{Solve a system of non-linear equations.}\\n\\nGiven an expression containing one or more linear equations, and an second expression containing\\nthe variables to solve for, determine the solutions. Returns a list of substitution rules for the \\nvariables that have been solved for.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 911768519859269492,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"from sympy.solvers.solveset import nonlinsolve as sympy_nonlinsolve\\n\\ndef nonlinsolve(exs, objs):\\n   ret = $@(exs)$\\n   obl = $@(objs)$\\n   if ret.head()!=r\\\"\\\\comma\\\":\\n      ret = $\\\\comma{ @(ret) }$\\n   if obl.head()!=r\\\"\\\\comma\\\":\\n      obl = $\\\\comma{ @(obl) }$\\n   sb = SympyBridge(ret)\\n   qq = sympy_nonlinsolve( sb.to_sympy(), objs._sympy_()) \\n   sb.from_sympy( sympy_nonlinsolve( sb.to_sympy(), objs._sympy_() ) )\\n   # The result is a list of solutions. Turn this into a list of\\n   # rules.\\n   nret = $\\\\comma{}$\\n   for i in range(len(ret)):\\n      tsol=$\\\\comma{}$\\n      for v in range(len(obl)):\\n         tmpv=obl[v]\\n         tmps=ret[i][v]\\n         tsol.top().append_child($ @(tmpv) -> @(tmps) $)\\n      nret.top().append_child(tsol)\\n   ret=nret\\n   return ret\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 4737965800086152437,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 17726577959155713331,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 16867347018516536039,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"(x)**2-1\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}{x}^{2\\\\,}\\\\discretionary{}{}{}-\\\\,1\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 7049263081588706730,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 14244270221802171944,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"{{x -> -1}, {x -> 1}}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\left[\\\\left[x \\\\rightarrow -\\\\,1\\\\right], \\\\discretionary{}{}{}\\\\left[x \\\\rightarrow 1\\\\right]\\\\right]\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"ignore_on_import\": true,\n\t\t\t\"source\": \"ex:= x**2-1;\\nsol=nonlinsolve(ex, $x$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 9068678982032793579,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 1679926337173325181,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 183493805300469498,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"0\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}0\\\\,\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"ignore_on_import\": true,\n\t\t\t\"source\": \"substitute(ex, sol[0])\\nsimplify(ex);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 14972222131526038404,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 10183612661385892278,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 7592274207501744189,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"(x)**2 + A_{m} B^{m} = 0\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}{x}^{2\\\\,}\\\\discretionary{}{}{}+A_{m} B^{m} = 0\\\\,\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9508219180757457848,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 6700441174221915549,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"{{x -> (-B^{m} A_{m})**( 1/2 )}, {x -> -(-B^{m} A_{m})**( 1/2 )}}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\left[\\\\left[x \\\\rightarrow \\\\sqrt{-\\\\,B^{m} A_{m}}\\\\right], \\\\discretionary{}{}{}\\\\left[x \\\\rightarrow -\\\\,\\\\sqrt{-\\\\,B^{m} A_{m}}\\\\right]\\\\right]\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"ignore_on_import\": true,\n\t\t\t\"source\": \"ex:= x**2 + A_{m} B^{m} = 0;\\nsol=nonlinsolve(ex, $x$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 3008341142464299938,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 18049567145713059104,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 877619584076577222,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"{(x)**2-1 = 0, (y)**2-2 = 0}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\left[{x}^{2\\\\,}\\\\discretionary{}{}{}-\\\\,1 = 0\\\\,, \\\\discretionary{}{}{}{y}^{2\\\\,}\\\\discretionary{}{}{}-2\\\\, = 0\\\\,\\\\right]\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 17361915992502167480,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 5211272471867728713,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"{{x -> -1, y -> 2**( 1/2 )}, {x -> 1, y -> 2**( 1/2 )}, {x -> -1, y -> -2**( 1/2 )}, {x -> 1, y -> -2**( 1/2 )}}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\left[\\\\left[x \\\\rightarrow -\\\\,1, \\\\discretionary{}{}{}y \\\\rightarrow \\\\sqrt{2\\\\,}\\\\right], \\\\discretionary{}{}{}\\\\left[x \\\\rightarrow 1, \\\\discretionary{}{}{}y \\\\rightarrow \\\\sqrt{2\\\\,}\\\\right], \\\\discretionary{}{}{}\\\\left[x \\\\rightarrow -\\\\,1, \\\\discretionary{}{}{}y \\\\rightarrow -\\\\,\\\\sqrt{2\\\\,}\\\\right], \\\\discretionary{}{}{}\\\\left[x \\\\rightarrow 1, \\\\discretionary{}{}{}y \\\\rightarrow -\\\\,\\\\sqrt{2\\\\,}\\\\right]\\\\right]\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"ignore_on_import\": true,\n\t\t\t\"source\": \"ex:= { x**2 - 1 = 0, y**2 - 2 =0 }; \\nnonlinsolve(ex, $x,y$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 6913007854354215623,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 11588338536455156616,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\algorithm{solve}{Solve an equation or system of equations.}\\n\\nGiven an expression containing one or more equations, and an second expression containing\\nthe variables to solve for, determine the solutions. Returns a list of substitution rules for the \\nvariables that have been solved for.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\algorithm{solve}{Solve an equation or system of equations.}\\n\\nGiven an expression containing one or more equations, and an second expression containing\\nthe variables to solve for, determine the solutions. Returns a list of substitution rules for the \\nvariables that have been solved for.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 6666887454489559442,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"from sympy import solve as sympy_solve\\n\\ndef solve(exs, objs):\\n   ret = $@(exs)$\\n   obl = $@(objs)$\\n   if ret.head()!=r\\\"\\\\comma\\\":\\n      ret = $\\\\comma{ @(ret) }$\\n   if obl.head()!=r\\\"\\\\comma\\\":\\n      obl = $\\\\comma{ @(obl) }$\\n   sb = SympyBridge(ret)\\n   sb.from_sympy( sympy_solve( sb.to_sympy(), objs._sympy_()) )\\n   # The result is a list of solutions. Turn this into a list of\\n   # rules.\\n   nret = $\\\\comma{}$\\n   for i in range(len(ret)):\\n      tsol=$\\\\comma{}$\\n      for v in range(len(obl)):\\n         tmpv=obl[v]\\n         tmps=ret[i][v]\\n         tsol.top().append_child($ @(tmpv) -> @(tmps) $)\\n      nret.top().append_child(tsol)\\n   ret=nret\\n   return ret\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 13789713952413725514,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 13932257768961801995,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 1522347131361413068,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"{{x -> -(y)**( 1/2 )}, {x -> (y)**( 1/2 )}}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\left[\\\\left[x \\\\rightarrow -\\\\,\\\\sqrt{y}\\\\right], \\\\discretionary{}{}{}\\\\left[x \\\\rightarrow \\\\sqrt{y}\\\\right]\\\\right]\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"ignore_on_import\": true,\n\t\t\t\"source\": \"solve($x**2=y$, $x$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 10348235580831042576,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"\"\n\t\t}\n\t],\n\t\"description\": \"Cadabra JSON notebook format\",\n\t\"flags\": {\n\t\t\"hide_input_cells\": false\n\t},\n\t\"version\": 1.0\n}\n"
  },
  {
    "path": "core/packages/cdb/utils/_algorithm.cc",
    "content": "#include <pybind11/pybind11.h>\n#include \"pythoncdb/py_algorithms.hh\"\n#include \"pythoncdb/py_kernel.hh\"\n#include \"Algorithm.hh\"\n\nusing namespace cadabra;\n\n// Virtual base class which uses ExNode instead of Ex::iterator so that\n// it can be extended in Python\nclass PyAlgorithm : public Algorithm\n{\npublic:\n\tPyAlgorithm(Ex_ptr ex)\n\t\t: Algorithm(*get_kernel_from_scope(), *ex)\n\t\t, ex(ex)\n\t{\n\n\t}\n\n\tresult_t py_apply_generic(bool deep, bool repeat, unsigned int depth)\n\t{\n\t\treturn apply_generic(deep, repeat, depth);\n\t}\n\n\tresult_t py_apply_pre_order(bool repeat)\n\t{\n\t\treturn apply_pre_order(repeat);\n\t}\n\n\tvirtual bool py_can_apply(ExNode node) = 0;\n\n\tbool can_apply(Ex::iterator it) override\n\t{\n\t\tExNode node(*get_kernel_from_scope(), ex);\n\t\tnode.ex = ex;\n\t\tnode.topit = it;\n\t\tnode.it = it;\n\t\tnode.stopit = it;\n\t\tnode.stopit.skip_children();\n\t\t++node.stopit;\n\t\tnode.update(true);\n\n\t\treturn py_can_apply(node);\n\t}\n\n\tvirtual Algorithm::result_t py_apply(ExNode node) = 0;\n\n\tAlgorithm::result_t apply(Ex::iterator& it) override\n\t{\n\t\tExNode node(*get_kernel_from_scope(), ex);\n\t\tnode.ex = ex;\n\t\tnode.topit = it;\n\t\tnode.it = it;\n\t\tnode.stopit = it;\n\t\tnode.stopit.skip_children();\n\t\t++node.stopit;\n\t\tnode.update(true);\n\n\t\tauto res = py_apply(node);\n\t\tit = node.it;\n\t\treturn res;\n\t}\n\nprivate:\n\tEx_ptr ex;\n};\n\n// Trampoline class which allows extending the virtual base class PyAlgorithm\n// inside Python\nclass PyAlgorithmTrampoline : public PyAlgorithm\n{\npublic:\n\tusing PyAlgorithm::PyAlgorithm;\n\n\tbool py_can_apply(ExNode node) override {\n\t\tPYBIND11_OVERRIDE_PURE_NAME(\n\t\t\tbool,\n\t\t\tPyAlgorithm,\n\t\t\t\"can_apply\",\n\t\t\tpy_can_apply,\n\t\t\tnode\n\t\t);\n\t}\n\n\tAlgorithm::result_t py_apply(ExNode node) override {\n\t\tPYBIND11_OVERRIDE_PURE_NAME(\n\t\t\tAlgorithm::result_t,\n\t\t\tPyAlgorithm,\n\t\t\t\"apply\",\n\t\t\tpy_apply,\n\t\t\tnode\n\t\t);\n\t}\n};\n\n\nPYBIND11_MODULE(_algorithm, m)\n{\n\tnamespace py = pybind11;\n\n\tpy::class_<PyAlgorithm, PyAlgorithmTrampoline>(m, \"Algorithm\")\n\t\t.def(py::init<Ex_ptr>())\n\t\t.def(\"can_apply\", &PyAlgorithm::py_can_apply)\n\t\t.def(\"apply\", &PyAlgorithm::py_apply)\n\t\t.def(\"apply_generic\", &PyAlgorithm::py_apply_generic,\n\t\t\tpy::arg(\"deep\") = true, py::arg(\"repeat\") = false, py::arg(\"depth\") = 0)\n\t\t.def(\"apply_pre_order\", &PyAlgorithm::py_apply_pre_order, py::arg(\"repeat\") = false);\n\n\tm.def(\"apply_algo_base\", apply_algo_base<PyAlgorithm>);\n}\n"
  },
  {
    "path": "core/packages/cdb/utils/develop.cnb",
    "content": "{\n\t\"cell_id\": 7900896013554414286,\n\t\"cells\": [\n\t\t{\n\t\t\t\"cell_id\": 3008518946232599177,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 798500217262993049,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\package{cdb.utils.develop}{Helper functions to aid development, debugging and testing}\\n\\nThis package contains some standardised functionality to aid in development of library code and Python algorithms\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\package{cdb.utils.develop}{Helper functions to aid development, debugging and testing}\\n\\nThis package contains some standardised functionality to aid in development of library code and Python algorithms\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 13348113113731925581,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"import inspect\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 13041134632829120942,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 17870137200133729598,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\algorithm{class Algorithm(ex: Ex)}{Base class for user defined tree-traversal algorithms}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\algorithm{class Algorithm(ex: Ex)}{Base class for user defined tree-traversal algorithms}\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 1319220678577630750,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"from cdb.utils._algorithm import Algorithm\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 13334862458884777602,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"from cdb.utils._algorithm import apply_algo_base as _apply_algo_base\\n\\ndef _cast_algo(apply, can_apply = lambda node: True):\\n\\tif len(inspect.getfullargspec(apply).args) != 1:\\n\\t\\traise TypeError(\\\"Failed to convert function to algorithm: function must only take one 'node' parameter\\\")\\n\\tif len(inspect.getfullargspec(can_apply).args) != 1:\\n\\t\\traise TypeError(\\\"Failed to convert function to algorithm: predicate must only take one 'node' parameter\\\")\\n\\treturn type(apply.__name__, (Algorithm, ), { \\n\\t\\t\\\"can_apply\\\": lambda self, node: can_apply(node), \\n\\t\\t\\\"apply\\\": lambda self, node: apply(node),\\n\\t\\t\\\"__doc__\\\": apply.__doc__\\n\\t})\\n\\ndef _create_algo(cls, pre_order):\\n\\tif Algorithm not in cls.__bases__:\\n\\t\\traise TypeError(\\\"Algorithm must derive from Algorithm type\\\")\\n\\tdef wrapper(ex, *args, deep=True, repeat=False, depth=0, **kwargs):\\n\\t\\tx = cls(ex, *args, **kwargs)\\n\\t\\treturn _apply_algo_base(x, ex, deep, repeat, depth, pre_order)\\n\\n\\t# Generate correct meta-information\\n\\twrapper.__name__ = cls.__name__\\n\\twrapper.__doc__ = cls.__doc__\\n\\t# Get argument list of Algorithm constructor\\n\\ttry:\\n\\t\\tparameters = list(inspect.signature(cls\\t.__init__).parameters.values())[1:]\\n\\texcept:\\n\\t\\tparameters = [ inspect.Parameter(\\\"ex\\\", inspect.Parameter.POSITIONAL_OR_KEYWORD) ]\\n\\t# Parameters of apply_algo_base\\n\\talgo_parameters = [\\n\\t\\tinspect.Parameter(\\\"deep\\\", inspect.Parameter.KEYWORD_ONLY, default=True),\\n\\t\\tinspect.Parameter(\\\"repeat\\\", inspect.Parameter.KEYWORD_ONLY, default=False),\\n\\t\\tinspect.Parameter(\\\"depth\\\", inspect.Parameter.KEYWORD_ONLY, default=0) ]\\n\\t# If parameters has a **kwargs at the end, algo_parameters must be inserted before this\\n\\tif parameters[-1].kind == inspect.Parameter.VAR_KEYWORD:\\n\\t\\twrapper.__signature__ = inspect.Signature(parameters[:-1] + algo_parameters + parameters[-1:])\\n\\telse:\\n\\t\\twrapper.__signature__ = inspect.Signature(parameters + algo_parameters)\\n\\treturn wrapper\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 2421359616022599147,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 16353153281984723823,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\algorithm{algo(pre_order: bool = False, pred: function = (node) -> True) -> function}{Decorator for creating tree-traversal algorithms}\\n\\nThis decorator takes a function or class derived from \\\\verb|cdb.utils.develop.Algorithm| and creates a tree-traversal algorithm which\\niterates through an expression applying the function or \\\\verb|apply| method of a class to each node in turn. It optionally takes the\\narguments \\\\verb|pre_order| which determines the order of traversal of the tree (\\\\verb|False| reverts to post-order iteration) and\\n\\\\verb|pred| which, if decorating a function, will be called at each node in the tree and the function only applied if the predicate\\nreturns true. If an \\\\verb|Algorithm| class is instead decorated, the behaviour of \\\\verb|pred| is implemented by the \\\\verb|can_apply|\\nmethod which must be overloaded\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\algorithm{algo(pre_order: bool = False, pred: function = (node) -> True) -> function}{Decorator for creating tree-traversal algorithms}\\n\\nThis decorator takes a function or class derived from \\\\verb|cdb.utils.develop.Algorithm| and creates a tree-traversal algorithm which\\niterates through an expression applying the function or \\\\verb|apply| method of a class to each node in turn. It optionally takes the\\narguments \\\\verb|pre_order| which determines the order of traversal of the tree (\\\\verb|False| reverts to post-order iteration) and\\n\\\\verb|pred| which, if decorating a function, will be called at each node in the tree and the function only applied if the predicate\\nreturns true. If an \\\\verb|Algorithm| class is instead decorated, the behaviour of \\\\verb|pred| is implemented by the \\\\verb|can_apply|\\nmethod which must be overloaded\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 8704625228430657301,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"def algo(*args, **kwargs):\\n\\t# Detect if we are called without arguments and therefore\\n\\t# get a single class or function instance. In this instance\\n\\t# default to post order and a predicate always returning true\\n\\tif len(args) == 1 and len(kwargs) == 0:\\n\\t\\tif inspect.isfunction(args[0]):\\n\\t\\t\\tcls = _cast_algo(args[0])\\n\\t\\telif inspect.isclass(args[0]):\\n\\t\\t\\tcls = args[0]\\n\\t\\telse:\\n\\t\\t\\traise ValueError(\\\"algo does not accept positional arguments\\\")\\n\\t\\treturn _create_algo(cls, pre_order=False)\\n\\n\\t# Otherwise we expect an empty *args and collect the keyword arguments\\n\\tif len(args) != 0:\\n\\t\\traise ValueError(\\\"algo does not accept positional arguments\\\")\\n\\tpre_order = kwargs.get('pre_order', False)\\n\\tpred = kwargs.get('pred', lambda node: True)\\n\\n\\t# Then we return a decorator with no arguments which will get applied\\n\\tdef unwrapped(arg):\\n\\t\\tif inspect.isfunction(arg):\\n\\t\\t\\tcls = _cast_algo(arg, pred)\\n\\t\\telse:\\n\\t\\t\\tif 'pred' in kwargs:\\n\\t\\t\\t\\traise ValueError(\\\"pred supplied to algo decorator, but this does not apply to class being decorated\\\")\\n\\t\\t\\tcls = arg\\n\\t\\treturn _create_algo(cls, pre_order=pre_order)\\n\\treturn unwrapped\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 2405738556624578142,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 15761994739137138802,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 17415156100168742565,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"A^{\\\\mu} + B^{\\\\mu}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}A^{\\\\mu}+B^{\\\\mu}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 15144194947899395553,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"output\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}Help on function switch_indices in module __main__:\\n\\nswitch_indices(ex, *, deep=True, repeat=False, depth=0)\\n    Switch positions on all indices\\n\\n\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"ignore_on_import\": true,\n\t\t\t\"source\": \"@algo\\ndef switch_indices(node):\\n\\t\\\"Switch positions on all indices\\\"\\n\\tif node.parent_rel == parent_rel_t.sub:\\n\\t\\tnode.parent_rel = parent_rel_t.super\\n\\t\\treturn result_t.changed\\n\\tif node.parent_rel == parent_rel_t.super:\\n\\t\\tnode.parent_rel = parent_rel_t.sub\\n\\t\\treturn result_t.changed\\n\\treturn result_t.unchanged\\n\\n# also takes optional 'deep', 'repeat' and 'depth' arguments\\nswitch_indices($A_{\\\\mu} + B_{\\\\mu}$);\\nhelp(switch_indices)\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 9340011096170931285,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 5850074756591759657,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 9620504524171758578,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"2y\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}2y\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 17850582158135921593,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"output\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}Help on function x_to_y in module __main__:\\n\\nx_to_y(ex, *, deep=True, repeat=False, depth=0)\\n\\n\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"ignore_on_import\": true,\n\t\t\t\"source\": \"@algo(pre_order=True, pred=lambda node: node.name == 'x')\\ndef x_to_y(node):\\n\\tnode.name = 'y'\\n\\treturn result_t.changed\\n\\nx_to_y($x + y$);\\nhelp(x_to_y)\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 15634397355979861807,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 14537821031780487327,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 3417601803473011010,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"2t_{\\\\mu}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}2t_{\\\\mu}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 17754394564063656935,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"output\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}Help on function a_to_b in module __main__:\\n\\na_to_b(ex, a, b, *args, deep=True, repeat=False, depth=0, **kwargs)\\n\\n\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"ignore_on_import\": true,\n\t\t\t\"source\": \"@algo\\nclass a_to_b(Algorithm):\\n\\tdef __init__(self, ex, a, b, *args, **kwargs):\\n\\t\\tAlgorithm.__init__(self, ex)\\n\\t\\tself.a, self.b = a, b\\n\\t\\n\\tdef can_apply(self, node):\\n\\t\\treturn node.name == self.a.head()\\n\\n\\tdef apply(self, node):\\n\\t\\tnode.name = self.b.head()\\n\\t\\treturn result_t.changed\\n\\na_to_b($s_{\\\\mu} + t_{\\\\mu}$, $s_{\\\\mu}$, $t_{\\\\mu}$);\\nhelp(a_to_b)\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 10135200674124616797,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"ignore_on_import\": true,\n\t\t\t\"source\": \"try:\\n\\t@algo\\n\\tdef function_with_too_many_arguments(a,b,c):\\n\\t\\tpass\\n\\traise AssertionError(\\\"TypeError not raised\\\")\\nexcept TypeError:\\n\\tpass\\n\\ntry:\\n\\t@algo\\n\\tclass does_not_inherit_from_Algorithm:\\n\\t\\tpass\\n\\traise AssertionError(\\\"TypeError not raised\\\")\\nexcept TypeError:\\n\\tpass\\n\\ntry:\\n\\t@algo(pred=lambda n: n.name == 'x')\\n\\tclass does_not_need_pred(Algorithm):\\n\\t\\tdef can_apply(self,node): return n.name =='x'\\n\\t\\tdef apply(self,node): return result_t.unchanged\\n\\traise AssertionError(\\\"ValueError not raised\\\")\\nexcept ValueError:\\n\\tpass\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 15845148038835594810,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 8739236297038682978,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\algorithm{time_algo(algo: function, ex: Ex, *args: <mixed>, iterations: int = 100) -> float}{Simple function to time the execution of an algorithm with given inputs.}\\n\\nThe arguments in *args are passed directly, but ex is copied before each\\ninvocation and so remains unmodified.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\algorithm{time_algo(algo: function, ex: Ex, *args: <mixed>, iterations: int = 100) -> float}{Simple function to time the execution of an algorithm with given inputs.}\\n\\nThe arguments in *args are passed directly, but ex is copied before each\\ninvocation and so remains unmodified.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 5937432672654218849,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"from datetime import timedelta\\n\\ndef time_algo(algo, ex, *args, iterations=100):\\n\\ts = Stopwatch()\\n\\tfor i in range(iterations):\\n\\t\\ttmp := @(ex);\\n\\t\\ts.start()\\n\\t\\talgo(tmp, *args)\\n\\t\\ts.stop()\\n\\treturn timedelta(seconds=s.seconds()/iterations, microseconds=s.useconds()/iterations)\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 17198486848786764579,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 6295148871247203489,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"verbatim\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}0:00:00.000875\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"ignore_on_import\": true,\n\t\t\t\"source\": \"time_algo(substitute, $a + b$, $a -> b$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 12791856048123301106,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 13532413926824958590,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"verbatim\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}0:00:00.000493\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"ignore_on_import\": true,\n\t\t\t\"source\": \"def times_2(ex):\\n\\treturn ex * $2$\\n\\ntime_algo(times_2, $a$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 15332315745938100730,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 8935506242999741244,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\algorithm{CadabraTestError}{Exception derived from AssertionError raised by testing functions when an assertion fails}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\algorithm{CadabraTestError}{Exception derived from AssertionError raised by testing functions when an assertion fails}\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 11180569447504398263,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"class CadabraTestError(AssertionError):\\n\\tpass\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 3479765664248597757,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 11588087231457837709,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\algorithm{test_algo(expected: Ex, throw_on_fail: bool)}{Decorator to aid defining unit tests for algorithms.}\\n\\nThis\\tadds the boilerplate code and adds an assert for the test.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\algorithm{test_algo(expected: Ex, throw_on_fail: bool)}{Decorator to aid defining unit tests for algorithms.}\\n\\nThis\\tadds the boilerplate code and adds an assert for the test.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 15123798302514262900,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"def test_algo(expected, throw_on_fail=False):\\n\\tdef decorator(func):\\n\\t\\tdef wrapper(*args, **kwargs):\\n\\t\\t\\tres = func(*args, **kwargs)\\n\\t\\t\\tif res == expected:\\n\\t\\t\\t\\tprint(func.__name__ + \\\" passed\\\")\\n\\t\\t\\telse:\\n\\t\\t\\t\\tprint(func.__name__ + \\\" FAILED\\\")\\n\\t\\t\\t\\tprint(\\\"  Expected: \\\" + str(expected))\\n\\t\\t\\t\\tprint(\\\"  Produced: \\\" + str(res))\\n\\t\\t\\t\\tif throw_on_fail: raise CadabraTestError\\n\\t\\t\\treturn res\\n\\t\\treturn wrapper\\n\\treturn decorator\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 2554539507442301090,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 4855635716783607432,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"output\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}sort_sum_test01 passed\\nsort_sum_test02 FAILED\\n  Expected: a + b\\n  Produced: a + c\\nsort_sum_test03 FAILED\\n  Expected: a + b\\n  Produced: a + c\\nRaised CadabraTestError\\n\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"ignore_on_import\": true,\n\t\t\t\"source\": \"@test_algo($a + b + c$)\\ndef sort_sum_test01():\\n\\tex := b + a + c.\\n\\treturn sort_sum(ex)\\nsort_sum_test01()\\n\\n@test_algo($a + b$)\\ndef sort_sum_test02():\\n\\tex := c + a.\\n\\treturn sort_sum(ex)\\nsort_sum_test02()\\n\\n@test_algo($a + b$, throw_on_fail=True)\\ndef sort_sum_test03():\\n\\tex := c + a.\\n\\treturn sort_sum(ex)\\n\\ntry:\\n\\tsort_sum_test03()\\n\\traise AssertionError(\\\"CadabraTestError not raised!\\\")\\nexcept CadabraTestError:\\n\\tprint(\\\"Raised CadabraTestError\\\")\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 17571440201905887785,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 12853042454041156620,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\algorithm{inherit_kernel() -> Kernel}{Find a kernel in the stack.}\\n\\nMove up stack frames until one which defines the \\\\verb|__cdbkernel__| variable is located and return \\nit. If no Kernel object is found then None is returned\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\algorithm{inherit_kernel() -> Kernel}{Find a kernel in the stack.}\\n\\nMove up stack frames until one which defines the \\\\verb|__cdbkernel__| variable is located and return \\nit. If no Kernel object is found then None is returned\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 460414117077303111,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"def inherit_kernel():\\n\\tframe = inspect.stack()[1][0]\\n\\twhile \\\"__cdbkernel__\\\" not in frame.f_locals:\\n\\t\\tframe = frame.f_back\\n\\t\\tif frame is None:\\n\\t\\t\\treturn None\\n\\treturn frame.f_locals[\\\"__cdbkernel__\\\"]\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 13850153861758424314,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"ignore_on_import\": true,\n\t\t\t\"source\": \"\"\n\t\t}\n\t],\n\t\"description\": \"Cadabra JSON notebook format\",\n\t\"version\": 1.0\n}\n"
  },
  {
    "path": "core/packages/cdb/utils/indices.cnb",
    "content": "{\n\t\"cell_id\": 15583880456908114958,\n\t\"cells\": [\n\t\t{\n\t\t\t\"cell_id\": 17303979617964142236,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"from cdb.utils.node import n_indices\\nfrom copy import copy\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 13419242331187320623,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 4122877639113717994,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\package{cdb.utils.indices}{Additional functionality to deal with indices}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\package{cdb.utils.indices}{Additional functionality to deal with indices}\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 13857590062838682174,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 18354051870315698989,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\algorithm{all_index_positions(ex: ExNode) -> Generator[Ex]}{Generate all possible combinations of covariant \\nand contravariant indices}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\algorithm{all_index_positions(ex: ExNode) -> Generator[Ex]}{Generate all possible combinations of covariant and contravariant indices}\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 10479853794613744564,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"def all_index_positions(ex_):\\n\\tex = copy(ex_)\\n\\tn = n_indices(ex.top())\\n\\tfor i in range(2**n):\\n\\t\\tfor height, index in zip(format(i, f\\\"0{n}b\\\"), ex.top().indices()):\\n\\t\\t\\tindex.parent_rel = parent_rel_t.sub if height == '0' else parent_rel_t.super\\n\\t\\tyield ex\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 1567279626437013803,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 10625918768741539985,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 5744285270842328701,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"A_{\\\\mu \\\\nu \\\\rho}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}A_{\\\\mu \\\\nu \\\\rho}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 808607824366024774,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 7391862823510323362,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"A_{\\\\mu \\\\nu}^{\\\\rho}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}A_{\\\\mu \\\\nu}\\\\,^{\\\\rho}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 17820102242399456702,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 4056150914491624274,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"A_{\\\\mu}^{\\\\nu}_{\\\\rho}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}A_{\\\\mu}\\\\,^{\\\\nu}\\\\,_{\\\\rho}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 11153558184430743234,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 4690332253586664815,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"A_{\\\\mu}^{\\\\nu \\\\rho}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}A_{\\\\mu}\\\\,^{\\\\nu \\\\rho}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 17054390684282561432,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 5447125216017949069,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"A^{\\\\mu}_{\\\\nu \\\\rho}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}A^{\\\\mu}\\\\,_{\\\\nu \\\\rho}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 13468401569599865394,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 399306766743001184,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"A^{\\\\mu}_{\\\\nu}^{\\\\rho}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}A^{\\\\mu}\\\\,_{\\\\nu}\\\\,^{\\\\rho}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 17321927018441561683,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 5814884726611788367,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"A^{\\\\mu \\\\nu}_{\\\\rho}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}A^{\\\\mu \\\\nu}\\\\,_{\\\\rho}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 16957255301193719326,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 5138394693482285977,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"A^{\\\\mu \\\\nu \\\\rho}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}A^{\\\\mu \\\\nu \\\\rho}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"ignore_on_import\": true,\n\t\t\t\"source\": \"ex := A_{\\\\mu \\\\nu \\\\rho}.\\nfor var in all_index_positions(ex):\\n\\tvar;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 10591913784695924168,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 7865695452725605118,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\algorithm{replace_index(ex: Ex, top_name: str, old_index: str, new_index: str) -> Ex}{Rename indices}\\n\\nRenames with \\\\texttt{new\\\\_index}\\nall occurences of indices named \\\\texttt{old\\\\_index} in any subtree whose top node is named \\\\texttt{top\\\\_name}\\n\\\\textbf{Note:}~This is useful for avoiding triple index-repeated errors due to the presence of tensor indices in the argument of\\nthe exponential function i.e. $\\\\exp(\\\\pm i k_\\\\lambda x^\\\\lambda)$\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\algorithm{replace_index(ex: Ex, top_name: str, old_index: str, new_index: str) -> Ex}{Rename indices}\\n\\nRenames with \\\\texttt{new\\\\_index}\\nall occurences of indices named \\\\texttt{old\\\\_index} in any subtree whose top node is named \\\\texttt{top\\\\_name}\\n\\\\textbf{Note:}~This is useful for avoiding triple index-repeated errors due to the presence of tensor indices in the argument of\\nthe exponential function i.e. $\\\\exp(\\\\pm i k_\\\\lambda x^\\\\lambda)$\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 12268357943789445408,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"def replace_index(ex, top_name, old_index, new_index):\\n\\tfor node in ex[top_name]:\\n\\t\\tfor match in node[old_index]:\\n\\t\\t\\tif match.parent_rel == parent_rel_t.super or match.parent_rel == parent_rel_t.sub:\\n\\t\\t\\t\\tmatch.name = new_index\\n\\treturn ex\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 17409970256726760074,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 13795957434526174235,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 13060781541372264531,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"h_{\\\\mu \\\\nu} = A_{\\\\mu \\\\nu} \\\\exp(i k_{\\\\mu} x^{\\\\mu})\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}h_{\\\\mu \\\\nu} = A_{\\\\mu \\\\nu} \\\\exp\\\\left(i k_{\\\\mu} x^{\\\\mu}\\\\right)\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9993906878758157671,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 17742477934095676240,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"h_{\\\\mu \\\\nu} = A_{\\\\mu \\\\nu} \\\\exp(i k_{\\\\alpha} x^{\\\\alpha})\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}h_{\\\\mu \\\\nu} = A_{\\\\mu \\\\nu} \\\\exp\\\\left(i k_{\\\\alpha} x^{\\\\alpha}\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"ignore_on_import\": true,\n\t\t\t\"source\": \"test := h_{\\\\mu\\\\nu} = A_{\\\\mu\\\\nu} \\\\exp(i*k_\\\\mu*x^{\\\\mu});\\ntest = replace_index(test,r\\\"\\\\exp\\\",r'\\\\mu',r'\\\\alpha');\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 11510030216175255073,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 1918773861692544849,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\algorithm{get_indices(node: ExNode) -> List[Ex]}{Return a list of all indices inside the given node}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\algorithm{get_indices(node: ExNode) -> List[Ex]}{Return a list of all indices inside the given node}\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 4114061066973510892,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"def get_indices(node):\\n\\t# Require monomial structure\\n\\tif isinstance(node, Ex):\\n\\t\\tnode = node.top()\\n\\tassert node.name != r\\\"\\\\sum\\\" and node.name != r\\\"\\\\equals\\\", f\\\"get_indices() requires a monomial structure, got {node.name}\\\"\\n\\n\\tindices = []\\n\\tinherits_indices = (IndexInherit.get(node) is not None)\\n\\n\\t# Walk through children collecting indices recursively\\n\\tfor child in node.children():\\n\\t\\tif child.parent_rel == parent_rel_t.super or child.parent_rel == parent_rel_t.sub:\\n\\t\\t\\t# Discard integers, symbols and coordinates\\n\\t\\t\\tsymb = Symbol.get(child)\\n\\t\\t\\tcoord = Coordinate.get(child)\\n\\t\\t\\tinteger = child.name == \\\"1\\\"\\n\\t\\t\\tif not (symb or coord or integer):\\n\\t\\t\\t\\tindex = child.ex()\\n\\t\\t\\t\\tindex.top().parent_rel = parent_rel_t.none\\n\\t\\t\\t\\tindices.append(index)\\n\\t\\telif inherits_indices:\\n\\t\\t\\tindices.extend(get_indices(child))\\n\\n\\treturn indices\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 7471126205299592191,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 3926702791067015050,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 3419282733763189790,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"a_{\\\\mu} \\\\partial_{\\\\sigma}(b_{\\\\mu} b_{\\\\lambda}) \\\\delta(p_{\\\\rho} p^{\\\\rho}) + g_{\\\\sigma \\\\lambda} g_{\\\\kappa} g^{\\\\kappa} = p_{\\\\sigma} p_{\\\\lambda}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}a_{\\\\mu} \\\\partial_{\\\\sigma}\\\\left(b_{\\\\mu} b_{\\\\lambda}\\\\right) \\\\delta\\\\left(p_{\\\\rho} p^{\\\\rho}\\\\right)+g_{\\\\sigma \\\\lambda} g_{\\\\kappa} g^{\\\\kappa} = p_{\\\\sigma} p_{\\\\lambda}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 467978901566468640,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"verbatim\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}Caught error\\\\end{verbatim}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9282048507038981528,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"{}$\\\\big[$$\\\\sigma$,\\\\discretionary{}{}{} $\\\\lambda$$\\\\big]$\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"ignore_on_import\": true,\n\t\t\t\"source\": \"\\\\partial{#}::Derivative.\\nex := 0 + a_{\\\\mu} \\\\partial_{\\\\sigma}{b_{\\\\mu}b_{\\\\lambda}} \\\\delta{p_{\\\\rho}p^{\\\\rho}} + g_{\\\\sigma\\\\lambda}g_{\\\\kappa}g^{\\\\kappa} = p_{\\\\sigma}p_{\\\\lambda};\\ntry: \\n\\tget_indices(ex);\\nexcept AssertionError:\\n\\t\\\"Caught error\\\";\\nget_indices(ex[1]);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 9875547432092551433,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 5657527890910142199,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\algorithm{get_dummy_indices(node: ExNode) -> List[Ex]}{Return a list of all dummy indices inside the given node}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\algorithm{get_dummy_indices(node: ExNode) -> List[Ex]}{Return a list of all dummy indices inside the given node}\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 16142500167825125558,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"def get_dummy_indices(node):\\n\\tindices = get_indices(node)\\n\\tdummies = []\\n\\tfor pos, idx in enumerate(indices):\\n\\t\\tif idx in dummies:\\n\\t\\t\\tcontinue\\n\\t\\ttry:\\n\\t\\t\\tother = indices.index(idx, pos + 1)\\n\\t\\t\\tdummies.append(idx)\\n\\t\\texcept ValueError:\\n\\t\\t\\tpass\\n\\treturn dummies\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 5826709331712786624,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 3965206875785443255,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 12964034287132943198,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"a_{\\\\mu} \\\\partial_{\\\\sigma}(b_{\\\\mu} b_{\\\\lambda}) \\\\delta(p_{\\\\rho} p^{\\\\rho})\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}a_{\\\\mu} \\\\partial_{\\\\sigma}\\\\left(b_{\\\\mu} b_{\\\\lambda}\\\\right) \\\\delta\\\\left(p_{\\\\rho} p^{\\\\rho}\\\\right)\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 5118101628968331098,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"{}$\\\\big[$$\\\\mu$$\\\\big]$\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"ignore_on_import\": true,\n\t\t\t\"source\": \"\\\\partial{#}::Derivative.\\nex := a_{\\\\mu} \\\\partial_{\\\\sigma}{b_{\\\\mu}b_{\\\\lambda}} \\\\delta{p_{\\\\rho}p^{\\\\rho}};\\nget_dummy_indices(ex);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 8198227195091703517,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 3586640425109646595,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\algorithm{get_free_indices(node: ExNode) -> List[Ex]}{Return a list of all free indices inside the given node}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\algorithm{get_free_indices(node: ExNode) -> List[Ex]}{Return a list of all free indices inside the given node}\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 12107868658700828741,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"def get_free_indices(node):\\n\\t# Find a monomial\\n\\tif isinstance(node, Ex):\\n\\t\\tnode = node.top()\\n\\twhile node.name == r\\\"\\\\sum\\\" or node.name == r\\\"\\\\equals\\\":\\n\\t\\tfor child in node.children():\\n\\t\\t\\tif child.name != \\\"1\\\":\\n\\t\\t\\t\\tnode = child\\n\\t\\t\\t\\tbreak\\n\\t\\telse:\\n\\t\\t\\treturn []\\n\\n\\tindices = []\\n\\tinherits_indices = (IndexInherit.get(node) is not None)\\n\\n\\t# Walk through children collecting indices recursively\\n\\tfor child in node.children():\\n\\t\\tif child.parent_rel == parent_rel_t.super or child.parent_rel == parent_rel_t.sub:\\n\\t\\t\\t# Discard integers, symbols and coordinates\\n\\t\\t\\tsymb = Symbol.get(child)\\n\\t\\t\\tcoord = Coordinate.get(child)\\n\\t\\t\\tinteger = child.name == \\\"1\\\"\\n\\t\\t\\tif not (symb or coord or integer):\\n\\t\\t\\t\\tindex = child.ex()\\n\\t\\t\\t\\tindex.top().parent_rel = parent_rel_t.none\\n\\t\\t\\t\\tindices.append(index)\\n\\t\\telif inherits_indices:\\n\\t\\t\\tindices.extend(get_free_indices(child))\\n\\n\\t# Find all repeated indices\\n\\tdummies = []\\n\\tfor pos, idx in enumerate(indices):\\n\\t\\tif idx in dummies:\\n\\t\\t\\tcontinue\\n\\t\\ttry:\\n\\t\\t\\tother = indices.index(idx, pos + 1)\\n\\t\\t\\tdummies.append(idx)\\n\\t\\texcept ValueError:\\n\\t\\t\\tpass\\n\\n\\t# Remove all instances of dummies from the set of indices and return\\n\\tfor dummy in dummies:\\n\\t\\tindices = [i for i in indices if i != dummy]\\n\\treturn indices\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 13119901376492792968,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 669024716363112975,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 6297175375627481469,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"a_{\\\\mu} \\\\partial_{\\\\sigma}(b_{\\\\mu} b_{\\\\lambda}) \\\\delta(p_{\\\\rho} p^{\\\\rho}) + g_{\\\\sigma \\\\lambda} g_{\\\\kappa} g^{\\\\kappa} = p_{\\\\sigma} p_{\\\\lambda}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}a_{\\\\mu} \\\\partial_{\\\\sigma}\\\\left(b_{\\\\mu} b_{\\\\lambda}\\\\right) \\\\delta\\\\left(p_{\\\\rho} p^{\\\\rho}\\\\right)+g_{\\\\sigma \\\\lambda} g_{\\\\kappa} g^{\\\\kappa} = p_{\\\\sigma} p_{\\\\lambda}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 4595981957722617540,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"{}$\\\\big[$$\\\\sigma$,\\\\discretionary{}{}{} $\\\\lambda$$\\\\big]$\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"ignore_on_import\": true,\n\t\t\t\"source\": \"\\\\partial{#}::Derivative.\\nex := 0 + a_{\\\\mu} \\\\partial_{\\\\sigma}{b_{\\\\mu}b_{\\\\lambda}} \\\\delta{p_{\\\\rho}p^{\\\\rho}} + g_{\\\\sigma\\\\lambda}g_{\\\\kappa}g^{\\\\kappa} = p_{\\\\sigma}p_{\\\\lambda};\\nget_free_indices(ex);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 1627815774396580848,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 7144980246086443385,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\algorithm{symmetrise_slots(ex: Ex, slots: list[int], antisym: bool = False)}{Symmetrise\\nor antisymmetrise an expression in the given slots}\\n\\nGiven an expression, iterates over all top level terms and symmetrises the indices in the\\ngiven \\\\texttt{slots}, so that e.g. \\\\verb|symmetrise_slots($A_{a b c}$, [0,1])|\\n$\\\\rightarrow$ $A_{a b c} + A_{b a c}$. For an expression containing a sum of terms,\\nall terms in the expression are symmetrised.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\algorithm{symmetrise_slots(ex: Ex, slots: list[int], antisym: bool = False)}{Symmetrise\\nor antisymmetrise an expression in the given slots}\\n\\nGiven an expression, iterates over all top level terms and symmetrises the indices in the\\ngiven \\\\texttt{slots}, so that e.g. \\\\verb|symmetrise_slots($A_{a b c}$, [0,1])|\\n$\\\\rightarrow$ $A_{a b c} + A_{b a c}$. For an expression containing a sum of terms,\\nall terms in the expression are symmetrised.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 16310576225572836586,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"from itertools import permutations\\n\\ndef symmetrise_slots(ex, slots, antisym=False):\\n\\tdef is_even(p):\\n\\t\\tif len(p) == 1: return True\\n\\t\\ttrans = 0\\n\\t\\tfor i in range(0,len(p)):\\n\\t\\t\\tj = i + 1\\n\\t\\t\\tfor j in range(j, len(p)):\\n\\t\\t\\t\\tif p[i] > p[j]: trans = trans + 1\\n\\t\\treturn ((trans % 2) == 0)\\n\\tdef _sym_slots(it, slots, antisym=False):\\n\\t\\trepl = $a$\\n\\t\\trepl.top().name = \\\"\\\\\\\\sum\\\"\\n\\t\\tindices = [$@(index)$ for index in it.indices()]\\n\\t\\trels = [index.parent_rel for index in it.indices()]\\n\\t\\tfor permutation in permutations(slots):\\n\\t\\t\\tnew_indices = [$@(index)$ for index in indices]\\n\\t\\t\\tnew_rels = [rel for rel in rels]\\n\\t\\t\\tfor a, b in zip(slots, permutation):\\n\\t\\t\\t\\tnew_indices[a] = indices[b]\\n\\t\\t\\t\\tnew_rels[a] = rels[b]\\n\\t\\t\\tif not antisym or is_even(permutation): new_term = $@(it)$\\n\\t\\t\\telse: new_term = $-@(it)$\\n\\t\\t\\tfor i, index in enumerate(new_term.top().indices()):\\n\\t\\t\\t\\tindex.replace(new_indices[i])\\n\\t\\t\\t\\tindex.parent_rel = new_rels[i]\\n\\t\\t\\trepl.top().append_child(new_term)\\n\\t\\tit.replace(repl)\\n\\tslots = sorted(slots)\\n\\tif ex.top().name == r\\\"\\\\sum\\\":\\n\\t\\tfor term in ex.top().children():\\n\\t\\t\\t_sym_slots(term, slots, antisym)\\n\\telse:\\n\\t\\t_sym_slots(ex.top(), slots, antisym)\\n\\tex.cleanup()\\n\\treturn ex\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 8743806279518418158,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 3660017727901812283,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 9316541226681817515,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"R_{a b c d}-R_{a b d c}-R_{a c d b} + R_{a d c b}-R_{b a c d} + R_{b a d c} + R_{b c d a}-R_{b d c a}-R_{c a b d} + R_{c b a d} + R_{c d a b}-R_{c d b a} + R_{d a b c}-R_{d b a c}-R_{d c a b} + R_{d c b a}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}R_{a b c d}-R_{a b d c}-R_{a c d b}+R_{a d c b}-R_{b a c d}+R_{b a d c}+R_{b c d a}-R_{b d c a}-R_{c a b d}+R_{c b a d}+R_{c d a b}-R_{c d b a}+R_{d a b c}-R_{d b a c}-R_{d c a b}+R_{d c b a}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 11071786508319260826,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 13751431965017289945,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"R_{a b c d}-R_{a b d c}-R_{a c d b} + R_{a d c b}-R_{b a c d} + R_{b a d c} + R_{b c d a}-R_{b d c a}-R_{c a b d} + R_{c b a d} + R_{c d a b}-R_{c d b a} + R_{d a b c}-R_{d b a c}-R_{d c a b} + R_{d c b a}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}R_{a b c d}-R_{a b d c}-R_{a c d b}+R_{a d c b}-R_{b a c d}+R_{b a d c}+R_{b c d a}-R_{b d c a}-R_{c a b d}+R_{c b a d}+R_{c d a b}-R_{c d b a}+R_{d a b c}-R_{d b a c}-R_{d c a b}+R_{d c b a}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"ignore_on_import\": true,\n\t\t\t\"source\": \"ex1 := R_{a b c d}:\\nsymmetrise_slots(ex1, [0,1], True)\\nsymmetrise_slots(ex1, [2,3], True)\\nsymmetrise_slots(ex1, [0,2])\\nsymmetrise_slots(ex1, [1,3])\\nsort_sum(ex1);\\n\\nR_{a b c d}::RiemannTensor.\\nex2 := 12 R_{a b c d}:\\nyoung_project_tensor(ex2)\\nsort_sum(ex2);\\n\\nassert ex1 == ex2\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 5089890689640016182,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"\"\n\t\t}\n\t],\n\t\"description\": \"Cadabra JSON notebook format\",\n\t\"flags\": {\n\t\t\"hide_input_cells\": false\n\t},\n\t\"version\": 1.0\n}\n"
  },
  {
    "path": "core/packages/cdb/utils/node.cnb",
    "content": "{\n\t\"cell_id\": 17512074313060748460,\n\t\"cells\": [\n\t\t{\n\t\t\t\"cell_id\": 15247747989752233954,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 1213666910347544194,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\package{cdb.utils.node}{Helper functions for working with ExNode objects}\\n\\nThis package contains numerous helper functions for examining, querying and creating ExNode objects\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\package{cdb.utils.node}{Helper functions for working with ExNode objects}\\n\\nThis package contains numerous helper functions for examining, querying and creating ExNode objects\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 8707393970919064424,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 2302073851195842048,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\algorithm{n_indices(ex_node: ExNode|Ex) -> int}{Return the number of first-level indices a node has}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\algorithm{n_indices(ex_node: ExNode|Ex) -> int}{Return the number of first-level indices a node has}\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 1753035616873629304,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"def n_indices(ex_node):\\n\\tif type(ex_node) is Ex:\\n\\t\\tex_node = ex_node.top()\\n\\treturn sum(1 for i in ex_node.indices())\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 16050091017712825754,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 3758324614433019034,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\algorithm{nth_index(ex_node: ExNode|Ex, n: int) -> ExNode}{Gets the nth index of an ExNode object}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\algorithm{nth_index(ex_node: ExNode|Ex, n: int) -> ExNode}{Gets the nth index of an ExNode object}\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 1668756240050354674,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"def nth_index(ex_node, n):\\n\\tif type(ex_node) is Ex:\\n\\t\\tex_node = ex_node.top()\\n\\tfor i, index in enumerate(ex_node.indices()):\\n\\t\\tif i == n:\\n\\t\\t\\treturn index\\n\\traise IndexError\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 14893455513982883060,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 5137071268020781653,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\algorithm{n_args(ex_node: ExNode|Ex) -> int}{Returns the number of first-level arguments a node has}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\algorithm{n_args(ex_node: ExNode|Ex) -> int}{Returns the number of first-level arguments a node has}\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 4541113739588128532,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"def n_args(ex_node):\\n\\tif type(ex_node) is Ex:\\n\\t\\tex_node = ex_node.top()\\n\\treturn sum(1 for i in ex_node.args())\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 1296289453444328705,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 10868576452574748356,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\algorithm{nth_arg(ex_node: ExNode|Ex, n: int) -> ExNode}{Gets the nth first-level argument of an ExNode object}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\algorithm{nth_arg(ex_node: ExNode|Ex, n: int) -> ExNode}{Gets the nth first-level argument of an ExNode object}\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 12002362360129662198,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"def nth_arg(ex_node, n):\\n\\tif type(ex_node) is Ex:\\n\\t\\tex_node = ex_node.top()\\n\\tfor i, arg in enumerate(ex_node.args()):\\n\\t\\tif i == n:\\n\\t\\t\\treturn arg\\n\\traise IndexError\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 7867168225214081120,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 15318580960104441515,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\algorithm{arg_tuple(ex_node: ExNode|Ex, n: int) -> tuple[ExNode]}{Returns a tuple containing the first n arguments of an ExNode object}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\algorithm{arg_tuple(ex_node: ExNode|Ex, n: int) -> tuple[ExNode]}{Returns a tuple containing the first n arguments of an ExNode object}\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 3905388232732922485,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"def arg_tuple(ex_node, n):\\n\\tif type(ex_node) is Ex:\\n\\t\\tex_node = ex_node.top()\\n\\treturn (nth_arg(ex_node, i)._latex_() for i in range(n))\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 5580540595633524661,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 6477025559129691750,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\algorithm{n_children(ex_node: ExNode|Ex) -> int}{Returns the number of first-level children a node has}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\algorithm{n_children(ex_node: ExNode|Ex) -> int}{Returns the number of first-level children a node has}\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 6625943265031471290,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"def n_children(ex_node):\\n\\tif type(ex_node) is Ex:\\n\\t\\tex_node = ex_node.top()\\n\\treturn sum(1 for i in ex_node.children())\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 10470381271085779836,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 8350148697092125558,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\algorithm{nth_child(ex_node: ExNode|Ex, n: int) -> ExNode}{Gets the nth first-level child of an ExNode object}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\algorithm{nth_child(ex_node: ExNode|Ex, n: int) -> ExNode}{Gets the nth first-level child of an ExNode object}\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 13783965533728989485,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"def nth_child(ex_node, n):\\n\\tif type(ex_node) is Ex:\\n\\t\\tex_node = ex_node.top()\\n\\n\\tfor i, child in enumerate(ex_node.children()):\\n\\t\\tif i == n:\\n\\t\\t\\treturn child\\n\\traise IndexError\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 10765803096551983959,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 402856110058782620,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\algorithm{child_tuple(ex_node : ExNode|Ex, n: int) -> tuple[ExNode]}{Returns a tuple containing the first n children of an ExNode object}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\algorithm{child_tuple(ex_node : ExNode|Ex, n: int) -> tuple[ExNode]}{Returns a tuple containing the first n children of an ExNode object}\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 6084336848221340877,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"def child_tuple(ex_node, n):\\n\\t\\\"\\\"\\\"\\\"\\\"\\\"\\n\\tif type(ex_node) is Ex:\\n\\t\\tex_node = ex_node.top()\\n\\n\\treturn (nth_child(ex_node, i)._latex_() for i in range(n))\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 14135986501232649833,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 8816228911771772273,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\algorithm{empty_sum() -> Ex}{Returns an Ex object with just one sum node with no children}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\algorithm{empty_sum() -> Ex}{Returns an Ex object with just one sum node with no children}\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 13241820287247340496,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"def empty_sum():\\n\\tex := a + b;\\n\\twhile n_children(ex.top()) != 0:\\n\\t\\tnth_child(ex.top(), 0).erase()\\n\\treturn ex\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 2942202388793883132,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 16075171543177567621,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\algorithm{empty_product() -> Ex}{Returns an Ex object with just one product node with no children}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\algorithm{empty_product() -> Ex}{Returns an Ex object with just one product node with no children}\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 7789116792134512028,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"def empty_product():\\n\\tex := a * b;\\n\\twhile n_children(ex.top()) != 0:\\n\\t\\tnth_child(ex.top(), 0).erase()\\n\\treturn ex\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 6834160618828137935,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 10463424941420234170,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"verbatim\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}a, b, c, d, e, f, g\\\\end{verbatim}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 4355001156256662151,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"verbatim\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}(a, b, c, d)\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"ignore_on_import\": true,\n\t\t\t\"source\": \"ex1 = $a, b, c, d, e, f, g$\\ndisplay(\\\", \\\".join(nth_arg(ex1, i)._latex_() for i in range(n_args(ex1))))\\ndisplay('(' + \\\", \\\".join(arg_tuple(ex1, 4)) + ')')\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 13524964813951039698,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"\"\n\t\t}\n\t],\n\t\"description\": \"Cadabra JSON notebook format\",\n\t\"flags\": {\n\t\t\"hide_input_cells\": false\n\t},\n\t\"version\": 1.0\n}\n"
  },
  {
    "path": "core/packages/cdb/utils/tableau.cnb",
    "content": "{\n\t\"cell_id\": 17439249385034091662,\n\t\"cells\": [\n\t\t{\n\t\t\t\"cell_id\": 8734995938305730404,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"from cdb.utils.node import n_indices, nth_child\\nfrom itertools import permutations\\nimport copy\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 10926153879009935420,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 655640036215962657,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\algorithm{fill_diagram(shape: tuple[int, ...], indices: tuple[int, ...]) -> tuple[tuple[int, ...], ...]}{Create a filled\\ntableau from a diagram shape and a list of indices to be entered left-to-right and top-to-bottom}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\algorithm{fill_diagram(shape: tuple[int, ...], indices: tuple[int, ...]) -> tuple[tuple[int, ...], ...]}{Create a filled\\ntableau from a diagram shape and a list of indices to be entered left-to-right and top-to-bottom}\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 4650101496488726068,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"def fill_diagram(shape, indices):\\n\\tpos = 0\\n\\tres = []\\n\\tfor row in shape:\\n\\t\\tres.append(tuple(indices[pos:pos+row]))\\n\\t\\tpos += row\\n\\treturn tuple(res)\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 6170261760868707497,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 4972547932551413900,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"verbatim\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}((0, 2), (1, 3))\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"ignore_on_import\": true,\n\t\t\t\"source\": \"fill_diagram((2,2), (0,2,1,3));\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 17257245543978409381,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 13645643897314952999,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\algorithm{get_shape(tab: tuple[tuple[int, ...], ...]) -> tuple[int, ...]}{Return the diagram shape of a filled tableau}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\algorithm{get_shape(tab: tuple[tuple[int, ...], ...]) -> tuple[int, ...]}{Return the diagram shape of a filled tableau}\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 18426422417848083334,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"def get_shape(tab):\\n\\treturn tuple(len(row) for row in tab)\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 12763722317612787858,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 4311011915341918303,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"verbatim\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}(2, 2)\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"ignore_on_import\": true,\n\t\t\t\"source\": \"get_shape([(0,2), (1,3)]);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 11184177818743178037,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 6424924232599460152,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\algorithm{get_indices(tab: tuple[tuple[int, ...], ...]) -> tuple[int, ...]}{Return the indices of a filled\\ntableau}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\algorithm{get_indices(tab: tuple[tuple[int, ...], ...]) -> tuple[int, ...]}{Return the indices of a filled\\ntableau}\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 12746646020864187123,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"def get_indices(tab):\\n\\treturn tuple(i for row in tab for i in row)\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 10387655419734127318,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 10039146017229501950,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"verbatim\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}(0, 3, 1, 2)\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"ignore_on_import\": true,\n\t\t\t\"source\": \"get_indices([(0,3), (1,2)]);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 17622104385795914714,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 2323026231863958281,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\algorithm{tableaux_to_ex(tuple[tuple[int, ...], ...], ...) -> Ex}{Convert tuple-representations of filled tableaux into an\\n\\\\texttt{Ex} object which can be passed to the \\\\texttt{TableauSymmetry} property}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\algorithm{tableaux_to_ex(tuple[tuple[int, ...], ...], ...) -> Ex}{Convert tuple-representations of filled tableaux into an\\n\\\\texttt{Ex} object which can be passed to the \\\\texttt{TableauSymmetry} property}\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 6770064243653586750,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"def tableaux_to_ex(*tabs):\\n\\tparts = []\\n\\tfor tab in tabs:\\n\\t\\tshape = [str(len(row)) for row in tab]\\n\\t\\tindices = [str(i) for row in tab for i in row]\\n\\t\\tparts.append(\\\"shape={\\\" + \\\",\\\".join(shape) + \\\"}, indices={\\\" + \\\",\\\".join(indices) + \\\"}\\\")\\n\\treturn Ex(\\\",\\\".join(parts)) \"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 12404871075510297773,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 4232949427795909670,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 5266415592967851707,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"{shape = {2, 2}, indices = {0, 2, 1, 3}, shape = 4, indices = {4, 5, 6, 7}, shape = {1, 1}, indices = {8, 9}}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\left[shape = \\\\left[2,~\\\\discretionary{}{}{} 2\\\\right],~\\\\discretionary{}{}{} indices = \\\\left[0,~\\\\discretionary{}{}{} 2,~\\\\discretionary{}{}{} 1,~\\\\discretionary{}{}{} 3\\\\right],~\\\\discretionary{}{}{} shape = 4,~\\\\discretionary{}{}{} indices = \\\\left[4,~\\\\discretionary{}{}{} 5,~\\\\discretionary{}{}{} 6,~\\\\discretionary{}{}{} 7\\\\right],~\\\\discretionary{}{}{} shape = \\\\left[1,~\\\\discretionary{}{}{} 1\\\\right],~\\\\discretionary{}{}{} indices = \\\\left[8,~\\\\discretionary{}{}{} 9\\\\right]\\\\right]\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"ignore_on_import\": true,\n\t\t\t\"source\": \"tableaux_to_ex([(0,2), (1,3)], [(4,5,6,7)], [(8,),(9,)]);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 14101893052762071849,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 5593239722411873632,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\algorithm{ex_to_tableaux(ex: Ex) -> list[tuple[tuple[int, ...], ...]]}{Covert an \\\\texttt{Ex} object consisting of\\n\\\\texttt{shape} and \\\\texttt{indices} nodes into tuple-representations of filled tableaux}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\algorithm{ex_to_tableaux(ex: Ex) -> list[tuple[tuple[int, ...], ...]]}{Covert an \\\\texttt{Ex} object consisting of\\n\\\\texttt{shape} and \\\\texttt{indices} nodes into tuple-representations of filled tableaux}\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 14782967466992548211,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"def ex_to_tableaux(ex):\\n\\ttab = { \\\"shape\\\": None, \\\"indices\\\": None }\\n\\ttabs = []\\n\\tfor node in ex.top().children():\\n\\t\\tl = []\\n\\t\\tfor k in nth_child(node, 1).children():\\n\\t\\t\\tl.append(int(k.multiplier))\\n\\t\\ttab[nth_child(node, 0).name] = l\\n\\t\\tif tab[\\\"shape\\\"] is not None and tab[\\\"indices\\\"] is not None:\\n\\t\\t\\ttabs.append(fill_diagram(tab[\\\"shape\\\"], tab[\\\"indices\\\"]))\\n\\t\\t\\ttab[\\\"shape\\\"] = None\\n\\t\\t\\ttab[\\\"indices\\\"] = None\\n\\treturn tabs\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 3409592937070762683,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 10461484522336609135,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"{}$\\\\big[$$\\\\verb|((0,), (1,))|$,\\\\discretionary{}{}{} $\\\\verb|((5, 3, 6), (4, 7))|$$\\\\big]$\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"ignore_on_import\": true,\n\t\t\t\"source\": \"ex_to_tableaux($shape={1,1}, indices={0,1}, shape={3,2}, indices={5,3,6,4,7}$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 1216030587752948593,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 18144390320621628896,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\algorithm{all_diagrams(n: int) -> Generator[tuple[int, ...]]}{Generate all possible tableau diagrams consisting of \\\\texttt{n} boxes}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\algorithm{all_diagrams(n: int) -> Generator[tuple[int, ...]]}{Generate all possible tableau diagrams consisting of \\\\texttt{n} boxes}\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 17251724056801448288,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"def all_diagrams(n):\\n\\tdef partitions(n, k):\\n\\t\\tyield (n,)\\n\\t\\tfor i in range(k, n//2 + 1):\\n\\t\\t\\tfor p in partitions(n-i, i):\\n\\t\\t\\t\\tyield (i, *p)\\n\\t# Yield all partitions sorted so that rows always decrease in length\\n\\tyield from (tuple(sorted(p, reverse=True)) for p in partitions(n, 1))\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 7533670825558258954,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 759495993201878641,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"output\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}(6,)\\n(5, 1)\\n(4, 1, 1)\\n(3, 1, 1, 1)\\n(2, 1, 1, 1, 1)\\n(1, 1, 1, 1, 1, 1)\\n(2, 2, 1, 1)\\n(3, 2, 1)\\n(4, 2)\\n(2, 2, 2)\\n(3, 3)\\n\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"ignore_on_import\": true,\n\t\t\t\"source\": \"for tableau in all_diagrams(6):\\n\\tprint(tableau)\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 17893376737970562489,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 12349308104187550257,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\algorithm{littlewood_richardson(a: tuple[int, ...], b: tuple[int, ...]) -> list[tuple[int, ...]]}{Do a Littlewood-Richardson\\ndecomposition on diagrams \\\\texttt{a} and \\\\texttt{b}}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\algorithm{littlewood_richardson(a: tuple[int, ...], b: tuple[int, ...]) -> list[tuple[int, ...]]}{Do a Littlewood-Richardson\\ndecomposition on diagrams \\\\texttt{a} and \\\\texttt{b}}\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 7784795496465730523,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"def _littlewood_validate(tab, max_index):\\n\\t# No two boxes in the same column are labelled with the same letter\\n\\tfor j in range(len(tab[0])):\\n\\t\\tcounts = [0] * max_index\\n\\t\\tfor i in range(len(tab)):\\n\\t\\t\\tif len(tab[i]) > j and tab[i][j] != 0:\\n\\t\\t\\t\\tcounts[tab[i][j] - 1] += 1\\n\\t\\tif any(i > 1 for i in counts):\\n\\t\\t\\t#print(f\\\"Discarding {tab} as two indices in same column\\\")\\n\\t\\t\\treturn False\\n\\t# The result is a legitimate Young diagram\\n\\tprev = len(tab[0])\\n\\tfor i in range(1, len(tab)):\\n\\t\\tcur = len(tab[i])\\n\\t\\tif cur > prev:\\n\\t\\t\\t#print(f\\\"Discarding {tab} as it is not a legitimate Young diagram\\\")\\n\\t\\t\\treturn False\\n\\t\\tprev = cur\\n\\t# If the letters are read right to left, there are never more is than js if i > j\\n\\tcounts = [0] * max_index\\n\\tfor row in tab:\\n\\t\\tfor elem in reversed(row):\\n\\t\\t\\tif elem != 0:\\n\\t\\t\\t\\tcounts[elem - 1] += 1\\n\\t\\t\\tif not all(i >= j for i, j in zip(counts, counts[1:])):\\n\\t\\t\\t\\t#print(f\\\"Discarding {tab} as a smaller index appears less times than a larger index\\\")\\n\\t\\t\\t\\treturn False\\n\\treturn True\\n\\ndef _littlewood(tab, indices, starting_row):\\n\\tif len(indices) == 0:\\n\\t\\tyield [len(row) for row in tab]\\n\\t\\treturn\\n\\tif tab[starting_row][-1] != indices[0]:\\n\\t\\tstarting_row = 0\\n\\tfor i in range(starting_row, len(tab)):\\n\\t\\tnewtab = copy.deepcopy(tab)\\n\\t\\tnewtab[i].append(indices[0])\\n\\t\\tif _littlewood_validate(newtab, indices[-1]):\\n\\t\\t\\tyield from _littlewood(newtab, indices[1:], i)\\n\\tnewtab = copy.deepcopy(tab)\\n\\tnewtab.append([indices[0]])\\n\\tif _littlewood_validate(newtab, indices[-1]):\\n\\t\\tyield from _littlewood(newtab, indices[1:], len(newtab) - 1)\\n\\ndef littlewood_richardson(a, b):\\n\\tindices = []\\n\\tfor i, r in enumerate(b, 1):\\n\\t\\tindices += [i] * r\\n\\ttab = [ [0]*r for r in a ]\\n\\treturn list(_littlewood(tab, indices, 0))\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 16873880143465727054,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 13592067450288467895,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"output\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}[[4, 4], [4, 3, 1], [4, 2, 2], [3, 3, 1, 1], [3, 2, 2, 1], [2, 2, 2, 2]]\\n\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"ignore_on_import\": true,\n\t\t\t\"source\": \"print(littlewood_richardson((2,2), (2,2)))\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 2074604220791874733,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 2234274075724592948,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\algorithm{conjugate(tab: tuple[tuple[int, ...], ...]) -> tuple[tuple[int, ...], ...]}{ Returns the conjugate\\nof a filled tableau, i.e. a reflection along the leading diagonal}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\algorithm{conjugate(tab: tuple[tuple[int, ...], ...]) -> tuple[tuple[int, ...], ...]}{ Returns the conjugate\\nof a filled tableau, i.e. a reflection along the leading diagonal}\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 11281111212979795399,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"def conjugate(tab):\\n\\ttranspose = []\\n\\tfor i in range(len(tab[0])):\\n\\t\\tcol = []\\n\\t\\tfor j in range(len(tab)):\\n\\t\\t\\tif len(tab[j]) > i:\\n\\t\\t\\t\\tcol.append(tab[j][i])\\n\\t\\ttranspose.append(col)\\n\\treturn transpose\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 17638329479369357761,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 16397270680577577158,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"output\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}[[0, 3, 5], [1, 4], [2]]\\n[[1], [2], [3]]\\n[[1, 2, 3]]\\n[[1]]\\n\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"ignore_on_import\": true,\n\t\t\t\"source\": \"print(conjugate([[0,1,2],[3,4],[5]]))\\nprint(conjugate([(1,2,3)]))\\nprint(conjugate([(1,),(2,),(3,)]))\\nprint(conjugate([(1,)]))\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 1098671556714192488,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 927467754716580389,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\algorithm{is_standard(tab: tuple[tuple[int, ...], ...]) -> bool}{Returns \\\\texttt{True} if a tableau is standard, \\ni.e. entries are strictly increasing south and east}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\algorithm{is_standard(tab: tuple[tuple[int, ...], ...]) -> bool}{Returns \\\\texttt{True} if a tableau is standard, \\ni.e. entries are strictly increasing south and east}\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 12557937237952354359,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"def is_standard(tab):\\n\\tdef check_rows(ftab):\\n\\t\\tfor row in ftab:\\n\\t\\t\\tif any(row[i] > row[i+1] for i in range(len(row)-1)):\\n\\t\\t\\t\\treturn False\\n\\t\\treturn True\\n\\treturn check_rows(tab) and check_rows(conjugate(tab))\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 11862270199667702553,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 14062871763396970276,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"verbatim\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}True\\\\end{verbatim}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 11953086304433101892,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"verbatim\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}True\\\\end{verbatim}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 10966144899066197072,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"verbatim\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}False\\\\end{verbatim}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 12211463845903837034,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"verbatim\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}True\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"ignore_on_import\": true,\n\t\t\t\"source\": \"is_standard([(0,2),(1,3)]);\\nis_standard([(0,1),(2,3)]);\\nis_standard([(1,2),(0,3)]);\\nis_standard([(1,2)]);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 3049852477480368486,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 10631683949309710340,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\algorithm{is_distinct(a: tuple[tuple[int, ...], ...], b: tuple[tuple[int, ...], ...]) -> bool}{Returns \\\\texttt{True} if\\n\\\\texttt{a} and \\\\texttt{b} are distinct, i.e. \\\\texttt{a} cannot be tranformed into \\\\texttt{b} by swapping rows or columns}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\algorithm{is_distinct(a: tuple[tuple[int, ...], ...], b: tuple[tuple[int, ...], ...]) -> bool}{Returns \\\\texttt{True} if\\n\\\\texttt{a} and \\\\texttt{b} are distinct, i.e. \\\\texttt{a} cannot be tranformed into \\\\texttt{b} by swapping rows or columns}\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 3288458276354221368,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"def is_distinct(a, b):\\n\\ta_rows = sorted(sorted(row) for row in a)\\n\\tb_rows = sorted(sorted(row) for row in b)\\n\\tif a_rows != b_rows:\\n\\t\\treturn True\\n\\ta_cols = sorted(sorted(col) for col in conjugate(a))\\n\\tb_cols = sorted(sorted(col) for col in conjugate(b))\\n\\tif a_cols != b_cols:\\n\\t\\treturn True\\n\\treturn False\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 4246334457930744633,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 14524990218026824931,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"verbatim\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}False\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"ignore_on_import\": true,\n\t\t\t\"source\": \"is_distinct([(0,2), (1,3)], [(1,3), (0,2)]);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 10379696668519694629,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 2563027422090506117,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\algorithm{all_distinct_fillings(diagram: tuple[int, ...]) -> Generator[tuple[tuple[int, ...], ...]]}{Generate all\\ndistinct fillings of \\\\texttt{diagram}}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\algorithm{all_distinct_fillings(diagram: tuple[int, ...]) -> Generator[tuple[tuple[int, ...], ...]]}{Generate all\\ndistinct fillings of \\\\texttt{diagram}}\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 5692032117368872571,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"def all_distinct_fillings(diagram):\\n\\tn = sum(diagram)\\n\\ttabs = []\\n\\tfor indices in permutations(range(n)):\\n\\t\\ttab = fill_diagram(diagram, indices)\\n\\t\\tif all(is_distinct(tab, other) for other in tabs):\\n\\t\\t\\tyield tab\\n\\t\\t\\ttabs.append(tab)\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 8693565799664488411,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 6528452269638973499,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"output\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}((0, 1), (2,))\\n((0, 2), (1,))\\n((1, 0), (2,))\\n((1, 2), (0,))\\n((2, 0), (1,))\\n((2, 1), (0,))\\n((0, 1),)\\n\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"ignore_on_import\": true,\n\t\t\t\"source\": \"for filling in all_distinct_fillings((2,1)):\\n\\tprint(filling)\\nfor filling in all_distinct_fillings((2,)):\\n\\tprint(filling)\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 7578262669365872009,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 5063735555955481709,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\algorithm{all_distinct_tableaux(n: int) -> Generator[tuple[tuple[int, ...], ...]]}{Generate all distinct tableaux with n boxes}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\algorithm{all_distinct_tableaux(n: int) -> Generator[tuple[tuple[int, ...], ...]]}{Generate all distinct tableaux with n boxes}\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 6646151790768196731,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"def all_distinct_tableaux(n):\\n\\tfor shape in all_diagrams(n):\\n\\t\\tyield from all_distinct_fillings(shape)\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 13638188473925948556,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 13434360698814515089,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"output\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}((0, 1, 2),)\\n((0, 1), (2,))\\n((0, 2), (1,))\\n((1, 0), (2,))\\n((1, 2), (0,))\\n((2, 0), (1,))\\n((2, 1), (0,))\\n((0,), (1,), (2,))\\n\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"ignore_on_import\": true,\n\t\t\t\"source\": \"for tab in all_distinct_tableaux(3):\\n\\tprint(tab)\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 7577618092493964110,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 11814110804417664209,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\algorithm{all_standard_fillings(diagram: tuple[int, ...]) -> Generator[tuple[tuple[int, ...], ...]]}{Generate all\\nstandard fillings of \\\\texttt{diagram}}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\algorithm{all_standard_fillings(diagram: tuple[int, ...]) -> Generator[tuple[tuple[int, ...], ...]]}{Generate all\\nstandard fillings of \\\\texttt{diagram}}\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 16549714018272565037,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"def all_standard_fillings(diagram):\\n\\tn = sum(diagram)\\n\\tfor indices in permutations(range(n)):\\n\\t\\ttab = fill_diagram(diagram, indices)\\n\\t\\tif is_standard(tab):\\n\\t\\t\\tyield tab\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 8034684310448471432,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 15883930492899180761,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"output\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}((0, 1), (2,))\\n((0, 2), (1,))\\n\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"ignore_on_import\": true,\n\t\t\t\"source\": \"for filling in all_standard_fillings((2,1)):\\n\\tprint(filling)\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 13138812445050867738,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 3414791383346547988,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\algorithm{all_standard_tableaux(n: int) -> Generator[tuple[tuple[int, ...], ...]]}{Generate all standard tableaux with\\n\\\\texttt{n} boxes}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\algorithm{all_standard_tableaux(n: int) -> Generator[tuple[tuple[int, ...], ...]]}{Generate all standard tableaux with\\n\\\\texttt{n} boxes}\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 15638995218729178626,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"def all_standard_tableaux(n):\\n\\tfor shape in all_diagrams(n):\\n\\t\\tyield from all_standard_fillings(shape)\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 5615984505213831895,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 2811724997650705139,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"output\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}((0, 1, 2, 3),)\\n((0, 1, 2), (3,))\\n((0, 1, 3), (2,))\\n((0, 2, 3), (1,))\\n((0, 1), (2,), (3,))\\n((0, 2), (1,), (3,))\\n((0, 3), (1,), (2,))\\n((0,), (1,), (2,), (3,))\\n((0, 1), (2, 3))\\n((0, 2), (1, 3))\\n\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"ignore_on_import\": true,\n\t\t\t\"source\": \"for tab in all_standard_tableaux(4):\\n\\tprint(tab)\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 4767728648789398550,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 13690048393920180737,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\algorithm{reduce_tableau(tab: tuple[tuple[int, ...], ...]) -> tuple[tuple[int, ...], ...]}{Return the tableau formed by\\nremoving the cell with the largest label}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\algorithm{reduce_tableau(tab: tuple[tuple[int, ...], ...]) -> tuple[tuple[int, ...], ...]}{Return the tableau formed by\\nremoving the cell with the largest label}\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 11319296881680315198,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"def reduce_tableau(tab):\\n\\tgreatest_elem = max(row[-1] for row in tab)\\n\\tres = []\\n\\tfor row in tab:\\n\\t\\tif row[-1] == greatest_elem:\\n\\t\\t\\tres.append(tuple(row[:-1]))\\n\\t\\telse:\\n\\t\\t\\tres.append(tuple(row))\\n\\treturn tuple(res)\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 2895358343697510309,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 15604320925891249630,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"verbatim\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}((0, 1, 2), (3,))\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"ignore_on_import\": true,\n\t\t\t\"source\": \"reduce_tableau([(0,1,2),(3,4)]);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 11724154751810140229,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 6932133234427607183,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\algorithm{augment_tableau(tab: tuple[tuple[int, ...], ...], label: int|None) -> list[tuple[tuple[int, ...], ...]]}{Return a list of all \\ntableaux formed by augmenting \\\\texttt{tab} by one cell containing \\\\texttt{label}, or if it is \\\\texttt{None} then the next \\nsmallest integer not appearing in \\\\texttt{tab}}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\algorithm{augment_tableau(tab: tuple[tuple[int, ...], ...], label: int|None) -> list[tuple[tuple[int, ...], ...]]}{Return a list of all \\ntableaux formed by augmenting \\\\texttt{tab} by one cell containing \\\\texttt{label}, or if it is \\\\texttt{None} then the next \\nsmallest integer not appearing in \\\\texttt{tab}}\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 6350568945503319497,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"def augment_tableau(tab, label=None):\\n\\tif label is None:\\n\\t\\tlabel = max(get_indices(tab)) + 1\\n\\tres = []\\n\\tl = len(tab[0]) + 1\\n\\tfor i, row in enumerate(tab):\\n\\t\\tif len(row) < l:\\n\\t\\t\\tt = [list(row) for row in tab]\\n\\t\\t\\tt[i].append(label)\\n\\t\\t\\tres.append(t)\\n\\t\\t\\tl = len(row)\\n\\tt = [list(row) for row in tab]\\n\\tt.append([label])\\n\\tres.append(t)\\n\\treturn res\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 3458439947979261072,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 16291607045970059826,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"output\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}[[[0, 1, 3], [2]], [[0, 1], [2, 3]], [[0, 1], [2], [3]]]\\n\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"ignore_on_import\": true,\n\t\t\t\"source\": \"print(augment_tableau([(0,1), (2,)]))\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 547223697396526441,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 10349327229214313701,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\algorithm{create_hermitian_tableau(tab: tuple[tuple[int, ...], ...]) -> list[tuple[tuple[int, ...], ...]]}{Creates a list\\nof tableaux such that the projection of the tensor product of these tableaux is a Hermitian operator}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\algorithm{create_hermitian_tableau(tab: tuple[tuple[int, ...], ...]) -> list[tuple[tuple[int, ...], ...]]}{Creates a list\\nof tableaux such that the projection of the tensor product of these tableaux is a Hermitian operator}\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 5738760520193255271,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"def create_hermitian_tableau(tab):\\n\\tassert is_standard(tab), \\\"tableau must be standard to create hermitian operator\\\"\\n\\tif sum(get_shape(tab)) <= 2:\\n\\t\\treturn [tab]\\n\\tgreatest_elem = max(get_indices(tab))\\n\\treduced_tab = []\\n\\tfor row in tab:\\n\\t\\treduced_row = list(row)\\n\\t\\tif greatest_elem in row:\\n\\t\\t\\treduced_row.remove(greatest_elem)\\n\\t\\t\\tif len(reduced_row) > 0:\\n\\t\\t\\t\\treduced_tab.append(tuple(reduced_row))\\n\\t\\telse:\\n\\t\\t\\treduced_tab.append(tuple(reduced_row))\\n\\treduced_herm = create_hermitian_tableau(tuple(reduced_tab))\\n\\treturn reduced_herm + [tab] + reduced_herm\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 3458821597999155122,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"ignore_on_import\": true,\n\t\t\t\"source\": \"print(create_hermitian_tableau([(0,1)]))\\nprint(create_hermitian_tableau([(0,1), (2,)]))\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 9747535794170023450,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 2245474417180971535,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\algorithm{construct_tableaux(ident: Ex, syms: Ex, standard_only: bool) -> Generator[Ex]}{Generate all distinct (or standard)\\ntableaux which when associated with \\\\texttt{ident} satisfy the symmetries given in \\\\texttt{syms} (a comma separated list \\nof expressions which equal 0)}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\algorithm{construct_tableaux(ident: Ex, syms: Ex, standard_only: bool) -> Generator[Ex]}{Generate all distinct (or standard)\\ntableaux which when associated with \\\\texttt{ident} satisfy the symmetries given in \\\\texttt{syms} (a comma separated list \\nof expressions which equal 0)}\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 439892239497663920,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"def construct_tableaux(ident, syms, standard_only=False):\\n\\t__cdbkernel__ = create_scope()\\n\\tn = n_indices(ident.top())\\n\\ttableaux = all_standard_tableaux(n) if standard_only else all_distinct_tableaux(n)\\n\\tfor tab in tableaux:\\n\\t\\tTableauSymmetry(ident, tableaux_to_ex(tab))\\n\\t\\tbroken = False\\n\\t\\tif syms.top().name == r\\\"\\\\comma\\\":\\n\\t\\t\\tfor symm in syms.top().children():\\n\\t\\t\\t\\tif meld($@(symm)$) != 0:\\n\\t\\t\\t\\t\\tbroken = True\\n\\t\\t\\t\\t\\tbreak\\n\\t\\telse:\\n\\t\\t\\tif meld($@(syms)$) != 0:\\n\\t\\t\\t\\tbroken = True\\n\\t\\tif not broken: \\n\\t\\t\\tyield tab\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 9509740741945359566,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 3634572458389941807,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"output\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}Pairwise antisymmetry:\\n((0,), (1,), (2,), (3,))\\n((0, 2), (1, 3))\\n((0, 3), (1, 2))\\nRiemann tensor symmetry:\\n((0, 2), (1, 3))\\n((0, 3), (1, 2))\\nRiemann tensor without Bianchi constraint:\\n((0,), (1,), (2,), (3,))\\n((0, 2), (1, 3))\\n((0, 3), (1, 2))\\nBianchi symmetries:\\n((1, 0, 2), (3,))\\n((1, 0, 3), (2,))\\n((2, 0, 1), (3,))\\n((2, 0, 3), (1,))\\n((3, 0, 1), (2,))\\n((3, 0, 2), (1,))\\n((0, 1), (2, 3))\\n((0, 1), (3, 2))\\n((0, 2), (1, 3))\\n((0, 2), (3, 1))\\n((0, 3), (1, 2))\\n((0, 3), (2, 1))\\n\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"ignore_on_import\": true,\n\t\t\t\"source\": \"pairwise_antisym := \\n\\tT_{a b c d} + T_{b a c d},\\n\\tT_{a b c d} + T_{a b d c}.\\nprint(\\\"Pairwise antisymmetry:\\\")\\nfor tableau in construct_tableaux($T_{a b c d}$, pairwise_antisym):\\n\\tprint(tableau)\\n\\nriemann := \\n\\tT_{a b c d} + T_{b a c d}, \\n\\tT_{a b c d} + T_{a b d c}, \\n\\tT_{a b c d} - T_{c d a b}, \\n\\tT_{a b c d} + T_{a c d b} + T_{a d b c}.\\nprint(\\\"Riemann tensor symmetry:\\\")\\nfor tableau in construct_tableaux($T_{a b c d}$, riemann):\\n\\tprint(tableau)\\n\\nriemann_no_bianchi :=\\n\\tT_{a b c d} + T_{b a c d},\\n\\tT_{a b c d} + T_{a b d c},\\n\\tT_{a b c d} - T_{c d a b}.\\nprint(\\\"Riemann tensor without Bianchi constraint:\\\")\\nfor tableau in construct_tableaux($T_{a b c d}$, riemann_no_bianchi):\\n\\tprint(tableau)\\n\\nbianchi := \\n\\tT_{a b c d} + T_{a c d b} + T_{a d b c}.\\nprint(\\\"Bianchi symmetries:\\\")\\nfor tableau in construct_tableaux($T_{a b c d}$, bianchi):\\n\\tprint(tableau)\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 2634122740391551161,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"R_{a b c d}::TableauSymmetry(shape={2,2}, indices={0,3,1,2}).\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 16983882067327749729,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"\"\n\t\t}\n\t],\n\t\"description\": \"Cadabra JSON notebook format\",\n\t\"version\": 1.0\n}\n"
  },
  {
    "path": "core/packages/cdb/utils/types.cnb",
    "content": "{\n\t\"cell_id\" : 3055175442602437687,\n\t\"cells\" : \n\t[\n\t\t{\n\t\t\t\"cell_id\" : 9256297574510892724,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 9256297574510892724,\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\package{cdb.utils.types}{Determining semantic properties of nodes}\\n\\nThis package contains simple wrappers for various useful checks on nodes to determine semantic information based on their name, \\nnumber of children, etc...\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\package{cdb.utils.types}{Determining semantic properties of nodes}\\n\\nThis package contains simple wrappers for various useful checks on nodes to determine semantic information based on their name, \\nnumber of children, etc...\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 5684905940070203990,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 14027713561723842750,\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\algorithm{is_relational_operator(node: ExNode) -> bool}{Returns True for $=$, $<$ and $>$ nodes}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\algorithm{is_relational_operator(node: ExNode) -> bool}{Returns True for $=$, $<$ and $>$ nodes}\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 1429712140485337784,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"def is_relational_operator(node):\\n\\treturn node.name in [r'\\\\equals', r'\\\\less', r'\\\\greater']\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 16326753075780368906,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 15503606750955089630,\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\algorithm{is_relational_expression(ex: Ex) -> bool}{Returns True for expressions which contain a top node which is a relational\\noperator and exactly two children}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\algorithm{is_relational_expression(ex: Ex) -> bool}{Returns True for expressions which contain a top node which is a relational\\noperator and exactly two children}\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 18335364954917430677,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"def is_relational_expression(ex):\\n\\treturn is_relational_operator(ex.top()) and n_args(ex.top()) == 2\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 5422877163838814435,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1\n}\n"
  },
  {
    "path": "core/passing.cc",
    "content": "\n#include <iostream>\n\nint k=5;\n\nvoid fun(int * &p)\n\t{\n\tp=&k;\n\t}\n\nint main()\n\t{\n\tint i=3;\n\tint *p = &i;\n\n\tstd::cout << *p << std::endl;\n\tfun(p);\n\tstd::cout << *p << std::endl;\n\t}\n"
  },
  {
    "path": "core/properties/Accent.cc",
    "content": "\n#include \"properties/Accent.hh\"\n\nusing namespace cadabra;\n\nAccent::~Accent()\n\t{\n\t}\n\nstd::string Accent::name() const\n\t{\n\treturn \"Accent\";\n\t}\n\n"
  },
  {
    "path": "core/properties/Accent.cnb",
    "content": "{\n\t\"cells\" : \n\t[\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\property{Accent}{Turn a symbol into an accent.}\\n\\nTurns a symbol into an accent. Accented objects inherit all properties\\nand indices from the objects which they wrap. Here is an example with\\ninherited coordinate dependence,\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\property{Accent}{Turn a symbol into an accent.}\\n\\nTurns a symbol into an accent. Accented objects inherit all properties\\nand indices from the objects which they wrap. Here is an example with\\ninherited coordinate dependence,\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Accent to~}\\\\widehat{\\\\#}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property PartialDerivative to~}\\\\partial{\\\\#}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Depends to~}A.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\partial\\\\left(A \\\\widehat{A} B\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"\\\\hat{#}::Accent;\\n\\\\partial{#}::PartialDerivative;\\nA::Depends(\\\\partial{#}, \\\\hat{#});\\nex:=\\\\partial(A \\\\hat{A} B);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\partial{A} \\\\widehat{A} B+A \\\\partial\\\\left(\\\\widehat{A}\\\\right) B+A \\\\widehat{A} \\\\partial{B}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"product_rule(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\partial{A} \\\\widehat{A} B+A \\\\partial\\\\left(\\\\widehat{A}\\\\right) B+A \\\\widehat{A} \\\\partial{B}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"unwrap(_, $\\\\partial{#}$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1\n}\n"
  },
  {
    "path": "core/properties/Accent.hh",
    "content": "\n#pragma once\n\n#include \"properties/IndexInherit.hh\"\n#include \"properties/NumericalFlat.hh\"\n\nnamespace cadabra {\n\n\t/**\n\t\t\t\t\\ingroup properties\n\n\tTurns a symbol into an accent. Accented objects inherit all properties\n\tand indices from the objects which they wrap.\n\t*/\n\n\tclass Accent : public PropertyInherit, public IndexInherit, public NumericalFlat, virtual public property {\n\t\tpublic:\n\t\t\tvirtual ~Accent();\n\t\t\tvirtual std::string name() const;\n\t\t};\n\n\n\t}\n"
  },
  {
    "path": "core/properties/Accent.tex",
    "content": "\\cdbproperty{Accent}{}\n\nTurns a symbol into an accent. Accented objects inherit all properties\nand indices from the objects which they wrap. Here is an example with\ninherited coordinate dependence:\n\\begin{screen}{1,2,3,4,5,6}\n\\hat{#}::Accent.\n\\partial{#}::PartialDerivative.\nA::Depends(\\partial).\n\\partial(A \\hat{A} B):\n@prodrule!(%):\n@unwrap!(%);\n\\partial(A) * A * B + A * \\partial(\\hat{A}) * B;\n\\end{screen}\nWithout the accent property, \\verb|\\hat{A}| object would be a\ncompletely independent object, unrelated to \\verb|A|.\n\n\\cdbseeprop{PropertyInherit}\n\\cdbseeprop{IndexInherit}\n\n"
  },
  {
    "path": "core/properties/AntiCommuting.cc",
    "content": "\n#include \"properties/AntiCommuting.hh\"\n\nusing namespace cadabra;\n\nAntiCommuting::~AntiCommuting()\n\t{\n\t}\n\nstd::string AntiCommuting::name() const\n\t{\n\treturn \"AntiCommuting\";\n\t}\n"
  },
  {
    "path": "core/properties/AntiCommuting.cnb",
    "content": "{\n\t\"cells\" : \n\t[\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\property{AntiCommuting}{Make objects anti-commuting.}\\n\\nMakes components anti-commuting, for example\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\property{AntiCommuting}{Make objects anti-commuting.}\\n\\nMakes components anti-commuting, for example\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property AntiCommuting to~}\\\\left[A,~\\\\discretionary{}{}{} B\\\\right].\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}B A\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}-A B\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"{A,B}::AntiCommuting;\\nex:=B A;\\nsort_product(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"It also works for objects with indices:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"It also works for objects with indices:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\psi_{m} \\\\chi \\\\psi_{n}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}-\\\\chi \\\\psi_{m} \\\\psi_{n}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"{\\\\psi_{m}, \\\\chi}::AntiCommuting.\\nex:= \\\\psi_{m} \\\\chi \\\\psi_{n};\\nsort_product(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"If you want a pattern like \\\\verb|\\\\psi_{m}| to anti-commute with\\nitself, you should use the \\\\prop{SelfAntiCommuting} property instead.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"If you want a pattern like \\\\verb|\\\\psi_{m}| to anti-commute with\\nitself, you should use the \\\\prop{SelfAntiCommuting} property instead.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"You can think about the difference\\nbetween \\\\prop{SelfAntiCommuting} and \\\\prop{AntiCommuting} in\\nthe following way. If \\\\verb|A_{m n}| is \\\\prop{SelfAntiCommuting}, it\\nmeans that for each value of the indices the expression \\\\verb|A_{m n}|\\nis an operator which anti-commutes with the operator for any other\\nvalue of the indices. The matrix~$A$ is thus a matrix of\\noperator-valued components which mutually anti-commute. On the other\\nhand, if \\\\verb|A| and\\n \\\\verb|B| are declared to\\nbe \\\\prop{AntiCommuting}, then these can be viewed as two matrices of\\ncommuting components, whose matrix product satisfies~$A B = - B A$.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"You can think about the difference\\nbetween \\\\prop{SelfAntiCommuting} and \\\\prop{AntiCommuting} in\\nthe following way. If \\\\verb|A_{m n}| is \\\\prop{SelfAntiCommuting}, it\\nmeans that for each value of the indices the expression \\\\verb|A_{m n}|\\nis an operator which anti-commutes with the operator for any other\\nvalue of the indices. The matrix~$A$ is thus a matrix of\\noperator-valued components which mutually anti-commute. On the other\\nhand, if \\\\verb|A| and\\n \\\\verb|B| are declared to\\nbe \\\\prop{AntiCommuting}, then these can be viewed as two matrices of\\ncommuting components, whose matrix product satisfies~$A B = - B A$.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"If you attach the \\\\prop{AntiCommuting} property to an object\\nwith an \\\\prop{ImplicitIndex} property, the commutation property does\\nnot refer to the object as a whole, but rather to its components. The\\nlogic behind that becomes clear when considering e.g.~spinor bilinears,\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"If you attach the \\\\prop{AntiCommuting} property to an object\\nwith an \\\\prop{ImplicitIndex} property, the commutation property does\\nnot refer to the object as a whole, but rather to its components. The\\nlogic behind that becomes clear when considering e.g.~spinor bilinears,\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Spinor to~}\\\\left[\\\\chi,~\\\\discretionary{}{}{} \\\\psi\\\\right].\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property AntiCommuting to~}\\\\left[\\\\chi,~\\\\discretionary{}{}{} \\\\psi\\\\right].\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property DiracBar to~}\\\\bar{\\\\#}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property GammaMatrix to~}\\\\Gamma\\\\left(\\\\#\\\\right).\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property SortOrder to~}\\\\left[\\\\chi,~\\\\discretionary{}{}{} \\\\psi\\\\right].\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\bar{\\\\psi} \\\\Gamma_{m n p} \\\\chi\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"{\\\\chi, \\\\psi}::Spinor(dimension=10, type=MajoranaWeyl);\\n{\\\\chi, \\\\psi}::AntiCommuting;\\n\\\\bar{#}::DiracBar;\\n\\\\Gamma{#}::GammaMatrix;\\n{\\\\chi, \\\\psi}::SortOrder;\\nex:=\\\\bar{\\\\psi} \\\\Gamma_{m n p} \\\\chi;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\bar{\\\\psi} \\\\Gamma_{m n p} \\\\chi\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"sort_product(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\bar{\\\\chi} \\\\Gamma_{m n p} \\\\psi\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"sort_spinors(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"Here \\\\algo{sort_product} did not act because both the spinors and\\nthe gamma matrices have the \\\\prop{ImplicitIndex} property and\\nthere are thus no simple rules for their re-ordering. However,\\nthe \\\\algo{sort_spinors} algorithm did act, and took into account\\nthe fact that the components of the spinors are anti-commuting.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"Here \\\\algo{sort_product} did not act because both the spinors and\\nthe gamma matrices have the \\\\prop{ImplicitIndex} property and\\nthere are thus no simple rules for their re-ordering. However,\\nthe \\\\algo{sort_spinors} algorithm did act, and took into account\\nthe fact that the components of the spinors are anti-commuting.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1\n}\n"
  },
  {
    "path": "core/properties/AntiCommuting.hh",
    "content": "\n#pragma once\n\n#include \"properties/CommutingBehaviour.hh\"\n\nnamespace cadabra {\n\n\tclass AntiCommuting : virtual public CommutingBehaviour {\n\t\tpublic:\n\t\t\tvirtual ~AntiCommuting();\n\t\t\tvirtual std::string name() const;\n\t\t\tvirtual int sign() const\n\t\t\t\t{\n\t\t\t\treturn -1;\n\t\t\t\t}\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/properties/AntiCommuting.tex",
    "content": "\\cdbproperty{AntiCommuting}{}\n\nMakes components anti-commuting. Example:\n\\begin{screen}{1,2}\n{A,B}::AntiCommuting.\nB A;\n@prodsort!(%);\n(-1) A B;\n\\end{screen}\nIt also works for objects with indices:\n\\begin{screen}{1,2}\n{\\psi_{m}, \\chi}::AntiCommuting.\n\\psi_{m} \\chi \\psi_{n};\n@prodsort!(%);\n(-1) \\chi \\psi_{m} \\psi_{n};\n\\end{screen}\nIf you want a pattern like \\verb|\\psi_{m}| to anti-commute with\nitself, you should use the \\subsprop{SelfAntiCommuting} property instead.\n\nYou can think about the difference\nbetween \\subsprop{SelfAntiCommuting} and \\subsprop{AntiCommuting} in\nthe following way. If \\verb|A_{m n}| is \\verb|SelfAntiCommuting|, it\nmeans that for each value of the indices the expression \\verb|A_{m n}|\nis an operator which anti-commutes with the operator for any other\nvalue of the indices. The matrix~$A$ is thus a matrix of\noperator-valued components which mutually anti-commute. On the other\nhand, if \\verb|A| and \\verb|B| are declared to\nbe \\verb|AntiCommuting|, then these can be viewed as two matrices of\ncommuting components, whose matrix product satisfies~$A B = - B A$.\n\nIf you attach the \\verb|AntiCommuting| property to an object\nwith an \\subsprop{ImplicitIndex} property, the commutation property does\nnot refer to the object as a whole, but rather to its components. The\nlogic behind that becomes clear when considering e.g.~spinor bilinears\n\\begin{screen}{1,2,3,4,5,6,7,9}\n{\\chi, \\psi}::Spinor(dimension=10, type=MajoranaWeyl).\n{\\chi, \\psi}::AntiCommuting.\n\\bar{#}::DiracBar.\n\\Gamma{#}::GammaMatrix.\n{\\chi, \\psi}::SortOrder.\n\\bar{\\psi} \\Gamma_{m n p} \\chi;\n@prodsort!(%);\n@prodsort: not applicable.\n@spinorsort!(%);\n\\bar{\\chi} \\Gamma_{m n p} \\psi;\n\\end{screen}\nHere \\subscommand{prodsort} did not act because both the spinors and\nthe gamma matrices have the \\subsprop{ImplicitIndex} property and\nthere are thus no simple rules for their re-ordering. However,\nthe \\subscommand{spinorsort} algorithm did act, and took into account\nthe fact that the components of the spinors are anti-commuting.\n\n\\cdbseealgo{prodsort}\n\\cdbseealgo{spinorsort}\n\\cdbseeprop{SelfAntiCommuting}\n\\cdbseeprop{Commuting}\n\\cdbseeprop{ImplicitIndex}\n"
  },
  {
    "path": "core/properties/AntiSelfDual.tex",
    "content": "\\cdbproperty{AntiSelfDual}{}\n\nMake a tensor fully anti-symmetric as well as anti-selfdual. The\nconventions used are that self-duality means\n\\begin{equation}\nF_{\\mu_1\\cdots \\mu_n}\n= - \\frac{1}{n!} \\epsilon_{\\mu_1\\cdots\\mu_n \\mu_{n+1}\\cdots \\mu_{2n}} F_{\\mu_{n+1}\\cdots\\mu_{2n}}\\,.\n\\end{equation}\nThis property used by the Young projection algorithms and\nthe \\subscommand{dualise\\_tensor} algorithm, among others.\n\n\\cdbseeprop{SelfDual}\n\\cdbseealgo{dualise_tensor}\n\\cdbseealgo{young_project_tensor}\n"
  },
  {
    "path": "core/properties/AntiSymmetric.cc",
    "content": "\n#include \"Algorithm.hh\"\n#include \"properties/AntiSymmetric.hh\"\n\nusing namespace cadabra;\n\nAntiSymmetric::~AntiSymmetric()\n\t{\n\t}\n\nstd::string AntiSymmetric::name() const\n\t{\n\treturn \"AntiSymmetric\";\n\t}\n\nunsigned int AntiSymmetric::size(const Properties&, Ex&, Ex::iterator) const\n\t{\n\treturn 1;\n\t}\n\nTableauBase::tab_t AntiSymmetric::get_tab(const Properties& pr, Ex& tr, Ex::iterator it, unsigned int num) const\n\t{\n\tassert(num==0);\n\n\tconst AntiSymmetric *pd;\n\tfor(;;) {\n\t\tpd=pr.get<AntiSymmetric>(it);\n\t\tif(!pd)\n\t\t\tit=tr.begin(it);\n\t\telse break;\n\t\t}\n\n\ttab_t tab;\n\tfor(unsigned int i=0; i<Algorithm::number_of_indices(pr, it); ++i)\n\t\ttab.add_box(i,i);\n\treturn tab;\n\t}\n\n"
  },
  {
    "path": "core/properties/AntiSymmetric.cnb",
    "content": "{\n\t\"cells\" : \n\t[\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\property{AntiSymmetric}{Make an object anti-symmetric in all indices.}\\n\\nMake an object anti-symmetric in all indices. This information is then\\nsubsequently used by various algorithms, for instance \\\\algo{canonicalise}. \\nAn example:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\property{AntiSymmetric}{Make an object anti-symmetric in all indices.}\\n\\nMake an object anti-symmetric in all indices. This information is then\\nsubsequently used by various algorithms, for instance \\\\algo{canonicalise}. \\nAn example:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}A_{m n} B_{m n}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"A_{m n}::AntiSymmetric.\\nB_{m n}::Symmetric.\\nex:=A_{m n} B_{m n};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}0\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"canonicalise(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"If you need anti-symmetry in only a subset of all indices of a tensor, you need to use the\\n\\\\prop{TableauSymmetry} property. A quick example:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"If you need anti-symmetry in only a subset of all indices of a tensor, you need to use the\\n\\\\prop{TableauSymmetry} property. A quick example:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property TableauSymmetry to~}C_{a n p}.\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"C_{a n p}::TableauSymmetry(shape={1,1}, indices={1,2});\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"This gives indices 1 and 2 (counting starts from 0) the symmetry of the Young Tableau\\nformed by two rows, each containing 1 box, which is the fully anti-symmetric representation of the \\npermutation group. Now you get, as expected,\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"This gives indices 1 and 2 (counting starts from 0) the symmetry of the Young Tableau\\nformed by two rows, each containing 1 box, which is the fully anti-symmetric representation of the \\npermutation group. Now you get, as expected,\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}C_{a n p}+C_{a p n}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex:=C_{a n p} + C_{a p n};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}0\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"canonicalise(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"For more information see the \\\\prop{TableauSymmetry} documentation.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"For more information see the \\\\prop{TableauSymmetry} documentation.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1\n}\n"
  },
  {
    "path": "core/properties/AntiSymmetric.hh",
    "content": "\n#pragma once\n\n\n#include \"properties/TableauBase.hh\"\n#include \"properties/Traceless.hh\"\n\nnamespace cadabra {\n\n\tclass AntiSymmetric : public TableauBase, public Traceless, virtual public property {\n\t\tpublic:\n\t\t\tvirtual ~AntiSymmetric();\n\t\t\tvirtual std::string name() const override;\n\n\t\t\tvirtual unsigned int size(const Properties&, Ex&, Ex::iterator) const override;\n\t\t\tvirtual tab_t        get_tab(const Properties&, Ex&, Ex::iterator, unsigned int) const override;\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/properties/AntiSymmetric.tex",
    "content": "\\cdbproperty{AntiSymmetric}{}\n\nMakes an object antisymmetric in all its indices. Example:\n\\begin{screen}{1,2,3,4}\nA_{m n}::AntiSymmetric.\nB_{m n}::Symmetric.\nA_{m n} B_{m n};\n@canonicalise!(%);\n0;\n\\end{screen}\nFor more complicated symmetries, use \\subsprop{TableauSymmetry}.\n\n\\cdbseealgo{canonicalise}\n\\cdbseeprop{Symmetric}\n\\cdbseeprop{TableauSymmetry}\n\\cdbseeprop{DAntiSymmetric}\n\n"
  },
  {
    "path": "core/properties/Commuting.cc",
    "content": "\n#include \"properties/Commuting.hh\"\n\nusing namespace cadabra;\n\nCommuting::~Commuting()\n\t{\n\t}\n\nstd::string Commuting::name() const\n\t{\n\treturn \"Commuting\";\n\t}\n"
  },
  {
    "path": "core/properties/Commuting.cnb",
    "content": "\n{\n\t\"cells\" : \n\t[\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\property{Commuting}{Make components commuting.}\\n\\nMakes components commuting. This is completely analogous\\nto \\\\prop{AntiCommuting} and in fact the default for all objects,\\nso usually does not need to be specified.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\property{Commuting}{Make components commuting.}\\n\\nMakes components commuting. This is completely analogous\\nto \\\\prop{AntiCommuting} and in fact the default for all objects,\\nso usually does not need to be specified.\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1.0\n}\n\n"
  },
  {
    "path": "core/properties/Commuting.hh",
    "content": "\n#pragma once\n\n#include \"properties/CommutingBehaviour.hh\"\n\nnamespace cadabra {\n\n\tclass Commuting : virtual public CommutingBehaviour {\n\t\tpublic:\n\t\t\tvirtual ~Commuting();\n\t\t\tvirtual std::string name() const;\n\t\t\tvirtual int sign() const\n\t\t\t\t{\n\t\t\t\treturn 1;\n\t\t\t\t}\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/properties/Commuting.tex",
    "content": "\\cdbproperty{Commuting}{}\n\nMakes components commuting. This is completely analogous\nto \\subsprop{AntiCommuting} and in fact the default for all objects,\nso usually does not need to be specified.\n\n\\cdbseeprop{AntiCommuting}\n\n"
  },
  {
    "path": "core/properties/CommutingAsProduct.cc",
    "content": "\n#include \"properties/CommutingAsProduct.hh\"\n\nusing namespace cadabra;\n\nstd::string CommutingAsProduct::name() const\n\t{\n\treturn \"CommutingAsProduct\";\n\t}\n\n"
  },
  {
    "path": "core/properties/CommutingAsProduct.cnb",
    "content": "\n{\n\t\"cells\" : \n\t[\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\property{CommutingAsProduct}{Makes an object behave as a product when commuting.}\\n\\nThis makes an object behave, for purposes of commutation rules, as a\\nproduct. That is, when trying to move another object through it, the\\nsign that is picked up is determined by moving the other object\\nthrough all the non-index children. \"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\property{CommutingAsProduct}{Makes an object behave as a product when commuting.}\\n\\nThis makes an object behave, for purposes of commutation rules, as a\\nproduct. That is, when trying to move another object through it, the\\nsign that is picked up is determined by moving the other object\\nthrough all the non-index children. \"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property CommutingAsProduct to~}A(\\\\#).\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property AntiCommuting to~}(Q, X, Y, Z).\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}A(Y Z Q) A(X)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"A(#)::CommutingAsProduct;\\n{Q,X,Y,Z}::AntiCommuting;\\nex:= A(Y)(Z)(Q)*A(X);\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}-A(X) A(Y Z Q)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"sort_product(_);\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"The minus sign arises because it would also have been present when\\nsorting \\\\verb|(Y*Z*Q)*X|. \"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"The minus sign arises because it would also have been present when\\nsorting \\\\verb|(Y*Z*Q)*X|. \"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1.0\n}\n\n"
  },
  {
    "path": "core/properties/CommutingAsProduct.hh",
    "content": "\n#pragma once\n\n#include \"Props.hh\"\n\nnamespace cadabra {\n\n\tclass CommutingAsProduct : virtual public property {\n\t\tpublic:\n\t\t\tvirtual std::string name() const;\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/properties/CommutingAsProduct.tex",
    "content": "\\cdbproperty{CommutingAsProduct}{}\n\nThis makes an object behave, for purposes of commutation rules, as a\nproduct. That is, when trying to move another object through it, the\nsign that is picked up is determined by moving the other object\nthrough all the non-index children. \n\nIn the example below, \n\\begin{screen}{1,2,3}\nA(#)::CommutingAsProduct.\n{Q,X,Y,Z}::AntiCommuting.\nA(Y)(Z)(Q)*A(X);\n@prodsort!(%);\n(-1) A(X) A(Y)(Z)(Q);\n\\end{screen}\nThe minus sign arises because it would also have been present when\nsorting {\\tt (Y*Z*Q)*X}. \n\nNote that this does not work when the arguments are given as a\nlist separated by commas, for instance as {\\tt A(Y,Z,Q)}. \n% \\begin{screen}{1,2,3}\n% A(#)::CommutingAsProduct.\n% \\comma{#}::CommutingAsProduct.\n% {Q,X,Y,Z}::AntiCommuting.\n% A(Y,Z,Q)*A(X);\n% @prodsort!(%);\n% (-1) A(X) A(Y)(Z)(Q);\n% \\end{screen}\n\n\\cdbseeprop{CommutingAsSum}\n\\cdbseeprop{AntiCommuting}\n\n"
  },
  {
    "path": "core/properties/CommutingAsSum.cc",
    "content": "\n#include \"properties/CommutingAsSum.hh\"\n\nusing namespace cadabra;\n\nstd::string CommutingAsSum::name() const\n\t{\n\treturn \"CommutingAsSum\";\n\t}\n\n"
  },
  {
    "path": "core/properties/CommutingAsSum.cnb",
    "content": "\n{\n\t\"cells\" : \n\t[\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\property{CommutingAsSum}{Makes an object behave as a sum when commuting.}\\n\\nThis makes an object behave, for purposes of commutation rules, as a\\nsum.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\property{CommutingAsSum}{Makes an object behave as a sum when commuting.}\\n\\nThis makes an object behave, for purposes of commutation rules, as a\\nsum.\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property CommutingAsSum to~}A(\\\\#).\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property AntiCommuting to~}(Q, X, Y, Z).\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}A(Y Z) A(X)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"A(#)::CommutingAsSum;\\n{Q,X,Y,Z}::AntiCommuting;\\nex:= A(Y)(Z)*A(X);\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}-A(X) A(Y Z)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"sort_product(_);\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"The minus sign arises because it would also have been present when\\nsorting the expression \\\\verb|(Y+Z)*X|.\\n\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"The minus sign arises because it would also have been present when\\nsorting the expression \\\\verb|(Y+Z)*X|.\\n\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1.0\n}\n\n"
  },
  {
    "path": "core/properties/CommutingAsSum.hh",
    "content": "\n#pragma once\n\n#include \"Props.hh\"\n\nnamespace cadabra {\n\n\tclass CommutingAsSum : virtual public property {\n\t\tpublic:\n\t\t\tvirtual std::string name() const;\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/properties/CommutingAsSum.tex",
    "content": "\\cdbproperty{CommutingAsSum}{}\n\nThis makes an object behave, for purposes of commutation rules, as a\nsum.\n\\begin{screen}{1,2,3}\nA(#)::CommutingAsSum.\n{Q,X,Y,Z}::AntiCommuting.\nA(Y)(Z)*A(X);\n@prodsort!(%);\n(-1) A(X) A(Y)(Z);\n\\end{screen}\nThe minus sign arises because it would also have been present when\nsorting the expression {\\tt (Y+Z)*X}. \n\nNote that this does not (yet) work when the arguments are given as a\nlist separated by commas, as in {\\tt A(Y,Z)}.\n\n\\cdbseeprop{CommutingAsProduct}\n\\cdbseeprop{AntiCommuting}\n\n"
  },
  {
    "path": "core/properties/CommutingBehaviour.cc",
    "content": "\n#include \"properties/CommutingBehaviour.hh\"\n\nusing namespace cadabra;\n\nproperty::match_t CommutingBehaviour::equals(const property *) const\n\t{\n\treturn no_match; // you can have as many of these as you like\n\t}\n\n"
  },
  {
    "path": "core/properties/CommutingBehaviour.hh",
    "content": "\n#pragma once\n\n#include \"Props.hh\"\n\nnamespace cadabra {\n\n\tclass CommutingBehaviour : virtual public list_property {\n\t\tpublic:\n\t\t\tvirtual int sign() const=0;\n\t\t\tvirtual match_t equals(const property *) const;\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/properties/Coordinate.cc",
    "content": "\n#include \"properties/Coordinate.hh\"\n#include \"properties/Indices.hh\"\n#include \"Exceptions.hh\"\n#include \"Kernel.hh\"\n#include \"Functional.hh\"\n\nusing namespace cadabra;\n\nstd::string Coordinate::name() const\n\t{\n\treturn \"Coordinate\";\n\t}\n\nvoid Coordinate::validate(Kernel& k, std::shared_ptr<Ex> ex) const\n\t{\n\tdo_list(*ex, ex->begin(),\n\t\t\t  [&k](Ex::iterator i)\n\t\t\t\t  {\n\t\t\t\t  Ex tmp(i);\n\t\t\t\t  tmp.begin()->fl.parent_rel=str_node::parent_rel_t::p_sub;\n\t\t\t\t  if(k.properties.get<Indices>(tmp.begin()))\n\t\t\t\t\t  throw ConsistencyException(\"Object already has an Indices property attached to it.\");\n\t\t\t\t  tmp.begin()->fl.parent_rel=str_node::parent_rel_t::p_super;\n\t\t\t\t  if(k.properties.get<Indices>(tmp.begin()))\n\t\t\t\t\t  throw ConsistencyException(\"Object already has an Indices property attached to it.\");\n\t\t\t\t  return true;\n\t\t\t\t  }\n\t\t\t  );\n\t}\n"
  },
  {
    "path": "core/properties/Coordinate.cnb",
    "content": "{\n\t\"cell_id\": 12308248189559892792,\n\t\"cells\": [\n\t\t{\n\t\t\t\"cell_id\": 6847719313692388189,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 12202434670886178648,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\property{Coordinate}{Declare a symbol to be a coordinate label.}\\n\\nDeclare a symbol to be a coordinate label (useful in combination\\nwith \\\\prop{Depends}). This is required if you want to write a\\nderivative with respect to a coordinate: if you write\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\property{Coordinate}{Declare a symbol to be a coordinate label.}\\n\\nDeclare a symbol to be a coordinate label (useful in combination\\nwith \\\\prop{Depends}). This is required if you want to write a\\nderivative with respect to a coordinate: if you write\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 13965430122641534132,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 2729351009933441984,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"error\",\n\t\t\t\t\t\"source\": \"{\\\\color{red}{\\\\begin{verbatim}RuntimeError: Free indices in different terms in a sum do not match.\\n\\nAt:\\n  Notebook Cell (Line 2): ex = Ex(r''' A(x,y) + \\\\partial_{x}{B(x,y)}'''); _=ex; display(ex)\\n\\\\end{verbatim}}}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"\\\\partial{#}::PartialDerivative.\\nex:= A(x,y) + \\\\partial_{x}{B(x,y)};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 4819941896955382090,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 13958906734848960010,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"will by default be seen as incorrect because the $x$ in the second\\nterm will be considered an index label, not a coordinate. The input\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"will by default be seen as incorrect because the $x$ in the second\\nterm will be considered an index label, not a coordinate. The input\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 14086010329010061981,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 10147094821929357556,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 3554707872972432039,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"A(x , y) + \\\\partial_{x}(B(x , y))\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}A\\\\left(x , \\\\discretionary{}{}{}y\\\\right)\\\\discretionary{}{}{}+\\\\partial_{x}{B\\\\left(x , \\\\discretionary{}{}{}y\\\\right)}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"{ x, y }::Coordinate.\\nex:=A(x,y) + \\\\partial_{x}{B(x,y)};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 16416609308264552501,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 17507747920193600578,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"is allowed and interpreted in the right way.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"is allowed and interpreted in the right way.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 12903276971402392966,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"\"\n\t\t}\n\t],\n\t\"description\": \"Cadabra JSON notebook format\",\n\t\"version\": 1.0\n}\n"
  },
  {
    "path": "core/properties/Coordinate.hh",
    "content": "\n#pragma once\n\n#include \"Props.hh\"\n\nnamespace cadabra {\n\n\tclass Coordinate : public property {\n\t\tpublic:\n\t\t\tvirtual std::string name() const;\n\t\t\tvirtual void        validate(Kernel&, std::shared_ptr<Ex>) const;\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/properties/Coordinate.tex",
    "content": "\\cdbproperty{Coordinate}{}\n\nDeclare a symbol to be a coordinate label (useful in combination\n  with \\subsprop{Depends}). This is required if you want to write a\n  derivative with respect to a coordinate: the input\n\\begin{screen}{1}\nA(x,x') + \\diff{B(x,x')}_{x};\n\\end{screen}\nwill by default be seen as incorrect because the $x$ in the second\nterm will be considered an index label, not a coordinate. The input\n\\begin{screen}{1,2}\n{ x, x' }::Coordinate.\nA(x,x') + \\diff{B(x,x')}_{x};\n\\end{screen}\nis allowed and interpreted in the right way.\n\n\\cdbseeprop{Symbol}\n"
  },
  {
    "path": "core/properties/DAntiSymmetric.cc",
    "content": "\n#include \"properties/DAntiSymmetric.hh\"\n\nusing namespace cadabra;\n\nstd::string DAntiSymmetric::name() const\n\t{\n\treturn \"DAntiSymmetric\";\n\t}\n\nunsigned int DAntiSymmetric::size(const Properties&, Ex&, Ex::iterator) const\n\t{\n\treturn 1;\n\t}\n\nTableauBase::tab_t DAntiSymmetric::get_tab(const Properties& properties, Ex& tr, Ex::iterator it, unsigned int num) const\n\t{\n\tassert(num==0);\n\n\tconst DAntiSymmetric *pd;\n\tfor(;;) {\n\t\tpd=properties.get<DAntiSymmetric>(it);\n\t\tif(!pd)\n\t\t\tit=tr.begin(it);\n\t\telse break;\n\t\t}\n\n\ttab_t tab;\n\ttab.add_box(0,1);\n\ttab.add_box(0,0); // these were in the wrong order!!!\n\tfor(unsigned int i=2; i<tr.number_of_children(it); ++i)\n\t\ttab.add_box(i-1,i);\n\treturn tab;\n\t}\n"
  },
  {
    "path": "core/properties/DAntiSymmetric.cnb",
    "content": "\n{\n\t\"cells\" : \n\t[\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\property{DAntiSymmetric}{Gives object the symmetries of the derivative of a fully antisymmetric tensor.}\\n\\nDeclares an object to have the symmetries of the derivative of a fully\\nanti-symmetric tensor, i.e.~to have a \\\\prop{TableauSymmetry}\\ncorresponding to a hook-shape Young tableau.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\property{DAntiSymmetric}{Gives object the symmetries of the derivative of a fully antisymmetric tensor.}\\n\\nDeclares an object to have the symmetries of the derivative of a fully\\nanti-symmetric tensor, i.e.~to have a \\\\prop{TableauSymmetry}\\ncorresponding to a hook-shape Young tableau.\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property DAntiSymmetric to~}{DF}_(mnpq).\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property AntiSymmetric to~}{A}_(mnpq).\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}DF_{m n p q} A^{m n p q}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"DF_{m n p q}::DAntiSymmetric;\\nA_{m n p q}::AntiSymmetric;\\nex:=DF_{m n p q} A^{m n p q};\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}DF^{m n p q} A_{m n p q}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"The symmetries can also be declared directly\\nusing \\\\prop{TableauSymmetry} but it is usually easier to read the\\n\\\\prop{DAntiSymmetric} form.\\n\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"The symmetries can also be declared directly\\nusing \\\\prop{TableauSymmetry} but it is usually easier to read the\\n\\\\prop{DAntiSymmetric} form.\\n\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1.0\n}\n\n"
  },
  {
    "path": "core/properties/DAntiSymmetric.hh",
    "content": "\n#pragma once\n\n#include \"properties/TableauBase.hh\"\n\nnamespace cadabra {\n\n\tclass DAntiSymmetric : public TableauBase, virtual public property {\n\t\tpublic:\n\t\t\tvirtual ~DAntiSymmetric() {};\n\t\t\tvirtual std::string name() const override;\n\n\t\t\tvirtual unsigned int size(const Properties&, Ex&, Ex::iterator) const override;\n\t\t\tvirtual tab_t        get_tab(const Properties&, Ex&, Ex::iterator, unsigned int) const override;\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/properties/DAntiSymmetric.tex",
    "content": "\\cdbproperty{DAntiSymmetric}{}\n\nDeclares an object to have the symmetries of the derivative of a fully\nanti-symmetric tensor, i.e.~to have a \\subsprop{TableauSymmetry}\ncorresponding to a hook-shape Young tableau.\n\\begin{screen}{1,2}\nDF_{m n p q}::DAntiSymmetric.\nA_{m n p q}::AntiSymmetric.\nDF_{m n p q} A^{m n p q};\n@impose_bianchi!(%);\n0;\n\\end{screen}\nThe symmetries can also be declared directly\nusing \\subsprop{TableauSymmetry} but it is usually easier to read the\n\\subsprop{DAntiSymmetric}\nform.\n\n\\cdbseeprop{TableauSymmetry}\n\\cdbseeprop{AntiSymmetric}\n"
  },
  {
    "path": "core/properties/Depends.cc",
    "content": "\n#include \"properties/Depends.hh\"\n#include \"properties/Indices.hh\"\n#include \"properties/Coordinate.hh\"\n#include \"properties/Derivative.hh\"\n#include \"properties/Accent.hh\"\n#include \"Exceptions.hh\"\n#include \"Kernel.hh\"\n\nusing namespace cadabra;\n\nstd::string Depends::name() const\n\t{\n\treturn \"Depends\";\n\t}\n\nbool Depends::parse(Kernel& kernel, keyval_t& kv)\n\t{\n\tconst Properties& pr=kernel.properties;\n\n\tkeyval_t::const_iterator it=kv.begin();\n\tdependencies_.set_head(str_node(\"\\\\comma\"));\n\tEx::iterator comma = dependencies_.begin();\n\t//\tEx::iterator comma = dependencies_.append_child(dependencies_.begin(), str_node(\"\\\\comma\"));\n\twhile(it!=kv.end()) {\n\t\tif(it->first==\"dependants\") {\n\t\t\tconst Indices    *dum=pr.get<Indices>(it->second.begin(), true);\n\t\t\tconst Coordinate *crd=pr.get<Coordinate>(it->second.begin());\n\t\t\tconst Derivative *der=pr.get<Derivative>(it->second.begin());\n\t\t\tconst Accent     *acc=pr.get<Accent>(it->second.begin());\n\t\t\tif(dum==0 && crd==0 && der==0 && acc==0) {\n\t\t\t\tthrow ArgumentException(std::string(\"Depends: \")+*it->second.begin()->name\n\t\t\t\t                        +\" lacks property Coordinate, Derivative, Accent or Indices.\\nIn 2.x, make sure to write dependence on a derivative\\nas A::Depends(\\\\partial{#}), note the '{#}'.\");\n\t\t\t\t}\n\t\t\t//\t\t\tstd::cout << \"adding \" << *it->second->name << \" to deps list\" << std::endl;\n\t\t\tdependencies_.append_child(comma, it->second.begin());\n\t\t\t}\n\t\t++it;\n\t\t}\n\n\treturn true;\n\t}\n\nEx Depends::dependencies(const Kernel&, Ex::iterator) const\n\t{\n\treturn dependencies_;\n\t}\n"
  },
  {
    "path": "core/properties/Depends.cnb",
    "content": "{\n\t\"cell_id\": 15383381436396341334,\n\t\"cells\": [\n\t\t{\n\t\t\t\"cell_id\": 6020749098024884238,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 4910824880255499277,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\property{Depends}{Makes an object implicitly dependent on other objects.}\\n\\nMakes an object implicitly dependent on other objects, i.e.~assumes\\nthat the indicated object is a function of the arguments of the\\nproperty. For example\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\property{Depends}{Makes an object implicitly dependent on other objects.}\\n\\nMakes an object implicitly dependent on other objects, i.e.~assumes\\nthat the indicated object is a function of the arguments of the\\nproperty. For example\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 10933035081687051752,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 17730837097666924186,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Attached property Coordinate to~}x.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 4424240274618919769,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Attached property Depends to~}\\\\phi.\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"x::Coordinate;\\n\\\\phi::Depends(x);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 2649437745767218223,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 16910720361941362315,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"makes $\\\\phi$ an implicit function of $x$. Instead of indicating the\\ncoordinate on which the object depends, it is also possible to\\nindicate which derivatives would yield a non-zero answer, as in\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"makes $\\\\phi$ an implicit function of $x$. Instead of indicating the\\ncoordinate on which the object depends, it is also possible to\\nindicate which derivatives would yield a non-zero answer, as in\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 2225917996266670719,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 17311460073182692618,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Attached property Derivative to~}\\\\nabla{\\\\#}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 17530187230455340883,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Attached property Depends to~}\\\\phi.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 18264881303581541750,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 5318602600250318696,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\nabla_{m}(\\\\phi c \\\\sin(y))\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\nabla_{m}\\\\left(\\\\phi c \\\\sin{y}\\\\right)\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 2519536452405989300,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 2105272590527625871,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"c \\\\sin(y) \\\\nabla_{m}(\\\\phi)\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}c \\\\sin{y} \\\\nabla_{m}{\\\\phi}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"\\\\nabla{#}::Derivative;\\n\\\\phi::Depends(\\\\nabla{#});\\nex:=\\\\nabla_{m}{\\\\phi c \\\\sin{y}};\\nunwrap(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 9917880054462086620,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 7573189513765282444,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"(Note: if you did this in Cadabra 1.x you could write \\\\verb|Depends(\\\\nabla)|; this is no longer \\npossible in 2.x and you need to write the full pattern \\\\verb|Depends(\\\\nabla{#})|). \\nFinally, it is possible to use an index name to indicate on which\\ncoordinates a field depends,\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"(Note: if you did this in Cadabra 1.x you could write \\\\verb|Depends(\\\\nabla)|; this is no longer \\npossible in 2.x and you need to write the full pattern \\\\verb|Depends(\\\\nabla{#})|). \\nFinally, it is possible to use an index name to indicate on which\\ncoordinates a field depends,\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 779241970792918393,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 2959988321147213328,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property Derivative attached to~}\\\\nabla{\\\\#}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 5778576878287523724,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property Indices(position=free) attached to~}\\\\left[\\\\mu,~\\\\discretionary{}{}{} \\\\nu\\\\right].\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 17728765352013426296,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property Depends attached to~}\\\\chi.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 16027798804825528227,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 16892754417118162490,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\nabla_{\\\\mu}(\\\\chi) + \\\\nabla_{\\\\mu}(\\\\rho)\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\nabla_{\\\\mu}{\\\\chi}+\\\\nabla_{\\\\mu}{\\\\rho}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 16911408471678705912,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 7695447514682173235,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\nabla_{\\\\mu}(\\\\chi)\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\nabla_{\\\\mu}{\\\\chi}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"\\\\nabla{#}::Derivative;\\n{\\\\mu,\\\\nu}::Indices;\\n\\\\chi::Depends(\\\\mu);\\nex:=\\\\nabla_{\\\\mu}{\\\\chi} + \\\\nabla_{\\\\mu}{\\\\rho};\\nunwrap(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 15454189233784161729,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 5207881987443951320,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"To make a tensor with any type and number of indices \\\\prop{Depend} on something else,\\nuse\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"To make a tensor with any type and number of indices \\\\prop{Depend} on something else,\\nuse\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 5208397427434026018,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 7796681554320905148,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Attached property Depends to~}h\\\\left(\\\\#\\\\right).\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 15888095070088685022,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 15103775522095930169,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\nabla_{m}(c d h^{0 t} h_{t 0} h^{0}_{0})\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\nabla_{m}\\\\left(c d h^{0 t} h_{t 0} h^{0}\\\\,_{0}\\\\right)\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 8327134344680474765,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 3527694145945193084,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"c d \\\\nabla_{m}(h^{0 t} h_{t 0} h^{0}_{0})\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}c d \\\\nabla_{m}\\\\left(h^{0 t} h_{t 0} h^{0}\\\\,_{0}\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"h{#}::Depends(\\\\nabla{#});\\nex:=\\\\nabla_{m}{ c d h^{0 t} h_{t 0} h^{0}_{0} };\\nunwrap(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 17340488615041470285,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 7339588896490186114,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Attached property Indices(position=free) to~}\\\\left[m,~\\\\discretionary{}{}{} n,~\\\\discretionary{}{}{} p,~\\\\discretionary{}{}{} q\\\\right].\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 13810305355999156769,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Attached property Depends to~}\\\\phi.\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"{m,n,p,q}::Indices(vector);\\n\\\\phi::Depends(m);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 12321058079793781466,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 17893413500898855549,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\nIf you want to make an object depend on more than one thing, you need\\nto specify them all in one \\\\prop{Depends} property. If you specify\\nthem in two separate properties, the last property will overwrite\\nthe previous one. Therefore, you get\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\nIf you want to make an object depend on more than one thing, you need\\nto specify them all in one \\\\prop{Depends} property. If you specify\\nthem in two separate properties, the last property will overwrite\\nthe previous one. Therefore, you get\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 8106929047029971935,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 15873721191759500494,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Attached property Accent to~}\\\\widehat{\\\\#}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 11321432652759574780,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Attached property Coordinate to~}\\\\left(x, \\\\linebreak[0] y\\\\right).\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 1058409645044592999,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Attached property PartialDerivative to~}\\\\partial{\\\\#}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 13844808077340533221,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Attached property Depends to~}A.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 13216314927744868318,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Attached property Depends to~}A.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 14657993155715685903,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\widehat{A}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 14452584277662090922,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}0\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"\\\\hat{#}::Accent;\\n{x,y}::Coordinate;\\n\\\\partial{#}::PartialDerivative;\\nA::Depends(\\\\hat{#});\\nA::Depends(x);\\nex:=\\\\hat{A};\\nunwrap(ex);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 17546269387797006387,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"\"\n\t\t}\n\t],\n\t\"description\": \"Cadabra JSON notebook format\",\n\t\"version\": 1.0\n}\n"
  },
  {
    "path": "core/properties/Depends.hh",
    "content": "#pragma once\n\n#include \"properties/DependsBase.hh\"\n\nnamespace cadabra {\n\n\tclass Depends : public DependsBase, virtual public property {\n\t\tpublic:\n\t\t\tvirtual std::string name() const override;\n\t\t\tvirtual bool parse(Kernel&, keyval_t&) override;\n\t\t\tvirtual Ex dependencies(const Kernel&, Ex::iterator) const override;\n\t\t\tvirtual std::string unnamed_argument() const override\n\t\t\t\t{\n\t\t\t\treturn \"dependants\";\n\t\t\t\t};\n\t\tprivate:\n\t\t\tEx dependencies_;\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/properties/Depends.tex",
    "content": "\\cdbproperty{Depends}{\\it comma separated list of indices,\ncoordinates, derivatives, accents}\n\nMakes an object implicitly dependent on other objects, i.e.~assumes\nthat the indicated object is a function of the arguments of the\nproperty. For example,\n\\begin{screen}{1,2}\nx::Coordinate.\n\\phi::Depends(x).\n\\end{screen}\nmakes $\\phi$ an implicit function of $x$. Instead of indicating the\ncoordinate on which the object depends, it is also possible to\nindicate which derivatives would yield a non-zero answer, as in\n\\begin{screen}{1,2}\n\\nabla{#}::Derivative.\n\\phi::Depends(\\nabla).\n\\end{screen}\nFinally, it is possible to use an index name to indicate on which\ncoordinates a field depends,\n\\begin{screen}{1,2}\n{m,n,p,q}::Indices(vector).\n\\phi::Depends(m).\n\\end{screen}\n\nTaking objects out of derivatives (because they do not depend on them)\nis handled using the \\subscommand{unwrap} algorithm.\n\nIf you want to make an object depend on more than one thing, you need\nto specify them all in one \\subsprop{Depends} property. If you specify\nthem in two separate properties, the last property will overwrite\nthe previous one. Therefore, you get\n\\begin{screen}{1,2,3,4,5,6}\n\\hat{#}::Accent.\n\\partial{#}::PartialDerivative.\nA::Depends(\\hat).\nA::Depends(\\partial).\n\\hat{A};\n@unwrap!(%);\nA;\n\\end{screen}\ninstead of \\verb|\\hat{A}| which you might have expected.\n\n\\cdbseealgo{unwrap}\n\\cdbseeprop{Derivative}\n\n"
  },
  {
    "path": "core/properties/DependsBase.hh",
    "content": "\n#pragma once\n\n#include \"Props.hh\"\n#include \"Kernel.hh\"\n\nnamespace cadabra {\n\n\t/// \\ingroup core\n\n\tclass DependsBase : virtual public property {\n\t\tpublic:\n\t\t\t/// Returns a tree of objects on which the given object depends.\n\t\t\tvirtual Ex dependencies(const Kernel&, Ex::iterator) const=0;\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/properties/DependsInherit.cc",
    "content": "\n#include \"properties/DependsInherit.hh\"\n\nusing namespace cadabra;\n\nstd::string DependsInherit::name() const\n\t{\n\treturn \"DependsInherit\";\n\t}\n\nEx DependsInherit::dependencies(const Kernel& kernel, Ex::iterator it) const\n\t{\n\t// std::cerr << \"DependsInherit::dependencies\" << std::endl;\n\tEx ret(\"\\\\comma\");\n\tEx::sibling_iterator sib=it.begin();\n\twhile(sib!=it.end()) {\n\t\tconst DependsBase *dep=kernel.properties.get<DependsBase>(sib);\n\t\tif(dep) {\n\t\t\t// std::cerr << \"found dep \" << dep->dependencies(kernel, sib) << \" for \" << *sib->name << std::endl;\n\t\t\tEx::iterator cn=ret.append_child(ret.begin(), dep->dependencies(kernel, sib).begin());\n\t\t\tret.flatten(cn);\n\t\t\tret.erase(cn);\n\t\t\t}\n\t\t++sib;\n\t\t}\n\treturn ret;\n\t}\n\n"
  },
  {
    "path": "core/properties/DependsInherit.hh",
    "content": "\n#pragma once\n\n#include \"properties/DependsBase.hh\"\n\nnamespace cadabra {\n\n\t/// \\ingroup properties\n\n\tclass DependsInherit : public DependsBase, virtual public property {\n\t\tpublic:\n\t\t\tvirtual std::string name() const override;\n\t\t\tvirtual Ex dependencies(const Kernel&, Ex::iterator) const override;\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/properties/DependsInherit.tex",
    "content": "\\cdbproperty{DependsInherit}{}\n\nMakes an object inherit all dependencies of the objects they\ncontain. This makes it possible to define functions of objects which\nbehave correctly inside derivatives.\n\\begin{screen}{1,2}\nf{#}::DependsInherit.\nx::Coordinate.\n\\partial{#}::PartialDerivative.\n\\phi::Depends(x).\n\\partial_{x}( g f(\\phi) );\n@unwrap!(%);\ng \\partial_{x}( f(\\phi) );\n\\end{screen}\n~\n\n\\cdbseealgo{unwrap}\n\\cdbseeprop{PartialDerivative}\n\n"
  },
  {
    "path": "core/properties/Derivative.cc",
    "content": "\n#include \"properties/Derivative.hh\"\n#include \"Props.hh\"\n#include \"Kernel.hh\"\n\nusing namespace cadabra;\n\nDerivative::~Derivative()\n\t{\n\t}\n\nbool Derivative::parse(Kernel&, std::shared_ptr<Ex>, keyval_t& keyvals)\n\t{\n\tkeyval_t::const_iterator ki=keyvals.begin();\n\twhile(ki!=keyvals.end()) {\n\t\tif(ki->first==\"to\") {\n\t\t\twith_respect_to=ki->second;\n\t\t\t}\n\t\t++ki;\n\t\t}\n\treturn true;\n\t}\n\t\t\t\nmultiplier_t Derivative::value(const Kernel& kernel, Ex::iterator it, const std::string& forcedlabel) const\n\t{\n\tconst Properties& properties=kernel.properties;\n\t//\ttxtout << \"!?!?\" << std::endl;\n\tmultiplier_t ret=0;\n\n\tEx::sibling_iterator sib=it.begin();\n\twhile(sib!=it.end()) {\n\t\tconst WeightBase *gnb=properties.get<WeightBase>(sib, forcedlabel);\n\t\tif(gnb) {\n\t\t\tmultiplier_t tmp=gnb->value(kernel, sib, forcedlabel);\n\t\t\tif(sib->is_index()) ret-=tmp;\n\t\t\telse                ret+=tmp;\n\t\t\t//\t\t\ttxtout << *sib->name << \" = \" << tmp << std::endl;\n\t\t\t}\n\t\t++sib;\n\t\t}\n\treturn ret;\n\t}\n\nstd::string Derivative::name() const\n\t{\n\treturn \"Derivative\";\n\t}\n\nunsigned int Derivative::size(const Properties& properties, Ex& tr, Ex::iterator it) const\n\t{\n\tit=properties.head<Derivative>(it);\n\treturn TableauInherit::size(properties, tr, it);\n\t}\n\nTableauBase::tab_t Derivative::get_tab(const Properties& properties, Ex& tr, Ex::iterator it, unsigned int num) const\n\t{\n\tit=properties.head<Derivative>(it);\n\treturn TableauInherit::get_tab(properties, tr, it, num);\n\t}\n"
  },
  {
    "path": "core/properties/Derivative.cnb",
    "content": "\n{\n\t\"cells\" : \n\t[\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\property{Derivative}{Declare an operator to satisfy the Leibnitz rule.}\\n\\nThis property representes an generic derivative object, satisfying the Leibnitz rule. These\\ngeneric derivatives do not have to commute\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\property{Derivative}{Declare an operator to satisfy the Leibnitz rule.}\\n\\nThis property representes an generic derivative object, satisfying the Leibnitz rule. These\\ngeneric derivatives do not have to commute\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Derivative to~}D(\\\\#).\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}D(A B C)\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}D(A) B C+A D(B) C+A B D(C)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"D{#}::Derivative;\\nex:= D(A B C);\\nproduct_rule(_);\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"Refer to the documentation of \\\\prop{PartialDerivative} on how to\\nwrite derivatives with respect to coordinate indices or coordinates.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"Refer to the documentation of \\\\prop{PartialDerivative} on how to\\nwrite derivatives with respect to coordinate indices or coordinates.\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"Make sure to declare the derivative either using the ``with any arguments''\\nnotation as used above (using the hash mark), or by giving an\\nappropriate pattern. The following does not work:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"Make sure to declare the derivative either using the ``with any arguments''\\nnotation as used above (using the hash mark), or by giving an\\nappropriate pattern. The following does not work:\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Derivative to~}D.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}D(A B C)\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}D(A B C)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"D::Derivative;\\nex:=D(A B C);\\nproduct_rule(_);\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"The pattern \\\\verb|D| above does not match the expression \\\\verb|D(A B C)| \\nand hence the algorithm does not know that \\\\verb|D(A B C)| is a\\nderivative acting on the product of three objects.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"The pattern \\\\verb|D| above does not match the expression \\\\verb|D(A B C)| \\nand hence the algorithm does not know that \\\\verb|D(A B C)| is a\\nderivative acting on the product of three objects.\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1.0\n}\n\n"
  },
  {
    "path": "core/properties/Derivative.hh",
    "content": "\n#pragma once\n\n#include \"properties/CommutingAsProduct.hh\"\n#include \"properties/NumericalFlat.hh\"\n#include \"properties/WeightBase.hh\"\n#include \"properties/TableauInherit.hh\"\n#include \"properties/Distributable.hh\"\n#include \"properties/DependsInherit.hh\"\n#include \"properties/IndexInherit.hh\"\n#include \"properties/SortOrder.hh\"\n#include \"properties/SelfCommutingBehaviour.hh\"\n\nnamespace cadabra {\n\n\tclass Derivative :\n\t\tpublic IndexInherit,\n\t\tpublic TableauInherit,\n\t\tpublic DependsInherit,\n\t\tpublic Inherit<SortOrder>,\n\t\tpublic Inherit<SelfCommutingBehaviour>,\n\t\tpublic CommutingAsProduct,\n\t\tpublic NumericalFlat,\n\t\tpublic WeightBase,\n//\t\tvirtual public TableauBase,\n\t\tpublic Distributable, virtual public property {\n\t\tpublic :\n\t\t\tvirtual ~Derivative();\n\t\t\tvirtual std::string name() const override;\n\n\t\t\tvirtual unsigned int size(const Properties&, Ex&, Ex::iterator) const override;\n\t\t\tvirtual tab_t        get_tab(const Properties&, Ex&, Ex::iterator, unsigned int) const override;\n\t\t\tvirtual multiplier_t value(const Kernel&, Ex::iterator, const std::string& forcedlabel) const override;\n\t\t\tvirtual bool         parse(Kernel&, std::shared_ptr<Ex>, keyval_t& keyvals) override;\n\t\t\tvirtual std::string unnamed_argument() const override\n\t\t\t\t{\n\t\t\t\treturn \"to\";\n\t\t\t\t};\n\t\n\t\t\tEx with_respect_to;\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/properties/Derivative.tex",
    "content": "\\cdbproperty{Derivative}{}\n\nAn generic derivative object, satisfying the Leibnitz rule. These\ngeneric derivatives do not have to commute.\n\\begin{screen}{1,2}\nD{#}::Derivative.\nD(A B C);\n@prodrule!(%);\nD(A) B C + A D(B) C + A B D(C);\n\\end{screen}\nRefer to the documentation of \\subsprop{PartialDerivative} on how to\nwrite derivatives with respect to coordinate indices or coordinates.\n\nMake sure to declare the derivative either using the ``with any arguments''\nnotation as used above (using the hash mark), or by giving an\nappropriate pattern. The following does not work:\n\\begin{screen}{1,2}\nD::Derivative.\nD(A B C);\n@prodrule!(%);\n@prodrule: not applicable.\n\\end{screen}\nThe pattern \\verb|D| above does not match the expression \\verb|D(A B C)| \nand hence the algorithm does not know that \\verb|D(A B C)| is a\nderivative acting on the product of three objects.\n\n\\cdbseealgo{prodrule}\n\\cdbseealgo{distribute}\n"
  },
  {
    "path": "core/properties/DerivativeOp.cc",
    "content": "\n#include \"properties/DerivativeOp.hh\"\n#include \"Props.hh\"\n#include \"Kernel.hh\"\n\nusing namespace cadabra;\n\nbool DerivativeOp::parse(Kernel&, std::shared_ptr<Ex>, keyval_t& keyvals)\n\t{\n\tkeyval_t::const_iterator ki=keyvals.begin();\n\tif(ki!=keyvals.end()) return false;\n\treturn true;\n\t}\n\nstd::string DerivativeOp::name() const\n\t{\n\treturn \"DerivativeOp\";\n\t}\n"
  },
  {
    "path": "core/properties/DerivativeOp.hh",
    "content": "\n#pragma once\n\n#include \"Props.hh\"\n\nnamespace cadabra {\n\t\n\tclass DerivativeOp : virtual public property {\n\t\tpublic :\n\t\t\tvirtual ~DerivativeOp() {};\n\t\t\tvirtual std::string name() const override;\n\t\t\tvirtual bool        parse(Kernel&, std::shared_ptr<Ex>, keyval_t& keyvals) override;\n\t};\n\t\n}\n"
  },
  {
    "path": "core/properties/Determinant.cc",
    "content": "\n#include \"Exceptions.hh\"\n#include \"properties/Determinant.hh\"\n\nusing namespace cadabra;\n\nDeterminant::Determinant()\n\t{\n\t}\n\nstd::string Determinant::name() const\n\t{\n\treturn \"Determinant\";\n\t}\n\nstd::string Determinant::unnamed_argument() const\n\t{\n\treturn \"object\";\n\t}\n\nbool Determinant::parse(Kernel&, keyval_t& keyvals)\n\t{\n\tkeyval_t::const_iterator kv=keyvals.find(\"object\");\n\tif(kv!=keyvals.end())\n\t\tobj = kv->second;\n\treturn true;\n\t}\n\nvoid Determinant::validate(Kernel&, std::shared_ptr<Ex> ) const\n\t{\n\t}\n\nvoid Determinant::latex(std::ostream& str) const\n\t{\n\tstr << name();\n\t}\n"
  },
  {
    "path": "core/properties/Determinant.cnb",
    "content": "{\n\t\"cells\" : \n\t[\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\property{Determinant}{Declares an object to be the determinant of a matrix or metric.}\\n\\nIn order to declare the name associated to the determinant of a matrix or metric, give it the\\n\\\\prop{Determinant} property, indicating the matrix or metric as an argument. This is mainly used\\nto compute determinants in components, but the property can also be used by algorithms which\\nonly deal with purely abstract properties, e.g.~covariant derivatives.\\n\\nThe following example shows how to declare a metric and its components, and then compute\\nthe determinant from there.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\property{Determinant}{Declares an object to be the determinant of a matrix or metric.}\\n\\nIn order to declare the name associated to the determinant of a matrix or metric, give it the\\n\\\\prop{Determinant} property, indicating the matrix or metric as an argument. This is mainly used\\nto compute determinants in components, but the property can also be used by algorithms which\\nonly deal with purely abstract properties, e.g.~covariant derivatives.\\n\\nThe following example shows how to declare a metric and its components, and then compute\\nthe determinant from there.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Coordinate to~}\\\\left[t,~\\\\discretionary{}{}{} r,~\\\\discretionary{}{}{} \\\\phi\\\\right].\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Indices(position=fixed) to~}\\\\left[m,~\\\\discretionary{}{}{} n,~\\\\discretionary{}{}{} p,~\\\\discretionary{}{}{} q\\\\right].\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Metric to~}g_{m n}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"{g_{t t} = -1, g_{r r} = 1, g_{\\\\phi \\\\phi} = (r)**2}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\left[g_{t t} = -1,~\\\\discretionary{}{}{} g_{r r} = 1,~\\\\discretionary{}{}{} g_{\\\\phi \\\\phi} = {r}^{2}\\\\right]\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"{t,r,\\\\phi}::Coordinate;\\n{m,n,p,q}::Indices(position=fixed, values={t,r,\\\\phi});\\ng_{m n}::Metric;\\nrl:= g_{t t} = -1, g_{r r} = 1, g_{\\\\phi \\\\phi} = r**2;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"Now we declare that $g$ denotes the determinant of the metric $g_{m n}$, and use \\\\algo{complete} to compute it\\ngiven the metric components.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"Now we declare that $g$ denotes the determinant of the metric $g_{m n}$, and use \\\\algo{complete} to compute it\\ngiven the metric components.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Determinant to~}g.\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"g::Determinant(g_{m n});\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"{g_{t t} = -1, g_{r r} = 1, g_{\\\\phi \\\\phi} = (r)**2, g = -(r)**2}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\left[g_{t t} = -1,~\\\\discretionary{}{}{} g_{r r} = 1,~\\\\discretionary{}{}{} g_{\\\\phi \\\\phi} = {r}^{2},~\\\\discretionary{}{}{} g = -{r}^{2}\\\\right]\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"complete(rl, $g$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1\n}\n"
  },
  {
    "path": "core/properties/Determinant.hh",
    "content": "\n#pragma once\n\n#include \"Props.hh\"\n#include \"properties/Symmetric.hh\"\n\nnamespace cadabra {\n\n\tclass Determinant : virtual public property {\n\t\tpublic:\n\t\t\tDeterminant();\n\t\t\tvirtual std::string name() const override;\n\t\t\tvirtual std::string unnamed_argument() const override;\n\t\t\tvirtual bool        parse(Kernel&, keyval_t&) override;\n\t\t\tvirtual void        validate(Kernel&, std::shared_ptr<Ex>) const override;\n\t\t\tvirtual void        latex(std::ostream&) const override;\n\n\t\t\tEx obj;\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/properties/Diagonal.cc",
    "content": "\n#include \"properties/Diagonal.hh\"\n\nusing namespace cadabra;\n\nstd::string Diagonal::name() const\n\t{\n\treturn \"Diagonal\";\n\t}\n\n"
  },
  {
    "path": "core/properties/Diagonal.cnb",
    "content": "\n{\n\t\"cells\" : \n\t[\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\property{Diagonal}{Declares a tensor to only have non-zero diagonal entries.}\\n\\nIndicates that the object to which the property is attached only has\\nnon-zero components on the diagonal, i.e.~when all indices take the\\nsame value. \"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\property{Diagonal}{Declares a tensor to only have non-zero diagonal entries.}\\n\\nIndicates that the object to which the property is attached only has\\nnon-zero components on the diagonal, i.e.~when all indices take the\\nsame value. \"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Diagonal to~}{\\\\delta}_(mn).\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\delta_{1 2} \\\\delta_{1 2}-\\\\delta_{1 1} \\\\delta_{2 2}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"\\\\delta_{m n}::Diagonal;\\nex:= \\\\delta_{1 2} \\\\delta_{1 2} - \\\\delta_{1 1} \\\\delta_{2 2};\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}-\\\\delta_{1 1} \\\\delta_{2 2}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"canonicalise(_);\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1.0\n}\n\n"
  },
  {
    "path": "core/properties/Diagonal.hh",
    "content": "\n#pragma once\n\n#include \"Props.hh\"\n#include \"properties/Symmetric.hh\"\n\nnamespace cadabra {\n\n\tclass Diagonal : public Symmetric {\n\t\tpublic:\n\t\t\tvirtual std::string name() const;\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/properties/Diagonal.tex",
    "content": "\\cdbproperty{Diagonal}{}\n\nIndicates that the object to which the property is attached only has\nnon-zero components on the diagonal, i.e.~when all indices take the\nsame value. \n\\begin{screen}{1,2}\n\\delta_{m n}::Diagonal.\n\\delta_{1 2} \\delta_{1 2} - \\delta_{1 1} \\delta_{2 2};\n@canonicalise!(%);\n- \\delta_{1 1}\\delta_{2 2};\n\\end{screen}\n~\n\n\\cdbseeprop{Coordinate}\n"
  },
  {
    "path": "core/properties/DifferentialForm.cc",
    "content": "\n#include \"DifferentialForm.hh\"\n\nusing namespace cadabra;\n\nDifferentialForm::~DifferentialForm()\n\t{\n\t}\n\nstd::string DifferentialForm::name() const\n\t{\n\treturn \"DifferentialForm\";\n\t}\n\nbool DifferentialForm::parse(Kernel&, keyval_t& keyvals)\n\t{\n\tfor(auto& kv: keyvals) {\n\t\tif(kv.first==\"degree\") {\n\t\t\tdegree_ = Ex(kv.second);\n\t\t\t}\n\t\t}\n\treturn true;\n\t}\n\nEx DifferentialForm::degree(const Properties&, Ex::iterator) const\n\t{\n\treturn degree_;\n\t}\n"
  },
  {
    "path": "core/properties/DifferentialForm.hh",
    "content": "\n#pragma once\n\n#include \"Props.hh\"\n#include \"properties/ImplicitIndex.hh\"\n#include \"properties/IndexInherit.hh\"\n#include \"properties/DifferentialFormBase.hh\"\n\nnamespace cadabra {\n\n\tclass DifferentialForm : public IndexInherit, public DifferentialFormBase {\n\t\tpublic:\n\t\t\tvirtual ~DifferentialForm();\n\t\t\tvirtual std::string name() const override;\n\t\t\tvirtual bool parse(Kernel&, keyval_t&) override;\n\n\t\t\tvirtual Ex degree(const Properties&, Ex::iterator) const override;\n\n\t\tprivate:\n\t\t\tEx degree_;\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/properties/DifferentialFormBase.hh",
    "content": "\n#pragma once\n\n#include \"Props.hh\"\n#include \"properties/ImplicitIndex.hh\"\n#include \"properties/IndexInherit.hh\"\n\nnamespace cadabra {\n\n\tclass DifferentialFormBase : virtual public property {\n\t\tpublic:\n\t\t\tvirtual Ex degree(const Properties&, Ex::iterator) const = 0;\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/properties/DiracBar.cc",
    "content": "\n#include \"DiracBar.hh\"\n\nusing namespace cadabra;\n\nDiracBar::~DiracBar()\n\t{\n\t}\n\nstd::string DiracBar::name() const\n\t{\n\treturn \"DiracBar\";\n\t}\n\n"
  },
  {
    "path": "core/properties/DiracBar.cnb",
    "content": "\n{\n\t\"cells\" : \n\t[\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\property{DiracBar}{An accent representing the Dirac conjugation operation.}\\n\\nDeclares an object to be the operator which applies the Dirac bar to a\\nspinor, i.e.~an operator which acts according to\\n\\\\begin{equation}\\n\\\\bar{\\\\psi} = i \\\\psi^\\\\dagger \\\\Gamma^0\\\\,.\\n\\\\end{equation}\\nFor more information see e.g.~\\\\algo{sort_spinors} or \\\\algo{fierz}.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\property{DiracBar}{An accent representing the Dirac conjugation operation.}\\n\\nDeclares an object to be the operator which applies the Dirac bar to a\\nspinor, i.e.~an operator which acts according to\\n\\\\begin{equation}\\n\\\\bar{\\\\psi} = i \\\\psi^\\\\dagger \\\\Gamma^0\\\\,.\\n\\\\end{equation}\\nFor more information see e.g.~\\\\algo{sort_spinors} or \\\\algo{fierz}.\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1.0\n}\n\n"
  },
  {
    "path": "core/properties/DiracBar.hh",
    "content": "\n#pragma once\n\n#include \"properties/Accent.hh\"\n#include \"properties/Distributable.hh\"\n\nnamespace cadabra {\n\n\tclass DiracBar : public Accent, public Distributable, virtual public property {\n\t\tpublic:\n\t\t\tvirtual ~DiracBar();\n\t\t\tvirtual std::string name() const;\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/properties/DiracBar.tex",
    "content": "\\cdbproperty{DiracBar}{}\n\nDeclares an object to be the operator which applies the Dirac bar to a\nspinor, i.e.~an operator which acts according to\n\\begin{equation}\n\\bar{\\psi} = i \\psi^\\dagger \\Gamma^0\\,.\n\\end{equation}\nFor more information see e.g.~\\subscommand{spinorsort} or \\subscommand{fierz}.\n\n\\cdbseeprop{Spinor}\n\\cdbseealgo{spinorsort}\n\\cdbseealgo{fierz}\n"
  },
  {
    "path": "core/properties/Distributable.cc",
    "content": "\n#include \"Distributable.hh\"\n\nusing namespace cadabra;\n\nstd::string Distributable::name() const\n\t{\n\treturn \"Distributable\";\n\t}\n\n"
  },
  {
    "path": "core/properties/Distributable.cnb",
    "content": "\n{\n\t\"cells\" : \n\t[\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\property{Distributable}{Make an operator distributable over its arguments.}\\n\\n Makes an operator distributable over its arguments, in the sense that when\\n  the object has a sum as argument, it can be distributed over the\\n  terms with \\\\algo{distribute}, as in\\n\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\property{Distributable}{Make an operator distributable over its arguments.}\\n\\n Makes an operator distributable over its arguments, in the sense that when\\n  the object has a sum as argument, it can be distributed over the\\n  terms with \\\\algo{distribute}, as in\\n\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Distributable to~}\\\\overline{\\\\#}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\overline{A+B+C D}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"\\\\overline{#}::Distributable;\\nex:= \\\\overline{A+B+C D};\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\overline{A}+\\\\overline{B}+\\\\overline{C D}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"distribute(_);\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1.0\n}\n\n"
  },
  {
    "path": "core/properties/Distributable.hh",
    "content": "\n#pragma once\n\n#include \"Props.hh\"\n\nnamespace cadabra {\n\n\tclass Distributable : virtual public  property {\n\t\tpublic:\n\t\t\tvirtual ~Distributable() {};\n\t\t\tvirtual std::string name() const;\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/properties/Distributable.tex",
    "content": "\\cdbproperty{Distributable}{}\n\n Makes an object distributable. When\n  the object has a sum as argument, it can be distributed over the\n  terms with \\subscommand{distribute}, as in\n\\begin{screen}{1,2,3}\n\\hat{#}::Distributable.\n\\hat{A+B+C D}:\n@distribute!(%);\n\\hat{A} + \\hat{B} + \\hat{C D};\n\\end{screen}\n~\n"
  },
  {
    "path": "core/properties/EpsilonTensor.cc",
    "content": "\n#include \"properties/EpsilonTensor.hh\"\n\nusing namespace cadabra;\n\nEpsilonTensor::~EpsilonTensor()\n\t{\n\t}\n\nstd::string EpsilonTensor::name() const\n\t{\n\treturn \"EpsilonTensor\";\n\t}\n\nbool EpsilonTensor::parse(Kernel&, keyval_t& keyvals)\n\t{\n\tkeyval_t::const_iterator kv=keyvals.find(\"metric\");\n\tif(kv!=keyvals.end()) metric=Ex(kv->second);\n\n\tkv=keyvals.find(\"delta\");\n\tif(kv!=keyvals.end()) krdelta=Ex(kv->second);\n\n\treturn true;\n\t}\n\n"
  },
  {
    "path": "core/properties/EpsilonTensor.cnb",
    "content": "\n{\n\t\"cells\" : \n\t[\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\property{EpsilonTensor}{A fully anti-symmetric tensor with constant components.}\\n\\nA fully anti-symmetric tensor, defined by\\n\\\\begin{equation}\\n\\\\epsilon_{m_1\\\\ldots m_k} := \\\\varepsilon_{m_1\\\\ldots m_k}\\\\,\\\\sqrt{|g|}\\\\,,\\n\\\\end{equation}\\nwhere the components of~$\\\\varepsilon_{m_1\\\\ldots m_k}$ are 0, $+1$ or $-1$\\nand~$\\\\varepsilon_{01\\\\cdots k}=1$,\\nindependent of the basis, and~$g$ denotes the metric\\ndeterminant. \\n\\nThis property optionally takes a tensor which indicates the symbol\\nwhich should be used as a \\\\prop{KroneckerDelta} symbol when\\nwriting out the product of two epsilon tensors. Additionally, it takes\\na tensor which is the associated metric, from which the signature can\\nbe extracted. See the documentation of \\\\algo{epsilon_to_delta}\\nfor more information on the use of these optional arguments.\\n\\nWhen the indices are in different positions it is understood that they\\nare simply raised with the metric. This in particular implies\\n\\\\begin{equation}\\n\\\\epsilon^{m_1\\\\ldots m_k} := g^{m_1 n_1} \\\\cdots g^{m_k n_k} \\n\\\\epsilon_{n_1\\\\ldots n_k} = \\\\frac{\\\\varepsilon^{m_1\\\\ldots m_k}}{\\\\sqrt{|g|}}\\\\,,\\n\\\\end{equation}\\nagain with~$\\\\varepsilon^{m_1\\\\ldots m_k}$ taking values 0, $+1$ or $-1$\\nand $\\\\varepsilon^{01\\\\cdots k}=\\\\pm 1$ depending on the signature of the\\nmetric.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\property{EpsilonTensor}{A fully anti-symmetric tensor with constant components.}\\n\\nA fully anti-symmetric tensor, defined by\\n\\\\begin{equation}\\n\\\\epsilon_{m_1\\\\ldots m_k} := \\\\varepsilon_{m_1\\\\ldots m_k}\\\\,\\\\sqrt{|g|}\\\\,,\\n\\\\end{equation}\\nwhere the components of~$\\\\varepsilon_{m_1\\\\ldots m_k}$ are 0, $+1$ or $-1$\\nand~$\\\\varepsilon_{01\\\\cdots k}=1$,\\nindependent of the basis, and~$g$ denotes the metric\\ndeterminant. \\n\\nThis property optionally takes a tensor which indicates the symbol\\nwhich should be used as a \\\\prop{KroneckerDelta} symbol when\\nwriting out the product of two epsilon tensors. Additionally, it takes\\na tensor which is the associated metric, from which the signature can\\nbe extracted. See the documentation of \\\\algo{epsilon_to_delta}\\nfor more information on the use of these optional arguments.\\n\\nWhen the indices are in different positions it is understood that they\\nare simply raised with the metric. This in particular implies\\n\\\\begin{equation}\\n\\\\epsilon^{m_1\\\\ldots m_k} := g^{m_1 n_1} \\\\cdots g^{m_k n_k} \\n\\\\epsilon_{n_1\\\\ldots n_k} = \\\\frac{\\\\varepsilon^{m_1\\\\ldots m_k}}{\\\\sqrt{|g|}}\\\\,,\\n\\\\end{equation}\\nagain with~$\\\\varepsilon^{m_1\\\\ldots m_k}$ taking values 0, $+1$ or $-1$\\nand $\\\\varepsilon^{01\\\\cdots k}=\\\\pm 1$ depending on the signature of the\\nmetric.\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1.0\n}\n\n"
  },
  {
    "path": "core/properties/EpsilonTensor.hh",
    "content": "\n#pragma once\n\n#include \"properties/AntiSymmetric.hh\"\n\nnamespace cadabra {\n\n\t/// \\ingroup properties\n\n\tclass EpsilonTensor : public AntiSymmetric, virtual public property {\n\t\tpublic:\n\t\t\tvirtual ~EpsilonTensor();\n\t\t\tvirtual std::string name() const override;\n\t\t\tvirtual bool parse(Kernel&, keyval_t&) override;\n\n\t\t\tEx metric, krdelta;\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/properties/EpsilonTensor.tex",
    "content": "\\cdbproperty{EpsilonTensor}{{\\it metric={\\sf metric object}, delta={\\sf\nKronecker delta name}}}\n\nA fully anti-symmetric tensor, defined by\n\\begin{equation}\n\\epsilon_{m_1\\ldots m_k} := \\varepsilon_{m_1\\ldots m_k}\\,\\sqrt{|g|}\\,,\n\\end{equation}\nwhere the components of~$\\varepsilon_{m_1\\ldots m_k}$ are 0, $+1$ or $-1$\nand~$\\varepsilon_{01\\cdots k}=1$,\nindependent of the basis, and~$g$ denotes the metric\ndeterminant. \n\nThis property optionally takes a tensor which indicates the symbol\nwhich should be used as a \\subsprop{KroneckerDelta} symbol when\nwriting out the product of two epsilon tensors. Additionally, it takes\na tensor which is the associated metric, from which the signature can\nbe extracted. See the documentation of \\subscommand{epsprod2gendelta}\nfor more information on the use of these optional arguments.\n\nWhen the indices are in different positions it is understood that they\nare simply raised with the metric. This in particular implies\n\\begin{equation}\n\\epsilon^{m_1\\ldots m_k} := g^{m_1 n_1} \\cdots g^{m_k n_k} \n\\epsilon_{n_1\\ldots n_k} = \\frac{\\varepsilon^{m_1\\ldots m_k}}{\\sqrt{|g|}}\\,,\n\\end{equation}\nagain with~$\\varepsilon^{m_1\\ldots m_k}$ taking values 0, $+1$ or $-1$\nand $\\varepsilon^{01\\cdots k}=\\pm 1$ depending on the signature of the\nmetric.\n\n\\cdbseealgo{epsprod2gendelta}\n"
  },
  {
    "path": "core/properties/ExteriorDerivative.cc",
    "content": "\n#include \"Exceptions.hh\"\n#include \"ExteriorDerivative.hh\"\n\nusing namespace cadabra;\n\nExteriorDerivative::~ExteriorDerivative()\n\t{\n\t}\n\nstd::string ExteriorDerivative::name() const\n\t{\n\treturn \"ExteriorDerivative\";\n\t}\n\nEx ExteriorDerivative::degree(const Properties& props, Ex::iterator it) const\n\t{\n\tauto sib=Ex::begin(it);\n\tint deg=1;\n\twhile(sib!=Ex::end(it)) {\n\t\tconst DifferentialFormBase *db = props.get<DifferentialFormBase>(sib);\n\t\tif(db) {\n\t\t\tauto thisdeg = db->degree(props, sib);\n\t\t\tif(thisdeg.is_rational()==false) {\n\t\t\t\t// std::cerr << thisdeg << std::endl;\n\t\t\t\tthrow NotYetImplemented(\"Cannot yet compute non-numerical form degrees.\");\n\t\t\t\t}\n\t\t\tdeg += to_long(thisdeg.to_rational());\n\t\t\t}\n\t\t++sib;\n\t\t}\n\treturn Ex(deg);\n\t}\n"
  },
  {
    "path": "core/properties/ExteriorDerivative.hh",
    "content": "\n#pragma once\n\n#include \"Props.hh\"\n#include \"properties/Derivative.hh\"\n#include \"properties/DifferentialFormBase.hh\"\n\nnamespace cadabra {\n\n\tclass ExteriorDerivative : public Derivative, public DifferentialFormBase {\n\t\tpublic:\n\t\t\tvirtual ~ExteriorDerivative();\n\t\t\tvirtual std::string name() const override;\n\n\t\t\tvirtual Ex degree(const Properties&, Ex::iterator) const override;\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/properties/FilledTableau.cc",
    "content": "\n#include \"properties/FilledTableau.hh\"\n\nusing namespace cadabra;\n\nstd::string FilledTableau::name() const\n\t{\n\treturn \"FilledTableau\";\n\t}\n\nbool FilledTableau::parse(Kernel&, keyval_t& keyvals)\n\t{\n\tkeyval_t::const_iterator kv=keyvals.find(\"dimension\");\n\tif(kv!=keyvals.end()) dimension=to_long(*(kv->second.begin()->multiplier));\n\telse dimension=-1;\n\treturn true;\n\t}\n"
  },
  {
    "path": "core/properties/FilledTableau.cnb",
    "content": "{\n\t\"cell_id\" : 3709770344770575223,\n\t\"cells\" : \n\t[\n\t\t{\n\t\t\t\"cell_id\" : 18315175544081447475,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 6317143617777149814,\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\property{Tableau}{A Young-tableau object with unlabelled boxes.}\\n\\nDeclares that the object carrying this property is used to label a Young tableau with\\nunlabelled boxes (Young diagram). The arguments of such objects denote the lenghts of the rows.\\nThe \\\\verb|dimension| argument of the property sets the dimension.\\n\\nCan be used in combination with the \\\\verb|lr_tensor| and \\\\verb|tab_dimension| algorithms\\nto compute tensor product representations.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\property{FilledTableau}{A Young-tableau object with labelled boxes.}\\n\\nDeclares that the object carrying this property is used to label a Young tableau with\\nlabelled boxes. The arguments of such objects are comma-separated lists of the contents\\nof the boxes in each row. The \\\\verb|dimension| argument of the property sets the dimension.\\n\\nCan be used in combination with the \\\\verb|lr_tensor| and \\\\verb|tab_dimension| algorithms\\nto compute tensor product representations.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 4814324193159731260,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 213677400209917287,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property FilledTableau to~}\\\\ytableaushort{{\\\\#}}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 9402199389898434983,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\" : 12576212416202906894,\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"\\\\tableau({c, c} , c) \\\\tableau({a, a} , b)\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\ytableaushort{{c}{c},{c}} \\\\otimes \\\\ytableaushort{{a}{a},{b}}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 13867533788213360416,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\" : 16962364561868398097,\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"\\\\tableau({c, c, a, a} , {c, b}) + \\\\tableau({c, c, a, a} , c , b) + \\\\tableau({c, c, a} , {c, a, b}) + \\\\tableau({c, c, a} , {c, a} , b) + \\\\tableau({c, c, a} , {c, b} , a) + \\\\tableau({c, c} , {c, a} , {a, b})\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\ytableaushort{{c}{c}{a}{a},{c}{b}} \\\\oplus \\\\ytableaushort{{c}{c}{a}{a},{c},{b}} \\\\oplus \\\\ytableaushort{{c}{c}{a},{c}{a}{b}} \\\\oplus \\\\ytableaushort{{c}{c}{a},{c}{a},{b}} \\\\oplus \\\\ytableaushort{{c}{c}{a},{c}{b},{a}} \\\\oplus \\\\ytableaushort{{c}{c},{c}{a},{a}{b}}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"\\\\tableau{#}::FilledTableau(dimension=3);\\nex:=\\\\tableau{c,c}{c}\\\\tableau{a,a}{b};\\nlr_tensor(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 6195976348837135823,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 697290612421312528,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"{}$\\\\big[$$\\\\verb|27|$,\\\\discretionary{}{}{} $\\\\verb|10|$,\\\\discretionary{}{}{} $\\\\verb|10|$,\\\\discretionary{}{}{} $\\\\verb|8|$,\\\\discretionary{}{}{} $\\\\verb|8|$,\\\\discretionary{}{}{} $\\\\verb|1|$$\\\\big]$\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"q=[int(tab_dimension(t.ex())) for t in ex.top().terms()];\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 10192517807076031993,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1\n}\n"
  },
  {
    "path": "core/properties/FilledTableau.hh",
    "content": "#pragma once\n\n#include \"Props.hh\"\n#include \"properties/ImplicitIndex.hh\"\n\nnamespace cadabra {\n\n\tclass FilledTableau : public ImplicitIndex, virtual public property {\n\t\tpublic:\n\t\t\tvirtual ~FilledTableau() {};\n\t\t\tvirtual std::string name() const override;\n\t\t\tvirtual bool        parse(Kernel&, keyval_t& keyvals) override;\n\n\t\t\tint dimension;\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/properties/FilledTableau.tex",
    "content": "\\cdbproperty{FilledTableau}{\\it dimension={\\sf integer}}\n\nIndicates that the object is a Young\n  tableau with labelled boxes. The arguments\n  of a \\subsprop{Tableau} property denote the contents, given as lists,\n\\begin{screen}{1,2}\n\\ftab{#}::FilledTableau.\n\\ftab{a,b,c}{d,e}{f};\n\\end{screen}\nIn the graphical interface this will display as\n\\begin{equation*}\n\\ftableau{a b c, d e, f}\n\\end{equation*}\nSee \\subsprop{Tableau} for information about adding the dimension of\nthe permutation group.\n\n"
  },
  {
    "path": "core/properties/GammaMatrix.cc",
    "content": "\n#include \"GammaMatrix.hh\"\n#include \"Kernel.hh\"\n\nusing namespace cadabra;\n\nGammaMatrix::~GammaMatrix()\n\t{\n\t}\n\nstd::string GammaMatrix::name() const\n\t{\n\treturn \"GammaMatrix\";\n\t}\n\nvoid GammaMatrix::latex(std::ostream& str) const\n\t{\n\tMatrix::latex(str);\n\t}\n\nbool GammaMatrix::parse(Kernel& kernel, keyval_t& keyvals)\n\t{\n\tkeyval_t::iterator kv=keyvals.find(\"metric\");\n\tif(kv!=keyvals.end()) {\n\t\tmetric=Ex(kv->second);\n\t\tkeyvals.erase(kv);\n\t\t}\n\n\tImplicitIndex::parse(kernel, keyvals);\n\tAntiSymmetric::parse(kernel, keyvals);\n\n\t//\tkv=keyvals.find(\"delta\");\n\t//\tif(kv!=keyvals.end()) delta=Ex(kv->second);\n\t//\n\treturn true;\n\t}\n"
  },
  {
    "path": "core/properties/GammaMatrix.cnb",
    "content": "\n{\n\t\"cells\" : \n\t[\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\property{GammaMatrix}{A generalised generator of a Clifford algebra.}\\n\\nA generalised generator of a Clifford algebra. With one vector index,\\n  it satisfies\\n\\\\begin{equation}\\n\\\\{ \\\\Gamma^m, \\\\Gamma^n \\\\} = 2\\\\,\\\\eta^{mn}\\\\,.\\n\\\\end{equation}\\nThe objects with more vector indices are defined as\\n\\\\begin{equation}\\n\\\\Gamma^{m_1\\\\ldots m_n} = \\\\Gamma^{[m_1}\\\\cdots \\\\Gamma^{m_n]}\\\\,,\\n\\\\end{equation}\\nwhere the anti-symmetrisation includes a division by~$n!$.\\nIf you intend to use the \\\\algo{join_gamma} algorithm, you have to add a\\nkey/value pair \\\\verb|metric| to set the name of the tensor which acts\\nas the unit element in the Clifford algebra.\\n\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\property{GammaMatrix}{A generalised generator of a Clifford algebra.}\\n\\nA generalised generator of a Clifford algebra. With one vector index,\\n  it satisfies\\n\\\\begin{equation}\\n\\\\{ \\\\Gamma^m, \\\\Gamma^n \\\\} = 2\\\\,\\\\eta^{mn}\\\\,.\\n\\\\end{equation}\\nThe objects with more vector indices are defined as\\n\\\\begin{equation}\\n\\\\Gamma^{m_1\\\\ldots m_n} = \\\\Gamma^{[m_1}\\\\cdots \\\\Gamma^{m_n]}\\\\,,\\n\\\\end{equation}\\nwhere the anti-symmetrisation includes a division by~$n!$.\\nIf you intend to use the \\\\algo{join_gamma} algorithm, you have to add a\\nkey/value pair \\\\verb|metric| to set the name of the tensor which acts\\nas the unit element in the Clifford algebra.\\n\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1.0\n}\n\n"
  },
  {
    "path": "core/properties/GammaMatrix.hh",
    "content": "\n#pragma once\n\n#include \"properties/Matrix.hh\"\n#include \"properties/AntiSymmetric.hh\"\n\nnamespace cadabra {\n\n\tclass GammaMatrix : public AntiSymmetric, public Matrix, virtual public property {\n\t\tpublic:\n\t\t\tvirtual ~GammaMatrix();\n\t\t\tvirtual std::string name() const override;\n\t\t\tvirtual void        latex(std::ostream&) const override;\n\t\t\tvirtual bool        parse(Kernel&, keyval_t& keyvals) override;\n\t\t\tvirtual std::string unnamed_argument() const override\n\t\t\t\t{\n\t\t\t\treturn \"explicit\";\n\t\t\t\t};\n\t\t\tEx metric;\n\t\t};\n\n\t}\n\n"
  },
  {
    "path": "core/properties/GammaMatrix.tex",
    "content": "\\cdbproperty{GammaMatrix}{\\it metric={\\sf metric name}}\n\nA generalised generator of a Clifford algebra. With one vector index,\n  it satisfies\n\\begin{equation}\n\\{ \\Gamma^m, \\Gamma^n \\} = 2\\,\\eta^{mn}\\,.\n\\end{equation}\nThe objects with more vector indices are defined as\n\\begin{equation}\n\\Gamma^{m_1\\ldots m_n} = \\Gamma^{[m_1}\\cdots \\Gamma^{m_n]}\\,,\n\\end{equation}\nwhere the anti-symmetrisation includes a division by~$n!$.\nIf you intend to use the \\subscommand{join} algorithm, you have to add a\nkey/value pair \\verb|metric| to set the name of the tensor which acts\nas the unit element in the Clifford algebra.\n"
  },
  {
    "path": "core/properties/GammaTraceless.cc",
    "content": "\n#include \"GammaTraceless.hh\"\n\nusing namespace cadabra;\n\nstd::string GammaTraceless::name() const\n\t{\n\treturn \"GammaTraceless\";\n\t}\n\n"
  },
  {
    "path": "core/properties/GammaTraceless.hh",
    "content": "\n#pragma once\n\n#include \"Props.hh\"\n\nnamespace cadabra {\n\n\tclass GammaTraceless : public property {\n\t\tpublic:\n\t\t\tvirtual ~GammaTraceless() {};\n\t\t\tvirtual std::string name() const;\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/properties/GammaTraceless.tex",
    "content": "\\cdbproperty{GammaTraceless}{}\n\nDeclares a spinor object with a vector index to be zero when it is\ncontracted with a gamma matrix.\n"
  },
  {
    "path": "core/properties/ImaginaryI.cc",
    "content": "\n#include \"properties/ImaginaryI.hh\"\n\nusing namespace cadabra;\n\nstd::string ImaginaryI::name() const\n\t{\n\treturn \"ImaginaryI\";\n\t}\n"
  },
  {
    "path": "core/properties/ImaginaryI.hh",
    "content": "\n#pragma once\n\n#include \"Props.hh\"\n\nnamespace cadabra {\n\n\tclass ImaginaryI : public property {\n\t\tpublic:\n\t\t\tvirtual std::string name() const override;\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/properties/ImplicitIndex.cc",
    "content": "\n#include \"properties/ImplicitIndex.hh\"\n#include \"Exceptions.hh\"\n\nusing namespace cadabra;\n\nstd::string ImplicitIndex::name() const\n\t{\n\treturn \"ImplicitIndex\";\n\t}\n\nbool ImplicitIndex::parse(Kernel&, keyval_t& keyvals)\n\t{\n\tkeyval_t::const_iterator ki=keyvals.begin();\n\twhile(ki!=keyvals.end()) {\n\t\t//\t\tstd::cout << \"ImplicitIndex: \" << ki->first << \" = \" << *ki->second->name << std::endl;\n\t\tif(ki->first==\"name\") {\n\t\t\tthrow std::logic_error(\"ImplicitIndex: argument 'name' no longer supported\");\n\t\t\t}\n\t\telse if(ki->first==\"explicit\") {\n\t\t\texplicit_form=ki->second;\n\t\t\t}\n\t\telse throw ConsistencyException(\"Property 'ImplicitIndex' does not accept key '\"+ki->first+\"'.\");\n\t\t++ki;\n\t\t}\n\n\treturn true;\n\t}\n\nvoid ImplicitIndex::latex(std::ostream& str) const\n\t{\n\tproperty::latex(str);\n\t//\tfor(size_t n=0; n<set_names.size(); ++n) {\n\t//\t\tif(n>0) str << \", \";\n\t//\t\tstr << set_names[n];\n\t//\t\t}\n\t}\n"
  },
  {
    "path": "core/properties/ImplicitIndex.cnb",
    "content": "\n{\n\t\"cells\" : \n\t[\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\property{ImplicitIndex}{Indicates that an object carries indices which are not written out.}\\n\\nIndicates that the object carries implicit indices, e.g.~for objects\\nrepresenting matrices or vectors. Such objects will not be moved\\nthrough each other, i.e.~they are mutually noncommuting.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\property{ImplicitIndex}{Indicates that an object carries indices which are not written out.}\\n\\nIndicates that the object carries implicit indices, e.g.~for objects\\nrepresenting matrices or vectors. Such objects will not be moved\\nthrough each other, i.e.~they are mutually noncommuting.\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property ImplicitIndex to~}(M, A).\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}M A\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}M A\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"{M,A}::ImplicitIndex;\\nex:=M A;\\nsort_product(_);\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"Without the \\\\prop{ImplicitIndex} property, \\\\algo{sort_product}\\nwould have freely moved the objects through each other.\\n\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"Without the \\\\prop{ImplicitIndex} property, \\\\algo{sort_product}\\nwould have freely moved the objects through each other.\\n\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"For more information on how to use matrices and vectors with implicit\\nindices, see \\\\algo{expand}.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"For more information on how to use matrices and vectors with implicit\\nindices, see \\\\algo{expand}.\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1.0\n}\n\n"
  },
  {
    "path": "core/properties/ImplicitIndex.hh",
    "content": "\n#pragma once\n\n#include \"Props.hh\"\n\nnamespace cadabra {\n\n\tclass ImplicitIndex : virtual public property {\n\t\tpublic:\n\t\t\tvirtual bool parse(Kernel&, keyval_t&) override;\n\t\t\tvirtual std::string name() const override;\n\t\t\tvirtual std::string unnamed_argument() const override\n\t\t\t\t{\n\t\t\t\treturn \"explicit\";\n\t\t\t\t};\n\t\t\tvirtual void latex(std::ostream& str) const override;\n\n\t\t\tEx explicit_form;\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/properties/ImplicitIndex.tex",
    "content": "\\cdbproperty{ImplicitIndex}{}\n\nIndicates that the object carries implicit indices, e.g.~for objects\nrepresenting matrices or vectors. Such objects will not be moved\nthrough each other, i.e.~they are mutually noncommuting.\n\\begin{screen}{1,2,3}\n{M,A}::ImplicitIndex;\nM A;\n@prodsort!(%);\nM A;\n\\end{screen}\nWithout the \\subsprop{ImplicitIndex} property, \\subscommand{prodsort}\nwould have freely moved the objects through each other.\n\nFor more information on how to use matrices and vectors with implicit\nindices, see \\subscommand{expand}.\n\n\\cdbseealgo{expand}\n"
  },
  {
    "path": "core/properties/IndexInherit.cc",
    "content": ""
  },
  {
    "path": "core/properties/IndexInherit.cnb",
    "content": "{\n\t\"cells\" : \n\t[\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\property{IndexInherit}{Make an object inherit all indices from its child objects.}\\n\\nIndicates that an object should inherit the indices of its child\\nobjects. This is useful mainly for operators. Matrix transposition,\\nfor instance, could be written as\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\property{IndexInherit}{Make an object inherit all indices from its child objects.}\\n\\nIndicates that an object should inherit the indices of its child\\nobjects. This is useful mainly for operators. Matrix transposition,\\nfor instance, could be written as\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property IndexInherit to~}T\\\\left(\\\\#\\\\right).\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"T(B_{m n}) + C_{m n}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}T\\\\left(B_{m n}\\\\right)+C_{m n}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"T{#}::IndexInherit;\\nex:=T(B_{m n}) + C_{m n};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"Without the \\\\prop{IndexInherit} property, the object \\n\\\\verb|T(B_{m n})| would be considered a scalar, without indices, and an index mismatch\\nerror would be reported. With the property, the first term has\\nexternal indices \\\\verb|m| and \\\\verb|n|, just like the second term.\\n\\nNote that indices which are 'direct indices' of the object still count, of course.\\nThis is also visible if you ask for the free indices directly, as the following\\nexample shows.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"Without the \\\\prop{IndexInherit} property, the object \\n\\\\verb|T(B_{m n})| would be considered a scalar, without indices, and an index mismatch\\nerror would be reported. With the property, the first term has\\nexternal indices \\\\verb|m| and \\\\verb|n|, just like the second term.\\n\\nNote that indices which are 'direct indices' of the object still count, of course.\\nThis is also visible if you ask for the free indices directly, as the following\\nexample shows.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"T_{m}(A_{n})\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}T_{m}\\\\left(A_{n}\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex:= T_{m}(A_{n});\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"verbatim\",\n\t\t\t\t\t\"source\" : \"\\\\begin{verbatim}m\\\\end{verbatim}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"verbatim\",\n\t\t\t\t\t\"source\" : \"\\\\begin{verbatim}n\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"for i in ex.top().free_indices(): \\n   display(i)\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1\n}\n"
  },
  {
    "path": "core/properties/IndexInherit.hh",
    "content": "\n#pragma once\n\n#include \"Props.hh\"\n#include \"properties/TableauBase.hh\"\n\nnamespace cadabra {\n\n\tclass IndexInherit : virtual public property {\n\t\tpublic:\n\t\t\tvirtual std::string name() const\n\t\t\t\t{\n\t\t\t\treturn std::string(\"IndexInherit\");\n\t\t\t\t};\n\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/properties/IndexInherit.tex",
    "content": "\\cdbproperty{IndexInherit}{}\n\nIndicates that an object should inherit the indices of its child\nobjects. This is useful mainly for operators. Matrix transposition,\nfor instance, could be written as \n\\begin{screen}{1,2,3}\nT{#}::IndexInherit.\nT(B_{m n}) + C_{m n};\n\\end{screen}\nWithout the \\subsprop{IndexInherit} property, the object \n\\verb|T(B_{m n})| would be considered a scalar, without indices, and an index mismatch\nerror would be reported. With the property, the first term has\nexternal indices \\verb|m| and \\verb|n|, just like the second term.\n\nThis property is automatically associated to all \\subsprop{Derivative} operators.\n\n\\cdbseeprop{Indices}\n\\cdbseeprop{Derivative}\n\\cdbseeprop{PartialDerivative}\n"
  },
  {
    "path": "core/properties/Indices.cc",
    "content": "\n#include \"Kernel.hh\"\n#include \"properties/Indices.hh\"\n#include \"properties/Integer.hh\"\n#include \"properties/Coordinate.hh\"\n#include \"Exceptions.hh\"\n#include \"Functional.hh\"\n\nusing namespace cadabra;\n\n#define MAX_INTEGER_RANGE 100\n\nIndices::Indices()\n\t: position_type(free)\n\t{\n\t}\n\nstd::string Indices::name() const\n\t{\n\treturn \"Indices\";\n\t}\n\nproperty::match_t Indices::equals(const property *other) const\n\t{\n\tconst Indices *cast_other = dynamic_cast<const Indices *>(other);\n\tif(cast_other) {\n\t\tif(set_name == cast_other->set_name) {\n\t\t\tif(parent_name == cast_other->parent_name && position_type == cast_other->position_type)\n\t\t\t\treturn exact_match;\n\t\t\telse\n\t\t\t\treturn id_match;\n\t\t\t}\n\t\treturn no_match;\n\t\t}\n\treturn property::equals(other);\n\t}\n\nbool Indices::parse(Kernel& kernel, std::shared_ptr<Ex> ex, keyval_t& keyvals)\n\t{\n\tkeyval_t::const_iterator ki=keyvals.begin();\n\twhile(ki!=keyvals.end()) {\n\t\tif(ki->first==\"name\") {\n\t\t\tif(*ki->second.begin()->multiplier!=1) \n\t\t\t\tthrow std::logic_error(\"Indices: use quotes to label names when they start with a number.\");\n\t\t\tif(!ki->second.is_string())\n\t\t\t\tthrow std::logic_error(\"Indices: label has to be a normal string, not a mathematical expression.\");\n\t\t\t\n\t\t\tset_name=*ki->second.begin()->name;\n\t\t\tif(set_name.size()>0) {\n\t\t\t\tif(set_name[0]=='\\\"' && set_name[set_name.size()-1]=='\\\"')\n\t\t\t\t\tset_name=set_name.substr(1,set_name.size()-2);\n\t\t\t\t}\n\t\t\t}\n\t\telse if(ki->first==\"parent\") {\n\t\t\tif(*ki->second.begin()->multiplier!=1) \n\t\t\t\tthrow std::logic_error(\"Indices: use quotes to label names when they start with a number.\");\n\t\t\tif(!ki->second.is_string())\n\t\t\t\tthrow std::logic_error(\"Indices: 'parent' has to be a normal string, not a mathematical expression.\");\n\n\t\t\tparent_name=*ki->second.begin()->name;\n\t\t\tif(parent_name.size()>0) {\n\t\t\t\tif(parent_name[0]=='\\\"' && parent_name[set_name.size()-1]=='\\\"')\n\t\t\t\t\tparent_name=parent_name.substr(1,parent_name.size()-2);\n\t\t\t\t}\n\t\t\t}\n\t\telse if(ki->first==\"position\") {\n\t\t\tif(ki->second.equals(\"free\"))\n\t\t\t\tposition_type=free;\n\t\t\telse if(ki->second.equals(\"fixed\"))\n\t\t\t\tposition_type=fixed;\n\t\t\telse if(ki->second.equals(\"independent\"))\n\t\t\t\tposition_type=independent;\n\t\t\telse throw ConsistencyException(\"Position type should be fixed, free or independent.\");\n\t\t\t}\n\t\telse if(ki->first==\"values\") {\n\t\t\t//std::cerr << \"got values keyword \" << *(ki->second->name) << std::endl;\n\t\t\tif(*ki->second.begin()->name==\"\\\\sequence\") {\n\t\t\t\t// Only accept a sequence if both start and end are explicit integers.\n\t\t\t\tEx::sibling_iterator sqit1 = Ex::child(ki->second.begin(), 0);\n\t\t\t\tEx::sibling_iterator sqit2 = Ex::child(ki->second.begin(), 1);\n\t\t\t\tif(!sqit1->is_integer() || !sqit2->is_integer()) \n\t\t\t\t\tthrow ConsistencyException(\"Value sequence for Indices property should contain explicit integers.\");\n\n\t\t\t\tauto args = std::make_shared<cadabra::Ex>(ki->second.begin());\n\t\t\t\tauto prop = new Integer();\n\t\t\t\tkernel.inject_property(prop, ex, args);\n\n\t\t\t\tif(prop->difference.to_integer() > MAX_INTEGER_RANGE)\n\t\t\t\t\tthrow ConsistencyException(\"Value sequence for Indices property spans too many elements.\");\n\n\t\t\t\tfor (int i=prop->from.to_integer(); i<=prop->to.to_integer(); ++i) {\n\t\t\t\t\tvalues_.push_back(Ex(i));\n\t\t\t\t\t}\n\t\t\t\t\n\t\t\t\t++ki;\n\t\t\t\tcontinue;\n\t\t\t\t}\n\n\t\t\tcollect_index_values(ki->second.begin());\n\t\t\t// If all values are integers, add an `Integer' property for the object,\n\t\t\t// listing these integers.\n\t\t\tbool is_number=true;\n\t\t\tbool is_continuous=false;\n\t\t\tfor(auto& val: values_)\n\t\t\t\tif(!val.begin()->is_integer()) {\n\t\t\t\t\tis_number=false;\n\t\t\t\t\tbreak;\n\t\t\t\t\t}\n\t\t\tif(is_number) {\n\t\t\t\tstd::sort(values_.begin(), values_.end(), [](Ex a, Ex b) {\n\t\t\t\t\treturn a.to_integer() < b.to_integer();\n\t\t\t\t\t});\n\t\t\t\tis_continuous = (int)values_.size() == (values_[values_.size() - 1].to_integer() - values_[0].to_integer() + 1);\n\t\t\t\t}\n\t\t\t// Do not apply Integer to a list of integers with gaps as\n\t\t\t// the former can only deal with continuous ranges.\n\t\t\tif(is_continuous) {\n//\t\t\t\tstd::cerr << \"Injecting Integer property\" << std::endl;\n\t\t\t\tkernel.inject_property(new Integer(), ex,\n\t\t\t\t\t\t\t\t\t\t\t  kernel.ex_from_string(std::to_string(values_[0].to_integer())+\"..\"\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t+std::to_string(values_[values_.size()-1].to_integer())\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t));\n\t\t\t\t}\n\t\t\t}\n\t\telse throw ConsistencyException(\"Property 'Indices' does not accept key '\"+ki->first+\"'.\");\n\t\t++ki;\n\t\t}\n\n\treturn true;\n\t}\n\nvoid Indices::latex(std::ostream& str) const\n\t{\n\tstr << \"Indices\";\n\tswitch(position_type) {\n\t\tcase free:\n\t\t\tstr << \"(position=free\";\n\t\t\tbreak;\n\t\tcase fixed:\n\t\t\tstr << \"(position=fixed\";\n\t\t\tbreak;\n\t\tcase independent:\n\t\t\tstr << \"(position=independent\";\n\t\t\tbreak;\n\t\t}\n\t// FIXME: here we would really need to know for *which*\n\t// index we are asking to print the property, otherwise\n\t// `values_` may not have been filled (if the value comes\n\t// in implicitly through an `Integer` property).\n\tif(values_.size()>0) {\n\t\tstr << \", values=\\\\{\";\n\t\tbool first=true;\n\t\tfor(const auto& v: values_) {\n\t\t\tif(first)\n\t\t\t\tfirst=false;\n\t\t\telse\n\t\t\t\tstr << \", \";\n\t\t\t// FIXME: this needs proper printing\n\t\t\tif(v.is_integer())\n\t\t\t\tstr << v.to_integer();\n\t\t\telse\n\t\t\t\tstr << v;\n\t\t\t}\n\t\tstr << \"\\\\})\";\n\t\t}\n\telse {\n\t\tstr << \")\";\n\t\t}\n\t}\n\nconst std::vector<Ex>& Indices::values(const Properties& properties, Ex::iterator sib) const\n\t{\n\tif(values_.size()!=0)\n\t\treturn values_;\n\t\t\t\n\t// Last attempt to get the values from an `Integer` property.\n\tconst Integer *iv = properties.get<Integer>(sib, true);\n\tif(iv==0)\n\t\treturn values_; // the user will have to check this for zero size!\n//\t\tthrow ArgumentException(\"No explicit values set for indices, and no Integer property found.\");\n\t\t\n\tif(!iv->from.is_integer() || !iv->to.is_integer()) \n\t\tthrow ArgumentException(\"Indices have integer property, but explicit range needed.\");\n\t\n\tfor(int val = iv->from.to_integer(); val <= iv->to.to_integer(); ++val)\n\t\tvalues_.push_back(Ex(val));\n\n\treturn values_;\n\t}\n\nvoid Indices::validate(Kernel& k, std::shared_ptr<Ex> ex) const\n\t{\n\tdo_list(*ex, ex->begin(),\n\t\t\t  [&k](Ex::iterator i)\n\t\t\t\t  {\n\t\t\t\t  if(k.properties.get<Coordinate>(i))\n\t\t\t\t\t  throw ConsistencyException(\"Object already has a Coordinate property attached to it.\");\n\t\t\t\t  return true;\n\t\t\t\t  }\n\t\t\t  );\n\t}\n\n\nvoid Indices::collect_index_values(Ex::iterator ind_values)\n\t{\n\tEx tmp;\n\tcadabra::do_list(tmp, ind_values, [&](Ex::iterator ind) {\n\t\tvalues_.push_back(Ex(ind));\n\t\t//\t\t\tauto name=ind_values.begin(ind);\n\t\t//\t\t\tsibling_iterator vals=name;\n\t\t//\t\t\t++vals;\n\t\t//\t\t\tindex_values[indprop]=cadabra::make_list(Ex(vals));\n\t\treturn true;\n\t\t});\n\t}\n\n"
  },
  {
    "path": "core/properties/Indices.cnb",
    "content": "{\n\t\"cell_id\": 9222280984339109129,\n\t\"cells\": [\n\t\t{\n\t\t\t\"cell_id\": 137989926080771703,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 15768001409649294644,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\property{Indices}{Declare names to be used as indices.}\\n\\nDeclare index names to be usable for dummy index\\npurposes. Typical usage is of the form\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\property{Indices}{Declare names to be used as indices.}\\n\\nDeclare index names to be usable for dummy index\\npurposes. Typical usage is of the form\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 4367690953385802217,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 5742890051355659833,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Attached property Indices(position=free) to~}(r, s, t).\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 12592366620725701587,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Attached property Indices(position=free) to~}(a, b, c, d).\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"{r,s,t}::Indices(vector);\\n{a,b,c,d}::Indices(spinor);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 1274492612593201931,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 16171049713142155210,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"This indicates the name of the index set (``vector'' resp.~``spinor''\\nin the example above). \"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"This indicates the name of the index set (``vector'' resp.~``spinor''\\nin the example above). \"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 4963803958092805750,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 17459461686941818730,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"Indices can occur as subscripts or superscripts, and you may use this\\nto indicate e.g.~covariant and contravariant transformation\\nbehaviour. In this case, use the additional\\nargument \\\\verb|position=fixed| to indicate that the position carries\\nmeaning. If you do not want cadabra to automatically raise or lower\\nindices when canonicalising expressions, or if upper and lower indices\\nare not related at all, use \\\\verb|position=independent|. The default is\\n\\\\verb|position=free|, which means that indices in a pair can be positioned anywhere and\\ntheir position carries no meaning. Be aware that this is not what you want if there\\nis a metric involved!\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"Indices can occur as subscripts or superscripts, and you may use this\\nto indicate e.g.~covariant and contravariant transformation\\nbehaviour. In this case, use the additional\\nargument \\\\verb|position=fixed| to indicate that the position carries\\nmeaning. If you do not want cadabra to automatically raise or lower\\nindices when canonicalising expressions, or if upper and lower indices\\nare not related at all, use \\\\verb|position=independent|. The default is\\n\\\\verb|position=free|, which means that indices in a pair can be positioned anywhere and\\ntheir position carries no meaning. Be aware that this is not what you want if there\\nis a metric involved!\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 6027867998309018678,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 16184606127486662925,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"When you work with vector spaces which are subspaces of larger spaces,\\nit is possible to indicate that a given set of indices take values in\\na subset of values of a larger set. An example makes this more\\nclear. Suppose we have one set of indices~$A,B,C$ which take values in\\na four-dimensional space, and another set of indices~$a,b,c$ which\\ntake values in a three-dimensional subspace. This is declared as\\n\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"When you work with vector spaces which are subspaces of larger spaces,\\nit is possible to indicate that a given set of indices take values in\\na subset of values of a larger set. An example makes this more\\nclear. Suppose we have one set of indices~$A,B,C$ which take values in\\na four-dimensional space, and another set of indices~$a,b,c$ which\\ntake values in a three-dimensional subspace. This is declared as\\n\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 5043963982261613752,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 602473294331448679,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Attached property Indices(position=free) to~}(A, B, C).\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 11107199374583441782,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Attached property Indices(position=free) to~}(a, b, c).\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"{A,B,C}::Indices(fourD);\\n{a,b,c}::Indices(threeD, parent=fourD);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 13826672473882943998,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 1910581516288308829,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"This will allow Cadabra to canonicalise expressions which contain mixed\\nindex types, as in\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"This will allow Cadabra to canonicalise expressions which contain mixed\\nindex types, as in\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 4648209960997019518,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 5192862143240553869,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Attached property Indices(position=free) to~}(A, B, C).\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9437564931888262343,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Attached property Indices(position=free) to~}(a, b, c).\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 18391389818505151790,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Attached property AntiSymmetric to~}{M}_(q?r?).\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 4413997982094884520,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}M_{a A}+M_{A a}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"{A,B,C}::Indices(fourD);\\n{a,b,c}::Indices(name=threeD, parent=fourD);\\nM_{q? r?}::AntiSymmetric;\\nex:=M_{a A} + M_{A a};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 13109355959044140599,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 3752435050457653649,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}0\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"canonicalise(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 1688052651963641722,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 2442249317402902113,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"Note the way in which the symmetry of the~$M$ tensor was declared here.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"Note the way in which the symmetry of the~$M$ tensor was declared here.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 4807718974397691090,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 4718875350833364286,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\subsection*{Index values}\\n\\nFor various algorithms (e.g. \\\\algo{evaluate}) it is necessary to specify the values that a particular\\nindex can take. The value of an index needs to be either a \\\\prop{Coordinate} or a \\\\prop{Symbol}, or \\nit can be an integer. The following are all valid:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\subsection*{Index values}\\n\\nFor various algorithms (e.g. \\\\algo{evaluate}) it is necessary to specify the values that a particular\\nindex can take. The value of an index needs to be either a \\\\prop{Coordinate} or a \\\\prop{Symbol}, or \\nit can be an integer. The following are all valid:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 9717721989471119742,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"{x,y,z}::Coordinate.\\n{a,b,c}::Indices(values={x,y,z}).\\n{d,e,f}::Indices(values={0,1,3}).\\n{m,n,p}::Indices(values={0,1,2}).\\n{q,r,s}::Indices(values={0..3}).\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 5245275082540183677,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 16921403430064941369,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"When values is a sequence or a list of integers with no gaps, an automatic \\n\\\\prop{Integer} property will be generated that reflects these values. So e.g. the \\nlast line above (but not the middle line) leads to an automatic attachment\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"When values is a sequence or a list of integers with no gaps, an automatic \\n\\\\prop{Integer} property will be generated that reflects these values. So e.g. the \\nlast line above (but not the middle line) leads to an automatic attachment\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 16647378988601399263,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"{m,n,p}::Integer(0..3).\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 1814948565060202401,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"\"\n\t\t}\n\t],\n\t\"description\": \"Cadabra JSON notebook format\",\n\t\"version\": 1.0\n}\n"
  },
  {
    "path": "core/properties/Indices.hh",
    "content": "\n#pragma once\n\n#include \"Props.hh\"\n\nnamespace cadabra {\n\n\tclass Indices : public list_property {\n\t\tpublic:\n\t\t\tIndices(); //const std::string& parent=\"\");\n\t\t\tvirtual bool parse(Kernel&, std::shared_ptr<Ex>, keyval_t&) override;\n\t\t\tvirtual std::string name() const override;\n\t\t\tvirtual std::string unnamed_argument() const override\n\t\t\t\t{\n\t\t\t\treturn \"name\";\n\t\t\t\t};\n\t\t\tvirtual match_t equals(const property *) const override;\n\t\t\tvirtual void    validate(Kernel&, std::shared_ptr<Ex>) const override;\n\t\t\t\n\t\t\t//\t\tvirtual void display(std::ostream&) const override;\n\t\t\tvirtual void latex(std::ostream&) const override;\n\n\t\t\tstd::string set_name, parent_name;\n\t\t\tenum position_t { free=0, fixed=1, independent=2 } position_type;\n\n\t\t\t/// List of possible values that indices of this type can\n\t\t\t/// take.  This gets collected from the `values` parameter,\n\t\t\t/// or determined from any `Integer` property. This can be\n\t\t\t/// empty if the values are not (yet) known so the caller\n\t\t\t/// needs to check that explicitly.\n\t\t\tconst std::vector<Ex>& values(const Properties&, Ex::iterator) const;\n\n\t\tprivate:\n\t\t\t/// Given the right-hand side of a 'values={...}' node, generate\n\t\t\t/// a list of all index values in index_values.\n\n\t\t\tvoid collect_index_values(Ex::iterator ind_values);\n\n\t\t\t// Explicit store of index values;\n\t\t\tmutable std::vector<Ex> values_;\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/properties/Indices.tex",
    "content": "\\cdbproperty{Indices}{\\it name={\\sf set name}, parent={\\sf parent set\nname}, position=free$\\vert$fixed$\\vert$independent}\n\nDeclare index names to be usable for dummy index\npurposes. Typical usage is of the form\n\\begin{screen}{1,2}\n{r,s,t}::Indices(vector).\n{a,b,c,d}::Indices(spinor).\n\\end{screen}\nThis indicates the name of the index set (``vector'' resp.~``spinor''\nin the example above). \n\nIndices can occur as subscripts or superscripts, and you may use this\nto indicate e.g.~covariant and contravariant transformation\nbehaviour. In this case, use the additional\nargument \\verb|position=fixed| to indicate that the position carries\nmeaning. If you do not want cadabra to automatically raise or lower\nindices when canonicalising expressions, or if upper and lower indices\nare not related at all, use \\verb|position=independent|.\n\nWhen you work with vector spaces which are subspaces of larger spaces,\nit is possible to indicate that a given set of indices take values in\na subset of values of a larger set. An example makes this more\nclear. Suppose we have one set of indices~$A,B,C$ which take values in\na four-dimensional space, and another set of indices~$a,b,c$ which\ntake values in a three-dimensional subspace. This is declared as\n\\begin{screen}{1,2}\n{A,B,C}::Indices(fourD).\n{a,b,c}::Indices(threeD, parent=fourD).\n\\end{screen}\nThis will allow cadabra to canonicalise expressions which contain mixed\nindex types, as in\n\\begin{screen}{1,2,3,4,5,6}\n{A,B,C}::Indices(fourD).\n{a,b,c}::Indices(threeD, parent=fourD).\nM_{q? r?}::AntiSymmetric.\nM_{a A} + M_{A a}:\n@canonicalise!(%):\n@collect_terms!(%);\n0;\n\\end{screen}\nNote the way in which the symmetry of the~$M$ tensor was declared here.\n\n\\cdbseealgo{split_index}\n\\cdbseeprop{Integer}\n"
  },
  {
    "path": "core/properties/Integer.cc",
    "content": "\n#include \"properties/Integer.hh\"\n#include \"Exceptions.hh\"\n#include \"Kernel.hh\"\n#include \"algorithms/collect_terms.hh\"\n\nusing namespace cadabra;\n\nstd::string Integer::name() const\n\t{\n\treturn \"Integer\";\n\t}\n\nbool Integer::parse(Kernel& kernel, keyval_t& keyvals)\n\t{\n\tkeyval_t::iterator kv=keyvals.find(\"range\");\n\tif(kv!=keyvals.end()) {\n\t\tif(*kv->second.begin()->name!=\"\\\\sequence\")\n\t\t\tthrow ConsistencyException(\"Integer range should use '..' notation.\");\n\n\t\tfrom=Ex(Ex::child(kv->second.begin(), 0));\n\t\tto  =Ex(Ex::child(kv->second.begin(), 1));\n\n\t\tEx::iterator sm=difference.set_head(str_node(\"\\\\sum\"));\n\t\tdifference.append_child(sm, to.begin())->fl.bracket=str_node::b_round;\n\t\tEx::iterator term2=difference.append_child(sm, from.begin());\n\t\tflip_sign(term2->multiplier);\n\t\tterm2->fl.bracket=str_node::b_round;\n\t\tdifference.append_child(sm, str_node(\"1\"))->fl.bracket=str_node::b_round;\n\n\t\tEx::sibling_iterator sib=difference.begin(sm);\n\t\twhile(sib!=difference.end(sm)) {\n\t\t\tif(*sib->name==\"\\\\sum\") {\n\t\t\t\tdifference.flatten(sib);\n\t\t\t\tsib=difference.erase(sib);\n\t\t\t\t}\n\t\t\telse ++sib;\n\t\t\t}\n\n\t\tcollect_terms ct(kernel, difference);\n\t\tct.apply(sm);\n\t\t}\n\n\t//\tEx::iterator top=difference.begin();\n\t//\tcleanup_dispatch(kernel, difference, top);\n\n\treturn true;\n\t}\n\nvoid Integer::display(std::ostream& str) const\n\t{\n\tstr << \"Integer\";\n\tif(from.begin()!=from.end()) {\n\t\tstr << \"(\" << *(from.begin()->multiplier) << \"..\"\n\t\t    << *(to.begin()->multiplier) << \")\";\n\t\t}\n\t}\n"
  },
  {
    "path": "core/properties/Integer.cnb",
    "content": "\n{\n\t\"cells\" : \n\t[\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\property{Integer}{Indicates that an object takes integer values.}\\n\\nIndicates that the object takes values in the integers. An optional\\nrange can be specified,\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\property{Integer}{Indicates that an object takes integer values.}\\n\\nIndicates that the object takes values in the integers. An optional\\nrange can be specified,\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Integer to~}p.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Integer to~}m.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Integer to~}n.\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"p::Integer;\\nm::Integer(1..10);\\nn::Integer(1..d-p);\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"This property is often used in combination with the \\\\prop{Indices}\\nproperty to indicate the range of numbers over which indices run.\\n\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"This property is often used in combination with the \\\\prop{Indices}\\nproperty to indicate the range of numbers over which indices run.\\n\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1.0\n}\n\n"
  },
  {
    "path": "core/properties/Integer.hh",
    "content": "\n#pragma once\n\n#include \"Props.hh\"\n\nnamespace cadabra {\n\n\t/// \\ingroup properties\n\t///\n\t/// Property indicating that a symbolic object always takes integer values.\n\t/// Optionally takes a range over which it runs, which can be symbolic.\n\n\tclass Integer : public property {\n\t\tpublic:\n\t\t\tvirtual ~Integer() {};\n\t\t\tvirtual std::string name() const override;\n\t\t\tvirtual bool        parse(Kernel&, keyval_t& keyvals) override;\n\t\t\t//\t\tvirtual bool parse(Ex&, Ex::iterator, Ex::iterator, keyval_t&);\n\t\t\tvirtual void display(std::ostream&) const;\n\t\t\tvirtual std::string unnamed_argument() const  override\n\t\t\t\t{\n\t\t\t\treturn \"range\";\n\t\t\t\t};\n\n\t\t\tEx from, to, difference;\n\t\t};\n\n\t}\n\n"
  },
  {
    "path": "core/properties/Integer.tex",
    "content": "\\cdbproperty{Integer}{\\sf range}\n\nIndicates that the object takes values in the integers. An optional\nrange can be specified,\n\\begin{screen}{1,2,3}\np::Integer;\nm::Integer(1..10);\nn::Integer(1..d-p);\n\\end{screen}\nThis property is often used in combination with the \\subsprop{Indices}\nproperty to indicate the range of numbers over which indices run.\n\n\\cdbseeprop{Indices}\n\n"
  },
  {
    "path": "core/properties/Integral.hh",
    "content": "#pragma once\n\n#include \"Props.hh\"\n\nnamespace cadabra {\n\n\t// Turns a symbol into an integration function, which takes two arguments,\n\t// the integrand and the coordinate over which to integrate, optionally\n\t// with a range.\n\n\tclass Integral : public property {\n\tpublic:\n\t\tvirtual ~Integral() {};\n\n\t\tvirtual std::string name() const;\n\t\tvirtual bool        parse(Kernel&, keyval_t& keyvals) override;\n\t\tvirtual void        display(std::ostream&) const;\n\t};\n\n}\n"
  },
  {
    "path": "core/properties/InverseMetric.cc",
    "content": "\n\n#include \"Exceptions.hh\"\n#include \"properties/InverseMetric.hh\"\n\nusing namespace cadabra;\n\nInverseMetric::InverseMetric()\n\t{\n\ttab_t tab;\n\ttab.add_box(0,0);\n\ttab.add_box(0,1);\n\ttabs.push_back(tab);\n\t}\n\nstd::string InverseMetric::name() const\n\t{\n\treturn \"InverseMetric\";\n\t}\n\nbool InverseMetric::parse(Kernel&, keyval_t& keyvals)\n\t{\n\tkeyval_t::const_iterator kv=keyvals.find(\"signature\");\n\tsignature=1;\n\tif(kv!=keyvals.end())\n\t\tsignature=to_long(*(kv->second.begin()->multiplier));\n\treturn true;\n\t}\n\nvoid InverseMetric::validate(Kernel&, std::shared_ptr<Ex> tr) const\n\t{\n\tif(tr->number_of_children(tr->begin())!=2)\n\t\tthrow ArgumentException(\"InverseMetric: needs exactly 2 indices.\");\n\t}\n"
  },
  {
    "path": "core/properties/InverseMetric.cnb",
    "content": "{\n\t\"cells\" : \n\t[\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\property{InverseMetric}{Make a two-tensor an inverse metric.}\\n\\nThis property is the partner of \\\\prop{Metric}. It makes the\\nassociated two-tensor symmetric and also indicates that it can be used\\nto raise or lower indices.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\property{InverseMetric}{Make a two-tensor an inverse metric.}\\n\\nThis property is the partner of \\\\prop{Metric}. It makes the\\nassociated two-tensor symmetric and also indicates that it can be used\\nto raise or lower indices.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}g_{m q} g^{m n} A_{n p}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"g^{m n}::InverseMetric.\\ng_{m n}::Metric.\\nex:=g_{m q} g^{m n} A_{n p};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}g_{q}\\\\,^{n} A_{n p}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"eliminate_metric(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"For more information, see \\\\prop{Metric}.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"For more information, see \\\\prop{Metric}.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1\n}\n"
  },
  {
    "path": "core/properties/InverseMetric.hh",
    "content": "\n#pragma once\n\n#include \"Props.hh\"\n#include \"properties/TableauSymmetry.hh\"\n\nnamespace cadabra {\n\n\tclass InverseMetric : public TableauSymmetry, virtual public property {\n\t\tpublic:\n\t\t\tInverseMetric();\n\t\t\tvirtual std::string name() const override;\n\t\t\tvirtual bool        parse(Kernel&, keyval_t&) override;\n\t\t\tvirtual void        validate(Kernel&, std::shared_ptr<Ex>) const override;\n\n\t\t\tint signature;\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/properties/InverseMetric.tex",
    "content": "\\cdbproperty{InverseMetric}{}\n\nThis property is the partner of \\subsprop{Metric}. It makes the\nassociated two-tensor symmetric and also indicates that it can be used\nto raise or lower indices.\n\\begin{screen}{1,2,3}\ng^{m n}::InverseMetric.\ng_{m n}::Metric.\ng_{m q} g^{m n} A_{n p};\n@eliminate_metric!(%);\nA_{q p};\n\\end{screen}\nFor more information, see \\subsprop{Metric}.\n\n\\cdbseealgo{eliminate_metric}\n\\cdbseeprop{Metric}\n\\cdbseeprop{Symmetric}\n"
  },
  {
    "path": "core/properties/InverseVielbein.cnb",
    "content": "{\n\t\"cell_id\" : 15071890539767200046,\n\t\"cells\" : \n\t[\n\t\t{\n\t\t\t\"cell_id\" : 6373255555275753029,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 13263267438977636121,\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\property{InverseVeilbein}{Makes a two-index object an inverse vielbein.}\\n\\nThe partner of \\\\verb|Vielbein|. See\\nthe \\\\verb|eliminate_vielbein| command for more information on\\ntypical usage patterns.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\property{InverseVeilbein}{Makes a two-index object an inverse vielbein.}\\n\\nThe partner of \\\\verb|Vielbein|. See\\nthe \\\\verb|eliminate_vielbein| command for more information on\\ntypical usage patterns.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 421681981131674138,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1\n}\n"
  },
  {
    "path": "core/properties/InverseVielbein.tex",
    "content": "\\cdbproperty{InverseVielbein}{}\n\nThe partner of \\subsprop{Vielbein}. See\nthe \\subscommand{eliminate\\_vielbein} command for more information on\ntypical usage patterns.\n\n\\cdbseeprop{Vielbein}\n\\cdbseealgo{eliminate_vielbein}\n"
  },
  {
    "path": "core/properties/KeepHistory.tex",
    "content": "\\cdbproperty{KeepHistory}{}\n\nThis is a global property. When set to false, only the last version of\neach expression is kept in memory, thereby reducing memory usage for\nvery large expressions. The default is ``true''. When set to\n``false'', \\subscommand{pop} is no longer available to return to\nprevious forms of the expression:\n\\begin{screen}{1,2,3,4}\n::KeepHistory(false).\n(a+b)*(c+d);\n@distribute!(%);\n@pop(%);\n@pop: not applicable.\n\\end{screen}\nIn general this is only useful to conserve memory when extremely long\nexpressions are manipulated.\n\n\\cdbseealgo{pop}\n"
  },
  {
    "path": "core/properties/KroneckerDelta.cc",
    "content": "\n#include \"properties/KroneckerDelta.hh\"\n#include \"Exceptions.hh\"\n\nusing namespace cadabra;\n\nstd::string KroneckerDelta::name() const\n\t{\n\treturn \"KroneckerDelta\";\n\t}\n\nunsigned int KroneckerDelta::size(const Properties&, Ex&, Ex::iterator) const\n\t{\n\treturn 1;\n\t}\n\nTableauBase::tab_t KroneckerDelta::get_tab(const Properties& properties, Ex& tr, Ex::iterator it, unsigned int num) const\n\t{\n\tassert(num==0);\n\n\tconst KroneckerDelta *pd;\n\tfor(;;) {\n\t\tpd=properties.get<KroneckerDelta>(it);\n\t\tif(!pd)\n\t\t\tit=tr.begin(it);\n\t\telse break;\n\t\t}\n\n\tif(tr.number_of_children(it)%2!=0)\n\t\tthrow ConsistencyException(\"Encountered a KroneckerDelta object with an odd number of indices.\");\n\n//\tbool onlytwo=false;\n//\tif(tr.number_of_children(it)==2)\n//\t\tonlytwo=true;\n\n\ttab_t tab;\n\tfor(unsigned int i=0; i<tr.number_of_children(it); i+=2) {\n\t\ttab.add_box(i/2,i);\n\t\t//\t\tif(onlytwo)\n\t\ttab.add_box(i/2,i+1);\n\t\t}\n\treturn tab;\n\t}\n"
  },
  {
    "path": "core/properties/KroneckerDelta.cnb",
    "content": "\n{\n\t\"cells\" : \n\t[\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\property{KroneckerDelta}{Turns an object into a generalised Kronecker delta symbol.}\\n\\nDenotes a generalised Kronecker\\n  delta symbol. When the symbol carries two indices, it is the usual\\n  Kronecker delta. When the number of indices is larger, the meaning\\n  is\\n\\\\begin{equation}\\n\\\\delta_{m_1}{}^{n_1}{}_{m_2}{}^{n_2}{}_{\\\\ldots m_k}{}^{n_k} =\\n\\\\delta_{[m 1}{}^{n_1} \\\\delta_{m_2}{}^{n_2} \\\\cdots \\\\delta_{m_k]}{}^{n_k} \\\\,,\\n\\\\end{equation}\\nwith unit weight anti-symmetrisation.  \\n\\nA symbol which is declared as a\\nKronecker delta has the property that it can be taken in and out of\\nderivatives. The algorithm \\\\algo{eliminate_kronecker} eliminates\\nnormal Kronecker deltas by appropriately renaming indices (in order to\\neliminate Kronecker deltas with more than two indices, first\\nuse \\\\algo{expand_delta}).\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\property{KroneckerDelta}{Turns an object into a generalised Kronecker delta symbol.}\\n\\nDenotes a generalised Kronecker\\n  delta symbol. When the symbol carries two indices, it is the usual\\n  Kronecker delta. When the number of indices is larger, the meaning\\n  is\\n\\\\begin{equation}\\n\\\\delta_{m_1}{}^{n_1}{}_{m_2}{}^{n_2}{}_{\\\\ldots m_k}{}^{n_k} =\\n\\\\delta_{[m 1}{}^{n_1} \\\\delta_{m_2}{}^{n_2} \\\\cdots \\\\delta_{m_k]}{}^{n_k} \\\\,,\\n\\\\end{equation}\\nwith unit weight anti-symmetrisation.  \\n\\nA symbol which is declared as a\\nKronecker delta has the property that it can be taken in and out of\\nderivatives. The algorithm \\\\algo{eliminate_kronecker} eliminates\\nnormal Kronecker deltas by appropriately renaming indices (in order to\\neliminate Kronecker deltas with more than two indices, first\\nuse \\\\algo{expand_delta}).\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1.0\n}\n\n"
  },
  {
    "path": "core/properties/KroneckerDelta.hh",
    "content": "\n#pragma once\n\n#include \"properties/TableauBase.hh\"\n\nnamespace cadabra {\n\n\tclass KroneckerDelta : public TableauBase, virtual public property {\n\t\tpublic:\n\t\t\tvirtual ~KroneckerDelta() {};\n\t\t\tvirtual std::string name() const;\n\n\t\t\tvirtual unsigned int size(const Properties&, Ex&, Ex::iterator) const;\n\t\t\tvirtual tab_t        get_tab(const Properties &, Ex&, Ex::iterator, unsigned int) const;\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/properties/KroneckerDelta.tex",
    "content": "\\cdbproperty{KroneckerDelta}{}\n\nDenotes a generalised Kronecker\n  delta symbol. When the symbol carries two indices, it is the usual\n  Kronecker delta. When the number of indices is larger, the meaning\n  is\n\\begin{equation}\n\\delta_{m_1}{}^{n_1}{}_{m_2}{}^{n_2}{}_{\\ldots m_k}{}^{n_k} =\n\\delta_{[m 1}{}^{n_1} \\delta_{m_2}{}^{n_2} \\cdots \\delta_{m_k]}{}^{n_k} \\,,\n\\end{equation}\nwith unit weight anti-symmetrisation.  \n\nA symbol which is declared as a\nKronecker delta has the property that it can be taken in and out of\nderivatives. The algorithm \\subscommand{eliminate\\_kr} eliminates\nnormal Kronecker deltas by appropriately renaming indices (in order to\neliminate Kronecker deltas with more than two indices, first\nuse \\subscommand{breakgendelta}).\n\n\\cdbseealgo{eliminate_kr}\n\\cdbseealgo{breakgendelta}\n"
  },
  {
    "path": "core/properties/LaTeXForm.cc",
    "content": "\n#include \"properties/LaTeXForm.hh\"\n\nusing namespace cadabra;\n\nstd::string LaTeXForm::name() const\n\t{\n\treturn \"LaTeXForm\";\n\t}\n\nstd::string LaTeXForm::unnamed_argument() const\n\t{\n\treturn \"latex\";\n\t}\n\nbool LaTeXForm::parse(Kernel&, keyval_t& keyvals)\n\t{\n//\tkeyval_t::const_iterator kv=keyvals.find(\"latex\");\n\tfor(const auto& kv: keyvals)\n\t\tlatex.push_back(kv.second);\n\n\t// Strip quotes. FIXME: handle errors.\n//\tlatex_=latex_.substr(1,latex_.size()-2);\n\treturn true;\n\t}\n\nstd::string LaTeXForm::latex_form() const\n\t{\n\treturn *(latex.begin()->begin()->name); // FIXME: deprecated\n\t}\n\n"
  },
  {
    "path": "core/properties/LaTeXForm.cnb",
    "content": "{\n\t\"cell_id\": 10332960512342882681,\n\t\"cells\": [\n\t\t{\n\t\t\t\"cell_id\": 16101808746726886949,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 17922711406420684199,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\property{LaTeXForm}{Changes the way in which expressions are displayed.}\\n\\nThe \\\\prop{LaTeXForm} property changes the way in which expressions are displayed in the graphical\\ninterface. In its simplest form, it acts just like a node rename operation,\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\property{LaTeXForm}{Changes the way in which expressions are displayed.}\\n\\nThe \\\\prop{LaTeXForm} property changes the way in which expressions are displayed in the graphical\\ninterface. In its simplest form, it acts just like a node rename operation,\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 8166426365570956951,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 14074699354269497242,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property LaTeXForm attached to {\\\\texttt{\\\\backslash{}del}}.}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 16923080146045210499,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 2021100724189033471,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\del_{m}(A)\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\partial_{m}\\\\!\\\\left(A\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"\\\\del{#}::LaTeXForm(\\\"\\\\partial\\\");\\nex:=\\\\del_{m}(A);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 12137153977390704291,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 1199599436471906871,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"This prints $\\\\partial_{m}(A);$ in the notebook, despite the fact\\nthat \\\\verb|\\\\del| is not a LaTeX{} command.\\n\\nIf you use this property to make a symbol printable, make sure to\\ndeclare it \\\\emph{before} any other properties are declared, otherwise\\nthe notebook will not know how to display the symbol and produce an\\nerror message.\\n\\nNote that the property is attached to a pattern (\\\\verb|\\\\del{#}| in\\nthis case) which matches the expression in which the replacement has\\nto be made. If the pattern matches, the replacement will be done on\\nthe head symbol (\\\\verb|\\\\del| in this case). A pattern \\\\verb|\\\\del|\\nwithout the argument wildcard \\\\verb|#| would only replace\\nwhen \\\\verb|\\\\del| occurs without any arguments (as in \\ne.g.~\\\\verb|\\\\del + A|).\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"This prints $\\\\partial_{m}(A);$ in the notebook, despite the fact\\nthat \\\\verb|\\\\del| is not a LaTeX{} command.\\n\\nIf you use this property to make a symbol printable, make sure to\\ndeclare it \\\\emph{before} any other properties are declared, otherwise\\nthe notebook will not know how to display the symbol and produce an\\nerror message.\\n\\nNote that the property is attached to a pattern (\\\\verb|\\\\del{#}| in\\nthis case) which matches the expression in which the replacement has\\nto be made. If the pattern matches, the replacement will be done on\\nthe head symbol (\\\\verb|\\\\del| in this case). A pattern \\\\verb|\\\\del|\\nwithout the argument wildcard \\\\verb|#| would only replace\\nwhen \\\\verb|\\\\del| occurs without any arguments (as in \\ne.g.~\\\\verb|\\\\del + A|).\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 16855295245100204448,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 12511356882212983496,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"If you want more control over the way in which elements of your original expression \\nare printed, you can use patterns like in the example below:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"If you want more control over the way in which elements of your original expression \\nare printed, you can use patterns like in the example below:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 5079904273003789391,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 2002807125132593468,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property LaTeXForm attached to {\\\\texttt{\\\\backslash{}ket}}.}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"\\\\ket{A??}{q??}::LaTeXForm(\\\"|\\\", A??, \\\"\\\\rangle_{\\\", q??, \\\"}\\\");\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 7082940046924425757,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 15029653052379928347,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 10178595622632027557,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\ket(n + 1 , a)\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}|n\\\\discretionary{}{}{}+1\\\\rangle_{a}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex:=\\\\ket{n+1}{a};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 9144468563272193427,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 2257828966897303850,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"The comma-separated list of arguments to \\\\prop{LaTeXForm} will be concatenated\\ninto a single LaTeX output string, with patterns replaced by their normal output\\nform.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"The comma-separated list of arguments to \\\\prop{LaTeXForm} will be concatenated\\ninto a single LaTeX output string, with patterns replaced by their normal output\\nform.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 4022895960666784505,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 5631816431885168242,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"Note that in all of the strings used inside the \\\\prop{LaTeXForm} property, you do not need to do any escaping of special characters: these strings are always interpreted as raw strings. Also note that you need to use double quotes, not single quotes.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"Note that in all of the strings used inside the \\\\prop{LaTeXForm} property, you do not need to do any escaping of special characters: these strings are always interpreted as raw strings. Also note that you need to use double quotes, not single quotes.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 386464782893588846,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"\"\n\t\t}\n\t],\n\t\"description\": \"Cadabra JSON notebook format\",\n\t\"flags\": {\n\t\t\"hide_input_cells\": false\n\t},\n\t\"version\": 1.0\n}\n"
  },
  {
    "path": "core/properties/LaTeXForm.hh",
    "content": "\n#pragma once\n\n#include \"Props.hh\"\n\nnamespace cadabra {\n\n\tclass LaTeXForm : virtual public property {\n\t\tpublic:\n\t\t\tvirtual std::string name() const override;\n\t\t\tvirtual bool parse(Kernel&, keyval_t&) override;\n\t\t\tvirtual std::string unnamed_argument() const override;\n\n\t\t\t/// Return the LaTeX string which should be used to display\n\t\t\t/// the object to which this property is associated. Will be\n\t\t\t/// interpreted by DisplayTeX because it can contain patterns\n\t\t\t/// (as e.g. in `a{b??}::LaTeXForm(\"| b?? \\rangle\")`).\n\t\t\tstd::string latex_form() const;\n\t\t\t\n\t\t\tstd::vector<Ex> latex;\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/properties/LaTeXForm.tex",
    "content": "\\cdbproperty{LaTeXForm}{\\sf valid \\LaTeX{} expression}\n\nChanges the way in which symbols are displayed in the graphical\ninterface. Example:\n\\begin{screen}{1,2}\n\\del{#}::LaTeXForm(\"\\partial\").\n\\del_{m}(A);\n\\end{screen}\nThis prints $\\partial_{m}(A);$ in the notebook, despite the fact\nthat \\verb|\\del| is not a \\LaTeX{} command.\n\nIf you use this property to make a symbol printable, make sure to\ndeclare it \\emph{before} any other properties are declared, otherwise\nthe notebook will not know how to display the symbol and produce an\nerror message.\n\nNote that the property is attached to a pattern (\\verb|\\del{#}| in\nthis case) which matches the expression in which the replacement has\nto be made. If the pattern matches, the replacement will be done on\nthe head symbol (\\verb|\\del| in this case). A pattern \\verb|\\del|\nwithout the argument wildcard \\verb|#| would only replace\nwhen \\verb|\\del| occurs without any arguments (as in \ne.g.~\\verb|\\del + A|).\n\nThese settings have no effect in the command-line version.\n\n"
  },
  {
    "path": "core/properties/Matrix.cc",
    "content": "\n#include \"Matrix.hh\"\n\nusing namespace cadabra;\n\nstd::string Matrix::name() const\n\t{\n\treturn \"Matrix\";\n\t}\n\n"
  },
  {
    "path": "core/properties/Matrix.hh",
    "content": "\n#pragma once\n\n#include \"properties/ImplicitIndex.hh\"\n\nnamespace cadabra {\n\n\tclass Matrix : public ImplicitIndex, virtual public property {\n\t\tpublic:\n\t\t\tvirtual ~Matrix() {};\n\t\t\tvirtual std::string name() const;\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/properties/Matrix.tex",
    "content": "\\cdbproperty{Matrix}{}\n\nDeclares an object to have two implicit indices, thus making it a\nmatrix object. This is useful in combination with the index bracket\nnotation. Example:\n\\begin{screen}{1,2}\n{m,n,p,q}::Indices.\nA::Matrix.\nV::ImplicitIndex.\n(A V)_{m};\n@expand!(%);\nA_{m n} V_{n};\n\\end{screen}\nObjects with the \\subsprop{Matrix} property automatically become\nnon-commuting among themselves, but retain their commutativity\nproperties with other objects.\n\\begin{screen}{1,2}\n{A,C}::Matrix.\nA C B A;\n@prodsort!(%);\nA B C A;\n\\end{screen}\n~\n\n\\cdbseealgo{prodsort}\n\\cdbseealgo{Spinor}\n\\cdbseeprop{ImplicitIndex}\n"
  },
  {
    "path": "core/properties/Metric.cc",
    "content": "\n#include \"Exceptions.hh\"\n#include \"IndexIterator.hh\"\n#include \"Kernel.hh\"\n#include \"properties/Metric.hh\"\n#include \"properties/Indices.hh\"\n\nusing namespace cadabra;\n\nMetric::Metric()\n\t{\n\t//\ttab_t tab;\n\t//\ttab.add_box(0,0);\n\t//\ttab.add_box(0,1);\n\t//\ttabs.push_back(tab);\n\t}\n\nstd::string Metric::name() const\n\t{\n\treturn \"Metric\";\n\t}\n\nbool Metric::parse(Kernel&, keyval_t& keyvals)\n\t{\n\tkeyval_t::const_iterator kv=keyvals.find(\"signature\");\n\tsignature=1;\n\tif(kv!=keyvals.end())\n\t\tsignature=to_long(*(kv->second.begin()->multiplier));\n\treturn true;\n\t}\n\nvoid Metric::validate(Kernel& kernel, std::shared_ptr<Ex> tr) const\n\t{\n\tauto st = index_iterator::begin(kernel.properties, tr->begin());\n\tauto nd = index_iterator::end(kernel.properties, tr->begin());\n\tsize_t num=0;\n\twhile(st != nd) {\n\t\tconst Indices *ind = kernel.properties.get<Indices>(st);\n\t\tif(ind==nullptr)\n\t\t\tthrow ArgumentException(\"Metric: indices of a metric object must have been declared as Indices.\");\n\n\t\tif(ind->position_type==Indices::position_t::free)\n\t\t\tthrow ArgumentException(\"Metric: indices of a metric object must have position 'fixed' or 'independent'.\");\n\n\t\t++num;\n\t\t++st;\n\t\t}\n\tif(num!=2) {\n\t\tthrow ArgumentException(\"Metric: needs exactly 2 indices.\");\n\t\t}\n\t}\n\nvoid Metric::latex(std::ostream& str) const\n\t{\n\tstr << name();\n\t}\n"
  },
  {
    "path": "core/properties/Metric.cnb",
    "content": "{\n\t\"cell_id\": 502887745135165894,\n\t\"cells\": [\n\t\t{\n\t\t\t\"cell_id\": 1870763346216562312,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 16590113103145697158,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\property{Metric}{Makes a two-tensor a metric.}\\n\\nLabels the object as a symmetric tensor, and optionally gives it the\\nindicated signature through the {\\\\tt signature} parameter.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\property{Metric}{Makes a two-tensor a metric.}\\n\\nLabels the object as a symmetric tensor, and optionally gives it the\\nindicated signature through the {\\\\tt signature} parameter.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 6115743091450954657,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 8587770812173137284,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 4066497848239046753,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"g_{m n} A^{n p}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}g_{m n} A^{n p}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9658144980223638993,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 8233761168233916260,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"A_{m}^{p}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}A_{m}\\\\,^{p}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"g_{m n}::Metric(signature=1).\\nex:= g_{m n} A^{n p};\\neliminate_metric(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 1399993026065074684,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 10234102992620672473,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"Objects declared as \\\\prop{Metric} can be used to automatically\\nraise or lower indices using the\\n\\\\algo{eliminate_metric} algorithm, as above.\\n\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"Objects declared as \\\\prop{Metric} can be used to automatically\\nraise or lower indices using the\\n\\\\algo{eliminate_metric} algorithm, as above.\\n\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 9140251695264754467,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"\"\n\t\t}\n\t],\n\t\"description\": \"Cadabra JSON notebook format\",\n\t\"version\": 1.0\n}\n"
  },
  {
    "path": "core/properties/Metric.hh",
    "content": "\n#pragma once\n\n#include \"Props.hh\"\n#include \"properties/Symmetric.hh\"\n\nnamespace cadabra {\n\n\tclass Metric : public Symmetric, virtual public property {\n\t\tpublic:\n\t\t\tMetric();\n\t\t\tvirtual std::string name() const override;\n\t\t\tvirtual bool        parse(Kernel&, keyval_t&) override;\n\t\t\tvirtual void        validate(Kernel&, std::shared_ptr<Ex>) const override;\n\t\t\tvirtual void        latex(std::ostream&) const override;\n\n\t\t\tint signature;\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/properties/Metric.tex",
    "content": "\\cdbproperty{Metric}{{\\it signature={\\sf integer}}}\n\nLabels the object as a symmetric tensor, and optionally gives it the\nindicated signature through the {\\tt signature} parameter.\n\\begin{screen}{1,2,3}\ng_{m n}::Metric(signature=1).\ng_{m n} A^{n p};\n@eliminate_metric!(%);\nA_{m}^{p};\n\\end{screen}\nObjects declared as \\subsprop{Metrics} can be used to automatically\nraise or lower indices using the\n\\subscommand{eliminate\\_metric} command.\n\n\\cdbseealgo{eliminate_metric}\n"
  },
  {
    "path": "core/properties/NonCommuting.cc",
    "content": "\n#include \"properties/NonCommuting.hh\"\n\nusing namespace cadabra;\n\nNonCommuting::~NonCommuting()\n\t{\n\t}\n\nstd::string NonCommuting::name() const\n\t{\n\treturn \"NonCommuting\";\n\t}\n"
  },
  {
    "path": "core/properties/NonCommuting.cnb",
    "content": "\n{\n\t\"cells\" : \n\t[\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\property{NonCommuting}{Makes components non-commuting.}\\n\\nMakes components non-commuting. See \\\\prop{AntiCommuting} for more\\ninformation on commutativity properties.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\property{NonCommuting}{Makes components non-commuting.}\\n\\nMakes components non-commuting. See \\\\prop{AntiCommuting} for more\\ninformation on commutativity properties.\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1.0\n}\n\n"
  },
  {
    "path": "core/properties/NonCommuting.hh",
    "content": "\n#pragma once\n\n#include \"properties/CommutingBehaviour.hh\"\n\nnamespace cadabra {\n\n\tclass NonCommuting : virtual public CommutingBehaviour {\n\t\tpublic:\n\t\t\tvirtual ~NonCommuting();\n\t\t\tvirtual std::string name() const;\n\t\t\tvirtual int sign() const\n\t\t\t\t{\n\t\t\t\treturn 0;\n\t\t\t\t}\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/properties/NonCommuting.tex",
    "content": "\\cdbproperty{NonCommuting}{}\n\nMakes components non-commuting. See \\subsprop{AntiCommuting} for more\ninformation on commutativity properties.\n\n\\cdbseeprop{AntiCommuting}\n\\cdbseeprop{SelfAntiCommuting}\n\\cdbseeprop{Commuting}\n\\cdbseeprop{ImplicitIndex}\n"
  },
  {
    "path": "core/properties/NumericalFlat.cc",
    "content": "\n#include \"properties/NumericalFlat.hh\"\n\nusing namespace cadabra;\n\nstd::string NumericalFlat::name() const\n\t{\n\treturn \"NumericalFlat\";\n\t}\n\n"
  },
  {
    "path": "core/properties/NumericalFlat.hh",
    "content": "\n#pragma once\n\n#include \"Props.hh\"\n\nnamespace cadabra {\n\n\t/// Property indicating that an operator is numerically flat, so that\n\t/// numerical factors in the argument can be taken outside.\n\n\tclass NumericalFlat : virtual public property {\n\t\tpublic:\n\t\t\tvirtual std::string name() const;\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/properties/NumericalFlat.tex",
    "content": "\\cdbproperty{NumericalFlat}{}\n\nIndicates that an operator is such that numerical factors can be taken\nout of its argument.\n\\begin{screen}{1,2}\nQ{#}::NumericalFlat.\nQ( 3 A ) + R( 3 A );\n@numerical_flatten!(%);\n3 Q( A ) + R( 3 A );\n\\end{screen}\n~\n\n\\cdbseeprop{Derivative}\n\\cdbseealgo{numerical_flatten}\n\\cdbseealgo{listflatten}\n"
  },
  {
    "path": "core/properties/PartialDerivative.cc",
    "content": "\n#include \"Algorithm.hh\"\n#include \"properties/PartialDerivative.hh\"\n\nusing namespace cadabra;\n\nPartialDerivative::~PartialDerivative()\n\t{\n\t}\n\nunsigned int PartialDerivative::size(const Properties& properties, Ex& tr, Ex::iterator it) const\n\t{\n\treturn Derivative::size(properties, tr, it)+1;\n\t}\n\n\nTableauBase::tab_t PartialDerivative::get_tab(const Properties& properties, Ex& tr, Ex::iterator it, unsigned int num) const\n\t{\n\tit=properties.head<PartialDerivative>(it);\n\n\tbool indices_first=tr.begin(it)->is_index();\n\tEx::sibling_iterator argnode=tr.begin(it);\n\tunsigned int number_of_indices=0;\n\twhile(argnode->is_index()) {\n\t\t++argnode;\n\t\t++number_of_indices;\n\t\t}\n\tunsigned int arg_indices=tr.number_of_children(argnode);\n\n\tif(num==0) { // symmetry of the derivative indices\n\t\ttab_t tab;\n\t\tint i=0;\n\t\tindex_iterator indit=index_iterator::begin(properties, it);\n\t\tif(!indices_first) {\n\t\t\tfor(unsigned int k=0; k<arg_indices; ++k) ++indit;\n\t\t\ti+=arg_indices;\n\t\t\t}\n\t\twhile(indit!=index_iterator::end(properties, it)) {\n\t\t\tif(tr.parent((Ex::iterator)indit)!=it) break;\n\t\t\t//\t\t\ttxtout << \"T: \" << i << \" \" << *indit->name << std::endl;\n\t\t\ttab.add_box(0, i);\n\t\t\t++i;\n\t\t\t++indit;\n\t\t\t}\n\t\treturn tab;\n\t\t}\n\telse {\n\t\treturn Derivative::get_tab(properties, tr, it, num-1);\n\t\t}\n\t}\n\nstd::string PartialDerivative::name() const\n\t{\n\treturn \"PartialDerivative\";\n\t}\n\n"
  },
  {
    "path": "core/properties/PartialDerivative.cnb",
    "content": "{\n\t\"cell_id\" : 5894066773150673170,\n\t\"cells\" : \n\t[\n\t\t{\n\t\t\t\"cell_id\" : 13525230147200416522,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 17709454361831274018,\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\property{PartialDerivative}{Makes an object a partial derivative.}\\n\\nMakes an object a partial derivative, i.e.~a derivative which\\ncommutes. The object on which it acts has to be a non-sub/superscript\\nchild, while all the sub- or superscript child nodes are interpreted\\nto be the variables with respect to which the derivative is taken.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\property{PartialDerivative}{Makes an object a partial derivative.}\\n\\nMakes an object a partial derivative, i.e.~a derivative which\\ncommutes. The object on which it acts has to be a non-sub/superscript\\nchild, while all the sub- or superscript child nodes are interpreted\\nto be the variables with respect to which the derivative is taken.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 8041028983535342531,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\\\\partial{#}::PartialDerivative.\\nA_{\\\\mu}::Depends(\\\\partial{#}).\\nex:= \\\\partial_{\\\\nu}{A_{\\\\mu} B_{\\\\rho}};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 11405585406750273487,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 9223372036854775813,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\partial_{\\\\nu}{A_{\\\\mu}} B_{\\\\rho}+A_{\\\\mu} \\\\partial_{\\\\nu}{B_{\\\\rho}}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"product_rule(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 8698124131347722985,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 9223372036854775816,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\" : 9223372036854775817,\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"\\\\partial_{\\\\nu}(A_{\\\\mu}) B_{\\\\rho}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\partial_{\\\\nu}{A_{\\\\mu}} B_{\\\\rho}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"unwrap(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 7814049592657967397,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 10367786712307776387,\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"Note that derivative objects do not necessarily need to have a sub- or\\nsuperscript child, they can be abstract derivatives as in\\n\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"Note that derivative objects do not necessarily need to have a sub- or\\nsuperscript child, they can be abstract derivatives as in\\n\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 16054494095843907264,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 9223372036854775819,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\" : 9223372036854775820,\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"cells\" : \n\t\t\t\t\t\t\t[\n\t\t\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\t\t\"cell_id\" : 9223372036854775821,\n\t\t\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\t\t\"source\" : \"\\\\partial(f g)\"\n\t\t\t\t\t\t\t\t}\n\t\t\t\t\t\t\t],\n\t\t\t\t\t\t\t\"source\" : \"D(c d e)\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}D\\\\left(c d e\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"D{#}::PartialDerivative.\\nex:= D(c d e);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 490912461791729791,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 9223372036854775822,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\" : 9223372036854775823,\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"D(c) d e + c D(d) e + c d D(e)\"\n\t\t\t\t\t\t},\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\" : 9223372036854775823,\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"g \\\\partial(f)\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}D{c} d e+c D{d} e+c d D{e}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"product_rule(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 6351980516135754406,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 7280252417494947409,\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"If you want to write a derivative with respect to a coordinate (instead\\nof with respect to an index, as in the first example above), refer to\\nthe \\\\prop{Coordinate} property.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"If you want to write a derivative with respect to a coordinate (instead\\nof with respect to an index, as in the first example above), refer to\\nthe \\\\prop{Coordinate} property.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 13304606490931490805,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 5525376504133299655,\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"It can be useful to specify what is the implicit coordinate with respect to which a\\nderivative acts. For instance, for a derivative in the $\\\\tau$ direction, we could\\nwrite\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"It can be useful to specify what is the implicit coordinate with respect to which a\\nderivative acts. For instance, for a derivative in the $\\\\tau$ direction, we could\\nwrite\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 593564993910242391,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 9223372036854775817,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Coordinate to~}\\\\tau.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 9223372036854775818,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Derivative to~}\\\\partial{\\\\#}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 9223372036854775819,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Depends to~}f.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 9223372036854775820,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\partial\\\\left(f g\\\\right)\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 9223372036854775822,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}g \\\\partial{f}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"\\\\tau::Coordinate;\\n\\\\partial{#}::Derivative(\\\\tau);\\nf::Depends(\\\\tau);\\nex:= \\\\partial{f g};\\nunwrap(ex);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 833494938170628554,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1\n}\n"
  },
  {
    "path": "core/properties/PartialDerivative.hh",
    "content": "\n#pragma once\n\n#include \"properties/Derivative.hh\"\n#include \"properties/Spinor.hh\"\n\nnamespace cadabra {\n\n\tclass PartialDerivative : public Derivative, public Inherit<Spinor>, virtual public property {\n\t\tpublic :\n\t\t\tvirtual ~PartialDerivative();\n\t\t\tvirtual std::string name() const;\n\n\t\t\tvirtual unsigned int size(const Properties&, Ex&, Ex::iterator) const;\n\t\t\tvirtual tab_t        get_tab(const Properties&, Ex&, Ex::iterator, unsigned int) const;\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/properties/PartialDerivative.tex",
    "content": "\\cdbproperty{PartialDerivative}{}\n\nMakes an object a partial derivative, i.e.~a derivative which\ncommutes. The object on which it acts has to be a non-sub/superscript\nchild, while all the sub- or superscript child nodes are interpreted\nto be the variables with respect to which the derivative is taken.\n\\begin{screen}{1,2,3,4}\n\\partial{#}::PartialDerivative.\nA_{\\mu}::Depends(\\partial).\n\\partial_{\\nu}{A_{\\mu} B_{\\rho}};\n@prodrule!(%);\n\\partial_{\\nu}{A_\\mu} B_{\\rho}\n\\end{screen}\nNote that derivative objects do not necessarily need to have a sub- or\nsuperscript child, they can be abstract derivatives as in\n\\begin{screen}{1,2,3}\nD(d?)::PartialDerivative.\nD(c d e);\n@prodrule!(%);\nD(c) d e + c D(d) e + c d D(e);\n\\end{screen}\nIf you want to write a derivative with respect to a coordinate (instead\nof with respect to an index, as in the first example above), refer to\nthe \\subsprop{Coordinate} property.\n\n\\cdbseeprop{Coordinate}\n"
  },
  {
    "path": "core/properties/PostDefaultRules.tex",
    "content": "\\cdbproperty{PostDefaultRules}{}\n\nSet the default rules, to be applied \\emph{after} every new input has\nbeen processed and active nodes have been executed. Use the inert form\nof active nodes for those ones that only have to be come active upon\nactual evaluation of the rule,\ni.e.~\\inertcommand{collect\\_terms!(\\%)}. Here is an example containing\nmore than one rule:\n\\begin{screen}{1,2}\n::PostDefaultRules( @@distribute!(%), @@prodsort!(%), @@collect_terms!(%) ).\nA*(B+C) + B*(A+C);\n2 A B + A C + B C;\n\\end{screen}\nNote that the rules have to be given in order; the list will only be\ntraversed once.\n\n\\cdbseeprop{PreDefaultRules}\n"
  },
  {
    "path": "core/properties/PreDefaultRules.tex",
    "content": "\\cdbproperty{PreDefaultRules}{}\n\nSet the default rules to be executed on all input \\emph{before} the\nactive nodes in that input are expanded. \n\n\\cdbseeprop{PostDefaultRules}\n\n"
  },
  {
    "path": "core/properties/PropertyInherit.tex",
    "content": "\\cdbproperty{PropertyInherit}{}\n\nIndicates that an object should inherit all properties of the objects\nthey wrap. In most cases, the use of \\subsprop{Accent} is more\nappropriate, since it also makes objects inherit indices.\n\n\\cdbseeprop{Accent}\n"
  },
  {
    "path": "core/properties/RiemannTensor.cc",
    "content": "\n#include \"IndexIterator.hh\"\n#include \"Exceptions.hh\"\n#include \"Kernel.hh\"\n#include \"Algorithm.hh\"\n#include \"properties/RiemannTensor.hh\"\n\n// #define DEBUG __FILE__\n#include \"Debug.hh\"\n\nusing namespace cadabra;\n\nRiemannTensor::RiemannTensor()\n\t{\n\ttab_t tab;\n\ttab.add_box(0,0);\n\ttab.add_box(0,2);\n\ttab.add_box(1,1);\n\ttab.add_box(1,3);\n\ttabs.push_back(tab);\n\t}\n\nstd::string RiemannTensor::name() const\n\t{\n\treturn \"RiemannTensor\";\n\t}\n\nvoid RiemannTensor::validate(Kernel& kernel, std::shared_ptr<Ex> pat) const\n\t{\n\tconst Properties& props=kernel.properties;\n\tif(Algorithm::number_of_indices(props, pat->begin())!=4)\n\t\tthrow ConsistencyException(\"RiemannTensor: need exactly 4 indices.\");\n\n\tint upper=0, lower=0;\n\n\tindex_iterator ii=index_iterator::begin(kernel.properties, pat->begin());\n\twhile(ii != index_iterator::end(kernel.properties, pat->begin()) ) {\n\t\tif(ii->fl.parent_rel==str_node::p_sub)        ++lower;\n\t\telse if(ii->fl.parent_rel==str_node::p_super) ++upper;\n\t\telse throw ConsistencyException(\"RiemannTensor: all indices need to be either upper or lower.\");\n\t\t++ii;\n\t\t}\n\tDEBUGLN( std::cerr << \"RiemannTensor:validate: found \" << upper << \"/\" << lower << \" upper/lower indices.\" << std::endl; );\n\tif(upper!=4 && lower!=4)\n\t\tthrow ConsistencyException(\"RiemannTensor: all indices need to be either upper or lower.\");\n\n\t// Also inject property with indices all moved to the other position.\n\tstd::shared_ptr<Ex> ex_other = std::make_shared<Ex>(pat->begin());\n\tEx::sibling_iterator sib=ex_other->begin(ex_other->begin());\n\twhile(sib!=ex_other->end(ex_other->begin())) {\n\t\tsib->fl.parent_rel = (upper==4 ? str_node::p_sub : str_node::p_super);\n\t\t++sib;\n\t\t}\n\tkernel.properties.master_insert(*ex_other, new RiemannTensor());\n\t}\n\n\n\n\n"
  },
  {
    "path": "core/properties/RiemannTensor.cnb",
    "content": "{\n\t\"cells\" : \n\t[\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\property{RiemannTensor}{Make an object a Riemann curvature tensor.}\\n\\nGives an object the symmetry properties of a Riemann tensor. This has implications for various\\nsimplification algorithms such as \\\\algo{canonicalise} or \\\\algo{young_project_tensor}.\\n\\nThe following is an example which makes use of the Ricci identity.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\property{RiemannTensor}{Make an object a Riemann curvature tensor.}\\n\\nGives an object the symmetry properties of a Riemann tensor. This has implications for various\\nsimplification algorithms such as \\\\algo{canonicalise} or \\\\algo{young_project_tensor}.\\n\\nThe following is an example which makes use of the Ricci identity.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property TableauSymmetry to~}R_{m n p q}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property AntiSymmetric to~}A^{m n p}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}A^{m n p} R_{m n p q}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"R_{m n p q}::RiemannTensor;\\nA^{m n p}::AntiSymmetric;\\nex:= A^{m n p} R_{m n p q};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}A^{m n p} \\\\left(\\\\frac{2}{3}R_{m n p q} - \\\\frac{1}{3}R_{m q n p}+\\\\frac{1}{3}R_{m p n q}\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"young_project_tensor(_, modulo_monoterm=True);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\frac{2}{3}A^{m n p} R_{m n p q} - \\\\frac{1}{3}A^{m n p} R_{m q n p}+\\\\frac{1}{3}A^{m n p} R_{m p n q}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"distribute(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}0\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"canonicalise(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1\n}\n"
  },
  {
    "path": "core/properties/RiemannTensor.hh",
    "content": "#pragma once\n\n#include \"properties/TableauSymmetry.hh\"\n\nnamespace cadabra {\n\n\tclass RiemannTensor : public TableauSymmetry, virtual public property {\n\t\tpublic:\n\t\t\tRiemannTensor();\n\t\t\tvirtual std::string name() const override;\n\t\t\tvirtual void        validate(Kernel&, std::shared_ptr<Ex>) const override;\n//\t\t\tvirtual bool        parse(Kernel&, std::shared_ptr<Ex>, keyval_t&) override;\n\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/properties/RiemannTensor.tex",
    "content": "\\cdbproperty{RiemannTensor}{}\n\nGives an object the symmetry properties of a Riemann tensor.\n\\begin{screen}{1,2}\nR_{m n p q}::RiemannTensor;\nA^{m n p}::AntiSymmetric.\nA^{m n p} R_{m n p q};\n@impose_bianchi!(%);\n0;\n\\end{screen}\nVarious other algorithms, such as \\subscommand{canonicalise}, also\ntake into account this property.\n\n\\cdbseealgo{canonicalise}\n\\cdbseealgo{impose_bianchi}\n"
  },
  {
    "path": "core/properties/SatisfiesBianchi.cc",
    "content": "\n#include \"properties/SatisfiesBianchi.hh\"\n#include \"Exceptions.hh\"\n#include \"IndexIterator.hh\"\n#include \"Kernel.hh\"\n#include \"properties/Derivative.hh\"\n\n// #define DEBUG __FILE__\n#include \"Debug.hh\"\n\nusing namespace cadabra;\n\nstd::string SatisfiesBianchi::name() const\n\t{\n\treturn \"SatisfiesBianchi\";\n\t}\n\nvoid SatisfiesBianchi::validate(Kernel& kernel, std::shared_ptr<Ex> pat) const \n\t{\n\tauto *der = kernel.properties.get<Derivative>(pat->begin());\n\tif(!der)\n\t\tthrow ArgumentException(\"SatisfiesBianchi: can only apply to objects with Derivative property.\");\n\n\tif(pat->number_of_children(pat->begin())!=2)\n\t\tthrow ArgumentException(\"SatisfiesBianchi: can only apply to a single Derivative acting on an explicit object.\");\n\t}\n\nunsigned int SatisfiesBianchi::size(const Properties& properties, Ex& tr, Ex::iterator it) const\n\t{\n\tEx::sibling_iterator chld=tr.begin(it);\n//\tbool indexfirst=false;\n\tif(chld->fl.parent_rel!=str_node::p_none) {\n//\t\tindexfirst=true;\n\t\t++chld;\n\t\t}\n\tassert(chld->fl.parent_rel==str_node::p_none);\n\tconst TableauBase *tb=properties.get<TableauBase>(chld);\n\n\tif(!tb) return 0;\n\n\tassert(tb->size(properties, tr, chld)==1); // Does this make sense otherwise?\n\n\treturn 1;\n\t}\n\nTableauBase::tab_t SatisfiesBianchi::get_tab(const Properties& properties, Ex& tr, Ex::iterator it, unsigned int) const\n\t{\n\t// Take the tableau of the child, increase all indices by\n\t// one if the derivative index sits on the first position,\n\t// and then add a box on the first row corresponding to the\n\t// derivative.\n\n\tEx::sibling_iterator chld=tr.begin(it);\n\tbool indexfirst=false;\n\tif(chld->fl.parent_rel!=str_node::p_none) {\n\t\tindexfirst=true;\n\t\t++chld;\n\t\t}\n\tassert(chld->fl.parent_rel==str_node::p_none);\n\t//\ttxtout << *chld->name << std::endl;\n\tconst TableauBase *tb=properties.get<TableauBase>(chld);\n\tassert(tb);\n\t//\ttxtout << \"got child TableauBase\" << std::endl;\n\n\tassert(tb->size(properties, tr, chld)==1);\n\ttab_t thetab=tb->get_tab(properties, tr, chld, 0);\n\t//\ttxtout << \"got child tab\" << std::endl;\n\tif(indexfirst) {\n\t\tfor(unsigned int r=0; r<thetab.number_of_rows(); ++r)\n\t\t\tfor(unsigned int c=0; c<thetab.row_size(r); ++c)\n\t\t\t\tthetab(r,c)+=1;\n\t\tthetab.add_box(0, 0);\n\t\t}\n\telse {\n\t\tindex_iterator ii=index_iterator::begin(properties, it);\n\t\tunsigned int pos=0;\n\t\twhile(ii!=index_iterator::end(properties, it)) {\n\t\t\t++ii;\n\t\t\t++pos;\n\t\t\t}\n\t\tthetab.add_box(0, pos-1);\n\t\t}\n\n\tDEBUGLN( std::cerr << thetab << std::endl; );\n\t\n\treturn thetab;\n\t}\n\n\n"
  },
  {
    "path": "core/properties/SatisfiesBianchi.cnb",
    "content": "{\n\t\"cell_id\": 8333782182685695692,\n\t\"cells\": [\n\t\t{\n\t\t\t\"cell_id\": 13023289047659747782,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 2993145575969842933,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\property{SatisfiesBianchi}{Make an object satisfy the generalised Bianchi identity.}\\n\\nIndicates that an object satisfies a (generalised) Bianchi\\nidentity. This is often used to link a derivative operator to a\\ncurvature tensor, as in\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\property{SatisfiesBianchi}{Make an object satisfy the generalised Bianchi identity.}\\n\\nIndicates that an object satisfies a (generalised) Bianchi\\nidentity. This is often used to link a derivative operator to a\\ncurvature tensor, as in\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 600502675255901832,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 7278336446640073669,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 12533235753225063125,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"D_{m}(R_{n p q r}) A^{m n p q}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}D_{m}\\\\!{R_{n p q r}} A^{m n p q}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"R_{m n p q}::RiemannTensor.\\nD{#}::Derivative.\\nD_{m}{ R_{n p q r} }::SatisfiesBianchi.\\nA^{m n p q}::AntiSymmetric.\\nex:= D_{m}{ R_{n p q r} } A^{m n p q};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 14138636317103115824,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 13508237173211391630,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 17690598400943458767,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"D_{m}( 1/12 R_{n p q r} +  1/12 R_{q p n r} +  1/12 R_{n r q p} +  1/12 R_{q r n p} -  1/12 R_{p n q r} -  1/12 R_{q n p r} -  1/12 R_{p r q n} -  1/12 R_{q r p n} -  1/12 R_{n p r q} -  1/12 R_{r p n q} -  1/12 R_{n q r p} -  1/12 R_{r q n p} +  1/12 R_{p n r q} +  1/12 R_{r n p q} +  1/12 R_{p q r n} +  1/12 R_{r q p n}) ( 1/24 A^{m n p q} -  1/24 A^{m n q p} -  1/24 A^{m p n q} +  1/24 A^{m p q n} +  1/24 A^{m q n p} -  1/24 A^{m q p n} -  1/24 A^{n m p q} +  1/24 A^{n m q p} +  1/24 A^{n p m q} -  1/24 A^{n p q m} -  1/24 A^{n q m p} +  1/24 A^{n q p m} +  1/24 A^{p m n q} -  1/24 A^{p m q n} -  1/24 A^{p n m q} +  1/24 A^{p n q m} +  1/24 A^{p q m n} -  1/24 A^{p q n m} -  1/24 A^{q m n p} +  1/24 A^{q m p n} +  1/24 A^{q n m p} -  1/24 A^{q n p m} -  1/24 A^{q p m n} +  1/24 A^{q p n m})\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}D_{m}\\\\!\\\\left(\\\\frac{1}{12}\\\\,R_{n p q r}\\\\discretionary{}{}{}+\\\\frac{1}{12}\\\\,R_{q p n r}\\\\discretionary{}{}{}+\\\\frac{1}{12}\\\\,R_{n r q p}\\\\discretionary{}{}{}+\\\\frac{1}{12}\\\\,R_{q r n p}\\\\discretionary{}{}{} - \\\\frac{1}{12}\\\\,R_{p n q r}\\\\discretionary{}{}{} - \\\\frac{1}{12}\\\\,R_{q n p r}\\\\discretionary{}{}{} - \\\\frac{1}{12}\\\\,R_{p r q n}\\\\discretionary{}{}{} - \\\\frac{1}{12}\\\\,R_{q r p n}\\\\discretionary{}{}{} - \\\\frac{1}{12}\\\\,R_{n p r q}\\\\discretionary{}{}{} - \\\\frac{1}{12}\\\\,R_{r p n q}\\\\discretionary{}{}{} - \\\\frac{1}{12}\\\\,R_{n q r p}\\\\discretionary{}{}{} - \\\\frac{1}{12}\\\\,R_{r q n p}\\\\discretionary{}{}{}+\\\\frac{1}{12}\\\\,R_{p n r q}\\\\discretionary{}{}{}+\\\\frac{1}{12}\\\\,R_{r n p q}\\\\discretionary{}{}{}+\\\\frac{1}{12}\\\\,R_{p q r n}\\\\discretionary{}{}{}+\\\\frac{1}{12}\\\\,R_{r q p n}\\\\right) \\\\left(\\\\frac{1}{24}\\\\,A^{m n p q}\\\\discretionary{}{}{} - \\\\frac{1}{24}\\\\,A^{m n q p}\\\\discretionary{}{}{} - \\\\frac{1}{24}\\\\,A^{m p n q}\\\\discretionary{}{}{}+\\\\frac{1}{24}\\\\,A^{m p q n}\\\\discretionary{}{}{}+\\\\frac{1}{24}\\\\,A^{m q n p}\\\\discretionary{}{}{} - \\\\frac{1}{24}\\\\,A^{m q p n}\\\\discretionary{}{}{} - \\\\frac{1}{24}\\\\,A^{n m p q}\\\\discretionary{}{}{}+\\\\frac{1}{24}\\\\,A^{n m q p}\\\\discretionary{}{}{}+\\\\frac{1}{24}\\\\,A^{n p m q}\\\\discretionary{}{}{} - \\\\frac{1}{24}\\\\,A^{n p q m}\\\\discretionary{}{}{} - \\\\frac{1}{24}\\\\,A^{n q m p}\\\\discretionary{}{}{}+\\\\frac{1}{24}\\\\,A^{n q p m}\\\\discretionary{}{}{}+\\\\frac{1}{24}\\\\,A^{p m n q}\\\\discretionary{}{}{} - \\\\frac{1}{24}\\\\,A^{p m q n}\\\\discretionary{}{}{} - \\\\frac{1}{24}\\\\,A^{p n m q}\\\\discretionary{}{}{}+\\\\frac{1}{24}\\\\,A^{p n q m}\\\\discretionary{}{}{}+\\\\frac{1}{24}\\\\,A^{p q m n}\\\\discretionary{}{}{} - \\\\frac{1}{24}\\\\,A^{p q n m}\\\\discretionary{}{}{} - \\\\frac{1}{24}\\\\,A^{q m n p}\\\\discretionary{}{}{}%\\n+\\\\frac{1}{24}\\\\,A^{q m p n}\\\\discretionary{}{}{}+\\\\frac{1}{24}\\\\,A^{q n m p}\\\\discretionary{}{}{} - \\\\frac{1}{24}\\\\,A^{q n p m}\\\\discretionary{}{}{} - \\\\frac{1}{24}\\\\,A^{q p m n}\\\\discretionary{}{}{}+\\\\frac{1}{24}\\\\,A^{q p n m}\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"young_project_tensor(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 1546185059476091385,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 7518520068568561488,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 12384204868021245284,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"0\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}0\\\\,\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"distribute(_)\\ncanonicalise(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 8290034210843708580,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"\"\n\t\t}\n\t],\n\t\"description\": \"Cadabra JSON notebook format\",\n\t\"flags\": {\n\t\t\"hide_input_cells\": false\n\t},\n\t\"version\": 1.0\n}\n"
  },
  {
    "path": "core/properties/SatisfiesBianchi.hh",
    "content": "\n#pragma once\n\n#include \"properties/TableauBase.hh\"\n\nnamespace cadabra {\n\n\tclass SatisfiesBianchi : public TableauBase, virtual public property {\n\t\tpublic:\n\t\t\t//\t\tvirtual bool parse(const Properties&, keyval_t&) override;\n\t\t\tvirtual std::string name() const override;\n\n\t\t\tvirtual unsigned int size(const Properties&, Ex&, Ex::iterator) const override;\n\t\t\tvirtual tab_t        get_tab(const Properties&, Ex&, Ex::iterator, unsigned int) const override;\n\t\t\tvirtual void         validate(Kernel&, std::shared_ptr<Ex>) const override;\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/properties/SatisfiesBianchi.tex",
    "content": "\\cdbproperty{SatisfiesBianchi}{}\n\nIndicates that an object satisfies a (generalised) Bianchi\nidentity. This is often used to link a derivative operator to a\ncurvature tensor, as in\n\\begin{screen}{1,2,3,4,5,6,8}\nR_{m n p q}::RiemannTensor;\nD{#}::Derivative.\nD_{m}{ R_{n p q r} }::SatisfiesBianchi.\nA^{m n p q}::AntiSymmetric.\nD_{m}{ R_{n p q r} } A^{m n p q};\n@canonicalise!(%);\n(-1) D_{m}{ R_{r n p q} } A^{m n p q};\n@impose_bianchi!(%);\n0;\n\\end{screen}\nThis general method allows one to handle more than one type of\nderivative object.\n\n\\cdbseeprop{RiemannTensor}\n\\cdbseealgo{canonicalise}\n\\cdbseealgo{impose_bianchi}\n"
  },
  {
    "path": "core/properties/SelfAntiCommuting.cc",
    "content": "\n#include \"properties/SelfAntiCommuting.hh\"\n\nusing namespace cadabra;\n\nSelfAntiCommuting::~SelfAntiCommuting()\n\t{\n\t}\n\nstd::string SelfAntiCommuting::name() const\n\t{\n\treturn \"SelfAntiCommuting\";\n\t}\n\nint SelfAntiCommuting::sign() const\n\t{\n\treturn -1;\n\t}\n"
  },
  {
    "path": "core/properties/SelfAntiCommuting.cnb",
    "content": "\n{\n\t\"cells\" : \n\t[\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\property{SelfAntiCommuting}{Make components of tensors anti-commute.}\\n\\nUsed to make objects with indices anti-commuting when their index\\nvalues are different. Example:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\property{SelfAntiCommuting}{Make components of tensors anti-commute.}\\n\\nUsed to make objects with indices anti-commuting when their index\\nvalues are different. Example:\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\psi^{\\\\nu} \\\\psi^{\\\\mu}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"\\\\psi^{\\\\mu}::SelfAntiCommuting.\\nex:= \\\\psi^{\\\\nu} \\\\psi^{\\\\mu};\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}-\\\\psi^{\\\\mu} \\\\psi^{\\\\nu}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"canonicalise(_);\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\psi^{\\\\mu} \\\\psi^{\\\\mu}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex:= \\\\psi^{\\\\mu} \\\\psi^{\\\\mu};\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}0\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"canonicalise(_);\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"This could not be handled with \\\\prop{AntiCommuting} because that\\nproperty handles the behaviour of \\\\emph{different} expression patterns.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"This could not be handled with \\\\prop{AntiCommuting} because that\\nproperty handles the behaviour of \\\\emph{different} expression patterns.\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1.0\n}\n\n"
  },
  {
    "path": "core/properties/SelfAntiCommuting.hh",
    "content": "\n#pragma once\n\n#include \"properties/SelfCommutingBehaviour.hh\"\n\nnamespace cadabra {\n\n\tclass SelfAntiCommuting : virtual public SelfCommutingBehaviour {\n\t\tpublic:\n\t\t\tvirtual ~SelfAntiCommuting();\n\t\t\tvirtual std::string name() const override;\n\t\t\tvirtual int sign() const override;\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/properties/SelfAntiCommuting.tex",
    "content": "\\cdbproperty{SelfAntiCommuting}{}\n\nUsed to make objects with indices anti-commuting when their index\nvalues are different. Example:\n\\begin{screen}{1,2,3,5,6}\n\\psi^{\\mu}::SelfAntiCommuting.\n\\psi^{\\nu} \\psi^{\\mu}:\n@prodsort!(%);\n(-1) \\psi^{\\mu} \\psi^{\\nu};\n\\psi^{\\mu} \\psi^{\\mu}:\n@canonicalise!(%);\n0;\n\\end{screen}\nThis could not be handled with \\subsprop{AntiCommuting} because that\nproperty handles the behaviour of \\emph{different} expression patterns.\n\n\\cdbseealgo{AntiCommuting}\n"
  },
  {
    "path": "core/properties/SelfCommuting.cc",
    "content": "\n#include \"properties/SelfCommuting.hh\"\n\nusing namespace cadabra;\n\nSelfCommuting::~SelfCommuting()\n\t{\n\t}\n\nstd::string SelfCommuting::name() const\n\t{\n\treturn \"SelfCommuting\";\n\t}\n\nint SelfCommuting::sign() const\n\t{\n\treturn 1;\n\t}\n"
  },
  {
    "path": "core/properties/SelfCommuting.cnb",
    "content": "\n{\n\t\"cells\" : \n\t[\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\property{SelfCommuting}{Make tensor components commute.}\\n\\nUsed to make objects with indices commuting when their index values\\nare different. This is the default, so usually not\\nneeded. See \\\\prop{SelfAntiCommuting} for more information.\\n\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\property{SelfCommuting}{Make tensor components commute.}\\n\\nUsed to make objects with indices commuting when their index values\\nare different. This is the default, so usually not\\nneeded. See \\\\prop{SelfAntiCommuting} for more information.\\n\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1.0\n}\n\n"
  },
  {
    "path": "core/properties/SelfCommuting.hh",
    "content": "\n\n#pragma once\n\n#include \"properties/SelfCommutingBehaviour.hh\"\n\nnamespace cadabra {\n\n\tclass SelfCommuting : virtual public SelfCommutingBehaviour {\n\t\tpublic:\n\t\t\tvirtual ~SelfCommuting();\n\t\t\tvirtual std::string name() const override;\n\t\t\tvirtual int sign() const override;\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/properties/SelfCommuting.tex",
    "content": "\\cdbproperty{SelfCommuting}{}\n\nUsed to make objects with indices commuting when their index values\nare different. This is the default, so usually not\nneeded. See \\subsprop{SelfAntiCommuting} for more information.\n\n\\cdbseealgo{SelfAntiCommuting}\n"
  },
  {
    "path": "core/properties/SelfCommutingBehaviour.hh",
    "content": "\n#pragma once\n\n#include \"Props.hh\"\n\nnamespace cadabra {\n\n\tclass SelfCommutingBehaviour : virtual public property {\n\t\tpublic:\n\t\t\tvirtual int sign() const=0;\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/properties/SelfDual.tex",
    "content": "\\cdbproperty{SelfDual}{}\n\nMake a tensor fully anti-symmetric as well as self-dual. The\nconventions used are that self-duality means\n\\begin{equation}\nF_{\\mu_1\\cdots \\mu_n}\n= \\frac{1}{n!} \\epsilon_{\\mu_1\\cdots\\mu_n \\mu_{n+1}\\cdots \\mu_{2n}} F_{\\mu_{n+1}\\cdots\\mu_{2n}}\\,.\n\\end{equation}\nThis property used by the Young projection algorithms and\nthe \\subscommand{dualise\\_tensor} algorithm, among others.\n\n\\cdbseeprop{AntiSelfDual}\n\\cdbseealgo{dualise_tensor}\n\\cdbseealgo{young_project_tensor}\n"
  },
  {
    "path": "core/properties/SelfNonCommuting.cc",
    "content": "\n#include \"properties/SelfNonCommuting.hh\"\n\nusing namespace cadabra;\n\nSelfNonCommuting::~SelfNonCommuting()\n\t{\n\t}\n\nstd::string SelfNonCommuting::name() const\n\t{\n\treturn \"SelfNonCommuting\";\n\t}\n\nint SelfNonCommuting::sign() const\n\t{\n\treturn 0;\n\t}\n"
  },
  {
    "path": "core/properties/SelfNonCommuting.cnb",
    "content": "\n{\n\t\"cells\" : \n\t[\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\property{SelfNonCommuting}{Make tensor components non-commuting.}\\n\\nUsed to make objects with indices non-commuting when their index\\nvalues are different. See \\\\prop{SelfAntiCommuting} for more\\ninformation.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\property{SelfNonCommuting}{Make tensor components non-commuting.}\\n\\nUsed to make objects with indices non-commuting when their index\\nvalues are different. See \\\\prop{SelfAntiCommuting} for more\\ninformation.\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}A_{n} A_{a} A_{m}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}A_{n} A_{a} A_{m}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"A_{m}::SelfNonCommuting.\\nex:= A_{n} A_{a} A_{m};\\nsort_product(_);\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1.0\n}\n\n"
  },
  {
    "path": "core/properties/SelfNonCommuting.hh",
    "content": "\n#pragma once\n\n#include \"properties/SelfCommutingBehaviour.hh\"\n\nnamespace cadabra {\n\n\tclass SelfNonCommuting : virtual public SelfCommutingBehaviour {\n\t\tpublic:\n\t\t\tvirtual ~SelfNonCommuting();\n\t\t\tvirtual std::string name() const override;\n\t\t\tvirtual int sign() const override;\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/properties/SelfNonCommuting.tex",
    "content": "\\cdbproperty{SelfNonCommuting}{}\n\nUsed to make objects with indices non-commuting when their index\nvalues are different. See \\subsprop{SelfAntiCommuting} for more\ninformation.\n\n\\cdbseealgo{SelfAntiCommuting}\n"
  },
  {
    "path": "core/properties/SigmaBarMatrix.tex",
    "content": "\\cdbproperty{SigmaBarMatrix}{}\n\nSee \\subsprop{SigmaMatrix} for details.\n\n\\cdbseeprop{SigmaMatrix}\n"
  },
  {
    "path": "core/properties/SigmaMatrix.hh",
    "content": "\n// 0812.1594v5.pdf\n"
  },
  {
    "path": "core/properties/SigmaMatrix.tex",
    "content": "\\cdbproperty{SigmaMatrix}{}\n\nThese are the invariant tensors relating the~$(\\tfrac{1}{2},\\tfrac{1}{2})$ to the vector representation of\nSO(3,1). \\Cdb uses the Wess~\\& Bagger conventions,\nwhich means that the metric has signature~$\\eta = {\\rm\n  diag}(-1,1,1,1)$ and\n\\begin{equation}\n(\\sigma^{\\mu})_{\\alpha\\dot{\\beta}} = ( -{\\mathbb 1}, \\vec\\sigma )_{\\alpha\\dot{\\beta}}\\,,\\quad\n(\\bar{\\sigma}^{\\mu})^{\\dot{\\alpha}\\beta} = (-{\\mathbb 1}, -\\vec\\sigma)^{\\dot{\\alpha}\\beta}\\,.\n\\end{equation}\nWhen the objects carry two vector indices, they are understood to be\n\\begin{equation}\n(\\sigma^{m n})_{\\alpha}{}^{\\beta} \\equiv \\frac{1}{4}( \\sigma^m\n  \\bar{\\sigma}^n - \\sigma^n \\bar{\\sigma}^m)_{\\alpha}{}^{\\beta}\\,,\\quad\\quad\n(\\bar{\\sigma}^{m n})^{\\dot{\\alpha}}{}_{\\dot{\\beta}} \\equiv\n  \\frac{1}{4}(\\bar{\\sigma}^m \\sigma^{n}\n- \\bar{\\sigma}^n \\sigma^{m})^{\\dot{\\alpha}}{}_{\\dot{\\beta}}\\,.\n\\end{equation}\nSee below for algorithms dealing with the conversion from indexed to\nindex-free notation.\n"
  },
  {
    "path": "core/properties/SortOrder.cc",
    "content": "\n#include \"properties/SortOrder.hh\"\n\nusing namespace cadabra;\n\nproperty::match_t SortOrder::equals(const property *) const\n\t{\n\treturn no_match; // you can have as many of these as you like\n\t}\n\nstd::string SortOrder::name() const\n\t{\n\treturn \"SortOrder\";\n\t}\n"
  },
  {
    "path": "core/properties/SortOrder.cnb",
    "content": "\n{\n\t\"cells\" : \n\t[\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\property{SortOrder}{Set sorting order of objects.}\\n\\nA list property which determines the preferred order of objects when\\na \\\\algo{sort_product} command is used. \"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\property{SortOrder}{Set sorting order of objects.}\\n\\nA list property which determines the preferred order of objects when\\na \\\\algo{sort_product} command is used. \"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}A A_{m} B C\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"{B,A,C,A_{m}}::SortOrder.\\nex:= A A_{m} B C;\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}B A C A_{m}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"sort_product(_);\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"As indicated in the example above, any type of object can appear in\\nthe list.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"As indicated in the example above, any type of object can appear in\\nthe list.\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1.0\n}\n\n"
  },
  {
    "path": "core/properties/SortOrder.hh",
    "content": "\n#pragma once\n\n#include \"Props.hh\"\n\nnamespace cadabra {\n\n\tclass SortOrder : public list_property {\n\t\tpublic:\n\t\t\tvirtual std::string name() const;\n\t\t\tvirtual match_t equals(const property *) const;\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/properties/SortOrder.tex",
    "content": "\\cdbproperty{SortOrder}{}\n\nA list property which determines the preferred order of objects when\na \\subscommand{prodsort} command is used. \n\\begin{screen}{1,2}\n{B,A,C,A_{m}}::SortOrder.\nA A_{m} B C;\n@prodsort!(%);\nB A C A_{m};\n\\end{screen}\nAs indicated in the example above, any type of object can appear in\nthe list.\n\n\\cdbseealgo{prodsort}\n\n"
  },
  {
    "path": "core/properties/Spinor.cc",
    "content": "\n#include \"Spinor.hh\"\n#include \"Exceptions.hh\"\n#include \"Kernel.hh\"\n\nusing namespace cadabra;\n\nSpinor::Spinor()\n\t: dimension(10), weyl(true), chirality(positive), majorana(true)\n\t{\n\t}\n\nstd::string Spinor::name() const\n\t{\n\treturn \"Spinor\";\n\t}\n\nbool Spinor::parse(Kernel& kernel, keyval_t& keyvals)\n\t{\n\tkeyval_t::iterator ki=keyvals.find(\"dimension\");\n\tif(ki!=keyvals.end()) {\n\t\tif(!ki->second.is_integer())\n\t\t\tthrow ConsistencyException(\"Spinor: dimension has to be an explicit integer.\");\n\t\tdimension=to_long(*ki->second.begin()->multiplier);\n\t\tkeyvals.erase(ki);\n\t\t}\n\telse dimension=10;\n\n\tki=keyvals.find(\"type\");\n\tif(ki!=keyvals.end()) {\n\t\tif(ki->second.equals(\"Weyl\")) {\n\t\t\tif(dimension%2!=0) {\n\t\t\t\tthrow ConsistencyException(\"Weyl spinors require the dimension to be even.\");\n\t\t\t\t}\n\t\t\tweyl=true;\n\t\t\t}\n\t\tif(ki->second.equals(\"Majorana\")) {\n\t\t\tweyl=false;\n\t\t\tif(dimension%8==2 || dimension%8==3 || dimension%8==4)\n\t\t\t\tmajorana=true;\n\t\t\telse {\n\t\t\t\tthrow ConsistencyException(\"Majorana spinors require the dimension to be 2,3,4 mod 8.\");\n\t\t\t\treturn false;\n\t\t\t\t}\n\t\t\t}\n\t\tif(ki->second.equals(\"MajoranaWeyl\")) {\n\t\t\tif(dimension%8==2) {\n\t\t\t\t//\t\t\t\ttxtout << \"setting to MajoranaWeyl\" << std::endl;\n\t\t\t\tweyl=true;\n\t\t\t\tmajorana=true;\n\t\t\t\t}\n\t\t\telse {\n\t\t\t\tthrow ConsistencyException(\"Majorana-Weyl spinors require the dimension to be 2 mod 8.\");\n\t\t\t\treturn false;\n\t\t\t\t}\n\t\t\t}\n\t\tkeyvals.erase(ki);\n\t\t}\n\n\tki=keyvals.find(\"chirality\");\n\tif(ki!=keyvals.end()) {\n\t\tif(ki->second.equals(\"Positive\")) chirality=positive;\n\t\tif(ki->second.equals(\"Negative\")) chirality=negative;\n\t\tkeyvals.erase(ki);\n\t\t}\n\n\tImplicitIndex::parse(kernel, keyvals);\n\n\treturn true;\n\t}\n\n"
  },
  {
    "path": "core/properties/Spinor.cnb",
    "content": "\n{\n\t\"cells\" : \n\t[\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\property{Spinor}{Declares an object to transform as a spinor.}\\n\\nDeclares an object to be a spinor, i.e.~transforming in one of the\\nspinor representations of the orthogonal or Lorentz group. The\\ndeclaration should involve an indication of the dimension, as in the\\nexample below. It can optionally have type indicators (these should be\\n{\\\\tt Majorana}, {\\\\tt Weyl} or {\\\\tt MajoranaWeyl}) and chirality\\nindicators for Weyl spinors ({\\\\tt Positive} or {\\\\tt Negative},\\nindicating the eigenvalue with respect to the generalised~$\\\\gamma_5$\\nmatrix). Here is an example:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\property{Spinor}{Declares an object to transform as a spinor.}\\n\\nDeclares an object to be a spinor, i.e.~transforming in one of the\\nspinor representations of the orthogonal or Lorentz group. The\\ndeclaration should involve an indication of the dimension, as in the\\nexample below. It can optionally have type indicators (these should be\\n{\\\\tt Majorana}, {\\\\tt Weyl} or {\\\\tt MajoranaWeyl}) and chirality\\nindicators for Weyl spinors ({\\\\tt Positive} or {\\\\tt Negative},\\nindicating the eigenvalue with respect to the generalised~$\\\\gamma_5$\\nmatrix). Here is an example:\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Spinor to~}\\\\psi.\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"\\\\psi::Spinor(dimension=11, type=Majorana);\\n\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"This property is taken into account by various algorithms such\\nas \\\\algo{fierz} and \\\\algo{sort_spinors}.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"This property is taken into account by various algorithms such\\nas \\\\algo{fierz} and \\\\algo{sort_spinors}.\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1.0\n}\n\n"
  },
  {
    "path": "core/properties/Spinor.hh",
    "content": "\n#pragma once\n\n#include \"properties/ImplicitIndex.hh\"\n\nnamespace cadabra {\n\n\tclass Spinor : public ImplicitIndex, virtual public property {\n\t\tpublic:\n\t\t\tSpinor();\n\t\t\tvirtual ~Spinor() {};\n\t\t\tvirtual std::string name() const override;\n\t\t\t//\t\tvirtual void        display(std::ostream&) const;\n\t\t\tvirtual bool        parse(Kernel&, keyval_t& keyvals) override;\n\n\t\t\tint  dimension;\n\t\t\tbool weyl;\n\t\t\tenum Chirality { positive, negative } chirality;  // only in combination with weyl\n\t\t\tbool majorana;\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/properties/Spinor.tex",
    "content": "\\cdbproperty{Spinor}{\\it dimension={\\sf integer},\ntype=Weyl$\\vert$Majorana$\\vert$MajoranaWeyl, chirality=Positive$\\vert$Negative}\n\nDeclares an object to be a spinor, i.e.~transforming in one of the\nspinor representations of the orthogonal or Lorentz group. The\ndeclaration should involve an indication of the dimension, as in the\nexample below. It can optionally have type indicators (these should be\n{\\tt Majorana}, {\\tt Weyl} or {\\tt MajoranaWeyl}) and chirality\nindicators for Weyl spinors ({\\tt Positive} or {\\tt Negative},\nindicating the eigenvalue with respect to the generalised~$\\gamma_5$\nmatrix). Here is an example:\n\\begin{screen}{1,2}\n\\psi::Spinor(dimension=11, type=Majorana).\n\\end{screen}\nThis property is taken into account by various algorithms such\nas \\subscommand{fierz} and \\subscommand{spinorsort}.\n\n\\cdbseeprop{DiracBar}\n\\cdbseealgo{fierz}\n\\cdbseealgo{spinorsort}\n"
  },
  {
    "path": "core/properties/Symbol.cc",
    "content": "\n#include \"properties/Symbol.hh\"\n\nusing namespace cadabra;\n\nstd::string Symbol::name() const\n\t{\n\treturn \"Symbol\";\n\t}\n\nconst Symbol *Symbol::get(const Properties& properties, Ex::iterator it, bool ignore_parent_rel)\n\t{\n\tif(*it->name==\"\\\\sum\") {\n\t\t// Check whether all siblings have the Symbol property.\n\t\tEx::sibling_iterator sib=it.begin();\n\t\tconst Symbol *s=0;\n\t\twhile(sib!=it.end()) {\n\t\t\ts = properties.get<Symbol>(sib, ignore_parent_rel);\n\t\t\tif(!s)\n\t\t\t\tbreak;\n\t\t\t++sib;\n\t\t\t}\n\t\treturn s;\n\t\t}\n\telse return properties.get<Symbol>(it, ignore_parent_rel);\n\t}\n"
  },
  {
    "path": "core/properties/Symbol.cnb",
    "content": "{\n\t\"cells\" : \n\t[\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\property{Symbol}{Make an object not count as index when it is a sub- or super-script}\\n\\nIf you want to attach symbols to tensors in sub- or superscript, as\\nin~$A^\\\\dagger$, you need to inform the system that this symbol is not\\nan index (otherwise it will interpret~$A^\\\\dagger A^\\\\dagger$ as two\\ncontracted vectors with vector indices~$\\\\dagger$). This is done by\\nassociating the \\\\prop{Symbol} property to the symbol; in this\\nexample\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\property{Symbol}{Make an object not count as index when it is a sub- or super-script}\\n\\nIf you want to attach symbols to tensors in sub- or superscript, as\\nin~$A^\\\\dagger$, you need to inform the system that this symbol is not\\nan index (otherwise it will interpret~$A^\\\\dagger A^\\\\dagger$ as two\\ncontracted vectors with vector indices~$\\\\dagger$). This is done by\\nassociating the \\\\prop{Symbol} property to the symbol; in this\\nexample\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Symbol to~}\\\\dagger.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}A^{\\\\dagger} A^{\\\\dagger}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"\\\\dagger::Symbol;\\nex:= A^{\\\\dagger} A^{\\\\dagger};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1\n}\n"
  },
  {
    "path": "core/properties/Symbol.hh",
    "content": "\n#pragma once\n\n#include \"Props.hh\"\n\nnamespace cadabra {\n\n\tclass Symbol : public property {\n\t\tpublic:\n\t\t\tvirtual std::string name() const;\n\n\t\t\tstatic const Symbol *get(const Properties&, Ex::iterator, bool ignore_parent_rel=false);\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/properties/Symmetric.cc",
    "content": "\n#include \"Algorithm.hh\"\n#include \"properties/Symmetric.hh\"\n\nusing namespace cadabra;\n\nstd::string Symmetric::name() const\n\t{\n\treturn \"Symmetric\";\n\t}\n\nunsigned int Symmetric::size(const Properties&, Ex&, Ex::iterator) const\n\t{\n\treturn 1;\n\t}\n\nTableauBase::tab_t Symmetric::get_tab(const Properties& pr, Ex& tr, Ex::iterator it, unsigned int num) const\n\t{\n\tassert(num==0);\n\n\tconst Symmetric *pd;\n\tfor(;;) {\n\t\tpd=pr.get<Symmetric>(it);\n\t\tif(!pd)\n\t\t\tit=tr.begin(it);\n\t\telse break;\n\t\t}\n\n\ttab_t tab;\n\tfor(unsigned int i=0; i<Algorithm::number_of_indices(pr, it); ++i)\n\t\ttab.add_box(0,i);\n\treturn tab;\n\t}\n\n"
  },
  {
    "path": "core/properties/Symmetric.cnb",
    "content": "{\n\t\"cells\" : \n\t[\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\property{Symmetric}{Make an object symmetric in all indices.}\\n\\nMake an object symmetric in all indices. This information is then\\nsubsequently used by various algorithms, for instance \\\\algo{canonicalise}. \\nAn example:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\property{Symmetric}{Make an object symmetric in all indices.}\\n\\nMake an object symmetric in all indices. This information is then\\nsubsequently used by various algorithms, for instance \\\\algo{canonicalise}. \\nAn example:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}A_{m n} B_{m n}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"A_{m n}::AntiSymmetric.\\nB_{m n}::Symmetric.\\nex:=A_{m n} B_{m n};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}0\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"canonicalise(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"If you need symmetry in only a subset of all indices of a tensor, you need to use the\\n\\\\prop{TableauSymmetry} property. A quick example:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"If you need symmetry in only a subset of all indices of a tensor, you need to use the\\n\\\\prop{TableauSymmetry} property. A quick example:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property TableauSymmetry to~}C_{a n p}.\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"C_{a n p}::TableauSymmetry(shape={2}, indices={1,2});\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"This gives indices 1 and 2 (counting starts from 0) the symmetry of the Young Tableau\\nformed by one row of 2 boxes, which is the fully symmetric representation of the \\npermutation group. Now you get, as expected,\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"This gives indices 1 and 2 (counting starts from 0) the symmetry of the Young Tableau\\nformed by one row of 2 boxes, which is the fully symmetric representation of the \\npermutation group. Now you get, as expected,\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}C_{a n p}-C_{a p n}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex:=C_{a n p} - C_{a p n};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}0\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"canonicalise(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"For more information see the \\\\prop{TableauSymmetry} documentation.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"For more information see the \\\\prop{TableauSymmetry} documentation.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1\n}\n"
  },
  {
    "path": "core/properties/Symmetric.hh",
    "content": "\n#pragma once\n\n#include \"properties/TableauBase.hh\"\n\nnamespace cadabra {\n\n\tclass Symmetric : public TableauBase, virtual public property {\n\t\tpublic:\n\t\t\tvirtual std::string  name() const override;\n\t\t\tvirtual unsigned int size(const Properties&, Ex&, Ex::iterator) const override;\n\t\t\tvirtual tab_t        get_tab(const Properties&, Ex&, Ex::iterator, unsigned int) const override;\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/properties/Symmetric.tex",
    "content": "\\cdbproperty{Symmetric}{}\n\nMakes an object symmetric in all its indices. For an example and more\ninformation, see \\subsprop{AntiSymmetric}.\n\n\\cdbseeprop{AntiSymmetric}\n\\cdbseealgo{canonicalise}\n\n"
  },
  {
    "path": "core/properties/Tableau.cc",
    "content": "\n#include \"properties/Tableau.hh\"\n\nusing namespace cadabra;\n\nstd::string Tableau::name() const\n\t{\n\treturn \"Tableau\";\n\t}\n\nbool Tableau::parse(Kernel&, keyval_t& keyvals)\n\t{\n\tkeyval_t::const_iterator kv=keyvals.find(\"dimension\");\n\tif(kv!=keyvals.end()) dimension=to_long(*(kv->second.begin()->multiplier));\n\telse dimension=-1;\n\treturn true;\n\t}\n\n"
  },
  {
    "path": "core/properties/Tableau.cnb",
    "content": "{\n\t\"cell_id\" : 3709770344770575223,\n\t\"cells\" : \n\t[\n\t\t{\n\t\t\t\"cell_id\" : 18315175544081447475,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 6317143617777149814,\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\property{Tableau}{A Young-tableau object with unlabelled boxes.}\\n\\nDeclares that the object carrying this property is used to label a Young tableau with\\nunlabelled boxes (Young diagram). The arguments of such objects denote the lenghts of the rows.\\nThe \\\\verb|dimension| argument of the property sets the dimension.\\n\\nCan be used in combination with the \\\\verb|lr_tensor| and \\\\verb|tab_dimension| algorithms\\nto compute tensor product representations.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\property{Tableau}{A Young-tableau object with unlabelled boxes.}\\n\\nDeclares that the object carrying this property is used to label a Young tableau with\\nunlabelled boxes (Young diagram). The arguments of such objects denote the lenghts of the rows.\\nThe \\\\verb|dimension| argument of the property sets the dimension.\\n\\nCan be used in combination with the \\\\verb|lr_tensor| and \\\\verb|tab_dimension| algorithms\\nto compute tensor product representations.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 4814324193159731260,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 5472831286544245,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Tableau to~}\\\\ydiagram{1}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 16824604591112637874,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\" : 10673774897090337872,\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"\\\\tableau(2 , 1) \\\\tableau(2 , 1)\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\ydiagram{2,1} \\\\otimes \\\\ydiagram{2,1}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 17444505558726063598,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\" : 8552454844429597034,\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"\\\\tableau(4 , 2) + \\\\tableau(4 , 1 , 1) + \\\\tableau(3 , 3) + 2\\\\tableau(3 , 2 , 1) + \\\\tableau(2 , 2 , 2)\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\ydiagram{4,2} \\\\oplus \\\\ydiagram{4,1,1} \\\\oplus \\\\ydiagram{3,3} \\\\oplus 2\\\\, \\\\ydiagram{3,2,1} \\\\oplus \\\\ydiagram{2,2,2}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"\\\\tableau{#}::Tableau(dimension=3);\\nex:=\\\\tableau{2}{1}\\\\tableau{2}{1};\\nlr_tensor(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 6195976348837135823,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 13849739628876949020,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"{}$\\\\big[$$\\\\verb|27|$,\\\\discretionary{}{}{} $\\\\verb|10|$,\\\\discretionary{}{}{} $\\\\verb|10|$,\\\\discretionary{}{}{} $\\\\verb|16|$,\\\\discretionary{}{}{} $\\\\verb|1|$$\\\\big]$\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"q=[int(tab_dimension(t.ex())) for t in ex.top().terms()];\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 10192517807076031993,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1\n}\n"
  },
  {
    "path": "core/properties/Tableau.hh",
    "content": "\n#pragma once\n\n#include \"Props.hh\"\n#include \"properties/ImplicitIndex.hh\"\n\nnamespace cadabra {\n\n\t/// Property representing a Young tableau with unlabelled\n\t/// boxes. Note the difference with TableauBase, which represents\n\t/// a (set of) Young tableaux and the map of the boxes to\n\t/// tensor indices.\n\n\tclass Tableau : public ImplicitIndex, virtual public property {\n\t\tpublic:\n\t\t\tvirtual ~Tableau() {};\n\t\t\tvirtual std::string name() const override;\n\t\t\tvirtual bool        parse(Kernel&, keyval_t& keyvals) override;\n\n\t\t\tint dimension;\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/properties/TableauBase.cc",
    "content": "\n#include \"properties/TableauBase.hh\"\n#include \"Exceptions.hh\"\n\nusing namespace cadabra;\n\nTableauBase::~TableauBase()\n\t{\n\t}\n\nstd::string TableauBase::name() const\n{\n\treturn \"TableauBase\";\n}\n\nint TableauBase::get_indexgroup(const Properties& pr, Ex& tr, Ex::iterator it, int indexnum) const\n\t{\n\tconst TableauBase *pd;\n\tfor(;;) {\n\t\tpd=pr.get<TableauBase>(it);\n\t\tif(!pd)\n\t\t\tit=tr.begin(it);\n\t\telse break;\n\t\t}\n\t//\tstd::cout << \"now at \" << *it->name << std::endl;\n\n\tunsigned int siz=size(pr, tr, it);\n\tif(siz!=1)\n\t\tthrow InternalError(\"TableauBase::get_indexgroup: does not yet work for multi-tab symmetries.\");\n\n\ttab_t tmptab=get_tab(pr, tr, it, 0);\n\t//\tdebugout << \"searching indexgroup for \" << *it->name <<  std::endl;\n\tif(tmptab.number_of_rows()==1) return 0;\n\n\tstd::pair<int,int> loc=tmptab.find(indexnum);\n\t//\tdebugout << \"searching indexgroup \" << loc.second << std::endl;\n\tassert(loc.first!=-1);\n\treturn loc.second;\n\t}\n\nbool TableauBase::is_simple_symmetry(const Properties& pr, Ex& tr, Ex::iterator it) const\n\t{\n\tconst TableauBase *pd;\n\tfor(;;) {\n\t\tpd=pr.get<TableauBase>(it);\n\t\tif(!pd)\n\t\t\tit=tr.begin(it);\n\t\telse break;\n\t\t}\n\n\tfor(unsigned int i=0; i<size(pr, tr, it); ++i) {\n\t\ttab_t tmptab=get_tab(pr, tr, it, i);\n\t\tif((tmptab.number_of_rows()==1 || tmptab.row_size(0)==1) && tmptab.selfdual_column==0)\n\t\t\treturn true;\n\t\t}\n\treturn false;\n\t}\n\n"
  },
  {
    "path": "core/properties/TableauBase.hh",
    "content": "\n#pragma once\n\n#include \"Props.hh\"\n#include \"YoungTab.hh\"\n\nnamespace cadabra {\n\n\tclass TableauBase : virtual public property {\n\t\tpublic:\n\t\t\tvirtual ~TableauBase();\n\t\t\ttypedef yngtab::filled_tableau<unsigned int> tab_t;\n\n\t\t\tvirtual std::string name() const;\n\n\t\t\tvirtual unsigned int size(const Properties&, Ex&, Ex::iterator) const=0;\n\t\t\tvirtual tab_t        get_tab(const Properties&, Ex&, Ex::iterator, unsigned int) const=0;\n\n\t\t\tvirtual bool         only_column_exchange() const\n\t\t\t\t{\n\t\t\t\treturn false;\n\t\t\t\t};\n\n\t\t\t// Indexgroups are groups of indices which can be sorted by application\n\t\t\t// of single-index monoterm symmetries. E.g. R_{m n p q} -> {m,n}:0, {p,q}:1.\n\t\t\tint                  get_indexgroup(const Properties&, Ex&, Ex::iterator, int) const;\n\n\t\t\t// Is the tableau either a single column or a single row, and without\n\t\t\t// duality projections?\n\t\t\tbool                 is_simple_symmetry(const Properties&, Ex&, Ex::iterator) const;\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/properties/TableauInherit.cc",
    "content": "\n\n#include \"properties/TableauInherit.hh\"\n#include \"Exceptions.hh\"\n\nusing namespace cadabra;\n\n// #define DEBUG 1\n\nTableauInherit::~TableauInherit()\n\t{\n\t}\n\nunsigned int TableauInherit::size(const Properties& properties, Ex& tr, Ex::iterator it) const\n\t{\n//\tit=properties.head<TableauInherit>(it);\n#ifdef DEBUG\n\tstd::cerr << \"TableauInherit::size\" << std::endl;\n#endif\n\n\tint ret=0;\n\tEx::sibling_iterator sib=tr.begin(it);\n\twhile(sib!=tr.end(it) && sib->is_index()) ++sib;\n\tif(sib!=tr.end(it)) {\n\t\tconst TableauBase *tb=properties.get<TableauBase>(sib);\n\t\tif(tb)\n\t\t\tret+=tb->size(properties, tr,sib);\n\t\t}\n\t\n#ifdef DEBUG\n\tstd::cerr << \"TableauInherit::size: tab size = \" << ret << std::endl;\n#endif\n\t\n\treturn ret;\n\t}\n\nTableauBase::tab_t TableauInherit::get_tab(const Properties& properties, Ex& tr, Ex::iterator it, unsigned int num) const\n\t{\n//\tit=properties.head<TableauInherit>(it);\n\n#ifdef DEBUG\n\tstd::cerr << \"TableauInherit::get_tab: \" << it << std::endl;\n#endif\n\n\t// Some algorithms call this without first calling `size`, so we\n\t// have to safeguard against that.\n\tif(size(properties, tr, it)==0)\n\t\tthrow InternalError(\"TableauInherit::get_tab called with incorrect index.\");\n\t\n\t//\tstd::cout << *it->name << \" is Derivative\" << std::endl;\n\t//\ttr.print_recursive_treeform(std::cout, it);\n\n\tbool indices_first=tr.begin(it)->is_index();\n\tEx::sibling_iterator argnode=tr.begin(it);\n\tunsigned int number_of_indices=0; // number of indices before the argument\n\twhile(argnode->is_index()) {\n\t\t//\t\tstd::cout << *argnode->name << std::endl;\n\t\t++argnode;\n\t\t++number_of_indices;\n\t\t}\n\n\t// Right now we only propagate information of a child node if it does\n\t// not contain a sum or product. FIXME: should handle more general info?\n\t// (note: this should, if at all, be handled by the product node which should\n\t// inherit TableauSymmetry and collect info from below, but this will make\n\t// still make things tricky when it comes to object exchange).\n\n\t// FIXME: should really use index iterators\n\t//\tunsigned int arg_indices=tr.number_of_children(argnode);\n\t//\ttxtout << \"for : \" << *it->name << std::endl;\n\t//\ttxtout << \"indices first \" << indices_first << std::endl;\n\t//\ttxtout << arg_indices << \" indices on argument\" << std::endl;\n\t//\ttxtout << number_of_indices << \" direct indices\" << std::endl;\n\n#ifdef DEBUG\n\tstd::cerr << \"TableauInherit::get_tab: offset indices by \" << number_of_indices << std::endl;\n#endif\n\n\t\n\t// symmetry of the argument on which \\diff acts\n\t//\t\ttxtout << \"computing rettab\" << std::endl;\n\n\t//\tstd::cout << *argnode->name << std::endl;\n\n\tconst TableauBase *tb=properties.get<TableauBase>(argnode);\n\tif(!tb) {\n\t\treturn TableauBase::tab_t(); // empty tableau\n\t\t}\n\tassert(tb);\n\tunsigned int othertabs=tb->size(properties, tr, argnode);\n\tif(num>=othertabs)\n\t\tthrow InternalError(\"TableauInherit::get_tab: inconsistent tableau size.\");\n\n\tTableauBase::tab_t rettab=tb->get_tab(properties, tr, argnode, num);\n\tif(indices_first) { // have to renumber the tableau\n\t\tfor(unsigned int rows=0; rows<rettab.number_of_rows(); ++rows)\n\t\t\tfor(unsigned int cols=0; cols<rettab.row_size(rows); ++cols) {\n\t\t\t\trettab(rows,cols)+=number_of_indices;\n\t\t\t\t//\t\t\t\ttxtout << \"C \" << rows << \",\" << cols << \": \" << rettab(rows,cols) << std::endl;\n\t\t\t\t}\n\t\t}\n\treturn rettab;\n\t}\n"
  },
  {
    "path": "core/properties/TableauInherit.hh",
    "content": "\n#pragma once\n\n#include \"Props.hh\"\n#include \"properties/TableauBase.hh\"\n\nnamespace cadabra {\n\n\t/// Property which makes a node inherit the TableauBase properties of\n\t/// child nodes. The `size` and `get_tab` functions translate the\n\t/// index numbers of the child nodes to index numbers of the\n\t/// wrapping node.\n\t\n\tclass TableauInherit : virtual public TableauBase, virtual public property {\n\t\tpublic:\n\t\t\tvirtual ~TableauInherit();\n\t\t\tvirtual std::string name() const\n\t\t\t\t{\n\t\t\t\treturn std::string(\"TableauInherit\");\n\t\t\t\t};\n\n\t\t\tvirtual unsigned int size(const Properties&, Ex&, Ex::iterator) const;\n\t\t\tvirtual tab_t        get_tab(const Properties&, Ex&, Ex::iterator, unsigned int) const;\n\t\t\t\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/properties/TableauSymmetry.cc",
    "content": "\n#include \"properties/TableauSymmetry.hh\"\n#include \"IndexIterator.hh\"\n#include \"Kernel.hh\"\n#include \"Exceptions.hh\"\n\nusing namespace cadabra;\n\nTableauSymmetry::~TableauSymmetry()\n\t{\n\t}\n\nstd::string TableauSymmetry::name() const\n\t{\n\treturn \"TableauSymmetry\";\n\t}\n\nbool TableauSymmetry::parse(Kernel&, keyval_t& keyvals)\n\t{\n\t// Scan for the tableaux.\n\tkeyval_t::const_iterator kvit=keyvals.begin();\n\n\tEx::iterator indices;\n\tEx::iterator shape;\n\tbool gotshape=false, gotindices=false;\n\n\twhile(kvit!=keyvals.end()) {\n\t\tif(kvit->first==\"shape\") {\n\t\t\tshape=kvit->second.begin();\n\t\t\tgotshape=true;\n\t\t\t}\n\t\tif(kvit->first==\"indices\") {\n\t\t\tgotindices=true;\n\t\t\tindices=kvit->second.begin();\n\t\t\t}\n\n\t\tif(gotshape && gotindices) {\n\t\t\tEx help;\n\t\t\t// Make sure the shape and indices lists have a \\comma node.\n\t\t\thelp.list_wrap_single_element(shape);\n\t\t\thelp.list_wrap_single_element(indices);\n\n\t\t\tEx::sibling_iterator si=shape.begin();\n\t\t\tEx::sibling_iterator ii=indices.begin();\n\n\t\t\ttab_t tab;\n\n\t\t\tkeyval_t::const_iterator tmp=kvit;\n\t\t\t++tmp;\n\t\t\tif(tmp!=keyvals.end()) {\n\t\t\t\tif(tmp->first==\"selfdual\")\n\t\t\t\t\ttab.selfdual_column=1;\n\t\t\t\telse if(tmp->first==\"antiselfdual\")\n\t\t\t\t\ttab.selfdual_column=-1;\n\t\t\t\t}\n\n\t\t\tint rowind=0;\n\t\t\tunsigned int tabdown=to_long(*si->multiplier);\n\t\t\t//\t\t\t unsigned int numindices=number_of_indices(properties, pat);\n\t\t\t// FIXME: we get the wrong pattern in case of a list! We should have\n\t\t\t// been fed each individual item in the list, not the list itself.\n\t\t\t//\t\t\t  std::cout << numindices << \" \" << *pat->name << std::endl;\n\t\t\twhile(ii!=indices.end()) {\n\t\t\t\t// FIXME: we cannot verify this at parse level, since we do not\n\t\t\t\t// get passed the pattern at that stage.\n\t\t\t\t// if(tabdown+1 > numindices) return false;\n\n\t\t\t\tif(si==shape.end()) return false;\n\t\t\t\ttab.add_box(rowind, to_long(*ii->multiplier));\n\t\t\t\t++ii;\n\t\t\t\tif((--tabdown)==0 && ii!=indices.end()) {\n\t\t\t\t\t++si;\n\t\t\t\t\tif(si==shape.end())\n\t\t\t\t\t\tthrow ConsistencyException(\"Number of indices larger than number of boxes in tableau.\");\n\t\t\t\t\t++rowind;\n\t\t\t\t\ttabdown=to_long(*si->multiplier);\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\ttabs.push_back(tab);\n\n\t\t\thelp.list_unwrap_single_element(shape);\n\t\t\thelp.list_unwrap_single_element(indices);\n\n\t\t\tgotshape=false;\n\t\t\tgotindices=false;\n\t\t\t}\n\t\t++kvit;\n\t\t}\n\n\treturn true;\n\t}\n\nvoid TableauSymmetry::latex(std::ostream& str) const\n\t{\n\tstr << \"TableauSymmetry\";\n\t//\tfor(unsigned int i=0; i<tabs.size(); ++i)\n\t//\t\tstr << tabs[i] << std::endl;\n\t}\n\nunsigned int TableauSymmetry::size(const Properties&, Ex&, Ex::iterator) const\n\t{\n\treturn tabs.size();\n\t}\n\nTableauBase::tab_t TableauSymmetry::get_tab(const Properties&, Ex&, Ex::iterator, unsigned int num) const\n\t{\n\tassert(num<tabs.size());\n\treturn tabs[num];\n\t}\n\nbool TableauSymmetry::only_column_exchange() const\n\t{\n\treturn only_col_;\n\t}\n"
  },
  {
    "path": "core/properties/TableauSymmetry.cnb",
    "content": "{\n\t\"cell_id\" : 16902783054956412060,\n\t\"cells\" : \n\t[\n\t\t{\n\t\t\t\"cell_id\" : 9336446995508430553,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 10808860181435822516,\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\property{TableauSymmetry}{Gives a tensor a generic Young tableau symmetry.}\\n\\nGives a tensor a generic Young tableau symmetry, as indicated by the arguments.\\nTakes lists of two key-value pairs as arguments, indicating the \\nshape of the Young tableau and the index slots associated to each box\\nin the tableau. The \\\\verb|shape| argument holds a list of row lengths, so that\\ne.g.~\\\\verb|shape={3,2}| indicates a tableau with 3 boxes in the first row and\\n2 boxes in the second.\\n\\nTo see this in action, consider for instance\\n\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\property{TableauSymmetry}{Gives a tensor a generic Young tableau symmetry.}\\n\\nGives a tensor a generic Young tableau symmetry, as indicated by the arguments.\\nTakes lists of two key-value pairs as arguments, indicating the \\nshape of the Young tableau and the index slots associated to each box\\nin the tableau. The \\\\verb|shape| argument holds a list of row lengths, so that\\ne.g.~\\\\verb|shape={3,2}| indicates a tableau with 3 boxes in the first row and\\n2 boxes in the second.\\n\\nTo see this in action, consider for instance\\n\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 6610164357862456051,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 10653642797126216062,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property TableauSymmetry to~}R_{a b c d}.\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"R_{a b c d}::TableauSymmetry( shape={2,2}, indices={0,2,1,3} );\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 5138385684117154843,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 8047288209152419328,\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"which yields the symmetries of the Riemann tensor, that is, the symmetries of a Young tableau\\nwith two rows of two boxes each. Note that indices are\\ncounted from zero. You can see that this works by showing that the cyclic identity \\nholds, using \\\\algo{young_project_tensor},\\n\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"which yields the symmetries of the Riemann tensor, that is, the symmetries of a Young tableau\\nwith two rows of two boxes each. Note that indices are\\ncounted from zero. You can see that this works by showing that the cyclic identity \\nholds, using \\\\algo{young_project_tensor},\\n\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 9169533688919721410,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 14102651060550901838,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}R_{a b c d}+R_{a c d b}+R_{a d b c}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex:= R_{a b c d} + R_{a c d b} + R_{a d b c};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 14155142464823892758,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 1401830329590754478,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}0\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"young_project_tensor(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 8316968334925093916,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 16743154458381615575,\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"Simple symmetry is imposed by using a tableau with one row, while simple anti-symmetry \\ncorresponds to a tableau with one column. See \\\\prop{Symmetric} and \\\\prop{AntiSymmetric} for\\nexamples. You can also obtain the same result using \\\\prop{TableauSymmetry}:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"Simple symmetry is imposed by using a tableau with one row, while simple anti-symmetry \\ncorresponds to a tableau with one column. See \\\\prop{Symmetric} and \\\\prop{AntiSymmetric} for\\nexamples. You can also obtain the same result using \\\\prop{TableauSymmetry}:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 2863296166973857653,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 9223372036854775809,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property TableauSymmetry to~}g_{a b}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 9223372036854775810,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property TableauSymmetry to~}A_{a b}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 9223372036854775811,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\" : 9223372036854775812,\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"g_{b a} + A_{b a}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}g_{b a}+A_{b a}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 9223372036854775813,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\" : 9223372036854775814,\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"g_{a b}-A_{a b}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}g_{a b}-A_{a b}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"g_{a b}::TableauSymmetry(shape={2}, indices={0,1});\\nA_{a b}::TableauSymmetry(shape={1,1}, indices={0,1});\\n\\nex:= g_{b a} + A_{b a};\\ncanonicalise(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 1981680061494751053,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 8003739705592496127,\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"The first two lines declare two two-index tensors, $g_{a b}$ symmetric, $A_{a b}$ anti-symmetric, as the last line confirms.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"The first two lines declare two two-index tensors, $g_{a b}$ symmetric, $A_{a b}$ anti-symmetric, as the last line confirms.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 10804208092567647702,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1\n}\n"
  },
  {
    "path": "core/properties/TableauSymmetry.hh",
    "content": "\n#pragma once\n\n#include \"properties/TableauBase.hh\"\n#include <vector>\n\nnamespace cadabra {\n\n\tclass TableauSymmetry : public TableauBase, virtual public property {\n\t\tpublic:\n\t\t\tvirtual ~TableauSymmetry();\n\n\t\t\tvirtual bool         parse(Kernel&, keyval_t&) override;\n\t\t\tvirtual std::string  name() const override;\n\t\t\tvirtual void         latex(std::ostream&) const override;\n\t\t\tvirtual unsigned int size(const Properties&, Ex&, Ex::iterator) const override;\n\t\t\tvirtual tab_t        get_tab(const Properties&, Ex&, Ex::iterator, unsigned int) const override;\n\t\t\tvirtual bool         only_column_exchange() const override;\n\n\t\t\tstd::vector<tab_t>   tabs;\n\n\t\tprivate:\n\t\t\tbool only_col_;\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/properties/TableauSymmetry.tex",
    "content": "\\cdbproperty{TableauSymmetry}{\\it shape={\\sf tableau shape},\nindices={\\sf index positions}, selfdual, antiselfdual}\n\nTakes lists of two key-value pairs as arguments, indicating the \nshape of the Young tableau and the index slots associated to each box\nin the tableau. For instance\n\\begin{screen}{1}\nR_{a b c d}::TableauSymmetry( shape={2,2}, indices={0,2,1,3} ).\n\\end{screen}\nyields the symmetries of the Riemann tensor. Note that indices are\ncounted from zero. It is also possible to label tensors as self-dual\nor anti-selfdual using the optional arguments.\n"
  },
  {
    "path": "core/properties/Trace.cc",
    "content": "\n#include \"Exceptions.hh\"\n#include \"properties/Trace.hh\"\n\nusing namespace cadabra;\n\nTrace::Trace()\n\t{\n\t}\n\nTrace::~Trace()\n\t{\n\t}\n\nstd::string Trace::name() const\n\t{\n\treturn \"Trace\";\n\t}\n\nstd::string Trace::unnamed_argument() const\n\t{\n\treturn \"object\";\n\t}\n\nbool Trace::parse(Kernel&, keyval_t& keyvals)\n\t{\n\tkeyval_t::const_iterator kv=keyvals.find(\"object\");\n\tif(kv!=keyvals.end())\n\t\tobj = kv->second;\n\tkv=keyvals.find(\"indices\");\n\tif(kv!=keyvals.end()) {\n\t\tif(kv->second.is_string())\n\t\t\tindex_set_name=*(kv->second.begin()->name);\n\t\telse\n\t\t\tthrow ConsistencyException(\"Trace: 'indices' argument should be a string.\");\n\t\t}\n\treturn true;\n\t}\n\nvoid Trace::validate(Kernel&, std::shared_ptr<Ex> ) const\n\t{\n\t}\n\nvoid Trace::latex(std::ostream& str) const\n\t{\n\tstr << name();\n\t}\n"
  },
  {
    "path": "core/properties/Trace.cnb",
    "content": "{\n\t\"cell_id\": 17765795687326672545,\n\t\"cells\": [\n\t\t{\n\t\t\t\"cell_id\": 5657055628871889371,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 15838817502290331855,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\property{Trace(indices: Ex)}{Declares a trace operator}\\n\\nDeclares the object to be a trace operator, optionally indicating the index set over which\\nthe trace acts. In the basic form, without argument, the trace will be understood to act on\\nall implicit index sets of objects inside it:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\property{Trace(indices: Ex)}{Declares a trace operator}\\n\\nDeclares the object to be a trace operator, optionally indicating the index set over which\\nthe trace acts. In the basic form, without argument, the trace will be understood to act on\\nall implicit index sets of objects inside it:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 16432476374370762544,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 14701796796581272745,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property Trace attached to~}Tr\\\\left(\\\\#\\\\right).\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 10467861451438837866,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property ImplicitIndex attached to~}\\\\left[A,~\\\\discretionary{}{}{} B\\\\right].\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 15736966627107438757,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 7868561666184191975,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"Tr(A B C)\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}{\\\\rm Tr}\\\\left(A B C\\\\right)\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 10051836574681228751,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 8920474380952069443,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"C Tr(A B)\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}C {\\\\rm Tr}\\\\left(A B\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"Tr{#}::Trace;\\nTr{#}::LaTeXForm(\\\"{\\\\rm Tr}\\\").\\n{A,B}::ImplicitIndex;\\nex:= Tr( A B C );\\nuntrace(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 8784944214298213045,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 4610301361330547467,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"If you have multiple implicit index sets, you can indicate the set over which you want to trace\\nby using the optional \\\\verb|indices| argument, as in:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"If you have multiple implicit index sets, you can indicate the set over which you want to trace\\nby using the optional \\\\verb|indices| argument, as in:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 4261831302810446873,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 3425732590941563836,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property Indices(position=free) attached to~}\\\\left[a,~\\\\discretionary{}{}{} b,~\\\\discretionary{}{}{} c,~\\\\discretionary{}{}{} d\\\\right].\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 14898627914478378462,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property Indices(position=free) attached to~}\\\\left[i,~\\\\discretionary{}{}{} j,~\\\\discretionary{}{}{} k,~\\\\discretionary{}{}{} l\\\\right].\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 11052125327420618799,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property Trace attached to~}tr\\\\left(\\\\#\\\\right).\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 14508075882197669737,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property ImplicitIndex attached to~}A.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 3292992286301537879,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property ImplicitIndex attached to~}B.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 16701574396990242092,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 427207694120458052,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"tr(A B)\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}tr\\\\left(A B\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"{a,b,c,d}::Indices(vector);\\n{i,j,k,l}::Indices(group);\\ntr{#}::Trace(indices=group);\\nA::ImplicitIndex(A_{i j});\\nB::ImplicitIndex(B_{a b});\\nex:= tr(A B);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 2995113146223563270,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 3067489343184685005,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 8398508392970649808,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"B tr(A)\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}B tr\\\\left(A\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"untrace(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 12526507910491638554,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"source\": \"\"\n\t\t}\n\t],\n\t\"description\": \"Cadabra JSON notebook format\",\n\t\"version\": 1.0\n}\n"
  },
  {
    "path": "core/properties/Trace.hh",
    "content": "\n#pragma once\n\n#include \"Props.hh\"\n#include \"properties/Symmetric.hh\"\n#include \"properties/Distributable.hh\"\n#include \"properties/IndexInherit.hh\"\n#include \"properties/TableauInherit.hh\"\n#include \"properties/NumericalFlat.hh\"\n\nnamespace cadabra {\n\n\tclass Trace :\n\t\t\tpublic Distributable,\n\t\t\tpublic IndexInherit,\n\t\t\tpublic TableauInherit,\n\t\t\tpublic NumericalFlat,\n\t\t\tvirtual public property {\n\t\tpublic:\n\t\t\tTrace();\n\t\t\tvirtual ~Trace();\n\t\t\tvirtual std::string name() const override;\n\t\t\tvirtual std::string unnamed_argument() const override;\n\t\t\tvirtual bool        parse(Kernel&, keyval_t&) override;\n\t\t\tvirtual void        validate(Kernel&, std::shared_ptr<Ex>) const override;\n\t\t\tvirtual void        latex(std::ostream&) const override;\n\n\t\t\tEx obj;\n\t\t\tstd::string index_set_name; // refers to Indices::set_name\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/properties/Traceless.cc",
    "content": "\n#include \"Traceless.hh\"\n#include \"Exceptions.hh\"\n\nusing namespace cadabra;\n\nstd::string Traceless::name() const\n\t{\n\treturn \"Traceless\";\n\t}\n\nbool Traceless::parse(Kernel&, keyval_t& keyvals)\n\t{\n\tkeyval_t::const_iterator kv=keyvals.begin();\n\twhile(kv!=keyvals.end()) {\n\t\tif(kv->first==\"indices\") {\n\t\t\tif(kv->second.is_string())\n\t\t\t\tindex_set_names.insert(*kv->second.begin()->name);\n\t\t\telse\n\t\t\t\tthrow ConsistencyException(\"Traceless: 'indices' argument should be a string.\");\n\t\t\t}\n\t\t++kv;\n\t\t}\n\treturn true;\n\t}\n"
  },
  {
    "path": "core/properties/Traceless.hh",
    "content": "\n#pragma once\n\n#include \"Props.hh\"\n\nnamespace cadabra {\n\n\tclass Traceless : virtual public property {\n\t\tpublic:\n\t\t\tvirtual ~Traceless() {};\n\t\t\tvirtual std::string name() const override;\n\t\t\tvirtual bool        parse(Kernel&, keyval_t&) override;\n\t\t\tvirtual std::string unnamed_argument() const override\n\t\t\t\t{\n\t\t\t\treturn \"indices\";\n\t\t\t\t};\n\n\t\t\tstd::set<std::string> index_set_names; // refers to Indices::set_name\n\t\t};\n\n\t}\n\n"
  },
  {
    "path": "core/properties/Traceless.tex",
    "content": "\\cdbproperty{Traceless}{}\n\nIndicates that the tensor is traceless:\n  any internal index contraction makes the tensor vanish.\n\\begin{screen}{1,2,3}\nA_{m n}::Traceless.\nA_{m}^{m};\n@canonicalise!(%);\n0;\n\\end{screen}\n~\n\n\\cdbseealgo{canonicalise}\n"
  },
  {
    "path": "core/properties/Vielbein.cc",
    "content": "\n#include \"properties/Vielbein.hh\"\n\nusing namespace cadabra;\n\nstd::string Vielbein::name() const\n\t{\n\treturn \"Vielbein\";\n\t}\n\nstd::string InverseVielbein::name() const\n\t{\n\treturn \"InverseVielbein\";\n\t}\n"
  },
  {
    "path": "core/properties/Vielbein.cnb",
    "content": "{\n\t\"cell_id\" : 8504522010490083117,\n\t\"cells\" : \n\t[\n\t\t{\n\t\t\t\"cell_id\" : 6571450582745955654,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 16207264670621719190,\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\property{Vielbein}{Makes a two-index object a vielbein.}\\n\\nIndicates that an object can be used to convert indices from one type\\nto another, i.e.~is a vielbein or tetrad. For more information, see\\n\\\\verb|eliminate_vielbein|.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\property{Vielbein}{Makes a two-index object a vielbein.}\\n\\nIndicates that an object can be used to convert indices from one type\\nto another, i.e.~is a vielbein or tetrad. For more information, see\\n\\\\verb|eliminate_vielbein|.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 15556941193362982862,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1\n}\n"
  },
  {
    "path": "core/properties/Vielbein.hh",
    "content": "\n#pragma once\n\n#include \"Props.hh\"\n\nnamespace cadabra {\n\n\tclass Vielbein : virtual public property {\n\t\tpublic:\n\t\t\tvirtual std::string name() const;\n\t\t};\n\n\tclass InverseVielbein : virtual public property {\n\t\tpublic:\n\t\t\tvirtual std::string name() const;\n\t\t};\n\n\t}\n\n"
  },
  {
    "path": "core/properties/Vielbein.tex",
    "content": "\\cdbproperty{Vielbein}{}\n\nIndicates that an object can be used to convert indices from one type\nto another, i.e.~is a vielbein or tetrad. For more information, see\n\\subscommand{eliminate\\_vielbein}.\n\n\\cdbseealgo{eliminate_vielbein}\n"
  },
  {
    "path": "core/properties/Weight.cc",
    "content": "\n#include \"Weight.hh\"\n#include \"Exceptions.hh\"\n\nusing namespace cadabra;\n\nWeight::~Weight()\n\t{\n\t}\n\nstd::string Weight::name() const\n\t{\n\treturn \"Weight\";\n\t}\n\nbool Weight::parse(Kernel& k, std::shared_ptr<Ex> ex, keyval_t& kv)\n\t{\n\tkeyval_t::const_iterator kvit=kv.find(\"value\");\n\tif(kvit!=kv.end()) {\n\t\tif(kvit->second.is_rational()==false)\n\t\t\tthrow ConsistencyException(\"Weight: weight should be an explicit rational.\");\n\t\tvalue_=*kvit->second.begin()->multiplier;\n\t\t}\n\telse value_=1;\n\n\treturn WeightBase::parse(k, ex, kv);\n\t}\n\nmultiplier_t Weight::value(const Kernel&, Ex::iterator, const std::string& forcedlabel) const\n\t{\n\tif(forcedlabel!=label) return -1;\n\treturn value_;\n\t}\n"
  },
  {
    "path": "core/properties/Weight.cnb",
    "content": "{\n\t\"cell_id\": 17594032342224758361,\n\t\"cells\": [\n\t\t{\n\t\t\t\"cell_id\": 2589219658710476359,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 10124450553688137587,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\property{Weight}{Attach a labelled weight to an object}\\n\\nAttach a labelled weight to an object, which can subsequently be used\\nin the algorithms \\\\algo{keep_weight} and \\\\algo{drop_weight} to select\\nparticular terms. See the documentation of those two algorithms\\nfor examples.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\property{Weight}{Attach a labelled weight to an object}\\n\\nAttach a labelled weight to an object, which can subsequently be used\\nin the algorithms \\\\algo{keep_weight} and \\\\algo{drop_weight} to select\\nparticular terms. See the documentation of those two algorithms\\nfor examples.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 442998546462730087,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"\"\n\t\t}\n\t],\n\t\"description\": \"Cadabra JSON notebook format\",\n\t\"version\": 1.0\n}\n"
  },
  {
    "path": "core/properties/Weight.hh",
    "content": "\n#pragma once\n\n#include \"properties/WeightBase.hh\"\n\nnamespace cadabra {\n\n\tclass Weight : virtual public WeightBase {\n\t\tpublic:\n\t\t\tvirtual ~Weight();\n\t\t\tvirtual multiplier_t  value(const Kernel&, Ex::iterator, const std::string& forcedlabel) const override;\n\t\t\tvirtual bool          parse(Kernel&, std::shared_ptr<Ex>, keyval_t&) override;\n\t\t\tvirtual std::string   unnamed_argument() const  override\n\t\t\t\t{\n\t\t\t\treturn \"value\";\n\t\t\t\t};\n\t\t\tvirtual std::string   name() const override;\n\t\tprivate:\n\t\t\tmultiplier_t value_;\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/properties/WeightBase.hh",
    "content": "\n#pragma once\n\n#include \"Props.hh\"\n\nnamespace cadabra {\n\n\tclass WeightBase : virtual public labelled_property {\n\t\tpublic:\n\t\t\tvirtual multiplier_t  value(const Kernel&, Ex::iterator, const std::string& forcedlabel) const=0;\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/properties/WeightInherit.cc",
    "content": "\n#include \"WeightInherit.hh\"\n#include \"Kernel.hh\"\n#include \"Exceptions.hh\"\n\nusing namespace cadabra;\n\nWeightInherit::~WeightInherit()\n\t{\n\t}\n\nstd::string WeightInherit::name() const\n\t{\n\treturn \"WeightInherit\";\n\t}\n\nWeightInherit::WeightException::WeightException(const std::string& str)\n\t: ConsistencyException(str)\n\t{\n\t}\n\nbool WeightInherit::parse(Kernel& k, std::shared_ptr<Ex> ex, keyval_t& kv)\n\t{\n\tkeyval_t::const_iterator tpit=kv.find(\"type\");\n\tif(tpit!=kv.end()) {\n\t\tif(tpit->second.equals(\"multiplicative\")) combination_type=multiplicative;\n\t\telse if(tpit->second.equals(\"additive\"))  combination_type=additive;\n\t\telse if(tpit->second.equals(\"power\"))     combination_type=power;\n\t\telse throw ArgumentException(\"weight type must be 'multiplicative', 'additive' or 'power'.\");\n\t\t}\n\telse combination_type=multiplicative;\n\n\ttpit = kv.find(\"self\");\n\tif(tpit!=kv.end()) {\n\t\tif(tpit->second.is_rational()==false)\n\t\t\tthrow ConsistencyException(\"WeightInherit: 'self' value should be an explicit rational.\");\n\t\t\n\t\tvalue_self=*tpit->second.begin()->multiplier;\n\t\t}\n\telse value_self=0;\n\n\tauto ret = WeightBase::parse(k, ex, kv);\n\treturn ret;\n\t}\n\nmultiplier_t WeightInherit::value(const Kernel& kernel, Ex::iterator it, const std::string& forcedlabel) const\n\t{\n\tconst Properties& properties=kernel.properties;\n\n\tmultiplier_t ret=0;\n\tbool first_term=true;\n\n\t// std::cerr << \"calling inherit on \" << *it->name << \" \" << &(*it) << \" \" << forcedlabel << std::endl;\n\tEx::sibling_iterator sib=it.begin();\n\twhile(sib!=it.end()) {\n\t\tif(!sib->is_index()) {\n\t\t\tswitch(combination_type) {\n\t\t\t\tcase multiplicative: {\n\t\t\t\t\tconst WeightBase *gnb=properties.get<WeightBase>(sib, forcedlabel);\n\t\t\t\t\t// std::cerr << \"finding weight for \" << Ex(sib) << std::endl;\n\t\t\t\t\tif(gnb) {\n\t\t\t\t\t\tmultiplier_t tmp=gnb->value(kernel, sib, forcedlabel);\n\t\t\t\t\t\tret+=tmp;\n\t\t\t\t\t\t}\n\t\t\t\t\t}\n\t\t\t\tbreak;\n\t\t\t\tcase additive: {\n\t\t\t\t\tmultiplier_t thisone=0;\n\t\t\t\t\tconst WeightBase *gnb=properties.get<WeightBase>(sib, forcedlabel);\n\t\t\t\t\tif(gnb) thisone=gnb->value(kernel, sib, forcedlabel);\n\t\t\t\t\telse    thisone=0;\n\t\t\t\t\tif(first_term) {\n\t\t\t\t\t\tfirst_term=false;\n\t\t\t\t\t\tret=thisone;\n\t\t\t\t\t\t}\n\t\t\t\t\telse if(ret!=thisone) {   // the weights in the sum are not uniform\n\t\t\t\t\t\tthrow WeightException(\"Encountered sum with un-equal weight terms.\");\n\t\t\t\t\t\t}\n\t\t\t\t\t}\n\t\t\t\tbreak;\n\t\t\t\tcase power: {\n\t\t\t\t\tconst WeightBase *gnb=properties.get<WeightBase>(sib, forcedlabel);\n\t\t\t\t\tif(gnb) {\n\t\t\t\t\t\tmultiplier_t tmp=gnb->value(kernel, sib, forcedlabel);\n\t\t\t\t\t\t++sib;\n\t\t\t\t\t\tif(sib==it.end() || sib->is_rational()==false)\n\t\t\t\t\t\t\tthrow RuntimeException(\"Can only handle numerical exponents for weight counting.\");\n\n\t\t\t\t\t\tret+=(*sib->multiplier)*tmp;\n\t\t\t\t\t\tsib=it.end();\n\t\t\t\t\t\tcontinue;\n\t\t\t\t\t\t}\n\t\t\t\t\t}\n\t\t\t\tbreak;\n\t\t\t\t}\n\t\t\t}\n\t\t++sib;\n\t\t}\n\n\tret+=value_self;  // Add our own weight.\n\n\treturn ret;\n\t}\n\n"
  },
  {
    "path": "core/properties/WeightInherit.cnb",
    "content": "{\n\t\"cells\" : \n\t[\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\property{WeightInherit}{Make object inherit weights from child nodes}\\n\\nIndicates that the object inherits all weights of its child nodes. The\\nlabel indicates which weights are inherited; use {\\\\tt all} to inherit\\nall weights. The type of inheritance determines whether weights of the\\nchild nodes should be added or multiplied. \\n\\nAdditive weight inheritance is used to assign a weight to sum-like\\nobjects. For example, if we declare\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\property{WeightInherit}{Make object inherit weights from child nodes}\\n\\nIndicates that the object inherits all weights of its child nodes. The\\nlabel indicates which weights are inherited; use {\\\\tt all} to inherit\\nall weights. The type of inheritance determines whether weights of the\\nchild nodes should be added or multiplied. \\n\\nAdditive weight inheritance is used to assign a weight to sum-like\\nobjects. For example, if we declare\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property WeightInherit to~}f\\\\left(\\\\#\\\\right).\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Weight to~}A.\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"f{#}::WeightInherit(label=all, type=Additive);\\nA::Weight(label=field, value=3);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"then the expression~\\\\verb|f{A}{A}| has weight~3. This is what would\\nhappen if `\\\\verb|f|' would be a sum: the weight of the sum is the same\\nas the weight of the terms (and is only defined if the weight of the\\nall terms is equal).\\n\\nMultiplicative weight inheritance is used to assign a weight to \\nproduct-like objects. For example, if we declare\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"then the expression~\\\\verb|f{A}{A}| has weight~3. This is what would\\nhappen if `\\\\verb|f|' would be a sum: the weight of the sum is the same\\nas the weight of the terms (and is only defined if the weight of the\\nall terms is equal).\\n\\nMultiplicative weight inheritance is used to assign a weight to \\nproduct-like objects. For example, if we declare\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property WeightInherit to~}g\\\\left(\\\\#\\\\right).\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Weight to~}B.\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"g{#}::WeightInherit(label=all, type=Multiplicative);\\nB::Weight(label=field, value=3);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"then the expression~\\\\verb|g{B}{B}| has weight~6. This is what would\\nhappen if `\\\\verb|g|' would be a product: the weight of the product is the same\\nas the sum of the weights of the factors.\\n\\nTerms can be selected based on their weight by using the\\n\\\\algo{keep_weight} or \\\\algo{drop_weight} algorithms.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"then the expression~\\\\verb|g{B}{B}| has weight~6. This is what would\\nhappen if `\\\\verb|g|' would be a product: the weight of the product is the same\\nas the sum of the weights of the factors.\\n\\nTerms can be selected based on their weight by using the\\n\\\\algo{keep_weight} or \\\\algo{drop_weight} algorithms.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1\n}\n"
  },
  {
    "path": "core/properties/WeightInherit.hh",
    "content": "\n#pragma once\n\n#include \"Exceptions.hh\"\n#include \"properties/WeightBase.hh\"\n\nnamespace cadabra {\n\n\tclass WeightInherit : virtual public WeightBase {\n\t\tpublic:\n\t\t\tvirtual ~WeightInherit();\n\t\t\t\n\t\t\t// The following exception class is thrown when 'value' cannot figure out the\n\t\t\t// weight because a sum contains terms of different weight.\n\t\t\tclass WeightException : public ConsistencyException {\n\t\t\t\tpublic:\n\t\t\t\t\tWeightException(const std::string&);\n\t\t\t\t};\n\n\t\t\tvirtual bool          parse(Kernel&, std::shared_ptr<Ex>, keyval_t&) override;\n\t\t\tvirtual multiplier_t  value(const Kernel&, Ex::iterator, const std::string& forcedlabel) const override;\n\t\t\tvirtual std::string   unnamed_argument() const override\n\t\t\t\t{\n\t\t\t\treturn \"type\";\n\t\t\t\t};\n\t\t\tvirtual std::string   name() const override;\n\n\t\t\tenum CombinationType { multiplicative, additive, power } combination_type;\n\n\t\t\tmultiplier_t value_self;\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/properties/WeylTensor.cc",
    "content": "\n#include \"IndexIterator.hh\"\n#include \"Exceptions.hh\"\n#include \"Kernel.hh\"\n#include \"Algorithm.hh\"\n#include \"properties/WeylTensor.hh\"\n\nusing namespace cadabra;\n\nWeylTensor::WeylTensor()\n\t{\n\ttab_t tab;\n\ttab.add_box(0,0);\n\ttab.add_box(0,2);\n\ttab.add_box(1,1);\n\ttab.add_box(1,3);\n\ttabs.push_back(tab);\n\t}\n\nWeylTensor::~WeylTensor()\n\t{\n\t}\n\nstd::string WeylTensor::name() const\n\t{\n\treturn \"WeylTensor\";\n\t}\n\n// Traceless and TableauSymetry args are overwritten elsewhere\nbool WeylTensor::parse(Kernel&, keyval_t& )\n\t{\n\treturn true;\n\t}\n\nvoid WeylTensor::validate(Kernel& kernel, std::shared_ptr<Ex> pat) const\n\t{\n\tif(Algorithm::number_of_indices(kernel.properties, pat->begin())!=4)\n\t\tthrow ConsistencyException(\"WeylTensor: need exactly 4 indices.\");\n\tindex_iterator indit=index_iterator::begin(kernel.properties, pat->begin());\n\tauto ind=kernel.properties.get<Indices>(indit, true);\n\t// We cannot access the right things from parse()\n\tif(ind) {\n\t\tWeylTensor *ptr = const_cast<WeylTensor*>(this);\n\t\tptr->index_set_names.insert(ind->set_name);\n\t\t}\n\t}\n\nvoid WeylTensor::latex(std::ostream& str) const\n\t{\n\tTableauSymmetry::latex(str);\n\tTraceless::latex(str);\n\t}\n\n"
  },
  {
    "path": "core/properties/WeylTensor.hh",
    "content": "\n#pragma once\n\n#include \"properties/TableauSymmetry.hh\"\n#include \"properties/Traceless.hh\"\n\nnamespace cadabra {\n\n\tclass WeylTensor : public TableauSymmetry, public Traceless, virtual public property {\n\t\tpublic:\n\t\t\tWeylTensor();\n\t\t\tvirtual ~WeylTensor();\n\t\t\tvirtual std::string name() const override;\n\t\t\tvirtual bool        parse(Kernel&, keyval_t&) override;\n\t\t\tvirtual void        validate(Kernel&, std::shared_ptr<Ex>) const override;\n\t\t\tvirtual void        latex(std::ostream&) const override;\n\t\t};\n\n\t}\n"
  },
  {
    "path": "core/properties/WeylTensor.tex",
    "content": "\\cdbproperty{WeylTensor}{}\n\nGives an object the symmetry properties of a Weyl tensor, i.e.~a\nRiemann tensor with an additional traceless condition. For more\ninformation, see \\subsprop{RiemannTensor}.\n\n\\cdbseeprop{RiemannTensor}\n\n"
  },
  {
    "path": "core/pythoncdb/py_algorithms.cc",
    "content": "#include \"py_algorithms.hh\"\n\n#include <pybind11/pybind11.h>\n#include <pybind11/stl.h>\n#include <pybind11/complex.h>\n\n#include \"../Algorithm.hh\"\n#include \"../NEvaluator.hh\"\n#include \"../NDSolver.hh\"\n#include \"../NIntegrator.hh\"\n#include \"../NTensor.hh\"\n#include \"../NInterpolatingFunction.hh\"\n\n#include \"../algorithms/canonicalise.hh\"\n#include \"../algorithms/collect_components.hh\"\n#include \"../algorithms/collect_factors.hh\"\n#include \"../algorithms/collect_terms.hh\"\n#include \"../algorithms/combine.hh\"\n#include \"../algorithms/complete.hh\"\n#include \"../algorithms/decompose.hh\"\n#include \"../algorithms/decompose_product.hh\"\n#include \"../algorithms/distribute.hh\"\n#include \"../algorithms/drop_weight.hh\"\n#include \"../algorithms/einsteinify.hh\"\n#include \"../algorithms/eliminate_kronecker.hh\"\n#include \"../algorithms/eliminate_metric.hh\"\n#include \"../algorithms/eliminate_vielbein.hh\"\n#include \"../algorithms/epsilon_to_delta.hh\"\n#include \"../algorithms/evaluate.hh\"\n#include \"../algorithms/expand.hh\"\n#include \"../algorithms/expand_delta.hh\"\n#include \"../algorithms/expand_diracbar.hh\"\n#include \"../algorithms/expand_dummies.hh\"\n#include \"../algorithms/expand_power.hh\"\n#include \"../algorithms/explicit_indices.hh\"\n#include \"../algorithms/factor_in.hh\"\n#include \"../algorithms/factor_out.hh\"\n#include \"../algorithms/fierz.hh\"\n#include \"../algorithms/first_order_form.hh\"\n#include \"../algorithms/flatten_sum.hh\"\n#include \"../algorithms/indexsort.hh\"\n#include \"../algorithms/integrate_by_parts.hh\"\n#include \"../algorithms/join_gamma.hh\"\n#include \"../algorithms/keep_terms.hh\"\n#include \"../algorithms/lower_free_indices.hh\"\n#include \"../algorithms/lr_tensor.hh\"\n#ifdef MATHEMATICA_FOUND\n#include \"../algorithms/map_mma.hh\"\n#endif\n#include \"../algorithms/map_sympy.hh\"\n#include \"../algorithms/meld.hh\"\n#include \"../algorithms/nevaluate.hh\"\n#include \"../algorithms/nval.hh\"\n#include \"../algorithms/order.hh\"\n#include \"../algorithms/product_rule.hh\"\n#include \"../algorithms/reduce_delta.hh\"\n#include \"../algorithms/rename_dummies.hh\"\n#include \"../algorithms/replace_match.hh\"\n#include \"../algorithms/rewrite_indices.hh\"\n#include \"../algorithms/simplify.hh\"\n#include \"../algorithms/sort_product.hh\"\n#include \"../algorithms/sort_spinors.hh\"\n#include \"../algorithms/sort_sum.hh\"\n#include \"../algorithms/split_gamma.hh\"\n#include \"../algorithms/split_index.hh\"\n#include \"../algorithms/substitute.hh\"\n#include \"../algorithms/sym.hh\"\n#include \"../algorithms/tab_dimension.hh\"\n#include \"../algorithms/take_match.hh\"\n#include \"../algorithms/unwrap.hh\"\n#include \"../algorithms/unzoom.hh\"\n#include \"../algorithms/untrace.hh\"\n#include \"../algorithms/vary.hh\"\n#include \"../algorithms/young_project.hh\"\n#include \"../algorithms/young_project_product.hh\"\n#include \"../algorithms/young_project_tensor.hh\"\n#include \"../algorithms/zoom.hh\"\n\n#include \"../properties/ImaginaryI.hh\"\n\nnamespace cadabra {\n\tnamespace py = pybind11;\n\n\tvoid                                                                set_variables(NEvaluator& evaluator, py::dict d);\n\tstd::tuple<Ex, NTensor, std::complex<double>, std::complex<double>> extract_var_range(py::dict d);\n\n\tvoid init_algorithms(py::module& m)\n\t\t{\n\t\tpybind11::enum_<Algorithm::result_t>(m, \"result_t\")\n\t\t.value(\"checkpointed\", Algorithm::result_t::l_checkpointed)\n\t\t.value(\"changed\", Algorithm::result_t::l_applied)\n\t\t.value(\"unchanged\", Algorithm::result_t::l_no_action)\n\t\t.value(\"error\", Algorithm::result_t::l_error)\n\t\t.export_values();\n\n\t\tdef_algo<canonicalise>(m, \"canonicalise\", true, false, 0);\n\t\tdef_algo<collect_components>(m, \"collect_components\", true, false, 0);\n\t\tdef_algo<collect_factors>(m, \"collect_factors\", true, false, 0);\n\t\tdef_algo<collect_terms>(m, \"collect_terms\", true, false, 0);\n\t\tdef_algo<decompose_product>(m, \"decompose_product\", true, false, 0);\n\t\tdef_algo<distribute>(m, \"distribute\", true, false, 0);\n\t\tdef_algo<eliminate_kronecker>(m, \"eliminate_kronecker\", true, false, 0);\n\t\tdef_algo<expand>(m, \"expand\", true, false, 0);\n\t\tdef_algo<expand_delta>(m, \"expand_delta\", true, false, 0);\n\t\tdef_algo<expand_diracbar>(m, \"expand_diracbar\", true, false, 0);\n\t\tdef_algo<expand_dummies, const Ex*, bool>(m, \"expand_dummies\", true, false, 0, py::arg(\"components\") = nullptr, py::arg(\"zero_missing_components\") = true);\n\t\tdef_algo<expand_power>(m, \"expand_power\", true, false, 0);\n\t\tdef_algo<explicit_indices>(m, \"explicit_indices\", true, false, 0);\n\t\tdef_algo<first_order_form, Ex>(m, \"first_order_form\", true, false, 0, py::arg(\"functions\") = Ex{});\n\t\tdef_algo<flatten_sum>(m, \"flatten_sum\", true, false, 0);\n\t\tdef_algo<indexsort>(m, \"indexsort\", true, false, 0);\n\t\tdef_algo<lr_tensor>(m, \"lr_tensor\", true, false, 0);\n\t\tdef_algo<product_rule>(m, \"product_rule\", true, false, 0);\n\t\tdef_algo<reduce_delta>(m, \"reduce_delta\", true, false, 0);\n\t\tdef_algo<sort_product>(m, \"sort_product\", true, false, 0);\n\t\tdef_algo<sort_spinors>(m, \"sort_spinors\", true, false, 0);\n\t\tdef_algo<sort_sum>(m, \"sort_sum\", true, false, 0);\n\t\tdef_algo<tabdimension>(m, \"tab_dimension\", true, false, 0);\n\t\tdef_algo<young_project_product>(m, \"young_project_product\", true, false, 0);\n\t\tdef_algo<combine, Ex>(m, \"combine\", true, false, 0, py::arg(\"trace_op\") = Ex{});\n\t\tdef_algo<complete, Ex>(m, \"complete\", false, false, 0, py::arg(\"add\"));\n\t\tdef_algo<decompose, Ex>(m, \"decompose\", false, false, 0, py::arg(\"basis\"));\n\t\tdef_algo<drop_weight, Ex>(m, \"drop_weight\", false, false, 0, py::arg(\"condition\") = Ex{});\n\t\tdef_algo<eliminate_metric, Ex,bool>(m, \"eliminate_metric\", true, false, 0, py::arg(\"preferred\") = Ex{}, py::arg(\"redundant\") = false);\n\t\tdef_algo<eliminate_vielbein, Ex,bool>(m, \"eliminate_vielbein\", true, false, 0, py::arg(\"preferred\") = Ex{},py::arg(\"redundant\")= false);\n\t\tdef_algo<keep_weight, Ex>(m, \"keep_weight\", false, false, 0, py::arg(\"condition\"));\n\t\tdef_algo<lower_free_indices, bool>(m, \"lower_free_indices\", true, false, 0, py::arg(\"lower\") = true);\n\t\tdef_algo<lower_free_indices, bool>(m, \"raise_free_indices\", true, false, 0, py::arg(\"lower\") = false);\n\t\tdef_algo<integrate_by_parts, Ex>(m, \"integrate_by_parts\", true, false, 0, py::arg(\"away_from\"));\n\t\tdef_algo<young_project_tensor, bool>(m, \"young_project_tensor\", true, false, 0, py::arg(\"modulo_monoterm\") = false);\n\t\tdef_algo<join_gamma, bool, bool>(m, \"join_gamma\", true, false, 0, py::arg(\"expand\") = true, py::arg(\"use_gendelta\") = false);\n\t\tdef_algo<einsteinify, Ex>(m, \"einsteinify\", true, false, 0, py::arg(\"metric\") = Ex{});\n\t\tdef_algo<evaluate, Ex, bool, bool>(m, \"evaluate\", false, false, 0, py::arg(\"components\") = Ex{}, py::arg(\"rhsonly\") = false, py::arg(\"simplify\") = true);\n\t\tdef_algo<keep_terms, std::vector<int>>(m, \"keep_terms\", true, false, 0, py::arg(\"terms\"));\n\t\tdef_algo<young_project, std::vector<int>, std::vector<int>>(m, \"young_project\", true, false, 0, py::arg(\"shape\"), py::arg(\"indices\"));\n\t\tdef_algo<simplify>(m, \"simplify\", false, false, 0);\n\t\tdef_algo<order, Ex, bool>(m, \"order\", true, false, 0, py::arg(\"factors\"), py::arg(\"anticommuting\") = false);\n\t\tdef_algo<epsilon_to_delta, bool>(m, \"epsilon_to_delta\", true, false, 0, py::arg(\"reduce\") = true);\n\t\tdef_algo<rename_dummies, std::string, std::string>(m, \"rename_dummies\", true, false, 0, py::arg(\"set\") = \"\", py::arg(\"to\") = \"\");\n\t\tdef_algo<sym, Ex, bool>(m, \"sym\", true, false, 0, py::arg(\"items\"), py::arg(\"antisymmetric\") = false);\n\t\tdef_algo<sym, Ex, bool>(m, \"asym\", true, false, 0, py::arg(\"items\"), py::arg(\"antisymmetric\") = true);\n\t\tdef_algo<sym, std::vector<unsigned int>, bool>(m, \"slot_sym\", true, false, 0, py::arg(\"items\"), py::arg(\"antisymmetric\") = false);\n\t\tdef_algo<sym, std::vector<unsigned int>, bool>(m, \"slot_asym\", true, false, 0, py::arg(\"items\"), py::arg(\"antisymmetric\") = true);\n\t\tdef_algo<factor_in, Ex>(m, \"factor_in\", true, false, 0, py::arg(\"factors\"));\n\t\tdef_algo<factor_out, Ex, bool>(m, \"factor_out\", true, false, 0, py::arg(\"factors\"), py::arg(\"right\") = false);\n\t\tdef_algo<fierz, Ex>(m, \"fierz\", true, false, 0, py::arg(\"spinors\"));\n\t\tdef_algo<substitute, Ex&, bool>(m, \"substitute\", true, false, 0, py::arg(\"rules\"), py::arg(\"partial\") = true);\n\t\tdef_algo<take_match, Ex&>(m, \"take_match\", true, false, 0, py::arg(\"rules\"));\n\t\tdef_algo<replace_match>(m, \"replace_match\", false, false, 0);\n\t\tdef_algo<zoom, Ex, bool>(m, \"zoom\", true, false, 0, py::arg(\"rules\"), py::arg(\"partial\") = true);\n\t\tdef_algo_preorder<unzoom>(m, \"unzoom\", true, false, 0);\n\t\tdef_algo<untrace>(m, \"untrace\", true, false, 0);\n\t\tdef_algo<rewrite_indices, Ex, Ex>(m, \"rewrite_indices\", true, false, 0, py::arg(\"preferred\"), py::arg(\"converters\"));\n\t\tdef_algo_preorder<vary, Ex&>(m, \"vary\", false, false, 0, py::arg(\"rules\"));\n\t\tdef_algo<split_gamma, bool>(m, \"split_gamma\", true, false, 0, py::arg(\"on_back\"));\n\t\tdef_algo<split_index, Ex>(m, \"split_index\", true, false, 0, py::arg(\"rules\"));\n\t\tdef_algo<unwrap, Ex>(m, \"unwrap\", true, false, 0, py::arg(\"wrapper\") = Ex{});\n//\t\tdef_algo_preorder<young_reduce, const Ex*>(m, \"young_reduce\", true, false, 0, py::arg(\"pattern\") = nullptr);\n//\t\tdef_algo_preorder<young_reduce_trace>(m, \"young_reduce_trace\", true, false, 0);\n\t\tdef_algo_preorder<meld, bool>(m, \"meld\", true, false, 0, py::arg(\"project_as_sum\") = false);\n\n//\t\tdef_algo<nevaluate>(m, \"nevaluate\", true, false, 0);\n\n\t\tm.def(\"nrange\", \n\t\t\t\t[](py::dict d) {\n\t\t\t\tauto ret = extract_var_range(d);\n\t\t\t\treturn std::make_pair(std::get<0>(ret), std::get<1>(ret));\n\t\t\t\t}\n\t\t\t\t);\n\n\t\tm.def(\"nval\",\n\t\t\t\t// We cannot use `def_algo` because we first need to\n\t\t\t\t// convert the Python dict into something that `nevaluate`\n\t\t\t\t// can handle (you cannot do that with pybind11\n\t\t\t\t// automagic).\n\t\t\t\t[](Ex_ptr ex, py::dict d) {\n\t\t\t\tstd::vector<std::pair<Ex, NTensor>> values;\n\t\t\t\tNEvaluator ev;\n\t\t\t\tset_variables(ev, d);\n\t\t\t\treturn apply_algo_preorder<nval>(ex, ev, true, false, 0);\n\t\t\t\t},\n\t\t\t\tpy::arg(\"ex\"),\n\t\t\t\tpy::arg(\"values\")=py::dict(),\n\t\t\t\tpybind11::doc(read_manual(m, \"algorithms\", \"nval\").c_str())\n\t\t\t\t);\n\t\t\n\t\tm.def(\"nevaluate\",\n\t\t\t\t// We cannot use `def_algo` because we first need to\n\t\t\t\t// convert the Python dict into something that `nevaluate`\n\t\t\t\t// can handle (you cannot do that with pybind11\n\t\t\t\t// automagic).\n\t\t\t\t[](Ex_ptr ex, py::dict d) {\n\t\t\t\tstd::vector<std::pair<Ex, NTensor>> values;\n\t\t\t\tNEvaluator ev((*ex).begin()); // FIXME: we do not know the entry point, it does not have to be top-level.\n\t\t\t\tset_variables(ev, d);\n\t\t\t\treturn ev.evaluate();\n//\t\t\t\treturn apply_algo<nevaluate>(ex, ev, false, false, 0);\n\t\t\t\t}\n\t\t\t\t);\n\t\t\n\t\tm.def(\"ndsolve\",\n\t\t\t\t[](Ex_ptr ex, py::dict initial, py::tuple range, Ex_ptr stop) {\n\t\t\t\tNDSolver nds(*ex);\n\t\t\t\t// initial values\n\t\t\t\tfor(const auto& iv: initial)\n\t\t\t\t\tnds.set_initial_value( py::cast<Ex>(iv.first), py::cast<double>(iv.second) );\n\n\t\t\t\tif(range.size()!=3)\n\t\t\t\t\tthrow ConsistencyException(\"ndsolve: integration range must have exactly three elements.\");\n\n\t\t\t\tnds.set_range( py::cast<Ex>(range[0]), py::cast<double>(range[1]), py::cast<double>(range[2]));\n\t\t\t\tnds.set_stop(*stop);\n\t\t\t\t\t\n\t\t\t\tauto res = nds.integrate();\n\t\t\t\tauto rexv = std::make_shared<Ex>(\"\\\\comma\");\n\n\t\t\t\tfor(size_t n=1; n<res.size(); ++n) {\n\t\t\t\t\tEx rex(\"\\\\equals\");\n\n\t\t\t\t\t// Create interpolating function.\n\t\t\t\t\tauto rif = std::make_shared<NInterpolatingFunction>();\n\t\t\t\t\trif->var = py::cast<Ex>(range[0]);\n\t\t\t\t\trif->var_values = res[0];\n\t\t\t\t\trif->fun_values = res[n];\n\n\t\t\t\t\t// Fill equality lhs and rhs;\n\t\t\t\t\trex.append_child(rex.begin(), nds.functions()[n-1].begin());\n\t\t\t\t\tauto rf = rex.append_child(rex.begin(), Ex(\"1\").begin());\n\t\t\t\t\trf->content = rif;\n\n\t\t\t\t\t// Add to list.\n\t\t\t\t\trexv->move_in_below(rexv->begin(), rex);\n\t\t\t\t\t}\n\t\t\t\t\n\t\t\t\treturn rexv;\n\t\t\t\t},\n\t\t\t\tpy::arg(\"ex\"),\n\t\t\t\tpy::arg(\"initial\"),\n\t\t\t\tpy::arg(\"range\"),\n\t\t\t\tpy::arg(\"stop\") = Ex{}\n\t\t\t\t);\n\n\t\tm.def(\"nintegrate\",\n\t\t\t\t[](Ex_ptr ex, py::dict ranges) {\n\t\t\t\tNIntegrator ni((*ex).begin());\n\n\t\t\t\t// Set all variables from the given dict entries.\n\t\t\t\tset_variables(ni.evaluator, ranges);\n\n\t\t\t\t// Set the integration range.\n\t\t\t\tauto var_range = extract_var_range(ranges);\n\t\t\t\tni.set_range( std::get<0>(var_range), std::get<2>(var_range).real(), std::get<3>(var_range).real() );\n\t\t\t\t\n\t\t\t\tauto res = ni.integrate();\n\t\t\t\t// FIXME: we need to have a better test for real integrands\n\t\t\t\tif(std::abs(res.imag()) > 5.0*std::numeric_limits<double>::epsilon())\n\t\t\t\t\treturn py::cast(res);\n\t\t\t\telse\n\t\t\t\t\treturn py::cast(res.real());\n\t\t\t\t}\n\t\t\t\t);\n\n\t\tm.def(\"Re\",\n\t\t\t\t[](Ex_ptr ex) {\n\t\t\t\tEx ret(ex->begin());\n\t\t\t\tret.wrap(ret.begin(), str_node(\"\\\\Re\"));\n\t\t\t\treturn ret;\n\t\t\t\t}\n\t\t\t\t);\n\t\t\n\t\tm.def(\"Im\",\n\t\t\t\t[](Ex_ptr ex) {\n\t\t\t\tEx ret(ex->begin());\n\t\t\t\tret.wrap(ret.begin(), str_node(\"\\\\Im\"));\n\t\t\t\treturn ret;\n\t\t\t\t}\n\t\t\t\t);\n\t\t\n\t\tm.def(\"get_num_rules\", []() {\n\t\t\treturn substitute::cache_size();\n\t\t\t});\n\t\t}\n\n\tvoid set_variables(NEvaluator& ev, py::dict d)\n\t\t{\n\t\t// For every variable in the dict, we can take either a numpy.array (or something that\n\t\t// auto-converts to it), a tuple (interpreted as a range) or a single complex/double\n\t\t// value. Figure out what it is, and convert to a vector of doubles.\n\t\t\n\t\tfor(const auto& dv: d) {\n\t\t\tpy::object type_obj = py::type::of(dv.second);\n\t\t\tstd::string type_name = py::str(type_obj.attr(\"__name__\"));\n\t\t\tif(type_name==\"float\") {\n\t\t\t\tstd::vector<double> vec;\n\t\t\t\tvec.push_back(py::cast<double>(dv.second));\n\t\t\t\tev.set_variable(py::cast<Ex>(dv.first), NTensor(vec));\n\t\t\t\t}\n\t\t\telse if(type_name==\"int\") {\n\t\t\t\tstd::vector<double> vec;\n\t\t\t\tvec.push_back(py::cast<int>(dv.second));\n\t\t\t\tev.set_variable(py::cast<Ex>(dv.first), NTensor(vec));\n\t\t\t\t}\n\t\t\telse if(type_name==\"complex\") {\n\t\t\t\tstd::vector<std::complex<double>> vec;\n\t\t\t\tvec.push_back(py::cast<std::complex<double>>(dv.second));\n\t\t\t\tev.set_variable(py::cast<Ex>(dv.first), NTensor(vec));\n\t\t\t\t}\n\t\t\telse if(type_name==\"tuple\") {\n\t\t\t\tstd::vector<double> rvec = py::cast<std::vector<double>>(dv.second);\n\t\t\t\tif(rvec.size()!=2)\n\t\t\t\t\tthrow ArgumentException(\"Range: value tuples must have exactly two elements (start, end); found \"+std::to_string(rvec.size())+\".\");\n\t\t\t\tauto range = NTensor::linspace(rvec[0], rvec[1], 100);\n\t\t\t\tev.set_variable(py::cast<Ex>(dv.first), range);\n\t\t\t\t}\n\t\t\telse {\n\t\t\t\tauto nt = NTensor(py::cast<std::vector<double>>(dv.second));\n\t\t\t\tif(nt.shape.size()==0 || nt.shape[0]==0)\n\t\t\t\t\tthrow ArgumentException(\"Range: value cannot be converted to a numerical range.\");\n\t\t\t\t\n\t\t\t\tev.set_variable(py::cast<Ex>(dv.first), nt);\n\t\t\t\t}\n\t\t\t}\n\t\tev.set_lookup_function([](const Ex& var) {\n\t\t\tKernel *kernel = get_kernel_from_scope();\n\t\t\tauto imaginaryI = kernel->properties.get<ImaginaryI>(var.begin());\n\t\t\tif(imaginaryI) return std::complex<double>(0, 1.0);\n\t\t\t\n\t\t\tthrow std::logic_error(\"No value.\");\n\t\t\t});\n\t\t}\n\n\tstd::tuple<Ex, NTensor, std::complex<double>, std::complex<double>> extract_var_range(py::dict d)\n\t\t{\n\t\t// Given a dict of variable to value mappings, extract the\n\t\t// single variable for which the value is an explicit or\n\t\t// implicit range, and return a tuple consisting of the\n\t\t// variable and the range. Throws an exception if there is\n\t\t// more than one range, or none.\n\t\tNTensor range(0);\n\t\tstd::complex<double> start, end;\n\t\tEx      rangevar;\n\t\tbool found=false;\n\t\tfor(const auto& dv: d) {\n\t\t\tpy::object type_obj = py::type::of(dv.second);\n\t\t\tstd::string type_name = py::str(type_obj.attr(\"__name__\"));\n\t\t\tif(!(type_name==\"float\" || type_name==\"complex\" || type_name==\"int\")) {\n\t\t\t\tif(found)\n\t\t\t\t\tthrow ArgumentException(\"nrange: found more than one variable with a value range.\");\n\t\t\t\t\n\t\t\t\trangevar = py::cast<Ex>(dv.first);\n\t\t\t\tif(type_name==\"tuple\") {\n\t\t\t\t\tstd::vector<double> rvec = py::cast<std::vector<double>>(dv.second);\n\t\t\t\t\tif(rvec.size()!=2)\n\t\t\t\t\t\tthrow ArgumentException(\"nrange: value tuples must have exactly two elements (start, end); found \"+std::to_string(rvec.size())+\".\");\n\t\t\t\t\trange = NTensor::linspace(rvec[0], rvec[1], 100);\n\t\t\t\t\tfound = true;\n\t\t\t\t\tstart = rvec[0];\n\t\t\t\t\tend   = rvec[1];\n\t\t\t\t\t}\n\t\t\t\telse {\n\t\t\t\t\tauto manrange = py::cast<std::vector<double>>(dv.second);\n\t\t\t\t\tstart = manrange[0];\n\t\t\t\t\tend   = manrange[manrange.size()-1];\n\t\t\t\t\trange = NTensor(manrange);\n\t\t\t\t\tfound = true;\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t}\n\t\tif(!found)\n\t\t\tthrow ArgumentException(\"nrange: not found any variable with a value range.\");\n\n\t\treturn std::make_tuple(rangevar, range, start, end);\n\t\t}\n}\n"
  },
  {
    "path": "core/pythoncdb/py_algorithms.hh",
    "content": "#pragma once\n\n#include <pybind11/pybind11.h>\n#include \"py_ex.hh\"\n#include \"py_helpers.hh\"\n#include \"py_kernel.hh\"\n#include \"py_progress.hh\"\n\nnamespace cadabra {\n\t\n\t/// \\ingroup pythoncore\n\t///\n\t/// Generic internal entry point for the Python side to execute a\n\t/// C++ algorithm. This gets called by the various apply_algo\n\t/// functions below, which in turn get called by the def_algo\n\t/// functions.\n\ttemplate <class Algo>\n\tEx_ptr apply_algo_base(Algo& algo, Ex_ptr ex, bool deep, bool repeat, unsigned int depth, bool pre_order=false)\n\t\t{\n\t\tEx::iterator it = ex->begin();\n\t\tif (ex->is_valid(it)) {\n\t\t\tProgressMonitor* pm = get_progress_monitor();\n\t\t\talgo.set_progress_monitor(pm);\n\t\t\tif(pre_order)\n\t\t\t\tex->update_state(algo.apply_pre_order(repeat));\n\t\t\telse\n\t\t\t\tex->update_state(algo.apply_generic(it, deep, repeat, depth));\n\t\t\tcall_post_process(*get_kernel_from_scope(), ex);\n\t\t\t}\n\n\t\treturn ex;\n\t\t}\n\n\ttemplate <class Algo>\n\tEx_ptr apply_algo(Ex_ptr ex, bool deep, bool repeat, unsigned int depth)\n\t\t{\n\t\tAlgo algo(*get_kernel_from_scope(), *ex);\n\t\treturn apply_algo_base(algo, ex, deep, repeat, depth, false);\n\t\t}\n\n\ttemplate <class Algo, typename Arg1>\n\tEx_ptr apply_algo(Ex_ptr ex, Arg1 arg1, bool deep, bool repeat, unsigned int depth)\n\t\t{\n\t\tAlgo algo(*get_kernel_from_scope(), *ex, arg1);\n\t\treturn apply_algo_base(algo, ex, deep, repeat, depth, false);\n\t\t}\n\n\ttemplate <class Algo, typename Arg1, typename Arg2>\n\tEx_ptr apply_algo(Ex_ptr ex, Arg1 arg1, Arg2 arg2, bool deep, bool repeat, unsigned int depth)\n\t\t{\n\t\tAlgo algo(*get_kernel_from_scope(), *ex, arg1, arg2);\n\t\treturn apply_algo_base(algo, ex, deep, repeat, depth, false);\n\t\t}\n\n\ttemplate <class Algo, typename Arg1, typename Arg2, typename Arg3>\n\tEx_ptr apply_algo(Ex_ptr ex, Arg1 arg1, Arg2 arg2, Arg3 arg3, bool deep, bool repeat, unsigned int depth)\n\t\t{\n\t\tAlgo algo(*get_kernel_from_scope(), *ex, arg1, arg2, arg3);\n\t\treturn apply_algo_base(algo, ex, deep, repeat, depth, false);\n\t\t}\n\n\n\t/// \\ingroup pythoncore\n\t///\n\t/// Method to declare a Python function with variable number of\n\t/// arguments, and make that call a C++ algorithm as specified in\n\t/// the Algo template parameter.  This will make the algorithm\n\t/// traverse post-order, that is to say, first on the innermost\n\t/// child (or leaf) of an expression tree, and then, if that fails,\n\t/// on parent nodes, and so on.\n\ttemplate<class Algo, typename... Args, typename... PyArgs>\n\tvoid def_algo(pybind11::module& m, const char* name, bool deep, bool repeat, unsigned int depth, PyArgs... pyargs)\n\t\t{\n\t\tm.def(name,\n\t\t      &apply_algo<Algo, Args...>,\n\t\t      pybind11::arg(\"ex\"),\n\t\t      std::forward<PyArgs>(pyargs)...,\n\t\t      pybind11::arg(\"deep\") = deep,\n\t\t      pybind11::arg(\"repeat\") = repeat,\n\t\t      pybind11::arg(\"depth\") = depth,\n\t\t      pybind11::doc(read_manual(m, \"algorithms\", name).c_str()),\n\t\t      pybind11::return_value_policy::reference_internal);\n\t\t}\n\n\ttemplate <class Algo>\n\tEx_ptr apply_algo_preorder(Ex_ptr ex, bool deep, bool repeat, unsigned int depth)\n\t\t{\n\t\tAlgo algo(*get_kernel_from_scope(), *ex);\n\t\treturn apply_algo_base(algo, ex, deep, repeat, depth, true);\n\t\t}\n\n\ttemplate <class Algo, typename Arg1>\n\tEx_ptr apply_algo_preorder(Ex_ptr ex, Arg1 arg1, bool deep, bool repeat, unsigned int depth)\n\t\t{\n\t\tAlgo algo(*get_kernel_from_scope(), *ex, arg1);\n\t\treturn apply_algo_base(algo, ex, deep, repeat, depth, true);\n\t\t}\n\n\ttemplate <class Algo, typename Arg1, typename Arg2>\n\tEx_ptr apply_algo_preorder(Ex_ptr ex, Arg1 arg1, Arg2 arg2, bool deep, bool repeat, unsigned int depth)\n\t\t{\n\t\tAlgo algo(*get_kernel_from_scope(), *ex, arg1, arg2);\n\t\treturn apply_algo_base(algo, ex, deep, repeat, depth, true);\n\t\t}\n\n\t/// \\ingroup pythoncore\n\t///\n\t/// Method to declare a Python function with variable number of arguments, and\n\t/// make that call a C++ algorithm as specified in the Algo template parameter.\n\t/// In contrast to def_algo, this one will apply the algorithm in pre-order\n\t/// traversal style, that is, it will first attempt to apply on a node itself\n\t/// before traversing further down the child nodes and attempting there.\n\ttemplate<class Algo, typename... Args, typename... PyArgs>\n\tvoid def_algo_preorder(pybind11::module& m, const char* name, bool deep, bool repeat, unsigned int depth, PyArgs... pyargs)\n\t\t{\n\t\tm.def(name,\n\t\t      &apply_algo_preorder<Algo, Args...>,\n\t\t      pybind11::arg(\"ex\"),\n\t\t      std::forward<PyArgs>(pyargs)...,\n\t\t      pybind11::arg(\"deep\") = deep,\n\t\t      pybind11::arg(\"repeat\") = repeat,\n\t\t      pybind11::arg(\"depth\") = depth,\n\t\t      pybind11::doc(read_manual(m, \"algorithms\", name).c_str()),\n\t\t      pybind11::return_value_policy::reference_internal);\n\t\t}\n\n\n\tvoid init_algorithms(pybind11::module& m);\n}\n"
  },
  {
    "path": "core/pythoncdb/py_ex.cc",
    "content": "\n#include \"Config.hh\"\n\n#include <pybind11/stl.h>\n\n#include \"py_ex.hh\"\n#include \"py_helpers.hh\"\n#include \"py_globals.hh\"\n#include \"py_kernel.hh\"\n#include \"py_algorithms.hh\"\n\n#include \"algorithms/map_sympy.hh\"\n#ifdef MATHEMATICA_FOUND\n#include \"algorithms/map_mma.hh\"\n#endif\n\n#include \"Exceptions.hh\"\n#include \"Parser.hh\"\n#include \"PreClean.hh\"\n#include \"Cleanup.hh\"\n#include \"Bridge.hh\"\n#include \"SympyCdb.hh\"\n#include \"NTensor.hh\"\n#include \"NInterpolatingFunction.hh\"\n\n// Includes for display routines\n#include <sstream>\n#include \"DisplayMMA.hh\"\n#include \"DisplayTeX.hh\"\n#include \"DisplaySympy.hh\"\n#include \"DisplayTerminal.hh\"\n\n#include <ios>\n#include <iomanip>\n\n// #define DEBUG 1\n\nnamespace cadabra {\n\n\tnamespace py = pybind11;\n\n\tbool Ex_compare(Ex_ptr one, Ex_ptr other)\n\t\t{\n\t\treturn tree_equal(&(get_kernel_from_scope()->properties), *one, *other);\n\t\t}\n\n\tbool Ex_compare(Ex_ptr one, int other)\n\t\t{\n\t\tauto ex = std::make_shared<Ex>(other);\n\t\treturn Ex_compare(one, ex);\n\t\t}\n\n\tEx_ptr Ex_add(const Ex_ptr ex1, const ExNode ex2)\n\t\t{\n\t\treturn Ex_add(ex1, ex2.ex, ex2.it);\n\n\t\t}\n\n\tEx_ptr Ex_add(const Ex_ptr ex1, const Ex_ptr ex2)\n\t\t{\n\t\treturn Ex_add(ex1, ex2, ex2->begin());\n\t\t}\n\n\tEx_ptr Ex_add(const Ex_ptr ex1, const Ex_ptr ex2, Ex::iterator top2)\n\t\t{\n\t\tif (ex1->size() == 0) return ex2;\n\t\tif (ex2->size() == 0) return ex1;\n\n\t\t// Using '+' for list addition is very illogical; it should add\n\t\t// componentwise.\n//\t\tbool comma1 = (*ex1->begin()->name == \"\\\\comma\");\n//\t\tbool comma2 = (*ex2->begin()->name == \"\\\\comma\");\n\n//\t\tif (comma1 || comma2) {\n//\t\t\tif (comma1) {\n//\t\t\t\tauto ret = std::make_shared<Ex>(*ex1);\n//\t\t\t\tauto loc = ret->append_child(ret->begin(), top2);\n//\t\t\t\tif (comma2)\n//\t\t\t\t\tret->flatten_and_erase(loc);\n//\t\t\t\treturn ret;\n//\t\t\t\t}\n//\t\t\telse {\n//\t\t\t\tauto ret = std::make_shared<Ex>(top2);\n//\t\t\t\tauto loc = ret->prepend_child(ret->begin(), ex1->begin());\n//\t\t\t\tif (comma1)\n//\t\t\t\t\tret->flatten_and_erase(loc);\n//\t\t\t\treturn ret;\n//\t\t\t\t}\n//\t\t\t}\n//\t\telse {\n\t\t\tauto ret = std::make_shared<Ex>(*ex1);\n\t\t\tif (*ret->begin()->name != \"\\\\sum\")\n\t\t\t\tret->wrap(ret->begin(), str_node(\"\\\\sum\"));\n\t\t\tret->append_child(ret->begin(), top2);\n\n\t\t\tauto it = ret->begin();\n\t\t\tcleanup_dispatch(*get_kernel_from_scope(), *ret, it);\n\t\t\treturn ret;\n//\t\t\t}\n\t\t}\n\n   Ex_ptr Ex_join(const Ex_ptr ex1, const Ex_ptr ex2)\n\t\t{\n\t\t// DEPRECATED: no longer in use, can be removed\n\t\tif (ex1->size() == 0) return ex2;\n\t\tif (ex2->size() == 0) return ex1;\n\n\t\tbool comma1 = (*ex1->begin()->name == \"\\\\comma\");\n\t\tbool comma2 = (*ex2->begin()->name == \"\\\\comma\");\n\n\t\tif(comma1 || comma2) {\n\t\t\tif (comma1) {\n\t\t\t\tauto ret = std::make_shared<Ex>(*ex1);\n\t\t\t\tauto loc = ret->append_child(ret->begin(), ex2->begin());\n\t\t\t\tif (comma2)\n\t\t\t\t\tret->flatten_and_erase(loc);\n\t\t\t\treturn ret;\n\t\t\t\t}\n\t\t\telse {\n\t\t\t\tauto ret = std::make_shared<Ex>(ex2->begin());\n\t\t\t\tauto loc = ret->prepend_child(ret->begin(), ex1->begin());\n\t\t\t\tif (comma1)\n\t\t\t\t\tret->flatten_and_erase(loc);\n\t\t\t\treturn ret;\n\t\t\t\t}\n\t\t\t}\n\t\telse {\n\t\t\tauto ret = std::make_shared<Ex>(*ex1);\n\t\t\tif (*ret->begin()->name != \"\\\\comma\")\n\t\t\t\tret->wrap(ret->begin(), str_node(\"\\\\comma\"));\n\t\t\tret->append_child(ret->begin(), ex2->begin());\n\n\t\t\tauto it = ret->begin();\n\t\t\tcleanup_dispatch(*get_kernel_from_scope(), *ret, it);\n\t\t\treturn ret;\n\t\t\t}\n\t\t}\n\n   Ex_ptr Ex_join(const std::vector<Ex_ptr>& exs)\n\t\t{\n\t\tauto ret = std::make_shared<Ex>(\"\\\\comma\");\n\n\t\tfor(const Ex_ptr& ex: exs) {\n\t\t\t// skip ex if empty\n\t\t\tif (ex->size() > 0) {\n\t\t\t\tauto loc = ret->append_child(ret->begin(), ex->begin());\n\t\t\t\tif(*ex->begin()->name==\"\\\\comma\") \n\t\t\t\t\tret->flatten_and_erase(loc);\n\t\t\t\t}\n\t\t\t}\n\t\t// Note: ret could still \\comma{} or \\comma{x}\n\t\tauto it = ret->begin();\n\t\tif (ret->number_of_children(it) < 2) {\n\t\t\tret->flatten_and_erase(it);\n\t\t\t}\n\t\treturn ret;\n\t\t}\n\t\n\tEx_ptr Ex_mul(const Ex_ptr ex1, const Ex_ptr ex2)\n\t\t{\n\t\treturn Ex_mul(ex1, ex2, ex2->begin());\n\t\t}\n\n\n\tEx_ptr Ex_mul(const Ex_ptr ex1, const Ex_ptr ex2, Ex::iterator top2)\n\t\t{\n\t\tif (ex1->size() == 0) return ex2;\n\t\tif (ex2->size() == 0) return ex1;\n\n\t\tauto ret = std::make_shared<Ex>(*ex1);\n\t\tif (*ret->begin()->name != \"\\\\prod\")\n\t\t\tret->wrap(ret->begin(), str_node(\"\\\\prod\"));\n\t\tret->append_child(ret->begin(), top2);\n\n\t\tauto it = ret->begin();\n\t\tcleanup_dispatch(*get_kernel_from_scope(), *ret, it);\n\t\treturn ret;\n\t\t}\n\n\tEx_ptr Ex_sub(const Ex_ptr ex1, const ExNode ex2)\n\t\t{\n\t\treturn Ex_sub(ex1, ex2.ex, ex2.it);\n\n\t\t}\n\n\tEx_ptr Ex_sub(const Ex_ptr ex1, const Ex_ptr ex2)\n\t\t{\n\t\treturn Ex_sub(ex1, ex2, ex2->begin());\n\t\t}\n\n\tEx_ptr Ex_sub(const Ex_ptr ex1, const Ex_ptr ex2, Ex::iterator top2)\n\t\t{\n\t\tif (ex1->size() == 0) {\n\t\t\tif (ex2->size() != 0) {\n\t\t\t\tauto ret = std::make_shared<Ex>(*ex2);\n\t\t\t\tmultiply(ex2->begin()->multiplier, -1);\n\t\t\t\tauto it = ret->begin();\n\t\t\t\tcleanup_dispatch(*get_kernel_from_scope(), *ret, it);\n\t\t\t\treturn ret;\n\t\t\t\t}\n\t\t\telse return ex2;\n\t\t\t}\n\t\tif (ex2->size() == 0) return ex1;\n\n\t\tauto ret = std::make_shared<Ex>(*ex1);\n\t\tif (*ret->begin()->name != \"\\\\sum\")\n\t\t\tret->wrap(ret->begin(), str_node(\"\\\\sum\"));\n\t\tauto it = ret->append_child(ret->begin(), top2);\n\t\tmultiply(it->multiplier, -1);\n\t\tcleanup_dispatch(*get_kernel_from_scope(), *ret, it);\n\n\t\tit = ret->begin();\n\t\tcleanup_dispatch(*get_kernel_from_scope(), *ret, it);\n\n\t\treturn ret;\n\t\t}\n\n\tEx_ptr fetch_from_python(const std::string& nm)\n\t\t{\n\t\tauto locals = get_locals();\n\t\tauto ret = fetch_from_python(nm, locals);\n\t\tif (!ret) {\n\t\t\tauto globals = get_globals();\n\t\t\tret = fetch_from_python(nm, globals);\n\t\t\t}\n\t\treturn ret;\n\t\t}\n\n\tEx_ptr fetch_from_python(const std::string& nm, pybind11::object scope)\n\t\t{\n\t\tif( !scope_has(scope, nm) ) {\n\t\t\treturn 0;\n\t\t\t}\n\t\tauto obj = scope[nm.c_str()];\n\n\t\t// Try 'Ex'\n\t\ttry {\n\t\t\treturn obj.cast<Ex_ptr>();\n\t\t\t}\n\t\tcatch (const pybind11::cast_error& e) {\n\t\t\t}\n\n\t\t// Try 'ExNode'\n\t\ttry {\n\t\t\tauto exnode = obj.cast<ExNode>();\n\t\t\tauto ret = std::make_shared<Ex>(exnode.it);\n\t\t\treturn ret;\n\t\t\t}\n\t\tcatch (const pybind11::cast_error& e) {\n\t\t\t}\n\n\t\t// Try float or int.\n\t\tif(pybind11::isinstance<py::int_>(obj)) {\n\t\t\tauto ret = std::make_shared<Ex>(pybind11::cast<int>(obj));\n\t\t\treturn ret;\n\t\t\t}\n\t\tif(pybind11::isinstance<py::float_>(obj)) {\n\t\t\tauto ret = std::make_shared<Ex>(pybind11::cast<float>(obj));\n\t\t\treturn ret;\n\t\t\t}\n\t\t\t\n\t\treturn 0;\n\t\t}\n\n\tstd::string Ex_as_str(Ex_ptr ex)\n\t\t{\n\t\tstd::ostringstream str;\n\t\t//\n\t\t// //\tif(state()==Algorithm::result_t::l_no_action)\n\t\t// //\t\tstr << \"(unchanged)\" << std::endl;\n\t\t// \tDisplayTeX dt(get_kernel_from_scope()->properties, ex);\n\n\t\tDisplayTerminal dt(*get_kernel_from_scope(), *ex, true);\n\t\tdt.output(str);\n\n\t\treturn str.str();\n\t\t}\n\n\tstd::string Ex_as_repr(Ex_ptr ex)\n\t\t{\n\t\tif (!ex) return \"\";\n\t\tif (ex->begin() == ex->end()) return \"\";\n\n\t\t//\t\tEx::iterator it = ex->begin();\n\t\tstd::ostringstream str;\n\t\tex->print_python(str, ex->begin());\n\t\treturn str.str();\n\t\t}\n\n\tstd::string Ex_as_latex(Ex_ptr ex)\n\t\t{\n\t\tif (!ex) return \"\";\n\t\tstd::ostringstream str;\n\t\tDisplayTeX dt(*get_kernel_from_scope(), *ex);\n\t\tdt.output(str);\n\t\treturn str.str();\n\t\t}\n\n\tpybind11::object Ex_as_sympy(Ex_ptr ex)\n\t\t{\n\t\t// Generate a string which can be parsed by Sympy.\n\t\tstd::string txt = Ex_as_sympy_string(ex);\n\n\t\t// Call sympify on a sympy-parseable  textual representation.\n\t\tpybind11::module sympy_parser = pybind11::module::import(\"sympy.parsing.sympy_parser\");\n\t\tauto parse = sympy_parser.attr(\"parse_expr\");\n#ifdef DEBUG\n\t\tstd::cerr << \"Feeding sympy: \" << txt << std::endl;\n#endif\n\t\tpybind11::object ret = parse(txt);\n\t\treturn ret;\n\t\t}\n\n\tpybind11::object ExNode_get_multiplier(const ExNode& ex)\n\t\t{\n\t\tif(!ex.is_valid())\n\t\t\tthrow ConsistencyException(\"Cannot get the multiplier of an iterator before the first 'next'.\");\n\n\t\tif(ex.it->multiplier->is_rational()) {\n\t\t\tpybind11::object mpq = pybind11::module::import(\"gmpy2\").attr(\"mpq\");\n\t\t\tauto m = ex.it->multiplier->get_rational();\n\t\t\tpybind11::object mult = mpq(m.get_num().get_si(), m.get_den().get_si());\n\t\t\treturn mult;\n\t\t\t}\n\t\telse {\n\t\t\treturn pybind11::cast(ex.it->multiplier->get_double());\n\t\t\t}\n\t\t}\n\t\n\tvoid ExNode_set_multiplier(ExNode& ex, pybind11::object mult)\n\t\t{\n\t\tif(!ex.is_valid())\n\t\t\tthrow ConsistencyException(\"Cannot set the multiplier of an iterator before the first 'next'.\");\n\n\t\t// FIXME: this assumes the python object is a rational, but it could be a double now.\n\t\tset(ex.it->multiplier, multiplier_t(mult.attr(\"numerator\").cast<long>(),\n\t\t\t\t\t\t\t\t\t\t\t\t\t\tmult.attr(\"denominator\").cast<long>()) );\n\t\t}\n\n\tpybind11::object ExNode_as_sympy(const ExNode& exnode)\n\t\t{\n\t\treturn Ex_as_sympy(exnode.ex);\n\t\t}\n\n\tstd::string Ex_as_sympy_string(Ex_ptr ex)\n\t\t{\n\t\t// Check to see if the expression is a scalar without dummy indices.\n\t\t//\tAlgorithm::index_map_t ind_free, ind_dummy;\n\t\t//\tAlgorithm::classify_indices(ex.begin(), ind_free, ind_dummy);\n\t\t//\tif(ind_dummy.size()>0)\n\t\t//\t\tthrow NonScalarException(\"Expression contains dummy indices.\");\n\t\t//\tif(ind_free.size()>0)\n\t\t//\t\tthrow NonScalarException(\"Expression contains free indices.\");\n\n\t\tif (!ex) return \"\";\n\t\tstd::ostringstream str;\n\t\tDisplaySympy dt(*get_kernel_from_scope(), *ex);\n\t\tdt.output(str);\n\t\treturn str.str();\n\t\t}\n\n\tstd::string Ex_as_input(Ex_ptr ex)\n\t\t{\n\t\tstd::ostringstream str;\n\t\t//\n\t\t// //\tif(state()==Algorithm::result_t::l_no_action)\n\t\t// //\t\tstr << \"(unchanged)\" << std::endl;\n\t\t// \tDisplayTeX dt(get_kernel_from_scope()->properties, ex);\n\n\t\tDisplayTerminal dt(*get_kernel_from_scope(), *ex, false);\n\t\tdt.output(str);\n\n\t\treturn str.str();\n\t\t}\n\n\tstd::string Ex_as_MMA(Ex_ptr ex, bool use_unicode)\n\t\t{\n\t\t// Check to see if the expression is a scalar without dummy indices.\n\t\t//\tAlgorithm::index_map_t ind_free, ind_dummy;\n\t\t//\tAlgorithm::classify_indices(ex.begin(), ind_free, ind_dummy);\n\t\t//\tif(ind_dummy.size()>0)\n\t\t//\t\tthrow NonScalarException(\"Expression contains dummy indices.\");\n\t\t//\tif(ind_free.size()>0)\n\t\t//\t\tthrow NonScalarException(\"Expression contains free indices.\");\n\n\t\tstd::ostringstream str;\n\t\tDisplayMMA dt(*get_kernel_from_scope(), *ex, use_unicode);\n\t\tdt.output(str);\n\n\t\treturn str.str();\n\t\t}\n\n\tEx_comparator::match_t ExNode_compare(const ExNode& lhs, const ExNode& rhs, const std::string& use_props, bool ignore_parent_rel)\n\t{\n\t\tEx_comparator comp(get_kernel_from_scope()->properties);\n\t\tEx_comparator::useprops_t up = Ex_comparator::useprops_t::always;\n\t\tif (use_props == \"not_at_top\")\n\t\t\tup = Ex_comparator::useprops_t::not_at_top;\n\t\telse if (use_props == \"never\")\n\t\t\tup = Ex_comparator::useprops_t::never;\n\t\treturn comp.equal_subtree(lhs.it, rhs.it, up, ignore_parent_rel);\n\t}\n\n\tstd::string print_tree(Ex *ex)\n\t\t{\n\t\tstd::ostringstream str;\n\t\tex->print_entire_tree(str);\n\t\treturn str.str();\n\t\t}\n\n\tEx lhs(Ex_ptr ex)\n\t\t{\n\t\tauto it = ex->begin();\n\t\tif (it == ex->end())\n\t\t\tthrow ArgumentException(\"Empty expression passed to 'lhs'.\");\n\n\t\tif (*it->name != \"\\\\equals\")\n\t\t\tthrow ArgumentException(\"Cannot take 'lhs' of expression which is not an equation.\");\n\n\t\treturn Ex(ex->begin(ex->begin()));\n\t\t}\n\n\tEx rhs(Ex_ptr ex)\n\t\t{\n\t\tauto it = ex->begin();\n\t\tif (it == ex->end())\n\t\t\tthrow ArgumentException(\"Empty expression passed to 'rhs'.\");\n\n\t\tif (*it->name != \"\\\\equals\")\n\t\t\tthrow ArgumentException(\"Cannot take 'rhs' of expression which is not an equation.\");\n\n\t\tauto sib = ex->begin(ex->begin());\n\t\t++sib;\n\t\treturn Ex(sib);\n\t\t}\n\n\tEx Ex_getslice(Ex_ptr ex, pybind11::slice slice)\n\t\t{\n\t\tEx result;\n\n\t\tpybind11::size_t start, stop, step, length;\n\t\t// std::cerr << \"SLICE object has \" << ex->number_of_children(ex->begin()) << \" elements\" << std::endl;\n\t\tslice.compute(ex->number_of_children(ex->begin()), &start, &stop, &step, &length);\n\t\t// std::cerr << \"SLICE: \" << start << \", \" << stop << \", \" << step << \", \" << length << std::endl;\n\t\tif (length == 0)\n\t\t\treturn result;\n\n\t\t// Set head\n\t\tauto it = result.set_head(*ex->begin());\n\n\t\t// Iterate over fully-closed range.\n\t\tfor (; start < stop; start += step) {\n\t\t\tEx::sibling_iterator toadd=ex->begin(ex->begin());\n\t\t\tstd::advance(toadd, start);\n\t\t\tresult.append_child(it, Ex::iterator(toadd));\n\t\t\t}\n\t\treturn result;\n\t\t}\n\n\tEx Ex_getitem(Ex &ex, int index)\n\t\t{\n\t\tEx::iterator it = ex.begin();\n\n\t\tsize_t num = ex.number_of_children(it);\n\t\tif (index >= 0 && (size_t)index < num)\n\t\t\treturn Ex(ex.child(it, index));\n\t\telse {\n\t\t\t//\t\tif(num==0 && index==0) {\n\t\t\t//\t\t\tstd::cerr << \"returning \" << ex << std::endl;\n\t\t\t//\t\t\treturn Ex(ex);\n\t\t\t//\t\t\t}\n\t\t\t//\t\telse\n\t\t\tthrow ArgumentException(\"index \" + std::to_string(index) + \" out of range, must be smaller than \" + std::to_string(num));\n\t\t\t}\n\t\t}\n\n\tvoid Ex_setitem(Ex_ptr ex, int index, Ex val)\n\t\t{\n\t\tEx::iterator it = ex->begin();\n\n\t\tsize_t num = ex->number_of_children(it);\n\t\tif (index >= 0 && (size_t)index < num)\n\t\t\tex->replace(ex->child(it, index), val.begin());\n\t\telse\n\t\t\tthrow ArgumentException(\"index \" + std::to_string(index) + \" out of range, must be smaller than \" + std::to_string(num));\n\t\t}\n\n\tvoid Ex_setitem_iterator(Ex_ptr ex, ExNode en, Ex_ptr val)\n\t\t{\n\t\tEx::iterator use;\n\t\tif (en.ex != ex) {\n\t\t\t//\t\tstd::cerr << \"Setitem need to convert iterator of\" << std::endl;\n\t\t\t//\t\tstd::cerr << en.it << std::endl;\n\t\t\t//\t\tstd::cerr << \"in \" << en.topit << std::endl;\n\t\t\t//\t\tstd::cerr << \"of \" << en.ex->begin() << std::endl;\n\t\t\tauto path = en.ex->path_from_iterator(en.it, en.topit);\n\t\t\t//\t\tfor(auto v: path)\n\t\t\t//\t\t\tstd::cerr << v << std::endl;\n\t\t\t//\t\tstd::cerr << \"for \" << ex->begin() << std::endl;\n\t\t\tuse = ex->iterator_from_path(path, ex->begin());\n\t\t\t//\t\tstd::cerr << \"which is \" << use << std::endl;\n\t\t\t}\n\t\telse {\n\t\t\tuse = en.it;\n\t\t\t}\n\n\t\tEx::iterator top = val->begin();\n\t\tif (*top->name == \"\")\n\t\t\ttop = val->begin(top);\n\n\t\tex->replace_index(use, top, true);\n\t\t}\n\n\tsize_t Ex_len(Ex_ptr ex)\n\t\t{\n\t\tEx::iterator it = ex->begin();\n\n\t\treturn ex->number_of_children(it);\n\t\t}\n\n\tlong Ex_int_cast(Ex_ptr ex)\n\t\t{\n\t\treturn ex->to_integer(); // this will throw an exception if the object is not integer\n\t\t}\n\n\tstd::string Ex_head(Ex_ptr ex)\n\t\t{\n\t\tif (ex->begin() == ex->end())\n\t\t\tthrow ArgumentException(\"Expression is empty, no head.\");\n\t\treturn *ex->begin()->name;\n\t\t}\n\n\tpybind11::object Ex_get_mult(Ex_ptr ex)\n\t\t{\n\t\tif (ex->begin() == ex->end())\n\t\t\tthrow ArgumentException(\"Expression is empty, no head.\");\n\t\tauto m = *ex->begin()->multiplier;\n\t\t//\treturn mpq(2,3);\n\n\t\tif(m.is_rational()) {\n\t\t\tpybind11::object mpq = pybind11::module::import(\"gmpy2\").attr(\"mpq\");\n\t\t\tpybind11::object mult = mpq(m.get_rational().get_num().get_si(), m.get_rational().get_den().get_si());\n\t\t\treturn mult;\n\t\t\t}\n\t\telse return pybind11::cast(m.get_double());\n\t\t}\n\n\tpybind11::list terms(Ex_ptr ex)\n\t\t{\n\t\tEx::iterator it = ex->begin();\n\n\t\tif (*it->name != \"\\\\sum\")\n\t\t\tthrow ArgumentException(\"terms() expected a sum expression.\");\n\n\t\tpybind11::list ret;\n\n\t\tauto sib = ex->begin(it);\n\t\twhile (sib != ex->end(it)) {\n\t\t\tret.append(Ex(sib));\n\t\t\t++sib;\n\t\t\t}\n\n\t\treturn ret;\n\t\t}\n\n\tstd::shared_ptr<sympy::SympyBridge> SympyBridge_init(std::shared_ptr<Ex> ex)\n\t\t{\n\t\tauto sb = std::make_shared<sympy::SympyBridge>(*get_kernel_from_scope(), ex);\n\t\treturn sb;\n\t\t}\n\n\tEx_ptr Ex_from_string(const std::string& ex_, bool, Kernel *kernel)\n\t\t{\n\t\tif (kernel == nullptr)\n\t\t\tkernel = get_kernel_from_scope();\n\n\t\tauto ptr = std::make_shared<Ex>();\n\t\t// Parse the string expression.\n\t\tParser parser(ptr);\n\t\tstd::stringstream str(ex_);\n\n\t\ttry {\n\t\t\tstr >> parser;\n\t\t\t}\n\t\tcatch (std::exception& except) {\n\t\t\tfor(size_t i=0; i<ex_.size(); ++i)\n\t\t\t\tstd::cerr << static_cast<int>(static_cast<uint8_t>(ex_[i])) << \" \";\n\t\t\tstd::cerr << std::endl;\n\t\t\tthrow ParseException(std::string(\"Cannot parse: \")+except.what());\n\t\t\t}\n\t\tparser.finalise();\n\n\t\t// First pull in any expressions referred to with @(...) notation, because the\n\t\t// full expression may not have consistent indices otherwise.\n\t\tpull_in(ptr, kernel);\n\t\t//\tstd::cerr << \"pulled in\" << std::endl;\n\n\t\t// Basic cleanup of rationals and subtractions, followed by\n\t\t// cleanup of nested sums and products.\n\t\tpre_clean_dispatch_deep(*kernel, *ptr);\n\t\tcleanup_dispatch_deep(*kernel, *ptr);\n\t\tcheck_index_consistency(*kernel, *ptr, (*ptr).begin());\n\t\tcall_post_process(*kernel, ptr);\n\t\t//\tstd::cerr << \"cleaned up\" << std::endl;\n\n\t\t// Now run all embedded python functions.\n\t\trun_python_functions(ptr, kernel);\n\n\t\treturn ptr;\n\t\t}\n\n\tEx_ptr Ex_from_int(int num, bool)\n\t\t{\n\t\tauto ptr = std::make_shared<Ex>(num);\n\t\treturn ptr;\n\t\t}\n\n\tEx_ptr Ex_from_float(double num, bool)\n\t\t{\n\t\tauto ptr = std::make_shared<Ex>(num);\n\t\treturn ptr;\n\t\t}\n\n\tvoid call_post_process(Kernel& kernel, Ex_ptr ex)\n\t\t{\n\t\t// Find the 'post_process' function, and if found, turn off\n\t\t// post-processing, then call the function on the current Ex.\n\t\tif (post_process_enabled) {\n\t\t\tif (ex->number_of_children(ex->begin()) == 0)\n\t\t\t\treturn;\n\n\t\t\tpost_process_enabled = false;\n\t\t\tpybind11::object post_process;\n\n\t\t\tauto locals = get_locals();\n\t\t\tif (scope_has(locals, \"post_process\")) {\n\t\t\t\tpost_process = locals[\"post_process\"];\n\t\t\t\t}\n\t\t\telse {\n\t\t\t\tauto globals = get_globals();\n\t\t\t\tif (scope_has(globals, \"post_process\"))\n\t\t\t\t\tpost_process = globals[\"post_process\"];\n\t\t\t\t}\n\t\t\tif (post_process) {\n\t\t\t\t// std::cerr << \"calling post-process\" << std::endl;\n\t\t\t\tpost_process(std::ref(kernel), ex);\n\t\t\t\t}\n\t\t\tpost_process_enabled = true;\n\t\t\t}\n\t\t}\n\n\tvoid Ex_cleanup(Ex_ptr ex)\n\t{\n\t\tKernel* kernel = get_kernel_from_scope();\n\t\tpre_clean_dispatch_deep(*kernel, *ex);\n\t\tcleanup_dispatch_deep(*kernel, *ex);\n\t\tcheck_index_consistency(*kernel, *ex, (*ex).begin());\n\t\tcall_post_process(*kernel, ex);\n\t}\n\n\tEx_ptr map_sympy_wrapper(Ex_ptr ex, std::string head, pybind11::args args)\n\t\t{\n\t\tstd::vector<std::string> av;\n\t\tfor (auto& arg : args)\n\t\t\tav.push_back(arg.cast<std::string>());\n\t\treturn apply_algo_preorder<map_sympy, std::string, std::vector<std::string>>(ex, head, av, false, false, 0);\n\t\t}\n\n\tvoid init_ex(py::module& m)\n\t\t{\n\t\tpybind11::enum_<str_node::parent_rel_t>(m, \"parent_rel_t\")\n\t\t.value(\"sub\", str_node::parent_rel_t::p_sub)\n\t\t.value(\"super\", str_node::parent_rel_t::p_super)\n\t\t.value(\"none\", str_node::parent_rel_t::p_none)\n\t\t.export_values()\n\t\t;\n\n\t\tpybind11::enum_<Ex_comparator::match_t>(m, \"match_t\")\n\t\t\t.value(\"node_match\", Ex_comparator::match_t::node_match)\n\t\t\t.value(\"subtree_match\", Ex_comparator::match_t::subtree_match)\n\t\t\t.value(\"match_index_less\", Ex_comparator::match_t::match_index_less)\n\t\t\t.value(\"match_index_greater\", Ex_comparator::match_t::match_index_greater)\n\t\t\t.value(\"no_match_indexpos_less\", Ex_comparator::match_t::no_match_indexpos_less)\n\t\t\t.value(\"no_match_indexpos_greater\", Ex_comparator::match_t::no_match_indexpos_greater)\n\t\t\t.value(\"no_match_less\", Ex_comparator::match_t::no_match_less)\n\t\t\t.value(\"no_match_greater\", Ex_comparator::match_t::no_match_greater);\n\n\t\tpybind11::class_<Ex, Ex_ptr >(m, \"Ex\", py::buffer_protocol())\n\t\t.def(py::init(&Ex_from_string), py::arg(\"input_form\"), py::arg(\"make_ref\") = true, py::arg(\"kernel\") = nullptr)\n\t\t.def(py::init(&Ex_from_int), py::arg(\"num\"), py::arg(\"make_ref\") = true)\n\t\t.def(py::init(&Ex_from_float), py::arg(\"num\"), py::arg(\"make_ref\") = true)\n\t\t.def(\"__str__\", &Ex_as_str)\n\t\t.def(\"_latex_\", &Ex_as_latex)\n\t\t.def(\"__repr__\", &Ex_as_repr)\n\t\t.def(\"__eq__\", static_cast<bool(*)(Ex_ptr, Ex_ptr)>(&Ex_compare))\n\t\t.def(\"__eq__\", static_cast<bool(*)(Ex_ptr, int)>(&Ex_compare))\n\t\t.def(\"_sympy_\", &Ex_as_sympy)\n\t\t.def(\"sympy_form\", &Ex_as_sympy_string)\n\t\t.def(\"mma_form\", &Ex_as_MMA, pybind11::arg(\"unicode\") = true)    // standardize on this\n\t\t.def(\"input_form\", &Ex_as_input)\n\t\t.def(\"__getitem__\", &Ex_getitem)\n\t\t.def(\"__getitem__\", &Ex_getitem_string)\n\t\t.def(\"__getitem__\", &Ex_getitem_iterator)\n\t\t.def(\"__getitem__\", &Ex_getslice)\n\t\t.def(\"__setitem__\", &Ex_setitem)\n\t\t.def(\"__setitem__\", &Ex_setitem_iterator)\n\t\t.def(\"__len__\", &Ex_len)\n\t\t.def(\"__int__\", &Ex_int_cast)\n\t\t.def(\"head\", &Ex_head)\n\t\t.def(\"mult\", &Ex_get_mult)\n\t\t.def(\"__iter__\", &Ex_iter)\n\t\t.def(\"top\", &Ex_top)\n\t\t.def(\"matches\", &Ex_matches)\n\t\t.def(\"matches\", &Ex_matches_Ex)\n\t\t.def(\"state\", &Ex::state)\n\t\t.def(\"reset\", &Ex::reset_state)\n\t\t.def(\"copy\", [](const Ex& ex) { return std::make_shared<Ex>(ex); })\n\t\t.def(\"changed\", &Ex::changed_state)\n\t\t.def(\"cleanup\", &Ex_cleanup)\n\t\t.def(\"__array__\", [](Ex& ex) {\n\t\t\tif(std::holds_alternative<std::shared_ptr<NTensor>>(ex.begin()->content)) {\n\t\t\t\tstd::shared_ptr<NTensor> ntp = std::get<std::shared_ptr<NTensor>>(ex.begin()->content);\n            py::object py_ntensor = py::cast(*ntp);\n\n\t\t\t\tif(!py::isinstance<py::buffer>(py_ntensor)) {\n\t\t\t\t\tthrow std::runtime_error(\"NTensor does not implement buffer protocol\");\n\t\t\t\t\t}\n\t\t\t\t\n\t\t\t\tpy::buffer  py_buffer  = py_ntensor.cast<py::buffer>();\n\t\t\t\tpy::module_ np = py::module_::import(\"numpy\");\n            \n            // Create a numpy array view of the buffer (no copy)\n            py::object array = np.attr(\"asarray\")(py_ntensor);\n\t\t\t\treturn array;\n \t\t\t\t}\n\t\t\telse {\n\t\t\t\tthrow ConsistencyException(\"Expression cannot be converted to numerical array.\");\n\t\t\t\t}\n\t\t\t})\n//\t\t.def_buffer([](Ex &ex) -> py::buffer_info {\n//\t\t\tthrow std::runtime_error(\"Help?\");\n//\t\t\t})\n//\t\t.def(\"__floordiv__\", [](const Ex& self, py::function func) {\n//\t\t\t   Ex expr_copy(self);\n//            py::object result = func(expr_copy);\n//            return result.cast<Ex>();\n//\t\t\t})\n\t\t.def(\"__hash__\", [](const Ex& ex) { return ex.calc_hash(ex.begin()); })\n\t\t.def(\"__add__\", static_cast<Ex_ptr(*)(const Ex_ptr, const ExNode)>(&Ex_add), py::is_operator{})\n\t\t.def(\"__add__\", static_cast<Ex_ptr(*)(const Ex_ptr, const Ex_ptr)>(&Ex_add), py::is_operator{})\n\t\t.def(\"__sub__\", static_cast<Ex_ptr(*)(const Ex_ptr, const ExNode)>(&Ex_sub), py::is_operator{})\n\t\t.def(\"__sub__\", static_cast<Ex_ptr(*)(const Ex_ptr, const Ex_ptr)>(&Ex_sub), py::is_operator{})\n\t\t.def(\"__mul__\", static_cast<Ex_ptr(*)(const Ex_ptr, const Ex_ptr)>(&Ex_mul), py::is_operator{})\n\t\t\t.def(py::pickle(\n\t\t\t[](const Ex_ptr& ex) { return py::make_tuple(Ex_as_input(ex)); },\n\t\t\t[](py::tuple t) { return Ex_from_string(t[0].cast<std::string>(), true, get_kernel_from_scope()); }\n\t\t));\n\n\t\tpybind11::class_<ExNode>(m, \"ExNode\", \"Iterator over elements of an Ex mathematical expression.\", py::buffer_protocol())\n\t\t\t.def(\"__iter__\", &ExNode::iter)\n\t\t\t.def(\"__next__\", &ExNode::next, pybind11::return_value_policy::reference_internal)\n\t\t\t.def(\"input_form\",  &ExNode::input_form)\n\t\t\t.def(\"__getitem__\", &ExNode::getitem_string)\n\t\t\t.def(\"__getitem__\", &ExNode::getitem_iterator)\n\t\t\t.def(\"__setitem__\", &ExNode::setitem_string)\n\t\t\t.def(\"__setitem__\", &ExNode::setitem_iterator)\n\t\t\t.def(\"_latex_\", &ExNode::_latex_)\n\t\t\t.def(\"__str__\", &ExNode::__str__)\n\t\t\t.def(\"_sympy_\", &ExNode_as_sympy)\n\t\t\t.def(\"terms\", &ExNode::terms, \"Return an ExNode iterator over all terms at the level of the current ExNode.\")\n\t\t\t.def(\"components\", &ExNode::components, \"Returns an ExNode iterator over all components of the tensor at the given ExNode.\")\n\t\t\t.def(\"factors\", &ExNode::factors, \"Return an ExNode iterator over all factors at the level of the current ExNode.\")\n\t\t\t.def(\"own_indices\", &ExNode::own_indices, \"Return an ExNode iterator over all indices which are not inherited from child nodes.\")\n\t\t\t.def(\"indices\", &ExNode::indices, \"Return an ExNode iterator over all indices.\")\n\t\t\t.def(\"free_indices\", &ExNode::free_indices, \"Return an ExNode iterator over all free indices.\")\n\t\t\t.def(\"args\", &ExNode::args)\n\t\t\t.def(\"children\", &ExNode::children)\n\t\t\t.def(\"replace\", &ExNode::replace, \"Replace the node pointed to by ExNode with the given Ex.\")\n\t\t\t.def(\"insert\", &ExNode::insert, \"Insert the given Ex in front of the node pointed to by the ExNode.\")\n\t\t\t.def(\"insert\", &ExNode::insert_it, \"Insert the node pointed to by the given ExNode in front of the ExNode.\")\n\t\t\t.def(\"append_child\", &ExNode::append_child, \"Append the given Ex as a child of the node pointed to by the ExNode.\")\n\t\t\t.def(\"append_child\", &ExNode::append_child_it, \"Append the node pointed to by the given ExNode as a child of the node pointed to by the ExNode.\")\n\t\t\t.def(\"erase\", &ExNode::erase, \"Erase the node pointed to by the ExNode.\")\n\t\t\t.def(\"ex\", &ExNode::get_ex, \"Obtain a copy of the node pointed to by the ExNode.\")\n\t\t\t.def(\"compare\", &ExNode_compare,\n\t\t\t\tpy::arg(\"other\"), py::arg(\"use_props\") = \"always\", py::arg(\"ignore_parent_rel\") = false)\n\t\t\t.def_property(\"name\", &ExNode::get_name, &ExNode::set_name, \"Set the name property of the node pointed to by the ExNode.\")\n\t\t\t.def_property(\"parent_rel\", &ExNode::get_parent_rel, &ExNode::set_parent_rel)\n\t\t\t.def_property(\"multiplier\", &ExNode_get_multiplier, &ExNode_set_multiplier)\n\t\t\t.def_buffer([](ExNode &exnode) -> py::buffer_info {\n\t\t\t\tthrow std::range_error(\"Do not call this on ExNode\");\n\t\t\t\t})\n\t\t\t.def(\"__add__\", [](ExNode a, Ex_ptr b) {\n\t\t\t\t\t\t\t\t return a.add_ex(b);\n\t\t\t\t\t\t\t\t }, pybind11::is_operator{});\n\n\t\tpybind11::class_<sympy::SympyBridge, std::shared_ptr<sympy::SympyBridge> >(m, \"SympyBridge\")\n\t\t.def(py::init(&SympyBridge_init))\n\t\t.def(\"to_sympy\", &sympy::SympyBridge::export_ex)\n\t\t.def(\"from_sympy\", &sympy::SympyBridge::import_ex)\n//\t\t.def(\"from_sympy_new\", &sympy::SympyBridge::import_ex_new)\t\t\t\n//\t\t.def(\"from_sympy_new\", &sympy::SympyBridge::import_ex_new)\n\t\t;\n\n\t\tm.def(\"join\", [](const Ex_ptr ex1, const Ex_ptr ex2, py::args args) {\n\t\t\tstd::vector<Ex_ptr> ex = {ex1, ex2};\n        \tfor (const auto& arg : args) {\n\t\t\t\tex.push_back(arg.cast<Ex_ptr>());\n\t\t\t\t}\n        \treturn Ex_join(ex);\n    \t\t});\n\n\t\tm.def(\"tree\", &print_tree);\n\n\t\tm.def(\"function_domain\", &cadabra::function_domain);\n\t\t\n\t\tm.def(\"map_sympy\", &map_sympy_wrapper,\n\t\t      pybind11::arg(\"ex\"),\n\t\t      pybind11::arg(\"function\") = \"\",\n\t\t      pybind11::return_value_policy::reference_internal);\n#ifdef MATHEMATICA_FOUND\n\t\tdef_algo<map_mma, std::string>(m, \"map_mma\", false, false, 0, pybind11::arg(\"function\") = \"\");\n#endif\n\n\t\tm.def(\"terms\", &terms);\n\n\t\tm.def(\"lhs\", &lhs);\n\t\tm.def(\"rhs\", &rhs);\n\n\t\t}\n\n\t}\n"
  },
  {
    "path": "core/pythoncdb/py_ex.hh",
    "content": "#pragma once\n\n#include <memory>\n\n#include \"../Storage.hh\"\n#include \"../ExNode.hh\"\n\nnamespace cadabra {\n\tusing Ex_ptr = std::shared_ptr<Ex>;\n\n\t/// \\ingroup pythoncore\n\t///\n\t/// Comparison operator for Ex objects in Python. Since comparison operators\n\t/// need a Properties object, we cannot have such operator== things in C++,\n\t/// but we can in Python since we can get the kernel in the current scope.\n\tbool Ex_compare(Ex_ptr, Ex_ptr);\n\tbool Ex_compare(Ex_ptr, int);\n\n\t/// \\ingroup pythoncore\n\t///\n\t/// Add two expressions, adding a top-level '\\sum' node if required.\n\n\tEx_ptr Ex_add(const Ex_ptr ex1, const ExNode ex2);\n\tEx_ptr Ex_add(const Ex_ptr ex1, const Ex_ptr ex2);\n\tEx_ptr Ex_add(const Ex_ptr ex1, const Ex_ptr ex2, Ex::iterator top2);\n\n\t/// \\ingroup pythoncore\n\t///\n\t/// Multiply two expressions, adding a top-level '\\prod' node if required.\n\tEx_ptr Ex_mul(const Ex_ptr ex1, const Ex_ptr ex2);\n\tEx_ptr Ex_mul(const Ex_ptr ex1, const Ex_ptr ex2, Ex::iterator top2);\n\n\t/// \\ingroup pythoncore\n\t///\n\t/// Subtract two expressions, adding a top-level '\\sum' node if required.\n\tEx_ptr Ex_sub(const Ex_ptr ex1, const ExNode ex2);\n\tEx_ptr Ex_sub(const Ex_ptr ex1, const Ex_ptr ex2);\n\tEx_ptr Ex_sub(const Ex_ptr ex1, const Ex_ptr ex2, Ex::iterator top2);\n\n\t/// \\ingroup pythoncore\n\t///\n\t/// Fetch an Ex object from the Python side using its Python identifier.\n\tEx_ptr fetch_from_python(const std::string& nm);\n\tEx_ptr fetch_from_python(const std::string& nm, pybind11::object scope);\n\n\t/// \\ingroup pythoncore\n\t///\n\t/// Generate the Python str() and repr() representation of the Ex object.\n\tstd::string Ex_as_str(Ex_ptr);\n\tstd::string Ex_as_repr(Ex_ptr);\n\n\t/// \\ingroup pythoncore\n\t///\n\t/// The Python 'print' function always calls the 'str' member on\n\t/// objects to be printed. This one is required to produce output\n\t/// which looks readable but is also still valid input. In order to\n\t/// produce proper LaTeX output, this is therefore not the right\n\t/// function to use, because Cadabra only reads a restricted subset\n\t/// of LaTeX (for instance, we output spacing commands like '\\,' but\n\t/// do not accept it on input).\n\t/// So we have a separate _latex_() member on each object, which\n\t///internally uses DisplayTeX to do the actual printing.\n\tstd::string Ex_as_latex(Ex_ptr);\n\n\t/// \\ingroup scalar\n\t///\n\t/// Outputs a Cadabra 'Ex' as a Sympy expression. This first converts the\n\t/// Cadabra expression to a string, and then reads that back in by calling\n\t/// sympy.parsing.sympy_parser.parse_expr. Is mapped to a '_sympy_()'\n\t/// function on each Ex object.\n\t/// When you feed an Ex object to a Sympy function, the Ex gets converted\n\t/// to a Sympy object in 'sympy.sympify' because the latter attempts to\n\t/// call __sympy__ on every object that you feed it.\n\tpybind11::object Ex_as_sympy(Ex_ptr);\n\n\t/// Similar to Ex_to_Sympy, but only producing a string which can be parsed\n\t/// by Sympy, instead of a full-fledged Sympy expression.\n\tstd::string Ex_as_sympy_string(Ex_ptr);\n\n\tstd::string Ex_as_input(Ex_ptr ex);\n\n\tstd::string Ex_as_MMA(Ex_ptr ex, bool use_unicode);\n\n\tstd::string Ex_as_tree(Ex *ex);\n\n\tcadabra::Ex lhs(Ex_ptr ex);\n\tcadabra::Ex rhs(Ex_ptr ex);\n\n\tEx Ex_getslice(Ex_ptr ex, pybind11::slice slice);\n\tEx Ex_getitem(Ex &ex, int index);\n\tvoid Ex_setitem(Ex_ptr ex, int index, Ex val);\n\tvoid Ex_setitem_iterator(Ex_ptr ex, ExNode en, Ex_ptr val);\n\tsize_t Ex_len(Ex_ptr ex);\n\tstd::string Ex_head(Ex_ptr ex);\n\tpybind11::object Ex_get_mult(Ex_ptr ex);\n\n\t// Split a 'sum' expression into its individual terms.\n\t// FIXME: now deprecated because we have operator[]?\n\tpybind11::list terms(Ex_ptr ex);\n\n\tEx_ptr Ex_from_string(const std::string& in, bool make_ref = true, Kernel * kernel = nullptr);\n\tEx_ptr Ex_from_int(int num, bool make_ref = true);\n\n\tEx_ptr map_sympy_wrapper(Ex_ptr ex, std::string head, pybind11::args args);\n#ifdef MATHEMATICA_FOUND\n\tEx_ptr map_mma_wrapper(Ex_ptr ex, std::string head);\n#endif\n\n\tvoid call_post_process(Kernel& kernel, Ex_ptr ex);\n\n\tvoid init_ex(pybind11::module& m);\n\t}\n"
  },
  {
    "path": "core/pythoncdb/py_globals.cc",
    "content": "#include \"py_globals.hh\"\n\nnamespace cadabra {\n\tbool post_process_enabled = true;\n\n\t}"
  },
  {
    "path": "core/pythoncdb/py_globals.hh",
    "content": "#pragma once\n\nnamespace cadabra {\n\textern bool post_process_enabled;\n\t}\n"
  },
  {
    "path": "core/pythoncdb/py_helpers.cc",
    "content": "#include \"../Config.hh\"\n#include \"../InstallPrefix.hh\"\n#include <fstream>\n#include \"py_helpers.hh\"\n#include <pybind11/embed.h>\n#include \"nlohmann/json.hpp\"\n#include <filesystem>\n#include <iostream>\n#include <regex>\n#include \"Kernel.hh\"\n\nnamespace py = pybind11;\n\nnamespace cadabra {\n\n\tpy::object get_locals()\n\t\t{\n\t\treturn py::reinterpret_borrow<py::object>(PyEval_GetLocals());\n\t\t}\n\n\tpy::object get_globals()\n\t\t{\n\t\treturn py::globals();\n\t\t}\n\n\tbool scope_has(const py::dict& dict, const std::string& obj)\n\t\t{\n\t\tfor (const auto& item : dict) {\n\t\t\tif (item.first.cast<std::string>() == obj) {\n\t\t\t\treturn true;\n\t\t\t\t}\n\t\t\t}\n\t\treturn false;\n\t\t}\n\n\t// The `install_prefix` function of `InstallPrefix.cc` will return the\n\t// installation prefix of the python interpreter when we run `cadabra2`\n\t// (the python script) or just import the cadabra2 module from a python\n\t// session. That is typically *not* where the manual pages are installed;\n\t// those are installed relative to the location of the cadabra2 module,\n\t// not relative to the python interpreter. We can get this location using\n\t// a bit of Python.\n\t\n\tstd::string install_prefix_of_module()\n\t\t{\n\t\tstatic std::string spath;\n\n\t\tif(spath==\"\") {\n\t\t\t// We have an empty helper module 'cdb.main' which we import\n\t\t\t// to figure out the location, as the __file__ attribute will\n\t\t\t// contain that after successful import.\n\t\t\tpy::module_ cdb = py::module_::import(\"cdb.main\");\n\t\t\tpy::object  result = cdb.attr(\"__file__\");\n\t\t\tstd::string tmp = result.cast<std::string>();\n\t\t\tauto dpath = std::filesystem::path(tmp).parent_path().parent_path();\n\t\t\tif(!std::filesystem::is_regular_file(dpath / \"cadabra2_defaults.py\")) {\n\t\t\t\tthrow std::logic_error(\"The cadabra2 binary module is in \"\n\t\t\t\t\t\t\t\t\t\t\t  +dpath.string()\n\t\t\t\t\t\t\t\t\t\t\t  +\" but the initialisation file 'cadabra2_defaults.py' is not there;\"\n\t\t\t\t\t\t\t\t\t\t\t  +\" giving up.\");\n\t\t\t\t}\n\t\t\tspath = dpath.string();\n\t\t\t}  \t\t\n\t\treturn spath;\n\t\t}\n\n\tstd::string read_manual(pybind11::module& m, const char* category, const char* name)\n\t\t{\n\t\t// If the module is installed in\n\t\t//\n\t\t//    /usr/local/lib/pythonX.YY/dist-packages/\n\t\t//\n\t\t// (which is `install_prefix_of_module()`) or\n\t\t//\n\t\t//    /usr/local/lib/pythonX.YY/site-packages/\n\t\t//\n\t\t// the manual pages can be found at\n\t\t//\n\t\t//    /usr/local/share/cadabra2/manual/\n\t\t\n\t\tstd::string manual_page = install_prefix_of_module()\n\t\t\t+ \"/../../../share/cadabra2/manual/\" + category + \"/\" + name + \".cnb\";\n\t\tstd::ifstream ifs(manual_page);\n\t\ttry {\n\t\t\tnlohmann::json root=nlohmann::json::parse(ifs);\n\t\t\tstd::string ret = (*root[\"cells\"].begin())[\"source\"].get<std::string>();\n\t\t\tret = std::regex_replace(ret, std::regex(R\"(\\\\algorithm\\{(.*)\\}\\{(.*)\\})\"), \"$2\");\n\t\t\tret = std::regex_replace(ret, std::regex(R\"(\\\\property\\{(.*)\\}\\{(.*)\\})\"), \"$2\");\n\t\t\tret = std::regex_replace(ret, std::regex(R\"(\\\\algo\\{([^\\}]*)\\})\"), \"$1\");\n\t\t\tret = std::regex_replace(ret, std::regex(R\"(\\\\prop\\{([^\\}]*)\\})\"), \"$1\");\n\t\t\tret = std::regex_replace(ret, std::regex(R\"(\\\\available\\{(.*)\\})\"), \"(available since: $1)\");\n\t\t\tret += \"\\n\\nFor more information see https://cadabra.science/manual/\"+std::string(name)+\".html\";\n\t\t\treturn ret;\n\t\t\t}\n\t\tcatch(nlohmann::json::exception& ex) {\n\t\t\treturn \"Failed to collect help information; no info at \"+manual_page+\".\";\n\t\t\t}\n\t\t}\n\n\t}\n"
  },
  {
    "path": "core/pythoncdb/py_helpers.hh",
    "content": "#pragma once\n\n#include <pybind11/pybind11.h>\n#include <memory>\n\nnamespace cadabra {\n\n\tpybind11::object get_locals();\n\tpybind11::object get_globals();\n\n\t/// Get the installation prefix of the binary cadabra2 module,\n\t/// typically something like `/usr/lib/pythonX.YY/site-packages/`.\n\tstd::string install_prefix_of_module();\n\n\t/// Determine whether the given python scope contains a variable\n\t/// with the given name.\n\tbool scope_has(const pybind11::dict& dict, const std::string& obj);\n\n\t/// Return the manual page for the category (\"property\"/\"algorithm\")\n\t/// and given name.\n\tstd::string read_manual(pybind11::module& m, const char* category, const char* name);\n\n}\n"
  },
  {
    "path": "core/pythoncdb/py_kernel.cc",
    "content": "#include \"properties/Distributable.hh\"\n#include \"properties/IndexInherit.hh\"\n#include \"properties/CommutingAsProduct.hh\"\n#include \"properties/DependsInherit.hh\"\n#include \"properties/NumericalFlat.hh\"\n#include \"properties/WeightInherit.hh\"\n#include \"properties/CommutingAsSum.hh\"\n#include \"properties/Derivative.hh\"\n#include \"properties/Accent.hh\"\n#include \"properties/Tableau.hh\"\n#include \"properties/FilledTableau.hh\"\n\n#include \"CdbPython.hh\"\n\n#include <pybind11/functional.h>\n#include \"py_globals.hh\"\n#include \"py_helpers.hh\"\n#include \"py_kernel.hh\"\n#include \"py_ex.hh\"\n\nnamespace cadabra {\n\tKernel *create_scope()\n\t\t{\n\t\tKernel *k = new Kernel(true);\n\t\treturn k;\n\t\t}\n\n\tKernel *create_scope_from_global()\n\t\t{\n\t\tKernel *k = create_empty_scope();\n\t\t// FIXME: copy global properties\n\t\treturn k;\n\t\t}\n\n\tKernel *create_empty_scope()\n\t\t{\n\t\tKernel *k = new Kernel(false);\n\t\treturn k;\n\t\t}\n\n\tKernel *get_kernel_from_scope()\n\t\t{\n\t\tKernel *kernel = nullptr;\n\n\t\t// Try and find the kernel in the local scope\n\t\tauto locals = get_locals();\n\t\tif (locals && scope_has(locals, \"__cdbkernel__\")) {\n\t\t\tkernel = locals[\"__cdbkernel__\"].cast<Kernel*>();\n\t\t\treturn kernel;\n\t\t\t}\n\n\t\t// No kernel in local scope, find one in global scope.\n\t\tauto globals = get_globals();\n\t\tif (globals && scope_has(globals, \"__cdbkernel__\")) {\n\t\t\tkernel = globals[\"__cdbkernel__\"].cast<Kernel*>();\n\t\t\treturn kernel;\n\t\t\t}\n\n\t\t// No kernel in local or global scope, construct a new global one\n\t\tkernel = create_scope();\n\t\tglobals[\"__cdbkernel__\"] = kernel;\n\t\treturn kernel;\n\t\t}\n\n\tvoid kernel_configure_warnings(Kernel& kernel, pybind11::kwargs kwargs)\n\t\t{\n\t\tif (kwargs) {\n\t\t\tfor (auto item : kwargs) {\n\t\t\t\tauto key = item.first.cast<std::string>();\n\t\t\t\tif (key == \"level\") {\n\t\t\t\t\ttry {\n\t\t\t\t\t\tauto value = item.second.cast<Kernel::warn_t>();\n\t\t\t\t\t\tkernel.warning_level = value;\n\t\t\t\t\t\t}\n\t\t\t\t\tcatch (pybind11::cast_error&) {\n\t\t\t\t\t\tthrow std::invalid_argument(\"named argument 'level' expected an integer\");\n\t\t\t\t\t\t}\n\t\t\t\t\t}\n\t\t\t\telse if (key == \"callback\") {\n\t\t\t\t\ttry {\n\t\t\t\t\t\tif (item.second.is_none()) {\n\t\t\t\t\t\t\tkernel.warning_callback = nullptr;\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\telse {\n\t\t\t\t\t\t\tauto value = item.second.cast<std::function<void(const std::string&)>>();\n\t\t\t\t\t\t\tkernel.warning_callback = value;\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\t}\n\t\t\t\t\tcatch (pybind11::cast_error&) {\n\t\t\t\t\t\tthrow std::invalid_argument(\"named argument 'callback' expected None or function with signature void(const std::string&)\");\n\t\t\t\t\t\t}\n\t\t\t\t\t}\n\t\t\t\telse {\n\t\t\t\t\tthrow std::invalid_argument(\"received unrecognised argument '\" + key + \"'\");\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t}\n\t\t}\n\n\tvoid init_kernel(pybind11::module& m)\n\t\t{\n\t\t// Declare the Kernel object for Python so we can store it in the local Python context.\n\t\t// We add a 'cadabra2.__cdbkernel__' object to the main module scope, and will\n\t\t// pull that into the interpreter scope in the 'cadabra2_default.py' file.\n\t\tpybind11::enum_<Kernel::scalar_backend_t>(m, \"scalar_backend_t\")\n\t\t\t.value(\"sympy\", Kernel::scalar_backend_t::sympy)\n\t\t\t.value(\"mathematica\", Kernel::scalar_backend_t::mathematica)\n\t\t\t.export_values();\n\n\t\tpybind11::enum_<Kernel::warn_t>(m, \"warn_t\")\n\t\t\t.value(\"notset\", Kernel::warn_t::notset)\n\t\t\t.value(\"info\", Kernel::warn_t::info)\n\t\t\t.value(\"debug\", Kernel::warn_t::debug)\n\t\t\t.value(\"warning\", Kernel::warn_t::warning)\n\t\t\t.value(\"error\", Kernel::warn_t::error)\n\t\t\t.value(\"critical\", Kernel::warn_t::critical);\n\n\t\tpybind11::class_<Kernel>(m, \"Kernel\", pybind11::dynamic_attr())\n\t\t\t.def(pybind11::init<bool>())\n\t\t\t.def_readonly_static(\"version\", &Kernel::version)\n\t\t\t.def_readonly_static(\"build\", &Kernel::build)\n\t\t\t.def_readwrite(\"display_fractions\", &Kernel::display_fractions)\n\t\t\t.def_readwrite(\"call_embedded_python_functions\", &Kernel::call_embedded_python_functions)\n\t\t\t.def_readwrite(\"scalar_backend\", &Kernel::scalar_backend)\n\t\t\t.def(\"warn\", &Kernel::warn, pybind11::arg(\"msg\"), pybind11::arg(\"level\") = 0)\n\t\t\t.def(\"configure_warnings\", kernel_configure_warnings);\n\n\t\tpybind11::class_<ConvertData>(m, \"ConvertData\")\n\t\t\t.def(pybind11::init<>())\n\t\t\t.def(pybind11::init<std::string, std::string, std::string, std::string>())\n\t\t\t.def_readwrite(\"lhs\", &ConvertData::lhs)\n\t\t\t.def_readwrite(\"rhs\", &ConvertData::rhs)\n\t\t\t.def_readwrite(\"op\", &ConvertData::op)\t\t\t\n\t\t\t.def_readwrite(\"indent\", &ConvertData::indent);\n\t\t\n\t\tKernel* kernel = create_scope();\n\t\tm.attr(\"__cdbkernel__\") = pybind11::cast(kernel);\n\n\t\tm.def(\"create_scope\", &create_scope,\n\t\t      pybind11::return_value_policy::take_ownership);\n\t\tm.def(\"create_scope_from_global\", &create_scope_from_global,\n\t\t      pybind11::return_value_policy::take_ownership);\n\t\tm.def(\"create_empty_scope\", &create_empty_scope,\n\t\t      pybind11::return_value_policy::take_ownership);\n\n\t\tm.def(\"cdb2python\", &cdb2python);\n\t\tm.def(\"cdb2python_string\", &cdb2python_string);\n\t\tm.def(\"convert_line\", &convert_line);\n\t\t}\n\n\t}\n"
  },
  {
    "path": "core/pythoncdb/py_kernel.hh",
    "content": "#pragma once\n\n#include <pybind11/pybind11.h>\n\n#include \"../Kernel.hh\"\n\nnamespace cadabra {\n\n\t/// \\ingroup pythoncore\n\t///\n\t/// Setup of kernels in current scope, callable from Python.\n\t/// When the decision was made to graft Cadabra onto Python, a choice had\n\t/// to be made about how Python variable scope would influence the\n\t/// visibility of Cadabra properties. It clearly makes sense to be able to\n\t/// declare properties which only hold inside a particular\n\t/// function. However Cadabra expressions and properties do not directly\n\t/// correspond to Python objects. Rather, declaring a property is more\n\t/// like a function call into the Cadabra module, which leaves its imprint\n\t/// on the state of the C++ part but does not change anything on the\n\t/// Python side, as you typically do not assign the created property to a\n\t/// Python symbol. Therefore, properties do not naturally inherit Python's\n\t/// scoping rules (this is different from e.g.~SymPy, in which\n\t///   mathematical objects are always in one-to-one correspondence with a\n\t///   Python object). A more fundamental problem is that properties can be\n\t/// attached to patterns, and those patterns can involve more than just\n\t/// the symbols which one passes into a function.\n\t///\n\t/// In order to not burden the user, properties are therefore by default\n\t/// global variables, stored in a single global Cadabra object\n\t/// `__cdbkernel__` which is initialised at import of the Cadabra module.\n\t/// If you add new properties inside a function scope, these will go\n\t/// into this already existing *global* property list by default.\n\t/// If you want to create a local scope for your computations, create a\n\t/// new `__cdbkernel__` as in\n\t/// ```\n\t/// def fun():\n\t///    __cdbkernel__ = cadabra.create_scope();\n\t///    [your code here]\n\t/// ```\n\t/// Now computations will not see the global properties at all.\n\t/// If you want to import the global properties, use instead\n\t/// ```\n\t/// def fun():\n\t///    __cdbkernel__ = cadabra.create_scope_from_global()\n\t///    [your code here]\n\t/// ```\n\t/// It is crucial that the\n\t/// `__cdbkernel__` symbol is referenced from within Python and visible to the bytecompiler, because\n\t/// it is not possible to create new variables on the local stack at runtime.\n\t/// Internally, the second version above fetches, at runtime, the\n\t/// `__cdbkernel__` from the globals stack, copies all properties in there\n\t/// into a new kernel, and returns the latter.\n\t///\n\t/// Both versions above do populate the newly created kernel with\n\t/// Cadabra's default properties. If you want a completely clean slate\n\t/// (for e.g.~testing purposes, or because you really do not want default\n\t/// rules for sums and products), use\n\t/// ```\n\t/// def fun():\n\t///    __cdbkernel__ = cadabra.create_empty_scope()\n\t///    [your code here]\n\t/// ```\n\t/// Note that in all these cases, changes to properties remain local and\n\t/// do not leak into the global property list.\n\t///\n\t/// All Cadabra algorithms, when called from Python, will first look for a\n\t/// kernel on the locals stack (i.e.~what `locals()` produces). If\n\t/// there is no kernel available locally, they will then revert to using\n\t/// the global kernel.\n\tKernel *create_scope();\n\tKernel *create_scope_from_global();\n\tKernel *create_empty_scope();\n\n\t/// \\ingroup pythoncore\n\t///\n\t/// Get a pointer to the currently visible kernel.\n\tKernel *get_kernel_from_scope();\n\n\n\tvoid init_kernel(pybind11::module& m);\n\n\t}\n"
  },
  {
    "path": "core/pythoncdb/py_media.cc",
    "content": "#include <pybind11/pybind11.h>\n#include \"Media.hh\"\n\nnamespace py = pybind11;\n\nnamespace cadabra {\n\tvoid init_media(py::module& m)\n\t\t{\n   \tpy::class_<LaTeXString>(m, \"LaTeXString\")\n\t\t\t.def(py::init<std::string>())\n\t\t\t.def(\"_latex_\", &LaTeXString::latex)\n\t\t\t.def(\"__str__\", &LaTeXString::latex)\n\t\t\t;\n\t\t}\n}\n"
  },
  {
    "path": "core/pythoncdb/py_media.hh",
    "content": "#pragma once\n\nnamespace cadabra {\n\n\tvoid init_media(pybind11::module& m);\n\n}\n"
  },
  {
    "path": "core/pythoncdb/py_module.cc",
    "content": "#include <pybind11/pybind11.h>\n#include <pybind11/embed.h>\n\n#include \"py_algorithms.hh\"\n#include \"py_ex.hh\"\n#include \"py_kernel.hh\"\n#include \"py_packages.hh\"\n#include \"py_progress.hh\"\n#include \"py_properties.hh\"\n#include \"py_stopwatch.hh\"\n#include \"py_tableau.hh\"\n#include \"py_ntensor.hh\"\n#include \"py_media.hh\"\n#include \"py_helpers.hh\"\n\n#include \"Kernel.hh\"\n\nnamespace cadabra {\n\tnamespace py = pybind11;\n\n\tstd::string init_ipython()\n\t\t{\n\t\tpy::exec(\"from IPython.display import Math\");\n\t\treturn \"Cadabra typeset output for IPython notebook initialised.\";\n\t\t}\n\n\tPYBIND11_MODULE(cadabra2, m)\n\t\t{\n\t\tpy::options options;\n\t\toptions.disable_function_signatures();\n\n//\t\tm.doc() = \"Cadabra symbolic computer algebra\";\n\t\tm.def(\"init_ipython\", &init_ipython);\n\n\t\t// These must be initialized in the order of which\n\t\t// symbols appear\n\t\tinit_packages(m);\n\t\tinit_kernel(m);\n\t\tinit_progress_monitor(m);\n\t\tinit_ntensor(m);\n\t\tinit_media(m);\n\t\tinit_stopwatch(m);\n\t\tinit_ex(m);\n\t\tinit_tableau(m);\n\t\tinit_algorithms(m);\n\t\tinit_properties(m);\n\t\t}\n\n\t}\n"
  },
  {
    "path": "core/pythoncdb/py_ntensor.cc",
    "content": "#include <pybind11/pybind11.h>\n#include \"NTensor.hh\"\n#include <sstream>\n\nnamespace py = pybind11;\n\n// #define DEBUG 1\n\nnamespace cadabra {\n\tvoid init_ntensor(py::module& m) {\n\tpy::class_<NTensor>(m, \"NTensor\", py::buffer_protocol())\n\t\t.def(\"is_real\", &NTensor::is_real)\n\t\t.def(\"__str__\", [](NTensor& nt) {\n\t\t\tstd::ostringstream str;\n\t\t\tstr << nt;\n\t\t\treturn str.str();\n\t\t\t})\n\t\t.def_buffer([](NTensor &nt) -> py::buffer_info {\n\t\t\tif(nt.is_real()) {\n\t\t\t\tsize_t stride=sizeof(std::complex<double>);\n\t\t\t\tstd::vector<size_t> strides(nt.shape.size(), 0);\n\t\t\t\tfor(size_t i=0; i<nt.shape.size(); i++) {\n\t\t\t\t\tstrides[nt.shape.size()-1-i] = stride;\n\t\t\t\t\tstride *= nt.shape[nt.shape.size()-1-i];\n\t\t\t\t\t}\n#ifdef DEBUG\n\t\t\t\tfor(size_t i=0; i<nt.shape.size(); ++i)\n\t\t\t\t\tstd::cerr << \"shape \" << i << \" = \" << nt.shape[i] << std::endl;\n\t\t\t\tfor(size_t i=0; i<strides.size(); ++i)\n\t\t\t\t\tstd::cerr << \"stride \" << i << \" = \" << strides[i] << std::endl;\n#endif\n\t\t\t\treturn py::buffer_info(\n\t\t\t\t\tnt.values.data(),                         /* Pointer to buffer */\n\t\t\t\t\tsizeof(double),                          /* Size of one scalar */\n\t\t\t\t\t\"d\", /* Python struct-style format descriptor */\n\t\t\t\t\tnt.shape.size(),                          /* Number of dimensions */\n\t\t\t\t\tnt.shape,                                 /* Buffer dimensions */\n\t\t\t\t\tstrides                                  /* Strides (in bytes) for each index */\n\t\t\t\t\t\t\t\t\t\t\t  );\n\t\t\t\t}\n\t\t\telse {\n#ifdef DEBUG\n\t\t\t\t//std::cerr << \"at(10,20) = \" << nt.at({10,20}) << std::endl;\n#endif\n\t\t\t\tsize_t stride=sizeof(std::complex<double>);\n\t\t\t\tstd::vector<size_t> strides(nt.shape.size(), 0);\n\t\t\t\tfor(size_t i=0; i<nt.shape.size(); i++) {\n\t\t\t\t\tstrides[nt.shape.size()-1-i] = stride;\n\t\t\t\t\tstride *= nt.shape[nt.shape.size()-1-i];\n\t\t\t\t\t}\n#ifdef DEBUG\n\t\t\t\tfor(size_t i=0; i<nt.shape.size(); ++i)\n\t\t\t\t\tstd::cerr << \"shape \" << i << \" = \" << nt.shape[i] << std::endl;\n\t\t\t\tfor(size_t i=0; i<strides.size(); ++i)\n\t\t\t\t\tstd::cerr << \"stride \" << i << \" = \" << strides[i] << std::endl;\n#endif\n\t\t\t\treturn py::buffer_info(\n\t\t\t\t\tnt.values.data(),                         /* Pointer to buffer */\n\t\t\t\t\tsizeof(std::complex<double>),                          /* Size of one scalar */\n\t\t\t\t\t\"Zd\", /* Python struct-style format descriptor */\n\t\t\t\t\tnt.shape.size(),                          /* Number of dimensions */\n\t\t\t\t\tnt.shape,                                 /* Buffer dimensions */\n\t\t\t\t\tstrides                                  /* Strides (in bytes) for each index */\n\t\t\t\t\t\t\t\t\t\t\t  );\n\t\t\t\t}\n\t\t\t});\n\t}\n}\n"
  },
  {
    "path": "core/pythoncdb/py_ntensor.hh",
    "content": "#pragma once\n\nnamespace cadabra {\n\n\tvoid init_ntensor(pybind11::module& m);\n\n}\n"
  },
  {
    "path": "core/pythoncdb/py_packages.cc",
    "content": "#include <fstream>\n#include <ctime>\n#include \"../CdbPython.hh\"\n\n#include \"py_packages.hh\"\n\nnamespace cadabra {\n\n\n\tvoid compile_package(const std::string& in_name, const std::string& out_name)\n\t\t{\n\t\t// Get current time info\n\t\t//\t\tstd::time_t t = std::time(nullptr);\n\t\t//\t\tstd::tm tm = *std::localtime(&t);\n\n\t\t// Only compile if the notebook is newer than the compiled package\n\t\tstruct stat f1, f2;\n\t\tif (stat(in_name.c_str(), &f1) == 0 && stat(out_name.c_str(), &f2) == 0 && f1.st_mtime < f2.st_mtime)\n\t\t\treturn;\n\n\t\tstd::string pystr;\n\t\tif(in_name.size()>3 && in_name.substr(in_name.size()-4)==\".cdb\")\n\t\t\tpystr = cadabra::cdb2python(in_name, false);\n\t\telse\n\t\t\tpystr = cadabra::cnb2python(in_name, false);\n\t\t\n\t\tif (pystr != \"\") {\n\t\t\tstd::ofstream ofs(out_name);\n\t\t\t//\t\tstd::ofstream ofs(name+\".py\");\n\t\t\tofs << pystr;\n\t\t\t}\n\t\t}\n\n\n\tvoid init_packages(pybind11::module& m)\n\t\t{\n\t\tm.def(\"compile_package__\", &compile_package);\n\t\t}\n\n\t}\n"
  },
  {
    "path": "core/pythoncdb/py_packages.hh",
    "content": "#pragma once\n\n#include <string>\n#include <pybind11/pybind11.h>\n\nnamespace cadabra {\n\t/// \\ingroup files\n\t///\n\t/// Convert a Cadabra notebook file to a python package which can be imported\n\t/// using standard 'import' notation. Doing this will ignore all cells\n\t/// which are labelled `ignore_on_import`.\n\n\tvoid compile_package(const std::string& in_name, const std::string& out_name);\n\n\tvoid init_packages(pybind11::module& m);\n\t}\n"
  },
  {
    "path": "core/pythoncdb/py_progress.cc",
    "content": "#include <iostream>\n\n#include \"py_progress.hh\"\n#include \"py_helpers.hh\"\n\nnamespace cadabra {\n\tnamespace py = pybind11;\n\n\tpy::list ProgressMonitor_totals_helper(ProgressMonitor& self)\n\t\t{\n\t\tpy::list list;\n\t\tauto totals = self.totals();\n\t\tfor (auto& total : totals)\n\t\t\tlist.append(total);\n\t\treturn list;\n\t\t}\n\n\tProgressMonitor *get_progress_monitor()\n\t\t{\n\t\ttry {\n\t\t\tpybind11::dict globals = get_globals();\n\t\t\tProgressMonitor* pm;\n\t\t\tif (scope_has(globals, \"__cdb_progress_monitor__\")) {\n\t\t\t\tpm = globals[\"__cdb_progress_monitor__\"].cast<ProgressMonitor*>();\n\t\t\t\t}\n\t\t\telse {\n\t\t\t\tif (scope_has(globals, \"server\") && py::hasattr(globals[\"server\"], \"send_progress_update\")) {\n\t\t\t\t\tpm = new ProgressMonitor(globals[\"server\"].attr(\"send_progress_update\"));\n\t\t\t\t}\n\t\t\t\telse\n\t\t\t\t\tpm = new ProgressMonitor();\n\t\t\t\tglobals[\"__cdb_progress_monitor__\"] = pm;\n\t\t\t\t}\n\t\t\treturn pm;\n\t\t\t}\n\t\tcatch (pybind11::error_already_set& ex) {\n\t\t\tstd::cerr << \"*!?!?\" << ex.what() << std::endl;\n\t\t\treturn nullptr;\n\t\t\t}\n\t\t}\n\n\n\tvoid init_progress_monitor(py::module& m)\n\t\t{\n\t\tpy::class_<ProgressMonitor>(m, \"ProgressMonitor\")\n\t\t.def(\"print\", &ProgressMonitor::print)\n\t\t.def(\"totals\", &ProgressMonitor_totals_helper);\n\n\t\tpybind11::class_<ProgressMonitor::Total>(m, \"Total\")\n\t\t.def_readonly(\"name\", &ProgressMonitor::Total::name)\n\t\t.def_readonly(\"call_count\", &ProgressMonitor::Total::call_count)\n\t\t.def_readonly(\"total_steps\", &ProgressMonitor::Total::total_steps)\n\t\t.def(\"__str__\", &ProgressMonitor::Total::str);\n\n\t\t}\n\n\t}\n"
  },
  {
    "path": "core/pythoncdb/py_progress.hh",
    "content": "#pragma once\n\n#include <pybind11/pybind11.h>\n\n#include \"../ProgressMonitor.hh\"\n\nnamespace cadabra {\n\n\tpybind11::list ProgressMonitor_totals_helper(ProgressMonitor& self);\n\tProgressMonitor *get_progress_monitor();\n\n\tvoid init_progress_monitor(pybind11::module& m);\n\n\t}\n"
  },
  {
    "path": "core/pythoncdb/py_properties.cc",
    "content": "#include \"py_properties.hh\"\n#include \"py_kernel.hh\"\n#include \"py_helpers.hh\"\n\n#include \"properties/Accent.hh\"\n#include \"properties/AntiCommuting.hh\"\n#include \"properties/AntiSymmetric.hh\"\n#include \"properties/Commuting.hh\"\n#include \"properties/Coordinate.hh\"\n#include \"properties/Depends.hh\"\n#include \"properties/DependsInherit.hh\"\n#include \"properties/Derivative.hh\"\n#include \"properties/DerivativeOp.hh\"\n#include \"properties/Determinant.hh\"\n#include \"properties/Diagonal.hh\"\n#include \"properties/DifferentialForm.hh\"\n#include \"properties/DiracBar.hh\"\n#include \"properties/GammaMatrix.hh\"\n#include \"properties/CommutingAsProduct.hh\"\n#include \"properties/CommutingAsSum.hh\"\n#include \"properties/DAntiSymmetric.hh\"\n#include \"properties/Diagonal.hh\"\n#include \"properties/Distributable.hh\"\n#include \"properties/EpsilonTensor.hh\"\n#include \"properties/ExteriorDerivative.hh\"\n#include \"properties/FilledTableau.hh\"\n#include \"properties/ImaginaryI.hh\"\n#include \"properties/ImplicitIndex.hh\"\n#include \"properties/Indices.hh\"\n#include \"properties/IndexInherit.hh\"\n#include \"properties/Integer.hh\"\n#include \"properties/InverseMetric.hh\"\n#include \"properties/KroneckerDelta.hh\"\n#include \"properties/LaTeXForm.hh\"\n#include \"properties/Matrix.hh\"\n#include \"properties/Metric.hh\"\n#include \"properties/NonCommuting.hh\"\n#include \"properties/NumericalFlat.hh\"\n#include \"properties/PartialDerivative.hh\"\n#include \"properties/RiemannTensor.hh\"\n#include \"properties/SatisfiesBianchi.hh\"\n#include \"properties/SelfAntiCommuting.hh\"\n#include \"properties/SelfCommuting.hh\"\n#include \"properties/SelfNonCommuting.hh\"\n#include \"properties/SortOrder.hh\"\n#include \"properties/Spinor.hh\"\n#include \"properties/Symbol.hh\"\n#include \"properties/Symmetric.hh\"\n#include \"properties/Tableau.hh\"\n#include \"properties/TableauInherit.hh\"\n#include \"properties/TableauSymmetry.hh\"\n#include \"properties/Trace.hh\"\n#include \"properties/Traceless.hh\"\n#include \"properties/Vielbein.hh\"\n#include \"properties/Weight.hh\"\n#include \"properties/WeightInherit.hh\"\n#include \"properties/WeylTensor.hh\"\n\n#include \"DisplayTeX.hh\"\n#include \"DisplayTerminal.hh\"\n#include \"Media.hh\"\n\nnamespace cadabra {\n\tnamespace py = pybind11;\n\n\tBoundPropertyBase::BoundPropertyBase()\n\t\t: prop(nullptr)\n\t\t, for_obj(nullptr)\n\t{\n\n\t}\n\n\tBoundPropertyBase::BoundPropertyBase(const property* prop, Ex_ptr for_obj)\n\t\t: prop(prop)\n\t\t, for_obj(for_obj)\n\t{\n\n\t}\n\n\tBoundPropertyBase::~BoundPropertyBase()\n\t{\n\n\t}\n\n\tstd::string BoundPropertyBase::str_() const\n\t{\n\t\tstd::ostringstream str;\n\t\tstr << \"Property \";\n//\t\tstd::cerr << \"going to print\" << std::endl;\n\t\tprop->latex(str); // FIXME: this should call 'str' on the property, which does not exist yet\n\t\tstr << \" attached to \" + Ex_as_str(for_obj) + \".\";\n\t\treturn str.str();\n\t}\n\n\tstd::string BoundPropertyBase::latex_() const\n\t{\n\t\tstd::ostringstream str;\n\n\t\t//\tHERE: this text should go away, property should just print itself in a python form,\n\t\t//   the decorating text should be printed in a separate place.\n\n\t\tstr << \"\\\\text{Property \";\n\t\tprop->latex(str);\n\t\tstd::string bare = Ex_as_latex(for_obj);\n\n\t\tif (dynamic_cast<const LaTeXForm*>(prop)) {\n\t\t\t// Since the LaTeXForm property has already been attached, the\n\t\t\t// Ex_as_latex call above will replace the original symbol and\n\t\t\t// replace it with the LaTeXForm. But we want to show the original\n\t\t\t// symbol!\n\t\t\tbare = *(for_obj->begin()->name);\n\t\t\tbare = std::regex_replace(bare, std::regex(R\"(#)\"), \"\\\\#\");\n\t\t\tbare = std::regex_replace(bare, std::regex(R\"(\\{)\"), \"\\\\{\");\n\t\t\tbare = std::regex_replace(bare, std::regex(R\"(\\})\"), \"\\\\}\");\n\t\t\tbare = std::regex_replace(bare, std::regex(R\"(\\\\)\"), \"\\\\backslash{}\");\n\t\t\tstr << \" attached to {\\\\texttt{\" + bare + \"}}.}\";\n\t\t}\n\t\telse {\n\t\t\tstr << \" attached to~}\" + bare + \".\";\n\t\t}\n\n\t\treturn str.str();\n\t}\n\n\tstd::string BoundPropertyBase::repr_() const\n\t{\n\t\t// FIXME: this needs work, it does not output things which can be fed back into python.\n\t\treturn \"Property::repr: \" + prop->name();\n\t}\n\n\tKernel& BoundPropertyBase::get_kernel()\n\t{\n\t\treturn *get_kernel_from_scope();\n\t}\n\n\tProperties& BoundPropertyBase::get_props()\n\t{\n\t\treturn get_kernel_from_scope()->properties;\n\t}\n\n\tEx& BoundPropertyBase::get_ex() const\n\t{\n\t\treturn *for_obj;\n\t}\n\n\tEx::iterator BoundPropertyBase::get_it() const\n\t{\n\t\treturn for_obj->begin();\n\t}\n\n\n\ttemplate <typename PropT, typename... ParentTs>\n\tBoundProperty<PropT, ParentTs...>::BoundProperty()\n\t\t: BoundPropertyBase()\n\t{\n\n\t}\n\n\ttemplate <typename PropT, typename... ParentTs>\n\tBoundProperty<PropT, ParentTs...>::BoundProperty(const PropT* prop, Ex_ptr for_obj)\n\t\t: BoundPropertyBase(prop, for_obj)\n\t{\n\n\t}\n\n\ttemplate <typename PropT, typename... ParentTs>\n\tBoundProperty<PropT, ParentTs...>::BoundProperty(Ex_ptr ex, Ex_ptr param)\n\t\t: BoundPropertyBase(nullptr, ex)\n\t{\n\t\tauto new_prop = new cpp_type();\n\t\tget_kernel_from_scope()->inject_property(new_prop, ex, param);\n\t\tBoundPropertyBase::prop = new_prop;\n\t}\n\n\n\ttemplate <typename PropT, typename... ParentTs>\n\tstd::shared_ptr<BoundProperty<PropT, ParentTs...>> BoundProperty<PropT, ParentTs...>::get_from_kernel(Ex::iterator it, const std::string& label, bool ignore_parent_rel)\n\n\t{\n\t\tint tmp;\n\t\tauto res = get_kernel_from_scope()->properties.get_with_pattern<PropT>(\n\t\t\tit, tmp, label, false, ignore_parent_rel);\n\n\t\tif (res.first) {\n\t\t\treturn std::make_shared<BoundProperty<PropT, ParentTs...>>(\n\t\t\t\tres.first,\n\t\t\t\tres.second ? std::make_shared<Ex>(res.second->obj) : nullptr);\n\t\t}\n\t\telse {\n\t\t\treturn nullptr;\n\t\t}\n\t}\n\n\n\ttemplate <typename PropT, typename... ParentTs>\n\tconst PropT* BoundProperty<PropT, ParentTs...>::get_prop() const\n\t{\n\treturn dynamic_cast<const PropT*>(BoundPropertyBase::prop);\n\t}\n\n\ttemplate <typename PropT, typename... ParentTs>\n\tvoid BoundProperty<PropT, ParentTs...>::attach(Ex_ptr obj) const\n\t\t{\n//\t\tstd::cerr << \"Attaching property to \" << obj << std::endl;\n\t\tKernel *kernel = get_kernel_from_scope();\n\t\tProperties& props = kernel->properties;\n\n\t\tconst auto *thisprop = get_prop();\n\t\tthisprop->validate(*kernel, obj);\n\t\tprops.master_insert(*obj, thisprop);\n\t\t}\n\n\ttemplate <typename PropT, typename... ParentTs>\n\tstd::string BoundProperty<PropT, ParentTs...>::str_() const\n\t\t{\n\t\treturn BoundPropertyBase::str_();\n\t\t}\n\n\ttemplate <typename PropT, typename... ParentTs>\n\tstd::string BoundProperty<PropT, ParentTs...>::latex_() const\n\t\t{\n\t\treturn BoundPropertyBase::latex_();\n\t\t}\n\n\ttemplate <typename PropT, typename... ParentTs>\n\tstd::string BoundProperty<PropT, ParentTs...>::repr_() const\n\t\t{\n\t\treturn BoundPropertyBase::str_();\n\t\t}\n\n\ttemplate <typename BoundPropT>\n\ttypename BoundPropT::py_type def_abstract_prop(pybind11::module& m, const std::string& name)\n\t{\n\t\tusing base_type = BoundPropT;\n//\t\tusing cpp_type = typename base_type::cpp_type;\n\t\tusing py_type = typename base_type::py_type;\n\n\t\treturn py_type(m, name.c_str(), py::multiple_inheritance(), read_manual(m, \"properties\", name.c_str()).c_str())\n\t\t\t.def_static(\"get\", [](Ex_ptr ex, const std::string& label, bool ipr) { return base_type::get_from_kernel(ex->begin(), label, ipr); }, py::arg(\"ex\"), py::arg(\"label\") = \"\", py::arg(\"ignore_parent_rel\") = false)\n\t\t\t.def_static(\"get\", [](ExNode node, const std::string& label, bool ipr) { return base_type::get_from_kernel(node.it, label, ipr); }, py::arg(\"exnode\"), py::arg(\"label\") = \"\", py::arg(\"ignore_parent_rel\") = false)\n\t\t\t.def(\"attach\", &BoundPropT::attach)\n\t\t\t.def(\"__str__\", &BoundPropT::str_)\n\t\t\t.def(\"__repr__\", &BoundPropT::repr_)\n\t\t\t.def(\"_latex_\", &BoundPropT::latex_);\n\t}\n\n\ttemplate <typename BoundPropT>\n\ttypename BoundPropT::py_type def_prop(pybind11::module& m)\n\t{\n\t\tusing base_type = BoundPropT;\n\t\tusing cpp_type = typename base_type::cpp_type;\n\t\tusing py_type = typename base_type::py_type;\n\n\t\treturn py_type(m, std::make_shared<cpp_type>()->name().c_str(), py::multiple_inheritance(), read_manual(m, \"properties\", std::make_shared<cpp_type>()->name().c_str()).c_str())\n\t\t\t.def(py::init<Ex_ptr, Ex_ptr>(), py::arg(\"ex\"), py::arg(\"param\")=Ex{})\n\n\t\t\t.def_static(\"get\", [](Ex_ptr ex, const std::string& label, bool ipr) { return base_type::get_from_kernel(ex->begin(), label, ipr); }, py::arg(\"ex\"), py::arg(\"label\") = \"\", py::arg(\"ignore_parent_rel\") = false)\n\t\t\t.def_static(\"get\", [](ExNode node, const std::string& label, bool ipr) { return base_type::get_from_kernel(node.it, label, ipr); }, py::arg(\"exnode\"), py::arg(\"label\") = \"\", py::arg(\"ignore_parent_rel\") = false)\n\t\t\t.def(\"attach\", &BoundPropT::attach)\n\t\t\t.def(\"__str__\", &BoundPropT::str_)\n\t\t\t.def(\"__repr__\", &BoundPropT::repr_)\n\t\t\t.def(\"_latex_\", &BoundPropT::latex_)\n\t\t\t;\n\t}\n\n\n\n\tpybind11::list list_properties()\n\t\t{\n\t\t// This function is fundamentally limited. We would *like* to return a list of\n\t\t// BoundProperties, so that you can do something with the output. But we cannot\n\t\t// walk the full property list and create a BoundProperty for each of them, as\n\t\t// we do not know the type (we can only dynamic_cast).\n\t\t//\n\t\t// So for now this is just returning a list of LaTeXStrings, obtained by asking\n\t\t// each property to print itself.\n\t\t\n\t\tKernel *kernel = get_kernel_from_scope();\n\t\tProperties& props = kernel->properties;\n\n\t\tpybind11::dict globals = get_globals();\n\t\tbool handles_latex_view = globals[\"server\"].attr(\"handles\")(pybind11::str(\"latex_view\")).cast<bool>();\n\t\t\n\t\tpybind11::list ret;\n\t\tstd::string res;\n\t\tbool multi = false;\n\t\tfor (auto it = props.pats.begin(); it != props.pats.end(); ++it) {\n\t\t\tif (it->first->hidden()) continue;\n\t\t\t\n\t\t\t// print the property name if we are at the end or if the next entry is for\n\t\t\t// a different property.\n\t\t\tdecltype(it) nxt = it;\n\t\t\t++nxt;\n\t\t\tif (res == \"\" && (nxt != props.pats.end() && it->first == nxt->first)) {\n\t\t\t\tif(handles_latex_view) res += \"\\\\{\";\n\t\t\t\telse                   res += \"{\";\n\t\t\t\tmulti = true;\n\t\t\t\t}\n\t\t\t\n\t\t\tstd::ostringstream str;\n\t\t\tif(handles_latex_view) {\n\t\t\t\tDisplayTeX dt(*get_kernel_from_scope(), it->second->obj);\n\t\t\t\tdt.output(str);\n\t\t\t\t}\n\t\t\telse {\n\t\t\t\tDisplayTerminal dt(*get_kernel_from_scope(), it->second->obj);\n\t\t\t\tdt.output(str);\n\t\t\t\t}\n\t\t\t\n\t\t\tres += str.str();\n\t\t\t\n\t\t\tif (nxt == props.pats.end() || it->first != nxt->first) {\n\t\t\t\tif (multi) {\n\t\t\t\t\tif(handles_latex_view) res += \"\\\\}\";\n\t\t\t\t\telse                   res += \"}\";\n\t\t\t\t\t}\n\t\t\t\tmulti = false;\n\t\t\t\tres += \"::\\\\texttt{\";\n\t\t\t\tres += (*it).first->name() + \"}\";\n\t\t\t\tret.append(LaTeXString(res));\n\t\t\t\tres = \"\";\n\t\t\t\t}\n\t\t\telse {\n\t\t\t\tres += \", \";\n\t\t\t\t}\n\t\t\t}\n\t\t\n\t\treturn ret;\n\t\t}\n\n\tstd::vector<Ex> indices_get_all(const Indices* indices, bool include_wildcards)\n\t{\n\t\tauto kernel = get_kernel_from_scope();\n\t\tauto its = kernel->properties.pats.equal_range(indices);\n\n\t\tstd::vector<Ex> res;\n\t\tfor (auto it = its.first; it != its.second; ++it) {\n\t\t\tif (it->second->obj.begin()->is_autodeclare_wildcard() && !include_wildcards)\n\t\t\t\tcontinue;\n\t\t\tres.push_back(it->second->obj);\n\t\t}\n\n\t\treturn res;\n\t}\n\n\tEx indices_get_dummy(const Indices* indices, const Ex_ptr& ex)\n\t{\n\t\tIndexClassifier ic(*get_kernel_from_scope());\n\t\treturn ic.get_dummy(indices, ex->begin());\n\t}\n\n\tvoid init_properties(py::module& m)\n\t\t{\n\n\t\tm.def(\"properties\", &list_properties);\n\n\t\tpy::class_<BoundPropertyBase, std::shared_ptr<BoundPropertyBase>>(m, \"Property\")\n\t\t\t.def_property_readonly(\"for_obj\", &BoundPropertyBase::get_ex);\n\n\n\t\t// Abstract base types = these are visible in Python but cannot be injected into the Kernel\n\t\tusing Py_list_property = BoundProperty<list_property, BoundPropertyBase>;\n\t\tusing Py_labelled_property = BoundProperty<labelled_property, BoundPropertyBase>;\n\t\tusing Py_CommutingBehaviour = BoundProperty<CommutingBehaviour, BoundPropertyBase>;\n\t\tusing Py_SelfCommutingBehaviour = BoundProperty<SelfCommutingBehaviour, BoundPropertyBase>;\n\t\tusing Py_TableauBase = BoundProperty<TableauBase, BoundPropertyBase>;\n\t\tusing Py_DependsBase = BoundProperty<DependsBase, BoundPropertyBase>;\n\t\tusing Py_WeightBase = BoundProperty<WeightBase, Py_labelled_property>;\n\t\tusing Py_DifferentialFormBase = BoundProperty<DifferentialFormBase, BoundPropertyBase>;\n\n\t\tdef_abstract_prop<Py_list_property>(m, \"list_property\");\n\t\tdef_abstract_prop<Py_labelled_property>(m, \"labelled_property\")\n\t\t\t.def_property_readonly(\"label\", [](const Py_labelled_property & p) { return p.get_prop()->label; });\n\t\tdef_abstract_prop<Py_CommutingBehaviour>(m, \"CommutingBehaviour\")\n\t\t\t.def(\"sign\", [](const Py_CommutingBehaviour & p) { return p.get_prop()->sign(); });\n\t\tdef_abstract_prop<Py_SelfCommutingBehaviour>(m, \"SelfCommutingBehaviour\")\n\t\t\t.def(\"sign\", [](const Py_SelfCommutingBehaviour & p) { return p.get_prop()->sign(); });\n\t\tdef_abstract_prop<Py_TableauBase>(m, \"TableauBase\")\n\t\t\t.def(\"size\", [](const Py_TableauBase & p) { return p.get_prop()->size(p.get_props(), p.get_ex(), p.get_it()); })\n\t\t\t.def(\"get_tab\", [](const Py_TableauBase & p, unsigned int num) { return p.get_prop()->get_tab(p.get_props(), p.get_ex(), p.get_it(), num); })\n\t\t\t.def(\"only_column_exchange\", [](const Py_TableauBase & p) { return p.get_prop()->only_column_exchange(); })\n\t\t\t.def(\"get_indexgroup\", [](const Py_TableauBase & p, int group) { return p.get_prop()->get_indexgroup(p.get_props(), p.get_ex(), p.get_it(), group); })\n\t\t\t.def(\"is_simple_symmetry\", [](const Py_TableauBase & p) { return p.get_prop()->is_simple_symmetry(p.get_props(), p.get_ex(), p.get_it()); });\n\t\tdef_abstract_prop<Py_DependsBase>(m, \"DependsBase\")\n\t\t\t.def(\"dependencies\", [](const Py_DependsBase & p) { return p.get_prop()->dependencies(p.get_kernel(), p.get_it()); });\n\t\tdef_abstract_prop<Py_WeightBase>(m, \"WeightBase\")\n\t\t\t.def(\"value\", [](const Py_WeightBase & p, const std::string& forcedLabel) {\n\t\t\t\tauto m = p.get_prop()->value(p.get_kernel(), p.get_it(), forcedLabel);\n\t\t\t\tif(m.is_rational()) {\n\t\t\t\t\t// This is mpq_class, convert to the Python equivalent.\n\t\t\t\t\tpybind11::object mpq = pybind11::module::import(\"gmpy2\").attr(\"mpq\");\n\t\t\t\t\tpybind11::object mult = mpq(m.get_rational().get_num().get_si(), m.get_rational().get_den().get_si());\n\t\t\t\t\treturn mult;\n\t\t\t\t\t}\n\t\t\t\telse return pybind11::cast(m.get_double());\n\t\t\t\t});\n\n\t\tdef_abstract_prop<Py_DifferentialFormBase>(m, \"DifferentialFormBase\")\n\t\t\t.def(\"degree\", [](const Py_DifferentialFormBase & p) { return p.get_prop()->degree(p.get_props(), p.get_it()); });\n\n\n\t\t// Base types - inherit only from BoundPropertyBase, list_property or labelled_property\n\t\tusing Py_IndexInherit = BoundProperty<IndexInherit, BoundPropertyBase>;\n\t\tusing Py_NumericalFlat = BoundProperty<NumericalFlat, BoundPropertyBase>;\n\t\tusing Py_Traceless = BoundProperty<Traceless, BoundPropertyBase>;\n\t\tusing Py_Coordinate = BoundProperty<Coordinate, BoundPropertyBase>;\n\t\tusing Py_CommutingAsProduct = BoundProperty<CommutingAsProduct, BoundPropertyBase>;\n\t\tusing Py_CommutingAsSum = BoundProperty<CommutingAsSum, BoundPropertyBase>;\n\t\tusing Py_Distributable = BoundProperty<Distributable, BoundPropertyBase>;\n\t\tusing Py_Determinant = BoundProperty<Determinant, BoundPropertyBase>;\n\t\tusing Py_DerivativeOp = BoundProperty<DerivativeOp, BoundPropertyBase>;\n\t\tusing Py_FilledTableau = BoundProperty<FilledTableau, BoundPropertyBase>;\n\t\tusing Py_ImplicitIndex = BoundProperty<ImplicitIndex, BoundPropertyBase>;\n\t\tusing Py_ImaginaryI = BoundProperty<ImaginaryI, BoundPropertyBase>;\n\t\tusing Py_Indices = BoundProperty<Indices, Py_list_property>;\n\t\tusing Py_Integer = BoundProperty<Integer, BoundPropertyBase>;\n\t\tusing Py_LaTeXForm = BoundProperty<LaTeXForm, BoundPropertyBase>;\n\t\tusing Py_SortOrder = BoundProperty<SortOrder, Py_list_property>;\n\t\tusing Py_Symbol = BoundProperty<Symbol, BoundPropertyBase>;\n\t\tusing Py_Tableau = BoundProperty<Tableau, BoundPropertyBase>;\n\t\tusing Py_TableauInherit = BoundProperty<TableauInherit, BoundPropertyBase>;\n\t\tusing Py_Vielbein = BoundProperty<Vielbein, BoundPropertyBase>;\n\t\tusing Py_InverseVielbein = BoundProperty<InverseVielbein, BoundPropertyBase>;\n\n\t\tdef_prop<Py_IndexInherit>(m);\n\t\tdef_prop<Py_NumericalFlat>(m);\n\t\tdef_prop<Py_Traceless>(m);\n\t\tdef_prop<Py_Coordinate>(m);\n\t\tdef_prop<Py_CommutingAsProduct>(m);\n\t\tdef_prop<Py_CommutingAsSum>(m);\n\t\tdef_prop<Py_Distributable>(m);\n\t\tdef_prop<Py_Determinant>(m)\n\t\t\t.def_property_readonly(\"obj\", [](const Py_Determinant & p) { return p.get_prop()->obj; });\n\t\tdef_prop<Py_DerivativeOp>(m);\n\t\tdef_prop<Py_FilledTableau>(m)\n\t\t\t.def_property_readonly(\"dimension\", [](const Py_FilledTableau & p) { return p.get_prop()->dimension; });\n\t\tdef_prop<Py_ImplicitIndex>(m)\n\t\t\t.def_property_readonly(\"explicit_form\", [](const Py_ImplicitIndex & p) { return p.get_prop()->explicit_form; });\n\t\tdef_prop<Py_ImaginaryI>(m);\n\t\tauto py_indices = def_prop<Py_Indices>(m)\n\t\t\t.def(\"get_indices\", [](const Py_Indices& p, bool wc) { return indices_get_all(p.get_prop(), wc); },\n\t\t\t\t  py::arg(\"include_wildcards\") = false)\n\t\t\t.def(\"get_dummy\", [](const Py_Indices& p, const Ex_ptr& ex) { return indices_get_dummy(p.get_prop(), ex);})\n\t\t\t.def_property_readonly(\"set_name\", [](const Py_Indices & p) { return p.get_prop()->set_name; })\n\t\t\t.def_property_readonly(\"parent_name\", [](const Py_Indices & p) { return p.get_prop()->parent_name; });\n//\t\t\t.def_property_readonly(\"values\", [](const Py_Indices & p) { return p.get_prop()->values(); });\n\t\tdef_prop<Py_Integer>(m)\n\t\t\t.def_property_readonly(\"from\", [](const Py_Integer & p) { return p.get_prop()->from; })\n\t\t\t.def_property_readonly(\"to\", [](const Py_Integer & p) { return p.get_prop()->to; })\n\t\t\t.def_property_readonly(\"difference\", [](const Py_Integer & p) { return p.get_prop()->difference; });\n\t\tdef_prop<Py_LaTeXForm>(m)\n\t\t\t.def(\"latex_form\", [](const Py_LaTeXForm & p) { return p.get_prop()->latex_form(); });\n\t\tdef_prop<Py_SortOrder>(m);\n\t\tdef_prop<Py_Symbol>(m);\n\t\tdef_prop<Py_Tableau>(m)\n\t\t\t.def_property_readonly(\"dimension\", [](const Py_Tableau & p) { return p.get_prop()->dimension; });\n\t\tdef_prop<Py_TableauInherit>(m);\n\t\tdef_prop<Py_Vielbein>(m);\n\t\tdef_prop<Py_InverseVielbein>(m);\n\n\t\tpy::enum_<Indices::position_t>(py_indices, \"position_t\", \"How to interpret the sub/super-script position of the indices.\")\n\t\t\t.value(\"free\", Indices::free,   \"Index positions are arbitrary.\")\n\t\t\t.value(\"fixed\", Indices::fixed, \"Index positions are fixed, but can be changed by canonicalisation.\")\n\t\t\t.value(\"independent\", Indices::independent, \"Index positions are independent and should never change.\")\n\t\t\t.export_values();\n\n\n\t\t// Derived types\n\t\tusing Py_Accent = BoundProperty<Accent, Py_IndexInherit, Py_NumericalFlat>;\n\t\tusing Py_AntiCommuting = BoundProperty<AntiCommuting, Py_CommutingBehaviour>;\n\t\tusing Py_Commuting = BoundProperty<Commuting, Py_CommutingBehaviour>;\n\t\tusing Py_AntiSymmetric = BoundProperty<AntiSymmetric, Py_TableauBase, Py_Traceless>;\n\t\tusing Py_DAntiSymmetric = BoundProperty<DAntiSymmetric, Py_TableauBase>;\n\t\tusing Py_Depends = BoundProperty<Depends, Py_DependsBase>;\n\t\tusing Py_Derivative = BoundProperty<Derivative, Py_IndexInherit, Py_CommutingAsProduct, Py_SelfCommutingBehaviour, Py_NumericalFlat, Py_TableauBase, Py_Distributable, Py_WeightBase>;\n\t\tusing Py_Symmetric = BoundProperty<Symmetric, Py_TableauBase>;\n\t\tusing Py_DifferentialForm = BoundProperty<DifferentialForm, Py_IndexInherit, Py_DifferentialFormBase>;\n\t\tusing Py_DiracBar = BoundProperty<DiracBar, Py_Accent, Py_Distributable>;\n\t\tusing Py_EpsilonTensor = BoundProperty<EpsilonTensor, Py_AntiSymmetric>;\n\t\tusing Py_ExteriorDerivative = BoundProperty<ExteriorDerivative, Py_Derivative, Py_DifferentialFormBase>;\n\t\tusing Py_Matrix = BoundProperty<Matrix, Py_ImplicitIndex>;\n\t\tusing Py_GammaMatrix = BoundProperty<GammaMatrix, Py_AntiSymmetric, Py_Matrix>;\n\t\tusing Py_TableauSymmetry = BoundProperty<TableauSymmetry, Py_TableauBase>;\n\t\tusing Py_InverseMetric = BoundProperty<InverseMetric, Py_TableauSymmetry>;\n\t\tusing Py_KroneckerDelta = BoundProperty<KroneckerDelta, Py_TableauBase>;\n\t\tusing Py_Metric = BoundProperty<Metric, Py_Symmetric>;\n\t\tusing Py_NonCommuting = BoundProperty<NonCommuting, Py_CommutingBehaviour>;\n\t\tusing Py_PartialDerivative = BoundProperty<PartialDerivative, Py_Derivative>;\n\t\tusing Py_RiemannTensor = BoundProperty<RiemannTensor, Py_TableauSymmetry>;\n\t\tusing Py_SatisfiesBianchi = BoundProperty<SatisfiesBianchi, Py_TableauBase>;\n\t\tusing Py_SelfAntiCommuting = BoundProperty<SelfAntiCommuting, Py_SelfCommutingBehaviour>;\n\t\tusing Py_SelfCommuting = BoundProperty<SelfCommuting, Py_SelfCommutingBehaviour>;\n\t\tusing Py_SelfNonCommuting = BoundProperty<SelfNonCommuting, Py_SelfCommutingBehaviour>;\n\t\tusing Py_Spinor = BoundProperty<Spinor, Py_ImplicitIndex>;\n\t\tusing Py_Trace = BoundProperty<Trace, Py_Distributable>;\n\t\tusing Py_Weight = BoundProperty<Weight, Py_WeightBase>;\n\t\tusing Py_WeightInherit = BoundProperty<WeightInherit, Py_WeightBase>;\n\t\tusing Py_WeylTensor = BoundProperty<WeylTensor, Py_TableauSymmetry, Py_Traceless>;\n\n\t\tdef_prop<Py_Accent>(m);\n\t\tdef_prop<Py_AntiCommuting>(m);\n\t\tdef_prop<Py_Commuting>(m);\n\t\tdef_prop<Py_AntiSymmetric>(m);\n\t\tdef_prop<Py_DAntiSymmetric>(m);\n\t\tdef_prop<Py_Depends>(m);\n\t\tdef_prop<Py_Derivative>(m);\n\t\tdef_prop<Py_Symmetric>(m);\n\t\tdef_prop<Py_DifferentialForm>(m);\n\t\tdef_prop<Py_DiracBar>(m);\n\t\tdef_prop<Py_EpsilonTensor>(m)\n\t\t\t.def_property_readonly(\"metric\", [](const Py_EpsilonTensor& p) { return p.get_prop()->metric; })\n\t\t\t.def_property_readonly(\"krdelta\", [](const Py_EpsilonTensor& p) { return p.get_prop()->krdelta; });\n\t\tdef_prop<Py_ExteriorDerivative>(m);\n\t\tdef_prop<Py_Matrix>(m);\n\t\tdef_prop<Py_GammaMatrix>(m)\n\t\t\t.def_property_readonly(\"metric\", [](const Py_GammaMatrix& p) { return p.get_prop()->metric; });\n\t\tdef_prop<Py_TableauSymmetry>(m);\n\t\tdef_prop<Py_InverseMetric>(m)\n\t\t\t.def_property_readonly(\"signature\", [](const Py_InverseMetric& p) { return p.get_prop()->signature; });\n\t\tdef_prop<Py_KroneckerDelta>(m);\n\t\tdef_prop<Py_Metric>(m)\n\t\t\t.def_property_readonly(\"signature\", [](const Py_Metric& p) { return p.get_prop()->signature; });;\n\t\tdef_prop<Py_NonCommuting>(m);\n\t\tdef_prop<Py_PartialDerivative>(m);\n\t\tdef_prop<Py_RiemannTensor>(m);\n\t\tdef_prop<Py_SatisfiesBianchi>(m);\n\t\tdef_prop<Py_SelfAntiCommuting>(m);\n\t\tdef_prop<Py_SelfCommuting>(m);\n\t\tdef_prop<Py_SelfNonCommuting>(m);\n\n\t\tusing Py_Diagonal = BoundProperty<Diagonal, Py_Symmetric>;\n\t\tdef_prop<Py_Diagonal>(m);\n\n\n\t\tauto py_spinor = def_prop<Py_Spinor>(m)\n\t\t\t.def_property_readonly(\"dimension\", [](const Py_Spinor& p) { return p.get_prop()->dimension; })\n\t\t\t.def_property_readonly(\"weyl\", [](const Py_Spinor& p) { return p.get_prop()->weyl; })\n\t\t\t.def_property_readonly(\"chirality\", [](const Py_Spinor& p) { return p.get_prop()->chirality; })\n\t\t\t.def_property_readonly(\"majorana\", [](const Py_Spinor& p) { return p.get_prop()->majorana; });\n\t\tdef_prop<Py_Trace>(m)\n\t\t\t.def_property_readonly(\"obj\", [](const Py_Trace& p) { return p.get_prop()->obj; })\n\t\t\t.def_property_readonly(\"index_set_name\", [](const Py_Trace& p) { return p.get_prop()->index_set_name; });\n\t\tdef_prop<Py_Weight>(m);\n\t\tauto py_weight_inherit = def_prop<Py_WeightInherit>(m)\n\t\t\t.def(\"combination_type\", [](const Py_WeightInherit& p) { return p.get_prop()->combination_type; });\n\t\tdef_prop<Py_WeylTensor>(m);\n\n\t\tpy::enum_<Spinor::Chirality>(py_spinor, \"Chirality\")\n\t\t\t.value(\"positive\", Spinor::positive)\n\t\t\t.value(\"negative\", Spinor::negative)\n\t\t\t.export_values();\n\n\t\tpy::enum_<WeightInherit::CombinationType>(py_weight_inherit, \"CombinationType\")\n\t\t\t.value(\"multiplicative\", WeightInherit::multiplicative)\n\t\t\t.value(\"additive\", WeightInherit::additive)\n\t\t\t.value(\"power\", WeightInherit::power)\n\t\t\t.export_values();\n\n\n\t\t}\n\t}\n"
  },
  {
    "path": "core/pythoncdb/py_properties.hh",
    "content": "#pragma once\n\n#include <string>\n#include <tuple>\n#include <sstream>\n#include <regex>\n#include <memory>\n#include <pybind11/pybind11.h>\n#include <pybind11/stl.h>\n#include \"py_ex.hh\"\n#include \"py_kernel.hh\"\n#include \"py_tableau.hh\"\n#include \"properties/LaTeXForm.hh\"\n\nnamespace cadabra {\n\tclass BoundPropertyBase\n\t\t: public std::enable_shared_from_this<BoundPropertyBase>\n\t{\n\tpublic:\n\t\tBoundPropertyBase();\n\t\tBoundPropertyBase(const property* prop, Ex_ptr for_obj);\n\t\tvirtual ~BoundPropertyBase();\n\n\t\t/// Human-readable form in text, i.e. no special formatting.\n\t\tstd::string str_() const;\n\t\t/// Human-readable form using LaTeX markup.\n\t\tstd::string latex_() const;\n\t\t/// Python-parseable form. FIXME: not correct right now.\n\t\tstd::string repr_() const;\n\n\t\tstatic Kernel& get_kernel();\n\t\tstatic Properties& get_props();\n\t\tEx& get_ex() const;\n\t\tEx::iterator get_it() const;\n\n\t\t// We keep a pointer to the C++ property, so it is possible to\n\t\t// query properties using the Python interface. However, this C++\n\t\t// object is owned by the C++ kernel and does not get destroyed\n\t\t// when the Python object goes out of scope.\n\t\tconst property* prop;\n\n\t\t// We also keep a shared pointer to the expression for which we\n\t\t// have defined this property, so that we can print sensible\n\t\t// information.\n\t\tEx_ptr for_obj;\n\t};\n\n\n\ttemplate <typename PropT, typename... ParentTs>\n\tclass BoundProperty\n\t\t: virtual public ParentTs...\n\t{\n\t\tpublic:\n\t\t\tusing cpp_type = PropT;\n\t\t\tusing py_type = pybind11::class_<BoundProperty, std::shared_ptr<BoundProperty>, ParentTs...>;\n\n\t\t\t// Default construct with null pointers\n\t\t\tBoundProperty();\n\t\t\t// Construct new property from expression and argument list\n\t\t\tBoundProperty(Ex_ptr ex, Ex_ptr param);\n\t\t\t// Construct from existing cpp property object\n\t\t\tBoundProperty(const PropT* prop, Ex_ptr for_obj);\n\n\t\t\t/// Human-readable form in text, i.e. no special formatting.\n\t\t\tstd::string str_() const;\n\t\t\t/// Human-readable form using LaTeX markup.\n\t\t\tstd::string latex_() const;\n\t\t\t/// Python-parseable form. FIXME: not correct right now.\n\t\t\tstd::string repr_() const;\n\t\t\t/// Attach this property to a different symbol.\n\t\t\tvoid attach(Ex_ptr ex) const;\n\t\t\t\n\t\t\t// Get existing cpp property by querying kernel\n\t\t\tstatic std::shared_ptr<BoundProperty> get_from_kernel(Ex::iterator ex, const std::string& label, bool ignore_parent_rel);\n\n\t\t\t// Return type is not the same as BoundPropertyBase, but this is ok\n\t\t\t// by the standard as cpp_type* is convertible to property*\n\t\t\tconst cpp_type* get_prop() const;\n\t\t};\n\n\ttemplate <typename PropT> std::string get_name();\n\n\ttemplate <typename BoundPropT> typename BoundPropT::py_type def_abstract_prop(pybind11::module& m);\n\ttemplate <typename BoundPropT> typename BoundPropT::py_type def_prop(pybind11::module& m);\n\n\tpybind11::list list_properties();\n\n\tvoid init_properties(pybind11::module& m);\n\n\t}\n"
  },
  {
    "path": "core/pythoncdb/py_stopwatch.cc",
    "content": "#include <sstream>\n#include \"../Stopwatch.hh\"\n\n#include \"py_stopwatch.hh\"\n\nnamespace cadabra {\n\tnamespace py = pybind11;\n\n\tvoid init_stopwatch(py::module& m)\n\t\t{\n\t\tpybind11::class_<Stopwatch>(m, \"Stopwatch\")\n\t\t.def(pybind11::init<>())\n\t\t.def(\"start\", &Stopwatch::start)\n\t\t.def(\"stop\", &Stopwatch::stop)\n\t\t.def(\"reset\", &Stopwatch::reset)\n\t\t.def(\"seconds\", &Stopwatch::seconds)\n\t\t.def(\"useconds\", &Stopwatch::useconds)\n\t\t.def(\"__str__\", [](const Stopwatch& s) {\n\t\t\tstd::stringstream ss;\n\t\t\tss << s;\n\t\t\treturn ss.str();\n\t\t\t});\n\t\t}\n\t}"
  },
  {
    "path": "core/pythoncdb/py_stopwatch.hh",
    "content": "#pragma once\n\n#include <pybind11/pybind11.h>\n\nnamespace cadabra {\n\tvoid init_stopwatch(pybind11::module& m);\n\t}\n"
  },
  {
    "path": "core/pythoncdb/py_tableau.cc",
    "content": "#include <sstream>\n#include \"py_tableau.hh\"\n#include \"../YoungTab.hh\"\n#include \"../properties/TableauBase.hh\"\nnamespace cadabra {\n\n\tnamespace py = pybind11;\n\tusing tab_t = TableauBase::tab_t;\n\n\tstd::string tab_str(const tab_t& tab)\n\t{\n\t\tstd::stringstream ss;\n\t\tss << \"( \";\n\t\tfor (size_t row = 0; row < tab.number_of_rows(); ++row) {\n\t\t\tss << \"(\";\n\t\t\tauto beg = tab.begin_row(row), next = std::next(tab.begin_row(row)), end = tab.end_row(row);\n\t\t\twhile (next != end) {\n\t\t\t\tss << *beg << \" \";\n\t\t\t\t++beg, ++next;\n\t\t\t}\n\t\t\tss << *beg << \") \";\n\t\t}\n\t\tss << \")\";\n\t\treturn ss.str();\n\t}\n\n\tvoid init_tableau(pybind11::module& m)\n\t{\n\t\tauto py_tab = py::class_<tab_t>(m, \"TableauObserver\")\n\t\t              .def(\"number_of_rows\", &tab_t::number_of_rows)\n\t\t              .def(\"row_size\", &tab_t::row_size)\n\t\t              .def(\"find\", &tab_t::find)\n\t\t              .def(\"__getitem__\", &tab_t::operator[])\n\t\t              .def(\"compare_without_multiplicity\", &tab_t::compare_without_multiplicity)\n\t\t              .def(\"has_nullifying_trace\", &tab_t::has_nullifying_trace)\n\t\t              .def(\"nonstandard_loc\", &tab_t::nonstandard_loc)\n\t\t.def(\"__iter__\", [](const tab_t & tab) {\n\t\t\treturn py::make_iterator(tab.begin(), tab.end());\n\t\t})\n\t\t.def(\"row\", [](const tab_t & tab, unsigned int row) {\n\t\t\treturn py::make_iterator(tab.begin_row(row), tab.end_row(row));\n\t\t})\n\t\t.def(\"column\", [](const tab_t & tab, unsigned int col) {\n\t\t\treturn py::make_iterator(tab.begin_column(col), tab.end_column(col));\n\t\t})\n\t\t.def(\"__str__\", &tab_str);\n\t}\n\n}\n"
  },
  {
    "path": "core/pythoncdb/py_tableau.hh",
    "content": "#pragma once\n\n#include <pybind11/pybind11.h>\n\nnamespace cadabra {\n\tvoid init_tableau(pybind11::module& m);\n}\n"
  },
  {
    "path": "core/test_benchmark.cc",
    "content": "\n#include \"Storage.hh\"\n#include \"NTensor.hh\"\n#include \"ExNode.hh\"\n#include <iostream>\n\nint main(int, char **)\n\t{\n\tstd::cerr << \"sizeof(str_node) = \" << sizeof(cadabra::str_node) << std::endl;\n\tstd::cerr << \"sizeof(NTensor)  = \" << sizeof(cadabra::NTensor) << std::endl;\n\tstd::cerr << \"sizeof(ExNode)   = \" << sizeof(ExNode) << std::endl;\n\tstd::cerr << \"sizeof(std::shared_ptr<NTensor>) = \" << sizeof(std::shared_ptr<cadabra::NTensor>) << std::endl;\n\tstd::cerr << \"sizeof(nset_t::iterator)         = \" << sizeof(cadabra::nset_t::iterator) << std::endl;\n\tstd::cerr << \"sizeof(multiplier_t)             = \" << sizeof(cadabra::multiplier_t) << std::endl;\n\tstd::cerr << \"sizeof(tree_node_<str_node>)     = \" << sizeof(tree_node_<cadabra::str_node>) << std::endl;\n\tstd::cerr << \"sizeof(variant<double, multiplier> = \" << sizeof(std::variant<double, cadabra::multiplier_t>) << std::endl;\n\t}\n"
  },
  {
    "path": "core/test_compile_command.py",
    "content": "import codeop\n\nstr1=\"\"\"for i in range(1000):\n   if i!=0:\n      sleep(0.001)\n   out=display(i+1, cell_id=out)\"\"\"\n\nstr2=\"\"\"for i in range(1000):\n   if i!=0:\n      sleep(0.001)\n   out=display(i+1, cell_id=out)\nend=time()\"\"\"\n\nprint(''.join(str2.rsplit('\\n', 1)[:-1]))\n\nres=codeop.compile_command(str1)\nprint(\"1 ok\", res)\nres=codeop.compile_command(str2)\nprint(\"2 ok\", res)\n"
  },
  {
    "path": "core/test_internals.cc",
    "content": "\n#include <catch2/catch_test_macros.hpp>\n\n#include \"Storage.hh\"\n#include \"Compare.hh\"\n#include \"Grouping.hh\"\n#include \"Kernel.hh\"\n\nusing namespace cadabra;\n\nTEST_CASE( \"C++: Ex equality\", \"[ex1]\" )\n\t{\n\tEx ex1(\"y\");\n\tEx ex2(\"y\");\n\t\n\tREQUIRE( ex1 == ex2 );\n\t}\n\nTEST_CASE(\"C++: Ex comparison\", \"[ex2]\")\n\t{\n\tEx ex1(\"y\");\n\tEx ex2(\"y\");\n\n\tstd::map<Ex, int, tree_exact_less_no_wildcards_obj> mp;\n\tmp[ex1]=3;\n\tmp[ex2]=4;\n\n\tREQUIRE( mp.size() == 1 );\n\t}\n\nTEST_CASE(\"C++: Ex grouping\", \"[group1]\")\n\t{\n\tKernel kernel(true);\n\tauto ex  = kernel.ex_from_string(\"{ A_{m n}, B_{m n}, A_{m n}, C_{m n}, B_{m n} }\");\n\tauto grp = group_by_equivalence(*ex, ex->begin());\n\t\n\tREQUIRE( grp.size() == 2 );\n\tREQUIRE( grp[ex->child(ex->begin(), 2)].second == ex->child(ex->begin(), 0) );\n\tREQUIRE( grp[ex->child(ex->begin(), 4)].second == ex->child(ex->begin(), 1) );\n\t}\n\nTEST_CASE(\"C++: advanced Ex grouping\", \"[group2]\")\n\t{\n\tKernel kernel(true);\n\n\tequiv_fun_t component_equiv = [](const Ex& ex, Ex::iterator it1, Ex::iterator it2) {\n\t\tit1 = ex.child(it1, 1);\n\t\tit2 = ex.child(it2, 1);\n\t\treturn ex.equal_subtree(it1, it2);\n\t\t};\n\t\n\tauto ex  = kernel.ex_from_string(\"{ [1, 2] = A_{m n}, [1, 3] = B_{m n}, [1, 4] = A_{m n}, [2, 3] = C_{m n}, [2, 4] = B_{m n} }\");\n\tauto grp2 = group_by_equivalence(*ex, ex->begin(), component_equiv);\n\t\n\tREQUIRE( grp2.size() == 2 );\n\tREQUIRE( grp2[ex->child(ex->begin(), 2)].second == ex->child(ex->begin(), 0) );\n\tREQUIRE( grp2[ex->child(ex->begin(), 4)].second == ex->child(ex->begin(), 1) );\n\t}\n\n"
  },
  {
    "path": "core/test_multiindex.cc",
    "content": "\n#include \"MultiIndex.hh\"\n\n#include <string>\n#include <iostream>\n\nint main()\n\t{\n\n\tMultiIndex<std::string> mi;\n\tmi.values.push_back( { \"a\", \"b\", \"c\" } );\n\tmi.values.push_back( { \"0\", \"1\", \"2\", \"3\" } );\n\tmi.values.push_back( { \"q\", \"r\" } );\n\n\tfor(mi.start(); !mi.end(); ++mi) {\n\t\tfor(std::size_t i=0; i<mi.values.size(); ++i)\n\t\t\tstd::cerr << mi[i] << \" \";\n\t\tstd::cerr << std::endl;\n\t\t}\n\t}\n"
  },
  {
    "path": "core/test_multiplier.cc",
    "content": "#include <catch2/catch_test_macros.hpp>\n\n#include <iostream>\n#include \"Multiplier.hh\"\n\nusing namespace cadabra;\n\nTEST_CASE(\"Multipliers\", \"[multiplier]\")\n\t{\n\t// Rational values\n\tmpq_class r1(1, 2); // 1/2\n\tmpq_class r2(3, 4); // 3/4\n   \n\tMultiplier m1(r1);\n\tMultiplier m2(r2);\n\tMultiplier m3(0.5);  // double\n   \n\tMultiplier sum_rational = m1 + m2;\n\tMultiplier sum_mixed = m1 + m3;\n\tMultiplier product = m1 * m2;\n\tMultiplier quotient = m1 / m3;\n\t\n\t// Operations with rational values\n\tREQUIRE( sum_rational.is_rational() == true );\n\tREQUIRE( sum_rational.get_rational() == mpq_class(5, 4) );\n\t\n\t// Operations involving a double should convert to double\n\tREQUIRE( sum_mixed.is_rational() == false );\n\tREQUIRE( std::abs( sum_mixed.get_double() - 1 ) < 1e-9 );\n\tREQUIRE( product.is_rational() == true );\n\tREQUIRE( product.get_rational() == mpq_class(3, 8) );\n\tREQUIRE( quotient.is_rational() == false );\n\tREQUIRE( std::abs( quotient.get_double() - 1 ) < 1e-9 );\n\t}\n"
  },
  {
    "path": "core/test_permutations.cc",
    "content": "\n#include \"Permutations.hh\"\n#include <iostream>\n\nint main()\n\t{\n\tstd::vector<int> one{ 3,6,8,9,2 };\n\tstd::vector<int> two{ 8,6,9,2,3 };\n\n\tPerm perm;\n\tperm.find_permutation(one.begin(), one.end(), two.begin(), two.end());\n\n\tfor(auto& i: perm.perm)\n\t\tstd::cout << i << \", \";\n\n\tstd::cout << std::endl;\n\t}\n"
  },
  {
    "path": "core/test_preprocessor.cc",
    "content": "/*\n\nCadabra: a field-theory motivated computer algebra system.\nCopyright (C) 2001-2020  Kasper Peeters <kasper.peeters@aei.mpg.de>\n\nThis program is free software: you can redistribute it and/or\nmodify it under the terms of the GNU General Public License as\n\tpublished by the Free Software Foundation, either version 3 of the\nLicense, or (at your option) any later version.\n\nThis program is distributed in the hope that it will be useful,\nbut WITHOUT ANY WARRANTY; without even the implied warranty of\nMERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU\nGeneral Public License for more details.\n\nYou should have received a copy of the GNU General Public License\nalong with this program.  If not, see <http://www.gnu.org/licenses/>.\n\n*/\n\n#include <stdlib.h>\n#include <stdexcept>\n#include <iostream>\n#include <internal/unistd.h>\n#include <sstream>\n#include \"PreProcessor.hh\"\n#include \"base64.hh\"\n\nbool testit(const std::string& input, const std::string& output)\n\t{\n\tstd::cout << \"testing: \" << input << \" ... \" << std::flush;\n\tstd::stringstream orig(input), res, res2;\n\tpreprocessor pp;\n\ttry {\n\t\torig >> pp;\n\t\tres << pp;\n\t\t}\n\tcatch(std::exception& ex) {\n\t\tif(output.size()==0) {\n\t\t\tstd::cout << \"ok (threw exception).\" << std::endl;\n\t\t\treturn true;\n\t\t\t}\n\t\t}\n\tif(res.str()!=output) {\n\t\tstd::cout << std::endl << std::endl << \"regression check **failed** for:\" << std::endl\n\t\t          << \" input :\" << input << std::endl\n\t\t          << \" wanted:\" << output << std::endl\n\t\t          << \" output:\" << res.str() << std::endl << std::endl;\n\t\treturn false;\n\t\t}\n\tpp.erase();\n\tres >> pp;\n\tres2 << pp;\n\tif(res.str()!=res2.str()) {\n\t\tstd::cout << std::endl << \"iterated regression check **failed** for:\" << std::endl\n\t\t          << \" input : \" << input << std::endl\n\t\t          << \" wanted: \" << res.str() << \"|\" << std::endl\n\t\t          << \" output: \" << res2.str() << \"|\" << std::endl;\n\t\treturn false;\n\t\t}\n\tstd::cout << std::endl\n\t          << \" result: \" << res.str() << \" ... ok.\" << std::endl;\n\treturn true;\n\t}\n\nint main(int, char **)\n\t{\n\tstd::stringstream orig, check;\n\tpreprocessor pp;\n\tint regression=1;\n\n\ttry {\n\t\tregression*=testit(\n\t\t               \"i k^{\\\\mu} ( lim_{z\\\\rightarrow w} (z-w)^{-1/2} \\\\psi_{\\\\mu}(w) S_{\\\\alpha}(z) )\",\n\t\t               \"\\\\prod{i}{k^{\\\\mu}}{\\\\prod(lim_{z \\\\rightarrow w})(\\\\sub(z)(w)^{\\\\sub{0}{\\\\frac{1}{2}}})(\\\\psi_{\\\\mu}(w))(S_{\\\\alpha}(z))}\");\n\t\tregression*=testit(\n\t\t               \"(a+b*c)\",\n\t\t               \"\\\\sum(a)(\\\\prod{b}{c})\");\n\n\t\tregression*=testit(\n\t\t               \"a+(b*c+e)\",\n\t\t               \"\\\\sum{a}{\\\\sum(\\\\prod{b}{c})(e)}\");\n\n\t\tregression*=testit(\n\t\t               \"a+(b)\",\n\t\t               \"\\\\sum{a}(b)\");\n\n\t\tregression*=testit(\n\t\t               \"sin(x)^2+cos(x)^2\",\n\t\t               \"\\\\sum{sin(x)^2}{cos(x)^2}\");\n\n\t\tregression*=testit(\n\t\t               \"[ T^1 T^2, T^3]\",\n\t\t               \"\\\\comma[\\\\prod{T^1}{T^2}][T^3]\");\n\n\t\t// This one was previously flagged as an error, but this does not make much sense\n\t\t// anymore, since the product 'y z' is perfectly fine within these brackets.\n\t\t//\t\tregression*=testit(\n\t\t//\t\t\t\"sin(cos(acos[asin{x + y z}]))\",\n\t\t//\t\t\t\"\");\n\n\t\tregression*=testit(\n\t\t               \"sin(cos(acos[asin[x + y z]]))\",\n\t\t               \"sin(cos(acos[asin[\\\\sum{x}{\\\\prod{y}{z}}]]))\");\n\n\t\tregression*=testit(\n\t\t               \"T^{mu nu}K_{mu rho} = V^{kappa} W_{kappa} M_{rho}\",\n\t\t               \"\\\\equals{\\\\prod{T^{mu nu}}{K_{mu rho}}}{\\\\prod{V^{kappa}}{W_{kappa}}{M_{rho}}}\");\n\n\t\tregression*=testit(\n\t\t               \"(T^{mu nu}K_{mu rho} + H^{nu}_{rho}) = V^{kappa} W_{kappa} M_{rho} + e_{rho}\",\n\t\t               \"\\\\equals{\\\\sum(\\\\prod{T^{mu nu}}{K_{mu rho}})(H^{nu}_{rho})}{\\\\sum{\\\\prod{V^{kappa}}{W_{kappa}}{M_{rho}}}{e_{rho}}}\");\n\n\t\tregression*=testit(\n\t\t               \"a = b c + e\",\n\t\t               \"\\\\equals{a}{\\\\sum{\\\\prod{b}{c}}{e}}\");\n\n\t\t// various forms of brackets and grouping\n\t\tregression*=testit(\n\t\t               \"sin(a-b+e)\",\n\t\t               \"sin(\\\\sum{\\\\sub{a}{b}}{e})\");\n\n\t\tregression*=testit(\n\t\t               \"a^{c-d+e}\",\n\t\t               \"a^{\\\\sum{\\\\sub{c}{d}}{e}}\");\n\n\t\tregression*=testit(\n\t\t               \"(a+b)\",\n\t\t               \"\\\\sum(a)(b)\");\n\n\t\tregression*=testit(\n\t\t               \"sin(a+b)\",\n\t\t               \"sin(\\\\sum{a}{b})\");\n\n\t\tregression*=testit(\n\t\t               \"(a+b)^2\",\n\t\t               \"\\\\sum(a)(b)^2\");\n\n\t\tregression*=testit(\n\t\t               \"(a+b)+(c+d)\",\n\t\t               \"\\\\sum{\\\\sum(a)(b)}{\\\\sum(c)(d)}\");\n\n\t\tregression*=testit(\n\t\t               \"((a+b)+(c+d))\",\n\t\t               \"\\\\sum(\\\\sum(a)(b))(\\\\sum(c)(d))\");\n\n\t\tregression*=testit(\n\t\t               \"thnu((-y1-y2)/2)\",\n\t\t               \"thnu(\\\\frac{\\\\sub(0)(y1)(y2)}{2})\");\n\n\t\tregression*=testit(\n\t\t               \"a^2b\",\n\t\t               \"\\\\prod{a^2}{b}\");\n\n\t\tregression*=testit(\n\t\t               \"Tensor[F,{}]\",\n\t\t               \"Tensor[F][{}]\");\n\n\t\tregression*=testit(\n\t\t               \"a^{} b\",\n\t\t               \"\\\\prod{a^{}}{b}\");\n\n\t\t// double brackets\n\n\t\tregression*=testit(\n\t\t               \"Tensor[{a}]\",\n\t\t               \"Tensor[{a}]\");\n\n\t\t// field theory constructions\n\t\tregression*=testit(\n\t\t               \"X^{\\\\mu}\",\n\t\t               \"X^{\\\\mu}\");\n\n\t\t// weird brackets\n\t\tregression*=testit(\n\t\t               \"delta[\\\\{a,b\\\\},\\\\{c,d\\\\}]\",\n\t\t               \"delta[\\\\comma\\\\{a\\\\}\\\\{b\\\\}][\\\\comma\\\\{c\\\\}\\\\{d\\\\}]\");\n\n\t\tregression*=testit(\n\t\t               \"q = a b + a(b)(c)\",\n\t\t               \"\\\\equals{q}{\\\\sum{\\\\prod{a}{b}}{a(b)(c)}}\");\n\n\t\tregression*=testit(\n\t\t               \"(a+b)_{\\\\mu}\",\n\t\t               \"\\\\sum(a)(b)_{\\\\mu}\");\n\n\t\tregression*=testit(\n\t\t               \"(a+b)_\\\\mu\",\n\t\t               \"\\\\sum(a)(b)_\\\\mu\");\n\n\t\tregression*=testit(\n\t\t               \"foo:= -a-b\",\n\t\t               \"\\\\declare{foo}{\\\\sub{0}{a}{b}}\");\n\n\t\tregression*=testit(\n\t\t               \"(\\\\Gamma_r)_{a b}\",\n\t\t               \"(\\\\Gamma_r)_{a b}\");\n\n\t\t// strings should never be expanded\n\t\tregression*=testit(\n\t\t               \"\\\"foo = bar\\\"\",\n\t\t               \"\\\"foo = bar\\\"\");\n\n\t\t// commands have special treatment\n\t\tregression*=testit(\n\t\t               \"@test_command!(something)\",\n\t\t               \"@test_command!(something)\");\n\n\t\t// multi-char relations\n\t\tregression*=testit(\n\t\t               \"a$VectorIndex(4)\",\n\t\t               \"a$VectorIndex(4)\");\n\n\t\tregression*=testit(\n\t\t               \"a::VectorIndex(4)\",\n\t\t               \"a$VectorIndex(4)\");\n\n\t\tregression*=testit(\n\t\t               \"A_{a b c} -> C_{a} D_{b c}\",\n\t\t               \"\\\\arrow{A_{a b c}}{\\\\prod{C_{a}}{D_{b c}}}\");\n\n\t\t// default whitespace->product\n\t\tregression*=testit(\n\t\t               \"{ a, b c f, d e }\",\n\t\t               \"\\\\comma{a}{\\\\prod{b}{c}{f}}{\\\\prod{d}{e}}\");\n\n\t\tregression*=testit(\n\t\t               \"{ a q, b c f, d e }\",\n\t\t               \"\\\\comma{\\\\prod{a}{q}}{\\\\prod{b}{c}{f}}{\\\\prod{d}{e}}\");\n\n\t\tregression*=testit(\n\t\t               \"\\\\partial_{a}{b c}\",\n\t\t               \"\\\\partial_{a}{\\\\prod{b}{c}}\");\n\n\t\tregression*=testit(\n\t\t               \"a*( (x^1)^2 + (x^2)^2 + (x^3)^2 )\",\n\t\t               \"\\\\prod{a}{\\\\sum((x^1)^2)((x^2)^2)((x^3)^2)}\");\n\n\t\tregression*=testit(\n\t\t               \"\\\\bar{\\\\diff{\\\\diff{A}_{\\\\nu}}_{\\\\rho}}\",\n\t\t               \"\\\\bar{\\\\diff{\\\\diff{A}_{\\\\nu}}_{\\\\rho}}\");\n\n\t\tregression*=testit(\n\t\t               \"A_{\\\\dot{a} \\\\dot{b}}\",\n\t\t               \"A_{\\\\dot{a} \\\\dot{b}}\");\n\n\t\tregression*=testit(\n\t\t               \"3..4\",\n\t\t               \"\\\\sequence{3}{4}\");\n\n\t\tregression*=testit(\n\t\t               \"3.14\",\n\t\t               \"3.14\");\n\n\t\tregression*=testit(\n\t\t               \"x**{2}\",\n\t\t               \"\\\\pow{x}{2}\");\n\n\t\tregression*=testit(\n\t\t               \"x**(2)\",\n\t\t               \"\\\\pow{x}(2)\");\n\n\t\tregression*=testit(\n\t\t               \"A(a,b)\",\n\t\t               \"A(a)(b)\");\n\n\t\tregression*=testit(\n\t\t               \"A(a,b,c)\",\n\t\t               \"A(a)(b)(c)\");\n\n\t\tregression*=testit(\n\t\t               \"A[a,b]\",\n\t\t               \"A[a][b]\");\n\n\t\tregression*=testit(\n\t\t               \"(a,b)\",\n\t\t               \"\\\\comma(a)(b)\");\n\n\t\tregression*=testit(\n\t\t               \"{a,b}\",\n\t\t               \"\\\\comma{a}{b}\");\n\n\t\tregression*=testit(\n\t\t               \"[a,b]\",\n\t\t               \"\\\\comma[a][b]\");\n\n\t\tregression*=testit(\n\t\t               \"sort_product( B A C )\",\n\t\t               \"sort_product(\\\\prod{B}{A}{C})\");\n\n\t\t//\t\t  regression*=testit(\n\t\t//\t\t\t  \"@substitute!(%){b_{p}->c_{p m n} A^{m n} + c_{p} }\",\n\t\t//\t\t\t  \"@substitute!(%){\\\\arrow{b_{p}}{\\\\sum{\\\\prod{c_{p m n}}{A^{m n}}{c_{p}}}}}\");\n\n\t\tif(!regression)\n\t\t\tstd::cout << \"*** Regression check failed; enter input or press CTRL-C ***\" << std::endl;\n\t\telse\n\t\t\tstd::cout << \"+++ Regression check ok; enter input or press CTRL-C +++\" << std::endl;\n\n\t\tstd::cin  >> pp;\n\t\torig  << pp;\n\t\tstd::cout << orig.str() << std::endl;\n\t\tpp.erase();\n\t\torig  >> pp;\n\t\tcheck << pp;\n\t\t}\n\tcatch(std::exception& ex) {\n\t\tstd::cerr << ex.what() << std::endl;\n\t\texit(1);\n\t\t}\n\n\tif(orig.str()==check.str()) std::cout << \"iteration is identical\" << std::endl;\n\telse std::cout << \"iteration is NOT identical:\" << std::endl\n\t\t               << check.str() << std::endl;\n\n\tif(regression) return 0;\n\telse return 1;\n\t}\n\n"
  },
  {
    "path": "core/test_wstp.cc",
    "content": "#include \"wstp.h\"\n#include <iostream>\n\n// https://reference.wolfram.com/legacy/language/v10.2/ref/c/WSLogStreamToFile.html\n// http://edenwaith.com/development/tutorials/mathlink/ML_Tut.pdf\n//\n// Run as\n//\n//    core/test_wstp -linkname 'math -mathlink' -linkmode launch\n\n\nint main(int argc, char **argv)\n\t{\n\tint errno;\n\tWSEnvironment stdenv;\n\tstdenv = WSInitialize((WSEnvironmentParameter)0);\n\tif(stdenv==0) {\n\t\tstd::cerr << \"Failed to initialise WSTP\" << std::endl;\n\t\treturn -1;\n\t\t}\n\t//\tauto lp = WSLoopbackOpen(stdenv, &errno);\n\tauto lp = WSOpenArgcArgv(stdenv, argc, argv, &errno);\n\tif(lp==0 || errno!=WSEOK) {\n\t\tstd::cerr << \"Failed to open loopback link \" << WSErrorMessage(lp) << std::endl;\n\t\treturn -1;\n\t\t}\n\n\tWSActivate(lp);\n\n\tconst char *fileName;\n\tauto res = WSLogFileNameForLink(lp, &fileName);\n\tif(! res) {\n\t\tstd::cerr << \"Failed to generate log file name\" << std::endl;\n\t\treturn -1;\n\t\t}\n\tres = WSLogStreamToFile(lp, fileName);\n\tstd::cerr << \"Logging to \" << fileName << std::endl;\n\n\tWSPutFunction(lp, \"EvaluatePacket\", 1L);\n\tWSPutFunction(lp, \"ToString\", 1L);\n\tWSPutFunction(lp, \"FullSimplify\", 1L);\n\tWSPutFunction(lp, \"ToExpression\", 1L);\n\tWSPutString(lp, \"Sin[x]^2 + Cos[x]^2 + Cos[x] Sin[x]\");\n\t//\tWSPutFunction(lp, \"Plus\", 2);\n\t//\tWSPutInteger(lp, 3);\n\t//\tWSPutInteger(lp, 8);\n\tWSEndPacket(lp);\n\tWSFlush(lp);\n\n\tint pkt=0;\n\twhile( (pkt = WSNextPacket(lp), pkt) && pkt != RETURNPKT ) {\n\t\tstd::cerr << \"received packet \" << pkt << std::endl;\n\t\tWSNewPacket(lp);\n\t\tif (WSError(lp)) {\n\t\t\tstd::cerr << \"error\" << std::endl;\n\t\t\t}\n\t\t}\n\tstd::cerr << \"packet now \" << pkt << std::endl;\n\n\tconst char *out;\n\tif(! WSGetString(lp, &out)) {\n\t\tprintf(\"Unable to read from link\\n\");\n\t\treturn -1;\n\t\t}\n\telse {\n\t\tstd::cerr << out << std::endl;\n\t\tWSReleaseString(lp, out);\n\t\t}\n\n\tWSReleaseLogFileNameForLink(lp, fileName);\n\n\tWSClose(lp);\n\tWSDeinitialize(stdenv);\n\t}\n"
  },
  {
    "path": "core/tree.hh",
    "content": "\n//\tSTL-like templated tree class.\n//\n// Copyright (C) 2001-2024 Kasper Peeters <kasper@phi-sci.com>\n// Distributed under the GNU General Public License version 3.\n//\n// Special permission to use tree.hh under the conditions of a \n// different license can be requested from the author.\n\n/** \\mainpage tree.hh\n    \\author   Kasper Peeters\n    \\version  3.20\n    \\date     2024-04-12\n    \\see      http://github.com/kpeeters/tree.hh/\n\n   The tree.hh library for C++ provides an STL-like container class\n   for n-ary trees, templated over the data stored at the\n   nodes. Various types of iterators are provided (post-order,\n   pre-order, and others). Where possible the access methods are\n   compatible with the STL or alternative algorithms are\n   available. \n*/\n\n\n#ifndef tree_hh_\n#define tree_hh_\n\n#include <cassert>\n#include <memory>\n#include <stdexcept>\n#include <iterator>\n#include <set>\n#include <queue>\n#include <algorithm>\n#include <cstddef>\n#include <string>\n\n/// A node in the tree, combining links to other nodes as well as the actual data.\ntemplate<class T>\nclass tree_node_ { // size: 5*4=20 bytes (on 32 bit arch), can be reduced by 8.\n\tpublic:\n\t\ttree_node_();\n\t\ttree_node_(const T&);\n\t\ttree_node_(T&&);\n\n\t\ttree_node_<T> *parent;\n\t   tree_node_<T> *first_child, *last_child;\n\t\ttree_node_<T> *prev_sibling, *next_sibling;\n\t\tT data;\n}; \n\ntemplate<class T>\ntree_node_<T>::tree_node_()\n\t: parent(0), first_child(0), last_child(0), prev_sibling(0), next_sibling(0)\n\t{\n\t}\n\ntemplate<class T>\ntree_node_<T>::tree_node_(const T& val)\n\t: parent(0), first_child(0), last_child(0), prev_sibling(0), next_sibling(0), data(val)\n\t{\n\t}\n\ntemplate<class T>\ntree_node_<T>::tree_node_(T&& val)\n\t: parent(0), first_child(0), last_child(0), prev_sibling(0), next_sibling(0), data(val)\n\t{\n\t}\n\n// Throw an exception with a stacktrace.\n\n//template <class E>\n//void throw_with_trace(const E& e)\n//\t{\n//\tthrow boost::enable_error_info(e)\n//\t\t<< traced(boost::stacktrace::stacktrace());\n//\t}\n\nclass navigation_error : public std::logic_error {\n\tpublic:\n\t\tnavigation_error(const std::string& s) : std::logic_error(s)\n\t\t\t{\n//\t\t\tassert(1==0);\n//\t\t\tstd::ostringstream str;\n//\t\t\tstd::cerr << boost::stacktrace::stacktrace() << std::endl;\n//\t\t\tstr << boost::stacktrace::stacktrace();\n//\t\t\tstacktrace=str.str();\n\t\t\t}\n\n//\t\tvirtual const char *what() const noexcept override\n//\t\t\t{\n//\t\t\treturn (std::logic_error::what()+std::string(\"; \")+stacktrace).c_str();\n//\t\t\t}\n//\n//\t\tstd::string stacktrace;\n};\n\t\t\ntemplate <class T, class tree_node_allocator = std::allocator<tree_node_<T> > >\nclass tree {\n\tprotected:\n\t\ttypedef tree_node_<T> tree_node;\n\tpublic:\n\t\t/// Value of the data stored at a node.\n\t\ttypedef T value_type;\n\n\t\tclass iterator_base;\n\t\tclass pre_order_iterator;\n\t\tclass post_order_iterator;\n\t\tclass sibling_iterator;\n      class leaf_iterator;\n\n\t\ttree();                                                                        // empty constructor\n\t\texplicit tree(const tree_node_allocator&);                                     // empty constructor with allocator\n\t\ttree(const T&);                                                                // constructor setting given element as head\n\t\ttree(const T&, const tree_node_allocator&);                                    // constructor setting given element as head with allocator\n\t\ttree(const iterator_base&);                                                    // create tree with copy of subtree at iterator\n\t\ttree(const iterator_base&, const tree_node_allocator&);                        // create tree with copy of subtree at iterator\n\t\ttree(const tree<T, tree_node_allocator>&);                                     // copy constructor\n\t\ttree(const tree<T, tree_node_allocator>&, const tree_node_allocator&);         // copy constructor\n\t\ttree(tree<T, tree_node_allocator>&&);                                          // move constructor\n\t\ttree(tree<T, tree_node_allocator>&&, const tree_node_allocator&);              // move constructor\n\t\t~tree();\n\t\ttree<T,tree_node_allocator>& operator=(const tree<T, tree_node_allocator>&);   // copy assignment\n\t\ttree<T,tree_node_allocator>& operator=(tree<T, tree_node_allocator>&&);        // move assignment\n\n\t\tvoid swap(tree& other);\n\n      /// Base class for iterators, only pointers stored, no traversal logic.\n#ifdef __SGI_STL_PORT\n\t\tclass iterator_base : public stlport::bidirectional_iterator<T, ptrdiff_t> {\n#else\n\t\tclass iterator_base {\n#endif\n\t\t\tpublic:\n\t\t\t\ttypedef T                               value_type;\n\t\t\t\ttypedef T*                              pointer;\n\t\t\t\ttypedef T&                              reference;\n\t\t\t\ttypedef size_t                          size_type;\n\t\t\t\ttypedef ptrdiff_t                       difference_type;\n\t\t\t\ttypedef std::bidirectional_iterator_tag iterator_category;\n\n\t\t\t\titerator_base();\n\t\t\t\titerator_base(tree_node *);\n\n\t\t\t\tT&             operator*() const;\n\t\t\t\tT*             operator->() const;\n\n            /// When called, the next increment/decrement skips children of this node.\n\t\t\t\tvoid         skip_children();\n\t\t\t\tvoid         skip_children(bool skip);\n\t\t\t\t/// Number of children of the node pointed to by the iterator.\n\t\t\t\tunsigned int number_of_children() const;\n\n\t\t\t\tsibling_iterator begin() const;\n\t\t\t\tsibling_iterator end() const;\n\n\t\t\t\ttree_node *node;\n\t\t\tprotected:\n\t\t\t\tbool skip_current_children_;\n\t\t};\n\n\t\t/// Depth-first iterator, first accessing the node, then its children.\n\t\tclass pre_order_iterator : public iterator_base { \n\t\t\tpublic:\n\t\t\t\tpre_order_iterator();\n\t\t\t\tpre_order_iterator(tree_node *);\n\t\t\t\tpre_order_iterator(const iterator_base&);\n\t\t\t\tpre_order_iterator(const sibling_iterator&);\n\n\t\t\t\tbool    operator==(const pre_order_iterator&) const;\n\t\t\t\tbool    operator!=(const pre_order_iterator&) const;\n\t\t\t\tpre_order_iterator&  operator++();\n\t\t\t   pre_order_iterator&  operator--();\n\t\t\t\tpre_order_iterator   operator++(int);\n\t\t\t\tpre_order_iterator   operator--(int);\n\t\t\t\tpre_order_iterator&  operator+=(unsigned int);\n\t\t\t\tpre_order_iterator&  operator-=(unsigned int);\n\n\t\t\t\tpre_order_iterator&  next_skip_children();\n\t\t};\n\n\t\t/// Depth-first iterator, first accessing the children, then the node itself.\n\t\tclass post_order_iterator : public iterator_base {\n\t\t\tpublic:\n\t\t\t\tpost_order_iterator();\n\t\t\t\tpost_order_iterator(tree_node *);\n\t\t\t\tpost_order_iterator(const iterator_base&);\n\t\t\t\tpost_order_iterator(const sibling_iterator&);\n\n\t\t\t\tbool    operator==(const post_order_iterator&) const;\n\t\t\t\tbool    operator!=(const post_order_iterator&) const;\n\t\t\t\tpost_order_iterator&  operator++();\n\t\t\t   post_order_iterator&  operator--();\n\t\t\t\tpost_order_iterator   operator++(int);\n\t\t\t\tpost_order_iterator   operator--(int);\n\t\t\t\tpost_order_iterator&  operator+=(unsigned int);\n\t\t\t\tpost_order_iterator&  operator-=(unsigned int);\n\n\t\t\t\t/// Set iterator to the first child as deep as possible down the tree.\n\t\t\t\tvoid descend_all();\n\t\t};\n\n\t\t/// Breadth-first iterator, using a queue\n\t\tclass breadth_first_queued_iterator : public iterator_base {\n\t\t\tpublic:\n\t\t\t\tbreadth_first_queued_iterator();\n\t\t\t\tbreadth_first_queued_iterator(tree_node *);\n\t\t\t\tbreadth_first_queued_iterator(const iterator_base&);\n\n\t\t\t\tbool    operator==(const breadth_first_queued_iterator&) const;\n\t\t\t\tbool    operator!=(const breadth_first_queued_iterator&) const;\n\t\t\t\tbreadth_first_queued_iterator&  operator++();\n\t\t\t\tbreadth_first_queued_iterator   operator++(int);\n\t\t\t\tbreadth_first_queued_iterator&  operator+=(unsigned int);\n\n\t\t\tprivate:\n\t\t\t\tstd::queue<tree_node *> traversal_queue;\n\t\t};\n\n\t\t/// The default iterator types throughout the tree class.\n\t\ttypedef pre_order_iterator            iterator;\n\t\ttypedef breadth_first_queued_iterator breadth_first_iterator;\n\n\t\t/// Iterator which traverses only the nodes at a given depth from the root.\n\t\tclass fixed_depth_iterator : public iterator_base {\n\t\t\tpublic:\n\t\t\t\tfixed_depth_iterator();\n\t\t\t\tfixed_depth_iterator(tree_node *);\n\t\t\t\tfixed_depth_iterator(const iterator_base&);\n\t\t\t\tfixed_depth_iterator(const sibling_iterator&);\n\t\t\t\tfixed_depth_iterator(const fixed_depth_iterator&);\n\n\t\t\t\tvoid swap(fixed_depth_iterator&, fixed_depth_iterator&);\n\t\t\t\tfixed_depth_iterator& operator=(fixed_depth_iterator);\n\n\t\t\t\tbool    operator==(const fixed_depth_iterator&) const;\n\t\t\t\tbool    operator!=(const fixed_depth_iterator&) const;\n\t\t\t\tfixed_depth_iterator&  operator++();\n\t\t\t   fixed_depth_iterator&  operator--();\n\t\t\t\tfixed_depth_iterator   operator++(int);\n\t\t\t\tfixed_depth_iterator   operator--(int);\n\t\t\t\tfixed_depth_iterator&  operator+=(unsigned int);\n\t\t\t\tfixed_depth_iterator&  operator-=(unsigned int);\n\n\t\t\t\ttree_node *top_node;\n\t\t};\n\n\t\t/// Iterator which traverses only the nodes which are siblings of each other.\n\t\tclass sibling_iterator : public iterator_base {\n\t\t\tpublic:\n\t\t\t\tsibling_iterator();\n\t\t\t\tsibling_iterator(tree_node *);\n\t\t\t\tsibling_iterator(const sibling_iterator&);\n\t\t\t\tsibling_iterator(const iterator_base&);\n\n\t\t\t\tvoid swap(sibling_iterator&, sibling_iterator&);\n\t\t\t\tsibling_iterator& operator=(sibling_iterator);\n\t\t\t\t\n\t\t\t\tbool    operator==(const sibling_iterator&) const;\n\t\t\t\tbool    operator!=(const sibling_iterator&) const;\n\t\t\t\tsibling_iterator&  operator++();\n\t\t\t\tsibling_iterator&  operator--();\n\t\t\t\tsibling_iterator   operator++(int);\n\t\t\t\tsibling_iterator   operator--(int);\n\t\t\t\tsibling_iterator&  operator+=(unsigned int);\n\t\t\t\tsibling_iterator&  operator-=(unsigned int);\n\n\t\t\t\ttree_node *range_first() const;\n\t\t\t\ttree_node *range_last() const;\n\t\t\t\ttree_node *parent_;\n\t\t\tprivate:\n\t\t\t\tvoid set_parent_();\n\t\t};\n\n      /// Iterator which traverses only the leaves.\n      class leaf_iterator : public iterator_base {\n         public:\n            leaf_iterator();\n            leaf_iterator(tree_node *, tree_node *top=0);\n            leaf_iterator(const sibling_iterator&);\n            leaf_iterator(const iterator_base&);\n\n            bool    operator==(const leaf_iterator&) const;\n            bool    operator!=(const leaf_iterator&) const;\n            leaf_iterator&  operator++();\n            leaf_iterator&  operator--();\n            leaf_iterator   operator++(int);\n            leaf_iterator   operator--(int);\n            leaf_iterator&  operator+=(unsigned int);\n            leaf_iterator&  operator-=(unsigned int);\n\t\t\tprivate:\n\t\t\t\ttree_node *top_node;\n      };\n\n\t\t/// Return iterator to the beginning of the tree.\n\t\tinline pre_order_iterator   begin() const;\n\t\t/// Return iterator to the end of the tree.\n\t\tinline pre_order_iterator   end() const;\n\t\t/// Return post-order iterator to the beginning of the tree.\n\t\tpost_order_iterator  begin_post() const;\n\t\t/// Return post-order end iterator of the tree.\n\t\tpost_order_iterator  end_post() const;\n\t\t/// Return fixed-depth iterator to the first node at a given depth from the given iterator.\n\t\t/// If 'walk_back=true', a depth=0 iterator will be taken from the beginning of the sibling\n\t\t/// range, not the current node.\n\t\tfixed_depth_iterator begin_fixed(const iterator_base&, unsigned int, bool walk_back=true) const;\n\t\t/// Return fixed-depth end iterator.\n\t\tfixed_depth_iterator end_fixed(const iterator_base&, unsigned int) const;\n\t\t/// Return breadth-first iterator to the first node at a given depth.\n\t\tbreadth_first_queued_iterator begin_breadth_first() const;\n\t\t/// Return breadth-first end iterator.\n\t\tbreadth_first_queued_iterator end_breadth_first() const;\n\t\t/// Return sibling iterator to the first child of given node.\n\t\tstatic sibling_iterator     begin(const iterator_base&);\n\t\t/// Return sibling end iterator for children of given node.\n\t\tstatic sibling_iterator     end(const iterator_base&);\n      /// Return leaf iterator to the first leaf of the tree.\n      leaf_iterator   begin_leaf() const;\n      /// Return leaf end iterator for entire tree.\n      leaf_iterator   end_leaf() const;\n      /// Return leaf iterator to the first leaf of the subtree at the given node.\n      leaf_iterator   begin_leaf(const iterator_base& top) const;\n      /// Return leaf end iterator for the subtree at the given node.\n      leaf_iterator   end_leaf(const iterator_base& top) const;\n\n\t\ttypedef std::vector<int> path_t;\n\t\t/// Return a path (to be taken from the 'top' node) corresponding to a node in the tree.\n\t\t/// The first integer in path_t is the number of steps you need to go 'right' in the sibling\n\t\t/// chain (so 0 if we go straight to the children).\n\t\tpath_t          path_from_iterator(const iterator_base& iter, const iterator_base& top) const;\n\t\t/// Return an iterator given a path from the 'top' node.\n\t\titerator        iterator_from_path(const path_t&, const iterator_base& top) const;\n\t\t\t\t\n\t\t/// Return iterator to the parent of a node. Throws a `navigation_error` if the node\n\t\t/// does not have a parent.\n\t\ttemplate<typename\titer> static iter parent(iter);\n\t\t/// Return iterator to the previous sibling of a node.\n\t\ttemplate<typename iter> static iter previous_sibling(iter);\n\t\t/// Return iterator to the next sibling of a node.\n\t\ttemplate<typename iter> static iter next_sibling(iter);\n\t\t/// Return iterator to the next node at a given depth.\n\t\ttemplate<typename iter> iter next_at_same_depth(iter) const;\n\n\t\t/// Erase all nodes of the tree.\n\t\tvoid     clear();\n\t\t/// Erase element at position pointed to by iterator, return incremented iterator.\n\t\ttemplate<typename iter> iter erase(iter);\n\t\t/// Erase all children of the node pointed to by iterator.\n\t\tvoid     erase_children(const iterator_base&);\n\t\t/// Erase all siblings to the right of the iterator.\n\t\tvoid     erase_right_siblings(const iterator_base&);\n\t\t/// Erase all siblings to the left of the iterator.\n\t\tvoid     erase_left_siblings(const iterator_base&);\n \n\t\t/// Insert empty node as last/first child of node pointed to by position.\n\t\ttemplate<typename iter> iter append_child(iter position); \n\t\ttemplate<typename iter> iter prepend_child(iter position); \n\t\t/// Insert node as last/first child of node pointed to by position.\n\t\ttemplate<typename iter> iter append_child(iter position, const T& x);\n\t\ttemplate<typename iter> iter append_child(iter position, T&& x);\n\t\ttemplate<typename iter> iter prepend_child(iter position, const T& x);\n\t\ttemplate<typename iter> iter prepend_child(iter position, T&& x);\n\t\t/// Append the node (plus its children) at other_position as last/first child of position.\n\t\ttemplate<typename iter> iter append_child(iter position, iter other_position);\n\t\ttemplate<typename iter> iter prepend_child(iter position, iter other_position);\n\t\t/// Append the nodes in the from-to range (plus their children) as last/first children of position.\n\t\ttemplate<typename iter> iter append_children(iter position, sibling_iterator from, sibling_iterator to);\n\t\ttemplate<typename iter> iter prepend_children(iter position, sibling_iterator from, sibling_iterator to);\n\n\t\t/// Short-hand to insert topmost node in otherwise empty tree.\n\t\tpre_order_iterator set_head(const T& x);\n\t\tpre_order_iterator set_head(T&& x);\n\t\t/// Insert node as previous sibling of node pointed to by position.\n\t\ttemplate<typename iter> iter insert(iter position, const T& x);\n\t\ttemplate<typename iter> iter insert(iter position, T&& x);\n\t\t/// Specialisation of previous member.\n\t\tsibling_iterator insert(sibling_iterator position, const T& x);\n\t\tsibling_iterator insert(sibling_iterator position, T&& x);\n\t\t/// Insert node (with children) pointed to by subtree as previous sibling of node pointed to by position.\n\t\t/// Does not change the subtree itself (use move_in or move_in_below for that).\n\t\ttemplate<typename iter> iter insert_subtree(iter position, const iterator_base& subtree);\n\t\t/// Insert node as next sibling of node pointed to by position.\n\t\ttemplate<typename iter> iter insert_after(iter position, const T& x);\n\t\ttemplate<typename iter> iter insert_after(iter position, T&& x);\n\t\t/// Insert node (with children) pointed to by subtree as next sibling of node pointed to by position.\n\t\ttemplate<typename iter> iter insert_subtree_after(iter position, const iterator_base& subtree);\n\n\t\t/// Replace node at 'position' with other node (keeping same children); 'position' becomes invalid.\n\t\ttemplate<typename iter> iter replace(iter position, const T& x);\n\t\t/// Replace node at 'position' with subtree starting at 'from' (do not erase subtree at 'from'); see above.\n\t\ttemplate<typename iter> iter replace(iter position, const iterator_base& from);\n\t\t/// Replace string of siblings (plus their children) with copy of a new string (with children); see above\n\t\tsibling_iterator replace(sibling_iterator orig_begin, sibling_iterator orig_end, \n\t\t\t\t\t\t\t\t\t\t sibling_iterator new_begin,  sibling_iterator new_end); \n\n\t\t/// Move all children of node at 'position' to be siblings, returns position.\n\t\ttemplate<typename iter> iter flatten(iter position);\n\t\t/// Move nodes in range to be children of 'position'.\n\t\ttemplate<typename iter> iter reparent(iter position, sibling_iterator begin, sibling_iterator end);\n\t\t/// Move all child nodes of 'from' to be children of 'position'.\n\t\ttemplate<typename iter> iter reparent(iter position, iter from);\n\n\t\t/// Replace node with a new node, making the old node (plus subtree) a child of the new node.\n\t\ttemplate<typename iter> iter wrap(iter position, const T& x);\n\t\t/// Replace the range of sibling nodes (plus subtrees), making these children of the new node.\n\t\ttemplate<typename iter> iter wrap(iter from, iter to, const T& x);\n\n\t\t/// Move 'source' node (plus its children) to become the next sibling of 'target'.\n\t\ttemplate<typename iter> iter move_after(iter target, iter source);\n\t\t/// Move 'source' node (plus its children) to become the previous sibling of 'target'.\n      template<typename iter> iter move_before(iter target, iter source);\n      sibling_iterator move_before(sibling_iterator target, sibling_iterator source);\n\t\t/// Move 'source' node (plus its children) to become the node at 'target' (erasing the node at 'target').\n\t\ttemplate<typename iter> iter move_ontop(iter target, iter source);\n\n\t\t/// Extract the subtree starting at the indicated node, removing it from the original tree.\n\t\ttree                         move_out(iterator);\n\t\t/// Inverse of take_out: inserts the given tree as previous sibling of indicated node by a \n\t\t/// move operation, that is, the given tree becomes empty. Returns iterator to the top node.\n\t\ttemplate<typename iter> iter move_in(iter, tree&);\n\t\t/// As above, but now make the tree the last child of the indicated node.\n\t\ttemplate<typename iter> iter move_in_below(iter, tree&);\n\t\t/// As above, but now make the tree the nth child of the indicated node (if possible).\n\t\ttemplate<typename iter> iter move_in_as_nth_child(iter, size_t, tree&);\n\n\t\t/// Merge with other tree, creating new branches and leaves only if they are not already present.\n\t\tvoid     merge(sibling_iterator, sibling_iterator, sibling_iterator, sibling_iterator, \n\t\t\t\t\t\t\tbool duplicate_leaves=false);\n\t\t/// As above, but using two trees with a single top node at the 'to' and 'from' positions.\n\t\tvoid     merge(iterator to, iterator from, bool duplicate_leaves);\n\t\t/// Sort (std::sort only moves values of nodes, this one moves children as well).\n\t\tvoid     sort(sibling_iterator from, sibling_iterator to, bool deep=false);\n\t\ttemplate<class StrictWeakOrdering>\n\t\tvoid     sort(sibling_iterator from, sibling_iterator to, StrictWeakOrdering comp, bool deep=false);\n\t\t/// Compare two ranges of nodes (compares nodes as well as tree structure).\n\t\ttemplate<typename iter>\n\t\tbool     equal(const iter& one, const iter& two, const iter& three) const;\n\t\ttemplate<typename iter, class BinaryPredicate>\n\t\tbool     equal(const iter& one, const iter& two, const iter& three, BinaryPredicate) const;\n\t\ttemplate<typename iter>\n\t\tbool     equal_subtree(const iter& one, const iter& two) const;\n\t\ttemplate<typename iter, class BinaryPredicate>\n\t\tbool     equal_subtree(const iter& one, const iter& two, BinaryPredicate) const;\n\t\t/// Extract a new tree formed by the range of siblings plus all their children.\n\t\ttree     subtree(sibling_iterator from, sibling_iterator to) const;\n\t\tvoid     subtree(tree&, sibling_iterator from, sibling_iterator to) const;\n\t\t/// Exchange the node (plus subtree) with its sibling node (do nothing if no sibling present).\n\t\tvoid     swap(sibling_iterator it);\n\t\t/// Exchange two nodes (plus subtrees). The iterators will remain valid and keep \n\t\t/// pointing to the same nodes, which now sit at different locations in the tree.\n\t   void     swap(iterator, iterator);\n\t\t\n\t\t/// Count the total number of nodes.\n\t\tsize_t   size() const;\n\t\t/// Count the total number of nodes below the indicated node (plus one).\n\t\tsize_t   size(const iterator_base&) const;\n\t\t/// Check if tree is empty.\n\t\tbool     empty() const;\n\t\t/// Compute the depth to the root or to a fixed other iterator.\n\t\tstatic int depth(const iterator_base&);\n\t\tstatic int depth(const iterator_base&, const iterator_base&);\n\t\t/// Compute the depth to the root, counting all levels for which predicate returns true.\n\t\ttemplate<class Predicate>\n\t\tstatic int depth(const iterator_base&, Predicate p);\n\t\t/// Compute the depth distance between two nodes, counting all levels for which predicate returns true.\n\t\ttemplate<class Predicate>\n\t\tstatic int distance(const iterator_base& top, const iterator_base& bottom, Predicate p);\n\t\t/// Determine the maximal depth of the tree. An empty tree has max_depth=-1.\n\t\tint      max_depth() const;\n\t\t/// Determine the maximal depth of the tree with top node at the given position.\n\t\tint      max_depth(const iterator_base&) const;\n\t\t/// Count the number of children of node at position.\n\t\tstatic unsigned int number_of_children(const iterator_base&);\n\t\t/// Count the number of siblings (left and right) of node at iterator. Total nodes at this level is +1.\n\t\tunsigned int number_of_siblings(const iterator_base&) const;\n\t\t/// Determine whether node at position is in the subtrees with indicated top node.\n   \tbool     is_in_subtree(const iterator_base& position, const iterator_base& top) const;\n\t\t/// Determine whether node at position is in the subtrees with root in the range.\n\t\tbool     is_in_subtree(const iterator_base& position, const iterator_base& begin, \n\t\t\t\t\t\t\t\t\t  const iterator_base& end) const;\n\t\t/// Determine whether the iterator is an 'end' iterator and thus not actually pointing to a node.\n\t\tbool     is_valid(const iterator_base&) const;\n\t\t/// Determine whether the iterator is one of the 'head' nodes at the top level, i.e. has no parent.\n\t\tstatic   bool is_head(const iterator_base&);\n\t\t/// Find the lowest common ancestor of two nodes, that is, the deepest node such that\n\t\t/// both nodes are descendants of it.\n\t\titerator lowest_common_ancestor(const iterator_base&, const iterator_base &) const;\n\n\t\t/// Determine the index of a node in the range of siblings to which it belongs.\n\t\tunsigned int index(sibling_iterator it) const;\n\t\t/// Inverse of 'index': return the n-th child of the node at position.\n\t\tstatic sibling_iterator child(const iterator_base& position, unsigned int);\n\t\t/// Return iterator to the sibling indicated by index\n\t\tsibling_iterator sibling(const iterator_base& position, unsigned int) const;  \t\t\t\t\n\t\t\n\t\t/// For debugging only: verify internal consistency by inspecting all pointers in the tree\n\t\t/// (which will also trigger a valgrind error in case something got corrupted).\n\t\tvoid debug_verify_consistency() const;\n\t\t\n\t\t/// Comparator class for iterators (compares pointer values; why doesn't this work automatically?)\n\t\tclass iterator_base_less {\n\t\t\tpublic:\n\t\t\t\tbool operator()(const typename tree<T, tree_node_allocator>::iterator_base& one,\n\t\t\t\t\t\t\t\t\t const typename tree<T, tree_node_allocator>::iterator_base& two) const\n\t\t\t\t\t{\n\t\t\t\t\treturn one.node < two.node;\n\t\t\t\t\t}\n\t\t};\n\t\ttree_node *head, *feet;    // head/feet are always dummy; if an iterator points to them it is invalid\n\tprivate:\n\t\ttree_node_allocator alloc_;\n\t\tvoid head_initialise_();\n\t\tvoid copy_(const tree<T, tree_node_allocator>& other);\n\n      /// Comparator class for two nodes of a tree (used for sorting and searching).\n\t\ttemplate<class StrictWeakOrdering>\n\t\tclass compare_nodes {\n\t\t\tpublic:\n\t\t\t\tcompare_nodes(StrictWeakOrdering comp) : comp_(comp) {}\n\t\t\t\t\n\t\t\t\tbool operator()(const tree_node *a, const tree_node *b) const\n\t\t\t\t\t{\n\t\t\t\t\treturn comp_(a->data, b->data);\n\t\t\t\t\t}\n\t\t\tprivate:\n\t\t\t\tStrictWeakOrdering comp_;\n\t\t};\n\t};\n\n//template <class T, class tree_node_allocator>\n//class iterator_base_less {\n//\tpublic:\n//\t\tbool operator()(const typename tree<T, tree_node_allocator>::iterator_base& one,\n//\t\t\t\t\t\t  const typename tree<T, tree_node_allocator>::iterator_base& two) const\n//\t\t\t{\n//\t\t\ttxtout << \"operatorclass<\" << one.node < two.node << std::endl;\n//\t\t\treturn one.node < two.node;\n//\t\t\t}\n//};\n\n// template <class T, class tree_node_allocator>\n// bool operator<(const typename tree<T, tree_node_allocator>::iterator& one,\n// \t\t\t\t\tconst typename tree<T, tree_node_allocator>::iterator& two)\n// \t{\n// \ttxtout << \"operator< \" << one.node < two.node << std::endl;\n// \tif(one.node < two.node) return true;\n// \treturn false;\n// \t}\n// \n// template <class T, class tree_node_allocator>\n// bool operator==(const typename tree<T, tree_node_allocator>::iterator& one,\n// \t\t\t\t\tconst typename tree<T, tree_node_allocator>::iterator& two)\n// \t{\n// \ttxtout << \"operator== \" << one.node == two.node << std::endl;\n// \tif(one.node == two.node) return true;\n// \treturn false;\n// \t}\n// \n// template <class T, class tree_node_allocator>\n// bool operator>(const typename tree<T, tree_node_allocator>::iterator_base& one,\n// \t\t\t\t\tconst typename tree<T, tree_node_allocator>::iterator_base& two)\n// \t{\n// \ttxtout << \"operator> \" << one.node < two.node << std::endl;\n// \tif(one.node > two.node) return true;\n// \treturn false;\n// \t}\n\n\n\n// Tree\n\ntemplate <class T, class tree_node_allocator>\ntree<T, tree_node_allocator>::tree()\n\t: alloc_()\n\t{\n\thead_initialise_();\n\t}\n\ntemplate <class T, class tree_node_allocator>\t\t\ntree<T, tree_node_allocator>::tree(const tree_node_allocator& alloc)\n\t: alloc_(alloc)\n\t{\n\thead_initialise_();\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntree<T, tree_node_allocator>::tree(const T& x)\n\t: alloc_()\n\t{\n\thead_initialise_();\n\tset_head(x);\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntree<T, tree_node_allocator>::tree(const T& x, const tree_node_allocator& alloc)\n\t: alloc_(alloc)\n\t{\n\thead_initialise_();\n\tset_head(x);\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntree<T, tree_node_allocator>::tree(tree<T, tree_node_allocator>&& x)\n\t: alloc_(std::move(x.alloc_))\n\t{\n\thead_initialise_();\n\tif(x.head->next_sibling!=x.feet) { // move tree if non-empty only\n\t\thead->next_sibling=x.head->next_sibling;\n\t\tfeet->prev_sibling=x.feet->prev_sibling;\n\t\tx.head->next_sibling->prev_sibling=head;\n\t\tx.feet->prev_sibling->next_sibling=feet;\n\t\tx.head->next_sibling=x.feet;\n\t\tx.feet->prev_sibling=x.head;\n\t\t}\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntree<T, tree_node_allocator>::tree(tree<T, tree_node_allocator>&& x, const tree_node_allocator& alloc)\n\t: alloc_(alloc)\n\t{\n\thead_initialise_();\n\tif(x.head->next_sibling!=x.feet) { // move tree if non-empty only\n\t\thead->next_sibling=x.head->next_sibling;\n\t\tfeet->prev_sibling=x.feet->prev_sibling;\n\t\tx.head->next_sibling->prev_sibling=head;\n\t\tx.feet->prev_sibling->next_sibling=feet;\n\t\tx.head->next_sibling=x.feet;\n\t\tx.feet->prev_sibling=x.head;\n\t\t}\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntree<T, tree_node_allocator>::tree(const iterator_base& other)\n\t: alloc_()\n\t{\n\thead_initialise_();\n\tset_head((*other));\n\treplace(begin(), other);\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntree<T, tree_node_allocator>::tree(const iterator_base& other, const tree_node_allocator& alloc)\n\t: alloc_(alloc)\n\t{\n\thead_initialise_();\n\tset_head((*other));\n\treplace(begin(), other);\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntree<T, tree_node_allocator>::~tree()\n\t{\n\tclear();\n\tstd::allocator_traits<decltype(alloc_)>::destroy(alloc_, head);\n\tstd::allocator_traits<decltype(alloc_)>::destroy(alloc_, feet);\n\tstd::allocator_traits<decltype(alloc_)>::deallocate(alloc_, head, 1);\n\tstd::allocator_traits<decltype(alloc_)>::deallocate(alloc_, feet, 1);\n\t}\n\ntemplate <class T, class tree_node_allocator>\nvoid tree<T, tree_node_allocator>::head_initialise_() \n   { \n   head = std::allocator_traits<decltype(alloc_)>::allocate(alloc_, 1, 0);\n   feet = std::allocator_traits<decltype(alloc_)>::allocate(alloc_, 1, 0);\n\tstd::allocator_traits<decltype(alloc_)>::construct(alloc_, head, tree_node_<T>());\n\tstd::allocator_traits<decltype(alloc_)>::construct(alloc_, feet, tree_node_<T>());\t\n\n   head->parent=0;\n   head->first_child=0;\n   head->last_child=0;\n   head->prev_sibling=0; //head;\n   head->next_sibling=feet; //head;\n\n\tfeet->parent=0;\n\tfeet->first_child=0;\n\tfeet->last_child=0;\n\tfeet->prev_sibling=head;\n\tfeet->next_sibling=0;\n   }\n\ntemplate <class T, class tree_node_allocator>\ntree<T,tree_node_allocator>& tree<T, tree_node_allocator>::operator=(const tree<T, tree_node_allocator>& other)\n\t{\n\tif(this != &other) {\n\t\t// Handle allocator propagation on copy assignment\n\t\tif constexpr(std::allocator_traits<tree_node_allocator>::propagate_on_container_copy_assignment::value) {\n\t\t\tif (alloc_ != other.alloc_) {\n\t\t\t\tclear();\n\t\t\t\talloc_ = other.alloc_;\n\t\t\t\t}\n\t\t\t}\n\t\tcopy_(other);\n\t\t}\n\treturn *this;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntree<T,tree_node_allocator>& tree<T, tree_node_allocator>::operator=(tree<T, tree_node_allocator>&& other)\n\t{\n\tif(this != &other) {\n      // Handle allocator propagation on move assignment  \n\t\tif constexpr(std::allocator_traits<tree_node_allocator>::propagate_on_container_move_assignment::value) {\n\t\t\tclear();\n\t\t\talloc_ = std::move(other.alloc_);\n\t\t\t// Move the tree structure...\n\t\t\t}\n\t\telse if (alloc_ == other.alloc_) {\n\t\t\t// Can move\n\t\t\tclear();\n\t\t\t// Move the tree structure...\n\t\t\t}\n\t\telse {\n\t\t\t// Must copy since allocators differ and don't propagate\n\t\t\tcopy_(other);\n\t\t\treturn *this;\n\t\t\t}\t\t\n\t\t\n\t\thead->next_sibling=other.head->next_sibling;\n\t\tfeet->prev_sibling=other.feet->prev_sibling;\n\t\tother.head->next_sibling->prev_sibling=head;\n\t\tother.feet->prev_sibling->next_sibling=feet;\n\t\tother.head->next_sibling=other.feet;\n\t\tother.feet->prev_sibling=other.head;\n\t\t}\n\treturn *this;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntree<T, tree_node_allocator>::tree(const tree<T, tree_node_allocator>& other)\n\t: alloc_(std::allocator_traits<tree_node_allocator>::select_on_container_copy_construction(other.alloc_))\n\t{\n\thead_initialise_();\n\tcopy_(other);\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntree<T, tree_node_allocator>::tree(const tree<T, tree_node_allocator>& other, const tree_node_allocator& alloc)\n\t: alloc_(alloc)\n\t{\n\thead_initialise_();\n\tcopy_(other);\n\t}\n\ntemplate <class T, class tree_node_allocator>\nvoid tree<T, tree_node_allocator>::copy_(const tree<T, tree_node_allocator>& other) \n\t{\n\tclear();\n\tpre_order_iterator it=other.begin(), to=begin();\n\twhile(it!=other.end()) {\n\t\tto=insert(to, (*it));\n\t\tit.skip_children();\n\t\t++it;\n\t\t}\n\tto=begin();\n\tit=other.begin();\n\twhile(it!=other.end()) {\n\t\tto=replace(to, it);\n\t\tto.skip_children();\n\t\tit.skip_children();\n\t\t++to;\n\t\t++it;\n\t\t}\n\t}\n\ntemplate <class T, class tree_node_allocator>\nvoid tree<T, tree_node_allocator>::clear()\n\t{\n\tif(head)\n\t\twhile(head->next_sibling!=feet)\n\t\t\terase(pre_order_iterator(head->next_sibling));\n\t}\n\ntemplate<class T, class tree_node_allocator> \nvoid tree<T, tree_node_allocator>::erase_children(const iterator_base& it)\n\t{\n//\tstd::cout << \"erase_children \" << it.node << std::endl;\n\tif(it.node==0) return;\n\n\ttree_node *cur=it.node->first_child;\n\ttree_node *prev=0;\n\n\twhile(cur!=0) {\n\t\tprev=cur;\n\t\tcur=cur->next_sibling;\n\t\terase_children(pre_order_iterator(prev));\n\t\tstd::allocator_traits<decltype(alloc_)>::destroy(alloc_, prev);\n\t\tstd::allocator_traits<decltype(alloc_)>::deallocate(alloc_, prev, 1);\n\t\t}\n\tit.node->first_child=0;\n\tit.node->last_child=0;\n//\tstd::cout << \"exit\" << std::endl;\n\t}\n\ntemplate<class T, class tree_node_allocator> \nvoid tree<T, tree_node_allocator>::erase_right_siblings(const iterator_base& it)\n\t{\n\tif(it.node==0) return;\n\n\ttree_node *cur=it.node->next_sibling;\n\ttree_node *prev=0;\n\n\twhile(cur!=0) {\n\t\tprev=cur;\n\t\tcur=cur->next_sibling;\n\t\terase_children(pre_order_iterator(prev));\n\t\tstd::allocator_traits<decltype(alloc_)>::destroy(alloc_, prev);\n\t\tstd::allocator_traits<decltype(alloc_)>::deallocate(alloc_, prev, 1);\n\t\t}\n\tit.node->next_sibling=0;\n\tif(it.node->parent!=0)\n\t\tit.node->parent->last_child=it.node;\n\t}\n\ntemplate<class T, class tree_node_allocator> \nvoid tree<T, tree_node_allocator>::erase_left_siblings(const iterator_base& it)\n\t{\n\tif(it.node==0) return;\n\n\ttree_node *cur=it.node->prev_sibling;\n\ttree_node *prev=0;\n\n\twhile(cur!=0) {\n\t\tprev=cur;\n\t\tcur=cur->prev_sibling;\n\t\terase_children(pre_order_iterator(prev));\n\t\tstd::allocator_traits<decltype(alloc_)>::destroy(alloc_, prev);\n\t\tstd::allocator_traits<decltype(alloc_)>::deallocate(alloc_, prev, 1);\n\t\t}\n\tit.node->prev_sibling=0;\n\tif(it.node->parent!=0)\n\t\tit.node->parent->first_child=it.node;\n\t}\n\ntemplate<class T, class tree_node_allocator> \ntemplate<class iter>\niter tree<T, tree_node_allocator>::erase(iter it)\n\t{\n\ttree_node *cur=it.node;\n\tassert(cur!=head);\n\titer ret=it;\n\tret.skip_children();\n\t++ret;\n\terase_children(it);\n\tif(cur->prev_sibling==0) {\n\t\tcur->parent->first_child=cur->next_sibling;\n\t\t}\n\telse {\n\t\tcur->prev_sibling->next_sibling=cur->next_sibling;\n\t\t}\n\tif(cur->next_sibling==0) {\n\t\tcur->parent->last_child=cur->prev_sibling;\n\t\t}\n\telse {\n\t\tcur->next_sibling->prev_sibling=cur->prev_sibling;\n\t\t}\n\n\tstd::allocator_traits<decltype(alloc_)>::destroy(alloc_, cur);\n\tstd::allocator_traits<decltype(alloc_)>::deallocate(alloc_, cur, 1);\n\treturn ret;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::pre_order_iterator tree<T, tree_node_allocator>::begin() const\n\t{\n\treturn pre_order_iterator(head->next_sibling);\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::pre_order_iterator tree<T, tree_node_allocator>::end() const\n\t{\n\treturn pre_order_iterator(feet);\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::breadth_first_queued_iterator tree<T, tree_node_allocator>::begin_breadth_first() const\n\t{\n\treturn breadth_first_queued_iterator(head->next_sibling);\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::breadth_first_queued_iterator tree<T, tree_node_allocator>::end_breadth_first() const\n\t{\n\treturn breadth_first_queued_iterator();\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::post_order_iterator tree<T, tree_node_allocator>::begin_post() const\n\t{\n\ttree_node *tmp=head->next_sibling;\n\tif(tmp!=feet) {\n\t\twhile(tmp->first_child)\n\t\t\ttmp=tmp->first_child;\n\t\t}\n\treturn post_order_iterator(tmp);\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::post_order_iterator tree<T, tree_node_allocator>::end_post() const\n\t{\n\treturn post_order_iterator(feet);\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::fixed_depth_iterator tree<T, tree_node_allocator>::begin_fixed(const iterator_base& pos, unsigned int dp, bool walk_back) const\n\t{\n\ttypename tree<T, tree_node_allocator>::fixed_depth_iterator ret;\n\tret.top_node=pos.node;\n\n\ttree_node *tmp=pos.node;\n\tunsigned int curdepth=0;\n\twhile(curdepth<dp) { // go down one level\n\t\twhile(tmp->first_child==0) {\n\t\t\tif(tmp->next_sibling==0) {\n\t\t\t\t// try to walk up and then right again\n\t\t\t\tdo {\n\t\t\t\t\tif(tmp==ret.top_node)\n\t\t\t\t\t   throw std::range_error(\"tree: begin_fixed out of range\");\n\t\t\t\t\ttmp=tmp->parent;\n               if(tmp==0) \n\t\t\t\t\t   throw std::range_error(\"tree: begin_fixed out of range\");\n               --curdepth;\n\t\t\t\t   } while(tmp->next_sibling==0);\n\t\t\t\t}\n\t\t\ttmp=tmp->next_sibling;\n\t\t\t}\n\t\ttmp=tmp->first_child;\n\t\t++curdepth;\n\t\t}\n\n\t// Now walk back to the first sibling in this range.\n\tif(walk_back)\n\twhile(tmp->prev_sibling!=0)\n\t\ttmp=tmp->prev_sibling;\t\n\t\n\tret.node=tmp;\n\treturn ret;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::fixed_depth_iterator tree<T, tree_node_allocator>::end_fixed(const iterator_base& pos, unsigned int dp) const\n\t{\n\tassert(1==0); // FIXME: not correct yet: use is_valid() as a temporary workaround \n\ttree_node *tmp=pos.node;\n\tunsigned int curdepth=1;\n\twhile(curdepth<dp) { // go down one level\n\t\twhile(tmp->first_child==0) {\n\t\t\ttmp=tmp->next_sibling;\n\t\t\tif(tmp==0)\n\t\t\t\tthrow std::range_error(\"tree: end_fixed out of range\");\n\t\t\t}\n\t\ttmp=tmp->first_child;\n\t\t++curdepth;\n\t\t}\n\treturn tmp;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::sibling_iterator tree<T, tree_node_allocator>::begin(const iterator_base& pos) \n\t{\n\tassert(pos.node!=0);\n\tif(pos.node->first_child==0) {\n\t\treturn end(pos);\n\t\t}\n\treturn pos.node->first_child;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::sibling_iterator tree<T, tree_node_allocator>::end(const iterator_base& pos) \n\t{\n\tsibling_iterator ret(0);\n\tret.parent_=pos.node;\n\treturn ret;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::leaf_iterator tree<T, tree_node_allocator>::begin_leaf() const\n   {\n   tree_node *tmp=head->next_sibling;\n   if(tmp!=feet) {\n      while(tmp->first_child)\n         tmp=tmp->first_child;\n      }\n   return leaf_iterator(tmp);\n   }\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::leaf_iterator tree<T, tree_node_allocator>::end_leaf() const\n   {\n   return leaf_iterator(feet);\n   }\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::path_t tree<T, tree_node_allocator>::path_from_iterator(const iterator_base& iter, const iterator_base& top) const\n\t{\n\tpath_t path;\n\ttree_node *walk=iter.node;\n\t\t\n\tdo {\n\t\tif(path.size()>0)\n\t\t\twalk=walk->parent;\n\t\tint num=0;\n\t\twhile(walk!=top.node && walk->prev_sibling!=0 && walk->prev_sibling!=head) {\n\t\t\t++num;\n\t\t\twalk=walk->prev_sibling;\n\t\t\t}\n\t\tpath.push_back(num);\n\t\t}\n\twhile(walk->parent!=0 && walk!=top.node);\n\n\tstd::reverse(path.begin(), path.end());\n\treturn path;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::iterator tree<T, tree_node_allocator>::iterator_from_path(const path_t& path, const iterator_base& top) const\n\t{\n\titerator it=top;\n\ttree_node *walk=it.node;\n\n\tfor(size_t step=0; step<path.size(); ++step) {\n\t\tif(step>0)\n\t\t\twalk=walk->first_child;\n\t\tif(walk==0)\n\t\t\tthrow std::range_error(\"tree::iterator_from_path: no more nodes at step \"+std::to_string(step));\n\n\t\tfor(int i=0; i<path[step]; ++i) {\n\t\t\twalk=walk->next_sibling;\n\t\t\tif(walk==0)\n\t\t\t\tthrow std::range_error(\"tree::iterator_from_path: out of siblings at step \"+std::to_string(step));\n\t\t\t}\n\t\t}\n\tit.node=walk;\n\treturn it;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::leaf_iterator tree<T, tree_node_allocator>::begin_leaf(const iterator_base& top) const\n   {\n\ttree_node *tmp=top.node;\n\twhile(tmp->first_child)\n\t\t tmp=tmp->first_child;\n   return leaf_iterator(tmp, top.node);\n   }\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::leaf_iterator tree<T, tree_node_allocator>::end_leaf(const iterator_base& top) const\n   {\n   return leaf_iterator(top.node, top.node);\n   }\n\ntemplate <class T, class tree_node_allocator>\ntemplate <typename iter>\niter tree<T, tree_node_allocator>::parent(iter position) \n\t{\n\tif(position.node==0)\n\t\tthrow navigation_error(\"tree: attempt to navigate from null iterator.\");\n\t \n\tif(position.node->parent==0) \n\t\tthrow navigation_error(\"tree: attempt to navigate up past head node.\");\n\n\treturn iter(position.node->parent);\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntemplate <typename iter>\niter tree<T, tree_node_allocator>::previous_sibling(iter position) \n\t{\n\tassert(position.node!=0);\n\titer ret(position);\n\tret.node=position.node->prev_sibling;\n\treturn ret;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntemplate <typename iter>\niter tree<T, tree_node_allocator>::next_sibling(iter position) \n\t{\n\tassert(position.node!=0);\n\titer ret(position);\n\tret.node=position.node->next_sibling;\n\treturn ret;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntemplate <typename iter>\niter tree<T, tree_node_allocator>::next_at_same_depth(iter position) const\n\t{\n\t// We make use of a temporary fixed_depth iterator to implement this.\n\n\ttypename tree<T, tree_node_allocator>::fixed_depth_iterator tmp(position.node);\n\n\t++tmp;\n\treturn iter(tmp);\n\n\t//\tassert(position.node!=0);\n\t//\titer ret(position);\n\t//\n\t//\tif(position.node->next_sibling) {\n\t//\t\tret.node=position.node->next_sibling;\n\t//\t\t}\n\t//\telse {\n\t//\t\tint relative_depth=0;\n\t//\t   upper:\n\t//\t\tdo {\n\t//\t\t\tret.node=ret.node->parent;\n\t//\t\t\tif(ret.node==0) return ret;\n\t//\t\t\t--relative_depth;\n\t//\t\t\t} while(ret.node->next_sibling==0);\n\t//\t   lower:\n\t//\t\tret.node=ret.node->next_sibling;\n\t//\t\twhile(ret.node->first_child==0) {\n\t//\t\t\tif(ret.node->next_sibling==0)\n\t//\t\t\t\tgoto upper;\n\t//\t\t\tret.node=ret.node->next_sibling;\n\t//\t\t\tif(ret.node==0) return ret;\n\t//\t\t\t}\n\t//\t\twhile(relative_depth<0 && ret.node->first_child!=0) {\n\t//\t\t\tret.node=ret.node->first_child;\n\t//\t\t\t++relative_depth;\n\t//\t\t\t}\n\t//\t\tif(relative_depth<0) {\n\t//\t\t\tif(ret.node->next_sibling==0) goto upper;\n\t//\t\t\telse                          goto lower;\n\t//\t\t\t}\n\t//\t\t}\n\t//\treturn ret;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntemplate <typename iter>\niter tree<T, tree_node_allocator>::append_child(iter position)\n \t{\n\tassert(position.node!=head);\n\tassert(position.node!=feet);\n\tassert(position.node);\n\n\ttree_node *tmp=std::allocator_traits<decltype(alloc_)>::allocate(alloc_, 1, 0);\n\tstd::allocator_traits<decltype(alloc_)>::construct(alloc_, tmp, tree_node_<T>());\n\ttmp->first_child=0;\n\ttmp->last_child=0;\n\n\ttmp->parent=position.node;\n\tif(position.node->last_child!=0) {\n\t\tposition.node->last_child->next_sibling=tmp;\n\t\t}\n\telse {\n\t\tposition.node->first_child=tmp;\n\t\t}\n\ttmp->prev_sibling=position.node->last_child;\n\tposition.node->last_child=tmp;\n\ttmp->next_sibling=0;\n\treturn tmp;\n \t}\n\ntemplate <class T, class tree_node_allocator>\ntemplate <typename iter>\niter tree<T, tree_node_allocator>::prepend_child(iter position)\n \t{\n\tassert(position.node!=head);\n\tassert(position.node!=feet);\n\tassert(position.node);\n\n\ttree_node *tmp=std::allocator_traits<decltype(alloc_)>::allocate(alloc_, 1, 0);\n\tstd::allocator_traits<decltype(alloc_)>::construct(alloc_, tmp, tree_node_<T>());\n\ttmp->first_child=0;\n\ttmp->last_child=0;\n\n\ttmp->parent=position.node;\n\tif(position.node->first_child!=0) {\n\t\tposition.node->first_child->prev_sibling=tmp;\n\t\t}\n\telse {\n\t\tposition.node->last_child=tmp;\n\t\t}\n\ttmp->next_sibling=position.node->first_child;\n\tposition.node->prev_child=tmp;\n\ttmp->prev_sibling=0;\n\treturn tmp;\n \t}\n\ntemplate <class T, class tree_node_allocator>\ntemplate <class iter>\niter tree<T, tree_node_allocator>::append_child(iter position, const T& x)\n\t{\n\t// If your program fails here you probably used 'append_child' to add the top\n\t// node to an empty tree. From version 1.45 the top element should be added\n\t// using 'insert'. See the documentation for further information, and sorry about\n\t// the API change.\n\tassert(position.node!=head);\n\tassert(position.node!=feet);\n\tassert(position.node);\n\n\ttree_node *tmp=std::allocator_traits<decltype(alloc_)>::allocate(alloc_, 1, 0);\n\tstd::allocator_traits<decltype(alloc_)>::construct(alloc_, tmp, x);\n\ttmp->first_child=0;\n\ttmp->last_child=0;\n\n\ttmp->parent=position.node;\n\tif(position.node->last_child!=0) {\n\t\tposition.node->last_child->next_sibling=tmp;\n\t\t}\n\telse {\n\t\tposition.node->first_child=tmp;\n\t\t}\n\ttmp->prev_sibling=position.node->last_child;\n\tposition.node->last_child=tmp;\n\ttmp->next_sibling=0;\n\treturn tmp;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntemplate <class iter>\niter tree<T, tree_node_allocator>::append_child(iter position, T&& x)\n\t{\n\tassert(position.node!=head);\n\tassert(position.node!=feet);\n\tassert(position.node);\n\n\ttree_node *tmp=std::allocator_traits<decltype(alloc_)>::allocate(alloc_, 1, 0);\n\tstd::allocator_traits<decltype(alloc_)>::construct(alloc_, tmp); // Here is where the move semantics kick in\n\n\tstd::swap(tmp->data, x);\n\t\n\ttmp->first_child=0;\n\ttmp->last_child=0;\n\n\ttmp->parent=position.node;\n\tif(position.node->last_child!=0) {\n\t\tposition.node->last_child->next_sibling=tmp;\n\t\t}\n\telse {\n\t\tposition.node->first_child=tmp;\n\t\t}\n\ttmp->prev_sibling=position.node->last_child;\n\tposition.node->last_child=tmp;\n\ttmp->next_sibling=0;\n\treturn tmp;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntemplate <class iter>\niter tree<T, tree_node_allocator>::prepend_child(iter position, const T& x)\n\t{\n\tassert(position.node!=head);\n\tassert(position.node!=feet);\n\tassert(position.node);\n\n\ttree_node *tmp=std::allocator_traits<decltype(alloc_)>::allocate(alloc_, 1, 0);\n\tstd::allocator_traits<decltype(alloc_)>::construct(alloc_, tmp, x);\n\ttmp->first_child=0;\n\ttmp->last_child=0;\n\n\ttmp->parent=position.node;\n\tif(position.node->first_child!=0) {\n\t\tposition.node->first_child->prev_sibling=tmp;\n\t\t}\n\telse {\n\t\tposition.node->last_child=tmp;\n\t\t}\n\ttmp->next_sibling=position.node->first_child;\n\tposition.node->first_child=tmp;\n\ttmp->prev_sibling=0;\n\treturn tmp;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntemplate <class iter>\niter tree<T, tree_node_allocator>::prepend_child(iter position, T&& x)\n\t{\n\tassert(position.node!=head);\n\tassert(position.node!=feet);\n\tassert(position.node);\n\n\ttree_node *tmp=std::allocator_traits<decltype(alloc_)>::allocate(alloc_, 1, 0);\n\tstd::allocator_traits<decltype(alloc_)>::construct(alloc_, tmp);\n\tstd::swap(tmp->data, x);\n\n\ttmp->first_child=0;\n\ttmp->last_child=0;\n\n\ttmp->parent=position.node;\n\tif(position.node->first_child!=0) {\n\t\tposition.node->first_child->prev_sibling=tmp;\n\t\t}\n\telse {\n\t\tposition.node->last_child=tmp;\n\t\t}\n\ttmp->next_sibling=position.node->first_child;\n\tposition.node->first_child=tmp;\n\ttmp->prev_sibling=0;\n\treturn tmp;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntemplate <class iter>\niter tree<T, tree_node_allocator>::append_child(iter position, iter other)\n\t{\n\tassert(position.node!=head);\n\tassert(position.node!=feet);\n\tassert(position.node);\n\n\tsibling_iterator aargh=append_child(position, value_type());\n\treturn replace(aargh, other);\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntemplate <class iter>\niter tree<T, tree_node_allocator>::prepend_child(iter position, iter other)\n\t{\n\tassert(position.node!=head);\n\tassert(position.node!=feet);\n\tassert(position.node);\n\n\tsibling_iterator aargh=prepend_child(position, value_type());\n\treturn replace(aargh, other);\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntemplate <class iter>\niter tree<T, tree_node_allocator>::append_children(iter position, sibling_iterator from, sibling_iterator to)\n\t{\n\tassert(position.node!=head);\n\tassert(position.node!=feet);\n\tassert(position.node);\n\n\titer ret=from;\n\n\twhile(from!=to) {\n\t\tinsert_subtree(position.end(), from);\n\t\t++from;\n\t\t}\n\treturn ret;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntemplate <class iter>\niter tree<T, tree_node_allocator>::prepend_children(iter position, sibling_iterator from, sibling_iterator to)\n\t{\n\tassert(position.node!=head);\n\tassert(position.node!=feet);\n\tassert(position.node);\n\n\tif(from==to) return from; // should return end of tree?\n\n\titer ret;\n\tdo {\n\t\t--to;\n\t\tret=insert_subtree(position.begin(), to);\n\t\t}\n\twhile(to!=from);\n\n\treturn ret;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::pre_order_iterator tree<T, tree_node_allocator>::set_head(const T& x)\n\t{\n\tassert(head->next_sibling==feet);\n\treturn insert(iterator(feet), x);\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::pre_order_iterator tree<T, tree_node_allocator>::set_head(T&& x)\n\t{\n\tassert(head->next_sibling==feet);\n\treturn insert(iterator(feet), x);\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntemplate <class iter>\niter tree<T, tree_node_allocator>::insert(iter position, const T& x)\n\t{\n\tif(position.node==0) {\n\t\tposition.node=feet; // Backward compatibility: when calling insert on a null node,\n\t\t                    // insert before the feet.\n\t\t}\n\tassert(position.node!=head); // Cannot insert before head.\n\n\ttree_node *tmp=std::allocator_traits<decltype(alloc_)>::allocate(alloc_, 1, 0);\n\tstd::allocator_traits<decltype(alloc_)>::construct(alloc_, tmp, x);\n\ttmp->first_child=0;\n\ttmp->last_child=0;\n\n\ttmp->parent=position.node->parent;\n\ttmp->next_sibling=position.node;\n\ttmp->prev_sibling=position.node->prev_sibling;\n\tposition.node->prev_sibling=tmp;\n\n\tif(tmp->prev_sibling==0) {\n\t\tif(tmp->parent) // when inserting nodes at the head, there is no parent\n\t\t\ttmp->parent->first_child=tmp;\n\t\t}\n\telse\n\t\ttmp->prev_sibling->next_sibling=tmp;\n\treturn tmp;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntemplate <class iter>\niter tree<T, tree_node_allocator>::insert(iter position, T&& x)\n\t{\n\tif(position.node==0) {\n\t\tposition.node=feet; // Backward compatibility: when calling insert on a null node,\n\t\t                    // insert before the feet.\n\t\t}\n\ttree_node *tmp=std::allocator_traits<decltype(alloc_)>::allocate(alloc_, 1, 0);\n\tstd::allocator_traits<decltype(alloc_)>::construct(alloc_, tmp);\n\tstd::swap(tmp->data, x); // Move semantics\n\ttmp->first_child=0;\n\ttmp->last_child=0;\n\n\ttmp->parent=position.node->parent;\n\ttmp->next_sibling=position.node;\n\ttmp->prev_sibling=position.node->prev_sibling;\n\tposition.node->prev_sibling=tmp;\n\n\tif(tmp->prev_sibling==0) {\n\t\tif(tmp->parent) // when inserting nodes at the head, there is no parent\n\t\t\ttmp->parent->first_child=tmp;\n\t\t}\n\telse\n\t\ttmp->prev_sibling->next_sibling=tmp;\n\treturn tmp;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::sibling_iterator tree<T, tree_node_allocator>::insert(sibling_iterator position, const T& x)\n\t{\n\ttree_node *tmp=std::allocator_traits<decltype(alloc_)>::allocate(alloc_, 1, 0);\n\tstd::allocator_traits<decltype(alloc_)>::construct(alloc_, tmp, x);\n\ttmp->first_child=0;\n\ttmp->last_child=0;\n\n\ttmp->next_sibling=position.node;\n\tif(position.node==0) { // iterator points to end of a subtree\n\t\ttmp->parent=position.parent_;\n\t\ttmp->prev_sibling=position.range_last();\n\t\ttmp->parent->last_child=tmp;\n\t\t}\n\telse {\n\t\ttmp->parent=position.node->parent;\n\t\ttmp->prev_sibling=position.node->prev_sibling;\n\t\tposition.node->prev_sibling=tmp;\n\t\t}\n\n\tif(tmp->prev_sibling==0) {\n\t\tif(tmp->parent) // when inserting nodes at the head, there is no parent\n\t\t\ttmp->parent->first_child=tmp;\n\t\t}\n\telse\n\t\ttmp->prev_sibling->next_sibling=tmp;\n\treturn tmp;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::sibling_iterator tree<T, tree_node_allocator>::insert(sibling_iterator position, T&& x)\n\t{\n\ttree_node *tmp=std::allocator_traits<decltype(alloc_)>::allocate(alloc_, 1, 0);\n\tstd::allocator_traits<decltype(alloc_)>::construct(alloc_, tmp);\n\tstd::swap(tmp->data, x); // Move semantics\n\n\ttmp->first_child=0;\n\ttmp->last_child=0;\n\n\ttmp->next_sibling=position.node;\n\tif(position.node==0) { // iterator points to end of a subtree\n\t\ttmp->parent=position.parent_;\n\t\ttmp->prev_sibling=position.range_last();\n\t\ttmp->parent->last_child=tmp;\n\t\t}\n\telse {\n\t\ttmp->parent=position.node->parent;\n\t\ttmp->prev_sibling=position.node->prev_sibling;\n\t\tposition.node->prev_sibling=tmp;\n\t\t}\n\n\tif(tmp->prev_sibling==0) {\n\t\tif(tmp->parent) // when inserting nodes at the head, there is no parent\n\t\t\ttmp->parent->first_child=tmp;\n\t\t}\n\telse\n\t\ttmp->prev_sibling->next_sibling=tmp;\n\treturn tmp;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntemplate <class iter>\niter tree<T, tree_node_allocator>::insert_after(iter position, const T& x)\n\t{\n\ttree_node *tmp=std::allocator_traits<decltype(alloc_)>::allocate(alloc_, 1, 0);\n\tstd::allocator_traits<decltype(alloc_)>::construct(alloc_, tmp, x);\n\ttmp->first_child=0;\n\ttmp->last_child=0;\n\n\ttmp->parent=position.node->parent;\n\ttmp->prev_sibling=position.node;\n\ttmp->next_sibling=position.node->next_sibling;\n\tposition.node->next_sibling=tmp;\n\n\tif(tmp->next_sibling==0) {\n\t\tif(tmp->parent) // when inserting nodes at the head, there is no parent\n\t\t\ttmp->parent->last_child=tmp;\n\t\t}\n\telse {\n\t\ttmp->next_sibling->prev_sibling=tmp;\n\t\t}\n\treturn tmp;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntemplate <class iter>\niter tree<T, tree_node_allocator>::insert_after(iter position, T&& x)\n\t{\n\ttree_node *tmp=std::allocator_traits<decltype(alloc_)>::allocate(alloc_, 1, 0);\n\tstd::allocator_traits<decltype(alloc_)>::construct(alloc_, tmp);\n\tstd::swap(tmp->data, x); // move semantics\n\ttmp->first_child=0;\n\ttmp->last_child=0;\n\n\ttmp->parent=position.node->parent;\n\ttmp->prev_sibling=position.node;\n\ttmp->next_sibling=position.node->next_sibling;\n\tposition.node->next_sibling=tmp;\n\n\tif(tmp->next_sibling==0) {\n\t\tif(tmp->parent) // when inserting nodes at the head, there is no parent\n\t\t\ttmp->parent->last_child=tmp;\n\t\t}\n\telse {\n\t\ttmp->next_sibling->prev_sibling=tmp;\n\t\t}\n\treturn tmp;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntemplate <class iter>\niter tree<T, tree_node_allocator>::insert_subtree(iter position, const iterator_base& subtree)\n\t{\n\t// insert dummy\n\titer it=insert(position, value_type());\n\t// replace dummy with subtree\n\treturn replace(it, subtree);\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntemplate <class iter>\niter tree<T, tree_node_allocator>::insert_subtree_after(iter position, const iterator_base& subtree)\n\t{\n\t// insert dummy\n\titer it=insert_after(position, value_type());\n\t// replace dummy with subtree\n\treturn replace(it, subtree);\n\t}\n\n// template <class T, class tree_node_allocator>\n// template <class iter>\n// iter tree<T, tree_node_allocator>::insert_subtree(sibling_iterator position, iter subtree)\n// \t{\n// \t// insert dummy\n// \titer it(insert(position, value_type()));\n// \t// replace dummy with subtree\n// \treturn replace(it, subtree);\n// \t}\n\ntemplate <class T, class tree_node_allocator>\ntemplate <class iter>\niter tree<T, tree_node_allocator>::replace(iter position, const T& x)\n\t{\n//\tkp::destructor(&position.node->data);\n//\tkp::constructor(&position.node->data, x);\n\tposition.node->data=x;\n//\talloc_.destroy(position.node);\n//\talloc_.construct(position.node, x);\n\treturn position;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntemplate <class iter>\niter tree<T, tree_node_allocator>::replace(iter position, const iterator_base& from)\n\t{\n\tassert(position.node!=head);\n\ttree_node *current_from=from.node;\n\ttree_node *start_from=from.node;\n\ttree_node *current_to  =position.node;\n\n\t// replace the node at position with head of the replacement tree at from\n//\tstd::cout << \"warning!\" << position.node << std::endl;\n\terase_children(position);\t\n//\tstd::cout << \"no warning!\" << std::endl;\n\ttree_node *tmp=std::allocator_traits<decltype(alloc_)>::allocate(alloc_, 1, 0);\n\tstd::allocator_traits<decltype(alloc_)>::construct(alloc_, tmp, (*from));\n\ttmp->first_child=0;\n\ttmp->last_child=0;\n\tif(current_to->prev_sibling==0) {\n\t\tif(current_to->parent!=0)\n\t\t\tcurrent_to->parent->first_child=tmp;\n\t\t}\n\telse {\n\t\tcurrent_to->prev_sibling->next_sibling=tmp;\n\t\t}\n\ttmp->prev_sibling=current_to->prev_sibling;\n\tif(current_to->next_sibling==0) {\n\t\tif(current_to->parent!=0)\n\t\t\tcurrent_to->parent->last_child=tmp;\n\t\t}\n\telse {\n\t\tcurrent_to->next_sibling->prev_sibling=tmp;\n\t\t}\n\ttmp->next_sibling=current_to->next_sibling;\n\ttmp->parent=current_to->parent;\n//\tkp::destructor(&current_to->data);\n\tstd::allocator_traits<decltype(alloc_)>::destroy(alloc_, current_to);\n\tstd::allocator_traits<decltype(alloc_)>::deallocate(alloc_, current_to, 1);\n\tcurrent_to=tmp;\n\t\n\t// only at this stage can we fix 'last'\n\ttree_node *last=from.node->next_sibling;\n\n\tpre_order_iterator toit=tmp;\n\t// copy all children\n\tdo {\n\t\tassert(current_from!=0);\n\t\tif(current_from->first_child != 0) {\n\t\t\tcurrent_from=current_from->first_child;\n\t\t\ttoit=append_child(toit, current_from->data);\n\t\t\t}\n\t\telse {\n\t\t\twhile(current_from->next_sibling==0 && current_from!=start_from) {\n\t\t\t\tcurrent_from=current_from->parent;\n\t\t\t\ttoit=parent(toit);\n\t\t\t\tassert(current_from!=0);\n\t\t\t\t}\n\t\t\tcurrent_from=current_from->next_sibling;\n\t\t\tif(current_from!=last) {\n\t\t\t\ttoit=append_child(parent(toit), current_from->data);\n\t\t\t\t}\n\t\t\t}\n\t\t}\n\twhile(current_from!=last);\n\n\treturn current_to;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::sibling_iterator tree<T, tree_node_allocator>::replace(\n\tsibling_iterator orig_begin, \n\tsibling_iterator orig_end, \n\tsibling_iterator new_begin, \n\tsibling_iterator new_end)\n\t{\n\ttree_node *orig_first=orig_begin.node;\n\ttree_node *new_first=new_begin.node;\n\ttree_node *orig_last=orig_first;\n\twhile((++orig_begin)!=orig_end)\n\t\torig_last=orig_last->next_sibling;\n\ttree_node *new_last=new_first;\n\twhile((++new_begin)!=new_end)\n\t\tnew_last=new_last->next_sibling;\n\n\t// insert all siblings in new_first..new_last before orig_first\n\tbool first=true;\n\tpre_order_iterator ret;\n\twhile(1==1) {\n\t\tpre_order_iterator tt=insert_subtree(pre_order_iterator(orig_first), pre_order_iterator(new_first));\n\t\tif(first) {\n\t\t\tret=tt;\n\t\t\tfirst=false;\n\t\t\t}\n\t\tif(new_first==new_last)\n\t\t\tbreak;\n\t\tnew_first=new_first->next_sibling;\n\t\t}\n\n\t// erase old range of siblings\n\tbool last=false;\n\ttree_node *next=orig_first;\n\twhile(1==1) {\n\t\tif(next==orig_last) \n\t\t\tlast=true;\n\t\tnext=next->next_sibling;\n\t\terase((pre_order_iterator)orig_first);\n\t\tif(last) \n\t\t\tbreak;\n\t\torig_first=next;\n\t\t}\n\treturn ret;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntemplate <typename iter>\niter tree<T, tree_node_allocator>::flatten(iter position)\n\t{\n\tif(position.node->first_child==0)\n\t\treturn position;\n\n\ttree_node *tmp=position.node->first_child;\n\twhile(tmp) {\n\t\ttmp->parent=position.node->parent;\n\t\ttmp=tmp->next_sibling;\n\t\t} \n\tif(position.node->next_sibling) {\n\t\tposition.node->last_child->next_sibling=position.node->next_sibling;\n\t\tposition.node->next_sibling->prev_sibling=position.node->last_child;\n\t\t}\n\telse {\n\t\tposition.node->parent->last_child=position.node->last_child;\n\t\t}\n\tposition.node->next_sibling=position.node->first_child;\n\tposition.node->next_sibling->prev_sibling=position.node;\n\tposition.node->first_child=0;\n\tposition.node->last_child=0;\n\n\treturn position;\n\t}\n\n\ntemplate <class T, class tree_node_allocator>\ntemplate <typename iter>\niter tree<T, tree_node_allocator>::reparent(iter position, sibling_iterator begin, sibling_iterator end)\n\t{\n\ttree_node *first=begin.node;\n\ttree_node *last=first;\n\n\tassert(first!=position.node);\n\t\n\tif(begin==end) return begin;\n\t// determine last node\n\twhile((++begin)!=end) {\n\t\tlast=last->next_sibling;\n\t\t}\n\t// move subtree\n\tif(first->prev_sibling==0) {\n\t\tfirst->parent->first_child=last->next_sibling;\n\t\t}\n\telse {\n\t\tfirst->prev_sibling->next_sibling=last->next_sibling;\n\t\t}\n\tif(last->next_sibling==0) {\n\t\tlast->parent->last_child=first->prev_sibling;\n\t\t}\n\telse {\n\t\tlast->next_sibling->prev_sibling=first->prev_sibling;\n\t\t}\n\tif(position.node->first_child==0) {\n\t\tposition.node->first_child=first;\n\t\tposition.node->last_child=last;\n\t\tfirst->prev_sibling=0;\n\t\t}\n\telse {\n\t\tposition.node->last_child->next_sibling=first;\n\t\tfirst->prev_sibling=position.node->last_child;\n\t\tposition.node->last_child=last;\n\t\t}\n\tlast->next_sibling=0;\n\n\ttree_node *pos=first;\n   for(;;) {\n\t\tpos->parent=position.node;\n\t\tif(pos==last) break;\n\t\tpos=pos->next_sibling;\n\t\t}\n\n\treturn first;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntemplate <typename iter> iter tree<T, tree_node_allocator>::reparent(iter position, iter from)\n\t{\n\tif(from.node->first_child==0) return position;\n\treturn reparent(position, from.node->first_child, end(from));\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntemplate <typename iter> iter tree<T, tree_node_allocator>::wrap(iter position, const T& x)\n\t{\n\tassert(position.node!=0);\n\tsibling_iterator fr=position, to=position;\n\t++to;\n\titer ret = insert(position, x);\n\treparent(ret, fr, to);\n\treturn ret;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntemplate <typename iter> iter tree<T, tree_node_allocator>::wrap(iter from, iter to, const T& x)\n\t{\n\tassert(from.node!=0);\n\titer ret = insert(from, x);\n\treparent(ret, from, to);\n\treturn ret;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntemplate <typename iter> iter tree<T, tree_node_allocator>::move_after(iter target, iter source)\n   {\n   tree_node *dst=target.node;\n   tree_node *src=source.node;\n   assert(dst);\n   assert(src);\n\n   if(dst==src) return source;\n\tif(dst->next_sibling)\n\t\tif(dst->next_sibling==src) // already in the right spot\n\t\t\treturn source;\n\n   // take src out of the tree\n   if(src->prev_sibling!=0) src->prev_sibling->next_sibling=src->next_sibling;\n   else                     src->parent->first_child=src->next_sibling;\n   if(src->next_sibling!=0) src->next_sibling->prev_sibling=src->prev_sibling;\n   else                     src->parent->last_child=src->prev_sibling;\n\n   // connect it to the new point\n   if(dst->next_sibling!=0) dst->next_sibling->prev_sibling=src;\n   else                     dst->parent->last_child=src;\n   src->next_sibling=dst->next_sibling;\n   dst->next_sibling=src;\n   src->prev_sibling=dst;\n   src->parent=dst->parent;\n   return src;\n   }\n\ntemplate <class T, class tree_node_allocator>\ntemplate <typename iter> iter tree<T, tree_node_allocator>::move_before(iter target, iter source)\n   {\n   tree_node *dst=target.node;\n   tree_node *src=source.node;\n   assert(dst);\n   assert(src);\n\n   if(dst==src) return source;\n\tif(dst->prev_sibling)\n\t\tif(dst->prev_sibling==src) // already in the right spot\n\t\t\treturn source;\n\n   // take src out of the tree\n   if(src->prev_sibling!=0) src->prev_sibling->next_sibling=src->next_sibling;\n   else                     src->parent->first_child=src->next_sibling;\n   if(src->next_sibling!=0) src->next_sibling->prev_sibling=src->prev_sibling;\n   else                     src->parent->last_child=src->prev_sibling;\n\n   // connect it to the new point\n   if(dst->prev_sibling!=0) dst->prev_sibling->next_sibling=src;\n   else                     dst->parent->first_child=src;\n   src->prev_sibling=dst->prev_sibling;\n   dst->prev_sibling=src;\n   src->next_sibling=dst;\n   src->parent=dst->parent;\n   return src;\n   }\n\n// specialisation for sibling_iterators\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::sibling_iterator tree<T, tree_node_allocator>::move_before(sibling_iterator target, \n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t  sibling_iterator source)\n\t{\n\ttree_node *dst=target.node;\n\ttree_node *src=source.node;\n\ttree_node *dst_prev_sibling;\n\tif(dst==0) { // must then be an end iterator\n\t\tdst_prev_sibling=target.parent_->last_child;\n\t\tassert(dst_prev_sibling);\n\t\t}\n\telse dst_prev_sibling=dst->prev_sibling;\n\tassert(src);\n\n\tif(dst==src) return source;\n\tif(dst_prev_sibling)\n\t\tif(dst_prev_sibling==src) // already in the right spot\n\t\t\treturn source;\n\n\t// take src out of the tree\n\tif(src->prev_sibling!=0) src->prev_sibling->next_sibling=src->next_sibling;\n\telse                     src->parent->first_child=src->next_sibling;\n\tif(src->next_sibling!=0) src->next_sibling->prev_sibling=src->prev_sibling;\n\telse                     src->parent->last_child=src->prev_sibling;\n\n\t// connect it to the new point\n\tif(dst_prev_sibling!=0) dst_prev_sibling->next_sibling=src;\n\telse                    target.parent_->first_child=src;\n\tsrc->prev_sibling=dst_prev_sibling;\n\tif(dst) {\n\t\tdst->prev_sibling=src;\n\t\tsrc->parent=dst->parent;\n\t\t}\n\telse {\n\t\tsrc->parent=dst_prev_sibling->parent;\n\t\t}\n\tsrc->next_sibling=dst;\n\treturn src;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntemplate <typename iter> iter tree<T, tree_node_allocator>::move_ontop(iter target, iter source)\n\t{\n\ttree_node *dst=target.node;\n\ttree_node *src=source.node;\n\tassert(dst);\n\tassert(src);\n\n\tif(dst==src) {\n//\t\tstd::cerr << \"MOVE ONTOP!\" << std::endl;\n\t\treturn source;\n\t\t}\n\n//\tif(dst==src->prev_sibling) {\n//\n//\t\t}\n\n\t// remember connection points\n\ttree_node *b_prev_sibling=dst->prev_sibling;\n\ttree_node *b_next_sibling=dst->next_sibling;\n\ttree_node *b_parent=dst->parent;\n\n\t// remove target\n\terase(target);\n\n\t// take src out of the tree\n\tif(src->prev_sibling!=0) src->prev_sibling->next_sibling=src->next_sibling;\n\telse {\n\t\tassert(src->parent!=0);\n\t\tsrc->parent->first_child=src->next_sibling;\n\t\t}\n\tif(src->next_sibling!=0) src->next_sibling->prev_sibling=src->prev_sibling;\n\telse {\n\t\tassert(src->parent!=0);\n\t\tsrc->parent->last_child=src->prev_sibling;\n\t\t}\n\n\t// connect it to the new point\n\tif(b_prev_sibling!=0) b_prev_sibling->next_sibling=src;\n\telse {\n\t\tassert(b_parent!=0);\n\t\tb_parent->first_child=src;\n\t\t}\n\tif(b_next_sibling!=0) b_next_sibling->prev_sibling=src;\n\telse {\n\t\tassert(b_parent!=0);\n\t\tb_parent->last_child=src;\n\t\t}\n\tsrc->prev_sibling=b_prev_sibling;\n\tsrc->next_sibling=b_next_sibling;\n\tsrc->parent=b_parent;\n\treturn src;\n\t}\n\n\ntemplate <class T, class tree_node_allocator>\ntree<T, tree_node_allocator> tree<T, tree_node_allocator>::move_out(iterator source)\n\t{\n\ttree ret;\n\n\t// Move source node into the 'ret' tree.\n\tret.head->next_sibling = source.node;\n\tret.feet->prev_sibling = source.node;\n\n\t// Close the links in the current tree.\n\tif(source.node->prev_sibling!=0) \n\t\tsource.node->prev_sibling->next_sibling = source.node->next_sibling;\n\n\tif(source.node->next_sibling!=0) \n\t\tsource.node->next_sibling->prev_sibling = source.node->prev_sibling;\n\n\t// If the moved-out node was a first or last child of\n\t// the parent, adjust those links.\n\tif(source.node->parent->first_child==source.node) { \n\t\tif(source.node->next_sibling!=0)\n\t\t\tsource.node->parent->first_child=source.node->next_sibling;\n\t\telse\n\t\t\tsource.node->parent->first_child=0;\n\t\t}\n\tif(source.node->parent->last_child==source.node) { \n\t\tif(source.node->prev_sibling!=0)\n\t\t\tsource.node->parent->last_child=source.node->prev_sibling;\n\t\telse\n\t\t\tsource.node->parent->last_child=0;\n\t\t}\n\tsource.node->parent=0;\n\t\n\t// Fix source prev/next links.\n\tsource.node->prev_sibling = ret.head;\n\tsource.node->next_sibling = ret.feet;\n\n\treturn ret; // A good compiler will move this, not copy.\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntemplate<typename iter> iter tree<T, tree_node_allocator>::move_in(iter loc, tree& other)\n\t{\n\tif(other.head->next_sibling==other.feet) return loc; // other tree is empty\n\n\ttree_node *other_first_head = other.head->next_sibling;\n\ttree_node *other_last_head  = other.feet->prev_sibling;\n\n\tsibling_iterator prev(loc);\n\t--prev;\n\t\n\tprev.node->next_sibling = other_first_head;\n\tloc.node->prev_sibling  = other_last_head;\n\tother_first_head->prev_sibling = prev.node;\n\tother_last_head->next_sibling  = loc.node;\n\n\t// Adjust parent pointers.\n\ttree_node *walk=other_first_head;\n\twhile(true) {\n\t\twalk->parent=loc.node->parent;\n\t\tif(walk==other_last_head)\n\t\t\tbreak;\n\t\twalk=walk->next_sibling;\n\t\t}\n\n\t// Close other tree.\n\tother.head->next_sibling=other.feet;\n\tother.feet->prev_sibling=other.head;\n\n\treturn other_first_head;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntemplate<typename iter> iter tree<T, tree_node_allocator>::move_in_below(iter loc, tree& other)\n\t{\n\tif(other.head->next_sibling==other.feet) return loc; // other tree is empty\n\n\tauto n = other.number_of_children(loc);\n\treturn move_in_as_nth_child(loc, n, other);\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntemplate<typename iter> iter tree<T, tree_node_allocator>::move_in_as_nth_child(iter loc, size_t n, tree& other)\n\t{\n\tif(other.head->next_sibling==other.feet) return loc; // other tree is empty\n\n\ttree_node *other_first_head = other.head->next_sibling;\n\ttree_node *other_last_head  = other.feet->prev_sibling;\n\n\tif(n==0) {\n\t\tif(loc.node->first_child==0) {\n\t\t\tloc.node->first_child=other_first_head;\n\t\t\tloc.node->last_child=other_last_head;\n\t\t\tother_last_head->next_sibling=0;\n\t\t\tother_first_head->prev_sibling=0;\n\t\t\t} \n\t\telse {\n\t\t\tloc.node->first_child->prev_sibling=other_last_head;\n\t\t\tother_last_head->next_sibling=loc.node->first_child;\n\t\t\tloc.node->first_child=other_first_head;\n\t\t\tother_first_head->prev_sibling=0;\n\t\t\t}\n\t\t}\n\telse {\n\t\t--n;\n\t\ttree_node *walk = loc.node->first_child;\n\t\twhile(true) {\n\t\t\tif(walk==0)\n\t\t\t\tthrow std::range_error(\"tree: move_in_as_nth_child position out of range\");\n\t\t\tif(n==0) \n\t\t\t\tbreak;\n\t\t\t--n;\n\t\t\twalk = walk->next_sibling;\n\t\t\t}\n\t\tif(walk->next_sibling==0) \n\t\t\tloc.node->last_child=other_last_head;\n\t\telse \n\t\t\twalk->next_sibling->prev_sibling=other_last_head;\n\t\tother_last_head->next_sibling=walk->next_sibling;\n\t\twalk->next_sibling=other_first_head;\n\t\tother_first_head->prev_sibling=walk;\n\t\t}\n\n\t// Adjust parent pointers.\n\ttree_node *walk=other_first_head;\n\twhile(true) {\n\t\twalk->parent=loc.node;\n\t\tif(walk==other_last_head)\n\t\t\tbreak;\n\t\twalk=walk->next_sibling;\n\t\t}\n\n\t// Close other tree.\n\tother.head->next_sibling=other.feet;\n\tother.feet->prev_sibling=other.head;\n\n\treturn other_first_head;\n\t}\n\n\ntemplate <class T, class tree_node_allocator>\nvoid tree<T, tree_node_allocator>::merge(sibling_iterator to1,   sibling_iterator to2,\n\t\t\t\t\t\t\t\t\t\t\t\t\t\tsibling_iterator from1, sibling_iterator from2,\n\t\t\t\t\t\t\t\t\t\t\t\t\t\tbool duplicate_leaves)\n\t{\n\tsibling_iterator fnd;\n\twhile(from1!=from2) {\n\t\tif((fnd=std::find(to1, to2, (*from1))) != to2) { // element found\n\t\t\tif(from1.begin()==from1.end()) { // full depth reached\n\t\t\t\tif(duplicate_leaves)\n\t\t\t\t\tappend_child(parent(to1), (*from1));\n\t\t\t\t}\n\t\t\telse { // descend further\n\t\t\t\tmerge(fnd.begin(), fnd.end(), from1.begin(), from1.end(), duplicate_leaves);\n\t\t\t\t}\n\t\t\t}\n\t\telse { // element missing\n\t\t\tinsert_subtree(to2, from1);\n\t\t\t}\n\t\t++from1;\n\t\t}\n\t}\n\ntemplate <class T, class tree_node_allocator>\nvoid tree<T, tree_node_allocator>::merge(iterator to, iterator from, bool duplicate_leaves)\n\t{\n\tsibling_iterator to1(to);\n\tsibling_iterator to2=to1;\n\t++to2;\n\tsibling_iterator from1(from);\n\tsibling_iterator from2=from1;\n\t++from2;\n\n\tmerge(to1, to2, from1, from2, duplicate_leaves);\n\t}\n\n\ntemplate <class T, class tree_node_allocator>\nvoid tree<T, tree_node_allocator>::sort(sibling_iterator from, sibling_iterator to, bool deep)\n\t{\n\tstd::less<T> comp;\n\tsort(from, to, comp, deep);\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntemplate <class StrictWeakOrdering>\nvoid tree<T, tree_node_allocator>::sort(sibling_iterator from, sibling_iterator to, \n\t\t\t\t\t\t\t\t\t\t\t\t\t StrictWeakOrdering comp, bool deep)\n\t{\n\tif(from==to) return;\n\t// make list of sorted nodes\n\t// CHECK: if multiset stores equivalent nodes in the order in which they\n\t// are inserted, then this routine should be called 'stable_sort'.\n\tstd::multiset<tree_node *, compare_nodes<StrictWeakOrdering> > nodes(comp);\n\tsibling_iterator it=from, it2=to;\n\twhile(it != to) {\n\t\tnodes.insert(it.node);\n\t\t++it;\n\t\t}\n\t// reassemble\n\t--it2;\n\n\t// prev and next are the nodes before and after the sorted range\n\ttree_node *prev=from.node->prev_sibling;\n\ttree_node *next=it2.node->next_sibling;\n\ttypename std::multiset<tree_node *, compare_nodes<StrictWeakOrdering> >::iterator nit=nodes.begin(), eit=nodes.end();\n\tif(prev==0) {\n\t\tif((*nit)->parent!=0) // to catch \"sorting the head\" situations, when there is no parent\n\t\t\t(*nit)->parent->first_child=(*nit);\n\t\t}\n\telse prev->next_sibling=(*nit);\n\n\t--eit;\n\twhile(nit!=eit) {\n\t\t(*nit)->prev_sibling=prev;\n\t\tif(prev)\n\t\t\tprev->next_sibling=(*nit);\n\t\tprev=(*nit);\n\t\t++nit;\n\t\t}\n\t// prev now points to the last-but-one node in the sorted range\n\tif(prev)\n\t\tprev->next_sibling=(*eit);\n\n\t// eit points to the last node in the sorted range.\n\t(*eit)->next_sibling=next;\n   (*eit)->prev_sibling=prev; // missed in the loop above\n\tif(next==0) {\n\t\tif((*eit)->parent!=0) // to catch \"sorting the head\" situations, when there is no parent\n\t\t\t(*eit)->parent->last_child=(*eit);\n\t\t}\n\telse next->prev_sibling=(*eit);\n\n\tif(deep) {\t// sort the children of each node too\n\t\tsibling_iterator bcs(*nodes.begin());\n\t\tsibling_iterator ecs(*eit);\n\t\t++ecs;\n\t\twhile(bcs!=ecs) {\n\t\t\tsort(begin(bcs), end(bcs), comp, deep);\n\t\t\t++bcs;\n\t\t\t}\n\t\t}\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntemplate <typename iter>\nbool tree<T, tree_node_allocator>::equal(const iter& one_, const iter& two, const iter& three_) const\n\t{\n\tstd::equal_to<T> comp;\n\treturn equal(one_, two, three_, comp);\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntemplate <typename iter>\nbool tree<T, tree_node_allocator>::equal_subtree(const iter& one_, const iter& two_) const\n\t{\n\tstd::equal_to<T> comp;\n\treturn equal_subtree(one_, two_, comp);\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntemplate <typename iter, class BinaryPredicate>\nbool tree<T, tree_node_allocator>::equal(const iter& one_, const iter& two, const iter& three_, BinaryPredicate fun) const\n\t{\n\tpre_order_iterator one(one_), three(three_);\n\n//\tif(one==two && is_valid(three) && three.number_of_children()!=0)\n//\t\treturn false;\n\twhile(one!=two && is_valid(three)) {\n\t\tif(!fun(*one,*three))\n\t\t\treturn false;\n\t\tif(one.number_of_children()!=three.number_of_children()) \n\t\t\treturn false;\n\t\t++one;\n\t\t++three;\n\t\t}\n\treturn true;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntemplate <typename iter, class BinaryPredicate>\nbool tree<T, tree_node_allocator>::equal_subtree(const iter& one_, const iter& two_, BinaryPredicate fun) const\n\t{\n\tpre_order_iterator one(one_), two(two_);\n\n\tif(!fun(*one,*two)) return false;\n\tif(number_of_children(one)!=number_of_children(two)) return false;\n\treturn equal(begin(one),end(one),begin(two),fun);\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntree<T, tree_node_allocator> tree<T, tree_node_allocator>::subtree(sibling_iterator from, sibling_iterator to) const\n\t{\n\tassert(from!=to); // if from==to, the range is empty, hence no tree to return.\n\n\ttree tmp;\n\ttmp.set_head(value_type());\n\ttmp.replace(tmp.begin(), tmp.end(), from, to);\n\treturn tmp;\n\t}\n\ntemplate <class T, class tree_node_allocator>\nvoid tree<T, tree_node_allocator>::subtree(tree& tmp, sibling_iterator from, sibling_iterator to) const\n\t{\n\tassert(from!=to); // if from==to, the range is empty, hence no tree to return.\n\n\ttmp.set_head(value_type());\n\ttmp.replace(tmp.begin(), tmp.end(), from, to);\n\t}\n\ntemplate <class T, class tree_node_allocator>\nsize_t tree<T, tree_node_allocator>::size() const\n\t{\n\tsize_t i=0;\n\tpre_order_iterator it=begin(), eit=end();\n\twhile(it!=eit) {\n\t\t++i;\n\t\t++it;\n\t\t}\n\treturn i;\n\t}\n\ntemplate <class T, class tree_node_allocator>\nsize_t tree<T, tree_node_allocator>::size(const iterator_base& top) const\n\t{\n\tsize_t i=0;\n\tpre_order_iterator it=top, eit=top;\n\teit.skip_children();\n\t++eit;\n\twhile(it!=eit) {\n\t\t++i;\n\t\t++it;\n\t\t}\n\treturn i;\n\t}\n\ntemplate <class T, class tree_node_allocator>\nbool tree<T, tree_node_allocator>::empty() const\n\t{\n\tpre_order_iterator it=begin(), eit=end();\n\treturn (it==eit);\n\t}\n\ntemplate <class T, class tree_node_allocator>\nint tree<T, tree_node_allocator>::depth(const iterator_base& it) \n\t{\n\ttree_node* pos=it.node;\n\tassert(pos!=0);\n\tint ret=0;\n\twhile(pos->parent!=0) {\n\t\tpos=pos->parent;\n\t\t++ret;\n\t\t}\n\treturn ret;\n\t}\n\ntemplate <class T, class tree_node_allocator>\nint tree<T, tree_node_allocator>::depth(const iterator_base& it, const iterator_base& root) \n\t{\n\ttree_node* pos=it.node;\n\tassert(pos!=0);\n\tint ret=0;\n\twhile(pos->parent!=0 && pos!=root.node) {\n\t\tpos=pos->parent;\n\t\t++ret;\n\t\t}\n\treturn ret;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntemplate <class Predicate>\nint tree<T, tree_node_allocator>::depth(const iterator_base& it, Predicate p) \n\t{\n\ttree_node* pos=it.node;\n\tassert(pos!=0);\n\tint ret=0;\n\twhile(pos->parent!=0) {\n\t\tpos=pos->parent;\n\t\tif(p(pos))\n\t\t\t++ret;\n\t\t}\n\treturn ret;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntemplate <class Predicate>\nint tree<T, tree_node_allocator>::distance(const iterator_base& top, const iterator_base& bottom, Predicate p) \n\t{\n\ttree_node* pos=bottom.node;\n\tassert(pos!=0);\n\tint ret=0;\n\twhile(pos->parent!=0 && pos!=top.node) {\n\t\tpos=pos->parent;\n\t\tif(p(pos))\n\t\t\t++ret;\n\t\t}\n\treturn ret;\n\t}\n\ntemplate <class T, class tree_node_allocator>\nint tree<T, tree_node_allocator>::max_depth() const\n\t{\n\tint maxd=-1;\n\tfor(tree_node *it = head->next_sibling; it!=feet; it=it->next_sibling)\n\t\tmaxd=std::max(maxd, max_depth(it));\n\n\treturn maxd;\n\t}\n\n\ntemplate <class T, class tree_node_allocator>\nint tree<T, tree_node_allocator>::max_depth(const iterator_base& pos) const\n\t{\n\ttree_node *tmp=pos.node;\n\n\tif(tmp==0 || tmp==head || tmp==feet) return -1;\n\n\tint curdepth=0, maxdepth=0;\n\twhile(true) { // try to walk the bottom of the tree\n\t\twhile(tmp->first_child==0) {\n\t\t\tif(tmp==pos.node) return maxdepth;\n\t\t\tif(tmp->next_sibling==0) {\n\t\t\t\t// try to walk up and then right again\n\t\t\t\tdo {\n\t\t\t\t\ttmp=tmp->parent;\n               if(tmp==0) return maxdepth;\n               --curdepth;\n\t\t\t\t\t}\n\t\t\t\twhile(tmp->next_sibling==0);\n\t\t\t\t}\n         if(tmp==pos.node) return maxdepth;\n\t\t\ttmp=tmp->next_sibling;\n\t\t\t}\n\t\ttmp=tmp->first_child;\n\t\t++curdepth;\n\t\tmaxdepth=std::max(curdepth, maxdepth);\n\t\t} \n\t}\n\ntemplate <class T, class tree_node_allocator>\nunsigned int tree<T, tree_node_allocator>::number_of_children(const iterator_base& it) \n\t{\n\ttree_node *pos=it.node->first_child;\n\tif(pos==0) return 0;\n\t\n\tunsigned int ret=1;\n//\t  while(pos!=it.node->last_child) {\n//\t\t  ++ret;\n//\t\t  pos=pos->next_sibling;\n//\t\t  }\n\twhile((pos=pos->next_sibling))\n\t\t++ret;\n\treturn ret;\n\t}\n\ntemplate <class T, class tree_node_allocator>\nunsigned int tree<T, tree_node_allocator>::number_of_siblings(const iterator_base& it) const\n\t{\n\ttree_node *pos=it.node;\n\tunsigned int ret=0;\n\t// count forward\n\twhile(pos->next_sibling && \n\t\t\tpos->next_sibling!=head &&\n\t\t\tpos->next_sibling!=feet) {\n\t\t++ret;\n\t\tpos=pos->next_sibling;\n\t\t}\n\t// count backward\n\tpos=it.node;\n\twhile(pos->prev_sibling && \n\t\t\tpos->prev_sibling!=head &&\n\t\t\tpos->prev_sibling!=feet) {\n\t\t++ret;\n\t\tpos=pos->prev_sibling;\n\t\t}\n\t\n\treturn ret;\n\t}\n\ntemplate<class T, class tree_node_allocator>\nvoid tree<T, tree_node_allocator>::swap(tree& other)\n\t{\n\tif constexpr(std::allocator_traits<tree_node_allocator>:: propagate_on_container_swap::value) {\n\t\tstd::swap(alloc_, other.alloc_);\n\t\t}\n\t// Swap tree structure (head, feet pointers)\n\tstd::swap(head, other.head);\n\tstd::swap(feet, other.feet);\n\t}\n\t\t\ntemplate <class T, class tree_node_allocator>\nvoid tree<T, tree_node_allocator>::swap(sibling_iterator it)\n\t{\n\ttree_node *nxt=it.node->next_sibling;\n\tif(nxt) {\n\t\tif(it.node->prev_sibling)\n\t\t\tit.node->prev_sibling->next_sibling=nxt;\n\t\telse\n\t\t\tit.node->parent->first_child=nxt;\n\t\tnxt->prev_sibling=it.node->prev_sibling;\n\t\ttree_node *nxtnxt=nxt->next_sibling;\n\t\tif(nxtnxt)\n\t\t\tnxtnxt->prev_sibling=it.node;\n\t\telse\n\t\t\tit.node->parent->last_child=it.node;\n\t\tnxt->next_sibling=it.node;\n\t\tit.node->prev_sibling=nxt;\n\t\tit.node->next_sibling=nxtnxt;\n\t\t}\n\t}\n\ntemplate <class T, class tree_node_allocator>\nvoid tree<T, tree_node_allocator>::swap(iterator one, iterator two)\n\t{\n\t// if one and two are adjacent siblings, use the sibling swap\n\tif(one.node->next_sibling==two.node) swap(one);\n\telse if(two.node->next_sibling==one.node) swap(two);\n\telse {\n\t\ttree_node *nxt1=one.node->next_sibling;\n\t\ttree_node *nxt2=two.node->next_sibling;\n\t\ttree_node *pre1=one.node->prev_sibling;\n\t\ttree_node *pre2=two.node->prev_sibling;\n\t\ttree_node *par1=one.node->parent;\n\t\ttree_node *par2=two.node->parent;\n\n\t\t// reconnect\n\t\tone.node->parent=par2;\n\t\tone.node->next_sibling=nxt2;\n\t\tif(nxt2) nxt2->prev_sibling=one.node;\n\t\telse     par2->last_child=one.node;\n\t\tone.node->prev_sibling=pre2;\n\t\tif(pre2) pre2->next_sibling=one.node;\n\t\telse     par2->first_child=one.node;    \n\n\t\ttwo.node->parent=par1;\n\t\ttwo.node->next_sibling=nxt1;\n\t\tif(nxt1) nxt1->prev_sibling=two.node;\n\t\telse     par1->last_child=two.node;\n\t\ttwo.node->prev_sibling=pre1;\n\t\tif(pre1) pre1->next_sibling=two.node;\n\t\telse     par1->first_child=two.node;\n\t\t}\n\t}\n\n// template <class BinaryPredicate>\n// tree<T, tree_node_allocator>::iterator tree<T, tree_node_allocator>::find_subtree(\n// \tsibling_iterator subfrom, sibling_iterator subto, iterator from, iterator to, \n// \tBinaryPredicate fun) const\n// \t{\n// \tassert(1==0); // this routine is not finished yet.\n// \twhile(from!=to) {\n// \t\tif(fun(*subfrom, *from)) {\n// \t\t\t\n// \t\t\t}\n// \t\t}\n// \treturn to;\n// \t}\n\ntemplate <class T, class tree_node_allocator>\nbool tree<T, tree_node_allocator>::is_in_subtree(const iterator_base& it, const iterator_base& top) const\n   {\n\tsibling_iterator first=top;\n\tsibling_iterator last=first;\n\t++last;\n\treturn is_in_subtree(it, first, last);\n\t}\n\ntemplate <class T, class tree_node_allocator>\nbool tree<T, tree_node_allocator>::is_in_subtree(const iterator_base& it, const iterator_base& begin, \n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t const iterator_base& end) const\n\t{\n\t// FIXME: this should be optimised.\n\tpre_order_iterator tmp=begin;\n\twhile(tmp!=end) {\n\t\tif(tmp==it) return true;\n\t\t++tmp;\n\t\t}\n\treturn false;\n\t}\n\ntemplate <class T, class tree_node_allocator>\nbool tree<T, tree_node_allocator>::is_valid(const iterator_base& it) const\n\t{\n\tif(it.node==0 || it.node==feet || it.node==head) return false;\n\telse return true;\n\t}\n\ntemplate <class T, class tree_node_allocator>\nbool tree<T, tree_node_allocator>::is_head(const iterator_base& it) \n  \t{\n\tif(it.node->parent==0) return true;\n\treturn false;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::iterator tree<T, tree_node_allocator>::lowest_common_ancestor(\n\tconst iterator_base& one, const iterator_base& two) const\n\t{\n\tstd::set<iterator, iterator_base_less> parents;\n\n\t// Walk up from 'one' storing all parents.\n\titerator walk=one;\n\tdo {\n\t\twalk=parent(walk);\n\t\tparents.insert(walk);\n\t\t}\n\twhile( walk.node->parent );\n\n\t// Walk up from 'two' until we encounter a node in parents.\n\twalk=two;\n\tdo {\n\t\twalk=parent(walk);\n\t\tif(parents.find(walk) != parents.end()) break;\n\t\t}\n\twhile( walk.node->parent );\n\n\treturn walk;\n\t}\n\ntemplate <class T, class tree_node_allocator>\nunsigned int tree<T, tree_node_allocator>::index(sibling_iterator it) const\n\t{\n\tunsigned int ind=0;\n\tif(it.node->parent==0) {\n\t\twhile(it.node->prev_sibling!=head) {\n\t\t\tit.node=it.node->prev_sibling;\n\t\t\t++ind;\n\t\t\t}\n\t\t}\n\telse {\n\t\twhile(it.node->prev_sibling!=0) {\n\t\t\tit.node=it.node->prev_sibling;\n\t\t\t++ind;\n\t\t\t}\n\t\t}\n\treturn ind;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::sibling_iterator tree<T, tree_node_allocator>::sibling(const iterator_base& it, unsigned int num) const\n   {\n   tree_node *tmp;\n   if(it.node->parent==0) {\n      tmp=head->next_sibling;\n      while(num) {\n         tmp = tmp->next_sibling;\n         --num;\n         }\n      }\n   else {\n      tmp=it.node->parent->first_child;\n      while(num) {\n         assert(tmp!=0);\n         tmp = tmp->next_sibling;\n         --num;\n         }\n      }\n   return tmp;\n   }\n \ntemplate <class T, class tree_node_allocator>\nvoid tree<T, tree_node_allocator>::debug_verify_consistency() const\n\t{\n\titerator it=begin();\n\twhile(it!=end()) {\n\t\t// std::cerr << *it << \" (\" << it.node << \")\" << std::endl;\n\t\tif(it.node->parent!=0) {\n\t\t\tif(it.node->prev_sibling==0) \n\t\t\t\tassert(it.node->parent->first_child==it.node);\n\t\t\telse \n\t\t\t\tassert(it.node->prev_sibling->next_sibling==it.node);\n\t\t\tif(it.node->next_sibling==0) \n\t\t\t\tassert(it.node->parent->last_child==it.node);\n\t\t\telse\n\t\t\t\tassert(it.node->next_sibling->prev_sibling==it.node);\n\t\t\t}\n\t\t++it;\n\t\t}\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::sibling_iterator tree<T, tree_node_allocator>::child(const iterator_base& it, unsigned int num) \n\t{\n\ttree_node *tmp=it.node->first_child;\n\twhile(num-- != 0) {\n\t\tif(tmp==0)\n\t\t\tthrow std::range_error(\"tree::child: reached null sibling with \"+std::to_string(num+1)+\" steps still to go\");\n\t\ttmp=tmp->next_sibling;\n\t\t}\n\tif(tmp==0)\n\t\tthrow std::range_error(\"tree::child: reached null sibling at final step\");\n\t\n\treturn tmp;\n\t}\n\n\n\n\n// Iterator base\n\ntemplate <class T, class tree_node_allocator>\ntree<T, tree_node_allocator>::iterator_base::iterator_base()\n\t: node(0), skip_current_children_(false)\n\t{\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntree<T, tree_node_allocator>::iterator_base::iterator_base(tree_node *tn)\n\t: node(tn), skip_current_children_(false)\n\t{\n\t}\n\ntemplate <class T, class tree_node_allocator>\nT& tree<T, tree_node_allocator>::iterator_base::operator*() const\n\t{\n\treturn node->data;\n\t}\n\ntemplate <class T, class tree_node_allocator>\nT* tree<T, tree_node_allocator>::iterator_base::operator->() const\n\t{\n\treturn &(node->data);\n\t}\n\ntemplate <class T, class tree_node_allocator>\nbool tree<T, tree_node_allocator>::post_order_iterator::operator!=(const post_order_iterator& other) const\n\t{\n\tif(other.node!=this->node) return true;\n\telse return false;\n\t}\n\ntemplate <class T, class tree_node_allocator>\nbool tree<T, tree_node_allocator>::post_order_iterator::operator==(const post_order_iterator& other) const\n\t{\n\tif(other.node==this->node) return true;\n\telse return false;\n\t}\n\ntemplate <class T, class tree_node_allocator>\nbool tree<T, tree_node_allocator>::pre_order_iterator::operator!=(const pre_order_iterator& other) const\n\t{\n\tif(other.node!=this->node) return true;\n\telse return false;\n\t}\n\ntemplate <class T, class tree_node_allocator>\nbool tree<T, tree_node_allocator>::pre_order_iterator::operator==(const pre_order_iterator& other) const\n\t{\n\tif(other.node==this->node) return true;\n\telse return false;\n\t}\n\ntemplate <class T, class tree_node_allocator>\nbool tree<T, tree_node_allocator>::sibling_iterator::operator!=(const sibling_iterator& other) const\n\t{\n\tif(other.node!=this->node) return true;\n\telse return false;\n\t}\n\ntemplate <class T, class tree_node_allocator>\nbool tree<T, tree_node_allocator>::sibling_iterator::operator==(const sibling_iterator& other) const\n\t{\n\tif(other.node==this->node) return true;\n\telse return false;\n\t}\n\ntemplate <class T, class tree_node_allocator>\nbool tree<T, tree_node_allocator>::leaf_iterator::operator!=(const leaf_iterator& other) const\n   {\n   if(other.node!=this->node) return true;\n   else return false;\n   }\n\ntemplate <class T, class tree_node_allocator>\nbool tree<T, tree_node_allocator>::leaf_iterator::operator==(const leaf_iterator& other) const\n   {\n   if(other.node==this->node && other.top_node==this->top_node) return true;\n   else return false;\n   }\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::sibling_iterator tree<T, tree_node_allocator>::iterator_base::begin() const\n\t{\n\tif(node->first_child==0) \n\t\treturn end();\n\n\tsibling_iterator ret(node->first_child);\n\tret.parent_=this->node;\n\treturn ret;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::sibling_iterator tree<T, tree_node_allocator>::iterator_base::end() const\n\t{\n\tsibling_iterator ret(0);\n\tret.parent_=node;\n\treturn ret;\n\t}\n\ntemplate <class T, class tree_node_allocator>\nvoid tree<T, tree_node_allocator>::iterator_base::skip_children()\n\t{\n\tskip_current_children_=true;\n\t}\n\ntemplate <class T, class tree_node_allocator>\nvoid tree<T, tree_node_allocator>::iterator_base::skip_children(bool skip)\n   {\n   skip_current_children_=skip;\n   }\n\ntemplate <class T, class tree_node_allocator>\nunsigned int tree<T, tree_node_allocator>::iterator_base::number_of_children() const\n\t{\n\ttree_node *pos=node->first_child;\n\tif(pos==0) return 0;\n\t\n\tunsigned int ret=1;\n\twhile(pos!=node->last_child) {\n\t\t++ret;\n\t\tpos=pos->next_sibling;\n\t\t}\n\treturn ret;\n\t}\n\n\n\n// Pre-order iterator\n\ntemplate <class T, class tree_node_allocator>\ntree<T, tree_node_allocator>::pre_order_iterator::pre_order_iterator() \n\t: iterator_base(0)\n\t{\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntree<T, tree_node_allocator>::pre_order_iterator::pre_order_iterator(tree_node *tn)\n\t: iterator_base(tn)\n\t{\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntree<T, tree_node_allocator>::pre_order_iterator::pre_order_iterator(const iterator_base &other)\n\t: iterator_base(other.node)\n\t{\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntree<T, tree_node_allocator>::pre_order_iterator::pre_order_iterator(const sibling_iterator& other)\n\t: iterator_base(other.node)\n\t{\n\tif(this->node==0) {\n\t\tif(other.range_last()!=0)\n\t\t\tthis->node=other.range_last();\n\t\telse \n\t\t\tthis->node=other.parent_;\n\t\tthis->skip_children();\n\t\t++(*this);\n\t\t}\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::pre_order_iterator& tree<T, tree_node_allocator>::pre_order_iterator::operator++()\n\t{\n\tassert(this->node!=0);\n\tif(!this->skip_current_children_ && this->node->first_child != 0) {\n\t\tthis->node=this->node->first_child;\n\t\t}\n\telse {\n\t\tthis->skip_current_children_=false;\n\t\twhile(this->node->next_sibling==0) {\n\t\t\tthis->node=this->node->parent;\n\t\t\tif(this->node==0)\n\t\t\t\treturn *this;\n\t\t\t}\n\t\tthis->node=this->node->next_sibling;\n\t\t}\n\treturn *this;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::pre_order_iterator& tree<T, tree_node_allocator>::pre_order_iterator::operator--()\n\t{\n\tassert(this->node!=0);\n\tif(this->node->prev_sibling) {\n\t\tthis->node=this->node->prev_sibling;\n\t\twhile(this->node->last_child)\n\t\t\tthis->node=this->node->last_child;\n\t\t}\n\telse {\n\t\tthis->node=this->node->parent;\n\t\tif(this->node==0)\n\t\t\treturn *this;\n\t\t}\n\treturn *this;\n}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::pre_order_iterator tree<T, tree_node_allocator>::pre_order_iterator::operator++(int)\n\t{\n\tpre_order_iterator copy = *this;\n\t++(*this);\n\treturn copy;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::pre_order_iterator& tree<T, tree_node_allocator>::pre_order_iterator::next_skip_children() \n   {\n\t(*this).skip_children();\n\t(*this)++;\n\treturn *this;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::pre_order_iterator tree<T, tree_node_allocator>::pre_order_iterator::operator--(int)\n{\n  pre_order_iterator copy = *this;\n  --(*this);\n  return copy;\n}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::pre_order_iterator& tree<T, tree_node_allocator>::pre_order_iterator::operator+=(unsigned int num)\n\t{\n\twhile(num>0) {\n\t\t++(*this);\n\t\t--num;\n\t\t}\n\treturn (*this);\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::pre_order_iterator& tree<T, tree_node_allocator>::pre_order_iterator::operator-=(unsigned int num)\n\t{\n\twhile(num>0) {\n\t\t--(*this);\n\t\t--num;\n\t\t}\n\treturn (*this);\n\t}\n\n\n\n// Post-order iterator\n\ntemplate <class T, class tree_node_allocator>\ntree<T, tree_node_allocator>::post_order_iterator::post_order_iterator() \n\t: iterator_base(0)\n\t{\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntree<T, tree_node_allocator>::post_order_iterator::post_order_iterator(tree_node *tn)\n\t: iterator_base(tn)\n\t{\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntree<T, tree_node_allocator>::post_order_iterator::post_order_iterator(const iterator_base &other)\n\t: iterator_base(other.node)\n\t{\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntree<T, tree_node_allocator>::post_order_iterator::post_order_iterator(const sibling_iterator& other)\n\t: iterator_base(other.node)\n\t{\n\tif(this->node==0) {\n\t\tif(other.range_last()!=0)\n\t\t\tthis->node=other.range_last();\n\t\telse \n\t\t\tthis->node=other.parent_;\n\t\tthis->skip_children();\n\t\t++(*this);\n\t\t}\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::post_order_iterator& tree<T, tree_node_allocator>::post_order_iterator::operator++()\n\t{\n\tassert(this->node!=0);\n\tif(this->node->next_sibling==0) {\n\t\tthis->node=this->node->parent;\n\t\tthis->skip_current_children_=false;\n\t\t}\n\telse {\n\t\tthis->node=this->node->next_sibling;\n\t\tif(this->skip_current_children_) {\n\t\t\tthis->skip_current_children_=false;\n\t\t\t}\n\t\telse {\n\t\t\twhile(this->node->first_child)\n\t\t\t\tthis->node=this->node->first_child;\n\t\t\t}\n\t\t}\n\treturn *this;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::post_order_iterator& tree<T, tree_node_allocator>::post_order_iterator::operator--()\n\t{\n\tassert(this->node!=0);\n\tif(this->skip_current_children_ || this->node->last_child==0) {\n\t\tthis->skip_current_children_=false;\n\t\twhile(this->node->prev_sibling==0)\n\t\t\tthis->node=this->node->parent;\n\t\tthis->node=this->node->prev_sibling;\n\t\t}\n\telse {\n\t\tthis->node=this->node->last_child;\n\t\t}\n\treturn *this;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::post_order_iterator tree<T, tree_node_allocator>::post_order_iterator::operator++(int)\n\t{\n\tpost_order_iterator copy = *this;\n\t++(*this);\n\treturn copy;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::post_order_iterator tree<T, tree_node_allocator>::post_order_iterator::operator--(int)\n\t{\n\tpost_order_iterator copy = *this;\n\t--(*this);\n\treturn copy;\n\t}\n\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::post_order_iterator& tree<T, tree_node_allocator>::post_order_iterator::operator+=(unsigned int num)\n\t{\n\twhile(num>0) {\n\t\t++(*this);\n\t\t--num;\n\t\t}\n\treturn (*this);\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::post_order_iterator& tree<T, tree_node_allocator>::post_order_iterator::operator-=(unsigned int num)\n\t{\n\twhile(num>0) {\n\t\t--(*this);\n\t\t--num;\n\t\t}\n\treturn (*this);\n\t}\n\ntemplate <class T, class tree_node_allocator>\nvoid tree<T, tree_node_allocator>::post_order_iterator::descend_all()\n\t{\n\tassert(this->node!=0);\n\twhile(this->node->first_child)\n\t\tthis->node=this->node->first_child;\n\t}\n\n\n// Breadth-first iterator\n\ntemplate <class T, class tree_node_allocator>\ntree<T, tree_node_allocator>::breadth_first_queued_iterator::breadth_first_queued_iterator()\n\t: iterator_base()\n\t{\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntree<T, tree_node_allocator>::breadth_first_queued_iterator::breadth_first_queued_iterator(tree_node *tn)\n\t: iterator_base(tn)\n\t{\n\ttraversal_queue.push(tn);\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntree<T, tree_node_allocator>::breadth_first_queued_iterator::breadth_first_queued_iterator(const iterator_base& other)\n\t: iterator_base(other.node)\n\t{\n\ttraversal_queue.push(other.node);\n\t}\n\ntemplate <class T, class tree_node_allocator>\nbool tree<T, tree_node_allocator>::breadth_first_queued_iterator::operator!=(const breadth_first_queued_iterator& other) const\n\t{\n\tif(other.node!=this->node) return true;\n\telse return false;\n\t}\n\ntemplate <class T, class tree_node_allocator>\nbool tree<T, tree_node_allocator>::breadth_first_queued_iterator::operator==(const breadth_first_queued_iterator& other) const\n\t{\n\tif(other.node==this->node) return true;\n\telse return false;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::breadth_first_queued_iterator& tree<T, tree_node_allocator>::breadth_first_queued_iterator::operator++()\n\t{\n\tassert(this->node!=0);\n\n\t// Add child nodes and pop current node\n\tsibling_iterator sib=this->begin();\n\twhile(sib!=this->end()) {\n\t\ttraversal_queue.push(sib.node);\n\t\t++sib;\n\t\t}\n\ttraversal_queue.pop();\n\tif(traversal_queue.size()>0)\n\t\tthis->node=traversal_queue.front();\n\telse \n\t\tthis->node=0;\n\treturn (*this);\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::breadth_first_queued_iterator tree<T, tree_node_allocator>::breadth_first_queued_iterator::operator++(int)\n\t{\n\tbreadth_first_queued_iterator copy = *this;\n\t++(*this);\n\treturn copy;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::breadth_first_queued_iterator& tree<T, tree_node_allocator>::breadth_first_queued_iterator::operator+=(unsigned int num)\n\t{\n\twhile(num>0) {\n\t\t++(*this);\n\t\t--num;\n\t\t}\n\treturn (*this);\n\t}\n\n\n\n// Fixed depth iterator\n\ntemplate <class T, class tree_node_allocator>\ntree<T, tree_node_allocator>::fixed_depth_iterator::fixed_depth_iterator()\n\t: iterator_base()\n\t{\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntree<T, tree_node_allocator>::fixed_depth_iterator::fixed_depth_iterator(tree_node *tn)\n\t: iterator_base(tn), top_node(0)\n\t{\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntree<T, tree_node_allocator>::fixed_depth_iterator::fixed_depth_iterator(const iterator_base& other)\n\t: iterator_base(other.node), top_node(0)\n\t{\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntree<T, tree_node_allocator>::fixed_depth_iterator::fixed_depth_iterator(const sibling_iterator& other)\n\t: iterator_base(other.node), top_node(0)\n\t{\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntree<T, tree_node_allocator>::fixed_depth_iterator::fixed_depth_iterator(const fixed_depth_iterator& other)\n\t: iterator_base(other.node), top_node(other.top_node)\n\t{\n\t}\n\ntemplate <class T, class tree_node_allocator>\nvoid tree<T, tree_node_allocator>::fixed_depth_iterator::swap(fixed_depth_iterator& first, fixed_depth_iterator& second) \n\t{\n\tstd::swap(first.node, second.node);\n\tstd::swap(first.skip_current_children_, second.skip_current_children_);\n\tstd::swap(first.top_node, second.top_node);\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::fixed_depth_iterator& tree<T, tree_node_allocator>::fixed_depth_iterator::operator=(fixed_depth_iterator other)\n\t{\n\tswap(*this, other);\n\treturn *this;\n\t}\n\t\t\ntemplate <class T, class tree_node_allocator>\nbool tree<T, tree_node_allocator>::fixed_depth_iterator::operator==(const fixed_depth_iterator& other) const\n\t{\n\tif(other.node==this->node && other.top_node==top_node) return true;\n\telse return false;\n\t}\n\ntemplate <class T, class tree_node_allocator>\nbool tree<T, tree_node_allocator>::fixed_depth_iterator::operator!=(const fixed_depth_iterator& other) const\n\t{\n\tif(other.node!=this->node || other.top_node!=top_node) return true;\n\telse return false;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::fixed_depth_iterator& tree<T, tree_node_allocator>::fixed_depth_iterator::operator++()\n\t{\n\tassert(this->node!=0);\n\n\tif(this->node->next_sibling) {\n\t\tthis->node=this->node->next_sibling;\n\t\t}\n\telse { \n\t\tint relative_depth=0;\n\t   upper:\n\t\tdo {\n\t\t\tif(this->node==this->top_node) {\n\t\t\t\tthis->node=0; // FIXME: return a proper fixed_depth end iterator once implemented\n\t\t\t\treturn *this;\n\t\t\t\t}\n\t\t\tthis->node=this->node->parent;\n\t\t\tif(this->node==0) return *this;\n\t\t\t--relative_depth;\n\t\t\t} while(this->node->next_sibling==0);\n\t   lower:\n\t\tthis->node=this->node->next_sibling;\n\t\twhile(this->node->first_child==0) {\n\t\t\tif(this->node->next_sibling==0)\n\t\t\t\tgoto upper;\n\t\t\tthis->node=this->node->next_sibling;\n\t\t\tif(this->node==0) return *this;\n\t\t\t}\n\t\twhile(relative_depth<0 && this->node->first_child!=0) {\n\t\t\tthis->node=this->node->first_child;\n\t\t\t++relative_depth;\n\t\t\t}\n\t\tif(relative_depth<0) {\n\t\t\tif(this->node->next_sibling==0) goto upper;\n\t\t\telse                          goto lower;\n\t\t\t}\n\t\t}\n\treturn *this;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::fixed_depth_iterator& tree<T, tree_node_allocator>::fixed_depth_iterator::operator--()\n\t{\n\tassert(this->node!=0);\n\n\tif(this->node->prev_sibling) {\n\t\tthis->node=this->node->prev_sibling;\n\t\t}\n\telse { \n\t\tint relative_depth=0;\n\t   upper:\n\t\tdo {\n\t\t\tif(this->node==this->top_node) {\n\t\t\t\tthis->node=0;\n\t\t\t\treturn *this;\n\t\t\t\t}\n\t\t\tthis->node=this->node->parent;\n\t\t\tif(this->node==0) return *this;\n\t\t\t--relative_depth;\n\t\t\t} while(this->node->prev_sibling==0);\n\t   lower:\n\t\tthis->node=this->node->prev_sibling;\n\t\twhile(this->node->last_child==0) {\n\t\t\tif(this->node->prev_sibling==0)\n\t\t\t\tgoto upper;\n\t\t\tthis->node=this->node->prev_sibling;\n\t\t\tif(this->node==0) return *this;\n\t\t\t}\n\t\twhile(relative_depth<0 && this->node->last_child!=0) {\n\t\t\tthis->node=this->node->last_child;\n\t\t\t++relative_depth;\n\t\t\t}\n\t\tif(relative_depth<0) {\n\t\t\tif(this->node->prev_sibling==0) goto upper;\n\t\t\telse                            goto lower;\n\t\t\t}\n\t\t}\n\treturn *this;\n\n//\n//\n//\tassert(this->node!=0);\n//\tif(this->node->prev_sibling!=0) {\n//\t\tthis->node=this->node->prev_sibling;\n//\t\tassert(this->node!=0);\n//\t\tif(this->node->parent==0 && this->node->prev_sibling==0) // head element\n//\t\t\tthis->node=0;\n//\t\t}\n//\telse {\n//\t\ttree_node *par=this->node->parent;\n//\t\tdo {\n//\t\t\tpar=par->prev_sibling;\n//\t\t\tif(par==0) { // FIXME: need to keep track of this!\n//\t\t\t\tthis->node=0;\n//\t\t\t\treturn *this;\n//\t\t\t\t}\n//\t\t\t} while(par->last_child==0);\n//\t\tthis->node=par->last_child;\n//\t\t}\n//\treturn *this;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::fixed_depth_iterator tree<T, tree_node_allocator>::fixed_depth_iterator::operator++(int)\n\t{\n\tfixed_depth_iterator copy = *this;\n\t++(*this);\n\treturn copy;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::fixed_depth_iterator tree<T, tree_node_allocator>::fixed_depth_iterator::operator--(int)\n   {\n\tfixed_depth_iterator copy = *this;\n\t--(*this);\n\treturn copy;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::fixed_depth_iterator& tree<T, tree_node_allocator>::fixed_depth_iterator::operator-=(unsigned int num)\n\t{\n\twhile(num>0) {\n\t\t--(*this);\n\t\t--(num);\n\t\t}\n\treturn (*this);\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::fixed_depth_iterator& tree<T, tree_node_allocator>::fixed_depth_iterator::operator+=(unsigned int num)\n\t{\n\twhile(num>0) {\n\t\t++(*this);\n\t\t--(num);\n\t\t}\n\treturn *this;\n\t}\n\n\n// Sibling iterator\n\ntemplate <class T, class tree_node_allocator>\ntree<T, tree_node_allocator>::sibling_iterator::sibling_iterator() \n\t: iterator_base()\n\t{\n\tset_parent_();\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntree<T, tree_node_allocator>::sibling_iterator::sibling_iterator(tree_node *tn)\n\t: iterator_base(tn)\n\t{\n\tset_parent_();\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntree<T, tree_node_allocator>::sibling_iterator::sibling_iterator(const iterator_base& other)\n\t: iterator_base(other.node)\n\t{\n\tset_parent_();\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntree<T, tree_node_allocator>::sibling_iterator::sibling_iterator(const sibling_iterator& other)\n\t: iterator_base(other), parent_(other.parent_)\n\t{\n\t}\n\ntemplate <class T, class tree_node_allocator>\nvoid tree<T, tree_node_allocator>::sibling_iterator::swap(sibling_iterator& first, sibling_iterator& second) \n\t{\n\tstd::swap(first.node, second.node);\n\tstd::swap(first.skip_current_children_, second.skip_current_children_);\n\tstd::swap(first.parent_, second.parent_);\n\t}\n\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::sibling_iterator& tree<T, tree_node_allocator>::sibling_iterator::operator=(sibling_iterator other)\n\t{\n\tswap(*this, other);\n\treturn *this;\n\t}\n\t\t\ntemplate <class T, class tree_node_allocator>\nvoid tree<T, tree_node_allocator>::sibling_iterator::set_parent_()\n\t{\n\tparent_=0;\n\tif(this->node==0) return;\n\tif(this->node->parent!=0)\n\t\tparent_=this->node->parent;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::sibling_iterator& tree<T, tree_node_allocator>::sibling_iterator::operator++()\n\t{\n\tif(this->node)\n\t\tthis->node=this->node->next_sibling;\n\treturn *this;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::sibling_iterator& tree<T, tree_node_allocator>::sibling_iterator::operator--()\n\t{\n\tif(this->node) this->node=this->node->prev_sibling;\n\telse {\n\t\tassert(parent_);\n\t\tthis->node=parent_->last_child;\n\t\t}\n\treturn *this;\n}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::sibling_iterator tree<T, tree_node_allocator>::sibling_iterator::operator++(int)\n\t{\n\tsibling_iterator copy = *this;\n\t++(*this);\n\treturn copy;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::sibling_iterator tree<T, tree_node_allocator>::sibling_iterator::operator--(int)\n\t{\n\tsibling_iterator copy = *this;\n\t--(*this);\n\treturn copy;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::sibling_iterator& tree<T, tree_node_allocator>::sibling_iterator::operator+=(unsigned int num)\n\t{\n\twhile(num>0) {\n\t\t++(*this);\n\t\t--num;\n\t\t}\n\treturn (*this);\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::sibling_iterator& tree<T, tree_node_allocator>::sibling_iterator::operator-=(unsigned int num)\n\t{\n\twhile(num>0) {\n\t\t--(*this);\n\t\t--num;\n\t\t}\n\treturn (*this);\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::tree_node *tree<T, tree_node_allocator>::sibling_iterator::range_first() const\n\t{\n\ttree_node *tmp=parent_->first_child;\n\treturn tmp;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::tree_node *tree<T, tree_node_allocator>::sibling_iterator::range_last() const\n\t{\n\treturn parent_->last_child;\n\t}\n\n// Leaf iterator\n\ntemplate <class T, class tree_node_allocator>\ntree<T, tree_node_allocator>::leaf_iterator::leaf_iterator() \n   : iterator_base(0), top_node(0)\n   {\n   }\n\ntemplate <class T, class tree_node_allocator>\ntree<T, tree_node_allocator>::leaf_iterator::leaf_iterator(tree_node *tn, tree_node *top)\n   : iterator_base(tn), top_node(top)\n   {\n   }\n\ntemplate <class T, class tree_node_allocator>\ntree<T, tree_node_allocator>::leaf_iterator::leaf_iterator(const iterator_base &other)\n   : iterator_base(other.node), top_node(0)\n   {\n   }\n\ntemplate <class T, class tree_node_allocator>\ntree<T, tree_node_allocator>::leaf_iterator::leaf_iterator(const sibling_iterator& other)\n   : iterator_base(other.node), top_node(0)\n   {\n   if(this->node==0) {\n      if(other.range_last()!=0)\n         this->node=other.range_last();\n      else \n         this->node=other.parent_;\n      ++(*this);\n      }\n   }\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::leaf_iterator& tree<T, tree_node_allocator>::leaf_iterator::operator++()\n   {\n\tassert(this->node!=0);\n\tif(this->node->first_child!=0) { // current node is no longer leaf (children got added)\n\t\t while(this->node->first_child) \n\t\t\t  this->node=this->node->first_child;\n\t\t }\n\telse {\n\t\t while(this->node->next_sibling==0) { \n\t\t\t  if (this->node->parent==0) return *this;\n\t\t\t  this->node=this->node->parent;\n\t\t\t  if (top_node != 0 && this->node==top_node) return *this;\n\t\t\t  }\n\t\t this->node=this->node->next_sibling;\n\t\t while(this->node->first_child)\n\t\t\t  this->node=this->node->first_child;\n\t\t }\n\treturn *this;\n   }\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::leaf_iterator& tree<T, tree_node_allocator>::leaf_iterator::operator--()\n   {\n\tassert(this->node!=0);\n\twhile (this->node->prev_sibling==0) {\n\t\tif (this->node->parent==0) return *this;\n\t\tthis->node=this->node->parent;\n\t\tif (top_node !=0 && this->node==top_node) return *this; \n\t\t}\n\tthis->node=this->node->prev_sibling;\n\twhile(this->node->last_child)\n\t\tthis->node=this->node->last_child;\n\treturn *this;\n\t}\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::leaf_iterator tree<T, tree_node_allocator>::leaf_iterator::operator++(int)\n   {\n   leaf_iterator copy = *this;\n   ++(*this);\n   return copy;\n   }\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::leaf_iterator tree<T, tree_node_allocator>::leaf_iterator::operator--(int)\n   {\n   leaf_iterator copy = *this;\n   --(*this);\n   return copy;\n   }\n\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::leaf_iterator& tree<T, tree_node_allocator>::leaf_iterator::operator+=(unsigned int num)\n   {\n   while(num>0) {\n      ++(*this);\n      --num;\n      }\n   return (*this);\n   }\n\ntemplate <class T, class tree_node_allocator>\ntypename tree<T, tree_node_allocator>::leaf_iterator& tree<T, tree_node_allocator>::leaf_iterator::operator-=(unsigned int num)\n   {\n   while(num>0) {\n      --(*this);\n      --num;\n      }\n   return (*this);\n   }\n\n#endif\n\n// Local variables:\n// tab-width: 3\n// End:\n"
  },
  {
    "path": "doc/.gitignore",
    "content": "algorithms\nproperties\n"
  },
  {
    "path": "doc/adjacency_form.md",
    "content": "\n# Adjacency matrix storage\n\nSo in order to prevent `young_reduce` from wasting time on manipulations\nwith Ex objects, I thought that one should store tensors internally in\nsome more compact form. Since all terms which we compare have the same\ntensor structure, the only thing you need to store is a list of indices\nand a list of contractions. E.g. `R_{a b c d} R_{e f c d}` could be \nrepresented as\n\n    a b c d e f c d .\n\n(I am ignoring upper/lower indices here; you can always correct that at\nthe very end by raising one index of a dummy pair). But this still has\nthe disadvantage that dummy indices have explicit labels. Better is a\nnotation in which a dummy contraction is indicated with the position of\nthe other index in the index position list. For the above example the\nindices are numbered\n\n    R_{a b c d} R_{e f c d}\n       0 1 2 3     4 5 6 7 \n\nand then you could represent this as\n\n    a b 6 7 e f 2 3\n\nIf you want to store this as a list of integers you could use negative\nones to indicate free indices (with their number referring to a table\nof free indices, e.g.)\n\n    -1 -2 6 7 -3 -4 2 3\n \n    -1: a\n    -2: b\n    -3: e\n    -4: f\n\nand then you do all young projection etc. on this array of integers.\n\n\n    class AdjEx {\n        public:\n            using index_t = short;\n            using adjform_t = std::vector<index_t>;\n    \n            /// Construct from a product in standard Ex notation.\n            AdjEx(const Ex&); \n            \n            /// Product an Ex from the adjacency form, given a list\n            /// of free indices.\n            Ex toEx() const;\n            \n            std::vector<Ex> factors; // with indices, so we can lookup types\n    };\n\n\n# Factoring\n\n    A_{m n} * D_{m p} * Q_{n p} + A_{m n} * E_{m p} * F_{p q} * Q_{n q};\n    \nDoes this become better in adj notation? First need to find\nintersection of factors, so we can put them in front.\n\n    A_{m n} Q_{n p} D_{m p}       A_{m n} Q_{n q} E_{m p} F_{p q}\n    \nBut this would work fine if we just rename dummies. So just aim for a\ncommand to move common factors to the front\n\n# Example\n\n\nPerhaps the following is a nicer example to try things out on, as it doesn't\nhave Riemann's in them. It comes from the computation that shows that\n\n   Tr( F ^ A ^ A ) = - Tr( A ^ F ^ A )                                (*)\n\nwhere A is a matrix-valued one-form and F is a matrix-valued two-form.\nSee e.g. Nakahara's \"Geometry, Topology and Physics\" chapter 10. To\nshow this, you could write it all out in indices; in Cadabra notation:\n\n    {a,b,c,d}::Indices(group);\n    {\\mu,\\nu,\\rho,\\sigma}::Indices(spacetime);\n    \\epsilon^{\\mu\\nu\\rho\\sigma}::EpsilonTensor;\n\n    ex1:=F^{a b}_{\\mu\\sigma} A^{b c}_{\\nu} A^{c a}_{\\rho} \\epsilon^{\\mu\\sigma\\nu\\rho}; \n    ex2:=A^{a b}_{\\mu} F^{b c}_{\\nu\\sigma} A^{c a}_{\\rho} \\epsilon^{\\mu\\nu\\sigma\\rho};\n\n    ex:= @(ex1) + @(ex2);\n\nAt the moment you can do \n\n    sort_product(_);\n    canonicalise(_);\n\nto make this vanish and prove (*). Now for the Young reduce approach, you would \nwrite ex1 and ex2 in 'F A A' form, and then the indices for these two expressions \nwould be\n\n          0 1 2  3     4 5 6  7 8 9   10 11    12    13  (index position)\n  \n     ex1: a b mu sigma b c nu c a rho mu sigma nu    rho\n     ex2: b c nu sigma a b mu c a rho mu nu    sigma rho\n          ============ ====== ======= ==================\n              F          A       A       \\epsilon\n\n(you'll need to read this with a fixed-width font). \nWithout referring to explicit index names, this turns into\n\n     ipos 0 1  2  3 4 5  6 7 8  9 10 11 12 13\n  \n     ex1: 8 4 10 11 1 7 12 5 0 13  2  3  6  9               (**)\n          ========= ====== ====== ===========\n              F       A      A      \\eps\n\nand similar for ex2. Nice and compact (you obviously only need to store\nthe tensor structure 'F A A', the line (**) and the numerical coefficient\nof this line, '1' in this case).\n\nNow comes the Young projection. In order to take into account that the \ntwo A tensors are the same, you need to symmetrise in the index blocks \nfor these two factors. This makes indices (4,5,6) become (7,8,9) and\nthe other way around.\n\n  ipos  0 1  2  3 4 5  6 7 8  9 10 11 12 13\n\n   ex1: 8 4 10 11 1 7 12 5 0 13  2  3  6  9  * (1/2)\n        5 7 10 11 8 0 13 1 4 12  2  3  9  6  * (1/2)\n        ========= ====== ====== ===========\n           F         A     A      \\eps\n\nSimilar for ex2. Now finally apply the 4! anti-symmetrisation on epsilon;\nhere are two terms:\n\n ipos  0 1  2  3 4 5  6 7 8  9 10 11 12 13\n\n   ex1: 5 7 10 11 8 0 13 1 4 12  2  3  9  6 *  (1/48)\n        5 7 10 11 8 0 13 1 4 12  2  9  3  6 * (-1/48)\n        ...\n        ========= ====== ====== ===========\n           F         A     A      \\eps\n\nSo after this you have 48 sets of 14 numbers for ex1, and ditto for ex2.\nNow do a linear decomposition of these sets, to find that ex1 is minus ex2.\n"
  },
  {
    "path": "doc/autogobble.sty",
    "content": "% LaTeX Package `lstautogobble`\n% Counts the leading spaces of the first line and sets `gobble` to this number\n% Copyright (c) 2011 by Martin Scharrer <martin@scharrer-online.de>\n% for http://tex.stackexchange.com/questions/19953/how-to-automatically-skip-leading-white-spaces-in-listings\n% This is free software under the LPPL v1.3c or later and was also posted under the CC BY-SA 3.0 license.\n\\ProvidesPackage{lstautogobble}[2012/02/04 v1.1 Implements 'autogobble' option for 'listings']\n\n% This is an add-on to the `listings` package\n\\RequirePackage{listings}\n\n% Counter for leading spaces\n\\newcount\\lstag@spacecount\n\n% Some macros for comparison:\n\\def\\lstag@activespace{\\lst@ProcessSpace}%  Definition of an active space\n\\def\\lstag@tabulator{\\lst@ProcessTabulator}%  Definition of an tabulator\n\n\\begingroup\n\\catcode`\\^^M=\\active%\n\\gdef\\lstag@activenl{^^M}%  Active CR (ASCII 13) character which is used as line break\n\\endgroup\n\n\n% Define `autogobble` option as boolean (by default off)\n\\lst@Key{autogobble}{false}[t]{\\lstKV@SetIf{#1}\\lst@ifautogobble}\n\n% `ungobble` option\n\\lst@Key{ungobble}{0}{\\def\\lst@ungobble{#1}}\n\n% Insert required code at environment init\n\\lst@AddToHook{Init}{\\lst@autogobble}\n\n% Autogobble init macro.\n% If the option is active and `gobble` is not set, init vars and overwrite the process macro with own definition.\n\\def\\lst@autogobble{%\n    \\lst@ifautogobble\n        \\ifnum\\lst@gobble>0\\else\n            \\def\\lst@gobble{\\lstag@gobble}%\n            \\def\\lstag@gobble{0}%\n            \\lstag@spacecount\\z@\n            \\def\\lstag@spaceaccu{}%\n            \\let\\lstag@restofline\\empty\n            \\let\\lstag@origlstenv@Process\\lstenv@Process\n            \\let\\lstenv@Process\\lstag@countleadingspaces\n        \\fi\n    \\fi\n}\n\n% Checks if the next following character (read as argument) is a line break (as it is supposed to be)\n% Otherwise there is some text direct after the `\\begin{<env>}[<options>]` which is dropped by `listings`.\n\\def\\lstag@countleadingspaces#1{%\n    \\expandafter\\ifx\\lstag@activenl#1\\relax\n        \\expandafter\\lstag@countleadingspaces@\n    \\else\n        \\def\\lstag@restofline{Dummy replacement of text after begin of listing to trigger original warning message}%\n        \\expandafter\\lstag@countleadingspaces\n    \\fi\n}\n\n% After the new line is found this macro counts the spaces and tabulators\n\\def\\lstag@countleadingspaces@#1{%\n    \\ifx\\lstag@activespace#1\\relax\n        \\advance\\lstag@spacecount by \\@ne\n        % Accumulate spaces (i.e. their definitions) for later re-insertion:\n        \\expandafter\\def\\expandafter\\lstag@spaceaccu\\expandafter{\\lstag@spaceaccu\\lst@ProcessSpace}%\n        \\let\\next\\lstag@countleadingspaces@\n    \\else% Character wasn't a space\n    \\ifx\\lstag@tabulator#1\\relax\n        \\advance\\lstag@spacecount by \\lst@tabsize\\relax\n        % Accumulate spaces (i.e. their definitions) for later re-insertion:\n        \\@tempcnta=\\lst@tabsize\\relax\n        \\loop\n        \\ifnum\\@tempcnta>\\z@\n            \\expandafter\\def\\expandafter\\lstag@spaceaccu\\expandafter{\\lstag@spaceaccu\\lst@ProcessSpace}%\n            \\advance\\@tempcnta\\m@ne\n        \\repeat\n        \\let\\next\\lstag@countleadingspaces@\n    \\else% Character wasn't a tabulator either\n        % Set gobble option (indirect):\n        \\xdef\\lstag@gobble{\\the\\numexpr\\lstag@spacecount-\\lst@ungobble\\relax}%\n        % Restore original definition of process macro:\n        \\global\\let\\lstenv@Process\\lstag@origlstenv@Process\n        % Re-insert all collected material or appropriate replacement material:\n        \\edef\\next{\\noexpand\\lstenv@Process\\lstag@restofline\\expandafter\\noexpand\\lstag@activenl\\expandafter\\unexpanded\\expandafter{\\lstag@spaceaccu}\\noexpand#1}%\n    \\fi\\fi\n    \\next\n}\n\n\\endinput"
  },
  {
    "path": "doc/cadabra2.tex",
    "content": "\\documentclass[11pt]{article}\n\\usepackage[textwidth=420pt,textheight=650pt,headheight=13.6pt,nofoot,includehead]{geometry}\n\\usepackage{bm}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage[colorlinks=true, citecolor=red, linkcolor=blue, urlcolor=red, plainpages=false, pdfpagelabels]{hyperref}\n\\usepackage{relsize}\n\\usepackage{xspace}\n\\usepackage{multicol}\n\\usepackage{nomencl}\n\\usepackage{titlesec}\n\\usepackage{titletoc}\n\\usepackage[bottom]{footmisc}\n\\usepackage{makeidx}\n\\usepackage{charter}\n\\usepackage{textfit}\n\\usepackage[numbers,sort&compress]{natbib}\n\\usepackage{hypernat}\n\\usepackage{fancyhdr}\n\\usepackage{fancyvrb}\n\\usepackage{bbold}\n\\usepackage[usenames]{color}\n\\usepackage{caption}\n\\renewcommand\\captionlabelfont{\\footnotesize\\upshape\\bfseries}\n\\renewcommand\\captionfont{\\footnotesize}\n\\makeindex\n\\usepackage{tableaux}\n\n\\newcommand{\\dcite}[1]{{\\citeauthor{#1}~\\cite{#1}}}\n\\newcommand{\\ddcite}[2]{{\\citeauthor{#1}~\\cite{#1,#2}}}\n\\setlength{\\skip\\footins}{15pt plus 4pt minus 2 pt}\n\n\\DeclareMathOperator{\\sgn}{sgn}\n\n% Screen environment, for display of verbatim material.\n\n\\makeatletter\n\\newcommand{\\kcomment}[2]{{\\bf [#1: #2]}}\n\\newcommand{\\bfcomment}[2]{{\\bf [#1: #2]}}\n\\newcommand{\\outdated}{{\\bfseries (documentation no longer correct!)}}\n\\fvset{frame=lines,framerule=0.1pt,framesep=6pt,numbers=none,xleftmargin=5ex,fontfamily=tt,fontsize=\\small}\n\\newenvironment{screen}[1]{\\hilitelines(#1)\\Verbatim}{\\endVerbatim}\n\\makeatother\n\n\\newif\\ifhilite\n\\def\\hilitelines(#1){%\n  \\def\\FancyVerbFormatLine##1{%\n    \\def\\fancylineinput{##1}%\n    \\hilitefalse\n    \\splitfirst #1,\\relax,%\n    \\ifhilite\\else\n      \\fancylineinput\n    \\fi}}\n\n\\def\\splitfirst#1,{%\n  \\ifx\\relax#1\\empty\\else\n    \\hiliteline{#1}{\\fancylineinput}\\expandafter\\splitfirst\n  \\fi}\n\n\\def\\hiliteline#1#2{%\n    \\ifhilite\\else\n      \\ifnum\\value{FancyVerbLine} = #1\n      \\llap{{\\smaller\\smaller \\raisebox{.8ex}{$\\vartriangleright$}}\\,\\,\\,}%\n      \\fi\n    \\fi}\n\n%        \\colourcmd{#2}\\hilitetrue\n%\\def\\colourcmd{\\colorbox{red}} \n\n% List layout.\n\n\\makenomenclature\n%glossary\n\\setlength{\\nomitemsep}{-\\parsep}\n%\\renewcommand{\\nomname}{\\hspace{-3mm}\\raisebox{3.2mm}{\\hbox{\\normalsize\\it %\n%      List of algorithms and properties:}}\\vspace{-7mm}}\n\\renewcommand{\\nomname}{\\vspace{-17mm}}\n\\renewcommand{\\nomlabel}[1]{{\\tt \\def\\cdbat{@}\\def\\cdbcc{::}\\def\\cdbbs{$\\backslash$}#1}\\hfill}\n\\renewcommand{\\pagedeclaration}[1]{#1~~~}\n\\renewcommand\\descriptionlabel[1]{\\hbox to \\textwidth{\\quad\\quad\\bf {#1}\\hfill}}\n\\newcommand{\\cdb}{{cadabra}\\xspace}\n\\newcommand{\\Cdb}{{Cadabra}\\xspace}\n\\newcommand{\\cdbii}{{Cadabra II}\\xspace}\n\\newcommand{\\Cdbii}{{Cadabra II}\\xspace}\n\\newcommand{\\fixme}[1]{{#1}\\marginpar{{\\bf\\smaller FIXME}}}\n\\newcommand{\\Cpp}{\\leavevmode\\rm{\\hbox{C\\hskip -0.1ex\\raise 0.5ex\\hbox{\\tiny ++}}}\\xspace}\n\n% Three macros to declare the main usage of a command, property or\n% member function (to appear in the table of contents of the module \n% section), and commands to use for every subsequent use in the\n% text (which may at some stage end up in the index at the end).\n\\newcommand{\\cdbcommand}[2]{\\nomenclature{\\cdbat#1}{\\hfill\\nomrefpage}{\\tt @#1}}\n\\newcommand{\\subscommand}[1]{{\\tt @#1}}\n\\newcommand{\\cdbprop}[2]{\\nomenclature{\\cdbcc#1}{\\hfill\\nomrefpage}{\\tt ::#1}}\n\n\\newenvironment{props}{\\par\\noindent{\\bf properties:}\\description}{\\enddescription}\n\\newenvironment{algs}{\\par\\noindent{\\bf algorithms:}\\description}{\\enddescription}\n\\newenvironment{reserved}{\\par\\noindent\\description}{\\enddescription}\n\n%\\newenvironment{props}{\\par\\noindent{\\bf properties:}\\\\[1ex]}{\\bigskip\\par}\n%\\newenvironment{algs}{\\par\\noindent{\\bf algorithms:}\\\\[1ex]}{\\bigskip\\par}\n\n\\newcommand{\\cdbalgorithm}[2]{\\nomenclature{\\cdbat#1}{\\hfill\\nomrefpage}\\item[{\\tt @#1}]}\n\\newcommand{\\cdbproperty}[2]{\\nomenclature{\\cdbcc#1}{\\hfill\\nomrefpage}\\item[{\\tt ::#1}\\if!#2!\\else(#2)\\fi]}\n\\newcommand{\\cdbreserved}[2]{\\nomenclature{\\cdbbs#1}{\\hfill\\nomrefpage}\\item[{\\tt $\\backslash$#1}\\if!#2!\\else\\{#2\\}\\fi]}\n\n%\\newcommand{\\cdbalgorithm}[2]{\\nomenclature{\\cdbat#1}{\\hfill\\refpage}\\noindent{\\tt @#1}\\\\}\n%\\newcommand{\\cdbproperty}[2]{\\nomenclature{\\cdbcc#1}{\\hfill\\refpage}\\noindent{\\tt ::#1}\\if#2{}\\else(#2)\\fi}\n\n\\newcommand{\\cdbseealgo}[1]{}\n\\newcommand{\\cdbseeprop}[1]{}\n\\newcommand{\\subsprop}[1]{{\\tt #1}}\n\\newcommand{\\cdbclass}[1]{{\\tt #1}}\n\\newcommand{\\cdbfile}[1]{{\\tt #1}}\n\\newcommand{\\member}[1]{{\\tt #1}}\n\\newcommand{\\subsmember}[1]{{\\tt #1}}\n\\newcommand{\\deprecated}{\\marginpar{{\\bf\\smaller deprecated}}}\n\n\\newcommand{\\inertcommand}[1]{{\\tt @@#1}}\n\\newcommand{\\texcommand}[1]{{\\tt $\\backslash$#1}}\n\\newcommand{\\ctri}{{\\smaller\\smaller$\\blacktriangleright$}}\n\\newcommand{\\boolargs}{{\\it true\\/}$|${\\it false\\/}}\n\\newcommand{\\listargs}{{\\it expression list\\/}}\n\n\\numberwithin{equation}{section}\n\n\\def\\mystrut{\\vbox to 8.5pt{}\\vtop to 3.5pt{}}\n\\def\\V{\\hskip10pt\\vrule\\hskip10pt}\n\\def\\T{\\hskip10pt\\vrule\\vrule height2.5pt depth -2.1pt width 10pt}\n\\def\\L{\\hskip10pt\\vrule height 8.5pt depth -2.1pt\n       \\vrule height2.5pt depth -2.1pt width 10pt}\n\\def\\N{\\hskip10pt\\phantom{\\vrule}\\hskip10pt}\n\\def\\hw{\\hskip-1000pt plus 1fil}\n\n% Courtesy of Donald Arsenau.\n\\makeatletter\n\\newenvironment{descerate}\n  {\\enumerate\n   \\@noitemargtrue \\let\\@noitemargfalse\\relax\n   \\renewcommand\\makelabel[1]{%\n     \\hspace\\labelwidth\n     \\llap{\\@itemlabel}%\n     \\hspace\\labelsep\n     \\textbf{##1}%\n   }%\n  }%\n  {\\endenumerate}\n\\makeatother\n%\\renewcommand{\\contentsname}{\\vspace{-3ex}}\n\n\n% Page layout style\n%\n\\pagestyle{fancy}\n\\renewcommand{\\sectionmark}[1]{\\markboth{{\\it\\small #1}}{}}%\n\\renewcommand{\\subsectionmark}[1]{\\markboth{{\\it\\small \\thesubsection.~#1}}{}}%\n\\fancyhf{}%\n\\fancyhead[L]{\\leftmark\\hspace{3cm}}\n\\fancyhead[R]{\\thepage}%\n\\renewcommand{\\headrulewidth}{.1pt}\n\\renewcommand{\\footrulewidth}{0pt}\n\\fancypagestyle{plain}{%\n \\fancyhead{}\n }\n\n\n%\\newcommand{\\sectionformat}[1]{\\colorbox[rgb]{.84,.84,.95}{$\\vcenter to 2.5ex{\\vspace{-.45ex}\\hbox\n%\t to 444pt{\\bfseries\\textcolor[rgb]{0,0,0}{\\Huge\\bfseries \\hspace{3mm}#1\\strut\\hfill}}}$}}\n%\\newcommand{\\subsectionformat}[1]{\\colorbox[rgb]{.9,.9,.98}{$\\vcenter to 1.5ex{\\hbox\n%\t to 444pt{\\bfseries\\textcolor[rgb]{0,0,0}{\\large\\bfseries \\hspace{3mm}\\thesubsection~~#1\\strut\\hfill}}}$}}\n\n\\newcommand{\\sectionformat}[1]{\\Huge\\bfseries \\hspace{3mm}#1}\n\\newcommand{\\subsectionformat}[1]{\\large\\bfseries \\hspace{3mm}\\thesubsection~~#1}\n\n% \\titlecontents{section}[0pt]{\\addvspace{1pc}\\itshape}%\n%    {\\contentsmargin{0pt}\\bfseries%\n%     \\makebox[0pt][r]{\\large\\thecontentslabel\\enspace}\\large}%\n%    {\\contentsmargin{0pt}\\large}\n%    {\\quad\\thepage}[\\addvspace{.5pc}]\n\\renewcommand{\\contentsname}{\\hspace{-30pt}Table of Contents}\n\n\\titleformat{\\section}[block]\n  {\\normalfont\\bfseries}{}{-30pt}{\\sectionformat}\n\\titleformat{\\subsection}[block]\n  {\\bfseries}{}{-30pt}{\\subsectionformat}\n\n\\begin{document}\n\\pagestyle{empty}\n\\begin{flushright}\n\\today\n\\end{flushright}\n\\vspace{6ex}\n\\hspace{-3mm}{\\bf \\scaletowidth{7cm}{Cadabra II}}~\\\\[.8ex] \n{\\it A field-theory motivated approach to symbolic computer algebra}\\\\[6ex]\n{\\large\\bf Copyright \\copyright~2001--2014 ~Kasper Peeters}\\\\[25ex]\n{\\huge\\bf Tutorial and reference guide}\n\\vfill\n\\noindent {\\smaller This manual is available under the terms of the GNU Free\nDocumentation License, version 1.2.\\\\\nThe accompanying software is available under the terms of the GNU\nGeneral Public License, version 3.}\n\\newpage\n\\pagestyle{fancy}\n\\noindent \\Cdb is a computer algebra system for the manipulation of\ntensorial mathematical expressions such as they occur in ``field\ntheory problems''. It is aimed at, but not necessarily restricted to,\nhigh-energy physicists. It is constructed as a simple\ntree-manipulating core, a large collection of standalone algorithmic\nmodules which act on the expression tree, and a set of modules\nresponsible for output of nodes in the tree. All of these parts are\nwritten in \\Cpp. The input and output formats closely follow \\TeX,\nwhich in many cases means that \\cdb is much simpler to use than other\nsimilar programs. It intentionally does not contain its own\nprogramming language; instead, new functionality is added by writing\nnew modules in \\Cpp.\\\\[2ex] This document contains a description of\nthe core program as well as a detailed listing of the functionality of\nthe currently available algorithm modules. Given the origin of \\cdb,\nthe bias is currently towards algorithms for problems in (quantum) field\ntheory, general relativity, group theory and related areas. The last\npart of this text consists of a user guide on how to implement new\nalgorithmic and\ndisplay modules and thereby extend the functionality of \\cdb.\\\\[3ex]\nThe software is available for download under the terms of the GNU\nGeneral Public License from\n\\url{http://cadabra.phi-sci.com/} .\\\\[3ex]\n\n\\noindent A paper describing the design of \\cdbii is\navailable as\n\\begin{center}\n\\begin{minipage}{.8\\textwidth}\n``\\emph{Introducing Cadabra: a symbolic computer algebra system for\\\\\n\t field theory problems}'',\\\\\nKasper Peeters,\nalso available as preprint {\\tt hep-th/0701238}.\n\\end{minipage}\n\\end{center}\nIf you use \\cdbii in your own work, please cite that paper.\n\n\n\\vfill\n\\noindent {\\large\\bf Copyright \\copyright~2001--2012 ~Kasper Peeters}\\\\[3ex]\n\\url{http://maths.dur.ac.uk/users/kasper.peeters/}\\\\[1ex]\n\\url{mailto:kasper.peeters@gmail.com}\n\\newpage\n\n\\pagestyle{empty}\n\\tableofcontents\n\\cleardoublepage\n\\pagestyle{fancy}\n\n\\section{Overview and motivation}\n\n% http://groups.google.com/groups?hl=en&lr=&ie=UTF-8&selm=281120021009129275%25sowell2%40cox.net\n%\n\\begin{flushright}\n{\\smaller\\smaller ``\\,}\\begin{minipage}[t]{220pt}\n\\smaller\\smaller{\\it I think that several of you are missing the obvious. The majority of\n people use these programs as symbolic calculators -- occasionally. As\n such they want their input and output to match what they would have\n written with pencil and paper.''}~  \\hfill\n \\href{https://groups.google.com/d/msg/comp.soft-sys.math.maple/7nfyE-aiYw0/GV2Q5pQtLMcJ}{\\tt\n   soft-sys.math.maple},~2002\n\\end{minipage}\n\\end{flushright}\n%\n%------------\n% \n% Things to be stressed here:\n%\n%   - Declaring a variable to be equal to something else and\n%     automatically substituting this something else for every\n%     occurence of the variable are two different things. You \n%     want to be able to write\n% \n%         W_{m} -> A_{m n} C^{n};\n%\n%         W_{m};\n%         @(W_{m});\n% \n%     or something like that. Aha erlebnis: yes, we will do it this\n%     way...\n%\n% - Intro: \n% \n%    - tensor expressions not trees, taking this into account afterwards is kludgy\n%      (automatic dummy index renaming, canonicalisation of expressions,\n%       handling of 'indexbracket' constructions; see the RuleUnique\n%       hack in MathTensor).\n%    - property lists are an essential ingredient in writing compact mathematical\n%      notation. They should be builtin, rather than added in the user-space language,\n%      because the algorithms need this property information.\n%    - tensor expressions are not naturally written in functional notation.\n%    - many _programming_ problems are not easiest to solve in Math or\n%      Maple language; a system that has open internals is required.\n\n\\noindent \\Cdb is a computer algebra system for the manipulation of\nwhat could loosely be called \\emph{tensorial expressions}. It is aimed\nat, but not necessarily restricted to, theoretical high-energy\nphysicists. The program's interface, storage system and underlying\nphilosophy differ substantially from other computer algebra systems.\nIts main characteristics are:\n\\begin{itemize}\n\\item[\\ctri] Usage of \\TeX{} notation for both input and output,\n  which eliminates many errors in transcribing problems from paper to\n  computer and back.\n\\item[\\ctri] Built-in understanding of dummy indices and dummy\n  symbols, including their automatic relabelling when necessary.\n  Powerful algorithms for canonicalisation of objects with index\n  symmetries, both mono-term and multi-term.\n\\item[\\ctri] A new way to deal with products of non-commuting objects,\n  enabling a notation which is identical to standard physicist's\n  notation (i.e.~no need for special non-commuting product operators).\n\\item[\\ctri] A flexible way to associate meaning (``type\n  information'') to tensors by attaching them to ``properties''.\n\\item[\\ctri] An optional unlimited undo system. Interactive calculations\n can be undone to arbitrary level without requiring a full\n re-evaluation of the entire calculation.\n\\item[\\ctri] A simple and documented way to add new algorithms in\n  the form of \\Cpp modules, which directly operate on the internal\n  expression tree.\n\\end{itemize}\n\n% There is a certain (large) class of problems in high-energy physics,\n% often classified as ``simple but tedious algebra'', for which existing\n% computer algebra systems are not very well suited. The most annoying\n% issues are typically related to the conversion of the physics problem\n% into computer language, and to the handling of expressions with many,\n% often implicit indices of various types. \\Cdb differs in essential\n% aspects from other systems, to take away these problems. The program\n% is somewhere in the middle between a general purpose system like\n% Mathematica and programs specialised for very particular tasks. \n% \\medskip\n\n% The design of \\cdb borrows many ideas from other computer algebra\n% programs.  The user interface was inspired to some extent by\n% H\\\"oglund's {\\tt Tensign}~\\cite{hogl1}. Another source of ideas, in\n% particular concerning the interactive user interface and the ``formula\n% history'' was the program {\\tt Abra}, written by de Roo. The idea of\n% using \\Cpp as the implementation language for algorithms (rather than\n% a home-brew language like most computer algebra systems do, or a\n% variant of LISP) can also be found in {\\tt GiNaC}, written by\n% \\dcite{e_baue1}. The use of one generic internal representation can\n% also be found in {\\tt Mathematica} and in fact most LISP-like systems,\n% although the one used by \\cdb is more tuned towards flexibility for\n% the user.  Some ideas about symbols being a-priori separate from their\n% meaning can also be found in {\\tt Yacas} by~\\dcite{e_pink1} and this\n% has to some extent been implemented as ``domains'' in {\\tt MuPAD}.\n% Finally, several of the modules were inspired by existing\n% software. For the manipulation of gamma matrix algebra, I have\n% borrowed from {\\tt GAMMA} by \\dcite{Gran:2001yh} as well as {\\tt\n% Abra}. The general relativity module uses many ideas of the {\\tt\n% GRtensorII} software by~\\dcite{e_grte1}.\n% \\medskip\n\nThis document contains a small tutorial, an extensive reference guide\nand a technical summary of the program's internals together with a\nguide on how to write new algorithm modules in \\Cpp.\n\n%Still discuss: Theorist (now Live Math Maker)~\\dcite{http://www.livemath.com/}\n%which has a mouse-based interface.\n%\n%\\url{http://poisson.dm.unipi.it/~cerulli/LAlgebrista/its2000.php?lang=en}\n%\n% Tensorial for mathematica:\n% http://home.earthlink.net/~djmp/Mathematica.html\n% See also the 'expression manipulation' thing there.\n\n\\vfill\n\\noindent\\begin{minipage}{\\textwidth}\n\\noindent {\\bfseries\\large Acknowledgements}\n\\medskip\n\n\\noindent This program uses code written by several other people. The\ntensor monomial canonicalisation routines rely on the {\\tt xPerm} code\nwritten by Jos\\'e Martin-Garcia~\\cite{e_xact}). All\nrepresentation-theory related problems are handled by the {\\tt LiE}\nsoftware by Marc van Leeuwen, Arjeh Cohen and Bert\nLisser~\\cite{e_cohe1}.  \\medskip\n\n\\noindent The name \\Cdb is an implicit acknowledgement to\n\\href{http://thep.housing.rug.nl/people/mees-de-roo}{Mees de Roo}, who\nintroduced me to his (so far unpublished) Pascal program {\\tt Abra} in\nthe fall of 2000. This program has an extremely physicist-friendly way\nof dealing with fermions and tensor symmetries, and a formula history\nmechanism still not found in any other comparable computer algebra\nsystem. \\Cdb was originally planned to be ``my private \\Cpp version of\n{\\tt Abra}'', and even though it does not show much similarity\nanymore, the development was to a large extent inspired by {\\tt Abra}.\n\\end{minipage}\n\\eject\n\n\\section{Tutorial}\n\nThe best way to explain the advantages of a new computer algebra\nsystem is to demonstrate its ease-of-use for a real-world problem.\nBut if you lack the patience to even read the tutorial on the next few\npages, at least read the remainder of this page for an absolute\nminimum of information. All input in the examples is prefixed\nwith a ``$\\vartriangleright$'' symbol.\n\\begin{itemize}\n\\item[\\ctri] Start the program by typing\n``{\\tt prompt cadabra}''. Quit with the ``\\subscommand{quit}'' command.\n\\item[\\ctri] Tensor expressions are entered as in \\TeX{}, with\n  subscripts and superscripts as you know them, e.g.\n\\begin{screen}{1}\nA_{m n} B^{m q} R^{n}_{q};\n\\end{screen}\nInput lines are terminated with ``;'', ``:'' or ``.'' punctuation; see\nsection~\\ref{s:input_format} on page~\\pageref{s:input_format} for\ninformation on what these characters mean.\n\\item[\\ctri] Tensors carry properties, such as ``being a Riemann\n  tensor''. These properties are attached by using a double-double\n  dot notation,\n\\begin{screen}{1,2,3}\nR_{m n p q}::RiemannTensor.\ng_{m n}::Metric.\n\\psi::Spinor.\n\\end{screen}\nA list of all properties and the place where they are described in\nthis manual can be found on page~\\pageref{s:modules}.\n\\item[\\ctri] For many operations \\cdb needs to know about the names\n  which it can use for `dummy' indices. You declare dummy indices as\n\\begin{screen}{1}\n{m,n,p,q}::Indices(vector).\n\\end{screen}\nwhere ``{\\tt vector}'' is a chosen name for this index set. See\nsection~\\ref{s:automaticdummies} on page~\\pageref{s:automaticdummies}. \n\\item[\\ctri] For many other operators, \\cdb needs to know the range\n  over which indices run. Set these index ranges by attaching\n  the \\subsprop{Integer} property to the indices, e.g.\n\\begin{screen}{1}\n{m,n,p,q}::Integer(0..10).\n\\end{screen}\n\\item[\\ctri] Expressions can be given a label so you can refer to them\n  again later; you do this by writing the label before the expression\n  and a ``:='' in between,\n\\begin{screen}{1}\nMaxwellEom:= \\diff{F^{m n}}_{n} = 0;\n\\end{screen}\n\\item[\\ctri] All things starting with `@' are commands (also called\n``active nodes'').  Some of the frequently used commands are\n\\subscommand{substitute} (page~\\pageref{loc_substitute}),\n\\subscommand{canonicalise} (page~\\pageref{loc_canonicalise}) and\n\\subscommand{collect\\_terms} (page~\\pageref{loc_collect_terms}).\n\\end{itemize}\n\\eject\n\n% \\subsection{Kaluza-Klein gravity}\n% \n% Starting from the Einstein-Hilbert action in four dimensions, a\n% reduction on a circle produces a theory in three dimensions which\n% contains two vector fields (one from the Kaluza-Klein vector and one\n% from the dualised Kaluza-Klein scalar). \n% \n% The interactive form of the program is started using the command\n% \\begin{screen}{0}\n% prompt cadabra\n% \\end{screen}\n% This produces a startup message and a prompt. We will go through a\n% simple example in general relativity to get used to the program.\n% First, we associate properties to the symbols which we will use:\n% \\begin{screen}{0}\n% m::Integer(0..d-1).\n% n::Integer(0..d-1).\n% g_{m n}::Metric.\n% \\Gamma^{m}_{n p}::ChristoffelSymbol.\n% R_{m n p q}::RiemannTensor.\n% \\end{screen}\n% In these expressions, the symbols {\\tt Integer}, {\\tt\n% ChristoffelSymbol} and {\\tt RiemannTensor} are so-called\n% ``properties'', which are known to \\cdb. A list of all known\n% properties can be found in section~\\ref{s:modules}. They are always\n% associated to names by using the ``::'' notation. The names to which\n% we associate these properties are arbitrary and we could have\n% e.g.~used a different symbol to denote a Riemann tensor. For more on\n% the input format, see section~\\ref{s:input_format}.\n% \n% \n% \n% (for more on the way in which active nodes act, see section~\\ref{s:active_nodes}).\n% \n% (this algorithm is provided by one of the many separate modules, see\n% section~\\ref{s:modules} for a description of the ones presently available).\n% \n\n\\subsection{Web tutorials and sample notebooks}\n\nApart from the tutorials listed below, there is a growing collection\nof sample notebooks available on the \\cdb web site. In addition, help\nis available through the mailing list.\n\n\n\\subsection{Tutorial 1: Tensor monomials and multi-term symmetries}\n\n\\Cdb contains powerful algorithms to bring any tensorial expression\ninto a canonical form. For multi-term symmetries, \\cdb relies on\nYoung tableau methods to generate a canonical form for tensor\nmonomials. \\footnote{The user interface for multi-term\n  symmetries is under active development and will simplify\n  substantially in upcoming releases.} \n\nAs an example, consider the identity\n\\begin{multline}\nW_{p q r s} W_{p t r u} W_{t v q w} W_{u v s w} \n- W_{p q r s} W_{p q t u} W_{r v t w} W_{s v u w} \\\\[1ex]\n= \n  W_{m n a b} W_{n p b c} W_{m s c d} W_{s p d a}\n- \\frac{1}{4} W_{m n a b} W_{p s b a} W_{m p c d} W_{n s d c}\\,.\n\\end{multline}\nin which~$W_{m n p q}$ is a Weyl tensor (all contracted indices have\nbeen written as subscripts for easier readability). Proving this\nidentity requires multiple uses of the Ricci cyclic identity,\n\\begin{equation}\nW_{m [n p q]} = 0 \\,.\n\\end{equation}\nWith \\cdb's Young tableau methods the proof is simple. We first\ndeclare our objects and input the identity which we want to prove,\n\\begin{screen}{1,2,4}\n{m,n,p,q,r,s,t,u,v,w,a,b,c,d,e,f}::Indices(vector).\nW_{m n p q}::WeylTensor.\n\nW_{p q r s} W_{p t r u} W_{t v q w} W_{u v s w} \n  - W_{p q r s} W_{p q t u} W_{r v t w} W_{s v u w}\n  - W_{m n a b} W_{n p b c} W_{m s c d} W_{s p d a}\n  + (1/4) W_{m n a b} W_{p s b a} W_{m p c d} W_{n s d c};\n\\end{screen}\nUsing a Young projector to project all Weyl tensors onto a form which\nshows the Ricci symmetry in manifest form is done with\n\\hilitelines(0)\n\\begin{screen}{1}\n@young_project_tensor!(%){ModuloMonoterm};\n\\end{screen}\nThis algorithm knows that the Weyl tensor sits in the~$\\displaystyle\\tilde{\\tableau{2 2}}$\nrepresentation of the rotation group~SO($d$), and effectively leads to\na replacement\n\\begin{equation}\nW_{m n p q} \\rightarrow \\frac{2}{3} W_{m n p q} - \\frac{1}{3} W_{m q n p} + \\frac{1}{3} W_{m p n q}\\,.\n\\end{equation}\nWe then expand the products of sums and canonicalise using mono-term\nsymmetries,\n\\begin{screen}{1,2,3,4}\n@distribute!(%):\n@canonicalise!(%):\n@rename_dummies!(%):\n@collect_terms!(%);\n\\end{screen}\nThe last line produces the expected ``zero''. A slightly more complicated\nmulti-term example can be found in \\TeX{}macs format in {\\tt texmacs/showcase1.tm}.\n\n\n\\subsection{Tutorial 2: Tensor monomials, part two}\n\nIt is easy to generate complete bases of tensor monomials, for any\narbitrary tensors (not necessarily for tensors in irreps, as in the\nprevious example). As an example, let us show how this works for a\nbasis constructed from three powers of the Riemann tensor. All that is\nrequired is\n\\begin{screen}{1,2,4,6,7}\n{m,n,p,q,r,s,t,u,v,w,a,b}::Indices(vector).\n{m,n,p,q,r,s,t,u,v,w,a,b}::Integer(0..9).\n\nR_{m n p q}::RiemannTensor.\n\nbasisR3:= R_{m n p q} R_{r s t u} R_{v w a b};\n@all_contractions(%);\n\\end{screen}\nThe result can be further simplified using\n\\begin{screen}{1,2,3,4,5}\n@canonicalise!(%):\n@substitute!(%)( R_{m n m n} -> R ):\n@substitute!(%)( R_{m n m p} -> R_{n p} ):\n@substitute!(%)( R_{n m p m} -> R_{n p} ):\n@substitute!(%)( R_{n m m p} -> R_{n p} );\n\\end{screen}\nwhich leads something like\\footnote{The algorithm involves a random\n  step which implies that the basis is not always the same, though it\n  is always complete. Further improvements are in preparation which\n  will eliminate this randomness (and also lead to a speedup).}\n\\begin{screen}{0}\nbasisR3:= \\{ R_{m n p q} * R_{m p r s} * R_{n r q s}, \n             R * R_{q r} * R_{q r}, \n             R_{n p} * R_{n q p r} * R_{q r}, \n             R_{n p} * R_{n q r s} * R_{p r q s}, \n             R * R_{p q r s} * R_{p q r s}, \n             R_{n p} * R_{n r} * R_{p r}, \n             R_{m n p q} * R_{m r p s} * R_{n r q s}, \n             R * R * R \\};\n\\end{screen}\nThis result is equivalent to the basis given in the ``${\\cal R}^0_{6,3}$''\ntable on page~1184 of~\\cite{Fulling:1992vm}.\n\n\n\\subsection{Tutorial 3: World-sheet supersymmetry}\n\\label{s:tut_worldsheet}\n\n\\Cdb not only deals with bosonic tensors, but also with fermionic\nobjects, i.e.~anti-commuting variables. A simple example on which to\nillustrate their use is the Ramond-Neveu-Schwarz superstring action.\nWe will here show how one uses \\cdb to show invariance of this action\nunder supersymmetry (a calculation which is easy to do by hand, but\nillustrates several aspects of \\cdb nicely). We will use a conformal\ngauge and complex coordinates.\n\nWe first define the properties of all the symbols which we will use,\n\\begin{screen}{1,2,3,4,5}\n{\\del{#}, \\delbar{#}}::Derivative.\n{\\Psi_\\mu, \\Psibar_\\mu, \\eps, \\epsbar}::AntiCommuting.\n{\\Psi_\\mu, \\Psibar_\\mu, \\eps, \\epsbar}::SelfAntiCommuting.\n{\\Psi_\\mu, \\Psibar_\\mu, X_\\mu}::Depends(\\del,\\delbar).\n{\\Psi_\\mu, \\Psibar_\\mu, \\eps, \\epsbar, X_\\mu, i}::SortOrder.\n\\end{screen}\nAll objects are by default commuting, so the bosons do not have to be\ndeclared separately.  You can at any time get a list of the declared\nproperties by using the command \\subscommand{proplist}.\n\nIf  you try this example in the graphical front-end, \\verb|\\\\del|,\n  \\verb|\\\\eps| and so\n  on would not print correctly as these are not valid \\LaTeX{}\n  symbols. However, you can tell \\cdb to print such symbols by using\n  the \\subsprop{LaTeXForm} property,\n\\begin{screen}{1,2,3,4,5}\n\\del{#}::LaTeXForm(\"\\partial\").\n\\delbar{#}::LaTeXForm(\"\\bar{\\partial}\").\n\\eps::LaTeXForm(\"\\epsilon\").\n\\epsbar::LaTeXForm(\"\\bar{\\epsilon}\").\n\\Psibar{#}::LaTeXForm(\"\\bar{\\Psi}\").\n\\end{screen}\nIf you use the command-line version, these \\subsprop{LaTeXForm}\nproperties are not needed.\n\nNow we have to input the action density (see~\\cite{kas_kystring} for\nthe conventions used here)\n\\begin{screen}{1}\naction:= \\del{X_\\mu} \\delbar{X_\\mu} \n        + i \\Psi_\\mu \\delbar{\\Psi_\\mu} + i \\Psibar_\\mu \\del{\\Psibar_\\mu};\n\\end{screen}\nObserve how we wrapped the \\texcommand{del} and \\texcommand{delbar}\noperators around the objects on which they are supposed to act. We are\nnow ready to perform the supersymmetry transformation. This is done by\nusing the \\subscommand{vary} algorithm, \n\\begin{screen}{1,5,6}\n@vary(%)( X_\\mu       ->   i \\epsbar \\Psi_\\mu + i \\eps \\Psibar_\\mu,\n          \\Psi_\\mu    -> - \\epsbar \\del{X_\\mu},\n          \\Psibar_\\mu -> - \\eps \\delbar{X_\\mu} );\n\n@distribute!(%);\n@prodrule!(%);\n\\end{screen}\nThe \\subscommand{prodrule} command has applied the Leibnitz rule on\nthe derivatives, so that the derivative of a product becomes a sum of\nterms. We expand again the products of sums, and use\n\\subscommand{unwrap} to take everything out of the derivatives which\ndoes not depend on it,\n\\begin{screen}{1,2,3}\n@distribute!(%);\n@unwrap!(%);\n@sort_product!(%);\n\\end{screen}\nAt this stage we are left with an expression which still contains\ndouble derivatives. In order to write this in a canonical form, we\neliminate all double derivatives by doing one partial\nintegration. This is done by first marking the derivatives which we\nwant to partially integrate, and then using \\subscommand{pintegrate},\n\\begin{screen}{1,2,3,4,5,6,7,8,9,10}\n@substitute!(%)( \\del{\\delbar{X_{\\mu}}} -> \\pdelbar{\\del{X_{\\mu}}} ):\n@substitute!(%)( \\delbar{\\del{X_{\\mu}}} -> \\pdel{\\delbar{X_{\\mu}}} ):\n@pintegrate!(%){ \\pdelbar }:\n@pintegrate!(%){ \\pdel }:\n@rename!(%){\"\\pdelbar\"}{\"\\delbar\"}:\n@rename!(%){\"\\pdel\"}{\"\\del\"};\n@prodrule!(%);\n@distribute!(%);\n@unwrap!(%);\n@sort_product!(%);\n\\end{screen}\nNotice how, after the partial integration, we renamed the partially\nintegrated derivatives back to normal ones (and again apply Leibnitz'\nrule).  If we now collect terms,\n\\begin{screen}{1}\n@collect_terms!(%);\n\\end{screen}\nwe indeed find that the total susy variation vanishes.\n\n\n\\subsection{Tutorial 4: Super-Maxwell}\n\nThe following example illustrates the use of a somewhat more\ncomplicated set of object properties. A \\TeX{}macs version of this\nproblem can be found in the distribution tarball in the file {\\tt\n  texmacs/showcase3.tm}. We start with the super-Maxwell action, given by\n\\begin{equation}\nS = \\int\\!{\\rm d^4}x\\, \\Big[ -\\frac{1}{4} (F_{ab})^2 -\n\\frac{1}{2}\\bar{\\lambda}\\gamma^a \\partial_a \\lambda\\Big]\\,,\n\\end{equation}\nIt is supposed to be invariant under the transformations\n\\begin{equation}\n\\delta A_a = \\bar{\\epsilon}\\gamma_a \\lambda\\,,\\quad\n\\delta \\lambda = -\\frac{1}{2} \\gamma^{a b} \\epsilon\\, F_{a b}\\,.\n\\end{equation}\nThe object properties for this problem are\n\\begin{screen}{1,2,3,4,5,6,7,8,9,10,11,12,13,14,15}\n{ a,b,c,d,e }::Indices(vector).\n\\bar{#}::DiracBar.\n{ \\partial{#}, \\ppartial{#} }::PartialDerivative.\n{ A_{a}, f_{a b} }::Depends(\\partial, \\ppartial).\n{ \\epsilon, \\gamma_{#} }::Depends(\\bar).\n\\lambda::Depends(\\bar, \\partial).\n{ \\lambda, \\gamma_{#} }::NonCommuting.\n{ \\lambda, \\epsilon }::Spinor(dimension=4, type=Majorana).\n{ \\epsilon, \\lambda }::SortOrder.\n{ \\epsilon, \\lambda }::AntiCommuting.\n\\lambda::SelfAntiCommuting.\n\\gamma_{#}::GammaMatrix(metric=\\delta).\n\\delta{#}::Accent.\nf_{a b}::AntiSymmetric.\n\\delta_{a b}::KroneckerDelta.\n\\end{screen}\nNote the use of two types of properties: those which apply to a single\nobject, like {\\tt Depends}, and those which are associated to a list\nof objects, like {\\tt AntiCommuting}. Clearly $\\partial_a \\lambda$ and\n$\\bar{\\epsilon}$ are anti-commuting too, but the program figures this out\nautomatically from the fact that {\\tt $\\backslash$partial} has an\nassociated {\\tt PartialDerivative} property associated to\nit.\\footnote{This is similar to Macsyma's types and features: the\nproperty which is attached to a symbol is like a `type', while all\nproperties which the symbol inherits from child nodes are like\n`features'.}\n\nThe actual calculation is an almost direct transcription of the\nformulas above. First we define the supersymmetry transformation rules,\n\\begin{screen}{1}\nsusy:= { \\delta{A_{a}} = \\bar{\\epsilon} \\gamma_{a} \\lambda, \n         \\delta{\\lambda} = -(1/2) \\gamma_{a b} \\epsilon f_{a b} };\n\\end{screen}\nThe action is also written just as it is typed in~\\TeX,\n\\begin{screen}{1}\nS:= -(1/4) f_{a b} f_{a b} \n              - (1/2) \\bar{\\lambda} \\gamma_{a} \\partial_{a}{\\lambda};\n\\end{screen}\nShowing invariance starts by applying a variational derivative,\n\\begin{screen}{1,5,6,7}\n@vary(%)( f_{a b} ->   \\partial_{a}{\\delta{A_{b}}} \n                     - \\partial_{b}{\\delta{A_{a}}},\n          \\lambda -> \\delta{\\lambda} );\n\n@distribute!(%):\n@substitute!(%)( @(susy) ): @prodrule!(%): @distribute!(%): @unwrap!(%);\n\\end{screen}\nAfter these steps, the result is (shown exactly as it appears in the \\TeX{}macs~\\cite{vdH:Gut} frontend)\n\\begin{equation}\nS = \\bar{\\epsilon} \\gamma_{a} \\partial_{b} \\lambda\\, f_{ab}\n  + \\frac{1}{4} \\overline{\\gamma_{cb} \\epsilon} \\gamma_{a}\n  \\partial_a\\lambda\\, f_{cb}\n  + \\frac{1}{4} \\bar{\\lambda}\\gamma_a \\gamma_{cd} \\epsilon \\partial_a f_{cb}\\,.\n\\end{equation}\nSince the program knows about the properties of gamma matrices it can\nrewrite the Dirac bar, and then we do one further partial integration,\n\\begin{screen}{1,2,3,4,5}\n@rewrite_diracbar!(%);\n@substitute!(%)( \\partial_{c}{f_{a b}} -> \\ppartial_{c}{f_{a b}} ):\n@pintegrate!(%){\\ppartial}: \n@rename!(%){\"\\ppartial\"}{\"\\partial\"}:\n@prodrule!(%): @unwrap!(%);\n\\end{screen}\nWhat remains is the gamma matrix algebra, sorting of spinors (which\nemploys inheritance of the {\\tt Spinor} and {\\tt AntiCommuting}\nproperties as already alluded to earlier) and a final canonicalisation\nof the index contractions,\n\\begin{screen}{1,2,4,5}\n@join!(%){expand}: @distribute!(%): @eliminate_kr!(%): @sort_product!(%);\n@substitute!(%)( \\partial_{a}{\\bar{\\lambda}}\n                                    -> \\bar{\\partial_{a}{\\lambda}} );\n@spinorsort!(%):\n@rename_dummies!(%): @canonicalise!(%): @collect_terms!(%);\n\\end{screen}\nThe result is a Bianchi identity on the field strength, and thus\ninvariance of the action.\n\n\n\n% \\subsection{BRST transformations}\n% \n% \\begin{equation}\n% \\begin{aligned}\n% \\delta A_\\mu^a   &= \\epsilon D_\\mu^{ab} c^b\\,,\\\\[1ex]\n% \\delta \\psi      &= i g\\, \\epsilon c^a t^a \\psi\\,,\\\\[1ex]\n% \\delta c^a       &= -\\tfrac{1}{2} g \\epsilon f^{abc} c^b c^c\\,,\\\\[1ex]\n% \\delta \\hat{c}^a &= \\epsilon B^a\\,,\\\\[1ex]\n% \\delta B^a       &= 0\\,.\n% \\end{aligned}\n% \\end{equation}\n% \n% \\begin{screen}{0}\n% {a, b, c, d, e, f, g}::Indices.\n% f^{a b c}::AntiSymmetric.\n% C^{a}::SelfAntiCommuting.\n% R_{a b d e}::RiemannTensor.\n% \n% #f^{a b c} f^{c d e} ( A_\\mu^b C^d C^e + A_\\mu^d C^e C^b + A_\\mu^e C^b C^d );\n% R_{a b d e} ( A_\\mu^b C^d C^e + A_\\mu^d C^e C^b + A_\\mu^e C^b C^d );\n% @distribute!(%);\n% @canonicalise!(%);\n% @rename_dummies!(%);\n% @collect_terms!(%);\n% \\end{screen}\n% \n%R_{a b d e} A_\\mu^b C^d C^e;\n\n% \\subsection{Perturbative gravity}\n% \n% % Perhaps the four-point vertex is nice to derive?\n% In perturbative Einstein gravity, we expand the metric around a fixed\n% background metric. This can get quite tedious at higher orders. Let us\n% first illustrate how such a perturbative expansion works at the lowest\n% order, for instance for~$R_{m n p q} R^{m n p q}$. This is obtained\n% with\n% \\begin{screen}{0}\n% {l, m, n, s, t, u, v}::Indices(vector).\n% R_{l m n s}::RiemannTensor.\n% h_{m n}::Symmetric.\n% \\diff{#}::PartialDerivative.\n% \n% 4 R_{l m n s} R_{l m n s};\n% \n% @substitute!(%)( R_{l m n s} -> \n%           @asym[ \\diff{ h_{l s} }_{m n} - \\diff{ h_{m s} }_{l n}]{_n, _s} );\n% \n% @distribute!(%):\n% @canonicalise!(%):\n% @collect_terms!(%);\n% \\end{screen}\n% The result is correct, but only because the inverse metrics which\n% contract the two Riemann tensors do \n\n\n% For next version: some way to write integrals and the like in\n% a natural notation.\n%\n% \\begin{screen}{0}\n% {l, m, n, r, s, t, u, v, w}::Indices(vector, position=fixed).\n% R_{l m n s}::RiemannTensor.\n% R::RicciScalar.\n% R_{l m n s}::Depends(x).\n% R::Depends(x).\n% \n% \\int_0^\\infty R dx;\n% \\end{screen}\n\n% some default input file which does collect_factors, collect_terms,\n% and so on as people expect.\n\n%   ::PostDefaultRules( @@sumflatten!(%), @@sort_product!(%), @@collect_factors!(%), @@collect_terms!(%) ).\n%   \n%   ( eta_{n m} + k h_{n m} )  ( eta^{m p} + k h0^{m p} + k**2 h1^{m p} + k**3 h2^{m p}) = \\delta_{n}^{p};\n%   @distribute!(%);\n%   @substitute!(%)( eta_{n m} eta^{m p} -> \\delta_{n}^{p} );\n%   # something to absorb eta, more elegantly than this. @eliminate_metric\n%   # would do, since we already have @eliminate_kr. That could handle all\n%   # such things, together with @eliminate_vielbein. \n%   @substitute!(%)( eta_{n m} A?^{m p} -> A?_{n}^{p} );\n%   @substitute!(%)( eta^{m n} A?_{p m} -> A?_{p}^{n} );\n%   @factorise!(%){ h0_{n}^{p}, h_{n}^{p}, h1_{n}^{p}, h2_{n}^{p} };\n%   @substitute!(%)( A?? = B?? -> A?? - B?? = 0 );\n%   # Raise indices with eta.\n%   # Some way to create substitution rules out of this.\n%   # so that we end up with { h0_{n}^{p} -> h_{n}^{p}, h1_{n}^{p} -> \n%   @coefficients(%){k};\n\n\n\n% \\begin{screen}{0}\n% {l, m, n, r, s, t, u, v, w}::Indices(vector, position=fixed).\n% R_{l m n s}::RiemannTensor.\n% R_{l m n s}::Depends(x).\n% h_{m n}::Symmetric.\n% g^{m n}::InverseMetric.\n% \\diff{#}::PartialDerivative.\n% \n% 4 R_{l m n s} R^{l m n s};\n% @rewrite_indices!(%){ R_{m n r s} }{ g^{m n} };\n% \n% @substitute!(%)( R_{l m n s} -> \n%           @asym[ \\diff{ h_{l s} }_{m n} - \\diff{ h_{m s} }_{l n}]{_n, _s} );\n% \n% @distribute!(%):\n% @canonicalise!(%):\n% @collect_terms!(%);\n% \\end{screen}\n% \n% \n% \n% \\subsection{Super-QED in two-component language}\n% \n% This example follows the example in appendix C of~\\cite{Lucic:1994nc},\n% see also \\cite{Ichinose:2006pc}.\n% \n% \\begin{screen}{0}\n% {\\alpha, \\gamma, \\delta, \\beta                        }::Indices(spinor).\n% {\\dot{\\delta}, \\dot{\\gamma}, \\dot{\\alpha}, \\dot{\\beta}}::Indices(dottedspinor).\n% {\\theta^{\\alpha}, \\psi^{\\beta}}::SelfAntiCommuting.\n% {\\theta^{\\alpha}, \\psi^{\\beta}}::AntiCommuting.\n% \\epsilon_{\\alpha\\beta}::AntiSymmetric.\n% {\\theta^{\\alpha}, \\epsilon_{\\alpha\\beta}, \\psi^{\\alpha}}::SortOrder;\n% \n% \\theta^{\\gamma} \\psi^{\\beta} \\epsilon_{\\delta\\gamma} \\theta^{\\delta};\n% @sort_product!(%);\n% @canonicalise!(%);\n% \n% {\\delta, \\gamma, \\alpha, \\beta}::SelfAntiCommuting.\n% \n% {m,n,p}::Indices(flat).\n% \n% D( \\theta^\\delta \\theta_\\delta F )_\\gamma;\n% @substitute!(%)( D( A?? )_{\\gamma} -> \\diff{ A?? }_{\\gamma} \n%     + i \\bar{\\theta}^{\\dot{\\alpha}} \\diff{ A?? }_{m} \\sigma^{m}_{\\gamma \\dot{\\alpha}} );\n% \n% @prodrule!(%);\n% @substitute!(%)( \\diff{\\theta^\\alpha}_{\\beta} = \\delta^{\\alpha}_{\\beta} );\n% @substitute!(%)( \\diff{\\theta^\\alpha}_{m}     = 0 );\n% \\end{screen}\n% \n% \n% \\subsection{Eleven-dimensional supergravity}\n% \n% The eleven-dimensional supergravity action was first worked out\n% by~\\dcite{crem1}. We would like to derive their form of the action by\n% constructing the most general supersymmetric action at two-derivative\n% level. \n% \n% The key new ingredient in this example is the use of the\n% \\subscommand{@canonicalise} algorithm.\n% \n\n\\vfill\\eject\n\n% \\subsection{Frequently asked questions}\n% \n% \n% This section discusses issues which rely on information from various\n% parts of the manual and are therefore less easy to find.\n% \\begin{descerate}\n% \\item[``How do \\cdb's expression lists compare to notebooks?'']~\\\\ In\n% \\cdb calculations are organised in a different way from standard\n% notebook-based computer algebra systems. The main feature is that\n% there is a more natural way of combining, into a group, all steps that\n% lead to the derivation of a certain result. In \\cdb, this is done by\n% having each expression carry with it a history of manipulations that\n% led to it. This structure mimicks more closely what one is used to do\n% when one manipulates expressions by hand: one takes a given expression\n% as input, and applies successive algorithms to it (using externally\n% derived other expressions) until a final form has been arrived at.\n% \n% Compare the following two common constructions:\\\\[-2ex]\n% \\begin{center}\n% \\begin{minipage}{.4\\textwidth}\n% \\begin{screen}{0}\n% expr:= (x+y)^2;\n% @expand(expr);\n% @factor(expr);\n% \\end{screen}\n% \\end{minipage}\n% \\begin{minipage}{.4\\textwidth}\n% \\begin{screen}{0}\n% expr:=(x+y)^2;\n% expr:=expand(expr);\n% expr:=factor(expr);\n% \\end{screen}\n% \\end{minipage}\n% \\end{center}\n% \\Cdb's form (on the left) more logically groups the manipulations of a\n% single expression.  A different way to understand the organisation is\n% to think of each expression (together with its history) as a\n% mini-notebook. Within each such mini-notebook you do calculations just\n% like in Maple or Mathematica. The starting input of each mini-notebook\n% can be a newly entered expression or something copied from the result\n% of a previously evaluated mini-notebook.\n% \\item[``How do I speed up large calculations?'']~\\\\ Turn off the\n% history. By default, a history is kept of all expressions, and the\n% {\\tt @pop} command can be used to access previous forms of an\n% expression. When a calculation contains large expressions and many\n% algorithms acting on them, this history quickly consumes a lot of\n% memory. Use the setting {\\tt ::KeepHistory(false)} to turn this off\n% altogether (see section~\\ref{s:builtin} for details).  Also, turn off\n% expression printing. By using the ``:'' delimiter instead of the ``;''\n% one, output is suppressed (see section~\\ref{s:input_format} for more\n% details). Not only does this make the output less messy, it also\n% speeds up the program.\n% \n% \\item[``Why did you not implement this in Mathematica?'']~\\\\\n% Many of the algorithms present in \\cdb could have been implemented in\n% an existing symbolic manipulator such as Mathematica. However, there\n% is a certain point beyond which the Mathematica code would become more\n% and more ugly and harder to maintain. Take for instance the example of\n% the rule {\\tt @eliminate\\_kr}. This one could be implemented as\n% \\begin{screen}{0}\n% eliminate_kr := { Delta[m_, m_] -> D }\n% \\end{screen}\n% But \\cdb does much more than this. It allows you to specify the\n% range of the indices (i.e.~the value of ``{\\tt D}'' above) and it also\n% does not require you to use {\\tt Delta} to represent the Kronecker\n% delta. So the appropriate rule is more like\n% \\begin{screen}{0}\n% eliminate_kr := { D_?deltaset[m_, m_] -> ... }\n% \\end{screen}\n% This becomes more and more complicated, and more importantly, diverges\n% more and more from an efficient and transparent rule-based system when\n% additional \\cdb features are implemented. At some point one reaches a\n% stage where a conventional programming language like \\Cpp shows its\n% advantages. \n% \n% \\item[``Why not a separate data and meta language?'']~\\\\ (The data\n% language is the language used to write the objects we want to\n% manipulate; the expression~\\verb|R_{m n p q}| is for instance part of\n% the data language. The meta language is the language which\n% describes what we want to do with these objects,\n% i.e.~\\verb|ricci_cycle|). In many cases, the input files would look\n% nicer if we would have a separate data and meta language. Compare\n% \\begin{center}\n% \\begin{minipage}{.4\\textwidth}\n% \\begin{screen}{0}\n% expr:= A+B;\n% @substitute!(expr)( B -> C );\n% \\end{screen}\n% \\end{minipage}\n% \\begin{minipage}{.4\\textwidth}\n% \\begin{screen}{0}\n% expr:= A+B;\n% substitute B -> C into expr;\n% \\end{screen}\n% \\end{minipage}\n% \\end{center}\n% However, the capability to pass any command or series of commands as\n% an argument to another command has great advantages (in fact, this is\n% one of the strengths of e.g.~LISP). Note that because \\cdb does not do\n% automatic substitution of expressions, you can write both \\verb|expr|\n% and \\verb|@(expr)| and these mean something different. This is not quite\n% possible in other systems which have the same data and meta\n% language. Thinking in terms of pointers (and pointers to algorithm\n% nodes) is very useful in this respect.\n% \\end{descerate}\n% \n% \n% \n% \\vfill\\eject\n\n\\section{Graphical user interface}\n\\subsection{General information}\n\nThe graphical user interface is called {\\tt\n  xcadabra}. \n\nContext-sensitive help is available: if you put your\ncursor on a command or property name and press F1 or the help button,\nyou will get a help screen (which is essentially the corresponding\nsection in this manual).\n\n\\subsection{Cell types}\n\nThere are \\emph{two} input cell types and \\emph{two} output cell\ntypes. Normal input cells contain \\cdb input. \\TeX{} input cells\ncontain comments which you can add to the notebook but which will not\nbe sent to \\cdb. Output cells can be either verbatim output, such as\nstatus messages, or \\TeX{} output of expressions. Output cells are\nassociated to input cells, so if you delete an input cell all the\nassociated output cells will be removed too.\n\nIn the current version there is no visual separation between\ncells. When you start a new blank notebook, your cursor is in the\nfirst input cell. After entering an expression there and pressing {\\tt\n  shift-enter}, this input cell will be evaluated and all output will\nbe placed below it in the first output cell. In addition, a new input\ncell will be created below the output cell.\n\nThe ``edit'' menu can be used to add input cells or delete them, and\nalso shows keyboard shortcuts.\n\n\\subsection{Editing, loading, saving, printing, exporting}\n\n% Use some screenshots to illustrate this.\nThe file format used by the front-end is a \\LaTeX{} compatible\nfile. If necessary, it can be edited by hand using a text editor.\n\nAs the file format which the front-end uses to save notebooks is a\n\\LaTeX{} compatible file, it is simple to print a notebook: simply\nsave it and run it through \\LaTeX{} as usual. You will need two\nspecial-purpose packages, {\\tt breqn} (which is separately packaged\nand also available from the AMS) and {\\tt tableaux} (which is included\nwith the \\cdb distribution). \n\nNotebooks can be exported to a normal \\cdb text input file. This\nresults in a file which contains only the input cells of the\nnotebook. Such a file can be fed into the command line version of \\cdb\nby using\n\\begin{screen}{1}\ncadabra --input [filename]\n\\end{screen}\n\nThe default extension for cadabra notebooks is {\\tt\n  .cnb}. \\index{.cnb} For cadabra input files (for the command line\nversion of \\cdb) it is {\\tt .cdb}.\\index{.cdb}\n\n\\subsection{Evaluating cells}\n\nIn order to evaluate cells, press {\\tt shift-enter} in an input\ncell. This will send the input to the kernel and display any results\nor informal messages below the input cell. \n\n\n\n\\subsection{Algorithm and property auto-completion}\n\nThe GUI has shell-like automatic completion of algorithm and property\nnames. If you type only part of an algorithm or property, and\nsubsequently press the \\verb|TAB| key, the name will be completed to\nin maximally unambiguous way. For instance, by typing \\verb|::Com| and\nhitting the \\verb|TAB| key, the input will be completed to\n\\verb|::Commuting|. By adding \\verb|AsP| and hitting TAB again, this\ngets completed to \\verb|::CommutingAsProduct|.\n\n\\subsection{Cutting and pasting}\n\nYou can select output cells and paste them back into input cells or\ninto some other application. The program offers two formats for\npasting, a \\LaTeX{} one which is useful to paste into a paper, and a\n\\cdb one which represents the way in which the expression can be\npasted back into the program. \n\nIn most cases, the format will be selected correctly\nautomatically. Under Emacs, a middle-mouse paste will paste the\n\\LaTeX{} version. You can paste the internal \\cdb format by adding the\nfollowing to your \\verb|.emacs| file:\n\\begin{screen}{0}\n(defun pastecdb ()\n   (interactive)\n   (insert (x-get-selection-internal 'PRIMARY 'cadabra)))\n\n(global-set-key (kbd \"C-x p\") 'pastecdb)\n\\end{screen}\nThis will make the combination ``Ctrl-x p'' insert the current\nselection in \\cdb internal format.\n\nFor more advanced users: the list of formats can be inspected using\n\\begin{screen}{1}\n(x-get-selection-internal 'PRIMARY 'TARGETS)\n[TIMESTAMP TARGETS MULTIPLE cadabra UTF8_STRING TEXT]\n\\end{screen}\nIf e.g.~an output cell with the content~\\verb|1/2 A_{m}^{n}| is\nselected, the two different paste formats can be obtained by\nevaluating the following two LISP expressions in a scratch buffer,\n\\begin{screen}{1}\n(x-get-selection-internal 'PRIMARY 'cadabra)\n#(\"1/2 A_{m}^{n};\" 0 14 (foreign-selection STRING))\n\\end{screen}\n\\begin{screen}{1}\n(x-get-selection-internal 'PRIMARY 'TEXT)\n#(\"1 := \\frac{1}{2}\\, A_{m}\\,^{n};\" 0 31 (foreign-selection COMPOUND_TEXT))\n\\end{screen}\nNote that the TEXT format contains markup such as spacing commands\nwhich make it more useful for papers. This is the default format when\nthe middle mouse button is pressed.\n\n\n\\vfill\\eject\n\\section{Reference guide}\n\n\\subsection{Basics about the input format}\n\n\\label{s:input_format}\nThe input format of \\cdb is closely related to the notation used by\n\\TeX{} to denote tensorial expressions. That is, one can use not only\nbracketed notation to denote child objects, like in \n\\begin{screen}{0}\nobject[child,child]\n\\end{screen}\nbut also the usual sub- and superscript notation like\n\\begin{screen}{0}\nobject^{child child}_{child}\n\\end{screen}\nOne can use backslashes in the names of objects as well, just as in\n\\TeX{}. All of the symbols that one enters this way are considered\n``passive'', that is, they will go into the expression tree just like\none has entered them. \n\n``Active nodes'', on the other hand, are symbols pre-fixed with a\n``@'' symbol. These are nodes which lead to an algorithm being applied\nto their children; they will thus not end up in the actual tree stored\nin memory, but instead get replaced with the output that their\nalgorithm produces (if any).  Finally, every non-empty expression that\none enters will labelled by a number. Additionally, one can give an\nexpression a label by entering it as ``\\mbox{{\\tt\nlabel-text:=~expression;}}''.  One can use either the expression\nnumber or the label to refer to an expression.\n\nNames of objects can contain any printable character, except for\nbrackets, sub- and super-script symbols and backslash characters (the\nlatter can only occur at the beginning of a name). The sole exception\nto this rule is the names of active nodes: these names \\emph{can}\ncontain underscores to separate words. The program can also deal with\n``accents'' added to symbol names, like\n\\begin{screen}{0}\n\\hat{A}\n\\bar{B}\n\\prime{Q}\n\\end{screen}\nThe precise way in which this works is explained in section~\\ref{s:accents}.\n\nInput lines always have to be terminated with either a ``;'', a ``:''\nor a ``.''. The first two of these delimiting symbols act in the same\nway as in Maple: the second form suppresses the output of the entered\nexpression (see section~\\ref{s:inputoutput} for additional information\non how to redirect output to files). The last delimiter has the effect\nof evaluating the resulting expression, and immediately discarding it,\nalso disabling printing.  Long expressions can, because of these\ndelimiters, be spread over many subsequent input lines. Any line\nstarting with a ``\\#'' sign is considered to be a comment (even when\nit appears within a multi-line expression). Comments are always\nignored completely (they do not end up in the expression\ntree).\\index{comments}\n\nAll internal storage is in prefix notation, but a converter is applied\nto the input which transforms normal infix notation for products and\nsums to prefix notation. \n\n%Objects do not have to be declared before they can be used, although\n%some algorithmic modules may not work in this case. See\n%section~\\ref{s:objprop} for more details.\n\n% TODO: - dX for differentials perhaps?\n%       - dX.Psi for inner products? (already implemented)\n\n\\subsection{Active nodes or ``commands''}\n\n\\label{s:active_nodes}\nActive nodes are nodes which lead to immediate evaluation after \nthe input has been entered; these could thus be called ``commands''.\nCommands always start with a ``@'' symbol, to distinguish them\nfrom normal, unevaluated input. Used in the standard ``notebook'' way, active nodes\nact on their first argument and get replaced with the result that they\ncompute. This form uses square brackets to denote the argument on\nwhich to act:\n\\begin{screen}{0}\n@command[expression]{arg1}{arg2}...{argn}\n\\end{screen}\nIf you want to re-use an existing expression as the argument, this can\nbe cloned by using the ``@'' operator itself:\n\\begin{screen}{0}\n@[equation number or label]\n\\end{screen}\nor (for convenience, as a single exception to the square bracket rule)\n\\begin{screen}{0}\n@(equation number or label)\n\\end{screen}\nboth evaluate to a copy of the expression to which they refer (one can\nuse the ``\\%'' character to denote the number of the last-used\nexpression). Note that all of these forms create a \\emph{new}\nexpression. One is advised \\emph{not} to refer to equation numbers\nusing this command, as this makes expressions tied together in a\nrather fragile way.\n\nAlgorithms can also be made to act on existing expressions such as to\nmodify the expression history (i.e.~in the language of the previous\nsection, to stay within a ``mini-notebook''). This is done by using\nround brackets instead of square ones:\n\\begin{screen}{0}\n@command(expression number or label){arg1}{arg2}...{argn} \n\\end{screen}\nHere it is no longer problematic to refer to equation numbers, as the\nresult of this command will appear in the history list of the\nindicated expression (and is therefore not tied to the particular\nnumber of the expression). \n% Finally, there is a form which acts on\n% ``marked'' expressions, which will be discussed later. This form does\n% not have any reference to an object on which to act, since there is\n% only one ``marker''; it thus looks like\n% \\begin{screen}{0}\n% @command{arg1}{arg2}...{argn}\n% \\end{screen}\n% The way in which (parts of) expressions get marked depends on the\n% particular user interface; more information can be found in \n% section~\\ref{s:marks}.\n\nAll of these commands act on the top of the argument subtree. You can\nmake them act subsequently on all nodes to which they apply by\npostfixing the name with an exclamation mark, as in\n\\begin{screen}{0}\n@command![expression]{arg1}{arg2}...{argn}\n\\end{screen}\nThis will search the tree in pre-order style, applying the algorithm\non every node to which the algorithm applies. \n\nIf you want an algorithm to act until the expression no longer\nchanges, use a double exclamation mark. Compare the single-exclamation\nmark version,\n\\begin{screen}{1,2}\nA_{m} B_{m} A_{n} B_{n};\n@substitute!(%)( A_{m} B_{n} -> Q);\nQ A_{n} B_{n};\n\\end{screen}\nwith the double-exclamation mark one,\n\\begin{screen}{1,2}\nA_{m} B_{m} A_{n} B_{n};\n@substitute!!(%)( A_{m} B_{n} -> Q );\nQ Q;\n\\end{screen}\nBe careful with this functionality, as there is currently no safeguard\nin case the expression keeps changing forever.\n\nInstead of acting only at the top of the argument subtree, or acting\non all nodes individually, it is also possible to act only a specific\nlevel of the expression. The notation for this is an exclamation mark\nwith an extra number attached to it, which indicates the level\n(starting at 1 for the highest level),\n\\begin{screen}{0}\n@command!level(expression number of label){arg1}{arg2}...{argn}\n\\end{screen}\nNote that \\verb|\\sum| and \\verb|\\prod| nodes in the expression tree\nalso count as a level.\n\n\n\\subsection{Object properties and declaration}\n\\label{s:objprop}\n\nSymbols in \\cdb have no a-priori ``meaning''. If you write\n\\verb|\\Gamma|, the program will not know that it is supposed to be,\nfor instance, a Clifford algebra generator.  You will have to declare\nthe properties of symbols, i.e.~you have to tell \\cdb explicitly that\nif you write \\verb|\\Gamma|, you actually mean a Clifford algebra\ngenerator. This indirect way of attaching a meaning to a symbol has\nthe advantage that you can use whatever notation you like; if you\nprefer to write \\verb|\\gamma|, or perhaps even \\verb|\\rho| if your\npaper uses that, then this is perfectly possible (object properties\nare a bit like ``attributes'' in {\\tt Mathematica} or ``domains'' in\n{\\tt Axiom} and {\\tt MuPAD}).\n\nProperties are all written using capitals to separate words, as in\n{\\tt AntiSymmetric}. This makes it easier to distinguish them from\ncommands. Properties of objects are declared by using the ``::''\ncharacters.  This can be done ``at first use'', i.e.~by just adding\nthe property to the object when it first appears in the input. As an\nexample, one can write\n\\begin{screen}{1}\nF_{m n p}::AntiSymmetric;\n\\end{screen}\nThis declares the object to be anti-symmetric in its indices and at\nthe same time creates a new expression with this object. The property\ninformation is stored separately, so that further appearances of the\n``\\verb|F_{m n p}|'' object will automatically share this property. It\nis of course also possible to keep object property declarations\nseparated (for instance at the top of an input file). This is done\nas follows:\n\\begin{screen}{1,2}\nF_{m n p}::AntiSymmetric.\nF_{m n p};\n\\end{screen}\nA list of all properties is available in the graphical interface\nthrough the Help menu, and can also be obtained using the\n\\subscommand{properties} command.\n\nNote that properties are attached to patterns. Therefore, you can have\n\\begin{screen}{1,2}\nR::RicciScalar.\nR_{m n p q}::RiemannTensor.\n\\end{screen}\nat the same time. The program will not warn you if you use\nincompatible properties, so if you make a declaration like above and\nthen later on do\n\\begin{screen}{1}\nR::Coordinate.\n\\end{screen}\nthis may lead to weird results.\n\nThe fact that objects are attached to patterns also means that you can\nuse something like wildcards. In the following declaration,\n\\begin{screen}{1}\n{ m#, n# }::Indices(vector).\n\\end{screen}\nthe entire infinite set of objects $m1, m2, m3, \\ldots$ and $n1, n2,\nn3, \\ldots$ are declared to be in the dummy index set\n``vector''.\\footnote{This way of declaring ranges of objects is\nsimilar to the \\index{autodeclare}``autodeclare'' declaration method\nof FORM~\\cite{Vermaseren:2000nd}.}\\index{autodeclare}\\index{\\#} Range\nwildcards can also be used to match one or more objects of a specific\ntype. In this case, they always start with a ``\\#'' sign, followed by\noptional additional information to specify the type of the object and\nthe number of them. The declaration\n\\begin{screen}{0}\n{m,n,p,q,r,s}::Indices(vector).\nA_{ #{m, 1..3} }::AntiSymmetric.\nB_{ #{m} }::Symmetric.\n\\end{screen}\nindicates that whenever the object \\verb|A| appears with one to three\nindices of the vector type, it is antisymmetric. If the index type\ndoes not match, or if there are zero or more than three indices, the\nproperty does not apply. Similarly, \\verb|B| is always symmetric when\nall of its indices are of the vector type.\\index{\\#}\\index{range wildcards} \n\nProperties can be assigned to an entire list of symbols with one\ncommand, namely by attaching the property to the list. For example,\n\\begin{screen}{1}\n{n, m, p, q}::Integer(1..d).\n\\end{screen}\nThis associates the property ``Integer'' to each and every symbol in\nthe list.  However, there is also a concept of ``list properties'',\nwhich are properties which are associated to the list as a\nwhole. Examples of list properties are ``AntiCommuting'' or\n``Indices''. See for a discussion of list properties\nsection~\\ref{s:list_properties}.\n\nObjects can have more than one property attached to them, and one\nshould therefore not confuse properties with the ``type'' of the\nobject. Consider for instance\n\\begin{screen}{1,2,3}\nx::Coordinate.\nW_{m n p q}::WeylTensor.\nW_{m n p q}::Depends(x).\n\\end{screen}\nThis attaches two completely independent properties to the pattern\n$W_{m n p q}$.\n\nIn the examples above, several properties had arguments\n(e.g. ``\\verb|vector|'' or ``\\verb|1..d|''). The general form of these\narguments is a set of key-value pairs, as in\n\\begin{screen}{1}\nT_{m n p q}::TableauSymmetry(shape={2,1}, indices={0,2,1}).\n\\end{screen}\nIn the simple cases discussed so far, the key and the equal sign was\nsuppressed. This is allowed because one of the keys plays the role of\nthe default key. Therefore, the following two are equivalent,\n\\begin{screen}{1,2}\n{ m, n }::Integer(range=0..d).\n{ m, n }::Integer(0..d).\n\\end{screen}\nSee the detailed documentation of the individual properties for\nallowed keys and the one which is taken as the default.\n\nFinally, there is a concept of ``inherited properties''. Consider\ne.g.~a sum of spinors, declared as\\index{properties!inheritance}\n\\begin{screen}{1,2}\n{\\psi_1, \\psi_2, \\psi_3}::Spinor.\n\\psi_1 + \\psi_2 + \\psi_33;\n\\end{screen}\nHere the sum has inherited the property ``Spinor'', even though it does\nnot have normal or intrinsic property of this type. Properties can\nalso inherit from each other, e.g.\n\\begin{screen}{1,2,3}\n\\Gamma_{#}::GammaMatrix.\n\\Gamma_{p o i u y};\n@indexsort!(%);\n\\end{screen}\nThe \\subsprop{GammaMatrix} property inherits from\n\\subsprop{AntiSymmetric} property, and therefore the {\\tt\n  $\\backslash$Gamma} object is automatically anti-symmetric in its\nindices. \n\nA list of all properties known to \\cdb can be obtained by using the\n\\subscommand{proplist} command.\\index{properties!list of all}\n\n% @exchange, which exchanges two terms in a product, should know\n% something about the commutator rule for two objects. But this is a\n% property of \\prod? NO, that leads to putting many rules on prod,\n% exactly the kind of problem Mathematica is also facing. \n\n% Refer to DeWitt's compact index notation; indices can take values in\n% the integers or in any continuous set.\n\n\n\n\\subsection{List properties and symbol groups}\n\\label{s:list_properties}\n\nSome properties are not naturally associated to a single symbol or\nobject, but have to do with collections of them. A simple example of\nsuch a property is \\subsprop{AntiCommuting}. Although it sometimes\nmakes sense to say that ``$\\psi_m$ is anticommuting'' (meaning that\n$\\psi_m \\psi_n = - \\psi_n \\psi_m$), it happens just as often that you\nwant to say ``$\\psi$ and $\\chi$ anticommute'' (meaning that $\\psi\\chi\n= - \\chi\\psi$). The latter property is clearly relating two different\nobjects. \n\nAnother example is dummy indices. While it may make sense to say that\n``$m$ is a dummy index'', this does not allow the program to\nsubstitute $m$ with another index when a clash of dummy index names\noccurs (e.g.~upon substitution of one expression into another). More\nuseful is to say that ``$m$, $n$, and $p$ are dummy indices of the\nsame type'', so that the program can relabel a pair of $m$'s into a\npair of $p$'s when necessary.\n\nIn \\cdb such properties are called ``list properties''. You can\nassociate a list property to a list of symbols by simply writing,\ne.g. for the first example above,\n\\begin{screen}{1}\n{ \\psi, \\chi }::AntiCommuting.\n\\end{screen}\nNote that, as described in section~\\ref{s:objprop}, you can also\nattach normal properties to multiple symbols in one go using this\nnotation. The program will figure out automatically whether you want\nto associate a normal property or a list property to the symbols in\nthe list.\n\nLists are ordered, although the ordering does not necessarily mean\nanything for all list properties (it is relevant for\ne.g.~\\subsprop{SortOrder} but irrelevant for e.g.~\\subsprop{AntiCommuting}).\n\n% When you `overwrite' a list property declaration, various things can\n% happen depending on the form of the list and the property used. Here\n% are some examples to illustrate this. In the first example, we\n% re-declare part of the objects in a previously declared set,\n% \\begin{screen}{1,2,3}\n% {a,b,c,d,e}::Indices(vector).\n% {a,b,c}::Indices(spinor).\n% \\end{screen}\n% This makes $a,b,c$ spinor indices and keeps $d,e$ as vector indices. A\n% similar example is\n% \\begin{screen}{1,2,3}\n% {a,b,c}::Indices(vector).\n% {a,b,c,d,e,f}::Indices(spinor).\n% \\end{screen}\n% in which all six indices become spinor indices.  The next example adds\n% elements to a property list,\n% \\begin{screen}{1,2}\n% {a,b,c}::Indices(vector).\n% {d,e}::Indices(vector).\n% \\end{screen}\n% All indices are now members of a common list of vector\n% indices. Finally, there are cases in which properties are declared\n% with additional arguments,\n% \\begin{screen}{1,2}\n% {a,b,c,d,e}::Indices(vector, position=free).\n% {a,b,c}::Indices(vector, position=fixed).\n% \\end{screen}\n% In this case the first line declares a set of indices with name\n% `vector' with free index positions, while the second line\n% re-declares this set to have fixed index positions. The result is that\n% $a,b,c$ are now members of this set, while the property for $d,e$ is\n% removed altogether (as it is not possible to have more than one set of\n% indices with the `vector' label).\n\n\n\\subsection{Indices, dummy indices and automatic index renaming}\n\\label{s:automaticdummies}\n\nIn \\cdb, all objects which occur as subscripts or superscripts\nare considered to be ``indices''. The names of indices are understood\nto be irrelevant when they occur in a pair, and automatic relabelling\nwill take place whenever necessary in order to avoid index clashes. \n\n\\Cdb knows about the differences between free and dummy indices. It \nchecks the input for consistency and displays a warning when the\nindex structure does not make sense. Thus, the input\n\\begin{screen}{1}\nA_{m n} + B_{m} = 0;\n\\end{screen}\nresults in an error message. \n\nThe location of indices is, by default, not considered to be\nrelevant. That is, you can write\n\\begin{screen}{1,2}\nA_{m} + A^{m};\nA_{m} B_{m};\n\\end{screen}\nas input and these are considered to be consistent expressions. If,\nhowever, the position of an index means something (like in general\nrelativity, where index lowering and raising implies contraction with\na metric), then you can declare index positions to be ``fixed''. This\nis done using\n\\begin{screen}{1}\n{m, n, p}::Indices(position=fixed).\n\\end{screen}\n\nWhen substituting an expression into another one, dummy indices will\nautomatically be relabelled when necessary. To see this in action,\nconsider the following example:\n\\begin{screen}{1,2,5}\n{p,q}::Indices(vector).\nF_{m n} F^{m n};\nF_{m n} F^{m n}\n\nG_{m n} @(1);\nG_{m n} F_{p q} F^{p q}\n\\end{screen}\nThe $m$ and $n$ indices have automatically been converted to $p$ and\n$q$ in order to avoid a conflict with the free indices on the $G_{m\n  n}$ object.\n\nRefer to section~\\ref{s:dummies} for commands that deal with dummy\nindices.\n\n%\\bfcomment{KP}{Explain the canonicalisation algorithm and compare with\n%other approaches in the literature}\n\n\\begin{table}[t]\n\\begin{center}\n\\begin{tabular}{rlll}\nargument    & whitespace  & dummy       & example \\\\[1ex]\n\\verb|{}|  & product      &            & \\verb|\\frac{a b}{c} = \\frac{a * b}{c}|\\\\ \n\\verb|()|  & product      &            & \\verb|sin(a b) = sin(a * b)|\\\\\n\\verb|_{}| & separator    & yes        & \\verb|M_{a b}  = M_{a}_{b}|\\\\\n\\verb|^{}| & separator    & yes        & \\verb|M^{a b}  = M^{a}^{b}|\\\\\n\\verb|_()| & separator    &            & \\verb|M_(a b)  = M_(a)_(b)|\\\\\n\\verb|^()| & separator    &            & \\verb|M^(a b)  = M^(a)^(b)|\\\\\n\\verb|[]|  & product      &            & \\verb|[a b, c] = [a * b, c]|\n\\end{tabular}\n\\caption{The implicit meaning of objects and whitespace inside the various\n  types of brackets.}\n\\label{t:argtypes}\n\\end{center}\n\\end{table}\n\n\n\\subsection{Exponents, indices and labels}\n\nExponents, indices and labels are traditionally all placed using\nsuper- or subscript notation, making these slightly ambiguous for a\ncomputer algebra system. Since this situation can become quite complex\n(how do you represent the third power of the first element of a\nvector?) \\cdb requires all powers to be entered with a double-star\n``$**$'' notation:\\footnote{Solutions involving the declaration of\n  which indices are exponents and which are indices have been\n  considered, but rejected in favour of the explicit ``$**$''\n  notation. Cases like ``the square of the second\n  component of a vector'' quickly become ambiguous even\n  with rather complicated property declarations, while the ``$**$''\n  notation remains transparent.}\n\\begin{screen}{1,2}\na**2;\na**(2 + 3b);\n\\end{screen}\nIn addition, all sub- or superscripts with \\emph{curly} braces\nindicate indices, to which the summation convention applies. In\nparticular, there are not allowed to be more than two identical\nindices in a single product. The summation convention does not apply\nto arguments with any other bracket types. In particular, sub- or\nsuperscripts with \\emph{square} or \\emph{pointy} brackets have (as of\nyet) no fixed meaning.\n\n\n\\subsection{Spacing and brackets}\n\n\\Cdb is reasonably flexible as far as spacing and brackets are\nconcerned, but the fact that objects do not have to be declared before\nthey can be used means that spaces have to be introduced in some cases\nto avoid ambiguity. As a general rule, all terms in a product have to\nbe separated by at least one whitespace character. Thus,\n\\begin{quote}\n\\begin{tabular}{ll}\n{\\tt A(B+C)}   & incorrect, (interpreted as {\\tt A} with argument {\\tt\n  B+C}), \\\\[1ex]\n{\\tt AB}       & incorrect, (interpreted as one object, not two) \\\\[1ex]\n{\\tt A (B+C)}  & correct, \\\\[1ex]\n{\\tt A*(B+C)}  & correct.\n\\end{tabular}\n\\end{quote}\nIf a whitespace character is absent, all brackets are interpreted as\nenclosing \\emph{argument} groups. Products of variables (e.g.~$AB$)\nhave to be separated by a space, otherwise the input will be read as\nthe name of a single variable.  However, spaces will automatically be\ninserted after numbers, between a closing bracket and a name or\nnumber, and between two names if the second name starts with a\nbackslash. The following expressions are therefore interpreted as one\nwould expect:\n\\begin{quote}\n\\begin{tabular}{ll}\n{\\tt 3A}     & interpreted as {\\tt 3*A}\\\\[1ex]\n{\\tt (A+B)C} & interpreted as {\\tt (A+B)*C}\\\\[1ex]\n{\\tt (A+B)3} & interpreted as {\\tt (A+B)*3}\\\\[1ex]\n{\\tt A$\\backslash$Gamma}& interpreted as {\\tt A*$\\Gamma$}\\\\[1ex]\n\\end{tabular}\n\\end{quote}\nThis conversion is done by the preprocessor. Finally, note that\nbrackets in the input \\emph{must} be balanced (a decision made to\nsimplify the parser; it means that \\cdb uses a different way to\nindicate groups of symmetric or anti-symmetric indices than one often\nencounters in the literature; see section~\\ref{s:tensor}).\n\n\\subsection{Implicit versus explicit indices}\n\nWhen writing expressions which involves vectors, spinors and matrices,\none often employs an implicit notation in which some or all of the\nindices are suppressed. Examples are\n\\begin{equation}\na = M b\\,,\\qquad\n\\bar{\\psi}\\gamma^{m}\\chi\\,,\n\\end{equation}\nwhere~$a$ and~$b$ are vectors, $\\psi$ and~$\\chi$ are spinors and~$M$\nand~$\\gamma^{m}$ are matrices. Clearly, the computer cannot know this\nwithout some further information. In \\cdb objects can carry implicit\nindices, through the \\subsprop{ImplicitIndex} property. There are\nderived forms of this, e.g.~\\subsprop{Matrix} and~\\subsprop{Spinor}, \n\\begin{screen}{1,2,3,4}\n{a,b}::ImplicitIndex;\nM::Matrix.\na = M b;\n@sort_product!(%);\n@sort_product: not applicable.\n\\end{screen}\nIf you had not made the property assignment in the first two lines,\nthe \\subscommand{sort\\_product} would have incorrectly swapped the matrix\nand vector, leading to a meaningless expression.\n\nIf you have more than one set of implicit indices, you can label them\njust like you can label explicit indices,\n\\begin{screen}{1,2,3,4,5}\n{a,b}::ImplicitIndex(type1);\n{c,d}::ImplicitIndex(type2);\nM::Matrix(type1).\na = M d c b;\n@sort_product!(%);\na = M b d c;\n\\end{screen}\n% It is also possible to declare that an object commutes with another\n% one even though they both carry implicit indices (e.g.~to indicate\n% that two matrices are commuting). \n% \n\n\\subsection{Index brackets}\n\nIndices can be associated to tensors, as in~$T_{\\mu\\nu}$, but it often\nalso happens that we want to associate indices to a sum or product of\ntensors, without writing all indices out explicitly. Examples are\n\\begin{equation}\n(A + B + C)_{\\alpha\\beta}\\,,\\quad\\text{or}\\quad\n(\\psi \\Gamma_{m n} \\Gamma_{p})_{\\beta}\\,.\n\\end{equation}\nHere the objects $A$, $B$, $C$ and~$\\Gamma$ are matrices, while~$\\psi$\nis a vector. Their explicit components are labelled with~$\\alpha$\nand~$\\beta$ indices, but the notation above keeps most of these vector\nindices implicit.\n\n\\Cdb can deal with such expressions through a construction which is\ncalled the ``indexbracket''. It is possible to convert from one form\nto the other by using the \\subscommand{combine} and\n\\subscommand{expand} algorithms. Combining terms goes like this,\n\\begin{screen}{1,2}\n(\\Gamma_r)_{\\alpha\\beta} (\\Gamma_{s t u})_{\\beta\\gamma}:\n@combine!(%);\n(\\Gamma_r \\Gamma_{s t u})_{\\alpha\\gamma};\n\\end{screen}\nor as in\n\\begin{screen}{1,2}\n(\\Gamma_r)_{\\alpha\\beta} Q_\\beta:\n@combine!(%);\n(\\Gamma_r Q)_{\\alpha};\n\\end{screen}\nIf the index bracket has only one index, either the first or the last\nargument should be a matrix, but not both:\n\\begin{screen}{1,2,4}\nA::Matrix.\n{m,n,p}::Indices(vector).\n(A B)_{m};\n@expand(%);\nA_{m n} B_{n};\n\\end{screen}\nIf the index bracket has two indices, all arguments should be matrices,\n\\begin{screen}{1,2,3}\n{A,B}::Matrix.\n{m,n,p}::Indices(vector).\n(A B)_{m n};\n@expand(%);\nA_{m p} B_{p n};\n\\end{screen}\nIf there are more arguments inside the bracket, these of course all\nneed to be matrices (and are assumed to be so by default).\n\n\n\\subsection{Derivatives and implicit dependence on coordinates}\n\\label{s:derivatives}\n\nThere is no fixed notation for derivatives; as with all other objects\nyou have to declare derivatives by associating a property to them, in\nthis case the \\subsprop{Derivative} property. \n\\begin{screen}{1}\n\\nabla{#}::Derivative.\n\\end{screen}\nDerivative objects can be used in various ways. You can just write the\nderivative symbol, as in\n\\begin{screen}{1}\n\\nabla{ A_{\\mu} };\n\\end{screen}\n(a notation used e.g.~in the tutorial example in\nsection~\\ref{s:tut_worldsheet}). Or you can write the coordinate with\nrespect to which the derivative is taken,\n\\begin{screen}{1,2,3}\ns::Coordinate.\nA_{\\mu}::Depends(s).\n\\nabla_{s}{ A_{\\mu} };\n\\end{screen}\nFinally, you can use an index as the subscript argument, as in\n\\begin{screen}{1,2}\n{ \\mu, \\nu }::Indices(vector).\n\\nabla_{\\nu}{ A_{\\mu} };\n\\end{screen}\n(in which case the first line is, for the purpose of using the\nderivative operator, actually unnecessary). \n\nThe main point of associating the \\subsprop{Derivative} property to an\nobject is to make the object obey the Leibnitz or product rule, as\nillustrated by the following example,\n\\begin{screen}{1,2,3}\n\\nabla{#}::Derivative.\n\\nabla{ A_{\\mu} * B_{\\nu} };\n@prodrule!(%);\n\\nabla{A_{\\mu}} B_{\\nu} + A_{\\mu} \\nabla{B_{\\nu}};\n\\end{screen}\nThis behaviour is a consequence of the fact that \\subsprop{Derivative}\nderives from \\subsprop{Distributable}. Note that the\n\\subsprop{Derivative} property does not automatically give you\ncommuting derivatives, so that you can e.g.~use it to write covariant\nderivatives. \n\nMore specific derivative types exist too. An example are partial\nderivatives, declared using the \\subsprop{PartialDerivative} property.\nPartial derivatives are commuting and therefore automatically\nsymmetric in their indices,\n\\begin{screen}{1,2,3,5,6}\n\\partial{#}::PartialDerivative.\n{a,b,m,n}::Indices(vector).\nC_{m n}::Symmetric.\n\nT^{b a} \\partial_{a b}( C_{m n} D_{n m} );\n@canonicalise!(%);\nT^{a b} \\partial_{a b}( C_{m n} D_{m n} );\n\\end{screen}\n\n\n\\subsection{Accents}\n\\label{s:accents}\n\nIt often occurs that you want to put a hat or tilde or some other\naccent on top of a symbol, as a means to indicate a slightly different\nobject. In most of these cases, the properties of the normal symbol\nand the accented symbol are identical. Such accents are declared using\nthe \\subsprop{Accent} property, as in\n\\begin{screen}{0}\n\\hat{#}::Accent.\n\\end{screen}\nThis automatically makes all symbols with hats inherit the properties\nof the unhatted symbols,\n\\begin{screen}{1,2,3,4,5}\n\\hat{#}::Accent.\n{\\psi, \\chi}::AntiCommuting.\n{\\psi, \\chi}::SortOrder.\n\\hat{\\chi} \\psi:\n@sort_product!(%);\n(-1) \\psi \\hat{\\chi};\n\\end{screen}\nIf you want to put an accent on an object with indices, wrap the\naccent around the entire object, do not leave the indices outside.\n\nNote that it is also possible to mark objects by attaching sub- or\nsuperscripted symbols to them, as in e.g.~$A^\\dagger$. This can be\ndone by declaring these symbols explicitly using the \\subsprop{Symbol}\nproperty,\n\\begin{screen}{1}\n\\dagger::Symbol.\n\\end{screen}\nIf you do not do this, \\texcommand{dagger} will be seen as an index\nand an error will be reported if it appears more than twice.\n\n\n\\subsection{Symbol ordering and commutation properties}\n\\label{s:symbol_ordering}\n\nA conventional way to sort factors in a product is to use\nlexographical ordering. However, this is almost never what one wants\nwhen transcribing a physics problem to the computer. Therefore, \\cdb\nallows you to specify the sort order of symbols yourself. This is done\nby associating the \\subsprop{SortOrder} list property to a list of\nsymbols, as in\n\\begin{screen}{1,2,3}\n{X,G,Y,A,B}::SortOrder.\nA*B*G*X*A*X:\n@sort_product(%);\nX*X*G*A*A*B;\n\\end{screen}\nMore complicated objects with indices are of course also allowed, such\nas in\n\\begin{screen}{1,2,3}\n{ W_{m n}, W_{m} }::SortOrder.\nW_{m n} W_{p} W_{q r} W_{s} W_{t}:\n@sort_product(%);\nW_{m n} * W_{q r} * W_{p} * W_{s} * W_{t};\n\\end{screen}\nFor the time being, it is not allowed to have more than one such set\ncontain the same symbol. Thus,\n\\begin{screen}{1,2}\n{X,G}::SortOrder.\n{X,A,B}::SortOrder.\n\\end{screen}\nis not allowed (and will, in fact, take $X$ out of the first list).\n%> A*B*G*X:\n%@sort_product(%);\n%X*A*B*G;\n%Beware that the program does not prevent you from constructing\n%mutually contradictory sort orders: when a product sort is performed\n%and two factors have to be compared, the program will simply look in\n%the lists until it finds one particular list which contains the two\n%factors. \n\nApart from the preferred sort order, there are more properties which\ninfluence the way in which products can be sorted. In particular, sort\norder is influenced by whether symbols commute or anti-commute with\neach other.  Physicists in general use a very implicit notation as far\nas commutativity of objects in a product is concerned. Consider for\ninstance a situation in which we deal with two operators $\\hat M$ and\n$\\hat N$, as well as some constants $q$ and $p$. These two expressions\nare equivalent:\n\\begin{equation}\n2q\\, \\hat M p \\hat N \\quad\\text{and}\\quad 2pq\\, \\hat M \\hat N \\,.\n\\end{equation}\nBut this is not obvious from the notation that has been used to\nindicate the product. In fact, the product symbol is usually left out\ncompletely.\n\nIn many other computer algebra systems, you have to introduce special\ntypes of ``non-commuting'' products (e.g.~the \\verb|&*| operator in\nMaple or the \\verb|**| operator in Mathematica). This can be rather\ncumbersome, for a variety of reasons. The main reason, however, is\nthat it does not match with what you do on paper. On paper, you never\nwrite special product symbols for objects which do not commute. You\njust string them together, and know from the properties of the symbols\nwhether objects can be moved through each other or not.\n\nIn order to make these sort of things possible in \\cdb, it is\nnecessary to declare ``sets'' of objects which mutually do not commute\n(i.e.~for which the order inside a product cannot be changed without\nconsequences) but which commute with objects of other sets. Many\ncomputer algebra systems only use one such set: objects are either\n``commuting'' or ``non-commuting''. This is often too restrictive. For\ninstance, when $\\Psi$ is a fermion and $\\Gamma$ denotes a Clifford\nalgebra element, a system with only one set of non-commuting objects\nis unable to see that\n\\begin{equation}\n\\bar\\Psi_a (\\Gamma_n\\Gamma_m)_{ab} \\Psi_b \\quad\\text{and}\\quad\n\\bar\\Psi_a \\Psi_b (\\Gamma_n\\Gamma_m)_{ab} \n\\end{equation}\nare equivalent. In \\cdb, one would simply put $\\Psi_{a}$ and\n$\\Gamma_{m}$ in two different sets, mutually commuting, but\nnon-commuting among themselves. To be precise, the example above is\nreproduced by\n\\begin{screen}{1,2,3,4,5}\n\\bar{#}::Accent.\n\\Psi_{a}::SelfNonCommuting.\n\\Gamma_{#}::GammaMatrix.\n\\bar{\\Psi_a} (\\Gamma_n \\Gamma_m)_{ab} \\Psi_b:\n@sort_product(%);\n\\bar{\\Psi_a} \\Psi_b (\\Gamma_n \\Gamma_m)_{ab};\n\\end{screen}\n(see section~\\ref{s:accents} for an explanation of the\n\\subsprop{Accent} property). \n\nCommutation properties always refer to components. If you associate an\n\\subsprop{ImplicitIndex} property to an object, then it will never\ncommute with itself or with any other such object. You can see this in\nthe example above, as the \\subscommand{sort\\_product} command kept the\norder of the two gamma matrices unchanged.\n\n%\\subsection{Component values and calculations}\n%\\label{s:component_values}\n%\n%(This section is preliminary and experimental.)\n\n% gammacomponents: { \\Gamma^{1}_{a b} = {{1,2,3},{1,2,4},..},\n%                    \\Gamma^{2}_{a b} = {{....} }\n%\n% \\bar{\\psi} \\Gamma^\\mu \\psi V_{\\mu}\n% @expand_index_bracket\n% @write_out!(%){ @(gammacomponents) }{ \\mu };\n\n% If you write out R_{m n p q} R_{m n p q} in components this leads\n% to d^4 terms. How can we reduce this so we do not double count?\n% The best way to minimise the number of terms is to assume that\n% we are, most of the time, contracting mostly-empty tensors.\n% (if you do not make that assumption then the computation will be\n% horrible anyway). \n%\n% R_{m n p q}               T_{m n p q}\n% {1,3,2,5}=exp1            {2,4,3,5}=exp2\n% {2,4,3,5}=exp3            {6,4,3,2}=exp3\n% ...\n%\n% determine the number of non-zero components for\n%   each tensor, taking into account Young projection.\n%   Use this to sort the loop order below (use tensor\n%   with lowest number of components in outer loop).\n% for(all non-zero components in tensor 1)\n%   for(all non-zero components in tensor 2)\n%     ...\n%       if(the index values match)\n%          multiply and store in sum.\n%\n% How do we instruct the program to compute components of\n% composite tensors?\n%\n% \\Gamma_{m n}^{p} = 1/2 g^{p q} (\\partial_{n}{g_{m q}} +\n%                                 \\partial_{m}{g_{n q}} -\n%                                 \\partial_{q}{g_{m n}}   );\n%\n% Here we need to associate coordinates to indices.\n% \n%  {t,r,phi,theta}::Coordinate(polar).\n%  {m,n,p,q,r}::Indices(vector, basis=polar).\n%  g_{m n}::Metric(polar).\n% \n% R_{m n p}^{q} = \\partial_{m}{\\Gamma\n\n\\subsection{Anti-commuting objects and derivatives}\n\nWe have discussed anti-commuting objects to some extend in the\nprevious section, but things become somewhat more hairy in combination\nwith derivatives. Hence the current section, in which we will look in\nmore detail at how to write properties which take care of\nanti-commuting derivatives (as they occur in e.g.~superspace field\ntheories).\n\nWe will use the \\subscommand{prodrule} command to show how the various\nproperty assignments work. \n\nThere are various ways in which you may want to write derivatives\nwhich are anti-commuting. One way is to use explicit indices, and\ndeclare them to be anti-commuting, as in\n\\begin{screen}{1,2,3,4}\n{\\alpha,\\beta,\\gamma}::Indices(spinor).\n{\\alpha,\\beta,\\gamma}::AntiCommuting.\nD{#}::Derivative.\nD_{\\alpha}{\\theta^\\beta \\theta^\\gamma};\nD_{\\alpha}{\\theta^{\\beta}} \\theta^{\\gamma} \n           - \\theta^{\\beta} D_{\\alpha}{\\theta^{\\gamma}};\n\\end{screen}\nNote the appearance of the minus sign for the second term. Writing\nthings in this way is the most straightforward way to handle\nanti-commuting derivatives, and only requires the assignment of the\n\\subsprop{AntiCommuting} property to the indices (second line above).\n\nHowever, one often deals with implicit indices when tackling problems\ninvolving anti-commuting variables. Here is an example to illustrate\nwhat is meant by this:\n\\begin{screen}{1,2,3}\ntest 19d does not do the right thing: it does not pick up a minus sign\nat the first step.\n\\end{screen}\n\n\\subsection{Input and output redirection}\n\\label{s:inputoutput}\n\nBy default, all generated output is displayed on the screen. As\nmentioned in section~\\ref{s:input_format}, the delimiter of a line\ndetermines whether output is suppressed or not. It is, however, also\npossible to write output to a file, by appending a file name to the\nline delimiter, as in\n\\begin{screen}{1}\na^2+b^2 = c^2; \"output_file\"\n\\end{screen}\n(note that there is no semi-colon following the file name).\nThis shows the filename ``output\\_file'' on the display, and writes \nto this file the expression\n\\begin{screen}{0}\n1:=  a^{2}+b^{2}=c^{2}\n\\end{screen}\nThis is exactly as it would have appeared on the display. If you need \na different kind of output, use the algorithms provided in the\n{\\tt output} module (see section~\\ref{s:output}).\n\nIt is also possible to read input from files instead of from the\nterminal: \n\\begin{screen}{1}\n< \"input_file\"\n\\end{screen}\nreads from the file ``input\\_file'' until the end or until a line\n\\verb|@end;| is found, whichever comes first. Input redirect can be\nnested. In case an error occurs, reading from the file is also aborted\nand input is taken from the terminal again.\n\n\\subsection{Default rules}\n\nBy default, \\cdb does very few things ``by itself'' with your\nexpressions. This goes as far as not collecting equal terms, so that\nyou can write\n\\begin{screen}{1}\nA + A;\n\\end{screen}\nand have this stored as a sum of two terms. However, you can add an\narbitrary number of default commands, which are run just after you\nhave entered an expression on the command line\n(\\subsprop{PreDefaultRules}) or just before the output is returned to\nyou (\\subsprop{PostDefaultRules}). So if you want terms to be\ncollected automatically, just enter\n\\begin{screen}{1}\n::PostDefaultRules( @@collect_terms!(%) ).\n\\end{screen}\nNote the double ``@@'' symbol, which prevents immediate execution of\nthe command. This post default rule will collect equal terms before\nthey ever make it to internal storage.\n\nMany more complicated things can be achieved with this feature. You\ncan, for instance, also use complicated substitution commands as\narguments to \\subsprop{PreDefaultRules} or\n\\subsprop{PostDefaultRules}. An example is\n\\begin{screen}{1,2,4}\n{m,n,p,q}::Indices(vector).\n::PreDefaultRules( @@substitute!(%)( A_{m n} -> B_{m q} B_{q n} ).\n\nA_{m n} A_{n m};\n\\end{screen}\nwhich immediately returns\n\\begin{screen}{0}\nB_{m q} B_{q n} B_{n p} B_{p m};\n\\end{screen}\nAs usual dummy indices have been relabelled appropriately.\n\n\n\\subsection{Patterns, conditionals and regular expressions}\n\nPatterns in \\cdb are quite a bit different from those in other\ncomputer algebra systems, because they are more tuned towards the\npattern matching of objects common in tensorial expressions, rather\nthan generic tree structures.\n\nName patterns are constructed by writing a single question mark behind\nthe name, as in\n\\begin{screen}{1}\n@substitute!(%)( A? + B? -> 0 );\n\\end{screen}\nwhich matches all sums with two terms, each of which is a single\nsymbol without indices or arguments. If you want to match instead any\nobject, with or without indices or arguments, use the double question\nmark instead. To see the difference more explicitly, compare the two\nsubstitute commands in the following example:\\index{?}\\index{??}\n\\begin{screen}{1,2,4}\nA_{m n} + B_{m n}:\n@substitute!(%)( A? + B? -> 0 );\nA_{m n} + B_{m n};\n@substitute!(%)( A?? + B?? -> 0 );\n0;\n\\end{screen}\nNote that it does not make sense to add arguments or indices to object\npatterns; a construction of the type ``\\verb|A??_{\\mu}(x)|'' is\nmeaningless and will be flagged as an error.\n\nThere is a special handling of objects which are dummy objects in the\nclassification of section~\\ref{s:automaticdummies} (see\ntable~\\ref{t:argtypes}). Objects of this type do not need the question\nmark, as their explicit name is never relevant. You can therefore\nwrite\n\\begin{screen}{1}\n@substitute!(%)( A_{m n} -> 0 );\n\\end{screen}\nto set all occurrances of the tensor~$A$ with two subscript indices to\nzero, regardless of the names of the indices (i.e.~this command sets\n$A_{p q}$ to zero).\n\nWhen replacing object wildcards with something else that involves\nthese objects, use the question mark notation also on the right-hand\nside of the rule. For instance,\n\\begin{screen}{1}\n@substitute!(%)( A? + B? -> A? A? );\n\\end{screen}\nreplaces all sums with two elements by the square of the first\nelement. The following example shows the difference between the\npresence or absence of question marks on the right-hand side:\n\\begin{screen}{1,2,4,5}\nC + D:\n@substitute!(%)( A? + B? -> A? A? );\nC * C;\n@pop(%);\n@substitute!(%)( A? + B? -> A A );\nA * A;\n\\end{screen}\nNote that you can also use patterns to remove or add indices or\narguments, as in\n\\begin{screen}{1,2,3,5}\n{\\mu,\\nu,\\rho}::Indices(vector).\nA_{\\mu} B_{\\nu} C_{\\nu} D_{\\mu};\n@substitute!!(%)( A?_{\\rho} B?_{\\rho} -> \\dot(A?)(B?) );\nA.D B.C;\n@substitute!!(%)( \\dot(A?)(B?) -> A?_{\\mu} B?_{\\mu} );\n\\end{screen}\n\nIn many algorithms, patterns can be supplemented by so-called\nconditionals. These are constraints on the objects that appear in the\npattern. For instance, the substitution command\\index{conditionals}\n\\begin{screen}{1}\n@substitute!(%)( A_{m n} B_{p q} | _{n}!=_{p} -> 0 );\n\\end{screen}\napplies the substitution rule only if the second index of $A$ and the\nfirst index of $B$ do not match. Note that the conditional follows\ndirectly after the pattern, not after the full substitution rule. A\nway to think about this is that the conditional is part of the\npattern, not of the rule. The reason why the conditional follows the\nfull pattern, and not directly the symbol to which it relates, is\nclear from the example above: the conditional is a ``global''\nconstraint on the pattern, not a local one on a single index.\n\nThese conditions can be used to match names of objects using\nregular\\index{regular expressions}\nexpressions. Consider the following example:\n\\begin{screen}{1,2}\nA + B3 + C7:\n@substitute!(%)( A + M? + N?  | { \\regex{M?}{\"B[0-9]*\"},\n                                \\regex{N?}{\"[A-Z]7\"} } -> sin(M? N?)/N? );\nsin(B3 C7)/C7;\n\\end{screen}\n\nIt is also possible to select objects based on whether or not they are\nassociated with a particular property, e.g.\\footnote{More compact\nnotations may look tempting, but were abandoned in favour of the\nconstraint-based notation, the reason being that more compact\nnotations tend to become hard to read when the constraint is more complicated.}\n\\begin{screen}{1,2,3}\nA::SelfAntiCommuting.\nA A + B B;\n@substitute!(%)( Q?? Q?? | \\hasprop{Q??}{SelfAntiCommuting} -> 0 );\nB B;\n\\end{screen}\nCombinations of different types of conditionals are of course also\npossible. This type of constraint can be used to construct replacement\nrules which act on objects of a certain type without knowing what\ntheir name is. The following example illustrates this.\n\\begin{screen}{1,2,3}\n\\sigma_{a?}::SigmaMatrix.\n\\sigma_{1}\\sigma_{2} + \\rho_{1} \\rho_{2};\n@substitute!(%)( S?_{1} S?_{2} | \\hasprop{S?_{1}}{SigmaMatrix} -> I*S?_{3}  );\nI \\sigma_{3} + \\rho_{1} \\rho_{2};\n\\end{screen}\nThis could also have been written without specifying the numerical\nvalues of the indices explicitly, \n\\begin{screen}{1,2,3}\n\\sigma_{a?}::SigmaMatrix.\n\\sigma_{1}\\sigma_{2} + \\rho_{1} \\rho_{2};\n@substitute!(%)( S?_{a?} S?_{b?} | \\hasprop{S?_{a?}}{SigmaMatrix} -> I*\\epsilon_{a? b? c} \\sigma_{c}  );\nI \\epsilon_{1 2 c} \\sigma_{c} + \\rho_{1} \\rho_{2};\n\\end{screen}\n\nAs a general rule, patterns on the right-hand side of a substitution\nrule get replaced even if their parent relation does not match the one\non the left-hand side,\n\\begin{screen}{1,2,3}\nq_{c d};\n@substitute!(%)( q_{a b} -> a Q_{a b} );\nc Q_{c d};\n\\end{screen}\nThis follows the general logic of explicit wildcards,\n\\begin{screen}{1,2,3}\nq_{c d};\n@substitute!(%)( q_{a? b?} -> a? Q_{a? b?} );\nc Q_{c d};\n\\end{screen}\nIf this is not what you want, just rename the dummy index labels,\n\\begin{screen}{1,2,3}\nq_{c d};\n@substitute!(%)( q_{e f} -> a Q_{e f} );\na Q_{c d};\n\\end{screen}\n\n\n%Note that declarations and substitution both use patterns, but the\n%latter are a superset of the former. That is, declarations at present\n%only accept dummy index patterns and range wildcards. A construction like\n%\\begin{screen}{0}\n%{ m? | \\regex{m?}{\"a[0-9]*\"} }::Integer.   INVALID\n%\\end{screen}\n%is not yet allowed.\n% This makes the symbols $a0$, $a1$, $a2$ and so on integers. Here one\n% sees once more that the conditional is part of the full pattern. The\n% entire expression inside the curly brackets should be considered a \n% pattern. Note that the following expressions are all equivalent:\n% \\begin{screen}{0}\n% { R?_{m? n? p? q?} | \\regex{R?}{\"R\"} }::RiemannTensor.\n% { R?_{m n p q} | \\regex{R?}{\"R\"} }::RiemannTensor.\n% R_{m? n? p? q?}::RiemannTensor.\n% R_{m n p q}::RiemannTensor.\n% \\end{screen}\n% The versions without the question marks on the indices match\n% any index names by virtue of the rule in section~\\ref{s:automaticdummies}.\n\n\\subsection{Procedures}\n\nAlthough the present version of \\cdb does not contain a full-fledged\nprogramming language, it does allow you to construct groups of\ncommands which can be applied term-by-term on a large sum. This is\nsometimes useful if e.g.~the application of a command on a single term\nalready leads to a large intermediate result.\n\nProcedures are defined by making use of the \\cdbcommand{procedure}{}\nconstruction. Here is an example, which distributes all products and\nperforms a substitution:\n\\begin{screen}{1,2,3,4,5}\n@procedure{ExpandAndCollect};\n@distribute!(%);\n@substitute!(%)( A C -> Q );\n@collect_terms!(%);\n@procedure_end;\n\\end{screen}\nA sample session which calls this procedure is\n\\begin{screen}{1,2,3,4}\n(A+C)*(B+C+A) + C*(E+A);\n@call{ExpandAndCollect};\n\\end{screen}\nThis produces some status output, followed by\n\\begin{screen}{0}\nA B + 2 Q + A A + C B + C C + C E + Q;\n\\end{screen}\nNote how the commands inside the procedure only act on each term in\nturn. The \\subscommand{collect\\_terms} command has only collected two\n\\verb|Q| symbols which arose from the first term. Note also that all\noutput of the commands inside the procedure has been suppressed,\ndespite the appearance of the semi-colon line delimiter.\n\n\n\\subsection{Reserved node names}\n\\label{s:reserved_names}\n\nThere is a small number of node names which is reserved to always mean\nthe same thing, i.e.~for which the properties are not determined by\nthe property system. These can be obtained using the `@reserved'\ncommand. Explicitly, they are\n%\n% If any of these change, they need to be changed in the output\n% routine of manipulator.cc as well.\n%\n\\begin{quote}\n\\texcommand{anticommutator},\n\\texcommand{arrow},\n\\texcommand{comma}, \n\\texcommand{commutator}, \n\\texcommand{conditional},\n\\texcommand{frac}, \n\\texcommand{cdot},\n\\texcommand{equals}, \n\\texcommand{expression},\n\\texcommand{factorial},\n\\texcommand{indexbracket}, \n\\texcommand{infty}, \n\\texcommand{label},\n\\texcommand{pow}, \n\\texcommand{prod}, \n\\texcommand{regex}, \n\\texcommand{sequence},\n\\texcommand{sum},\n\\texcommand{unequals}.\n\\end{quote}\nMoreover, \\cdb uses a number of standard names for mathematical\noperators as reserved keywords, to wit\n\\begin{quote}\n\\texcommand{sin},\n\\texcommand{cos},\n\\texcommand{tan},\n\\texcommand{sinh},\n\\texcommand{cosh},\n\\texcommand{tanh},\n\\texcommand{arcsin},\n\\texcommand{arccos},\n\\texcommand{arctan},\n\\texcommand{sqrt}\n\\end{quote}\nSome properties of these nodes are still obtained from the property\nsystem in order to make algorithms look more uniform, but the names of\nthese reserved nodes can not be changed. \n\n\\begin{reserved}\n\\input{reserved/anticommutator.tex}\n\\input{reserved/arrow.tex}\n\\input{reserved/comma.tex}\n\\input{reserved/commutator.tex}\n\\input{reserved/conditional.tex}\n\\input{reserved/frac.tex}\n\\input{reserved/cdot.tex}\n\\input{reserved/equals.tex}\n\\input{reserved/expression.tex}\n\\input{reserved/factorial.tex}\n\\input{reserved/indexbracket.tex}\n\\input{reserved/infty.tex}\n\\input{reserved/label.tex}\n\\input{reserved/pow.tex}\n\\input{reserved/prod.tex}\n\\input{reserved/regex.tex}\n\\input{reserved/sequence.tex}\n\\input{reserved/sum.tex}\n\\input{reserved/unequals.tex}\n\\end{reserved}\n\n\n\\subsection{Startup and program options}\n\nThere are a few startup options for the command line version of \\cdb.\nIf present, a startup file {\\tt \\verb|~/.cadabra|}\n\\index{.cadabra}\\index{startup file} will be read when the program is\nstarted (only when running cadabra in command-line mode). This file\ncan contain any \\cdb input.\n\\begin{description}\n\\item[{\\tt -{}-{}bare}] Disable reading of the startup file\n  \\verb|~/.cadabra|.\n\\item[{\\tt -{}-{}silent}] Disable normal output (so that the only\n  remaining output is through output redirection into files).\n\\item[{\\tt -{}-{}input [filename]}] Before switching to interactive mode, first\n  read and process the indicated file.\n\\item[{\\tt -{}-{}prompt [string]}] Set the \\cdb prompt to the given\n  string.\n\\item[{\\tt -{}-{}silentfail}] Silently fail (i.e. do not complain) if\n  an algorithm is activated which cannot be applied.\n\\item[{\\tt -{}-{}loginput}] Write the input into the debug file as\n  well.\n\\item[{\\tt -{}-{}nowarnings}] Suppress displaying of any warnings\n  which are not fatal errors.\n\\item[{\\tt -{}-{}texmacs}] Send output in TeXmacs format.\n\\end{description}\nIn order to have command-line editing functionality, the {\\tt prompt}\nprogram is provided. So the two ways of starting \\cdb are\n\\begin{screen}{0}\ncadabra\nprompt cadabra\n\\end{screen}\nthe second of which gives cursor control and an editing history. There\nare various other settings of \\cdb which can be influenced through\nenvironment variables; see section~\\ref{s:environment_variables} for\ndetails.\n\n\n\\subsection{Environment variables}\n\\label{s:environment_variables}\n\n\\index{environment variables}There are a few environment variables which may be set to influence\nthe behaviour of cadabra:\n\\begin{descerate}\n\\item[CDB\\_LOG] \\index{CDB\\_LOG} When set, debug logging will be\n  enabled.\n%\\item[CDB\\_CHECK\\_INPUT] \\index{CDB\\_CHECK\\_INPUT} If set, check all\n%  input lines for index consistency.\n\\item[CDB\\_ERRORS\\_ARE\\_FATAL] \\index{CDB\\_ERRORS\\_ARE\\_FATAL} If this\n  variable is set, errors (inconsistency of the tree or attempted use\n  of non-existing algorithm) will abort the program  (the default\n  action, when this variable is unset, is to ignore the offending input line).\n\\item[CDB\\_PARANOID] \\index{CDB\\_PARANOID} Perform extensive consistency checks on the\n  internal data format after each algorithm has been applied (only\n  useful for debugging).\n\\item[CDB\\_PRINTSTAR] \\index{CDB\\_PRINTSTAR} Determines whether or not multiplication star\n  symbols are displayed.\n\\item[CDB\\_TIGHTSTAR] \\index{CDB\\_TIGHTSTAR} Make output of multiplication symbols more compact.\n\\item[CDB\\_TIGHTBRACKETS] \\index{CDB\\_TIGHTBRACKETS} Make output of bracketed expressions more\n  compact.\n\\item[CDB\\_USE\\_UTF8] \\index{CDB\\_USE\\_UTF8} Use UTF8 line breaking characters in the output.\n\\end{descerate}\n\n% \\subsection{Future plans}\n% \n% Now that the program is beginning to reach a usable and stable state,\n% a number of directions for future work suggest themselves:\n% \\begin{itemize}\n% \\item A new parser; the current one was hand-written for many reasons,\n%   and is messy and not entirely correct. Now that the input format has\n%   stabilised it is time for a parser which is easier to debug,\n%   e.g.~one based on {\\tt lex} \\& {\\tt yacc}.\n% \\item Inclusion of proper program flow including loops and\n%   subroutines. \n% \\end{itemize}\n% Any suggestions on these or other topics are welcome.\n\n%-----------------------------------------------------------------\n\\vfill\\eject\n\\section{Algorithm modules}\n\n\\label{s:modules}\n\nAll algorithms are stored in modules separate from the core of the\nprogram. These are at present all distributed together with the main\nprogram, but will in the future be available separately as binary or\nsource plugin modules that can be loaded on demand.\n\nAny expression that starts with a name beginning with an ``@'' symbol\nis interpreted as a command. Commands act on the currently selected\nobjects in an expression or on the expression for which the label or\nnumber is given as the first argument. See\nsection~\\ref{s:active_nodes} for more details on how to apply\nalgorithms to expressions.\n\n\\begin{multicols}{2}\n\\printnomenclature\n%\\printglossary\n\\end{multicols}\n\\vfill\\eject\n\n% \\subsection{Built-in core algorithms}\n% \n% \\label{s:builtin}\n% There is a very small number of properties and algorithms built into\n% the core program. These have to do with global memory management and\n% global output settings.\n% \\bigskip\n% \n% \\begin{props}\n% \\input{properties/KeepHistory.tex}\n% \\input{properties/PreDefaultRules.tex}\n% \\input{properties/PostDefaultRules.tex}\n% \\end{props}\n% \\bigskip\n% \n% \\begin{algs}\n% \\input{algorithms/pop.tex}\n% \\input{algorithms/amnesia.tex}\n% \\input{algorithms/algorithms.tex}\n% \\input{algorithms/properties.tex}\n% \\input{algorithms/timing.tex}\n% \\input{algorithms/output_format.tex}\n% \\input{algorithms/quit.tex}\n% \\input{algorithms/end.tex}\n% \\input{algorithms/reset.tex}\n% \\input{algorithms/xterm_title.tex}\n% %\\item[\\cdbcommand{utf8\\_output\\{true|false\\}}{}] Determines whether\n% %the output should contain UTF8 encoded Unicode control characters for \n% %line-breaking and object grouping. This output format is used by the\n% %graphical front-end.\n% \\end{algs}\n% \n% \\vfill\\eject\n% \n% \n% \\subsection{Rationals, complex numbers and other numerics}\n% \n% \\begin{props}\n% %\\item[\\cdbprop{ImaginaryI}{}] Indicates that the object squares to\n% %  $-1$. \n% %\\item[\\cdbprop{Real}{}]\n% %\\item[\\cdbprop{Imaginary}{}]\n% %\\item[\\cdbprop{Complex}{}]\n% \\input{properties/Integer.tex}\n% \\input{properties/NumericalFlat.tex}\n% \\end{props}\n% \\bigskip\n% \\begin{algs}\n% %\\item[\\cdbcommand{eval\\_factorial}{}] Evaluate the numerical value of \n% %a factorial expression, e.g.~turn $5!$ into $120$.\\kcomment{KP}{Not\n% %yet implemented}\n% \\input{algorithms/numerical_flatten.tex}\n% \\end{algs}\n% \n% \\vfill\\eject\n% \n% \\subsection{Sums and products}\n% \n% \\label{m:algebra}\n% This module handles expansion of sums and products as well as\n% distributing products over sums and similar algorithms. It recognises\n% \\bigskip\n% \\begin{props}\n% \\input{properties/Matrix.tex}\n% \\input{properties/ImplicitIndex.tex}\n% \\input{properties/Diagonal.tex}\n% \\input{properties/SelfAntiCommuting.tex}\n% \\input{properties/SelfNonCommuting.tex}\n% \\input{properties/SelfCommuting.tex}\n% \\input{properties/Distributable.tex}\n% \\input{properties/AntiSymmetric.tex}\n% \\input{properties/Symmetric.tex}\n% \\input{properties/TableauSymmetry.tex}\n% \\input{properties/DAntiSymmetric.tex}\n% \\input{properties/Commuting.tex}\n% \\input{properties/NonCommuting.tex}\n% \\input{properties/AntiCommuting.tex}\n% \\input{properties/CommutingAsProduct.tex}\n% \\input{properties/CommutingAsSum.tex}\n% \\input{properties/Traceless.tex}\n% \\input{properties/KroneckerDelta.tex}\n% \\input{properties/EpsilonTensor.tex}\n% \\input{properties/SortOrder.tex}\n% \\input{properties/Derivative.tex}\n% \\input{properties/PartialDerivative.tex}\n% \\end{props}\n% \\begin{algs}\n% \\input{algorithms/prodflatten.tex}\n% \\input{algorithms/sumflatten.tex}\n% \\input{algorithms/remove_indexbracket.tex}\n% \\input{algorithms/expand_power.tex}\n% %\\input{algorithms/drop.tex}\n% \\input{algorithms/drop_weight.tex}\n% \\input{algorithms/keep_weight.tex}\n% \\input{algorithms/distribute.tex}\n% \\input{algorithms/prodrule.tex}\n% \\input{algorithms/sumsort.tex}\n% \\input{algorithms/sort_product.tex}\n% \\input{algorithms/collect_factors.tex}\n% \\input{algorithms/collect_terms.tex}\n% \\input{algorithms/factor_out.tex}\n% \\input{algorithms/factor_in.tex}\n% \\input{algorithms/canonicalise.tex}\n% \\input{algorithms/reduce.tex}\n% \\input{algorithms/young_project.tex}\n% \\input{algorithms/all_contractions.tex}\n% \\end{algs}\n\n\\vfill\\eject\n\\subsection{Young tableaux}\n\nYoung diagrams (with unlabelled boxes) and Young tableaux (with\nlabelled boxes) can be manipulated directly, and \\cdb contains\nroutines to e.g.~compute tensor products or to put tableaux in\nstandard form using all their symmetries. In order to avoid confusion\nabout the meaning of ``diagram'' and ``tableau'', a Young tableau with\nlabelled boxes is called a ``FilledTableau'' in \\cdb, while a tableau\nwithout any labels in the boxes is a ``Tableau''.\n\\bigskip\n\n% \\begin{props}\n% \\input{properties/Tableau.tex}\n% \\input{properties/FilledTableau.tex}\n% \\end{props}\n% \n% \\begin{algs}\n% \\input{algorithms/tabdimension.tex}\n% \\input{algorithms/tabcanonicalise.tex}\n% \\input{algorithms/tabstandardform.tex}\n% \\input{algorithms/lr_tensor.tex}\n% \\input{algorithms/decompose.tex}\n% \\input{algorithms/decompose_product.tex}\n% \\end{algs}\n\n\\vfill\\eject\n\n\\subsection{Lists and ranges}\n\nWhen using list algorithms, be aware of the fact that when they act on\nan argument, they actually replace the argument, not generate a new\none. Therefore, to generate a new expression which contains the length\nof another expression, \n\\begin{screen}{1,3}\nA+B+C+D;\n1:= A+B+C+D;\n@length[@(1)];\n2:= 4;\n\\end{screen}\nThis is to be compared with\n\\begin{screen}{1,3}\nA+B+C+D;\n1:= A+B+C+D;\n@length(1);\n1:= 4;\n\\end{screen}\nin which case the first expression gets replaced by its length.\n\\medskip\n\n% \\begin{algs}\n% \\input{algorithms/length.tex}\n% \\input{algorithms/take.tex}\n% \\input{algorithms/range.tex}\n% \\input{algorithms/inner.tex}\n% \\input{algorithms/list_sum.tex}\n% \\input{algorithms/listflatten.tex}\n% \\input{algorithms/permute.tex}\n% \\end{algs}\n\n\\vfill\\eject\n\n%\\subsection{Differential geometry}\n%\n%\\label{s:diff_geom}\n%\\begin{props}\n%\\item[\\cdbprop{DifferentialForm}{}]\n%\\end{props}\n%\\bigskip\n\n%\\begin{algs}\n%\\end{algs}\n\n\n\\subsection{Properties}\n\n\\label{s:properties}\n% \\begin{props}\n% \\input{properties/PropertyInherit.tex}\n% \\input{properties/IndexInherit.tex}\n% \\end{props}\n%\\begin{algs}\n%\\item[\\cdbcommand{extract\\_properties}{}] An algorithm mainly useful \n%in internal routines: it extracts properties attached to a symbol and\n%adds them to the global property list. Gets called automatically on\n%input.\n%\\end{algs}\n%\n\\vfill\\eject\n\n\\subsection{Dummy indices}\n\n\\label{s:dummies}\nDummy indices are a subject by itself. There are various problems with\nmost implementations of dummy indices in computer algebra software. In\nmany cases, dummy indices are added as an afterthought, leading to\nsituations were illegal expressions (e.g. with a more than twice\nrepeated dummy index) can be entered. Even if this is flagged, most\nprograms do not know about different index types (which leads to\nproblems when there is more than one type of contraction, or a sum\nover only part of the index range). In \\cdb, the system knows about\ndummy index \\emph{sets}, and all algorithms can request new dummy\nindices very easily. This is handled through the {\\tt dummies} module. \n\\bigskip\n\n% \\begin{props}\n% \\input{properties/Indices.tex}\n% \\end{props}\n% \\begin{algs}\n% \\input{algorithms/rename_dummies.tex}\n% \\end{algs}\n\n\\vfill\\eject\n\n\\subsection{Symmetrisation and anti-symmetrisation}\n% This is actually implemented in algebra.cc, the sym.cc is empty\n\nThis module contains algorithms for the symmetrisation or\nanti-symmetrisation of expressions in their elements, and for the\ninverse procedure, whereby object trees are identified when they\ndiffer only by certain symmetrisations or anti-symmetrisations.\n%This module relies strongly on the {\\tt combinatorics.hh} header file,\n%which contains algorithms that generate various combinations and\n%permutations of sets.\n%\\url{http://dogma.net/markn/articles/Permutations/}\n\\bigskip\n\n% \\begin{algs}\n% \\input{algorithms/sym.tex}\n% \\input{algorithms/asym.tex}\n% \\input{algorithms/canonicalorder.tex}\n% \\input{algorithms/impose_asym.tex}\n% \\input{algorithms/asymprop.tex}\n% \\end{algs}\n\n\\vfill\\eject\n\n\\subsection{Field theory}\n\n\\label{s:tensor}\n\n\\bigskip\n% \\begin{props}\n% \\input{properties/SelfDual.tex}\n% \\input{properties/AntiSelfDual.tex}\n% \\input{properties/Depends.tex}\n% \\input{properties/DependsInherit.tex}\n% \\input{properties/Weight.tex}\n% \\input{properties/WeightInherit.tex}\n% \\input{properties/Symbol.tex}\n% \\input{properties/Coordinate.tex}\n% \\input{properties/Accent.tex}\n% \\input{properties/SatisfiesBianchi.tex}\n% \\end{props}\n% \\bigskip\n% \\begin{algs}\n% \\input{algorithms/unwrap.tex}\n% \\input{algorithms/eliminate_kronecker.tex}\n% \\input{algorithms/eliminateeps.tex}\n% \\input{algorithms/epsprod2gendelta.tex}\n% \\input{algorithms/dualise_tensor.tex}\n% \\input{algorithms/reduce_gendelta.tex}\n% \\input{algorithms/product_shorthand.tex}\n% \\input{algorithms/expand_product_shorthand.tex}\n% \\input{algorithms/pintegrate.tex}\n% \\input{algorithms/impose_bianchi.tex}\n% \\input{algorithms/einsteinify.tex}\n% \\input{algorithms/combine.tex}\n% \\input{algorithms/expand.tex}\n% \\end{algs}\n~\n\n\\vfill\\eject\n\n\\subsection{Output routines}\n\n\\label{s:output}\nThe core of \\cdb only knows how to output its internal tree format in\ninfix notation, and by default displays the result of every input line\nin this way (labelled by the expression number and label, if any).\nFor more complicated output, for instance to feed \\cdb expressions to\nother programs, or to see the internal tree form, routines are\navailable in the {\\tt output} module. Note that these modules do not\ntransform the tree or generate new expressions; they \\emph{only}\ngenerate output.\n\nRelated but \\emph{different} functionality is present in the {\\tt\nconvert} module, which contains transformation algorithms which\ntransform the internal tree to other conventions (e.g.~in order to\nconvert a \\cdb tree to a tree which can be understood by Maple or\nMathematica).\n\\bigskip\n\n% \\begin{props}\n% \\input{properties/LaTeXForm.tex}\n% \\end{props}\n% \\bigskip\n% \\begin{algs}\n% \\input{algorithms/depprint.tex}\n% \\input{algorithms/print.tex}\n% \\input{algorithms/number_of_terms.tex}\n% \\input{algorithms/proplist.tex}\n% \\input{algorithms/assert.tex}\n% \\end{algs}\n% \\bigskip\\bigskip\n\n\\noindent Furthermore, there are a few algorithms which are mainly useful for\ndebugging purposes, as they display information about the internal\nrepresentation of the expression tree. More information on the\ninternal data structures can be found in\nsection~\\ref{s:internal_storage}.\n\\bigskip\n\n% \\begin{algs}\n% \\input{algorithms/tree.tex}\n% \\input{algorithms/indexlist.tex}\n% \\end{algs}\n\n\\vfill\\eject\n\n% \\subsection{Perturbative string theory ({\\tt pertstring})}\n% \n% \n% This module contains useful routines for the computation of\n% perturbative string amplitudes, that is, it contains information about\n% Jacobi theta functions and assorted things.\n% \\bigskip\n% \\begin{algs}\n% \\item[\\cdbcommand{aticksen}{}] Work out a fermionic correlator according to\n% \\dcite{Atick:1987rs}. These correlators contain SO(2) spinors\n% represented in the form of a complex fermion $\\Psi$ and $\\bar\\Psi$, as\n% well as spin fields $S_+$ and $S_-$ \\kcomment{KP}{Lacking\n% ``properties'', these currently have to be written as {\\tt Psi}, {\\tt\n% Psibar}, {\\tt Splus} and {\\tt Sminus}.}. Correlators of these are written as\n% {\\tt \\\\corr\\{...\\}}, where the dots contain an arbitrary number of these\n% fermionic fields, together with their dependence on insertion points. \n% The algorithm converts these correlators to Jacobi theta function expressions,\n% (ignoring a normalisation constant) using the expression\n% \\begin{equation}\n% \\begin{aligned}[t] \\Big\\langle \\prod_{i=1}^{N_1}& S^+(\\tilde y_i)\n% \\prod_{i=1}^{N_2} S^-(y_i) \\prod_{i=1}^{N_3} \\bar\\Psi(\\tilde z_i)\n% \\prod_{i=1}^{N_4} \\Psi(z_i)\\Big\\rangle_\\nu \\\\[1ex]\n% {} & = K_\\nu  \\frac{\\displaystyle \\prod_{i<j}\\theta_1(\\tilde y_i-\\tilde y_j)^{\\tfrac{1}{4}}\n% \\prod_{i<j} \\theta_1(y_i-y_j)^{\\tfrac{1}{4}} \n% \\prod_{i<j} \\theta_1(\\tilde z_i-\\tilde z_j)\n% \\prod_{i<j} \\theta_1(z_i- z_j)}{\\displaystyle\n%   \\prod_{i,j} \\theta_1(y_i-\\tilde y_j)^{\\tfrac{1}{4}}\n%   \\prod_{i,j} \\theta_1(z_i-\\tilde z_i)\n% } \\\\[1ex]\n% & \\quad\\quad\\times \n% \\frac{ \\displaystyle\n%   \\prod_{i,j} \\theta_1(z_i-\\tilde y_j)^{\\tfrac{1}{2}}\n%   \\prod_{i,j} \\theta_1(\\tilde z_i - y_j)^{\\tfrac{1}{2}}}{\\displaystyle\n%   \\prod_{i,j} \\theta_1(\\tilde z_i- \\tilde y_j)^{\\tfrac{1}{2}}\n%   \\prod_{i,j} \\theta_1(z_i-y_j)^{\\tfrac{1}{2}}\n% }\\\\[1ex]\n% &\\quad\\quad\\times\n% \\theta_\\nu\\left( \\frac{1}{2}\\sum_i \\tilde y_i - \\frac{1}{2}\\sum_i y_i \n% + \\sum_i z_i - \\sum_i \\tilde z_i\\right)\\, .\n% \\end{aligned}\n% \\end{equation}\n% \n% \\item[\\cdbcommand{riemannid}{}] Implement the Riemann identity for\n% a sum over spin structures of a product of four theta functions on the\n% torus. That is, it implements\n% \\begin{multline}\n% \\sum_{\\nu=1,2,3,4} (-)^{\\nu-1}\\, \\theta_\\nu(z_1|\\tau) \\theta_\\nu(z_2|\\tau)\n% \\theta_\\nu(z_3|\\tau) \\theta_\\nu(z_4|\\tau) \\\\[1ex] = \n% 2\\,\n% \\theta_1\\left(\\frac{z_1+z_2+z_3+z_4}{2}\\Big|\\tau\\right)\n% \\theta_1\\left(\\frac{z_1+z_2-z_3-z_4}{2}\\Big|\\tau\\right)\\\\[1ex]\n% \\times\\theta_1\\left(\\frac{z_1-z_2-z_3+z_4}{2}\\Big|\\tau\\right)\n% \\theta_1\\left(\\frac{z_1-z_2+z_3-z_4}{2}\\Big|\\tau\\right)\\, .\n% \\end{multline}\n% In particular, if any the arguments coincide pairwise (e.g.~$z_1=z_2$\n% and $z_3=z_4$) the right-hand side vanishes because $\\theta_1$ is odd.\n% \\end{algs}\n% \n% \\vfill\\eject\n\n\\subsection{General relativity}\n\nThis module deals with special tensors relevant for general\nrelativity. See in particular also the {\\tt canonicalise} algorithm in\nsection~\\ref{m:algebra}.\n\\bigskip\n% \\begin{props}\n% \\input{properties/Metric.tex}\n% \\input{properties/InverseMetric.tex}\n% \\input{properties/Vielbein.tex}\n% \\input{properties/InverseVielbein.tex}\n% \\input{properties/RiemannTensor.tex}\n% \\input{properties/WeylTensor.tex}\n% \\end{props}\n% \\bigskip\n% \\begin{algs}\n% \\input{algorithms/rewrite_indices.tex}\n% \\input{algorithms/riemann_index_regroup.tex}\n% %\\input{algorithms/ricci_can_order.tex}\n% \\input{algorithms/split_index.tex}\n% \\input{algorithms/split_index.tex}\n% \\input{algorithms/eliminate_vielbein.tex}\n% \\input{algorithms/eliminate_metric.tex}\n% \\end{algs}\n\n\\vfill\\eject\n\n\\subsection{Substitution}\n\nSubstitution of expressions into other ones is a subtle issue. One\nproblem, namely that of relabelling of dummy indices, is addressed by\nthe core routines and has been discussed in section~\\ref{s:dummies}. \nHere we will discuss how \\cdb handles the issue of pattern matching.\n\n%index label matching and product factor and sum term re-ordering.\n\\bigskip\n\n\\begin{algs}\n\\item[\\cdbcommand{}{}] Given an expression number of label, this node\nreplaces itself with a copy of this expression. As with any active\nnode, this one takes care of dummy index relabelling automatically\n(see section~\\ref{s:dummies}).\n\\item[\\cdbcommand{rename}{}] \\outdated Renames objects and numbered objects,\nbut only on a fixed level, i.e.~does not do pattern matching at all.\nFor instance,\n\\begin{screen}{1,3}\nF_{m1 m2 m3};\nF_{m1 m2 m3}\n@rename!(%){m}{r};\nF_{r1 r2 r3}\n\\end{screen}\nIt will not prevent you from introducing dummy pairs:\n\\begin{screen}{1,2}\nF_{m n};\n@rename!(%){m}{n};\nF_{n n};\n\\end{screen}\nHowever, it will relabel already existing dummy pairs if you rename an\nopen index in such a way that it would conflict with the dummy pair:\n\\begin{screen}{1,2,3}\n{m,n,p,q,r,s}::Indices(vector).\nF_{m n} G_{n q};\n@rename!(%){m}{n};\nF_{n p} G_{p q};\n\\end{screen}\n~\n% \\input{algorithms/substitute.tex}\n% \\input{algorithms/vary.tex}\n% \\input{algorithms/take_match.tex}\n% \\input{algorithms/replace_match.tex}\n\\end{algs}\n\n\\vfill\\eject\n\n\\subsection{Linear algebra}\n\n% \\begin{algs}\n% \\input{algorithms/lsolve.tex}\n% \\end{algs}\n\n\\vfill\\eject\n\n\\subsection{Gamma matrix algebra and fermions}\n\nThis module deals with manipulations of the Clifford algebra, spinor\nrepresentations of the Lorentz group and related issues. Cadabra\nfollows the conventions of Sevrin's appendix~1.5, except for the fact\nthat we call the time-like component zero and the product of all gamma\nmatrices~$\\tilde\\Gamma$.\n\\bigskip\n% \\begin{props}\n% \\input{properties/Spinor.tex}\n% \\input{properties/DiracBar.tex}\n% \\input{properties/GammaMatrix.tex}\n% \\input{properties/GammaTraceless.tex}\n% \\input{properties/SigmaMatrix.tex}\n% \\input{properties/SigmaBarMatrix.tex}\n% \\end{props}\n% \\bigskip\n% \\begin{algs}\n% \\input{algorithms/join_gamma.tex}\n% \\input{algorithms/gammasplit.tex}\n% \\input{algorithms/rewrite_diracbar.tex}\n% \\input{algorithms/projweyl.tex}\n% \\input{algorithms/spinorsort.tex}\n% \\end{algs}\n\n\n\\vfill\\eject\n\n\\subsection{Conversion from/to other formats}\n\n\\Cdb's syntax is a superset of the Maple and Mathematica formats, in\nthe sense that the internal tree representation of \\cdb can store\ninput for both of these systems. However, this may not always be the\nmost convenient way of storage, as \\cdb often has more compact or\nexpressive ways to store tensors. The {\\tt convert} module provides\nconversion algorithms from and to these two formats.\n\\bigskip\n\n% \\begin{algs}\n% \\input{algorithms/run.tex}\n% \\input{algorithms/maxima.tex}\n% \\input{algorithms/maple.tex}\n% \\item[{\\cdbcommand{from\\_math}{}[expression]}] Reads mathematica input\n% format as used by GAMMA~\\cite{Gran:2001yh}. Fully anti-symmetric\n% tensors are denoted with\n% \\begin{screen}{0}\n% Tensor[name,{indices}]\n% \\end{screen}\n% Tensors with property ``weyltensor'' are printed as\n% \\begin{screen}{1}\n% W_{r1 r2 r3 r4}  \n% Weyl[{r1,r2}, {r3,r4}]\n% \\end{screen}\n% (warning, this removes the tensor name).\n% \\item[{\\cdbcommand{to\\_math}{}[expression]}] Converts the mathematica expression\n% to a \\cdb one. See above for details about the conversion process.\n% \\end{algs}\n\n\n\n\\vfill\\eject\n\n\\section{Core functionality}\n\n\\subsection{Source file description}\n\nThe files in the {\\tt src} directory build up the core of the program\nand are described below. Algorithm-specific code is in the {\\tt\nsrc/modules} subdirectory and a description of those files can be\nfound in section~\\ref{s:modules}. The files below should not be\nchanged when adding new modules.\n\\begin{description}\n\\item[{\\tt main.cc}] Startup routines; initialises the I/O streams,\nsets up the signal handlers for control-C and window resize signals\nand starts the main event loop.\n\n\\item[{\\tt manipulator.cc}, {\\tt manipulator.hh}] Contains the object\n  that processes the input line by line, activates the parser on it,\n  and scans the tree for active nodes. A few very low-level commands\n  (see section~\\ref{s:builtin}) are handled in this class, while the\n  other ones are dispatched to external modules.\n\n\\item[{\\tt preprocessor.cc}, {\\tt preprocessor.hh}] The code for\nconversion of human editable infix input to the tree-form handled by\nthe other parts of the program. This is a text-to-text filter forming\nthe first pass of the parser. All functionality can be tested using\n\\verb|test_preprocessor.cc|.\n\n\\item[{\\tt storage.cc}, {\\tt storage.hh}] The node and tree classes\nfor storage of the tree form of expressions. These are the classes on \nwhich actual symbolic manipulation takes place. See also the separate\n\\verb|tree.hh| class.\n\n\\item[{\\tt parser.cc}, {\\tt parser.hh}] The class which contains the\nparsing algorithms that turns output of the preprocessor class into a\ntree form.\n\n\\item[{\\tt algorithm.cc}, {\\tt algorithm.hh}] The base class for all\nthe classes defined in the modules subdirectory. Plus the\nimplementation of scanning for command arguments and the necessary\nlogic to create the undo information, apply an algorithm until it no\nlonger changes the expression and other things which are independent\nof the particular command.\n\n\\item[{\\tt combinatorics.hh}] General routines for the generation of\ncombinations and permutations of elements in a vector. Consists\nof a single class {\\tt combinations<$\\ldots$>} templated over the\ntype of the objects to be permuted. This class acts as a container\nholding both the original vector (in the {\\tt storage} member), the\npermutation patterns (in the {\\tt sublengths} vector, more on this\nlater) as well as the resulting permuted vectors (accessible through \n{\\tt operator[]}; the total number of combinations is given by\n{\\tt size()}).\n\\end{description}\n\n\\subsection{Tree representation of expressions}\n\\label{s:internal_storage}\n\nExpressions are internally stored in a tree container class, based on\nthe {\\tt tree.hh} library~\\cite{kas_tree}. The present section\ndescribes the tree format in some more detail. \n\nLet us start with a couple of remarks on the motivation which has led\nto the current implementation. An important requirement for the\nstorage format is that symbols should not have a fixed meaning, but\nrather be like variables in a computer program: they can be declared\nto represent objects of a certain type. Similarly, the user should be\nfree to use arbitrary bracket types and sub- and superscript\nindicators (these should in addition be kept during the algebraic\nmanipulations). The first issue is resolved with the property system,\nbut the second one needs support directly in the storage tree.\n\nSecondly, storage should be such that a trivial (often occurring)\nextensions from one object to another should not lead to blowup. For\ninstance, the difference between \\verb|A_\\mu| and \\verb|A_{\\mu \\nu}|\nshould preferably not introduce a new layer between the \\verb|A| node\nand the \\verb|\\mu| node. This is achieved by adding the bracket type\nto the \\emph{child} node rather than the parent (in the example above,\nthe curly brackets are part of the \\verb|\\mu| and \\verb|\\nu|\nnodes). This applies also to e.g.~sums: in \\verb|(A+B)| (which is\nconverted by the preprocessor to \\verb|\\sum(A)(B)| ), the round\nbrackets are part of the child nodes of the \\verb|\\+|\nnode.\\footnote{Subsequent child nodes with the same bracket type\nassociated to them are taken to be part of the same group; the input\n{\\tt A\\_\\{$\\backslash$mu\\}\\_\\{$\\backslash$nu\\}} will therefore be\nprinted as {\\tt A\\_\\{$\\backslash$mu $\\backslash$nu\\}}. Similarly,\nthere is no way to represent $(a)+(b)$ since the internal storage\nformat automatically turns this into $(a+b)$.} Similarly, extending\n\\verb|q| to \\verb|3q| should not introduce new intermediate layers to\ngroup the two symbols together. This has been achieved by giving each\nnode a multiplier field (this holds true even for products,\ni.e.~\\verb|3(a+b)| is represented as a sum node with multiplier 3 (in\naddition, such numerical factors are always commuted to the front of\nthe expression).\\footnote{The multiplier field is a rational, and is\n  intended to stay that way. It is not a good idea to make it\n  complex, otherwise we will end up with octonionic multipliers at \nsome stage. }\n%We need some pre-defined symbols\n%for $i$ and so on though, and rules to simplify products of\n%them. These rules can be kept explicit and user-switchable to be\n%automatic.}\n\nIt should also be possible to make expressions arbitrarily deeply\nnested; one should be able to write \\verb|a+b| as well as\n\\verb|\\sin(a+b)|. This is in contrast to programs such as \n{\\tt Abra} and {\\tt FORM} which store their input as sums of products \nof factors, i.e.~without further nesting.\n\nFinally, tt should be posssible to store the history of an expression,\nin order to implement unlimited undo. \n\nThe data stored at each tree node is further explained in\nsection~\\ref{s:writing_new}, see in particular the excerpt from the {\\tt\n  storage.hh} file in figure~\\ref{f:str_node}. The structure of the\nactual tree is illustrated in figure~\\ref{f:example_history}. \nEach expression starts with a {\\tt history} node. The label of the\nexpression is given in a subnode {\\tt label}. All remaining child\nnodes of the {\\tt history} nodes represent the history of the\nexpression. The most often encountered node here is the {\\tt\n  expression} node, which contains the actual expression. However,\nthere are other nodes as well, for instance {\\tt asymimplicit} which\ncontains information about the symmetry structure of an expression\n(this feature is not yet enabled).\n\n\\begin{figure}[t]\n\\begin{equation*}\n\\vcenter{\\offinterlineskip\n\\halign{&#\\mystrut\\hfil\\cr\n\\texcommand{history} \\cr\n\\T  \\texcommand{label}\\cr\n\\V  \\L  apple \\cr\n\\T  \\texcommand{expression} \\cr\n\\V  \\L  \\texcommand{prod} \\cr\n\\V  \\N \\T  a \\cr\n\\V  \\N \\L  \\texcommand{sum} \\cr\n\\V  \\N \\N \\T  b \\cr\n\\V  \\N \\N \\L  c \\cr\n\\L  \\texcommand{expression} \\cr\n\\N  \\L  \\texcommand{sum} \\cr\n\\N  \\N  \\T  \\texcommand{prod} \\cr\n\\N  \\N  \\V  \\T  a \\cr\n\\N  \\N  \\V  \\L  b \\cr\n\\N  \\N  \\L  \\texcommand{prod} \\cr\n\\N  \\N  \\N  \\T  a \\cr\n\\N  \\N  \\N  \\L  c \\cr }}\n\\end{equation*}\n\\caption{Example history tree for a single expression.  Here, the\nprogram started with the user entering the expression $a (b+c)$. This\nexpression was then manipulated by applying the\n\\subscommand{distribute} algorithm. The nodes at the top of the\nexpression tree are all of the {\\tt history} type.\n\\label{f:example_history}}\n\\end{figure}\n% \\T \\texcommand{action}\\cr\n% \\V  \\T \\subscommand{exchange}\\cr\n% \\V  \\N  \\T a\\cr\n% \\V  \\N  \\L b\\cr\n% \\quad\\quad\\longleftrightarrow\\quad\\quad\n% \\vcenter{\n% \\offinterlineskip\n% \\halign{&#\\mystrut\\hfil\\cr\n% (1) $a+b$ \\cr\n% \\T  exchange \\cr\n% \\V  \\L \\,$b+a$\\cr\n% \\V  \\N \\,rmult $d$\\cr\n% \\V  \\N \\L \\,$(b+a) d$ $\\bullet$\\cr\n% \\L  lmult $c$\\cr\n% \\N  \\L \\,$c(a+b)$ \\cr}}\n\n\\subsection{Nested sums, products and pure numbers}\n\nNested sum and product nodes require some explanation, as the way in\nwhich \\cdb handles and stores these determines how brackets can appear\nin sums and products. As a general rule, sums within sums which are\nsuch that all child nodes have the same, non-visible bracket are not\nallowed, and automatically converted to a single sum. In other words\n\\begin{screen}{0}\n(\\sum{a}{b}+\\sum{c}{d})\n\\end{screen}\nis not allowed, since it would print as \\verb|(a+b+c+d)| which is\nindistinguishable from \n\\begin{screen}{0}\n(\\sum{a}{b}{c}{d}) .\n\\end{screen}\nThe first expression is therefore internally always converted to the\nsecond one before it is stored. A similar situation occurs with\nproducts, where\n\\begin{screen}{0}\n\\prod{a}{\\prod{b}{c}}\n\\end{screen}\nis not allowed and ``flattened'' to the simpler\n\\begin{screen}{0}\n\\prod{a}{b}{c} .\n\\end{screen}\nThe general rule is that nested sums and products are converted to\nflattened form if these two forms are indistinguishable in the\nstandard output format. Nested sums and products can occur, but they\nhave to have different or non-empty bracket types for their\nchildren. An example is\n\\begin{screen}{0}\n\\prod{a}{\\prod(b)(c)}\n\\end{screen}\nwhich prints as \\verb|a*(b*c)|. This is not automatically converted to\n\\verb|a*b*c|. Note that this form is \\emph{not} represented as\n\\begin{screen}{0}\n\\prod{a}(b)(c)    (wrong)\n\\end{screen}\nThis is a consequence of the second rule: all child nodes of product\nor sum nodes must have the same bracket type.  In summary, automatic\nflattening of nested sum or product trees do not automatically occur\nover bracket boundaries. You can then write and keep\n$(\\sin(x)+\\cos(x)) + (\\sin(x) + 3 \\cos(x))$, which will be stored as\n\\begin{screen}{0}\n\\sum{\\sum(sin(x))(cos(x))}{\\sum(sin(x))(cos(x))}\n\\end{screen}\nIn order to remove brackets, one uses the \\subscommand{sumflatten} \nand \\subscommand{prodflatten} commands, see section~\\ref{m:algebra}.\n\nProducts and sums with sub- or superscripts which apply to one or more\nof the child nodes are internally represented using\n\\verb|\\indexbracket| nodes. That is, the input\n\\begin{screen}{0}\nq (a+b)_\\mu\n\\end{screen}\nis represented as\n\\begin{screen}{0}\n\\prod{q}{\\indexbracket{\\sum(a)(b)}_{\\mu}}\n\\end{screen}\n(note the way in which the bracket types are inherited).\nIn fact, such indexbracket constructions apply for any content inside\nthe brackets; in the example above, an indexbracket would be generated\neven without the \\verb|\\sum| node: the input\n\\begin{screen}{0}\nq (\\Gamma^r)_{a b}\n\\end{screen}\nis stored as\n\\begin{screen}{0}\n\\prod{q}{\\indexbracket(\\Gamma^r)_{a b}}\n\\end{screen}\nThe result of the indexbracket way of storing expressions is that\n``index free'' manipulations apply directly inside the indexbracket\nargument and no special algorithms are needed. Input will\nautomatically be converted to this form. Getting rid of indexbrackets\naround single symbols is done using \\subscommand{remove\\_indexbracket}.\n\nAnother issue is the storage of numbers.  Since pure numerical factors\nare only allowed to appear in the multiplier field of a node, a pure\nnumber is stored as ``1'' with its multiplier equal to the\nnumber. Product nodes with two arguments of which one is a number are\nnot allowed and will be converted to a single node with multiplier\nfield, automatically.\n\nIn order to eliminate ambiguities concerning multipliers in sum and\nproduct nodes, the following rules should be obeyed: sum nodes always\nhave unit multiplier (i.e.~non-trivial multipliers are associated to\nthe children) and children of product nodes should also always have\nunit multiplier (i.e.~the multipliers of all the children should in\nthis case be collected in the prod node itself).\n\n\\subsection{External scalar engine interface}\n\n\\Cdb is a tensor computer algebra system, without much functionality\nfor simplification or manipulation of scalar expressions. Other\nsystems exist which handle this much better, and it is a waste to\nduplicate those efforts. Therefore, the \\cdbclass{algorithm} class\ncontains functionality to isolate scalar factors from a tensorial\nexpression, manipulate them using an external scalar CAS, and\nre-insert them into the internal \\cdb tree.\n\nScalar expressions are defined to be sums or (subsets of factors of)\nproducts which contain no objects with subscript or superscript\nchildren (i.e.~contain no tensors). \n\nExporting a scalar expression to an external CAS requires a rewriting\nstep before and after the export. At present only Maxima's format is\nsupported.\n\n\n\n\\vfill\\eject\n\n\\section{Module implementation guide}\n\n\n\\subsection{Storage of numbers and strings}\n\nThere is a special memory area for the storage of rational numbers\n(with arbitrary-length integers for the numerator and denominator) as\nwell as for the storage of strings. \n\n\\subsection{Accessing indices}\n\nIndices are stored as ordinary child nodes. However, there are various\nways to iterate over all indices in a factor, which are more useful\nthan a simple iteration over all child nodes. \n\n\\subsection{Object properties}\n\nThe properties attached to a node in the tree can be queried by using\na lookup method in the {\\tt properties} namespace. Object properties\nare child classes of the {\\tt property} class, and contain the\nproperty information in a parsed form. The following code snippet\nillustrates how properties are dealt with:\n\\begin{screen}{0}\nAntiSymmetry *s=properties::get<AntiSymmetry>(it)\nif(s) {\n   // do something with the property info\n   }\n\\end{screen}\nHere we used a property called {\\tt AntiSymmetry}, which is declared\nin the the module header {\\tt modules/algebra.hh} (see the other\nheader files of the various modules for information about the\navailable property types). If the node pointed to by {\\tt it} has this\nproperty associated to it, the pointer {\\tt s} will be set to point to\nthe associated property node.  \\bfcomment{KP}{Better to use a property\n  example where the property node contains some additional\n  information, which can then be used.}\n\nIt is also possible to do this search in the other direction, that is,\nto find an object with a given property. \n\\begin{screen}{0}\nproperties::property_map_t::iterator \n               it=properties::get_pattern<GammaMatrix>();\nif(it!=properties::props.end()) {\n   // Now *(it->first) contains the name of a GammaMatrix object.\n   }\n\\end{screen}\n\\bfcomment{KP}{Instead of checking these things, it is better to throw\nexceptions, since that will make the code more readable and also the\nerror handling more uniform (it can go in one place instead of being\nrepeated).}\n\nSums and products inherit, in a certain way, properties of the terms\nand factors from which they are built up. This is true also for other\nfunctions. If you want to know whether a given node has such\n\\emph{inherited properties}, a simple call to \\verb|get<...>| is not\nsufficient. Instead, use the following construction:\n\\begin{screen}{0}\nMatrix *m=properties::get_composite<Matrix>(it)\nif(m) {\n   // do something with the property info\n   }\n\\end{screen}\nThese inheritance rules for composite objects are at present\nhard-coded but will be user-defineable at a later stage.\n\nIn addition to querying for object properties, some algorithms\nalso act on objects which encode their\nproperty in a special reserved node name. As an example, the \n\\subscommand{prodrule} acts on objects which carry a \\subsprop{Derivative}\nproperty, but it also acts on \\subscommand{cdb\\_Derivative} objects. This\nallows e.g.~the \\subscommand{vary} algorithm to wrap a derivative-like\nobject around powers and have \\subscommand{prodrule} expand that\n\n% \\begin{sectionunit}\n% \\title{Labelling and selection of expressions}\n% \n% \n% The kernel of \\cdb is completely separated from its user interface,\n% but the communication between the two uses a human-readable format.\n% In order to allow the front-end to refer to individual elements of\n% the expressions, a simple labelling scheme is used for every \n% node in an expression. The \\cdb kernel output thus looks like\n% \\begin{screen}{0}\n% \\Gamma@1_{m@2} \\Gamma@3_{n@4} \\Gamma@5_{p@6}\n% \\end{screen}\n% All symbols have been labelled with a unique\n% numerical identifier. When you select the two gamma symbols, the\n% front-end notifies the core of this action by sending back the\n% identifiers ``1'' and ``3''. Upon receipt of the command {\\tt @join}\n% the core then knows to which objects this algorithm should apply.  In\n% the absence of a front-end, you can do the selection by hand: just\n% send the command {\\tt @select} to the core, followed by a comma\n% separated bracketed argument list of numerical identifiers. There also\n% exist an {\\tt @unselect} command.\n% \n% \n% \n\n\\subsection{Writing a new algorithm module}\n\\label{s:writing_new}\n\nAll functionality of cadabra that goes beyond storage of the\nexpression trees is located in separate modules, stored in the\n\\verb|src/modules| subdirectory. New functionality can easily be added\nby writing new modules. All algorithm objects derive from the\n\\verb|algorithm| object defined in \\verb|src/algorithm.hh|, and only\na couple of virtual members have to be implemented.\n\\begin{figure}[p!]\n\\begin{screen}{0}\nclass str_node {\n   public:\n      ...\n};\n\\end{screen}\n\\caption{The node class.\\label{f:str_node}}\n\\end{figure}\n\\begin{figure}[p!]\n\\begin{screen}{0}\nclass algorithm {\n  public:\n    typedef exptree::iterator         iterator;\n    typedef exptree::sibling_iterator sibling_iterator;\n  \n    algorithm(exptree&, iterator&);\n  \n    virtual void     description() const=0;\n    virtual bool     can_apply(iterator&);\n    virtual bool     can_apply(sibling_iterator&, sibling_iterator&);\n    virtual result_t apply(iterator&);\n    virtual result_t apply(sibling_iterator&, sibling_iterator&);\n\n    sibling_iterator args_begin() const;\n    sibling_iterator args_end() const;\n    unsigned int     number_of_args() const;\n\n    exptree&  tr;\n    iterator this_command;\n};\n\\end{screen}\n\\caption{The relevant members of the class interface for the {\\tt algorithm}\n  object. The virtual members and the constructor have to be\n  implemented in new algorithm objects; see the main text for an\n  explanation of the two versions of {\\tt can\\_apply} and {\\tt apply}.}\n\\label{f:algorithm}\n\\end{figure}\n\\begin{figure}[p!]\n\\begin{screen}{0}\nclass exptree {\n  public:\n    sibling_iterator arg(iterator, unsigned int) const;\n    unsigned int     arg_size(sibling_iterator) const;\n    multiplier_t     arg_to_num(sibling_iterator, unsigned int) const;\n};\n\\end{screen}\n\\caption{The relevant members of the class interface for the {\\tt exptree}\nobject.}\n\\end{figure}\n\nThe class interface for the algorithm object is shown in\nfigure~\\ref{f:algorithm}.  The members which any class derived from\n{\\tt algorithm} should implement are described below.\n\\begin{description}\n\\item[{\\tt constructor(exptree\\&, iterator)}] Algorithm objects get\ninitialised with a reference {\\tt tr} to the expression tree on which\nthey act, together with an iterator {\\tt this\\_command} pointing to\nthe associated command node. By looking at the child nodes of the\nlatter, the arguments of the command can be obtained. The simplest way\nto do this is to use the sibling iterators returned by\n\\verb|args_begin()| and \\verb|args_end()|; these automatically skip\nthe argument which refers to the equation number (i.e.~they skip the\n\\verb|(5)| argument in \\verb|@command(5){arg1}{arg2}|). The\nconstructor is a good place to parse the command arguments, since that\nwill in general only be required once. Do not do anything in the\nconstructor that has to be done on every invocation of the same\ncommand on different expressions.\n\nIf you discover that the arguments passed to an algorithm are \nnot legal, you have to throw an {\\tt algorithm::constructor\\_error}\nexception.\n\\item[{\\tt description()}] Should display an explanation of the\nfunctionality of the algorithm on the {\\tt txtout} stream. Do not\nadd \\verb|std::endl| newlines by hand, these will be inserted\nautomatically.\n\\item[\\hbox{\\tt bool can\\_apply(iterator)}] \nDetermines whether the algorithm has a chance\nof acting on the given expression. This is an \\emph{estimate} but is\nrequired to return {\\tt true} if there is a possibility that the\nalgorithm would yield a change. It is allowed to return {\\tt true}\nand then still not do anything when {\\tt apply} is called.\n\nIt takes an {\\tt iterator} as argument, which indicates the node at\nwhich the algorithm is supposed to act.\n\nSince {\\tt can\\_apply} is guaranteed to be called before {\\tt apply},\nit is allowed for the {\\tt can\\_apply} member to store results for later use in\n{\\tt apply}. However, multiple calls can be made to this combo, so\nany data stored should be erased upon each call to {\\tt can\\_apply}.\n\\item[\\hbox{\\tt apply\\_result apply(iterator\\&)}]\nThis is where the actual algorithm is applied. It is allowed to\nmodify the iterator if necessary. No elements in the tree which sit\nabove the entry point should ever be changed. \n\n\\fixme{It should also be disallowed that an algorithm unwraps the\n  single node which it has been given into multiple nodes, because\n  the returned iterator cannot propagate this information to the\n  caller. {\\tt cleanup\\_nests} does this wrong.}\n\nBefore exiting this function, the member variable {\\tt\nexpression\\_modified} has to be set according to whether or not the\napply call made any changes to the expression.\n\nIf the algorithm can take a long time to complete and you want to give\nthe user the option of interrupting it with control-C, you can check\n(at points where the algorithm can be interrupted) the global variable\n{\\tt interrupted}. If it is set, you should immediately throw an\nexception of type {\\tt algorithm\\_interrupted}, preferably with a\nshort string describing the location or algorithm at which the\ninterrupt occurred. The exception will be handled at the top level in\nthe {\\tt manipulator.cc} code, where the current expression will be\nremoved. \n%\n%Do not forget to unset it afterwards. If you exit an\n%algorithm this way, your module should leave the expression tree in\n%exactly the same way as it was when the {\\tt apply} member was\n%entered. Return \\verb|l_error| to signal failure.\n\nAlgorithms can write progress information to the stream {\\tt txtout}\nand debug information (which will go into a separate file on disk) to\n{\\tt debugout}. These are global objects. Do not use the \\Cpp streams\n{\\tt std::cout} and {\\tt std::cerr} for this purpose.\n\\end{description}\nAn algorithm is \\emph{never} allowed to modify the tree above the node\nor range of sibling nodes which were passed to the \\verb|apply|\ncall. In other words, siblings and parent nodes should never be\ntouched, and the nodes should not be removed from the tree\ndirectly. If you want to remove nodes, this can be done by setting\ntheir multiplier field to zero; the core routines will take care of\nactually removing the nodes from the tree. It is allowed to inspect\nthe tree above the given nodes, but this is discouraged. \\fixme{What\n  does this mean?}\n\nUpon any exit from an algorithm module, the tree is required to be in\na valid state. In many cases, it is useful to clean up modifications\nto the tree by calling the utility function {\\tt cleanup\\_expression}\n(see section~\\ref{s:utility} for more information).\n\n\n\\subsection{Adding the module to the system}\n\nOnce you have written the \\verb|.hh| and \\verb|.cc| files associated\nto your new algorithm, it has to be added to the build process and the\ncore program. First, add the header to the master header file\n\\verb|src/modules/modules.hh| file; this one looks like\n\\begin{screen}{0}\nsrc/modules/modules.hh:\n\n#include \"algebra.hh\"\n#include \"pertstring.hh\"\n#include \"select.hh\"\n...\n\\end{screen}\nYou also have to add it to the \\verb|src/Makefile.in|. Near the top of\nthis file you find a line looking somewhat like\n\\begin{screen}{0}\nsrc/Makefile.in:\n\n...\nMOBJS=modules/algebra.o modules/pertstring.o modules/convert.o \\\n      modules/field_theory.o modules/select.o modules/dummies.o \\\n      modules/properties.o modules/relativity.o modules/substitute.o\n...\n\\end{screen}\nand this is where your module has to be added. Finally, you have to\nmake the algorithm visible to the core program. This is done in the\n\\verb|src/manipulator.cc| file. In the constructor of the\n\\verb|manipulator| class (defined somewhere near the top), you see a\nmap of names to algorithm classes. A small piece is listed below:\n\\begin{screen}{0}\nsrc/manipulator.cc:\n\n...\n// pertstring\nalgorithms[\"@aticksen\"]       =&create<aticksen>;\nalgorithms[\"@riemannid\"]      =&create<riemannid>;\n\n// algebra\nalgorithms[\"@distribute\"]     =&create<distribute>; \n ...\n\\end{screen}\nAdd your algorithm here; it does not have to have the same name as the\nobject class name. Once this is all done, rerun configure and make.\n\n\n\\subsection{Adding new properties}\n\n\\begin{figure}[t]\n\\begin{screen}{0}\nclass property\\_base{\n  public:\n    virtual bool        parse(exptree&, iterator pat, iterator prop);\n    virtual std::string name() const=0;\n    virtual void        display(std::ostream&) const;\n};\n\nclass property      : public property\\_base {};\nclass list\\_property : public property\\_base {};\n\nclass labelled\\_property : public property {\n  public:\n    std::string label;\n};\n\\end{screen}\n\\caption{The relevant members of the class interface for the {\\tt\n\t property\\_base} object and the derived objects.}\n\\end{figure}\n\n\\bfcomment{KP}{Discuss the various member functions of property, in\nparticular the way in which parse is supposed to behave, and the way\nin which properties should be registered.}\nSince algorithms rely crucially on a \\emph{fixed} set of properties\nwhich they provide themselves, we store these things in a \\Cpp way,\nrather than using strings. Another motivation: we do not want to parse\n(and check) these property trees every time they are accessed. \n\nProperties typically carry key/value pairs which further specify \nthe characteristics of the property. When the property object is\ncreated, the core calls the \\verb|parse()| method of the property, in\nwhich you are responsible for scanning through the list of key/value\npairs. This is rather simple: just call the \\verb|find()| member of\nthe \\verb|keyval| argument,\n\\begin{screen}{0}\nkeyval_t::iterator ki=keyvals.find(\"dimension\");\nif(ki!=keyvals.end()) {\n    // now ki->second is an iterator to an expression subtree\n    }\n\\end{screen}\nYou are supposed to remove any handled keyval pair from the list by\nusing the \\verb|erase()| member, so that the system can keep track of\nunhandled pairs.  Do not forget to call the \\verb|parse()| method of\nall parent classes at the end.\n\nOnce this is all done, register the property with the system by adding\nan appropriate call to the module's \\verb|register_properties()|\nmethod, found at the top of each module.\n\n\\subsection{Throwing errors}\n\nIf, at any stage, an inconsistent expression is encountered, the safe\nway to return to the top level of the manipulator is to throw the\nexception class \\cdbclass{consistency\\_error} (defined in \\cdbfile{algorithm.hh}).\n\n\n\\subsection{Manipulating the expression tree}\n\nThe \\cdbclass{exptree} class contains a number of tree access routines\nwhich enhance the functionality of the {\\tt tree.hh} library. \n\\begin{description}\n\\item[\\member{index\\_iterator}] \n\\item[\\member{index\\_map\\_t}]\n\\end{description}\n\n\\subsubsection{Acting on products or single terms}\n\nuse \\member{is\\_single\\_term} inside \\member{can\\_apply} to test for\nthis case. Then in \\member{apply} call\n\\member{prod\\_wrap\\_single\\_term} (which will be harmless for proper\nproducts). At the very end of \\member{apply}, call\n\\member{prod\\_unwrap\\_single\\_term} to remove the product again.\n\n\n\\subsection{Utility functions}\n\n\\label{s:utility}\nThere are also various useful helper functions in the {\\tt exptree} \nclass, mainly dealing with the conversion of expression numbers or\nlabels to iterators that point to the actual expression in the tree.\n\\begin{description}\n\\item[\\vbox{\\hbox{\\member{cleanup\\_expression(exptree\\&)}}\n            \\hbox{\\member{cleanup\\_expression(exptree\\&, iterator)}}}]\nConverts an expression (or part of it below the indicated node) to\na valid form. That is, it calls various simplification algorithms\non the expression, among which {\\tt sumflatten} and {\\tt prodcollectnum}. \n\n\\item[\\member{cleanup\\_nests}] When called on a product inside a\n  product, or a sum inside a sum, and the bracket types of both node\n  and parent are the same, flatten the tree. Adjusts the iterator to\n  point to the product or sum node which remains.\n\n\\item[\\member{equation\\_by\\_number\\_or\\_name}] Given an iterator\nto a node that represents an expression number or expression label,\nthis member returns an iterator that points to the actual node\n(to be precise: to the \\verb|\\history| node of the expression).\n\n\\item[\\vbox{\\hbox{\\member{arg\\_size(sibling\\_iterator)}}\n      \\hbox{\\member{arg(iterator, unsigned int)}}}]\nMany algorithms require one \\emph{or more} objects as arguments. These\nare usually passed as lists, and therefore end up being of two forms:\neither they are single objects or they are {\\tt comma} objects\nrepresenting a list. In order to avoid having to check for these two\ncases, one can use these two member functions.\n\nThe iterator arguments of these two member functions should point to\nthe child which is either a single argument or a \\texcommand{comma}\nnode.\n\n\\item[\\member{pushup\\_multiplier}] Can be called on any node. If the\n  node has a non-unit multiplier and the storage conventions exclude\n  this, the algorithm will push the multiplier up the tree.\n\\end{description}\n% \\begin{itemize}\n% \\item The various comparison functions in str\\_node.\n% \\item Members of active\\_node and algorithm.\n% \\item Multiply, add, zero and one in these classes.\n% \\end{itemize}\n\n\n\\subsection{Writing a new output module}\n\n\n\\kcomment{KP}{Structure is different now: one inherits from {\\tt\noutput\\_exptree} and then has printing stuff at ones disposal. Still\nwould be nice to be able to change the printing objects for a given\nnode type, i.e.~modify the map of node names to printing objects.}\n\n\\kcomment{KP}{Also do something intelligent with the Mathematica\noutput flags}.\n\n\n\\subsection{Namespaces and global objects}\n\nThe following objects are global:\n\\begin{description}\n\\item[{\\tt modglue::opipe txtout}] \nThe normal output stream, to which you should communicate with the user.\n\\item[{\\tt std::ofstream debugout}]\nThe debug output stream, which normally writes to a file, and should\nonly be used to write output which is useful for debugging purposes.\n\\item[{\\tt nset\\_t name\\_set}]\nThe global collection of all strings. Nodes in the expression tree\ncontain an iterator into this map (see in particular figure~\\ref{f:str_node}).\n\\item[{\\tt rset\\_t rat\\_set}]\nThe global collection of all rational numbers. Nodes in the expression\ntree contain an iterator into this map (see in particular figure~\\ref{f:str_node}).\n\\item[{\\tt bool interrupted}]\nA global flag which indicates that the user has requested the\ncomputation to be interrupted. See section~\\ref{s:writing_new} for\nmore information on this variable.\n\\item[{\\tt stopwatch globaltime}]\nThe wall time since program start.\n\\item[{\\tt unsigned int size\\_x, size\\_y}] The size of the current\n  output window.\n\\end{description}\n\n% \\subsection{Troubleshooting}\n% \n% \\begin{description}\n% \\item[Problems getting expressions in canonical form]\n% There are various canonical places to look for errors. One of\n% them is the routine {\\tt propagate\\_zeroes}, which may still not remove\n% zeroes properly but leave an inconsistent tree. Another place\n% is {\\tt cleanup\\_nests}.\n% \\end{description}\n\\vfill\\eject\n\n% \\section{Future plans}\n% \\subsection{Front-ends}\n% \n% \n% %The text-mode front-end will be based on {\\tt eqascii} by\n% %\\dcite{e_bori1}, while the graphical front-end will use \n% %\\TeX{} for typesetting.\n% \n% \\subsection{Component calculations}\n\n%\\vfill\\eject\n\n\n% \\begin{sectionunit}\n% \\title{Using the history mechanism}\n% \n% Let us first discuss an example which shows the way in which the \\cdb\n% history mechanism works, and also exhibits the selection mechanism. \n% As with all other data structures in \\cdb, the history is also a\n% tree-like structure. Expressions and commands get appended as children\n% of each other. When you backtrack by going to a previous expression in\n% the history, any new commands get added as child, thereby keeping\n% the previous calculations based on that node accessible. An\n% example illustrates how this works.\n% \\begin{screen}{0}\n% > \\Gamma_{m} \\Gamma_{n}\n% \t (1)    : \\Gamma_{m} \\Gamma_{n}\n% > @join{(1), 1, 2}\n% \t (1)    : \\Gamma_{m n} + \\eta_{m n}\n% > \\Gamma_{m n} = \\epsilon_{p q r s} \\Gamma^{p q r s} \\tilde\\Gamma\n% \t (1)    : \\Gamma_{m n} + \\eta_{m n}\n% \t (2)    : \\Gamma_{m n} = \\epsilon_{p q r s m n} \\Gamma^{p q r s} \\tilde\\Gamma\n% > @subs{(2), (1)}\n% \t (1)    : \\epsilon_{p q r s m n}\\Gamma^{p q r s}\\tilde\\Gamma + \\eta_{m n}\n% \t (2)    : \\Gamma_{m n} = \\epsilon_{p q r s} \\Gamma^{p q r s} \\tilde\\Gamma\n% > \\eta_{m n} = 0\n% \t (1)    : \\epsilon_{p q r s m n}\\Gamma^{p q r s}\\tilde\\Gamma + \\eta_{m n}\n% \t (2)    : \\Gamma_{m n} = \\epsilon_{p q r s} \\Gamma^{p q r s} \\tilde\\Gamma\n% \t (3)    : \\eta_{m n} = 0\n% > @up((1))\n% \t (1)    : \\Gamma_{m n} + \\eta_{m n}\n% > @subs{(3), (1)}\n% \t (1)    : \\Gamma_{m n}\n% \t (2)    : \\Gamma_{m n} = \\epsilon_{p q r s} \\Gamma^{p q r s} \\tilde\\Gamma\n% \t (3)    : \\eta_{m n} = 0\n% \\end{screen}\n% Notice how the modification of equation~(1) has produced a new\n% equation, but it has kept the original expression in memory as well.\n% You can see the history of an equation by doing\n% \\begin{screen}{0}\n% > @showtree((1))\n% \t input\n% \t (1)         : \\Gamma_{m} \\Gamma_{n}\n% \t\tjoin\n% \t\t(1.1)     : \\Gamma_{m n} + \\eta_{m n}\n% \t\t  subs\n% \t\t  (1.1.1) : \\epsilon_{p q r s m n}\\Gamma^{p q r s}\\tilde\\Gamma + \\eta_{m n}\n% \t\t  subs\n% \t\t  (1.1.2)*: \\Gamma_{m n}\n% \\end{screen}\n% The star indicates which equation is currently denoted with~(1) in the\n% compact output. If you are not interested in the paths that led to\n% other expressions, then it is sufficient to do\n% \\begin{screen}{0}\n% > @showhistory((1))\n% \t input  : \\Gamma_{m} \\Gamma_{n}\n% \t join   : \\Gamma_{m n} + \\eta_{m n}\n% \t subs   : \\Gamma_{m n}\n% \\end{screen}\n% This can be used to generate a clean report of all the manipulations\n% that lead up to a certain result. If you are confident that you do not\n% anymore need any of the branches except the one that leads to the\n% last result, you can enter the \\verb|@cleanhistory| command.\n% \n\n\n\n\n\\printindex\n\\bibliographystyle{kasper}\n\\bibliography{kasbib}\n\\end{document}\n\n\n\n\n\n% \\begin{sectionunit}\n% \\title{Cursor mode}\n% \n% At any time, pressing `escape' will jump to the `cursor' mode. In this\n% mode, one can select and unselects parts of the expression. Available\n% commands:\n% \\begin{center}\n% \\begin{tabular}{ll}\n% cursor-right & move cursor to next object on this level \\\\[1ex]\n% cursor-left  & move cursor to previous object on this level \\\\[1ex]\n% cursor-down  & move cursor to the arguments of the current\n% objects\\\\[1ex]\n% cursor-up    & move cursor to the parent of the current object\\\\[1ex]\n% page-down    & enlarge cursor size \\\\[1ex]\n% page-up      & shrink cursor size \\\\[1ex]\n% e            & remove all selections \\\\[1ex]\n% space        & select the objects currently under the cursor\n% \\end{tabular}\n% \\end{center}\n% \n\n\n\\begin{enumerate}\n\\item Work both with abstract component tensors as well as individual\ncomponents. The algorithms for e.g.~gamma matrix manipulation have to\nrecognise this (not just flip indices around, but actually use\n$\\Gamma^1 \\Gamma^1=1$ and so on).\n\n\\end{enumerate}\n"
  },
  {
    "path": "doc/cadabra2_hep.tex",
    "content": "\\documentclass[11pt]{article}\n\\usepackage[textwidth=460pt,textheight=660pt]{geometry}\n\\usepackage[usenames,dvipsnames]{color}\n\\usepackage{fancyvrb}\n\\usepackage{relsize}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage{graphicx}\n\\usepackage[urlcolor=blue,citecolor=blue,colorlinks]{hyperref}\n\\usepackage{fleqn}\n\\usepackage{xspace}\n\\usepackage[bottom]{footmisc}\n\\usepackage[numbers,sort&compress]{natbib}\n\\usepackage{tableaux}\n\n\\fvset{frame=none,framerule=0.1pt,framesep=6pt,numbers=left,xleftmargin=25pt,fontfamily=tt,fontsize=\\small}\n\\newenvironment{hanging}\n    {\\begin{list}{}{\\setlength\\itemsep{0pt}%\n \\setlength\\topsep{0pt}%\n \\setlength\\leftmargin{25pt}%\n \\setlength\\itemindent{0pt}%\n \\setlength\\listparindent{\\itemindent}}%\n     \\item[]}\n    {\\end{list}}\n\n\\newcommand{\\toprule}{\\par\\vspace{1ex}\\noindent\\hspace{25pt}\\rule{435pt}{.1pt}}\n\\newcommand{\\botrule}{\\noindent\\hspace{25pt}\\rule{435pt}{.1pt}\\\\[2ex]}\n\\newcommand{\\botrulem}{\\noindent\\hspace{25pt}\\rule{435pt}{.1pt}}\n\\newenvironment{cdbin}{\\fvset{firstnumber=1}\\color[named]{Blue}\\Verbatim}{\\endVerbatim}\n\\newenvironment{cdbcont}{\\fvset{firstnumber=last}\\color[named]{Blue}\\Verbatim}{\\endVerbatim}\n\\newenvironment{cdbout}{\\vspace{-1.4ex}\\begin{equation}}{\\end{equation}\\vspace{-1.4ex}}\n\\newenvironment{cdbcom}{\\begin{hanging}}{\\end{hanging}}\n\\setlength{\\abovedisplayskip}{0pt}\n\\setlength{\\abovedisplayshortskip}{0pt}\n\\setlength{\\belowdisplayskip}{-5pt}\n\\setlength{\\belowdisplayshortskip}{-5pt}\n\n\\newcommand{\\cdb}{{cadabra}\\xspace}\n\\newcommand{\\Cdb}{{Cadabra}\\xspace}\n\n\\begin{document}\n\\pagestyle{empty}\n\\begin{flushright}\n%SPIN-06/46\\\\\n%ITP-UU-06/56\\\\\nhep-th/0701238\\\\\n25 January 2007\\\\\n3 April 2018 (update for v2 syntax)\n\\end{flushright}\n\\vskip 7ex\n\n\\begin{center}\n\\begin{minipage}{.95\\textwidth}\n{\\huge\\bf Introducing Cadabra: a symbolic computer\\\\[1ex]  \nalgebra system for field theory problems}\\\\[7ex]\n{\\large\\bf Kasper Peeters}\\\\[5ex]\nDepartment of Mathematical Sciences\\\\\nDurham University\\\\\nSouth Road\\\\\nDurham DH1 3LE\\\\\nUnited Kingdom\\\\[3ex]\n%Institute for Theoretical Physics\\\\\n%Utrecht University\\\\\n%P.O.~Box 80.195\\\\\n%3508 TD Utrecht,\\\\\n%The Netherlands\\\\[3ex]\n{\\tt kasper.peeters@durham.ac.uk}\n\\vskip 9ex\n\n{\\bf Abstract:}\\\\[1ex] Cadabra is a new computer algebra system\ndesigned specifically for the solution of problems encountered in\nfield theory. It has extensive functionality for tensor polynomial\nsimplification taking care of Bianchi and Schouten identities, for\nfermions and anti-commuting variables, Clifford algebras and Fierz\ntransformations, implicit coordinate dependence, multiple index types\nand many other field theory related concepts. The input format is a\nsubset of \\TeX{} and thus easy to learn. Both a command-line and a\ngraphical interface are available. The present paper is an\nintroduction to the program using several concrete problems from\ngravity, supergravity and quantum field theory.\n\\end{minipage}\n\\vfill\\vfill\n\n\\begin{minipage}{0.95\\textwidth}\n\\noindent{\\smaller\\smaller This paper originally appeared in 2007. It\n  has been updated to reflect the syntax changes introduced with\n  Cadabra~2.x (first released in 2016), but is otherwise essentially\n  unchanged. A more in-depth discussion of the changes of the 2.x\n  series will appear in an upcoming paper. The software itself,\n  including source code, can be obtained from the web site\n  \\url{http://cadabra.science/} where further documentation and\n  tutorial notebooks can also be found.}\n\\end{minipage}\n\\end{center}\n\\eject\n\\pagestyle{plain}\n\\hrule\n\\tableofcontents\n\\vspace{4ex}\n\\hrule\n\\bigskip\n\n\\section{Introduction}\n\nThe currently available spectrum of symbolic computer algebra software\nexhibits, from the perspective of a high-energy physicist, an\nunfortunate deficiency. On the one hand, problems dealing with\ndifferential equations, symbolic matrix algebra, special functions,\nseries expansions, polynomial algebra and so on are adequately\ncovered, often by several different systems. It is not too hard to\ntranslate a give physics problem in these classes from paper to\ncomputer and back. Other common problems, on the other hand, such as\napplying symmetry transformations to Lagrangians, computing Poisson\nbrackets, deriving field equations, canonicalising tensor expressions\nor performing Fierz transformations, are much harder to handle using\nexisting symbolic computer algebra tools. For these classes of problems,\nwhich one could label as ``field theory problems'', it typically takes\nmuch more effort to convert them from paper and solve them on the computer.\n\nGranted, there are many smaller systems, often built on top of general\npurpose systems such as Mathematica or Maple, which solve one or more\nof these problems.\\footnote{Among the more often-used recently written\npackages there is {\\tt GAMMA} for gamma matrix\nalgebra~\\cite{Gran:2001yh}, {\\tt grassmann.m} for handling of\nanti-commuting variables~\\cite{e_grassmann} and the extensive {\\tt\nxAct} for tensor manipulation~\\cite{e_xact}. This list is far from\ncomplete and only meant to illustrate how much work one has to do in\norder to teach a general-purpose symbolic computer algebra system\nabout even the simplest concepts which occur in field theory.}\nHowever, writing such packages, or even adapting them for slightly\nmore complicated situations than for which they were intended, is\noften far from easy, and requires a substantial knowledge of the\nunderlying computer algebra system. Moreover, combining them, such\nthat e.g.~a tensor manipulating package can deal with fermions too, is\ntypically a tedious exercise, if possible at all. There are clear\ntechnical reasons for this, rooted in the design of general purpose\ncomputer algebra systems. However, rather than dwelling on these\ndeficiencies, it is more productive to actually come up with a better\nsolution.\n\nThe present paper is an introduction to a new computer algebra system,\ncalled ``Cadabra'', which is designed from the start with field theory\nproblems in mind. By discussing a number of explicit sample problems\nrepresentative of the ``field theory'' class vaguely defined above,\nthis paper is intended as a guide for users rather than computer\nscientists (for those interested, a description of the technical\nimplementation and code design goals has appeared\nin~\\cite{Peeters:2006kp}).\n\n\\medskip\n\nIn which sense does \\Cdb differ from other computer algebra systems?\nThe first and most easily visible feature is that all expression input is in\nthe form of a subset of \\TeX. Tensor indices, Dirac conjugation,\nderivative operators, commutators, fermion products and so on are all\nwritten just as in \\TeX.  With a little bit of discipline, one can\ncut-and-paste expressions straight from a paper into a \\Cdb\nnotebook. The output, similarly, is typeset as \\TeX{} would do it, and\n\\Cdb notebook files are in fact at the same time also valid \\TeX{}\nfiles (the program comes with a graphical notebook interface, but can\nalso be used from the command line).\n\nSecondly, \\Cdb contains some of the most powerful tensor expression\nsimplification routines available at present. Not only does it use\nsimple symmetry or anti-symmetry of tensors or tensor indices in order\nto simplify expressions\\footnote{I am grateful to Jos\\'e\nMart\\'\\i{}n-Garc\\'\\i{}a for allowing me to use his excellent {\\tt\nxPerm} code~\\cite{e_xact} for this purpose.}, it also takes into\naccount multi-term relations such as the Bianchi identity, as well as\ndimension-dependent relations such as the Schouten identity\n(section~\\ref{s:bianchi}). The program handles commuting as well as\nanti-commuting tensors, allows for multiple index sets\n(section~\\ref{s:example2}), and knows about the concept of a dummy\nindex so that no special wildcard notation is ever needed when\nhandling tensor indices.\n\nThirdly, the program knows about many concepts which are common in\nfield theory. It handles anti-commuting and non-commuting objects\nwithout special notations for their products (section~\\ref{s:other}),\nit knows about gamma matrix algebra (section~\\ref{s:gamma}), Fierz\nidentities (section~\\ref{s:example3}), Dirac conjugation, vielbeine,\nflat and curved, covariant and contravariant indices\n(section~\\ref{s:other}), implicit dependence of tensors on\ncoordinates, partial and covariant derivatives\n(section~\\ref{s:derivatives}). It has extensive facilities for handling\nof field theory expressions, e.g.~dealing with variational\nderivatives. It features a substitution command which correctly\nhandles anti-commuting objects and dummy indices and offers a wide\nvariety of pattern matching situations which occur in field theory.\n\nFourthly, the program has special support that allows the user to\nwrite (and keep) expressions in any desired form, e.g.~to specify the\npreferred order of objects. The program does not try to do anything\nsmart unless it is explicitly told to do so. However, when desired, it\nis always possible to add any arbitrary simplification step to a list\nof commands which is executed at every step of the calculation.  In\nthis way one has precise control over the level of verbosity of\nthe intermediate results of a computation.\n\nFinally, the source code of the program is freely available, with\nextensive documentation on how to extend it with new algorithms and\nnew data types (e.g.~twistor variables are planned for an upcoming\nrelease). The program is completely independent of commercial software\nand relies only on a few other open source libraries and programs. It\nruns on Linux, Mac~OS~X, Windows and various BSD flavours and the\nsource code as well as binary packages can be downloaded from the web\nsite.\n\n\\medskip\n\nThe following sections discuss these characteristic features of \\Cdb,\nillustrated with many explicit calculations and several longer\nexamples (see in particular the Riemann tensor polynomial problem in\nsection~\\ref{s:example1}, the Kaluza-Klein gravity problem in\nsection~\\ref{s:example2} and the fermion Fierz problem in\nsection~\\ref{s:example3}). These examples were chosen to illustrate\nthe typical use of \\Cdb, in particular the way in which it fills a gap\nin the existing spectrum of computer algebra software. The web site\noffers a growing collection of longer sample calculations for those\nreaders who are interested in applications to more advanced problems.\nThe program is under active development and information about updates\nand new features can also be obtained from there.\n\n\\section{Bosonic basics}\n\\subsection{Tensors, indices and symmetries}\n\nBefore discussing actual calculations, let us start with a few words\nconcerning notation. This discussion can be short because, as\nmentioned in the introduction, mathematical expressions are entered\nessentially as one would enter them in \\TeX{} (with a few restrictions\nto avoid ambiguities, which we will discuss as we go along). In order\nto manipulate expressions, \\Cdb often needs to know a bit more about\nproperties of tensors or other symbols. Such properties are entered\nusing the `\\verb|::|' symbol. A simple example is the declaration of\nindex sets, useful for automatic dummy index relabelling. An example\nwill clarify this,\\footnote{The input and output shown in this paper\nare essentially identical to those in the graphical interface which\ncomes with \\Cdb, the only difference being the added line numbers and\nsome minor typographical modifications.}  \\toprule\n\\begin{cdbin}\n{ a, b, c, d }::Indices.\nex:= A_{a b} B_{b c};\n\\end{cdbin}\n\\begin{cdbout}\nA_{a b} B_{b c};\n\\end{cdbout}\n\\begin{cdbcont}\nsubstitute(_, $B_{a b} ->  C_{a b c} D_{c}$ );\n\\end{cdbcont}\n\\begin{cdbout}\nA_{a b} \\, C_{b c d} \\, D_{d};\n\\end{cdbout}\n\\botrule\nThe automatic index relabelling which has taken place in this\nsubstitute command was clearly only possible because of the property\ndeclaration in the first line. Note how the substitute command has\nalso figured out that \\verb|B_{a b}| on the left-hand side is\nequivalent to \\verb|B_{b c}|, without any explicit wildcards or\npatterns. We will see more of this type of field-theory motivated\nlogic throughout the paper.\n\nIndices can be simple letters, as in the example above, but it is also\nperfectly possible to put accents on them. This can be useful for\ne.g.~notations involving chiral spinors. The following example\nillustrates the use of accents on indices.\n\\toprule\n\\begin{cdbin}\nA_{\\dot{a} \\dot{b}}::AntiSymmetric.\nex:= A_{\\dot{b} \\dot{a}};\n\\end{cdbin}\n\\begin{cdbout}\nA_{\\dot{b} \\dot{a}};\n\\end{cdbout}\n\\begin{cdbcont}\ncanonicalise(_);\n\\end{cdbcont}\n\\begin{cdbout}\n(-1)\\,A_{\\dot{a} \\dot{b}};\n\\end{cdbout}\n\\botrule Here we also see a second usage of property declarations: the\nconstruction in the first line declares that the $A_{\\dot{a} \\dot{b}}$\ntensor is antisymmetric in its indices. The canonicalise command\nsubsequently writes the input in a canonical form, which in this\ntrivial example simply means that the indices gets sorted in\nalphabetical order.  Continuing the example above, one can also use\nsubscripts or superscripts on indices, as in the example below.\n\\vfill\\eject\n\\toprule\n\\begin{cdbin}\n{ a_{1}, a_{2}, a_{3}, a_{4} }::Indices(vector).\nex:= V_{a_{1}} W_{a_{1}}:\nsubstitute(_, $V_{a_{2}} -> M_{a_{2} a_{1}} N_{a_{1}}$ );\n\\end{cdbin}\n\\begin{cdbout}\nM_{a_{1} a_{2}} \\, N_{a_{2}} \\, W_{a_{1}};\n\\end{cdbout}\n\\botrule As this example shows in some more detail, the input format\nis a mixture of Cadabra's own LaTeX-like language for the description\nof mathematical expressions, and Python. The underscore symbol\n`\\verb|_|' always refers to the last-used expression.\n\nA guiding principle in \\Cdb is that nothing ever has to be declared\nunless this is absolutely needed. This is in contrast to many other\nsystems, where for instance one has to declare manifolds and index\nsets and so on before one can even enter a tensor expression. This\nmakes code hard to read, but more importantly, such additional\ndeclarations are hard to remember. As an example of how \\Cdb works,\none can e.g.~input tensor expressions and perform substitution on them,\nwithout ever declaring the symbols used for indices. Only when the\nprogram needs to generate new dummy indices does one need to declare\nindex sets, so that dummy indices can be taken out of the right\nset. The general guideline is that ``one only\nneeds to tell the program about the meaning of symbols when this is\nactually required to do the manipulation correctly''.\n\nIn order to declare symmetries of tensors, it is possible to use\nsimple shorthands like the \\verb|AntiSymmetric| in the example above. \nMore generally, symmetries can be declared using  a generic Young\ntableau notation. An object with the symmetries of a Riemann tensor,\nfor example, can be declared as in the following example.\n\\toprule\n\\begin{cdbin}\nR_{a b c d}::TableauSymmetry(shape={2,2}, indices={0,2,1,3}).\nex:=R_{a b c d} R_{d c a b}:\ncanonicalise(_);\n\\end{cdbin}\n\\begin{cdbout}\n(-1)\\, R_{a b c d}\\, R_{a b c d};\n\\end{cdbout}\n\\botrule\nThe first line indicates that the tensor has the symmetries of the\n\\raisebox{2ex}{$\\ftableau{ac,bd}$} tableau (the numbers in the \\verb|indices| argument\nrefer to the index positions). The \\verb|canonicalise| algorithm writes\nthe input in canonical form with respect to mono-term symmetries\n(anti-symmetry in the two index pairs and symmetry under pair\nexchange). The Ricci symmetry is also encoded in the Young tableau and\nwill be discussed later. Many tensor symmetries have shorthand\nnotations, so one often does not have spell out the tableau (e.g.~\\verb|RiemannTensor| or \\verb|SatisfiesBianchi|).\n\n\\subsection{Derivatives and dependencies}\n\\label{s:derivatives}\n\nThere are relatively few surprises when it comes to derivatives.\nIt is possible to write derivatives with respect to coordinates,\ni.e.~write~$\\partial_x$ where~$x$ is a coordinate, but\nit is also possible to use indices, as in~$\\partial_i$ with $i$ being\na vector index. It is also possible to make objects implicitly\ndependent on a derivative operator, so that one can write~$\\partial\nA$ without an explicit specification of the coordinate which is\ninvolved here. \n\nIn order to make this possible, however, derivative objects have to be\ndeclared just like indices, otherwise the system does not know which\nsymbol ($\\partial$, $D$, $d$, $\\nabla$, \\ldots) one wants to use for\nthem. Implicit dependencies of objects on coordinates associated to\nderivatives is indicated through a \\verb|Depends| property. Here is an\nexample to illustrate all this: \\toprule\n\\begin{cdbin}\n\\nabla{#}::Derivative.\n\\partial{#}::PartialDerivative.\nA_{m n}::AntiSymmetric.\nV_{m}::Depends(\\nabla{#}).\n\nex:= \\partial_{m p}( A_{q r} V_{n} ) A^{p m};\n\\end{cdbin}\n\\begin{cdbout}\n\\partial_{m p}( A_{q r} V_{n} ) A^{p m};\n\\end{cdbout}\n\\begin{cdbcont}\ncanonicalise(_);\n\\end{cdbcont}\n\\begin{cdbout}\n0;\n\\end{cdbout}\n\\begin{cdbcont}\nex:=\\nabla_{m p}( A_{q r} V_{n} ) A^{p m};\ncanonicalise(_);\n\\end{cdbcont}\n\\begin{cdbout}\n(-1) \\nabla_{m p}( A_{q r} V_{n} ) A^{m p};\n\\end{cdbout}\n\\begin{cdbcont}\nunwrap(_);\n\\end{cdbcont}\n\\begin{cdbout}\n(-1) A_{q r} \\nabla_{m p}{ V_{n} } A^{m p};\n\\end{cdbout}\n\\botrule\nNote how the symmetry of a double partial derivative has automatically\nbeen taken into account (it\nis part of the \\verb|PartialDerivative| property). This is called\n``property inheritance''.\n\n\n\\subsection{Bianchi, Ricci and Schouten identities}\n\\label{s:bianchi}\n\nSo far we have seen several examples of so-called ``mono-term''\ncanonicalisation, in which simple symmetries of tensors are used,\nwhich relate one particular term to one particular other term. More\ncomplicated symmetries are Ricci or Bianchi identities, which relate\nmore than two terms (``multi-term'' symmetries). Such identities can\nbe taken into account using Young tableau projectors. Here is an\nexample to show how this works.  \n\\toprule\n\\begin{cdbin}\n{m,n,p,q,r,s,t#}::Indices(vector).\n\\nabla{#}::Derivative.\nR_{m n p q}::RiemannTensor.\n\\nabla_{m}{R_{p q r s}}::SatisfiesBianchi.\n\\end{cdbin}\n\\begin{cdbcom}\nThe last line is a shorthand, but internally does nothing more than to\nassociate a particular Young tableau symmetry to the given\ntensor.\\footnote{The alternative is\n{\\tt $\\backslash$nabla\\_\\{m\\}\\{R\\_\\{p q r s\\}\\}::TableauSymmetry( shape=\\{3,2\\}, indices=\\{1,3,0,2,4\\} ).} \nwhich makes use of the more general tableau symmetry property which we\nhave seen earlier.} Here it effectively associates the $\\nabla$\noperator to the Riemann tensor. We can see this in action, for\ninstance, by verifying that the Bianchi identity indeed holds,\n\\footnote{The {\\tt depth=1} parameter of the\n  {\\tt young\\_project\\_tensor} algorithm indicates that this command\n  should only be applied at ``level 1'' of the expression, i.e.~at the\n  level of the terms of the sum.}\n\\end{cdbcom}\n\\begin{cdbcont}\nex:= \\nabla_{m}{R_{p q r s}} + \\nabla_{p}{R_{q m r s}} + \\nabla_{q}{R_{m p r s}}:\nyoung_project_tensor(_, depth=1, modulo_monoterm=True);\n\\end{cdbcont}\n\\begin{cdbout}\n0\n\\end{cdbout}\n\\botrule\nAs expected, by Young-projecting the expression, the Bianchi identity\nbecomes manifest~\\cite{Green:2005qr}.\n\nA similar logic can also be used~\\cite{kas_dimdep} to take into\naccount dimension-dependent identities, more generally known as\nSchouten identities or Lovelock identities. Take as an example two\nanti-symmetric tensors~$A_{m n p}$ and~$B_{m n p}$. Then we have\n\\begin{equation}\nA_{m n p} B_{m n q} - A_{m n q} B_{m n p} = 0 \\quad\\text{in $d=3$,}\n\\end{equation}\nwhich is conventionally proved by using the fact that\nanti-symmetrising in four indices yields zero in three dimensions.\n\\Cdb instead uses Young tableau product rules to accomplish the same\nresult~\\cite{kas_dimdep}. \n\\toprule\n\\begin{cdbin}\n{ m, n, p, q }::Indices(vector).\n{ A_{m n p}, B_{m n p} }::AntiSymmetric.\nA_{m n p} B_{m n q} - A_{m n q} B_{m n p};\n\\end{cdbin}\n\\begin{cdbout}\nex:= A_{m n p} B_{m n q} - A_{m n q} B_{m n p};\n\\end{cdbout}\n\\begin{cdbcom}\nIn four dimensions or higher, this product cannot be simplified any\nfurther. Decomposing the product using Young projectors and\ncanonicalising with respect to monoterm symmetries gives back the input,\n\\end{cdbcom}\n\\begin{cdbcont}\n{ m, n, p, q }::Integer(1..4).\ndecompose_product(_)\ncanonicalise(_);\n\\end{cdbcont}\n\\begin{cdbout}\nA_{p m n} B_{q m n} - A_{q m n} B_{p m n};\n\\end{cdbout}\n\\begin{cdbcom}\nIn three dimensions, however, the expression vanishes by virtue of the\nSchouten identity. The same procedure as above now indeed produces a zero,\n\\end{cdbcom}\n\\begin{cdbcont}\n{ m, n, p, q }::Integer(1..3).\ndecompose_product(_)\ncanonicalise(_);\n\\end{cdbcont}\n\\begin{cdbout}\n0; \n\\end{cdbout}\n\\botrule\nSome more examples can be found in~\\cite{Peeters:2006kp} and in the reference manual.\n\nAs an added bonus, the Young tableau routines which are used\ninternally can also be used directly. There are properties both for\nfilled and unfilled tableaux. The following example shows an example\nof the latter, together with the Littlewood-Richardson algorithm and\nthe use of the hook formula to compute dimensions of representations,\n\\eject\n\n\\toprule\n\\begin{cdbin}\n\\ftableau{#}::FilledTableau(dimension=10).\nex:=\\ftableau{0,0}{1,1} \\ftableau{a,a}{b,b}:\nlr_tensor(_);\n\\end{cdbin}\n\\begin{cdbout}\n\\ftableau{{0}{0}{a}{a},{1}{1}{b}{b}} \\oplus \\ftableau{{0}{0}{a}{a},{1}{1}{b},{b}} \\oplus \\ftableau{{0}{0}{a}{a},{1}{1},{b}{b}} \\oplus \\ftableau{{0}{0}{a},{1}{1}{b},{a},{b}} \\oplus \\ftableau{{0}{0}{a},{1}{1},{a}{b},{b}} \\oplus \\ftableau{{0}{0},{1}{1},{a}{a},{b}{b}};\n\\end{cdbout}\n\\begin{cdbcont}\ntab_dimension(_);\n\\end{cdbcont}\n\\begin{cdbout}\n70785 \\oplus 235950 \\oplus 154440 \\oplus 101640 \\oplus 103950 \\oplus 13860;\n\\end{cdbout}\n\\botrule\n\n\n\\subsection{A Riemann tensor polynomial example}\n\\label{s:example1}\n\nLet us now discuss a somewhat more complicated example of bosonic\ntensor algebra, which shows not only how symmetries of tensors are\nused, but also how repeated derivative operators work and how\nmore complicated canonicalisation problems are solved.\n\nTo this extent we will discuss a certain identity, a\nproof of which can be found in appendix~A of~\\cite{Frolov:2001jh}.\nConcretely, the problem concerns two particular third-order\npolynomials in the Weyl tensor~$C_{m n p q}$, given by\n\\begin{equation}\n\\begin{aligned}\nE_{ij} &= - C_{i}{}^{mkl} C_{jpkq} C_{l}{}^{pmq}\n+ \\frac{1}{4} C_{i}{}^{mkl} C_{jmpq} C_{kl}{}^{pq}\n- \\frac{1}{2} C_{ikjl} C^{kmpq} C^{l}{}_{mpq}\\,,\\\\[1ex]\nE &= C_{jmnk} C^{mpqn} C_{p}{}^{jk}{}_q + \\frac{1}{2} C_{jkmn} C^{pqmn} C^{jk}{}_{pq}\\,.\n\\end{aligned}\n\\end{equation}\nWhen evaluated on an Einstein space, these polynomials are supposed to\nsatisfy the identity\n\\begin{equation}\n\\label{e:Frolovid}\n\\nabla_i \\nabla_j E_{ij} - \\frac{1}{6} \\nabla_i \\nabla_i E = 0\\,.\n\\end{equation}\nProving this is a tedious exercise with Bianchi identities when done by\nhand. With \\Cdb the proof is straightforward; the notebook is depicted\nbelow.\n\nThe key elements in this example are the declaration of the Weyl\ntensor as well as the covariant derivative, together with the 4th line\nwhich links the two, by stating that the covariant derivative of the\nWeyl tensor satisfies the Bianchi identity. \n\\vfill\\eject\n\n\\toprule\n\\begin{cdbin}\n{i,j,m,n,k,p,q,l,r,r#}::Indices(vector).\nC_{m n p q}::WeylTensor.\n\\nabla{#}::Derivative.\n\\nabla_{r}{ C_{m n p q} }::SatisfiesBianchi.\n\nEij:=- C_{i m k l} C_{j p k q} C_{l p m q} + 1/4 C_{i m k l} C_{j m p q} C_{k l p q}\n     - 1/2 C_{i k j l} C_{k m p q} C_{l m p q}:\n\nE:=  C_{j m n k} C_{m p q n} C_{p j k q} + 1/2 C_{j k m n} C_{p q m n} C_{j k p q}:\n\nexp:= \\nabla_{i}{\\nabla_{j}{ @(Eij) }} - 1/6 \\nabla_{i}{\\nabla_{i}{ @(E) }}:\n\\end{cdbin}\n\\begin{cdbcom}\nWe now need to apply (twice) the Leibniz rule to expand the\nderivatives, and then sort the tensors and write the result in\ncanonical form with respect to mono-term symmetries,\n\\end{cdbcom}\n\\begin{cdbcont}\ndistribute(_); product_rule(_);\ndistribute(_); product_rule(_);  \n\nsort_product(_); canonicalise(_);\nrename_dummies(_);\n\\end{cdbcont}\n\\begin{cdbcom}\nBecause the identity which we intend to prove is only supposed to hold\non Einstein spaces, we set the divergence of the Weyl tensor to zero,\n\\end{cdbcom}\n\\begin{cdbcont}\nsubstitute(_, $\\nabla_{i}{C_{k i l m}} -> 0 , \\nabla_{i}{C_{k m l i}} -> 0$ );\n\\end{cdbcont}\n\\begin{cdbout}\n\\begin{aligned}\n& ~~~~ C_{i j m n} C_{i k m p} \\nabla_{q}{\\nabla_{j}{C_{n k p q}}} \n- C_{i j m n} \\nabla_{k}{C_{i p m q}} \\nabla_{p}{C_{j q n k}} \n- 2 C_{i j m n} \\nabla_{i}{C_{m k p q}} \\nabla_{p}{C_{j k n q}} \\\\\n&- C_{i j m n} C_{i k p q} \\nabla_{m}{\\nabla_{p}{C_{j q n k}}} \n- \\frac{1}{4} C_{i j m n} C_{i j k p} \\nabla_{q}{\\nabla_{m}{C_{n q k p}}} \n+ \\frac{1}{4} C_{i j m n} \\nabla_{k}{C_{i j p q}} \\nabla_{p}{C_{m n k q}} \\\\\n&- \\frac{1}{2} C_{i j m n} \\nabla_{i}{C_{j k p q}} \\nabla_{k}{C_{m n p q}} \n+ \\frac{1}{4} C_{i j m n} C_{i k p q} \\nabla_{j}{\\nabla_{k}{C_{m n p q}}} \n+ \\frac{1}{2} C_{i j m n} C_{i k p q} \\nabla_{m}{\\nabla_{j}{C_{n k p q}}} \\\\\n&+ \\frac{1}{2} C_{i j m n} \\nabla_{i}{C_{m k p q}} \\nabla_{n}{C_{j k p q}} \n- \\frac{1}{2} C_{i j m n} \\nabla_{i}{C_{j k p q}} \\nabla_{m}{C_{n k p q}} \n+ \\frac{1}{2} C_{i j m n} C_{i k p q} \\nabla_{j}{\\nabla_{m}{C_{n k p q}}}\\\\ \n&+ \\frac{1}{2} C_{i j m n} C_{i k m p} \\nabla_{q}{\\nabla_{q}{C_{j k n p}}} \n+ C_{i j m n} \\nabla_{k}{C_{i p m q}} \\nabla_{k}{C_{j p n q}} \n- \\frac{1}{4} C_{i j m n} C_{i j k p} \\nabla_{q}{\\nabla_{q}{C_{m n k p}}} \\\\\n&- \\frac{1}{2} C_{i j m n} \\nabla_{k}{C_{i j p q}} \\nabla_{k}{C_{m n p q}};\n\\end{aligned}\n\\end{cdbout}\n\\begin{cdbcom}\nThis expression should vanish upon use of the Bianchi identity. By\nexpanding all tensors using their Young projectors, this becomes manifest,\n\\end{cdbcom}\n\\begin{cdbcont}\nyoung_project_product(_);\n\\end{cdbcont}\n\\begin{cdbout}\n0;\n\\end{cdbout}\n\\begin{cdbcom}\nThis proves the identity~\\eqref{e:Frolovid}.\n\\end{cdbcom}\n\\botrule\nThe use of Young projector methods also allows for other calculations\nwhich are computationally intensive when done by hand. An example is\nthe problem of generating a complete basis of monomials of Riemann\ntensors, discussed in~\\cite{Peeters:2006kp}. \n\n% @young_project_tensor!3(%){ModuloMonoterm};\n% @distribute!(%):\n% @prodsort!(%):\n% @canonicalise!(%):\n% @rename_dummies!(%):\n\n\\subsection{Index ranges and subspaces, Kaluza-Klein gravity}\n\\label{s:example2}\n\nWe have so far seen rather simple uses of indices, in which only a\nsingle vector space was used. \\Cdb contains functionality to deal with\nmore complicated situations though. In section~\\ref{s:fermions} we\nwill discuss the use of multiple index types as well as implicit\nindices. Here we will discuss another index feature, namely the\npossibility to ``split'' indices into two or more subspaces. Let us\nfirst illustrate this with a simple example.\n\\toprule\n\\begin{cdbin}\n{M, N, P}::Indices(space).\n{m, n, p}::Indices(subspace1).\n{a, b, c}::Indices(subspace2).\n\nex:= A_{M N} B_{N P};\nsplit_index(_, $M, m, a$);\n\\end{cdbin}\n\\begin{cdbout}\nA_{M m} \\, B_{m P} + A_{M a}\\, B_{a P}\\,;\n\\end{cdbout}\n\\botrule \nThe first three lines declare three types of indices, labelled as\n``space'', ``subspace1'' and ``subspace2'' respectively. The last line\nof the input performs the split of the dummy index into the two\nsubspaces. Instead of using two subspaces labelled by indices, it is\nalso possible to use a one-dimensional subspace. An example of how\nthis works can be found in the Kaluza-Klein problem discussed below.\n\nThe index split functionality is particularly useful for Kaluza-Klein\ntype problems, in which the metric is decomposed according to\n\\begin{equation}\n\\label{e:KKansatz}\ng_{\\mu\\nu} = \\begin{pmatrix}\n \\phi^{-1}\\, h_{m n} + \\phi\\, A_{m} A_{n}  & \\phi\\, A_{m} \\\\\n\\phi\\, A_{n} & \\phi \n\\end{pmatrix}\\,,\n\\end{equation}\n(where the usual conventions in four space-time dimensions were used).\nIt is a somewhat tedious exercise to compute the Riemann tensor\ncomponents for this particular metric ansatz. One finds for instance\nthat \n\\begin{equation}\n\\begin{aligned}\n\\label{e:Rm4n4}\nR_{m 4 n 4} &=  - \\frac{1}{2}  \\nabla_{m}\\partial_{n}{\\phi} \n - \\frac{1}{4} \\partial_{m}{\\phi} \\partial_{n}{\\phi}\\, \\phi^{-1} \n + \\frac{1}{4} \\partial_{p}{\\phi} \\partial_{q}{\\phi} \\phi^{-1} h_{m n} h^{p q} \n + \\frac{1}{4} F_{m p} F_{n q} \\phi^{3} h^{p q} \\,,\n\\end{aligned}\n\\end{equation}\nwhere $F_{mn}$ is the field strength of~$A_{m}$.\nThe following notebook computes this expression using \\Cdb and the\nindex splitting functionality. All intermediate output is suppressed\nas it tends to get rather lengthy.\n\\toprule\n\\begin{cdbin}\n{\\mu,\\nu,\\rho,\\sigma,\\kappa,\\lambda,\\eta,\\chi#}::Indices(full, position=fixed).\n{m,n,p,q,r,s,t,u,v,m#}::Indices(subspace, position=fixed, parent=full).\n\\end{cdbin}\n\\begin{cdbcom}\nNote the appearance of \\verb|parent=full|. This indicates that the\nindices in the second set span a subspace of the indices in the first\nset. The remaining declarations are standard,\n\\end{cdbcom}\n\\begin{cdbcont}\n\\partial{#}::PartialDerivative.\ng_{\\mu\\nu}::Metric.\ng^{\\mu\\nu}::InverseMetric.\ng_{\\mu? \\nu?}::Symmetric.\ng^{\\mu? \\nu?}::Symmetric.\nh_{m n}::Metric.\nh^{m n}::InverseMetric.\n\\delta^{\\mu?}_{\\nu?}::KroneckerDelta.\n\\delta_{\\mu?}^{\\nu?}::KroneckerDelta.\nF_{m n}::AntiSymmetric.\n\\end{cdbcont}\n\\begin{cdbcom}\nWe will want to expand the Riemann tensor in terms of the metric. The\nfollowing two substitution rules do the conversion from Riemann tensor\nto Christoffel symbol and from Christoffel symbol to\nmetric.\\footnote{Cadabra 2.x contains a growing library of packages\n  with expressions of this type, but we will here not rely on that\n  library facility.} Index patterns like \\verb|\\lambda?| match both four- and\nthree-dimensional indices.\n\\end{cdbcom}\n\\begin{cdbcont}\nRtoG:= R^{\\lambda?}_{\\mu?\\nu?\\kappa?} -> \n - \\partial_{\\kappa?}{ \\Gamma^{\\lambda?}_{\\mu?\\nu?} }\n + \\partial_{\\nu?}{ \\Gamma^{\\lambda?}_{\\mu?\\kappa?} }\n - \\Gamma^{\\eta}_{\\mu?\\nu?} \\Gamma^{\\lambda?}_{\\kappa?\\eta}\n + \\Gamma^{\\eta}_{\\mu?\\kappa?} \\Gamma^{\\lambda?}_{\\nu?\\eta}:\n\nGtog:= \\Gamma^{\\lambda?}_{\\mu?\\nu?} ->\n  (1/2) * g^{\\lambda?\\kappa} ( \n        \\partial_{\\nu?}{ g_{\\kappa\\mu?} } + \\partial_{\\mu?}{g_{\\kappa\\nu?} } \n                                       - \\partial_{\\kappa}{ g_{\\mu?\\nu?} } ):\n\\end{cdbcont}\n\\begin{cdbcom}\nNow input the $R_{m 4 n 4}$ component and do the substitution. After\neach substitution, we distribute products over sums. We also apply the\nproduct rule to distribute derivatives over factors in a product.\n\\end{cdbcom}\n\\begin{cdbcont}\ntodo:= g_{m1 m} R^{m1}_{4 n 4} + g_{4 m} R^{4}_{4 n 4};\nsubstitute(_, RtoG)\nsubstitute(_, Gtog)\ndistribute(_)\nproduct_rule(_)\ndistribute(_)\nsort_product(_)\n\\end{cdbcont}\n\\begin{cdbcom}\nWe now split the $\\mu$ index into a $m$ part and the remaining $4$\ndirection (the \\verb|!!| version of the command makes it apply until\nthe result no longer changes).  After that, we remove $x^4$ derivatives of the gauge\nfield and write the expression in canonical form,\n\\end{cdbcom}\n\\begin{cdbcont}\nsplit_index(_, $\\mu, m1, 4$, repeat=True)\nsubstitute(_, $\\partial_{4}{A??} -> 0$, repeat=True)\nsubstitute(_, $\\partial_{4 m?}{A??} -> 0$, repeat=True)\nsubstitute(_, $\\partial_{m? 4}{A??} -> 0$, repeat=True)\ncanonicalise(_);\n\\end{cdbcont}\n\\begin{cdbcom}\nIn the next step, we insert the metric ansatz~\\eqref{e:KKansatz} and\nsimplify the result as much as possible.\n\\end{cdbcom}\n\\begin{cdbcont}\nsubstitute(_, $g_{4 4} -> \\phi$ )\nsubstitute(_, $g_{m 4} -> \\phi A_{m}$ )\nsubstitute(_, $g_{4 m} -> \\phi A_{m}$ )\nsubstitute(_, $g_{m n} -> \\phi**{-1} h_{m n} + \\phi A_{m} A_{n}$ )\nsubstitute(_, $g^{4 4} -> \\phi**{-1} + \\phi A_{m} h^{m n} A_{n}$ )\nsubstitute(_, $g^{m 4} -> - \\phi h^{m n} A_{n}$ )\nsubstitute(_, $g^{4 m} -> - \\phi h^{m n} A_{n}$ )\nsubstitute(_, $g^{m n} -> \\phi h^{m n}$ );\n\\end{cdbcont}\n\\begin{cdbcom}\nSome derivatives have to be rewritten to a canonical form,\n\\end{cdbcom}\n\\begin{cdbcont}\nconverge(todo):\n   distribute(_)\n   product_rule(_)\n   canonicalise(_)\n\\end{cdbcont}\n\\begin{cdbcom}\nThe above shows the use of a Cadabra extension \\verb|converge|, which\napplies a list of algorithms to an expression until it no longer\nchanges. We now rewrite derivatives of inverse metrics,\n\\end{cdbcom}\n\\begin{cdbcont}\nsubstitute(_, $\\partial_{p}{h^{n m}} h_{q m} -> - \\partial_{p}{h_{q m}} h^{n m}$ )\ncollect_factors(_)\nsort_product(_)\nconverge(todo):\n   substitute(_, $h_{m1 m2} h^{m3 m2} -> \\delta_{m1}^{m3}$, repeat=True )\n   eliminate_kronecker(_)\n   canonicalise(_)\n\\end{cdbcont}\n\\begin{cdbcom}\nFinally, we replace the derivative of the gauge field with the field\nstrength,\n\\end{cdbcom}\n\\begin{cdbcont}\nsubstitute(_, $\\partial_{n}{A_{m}} -> 1/2*\\partial_{n}{A_{m}}\n               + 1/2*F_{n m} + 1/2*\\partial_{m}{A_{n}}$ )\ndistribute(_)\nsort_product(_)\ncanonicalise(_)\nrename_dummies(_);\n\\end{cdbcont}\n\\begin{cdbout}\n\\begin{aligned}\n{}& - \\frac{1}{4} \\partial_{m}{\\phi} \\partial_{n}{\\phi} \\phi^{-1} \n + \\frac{1}{4} \\partial_{p}{\\phi} \\partial_{n}{h_{m q}} h^{p q} \n - \\frac{1}{2} \\partial_{m n}{\\phi} \n + \\frac{1}{4} F_{m p} F_{n q} \\phi^{3} h^{p q} \\\\\n{}& + \\frac{1}{4} \\partial_{p}{\\phi} \\partial_{q}{\\phi} \\phi^{-1} h_{m n} h^{p q} \n - \\frac{1}{4} \\partial_{p}{\\phi} \\partial_{q}{h_{m n}} h^{p q} \n + \\frac{1}{4} \\partial_{p}{\\phi} \\partial_{m}{h_{n q}} h^{p q};\n\\end{aligned}\n\\end{cdbout}\n\\begin{cdbcom}\nThis is indeed equivalent to~\\eqref{e:Rm4n4} upon writing out the\ncovariant derivative in the first term of that equation.\n\\end{cdbcom}\n\\botrule\nIf required, some of these calculations can be done with fewer lines\nof input by adding a number of default simplification rules; an\nexample of such default rules will be discussed in the next section. \nWe will end here the discussion of purely bosonic problems and move on\nto fermions and anti-commuting tensors.\n\n\\vfill\\eject\n\\section{Fermions, Dirac algebra and Fierz transformations}\n\\label{s:fermions}\n\\subsection{Simple gamma matrix algebra}\n\\label{s:gamma}\n\n\\Cdb has built-in algorithms for the manipulation of anti-commuting\nobjects, spinors and gamma matrices in any dimension. Combined with\nthe option of ``suppressing'' indices (in our examples below we will\nsuppress spinor indices), it becomes possible to write calculations in\na natural and compact way. All anti-commuting and fermionic objects as\nusual need to be declared by attaching the appropriate properties to\nthem; we will see many examples of this.\n\nLet us start, however, with some simple gamma matrix algebra. As an\nexample, we will expand the product $\\Gamma_{s r} \\Gamma_{r l}\n\\Gamma_{k m} \\Gamma_{m s}$ in arbitrary dimensions in terms of the\nirreducible~$\\Gamma_{kl}$ and $\\delta_{kl}$ components.  \n\\toprule\n\\begin{cdbcom}\nWe first declare the vector indices, their range, and the symbols used for\ngamma matrices and Kronecker deltas.\n\\end{cdbcom}\n\\begin{cdbcont}\n{s,r,l,k,m,n}::Indices(vector).\n{s,r,l,k,m,n}::Integer(0..d-1).\n\\Gamma_{#}::GammaMatrix(metric=\\delta).\n\\delta_{m n}::KroneckerDelta.\n\\end{cdbcont}\n\\begin{cdbcom}\nThe declaration for the gamma matrix shows that we are defining an\nobject with implicit indices: the spinor indices will be\nsuppressed. The notation \\verb|_{#}| denotes the presence of an\narbitrary number of indices.\n\nIt is useful to let Cadabra do a bit more simplification at every step\n(more than the default of simply collecting equal terms). This can be\nachieved by re-defining the \\verb|post_process| function, which gets\ncalled after every step of the computation.\n\\end{cdbcom}\n\\begin{cdbin}\ndef post_process(ex):\n   sort_product(ex)\n   eliminate_kronecker(ex)\n   canonicalise(ex)\n   collect_terms(ex)\n\\end{cdbin}\n\\begin{cdbcom}\nThis sorts the product, eliminate Kronecker delta's, writes indices in\ncanonical order and then finally collects equal terms.\n  \nNext follows the actual computation. We write down the gamma matrix\nproduct and join gamma matrices three times,\n\\end{cdbcom}\n\\begin{cdbcont}\nex:= \\Gamma_{s r} \\Gamma_{r l} \\Gamma_{k m} \\Gamma_{m s};\nfor i in range(3):\n   join_gamma(_)\n   distribute(_)\n\\end{cdbcont}\n\\begin{cdbcom}\n  Note once more how we are mixing ordinary Python loop constructions\n  with Cadabra code here. \n\\end{cdbcom}\n\\begin{cdbout}\n\\label{e:gam1}\n-18 \\Gamma_{kl} d + 8 \\Gamma_{kl} d d + 12 \\Gamma_{kl} - 3\\delta_{kl}\n+ 6 \\delta_{kl} d - 4 \\delta_{kl} d d - \\Gamma_{k l} d d d +\n\\delta_{kl} d d d\n\\end{cdbout}\n\\begin{cdbcont}\nfactor_in(_, $d$)\ncollect_factors(_)\n\\end{cdbcont}\n\\begin{cdbout}\n\\Gamma_{k l} (- 18 d + 8 d^2 + 12 - d^3) + \\delta_{k l} ( - 3 + 6 d - 4 d^2 + d^3);\n\\end{cdbout}\n\\botrule \nThe key ingredient here is the \\verb|join_gamma| algorithm, which\ntakes two adjacent generalised gamma matrices and expands their product in terms of\na basis of fully antisymmetrised gamma matrices. In the step\nbefore~\\eqref{e:gam1} the Python loop performs such a join three times\nand expands out the resulting product. \n\nIn the example above, the spinor indices on the gamma matrices were\nsuppressed. The \\verb|GammaMatrix| property has turned the gamma\nsymbols into non-commuting objects, which will not change order when\nsorting symbols in a product. It is, however, possible to add the\nspinor indices back in, and use explicit indices. For this purpose,\n\\Cdb knows the concept of an ``index bracket'', which associates\nindices to matrix objects like the gamma matrices above, or to\ne.g.~vectors or spinors. Here is a somewhat simpler example:\n\\toprule\n\\begin{cdbin}\n{a,b,c,d#}::Indices(spinor).\n\\Gamma_{#}::GammaMatrix(metric=\\delta).\n(\\Gamma_{m n})_{a b} (\\Gamma_{n p})_{b c};\ncombine(_);\n\\end{cdbin}\n\\begin{cdbout}\n(\\Gamma_{m n}\\, \\Gamma_{n p})_{a c};\n\\end{cdbout}\n\\begin{cdbcont}\njoin_gamma(_)\ncanonicalise(_);\n\\end{cdbcont}\n\\begin{cdbout}\n (\\Gamma_{m p} \\delta_{n n} - \\Gamma_{m n} \\delta_{n p} + \\Gamma_{p n} \\delta_{m n} \n+ \\delta_{m p} \\delta_{n n} - \\delta_{m n} \\delta_{n p})_{a c};\n\\end{cdbout}\n\\botrule\nThe join algorithm has acted `inside' the index bracket, on the matrix\nobjects themselves. Conversely, index brackets can\nbe distributed over elements in the sum, and objects can be taken out\nof the index bracket when they are known not to contain implicit\nindices:\n\\toprule\n\\begin{cdbcont}\ndistribute(_)\nexpand(_);\n\\end{cdbcont}\n\\begin{cdbout}\n (\\Gamma_{m p})_{a c} \\delta_{n n} - (\\Gamma_{m n})_{a c} \\delta_{n p} \n+ (\\Gamma_{p n})_{a c} \\delta_{m n} + (\\delta_{m p} \\delta_{n n})_{a c} \n- (\\delta_{m n} \\delta_{n p})_{a c};\n\\end{cdbout}\n\\botrule\nIn this way, matrix operations can be switched between abstract and\nindex notation at will.\n\n\\subsection{Fierz transformations}\n\\label{s:example3}\n\n\\Cdb can apply Fierz transformations in any dimension to re-order\nfour-fermion terms. As an example, consider the following identity for\nMajorana spinors in eleven dimensions~\\cite{deWit:1998tk},\n\\begin{equation}\n\\begin{aligned}\n\\label{e:fierzthing}\n-e_{[\\nu}{}^s (\\bar \\theta \\Gamma^{rs} \\psi_\\rho)(\\bar\\psi_{\\mu]} \\Gamma^r \\epsilon) &=\n\\sum_{n} \\frac{1}{2^5\\; n!} (\\bar\\psi_\\mu \\Gamma^{i_1\\ldots i_n} \\psi_\\rho)\n(\\bar\\theta \\Gamma^{rs} \\Gamma^{i_n\\ldots i_1} \\Gamma^{r} \\epsilon) \\\\\n&= \\frac{1}{2^5} \\bar\\psi_{[\\mu} \\Gamma_m \\psi_\\rho e_{\\nu]}{}^s \\left( 8 \\bar\\theta \\Gamma^{sm}\\epsilon\n+ 10 \\eta^{sm} \\bar\\theta\\epsilon\\right) \\\\\n&\\quad - \\frac{1}{2^5\\; 2!} \\bar\\psi_{[\\mu}\\Gamma_{mn} \\psi_\\rho e_{\\nu]}{}^s\\left(\n-6 \\bar\\theta\\Gamma^{smn} \\epsilon + 16\\bar\\theta \\Gamma^{[m} \\epsilon \\eta^{n]s}\\right)\\\\\n&\\quad + \\frac{1}{2^5\\; 5!} \\bar\\psi_{[\\mu}\\Gamma_{mnopq} \\psi_\\rho e_{\\nu]}{}^s \\left(\n10 \\eta^{s[m} \\bar\\theta\\Gamma^{nopq]} \\epsilon\\right) \\, .\n\\end{aligned}\n\\end{equation}\nWith conventional tools, it would take some time to convert this\nproblem to the computer. Proving this with \\Cdb, on the other hand,\nrequires little more than defining symbols properly and inputting the\nexpression on the left-hand side as one would type it in a\npaper. Moreover, reading off the output is simple as well, because \\Cdb produces\noutput which is virtually identical to the right-hand side of the\nequation above. The notebook with comments is displayed below.\n\\toprule\n\\begin{cdbin}\n{\\mu,\\nu,\\rho}::Indices(curved, position=fixed).\n{m,n,p,q,r,s,t,u,v}::Indices(flat, position=independent).\n{m,n,p,q,r,s,t,u,v}::Integer(0..10).\nT^{#{\\mu}}::AntiSymmetric.\n\\psi_{\\mu}::SelfAntiCommuting.\n\\psi_{\\mu}::Spinor(dimension=11, type=Majorana).\n\\theta::Spinor(dimension=11, type=Majorana).\n\\epsilon::Spinor(dimension=11, type=Majorana).\n{\\theta,\\epsilon,\\psi_{\\mu}}::AntiCommuting.\n\\bar{#}::DiracBar.\n\\delta^{m n}::KroneckerDelta.\n\\Gamma^{#{m}}::GammaMatrix(metric=\\delta).\\end{cdbin}\n\\begin{cdbcom}\nThese lines define the properties of all the symbols. We now\ninput (minus) the left-hand side of~\\eqref{e:fierzthing}, and do a Fierz\ntransformation to bring the~$\\theta$ and~$\\epsilon$ spinors together,\n\\end{cdbcom}\n\\begin{cdbcont}\nex:= T^{\\mu\\nu\\rho} e_{\\nu}^{s}\n     \\bar{\\theta} \\Gamma^{r s} \\psi_{\\rho}\n     \\bar{\\psi_{\\mu}} \\Gamma^{r} \\epsilon;\n\nfierz(ex, $\\theta, \\epsilon, \\psi_{\\mu}, \\psi_{\\rho}$ );\n\\end{cdbcont}\n\\begin{cdbout}\n\\begin{aligned}\n&{}- \\frac{1}{32} T^{\\mu \\nu \\rho} e_{\\nu}^{s} \\bar{\\theta} \\Gamma^{r s}\n\\Gamma^{r} \\epsilon \\bar{\\psi_{\\mu}} \\psi_{\\rho} \n{}- \\frac{1}{32} T^{\\mu \\nu \\rho} e_{\\nu}^{s} \\bar{\\theta} \\Gamma^{r s}\n\\Gamma^{m} \\Gamma^{r} \\epsilon \\bar{\\psi_{\\mu}} \\Gamma_{m} \\psi_{\\rho} \\\\[1ex]\n&{}- \\frac{1}{64} T^{\\mu \\nu \\rho} e_{\\nu}^{s} \\bar{\\theta} \\Gamma^{r s}\n\\Gamma^{m n} \\Gamma^{r} \\epsilon \\bar{\\psi_{\\mu}} \\Gamma_{n m}\n\\psi_{\\rho} \n{}- \\frac{1}{192} T^{\\mu \\nu \\rho} e_{\\nu}^{s} \\bar{\\theta} \\Gamma^{r s}\n\\Gamma^{m n p} \\Gamma^{r} \\epsilon \\bar{\\psi_{\\mu}} \\Gamma_{p n m}\n\\psi_{\\rho} \\\\[1ex]\n&{}- \\frac{1}{768} T^{\\mu \\nu \\rho} e_{\\nu}^{s} \\bar{\\theta} \\Gamma^{r s}\n\\Gamma^{m n p q} \\Gamma^{r} \\epsilon \\bar{\\psi_{\\mu}} \\Gamma_{q p n m}\n\\psi_{\\rho} \n{}- \\frac{1}{3840} T^{\\mu \\nu \\rho} e_{\\nu}^{s} \\bar{\\theta} \\Gamma^{r s}\n\\Gamma^{m n p q t1} \\Gamma^{r} \\epsilon \\bar{\\psi_{\\mu}} \\Gamma_{t1 q\n  p n m} \\psi_{\\rho};\n\\end{aligned}\n\\end{cdbout}\n\\begin{cdbcom}\nThis is not yet in the desired form, so we join gamma matrices\nuntil we are left with fully anti-symmetrised gamma matrix products, \n\\end{cdbcom}\n\\begin{cdbcont}\nconverge(obj):\n   join_gamma(_)\n   distribute(_)\n   eliminate_kronecker(_)\n\ncanonicalise(_)\nrename_dummies(_);\n\\end{cdbcont}\n\\begin{cdbout}\n\\begin{aligned}\n& \\frac{1}{4}\\, T^{\\mu \\nu \\rho} e_{\\mu}\\,^{m} \\bar{\\theta} \\Gamma^{m n}\n\\epsilon \\bar{\\psi_{\\nu}} \\Gamma_{n} \\psi_{\\rho} \n+ \\frac{5}{16}\\, T^{\\mu \\nu \\rho} e_{\\mu}\\,^{m} \\bar{\\theta} \\epsilon\n\\bar{\\psi_{\\nu}} \\Gamma_{m} \\psi_{\\rho} \n+ \\frac{3}{32}\\, T^{\\mu \\nu\n  \\rho} e_{\\mu}\\,^{m} \\bar{\\theta} \\Gamma^{m n p} \\epsilon\n\\bar{\\psi_{\\nu}} \\Gamma_{n p} \\psi_{\\rho} \\\\[1ex]\n&+ \\frac{1}{4}\\, T^{\\mu \\nu \\rho} e_{\\mu}\\,^{m} \\bar{\\theta} \\Gamma^{n}\n\\epsilon \\bar{\\psi_{\\nu}} \\Gamma_{m n} \\psi_{\\rho} \n+ \\frac{1}{384}\\, T^{\\mu \\nu \\rho} e_{\\mu}\\,^{m} \\bar{\\theta}\n\\Gamma^{n p q r} \\epsilon \\bar{\\psi_{\\nu}} \\Gamma_{m n p q r}\n\\psi_{\\rho};\n\\end{aligned}\n\\end{cdbout}\n\\begin{cdbcom}\nThis is indeed equivalent to the right-hand side of~\\eqref{e:fierzthing}.\n\\end{cdbcom}\n\\botrule Note in particular once more the simplicity of the input on\nline~12-14. As advertised, very little knowledge of the program is\nneeded in order to be able to read and follow a calculation in a \\Cdb\nnotebook.\n\n\\subsection{Other assorted topics}\n\\label{s:other} \n\nSo far we have only seen the substitution command in action on bosonic\nobjects. However, the substitution command in \\Cdb is aware of\nanti-commuting objects as well, and will take care of signs whenever products\nin the pattern and the expression are not ordered in the same way. It\nwill also refuse to match a pattern if two symbols are declared\nnon-commuting, and do not appear in the same order in the pattern and\nin the expression. \n\nAnti-commutativity comes in two flavours: self-anticommutativity and\nmutual anti-com\\-muta\\-tivity. The first is used for objects which carry\nan index: if $\\psi_{\\mu}$ is declared self-anticommuting, it means\nthat $\\psi_{\\mu}\\psi_{\\nu} = - \\psi_{\\nu} \\psi_{\\mu}$. Below is an\nexample to illustrate these concepts and the substitution\nfunctionality: \\toprule\n\\begin{cdbin}\n\\psi_{\\mu}::SelfAntiCommuting.\n{ \\chi, \\psi_{\\mu} }::AntiCommuting.\nex:= \\chi A^{\\mu\\nu} \\psi_{\\mu} \\chi \\psi_{\\nu};\n\\end{cdbin}\n\\begin{cdbout}\n\\chi A^{\\mu\\nu} \\psi_{\\mu} \\chi \\psi_{\\nu};\n\\end{cdbout}\n\\begin{cdbin}\nsubstitute(_, $\\psi_{\\mu} \\psi_{nu} -> B_{\\mu\\nu}$ );\n\\end{cdbin}\n\\begin{cdbout}\n- \\chi \\, A^{\\mu \\nu} \\, B_{\\mu \\nu} \\, \\chi;\n\\end{cdbout}\n\\begin{cdbcom}\nBy declaring $\\chi$ and $\\psi_{\\mu}$ to be mutually anti-commuting, \n\\Cdb knows that a sign should be picked up when doing the\nsubstitution. \n\nIn order to illustrate the meaning of \\verb|SelfAntiCommuting|, we\ndeclare $A^{\\mu\\nu}$ to be symmetric and canonicalise the\nexpression,\n\\end{cdbcom}\n\\begin{cdbin}\nA^{\\mu\\nu}::Symmetric.\nex:= \\chi A^{\\mu\\nu} \\psi_{\\mu} \\chi \\psi_{\\nu};  \ncanonicalise(_);\n\\end{cdbin}\n\\begin{cdbout}\n0;\n\\end{cdbout}\n\\begin{cdbcom}\nBecause $\\psi_{\\mu}$ has been declared \\verb|SelfAntiCommuting|, the\nprogram knows that $\\psi_{\\mu}\\psi_{\\nu}$ is anti-symmetric in its two\nindices, and has used this to simplify the expression.\n\\end{cdbcom}\n\\botrule\n\nTo conclude, let us discuss one more calculation which combines some\nof the functionality of \\Cdb discussed above, and also shows how to\nhandle variational problems, especially those involving fermionic\nobjects. An example is the variation of a Lagrangian under\nsupersymmetry transformations.  Consider the following sample\ncalculation,\n\\eject\n\n\\toprule\n\\begin{cdbin}\ndef post_process(ex):\n   eliminate_kronecker(_)\n   sort_product(_)\n   collect_terms(_)\n\\end{cdbin}\n%\\begin{cdbcom}\n%Declaration of indices and derivatives,\n%\\end{cdbcom}\n\\begin{cdbcont}\nD{#}::Derivative.\n\\bar{#}::DiracBar.\n\\delta{A??}::Derivative.\n{m,n,p,q,r,s,t,u,m#}::Indices(flat).\n{m,n,p,q,r,s,t,u,m#}::Integer(0..3).\n{\\mu,\\nu,\\rho,\\sigma,\\kappa,\\lambda,\\alpha,\\beta}::Indices(curved,position=fixed).\n{\\mu,\\nu,\\rho,\\sigma,\\kappa,\\lambda,\\alpha,\\beta}::Integer(0..3).\n\\end{cdbcont}\n\\begin{cdbcom}\nDeclaration of bosonic fields,\n\\end{cdbcom}\n\\begin{cdbcont}\ne^{m \\mu}::Vielbein.\ne_{m \\mu}::InverseVielbein.\ng^{\\mu\\nu}::InverseMetric.\ng_{\\mu\\nu}::Metric.\n\\end{cdbcont}\n\\begin{cdbcom}\nDeclaration of fermionic fields,\n\\end{cdbcom}\n\\begin{cdbcont}\n{ \\epsilon,\\psi_{\\mu},\\psi_{\\mu\\nu} }::Spinor(dimension=4, type=Majorana).\n\\Gamma_{#{m}}::GammaMatrix(metric=\\delta).\n{ \\psi_{\\mu\\nu}, \\psi_{\\mu}, \\epsilon }::AntiCommuting.\n{ \\psi_{\\mu}, \\psi_{\\mu\\nu} }::SelfAntiCommuting.\n{ \\epsilon, \\psi_{\\mu}, \\psi_{\\mu\\nu} }::SortOrder.\n\\Gamma_{#}::Depends(\\bar{#}).\n\\psi_{\\mu\\nu}::AntiSymmetric.\n\\end{cdbcont}\n\\begin{cdbcom}\nInput of the Lagrangian and rewriting such that all indices on gamma\nmatrices are flat,\n\\end{cdbcom}\n\\begin{cdbcont}\nL:= -1/2 e e^{n \\nu} e^{m \\mu} R_{\\mu\\nu n m} \n                 - 1/2 e \\bar{\\psi_\\mu} \\Gamma^{\\mu\\nu\\rho} D_{\\nu}{\\psi_{\\rho}}:\nrewrite_indices(_, $\\Gamma^{m n p}$, $e^{n \\mu}$);\n\\end{cdbcont}\n\\begin{cdbout}\nL := -\\frac{1}{2} R_{\\mu\\nu n m} e e^{m\\mu} e^{n \\nu} - \\frac{1}{2}\n \\bar{\\psi}_\\mu \\Gamma^{mnp} D_{\\nu}\\psi_{\\rho} e e^{m \\mu} e^{n \\nu}\n e^{p \\rho}\\,;\n\\end{cdbout}\n\\begin{cdbcom}\nIn the 1.5th~order formalism, the supersymmetry transformation rules\nare given by\n\\end{cdbcom}\n\\begin{cdbcont}\nsusy:= { e^{n \\mu} -> -\\bar{\\epsilon} \\Gamma^m \\psi_\\nu e^{m \\mu} e^{n \\nu},\n         e         -> e \\bar{\\epsilon} \\Gamma^n \\psi_\\mu e^{n\\mu},\n         \\psi_\\mu  -> D_{\\mu}{\\epsilon} }:\n\\end{cdbcont}\n\\begin{cdbcom}\nVarying under supersymmetry is now a simple matter of using the\n\\verb|vary| command, giving it the rules defined above. This will\nautomatically assume infinitesimal variations.\n\\end{cdbcom}\n\\begin{cdbcont}\nvary(L, susy);\n\\end{cdbcont}\n\\begin{cdbout}\n\\begin{aligned}\nL := & - \\frac{1}{2}\\, R_{\\mu \\nu n m} \\overline{\\epsilon} \\Gamma^{p} \\psi_{\\rho} e e^{p \\rho} e^{m \\mu} e^{n \\nu} \n+ \\frac{1}{2}\\, R_{\\mu \\nu n m} e \\overline{\\epsilon} \\Gamma^{p} \\psi_{\\rho} e^{p \\mu} e^{m \\rho} e^{n \\nu} \\\\\n&+ \\frac{1}{2}\\, R_{\\mu \\nu n m} e e^{m \\mu} \\overline{\\epsilon} \\Gamma^{p} \\psi_{\\rho} e^{p \\nu} e^{n \\rho} \n - \\frac{1}{2}\\, \\Gamma^{m n p} \\overline{D_{\\mu}{\\epsilon}}\nD_{\\nu}{\\psi_{\\rho}} e e^{m \\mu} e^{n \\nu} e^{p \\rho} \\\\\n& - \\frac{1}{2}\\, \\Gamma^{m n p} \\overline{\\psi_{\\mu}}\nD_{\\nu}{D_{\\rho}{\\epsilon}} e e^{m \\mu} e^{n \\nu} e^{p \\rho} \n- \\frac{1}{2}\\, \\Gamma^{m n p} \\overline{\\psi_{\\mu}} D_{\\nu}{\\psi_{\\rho}}\n\\overline{\\epsilon} \\Gamma^{q} \\psi_{\\sigma} e e^{q \\sigma} e^{m \\mu} e^{n\n  \\nu} e^{p \\rho} \\\\\n&+ \\frac{1}{2}\\, \\Gamma^{m n p} \\overline{\\psi_{\\mu}} D_{\\nu}{\\psi_{\\rho}} e\n\\overline{\\epsilon} \\Gamma^{q} \\psi_{\\sigma} e^{q \\mu} e^{m \\sigma} e^{n\n  \\nu} e^{p \\rho} \n+ \\frac{1}{2}\\, \\Gamma^{m n p} \\overline{\\psi_{\\mu}} D_{\\nu}{\\psi_{\\rho}} e\ne^{m \\mu} \\overline{\\epsilon} \\Gamma^{q} \\psi_{\\sigma} e^{q \\nu} e^{n\n  \\sigma} e^{p \\rho} \\\\\n&+ \\frac{1}{2}\\, \\Gamma^{m n p} \\overline{\\psi_{\\mu}} D_{\\nu}{\\psi_{\\rho}} e e^{m \\mu} e^{n \\nu} \\overline{\\epsilon} \\Gamma^{q} \\psi_{\\sigma} e^{q \\rho} e^{p \\sigma};\n\\end{aligned}\n\\end{cdbout}\n\\botrule \n(The rest of the calculation, in which the result is rewritten using\npartial integration and a Fierz identity to show that it vanishes, can\nbe found in a more extensive notebook on $N=1$ supergravity in four\ndimensions, available from the web site).\n\nVarious aspects of \\Cdb are visible here: the use of multiple\nindex types and conversion between them, the user-specified sort order\nof fields which takes into account commutativity properties of\ntensors, the pattern matching routines which automatically deal with dummy\nindex relabelling, the readability of input/output and so on. \n\n\n\\section{Conclusions}\n\nWe have discussed the capabilities of the new computer algebra system\n``\\Cdb'', by applying it to a number of concrete calculations. There are\nseveral aspects of this system which make it particularly well-suited\nto solve field-theory problems. Firstly, it uses (a subset of)~\\TeX{}\nnot only for output, but also for input. Compared to other computer\nalgebra systems, this makes it much easier to input complicated\nexpressions without errors, as there is hardly any new syntax to be\nlearnt. Secondly, the program has built-in facilities for many\nconcepts which occur in field theory, like anti-commuting variables,\ngamma matrix algebra, implicit dependence on coordinates, accents,\nmultiple dummy index sets, canonicalisation of tensor expressions and\nso on. Although there exist other systems which share some of the\nfunctionality of \\Cdb, the implementation in \\Cdb was designed from\nscratch so as to make problem solving resemble as close as possible\nthe steps one would follow with pencil and paper.\n\nThe program is entirely built on freely distributable software\nlibraries, i.e.~it does not make use of any proprietary computer\nalgebra system.  The system is available in source code for all\nsupported platforms, as well as in binary form for Linux and Windows\ncomputers; the reader is referred to the web\nsite~\\url{http://cadabra.science} for download and installation\ninstructions as well as the help forum.\n\nGiven the program's scope and size, there of course remains quite some\nroom for improvements and additions. An upcoming paper will describe\nthe improvements introduced in the 2.x series.\n\\vfill\\eject\n\n\\section*{Acknowledgements}\n\nThe development of Cadabra was made possible by support from\nDAMTP at Cambridge University, from CERN and in particular from the\nAlbert-Einstein-Institute in Potsdam.  This work was also sponsored in\npart by VIDI grant 016.069.313 from the Dutch Organisation for\nScientific Research (NWO).  I am grateful to the Department of\nMathematical Sciences at Durham University for hospitality while this\nwork was being completed. Many thanks to Marcus Berg for comments on\nthe first version of this paper.\n\n%\\begin{smaller}\n%\\bibliographystyle{kasper}\n%\\bibliography{kasbib}\n\\begingroup\\raggedright\\begin{thebibliography}{8}\n\\expandafter\\ifx\\csname natexlab\\endcsname\\relax\\def\\natexlab#1{#1}\\fi\n\n\\bibitem[Gran(2001)]{Gran:2001yh}\nU.~Gran, ``{GAMMA}: A {Mathematica} package for performing gamma-matrix algebra\n  and {Fierz} transformations in arbitrary dimensions'',\n  \\href{http://xxx.lanl.gov/abs/hep-th/0105086}{{\\tt hep-th/0105086}},\n\\url{http://fy.chalmers.se/~gran/GAMMA/}.\n%%CITATION = HEP-TH 0105086;%%.\n\n\\bibitem[Headrick(????)]{e_grassmann}\nM.~Headrick, ``grassmann.m'',\n  \\url{http://www.stanford.edu/~headrick/physics/index.html}.\n\n\\bibitem[{Mart\\'\\i{}n-Garc\\'\\i{}a}(????)]{e_xact}\nJ.~{Mart\\'\\i{}n-Garc\\'\\i{}a}, ``{xPerm and xAct}'',\n  \\url{http://metric.iem.csic.es/Martin-Garcia/xAct/index.html}.\n\n\\bibitem[Peeters(2006)]{Peeters:2006kp}\nK.~Peeters, ``A field-theory motivated approach to symbolic computer algebra'',\n  {\\em Comp.\\ Phys.\\ Commun.} {\\bf 176} (2006) 550--558,\n  \\href{http://xxx.lanl.gov/abs/cs.sc/0608005}{{\\tt cs.sc/0608005}}.\n%%CITATION = CS.SC 0608005;%%\n\n\\bibitem[Green et~al.(2005)Green, Peeters, and Stahn]{Green:2005qr}\nM.~B. Green, K.~Peeters, and C.~Stahn, ``Superfield integrals in high\n  dimensions'', {\\em JHEP\\,} {\\bf 08} (2005) 093,\n\\href{http://xxx.lanl.gov/abs/hep-th/0506161}{{\\tt hep-th/0506161}}.\n%%CITATION = HEP-TH 0506161;%%.\n\n\\bibitem[Peeters(????)]{kas_dimdep}\nK.~Peeters, ``A {Young} tableau based algorithm for dimensionally dependent\n  identities'', in preparation.\n\n\\bibitem[Frolov and Tseytlin(2002)]{Frolov:2001jh}\nS.~Frolov and A.~A. Tseytlin, ``{$R^4$ corrections to conifolds and $G(2)$\n  holonomy metrics}'', {\\em Nucl.\\ Phys.} {\\bf B632} (2002) 69--100,\n\\href{http://xxx.lanl.gov/abs/hep-th/0111128}{{\\tt hep-th/0111128}}.\n%%CITATION = HEP-TH 0111128;%%.\n\n\\bibitem[de~Wit et~al.(1998)de~Wit, Peeters, and Plefka]{deWit:1998tk}\nB.~de~Wit, K.~Peeters, and J.~Plefka, ``Superspace geometry for supermembrane\n  backgrounds'', {\\em Nucl.\\ Phys.} {\\bf B532} (1998) 99,\n\\href{http://xxx.lanl.gov/abs/hep-th/9803209}{{\\tt hep-th/9803209}}.\n%%CITATION = NUPHA,B532,99;%%.\n\n\\end{thebibliography}\\endgroup\n%\\end{smaller}\n\\end{document}\n\n\n\n\n"
  },
  {
    "path": "doc/description",
    "content": "Cadabra is a computer algebra system designed specifically for the\nsolution of problems encountered in field theory. It has extensive\nfunctionality for tensor polynomial simplification including\nmulti-term symmetries, fermions and anti-commuting variables,\nClifford algebras and Fierz transformations, implicit coordinate\ndependence, multiple index types and many more. The input format is\na subset of TeX. This is the 2.x series of the software.\n"
  },
  {
    "path": "doc/license.txt",
    "content": "                    GNU GENERAL PUBLIC LICENSE\n                       Version 3, 29 June 2007\n\n Copyright (C) 2007 Free Software Foundation, Inc. <http://fsf.org/>\n Everyone is permitted to copy and distribute verbatim copies\n of this license document, but changing it is not allowed.\n\n                            Preamble\n\n  The GNU General Public License is a free, copyleft license for\nsoftware and other kinds of works.\n\n  The licenses for most software and other practical works are designed\nto take away your freedom to share and change the works.  By contrast,\nthe GNU General Public License is intended to guarantee your freedom to\nshare and change all versions of a program--to make sure it remains free\nsoftware for all its users.  We, the Free Software Foundation, use the\nGNU General Public License for most of our software; it applies also to\nany other work released this way by its authors.  You can apply it to\nyour programs, too.\n\n  When we speak of free software, we are referring to freedom, not\nprice.  Our General Public Licenses are designed to make sure that you\nhave the freedom to distribute copies of free software (and charge for\nthem if you wish), that you receive source code or can get it if you\nwant it, that you can change the software or use pieces of it in new\nfree programs, and that you know you can do these things.\n\n  To protect your rights, we need to prevent others from denying you\nthese rights or asking you to surrender the rights.  Therefore, you have\ncertain responsibilities if you distribute copies of the software, or if\nyou modify it: responsibilities to respect the freedom of others.\n\n  For example, if you distribute copies of such a program, whether\ngratis or for a fee, you must pass on to the recipients the same\nfreedoms that you received.  You must make sure that they, too, receive\nor can get the source code.  And you must show them these terms so they\nknow their rights.\n\n  Developers that use the GNU GPL protect your rights with two steps:\n(1) assert copyright on the software, and (2) offer you this License\ngiving you legal permission to copy, distribute and/or modify it.\n\n  For the developers' and authors' protection, the GPL clearly explains\nthat there is no warranty for this free software.  For both users' and\nauthors' sake, the GPL requires that modified versions be marked as\nchanged, so that their problems will not be attributed erroneously to\nauthors of previous versions.\n\n  Some devices are designed to deny users access to install or run\nmodified versions of the software inside them, although the manufacturer\ncan do so.  This is fundamentally incompatible with the aim of\nprotecting users' freedom to change the software.  The systematic\npattern of such abuse occurs in the area of products for individuals to\nuse, which is precisely where it is most unacceptable.  Therefore, we\nhave designed this version of the GPL to prohibit the practice for those\nproducts.  If such problems arise substantially in other domains, we\nstand ready to extend this provision to those domains in future versions\nof the GPL, as needed to protect the freedom of users.\n\n  Finally, every program is threatened constantly by software patents.\nStates should not allow patents to restrict development and use of\nsoftware on general-purpose computers, but in those that do, we wish to\navoid the special danger that patents applied to a free program could\nmake it effectively proprietary.  To prevent this, the GPL assures that\npatents cannot be used to render the program non-free.\n\n  The precise terms and conditions for copying, distribution and\nmodification follow.\n\n                       TERMS AND CONDITIONS\n\n  0. Definitions.\n\n  \"This License\" refers to version 3 of the GNU General Public License.\n\n  \"Copyright\" also means copyright-like laws that apply to other kinds of\nworks, such as semiconductor masks.\n\n  \"The Program\" refers to any copyrightable work licensed under this\nLicense.  Each licensee is addressed as \"you\".  \"Licensees\" and\n\"recipients\" may be individuals or organizations.\n\n  To \"modify\" a work means to copy from or adapt all or part of the work\nin a fashion requiring copyright permission, other than the making of an\nexact copy.  The resulting work is called a \"modified version\" of the\nearlier work or a work \"based on\" the earlier work.\n\n  A \"covered work\" means either the unmodified Program or a work based\non the Program.\n\n  To \"propagate\" a work means to do anything with it that, without\npermission, would make you directly or secondarily liable for\ninfringement under applicable copyright law, except executing it on a\ncomputer or modifying a private copy.  Propagation includes copying,\ndistribution (with or without modification), making available to the\npublic, and in some countries other activities as well.\n\n  To \"convey\" a work means any kind of propagation that enables other\nparties to make or receive copies.  Mere interaction with a user through\na computer network, with no transfer of a copy, is not conveying.\n\n  An interactive user interface displays \"Appropriate Legal Notices\"\nto the extent that it includes a convenient and prominently visible\nfeature that (1) displays an appropriate copyright notice, and (2)\ntells the user that there is no warranty for the work (except to the\nextent that warranties are provided), that licensees may convey the\nwork under this License, and how to view a copy of this License.  If\nthe interface presents a list of user commands or options, such as a\nmenu, a prominent item in the list meets this criterion.\n\n  1. Source Code.\n\n  The \"source code\" for a work means the preferred form of the work\nfor making modifications to it.  \"Object code\" means any non-source\nform of a work.\n\n  A \"Standard Interface\" means an interface that either is an official\nstandard defined by a recognized standards body, or, in the case of\ninterfaces specified for a particular programming language, one that\nis widely used among developers working in that language.\n\n  The \"System Libraries\" of an executable work include anything, other\nthan the work as a whole, that (a) is included in the normal form of\npackaging a Major Component, but which is not part of that Major\nComponent, and (b) serves only to enable use of the work with that\nMajor Component, or to implement a Standard Interface for which an\nimplementation is available to the public in source code form.  A\n\"Major Component\", in this context, means a major essential component\n(kernel, window system, and so on) of the specific operating system\n(if any) on which the executable work runs, or a compiler used to\nproduce the work, or an object code interpreter used to run it.\n\n  The \"Corresponding Source\" for a work in object code form means all\nthe source code needed to generate, install, and (for an executable\nwork) run the object code and to modify the work, including scripts to\ncontrol those activities.  However, it does not include the work's\nSystem Libraries, or general-purpose tools or generally available free\nprograms which are used unmodified in performing those activities but\nwhich are not part of the work.  For example, Corresponding Source\nincludes interface definition files associated with source files for\nthe work, and the source code for shared libraries and dynamically\nlinked subprograms that the work is specifically designed to require,\nsuch as by intimate data communication or control flow between those\nsubprograms and other parts of the work.\n\n  The Corresponding Source need not include anything that users\ncan regenerate automatically from other parts of the Corresponding\nSource.\n\n  The Corresponding Source for a work in source code form is that\nsame work.\n\n  2. Basic Permissions.\n\n  All rights granted under this License are granted for the term of\ncopyright on the Program, and are irrevocable provided the stated\nconditions are met.  This License explicitly affirms your unlimited\npermission to run the unmodified Program.  The output from running a\ncovered work is covered by this License only if the output, given its\ncontent, constitutes a covered work.  This License acknowledges your\nrights of fair use or other equivalent, as provided by copyright law.\n\n  You may make, run and propagate covered works that you do not\nconvey, without conditions so long as your license otherwise remains\nin force.  You may convey covered works to others for the sole purpose\nof having them make modifications exclusively for you, or provide you\nwith facilities for running those works, provided that you comply with\nthe terms of this License in conveying all material for which you do\nnot control copyright.  Those thus making or running the covered works\nfor you must do so exclusively on your behalf, under your direction\nand control, on terms that prohibit them from making any copies of\nyour copyrighted material outside their relationship with you.\n\n  Conveying under any other circumstances is permitted solely under\nthe conditions stated below.  Sublicensing is not allowed; section 10\nmakes it unnecessary.\n\n  3. Protecting Users' Legal Rights From Anti-Circumvention Law.\n\n  No covered work shall be deemed part of an effective technological\nmeasure under any applicable law fulfilling obligations under article\n11 of the WIPO copyright treaty adopted on 20 December 1996, or\nsimilar laws prohibiting or restricting circumvention of such\nmeasures.\n\n  When you convey a covered work, you waive any legal power to forbid\ncircumvention of technological measures to the extent such circumvention\nis effected by exercising rights under this License with respect to\nthe covered work, and you disclaim any intention to limit operation or\nmodification of the work as a means of enforcing, against the work's\nusers, your or third parties' legal rights to forbid circumvention of\ntechnological measures.\n\n  4. Conveying Verbatim Copies.\n\n  You may convey verbatim copies of the Program's source code as you\nreceive it, in any medium, provided that you conspicuously and\nappropriately publish on each copy an appropriate copyright notice;\nkeep intact all notices stating that this License and any\nnon-permissive terms added in accord with section 7 apply to the code;\nkeep intact all notices of the absence of any warranty; and give all\nrecipients a copy of this License along with the Program.\n\n  You may charge any price or no price for each copy that you convey,\nand you may offer support or warranty protection for a fee.\n\n  5. Conveying Modified Source Versions.\n\n  You may convey a work based on the Program, or the modifications to\nproduce it from the Program, in the form of source code under the\nterms of section 4, provided that you also meet all of these conditions:\n\n    a) The work must carry prominent notices stating that you modified\n    it, and giving a relevant date.\n\n    b) The work must carry prominent notices stating that it is\n    released under this License and any conditions added under section\n    7.  This requirement modifies the requirement in section 4 to\n    \"keep intact all notices\".\n\n    c) You must license the entire work, as a whole, under this\n    License to anyone who comes into possession of a copy.  This\n    License will therefore apply, along with any applicable section 7\n    additional terms, to the whole of the work, and all its parts,\n    regardless of how they are packaged.  This License gives no\n    permission to license the work in any other way, but it does not\n    invalidate such permission if you have separately received it.\n\n    d) If the work has interactive user interfaces, each must display\n    Appropriate Legal Notices; however, if the Program has interactive\n    interfaces that do not display Appropriate Legal Notices, your\n    work need not make them do so.\n\n  A compilation of a covered work with other separate and independent\nworks, which are not by their nature extensions of the covered work,\nand which are not combined with it such as to form a larger program,\nin or on a volume of a storage or distribution medium, is called an\n\"aggregate\" if the compilation and its resulting copyright are not\nused to limit the access or legal rights of the compilation's users\nbeyond what the individual works permit.  Inclusion of a covered work\nin an aggregate does not cause this License to apply to the other\nparts of the aggregate.\n\n  6. Conveying Non-Source Forms.\n\n  You may convey a covered work in object code form under the terms\nof sections 4 and 5, provided that you also convey the\nmachine-readable Corresponding Source under the terms of this License,\nin one of these ways:\n\n    a) Convey the object code in, or embodied in, a physical product\n    (including a physical distribution medium), accompanied by the\n    Corresponding Source fixed on a durable physical medium\n    customarily used for software interchange.\n\n    b) Convey the object code in, or embodied in, a physical product\n    (including a physical distribution medium), accompanied by a\n    written offer, valid for at least three years and valid for as\n    long as you offer spare parts or customer support for that product\n    model, to give anyone who possesses the object code either (1) a\n    copy of the Corresponding Source for all the software in the\n    product that is covered by this License, on a durable physical\n    medium customarily used for software interchange, for a price no\n    more than your reasonable cost of physically performing this\n    conveying of source, or (2) access to copy the\n    Corresponding Source from a network server at no charge.\n\n    c) Convey individual copies of the object code with a copy of the\n    written offer to provide the Corresponding Source.  This\n    alternative is allowed only occasionally and noncommercially, and\n    only if you received the object code with such an offer, in accord\n    with subsection 6b.\n\n    d) Convey the object code by offering access from a designated\n    place (gratis or for a charge), and offer equivalent access to the\n    Corresponding Source in the same way through the same place at no\n    further charge.  You need not require recipients to copy the\n    Corresponding Source along with the object code.  If the place to\n    copy the object code is a network server, the Corresponding Source\n    may be on a different server (operated by you or a third party)\n    that supports equivalent copying facilities, provided you maintain\n    clear directions next to the object code saying where to find the\n    Corresponding Source.  Regardless of what server hosts the\n    Corresponding Source, you remain obligated to ensure that it is\n    available for as long as needed to satisfy these requirements.\n\n    e) Convey the object code using peer-to-peer transmission, provided\n    you inform other peers where the object code and Corresponding\n    Source of the work are being offered to the general public at no\n    charge under subsection 6d.\n\n  A separable portion of the object code, whose source code is excluded\nfrom the Corresponding Source as a System Library, need not be\nincluded in conveying the object code work.\n\n  A \"User Product\" is either (1) a \"consumer product\", which means any\ntangible personal property which is normally used for personal, family,\nor household purposes, or (2) anything designed or sold for incorporation\ninto a dwelling.  In determining whether a product is a consumer product,\ndoubtful cases shall be resolved in favor of coverage.  For a particular\nproduct received by a particular user, \"normally used\" refers to a\ntypical or common use of that class of product, regardless of the status\nof the particular user or of the way in which the particular user\nactually uses, or expects or is expected to use, the product.  A product\nis a consumer product regardless of whether the product has substantial\ncommercial, industrial or non-consumer uses, unless such uses represent\nthe only significant mode of use of the product.\n\n  \"Installation Information\" for a User Product means any methods,\nprocedures, authorization keys, or other information required to install\nand execute modified versions of a covered work in that User Product from\na modified version of its Corresponding Source.  The information must\nsuffice to ensure that the continued functioning of the modified object\ncode is in no case prevented or interfered with solely because\nmodification has been made.\n\n  If you convey an object code work under this section in, or with, or\nspecifically for use in, a User Product, and the conveying occurs as\npart of a transaction in which the right of possession and use of the\nUser Product is transferred to the recipient in perpetuity or for a\nfixed term (regardless of how the transaction is characterized), the\nCorresponding Source conveyed under this section must be accompanied\nby the Installation Information.  But this requirement does not apply\nif neither you nor any third party retains the ability to install\nmodified object code on the User Product (for example, the work has\nbeen installed in ROM).\n\n  The requirement to provide Installation Information does not include a\nrequirement to continue to provide support service, warranty, or updates\nfor a work that has been modified or installed by the recipient, or for\nthe User Product in which it has been modified or installed.  Access to a\nnetwork may be denied when the modification itself materially and\nadversely affects the operation of the network or violates the rules and\nprotocols for communication across the network.\n\n  Corresponding Source conveyed, and Installation Information provided,\nin accord with this section must be in a format that is publicly\ndocumented (and with an implementation available to the public in\nsource code form), and must require no special password or key for\nunpacking, reading or copying.\n\n  7. Additional Terms.\n\n  \"Additional permissions\" are terms that supplement the terms of this\nLicense by making exceptions from one or more of its conditions.\nAdditional permissions that are applicable to the entire Program shall\nbe treated as though they were included in this License, to the extent\nthat they are valid under applicable law.  If additional permissions\napply only to part of the Program, that part may be used separately\nunder those permissions, but the entire Program remains governed by\nthis License without regard to the additional permissions.\n\n  When you convey a copy of a covered work, you may at your option\nremove any additional permissions from that copy, or from any part of\nit.  (Additional permissions may be written to require their own\nremoval in certain cases when you modify the work.)  You may place\nadditional permissions on material, added by you to a covered work,\nfor which you have or can give appropriate copyright permission.\n\n  Notwithstanding any other provision of this License, for material you\nadd to a covered work, you may (if authorized by the copyright holders of\nthat material) supplement the terms of this License with terms:\n\n    a) Disclaiming warranty or limiting liability differently from the\n    terms of sections 15 and 16 of this License; or\n\n    b) Requiring preservation of specified reasonable legal notices or\n    author attributions in that material or in the Appropriate Legal\n    Notices displayed by works containing it; or\n\n    c) Prohibiting misrepresentation of the origin of that material, or\n    requiring that modified versions of such material be marked in\n    reasonable ways as different from the original version; or\n\n    d) Limiting the use for publicity purposes of names of licensors or\n    authors of the material; or\n\n    e) Declining to grant rights under trademark law for use of some\n    trade names, trademarks, or service marks; or\n\n    f) Requiring indemnification of licensors and authors of that\n    material by anyone who conveys the material (or modified versions of\n    it) with contractual assumptions of liability to the recipient, for\n    any liability that these contractual assumptions directly impose on\n    those licensors and authors.\n\n  All other non-permissive additional terms are considered \"further\nrestrictions\" within the meaning of section 10.  If the Program as you\nreceived it, or any part of it, contains a notice stating that it is\ngoverned by this License along with a term that is a further\nrestriction, you may remove that term.  If a license document contains\na further restriction but permits relicensing or conveying under this\nLicense, you may add to a covered work material governed by the terms\nof that license document, provided that the further restriction does\nnot survive such relicensing or conveying.\n\n  If you add terms to a covered work in accord with this section, you\nmust place, in the relevant source files, a statement of the\nadditional terms that apply to those files, or a notice indicating\nwhere to find the applicable terms.\n\n  Additional terms, permissive or non-permissive, may be stated in the\nform of a separately written license, or stated as exceptions;\nthe above requirements apply either way.\n\n  8. Termination.\n\n  You may not propagate or modify a covered work except as expressly\nprovided under this License.  Any attempt otherwise to propagate or\nmodify it is void, and will automatically terminate your rights under\nthis License (including any patent licenses granted under the third\nparagraph of section 11).\n\n  However, if you cease all violation of this License, then your\nlicense from a particular copyright holder is reinstated (a)\nprovisionally, unless and until the copyright holder explicitly and\nfinally terminates your license, and (b) permanently, if the copyright\nholder fails to notify you of the violation by some reasonable means\nprior to 60 days after the cessation.\n\n  Moreover, your license from a particular copyright holder is\nreinstated permanently if the copyright holder notifies you of the\nviolation by some reasonable means, this is the first time you have\nreceived notice of violation of this License (for any work) from that\ncopyright holder, and you cure the violation prior to 30 days after\nyour receipt of the notice.\n\n  Termination of your rights under this section does not terminate the\nlicenses of parties who have received copies or rights from you under\nthis License.  If your rights have been terminated and not permanently\nreinstated, you do not qualify to receive new licenses for the same\nmaterial under section 10.\n\n  9. Acceptance Not Required for Having Copies.\n\n  You are not required to accept this License in order to receive or\nrun a copy of the Program.  Ancillary propagation of a covered work\noccurring solely as a consequence of using peer-to-peer transmission\nto receive a copy likewise does not require acceptance.  However,\nnothing other than this License grants you permission to propagate or\nmodify any covered work.  These actions infringe copyright if you do\nnot accept this License.  Therefore, by modifying or propagating a\ncovered work, you indicate your acceptance of this License to do so.\n\n  10. Automatic Licensing of Downstream Recipients.\n\n  Each time you convey a covered work, the recipient automatically\nreceives a license from the original licensors, to run, modify and\npropagate that work, subject to this License.  You are not responsible\nfor enforcing compliance by third parties with this License.\n\n  An \"entity transaction\" is a transaction transferring control of an\norganization, or substantially all assets of one, or subdividing an\norganization, or merging organizations.  If propagation of a covered\nwork results from an entity transaction, each party to that\ntransaction who receives a copy of the work also receives whatever\nlicenses to the work the party's predecessor in interest had or could\ngive under the previous paragraph, plus a right to possession of the\nCorresponding Source of the work from the predecessor in interest, if\nthe predecessor has it or can get it with reasonable efforts.\n\n  You may not impose any further restrictions on the exercise of the\nrights granted or affirmed under this License.  For example, you may\nnot impose a license fee, royalty, or other charge for exercise of\nrights granted under this License, and you may not initiate litigation\n(including a cross-claim or counterclaim in a lawsuit) alleging that\nany patent claim is infringed by making, using, selling, offering for\nsale, or importing the Program or any portion of it.\n\n  11. Patents.\n\n  A \"contributor\" is a copyright holder who authorizes use under this\nLicense of the Program or a work on which the Program is based.  The\nwork thus licensed is called the contributor's \"contributor version\".\n\n  A contributor's \"essential patent claims\" are all patent claims\nowned or controlled by the contributor, whether already acquired or\nhereafter acquired, that would be infringed by some manner, permitted\nby this License, of making, using, or selling its contributor version,\nbut do not include claims that would be infringed only as a\nconsequence of further modification of the contributor version.  For\npurposes of this definition, \"control\" includes the right to grant\npatent sublicenses in a manner consistent with the requirements of\nthis License.\n\n  Each contributor grants you a non-exclusive, worldwide, royalty-free\npatent license under the contributor's essential patent claims, to\nmake, use, sell, offer for sale, import and otherwise run, modify and\npropagate the contents of its contributor version.\n\n  In the following three paragraphs, a \"patent license\" is any express\nagreement or commitment, however denominated, not to enforce a patent\n(such as an express permission to practice a patent or covenant not to\nsue for patent infringement).  To \"grant\" such a patent license to a\nparty means to make such an agreement or commitment not to enforce a\npatent against the party.\n\n  If you convey a covered work, knowingly relying on a patent license,\nand the Corresponding Source of the work is not available for anyone\nto copy, free of charge and under the terms of this License, through a\npublicly available network server or other readily accessible means,\nthen you must either (1) cause the Corresponding Source to be so\navailable, or (2) arrange to deprive yourself of the benefit of the\npatent license for this particular work, or (3) arrange, in a manner\nconsistent with the requirements of this License, to extend the patent\nlicense to downstream recipients.  \"Knowingly relying\" means you have\nactual knowledge that, but for the patent license, your conveying the\ncovered work in a country, or your recipient's use of the covered work\nin a country, would infringe one or more identifiable patents in that\ncountry that you have reason to believe are valid.\n\n  If, pursuant to or in connection with a single transaction or\narrangement, you convey, or propagate by procuring conveyance of, a\ncovered work, and grant a patent license to some of the parties\nreceiving the covered work authorizing them to use, propagate, modify\nor convey a specific copy of the covered work, then the patent license\nyou grant is automatically extended to all recipients of the covered\nwork and works based on it.\n\n  A patent license is \"discriminatory\" if it does not include within\nthe scope of its coverage, prohibits the exercise of, or is\nconditioned on the non-exercise of one or more of the rights that are\nspecifically granted under this License.  You may not convey a covered\nwork if you are a party to an arrangement with a third party that is\nin the business of distributing software, under which you make payment\nto the third party based on the extent of your activity of conveying\nthe work, and under which the third party grants, to any of the\nparties who would receive the covered work from you, a discriminatory\npatent license (a) in connection with copies of the covered work\nconveyed by you (or copies made from those copies), or (b) primarily\nfor and in connection with specific products or compilations that\ncontain the covered work, unless you entered into that arrangement,\nor that patent license was granted, prior to 28 March 2007.\n\n  Nothing in this License shall be construed as excluding or limiting\nany implied license or other defenses to infringement that may\notherwise be available to you under applicable patent law.\n\n  12. No Surrender of Others' Freedom.\n\n  If conditions are imposed on you (whether by court order, agreement or\notherwise) that contradict the conditions of this License, they do not\nexcuse you from the conditions of this License.  If you cannot convey a\ncovered work so as to satisfy simultaneously your obligations under this\nLicense and any other pertinent obligations, then as a consequence you may\nnot convey it at all.  For example, if you agree to terms that obligate you\nto collect a royalty for further conveying from those to whom you convey\nthe Program, the only way you could satisfy both those terms and this\nLicense would be to refrain entirely from conveying the Program.\n\n  13. Use with the GNU Affero General Public License.\n\n  Notwithstanding any other provision of this License, you have\npermission to link or combine any covered work with a work licensed\nunder version 3 of the GNU Affero General Public License into a single\ncombined work, and to convey the resulting work.  The terms of this\nLicense will continue to apply to the part which is the covered work,\nbut the special requirements of the GNU Affero General Public License,\nsection 13, concerning interaction through a network will apply to the\ncombination as such.\n\n  14. Revised Versions of this License.\n\n  The Free Software Foundation may publish revised and/or new versions of\nthe GNU General Public License from time to time.  Such new versions will\nbe similar in spirit to the present version, but may differ in detail to\naddress new problems or concerns.\n\n  Each version is given a distinguishing version number.  If the\nProgram specifies that a certain numbered version of the GNU General\nPublic License \"or any later version\" applies to it, you have the\noption of following the terms and conditions either of that numbered\nversion or of any later version published by the Free Software\nFoundation.  If the Program does not specify a version number of the\nGNU General Public License, you may choose any version ever published\nby the Free Software Foundation.\n\n  If the Program specifies that a proxy can decide which future\nversions of the GNU General Public License can be used, that proxy's\npublic statement of acceptance of a version permanently authorizes you\nto choose that version for the Program.\n\n  Later license versions may give you additional or different\npermissions.  However, no additional obligations are imposed on any\nauthor or copyright holder as a result of your choosing to follow a\nlater version.\n\n  15. Disclaimer of Warranty.\n\n  THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY\nAPPLICABLE LAW.  EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT\nHOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM \"AS IS\" WITHOUT WARRANTY\nOF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO,\nTHE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR\nPURPOSE.  THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM\nIS WITH YOU.  SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF\nALL NECESSARY SERVICING, REPAIR OR CORRECTION.\n\n  16. Limitation of Liability.\n\n  IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING\nWILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS\nTHE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY\nGENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE\nUSE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF\nDATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD\nPARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS),\nEVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF\nSUCH DAMAGES.\n\n  17. Interpretation of Sections 15 and 16.\n\n  If the disclaimer of warranty and limitation of liability provided\nabove cannot be given local legal effect according to their terms,\nreviewing courts shall apply local law that most closely approximates\nan absolute waiver of all civil liability in connection with the\nProgram, unless a warranty or assumption of liability accompanies a\ncopy of the Program in return for a fee.\n\n                     END OF TERMS AND CONDITIONS\n\n            How to Apply These Terms to Your New Programs\n\n  If you develop a new program, and you want it to be of the greatest\npossible use to the public, the best way to achieve this is to make it\nfree software which everyone can redistribute and change under these terms.\n\n  To do so, attach the following notices to the program.  It is safest\nto attach them to the start of each source file to most effectively\nstate the exclusion of warranty; and each file should have at least\nthe \"copyright\" line and a pointer to where the full notice is found.\n\n    <one line to give the program's name and a brief idea of what it does.>\n    Copyright (C) <year>  <name of author>\n\n    This program is free software: you can redistribute it and/or modify\n    it under the terms of the GNU General Public License as published by\n    the Free Software Foundation, either version 3 of the License, or\n    (at your option) any later version.\n\n    This program is distributed in the hope that it will be useful,\n    but WITHOUT ANY WARRANTY; without even the implied warranty of\n    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n    GNU General Public License for more details.\n\n    You should have received a copy of the GNU General Public License\n    along with this program.  If not, see <http://www.gnu.org/licenses/>.\n\nAlso add information on how to contact you by electronic and paper mail.\n\n  If the program does terminal interaction, make it output a short\nnotice like this when it starts in an interactive mode:\n\n    <program>  Copyright (C) <year>  <name of author>\n    This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'.\n    This is free software, and you are welcome to redistribute it\n    under certain conditions; type `show c' for details.\n\nThe hypothetical commands `show w' and `show c' should show the appropriate\nparts of the General Public License.  Of course, your program's commands\nmight be different; for a GUI interface, you would use an \"about box\".\n\n  You should also get your employer (if you work as a programmer) or school,\nif any, to sign a \"copyright disclaimer\" for the program, if necessary.\nFor more information on this, and how to apply and follow the GNU GPL, see\n<http://www.gnu.org/licenses/>.\n\n  The GNU General Public License does not permit incorporating your program\ninto proprietary programs.  If your program is a subroutine library, you\nmay consider it more useful to permit linking proprietary applications with\nthe library.  If this is what you want to do, use the GNU Lesser General\nPublic License instead of this License.  But first, please read\n<http://www.gnu.org/philosophy/why-not-lgpl.html>.\n"
  },
  {
    "path": "doc/main.md",
    "content": "Cadabra                                         {#mainpage}\n=======\n\n\\author  Kasper Peeters\n\\version 2.x series\n\\see     http://cadabra.science\n\n\nThis repository holds the 2.x series of the Cadabra computer\nalgebra system. \n\nCadabra was designed specifically for the solution of problems\nencountered in field theory. It has extensive functionality for tensor\ncomputer algebra, tensor polynomial simplification including\nmulti-term symmetries, fermions and anti-commuting variables, Clifford\nalgebras and Fierz transformations, implicit coordinate dependence,\nmultiple index types and many more. The input format is a subset of\nTeX. Both a command-line and a graphical interface are available.\n\nThe Cadabra system is built around the C++ expression storage class\ncadabra::Ex.  This stores mathematical expressions in the form of a\nsymbol tree. Properties, derived from cadabra::property, can be\nattached to symbols inside the tree.  Algorithms, derived from\ncadabra::Algorithm, act on the cadabra::Ex objects, transforming their\ncontent by making use of the property information.\n\nThe C++ objects and algorithms can be accessed via Python (via the\ncadabra2 Python module built with the various files of the \\ref\npythoncore module), or they can be used directly through the use of\nCadabra-as-a-library.\n\nTo get started with the source code documentation, navigate to the\n\\ref modules overview.\n"
  },
  {
    "path": "doc/modules.dox",
    "content": "/// \\defgroup core Core\n/// All computer algebra functionality in the form of C++ classes.\n///\n/// \\defgroup cleanup Cleanup\n/// Functionality to clean up expressions so that they satisfy the requirements\n/// of a consistent expression tree.\n/// \\ingroup core\n///\n/// \\defgroup display Expression display\n/// Classes to handle printing of expressions in various formats.\n///\n/// There are several different requirements for printing, depending on whether\n/// output is to the console, the graphical notebook, or to a different\n/// computer algebra system. In the latter case, one typically also needs\n/// to be able to convert the output of that external system back into\n/// Cadabra-parsable format, which is what e.g. the DisplayMMA::import\n/// and DisplaySympy::import member functions do. \n/// \\ingroup core\n///\n///\n/// \\defgroup compare Expression comparison\n/// Functions to compare and match expressions stored in Ex objects. \n///\n/// These can involve wildcards and dummy indices, and matching may depend on \n/// the properties attached to symbols.\n/// This is an important bit of functionality used widely throughout the Cadabra core.\n/// All substitution and component evaluation logic depends on this module.\n/// \\ingroup core\n///\n/// \\defgroup files Notebooks and packages\n/// Graphical notebook interface and Cadabra packages.\n///\n/// Functionality to store and manipulate Cadabra notebooks and use them as\n/// packages inside other notebooks or scripts. \n/// \\ingroup core\n\n/// \\defgroup pythoncore Python Core\n/// Python wrapper around the C++ core module.\n///\n/// This wrapper makes the entire \n/// functionality of Cadabra accessible from Python. This consists of two\n/// parts. One is core/cadabra2_defaults.py, which is a pure-python file.\n/// It contains the display function to show Cadabra objects to the user\n/// in a UI-independent way (e.g. switching between a text representation\n/// on the command line and a LaTeX representation when running in a notebook).\n/// The other part are the various files in core/pythoncdb, which build\n/// the cadabra2 module for python, to be imported with 'from cadabra2 import *'.\n///\n/// The Python module has functionality to import Cadabra notebooks using\n/// standard Python import syntax. This functionality is part of the\n/// \\ref files module and described there.\n/// \\ingroup core\n\n/// \\defgroup scalar Scalar algebra\n/// Functionality to make Cadabra interface with scalar computer\n/// algebra systems such as Sympy or Mathematica.\n///\n/// It converts scalar\n/// parts of Cadabra expressions ('things without indices') to one of\n/// these systems, runs them through, and then converts back to Cadabra\n/// notation. Currently available are SymPy and Mathematica backends.\n/// \\ingroup core\n\n/// \\defgroup numerical Numerical evaluation\n/// Functionality to evaluate mathematical expressions numerically.\n/// \n/// Cadabra's symbolic expressions can be evaluated numerically,\n/// e.g. when you want to plot a function. Cadabra contains its own\n/// fast numerical evaluator and its own numerical tensor types.\n/// \\ingroup core\n\n/// \\defgroup algorithms Algorithms\n/// Containing all algorithms acting on symbolic expression trees.\n/// \\ingroup core\n///\n/// \\defgroup properties Properties\n/// Containing all properties that can be attached to symbolic expressions.\n/// \\ingroup core\n///\n/// \\defgroup clientserver Client-Server \n///\n/// Base classes (independent of any GUI toolkit) to write Cadabra\n/// clients and servers.\n///\n/// All clients use two threads. One is the main thread and runs\n/// most of the logic in the DocumentThread object. The other one is\n/// a thread which communicates with the server process; code for\n/// this thread is in the ComputeThread object.  One typically\n/// subclasses the former into a full-fledged object driving the\n/// graphical user interface.\n/// \n/// All functionality that deals with GUI updates is isolated in\n/// GUIBase. A client should derive from this abstract base class\n/// and implement the methods there. Clients should also derive from\n/// DocumentThread, but there are no abstract virtual members\n/// to implemented from this base class.\n/// \n/// All actual updates to the document stored in the\n/// DocumentThread::dtree member are made on the GUI thread as\n/// well. The compute thread merely puts requests to change the\n/// document onto a stack, and then requests that the GUI updates\n/// the document.\n///\n/// In order to enable undo/redo, all updates to DocumentThread::dtree \n/// are made by putting objects derived from ActionBase onto the \n/// action stack. See DocumentThread::queue_action for details.\n/// These ActionBase objects (among which ActionAddCell, ActionRemoveCell, \n/// ActionInsertText, etc) get executed on the GUI thread, and contain\n/// the actual logic to perform updates to the document and related\n/// GUI elements. \n///\n///\n/// \\defgroup libcadabra2 Cadabra C++ library\n///\n/// All Cadabra functionality can be used directly from C++ programs without\n/// using the Python frontend. A sample program can be found in\n/// c++lib/simple.cc:\n/// \\include c++lib/simple.cc\n///\n///\n/// \\defgroup frontend Front-end\n/// All code which implements graphical front-end notebook interfaces.\n\n"
  },
  {
    "path": "doc/random.md",
    "content": "# on macOS\nhttps://stackoverflow.com/questions/57535924/shipping-gtk-apps-for-macos-with-xcode\n\n\n# \n# Test 1:= keep_terms\n\nfrom cadabra import *;\n\nobj = Ex('a*(b+c)')\ndistribute(obj,True)\n\n\n\nHow do we do this on the C++ side? \n\n\n\n-----\n\nWith a preprocessor we could turn\n\nobj := A_{m n} B_{n p};\n\ninto \n\nobj = Ex('A_{m n} B_{n p}');\n\nvery easily and then all problems would go away. Ditto for\n\ndistribute!(obj);\n\nto \n\ndistribute(obj, all=True);\n\nalgo options:\n\n all:      like !  synonym for deep\n deep:     like !  make deep=True the default\n   actually, we could make this algo dependent; for some algorithms\n   like vary it does not make sense to do a deep default.\n repeat:   like !! make repeat=False the default\n\nWe could also wrap\n\ndistribute(%);\n\nsince (% is not a valid python sequence of characters anyway.\n\n\nProperties:\n\n  A_{m n}::Distributable(name='vector');\n\nto\n \n  Distributable('A_{m n}', name='vector');\n\n\nsed -e 's/\\(((\\?!:=).)*\\):=\\(.*\\)/\\1 = Ex(\"\\2\")/'\n\n---------------------\n\nIndices('m,n,p,q,r', name='vector');\nex = 'A_{m n} B_{m n}';\nsubstitute(ex, 'B_{p q} -> C_{p} C_{q}');\n\n\n\n\nobj1 = Ex('a1 + a2 + a3 + a4 + a5 + a6 + a7');\nobj1 = Algo(obj1, True);\n\nobj1 = keep_terms(obj1, {2,4});  // auto-converts string to ex\n// it is pass by reference, so obj1 gets modified. None of\n// this silly obj1 = blabla(obj1) nonsense.\ntst1 = 'a3 + a4 + a5 - obj1'; // python objects are known on the cdb side.\ncollect_terms(tst1);\nassert(tst1);\n\nex = keep_terms('a1 + a2 + a3 + a4 + a5 + a6 + a7', {2,4});\n\n\n@keep_terms(%){2}{4};\ntst1:= a3 + a4 + a5 - @(obj1);\n@collect_terms!(%);\n@assert(tst1);\n\n\n-----\n\na:=A*(B+C);\ndistribute(a, repeat=True);\nb:=A_{m n} (B^{n p} + C^{n p});\ndistribute(b);\ndistribute('A_{m n} (B^{n p} + C^{n p})');\n\n{a,b,c,d}::Indices;\nex:=A_{c d} C^{d};\nrename_dummies(ex);\n\nsort_product(ex)\nex:=B\nex:=A B A D C;\nrl:= B -> Q;\nsubstitute(ex, rl, True)\n\n{m,n,p,a,b}::Indices.\nex:=A_{m n} ( C^{n p} + D^{n p} );\nrl:= C^{a b} -> M_{m} D^{m a b};\nsubstitute(ex, rl)\n\nfrom cadabra import *\nIndices(Ex('{m,n,p,a,b}'))\nex=Ex('A_{m n} ( C^{n p} + D^{n p} )')\nrule=Ex('C^{a b} -> M_{m} D^{m a b}')\nsubstitute(ex, rule, True)\n\nsubstitute(ex, rl, True)\n\n\nex:= B + A B A D C + A A D C;\nrl:= B -> 2;\nsubstitute(ex, rl)\nrl2:= A A D C -> 9\nsubstitute(ex, rl2)\nex:= B + A B A D C + A A D C;\nsubstitute(ex, rl)\nrl:= B -> 2;\nsubstitute(ex, rl2)\n\n{m,n,p,a,b}::Indices.\nex:=A_{m n} ( C^{n p} + D^{n p} );\nrl:= C^{a b} -> D^{a b};\nsubstitute(ex, rl)\n\n\nex1=Ex(0)\nex2=Ex('0')\nex3=Ex('1')\nprint ex1==ex2\nprint ex2==ex3\nprint ex1==Ex(0)\n\ndef test():\n\t{m,n,p,a,b}::AntiCommuting.\n\tex:=p m n a;\n\tsort_product(ex);\n\tprint(ex);\n\tex2:= A*(B+C);\n\tdistribute(ex2);\t\n\ttst2:= A B + A C - @(ex2)\n\tprint(tst2)\n\tcollect_terms(tst2)\n        if tst==Ex(0):\n       \n\tprint(tree(tst2))\n\tprint(tree(Ex(0))\n\ntest()\n\n# This does not see the property declared in test():\nex3:=p m n a;\nsort_product(ex3);\nprint(ex3);\n\n\n\na=3\nex:= A_{m n} @(a)\n"
  },
  {
    "path": "doc/reserved/anticommutator.tex",
    "content": "\\cdbreserved{anticommutator}{}\n\nDenotes the anti-commutator of two objects.\n\nThe default properties of \\verb|\\anticommutator| are\n\\begin{verbatim}\n\\anticommutator{#}::IndexInherit.\n\\anticommutator{#}::Derivative.\n\\end{verbatim}\n\n\n\n\n"
  },
  {
    "path": "doc/reserved/arrow.tex",
    "content": "\\cdbreserved{arrow}{}\n\nDenotes a substitution rule.\n\n"
  },
  {
    "path": "doc/reserved/cdot.tex",
    "content": "\\cdbreserved{cdot}{}\n\nDenotes a dot product of vectors in which the contracted indices are\nsuppressed. Displays as an infix dot.\n\n\n\n"
  },
  {
    "path": "doc/reserved/comma.tex",
    "content": "\\cdbreserved{comma}{}\n\nDenotes comma-separated objects.  The parser rewrites any set of \nobjects which are separated by an infix comma using the \\verb|\\comma| object.\n\n\n\n"
  },
  {
    "path": "doc/reserved/commutator.tex",
    "content": "\\cdbreserved{commutator}{}\n\nDenotes the commutator of two objects.\n\nThe default properties of \\verb|\\commutator| are\n\\begin{verbatim}\n\\commutator{#}::IndexInherit.\n\\commutator{#}::Derivative.\n\\end{verbatim}\n\n\n\n\n"
  },
  {
    "path": "doc/reserved/conditional.tex",
    "content": "\\cdbreserved{conditional}{}\n\nDenotes a conditional pattern. The parser rewrites an infix vertical bar operator\nusing a \\verb|\\conditional| object, in which the first argument is the\npattern and the second argument is the condition under which the\npattern holds.\n\n"
  },
  {
    "path": "doc/reserved/equals.tex",
    "content": "\\cdbreserved{equals}{}\n\nDenotes equalities. The parser rewrites an infix \\verb|=| operator\nusing an \\verb|\\equals| object.\n\n\n\n"
  },
  {
    "path": "doc/reserved/expression.tex",
    "content": "\\cdbreserved{expression}{}\n\nDenotes the top-level node of an expression.\n\n"
  },
  {
    "path": "doc/reserved/factorial.tex",
    "content": "\\cdbreserved{factorial}{}\n\nDenotes the factorial of an object. The parser rewrites a post-fix\nexclamation mark as a \\verb|\\factorial| object.\n\n\n\n"
  },
  {
    "path": "doc/reserved/frac.tex",
    "content": "\\cdbreserved{frac}{}\n\nDenotes a generic ratio of objects. \n"
  },
  {
    "path": "doc/reserved/indexbracket.tex",
    "content": "\\cdbreserved{indexbracket}{}\n\nDenotes a group of objects with indices which are collectively\nwritten, as in~\\mbox{$(A + B + C)_{m n}$}.\n\nThe default properties of \\verb|\\indexbracket| are\n\\begin{verbatim}\n\\indexbracket{#}::Distributable.\n\\indexbracket{#}::IndexInherit.\n\\end{verbatim}\n~\n\n\n"
  },
  {
    "path": "doc/reserved/infty.tex",
    "content": "\\cdbreserved{infty}{}\n\nDenotes infinity.\n\n\n\n"
  },
  {
    "path": "doc/reserved/label.tex",
    "content": "\\cdbreserved{label}{}\n\nDenotes the label of an expression.\n\n\n\n"
  },
  {
    "path": "doc/reserved/matrix.tex",
    "content": "\\cdbreserved{matrix}{}\n\nGeneric dense matrix of component values.\n\n\n\n"
  },
  {
    "path": "doc/reserved/pow.tex",
    "content": "\\cdbreserved{pow}{}\n\nDenotes a generic exponent of one object raised to the power of\nanother object. The parser translates the infix ``\\verb|**|''\nto \\verb|\\pow|.\n\nThe default properties of \\verb|\\prod| are\n\\begin{verbatim}\n\\pow{#}::DependsInherit.\n\\end{verbatim}\n~\n\n\n"
  },
  {
    "path": "doc/reserved/prod.tex",
    "content": "\\cdbreserved{prod}{}\n\nDenotes a generic product of objects. The parser translates objects\nseparated by whitespace or by a ``\\verb|*|'' symbol to products. \n\nThe default properties of \\verb|\\prod| are\n\\begin{verbatim}\n\\prod{#}::Distributable.\n\\prod{#}::IndexInherit.\n\\prod{#}::CommutingAsProduct.\n\\prod{#}::DependsInherit.\n\\prod{#}::WeightInherit(label=all, type=Multiplicative).\n\\prod{#}::NumericalFlat.\n\\end{verbatim}\n~\n\n\\cdbseeprop{AntiCommuting}\n\\cdbseeprop{NonCommuting}\n\\cdbseealgo{prodsort}\n"
  },
  {
    "path": "doc/reserved/regex.tex",
    "content": "\\cdbreserved{regex}{}\n\nDenotes a regular expression name pattern. The first argument is a\nsymbol and the second argument is a string containing the regular\nexpression.\n\n"
  },
  {
    "path": "doc/reserved/sequence.tex",
    "content": "\\cdbreserved{sequence}{}\n\nDenotes a sequence or range of objects. The parser rewrites an\ninfix \\verb|..| operator (two dots) using a \\verb|\\sequence| object.\n\n\n\n"
  },
  {
    "path": "doc/reserved/sum.tex",
    "content": "\\cdbreserved{sum}{}\n\nDenotes a generic sum of objects. The parser translates objects\nseparated by a ``$+$'' symbol tol sums.\n\nThe default properties of \\verb|\\sum| are\n\\begin{verbatim}\n\\sum{#}::CommutingAsSum.\n\\sum{#}::DependsInherit.\n\\sum{#}::IndexInherit.\n\\sum{#}::WeightInherit(label=all, type=Additive).\n\\end{verbatim}\n~\n\n\n\\cdbseealgo{sumsort}\n"
  },
  {
    "path": "doc/reserved/unequals.tex",
    "content": "\\cdbreserved{unequals}{}\n\nDenotes inequalities. The parser rewrites an infix \\verb|!=| operator\nusing an \\verb|\\unequals| object.\n\n\n\n"
  },
  {
    "path": "doc/tableaux.sty",
    "content": "%\n% tableaux.sty  version 1.0\n% Copyright (C) 2007-2025  by Kasper Peeters\n%\n% A LaTeX style file for drawing Young diagrams and Young tableaux.\n%\n% This file is (well, was) part of the Cadabra computer algebra system,\n%\n%   https://cadabra.science/\n%\n% but may be distributed /or modified under the conditions of the\n% LaTeX Project Public License, either version 1.3 of this license or\n% (at your option) any later version. The latest version of this\n% license is in\n%\n%   http://www.latex-project.org/lppl.txt\n%\n% and version 1.3 or later is part of all distributions of LaTeX\n% version 2005/12/01 or later.\n%\n% This work has the LPPL maintenance status `maintained'.\n% The current maintainer of this work is Kasper Peeters.\n%\n\n\\def\\@forc#1#2#3{\\expandafter\\f@rc\\expandafter#1{#2 \\^}{#3}}\n\\def\\f@@rc#1#2#3\\f@@rc#4{\\def#1{#2}#4\\f@rc#1{#3}{#4}}\n\\long\\def\\ReturnAfterFi#1\\fi{\\fi#1}\n    \\def\\f@rc#1#2#3{%\n      \\def\\temp@ty{#2}%\n      \\ifx\\@empty\\temp@ty\n      \\else\n        \\ReturnAfterFi{%\n          \\f@@rc#1#2\\f@@rc{#3}%\n        }%\n      \\fi\n    }%\n\n% Sorry, some global registers...\n\\newdimen\\ytsize\\ytsize=2mm\n\\newdimen\\ytfsize\\ytfsize=4mm\n\\newcount\\repcnt\n\\newdimen\\acchspace\n\\newdimen\\accvspace\n\\newdimen\\raiseh\n\\newdimen\\maxw\n\n\\newcommand\\phrule[1]{\\hbox{\\vbox to0pt{\\hrule height .2pt width#1\\vss}}}\n%\\newcommand\\pvrule{\\vbox{\\hbox to0pt{\\vrule width .2pt height\\ytsize\\hss}}}\n\n\\newcommand\\ftableau[1]{%\n\\def\\ctest{,}\n\\def\\Ktest{\\^}\n\\acchspace=0ex\n\\accvspace=0ex\n\\maxw=0ex\n\\vbox{\\hbox{%\n\\@forc\\thisel{#1}{%\n \\ifx\\thisel\\Ktest{%\n     \\ifnum\\maxw=0\\maxw=\\acchspace\\fi%\n     \\raisebox{\\accvspace}{\\vbox to \\ytfsize{\\hbox to\n\t\t 0pt{\\vrule height \\ytfsize\\hss}}}\\kern\\acchspace\\kern-\\maxw}\n \\else\\ifx\\thisel\\ctest\n     \\ifnum\\maxw=0\\maxw=\\acchspace\\fi%\n     \\raisebox{\\accvspace}{\\vbox to \\ytfsize{\\hbox to 0pt{\\vrule height \\ytfsize\\hss}}}%\n     \\kern\\acchspace\\acchspace=0ex\n\t  \\advance\\accvspace by -\\ytfsize\n \\else\n     \\setbox3=\\hbox{$\\thisel$}%\n\t  \\raiseh=\\ytfsize%\n\t  \\advance\\raiseh by -1ex%\n\t  \\divide\\raiseh by 2%\n     \\advance\\acchspace by-\\ytfsize%\n     \\raisebox{\\accvspace}{\\vbox to \\ytfsize{\\hrule\\hbox to%\n        \\ytfsize{\\vrule height \\ytfsize\\hskip.5ex%\n         \\raisebox{\\raiseh}{\\tiny$\\thisel$}\\hss}\\vss\\phrule{\\ytfsize}}}%\n \\fi\\fi}}}}\n\n\\newcommand\\tableau[1]{%\n\\def\\stest{ }\n\\def\\Ktest{\\^}\n\\acchspace=0ex\n\\accvspace=0ex\n\\maxw=0ex\n\\hbox{%\n\\@forc\\thisel{#1}{%\n \\ifx\\thisel\\Ktest{}\n \\else\n     \\repcnt=\\thisel%\n     \\loop{}%\n     \\advance\\acchspace by-\\ytsize%\n     \\raisebox{\\accvspace}{\\vbox to \\ytsize{\\hrule \\hbox to%\n\t\t\t\\ytsize{\\vrule height \\ytsize\\hss}\\vss\\phrule{\\ytsize}}}%\n     \\advance\\repcnt by -1\\ifnum\\repcnt>1{}\\repeat%\n     \\ifnum\\maxw=0\\maxw=\\acchspace\\fi%\n     \\raisebox{\\accvspace}{\\vbox to \\ytsize{\\hbox to 0pt{\\vrule height \\ytsize\\hss}}}%\n     \\kern\\acchspace\\acchspace=0ex%\n\t  \\advance\\accvspace by -\\ytsize%\n \\fi}\\kern-\\maxw}}\n\n\n"
  },
  {
    "path": "doc/the_cadabra_book.bib",
    "content": "@article{kas_cdb_hep,\n   author  = \"Peeters, Kasper\",\n   title   = \"{Introducing Cadabra: a symbolic computer algebra system for field theory problems}\",\n   eprint  = \"hep-th/0701238\",\n   year    = \"2007\"\n}\n@Article{Peeters:2003pv,\n     author    = \"Peeters, Kasper and Westerberg, Anders\",\n     title     = \"{The Ramond-Ramond sector of string theory beyond leading order}\",\n     journal   = \"Class. Quant. Grav.\",\n     volume    = \"21\",\n     year      = \"2004\",\n     pages     = \"1643-1666\",\n     eprint    = \"hep-th/0307298\",\n     SLACcitation  = \"%%CITATION = HEP-TH 0307298;%%\"\n}\n@Article{Peeters:2000qj,\n   author    = \"Kasper Peeters and Pierre Vanhove and Anders Westerberg\",\n   title     = \"Supersymmetric higher-derivative actions in ten and eleven\n                dimensions,  the associated superalgebras and their\n                formulation in superspace\",\n   journal   = \"Class. Quant. Grav\",\n   volume    = \"18\",\n   year      = \"2001\",\n   pages     = \"843-889\",\n   eprint    = \"hep-th/0010167\",\n   SLACcitation  = \"%%CITATION = HEP-TH 0010167;%%\"\n}\n@article{Peeters:2018dyg,\n    author = \"Peeters, Kasper\",\n    title = \"{Cadabra2: computer algebra for field theory revisited}\",\n    doi = \"10.21105/joss.01118\",\n    journal = \"J. Open Source Softw.\",\n    volume = \"3\",\n    number = \"32\",\n    pages = \"1118\",\n    year = \"2018\"\n}\n"
  },
  {
    "path": "doc/the_cadabra_book.tex",
    "content": "\\documentclass[11pt]{book}\n\\usepackage[scale=.7]{geometry}\n\\usepackage{charter}\n\\usepackage[backend=biber, sorting=none]{biblatex}\n\\usepackage{textfit}\n\\usepackage{relsize}\n\\usepackage{setspace}\n\\usepackage{fancyhdr}\n\\usepackage{ytableau}\n\\usepackage{listings}\n\\usepackage[fleqn]{amsmath}\n\\usepackage{color}\n\\usepackage{changepage}\n\\usepackage[colorlinks=true, linkcolor=red, citecolor=red, urlcolor=black, plainpages=false, pdfpagelabels]{hyperref}\n\\usepackage{etoolbox}\n\\usepackage{amssymb}\n\\usepackage[parfill]{parskip}\n\\usepackage{graphicx}\n\\usepackage{wallpaper}\n\\def\\specialcolon{\\mathrel{\\mathop{:}}\\hspace{-.5em}}\n\\renewcommand{\\bar}[1]{\\overline{#1}}\n%\\newcommand{\\algorithm}[2]{{\\tt\\Large\\detokenize{#1}}\\\\[1ex]\n%  {\\emph{#2}}\\\\[1ex]\n%}\n\\usepackage{cprotect}\n\\newcommand{\\algorithm}[2]{\\subsection{\\texttt{#1}}\n{\\emph{#2}}\\\\\n}\n\\newcommand{\\property}[2]{{\\tt\\Large\\detokenize{#1}}\\\\[1ex]\n{\\emph{#2}}\\\\[1ex]\n}\n\\newcommand{\\algo}[1]{{\\tt \\detokenize{#1}}}\n\\newcommand{\\prop}[1]{{\\tt \\detokenize{#1}}}\n\\renewcommand{\\author}[1]{{\\bfseries #1}}\n\\newcommand{\\email}[1]{, {\\tt #1}}\n\n% Math expressions wrapped in \\brwrap will get typeset with\n% round brackets around them, which have the appropriate size.\n% The expression itself can still be broken over multiple lines.\n\n\\newcommand\\brwrap[3]{%\n  \\setbox0=\\hbox{$#2$}\n  \\left#1\\vbox to \\the\\ht0{\\hbox to 0pt{}}\\right.\\kern-.2em\n  \\begingroup #2\\endgroup\\kern-.15em\n  \\left.\\vbox to \\the\\ht0{\\hbox to 0pt{}}\\right#3\n}\n\n\\renewcommand{\\arraystretch}{1.2}\n\\tolerance=10000\n\\relpenalty=10\n\\binoppenalty=10\n\\hyphenpenalty=10\n%\\raggedright\n\n%\\usepackage[most]{tcolorbox}\n\n\\definecolor{backcolour}{rgb}{0.95,0.95,0.92}\n\\lstnewenvironment{python}[1][]{\\lstset{language=python,\n   columns=fullflexible,\n   xleftmargin=1em,\n   belowskip=0pt,\n%   aboveskip=5pt,\n   tabsize=3,\n   backgroundcolor=\\color{backcolour},   \n   commentstyle={}, % otherwise {#} cadabra arguments look ugly\n   breaklines=true,   \n   basicstyle=\\small\\ttfamily\\color{blue},\n   keywordstyle={}\n}}{}\n  \n\n\\everymath{\\displaystyle}\n\n% Page numbers\n\\pagestyle{fancy}\n\\fancyhf{} % clear all header and footer fields\n\\renewcommand{\\headrulewidth}{0pt}\n\\renewcommand{\\footrulewidth}{0pt}\n\\fancyfoot[LE,RO]{{\\small\\thepage}}\n\\fancyfoot[LO,RE]{}\n\n% \\makeatletter\\def\\old@comma{,}\\catcode`\\,=13 \\def,{%\n% \\ifmmode\\old@comma\\discretionary{}{}{}\\else\\old@comma\\fi}\\makeatother\n\n% Ensure that maths broken over multiple lines has a bit of spacing\n% between lines.\n\\lineskiplimit=0mm\n\\lineskip=1.5ex\n\n\\ytableausetup{centertableaux} % smalltableaux\n\n% Chapter and section headers.\n\\usepackage[compact]{titlesec}\n\n\\newcommand{\\chapterformat}[1]{\\LARGE\\larger\\bfseries \\hspace{3mm}#1}\n\n\\titleformat{\\chapter}[block]\n  {\\large\\bfseries}{}{0pt}{\\hfill{\\color[rgb]{.5,.5,.5}{%\n  \\bfseries\\scaletoheight{2cm}{\\thechapter}}}%\n\\\\\\hbox{~}\\hfill\\chapterformat}\n\n\n\n\\bibliography{the_cadabra_book}\n\n\n\\begin{document}\n\\pagestyle{empty}\n\\ThisLRCornerWallPaper{1.0}{book_cover}\n\\begin{flushright}\n\\today\n\\end{flushright}\n\\vspace{6ex}\n{\\bf \\scaletowidth{15cm}{The Cadabra Book}}~\\\\[.8ex] \n{\\it\\large A field-theory motivated approach to symbolic computer algebra}\\\\[6ex]\n{\\bf \\scaletowidth{5cm}{Kasper Peeters}}\n\\newpage\n\\pagestyle{empty}\n\\hbox{~}\n\\noindent {\\smaller This book is available under the terms of the GNU Free\nDocumentation License, version~1.2.\\\\\nThe Cadabra software is available under the terms of the GNU\nGeneral Public License, version~3.}\n\\vfill\n\\noindent {\\large\\bf Copyright \\copyright~2001-2025 ~Kasper Peeters}\\\\[3ex]\n\\href{mailto:kasper.peeters@cadabra.science}{kasper.peeters@cadabra.science}\n\n\\tableofcontents\n\n\\pagestyle{fancy} \n\n\\chapter{Introduction and overview}\n\\section{Bird's eye overview}\n\nCadabra is a symbolic computer algebra system (CAS) designed to solve\nproblems in physics, in particular (but not limited to) those which\ndeal with classical and quantum field theory. Its input format is a\nsubset of TeX, which means that throughout your computations the maths\nwill all stay in a form which is hopefully already familiar to you.\nIt has a large number of facilities which make it easy to work with\ntensors, anti-commuting objects, implicit indices, implicit coordinate\ndependence and so on; things which help to keep mathematical\nexpressions compact and readable, so that your notebooks resemble what\nyou would do with pen-and-paper.\n\n% Concrete types of problems you can solve include:\n% \\begin{itemize}\n%   \\item \n% \\end{itemize}\n\nCadabra is at its core a Python module (written in C++ and exposed to\nPython using pybind11), which also contains a pre-parser which turns\nCadabra's language into pure Python. You can use through a command\nline client, a graphical notebook interface, or via Jupyter through\nthe Cadabra kernel. You can, if you want to, also use it from Python\ndirectly, or as a C++ library.\n\n\n\\section{Cadabra's design philosophy}\n\nCadabra is built around the fact that many computations do not have\none single and unique path between the starting point and the end\nresult. When we do computations on paper, we often take bits of an\nexpression apart, do some manipulations on them, stick them back into\nthe main expression, and so on. Often, the manipulations that we do\nare far from uniquely determined by the problem, and often there is no\nway even in principle for a computer to figure out what is 'the best'\nthing to do.\n\nWhat we need the computer to do, in such a case, is to be good at\nperforming simple but tedious steps, without enforcing on the user how\nto do a particular computation. In other words, we want the computer\nalgebra system to be a scratchpad, leaving us in control of which\nsteps to take, not forcing us to return to a 'canonical' expression at\nevery stage.\n\nMost existing computer algebra systems allow for this kind of work\nflow only by requiring to stick clumsy 'inert' or 'hold' arguments\nonto expressions, by default always 'simplifying' every input to some\nform they think is best. Cadabra starts from the other end of the\nspectrum, and as a general rule keeps your expression untouched,\nunless you explicitly ask for something to be done to it.\n\nAnother key issue in the design of symbolic computer algebra systems\nhas always been whether or not there should be a distinction between\nthe 'data language' (the language used to write down mathematical\nexpressions), the 'manipulation language' (the language used to write\ndown what you want to do with those expressions) and the\n'implementation language' (the language used to implement algorithms\nwhich act on mathematical expressions). Many computer algebra systems\ntake the approach in which these languages are the same (Axiom,\nReduce, Sympy) or mostly the same apart from a small core which uses a\ndifferent implementation language (Mathematica, Maple). The Cadabra\nproject is rooted in the idea that for many applications, it is better\nto keep a clean distinction between these three languages. Cadabra\nwrites mathematics using LaTeX, is programmable in Python, and is\nunder the hood largely written in C++.\n\n\\section{History}\n\nCadabra was originally written around 2001 to solve a number of\nproblems related to higher-derivative\nsupergravity~\\cite{Peeters:2000qj,Peeters:2003pv}. It was then\nexpanded and polished, and first saw its public release in\n2007~\\cite{kas_cdb_hep}.  During the years that followed, it became\nclear that several design decisions were not ideal, such as the use of\na custom programming language and the lack of functionality for\ncomponent computations. Over the course of 2015-2016 a large rewrite\ntook place, which resulted in Cadabra 2.x~\\cite{Peeters:2018dyg}.\nThis new version is programmable in Python and does both abstract and\ncomponent computations. From 2017 to 2022 Dominic Price joined the\nteam. He was responsible for many improvements, such as the add-on\npackage system, the conversion to pybind11 for the Python bindings,\nthe implementation of the {\\tt meld} algorithm and many others. From\n2022 onwards the emphasis has been on making it easier to run Cadabra\n(for instance by the introduction of a publically available Jupyter\nserver with the Cadabra kernel, and by making it much easier to\ninstall the software locally on all platforms). From 2024 the focus is\nagain on adding more physics functionality as well as tutorials.\n\n\n%==================================================================\n\\chapter{The input format}\n\\input{input_format.tex}\n\\input{ref_printing.tex}\n\\input{ref_properties.tex}\n\\input{ref_indices.tex}\n\\input{ref_exponents.tex}\n\\input{ref_spacing.tex}\n\\input{ref_implicit_versus_explicit.tex}\n\\input{ref_indexbrackets}\n\n%==================================================================\n\\chapter{Mathematical properties}\n\\input{ref_derivatives.tex}\n\\input{ref_accents.tex}\n\\input{ref_ordering.tex}\n\n%==================================================================\n\\chapter{Manipulating expressions}\n\\input{ref_selecting.tex}\n\\input{ref_import.tex}\n\\input{ref_default_simplification}\n\\input{ref_patterns}\n\\input{ref_numerical}\n\\input{ref_dynamical_updates}\n\\input{ref_plotting}\n\\input{ref_ndsolve}\n\n%==================================================================\n\\chapter{Writing your own packages}\n\\input{ref_programming}\n\\input{ref_sympy}\n\\input{ref_kernel}\n\\input{ref_c++_library}\n\\input{ref_flags_variables}\n\n%==================================================================\n\\chapter{Algorithms}\n\n\\section{Substitution and variation}\n\n\\input{distribute}\n\\input{product_rule}\n\\input{substitute}\n\\input{vary}\n\\input{expand_power}\n\\input{unwrap}\n\\input{integrate_by_parts}\n\n\\section{Metrics and bundles}\n\n\\input{eliminate_kronecker}\n\\input{eliminate_metric}\n\\input{eliminate_vielbein}\n\\input{einsteinify}\n\\input{epsilon_to_delta}\n\\input{expand_delta}\n\\input{reduce_delta}\n\n\\section{Index manipulations}\n\n\\input{combine}\n\\input{explicit_indices}\n\\input{lower_free_indices}\n\\input{raise_free_indices}\n\\input{split_index}\n\\input{untrace}\n\\input{rename_dummies}\n\\input{rewrite_indices}\n\\input{expand}\n\n\\section{Tensor component values}\n\n\\input{complete}\n\\input{evaluate}\n\n\\section{Factorisation}\n\n\\input{factor_in}\n\\input{factor_out}\n\n\\section{Spinors and fermions}\n\n\\input{expand_diracbar}\n\\input{fierz}\n\\input{join_gamma}\n\\input{sort_spinors}\n\\input{split_gamma}\n\n\\section{Sorting and canonicalisation}\n  \n\\input{asym}\n\\input{canonicalise}\n\\input{young_project_product}\n\\input{young_project_tensor}\n\\input{meld}\n\\input{sort_product}\n\\input{sort_sum}\n\n\\section{Weights and perturbations}\n\n\\input{drop_weight}\n\\input{keep_weight}\n\n\\section{Simplification}\n\n\\input{collect_factors}\n\\input{collect_terms}\n\\input{map_sympy}\n\\input{simplify}\n\n\\section{Representations}\n\n\\input{decompose}\n\\input{decompose_product}\n\\input{lr_tensor}\n\n\\section{Sub-expression manipulation}\n\n\\input{replace_match}\n\\input{take_match}\n\\input{zoom}\n\n\\printbibliography\n\n\\end{document}\n"
  },
  {
    "path": "doc/users/command_line.tex",
    "content": "\n\\section{Command line interface}\n\\subsection{Options}\n\n\\begin{tabularx}{.8\\textwidth}{lX}\n\\verb|-d| & Run in debug mode, in which a Cadabra crash will land you in gdb\n            from which you can inspect stack traces and so on (only useful for\n            developers).\n\\end{tabularx}\n\n\n\n\\subsection{Editing facilities}\n\nWhen entering a Cadabra expression, that is, when a line contains a\n\\verb|:=| or \\verb|::| token indicating an expression or property\ndeclaration respectively, Cadabra enters a multi-line input mode which\nis somewhat different from the Python editing mode. As long as the\ninput does not end on a colon \\verb|:| or semi-colon \\verb|;| new\nlines will be requested, and this is indicated by the prompt becoming\na vertical bar. Multi-line input is strung together as one line before\nbeing fed to the Cadabra parser.\n"
  },
  {
    "path": "doc/users/comparison.tex",
    "content": "\nhttps://github.com/Jutho/TensorOperations.jl\n  (limited)\n\nhttp://hz2.org/blog/einstein_notation.html\n"
  },
  {
    "path": "doc/users/components.tex",
    "content": "\n\ng_{a b} -> \\eta_{a b} + l_a l_b\n\n\n\n\ng_{a b} => \\diag{ -1, 1, 1, 1 }_{a b}\n\n\n\n"
  },
  {
    "path": "doc/users/input.tex",
    "content": "\\section{Input format}\n\nThe input format of Cadabra~II follows the Python language\nspecification, with the following additional rules:\n\\begin{enumerate}\n\\item A line containing a \\verb|:=| token is interpreted as a Cadabra\n  expression declaration. If the line does not end with a semi-colon\n  \\verb|;| following lines are added until a line is found which does\n  end with a semi-colon. The newlines between these lines are replaced\n  with a single space character.\n\n  [example]\n\n  This is translated to the following expression before it is being\n  handed to the Python interpreter.\n\n  [translation]\n\n\\item A line containing a \\verb|::| token is interpreted as a Cadabra\n  property declaration. The same rule for line continuation is used.\n\n\\item Anything inbetween two dollar symbols is interpreted as a\n  Cadabra expression (just like \\TeX{} handles mathematical\n  expressions).\n\n\\item A line ending with a semi-colon \\verb|;| will lead to the output\n  of the last-used expression being printed. To be precise, it will\n  insert a \\verb|print(latex(_))| into the input.\n\\end{enumerate}\nThe interactive shell \\verb|cadabra2| will indicate Cadabra line\ncontinuations by showing a `|' symbol as prompt (instead of the\n`\\verb|>|' shown for new lines.\n"
  },
  {
    "path": "doc/users/notebook_comparisons.tex",
    "content": "\\section{Comparison with other notebook systems}\n\nCadabra is not built on IPython or Sage notebook. There are various\nreasons for this, but the most important one is probably that I am not\na strong believer in the idea that ``the Mathematica and Maple\nnotebook interfaces are the ideal to strive for''. In fact, I think\nthere are many things wrong with these interfaces, not\n\nBy tacking on to IPython on Sage, I would not be free to experiment\nwith different basic structure. \n\nSimple shortcomings: Most notebook systems lack a multiple view facility.\nMany lack an unlimited undo/redo stack, which tracks complete changes\nto the document, not just within a single cell.\n\nStructural shortcomings: \n"
  },
  {
    "path": "doc/writing_algorithms.tex",
    "content": "% Basic document style\n\\documentclass{article}\n\\usepackage[utf8]{inputenc}\n\\usepackage[margin=1in]{geometry}\n\\usepackage{inconsolata} % prettier texttt\n\\renewcommand{\\familydefault}{\\sfdefault}\n\n% Graphics, tables and figures\n\\usepackage{enumitem}\n\\usepackage{hyperref}\n\\usepackage{float}\n\\usepackage[table, x11names]{xcolor}\n\\usepackage{graphicx}\n\\usepackage{listings}\n\\usepackage{autogobble}\n\\usepackage{tikz}\n\n\\lstset{\n\tbasicstyle=\\footnotesize\\color{black}\\ttfamily,\n\tbelowcaptionskip=1\\baselineskip,\n\tbreaklines=true,\n\txleftmargin=\\parindent,\n\txrightmargin=\\parindent,\n\tshowstringspaces=false,\n\tkeywordstyle=\\color{Firebrick3},\n\tkeywordstyle=[2]\\color{DodgerBlue4},\n\tcommentstyle=\\color{MistyRose4},\n\tstringstyle=\\color{Green4},\n\trulecolor=\\color{black!50},\n\ttabsize=4,\n\tautogobble,\n\tframe=l,\n\tframerule=2pt\n}\n\\lstdefinestyle{cdb}{ language=Python, rulecolor=\\color{blue!50}, moredelim=[is][\\color{Goldenrod4}]{<m>}{</m>}, moredelim=[s][\\color{Goldenrod4}]{\\$}{\\$}, morekeywords={ assert }, keywords=[2]{ sym, cdb2python_string, explicit_indices, rhs, simplify, young_project, einsteinify, collect_terms, compile_package__, slot_sym, factor_in, young_project_tensor, eliminate_metric, cdb2python, init_ipython, zoom, take_match, collect_factors, slot_asym, expand_dummies, untrace, sort_sum, product_rule, lhs, split_gamma, epsilon_to_delta, rename_dummies, unwrap, decompose, eliminate_vielbein, create_scope, drop_weight, order, eliminate_kronecker, join_gamma, reduce_delta, distribute, integrate_by_parts, evaluate, rewrite_indices, expand_delta, vary, sort_spinors, asym, kernel, map_sympy, split_index, decompose_product, young_project_product, substitute, lower_free_indices, replace_match, expand_diracbar, complete, collect_components, tree, keep_weight, unzoom, meld, create_scope_from_global, terms, fierz, create_empty_scope, keep_terms, sort_product, raise_free_indices, properties, indexsort, expand, tab_dimension, expand_power, lr_tensor, canonicalise, combine, flatten_sum, factor_out, Distributable, AntiSymmetric, Accent, SelfCommutingBehaviour, WeightInherit, SelfCommuting, KroneckerDelta, AntiCommuting, Weight, Spinor, CommutingBehaviour, InverseMetric, DAntiSymmetric, SelfNonCommuting, Vielbein, Coordinate, scalar_backend_t, Diagonal, NumericalFlat, TableauInherit, Traceless, DependsBase, SortOrder, InverseVielbein, match_t, Indices, WeightBase, Derivative, WeylTensor, DifferentialFormBase, FilledTableau, CommutingAsProduct, ProgressMonitor, Tableau, CommutingAsSum, LaTeXForm, RiemannTensor, TableauSymmetry, list_property, SatisfiesBianchi, Metric, ExNode, Commuting, warn_t, TableauObserver, ExteriorDerivative, Total, Symmetric, Integer, SelfAntiCommuting, Trace, result_t, Ex, labelled_property, Stopwatch, DifferentialForm, NonCommuting, EpsilonTensor, PartialDerivative, Property, Symbol, ImaginaryI, TableauBase, IndexInherit, SympyBridge, Determinant, GammaMatrix, ImplicitIndex, Kernel, DiracBar, Matrix, Depends, parent_rel_t, } }\n\\lstnewenvironment{lstcdb}{\\lstset{style=cdb}}{}\n\\lstnewenvironment{lstverb}{\\lstset{moredelim=[is][\\bfseries\\color{Green3}]{<add>}{</add>}}}{}\n\\lstnewenvironment{lstlatex}{\\lstset{ rulecolor=\\color{Green4!50}, morekeywords={ \\algorithm, \\texttt } } }{}\n\\lstnewenvironment{lstcpp}{\\lstset{ language=C++, moredelim=[is][\\bfseries\\color{Green3}]{<add>}{</add>}, morekeywords={override}, rulecolor=\\color{LightPink2}}}{}\n\n% Copied from the cadabra preamble.tex\n\\newcommand{\\algorithm}[2]{{\\tt\\Large\\detokenize{#1}}\\\\[1ex]\n{\\emph{#2}}\\\\[1ex]\n}\n\n\n% Maths \n\\usepackage{amsmath}\n\\usepackage{amssymb}\n\\usepackage[vcentermath]{youngtab}\n\n\\title{Writing Algorithms in Cadabra2}\n\\author{Dominic Price}\n\\date{}\n\n\\begin{document}\n\\maketitle\n\nCadabra is a powerful computer algebra system which is specialised for handling tensor field calculations\nand is built on top of Python. By using Python as a foundation, it is very easy to extend the functionality of\nCadabra with custom algorithms to perform specific tasks as well as very generic routines which can use the \nincredibly flexible and reflective language features of Python to dynamically respond to different inputs.\n\nThis is a brief introduction to writing algorithms in Cadabra, introducing some of the typical idioms which allow\nuser algorithms to behave like the inbuilt routines as well as the various language features and technical \nconsiderations of writing algorithms.\n\nThe first section is a purely Python centred guide and assumes a basic familiarity with both Cadabra and Python\nwith any more advanced language features being explained and external resources to provide more details linked.\nIn the second section, the infrastructure of the underlying C++ codebase is explained and directions on how to\nextend Cadabra using C++ is covered. This is a slightly more advanced discussion although it is aimed to be\naccessible for casual users of C++. \n\n\\section{What is an algorithm in Cadabra?}\n\nBefore diving into the ins and outs of \\emph{how} to write an algorithm for Cadabra, it is first worth discussing exactly\nwhat specifically we are talking about as the term `algorithm' is quite general. For the purposes of this tutorial, when\ntalking about an algorithm we are specifically talking about a function which satisfies some criteria:\n\\begin{enumerate}\n\t\\item The number of argument it takes can vary, but its first argument must be a \\verb|Ex| object\n\t\\item It should apply transformations on this expression\n\t\\item It then returns a reference to this expression\n\\end{enumerate}\nThe functions in the Cadabra core all satisfy this format, and most of the functions found in the \\verb|cdb.*| libraries are\ntoo although occasionally they will instead create a copy of the input expression instead of modifying it. An example of an\nalgorithm which acts like this is \\verb|get_component| from the \\verb|cdb.core.component| library which resolves the free\nindices of an expression into specified components.\n\nWhile it is of course possible to write functions which modify expression and which \\emph{don't} follow these\ncriteria, if you are planning to release your algorithm to the wider community or even are collaborating on a \nproject then by making sure that you follow these requirements your code will be far more intuitive for others to\nfollow and will be able to be used alongside the inbuilt Cadabra algorithms seamlessly. To illustrate, the \nfollowing function\n\\begin{lstcdb}\n\tdef distribute_excluding(subex, ex):\n\t\tsubstitute(ex, $@(subex) -> qqq$)\n\t\tdistribute(ex)\n\t\tsubstitute(ex, $qqq -> @(subex)$)\n\t\treturn True\n\\end{lstcdb}\nwhich takes the `acting' expression as a second parameter and returns a \\verb|bool| is almost certain to be a common source\nof bugs and look out of place in a list of algorithm calls:\n\\begin{lstcdb}\n\t...\n\tunwrap(ex)\n\tsubstitute(ex, $\\partial_{\\mu}{p} -> 0$)\n\tdistribute_excluding($t - s$, ex)\n\t...\n\\end{lstcdb}\nand also prevents users from immediately viewing the results of the algorithm:\n\\begin{lstcdb}\n\tex := (x + y)*(a + b)*(c + d)\n\tsubstitute(ex, $a + b -> 1$); # Displays $(x+y)(c+d)$\n\tdistribute_excluding($x + y$, ex); # Displays 'True'\n\\end{lstcdb}\n\n\n\\section{Writing Cadabra algorithms in Python}\n\nHaving covered what an algorithm is, we can now start looking at ways to implement them. Using pure Python, there\nare two basic constructions which can be used for interfacing an algorithm: the simplest method is by using a \nPython function definition which satisfies the criteria given above. The second method is by using the special\n\\verb|@algo| decorator defined in \\verb|cdb.util.develop| which allows \\emph{tree-traversal} algorithms to be\neasily created.\n\n\\subsection{Iterating through the expression tree}\n\nOften, we may want to write a routine which does something completely different to what the inbuilt functions\nprovide and will require a lower-level look at the expression. In order to handle this, Cadabra provides methods\nfor iterating over the \\emph{expression tree}, which is the internal representation of the expression which\nCadabra keeps. You can get a basic visualisation of this tree, for example typing\n\\begin{lstcdb}\n\tex := <m>2k * (a_{\\mu} + b_{\\mu})</m>.\n\ttree(ex);\n\\end{lstcdb}\nwill show you the output\n\\begin{lstverb}\n\t{\\prod}  2  (4 000001E82DF51F60)\n\t  1:{k}  (4 000001E82DF510B0)\n\t  2:{\\sum}  (4 000001E82DF51560)\n\t  3:  {a}  (4 000001E82DF51650)\n\t  4:    _{\\mu}  (4 000001E82DF51790)\n\t  5:  {b}  (4 000001E82DF518D0)\n\t  6:    _{\\mu}  (4 000001E82DF51920)\n\\end{lstverb}\nThe \\texttt{tree} command is mainly for debugging purposes and so isn't the most friendly of layouts --- the\nname of the node is shown inside brackets (usually curly, but this reflects the bracket type of the node) and\nis optionally preceded by a symbol (usually \\verb|_| or \\verb|^|) reflecting its relation to the parent node,\nthis is followed by a number representing the rational multiplier of the node if it is non-unitary, and then\nin brackets is some extra information about the pointer location. Nodes representing operators are not denoted\nby symbols but are given names, thus in this diagram we can see \\texttt{*} $\\rightarrow$ \\verb|\\prod| and\n\\texttt{+} $\\rightarrow$ \\verb|\\sum|. A list of these special node names is given in Appendix \\ref{app:nodenames}.\nLets look at a diagrammatic representation to make it clearer what is being shown:\n\n\\begin{figure}[H]\n\t\\centering\n\t\\begin{tikzpicture}[\n\t\tsibling distance=10em,\n\t\tevery node/.style = {shape=rectangle, draw, align=center, fill=gray!20}]\n\t\t\\node {\\texttt{2 * \\textbackslash prod}}\n\t\t\tchild { node {\\texttt{k}} }\n\t\t\tchild { node {\\texttt{\\textbackslash sum}}\n\t\t\t\tchild { node {\\texttt{a}}\n\t\t\t\t\tchild { node {\\texttt{\\_\\textbackslash mu}} } }\n\t\t\t\tchild { node {\\texttt{b}}\n\t\t\t\t\tchild { node {\\texttt{\\_\\textbackslash mu}} } } };\n\t\\end{tikzpicture}\n\\end{figure}\n\nIf the relation between this and the expression $2k(a_{\\mu} + b_{\\mu})$ is unclear then there is a good\nexplanation of how to build up these trees on the Mathematics StackExchange\\footnote{\n\\url{https://math.stackexchange.com/a/369807}} and the Wikipedia article for binary trees\\footnote{\n\\url{https://en.wikipedia.org/wiki/Binary_expression_tree}} although it should be remembered that operator nodes\nin the Cadabra expression tree are not limited to two children.\n\nAccess to this tree in Python allows arbitrary manipulation of expressions. The tree can be traversed in\nnumerous ways, with \\texttt{ExNode} objects providing an interface to the nodes in the tree. These both expose\nvarious properties of the tree as well as methods which allow the insertion, modification and removal of nodes:\nthese methods are enumerated in Appendix \\ref{app:exnode}. \n\nThere are three main ways of obtaining references to nodes in the tree:\n\\begin{enumerate}[label=\\textbf{\\arabic*}.]\n\t\\item \\textbf{\\texttt{Ex.top()}}\n\t\n\tThe node representing the top node of a tree can be obtained by using the \\texttt{top} method of a\n\t\\texttt{Ex} object. From this, the tree can be further explored by using one of the \\texttt{ExNode} methods\n\twhich returns an iterator, for example\n\t\\begin{lstcdb}\n\t\tfor node in ex.top().children():\n\t\t\tprint(node.name)\n\t\\end{lstcdb}\n\twhich for the expression above prints\n\t\\begin{lstverb}\n\t\tk\n\t\t\\sum\n\t\\end{lstverb}\n\n\t\\item \\textbf{Name search}\n\t\n\tIt is possible to iterate over nodes based on their name as in the following example:\n\t\\begin{lstcdb}\n\t\tex := <m>v_{\\mu} v^{\\mu} \\gamma_{\\rho \\lambda} + T_{\\rho \\lambda}</m>;\n\t\tfor node in ex[r'\\mu']:\n\t\t\tnode.name = r'\\nu'\n\t\\end{lstcdb}\n\twhere the expression now reads $v_{\\nu} v^{\\nu} \\gamma_{\\rho \\lambda} + T_{\\rho \\lambda}$\n\t\\item \\textbf{Whole tree traversal}\n\t\n\tThe simplest traversal method is to visit the whole tree using a for loop:\n\t\\begin{lstcdb}\n\t\tfor node in ex:\n\t\t\tprint(node.name)\n\t\\end{lstcdb}\n\tFor the expression above this prints\n\t\\begin{lstverb}\n\t\t\\prod\n\t\tk\n\t\t\\sum\n\t\ta\n\t\t\\mu\n\t\tb\n\t\t\\mu\n\t\\end{lstverb}\n\tThis is known as \\emph{preorder} iteration, i.e. each node is returned before its children are visited.\t\n\\end{enumerate}\n\n\n\\subsection{Accessing property information}\n\nIn many cases, in order for a algorithm to work correctly we need to be able to query subexpressions to see\nwhich properties they have assigned. This can be done using the \\texttt{.get(ex)} method of a property which\nreturns the corresponding property object if it assigned to the expression or \\texttt{None} otherwise. In the\nfollowing example this lets us check whether various objects are defined as coordinates:\n\\begin{lstcdb}\n\t<m>{t, x, y, z}</m>::Coordinate.\n\tCoordinate.get($t$);\n\tCoordinate.get($\\phi$);\n\tfor node in $x, r$.top().children():\n\t\tCoordinate.get(node);\n\\end{lstcdb}\n\\begin{lstverb}\n\tProperty Coordinate attached to t.\n\tNone\n\tProperty Coordinate attached to x\n\tNone\n\\end{lstverb}\nNote that some properties, such as \\texttt{Coordinate}, can be dependent upon their parent relationship, for\nexample the $t$ in $v_t$ is still a coordinate but the following returns \\texttt{None}:\n\\begin{lstcdb}\n\tex := <m>v_{t}</m>.\n\tfor node in ex['t']:\n\t\tCoordinate.get(node);\n\\end{lstcdb}\n\tIn this instance, we can pass the optional argument \\verb|ignore_parent_rel=True| to allow Cadabra to make the\n\tmatch:\n\\begin{lstcdb}\n\tfor node in ex['t']:\n\t\tCoordinate.get(node, ignore_parent_rel=True);\n\\end{lstcdb}\nMany property object have extra methods which provide extra information, usually these are from attributes\npassed when the property was declared. In the following example we can use this to see which values various\nindices run over:\n\\begin{lstcdb}\n\t<m>{i, j, k, l}</m>::Indices(<m>cartesian, values={x,y,z}</m>).\n\t<m>{\\mu, \\nu, \\rho, \\lambda}</m>::Indices(<m>polar, values={r, \\phi, \\theta}</m>).\n\tex := <m>x^{i}x^{i} + p_{\\mu}p^{\\mu}</m>.\n\tfor node in ex:\n\t\tprop = Indices.get(node)\n\t\tif prop is not None:\n\t\t\tprint(node.name, prop.values)\n\\end{lstcdb}\n\\begin{lstverb}\n\ti [x, y, z]\n\ti [x, y, z]\n\t\\mu [r, \\phi, \\theta]\n\t\\mu [r, \\phi, \\theta]\n\\end{lstverb}\nTo get a list of which extra methods a property defines you can use \\verb|dir| or \\verb|help| to list all the\nmethods it defines.\n\n\\subsection{Algorithms using \\texttt{def}}\n\nFor almost all situations you are likely to come across, a simple definition of an algorithm using a Python\nfunction will be sufficient. We already saw a bad example of this in the previous section with \n\\verb|distribute_excluding|; lets rewrite that now to make it more conventional:\n\\begin{lstcdb}\n\tdef distribute_excluding(ex, subex):\n\t\tsubstitute(ex, $@(subex) -> qqq$)\n\t\tdistribute(ex)\n\t\tsubstitute(ex, $qqq -> @(subex)$)\n\t\treturn ex\n\\end{lstcdb}\nThis is a simple routine which allows us to limit the effects of \\verb|distribute| on an expression which can\nbe useful if there are some common factors containing sums which we want to preserve, for example in\nSchwarzchild space-time where factors of $2M - r$ are common. Of course, this is a slightly na\\\"ive way of\nwriting this (it will cause unexpected behaviour in the event someone uses \\texttt{qqq} as a variable name and\nis limited to only allowing one expression to be excluded) but illustrates a common technique for writing\nalgorithms quite nicely: more complicated manipulations can often be produced simply by combining the\ninbuilt algorithms like this to suit specific needs. \n\n\\subsection{Algorithms using \\texttt{@algo}}\n\nA common technique for writing algorithms is to traverse the expression tree checking each node against a criteria and applying\na function to it if the criteria is satisfied. The entire collection of core algorithms is built in this manner and the pattern\nis implemented in the \\texttt{Algorithm} class. This is a abstract base class with two pure virtual methods: \\verb|can_apply|\nwhich implements the predicate checking if an operation can be applied to a tree node, and \\verb|apply| which then carries out\nthe actual operation. \n\nThe class itself is, however, usually not directly visible to users --- instead its behaviour is wrapped inside of a function\nwhich takes care of iterating through the tree, calling \\verb|can_apply| and \\verb|apply|, and ensuring that the tree is in\na normalised state after the operation. In Python this wrapping is implemented with the \\verb|@algo| decorator which\nautomatically converts the class into an appropriate function call. A very simple example is the following \\verb|x_to_y|\nalgorithm. We first need to import the relevant objects from the \\verb|cdb.utils.develop| library:  \n\\begin{lstcdb}\n\tfrom cdb.utils.develop import algo, Algorithm\n\\end{lstcdb} \nWe then define a decorated class which inherits from \\verb|Algorithm| and overrides the two virtual functions:\n\\begin{lstcdb}\n\t@algo\n\tclass x_to_y(Algorithm):\n\t\tdef can_apply(self, node):\n\t\t\treturn node.name == 'x'\n\t\tdef apply(self, node):\n\t\t\tnode.name = 'y'\n\t\t\treturn result_t.changed\n\\end{lstcdb}\nThe predicate in this instance simply checks the name of the node, but in all cases it should return a boolean type. Any node\nfor which the result is \\verb|False| is skipped and so the \\verb|apply| method can make assumptions about node it receives as\na parameter based on this. In this case, it knows that it can change the name to \\texttt{y}. The return value of the \n\\verb|apply| method is of type \\verb|result_t| which should take on the value \\texttt{changed} if some transformation was\napplied, \\texttt{error} if some error occurred inside the method or \\texttt{unchanged} if \\verb|apply| ended up making no\nmodifications to the tree. \\verb|apply| \\emph{must} return a \\verb|result_t| or an exception will be raised when the algorithm\nis called that the function signature is incorrect.\n\nThe \\verb|@algo| decorator converts this into a function so we call this algorithm as any other algorithm in Cadabra:\n\\begin{lstcdb}\n\tx_to_y($x + y$)\n\\end{lstcdb}\n\\begin{lstverb}\n\t2y\n\\end{lstverb}\nNotice that various cleanup routines are automatically called after the algorithm is applied which simplifies the expression\nfrom $y + y$ into $2y$. \n\nThe function is also given the optional keyword arguments \\verb|deep|, \\verb|repeat| and \\verb|depth| with the same behaviour\nas the core algorithms.\n\n\\subsubsection*{Stateful algorithms}\nSometimes it is necessary for an algorithm to be stateful, that is either be passed extra information through parameters when\nit is called or to retain some information between various calls to \\verb|apply|. This can be done by overriding the \n\\verb|__init__| method of the class; any arguments passed to the function call (other than \\verb|deep|, \\verb|repeat| and\n\\verb|depth|) are forwarded onto this constructor.  Let's use this to extend our \\verb|x_to_y| algorithm into one where we can\nspecify other values for \\verb|x| and \\verb|y|:\n\\begin{lstcdb}\n\t@algo\n\tclass x_to_y(Algorithm):\n\t\tdef __init__(self, ex, x='x', y='y'):\n\t\t\tAlgorithm.__init__(self, ex)\n\t\t\tself.x = x\n\t\t\tself.y = y\n\t\tdef can_apply(self, node):\n\t\t\treturn node.name == self.x\n\t\tdef apply(self, node):\n\t\t\tnode.name = self.y\n\t\t\treturn result_t.changed\n\\end{lstcdb}\nWe can now use this as a `y-to-x' algorithm too:\n\\begin{lstcdb}\n\tx_to_y($x + y$, x='y', y='x');\n\\end{lstcdb}\n\\begin{lstverb}\n\t2x\n\\end{lstverb}\nIts important to ensure that the first argument to the \\verb|__init__| method is the \\verb|Ex| object on which the algorithm\nis called, and to remember to call the base \\verb|Algorithm| constructor too.\n\n\\subsubsection*{Functional shortcut}\nFor simple algorithms such as our \\verb|x_to_y| example here, instead of defining an entire class we can also just supply\n\\verb|@algo| with a function and it will automatically generate the class definition using the function body for the\n\\verb|apply| method:\n\\begin{lstcdb}\n\t@algo\n\tdef x_to_y(node):\n\t\tif node.name == 'x':\n\t\t\tnode.name = 'y'\n\t\t\treturn result_t.changed\n\t\treturn result_t.unchanged\n\\end{lstcdb}\nNote that it is not possible to create a stateful algorithm using this method, the definition using a class as shown above must\nbe used if this is desired.\nAnoher drawback to this approach is that the predicate is now inside the body of \\verb|apply| which results in slightly less\nefficient code being produced, but this is negligible for simple algorithms such as this for which the shorthand is intended.\nIf this does become a concern, it is also possible to supply \\verb|algo| with a verb|pred| parameter which it will use as the\nbody for \\verb|can_apply| eliminating the need to perform this check inside the function body:\n\\begin{lstcdb}\n\t@algo(pred=lambda node: node.name == 'x')\n\tdef x_to_y(node):\n\t\tnode.name = 'y'\n\t\treturn result_t.changed\n\\end{lstcdb}\nThis produces code which is identical to the first class definition we discussed above. \n\n\\subsection{Documenting algorithms}\n\nAs notebooks can be imported from other notebooks using Python's \\texttt{import} statement, many Cadabra packages are written\nin notebooks which allows the documentation to be provided in accompanying \\LaTeX{} cells. In order to format this documentation\nthe \\texttt{algorithm} command is provided which takes two arguments: the signature of the algorithm's function call and a\nbrief description of its use and application. \n\nThe signature should contain the types of all the arguments and the return value using Python's type hinting style, for \nexample a function which takes a \\texttt{Ex} object and a \\texttt{int} and returns a \\texttt{Ex} might be documented like\n\\begin{lstlatex}\n\\algorithm{my_algo(ex: Ex, n: int) -> Ex}{Does some transformation to \\texttt{ex} which involves \\texttt{n}}\n\\end{lstlatex}\n\\fcolorbox{gray!50}{white}{%\n\t\\begin{minipage}{\\textwidth}\n\t\t\\vspace{1mm}\n\t\t\\algorithm{my_algo(ex: Ex, n: int) -> Ex}{Does some transformation to \\texttt{ex} which involves \\texttt{n}}\n\t\\end{minipage}\t\n}\n\n\\section{Writing Cadabra algorithms in C++}\n\nAlthough one of the greatest strengths of Cadabra is how easy it is to extend using Python, efficiency can sometimes cause \nissues either on very large expressions or when algorithms reach a certain level of complexity and are hindered by the\nPython interpreted runtime. In these instances, writing the algorithm in C++ is almost certainly the necessary solution. It is\nnot a common occurrence for users to contribute C++ algorithms and so no specific functionality has been developed in order to\nfacilitate the writing of external libraries and so it is necessary to build Cadabra from source and develop the algorithm\ninside the core codebase, however Cadabra always welcomes community contributions and if the algorithm proves to be useful then\nit may well be included in a future release of Cadabra.\n\nThere are two ways of placing a C++ algorithm into Cadabra: either by extending the list of core algorithms, or by placing the\ncode in a library package. In either instance, the first step is to get the Cadabra code base from github\n\\footnote{\\url{https://github.com/kpeeters/cadabra2}} and follow the build instructions for your OS. The next optional\n(but recommended especially if you are planning of submitting a pull request) is to set up a new git branch to perform your\ndevelopment on. \n\n\\subsection{Writing a core algorithm}\n\nAs with the \\verb|@algo| style of algorithm definition in Python, the core algorithms in C++ all derive from the C++\n\\verb|Algorithm| class. First, you should create a header and source file where the code for you algorithm will live. As with\nthe previous example, we will create the simple \\verb|x_to_y| algorithm and so we create the files \n\\verb|core/algorithms/x_to_y.hh| and \\verb|core/algorithms/x_to_.cc|. We also need to tell CMake about the new source file by\nadding a line to the \\verb|ALGORITHM_SRC_FILES| variable in \\verb|core/CMakeLists.txt|:\n\\begin{lstverb}\nSET(ALGORITHM_SRC_FILES\n   algorithms/canonicalise.cc\n   algorithms/collect_components.cc\n   algorithms/collect_factors.cc\n   ...\n   algorithms/unwrap.cc\n   algorithms/unzoom.cc\n   algorithms/untrace.cc\n   <add>algorithms/x_to_y.cc</add>\n   algorithms/vary.cc\n   algorithms/young_project.cc\n   algorithms/young_project_product.cc\n)\n\\end{lstverb}\nNext we need to define the \\verb|x_to_y| class in the header file \\verb|core/algorithms/x_to_y.hh| we just created:\n\\begin{lstcpp}\n\t#pragma once\n\t#include <Algorithm.hh>\n\t\n\tnamespace cadabra {\n\t\tclass x_to_y : public Algorithm {\n\t\t\tpublic:\n\t\t\t\tx_to_y(const Kernel& kernel, Ex& ex);\n\t\n\t\t\t\tbool can_apply(Ex::iterator it) override;\n\t\t\t\tresult_t apply(Ex::iterator& it) override;\n\t\t\t};\n\t\t}\n\\end{lstcpp}\nThis should be fairly understandable, the signatures of all the class methods must be the same as in this example but you\nmay add more parameters to the constructor after the \\verb|Ex| reference (as we will do later). We can now move on to the\nimplementation which goes into \\verb|core/algorithms/x_to_y.cc|. We start by importing the header and for convenience \npulling \\verb|cadabra| into the global namespace:\n\\begin{lstcpp}\n\t#include \"algorithms/x_to_y.hh\"\n\t\n\tusing namespace cadabra;\n\\end{lstcpp}\nFor the simple algorithm we are writing, we will simply forward the constructor arguments onto the \\verb|Algorithm| constructor:\n\\begin{lstcpp}\n\tx_to_y::x_to_y(const Kernel& kernel, Ex& ex)\n\t\t: Algorithm(kernel, ex)\n\t\t{\n\t\n\t\t}\n\\end{lstcpp}\nNext we write in our implementation of \\verb|can_apply|. This is a very straightforward function, the only thing to keep in \nmind is that node names in Cadabra are interned and so to access the \\verb|std::string| representation of them they must\nbe dereferenced:\n\\begin{lstcpp}\n\tbool x_to_y::can_apply(Ex::iterator it)\n\t\t{\n\t\treturn *it->name == \"x\";\n\t\t}\n\\end{lstcpp}\nThe last bit of code we need to write in this file is the implementation of \\verb|apply|. Again, as the strings are interned\ninstead of assigning a string we must query the global \\verb|name_set| for an iterator and store the value this returns to us:\n\\begin{lstcpp}\n\tAlgorithm::result_t x_to_y::apply(Ex::iterator& it)\n\t\t{\n\t\tit->name = name_set.insert(\"y\").first;\n\t\treturn result_t::l_applied;\n\t\t}\n\\end{lstcpp}\nIt is also worth mentioning that the \\verb|result_t| names differ between the Python and C++ interfaces; whereas before we\nused \\verb|changed| and \\verb|unchanged| in C++ we use \\verb|l_applied| and \\verb|l_no_action| respectively.\n\nThe final step we need to perform is the Python interfacing code in \\verb|core/pythoncdb/py_algorithms.cc|. We first add our\nheader file to the list of includes at the top:\n\\begin{lstcpp}\n\t...\n\t#include \"../algorithms/unwrap.hh\"\n\t#include \"../algorithms/unzoom.hh\"\n\t#include \"../algorithms/untrace.hh\"\n\t<add>#include \"../algorithms/x_to_y.hh\"</add>\n\t#include \"../algorithms/vary.hh\"\n\t#include \"../algorithms/young_project.hh\"\n\t#include \"../algorithms/young_project_product.hh\"\n\t#include \"../algorithms/young_project_tensor.hh\"\n\t...\n\\end{lstcpp}\nThe final step before building is then the actual binding code. This is the least intuitive part of the process, but most of\nthe technical details are hidden and all that needs to be done is to call \\verb|def_algo| templated against the\n\\verb|x_to_y| class. You can add this line to the end of the list of \\verb|def_algo| declarations in the \n\\verb|init_algorithms| function:\n\\begin{lstcpp}\n\tvoid init_algorithms(py::module& m)\n\t\t{\n\t\tpybind11::enum_<Algorithm::result_t>(m, \"result_t\")\n\t\t.value(\"checkpointed\", Algorithm::result_t::l_checkpointed)\n\t\t...\n\t\tdef_algo_preorder<meld, bool>(m, \"meld\", true, false, 0, py::arg(\"project_as_sum\") = false);\n\t\t<add>def_algo<x_to_y>(m, \"x_to_y\", true, false, 0);</add>\n\t\t}\n\\end{lstcpp}\nThe first argument is a handle to the \\verb|cadabra2| Python module and the second is the name of the function on the \nPython side, this should be the same as the C++ name to avoid confusion. The next three parameters are the default values of\nthe \\verb|deep|, \\verb|repeat| and \\verb|depth| parameters but these can be changed in Python when calling the algorithm\nby using the optional keyword arguments.\n\nIt's now time to build Cadabra again and try out the new algorithm. The algorithm will be imported into the global scope at\nlaunch:\n\\begin{lstcdb}\n\tx_to_y($x + y$);\n\\end{lstcdb}\n\\begin{lstverb}\n\t2y\n\\end{lstverb}\n\n\\subsubsection*{Adding extra constructor parameters}\n\nAs with our \\verb|x_to_y| function from the Python section, a natural extension would be to allow users to provide values of\n\\verb|x| and \\verb|y|. This only requires a few alterations to the code we have written: first the constructor must be \naltered to take the new parameters and the class definition extended to include the two new variables \\verb|x| and \\verb|y|. We will store these as interned strings and so we declare them as \\verb|nset_t::iterator| variables. The new class definition in \n\\verb|x_to_y.hh| now looks as follows\n\\begin{lstcpp}\n\tclass x_to_y : public Algorithm {\n\t\tpublic:\n\t\t\tx_to_y(const Kernel& kernel, Ex& ex, const std::string& x, const std::string& y);\n\n\t\t\tbool can_apply(Ex::iterator it) override;\n\t\t\tresult_t apply(Ex::iterator& it) override;\n\n\t\tprivate:\n\t\t\tnset_t::iterator x, y;\n\t\t};\n\\end{lstcpp}\nMoving onto \\verb|x_to_y.cc|, we now also change the constructor signature here and initialise \\verb|x| and \\verb|y|:\n\\begin{lstcpp}\n\tx_to_y::x_to_y(const Kernel& kernel, Ex& ex, const std::string& x, const std::string& y)\n\t\t: Algorithm(kernel, ex)\n\t\t, x(name_set.insert(x).first)\n\t\t, y(name_set.insert(y).first)\n\t\t{\n\t\n\t\t}\n\\end{lstcpp}\nThe \\verb|can_apply| and \\verb|apply| function definitions also need to use the stored values instead of the hardcoded\nvalues of \\verb|x| and \\verb|y|:\n\\begin{lstcpp}\n\tbool x_to_y::can_apply(Ex::iterator it)\n\t{\n\t\treturn it->name == x;\n\t}\n\t\n\tAlgorithm::result_t x_to_y::apply(Ex::iterator& it)\n\t{\n\t\tit->name = y;\n\t\treturn result_t::l_applied;\n\t}\n\\end{lstcpp}\nAlmost done: just one more line to change, the Python binding code. In order to make Python aware that the function now takes\ntwo extra arguments, we need to add the types of these these extra arguments to the list of template parameters of \n\\verb|def_algo|. We also need to give these extra arguments Python names, which is done by adding a \\verb|py::arg| object\nparameter onto the end of the list of \\verb|def_algo|'s parameters for each argument. The final binding code should look like\nthis:\n\\begin{lstcpp}\n\tdef_algo<x_to_y, const std::string&, const std::string&>(\n\t\tm, \"x_to_y\", true, false, 0, \n\t\tpy::arg(\"x\"), py::arg(\"y\"));\n\\end{lstcpp}\nAfter building, this is now accessible from Cadabra:\n\\begin{lstcdb}\n\tx_to_y($x + y$, 'y', 'x')\n\\end{lstcdb}\n\\begin{lstverb}\n\t2x\n\\end{lstverb}\n\n\\subsection{Writing a package algorithm}\n\nRecently, additions to the binding code have allowed the possibility of creating Cadabra packages in C++. There is currently\nonly support in the build system for creating libraries for the builtin \\verb|cdb.*| libraries. This can be used to refactor\nalgorithms contained in these libraries which are currently implemented in Python into C++ routines, or to provide `non-core'\nfunctionality in an easily accessible location without polluting the global namespace.\n\nIt is recommended that the C++ library is prefixed with an underscore, and the relevant functions, classes or other definitions\nwhich it provides imported into a Cadabra notebook with the documentation attached there. Therefore, if we wanted to create\na \\verb|cdb.core.subs| module for our \\verb|x_to_y| algorithm, we would create the C++ module \\verb|cdb.core._subs| and then\nhave a notebook \\verb|cdb.core.subs| with the contents\n\\begin{lstlatex}\n\\algorithm{x_to_y(ex: Ex) -> Ex}{Renames all nodes names x to y}\n\\end{lstlatex}\n\\begin{lstcdb}\nfrom cdb.core._subs import x_to_y\n\\end{lstcdb}\n\nTo create the package, we first need to make a file \\verb|core/packages/cdb/core/_subs.cc|. To make the build system aware\nof the package, we need to add it to the \\verb|COMPILED_PACKAGES| variable in the build script located at\n\\verb|core/packages/CMakeLists.txt|:\n\\begin{lstverb}\nset(COMPILED_PACKAGES\n  core/_component.cc\n  utils/_algorithm.cc\n  <add>core/_subs.cc</add>\n  )\n\\end{lstverb}\nThe contents of the file \\verb|_subs.cc| is very similar to the code used for implementing a core algorithm. We begin by\nimporting the functionality from the \\verb|py_algorithms.hh| header which will also give us access to the \\verb|Algorithm|\nclass, and we will then bring it into scope by importing all the names from the \\verb|cadabra| namespace:\n\\begin{lstcpp}\n\t#include \"pythoncdb/py_algorithms.cc\"\n\t\n\tusing namespace cadabra;\n\\end{lstcpp}\nWe can then implement the \\verb|x_to_y| class as before, here we use inline function definitions for brevity:\n\\begin{lstcpp}\n\tclass x_to_y : public Algorithm {\n\t\tpublic:\n\t\t\tx_to_y(const Kernel& kernel, Ex& ex)\n\t\t\t\t: Algorithm(kernel, ex)\n\t\t\t\t{\n\t\n\t\t\t\t}\n\t\n\t\t\tbool can_apply(Ex::iterator it) override\n\t\t\t\t{\n\t\t\t\treturn *it->name == \"x\";\n\t\t\t\t}\n\t\n\t\t\tresult_t apply(Ex::iterator& it) override\n\t\t\t\t{\n\t\t\t\tit->name = name_set.insert(\"y\").first;\n\t\t\t\t}\n\t\t};\n\\end{lstcpp}\nFinally we create the Python module itself using the \\verb|PYBIND11_MODULE| macro. The first argument must match the filename\nas this will be the name of the module, the second argument can be any valid identifier. We can then call \\verb|def_algo|\njust as before:\n\n\\begin{lstcpp}\n\tPYBIND11_MODULE(_subs, m)\n\t{\n\t\tdef_algo<x_to_y>(m, \"x_to_y\", true, false, 0);\n\t}\n\\end{lstcpp}\nAfter building, this will now be available to import into Cadabra. Assuming we have also created the \\verb|subs| notebook as\ndescribed above, we can now call the \\verb|x_to_y| from there:\n\\begin{lstcdb}\n\tx + y\n\\end{lstcdb}\n\\begin{lstverb}\n\t2y\n\\end{lstverb}\nExtending this to the alternate form of \\verb|x_to_y| with extra arguments is done exactly as for the case when writing a \ncore algorithm was discussed.\n\nCircling back to the very beginning of this tutorial, it is of course also possible to create a function which does this\nby accepting and returning a \\verb|Ex_ptr| (a convenience typedef for the \\verb|Ex| pointer type exposed to Python):\n\\begin{lstcpp}\n\tEx_ptr x_to_y(Ex_ptr ex)\n\t\t{\n\t\tfor (Ex::iterator beg = ex->begin(), end = ex->end(); beg != end; ++beg) {\n\t\t\tif (*beg->name == \"x\")\n\t\t\t\tbeg->name = name_set.insert(\"y\").first;\n\t\t\t}\n\t\treturn ex;\n\t\t}\n\\end{lstcpp}\nwith the binding code\n\\begin{lstcpp}\n\tm.def(\"x_to_y\", x_to_y);\n\\end{lstcpp}\n\n\n\\appendix\n\n\\newpage\n\\section{Reserved node names}\n\\label{app:nodenames}\n\nMore information on the behaviour of these nodes can be found in the Cadabra documentation.\n\n\\begin{table}[H]\n\t\\centering\n\t\\renewcommand{\\arraystretch}{1.5}\n\t\\begin{tabular}{|c|c|c|}\n\t\\hline\n\t\\rowcolor[HTML]{C0C0C0} \n\tSymbol & Node name & Brief description    \\\\ \\hline\n\t$\\times$ & \\verb|\\prod| \n\t\t& Product of children\\\\ \\hline\n\t$+$ & \\verb|\\sum| \n\t\t& Sum of children  \\\\ \\hline\n\t$\\oplus$ & \\verb|\\oplus| \n\t\t& Tensor sum of children \\\\ \\hline\n\t$\\frac{x}{y}$ & \\verb|\\frac| \n\t\t& Quotient of children (internal use only)  \\\\ \\hline\n\t$,$ & \\verb|\\comma| \n\t\t& List of children as independent expressions \\\\ \\hline\n\t$\\rightarrow$ & \\verb|\\arrow| \n\t\t& Substitution rule from first child to second \\\\ \\hline\n\t$\\cdot$ & \\verb|\\inner| \n\t\t& Inner product of children \\\\ \\hline\n\t$x^y$ & \\verb|\\pow| \n\t\t& First child to power of second child \\\\ \\hline\n\t$\\int$ & \\verb|\\int| \n\t\t& Integral of first child w.r.t second child \\\\ \\hline\n\t$=$ & \\verb|\\equals| \n\t\t& First child equals second child \\\\ \\hline\n\t$\\neq$ & \\verb|\\unequals| \n\t\t& First child does not equal second child \\\\ \\hline\n\t$[a, b]$ & \\verb|\\commutator| \n\t\t& Commutator between two children \\\\ \\hline\n\t$\\{a, b\\}$ & \\verb|\\anticommutator| \n\t\t& Anticommutator between  two children \\\\ \\hline\n\t$\\left\\{\\begin{aligned}\\square_t &= \\cdots \\\\ &\\cdots\\end{aligned}\\right.$ & \\verb|\\components|\n\t\t& Component values of free indices \\\\ \\hline\n\t$\\wedge$ & \\verb|\\wedge| \n\t\t& Wedge product of children \\\\ \\hline\n\t$x\\quad\\text{with}\\quad y$ & \\verb|\\conditional| \n\t\t& First child as pattern which holds under second child \\\\ \\hline\n\t$<$ & \\verb|\\less| \n\t\t& First child is less than second child\\\\ \\hline\n\t$>$ & \\verb|\\greater| \n\t\t& First child is greater than second child\\\\ \\hline\n\t$(A+B+C)_\\mu$ & \\verb|\\indexbracket|\n\t\t& First child is an object with indices given by the remaining children \\\\ \\hline\n\t$\\cdots$ & \\verb|\\ldots|\n\t\t& Suppressed terms \\\\ \\hline\n\t\n\t\\end{tabular}\n\\end{table}\n\n\\newpage\n\\section{\\texttt{ExNode} methods and properties}\n\\label{app:exnode}\n\n\\renewcommand{\\descriptionlabel}[1]{\\hspace{\\labelsep}\\textbf{\\texttt{#1}}}\n\\subsection{Properties}\n\\begin{description}\n\t\\item[name] \n\t\tThe name of the current node\n\t\\item[parent\\_rel] \n\t\tThe relationship of the current node to its parent\n\t\\item[multiplier]\n\t\tThe rational multiplier attached to the current node\n\\end{description}\n\\subsection{Methods}\n\\begin{description}\n\t\\item[args()]\n\t\tReturn an iterator over all arguments of the current node\n\t\\item[append\\_child(other)] \n\t\tAppend a \\texttt{Ex} or \\texttt{ExNode} as a child of the current node\n\t\\item[children()]\n\t\tReturn an iterator over all children of the current node\n\t\\item[compare(other, use\\_props, ignore\\_parent\\_rel] \n\t\tCompare to another \\texttt{ExNode}. Returns a \\texttt{match\\_t} object.\n\t\\item[erase()] \n\t\tErase the current node\n\t\\item[ex()] \n\t\tReturn a copy of the current node as a \\texttt{Ex} object\n\t\\item[factors()]\n\t\tReturn an iterator over all factors at the level of the current node\n\t\\item[free\\_indices()]\n\t\tReturn an iterator over all free indices of the current node\n\t\\item[indices()]\n\t\tReturn an iterator over all indices of the current node\n\t\\item[insert(other)]\n\t\tInsert a \\texttt{Ex} or \\texttt{ExNode} object in front of the current node\n\t\\item[own\\_indices()]\n\t\tReturn an iterator over all indices of the current node which are not inherited from child nodes\n\t\\item[replace(ex)]\n\t\tReplace the current node with a \\texttt{Ex} object\n\t\\item[terms()]\n\t\tReturn an iterator over all terms at the level of the current node\n\\end{description}\n\n\\end{document}\n"
  },
  {
    "path": "docker/Dockerfile",
    "content": "# Dockerfile to build a docker container with Cadabra running as a Jupyter\n# kernel inside JupyterLab.\n#\n# Based on https://github.com/fjebaker/cadabra-resources\n#      and https://hub.docker.com/r/flavleger/cadabra\n#\n#\n# Build with\n#\n#    docker build . -t cadabra2-jupyter\n#\n# Then run with\n#\n#    docker run -p 9057:9057 -v $(pwd)/notebooks:/home/cadabra cadabra2-jupyter\n\nFROM python:3.11-slim-bookworm AS builder\nUSER root\nARG DEBIAN_FRONTEND=noninteractive\nRUN apt update && apt install -y \\\n    git cmake pkgconf libpython3-dev python3-dev g++ \\\n    libgmp3-dev libglibmm-2.4-dev libboost-all-dev libssl-dev libgmp-dev libsqlite3-dev uuid-dev  \\\n    python3-matplotlib python3-mpmath python3-sympy python3-gmpy2 python3-pip\nRUN pip install jupyter\nRUN git clone -b \"master\" --depth 1 https://github.com/kpeeters/cadabra2 && \\\n    mkdir -p cadabra2/build && cd cadabra2/build && \\\n    cmake .. -DENABLE_FRONTEND=&& \\\n    make -j `nproc` && \\\n    make install\n\nFROM python:3.11-slim-bookworm\nUSER root\nARG DEBIAN_FRONTEND=noninteractive\nRUN apt update && apt install -y \\\n    libgmp10 \\\n    libgmpxx4ldbl \\\n    libsqlite3-0 \\\n    python3 \\\n    python3-gmpy2 \\\n    python3-pip \\\n    uuid \\\n && rm -rf /var/lib/apt/lists/*\nRUN pip install jupyter\nCOPY --from=builder /usr/local/bin/cadabra* /usr/local/bin/\nCOPY --from=builder /usr/local/lib/python3.11/site-packages /usr/local/lib/python3.11/site-packages\nCOPY --from=builder /usr/local/share/cadabra2 /usr/local/share/cadabra2\nCOPY --from=builder /usr/local/share/jupyter/kernels/cadabra2 /usr/local/share/jupyter/kernels/cadabra2\n\n# Cleanup things not necessary for running the container.\nRUN apt-get remove -y gcc && apt-get autoremove -y\n\nEXPOSE 9057\nWORKDIR /home/cadabra\nCOPY docker/entrypoint.sh /entrypoint.sh\nRUN chmod +x /entrypoint.sh\nENTRYPOINT [\"/entrypoint.sh\", \"--port=9057\"]\n"
  },
  {
    "path": "docker/entrypoint.sh",
    "content": "#!/bin/sh\n\n# amend python path\nexport PYTHONPATH=${PYTHONPATH}:/usr/local/lib/python3.11/dist-packages\njupyter notebook --ip=0.0.0.0 --allow-root $@\n"
  },
  {
    "path": "examples/.gitignore",
    "content": "library.py\n"
  },
  {
    "path": "examples/auto_meld.cnb",
    "content": "{\n\t\"cell_id\" : 12286062114484406453,\n\t\"cells\" : \n\t[\n\t\t{\n\t\t\t\"cell_id\" : 14628779505962182789,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"def post_process(ex):\\n    meld(ex)\\n    collect_terms(ex)\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 17732859429837154320,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 9223372036854775810,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property TableauSymmetry to~}R_{a b c d}.\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"R_{a b c d}::RiemannTensor;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 8054626802115821673,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 9223372036854775812,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\" : 9223372036854775813,\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"0\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}0\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex:=R_{a b c d} + R_{a c d b} + R_{a d b c};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 8540820496130751966,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"W_{m n p q}::WeylTensor.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 8245654388093335992,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 9223372036854775816,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\" : 9223372036854775817,\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"0\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}0\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex:= W_{p q r s} W_{p t r u} W_{t v q w} W_{u v s w} \\n  - W_{p q r s} W_{p q t u} W_{r v t w} W_{s v u w}\\n  - W_{m n a b} W_{n p b c} W_{m s c d} W_{s p d a}\\n  + (1/4) W_{m n a b} W_{p s b a} W_{m p c d} W_{n s d c};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 14294698861693786241,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 9223372036854775819,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Symmetric to~}S_{m n p}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 9223372036854775820,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property AntiSymmetric to~}A^{m n p}.\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"S_{m n p}::Symmetric;\\nA^{m n p}::AntiSymmetric;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 17887186645587646211,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 9223372036854775822,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\" : 9223372036854775823,\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"0\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}0\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex:=R_{a b c d} A^{b c d};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 8808759323842202056,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1\n}\n"
  },
  {
    "path": "examples/automatic_multiterm.cnb",
    "content": "{\n\t\"cell_id\": 3391536610896426838,\n\t\"cells\": [\n\t\t{\n\t\t\t\"cell_id\": 9970128145502107243,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 16204355368752002978,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"This notebook illustrates how the automatic multi-term simplification algorithm \\\\algo{meld} can\\nbe used in a \\\\verb|post_process| function to simplify expressions immediately.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"This notebook illustrates how the automatic multi-term simplification algorithm \\\\algo{meld} can\\nbe used in a \\\\verb|post_process| function to simplify expressions immediately.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 16589852709921553693,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"def post_process(ex):\\n    meld(ex)\\n    collect_terms(ex)\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 1137909878511905740,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 3984991681506874828,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property TableauSymmetry attached to~}R_{a b c d}.\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"R_{a b c d}::RiemannTensor;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 10442559150589961051,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 16272566471204925814,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 1708705026185000243,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"R_{a b c d} + R_{b c a d} + R_{c a b d}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}R_{a b c d}+R_{b c a d}+R_{c a b d}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex:=R_{a b c d} + R_{b c a d} + R_{c a b d};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 17665426107502293019,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 4864102099047927703,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property AntiSymmetric attached to~}A^{a b c}.\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"A^{a b c}::AntiSymmetric;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 11231869119195730671,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 775906003630772013,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property Symmetric attached to~}S_{a b c}.\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"S_{a b c}::Symmetric;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 15440997254477550604,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 228473189702070848,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 9500934661811827513,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"R_{a b c d} A^{a b c}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}R_{a b c d} A^{a b c}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex:=R_{a b c d} A^{a b c};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 6001193804290926265,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 16452054599630373227,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 17144787782815941213,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"(A^{a b c} + A^{c a b}) S_{a b c}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\left(A^{a b c}+A^{c a b}\\\\right) S_{a b c}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex:= (A^{a b c} + A^{c a b}) S_{a b c};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 14929753163657422384,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 1137671033037866650,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 1039654011058708309,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"2A^{a b c} S_{a b c}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}2A^{a b c} S_{a b c}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"meld(ex, repeat=True);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 10182337157813236277,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 16001156654425651111,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 15399389374269644662,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"(a-b) A^{a b c}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\left(a-b\\\\right) A^{a b c}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex:= a A^{a b c} + b A^{b a c};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 2655562479605535632,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 3165433391968790005,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 14527276633063001349,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \" 3/2 R_{a b c d} R_{a b c d}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\frac{3}{2}R_{a b c d} R_{a b c d}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex:=R_{a b c d} R_{a b c d} + R_{a b c d} R_{a c b d};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 12588425984072827898,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"\"\n\t\t}\n\t],\n\t\"description\": \"Cadabra JSON notebook format\",\n\t\"version\": 1.0\n}\n"
  },
  {
    "path": "examples/beginners.cnb",
    "content": "{\n\t\"cell_id\": 14431655003681514184,\n\t\"cells\": [\n\t\t{\n\t\t\t\"cell_id\": 8633778387409141299,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 1555447978250595260,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\section*{Introduction to Cadabra for beginners}\\n\\nThis notebook introduces Cadabra to people who have never used it before, or who have\\nused one of the old 1.x versions. It will show you how to enter expressions, attach\\nproperties to patterns, perform simple substitutions and so on. \\n\\nIf you need help, do not hesitate to email \\\\href{mailto:help@cadabra.science}{help@cadabra.science} or visit\\nthe web site at \\\\url{http://cadabra.science/}.\\n\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\section*{Introduction to Cadabra for beginners}\\n\\nThis notebook introduces Cadabra to people who have never used it before, or who have\\nused one of the old 1.x versions. It will show you how to enter expressions, attach\\nproperties to patterns, perform simple substitutions and so on. \\n\\nIf you need help, do not hesitate to email \\\\href{mailto:help@cadabra.science}{help@cadabra.science} or visit\\nthe web site at \\\\url{http://cadabra.science/}.\\n\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 627033528208718509,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 696614165692401843,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\section*{Equations of motion}\\n\\nA good example to illustrate a number of Cadabra manipulations is to derive the equations of\\nmotion of a field theory from an action. Below we discuss the Maxwell equations, just for\\nsimplicity.\\n\\nIn Cadabra, the default setting is to do very little automatic simplification (essentially, only\\nequal terms are collected). You can change this, however, by writing a \\\\verb|post_process|\\nfunction which contains all the algorithms which you want to run at every step of your notebook.\\nBelow is an example:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\section*{Equations of motion}\\n\\nA good example to illustrate a number of Cadabra manipulations is to derive the equations of\\nmotion of a field theory from an action. Below we discuss the Maxwell equations, just for\\nsimplicity.\\n\\nIn Cadabra, the default setting is to do very little automatic simplification (essentially, only\\nequal terms are collected). You can change this, however, by writing a \\\\verb|post_process|\\nfunction which contains all the algorithms which you want to run at every step of your notebook.\\nBelow is an example:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 90834408152362928,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"def post_process(ex):\\n\\tsort_product(ex)\\n\\tcanonicalise(ex)\\n\\tcollect_terms(ex)\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 10158155746608638325,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9282208752232173974,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"As you can see, this sorts factors in a product (alphabetically, you can change this if you want), then \\nwrites indices in canonical form, and collects equal terms.\\n\\nBefore we can enter our Maxwell action, we need to declare some properties of the symbols which we\\nwant to use. Cadabra is fairly minimalistic with this; you typically only have to declare what\\nyou are going to use. Below we declare that $\\\\mu$, $\\\\nu$, $\\\\rho$ are indices, $x$ is a coordinate\\nlabel, and \\\\verb|\\\\partial| indicates a partial derivative. We then declare properties of the field \\nstrength and the gauge potential. This should all read fairly naturally.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"As you can see, this sorts factors in a product (alphabetically, you can change this if you want), then \\nwrites indices in canonical form, and collects equal terms.\\n\\nBefore we can enter our Maxwell action, we need to declare some properties of the symbols which we\\nwant to use. Cadabra is fairly minimalistic with this; you typically only have to declare what\\nyou are going to use. Below we declare that $\\\\mu$, $\\\\nu$, $\\\\rho$ are indices, $x$ is a coordinate\\nlabel, and \\\\verb|\\\\partial| indicates a partial derivative. We then declare properties of the field \\nstrength and the gauge potential. This should all read fairly naturally.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 4208974568806994639,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 13613676846232812259,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property AntiSymmetric attached to~}F_{\\\\mu \\\\nu}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 13919415251796785283,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property Accent attached to~}\\\\backslash\\\\texttt{delta}\\\\{\\\\#\\\\}.\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"{\\\\mu,\\\\nu,\\\\rho}::Indices(position=free).\\nx::Coordinate.\\n\\\\partial{#}::Derivative.\\n\\nF_{\\\\mu\\\\nu}::AntiSymmetric;\\nF_{\\\\mu\\\\nu}::Depends(x).\\nA_{\\\\mu}::Depends(x,\\\\partial{#}).\\n\\\\delta{#}::Accent;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 11926884762139224888,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 8683329568142568829,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"Note how lines ending in a semi-colon get their output printed, while those ending in a period do not.\\n\\nWe are now ready to write down our action, very similar to what you would write down in \\\\LaTeX{}. We also \\nwrite down a rule which says how the field strength is related to the gauge potential. Note how this rule\\ndoes not automatically get inserted into the action; you need to tell Cadabra to do that.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"Note how lines ending in a semi-colon get their output printed, while those ending in a period do not.\\n\\nWe are now ready to write down our action, very similar to what you would write down in \\\\LaTeX{}. We also \\nwrite down a rule which says how the field strength is related to the gauge potential. Note how this rule\\ndoes not automatically get inserted into the action; you need to tell Cadabra to do that.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 7027547302954400198,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 16997158852528836304,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 12321753324994697114,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \" -  1/4 \\\\int{F^{\\\\mu \\\\nu} F_{\\\\mu \\\\nu}}{x}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{} - \\\\frac{1}{4}\\\\,\\\\int F^{\\\\mu \\\\nu} F_{\\\\mu \\\\nu}\\\\,\\\\,{\\\\rm d}x\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"S:= -1/4 \\\\int{ F_{\\\\mu\\\\nu} F^{\\\\mu\\\\nu} }{x};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 10675064917502417815,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 16736008621728755559,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 2841730090277576112,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"F_{\\\\mu \\\\nu} = \\\\partial_{\\\\mu}(A_{\\\\nu})-\\\\partial_{\\\\nu}(A_{\\\\mu})\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}F_{\\\\mu \\\\nu} = \\\\partial_{\\\\mu}{A_{\\\\nu}}\\\\discretionary{}{}{}-\\\\,\\\\partial_{\\\\nu}{A_{\\\\mu}}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"rl:= F_{\\\\mu\\\\nu} = \\\\partial_{\\\\mu}{A_{\\\\nu}} - \\\\partial_{\\\\nu}{A_{\\\\mu}};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 15590188229061212795,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 5152435344052724921,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 17374414118717229867,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \" -  1/4 \\\\int{(\\\\partial_{\\\\mu}(A_{\\\\nu})-\\\\partial_{\\\\nu}(A_{\\\\mu})) (\\\\partial^{\\\\mu}(A^{\\\\nu})-\\\\partial^{\\\\nu}(A^{\\\\mu}))}{x}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{} - \\\\frac{1}{4}\\\\,\\\\int \\\\left(\\\\partial_{\\\\mu}{A_{\\\\nu}}\\\\discretionary{}{}{}-\\\\,\\\\partial_{\\\\nu}{A_{\\\\mu}}\\\\right) \\\\left(\\\\partial^{\\\\mu}{A^{\\\\nu}}\\\\discretionary{}{}{}-\\\\,\\\\partial^{\\\\nu}{A^{\\\\mu}}\\\\right)\\\\,\\\\,{\\\\rm d}x\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"substitute(S, rl);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 6752128996868095190,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 15882477026481653294,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"Note how this has automatically replaced the field strength with upper as well as\\nlower indices, by virtue of the fact that the index position was declared with \\\\verb|position=free|.\\n\\nWe can now compute a variational derivative of this object with respect to $A_\\\\mu$.\\nNote the use of inline formulas using the standard \\\\TeX{} \\\\$\\\\ldots\\\\$ construction.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"Note how this has automatically replaced the field strength with upper as well as\\nlower indices, by virtue of the fact that the index position was declared with \\\\verb|position=free|.\\n\\nWe can now compute a variational derivative of this object with respect to $A_\\\\mu$.\\nNote the use of inline formulas using the standard \\\\TeX{} \\\\$\\\\ldots\\\\$ construction.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 1032054412087685768,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 14362926650555376717,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 17180071277917949034,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \" -  1/4 \\\\int{(\\\\partial^{\\\\mu}(A^{\\\\nu})-\\\\partial^{\\\\nu}(A^{\\\\mu})) (\\\\partial_{\\\\mu}(\\\\delta{A_{\\\\nu}})-\\\\partial_{\\\\nu}(\\\\delta{A_{\\\\mu}})) + (\\\\partial_{\\\\mu}(A_{\\\\nu})-\\\\partial_{\\\\nu}(A_{\\\\mu})) (\\\\partial^{\\\\mu}(\\\\delta{A^{\\\\nu}})-\\\\partial^{\\\\nu}(\\\\delta{A^{\\\\mu}}))}{x}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{} - \\\\frac{1}{4}\\\\,\\\\int \\\\left(\\\\left(\\\\partial^{\\\\mu}{A^{\\\\nu}}\\\\discretionary{}{}{}-\\\\,\\\\partial^{\\\\nu}{A^{\\\\mu}}\\\\right) \\\\left(\\\\partial_{\\\\mu}{\\\\delta{A_{\\\\nu}}}\\\\discretionary{}{}{}-\\\\,\\\\partial_{\\\\nu}{\\\\delta{A_{\\\\mu}}}\\\\right)\\\\discretionary{}{}{}+\\\\left(\\\\partial_{\\\\mu}{A_{\\\\nu}}\\\\discretionary{}{}{}-\\\\,\\\\partial_{\\\\nu}{A_{\\\\mu}}\\\\right) \\\\left(\\\\partial^{\\\\mu}{\\\\delta{A^{\\\\nu}}}\\\\discretionary{}{}{}-\\\\,\\\\partial^{\\\\nu}{\\\\delta{A^{\\\\mu}}}\\\\right)\\\\right)\\\\,\\\\,{\\\\rm d}x\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"vary(S, $A_{\\\\mu} -> \\\\delta{A_{\\\\mu}}$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 11763321768686026380,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 1761458177367932910,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"We need to distribute the products over the sums, and then integrate by parts, away from\\nthe $\\\\delta{A_{\\\\mu}}$ factors:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"We need to distribute the products over the sums, and then integrate by parts, away from\\nthe $\\\\delta{A_{\\\\mu}}$ factors:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 14213161442110619124,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 5715478533428538365,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 4881724907362652245,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \" -  1/4 \\\\int{4\\\\partial^{\\\\mu}(A^{\\\\nu}) \\\\partial_{\\\\mu}(\\\\delta{A_{\\\\nu}})-4\\\\partial^{\\\\mu}(A^{\\\\nu}) \\\\partial_{\\\\nu}(\\\\delta{A_{\\\\mu}})}{x}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{} - \\\\frac{1}{4}\\\\,\\\\int \\\\left(4\\\\,\\\\partial^{\\\\mu}{A^{\\\\nu}} \\\\partial_{\\\\mu}{\\\\delta{A_{\\\\nu}}}\\\\discretionary{}{}{}-4\\\\,\\\\partial^{\\\\mu}{A^{\\\\nu}} \\\\partial_{\\\\nu}{\\\\delta{A_{\\\\mu}}}\\\\right)\\\\,\\\\,{\\\\rm d}x\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 17979031693467390065,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 4133979830334364856,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \" -  1/4 \\\\int{-4\\\\delta{A^{\\\\mu}} \\\\partial^{\\\\nu}(\\\\partial_{\\\\nu}(A_{\\\\mu})) + 4\\\\delta{A^{\\\\mu}} \\\\partial^{\\\\nu}(\\\\partial_{\\\\mu}(A_{\\\\nu}))}{x}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{} - \\\\frac{1}{4}\\\\,\\\\int \\\\left(-4\\\\,\\\\delta{A^{\\\\mu}} \\\\partial^{\\\\nu}\\\\left(\\\\partial_{\\\\nu}{A_{\\\\mu}}\\\\right)\\\\discretionary{}{}{}+4\\\\,\\\\delta{A^{\\\\mu}} \\\\partial^{\\\\nu}\\\\left(\\\\partial_{\\\\mu}{A_{\\\\nu}}\\\\right)\\\\right)\\\\,\\\\,{\\\\rm d}x\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"distribute(S);\\nintegrate_by_parts(S, $\\\\delta{A_{\\\\mu}}$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 17318140548827299932,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 10762713754364626884,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"Finally, in order to write this back in terms of the field strength, we use the following rewriting trick,\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"Finally, in order to write this back in terms of the field strength, we use the following rewriting trick,\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 9283526757247180971,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 14318599050902391252,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 2867222870137387221,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \" -  1/4 \\\\int{-4\\\\delta{A^{\\\\mu}} \\\\partial^{\\\\nu}(( 1/2 \\\\partial_{\\\\nu}(A_{\\\\mu}) -  1/2 F_{\\\\mu \\\\nu} +  1/2 \\\\partial_{\\\\mu}(A_{\\\\nu}))) + 4\\\\delta{A^{\\\\mu}} \\\\partial^{\\\\nu}(( 1/2 \\\\partial_{\\\\mu}(A_{\\\\nu}) +  1/2 F_{\\\\mu \\\\nu} +  1/2 \\\\partial_{\\\\nu}(A_{\\\\mu})))}{x}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{} - \\\\frac{1}{4}\\\\,\\\\int \\\\left(-4\\\\,\\\\delta{A^{\\\\mu}} \\\\partial^{\\\\nu}\\\\left(\\\\frac{1}{2}\\\\,\\\\partial_{\\\\nu}{A_{\\\\mu}}\\\\discretionary{}{}{} - \\\\frac{1}{2}\\\\,F_{\\\\mu \\\\nu}\\\\discretionary{}{}{}+\\\\frac{1}{2}\\\\,\\\\partial_{\\\\mu}{A_{\\\\nu}}\\\\right)\\\\discretionary{}{}{}+4\\\\,\\\\delta{A^{\\\\mu}} \\\\partial^{\\\\nu}\\\\left(\\\\frac{1}{2}\\\\,\\\\partial_{\\\\mu}{A_{\\\\nu}}\\\\discretionary{}{}{}+\\\\frac{1}{2}\\\\,F_{\\\\mu \\\\nu}\\\\discretionary{}{}{}+\\\\frac{1}{2}\\\\,\\\\partial_{\\\\nu}{A_{\\\\mu}}\\\\right)\\\\right)\\\\,\\\\,{\\\\rm d}x\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"substitute(_, $\\\\partial_{\\\\mu}{A_{\\\\nu}} -> 1/2 \\\\partial_{\\\\mu}{A_{\\\\nu}} + 1/2 F_{\\\\mu\\\\nu} + 1/2 \\\\partial_{\\\\nu}{A_{\\\\mu}}$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 4266606467681726283,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 5980744749295532304,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 17065827744344474700,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"-\\\\int{\\\\delta{A^{\\\\mu}} \\\\partial^{\\\\nu}(F_{\\\\mu \\\\nu})}{x}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}-\\\\,\\\\int \\\\delta{A^{\\\\mu}} \\\\partial^{\\\\nu}{F_{\\\\mu \\\\nu}}\\\\,\\\\,{\\\\rm d}x\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"distribute(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 17735099200715511822,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 602741357312734805,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"This isolates the equations of motion $\\\\partial^\\\\nu F_{\\\\mu\\\\nu}=0$ in the integrand.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"This isolates the equations of motion $\\\\partial^\\\\nu F_{\\\\mu\\\\nu}=0$ in the integrand.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 16532030718140923636,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"\"\n\t\t}\n\t],\n\t\"description\": \"Cadabra JSON notebook format\",\n\t\"flags\": {\n\t\t\"hide_input_cells\": false\n\t},\n\t\"version\": 1.0\n}\n"
  },
  {
    "path": "examples/bianchi_identities.cnb",
    "content": "{\n\t\"cells\" : \n\t[\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\section*{A higher-derivative Bianchi identity}\\n\\nThe identity which we will prove here comes from appendix A of hep-th/0111128. It shows that a particular\\ncubic polynomial of Weyl tensors vanishes by virtue of the Weyl tensor multi-term symmetries. The declaration\\nof the indices, Weyl tensor and covariant derivative is done with:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\section*{A higher-derivative Bianchi identity}\\n\\nThe identity which we will prove here comes from appendix A of hep-th/0111128. It shows that a particular\\ncubic polynomial of Weyl tensors vanishes by virtue of the Weyl tensor multi-term symmetries. The declaration\\nof the indices, Weyl tensor and covariant derivative is done with:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}-C_{i m k l} C_{j p k q} C_{l p m q}%\\n+\\\\frac{1}{4}C_{i m k l} C_{j m p q} C_{k l p q}%\\n - \\\\frac{1}{2}C_{i k j l} C_{k m p q} C_{l m p q}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\nabla_{i}\\\\left(\\\\nabla_{j}\\\\left(-C_{i m k l} C_{j p k q} C_{l p m q}%\\n+\\\\frac{1}{4}C_{i m k l} C_{j m p q} C_{k l p q}%\\n - \\\\frac{1}{2}C_{i k j l} C_{k m p q} C_{l m p q}\\\\right)\\\\right)%\\n - \\\\frac{1}{6}\\\\nabla_{i}\\\\left(\\\\nabla_{i}\\\\left(C_{j m n k} C_{m p q n} C_{p j k q}%\\n+\\\\frac{1}{2}C_{j k m n} C_{p q m n} C_{j k p q}\\\\right)\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"{i,j,m,n,k,p,q,l,r,r#}::Indices(vector).\\nC_{m n p q}::WeylTensor.\\n\\\\nabla{#}::Derivative.\\n\\\\nabla_{r}{ C_{m n p q} }::SatisfiesBianchi.\\n\\\\delta_{i j}::KroneckerDelta.\\n\\nEij:=- C_{i m k l} C_{j p k q} C_{l p m q} + 1/4 C_{i m k l} C_{j m p q} C_{k l p q}\\n     - 1/2 C_{i k j l} C_{k m p q} C_{l m p q}:\\n\\nE:=  C_{j m n k} C_{m p q n} C_{p j k q} + 1/2 C_{j k m n} C_{p q m n} C_{j k p q}:\\n\\nexp:= \\\\nabla_{i}{\\\\nabla_{j}{ @(Eij) }} - 1/6 \\\\nabla_{i}{\\\\nabla_{i}{ @(E) }};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"First apply the product rule twice to write out derivatives:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"First apply the product rule twice to write out derivatives:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}C_{i j m n} C_{i k m p} \\\\nabla_{q}\\\\left(\\\\nabla_{j}{C_{n k p q}}\\\\right)%\\n-C_{i j m n} \\\\nabla_{k}{C_{i p m q}} \\\\nabla_{p}{C_{j q n k}}%\\n-2C_{i j m n} \\\\nabla_{i}{C_{m k p q}} \\\\nabla_{p}{C_{j k n q}}%\\n-C_{i j m n} \\\\nabla_{k}{C_{i k m p}} \\\\nabla_{q}{C_{j p n q}}%\\n+C_{i j m n} C_{i k m p} \\\\nabla_{j}\\\\left(\\\\nabla_{q}{C_{n k p q}}\\\\right)%\\n-2C_{i j m n} \\\\nabla_{i}{C_{j k m p}} \\\\nabla_{q}{C_{n k p q}}%\\n-C_{i j m n} C_{i k p q} \\\\nabla_{m}\\\\left(\\\\nabla_{p}{C_{j q n k}}\\\\right)%\\n - \\\\frac{1}{4}C_{i j m n} C_{i j k p} \\\\nabla_{q}\\\\left(\\\\nabla_{m}{C_{n q k p}}\\\\right)%\\n+\\\\frac{1}{4}C_{i j m n} \\\\nabla_{k}{C_{i j p q}} \\\\nabla_{p}{C_{m n k q}}%\\n - \\\\frac{1}{2}C_{i j m n} \\\\nabla_{i}{C_{j k p q}} \\\\nabla_{k}{C_{m n p q}}%\\n - \\\\frac{1}{4}C_{i j m n} \\\\nabla_{k}{C_{i j k p}} \\\\nabla_{q}{C_{m n p q}}%\\n - \\\\frac{1}{4}C_{i j m n} C_{i j k p} \\\\nabla_{m}\\\\left(\\\\nabla_{q}{C_{n q k p}}\\\\right)%\\n - \\\\frac{1}{2}C_{i j m n} \\\\nabla_{i}{C_{m n k p}} \\\\nabla_{q}{C_{j q k p}}%\\n+\\\\frac{1}{4}C_{i j m n} C_{i k p q} \\\\nabla_{j}\\\\left(\\\\nabla_{k}{C_{m n p q}}\\\\right)%\\n - \\\\frac{1}{2}C_{i j m n} C_{i j m k} \\\\nabla_{p}\\\\left(\\\\nabla_{q}{C_{n p k q}}\\\\right)%\\n+C_{i j m n} \\\\nabla_{k}{C_{i j m p}} \\\\nabla_{q}{C_{n q k p}}%\\n-C_{i j m n} \\\\nabla_{k}{C_{i j m p}} \\\\nabla_{q}{C_{n k p q}}%\\n+\\\\frac{1}{2}C_{i j m n} C_{i k p q} \\\\nabla_{m}\\\\left(\\\\nabla_{j}{C_{n k p q}}\\\\right)%\\n+\\\\frac{1}{2}C_{i j m n} \\\\nabla_{i}{C_{m k p q}} \\\\nabla_{n}{C_{j k p q}}%\\n - \\\\frac{1}{2}C_{i j m n} \\\\nabla_{i}{C_{j k p q}} \\\\nabla_{m}{C_{n k p q}}%\\n+\\\\frac{1}{2}C_{i j m n} C_{i k p q} \\\\nabla_{j}\\\\left(\\\\nabla_{m}{C_{n k p q}}\\\\right)%\\n+\\\\frac{1}{2}C_{i j m n} C_{i k m p} \\\\nabla_{q}\\\\left(\\\\nabla_{q}{C_{j k n p}}\\\\right)%\\n+C_{i j m n} \\\\nabla_{k}{C_{i p m q}} \\\\nabla_{k}{C_{j p n q}}%\\n - \\\\frac{1}{4}C_{i j m n} C_{i j k p} \\\\nabla_{q}\\\\left(\\\\nabla_{q}{C_{m n k p}}\\\\right)%\\n - \\\\frac{1}{2}C_{i j m n} \\\\nabla_{k}{C_{i j p q}} \\\\nabla_{k}{C_{m n p q}}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"distribute(_); product_rule(_); distribute(_); product_rule(_)\\nsort_product(_); canonicalise(_)\\nrename_dummies(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"Because the identity which we intend to prove is only supposed to hold on Einstein spaces, we\\nset the divergence of the Weyl tensor to zero,\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"Because the identity which we intend to prove is only supposed to hold on Einstein spaces, we\\nset the divergence of the Weyl tensor to zero,\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}C_{i j m n} C_{i k m p} \\\\nabla_{q}\\\\left(\\\\nabla_{j}{C_{n k p q}}\\\\right)%\\n-C_{i j m n} \\\\nabla_{k}{C_{i p m q}} \\\\nabla_{p}{C_{j q n k}}%\\n-2C_{i j m n} \\\\nabla_{i}{C_{m k p q}} \\\\nabla_{p}{C_{j k n q}}%\\n-C_{i j m n} C_{i k p q} \\\\nabla_{m}\\\\left(\\\\nabla_{p}{C_{j q n k}}\\\\right)%\\n - \\\\frac{1}{4}C_{i j m n} C_{i j k p} \\\\nabla_{q}\\\\left(\\\\nabla_{m}{C_{n q k p}}\\\\right)%\\n+\\\\frac{1}{4}C_{i j m n} \\\\nabla_{k}{C_{i j p q}} \\\\nabla_{p}{C_{m n k q}}%\\n - \\\\frac{1}{2}C_{i j m n} \\\\nabla_{i}{C_{j k p q}} \\\\nabla_{k}{C_{m n p q}}%\\n+\\\\frac{1}{4}C_{i j m n} C_{i k p q} \\\\nabla_{j}\\\\left(\\\\nabla_{k}{C_{m n p q}}\\\\right)%\\n+\\\\frac{1}{2}C_{i j m n} C_{i k p q} \\\\nabla_{m}\\\\left(\\\\nabla_{j}{C_{n k p q}}\\\\right)%\\n+\\\\frac{1}{2}C_{i j m n} \\\\nabla_{i}{C_{m k p q}} \\\\nabla_{n}{C_{j k p q}}%\\n - \\\\frac{1}{2}C_{i j m n} \\\\nabla_{i}{C_{j k p q}} \\\\nabla_{m}{C_{n k p q}}%\\n+\\\\frac{1}{2}C_{i j m n} C_{i k p q} \\\\nabla_{j}\\\\left(\\\\nabla_{m}{C_{n k p q}}\\\\right)%\\n+\\\\frac{1}{2}C_{i j m n} C_{i k m p} \\\\nabla_{q}\\\\left(\\\\nabla_{q}{C_{j k n p}}\\\\right)%\\n+C_{i j m n} \\\\nabla_{k}{C_{i p m q}} \\\\nabla_{k}{C_{j p n q}}%\\n - \\\\frac{1}{4}C_{i j m n} C_{i j k p} \\\\nabla_{q}\\\\left(\\\\nabla_{q}{C_{m n k p}}\\\\right)%\\n - \\\\frac{1}{2}C_{i j m n} \\\\nabla_{k}{C_{i j p q}} \\\\nabla_{k}{C_{m n p q}}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"substitute(_, $\\\\nabla_{i}{ C_{k i l m} } -> 0, \\\\nabla_{i}{ C_{k m l i} } -> 0$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"This expression should vanish upon use of the Bianchi identity. By expanding all tensors using\\ntheir Young projectors, this becomes manifest; a few seconds of computation produces:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"This expression should vanish upon use of the Bianchi identity. By expanding all tensors using\\ntheir Young projectors, this becomes manifest; a few seconds of computation produces:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}0\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"young_project_product(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"This proves the identity.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"This proves the identity.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1\n}\n"
  },
  {
    "path": "examples/canonicalise.cnb",
    "content": "\n{\n\t\"cells\" : \n\t[\n\t\t\n\t\t{\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_type\" : \"output\",\n\t\t\t\t\t\"id\" : 10,\n\t\t\t\t\t\"source\" : \"$A_{m n} B_{m n}\\n$\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"id\" : 3,\n\t\t\t\"source\" : \"A_{m n}::Symmetric.\\nB_{m n}::AntiSymmetric.\\nex:=A_{m n} B_{m n};\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_type\" : \"output\",\n\t\t\t\t\t\"id\" : 13,\n\t\t\t\t\t\"source\" : \"$0\\n$\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"id\" : 5,\n\t\t\t\"source\" : \"canonicalise(_);\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"id\" : 6,\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1.0\n}\n\n"
  },
  {
    "path": "examples/cell_ids.cnb",
    "content": "{\n\t\"cell_id\": 11301361161958322865,\n\t\"cells\": [\n\t\t{\n\t\t\t\"cell_id\": 3209737360045897807,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 1275646209966621667,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"The \\\\verb|display| function will return the ID of the output cell. Using this ID it \\nis possible to send subsequent output to the same output cell. This allows for \\ndynamical updating (e.g. counters or progress bars).\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"The \\\\verb|display| function will return the ID of the output cell. Using this ID it \\nis possible to send subsequent output to the same output cell. This allows for \\ndynamical updating (e.g. counters or progress bars).\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 2543726846254358456,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 689965496974128564,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 9610737522023299257,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"A_{m n}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}A_{m n}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 2823807190979596582,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 15966417375204997629,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"B_{p q}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}B_{p q}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex:=A_{m n};\\nex2:=B_{p q};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 13771311687216592030,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 12160042253445624459,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 4777631753974189465,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"A_{m n}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}A_{m n}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"c1=display(ex)\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 13687948512684403628,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9350841598844205305,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 10397374464617081800,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"B_{p q}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}B_{p q}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"c2=display(ex2)\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 1243683661280339692,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 11419632574425512943,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"The above used the default \\\\verb|cell_id| parameter of \\\\verb|display| (zero), which led to the \\ncreation of a new output cell. However, if we pass this ID to the \\\\verb|display| function, we \\ncan overwrite an existing output cell:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"The above used the default \\\\verb|cell_id| parameter of \\\\verb|display| (zero), which led to the \\ncreation of a new output cell. However, if we pass this ID to the \\\\verb|display| function, we \\ncan overwrite an existing output cell:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 14484998934473877948,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 10270840374210630885,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 2471321157843722375,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"A_{m n}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}A_{m n}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"display(ex, cell_id=c2)\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 13671896224003488670,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"\"\n\t\t}\n\t],\n\t\"description\": \"Cadabra JSON notebook format\",\n\t\"version\": 1.0\n}\n"
  },
  {
    "path": "examples/component_evaluation.cnb",
    "content": "{\n\t\"cell_id\": 8545880230937607412,\n\t\"cells\": [\n\t\t{\n\t\t\t\"cell_id\": 2484385849359819743,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 14721630884910007993,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property Indices(position=fixed, values=\\\\{{1}  0\\n, {1}\\n, {1}  2\\n, {1}  3\\n\\\\}) attached to~}\\\\left[\\\\mu, \\\\discretionary{}{}{}\\\\nu, \\\\discretionary{}{}{}\\\\rho\\\\right].\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 4369391074336507261,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property PartialDerivative attached to~}\\\\backslash\\\\texttt{partial}\\\\{\\\\#\\\\}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 1886096681860453553,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property AntiSymmetric attached to~}F_{\\\\mu \\\\nu}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 8745885633650528229,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property Depends attached to~}A^{\\\\mu}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 16027540428004546439,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 16565301818321321197,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\partial_{\\\\mu}(F^{\\\\mu \\\\nu}) = 0\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\partial_{\\\\mu}\\\\!{F^{\\\\mu \\\\nu}} = 0\\\\,\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"{\\\\mu,\\\\nu,\\\\rho}::Indices(position=fixed, values={0,1,2,3});\\n\\\\partial{#}::PartialDerivative;\\nF_{\\\\mu\\\\nu}::AntiSymmetric;\\nA^{\\\\mu}::Depends(\\\\partial{#});\\neom:=\\\\partial_{\\\\mu}{ F^{\\\\mu\\\\nu} } = 0;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 9150919648533741901,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 7106101853783883831,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 7391230446999123982,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"F^{\\\\mu \\\\nu} = \\\\partial^{\\\\mu}(A^{\\\\nu})-\\\\partial^{\\\\nu}(A^{\\\\mu})\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}F^{\\\\mu \\\\nu} = \\\\partial^{\\\\mu}\\\\!{A^{\\\\nu}}\\\\discretionary{}{}{}-\\\\,\\\\partial^{\\\\nu}\\\\!{A^{\\\\mu}}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"fdef:= F^{\\\\mu\\\\nu} = \\\\partial^{\\\\mu}{A^{\\\\nu}} - \\\\partial^{\\\\nu}{A^{\\\\mu}};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 1512979895180218637,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 1934436528941262476,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 13847813662922193907,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\partial_{\\\\mu}((\\\\partial^{\\\\mu}(A^{\\\\nu})-\\\\partial^{\\\\nu}(A^{\\\\mu}))) = 0\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\partial_{\\\\mu}\\\\!\\\\left(\\\\partial^{\\\\mu}\\\\!{A^{\\\\nu}}\\\\discretionary{}{}{}-\\\\,\\\\partial^{\\\\nu}\\\\!{A^{\\\\mu}}\\\\right) = 0\\\\,\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"substitute(eom, fdef);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 13569802970605986146,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 11291669789095251908,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 10465252941124039466,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"{A^{0} = A^{0}, A^{1} = A^{1}, A^{2} = A^{2}, A^{3} = A^{3}}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\left[A^{0\\\\,} = A^{0\\\\,}, \\\\discretionary{}{}{}A^{1} = A^{1}, \\\\discretionary{}{}{}A^{2\\\\,} = A^{2\\\\,}, \\\\discretionary{}{}{}A^{3\\\\,} = A^{3\\\\,}\\\\right]\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"cmp:= {A^0 = A^0, A^1 = A^1, A^2 = A^2, A^3 = A^3 };\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 1512358898708328731,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 620585941810530269,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"error\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}RuntimeError: All indices on derivatives need to be lowered first.\\n\\nAt:\\n  Notebook Cell (Line 1): _ = evaluate(eom, cmp)\\n\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"evaluate(eom, cmp);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 14179130772924741170,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 1178977843759317861,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 10334284518408387447,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\partial_{\\\\mu}(A^{2})\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\partial_{\\\\mu}\\\\!{A^{2\\\\,}}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"tst:=\\\\partial_{\\\\mu}{A^{2}};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 17593745836886198907,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 6550553018172750450,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 12140324784168685421,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\partial_{\\\\mu}(A^{2})\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\partial_{\\\\mu}\\\\!{A^{2\\\\,}}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"unwrap(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 9182466992467207261,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 4488857471632381307,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 17695006672676772130,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\components_{\\\\mu}({{3} = \\\\partial_{3}(A^{2}), {2} = \\\\partial_{2}(A^{2}), {1} = \\\\partial_{1}(A^{2}), {0} = \\\\partial_{0}(A^{2})})\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\square{}_{\\\\mu}\\\\left\\\\{\\\\begin{aligned}\\\\square{}_{3\\\\,}& = \\\\partial_{3\\\\,}\\\\!{A^{2\\\\,}}\\\\\\\\[-.5ex]\\n\\\\square{}_{2\\\\,}& = \\\\partial_{2\\\\,}\\\\!{A^{2\\\\,}}\\\\\\\\[-.5ex]\\n\\\\square{}_{1}& = \\\\partial_{1}\\\\!{A^{2\\\\,}}\\\\\\\\[-.5ex]\\n\\\\square{}_{0\\\\,}& = \\\\partial_{0\\\\,}\\\\!{A^{2\\\\,}}\\\\\\\\[-.5ex]\\n\\\\end{aligned}\\\\right.\\n\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"evaluate(tst);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 8436557046968158716,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"\"\n\t\t}\n\t],\n\t\"description\": \"Cadabra JSON notebook format\",\n\t\"flags\": {\n\t\t\"hide_input_cells\": false\n\t},\n\t\"version\": 1.0\n}\n"
  },
  {
    "path": "examples/components2.cnb",
    "content": "\n{\n\t\"cells\" : \n\t[\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}A_{n m} B_{m n p} (C_{p s} + D_{s p})\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}{A_{r t} = 3, B_{t r t} = 2, B_{t r r} = 5, C_{t r} = 1, D_{r t} = r^{2} t, D_{t r} = t^{2}}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}s = \\\\left\\\\{\\\\begin{aligned}{r}: & (6\\\\, r^{2} t + 6)\\\\\\\\\\n{t}: & 15\\\\, t^{2}\\\\\\\\\\n\\\\end{aligned}\\\\right.\\n\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"{r,t}::Coordinate.\\n{m,n,p,s}::Indices(values={t,r}).\\n\\\\partial{#}::PartialDerivative.\\nC::Depends(r,t).\\n#ex:= A_{m n} B_{m n p} ( \\\\partial_{p}{C} + \\\\partial_{p}{E(t)} + D_{p} );\\nex:= A_{n m} B_{m n p} ( C_{p s} + D_{s p} );\\n#rl:= [ A_{t r} = 3, B_{t r t} = 2, B_{t r r} = 5, C_{t} + D_{t} = 1 ];\\nrl:= [ A_{r t} = 3, B_{t r t} = 2, B_{t r r} = 5, C_{t r} = 1, D_{r t} = r**2*t, D_{t r}=t**2 ];\\nevaluate(ex, rl);\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\Gamma^{\\\\mu}\\\\,_{\\\\nu \\\\rho}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\Gamma^{\\\\mu}\\\\,_{\\\\nu \\\\rho} = \\\\frac{1}{2}\\\\, g^{\\\\mu \\\\sigma} (\\\\partial_{\\\\rho}{g_{\\\\nu \\\\sigma}} + \\\\partial_{\\\\nu}{g_{\\\\rho \\\\sigma}} - \\\\partial_{\\\\sigma}{g_{\\\\nu \\\\rho}})\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\frac{1}{2}\\\\, g^{\\\\mu \\\\sigma} (\\\\partial_{\\\\rho}{g_{\\\\nu \\\\sigma}} + \\\\partial_{\\\\nu}{g_{\\\\rho \\\\sigma}} - \\\\partial_{\\\\sigma}{g_{\\\\nu \\\\rho}})\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\mu\\\\nu\\\\rho = \\\\left\\\\{\\\\begin{aligned}{t, t, r}: & \\\\frac{M}{(r^{2} ( - 2\\\\, (\\\\frac{M}{r}) + 1))}\\\\\\\\\\n{t, r, t}: & \\\\frac{M}{(r^{2} ( - 2\\\\, (\\\\frac{M}{r}) + 1))}\\\\\\\\\\n{r, r, r}: & M \\\\frac{(2\\\\, (\\\\frac{M}{r}) - 1)}{(r^{2} ( - 2\\\\, (\\\\frac{M}{r}) + 1)^{2})}\\\\\\\\\\n{r, \\\\phi, \\\\phi}: & r (2\\\\, (\\\\frac{M}{r}) - 1) \\\\sin(\\\\theta)^{2}\\\\\\\\\\n{r, \\\\theta, \\\\theta}: & r (2\\\\, (\\\\frac{M}{r}) - 1)\\\\\\\\\\n{r, t, t}: & M \\\\frac{( - 2\\\\, (\\\\frac{M}{r}) + 1)}{r^{2}}\\\\\\\\\\n{\\\\theta, \\\\theta, r}: & \\\\frac{1}{r}\\\\\\\\\\n{\\\\theta, r, \\\\theta}: & \\\\frac{1}{r}\\\\\\\\\\n{\\\\theta, \\\\phi, \\\\phi}: & -\\\\sin(\\\\theta) \\\\cos(\\\\theta)\\\\\\\\\\n{\\\\phi, \\\\phi, r}: & \\\\frac{1}{r}\\\\\\\\\\n{\\\\phi, \\\\phi, \\\\theta}: & \\\\frac{\\\\cos(\\\\theta)}{\\\\sin(\\\\theta)}\\\\\\\\\\n{\\\\phi, r, \\\\phi}: & \\\\frac{1}{r}\\\\\\\\\\n{\\\\phi, \\\\theta, \\\\phi}: & \\\\frac{\\\\cos(\\\\theta)}{\\\\sin(\\\\theta)}\\\\\\\\\\n\\\\end{aligned}\\\\right.\\n\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"{r,t,\\\\phi,\\\\theta}::Coordinate.\\n{\\\\mu,\\\\nu,\\\\rho,\\\\sigma}::Indices(values={t,r,\\\\phi,\\\\theta}, position=fixed).\\n\\\\partial{#}::PartialDerivative.\\n         \\nex:= \\\\Gamma^{\\\\mu}_{\\\\nu\\\\rho};\\nrl:= \\\\Gamma^{\\\\mu}_{\\\\nu\\\\rho} = 1/2 g^{\\\\mu\\\\sigma} ( \\\\partial_{\\\\rho}{g_{\\\\nu\\\\sigma}} +\\\\partial_{\\\\nu}{g_{\\\\rho\\\\sigma}}-\\\\partial_{\\\\sigma}{g_{\\\\nu\\\\rho}} );\\n                          \\nss:= { g_{t t} = -(1-2 M/r),   g_{r r} = 1/(1-2 M/r), g_{\\\\theta\\\\theta} = r**2,    g_{\\\\phi\\\\phi}=r**2 \\\\sin(\\\\theta)**2,\\n       g^{t t} = -1/(1-2 M/r), g^{r r} = 1-2 M/r,     g^{\\\\theta\\\\theta} = r**(-2), g^{\\\\phi\\\\phi}=r**(-2) \\\\sin(\\\\theta)**(-2) };\\nsubstitute(ex, rl);\\nevaluate(ex, ss);\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1.0\n}\n\n"
  },
  {
    "path": "examples/converge.cnb",
    "content": "{\n\t\"cell_id\": 16364440255809670543,\n\t\"cells\": [\n\t\t{\n\t\t\t\"cell_id\": 4560948911837856818,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 8096814962229094915,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\section*{Applying operations until convergence}\\n\\nIt often happens that you want to perform a series of operations on an expression, until\\nthe expression no longer changes. If it is just a single operation, you can use the \\\\verb|repeat=True|\\nparameter to the algorithm. Let us have a look at a simple example:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\section*{Applying operations until convergence}\\n\\nIt often happens that you want to perform a series of operations on an expression, until\\nthe expression no longer changes. If it is just a single operation, you can use the \\\\verb|repeat=True|\\nparameter to the algorithm. Let us have a look at a simple example:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 8484402117747940808,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 6102843015116529563,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}Q Q Q Q Q Q\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 5930843567868132618,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\left(A%\\n+B\\\\right) \\\\left(A%\\n+B\\\\right) \\\\left(A%\\n+B\\\\right) \\\\left(A%\\n+B\\\\right) \\\\left(A%\\n+B\\\\right) \\\\left(A%\\n+B\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex:=Q Q Q Q Q Q;\\nsubstitute(ex, $Q->A+B, A->3, B->5$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 17394728300667667090,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 12831285945235543173,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"Here the \\\\verb|A->3| and \\\\verb|B->5| bits of the substitution rule did not get applied because substitute\\nonly ran once. By adding the \\\\verb|repeat=True| flag you get the expected result:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"Here the \\\\verb|A->3| and \\\\verb|B->5| bits of the substitution rule did not get applied because substitute\\nonly ran once. By adding the \\\\verb|repeat=True| flag you get the expected result:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 5405106106766922936,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 1105927374242350850,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}Q Q Q Q Q Q\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9385640161226065943,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}262144\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex:=Q Q Q Q Q Q;\\nsubstitute(ex, $Q->A+B, A->3, B->5$, repeat=True);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 9537143133737954222,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 13101155018156104120,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"However, this only works if you have a single algorithm to work with. If you want to apply a series of \\nalgorithms, you need to use the Cadabra specific \\\\verb|converge| construction (which is an extension of Python). \\nIt works very similar to a \\\\verb|while| loop, and will run until the indicated expression no longer changes. Here is an example:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"However, this only works if you have a single algorithm to work with. If you want to apply a series of \\nalgorithms, you need to use the Cadabra specific \\\\verb|converge| construction (which is an extension of Python). \\nIt works very similar to a \\\\verb|while| loop, and will run until the indicated expression no longer changes. Here is an example:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 18076787751473649262,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 7473100367640179464,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 1356417453824935185,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"Q Q Q Q Q Q\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}Q Q Q Q Q Q\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 5881110624344566499,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 18420178688487594231,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"(A + B) (A + B) (A + B) (A + B) (A + B) (A + B)\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\left(A\\\\discretionary{}{}{}+B\\\\right) \\\\left(A\\\\discretionary{}{}{}+B\\\\right) \\\\left(A\\\\discretionary{}{}{}+B\\\\right) \\\\left(A\\\\discretionary{}{}{}+B\\\\right) \\\\left(A\\\\discretionary{}{}{}+B\\\\right) \\\\left(A\\\\discretionary{}{}{}+B\\\\right)\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 15799923042721325090,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 17480327659062318542,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"A A A A A A + A A A A A B + A A A A B A + A A A A B B + A A A B A A + A A A B A B + A A A B B A + A A A B B B + A A B A A A + A A B A A B + A A B A B A + A A B A B B + A A B B A A + A A B B A B + A A B B B A + A A B B B B + A B A A A A + A B A A A B + A B A A B A + A B A A B B + A B A B A A + A B A B A B + A B A B B A + A B A B B B + A B B A A A + A B B A A B + A B B A B A + A B B A B B + A B B B A A + A B B B A B + A B B B B A + A B B B B B + B A A A A A + B A A A A B + B A A A B A + B A A A B B + B A A B A A + B A A B A B + B A A B B A + B A A B B B + B A B A A A + B A B A A B + B A B A B A + B A B A B B + B A B B A A + B A B B A B + B A B B B A + B A B B B B + B B A A A A + B B A A A B + B B A A B A + B B A A B B + B B A B A A + B B A B A B + B B A B B A + B B A B B B + B B B A A A + B B B A A B + B B B A B A + B B B A B B + B B B B A A + B B B B A B + B B B B B A + B B B B B B\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}A A A A A A\\\\discretionary{}{}{}+A A A A A B\\\\discretionary{}{}{}+A A A A B A\\\\discretionary{}{}{}+A A A A B B\\\\discretionary{}{}{}+A A A B A A\\\\discretionary{}{}{}+A A A B A B\\\\discretionary{}{}{}+A A A B B A\\\\discretionary{}{}{}+A A A B B B\\\\discretionary{}{}{}+A A B A A A\\\\discretionary{}{}{}+A A B A A B\\\\discretionary{}{}{}+A A B A B A\\\\discretionary{}{}{}+A A B A B B\\\\discretionary{}{}{}+A A B B A A\\\\discretionary{}{}{}+A A B B A B\\\\discretionary{}{}{}+A A B B B A\\\\discretionary{}{}{}+A A B B B B\\\\discretionary{}{}{}+A B A A A A\\\\discretionary{}{}{}+A B A A A B\\\\discretionary{}{}{}+A B A A B A\\\\discretionary{}{}{}%\\n+A B A A B B\\\\discretionary{}{}{}+A B A B A A\\\\discretionary{}{}{}+A B A B A B\\\\discretionary{}{}{}+A B A B B A\\\\discretionary{}{}{}+A B A B B B\\\\discretionary{}{}{}+A B B A A A\\\\discretionary{}{}{}+A B B A A B\\\\discretionary{}{}{}+A B B A B A\\\\discretionary{}{}{}+A B B A B B\\\\discretionary{}{}{}+A B B B A A\\\\discretionary{}{}{}+A B B B A B\\\\discretionary{}{}{}+A B B B B A\\\\discretionary{}{}{}+A B B B B B\\\\discretionary{}{}{}+B A A A A A\\\\discretionary{}{}{}+B A A A A B\\\\discretionary{}{}{}+B A A A B A\\\\discretionary{}{}{}+B A A A B B\\\\discretionary{}{}{}+B A A B A A\\\\discretionary{}{}{}+B A A B A B\\\\discretionary{}{}{}%\\n+B A A B B A\\\\discretionary{}{}{}+B A A B B B\\\\discretionary{}{}{}+B A B A A A\\\\discretionary{}{}{}+B A B A A B\\\\discretionary{}{}{}+B A B A B A\\\\discretionary{}{}{}+B A B A B B\\\\discretionary{}{}{}+B A B B A A\\\\discretionary{}{}{}+B A B B A B\\\\discretionary{}{}{}+B A B B B A\\\\discretionary{}{}{}+B A B B B B\\\\discretionary{}{}{}+B B A A A A\\\\discretionary{}{}{}+B B A A A B\\\\discretionary{}{}{}+B B A A B A\\\\discretionary{}{}{}+B B A A B B\\\\discretionary{}{}{}+B B A B A A\\\\discretionary{}{}{}+B B A B A B\\\\discretionary{}{}{}+B B A B B A\\\\discretionary{}{}{}+B B A B B B\\\\discretionary{}{}{}+B B B A A A\\\\discretionary{}{}{}%\\n+B B B A A B\\\\discretionary{}{}{}+B B B A B A\\\\discretionary{}{}{}+B B B A B B\\\\discretionary{}{}{}+B B B B A A\\\\discretionary{}{}{}+B B B B A B\\\\discretionary{}{}{}+B B B B B A\\\\discretionary{}{}{}+B B B B B B\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 12899213816227628911,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 15954440784425493878,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"A A A A A A + 18A A A A + 135A A + 540 + 135B B + 18B B B B + B B B B B B\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}A A A A A A\\\\discretionary{}{}{}+18A A A A\\\\discretionary{}{}{}+135A A\\\\discretionary{}{}{}+540\\\\discretionary{}{}{}+135B B\\\\discretionary{}{}{}+18B B B B\\\\discretionary{}{}{}+B B B B B B\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 12278366585207225484,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 1380703068642686843,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"A A A A A A + 18A A A A + 135A A + 540 + 135B B + 18B B B B + B B B B B B\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}A A A A A A\\\\discretionary{}{}{}+18A A A A\\\\discretionary{}{}{}+135A A\\\\discretionary{}{}{}+540\\\\discretionary{}{}{}+135B B\\\\discretionary{}{}{}+18B B B B\\\\discretionary{}{}{}+B B B B B B\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 6644706389115648256,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 8158280886788049335,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"A A A A A A + 18A A A A + 135A A + 540 + 135B B + 18B B B B + B B B B B B\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}A A A A A A\\\\discretionary{}{}{}+18A A A A\\\\discretionary{}{}{}+135A A\\\\discretionary{}{}{}+540\\\\discretionary{}{}{}+135B B\\\\discretionary{}{}{}+18B B B B\\\\discretionary{}{}{}+B B B B B B\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 16485223424872350895,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 4033380256338516245,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"A A A A A A + 18A A A A + 135A A + 540 + 135B B + 18B B B B + B B B B B B\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}A A A A A A\\\\discretionary{}{}{}+18A A A A\\\\discretionary{}{}{}+135A A\\\\discretionary{}{}{}+540\\\\discretionary{}{}{}+135B B\\\\discretionary{}{}{}+18B B B B\\\\discretionary{}{}{}+B B B B B B\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex:=Q Q Q Q Q Q;\\n\\nconverge(ex):\\n\\tsubstitute(_, $Q->A+B, A B->3$, repeat=True);\\n\\tdistribute(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 12146602346513886272,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 3425231414405124914,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"We have added semicolons to every line in order to show precisely what happens: in the first iteration, the substitution \\nexpands $Q$ to $A+B$. This gives an expression in which there are no $AB$ factors yet. Those arise only once\\nthe \\\\verb|distribute| algorithm is called. At the second iteration, the substitution algorithm then \\nreplaces the~$AB$ product with~$3$.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"We have added semicolons to every line in order to show precisely what happens: in the first iteration, the substitution \\nexpands $Q$ to $A+B$. This gives an expression in which there are no $AB$ factors yet. Those arise only once\\nthe \\\\verb|distribute| algorithm is called. At the second iteration, the substitution algorithm then \\nreplaces the~$AB$ product with~$3$.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 14872399896822144370,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 17479584531350384548,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"As far as the output is concerned, the last line is repeated 4 times. First as the\\nresult of the working substitute, then because of the \\\\verb|distribute| call which\\nfollows (and does nothing). The loop then runs once more because the expression has\\nchanged, creating two more output lines. As this is a bit verbose, one would normally\\nsuppress the printing inside the \\\\verb|converge| block and only print at the end, as in:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"As far as the output is concerned, the last line is repeated 4 times. First as the\\nresult of the working substitute, then because of the \\\\verb|distribute| call which\\nfollows (and does nothing). The loop then runs once more because the expression has\\nchanged, creating two more output lines. As this is a bit verbose, one would normally\\nsuppress the printing inside the \\\\verb|converge| block and only print at the end, as in:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 4018472621299398286,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 1255485117432132129,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}Q Q Q Q Q Q\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 8477564085412428496,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}A A A A A A%\\n+18A A A A%\\n+135A A%\\n+540%\\n+135B B%\\n+18B B B B%\\n+B B B B B B\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex:=Q Q Q Q Q Q;\\n\\nconverge(ex):\\n\\tsubstitute(_, $Q->A+B, A B->3$, repeat=True)\\n\\tdistribute(_)\\n;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 13979277305687164122,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 10078366637322340715,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"Note the semi-colon \\\\verb|;| at the very end of the \\\\verb|converge| block, which triggers printing of the final result.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"Note the semi-colon \\\\verb|;| at the very end of the \\\\verb|converge| block, which triggers printing of the final result.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 2586718299574850030,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"\"\n\t\t}\n\t],\n\t\"description\": \"Cadabra JSON notebook format\",\n\t\"version\": 1.0\n}\n"
  },
  {
    "path": "examples/covariant_derivative.cdb",
    "content": "ex:= A_{m n} B_{n} + C_{m n p} D_{n p};\nfor i in ex.top().indices():\n    print(i)\n\nfor i in ex.top().free_indices():\n    print(i)\n\nprint(\"---\")\nfor term in ex.top().terms():\n    print(str(term)+\" has indices:\")\n    for i in term.indices():\n        print(i)\n        \n    \ndef expand_nabla(ex):\n    for nabla in ex[r'\\nabla']:\n        nabla.name=r'\\partial'\n        dindex = nabla.indices().__next__()   # need .index() to give direct single index without __next()__.\n        for arg in nabla.args():              # need .arg() to give direct single argument without __next()__.\n            ret:=0;\n            for index in arg.free_indices():\n                t2:= @(arg);\n                if index.parent_rel==sub:\n                    t1:= -\\Gamma^{p}_{@(dindex) @(index)};\n                    t2[index]:= _{p};\n                else:\n                    t1:=  \\Gamma^{@(index)}_{@(dindex) p};\n                    t2[index]:= ^{p};\n                ret += t1 * t2\n            nabla += ret\n    return ex\n\n\\nabla{#}::Derivative;\n\\hat{#}::Accent;\nex:= \\nabla_{a}{ h^{b}_{c} }; \nexpand_nabla(ex);\n\nex:= \\nabla_{a}{ v_{b} w^{b} };\nexpand_nabla(ex);\n    \nex:= \\nabla_{\\hat{a}}{ h_{b c} v_{d} } + \\nabla_{b}{ h_{\\hat{a} c d } } + T_{\\hat{a} b c d};\nexpand_nabla(ex);\n\n    \n\n"
  },
  {
    "path": "examples/equations_of_motion.cnb",
    "content": "{\n\t\"cells\" : \n\t[\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property PartialDerivative to~}\\\\partial{\\\\#}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Indices(position=fixed) to~}\\\\left\\\\{\\\\mu,~\\\\linebreak[0] \\\\nu\\\\right\\\\}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\int\\\\sqrt{-g} \\\\left(\\\\frac{1}{2}g^{\\\\mu \\\\nu} \\\\partial_{\\\\mu}{\\\\phi} \\\\partial_{\\\\nu}{\\\\phi}+V\\\\right)\\\\,\\\\,{\\\\rm d}x\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"\\\\partial{#}::PartialDerivative;\\n{\\\\mu,\\\\nu}::Indices(position=fixed);\\nS:= \\\\int{ \\\\sqrt{-g} ( 1/2 g^{\\\\mu\\\\nu}\\\\partial_{\\\\mu}{\\\\phi} \\\\partial_{\\\\nu}{\\\\phi} + V )}{x};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Accent to~}\\\\delta{\\\\#}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Symmetric to~}g^{\\\\mu \\\\nu}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\left\\\\{\\\\phi \\\\rightarrow \\\\delta{\\\\phi},~\\\\linebreak[0] V \\\\rightarrow V' \\\\delta{\\\\phi}\\\\right\\\\}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"\\\\delta{#}::Accent;\\ng^{\\\\mu\\\\nu}::Symmetric;\\nrl:= \\\\phi -> \\\\delta{\\\\phi}, V -> V' \\\\delta{\\\\phi};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\int\\\\sqrt{-g} \\\\left(\\\\frac{1}{2}g^{\\\\mu \\\\nu} \\\\partial_{\\\\mu}{\\\\delta{\\\\phi}} \\\\partial_{\\\\nu}{\\\\phi}+\\\\frac{1}{2}g^{\\\\mu \\\\nu} \\\\partial_{\\\\mu}{\\\\phi} \\\\partial_{\\\\nu}{\\\\delta{\\\\phi}}+V' \\\\delta{\\\\phi}\\\\right)\\\\,\\\\,{\\\\rm d}x\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"vary(S, rl);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\int\\\\sqrt{-g} \\\\left(\\\\partial_{\\\\mu}{\\\\delta{\\\\phi}} \\\\partial_{\\\\nu}{\\\\phi} g^{\\\\mu \\\\nu}+V' \\\\delta{\\\\phi}\\\\right)\\\\,\\\\,{\\\\rm d}x\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"sort_product(_)\\ncanonicalise(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\int\\\\left(\\\\sqrt{-g} \\\\partial_{\\\\mu}{\\\\delta{\\\\phi}} \\\\partial_{\\\\nu}{\\\\phi} g^{\\\\mu \\\\nu}+\\\\sqrt{-g} V' \\\\delta{\\\\phi}\\\\right)\\\\,\\\\,{\\\\rm d}x\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"distribute(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\int\\\\left(-\\\\partial_{\\\\mu}\\\\left(\\\\sqrt{-g}\\\\right) \\\\delta{\\\\phi} \\\\partial_{\\\\nu}{\\\\phi} g^{\\\\mu \\\\nu}-\\\\sqrt{-g} \\\\delta{\\\\phi} \\\\partial_{\\\\mu}\\\\left(\\\\partial_{\\\\nu}{\\\\phi} g^{\\\\mu \\\\nu}\\\\right)+\\\\sqrt{-g} V' \\\\delta{\\\\phi}\\\\right)\\\\,\\\\,{\\\\rm d}x\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"integrate_by_parts(_, $\\\\delta{\\\\phi}$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\int\\\\delta{\\\\phi} \\\\left(-\\\\partial_{\\\\mu}\\\\left(\\\\sqrt{-g}\\\\right) \\\\partial_{\\\\nu}{\\\\phi} g^{\\\\mu \\\\nu}-\\\\sqrt{-g} \\\\partial_{\\\\mu}\\\\left(\\\\partial_{\\\\nu}{\\\\phi} g^{\\\\mu \\\\nu}\\\\right)+\\\\sqrt{-g} V'\\\\right)\\\\,\\\\,{\\\\rm d}x\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"factor_out(_, $\\\\delta{\\\\phi}$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1\n}\n"
  },
  {
    "path": "examples/exterior.cnb",
    "content": "{\n\t\"cell_id\": 17942456533940163234,\n\t\"cells\": [\n\t\t{\n\t\t\t\"cell_id\": 11340042467900394662,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9417804978734591005,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\section*{Differential forms}\\n\\nCadabra can handle the calculus of differential forms. Differential forms are declared by attaching\\nthe property \\\\prop{DifferentialForm} to an object, as in the example below, where we declare\\nfour forms, with degree 0 to 3, and one form with symbolic degree $p$.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\section*{Differential forms}\\n\\nCadabra can handle the calculus of differential forms. Differential forms are declared by attaching\\nthe property \\\\prop{DifferentialForm} to an object, as in the example below, where we declare\\nfour forms, with degree 0 to 3, and one form with symbolic degree $p$.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 8887426986920168478,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 13073359310491379889,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property DifferentialForm attached to~}A^{(0)}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 10593507904057100864,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property DifferentialForm attached to~}A^{(1)}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 6537944391875026508,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property DifferentialForm attached to~}A^{(2)}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 12647633650928800632,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property DifferentialForm attached to~}A^{(3)}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 12487424283125203977,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property DifferentialForm attached to~}B^{(p)}.\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"A0::LaTeXForm(\\\"A^{(0)}\\\").\\nA1::LaTeXForm(\\\"A^{(1)}\\\").\\nA2::LaTeXForm(\\\"A^{(2)}\\\").\\nA3::LaTeXForm(\\\"A^{(3)}\\\").\\nBp::LaTeXForm(\\\"B^{(p)}\\\").\\nA0::DifferentialForm(degree=0);\\nA1::DifferentialForm(degree=1);\\nA2::DifferentialForm(degree=2);\\nA3::DifferentialForm(degree=3);\\nBp::DifferentialForm(degree=p);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 9245929567340263576,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 10731088970142001207,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"The exterior product (or wedge product) of forms is denoted with a \\\\verb|^| symbol (make sure to put a space\\nbefore and after this symbol to avoid confusion with a superscript).\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"The exterior product (or wedge product) of forms is denoted with a \\\\verb|^| symbol (make sure to put a space\\nbefore and after this symbol to avoid confusion with a superscript).\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 4953780234914878080,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 6923194141810237783,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 17082687383703456280,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"A1 ^ A2 + A2 ^ A1\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}A^{(1)}\\\\wedge A^{(2)}\\\\discretionary{}{}{}+A^{(2)}\\\\wedge A^{(1)}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex:=A1 ^ A2 + A2 ^ A1;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 1319382506597754390,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 2881774846106643562,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 4676872922717938419,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"2A1 ^ A2\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}2\\\\,A^{(1)}\\\\wedge A^{(2)}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"sort_product(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 9265232820241736682,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 502579766510955272,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 7323600331052651947,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"A1 ^ A2 ^ A1\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}A^{(1)}\\\\wedge A^{(2)}\\\\wedge A^{(1)}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 11601682801055726062,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 17096746244275086715,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"0\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}0\\\\,\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex:=A1 ^ A2 ^ A1;\\nsort_product(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 4020737267376578434,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 553403799738640895,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 5981656483791278698,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"A3 ^ A2 ^ A1 ^ A2\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}A^{(3)}\\\\wedge A^{(2)}\\\\wedge A^{(1)}\\\\wedge A^{(2)}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 1138853092500522538,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 15420789810314368702,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"-A1 ^ A2 ^ A2 ^ A3\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}-\\\\,A^{(1)}\\\\wedge A^{(2)}\\\\wedge A^{(2)}\\\\wedge A^{(3)}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex:= A3 ^ A2 ^ A1 ^ A2;\\nsort_product(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 14722099834296306032,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 15780429776499677377,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"An exterior derivative can be declared by using the \\\\prop{ExteriorDerivative} property. Applying an exterior\\nderivative twice produces zero, and it obeys the product rule taking into account the degree of differential forms.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"An exterior derivative can be declared by using the \\\\prop{ExteriorDerivative} property. Applying an exterior\\nderivative twice produces zero, and it obeys the product rule taking into account the degree of differential forms.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 15528343336642185683,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 14425756794755688154,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property ExteriorDerivative attached to~}d{\\\\#}.\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"d{#}::ExteriorDerivative;\\nd{#}::LaTeXForm(\\\"{\\\\rm d}\\\").\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 1144807404142193736,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 14316627591008813729,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 12449235750573262389,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"-d(A1 ^ A2 ^ A2 ^ A3)\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}-\\\\,{\\\\rm d}\\\\left(A^{(1)}\\\\wedge A^{(2)}\\\\wedge A^{(2)}\\\\wedge A^{(3)}\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex2:= d{ @(ex) };\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 12023467755791252355,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 548029278717630328,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 13065435639143390826,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"-d(A1) ^ A2 ^ A2 ^ A3 + A1 ^ d(A2) ^ A2 ^ A3 + A1 ^ A2 ^ d(A2) ^ A3 + A1 ^ A2 ^ A2 ^ d(A3)\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}-\\\\,{\\\\rm d}{A^{(1)}}\\\\wedge A^{(2)}\\\\wedge A^{(2)}\\\\wedge A^{(3)}\\\\discretionary{}{}{}+A^{(1)}\\\\wedge {\\\\rm d}{A^{(2)}}\\\\wedge A^{(2)}\\\\wedge A^{(3)}\\\\discretionary{}{}{}+A^{(1)}\\\\wedge A^{(2)}\\\\wedge {\\\\rm d}{A^{(2)}}\\\\wedge A^{(3)}\\\\discretionary{}{}{}+A^{(1)}\\\\wedge A^{(2)}\\\\wedge A^{(2)}\\\\wedge {\\\\rm d}{A^{(3)}}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"product_rule(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 8520254541109020363,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 17389198675231273418,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 6379329424106536610,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"d(A1 ^ A2 ^ d(A3))\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}{\\\\rm d}\\\\left(A^{(1)}\\\\wedge A^{(2)}\\\\wedge {\\\\rm d}{A^{(3)}}\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex:= d{ A1 ^ A2 ^ d{ A3 } };\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 9883512770807428270,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 6479707434524814266,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 11224304011160064339,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"d(A1) ^ A2 ^ d(A3)-A1 ^ d(A2) ^ d(A3)\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}{\\\\rm d}{A^{(1)}}\\\\wedge A^{(2)}\\\\wedge {\\\\rm d}{A^{(3)}}\\\\discretionary{}{}{}-\\\\,A^{(1)}\\\\wedge {\\\\rm d}{A^{(2)}}\\\\wedge {\\\\rm d}{A^{(3)}}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"product_rule(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 3882037680778395718,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 10144537675020775443,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 7972450390527612306,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"A2 ^ d(A1) ^ d(A3)-A1 ^ d(A2) ^ d(A3)\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}A^{(2)}\\\\wedge {\\\\rm d}{A^{(1)}}\\\\wedge {\\\\rm d}{A^{(3)}}\\\\discretionary{}{}{}-\\\\,A^{(1)}\\\\wedge {\\\\rm d}{A^{(2)}}\\\\wedge {\\\\rm d}{A^{(3)}}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"sort_product(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 7388374175146732527,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 7893177832322756865,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"Two forms in a product can only be swapped around if one of their degrees is zero:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"Two forms in a product can only be swapped around if one of their degrees is zero:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 7517601938794019119,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9355352882446994084,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 9014306377047625861,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"A2 A0 + A0 A2\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}A^{(2)} A^{(0)}\\\\discretionary{}{}{}+A^{(0)} A^{(2)}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 4376895380066575997,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 14683582997119667726,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"2A0 A2\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}2\\\\,A^{(0)} A^{(2)}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex4:= A2 A0 + A0 A2;\\nsort_product(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 4180056803145046336,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 4007756470112194266,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"In a wedge product, forms can be swapped around taking into account their degree:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"In a wedge product, forms can be swapped around taking into account their degree:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 1994676414667850866,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 3259713259784367660,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 3523049251192430421,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"A3 ^ A1-A1 ^ A3 + A2 ^ A2 ^ A0\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}A^{(3)}\\\\wedge A^{(1)}\\\\discretionary{}{}{}-\\\\,A^{(1)}\\\\wedge A^{(3)}\\\\discretionary{}{}{}+A^{(2)}\\\\wedge A^{(2)}\\\\wedge A^{(0)}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 14428638432251725402,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 1966350038726147102,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"-2A1 ^ A3 + A0 ^ A2 ^ A2\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}-2\\\\,A^{(1)}\\\\wedge A^{(3)}\\\\discretionary{}{}{}+A^{(0)}\\\\wedge A^{(2)}\\\\wedge A^{(2)}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex5:= A3 ^ A1 - A1 ^ A3 + A2 ^ A2 ^ A0;\\nsort_product(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 3478897637566888729,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 13125406793319040163,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"Differential forms can have tensor indices, e.g.~for vielbeine or spin connections. In the example below the spin connection is a one-form:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"Differential forms can have tensor indices, e.g.~for vielbeine or spin connections. In the example below the spin connection is a one-form:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 16323106096533524039,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 793962738078864164,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property Indices(position=free) attached to~}\\\\left[a, \\\\discretionary{}{}{}b, \\\\discretionary{}{}{}c\\\\right].\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 4917464210514929957,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property DifferentialForm attached to~}\\\\left[e^{a}, \\\\discretionary{}{}{}\\\\omega^{a}\\\\,_\\\\!{b}\\\\right].\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"{a,b,c}::Indices;\\n{e^{a}, \\\\omega^{a}_{b}}::DifferentialForm(degree=1);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 569944791880263975,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 12875217671457157494,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 3367952966686115973,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"d(e^{a}) = -\\\\omega^{a}_{b} ^ e^{b}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}{\\\\rm d}{e^{a}} = -\\\\,\\\\omega^{a}\\\\,_\\\\!{b}\\\\wedge e^{b}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex:=d{e^{a}} = - \\\\omega^{a}_{b} ^ e^{b};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 15096640937298439073,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 4180290509943711364,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 17052694519576749752,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"0 = -d(\\\\omega^{a}_{b} ^ e^{b})\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}0\\\\, = -\\\\,{\\\\rm d}\\\\left(\\\\omega^{a}\\\\,_\\\\!{b}\\\\wedge e^{b}\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"cv:= d{ @(ex) };\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 2802247552303887267,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 14109098586816485661,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 5057550769214572062,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"0 = -d(\\\\omega^{a}_{b} ^ e^{b})\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}0\\\\, = -\\\\,{\\\\rm d}\\\\left(\\\\omega^{a}\\\\,_\\\\!{b}\\\\wedge e^{b}\\\\right)\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 16768635483364701468,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 9100291738975759978,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"0 = -d(\\\\omega^{a}_{b}) ^ e^{b} + \\\\omega^{a}_{b} ^ d(e^{b})\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}0\\\\, = -\\\\,{\\\\rm d}{\\\\omega^{a}\\\\,_\\\\!{b}}\\\\wedge e^{b}\\\\discretionary{}{}{}+\\\\omega^{a}\\\\,_\\\\!{b}\\\\wedge {\\\\rm d}{e^{b}}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"distribute(cv);\\nproduct_rule(cv);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 16406542458279560327,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 6908270652899820190,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 7722778083774726111,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"0 = -d(\\\\omega^{a}_{b}) ^ e^{b}-\\\\omega^{a}_{b} ^ \\\\omega^{b}_{c} ^ e^{c}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}0\\\\, = -\\\\,{\\\\rm d}{\\\\omega^{a}\\\\,_\\\\!{b}}\\\\wedge e^{b}\\\\discretionary{}{}{}-\\\\,\\\\omega^{a}\\\\,_\\\\!{b}\\\\wedge \\\\omega^{b}\\\\,_\\\\!{c}\\\\wedge e^{c}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"substitute(cv, ex);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 10258893899376774313,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 2550465529160061943,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 12120344385952314056,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"0 = -d(\\\\omega^{a}_{b}) ^ e^{b}-\\\\omega^{a}_{b} ^ \\\\omega^{b}_{c} ^ e^{c}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}0\\\\, = -\\\\,{\\\\rm d}{\\\\omega^{a}\\\\,_\\\\!{b}}\\\\wedge e^{b}\\\\discretionary{}{}{}-\\\\,\\\\omega^{a}\\\\,_\\\\!{b}\\\\wedge \\\\omega^{b}\\\\,_\\\\!{c}\\\\wedge e^{c}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"rename_dummies(cv);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 16913818003335919797,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 6957951781041518552,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"Some more random assorted ramblings below, not finished yet!!!\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"Some more random assorted ramblings below, not finished yet!!!\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 5914123710050700613,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 5157664565284124436,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 16426374208311443500,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"d(-2A1 ^ A3 + A0 ^ A2 ^ A2)\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}{\\\\rm d}\\\\left(-2\\\\,A^{(1)}\\\\wedge A^{(3)}\\\\discretionary{}{}{}+A^{(0)}\\\\wedge A^{(2)}\\\\wedge A^{(2)}\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex4:= d{ @(ex5) };\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 6700747750860875507,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 14976239101849367835,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 5100631419153999072,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"-2d(A1 ^ A3) + d(A0 ^ A2 ^ A2)\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}-2\\\\,{\\\\rm d}\\\\left(A^{(1)}\\\\wedge A^{(3)}\\\\right)\\\\discretionary{}{}{}+{\\\\rm d}\\\\left(A^{(0)}\\\\wedge A^{(2)}\\\\wedge A^{(2)}\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"distribute(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 15415966661854912494,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 17651714335568080313,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 7631791663732561426,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"-2d(A1) ^ A3 + 2A1 ^ d(A3) + d(A0) ^ A2 ^ A2 + A0 ^ d(A2) ^ A2 + A0 ^ A2 ^ d(A2)\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}-2\\\\,{\\\\rm d}{A^{(1)}}\\\\wedge A^{(3)}\\\\discretionary{}{}{}+2\\\\,A^{(1)}\\\\wedge {\\\\rm d}{A^{(3)}}\\\\discretionary{}{}{}+{\\\\rm d}{A^{(0)}}\\\\wedge A^{(2)}\\\\wedge A^{(2)}\\\\discretionary{}{}{}+A^{(0)}\\\\wedge {\\\\rm d}{A^{(2)}}\\\\wedge A^{(2)}\\\\discretionary{}{}{}+A^{(0)}\\\\wedge A^{(2)}\\\\wedge {\\\\rm d}{A^{(2)}}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"product_rule(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 4457834258149327361,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9640802863015191596,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 12235520319002832933,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"-2A3 ^ d(A1) + 2A1 ^ d(A3) + A2 ^ A2 ^ d(A0) + 2A0 ^ A2 ^ d(A2)\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}-2\\\\,A^{(3)}\\\\wedge {\\\\rm d}{A^{(1)}}\\\\discretionary{}{}{}+2\\\\,A^{(1)}\\\\wedge {\\\\rm d}{A^{(3)}}\\\\discretionary{}{}{}+A^{(2)}\\\\wedge A^{(2)}\\\\wedge {\\\\rm d}{A^{(0)}}\\\\discretionary{}{}{}+2\\\\,A^{(0)}\\\\wedge A^{(2)}\\\\wedge {\\\\rm d}{A^{(2)}}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"sort_product(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 4984116761811257240,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 14122369766595653625,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property Indices(position=free, values=\\\\{{1}\\n, {1}  2\\n, {1}  3\\n\\\\}) attached to~}\\\\left[i, \\\\discretionary{}{}{}j, \\\\discretionary{}{}{}k, \\\\discretionary{}{}{}l\\\\right].\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 17837628204179838226,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property Integer attached to~}\\\\left[i, \\\\discretionary{}{}{}j, \\\\discretionary{}{}{}k, \\\\discretionary{}{}{}l\\\\right].\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 4664208718734190365,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property EpsilonTensor attached to~}\\\\epsilon^{i j k}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 3701034086881586022,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property ExteriorDerivative attached to~}{\\\\rm d}{\\\\#}.\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"{i,j,k,l}::Indices(values={1,2,3});\\n{i,j,k,l}::Integer(1..3);\\n\\\\epsilon^{i j k}::EpsilonTensor;\\nd{#}::ExteriorDerivative;\\nd{#}::LaTeXForm(\\\"{\\\\rm d}\\\").\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 6955768955919678707,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 10282786757027507880,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 1625005921047992761,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\epsilon^{i j k}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\epsilon^{i j k}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex:=\\\\epsilon^{i j k};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 146115869353297447,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 7899861340471311518,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 15504944998596185971,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\components^{i j k}({{1, 2, 3} = 1, {1, 3, 2} = -1, {2, 1, 3} = -1, {2, 3, 1} = 1, {3, 1, 2} = 1, {3, 2, 1} = -1})\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\square{}^{i}{}^{j}{}^{k}\\\\left\\\\{\\\\begin{aligned}\\\\square{}^{1}{}^{2\\\\,}{}^{3\\\\,}& = 1\\\\\\\\[-.5ex]\\n\\\\square{}^{1}{}^{3\\\\,}{}^{2\\\\,}& = -\\\\,1\\\\\\\\[-.5ex]\\n\\\\square{}^{2\\\\,}{}^{1}{}^{3\\\\,}& = -\\\\,1\\\\\\\\[-.5ex]\\n\\\\square{}^{2\\\\,}{}^{3\\\\,}{}^{1}& = 1\\\\\\\\[-.5ex]\\n\\\\square{}^{3\\\\,}{}^{1}{}^{2\\\\,}& = 1\\\\\\\\[-.5ex]\\n\\\\square{}^{3\\\\,}{}^{2\\\\,}{}^{1}& = -\\\\,1\\\\\\\\[-.5ex]\\n\\\\end{aligned}\\\\right.\\n\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"evaluate(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 6999986821528213344,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9223372036854775820,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 9223372036854775821,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"{\\\\Sigma^{1} = \\\\cos(\\\\psi) d(\\\\theta) + \\\\sin(\\\\psi) \\\\sin(\\\\theta) d(\\\\phi), \\\\Sigma^{2} = -\\\\sin(\\\\psi) d(\\\\theta) + \\\\cos(\\\\psi) \\\\sin(\\\\theta) d(\\\\phi), \\\\Sigma^{3} = \\\\cos(\\\\theta) d(\\\\phi) + d(\\\\psi)}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\left[\\\\Sigma^{1} = \\\\cos{\\\\psi} {\\\\rm d}{\\\\theta}+\\\\sin{\\\\psi} \\\\sin{\\\\theta} {\\\\rm d}{\\\\phi},~\\\\discretionary{}{}{} \\\\Sigma^{2} = -\\\\sin{\\\\psi} {\\\\rm d}{\\\\theta}+\\\\cos{\\\\psi} \\\\sin{\\\\theta} {\\\\rm d}{\\\\phi},~\\\\discretionary{}{}{} \\\\Sigma^{3} = \\\\cos{\\\\theta} {\\\\rm d}{\\\\phi}+{\\\\rm d}{\\\\psi}\\\\right]\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"rl:= { \\\\Sigma^{1} =  \\\\cos{\\\\psi} d{\\\\theta} + \\\\sin{\\\\psi} \\\\sin{\\\\theta} d{\\\\phi},\\n       \\\\Sigma^{2} = -\\\\sin{\\\\psi} d{\\\\theta} + \\\\cos{\\\\psi} \\\\sin{\\\\theta} d{\\\\phi},\\n       \\\\Sigma^{3} =  \\\\cos{\\\\theta} d{\\\\phi} + d{\\\\psi} };\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 2266077326488286745,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9223372036854775823,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{} - \\\\frac{1}{2}\\\\epsilon^{i j k} \\\\Sigma^{j}\\\\wedge \\\\Sigma^{k}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"tst:= -1/2 \\\\epsilon^{i j k} \\\\Sigma^{j} ^ \\\\Sigma^{k};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 11941205435825729702,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9223372036854775826,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}0\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"evaluate(tst, rl);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 8836380534498282216,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"\"\n\t\t}\n\t],\n\t\"description\": \"Cadabra JSON notebook format\",\n\t\"flags\": {\n\t\t\"hide_input_cells\": false\n\t},\n\t\"version\": 1.0\n}\n"
  },
  {
    "path": "examples/fermionic_oscillator_algebra.cnb",
    "content": "{\n\t\"cells\" : \n\t[\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Indices(position=free) to~}\\\\left[n,~\\\\discretionary{}{}{} m,~\\\\discretionary{}{}{} p\\\\right].\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property SelfAntiCommuting to~}a_{n}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property SelfAntiCommuting to~}ad_{n}.\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"{n,m,p}::Indices(position=free);\\na_{n}::SelfAntiCommuting;\\nad_{n}::SelfAntiCommuting;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"ad_{n}::LaTeXForm(\\\"a^\\\\dagger\\\").\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property NonCommuting to~}\\\\left[a_{n},~\\\\discretionary{}{}{} a^\\\\dagger_{m}\\\\right].\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"{a_{n},ad_{m} }::NonCommuting;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"a_{n} a_{m}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}a_{n} a_{m}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"-a_{m} a_{n}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}-a_{m} a_{n}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex1:= a_{n} a_{m};\\nsort_product(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"0\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}0\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex2:= a_{n} a_{n};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"a_{n} ad_{n}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}a_{n} a^\\\\dagger_{n}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"a_{n} ad_{n}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}a_{n} a^\\\\dagger_{n}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex3:= a_{n} ad_{n};\\nsort_product(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"ad_{n} a_{n}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}a^\\\\dagger_{n} a_{n}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"ad_{n} a_{n}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}a^\\\\dagger_{n} a_{n}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex3:= ad_{n} a_{n};\\nsort_product(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"a_{n} ad_{m}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}a_{n} a^\\\\dagger_{m}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"a_{n} ad_{m}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}a_{n} a^\\\\dagger_{m}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex4:= a_{n} ad_{m};\\nsort_product(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property KroneckerDelta to~}\\\\delta_{m n}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"a_{m} ad_{n} → -ad_{n} a_{m} + \\\\delta_{n m}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}a_{m} a^\\\\dagger_{n} \\\\rightarrow -a^\\\\dagger_{n} a_{m}+\\\\delta_{n m}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"\\\\delta_{m n}::KroneckerDelta;\\nrl:= a_{m} ad_{n} -> - ad_{n} a_{m} + \\\\delta_{n m};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"a_{n} a_{m} ad_{m} a_{n}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}a_{n} a_{m} a^\\\\dagger_{m} a_{n}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex5:= a_{n} a_{m} ad_{m} a_{n};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"-(-ad_{m} a_{n} + \\\\delta_{m n}) a_{m} a_{n}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}-\\\\left(-a^\\\\dagger_{m} a_{n}+\\\\delta_{m n}\\\\right) a_{m} a_{n}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"substitute(ex5, rl);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"def post_process(ex):\\n   # move all a^\\\\dagger operators to the right\\n   converge(ex):\\n      substitute(ex, rl)\\n      distribute(ex)\\n      eliminate_kronecker(ex)\\n   sort_product(ex)\\n   collect_terms(ex)\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"-ad_{m} a_{m} a_{p} + \\\\delta_{m m} a_{p}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}-a^\\\\dagger_{m} a_{m} a_{p}+\\\\delta_{m m} a_{p}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex:= a_{n} ad_{p} a_{m} ad_{m} a_{n};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1\n}\n"
  },
  {
    "path": "examples/fierz.cnb",
    "content": "{\n\t\"cells\" : \n\t[\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"{\\\\mu,\\\\nu,\\\\rho}::Indices(curved, position=fixed).\\n{m,n,p,q,r,s,t,u,v}::Indices(flat, position=independent).\\n{m,n,p,q,r,s,t,u,v}::Integer(0..10).\\nT^{#{\\\\mu}}::AntiSymmetric.\\n\\\\psi_{\\\\mu}::SelfAntiCommuting.\\n\\\\psi_{\\\\mu}::Spinor(dimension=11, type=Majorana).\\n\\\\theta::Spinor(dimension=11, type=Majorana).\\n\\\\epsilon::Spinor(dimension=11, type=Majorana).\\n{\\\\theta,\\\\epsilon,\\\\psi_{\\\\mu}}::AntiCommuting.\\n\\\\bar{#}::DiracBar.\\n\\\\delta^{m n}::KroneckerDelta.\\n\\\\Gamma^{#{m}}::GammaMatrix(metric=\\\\delta).\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}T^{\\\\mu \\\\nu \\\\rho} e_{\\\\nu}\\\\,^{s} \\\\bar{\\\\theta} \\\\Gamma^{r s} \\\\psi_{\\\\rho} \\\\bar{\\\\psi_{\\\\mu}} \\\\Gamma^{r} \\\\epsilon\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"obj:= T^{\\\\mu\\\\nu\\\\rho} e_{\\\\nu}^{s}\\n     \\\\bar{\\\\theta} \\\\Gamma^{r s} \\\\psi_{\\\\rho}\\n     \\\\bar{\\\\psi_{\\\\mu}} \\\\Gamma^{r} \\\\epsilon;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{} - \\\\frac{1}{32}T^{\\\\mu \\\\nu \\\\rho} e_{\\\\nu}\\\\,^{s} \\\\bar{\\\\theta} \\\\Gamma^{r s} \\\\Gamma^{r} \\\\epsilon \\\\bar{\\\\psi_{\\\\mu}} \\\\psi_{\\\\rho} - \\\\frac{1}{32}T^{\\\\mu \\\\nu \\\\rho} e_{\\\\nu}\\\\,^{s} \\\\bar{\\\\theta} \\\\Gamma^{r s} \\\\Gamma^{m} \\\\Gamma^{r} \\\\epsilon \\\\bar{\\\\psi_{\\\\mu}} \\\\Gamma_{m} \\\\psi_{\\\\rho} - \\\\frac{1}{64}T^{\\\\mu \\\\nu \\\\rho} e_{\\\\nu}\\\\,^{s} \\\\bar{\\\\theta} \\\\Gamma^{r s} \\\\Gamma^{m n} \\\\Gamma^{r} \\\\epsilon \\\\bar{\\\\psi_{\\\\mu}} \\\\Gamma_{n m} \\\\psi_{\\\\rho} - \\\\frac{1}{192}T^{\\\\mu \\\\nu \\\\rho} e_{\\\\nu}\\\\,^{s} \\\\bar{\\\\theta} \\\\Gamma^{r s} \\\\Gamma^{m n p} \\\\Gamma^{r} \\\\epsilon \\\\bar{\\\\psi_{\\\\mu}} \\\\Gamma_{p n m} \\\\psi_{\\\\rho} - \\\\frac{1}{768}T^{\\\\mu \\\\nu \\\\rho} e_{\\\\nu}\\\\,^{s} \\\\bar{\\\\theta} \\\\Gamma^{r s} \\\\Gamma^{m n p q} \\\\Gamma^{r} \\\\epsilon \\\\bar{\\\\psi_{\\\\mu}} \\\\Gamma_{q p n m} \\\\psi_{\\\\rho} - \\\\frac{1}{3840}T^{\\\\mu \\\\nu \\\\rho} e_{\\\\nu}\\\\,^{s} \\\\bar{\\\\theta} \\\\Gamma^{r s} \\\\Gamma^{m n p q t} \\\\Gamma^{r} \\\\epsilon \\\\bar{\\\\psi_{\\\\mu}} \\\\Gamma_{t q p n m} \\\\psi_{\\\\rho}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"fierz(_, $\\\\theta, \\\\epsilon, \\\\psi_{\\\\mu}, \\\\psi_{\\\\rho}$ );\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\frac{1}{4}T^{\\\\mu \\\\nu \\\\rho} e_{\\\\mu}\\\\,^{m} \\\\bar{\\\\theta} \\\\Gamma_{m}\\\\,^{n} \\\\epsilon \\\\bar{\\\\psi_{\\\\nu}} \\\\Gamma^{n} \\\\psi_{\\\\rho}+\\\\frac{5}{16}T^{\\\\mu \\\\nu \\\\rho} e_{\\\\mu}\\\\,^{m} \\\\bar{\\\\theta} \\\\epsilon \\\\bar{\\\\psi_{\\\\nu}} \\\\Gamma_{m} \\\\psi_{\\\\rho}+\\\\frac{3}{32}T^{\\\\mu \\\\nu \\\\rho} e_{\\\\mu}\\\\,^{m} \\\\bar{\\\\theta} \\\\Gamma_{m}\\\\,^{n p} \\\\epsilon \\\\bar{\\\\psi_{\\\\nu}} \\\\Gamma_{n}\\\\,^{p} \\\\psi_{\\\\rho}+\\\\frac{1}{4}T^{\\\\mu \\\\nu \\\\rho} e_{\\\\mu}\\\\,^{n} \\\\bar{\\\\theta} \\\\Gamma^{m} \\\\epsilon \\\\bar{\\\\psi_{\\\\nu}} \\\\Gamma_{n m} \\\\psi_{\\\\rho}+\\\\frac{1}{384}T^{\\\\mu \\\\nu \\\\rho} e_{\\\\mu}\\\\,^{r} \\\\bar{\\\\theta} \\\\Gamma^{m n p q} \\\\epsilon \\\\bar{\\\\psi_{\\\\nu}} \\\\Gamma_{r m n p q} \\\\psi_{\\\\rho}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"converge(obj):\\n   join_gamma(_)\\n   distribute(_)\\n   eliminate_kronecker(_)\\ncanonicalise(_)\\nrename_dummies(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\frac{1}{4}T^{\\\\mu \\\\nu \\\\rho} e_{\\\\mu}\\\\,^{m} \\\\bar{\\\\theta} \\\\Gamma^{m n} \\\\epsilon \\\\bar{\\\\psi_{\\\\nu}} \\\\Gamma_{n} \\\\psi_{\\\\rho}+\\\\frac{5}{16}T^{\\\\mu \\\\nu \\\\rho} e_{\\\\mu}\\\\,^{m} \\\\bar{\\\\theta} \\\\epsilon \\\\bar{\\\\psi_{\\\\nu}} \\\\Gamma_{m} \\\\psi_{\\\\rho}+\\\\frac{3}{32}T^{\\\\mu \\\\nu \\\\rho} e_{\\\\mu}\\\\,^{m} \\\\bar{\\\\theta} \\\\Gamma^{m n p} \\\\epsilon \\\\bar{\\\\psi_{\\\\nu}} \\\\Gamma_{n p} \\\\psi_{\\\\rho}+\\\\frac{1}{4}T^{\\\\mu \\\\nu \\\\rho} e_{\\\\mu}\\\\,^{m} \\\\bar{\\\\theta} \\\\Gamma^{n} \\\\epsilon \\\\bar{\\\\psi_{\\\\nu}} \\\\Gamma_{m n} \\\\psi_{\\\\rho}+\\\\frac{1}{384}T^{\\\\mu \\\\nu \\\\rho} e_{\\\\mu}\\\\,^{m} \\\\bar{\\\\theta} \\\\Gamma^{n p q r} \\\\epsilon \\\\bar{\\\\psi_{\\\\nu}} \\\\Gamma_{m n p q r} \\\\psi_{\\\\rho}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"tst:=1/4 T^{\\\\mu \\\\nu \\\\rho} e_{\\\\mu}^{m} \\\\bar{\\\\theta} \\\\Gamma^{m n}\\n\\\\epsilon \\\\bar{\\\\psi_{\\\\nu}} \\\\Gamma_{n} \\\\psi_{\\\\rho} \\n+ 5/16 T^{\\\\mu \\\\nu \\\\rho} e_{\\\\mu}^{m} \\\\bar{\\\\theta} \\\\epsilon\\n\\\\bar{\\\\psi_{\\\\nu}} \\\\Gamma_{m} \\\\psi_{\\\\rho} \\n+ 3/32 T^{\\\\mu \\\\nu \\\\rho} e_{\\\\mu}^{m} \\\\bar{\\\\theta} \\\\Gamma^{m n p} \\\\epsilon\\n\\\\bar{\\\\psi_{\\\\nu}} \\\\Gamma_{n p} \\\\psi_{\\\\rho} \\n+ 1/4 T^{\\\\mu \\\\nu \\\\rho} e_{\\\\mu}^{m} \\\\bar{\\\\theta} \\\\Gamma^{n}\\n\\\\epsilon \\\\bar{\\\\psi_{\\\\nu}} \\\\Gamma_{m n} \\\\psi_{\\\\rho} \\n+ 1/384 T^{\\\\mu \\\\nu \\\\rho} e_{\\\\mu}^{m} \\\\bar{\\\\theta}\\n\\\\Gamma^{n p q r} \\\\epsilon \\\\bar{\\\\psi_{\\\\nu}} \\\\Gamma_{m n p q r} \\\\psi_{\\\\rho};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1\n}\n"
  },
  {
    "path": "examples/for_previous_users.cnb",
    "content": "{\n\t\"cells\" : \n\t[\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\section*{Cadabra for loyal users}\\n\\nThis notebook explains various aspects of Cadabra 2 for users of earlier versions. But even if \\nyou have never used Cadabra before, this is probably a useful notebook to read through.\\n\\nUnder the hood, many things have changed, most notably the fact that you can now freely\\nmix mathematical expressions with proper Python code to manipulate them. But let's get\\nstarted at the beginning. Just like in the old Cadabra, you enter expressions by using\\nthe \\\\verb|:=| assignment operator. \"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\section*{Cadabra for loyal users}\\n\\nThis notebook explains various aspects of Cadabra 2 for users of earlier versions. But even if \\nyou have never used Cadabra before, this is probably a useful notebook to read through.\\n\\nUnder the hood, many things have changed, most notably the fact that you can now freely\\nmix mathematical expressions with proper Python code to manipulate them. But let's get\\nstarted at the beginning. Just like in the old Cadabra, you enter expressions by using\\nthe \\\\verb|:=| assignment operator. \"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}A_{m n} B_{m n}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex := A_{m n} B_{m n};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"Here `\\\\verb|ex|' is, as before, the label that will be assigned to this expression.\\nCadabra's default has always been to display every line that ends in a semi-colon, `\\\\verb|;|',\\nand that rule has not changed. The difference is how things are implemented now. While \\n`\\\\verb|ex|' used to be simply a label, in Cadabra 2 it is a full-fledged Python object. You \\ncan see this by e.g.~asking for its type:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"Here `\\\\verb|ex|' is, as before, the label that will be assigned to this expression.\\nCadabra's default has always been to display every line that ends in a semi-colon, `\\\\verb|;|',\\nand that rule has not changed. The difference is how things are implemented now. While \\n`\\\\verb|ex|' used to be simply a label, in Cadabra 2 it is a full-fledged Python object. You \\ncan see this by e.g.~asking for its type:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"verbatim\",\n\t\t\t\t\t\"source\" : \"\\\\begin{verbatim}<class 'cadabra2.Ex'>\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"type(ex);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"Note how we again used the `\\\\verb|;|' line ending to instruct Cadabra to display the result. \\nIf you had left it off, you would get no output (try it!). Note how you have used a bit of Python\\n(the \\\\verb|type| function call) without telling Cadabra that this was actually Python, not a \\nCadabra expression. How that works will become clear in a minute.\\n\\nProperties of mathematical symbols can, as before, be entered by using the `\\\\verb|::|' operator, \\nas the following shows.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"Note how we again used the `\\\\verb|;|' line ending to instruct Cadabra to display the result. \\nIf you had left it off, you would get no output (try it!). Note how you have used a bit of Python\\n(the \\\\verb|type| function call) without telling Cadabra that this was actually Python, not a \\nCadabra expression. How that works will become clear in a minute.\\n\\nProperties of mathematical symbols can, as before, be entered by using the `\\\\verb|::|' operator, \\nas the following shows.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Symmetric to~}A_{m n}.\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"A_{m n}::Symmetric;\\nB_{m n}::AntiSymmetric.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"Notice how we suppressed printing of the property assignment on the second line, by using a period instead of a semi-colon.\\nThe main notational difference with respect to the old Cadabra comes when running algorithms on expressions. \\nAlgorithms have become Python functions, and the somewhat esoteric algorithm calling convention of the old Cadabra\\n(with an ampersand, like in `\\\\verb|@canonicalise!(%)|' is now replaced by a cleaner looking Pythonesque form:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"Notice how we suppressed printing of the property assignment on the second line, by using a period instead of a semi-colon.\\nThe main notational difference with respect to the old Cadabra comes when running algorithms on expressions. \\nAlgorithms have become Python functions, and the somewhat esoteric algorithm calling convention of the old Cadabra\\n(with an ampersand, like in `\\\\verb|@canonicalise!(%)|' is now replaced by a cleaner looking Pythonesque form:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}0\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"canonicalise(ex);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"As you can see, simply call the function and pass in the Python object corresponding to the mathematical expression\\nyou want to act on. \\n\\nWith Python at your disposal, you can now do things which were impossible or at the least very clumsy with the old\\n\\\\verb|@procedure| construction. For instance, you can now use loop constructions like the following:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"As you can see, simply call the function and pass in the Python object corresponding to the mathematical expression\\nyou want to act on. \\n\\nWith Python at your disposal, you can now do things which were impossible or at the least very clumsy with the old\\n\\\\verb|@procedure| construction. For instance, you can now use loop constructions like the following:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}A_{m n} B_{m n}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}A_{m n} \\\\rightarrow A_{m n}+C_{m n}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\left(A_{m n}+C_{m n}\\\\right) B_{m n}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\left(A_{m n}+2C_{m n}\\\\right) B_{m n}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\left(A_{m n}+3C_{m n}\\\\right) B_{m n}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex  := A_{m n} B_{m n};\\nrule:= A_{m n} -> A_{m n} + C_{m n};\\nfor i in range(3):\\n\\tsubstitute(ex, rule);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1\n}\n"
  },
  {
    "path": "examples/frw.cnb",
    "content": "{\n\t\"cell_id\": 17568846475961250656,\n\t\"cells\": [\n\t\t{\n\t\t\t\"cell_id\": 18357667773937998514,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"__cdbkernel__.display_fractions=True\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 9459132517554293622,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 6278840647255743935,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property Coordinate attached to~}\\\\left[t, \\\\discretionary{}{}{}r, \\\\discretionary{}{}{}\\\\theta, \\\\discretionary{}{}{}\\\\phi\\\\right].\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 6846866674437952589,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property Indices(position=fixed, values=\\\\{{t}\\n, {r}\\n, {\\\\theta}\\n, {\\\\phi}\\n\\\\}) attached to~}\\\\left[\\\\mu, \\\\discretionary{}{}{}\\\\nu, \\\\discretionary{}{}{}\\\\rho, \\\\discretionary{}{}{}\\\\sigma, \\\\discretionary{}{}{}\\\\kappa, \\\\discretionary{}{}{}\\\\lambda\\\\right].\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"{t, r, \\\\theta, \\\\phi}::Coordinate();\\n{\\\\mu,\\\\nu,\\\\rho,\\\\sigma,\\\\kappa,\\\\lambda}::Indices(values={t, r, \\\\theta, \\\\phi}, position=fixed);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 14762501784556844760,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 6042237038597741993,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property Depends attached to~}a.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 5727658145276422944,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property PartialDerivative attached to~}\\\\backslash\\\\texttt{partial}\\\\{\\\\#\\\\}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 14992956572435558237,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property LaTeXForm attached to {\\\\texttt{\\\\backslash{}partial}}.}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 14748187663173571912,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property LaTeXForm attached to {\\\\texttt{\\\\backslash{}partial}}.}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"a::Depends(t);\\n\\\\partial{#}::PartialDerivative;\\n\\\\partial_{t}{A??}::LaTeXForm(\\\"\\\\dot{\\\", A??, \\\"}\\\");\\n\\\\partial_{t t}{A??}::LaTeXForm(\\\"\\\\ddot{\\\", A??, \\\"}\\\");\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 419255393453167370,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 4547194245541305689,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property Metric attached to~}g_{\\\\mu \\\\nu}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9810108694561868228,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property TableauSymmetry attached to~}g^{\\\\mu \\\\nu}.\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"g_{\\\\mu\\\\nu}::Metric;\\ng^{\\\\mu\\\\nu}::InverseMetric;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 4501579731258922918,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 6139535987905113585,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 766435461356623527,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"{g_{t t} = -1, g_{r r} = (a)**2 (1-k (r)**2)**(-1), g_{\\\\theta \\\\theta} = (a)**2 (r)**2, g_{\\\\phi \\\\phi} = (a)**2 (r)**2 (\\\\sin(\\\\theta))**2}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\left[g_{t t} = -\\\\,1, \\\\discretionary{}{}{}g_{r r} = \\\\frac{{a}^{2\\\\,}}{\\\\left(1\\\\discretionary{}{}{}-\\\\,k {r}^{2\\\\,}\\\\right)}, \\\\discretionary{}{}{}g_{\\\\theta \\\\theta} = {a}^{2\\\\,} {r}^{2\\\\,}, \\\\discretionary{}{}{}g_{\\\\phi \\\\phi} = {a}^{2\\\\,} {r}^{2\\\\,} {\\\\left(\\\\sin{\\\\theta}\\\\right)}^{2\\\\,}\\\\right]\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"metric:= { g_{t t} = -1, \\n           g_{r r} = a**2 / (1 - k r**2), \\n           g_{\\\\theta\\\\theta} = a**2 r**2, \\n           g_{\\\\phi\\\\phi} = a**2 r**2 \\\\sin(\\\\theta)**2 };\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 15020289295702173224,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 16350274063269046608,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 2041974376356296988,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"{g_{t t} = -1, g_{r r} = (a)**2 (1-k (r)**2)**(-1), g_{\\\\theta \\\\theta} = (a)**2 (r)**2, g_{\\\\phi \\\\phi} = (a)**2 (r)**2 (\\\\sin(\\\\theta))**2, g^{t t} = -1, g^{r r} = (-k (r)**2 + 1) (a)**(-2), g^{\\\\theta \\\\theta} = ((r)**2 (a)**2)**(-1), g^{\\\\phi \\\\phi} = ((r)**2 (a)**2 (\\\\sin(\\\\theta))**2)**(-1)}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\left[g_{t t} = -\\\\,1, \\\\discretionary{}{}{}g_{r r} = \\\\frac{{a}^{2\\\\,}}{\\\\left(1\\\\discretionary{}{}{}-\\\\,k {r}^{2\\\\,}\\\\right)}, \\\\discretionary{}{}{}g_{\\\\theta \\\\theta} = {a}^{2\\\\,} {r}^{2\\\\,}, \\\\discretionary{}{}{}g_{\\\\phi \\\\phi} = {a}^{2\\\\,} {r}^{2\\\\,} {\\\\left(\\\\sin{\\\\theta}\\\\right)}^{2\\\\,}, \\\\discretionary{}{}{}g^{t t} = -\\\\,1, \\\\discretionary{}{}{}g^{r r} = \\\\frac{\\\\left(-\\\\,k {r}^{2\\\\,}\\\\discretionary{}{}{}+1\\\\right)}{{a}^{2\\\\,}}, \\\\discretionary{}{}{}g^{\\\\theta \\\\theta} = \\\\frac{1}{{r}^{2\\\\,} {a}^{2\\\\,}}, \\\\discretionary{}{}{}g^{\\\\phi \\\\phi} = \\\\frac{1}{{r}^{2\\\\,} {a}^{2\\\\,} {\\\\left(\\\\sin{\\\\theta}\\\\right)}^{2\\\\,}}\\\\right]\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"complete(metric, $g^{\\\\mu\\\\nu}$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 10589649882254774352,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 3739387488082977978,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 13904654066456474925,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\Gamma^{\\\\sigma}_{\\\\mu \\\\nu} =  1/2 g^{\\\\sigma \\\\rho} (\\\\partial_{\\\\mu}(g_{\\\\nu \\\\rho}) + \\\\partial_{\\\\nu}(g_{\\\\mu \\\\rho})-\\\\partial_{\\\\rho}(g_{\\\\mu \\\\nu}))\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\Gamma^{\\\\sigma}\\\\,_{\\\\mu \\\\nu} = \\\\frac{1}{2}\\\\,g^{\\\\sigma \\\\rho} \\\\left(\\\\partial_{\\\\mu}{g_{\\\\nu \\\\rho}}\\\\discretionary{}{}{}+\\\\partial_{\\\\nu}{g_{\\\\mu \\\\rho}}\\\\discretionary{}{}{}-\\\\,\\\\partial_{\\\\rho}{g_{\\\\mu \\\\nu}}\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"chr:= \\\\Gamma^{\\\\sigma}_{\\\\mu\\\\nu} = 1/2 g^{\\\\sigma\\\\rho} ( \\\\partial_{\\\\mu}{g_{\\\\nu\\\\rho}} + \\\\partial_{\\\\nu}{g_{\\\\mu\\\\rho}}\\n                                                           - \\\\partial_{\\\\rho}{g_{\\\\mu\\\\nu}} );\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 13871245615379157968,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 4591549504333152962,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 11051608797055996367,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\Gamma^{\\\\sigma}_{\\\\mu \\\\nu} = \\\\components_{\\\\nu \\\\mu}^{\\\\sigma}({{\\\\phi, t, \\\\phi} = \\\\partial_{t}(a) (a)**(-1), {\\\\phi, r, \\\\phi} = (r)**(-1), {\\\\phi, \\\\theta, \\\\phi} = (\\\\tan(\\\\theta))**(-1), {\\\\theta, t, \\\\theta} = \\\\partial_{t}(a) (a)**(-1), {\\\\theta, r, \\\\theta} = (r)**(-1), {r, t, r} = \\\\partial_{t}(a) (a)**(-1), {r, r, r} = -k r (k (r)**2-1)**(-1), {t, \\\\phi, \\\\phi} = \\\\partial_{t}(a) (a)**(-1), {r, \\\\phi, \\\\phi} = (r)**(-1), {\\\\theta, \\\\phi, \\\\phi} = (\\\\tan(\\\\theta))**(-1), {t, \\\\theta, \\\\theta} = \\\\partial_{t}(a) (a)**(-1), {r, \\\\theta, \\\\theta} = (r)**(-1), {t, r, r} = \\\\partial_{t}(a) (a)**(-1), {\\\\phi, \\\\phi, t} = (r)**2 a (\\\\sin(\\\\theta))**2 \\\\partial_{t}(a), {\\\\phi, \\\\phi, r} = r (k (r)**2-1) (\\\\sin(\\\\theta))**2, {\\\\phi, \\\\phi, \\\\theta} =  -  1/2 \\\\sin(2\\\\theta), {\\\\theta, \\\\theta, t} = (r)**2 a \\\\partial_{t}(a), {\\\\theta, \\\\theta, r} = k (r)**3-r, {r, r, t} = -a \\\\partial_{t}(a) (k (r)**2-1)**(-1)})\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\Gamma^{\\\\sigma}\\\\,_{\\\\mu \\\\nu} = \\\\square{}_{\\\\nu}{}_{\\\\mu}{}^{\\\\sigma}\\\\left\\\\{\\\\begin{aligned}\\\\square{}_{\\\\phi}{}_{t}{}^{\\\\phi}& = \\\\square{}_{t}{}_{\\\\phi}{}^{\\\\phi} = \\\\square{}_{r}{}_{t}{}^{r} = \\\\square{}_{t}{}_{\\\\theta}{}^{\\\\theta} = \\\\square{}_{t}{}_{r}{}^{r} = \\\\square{}_{\\\\theta}{}_{t}{}^{\\\\theta} = \\\\frac{\\\\dot{a}}{a}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{r}{}^{\\\\phi}& = \\\\square{}_{r}{}_{\\\\phi}{}^{\\\\phi} = \\\\square{}_{r}{}_{\\\\theta}{}^{\\\\theta} = \\\\square{}_{\\\\theta}{}_{r}{}^{\\\\theta} = \\\\frac{1}{r}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{\\\\theta}{}^{\\\\phi}& = \\\\square{}_{\\\\theta}{}_{\\\\phi}{}^{\\\\phi} = \\\\frac{1}{\\\\tan{\\\\theta}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{r}{}^{r}& = -\\\\frac{k r}{\\\\left(k {r}^{2\\\\,}\\\\discretionary{}{}{}-\\\\,1\\\\right)}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{\\\\phi}{}^{t}& = {r}^{2\\\\,} a {\\\\left(\\\\sin{\\\\theta}\\\\right)}^{2\\\\,} \\\\dot{a}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{\\\\phi}{}^{r}& = r \\\\left(k {r}^{2\\\\,}\\\\discretionary{}{}{}-\\\\,1\\\\right) {\\\\left(\\\\sin{\\\\theta}\\\\right)}^{2\\\\,}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{\\\\phi}{}^{\\\\theta}& =  - \\\\frac{1}{2}\\\\,\\\\sin\\\\left(2\\\\,\\\\theta\\\\right)\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{\\\\theta}{}^{t}& = {r}^{2\\\\,} a \\\\dot{a}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{\\\\theta}{}^{r}& = k {r}^{3\\\\,}\\\\discretionary{}{}{}-\\\\,r\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{r}{}^{t}& = -\\\\frac{a \\\\dot{a}}{\\\\left(k {r}^{2\\\\,}\\\\discretionary{}{}{}-\\\\,1\\\\right)}\\\\\\\\[-.5ex]\\n\\\\end{aligned}\\\\right\\\\}\\n\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"evaluate(chr, metric, rhsonly=True);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 13296679705463885674,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 18387406634533306773,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 9015241021054378139,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"R^{\\\\rho}_{\\\\sigma \\\\mu \\\\nu} = \\\\partial_{\\\\mu}(\\\\Gamma^{\\\\rho}_{\\\\sigma \\\\nu})-\\\\partial_{\\\\nu}(\\\\Gamma^{\\\\rho}_{\\\\sigma \\\\mu}) + \\\\Gamma^{\\\\rho}_{\\\\mu \\\\lambda} \\\\Gamma^{\\\\lambda}_{\\\\nu \\\\sigma}-\\\\Gamma^{\\\\rho}_{\\\\nu \\\\lambda} \\\\Gamma^{\\\\lambda}_{\\\\mu \\\\sigma}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}R^{\\\\rho}\\\\,_{\\\\sigma \\\\mu \\\\nu} = \\\\partial_{\\\\mu}{\\\\Gamma^{\\\\rho}\\\\,_{\\\\sigma \\\\nu}}\\\\discretionary{}{}{}-\\\\,\\\\partial_{\\\\nu}{\\\\Gamma^{\\\\rho}\\\\,_{\\\\sigma \\\\mu}}\\\\discretionary{}{}{}+\\\\Gamma^{\\\\rho}\\\\,_{\\\\mu \\\\lambda} \\\\Gamma^{\\\\lambda}\\\\,_{\\\\nu \\\\sigma}\\\\discretionary{}{}{}-\\\\,\\\\Gamma^{\\\\rho}\\\\,_{\\\\nu \\\\lambda} \\\\Gamma^{\\\\lambda}\\\\,_{\\\\mu \\\\sigma}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"riem:= R^{\\\\rho}_{\\\\sigma\\\\mu\\\\nu} = \\\\partial_{\\\\mu}{\\\\Gamma^{\\\\rho}_{\\\\sigma\\\\nu}} - \\\\partial_{\\\\nu}{\\\\Gamma^{\\\\rho}_{\\\\sigma\\\\mu}}\\n                                 + \\\\Gamma^{\\\\rho}_{\\\\mu\\\\lambda} \\\\Gamma^{\\\\lambda}_{\\\\nu\\\\sigma}\\n                                 - \\\\Gamma^{\\\\rho}_{\\\\nu\\\\lambda} \\\\Gamma^{\\\\lambda}_{\\\\mu\\\\sigma};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 3943846146251824820,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"substitute(riem, chr)\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 2490355670880792435,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 17270529304093918135,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 15939039594621404881,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"R^{\\\\rho}_{\\\\sigma \\\\mu \\\\nu} = \\\\components_{\\\\nu \\\\sigma}^{\\\\rho}_{\\\\mu}({{r, r, t, t} = -a \\\\partial_{t t}(a) (k (r)**2-1)**(-1), {\\\\theta, \\\\theta, r, r} = (r)**2 (k + (\\\\partial_{t}(a))**2), {\\\\theta, \\\\theta, t, t} = (r)**2 a \\\\partial_{t t}(a), {\\\\phi, \\\\phi, \\\\theta, \\\\theta} = (r)**2 (k + (\\\\partial_{t}(a))**2) (\\\\sin(\\\\theta))**2, {\\\\phi, \\\\phi, r, r} = (r)**2 (k + (\\\\partial_{t}(a))**2) (\\\\sin(\\\\theta))**2, {\\\\phi, \\\\phi, t, t} = (r)**2 a (\\\\sin(\\\\theta))**2 \\\\partial_{t t}(a), {r, t, r, t} = \\\\partial_{t t}(a) (a)**(-1), {\\\\theta, t, \\\\theta, t} = \\\\partial_{t t}(a) (a)**(-1), {\\\\phi, \\\\theta, \\\\phi, \\\\theta} = (r)**2 (-k-(\\\\partial_{t}(a))**2), {\\\\phi, t, \\\\phi, t} = \\\\partial_{t t}(a) (a)**(-1), {t, r, t, r} = a \\\\partial_{t t}(a) (k (r)**2-1)**(-1), {r, \\\\theta, r, \\\\theta} = (r)**2 (-k-(\\\\partial_{t}(a))**2), {t, \\\\theta, t, \\\\theta} = -(r)**2 a \\\\partial_{t t}(a), {\\\\theta, \\\\phi, \\\\theta, \\\\phi} = -(r)**2 (k + (\\\\partial_{t}(a))**2) (\\\\sin(\\\\theta))**2, {r, \\\\phi, r, \\\\phi} = (r)**2 (-k-(\\\\partial_{t}(a))**2) (\\\\sin(\\\\theta))**2, {t, \\\\phi, t, \\\\phi} = -(r)**2 a (\\\\sin(\\\\theta))**2 \\\\partial_{t t}(a), {t, t, r, r} = -\\\\partial_{t t}(a) (a)**(-1), {r, r, \\\\theta, \\\\theta} = (-k-(\\\\partial_{t}(a))**2) (k (r)**2-1)**(-1), {t, t, \\\\theta, \\\\theta} = -\\\\partial_{t t}(a) (a)**(-1), {\\\\theta, \\\\theta, \\\\phi, \\\\phi} = (r)**2 (k + (\\\\partial_{t}(a))**2), {r, r, \\\\phi, \\\\phi} = (-k-(\\\\partial_{t}(a))**2) (k (r)**2-1)**(-1), {t, t, \\\\phi, \\\\phi} = -\\\\partial_{t t}(a) (a)**(-1), {\\\\phi, r, \\\\phi, r} = (k + (\\\\partial_{t}(a))**2) (k (r)**2-1)**(-1), {\\\\theta, r, \\\\theta, r} = (k + (\\\\partial_{t}(a))**2) (k (r)**2-1)**(-1)})\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}R^{\\\\rho}\\\\,_{\\\\sigma \\\\mu \\\\nu} = \\\\square{}_{\\\\nu}{}_{\\\\sigma}{}^{\\\\rho}{}_{\\\\mu}\\\\left\\\\{\\\\begin{aligned}\\\\square{}_{r}{}_{r}{}^{t}{}_{t}& = -\\\\frac{a \\\\ddot{a}}{\\\\left(k {r}^{2\\\\,}\\\\discretionary{}{}{}-\\\\,1\\\\right)}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{\\\\theta}{}^{r}{}_{r}& = \\\\square{}_{\\\\theta}{}_{\\\\theta}{}^{\\\\phi}{}_{\\\\phi} = {r}^{2\\\\,} \\\\left(k\\\\discretionary{}{}{}+{\\\\left(\\\\dot{a}\\\\right)}^{2\\\\,}\\\\right)\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{\\\\theta}{}^{t}{}_{t}& = {r}^{2\\\\,} a \\\\ddot{a}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{\\\\phi}{}^{\\\\theta}{}_{\\\\theta}& = \\\\square{}_{\\\\phi}{}_{\\\\phi}{}^{r}{}_{r} = {r}^{2\\\\,} \\\\left(k\\\\discretionary{}{}{}+{\\\\left(\\\\dot{a}\\\\right)}^{2\\\\,}\\\\right) {\\\\left(\\\\sin{\\\\theta}\\\\right)}^{2\\\\,}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{\\\\phi}{}^{t}{}_{t}& = {r}^{2\\\\,} a {\\\\left(\\\\sin{\\\\theta}\\\\right)}^{2\\\\,} \\\\ddot{a}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{t}{}^{r}{}_{t}& = \\\\square{}_{\\\\phi}{}_{t}{}^{\\\\phi}{}_{t} = \\\\square{}_{\\\\theta}{}_{t}{}^{\\\\theta}{}_{t} = \\\\frac{\\\\ddot{a}}{a}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{\\\\theta}{}^{\\\\phi}{}_{\\\\theta}& = \\\\square{}_{r}{}_{\\\\theta}{}^{r}{}_{\\\\theta} = {r}^{2\\\\,} \\\\left(-\\\\,k\\\\discretionary{}{}{}-\\\\,{\\\\left(\\\\dot{a}\\\\right)}^{2\\\\,}\\\\right)\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}_{r}{}^{t}{}_{r}& = \\\\frac{a \\\\ddot{a}}{\\\\left(k {r}^{2\\\\,}\\\\discretionary{}{}{}-\\\\,1\\\\right)}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}_{\\\\theta}{}^{t}{}_{\\\\theta}& = -\\\\,{r}^{2\\\\,} a \\\\ddot{a}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{\\\\phi}{}^{\\\\theta}{}_{\\\\phi}& = -\\\\,{r}^{2\\\\,} \\\\left(k\\\\discretionary{}{}{}+{\\\\left(\\\\dot{a}\\\\right)}^{2\\\\,}\\\\right) {\\\\left(\\\\sin{\\\\theta}\\\\right)}^{2\\\\,}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{\\\\phi}{}^{r}{}_{\\\\phi}& = {r}^{2\\\\,} \\\\left(-\\\\,k\\\\discretionary{}{}{}-\\\\,{\\\\left(\\\\dot{a}\\\\right)}^{2\\\\,}\\\\right) {\\\\left(\\\\sin{\\\\theta}\\\\right)}^{2\\\\,}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}_{\\\\phi}{}^{t}{}_{\\\\phi}& = -\\\\,{r}^{2\\\\,} a {\\\\left(\\\\sin{\\\\theta}\\\\right)}^{2\\\\,} \\\\ddot{a}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}_{t}{}^{r}{}_{r}& = \\\\square{}_{t}{}_{t}{}^{\\\\theta}{}_{\\\\theta} = \\\\square{}_{t}{}_{t}{}^{\\\\phi}{}_{\\\\phi} = -\\\\frac{\\\\ddot{a}}{a}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{r}{}^{\\\\theta}{}_{\\\\theta}& = \\\\square{}_{r}{}_{r}{}^{\\\\phi}{}_{\\\\phi} = \\\\frac{\\\\left(-\\\\,k\\\\discretionary{}{}{}-\\\\,{\\\\left(\\\\dot{a}\\\\right)}^{2\\\\,}\\\\right)}{\\\\left(k {r}^{2\\\\,}\\\\discretionary{}{}{}-\\\\,1\\\\right)}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{r}{}^{\\\\phi}{}_{r}& = \\\\square{}_{\\\\theta}{}_{r}{}^{\\\\theta}{}_{r} = \\\\frac{\\\\left(k\\\\discretionary{}{}{}+{\\\\left(\\\\dot{a}\\\\right)}^{2\\\\,}\\\\right)}{\\\\left(k {r}^{2\\\\,}\\\\discretionary{}{}{}-\\\\,1\\\\right)}\\\\\\\\[-.5ex]\\n\\\\end{aligned}\\\\right\\\\}\\n\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"evaluate(riem, metric, rhsonly=True);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 16551477785137702532,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 8055576766416093956,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 17976892358335415207,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"R_{\\\\mu \\\\nu} = R^{\\\\rho}_{\\\\mu \\\\nu \\\\rho}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}R_{\\\\mu \\\\nu} = R^{\\\\rho}\\\\,_{\\\\mu \\\\nu \\\\rho}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ricc:= R_{\\\\mu\\\\nu} = R^{\\\\rho}_{\\\\mu\\\\nu\\\\rho};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 12797918887183114173,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 18424815107255673273,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 15285328043211694640,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"R_{\\\\mu \\\\nu} = \\\\components_{\\\\mu \\\\nu}({{t, t} = 3\\\\partial_{t t}(a) (a)**(-1), {\\\\theta, \\\\theta} = (r)**2 (-2k-a \\\\partial_{t t}(a)-2(\\\\partial_{t}(a))**2), {r, r} = (2k + a \\\\partial_{t t}(a) + 2(\\\\partial_{t}(a))**2) (k (r)**2-1)**(-1), {\\\\phi, \\\\phi} = (r)**2 (-2k-a \\\\partial_{t t}(a)-2(\\\\partial_{t}(a))**2) (\\\\sin(\\\\theta))**2})\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}R_{\\\\mu \\\\nu} = \\\\square{}_{\\\\mu}{}_{\\\\nu}\\\\left\\\\{\\\\begin{aligned}\\\\square{}_{t}{}_{t}& = \\\\frac{3\\\\,\\\\ddot{a}}{a}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{\\\\theta}& = {r}^{2\\\\,} \\\\left(-2\\\\,k\\\\discretionary{}{}{}-\\\\,a \\\\ddot{a}\\\\discretionary{}{}{}-2\\\\,{\\\\left(\\\\dot{a}\\\\right)}^{2\\\\,}\\\\right)\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{r}& = \\\\frac{\\\\left(2\\\\,k\\\\discretionary{}{}{}+a \\\\ddot{a}\\\\discretionary{}{}{}+2\\\\,{\\\\left(\\\\dot{a}\\\\right)}^{2\\\\,}\\\\right)}{\\\\left(k {r}^{2\\\\,}\\\\discretionary{}{}{}-\\\\,1\\\\right)}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{\\\\phi}& = {r}^{2\\\\,} \\\\left(-2\\\\,k\\\\discretionary{}{}{}-\\\\,a \\\\ddot{a}\\\\discretionary{}{}{}-2\\\\,{\\\\left(\\\\dot{a}\\\\right)}^{2\\\\,}\\\\right) {\\\\left(\\\\sin{\\\\theta}\\\\right)}^{2\\\\,}\\\\\\\\[-.5ex]\\n\\\\end{aligned}\\\\right\\\\}\\n\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"substitute(ricc, riem)\\nevaluate(ricc, metric, rhsonly=True);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 18439898758683516277,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 17764669073962124504,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 6449485821058317619,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"R = g^{\\\\mu \\\\nu} R_{\\\\mu \\\\nu}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}R = g^{\\\\mu \\\\nu} R_{\\\\mu \\\\nu}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"rsc:= R = g^{\\\\mu\\\\nu} R_{\\\\mu\\\\nu};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 7536224625176264330,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 14598921007266714213,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 17619451859496771489,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"R = 6(-k-a \\\\partial_{t t}(a)-(\\\\partial_{t}(a))**2) (a)**(-2)\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}R = \\\\frac{6\\\\,\\\\left(-\\\\,k\\\\discretionary{}{}{}-\\\\,a \\\\ddot{a}\\\\discretionary{}{}{}-\\\\,{\\\\left(\\\\dot{a}\\\\right)}^{2\\\\,}\\\\right)}{{a}^{2\\\\,}}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"substitute(rsc, ricc)\\nevaluate(rsc, metric, rhsonly=True);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 14251455638551275443,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 3040197892620593075,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"Let's compute the Einstein tensor, as we will need that to compute equations of motion for the scale factor. Start with the definition,\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"Let's compute the Einstein tensor, as we will need that to compute equations of motion for the scale factor. Start with the definition,\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 12320538355060283436,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 13673596348289381928,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 17786104397218562362,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"G_{\\\\mu \\\\nu} = R_{\\\\mu \\\\nu} -  1/2 g_{\\\\mu \\\\nu} R\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}G_{\\\\mu \\\\nu} = R_{\\\\mu \\\\nu}\\\\discretionary{}{}{} - \\\\frac{1}{2}\\\\,g_{\\\\mu \\\\nu} R\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"einstein:= G_{\\\\mu\\\\nu} = R_{\\\\mu\\\\nu} - 1/2 g_{\\\\mu\\\\nu} R;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 8363691169720324631,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 10277930022379001609,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"Substitute the components for the Ricci tensor and scalar computed above, and then use the metric at the last step to finish the computation,\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"Substitute the components for the Ricci tensor and scalar computed above, and then use the metric at the last step to finish the computation,\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 10782175449488819360,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 2035524564443219634,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 11692588637972694010,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"G_{\\\\mu \\\\nu} = \\\\components_{\\\\mu \\\\nu}({{t, t} = 3(-k-(\\\\partial_{t}(a))**2) (a)**(-2), {\\\\theta, \\\\theta} = (r)**2 (k + 2a \\\\partial_{t t}(a) + (\\\\partial_{t}(a))**2), {r, r} = (-k-2a \\\\partial_{t t}(a)-(\\\\partial_{t}(a))**2) (k (r)**2-1)**(-1), {\\\\phi, \\\\phi} = (r)**2 (k + 2a \\\\partial_{t t}(a) + (\\\\partial_{t}(a))**2) (\\\\sin(\\\\theta))**2})\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}G_{\\\\mu \\\\nu} = \\\\square{}_{\\\\mu}{}_{\\\\nu}\\\\left\\\\{\\\\begin{aligned}\\\\square{}_{t}{}_{t}& = \\\\frac{3\\\\,\\\\left(-\\\\,k\\\\discretionary{}{}{}-\\\\,{\\\\left(\\\\dot{a}\\\\right)}^{2\\\\,}\\\\right)}{{a}^{2\\\\,}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{\\\\theta}& = {r}^{2\\\\,} \\\\left(k\\\\discretionary{}{}{}+2\\\\,a \\\\ddot{a}\\\\discretionary{}{}{}+{\\\\left(\\\\dot{a}\\\\right)}^{2\\\\,}\\\\right)\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{r}& = \\\\frac{\\\\left(-\\\\,k\\\\discretionary{}{}{}-2\\\\,a \\\\ddot{a}\\\\discretionary{}{}{}-\\\\,{\\\\left(\\\\dot{a}\\\\right)}^{2\\\\,}\\\\right)}{\\\\left(k {r}^{2\\\\,}\\\\discretionary{}{}{}-\\\\,1\\\\right)}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{\\\\phi}& = {r}^{2\\\\,} \\\\left(k\\\\discretionary{}{}{}+2\\\\,a \\\\ddot{a}\\\\discretionary{}{}{}+{\\\\left(\\\\dot{a}\\\\right)}^{2\\\\,}\\\\right) {\\\\left(\\\\sin{\\\\theta}\\\\right)}^{2\\\\,}\\\\\\\\[-.5ex]\\n\\\\end{aligned}\\\\right\\\\}\\n\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"substitute(einstein, ricc)\\nsubstitute(einstein, rsc)\\nevaluate(einstein, metric, rhsonly=True);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 251939380337894963,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 6375792474797107374,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"Let's compute the Einstein tensor with mixed indices by simply raising one:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"Let's compute the Einstein tensor with mixed indices by simply raising one:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 11152058718401270058,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 2331349124689904645,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 12620239727471059401,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"G^{\\\\mu}_{\\\\nu} = \\\\components_{\\\\nu}^{\\\\mu}({{t, t} = 3(k + (\\\\partial_{t}(a))**2) (a)**(-2), {\\\\theta, \\\\theta} = (k + 2a \\\\partial_{t t}(a) + (\\\\partial_{t}(a))**2) (a)**(-2), {r, r} = (k + 2a \\\\partial_{t t}(a) + (\\\\partial_{t}(a))**2) (a)**(-2), {\\\\phi, \\\\phi} = (k + 2a \\\\partial_{t t}(a) + (\\\\partial_{t}(a))**2) (a)**(-2)})\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}G^{\\\\mu}\\\\,_{\\\\nu} = \\\\square{}_{\\\\nu}{}^{\\\\mu}\\\\left\\\\{\\\\begin{aligned}\\\\square{}_{t}{}^{t}& = \\\\frac{3\\\\,\\\\left(k\\\\discretionary{}{}{}+{\\\\left(\\\\dot{a}\\\\right)}^{2\\\\,}\\\\right)}{{a}^{2\\\\,}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}^{\\\\theta}& = \\\\square{}_{r}{}^{r} = \\\\square{}_{\\\\phi}{}^{\\\\phi} = \\\\frac{\\\\left(k\\\\discretionary{}{}{}+2\\\\,a \\\\ddot{a}\\\\discretionary{}{}{}+{\\\\left(\\\\dot{a}\\\\right)}^{2\\\\,}\\\\right)}{{a}^{2\\\\,}}\\\\\\\\[-.5ex]\\n\\\\end{aligned}\\\\right\\\\}\\n\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"evaluate(substitute($G^{\\\\mu}_{\\\\nu} = g^{\\\\mu\\\\rho} G_{\\\\rho\\\\nu}$, einstein), metric, rhsonly=True);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 17244476709214870349,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 16335368620656234184,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 11282213324064228681,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"G^{\\\\mu}_{\\\\nu} = g^{\\\\mu \\\\rho} G_{\\\\rho \\\\nu}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}G^{\\\\mu}\\\\,_{\\\\nu} = g^{\\\\mu \\\\rho} G_{\\\\rho \\\\nu}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"einsteinmixed:= G^{\\\\mu}_{\\\\nu} = g^{\\\\mu\\\\rho} G_{\\\\rho\\\\nu};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 275681027250199802,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 13888328276992074924,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 10143560440639855835,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"G^{\\\\mu}_{\\\\nu} = \\\\components_{\\\\nu}^{\\\\mu}({{t, t} = 3(k + (\\\\partial_{t}(a))**2) (a)**(-2), {\\\\theta, \\\\theta} = (k + 2a \\\\partial_{t t}(a) + (\\\\partial_{t}(a))**2) (a)**(-2), {r, r} = (k + 2a \\\\partial_{t t}(a) + (\\\\partial_{t}(a))**2) (a)**(-2), {\\\\phi, \\\\phi} = (k + 2a \\\\partial_{t t}(a) + (\\\\partial_{t}(a))**2) (a)**(-2)})\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}G^{\\\\mu}\\\\,_{\\\\nu} = \\\\square{}_{\\\\nu}{}^{\\\\mu}\\\\left\\\\{\\\\begin{aligned}\\\\square{}_{t}{}^{t}& = \\\\frac{3\\\\,\\\\left(k\\\\discretionary{}{}{}+{\\\\left(\\\\dot{a}\\\\right)}^{2\\\\,}\\\\right)}{{a}^{2\\\\,}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}^{\\\\theta}& = \\\\square{}_{r}{}^{r} = \\\\square{}_{\\\\phi}{}^{\\\\phi} = \\\\frac{\\\\left(k\\\\discretionary{}{}{}+2\\\\,a \\\\ddot{a}\\\\discretionary{}{}{}+{\\\\left(\\\\dot{a}\\\\right)}^{2\\\\,}\\\\right)}{{a}^{2\\\\,}}\\\\\\\\[-.5ex]\\n\\\\end{aligned}\\\\right\\\\}\\n\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"substitute(einsteinmixed, einstein)\\nevaluate(einsteinmixed, metric, rhsonly=True);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 14767310302042208122,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 13707870999398618981,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"Now on to the Friedmann equations. We need the Einstein equations first (could have used the pre-computed Einstein tensor above),\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"Now on to the Friedmann equations. We need the Einstein equations first (could have used the pre-computed Einstein tensor above),\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 2707163638401030064,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 6893369584150017871,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 11109506132705913347,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"R_{\\\\mu \\\\nu} -  1/2 g_{\\\\mu \\\\nu} = T_{\\\\mu \\\\nu}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}R_{\\\\mu \\\\nu}\\\\discretionary{}{}{} - \\\\frac{1}{2}\\\\,g_{\\\\mu \\\\nu} = T_{\\\\mu \\\\nu}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"frw:= R_{\\\\mu\\\\nu} - 1/2 g_{\\\\mu\\\\nu} = T_{\\\\mu\\\\nu};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 8727094230579310444,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 4800274537670768984,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 1873151167832302103,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"{T_{t t} = \\\\rho, T_{r r} = p g_{r r}, T_{\\\\phi \\\\phi} = p g_{\\\\phi \\\\phi}, T_{\\\\theta \\\\theta} = p g_{\\\\theta \\\\theta}}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\left[T_{t t} = \\\\rho, \\\\discretionary{}{}{}T_{r r} = p g_{r r}, \\\\discretionary{}{}{}T_{\\\\phi \\\\phi} = p g_{\\\\phi \\\\phi}, \\\\discretionary{}{}{}T_{\\\\theta \\\\theta} = p g_{\\\\theta \\\\theta}\\\\right]\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"stress:= { T_{t t} = \\\\rho, T_{r r} = p g_{r r}, T_{\\\\phi\\\\phi} = p g_{\\\\phi\\\\phi}, T_{\\\\theta\\\\theta} = p g_{\\\\theta\\\\theta} };\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 10259894831905811945,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 12012379353390368245,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 7775411517433978780,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\components_{\\\\mu \\\\nu}({{t, t} = 3\\\\partial_{t t}(a) (a)**(-1), {\\\\theta, \\\\theta} = (r)**2 (-2k-a \\\\partial_{t t}(a)-2(\\\\partial_{t}(a))**2), {r, r} = (2k + a \\\\partial_{t t}(a) + 2(\\\\partial_{t}(a))**2) (k (r)**2-1)**(-1), {\\\\phi, \\\\phi} = (r)**2 (-2k-a \\\\partial_{t t}(a)-2(\\\\partial_{t}(a))**2) (\\\\sin(\\\\theta))**2}) -  1/2 g_{\\\\mu \\\\nu} = T_{\\\\mu \\\\nu}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\square{}_{\\\\mu}{}_{\\\\nu}\\\\left\\\\{\\\\begin{aligned}\\\\square{}_{t}{}_{t}& = \\\\frac{3\\\\,\\\\ddot{a}}{a}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{\\\\theta}& = {r}^{2\\\\,} \\\\left(-2\\\\,k\\\\discretionary{}{}{}-\\\\,a \\\\ddot{a}\\\\discretionary{}{}{}-2\\\\,{\\\\left(\\\\dot{a}\\\\right)}^{2\\\\,}\\\\right)\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{r}& = \\\\frac{\\\\left(2\\\\,k\\\\discretionary{}{}{}+a \\\\ddot{a}\\\\discretionary{}{}{}+2\\\\,{\\\\left(\\\\dot{a}\\\\right)}^{2\\\\,}\\\\right)}{\\\\left(k {r}^{2\\\\,}\\\\discretionary{}{}{}-\\\\,1\\\\right)}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{\\\\phi}& = {r}^{2\\\\,} \\\\left(-2\\\\,k\\\\discretionary{}{}{}-\\\\,a \\\\ddot{a}\\\\discretionary{}{}{}-2\\\\,{\\\\left(\\\\dot{a}\\\\right)}^{2\\\\,}\\\\right) {\\\\left(\\\\sin{\\\\theta}\\\\right)}^{2\\\\,}\\\\\\\\[-.5ex]\\n\\\\end{aligned}\\\\right\\\\}\\n\\\\discretionary{}{}{} - \\\\frac{1}{2}\\\\,g_{\\\\mu \\\\nu} = T_{\\\\mu \\\\nu}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"substitute(frw, ricc);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 34337683364647191,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 1865938083906276254,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 12273741059518738884,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\components_{\\\\mu \\\\nu}({{t, t} =  1/2  + 3\\\\partial_{t t}(a) (a)**(-1), {\\\\theta, \\\\theta} = (r)**2 (-2k -  1/2 (a)**2-a \\\\partial_{t t}(a)-2(\\\\partial_{t}(a))**2), {r, r} = (2k +  1/2 (a)**2 + a \\\\partial_{t t}(a) + 2(\\\\partial_{t}(a))**2) (k (r)**2-1)**(-1), {\\\\phi, \\\\phi} = (r)**2 (-2k -  1/2 (a)**2-a \\\\partial_{t t}(a)-2(\\\\partial_{t}(a))**2) (\\\\sin(\\\\theta))**2}) = \\\\components_{\\\\mu \\\\nu}({{t, t} = \\\\rho, {r, r} = p g_{r r}, {\\\\phi, \\\\phi} = p g_{\\\\phi \\\\phi}, {\\\\theta, \\\\theta} = p g_{\\\\theta \\\\theta}})\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\square{}_{\\\\mu}{}_{\\\\nu}\\\\left\\\\{\\\\begin{aligned}\\\\square{}_{t}{}_{t}& = \\\\frac{1}{2}\\\\,\\\\discretionary{}{}{}+\\\\frac{3\\\\,\\\\ddot{a}}{a}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{\\\\theta}& = {r}^{2\\\\,} \\\\left(-2\\\\,k\\\\discretionary{}{}{} - \\\\frac{1}{2}\\\\,{a}^{2\\\\,}\\\\discretionary{}{}{}-\\\\,a \\\\ddot{a}\\\\discretionary{}{}{}-2\\\\,{\\\\left(\\\\dot{a}\\\\right)}^{2\\\\,}\\\\right)\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{r}& = \\\\frac{\\\\left(2\\\\,k\\\\discretionary{}{}{}+\\\\frac{1}{2}\\\\,{a}^{2\\\\,}\\\\discretionary{}{}{}+a \\\\ddot{a}\\\\discretionary{}{}{}+2\\\\,{\\\\left(\\\\dot{a}\\\\right)}^{2\\\\,}\\\\right)}{\\\\left(k {r}^{2\\\\,}\\\\discretionary{}{}{}-\\\\,1\\\\right)}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{\\\\phi}& = {r}^{2\\\\,} \\\\left(-2\\\\,k\\\\discretionary{}{}{} - \\\\frac{1}{2}\\\\,{a}^{2\\\\,}\\\\discretionary{}{}{}-\\\\,a \\\\ddot{a}\\\\discretionary{}{}{}-2\\\\,{\\\\left(\\\\dot{a}\\\\right)}^{2\\\\,}\\\\right) {\\\\left(\\\\sin{\\\\theta}\\\\right)}^{2\\\\,}\\\\\\\\[-.5ex]\\n\\\\end{aligned}\\\\right\\\\}\\n = \\\\square{}_{\\\\mu}{}_{\\\\nu}\\\\left\\\\{\\\\begin{aligned}\\\\square{}_{t}{}_{t}& = \\\\rho\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{r}& = p g_{r r}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{\\\\phi}& = p g_{\\\\phi \\\\phi}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{\\\\theta}& = p g_{\\\\theta \\\\theta}\\\\\\\\[-.5ex]\\n\\\\end{aligned}\\\\right\\\\}\\n\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"evaluate(frw, join(metric, stress));\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 3927714376445781014,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 2243419952119428589,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 17061535033441028440,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\components_{\\\\mu \\\\nu}({{t, t} =  1/2  + 3\\\\partial_{t t}(a) (a)**(-1), {\\\\theta, \\\\theta} = (r)**2 (-2k -  1/2 (a)**2-a \\\\partial_{t t}(a)-2(\\\\partial_{t}(a))**2), {r, r} = (2k +  1/2 (a)**2 + a \\\\partial_{t t}(a) + 2(\\\\partial_{t}(a))**2) (k (r)**2-1)**(-1), {\\\\phi, \\\\phi} = (r)**2 (-2k -  1/2 (a)**2-a \\\\partial_{t t}(a)-2(\\\\partial_{t}(a))**2) (\\\\sin(\\\\theta))**2}) = \\\\components_{\\\\mu \\\\nu}({{t, t} = \\\\rho, {r, r} = p (a)**2 (1-k (r)**2)**(-1), {\\\\phi, \\\\phi} = p (a)**2 (r)**2 (\\\\sin(\\\\theta))**2, {\\\\theta, \\\\theta} = p (a)**2 (r)**2})\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\square{}_{\\\\mu}{}_{\\\\nu}\\\\left\\\\{\\\\begin{aligned}\\\\square{}_{t}{}_{t}& = \\\\frac{1}{2}\\\\,\\\\discretionary{}{}{}+\\\\frac{3\\\\,\\\\ddot{a}}{a}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{\\\\theta}& = {r}^{2\\\\,} \\\\left(-2\\\\,k\\\\discretionary{}{}{} - \\\\frac{1}{2}\\\\,{a}^{2\\\\,}\\\\discretionary{}{}{}-\\\\,a \\\\ddot{a}\\\\discretionary{}{}{}-2\\\\,{\\\\left(\\\\dot{a}\\\\right)}^{2\\\\,}\\\\right)\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{r}& = \\\\frac{\\\\left(2\\\\,k\\\\discretionary{}{}{}+\\\\frac{1}{2}\\\\,{a}^{2\\\\,}\\\\discretionary{}{}{}+a \\\\ddot{a}\\\\discretionary{}{}{}+2\\\\,{\\\\left(\\\\dot{a}\\\\right)}^{2\\\\,}\\\\right)}{\\\\left(k {r}^{2\\\\,}\\\\discretionary{}{}{}-\\\\,1\\\\right)}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{\\\\phi}& = {r}^{2\\\\,} \\\\left(-2\\\\,k\\\\discretionary{}{}{} - \\\\frac{1}{2}\\\\,{a}^{2\\\\,}\\\\discretionary{}{}{}-\\\\,a \\\\ddot{a}\\\\discretionary{}{}{}-2\\\\,{\\\\left(\\\\dot{a}\\\\right)}^{2\\\\,}\\\\right) {\\\\left(\\\\sin{\\\\theta}\\\\right)}^{2\\\\,}\\\\\\\\[-.5ex]\\n\\\\end{aligned}\\\\right\\\\}\\n = \\\\square{}_{\\\\mu}{}_{\\\\nu}\\\\left\\\\{\\\\begin{aligned}\\\\square{}_{t}{}_{t}& = \\\\rho\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{r}& = \\\\frac{p {a}^{2\\\\,}}{\\\\left(1\\\\discretionary{}{}{}-\\\\,k {r}^{2\\\\,}\\\\right)}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{\\\\phi}& = p {a}^{2\\\\,} {r}^{2\\\\,} {\\\\left(\\\\sin{\\\\theta}\\\\right)}^{2\\\\,}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{\\\\theta}& = p {a}^{2\\\\,} {r}^{2\\\\,}\\\\\\\\[-.5ex]\\n\\\\end{aligned}\\\\right\\\\}\\n\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"substitute(frw, metric);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 8846808630722024465,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"from cdb.core.manip import *\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 5474709602832868120,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 5928231195483670410,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 3750470487921315635,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\components_{\\\\mu \\\\nu}({{t, t} =  1/2  + 3\\\\partial_{t t}(a) (a)**(-1), {\\\\theta, \\\\theta} = (r)**2 (-2k -  1/2 (a)**2-a \\\\partial_{t t}(a)-2(\\\\partial_{t}(a))**2), {r, r} = (2k +  1/2 (a)**2 + a \\\\partial_{t t}(a) + 2(\\\\partial_{t}(a))**2) (k (r)**2-1)**(-1), {\\\\phi, \\\\phi} = (r)**2 (-2k -  1/2 (a)**2-a \\\\partial_{t t}(a)-2(\\\\partial_{t}(a))**2) (\\\\sin(\\\\theta))**2}) + \\\\components_{\\\\mu \\\\nu}({{t, t} = -\\\\rho, {r, r} = -p (a)**2 (1-k (r)**2)**(-1), {\\\\phi, \\\\phi} = -p (a)**2 (r)**2 (\\\\sin(\\\\theta))**2, {\\\\theta, \\\\theta} = -p (a)**2 (r)**2})\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\square{}_{\\\\mu}{}_{\\\\nu}\\\\left\\\\{\\\\begin{aligned}\\\\square{}_{t}{}_{t}& = \\\\frac{1}{2}\\\\,\\\\discretionary{}{}{}+\\\\frac{3\\\\,\\\\ddot{a}}{a}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{\\\\theta}& = {r}^{2\\\\,} \\\\left(-2\\\\,k\\\\discretionary{}{}{} - \\\\frac{1}{2}\\\\,{a}^{2\\\\,}\\\\discretionary{}{}{}-\\\\,a \\\\ddot{a}\\\\discretionary{}{}{}-2\\\\,{\\\\left(\\\\dot{a}\\\\right)}^{2\\\\,}\\\\right)\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{r}& = \\\\frac{\\\\left(2\\\\,k\\\\discretionary{}{}{}+\\\\frac{1}{2}\\\\,{a}^{2\\\\,}\\\\discretionary{}{}{}+a \\\\ddot{a}\\\\discretionary{}{}{}+2\\\\,{\\\\left(\\\\dot{a}\\\\right)}^{2\\\\,}\\\\right)}{\\\\left(k {r}^{2\\\\,}\\\\discretionary{}{}{}-\\\\,1\\\\right)}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{\\\\phi}& = {r}^{2\\\\,} \\\\left(-2\\\\,k\\\\discretionary{}{}{} - \\\\frac{1}{2}\\\\,{a}^{2\\\\,}\\\\discretionary{}{}{}-\\\\,a \\\\ddot{a}\\\\discretionary{}{}{}-2\\\\,{\\\\left(\\\\dot{a}\\\\right)}^{2\\\\,}\\\\right) {\\\\left(\\\\sin{\\\\theta}\\\\right)}^{2\\\\,}\\\\\\\\[-.5ex]\\n\\\\end{aligned}\\\\right\\\\}\\n\\\\discretionary{}{}{}+\\\\square{}_{\\\\mu}{}_{\\\\nu}\\\\left\\\\{\\\\begin{aligned}\\\\square{}_{t}{}_{t}& = -\\\\,\\\\rho\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{r}& = -\\\\frac{p {a}^{2\\\\,}}{\\\\left(1\\\\discretionary{}{}{}-\\\\,k {r}^{2\\\\,}\\\\right)}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{\\\\phi}& = -\\\\,p {a}^{2\\\\,} {r}^{2\\\\,} {\\\\left(\\\\sin{\\\\theta}\\\\right)}^{2\\\\,}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{\\\\theta}& = -\\\\,p {a}^{2\\\\,} {r}^{2\\\\,}\\\\\\\\[-.5ex]\\n\\\\end{aligned}\\\\right\\\\}\\n\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"q=lhs(frw) - rhs(frw);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 1418128123064669014,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 11029541099087982197,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 68213334860507748,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\components_{\\\\mu \\\\nu}({{t, t} = -\\\\rho +  1/2  + 3\\\\partial_{t t}(a) (a)**(-1), {\\\\theta, \\\\theta} = (r)**2 (-2k-p (a)**2 -  1/2 (a)**2-a \\\\partial_{t t}(a)-2(\\\\partial_{t}(a))**2), {r, r} = (2k + p (a)**2 +  1/2 (a)**2 + a \\\\partial_{t t}(a) + 2(\\\\partial_{t}(a))**2) (k (r)**2-1)**(-1), {\\\\phi, \\\\phi} = (r)**2 (-2k-p (a)**2 -  1/2 (a)**2-a \\\\partial_{t t}(a)-2(\\\\partial_{t}(a))**2) (\\\\sin(\\\\theta))**2})\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\square{}_{\\\\mu}{}_{\\\\nu}\\\\left\\\\{\\\\begin{aligned}\\\\square{}_{t}{}_{t}& = -\\\\,\\\\rho\\\\discretionary{}{}{}+\\\\frac{1}{2}\\\\,\\\\discretionary{}{}{}+\\\\frac{3\\\\,\\\\ddot{a}}{a}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{\\\\theta}& = {r}^{2\\\\,} \\\\left(-2\\\\,k\\\\discretionary{}{}{}-\\\\,p {a}^{2\\\\,}\\\\discretionary{}{}{} - \\\\frac{1}{2}\\\\,{a}^{2\\\\,}\\\\discretionary{}{}{}-\\\\,a \\\\ddot{a}\\\\discretionary{}{}{}-2\\\\,{\\\\left(\\\\dot{a}\\\\right)}^{2\\\\,}\\\\right)\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{r}& = \\\\frac{\\\\left(2\\\\,k\\\\discretionary{}{}{}+p {a}^{2\\\\,}\\\\discretionary{}{}{}+\\\\frac{1}{2}\\\\,{a}^{2\\\\,}\\\\discretionary{}{}{}+a \\\\ddot{a}\\\\discretionary{}{}{}+2\\\\,{\\\\left(\\\\dot{a}\\\\right)}^{2\\\\,}\\\\right)}{\\\\left(k {r}^{2\\\\,}\\\\discretionary{}{}{}-\\\\,1\\\\right)}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{\\\\phi}& = {r}^{2\\\\,} \\\\left(-2\\\\,k\\\\discretionary{}{}{}-\\\\,p {a}^{2\\\\,}\\\\discretionary{}{}{} - \\\\frac{1}{2}\\\\,{a}^{2\\\\,}\\\\discretionary{}{}{}-\\\\,a \\\\ddot{a}\\\\discretionary{}{}{}-2\\\\,{\\\\left(\\\\dot{a}\\\\right)}^{2\\\\,}\\\\right) {\\\\left(\\\\sin{\\\\theta}\\\\right)}^{2\\\\,}\\\\\\\\[-.5ex]\\n\\\\end{aligned}\\\\right\\\\}\\n\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"collect_components(q);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 11004659051713845606,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"from cdb.core.manip import *\\nfrom cdb.core.component import *\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 17270391563431783644,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 11247039435171374167,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 16043885347605951914,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\components_{\\\\mu \\\\nu}({{t, t} = -\\\\rho +  1/2  + 3\\\\partial_{t t}(a) (a)**(-1), {\\\\theta, \\\\theta} = (r)**2 (-2k-p (a)**2 -  1/2 (a)**2-a \\\\partial_{t t}(a)-2(\\\\partial_{t}(a))**2), {r, r} = (2k + p (a)**2 +  1/2 (a)**2 + a \\\\partial_{t t}(a) + 2(\\\\partial_{t}(a))**2) (k (r)**2-1)**(-1), {\\\\phi, \\\\phi} = (r)**2 (-2k-p (a)**2 -  1/2 (a)**2-a \\\\partial_{t t}(a)-2(\\\\partial_{t}(a))**2) (\\\\sin(\\\\theta))**2})\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\square{}_{\\\\mu}{}_{\\\\nu}\\\\left\\\\{\\\\begin{aligned}\\\\square{}_{t}{}_{t}& = -\\\\,\\\\rho\\\\discretionary{}{}{}+\\\\frac{1}{2}\\\\,\\\\discretionary{}{}{}+\\\\frac{3\\\\,\\\\ddot{a}}{a}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{\\\\theta}& = {r}^{2\\\\,} \\\\left(-2\\\\,k\\\\discretionary{}{}{}-\\\\,p {a}^{2\\\\,}\\\\discretionary{}{}{} - \\\\frac{1}{2}\\\\,{a}^{2\\\\,}\\\\discretionary{}{}{}-\\\\,a \\\\ddot{a}\\\\discretionary{}{}{}-2\\\\,{\\\\left(\\\\dot{a}\\\\right)}^{2\\\\,}\\\\right)\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{r}& = \\\\frac{\\\\left(2\\\\,k\\\\discretionary{}{}{}+p {a}^{2\\\\,}\\\\discretionary{}{}{}+\\\\frac{1}{2}\\\\,{a}^{2\\\\,}\\\\discretionary{}{}{}+a \\\\ddot{a}\\\\discretionary{}{}{}+2\\\\,{\\\\left(\\\\dot{a}\\\\right)}^{2\\\\,}\\\\right)}{\\\\left(k {r}^{2\\\\,}\\\\discretionary{}{}{}-\\\\,1\\\\right)}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{\\\\phi}& = {r}^{2\\\\,} \\\\left(-2\\\\,k\\\\discretionary{}{}{}-\\\\,p {a}^{2\\\\,}\\\\discretionary{}{}{} - \\\\frac{1}{2}\\\\,{a}^{2\\\\,}\\\\discretionary{}{}{}-\\\\,a \\\\ddot{a}\\\\discretionary{}{}{}-2\\\\,{\\\\left(\\\\dot{a}\\\\right)}^{2\\\\,}\\\\right) {\\\\left(\\\\sin{\\\\theta}\\\\right)}^{2\\\\,}\\\\\\\\[-.5ex]\\n\\\\end{aligned}\\\\right\\\\}\\n\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"unzoom(q);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 14083269657824155624,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 4871449050226298094,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 13725429586557322669,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"(r)**2 (-2k-p (a)**2 -  1/2 (a)**2-a \\\\partial_{t t}(a)-2(\\\\partial_{t}(a))**2)\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}{r}^{2\\\\,} \\\\left(-2\\\\,k\\\\discretionary{}{}{}-\\\\,p {a}^{2\\\\,}\\\\discretionary{}{}{} - \\\\frac{1}{2}\\\\,{a}^{2\\\\,}\\\\discretionary{}{}{}-\\\\,a \\\\ddot{a}\\\\discretionary{}{}{}-2\\\\,{\\\\left(\\\\dot{a}\\\\right)}^{2\\\\,}\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"e1=get_component(q, $\\\\theta, \\\\theta$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 16007315346860473479,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9151203916009267879,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 11701340608753929026,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"-\\\\rho +  1/2  + 3\\\\partial_{t t}(a) (a)**(-1)\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}-\\\\,\\\\rho\\\\discretionary{}{}{}+\\\\frac{1}{2}\\\\,\\\\discretionary{}{}{}+\\\\frac{3\\\\,\\\\ddot{a}}{a}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"e2=get_component(q, $t, t$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 6464136259393658645,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"\"\n\t\t}\n\t],\n\t\"description\": \"Cadabra JSON notebook format\",\n\t\"flags\": {\n\t\t\"hide_input_cells\": false\n\t},\n\t\"version\": 1.0\n}\n"
  },
  {
    "path": "examples/gamma_matrix_algebra.cnb",
    "content": "{\n\t\"cell_id\": 7836342630161262192,\n\t\"cells\": [\n\t\t{\n\t\t\t\"cell_id\": 15181707112407147179,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 6516150315733905146,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\section*{Gamma matrix algebra (Clifford algebras)}\\n\\nCadabra can do gamma matrix algebra in an arbitrary number of dimensions. The example below shows how to work out \\nthe particular gamma matrix contraction\\n\\\\begin{equation*}\\n\\\\Gamma_{s r} \\\\Gamma_{r l} \\\\Gamma_{k m} \\\\Gamma_{m s}\\\\,,\\n\\\\end{equation*}\\nwhich is not impossible to do by hand, but certainly much nicer with Cadabra. As always, we first need to declare\\nthe symbols we are going to use. \"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\section*{Gamma matrix algebra (Clifford algebras)}\\n\\nCadabra can do gamma matrix algebra in an arbitrary number of dimensions. The example below shows how to work out \\nthe particular gamma matrix contraction\\n\\\\begin{equation*}\\n\\\\Gamma_{s r} \\\\Gamma_{r l} \\\\Gamma_{k m} \\\\Gamma_{m s}\\\\,,\\n\\\\end{equation*}\\nwhich is not impossible to do by hand, but certainly much nicer with Cadabra. As always, we first need to declare\\nthe symbols we are going to use. \"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 13736011136748361918,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 16359960956223444064,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property Indices(position=free) attached to~}\\\\left[s, \\\\discretionary{}{}{}r, \\\\discretionary{}{}{}l, \\\\discretionary{}{}{}k, \\\\discretionary{}{}{}m, \\\\discretionary{}{}{}n\\\\right].\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 17463746679506917715,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property Integer attached to~}\\\\left[s, \\\\discretionary{}{}{}r, \\\\discretionary{}{}{}l, \\\\discretionary{}{}{}k, \\\\discretionary{}{}{}m, \\\\discretionary{}{}{}n\\\\right].\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9131536127881142319,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property GammaMatrix attached to~}\\\\backslash\\\\texttt{Gamma}\\\\{\\\\#\\\\}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9970177242382691336,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property KroneckerDelta attached to~}\\\\delta_{m n}.\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"{s,r,l,k,m,n}::Indices(vector);\\n{s,r,l,k,m,n}::Integer(0..d-1);\\n\\\\Gamma_{#}::GammaMatrix(metric=\\\\delta);\\n\\\\delta_{m n}::KroneckerDelta;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 14916208636544326190,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 14194647839644370116,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"After every step in which we work out the product of two generalised gamma matrices, we need a number of algorithms\\nto simplify the result. We will use the mechanism of defining a \\\\verb|post_process| function, which gets called after\\nevery Cadabra function call. Note how every algorithm that is called in here acts on the same expression; you do not have to \\ndo things like \\\\verb|ex = sort_product(ex)|.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"After every step in which we work out the product of two generalised gamma matrices, we need a number of algorithms\\nto simplify the result. We will use the mechanism of defining a \\\\verb|post_process| function, which gets called after\\nevery Cadabra function call. Note how every algorithm that is called in here acts on the same expression; you do not have to \\ndo things like \\\\verb|ex = sort_product(ex)|.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 12607813013912134810,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"def post_process(ex):\\n\\tsort_product(ex)\\n\\teliminate_kronecker(ex)\\n\\tcanonicalise(ex)\\n\\tcollect_terms(ex)\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 1785829096969371759,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 17004817770334712017,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"The expression which we want to simplify reads\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"The expression which we want to simplify reads\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 2205276562613272511,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 82935383606815926,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 13260894866853173166,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"-\\\\Gamma_{m r} \\\\Gamma_{l m} \\\\Gamma_{k s} \\\\Gamma_{r s}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}-\\\\,\\\\Gamma_{m r} \\\\Gamma_{l m} \\\\Gamma_{k s} \\\\Gamma_{r s}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex:=\\\\Gamma_{s r} \\\\Gamma_{r l} \\\\Gamma_{k m} \\\\Gamma_{m s};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 2748886865497035333,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 7565631776140811989,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"We need to join and distribute three times to merge all four generalised gamma matrices, so\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"We need to join and distribute three times to merge all four generalised gamma matrices, so\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 10942172291160346011,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 11701630706278017846,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 7267858631944983333,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\Gamma_{k l} (-18d + 8d d + 12-d d d) + \\\\delta_{k l} (-3 + 6d-4d d + d d d)\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\Gamma_{k l} \\\\left(-18\\\\,d\\\\discretionary{}{}{}+8\\\\,d d\\\\discretionary{}{}{}+12\\\\,\\\\discretionary{}{}{}-\\\\,d d d\\\\right)\\\\discretionary{}{}{}+\\\\delta_{k l} \\\\left(-3\\\\,\\\\discretionary{}{}{}+6\\\\,d\\\\discretionary{}{}{}-4\\\\,d d\\\\discretionary{}{}{}+d d d\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"for i in range(3):\\n\\tjoin_gamma(_)\\n\\tdistribute(_)\\nfactor_in(_, $d$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 1938335043474642649,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 647755519203709355,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 10879512807052220584,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\Gamma_{k l} (-18d + 8(d)**2 + 12-(d)**3) + \\\\delta_{k l} (-3 + 6d-4(d)**2 + (d)**3)\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\Gamma_{k l} \\\\left(-18\\\\,d\\\\discretionary{}{}{}+8\\\\,{d}^{2\\\\,}\\\\discretionary{}{}{}+12\\\\,\\\\discretionary{}{}{}-\\\\,{d}^{3\\\\,}\\\\right)\\\\discretionary{}{}{}+\\\\delta_{k l} \\\\left(-3\\\\,\\\\discretionary{}{}{}+6\\\\,d\\\\discretionary{}{}{}-4\\\\,{d}^{2\\\\,}\\\\discretionary{}{}{}+{d}^{3\\\\,}\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"collect_factors(ex);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 4783681678151271461,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 2436902490514838396,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"That's the answer we wanted to compute, much easier than by hand.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"That's the answer we wanted to compute, much easier than by hand.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 10887901339884211899,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"\"\n\t\t}\n\t],\n\t\"description\": \"Cadabra JSON notebook format\",\n\t\"flags\": {\n\t\t\"hide_input_cells\": false\n\t},\n\t\"version\": 1.0\n}\n"
  },
  {
    "path": "examples/gamma_traces.cnb",
    "content": "{\n\t\"cells\" : \n\t[\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property GammaMatrix to~}\\\\gamma\\\\left(\\\\#\\\\right).\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property KroneckerDelta to~}\\\\delta\\\\left(\\\\#\\\\right).\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Indices(position=free) to~}\\\\left\\\\{a,~\\\\linebreak[0] b,~\\\\linebreak[0] c,~\\\\linebreak[0] d,~\\\\linebreak[0] e,~\\\\linebreak[0] f,~\\\\linebreak[0] g,~\\\\linebreak[0] h,~\\\\linebreak[0] i\\\\right\\\\}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Integer to~}\\\\left\\\\{a,~\\\\linebreak[0] b,~\\\\linebreak[0] c,~\\\\linebreak[0] d,~\\\\linebreak[0] e,~\\\\linebreak[0] f,~\\\\linebreak[0] g,~\\\\linebreak[0] h,~\\\\linebreak[0] i\\\\right\\\\}.\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"\\\\gamma{#}::GammaMatrix(metric=\\\\delta);\\n\\\\delta{#}::KroneckerDelta;\\n{a,b,c,d,e,f,g,h,i}::Indices(position=free);\\n{a,b,c,d,e,f,g,h,i}::Integer(0..3);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\gamma_{a} \\\\gamma_{b} \\\\gamma_{c} \\\\gamma_{d}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"E47:=\\\\gamma_{a}\\\\gamma_{b}\\\\gamma_{c}\\\\gamma_{d};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"def red(ex):\\n   converge(ex):\\n      join_gamma(ex)\\n      distribute(ex)\\n      eliminate_kronecker(ex)\\n      sort_product(ex)\\n   return ex\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\gamma_{a b c d}+\\\\delta_{c d} \\\\gamma_{a b}-\\\\delta_{b d} \\\\gamma_{a c}+\\\\delta_{a d} \\\\gamma_{b c}+\\\\delta_{b c} \\\\gamma_{a d}+\\\\delta_{a d} \\\\delta_{b c}-\\\\delta_{a c} \\\\gamma_{b d}-\\\\delta_{a c} \\\\delta_{b d}+\\\\delta_{a b} \\\\gamma_{c d}+\\\\delta_{a b} \\\\delta_{c d}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"red(E47);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\delta_{a d} \\\\delta_{b c}-\\\\delta_{a c} \\\\delta_{b d}+\\\\delta_{a b} \\\\delta_{c d}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"substitute(E47, $\\\\gamma_{a b}->0, \\\\gamma_{a b c d}->0$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\gamma_{a} \\\\gamma_{b} \\\\gamma_{c} \\\\gamma_{d} \\\\gamma_{e} \\\\gamma_{f}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"E53:=\\\\gamma_{a}\\\\gamma_{b}\\\\gamma_{c}\\\\gamma_{d}\\\\gamma_{e}\\\\gamma_{f};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\delta_{d e} \\\\gamma_{a b c f}+\\\\delta_{c f} \\\\delta_{d e} \\\\gamma_{a b}-\\\\delta_{b f} \\\\delta_{d e} \\\\gamma_{a c}+\\\\delta_{a f} \\\\delta_{d e} \\\\gamma_{b c}-\\\\delta_{c e} \\\\gamma_{a b d f}-\\\\delta_{c e} \\\\delta_{d f} \\\\gamma_{a b}+\\\\delta_{b f} \\\\delta_{c e} \\\\gamma_{a d}-\\\\delta_{a f} \\\\delta_{c e} \\\\gamma_{b d}+\\\\delta_{b e} \\\\gamma_{a c d f}+\\\\delta_{b e} \\\\delta_{d f} \\\\gamma_{a c}-\\\\delta_{b e} \\\\delta_{c f} \\\\gamma_{a d}+\\\\delta_{a f} \\\\delta_{b e} \\\\gamma_{c d}-\\\\delta_{a e} \\\\gamma_{b c d f}-\\\\delta_{a e} \\\\delta_{d f} \\\\gamma_{b c}+\\\\delta_{a e} \\\\delta_{c f} \\\\gamma_{b d}-\\\\delta_{a e} \\\\delta_{b f} \\\\gamma_{c d}+\\\\delta_{c d} \\\\gamma_{a b e f}+\\\\delta_{c d} \\\\delta_{e f} \\\\gamma_{a b}-\\\\delta_{b f} \\\\delta_{c d} \\\\gamma_{a e}%\\n+\\\\delta_{a f} \\\\delta_{c d} \\\\gamma_{b e}+\\\\delta_{b e} \\\\delta_{c d} \\\\gamma_{a f}+\\\\delta_{a f} \\\\delta_{b e} \\\\delta_{c d}-\\\\delta_{a e} \\\\delta_{c d} \\\\gamma_{b f}-\\\\delta_{a e} \\\\delta_{b f} \\\\delta_{c d}-\\\\delta_{b d} \\\\gamma_{a c e f}-\\\\delta_{b d} \\\\delta_{e f} \\\\gamma_{a c}+\\\\delta_{b d} \\\\delta_{c f} \\\\gamma_{a e}-\\\\delta_{a f} \\\\delta_{b d} \\\\gamma_{c e}-\\\\delta_{b d} \\\\delta_{c e} \\\\gamma_{a f}-\\\\delta_{a f} \\\\delta_{b d} \\\\delta_{c e}+\\\\delta_{a e} \\\\delta_{b d} \\\\gamma_{c f}+\\\\delta_{a e} \\\\delta_{b d} \\\\delta_{c f}+\\\\delta_{a d} \\\\gamma_{b c e f}+\\\\delta_{a d} \\\\delta_{e f} \\\\gamma_{b c}-\\\\delta_{a d} \\\\delta_{c f} \\\\gamma_{b e}+\\\\delta_{a d} \\\\delta_{b f} \\\\gamma_{c e}+\\\\delta_{a d} \\\\delta_{c e} \\\\gamma_{b f}+\\\\delta_{a d} \\\\delta_{b f} \\\\delta_{c e}-\\\\delta_{a d} \\\\delta_{b e} \\\\gamma_{c f}%\\n-\\\\delta_{a d} \\\\delta_{b e} \\\\delta_{c f}+\\\\delta_{b c} \\\\gamma_{a d e f}+\\\\delta_{b c} \\\\delta_{e f} \\\\gamma_{a d}-\\\\delta_{b c} \\\\delta_{d f} \\\\gamma_{a e}+\\\\delta_{a f} \\\\delta_{b c} \\\\gamma_{d e}+\\\\delta_{b c} \\\\delta_{d e} \\\\gamma_{a f}+\\\\delta_{a f} \\\\delta_{b c} \\\\delta_{d e}-\\\\delta_{a e} \\\\delta_{b c} \\\\gamma_{d f}-\\\\delta_{a e} \\\\delta_{b c} \\\\delta_{d f}+\\\\delta_{a d} \\\\delta_{b c} \\\\gamma_{e f}+\\\\delta_{a d} \\\\delta_{b c} \\\\delta_{e f}-\\\\delta_{a c} \\\\gamma_{b d e f}-\\\\delta_{a c} \\\\delta_{e f} \\\\gamma_{b d}+\\\\delta_{a c} \\\\delta_{d f} \\\\gamma_{b e}-\\\\delta_{a c} \\\\delta_{b f} \\\\gamma_{d e}-\\\\delta_{a c} \\\\delta_{d e} \\\\gamma_{b f}-\\\\delta_{a c} \\\\delta_{b f} \\\\delta_{d e}+\\\\delta_{a c} \\\\delta_{b e} \\\\gamma_{d f}+\\\\delta_{a c} \\\\delta_{b e} \\\\delta_{d f}-\\\\delta_{a c} \\\\delta_{b d} \\\\gamma_{e f}%\\n-\\\\delta_{a c} \\\\delta_{b d} \\\\delta_{e f}+\\\\delta_{a b} \\\\gamma_{c d e f}+\\\\delta_{a b} \\\\delta_{e f} \\\\gamma_{c d}-\\\\delta_{a b} \\\\delta_{d f} \\\\gamma_{c e}+\\\\delta_{a b} \\\\delta_{c f} \\\\gamma_{d e}+\\\\delta_{a b} \\\\delta_{d e} \\\\gamma_{c f}+\\\\delta_{a b} \\\\delta_{c f} \\\\delta_{d e}-\\\\delta_{a b} \\\\delta_{c e} \\\\gamma_{d f}-\\\\delta_{a b} \\\\delta_{c e} \\\\delta_{d f}+\\\\delta_{a b} \\\\delta_{c d} \\\\gamma_{e f}+\\\\delta_{a b} \\\\delta_{c d} \\\\delta_{e f}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"red(E53);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\delta_{a f} \\\\delta_{b e} \\\\delta_{c d}-\\\\delta_{a e} \\\\delta_{b f} \\\\delta_{c d}-\\\\delta_{a f} \\\\delta_{b d} \\\\delta_{c e}+\\\\delta_{a e} \\\\delta_{b d} \\\\delta_{c f}+\\\\delta_{a d} \\\\delta_{b f} \\\\delta_{c e}-\\\\delta_{a d} \\\\delta_{b e} \\\\delta_{c f}+\\\\delta_{a f} \\\\delta_{b c} \\\\delta_{d e}-\\\\delta_{a e} \\\\delta_{b c} \\\\delta_{d f}+\\\\delta_{a d} \\\\delta_{b c} \\\\delta_{e f}-\\\\delta_{a c} \\\\delta_{b f} \\\\delta_{d e}+\\\\delta_{a c} \\\\delta_{b e} \\\\delta_{d f}-\\\\delta_{a c} \\\\delta_{b d} \\\\delta_{e f}+\\\\delta_{a b} \\\\delta_{c f} \\\\delta_{d e}-\\\\delta_{a b} \\\\delta_{c e} \\\\delta_{d f}+\\\\delta_{a b} \\\\delta_{c d} \\\\delta_{e f}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"substitute(E53, $\\\\gamma_{a b}->0, \\\\gamma_{a b c d}->0, \\\\gamma_{a b c d e f}->0$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\gamma_{0 1 2 3} \\\\gamma_{a} \\\\gamma_{b} \\\\gamma_{c} \\\\gamma_{d}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"E59:= \\\\gamma_{0 1 2 3} \\\\gamma_{a}\\\\gamma_{b}\\\\gamma_{c}\\\\gamma_{d};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\gamma_{0 1 2 3 a b c d}+\\\\delta_{c d} \\\\gamma_{0 1 2 3 a b}-\\\\delta_{b d} \\\\gamma_{0 1 2 3 a c}+\\\\delta_{a d} \\\\gamma_{0 1 2 3 b c}-\\\\delta_{3 d} \\\\gamma_{0 1 2 a b c}+\\\\delta_{2 d} \\\\gamma_{0 1 3 a b c}-\\\\delta_{1 d} \\\\gamma_{0 2 3 a b c}+\\\\delta_{0 d} \\\\gamma_{1 2 3 a b c}+\\\\delta_{b c} \\\\gamma_{0 1 2 3 a d}+\\\\delta_{a d} \\\\delta_{b c} \\\\gamma_{0 1 2 3}-\\\\delta_{3 d} \\\\delta_{b c} \\\\gamma_{0 1 2 a}+\\\\delta_{2 d} \\\\delta_{b c} \\\\gamma_{0 1 3 a}-\\\\delta_{1 d} \\\\delta_{b c} \\\\gamma_{0 2 3 a}+\\\\delta_{0 d} \\\\delta_{b c} \\\\gamma_{1 2 3 a}-\\\\delta_{a c} \\\\gamma_{0 1 2 3 b d}-\\\\delta_{a c} \\\\delta_{b d} \\\\gamma_{0 1 2 3}+\\\\delta_{3 d} \\\\delta_{a c} \\\\gamma_{0 1 2 b}-\\\\delta_{2 d} \\\\delta_{a c} \\\\gamma_{0 1 3 b}+\\\\delta_{1 d} \\\\delta_{a c} \\\\gamma_{0 2 3 b}%\\n-\\\\delta_{0 d} \\\\delta_{a c} \\\\gamma_{1 2 3 b}+\\\\delta_{3 c} \\\\gamma_{0 1 2 a b d}+\\\\delta_{3 c} \\\\delta_{b d} \\\\gamma_{0 1 2 a}-\\\\delta_{3 c} \\\\delta_{a d} \\\\gamma_{0 1 2 b}+\\\\delta_{2 d} \\\\delta_{3 c} \\\\gamma_{0 1 a b}-\\\\delta_{1 d} \\\\delta_{3 c} \\\\gamma_{0 2 a b}+\\\\delta_{0 d} \\\\delta_{3 c} \\\\gamma_{1 2 a b}-\\\\delta_{2 c} \\\\gamma_{0 1 3 a b d}-\\\\delta_{2 c} \\\\delta_{b d} \\\\gamma_{0 1 3 a}+\\\\delta_{2 c} \\\\delta_{a d} \\\\gamma_{0 1 3 b}-\\\\delta_{2 c} \\\\delta_{3 d} \\\\gamma_{0 1 a b}+\\\\delta_{1 d} \\\\delta_{2 c} \\\\gamma_{0 3 a b}-\\\\delta_{0 d} \\\\delta_{2 c} \\\\gamma_{1 3 a b}+\\\\delta_{1 c} \\\\gamma_{0 2 3 a b d}+\\\\delta_{1 c} \\\\delta_{b d} \\\\gamma_{0 2 3 a}-\\\\delta_{1 c} \\\\delta_{a d} \\\\gamma_{0 2 3 b}+\\\\delta_{1 c} \\\\delta_{3 d} \\\\gamma_{0 2 a b}-\\\\delta_{1 c} \\\\delta_{2 d} \\\\gamma_{0 3 a b}+\\\\delta_{0 d} \\\\delta_{1 c} \\\\gamma_{2 3 a b}-\\\\delta_{0 c} \\\\gamma_{1 2 3 a b d}%\\n-\\\\delta_{0 c} \\\\delta_{b d} \\\\gamma_{1 2 3 a}+\\\\delta_{0 c} \\\\delta_{a d} \\\\gamma_{1 2 3 b}-\\\\delta_{0 c} \\\\delta_{3 d} \\\\gamma_{1 2 a b}+\\\\delta_{0 c} \\\\delta_{2 d} \\\\gamma_{1 3 a b}-\\\\delta_{0 c} \\\\delta_{1 d} \\\\gamma_{2 3 a b}+\\\\delta_{a b} \\\\gamma_{0 1 2 3 c d}+\\\\delta_{a b} \\\\delta_{c d} \\\\gamma_{0 1 2 3}-\\\\delta_{3 d} \\\\delta_{a b} \\\\gamma_{0 1 2 c}+\\\\delta_{2 d} \\\\delta_{a b} \\\\gamma_{0 1 3 c}-\\\\delta_{1 d} \\\\delta_{a b} \\\\gamma_{0 2 3 c}+\\\\delta_{0 d} \\\\delta_{a b} \\\\gamma_{1 2 3 c}+\\\\delta_{3 c} \\\\delta_{a b} \\\\gamma_{0 1 2 d}+\\\\delta_{2 d} \\\\delta_{3 c} \\\\delta_{a b} \\\\gamma_{0 1}-\\\\delta_{1 d} \\\\delta_{3 c} \\\\delta_{a b} \\\\gamma_{0 2}+\\\\delta_{0 d} \\\\delta_{3 c} \\\\delta_{a b} \\\\gamma_{1 2}-\\\\delta_{2 c} \\\\delta_{a b} \\\\gamma_{0 1 3 d}-\\\\delta_{2 c} \\\\delta_{3 d} \\\\delta_{a b} \\\\gamma_{0 1}+\\\\delta_{1 d} \\\\delta_{2 c} \\\\delta_{a b} \\\\gamma_{0 3}-\\\\delta_{0 d} \\\\delta_{2 c} \\\\delta_{a b} \\\\gamma_{1 3}+\\\\delta_{1 c} \\\\delta_{a b} \\\\gamma_{0 2 3 d}%\\n+\\\\delta_{1 c} \\\\delta_{3 d} \\\\delta_{a b} \\\\gamma_{0 2}-\\\\delta_{1 c} \\\\delta_{2 d} \\\\delta_{a b} \\\\gamma_{0 3}+\\\\delta_{0 d} \\\\delta_{1 c} \\\\delta_{a b} \\\\gamma_{2 3}-\\\\delta_{0 c} \\\\delta_{a b} \\\\gamma_{1 2 3 d}-\\\\delta_{0 c} \\\\delta_{3 d} \\\\delta_{a b} \\\\gamma_{1 2}+\\\\delta_{0 c} \\\\delta_{2 d} \\\\delta_{a b} \\\\gamma_{1 3}-\\\\delta_{0 c} \\\\delta_{1 d} \\\\delta_{a b} \\\\gamma_{2 3}-\\\\delta_{3 b} \\\\gamma_{0 1 2 a c d}-\\\\delta_{3 b} \\\\delta_{c d} \\\\gamma_{0 1 2 a}+\\\\delta_{3 b} \\\\delta_{a d} \\\\gamma_{0 1 2 c}-\\\\delta_{2 d} \\\\delta_{3 b} \\\\gamma_{0 1 a c}+\\\\delta_{1 d} \\\\delta_{3 b} \\\\gamma_{0 2 a c}-\\\\delta_{0 d} \\\\delta_{3 b} \\\\gamma_{1 2 a c}-\\\\delta_{3 b} \\\\delta_{a c} \\\\gamma_{0 1 2 d}-\\\\delta_{2 d} \\\\delta_{3 b} \\\\delta_{a c} \\\\gamma_{0 1}+\\\\delta_{1 d} \\\\delta_{3 b} \\\\delta_{a c} \\\\gamma_{0 2}-\\\\delta_{0 d} \\\\delta_{3 b} \\\\delta_{a c} \\\\gamma_{1 2}+\\\\delta_{2 c} \\\\delta_{3 b} \\\\gamma_{0 1 a d}+\\\\delta_{2 c} \\\\delta_{3 b} \\\\delta_{a d} \\\\gamma_{0 1}-\\\\delta_{1 d} \\\\delta_{2 c} \\\\delta_{3 b} \\\\gamma_{0 a}%\\n+\\\\delta_{0 d} \\\\delta_{2 c} \\\\delta_{3 b} \\\\gamma_{1 a}-\\\\delta_{1 c} \\\\delta_{3 b} \\\\gamma_{0 2 a d}-\\\\delta_{1 c} \\\\delta_{3 b} \\\\delta_{a d} \\\\gamma_{0 2}+\\\\delta_{1 c} \\\\delta_{2 d} \\\\delta_{3 b} \\\\gamma_{0 a}-\\\\delta_{0 d} \\\\delta_{1 c} \\\\delta_{3 b} \\\\gamma_{2 a}+\\\\delta_{0 c} \\\\delta_{3 b} \\\\gamma_{1 2 a d}+\\\\delta_{0 c} \\\\delta_{3 b} \\\\delta_{a d} \\\\gamma_{1 2}-\\\\delta_{0 c} \\\\delta_{2 d} \\\\delta_{3 b} \\\\gamma_{1 a}+\\\\delta_{0 c} \\\\delta_{1 d} \\\\delta_{3 b} \\\\gamma_{2 a}+\\\\delta_{2 b} \\\\gamma_{0 1 3 a c d}+\\\\delta_{2 b} \\\\delta_{c d} \\\\gamma_{0 1 3 a}-\\\\delta_{2 b} \\\\delta_{a d} \\\\gamma_{0 1 3 c}+\\\\delta_{2 b} \\\\delta_{3 d} \\\\gamma_{0 1 a c}-\\\\delta_{1 d} \\\\delta_{2 b} \\\\gamma_{0 3 a c}+\\\\delta_{0 d} \\\\delta_{2 b} \\\\gamma_{1 3 a c}+\\\\delta_{2 b} \\\\delta_{a c} \\\\gamma_{0 1 3 d}+\\\\delta_{2 b} \\\\delta_{3 d} \\\\delta_{a c} \\\\gamma_{0 1}-\\\\delta_{1 d} \\\\delta_{2 b} \\\\delta_{a c} \\\\gamma_{0 3}+\\\\delta_{0 d} \\\\delta_{2 b} \\\\delta_{a c} \\\\gamma_{1 3}-\\\\delta_{2 b} \\\\delta_{3 c} \\\\gamma_{0 1 a d}%\\n-\\\\delta_{2 b} \\\\delta_{3 c} \\\\delta_{a d} \\\\gamma_{0 1}+\\\\delta_{1 d} \\\\delta_{2 b} \\\\delta_{3 c} \\\\gamma_{0 a}-\\\\delta_{0 d} \\\\delta_{2 b} \\\\delta_{3 c} \\\\gamma_{1 a}+\\\\delta_{1 c} \\\\delta_{2 b} \\\\gamma_{0 3 a d}+\\\\delta_{1 c} \\\\delta_{2 b} \\\\delta_{a d} \\\\gamma_{0 3}-\\\\delta_{1 c} \\\\delta_{2 b} \\\\delta_{3 d} \\\\gamma_{0 a}+\\\\delta_{0 d} \\\\delta_{1 c} \\\\delta_{2 b} \\\\gamma_{3 a}-\\\\delta_{0 c} \\\\delta_{2 b} \\\\gamma_{1 3 a d}-\\\\delta_{0 c} \\\\delta_{2 b} \\\\delta_{a d} \\\\gamma_{1 3}+\\\\delta_{0 c} \\\\delta_{2 b} \\\\delta_{3 d} \\\\gamma_{1 a}-\\\\delta_{0 c} \\\\delta_{1 d} \\\\delta_{2 b} \\\\gamma_{3 a}-\\\\delta_{1 b} \\\\gamma_{0 2 3 a c d}-\\\\delta_{1 b} \\\\delta_{c d} \\\\gamma_{0 2 3 a}+\\\\delta_{1 b} \\\\delta_{a d} \\\\gamma_{0 2 3 c}-\\\\delta_{1 b} \\\\delta_{3 d} \\\\gamma_{0 2 a c}+\\\\delta_{1 b} \\\\delta_{2 d} \\\\gamma_{0 3 a c}-\\\\delta_{0 d} \\\\delta_{1 b} \\\\gamma_{2 3 a c}-\\\\delta_{1 b} \\\\delta_{a c} \\\\gamma_{0 2 3 d}-\\\\delta_{1 b} \\\\delta_{3 d} \\\\delta_{a c} \\\\gamma_{0 2}+\\\\delta_{1 b} \\\\delta_{2 d} \\\\delta_{a c} \\\\gamma_{0 3}%\\n-\\\\delta_{0 d} \\\\delta_{1 b} \\\\delta_{a c} \\\\gamma_{2 3}+\\\\delta_{1 b} \\\\delta_{3 c} \\\\gamma_{0 2 a d}+\\\\delta_{1 b} \\\\delta_{3 c} \\\\delta_{a d} \\\\gamma_{0 2}-\\\\delta_{1 b} \\\\delta_{2 d} \\\\delta_{3 c} \\\\gamma_{0 a}+\\\\delta_{0 d} \\\\delta_{1 b} \\\\delta_{3 c} \\\\gamma_{2 a}-\\\\delta_{1 b} \\\\delta_{2 c} \\\\gamma_{0 3 a d}-\\\\delta_{1 b} \\\\delta_{2 c} \\\\delta_{a d} \\\\gamma_{0 3}+\\\\delta_{1 b} \\\\delta_{2 c} \\\\delta_{3 d} \\\\gamma_{0 a}-\\\\delta_{0 d} \\\\delta_{1 b} \\\\delta_{2 c} \\\\gamma_{3 a}+\\\\delta_{0 c} \\\\delta_{1 b} \\\\gamma_{2 3 a d}+\\\\delta_{0 c} \\\\delta_{1 b} \\\\delta_{a d} \\\\gamma_{2 3}-\\\\delta_{0 c} \\\\delta_{1 b} \\\\delta_{3 d} \\\\gamma_{2 a}+\\\\delta_{0 c} \\\\delta_{1 b} \\\\delta_{2 d} \\\\gamma_{3 a}+\\\\delta_{0 b} \\\\gamma_{1 2 3 a c d}+\\\\delta_{0 b} \\\\delta_{c d} \\\\gamma_{1 2 3 a}-\\\\delta_{0 b} \\\\delta_{a d} \\\\gamma_{1 2 3 c}+\\\\delta_{0 b} \\\\delta_{3 d} \\\\gamma_{1 2 a c}-\\\\delta_{0 b} \\\\delta_{2 d} \\\\gamma_{1 3 a c}+\\\\delta_{0 b} \\\\delta_{1 d} \\\\gamma_{2 3 a c}+\\\\delta_{0 b} \\\\delta_{a c} \\\\gamma_{1 2 3 d}%\\n+\\\\delta_{0 b} \\\\delta_{3 d} \\\\delta_{a c} \\\\gamma_{1 2}-\\\\delta_{0 b} \\\\delta_{2 d} \\\\delta_{a c} \\\\gamma_{1 3}+\\\\delta_{0 b} \\\\delta_{1 d} \\\\delta_{a c} \\\\gamma_{2 3}-\\\\delta_{0 b} \\\\delta_{3 c} \\\\gamma_{1 2 a d}-\\\\delta_{0 b} \\\\delta_{3 c} \\\\delta_{a d} \\\\gamma_{1 2}+\\\\delta_{0 b} \\\\delta_{2 d} \\\\delta_{3 c} \\\\gamma_{1 a}-\\\\delta_{0 b} \\\\delta_{1 d} \\\\delta_{3 c} \\\\gamma_{2 a}+\\\\delta_{0 b} \\\\delta_{2 c} \\\\gamma_{1 3 a d}+\\\\delta_{0 b} \\\\delta_{2 c} \\\\delta_{a d} \\\\gamma_{1 3}-\\\\delta_{0 b} \\\\delta_{2 c} \\\\delta_{3 d} \\\\gamma_{1 a}+\\\\delta_{0 b} \\\\delta_{1 d} \\\\delta_{2 c} \\\\gamma_{3 a}-\\\\delta_{0 b} \\\\delta_{1 c} \\\\gamma_{2 3 a d}-\\\\delta_{0 b} \\\\delta_{1 c} \\\\delta_{a d} \\\\gamma_{2 3}+\\\\delta_{0 b} \\\\delta_{1 c} \\\\delta_{3 d} \\\\gamma_{2 a}-\\\\delta_{0 b} \\\\delta_{1 c} \\\\delta_{2 d} \\\\gamma_{3 a}+\\\\delta_{3 a} \\\\gamma_{0 1 2 b c d}+\\\\delta_{3 a} \\\\delta_{c d} \\\\gamma_{0 1 2 b}-\\\\delta_{3 a} \\\\delta_{b d} \\\\gamma_{0 1 2 c}+\\\\delta_{2 d} \\\\delta_{3 a} \\\\gamma_{0 1 b c}-\\\\delta_{1 d} \\\\delta_{3 a} \\\\gamma_{0 2 b c}%\\n+\\\\delta_{0 d} \\\\delta_{3 a} \\\\gamma_{1 2 b c}+\\\\delta_{3 a} \\\\delta_{b c} \\\\gamma_{0 1 2 d}+\\\\delta_{2 d} \\\\delta_{3 a} \\\\delta_{b c} \\\\gamma_{0 1}-\\\\delta_{1 d} \\\\delta_{3 a} \\\\delta_{b c} \\\\gamma_{0 2}+\\\\delta_{0 d} \\\\delta_{3 a} \\\\delta_{b c} \\\\gamma_{1 2}-\\\\delta_{2 c} \\\\delta_{3 a} \\\\gamma_{0 1 b d}-\\\\delta_{2 c} \\\\delta_{3 a} \\\\delta_{b d} \\\\gamma_{0 1}+\\\\delta_{1 d} \\\\delta_{2 c} \\\\delta_{3 a} \\\\gamma_{0 b}-\\\\delta_{0 d} \\\\delta_{2 c} \\\\delta_{3 a} \\\\gamma_{1 b}+\\\\delta_{1 c} \\\\delta_{3 a} \\\\gamma_{0 2 b d}+\\\\delta_{1 c} \\\\delta_{3 a} \\\\delta_{b d} \\\\gamma_{0 2}-\\\\delta_{1 c} \\\\delta_{2 d} \\\\delta_{3 a} \\\\gamma_{0 b}+\\\\delta_{0 d} \\\\delta_{1 c} \\\\delta_{3 a} \\\\gamma_{2 b}-\\\\delta_{0 c} \\\\delta_{3 a} \\\\gamma_{1 2 b d}-\\\\delta_{0 c} \\\\delta_{3 a} \\\\delta_{b d} \\\\gamma_{1 2}+\\\\delta_{0 c} \\\\delta_{2 d} \\\\delta_{3 a} \\\\gamma_{1 b}-\\\\delta_{0 c} \\\\delta_{1 d} \\\\delta_{3 a} \\\\gamma_{2 b}+\\\\delta_{2 b} \\\\delta_{3 a} \\\\gamma_{0 1 c d}+\\\\delta_{2 b} \\\\delta_{3 a} \\\\delta_{c d} \\\\gamma_{0 1}-\\\\delta_{1 d} \\\\delta_{2 b} \\\\delta_{3 a} \\\\gamma_{0 c}%\\n+\\\\delta_{0 d} \\\\delta_{2 b} \\\\delta_{3 a} \\\\gamma_{1 c}+\\\\delta_{1 c} \\\\delta_{2 b} \\\\delta_{3 a} \\\\gamma_{0 d}+\\\\delta_{0 d} \\\\delta_{1 c} \\\\delta_{2 b} \\\\delta_{3 a}-\\\\delta_{0 c} \\\\delta_{2 b} \\\\delta_{3 a} \\\\gamma_{1 d}-\\\\delta_{0 c} \\\\delta_{1 d} \\\\delta_{2 b} \\\\delta_{3 a}-\\\\delta_{1 b} \\\\delta_{3 a} \\\\gamma_{0 2 c d}-\\\\delta_{1 b} \\\\delta_{3 a} \\\\delta_{c d} \\\\gamma_{0 2}+\\\\delta_{1 b} \\\\delta_{2 d} \\\\delta_{3 a} \\\\gamma_{0 c}-\\\\delta_{0 d} \\\\delta_{1 b} \\\\delta_{3 a} \\\\gamma_{2 c}-\\\\delta_{1 b} \\\\delta_{2 c} \\\\delta_{3 a} \\\\gamma_{0 d}-\\\\delta_{0 d} \\\\delta_{1 b} \\\\delta_{2 c} \\\\delta_{3 a}+\\\\delta_{0 c} \\\\delta_{1 b} \\\\delta_{3 a} \\\\gamma_{2 d}+\\\\delta_{0 c} \\\\delta_{1 b} \\\\delta_{2 d} \\\\delta_{3 a}+\\\\delta_{0 b} \\\\delta_{3 a} \\\\gamma_{1 2 c d}+\\\\delta_{0 b} \\\\delta_{3 a} \\\\delta_{c d} \\\\gamma_{1 2}-\\\\delta_{0 b} \\\\delta_{2 d} \\\\delta_{3 a} \\\\gamma_{1 c}+\\\\delta_{0 b} \\\\delta_{1 d} \\\\delta_{3 a} \\\\gamma_{2 c}+\\\\delta_{0 b} \\\\delta_{2 c} \\\\delta_{3 a} \\\\gamma_{1 d}+\\\\delta_{0 b} \\\\delta_{1 d} \\\\delta_{2 c} \\\\delta_{3 a}-\\\\delta_{0 b} \\\\delta_{1 c} \\\\delta_{3 a} \\\\gamma_{2 d}%\\n-\\\\delta_{0 b} \\\\delta_{1 c} \\\\delta_{2 d} \\\\delta_{3 a}-\\\\delta_{2 a} \\\\gamma_{0 1 3 b c d}-\\\\delta_{2 a} \\\\delta_{c d} \\\\gamma_{0 1 3 b}+\\\\delta_{2 a} \\\\delta_{b d} \\\\gamma_{0 1 3 c}-\\\\delta_{2 a} \\\\delta_{3 d} \\\\gamma_{0 1 b c}+\\\\delta_{1 d} \\\\delta_{2 a} \\\\gamma_{0 3 b c}-\\\\delta_{0 d} \\\\delta_{2 a} \\\\gamma_{1 3 b c}-\\\\delta_{2 a} \\\\delta_{b c} \\\\gamma_{0 1 3 d}-\\\\delta_{2 a} \\\\delta_{3 d} \\\\delta_{b c} \\\\gamma_{0 1}+\\\\delta_{1 d} \\\\delta_{2 a} \\\\delta_{b c} \\\\gamma_{0 3}-\\\\delta_{0 d} \\\\delta_{2 a} \\\\delta_{b c} \\\\gamma_{1 3}+\\\\delta_{2 a} \\\\delta_{3 c} \\\\gamma_{0 1 b d}+\\\\delta_{2 a} \\\\delta_{3 c} \\\\delta_{b d} \\\\gamma_{0 1}-\\\\delta_{1 d} \\\\delta_{2 a} \\\\delta_{3 c} \\\\gamma_{0 b}+\\\\delta_{0 d} \\\\delta_{2 a} \\\\delta_{3 c} \\\\gamma_{1 b}-\\\\delta_{1 c} \\\\delta_{2 a} \\\\gamma_{0 3 b d}-\\\\delta_{1 c} \\\\delta_{2 a} \\\\delta_{b d} \\\\gamma_{0 3}+\\\\delta_{1 c} \\\\delta_{2 a} \\\\delta_{3 d} \\\\gamma_{0 b}-\\\\delta_{0 d} \\\\delta_{1 c} \\\\delta_{2 a} \\\\gamma_{3 b}+\\\\delta_{0 c} \\\\delta_{2 a} \\\\gamma_{1 3 b d}%\\n+\\\\delta_{0 c} \\\\delta_{2 a} \\\\delta_{b d} \\\\gamma_{1 3}-\\\\delta_{0 c} \\\\delta_{2 a} \\\\delta_{3 d} \\\\gamma_{1 b}+\\\\delta_{0 c} \\\\delta_{1 d} \\\\delta_{2 a} \\\\gamma_{3 b}-\\\\delta_{2 a} \\\\delta_{3 b} \\\\gamma_{0 1 c d}-\\\\delta_{2 a} \\\\delta_{3 b} \\\\delta_{c d} \\\\gamma_{0 1}+\\\\delta_{1 d} \\\\delta_{2 a} \\\\delta_{3 b} \\\\gamma_{0 c}-\\\\delta_{0 d} \\\\delta_{2 a} \\\\delta_{3 b} \\\\gamma_{1 c}-\\\\delta_{1 c} \\\\delta_{2 a} \\\\delta_{3 b} \\\\gamma_{0 d}-\\\\delta_{0 d} \\\\delta_{1 c} \\\\delta_{2 a} \\\\delta_{3 b}+\\\\delta_{0 c} \\\\delta_{2 a} \\\\delta_{3 b} \\\\gamma_{1 d}+\\\\delta_{0 c} \\\\delta_{1 d} \\\\delta_{2 a} \\\\delta_{3 b}+\\\\delta_{1 b} \\\\delta_{2 a} \\\\gamma_{0 3 c d}+\\\\delta_{1 b} \\\\delta_{2 a} \\\\delta_{c d} \\\\gamma_{0 3}-\\\\delta_{1 b} \\\\delta_{2 a} \\\\delta_{3 d} \\\\gamma_{0 c}+\\\\delta_{0 d} \\\\delta_{1 b} \\\\delta_{2 a} \\\\gamma_{3 c}+\\\\delta_{1 b} \\\\delta_{2 a} \\\\delta_{3 c} \\\\gamma_{0 d}+\\\\delta_{0 d} \\\\delta_{1 b} \\\\delta_{2 a} \\\\delta_{3 c}-\\\\delta_{0 c} \\\\delta_{1 b} \\\\delta_{2 a} \\\\gamma_{3 d}-\\\\delta_{0 c} \\\\delta_{1 b} \\\\delta_{2 a} \\\\delta_{3 d}-\\\\delta_{0 b} \\\\delta_{2 a} \\\\gamma_{1 3 c d}%\\n-\\\\delta_{0 b} \\\\delta_{2 a} \\\\delta_{c d} \\\\gamma_{1 3}+\\\\delta_{0 b} \\\\delta_{2 a} \\\\delta_{3 d} \\\\gamma_{1 c}-\\\\delta_{0 b} \\\\delta_{1 d} \\\\delta_{2 a} \\\\gamma_{3 c}-\\\\delta_{0 b} \\\\delta_{2 a} \\\\delta_{3 c} \\\\gamma_{1 d}-\\\\delta_{0 b} \\\\delta_{1 d} \\\\delta_{2 a} \\\\delta_{3 c}+\\\\delta_{0 b} \\\\delta_{1 c} \\\\delta_{2 a} \\\\gamma_{3 d}+\\\\delta_{0 b} \\\\delta_{1 c} \\\\delta_{2 a} \\\\delta_{3 d}+\\\\delta_{1 a} \\\\gamma_{0 2 3 b c d}+\\\\delta_{1 a} \\\\delta_{c d} \\\\gamma_{0 2 3 b}-\\\\delta_{1 a} \\\\delta_{b d} \\\\gamma_{0 2 3 c}+\\\\delta_{1 a} \\\\delta_{3 d} \\\\gamma_{0 2 b c}-\\\\delta_{1 a} \\\\delta_{2 d} \\\\gamma_{0 3 b c}+\\\\delta_{0 d} \\\\delta_{1 a} \\\\gamma_{2 3 b c}+\\\\delta_{1 a} \\\\delta_{b c} \\\\gamma_{0 2 3 d}+\\\\delta_{1 a} \\\\delta_{3 d} \\\\delta_{b c} \\\\gamma_{0 2}-\\\\delta_{1 a} \\\\delta_{2 d} \\\\delta_{b c} \\\\gamma_{0 3}+\\\\delta_{0 d} \\\\delta_{1 a} \\\\delta_{b c} \\\\gamma_{2 3}-\\\\delta_{1 a} \\\\delta_{3 c} \\\\gamma_{0 2 b d}-\\\\delta_{1 a} \\\\delta_{3 c} \\\\delta_{b d} \\\\gamma_{0 2}+\\\\delta_{1 a} \\\\delta_{2 d} \\\\delta_{3 c} \\\\gamma_{0 b}%\\n-\\\\delta_{0 d} \\\\delta_{1 a} \\\\delta_{3 c} \\\\gamma_{2 b}+\\\\delta_{1 a} \\\\delta_{2 c} \\\\gamma_{0 3 b d}+\\\\delta_{1 a} \\\\delta_{2 c} \\\\delta_{b d} \\\\gamma_{0 3}-\\\\delta_{1 a} \\\\delta_{2 c} \\\\delta_{3 d} \\\\gamma_{0 b}+\\\\delta_{0 d} \\\\delta_{1 a} \\\\delta_{2 c} \\\\gamma_{3 b}-\\\\delta_{0 c} \\\\delta_{1 a} \\\\gamma_{2 3 b d}-\\\\delta_{0 c} \\\\delta_{1 a} \\\\delta_{b d} \\\\gamma_{2 3}+\\\\delta_{0 c} \\\\delta_{1 a} \\\\delta_{3 d} \\\\gamma_{2 b}-\\\\delta_{0 c} \\\\delta_{1 a} \\\\delta_{2 d} \\\\gamma_{3 b}+\\\\delta_{1 a} \\\\delta_{3 b} \\\\gamma_{0 2 c d}+\\\\delta_{1 a} \\\\delta_{3 b} \\\\delta_{c d} \\\\gamma_{0 2}-\\\\delta_{1 a} \\\\delta_{2 d} \\\\delta_{3 b} \\\\gamma_{0 c}+\\\\delta_{0 d} \\\\delta_{1 a} \\\\delta_{3 b} \\\\gamma_{2 c}+\\\\delta_{1 a} \\\\delta_{2 c} \\\\delta_{3 b} \\\\gamma_{0 d}+\\\\delta_{0 d} \\\\delta_{1 a} \\\\delta_{2 c} \\\\delta_{3 b}-\\\\delta_{0 c} \\\\delta_{1 a} \\\\delta_{3 b} \\\\gamma_{2 d}-\\\\delta_{0 c} \\\\delta_{1 a} \\\\delta_{2 d} \\\\delta_{3 b}-\\\\delta_{1 a} \\\\delta_{2 b} \\\\gamma_{0 3 c d}-\\\\delta_{1 a} \\\\delta_{2 b} \\\\delta_{c d} \\\\gamma_{0 3}+\\\\delta_{1 a} \\\\delta_{2 b} \\\\delta_{3 d} \\\\gamma_{0 c}%\\n-\\\\delta_{0 d} \\\\delta_{1 a} \\\\delta_{2 b} \\\\gamma_{3 c}-\\\\delta_{1 a} \\\\delta_{2 b} \\\\delta_{3 c} \\\\gamma_{0 d}-\\\\delta_{0 d} \\\\delta_{1 a} \\\\delta_{2 b} \\\\delta_{3 c}+\\\\delta_{0 c} \\\\delta_{1 a} \\\\delta_{2 b} \\\\gamma_{3 d}+\\\\delta_{0 c} \\\\delta_{1 a} \\\\delta_{2 b} \\\\delta_{3 d}+\\\\delta_{0 b} \\\\delta_{1 a} \\\\gamma_{2 3 c d}+\\\\delta_{0 b} \\\\delta_{1 a} \\\\delta_{c d} \\\\gamma_{2 3}-\\\\delta_{0 b} \\\\delta_{1 a} \\\\delta_{3 d} \\\\gamma_{2 c}+\\\\delta_{0 b} \\\\delta_{1 a} \\\\delta_{2 d} \\\\gamma_{3 c}+\\\\delta_{0 b} \\\\delta_{1 a} \\\\delta_{3 c} \\\\gamma_{2 d}+\\\\delta_{0 b} \\\\delta_{1 a} \\\\delta_{2 d} \\\\delta_{3 c}-\\\\delta_{0 b} \\\\delta_{1 a} \\\\delta_{2 c} \\\\gamma_{3 d}-\\\\delta_{0 b} \\\\delta_{1 a} \\\\delta_{2 c} \\\\delta_{3 d}-\\\\delta_{0 a} \\\\gamma_{1 2 3 b c d}-\\\\delta_{0 a} \\\\delta_{c d} \\\\gamma_{1 2 3 b}+\\\\delta_{0 a} \\\\delta_{b d} \\\\gamma_{1 2 3 c}-\\\\delta_{0 a} \\\\delta_{3 d} \\\\gamma_{1 2 b c}+\\\\delta_{0 a} \\\\delta_{2 d} \\\\gamma_{1 3 b c}-\\\\delta_{0 a} \\\\delta_{1 d} \\\\gamma_{2 3 b c}-\\\\delta_{0 a} \\\\delta_{b c} \\\\gamma_{1 2 3 d}%\\n-\\\\delta_{0 a} \\\\delta_{3 d} \\\\delta_{b c} \\\\gamma_{1 2}+\\\\delta_{0 a} \\\\delta_{2 d} \\\\delta_{b c} \\\\gamma_{1 3}-\\\\delta_{0 a} \\\\delta_{1 d} \\\\delta_{b c} \\\\gamma_{2 3}+\\\\delta_{0 a} \\\\delta_{3 c} \\\\gamma_{1 2 b d}+\\\\delta_{0 a} \\\\delta_{3 c} \\\\delta_{b d} \\\\gamma_{1 2}-\\\\delta_{0 a} \\\\delta_{2 d} \\\\delta_{3 c} \\\\gamma_{1 b}+\\\\delta_{0 a} \\\\delta_{1 d} \\\\delta_{3 c} \\\\gamma_{2 b}-\\\\delta_{0 a} \\\\delta_{2 c} \\\\gamma_{1 3 b d}-\\\\delta_{0 a} \\\\delta_{2 c} \\\\delta_{b d} \\\\gamma_{1 3}+\\\\delta_{0 a} \\\\delta_{2 c} \\\\delta_{3 d} \\\\gamma_{1 b}-\\\\delta_{0 a} \\\\delta_{1 d} \\\\delta_{2 c} \\\\gamma_{3 b}+\\\\delta_{0 a} \\\\delta_{1 c} \\\\gamma_{2 3 b d}+\\\\delta_{0 a} \\\\delta_{1 c} \\\\delta_{b d} \\\\gamma_{2 3}-\\\\delta_{0 a} \\\\delta_{1 c} \\\\delta_{3 d} \\\\gamma_{2 b}+\\\\delta_{0 a} \\\\delta_{1 c} \\\\delta_{2 d} \\\\gamma_{3 b}-\\\\delta_{0 a} \\\\delta_{3 b} \\\\gamma_{1 2 c d}-\\\\delta_{0 a} \\\\delta_{3 b} \\\\delta_{c d} \\\\gamma_{1 2}+\\\\delta_{0 a} \\\\delta_{2 d} \\\\delta_{3 b} \\\\gamma_{1 c}-\\\\delta_{0 a} \\\\delta_{1 d} \\\\delta_{3 b} \\\\gamma_{2 c}-\\\\delta_{0 a} \\\\delta_{2 c} \\\\delta_{3 b} \\\\gamma_{1 d}%\\n-\\\\delta_{0 a} \\\\delta_{1 d} \\\\delta_{2 c} \\\\delta_{3 b}+\\\\delta_{0 a} \\\\delta_{1 c} \\\\delta_{3 b} \\\\gamma_{2 d}+\\\\delta_{0 a} \\\\delta_{1 c} \\\\delta_{2 d} \\\\delta_{3 b}+\\\\delta_{0 a} \\\\delta_{2 b} \\\\gamma_{1 3 c d}+\\\\delta_{0 a} \\\\delta_{2 b} \\\\delta_{c d} \\\\gamma_{1 3}-\\\\delta_{0 a} \\\\delta_{2 b} \\\\delta_{3 d} \\\\gamma_{1 c}+\\\\delta_{0 a} \\\\delta_{1 d} \\\\delta_{2 b} \\\\gamma_{3 c}+\\\\delta_{0 a} \\\\delta_{2 b} \\\\delta_{3 c} \\\\gamma_{1 d}+\\\\delta_{0 a} \\\\delta_{1 d} \\\\delta_{2 b} \\\\delta_{3 c}-\\\\delta_{0 a} \\\\delta_{1 c} \\\\delta_{2 b} \\\\gamma_{3 d}-\\\\delta_{0 a} \\\\delta_{1 c} \\\\delta_{2 b} \\\\delta_{3 d}-\\\\delta_{0 a} \\\\delta_{1 b} \\\\gamma_{2 3 c d}-\\\\delta_{0 a} \\\\delta_{1 b} \\\\delta_{c d} \\\\gamma_{2 3}+\\\\delta_{0 a} \\\\delta_{1 b} \\\\delta_{3 d} \\\\gamma_{2 c}-\\\\delta_{0 a} \\\\delta_{1 b} \\\\delta_{2 d} \\\\gamma_{3 c}-\\\\delta_{0 a} \\\\delta_{1 b} \\\\delta_{3 c} \\\\gamma_{2 d}-\\\\delta_{0 a} \\\\delta_{1 b} \\\\delta_{2 d} \\\\delta_{3 c}+\\\\delta_{0 a} \\\\delta_{1 b} \\\\delta_{2 c} \\\\gamma_{3 d}+\\\\delta_{0 a} \\\\delta_{1 b} \\\\delta_{2 c} \\\\delta_{3 d}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"red(E59);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1\n}\n"
  },
  {
    "path": "examples/graphical_user_interface.cnb",
    "content": "{\n\t\"cells\" : \n\t[\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\section*{Graphical user interface}\\n\\nThe graphical notebook user interface of Cadabra is called \\\\verb|cadabra2-gtk|. \\nContext-sensitive help is available : if you put your\\ncursor on a command or property name and press F1 or the help button,\\nyou will get a help screen (which is essentially the corresponding\\nsection in this manual).\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\section*{Graphical user interface}\\n\\nThe graphical notebook user interface of Cadabra is called \\\\verb|cadabra2-gtk|. \\nContext-sensitive help is available : if you put your\\ncursor on a command or property name and press F1 or the help button,\\nyou will get a help screen (which is essentially the corresponding\\nsection in this manual).\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\subsection*{Cell types}\\n\\nThere are \\\\emph{two} input cell types and \\\\emph{two} output cell\\ntypes. Normal input cells contain Cadabra input. \\\\LaTeX{} input cells\\ncontain comments which you can add to the notebook but which will not\\nbe sent to Cadabra. Output cells can be either verbatim output, such as\\nstatus messages, or \\\\LaTeX{} output of expressions. Output cells are\\nassociated to input cells, so if you delete an input cell all the\\nassociated output cells will be removed too. You can switch a cell from one\\ntype to the other by using the `Edit' menu.\\n\\nIn the current version there is no visual separation between\\ncells. When you start a new blank notebook, your cursor is in the\\nfirst input cell. After entering an expression there and pressing {\\\\tt\\n  shift-enter}, this input cell will be evaluated and all output will\\nbe placed below it in the first output cell. In addition, a new input\\ncell will be created below the output cell.\\n\\nThe ``edit'' menu can be used to add input cells or delete them, and\\nalso shows keyboard shortcuts.\\n\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\subsection*{Cell types}\\n\\nThere are \\\\emph{two} input cell types and \\\\emph{two} output cell\\ntypes. Normal input cells contain Cadabra input. \\\\LaTeX{} input cells\\ncontain comments which you can add to the notebook but which will not\\nbe sent to Cadabra. Output cells can be either verbatim output, such as\\nstatus messages, or \\\\LaTeX{} output of expressions. Output cells are\\nassociated to input cells, so if you delete an input cell all the\\nassociated output cells will be removed too. You can switch a cell from one\\ntype to the other by using the `Edit' menu.\\n\\nIn the current version there is no visual separation between\\ncells. When you start a new blank notebook, your cursor is in the\\nfirst input cell. After entering an expression there and pressing {\\\\tt\\n  shift-enter}, this input cell will be evaluated and all output will\\nbe placed below it in the first output cell. In addition, a new input\\ncell will be created below the output cell.\\n\\nThe ``edit'' menu can be used to add input cells or delete them, and\\nalso shows keyboard shortcuts.\\n\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\subsection*{Editing, loading, saving, printing, exporting}\\n\\nThe notebook file format (preferred extension \\\\verb|.cnb|) is a JSON file (in contrast to the format in 1.x, which was \\\\LaTeX{}). \\nYou can export your notebook for viewing on any modern browser by exporting to standalone HTML. \\n\\nNotebooks can also be exported to a normal Cadabra text input file (preferred extension \\\\verb|.cdb|), which can be read by the command line version.\\nYou can feed it by simply using\\n\\n\\\\begin{verbatim}\\ncadabra2 < filename.cdb\\n\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\subsection*{Editing, loading, saving, printing, exporting}\\n\\nThe notebook file format (preferred extension \\\\verb|.cnb|) is a JSON file (in contrast to the format in 1.x, which was \\\\LaTeX{}). \\nYou can export your notebook for viewing on any modern browser by exporting to standalone HTML. \\n\\nNotebooks can also be exported to a normal Cadabra text input file (preferred extension \\\\verb|.cdb|), which can be read by the command line version.\\nYou can feed it by simply using\\n\\n\\\\begin{verbatim}\\ncadabra2 < filename.cdb\\n\\\\end{verbatim}\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1\n}\n"
  },
  {
    "path": "examples/ho.cnb",
    "content": "{\n\t\"cells\" : \n\t[\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property NonCommuting to~}\\\\left\\\\{b,~\\\\linebreak[0] bd\\\\right\\\\}.\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"{b,bd}::NonCommuting;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"bd::LaTeXForm(\\\"b^\\\\dagger\\\").\\nvs::LaTeXForm(\\\"|0\\\\rangle\\\").\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}b^\\\\dagger b\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"N:= bd b;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}b^\\\\dagger b b^\\\\dagger b^\\\\dagger b^\\\\dagger |0\\\\rangle\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex:= @(N) bd bd bd vs;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\left\\\\{b b^\\\\dagger = b^\\\\dagger b+1,~\\\\linebreak[0] b |0\\\\rangle = 0\\\\right\\\\}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"rl:= b bd = bd b + 1, b vs = 0;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}8b^\\\\dagger b^\\\\dagger |0\\\\rangle+4b^\\\\dagger b^\\\\dagger b^\\\\dagger b^\\\\dagger |0\\\\rangle\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"converge(ex):\\n   substitute(ex, rl)\\n   distribute(ex)\\n;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}f\\\\left(x , y\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex:=f(x,y);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}b^\\\\dagger b \\\\left(b+b^\\\\dagger\\\\right)^{4} |0\\\\rangle\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex:= @(N) (b + bd)**4 vs;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}b^\\\\dagger b \\\\left(b+b^\\\\dagger\\\\right) \\\\left(b+b^\\\\dagger\\\\right) \\\\left(b+b^\\\\dagger\\\\right) \\\\left(b+b^\\\\dagger\\\\right) |0\\\\rangle\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"expand_power(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}b^\\\\dagger b b b b b |0\\\\rangle+b^\\\\dagger b b b b b^\\\\dagger |0\\\\rangle+b^\\\\dagger b b b b^\\\\dagger b |0\\\\rangle+b^\\\\dagger b b b b^\\\\dagger b^\\\\dagger |0\\\\rangle+b^\\\\dagger b b b^\\\\dagger b b |0\\\\rangle+b^\\\\dagger b b b^\\\\dagger b b^\\\\dagger |0\\\\rangle+b^\\\\dagger b b b^\\\\dagger b^\\\\dagger b |0\\\\rangle+b^\\\\dagger b b b^\\\\dagger b^\\\\dagger b^\\\\dagger |0\\\\rangle+b^\\\\dagger b b^\\\\dagger b b b |0\\\\rangle+b^\\\\dagger b b^\\\\dagger b b b^\\\\dagger |0\\\\rangle+b^\\\\dagger b b^\\\\dagger b b^\\\\dagger b |0\\\\rangle+b^\\\\dagger b b^\\\\dagger b b^\\\\dagger b^\\\\dagger |0\\\\rangle+b^\\\\dagger b b^\\\\dagger b^\\\\dagger b b |0\\\\rangle+b^\\\\dagger b b^\\\\dagger b^\\\\dagger b b^\\\\dagger |0\\\\rangle+b^\\\\dagger b b^\\\\dagger b^\\\\dagger b^\\\\dagger b |0\\\\rangle+b^\\\\dagger b b^\\\\dagger b^\\\\dagger b^\\\\dagger b^\\\\dagger |0\\\\rangle\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"distribute(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1\n}\n"
  },
  {
    "path": "examples/indexing_expressions.cnb",
    "content": "{\n\t\"cell_id\": 6102482626991130957,\n\t\"cells\": [\n\t\t{\n\t\t\t\"cell_id\": 6577700479364638575,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 3171107741548752808,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 2466075911107495190,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"B A + C A + D B\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}B A\\\\discretionary{}{}{}+C A\\\\discretionary{}{}{}+D B\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex:=B*A+C*A+D*B;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 9062355444764525002,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 17526409358088580338,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 1992012689652851717,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"B D\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}B D\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex[2]=sort_product(ex[2]);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 11492451290551663363,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 6860723093135118091,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 18265426190443569502,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"B A + C A + B D\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}B A\\\\discretionary{}{}{}+C A\\\\discretionary{}{}{}+B D\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 3806815117901505855,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 5981219590368000673,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 2500060301239934324,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\int{A + B + C + D}{x}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\int \\\\left(A\\\\discretionary{}{}{}+B\\\\discretionary{}{}{}+C\\\\discretionary{}{}{}+D\\\\right)\\\\,\\\\,{\\\\rm d}x\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex:=\\\\int{ A + B + C + D}{x};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 4732494028466308286,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 7759897485750795908,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 11505880187291561388,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"C\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}C\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex[0][2];\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 9135295628618278121,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 13702029404215408146,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 2582319247121309960,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"Q\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}Q\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 16475775774377124278,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 18098087045568801557,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\int{A + B + C + D}{x}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\int \\\\left(A\\\\discretionary{}{}{}+B\\\\discretionary{}{}{}+C\\\\discretionary{}{}{}+D\\\\right)\\\\,\\\\,{\\\\rm d}x\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex[0][2]=substitute(ex[0][2], $C->Q$);\\nex;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 16415187349600585453,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 12929615604662702514,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 9072927387460019282,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"A\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}A\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 16681211654891441967,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 1232829287611183041,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"A + A_{0} + A_{1} + A_{2} + A_{3} + A_{4} + A_{5} + A_{6} + A_{7} + A_{8} + A_{9}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}A\\\\discretionary{}{}{}+A_{0\\\\,}\\\\discretionary{}{}{}+A_{1}\\\\discretionary{}{}{}+A_{2\\\\,}\\\\discretionary{}{}{}+A_{3\\\\,}\\\\discretionary{}{}{}+A_{4\\\\,}\\\\discretionary{}{}{}+A_{5\\\\,}\\\\discretionary{}{}{}+A_{6\\\\,}\\\\discretionary{}{}{}+A_{7\\\\,}\\\\discretionary{}{}{}+A_{8\\\\,}\\\\discretionary{}{}{}+A_{9\\\\,}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex3:=A;\\nfor i in range(10):\\n\\tex3 = ex3 + Ex('A_{'+str(i)+'}')\\nex3;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 7306560746347034792,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 7730748263181081632,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 3041551120754941543,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"C-D\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}C\\\\discretionary{}{}{}-\\\\,D\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex4:=C - D;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 7379252608352902607,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 199127150708909635,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 11345401835432704654,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"A + A_{0} + A_{1} + A_{2} + A_{3} + A_{4} + A_{5} + A_{6} + A_{7} + A_{8} + A_{9}-C + D\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}A\\\\discretionary{}{}{}+A_{0\\\\,}\\\\discretionary{}{}{}+A_{1}\\\\discretionary{}{}{}+A_{2\\\\,}\\\\discretionary{}{}{}+A_{3\\\\,}\\\\discretionary{}{}{}+A_{4\\\\,}\\\\discretionary{}{}{}+A_{5\\\\,}\\\\discretionary{}{}{}+A_{6\\\\,}\\\\discretionary{}{}{}+A_{7\\\\,}\\\\discretionary{}{}{}+A_{8\\\\,}\\\\discretionary{}{}{}+A_{9\\\\,}\\\\discretionary{}{}{}-\\\\,C\\\\discretionary{}{}{}+D\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex5=ex3-ex4;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 855278985929013194,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 620138231639540893,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 95419599768450119,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"A + B_{0} + B_{1} + B_{2} + B_{3}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}A\\\\discretionary{}{}{}+B_{0\\\\,}\\\\discretionary{}{}{}+B_{1}\\\\discretionary{}{}{}+B_{2\\\\,}\\\\discretionary{}{}{}+B_{3\\\\,}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"substitute(ex5[:5], $A_{a?}->B_{a?}$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 9349378173800162609,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 17382437692800678210,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"error\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}RuntimeError: index 15 out of range, must be smaller than 13\\n\\nAt:\\n  Notebook Cell (Line 1): _ = ex5[15]\\n\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex5[15];\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 1206876666605987021,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"\"\n\t\t}\n\t],\n\t\"description\": \"Cadabra JSON notebook format\",\n\t\"flags\": {\n\t\t\"hide_input_cells\": false\n\t},\n\t\"version\": 1.0\n}\n"
  },
  {
    "path": "examples/input_format.cnb",
    "content": "{\n\t\"cell_id\": 17995742875800745261,\n\t\"cells\": [\n\t\t{\n\t\t\t\"cell_id\": 7233586445452571067,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 17102240285307488534,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\section*{Input format}\\n\\\\subsection*{General structure}\\n\\nCadabra uses LaTeX for the input of mathematical expressions, and Python to\\nwrite out actions and algorithms which act on these expressions. In order to make it \\nsimpler to mix LaTeX and Python code, the cadabra2 command-line client and the\\ncadabra2-gtk notebook interface use a pre-processor which accepts this mixture\\nand converts it to pure Python. This happens under the hood and most people will\\nnot need to know more about this, other than that it works.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\section*{Input format}\\n\\\\subsection*{General structure}\\n\\nCadabra uses LaTeX for the input of mathematical expressions, and Python to\\nwrite out actions and algorithms which act on these expressions. In order to make it \\nsimpler to mix LaTeX and Python code, the cadabra2 command-line client and the\\ncadabra2-gtk notebook interface use a pre-processor which accepts this mixture\\nand converts it to pure Python. This happens under the hood and most people will\\nnot need to know more about this, other than that it works.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 3565968931941232174,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 5264915254736913146,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"Expressions are entered by using the '\\\\verb|:=|' operator, as in\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"Expressions are entered by using the '\\\\verb|:=|' operator, as in\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 11168178429144848554,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 162743159304939194,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 8867733089192382465,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"A + B + C_{m} C^{m}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}A+B+C_{m} C^{m}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex:=A+B+C_{m} C^{m};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 1591872224667350552,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 6796051197936084455,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"The \\\\verb|ex| identifier is a Python variable, and the above line assigns it the mathematical\\nexpression which follows the '\\\\verb|:=|' operator. Internally, objects like \\\\verb|ex| are \\nordinary Python objects (of type \\\\verb|cadabra2.Ex|), and their names can thus only contain normal \\nalphanumeric symbols. \"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"The \\\\verb|ex| identifier is a Python variable, and the above line assigns it the mathematical\\nexpression which follows the '\\\\verb|:=|' operator. Internally, objects like \\\\verb|ex| are \\nordinary Python objects (of type \\\\verb|cadabra2.Ex|), and their names can thus only contain normal \\nalphanumeric symbols. \"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 4694010193013820647,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 2256005163083726401,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"verbatim\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}<class 'cadabra2.Ex'>\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"type(ex);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 1369026216775059075,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 17589432926926272817,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"Lines containing mathematical expressions like the above always have to be terminated with either a ';' or a ':'\\n(or a '.', which acts in the same way as ':'). \\nThese delimiting symbols act in the same way as in Maple: the second form suppresses the output of the entered\\nexpression. Long expressions can, because of these\\ndelimiters, be spread over many subsequent input lines. As in ordinary Python, any line\\nstarting with a ``\\\\#'' sign is considered to be a comment (even when\\nit appears within a multi-line expression). \"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"Lines containing mathematical expressions like the above always have to be terminated with either a ';' or a ':'\\n(or a '.', which acts in the same way as ':'). \\nThese delimiting symbols act in the same way as in Maple: the second form suppresses the output of the entered\\nexpression. Long expressions can, because of these\\ndelimiters, be spread over many subsequent input lines. As in ordinary Python, any line\\nstarting with a ``\\\\#'' sign is considered to be a comment (even when\\nit appears within a multi-line expression). \"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 9939973578136241108,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 218911297618970187,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"When entering maths as above (using the `\\\\verb|:=|' assignment operator) you do not need to indicate that\\nthe right-hand side is mathematics. There are situations, however, when you do need to give Cadabra a hint\\nthat what you type is maths, not Python, namely when you want to write maths without assigning it to\\na Python variable. In this case, you add dollar symbols, just as in LaTeX:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"When entering maths as above (using the `\\\\verb|:=|' assignment operator) you do not need to indicate that\\nthe right-hand side is mathematics. There are situations, however, when you do need to give Cadabra a hint\\nthat what you type is maths, not Python, namely when you want to write maths without assigning it to\\na Python variable. In this case, you add dollar symbols, just as in LaTeX:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 7824582319615562940,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 13761891641704533245,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 13355639495689827370,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"A + B + D\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}A+B+D\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"substitute($A + B + C$, $C -> D$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 8279289810202898585,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 13481872891682365066,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"As you can see, this uses an `inline' definition of a mathematical expression, without giving it a name.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"As you can see, this uses an `inline' definition of a mathematical expression, without giving it a name.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 11333938729236975341,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 5940099392058433169,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\subsection*{Algorithms acting on mathematical expressions}\\n\\nMathematical expressions are manipulated by using ordinary Python functions, which act on \\\\verb|cadabra2.Ex| objects. \\nYou have already seen an\\nexample of this above: when we wrote \\\\verb|substitute(...)|, this is a normal Python function, and it\\nacts on the \\\\verb|cadabra2.Ex| object which contains the mathematical expression $A+B+C$. It also gets\\npassed a second argument, which is the substitution rule, in the example above given by $C \\\\rightarrow D$.\\nIn both cases we have in-lined this expression using the LaTeX dollar notation. \\n\\nAn alternative way to write the above is to first define the two expressions, and then \\nfeed those (as Python objects) to the substitute algorithm. This looks as follows:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\subsection*{Algorithms acting on mathematical expressions}\\n\\nMathematical expressions are manipulated by using ordinary Python functions, which act on \\\\verb|cadabra2.Ex| objects. \\nYou have already seen an\\nexample of this above: when we wrote \\\\verb|substitute(...)|, this is a normal Python function, and it\\nacts on the \\\\verb|cadabra2.Ex| object which contains the mathematical expression $A+B+C$. It also gets\\npassed a second argument, which is the substitution rule, in the example above given by $C \\\\rightarrow D$.\\nIn both cases we have in-lined this expression using the LaTeX dollar notation. \\n\\nAn alternative way to write the above is to first define the two expressions, and then \\nfeed those (as Python objects) to the substitute algorithm. This looks as follows:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 17499779172771751965,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 13508214564903569542,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 9670337921159490001,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"A + B + C\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}A\\\\discretionary{}{}{}+B\\\\discretionary{}{}{}+C\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 15947743082636131503,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 15854571327032704552,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"C -> D\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}C \\\\rightarrow D\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 495408491245815016,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 14065503871271261469,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"A + B + D\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}A\\\\discretionary{}{}{}+B\\\\discretionary{}{}{}+D\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex   := A+B+C;\\nrule := C -> D;\\nsubstitute(ex, rule);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 7336055377022334854,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 7249506248577668324,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"Observe how we do not put dollar signs around the \\\\verb|ex| and \\\\verb|rule| arguments of the \\\\verb|substitute|\\nfunction call: these things are Python objects, and therefore that last line above is just a standard\\nPython function acting on Python objects. The only non-standard thing is the semi-colon at the end: it ensures\\nthat when we execute the cell, the result of that function call gets displayed.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"Observe how we do not put dollar signs around the \\\\verb|ex| and \\\\verb|rule| arguments of the \\\\verb|substitute|\\nfunction call: these things are Python objects, and therefore that last line above is just a standard\\nPython function acting on Python objects. The only non-standard thing is the semi-colon at the end: it ensures\\nthat when we execute the cell, the result of that function call gets displayed.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 14142924753738253554,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 12968643109865116887,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\subsection*{Function calls inside mathematical expressions}\\n\\nMany computer algebra systems do not make a distinction between the language used to write the mathematical\\nexpressions and the language used to write the actions and algorithms acting on them. If you prefer that\\nnotation, you can instruct Cadabra to allow in-line Python code in mathematical expressions, by using\\na particular kernel option:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\subsection*{Function calls inside mathematical expressions}\\n\\nMany computer algebra systems do not make a distinction between the language used to write the mathematical\\nexpressions and the language used to write the actions and algorithms acting on them. If you prefer that\\nnotation, you can instruct Cadabra to allow in-line Python code in mathematical expressions, by using\\na particular kernel option:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 14839438110559465856,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"__cdbkernel__.call_embedded_python_functions=True\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 13320774661377944897,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 3868658765204075874,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"You can now write the above example in an even more compact form, as\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"You can now write the above example in an even more compact form, as\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 9105043797411706950,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 17277331614704024525,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 1818314009831986771,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"A + B + D\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}A\\\\discretionary{}{}{}+B\\\\discretionary{}{}{}+D\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex:= substitute( A+B+C, C->D );\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 11677281993501439788,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 1718801022189349523,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"Note that the entire line after the '\\\\verb|:=|' operator is considered a mathematical expression, but Cadabra has \\nautomatically applied the \\\\verb|substitute| Python function on the two sub-expressions. The result is stored \\nin the Python object \\\\verb|ex|. \\n\\nNote that with this option turned on, \\\\emph{any} function with a name two or more characters long will be treated\\nas a Python function and Cadabra will attempt to run it. If your mathematical expressions contain such functions\\nas mathematics (not Python), then you will need to keep this functionality turned off.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"Note that the entire line after the '\\\\verb|:=|' operator is considered a mathematical expression, but Cadabra has \\nautomatically applied the \\\\verb|substitute| Python function on the two sub-expressions. The result is stored \\nin the Python object \\\\verb|ex|. \\n\\nNote that with this option turned on, \\\\emph{any} function with a name two or more characters long will be treated\\nas a Python function and Cadabra will attempt to run it. If your mathematical expressions contain such functions\\nas mathematics (not Python), then you will need to keep this functionality turned off.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 16834549477742454181,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"__cdbkernel__.call_embedded_python_functions=False\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 13066277311614345372,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 6858387052763340044,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\subsection*{Similarity and difference with LaTeX}\\n\\nInside mathematical expressions you can use most of the standard LaTeX notation. You can write mathematical\\nfunctions acting on variables, use special functions, and things like integrals. In some cases this deviates\\nslightly from what you are used to, mostly in order to remove ambiguities in the LaTeX notation, as the\\nexample below shows:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\subsection*{Similarity and difference with LaTeX}\\n\\nInside mathematical expressions you can use most of the standard LaTeX notation. You can write mathematical\\nfunctions acting on variables, use special functions, and things like integrals. In some cases this deviates\\nslightly from what you are used to, mostly in order to remove ambiguities in the LaTeX notation, as the\\nexample below shows:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 7769968518645043704,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 2026161499493210645,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 11841803707237998635,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"f(x) \\\\sin(x) \\\\int{\\\\cos(y)}{{y, 0, x}}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}f\\\\left(x\\\\right) \\\\sin{x} \\\\int_{0}^{x} \\\\cos{y}\\\\,\\\\,{\\\\rm d}y\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex:= f(x) \\\\sin(x) \\\\int{ \\\\cos(y) }{y, 0, x}; \"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 9760342780766748218,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 10359152349042096761,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"Cadabra always uses standard sub- and super-script notation for vector, spinor and other tensor indices, \"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"Cadabra always uses standard sub- and super-script notation for vector, spinor and other tensor indices, \"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 16884170432113302203,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9536246187304007274,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 6733921305923967445,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"R^{m} _{n p q} v^{p} v^{q}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}R^{m} _{n p q} v^{p} v^{q}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex:= R^m_{n p q} v^p v^q;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 4134420176076535633,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 16419948048587530591,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"Be careful that you will in general may need to be a little bit more generous in providing curly braces to \\ngroup these sub- and superscripts; sometimes it is best to be on the cautious side. Also be aware that \\nwhile Cadabra tries hard to figure out products of symbols even when you do not write a multiplication sign,\\nyou need to give it some hints by using spaces appropriately. If you write '\\\\verb|mn|' this is treated as\\none symbol, not the product of '\\\\verb|m|' and '\\\\verb|n|'. If you want the latter, put a space inbetween.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"Be careful that you will in general may need to be a little bit more generous in providing curly braces to \\ngroup these sub- and superscripts; sometimes it is best to be on the cautious side. Also be aware that \\nwhile Cadabra tries hard to figure out products of symbols even when you do not write a multiplication sign,\\nyou need to give it some hints by using spaces appropriately. If you write '\\\\verb|mn|' this is treated as\\none symbol, not the product of '\\\\verb|m|' and '\\\\verb|n|'. If you want the latter, put a space inbetween.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 961384143615778850,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"\"\n\t\t}\n\t],\n\t\"description\": \"Cadabra JSON notebook format\",\n\t\"version\": 1.0\n}\n"
  },
  {
    "path": "examples/kaluza_klein.cnb",
    "content": "{\n\t\"cells\" : \n\t[\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\section*{The Kaluza-Klein example from section 2.5 of hep-th/0701238}\\n\\nThis example shows how to use \\\\algo{split_index} in a somewhat more complicated setting. \\nWe first declare the indices that we will use.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\section*{The Kaluza-Klein example from section 2.5 of hep-th/0701238}\\n\\nThis example shows how to use \\\\algo{split_index} in a somewhat more complicated setting. \\nWe first declare the indices that we will use.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Indices(position=independent) to~}\\\\left[\\\\mu,~\\\\discretionary{}{}{} \\\\nu,~\\\\discretionary{}{}{} \\\\rho,~\\\\discretionary{}{}{} \\\\sigma,~\\\\discretionary{}{}{} \\\\kappa,~\\\\discretionary{}{}{} \\\\lambda,~\\\\discretionary{}{}{} \\\\eta,~\\\\discretionary{}{}{} \\\\chi\\\\#\\\\right].\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Indices(position=independent) to~}\\\\left[m,~\\\\discretionary{}{}{} n,~\\\\discretionary{}{}{} p,~\\\\discretionary{}{}{} q,~\\\\discretionary{}{}{} r,~\\\\discretionary{}{}{} s,~\\\\discretionary{}{}{} t,~\\\\discretionary{}{}{} u,~\\\\discretionary{}{}{} v,~\\\\discretionary{}{}{} w,~\\\\discretionary{}{}{} x,~\\\\discretionary{}{}{} y,~\\\\discretionary{}{}{} z,~\\\\discretionary{}{}{} m\\\\#\\\\right].\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"{\\\\mu,\\\\nu,\\\\rho,\\\\sigma,\\\\kappa,\\\\lambda,\\\\eta,\\\\chi#}::Indices(full, position=independent);\\n{m,n,p,q,r,s,t,u,v,w,x,y,z,m#}::Indices(subspace, position=independent, parent=full);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"Note the appearance of \\\\verb|parent=full|. This indicates that the indices in the second set\\nspan a subspace of the indices in the first set. Also note that we have declared the indices\\nas \\\\verb|position=independent|, to prevent Cadabra from automatically raising or lowering them \\nwhen canonicalising (as this does not really help us here).\\n\\nThe remaining declarations are standard,\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"Note the appearance of \\\\verb|parent=full|. This indicates that the indices in the second set\\nspan a subspace of the indices in the first set. Also note that we have declared the indices\\nas \\\\verb|position=independent|, to prevent Cadabra from automatically raising or lowering them \\nwhen canonicalising (as this does not really help us here).\\n\\nThe remaining declarations are standard,\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\\\\partial{#}::PartialDerivative.\\ng_{\\\\mu\\\\nu}::Metric.\\ng^{\\\\mu\\\\nu}::InverseMetric.\\ng_{\\\\mu? \\\\nu?}::Symmetric.\\ng^{\\\\mu? \\\\nu?}::Symmetric.\\nh_{m n}::Metric.\\nh^{m n}::InverseMetric.\\n\\\\delta^{\\\\mu?}_{\\\\nu?}::KroneckerDelta.\\n\\\\delta_{\\\\mu?}^{\\\\nu?}::KroneckerDelta.\\nF_{m n}::AntiSymmetric.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"We will want to expand the Riemann tensor in terms of the metric. The following two substitution\\nrules do the conversion from Riemann tensor to Christoffel symbol and from Christoffel symbol\\nto metric (a library with common substitution rules like these is in preparation).\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"We will want to expand the Riemann tensor in terms of the metric. The following two substitution\\nrules do the conversion from Riemann tensor to Christoffel symbol and from Christoffel symbol\\nto metric (a library with common substitution rules like these is in preparation).\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}R^{\\\\lambda?}\\\\,_{\\\\mu? \\\\nu? \\\\kappa?} \\\\rightarrow -\\\\partial_{\\\\kappa?}{\\\\Gamma^{\\\\lambda?}\\\\,_{\\\\mu? \\\\nu?}}+\\\\partial_{\\\\nu?}{\\\\Gamma^{\\\\lambda?}\\\\,_{\\\\mu? \\\\kappa?}}-\\\\Gamma^{\\\\eta}\\\\,_{\\\\mu? \\\\nu?} \\\\Gamma^{\\\\lambda?}\\\\,_{\\\\kappa? \\\\eta}+\\\\Gamma^{\\\\eta}\\\\,_{\\\\mu? \\\\kappa?} \\\\Gamma^{\\\\lambda?}\\\\,_{\\\\nu? \\\\eta}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\Gamma^{\\\\lambda?}\\\\,_{\\\\mu? \\\\nu?} \\\\rightarrow \\\\frac{1}{2}g^{\\\\lambda? \\\\kappa} \\\\left(\\\\partial_{\\\\nu?}{g_{\\\\kappa \\\\mu?}}+\\\\partial_{\\\\mu?}{g_{\\\\kappa \\\\nu?}}-\\\\partial_{\\\\kappa}{g_{\\\\mu? \\\\nu?}}\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"RtoG:= R^{\\\\lambda?}_{\\\\mu?\\\\nu?\\\\kappa?} -> \\n - \\\\partial_{\\\\kappa?}{ \\\\Gamma^{\\\\lambda?}_{\\\\mu?\\\\nu?} }\\n + \\\\partial_{\\\\nu?}{ \\\\Gamma^{\\\\lambda?}_{\\\\mu?\\\\kappa?} }\\n - \\\\Gamma^{\\\\eta}_{\\\\mu?\\\\nu?} \\\\Gamma^{\\\\lambda?}_{\\\\kappa?\\\\eta}\\n + \\\\Gamma^{\\\\eta}_{\\\\mu?\\\\kappa?} \\\\Gamma^{\\\\lambda?}_{\\\\nu?\\\\eta};\\n\\nGtog:= \\\\Gamma^{\\\\lambda?}_{\\\\mu?\\\\nu?} ->\\n  (1/2) * g^{\\\\lambda?\\\\kappa} ( \\n        \\\\partial_{\\\\nu?}{ g_{\\\\kappa\\\\mu?} } + \\\\partial_{\\\\mu?}{ g_{\\\\kappa\\\\nu?} } - \\\\partial_{\\\\kappa}{ g_{\\\\mu?\\\\nu?} } );\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"In this example we want to compute the Kaluza-Klein reduction of the $R_{m 4 n 4}$ component of the\\nRiemann tensor. So we enter this component and do the substitution that takes the Riemann tensor\\nto metrics. After each substitution, we distribute\\nproducts over sums. We also apply the product rule to distribute derivatives over factors in a\\nproduct.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"In this example we want to compute the Kaluza-Klein reduction of the $R_{m 4 n 4}$ component of the\\nRiemann tensor. So we enter this component and do the substitution that takes the Riemann tensor\\nto metrics. After each substitution, we distribute\\nproducts over sums. We also apply the product rule to distribute derivatives over factors in a\\nproduct.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}g_{m1 m} R^{m1}\\\\,_{4 n 4}+g_{4 m} R^{4}\\\\,_{4 n 4}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"todo:= g_{m1 m} R^{m1}_{4 n 4} + g_{4 m} R^{4}_{4 n 4};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{} - \\\\frac{1}{2}\\\\partial_{n}{g_{\\\\kappa 4}} \\\\partial_{4}{g^{m1 \\\\kappa}} g_{m1 m} - \\\\frac{1}{2}\\\\partial_{4 n}{g_{\\\\kappa 4}} g_{m1 m} g^{m1 \\\\kappa} - \\\\frac{1}{2}\\\\partial_{4}{g^{m1 \\\\kappa}} \\\\partial_{4}{g_{\\\\kappa n}} g_{m1 m} - \\\\frac{1}{2}\\\\partial_{4 4}{g_{\\\\kappa n}} g_{m1 m} g^{m1 \\\\kappa}+\\\\frac{1}{2}\\\\partial_{\\\\kappa}{g_{4 n}} \\\\partial_{4}{g^{m1 \\\\kappa}} g_{m1 m}+\\\\frac{1}{2}\\\\partial_{4 \\\\kappa}{g_{4 n}} g_{m1 m} g^{m1 \\\\kappa}+\\\\partial_{n}{g^{m1 \\\\kappa}} \\\\partial_{4}{g_{\\\\kappa 4}} g_{m1 m}+\\\\partial_{n 4}{g_{\\\\kappa 4}} g_{m1 m} g^{m1 \\\\kappa} - \\\\frac{1}{2}\\\\partial_{\\\\kappa}{g_{4 4}} \\\\partial_{n}{g^{m1 \\\\kappa}} g_{m1 m} - \\\\frac{1}{2}\\\\partial_{n \\\\kappa}{g_{4 4}} g_{m1 m} g^{m1 \\\\kappa} - \\\\frac{1}{4}\\\\partial_{\\\\eta}{g_{\\\\mu 4}} \\\\partial_{n}{g_{\\\\kappa 4}} g_{m1 m} g^{\\\\eta \\\\kappa} g^{m1 \\\\mu} - \\\\frac{1}{4}\\\\partial_{n}{g_{\\\\kappa 4}} \\\\partial_{4}{g_{\\\\mu \\\\eta}} g_{m1 m} g^{\\\\eta \\\\kappa} g^{m1 \\\\mu}+\\\\frac{1}{4}\\\\partial_{\\\\mu}{g_{4 \\\\eta}} \\\\partial_{n}{g_{\\\\kappa 4}} g_{m1 m} g^{\\\\eta \\\\kappa} g^{m1 \\\\mu} - \\\\frac{1}{4}\\\\partial_{\\\\eta}{g_{\\\\mu 4}} \\\\partial_{4}{g_{\\\\kappa n}} g_{m1 m} g^{\\\\eta \\\\kappa} g^{m1 \\\\mu} - \\\\frac{1}{4}\\\\partial_{4}{g_{\\\\mu \\\\eta}} \\\\partial_{4}{g_{\\\\kappa n}} g_{m1 m} g^{\\\\eta \\\\kappa} g^{m1 \\\\mu}+\\\\frac{1}{4}\\\\partial_{\\\\mu}{g_{4 \\\\eta}} \\\\partial_{4}{g_{\\\\kappa n}} g_{m1 m} g^{\\\\eta \\\\kappa} g^{m1 \\\\mu}+\\\\frac{1}{4}\\\\partial_{\\\\eta}{g_{\\\\mu 4}} \\\\partial_{\\\\kappa}{g_{4 n}} g_{m1 m} g^{\\\\eta \\\\kappa} g^{m1 \\\\mu}+\\\\frac{1}{4}\\\\partial_{\\\\kappa}{g_{4 n}} \\\\partial_{4}{g_{\\\\mu \\\\eta}} g_{m1 m} g^{\\\\eta \\\\kappa} g^{m1 \\\\mu} - \\\\frac{1}{4}\\\\partial_{\\\\mu}{g_{4 \\\\eta}} \\\\partial_{\\\\kappa}{g_{4 n}} g_{m1 m} g^{\\\\eta \\\\kappa} g^{m1 \\\\mu}%\\n+\\\\frac{1}{2}\\\\partial_{\\\\eta}{g_{\\\\mu n}} \\\\partial_{4}{g_{\\\\kappa 4}} g_{m1 m} g^{\\\\eta \\\\kappa} g^{m1 \\\\mu}+\\\\frac{1}{2}\\\\partial_{n}{g_{\\\\mu \\\\eta}} \\\\partial_{4}{g_{\\\\kappa 4}} g_{m1 m} g^{\\\\eta \\\\kappa} g^{m1 \\\\mu} - \\\\frac{1}{2}\\\\partial_{\\\\mu}{g_{n \\\\eta}} \\\\partial_{4}{g_{\\\\kappa 4}} g_{m1 m} g^{\\\\eta \\\\kappa} g^{m1 \\\\mu} - \\\\frac{1}{4}\\\\partial_{\\\\eta}{g_{\\\\mu n}} \\\\partial_{\\\\kappa}{g_{4 4}} g_{m1 m} g^{\\\\eta \\\\kappa} g^{m1 \\\\mu} - \\\\frac{1}{4}\\\\partial_{\\\\kappa}{g_{4 4}} \\\\partial_{n}{g_{\\\\mu \\\\eta}} g_{m1 m} g^{\\\\eta \\\\kappa} g^{m1 \\\\mu}+\\\\frac{1}{4}\\\\partial_{\\\\mu}{g_{n \\\\eta}} \\\\partial_{\\\\kappa}{g_{4 4}} g_{m1 m} g^{\\\\eta \\\\kappa} g^{m1 \\\\mu} - \\\\frac{1}{2}\\\\partial_{n}{g_{\\\\kappa 4}} \\\\partial_{4}{g^{4 \\\\kappa}} g_{4 m} - \\\\frac{1}{2}\\\\partial_{4 n}{g_{\\\\kappa 4}} g_{4 m} g^{4 \\\\kappa} - \\\\frac{1}{2}\\\\partial_{4}{g^{4 \\\\kappa}} \\\\partial_{4}{g_{\\\\kappa n}} g_{4 m} - \\\\frac{1}{2}\\\\partial_{4 4}{g_{\\\\kappa n}} g_{4 m} g^{4 \\\\kappa}+\\\\frac{1}{2}\\\\partial_{\\\\kappa}{g_{4 n}} \\\\partial_{4}{g^{4 \\\\kappa}} g_{4 m}+\\\\frac{1}{2}\\\\partial_{4 \\\\kappa}{g_{4 n}} g_{4 m} g^{4 \\\\kappa}+\\\\partial_{n}{g^{4 \\\\kappa}} \\\\partial_{4}{g_{\\\\kappa 4}} g_{4 m}+\\\\partial_{n 4}{g_{\\\\kappa 4}} g_{4 m} g^{4 \\\\kappa} - \\\\frac{1}{2}\\\\partial_{\\\\kappa}{g_{4 4}} \\\\partial_{n}{g^{4 \\\\kappa}} g_{4 m} - \\\\frac{1}{2}\\\\partial_{n \\\\kappa}{g_{4 4}} g_{4 m} g^{4 \\\\kappa} - \\\\frac{1}{4}\\\\partial_{\\\\eta}{g_{\\\\mu 4}} \\\\partial_{n}{g_{\\\\kappa 4}} g_{4 m} g^{\\\\eta \\\\kappa} g^{4 \\\\mu} - \\\\frac{1}{4}\\\\partial_{n}{g_{\\\\kappa 4}} \\\\partial_{4}{g_{\\\\mu \\\\eta}} g_{4 m} g^{\\\\eta \\\\kappa} g^{4 \\\\mu}+\\\\frac{1}{4}\\\\partial_{\\\\mu}{g_{4 \\\\eta}} \\\\partial_{n}{g_{\\\\kappa 4}} g_{4 m} g^{\\\\eta \\\\kappa} g^{4 \\\\mu} - \\\\frac{1}{4}\\\\partial_{\\\\eta}{g_{\\\\mu 4}} \\\\partial_{4}{g_{\\\\kappa n}} g_{4 m} g^{\\\\eta \\\\kappa} g^{4 \\\\mu}%\\n - \\\\frac{1}{4}\\\\partial_{4}{g_{\\\\mu \\\\eta}} \\\\partial_{4}{g_{\\\\kappa n}} g_{4 m} g^{\\\\eta \\\\kappa} g^{4 \\\\mu}+\\\\frac{1}{4}\\\\partial_{\\\\mu}{g_{4 \\\\eta}} \\\\partial_{4}{g_{\\\\kappa n}} g_{4 m} g^{\\\\eta \\\\kappa} g^{4 \\\\mu}+\\\\frac{1}{4}\\\\partial_{\\\\eta}{g_{\\\\mu 4}} \\\\partial_{\\\\kappa}{g_{4 n}} g_{4 m} g^{\\\\eta \\\\kappa} g^{4 \\\\mu}+\\\\frac{1}{4}\\\\partial_{\\\\kappa}{g_{4 n}} \\\\partial_{4}{g_{\\\\mu \\\\eta}} g_{4 m} g^{\\\\eta \\\\kappa} g^{4 \\\\mu} - \\\\frac{1}{4}\\\\partial_{\\\\mu}{g_{4 \\\\eta}} \\\\partial_{\\\\kappa}{g_{4 n}} g_{4 m} g^{\\\\eta \\\\kappa} g^{4 \\\\mu}+\\\\frac{1}{2}\\\\partial_{\\\\eta}{g_{\\\\mu n}} \\\\partial_{4}{g_{\\\\kappa 4}} g_{4 m} g^{\\\\eta \\\\kappa} g^{4 \\\\mu}+\\\\frac{1}{2}\\\\partial_{n}{g_{\\\\mu \\\\eta}} \\\\partial_{4}{g_{\\\\kappa 4}} g_{4 m} g^{\\\\eta \\\\kappa} g^{4 \\\\mu} - \\\\frac{1}{2}\\\\partial_{\\\\mu}{g_{n \\\\eta}} \\\\partial_{4}{g_{\\\\kappa 4}} g_{4 m} g^{\\\\eta \\\\kappa} g^{4 \\\\mu} - \\\\frac{1}{4}\\\\partial_{\\\\eta}{g_{\\\\mu n}} \\\\partial_{\\\\kappa}{g_{4 4}} g_{4 m} g^{\\\\eta \\\\kappa} g^{4 \\\\mu} - \\\\frac{1}{4}\\\\partial_{\\\\kappa}{g_{4 4}} \\\\partial_{n}{g_{\\\\mu \\\\eta}} g_{4 m} g^{\\\\eta \\\\kappa} g^{4 \\\\mu}+\\\\frac{1}{4}\\\\partial_{\\\\mu}{g_{n \\\\eta}} \\\\partial_{\\\\kappa}{g_{4 4}} g_{4 m} g^{\\\\eta \\\\kappa} g^{4 \\\\mu}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"substitute(_, RtoG)\\nsubstitute(_, Gtog)\\ndistribute(_)\\nproduct_rule(_)\\ndistribute(_)\\nsort_product(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"We then split the greek indices into roman indices and the 4-th direction. Notice the use\\nof \\\\verb|repeat=True| which will keep doing this substitution until all greek indices\\nhave been split. After that we again have to set all derivatives in the 4-th direction to zero.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"We then split the greek indices into roman indices and the 4-th direction. Notice the use\\nof \\\\verb|repeat=True| which will keep doing this substitution until all greek indices\\nhave been split. After that we again have to set all derivatives in the 4-th direction to zero.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{} - \\\\frac{1}{2}\\\\partial_{m1}{g_{4 4}} \\\\partial_{n}{g^{m1 p}} g_{m p} - \\\\frac{1}{2}\\\\partial_{n m1}{g_{4 4}} g_{m p} g^{m1 p} - \\\\frac{1}{4}\\\\partial_{n}{g_{4 m1}} \\\\partial_{p}{g_{4 q}} g_{m r} g^{m1 p} g^{q r} - \\\\frac{1}{2}\\\\partial_{m1}{g_{4 4}} \\\\partial_{n}{g_{4 p}} g_{m q} g^{m1 p} g^{4 q} - \\\\frac{1}{4}\\\\partial_{m1}{g_{4 p}} \\\\partial_{n}{g_{4 4}} g_{m q} g^{4 m1} g^{p q} - \\\\frac{1}{2}\\\\partial_{n}{g_{4 4}} \\\\partial_{m1}{g_{4 4}} g_{m p} g^{4 m1} g^{4 p}+\\\\frac{1}{4}\\\\partial_{m1}{g_{4 p}} \\\\partial_{n}{g_{4 q}} g_{m r} g^{m1 r} g^{p q}+\\\\frac{1}{4}\\\\partial_{m1}{g_{4 p}} \\\\partial_{n}{g_{4 4}} g_{m q} g^{4 p} g^{m1 q}+\\\\frac{1}{4}\\\\partial_{m1}{g_{4 4}} \\\\partial_{n}{g_{4 p}} g_{m q} g^{4 p} g^{m1 q}+\\\\frac{1}{4}\\\\partial_{n}{g_{4 4}} \\\\partial_{m1}{g_{4 4}} g_{m p} g^{4 4} g^{m1 p}+\\\\frac{1}{4}\\\\partial_{m1}{g_{4 p}} \\\\partial_{q}{g_{n 4}} g_{m r} g^{m1 q} g^{p r}+\\\\frac{1}{4}\\\\partial_{m1}{g_{4 4}} \\\\partial_{p}{g_{n 4}} g_{m q} g^{m1 p} g^{4 q} - \\\\frac{1}{4}\\\\partial_{m1}{g_{n 4}} \\\\partial_{p}{g_{4 q}} g_{m r} g^{m1 q} g^{p r} - \\\\frac{1}{4}\\\\partial_{m1}{g_{4 4}} \\\\partial_{p}{g_{n 4}} g_{m q} g^{4 p} g^{m1 q} - \\\\frac{1}{4}\\\\partial_{m1}{g_{n p}} \\\\partial_{q}{g_{4 4}} g_{m r} g^{m1 q} g^{p r} - \\\\frac{1}{4}\\\\partial_{m1}{g_{n 4}} \\\\partial_{p}{g_{4 4}} g_{m q} g^{m1 p} g^{4 q} - \\\\frac{1}{4}\\\\partial_{m1}{g_{4 4}} \\\\partial_{n}{g_{p q}} g_{m r} g^{m1 p} g^{q r} - \\\\frac{1}{4}\\\\partial_{m1}{g_{4 4}} \\\\partial_{n}{g_{4 p}} g_{m q} g^{4 m1} g^{p q}+\\\\frac{1}{4}\\\\partial_{m1}{g_{n p}} \\\\partial_{q}{g_{4 4}} g_{m r} g^{m1 r} g^{p q}%\\n+\\\\frac{1}{4}\\\\partial_{m1}{g_{n 4}} \\\\partial_{p}{g_{4 4}} g_{m q} g^{4 p} g^{m1 q} - \\\\frac{1}{2}\\\\partial_{p}{g_{4 4}} \\\\partial_{n}{g^{4 p}} g_{m 4} - \\\\frac{1}{2}\\\\partial_{n p}{g_{4 4}} g_{m 4} g^{4 p} - \\\\frac{1}{4}\\\\partial_{n}{g_{4 p}} \\\\partial_{q}{g_{4 r}} g_{m 4} g^{p q} g^{4 r} - \\\\frac{1}{2}\\\\partial_{p}{g_{4 4}} \\\\partial_{n}{g_{4 q}} g_{m 4} g^{p q} g^{4 4} - \\\\frac{1}{4}\\\\partial_{p}{g_{4 q}} \\\\partial_{n}{g_{4 4}} g_{m 4} g^{4 p} g^{4 q} - \\\\frac{1}{2}\\\\partial_{n}{g_{4 4}} \\\\partial_{p}{g_{4 4}} g_{m 4} g^{4 p} g^{4 4}+\\\\frac{1}{4}\\\\partial_{p}{g_{4 q}} \\\\partial_{n}{g_{4 r}} g_{m 4} g^{q r} g^{4 p}+\\\\frac{1}{4}\\\\partial_{p}{g_{4 q}} \\\\partial_{n}{g_{4 4}} g_{m 4} g^{4 q} g^{4 p}+\\\\frac{1}{4}\\\\partial_{n}{g_{4 4}} \\\\partial_{p}{g_{4 4}} g_{m 4} g^{4 4} g^{4 p}+\\\\frac{1}{4}\\\\partial_{p}{g_{4 q}} \\\\partial_{r}{g_{n 4}} g_{m 4} g^{p r} g^{4 q}+\\\\frac{1}{4}\\\\partial_{p}{g_{4 4}} \\\\partial_{q}{g_{n 4}} g_{m 4} g^{p q} g^{4 4} - \\\\frac{1}{4}\\\\partial_{p}{g_{n 4}} \\\\partial_{q}{g_{4 r}} g_{m 4} g^{p r} g^{4 q} - \\\\frac{1}{4}\\\\partial_{p}{g_{4 4}} \\\\partial_{q}{g_{n 4}} g_{m 4} g^{4 p} g^{4 q} - \\\\frac{1}{4}\\\\partial_{p}{g_{n q}} \\\\partial_{r}{g_{4 4}} g_{m 4} g^{p r} g^{4 q} - \\\\frac{1}{4}\\\\partial_{p}{g_{n 4}} \\\\partial_{q}{g_{4 4}} g_{m 4} g^{p q} g^{4 4} - \\\\frac{1}{4}\\\\partial_{p}{g_{4 4}} \\\\partial_{n}{g_{q r}} g_{m 4} g^{p q} g^{4 r}+\\\\frac{1}{4}\\\\partial_{p}{g_{n q}} \\\\partial_{r}{g_{4 4}} g_{m 4} g^{q r} g^{4 p}+\\\\frac{1}{4}\\\\partial_{p}{g_{n 4}} \\\\partial_{q}{g_{4 4}} g_{m 4} g^{4 p} g^{4 q}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"split_index(_, $\\\\mu, m1, 4$, repeat=True)\\nsubstitute(_, $\\\\partial_{4}{A??} -> 0$, repeat=True)\\nsubstitute(_, $\\\\partial_{4 m?}{A??} -> 0$, repeat=True)\\nsubstitute(_, $\\\\partial_{m? 4}{A??} -> 0$, repeat=True)\\ncanonicalise(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"Now comes the ansatz of the metric in terms of the Kaluza-Klein gauge field $A_\\\\mu$ and the scalar $\\\\phi$. \\nWe substitute this with the lines below. The output is not particularly enlightening...\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"Now comes the ansatz of the metric in terms of the Kaluza-Klein gauge field $A_\\\\mu$ and the scalar $\\\\phi$. \\nWe substitute this with the lines below. The output is not particularly enlightening...\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{} - \\\\frac{1}{2}\\\\partial_{m1}{\\\\phi} \\\\partial_{n}\\\\left(\\\\phi h^{m1 p}\\\\right) \\\\left({\\\\phi}^{-1} h_{m p}+\\\\phi A_{m} A_{p}\\\\right) - \\\\frac{1}{2}\\\\partial_{n m1}{\\\\phi} \\\\left({\\\\phi}^{-1} h_{m p}+\\\\phi A_{m} A_{p}\\\\right) \\\\phi h^{m1 p} - \\\\frac{1}{4}\\\\partial_{n}\\\\left(\\\\phi A_{m1}\\\\right) \\\\partial_{p}\\\\left(\\\\phi A_{q}\\\\right) \\\\left({\\\\phi}^{-1} h_{m r}+\\\\phi A_{m} A_{r}\\\\right) \\\\phi h^{m1 p} \\\\phi h^{q r}+\\\\frac{1}{2}\\\\partial_{m1}{\\\\phi} \\\\partial_{n}\\\\left(\\\\phi A_{p}\\\\right) \\\\left({\\\\phi}^{-1} h_{m q}+\\\\phi A_{m} A_{q}\\\\right) \\\\phi h^{m1 p} \\\\phi h^{q r} A_{r}+\\\\frac{1}{4}\\\\partial_{m1}\\\\left(\\\\phi A_{p}\\\\right) \\\\partial_{n}{\\\\phi} \\\\left({\\\\phi}^{-1} h_{m q}+\\\\phi A_{m} A_{q}\\\\right) \\\\phi h^{m1 r} A_{r} \\\\phi h^{p q} - \\\\frac{1}{2}\\\\partial_{n}{\\\\phi} \\\\partial_{m1}{\\\\phi} \\\\left({\\\\phi}^{-1} h_{m p}+\\\\phi A_{m} A_{p}\\\\right) \\\\phi h^{m1 q} A_{q} \\\\phi h^{p r} A_{r}+\\\\frac{1}{4}\\\\partial_{m1}\\\\left(\\\\phi A_{p}\\\\right) \\\\partial_{n}\\\\left(\\\\phi A_{q}\\\\right) \\\\left({\\\\phi}^{-1} h_{m r}+\\\\phi A_{m} A_{r}\\\\right) \\\\phi h^{m1 r} \\\\phi h^{p q} - \\\\frac{1}{4}\\\\partial_{m1}\\\\left(\\\\phi A_{p}\\\\right) \\\\partial_{n}{\\\\phi} \\\\left({\\\\phi}^{-1} h_{m q}+\\\\phi A_{m} A_{q}\\\\right) \\\\phi h^{p r} A_{r} \\\\phi h^{m1 q} - \\\\frac{1}{4}\\\\partial_{m1}{\\\\phi} \\\\partial_{n}\\\\left(\\\\phi A_{p}\\\\right) \\\\left({\\\\phi}^{-1} h_{m q}+\\\\phi A_{m} A_{q}\\\\right) \\\\phi h^{p r} A_{r} \\\\phi h^{m1 q}+\\\\frac{1}{4}\\\\partial_{n}{\\\\phi} \\\\partial_{m1}{\\\\phi} \\\\left({\\\\phi}^{-1} h_{m p}+\\\\phi A_{m} A_{p}\\\\right) \\\\left({\\\\phi}^{-1}+\\\\phi A_{q} h^{q r} A_{r}\\\\right) \\\\phi h^{m1 p}+\\\\frac{1}{4}\\\\partial_{m1}\\\\left(\\\\phi A_{p}\\\\right) \\\\partial_{q}\\\\left(\\\\phi A_{n}\\\\right) \\\\left({\\\\phi}^{-1} h_{m r}+\\\\phi A_{m} A_{r}\\\\right) \\\\phi h^{m1 q} \\\\phi h^{p r} - \\\\frac{1}{4}\\\\partial_{m1}{\\\\phi} \\\\partial_{p}\\\\left(\\\\phi A_{n}\\\\right) \\\\left({\\\\phi}^{-1} h_{m q}+\\\\phi A_{m} A_{q}\\\\right) \\\\phi h^{m1 p} \\\\phi h^{q r} A_{r} - \\\\frac{1}{4}\\\\partial_{m1}\\\\left(\\\\phi A_{n}\\\\right) \\\\partial_{p}\\\\left(\\\\phi A_{q}\\\\right) \\\\left({\\\\phi}^{-1} h_{m r}+\\\\phi A_{m} A_{r}\\\\right) \\\\phi h^{m1 q} \\\\phi h^{p r}+\\\\frac{1}{4}\\\\partial_{m1}{\\\\phi} \\\\partial_{p}\\\\left(\\\\phi A_{n}\\\\right) \\\\left({\\\\phi}^{-1} h_{m q}+\\\\phi A_{m} A_{q}\\\\right) \\\\phi h^{p r} A_{r} \\\\phi h^{m1 q} - \\\\frac{1}{4}\\\\partial_{m1}\\\\left({\\\\phi}^{-1} h_{n p}+\\\\phi A_{n} A_{p}\\\\right) \\\\partial_{q}{\\\\phi} \\\\left({\\\\phi}^{-1} h_{m r}+\\\\phi A_{m} A_{r}\\\\right) \\\\phi h^{m1 q} \\\\phi h^{p r}+\\\\frac{1}{4}\\\\partial_{m1}\\\\left(\\\\phi A_{n}\\\\right) \\\\partial_{p}{\\\\phi} \\\\left({\\\\phi}^{-1} h_{m q}+\\\\phi A_{m} A_{q}\\\\right) \\\\phi h^{m1 p} \\\\phi h^{q r} A_{r} - \\\\frac{1}{4}\\\\partial_{m1}{\\\\phi} \\\\partial_{n}\\\\left({\\\\phi}^{-1} h_{p q}+\\\\phi A_{p} A_{q}\\\\right) \\\\left({\\\\phi}^{-1} h_{m r}+\\\\phi A_{m} A_{r}\\\\right) \\\\phi h^{m1 p} \\\\phi h^{q r}+\\\\frac{1}{4}\\\\partial_{m1}{\\\\phi} \\\\partial_{n}\\\\left(\\\\phi A_{p}\\\\right) \\\\left({\\\\phi}^{-1} h_{m q}+\\\\phi A_{m} A_{q}\\\\right) \\\\phi h^{m1 r} A_{r} \\\\phi h^{p q}+\\\\frac{1}{4}\\\\partial_{m1}\\\\left({\\\\phi}^{-1} h_{n p}+\\\\phi A_{n} A_{p}\\\\right) \\\\partial_{q}{\\\\phi} \\\\left({\\\\phi}^{-1} h_{m r}+\\\\phi A_{m} A_{r}\\\\right) \\\\phi h^{m1 r} \\\\phi h^{p q}%\\n - \\\\frac{1}{4}\\\\partial_{m1}\\\\left(\\\\phi A_{n}\\\\right) \\\\partial_{p}{\\\\phi} \\\\left({\\\\phi}^{-1} h_{m q}+\\\\phi A_{m} A_{q}\\\\right) \\\\phi h^{p r} A_{r} \\\\phi h^{m1 q}+\\\\frac{1}{2}\\\\partial_{p}{\\\\phi} \\\\partial_{n}\\\\left(\\\\phi h^{p q} A_{q}\\\\right) \\\\phi A_{m}+\\\\frac{1}{2}\\\\partial_{n p}{\\\\phi} \\\\phi A_{m} \\\\phi h^{p q} A_{q}+\\\\frac{1}{4}\\\\partial_{n}\\\\left(\\\\phi A_{p}\\\\right) \\\\partial_{q}\\\\left(\\\\phi A_{r}\\\\right) \\\\phi A_{m} \\\\phi h^{p q} \\\\phi h^{r s} A_{s} - \\\\frac{1}{2}\\\\partial_{p}{\\\\phi} \\\\partial_{n}\\\\left(\\\\phi A_{q}\\\\right) \\\\phi A_{m} \\\\phi h^{p q} \\\\left({\\\\phi}^{-1}+\\\\phi A_{r} h^{r s} A_{s}\\\\right) - \\\\frac{1}{4}\\\\partial_{p}\\\\left(\\\\phi A_{q}\\\\right) \\\\partial_{n}{\\\\phi} \\\\phi A_{m} \\\\phi h^{p r} A_{r} \\\\phi h^{q s} A_{s}+\\\\frac{1}{2}\\\\partial_{n}{\\\\phi} \\\\partial_{p}{\\\\phi} \\\\phi A_{m} \\\\phi h^{p s} A_{s} \\\\left({\\\\phi}^{-1}+\\\\phi A_{q} h^{q r} A_{r}\\\\right) - \\\\frac{1}{4}\\\\partial_{p}\\\\left(\\\\phi A_{q}\\\\right) \\\\partial_{n}\\\\left(\\\\phi A_{r}\\\\right) \\\\phi A_{m} \\\\phi h^{q r} \\\\phi h^{p s} A_{s}+\\\\frac{1}{4}\\\\partial_{p}\\\\left(\\\\phi A_{q}\\\\right) \\\\partial_{n}{\\\\phi} \\\\phi A_{m} \\\\phi h^{q r} A_{r} \\\\phi h^{p s} A_{s} - \\\\frac{1}{4}\\\\partial_{n}{\\\\phi} \\\\partial_{p}{\\\\phi} \\\\phi A_{m} \\\\left({\\\\phi}^{-1}+\\\\phi A_{q} h^{q r} A_{r}\\\\right) \\\\phi h^{p s} A_{s} - \\\\frac{1}{4}\\\\partial_{p}\\\\left(\\\\phi A_{q}\\\\right) \\\\partial_{r}\\\\left(\\\\phi A_{n}\\\\right) \\\\phi A_{m} \\\\phi h^{p r} \\\\phi h^{q s} A_{s}+\\\\frac{1}{4}\\\\partial_{p}{\\\\phi} \\\\partial_{q}\\\\left(\\\\phi A_{n}\\\\right) \\\\phi A_{m} \\\\phi h^{p q} \\\\left({\\\\phi}^{-1}+\\\\phi A_{r} h^{r s} A_{s}\\\\right)+\\\\frac{1}{4}\\\\partial_{p}\\\\left(\\\\phi A_{n}\\\\right) \\\\partial_{q}\\\\left(\\\\phi A_{r}\\\\right) \\\\phi A_{m} \\\\phi h^{p r} \\\\phi h^{q s} A_{s} - \\\\frac{1}{4}\\\\partial_{p}{\\\\phi} \\\\partial_{q}\\\\left(\\\\phi A_{n}\\\\right) \\\\phi A_{m} \\\\phi h^{p r} A_{r} \\\\phi h^{q s} A_{s}+\\\\frac{1}{4}\\\\partial_{p}\\\\left({\\\\phi}^{-1} h_{n q}+\\\\phi A_{n} A_{q}\\\\right) \\\\partial_{r}{\\\\phi} \\\\phi A_{m} \\\\phi h^{p r} \\\\phi h^{q s} A_{s} - \\\\frac{1}{4}\\\\partial_{p}\\\\left(\\\\phi A_{n}\\\\right) \\\\partial_{q}{\\\\phi} \\\\phi A_{m} \\\\phi h^{p q} \\\\left({\\\\phi}^{-1}+\\\\phi A_{r} h^{r s} A_{s}\\\\right)+\\\\frac{1}{4}\\\\partial_{p}{\\\\phi} \\\\partial_{n}\\\\left({\\\\phi}^{-1} h_{q r}+\\\\phi A_{q} A_{r}\\\\right) \\\\phi A_{m} \\\\phi h^{p q} \\\\phi h^{r s} A_{s} - \\\\frac{1}{4}\\\\partial_{p}\\\\left({\\\\phi}^{-1} h_{n q}+\\\\phi A_{n} A_{q}\\\\right) \\\\partial_{r}{\\\\phi} \\\\phi A_{m} \\\\phi h^{q r} \\\\phi h^{p s} A_{s}+\\\\frac{1}{4}\\\\partial_{p}\\\\left(\\\\phi A_{n}\\\\right) \\\\partial_{q}{\\\\phi} \\\\phi A_{m} \\\\phi h^{p r} A_{r} \\\\phi h^{q s} A_{s}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"substitute(_, $g_{4 4} -> \\\\phi$ )\\nsubstitute(_, $g_{m 4} -> \\\\phi A_{m}$ )\\nsubstitute(_, $g_{4 m} -> \\\\phi A_{m}$ )\\nsubstitute(_, $g_{m n} -> \\\\phi**{-1} h_{m n} + \\\\phi A_{m} A_{n}$ )\\nsubstitute(_, $g^{4 4} -> \\\\phi**{-1} + \\\\phi A_{m} h^{m n} A_{n}$ )\\nsubstitute(_, $g^{m 4} -> - \\\\phi h^{m n} A_{n}$ )\\nsubstitute(_, $g^{4 m} -> - \\\\phi h^{m n} A_{n}$ )\\nsubstitute(_, $g^{m n} -> \\\\phi h^{m n}$ );\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"We now need to distribute derivatives over sums and use the product rule. This has to be done a few times,\\nso we wrap this in a \\\\verb|converge| block which applies the operations until the result no longer changes. The output \\nof those operations is quite large, so we suppress it (by not writing semi-colons after the \\nfunction calls or after the converge block).\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"We now need to distribute derivatives over sums and use the product rule. This has to be done a few times,\\nso we wrap this in a \\\\verb|converge| block which applies the operations until the result no longer changes. The output \\nof those operations is quite large, so we suppress it (by not writing semi-colons after the \\nfunction calls or after the converge block).\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"converge(todo):\\n   distribute(_)\\n   product_rule(_)\\n   canonicalise(_)\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"We then convert derivatives of the inverse metric to derivatives of the metric, and cleanup contractions\\nwhich lead to Kronecker deltas.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"We then convert derivatives of the inverse metric to derivatives of the metric, and cleanup contractions\\nwhich lead to Kronecker deltas.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{} - \\\\frac{1}{4}\\\\partial_{m}{\\\\phi} \\\\partial_{n}{\\\\phi} {\\\\phi}^{-1}+\\\\frac{1}{4}\\\\partial_{m1}{\\\\phi} \\\\partial_{n}{h_{m p}} h^{m1 p} - \\\\frac{3}{4}A_{m} A_{m1} \\\\partial_{n}{\\\\phi} \\\\partial_{p}{\\\\phi} \\\\phi h^{m1 p} - \\\\frac{1}{2}A_{m} A_{m1} \\\\partial_{p}{\\\\phi} \\\\partial_{n}{h^{m1 p}} {\\\\phi}^{2} - \\\\frac{1}{2}\\\\partial_{m n}{\\\\phi} - \\\\frac{1}{2}A_{m} A_{m1} \\\\partial_{n p}{\\\\phi} {\\\\phi}^{2} h^{m1 p} - \\\\frac{1}{4}A_{m1} \\\\partial_{p}{A_{m}} \\\\partial_{n}{\\\\phi} {\\\\phi}^{2} h^{m1 p} - \\\\frac{1}{2}A_{m} \\\\partial_{n}{A_{m1}} \\\\partial_{p}{\\\\phi} {\\\\phi}^{2} h^{m1 p} - \\\\frac{1}{4}\\\\partial_{n}{A_{m1}} \\\\partial_{p}{A_{m}} {\\\\phi}^{3} h^{m1 p} - \\\\frac{1}{4}A_{m} A_{m1} \\\\partial_{n}{A_{p}} \\\\partial_{q}{A_{r}} {\\\\phi}^{5} h^{m1 r} h^{p q}+\\\\frac{3}{4}A_{m} A_{m1} \\\\partial_{n}{\\\\phi} \\\\partial_{q}{\\\\phi} \\\\phi h^{m1 q}+\\\\frac{1}{2}A_{m} \\\\partial_{n}{A_{p}} \\\\partial_{q}{\\\\phi} {\\\\phi}^{2} h^{p q}+\\\\frac{1}{4}A_{m1} \\\\partial_{r}{A_{m}} \\\\partial_{n}{\\\\phi} {\\\\phi}^{2} h^{m1 r}+\\\\frac{1}{4}A_{m1} A_{q} \\\\partial_{m}{\\\\phi} \\\\partial_{n}{\\\\phi} \\\\phi h^{m1 q}+\\\\frac{1}{4}A_{p} \\\\partial_{n}{A_{q}} \\\\partial_{m}{\\\\phi} {\\\\phi}^{2} h^{p q}+\\\\frac{1}{4}A_{p} \\\\partial_{m}{A_{q}} \\\\partial_{n}{\\\\phi} {\\\\phi}^{2} h^{p q}+\\\\frac{1}{4}\\\\partial_{m}{A_{m1}} \\\\partial_{n}{A_{q}} {\\\\phi}^{3} h^{m1 q}+\\\\frac{1}{4}A_{m} A_{m1} \\\\partial_{n}{A_{p}} \\\\partial_{q}{A_{r}} {\\\\phi}^{5} h^{m1 q} h^{p r} - \\\\frac{1}{4}A_{m1} A_{r} \\\\partial_{m}{\\\\phi} \\\\partial_{n}{\\\\phi} \\\\phi h^{m1 r}%\\n - \\\\frac{1}{4}A_{p} \\\\partial_{m}{A_{r}} \\\\partial_{n}{\\\\phi} {\\\\phi}^{2} h^{p r} - \\\\frac{1}{4}A_{p} A_{r} \\\\partial_{m}{\\\\phi} \\\\partial_{n}{\\\\phi} \\\\phi h^{p r} - \\\\frac{1}{4}A_{p} \\\\partial_{n}{A_{r}} \\\\partial_{m}{\\\\phi} {\\\\phi}^{2} h^{p r}+\\\\frac{1}{4}A_{q} A_{r} \\\\partial_{m}{\\\\phi} \\\\partial_{n}{\\\\phi} \\\\phi h^{q r}+\\\\frac{1}{4}A_{m} A_{n} \\\\partial_{m1}{\\\\phi} \\\\partial_{p}{\\\\phi} \\\\phi h^{m1 p}+\\\\frac{1}{4}\\\\partial_{m1}{A_{m}} \\\\partial_{p}{A_{n}} {\\\\phi}^{3} h^{m1 p}+\\\\frac{1}{4}A_{m} A_{m1} \\\\partial_{p}{A_{n}} \\\\partial_{q}{A_{r}} {\\\\phi}^{5} h^{m1 r} h^{p q} - \\\\frac{1}{4}A_{n} A_{m1} \\\\partial_{m}{\\\\phi} \\\\partial_{q}{\\\\phi} \\\\phi h^{m1 q} - \\\\frac{1}{4}A_{n} \\\\partial_{m}{A_{m1}} \\\\partial_{q}{\\\\phi} {\\\\phi}^{2} h^{m1 q} - \\\\frac{1}{4}A_{m1} \\\\partial_{q}{A_{n}} \\\\partial_{m}{\\\\phi} {\\\\phi}^{2} h^{m1 q} - \\\\frac{1}{4}\\\\partial_{m}{A_{m1}} \\\\partial_{q}{A_{n}} {\\\\phi}^{3} h^{m1 q} - \\\\frac{1}{4}A_{m} A_{m1} \\\\partial_{p}{A_{n}} \\\\partial_{q}{A_{r}} {\\\\phi}^{5} h^{m1 q} h^{p r}+\\\\frac{1}{4}A_{p} \\\\partial_{r}{A_{n}} \\\\partial_{m}{\\\\phi} {\\\\phi}^{2} h^{p r}+\\\\frac{1}{4}\\\\partial_{m1}{\\\\phi} \\\\partial_{q}{\\\\phi} {\\\\phi}^{-1} h_{m n} h^{m1 q} - \\\\frac{1}{4}\\\\partial_{m1}{\\\\phi} \\\\partial_{q}{h_{m n}} h^{m1 q}+\\\\frac{1}{4}A_{m} A_{n} \\\\partial_{p}{\\\\phi} \\\\partial_{q}{\\\\phi} \\\\phi h^{p q} - \\\\frac{1}{4}A_{m} A_{m1} \\\\partial_{p}{\\\\phi} \\\\partial_{q}{h_{n r}} {\\\\phi}^{2} h^{m1 r} h^{p q} - \\\\frac{1}{4}A_{m} A_{n} \\\\partial_{m1}{\\\\phi} \\\\partial_{q}{\\\\phi} \\\\phi h^{m1 q} - \\\\frac{1}{4}A_{m} A_{m1} \\\\partial_{p}{\\\\phi} \\\\partial_{n}{h_{q r}} {\\\\phi}^{2} h^{m1 q} h^{p r} - \\\\frac{1}{4}A_{m1} \\\\partial_{n}{A_{m}} \\\\partial_{p}{\\\\phi} {\\\\phi}^{2} h^{m1 p}%\\n+\\\\frac{1}{4}A_{m1} \\\\partial_{n}{A_{m}} \\\\partial_{r}{\\\\phi} {\\\\phi}^{2} h^{m1 r}+\\\\frac{1}{4}\\\\partial_{p}{\\\\phi} \\\\partial_{m}{h_{n q}} h^{p q} - \\\\frac{1}{4}A_{m} A_{q} \\\\partial_{n}{\\\\phi} \\\\partial_{r}{\\\\phi} \\\\phi h^{q r}+\\\\frac{1}{4}A_{m} A_{m1} \\\\partial_{p}{\\\\phi} \\\\partial_{q}{h_{n r}} {\\\\phi}^{2} h^{m1 q} h^{p r}+\\\\frac{1}{4}A_{n} A_{m1} \\\\partial_{m}{\\\\phi} \\\\partial_{p}{\\\\phi} \\\\phi h^{m1 p}+\\\\frac{1}{4}A_{p} \\\\partial_{m}{A_{n}} \\\\partial_{q}{\\\\phi} {\\\\phi}^{2} h^{p q}+\\\\frac{1}{4}A_{n} \\\\partial_{m}{A_{p}} \\\\partial_{q}{\\\\phi} {\\\\phi}^{2} h^{p q} - \\\\frac{1}{4}A_{p} \\\\partial_{m}{A_{n}} \\\\partial_{r}{\\\\phi} {\\\\phi}^{2} h^{p r}+\\\\frac{1}{2}A_{m} A_{p} \\\\partial_{q}{\\\\phi} \\\\partial_{n}{h^{p q}} {\\\\phi}^{2}+\\\\frac{1}{2}A_{m} A_{p} \\\\partial_{n q}{\\\\phi} {\\\\phi}^{2} h^{p q}+\\\\frac{1}{4}A_{m} A_{p} \\\\partial_{n}{A_{q}} \\\\partial_{r}{A_{s}} {\\\\phi}^{5} h^{p s} h^{q r}+\\\\frac{1}{4}A_{m} A_{p} \\\\partial_{n}{\\\\phi} \\\\partial_{s}{\\\\phi} \\\\phi h^{p s} - \\\\frac{1}{4}A_{m} A_{p} \\\\partial_{n}{A_{q}} \\\\partial_{r}{A_{s}} {\\\\phi}^{5} h^{p r} h^{q s} - \\\\frac{1}{4}A_{m} A_{p} \\\\partial_{q}{A_{n}} \\\\partial_{r}{A_{s}} {\\\\phi}^{5} h^{p s} h^{q r}+\\\\frac{1}{4}A_{m} A_{p} \\\\partial_{q}{A_{n}} \\\\partial_{r}{A_{s}} {\\\\phi}^{5} h^{p r} h^{q s} - \\\\frac{1}{4}A_{m} A_{n} \\\\partial_{q}{\\\\phi} \\\\partial_{r}{\\\\phi} \\\\phi h^{q r}+\\\\frac{1}{4}A_{m} A_{p} \\\\partial_{q}{\\\\phi} \\\\partial_{r}{h_{n s}} {\\\\phi}^{2} h^{p s} h^{q r} - \\\\frac{1}{4}A_{m} A_{p} \\\\partial_{n}{\\\\phi} \\\\partial_{r}{\\\\phi} \\\\phi h^{p r}+\\\\frac{1}{4}A_{m} A_{p} \\\\partial_{q}{\\\\phi} \\\\partial_{n}{h_{r s}} {\\\\phi}^{2} h^{p r} h^{q s}+\\\\frac{1}{4}A_{m} A_{r} \\\\partial_{n}{\\\\phi} \\\\partial_{s}{\\\\phi} \\\\phi h^{r s}%\\n - \\\\frac{1}{4}A_{m} A_{p} \\\\partial_{q}{\\\\phi} \\\\partial_{r}{h_{n s}} {\\\\phi}^{2} h^{p r} h^{q s}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"substitute(_, $\\\\partial_{p}{h^{n m}} h_{q m} -> - \\\\partial_{p}{h_{q m}} h^{n m}$ )\\ncollect_factors(_)\\nsort_product(_)\\nconverge(todo):\\n\\tsubstitute(_, $h_{m1 m2} h^{m3 m2} -> \\\\delta_{m1}^{m3}$, repeat=True )\\n\\teliminate_kronecker(_)\\n\\tcanonicalise(_)\\n;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"This is almost the finaly result, but one would normally write it in terms of the field strength,\\nnot the gauge potential. This can be done with one further substitution and some simplification, to \\nget the result\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"This is almost the finaly result, but one would normally write it in terms of the field strength,\\nnot the gauge potential. This can be done with one further substitution and some simplification, to \\nget the result\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{} - \\\\frac{1}{4}\\\\partial_{m}{\\\\phi} \\\\partial_{n}{\\\\phi} {\\\\phi}^{-1}+\\\\frac{1}{4}\\\\partial_{p}{\\\\phi} \\\\partial_{n}{h_{m q}} h^{p q} - \\\\frac{1}{2}\\\\partial_{m n}{\\\\phi}+\\\\frac{1}{4}F_{m p} F_{n q} {\\\\phi}^{3} h^{p q}+\\\\frac{1}{4}\\\\partial_{p}{\\\\phi} \\\\partial_{q}{\\\\phi} {\\\\phi}^{-1} h_{m n} h^{p q} - \\\\frac{1}{4}\\\\partial_{p}{\\\\phi} \\\\partial_{q}{h_{m n}} h^{p q}+\\\\frac{1}{4}\\\\partial_{p}{\\\\phi} \\\\partial_{m}{h_{n q}} h^{p q}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"substitute(_, $\\\\partial_{n}{A_{m}} -> 1/2*\\\\partial_{n}{A_{m}} + 1/2*F_{n m} + 1/2*\\\\partial_{m}{A_{n}}$ )\\ndistribute(_)\\nsort_product(_)\\ncanonicalise(_)\\nrename_dummies(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1\n}\n"
  },
  {
    "path": "examples/kerr.cnb",
    "content": "{\n\t\"cells\" : \n\t[\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Coordinate to~}\\\\left[t,~\\\\discretionary{}{}{} r,~\\\\discretionary{}{}{} \\\\theta,~\\\\discretionary{}{}{} \\\\phi\\\\right].\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Metric to~}g_{\\\\mu \\\\nu}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property TableauSymmetry to~}g^{\\\\mu \\\\nu}.\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"{t,r,\\\\theta,\\\\phi}::Coordinate;\\n{\\\\mu,\\\\nu,\\\\rho,\\\\sigma,\\\\lambda,\\\\kappa}::Indices(values={t,r,\\\\phi,\\\\theta}, position=fixed).\\nrs::LaTeXForm(\\\"r_s\\\").\\ng_{\\\\mu\\\\nu}::Metric;\\ng^{\\\\mu\\\\nu}::InverseMetric;\\n\\\\partial{#}::PartialDerivative.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Depends to~}\\\\Delta.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Depends to~}\\\\Sigma.\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"\\\\Delta::Depends(r);\\n\\\\Sigma::Depends(r, \\\\theta);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\left[g_{t t} = -1+r_s \\\\frac{r}{\\\\Sigma},~\\\\discretionary{}{}{} g_{t \\\\phi} = -r_s a r \\\\frac{\\\\sin{\\\\theta}^{2}}{\\\\Sigma},~\\\\discretionary{}{}{} g_{\\\\phi t} = -r_s a r \\\\frac{\\\\sin{\\\\theta}^{2}}{\\\\Sigma},~\\\\discretionary{}{}{} g_{r r} = \\\\frac{\\\\Sigma}{\\\\Delta},~\\\\discretionary{}{}{} g_{\\\\theta \\\\theta} = \\\\Sigma,~\\\\discretionary{}{}{} g_{\\\\phi \\\\phi} = \\\\left(r^{2}+a^{2}+r_s a^{2} r \\\\frac{\\\\sin{\\\\theta}^{2}}{\\\\Sigma}\\\\right) \\\\sin{\\\\theta}^{2}\\\\right]\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"kerr:= { g_{t t}            = - (1 - rs r / \\\\Sigma),\\n         g_{t \\\\phi}         = - rs a r \\\\sin(\\\\theta)**2 / \\\\Sigma,\\n         g_{\\\\phi t}         = - rs a r \\\\sin(\\\\theta)**2 / \\\\Sigma,\\n         g_{r r}            = \\\\Sigma / \\\\Delta,\\n         g_{\\\\theta \\\\theta } = \\\\Sigma,\\n         g_{\\\\phi \\\\phi}      = ( r**2 + a**2 + rs a**2 r \\\\sin(\\\\theta)**2 / \\\\Sigma ) \\\\sin(\\\\theta)**2 };\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\left[g_{t t} = -1+r_s \\\\frac{r}{\\\\Sigma},~\\\\discretionary{}{}{} g_{t \\\\phi} = -r_s a r \\\\frac{\\\\sin{\\\\theta}^{2}}{\\\\Sigma},~\\\\discretionary{}{}{} g_{\\\\phi t} = -r_s a r \\\\frac{\\\\sin{\\\\theta}^{2}}{\\\\Sigma},~\\\\discretionary{}{}{} g_{r r} = \\\\frac{\\\\Sigma}{\\\\Delta},~\\\\discretionary{}{}{} g_{\\\\theta \\\\theta} = \\\\Sigma,~\\\\discretionary{}{}{} g_{\\\\phi \\\\phi} = \\\\left(r^{2}+a^{2}+r_s a^{2} r \\\\frac{\\\\sin{\\\\theta}^{2}}{\\\\Sigma}\\\\right) \\\\sin{\\\\theta}^{2},~\\\\discretionary{}{}{} g^{t t} = a^{2} r^{2} r_s^{2} \\\\left(r r_s-\\\\Sigma\\\\right) \\\\frac{\\\\sin{\\\\theta}^{2}}{\\\\left(r \\\\frac{r_s}{\\\\Sigma}-1\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{2}}+\\\\frac{1}{r \\\\frac{r_s}{\\\\Sigma}-1},~\\\\discretionary{}{}{} g^{t \\\\phi} = a r r_s \\\\frac{r r_s-\\\\Sigma}{\\\\left(r \\\\frac{r_s}{\\\\Sigma}-1\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma},~\\\\discretionary{}{}{} g^{r r} = \\\\frac{\\\\Delta}{\\\\Sigma},~\\\\discretionary{}{}{} g^{\\\\phi t} = a r r_s \\\\frac{r r_s-\\\\Sigma}{\\\\left(r \\\\frac{r_s}{\\\\Sigma}-1\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma},~\\\\discretionary{}{}{} g^{\\\\phi \\\\phi} = \\\\frac{r r_s-\\\\Sigma}{\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\sin{\\\\theta}^{2}},~\\\\discretionary{}{}{} g^{\\\\theta \\\\theta} = \\\\frac{1}{\\\\Sigma}\\\\right]\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"complete(kerr, $g^{\\\\mu\\\\nu}$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"import cdb.relativity as gr\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Indices(position=fixed) to~}\\\\left[\\\\mu,~\\\\discretionary{}{}{} \\\\nu,~\\\\discretionary{}{}{} \\\\rho,~\\\\discretionary{}{}{} \\\\sigma,~\\\\discretionary{}{}{} \\\\kappa,~\\\\discretionary{}{}{} \\\\gamma,~\\\\discretionary{}{}{} \\\\lambda\\\\right].\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\Gamma^{\\\\lambda}\\\\,_{\\\\mu \\\\nu} = \\\\frac{1}{2}g^{\\\\lambda \\\\kappa} \\\\left(\\\\partial_{\\\\mu}{g_{\\\\kappa \\\\nu}}+\\\\partial_{\\\\nu}{g_{\\\\kappa \\\\mu}}-\\\\partial_{\\\\kappa}{g_{\\\\mu \\\\nu}}\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ch = gr.christoffel_from_metric();\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"evaluate(ch, kerr, rhsonly=True)\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\Gamma^{\\\\lambda}\\\\,_{\\\\mu \\\\nu} = \\\\left\\\\{\\\\begin{aligned}\\\\square{}_{\\\\phi}{}_{r}{}^{t}= & a r_s \\\\left(2a^{2} r^{2} r_s r-a^{2} r r_s \\\\Sigma-2a^{2} r \\\\Sigma r+a^{2} \\\\Sigma^{2}+2r^{4} r_s r+r^{3} r_s \\\\Sigma-2r^{3} \\\\Sigma r-r^{2} \\\\Sigma^{2}\\\\right) \\\\frac{\\\\sin{\\\\theta}^{2}}{2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{r}{}^{\\\\phi}= & \\\\frac{a^{2} r r_s \\\\sin{\\\\theta}^{2} r - \\\\frac{1}{2}a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+r^{2} r_s \\\\Sigma-r \\\\Sigma^{2}}{\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{\\\\theta}{}^{t}= & a r r_s \\\\left(2a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta} \\\\cos{\\\\theta}-2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta} \\\\cos{\\\\theta}-2a^{2} r r_s a^{2} \\\\cos{\\\\theta} \\\\sin{\\\\theta}+2a^{2} \\\\Sigma a^{2} \\\\cos{\\\\theta} \\\\sin{\\\\theta}-2r^{3} r_s a^{2} \\\\cos{\\\\theta} \\\\sin{\\\\theta}+2r^{2} \\\\Sigma a^{2} \\\\cos{\\\\theta} \\\\sin{\\\\theta}\\\\right) \\\\frac{\\\\sin{\\\\theta}^{2}}{2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(-a^{2} r r_s \\\\sin{\\\\theta}^{2}+a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{\\\\theta}{}^{\\\\phi}= & \\\\frac{-a^{2} r^{2} r_s^{2} \\\\left(2\\\\Sigma \\\\cos{\\\\theta}+2\\\\sin{\\\\theta} a^{2} \\\\cos{\\\\theta} \\\\sin{\\\\theta}\\\\right) \\\\sin{\\\\theta}^{2}+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(4a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}+2a^{2} r r_s \\\\sin{\\\\theta}^{3} a^{2} \\\\cos{\\\\theta} \\\\sin{\\\\theta}+2\\\\left(a^{2}+r^{2}\\\\right) \\\\Sigma^{2} \\\\cos{\\\\theta}\\\\right)}{2\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{2} \\\\sin{\\\\theta}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{r}{}^{\\\\theta}= & \\\\frac{2r}{2\\\\Sigma}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{\\\\theta}{}^{\\\\theta}= & \\\\frac{-2a^{2} \\\\cos{\\\\theta} \\\\sin{\\\\theta}}{2\\\\Sigma}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{r}{}^{r}= & \\\\frac{2r}{2\\\\Sigma} - \\\\frac{2r-r_s}{2\\\\Delta}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{\\\\theta}{}^{r}= & \\\\frac{-2a^{2} \\\\cos{\\\\theta} \\\\sin{\\\\theta}}{2\\\\Sigma}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}_{r}{}^{t}= & r_s \\\\left(2r r-\\\\Sigma\\\\right) \\\\frac{-a^{2} r r_s+a^{2} \\\\Sigma-r^{3} r_s+r^{2} \\\\Sigma}{2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}_{r}{}^{\\\\phi}= & -a r_s \\\\frac{2r r-\\\\Sigma}{2\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}_{\\\\theta}{}^{t}= & r r_s \\\\frac{-a^{2} r^{2} r_s^{2} \\\\sin{2\\\\theta}+a^{2} r r_s \\\\Sigma \\\\sin{2\\\\theta}+2a^{2} r r_s a^{2} \\\\cos{\\\\theta} \\\\sin{\\\\theta}-2a^{2} \\\\Sigma a^{2} \\\\cos{\\\\theta} \\\\sin{\\\\theta}+2r^{3} r_s a^{2} \\\\cos{\\\\theta} \\\\sin{\\\\theta}-2r^{2} \\\\Sigma a^{2} \\\\cos{\\\\theta} \\\\sin{\\\\theta}}{2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}_{\\\\theta}{}^{\\\\phi}= & a r r_s \\\\frac{-2r \\\\frac{r_s}{\\\\tan{\\\\theta}}+\\\\frac{2\\\\Sigma}{\\\\tan{\\\\theta}}+2a^{2} \\\\cos{\\\\theta} \\\\sin{\\\\theta}}{2\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{\\\\phi}{}^{t}= & a r_s \\\\left(2a^{2} r^{2} r_s r-a^{2} r r_s \\\\Sigma-2a^{2} r \\\\Sigma r+a^{2} \\\\Sigma^{2}+2r^{4} r_s r+r^{3} r_s \\\\Sigma-2r^{3} \\\\Sigma r-r^{2} \\\\Sigma^{2}\\\\right) \\\\frac{\\\\sin{\\\\theta}^{2}}{2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{\\\\phi}{}^{\\\\phi}= & \\\\frac{a^{2} r r_s \\\\sin{\\\\theta}^{2} r - \\\\frac{1}{2}a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+r^{2} r_s \\\\Sigma-r \\\\Sigma^{2}}{\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{\\\\phi}{}^{t}= & a r r_s \\\\left(2a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta} \\\\cos{\\\\theta}-2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta} \\\\cos{\\\\theta}-2a^{2} r r_s a^{2} \\\\cos{\\\\theta} \\\\sin{\\\\theta}+2a^{2} \\\\Sigma a^{2} \\\\cos{\\\\theta} \\\\sin{\\\\theta}-2r^{3} r_s a^{2} \\\\cos{\\\\theta} \\\\sin{\\\\theta}+2r^{2} \\\\Sigma a^{2} \\\\cos{\\\\theta} \\\\sin{\\\\theta}\\\\right) \\\\frac{\\\\sin{\\\\theta}^{2}}{2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(-a^{2} r r_s \\\\sin{\\\\theta}^{2}+a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{\\\\phi}{}^{\\\\phi}= & \\\\frac{-a^{2} r^{2} r_s^{2} \\\\left(2\\\\Sigma \\\\cos{\\\\theta}+2\\\\sin{\\\\theta} a^{2} \\\\cos{\\\\theta} \\\\sin{\\\\theta}\\\\right) \\\\sin{\\\\theta}^{2}+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(4a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}+2a^{2} r r_s \\\\sin{\\\\theta}^{3} a^{2} \\\\cos{\\\\theta} \\\\sin{\\\\theta}+2\\\\left(a^{2}+r^{2}\\\\right) \\\\Sigma^{2} \\\\cos{\\\\theta}\\\\right)}{2\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{2} \\\\sin{\\\\theta}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{\\\\theta}{}^{\\\\theta}= & \\\\frac{2r}{2\\\\Sigma}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{r}{}^{r}= & \\\\frac{-2a^{2} \\\\cos{\\\\theta} \\\\sin{\\\\theta}}{2\\\\Sigma}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{t}{}^{t}= & r_s \\\\left(2r r-\\\\Sigma\\\\right) \\\\frac{-a^{2} r r_s+a^{2} \\\\Sigma-r^{3} r_s+r^{2} \\\\Sigma}{2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{t}{}^{\\\\phi}= & -a r_s \\\\frac{2r r-\\\\Sigma}{2\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{t}{}^{t}= & r r_s \\\\frac{-a^{2} r^{2} r_s^{2} \\\\sin{2\\\\theta}+a^{2} r r_s \\\\Sigma \\\\sin{2\\\\theta}+2a^{2} r r_s a^{2} \\\\cos{\\\\theta} \\\\sin{\\\\theta}-2a^{2} \\\\Sigma a^{2} \\\\cos{\\\\theta} \\\\sin{\\\\theta}+2r^{3} r_s a^{2} \\\\cos{\\\\theta} \\\\sin{\\\\theta}-2r^{2} \\\\Sigma a^{2} \\\\cos{\\\\theta} \\\\sin{\\\\theta}}{2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{t}{}^{\\\\phi}= & a r r_s \\\\frac{-2r \\\\frac{r_s}{\\\\tan{\\\\theta}}+\\\\frac{2\\\\Sigma}{\\\\tan{\\\\theta}}+2a^{2} \\\\cos{\\\\theta} \\\\sin{\\\\theta}}{2\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{\\\\phi}{}^{r}= & \\\\left(2a^{2} r r_s \\\\sin{\\\\theta}^{4} r-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{4}-2r \\\\Sigma^{2} \\\\sin{\\\\theta}^{2}\\\\right) \\\\frac{\\\\Delta}{2\\\\Sigma^{3}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{\\\\phi}{}^{\\\\theta}= & -\\\\left(4a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}+2a^{2} r r_s \\\\sin{\\\\theta}^{3} a^{2} \\\\cos{\\\\theta} \\\\sin{\\\\theta}+2\\\\left(a^{2}+r^{2}\\\\right) \\\\Sigma^{2} \\\\cos{\\\\theta}\\\\right) \\\\frac{\\\\sin{\\\\theta}}{2\\\\Sigma^{3}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{\\\\theta}{}^{r}= & -\\\\Delta \\\\frac{2r}{2\\\\Sigma}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{r}{}^{\\\\theta}= &  - \\\\frac{-2a^{2} \\\\cos{\\\\theta} \\\\sin{\\\\theta}}{2\\\\Delta \\\\Sigma}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}_{\\\\phi}{}^{r}= & -a r_s \\\\left(2r r-\\\\Sigma\\\\right) \\\\Delta \\\\frac{\\\\sin{\\\\theta}^{2}}{2\\\\Sigma^{3}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}_{\\\\phi}{}^{\\\\theta}= & a r r_s \\\\frac{2\\\\Sigma \\\\sin{2\\\\theta}-2\\\\cos{2\\\\theta} a^{2} \\\\cos{\\\\theta} \\\\sin{\\\\theta}+2a^{2} \\\\cos{\\\\theta} \\\\sin{\\\\theta}}{4\\\\Sigma^{3}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{t}{}^{r}= & -a r_s \\\\left(2r r-\\\\Sigma\\\\right) \\\\Delta \\\\frac{\\\\sin{\\\\theta}^{2}}{2\\\\Sigma^{3}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{t}{}^{\\\\theta}= & a r r_s \\\\frac{2\\\\Sigma \\\\sin{2\\\\theta}-2\\\\cos{2\\\\theta} a^{2} \\\\cos{\\\\theta} \\\\sin{\\\\theta}+2a^{2} \\\\cos{\\\\theta} \\\\sin{\\\\theta}}{4\\\\Sigma^{3}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}_{t}{}^{r}= & r_s \\\\left(2r r-\\\\Sigma\\\\right) \\\\frac{\\\\Delta}{2\\\\Sigma^{3}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}_{t}{}^{\\\\theta}= & r r_s \\\\frac{-2a^{2} \\\\cos{\\\\theta} \\\\sin{\\\\theta}}{2\\\\Sigma^{3}}\\\\\\\\[-.5ex]\\n\\\\end{aligned}\\\\right.\\n\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"substitute(ch, $\\\\partial_{r}{\\\\Sigma} = 2 r$)\\nsubstitute(ch, $\\\\partial_{\\\\theta}{\\\\Sigma} = -2 a**2 \\\\cos{\\\\theta} \\\\sin{\\\\theta}$)\\nsubstitute(ch, $\\\\partial_{r}{\\\\Delta} = 2 r - rs$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\partial_{\\\\mu}{\\\\Gamma^{\\\\rho}\\\\,_{\\\\nu \\\\sigma}}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\Gamma^{\\\\rho}\\\\,_{\\\\mu \\\\lambda} \\\\Gamma^{\\\\lambda}\\\\,_{\\\\nu \\\\sigma}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}-\\\\partial_{\\\\nu}{\\\\Gamma^{\\\\rho}\\\\,_{\\\\mu \\\\sigma}}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}-\\\\Gamma^{\\\\rho}\\\\,_{\\\\nu \\\\lambda} \\\\Gamma^{\\\\lambda}\\\\,_{\\\\mu \\\\sigma}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"tst1:=\\\\partial_{\\\\mu}{\\\\Gamma^{\\\\rho}_{\\\\nu\\\\sigma}};\\ntst2:=\\\\Gamma^{\\\\rho}_{\\\\mu\\\\lambda} \\\\Gamma^{\\\\lambda}_{\\\\nu\\\\sigma};\\ntst3:=-\\\\partial_{\\\\nu}{\\\\Gamma^{\\\\rho}_{\\\\mu\\\\sigma}};\\ntst4:=-\\\\Gamma^{\\\\rho}_{\\\\nu\\\\lambda} \\\\Gamma^{\\\\lambda}_{\\\\mu\\\\sigma};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\left\\\\{\\\\begin{aligned}\\\\square{}_{t}{}_{t}{}^{\\\\theta}{}_{r}= & a^{2} r_s \\\\left(3r \\\\partial_{r}{\\\\Sigma}-\\\\Sigma\\\\right) \\\\frac{\\\\sin{2\\\\theta}}{2\\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}_{t}{}^{\\\\theta}{}_{\\\\theta}= & a^{2} r r_s \\\\frac{-\\\\Sigma \\\\cos{2\\\\theta}+\\\\frac{3}{2}\\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}}{\\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}_{t}{}^{r}{}_{r}= & r_s \\\\frac{-3\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\Delta \\\\partial_{r}{\\\\Sigma}+\\\\left(\\\\left(4r-\\\\partial_{r}{\\\\Sigma}\\\\right) \\\\Delta+\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\partial_{r}{\\\\Delta}\\\\right) \\\\Sigma}{2\\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}_{t}{}^{r}{}_{\\\\theta}= & r_s \\\\left(-3r^{2}+\\\\Sigma\\\\right) \\\\Delta \\\\frac{\\\\partial_{\\\\theta}{\\\\Sigma}}{\\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{t}{}^{\\\\theta}{}_{r}= & a r_s \\\\left(-3a^{2} r \\\\sin{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}+a^{2} \\\\Sigma \\\\sin{\\\\theta}^{2}-2r \\\\Sigma \\\\partial_{r}{\\\\Sigma}+\\\\Sigma^{2}\\\\right) \\\\sin{\\\\theta} \\\\frac{\\\\cos{\\\\theta}}{\\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{t}{}^{\\\\theta}{}_{\\\\theta}= & a r r_s \\\\frac{-2a^{2} \\\\left(-\\\\cos{2\\\\theta}+1\\\\right)^{2} \\\\Sigma-3a^{2} \\\\Sigma \\\\cos{2\\\\theta}+3a^{2} \\\\Sigma - \\\\frac{3}{2}a^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}+\\\\frac{3}{4}a^{2} \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}+2\\\\Sigma^{2} \\\\cos{2\\\\theta}-2\\\\Sigma \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}}{2\\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{t}{}^{r}{}_{r}= & a r_s \\\\left(3\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\Delta \\\\partial_{r}{\\\\Sigma}-\\\\left(\\\\left(4r-\\\\partial_{r}{\\\\Sigma}\\\\right) \\\\Delta+\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\partial_{r}{\\\\Delta}\\\\right) \\\\Sigma\\\\right) \\\\frac{\\\\sin{\\\\theta}^{2}}{2\\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{t}{}^{r}{}_{\\\\theta}= & a r_s \\\\left(3\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\sin{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}+\\\\left(\\\\left(-4r^{2}+2\\\\Sigma\\\\right) \\\\cos{\\\\theta}+\\\\sin{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\Sigma\\\\right) \\\\Delta \\\\frac{\\\\sin{\\\\theta}}{2\\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}_{\\\\phi}{}^{\\\\theta}{}_{r}= & a r_s \\\\left(-3a^{2} r \\\\sin{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}+a^{2} \\\\Sigma \\\\sin{\\\\theta}^{2}-2r \\\\Sigma \\\\partial_{r}{\\\\Sigma}+\\\\Sigma^{2}\\\\right) \\\\sin{\\\\theta} \\\\frac{\\\\cos{\\\\theta}}{\\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}_{\\\\phi}{}^{\\\\theta}{}_{\\\\theta}= & a r r_s \\\\frac{-2a^{2} \\\\left(-\\\\cos{2\\\\theta}+1\\\\right)^{2} \\\\Sigma-3a^{2} \\\\Sigma \\\\cos{2\\\\theta}+3a^{2} \\\\Sigma - \\\\frac{3}{2}a^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}+\\\\frac{3}{4}a^{2} \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}+2\\\\Sigma^{2} \\\\cos{2\\\\theta}-2\\\\Sigma \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}}{2\\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}_{\\\\phi}{}^{r}{}_{r}= & a r_s \\\\left(3\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\Delta \\\\partial_{r}{\\\\Sigma}-\\\\left(\\\\left(4r-\\\\partial_{r}{\\\\Sigma}\\\\right) \\\\Delta+\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\partial_{r}{\\\\Delta}\\\\right) \\\\Sigma\\\\right) \\\\frac{\\\\sin{\\\\theta}^{2}}{2\\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}_{\\\\phi}{}^{r}{}_{\\\\theta}= & a r_s \\\\left(3\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\sin{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}+\\\\left(\\\\left(-4r^{2}+2\\\\Sigma\\\\right) \\\\cos{\\\\theta}+\\\\sin{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\Sigma\\\\right) \\\\Delta \\\\frac{\\\\sin{\\\\theta}}{2\\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{r}{}^{\\\\theta}{}_{r}= & -a^{2} \\\\left(\\\\Delta \\\\partial_{r}{\\\\Sigma}+\\\\Sigma \\\\partial_{r}{\\\\Delta}\\\\right) \\\\frac{\\\\sin{2\\\\theta}}{2\\\\Delta^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{r}{}^{\\\\theta}{}_{\\\\theta}= & a^{2} \\\\frac{\\\\Sigma \\\\cos{2\\\\theta} - \\\\frac{1}{2}\\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}}{\\\\Delta \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{\\\\theta}{}^{r}{}_{r}= & \\\\frac{r \\\\Delta \\\\partial_{r}{\\\\Sigma}-\\\\left(r \\\\partial_{r}{\\\\Delta}+\\\\Delta\\\\right) \\\\Sigma}{\\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{\\\\theta}{}^{r}{}_{\\\\theta}= & r \\\\Delta \\\\frac{\\\\partial_{\\\\theta}{\\\\Sigma}}{\\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{\\\\phi}{}^{\\\\theta}{}_{r}= & \\\\left(3a^{4} r r_s \\\\sin{\\\\theta}^{4} \\\\partial_{r}{\\\\Sigma}-a^{4} r_s \\\\Sigma \\\\sin{\\\\theta}^{4}+4a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}-2a^{2} r_s \\\\Sigma^{2} \\\\sin{\\\\theta}^{2}+a^{2} \\\\Sigma^{2} \\\\partial_{r}{\\\\Sigma}+r^{2} \\\\Sigma^{2} \\\\partial_{r}{\\\\Sigma}-2r \\\\Sigma^{3}\\\\right) \\\\sin{\\\\theta} \\\\frac{\\\\cos{\\\\theta}}{\\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{\\\\phi}{}^{\\\\theta}{}_{\\\\theta}= & \\\\frac{\\\\frac{3}{4}a^{4} r r_s \\\\left(-\\\\cos{2\\\\theta}+1\\\\right)^{3} \\\\Sigma - \\\\frac{5}{4}a^{4} r r_s \\\\left(-\\\\cos{2\\\\theta}+1\\\\right)^{2} \\\\Sigma+\\\\frac{3}{8}a^{4} r r_s \\\\left(-\\\\cos{2\\\\theta}+1\\\\right)^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}+2a^{2} r r_s \\\\left(-\\\\cos{2\\\\theta}+1\\\\right)^{2} \\\\Sigma^{2}+3a^{2} r r_s \\\\Sigma^{2} \\\\cos{2\\\\theta}-3a^{2} r r_s \\\\Sigma^{2}+a^{2} r r_s \\\\Sigma \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma} - \\\\frac{1}{2}a^{2} r r_s \\\\Sigma \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}-a^{2} \\\\Sigma^{3} \\\\cos{2\\\\theta}+\\\\frac{1}{2}a^{2} \\\\Sigma^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}-r^{2} \\\\Sigma^{3} \\\\cos{2\\\\theta}+\\\\frac{1}{2}r^{2} \\\\Sigma^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}}{\\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{\\\\phi}{}^{r}{}_{r}= & \\\\left(-3a^{2} r^{2} r_s \\\\Delta \\\\sin{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}+a^{2} r^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2} \\\\partial_{r}{\\\\Delta}+2a^{2} r r_s \\\\Delta \\\\Sigma \\\\sin{\\\\theta}^{2}+a^{2} r_s \\\\Delta \\\\Sigma \\\\sin{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma} - \\\\frac{1}{2}a^{2} r_s \\\\Sigma^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{r}{\\\\Delta}+r \\\\Delta \\\\Sigma^{2} \\\\partial_{r}{\\\\Sigma}-r \\\\Sigma^{3} \\\\partial_{r}{\\\\Delta}-\\\\Delta \\\\Sigma^{3}\\\\right) \\\\frac{\\\\sin{\\\\theta}^{2}}{\\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{\\\\phi}{}^{r}{}_{\\\\theta}= & \\\\left(4a^{2} r^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}-3a^{2} r^{2} r_s \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}{\\\\Sigma}-2a^{2} r_s \\\\Sigma^{2} \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}+a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}{\\\\Sigma}-2r \\\\Sigma^{3} \\\\cos{\\\\theta}+r \\\\Sigma^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\Delta \\\\frac{\\\\sin{\\\\theta}}{\\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{t}{}^{\\\\phi}{}_{r}= & a r_s \\\\frac{-r \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\partial_{r}{\\\\Sigma}+r \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right) \\\\left(-a^{2} r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\partial_{r}{\\\\Sigma}-3r^{2} r_s+r^{2} \\\\partial_{r}{\\\\Sigma}+2r \\\\Sigma\\\\right) \\\\Sigma+\\\\left(a^{2} \\\\sin{\\\\theta}^{2}-2r r_s+r \\\\partial_{r}{\\\\Sigma}+\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma}{\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2} \\\\tan{\\\\theta}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{t}{}^{\\\\phi}{}_{\\\\theta}= & a r r_s \\\\frac{\\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\sin{2\\\\theta}+a^{2} \\\\partial_{\\\\theta}{\\\\Sigma}+r^{2} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\Sigma \\\\tan{\\\\theta}-\\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\tan{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}+\\\\left(a^{2} \\\\cos{2\\\\theta} \\\\tan{\\\\theta}^{2}+\\\\frac{r r_s-\\\\Sigma}{\\\\cos{\\\\theta}^{2}}+\\\\tan{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma}{\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2} \\\\tan{\\\\theta}^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{t}{}^{t}{}_{r}= & -a^{2} r_s \\\\left(a^{4} r^{2} r_s \\\\cos{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}-2a^{4} r \\\\Sigma \\\\partial_{r}{\\\\Sigma}+a^{4} \\\\Sigma^{2}+a^{2} r^{4} r_s \\\\cos{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}+a^{2} r^{4} r_s \\\\partial_{r}{\\\\Sigma}-a^{2} r^{3} r_s^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}-2a^{2} r^{3} r_s \\\\Sigma \\\\cos{\\\\theta}^{2}+2a^{2} r^{3} r_s \\\\Sigma-4a^{2} r^{3} \\\\Sigma \\\\partial_{r}{\\\\Sigma}+a^{2} r^{2} r_s^{2} \\\\Sigma \\\\cos{\\\\theta}^{2}+2a^{2} r^{2} r_s \\\\Sigma \\\\partial_{r}{\\\\Sigma}+2a^{2} r^{2} \\\\Sigma^{2}-2a^{2} r r_s \\\\Sigma^{2}+r^{6} r_s \\\\partial_{r}{\\\\Sigma}-r^{5} r_s^{2} \\\\partial_{r}{\\\\Sigma}-2r^{5} \\\\Sigma \\\\partial_{r}{\\\\Sigma}-r^{4} r_s^{2} \\\\Sigma+2r^{4} r_s \\\\Sigma \\\\partial_{r}{\\\\Sigma}+r^{4} \\\\Sigma^{2}\\\\right) \\\\sin{\\\\theta} \\\\frac{\\\\cos{\\\\theta}}{\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{t}{}^{t}{}_{\\\\theta}= & a^{2} r r_s \\\\frac{\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\sin{2\\\\theta}+a^{2} \\\\partial_{\\\\theta}{\\\\Sigma}+r^{2} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\Sigma \\\\sin{2\\\\theta}-\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}-\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(-2a^{2} r r_s \\\\cos{2\\\\theta}+2a^{2} \\\\Sigma \\\\cos{2\\\\theta}+a^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}-2r^{3} r_s \\\\cos{2\\\\theta}+2r^{2} r_s^{2} \\\\cos{2\\\\theta}+2r^{2} \\\\Sigma \\\\cos{2\\\\theta}+r^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}-2r r_s \\\\Sigma \\\\cos{2\\\\theta}-r r_s \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\Sigma+\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\Sigma \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}}{2\\\\left(r r_s-\\\\Sigma\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{t}{}^{\\\\phi}{}_{r}= & a r_s \\\\frac{-\\\\left(4r-\\\\partial_{r}{\\\\Sigma}\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma+\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\partial_{r}{\\\\Sigma}-\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(-a^{2} r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\partial_{r}{\\\\Sigma}-3r^{2} r_s+r^{2} \\\\partial_{r}{\\\\Sigma}+2r \\\\Sigma\\\\right) \\\\Sigma}{2\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{t}{}^{\\\\phi}{}_{\\\\theta}= & a r_s \\\\frac{-\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\sin{2\\\\theta}+a^{2} \\\\partial_{\\\\theta}{\\\\Sigma}+r^{2} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\Sigma+\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\partial_{\\\\theta}{\\\\Sigma}+\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma \\\\partial_{\\\\theta}{\\\\Sigma}}{2\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{t}{}^{t}{}_{r}= & r_s \\\\frac{\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(r_s-\\\\partial_{r}{\\\\Sigma}\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma+\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\partial_{r}{\\\\Sigma}-\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(-a^{2} r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\partial_{r}{\\\\Sigma}-3r^{2} r_s+r^{2} \\\\partial_{r}{\\\\Sigma}+2r \\\\Sigma\\\\right) \\\\Sigma+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(-\\\\left(4r-\\\\partial_{r}{\\\\Sigma}\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)+\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(-a^{2} r_s+a^{2} \\\\partial_{r}{\\\\Sigma}-3r^{2} r_s+r^{2} \\\\partial_{r}{\\\\Sigma}+2r \\\\Sigma\\\\right)\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma}{2\\\\left(r r_s-\\\\Sigma\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{t}{}^{t}{}_{\\\\theta}= & r_s \\\\frac{-\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\sin{2\\\\theta}+a^{2} \\\\partial_{\\\\theta}{\\\\Sigma}+r^{2} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma+\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\partial_{\\\\theta}{\\\\Sigma}-\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma \\\\partial_{\\\\theta}{\\\\Sigma}+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma+\\\\left(a^{2}+r^{2}\\\\right) \\\\left(2r^{2}-\\\\Sigma\\\\right)\\\\right) \\\\Sigma \\\\partial_{\\\\theta}{\\\\Sigma}}{2\\\\left(r r_s-\\\\Sigma\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{r}{}^{r}{}_{r}= & a^{2} \\\\sin{2\\\\theta} \\\\frac{\\\\partial_{r}{\\\\Sigma}}{2\\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{r}{}^{r}{}_{\\\\theta}= & a^{2} \\\\frac{-\\\\Sigma \\\\cos{2\\\\theta}+\\\\frac{1}{2}\\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}}{\\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{\\\\theta}{}^{\\\\theta}{}_{r}= & \\\\frac{-r \\\\partial_{r}{\\\\Sigma}+\\\\Sigma}{\\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{\\\\theta}{}^{\\\\theta}{}_{\\\\theta}= & -r \\\\frac{\\\\partial_{\\\\theta}{\\\\Sigma}}{\\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{\\\\phi}{}^{\\\\phi}{}_{r}= & a^{2} r_s \\\\left(-a^{4} r^{2} r_s \\\\sin{\\\\theta}^{4} \\\\partial_{r}{\\\\Sigma}+a^{4} r^{2} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}-2a^{4} r \\\\Sigma \\\\sin{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}+a^{4} \\\\Sigma^{2} \\\\sin{\\\\theta}^{2}+a^{2} r^{4} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}+a^{2} r^{3} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}-a^{2} r^{3} r_s^{2} \\\\partial_{r}{\\\\Sigma}+2a^{2} r^{3} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-2a^{2} r^{3} \\\\Sigma \\\\sin{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}-a^{2} r^{2} r_s^{2} \\\\Sigma \\\\sin{\\\\theta}^{2}+a^{2} r^{2} r_s^{2} \\\\Sigma+2a^{2} r^{2} r_s \\\\Sigma \\\\partial_{r}{\\\\Sigma}-a^{2} r^{2} \\\\Sigma^{2} \\\\sin{\\\\theta}^{2}-2a^{2} r r_s \\\\Sigma^{2}-a^{2} r \\\\Sigma^{2} \\\\partial_{r}{\\\\Sigma}+a^{2} \\\\Sigma^{3}-r^{5} r_s^{2} \\\\partial_{r}{\\\\Sigma}-r^{4} r_s^{2} \\\\Sigma+2r^{4} r_s \\\\Sigma \\\\partial_{r}{\\\\Sigma}%\\n+2r^{3} r_s \\\\Sigma^{2}-r^{3} \\\\Sigma^{2} \\\\partial_{r}{\\\\Sigma}-r^{2} \\\\Sigma^{3}\\\\right) \\\\sin{\\\\theta} \\\\frac{\\\\cos{\\\\theta}}{\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{\\\\phi}{}^{\\\\phi}{}_{\\\\theta}= & \\\\frac{-\\\\left(a^{2} r r_s \\\\sin{2\\\\theta}+a^{2} \\\\partial_{\\\\theta}{\\\\Sigma}+r^{2} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right) \\\\Sigma \\\\sin{\\\\theta} \\\\cos{\\\\theta}+\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right) \\\\Sigma \\\\cos{\\\\theta}^{2}+2\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right) \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}+\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(5a^{4} r r_s \\\\Sigma \\\\sin{\\\\theta}^{5}-4a^{4} r r_s \\\\Sigma \\\\sin{\\\\theta}^{3}-a^{4} r r_s \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}-3a^{2} r^{2} r_s^{2} \\\\Sigma \\\\sin{\\\\theta}^{3}+2a^{2} r^{2} r_s^{2} \\\\Sigma \\\\sin{\\\\theta}-a^{2} r^{2} r_s^{2} \\\\cos{\\\\theta}^{3} \\\\partial_{\\\\theta}{\\\\Sigma}+a^{2} r^{2} r_s^{2} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}+6a^{2} r r_s \\\\Sigma^{2} \\\\sin{\\\\theta}^{3}-5a^{2} r r_s \\\\Sigma^{2} \\\\sin{\\\\theta}+4a^{2} r r_s \\\\Sigma \\\\cos{\\\\theta}^{3} \\\\partial_{\\\\theta}{\\\\Sigma}-2a^{2} r r_s \\\\Sigma \\\\cos{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}+a^{2} \\\\Sigma^{3} \\\\sin{\\\\theta}-3a^{2} \\\\Sigma^{2} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}-r^{3} r_s \\\\Sigma^{2} \\\\sin{\\\\theta}+2r^{3} r_s \\\\Sigma \\\\cos{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}+r^{2} \\\\Sigma^{3} \\\\sin{\\\\theta}-3r^{2} \\\\Sigma^{2} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\sin{\\\\theta}}{\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2} \\\\sin{\\\\theta}^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{\\\\phi}{}^{t}{}_{r}= & a^{3} r_s \\\\left(-r \\\\left(r_s-\\\\partial_{r}{\\\\Sigma}\\\\right) \\\\left(-a^{2} r r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\Sigma-r^{3} r_s+r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\Sigma-r \\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(-a^{2} r r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\Sigma-r^{3} r_s+r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\partial_{r}{\\\\Sigma}-r \\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(-a^{2} r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\partial_{r}{\\\\Sigma}-3r^{2} r_s+r^{2} \\\\partial_{r}{\\\\Sigma}+2r \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\Sigma+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(-a^{2} r r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\Sigma-r^{3} r_s+r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma+r \\\\left(a^{2} r_s-a^{2} \\\\partial_{r}{\\\\Sigma}+3r^{2} r_s-r^{2} \\\\partial_{r}{\\\\Sigma}-2r r_s^{2}+r r_s \\\\partial_{r}{\\\\Sigma}-2r \\\\Sigma+r_s \\\\Sigma\\\\right)\\\\right) \\\\Sigma\\\\right) \\\\sin{\\\\theta}^{3} \\\\frac{\\\\cos{\\\\theta}}{\\\\left(r r_s-\\\\Sigma\\\\right)^{2} \\\\left(-a^{2} r r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\Sigma-r^{3} r_s+r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{\\\\phi}{}^{t}{}_{\\\\theta}= & a^{3} r r_s \\\\left(-\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\sin{2\\\\theta}+a^{2} \\\\partial_{\\\\theta}{\\\\Sigma}+r^{2} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\Sigma \\\\sin{\\\\theta} \\\\cos{\\\\theta}-\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(-a^{2} r r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\Sigma-r^{3} r_s+r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(-a^{2} r r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\Sigma-r^{3} r_s+r^{2} \\\\Sigma\\\\right) \\\\left(2a^{2} r r_s \\\\cos{2\\\\theta}+a^{2} r r_s-2a^{2} \\\\Sigma \\\\cos{2\\\\theta}-a^{2} \\\\Sigma - \\\\frac{1}{2}a^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}+2r^{3} r_s \\\\cos{2\\\\theta}+r^{3} r_s-2r^{2} r_s^{2} \\\\cos{2\\\\theta}-r^{2} r_s^{2}-2r^{2} \\\\Sigma \\\\cos{2\\\\theta}-r^{2} \\\\Sigma - \\\\frac{1}{2}r^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}+2r r_s \\\\Sigma \\\\cos{2\\\\theta}+r r_s \\\\Sigma+\\\\frac{1}{2}r r_s \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\Sigma+\\\\left(-a^{2} r r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\Sigma-r^{3} r_s+r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\Sigma \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\frac{\\\\sin{\\\\theta}^{2}}{\\\\left(r r_s-\\\\Sigma\\\\right)^{2} \\\\left(-a^{2} r r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\Sigma-r^{3} r_s+r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{\\\\phi}{}^{\\\\phi}{}_{r}= & \\\\frac{-\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right) \\\\partial_{r}{\\\\Sigma}+\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(4a^{2} r r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}+2r^{2} r_s \\\\partial_{r}{\\\\Sigma}+4r r_s \\\\Sigma-4r \\\\Sigma \\\\partial_{r}{\\\\Sigma}-2\\\\Sigma^{2}\\\\right) \\\\Sigma+\\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right) \\\\left(-a^{2} r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\partial_{r}{\\\\Sigma}-3r^{2} r_s+r^{2} \\\\partial_{r}{\\\\Sigma}+2r \\\\Sigma\\\\right) \\\\Sigma}{2\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{\\\\phi}{}^{\\\\phi}{}_{\\\\theta}= & \\\\frac{\\\\left(a^{2} r r_s \\\\sin{2\\\\theta}+a^{2} \\\\partial_{\\\\theta}{\\\\Sigma}+r^{2} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right) \\\\Sigma-\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right) \\\\partial_{\\\\theta}{\\\\Sigma}+\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{2\\\\theta}-a^{2} r_s \\\\Sigma \\\\sin{2\\\\theta}-a^{2} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{\\\\theta}{\\\\Sigma}+2r^{2} r_s \\\\partial_{\\\\theta}{\\\\Sigma}-4r \\\\Sigma \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\Sigma}{2\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{\\\\phi}{}^{t}{}_{r}= & -a r_s \\\\left(2a^{4} r^{3} r_s \\\\cos{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}-2a^{4} r^{2} r_s \\\\Sigma \\\\cos{\\\\theta}^{2}-4a^{4} r^{2} \\\\Sigma \\\\partial_{r}{\\\\Sigma}+4a^{4} r \\\\Sigma^{2}-a^{4} r_s \\\\Sigma^{2} \\\\cos{\\\\theta}^{2}+a^{4} \\\\Sigma^{2} \\\\partial_{r}{\\\\Sigma}+2a^{2} r^{5} r_s \\\\cos{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}+2a^{2} r^{5} r_s \\\\partial_{r}{\\\\Sigma}-6a^{2} r^{4} r_s \\\\Sigma \\\\cos{\\\\theta}^{2}+2a^{2} r^{4} r_s \\\\Sigma-8a^{2} r^{4} \\\\Sigma \\\\partial_{r}{\\\\Sigma}+8a^{2} r^{3} \\\\Sigma^{2}-a^{2} r^{2} r_s \\\\Sigma^{2} \\\\cos{\\\\theta}^{2}-3a^{2} r^{2} r_s \\\\Sigma^{2}+4a^{2} r \\\\Sigma^{3}+2r^{7} r_s \\\\partial_{r}{\\\\Sigma}-2r^{6} r_s \\\\Sigma-4r^{6} \\\\Sigma \\\\partial_{r}{\\\\Sigma}+4r^{5} \\\\Sigma^{2}%\\n+r^{4} r_s \\\\Sigma^{2}-r^{4} \\\\Sigma^{2} \\\\partial_{r}{\\\\Sigma}\\\\right) \\\\frac{\\\\sin{\\\\theta}^{2}}{2\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{\\\\phi}{}^{t}{}_{\\\\theta}= & a r_s \\\\left(\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(-\\\\left(2a^{2} r^{2}+a^{2} r r_s-2a^{2} \\\\Sigma+2r^{4}-r^{3} r_s+2r^{2} \\\\Sigma\\\\right) \\\\sin{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}+2\\\\left(2a^{2} r^{3} r_s-2a^{2} r^{2} \\\\Sigma-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}+2r^{5} r_s-2r^{4} \\\\Sigma+r^{3} r_s \\\\Sigma-r^{2} \\\\Sigma^{2}\\\\right) \\\\cos{\\\\theta}\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\sin{2\\\\theta}+a^{2} \\\\partial_{\\\\theta}{\\\\Sigma}+r^{2} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\left(2a^{2} r^{3} r_s-2a^{2} r^{2} \\\\Sigma-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}+2r^{5} r_s-2r^{4} \\\\Sigma+r^{3} r_s \\\\Sigma-r^{2} \\\\Sigma^{2}\\\\right) \\\\Sigma \\\\sin{\\\\theta}-\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(2a^{2} r^{3} r_s-2a^{2} r^{2} \\\\Sigma-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}+2r^{5} r_s-2r^{4} \\\\Sigma+r^{3} r_s \\\\Sigma-r^{2} \\\\Sigma^{2}\\\\right) \\\\sin{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}+\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(2a^{2} r^{3} r_s-2a^{2} r^{2} \\\\Sigma-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}+2r^{5} r_s-2r^{4} \\\\Sigma+r^{3} r_s \\\\Sigma-r^{2} \\\\Sigma^{2}\\\\right) \\\\Sigma \\\\sin{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\frac{\\\\sin{\\\\theta}}{2\\\\left(r r_s-\\\\Sigma\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}_{\\\\theta}{}^{\\\\phi}{}_{r}= & a r_s \\\\frac{-r \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\partial_{r}{\\\\Sigma}+r \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right) \\\\left(-a^{2} r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\partial_{r}{\\\\Sigma}-3r^{2} r_s+r^{2} \\\\partial_{r}{\\\\Sigma}+2r \\\\Sigma\\\\right) \\\\Sigma+\\\\left(a^{2} \\\\sin{\\\\theta}^{2}-2r r_s+r \\\\partial_{r}{\\\\Sigma}+\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma}{\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2} \\\\tan{\\\\theta}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}_{\\\\theta}{}^{\\\\phi}{}_{\\\\theta}= & a r r_s \\\\frac{\\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\sin{2\\\\theta}+a^{2} \\\\partial_{\\\\theta}{\\\\Sigma}+r^{2} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\Sigma \\\\tan{\\\\theta}-\\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\tan{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}+\\\\left(a^{2} \\\\cos{2\\\\theta} \\\\tan{\\\\theta}^{2}+\\\\frac{r r_s-\\\\Sigma}{\\\\cos{\\\\theta}^{2}}+\\\\tan{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma}{\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2} \\\\tan{\\\\theta}^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}_{\\\\theta}{}^{t}{}_{r}= & -a^{2} r_s \\\\left(a^{4} r^{2} r_s \\\\cos{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}-2a^{4} r \\\\Sigma \\\\partial_{r}{\\\\Sigma}+a^{4} \\\\Sigma^{2}+a^{2} r^{4} r_s \\\\cos{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}+a^{2} r^{4} r_s \\\\partial_{r}{\\\\Sigma}-a^{2} r^{3} r_s^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}-2a^{2} r^{3} r_s \\\\Sigma \\\\cos{\\\\theta}^{2}+2a^{2} r^{3} r_s \\\\Sigma-4a^{2} r^{3} \\\\Sigma \\\\partial_{r}{\\\\Sigma}+a^{2} r^{2} r_s^{2} \\\\Sigma \\\\cos{\\\\theta}^{2}+2a^{2} r^{2} r_s \\\\Sigma \\\\partial_{r}{\\\\Sigma}+2a^{2} r^{2} \\\\Sigma^{2}-2a^{2} r r_s \\\\Sigma^{2}+r^{6} r_s \\\\partial_{r}{\\\\Sigma}-r^{5} r_s^{2} \\\\partial_{r}{\\\\Sigma}-2r^{5} \\\\Sigma \\\\partial_{r}{\\\\Sigma}-r^{4} r_s^{2} \\\\Sigma+2r^{4} r_s \\\\Sigma \\\\partial_{r}{\\\\Sigma}+r^{4} \\\\Sigma^{2}\\\\right) \\\\sin{\\\\theta} \\\\frac{\\\\cos{\\\\theta}}{\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}_{\\\\theta}{}^{t}{}_{\\\\theta}= & a^{2} r r_s \\\\frac{\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\sin{2\\\\theta}+a^{2} \\\\partial_{\\\\theta}{\\\\Sigma}+r^{2} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\Sigma \\\\sin{2\\\\theta}-\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}-\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(-2a^{2} r r_s \\\\cos{2\\\\theta}+2a^{2} \\\\Sigma \\\\cos{2\\\\theta}+a^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}-2r^{3} r_s \\\\cos{2\\\\theta}+2r^{2} r_s^{2} \\\\cos{2\\\\theta}+2r^{2} \\\\Sigma \\\\cos{2\\\\theta}+r^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}-2r r_s \\\\Sigma \\\\cos{2\\\\theta}-r r_s \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\Sigma+\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\Sigma \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}}{2\\\\left(r r_s-\\\\Sigma\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}_{r}{}^{\\\\phi}{}_{r}= & a r_s \\\\frac{-\\\\left(4r-\\\\partial_{r}{\\\\Sigma}\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma+\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\partial_{r}{\\\\Sigma}-\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(-a^{2} r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\partial_{r}{\\\\Sigma}-3r^{2} r_s+r^{2} \\\\partial_{r}{\\\\Sigma}+2r \\\\Sigma\\\\right) \\\\Sigma}{2\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}_{r}{}^{\\\\phi}{}_{\\\\theta}= & a r_s \\\\frac{-\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\sin{2\\\\theta}+a^{2} \\\\partial_{\\\\theta}{\\\\Sigma}+r^{2} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\Sigma+\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\partial_{\\\\theta}{\\\\Sigma}+\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma \\\\partial_{\\\\theta}{\\\\Sigma}}{2\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}_{r}{}^{t}{}_{r}= & r_s \\\\frac{\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(r_s-\\\\partial_{r}{\\\\Sigma}\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma+\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\partial_{r}{\\\\Sigma}-\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(-a^{2} r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\partial_{r}{\\\\Sigma}-3r^{2} r_s+r^{2} \\\\partial_{r}{\\\\Sigma}+2r \\\\Sigma\\\\right) \\\\Sigma+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(-\\\\left(4r-\\\\partial_{r}{\\\\Sigma}\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)+\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(-a^{2} r_s+a^{2} \\\\partial_{r}{\\\\Sigma}-3r^{2} r_s+r^{2} \\\\partial_{r}{\\\\Sigma}+2r \\\\Sigma\\\\right)\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma}{2\\\\left(r r_s-\\\\Sigma\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}_{r}{}^{t}{}_{\\\\theta}= & r_s \\\\frac{-\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\sin{2\\\\theta}+a^{2} \\\\partial_{\\\\theta}{\\\\Sigma}+r^{2} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma+\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\partial_{\\\\theta}{\\\\Sigma}-\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma \\\\partial_{\\\\theta}{\\\\Sigma}+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma+\\\\left(a^{2}+r^{2}\\\\right) \\\\left(2r^{2}-\\\\Sigma\\\\right)\\\\right) \\\\Sigma \\\\partial_{\\\\theta}{\\\\Sigma}}{2\\\\left(r r_s-\\\\Sigma\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{\\\\theta}{}^{r}{}_{r}= & a^{2} \\\\sin{2\\\\theta} \\\\frac{\\\\partial_{r}{\\\\Sigma}}{2\\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{\\\\theta}{}^{r}{}_{\\\\theta}= & a^{2} \\\\frac{-\\\\Sigma \\\\cos{2\\\\theta}+\\\\frac{1}{2}\\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}}{\\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{r}{}^{r}{}_{r}= & -r \\\\frac{\\\\partial_{r}{\\\\Sigma}}{\\\\Sigma^{2}}+r \\\\frac{\\\\partial_{r}{\\\\Delta}}{\\\\Delta^{2}}-r_s \\\\frac{\\\\partial_{r}{\\\\Delta}}{2\\\\Delta^{2}}+\\\\frac{1}{\\\\Sigma} - \\\\frac{1}{\\\\Delta}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{r}{}^{r}{}_{\\\\theta}= & -r \\\\frac{\\\\partial_{\\\\theta}{\\\\Sigma}}{\\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{\\\\theta}{}^{\\\\theta}{}_{r}= & a^{2} \\\\sin{2\\\\theta} \\\\frac{\\\\partial_{r}{\\\\Sigma}}{2\\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{\\\\theta}{}^{\\\\theta}{}_{\\\\theta}= & a^{2} \\\\frac{-\\\\Sigma \\\\cos{2\\\\theta}+\\\\frac{1}{2}\\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}}{\\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{r}{}^{\\\\theta}{}_{r}= & \\\\frac{-r \\\\partial_{r}{\\\\Sigma}+\\\\Sigma}{\\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{r}{}^{\\\\theta}{}_{\\\\theta}= & -r \\\\frac{\\\\partial_{\\\\theta}{\\\\Sigma}}{\\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{\\\\theta}{}^{\\\\phi}{}_{r}= & a^{2} r_s \\\\left(-a^{4} r^{2} r_s \\\\sin{\\\\theta}^{4} \\\\partial_{r}{\\\\Sigma}+a^{4} r^{2} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}-2a^{4} r \\\\Sigma \\\\sin{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}+a^{4} \\\\Sigma^{2} \\\\sin{\\\\theta}^{2}+a^{2} r^{4} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}+a^{2} r^{3} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}-a^{2} r^{3} r_s^{2} \\\\partial_{r}{\\\\Sigma}+2a^{2} r^{3} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-2a^{2} r^{3} \\\\Sigma \\\\sin{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}-a^{2} r^{2} r_s^{2} \\\\Sigma \\\\sin{\\\\theta}^{2}+a^{2} r^{2} r_s^{2} \\\\Sigma+2a^{2} r^{2} r_s \\\\Sigma \\\\partial_{r}{\\\\Sigma}-a^{2} r^{2} \\\\Sigma^{2} \\\\sin{\\\\theta}^{2}-2a^{2} r r_s \\\\Sigma^{2}-a^{2} r \\\\Sigma^{2} \\\\partial_{r}{\\\\Sigma}+a^{2} \\\\Sigma^{3}-r^{5} r_s^{2} \\\\partial_{r}{\\\\Sigma}-r^{4} r_s^{2} \\\\Sigma+2r^{4} r_s \\\\Sigma \\\\partial_{r}{\\\\Sigma}%\\n+2r^{3} r_s \\\\Sigma^{2}-r^{3} \\\\Sigma^{2} \\\\partial_{r}{\\\\Sigma}-r^{2} \\\\Sigma^{3}\\\\right) \\\\sin{\\\\theta} \\\\frac{\\\\cos{\\\\theta}}{\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{\\\\theta}{}^{\\\\phi}{}_{\\\\theta}= & \\\\frac{-\\\\left(a^{2} r r_s \\\\sin{2\\\\theta}+a^{2} \\\\partial_{\\\\theta}{\\\\Sigma}+r^{2} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right) \\\\Sigma \\\\sin{\\\\theta} \\\\cos{\\\\theta}+\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right) \\\\Sigma \\\\cos{\\\\theta}^{2}+2\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right) \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}+\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(5a^{4} r r_s \\\\Sigma \\\\sin{\\\\theta}^{5}-4a^{4} r r_s \\\\Sigma \\\\sin{\\\\theta}^{3}-a^{4} r r_s \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}-3a^{2} r^{2} r_s^{2} \\\\Sigma \\\\sin{\\\\theta}^{3}+2a^{2} r^{2} r_s^{2} \\\\Sigma \\\\sin{\\\\theta}-a^{2} r^{2} r_s^{2} \\\\cos{\\\\theta}^{3} \\\\partial_{\\\\theta}{\\\\Sigma}+a^{2} r^{2} r_s^{2} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}+6a^{2} r r_s \\\\Sigma^{2} \\\\sin{\\\\theta}^{3}-5a^{2} r r_s \\\\Sigma^{2} \\\\sin{\\\\theta}+4a^{2} r r_s \\\\Sigma \\\\cos{\\\\theta}^{3} \\\\partial_{\\\\theta}{\\\\Sigma}-2a^{2} r r_s \\\\Sigma \\\\cos{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}+a^{2} \\\\Sigma^{3} \\\\sin{\\\\theta}-3a^{2} \\\\Sigma^{2} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}-r^{3} r_s \\\\Sigma^{2} \\\\sin{\\\\theta}+2r^{3} r_s \\\\Sigma \\\\cos{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}+r^{2} \\\\Sigma^{3} \\\\sin{\\\\theta}-3r^{2} \\\\Sigma^{2} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\sin{\\\\theta}}{\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2} \\\\sin{\\\\theta}^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{\\\\theta}{}^{t}{}_{r}= & a^{3} r_s \\\\left(-r \\\\left(r_s-\\\\partial_{r}{\\\\Sigma}\\\\right) \\\\left(-a^{2} r r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\Sigma-r^{3} r_s+r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\Sigma-r \\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(-a^{2} r r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\Sigma-r^{3} r_s+r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\partial_{r}{\\\\Sigma}-r \\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(-a^{2} r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\partial_{r}{\\\\Sigma}-3r^{2} r_s+r^{2} \\\\partial_{r}{\\\\Sigma}+2r \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\Sigma+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(-a^{2} r r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\Sigma-r^{3} r_s+r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma+r \\\\left(a^{2} r_s-a^{2} \\\\partial_{r}{\\\\Sigma}+3r^{2} r_s-r^{2} \\\\partial_{r}{\\\\Sigma}-2r r_s^{2}+r r_s \\\\partial_{r}{\\\\Sigma}-2r \\\\Sigma+r_s \\\\Sigma\\\\right)\\\\right) \\\\Sigma\\\\right) \\\\sin{\\\\theta}^{3} \\\\frac{\\\\cos{\\\\theta}}{\\\\left(r r_s-\\\\Sigma\\\\right)^{2} \\\\left(-a^{2} r r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\Sigma-r^{3} r_s+r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{\\\\theta}{}^{t}{}_{\\\\theta}= & a^{3} r r_s \\\\left(-\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\sin{2\\\\theta}+a^{2} \\\\partial_{\\\\theta}{\\\\Sigma}+r^{2} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\Sigma \\\\sin{\\\\theta} \\\\cos{\\\\theta}-\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(-a^{2} r r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\Sigma-r^{3} r_s+r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(-a^{2} r r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\Sigma-r^{3} r_s+r^{2} \\\\Sigma\\\\right) \\\\left(2a^{2} r r_s \\\\cos{2\\\\theta}+a^{2} r r_s-2a^{2} \\\\Sigma \\\\cos{2\\\\theta}-a^{2} \\\\Sigma - \\\\frac{1}{2}a^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}+2r^{3} r_s \\\\cos{2\\\\theta}+r^{3} r_s-2r^{2} r_s^{2} \\\\cos{2\\\\theta}-r^{2} r_s^{2}-2r^{2} \\\\Sigma \\\\cos{2\\\\theta}-r^{2} \\\\Sigma - \\\\frac{1}{2}r^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}+2r r_s \\\\Sigma \\\\cos{2\\\\theta}+r r_s \\\\Sigma+\\\\frac{1}{2}r r_s \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\Sigma+\\\\left(-a^{2} r r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\Sigma-r^{3} r_s+r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\Sigma \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\frac{\\\\sin{\\\\theta}^{2}}{\\\\left(r r_s-\\\\Sigma\\\\right)^{2} \\\\left(-a^{2} r r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\Sigma-r^{3} r_s+r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{r}{}^{\\\\phi}{}_{r}= & \\\\frac{-\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right) \\\\partial_{r}{\\\\Sigma}+\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(4a^{2} r r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}+2r^{2} r_s \\\\partial_{r}{\\\\Sigma}+4r r_s \\\\Sigma-4r \\\\Sigma \\\\partial_{r}{\\\\Sigma}-2\\\\Sigma^{2}\\\\right) \\\\Sigma+\\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right) \\\\left(-a^{2} r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\partial_{r}{\\\\Sigma}-3r^{2} r_s+r^{2} \\\\partial_{r}{\\\\Sigma}+2r \\\\Sigma\\\\right) \\\\Sigma}{2\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{r}{}^{\\\\phi}{}_{\\\\theta}= & \\\\frac{\\\\left(a^{2} r r_s \\\\sin{2\\\\theta}+a^{2} \\\\partial_{\\\\theta}{\\\\Sigma}+r^{2} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right) \\\\Sigma-\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right) \\\\partial_{\\\\theta}{\\\\Sigma}+\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{2\\\\theta}-a^{2} r_s \\\\Sigma \\\\sin{2\\\\theta}-a^{2} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{\\\\theta}{\\\\Sigma}+2r^{2} r_s \\\\partial_{\\\\theta}{\\\\Sigma}-4r \\\\Sigma \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\Sigma}{2\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{r}{}^{t}{}_{r}= & -a r_s \\\\left(2a^{4} r^{3} r_s \\\\cos{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}-2a^{4} r^{2} r_s \\\\Sigma \\\\cos{\\\\theta}^{2}-4a^{4} r^{2} \\\\Sigma \\\\partial_{r}{\\\\Sigma}+4a^{4} r \\\\Sigma^{2}-a^{4} r_s \\\\Sigma^{2} \\\\cos{\\\\theta}^{2}+a^{4} \\\\Sigma^{2} \\\\partial_{r}{\\\\Sigma}+2a^{2} r^{5} r_s \\\\cos{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}+2a^{2} r^{5} r_s \\\\partial_{r}{\\\\Sigma}-6a^{2} r^{4} r_s \\\\Sigma \\\\cos{\\\\theta}^{2}+2a^{2} r^{4} r_s \\\\Sigma-8a^{2} r^{4} \\\\Sigma \\\\partial_{r}{\\\\Sigma}+8a^{2} r^{3} \\\\Sigma^{2}-a^{2} r^{2} r_s \\\\Sigma^{2} \\\\cos{\\\\theta}^{2}-3a^{2} r^{2} r_s \\\\Sigma^{2}+4a^{2} r \\\\Sigma^{3}+2r^{7} r_s \\\\partial_{r}{\\\\Sigma}-2r^{6} r_s \\\\Sigma-4r^{6} \\\\Sigma \\\\partial_{r}{\\\\Sigma}+4r^{5} \\\\Sigma^{2}%\\n+r^{4} r_s \\\\Sigma^{2}-r^{4} \\\\Sigma^{2} \\\\partial_{r}{\\\\Sigma}\\\\right) \\\\frac{\\\\sin{\\\\theta}^{2}}{2\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{r}{}^{t}{}_{\\\\theta}= & a r_s \\\\left(\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(-\\\\left(2a^{2} r^{2}+a^{2} r r_s-2a^{2} \\\\Sigma+2r^{4}-r^{3} r_s+2r^{2} \\\\Sigma\\\\right) \\\\sin{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}+2\\\\left(2a^{2} r^{3} r_s-2a^{2} r^{2} \\\\Sigma-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}+2r^{5} r_s-2r^{4} \\\\Sigma+r^{3} r_s \\\\Sigma-r^{2} \\\\Sigma^{2}\\\\right) \\\\cos{\\\\theta}\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\sin{2\\\\theta}+a^{2} \\\\partial_{\\\\theta}{\\\\Sigma}+r^{2} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\left(2a^{2} r^{3} r_s-2a^{2} r^{2} \\\\Sigma-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}+2r^{5} r_s-2r^{4} \\\\Sigma+r^{3} r_s \\\\Sigma-r^{2} \\\\Sigma^{2}\\\\right) \\\\Sigma \\\\sin{\\\\theta}-\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(2a^{2} r^{3} r_s-2a^{2} r^{2} \\\\Sigma-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}+2r^{5} r_s-2r^{4} \\\\Sigma+r^{3} r_s \\\\Sigma-r^{2} \\\\Sigma^{2}\\\\right) \\\\sin{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}+\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(2a^{2} r^{3} r_s-2a^{2} r^{2} \\\\Sigma-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}+2r^{5} r_s-2r^{4} \\\\Sigma+r^{3} r_s \\\\Sigma-r^{2} \\\\Sigma^{2}\\\\right) \\\\Sigma \\\\sin{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\frac{\\\\sin{\\\\theta}}{2\\\\left(r r_s-\\\\Sigma\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\end{aligned}\\\\right.\\n\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"substitute(tst1,ch)\\nevaluate(tst1, kerr);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\left\\\\{\\\\begin{aligned}\\\\square{}_{r}{}^{t}{}_{\\\\phi}{}_{r}= & a r_s \\\\left(-r_s \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right)\\\\right) \\\\left(2a^{2} r^{3} r_s-2a^{2} r^{2} \\\\Sigma-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}+2r^{5} r_s-2r^{4} \\\\Sigma+r^{3} r_s \\\\Sigma-r^{2} \\\\Sigma^{2}\\\\right) \\\\frac{\\\\sin{\\\\theta}^{2}}{4\\\\left(r r_s-\\\\Sigma\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}^{t}{}_{\\\\phi}{}_{\\\\theta}= & a r_s \\\\left(a^{2} r r_s \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{\\\\theta}^{2}-\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right) \\\\left(2a^{2} r^{3} r_s-2a^{2} r^{2} \\\\Sigma-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}+2r^{5} r_s-2r^{4} \\\\Sigma+r^{3} r_s \\\\Sigma-r^{2} \\\\Sigma^{2}\\\\right)\\\\right) \\\\sin{\\\\theta} \\\\frac{\\\\cos{\\\\theta}}{2\\\\left(r r_s-\\\\Sigma\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{3} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}^{t}{}_{t}{}_{r}= & r_s^{2} \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\frac{-a^{2} \\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(2a^{2} r^{3} r_s-2a^{2} r^{2} \\\\Sigma-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}+2r^{5} r_s-2r^{4} \\\\Sigma+r^{3} r_s \\\\Sigma-r^{2} \\\\Sigma^{2}\\\\right) \\\\sin{\\\\theta}^{2}+\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2}}{4\\\\left(r r_s-\\\\Sigma\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}^{t}{}_{t}{}_{\\\\theta}= & a^{2} r r_s^{2} \\\\frac{-\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right) \\\\left(2a^{2} r^{3} r_s-2a^{2} r^{2} \\\\Sigma-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}+2r^{5} r_s-2r^{4} \\\\Sigma+r^{3} r_s \\\\Sigma-r^{2} \\\\Sigma^{2}\\\\right) \\\\sin{\\\\theta}^{2}}{4\\\\left(r r_s-\\\\Sigma\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2} \\\\tan{\\\\theta}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}^{t}{}_{r}{}_{\\\\phi}= & a r_s \\\\left(-r_s \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right)\\\\right) \\\\left(2a^{2} r^{3} r_s-2a^{2} r^{2} \\\\Sigma-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}+2r^{5} r_s-2r^{4} \\\\Sigma+r^{3} r_s \\\\Sigma-r^{2} \\\\Sigma^{2}\\\\right) \\\\frac{\\\\sin{\\\\theta}^{2}}{4\\\\left(r r_s-\\\\Sigma\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}^{t}{}_{\\\\theta}{}_{\\\\phi}= & a r_s \\\\left(a^{2} r r_s \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{\\\\theta}^{2}-\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right) \\\\left(2a^{2} r^{3} r_s-2a^{2} r^{2} \\\\Sigma-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}+2r^{5} r_s-2r^{4} \\\\Sigma+r^{3} r_s \\\\Sigma-r^{2} \\\\Sigma^{2}\\\\right)\\\\right) \\\\sin{\\\\theta} \\\\frac{\\\\cos{\\\\theta}}{2\\\\left(r r_s-\\\\Sigma\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{3} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}^{t}{}_{r}{}_{t}= & r_s^{2} \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\frac{-a^{2} \\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(2a^{2} r^{3} r_s-2a^{2} r^{2} \\\\Sigma-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}+2r^{5} r_s-2r^{4} \\\\Sigma+r^{3} r_s \\\\Sigma-r^{2} \\\\Sigma^{2}\\\\right) \\\\sin{\\\\theta}^{2}+\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2}}{4\\\\left(r r_s-\\\\Sigma\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}^{t}{}_{\\\\theta}{}_{t}= & a^{2} r r_s^{2} \\\\frac{-\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right) \\\\left(2a^{2} r^{3} r_s-2a^{2} r^{2} \\\\Sigma-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}+2r^{5} r_s-2r^{4} \\\\Sigma+r^{3} r_s \\\\Sigma-r^{2} \\\\Sigma^{2}\\\\right) \\\\sin{\\\\theta}^{2}}{4\\\\left(r r_s-\\\\Sigma\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2} \\\\tan{\\\\theta}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}^{\\\\phi}{}_{\\\\phi}{}_{r}= & \\\\frac{-a^{2} r_s^{2} \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(2a^{2} r^{3} r_s-2a^{2} r^{2} \\\\Sigma-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}+2r^{5} r_s-2r^{4} \\\\Sigma+r^{3} r_s \\\\Sigma-r^{2} \\\\Sigma^{2}\\\\right) \\\\sin{\\\\theta}^{2}+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right)^{2}}{4\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}^{\\\\phi}{}_{\\\\phi}{}_{\\\\theta}= & \\\\frac{a^{4} r r_s^{2} \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{\\\\theta}^{4}-\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right)}{2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{3} \\\\Sigma^{2} \\\\tan{\\\\theta}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}^{\\\\phi}{}_{t}{}_{r}= & a r_s \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\frac{r_s \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)+\\\\left(-r r_s+\\\\Sigma\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right)}{4\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}^{\\\\phi}{}_{t}{}_{\\\\theta}= & a r r_s \\\\frac{-a^{2} r_s \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right)}{4\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2} \\\\tan{\\\\theta}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}^{\\\\phi}{}_{r}{}_{\\\\phi}= & \\\\frac{-a^{2} r_s^{2} \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(2a^{2} r^{3} r_s-2a^{2} r^{2} \\\\Sigma-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}+2r^{5} r_s-2r^{4} \\\\Sigma+r^{3} r_s \\\\Sigma-r^{2} \\\\Sigma^{2}\\\\right) \\\\sin{\\\\theta}^{2}+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right)^{2}}{4\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}^{\\\\phi}{}_{\\\\theta}{}_{\\\\phi}= & \\\\frac{a^{4} r r_s^{2} \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{\\\\theta}^{4}-\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right)}{2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{3} \\\\Sigma^{2} \\\\tan{\\\\theta}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}^{\\\\phi}{}_{r}{}_{t}= & a r_s \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\frac{r_s \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)+\\\\left(-r r_s+\\\\Sigma\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right)}{4\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}^{\\\\phi}{}_{\\\\theta}{}_{t}= & a r r_s \\\\frac{-a^{2} r_s \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right)}{4\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2} \\\\tan{\\\\theta}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}^{t}{}_{\\\\phi}{}_{r}= & a^{3} r r_s \\\\left(2a^{4} r^{2} r_s \\\\cos{\\\\theta}^{2}-a^{4} r_s \\\\Sigma \\\\cos{\\\\theta}^{2}+2a^{2} r^{4} r_s \\\\cos{\\\\theta}^{2}+2a^{2} r^{4} r_s-2a^{2} r^{3} r_s^{2} \\\\cos{\\\\theta}^{2}-a^{2} r^{2} r_s \\\\Sigma \\\\cos{\\\\theta}^{2}-a^{2} r^{2} r_s \\\\Sigma+a^{2} r r_s^{2} \\\\Sigma \\\\cos{\\\\theta}^{2}+2a^{2} r \\\\Sigma^{2}+2r^{6} r_s-2r^{5} r_s^{2}-r^{4} r_s \\\\Sigma+r^{3} r_s^{2} \\\\Sigma+2r^{3} \\\\Sigma^{2}-2r^{2} r_s \\\\Sigma^{2}\\\\right) \\\\sin{\\\\theta}^{3} \\\\frac{\\\\cos{\\\\theta}}{2\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}^{t}{}_{\\\\phi}{}_{\\\\theta}= & -a^{3} r r_s \\\\left(a^{2} r r_s \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{\\\\theta} \\\\sin{2\\\\theta}-2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right) \\\\cos{\\\\theta}\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{\\\\theta}^{2} \\\\frac{\\\\cos{\\\\theta}}{2\\\\left(r r_s-\\\\Sigma\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}^{t}{}_{t}{}_{r}= & a^{2} r r_s^{2} \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(-a^{4} \\\\cos{\\\\theta}^{2}-a^{2} r^{2} \\\\cos{\\\\theta}^{2}-a^{2} r^{2}+a^{2} r r_s \\\\cos{\\\\theta}^{2}-r^{4}+r^{3} r_s\\\\right) \\\\sin{\\\\theta} \\\\frac{\\\\cos{\\\\theta}}{2\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}^{t}{}_{t}{}_{\\\\theta}= & a^{4} r^{2} r_s^{2} \\\\left(\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)+\\\\left(-a^{2} r r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\Sigma-r^{3} r_s+r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right)\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{\\\\theta}^{2} \\\\frac{\\\\cos{\\\\theta}^{2}}{\\\\left(r r_s-\\\\Sigma\\\\right)^{2} \\\\left(-a^{2} r r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\Sigma-r^{3} r_s+r^{2} \\\\Sigma\\\\right)^{3} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}^{t}{}_{r}{}_{\\\\phi}= & a^{3} r r_s \\\\left(2a^{4} r^{2} r_s \\\\cos{\\\\theta}^{2}-a^{4} r_s \\\\Sigma \\\\cos{\\\\theta}^{2}+2a^{2} r^{4} r_s \\\\cos{\\\\theta}^{2}+2a^{2} r^{4} r_s-2a^{2} r^{3} r_s^{2} \\\\cos{\\\\theta}^{2}-a^{2} r^{2} r_s \\\\Sigma \\\\cos{\\\\theta}^{2}-a^{2} r^{2} r_s \\\\Sigma+a^{2} r r_s^{2} \\\\Sigma \\\\cos{\\\\theta}^{2}+2a^{2} r \\\\Sigma^{2}+2r^{6} r_s-2r^{5} r_s^{2}-r^{4} r_s \\\\Sigma+r^{3} r_s^{2} \\\\Sigma+2r^{3} \\\\Sigma^{2}-2r^{2} r_s \\\\Sigma^{2}\\\\right) \\\\sin{\\\\theta}^{3} \\\\frac{\\\\cos{\\\\theta}}{2\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}^{t}{}_{\\\\theta}{}_{\\\\phi}= & -a^{3} r r_s \\\\left(a^{2} r r_s \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{\\\\theta} \\\\sin{2\\\\theta}-2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right) \\\\cos{\\\\theta}\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{\\\\theta}^{2} \\\\frac{\\\\cos{\\\\theta}}{2\\\\left(r r_s-\\\\Sigma\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}^{t}{}_{r}{}_{t}= & a^{2} r r_s^{2} \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(-a^{4} \\\\cos{\\\\theta}^{2}-a^{2} r^{2} \\\\cos{\\\\theta}^{2}-a^{2} r^{2}+a^{2} r r_s \\\\cos{\\\\theta}^{2}-r^{4}+r^{3} r_s\\\\right) \\\\sin{\\\\theta} \\\\frac{\\\\cos{\\\\theta}}{2\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}^{t}{}_{\\\\theta}{}_{t}= & a^{4} r^{2} r_s^{2} \\\\left(\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)+\\\\left(-a^{2} r r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\Sigma-r^{3} r_s+r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right)\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{\\\\theta}^{2} \\\\frac{\\\\cos{\\\\theta}^{2}}{\\\\left(r r_s-\\\\Sigma\\\\right)^{2} \\\\left(-a^{2} r r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\Sigma-r^{3} r_s+r^{2} \\\\Sigma\\\\right)^{3} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}^{\\\\phi}{}_{\\\\phi}{}_{r}= & \\\\frac{a^{2} r r_s^{2} \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right) \\\\left(2a^{2} r^{3} r_s-2a^{2} r^{2} \\\\Sigma-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}+2r^{5} r_s-2r^{4} \\\\Sigma+r^{3} r_s \\\\Sigma-r^{2} \\\\Sigma^{2}\\\\right) \\\\sin{\\\\theta}^{3}-\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right) \\\\sin{\\\\theta}}{2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2} \\\\sin{\\\\theta} \\\\tan{\\\\theta}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}^{\\\\phi}{}_{\\\\phi}{}_{\\\\theta}= & \\\\frac{a^{4} r^{2} r_s^{2} \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{\\\\theta}^{4}+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(-a^{2} r r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\Sigma-r^{3} r_s+r^{2} \\\\Sigma\\\\right) \\\\left(-a^{4} r r_s \\\\left(-\\\\cos{\\\\theta}^{2}+1\\\\right)^{2}-a^{2} r^{2} r_s^{2} \\\\cos{\\\\theta}^{2}+a^{2} r^{2} r_s^{2}+2a^{2} r r_s \\\\Sigma \\\\cos{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma-a^{2} \\\\Sigma^{2}+r^{3} r_s \\\\Sigma-r^{2} \\\\Sigma^{2}\\\\right)^{2}}{\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(-a^{2} r r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\Sigma-r^{3} r_s+r^{2} \\\\Sigma\\\\right)^{3} \\\\Sigma^{2} \\\\tan{\\\\theta}^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}^{\\\\phi}{}_{t}{}_{r}= & a r_s \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\frac{-r r_s \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right)}{2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2} \\\\tan{\\\\theta}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}^{\\\\phi}{}_{t}{}_{\\\\theta}= & a r r_s \\\\left(a^{2} r r_s \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{\\\\theta} \\\\sin{2\\\\theta}-2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right) \\\\cos{\\\\theta}\\\\right) \\\\frac{a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma}{2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2} \\\\sin{\\\\theta} \\\\tan{\\\\theta}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}^{\\\\phi}{}_{r}{}_{\\\\phi}= & \\\\frac{a^{2} r r_s^{2} \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right) \\\\left(2a^{2} r^{3} r_s-2a^{2} r^{2} \\\\Sigma-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}+2r^{5} r_s-2r^{4} \\\\Sigma+r^{3} r_s \\\\Sigma-r^{2} \\\\Sigma^{2}\\\\right) \\\\sin{\\\\theta}^{3}-\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right) \\\\sin{\\\\theta}}{2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2} \\\\sin{\\\\theta} \\\\tan{\\\\theta}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}^{\\\\phi}{}_{\\\\theta}{}_{\\\\phi}= & \\\\frac{a^{4} r^{2} r_s^{2} \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{\\\\theta}^{4}+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(-a^{2} r r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\Sigma-r^{3} r_s+r^{2} \\\\Sigma\\\\right) \\\\left(-a^{4} r r_s \\\\left(-\\\\cos{\\\\theta}^{2}+1\\\\right)^{2}-a^{2} r^{2} r_s^{2} \\\\cos{\\\\theta}^{2}+a^{2} r^{2} r_s^{2}+2a^{2} r r_s \\\\Sigma \\\\cos{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma-a^{2} \\\\Sigma^{2}+r^{3} r_s \\\\Sigma-r^{2} \\\\Sigma^{2}\\\\right)^{2}}{\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(-a^{2} r r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\Sigma-r^{3} r_s+r^{2} \\\\Sigma\\\\right)^{3} \\\\Sigma^{2} \\\\tan{\\\\theta}^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}^{\\\\phi}{}_{r}{}_{t}= & a r_s \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\frac{-r r_s \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right)}{2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2} \\\\tan{\\\\theta}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}^{\\\\phi}{}_{\\\\theta}{}_{t}= & a r r_s \\\\left(a^{2} r r_s \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{\\\\theta} \\\\sin{2\\\\theta}-2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right) \\\\cos{\\\\theta}\\\\right) \\\\frac{a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma}{2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2} \\\\sin{\\\\theta} \\\\tan{\\\\theta}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}^{\\\\theta}{}_{\\\\theta}{}_{r}= & \\\\frac{-a^{4} \\\\left( - \\\\frac{1}{8}\\\\cos{4\\\\theta}+\\\\frac{1}{8}\\\\right)+r^{2} \\\\Delta}{\\\\Delta \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}^{\\\\theta}{}_{\\\\theta}{}_{\\\\theta}= & -a^{2} r \\\\frac{\\\\sin{2\\\\theta}}{\\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}^{\\\\theta}{}_{r}{}_{\\\\theta}= & \\\\frac{-a^{4} \\\\left( - \\\\frac{1}{8}\\\\cos{4\\\\theta}+\\\\frac{1}{8}\\\\right)+r^{2} \\\\Delta}{\\\\Delta \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}^{\\\\theta}{}_{\\\\phi}{}_{\\\\phi}= & -\\\\left(a^{4} r_s \\\\sin{\\\\theta}^{4}+4a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}+2a^{2} r \\\\Sigma \\\\sin{\\\\theta}^{2}+2a^{2} r \\\\Sigma+2r^{3} \\\\Sigma\\\\right) \\\\sin{\\\\theta} \\\\frac{\\\\cos{\\\\theta}}{2\\\\Sigma^{3}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}^{\\\\theta}{}_{r}{}_{r}= & a^{2} \\\\left(4r \\\\Delta+\\\\left(-2r+r_s\\\\right) \\\\Sigma\\\\right) \\\\frac{\\\\sin{2\\\\theta}}{4\\\\Delta^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}^{\\\\theta}{}_{t}{}_{\\\\phi}= & a r_s \\\\left(a^{2} \\\\sin{\\\\theta}^{2}+2r^{2}\\\\right) \\\\sin{\\\\theta} \\\\frac{\\\\cos{\\\\theta}}{2\\\\Sigma^{3}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}^{\\\\theta}{}_{\\\\phi}{}_{t}= & a r_s \\\\left(a^{2} \\\\sin{\\\\theta}^{2}+2r^{2}\\\\right) \\\\sin{\\\\theta} \\\\frac{\\\\cos{\\\\theta}}{2\\\\Sigma^{3}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}^{\\\\theta}{}_{t}{}_{t}= & -a^{2} r_s \\\\frac{\\\\sin{2\\\\theta}}{4\\\\Sigma^{3}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}^{\\\\theta}{}_{\\\\theta}{}_{r}= & -a^{2} r \\\\frac{\\\\sin{2\\\\theta}}{\\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}^{\\\\theta}{}_{\\\\theta}{}_{\\\\theta}= & \\\\frac{a^{4} \\\\left( - \\\\frac{1}{8}\\\\cos{4\\\\theta}+\\\\frac{1}{8}\\\\right)-r^{2} \\\\Delta}{\\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}^{\\\\theta}{}_{r}{}_{\\\\theta}= & -a^{2} r \\\\frac{\\\\sin{2\\\\theta}}{\\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}^{\\\\theta}{}_{\\\\phi}{}_{\\\\phi}= & \\\\left(2a^{2} \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+\\\\left(a^{2}+r^{2}\\\\right) \\\\Sigma^{2}\\\\right) \\\\cos{\\\\theta}^{2}-r \\\\left(-2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}+a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r \\\\Sigma^{2}\\\\right) \\\\Delta\\\\right) \\\\frac{\\\\sin{\\\\theta}^{2}}{2\\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}^{\\\\theta}{}_{r}{}_{r}= & \\\\frac{-a^{4} \\\\left( - \\\\frac{1}{4}\\\\cos{4\\\\theta}+\\\\frac{1}{4}\\\\right)+r \\\\left(2r \\\\Delta+\\\\left(-2r+r_s\\\\right) \\\\Sigma\\\\right)}{2\\\\Delta \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}^{\\\\theta}{}_{t}{}_{\\\\phi}= & a r r_s \\\\left(2a^{4} \\\\sin{\\\\theta}^{4}-2a^{4} \\\\sin{\\\\theta}^{2}+2a^{2} \\\\Sigma \\\\sin{\\\\theta}^{2}-2a^{2} \\\\Sigma-2r^{2} \\\\Delta+\\\\Delta \\\\Sigma\\\\right) \\\\frac{\\\\sin{\\\\theta}^{2}}{2\\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}^{\\\\theta}{}_{\\\\phi}{}_{t}= & a r r_s \\\\left(2a^{4} \\\\sin{\\\\theta}^{4}-2a^{4} \\\\sin{\\\\theta}^{2}+2a^{2} \\\\Sigma \\\\sin{\\\\theta}^{2}-2a^{2} \\\\Sigma-2r^{2} \\\\Delta+\\\\Delta \\\\Sigma\\\\right) \\\\frac{\\\\sin{\\\\theta}^{2}}{2\\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}^{\\\\theta}{}_{t}{}_{t}= & r r_s \\\\frac{a^{4} \\\\left( - \\\\frac{1}{4}\\\\cos{4\\\\theta}+\\\\frac{1}{4}\\\\right)+\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\Delta}{2\\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}^{r}{}_{r}{}_{r}= & \\\\frac{ - \\\\frac{1}{2}a^{4} \\\\left(-\\\\cos{4\\\\theta}+1\\\\right) \\\\Delta+\\\\left(2r \\\\Delta+\\\\left(-2r+r_s\\\\right) \\\\Sigma\\\\right)^{2}}{4\\\\Delta^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}^{r}{}_{r}{}_{\\\\theta}= & -a^{2} \\\\left(4r \\\\Delta-\\\\left(2r-r_s\\\\right) \\\\Sigma\\\\right) \\\\frac{\\\\sin{2\\\\theta}}{4\\\\Delta \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}^{r}{}_{\\\\theta}{}_{r}= & -a^{2} \\\\left(4r \\\\Delta-\\\\left(2r-r_s\\\\right) \\\\Sigma\\\\right) \\\\frac{\\\\sin{2\\\\theta}}{4\\\\Delta \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}^{r}{}_{\\\\phi}{}_{\\\\phi}= & \\\\left(4a^{2} \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+\\\\left(a^{2}+r^{2}\\\\right) \\\\Sigma^{2}\\\\right) \\\\cos{\\\\theta}^{2}-\\\\left(2r \\\\Delta+\\\\left(-2r+r_s\\\\right) \\\\Sigma\\\\right) \\\\left(-2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}+a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r \\\\Sigma^{2}\\\\right)\\\\right) \\\\frac{\\\\sin{\\\\theta}^{2}}{4\\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}^{r}{}_{\\\\theta}{}_{\\\\theta}= & \\\\frac{a^{4} \\\\left( - \\\\frac{1}{4}\\\\cos{4\\\\theta}+\\\\frac{1}{4}\\\\right)-r \\\\left(2r \\\\Delta+\\\\left(-2r+r_s\\\\right) \\\\Sigma\\\\right)}{2\\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}^{r}{}_{t}{}_{\\\\phi}= & a r_s \\\\left(4a^{4} r \\\\sin{\\\\theta}^{4}-4a^{4} r \\\\sin{\\\\theta}^{2}+4a^{2} r \\\\Sigma \\\\sin{\\\\theta}^{2}-4a^{2} r \\\\Sigma-4r^{3} \\\\Delta+4r^{3} \\\\Sigma-2r^{2} r_s \\\\Sigma+2r \\\\Delta \\\\Sigma-2r \\\\Sigma^{2}+r_s \\\\Sigma^{2}\\\\right) \\\\frac{\\\\sin{\\\\theta}^{2}}{4\\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}^{r}{}_{\\\\phi}{}_{t}= & a r_s \\\\left(4a^{4} r \\\\sin{\\\\theta}^{4}-4a^{4} r \\\\sin{\\\\theta}^{2}+4a^{2} r \\\\Sigma \\\\sin{\\\\theta}^{2}-4a^{2} r \\\\Sigma-4r^{3} \\\\Delta+4r^{3} \\\\Sigma-2r^{2} r_s \\\\Sigma+2r \\\\Delta \\\\Sigma-2r \\\\Sigma^{2}+r_s \\\\Sigma^{2}\\\\right) \\\\frac{\\\\sin{\\\\theta}^{2}}{4\\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}^{r}{}_{t}{}_{t}= & r_s \\\\frac{a^{4} r \\\\left( - \\\\frac{1}{2}\\\\cos{4\\\\theta}+\\\\frac{1}{2}\\\\right)+\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(2r \\\\Delta+\\\\left(-2r+r_s\\\\right) \\\\Sigma\\\\right)}{4\\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}^{r}{}_{r}{}_{r}= & -a^{2} \\\\left(4r \\\\Delta-\\\\left(2r-r_s\\\\right) \\\\Sigma\\\\right) \\\\frac{\\\\sin{2\\\\theta}}{4\\\\Delta \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}^{r}{}_{r}{}_{\\\\theta}= & \\\\frac{a^{4} \\\\left( - \\\\frac{1}{8}\\\\cos{4\\\\theta}+\\\\frac{1}{8}\\\\right)-r^{2} \\\\Delta}{\\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}^{r}{}_{\\\\theta}{}_{r}= & \\\\frac{a^{4} \\\\left( - \\\\frac{1}{8}\\\\cos{4\\\\theta}+\\\\frac{1}{8}\\\\right)-r^{2} \\\\Delta}{\\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}^{r}{}_{\\\\phi}{}_{\\\\phi}= & \\\\left(a^{4} r_s \\\\sin{\\\\theta}^{4}+4a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}+2a^{2} r \\\\Sigma \\\\sin{\\\\theta}^{2}+2a^{2} r \\\\Sigma+2r^{3} \\\\Sigma\\\\right) \\\\Delta \\\\sin{\\\\theta} \\\\frac{\\\\cos{\\\\theta}}{2\\\\Sigma^{3}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}^{r}{}_{\\\\theta}{}_{\\\\theta}= & a^{2} r \\\\Delta \\\\frac{\\\\sin{2\\\\theta}}{\\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}^{r}{}_{t}{}_{\\\\phi}= & -a r_s \\\\left(a^{2} \\\\sin{\\\\theta}^{2}+2r^{2}\\\\right) \\\\Delta \\\\sin{\\\\theta} \\\\frac{\\\\cos{\\\\theta}}{2\\\\Sigma^{3}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}^{r}{}_{\\\\phi}{}_{t}= & -a r_s \\\\left(a^{2} \\\\sin{\\\\theta}^{2}+2r^{2}\\\\right) \\\\Delta \\\\sin{\\\\theta} \\\\frac{\\\\cos{\\\\theta}}{2\\\\Sigma^{3}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}^{r}{}_{t}{}_{t}= & a^{2} r_s \\\\Delta \\\\frac{\\\\sin{2\\\\theta}}{4\\\\Sigma^{3}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}^{t}{}_{r}{}_{r}= & -a r_s \\\\left(4a^{4} r \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{2}-\\\\left(2r \\\\Delta-\\\\left(2r-r_s\\\\right) \\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(2a^{2} r^{3} r_s-2a^{2} r^{2} \\\\Sigma-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}+2r^{5} r_s-2r^{4} \\\\Sigma+r^{3} r_s \\\\Sigma-r^{2} \\\\Sigma^{2}\\\\right)\\\\right) \\\\frac{\\\\sin{\\\\theta}^{2}}{4\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Delta \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}^{t}{}_{r}{}_{\\\\theta}= & a^{3} r_s \\\\left(-4a^{2} r^{3} r_s+4a^{2} r^{2} \\\\Sigma+a^{2} r r_s \\\\Sigma-a^{2} \\\\Sigma^{2}-4r^{5} r_s+2r^{4} r_s^{2}+4r^{4} \\\\Sigma-3r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right) \\\\sin{\\\\theta}^{3} \\\\frac{\\\\cos{\\\\theta}}{2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}^{t}{}_{\\\\theta}{}_{r}= & a^{3} r_s \\\\left(-4a^{2} r^{3} r_s+4a^{2} r^{2} \\\\Sigma+a^{2} r r_s \\\\Sigma-a^{2} \\\\Sigma^{2}-4r^{5} r_s+2r^{4} r_s^{2}+4r^{4} \\\\Sigma-3r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right) \\\\sin{\\\\theta}^{3} \\\\frac{\\\\cos{\\\\theta}}{2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}^{t}{}_{\\\\phi}{}_{\\\\phi}= & a r_s \\\\left(4a^{2} r \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+\\\\left(a^{2}+r^{2}\\\\right) \\\\Sigma^{2}\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\cos{\\\\theta}^{2}+\\\\left(-2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}+a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r \\\\Sigma^{2}\\\\right) \\\\left(-a^{2} r r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\Sigma-r^{3} r_s+r^{2} \\\\Sigma\\\\right) \\\\left(2a^{2} r^{3} r_s-2a^{2} r^{2} \\\\Sigma-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}+2r^{5} r_s-2r^{4} \\\\Sigma+r^{3} r_s \\\\Sigma-r^{2} \\\\Sigma^{2}\\\\right) \\\\Delta\\\\right) \\\\frac{\\\\sin{\\\\theta}^{4}}{4\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(-a^{2} r r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\Sigma-r^{3} r_s+r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}^{t}{}_{\\\\theta}{}_{\\\\theta}= & a r r_s \\\\left(2a^{4} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{2}+\\\\left(-a^{2} r r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\Sigma-r^{3} r_s+r^{2} \\\\Sigma\\\\right) \\\\left(2a^{2} r^{3} r_s-2a^{2} r^{2} \\\\Sigma-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}+2r^{5} r_s-2r^{4} \\\\Sigma+r^{3} r_s \\\\Sigma-r^{2} \\\\Sigma^{2}\\\\right) \\\\Delta\\\\right) \\\\frac{\\\\sin{\\\\theta}^{2}}{2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(-a^{2} r r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\Sigma-r^{3} r_s+r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}^{t}{}_{t}{}_{\\\\phi}= & a^{2} r_s^{2} \\\\left(-a^{2} r^{2} \\\\left(a^{2} \\\\sin{\\\\theta}^{2}+\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\cos{\\\\theta}^{2}+\\\\frac{1}{4}\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(-a^{2} r r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\Sigma-r^{3} r_s+r^{2} \\\\Sigma\\\\right) \\\\left(2a^{2} r^{3} r_s-2a^{2} r^{2} \\\\Sigma-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}+2r^{5} r_s-2r^{4} \\\\Sigma+r^{3} r_s \\\\Sigma-r^{2} \\\\Sigma^{2}\\\\right) \\\\Delta\\\\right) \\\\frac{\\\\sin{\\\\theta}^{4}}{\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(-a^{2} r r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\Sigma-r^{3} r_s+r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}^{t}{}_{\\\\phi}{}_{t}= & a^{2} r_s^{2} \\\\left(-a^{2} r^{2} \\\\left(a^{2} \\\\sin{\\\\theta}^{2}+\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\cos{\\\\theta}^{2}+\\\\frac{1}{4}\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(-a^{2} r r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\Sigma-r^{3} r_s+r^{2} \\\\Sigma\\\\right) \\\\left(2a^{2} r^{3} r_s-2a^{2} r^{2} \\\\Sigma-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}+2r^{5} r_s-2r^{4} \\\\Sigma+r^{3} r_s \\\\Sigma-r^{2} \\\\Sigma^{2}\\\\right) \\\\Delta\\\\right) \\\\frac{\\\\sin{\\\\theta}^{4}}{\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(-a^{2} r r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\Sigma-r^{3} r_s+r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}^{t}{}_{t}{}_{t}= & a r_s^{2} \\\\left(4a^{4} r^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{2}+\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(2a^{2} r^{3} r_s-2a^{2} r^{2} \\\\Sigma-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}+2r^{5} r_s-2r^{4} \\\\Sigma+r^{3} r_s \\\\Sigma-r^{2} \\\\Sigma^{2}\\\\right) \\\\Delta\\\\right) \\\\frac{\\\\sin{\\\\theta}^{2}}{4\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}^{\\\\phi}{}_{r}{}_{r}= & \\\\frac{-a^{2} \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right) \\\\cos{\\\\theta}^{2}+\\\\left(2r \\\\Delta+\\\\left(-2r+r_s\\\\right) \\\\Sigma\\\\right) \\\\left(\\\\frac{1}{2}a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2} - \\\\frac{1}{4}a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+\\\\frac{1}{2}r^{2} r_s \\\\Sigma - \\\\frac{1}{2}r \\\\Sigma^{2}\\\\right)}{\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Delta \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}^{\\\\phi}{}_{r}{}_{\\\\theta}= & \\\\frac{-4a^{4} r^{2} r_s \\\\sin{\\\\theta}^{4}+a^{4} r_s \\\\Sigma \\\\sin{\\\\theta}^{4}+2a^{2} r^{3} r_s^{2} \\\\sin{\\\\theta}^{2}-6a^{2} r^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2a^{2} r^{2} r_s \\\\Sigma+2a^{2} r \\\\Sigma^{2} \\\\sin{\\\\theta}^{2}-2a^{2} r \\\\Sigma^{2}+2r^{4} r_s \\\\Sigma-2r^{3} \\\\Sigma^{2}}{2\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{2} \\\\tan{\\\\theta}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}^{\\\\phi}{}_{\\\\theta}{}_{r}= & \\\\frac{-4a^{4} r^{2} r_s \\\\sin{\\\\theta}^{4}+a^{4} r_s \\\\Sigma \\\\sin{\\\\theta}^{4}+2a^{2} r^{3} r_s^{2} \\\\sin{\\\\theta}^{2}-6a^{2} r^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2a^{2} r^{2} r_s \\\\Sigma+2a^{2} r \\\\Sigma^{2} \\\\sin{\\\\theta}^{2}-2a^{2} r \\\\Sigma^{2}+2r^{4} r_s \\\\Sigma-2r^{3} \\\\Sigma^{2}}{2\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{2} \\\\tan{\\\\theta}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}^{\\\\phi}{}_{\\\\phi}{}_{\\\\phi}= & \\\\frac{ - \\\\frac{1}{4}\\\\left(-2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}+a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r \\\\Sigma^{2}\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right) \\\\Delta \\\\sin{\\\\theta}^{2}+\\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+\\\\left(a^{2}+r^{2}\\\\right) \\\\Sigma^{2}\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right) \\\\cos{\\\\theta}^{2}}{\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}^{\\\\phi}{}_{\\\\theta}{}_{\\\\theta}= & \\\\frac{a^{2} \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right) \\\\cos{\\\\theta}^{2} - \\\\frac{1}{2}r \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right) \\\\Delta}{\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}^{\\\\phi}{}_{t}{}_{\\\\phi}= & -a r_s \\\\frac{4r \\\\left(a^{2} \\\\sin{\\\\theta}^{2}+\\\\Sigma\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right) \\\\cos{\\\\theta}^{2}+\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right) \\\\Delta \\\\sin{\\\\theta}^{2}}{4\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}^{\\\\phi}{}_{\\\\phi}{}_{t}= & -a r_s \\\\frac{4r \\\\left(a^{2} \\\\sin{\\\\theta}^{2}+\\\\Sigma\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right) \\\\cos{\\\\theta}^{2}+\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right) \\\\Delta \\\\sin{\\\\theta}^{2}}{4\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}^{\\\\phi}{}_{t}{}_{t}= & r_s \\\\frac{4a^{2} r \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right) \\\\cos{\\\\theta}^{2}+\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right) \\\\Delta}{4\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}^{t}{}_{r}{}_{r}= & r_s \\\\frac{a^{4} r \\\\left(-\\\\cos{4\\\\theta}+1\\\\right) \\\\left(\\\\frac{1}{2}a^{2} r r_s - \\\\frac{1}{2}a^{2} \\\\Sigma+\\\\frac{1}{2}r^{3} r_s - \\\\frac{1}{2}r^{2} r_s^{2} - \\\\frac{1}{2}r^{2} \\\\Sigma+\\\\frac{1}{2}r r_s \\\\Sigma\\\\right)-\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(2r \\\\Delta+\\\\left(-2r+r_s\\\\right) \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)}{4\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Delta \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}^{t}{}_{r}{}_{\\\\theta}= & a^{2} r_s \\\\left(2a^{2} r^{2} - \\\\frac{1}{2}a^{2} \\\\Sigma+2r^{4}-r^{3} r_s - \\\\frac{1}{2}r^{2} \\\\Sigma\\\\right) \\\\frac{\\\\sin{2\\\\theta}}{2\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}^{t}{}_{\\\\theta}{}_{r}= & a^{2} r_s \\\\left(2a^{2} r^{2} - \\\\frac{1}{2}a^{2} \\\\Sigma+2r^{4}-r^{3} r_s - \\\\frac{1}{2}r^{2} \\\\Sigma\\\\right) \\\\frac{\\\\sin{2\\\\theta}}{2\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}^{t}{}_{\\\\phi}{}_{\\\\phi}= & r_s \\\\left(-2a^{2} r \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+\\\\left(a^{2}+r^{2}\\\\right) \\\\Sigma^{2}\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{2\\\\theta} \\\\cos{\\\\theta}+\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(-2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{3}+a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{3}+2r \\\\Sigma^{2} \\\\sin{\\\\theta}\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Delta\\\\right) \\\\frac{\\\\sin{\\\\theta}}{4\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}^{t}{}_{\\\\theta}{}_{\\\\theta}= & r r_s \\\\frac{-a^{6} \\\\left( - \\\\frac{1}{4}\\\\cos{4\\\\theta}+\\\\frac{1}{4}\\\\right)-a^{4} r^{2} \\\\left( - \\\\frac{1}{4}\\\\cos{4\\\\theta}+\\\\frac{1}{4}\\\\right)+a^{4} r r_s \\\\left( - \\\\frac{1}{4}\\\\cos{4\\\\theta}+\\\\frac{1}{4}\\\\right)+2a^{2} r^{2} \\\\Delta-a^{2} \\\\Delta \\\\Sigma+2r^{4} \\\\Delta-r^{2} \\\\Delta \\\\Sigma}{2\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}^{t}{}_{t}{}_{\\\\phi}= & a r_s^{2} \\\\left(4a^{2} r^{2} \\\\left(a^{2} \\\\sin{\\\\theta}^{2}+\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\cos{\\\\theta}^{2}+\\\\left(2r^{2}-\\\\Sigma\\\\right)^{2} \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Delta\\\\right) \\\\frac{\\\\sin{\\\\theta}^{2}}{4\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}^{t}{}_{\\\\phi}{}_{t}= & a r_s^{2} \\\\left(4a^{2} r^{2} \\\\left(a^{2} \\\\sin{\\\\theta}^{2}+\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\cos{\\\\theta}^{2}+\\\\left(2r^{2}-\\\\Sigma\\\\right)^{2} \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Delta\\\\right) \\\\frac{\\\\sin{\\\\theta}^{2}}{4\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}^{t}{}_{t}{}_{t}= & -r_s^{2} \\\\frac{-a^{6} r^{2} \\\\left(\\\\frac{1}{2}\\\\cos{4\\\\theta} - \\\\frac{1}{2}\\\\right)-a^{4} r^{4} \\\\left(\\\\frac{1}{2}\\\\cos{4\\\\theta} - \\\\frac{1}{2}\\\\right)+a^{4} r^{3} r_s \\\\left(\\\\frac{1}{2}\\\\cos{4\\\\theta} - \\\\frac{1}{2}\\\\right)+4a^{2} r^{4} \\\\Delta-4a^{2} r^{2} \\\\Delta \\\\Sigma+a^{2} \\\\Delta \\\\Sigma^{2}+4r^{6} \\\\Delta-4r^{4} \\\\Delta \\\\Sigma+r^{2} \\\\Delta \\\\Sigma^{2}}{4\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}^{\\\\phi}{}_{r}{}_{r}= & a r_s \\\\frac{4a^{2} r \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right) \\\\sin{\\\\theta} \\\\cos{\\\\theta}-\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(2r \\\\Delta+\\\\left(-2r+r_s\\\\right) \\\\Sigma\\\\right) \\\\tan{\\\\theta}}{4\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Delta \\\\Sigma^{2} \\\\tan{\\\\theta}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}^{\\\\phi}{}_{r}{}_{\\\\theta}= & a r_s \\\\frac{a^{2} \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\sin{\\\\theta}^{2}+2r^{2} \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right)}{2\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{2} \\\\tan{\\\\theta}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}^{\\\\phi}{}_{\\\\theta}{}_{r}= & a r_s \\\\frac{a^{2} \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\sin{\\\\theta}^{2}+2r^{2} \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right)}{2\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{2} \\\\tan{\\\\theta}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}^{\\\\phi}{}_{\\\\phi}{}_{\\\\phi}= & a r_s \\\\left(-4r \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+\\\\left(a^{2}+r^{2}\\\\right) \\\\Sigma^{2}\\\\right) \\\\cos{\\\\theta}+\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(-2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}+a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r \\\\Sigma^{2}\\\\right) \\\\Delta \\\\frac{\\\\sin{\\\\theta}^{2}}{\\\\cos{\\\\theta}}\\\\right) \\\\frac{\\\\cos{\\\\theta}}{4\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}^{\\\\phi}{}_{\\\\theta}{}_{\\\\theta}= & a r r_s \\\\frac{-2a^{2} \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right) \\\\sin{\\\\theta} \\\\cos{\\\\theta}+\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\Delta \\\\tan{\\\\theta}}{2\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{2} \\\\tan{\\\\theta}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}^{\\\\phi}{}_{t}{}_{\\\\phi}= & a^{2} r_s^{2} \\\\left(r^{2} \\\\left(a^{2} \\\\sin{\\\\theta}^{2}+\\\\Sigma\\\\right) \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right) \\\\cos{\\\\theta}+\\\\left(2r^{2}-\\\\Sigma\\\\right)^{2} \\\\Delta \\\\frac{\\\\sin{\\\\theta}^{2}}{4\\\\cos{\\\\theta}}\\\\right) \\\\frac{\\\\cos{\\\\theta}}{\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}^{\\\\phi}{}_{\\\\phi}{}_{t}= & a^{2} r_s^{2} \\\\left(r^{2} \\\\left(a^{2} \\\\sin{\\\\theta}^{2}+\\\\Sigma\\\\right) \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right) \\\\cos{\\\\theta}+\\\\left(2r^{2}-\\\\Sigma\\\\right)^{2} \\\\Delta \\\\frac{\\\\sin{\\\\theta}^{2}}{4\\\\cos{\\\\theta}}\\\\right) \\\\frac{\\\\cos{\\\\theta}}{\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}^{\\\\phi}{}_{t}{}_{t}= & -a r_s^{2} \\\\frac{4a^{2} r^{2} \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right) \\\\sin{\\\\theta} \\\\cos{\\\\theta}+\\\\left(2r^{2}-\\\\Sigma\\\\right)^{2} \\\\Delta \\\\tan{\\\\theta}}{4\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4} \\\\tan{\\\\theta}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}^{r}{}_{\\\\phi}{}_{r}= & \\\\left(-a^{2} r_s^{2} \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(2a^{2} r^{3} r_s-2a^{2} r^{2} \\\\Sigma-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}+2r^{5} r_s-2r^{4} \\\\Sigma+r^{3} r_s \\\\Sigma-r^{2} \\\\Sigma^{2}\\\\right) \\\\sin{\\\\theta}^{2}+\\\\left(-r r_s+\\\\Sigma\\\\right) \\\\left(-2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}+a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r \\\\Sigma^{2}\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right)\\\\right) \\\\Delta \\\\frac{\\\\sin{\\\\theta}^{2}}{4\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}^{r}{}_{\\\\phi}{}_{\\\\theta}= & \\\\left(a^{4} r r_s^{2} \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{\\\\theta}^{4}+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(-2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}+a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r \\\\Sigma^{2}\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right)\\\\right) \\\\Delta \\\\sin{\\\\theta} \\\\frac{\\\\cos{\\\\theta}}{2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}^{r}{}_{t}{}_{r}= & a r_s \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(r_s \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(-2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}+a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r \\\\Sigma^{2}\\\\right)\\\\right) \\\\Delta \\\\frac{\\\\sin{\\\\theta}^{2}}{4\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}^{r}{}_{t}{}_{\\\\theta}= & a r r_s \\\\left(-a^{2} r_s \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+2\\\\left(-r r_s+\\\\Sigma\\\\right) \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right) \\\\left(-2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}+a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r \\\\Sigma^{2}\\\\right)\\\\right) \\\\Delta \\\\frac{\\\\sin{\\\\theta}^{2}}{4\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4} \\\\tan{\\\\theta}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}^{r}{}_{r}{}_{\\\\phi}= & \\\\left(-a^{2} r_s^{2} \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(2a^{2} r^{3} r_s-2a^{2} r^{2} \\\\Sigma-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}+2r^{5} r_s-2r^{4} \\\\Sigma+r^{3} r_s \\\\Sigma-r^{2} \\\\Sigma^{2}\\\\right) \\\\sin{\\\\theta}^{2}+\\\\left(-r r_s+\\\\Sigma\\\\right) \\\\left(-2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}+a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r \\\\Sigma^{2}\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right)\\\\right) \\\\Delta \\\\frac{\\\\sin{\\\\theta}^{2}}{4\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}^{r}{}_{\\\\theta}{}_{\\\\phi}= & \\\\left(a^{4} r r_s^{2} \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{\\\\theta}^{4}+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(-2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}+a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r \\\\Sigma^{2}\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right)\\\\right) \\\\Delta \\\\sin{\\\\theta} \\\\frac{\\\\cos{\\\\theta}}{2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}^{r}{}_{r}{}_{t}= & a r_s \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(r_s \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(-2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}+a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r \\\\Sigma^{2}\\\\right)\\\\right) \\\\Delta \\\\frac{\\\\sin{\\\\theta}^{2}}{4\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}^{r}{}_{\\\\theta}{}_{t}= & a r r_s \\\\left(-a^{2} r_s \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+2\\\\left(-r r_s+\\\\Sigma\\\\right) \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right) \\\\left(-2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}+a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r \\\\Sigma^{2}\\\\right)\\\\right) \\\\Delta \\\\frac{\\\\sin{\\\\theta}^{2}}{4\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4} \\\\tan{\\\\theta}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}^{\\\\theta}{}_{\\\\phi}{}_{r}= & \\\\left(a^{2} r r_s^{2} \\\\left(a^{2} \\\\sin{\\\\theta}^{2}+\\\\Sigma\\\\right) \\\\left(2a^{2} r^{3} r_s-2a^{2} r^{2} \\\\Sigma-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}+2r^{5} r_s-2r^{4} \\\\Sigma+r^{3} r_s \\\\Sigma-r^{2} \\\\Sigma^{2}\\\\right) \\\\sin{\\\\theta}^{2}+\\\\left(-r r_s+\\\\Sigma\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+\\\\left(a^{2}+r^{2}\\\\right) \\\\Sigma^{2}\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right)\\\\right) \\\\sin{\\\\theta} \\\\frac{\\\\cos{\\\\theta}}{2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}^{\\\\theta}{}_{\\\\phi}{}_{\\\\theta}= & -\\\\left(a^{4} r^{2} r_s^{2} \\\\left(a^{2} \\\\sin{\\\\theta}^{2}+\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{\\\\theta}^{4}-\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+\\\\left(a^{2}+r^{2}\\\\right) \\\\Sigma^{2}\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right)\\\\right) \\\\frac{\\\\cos{\\\\theta}^{2}}{\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}^{\\\\theta}{}_{t}{}_{r}= & a r_s \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(-r r_s \\\\left(a^{2} \\\\sin{\\\\theta}^{2}+\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+\\\\left(a^{2}+r^{2}\\\\right) \\\\Sigma^{2}\\\\right)\\\\right) \\\\sin{\\\\theta} \\\\frac{\\\\cos{\\\\theta}}{2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}^{\\\\theta}{}_{t}{}_{\\\\theta}= & a r r_s \\\\left(a^{2} r r_s \\\\left(a^{2} \\\\sin{\\\\theta}^{2}+\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{\\\\theta}^{2}+\\\\left(-r r_s+\\\\Sigma\\\\right) \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+\\\\left(a^{2}+r^{2}\\\\right) \\\\Sigma^{2}\\\\right)\\\\right) \\\\frac{\\\\cos{\\\\theta}^{2}}{\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}^{\\\\theta}{}_{r}{}_{\\\\phi}= & \\\\left(a^{2} r r_s^{2} \\\\left(a^{2} \\\\sin{\\\\theta}^{2}+\\\\Sigma\\\\right) \\\\left(2a^{2} r^{3} r_s-2a^{2} r^{2} \\\\Sigma-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}+2r^{5} r_s-2r^{4} \\\\Sigma+r^{3} r_s \\\\Sigma-r^{2} \\\\Sigma^{2}\\\\right) \\\\sin{\\\\theta}^{2}+\\\\left(-r r_s+\\\\Sigma\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+\\\\left(a^{2}+r^{2}\\\\right) \\\\Sigma^{2}\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right)\\\\right) \\\\sin{\\\\theta} \\\\frac{\\\\cos{\\\\theta}}{2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}^{\\\\theta}{}_{\\\\theta}{}_{\\\\phi}= & -\\\\left(a^{4} r^{2} r_s^{2} \\\\left(a^{2} \\\\sin{\\\\theta}^{2}+\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{\\\\theta}^{4}-\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+\\\\left(a^{2}+r^{2}\\\\right) \\\\Sigma^{2}\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right)\\\\right) \\\\frac{\\\\cos{\\\\theta}^{2}}{\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}^{\\\\theta}{}_{r}{}_{t}= & a r_s \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(-r r_s \\\\left(a^{2} \\\\sin{\\\\theta}^{2}+\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+\\\\left(a^{2}+r^{2}\\\\right) \\\\Sigma^{2}\\\\right)\\\\right) \\\\sin{\\\\theta} \\\\frac{\\\\cos{\\\\theta}}{2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}^{\\\\theta}{}_{\\\\theta}{}_{t}= & a r r_s \\\\left(a^{2} r r_s \\\\left(a^{2} \\\\sin{\\\\theta}^{2}+\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{\\\\theta}^{2}+\\\\left(-r r_s+\\\\Sigma\\\\right) \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+\\\\left(a^{2}+r^{2}\\\\right) \\\\Sigma^{2}\\\\right)\\\\right) \\\\frac{\\\\cos{\\\\theta}^{2}}{\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}^{r}{}_{\\\\phi}{}_{r}= & a r_s \\\\left(4a^{2} r^{4} r_s \\\\cos{\\\\theta}^{2}-4a^{2} r^{2} r_s \\\\Sigma \\\\cos{\\\\theta}^{2}+a^{2} r_s \\\\Sigma^{2} \\\\cos{\\\\theta}^{2}+4r^{6} r_s-4r^{4} r_s \\\\Sigma+4r^{3} \\\\Sigma^{2}+r^{2} r_s \\\\Sigma^{2}-2r \\\\Sigma^{3}\\\\right) \\\\Delta \\\\frac{\\\\sin{\\\\theta}^{2}}{4\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}^{r}{}_{\\\\phi}{}_{\\\\theta}= & -a r_s \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{\\\\theta}^{2}-\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right)\\\\right) \\\\Delta \\\\sin{\\\\theta} \\\\frac{\\\\cos{\\\\theta}}{2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}^{r}{}_{t}{}_{r}= & r_s^{2} \\\\left(2r^{2}-\\\\Sigma\\\\right)^{2} \\\\left(-a^{2} r r_s+a^{2} \\\\left(r r_s-\\\\Sigma\\\\right) \\\\sin{\\\\theta}^{2}+a^{2} \\\\Sigma-r^{3} r_s+r^{2} \\\\Sigma\\\\right) \\\\frac{\\\\Delta}{4\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}^{r}{}_{t}{}_{\\\\theta}= & a^{2} r r_s^{2} \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma \\\\cos{\\\\theta}^{2}+r^{3} r_s-r^{2} \\\\Sigma-r r_s \\\\Sigma+\\\\Sigma^{2}\\\\right) \\\\Delta \\\\sin{\\\\theta} \\\\frac{\\\\cos{\\\\theta}}{2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}^{r}{}_{r}{}_{\\\\phi}= & a r_s \\\\left(4a^{2} r^{4} r_s \\\\cos{\\\\theta}^{2}-4a^{2} r^{2} r_s \\\\Sigma \\\\cos{\\\\theta}^{2}+a^{2} r_s \\\\Sigma^{2} \\\\cos{\\\\theta}^{2}+4r^{6} r_s-4r^{4} r_s \\\\Sigma+4r^{3} \\\\Sigma^{2}+r^{2} r_s \\\\Sigma^{2}-2r \\\\Sigma^{3}\\\\right) \\\\Delta \\\\frac{\\\\sin{\\\\theta}^{2}}{4\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}^{r}{}_{\\\\theta}{}_{\\\\phi}= & -a r_s \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{\\\\theta}^{2}-\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right)\\\\right) \\\\Delta \\\\sin{\\\\theta} \\\\frac{\\\\cos{\\\\theta}}{2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}^{r}{}_{r}{}_{t}= & r_s^{2} \\\\left(2r^{2}-\\\\Sigma\\\\right)^{2} \\\\left(-a^{2} r r_s+a^{2} \\\\left(r r_s-\\\\Sigma\\\\right) \\\\sin{\\\\theta}^{2}+a^{2} \\\\Sigma-r^{3} r_s+r^{2} \\\\Sigma\\\\right) \\\\frac{\\\\Delta}{4\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}^{r}{}_{\\\\theta}{}_{t}= & a^{2} r r_s^{2} \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma \\\\cos{\\\\theta}^{2}+r^{3} r_s-r^{2} \\\\Sigma-r r_s \\\\Sigma+\\\\Sigma^{2}\\\\right) \\\\Delta \\\\sin{\\\\theta} \\\\frac{\\\\cos{\\\\theta}}{2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}^{\\\\theta}{}_{\\\\phi}{}_{r}= & a r r_s \\\\left(-a^{2} r_s \\\\left(2a^{2} r^{3} r_s-2a^{2} r^{2} \\\\Sigma-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}+2r^{5} r_s-2r^{4} \\\\Sigma+r^{3} r_s \\\\Sigma-r^{2} \\\\Sigma^{2}\\\\right) \\\\sin{\\\\theta}^{2}+\\\\left(a^{2} \\\\sin{\\\\theta}^{2}+\\\\Sigma\\\\right) \\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right)\\\\right) \\\\sin{\\\\theta} \\\\frac{\\\\cos{\\\\theta}}{2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}^{\\\\theta}{}_{\\\\phi}{}_{\\\\theta}= & a r r_s \\\\left(a^{4} r r_s \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{\\\\theta}^{4}+\\\\left(a^{2} \\\\sin{\\\\theta}^{2}+\\\\Sigma\\\\right) \\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(-a^{2} r r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\Sigma-r^{3} r_s+r^{2} \\\\Sigma\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right)\\\\right) \\\\frac{\\\\cos{\\\\theta}^{2}}{\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(-a^{2} r r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\Sigma-r^{3} r_s+r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}^{\\\\theta}{}_{t}{}_{r}= & a^{2} r r_s^{2} \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma \\\\cos{\\\\theta}^{2}+r^{3} r_s-r^{2} \\\\Sigma-r r_s \\\\Sigma+\\\\Sigma^{2}\\\\right) \\\\sin{\\\\theta} \\\\frac{\\\\cos{\\\\theta}}{2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}^{\\\\theta}{}_{t}{}_{\\\\theta}= & a^{2} r^{2} r_s^{2} \\\\left(-a^{2} \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{\\\\theta}^{2}+\\\\left(a^{2} \\\\sin{\\\\theta}^{2}+\\\\Sigma\\\\right) \\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right)\\\\right) \\\\frac{\\\\cos{\\\\theta}^{2}}{\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}^{\\\\theta}{}_{r}{}_{\\\\phi}= & a r r_s \\\\left(-a^{2} r_s \\\\left(2a^{2} r^{3} r_s-2a^{2} r^{2} \\\\Sigma-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}+2r^{5} r_s-2r^{4} \\\\Sigma+r^{3} r_s \\\\Sigma-r^{2} \\\\Sigma^{2}\\\\right) \\\\sin{\\\\theta}^{2}+\\\\left(a^{2} \\\\sin{\\\\theta}^{2}+\\\\Sigma\\\\right) \\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right)\\\\right) \\\\sin{\\\\theta} \\\\frac{\\\\cos{\\\\theta}}{2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}^{\\\\theta}{}_{\\\\theta}{}_{\\\\phi}= & a r r_s \\\\left(a^{4} r r_s \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{\\\\theta}^{4}+\\\\left(a^{2} \\\\sin{\\\\theta}^{2}+\\\\Sigma\\\\right) \\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(-a^{2} r r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\Sigma-r^{3} r_s+r^{2} \\\\Sigma\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right)\\\\right) \\\\frac{\\\\cos{\\\\theta}^{2}}{\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(-a^{2} r r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\Sigma-r^{3} r_s+r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}^{\\\\theta}{}_{r}{}_{t}= & a^{2} r r_s^{2} \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma \\\\cos{\\\\theta}^{2}+r^{3} r_s-r^{2} \\\\Sigma-r r_s \\\\Sigma+\\\\Sigma^{2}\\\\right) \\\\sin{\\\\theta} \\\\frac{\\\\cos{\\\\theta}}{2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}^{\\\\theta}{}_{\\\\theta}{}_{t}= & a^{2} r^{2} r_s^{2} \\\\left(-a^{2} \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{\\\\theta}^{2}+\\\\left(a^{2} \\\\sin{\\\\theta}^{2}+\\\\Sigma\\\\right) \\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right)\\\\right) \\\\frac{\\\\cos{\\\\theta}^{2}}{\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\end{aligned}\\\\right.\\n\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"substitute(tst2,ch)\\nevaluate(tst2, kerr);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\left\\\\{\\\\begin{aligned}\\\\square{}_{t}{}_{t}{}^{\\\\theta}{}_{r}= & a^{2} r_s \\\\left(-3r \\\\partial_{r}{\\\\Sigma}+\\\\Sigma\\\\right) \\\\frac{\\\\sin{2\\\\theta}}{2\\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}_{t}{}^{\\\\theta}{}_{\\\\theta}= & a^{2} r r_s \\\\frac{\\\\Sigma \\\\cos{2\\\\theta} - \\\\frac{3}{2}\\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}}{\\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}_{t}{}^{r}{}_{r}= & r_s \\\\frac{3\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\Delta \\\\partial_{r}{\\\\Sigma}-\\\\left(\\\\left(4r-\\\\partial_{r}{\\\\Sigma}\\\\right) \\\\Delta+\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\partial_{r}{\\\\Delta}\\\\right) \\\\Sigma}{2\\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}_{t}{}^{r}{}_{\\\\theta}= & r_s \\\\left(3r^{2}-\\\\Sigma\\\\right) \\\\Delta \\\\frac{\\\\partial_{\\\\theta}{\\\\Sigma}}{\\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{t}{}^{\\\\theta}{}_{r}= & a r_s \\\\left(3a^{2} r \\\\sin{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}-a^{2} \\\\Sigma \\\\sin{\\\\theta}^{2}+2r \\\\Sigma \\\\partial_{r}{\\\\Sigma}-\\\\Sigma^{2}\\\\right) \\\\sin{\\\\theta} \\\\frac{\\\\cos{\\\\theta}}{\\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{t}{}^{\\\\theta}{}_{\\\\theta}= & a r r_s \\\\frac{2a^{2} \\\\left(-\\\\cos{2\\\\theta}+1\\\\right)^{2} \\\\Sigma+3a^{2} \\\\Sigma \\\\cos{2\\\\theta}-3a^{2} \\\\Sigma+\\\\frac{3}{2}a^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma} - \\\\frac{3}{4}a^{2} \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}-2\\\\Sigma^{2} \\\\cos{2\\\\theta}+2\\\\Sigma \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}}{2\\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{t}{}^{r}{}_{r}= & a r_s \\\\left(-3\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\Delta \\\\partial_{r}{\\\\Sigma}+\\\\left(\\\\left(4r-\\\\partial_{r}{\\\\Sigma}\\\\right) \\\\Delta+\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\partial_{r}{\\\\Delta}\\\\right) \\\\Sigma\\\\right) \\\\frac{\\\\sin{\\\\theta}^{2}}{2\\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{t}{}^{r}{}_{\\\\theta}= & a r_s \\\\left(-3\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\sin{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}+\\\\left(\\\\left(4r^{2}-2\\\\Sigma\\\\right) \\\\cos{\\\\theta}-\\\\sin{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\Sigma\\\\right) \\\\Delta \\\\frac{\\\\sin{\\\\theta}}{2\\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}_{\\\\phi}{}^{\\\\theta}{}_{r}= & a r_s \\\\left(3a^{2} r \\\\sin{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}-a^{2} \\\\Sigma \\\\sin{\\\\theta}^{2}+2r \\\\Sigma \\\\partial_{r}{\\\\Sigma}-\\\\Sigma^{2}\\\\right) \\\\sin{\\\\theta} \\\\frac{\\\\cos{\\\\theta}}{\\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}_{\\\\phi}{}^{\\\\theta}{}_{\\\\theta}= & a r r_s \\\\frac{2a^{2} \\\\left(-\\\\cos{2\\\\theta}+1\\\\right)^{2} \\\\Sigma+3a^{2} \\\\Sigma \\\\cos{2\\\\theta}-3a^{2} \\\\Sigma+\\\\frac{3}{2}a^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma} - \\\\frac{3}{4}a^{2} \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}-2\\\\Sigma^{2} \\\\cos{2\\\\theta}+2\\\\Sigma \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}}{2\\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}_{\\\\phi}{}^{r}{}_{r}= & a r_s \\\\left(-3\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\Delta \\\\partial_{r}{\\\\Sigma}+\\\\left(\\\\left(4r-\\\\partial_{r}{\\\\Sigma}\\\\right) \\\\Delta+\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\partial_{r}{\\\\Delta}\\\\right) \\\\Sigma\\\\right) \\\\frac{\\\\sin{\\\\theta}^{2}}{2\\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}_{\\\\phi}{}^{r}{}_{\\\\theta}= & a r_s \\\\left(-3\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\sin{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}+\\\\left(\\\\left(4r^{2}-2\\\\Sigma\\\\right) \\\\cos{\\\\theta}-\\\\sin{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\Sigma\\\\right) \\\\Delta \\\\frac{\\\\sin{\\\\theta}}{2\\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{r}{}^{\\\\theta}{}_{r}= & a^{2} \\\\left(\\\\Delta \\\\partial_{r}{\\\\Sigma}+\\\\Sigma \\\\partial_{r}{\\\\Delta}\\\\right) \\\\frac{\\\\sin{2\\\\theta}}{2\\\\Delta^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{r}{}^{\\\\theta}{}_{\\\\theta}= & a^{2} \\\\frac{-\\\\Sigma \\\\cos{2\\\\theta}+\\\\frac{1}{2}\\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}}{\\\\Delta \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{\\\\theta}{}^{r}{}_{r}= & \\\\frac{-r \\\\Delta \\\\partial_{r}{\\\\Sigma}+\\\\left(r \\\\partial_{r}{\\\\Delta}+\\\\Delta\\\\right) \\\\Sigma}{\\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{\\\\theta}{}^{r}{}_{\\\\theta}= & -r \\\\Delta \\\\frac{\\\\partial_{\\\\theta}{\\\\Sigma}}{\\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{\\\\phi}{}^{\\\\theta}{}_{r}= & -\\\\left(3a^{4} r r_s \\\\sin{\\\\theta}^{4} \\\\partial_{r}{\\\\Sigma}-a^{4} r_s \\\\Sigma \\\\sin{\\\\theta}^{4}+4a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}-2a^{2} r_s \\\\Sigma^{2} \\\\sin{\\\\theta}^{2}+a^{2} \\\\Sigma^{2} \\\\partial_{r}{\\\\Sigma}+r^{2} \\\\Sigma^{2} \\\\partial_{r}{\\\\Sigma}-2r \\\\Sigma^{3}\\\\right) \\\\sin{\\\\theta} \\\\frac{\\\\cos{\\\\theta}}{\\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{\\\\phi}{}^{\\\\theta}{}_{\\\\theta}= & \\\\frac{ - \\\\frac{3}{4}a^{4} r r_s \\\\left(-\\\\cos{2\\\\theta}+1\\\\right)^{3} \\\\Sigma+\\\\frac{5}{4}a^{4} r r_s \\\\left(-\\\\cos{2\\\\theta}+1\\\\right)^{2} \\\\Sigma - \\\\frac{3}{8}a^{4} r r_s \\\\left(-\\\\cos{2\\\\theta}+1\\\\right)^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}-2a^{2} r r_s \\\\left(-\\\\cos{2\\\\theta}+1\\\\right)^{2} \\\\Sigma^{2}-3a^{2} r r_s \\\\Sigma^{2} \\\\cos{2\\\\theta}+3a^{2} r r_s \\\\Sigma^{2}-a^{2} r r_s \\\\Sigma \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}+\\\\frac{1}{2}a^{2} r r_s \\\\Sigma \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}+a^{2} \\\\Sigma^{3} \\\\cos{2\\\\theta} - \\\\frac{1}{2}a^{2} \\\\Sigma^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}+r^{2} \\\\Sigma^{3} \\\\cos{2\\\\theta} - \\\\frac{1}{2}r^{2} \\\\Sigma^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}}{\\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{\\\\phi}{}^{r}{}_{r}= & \\\\left(3a^{2} r^{2} r_s \\\\Delta \\\\sin{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}-a^{2} r^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2} \\\\partial_{r}{\\\\Delta}-2a^{2} r r_s \\\\Delta \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Delta \\\\Sigma \\\\sin{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}+\\\\frac{1}{2}a^{2} r_s \\\\Sigma^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{r}{\\\\Delta}-r \\\\Delta \\\\Sigma^{2} \\\\partial_{r}{\\\\Sigma}+r \\\\Sigma^{3} \\\\partial_{r}{\\\\Delta}+\\\\Delta \\\\Sigma^{3}\\\\right) \\\\frac{\\\\sin{\\\\theta}^{2}}{\\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{\\\\phi}{}^{r}{}_{\\\\theta}= & \\\\left(-4a^{2} r^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}+3a^{2} r^{2} r_s \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}{\\\\Sigma}+2a^{2} r_s \\\\Sigma^{2} \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}{\\\\Sigma}+2r \\\\Sigma^{3} \\\\cos{\\\\theta}-r \\\\Sigma^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\Delta \\\\frac{\\\\sin{\\\\theta}}{\\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{t}{}^{\\\\phi}{}_{r}= & a r_s \\\\frac{r \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\partial_{r}{\\\\Sigma}-r \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right) \\\\left(-a^{2} r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\partial_{r}{\\\\Sigma}-3r^{2} r_s+r^{2} \\\\partial_{r}{\\\\Sigma}+2r \\\\Sigma\\\\right) \\\\Sigma+\\\\left(-a^{2} \\\\sin{\\\\theta}^{2}+2r r_s-r \\\\partial_{r}{\\\\Sigma}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma}{\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2} \\\\tan{\\\\theta}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{t}{}^{\\\\phi}{}_{\\\\theta}= & a r r_s \\\\frac{-\\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\sin{2\\\\theta}+a^{2} \\\\partial_{\\\\theta}{\\\\Sigma}+r^{2} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\Sigma \\\\tan{\\\\theta}+\\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\tan{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}-\\\\left(a^{2} \\\\cos{2\\\\theta} \\\\tan{\\\\theta}^{2}+\\\\frac{r r_s-\\\\Sigma}{\\\\cos{\\\\theta}^{2}}+\\\\tan{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma}{\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2} \\\\tan{\\\\theta}^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{t}{}^{t}{}_{r}= & a^{2} r_s \\\\left(a^{4} r^{2} r_s \\\\cos{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}-2a^{4} r \\\\Sigma \\\\partial_{r}{\\\\Sigma}+a^{4} \\\\Sigma^{2}+a^{2} r^{4} r_s \\\\cos{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}+a^{2} r^{4} r_s \\\\partial_{r}{\\\\Sigma}-a^{2} r^{3} r_s^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}-2a^{2} r^{3} r_s \\\\Sigma \\\\cos{\\\\theta}^{2}+2a^{2} r^{3} r_s \\\\Sigma-4a^{2} r^{3} \\\\Sigma \\\\partial_{r}{\\\\Sigma}+a^{2} r^{2} r_s^{2} \\\\Sigma \\\\cos{\\\\theta}^{2}+2a^{2} r^{2} r_s \\\\Sigma \\\\partial_{r}{\\\\Sigma}+2a^{2} r^{2} \\\\Sigma^{2}-2a^{2} r r_s \\\\Sigma^{2}+r^{6} r_s \\\\partial_{r}{\\\\Sigma}-r^{5} r_s^{2} \\\\partial_{r}{\\\\Sigma}-2r^{5} \\\\Sigma \\\\partial_{r}{\\\\Sigma}-r^{4} r_s^{2} \\\\Sigma+2r^{4} r_s \\\\Sigma \\\\partial_{r}{\\\\Sigma}+r^{4} \\\\Sigma^{2}\\\\right) \\\\sin{\\\\theta} \\\\frac{\\\\cos{\\\\theta}}{\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{t}{}^{t}{}_{\\\\theta}= & a^{2} r r_s \\\\frac{-\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\sin{2\\\\theta}+a^{2} \\\\partial_{\\\\theta}{\\\\Sigma}+r^{2} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\Sigma \\\\sin{2\\\\theta}+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(-2a^{2} r r_s \\\\cos{2\\\\theta}+2a^{2} \\\\Sigma \\\\cos{2\\\\theta}+a^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}-2r^{3} r_s \\\\cos{2\\\\theta}+2r^{2} r_s^{2} \\\\cos{2\\\\theta}+2r^{2} \\\\Sigma \\\\cos{2\\\\theta}+r^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}-2r r_s \\\\Sigma \\\\cos{2\\\\theta}-r r_s \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\Sigma-\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\Sigma \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}}{2\\\\left(r r_s-\\\\Sigma\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{t}{}^{\\\\phi}{}_{r}= & a r_s \\\\frac{\\\\left(4r-\\\\partial_{r}{\\\\Sigma}\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma-\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\partial_{r}{\\\\Sigma}+\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(-a^{2} r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\partial_{r}{\\\\Sigma}-3r^{2} r_s+r^{2} \\\\partial_{r}{\\\\Sigma}+2r \\\\Sigma\\\\right) \\\\Sigma}{2\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{t}{}^{\\\\phi}{}_{\\\\theta}= & a r_s \\\\frac{\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\sin{2\\\\theta}+a^{2} \\\\partial_{\\\\theta}{\\\\Sigma}+r^{2} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\Sigma-\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\partial_{\\\\theta}{\\\\Sigma}-\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma \\\\partial_{\\\\theta}{\\\\Sigma}}{2\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{t}{}^{t}{}_{r}= & r_s \\\\frac{-\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(r_s-\\\\partial_{r}{\\\\Sigma}\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma-\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\partial_{r}{\\\\Sigma}+\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(-a^{2} r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\partial_{r}{\\\\Sigma}-3r^{2} r_s+r^{2} \\\\partial_{r}{\\\\Sigma}+2r \\\\Sigma\\\\right) \\\\Sigma+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(\\\\left(4r-\\\\partial_{r}{\\\\Sigma}\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)-\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(-a^{2} r_s+a^{2} \\\\partial_{r}{\\\\Sigma}-3r^{2} r_s+r^{2} \\\\partial_{r}{\\\\Sigma}+2r \\\\Sigma\\\\right)\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma}{2\\\\left(r r_s-\\\\Sigma\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{t}{}^{t}{}_{\\\\theta}= & r_s \\\\frac{\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\sin{2\\\\theta}+a^{2} \\\\partial_{\\\\theta}{\\\\Sigma}+r^{2} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma-\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\partial_{\\\\theta}{\\\\Sigma}+\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma \\\\partial_{\\\\theta}{\\\\Sigma}+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(-a^{2} r r_s+a^{2} \\\\Sigma-r^{3} r_s+r^{2} \\\\Sigma-\\\\left(a^{2}+r^{2}\\\\right) \\\\left(2r^{2}-\\\\Sigma\\\\right)\\\\right) \\\\Sigma \\\\partial_{\\\\theta}{\\\\Sigma}}{2\\\\left(r r_s-\\\\Sigma\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{r}{}^{r}{}_{r}= & -a^{2} \\\\sin{2\\\\theta} \\\\frac{\\\\partial_{r}{\\\\Sigma}}{2\\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{r}{}^{r}{}_{\\\\theta}= & a^{2} \\\\frac{\\\\Sigma \\\\cos{2\\\\theta} - \\\\frac{1}{2}\\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}}{\\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{\\\\theta}{}^{\\\\theta}{}_{r}= & \\\\frac{r \\\\partial_{r}{\\\\Sigma}-\\\\Sigma}{\\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{\\\\theta}{}^{\\\\theta}{}_{\\\\theta}= & r \\\\frac{\\\\partial_{\\\\theta}{\\\\Sigma}}{\\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{\\\\phi}{}^{\\\\phi}{}_{r}= & a^{2} r_s \\\\left(a^{4} r^{2} r_s \\\\sin{\\\\theta}^{4} \\\\partial_{r}{\\\\Sigma}-a^{4} r^{2} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}+2a^{4} r \\\\Sigma \\\\sin{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}-a^{4} \\\\Sigma^{2} \\\\sin{\\\\theta}^{2}-a^{2} r^{4} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}-a^{2} r^{3} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}+a^{2} r^{3} r_s^{2} \\\\partial_{r}{\\\\Sigma}-2a^{2} r^{3} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2a^{2} r^{3} \\\\Sigma \\\\sin{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}+a^{2} r^{2} r_s^{2} \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r^{2} r_s^{2} \\\\Sigma-2a^{2} r^{2} r_s \\\\Sigma \\\\partial_{r}{\\\\Sigma}+a^{2} r^{2} \\\\Sigma^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma^{2}+a^{2} r \\\\Sigma^{2} \\\\partial_{r}{\\\\Sigma}-a^{2} \\\\Sigma^{3}+r^{5} r_s^{2} \\\\partial_{r}{\\\\Sigma}+r^{4} r_s^{2} \\\\Sigma-2r^{4} r_s \\\\Sigma \\\\partial_{r}{\\\\Sigma}%\\n-2r^{3} r_s \\\\Sigma^{2}+r^{3} \\\\Sigma^{2} \\\\partial_{r}{\\\\Sigma}+r^{2} \\\\Sigma^{3}\\\\right) \\\\sin{\\\\theta} \\\\frac{\\\\cos{\\\\theta}}{\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{\\\\phi}{}^{\\\\phi}{}_{\\\\theta}= & \\\\frac{\\\\left(a^{2} r r_s \\\\sin{2\\\\theta}+a^{2} \\\\partial_{\\\\theta}{\\\\Sigma}+r^{2} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right) \\\\Sigma \\\\sin{\\\\theta} \\\\cos{\\\\theta}-\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right) \\\\Sigma \\\\cos{\\\\theta}^{2}-2\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right) \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}+\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(-5a^{4} r r_s \\\\Sigma \\\\sin{\\\\theta}^{5}+4a^{4} r r_s \\\\Sigma \\\\sin{\\\\theta}^{3}+a^{4} r r_s \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}+3a^{2} r^{2} r_s^{2} \\\\Sigma \\\\sin{\\\\theta}^{3}-2a^{2} r^{2} r_s^{2} \\\\Sigma \\\\sin{\\\\theta}+a^{2} r^{2} r_s^{2} \\\\cos{\\\\theta}^{3} \\\\partial_{\\\\theta}{\\\\Sigma}-a^{2} r^{2} r_s^{2} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}-6a^{2} r r_s \\\\Sigma^{2} \\\\sin{\\\\theta}^{3}+5a^{2} r r_s \\\\Sigma^{2} \\\\sin{\\\\theta}-4a^{2} r r_s \\\\Sigma \\\\cos{\\\\theta}^{3} \\\\partial_{\\\\theta}{\\\\Sigma}+2a^{2} r r_s \\\\Sigma \\\\cos{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}-a^{2} \\\\Sigma^{3} \\\\sin{\\\\theta}+3a^{2} \\\\Sigma^{2} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}+r^{3} r_s \\\\Sigma^{2} \\\\sin{\\\\theta}-2r^{3} r_s \\\\Sigma \\\\cos{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}-r^{2} \\\\Sigma^{3} \\\\sin{\\\\theta}+3r^{2} \\\\Sigma^{2} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\sin{\\\\theta}}{\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2} \\\\sin{\\\\theta}^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{\\\\phi}{}^{t}{}_{r}= & a^{3} r_s \\\\left(r \\\\left(r_s-\\\\partial_{r}{\\\\Sigma}\\\\right) \\\\left(-a^{2} r r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\Sigma-r^{3} r_s+r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\Sigma+r \\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(-a^{2} r r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\Sigma-r^{3} r_s+r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\partial_{r}{\\\\Sigma}+r \\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(-a^{2} r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\partial_{r}{\\\\Sigma}-3r^{2} r_s+r^{2} \\\\partial_{r}{\\\\Sigma}+2r \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\Sigma+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(-a^{2} r r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\Sigma-r^{3} r_s+r^{2} \\\\Sigma\\\\right) \\\\left(-a^{2} r r_s+a^{2} \\\\Sigma-r^{3} r_s+r^{2} r_s^{2}+r^{2} \\\\Sigma-r r_s \\\\Sigma-r \\\\left(a^{2} r_s-a^{2} \\\\partial_{r}{\\\\Sigma}+3r^{2} r_s-r^{2} \\\\partial_{r}{\\\\Sigma}-2r r_s^{2}+r r_s \\\\partial_{r}{\\\\Sigma}-2r \\\\Sigma+r_s \\\\Sigma\\\\right)\\\\right) \\\\Sigma\\\\right) \\\\sin{\\\\theta}^{3} \\\\frac{\\\\cos{\\\\theta}}{\\\\left(r r_s-\\\\Sigma\\\\right)^{2} \\\\left(-a^{2} r r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\Sigma-r^{3} r_s+r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{\\\\phi}{}^{t}{}_{\\\\theta}= & a^{3} r r_s \\\\left(\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\sin{2\\\\theta}+a^{2} \\\\partial_{\\\\theta}{\\\\Sigma}+r^{2} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\Sigma \\\\sin{\\\\theta} \\\\cos{\\\\theta}+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(-a^{2} r r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\Sigma-r^{3} r_s+r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(-a^{2} r r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\Sigma-r^{3} r_s+r^{2} \\\\Sigma\\\\right) \\\\left(-2a^{2} r r_s \\\\cos{2\\\\theta}-a^{2} r r_s+2a^{2} \\\\Sigma \\\\cos{2\\\\theta}+a^{2} \\\\Sigma+\\\\frac{1}{2}a^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}-2r^{3} r_s \\\\cos{2\\\\theta}-r^{3} r_s+2r^{2} r_s^{2} \\\\cos{2\\\\theta}+r^{2} r_s^{2}+2r^{2} \\\\Sigma \\\\cos{2\\\\theta}+r^{2} \\\\Sigma+\\\\frac{1}{2}r^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}-2r r_s \\\\Sigma \\\\cos{2\\\\theta}-r r_s \\\\Sigma - \\\\frac{1}{2}r r_s \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\Sigma-\\\\left(-a^{2} r r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\Sigma-r^{3} r_s+r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\Sigma \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\frac{\\\\sin{\\\\theta}^{2}}{\\\\left(r r_s-\\\\Sigma\\\\right)^{2} \\\\left(-a^{2} r r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\Sigma-r^{3} r_s+r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{\\\\phi}{}^{\\\\phi}{}_{r}= & \\\\frac{\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right) \\\\partial_{r}{\\\\Sigma}+\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(-4a^{2} r r_s \\\\sin{\\\\theta}^{2}+a^{2} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}-2r^{2} r_s \\\\partial_{r}{\\\\Sigma}-4r r_s \\\\Sigma+4r \\\\Sigma \\\\partial_{r}{\\\\Sigma}+2\\\\Sigma^{2}\\\\right) \\\\Sigma-\\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right) \\\\left(-a^{2} r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\partial_{r}{\\\\Sigma}-3r^{2} r_s+r^{2} \\\\partial_{r}{\\\\Sigma}+2r \\\\Sigma\\\\right) \\\\Sigma}{2\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{\\\\phi}{}^{\\\\phi}{}_{\\\\theta}= & \\\\frac{-\\\\left(a^{2} r r_s \\\\sin{2\\\\theta}+a^{2} \\\\partial_{\\\\theta}{\\\\Sigma}+r^{2} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right) \\\\Sigma+\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right) \\\\partial_{\\\\theta}{\\\\Sigma}+\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(-2a^{2} r^{2} r_s \\\\sin{2\\\\theta}+a^{2} r_s \\\\Sigma \\\\sin{2\\\\theta}+a^{2} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{\\\\theta}{\\\\Sigma}-2r^{2} r_s \\\\partial_{\\\\theta}{\\\\Sigma}+4r \\\\Sigma \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\Sigma}{2\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{\\\\phi}{}^{t}{}_{r}= & a r_s \\\\left(2a^{4} r^{3} r_s \\\\cos{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}-2a^{4} r^{2} r_s \\\\Sigma \\\\cos{\\\\theta}^{2}-4a^{4} r^{2} \\\\Sigma \\\\partial_{r}{\\\\Sigma}+4a^{4} r \\\\Sigma^{2}-a^{4} r_s \\\\Sigma^{2} \\\\cos{\\\\theta}^{2}+a^{4} \\\\Sigma^{2} \\\\partial_{r}{\\\\Sigma}+2a^{2} r^{5} r_s \\\\cos{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}+2a^{2} r^{5} r_s \\\\partial_{r}{\\\\Sigma}-6a^{2} r^{4} r_s \\\\Sigma \\\\cos{\\\\theta}^{2}+2a^{2} r^{4} r_s \\\\Sigma-8a^{2} r^{4} \\\\Sigma \\\\partial_{r}{\\\\Sigma}+8a^{2} r^{3} \\\\Sigma^{2}-a^{2} r^{2} r_s \\\\Sigma^{2} \\\\cos{\\\\theta}^{2}-3a^{2} r^{2} r_s \\\\Sigma^{2}+4a^{2} r \\\\Sigma^{3}+2r^{7} r_s \\\\partial_{r}{\\\\Sigma}-2r^{6} r_s \\\\Sigma-4r^{6} \\\\Sigma \\\\partial_{r}{\\\\Sigma}+4r^{5} \\\\Sigma^{2}%\\n+r^{4} r_s \\\\Sigma^{2}-r^{4} \\\\Sigma^{2} \\\\partial_{r}{\\\\Sigma}\\\\right) \\\\frac{\\\\sin{\\\\theta}^{2}}{2\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{\\\\phi}{}^{t}{}_{\\\\theta}= & a r_s \\\\left(\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(\\\\left(2a^{2} r^{2}+a^{2} r r_s-2a^{2} \\\\Sigma+2r^{4}-r^{3} r_s+2r^{2} \\\\Sigma\\\\right) \\\\sin{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}+2\\\\left(-2a^{2} r^{3} r_s+2a^{2} r^{2} \\\\Sigma+a^{2} r r_s \\\\Sigma-a^{2} \\\\Sigma^{2}-2r^{5} r_s+2r^{4} \\\\Sigma-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right) \\\\cos{\\\\theta}\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma-\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\sin{2\\\\theta}+a^{2} \\\\partial_{\\\\theta}{\\\\Sigma}+r^{2} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\left(2a^{2} r^{3} r_s-2a^{2} r^{2} \\\\Sigma-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}+2r^{5} r_s-2r^{4} \\\\Sigma+r^{3} r_s \\\\Sigma-r^{2} \\\\Sigma^{2}\\\\right) \\\\Sigma \\\\sin{\\\\theta}+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(2a^{2} r^{3} r_s-2a^{2} r^{2} \\\\Sigma-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}+2r^{5} r_s-2r^{4} \\\\Sigma+r^{3} r_s \\\\Sigma-r^{2} \\\\Sigma^{2}\\\\right) \\\\sin{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}-\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(2a^{2} r^{3} r_s-2a^{2} r^{2} \\\\Sigma-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}+2r^{5} r_s-2r^{4} \\\\Sigma+r^{3} r_s \\\\Sigma-r^{2} \\\\Sigma^{2}\\\\right) \\\\Sigma \\\\sin{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\frac{\\\\sin{\\\\theta}}{2\\\\left(r r_s-\\\\Sigma\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}_{\\\\theta}{}^{\\\\phi}{}_{r}= & a r_s \\\\frac{r \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\partial_{r}{\\\\Sigma}-r \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right) \\\\left(-a^{2} r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\partial_{r}{\\\\Sigma}-3r^{2} r_s+r^{2} \\\\partial_{r}{\\\\Sigma}+2r \\\\Sigma\\\\right) \\\\Sigma+\\\\left(-a^{2} \\\\sin{\\\\theta}^{2}+2r r_s-r \\\\partial_{r}{\\\\Sigma}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma}{\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2} \\\\tan{\\\\theta}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}_{\\\\theta}{}^{\\\\phi}{}_{\\\\theta}= & a r r_s \\\\frac{-\\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\sin{2\\\\theta}+a^{2} \\\\partial_{\\\\theta}{\\\\Sigma}+r^{2} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\Sigma \\\\tan{\\\\theta}+\\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\tan{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}-\\\\left(a^{2} \\\\cos{2\\\\theta} \\\\tan{\\\\theta}^{2}+\\\\frac{r r_s-\\\\Sigma}{\\\\cos{\\\\theta}^{2}}+\\\\tan{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma}{\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2} \\\\tan{\\\\theta}^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}_{\\\\theta}{}^{t}{}_{r}= & a^{2} r_s \\\\left(a^{4} r^{2} r_s \\\\cos{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}-2a^{4} r \\\\Sigma \\\\partial_{r}{\\\\Sigma}+a^{4} \\\\Sigma^{2}+a^{2} r^{4} r_s \\\\cos{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}+a^{2} r^{4} r_s \\\\partial_{r}{\\\\Sigma}-a^{2} r^{3} r_s^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}-2a^{2} r^{3} r_s \\\\Sigma \\\\cos{\\\\theta}^{2}+2a^{2} r^{3} r_s \\\\Sigma-4a^{2} r^{3} \\\\Sigma \\\\partial_{r}{\\\\Sigma}+a^{2} r^{2} r_s^{2} \\\\Sigma \\\\cos{\\\\theta}^{2}+2a^{2} r^{2} r_s \\\\Sigma \\\\partial_{r}{\\\\Sigma}+2a^{2} r^{2} \\\\Sigma^{2}-2a^{2} r r_s \\\\Sigma^{2}+r^{6} r_s \\\\partial_{r}{\\\\Sigma}-r^{5} r_s^{2} \\\\partial_{r}{\\\\Sigma}-2r^{5} \\\\Sigma \\\\partial_{r}{\\\\Sigma}-r^{4} r_s^{2} \\\\Sigma+2r^{4} r_s \\\\Sigma \\\\partial_{r}{\\\\Sigma}+r^{4} \\\\Sigma^{2}\\\\right) \\\\sin{\\\\theta} \\\\frac{\\\\cos{\\\\theta}}{\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}_{\\\\theta}{}^{t}{}_{\\\\theta}= & a^{2} r r_s \\\\frac{-\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\sin{2\\\\theta}+a^{2} \\\\partial_{\\\\theta}{\\\\Sigma}+r^{2} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\Sigma \\\\sin{2\\\\theta}+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(-2a^{2} r r_s \\\\cos{2\\\\theta}+2a^{2} \\\\Sigma \\\\cos{2\\\\theta}+a^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}-2r^{3} r_s \\\\cos{2\\\\theta}+2r^{2} r_s^{2} \\\\cos{2\\\\theta}+2r^{2} \\\\Sigma \\\\cos{2\\\\theta}+r^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}-2r r_s \\\\Sigma \\\\cos{2\\\\theta}-r r_s \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\Sigma-\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\Sigma \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}}{2\\\\left(r r_s-\\\\Sigma\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}_{r}{}^{\\\\phi}{}_{r}= & a r_s \\\\frac{\\\\left(4r-\\\\partial_{r}{\\\\Sigma}\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma-\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\partial_{r}{\\\\Sigma}+\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(-a^{2} r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\partial_{r}{\\\\Sigma}-3r^{2} r_s+r^{2} \\\\partial_{r}{\\\\Sigma}+2r \\\\Sigma\\\\right) \\\\Sigma}{2\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}_{r}{}^{\\\\phi}{}_{\\\\theta}= & a r_s \\\\frac{\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\sin{2\\\\theta}+a^{2} \\\\partial_{\\\\theta}{\\\\Sigma}+r^{2} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\Sigma-\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\partial_{\\\\theta}{\\\\Sigma}-\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma \\\\partial_{\\\\theta}{\\\\Sigma}}{2\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}_{r}{}^{t}{}_{r}= & r_s \\\\frac{-\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(r_s-\\\\partial_{r}{\\\\Sigma}\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma-\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\partial_{r}{\\\\Sigma}+\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(-a^{2} r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\partial_{r}{\\\\Sigma}-3r^{2} r_s+r^{2} \\\\partial_{r}{\\\\Sigma}+2r \\\\Sigma\\\\right) \\\\Sigma+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(\\\\left(4r-\\\\partial_{r}{\\\\Sigma}\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)-\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(-a^{2} r_s+a^{2} \\\\partial_{r}{\\\\Sigma}-3r^{2} r_s+r^{2} \\\\partial_{r}{\\\\Sigma}+2r \\\\Sigma\\\\right)\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma}{2\\\\left(r r_s-\\\\Sigma\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}_{r}{}^{t}{}_{\\\\theta}= & r_s \\\\frac{\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\sin{2\\\\theta}+a^{2} \\\\partial_{\\\\theta}{\\\\Sigma}+r^{2} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma-\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\partial_{\\\\theta}{\\\\Sigma}+\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma \\\\partial_{\\\\theta}{\\\\Sigma}+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(-a^{2} r r_s+a^{2} \\\\Sigma-r^{3} r_s+r^{2} \\\\Sigma-\\\\left(a^{2}+r^{2}\\\\right) \\\\left(2r^{2}-\\\\Sigma\\\\right)\\\\right) \\\\Sigma \\\\partial_{\\\\theta}{\\\\Sigma}}{2\\\\left(r r_s-\\\\Sigma\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{\\\\theta}{}^{r}{}_{r}= & -a^{2} \\\\sin{2\\\\theta} \\\\frac{\\\\partial_{r}{\\\\Sigma}}{2\\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{\\\\theta}{}^{r}{}_{\\\\theta}= & a^{2} \\\\frac{\\\\Sigma \\\\cos{2\\\\theta} - \\\\frac{1}{2}\\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}}{\\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{r}{}^{r}{}_{r}= & r \\\\frac{\\\\partial_{r}{\\\\Sigma}}{\\\\Sigma^{2}}-r \\\\frac{\\\\partial_{r}{\\\\Delta}}{\\\\Delta^{2}}+r_s \\\\frac{\\\\partial_{r}{\\\\Delta}}{2\\\\Delta^{2}} - \\\\frac{1}{\\\\Sigma}+\\\\frac{1}{\\\\Delta}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{r}{}^{r}{}_{\\\\theta}= & r \\\\frac{\\\\partial_{\\\\theta}{\\\\Sigma}}{\\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{\\\\theta}{}^{\\\\theta}{}_{r}= & -a^{2} \\\\sin{2\\\\theta} \\\\frac{\\\\partial_{r}{\\\\Sigma}}{2\\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{\\\\theta}{}^{\\\\theta}{}_{\\\\theta}= & a^{2} \\\\frac{\\\\Sigma \\\\cos{2\\\\theta} - \\\\frac{1}{2}\\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}}{\\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{r}{}^{\\\\theta}{}_{r}= & \\\\frac{r \\\\partial_{r}{\\\\Sigma}-\\\\Sigma}{\\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{r}{}^{\\\\theta}{}_{\\\\theta}= & r \\\\frac{\\\\partial_{\\\\theta}{\\\\Sigma}}{\\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{\\\\theta}{}^{\\\\phi}{}_{r}= & a^{2} r_s \\\\left(a^{4} r^{2} r_s \\\\sin{\\\\theta}^{4} \\\\partial_{r}{\\\\Sigma}-a^{4} r^{2} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}+2a^{4} r \\\\Sigma \\\\sin{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}-a^{4} \\\\Sigma^{2} \\\\sin{\\\\theta}^{2}-a^{2} r^{4} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}-a^{2} r^{3} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}+a^{2} r^{3} r_s^{2} \\\\partial_{r}{\\\\Sigma}-2a^{2} r^{3} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2a^{2} r^{3} \\\\Sigma \\\\sin{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}+a^{2} r^{2} r_s^{2} \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r^{2} r_s^{2} \\\\Sigma-2a^{2} r^{2} r_s \\\\Sigma \\\\partial_{r}{\\\\Sigma}+a^{2} r^{2} \\\\Sigma^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma^{2}+a^{2} r \\\\Sigma^{2} \\\\partial_{r}{\\\\Sigma}-a^{2} \\\\Sigma^{3}+r^{5} r_s^{2} \\\\partial_{r}{\\\\Sigma}+r^{4} r_s^{2} \\\\Sigma-2r^{4} r_s \\\\Sigma \\\\partial_{r}{\\\\Sigma}%\\n-2r^{3} r_s \\\\Sigma^{2}+r^{3} \\\\Sigma^{2} \\\\partial_{r}{\\\\Sigma}+r^{2} \\\\Sigma^{3}\\\\right) \\\\sin{\\\\theta} \\\\frac{\\\\cos{\\\\theta}}{\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{\\\\theta}{}^{\\\\phi}{}_{\\\\theta}= & \\\\frac{\\\\left(a^{2} r r_s \\\\sin{2\\\\theta}+a^{2} \\\\partial_{\\\\theta}{\\\\Sigma}+r^{2} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right) \\\\Sigma \\\\sin{\\\\theta} \\\\cos{\\\\theta}-\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right) \\\\Sigma \\\\cos{\\\\theta}^{2}-2\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right) \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}+\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(-5a^{4} r r_s \\\\Sigma \\\\sin{\\\\theta}^{5}+4a^{4} r r_s \\\\Sigma \\\\sin{\\\\theta}^{3}+a^{4} r r_s \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}+3a^{2} r^{2} r_s^{2} \\\\Sigma \\\\sin{\\\\theta}^{3}-2a^{2} r^{2} r_s^{2} \\\\Sigma \\\\sin{\\\\theta}+a^{2} r^{2} r_s^{2} \\\\cos{\\\\theta}^{3} \\\\partial_{\\\\theta}{\\\\Sigma}-a^{2} r^{2} r_s^{2} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}-6a^{2} r r_s \\\\Sigma^{2} \\\\sin{\\\\theta}^{3}+5a^{2} r r_s \\\\Sigma^{2} \\\\sin{\\\\theta}-4a^{2} r r_s \\\\Sigma \\\\cos{\\\\theta}^{3} \\\\partial_{\\\\theta}{\\\\Sigma}+2a^{2} r r_s \\\\Sigma \\\\cos{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}-a^{2} \\\\Sigma^{3} \\\\sin{\\\\theta}+3a^{2} \\\\Sigma^{2} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}+r^{3} r_s \\\\Sigma^{2} \\\\sin{\\\\theta}-2r^{3} r_s \\\\Sigma \\\\cos{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}-r^{2} \\\\Sigma^{3} \\\\sin{\\\\theta}+3r^{2} \\\\Sigma^{2} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\sin{\\\\theta}}{\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2} \\\\sin{\\\\theta}^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{\\\\theta}{}^{t}{}_{r}= & a^{3} r_s \\\\left(r \\\\left(r_s-\\\\partial_{r}{\\\\Sigma}\\\\right) \\\\left(-a^{2} r r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\Sigma-r^{3} r_s+r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\Sigma+r \\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(-a^{2} r r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\Sigma-r^{3} r_s+r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\partial_{r}{\\\\Sigma}+r \\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(-a^{2} r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\partial_{r}{\\\\Sigma}-3r^{2} r_s+r^{2} \\\\partial_{r}{\\\\Sigma}+2r \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\Sigma+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(-a^{2} r r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\Sigma-r^{3} r_s+r^{2} \\\\Sigma\\\\right) \\\\left(-a^{2} r r_s+a^{2} \\\\Sigma-r^{3} r_s+r^{2} r_s^{2}+r^{2} \\\\Sigma-r r_s \\\\Sigma-r \\\\left(a^{2} r_s-a^{2} \\\\partial_{r}{\\\\Sigma}+3r^{2} r_s-r^{2} \\\\partial_{r}{\\\\Sigma}-2r r_s^{2}+r r_s \\\\partial_{r}{\\\\Sigma}-2r \\\\Sigma+r_s \\\\Sigma\\\\right)\\\\right) \\\\Sigma\\\\right) \\\\sin{\\\\theta}^{3} \\\\frac{\\\\cos{\\\\theta}}{\\\\left(r r_s-\\\\Sigma\\\\right)^{2} \\\\left(-a^{2} r r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\Sigma-r^{3} r_s+r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{\\\\theta}{}^{t}{}_{\\\\theta}= & a^{3} r r_s \\\\left(\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\sin{2\\\\theta}+a^{2} \\\\partial_{\\\\theta}{\\\\Sigma}+r^{2} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\Sigma \\\\sin{\\\\theta} \\\\cos{\\\\theta}+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(-a^{2} r r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\Sigma-r^{3} r_s+r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(-a^{2} r r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\Sigma-r^{3} r_s+r^{2} \\\\Sigma\\\\right) \\\\left(-2a^{2} r r_s \\\\cos{2\\\\theta}-a^{2} r r_s+2a^{2} \\\\Sigma \\\\cos{2\\\\theta}+a^{2} \\\\Sigma+\\\\frac{1}{2}a^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}-2r^{3} r_s \\\\cos{2\\\\theta}-r^{3} r_s+2r^{2} r_s^{2} \\\\cos{2\\\\theta}+r^{2} r_s^{2}+2r^{2} \\\\Sigma \\\\cos{2\\\\theta}+r^{2} \\\\Sigma+\\\\frac{1}{2}r^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}-2r r_s \\\\Sigma \\\\cos{2\\\\theta}-r r_s \\\\Sigma - \\\\frac{1}{2}r r_s \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\Sigma-\\\\left(-a^{2} r r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\Sigma-r^{3} r_s+r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\Sigma \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\frac{\\\\sin{\\\\theta}^{2}}{\\\\left(r r_s-\\\\Sigma\\\\right)^{2} \\\\left(-a^{2} r r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\Sigma-r^{3} r_s+r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{r}{}^{\\\\phi}{}_{r}= & \\\\frac{\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right) \\\\partial_{r}{\\\\Sigma}+\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(-4a^{2} r r_s \\\\sin{\\\\theta}^{2}+a^{2} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}-2r^{2} r_s \\\\partial_{r}{\\\\Sigma}-4r r_s \\\\Sigma+4r \\\\Sigma \\\\partial_{r}{\\\\Sigma}+2\\\\Sigma^{2}\\\\right) \\\\Sigma-\\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right) \\\\left(-a^{2} r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\partial_{r}{\\\\Sigma}-3r^{2} r_s+r^{2} \\\\partial_{r}{\\\\Sigma}+2r \\\\Sigma\\\\right) \\\\Sigma}{2\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{r}{}^{\\\\phi}{}_{\\\\theta}= & \\\\frac{-\\\\left(a^{2} r r_s \\\\sin{2\\\\theta}+a^{2} \\\\partial_{\\\\theta}{\\\\Sigma}+r^{2} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right) \\\\Sigma+\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right) \\\\partial_{\\\\theta}{\\\\Sigma}+\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(-2a^{2} r^{2} r_s \\\\sin{2\\\\theta}+a^{2} r_s \\\\Sigma \\\\sin{2\\\\theta}+a^{2} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{\\\\theta}{\\\\Sigma}-2r^{2} r_s \\\\partial_{\\\\theta}{\\\\Sigma}+4r \\\\Sigma \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\Sigma}{2\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{r}{}^{t}{}_{r}= & a r_s \\\\left(2a^{4} r^{3} r_s \\\\cos{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}-2a^{4} r^{2} r_s \\\\Sigma \\\\cos{\\\\theta}^{2}-4a^{4} r^{2} \\\\Sigma \\\\partial_{r}{\\\\Sigma}+4a^{4} r \\\\Sigma^{2}-a^{4} r_s \\\\Sigma^{2} \\\\cos{\\\\theta}^{2}+a^{4} \\\\Sigma^{2} \\\\partial_{r}{\\\\Sigma}+2a^{2} r^{5} r_s \\\\cos{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}+2a^{2} r^{5} r_s \\\\partial_{r}{\\\\Sigma}-6a^{2} r^{4} r_s \\\\Sigma \\\\cos{\\\\theta}^{2}+2a^{2} r^{4} r_s \\\\Sigma-8a^{2} r^{4} \\\\Sigma \\\\partial_{r}{\\\\Sigma}+8a^{2} r^{3} \\\\Sigma^{2}-a^{2} r^{2} r_s \\\\Sigma^{2} \\\\cos{\\\\theta}^{2}-3a^{2} r^{2} r_s \\\\Sigma^{2}+4a^{2} r \\\\Sigma^{3}+2r^{7} r_s \\\\partial_{r}{\\\\Sigma}-2r^{6} r_s \\\\Sigma-4r^{6} \\\\Sigma \\\\partial_{r}{\\\\Sigma}+4r^{5} \\\\Sigma^{2}%\\n+r^{4} r_s \\\\Sigma^{2}-r^{4} \\\\Sigma^{2} \\\\partial_{r}{\\\\Sigma}\\\\right) \\\\frac{\\\\sin{\\\\theta}^{2}}{2\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{r}{}^{t}{}_{\\\\theta}= & a r_s \\\\left(\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(\\\\left(2a^{2} r^{2}+a^{2} r r_s-2a^{2} \\\\Sigma+2r^{4}-r^{3} r_s+2r^{2} \\\\Sigma\\\\right) \\\\sin{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}+2\\\\left(-2a^{2} r^{3} r_s+2a^{2} r^{2} \\\\Sigma+a^{2} r r_s \\\\Sigma-a^{2} \\\\Sigma^{2}-2r^{5} r_s+2r^{4} \\\\Sigma-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right) \\\\cos{\\\\theta}\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma-\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\sin{2\\\\theta}+a^{2} \\\\partial_{\\\\theta}{\\\\Sigma}+r^{2} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\left(2a^{2} r^{3} r_s-2a^{2} r^{2} \\\\Sigma-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}+2r^{5} r_s-2r^{4} \\\\Sigma+r^{3} r_s \\\\Sigma-r^{2} \\\\Sigma^{2}\\\\right) \\\\Sigma \\\\sin{\\\\theta}+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(2a^{2} r^{3} r_s-2a^{2} r^{2} \\\\Sigma-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}+2r^{5} r_s-2r^{4} \\\\Sigma+r^{3} r_s \\\\Sigma-r^{2} \\\\Sigma^{2}\\\\right) \\\\sin{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}-\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(2a^{2} r^{3} r_s-2a^{2} r^{2} \\\\Sigma-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}+2r^{5} r_s-2r^{4} \\\\Sigma+r^{3} r_s \\\\Sigma-r^{2} \\\\Sigma^{2}\\\\right) \\\\Sigma \\\\sin{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\frac{\\\\sin{\\\\theta}}{2\\\\left(r r_s-\\\\Sigma\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\end{aligned}\\\\right.\\n\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"substitute(tst3, ch)\\nevaluate(tst3, kerr);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\left\\\\{\\\\begin{aligned}\\\\square{}_{r}{}^{t}{}_{\\\\phi}{}_{r}= & a r_s \\\\left(r_s \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)+\\\\left(-r r_s+\\\\Sigma\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right)\\\\right) \\\\left(2a^{2} r^{3} r_s-2a^{2} r^{2} \\\\Sigma-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}+2r^{5} r_s-2r^{4} \\\\Sigma+r^{3} r_s \\\\Sigma-r^{2} \\\\Sigma^{2}\\\\right) \\\\frac{\\\\sin{\\\\theta}^{2}}{4\\\\left(r r_s-\\\\Sigma\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}^{t}{}_{\\\\phi}{}_{\\\\theta}= & a r_s \\\\left(a^{2} r r_s \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{\\\\theta}^{2}+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(-a^{2} r r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\Sigma-r^{3} r_s+r^{2} \\\\Sigma\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right) \\\\left(2a^{2} r^{3} r_s-2a^{2} r^{2} \\\\Sigma-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}+2r^{5} r_s-2r^{4} \\\\Sigma+r^{3} r_s \\\\Sigma-r^{2} \\\\Sigma^{2}\\\\right)\\\\right) \\\\sin{\\\\theta} \\\\frac{\\\\cos{\\\\theta}}{2\\\\left(r r_s-\\\\Sigma\\\\right)^{2} \\\\left(-a^{2} r r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\Sigma-r^{3} r_s+r^{2} \\\\Sigma\\\\right)^{3} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}^{t}{}_{t}{}_{r}= & r_s^{2} \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\frac{a^{2} \\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(2a^{2} r^{3} r_s-2a^{2} r^{2} \\\\Sigma-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}+2r^{5} r_s-2r^{4} \\\\Sigma+r^{3} r_s \\\\Sigma-r^{2} \\\\Sigma^{2}\\\\right) \\\\sin{\\\\theta}^{2}-\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2}}{4\\\\left(r r_s-\\\\Sigma\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}^{t}{}_{t}{}_{\\\\theta}= & a^{2} r r_s^{2} \\\\frac{\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right) \\\\left(2a^{2} r^{3} r_s-2a^{2} r^{2} \\\\Sigma-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}+2r^{5} r_s-2r^{4} \\\\Sigma+r^{3} r_s \\\\Sigma-r^{2} \\\\Sigma^{2}\\\\right) \\\\sin{\\\\theta}^{2}}{4\\\\left(r r_s-\\\\Sigma\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2} \\\\tan{\\\\theta}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}^{t}{}_{r}{}_{\\\\phi}= & a r_s \\\\left(r_s \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)+\\\\left(-r r_s+\\\\Sigma\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right)\\\\right) \\\\left(2a^{2} r^{3} r_s-2a^{2} r^{2} \\\\Sigma-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}+2r^{5} r_s-2r^{4} \\\\Sigma+r^{3} r_s \\\\Sigma-r^{2} \\\\Sigma^{2}\\\\right) \\\\frac{\\\\sin{\\\\theta}^{2}}{4\\\\left(r r_s-\\\\Sigma\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}^{t}{}_{\\\\theta}{}_{\\\\phi}= & a r_s \\\\left(a^{2} r r_s \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{\\\\theta}^{2}+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(-a^{2} r r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\Sigma-r^{3} r_s+r^{2} \\\\Sigma\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right) \\\\left(2a^{2} r^{3} r_s-2a^{2} r^{2} \\\\Sigma-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}+2r^{5} r_s-2r^{4} \\\\Sigma+r^{3} r_s \\\\Sigma-r^{2} \\\\Sigma^{2}\\\\right)\\\\right) \\\\sin{\\\\theta} \\\\frac{\\\\cos{\\\\theta}}{2\\\\left(r r_s-\\\\Sigma\\\\right)^{2} \\\\left(-a^{2} r r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\Sigma-r^{3} r_s+r^{2} \\\\Sigma\\\\right)^{3} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}^{t}{}_{r}{}_{t}= & r_s^{2} \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\frac{a^{2} \\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(2a^{2} r^{3} r_s-2a^{2} r^{2} \\\\Sigma-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}+2r^{5} r_s-2r^{4} \\\\Sigma+r^{3} r_s \\\\Sigma-r^{2} \\\\Sigma^{2}\\\\right) \\\\sin{\\\\theta}^{2}-\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2}}{4\\\\left(r r_s-\\\\Sigma\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}^{t}{}_{\\\\theta}{}_{t}= & a^{2} r r_s^{2} \\\\frac{\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right) \\\\left(2a^{2} r^{3} r_s-2a^{2} r^{2} \\\\Sigma-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}+2r^{5} r_s-2r^{4} \\\\Sigma+r^{3} r_s \\\\Sigma-r^{2} \\\\Sigma^{2}\\\\right) \\\\sin{\\\\theta}^{2}}{4\\\\left(r r_s-\\\\Sigma\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2} \\\\tan{\\\\theta}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}^{\\\\phi}{}_{\\\\phi}{}_{r}= & \\\\frac{a^{2} r_s^{2} \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(2a^{2} r^{3} r_s-2a^{2} r^{2} \\\\Sigma-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}+2r^{5} r_s-2r^{4} \\\\Sigma+r^{3} r_s \\\\Sigma-r^{2} \\\\Sigma^{2}\\\\right) \\\\sin{\\\\theta}^{2}+\\\\left(-r r_s+\\\\Sigma\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right)^{2}}{4\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}^{\\\\phi}{}_{\\\\phi}{}_{\\\\theta}= & \\\\frac{a^{4} r r_s^{2} \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{\\\\theta}^{4}+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(-a^{2} r r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\Sigma-r^{3} r_s+r^{2} \\\\Sigma\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right)}{2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(-a^{2} r r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\Sigma-r^{3} r_s+r^{2} \\\\Sigma\\\\right)^{3} \\\\Sigma^{2} \\\\tan{\\\\theta}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}^{\\\\phi}{}_{t}{}_{r}= & a r_s \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\frac{-r_s \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right)}{4\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}^{\\\\phi}{}_{t}{}_{\\\\theta}= & a r r_s \\\\frac{a^{2} r_s \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+2\\\\left(-r r_s+\\\\Sigma\\\\right) \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right)}{4\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2} \\\\tan{\\\\theta}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}^{\\\\phi}{}_{r}{}_{\\\\phi}= & \\\\frac{a^{2} r_s^{2} \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(2a^{2} r^{3} r_s-2a^{2} r^{2} \\\\Sigma-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}+2r^{5} r_s-2r^{4} \\\\Sigma+r^{3} r_s \\\\Sigma-r^{2} \\\\Sigma^{2}\\\\right) \\\\sin{\\\\theta}^{2}+\\\\left(-r r_s+\\\\Sigma\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right)^{2}}{4\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}^{\\\\phi}{}_{\\\\theta}{}_{\\\\phi}= & \\\\frac{a^{4} r r_s^{2} \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{\\\\theta}^{4}+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(-a^{2} r r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\Sigma-r^{3} r_s+r^{2} \\\\Sigma\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right)}{2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(-a^{2} r r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\Sigma-r^{3} r_s+r^{2} \\\\Sigma\\\\right)^{3} \\\\Sigma^{2} \\\\tan{\\\\theta}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}^{\\\\phi}{}_{r}{}_{t}= & a r_s \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\frac{-r_s \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right)}{4\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}^{\\\\phi}{}_{\\\\theta}{}_{t}= & a r r_s \\\\frac{a^{2} r_s \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+2\\\\left(-r r_s+\\\\Sigma\\\\right) \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right)}{4\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2} \\\\tan{\\\\theta}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}^{t}{}_{\\\\phi}{}_{r}= & a^{3} r r_s \\\\left(-2a^{4} r^{2} r_s \\\\cos{\\\\theta}^{2}+a^{4} r_s \\\\Sigma \\\\cos{\\\\theta}^{2}-2a^{2} r^{4} r_s \\\\cos{\\\\theta}^{2}-2a^{2} r^{4} r_s+2a^{2} r^{3} r_s^{2} \\\\cos{\\\\theta}^{2}+a^{2} r^{2} r_s \\\\Sigma \\\\cos{\\\\theta}^{2}+a^{2} r^{2} r_s \\\\Sigma-a^{2} r r_s^{2} \\\\Sigma \\\\cos{\\\\theta}^{2}-2a^{2} r \\\\Sigma^{2}-2r^{6} r_s+2r^{5} r_s^{2}+r^{4} r_s \\\\Sigma-r^{3} r_s^{2} \\\\Sigma-2r^{3} \\\\Sigma^{2}+2r^{2} r_s \\\\Sigma^{2}\\\\right) \\\\sin{\\\\theta}^{3} \\\\frac{\\\\cos{\\\\theta}}{2\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}^{t}{}_{\\\\phi}{}_{\\\\theta}= & a^{3} r r_s \\\\left(a^{2} r r_s \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{\\\\theta} \\\\sin{2\\\\theta}-2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right) \\\\cos{\\\\theta}\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{\\\\theta}^{2} \\\\frac{\\\\cos{\\\\theta}}{2\\\\left(r r_s-\\\\Sigma\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}^{t}{}_{t}{}_{r}= & a^{2} r r_s^{2} \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{4} \\\\cos{\\\\theta}^{2}+a^{2} r^{2} \\\\cos{\\\\theta}^{2}+a^{2} r^{2}-a^{2} r r_s \\\\cos{\\\\theta}^{2}+r^{4}-r^{3} r_s\\\\right) \\\\sin{\\\\theta} \\\\frac{\\\\cos{\\\\theta}}{2\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}^{t}{}_{t}{}_{\\\\theta}= & a^{4} r^{2} r_s^{2} \\\\left(\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)-\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right)\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{\\\\theta}^{2} \\\\frac{\\\\cos{\\\\theta}^{2}}{\\\\left(r r_s-\\\\Sigma\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{3} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}^{t}{}_{r}{}_{\\\\phi}= & a^{3} r r_s \\\\left(-2a^{4} r^{2} r_s \\\\cos{\\\\theta}^{2}+a^{4} r_s \\\\Sigma \\\\cos{\\\\theta}^{2}-2a^{2} r^{4} r_s \\\\cos{\\\\theta}^{2}-2a^{2} r^{4} r_s+2a^{2} r^{3} r_s^{2} \\\\cos{\\\\theta}^{2}+a^{2} r^{2} r_s \\\\Sigma \\\\cos{\\\\theta}^{2}+a^{2} r^{2} r_s \\\\Sigma-a^{2} r r_s^{2} \\\\Sigma \\\\cos{\\\\theta}^{2}-2a^{2} r \\\\Sigma^{2}-2r^{6} r_s+2r^{5} r_s^{2}+r^{4} r_s \\\\Sigma-r^{3} r_s^{2} \\\\Sigma-2r^{3} \\\\Sigma^{2}+2r^{2} r_s \\\\Sigma^{2}\\\\right) \\\\sin{\\\\theta}^{3} \\\\frac{\\\\cos{\\\\theta}}{2\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}^{t}{}_{\\\\theta}{}_{\\\\phi}= & a^{3} r r_s \\\\left(a^{2} r r_s \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{\\\\theta} \\\\sin{2\\\\theta}-2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right) \\\\cos{\\\\theta}\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{\\\\theta}^{2} \\\\frac{\\\\cos{\\\\theta}}{2\\\\left(r r_s-\\\\Sigma\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}^{t}{}_{r}{}_{t}= & a^{2} r r_s^{2} \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{4} \\\\cos{\\\\theta}^{2}+a^{2} r^{2} \\\\cos{\\\\theta}^{2}+a^{2} r^{2}-a^{2} r r_s \\\\cos{\\\\theta}^{2}+r^{4}-r^{3} r_s\\\\right) \\\\sin{\\\\theta} \\\\frac{\\\\cos{\\\\theta}}{2\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}^{t}{}_{\\\\theta}{}_{t}= & a^{4} r^{2} r_s^{2} \\\\left(\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)-\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right)\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{\\\\theta}^{2} \\\\frac{\\\\cos{\\\\theta}^{2}}{\\\\left(r r_s-\\\\Sigma\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{3} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}^{\\\\phi}{}_{\\\\phi}{}_{r}= & \\\\frac{-a^{2} r r_s^{2} \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right) \\\\left(2a^{2} r^{3} r_s-2a^{2} r^{2} \\\\Sigma-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}+2r^{5} r_s-2r^{4} \\\\Sigma+r^{3} r_s \\\\Sigma-r^{2} \\\\Sigma^{2}\\\\right) \\\\sin{\\\\theta}^{3}+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right) \\\\sin{\\\\theta}}{2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2} \\\\sin{\\\\theta} \\\\tan{\\\\theta}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}^{\\\\phi}{}_{\\\\phi}{}_{\\\\theta}= & \\\\frac{a^{4} r^{2} r_s^{2} \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{\\\\theta}^{4}-\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{4} r r_s \\\\left(\\\\cos{\\\\theta}^{2}-1\\\\right)^{2}+a^{2} r^{2} r_s^{2} \\\\cos{\\\\theta}^{2}-a^{2} r^{2} r_s^{2}-2a^{2} r r_s \\\\Sigma \\\\cos{\\\\theta}^{2}+a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right)^{2}}{\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{3} \\\\Sigma^{2} \\\\tan{\\\\theta}^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}^{\\\\phi}{}_{t}{}_{r}= & a r_s \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\frac{r r_s \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)-\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right)}{2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2} \\\\tan{\\\\theta}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}^{\\\\phi}{}_{t}{}_{\\\\theta}= & a r r_s \\\\left(-a^{2} r r_s \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{\\\\theta} \\\\sin{2\\\\theta}+2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right) \\\\cos{\\\\theta}\\\\right) \\\\frac{a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma}{2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2} \\\\sin{\\\\theta} \\\\tan{\\\\theta}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}^{\\\\phi}{}_{r}{}_{\\\\phi}= & \\\\frac{-a^{2} r r_s^{2} \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right) \\\\left(2a^{2} r^{3} r_s-2a^{2} r^{2} \\\\Sigma-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}+2r^{5} r_s-2r^{4} \\\\Sigma+r^{3} r_s \\\\Sigma-r^{2} \\\\Sigma^{2}\\\\right) \\\\sin{\\\\theta}^{3}+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right) \\\\sin{\\\\theta}}{2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2} \\\\sin{\\\\theta} \\\\tan{\\\\theta}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}^{\\\\phi}{}_{\\\\theta}{}_{\\\\phi}= & \\\\frac{a^{4} r^{2} r_s^{2} \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{\\\\theta}^{4}-\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{4} r r_s \\\\left(\\\\cos{\\\\theta}^{2}-1\\\\right)^{2}+a^{2} r^{2} r_s^{2} \\\\cos{\\\\theta}^{2}-a^{2} r^{2} r_s^{2}-2a^{2} r r_s \\\\Sigma \\\\cos{\\\\theta}^{2}+a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right)^{2}}{\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{3} \\\\Sigma^{2} \\\\tan{\\\\theta}^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}^{\\\\phi}{}_{r}{}_{t}= & a r_s \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\frac{r r_s \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)-\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right)}{2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2} \\\\tan{\\\\theta}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}^{\\\\phi}{}_{\\\\theta}{}_{t}= & a r r_s \\\\left(-a^{2} r r_s \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{\\\\theta} \\\\sin{2\\\\theta}+2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right) \\\\cos{\\\\theta}\\\\right) \\\\frac{a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma}{2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2} \\\\sin{\\\\theta} \\\\tan{\\\\theta}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}^{\\\\theta}{}_{\\\\theta}{}_{r}= & \\\\frac{a^{4} \\\\left( - \\\\frac{1}{8}\\\\cos{4\\\\theta}+\\\\frac{1}{8}\\\\right)-r^{2} \\\\Delta}{\\\\Delta \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}^{\\\\theta}{}_{\\\\theta}{}_{\\\\theta}= & a^{2} r \\\\frac{\\\\sin{2\\\\theta}}{\\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}^{\\\\theta}{}_{r}{}_{\\\\theta}= & \\\\frac{a^{4} \\\\left( - \\\\frac{1}{8}\\\\cos{4\\\\theta}+\\\\frac{1}{8}\\\\right)-r^{2} \\\\Delta}{\\\\Delta \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}^{\\\\theta}{}_{\\\\phi}{}_{\\\\phi}= & \\\\left(a^{4} r_s \\\\sin{\\\\theta}^{4}+4a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}+2a^{2} r \\\\Sigma \\\\sin{\\\\theta}^{2}+2a^{2} r \\\\Sigma+2r^{3} \\\\Sigma\\\\right) \\\\sin{\\\\theta} \\\\frac{\\\\cos{\\\\theta}}{2\\\\Sigma^{3}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}^{\\\\theta}{}_{r}{}_{r}= & -a^{2} \\\\left(4r \\\\Delta-\\\\left(2r-r_s\\\\right) \\\\Sigma\\\\right) \\\\frac{\\\\sin{2\\\\theta}}{4\\\\Delta^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}^{\\\\theta}{}_{t}{}_{\\\\phi}= & -a r_s \\\\left(a^{2} \\\\sin{\\\\theta}^{2}+2r^{2}\\\\right) \\\\sin{\\\\theta} \\\\frac{\\\\cos{\\\\theta}}{2\\\\Sigma^{3}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}^{\\\\theta}{}_{\\\\phi}{}_{t}= & -a r_s \\\\left(a^{2} \\\\sin{\\\\theta}^{2}+2r^{2}\\\\right) \\\\sin{\\\\theta} \\\\frac{\\\\cos{\\\\theta}}{2\\\\Sigma^{3}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}^{\\\\theta}{}_{t}{}_{t}= & a^{2} r_s \\\\frac{\\\\sin{2\\\\theta}}{4\\\\Sigma^{3}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}^{\\\\theta}{}_{\\\\theta}{}_{r}= & a^{2} r \\\\frac{\\\\sin{2\\\\theta}}{\\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}^{\\\\theta}{}_{\\\\theta}{}_{\\\\theta}= & \\\\frac{-a^{4} \\\\left( - \\\\frac{1}{8}\\\\cos{4\\\\theta}+\\\\frac{1}{8}\\\\right)+r^{2} \\\\Delta}{\\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}^{\\\\theta}{}_{r}{}_{\\\\theta}= & a^{2} r \\\\frac{\\\\sin{2\\\\theta}}{\\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}^{\\\\theta}{}_{\\\\phi}{}_{\\\\phi}= & \\\\left(-2a^{2} \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+\\\\left(a^{2}+r^{2}\\\\right) \\\\Sigma^{2}\\\\right) \\\\cos{\\\\theta}^{2}+r \\\\left(-2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}+a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r \\\\Sigma^{2}\\\\right) \\\\Delta\\\\right) \\\\frac{\\\\sin{\\\\theta}^{2}}{2\\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}^{\\\\theta}{}_{r}{}_{r}= & \\\\frac{a^{4} \\\\left( - \\\\frac{1}{4}\\\\cos{4\\\\theta}+\\\\frac{1}{4}\\\\right)-r \\\\left(2r \\\\Delta+\\\\left(-2r+r_s\\\\right) \\\\Sigma\\\\right)}{2\\\\Delta \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}^{\\\\theta}{}_{t}{}_{\\\\phi}= & a r r_s \\\\left(-2a^{4} \\\\sin{\\\\theta}^{4}+2a^{4} \\\\sin{\\\\theta}^{2}-2a^{2} \\\\Sigma \\\\sin{\\\\theta}^{2}+2a^{2} \\\\Sigma+2r^{2} \\\\Delta-\\\\Delta \\\\Sigma\\\\right) \\\\frac{\\\\sin{\\\\theta}^{2}}{2\\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}^{\\\\theta}{}_{\\\\phi}{}_{t}= & a r r_s \\\\left(-2a^{4} \\\\sin{\\\\theta}^{4}+2a^{4} \\\\sin{\\\\theta}^{2}-2a^{2} \\\\Sigma \\\\sin{\\\\theta}^{2}+2a^{2} \\\\Sigma+2r^{2} \\\\Delta-\\\\Delta \\\\Sigma\\\\right) \\\\frac{\\\\sin{\\\\theta}^{2}}{2\\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}^{\\\\theta}{}_{t}{}_{t}= & -r r_s \\\\frac{-a^{4} \\\\left(\\\\frac{1}{4}\\\\cos{4\\\\theta} - \\\\frac{1}{4}\\\\right)+\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\Delta}{2\\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}^{r}{}_{r}{}_{r}= & \\\\frac{\\\\frac{1}{2}a^{4} \\\\left(-\\\\cos{4\\\\theta}+1\\\\right) \\\\Delta-\\\\left(2r \\\\Delta+\\\\left(-2r+r_s\\\\right) \\\\Sigma\\\\right)^{2}}{4\\\\Delta^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}^{r}{}_{r}{}_{\\\\theta}= & a^{2} \\\\left(4r \\\\Delta+\\\\left(-2r+r_s\\\\right) \\\\Sigma\\\\right) \\\\frac{\\\\sin{2\\\\theta}}{4\\\\Delta \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}^{r}{}_{\\\\theta}{}_{r}= & a^{2} \\\\left(4r \\\\Delta+\\\\left(-2r+r_s\\\\right) \\\\Sigma\\\\right) \\\\frac{\\\\sin{2\\\\theta}}{4\\\\Delta \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}^{r}{}_{\\\\phi}{}_{\\\\phi}= & \\\\left(-4a^{2} \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+\\\\left(a^{2}+r^{2}\\\\right) \\\\Sigma^{2}\\\\right) \\\\cos{\\\\theta}^{2}+\\\\left(2r \\\\Delta+\\\\left(-2r+r_s\\\\right) \\\\Sigma\\\\right) \\\\left(-2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}+a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r \\\\Sigma^{2}\\\\right)\\\\right) \\\\frac{\\\\sin{\\\\theta}^{2}}{4\\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}^{r}{}_{\\\\theta}{}_{\\\\theta}= & \\\\frac{-a^{4} \\\\left( - \\\\frac{1}{4}\\\\cos{4\\\\theta}+\\\\frac{1}{4}\\\\right)+r \\\\left(2r \\\\Delta+\\\\left(-2r+r_s\\\\right) \\\\Sigma\\\\right)}{2\\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}^{r}{}_{t}{}_{\\\\phi}= & a r_s \\\\left(-4a^{4} r \\\\sin{\\\\theta}^{4}+4a^{4} r \\\\sin{\\\\theta}^{2}-4a^{2} r \\\\Sigma \\\\sin{\\\\theta}^{2}+4a^{2} r \\\\Sigma+4r^{3} \\\\Delta-4r^{3} \\\\Sigma+2r^{2} r_s \\\\Sigma-2r \\\\Delta \\\\Sigma+2r \\\\Sigma^{2}-r_s \\\\Sigma^{2}\\\\right) \\\\frac{\\\\sin{\\\\theta}^{2}}{4\\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}^{r}{}_{\\\\phi}{}_{t}= & a r_s \\\\left(-4a^{4} r \\\\sin{\\\\theta}^{4}+4a^{4} r \\\\sin{\\\\theta}^{2}-4a^{2} r \\\\Sigma \\\\sin{\\\\theta}^{2}+4a^{2} r \\\\Sigma+4r^{3} \\\\Delta-4r^{3} \\\\Sigma+2r^{2} r_s \\\\Sigma-2r \\\\Delta \\\\Sigma+2r \\\\Sigma^{2}-r_s \\\\Sigma^{2}\\\\right) \\\\frac{\\\\sin{\\\\theta}^{2}}{4\\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}^{r}{}_{t}{}_{t}= & -r_s \\\\frac{-a^{4} r \\\\left(\\\\frac{1}{2}\\\\cos{4\\\\theta} - \\\\frac{1}{2}\\\\right)+\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(2r \\\\Delta-\\\\left(2r-r_s\\\\right) \\\\Sigma\\\\right)}{4\\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}^{r}{}_{r}{}_{r}= & a^{2} \\\\left(4r \\\\Delta+\\\\left(-2r+r_s\\\\right) \\\\Sigma\\\\right) \\\\frac{\\\\sin{2\\\\theta}}{4\\\\Delta \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}^{r}{}_{r}{}_{\\\\theta}= & \\\\frac{-a^{4} \\\\left( - \\\\frac{1}{8}\\\\cos{4\\\\theta}+\\\\frac{1}{8}\\\\right)+r^{2} \\\\Delta}{\\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}^{r}{}_{\\\\theta}{}_{r}= & \\\\frac{-a^{4} \\\\left( - \\\\frac{1}{8}\\\\cos{4\\\\theta}+\\\\frac{1}{8}\\\\right)+r^{2} \\\\Delta}{\\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}^{r}{}_{\\\\phi}{}_{\\\\phi}= & -\\\\left(a^{4} r_s \\\\sin{\\\\theta}^{4}+4a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}+2a^{2} r \\\\Sigma \\\\sin{\\\\theta}^{2}+2a^{2} r \\\\Sigma+2r^{3} \\\\Sigma\\\\right) \\\\Delta \\\\sin{\\\\theta} \\\\frac{\\\\cos{\\\\theta}}{2\\\\Sigma^{3}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}^{r}{}_{\\\\theta}{}_{\\\\theta}= & -a^{2} r \\\\Delta \\\\frac{\\\\sin{2\\\\theta}}{\\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}^{r}{}_{t}{}_{\\\\phi}= & a r_s \\\\left(a^{2} \\\\sin{\\\\theta}^{2}+2r^{2}\\\\right) \\\\Delta \\\\sin{\\\\theta} \\\\frac{\\\\cos{\\\\theta}}{2\\\\Sigma^{3}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}^{r}{}_{\\\\phi}{}_{t}= & a r_s \\\\left(a^{2} \\\\sin{\\\\theta}^{2}+2r^{2}\\\\right) \\\\Delta \\\\sin{\\\\theta} \\\\frac{\\\\cos{\\\\theta}}{2\\\\Sigma^{3}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}^{r}{}_{t}{}_{t}= & -a^{2} r_s \\\\Delta \\\\frac{\\\\sin{2\\\\theta}}{4\\\\Sigma^{3}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}^{t}{}_{r}{}_{r}= & a r_s \\\\left(4a^{4} r \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{2}+\\\\left(2r \\\\Delta+\\\\left(-2r+r_s\\\\right) \\\\Sigma\\\\right) \\\\left(-a^{2} r r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\Sigma-r^{3} r_s+r^{2} \\\\Sigma\\\\right) \\\\left(2a^{2} r^{3} r_s-2a^{2} r^{2} \\\\Sigma-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}+2r^{5} r_s-2r^{4} \\\\Sigma+r^{3} r_s \\\\Sigma-r^{2} \\\\Sigma^{2}\\\\right)\\\\right) \\\\frac{\\\\sin{\\\\theta}^{2}}{4\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(-a^{2} r r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\Sigma-r^{3} r_s+r^{2} \\\\Sigma\\\\right)^{2} \\\\Delta \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}^{t}{}_{r}{}_{\\\\theta}= & a^{3} r_s \\\\left(4a^{2} r^{3} r_s-4a^{2} r^{2} \\\\Sigma-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}+4r^{5} r_s-2r^{4} r_s^{2}-4r^{4} \\\\Sigma+3r^{3} r_s \\\\Sigma-r^{2} \\\\Sigma^{2}\\\\right) \\\\sin{\\\\theta}^{3} \\\\frac{\\\\cos{\\\\theta}}{2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}^{t}{}_{\\\\theta}{}_{r}= & a^{3} r_s \\\\left(4a^{2} r^{3} r_s-4a^{2} r^{2} \\\\Sigma-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}+4r^{5} r_s-2r^{4} r_s^{2}-4r^{4} \\\\Sigma+3r^{3} r_s \\\\Sigma-r^{2} \\\\Sigma^{2}\\\\right) \\\\sin{\\\\theta}^{3} \\\\frac{\\\\cos{\\\\theta}}{2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}^{t}{}_{\\\\phi}{}_{\\\\phi}= & -a r_s \\\\left(4a^{2} r \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+\\\\left(a^{2}+r^{2}\\\\right) \\\\Sigma^{2}\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\cos{\\\\theta}^{2}-\\\\left(-2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}+a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r \\\\Sigma^{2}\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(2a^{2} r^{3} r_s-2a^{2} r^{2} \\\\Sigma-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}+2r^{5} r_s-2r^{4} \\\\Sigma+r^{3} r_s \\\\Sigma-r^{2} \\\\Sigma^{2}\\\\right) \\\\Delta\\\\right) \\\\frac{\\\\sin{\\\\theta}^{4}}{4\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}^{t}{}_{\\\\theta}{}_{\\\\theta}= & -a r r_s \\\\left(2a^{4} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{2}-\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(2a^{2} r^{3} r_s-2a^{2} r^{2} \\\\Sigma-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}+2r^{5} r_s-2r^{4} \\\\Sigma+r^{3} r_s \\\\Sigma-r^{2} \\\\Sigma^{2}\\\\right) \\\\Delta\\\\right) \\\\frac{\\\\sin{\\\\theta}^{2}}{2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}^{t}{}_{t}{}_{\\\\phi}= & a^{2} r_s^{2} \\\\left(a^{2} r^{2} \\\\left(a^{2} \\\\sin{\\\\theta}^{2}+\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\cos{\\\\theta}^{2} - \\\\frac{1}{4}\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(-a^{2} r r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\Sigma-r^{3} r_s+r^{2} \\\\Sigma\\\\right) \\\\left(2a^{2} r^{3} r_s-2a^{2} r^{2} \\\\Sigma-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}+2r^{5} r_s-2r^{4} \\\\Sigma+r^{3} r_s \\\\Sigma-r^{2} \\\\Sigma^{2}\\\\right) \\\\Delta\\\\right) \\\\frac{\\\\sin{\\\\theta}^{4}}{\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(-a^{2} r r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\Sigma-r^{3} r_s+r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}^{t}{}_{\\\\phi}{}_{t}= & a^{2} r_s^{2} \\\\left(a^{2} r^{2} \\\\left(a^{2} \\\\sin{\\\\theta}^{2}+\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\cos{\\\\theta}^{2} - \\\\frac{1}{4}\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(-a^{2} r r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\Sigma-r^{3} r_s+r^{2} \\\\Sigma\\\\right) \\\\left(2a^{2} r^{3} r_s-2a^{2} r^{2} \\\\Sigma-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}+2r^{5} r_s-2r^{4} \\\\Sigma+r^{3} r_s \\\\Sigma-r^{2} \\\\Sigma^{2}\\\\right) \\\\Delta\\\\right) \\\\frac{\\\\sin{\\\\theta}^{4}}{\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(-a^{2} r r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\Sigma-r^{3} r_s+r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}^{t}{}_{t}{}_{t}= & -a r_s^{2} \\\\left(4a^{4} r^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{2}+\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(2a^{2} r^{3} r_s-2a^{2} r^{2} \\\\Sigma-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}+2r^{5} r_s-2r^{4} \\\\Sigma+r^{3} r_s \\\\Sigma-r^{2} \\\\Sigma^{2}\\\\right) \\\\Delta\\\\right) \\\\frac{\\\\sin{\\\\theta}^{2}}{4\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}^{\\\\phi}{}_{r}{}_{r}= & \\\\frac{a^{2} \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right) \\\\cos{\\\\theta}^{2}-\\\\left(2r \\\\Delta+\\\\left(-2r+r_s\\\\right) \\\\Sigma\\\\right) \\\\left(\\\\frac{1}{2}a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2} - \\\\frac{1}{4}a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+\\\\frac{1}{2}r^{2} r_s \\\\Sigma - \\\\frac{1}{2}r \\\\Sigma^{2}\\\\right)}{\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Delta \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}^{\\\\phi}{}_{r}{}_{\\\\theta}= & \\\\frac{4a^{4} r^{2} r_s \\\\sin{\\\\theta}^{4}-a^{4} r_s \\\\Sigma \\\\sin{\\\\theta}^{4}-2a^{2} r^{3} r_s^{2} \\\\sin{\\\\theta}^{2}+6a^{2} r^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-2a^{2} r^{2} r_s \\\\Sigma-2a^{2} r \\\\Sigma^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r \\\\Sigma^{2}-2r^{4} r_s \\\\Sigma+2r^{3} \\\\Sigma^{2}}{2\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{2} \\\\tan{\\\\theta}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}^{\\\\phi}{}_{\\\\theta}{}_{r}= & \\\\frac{4a^{4} r^{2} r_s \\\\sin{\\\\theta}^{4}-a^{4} r_s \\\\Sigma \\\\sin{\\\\theta}^{4}-2a^{2} r^{3} r_s^{2} \\\\sin{\\\\theta}^{2}+6a^{2} r^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-2a^{2} r^{2} r_s \\\\Sigma-2a^{2} r \\\\Sigma^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r \\\\Sigma^{2}-2r^{4} r_s \\\\Sigma+2r^{3} \\\\Sigma^{2}}{2\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{2} \\\\tan{\\\\theta}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}^{\\\\phi}{}_{\\\\phi}{}_{\\\\phi}= & \\\\frac{\\\\frac{1}{4}\\\\left(-2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}+a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r \\\\Sigma^{2}\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right) \\\\Delta \\\\sin{\\\\theta}^{2}-\\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+\\\\left(a^{2}+r^{2}\\\\right) \\\\Sigma^{2}\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right) \\\\cos{\\\\theta}^{2}}{\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}^{\\\\phi}{}_{\\\\theta}{}_{\\\\theta}= & \\\\frac{-a^{2} \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right) \\\\cos{\\\\theta}^{2}+\\\\frac{1}{2}r \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right) \\\\Delta}{\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}^{\\\\phi}{}_{t}{}_{\\\\phi}= & a r_s \\\\frac{4r \\\\left(a^{2} \\\\sin{\\\\theta}^{2}+\\\\Sigma\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right) \\\\cos{\\\\theta}^{2}+\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right) \\\\Delta \\\\sin{\\\\theta}^{2}}{4\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}^{\\\\phi}{}_{\\\\phi}{}_{t}= & a r_s \\\\frac{4r \\\\left(a^{2} \\\\sin{\\\\theta}^{2}+\\\\Sigma\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right) \\\\cos{\\\\theta}^{2}+\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right) \\\\Delta \\\\sin{\\\\theta}^{2}}{4\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}^{\\\\phi}{}_{t}{}_{t}= & -r_s \\\\frac{4a^{2} r \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right) \\\\cos{\\\\theta}^{2}+\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right) \\\\Delta}{4\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}^{t}{}_{r}{}_{r}= & r_s \\\\frac{-a^{4} r \\\\left(-\\\\cos{4\\\\theta}+1\\\\right) \\\\left(\\\\frac{1}{2}a^{2} r r_s - \\\\frac{1}{2}a^{2} \\\\Sigma+\\\\frac{1}{2}r^{3} r_s - \\\\frac{1}{2}r^{2} r_s^{2} - \\\\frac{1}{2}r^{2} \\\\Sigma+\\\\frac{1}{2}r r_s \\\\Sigma\\\\right)+\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(2r \\\\Delta+\\\\left(-2r+r_s\\\\right) \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)}{4\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Delta \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}^{t}{}_{r}{}_{\\\\theta}= & a^{2} r_s \\\\left(-2a^{2} r^{2}+\\\\frac{1}{2}a^{2} \\\\Sigma-2r^{4}+r^{3} r_s+\\\\frac{1}{2}r^{2} \\\\Sigma\\\\right) \\\\frac{\\\\sin{2\\\\theta}}{2\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}^{t}{}_{\\\\theta}{}_{r}= & a^{2} r_s \\\\left(-2a^{2} r^{2}+\\\\frac{1}{2}a^{2} \\\\Sigma-2r^{4}+r^{3} r_s+\\\\frac{1}{2}r^{2} \\\\Sigma\\\\right) \\\\frac{\\\\sin{2\\\\theta}}{2\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}^{t}{}_{\\\\phi}{}_{\\\\phi}= & r_s \\\\left(2a^{2} r \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+\\\\left(a^{2}+r^{2}\\\\right) \\\\Sigma^{2}\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{2\\\\theta} \\\\cos{\\\\theta}-\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(-2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{3}+a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{3}+2r \\\\Sigma^{2} \\\\sin{\\\\theta}\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Delta\\\\right) \\\\frac{\\\\sin{\\\\theta}}{4\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}^{t}{}_{\\\\theta}{}_{\\\\theta}= & r r_s \\\\frac{-a^{6} \\\\left(\\\\frac{1}{4}\\\\cos{4\\\\theta} - \\\\frac{1}{4}\\\\right)-a^{4} r^{2} \\\\left(\\\\frac{1}{4}\\\\cos{4\\\\theta} - \\\\frac{1}{4}\\\\right)+a^{4} r r_s \\\\left(\\\\frac{1}{4}\\\\cos{4\\\\theta} - \\\\frac{1}{4}\\\\right)-2a^{2} r^{2} \\\\Delta+a^{2} \\\\Delta \\\\Sigma-2r^{4} \\\\Delta+r^{2} \\\\Delta \\\\Sigma}{2\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}^{t}{}_{t}{}_{\\\\phi}= & -a r_s^{2} \\\\left(4a^{2} r^{2} \\\\left(a^{2} \\\\sin{\\\\theta}^{2}+\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\cos{\\\\theta}^{2}+\\\\left(2r^{2}-\\\\Sigma\\\\right)^{2} \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Delta\\\\right) \\\\frac{\\\\sin{\\\\theta}^{2}}{4\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}^{t}{}_{\\\\phi}{}_{t}= & -a r_s^{2} \\\\left(4a^{2} r^{2} \\\\left(a^{2} \\\\sin{\\\\theta}^{2}+\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\cos{\\\\theta}^{2}+\\\\left(2r^{2}-\\\\Sigma\\\\right)^{2} \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Delta\\\\right) \\\\frac{\\\\sin{\\\\theta}^{2}}{4\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}^{t}{}_{t}{}_{t}= & r_s^{2} \\\\frac{a^{6} r^{2} \\\\left( - \\\\frac{1}{2}\\\\cos{4\\\\theta}+\\\\frac{1}{2}\\\\right)+a^{4} r^{4} \\\\left( - \\\\frac{1}{2}\\\\cos{4\\\\theta}+\\\\frac{1}{2}\\\\right)-a^{4} r^{3} r_s \\\\left( - \\\\frac{1}{2}\\\\cos{4\\\\theta}+\\\\frac{1}{2}\\\\right)+4a^{2} r^{4} \\\\Delta-4a^{2} r^{2} \\\\Delta \\\\Sigma+a^{2} \\\\Delta \\\\Sigma^{2}+4r^{6} \\\\Delta-4r^{4} \\\\Delta \\\\Sigma+r^{2} \\\\Delta \\\\Sigma^{2}}{4\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}^{\\\\phi}{}_{r}{}_{r}= & a r_s \\\\frac{-4a^{2} r \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right) \\\\sin{\\\\theta} \\\\cos{\\\\theta}+\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(2r \\\\Delta+\\\\left(-2r+r_s\\\\right) \\\\Sigma\\\\right) \\\\tan{\\\\theta}}{4\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Delta \\\\Sigma^{2} \\\\tan{\\\\theta}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}^{\\\\phi}{}_{r}{}_{\\\\theta}= & -a r_s \\\\frac{a^{2} \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\sin{\\\\theta}^{2}+2r^{2} \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right)}{2\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{2} \\\\tan{\\\\theta}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}^{\\\\phi}{}_{\\\\theta}{}_{r}= & -a r_s \\\\frac{a^{2} \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\sin{\\\\theta}^{2}+2r^{2} \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right)}{2\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{2} \\\\tan{\\\\theta}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}^{\\\\phi}{}_{\\\\phi}{}_{\\\\phi}= & a r_s \\\\left(4r \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+\\\\left(a^{2}+r^{2}\\\\right) \\\\Sigma^{2}\\\\right) \\\\cos{\\\\theta}-\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(-2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}+a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r \\\\Sigma^{2}\\\\right) \\\\Delta \\\\frac{\\\\sin{\\\\theta}^{2}}{\\\\cos{\\\\theta}}\\\\right) \\\\frac{\\\\cos{\\\\theta}}{4\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}^{\\\\phi}{}_{\\\\theta}{}_{\\\\theta}= & a r r_s \\\\frac{2a^{2} \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right) \\\\sin{\\\\theta} \\\\cos{\\\\theta}-\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\Delta \\\\tan{\\\\theta}}{2\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{2} \\\\tan{\\\\theta}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}^{\\\\phi}{}_{t}{}_{\\\\phi}= & -a^{2} r_s^{2} \\\\left(r^{2} \\\\left(a^{2} \\\\sin{\\\\theta}^{2}+\\\\Sigma\\\\right) \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right) \\\\cos{\\\\theta}+\\\\left(2r^{2}-\\\\Sigma\\\\right)^{2} \\\\Delta \\\\frac{\\\\sin{\\\\theta}^{2}}{4\\\\cos{\\\\theta}}\\\\right) \\\\frac{\\\\cos{\\\\theta}}{\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}^{\\\\phi}{}_{\\\\phi}{}_{t}= & -a^{2} r_s^{2} \\\\left(r^{2} \\\\left(a^{2} \\\\sin{\\\\theta}^{2}+\\\\Sigma\\\\right) \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right) \\\\cos{\\\\theta}+\\\\left(2r^{2}-\\\\Sigma\\\\right)^{2} \\\\Delta \\\\frac{\\\\sin{\\\\theta}^{2}}{4\\\\cos{\\\\theta}}\\\\right) \\\\frac{\\\\cos{\\\\theta}}{\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}^{\\\\phi}{}_{t}{}_{t}= & a r_s^{2} \\\\frac{4a^{2} r^{2} \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right) \\\\sin{\\\\theta} \\\\cos{\\\\theta}+\\\\left(2r^{2}-\\\\Sigma\\\\right)^{2} \\\\Delta \\\\tan{\\\\theta}}{4\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4} \\\\tan{\\\\theta}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}^{r}{}_{\\\\phi}{}_{r}= & \\\\left(a^{2} r_s^{2} \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(2a^{2} r^{3} r_s-2a^{2} r^{2} \\\\Sigma-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}+2r^{5} r_s-2r^{4} \\\\Sigma+r^{3} r_s \\\\Sigma-r^{2} \\\\Sigma^{2}\\\\right) \\\\sin{\\\\theta}^{2}+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(-2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}+a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r \\\\Sigma^{2}\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right)\\\\right) \\\\Delta \\\\frac{\\\\sin{\\\\theta}^{2}}{4\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}^{r}{}_{\\\\phi}{}_{\\\\theta}= & -\\\\left(a^{4} r r_s^{2} \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{\\\\theta}^{4}+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(-2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}+a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r \\\\Sigma^{2}\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right)\\\\right) \\\\Delta \\\\sin{\\\\theta} \\\\frac{\\\\cos{\\\\theta}}{2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}^{r}{}_{t}{}_{r}= & a r_s \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(-r_s \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)+\\\\left(-r r_s+\\\\Sigma\\\\right) \\\\left(-2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}+a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r \\\\Sigma^{2}\\\\right)\\\\right) \\\\Delta \\\\frac{\\\\sin{\\\\theta}^{2}}{4\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}^{r}{}_{t}{}_{\\\\theta}= & a r r_s \\\\left(a^{2} r_s \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right) \\\\left(-2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}+a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r \\\\Sigma^{2}\\\\right)\\\\right) \\\\Delta \\\\frac{\\\\sin{\\\\theta}^{2}}{4\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4} \\\\tan{\\\\theta}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}^{r}{}_{r}{}_{\\\\phi}= & \\\\left(a^{2} r_s^{2} \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(2a^{2} r^{3} r_s-2a^{2} r^{2} \\\\Sigma-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}+2r^{5} r_s-2r^{4} \\\\Sigma+r^{3} r_s \\\\Sigma-r^{2} \\\\Sigma^{2}\\\\right) \\\\sin{\\\\theta}^{2}+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(-2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}+a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r \\\\Sigma^{2}\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right)\\\\right) \\\\Delta \\\\frac{\\\\sin{\\\\theta}^{2}}{4\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}^{r}{}_{\\\\theta}{}_{\\\\phi}= & -\\\\left(a^{4} r r_s^{2} \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{\\\\theta}^{4}+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(-2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}+a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r \\\\Sigma^{2}\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right)\\\\right) \\\\Delta \\\\sin{\\\\theta} \\\\frac{\\\\cos{\\\\theta}}{2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}^{r}{}_{r}{}_{t}= & a r_s \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(-r_s \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)+\\\\left(-r r_s+\\\\Sigma\\\\right) \\\\left(-2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}+a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r \\\\Sigma^{2}\\\\right)\\\\right) \\\\Delta \\\\frac{\\\\sin{\\\\theta}^{2}}{4\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}^{r}{}_{\\\\theta}{}_{t}= & a r r_s \\\\left(a^{2} r_s \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right) \\\\left(-2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}+a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r \\\\Sigma^{2}\\\\right)\\\\right) \\\\Delta \\\\frac{\\\\sin{\\\\theta}^{2}}{4\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4} \\\\tan{\\\\theta}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}^{\\\\theta}{}_{\\\\phi}{}_{r}= & \\\\left(-a^{2} r r_s^{2} \\\\left(a^{2} \\\\sin{\\\\theta}^{2}+\\\\Sigma\\\\right) \\\\left(2a^{2} r^{3} r_s-2a^{2} r^{2} \\\\Sigma-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}+2r^{5} r_s-2r^{4} \\\\Sigma+r^{3} r_s \\\\Sigma-r^{2} \\\\Sigma^{2}\\\\right) \\\\sin{\\\\theta}^{2}+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+\\\\left(a^{2}+r^{2}\\\\right) \\\\Sigma^{2}\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right)\\\\right) \\\\sin{\\\\theta} \\\\frac{\\\\cos{\\\\theta}}{2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}^{\\\\theta}{}_{\\\\phi}{}_{\\\\theta}= & \\\\left(a^{4} r^{2} r_s^{2} \\\\left(a^{2} \\\\sin{\\\\theta}^{2}+\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{\\\\theta}^{4}+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+\\\\left(a^{2}+r^{2}\\\\right) \\\\Sigma^{2}\\\\right) \\\\left(-a^{2} r r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\Sigma-r^{3} r_s+r^{2} \\\\Sigma\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right)\\\\right) \\\\frac{\\\\cos{\\\\theta}^{2}}{\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(-a^{2} r r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\Sigma-r^{3} r_s+r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}^{\\\\theta}{}_{t}{}_{r}= & a r_s \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(r r_s \\\\left(a^{2} \\\\sin{\\\\theta}^{2}+\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)+\\\\left(-r r_s+\\\\Sigma\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+\\\\left(a^{2}+r^{2}\\\\right) \\\\Sigma^{2}\\\\right)\\\\right) \\\\sin{\\\\theta} \\\\frac{\\\\cos{\\\\theta}}{2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}^{\\\\theta}{}_{t}{}_{\\\\theta}= & a r r_s \\\\left(-a^{2} r r_s \\\\left(a^{2} \\\\sin{\\\\theta}^{2}+\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{\\\\theta}^{2}+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+\\\\left(a^{2}+r^{2}\\\\right) \\\\Sigma^{2}\\\\right)\\\\right) \\\\frac{\\\\cos{\\\\theta}^{2}}{\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}^{\\\\theta}{}_{r}{}_{\\\\phi}= & \\\\left(-a^{2} r r_s^{2} \\\\left(a^{2} \\\\sin{\\\\theta}^{2}+\\\\Sigma\\\\right) \\\\left(2a^{2} r^{3} r_s-2a^{2} r^{2} \\\\Sigma-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}+2r^{5} r_s-2r^{4} \\\\Sigma+r^{3} r_s \\\\Sigma-r^{2} \\\\Sigma^{2}\\\\right) \\\\sin{\\\\theta}^{2}+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+\\\\left(a^{2}+r^{2}\\\\right) \\\\Sigma^{2}\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right)\\\\right) \\\\sin{\\\\theta} \\\\frac{\\\\cos{\\\\theta}}{2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}^{\\\\theta}{}_{\\\\theta}{}_{\\\\phi}= & \\\\left(a^{4} r^{2} r_s^{2} \\\\left(a^{2} \\\\sin{\\\\theta}^{2}+\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{\\\\theta}^{4}+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+\\\\left(a^{2}+r^{2}\\\\right) \\\\Sigma^{2}\\\\right) \\\\left(-a^{2} r r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\Sigma-r^{3} r_s+r^{2} \\\\Sigma\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right)\\\\right) \\\\frac{\\\\cos{\\\\theta}^{2}}{\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(-a^{2} r r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\Sigma-r^{3} r_s+r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}^{\\\\theta}{}_{r}{}_{t}= & a r_s \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(r r_s \\\\left(a^{2} \\\\sin{\\\\theta}^{2}+\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)+\\\\left(-r r_s+\\\\Sigma\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+\\\\left(a^{2}+r^{2}\\\\right) \\\\Sigma^{2}\\\\right)\\\\right) \\\\sin{\\\\theta} \\\\frac{\\\\cos{\\\\theta}}{2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}^{\\\\theta}{}_{\\\\theta}{}_{t}= & a r r_s \\\\left(-a^{2} r r_s \\\\left(a^{2} \\\\sin{\\\\theta}^{2}+\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{\\\\theta}^{2}+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+\\\\left(a^{2}+r^{2}\\\\right) \\\\Sigma^{2}\\\\right)\\\\right) \\\\frac{\\\\cos{\\\\theta}^{2}}{\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}^{r}{}_{\\\\phi}{}_{r}= & -a r_s \\\\left(4a^{2} r^{4} r_s \\\\cos{\\\\theta}^{2}-4a^{2} r^{2} r_s \\\\Sigma \\\\cos{\\\\theta}^{2}+a^{2} r_s \\\\Sigma^{2} \\\\cos{\\\\theta}^{2}+4r^{6} r_s-4r^{4} r_s \\\\Sigma+4r^{3} \\\\Sigma^{2}+r^{2} r_s \\\\Sigma^{2}-2r \\\\Sigma^{3}\\\\right) \\\\Delta \\\\frac{\\\\sin{\\\\theta}^{2}}{4\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}^{r}{}_{\\\\phi}{}_{\\\\theta}= & a r_s \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{\\\\theta}^{2}+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(-a^{2} r r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\Sigma-r^{3} r_s+r^{2} \\\\Sigma\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right)\\\\right) \\\\Delta \\\\sin{\\\\theta} \\\\frac{\\\\cos{\\\\theta}}{2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(-a^{2} r r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\Sigma-r^{3} r_s+r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}^{r}{}_{t}{}_{r}= & r_s^{2} \\\\left(2r^{2}-\\\\Sigma\\\\right)^{2} \\\\left(a^{2} r r_s-a^{2} \\\\left(r r_s-\\\\Sigma\\\\right) \\\\sin{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\frac{\\\\Delta}{4\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}^{r}{}_{t}{}_{\\\\theta}= & a^{2} r r_s^{2} \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(-a^{2} r r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\Sigma \\\\cos{\\\\theta}^{2}-r^{3} r_s+r^{2} \\\\Sigma+r r_s \\\\Sigma-\\\\Sigma^{2}\\\\right) \\\\Delta \\\\sin{\\\\theta} \\\\frac{\\\\cos{\\\\theta}}{2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}^{r}{}_{r}{}_{\\\\phi}= & -a r_s \\\\left(4a^{2} r^{4} r_s \\\\cos{\\\\theta}^{2}-4a^{2} r^{2} r_s \\\\Sigma \\\\cos{\\\\theta}^{2}+a^{2} r_s \\\\Sigma^{2} \\\\cos{\\\\theta}^{2}+4r^{6} r_s-4r^{4} r_s \\\\Sigma+4r^{3} \\\\Sigma^{2}+r^{2} r_s \\\\Sigma^{2}-2r \\\\Sigma^{3}\\\\right) \\\\Delta \\\\frac{\\\\sin{\\\\theta}^{2}}{4\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}^{r}{}_{\\\\theta}{}_{\\\\phi}= & a r_s \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{\\\\theta}^{2}+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(-a^{2} r r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\Sigma-r^{3} r_s+r^{2} \\\\Sigma\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right)\\\\right) \\\\Delta \\\\sin{\\\\theta} \\\\frac{\\\\cos{\\\\theta}}{2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(-a^{2} r r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\Sigma-r^{3} r_s+r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}^{r}{}_{r}{}_{t}= & r_s^{2} \\\\left(2r^{2}-\\\\Sigma\\\\right)^{2} \\\\left(a^{2} r r_s-a^{2} \\\\left(r r_s-\\\\Sigma\\\\right) \\\\sin{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\frac{\\\\Delta}{4\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}^{r}{}_{\\\\theta}{}_{t}= & a^{2} r r_s^{2} \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(-a^{2} r r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\Sigma \\\\cos{\\\\theta}^{2}-r^{3} r_s+r^{2} \\\\Sigma+r r_s \\\\Sigma-\\\\Sigma^{2}\\\\right) \\\\Delta \\\\sin{\\\\theta} \\\\frac{\\\\cos{\\\\theta}}{2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}^{\\\\theta}{}_{\\\\phi}{}_{r}= & a r r_s \\\\left(a^{2} r_s \\\\left(2a^{2} r^{3} r_s-2a^{2} r^{2} \\\\Sigma-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}+2r^{5} r_s-2r^{4} \\\\Sigma+r^{3} r_s \\\\Sigma-r^{2} \\\\Sigma^{2}\\\\right) \\\\sin{\\\\theta}^{2}+\\\\left(a^{2} \\\\sin{\\\\theta}^{2}+\\\\Sigma\\\\right) \\\\left(-r r_s+\\\\Sigma\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right)\\\\right) \\\\sin{\\\\theta} \\\\frac{\\\\cos{\\\\theta}}{2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}^{\\\\theta}{}_{\\\\phi}{}_{\\\\theta}= & -a r r_s \\\\left(a^{4} r r_s \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{\\\\theta}^{4}-\\\\left(a^{2} \\\\sin{\\\\theta}^{2}+\\\\Sigma\\\\right) \\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right)\\\\right) \\\\frac{\\\\cos{\\\\theta}^{2}}{\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}^{\\\\theta}{}_{t}{}_{r}= & a^{2} r r_s^{2} \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(-a^{2} r r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\Sigma \\\\cos{\\\\theta}^{2}-r^{3} r_s+r^{2} \\\\Sigma+r r_s \\\\Sigma-\\\\Sigma^{2}\\\\right) \\\\sin{\\\\theta} \\\\frac{\\\\cos{\\\\theta}}{2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}^{\\\\theta}{}_{t}{}_{\\\\theta}= & a^{2} r^{2} r_s^{2} \\\\left(a^{2} \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{\\\\theta}^{2}+\\\\left(a^{2} \\\\sin{\\\\theta}^{2}+\\\\Sigma\\\\right) \\\\left(-r r_s+\\\\Sigma\\\\right) \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right)\\\\right) \\\\frac{\\\\cos{\\\\theta}^{2}}{\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}^{\\\\theta}{}_{r}{}_{\\\\phi}= & a r r_s \\\\left(a^{2} r_s \\\\left(2a^{2} r^{3} r_s-2a^{2} r^{2} \\\\Sigma-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}+2r^{5} r_s-2r^{4} \\\\Sigma+r^{3} r_s \\\\Sigma-r^{2} \\\\Sigma^{2}\\\\right) \\\\sin{\\\\theta}^{2}+\\\\left(a^{2} \\\\sin{\\\\theta}^{2}+\\\\Sigma\\\\right) \\\\left(-r r_s+\\\\Sigma\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right)\\\\right) \\\\sin{\\\\theta} \\\\frac{\\\\cos{\\\\theta}}{2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}^{\\\\theta}{}_{\\\\theta}{}_{\\\\phi}= & -a r r_s \\\\left(a^{4} r r_s \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{\\\\theta}^{4}-\\\\left(a^{2} \\\\sin{\\\\theta}^{2}+\\\\Sigma\\\\right) \\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right)\\\\right) \\\\frac{\\\\cos{\\\\theta}^{2}}{\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}^{\\\\theta}{}_{r}{}_{t}= & a^{2} r r_s^{2} \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(-a^{2} r r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\Sigma \\\\cos{\\\\theta}^{2}-r^{3} r_s+r^{2} \\\\Sigma+r r_s \\\\Sigma-\\\\Sigma^{2}\\\\right) \\\\sin{\\\\theta} \\\\frac{\\\\cos{\\\\theta}}{2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}^{\\\\theta}{}_{\\\\theta}{}_{t}= & a^{2} r^{2} r_s^{2} \\\\left(a^{2} \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{\\\\theta}^{2}+\\\\left(a^{2} \\\\sin{\\\\theta}^{2}+\\\\Sigma\\\\right) \\\\left(-r r_s+\\\\Sigma\\\\right) \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right)\\\\right) \\\\frac{\\\\cos{\\\\theta}^{2}}{\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\end{aligned}\\\\right.\\n\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"substitute(tst4,ch)\\nevaluate(tst4, kerr);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}R^{\\\\rho}\\\\,_{\\\\sigma \\\\mu \\\\nu} = \\\\left\\\\{\\\\begin{aligned}\\\\square{}_{t}{}_{t}{}^{\\\\theta}{}_{r}= & a^{2} r_s \\\\frac{-2r r_s \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma \\\\cos{\\\\theta}^{2}+r^{3} r_s-r^{2} \\\\Sigma-r r_s \\\\Sigma+\\\\Sigma^{2}\\\\right) \\\\sin{\\\\theta} \\\\cos{\\\\theta}+3\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(2r \\\\partial_{r}{\\\\Sigma}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\sin{2\\\\theta}}{4\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}_{t}{}^{\\\\theta}{}_{\\\\theta}= & r r_s \\\\frac{8a^{2} r r_s \\\\left(a^{2} \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{\\\\theta}^{2}+\\\\left(a^{2} \\\\sin{\\\\theta}^{2}+\\\\Sigma\\\\right) \\\\left(-r r_s+\\\\Sigma\\\\right) \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right)\\\\right) \\\\cos{\\\\theta}^{2}+\\\\left(-r r_s+\\\\Sigma\\\\right) \\\\left(a^{4} \\\\left(\\\\cos{4\\\\theta}-1\\\\right)+a^{2} \\\\left(8\\\\Sigma \\\\cos{2\\\\theta}-12\\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right)-4\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\Delta\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)}{8\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}_{t}{}^{r}{}_{r}= & r_s \\\\frac{-2r_s \\\\left(2r^{2}-\\\\Sigma\\\\right)^{2} \\\\left(-a^{2} r r_s+a^{2} \\\\left(r r_s-\\\\Sigma\\\\right) \\\\sin{\\\\theta}^{2}+a^{2} \\\\Sigma-r^{3} r_s+r^{2} \\\\Sigma\\\\right) \\\\Delta+\\\\left(-r r_s+\\\\Sigma\\\\right) \\\\left(a^{4} r \\\\left(\\\\cos{4\\\\theta}-1\\\\right)-2\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(2r \\\\Delta-\\\\left(2r-r_s\\\\right) \\\\Sigma\\\\right)+12\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\Delta \\\\partial_{r}{\\\\Sigma}-4\\\\left(\\\\left(4r-\\\\partial_{r}{\\\\Sigma}\\\\right) \\\\Delta+\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\partial_{r}{\\\\Delta}\\\\right) \\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)}{8\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}_{t}{}^{r}{}_{\\\\theta}= & r_s \\\\left(-2a^{2} r r_s \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma \\\\cos{\\\\theta}^{2}+r^{3} r_s-r^{2} \\\\Sigma-r r_s \\\\Sigma+\\\\Sigma^{2}\\\\right) \\\\sin{\\\\theta} \\\\cos{\\\\theta}+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} \\\\Sigma \\\\sin{2\\\\theta}-4\\\\left(3r^{2}-\\\\Sigma\\\\right) \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)\\\\right) \\\\frac{\\\\Delta}{4\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{t}{}^{\\\\theta}{}_{r}= & a r_s \\\\left(r \\\\left(a^{2} r_s \\\\left(2a^{2} r^{3} r_s-2a^{2} r^{2} \\\\Sigma-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}+2r^{5} r_s-2r^{4} \\\\Sigma+r^{3} r_s \\\\Sigma-r^{2} \\\\Sigma^{2}\\\\right) \\\\sin{\\\\theta}^{2}+\\\\left(a^{2} \\\\sin{\\\\theta}^{2}+\\\\Sigma\\\\right) \\\\left(-r r_s+\\\\Sigma\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right)\\\\right)+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(-6a^{2} r \\\\sin{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}+3a^{2} \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} \\\\Sigma-4r \\\\Sigma \\\\partial_{r}{\\\\Sigma}+2\\\\Sigma^{2}\\\\right)\\\\right) \\\\sin{\\\\theta} \\\\frac{\\\\cos{\\\\theta}}{2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{t}{}^{\\\\theta}{}_{\\\\theta}= & a r r_s \\\\frac{\\\\left(-r r_s+\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(-8a^{4} \\\\sin{\\\\theta}^{6}+8a^{4} \\\\sin{\\\\theta}^{4}+24a^{2} \\\\Sigma \\\\sin{\\\\theta}^{4}+8a^{2} \\\\Sigma \\\\cos{2\\\\theta}-8a^{2} \\\\Sigma+6a^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}-3a^{2} \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}-4r^{2} \\\\Delta \\\\cos{2\\\\theta}+4r^{2} \\\\Delta+2\\\\Delta \\\\Sigma \\\\cos{2\\\\theta}-2\\\\Delta \\\\Sigma-8\\\\Sigma^{2} \\\\cos{2\\\\theta}+8\\\\Sigma \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right)-8\\\\left(a^{4} r r_s \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{\\\\theta}^{4}+\\\\left(a^{2} \\\\sin{\\\\theta}^{2}+\\\\Sigma\\\\right) \\\\left(-r r_s+\\\\Sigma\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right)\\\\right) \\\\cos{\\\\theta}^{2}}{8\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{t}{}^{r}{}_{r}= & a r_s \\\\left(\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(4a^{4} r \\\\sin{\\\\theta}^{4}-4a^{4} r \\\\sin{\\\\theta}^{2}+4a^{2} r \\\\Sigma \\\\sin{\\\\theta}^{2}-4a^{2} r \\\\Sigma-4r^{3} \\\\Delta+4r^{3} \\\\Sigma-2r^{2} r_s \\\\Sigma+2r \\\\Delta \\\\Sigma-2r \\\\Sigma^{2}+r_s \\\\Sigma^{2}+6\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\Delta \\\\partial_{r}{\\\\Sigma}-2\\\\left(\\\\left(4r-\\\\partial_{r}{\\\\Sigma}\\\\right) \\\\Delta+\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\partial_{r}{\\\\Delta}\\\\right) \\\\Sigma\\\\right)-\\\\left(4a^{2} r^{4} r_s \\\\cos{\\\\theta}^{2}-4a^{2} r^{2} r_s \\\\Sigma \\\\cos{\\\\theta}^{2}+a^{2} r_s \\\\Sigma^{2} \\\\cos{\\\\theta}^{2}+4r^{6} r_s-4r^{4} r_s \\\\Sigma+4r^{3} \\\\Sigma^{2}+r^{2} r_s \\\\Sigma^{2}-2r \\\\Sigma^{3}\\\\right) \\\\Delta\\\\right) \\\\frac{\\\\sin{\\\\theta}^{2}}{4\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{t}{}^{r}{}_{\\\\theta}= & a r_s \\\\left(\\\\left(16r^{2}-8\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{\\\\theta}^{2}+\\\\left(-r r_s+\\\\Sigma\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right)\\\\right) \\\\sin{\\\\theta} \\\\cos{\\\\theta}+\\\\left(-r r_s+\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(2a^{2} \\\\Sigma \\\\sin{2\\\\theta}-a^{2} \\\\Sigma \\\\sin{4\\\\theta}+24r^{2} \\\\Sigma \\\\sin{2\\\\theta}+24r^{2} \\\\cos{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}-24r^{2} \\\\partial_{\\\\theta}{\\\\Sigma}-8\\\\Sigma^{2} \\\\sin{2\\\\theta}-8\\\\Sigma \\\\cos{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}+8\\\\Sigma \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right)\\\\right) \\\\frac{\\\\Delta}{16\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}_{\\\\phi}{}^{\\\\theta}{}_{r}= & a r_s \\\\left(\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(r r_s \\\\left(a^{2} \\\\sin{\\\\theta}^{2}+\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)+\\\\left(-r r_s+\\\\Sigma\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+\\\\left(a^{2}+r^{2}\\\\right) \\\\Sigma^{2}\\\\right)\\\\right)+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(-6a^{2} r \\\\sin{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}+3a^{2} \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} \\\\Sigma-4r \\\\Sigma \\\\partial_{r}{\\\\Sigma}+2\\\\Sigma^{2}\\\\right)\\\\right) \\\\sin{\\\\theta} \\\\frac{\\\\cos{\\\\theta}}{2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}_{\\\\phi}{}^{\\\\theta}{}_{\\\\theta}= & a r r_s \\\\frac{\\\\left(-r r_s+\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(-8a^{4} \\\\sin{\\\\theta}^{6}+8a^{4} \\\\sin{\\\\theta}^{4}+24a^{2} \\\\Sigma \\\\sin{\\\\theta}^{4}+8a^{2} \\\\Sigma \\\\cos{2\\\\theta}-8a^{2} \\\\Sigma+6a^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}-3a^{2} \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}-4r^{2} \\\\Delta \\\\cos{2\\\\theta}+4r^{2} \\\\Delta+2\\\\Delta \\\\Sigma \\\\cos{2\\\\theta}-2\\\\Delta \\\\Sigma-8\\\\Sigma^{2} \\\\cos{2\\\\theta}+8\\\\Sigma \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right)-8\\\\left(a^{2} r r_s \\\\left(a^{2} \\\\sin{\\\\theta}^{2}+\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{\\\\theta}^{2}+\\\\left(-r r_s+\\\\Sigma\\\\right) \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+\\\\left(a^{2}+r^{2}\\\\right) \\\\Sigma^{2}\\\\right)\\\\right) \\\\cos{\\\\theta}^{2}}{8\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}_{\\\\phi}{}^{r}{}_{r}= & a r_s \\\\left(-\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(r_s \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(-2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}+a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r \\\\Sigma^{2}\\\\right)\\\\right) \\\\Delta+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(4a^{4} r \\\\sin{\\\\theta}^{4}-4a^{4} r \\\\sin{\\\\theta}^{2}+4a^{2} r \\\\Sigma \\\\sin{\\\\theta}^{2}-4a^{2} r \\\\Sigma-4r^{3} \\\\Delta+4r^{3} \\\\Sigma-2r^{2} r_s \\\\Sigma+2r \\\\Delta \\\\Sigma-2r \\\\Sigma^{2}+r_s \\\\Sigma^{2}+6\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\Delta \\\\partial_{r}{\\\\Sigma}-2\\\\left(\\\\left(4r-\\\\partial_{r}{\\\\Sigma}\\\\right) \\\\Delta+\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\partial_{r}{\\\\Delta}\\\\right) \\\\Sigma\\\\right)\\\\right) \\\\frac{\\\\sin{\\\\theta}^{2}}{4\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}_{\\\\phi}{}^{r}{}_{\\\\theta}= & a r_s \\\\left(4r \\\\left(a^{2} r_s \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right) \\\\left(-2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}+a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r \\\\Sigma^{2}\\\\right)\\\\right) \\\\sin{\\\\theta}^{2}+\\\\left(-r r_s+\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(2a^{2} \\\\Sigma \\\\sin{2\\\\theta}-a^{2} \\\\Sigma \\\\sin{4\\\\theta}+24r^{2} \\\\Sigma \\\\sin{2\\\\theta}+24r^{2} \\\\cos{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}-24r^{2} \\\\partial_{\\\\theta}{\\\\Sigma}-8\\\\Sigma^{2} \\\\sin{2\\\\theta}-8\\\\Sigma \\\\cos{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}+8\\\\Sigma \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\tan{\\\\theta}\\\\right) \\\\frac{\\\\Delta}{16\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4} \\\\tan{\\\\theta}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{r}{}^{\\\\theta}{}_{\\\\theta}= & \\\\frac{a^{2} \\\\Sigma \\\\cos{2\\\\theta} - \\\\frac{1}{2}a^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}-r^{2} \\\\Sigma+\\\\frac{1}{2}r r_s \\\\Sigma+r \\\\Delta \\\\partial_{r}{\\\\Sigma}-\\\\Delta \\\\Sigma}{\\\\Delta \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{\\\\theta}{}^{r}{}_{r}= & \\\\frac{a^{2} \\\\Sigma \\\\cos{2\\\\theta} - \\\\frac{1}{2}a^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}+r^{2} \\\\Sigma - \\\\frac{1}{2}r r_s \\\\Sigma+r \\\\Delta \\\\partial_{r}{\\\\Sigma}-r \\\\Sigma \\\\partial_{r}{\\\\Delta}-\\\\Delta \\\\Sigma}{\\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{\\\\phi}{}^{\\\\theta}{}_{r}= & \\\\left(-a^{2} r r_s^{2} \\\\left(a^{2} \\\\sin{\\\\theta}^{2}+\\\\Sigma\\\\right) \\\\left(2a^{2} r^{3} r_s-2a^{2} r^{2} \\\\Sigma-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}+2r^{5} r_s-2r^{4} \\\\Sigma+r^{3} r_s \\\\Sigma-r^{2} \\\\Sigma^{2}\\\\right) \\\\sin{\\\\theta}^{2}+\\\\left(-r r_s+\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(-6a^{4} r r_s \\\\sin{\\\\theta}^{4} \\\\partial_{r}{\\\\Sigma}+3a^{4} r_s \\\\Sigma \\\\sin{\\\\theta}^{4}+4a^{2} r^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-8a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}+2a^{2} r \\\\Sigma^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r \\\\Sigma^{2}+4a^{2} r_s \\\\Sigma^{2} \\\\sin{\\\\theta}^{2}-2a^{2} \\\\Sigma^{2} \\\\partial_{r}{\\\\Sigma}+2r^{3} \\\\Sigma^{2}-2r^{2} \\\\Sigma^{2} \\\\partial_{r}{\\\\Sigma}+4r \\\\Sigma^{3}\\\\right)+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+\\\\left(a^{2}+r^{2}\\\\right) \\\\Sigma^{2}\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right)\\\\right) \\\\sin{\\\\theta} \\\\frac{\\\\cos{\\\\theta}}{2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{\\\\phi}{}^{\\\\theta}{}_{\\\\theta}= & \\\\frac{\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(12a^{4} r r_s \\\\Sigma \\\\sin{\\\\theta}^{6}-10a^{4} r r_s \\\\Sigma \\\\sin{\\\\theta}^{4}+6a^{4} r r_s \\\\sin{\\\\theta}^{5} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}+16a^{2} r r_s \\\\Sigma^{2} \\\\sin{\\\\theta}^{4}+6a^{2} r r_s \\\\Sigma^{2} \\\\cos{2\\\\theta}-6a^{2} r r_s \\\\Sigma^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}-a^{2} r r_s \\\\Sigma \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}-2a^{2} \\\\Sigma^{3} \\\\cos{2\\\\theta}+a^{2} \\\\Sigma^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}-2r^{2} \\\\Sigma^{3} \\\\cos{2\\\\theta}+r^{2} \\\\Sigma^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}+\\\\left(2a^{2} \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+\\\\left(a^{2}+r^{2}\\\\right) \\\\Sigma^{2}\\\\right) \\\\cos{\\\\theta}^{2}-r \\\\left(-2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}+a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r \\\\Sigma^{2}\\\\right) \\\\Delta\\\\right) \\\\sin{\\\\theta}^{2}\\\\right)+2\\\\left(a^{4} r^{2} r_s^{2} \\\\left(a^{2} \\\\sin{\\\\theta}^{2}+\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{\\\\theta}^{4}+\\\\left(-r r_s+\\\\Sigma\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+\\\\left(a^{2}+r^{2}\\\\right) \\\\Sigma^{2}\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right)\\\\right) \\\\cos{\\\\theta}^{2}}{2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{\\\\phi}{}^{r}{}_{r}= & \\\\left(\\\\left(-r r_s+\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(12a^{2} r^{2} r_s \\\\Delta \\\\sin{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}-4a^{2} r^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2} \\\\partial_{r}{\\\\Delta}-8a^{2} r r_s \\\\Delta \\\\Sigma \\\\sin{\\\\theta}^{2}-4a^{2} r_s \\\\Delta \\\\Sigma \\\\sin{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}+2a^{2} r_s \\\\Sigma^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{r}{\\\\Delta}-4a^{2} \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+\\\\left(a^{2}+r^{2}\\\\right) \\\\Sigma^{2}\\\\right) \\\\cos{\\\\theta}^{2}-4r \\\\Delta \\\\Sigma^{2} \\\\partial_{r}{\\\\Sigma}+4r \\\\Sigma^{3} \\\\partial_{r}{\\\\Delta}+\\\\left(2r \\\\Delta-\\\\left(2r-r_s\\\\right) \\\\Sigma\\\\right) \\\\left(-2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}+a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r \\\\Sigma^{2}\\\\right)+4\\\\Delta \\\\Sigma^{3}\\\\right)+\\\\left(a^{2} r_s^{2} \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(2a^{2} r^{3} r_s-2a^{2} r^{2} \\\\Sigma-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}+2r^{5} r_s-2r^{4} \\\\Sigma+r^{3} r_s \\\\Sigma-r^{2} \\\\Sigma^{2}\\\\right) \\\\sin{\\\\theta}^{2}+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(-2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}+a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r \\\\Sigma^{2}\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right)\\\\right) \\\\Delta\\\\right) \\\\frac{\\\\sin{\\\\theta}^{2}}{4\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{\\\\phi}{}^{r}{}_{\\\\theta}= & \\\\left(\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(8a^{2} r^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}-6a^{2} r^{2} r_s \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}{\\\\Sigma}-4a^{2} r_s \\\\Sigma^{2} \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}+2a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}{\\\\Sigma}-4r \\\\Sigma^{3} \\\\cos{\\\\theta}+2r \\\\Sigma^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}+\\\\left(a^{4} r_s \\\\sin{\\\\theta}^{4}+4a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}+2a^{2} r \\\\Sigma \\\\sin{\\\\theta}^{2}+2a^{2} r \\\\Sigma+2r^{3} \\\\Sigma\\\\right) \\\\Sigma \\\\cos{\\\\theta}\\\\right)-\\\\left(a^{4} r r_s^{2} \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{\\\\theta}^{4}+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(-2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}+a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r \\\\Sigma^{2}\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right)\\\\right) \\\\cos{\\\\theta}\\\\right) \\\\Delta \\\\frac{\\\\sin{\\\\theta}}{2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{t}{}^{\\\\phi}{}_{r}= & a r_s \\\\frac{-r \\\\left(a^{2} r_s \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+2\\\\left(-r r_s+\\\\Sigma\\\\right) \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right)\\\\right)+2\\\\left(-r r_s+\\\\Sigma\\\\right) \\\\left(a^{2} \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\sin{\\\\theta}^{2}+2r^{2} \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right)\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)+4\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(-r \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\partial_{r}{\\\\Sigma}+r \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right) \\\\left(-a^{2} r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\partial_{r}{\\\\Sigma}-3r^{2} r_s+r^{2} \\\\partial_{r}{\\\\Sigma}+2r \\\\Sigma\\\\right) \\\\Sigma+\\\\left(a^{2} \\\\sin{\\\\theta}^{2}-2r r_s+r \\\\partial_{r}{\\\\Sigma}+\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma\\\\right)}{4\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2} \\\\tan{\\\\theta}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{t}{}^{\\\\phi}{}_{\\\\theta}= & a r r_s \\\\frac{\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(2a^{2} \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right) \\\\sin{\\\\theta} \\\\cos{\\\\theta}-\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\Delta \\\\tan{\\\\theta}\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\sin{\\\\theta}^{2}+\\\\left(\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(2\\\\left(\\\\left(a^{2} r r_s \\\\sin{2\\\\theta}+a^{2} \\\\partial_{\\\\theta}{\\\\Sigma}+r^{2} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\Sigma-\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right) \\\\sin{\\\\theta} \\\\cos{\\\\theta}-\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(4a^{2} \\\\sin{\\\\theta}^{4}+a^{2} \\\\cos{2\\\\theta}-a^{2}-2r r_s+2\\\\Sigma-\\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\Sigma\\\\right)+\\\\left(a^{2} r r_s \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{\\\\theta} \\\\sin{2\\\\theta}+2\\\\left(-r r_s+\\\\Sigma\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right) \\\\cos{\\\\theta}\\\\right) \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right) \\\\cos{\\\\theta}\\\\right) \\\\tan{\\\\theta}}{2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{t}{}^{t}{}_{r}= & a^{2} r_s \\\\left(-6a^{4} r^{3} r_s \\\\cos{\\\\theta}^{2}-2a^{4} r^{2} r_s \\\\cos{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}+4a^{4} r^{2} \\\\Sigma+2a^{4} r r_s \\\\Sigma \\\\cos{\\\\theta}^{2}+4a^{4} r \\\\Sigma \\\\partial_{r}{\\\\Sigma}-3a^{4} \\\\Sigma^{2}-6a^{2} r^{5} r_s \\\\cos{\\\\theta}^{2}-6a^{2} r^{5} r_s+2a^{2} r^{4} r_s^{2} \\\\cos{\\\\theta}^{2}-2a^{2} r^{4} r_s \\\\cos{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}-2a^{2} r^{4} r_s \\\\partial_{r}{\\\\Sigma}+8a^{2} r^{4} \\\\Sigma+2a^{2} r^{3} r_s^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}+4a^{2} r^{3} r_s \\\\Sigma \\\\cos{\\\\theta}^{2}+8a^{2} r^{3} \\\\Sigma \\\\partial_{r}{\\\\Sigma}-2a^{2} r^{2} r_s^{2} \\\\Sigma \\\\cos{\\\\theta}^{2}-4a^{2} r^{2} r_s \\\\Sigma \\\\partial_{r}{\\\\Sigma}-6a^{2} r^{2} \\\\Sigma^{2}+3a^{2} r r_s \\\\Sigma^{2}%\\n-6r^{7} r_s+2r^{6} r_s^{2}-2r^{6} r_s \\\\partial_{r}{\\\\Sigma}+4r^{6} \\\\Sigma+2r^{5} r_s^{2} \\\\partial_{r}{\\\\Sigma}+2r^{5} r_s \\\\Sigma+4r^{5} \\\\Sigma \\\\partial_{r}{\\\\Sigma}-4r^{4} r_s \\\\Sigma \\\\partial_{r}{\\\\Sigma}-3r^{4} \\\\Sigma^{2}+r^{3} r_s \\\\Sigma^{2}\\\\right) \\\\sin{\\\\theta} \\\\frac{\\\\cos{\\\\theta}}{2\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{t}{}^{t}{}_{\\\\theta}= & -r r_s \\\\frac{4a^{2} \\\\left(2a^{2} r r_s \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\left(-a^{2} r r_s+a^{2} \\\\Sigma-r^{3} r_s+r^{2} r_s^{2}+r^{2} \\\\Sigma-r r_s \\\\Sigma+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right)\\\\right) \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{2}-\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\sin{2\\\\theta}+a^{2} \\\\partial_{\\\\theta}{\\\\Sigma}+r^{2} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\Sigma \\\\sin{2\\\\theta}+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(-2a^{2} r r_s \\\\cos{2\\\\theta}+2a^{2} \\\\Sigma \\\\cos{2\\\\theta}+a^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}-2r^{3} r_s \\\\cos{2\\\\theta}+2r^{2} r_s^{2} \\\\cos{2\\\\theta}+2r^{2} \\\\Sigma \\\\cos{2\\\\theta}+r^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}-2r r_s \\\\Sigma \\\\cos{2\\\\theta}-r r_s \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\Sigma-\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\Sigma \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right)+\\\\left(r r_s-\\\\Sigma\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{6} \\\\left(\\\\cos{4\\\\theta}-1\\\\right)+a^{4} r^{2} \\\\left(\\\\cos{4\\\\theta}-1\\\\right)-a^{4} r r_s \\\\left(\\\\cos{4\\\\theta}-1\\\\right)+8a^{2} r^{2} \\\\Delta-4a^{2} \\\\Delta \\\\Sigma+8r^{4} \\\\Delta-4r^{2} \\\\Delta \\\\Sigma\\\\right)}{8\\\\left(r r_s-\\\\Sigma\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{t}{}^{\\\\phi}{}_{r}= & a r_s \\\\frac{\\\\left(-r r_s+\\\\Sigma\\\\right) \\\\left(4a^{2} r \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right) \\\\sin{\\\\theta} \\\\cos{\\\\theta}-\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(2r \\\\Delta-\\\\left(2r-r_s\\\\right) \\\\Sigma\\\\right) \\\\tan{\\\\theta}\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)+\\\\left(\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(r_s \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)+\\\\left(-r r_s+\\\\Sigma\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right)\\\\right)+2\\\\left(-r r_s+\\\\Sigma\\\\right) \\\\left(\\\\left(4r-\\\\partial_{r}{\\\\Sigma}\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma-\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\partial_{r}{\\\\Sigma}+\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(-a^{2} r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\partial_{r}{\\\\Sigma}-3r^{2} r_s+r^{2} \\\\partial_{r}{\\\\Sigma}+2r \\\\Sigma\\\\right) \\\\Sigma\\\\right)\\\\right) \\\\Delta \\\\tan{\\\\theta}}{4\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Delta \\\\Sigma^{2} \\\\tan{\\\\theta}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{t}{}^{\\\\phi}{}_{\\\\theta}= & a r_s \\\\frac{\\\\left(-2r^{2}+\\\\Sigma\\\\right) \\\\left(r r_s \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)+\\\\left(-r r_s+\\\\Sigma\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right)\\\\right)+\\\\left(-r r_s+\\\\Sigma\\\\right) \\\\left(a^{2} \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\sin{\\\\theta}^{2}+2r^{2} \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right)\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(-\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\sin{2\\\\theta}+a^{2} \\\\partial_{\\\\theta}{\\\\Sigma}+r^{2} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\Sigma+\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\partial_{\\\\theta}{\\\\Sigma}+\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\tan{\\\\theta}}{2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2} \\\\tan{\\\\theta}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{t}{}^{t}{}_{r}= & r_s \\\\frac{\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{4} r \\\\left(\\\\cos{4\\\\theta}-1\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right)+2\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(2r \\\\Delta-\\\\left(2r-r_s\\\\right) \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)-2\\\\left(r_s \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} \\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(2a^{2} r^{3} r_s-2a^{2} r^{2} \\\\Sigma-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}+2r^{5} r_s-2r^{4} \\\\Sigma+r^{3} r_s \\\\Sigma-r^{2} \\\\Sigma^{2}\\\\right) \\\\sin{\\\\theta}^{2}+\\\\left(-2r^{2}+\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2}\\\\right)-2\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(r_s-\\\\partial_{r}{\\\\Sigma}\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma-2\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\partial_{r}{\\\\Sigma}+2\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(-a^{2} r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\partial_{r}{\\\\Sigma}-3r^{2} r_s+r^{2} \\\\partial_{r}{\\\\Sigma}+2r \\\\Sigma\\\\right) \\\\Sigma+2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(\\\\left(4r-\\\\partial_{r}{\\\\Sigma}\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)-\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(-a^{2} r_s+a^{2} \\\\partial_{r}{\\\\Sigma}-3r^{2} r_s+r^{2} \\\\partial_{r}{\\\\Sigma}+2r \\\\Sigma\\\\right)\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma\\\\right) \\\\Delta}{8\\\\left(r r_s-\\\\Sigma\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Delta \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{t}{}^{t}{}_{\\\\theta}= & r_s \\\\frac{-2a^{2} r r_s \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(r r_s-\\\\Sigma\\\\right)^{2} \\\\left(a^{4} \\\\cos{\\\\theta}^{2}+a^{2} r^{2} \\\\cos{\\\\theta}^{2}+a^{2} r^{2}-a^{2} r r_s \\\\cos{\\\\theta}^{2}+r^{4}-r^{3} r_s\\\\right) \\\\sin{\\\\theta} \\\\cos{\\\\theta}+a^{2} \\\\left(r r_s-\\\\Sigma\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(-4a^{2} r^{2}+a^{2} \\\\Sigma-4r^{4}+2r^{3} r_s+r^{2} \\\\Sigma\\\\right) \\\\sin{2\\\\theta}-2\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\sin{2\\\\theta}+a^{2} \\\\partial_{\\\\theta}{\\\\Sigma}+r^{2} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma+2\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\partial_{\\\\theta}{\\\\Sigma}-2\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma \\\\partial_{\\\\theta}{\\\\Sigma}+2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma+\\\\left(a^{2}+r^{2}\\\\right) \\\\left(2r^{2}-\\\\Sigma\\\\right)\\\\right) \\\\Sigma \\\\partial_{\\\\theta}{\\\\Sigma}}{4\\\\left(r r_s-\\\\Sigma\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{r}{}^{r}{}_{\\\\theta}= & \\\\frac{-a^{2} \\\\Sigma \\\\cos{2\\\\theta}+\\\\frac{1}{2}a^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}-r^{2} \\\\Sigma+\\\\frac{1}{2}r r_s \\\\Sigma-r \\\\Delta \\\\partial_{r}{\\\\Sigma}+r \\\\Sigma \\\\partial_{r}{\\\\Delta}+\\\\Delta \\\\Sigma}{\\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{\\\\theta}{}^{\\\\theta}{}_{r}= & \\\\frac{-a^{2} \\\\Sigma \\\\cos{2\\\\theta}+\\\\frac{1}{2}a^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}+r^{2} \\\\Sigma - \\\\frac{1}{2}r r_s \\\\Sigma-r \\\\Delta \\\\partial_{r}{\\\\Sigma}+\\\\Delta \\\\Sigma}{\\\\Delta \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{\\\\phi}{}^{\\\\phi}{}_{r}= & \\\\frac{a^{4} r r_s^{2} \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{\\\\theta}^{4}-2a^{2} r_s \\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{4} r^{2} r_s \\\\sin{\\\\theta}^{4} \\\\partial_{r}{\\\\Sigma}-a^{4} r^{2} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}+2a^{4} r \\\\Sigma \\\\sin{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}-a^{4} \\\\Sigma^{2} \\\\sin{\\\\theta}^{2}-a^{2} r^{4} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}-a^{2} r^{3} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}+a^{2} r^{3} r_s^{2} \\\\partial_{r}{\\\\Sigma}-2a^{2} r^{3} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2a^{2} r^{3} \\\\Sigma \\\\sin{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}+a^{2} r^{2} r_s^{2} \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r^{2} r_s^{2} \\\\Sigma-2a^{2} r^{2} r_s \\\\Sigma \\\\partial_{r}{\\\\Sigma}+a^{2} r^{2} \\\\Sigma^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma^{2}+a^{2} r \\\\Sigma^{2} \\\\partial_{r}{\\\\Sigma}-a^{2} \\\\Sigma^{3}+r^{5} r_s^{2} \\\\partial_{r}{\\\\Sigma}+r^{4} r_s^{2} \\\\Sigma-2r^{4} r_s \\\\Sigma \\\\partial_{r}{\\\\Sigma}%\\n-2r^{3} r_s \\\\Sigma^{2}+r^{3} \\\\Sigma^{2} \\\\partial_{r}{\\\\Sigma}+r^{2} \\\\Sigma^{3}\\\\right) \\\\sin{\\\\theta}^{2}+\\\\left(-r r_s+\\\\Sigma\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right)+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(4a^{4} r^{2} r_s \\\\sin{\\\\theta}^{4}-a^{4} r_s \\\\Sigma \\\\sin{\\\\theta}^{4}-2a^{2} r^{3} r_s^{2} \\\\sin{\\\\theta}^{2}+6a^{2} r^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-2a^{2} r^{2} r_s \\\\Sigma-2a^{2} r \\\\Sigma^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r \\\\Sigma^{2}-2r^{4} r_s \\\\Sigma+2r^{3} \\\\Sigma^{2}\\\\right)}{2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2} \\\\tan{\\\\theta}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{\\\\phi}{}^{\\\\phi}{}_{\\\\theta}= & \\\\frac{2\\\\left(-r r_s+\\\\Sigma\\\\right) \\\\left(\\\\left(a^{2} r r_s \\\\sin{2\\\\theta}+a^{2} \\\\partial_{\\\\theta}{\\\\Sigma}+r^{2} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right) \\\\Sigma \\\\sin{\\\\theta} \\\\cos{\\\\theta}-\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right) \\\\Sigma \\\\cos{\\\\theta}^{2}-2\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right) \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}+\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(-5a^{4} r r_s \\\\Sigma \\\\sin{\\\\theta}^{5}+4a^{4} r r_s \\\\Sigma \\\\sin{\\\\theta}^{3}+a^{4} r r_s \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}+3a^{2} r^{2} r_s^{2} \\\\Sigma \\\\sin{\\\\theta}^{3}-2a^{2} r^{2} r_s^{2} \\\\Sigma \\\\sin{\\\\theta}+a^{2} r^{2} r_s^{2} \\\\cos{\\\\theta}^{3} \\\\partial_{\\\\theta}{\\\\Sigma}-a^{2} r^{2} r_s^{2} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}-6a^{2} r r_s \\\\Sigma^{2} \\\\sin{\\\\theta}^{3}+5a^{2} r r_s \\\\Sigma^{2} \\\\sin{\\\\theta}-4a^{2} r r_s \\\\Sigma \\\\cos{\\\\theta}^{3} \\\\partial_{\\\\theta}{\\\\Sigma}+2a^{2} r r_s \\\\Sigma \\\\cos{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}-a^{2} \\\\Sigma^{3} \\\\sin{\\\\theta}+3a^{2} \\\\Sigma^{2} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}+r^{3} r_s \\\\Sigma^{2} \\\\sin{\\\\theta}-2r^{3} r_s \\\\Sigma \\\\cos{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}-r^{2} \\\\Sigma^{3} \\\\sin{\\\\theta}+3r^{2} \\\\Sigma^{2} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\sin{\\\\theta}\\\\right) \\\\tan{\\\\theta}^{2}+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(2a^{2} \\\\left(-a^{4} r r_s \\\\sin{\\\\theta}^{4}+a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}-2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+a^{2} r r_s \\\\Sigma-a^{2} \\\\Sigma^{2}+r^{3} r_s \\\\Sigma-r^{2} \\\\Sigma^{2}\\\\right) \\\\cos{\\\\theta}^{2}+r \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right) \\\\Delta\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+2\\\\left(-a^{4} r^{2} r_s^{2} \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{\\\\theta}^{4}+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right)^{2}\\\\right) \\\\sin{\\\\theta}^{2}}{2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{\\\\phi}{}^{t}{}_{r}= & a r_s \\\\left(a^{2} r r_s \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{\\\\theta}^{2}-a^{2} \\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(-4a^{2} r^{3} r_s+4a^{2} r^{2} \\\\Sigma+a^{2} r r_s \\\\Sigma-a^{2} \\\\Sigma^{2}-4r^{5} r_s+2r^{4} r_s^{2}+4r^{4} \\\\Sigma-3r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right) \\\\sin{\\\\theta}^{2}+2a^{2} \\\\left(r \\\\left(r_s-\\\\partial_{r}{\\\\Sigma}\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\Sigma+r \\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\partial_{r}{\\\\Sigma}-r \\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(-a^{2} r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\partial_{r}{\\\\Sigma}-3r^{2} r_s+r^{2} \\\\partial_{r}{\\\\Sigma}+2r \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\Sigma-\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma+r \\\\left(a^{2} r_s-a^{2} \\\\partial_{r}{\\\\Sigma}+3r^{2} r_s-r^{2} \\\\partial_{r}{\\\\Sigma}-2r r_s^{2}+r r_s \\\\partial_{r}{\\\\Sigma}-2r \\\\Sigma+r_s \\\\Sigma\\\\right)\\\\right) \\\\Sigma\\\\right) \\\\sin{\\\\theta}^{2}-\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right) \\\\left(2a^{2} r^{3} r_s-2a^{2} r^{2} \\\\Sigma-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}+2r^{5} r_s-2r^{4} \\\\Sigma+r^{3} r_s \\\\Sigma-r^{2} \\\\Sigma^{2}\\\\right)\\\\right) \\\\sin{\\\\theta} \\\\frac{\\\\cos{\\\\theta}}{2\\\\left(r r_s-\\\\Sigma\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{\\\\phi}{}^{t}{}_{\\\\theta}= & a r r_s \\\\left(-a^{2} \\\\left(2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\sin{2\\\\theta}+a^{2} \\\\partial_{\\\\theta}{\\\\Sigma}+r^{2} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\Sigma \\\\sin{\\\\theta} \\\\cos{\\\\theta}-2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}-\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(-4a^{2} r r_s \\\\cos{2\\\\theta}-2a^{2} r r_s+4a^{2} \\\\Sigma \\\\cos{2\\\\theta}+2a^{2} \\\\Sigma+a^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}-4r^{3} r_s \\\\cos{2\\\\theta}-2r^{3} r_s+4r^{2} r_s^{2} \\\\cos{2\\\\theta}+2r^{2} r_s^{2}+4r^{2} \\\\Sigma \\\\cos{2\\\\theta}+2r^{2} \\\\Sigma+r^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}-4r r_s \\\\Sigma \\\\cos{2\\\\theta}-2r r_s \\\\Sigma-r r_s \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\Sigma+\\\\left(a^{2} r r_s \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{\\\\theta} \\\\sin{2\\\\theta}+\\\\left(-2r r_s+2\\\\Sigma\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right) \\\\cos{\\\\theta}\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\cos{\\\\theta}+2\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\Sigma \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right)+\\\\left(-r r_s+\\\\Sigma\\\\right) \\\\left(a^{4} \\\\left(-\\\\cos{4\\\\theta}+1\\\\right) \\\\left(\\\\frac{1}{4}a^{2} r r_s - \\\\frac{1}{4}a^{2} \\\\Sigma+\\\\frac{1}{4}r^{3} r_s - \\\\frac{1}{4}r^{2} r_s^{2} - \\\\frac{1}{4}r^{2} \\\\Sigma+\\\\frac{1}{4}r r_s \\\\Sigma\\\\right)-\\\\left(2a^{2} r^{3} r_s-2a^{2} r^{2} \\\\Sigma-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}+2r^{5} r_s-2r^{4} \\\\Sigma+r^{3} r_s \\\\Sigma-r^{2} \\\\Sigma^{2}\\\\right) \\\\Delta\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)\\\\right) \\\\frac{\\\\sin{\\\\theta}^{2}}{2\\\\left(r r_s-\\\\Sigma\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{\\\\phi}{}^{\\\\phi}{}_{r}= & \\\\frac{\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(4a^{2} \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right) \\\\cos{\\\\theta}^{2}+\\\\left(-2r \\\\Delta+\\\\left(2r-r_s\\\\right) \\\\Sigma\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right)\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)+\\\\left(-a^{2} r_s^{2} \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(2a^{2} r^{3} r_s-2a^{2} r^{2} \\\\Sigma-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}+2r^{5} r_s-2r^{4} \\\\Sigma+r^{3} r_s \\\\Sigma-r^{2} \\\\Sigma^{2}\\\\right) \\\\sin{\\\\theta}^{2}+2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(-\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right) \\\\partial_{r}{\\\\Sigma}+\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(4a^{2} r r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}+2r^{2} r_s \\\\partial_{r}{\\\\Sigma}+4r r_s \\\\Sigma-4r \\\\Sigma \\\\partial_{r}{\\\\Sigma}-2\\\\Sigma^{2}\\\\right) \\\\Sigma+\\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right) \\\\left(-a^{2} r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\partial_{r}{\\\\Sigma}-3r^{2} r_s+r^{2} \\\\partial_{r}{\\\\Sigma}+2r \\\\Sigma\\\\right) \\\\Sigma\\\\right)+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right)^{2}\\\\right) \\\\Delta}{4\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Delta \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{\\\\phi}{}^{\\\\phi}{}_{\\\\theta}= & \\\\frac{a^{2} r r_s^{2} \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right) \\\\left(2a^{2} r^{3} r_s-2a^{2} r^{2} \\\\Sigma-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}+2r^{5} r_s-2r^{4} \\\\Sigma+r^{3} r_s \\\\Sigma-r^{2} \\\\Sigma^{2}\\\\right) \\\\sin{\\\\theta}^{2}+\\\\left(-r r_s+\\\\Sigma\\\\right) \\\\left(-\\\\left(a^{2} r r_s \\\\sin{2\\\\theta}+a^{2} \\\\partial_{\\\\theta}{\\\\Sigma}+r^{2} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right) \\\\Sigma+\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right) \\\\partial_{\\\\theta}{\\\\Sigma}+\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(-2a^{2} r^{2} r_s \\\\sin{2\\\\theta}+a^{2} r_s \\\\Sigma \\\\sin{2\\\\theta}+a^{2} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{\\\\theta}{\\\\Sigma}-2r^{2} r_s \\\\partial_{\\\\theta}{\\\\Sigma}+4r \\\\Sigma \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\Sigma\\\\right) \\\\tan{\\\\theta}+\\\\left(-r r_s+\\\\Sigma\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right)+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(4a^{4} r^{2} r_s \\\\sin{\\\\theta}^{4}-a^{4} r_s \\\\Sigma \\\\sin{\\\\theta}^{4}-2a^{2} r^{3} r_s^{2} \\\\sin{\\\\theta}^{2}+6a^{2} r^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-2a^{2} r^{2} r_s \\\\Sigma-2a^{2} r \\\\Sigma^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r \\\\Sigma^{2}-2r^{4} r_s \\\\Sigma+2r^{3} \\\\Sigma^{2}\\\\right)}{2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2} \\\\tan{\\\\theta}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{\\\\phi}{}^{t}{}_{r}= & a r_s \\\\left(-\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(4a^{4} r^{4} r_s \\\\cos{\\\\theta}^{2}+4a^{4} r^{3} r_s \\\\cos{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}-8a^{4} r^{2} r_s \\\\Sigma \\\\cos{\\\\theta}^{2}-8a^{4} r^{2} \\\\Sigma \\\\partial_{r}{\\\\Sigma}+8a^{4} r \\\\Sigma^{2}-a^{4} r_s \\\\Sigma^{2} \\\\cos{\\\\theta}^{2}+2a^{4} \\\\Sigma^{2} \\\\partial_{r}{\\\\Sigma}+4a^{2} r^{6} r_s \\\\cos{\\\\theta}^{2}+4a^{2} r^{6} r_s+4a^{2} r^{5} r_s \\\\cos{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}+4a^{2} r^{5} r_s \\\\partial_{r}{\\\\Sigma}-12a^{2} r^{4} r_s \\\\Sigma \\\\cos{\\\\theta}^{2}-4a^{2} r^{4} r_s \\\\Sigma-16a^{2} r^{4} \\\\Sigma \\\\partial_{r}{\\\\Sigma}+20a^{2} r^{3} \\\\Sigma^{2}-3a^{2} r^{2} r_s \\\\Sigma^{2} \\\\cos{\\\\theta}^{2}-3a^{2} r^{2} r_s \\\\Sigma^{2}+6a^{2} r \\\\Sigma^{3}+4r^{8} r_s%\\n+4r^{7} r_s \\\\partial_{r}{\\\\Sigma}-8r^{6} r_s \\\\Sigma-8r^{6} \\\\Sigma \\\\partial_{r}{\\\\Sigma}+12r^{5} \\\\Sigma^{2}-r^{4} r_s \\\\Sigma^{2}-2r^{4} \\\\Sigma^{2} \\\\partial_{r}{\\\\Sigma}+2r^{3} \\\\Sigma^{3}\\\\right) \\\\Delta+\\\\left(a^{4} r \\\\left(-\\\\cos{4\\\\theta}+1\\\\right) \\\\left(\\\\frac{1}{2}a^{2} r r_s - \\\\frac{1}{2}a^{2} \\\\Sigma+\\\\frac{1}{2}r^{3} r_s - \\\\frac{1}{2}r^{2} r_s^{2} - \\\\frac{1}{2}r^{2} \\\\Sigma+\\\\frac{1}{2}r r_s \\\\Sigma\\\\right)-\\\\left(2r \\\\Delta-\\\\left(2r-r_s\\\\right) \\\\Sigma\\\\right) \\\\left(2a^{2} r^{3} r_s-2a^{2} r^{2} \\\\Sigma-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}+2r^{5} r_s-2r^{4} \\\\Sigma+r^{3} r_s \\\\Sigma-r^{2} \\\\Sigma^{2}\\\\right)\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)\\\\right) \\\\frac{\\\\sin{\\\\theta}^{2}}{4\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Delta \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{\\\\phi}{}^{t}{}_{\\\\theta}= & a r_s \\\\left(a^{2} r \\\\left(r r_s-\\\\Sigma\\\\right)^{2} \\\\left(2a^{4} r^{2} r_s \\\\cos{\\\\theta}^{2}-a^{4} r_s \\\\Sigma \\\\cos{\\\\theta}^{2}+2a^{2} r^{4} r_s \\\\cos{\\\\theta}^{2}+2a^{2} r^{4} r_s-2a^{2} r^{3} r_s^{2} \\\\cos{\\\\theta}^{2}-a^{2} r^{2} r_s \\\\Sigma \\\\cos{\\\\theta}^{2}-a^{2} r^{2} r_s \\\\Sigma+a^{2} r r_s^{2} \\\\Sigma \\\\cos{\\\\theta}^{2}+2a^{2} r \\\\Sigma^{2}+2r^{6} r_s-2r^{5} r_s^{2}-r^{4} r_s \\\\Sigma+r^{3} r_s^{2} \\\\Sigma+2r^{3} \\\\Sigma^{2}-2r^{2} r_s \\\\Sigma^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}-a^{2} \\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(-4a^{2} r^{3} r_s+4a^{2} r^{2} \\\\Sigma+a^{2} r r_s \\\\Sigma-a^{2} \\\\Sigma^{2}-4r^{5} r_s+2r^{4} r_s^{2}+4r^{4} \\\\Sigma-3r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}-\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(\\\\left(2a^{2} r^{2}+a^{2} r r_s-2a^{2} \\\\Sigma+2r^{4}-r^{3} r_s+2r^{2} \\\\Sigma\\\\right) \\\\sin{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}+2\\\\left(-2a^{2} r^{3} r_s+2a^{2} r^{2} \\\\Sigma+a^{2} r r_s \\\\Sigma-a^{2} \\\\Sigma^{2}-2r^{5} r_s+2r^{4} \\\\Sigma-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right) \\\\cos{\\\\theta}\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\sin{2\\\\theta}+a^{2} \\\\partial_{\\\\theta}{\\\\Sigma}+r^{2} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\left(2a^{2} r^{3} r_s-2a^{2} r^{2} \\\\Sigma-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}+2r^{5} r_s-2r^{4} \\\\Sigma+r^{3} r_s \\\\Sigma-r^{2} \\\\Sigma^{2}\\\\right) \\\\Sigma \\\\sin{\\\\theta}-\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(2a^{2} r^{3} r_s-2a^{2} r^{2} \\\\Sigma-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}+2r^{5} r_s-2r^{4} \\\\Sigma+r^{3} r_s \\\\Sigma-r^{2} \\\\Sigma^{2}\\\\right) \\\\sin{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}+\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(2a^{2} r^{3} r_s-2a^{2} r^{2} \\\\Sigma-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}+2r^{5} r_s-2r^{4} \\\\Sigma+r^{3} r_s \\\\Sigma-r^{2} \\\\Sigma^{2}\\\\right) \\\\Sigma \\\\sin{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\frac{\\\\sin{\\\\theta}}{2\\\\left(r r_s-\\\\Sigma\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}_{\\\\theta}{}^{\\\\phi}{}_{r}= & a r_s \\\\frac{-r \\\\left(a^{2} r_s \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+2\\\\left(-r r_s+\\\\Sigma\\\\right) \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right)\\\\right)+2\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(r r_s \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)+\\\\left(-r r_s+\\\\Sigma\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right)\\\\right)+2\\\\left(-r r_s+\\\\Sigma\\\\right) \\\\left(-\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\sin{2\\\\theta}+a^{2} \\\\partial_{\\\\theta}{\\\\Sigma}+r^{2} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\Sigma+\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\partial_{\\\\theta}{\\\\Sigma}+\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\tan{\\\\theta}+4\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(-r \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\partial_{r}{\\\\Sigma}+r \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right) \\\\left(-a^{2} r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\partial_{r}{\\\\Sigma}-3r^{2} r_s+r^{2} \\\\partial_{r}{\\\\Sigma}+2r \\\\Sigma\\\\right) \\\\Sigma+\\\\left(a^{2} \\\\sin{\\\\theta}^{2}-2r r_s+r \\\\partial_{r}{\\\\Sigma}+\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma\\\\right)}{4\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2} \\\\tan{\\\\theta}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}_{\\\\theta}{}^{t}{}_{r}= & r_s \\\\frac{a^{2} r r_s \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(r r_s-\\\\Sigma\\\\right)^{2} \\\\left(a^{4} \\\\cos{\\\\theta}^{2}+a^{2} r^{2} \\\\cos{\\\\theta}^{2}+a^{2} r^{2}-a^{2} r r_s \\\\cos{\\\\theta}^{2}+r^{4}-r^{3} r_s\\\\right) \\\\sin{\\\\theta} \\\\cos{\\\\theta}-a^{2} \\\\left(r r_s-\\\\Sigma\\\\right)^{2} \\\\left(2a^{4} r^{3} r_s \\\\cos{\\\\theta}^{2}+2a^{4} r^{2} r_s \\\\cos{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}-a^{4} r r_s \\\\Sigma \\\\cos{\\\\theta}^{2}-4a^{4} r \\\\Sigma \\\\partial_{r}{\\\\Sigma}+2a^{4} \\\\Sigma^{2}+2a^{2} r^{5} r_s \\\\cos{\\\\theta}^{2}+2a^{2} r^{5} r_s+2a^{2} r^{4} r_s \\\\cos{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}+2a^{2} r^{4} r_s \\\\partial_{r}{\\\\Sigma}-2a^{2} r^{3} r_s^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}-3a^{2} r^{3} r_s \\\\Sigma \\\\cos{\\\\theta}^{2}-a^{2} r^{3} r_s \\\\Sigma-8a^{2} r^{3} \\\\Sigma \\\\partial_{r}{\\\\Sigma}+2a^{2} r^{2} r_s^{2} \\\\Sigma \\\\cos{\\\\theta}^{2}+4a^{2} r^{2} r_s \\\\Sigma \\\\partial_{r}{\\\\Sigma}+4a^{2} r^{2} \\\\Sigma^{2}-3a^{2} r r_s \\\\Sigma^{2}+2r^{7} r_s+2r^{6} r_s \\\\partial_{r}{\\\\Sigma}%\\n-2r^{5} r_s^{2} \\\\partial_{r}{\\\\Sigma}-3r^{5} r_s \\\\Sigma-4r^{5} \\\\Sigma \\\\partial_{r}{\\\\Sigma}+4r^{4} r_s \\\\Sigma \\\\partial_{r}{\\\\Sigma}+2r^{4} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma^{2}\\\\right) \\\\sin{\\\\theta} \\\\cos{\\\\theta}+\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\sin{2\\\\theta}+a^{2} \\\\partial_{\\\\theta}{\\\\Sigma}+r^{2} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma-\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\partial_{\\\\theta}{\\\\Sigma}+\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma \\\\partial_{\\\\theta}{\\\\Sigma}-\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma+\\\\left(a^{2}+r^{2}\\\\right) \\\\left(2r^{2}-\\\\Sigma\\\\right)\\\\right) \\\\Sigma \\\\partial_{\\\\theta}{\\\\Sigma}}{2\\\\left(r r_s-\\\\Sigma\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}_{r}{}^{\\\\phi}{}_{\\\\theta}= & a r_s \\\\frac{r \\\\left(a^{2} r_s \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+2\\\\left(-r r_s+\\\\Sigma\\\\right) \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right)\\\\right)+2\\\\left(-2r^{2}+\\\\Sigma\\\\right) \\\\left(r r_s \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)+\\\\left(-r r_s+\\\\Sigma\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right)\\\\right)+4\\\\left(-r r_s+\\\\Sigma\\\\right) \\\\left(-r \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\partial_{r}{\\\\Sigma}+r \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right) \\\\left(-a^{2} r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\partial_{r}{\\\\Sigma}-3r^{2} r_s+r^{2} \\\\partial_{r}{\\\\Sigma}+2r \\\\Sigma\\\\right) \\\\Sigma+\\\\left(a^{2} \\\\sin{\\\\theta}^{2}-2r r_s+r \\\\partial_{r}{\\\\Sigma}+\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma\\\\right)+2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(-\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\sin{2\\\\theta}+a^{2} \\\\partial_{\\\\theta}{\\\\Sigma}+r^{2} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\Sigma+\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\partial_{\\\\theta}{\\\\Sigma}+\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\tan{\\\\theta}}{4\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2} \\\\tan{\\\\theta}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}_{r}{}^{t}{}_{\\\\theta}= & r_s \\\\frac{a^{2} r r_s \\\\left(\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right) \\\\left(2a^{2} r^{3} r_s-2a^{2} r^{2} \\\\Sigma-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}+2r^{5} r_s-2r^{4} \\\\Sigma+r^{3} r_s \\\\Sigma-r^{2} \\\\Sigma^{2}\\\\right) \\\\sin{\\\\theta}^{2}\\\\right)-2\\\\left(a^{2} r r_s \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(r r_s-\\\\Sigma\\\\right)^{2} \\\\left(a^{4} \\\\cos{\\\\theta}^{2}+a^{2} r^{2} \\\\cos{\\\\theta}^{2}+a^{2} r^{2}-a^{2} r r_s \\\\cos{\\\\theta}^{2}+r^{4}-r^{3} r_s\\\\right) \\\\sin{\\\\theta} \\\\cos{\\\\theta}-2a^{2} \\\\left(r r_s-\\\\Sigma\\\\right)^{2} \\\\left(a^{4} r^{2} r_s \\\\cos{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}-2a^{4} r \\\\Sigma \\\\partial_{r}{\\\\Sigma}+a^{4} \\\\Sigma^{2}+a^{2} r^{4} r_s \\\\cos{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}+a^{2} r^{4} r_s \\\\partial_{r}{\\\\Sigma}-a^{2} r^{3} r_s^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}-2a^{2} r^{3} r_s \\\\Sigma \\\\cos{\\\\theta}^{2}+2a^{2} r^{3} r_s \\\\Sigma-4a^{2} r^{3} \\\\Sigma \\\\partial_{r}{\\\\Sigma}+a^{2} r^{2} r_s^{2} \\\\Sigma \\\\cos{\\\\theta}^{2}+2a^{2} r^{2} r_s \\\\Sigma \\\\partial_{r}{\\\\Sigma}+2a^{2} r^{2} \\\\Sigma^{2}-2a^{2} r r_s \\\\Sigma^{2}+r^{6} r_s \\\\partial_{r}{\\\\Sigma}-r^{5} r_s^{2} \\\\partial_{r}{\\\\Sigma}-2r^{5} \\\\Sigma \\\\partial_{r}{\\\\Sigma}-r^{4} r_s^{2} \\\\Sigma+2r^{4} r_s \\\\Sigma \\\\partial_{r}{\\\\Sigma}+r^{4} \\\\Sigma^{2}\\\\right) \\\\sin{\\\\theta} \\\\cos{\\\\theta}+\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\sin{2\\\\theta}+a^{2} \\\\partial_{\\\\theta}{\\\\Sigma}+r^{2} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma-\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\partial_{\\\\theta}{\\\\Sigma}+\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma \\\\partial_{\\\\theta}{\\\\Sigma}-\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma+\\\\left(a^{2}+r^{2}\\\\right) \\\\left(2r^{2}-\\\\Sigma\\\\right)\\\\right) \\\\Sigma \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\tan{\\\\theta}}{4\\\\left(r r_s-\\\\Sigma\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2} \\\\tan{\\\\theta}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{\\\\theta}{}^{r}{}_{r}= & \\\\frac{\\\\frac{1}{2}a^{2} \\\\sin{2\\\\theta} \\\\partial_{r}{\\\\Sigma}+r \\\\partial_{\\\\theta}{\\\\Sigma}}{\\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{r}{}^{r}{}_{\\\\theta}= &  - \\\\frac{\\\\frac{1}{2}a^{2} \\\\sin{2\\\\theta} \\\\partial_{r}{\\\\Sigma}+r \\\\partial_{\\\\theta}{\\\\Sigma}}{\\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{\\\\theta}{}^{\\\\theta}{}_{r}= & \\\\frac{\\\\frac{1}{2}a^{2} \\\\sin{2\\\\theta} \\\\partial_{r}{\\\\Sigma}+r \\\\partial_{\\\\theta}{\\\\Sigma}}{\\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{r}{}^{\\\\theta}{}_{\\\\theta}= &  - \\\\frac{\\\\frac{1}{2}a^{2} \\\\sin{2\\\\theta} \\\\partial_{r}{\\\\Sigma}+r \\\\partial_{\\\\theta}{\\\\Sigma}}{\\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{\\\\theta}{}^{\\\\phi}{}_{r}= & \\\\frac{a^{4} r r_s^{2} \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{\\\\theta}^{4}-a^{2} r r_s^{2} \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right) \\\\left(2a^{2} r^{3} r_s-2a^{2} r^{2} \\\\Sigma-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}+2r^{5} r_s-2r^{4} \\\\Sigma+r^{3} r_s \\\\Sigma-r^{2} \\\\Sigma^{2}\\\\right) \\\\sin{\\\\theta}^{2}-2a^{2} r_s \\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{4} r^{2} r_s \\\\sin{\\\\theta}^{4} \\\\partial_{r}{\\\\Sigma}-a^{4} r^{2} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}+2a^{4} r \\\\Sigma \\\\sin{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}-a^{4} \\\\Sigma^{2} \\\\sin{\\\\theta}^{2}-a^{2} r^{4} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}-a^{2} r^{3} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}+a^{2} r^{3} r_s^{2} \\\\partial_{r}{\\\\Sigma}-2a^{2} r^{3} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2a^{2} r^{3} \\\\Sigma \\\\sin{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}+a^{2} r^{2} r_s^{2} \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r^{2} r_s^{2} \\\\Sigma-2a^{2} r^{2} r_s \\\\Sigma \\\\partial_{r}{\\\\Sigma}+a^{2} r^{2} \\\\Sigma^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma^{2}+a^{2} r \\\\Sigma^{2} \\\\partial_{r}{\\\\Sigma}-a^{2} \\\\Sigma^{3}+r^{5} r_s^{2} \\\\partial_{r}{\\\\Sigma}+r^{4} r_s^{2} \\\\Sigma-2r^{4} r_s \\\\Sigma \\\\partial_{r}{\\\\Sigma}%\\n-2r^{3} r_s \\\\Sigma^{2}+r^{3} \\\\Sigma^{2} \\\\partial_{r}{\\\\Sigma}+r^{2} \\\\Sigma^{3}\\\\right) \\\\sin{\\\\theta}^{2}+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(-\\\\left(a^{2} r r_s \\\\sin{2\\\\theta}+a^{2} \\\\partial_{\\\\theta}{\\\\Sigma}+r^{2} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right) \\\\Sigma+\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right) \\\\partial_{\\\\theta}{\\\\Sigma}+\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(-2a^{2} r^{2} r_s \\\\sin{2\\\\theta}+a^{2} r_s \\\\Sigma \\\\sin{2\\\\theta}+a^{2} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{\\\\theta}{\\\\Sigma}-2r^{2} r_s \\\\partial_{\\\\theta}{\\\\Sigma}+4r \\\\Sigma \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\Sigma\\\\right) \\\\tan{\\\\theta}}{2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2} \\\\tan{\\\\theta}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{\\\\theta}{}^{t}{}_{r}= & a r_s \\\\left(-2a^{6} r^{3} r_s \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}+2a^{6} r^{3} r_s \\\\cos{\\\\theta}^{5}-4a^{6} r^{3} r_s \\\\cos{\\\\theta}^{3}+2a^{6} r^{3} r_s \\\\cos{\\\\theta}-2a^{6} r^{2} r_s \\\\cos{\\\\theta}^{5} \\\\partial_{r}{\\\\Sigma}+2a^{6} r^{2} r_s \\\\cos{\\\\theta}^{3} \\\\partial_{r}{\\\\Sigma}+a^{6} r r_s \\\\Sigma \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}-a^{6} r r_s \\\\Sigma \\\\cos{\\\\theta}^{5}+2a^{6} r r_s \\\\Sigma \\\\cos{\\\\theta}^{3}-a^{6} r r_s \\\\Sigma \\\\cos{\\\\theta}+4a^{6} r \\\\Sigma \\\\cos{\\\\theta}^{3} \\\\partial_{r}{\\\\Sigma}-4a^{6} r \\\\Sigma \\\\cos{\\\\theta} \\\\partial_{r}{\\\\Sigma}-2a^{6} \\\\Sigma^{2} \\\\cos{\\\\theta}^{3}+2a^{6} \\\\Sigma^{2} \\\\cos{\\\\theta}-2a^{4} r^{5} r_s \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}+2a^{4} r^{5} r_s \\\\cos{\\\\theta}^{5}-4a^{4} r^{5} r_s \\\\cos{\\\\theta}^{3}+2a^{4} r^{5} r_s \\\\cos{\\\\theta}-2a^{4} r^{4} r_s^{2} \\\\cos{\\\\theta}^{5}%\\n+2a^{4} r^{4} r_s^{2} \\\\cos{\\\\theta}^{3}-2a^{4} r^{4} r_s \\\\cos{\\\\theta}^{5} \\\\partial_{r}{\\\\Sigma}+2a^{4} r^{4} r_s \\\\cos{\\\\theta} \\\\partial_{r}{\\\\Sigma}+2a^{4} r^{3} r_s^{2} \\\\cos{\\\\theta}^{5} \\\\partial_{r}{\\\\Sigma}-2a^{4} r^{3} r_s^{2} \\\\cos{\\\\theta}^{3} \\\\partial_{r}{\\\\Sigma}-a^{4} r^{3} r_s \\\\Sigma \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}+3a^{4} r^{3} r_s \\\\Sigma \\\\cos{\\\\theta}^{5}-2a^{4} r^{3} r_s \\\\Sigma \\\\cos{\\\\theta}^{3}-3a^{4} r^{3} r_s \\\\Sigma \\\\cos{\\\\theta}-2a^{4} r^{3} r_s \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}{\\\\Sigma}+2a^{4} r^{3} r_s \\\\sin{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}+8a^{4} r^{3} \\\\Sigma \\\\cos{\\\\theta}^{3} \\\\partial_{r}{\\\\Sigma}-8a^{4} r^{3} \\\\Sigma \\\\cos{\\\\theta} \\\\partial_{r}{\\\\Sigma}-a^{4} r^{2} r_s^{2} \\\\Sigma \\\\cos{\\\\theta}^{5}+a^{4} r^{2} r_s^{2} \\\\Sigma \\\\cos{\\\\theta}^{3}-4a^{4} r^{2} r_s \\\\Sigma \\\\cos{\\\\theta}^{3} \\\\partial_{r}{\\\\Sigma}+4a^{4} r^{2} r_s \\\\Sigma \\\\cos{\\\\theta} \\\\partial_{r}{\\\\Sigma}-2a^{4} r^{2} \\\\Sigma^{2} \\\\cos{\\\\theta}^{3}+4a^{4} r^{2} \\\\Sigma^{2} \\\\cos{\\\\theta}-4a^{4} r^{2} \\\\Sigma \\\\sin{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}%\\n+2a^{4} r r_s \\\\Sigma^{2} \\\\cos{\\\\theta}^{3}-a^{4} r r_s \\\\Sigma^{2} \\\\cos{\\\\theta}-a^{4} \\\\Sigma^{3} \\\\cos{\\\\theta}+a^{4} \\\\Sigma^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}-2a^{2} r^{6} r_s^{2} \\\\cos{\\\\theta}^{3}+2a^{2} r^{6} r_s^{2} \\\\cos{\\\\theta}-2a^{2} r^{6} r_s \\\\cos{\\\\theta}^{3} \\\\partial_{r}{\\\\Sigma}+2a^{2} r^{6} r_s \\\\cos{\\\\theta} \\\\partial_{r}{\\\\Sigma}+2a^{2} r^{5} r_s^{2} \\\\cos{\\\\theta}^{3} \\\\partial_{r}{\\\\Sigma}-2a^{2} r^{5} r_s^{2} \\\\cos{\\\\theta} \\\\partial_{r}{\\\\Sigma}+4a^{2} r^{5} r_s \\\\Sigma \\\\cos{\\\\theta}^{3}-8a^{2} r^{5} r_s \\\\Sigma \\\\cos{\\\\theta}-2a^{2} r^{5} r_s \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}{\\\\Sigma}+4a^{2} r^{5} r_s \\\\sin{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}+4a^{2} r^{5} \\\\Sigma \\\\cos{\\\\theta}^{3} \\\\partial_{r}{\\\\Sigma}-4a^{2} r^{5} \\\\Sigma \\\\cos{\\\\theta} \\\\partial_{r}{\\\\Sigma}+a^{2} r^{4} r_s^{2} \\\\Sigma \\\\cos{\\\\theta}^{3}-a^{2} r^{4} r_s^{2} \\\\Sigma \\\\cos{\\\\theta}-4a^{2} r^{4} r_s \\\\Sigma \\\\cos{\\\\theta}^{3} \\\\partial_{r}{\\\\Sigma}+4a^{2} r^{4} r_s \\\\Sigma \\\\cos{\\\\theta} \\\\partial_{r}{\\\\Sigma}%\\n+4a^{2} r^{4} \\\\Sigma^{2} \\\\cos{\\\\theta}-8a^{2} r^{4} \\\\Sigma \\\\sin{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}-2r^{7} r_s \\\\Sigma \\\\cos{\\\\theta}+2r^{7} r_s \\\\sin{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}+2r^{6} \\\\Sigma^{2} \\\\cos{\\\\theta}-4r^{6} \\\\Sigma \\\\sin{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}-r^{5} r_s \\\\Sigma^{2} \\\\cos{\\\\theta}+r^{4} \\\\Sigma^{3} \\\\cos{\\\\theta}-r^{4} \\\\Sigma^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\frac{\\\\sin{\\\\theta}}{2\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{r}{}^{\\\\phi}{}_{\\\\theta}= & \\\\frac{-a^{4} r r_s^{2} \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{\\\\theta}^{4}+a^{2} r r_s^{2} \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right) \\\\left(2a^{2} r^{3} r_s-2a^{2} r^{2} \\\\Sigma-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}+2r^{5} r_s-2r^{4} \\\\Sigma+r^{3} r_s \\\\Sigma-r^{2} \\\\Sigma^{2}\\\\right) \\\\sin{\\\\theta}^{2}+2a^{2} r_s \\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{4} r^{2} r_s \\\\sin{\\\\theta}^{4} \\\\partial_{r}{\\\\Sigma}-a^{4} r^{2} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}+2a^{4} r \\\\Sigma \\\\sin{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}-a^{4} \\\\Sigma^{2} \\\\sin{\\\\theta}^{2}-a^{2} r^{4} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}-a^{2} r^{3} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}+a^{2} r^{3} r_s^{2} \\\\partial_{r}{\\\\Sigma}-2a^{2} r^{3} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2a^{2} r^{3} \\\\Sigma \\\\sin{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}+a^{2} r^{2} r_s^{2} \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r^{2} r_s^{2} \\\\Sigma-2a^{2} r^{2} r_s \\\\Sigma \\\\partial_{r}{\\\\Sigma}+a^{2} r^{2} \\\\Sigma^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma^{2}+a^{2} r \\\\Sigma^{2} \\\\partial_{r}{\\\\Sigma}-a^{2} \\\\Sigma^{3}+r^{5} r_s^{2} \\\\partial_{r}{\\\\Sigma}+r^{4} r_s^{2} \\\\Sigma-2r^{4} r_s \\\\Sigma \\\\partial_{r}{\\\\Sigma}%\\n-2r^{3} r_s \\\\Sigma^{2}+r^{3} \\\\Sigma^{2} \\\\partial_{r}{\\\\Sigma}+r^{2} \\\\Sigma^{3}\\\\right) \\\\sin{\\\\theta}^{2}+\\\\left(-r r_s+\\\\Sigma\\\\right) \\\\left(-\\\\left(a^{2} r r_s \\\\sin{2\\\\theta}+a^{2} \\\\partial_{\\\\theta}{\\\\Sigma}+r^{2} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right) \\\\Sigma+\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right) \\\\partial_{\\\\theta}{\\\\Sigma}+\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(-2a^{2} r^{2} r_s \\\\sin{2\\\\theta}+a^{2} r_s \\\\Sigma \\\\sin{2\\\\theta}+a^{2} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{\\\\theta}{\\\\Sigma}-2r^{2} r_s \\\\partial_{\\\\theta}{\\\\Sigma}+4r \\\\Sigma \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\Sigma\\\\right) \\\\tan{\\\\theta}}{2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2} \\\\tan{\\\\theta}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{r}{}^{t}{}_{\\\\theta}= & a r_s \\\\left(2a^{6} r^{3} r_s \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}-2a^{6} r^{3} r_s \\\\cos{\\\\theta}^{5}+4a^{6} r^{3} r_s \\\\cos{\\\\theta}^{3}-2a^{6} r^{3} r_s \\\\cos{\\\\theta}+2a^{6} r^{2} r_s \\\\cos{\\\\theta}^{5} \\\\partial_{r}{\\\\Sigma}-2a^{6} r^{2} r_s \\\\cos{\\\\theta}^{3} \\\\partial_{r}{\\\\Sigma}-a^{6} r r_s \\\\Sigma \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}+a^{6} r r_s \\\\Sigma \\\\cos{\\\\theta}^{5}-2a^{6} r r_s \\\\Sigma \\\\cos{\\\\theta}^{3}+a^{6} r r_s \\\\Sigma \\\\cos{\\\\theta}-4a^{6} r \\\\Sigma \\\\cos{\\\\theta}^{3} \\\\partial_{r}{\\\\Sigma}+4a^{6} r \\\\Sigma \\\\cos{\\\\theta} \\\\partial_{r}{\\\\Sigma}+2a^{6} \\\\Sigma^{2} \\\\cos{\\\\theta}^{3}-2a^{6} \\\\Sigma^{2} \\\\cos{\\\\theta}+2a^{4} r^{5} r_s \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}-2a^{4} r^{5} r_s \\\\cos{\\\\theta}^{5}+4a^{4} r^{5} r_s \\\\cos{\\\\theta}^{3}-2a^{4} r^{5} r_s \\\\cos{\\\\theta}+2a^{4} r^{4} r_s^{2} \\\\cos{\\\\theta}^{5}%\\n-2a^{4} r^{4} r_s^{2} \\\\cos{\\\\theta}^{3}+2a^{4} r^{4} r_s \\\\cos{\\\\theta}^{5} \\\\partial_{r}{\\\\Sigma}-2a^{4} r^{4} r_s \\\\cos{\\\\theta} \\\\partial_{r}{\\\\Sigma}-2a^{4} r^{3} r_s^{2} \\\\cos{\\\\theta}^{5} \\\\partial_{r}{\\\\Sigma}+2a^{4} r^{3} r_s^{2} \\\\cos{\\\\theta}^{3} \\\\partial_{r}{\\\\Sigma}+a^{4} r^{3} r_s \\\\Sigma \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}-3a^{4} r^{3} r_s \\\\Sigma \\\\cos{\\\\theta}^{5}+2a^{4} r^{3} r_s \\\\Sigma \\\\cos{\\\\theta}^{3}+3a^{4} r^{3} r_s \\\\Sigma \\\\cos{\\\\theta}+2a^{4} r^{3} r_s \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}{\\\\Sigma}-2a^{4} r^{3} r_s \\\\sin{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}-8a^{4} r^{3} \\\\Sigma \\\\cos{\\\\theta}^{3} \\\\partial_{r}{\\\\Sigma}+8a^{4} r^{3} \\\\Sigma \\\\cos{\\\\theta} \\\\partial_{r}{\\\\Sigma}+a^{4} r^{2} r_s^{2} \\\\Sigma \\\\cos{\\\\theta}^{5}-a^{4} r^{2} r_s^{2} \\\\Sigma \\\\cos{\\\\theta}^{3}+4a^{4} r^{2} r_s \\\\Sigma \\\\cos{\\\\theta}^{3} \\\\partial_{r}{\\\\Sigma}-4a^{4} r^{2} r_s \\\\Sigma \\\\cos{\\\\theta} \\\\partial_{r}{\\\\Sigma}+2a^{4} r^{2} \\\\Sigma^{2} \\\\cos{\\\\theta}^{3}-4a^{4} r^{2} \\\\Sigma^{2} \\\\cos{\\\\theta}+4a^{4} r^{2} \\\\Sigma \\\\sin{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}%\\n-2a^{4} r r_s \\\\Sigma^{2} \\\\cos{\\\\theta}^{3}+a^{4} r r_s \\\\Sigma^{2} \\\\cos{\\\\theta}+a^{4} \\\\Sigma^{3} \\\\cos{\\\\theta}-a^{4} \\\\Sigma^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}+2a^{2} r^{6} r_s^{2} \\\\cos{\\\\theta}^{3}-2a^{2} r^{6} r_s^{2} \\\\cos{\\\\theta}+2a^{2} r^{6} r_s \\\\cos{\\\\theta}^{3} \\\\partial_{r}{\\\\Sigma}-2a^{2} r^{6} r_s \\\\cos{\\\\theta} \\\\partial_{r}{\\\\Sigma}-2a^{2} r^{5} r_s^{2} \\\\cos{\\\\theta}^{3} \\\\partial_{r}{\\\\Sigma}+2a^{2} r^{5} r_s^{2} \\\\cos{\\\\theta} \\\\partial_{r}{\\\\Sigma}-4a^{2} r^{5} r_s \\\\Sigma \\\\cos{\\\\theta}^{3}+8a^{2} r^{5} r_s \\\\Sigma \\\\cos{\\\\theta}+2a^{2} r^{5} r_s \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}{\\\\Sigma}-4a^{2} r^{5} r_s \\\\sin{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}-4a^{2} r^{5} \\\\Sigma \\\\cos{\\\\theta}^{3} \\\\partial_{r}{\\\\Sigma}+4a^{2} r^{5} \\\\Sigma \\\\cos{\\\\theta} \\\\partial_{r}{\\\\Sigma}-a^{2} r^{4} r_s^{2} \\\\Sigma \\\\cos{\\\\theta}^{3}+a^{2} r^{4} r_s^{2} \\\\Sigma \\\\cos{\\\\theta}+4a^{2} r^{4} r_s \\\\Sigma \\\\cos{\\\\theta}^{3} \\\\partial_{r}{\\\\Sigma}-4a^{2} r^{4} r_s \\\\Sigma \\\\cos{\\\\theta} \\\\partial_{r}{\\\\Sigma}%\\n-4a^{2} r^{4} \\\\Sigma^{2} \\\\cos{\\\\theta}+8a^{2} r^{4} \\\\Sigma \\\\sin{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}+2r^{7} r_s \\\\Sigma \\\\cos{\\\\theta}-2r^{7} r_s \\\\sin{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}-2r^{6} \\\\Sigma^{2} \\\\cos{\\\\theta}+4r^{6} \\\\Sigma \\\\sin{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}+r^{5} r_s \\\\Sigma^{2} \\\\cos{\\\\theta}-r^{4} \\\\Sigma^{3} \\\\cos{\\\\theta}+r^{4} \\\\Sigma^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\frac{\\\\sin{\\\\theta}}{2\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{r}{}^{t}{}_{\\\\phi}= & a r_s \\\\left(\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(4\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(2a^{4} r^{3} r_s \\\\cos{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}-2a^{4} r^{2} r_s \\\\Sigma \\\\cos{\\\\theta}^{2}-4a^{4} r^{2} \\\\Sigma \\\\partial_{r}{\\\\Sigma}+4a^{4} r \\\\Sigma^{2}-a^{4} r_s \\\\Sigma^{2} \\\\cos{\\\\theta}^{2}+a^{4} \\\\Sigma^{2} \\\\partial_{r}{\\\\Sigma}+2a^{2} r^{5} r_s \\\\cos{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}+2a^{2} r^{5} r_s \\\\partial_{r}{\\\\Sigma}-6a^{2} r^{4} r_s \\\\Sigma \\\\cos{\\\\theta}^{2}+2a^{2} r^{4} r_s \\\\Sigma-8a^{2} r^{4} \\\\Sigma \\\\partial_{r}{\\\\Sigma}+8a^{2} r^{3} \\\\Sigma^{2}-a^{2} r^{2} r_s \\\\Sigma^{2} \\\\cos{\\\\theta}^{2}-3a^{2} r^{2} r_s \\\\Sigma^{2}+4a^{2} r \\\\Sigma^{3}+2r^{7} r_s \\\\partial_{r}{\\\\Sigma}-2r^{6} r_s \\\\Sigma-4r^{6} \\\\Sigma \\\\partial_{r}{\\\\Sigma}+4r^{5} \\\\Sigma^{2}%\\n+r^{4} r_s \\\\Sigma^{2}-r^{4} \\\\Sigma^{2} \\\\partial_{r}{\\\\Sigma}\\\\right) \\\\Delta+\\\\left(a^{4} r \\\\left(\\\\cos{4\\\\theta}-1\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right)+2\\\\left(2r \\\\Delta-\\\\left(2r-r_s\\\\right) \\\\Sigma\\\\right) \\\\left(2a^{2} r^{3} r_s-2a^{2} r^{2} \\\\Sigma-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}+2r^{5} r_s-2r^{4} \\\\Sigma+r^{3} r_s \\\\Sigma-r^{2} \\\\Sigma^{2}\\\\right)\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)\\\\right)+2\\\\left(r_s \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)+\\\\left(-r r_s+\\\\Sigma\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right)\\\\right) \\\\left(2a^{2} r^{3} r_s-2a^{2} r^{2} \\\\Sigma-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}+2r^{5} r_s-2r^{4} \\\\Sigma+r^{3} r_s \\\\Sigma-r^{2} \\\\Sigma^{2}\\\\right) \\\\Delta\\\\right) \\\\frac{\\\\sin{\\\\theta}^{2}}{8\\\\left(r r_s-\\\\Sigma\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Delta \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{\\\\theta}{}^{t}{}_{\\\\phi}= & a r_s \\\\left(-a^{2} r \\\\left(r r_s-\\\\Sigma\\\\right)^{2} \\\\left(2a^{4} r^{2} r_s \\\\cos{\\\\theta}^{2}-a^{4} r_s \\\\Sigma \\\\cos{\\\\theta}^{2}+2a^{2} r^{4} r_s \\\\cos{\\\\theta}^{2}+2a^{2} r^{4} r_s-2a^{2} r^{3} r_s^{2} \\\\cos{\\\\theta}^{2}-a^{2} r^{2} r_s \\\\Sigma \\\\cos{\\\\theta}^{2}-a^{2} r^{2} r_s \\\\Sigma+a^{2} r r_s^{2} \\\\Sigma \\\\cos{\\\\theta}^{2}+2a^{2} r \\\\Sigma^{2}+2r^{6} r_s-2r^{5} r_s^{2}-r^{4} r_s \\\\Sigma+r^{3} r_s^{2} \\\\Sigma+2r^{3} \\\\Sigma^{2}-2r^{2} r_s \\\\Sigma^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}-a^{2} \\\\left(r r_s-\\\\Sigma\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(4a^{2} r^{2}-a^{2} \\\\Sigma+4r^{4}-2r^{3} r_s+r^{2} \\\\Sigma\\\\right) \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(\\\\left(2a^{2} r^{2}+a^{2} r r_s-2a^{2} \\\\Sigma+2r^{4}-r^{3} r_s+2r^{2} \\\\Sigma\\\\right) \\\\sin{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}+2\\\\left(-2a^{2} r^{3} r_s+2a^{2} r^{2} \\\\Sigma+a^{2} r r_s \\\\Sigma-a^{2} \\\\Sigma^{2}-2r^{5} r_s+2r^{4} \\\\Sigma-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right) \\\\cos{\\\\theta}\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma-\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\sin{2\\\\theta}+a^{2} \\\\partial_{\\\\theta}{\\\\Sigma}+r^{2} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\left(2a^{2} r^{3} r_s-2a^{2} r^{2} \\\\Sigma-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}+2r^{5} r_s-2r^{4} \\\\Sigma+r^{3} r_s \\\\Sigma-r^{2} \\\\Sigma^{2}\\\\right) \\\\Sigma \\\\sin{\\\\theta}+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(2a^{2} r^{3} r_s-2a^{2} r^{2} \\\\Sigma-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}+2r^{5} r_s-2r^{4} \\\\Sigma+r^{3} r_s \\\\Sigma-r^{2} \\\\Sigma^{2}\\\\right) \\\\sin{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}-\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(2a^{2} r^{3} r_s-2a^{2} r^{2} \\\\Sigma-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}+2r^{5} r_s-2r^{4} \\\\Sigma+r^{3} r_s \\\\Sigma-r^{2} \\\\Sigma^{2}\\\\right) \\\\Sigma \\\\sin{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\frac{\\\\sin{\\\\theta}}{2\\\\left(r r_s-\\\\Sigma\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{r}{}^{t}{}_{\\\\phi}= & a r_s \\\\left(-a^{2} r r_s \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{\\\\theta}^{2}-a^{2} \\\\left(2r \\\\left(r_s-\\\\partial_{r}{\\\\Sigma}\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\Sigma+2r \\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\partial_{r}{\\\\Sigma}-2r \\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(-a^{2} r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\partial_{r}{\\\\Sigma}-3r^{2} r_s+r^{2} \\\\partial_{r}{\\\\Sigma}+2r \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\Sigma+\\\\left(r r_s-\\\\Sigma\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(4a^{2} r^{2}-a^{2} \\\\Sigma+4r^{4}-2r^{3} r_s+r^{2} \\\\Sigma\\\\right)-2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma+r \\\\left(a^{2} r_s-a^{2} \\\\partial_{r}{\\\\Sigma}+3r^{2} r_s-r^{2} \\\\partial_{r}{\\\\Sigma}-2r r_s^{2}+r r_s \\\\partial_{r}{\\\\Sigma}-2r \\\\Sigma+r_s \\\\Sigma\\\\right)\\\\right) \\\\Sigma\\\\right) \\\\sin{\\\\theta}^{2}+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right) \\\\left(2a^{2} r^{3} r_s-2a^{2} r^{2} \\\\Sigma-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}+2r^{5} r_s-2r^{4} \\\\Sigma+r^{3} r_s \\\\Sigma-r^{2} \\\\Sigma^{2}\\\\right)\\\\right) \\\\sin{\\\\theta} \\\\frac{\\\\cos{\\\\theta}}{2\\\\left(r r_s-\\\\Sigma\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{\\\\theta}{}^{t}{}_{\\\\phi}= & a r r_s \\\\left(4a^{2} \\\\left(a^{2} r r_s \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{\\\\theta} \\\\sin{2\\\\theta}+2\\\\left(-r r_s+\\\\Sigma\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right) \\\\cos{\\\\theta}\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\cos{\\\\theta}-4a^{2} \\\\left(-2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\sin{2\\\\theta}+a^{2} \\\\partial_{\\\\theta}{\\\\Sigma}+r^{2} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\Sigma \\\\sin{\\\\theta} \\\\cos{\\\\theta}+2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(-4a^{2} r r_s \\\\cos{2\\\\theta}-2a^{2} r r_s+4a^{2} \\\\Sigma \\\\cos{2\\\\theta}+2a^{2} \\\\Sigma+a^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}-4r^{3} r_s \\\\cos{2\\\\theta}-2r^{3} r_s+4r^{2} r_s^{2} \\\\cos{2\\\\theta}+2r^{2} r_s^{2}+4r^{2} \\\\Sigma \\\\cos{2\\\\theta}+2r^{2} \\\\Sigma+r^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}-4r r_s \\\\Sigma \\\\cos{2\\\\theta}-2r r_s \\\\Sigma-r r_s \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\Sigma-2\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\Sigma \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right)-\\\\left(r r_s-\\\\Sigma\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{6} \\\\left(\\\\cos{4\\\\theta}-1\\\\right)+a^{4} r^{2} \\\\left(\\\\cos{4\\\\theta}-1\\\\right)-a^{4} r r_s \\\\left(\\\\cos{4\\\\theta}-1\\\\right)+8a^{2} r^{2} \\\\Delta-4a^{2} \\\\Delta \\\\Sigma+8r^{4} \\\\Delta+4r^{2} \\\\Delta \\\\Sigma\\\\right)\\\\right) \\\\frac{\\\\sin{\\\\theta}^{2}}{8\\\\left(r r_s-\\\\Sigma\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{t}{}^{t}{}_{\\\\phi}= & r_s \\\\left(2a^{2} r \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+\\\\left(a^{2}+r^{2}\\\\right) \\\\Sigma^{2}\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{2\\\\theta} \\\\cos{\\\\theta}-a^{2} r_s \\\\left(4a^{2} r^{2} \\\\left(a^{2} \\\\sin{\\\\theta}^{2}+\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\cos{\\\\theta}^{2}+\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(2a^{2} r^{3} r_s-2a^{2} r^{2} \\\\Sigma-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}+2r^{5} r_s-2r^{4} \\\\Sigma+r^{3} r_s \\\\Sigma-r^{2} \\\\Sigma^{2}\\\\right) \\\\Delta\\\\right) \\\\sin{\\\\theta}^{3}-\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(-2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}+a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r \\\\Sigma^{2}\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Delta \\\\sin{\\\\theta}\\\\right) \\\\frac{\\\\sin{\\\\theta}}{4\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}_{t}{}^{t}{}_{\\\\phi}= & -a r^{2} r_s^{2} \\\\left(2a^{4} \\\\cos{\\\\theta}^{2}+2a^{2} r^{2} \\\\cos{\\\\theta}^{2}-2a^{2} r r_s \\\\cos{\\\\theta}^{2}-2r^{2} \\\\Delta+\\\\Delta \\\\Sigma\\\\right) \\\\frac{\\\\sin{\\\\theta}^{2}}{2\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{3}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{r}{}^{\\\\phi}{}_{\\\\phi}= & \\\\frac{-\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(\\\\left(4a^{2} \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right) \\\\cos{\\\\theta}^{2}+\\\\left(-2r \\\\Delta+\\\\left(2r-r_s\\\\right) \\\\Sigma\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right)\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)+2\\\\left(-\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right) \\\\partial_{r}{\\\\Sigma}+\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(4a^{2} r r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}+2r^{2} r_s \\\\partial_{r}{\\\\Sigma}+4r r_s \\\\Sigma-4r \\\\Sigma \\\\partial_{r}{\\\\Sigma}-2\\\\Sigma^{2}\\\\right) \\\\Sigma+\\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right) \\\\left(-a^{2} r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\partial_{r}{\\\\Sigma}-3r^{2} r_s+r^{2} \\\\partial_{r}{\\\\Sigma}+2r \\\\Sigma\\\\right) \\\\Sigma\\\\right) \\\\Delta\\\\right)+\\\\left(a^{2} r_s^{2} \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(2a^{2} r^{3} r_s-2a^{2} r^{2} \\\\Sigma-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}+2r^{5} r_s-2r^{4} \\\\Sigma+r^{3} r_s \\\\Sigma-r^{2} \\\\Sigma^{2}\\\\right) \\\\sin{\\\\theta}^{2}+\\\\left(-r r_s+\\\\Sigma\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right)^{2}\\\\right) \\\\Delta}{4\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Delta \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{\\\\theta}{}^{\\\\phi}{}_{\\\\phi}= & \\\\frac{-a^{2} r r_s^{2} \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right) \\\\left(2a^{2} r^{3} r_s-2a^{2} r^{2} \\\\Sigma-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}+2r^{5} r_s-2r^{4} \\\\Sigma+r^{3} r_s \\\\Sigma-r^{2} \\\\Sigma^{2}\\\\right) \\\\sin{\\\\theta}^{2}+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(\\\\left(-\\\\left(a^{2} r r_s \\\\sin{2\\\\theta}+a^{2} \\\\partial_{\\\\theta}{\\\\Sigma}+r^{2} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right) \\\\Sigma+\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right) \\\\partial_{\\\\theta}{\\\\Sigma}+\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(-2a^{2} r^{2} r_s \\\\sin{2\\\\theta}+a^{2} r_s \\\\Sigma \\\\sin{2\\\\theta}+a^{2} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{\\\\theta}{\\\\Sigma}-2r^{2} r_s \\\\partial_{\\\\theta}{\\\\Sigma}+4r \\\\Sigma \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\Sigma\\\\right) \\\\tan{\\\\theta}+\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(-4a^{4} r^{2} r_s \\\\sin{\\\\theta}^{4}+a^{4} r_s \\\\Sigma \\\\sin{\\\\theta}^{4}+2a^{2} r^{3} r_s^{2} \\\\sin{\\\\theta}^{2}-6a^{2} r^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2a^{2} r^{2} r_s \\\\Sigma+2a^{2} r \\\\Sigma^{2} \\\\sin{\\\\theta}^{2}-2a^{2} r \\\\Sigma^{2}+2r^{4} r_s \\\\Sigma-2r^{3} \\\\Sigma^{2}\\\\right)\\\\right)+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right)}{2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2} \\\\tan{\\\\theta}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{r}{}^{\\\\phi}{}_{\\\\phi}= & \\\\frac{-a^{4} r r_s^{2} \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{\\\\theta}^{4}+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(2a^{2} r_s \\\\left(a^{4} r^{2} r_s \\\\sin{\\\\theta}^{4} \\\\partial_{r}{\\\\Sigma}-a^{4} r^{2} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}+2a^{4} r \\\\Sigma \\\\sin{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}-a^{4} \\\\Sigma^{2} \\\\sin{\\\\theta}^{2}-a^{2} r^{4} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}-a^{2} r^{3} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}+a^{2} r^{3} r_s^{2} \\\\partial_{r}{\\\\Sigma}-2a^{2} r^{3} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2a^{2} r^{3} \\\\Sigma \\\\sin{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}+a^{2} r^{2} r_s^{2} \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r^{2} r_s^{2} \\\\Sigma-2a^{2} r^{2} r_s \\\\Sigma \\\\partial_{r}{\\\\Sigma}+a^{2} r^{2} \\\\Sigma^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma^{2}+a^{2} r \\\\Sigma^{2} \\\\partial_{r}{\\\\Sigma}-a^{2} \\\\Sigma^{3}+r^{5} r_s^{2} \\\\partial_{r}{\\\\Sigma}+r^{4} r_s^{2} \\\\Sigma-2r^{4} r_s \\\\Sigma \\\\partial_{r}{\\\\Sigma}%\\n-2r^{3} r_s \\\\Sigma^{2}+r^{3} \\\\Sigma^{2} \\\\partial_{r}{\\\\Sigma}+r^{2} \\\\Sigma^{3}\\\\right) \\\\sin{\\\\theta}^{2}+\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(-4a^{4} r^{2} r_s \\\\sin{\\\\theta}^{4}+a^{4} r_s \\\\Sigma \\\\sin{\\\\theta}^{4}+2a^{2} r^{3} r_s^{2} \\\\sin{\\\\theta}^{2}-6a^{2} r^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2a^{2} r^{2} r_s \\\\Sigma+2a^{2} r \\\\Sigma^{2} \\\\sin{\\\\theta}^{2}-2a^{2} r \\\\Sigma^{2}+2r^{4} r_s \\\\Sigma-2r^{3} \\\\Sigma^{2}\\\\right)\\\\right)+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right)}{2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2} \\\\tan{\\\\theta}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{\\\\theta}{}^{\\\\phi}{}_{\\\\phi}= & \\\\frac{\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(\\\\left(2a^{2} \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right) \\\\cos{\\\\theta}^{2}-r \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right) \\\\Delta\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\sin{\\\\theta}^{2}+2\\\\left(a^{2} r r_s \\\\sin{2\\\\theta}+a^{2} \\\\partial_{\\\\theta}{\\\\Sigma}+r^{2} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right) \\\\Sigma \\\\sin{\\\\theta} \\\\cos{\\\\theta}-2\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right) \\\\Sigma \\\\cos{\\\\theta}^{2}-4\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right) \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}+2\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(-5a^{4} r r_s \\\\Sigma \\\\sin{\\\\theta}^{5}+4a^{4} r r_s \\\\Sigma \\\\sin{\\\\theta}^{3}+a^{4} r r_s \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}+3a^{2} r^{2} r_s^{2} \\\\Sigma \\\\sin{\\\\theta}^{3}-2a^{2} r^{2} r_s^{2} \\\\Sigma \\\\sin{\\\\theta}+a^{2} r^{2} r_s^{2} \\\\cos{\\\\theta}^{3} \\\\partial_{\\\\theta}{\\\\Sigma}-a^{2} r^{2} r_s^{2} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}-6a^{2} r r_s \\\\Sigma^{2} \\\\sin{\\\\theta}^{3}+5a^{2} r r_s \\\\Sigma^{2} \\\\sin{\\\\theta}-4a^{2} r r_s \\\\Sigma \\\\cos{\\\\theta}^{3} \\\\partial_{\\\\theta}{\\\\Sigma}+2a^{2} r r_s \\\\Sigma \\\\cos{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}-a^{2} \\\\Sigma^{3} \\\\sin{\\\\theta}+3a^{2} \\\\Sigma^{2} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}+r^{3} r_s \\\\Sigma^{2} \\\\sin{\\\\theta}-2r^{3} r_s \\\\Sigma \\\\cos{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}-r^{2} \\\\Sigma^{3} \\\\sin{\\\\theta}+3r^{2} \\\\Sigma^{2} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\sin{\\\\theta}\\\\right) \\\\tan{\\\\theta}^{2}+2\\\\left(a^{4} r^{2} r_s^{2} \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{\\\\theta}^{4}+\\\\left(-r r_s+\\\\Sigma\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right)^{2}\\\\right) \\\\sin{\\\\theta}^{2}}{2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{t}{}^{\\\\phi}{}_{\\\\phi}= & a r^{2} r_s^{2} \\\\left(2a^{4} \\\\cos{\\\\theta}^{2}+2a^{2} r^{2} \\\\cos{\\\\theta}^{2}-2a^{2} r r_s \\\\cos{\\\\theta}^{2}-2r^{2} \\\\Delta+\\\\Delta \\\\Sigma\\\\right) \\\\frac{\\\\sin{\\\\theta}^{2}}{2\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{3}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}_{t}{}^{\\\\phi}{}_{\\\\phi}= & -r r_s \\\\frac{2a^{4} r r_s \\\\cos{\\\\theta}^{2}-2a^{4} \\\\Sigma \\\\cos{\\\\theta}^{2}+2a^{2} r^{3} r_s \\\\cos{\\\\theta}^{2}-2a^{2} r^{2} r_s^{2} \\\\cos{\\\\theta}^{2}-2a^{2} r^{2} \\\\Sigma \\\\cos{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\cos{\\\\theta}^{2}-2r^{3} r_s \\\\Delta+2r^{2} \\\\Delta \\\\Sigma+r r_s \\\\Delta \\\\Sigma-\\\\Delta \\\\Sigma^{2}}{2\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{3}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{r}{}^{t}{}_{t}= & r_s \\\\frac{2r_s \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} \\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(2a^{2} r^{3} r_s-2a^{2} r^{2} \\\\Sigma-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}+2r^{5} r_s-2r^{4} \\\\Sigma+r^{3} r_s \\\\Sigma-r^{2} \\\\Sigma^{2}\\\\right) \\\\sin{\\\\theta}^{2}+\\\\left(-2r^{2}+\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2}\\\\right) \\\\Delta+\\\\left(-r r_s+\\\\Sigma\\\\right) \\\\left(a^{4} r \\\\left(\\\\cos{4\\\\theta}-1\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right)+2\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(2r \\\\Delta-\\\\left(2r-r_s\\\\right) \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)-4\\\\left(\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(r_s-\\\\partial_{r}{\\\\Sigma}\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma+\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\partial_{r}{\\\\Sigma}-\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(-a^{2} r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\partial_{r}{\\\\Sigma}-3r^{2} r_s+r^{2} \\\\partial_{r}{\\\\Sigma}+2r \\\\Sigma\\\\right) \\\\Sigma-\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(\\\\left(4r-\\\\partial_{r}{\\\\Sigma}\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)-\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(-a^{2} r_s+a^{2} \\\\partial_{r}{\\\\Sigma}-3r^{2} r_s+r^{2} \\\\partial_{r}{\\\\Sigma}+2r \\\\Sigma\\\\right)\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma\\\\right) \\\\Delta}{8\\\\left(r r_s-\\\\Sigma\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Delta \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{\\\\theta}{}^{t}{}_{t}= & r_s \\\\frac{2a^{2} r r_s \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(r r_s-\\\\Sigma\\\\right)^{2} \\\\left(a^{4} \\\\cos{\\\\theta}^{2}+a^{2} r^{2} \\\\cos{\\\\theta}^{2}+a^{2} r^{2}-a^{2} r r_s \\\\cos{\\\\theta}^{2}+r^{4}-r^{3} r_s\\\\right) \\\\sin{\\\\theta} \\\\cos{\\\\theta}-a^{2} \\\\left(r r_s-\\\\Sigma\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(-4a^{2} r^{2}+a^{2} \\\\Sigma-4r^{4}+2r^{3} r_s+r^{2} \\\\Sigma\\\\right) \\\\sin{2\\\\theta}+2\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\sin{2\\\\theta}+a^{2} \\\\partial_{\\\\theta}{\\\\Sigma}+r^{2} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma-2\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\partial_{\\\\theta}{\\\\Sigma}+2\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma \\\\partial_{\\\\theta}{\\\\Sigma}-2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma+\\\\left(a^{2}+r^{2}\\\\right) \\\\left(2r^{2}-\\\\Sigma\\\\right)\\\\right) \\\\Sigma \\\\partial_{\\\\theta}{\\\\Sigma}}{4\\\\left(r r_s-\\\\Sigma\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{r}{}^{t}{}_{t}= & a^{2} r_s \\\\left(6a^{4} r^{3} r_s \\\\cos{\\\\theta}^{2}+2a^{4} r^{2} r_s \\\\cos{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}-4a^{4} r^{2} \\\\Sigma-2a^{4} r r_s \\\\Sigma \\\\cos{\\\\theta}^{2}-4a^{4} r \\\\Sigma \\\\partial_{r}{\\\\Sigma}+3a^{4} \\\\Sigma^{2}+6a^{2} r^{5} r_s \\\\cos{\\\\theta}^{2}+6a^{2} r^{5} r_s-2a^{2} r^{4} r_s^{2} \\\\cos{\\\\theta}^{2}+2a^{2} r^{4} r_s \\\\cos{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}+2a^{2} r^{4} r_s \\\\partial_{r}{\\\\Sigma}-8a^{2} r^{4} \\\\Sigma-2a^{2} r^{3} r_s^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}-4a^{2} r^{3} r_s \\\\Sigma \\\\cos{\\\\theta}^{2}-8a^{2} r^{3} \\\\Sigma \\\\partial_{r}{\\\\Sigma}+2a^{2} r^{2} r_s^{2} \\\\Sigma \\\\cos{\\\\theta}^{2}+4a^{2} r^{2} r_s \\\\Sigma \\\\partial_{r}{\\\\Sigma}+6a^{2} r^{2} \\\\Sigma^{2}-3a^{2} r r_s \\\\Sigma^{2}%\\n+6r^{7} r_s-2r^{6} r_s^{2}+2r^{6} r_s \\\\partial_{r}{\\\\Sigma}-4r^{6} \\\\Sigma-2r^{5} r_s^{2} \\\\partial_{r}{\\\\Sigma}-2r^{5} r_s \\\\Sigma-4r^{5} \\\\Sigma \\\\partial_{r}{\\\\Sigma}+4r^{4} r_s \\\\Sigma \\\\partial_{r}{\\\\Sigma}+3r^{4} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma^{2}\\\\right) \\\\sin{\\\\theta} \\\\frac{\\\\cos{\\\\theta}}{2\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{\\\\phi}{}^{t}{}_{t}= & r_s \\\\left(-2a^{2} r \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+\\\\left(a^{2}+r^{2}\\\\right) \\\\Sigma^{2}\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{2\\\\theta} \\\\cos{\\\\theta}+a^{2} r_s \\\\left(4a^{2} r^{2} \\\\left(a^{2} \\\\sin{\\\\theta}^{2}+\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\cos{\\\\theta}^{2}+\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(2a^{2} r^{3} r_s-2a^{2} r^{2} \\\\Sigma-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}+2r^{5} r_s-2r^{4} \\\\Sigma+r^{3} r_s \\\\Sigma-r^{2} \\\\Sigma^{2}\\\\right) \\\\Delta\\\\right) \\\\sin{\\\\theta}^{3}+\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(-2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{3}+a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{3}+2r \\\\Sigma^{2} \\\\sin{\\\\theta}\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Delta\\\\right) \\\\frac{\\\\sin{\\\\theta}}{4\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{\\\\theta}{}^{t}{}_{t}= & r r_s \\\\frac{8a^{4} r r_s \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\left(-a^{2} r r_s+a^{2} \\\\Sigma-r^{3} r_s+r^{2} r_s^{2}+r^{2} \\\\Sigma-r r_s \\\\Sigma+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right)\\\\right) \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{2}-4a^{2} \\\\left(\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\sin{2\\\\theta}+a^{2} \\\\partial_{\\\\theta}{\\\\Sigma}+r^{2} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\Sigma \\\\sin{2\\\\theta}-\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}-\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(-2a^{2} r r_s \\\\cos{2\\\\theta}+2a^{2} \\\\Sigma \\\\cos{2\\\\theta}+a^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}-2r^{3} r_s \\\\cos{2\\\\theta}+2r^{2} r_s^{2} \\\\cos{2\\\\theta}+2r^{2} \\\\Sigma \\\\cos{2\\\\theta}+r^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}-2r r_s \\\\Sigma \\\\cos{2\\\\theta}-r r_s \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\Sigma+\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\Sigma \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right)+\\\\left(r r_s-\\\\Sigma\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{6} \\\\left(\\\\cos{4\\\\theta}-1\\\\right)+a^{4} r^{2} \\\\left(\\\\cos{4\\\\theta}-1\\\\right)-a^{4} r r_s \\\\left(\\\\cos{4\\\\theta}-1\\\\right)+8a^{2} r^{2} \\\\Delta-4a^{2} \\\\Delta \\\\Sigma+8r^{4} \\\\Delta-4r^{2} \\\\Delta \\\\Sigma\\\\right)}{8\\\\left(r r_s-\\\\Sigma\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}_{\\\\phi}{}^{t}{}_{t}= & a r^{2} r_s^{2} \\\\left(2a^{4} \\\\cos{\\\\theta}^{2}+2a^{2} r^{2} \\\\cos{\\\\theta}^{2}-2a^{2} r r_s \\\\cos{\\\\theta}^{2}-2r^{2} \\\\Delta+\\\\Delta \\\\Sigma\\\\right) \\\\frac{\\\\sin{\\\\theta}^{2}}{2\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{3}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{r}{}^{\\\\phi}{}_{t}= & a r_s \\\\frac{-\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(r_s \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)+\\\\left(-r r_s+\\\\Sigma\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right)\\\\right) \\\\Delta \\\\tan{\\\\theta}+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(\\\\left(4a^{2} r \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right) \\\\sin{\\\\theta} \\\\cos{\\\\theta}-\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(2r \\\\Delta-\\\\left(2r-r_s\\\\right) \\\\Sigma\\\\right) \\\\tan{\\\\theta}\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)+2\\\\left(\\\\left(4r-\\\\partial_{r}{\\\\Sigma}\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma-\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\partial_{r}{\\\\Sigma}+\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(-a^{2} r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\partial_{r}{\\\\Sigma}-3r^{2} r_s+r^{2} \\\\partial_{r}{\\\\Sigma}+2r \\\\Sigma\\\\right) \\\\Sigma\\\\right) \\\\Delta \\\\tan{\\\\theta}\\\\right)}{4\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Delta \\\\Sigma^{2} \\\\tan{\\\\theta}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{\\\\theta}{}^{\\\\phi}{}_{t}= & a r_s \\\\frac{\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(r r_s \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)+\\\\left(-r r_s+\\\\Sigma\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right)\\\\right)+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(\\\\left(a^{2} \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\sin{\\\\theta}^{2}+2r^{2} \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right)\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)-\\\\left(-\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\sin{2\\\\theta}+a^{2} \\\\partial_{\\\\theta}{\\\\Sigma}+r^{2} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\Sigma+\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\partial_{\\\\theta}{\\\\Sigma}+\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\tan{\\\\theta}\\\\right)}{2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2} \\\\tan{\\\\theta}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{r}{}^{\\\\phi}{}_{t}= & a r_s \\\\frac{r \\\\left(a^{2} r_s \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+2\\\\left(-r r_s+\\\\Sigma\\\\right) \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right)\\\\right)+2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(2r \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\partial_{r}{\\\\Sigma}-2r \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right) \\\\left(-a^{2} r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\partial_{r}{\\\\Sigma}-3r^{2} r_s+r^{2} \\\\partial_{r}{\\\\Sigma}+2r \\\\Sigma\\\\right) \\\\Sigma+\\\\left(a^{2} \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\sin{\\\\theta}^{2}+2r^{2} \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right)\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)-2\\\\left(a^{2} \\\\sin{\\\\theta}^{2}-2r r_s+r \\\\partial_{r}{\\\\Sigma}+\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma\\\\right)}{4\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2} \\\\tan{\\\\theta}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{\\\\phi}{}^{\\\\phi}{}_{t}= & -a r^{2} r_s^{2} \\\\left(2a^{4} \\\\cos{\\\\theta}^{2}+2a^{2} r^{2} \\\\cos{\\\\theta}^{2}-2a^{2} r r_s \\\\cos{\\\\theta}^{2}-2r^{2} \\\\Delta+\\\\Delta \\\\Sigma\\\\right) \\\\frac{\\\\sin{\\\\theta}^{2}}{2\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{3}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{\\\\theta}{}^{\\\\phi}{}_{t}= & a r r_s \\\\frac{\\\\left(-r r_s+\\\\Sigma\\\\right) \\\\left(2\\\\left(\\\\left(a^{2} r r_s \\\\sin{2\\\\theta}+a^{2} \\\\partial_{\\\\theta}{\\\\Sigma}+r^{2} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\Sigma-\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right) \\\\sin{\\\\theta} \\\\cos{\\\\theta}+\\\\left(2a^{2} \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right) \\\\sin{\\\\theta} \\\\cos{\\\\theta}-\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\Delta \\\\tan{\\\\theta}\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\sin{\\\\theta} \\\\cos{\\\\theta}-\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(4a^{2} \\\\sin{\\\\theta}^{4}+a^{2} \\\\cos{2\\\\theta}-a^{2}-2r r_s+2\\\\Sigma-\\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\Sigma\\\\right) \\\\sin{\\\\theta}-\\\\left(a^{2} r r_s \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{\\\\theta} \\\\sin{2\\\\theta}+2\\\\left(-r r_s+\\\\Sigma\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right) \\\\cos{\\\\theta}\\\\right) \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right) \\\\sin{\\\\theta} \\\\cos{\\\\theta}}{2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2} \\\\sin{\\\\theta}^{3}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}_{\\\\phi}{}^{\\\\phi}{}_{t}= & r r_s \\\\frac{2a^{4} r r_s \\\\cos{\\\\theta}^{2}-2a^{4} \\\\Sigma \\\\cos{\\\\theta}^{2}+2a^{2} r^{3} r_s \\\\cos{\\\\theta}^{2}-2a^{2} r^{2} r_s^{2} \\\\cos{\\\\theta}^{2}-2a^{2} r^{2} \\\\Sigma \\\\cos{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\cos{\\\\theta}^{2}-2r^{3} r_s \\\\Delta+2r^{2} \\\\Delta \\\\Sigma+r r_s \\\\Delta \\\\Sigma-\\\\Delta \\\\Sigma^{2}}{2\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{3}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{r}{}^{r}{}_{\\\\phi}= & \\\\left(\\\\left(-r r_s+\\\\Sigma\\\\right) \\\\left(4a^{2} \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+\\\\left(a^{2}+r^{2}\\\\right) \\\\Sigma^{2}\\\\right) \\\\cos{\\\\theta}^{2}+\\\\left(-2r \\\\Delta+\\\\left(2r-r_s\\\\right) \\\\Sigma\\\\right) \\\\left(-2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}+a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r \\\\Sigma^{2}\\\\right)\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)+2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(6a^{2} r^{2} r_s \\\\Delta \\\\sin{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}-2a^{2} r^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2} \\\\partial_{r}{\\\\Delta}-4a^{2} r r_s \\\\Delta \\\\Sigma \\\\sin{\\\\theta}^{2}-2a^{2} r_s \\\\Delta \\\\Sigma \\\\sin{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}+a^{2} r_s \\\\Sigma^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{r}{\\\\Delta}-2r \\\\Delta \\\\Sigma^{2} \\\\partial_{r}{\\\\Sigma}+2r \\\\Sigma^{3} \\\\partial_{r}{\\\\Delta}+2\\\\Delta \\\\Sigma^{3}\\\\right)-\\\\left(a^{2} r_s^{2} \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(2a^{2} r^{3} r_s-2a^{2} r^{2} \\\\Sigma-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}+2r^{5} r_s-2r^{4} \\\\Sigma+r^{3} r_s \\\\Sigma-r^{2} \\\\Sigma^{2}\\\\right) \\\\sin{\\\\theta}^{2}+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(-2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}+a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r \\\\Sigma^{2}\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right)\\\\right) \\\\Delta\\\\right) \\\\frac{\\\\sin{\\\\theta}^{2}}{4\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{\\\\theta}{}^{r}{}_{\\\\phi}= & \\\\left(2\\\\left(-r r_s+\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(4a^{2} r^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}-3a^{2} r^{2} r_s \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}{\\\\Sigma}-2a^{2} r_s \\\\Sigma^{2} \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}+a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}{\\\\Sigma}-2r \\\\Sigma^{3} \\\\cos{\\\\theta}+r \\\\Sigma^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right)-\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{4} r_s \\\\sin{\\\\theta}^{4}+4a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}+2a^{2} r \\\\Sigma \\\\sin{\\\\theta}^{2}+2a^{2} r \\\\Sigma+2r^{3} \\\\Sigma\\\\right) \\\\Sigma \\\\cos{\\\\theta}+\\\\left(a^{4} r r_s^{2} \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{\\\\theta}^{4}+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(-2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}+a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r \\\\Sigma^{2}\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right)\\\\right) \\\\cos{\\\\theta}\\\\right) \\\\Delta \\\\frac{\\\\sin{\\\\theta}}{2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}_{r}{}^{r}{}_{\\\\phi}= & a r_s \\\\left(\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(r_s \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(-2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}+a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r \\\\Sigma^{2}\\\\right)\\\\right) \\\\Delta+\\\\left(-r r_s+\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(4a^{4} r \\\\sin{\\\\theta}^{4}-4a^{4} r \\\\sin{\\\\theta}^{2}+4a^{2} r \\\\Sigma \\\\sin{\\\\theta}^{2}-4a^{2} r \\\\Sigma-4r^{3} \\\\Delta+4r^{3} \\\\Sigma-2r^{2} r_s \\\\Sigma+2r \\\\Delta \\\\Sigma-2r \\\\Sigma^{2}+r_s \\\\Sigma^{2}\\\\right)-2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(3\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\Delta \\\\partial_{r}{\\\\Sigma}-\\\\left(\\\\left(4r-\\\\partial_{r}{\\\\Sigma}\\\\right) \\\\Delta+\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\partial_{r}{\\\\Delta}\\\\right) \\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)\\\\right) \\\\frac{\\\\sin{\\\\theta}^{2}}{4\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}_{\\\\theta}{}^{r}{}_{\\\\phi}= & a r_s \\\\left(-r \\\\left(a^{2} r_s \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right) \\\\left(-2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}+a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r \\\\Sigma^{2}\\\\right)\\\\right) \\\\sin{\\\\theta}+2\\\\left(a^{2} \\\\sin{\\\\theta}^{2}+2r^{2}\\\\right) \\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma \\\\sin{\\\\theta}+2\\\\left(-r r_s+\\\\Sigma\\\\right) \\\\left(3\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\sin{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}-\\\\left(2\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\cos{\\\\theta}-\\\\sin{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\tan{\\\\theta}\\\\right) \\\\Delta \\\\frac{\\\\sin{\\\\theta}}{4\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4} \\\\tan{\\\\theta}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{t}{}^{r}{}_{\\\\phi}= & a r_s \\\\left(2a^{2} r^{4} r_s^{2} \\\\cos{\\\\theta}^{2}-4a^{2} r^{3} r_s \\\\Sigma-a^{2} r^{2} r_s^{2} \\\\Sigma \\\\cos{\\\\theta}^{2}-2a^{2} r^{2} \\\\Sigma^{2} \\\\cos{\\\\theta}^{2}+4a^{2} r^{2} \\\\Sigma^{2}+a^{2} r r_s \\\\Sigma^{2} \\\\cos{\\\\theta}^{2}+a^{2} r r_s \\\\Sigma^{2}-a^{2} \\\\Sigma^{3}+2r^{6} r_s^{2}-4r^{5} r_s \\\\Sigma+r^{4} r_s^{2} \\\\Sigma+2r^{4} \\\\Sigma^{2}-2r^{3} r_s \\\\Sigma^{2}+r^{2} \\\\Sigma^{3}\\\\right) \\\\Delta \\\\sin{\\\\theta} \\\\frac{\\\\cos{\\\\theta}}{2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{3}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{r}{}^{\\\\theta}{}_{\\\\phi}= & \\\\left(a^{2} r r_s^{2} \\\\left(a^{2} \\\\sin{\\\\theta}^{2}+\\\\Sigma\\\\right) \\\\left(2a^{2} r^{3} r_s-2a^{2} r^{2} \\\\Sigma-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}+2r^{5} r_s-2r^{4} \\\\Sigma+r^{3} r_s \\\\Sigma-r^{2} \\\\Sigma^{2}\\\\right) \\\\sin{\\\\theta}^{2}+\\\\left(-r r_s+\\\\Sigma\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+\\\\left(a^{2}+r^{2}\\\\right) \\\\Sigma^{2}\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right)+2\\\\left(-r r_s+\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(3a^{4} r r_s \\\\sin{\\\\theta}^{4} \\\\partial_{r}{\\\\Sigma}-a^{4} r_s \\\\Sigma \\\\sin{\\\\theta}^{4}+4a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}-2a^{2} r_s \\\\Sigma^{2} \\\\sin{\\\\theta}^{2}+a^{2} \\\\Sigma^{2} \\\\partial_{r}{\\\\Sigma}+r^{2} \\\\Sigma^{2} \\\\partial_{r}{\\\\Sigma}-2r \\\\Sigma^{3}\\\\right)+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{4} r_s \\\\sin{\\\\theta}^{4}+4a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}+2a^{2} r \\\\Sigma \\\\sin{\\\\theta}^{2}+2a^{2} r \\\\Sigma+2r^{3} \\\\Sigma\\\\right) \\\\Sigma\\\\right) \\\\sin{\\\\theta} \\\\frac{\\\\cos{\\\\theta}}{2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{\\\\theta}{}^{\\\\theta}{}_{\\\\phi}= & \\\\frac{\\\\left(-r r_s+\\\\Sigma\\\\right) \\\\left(2a^{2} \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+\\\\left(a^{2}+r^{2}\\\\right) \\\\Sigma^{2}\\\\right) \\\\cos{\\\\theta}^{2}-r \\\\left(-2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}+a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r \\\\Sigma^{2}\\\\right) \\\\Delta\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\sin{\\\\theta}^{2}+\\\\left(-r r_s+\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(12a^{4} r r_s \\\\Sigma \\\\sin{\\\\theta}^{6}-10a^{4} r r_s \\\\Sigma \\\\sin{\\\\theta}^{4}+6a^{4} r r_s \\\\sin{\\\\theta}^{5} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}+16a^{2} r r_s \\\\Sigma^{2} \\\\sin{\\\\theta}^{4}+6a^{2} r r_s \\\\Sigma^{2} \\\\cos{2\\\\theta}-6a^{2} r r_s \\\\Sigma^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}-a^{2} r r_s \\\\Sigma \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}-2a^{2} \\\\Sigma^{3} \\\\cos{2\\\\theta}+a^{2} \\\\Sigma^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}-2r^{2} \\\\Sigma^{3} \\\\cos{2\\\\theta}+r^{2} \\\\Sigma^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right)+2\\\\left(-a^{4} r^{2} r_s^{2} \\\\left(a^{2} \\\\sin{\\\\theta}^{2}+\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{\\\\theta}^{4}+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+\\\\left(a^{2}+r^{2}\\\\right) \\\\Sigma^{2}\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right)\\\\right) \\\\cos{\\\\theta}^{2}}{2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}_{r}{}^{\\\\theta}{}_{\\\\phi}= & a r_s \\\\left(\\\\left(-2r^{2}+\\\\Sigma\\\\right) \\\\left(r r_s \\\\left(a^{2} \\\\sin{\\\\theta}^{2}+\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)+\\\\left(-r r_s+\\\\Sigma\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+\\\\left(a^{2}+r^{2}\\\\right) \\\\Sigma^{2}\\\\right)\\\\right)-\\\\left(a^{2} \\\\sin{\\\\theta}^{2}+2r^{2}\\\\right) \\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma+2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(3a^{2} r \\\\sin{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}-a^{2} \\\\Sigma \\\\sin{\\\\theta}^{2}+2r \\\\Sigma \\\\partial_{r}{\\\\Sigma}-\\\\Sigma^{2}\\\\right)\\\\right) \\\\sin{\\\\theta} \\\\frac{\\\\cos{\\\\theta}}{2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}_{\\\\theta}{}^{\\\\theta}{}_{\\\\phi}= & a r r_s \\\\frac{4\\\\left(-r r_s+\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(2a^{4} \\\\sin{\\\\theta}^{4}-2a^{4} \\\\sin{\\\\theta}^{2}+2a^{2} \\\\Sigma \\\\sin{\\\\theta}^{2}-2a^{2} \\\\Sigma-2r^{2} \\\\Delta+\\\\Delta \\\\Sigma\\\\right) \\\\sin{\\\\theta}^{2}+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(32a^{2} \\\\Sigma \\\\sin{\\\\theta}^{4}+12a^{2} \\\\Sigma \\\\cos{2\\\\theta}-12a^{2} \\\\Sigma+6a^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}-3a^{2} \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}-8\\\\Sigma^{2} \\\\cos{2\\\\theta}+8\\\\Sigma \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right)+8\\\\left(a^{2} r r_s \\\\left(a^{2} \\\\sin{\\\\theta}^{2}+\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{\\\\theta}^{2}+\\\\left(-r r_s+\\\\Sigma\\\\right) \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+\\\\left(a^{2}+r^{2}\\\\right) \\\\Sigma^{2}\\\\right)\\\\right) \\\\cos{\\\\theta}^{2}}{8\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{t}{}^{\\\\theta}{}_{\\\\phi}= & -a r_s \\\\left(2a^{2} r^{3} r_s \\\\cos{\\\\theta}^{2}+2a^{2} r^{2} \\\\Sigma \\\\cos{\\\\theta}^{2}-4a^{2} r^{2} \\\\Sigma-a^{2} r r_s \\\\Sigma \\\\cos{\\\\theta}^{2}+a^{2} \\\\Sigma^{2}+2r^{5} r_s-2r^{4} \\\\Sigma+r^{3} r_s \\\\Sigma-r^{2} \\\\Sigma^{2}\\\\right) \\\\sin{\\\\theta} \\\\frac{\\\\cos{\\\\theta}}{2\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{3}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{r}{}^{r}{}_{t}= & a r_s \\\\left(\\\\left(-6\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\Delta \\\\partial_{r}{\\\\Sigma}+2\\\\left(\\\\left(4r-\\\\partial_{r}{\\\\Sigma}\\\\right) \\\\Delta+\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\partial_{r}{\\\\Delta}\\\\right) \\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)-\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(4a^{4} r \\\\sin{\\\\theta}^{4}-4a^{4} r \\\\sin{\\\\theta}^{2}+4a^{2} r \\\\Sigma \\\\sin{\\\\theta}^{2}-4a^{2} r \\\\Sigma-4r^{3} \\\\Delta+4r^{3} \\\\Sigma-2r^{2} r_s \\\\Sigma+2r \\\\Delta \\\\Sigma-2r \\\\Sigma^{2}+r_s \\\\Sigma^{2}\\\\right)+\\\\left(4a^{2} r^{4} r_s \\\\cos{\\\\theta}^{2}-4a^{2} r^{2} r_s \\\\Sigma \\\\cos{\\\\theta}^{2}+a^{2} r_s \\\\Sigma^{2} \\\\cos{\\\\theta}^{2}+4r^{6} r_s-4r^{4} r_s \\\\Sigma+4r^{3} \\\\Sigma^{2}+r^{2} r_s \\\\Sigma^{2}-2r \\\\Sigma^{3}\\\\right) \\\\Delta\\\\right) \\\\frac{\\\\sin{\\\\theta}^{2}}{4\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{\\\\theta}{}^{r}{}_{t}= & a r_s \\\\left(\\\\left(-2r^{2}+\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{\\\\theta}^{2}+\\\\left(-r r_s+\\\\Sigma\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right)\\\\right) \\\\cos{\\\\theta}+\\\\left(a^{2} \\\\sin{\\\\theta}^{2}+2r^{2}\\\\right) \\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma \\\\cos{\\\\theta}+\\\\left(-r r_s+\\\\Sigma\\\\right) \\\\left(3\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\sin{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}-\\\\left(\\\\left(4r^{2}-2\\\\Sigma\\\\right) \\\\cos{\\\\theta}-\\\\sin{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)\\\\right) \\\\Delta \\\\frac{\\\\sin{\\\\theta}}{2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}_{r}{}^{r}{}_{t}= & r_s \\\\frac{2r_s \\\\left(2r^{2}-\\\\Sigma\\\\right)^{2} \\\\left(-a^{2} r r_s+a^{2} \\\\left(r r_s-\\\\Sigma\\\\right) \\\\sin{\\\\theta}^{2}+a^{2} \\\\Sigma-r^{3} r_s+r^{2} \\\\Sigma\\\\right) \\\\Delta+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{4} r \\\\left(\\\\cos{4\\\\theta}-1\\\\right)-2\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(2r \\\\Delta-\\\\left(2r-r_s\\\\right) \\\\Sigma\\\\right)\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)+4\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(3\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\Delta \\\\partial_{r}{\\\\Sigma}-\\\\left(\\\\left(4r-\\\\partial_{r}{\\\\Sigma}\\\\right) \\\\Delta+\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\partial_{r}{\\\\Delta}\\\\right) \\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)}{8\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}_{\\\\theta}{}^{r}{}_{t}= & r_s \\\\left(2a^{2} r r_s \\\\left(2a^{2} r^{2} \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma \\\\cos{\\\\theta}^{2}+2r^{4}-3r^{2} \\\\Sigma+\\\\Sigma^{2}\\\\right) \\\\sin{\\\\theta} \\\\cos{\\\\theta}-a^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma \\\\sin{2\\\\theta}+4\\\\left(3r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\frac{\\\\Delta}{4\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{\\\\phi}{}^{r}{}_{t}= & a r_s \\\\left(-2a^{2} r^{4} r_s^{2} \\\\cos{\\\\theta}^{2}+4a^{2} r^{3} r_s \\\\Sigma+a^{2} r^{2} r_s^{2} \\\\Sigma \\\\cos{\\\\theta}^{2}+2a^{2} r^{2} \\\\Sigma^{2} \\\\cos{\\\\theta}^{2}-4a^{2} r^{2} \\\\Sigma^{2}-a^{2} r r_s \\\\Sigma^{2} \\\\cos{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma^{2}+a^{2} \\\\Sigma^{3}-2r^{6} r_s^{2}+4r^{5} r_s \\\\Sigma-r^{4} r_s^{2} \\\\Sigma-2r^{4} \\\\Sigma^{2}+2r^{3} r_s \\\\Sigma^{2}-r^{2} \\\\Sigma^{3}\\\\right) \\\\Delta \\\\sin{\\\\theta} \\\\frac{\\\\cos{\\\\theta}}{2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{3}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{r}{}^{\\\\theta}{}_{t}= & a r_s \\\\left(-r \\\\left(-2a^{4} r^{2} r_s \\\\sin{\\\\theta}^{4}+2a^{4} r^{2} r_s \\\\sin{\\\\theta}^{2}+a^{4} r_s \\\\Sigma \\\\sin{\\\\theta}^{4}-a^{4} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2a^{2} r^{4} r_s \\\\sin{\\\\theta}^{2}-3a^{2} r^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2a^{2} r \\\\Sigma^{2} \\\\sin{\\\\theta}^{2}+a^{2} r_s \\\\Sigma^{2} \\\\sin{\\\\theta}^{2}-2r^{2} r_s \\\\Sigma^{2}+2r \\\\Sigma^{3}\\\\right)-\\\\left(a^{2} \\\\sin{\\\\theta}^{2}+2r^{2}\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma+2\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(3a^{2} r \\\\sin{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}-a^{2} \\\\Sigma \\\\sin{\\\\theta}^{2}+2r \\\\Sigma \\\\partial_{r}{\\\\Sigma}-\\\\Sigma^{2}\\\\right)\\\\right) \\\\sin{\\\\theta} \\\\frac{\\\\cos{\\\\theta}}{2\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{\\\\theta}{}^{\\\\theta}{}_{t}= & a r r_s \\\\frac{4\\\\left(-r r_s+\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(2a^{4} \\\\sin{\\\\theta}^{4}-2a^{4} \\\\sin{\\\\theta}^{2}+2a^{2} \\\\Sigma \\\\sin{\\\\theta}^{2}-2a^{2} \\\\Sigma-2r^{2} \\\\Delta+\\\\Delta \\\\Sigma\\\\right) \\\\sin{\\\\theta}^{2}+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(32a^{2} \\\\Sigma \\\\sin{\\\\theta}^{4}+12a^{2} \\\\Sigma \\\\cos{2\\\\theta}-12a^{2} \\\\Sigma+6a^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}-3a^{2} \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}-8\\\\Sigma^{2} \\\\cos{2\\\\theta}+8\\\\Sigma \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right)+8\\\\left(a^{4} r r_s \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{\\\\theta}^{4}+\\\\left(a^{2} \\\\sin{\\\\theta}^{2}+\\\\Sigma\\\\right) \\\\left(-r r_s+\\\\Sigma\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right)\\\\right) \\\\cos{\\\\theta}^{2}}{8\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}_{r}{}^{\\\\theta}{}_{t}= & a^{2} r_s \\\\left(2a^{2} r^{3} r_s \\\\cos{\\\\theta}^{2}-6a^{2} r^{2} r_s \\\\cos{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}+2a^{2} r r_s \\\\Sigma \\\\cos{\\\\theta}^{2}+6a^{2} r \\\\Sigma \\\\partial_{r}{\\\\Sigma}-3a^{2} \\\\Sigma^{2}+2r^{5} r_s-6r^{4} r_s \\\\partial_{r}{\\\\Sigma}+6r^{3} \\\\Sigma \\\\partial_{r}{\\\\Sigma}-3r^{2} \\\\Sigma^{2}+r r_s \\\\Sigma^{2}\\\\right) \\\\sin{\\\\theta} \\\\frac{\\\\cos{\\\\theta}}{2\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}_{\\\\theta}{}^{\\\\theta}{}_{t}= & r r_s \\\\frac{4a^{2} \\\\left(2r r_s \\\\left(a^{4} \\\\sin{\\\\theta}^{4}-a^{4} \\\\sin{\\\\theta}^{2}-a^{2} r^{2} \\\\sin{\\\\theta}^{2}+2a^{2} \\\\Sigma \\\\sin{\\\\theta}^{2}-r r_s \\\\Sigma+\\\\Sigma^{2}\\\\right) \\\\cos{\\\\theta}^{2}+\\\\left(2\\\\Sigma \\\\cos{2\\\\theta}-3\\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)\\\\right)+\\\\left(a^{4} \\\\left(\\\\cos{4\\\\theta}-1\\\\right)-4\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\Delta\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)}{8\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{\\\\phi}{}^{\\\\theta}{}_{t}= & a r_s \\\\left(2a^{2} r^{3} r_s \\\\cos{\\\\theta}^{2}+2a^{2} r^{2} \\\\Sigma \\\\cos{\\\\theta}^{2}-4a^{2} r^{2} \\\\Sigma-a^{2} r r_s \\\\Sigma \\\\cos{\\\\theta}^{2}+a^{2} \\\\Sigma^{2}+2r^{5} r_s-2r^{4} \\\\Sigma+r^{3} r_s \\\\Sigma-r^{2} \\\\Sigma^{2}\\\\right) \\\\sin{\\\\theta} \\\\frac{\\\\cos{\\\\theta}}{2\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{3}}\\\\\\\\[-.5ex]\\n\\\\end{aligned}\\\\right.\\n\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"rm:= R^{\\\\rho}_{\\\\sigma\\\\mu\\\\nu} = @(tst1) + @(tst2) + @(tst3) + @(tst4).\\ncollect_components(rm);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}R_{\\\\sigma \\\\nu} = R^{\\\\rho}\\\\,_{\\\\sigma \\\\rho \\\\nu}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}R_{\\\\sigma \\\\nu} = \\\\left\\\\{\\\\begin{aligned}\\\\square{}_{t}{}_{t}= & r_s \\\\frac{-4r \\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(2a^{4} r r_s \\\\cos{\\\\theta}^{2}-2a^{4} \\\\Sigma \\\\cos{\\\\theta}^{2}+2a^{2} r^{3} r_s \\\\cos{\\\\theta}^{2}-2a^{2} r^{2} r_s^{2} \\\\cos{\\\\theta}^{2}-2a^{2} r^{2} \\\\Sigma \\\\cos{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\cos{\\\\theta}^{2}-2r^{3} r_s \\\\Delta+2r^{2} \\\\Delta \\\\Sigma+r r_s \\\\Delta \\\\Sigma-\\\\Delta \\\\Sigma^{2}\\\\right) \\\\Sigma+r \\\\left(8a^{2} r r_s \\\\left(a^{2} \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{\\\\theta}^{2}+\\\\left(a^{2} \\\\sin{\\\\theta}^{2}+\\\\Sigma\\\\right) \\\\left(-r r_s+\\\\Sigma\\\\right) \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right)\\\\right) \\\\cos{\\\\theta}^{2}+\\\\left(-r r_s+\\\\Sigma\\\\right) \\\\left(a^{4} \\\\left(\\\\cos{4\\\\theta}-1\\\\right)+a^{2} \\\\left(8\\\\Sigma \\\\cos{2\\\\theta}-12\\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right)-4\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\Delta\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)\\\\right)-2r_s \\\\left(2r^{2}-\\\\Sigma\\\\right)^{2} \\\\left(-a^{2} r r_s+a^{2} \\\\left(r r_s-\\\\Sigma\\\\right) \\\\sin{\\\\theta}^{2}+a^{2} \\\\Sigma-r^{3} r_s+r^{2} \\\\Sigma\\\\right) \\\\Delta+\\\\left(-r r_s+\\\\Sigma\\\\right) \\\\left(a^{4} r \\\\left(\\\\cos{4\\\\theta}-1\\\\right)-2\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(2r \\\\Delta-\\\\left(2r-r_s\\\\right) \\\\Sigma\\\\right)+12\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\Delta \\\\partial_{r}{\\\\Sigma}-4\\\\left(\\\\left(4r-\\\\partial_{r}{\\\\Sigma}\\\\right) \\\\Delta+\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\partial_{r}{\\\\Delta}\\\\right) \\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)}{8\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{t}= & a r_s \\\\frac{4r^{2} r_s \\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(2a^{4} \\\\cos{\\\\theta}^{2}+2a^{2} r^{2} \\\\cos{\\\\theta}^{2}-2a^{2} r r_s \\\\cos{\\\\theta}^{2}-2r^{2} \\\\Delta+\\\\Delta \\\\Sigma\\\\right) \\\\Sigma \\\\sin{\\\\theta}^{2}-r \\\\left(\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(-8a^{4} \\\\sin{\\\\theta}^{6}+8a^{4} \\\\sin{\\\\theta}^{4}+24a^{2} \\\\Sigma \\\\sin{\\\\theta}^{4}+8a^{2} \\\\Sigma \\\\cos{2\\\\theta}-8a^{2} \\\\Sigma+6a^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}-3a^{2} \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}-4r^{2} \\\\Delta \\\\cos{2\\\\theta}+4r^{2} \\\\Delta+2\\\\Delta \\\\Sigma \\\\cos{2\\\\theta}-2\\\\Delta \\\\Sigma-8\\\\Sigma^{2} \\\\cos{2\\\\theta}+8\\\\Sigma \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right)+8\\\\left(a^{4} r r_s \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{\\\\theta}^{4}+\\\\left(a^{2} \\\\sin{\\\\theta}^{2}+\\\\Sigma\\\\right) \\\\left(-r r_s+\\\\Sigma\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right)\\\\right) \\\\cos{\\\\theta}^{2}\\\\right)+2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(4a^{4} r \\\\sin{\\\\theta}^{4}-4a^{4} r \\\\sin{\\\\theta}^{2}+4a^{2} r \\\\Sigma \\\\sin{\\\\theta}^{2}-4a^{2} r \\\\Sigma-4r^{3} \\\\Delta+4r^{3} \\\\Sigma-2r^{2} r_s \\\\Sigma+2r \\\\Delta \\\\Sigma-2r \\\\Sigma^{2}+r_s \\\\Sigma^{2}+6\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\Delta \\\\partial_{r}{\\\\Sigma}-2\\\\left(\\\\left(4r-\\\\partial_{r}{\\\\Sigma}\\\\right) \\\\Delta+\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\partial_{r}{\\\\Delta}\\\\right) \\\\Sigma\\\\right)-\\\\left(4a^{2} r^{4} r_s \\\\cos{\\\\theta}^{2}-4a^{2} r^{2} r_s \\\\Sigma \\\\cos{\\\\theta}^{2}+a^{2} r_s \\\\Sigma^{2} \\\\cos{\\\\theta}^{2}+4r^{6} r_s-4r^{4} r_s \\\\Sigma+4r^{3} \\\\Sigma^{2}+r^{2} r_s \\\\Sigma^{2}-2r \\\\Sigma^{3}\\\\right) \\\\Delta\\\\right) \\\\sin{\\\\theta}^{2}}{8\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}_{\\\\phi}= & a r_s \\\\frac{4r^{2} r_s \\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(2a^{4} \\\\cos{\\\\theta}^{2}+2a^{2} r^{2} \\\\cos{\\\\theta}^{2}-2a^{2} r r_s \\\\cos{\\\\theta}^{2}-2r^{2} \\\\Delta+\\\\Delta \\\\Sigma\\\\right) \\\\Sigma \\\\sin{\\\\theta}^{2}-r \\\\left(\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(-8a^{4} \\\\sin{\\\\theta}^{6}+8a^{4} \\\\sin{\\\\theta}^{4}+24a^{2} \\\\Sigma \\\\sin{\\\\theta}^{4}+8a^{2} \\\\Sigma \\\\cos{2\\\\theta}-8a^{2} \\\\Sigma+6a^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}-3a^{2} \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}-4r^{2} \\\\Delta \\\\cos{2\\\\theta}+4r^{2} \\\\Delta+2\\\\Delta \\\\Sigma \\\\cos{2\\\\theta}-2\\\\Delta \\\\Sigma-8\\\\Sigma^{2} \\\\cos{2\\\\theta}+8\\\\Sigma \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right)+8\\\\left(a^{2} r r_s \\\\left(a^{2} \\\\sin{\\\\theta}^{2}+\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{\\\\theta}^{2}+\\\\left(-r r_s+\\\\Sigma\\\\right) \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+\\\\left(a^{2}+r^{2}\\\\right) \\\\Sigma^{2}\\\\right)\\\\right) \\\\cos{\\\\theta}^{2}\\\\right)-2\\\\left(\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(r_s \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(-2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}+a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r \\\\Sigma^{2}\\\\right)\\\\right) \\\\Delta+\\\\left(-r r_s+\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(4a^{4} r \\\\sin{\\\\theta}^{4}-4a^{4} r \\\\sin{\\\\theta}^{2}+4a^{2} r \\\\Sigma \\\\sin{\\\\theta}^{2}-4a^{2} r \\\\Sigma-4r^{3} \\\\Delta+4r^{3} \\\\Sigma-2r^{2} r_s \\\\Sigma+2r \\\\Delta \\\\Sigma-2r \\\\Sigma^{2}+r_s \\\\Sigma^{2}+6\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\Delta \\\\partial_{r}{\\\\Sigma}-2\\\\left(\\\\left(4r-\\\\partial_{r}{\\\\Sigma}\\\\right) \\\\Delta+\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\partial_{r}{\\\\Delta}\\\\right) \\\\Sigma\\\\right)\\\\right) \\\\sin{\\\\theta}^{2}}{8\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{r}= & \\\\frac{-r_s \\\\left(-2r_s \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} \\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(2a^{2} r^{3} r_s-2a^{2} r^{2} \\\\Sigma-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}+2r^{5} r_s-2r^{4} \\\\Sigma+r^{3} r_s \\\\Sigma-r^{2} \\\\Sigma^{2}\\\\right) \\\\sin{\\\\theta}^{2}+\\\\left(-2r^{2}+\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2}\\\\right) \\\\Delta+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{4} r \\\\left(\\\\cos{4\\\\theta}-1\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right)+2\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(2r \\\\Delta-\\\\left(2r-r_s\\\\right) \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)+4\\\\left(\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(r_s-\\\\partial_{r}{\\\\Sigma}\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma+\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\partial_{r}{\\\\Sigma}-\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(-a^{2} r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\partial_{r}{\\\\Sigma}-3r^{2} r_s+r^{2} \\\\partial_{r}{\\\\Sigma}+2r \\\\Sigma\\\\right) \\\\Sigma-\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(\\\\left(4r-\\\\partial_{r}{\\\\Sigma}\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)-\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(-a^{2} r_s+a^{2} \\\\partial_{r}{\\\\Sigma}-3r^{2} r_s+r^{2} \\\\partial_{r}{\\\\Sigma}+2r \\\\Sigma\\\\right)\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma\\\\right) \\\\Delta\\\\right)+4\\\\left(r r_s-\\\\Sigma\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\left(2a^{2} \\\\Sigma \\\\cos{2\\\\theta}-a^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}-2r^{2} \\\\Sigma+r r_s \\\\Sigma+2r \\\\Delta \\\\partial_{r}{\\\\Sigma}-2\\\\Delta \\\\Sigma\\\\right)+2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(\\\\left(-r r_s+\\\\Sigma\\\\right) \\\\left(\\\\left(4a^{2} \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right) \\\\cos{\\\\theta}^{2}+\\\\left(-2r \\\\Delta+\\\\left(2r-r_s\\\\right) \\\\Sigma\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right)\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)+2\\\\left(-\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right) \\\\partial_{r}{\\\\Sigma}+\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(4a^{2} r r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}+2r^{2} r_s \\\\partial_{r}{\\\\Sigma}+4r r_s \\\\Sigma-4r \\\\Sigma \\\\partial_{r}{\\\\Sigma}-2\\\\Sigma^{2}\\\\right) \\\\Sigma+\\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right) \\\\left(-a^{2} r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\partial_{r}{\\\\Sigma}-3r^{2} r_s+r^{2} \\\\partial_{r}{\\\\Sigma}+2r \\\\Sigma\\\\right) \\\\Sigma\\\\right) \\\\Delta\\\\right)+\\\\left(a^{2} r_s^{2} \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(2a^{2} r^{3} r_s-2a^{2} r^{2} \\\\Sigma-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}+2r^{5} r_s-2r^{4} \\\\Sigma+r^{3} r_s \\\\Sigma-r^{2} \\\\Sigma^{2}\\\\right) \\\\sin{\\\\theta}^{2}+\\\\left(-r r_s+\\\\Sigma\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right)^{2}\\\\right) \\\\Delta\\\\right)}{8\\\\left(r r_s-\\\\Sigma\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Delta \\\\Sigma^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{\\\\theta}= & \\\\frac{r r_s \\\\left(8a^{4} r r_s \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\left(-a^{2} r r_s+a^{2} \\\\Sigma-r^{3} r_s+r^{2} r_s^{2}+r^{2} \\\\Sigma-r r_s \\\\Sigma+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right)\\\\right) \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{2}+4a^{2} \\\\left(-\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\sin{2\\\\theta}+a^{2} \\\\partial_{\\\\theta}{\\\\Sigma}+r^{2} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\Sigma \\\\sin{2\\\\theta}+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(-2a^{2} r r_s \\\\cos{2\\\\theta}+2a^{2} \\\\Sigma \\\\cos{2\\\\theta}+a^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}-2r^{3} r_s \\\\cos{2\\\\theta}+2r^{2} r_s^{2} \\\\cos{2\\\\theta}+2r^{2} \\\\Sigma \\\\cos{2\\\\theta}+r^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}-2r r_s \\\\Sigma \\\\cos{2\\\\theta}-r r_s \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\Sigma-\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\Sigma \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right)+\\\\left(r r_s-\\\\Sigma\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{6} \\\\left(\\\\cos{4\\\\theta}-1\\\\right)+a^{4} r^{2} \\\\left(\\\\cos{4\\\\theta}-1\\\\right)-a^{4} r r_s \\\\left(\\\\cos{4\\\\theta}-1\\\\right)+8a^{2} r^{2} \\\\Delta-4a^{2} \\\\Delta \\\\Sigma+8r^{4} \\\\Delta-4r^{2} \\\\Delta \\\\Sigma\\\\right)\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+4\\\\left(r r_s-\\\\Sigma\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\left(2a^{2} \\\\Sigma \\\\cos{2\\\\theta}-a^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}+2r^{2} \\\\Sigma-r r_s \\\\Sigma+2r \\\\Delta \\\\partial_{r}{\\\\Sigma}-2r \\\\Sigma \\\\partial_{r}{\\\\Delta}-2\\\\Delta \\\\Sigma\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+4\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(\\\\left(2a^{2} \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right) \\\\cos{\\\\theta}^{2}-r \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right) \\\\Delta\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\sin{\\\\theta}^{2}+2\\\\left(a^{2} r r_s \\\\sin{2\\\\theta}+a^{2} \\\\partial_{\\\\theta}{\\\\Sigma}+r^{2} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right) \\\\Sigma \\\\sin{\\\\theta} \\\\cos{\\\\theta}-2\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right) \\\\Sigma \\\\cos{\\\\theta}^{2}-4\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right) \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}+2\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(-5a^{4} r r_s \\\\Sigma \\\\sin{\\\\theta}^{5}+4a^{4} r r_s \\\\Sigma \\\\sin{\\\\theta}^{3}+a^{4} r r_s \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}+3a^{2} r^{2} r_s^{2} \\\\Sigma \\\\sin{\\\\theta}^{3}-2a^{2} r^{2} r_s^{2} \\\\Sigma \\\\sin{\\\\theta}+a^{2} r^{2} r_s^{2} \\\\cos{\\\\theta}^{3} \\\\partial_{\\\\theta}{\\\\Sigma}-a^{2} r^{2} r_s^{2} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}-6a^{2} r r_s \\\\Sigma^{2} \\\\sin{\\\\theta}^{3}+5a^{2} r r_s \\\\Sigma^{2} \\\\sin{\\\\theta}-4a^{2} r r_s \\\\Sigma \\\\cos{\\\\theta}^{3} \\\\partial_{\\\\theta}{\\\\Sigma}+2a^{2} r r_s \\\\Sigma \\\\cos{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}-a^{2} \\\\Sigma^{3} \\\\sin{\\\\theta}+3a^{2} \\\\Sigma^{2} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}+r^{3} r_s \\\\Sigma^{2} \\\\sin{\\\\theta}-2r^{3} r_s \\\\Sigma \\\\cos{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}-r^{2} \\\\Sigma^{3} \\\\sin{\\\\theta}+3r^{2} \\\\Sigma^{2} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\sin{\\\\theta}\\\\right) \\\\tan{\\\\theta}^{2}+2\\\\left(a^{4} r^{2} r_s^{2} \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{\\\\theta}^{4}+\\\\left(-r r_s+\\\\Sigma\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right)^{2}\\\\right) \\\\sin{\\\\theta}^{2}\\\\right)}{8\\\\left(r r_s-\\\\Sigma\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{\\\\phi}= & \\\\frac{2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(12a^{4} r r_s \\\\Sigma \\\\sin{\\\\theta}^{6}-10a^{4} r r_s \\\\Sigma \\\\sin{\\\\theta}^{4}+6a^{4} r r_s \\\\sin{\\\\theta}^{5} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}+16a^{2} r r_s \\\\Sigma^{2} \\\\sin{\\\\theta}^{4}+6a^{2} r r_s \\\\Sigma^{2} \\\\cos{2\\\\theta}-6a^{2} r r_s \\\\Sigma^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}-a^{2} r r_s \\\\Sigma \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}-2a^{2} \\\\Sigma^{3} \\\\cos{2\\\\theta}+a^{2} \\\\Sigma^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}-2r^{2} \\\\Sigma^{3} \\\\cos{2\\\\theta}+r^{2} \\\\Sigma^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}{\\\\Sigma}+\\\\left(2a^{2} \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+\\\\left(a^{2}+r^{2}\\\\right) \\\\Sigma^{2}\\\\right) \\\\cos{\\\\theta}^{2}-r \\\\left(-2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}+a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r \\\\Sigma^{2}\\\\right) \\\\Delta\\\\right) \\\\sin{\\\\theta}^{2}\\\\right)+\\\\left(r_s \\\\left(-2a^{2} r \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+\\\\left(a^{2}+r^{2}\\\\right) \\\\Sigma^{2}\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{2\\\\theta} \\\\cos{\\\\theta}+a^{2} r_s \\\\left(4a^{2} r^{2} \\\\left(a^{2} \\\\sin{\\\\theta}^{2}+\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\cos{\\\\theta}^{2}+\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(2a^{2} r^{3} r_s-2a^{2} r^{2} \\\\Sigma-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}+2r^{5} r_s-2r^{4} \\\\Sigma+r^{3} r_s \\\\Sigma-r^{2} \\\\Sigma^{2}\\\\right) \\\\Delta\\\\right) \\\\sin{\\\\theta}^{3}+\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(-2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}+a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r \\\\Sigma^{2}\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Delta \\\\sin{\\\\theta}\\\\right)+\\\\left(\\\\left(-r r_s+\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(12a^{2} r^{2} r_s \\\\Delta \\\\sin{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}-4a^{2} r^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2} \\\\partial_{r}{\\\\Delta}-8a^{2} r r_s \\\\Delta \\\\Sigma \\\\sin{\\\\theta}^{2}-4a^{2} r_s \\\\Delta \\\\Sigma \\\\sin{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}+2a^{2} r_s \\\\Sigma^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{r}{\\\\Delta}-4a^{2} \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+\\\\left(a^{2}+r^{2}\\\\right) \\\\Sigma^{2}\\\\right) \\\\cos{\\\\theta}^{2}-4r \\\\Delta \\\\Sigma^{2} \\\\partial_{r}{\\\\Sigma}+4r \\\\Sigma^{3} \\\\partial_{r}{\\\\Delta}+\\\\left(2r \\\\Delta-\\\\left(2r-r_s\\\\right) \\\\Sigma\\\\right) \\\\left(-2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}+a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r \\\\Sigma^{2}\\\\right)+4\\\\Delta \\\\Sigma^{3}\\\\right)+\\\\left(a^{2} r_s^{2} \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(2a^{2} r^{3} r_s-2a^{2} r^{2} \\\\Sigma-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}+2r^{5} r_s-2r^{4} \\\\Sigma+r^{3} r_s \\\\Sigma-r^{2} \\\\Sigma^{2}\\\\right) \\\\sin{\\\\theta}^{2}+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(-2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}+a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r \\\\Sigma^{2}\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right)\\\\right) \\\\Delta\\\\right) \\\\sin{\\\\theta}\\\\right) \\\\sin{\\\\theta}+4\\\\left(a^{4} r^{2} r_s^{2} \\\\left(a^{2} \\\\sin{\\\\theta}^{2}+\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{\\\\theta}^{4}+\\\\left(-r r_s+\\\\Sigma\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+\\\\left(a^{2}+r^{2}\\\\right) \\\\Sigma^{2}\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right)\\\\right) \\\\cos{\\\\theta}^{2}}{4\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{\\\\theta}= & \\\\frac{r_s \\\\left(2a^{2} r r_s \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(r r_s-\\\\Sigma\\\\right)^{2} \\\\left(a^{4} \\\\cos{\\\\theta}^{2}+a^{2} r^{2} \\\\cos{\\\\theta}^{2}+a^{2} r^{2}-a^{2} r r_s \\\\cos{\\\\theta}^{2}+r^{4}-r^{3} r_s\\\\right) \\\\sin{\\\\theta} \\\\cos{\\\\theta}-a^{2} \\\\left(r r_s-\\\\Sigma\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(-4a^{2} r^{2}+a^{2} \\\\Sigma-4r^{4}+2r^{3} r_s+r^{2} \\\\Sigma\\\\right) \\\\sin{2\\\\theta}+2\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\sin{2\\\\theta}+a^{2} \\\\partial_{\\\\theta}{\\\\Sigma}+r^{2} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma-2\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\partial_{\\\\theta}{\\\\Sigma}+2\\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\Sigma \\\\partial_{\\\\theta}{\\\\Sigma}-2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma+\\\\left(a^{2}+r^{2}\\\\right) \\\\left(2r^{2}-\\\\Sigma\\\\right)\\\\right) \\\\Sigma \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\tan{\\\\theta}+2\\\\left(r r_s-\\\\Sigma\\\\right)^{2} \\\\left(a^{2} \\\\sin{2\\\\theta} \\\\partial_{r}{\\\\Sigma}+2r \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\tan{\\\\theta}+2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(-a^{2} r r_s^{2} \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+\\\\Sigma\\\\right) \\\\left(2a^{2} r^{3} r_s-2a^{2} r^{2} \\\\Sigma-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}+2r^{5} r_s-2r^{4} \\\\Sigma+r^{3} r_s \\\\Sigma-r^{2} \\\\Sigma^{2}\\\\right) \\\\sin{\\\\theta}^{2}+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(\\\\left(-\\\\left(a^{2} r r_s \\\\sin{2\\\\theta}+a^{2} \\\\partial_{\\\\theta}{\\\\Sigma}+r^{2} \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right) \\\\Sigma+\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right) \\\\partial_{\\\\theta}{\\\\Sigma}+\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(-2a^{2} r^{2} r_s \\\\sin{2\\\\theta}+a^{2} r_s \\\\Sigma \\\\sin{2\\\\theta}+a^{2} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{\\\\theta}{\\\\Sigma}-2r^{2} r_s \\\\partial_{\\\\theta}{\\\\Sigma}+4r \\\\Sigma \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\Sigma\\\\right) \\\\tan{\\\\theta}+\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(-4a^{4} r^{2} r_s \\\\sin{\\\\theta}^{4}+a^{4} r_s \\\\Sigma \\\\sin{\\\\theta}^{4}+2a^{2} r^{3} r_s^{2} \\\\sin{\\\\theta}^{2}-6a^{2} r^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2a^{2} r^{2} r_s \\\\Sigma+2a^{2} r \\\\Sigma^{2} \\\\sin{\\\\theta}^{2}-2a^{2} r \\\\Sigma^{2}+2r^{4} r_s \\\\Sigma-2r^{3} \\\\Sigma^{2}\\\\right)\\\\right)+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right)\\\\right)}{4\\\\left(r r_s-\\\\Sigma\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2} \\\\tan{\\\\theta}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{r}= & \\\\frac{-a^{4} r r_s^{2} \\\\left(2r^{2}-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\Sigma+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\Sigma+r r_s \\\\Sigma\\\\right) \\\\sin{\\\\theta}^{4}-a^{2} r_s \\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(-6a^{4} r^{3} r_s \\\\cos{\\\\theta}^{2}-2a^{4} r^{2} r_s \\\\cos{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}+4a^{4} r^{2} \\\\Sigma+2a^{4} r r_s \\\\Sigma \\\\cos{\\\\theta}^{2}+4a^{4} r \\\\Sigma \\\\partial_{r}{\\\\Sigma}-3a^{4} \\\\Sigma^{2}-6a^{2} r^{5} r_s \\\\cos{\\\\theta}^{2}-6a^{2} r^{5} r_s+2a^{2} r^{4} r_s^{2} \\\\cos{\\\\theta}^{2}-2a^{2} r^{4} r_s \\\\cos{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}-2a^{2} r^{4} r_s \\\\partial_{r}{\\\\Sigma}+8a^{2} r^{4} \\\\Sigma+2a^{2} r^{3} r_s^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}+4a^{2} r^{3} r_s \\\\Sigma \\\\cos{\\\\theta}^{2}+8a^{2} r^{3} \\\\Sigma \\\\partial_{r}{\\\\Sigma}-2a^{2} r^{2} r_s^{2} \\\\Sigma \\\\cos{\\\\theta}^{2}-4a^{2} r^{2} r_s \\\\Sigma \\\\partial_{r}{\\\\Sigma}-6a^{2} r^{2} \\\\Sigma^{2}+3a^{2} r r_s \\\\Sigma^{2}%\\n-6r^{7} r_s+2r^{6} r_s^{2}-2r^{6} r_s \\\\partial_{r}{\\\\Sigma}+4r^{6} \\\\Sigma+2r^{5} r_s^{2} \\\\partial_{r}{\\\\Sigma}+2r^{5} r_s \\\\Sigma+4r^{5} \\\\Sigma \\\\partial_{r}{\\\\Sigma}-4r^{4} r_s \\\\Sigma \\\\partial_{r}{\\\\Sigma}-3r^{4} \\\\Sigma^{2}+r^{3} r_s \\\\Sigma^{2}\\\\right) \\\\sin{\\\\theta}^{2}+\\\\left(-r r_s+\\\\Sigma\\\\right) \\\\left(a^{2} \\\\sin{2\\\\theta} \\\\partial_{r}{\\\\Sigma}+2r \\\\partial_{\\\\theta}{\\\\Sigma}\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\tan{\\\\theta}+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(2a^{2} r_s \\\\left(a^{4} r^{2} r_s \\\\sin{\\\\theta}^{4} \\\\partial_{r}{\\\\Sigma}-a^{4} r^{2} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}+2a^{4} r \\\\Sigma \\\\sin{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}-a^{4} \\\\Sigma^{2} \\\\sin{\\\\theta}^{2}-a^{2} r^{4} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}-a^{2} r^{3} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}+a^{2} r^{3} r_s^{2} \\\\partial_{r}{\\\\Sigma}-2a^{2} r^{3} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2a^{2} r^{3} \\\\Sigma \\\\sin{\\\\theta}^{2} \\\\partial_{r}{\\\\Sigma}+a^{2} r^{2} r_s^{2} \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r^{2} r_s^{2} \\\\Sigma-2a^{2} r^{2} r_s \\\\Sigma \\\\partial_{r}{\\\\Sigma}+a^{2} r^{2} \\\\Sigma^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma^{2}+a^{2} r \\\\Sigma^{2} \\\\partial_{r}{\\\\Sigma}-a^{2} \\\\Sigma^{3}+r^{5} r_s^{2} \\\\partial_{r}{\\\\Sigma}+r^{4} r_s^{2} \\\\Sigma-2r^{4} r_s \\\\Sigma \\\\partial_{r}{\\\\Sigma}%\\n-2r^{3} r_s \\\\Sigma^{2}+r^{3} \\\\Sigma^{2} \\\\partial_{r}{\\\\Sigma}+r^{2} \\\\Sigma^{3}\\\\right) \\\\sin{\\\\theta}^{2}+\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right) \\\\left(-4a^{4} r^{2} r_s \\\\sin{\\\\theta}^{4}+a^{4} r_s \\\\Sigma \\\\sin{\\\\theta}^{4}+2a^{2} r^{3} r_s^{2} \\\\sin{\\\\theta}^{2}-6a^{2} r^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2a^{2} r^{2} r_s \\\\Sigma+2a^{2} r \\\\Sigma^{2} \\\\sin{\\\\theta}^{2}-2a^{2} r \\\\Sigma^{2}+2r^{4} r_s \\\\Sigma-2r^{3} \\\\Sigma^{2}\\\\right)\\\\right)+\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\Sigma \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\Sigma-2r \\\\Sigma^{2}\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\Sigma \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\Sigma+a^{2} \\\\Sigma^{2}-r^{3} r_s \\\\Sigma+r^{2} \\\\Sigma^{2}\\\\right)}{2\\\\left(r r_s-\\\\Sigma\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\Sigma+r^{3} r_s-r^{2} \\\\Sigma\\\\right)^{2} \\\\Sigma^{2} \\\\tan{\\\\theta}}\\\\\\\\[-.5ex]\\n\\\\end{aligned}\\\\right.\\n\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"rc:= R_{\\\\sigma\\\\nu} = R^{\\\\rho}_{\\\\sigma\\\\rho\\\\nu};\\nsubstitute(rc, rm)\\nevaluate(rc, kerr, rhsonly=True);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}R_{\\\\sigma \\\\nu} = \\\\left\\\\{\\\\begin{aligned}\\\\square{}_{t}{}_{t}= & r_s \\\\frac{-4r \\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(2a^{4} r r_s \\\\cos{\\\\theta}^{2}-2a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2}+2a^{2} r^{3} r_s \\\\cos{\\\\theta}^{2}-2a^{2} r^{2} r_s^{2} \\\\cos{\\\\theta}^{2}-2a^{2} r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2}+2a^{2} r r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2}-2r^{3} r_s \\\\left(r^{2}-r_s r+a^{2}\\\\right)+2r^{2} \\\\left(r^{2}-r_s r+a^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r r_s \\\\left(r^{2}-r_s r+a^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-\\\\left(r^{2}-r_s r+a^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r \\\\left(8a^{2} r r_s \\\\left(a^{2} \\\\left(a^{2} r r_s-a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right) \\\\sin{\\\\theta}^{2}+\\\\left(a^{2} \\\\sin{\\\\theta}^{2}+r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(-r r_s+r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right) \\\\cos{\\\\theta}^{2}+\\\\left(-r r_s+r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(a^{4} \\\\left(\\\\cos{4\\\\theta}-1\\\\right)+a^{2} \\\\left(8\\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{2\\\\theta}-12\\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right)-4\\\\left(r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(r^{2}-r_s r+a^{2}\\\\right)\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r^{3} r_s-r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right)\\\\right)-2r_s \\\\left(r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\left(-a^{2} r r_s+a^{2} \\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-r^{3} r_s+r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right) \\\\left(r^{2}-r_s r+a^{2}\\\\right)+\\\\left(-r r_s+r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(a^{4} r \\\\left(\\\\cos{4\\\\theta}-1\\\\right)-2\\\\left(r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(2r \\\\left(r^{2}-r_s r+a^{2}\\\\right)-\\\\left(2r-r_s\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right)+12\\\\left(r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(r^{2}-r_s r+a^{2}\\\\right) \\\\partial_{r}\\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-4\\\\left(\\\\left(4r-\\\\partial_{r}\\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right) \\\\left(r^{2}-r_s r+a^{2}\\\\right)+\\\\left(r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\partial_{r}\\\\left(r^{2}-r_s r+a^{2}\\\\right)\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r^{3} r_s-r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right)}{8\\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r^{3} r_s-r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{t}= & a r_s \\\\frac{4r^{2} r_s \\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(2a^{4} \\\\cos{\\\\theta}^{2}+2a^{2} r^{2} \\\\cos{\\\\theta}^{2}-2a^{2} r r_s \\\\cos{\\\\theta}^{2}-2r^{2} \\\\left(r^{2}-r_s r+a^{2}\\\\right)+\\\\left(r^{2}-r_s r+a^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-r \\\\left(\\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r^{3} r_s-r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right) \\\\left(-8a^{4} \\\\sin{\\\\theta}^{6}+8a^{4} \\\\sin{\\\\theta}^{4}+24a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{4}+8a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{2\\\\theta}-8a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+6a^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-3a^{2} \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-4r^{2} \\\\left(r^{2}-r_s r+a^{2}\\\\right) \\\\cos{2\\\\theta}+4r^{2} \\\\left(r^{2}-r_s r+a^{2}\\\\right)+2\\\\left(r^{2}-r_s r+a^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{2\\\\theta}-2\\\\left(r^{2}-r_s r+a^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-8\\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{2\\\\theta}+8\\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right)+8\\\\left(a^{4} r r_s \\\\left(a^{2} r r_s-a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right) \\\\sin{\\\\theta}^{4}+\\\\left(a^{2} \\\\sin{\\\\theta}^{2}+r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(-r r_s+r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-r^{3} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}\\\\right)\\\\right) \\\\cos{\\\\theta}^{2}\\\\right)+2\\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r^{3} r_s-r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right) \\\\left(4a^{4} r \\\\sin{\\\\theta}^{4}-4a^{4} r \\\\sin{\\\\theta}^{2}+4a^{2} r \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4a^{2} r \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-4r^{3} \\\\left(r^{2}-r_s r+a^{2}\\\\right)+4r^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-2r^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+2r \\\\left(r^{2}-r_s r+a^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-2r \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+6\\\\left(r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(r^{2}-r_s r+a^{2}\\\\right) \\\\partial_{r}\\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-2\\\\left(\\\\left(4r-\\\\partial_{r}\\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right) \\\\left(r^{2}-r_s r+a^{2}\\\\right)+\\\\left(r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\partial_{r}\\\\left(r^{2}-r_s r+a^{2}\\\\right)\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right)-\\\\left(4a^{2} r^{4} r_s \\\\cos{\\\\theta}^{2}-4a^{2} r^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2}+a^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{2}+4r^{6} r_s-4r^{4} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+4r^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+r^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-2r \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3}\\\\right) \\\\left(r^{2}-r_s r+a^{2}\\\\right)\\\\right) \\\\sin{\\\\theta}^{2}}{8\\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r^{3} r_s-r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}_{\\\\phi}= & a r_s \\\\frac{4r^{2} r_s \\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(2a^{4} \\\\cos{\\\\theta}^{2}+2a^{2} r^{2} \\\\cos{\\\\theta}^{2}-2a^{2} r r_s \\\\cos{\\\\theta}^{2}-2r^{2} \\\\left(r^{2}-r_s r+a^{2}\\\\right)+\\\\left(r^{2}-r_s r+a^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-r \\\\left(\\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r^{3} r_s-r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right) \\\\left(-8a^{4} \\\\sin{\\\\theta}^{6}+8a^{4} \\\\sin{\\\\theta}^{4}+24a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{4}+8a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{2\\\\theta}-8a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+6a^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-3a^{2} \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-4r^{2} \\\\left(r^{2}-r_s r+a^{2}\\\\right) \\\\cos{2\\\\theta}+4r^{2} \\\\left(r^{2}-r_s r+a^{2}\\\\right)+2\\\\left(r^{2}-r_s r+a^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{2\\\\theta}-2\\\\left(r^{2}-r_s r+a^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-8\\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{2\\\\theta}+8\\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right)+8\\\\left(a^{2} r r_s \\\\left(a^{2} \\\\sin{\\\\theta}^{2}+r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right) \\\\sin{\\\\theta}^{2}+\\\\left(-r r_s+r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}+2a^{2} r r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+\\\\left(a^{2}+r^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}\\\\right)\\\\right) \\\\cos{\\\\theta}^{2}\\\\right)-2\\\\left(\\\\left(r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(r_s \\\\left(r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r^{3} r_s-r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right)+\\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(-2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}+a^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+2r \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}\\\\right)\\\\right) \\\\left(r^{2}-r_s r+a^{2}\\\\right)+\\\\left(-r r_s+r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r^{3} r_s-r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right) \\\\left(4a^{4} r \\\\sin{\\\\theta}^{4}-4a^{4} r \\\\sin{\\\\theta}^{2}+4a^{2} r \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4a^{2} r \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-4r^{3} \\\\left(r^{2}-r_s r+a^{2}\\\\right)+4r^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-2r^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+2r \\\\left(r^{2}-r_s r+a^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-2r \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+6\\\\left(r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(r^{2}-r_s r+a^{2}\\\\right) \\\\partial_{r}\\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-2\\\\left(\\\\left(4r-\\\\partial_{r}\\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right) \\\\left(r^{2}-r_s r+a^{2}\\\\right)+\\\\left(r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\partial_{r}\\\\left(r^{2}-r_s r+a^{2}\\\\right)\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right)\\\\right) \\\\sin{\\\\theta}^{2}}{8\\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r^{3} r_s-r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{r}= & \\\\frac{-r_s \\\\left(-2r_s \\\\left(r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(a^{2} \\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(2a^{2} r^{3} r_s-2a^{2} r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-a^{2} r r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+2r^{5} r_s-2r^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r^{3} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}\\\\right) \\\\sin{\\\\theta}^{2}+\\\\left(-r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r^{3} r_s-r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right)^{2}\\\\right) \\\\left(r^{2}-r_s r+a^{2}\\\\right)+\\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(a^{4} r \\\\left(\\\\cos{4\\\\theta}-1\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right)+2\\\\left(r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(2r \\\\left(r^{2}-r_s r+a^{2}\\\\right)-\\\\left(2r-r_s\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r^{3} r_s-r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right)\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r^{3} r_s-r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right)+4\\\\left(\\\\left(r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(r_s-\\\\partial_{r}\\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r^{3} r_s-r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r^{3} r_s-r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+\\\\left(r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r^{3} r_s-r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r^{3} r_s-r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right) \\\\partial_{r}\\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-\\\\left(r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r^{3} r_s-r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right) \\\\left(-a^{2} r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\partial_{r}\\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-3r^{2} r_s+r^{2} \\\\partial_{r}\\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+2r \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-\\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(\\\\left(4r-\\\\partial_{r}\\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r^{3} r_s-r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right)-\\\\left(r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(-a^{2} r_s+a^{2} \\\\partial_{r}\\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-3r^{2} r_s+r^{2} \\\\partial_{r}\\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+2r \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right)\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r^{3} r_s-r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right) \\\\left(r^{2}-r_s r+a^{2}\\\\right)\\\\right)+4\\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r^{3} r_s-r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right)^{2} \\\\left(2a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{2\\\\theta}-a^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-2r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+2r \\\\left(r^{2}-r_s r+a^{2}\\\\right) \\\\partial_{r}\\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-2\\\\left(r^{2}-r_s r+a^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right)+2\\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(\\\\left(-r r_s+r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(\\\\left(4a^{2} \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-r^{3} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}\\\\right) \\\\cos{\\\\theta}^{2}+\\\\left(-2r \\\\left(r^{2}-r_s r+a^{2}\\\\right)+\\\\left(2r-r_s\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-2r \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}\\\\right)\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r^{3} r_s-r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right)+2\\\\left(-\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r^{3} r_s-r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-2r \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}\\\\right) \\\\partial_{r}\\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r^{3} r_s-r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right) \\\\left(4a^{2} r r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+2r^{2} r_s \\\\partial_{r}\\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+4r r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-4r \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\partial_{r}\\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-2\\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+\\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-2r \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}\\\\right) \\\\left(-a^{2} r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\partial_{r}\\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-3r^{2} r_s+r^{2} \\\\partial_{r}\\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+2r \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right) \\\\left(r^{2}-r_s r+a^{2}\\\\right)\\\\right)+\\\\left(a^{2} r_s^{2} \\\\left(r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(2a^{2} r^{3} r_s-2a^{2} r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-a^{2} r r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+2r^{5} r_s-2r^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r^{3} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}\\\\right) \\\\sin{\\\\theta}^{2}+\\\\left(-r r_s+r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-2r \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}\\\\right)^{2}\\\\right) \\\\left(r^{2}-r_s r+a^{2}\\\\right)\\\\right)}{8\\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r^{3} r_s-r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right)^{2} \\\\left(r^{2}-r_s r+a^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{\\\\theta}= & \\\\frac{r r_s \\\\left(8a^{4} r r_s \\\\left(a^{2} r r_s-a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right) \\\\left(-a^{2} r r_s+a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-r^{3} r_s+r^{2} r_s^{2}+r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-r r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+\\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right) \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{2}+4a^{2} \\\\left(-\\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(a^{2} r r_s \\\\sin{2\\\\theta}+a^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{2\\\\theta}+\\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r^{3} r_s-r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right) \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+\\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r^{3} r_s-r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right) \\\\left(-2a^{2} r r_s \\\\cos{2\\\\theta}+2a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{2\\\\theta}+a^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-2r^{3} r_s \\\\cos{2\\\\theta}+2r^{2} r_s^{2} \\\\cos{2\\\\theta}+2r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{2\\\\theta}+r^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-2r r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{2\\\\theta}-r r_s \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r^{3} r_s-r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right)+\\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r^{3} r_s-r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right) \\\\left(a^{6} \\\\left(\\\\cos{4\\\\theta}-1\\\\right)+a^{4} r^{2} \\\\left(\\\\cos{4\\\\theta}-1\\\\right)-a^{4} r r_s \\\\left(\\\\cos{4\\\\theta}-1\\\\right)+8a^{2} r^{2} \\\\left(r^{2}-r_s r+a^{2}\\\\right)-4a^{2} \\\\left(r^{2}-r_s r+a^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+8r^{4} \\\\left(r^{2}-r_s r+a^{2}\\\\right)-4r^{2} \\\\left(r^{2}-r_s r+a^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right)\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+4\\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r^{3} r_s-r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right)^{2} \\\\left(2a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{2\\\\theta}-a^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+2r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-r r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+2r \\\\left(r^{2}-r_s r+a^{2}\\\\right) \\\\partial_{r}\\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-2r \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\partial_{r}\\\\left(r^{2}-r_s r+a^{2}\\\\right)-2\\\\left(r^{2}-r_s r+a^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+4\\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(\\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(\\\\left(2a^{2} \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-r^{3} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}\\\\right) \\\\cos{\\\\theta}^{2}-r \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-2r \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}\\\\right) \\\\left(r^{2}-r_s r+a^{2}\\\\right)\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r^{3} r_s-r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right) \\\\sin{\\\\theta}^{2}+2\\\\left(a^{2} r r_s \\\\sin{2\\\\theta}+a^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-r^{3} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\cos{\\\\theta}-2\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r^{3} r_s-r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-r^{3} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2}-4\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r^{3} r_s-r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-r^{3} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}\\\\right) \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+2\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r^{3} r_s-r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right) \\\\left(-5a^{4} r r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{5}+4a^{4} r r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{3}+a^{4} r r_s \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+3a^{2} r^{2} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{3}-2a^{2} r^{2} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}+a^{2} r^{2} r_s^{2} \\\\cos{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-a^{2} r^{2} r_s^{2} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-6a^{2} r r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{3}+5a^{2} r r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}-4a^{2} r r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+2a^{2} r r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}+3a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r^{3} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}-2r^{3} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}+3r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right) \\\\sin{\\\\theta}\\\\right) \\\\tan{\\\\theta}^{2}+2\\\\left(a^{4} r^{2} r_s^{2} \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right) \\\\sin{\\\\theta}^{4}+\\\\left(-r r_s+r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-r^{3} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}\\\\right)^{2}\\\\right) \\\\sin{\\\\theta}^{2}\\\\right)}{8\\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r^{3} r_s-r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right)^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{\\\\phi}= & \\\\frac{2\\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r^{3} r_s-r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right) \\\\left(12a^{4} r r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{6}-10a^{4} r r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{4}+6a^{4} r r_s \\\\sin{\\\\theta}^{5} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+16a^{2} r r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4}+6a^{2} r r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{2\\\\theta}-6a^{2} r r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+2a^{2} r r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-a^{2} r r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-2a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\cos{2\\\\theta}+a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-2r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\cos{2\\\\theta}+r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+\\\\left(2a^{2} \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}+2a^{2} r r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+\\\\left(a^{2}+r^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}\\\\right) \\\\cos{\\\\theta}^{2}-r \\\\left(-2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}+a^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+2r \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}\\\\right) \\\\left(r^{2}-r_s r+a^{2}\\\\right)\\\\right) \\\\sin{\\\\theta}^{2}\\\\right)+\\\\left(r_s \\\\left(-2a^{2} r \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}+2a^{2} r r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+\\\\left(a^{2}+r^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right) \\\\sin{2\\\\theta} \\\\cos{\\\\theta}+a^{2} r_s \\\\left(4a^{2} r^{2} \\\\left(a^{2} \\\\sin{\\\\theta}^{2}+r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right) \\\\cos{\\\\theta}^{2}+\\\\left(r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(2a^{2} r^{3} r_s-2a^{2} r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-a^{2} r r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+2r^{5} r_s-2r^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r^{3} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}\\\\right) \\\\left(r^{2}-r_s r+a^{2}\\\\right)\\\\right) \\\\sin{\\\\theta}^{3}+\\\\left(r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(-2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}+a^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+2r \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r^{3} r_s-r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right) \\\\left(r^{2}-r_s r+a^{2}\\\\right) \\\\sin{\\\\theta}\\\\right)+\\\\left(\\\\left(-r r_s+r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r^{3} r_s-r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right) \\\\left(12a^{2} r^{2} r_s \\\\left(r^{2}-r_s r+a^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-4a^{2} r^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}-r_s r+a^{2}\\\\right)-8a^{2} r r_s \\\\left(r^{2}-r_s r+a^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4a^{2} r_s \\\\left(r^{2}-r_s r+a^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+2a^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}-r_s r+a^{2}\\\\right)-4a^{2} \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}+2a^{2} r r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+\\\\left(a^{2}+r^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}\\\\right) \\\\cos{\\\\theta}^{2}-4r \\\\left(r^{2}-r_s r+a^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+4r \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\partial_{r}\\\\left(r^{2}-r_s r+a^{2}\\\\right)+\\\\left(2r \\\\left(r^{2}-r_s r+a^{2}\\\\right)-\\\\left(2r-r_s\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right) \\\\left(-2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}+a^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+2r \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}\\\\right)+4\\\\left(r^{2}-r_s r+a^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3}\\\\right)+\\\\left(a^{2} r_s^{2} \\\\left(r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(2a^{2} r^{3} r_s-2a^{2} r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-a^{2} r r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+2r^{5} r_s-2r^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r^{3} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}\\\\right) \\\\sin{\\\\theta}^{2}+\\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(-2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}+a^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+2r \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-2r \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}\\\\right)\\\\right) \\\\left(r^{2}-r_s r+a^{2}\\\\right)\\\\right) \\\\sin{\\\\theta}\\\\right) \\\\sin{\\\\theta}+4\\\\left(a^{4} r^{2} r_s^{2} \\\\left(a^{2} \\\\sin{\\\\theta}^{2}+r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right) \\\\sin{\\\\theta}^{4}+\\\\left(-r r_s+r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}+2a^{2} r r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+\\\\left(a^{2}+r^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-r^{3} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}\\\\right)\\\\right) \\\\cos{\\\\theta}^{2}}{4\\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r^{3} r_s-r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{\\\\theta}= & \\\\frac{r_s \\\\left(2a^{2} r r_s \\\\left(r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\left(a^{4} \\\\cos{\\\\theta}^{2}+a^{2} r^{2} \\\\cos{\\\\theta}^{2}+a^{2} r^{2}-a^{2} r r_s \\\\cos{\\\\theta}^{2}+r^{4}-r^{3} r_s\\\\right) \\\\sin{\\\\theta} \\\\cos{\\\\theta}-a^{2} \\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r^{3} r_s-r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right) \\\\left(-4a^{2} r^{2}+a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-4r^{4}+2r^{3} r_s+r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right) \\\\sin{2\\\\theta}+2\\\\left(r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(a^{2} r r_s \\\\sin{2\\\\theta}+a^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r^{3} r_s-r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-2\\\\left(r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r^{3} r_s-r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r^{3} r_s-r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right) \\\\partial_{\\\\theta}\\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+2\\\\left(r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r^{3} r_s-r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r^{3} r_s-r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\partial_{\\\\theta}\\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-2\\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r^{3} r_s-r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r^{3} r_s-r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+\\\\left(a^{2}+r^{2}\\\\right) \\\\left(r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\partial_{\\\\theta}\\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right) \\\\tan{\\\\theta}+2\\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\left(a^{2} \\\\sin{2\\\\theta} \\\\partial_{r}\\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+2r \\\\partial_{\\\\theta}\\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r^{3} r_s-r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right)^{2} \\\\tan{\\\\theta}+2\\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(-a^{2} r r_s^{2} \\\\left(a^{2} \\\\sin{\\\\theta}^{2}-r r_s+r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(2a^{2} r^{3} r_s-2a^{2} r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-a^{2} r r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+2r^{5} r_s-2r^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r^{3} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}\\\\right) \\\\sin{\\\\theta}^{2}+\\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(\\\\left(-\\\\left(a^{2} r r_s \\\\sin{2\\\\theta}+a^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-2r \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r^{3} r_s-r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-2r \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}\\\\right) \\\\partial_{\\\\theta}\\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r^{3} r_s-r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right) \\\\left(-2a^{2} r^{2} r_s \\\\sin{2\\\\theta}+a^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{2\\\\theta}+a^{2} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-2r^{2} r_s \\\\partial_{\\\\theta}\\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+4r \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\partial_{\\\\theta}\\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right) \\\\tan{\\\\theta}+\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r^{3} r_s-r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right) \\\\left(-4a^{4} r^{2} r_s \\\\sin{\\\\theta}^{4}+a^{4} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{4}+2a^{2} r^{3} r_s^{2} \\\\sin{\\\\theta}^{2}-6a^{2} r^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+2a^{2} r^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+2a^{2} r \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-2a^{2} r \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+2r^{4} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-2r^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}\\\\right)\\\\right)+\\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-2r \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-r^{3} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}\\\\right)\\\\right)}{4\\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r^{3} r_s-r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right)^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{r}= & \\\\frac{-a^{4} r r_s^{2} \\\\left(r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(a^{2} r r_s-a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r^{3} r_s-r^{2} r_s^{2}-r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right) \\\\sin{\\\\theta}^{4}-a^{2} r_s \\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(-6a^{4} r^{3} r_s \\\\cos{\\\\theta}^{2}-2a^{4} r^{2} r_s \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+4a^{4} r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+2a^{4} r r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2}+4a^{4} r \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\partial_{r}\\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-3a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-6a^{2} r^{5} r_s \\\\cos{\\\\theta}^{2}-6a^{2} r^{5} r_s+2a^{2} r^{4} r_s^{2} \\\\cos{\\\\theta}^{2}-2a^{2} r^{4} r_s \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-2a^{2} r^{4} r_s \\\\partial_{r}\\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+8a^{2} r^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+2a^{2} r^{3} r_s^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+4a^{2} r^{3} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2}+8a^{2} r^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\partial_{r}\\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-2a^{2} r^{2} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2}-4a^{2} r^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\partial_{r}\\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-6a^{2} r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+3a^{2} r r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}%\\n-6r^{7} r_s+2r^{6} r_s^{2}-2r^{6} r_s \\\\partial_{r}\\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+4r^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+2r^{5} r_s^{2} \\\\partial_{r}\\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+2r^{5} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+4r^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\partial_{r}\\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-4r^{4} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\partial_{r}\\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-3r^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+r^{3} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}\\\\right) \\\\sin{\\\\theta}^{2}+\\\\left(-r r_s+r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(a^{2} \\\\sin{2\\\\theta} \\\\partial_{r}\\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+2r \\\\partial_{\\\\theta}\\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r^{3} r_s-r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right)^{2} \\\\tan{\\\\theta}+\\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(2a^{2} r_s \\\\left(a^{4} r^{2} r_s \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-a^{4} r^{2} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+2a^{4} r \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-a^{2} r^{4} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-a^{2} r^{3} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+a^{2} r^{3} r_s^{2} \\\\partial_{r}\\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-2a^{2} r^{3} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+2a^{2} r^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+a^{2} r^{2} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-a^{2} r^{2} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-2a^{2} r^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\partial_{r}\\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+a^{2} r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+a^{2} r \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3}+r^{5} r_s^{2} \\\\partial_{r}\\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r^{4} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-2r^{4} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\partial_{r}\\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)%\\n-2r^{3} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+r^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3}\\\\right) \\\\sin{\\\\theta}^{2}+\\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r^{3} r_s-r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right) \\\\left(-4a^{4} r^{2} r_s \\\\sin{\\\\theta}^{4}+a^{4} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{4}+2a^{2} r^{3} r_s^{2} \\\\sin{\\\\theta}^{2}-6a^{2} r^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+2a^{2} r^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+2a^{2} r \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-2a^{2} r \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+2r^{4} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-2r^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}\\\\right)\\\\right)+\\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+2r^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-2r \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}\\\\right) \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-a^{2} r r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-r^{3} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}\\\\right)}{2\\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r^{3} r_s-r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)\\\\right)^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}}\\\\\\\\[-.5ex]\\n\\\\end{aligned}\\\\right.\\n\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"substitute(rc, $\\\\Sigma = r**2 + a**2 \\\\cos{\\\\theta}**2, \\\\Delta = r**2 - rs r + a**2$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}R_{\\\\sigma \\\\nu} = \\\\left\\\\{\\\\begin{aligned}\\\\square{}_{t}{}_{t}= & r_s \\\\frac{54r^{5} r_s^{2} a^{4} \\\\cos{\\\\theta}^{2}+6r^{3} r_s^{2} a^{6} \\\\cos{\\\\theta}^{4}-104r^{6} r_s a^{4} \\\\cos{\\\\theta}^{2}-22r^{4} r_s a^{6} \\\\cos{\\\\theta}^{4}+4r^{2} r_s a^{8} \\\\cos{\\\\theta}^{6}+94r^{7} r_s^{2} a^{2} \\\\cos{\\\\theta}^{2}+12r^{5} r_s^{2} a^{4} \\\\cos{\\\\theta}^{4}-22r^{6} r_s^{3} a^{2} \\\\cos{\\\\theta}^{2}+2r^{4} r_s^{3} a^{4} \\\\cos{\\\\theta}^{4}-88r^{8} r_s a^{2} \\\\cos{\\\\theta}^{2}-22r^{6} r_s a^{4} \\\\cos{\\\\theta}^{4}+4r^{4} r_s a^{6} \\\\cos{\\\\theta}^{6}-2r^{3} r_s^{2} a^{6} \\\\cos{\\\\theta}^{6}+80r^{9} r_s^{2}-26r^{8} r_s^{3}+50r^{7} r_s^{2} a^{2}-82r^{10} r_s-78r^{8} r_s a^{2}+8r^{6} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}%\\n+8r^{4} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} \\\\cos{\\\\theta}^{2}-4r^{5} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-4r^{3} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} \\\\cos{\\\\theta}^{2}+4r^{4} r_s a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+4r^{2} r_s a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{2}-16r^{6} a^{4} r_s \\\\cos{\\\\theta}^{2}+8r^{4} a^{6} r_s \\\\cos{\\\\theta}^{4}+84r^{7} a^{4} \\\\cos{\\\\theta}^{2}+20r^{5} a^{6} \\\\cos{\\\\theta}^{4}-20r^{3} a^{8} \\\\cos{\\\\theta}^{6}+4r^{8} a^{2} r_s \\\\cos{\\\\theta}^{2}+48r^{6} a^{4} r_s \\\\cos{\\\\theta}^{4}-24r^{7} a^{2} r_s^{2} \\\\cos{\\\\theta}^{2}-40r^{5} a^{4} r_s^{2} \\\\cos{\\\\theta}^{4}+48r^{9} a^{2} \\\\cos{\\\\theta}^{2}+12r^{7} a^{4} \\\\cos{\\\\theta}^{4}-16r^{5} a^{6} \\\\cos{\\\\theta}^{6}+32r^{4} a^{6} r_s \\\\cos{\\\\theta}^{6}+28r^{11}+52r^{9} a^{2}%\\n-4r^{7} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-4r^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} \\\\cos{\\\\theta}^{2}-4r^{5} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-4r^{3} a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{2}+4r^{4} a^{6} \\\\cos{\\\\theta}^{4} r_s+18r^{2} a^{8} \\\\cos{\\\\theta}^{6} r_s-8r a^{10} \\\\cos{\\\\theta}^{8}-8r^{6} a^{4} \\\\cos{\\\\theta}^{4} r_s+22r^{4} a^{6} \\\\cos{\\\\theta}^{6} r_s-12r^{5} a^{4} \\\\cos{\\\\theta}^{4} r_s^{2}-14r^{3} a^{6} \\\\cos{\\\\theta}^{6} r_s^{2}-8r^{3} a^{8} \\\\cos{\\\\theta}^{8}+8r^{2} a^{8} \\\\cos{\\\\theta}^{8} r_s-22r^{8} a^{2} \\\\cos{\\\\theta}^{2} r_s+2r^{7} a^{2} \\\\cos{\\\\theta}^{2} r_s^{2}-14r^{6} a^{4} \\\\cos{\\\\theta}^{2} r_s-4r^{5} a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-4r^{3} a^{4} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+4r^{4} a^{2} \\\\cos{\\\\theta}^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+4r^{2} a^{4} \\\\cos{\\\\theta}^{4} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}%\\n-4r^{3} a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-4r a^{6} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+8r^{3} a^{6} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{2}-8r^{4} a^{6} r_s \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{2}-8r^{2} a^{8} r_s \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2}-8r^{5} a^{4} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{2}+8r^{6} a^{4} r_s \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{2}+8r^{4} a^{6} r_s \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2}-8r^{3} a^{6} r_s^{2} \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}^{2}-16r^{3} a^{6} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{4}+8r^{4} a^{6} r_s \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}^{2}+16r^{4} a^{6} r_s \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{4}+8r^{2} a^{8} r_s \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}^{4}+8r^{2} a^{8} r_s \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{6}+8r^{6} a^{2} r_s^{3} \\\\cos{\\\\theta}^{2}+8r^{4} a^{4} r_s^{3} \\\\cos{\\\\theta}^{4}-16r^{3} a^{6} r_s^{2} \\\\cos{\\\\theta}^{6}+8r^{2} a^{8} r_s \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2}+8r^{2} a^{8} r_s \\\\cos{\\\\theta}^{8}-2r^{3} r_s^{2} a^{6} \\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{2}%\\n+2r^{4} r_s a^{6} \\\\cos{4\\\\theta}+2r^{2} r_s a^{8} \\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{2}-2r^{5} r_s^{2} a^{4} \\\\cos{4\\\\theta}+2r^{6} r_s a^{4} \\\\cos{4\\\\theta}+2r^{4} r_s a^{6} \\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{2}+2r^{3} r_s^{2} a^{6} \\\\cos{\\\\theta}^{2}-2r^{4} r_s a^{6}-2r^{2} r_s a^{8} \\\\cos{\\\\theta}^{2}+2r^{5} r_s^{2} a^{4}-26r^{6} r_s a^{4}-34r^{4} r_s a^{6} \\\\cos{\\\\theta}^{2}-8r^{5} r_s^{2} a^{4} \\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2}+8r^{6} r_s a^{4} \\\\cos{2\\\\theta}+8r^{4} r_s a^{6} \\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2}-8r^{7} r_s^{2} a^{2} \\\\cos{2\\\\theta}+8r^{8} r_s a^{2} \\\\cos{2\\\\theta}+8r^{6} r_s a^{4} \\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2}-8r^{3} r_s^{2} a^{6} \\\\cos{\\\\theta}^{4} \\\\cos{2\\\\theta}+8r^{4} r_s a^{6} \\\\cos{\\\\theta}^{2} \\\\cos{2\\\\theta}+8r^{2} r_s a^{8} \\\\cos{\\\\theta}^{4} \\\\cos{2\\\\theta}%\\n-8r^{5} r_s^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\cos{2\\\\theta}+8r^{6} r_s a^{4} \\\\cos{\\\\theta}^{2} \\\\cos{2\\\\theta}+8r^{4} r_s a^{6} \\\\cos{\\\\theta}^{4} \\\\cos{2\\\\theta}+12r^{3} r_s^{2} a^{4} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2}-12r^{4} r_s a^{4} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)-12r^{2} r_s a^{6} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2}+12r^{5} r_s^{2} a^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)-12r^{6} r_s a^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)-12r^{4} r_s a^{4} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2}+12r^{3} r_s^{2} a^{4} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2}-12r^{4} r_s a^{4} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-12r^{2} r_s a^{6} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2}+12r^{5} r_s^{2} a^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-12r^{6} r_s a^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-12r^{4} r_s a^{4} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2}-8r^{2} r_s a^{8} \\\\cos{\\\\theta}^{4}+2r^{4} a^{6} \\\\cos{4\\\\theta} r_s \\\\cos{\\\\theta}^{2}-2r^{5} a^{6} \\\\cos{4\\\\theta}-2r^{3} a^{8} \\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{2}+2r^{6} a^{4} \\\\cos{4\\\\theta} r_s%\\n-2r^{7} a^{4} \\\\cos{4\\\\theta}-2r^{5} a^{6} \\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{2}-2r^{4} a^{6} r_s \\\\cos{\\\\theta}^{2}+2r^{5} a^{6}+3r^{3} a^{8} \\\\cos{\\\\theta}^{2}-2r^{6} a^{4} r_s+26r^{7} a^{4}+39r^{5} a^{6} \\\\cos{\\\\theta}^{2}+8r^{6} a^{4} \\\\cos{2\\\\theta} r_s \\\\cos{\\\\theta}^{2}-8r^{7} a^{4} \\\\cos{2\\\\theta}-8r^{5} a^{6} \\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2}+8r^{8} a^{2} \\\\cos{2\\\\theta} r_s-8r^{9} a^{2} \\\\cos{2\\\\theta}-8r^{7} a^{4} \\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2}+24r^{4} a^{6} \\\\cos{\\\\theta}^{4} \\\\cos{2\\\\theta} r_s-16r^{5} a^{6} \\\\cos{\\\\theta}^{2} \\\\cos{2\\\\theta}-24r^{3} a^{8} \\\\cos{\\\\theta}^{4} \\\\cos{2\\\\theta}+16r^{6} a^{4} \\\\cos{\\\\theta}^{2} \\\\cos{2\\\\theta} r_s-16r^{7} a^{4} \\\\cos{\\\\theta}^{2} \\\\cos{2\\\\theta}-24r^{5} a^{6} \\\\cos{\\\\theta}^{4} \\\\cos{2\\\\theta}%\\n-12r^{4} a^{4} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s \\\\cos{\\\\theta}^{2}+12r^{5} a^{4} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+12r^{3} a^{6} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2}-12r^{6} a^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s+12r^{7} a^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+12r^{5} a^{4} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2}-12r^{4} a^{4} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\cos{\\\\theta}^{2}+12r^{5} a^{4} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+12r^{3} a^{6} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2}-12r^{6} a^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s+12r^{7} a^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+12r^{5} a^{4} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2}-24r^{8} a^{2} r_s+9r^{3} a^{8} \\\\cos{\\\\theta}^{4}+r^{2} a^{8} \\\\cos{\\\\theta}^{4} \\\\cos{4\\\\theta} r_s-r^{3} a^{8} \\\\cos{\\\\theta}^{2} \\\\cos{4\\\\theta}-r a^{10} \\\\cos{\\\\theta}^{4} \\\\cos{4\\\\theta}+r^{4} a^{6} \\\\cos{\\\\theta}^{2} \\\\cos{4\\\\theta} r_s-r^{5} a^{6} \\\\cos{\\\\theta}^{2} \\\\cos{4\\\\theta}-r^{3} a^{8} \\\\cos{\\\\theta}^{4} \\\\cos{4\\\\theta}%\\n-r^{2} a^{8} \\\\cos{\\\\theta}^{4} r_s+r a^{10} \\\\cos{\\\\theta}^{4}-r^{4} a^{6} \\\\cos{\\\\theta}^{2} r_s+8r^{2} a^{8} \\\\cos{\\\\theta}^{6} \\\\cos{2\\\\theta} r_s-8r a^{10} \\\\cos{\\\\theta}^{6} \\\\cos{2\\\\theta}-8r^{3} a^{8} \\\\cos{\\\\theta}^{6} \\\\cos{2\\\\theta}-12r^{2} a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s+12r^{3} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+12r a^{8} \\\\cos{\\\\theta}^{4} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)-12r^{4} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s+12r^{5} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+12r^{3} a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)-12r^{2} a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s+12r^{3} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+12r a^{8} \\\\cos{\\\\theta}^{4} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-12r^{4} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s+12r^{5} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+12r^{3} a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-4r a^{10} \\\\cos{\\\\theta}^{6}+4r_s^{2} \\\\left(r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} r^{3}%\\n-2r_s^{3} \\\\left(r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} r^{2}+2r_s^{2} \\\\left(r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{4} r-4r_s^{2} \\\\left(r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} r^{3} \\\\sin{\\\\theta}^{2}+2r_s^{3} \\\\left(r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} r^{2} \\\\sin{\\\\theta}^{2}-2r_s^{2} \\\\left(r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{4} r \\\\sin{\\\\theta}^{2}+2r_s \\\\left(r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} r^{4} \\\\sin{\\\\theta}^{2}+2r_s \\\\left(r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{4} r^{2} \\\\sin{\\\\theta}^{2}+2r_s \\\\left(r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} r^{2}-2r_s^{2} \\\\left(r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} r+2r_s \\\\left(r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}-2r_s \\\\left(r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} r^{4}-2r_s \\\\left(r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{4} r^{2}-2r_s \\\\left(r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{4} \\\\cos{\\\\theta}^{2} r^{2}+2r_s^{2} \\\\left(r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{4} \\\\cos{\\\\theta}^{2} r-2r_s \\\\left(r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{6} \\\\cos{\\\\theta}^{2}+4r_s^{2} \\\\left(r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r^{5}-2r_s^{3} \\\\left(r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r^{4}+2r_s^{2} \\\\left(r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r^{3} a^{2}-2r_s \\\\left(r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r^{6}-2r_s \\\\left(r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r^{4} a^{2}%\\n-2r_s \\\\left(r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r^{4} a^{2} \\\\cos{\\\\theta}^{2}+2r_s^{2} \\\\left(r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r^{3} a^{2} \\\\cos{\\\\theta}^{2}-2r_s \\\\left(r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r^{2} a^{4} \\\\cos{\\\\theta}^{2}-2r^{2} r_s^{3} a^{6} \\\\cos{\\\\theta}^{6}+2r r_s^{2} a^{8} \\\\cos{\\\\theta}^{6}-44r^{6} r_s^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{2} \\\\cos{\\\\theta}^{2}+28r^{7} r_s \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{2}+32r^{5} r_s \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{4} \\\\cos{\\\\theta}^{2}-40r^{8} r_s^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+24r^{9} r_s \\\\partial_{r}\\\\left(r^{2}\\\\right)+24r^{7} r_s \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{2} \\\\cos{\\\\theta}^{2}-52r^{6} r_s^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{2} \\\\cos{\\\\theta}^{2}+32r^{7} r_s \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{2}+40r^{5} r_s \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{4} \\\\cos{\\\\theta}^{2}-44r^{8} r_s^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+28r^{9} r_s \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+32r^{7} r_s \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{2} \\\\cos{\\\\theta}^{2}+20r^{5} r_s^{3} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{2} \\\\cos{\\\\theta}^{2}-20r^{6} r_s^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{2}-28r^{4} r_s^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{4} \\\\cos{\\\\theta}^{2}%\\n+16r^{7} r_s^{3} \\\\partial_{r}\\\\left(r^{2}\\\\right)+20r^{5} r_s^{3} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{2} \\\\cos{\\\\theta}^{2}-20r^{6} r_s^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{2}-28r^{4} r_s^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{4} \\\\cos{\\\\theta}^{2}+16r^{7} r_s^{3} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-12r^{4} r_s^{2} a^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2}+12r^{5} r_s a^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)+12r^{3} r_s a^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2}-12r^{6} r_s^{2} a^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+12r^{7} r_s a^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+12r^{5} r_s a^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2}-12r^{4} r_s^{2} a^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2}+12r^{5} r_s a^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+12r^{3} r_s a^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2}-12r^{6} r_s^{2} a^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+12r^{7} r_s a^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+12r^{5} r_s a^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2}+16r^{4} r_s^{2} a^{4} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)-20r^{5} r_s a^{4} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-16r^{3} r_s a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)%\\n+20r^{6} r_s^{2} a^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-8r^{7} r_s a^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-4r^{5} r_s a^{4} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)+24r^{4} r_s^{2} a^{4} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-24r^{5} r_s a^{4} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-24r^{3} r_s a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+24r^{6} r_s^{2} a^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-12r^{7} r_s a^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-12r^{5} r_s a^{4} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-12r^{3} r_s^{3} a^{4} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)+24r^{4} r_s^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+24r^{2} r_s^{2} a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)-12r^{5} r_s^{3} a^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-12r^{3} r_s^{3} a^{4} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+24r^{4} r_s^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+24r^{2} r_s^{2} a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-12r^{5} r_s^{3} a^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-12r^{3} r_s a^{6} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-12r r_s a^{8} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)-12r^{3} r_s a^{6} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)%\\n-12r r_s a^{8} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-4r^{4} r_s^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{4} \\\\cos{\\\\theta}^{4}+4r^{3} r_s \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{6} \\\\cos{\\\\theta}^{4}+4r^{3} r_s^{3} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{4} \\\\cos{\\\\theta}^{4}-8r^{2} r_s^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{6} \\\\cos{\\\\theta}^{4}+4r^{5} r_s \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{4}+8r^{3} r_s \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{6} \\\\cos{\\\\theta}^{2}+4r r_s \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{8} \\\\cos{\\\\theta}^{4}-8r^{4} r_s^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{4} \\\\cos{\\\\theta}^{4}+8r^{3} r_s \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{6} \\\\cos{\\\\theta}^{4}+4r^{5} r_s \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{4} \\\\cos{\\\\theta}^{4}+4r^{3} r_s^{3} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{4} \\\\cos{\\\\theta}^{4}-8r^{2} r_s^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{6} \\\\cos{\\\\theta}^{4}+4r^{5} r_s \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{4}+8r^{3} r_s \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{6} \\\\cos{\\\\theta}^{2}+4r r_s \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{8} \\\\cos{\\\\theta}^{4}-8r^{6} r_s^{2} \\\\partial_{r}\\\\left(r_s r\\\\right) a^{2} \\\\cos{\\\\theta}^{2}+4r^{7} r_s \\\\partial_{r}\\\\left(r_s r\\\\right) a^{2}+8r^{5} r_s \\\\partial_{r}\\\\left(r_s r\\\\right) a^{4} \\\\cos{\\\\theta}^{2}-4r^{8} r_s^{2} \\\\partial_{r}\\\\left(r_s r\\\\right)%\\n+4r^{9} r_s \\\\partial_{r}\\\\left(r_s r\\\\right)+8r^{7} r_s \\\\partial_{r}\\\\left(r_s r\\\\right) a^{2} \\\\cos{\\\\theta}^{2}-4r^{4} r_s^{2} \\\\partial_{r}\\\\left(r_s r\\\\right) a^{4} \\\\cos{\\\\theta}^{4}+4r^{3} r_s \\\\partial_{r}\\\\left(r_s r\\\\right) a^{6} \\\\cos{\\\\theta}^{4}+4r^{5} r_s \\\\partial_{r}\\\\left(r_s r\\\\right) a^{4} \\\\cos{\\\\theta}^{4}+8r^{6} r_s^{2} \\\\partial_{r}\\\\left(a^{2}\\\\right) a^{2} \\\\cos{\\\\theta}^{2}-4r^{7} r_s \\\\partial_{r}\\\\left(a^{2}\\\\right) a^{2}-8r^{5} r_s \\\\partial_{r}\\\\left(a^{2}\\\\right) a^{4} \\\\cos{\\\\theta}^{2}+4r^{8} r_s^{2} \\\\partial_{r}\\\\left(a^{2}\\\\right)-4r^{9} r_s \\\\partial_{r}\\\\left(a^{2}\\\\right)-8r^{7} r_s \\\\partial_{r}\\\\left(a^{2}\\\\right) a^{2} \\\\cos{\\\\theta}^{2}+4r^{4} r_s^{2} \\\\partial_{r}\\\\left(a^{2}\\\\right) a^{4} \\\\cos{\\\\theta}^{4}-4r^{3} r_s \\\\partial_{r}\\\\left(a^{2}\\\\right) a^{6} \\\\cos{\\\\theta}^{4}-4r^{5} r_s \\\\partial_{r}\\\\left(a^{2}\\\\right) a^{4} \\\\cos{\\\\theta}^{4}-4r^{2} r_s^{2} a^{6} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right)+4r r_s a^{8} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right)+4r^{3} r_s a^{6} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right)+8r^{4} r_s^{2} a^{4} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r_s r\\\\right)-4r^{5} r_s a^{4} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r_s r\\\\right)-8r^{3} r_s a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r_s r\\\\right)%\\n+4r^{6} r_s^{2} a^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r_s r\\\\right)-4r^{7} r_s a^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r_s r\\\\right)-8r^{5} r_s a^{4} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r_s r\\\\right)+4r^{2} r_s^{2} a^{6} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(r_s r\\\\right)-4r r_s a^{8} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(r_s r\\\\right)-4r^{3} r_s a^{6} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(r_s r\\\\right)-8r^{4} r_s^{2} a^{4} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2}\\\\right)+4r^{5} r_s a^{4} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2}\\\\right)+8r^{3} r_s a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2}\\\\right)-4r^{6} r_s^{2} a^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2}\\\\right)+4r^{7} r_s a^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2}\\\\right)+8r^{5} r_s a^{4} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2}\\\\right)-4r^{2} r_s^{2} a^{6} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(a^{2}\\\\right)+4r r_s a^{8} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(a^{2}\\\\right)+4r^{3} r_s a^{6} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(a^{2}\\\\right)+12r^{7} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{2} r_s \\\\cos{\\\\theta}^{2}-16r^{8} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{2}-20r^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{4} \\\\cos{\\\\theta}^{2}+16r^{9} \\\\partial_{r}\\\\left(r^{2}\\\\right) r_s-12r^{10} \\\\partial_{r}\\\\left(r^{2}\\\\right)%\\n-12r^{8} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{2} \\\\cos{\\\\theta}^{2}+16r^{7} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{2} r_s \\\\cos{\\\\theta}^{2}-20r^{8} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{2}-28r^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{4} \\\\cos{\\\\theta}^{2}+20r^{9} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s-16r^{10} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-20r^{8} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{2} \\\\cos{\\\\theta}^{2}+12r^{5} a^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right) r_s \\\\cos{\\\\theta}^{2}-12r^{6} a^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)-12r^{4} a^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2}+12r^{7} a^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) r_s-12r^{8} a^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-12r^{6} a^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2}+12r^{5} a^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\cos{\\\\theta}^{2}-12r^{6} a^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-12r^{4} a^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2}+12r^{7} a^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s-12r^{8} a^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-12r^{6} a^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2}-4r^{5} a^{4} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right) r_s%\\n+20r^{6} a^{4} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+16r^{4} a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)-8r^{7} a^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) r_s+8r^{8} a^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+4r^{6} a^{4} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)-12r^{5} a^{4} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s+24r^{6} a^{4} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+24r^{4} a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-12r^{7} a^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s+12r^{8} a^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+12r^{6} a^{4} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+12r^{4} a^{4} \\\\cos{\\\\theta}^{4} r_s^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-12r^{5} a^{4} \\\\cos{\\\\theta}^{2} r_s \\\\partial_{r}\\\\left(r^{2}\\\\right)-12r^{3} a^{6} \\\\cos{\\\\theta}^{4} r_s \\\\partial_{r}\\\\left(r^{2}\\\\right)+12r^{6} a^{2} \\\\cos{\\\\theta}^{2} r_s^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-12r^{7} a^{2} \\\\cos{\\\\theta}^{2} r_s \\\\partial_{r}\\\\left(r^{2}\\\\right)-12r^{5} a^{4} \\\\cos{\\\\theta}^{4} r_s \\\\partial_{r}\\\\left(r^{2}\\\\right)+12r^{4} a^{4} \\\\cos{\\\\theta}^{4} r_s^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-12r^{5} a^{4} \\\\cos{\\\\theta}^{2} r_s \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-12r^{3} a^{6} \\\\cos{\\\\theta}^{4} r_s \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)%\\n+12r^{6} a^{2} \\\\cos{\\\\theta}^{2} r_s^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-12r^{7} a^{2} \\\\cos{\\\\theta}^{2} r_s \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-12r^{5} a^{4} \\\\cos{\\\\theta}^{4} r_s \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-12r^{3} a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right) r_s+12r^{4} a^{6} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+12r^{2} a^{8} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)-12r^{5} a^{4} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) r_s-12r^{3} a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s+12r^{4} a^{6} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+12r^{2} a^{8} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-12r^{5} a^{4} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s-4r^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{6} \\\\cos{\\\\theta}^{4}-8r^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right) r_s^{2} a^{2} \\\\cos{\\\\theta}^{2}+4r^{7} \\\\partial_{r}\\\\left(r^{2}\\\\right) r_s a^{2}+8r^{5} \\\\partial_{r}\\\\left(r^{2}\\\\right) r_s a^{4} \\\\cos{\\\\theta}^{2}-4r^{8} \\\\partial_{r}\\\\left(r^{2}\\\\right) r_s^{2}+8r^{7} \\\\partial_{r}\\\\left(r^{2}\\\\right) r_s a^{2} \\\\cos{\\\\theta}^{2}-4r^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right) r_s^{2} a^{4} \\\\cos{\\\\theta}^{4}+4r^{3} \\\\partial_{r}\\\\left(r^{2}\\\\right) r_s a^{6} \\\\cos{\\\\theta}^{4}+4r^{5} \\\\partial_{r}\\\\left(r^{2}\\\\right) r_s a^{4} \\\\cos{\\\\theta}^{4}%\\n+4r^{5} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{4} r_s \\\\cos{\\\\theta}^{2}-4r^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{4}-8r^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{6} \\\\cos{\\\\theta}^{2}+4r^{7} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{2} r_s+4r^{3} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{6} \\\\cos{\\\\theta}^{4} r_s-4r^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{8} \\\\cos{\\\\theta}^{4}+4r^{5} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{4} \\\\cos{\\\\theta}^{2} r_s+4r^{5} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{4} \\\\cos{\\\\theta}^{4} r_s-8r^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{6} \\\\cos{\\\\theta}^{4}+4r^{7} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{2} \\\\cos{\\\\theta}^{2} r_s-4r^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{4} \\\\cos{\\\\theta}^{4}-8r^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s^{2} a^{2} \\\\cos{\\\\theta}^{2}+4r^{7} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s a^{2}+8r^{5} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s a^{4} \\\\cos{\\\\theta}^{2}-4r^{8} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s^{2}+8r^{7} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s a^{2} \\\\cos{\\\\theta}^{2}-4r^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s^{2} a^{4} \\\\cos{\\\\theta}^{4}+4r^{3} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s a^{6} \\\\cos{\\\\theta}^{4}+4r^{5} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s a^{4} \\\\cos{\\\\theta}^{4}+4r^{5} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{4} r_s \\\\cos{\\\\theta}^{2}%\\n-4r^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{4}-8r^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{6} \\\\cos{\\\\theta}^{2}+4r^{7} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{2} r_s+4r^{3} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{6} \\\\cos{\\\\theta}^{4} r_s-4r^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{8} \\\\cos{\\\\theta}^{4}+4r^{5} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{4} \\\\cos{\\\\theta}^{2} r_s+4r^{7} \\\\partial_{r}\\\\left(r_s r\\\\right) a^{2} r_s \\\\cos{\\\\theta}^{2}-4r^{8} \\\\partial_{r}\\\\left(r_s r\\\\right) a^{2}-8r^{6} \\\\partial_{r}\\\\left(r_s r\\\\right) a^{4} \\\\cos{\\\\theta}^{2}+4r^{9} \\\\partial_{r}\\\\left(r_s r\\\\right) r_s-4r^{10} \\\\partial_{r}\\\\left(r_s r\\\\right)-8r^{8} \\\\partial_{r}\\\\left(r_s r\\\\right) a^{2} \\\\cos{\\\\theta}^{2}+4r^{5} \\\\partial_{r}\\\\left(r_s r\\\\right) a^{4} \\\\cos{\\\\theta}^{4} r_s-4r^{4} \\\\partial_{r}\\\\left(r_s r\\\\right) a^{6} \\\\cos{\\\\theta}^{4}+4r^{7} \\\\partial_{r}\\\\left(r_s r\\\\right) a^{2} \\\\cos{\\\\theta}^{2} r_s-4r^{6} \\\\partial_{r}\\\\left(r_s r\\\\right) a^{4} \\\\cos{\\\\theta}^{4}-4r^{7} \\\\partial_{r}\\\\left(a^{2}\\\\right) a^{2} r_s \\\\cos{\\\\theta}^{2}+4r^{8} \\\\partial_{r}\\\\left(a^{2}\\\\right) a^{2}+8r^{6} \\\\partial_{r}\\\\left(a^{2}\\\\right) a^{4} \\\\cos{\\\\theta}^{2}-4r^{9} \\\\partial_{r}\\\\left(a^{2}\\\\right) r_s%\\n+4r^{10} \\\\partial_{r}\\\\left(a^{2}\\\\right)+8r^{8} \\\\partial_{r}\\\\left(a^{2}\\\\right) a^{2} \\\\cos{\\\\theta}^{2}-4r^{5} \\\\partial_{r}\\\\left(a^{2}\\\\right) a^{4} \\\\cos{\\\\theta}^{4} r_s+4r^{4} \\\\partial_{r}\\\\left(a^{2}\\\\right) a^{6} \\\\cos{\\\\theta}^{4}-4r^{7} \\\\partial_{r}\\\\left(a^{2}\\\\right) a^{2} \\\\cos{\\\\theta}^{2} r_s+4r^{6} \\\\partial_{r}\\\\left(a^{2}\\\\right) a^{4} \\\\cos{\\\\theta}^{4}+4r^{3} a^{6} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right) r_s-4r^{2} a^{8} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right)-4r^{4} a^{6} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right)-8r^{5} a^{4} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r_s r\\\\right) r_s+4r^{6} a^{4} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r_s r\\\\right)+8r^{4} a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r_s r\\\\right)-4r^{7} a^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r_s r\\\\right) r_s+4r^{8} a^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r_s r\\\\right)+8r^{6} a^{4} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r_s r\\\\right)-4r^{3} a^{6} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(r_s r\\\\right) r_s+4r^{2} a^{8} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(r_s r\\\\right)+4r^{4} a^{6} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(r_s r\\\\right)+8r^{5} a^{4} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2}\\\\right) r_s-4r^{6} a^{4} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2}\\\\right)%\\n-8r^{4} a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2}\\\\right)+4r^{7} a^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2}\\\\right) r_s-4r^{8} a^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2}\\\\right)-8r^{6} a^{4} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2}\\\\right)+4r^{3} a^{6} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(a^{2}\\\\right) r_s-4r^{2} a^{8} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(a^{2}\\\\right)-4r^{4} a^{6} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(a^{2}\\\\right)+a^{8} \\\\cos{\\\\theta}^{4} r^{2} \\\\cos{4\\\\theta} r_s-a^{8} \\\\cos{\\\\theta}^{2} r^{3} \\\\cos{4\\\\theta}-a^{10} \\\\cos{\\\\theta}^{4} r \\\\cos{4\\\\theta}+a^{6} \\\\cos{\\\\theta}^{2} r^{4} \\\\cos{4\\\\theta} r_s-a^{6} \\\\cos{\\\\theta}^{2} r^{5} \\\\cos{4\\\\theta}-a^{8} \\\\cos{\\\\theta}^{4} r^{3} \\\\cos{4\\\\theta}-a^{8} \\\\cos{\\\\theta}^{4} r^{2} r_s+a^{8} \\\\cos{\\\\theta}^{2} r^{3}+a^{10} \\\\cos{\\\\theta}^{4} r-a^{6} \\\\cos{\\\\theta}^{2} r^{4} r_s+21a^{6} \\\\cos{\\\\theta}^{2} r^{5}+33a^{8} \\\\cos{\\\\theta}^{4} r^{3}+28a^{4} \\\\cos{\\\\theta}^{4} r^{5} r_s^{2}%\\n-38a^{4} \\\\cos{\\\\theta}^{2} r^{6} r_s-60a^{6} \\\\cos{\\\\theta}^{4} r^{4} r_s+18a^{2} \\\\cos{\\\\theta}^{2} r^{7} r_s^{2}-34a^{2} \\\\cos{\\\\theta}^{2} r^{8} r_s-56a^{4} \\\\cos{\\\\theta}^{4} r^{6} r_s+36a^{4} \\\\cos{\\\\theta}^{2} r^{7}+60a^{6} \\\\cos{\\\\theta}^{4} r^{5}-26a^{6} \\\\cos{\\\\theta}^{6} r^{4} r_s+28a^{8} \\\\cos{\\\\theta}^{6} r^{3}+28a^{4} \\\\cos{\\\\theta}^{4} r^{7}+16a^{6} \\\\cos{\\\\theta}^{6} r^{5}+10a^{6} \\\\cos{\\\\theta}^{6} r^{3} r_s^{2}-22a^{8} \\\\cos{\\\\theta}^{6} r^{2} r_s+12a^{10} \\\\cos{\\\\theta}^{6} r-4a^{8} \\\\cos{\\\\theta}^{8} r^{2} r_s+4a^{10} \\\\cos{\\\\theta}^{8} r+4a^{8} \\\\cos{\\\\theta}^{8} r^{3}+4a^{6} \\\\cos{\\\\theta}^{6} r_s^{2} r^{3}-2a^{6} \\\\cos{\\\\theta}^{4} r_s r^{4}-4a^{8} \\\\cos{\\\\theta}^{6} r_s r^{2}%\\n+2a^{4} \\\\cos{\\\\theta}^{4} r_s^{2} r^{5}-2a^{4} \\\\cos{\\\\theta}^{4} r_s r^{6}-4a^{6} \\\\cos{\\\\theta}^{6} r_s r^{4}+2a^{8} \\\\cos{\\\\theta}^{8} r_s^{2} r-2a^{10} \\\\cos{\\\\theta}^{8} r_s-2a^{8} \\\\cos{\\\\theta}^{8} r_s r^{2}-8a^{4} \\\\cos{\\\\theta}^{4} r^{5} \\\\partial_{r}\\\\left(r^{2}\\\\right) r_s-20a^{4} \\\\cos{\\\\theta}^{2} r^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right)-4a^{6} \\\\cos{\\\\theta}^{4} r^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)+8a^{2} \\\\cos{\\\\theta}^{2} r^{7} \\\\partial_{r}\\\\left(r^{2}\\\\right) r_s-8a^{2} \\\\cos{\\\\theta}^{2} r^{8} \\\\partial_{r}\\\\left(r^{2}\\\\right)+8a^{4} \\\\cos{\\\\theta}^{4} r^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right)-24a^{4} \\\\cos{\\\\theta}^{2} r^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-12a^{6} \\\\cos{\\\\theta}^{4} r^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+12a^{2} \\\\cos{\\\\theta}^{2} r^{7} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s-12a^{2} \\\\cos{\\\\theta}^{2} r^{8} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-12a^{4} \\\\cos{\\\\theta}^{4} r^{4} r_s^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+12a^{4} \\\\cos{\\\\theta}^{2} r^{5} r_s \\\\partial_{r}\\\\left(r^{2}\\\\right)+12a^{6} \\\\cos{\\\\theta}^{4} r^{3} r_s \\\\partial_{r}\\\\left(r^{2}\\\\right)-12a^{2} \\\\cos{\\\\theta}^{2} r^{6} r_s^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)%\\n+12a^{2} \\\\cos{\\\\theta}^{2} r^{7} r_s \\\\partial_{r}\\\\left(r^{2}\\\\right)+12a^{4} \\\\cos{\\\\theta}^{4} r^{5} r_s \\\\partial_{r}\\\\left(r^{2}\\\\right)-12a^{4} \\\\cos{\\\\theta}^{4} r^{4} r_s^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+12a^{4} \\\\cos{\\\\theta}^{2} r^{5} r_s \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+12a^{6} \\\\cos{\\\\theta}^{4} r^{3} r_s \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-12a^{2} \\\\cos{\\\\theta}^{2} r^{6} r_s^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+12a^{2} \\\\cos{\\\\theta}^{2} r^{7} r_s \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+12a^{4} \\\\cos{\\\\theta}^{4} r^{5} r_s \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+12a^{6} \\\\cos{\\\\theta}^{4} r^{3} \\\\partial_{r}\\\\left(r^{2}\\\\right) r_s-12a^{6} \\\\cos{\\\\theta}^{2} r^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)-12a^{8} \\\\cos{\\\\theta}^{4} r^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+12a^{4} \\\\cos{\\\\theta}^{2} r^{5} \\\\partial_{r}\\\\left(r^{2}\\\\right) r_s+12a^{6} \\\\cos{\\\\theta}^{4} r^{3} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s-12a^{6} \\\\cos{\\\\theta}^{2} r^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-12a^{8} \\\\cos{\\\\theta}^{4} r^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+12a^{4} \\\\cos{\\\\theta}^{2} r^{5} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s-16a^{6} \\\\cos{\\\\theta}^{6} r^{3} \\\\partial_{r}\\\\left(r^{2}\\\\right) r_s+16a^{8} \\\\cos{\\\\theta}^{6} r^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+16a^{6} \\\\cos{\\\\theta}^{6} r^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)-12a^{6} \\\\cos{\\\\theta}^{6} r^{3} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s%\\n+12a^{8} \\\\cos{\\\\theta}^{6} r^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+12a^{6} \\\\cos{\\\\theta}^{6} r^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+12a^{6} \\\\cos{\\\\theta}^{6} r_s^{2} r^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-12a^{6} \\\\cos{\\\\theta}^{4} r_s r^{3} \\\\partial_{r}\\\\left(r^{2}\\\\right)-12a^{8} \\\\cos{\\\\theta}^{6} r_s r \\\\partial_{r}\\\\left(r^{2}\\\\right)+12a^{4} \\\\cos{\\\\theta}^{4} r_s^{2} r^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)-12a^{4} \\\\cos{\\\\theta}^{4} r_s r^{5} \\\\partial_{r}\\\\left(r^{2}\\\\right)-12a^{6} \\\\cos{\\\\theta}^{6} r_s r^{3} \\\\partial_{r}\\\\left(r^{2}\\\\right)+12a^{6} \\\\cos{\\\\theta}^{6} r_s^{2} r^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-12a^{6} \\\\cos{\\\\theta}^{4} r_s r^{3} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-12a^{8} \\\\cos{\\\\theta}^{6} r_s r \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+12a^{4} \\\\cos{\\\\theta}^{4} r_s^{2} r^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-12a^{4} \\\\cos{\\\\theta}^{4} r_s r^{5} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-12a^{6} \\\\cos{\\\\theta}^{6} r_s r^{3} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-8a^{8} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right) r r_s+4a^{8} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right) r^{2}+8a^{10} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right)-4a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right) r^{3} r_s-8a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right) r^{4}-4a^{8} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right) r^{2}%\\n-8a^{8} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r r_s+4a^{8} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r^{2}+8a^{10} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-4a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r^{3} r_s-4a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r^{4}+4a^{8} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r^{2}+16a^{2} \\\\cos{\\\\theta}^{2} r^{9}+12a^{4} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right) r^{5} r_s-8a^{4} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) r^{6}+4a^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) r^{7} r_s-4a^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) r^{8}-12a^{4} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right) r^{6}+12a^{6} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right) r^{3} r_s-12a^{6} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right) r^{4}-8a^{4} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right) r_s^{2} r^{4}+4a^{4} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) r_s r^{5}+8a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right) r_s r^{3}-4a^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) r_s^{2} r^{6}+4a^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) r_s r^{7}+8a^{4} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right) r_s r^{5}%\\n-4a^{6} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right) r_s^{2} r^{2}+4a^{8} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right) r_s r+4a^{6} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right) r_s r^{3}-4a^{6} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) r^{4}+4a^{4} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) r^{5} r_s+8a^{4} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r^{5} r_s-8a^{4} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r^{6}+4a^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r^{7} r_s-4a^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r^{8}-8a^{4} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r^{6}+4a^{6} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r^{3} r_s-4a^{6} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r^{4}-8a^{4} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s^{2} r^{4}+4a^{4} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s r^{5}+8a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s r^{3}-4a^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s^{2} r^{6}+4a^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s r^{7}+8a^{4} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s r^{5}-4a^{6} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s^{2} r^{2}+4a^{8} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s r%\\n+4a^{6} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s r^{3}-4a^{6} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r^{4}+4a^{4} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r^{5} r_s+8a^{4} \\\\cos{\\\\theta}^{4} r^{5} \\\\partial_{r}\\\\left(r_s r\\\\right) r_s-4a^{4} \\\\cos{\\\\theta}^{2} r^{6} \\\\partial_{r}\\\\left(r_s r\\\\right)-8a^{6} \\\\cos{\\\\theta}^{4} r^{4} \\\\partial_{r}\\\\left(r_s r\\\\right)+4a^{2} \\\\cos{\\\\theta}^{2} r^{7} \\\\partial_{r}\\\\left(r_s r\\\\right) r_s-4a^{2} \\\\cos{\\\\theta}^{2} r^{8} \\\\partial_{r}\\\\left(r_s r\\\\right)-8a^{4} \\\\cos{\\\\theta}^{4} r^{6} \\\\partial_{r}\\\\left(r_s r\\\\right)+4a^{6} \\\\cos{\\\\theta}^{6} r^{3} \\\\partial_{r}\\\\left(r_s r\\\\right) r_s-4a^{8} \\\\cos{\\\\theta}^{6} r^{2} \\\\partial_{r}\\\\left(r_s r\\\\right)-4a^{6} \\\\cos{\\\\theta}^{6} r^{4} \\\\partial_{r}\\\\left(r_s r\\\\right)-8a^{4} \\\\cos{\\\\theta}^{4} r^{5} \\\\partial_{r}\\\\left(a^{2}\\\\right) r_s+4a^{4} \\\\cos{\\\\theta}^{2} r^{6} \\\\partial_{r}\\\\left(a^{2}\\\\right)+8a^{6} \\\\cos{\\\\theta}^{4} r^{4} \\\\partial_{r}\\\\left(a^{2}\\\\right)-4a^{2} \\\\cos{\\\\theta}^{2} r^{7} \\\\partial_{r}\\\\left(a^{2}\\\\right) r_s+4a^{2} \\\\cos{\\\\theta}^{2} r^{8} \\\\partial_{r}\\\\left(a^{2}\\\\right)+8a^{4} \\\\cos{\\\\theta}^{4} r^{6} \\\\partial_{r}\\\\left(a^{2}\\\\right)-4a^{6} \\\\cos{\\\\theta}^{6} r^{3} \\\\partial_{r}\\\\left(a^{2}\\\\right) r_s+4a^{8} \\\\cos{\\\\theta}^{6} r^{2} \\\\partial_{r}\\\\left(a^{2}\\\\right)%\\n+4a^{6} \\\\cos{\\\\theta}^{6} r^{4} \\\\partial_{r}\\\\left(a^{2}\\\\right)+4a^{8} \\\\cos{\\\\theta}^{8} \\\\partial_{r}\\\\left(r^{2}\\\\right) r r_s-4a^{10} \\\\cos{\\\\theta}^{8} \\\\partial_{r}\\\\left(r^{2}\\\\right)-4a^{8} \\\\cos{\\\\theta}^{8} \\\\partial_{r}\\\\left(r^{2}\\\\right) r^{2}-8a^{6} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(r_s r\\\\right) r^{3} r_s+4a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r_s r\\\\right) r^{4}+8a^{8} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(r_s r\\\\right) r^{2}-4a^{4} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r_s r\\\\right) r^{5} r_s+4a^{4} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r_s r\\\\right) r^{6}+8a^{6} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(r_s r\\\\right) r^{4}-4a^{8} \\\\cos{\\\\theta}^{8} \\\\partial_{r}\\\\left(r_s r\\\\right) r r_s+4a^{10} \\\\cos{\\\\theta}^{8} \\\\partial_{r}\\\\left(r_s r\\\\right)+4a^{8} \\\\cos{\\\\theta}^{8} \\\\partial_{r}\\\\left(r_s r\\\\right) r^{2}+8a^{6} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(a^{2}\\\\right) r^{3} r_s-4a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2}\\\\right) r^{4}-8a^{8} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(a^{2}\\\\right) r^{2}+4a^{4} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2}\\\\right) r^{5} r_s-4a^{4} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2}\\\\right) r^{6}-8a^{6} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(a^{2}\\\\right) r^{4}+4a^{8} \\\\cos{\\\\theta}^{8} \\\\partial_{r}\\\\left(a^{2}\\\\right) r r_s%\\n-4a^{10} \\\\cos{\\\\theta}^{8} \\\\partial_{r}\\\\left(a^{2}\\\\right)-4a^{8} \\\\cos{\\\\theta}^{8} \\\\partial_{r}\\\\left(a^{2}\\\\right) r^{2}}{8r^{2} r_s^{2} a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4}-8r^{3} r_s a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4}-8r r_s a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4}+8r^{4} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4}-16r^{5} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4}-8r^{3} r_s a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4}-8r^{3} a^{2} r_s \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4}+8r^{4} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4}+8r^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4}+8r^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4}+8r^{4} a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4}-8a^{4} \\\\cos{\\\\theta}^{4} r r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4}+8a^{4} \\\\cos{\\\\theta}^{2} r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4}+8a^{6} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4}-8a^{2} \\\\cos{\\\\theta}^{2} r^{3} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4}+8a^{2} \\\\cos{\\\\theta}^{2} r^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4}+8a^{4} \\\\cos{\\\\theta}^{4} r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{t}= & a r_s \\\\frac{-56r^{5} r_s^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}-8r^{3} r_s^{2} a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2}-20r^{7} r_s^{2} a^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+44r^{5} r_s^{2} a^{4} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2}+8r^{6} r_s^{3} a^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}-12r^{4} r_s^{3} a^{4} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2}-52r^{9} r_s^{2} \\\\sin{\\\\theta}^{2}+20r^{8} r_s^{3} \\\\sin{\\\\theta}^{2}-48r^{7} r_s^{2} a^{2} \\\\sin{\\\\theta}^{2}+72r^{6} r_s a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+4r^{4} r_s a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2}+16r^{8} r_s a^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}-16r^{6} r_s a^{4} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2}+44r^{10} r_s \\\\sin{\\\\theta}^{2}+72r^{8} r_s a^{2} \\\\sin{\\\\theta}^{2}-12r^{2} r_s a^{8} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2}-12r^{4} r_s a^{6} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2}+12r^{3} r_s^{2} a^{6} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2}+16r^{3} r_s^{2} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6}%\\n-16r^{3} r_s^{2} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4}-32r^{5} r_s^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4}-16r^{3} r_s^{2} a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4}-16r^{5} r_s^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\cos{2\\\\theta}-12r^{3} r_s^{2} a^{6} \\\\cos{\\\\theta}^{4} \\\\cos{2\\\\theta}+16r^{5} r_s^{2} a^{4} \\\\cos{\\\\theta}^{2}+12r^{3} r_s^{2} a^{6} \\\\cos{\\\\theta}^{4}-6r^{3} r_s^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)-6r^{3} r_s^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+3r^{3} r_s^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+3r^{3} r_s^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-2r^{7} r_s^{2} a^{2} \\\\cos{\\\\theta}^{2} \\\\cos{2\\\\theta}-6r^{7} r_s^{2} a^{2} \\\\cos{\\\\theta}^{2}-4r^{5} r_s^{2} a^{4} \\\\cos{\\\\theta}^{4} \\\\cos{2\\\\theta}+2r^{4} r_s^{3} a^{4} \\\\cos{\\\\theta}^{4} \\\\cos{2\\\\theta}-4r^{5} r_s^{2} a^{4} \\\\cos{\\\\theta}^{4}-2r^{4} r_s^{3} a^{4} \\\\cos{\\\\theta}^{4}+8r^{3} r_s^{2} a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{2\\\\theta}-16r^{5} r_s^{2} a^{2} \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)-16r^{5} r_s^{2} a^{2} \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)%\\n-8r^{3} r_s^{2} a^{4} \\\\cos{\\\\theta}^{4} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)-8r^{3} r_s^{2} a^{4} \\\\cos{\\\\theta}^{4} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-16r^{4} r_s a^{6} \\\\sin{\\\\theta}^{6}+16r^{4} r_s a^{6} \\\\sin{\\\\theta}^{4}+48r^{6} r_s a^{4} \\\\sin{\\\\theta}^{4}+48r^{4} r_s a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4}+6r^{6} r_s a^{4} \\\\cos{2\\\\theta}+16r^{4} r_s a^{6} \\\\cos{\\\\theta}^{2} \\\\cos{2\\\\theta}-6r^{6} r_s a^{4}-16r^{4} r_s a^{6} \\\\cos{\\\\theta}^{2}+6r^{4} r_s a^{4} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+6r^{4} r_s a^{4} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-3r^{4} r_s a^{4} \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)-3r^{4} r_s a^{4} \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+10r^{8} r_s a^{2} \\\\cos{2\\\\theta}-4r^{7} r_s^{2} a^{2} \\\\cos{2\\\\theta}-10r^{8} r_s a^{2}+4r^{7} r_s^{2} a^{2}+26r^{6} r_s a^{4} \\\\cos{\\\\theta}^{2} \\\\cos{2\\\\theta}-26r^{6} r_s a^{4} \\\\cos{\\\\theta}^{2}%\\n-8r^{4} r_s a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{2\\\\theta}+20r^{6} r_s a^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+20r^{6} r_s a^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+22r^{4} r_s a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+22r^{4} r_s a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-16r^{2} r_s a^{8} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6}+16r^{2} r_s a^{8} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4}+16r^{2} r_s a^{8} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4}+10r^{2} r_s a^{8} \\\\cos{\\\\theta}^{4} \\\\cos{2\\\\theta}-10r^{2} r_s a^{8} \\\\cos{\\\\theta}^{4}+6r^{2} r_s a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+6r^{2} r_s a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-3r^{2} r_s a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)-3r^{2} r_s a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+12r^{4} r_s a^{6} \\\\cos{\\\\theta}^{4} \\\\cos{2\\\\theta}-12r^{4} r_s a^{6} \\\\cos{\\\\theta}^{4}-8r^{2} r_s a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{2\\\\theta}+8r^{2} r_s a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+8r^{2} r_s a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+16r^{5} r_s^{2} a^{4} \\\\sin{\\\\theta}^{6}%\\n-16r^{5} r_s^{2} a^{4} \\\\sin{\\\\theta}^{4}-16r^{7} r_s^{2} a^{2} \\\\sin{\\\\theta}^{4}-6r^{5} r_s^{2} a^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)-6r^{5} r_s^{2} a^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+3r^{5} r_s^{2} a^{2} \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+3r^{5} r_s^{2} a^{2} \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+6r^{9} r_s^{2} \\\\cos{2\\\\theta}-2r^{8} r_s^{3} \\\\cos{2\\\\theta}-6r^{9} r_s^{2}+2r^{8} r_s^{3}+8r^{5} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{2\\\\theta}-8r^{7} r_s^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)-8r^{7} r_s^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-32r^{6} r_s a^{4} \\\\sin{\\\\theta}^{6}+32r^{8} r_s a^{2} \\\\sin{\\\\theta}^{4}+48r^{6} r_s a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4}-6r^{6} r_s a^{2} \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)-6r^{6} r_s a^{2} \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-6r^{10} r_s \\\\cos{2\\\\theta}+6r^{10} r_s%\\n+4r^{8} r_s a^{2} \\\\cos{\\\\theta}^{2} \\\\cos{2\\\\theta}-4r^{8} r_s a^{2} \\\\cos{\\\\theta}^{2}-16r^{6} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{2\\\\theta}+16r^{8} r_s \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+16r^{8} r_s \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+24r^{6} r_s a^{2} \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+24r^{6} r_s a^{2} \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-16r^{4} r_s a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6}+16r^{4} r_s a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4}-3r^{4} r_s a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)-3r^{4} r_s a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+2r^{6} r_s a^{4} \\\\cos{\\\\theta}^{4} \\\\cos{2\\\\theta}-2r^{6} r_s a^{4} \\\\cos{\\\\theta}^{4}-8r^{4} r_s a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{2\\\\theta}+8r^{4} r_s a^{4} \\\\cos{\\\\theta}^{4} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+8r^{4} r_s a^{4} \\\\cos{\\\\theta}^{4} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-16r^{4} a^{6} r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6}+16r^{4} a^{6} r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4}+16r^{6} a^{4} r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4}+24r^{4} a^{6} r_s \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4}%\\n+8r^{6} a^{4} r_s \\\\cos{\\\\theta}^{2} \\\\cos{2\\\\theta}+10r^{4} a^{6} r_s \\\\cos{\\\\theta}^{4} \\\\cos{2\\\\theta}-8r^{6} a^{4} r_s \\\\cos{\\\\theta}^{2}-10r^{4} a^{6} r_s \\\\cos{\\\\theta}^{4}+6r^{4} a^{4} r_s \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+6r^{4} a^{4} r_s \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-3r^{4} a^{4} r_s \\\\cos{\\\\theta}^{2} \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)-3r^{4} a^{4} r_s \\\\cos{\\\\theta}^{2} \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-2r^{8} a^{2} r_s \\\\cos{\\\\theta}^{2} \\\\cos{2\\\\theta}+2r^{7} a^{2} r_s^{2} \\\\cos{\\\\theta}^{2} \\\\cos{2\\\\theta}+10r^{8} a^{2} r_s \\\\cos{\\\\theta}^{2}-2r^{7} a^{2} r_s^{2} \\\\cos{\\\\theta}^{2}+2r^{6} a^{4} r_s \\\\cos{\\\\theta}^{4} \\\\cos{2\\\\theta}-2r^{5} a^{4} r_s^{2} \\\\cos{\\\\theta}^{4} \\\\cos{2\\\\theta}+6r^{6} a^{4} r_s \\\\cos{\\\\theta}^{4}+2r^{5} a^{4} r_s^{2} \\\\cos{\\\\theta}^{4}-8r^{4} a^{2} r_s \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{2\\\\theta}+8r^{6} a^{2} r_s \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+8r^{6} a^{2} r_s \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+8r^{4} a^{4} r_s \\\\cos{\\\\theta}^{4} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)%\\n+8r^{4} a^{4} r_s \\\\cos{\\\\theta}^{4} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+16r^{5} a^{6} \\\\sin{\\\\theta}^{6}-16r^{5} a^{6} \\\\sin{\\\\theta}^{4}-32r^{7} a^{4} \\\\sin{\\\\theta}^{4}-80r^{5} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4}-6r^{7} a^{4} \\\\cos{2\\\\theta}-22r^{5} a^{6} \\\\cos{\\\\theta}^{2} \\\\cos{2\\\\theta}+6r^{7} a^{4}+22r^{5} a^{6} \\\\cos{\\\\theta}^{2}-6r^{5} a^{4} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)-6r^{5} a^{4} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+3r^{5} a^{4} \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+3r^{5} a^{4} \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-4r^{9} a^{2} \\\\cos{2\\\\theta}-2r^{8} a^{2} r_s \\\\cos{2\\\\theta}+4r^{9} a^{2}+2r^{8} a^{2} r_s-20r^{7} a^{4} \\\\cos{\\\\theta}^{2} \\\\cos{2\\\\theta}+20r^{7} a^{4} \\\\cos{\\\\theta}^{2}+8r^{5} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{2\\\\theta}%\\n-14r^{7} a^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)-14r^{7} a^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-36r^{5} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)-36r^{5} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+24r^{3} a^{8} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6}-24r^{3} a^{8} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4}-72r^{3} a^{8} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4}-26r^{3} a^{8} \\\\cos{\\\\theta}^{4} \\\\cos{2\\\\theta}+26r^{3} a^{8} \\\\cos{\\\\theta}^{4}-12r^{3} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)-12r^{3} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+6r^{3} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+6r^{3} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+2r^{6} a^{4} \\\\cos{\\\\theta}^{2} r_s \\\\cos{2\\\\theta}-2r^{6} a^{4} \\\\cos{\\\\theta}^{2} r_s-28r^{5} a^{6} \\\\cos{\\\\theta}^{4} \\\\cos{2\\\\theta}+18r^{4} a^{6} \\\\cos{\\\\theta}^{4} r_s \\\\cos{2\\\\theta}+28r^{5} a^{6} \\\\cos{\\\\theta}^{4}-18r^{4} a^{6} \\\\cos{\\\\theta}^{4} r_s+16r^{3} a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{2\\\\theta}%\\n-30r^{3} a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)-30r^{3} a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+16r^{7} a^{4} \\\\sin{\\\\theta}^{6}-16r^{9} a^{2} \\\\sin{\\\\theta}^{4}-56r^{7} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4}+3r^{7} a^{2} \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+3r^{7} a^{2} \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+2r^{11} \\\\cos{2\\\\theta}-2r^{11}+2r^{9} a^{2} \\\\cos{\\\\theta}^{2} \\\\cos{2\\\\theta}-2r^{9} a^{2} \\\\cos{\\\\theta}^{2}+8r^{7} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{2\\\\theta}-8r^{9} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)-8r^{9} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-24r^{7} a^{2} \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)-24r^{7} a^{2} \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+24r^{5} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6}-64r^{5} a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4}+6r^{5} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+6r^{5} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)%\\n-6r^{8} a^{2} \\\\cos{\\\\theta}^{2} r_s \\\\cos{2\\\\theta}+6r^{8} a^{2} \\\\cos{\\\\theta}^{2} r_s-2r^{7} a^{4} \\\\cos{\\\\theta}^{4} \\\\cos{2\\\\theta}+2r^{6} a^{4} \\\\cos{\\\\theta}^{4} r_s \\\\cos{2\\\\theta}+2r^{7} a^{4} \\\\cos{\\\\theta}^{4}+14r^{6} a^{4} \\\\cos{\\\\theta}^{4} r_s+16r^{5} a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{2\\\\theta}-24r^{5} a^{4} \\\\cos{\\\\theta}^{4} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)-24r^{5} a^{4} \\\\cos{\\\\theta}^{4} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-8r^{2} a^{8} \\\\cos{\\\\theta}^{4} r_s \\\\sin{\\\\theta}^{6}+8r^{2} a^{8} \\\\cos{\\\\theta}^{4} r_s \\\\sin{\\\\theta}^{4}+32r^{4} a^{6} \\\\cos{\\\\theta}^{4} r_s \\\\sin{\\\\theta}^{4}+16r^{2} a^{8} \\\\cos{\\\\theta}^{6} r_s \\\\sin{\\\\theta}^{4}+12r^{2} a^{8} \\\\cos{\\\\theta}^{6} r_s \\\\cos{2\\\\theta}-12r^{2} a^{8} \\\\cos{\\\\theta}^{6} r_s+6r^{2} a^{6} \\\\cos{\\\\theta}^{4} r_s \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+6r^{2} a^{6} \\\\cos{\\\\theta}^{4} r_s \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-3r^{2} a^{6} \\\\cos{\\\\theta}^{4} r_s \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)-3r^{2} a^{6} \\\\cos{\\\\theta}^{4} r_s \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-8r^{5} a^{4} \\\\cos{\\\\theta}^{4} r_s^{2}%\\n+4r^{4} a^{6} \\\\cos{\\\\theta}^{6} r_s \\\\cos{2\\\\theta}-2r^{3} a^{6} \\\\cos{\\\\theta}^{6} r_s^{2} \\\\cos{2\\\\theta}+20r^{4} a^{6} \\\\cos{\\\\theta}^{6} r_s-6r^{3} a^{6} \\\\cos{\\\\theta}^{6} r_s^{2}-8r^{2} a^{4} \\\\cos{\\\\theta}^{4} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{2\\\\theta}+16r^{4} a^{4} \\\\cos{\\\\theta}^{4} r_s \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+16r^{4} a^{4} \\\\cos{\\\\theta}^{4} r_s \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+8r^{2} a^{6} \\\\cos{\\\\theta}^{6} r_s \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+8r^{2} a^{6} \\\\cos{\\\\theta}^{6} r_s \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+8r a^{10} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{6}-8r a^{10} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4}-24r a^{10} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4}-10r a^{10} \\\\cos{\\\\theta}^{6} \\\\cos{2\\\\theta}+10r a^{10} \\\\cos{\\\\theta}^{6}-6r a^{8} \\\\cos{\\\\theta}^{4} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)-6r a^{8} \\\\cos{\\\\theta}^{4} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+3r a^{8} \\\\cos{\\\\theta}^{4} \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+3r a^{8} \\\\cos{\\\\theta}^{4} \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-12r^{3} a^{8} \\\\cos{\\\\theta}^{6} \\\\cos{2\\\\theta}+12r^{3} a^{8} \\\\cos{\\\\theta}^{6}%\\n+8r a^{6} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{2\\\\theta}-8r a^{8} \\\\cos{\\\\theta}^{6} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)-8r a^{8} \\\\cos{\\\\theta}^{6} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-8r^{4} a^{6} \\\\cos{\\\\theta}^{2} r_s \\\\sin{\\\\theta}^{6}+8r^{4} a^{6} \\\\cos{\\\\theta}^{2} r_s \\\\sin{\\\\theta}^{4}+24r^{6} a^{4} \\\\cos{\\\\theta}^{2} r_s \\\\sin{\\\\theta}^{4}+6r^{4} a^{4} \\\\cos{\\\\theta}^{2} r_s \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+6r^{4} a^{4} \\\\cos{\\\\theta}^{2} r_s \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-3r^{4} a^{4} \\\\cos{\\\\theta}^{2} r_s \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)-3r^{4} a^{4} \\\\cos{\\\\theta}^{2} r_s \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+2r^{7} a^{2} \\\\cos{\\\\theta}^{2} r_s^{2} \\\\cos{2\\\\theta}-2r^{7} a^{2} \\\\cos{\\\\theta}^{2} r_s^{2}-8r^{4} a^{2} \\\\cos{\\\\theta}^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{2\\\\theta}+8r^{6} a^{2} \\\\cos{\\\\theta}^{2} r_s \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+8r^{6} a^{2} \\\\cos{\\\\theta}^{2} r_s \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+8r^{3} a^{8} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{6}-24r^{3} a^{8} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4}+3r^{3} a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+3r^{3} a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-2r^{5} a^{6} \\\\cos{\\\\theta}^{6} \\\\cos{2\\\\theta}%\\n+2r^{5} a^{6} \\\\cos{\\\\theta}^{6}+8r^{3} a^{4} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{2\\\\theta}-8r^{3} a^{6} \\\\cos{\\\\theta}^{6} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)-8r^{3} a^{6} \\\\cos{\\\\theta}^{6} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-8r^{3} a^{6} r_s^{2} \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}^{2}+8r^{4} a^{6} r_s \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}^{2}+8r^{2} a^{8} r_s \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4}-16r^{5} a^{4} r_s^{2} \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}^{2}+8r^{4} a^{4} r_s^{3} \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}^{2}-8r^{3} a^{6} r_s^{2} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4}+8r^{3} a^{6} \\\\sin{\\\\theta}^{6} r_s^{2} \\\\cos{\\\\theta}^{2}-8r^{4} a^{4} \\\\sin{\\\\theta}^{4} r_s^{3} \\\\cos{\\\\theta}^{2}+24r^{5} a^{4} \\\\sin{\\\\theta}^{4} r_s^{2} \\\\cos{\\\\theta}^{2}+16r^{3} a^{6} \\\\sin{\\\\theta}^{4} r_s^{2} \\\\cos{\\\\theta}^{4}-8r^{5} a^{4} \\\\sin{\\\\theta}^{2} r_s^{2} \\\\cos{\\\\theta}^{2}-8r^{3} a^{6} \\\\sin{\\\\theta}^{2} r_s^{2} \\\\cos{\\\\theta}^{4}+8r^{2} a^{4} \\\\sin{\\\\theta}^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{2}-8r^{7} a^{2} \\\\sin{\\\\theta}^{2} r_s^{2} \\\\cos{\\\\theta}^{2}-8r^{5} a^{4} \\\\sin{\\\\theta}^{2} r_s^{2} \\\\cos{\\\\theta}^{4}+8r^{4} a^{2} \\\\sin{\\\\theta}^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{2}%\\n-8r^{4} a^{6} \\\\sin{\\\\theta}^{6} r_s \\\\cos{\\\\theta}^{2}-16r^{6} a^{4} \\\\sin{\\\\theta}^{4} r_s \\\\cos{\\\\theta}^{2}-16r^{4} a^{6} \\\\sin{\\\\theta}^{4} r_s \\\\cos{\\\\theta}^{4}+8r^{6} a^{4} \\\\sin{\\\\theta}^{2} r_s \\\\cos{\\\\theta}^{2}+8r^{4} a^{6} \\\\sin{\\\\theta}^{2} r_s \\\\cos{\\\\theta}^{4}-8r^{3} a^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{2}+8r^{8} a^{2} \\\\sin{\\\\theta}^{2} r_s \\\\cos{\\\\theta}^{2}+8r^{6} a^{4} \\\\sin{\\\\theta}^{2} r_s \\\\cos{\\\\theta}^{4}-8r^{5} a^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{2}-8r^{2} a^{8} \\\\sin{\\\\theta}^{6} \\\\cos{\\\\theta}^{4} r_s+8r^{3} a^{6} \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}^{4} r_s^{2}-16r^{4} a^{6} \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}^{4} r_s-16r^{2} a^{8} \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}^{6} r_s+8r^{4} a^{6} \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{4} r_s+8r^{2} a^{8} \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{6} r_s-8r a^{6} \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+8r^{6} a^{4} \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{4} r_s+8r^{4} a^{6} \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{6} r_s-8r^{3} a^{4} \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+8r^{5} r_s^{2} a^{4} \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}^{2}%\\n-8r^{6} r_s^{3} a^{2} \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{2}+16r^{7} r_s^{2} a^{2} \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{2}+8r^{4} r_s a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{2}-8r^{9} r_s^{2} \\\\cos{\\\\theta}^{2}-8r^{7} r_s^{2} a^{2} \\\\cos{\\\\theta}^{4}+8r^{6} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{2}+8r^{7} a^{2} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{2}-16r^{8} a^{2} r_s \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{2}-20r^{6} a^{4} r_s \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2}-8r^{5} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{2}+8r^{10} r_s \\\\cos{\\\\theta}^{2}+8r^{8} r_s a^{2} \\\\cos{\\\\theta}^{4}-8r^{7} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{2}+32r^{5} a^{4} \\\\cos{\\\\theta}^{4} r_s^{2} \\\\sin{\\\\theta}^{2}-24r^{6} a^{4} \\\\cos{\\\\theta}^{4} r_s \\\\sin{\\\\theta}^{2}-48r^{4} a^{6} \\\\cos{\\\\theta}^{6} r_s \\\\sin{\\\\theta}^{2}-16r^{3} a^{4} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+16r^{8} a^{2} \\\\cos{\\\\theta}^{4} r_s+24r^{6} a^{4} \\\\cos{\\\\theta}^{6} r_s-16r^{5} a^{2} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}%\\n+8r^{3} a^{6} \\\\cos{\\\\theta}^{4} r_s^{2} \\\\sin{\\\\theta}^{4}-8r^{4} a^{4} \\\\cos{\\\\theta}^{4} r_s^{3} \\\\sin{\\\\theta}^{2}+24r^{3} a^{6} \\\\cos{\\\\theta}^{6} r_s^{2} \\\\sin{\\\\theta}^{2}+8r^{2} a^{4} \\\\cos{\\\\theta}^{4} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-8r^{7} a^{2} \\\\cos{\\\\theta}^{4} r_s^{2}-8r^{5} a^{4} \\\\cos{\\\\theta}^{6} r_s^{2}+8r^{4} a^{2} \\\\cos{\\\\theta}^{4} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-16r^{2} a^{8} \\\\cos{\\\\theta}^{8} r_s \\\\sin{\\\\theta}^{2}+8r^{2} a^{8} \\\\cos{\\\\theta}^{8} r_s-8r a^{6} \\\\cos{\\\\theta}^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+8r^{4} a^{6} \\\\cos{\\\\theta}^{8} r_s-8r^{3} a^{4} \\\\cos{\\\\theta}^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-6r^{3} r_s^{2} a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+2r^{2} r_s^{3} a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-4r^{6} r_s^{2} a^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4r^{6} r_s^{2} a^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4r^{5} r_s^{3} a^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4r^{5} r_s^{3} a^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+8r^{4} r_s^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+8r^{4} r_s^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}%\\n-12r^{4} r_s^{2} a^{4} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}-16r^{4} r_s^{2} a^{4} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+8r^{3} r_s^{3} a^{4} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+8r^{3} r_s^{3} a^{4} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-16r^{2} r_s^{2} a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}-16r^{2} r_s^{2} a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4r^{4} r_s^{2} a^{4} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r_s r\\\\right) \\\\sin{\\\\theta}^{2}+4r^{4} r_s^{2} a^{4} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2}+4r^{2} r_s^{2} a^{6} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4r^{2} r_s^{2} a^{6} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(r_s r\\\\right) \\\\sin{\\\\theta}^{2}+4r^{2} r_s^{2} a^{6} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2}+28r^{6} r_s a^{4} \\\\sin{\\\\theta}^{2}+48r^{4} r_s a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+4r^{4} r_s a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-2r^{3} r_s^{2} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-36r^{7} r_s a^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}-40r^{7} r_s a^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+28r^{6} r_s^{2} a^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+28r^{6} r_s^{2} a^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-16r^{5} r_s a^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}%\\n-16r^{5} r_s a^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+4r^{5} r_s a^{4} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+4r^{5} r_s a^{4} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4r^{3} r_s a^{6} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4r^{3} r_s a^{6} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+4r^{4} r_s^{2} a^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}-4r^{3} r_s a^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}-4r^{5} r_s a^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+4r^{4} r_s^{2} a^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}-4r^{3} r_s a^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}-4r^{7} r_s a^{2} \\\\partial_{r}\\\\left(r_s r\\\\right) \\\\sin{\\\\theta}^{2}-4r^{5} r_s a^{4} \\\\partial_{r}\\\\left(r_s r\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+4r^{7} r_s a^{2} \\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2}+4r^{5} r_s a^{4} \\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+12r^{3} r_s a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+4r^{3} r_s a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r_s r\\\\right) \\\\sin{\\\\theta}^{2}-4r^{3} r_s a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2}+20r^{2} r_s a^{8} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2}+4r^{2} r_s a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-2r r_s^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}%\\n+16r^{3} r_s a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+8r r_s a^{8} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+8r r_s a^{8} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4r r_s a^{8} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+4r r_s a^{8} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(r_s r\\\\right) \\\\sin{\\\\theta}^{2}-4r r_s a^{8} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4r^{5} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+4r^{4} r_s^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+44r^{8} r_s^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+48r^{8} r_s^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-16r^{7} r_s^{3} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}-16r^{7} r_s^{3} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+8r^{6} r_s^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}-4r^{5} r_s^{3} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+4r^{6} r_s^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{2} \\\\sin{\\\\theta}^{2}+4r^{4} r_s^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+12r^{6} r_s^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}-4r^{5} r_s^{3} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+4r^{6} r_s^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{2} \\\\sin{\\\\theta}^{2}+4r^{4} r_s^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}%\\n+4r^{8} r_s^{2} \\\\partial_{r}\\\\left(r_s r\\\\right) \\\\sin{\\\\theta}^{2}+4r^{6} r_s^{2} \\\\partial_{r}\\\\left(r_s r\\\\right) a^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}-4r^{8} r_s^{2} \\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4r^{6} r_s^{2} \\\\partial_{r}\\\\left(a^{2}\\\\right) a^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+4r^{6} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-36r^{9} r_s \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}-44r^{9} r_s \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+4r^{7} r_s a^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+8r^{7} r_s a^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-8r^{7} r_s \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{2} \\\\sin{\\\\theta}^{2}-8r^{5} r_s \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}-8r^{7} r_s \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}-8r^{7} r_s \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{2} \\\\sin{\\\\theta}^{2}-8r^{5} r_s \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}-8r^{9} r_s \\\\partial_{r}\\\\left(r_s r\\\\right) \\\\sin{\\\\theta}^{2}-8r^{7} r_s \\\\partial_{r}\\\\left(r_s r\\\\right) a^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+8r^{9} r_s \\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2}+8r^{7} r_s \\\\partial_{r}\\\\left(a^{2}\\\\right) a^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+4r^{7} r_s a^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r_s r\\\\right) \\\\sin{\\\\theta}^{2}+8r^{5} r_s a^{4} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r_s r\\\\right) \\\\sin{\\\\theta}^{2}%\\n-4r^{7} r_s a^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2}-8r^{5} r_s a^{4} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2}+4r^{4} r_s a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+8r^{5} r_s a^{4} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4r^{3} r_s a^{6} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+4r^{3} r_s a^{6} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(r_s r\\\\right) \\\\sin{\\\\theta}^{2}-4r^{3} r_s a^{6} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2}-2r^{3} r_s^{2} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+2r^{2} r_s^{3} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}-2r r_s^{2} a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}-6r^{4} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} \\\\sin{\\\\theta}^{2}-2r^{3} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} \\\\sin{\\\\theta}^{2}+4r^{4} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2}-4r^{3} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2}+4r^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} a^{2} \\\\sin{\\\\theta}^{2}+36r^{6} a^{4} r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+12r^{4} a^{6} r_s \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2}-16r^{7} a^{2} r_s^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+12r^{8} a^{2} r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+4r^{4} a^{2} r_s \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}%\\n-2r^{3} a^{2} r_s^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-12r^{7} a^{2} r_s \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}-16r^{7} a^{2} r_s \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+16r^{6} a^{2} r_s^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+16r^{6} a^{2} r_s^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-16r^{5} a^{4} r_s \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}-16r^{5} a^{4} r_s \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+8r^{5} a^{4} r_s \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+8r^{5} a^{4} r_s \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-8r^{4} a^{4} r_s^{2} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}-8r^{4} a^{4} r_s^{2} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+8r^{3} a^{6} r_s \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+8r^{3} a^{6} r_s \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4r^{7} a^{2} r_s \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r_s r\\\\right) \\\\sin{\\\\theta}^{2}+4r^{7} a^{2} r_s \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4r^{3} a^{6} r_s \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+4r^{3} a^{6} r_s \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(r_s r\\\\right) \\\\sin{\\\\theta}^{2}-4r^{3} a^{6} r_s \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2}-28r^{7} a^{4} \\\\sin{\\\\theta}^{2}-48r^{5} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}%\\n+16r^{8} a^{2} r_s \\\\sin{\\\\theta}^{2}-64r^{7} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}-40r^{9} a^{2} \\\\sin{\\\\theta}^{2}-4r^{5} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+2r^{4} a^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+24r^{8} a^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+28r^{8} a^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-12r^{7} a^{2} r_s \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}-12r^{7} a^{2} r_s \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+16r^{6} a^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+16r^{6} a^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+8r^{6} a^{4} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+8r^{6} a^{4} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+4r^{4} a^{6} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+4r^{4} a^{6} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4r^{7} a^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) r_s \\\\sin{\\\\theta}^{2}-4r^{5} a^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right) r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+4r^{4} a^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+4r^{6} a^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}-4r^{7} a^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\sin{\\\\theta}^{2}%\\n-4r^{5} a^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+4r^{4} a^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+4r^{8} a^{2} \\\\partial_{r}\\\\left(r_s r\\\\right) \\\\sin{\\\\theta}^{2}+4r^{6} a^{4} \\\\partial_{r}\\\\left(r_s r\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}-4r^{8} a^{2} \\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4r^{6} a^{4} \\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}-12r^{4} a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4r^{4} a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r_s r\\\\right) \\\\sin{\\\\theta}^{2}+4r^{4} a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2}-20r^{3} a^{8} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2}+16r^{6} a^{4} \\\\cos{\\\\theta}^{2} r_s \\\\sin{\\\\theta}^{2}-24r^{5} a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2}+8r^{4} a^{6} \\\\cos{\\\\theta}^{4} r_s \\\\sin{\\\\theta}^{2}-4r^{3} a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+2r^{2} a^{4} \\\\cos{\\\\theta}^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-16r^{4} a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+12r^{3} a^{6} \\\\cos{\\\\theta}^{4} r_s \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+12r^{3} a^{6} \\\\cos{\\\\theta}^{4} r_s \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-8r^{2} a^{8} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}-8r^{2} a^{8} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}%\\n-4r^{5} a^{4} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) r_s \\\\sin{\\\\theta}^{2}-4r^{3} a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right) r_s \\\\sin{\\\\theta}^{2}-4r^{5} a^{4} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\sin{\\\\theta}^{2}-4r^{3} a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\sin{\\\\theta}^{2}+4r^{2} a^{8} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4r^{2} a^{8} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(r_s r\\\\right) \\\\sin{\\\\theta}^{2}+4r^{2} a^{8} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2}-16r^{9} a^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}-12r^{11} \\\\sin{\\\\theta}^{2}+4r^{7} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+12r^{10} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+16r^{10} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+4r^{8} a^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+4r^{8} a^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4r^{9} \\\\partial_{r}\\\\left(r^{2}\\\\right) r_s \\\\sin{\\\\theta}^{2}-4r^{7} \\\\partial_{r}\\\\left(r^{2}\\\\right) r_s a^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+4r^{8} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{2} \\\\sin{\\\\theta}^{2}+4r^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+4r^{8} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}-4r^{9} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\sin{\\\\theta}^{2}%\\n-4r^{7} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s a^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+4r^{8} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{2} \\\\sin{\\\\theta}^{2}+4r^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+4r^{10} \\\\partial_{r}\\\\left(r_s r\\\\right) \\\\sin{\\\\theta}^{2}+4r^{8} \\\\partial_{r}\\\\left(r_s r\\\\right) a^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}-4r^{10} \\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4r^{8} \\\\partial_{r}\\\\left(a^{2}\\\\right) a^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}-4r^{6} a^{4} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4r^{6} a^{4} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r_s r\\\\right) \\\\sin{\\\\theta}^{2}+4r^{6} a^{4} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2}+16r^{8} a^{2} \\\\cos{\\\\theta}^{2} r_s \\\\sin{\\\\theta}^{2}-4r^{7} a^{4} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2}-4r^{5} a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+2r^{4} a^{2} \\\\cos{\\\\theta}^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-8r^{6} a^{4} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+12r^{5} a^{4} \\\\cos{\\\\theta}^{4} r_s \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+12r^{5} a^{4} \\\\cos{\\\\theta}^{4} r_s \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4r^{7} a^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) r_s \\\\sin{\\\\theta}^{2}-4r^{5} a^{4} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right) r_s \\\\sin{\\\\theta}^{2}-4r^{7} a^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\sin{\\\\theta}^{2}%\\n-4r^{5} a^{4} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\sin{\\\\theta}^{2}+4r^{4} a^{6} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4r^{4} a^{6} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(r_s r\\\\right) \\\\sin{\\\\theta}^{2}+4r^{4} a^{6} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2}+2r^{4} a^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}-2r^{3} a^{2} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+2r^{2} a^{4} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}-8r^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s \\\\sin{\\\\theta}^{2}+8r^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} \\\\sin{\\\\theta}^{2}-4r^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2}+4r^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} r_s \\\\sin{\\\\theta}^{2}-4r^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} a^{2} \\\\sin{\\\\theta}^{2}-8a^{8} \\\\cos{\\\\theta}^{4} r^{2} r_s \\\\sin{\\\\theta}^{6}+8a^{8} \\\\cos{\\\\theta}^{4} r^{2} r_s \\\\sin{\\\\theta}^{4}-16a^{6} \\\\cos{\\\\theta}^{4} r^{4} r_s \\\\sin{\\\\theta}^{4}-8a^{8} \\\\cos{\\\\theta}^{6} r^{2} r_s \\\\sin{\\\\theta}^{4}+64a^{6} \\\\cos{\\\\theta}^{4} r^{4} r_s \\\\sin{\\\\theta}^{2}+20a^{8} \\\\cos{\\\\theta}^{6} r^{2} r_s \\\\sin{\\\\theta}^{2}-16a^{4} \\\\cos{\\\\theta}^{4} r^{5} r_s^{2} \\\\sin{\\\\theta}^{2}+4a^{6} \\\\cos{\\\\theta}^{6} r^{4} r_s \\\\sin{\\\\theta}^{2}%\\n+32a^{4} \\\\cos{\\\\theta}^{4} r^{6} r_s \\\\sin{\\\\theta}^{2}+6a^{4} \\\\cos{\\\\theta}^{4} r^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-2a^{4} \\\\cos{\\\\theta}^{4} r r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-4a^{4} \\\\cos{\\\\theta}^{4} r^{5} r_s \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}-8a^{4} \\\\cos{\\\\theta}^{4} r^{5} r_s \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+8a^{4} \\\\cos{\\\\theta}^{4} r^{4} r_s^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+8a^{4} \\\\cos{\\\\theta}^{4} r^{4} r_s^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-8a^{6} \\\\cos{\\\\theta}^{4} r^{3} r_s \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}-8a^{6} \\\\cos{\\\\theta}^{4} r^{3} r_s \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+16a^{6} \\\\cos{\\\\theta}^{6} r^{3} r_s \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+20a^{6} \\\\cos{\\\\theta}^{6} r^{3} r_s \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-8a^{6} \\\\cos{\\\\theta}^{6} r^{2} r_s^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}-8a^{6} \\\\cos{\\\\theta}^{6} r^{2} r_s^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+8a^{8} \\\\cos{\\\\theta}^{6} r r_s \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+8a^{8} \\\\cos{\\\\theta}^{6} r r_s \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4a^{4} \\\\cos{\\\\theta}^{4} r^{5} r_s \\\\partial_{r}\\\\left(r_s r\\\\right) \\\\sin{\\\\theta}^{2}+4a^{6} \\\\cos{\\\\theta}^{6} r^{3} r_s \\\\partial_{r}\\\\left(r_s r\\\\right) \\\\sin{\\\\theta}^{2}+4a^{4} \\\\cos{\\\\theta}^{4} r^{5} r_s \\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4a^{6} \\\\cos{\\\\theta}^{6} r^{3} r_s \\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4a^{8} \\\\cos{\\\\theta}^{8} r r_s \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}%\\n+4a^{8} \\\\cos{\\\\theta}^{8} r r_s \\\\partial_{r}\\\\left(r_s r\\\\right) \\\\sin{\\\\theta}^{2}-4a^{8} \\\\cos{\\\\theta}^{8} r r_s \\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2}+8a^{8} \\\\cos{\\\\theta}^{2} r^{3} \\\\sin{\\\\theta}^{6}-8a^{8} \\\\cos{\\\\theta}^{2} r^{3} \\\\sin{\\\\theta}^{4}+8a^{8} \\\\cos{\\\\theta}^{4} r^{3} \\\\sin{\\\\theta}^{4}-28a^{6} \\\\cos{\\\\theta}^{2} r^{5} \\\\sin{\\\\theta}^{2}-48a^{8} \\\\cos{\\\\theta}^{4} r^{3} \\\\sin{\\\\theta}^{2}+44a^{4} \\\\cos{\\\\theta}^{2} r^{6} r_s \\\\sin{\\\\theta}^{2}-64a^{6} \\\\cos{\\\\theta}^{4} r^{5} \\\\sin{\\\\theta}^{2}-40a^{4} \\\\cos{\\\\theta}^{2} r^{7} \\\\sin{\\\\theta}^{2}+4a^{4} \\\\cos{\\\\theta}^{2} r^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+4a^{4} \\\\cos{\\\\theta}^{2} r^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+28a^{4} \\\\cos{\\\\theta}^{2} r^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+32a^{4} \\\\cos{\\\\theta}^{2} r^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-28a^{4} \\\\cos{\\\\theta}^{2} r^{5} r_s \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}-28a^{4} \\\\cos{\\\\theta}^{2} r^{5} r_s \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+16a^{6} \\\\cos{\\\\theta}^{2} r^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+16a^{6} \\\\cos{\\\\theta}^{2} r^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+8a^{6} \\\\cos{\\\\theta}^{4} r^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+12a^{6} \\\\cos{\\\\theta}^{4} r^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}%\\n+4a^{8} \\\\cos{\\\\theta}^{4} r^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+4a^{8} \\\\cos{\\\\theta}^{4} r^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4a^{4} \\\\cos{\\\\theta}^{2} r^{5} \\\\partial_{r}\\\\left(r^{2}\\\\right) r_s \\\\sin{\\\\theta}^{2}-4a^{6} \\\\cos{\\\\theta}^{4} r^{3} \\\\partial_{r}\\\\left(r^{2}\\\\right) r_s \\\\sin{\\\\theta}^{2}-4a^{4} \\\\cos{\\\\theta}^{2} r^{5} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\sin{\\\\theta}^{2}-4a^{6} \\\\cos{\\\\theta}^{4} r^{3} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\sin{\\\\theta}^{2}+4a^{4} \\\\cos{\\\\theta}^{2} r^{6} \\\\partial_{r}\\\\left(r_s r\\\\right) \\\\sin{\\\\theta}^{2}+4a^{6} \\\\cos{\\\\theta}^{4} r^{4} \\\\partial_{r}\\\\left(r_s r\\\\right) \\\\sin{\\\\theta}^{2}-4a^{4} \\\\cos{\\\\theta}^{2} r^{6} \\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4a^{6} \\\\cos{\\\\theta}^{4} r^{4} \\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2}-20a^{8} \\\\cos{\\\\theta}^{6} r^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+8a^{10} \\\\cos{\\\\theta}^{4} r \\\\sin{\\\\theta}^{6}-8a^{10} \\\\cos{\\\\theta}^{4} r \\\\sin{\\\\theta}^{4}+8a^{10} \\\\cos{\\\\theta}^{6} r \\\\sin{\\\\theta}^{4}-20a^{10} \\\\cos{\\\\theta}^{6} r \\\\sin{\\\\theta}^{2}-24a^{8} \\\\cos{\\\\theta}^{6} r^{3} \\\\sin{\\\\theta}^{2}-4a^{6} \\\\cos{\\\\theta}^{4} r \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+4a^{6} \\\\cos{\\\\theta}^{4} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-20a^{8} \\\\cos{\\\\theta}^{6} r^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+12a^{8} \\\\cos{\\\\theta}^{6} r_s r \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}%\\n+12a^{8} \\\\cos{\\\\theta}^{6} r_s r \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-8a^{10} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}-8a^{10} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+4a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right) r^{4} \\\\sin{\\\\theta}^{2}+8a^{8} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right) r^{2} \\\\sin{\\\\theta}^{2}-4a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right) r_s r^{3} \\\\sin{\\\\theta}^{2}-4a^{8} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right) r_s r \\\\sin{\\\\theta}^{2}+4a^{8} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right) r^{2} \\\\sin{\\\\theta}^{2}+4a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r^{4} \\\\sin{\\\\theta}^{2}+4a^{8} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r^{2} \\\\sin{\\\\theta}^{2}-4a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s r^{3} \\\\sin{\\\\theta}^{2}-4a^{8} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s r \\\\sin{\\\\theta}^{2}+4a^{8} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r^{2} \\\\sin{\\\\theta}^{2}+4a^{10} \\\\cos{\\\\theta}^{8} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4a^{8} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(r_s r\\\\right) r^{2} \\\\sin{\\\\theta}^{2}-4a^{10} \\\\cos{\\\\theta}^{8} \\\\partial_{r}\\\\left(r_s r\\\\right) \\\\sin{\\\\theta}^{2}+4a^{8} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(a^{2}\\\\right) r^{2} \\\\sin{\\\\theta}^{2}+4a^{10} \\\\cos{\\\\theta}^{8} \\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2}-8a^{6} \\\\cos{\\\\theta}^{2} r^{4} r_s \\\\sin{\\\\theta}^{6}+8a^{6} \\\\cos{\\\\theta}^{2} r^{4} r_s \\\\sin{\\\\theta}^{4}%\\n-8a^{4} \\\\cos{\\\\theta}^{2} r^{6} r_s \\\\sin{\\\\theta}^{4}-16a^{2} \\\\cos{\\\\theta}^{2} r^{7} r_s^{2} \\\\sin{\\\\theta}^{2}+28a^{2} \\\\cos{\\\\theta}^{2} r^{8} r_s \\\\sin{\\\\theta}^{2}+8a^{2} \\\\cos{\\\\theta}^{2} r^{4} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-4a^{2} \\\\cos{\\\\theta}^{2} r^{3} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-24a^{2} \\\\cos{\\\\theta}^{2} r^{7} r_s \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}-28a^{2} \\\\cos{\\\\theta}^{2} r^{7} r_s \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+16a^{2} \\\\cos{\\\\theta}^{2} r^{6} r_s^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+16a^{2} \\\\cos{\\\\theta}^{2} r^{6} r_s^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4a^{2} \\\\cos{\\\\theta}^{2} r^{7} r_s \\\\partial_{r}\\\\left(r_s r\\\\right) \\\\sin{\\\\theta}^{2}+4a^{2} \\\\cos{\\\\theta}^{2} r^{7} r_s \\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2}+8a^{6} \\\\cos{\\\\theta}^{2} r^{5} \\\\sin{\\\\theta}^{6}+8a^{4} \\\\cos{\\\\theta}^{2} r^{7} \\\\sin{\\\\theta}^{4}+16a^{6} \\\\cos{\\\\theta}^{4} r^{5} \\\\sin{\\\\theta}^{4}-16a^{4} \\\\cos{\\\\theta}^{4} r^{7} \\\\sin{\\\\theta}^{2}-12a^{2} \\\\cos{\\\\theta}^{2} r^{9} \\\\sin{\\\\theta}^{2}+4a^{2} \\\\cos{\\\\theta}^{2} r^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+12a^{2} \\\\cos{\\\\theta}^{2} r^{8} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+16a^{2} \\\\cos{\\\\theta}^{2} r^{8} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+4a^{4} \\\\cos{\\\\theta}^{4} r^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}%\\n+8a^{4} \\\\cos{\\\\theta}^{4} r^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4a^{2} \\\\cos{\\\\theta}^{2} r^{7} \\\\partial_{r}\\\\left(r^{2}\\\\right) r_s \\\\sin{\\\\theta}^{2}-8a^{4} \\\\cos{\\\\theta}^{4} r^{5} \\\\partial_{r}\\\\left(r^{2}\\\\right) r_s \\\\sin{\\\\theta}^{2}-4a^{2} \\\\cos{\\\\theta}^{2} r^{7} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\sin{\\\\theta}^{2}-8a^{4} \\\\cos{\\\\theta}^{4} r^{5} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\sin{\\\\theta}^{2}+4a^{2} \\\\cos{\\\\theta}^{2} r^{8} \\\\partial_{r}\\\\left(r_s r\\\\right) \\\\sin{\\\\theta}^{2}+4a^{4} \\\\cos{\\\\theta}^{4} r^{6} \\\\partial_{r}\\\\left(r_s r\\\\right) \\\\sin{\\\\theta}^{2}-4a^{2} \\\\cos{\\\\theta}^{2} r^{8} \\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4a^{4} \\\\cos{\\\\theta}^{4} r^{6} \\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4a^{6} \\\\cos{\\\\theta}^{6} r^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4a^{6} \\\\cos{\\\\theta}^{6} r^{4} \\\\partial_{r}\\\\left(r_s r\\\\right) \\\\sin{\\\\theta}^{2}+4a^{6} \\\\cos{\\\\theta}^{6} r^{4} \\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2}+8a^{8} \\\\cos{\\\\theta}^{4} r^{3} \\\\sin{\\\\theta}^{6}+8a^{8} \\\\cos{\\\\theta}^{6} r^{3} \\\\sin{\\\\theta}^{4}-4a^{6} \\\\cos{\\\\theta}^{6} r^{5} \\\\sin{\\\\theta}^{2}-4a^{4} \\\\cos{\\\\theta}^{4} r^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-8a^{6} \\\\cos{\\\\theta}^{6} r^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4a^{6} \\\\cos{\\\\theta}^{6} r^{3} \\\\partial_{r}\\\\left(r^{2}\\\\right) r_s \\\\sin{\\\\theta}^{2}-4a^{6} \\\\cos{\\\\theta}^{6} r^{3} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\sin{\\\\theta}^{2}+4a^{8} \\\\cos{\\\\theta}^{8} r^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}%\\n-4a^{8} \\\\cos{\\\\theta}^{8} r^{2} \\\\partial_{r}\\\\left(r_s r\\\\right) \\\\sin{\\\\theta}^{2}+4a^{8} \\\\cos{\\\\theta}^{8} r^{2} \\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2}+2a^{4} \\\\cos{\\\\theta}^{4} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r^{2} \\\\sin{\\\\theta}^{2}-2a^{4} \\\\cos{\\\\theta}^{4} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r \\\\sin{\\\\theta}^{2}-8a^{2} \\\\cos{\\\\theta}^{2} r^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s \\\\sin{\\\\theta}^{2}-4a^{2} \\\\cos{\\\\theta}^{2} r^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2}+4a^{2} \\\\cos{\\\\theta}^{2} r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} r_s \\\\sin{\\\\theta}^{2}-4a^{4} \\\\cos{\\\\theta}^{2} r \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2}}{8r^{2} r_s^{2} a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4}-8r^{3} r_s a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4}-8r r_s a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4}+8r^{4} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4}-16r^{5} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4}-8r^{3} r_s a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4}-8r^{3} a^{2} r_s \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4}+8r^{4} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4}+8r^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4}+8r^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4}+8r^{4} a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4}-8a^{4} \\\\cos{\\\\theta}^{4} r r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4}+8a^{4} \\\\cos{\\\\theta}^{2} r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4}+8a^{6} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4}-8a^{2} \\\\cos{\\\\theta}^{2} r^{3} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4}+8a^{2} \\\\cos{\\\\theta}^{2} r^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4}+8a^{4} \\\\cos{\\\\theta}^{4} r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}_{\\\\phi}= & a r_s \\\\frac{-60r^{5} r_s^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}-14r^{3} r_s^{2} a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2}-34r^{7} r_s^{2} a^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+70r^{5} r_s^{2} a^{4} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2}+14r^{6} r_s^{3} a^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}-20r^{4} r_s^{3} a^{4} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2}-56r^{9} r_s^{2} \\\\sin{\\\\theta}^{2}+22r^{8} r_s^{3} \\\\sin{\\\\theta}^{2}-54r^{7} r_s^{2} a^{2} \\\\sin{\\\\theta}^{2}+80r^{6} r_s a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+24r^{8} r_s a^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}-18r^{6} r_s a^{4} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2}+46r^{10} r_s \\\\sin{\\\\theta}^{2}+76r^{8} r_s a^{2} \\\\sin{\\\\theta}^{2}-12r^{2} r_s a^{8} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2}-12r^{4} r_s a^{6} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2}+28r^{3} r_s^{2} a^{6} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2}+16r^{3} r_s^{2} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6}-18r^{3} r_s^{2} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4}%\\n-34r^{5} r_s^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4}-8r^{3} r_s^{2} a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4}-16r^{5} r_s^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\cos{2\\\\theta}-12r^{3} r_s^{2} a^{6} \\\\cos{\\\\theta}^{4} \\\\cos{2\\\\theta}+16r^{5} r_s^{2} a^{4} \\\\cos{\\\\theta}^{2}+12r^{3} r_s^{2} a^{6} \\\\cos{\\\\theta}^{4}-6r^{3} r_s^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)-6r^{3} r_s^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+3r^{3} r_s^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+3r^{3} r_s^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-2r^{7} r_s^{2} a^{2} \\\\cos{\\\\theta}^{2} \\\\cos{2\\\\theta}+2r^{7} r_s^{2} a^{2} \\\\cos{\\\\theta}^{2}-4r^{5} r_s^{2} a^{4} \\\\cos{\\\\theta}^{4} \\\\cos{2\\\\theta}+2r^{4} r_s^{3} a^{4} \\\\cos{\\\\theta}^{4} \\\\cos{2\\\\theta}+4r^{5} r_s^{2} a^{4} \\\\cos{\\\\theta}^{4}-2r^{4} r_s^{3} a^{4} \\\\cos{\\\\theta}^{4}+8r^{3} r_s^{2} a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{2\\\\theta}-16r^{5} r_s^{2} a^{2} \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)-16r^{5} r_s^{2} a^{2} \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-8r^{3} r_s^{2} a^{4} \\\\cos{\\\\theta}^{4} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)%\\n-8r^{3} r_s^{2} a^{4} \\\\cos{\\\\theta}^{4} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-16r^{4} r_s a^{6} \\\\sin{\\\\theta}^{6}+16r^{4} r_s a^{6} \\\\sin{\\\\theta}^{4}+48r^{6} r_s a^{4} \\\\sin{\\\\theta}^{4}+48r^{4} r_s a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4}+6r^{6} r_s a^{4} \\\\cos{2\\\\theta}+16r^{4} r_s a^{6} \\\\cos{\\\\theta}^{2} \\\\cos{2\\\\theta}-6r^{6} r_s a^{4}-16r^{4} r_s a^{6} \\\\cos{\\\\theta}^{2}+6r^{4} r_s a^{4} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+6r^{4} r_s a^{4} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-3r^{4} r_s a^{4} \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)-3r^{4} r_s a^{4} \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+10r^{8} r_s a^{2} \\\\cos{2\\\\theta}-4r^{7} r_s^{2} a^{2} \\\\cos{2\\\\theta}-10r^{8} r_s a^{2}+4r^{7} r_s^{2} a^{2}+26r^{6} r_s a^{4} \\\\cos{\\\\theta}^{2} \\\\cos{2\\\\theta}-26r^{6} r_s a^{4} \\\\cos{\\\\theta}^{2}-8r^{4} r_s a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{2\\\\theta}%\\n+20r^{6} r_s a^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+20r^{6} r_s a^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+22r^{4} r_s a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+22r^{4} r_s a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-16r^{2} r_s a^{8} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6}+16r^{2} r_s a^{8} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4}+16r^{2} r_s a^{8} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4}+10r^{2} r_s a^{8} \\\\cos{\\\\theta}^{4} \\\\cos{2\\\\theta}-10r^{2} r_s a^{8} \\\\cos{\\\\theta}^{4}+6r^{2} r_s a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+6r^{2} r_s a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-3r^{2} r_s a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)-3r^{2} r_s a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+12r^{4} r_s a^{6} \\\\cos{\\\\theta}^{4} \\\\cos{2\\\\theta}-12r^{4} r_s a^{6} \\\\cos{\\\\theta}^{4}-8r^{2} r_s a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{2\\\\theta}+8r^{2} r_s a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+8r^{2} r_s a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+16r^{5} r_s^{2} a^{4} \\\\sin{\\\\theta}^{6}-14r^{5} r_s^{2} a^{4} \\\\sin{\\\\theta}^{4}%\\n-14r^{7} r_s^{2} a^{2} \\\\sin{\\\\theta}^{4}-6r^{5} r_s^{2} a^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)-6r^{5} r_s^{2} a^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+3r^{5} r_s^{2} a^{2} \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+3r^{5} r_s^{2} a^{2} \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+6r^{9} r_s^{2} \\\\cos{2\\\\theta}-2r^{8} r_s^{3} \\\\cos{2\\\\theta}-6r^{9} r_s^{2}+2r^{8} r_s^{3}+8r^{5} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{2\\\\theta}-8r^{7} r_s^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)-8r^{7} r_s^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-32r^{6} r_s a^{4} \\\\sin{\\\\theta}^{6}+32r^{8} r_s a^{2} \\\\sin{\\\\theta}^{4}+48r^{6} r_s a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4}-6r^{6} r_s a^{2} \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)-6r^{6} r_s a^{2} \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-6r^{10} r_s \\\\cos{2\\\\theta}+6r^{10} r_s+4r^{8} r_s a^{2} \\\\cos{\\\\theta}^{2} \\\\cos{2\\\\theta}%\\n-4r^{8} r_s a^{2} \\\\cos{\\\\theta}^{2}-16r^{6} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{2\\\\theta}+16r^{8} r_s \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+16r^{8} r_s \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+24r^{6} r_s a^{2} \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+24r^{6} r_s a^{2} \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-16r^{4} r_s a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6}+16r^{4} r_s a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4}-3r^{4} r_s a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)-3r^{4} r_s a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+2r^{6} r_s a^{4} \\\\cos{\\\\theta}^{4} \\\\cos{2\\\\theta}-2r^{6} r_s a^{4} \\\\cos{\\\\theta}^{4}-8r^{4} r_s a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{2\\\\theta}+8r^{4} r_s a^{4} \\\\cos{\\\\theta}^{4} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+8r^{4} r_s a^{4} \\\\cos{\\\\theta}^{4} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-16r^{4} a^{6} r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6}+18r^{4} a^{6} r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4}+18r^{6} a^{4} r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4}+16r^{4} a^{6} r_s \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4}+8r^{6} a^{4} r_s \\\\cos{\\\\theta}^{2} \\\\cos{2\\\\theta}%\\n+10r^{4} a^{6} r_s \\\\cos{\\\\theta}^{4} \\\\cos{2\\\\theta}-8r^{6} a^{4} r_s \\\\cos{\\\\theta}^{2}-10r^{4} a^{6} r_s \\\\cos{\\\\theta}^{4}+6r^{4} a^{4} r_s \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+6r^{4} a^{4} r_s \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-3r^{4} a^{4} r_s \\\\cos{\\\\theta}^{2} \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)-3r^{4} a^{4} r_s \\\\cos{\\\\theta}^{2} \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-2r^{8} a^{2} r_s \\\\cos{\\\\theta}^{2} \\\\cos{2\\\\theta}+2r^{7} a^{2} r_s^{2} \\\\cos{\\\\theta}^{2} \\\\cos{2\\\\theta}+2r^{8} a^{2} r_s \\\\cos{\\\\theta}^{2}-2r^{7} a^{2} r_s^{2} \\\\cos{\\\\theta}^{2}+2r^{6} a^{4} r_s \\\\cos{\\\\theta}^{4} \\\\cos{2\\\\theta}-2r^{5} a^{4} r_s^{2} \\\\cos{\\\\theta}^{4} \\\\cos{2\\\\theta}-2r^{6} a^{4} r_s \\\\cos{\\\\theta}^{4}+2r^{5} a^{4} r_s^{2} \\\\cos{\\\\theta}^{4}-8r^{4} a^{2} r_s \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{2\\\\theta}+8r^{6} a^{2} r_s \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+8r^{6} a^{2} r_s \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+8r^{4} a^{4} r_s \\\\cos{\\\\theta}^{4} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+8r^{4} a^{4} r_s \\\\cos{\\\\theta}^{4} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)%\\n+16r^{5} a^{6} \\\\sin{\\\\theta}^{6}-16r^{5} a^{6} \\\\sin{\\\\theta}^{4}-32r^{7} a^{4} \\\\sin{\\\\theta}^{4}-80r^{5} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4}-6r^{7} a^{4} \\\\cos{2\\\\theta}-22r^{5} a^{6} \\\\cos{\\\\theta}^{2} \\\\cos{2\\\\theta}+6r^{7} a^{4}+22r^{5} a^{6} \\\\cos{\\\\theta}^{2}-6r^{5} a^{4} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)-6r^{5} a^{4} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+3r^{5} a^{4} \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+3r^{5} a^{4} \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-4r^{9} a^{2} \\\\cos{2\\\\theta}-2r^{8} a^{2} r_s \\\\cos{2\\\\theta}+4r^{9} a^{2}+2r^{8} a^{2} r_s-20r^{7} a^{4} \\\\cos{\\\\theta}^{2} \\\\cos{2\\\\theta}+20r^{7} a^{4} \\\\cos{\\\\theta}^{2}+8r^{5} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{2\\\\theta}-14r^{7} a^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)%\\n-14r^{7} a^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-36r^{5} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)-36r^{5} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+24r^{3} a^{8} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6}-24r^{3} a^{8} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4}-72r^{3} a^{8} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4}-26r^{3} a^{8} \\\\cos{\\\\theta}^{4} \\\\cos{2\\\\theta}+26r^{3} a^{8} \\\\cos{\\\\theta}^{4}-12r^{3} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)-12r^{3} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+6r^{3} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+6r^{3} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+2r^{6} a^{4} \\\\cos{\\\\theta}^{2} r_s \\\\cos{2\\\\theta}-2r^{6} a^{4} \\\\cos{\\\\theta}^{2} r_s-28r^{5} a^{6} \\\\cos{\\\\theta}^{4} \\\\cos{2\\\\theta}+18r^{4} a^{6} \\\\cos{\\\\theta}^{4} r_s \\\\cos{2\\\\theta}+28r^{5} a^{6} \\\\cos{\\\\theta}^{4}-18r^{4} a^{6} \\\\cos{\\\\theta}^{4} r_s+16r^{3} a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{2\\\\theta}-30r^{3} a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)%\\n-30r^{3} a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+16r^{7} a^{4} \\\\sin{\\\\theta}^{6}-16r^{9} a^{2} \\\\sin{\\\\theta}^{4}-56r^{7} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4}+3r^{7} a^{2} \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+3r^{7} a^{2} \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+2r^{11} \\\\cos{2\\\\theta}-2r^{11}+2r^{9} a^{2} \\\\cos{\\\\theta}^{2} \\\\cos{2\\\\theta}-2r^{9} a^{2} \\\\cos{\\\\theta}^{2}+8r^{7} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{2\\\\theta}-8r^{9} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)-8r^{9} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-24r^{7} a^{2} \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)-24r^{7} a^{2} \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+24r^{5} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6}-64r^{5} a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4}+6r^{5} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+6r^{5} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-6r^{8} a^{2} \\\\cos{\\\\theta}^{2} r_s \\\\cos{2\\\\theta}%\\n+6r^{8} a^{2} \\\\cos{\\\\theta}^{2} r_s-2r^{7} a^{4} \\\\cos{\\\\theta}^{4} \\\\cos{2\\\\theta}+2r^{6} a^{4} \\\\cos{\\\\theta}^{4} r_s \\\\cos{2\\\\theta}+2r^{7} a^{4} \\\\cos{\\\\theta}^{4}-2r^{6} a^{4} \\\\cos{\\\\theta}^{4} r_s+16r^{5} a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{2\\\\theta}-24r^{5} a^{4} \\\\cos{\\\\theta}^{4} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)-24r^{5} a^{4} \\\\cos{\\\\theta}^{4} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-8r^{2} a^{8} \\\\cos{\\\\theta}^{4} r_s \\\\sin{\\\\theta}^{6}+10r^{2} a^{8} \\\\cos{\\\\theta}^{4} r_s \\\\sin{\\\\theta}^{4}+34r^{4} a^{6} \\\\cos{\\\\theta}^{4} r_s \\\\sin{\\\\theta}^{4}+16r^{2} a^{8} \\\\cos{\\\\theta}^{6} r_s \\\\sin{\\\\theta}^{4}+12r^{2} a^{8} \\\\cos{\\\\theta}^{6} r_s \\\\cos{2\\\\theta}-12r^{2} a^{8} \\\\cos{\\\\theta}^{6} r_s+6r^{2} a^{6} \\\\cos{\\\\theta}^{4} r_s \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+6r^{2} a^{6} \\\\cos{\\\\theta}^{4} r_s \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-3r^{2} a^{6} \\\\cos{\\\\theta}^{4} r_s \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)-3r^{2} a^{6} \\\\cos{\\\\theta}^{4} r_s \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+4r^{4} a^{6} \\\\cos{\\\\theta}^{6} r_s \\\\cos{2\\\\theta}-2r^{3} a^{6} \\\\cos{\\\\theta}^{6} r_s^{2} \\\\cos{2\\\\theta}%\\n-4r^{4} a^{6} \\\\cos{\\\\theta}^{6} r_s+2r^{3} a^{6} \\\\cos{\\\\theta}^{6} r_s^{2}-8r^{2} a^{4} \\\\cos{\\\\theta}^{4} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{2\\\\theta}+16r^{4} a^{4} \\\\cos{\\\\theta}^{4} r_s \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+16r^{4} a^{4} \\\\cos{\\\\theta}^{4} r_s \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+8r^{2} a^{6} \\\\cos{\\\\theta}^{6} r_s \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+8r^{2} a^{6} \\\\cos{\\\\theta}^{6} r_s \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+8r a^{10} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{6}-8r a^{10} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4}-24r a^{10} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4}-10r a^{10} \\\\cos{\\\\theta}^{6} \\\\cos{2\\\\theta}+10r a^{10} \\\\cos{\\\\theta}^{6}-6r a^{8} \\\\cos{\\\\theta}^{4} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)-6r a^{8} \\\\cos{\\\\theta}^{4} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+3r a^{8} \\\\cos{\\\\theta}^{4} \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+3r a^{8} \\\\cos{\\\\theta}^{4} \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-12r^{3} a^{8} \\\\cos{\\\\theta}^{6} \\\\cos{2\\\\theta}+12r^{3} a^{8} \\\\cos{\\\\theta}^{6}+8r a^{6} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{2\\\\theta}-8r a^{8} \\\\cos{\\\\theta}^{6} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)%\\n-8r a^{8} \\\\cos{\\\\theta}^{6} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-8r^{4} a^{6} \\\\cos{\\\\theta}^{2} r_s \\\\sin{\\\\theta}^{6}+6r^{4} a^{6} \\\\cos{\\\\theta}^{2} r_s \\\\sin{\\\\theta}^{4}+22r^{6} a^{4} \\\\cos{\\\\theta}^{2} r_s \\\\sin{\\\\theta}^{4}+6r^{4} a^{4} \\\\cos{\\\\theta}^{2} r_s \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+6r^{4} a^{4} \\\\cos{\\\\theta}^{2} r_s \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-3r^{4} a^{4} \\\\cos{\\\\theta}^{2} r_s \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)-3r^{4} a^{4} \\\\cos{\\\\theta}^{2} r_s \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+2r^{7} a^{2} \\\\cos{\\\\theta}^{2} r_s^{2} \\\\cos{2\\\\theta}-2r^{7} a^{2} \\\\cos{\\\\theta}^{2} r_s^{2}-8r^{4} a^{2} \\\\cos{\\\\theta}^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{2\\\\theta}+8r^{6} a^{2} \\\\cos{\\\\theta}^{2} r_s \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+8r^{6} a^{2} \\\\cos{\\\\theta}^{2} r_s \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+8r^{3} a^{8} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{6}-24r^{3} a^{8} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4}+3r^{3} a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+3r^{3} a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-2r^{5} a^{6} \\\\cos{\\\\theta}^{6} \\\\cos{2\\\\theta}+2r^{5} a^{6} \\\\cos{\\\\theta}^{6}+8r^{3} a^{4} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{2\\\\theta}%\\n-8r^{3} a^{6} \\\\cos{\\\\theta}^{6} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)-8r^{3} a^{6} \\\\cos{\\\\theta}^{6} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-8r^{3} a^{6} r_s^{2} \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}^{2}+8r^{4} a^{6} r_s \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}^{2}+8r^{2} a^{8} r_s \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}^{4}-16r^{5} a^{4} r_s^{2} \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}^{2}+8r^{4} a^{4} r_s^{3} \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}^{2}+8r^{4} a^{6} r_s \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}^{4}-8r^{3} a^{6} r_s^{2} \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}^{4}-8r^{5} a^{4} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{2}+8r^{6} a^{4} r_s \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{2}+36r^{4} a^{6} r_s \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2}-16r^{7} a^{2} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{2}+8r^{6} a^{2} r_s^{3} \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{2}-8r^{8} a^{2} r_s \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{2}+4r^{6} a^{4} r_s \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2}-32r^{5} a^{4} r_s^{2} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2}-8r^{3} a^{6} r_s^{2} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2}+8r^{2} a^{8} r_s \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2}+8r^{4} a^{4} r_s^{3} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2}%\\n+8r^{4} a^{6} r_s \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2}-8r^{3} a^{6} r_s^{2} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2}+8r^{3} r_s^{2} a^{6} \\\\sin{\\\\theta}^{6} \\\\cos{\\\\theta}^{2}+32r^{5} r_s^{2} a^{4} \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}^{2}+16r^{3} r_s^{2} a^{6} \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}^{4}+8r^{2} r_s a^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{2}+8r^{4} r_s a^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{2}-8r^{4} r_s^{3} a^{4} \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}^{2}-16r^{6} r_s^{3} a^{2} \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{2}-8r^{3} r_s^{2} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{2}-8r^{5} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{2}+32r^{7} r_s^{2} a^{2} \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{2}+16r^{4} r_s a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{2}+16r^{6} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{2}+8r^{2} r_s a^{4} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+8r^{4} r_s a^{2} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-8r^{4} a^{6} \\\\sin{\\\\theta}^{6} r_s \\\\cos{\\\\theta}^{2}-16r^{6} a^{4} \\\\sin{\\\\theta}^{4} r_s \\\\cos{\\\\theta}^{2}-16r^{4} a^{6} \\\\sin{\\\\theta}^{4} r_s \\\\cos{\\\\theta}^{4}-8r^{3} a^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{2}%\\n-8r^{5} a^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{2}-8r^{5} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{2}-8r^{7} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{2}-24r^{6} a^{4} \\\\cos{\\\\theta}^{4} r_s \\\\sin{\\\\theta}^{2}-48r^{4} a^{6} \\\\cos{\\\\theta}^{6} r_s \\\\sin{\\\\theta}^{2}-16r^{3} a^{4} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-16r^{5} a^{2} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-8r^{2} a^{8} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{6} r_s-16r^{4} a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} r_s-16r^{2} a^{8} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} r_s-8r a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-8r^{3} a^{4} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+6r^{3} a^{6} \\\\cos{\\\\theta}^{4} r_s^{2} \\\\sin{\\\\theta}^{4}+16r^{5} a^{4} \\\\cos{\\\\theta}^{4} r_s^{2} \\\\sin{\\\\theta}^{2}+16r^{3} a^{6} \\\\cos{\\\\theta}^{6} r_s^{2} \\\\sin{\\\\theta}^{2}+8r^{2} a^{4} \\\\cos{\\\\theta}^{4} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+8r^{4} a^{2} \\\\cos{\\\\theta}^{4} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-16r^{2} a^{8} \\\\cos{\\\\theta}^{8} r_s \\\\sin{\\\\theta}^{2}-8r a^{6} \\\\cos{\\\\theta}^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-8r^{3} a^{4} \\\\cos{\\\\theta}^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}%\\n+2r^{6} r_s^{3} a^{2} \\\\sin{\\\\theta}^{2}-2r^{5} r_s^{2} a^{4} \\\\sin{\\\\theta}^{2}+30r^{6} r_s a^{4} \\\\sin{\\\\theta}^{2}+48r^{4} r_s a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}-2r^{4} r_s^{3} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+2r^{3} r_s^{2} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+18r^{2} r_s a^{8} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2}-2r^{6} r_s^{3} a^{2} \\\\sin{\\\\theta}^{4}+2r^{4} r_s^{3} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4}+6r^{6} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-4r^{5} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-4r^{4} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} \\\\sin{\\\\theta}^{2}-2r^{8} a^{2} r_s \\\\sin{\\\\theta}^{4}+2r^{7} a^{2} r_s^{2} \\\\sin{\\\\theta}^{4}-2r^{6} a^{4} r_s \\\\sin{\\\\theta}^{4}-2r^{5} a^{4} r_s^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4}-4r^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s \\\\sin{\\\\theta}^{2}+4r^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} \\\\sin{\\\\theta}^{2}+2r^{5} a^{4} \\\\cos{\\\\theta}^{2} r_s^{2} \\\\sin{\\\\theta}^{4}-4r^{4} a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s \\\\sin{\\\\theta}^{2}%\\n+6a^{4} \\\\cos{\\\\theta}^{2} r_s^{2} r^{5} \\\\sin{\\\\theta}^{2}-2a^{4} \\\\cos{\\\\theta}^{2} r_s^{3} r^{4} \\\\sin{\\\\theta}^{2}+2a^{6} \\\\cos{\\\\theta}^{2} r_s^{2} r^{3} \\\\sin{\\\\theta}^{2}-4a^{4} \\\\cos{\\\\theta}^{2} r_s r^{6} \\\\sin{\\\\theta}^{2}-2a^{6} \\\\cos{\\\\theta}^{2} r_s r^{4} \\\\sin{\\\\theta}^{2}-4a^{6} \\\\cos{\\\\theta}^{4} r_s^{2} r^{3} \\\\sin{\\\\theta}^{2}+4a^{2} \\\\cos{\\\\theta}^{2} r_s^{2} r^{7} \\\\sin{\\\\theta}^{2}-2a^{2} \\\\cos{\\\\theta}^{2} r_s^{3} r^{6} \\\\sin{\\\\theta}^{2}-2a^{2} \\\\cos{\\\\theta}^{2} r_s r^{8} \\\\sin{\\\\theta}^{2}-2a^{4} \\\\cos{\\\\theta}^{4} r_s^{2} r^{5} \\\\sin{\\\\theta}^{2}+2a^{6} \\\\cos{\\\\theta}^{4} r_s^{3} r^{2} \\\\sin{\\\\theta}^{2}-2a^{8} \\\\cos{\\\\theta}^{4} r_s^{2} r \\\\sin{\\\\theta}^{2}+4a^{8} \\\\cos{\\\\theta}^{6} r_s r^{2} \\\\sin{\\\\theta}^{2}-2a^{8} \\\\cos{\\\\theta}^{6} r_s^{2} r \\\\sin{\\\\theta}^{2}+2a^{10} \\\\cos{\\\\theta}^{6} r_s \\\\sin{\\\\theta}^{2}+2a^{4} \\\\cos{\\\\theta}^{4} r_s^{3} r^{4} \\\\sin{\\\\theta}^{2}+2a^{6} \\\\cos{\\\\theta}^{6} r_s r^{4} \\\\sin{\\\\theta}^{2}-2a^{6} \\\\cos{\\\\theta}^{6} r_s^{2} r^{3} \\\\sin{\\\\theta}^{2}-4a^{4} \\\\cos{\\\\theta}^{2} r^{5} r_s^{2} \\\\sin{\\\\theta}^{4}+2a^{4} \\\\cos{\\\\theta}^{2} r^{4} r_s^{3} \\\\sin{\\\\theta}^{4}%\\n-2a^{6} \\\\cos{\\\\theta}^{2} r^{3} r_s^{2} \\\\sin{\\\\theta}^{4}-2a^{6} \\\\cos{\\\\theta}^{4} r^{2} r_s^{3} \\\\sin{\\\\theta}^{4}+2a^{8} \\\\cos{\\\\theta}^{4} r r_s^{2} \\\\sin{\\\\theta}^{4}+10a^{2} \\\\cos{\\\\theta}^{2} r^{4} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-6a^{2} \\\\cos{\\\\theta}^{2} r^{3} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+6a^{4} \\\\cos{\\\\theta}^{2} r^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-6a^{4} \\\\cos{\\\\theta}^{2} r^{6} r_s \\\\sin{\\\\theta}^{4}+10a^{6} \\\\cos{\\\\theta}^{2} r^{4} r_s \\\\sin{\\\\theta}^{4}-14a^{6} \\\\cos{\\\\theta}^{4} r^{4} r_s \\\\sin{\\\\theta}^{4}+10a^{8} \\\\cos{\\\\theta}^{4} r^{2} r_s \\\\sin{\\\\theta}^{4}-8a^{2} \\\\cos{\\\\theta}^{2} r^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+4a^{2} \\\\cos{\\\\theta}^{2} r^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s \\\\sin{\\\\theta}^{2}-8a^{4} \\\\cos{\\\\theta}^{2} r^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-2a^{6} \\\\cos{\\\\theta}^{4} r_s r^{4} \\\\sin{\\\\theta}^{4}+2a^{6} \\\\cos{\\\\theta}^{4} r_s^{2} r^{3} \\\\sin{\\\\theta}^{4}-2a^{8} \\\\cos{\\\\theta}^{4} r_s r^{2} \\\\sin{\\\\theta}^{4}-2a^{8} \\\\cos{\\\\theta}^{6} r_s \\\\sin{\\\\theta}^{4} r^{2}+2a^{8} \\\\cos{\\\\theta}^{6} r_s^{2} \\\\sin{\\\\theta}^{4} r-2a^{10} \\\\cos{\\\\theta}^{6} r_s \\\\sin{\\\\theta}^{4}-8a^{4} \\\\cos{\\\\theta}^{4} r^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}%\\n+4a^{4} \\\\cos{\\\\theta}^{4} r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s \\\\sin{\\\\theta}^{2}-8a^{6} \\\\cos{\\\\theta}^{4} r \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-6r^{3} r_s^{2} a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+2r^{2} r_s^{3} a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-4r^{6} r_s^{2} a^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4r^{6} r_s^{2} a^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4r^{5} r_s^{3} a^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4r^{5} r_s^{3} a^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+8r^{4} r_s^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+8r^{4} r_s^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-12r^{4} r_s^{2} a^{4} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}-16r^{4} r_s^{2} a^{4} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+8r^{3} r_s^{3} a^{4} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+8r^{3} r_s^{3} a^{4} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-16r^{2} r_s^{2} a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}-16r^{2} r_s^{2} a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4r^{4} r_s^{2} a^{4} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r_s r\\\\right) \\\\sin{\\\\theta}^{2}+4r^{4} r_s^{2} a^{4} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2}+4r^{2} r_s^{2} a^{6} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4r^{2} r_s^{2} a^{6} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(r_s r\\\\right) \\\\sin{\\\\theta}^{2}%\\n+4r^{2} r_s^{2} a^{6} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2}+4r^{4} r_s a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-2r^{3} r_s^{2} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-36r^{7} r_s a^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}-40r^{7} r_s a^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+28r^{6} r_s^{2} a^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+28r^{6} r_s^{2} a^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-16r^{5} r_s a^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}-16r^{5} r_s a^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+4r^{5} r_s a^{4} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+4r^{5} r_s a^{4} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4r^{3} r_s a^{6} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4r^{3} r_s a^{6} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+4r^{4} r_s^{2} a^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}-4r^{3} r_s a^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}-4r^{5} r_s a^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+4r^{4} r_s^{2} a^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}-4r^{3} r_s a^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}-4r^{7} r_s a^{2} \\\\partial_{r}\\\\left(r_s r\\\\right) \\\\sin{\\\\theta}^{2}-4r^{5} r_s a^{4} \\\\partial_{r}\\\\left(r_s r\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}%\\n+4r^{7} r_s a^{2} \\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2}+4r^{5} r_s a^{4} \\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+12r^{3} r_s a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+4r^{3} r_s a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r_s r\\\\right) \\\\sin{\\\\theta}^{2}-4r^{3} r_s a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2}+4r^{2} r_s a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-2r r_s^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+16r^{3} r_s a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+8r r_s a^{8} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+8r r_s a^{8} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4r r_s a^{8} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+4r r_s a^{8} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(r_s r\\\\right) \\\\sin{\\\\theta}^{2}-4r r_s a^{8} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2}+2r^{4} r_s^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+44r^{8} r_s^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+48r^{8} r_s^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-16r^{7} r_s^{3} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}-16r^{7} r_s^{3} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+8r^{6} r_s^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}-4r^{5} r_s^{3} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}%\\n+4r^{6} r_s^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{2} \\\\sin{\\\\theta}^{2}+4r^{4} r_s^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+12r^{6} r_s^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}-4r^{5} r_s^{3} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+4r^{6} r_s^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{2} \\\\sin{\\\\theta}^{2}+4r^{4} r_s^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+4r^{8} r_s^{2} \\\\partial_{r}\\\\left(r_s r\\\\right) \\\\sin{\\\\theta}^{2}+4r^{6} r_s^{2} \\\\partial_{r}\\\\left(r_s r\\\\right) a^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}-4r^{8} r_s^{2} \\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4r^{6} r_s^{2} \\\\partial_{r}\\\\left(a^{2}\\\\right) a^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}-36r^{9} r_s \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}-44r^{9} r_s \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+4r^{7} r_s a^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+8r^{7} r_s a^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-8r^{7} r_s \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{2} \\\\sin{\\\\theta}^{2}-8r^{5} r_s \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}-8r^{7} r_s \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}-8r^{7} r_s \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{2} \\\\sin{\\\\theta}^{2}-8r^{5} r_s \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}-8r^{9} r_s \\\\partial_{r}\\\\left(r_s r\\\\right) \\\\sin{\\\\theta}^{2}%\\n-8r^{7} r_s \\\\partial_{r}\\\\left(r_s r\\\\right) a^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+8r^{9} r_s \\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2}+8r^{7} r_s \\\\partial_{r}\\\\left(a^{2}\\\\right) a^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+4r^{7} r_s a^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r_s r\\\\right) \\\\sin{\\\\theta}^{2}+8r^{5} r_s a^{4} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r_s r\\\\right) \\\\sin{\\\\theta}^{2}-4r^{7} r_s a^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2}-8r^{5} r_s a^{4} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2}+4r^{4} r_s a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+8r^{5} r_s a^{4} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4r^{3} r_s a^{6} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+4r^{3} r_s a^{6} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(r_s r\\\\right) \\\\sin{\\\\theta}^{2}-4r^{3} r_s a^{6} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2}+36r^{6} a^{4} r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}-16r^{7} a^{2} r_s^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+12r^{8} a^{2} r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+4r^{4} a^{2} r_s \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-2r^{3} a^{2} r_s^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-12r^{7} a^{2} r_s \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}-16r^{7} a^{2} r_s \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+16r^{6} a^{2} r_s^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}%\\n+16r^{6} a^{2} r_s^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-16r^{5} a^{4} r_s \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}-16r^{5} a^{4} r_s \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+8r^{5} a^{4} r_s \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+8r^{5} a^{4} r_s \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-8r^{4} a^{4} r_s^{2} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}-8r^{4} a^{4} r_s^{2} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+8r^{3} a^{6} r_s \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+8r^{3} a^{6} r_s \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4r^{7} a^{2} r_s \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r_s r\\\\right) \\\\sin{\\\\theta}^{2}+4r^{7} a^{2} r_s \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4r^{3} a^{6} r_s \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+4r^{3} a^{6} r_s \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(r_s r\\\\right) \\\\sin{\\\\theta}^{2}-4r^{3} a^{6} r_s \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2}-28r^{7} a^{4} \\\\sin{\\\\theta}^{2}-48r^{5} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+16r^{8} a^{2} r_s \\\\sin{\\\\theta}^{2}-64r^{7} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}-40r^{9} a^{2} \\\\sin{\\\\theta}^{2}-4r^{5} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}%\\n+2r^{4} a^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+24r^{8} a^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+28r^{8} a^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-12r^{7} a^{2} r_s \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}-12r^{7} a^{2} r_s \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+16r^{6} a^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+16r^{6} a^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+8r^{6} a^{4} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+8r^{6} a^{4} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+4r^{4} a^{6} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+4r^{4} a^{6} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4r^{7} a^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) r_s \\\\sin{\\\\theta}^{2}-4r^{5} a^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right) r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+4r^{4} a^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+4r^{6} a^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}-4r^{7} a^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\sin{\\\\theta}^{2}-4r^{5} a^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+4r^{4} a^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+4r^{8} a^{2} \\\\partial_{r}\\\\left(r_s r\\\\right) \\\\sin{\\\\theta}^{2}+4r^{6} a^{4} \\\\partial_{r}\\\\left(r_s r\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}%\\n-4r^{8} a^{2} \\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4r^{6} a^{4} \\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}-12r^{4} a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4r^{4} a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r_s r\\\\right) \\\\sin{\\\\theta}^{2}+4r^{4} a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2}-20r^{3} a^{8} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2}+16r^{6} a^{4} \\\\cos{\\\\theta}^{2} r_s \\\\sin{\\\\theta}^{2}-24r^{5} a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2}+8r^{4} a^{6} \\\\cos{\\\\theta}^{4} r_s \\\\sin{\\\\theta}^{2}+2r^{2} a^{4} \\\\cos{\\\\theta}^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-16r^{4} a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+12r^{3} a^{6} \\\\cos{\\\\theta}^{4} r_s \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+12r^{3} a^{6} \\\\cos{\\\\theta}^{4} r_s \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-8r^{2} a^{8} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}-8r^{2} a^{8} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4r^{5} a^{4} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) r_s \\\\sin{\\\\theta}^{2}-4r^{3} a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right) r_s \\\\sin{\\\\theta}^{2}-4r^{5} a^{4} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\sin{\\\\theta}^{2}-4r^{3} a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\sin{\\\\theta}^{2}+4r^{2} a^{8} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}%\\n-4r^{2} a^{8} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(r_s r\\\\right) \\\\sin{\\\\theta}^{2}+4r^{2} a^{8} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2}-16r^{9} a^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}-12r^{11} \\\\sin{\\\\theta}^{2}+12r^{10} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+16r^{10} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+4r^{8} a^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+4r^{8} a^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4r^{9} \\\\partial_{r}\\\\left(r^{2}\\\\right) r_s \\\\sin{\\\\theta}^{2}-4r^{7} \\\\partial_{r}\\\\left(r^{2}\\\\right) r_s a^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+4r^{8} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{2} \\\\sin{\\\\theta}^{2}+4r^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+4r^{8} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}-4r^{9} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\sin{\\\\theta}^{2}-4r^{7} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s a^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+4r^{8} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{2} \\\\sin{\\\\theta}^{2}+4r^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+4r^{10} \\\\partial_{r}\\\\left(r_s r\\\\right) \\\\sin{\\\\theta}^{2}+4r^{8} \\\\partial_{r}\\\\left(r_s r\\\\right) a^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}-4r^{10} \\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2}%\\n-4r^{8} \\\\partial_{r}\\\\left(a^{2}\\\\right) a^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}-4r^{6} a^{4} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4r^{6} a^{4} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r_s r\\\\right) \\\\sin{\\\\theta}^{2}+4r^{6} a^{4} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2}+16r^{8} a^{2} \\\\cos{\\\\theta}^{2} r_s \\\\sin{\\\\theta}^{2}-4r^{7} a^{4} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2}+2r^{4} a^{2} \\\\cos{\\\\theta}^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-8r^{6} a^{4} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+12r^{5} a^{4} \\\\cos{\\\\theta}^{4} r_s \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+12r^{5} a^{4} \\\\cos{\\\\theta}^{4} r_s \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4r^{7} a^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) r_s \\\\sin{\\\\theta}^{2}-4r^{5} a^{4} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right) r_s \\\\sin{\\\\theta}^{2}-4r^{7} a^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\sin{\\\\theta}^{2}-4r^{5} a^{4} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\sin{\\\\theta}^{2}+4r^{4} a^{6} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4r^{4} a^{6} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(r_s r\\\\right) \\\\sin{\\\\theta}^{2}+4r^{4} a^{6} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2}-8a^{8} \\\\cos{\\\\theta}^{4} r^{2} r_s \\\\sin{\\\\theta}^{6}-8a^{8} \\\\cos{\\\\theta}^{6} r^{2} r_s \\\\sin{\\\\theta}^{4}+72a^{6} \\\\cos{\\\\theta}^{4} r^{4} r_s \\\\sin{\\\\theta}^{2}%\\n+28a^{8} \\\\cos{\\\\theta}^{6} r^{2} r_s \\\\sin{\\\\theta}^{2}-24a^{4} \\\\cos{\\\\theta}^{4} r^{5} r_s^{2} \\\\sin{\\\\theta}^{2}+12a^{6} \\\\cos{\\\\theta}^{6} r^{4} r_s \\\\sin{\\\\theta}^{2}-8a^{6} \\\\cos{\\\\theta}^{6} r^{3} r_s^{2} \\\\sin{\\\\theta}^{2}+40a^{4} \\\\cos{\\\\theta}^{4} r^{6} r_s \\\\sin{\\\\theta}^{2}+6a^{4} \\\\cos{\\\\theta}^{4} r^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-2a^{4} \\\\cos{\\\\theta}^{4} r r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-4a^{4} \\\\cos{\\\\theta}^{4} r^{5} r_s \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}-8a^{4} \\\\cos{\\\\theta}^{4} r^{5} r_s \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+8a^{4} \\\\cos{\\\\theta}^{4} r^{4} r_s^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+8a^{4} \\\\cos{\\\\theta}^{4} r^{4} r_s^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-8a^{6} \\\\cos{\\\\theta}^{4} r^{3} r_s \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}-8a^{6} \\\\cos{\\\\theta}^{4} r^{3} r_s \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+16a^{6} \\\\cos{\\\\theta}^{6} r^{3} r_s \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+20a^{6} \\\\cos{\\\\theta}^{6} r^{3} r_s \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-8a^{6} \\\\cos{\\\\theta}^{6} r^{2} r_s^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}-8a^{6} \\\\cos{\\\\theta}^{6} r^{2} r_s^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+8a^{8} \\\\cos{\\\\theta}^{6} r r_s \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+8a^{8} \\\\cos{\\\\theta}^{6} r r_s \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4a^{4} \\\\cos{\\\\theta}^{4} r^{5} r_s \\\\partial_{r}\\\\left(r_s r\\\\right) \\\\sin{\\\\theta}^{2}%\\n+4a^{6} \\\\cos{\\\\theta}^{6} r^{3} r_s \\\\partial_{r}\\\\left(r_s r\\\\right) \\\\sin{\\\\theta}^{2}+4a^{4} \\\\cos{\\\\theta}^{4} r^{5} r_s \\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4a^{6} \\\\cos{\\\\theta}^{6} r^{3} r_s \\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4a^{8} \\\\cos{\\\\theta}^{8} r r_s \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+4a^{8} \\\\cos{\\\\theta}^{8} r r_s \\\\partial_{r}\\\\left(r_s r\\\\right) \\\\sin{\\\\theta}^{2}-4a^{8} \\\\cos{\\\\theta}^{8} r r_s \\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2}+8a^{8} \\\\cos{\\\\theta}^{2} r^{3} \\\\sin{\\\\theta}^{6}-8a^{8} \\\\cos{\\\\theta}^{2} r^{3} \\\\sin{\\\\theta}^{4}+8a^{8} \\\\cos{\\\\theta}^{4} r^{3} \\\\sin{\\\\theta}^{4}-28a^{6} \\\\cos{\\\\theta}^{2} r^{5} \\\\sin{\\\\theta}^{2}-48a^{8} \\\\cos{\\\\theta}^{4} r^{3} \\\\sin{\\\\theta}^{2}+44a^{4} \\\\cos{\\\\theta}^{2} r^{6} r_s \\\\sin{\\\\theta}^{2}-64a^{6} \\\\cos{\\\\theta}^{4} r^{5} \\\\sin{\\\\theta}^{2}-40a^{4} \\\\cos{\\\\theta}^{2} r^{7} \\\\sin{\\\\theta}^{2}+28a^{4} \\\\cos{\\\\theta}^{2} r^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+32a^{4} \\\\cos{\\\\theta}^{2} r^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-28a^{4} \\\\cos{\\\\theta}^{2} r^{5} r_s \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}-28a^{4} \\\\cos{\\\\theta}^{2} r^{5} r_s \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+16a^{6} \\\\cos{\\\\theta}^{2} r^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+16a^{6} \\\\cos{\\\\theta}^{2} r^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}%\\n+8a^{6} \\\\cos{\\\\theta}^{4} r^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+12a^{6} \\\\cos{\\\\theta}^{4} r^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+4a^{8} \\\\cos{\\\\theta}^{4} r^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+4a^{8} \\\\cos{\\\\theta}^{4} r^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4a^{4} \\\\cos{\\\\theta}^{2} r^{5} \\\\partial_{r}\\\\left(r^{2}\\\\right) r_s \\\\sin{\\\\theta}^{2}-4a^{6} \\\\cos{\\\\theta}^{4} r^{3} \\\\partial_{r}\\\\left(r^{2}\\\\right) r_s \\\\sin{\\\\theta}^{2}-4a^{4} \\\\cos{\\\\theta}^{2} r^{5} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\sin{\\\\theta}^{2}-4a^{6} \\\\cos{\\\\theta}^{4} r^{3} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\sin{\\\\theta}^{2}+4a^{4} \\\\cos{\\\\theta}^{2} r^{6} \\\\partial_{r}\\\\left(r_s r\\\\right) \\\\sin{\\\\theta}^{2}+4a^{6} \\\\cos{\\\\theta}^{4} r^{4} \\\\partial_{r}\\\\left(r_s r\\\\right) \\\\sin{\\\\theta}^{2}-4a^{4} \\\\cos{\\\\theta}^{2} r^{6} \\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4a^{6} \\\\cos{\\\\theta}^{4} r^{4} \\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2}-20a^{8} \\\\cos{\\\\theta}^{6} r^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+8a^{10} \\\\cos{\\\\theta}^{4} r \\\\sin{\\\\theta}^{6}-8a^{10} \\\\cos{\\\\theta}^{4} r \\\\sin{\\\\theta}^{4}+8a^{10} \\\\cos{\\\\theta}^{6} r \\\\sin{\\\\theta}^{4}-20a^{10} \\\\cos{\\\\theta}^{6} r \\\\sin{\\\\theta}^{2}-24a^{8} \\\\cos{\\\\theta}^{6} r^{3} \\\\sin{\\\\theta}^{2}+2a^{6} \\\\cos{\\\\theta}^{4} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-20a^{8} \\\\cos{\\\\theta}^{6} r^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}%\\n+12a^{8} \\\\cos{\\\\theta}^{6} r_s r \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+12a^{8} \\\\cos{\\\\theta}^{6} r_s r \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-8a^{10} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}-8a^{10} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+4a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right) r^{4} \\\\sin{\\\\theta}^{2}+8a^{8} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right) r^{2} \\\\sin{\\\\theta}^{2}-4a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right) r_s r^{3} \\\\sin{\\\\theta}^{2}-4a^{8} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right) r_s r \\\\sin{\\\\theta}^{2}+4a^{8} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right) r^{2} \\\\sin{\\\\theta}^{2}+4a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r^{4} \\\\sin{\\\\theta}^{2}+4a^{8} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r^{2} \\\\sin{\\\\theta}^{2}-4a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s r^{3} \\\\sin{\\\\theta}^{2}-4a^{8} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s r \\\\sin{\\\\theta}^{2}+4a^{8} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r^{2} \\\\sin{\\\\theta}^{2}+4a^{10} \\\\cos{\\\\theta}^{8} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4a^{8} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(r_s r\\\\right) r^{2} \\\\sin{\\\\theta}^{2}-4a^{10} \\\\cos{\\\\theta}^{8} \\\\partial_{r}\\\\left(r_s r\\\\right) \\\\sin{\\\\theta}^{2}+4a^{8} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(a^{2}\\\\right) r^{2} \\\\sin{\\\\theta}^{2}+4a^{10} \\\\cos{\\\\theta}^{8} \\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2}-8a^{6} \\\\cos{\\\\theta}^{2} r^{4} r_s \\\\sin{\\\\theta}^{6}%\\n-16a^{2} \\\\cos{\\\\theta}^{2} r^{7} r_s^{2} \\\\sin{\\\\theta}^{2}+28a^{2} \\\\cos{\\\\theta}^{2} r^{8} r_s \\\\sin{\\\\theta}^{2}-24a^{2} \\\\cos{\\\\theta}^{2} r^{7} r_s \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}-28a^{2} \\\\cos{\\\\theta}^{2} r^{7} r_s \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+16a^{2} \\\\cos{\\\\theta}^{2} r^{6} r_s^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+16a^{2} \\\\cos{\\\\theta}^{2} r^{6} r_s^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4a^{2} \\\\cos{\\\\theta}^{2} r^{7} r_s \\\\partial_{r}\\\\left(r_s r\\\\right) \\\\sin{\\\\theta}^{2}+4a^{2} \\\\cos{\\\\theta}^{2} r^{7} r_s \\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2}+8a^{6} \\\\cos{\\\\theta}^{2} r^{5} \\\\sin{\\\\theta}^{6}+8a^{4} \\\\cos{\\\\theta}^{2} r^{7} \\\\sin{\\\\theta}^{4}+16a^{6} \\\\cos{\\\\theta}^{4} r^{5} \\\\sin{\\\\theta}^{4}-16a^{4} \\\\cos{\\\\theta}^{4} r^{7} \\\\sin{\\\\theta}^{2}-12a^{2} \\\\cos{\\\\theta}^{2} r^{9} \\\\sin{\\\\theta}^{2}+12a^{2} \\\\cos{\\\\theta}^{2} r^{8} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+16a^{2} \\\\cos{\\\\theta}^{2} r^{8} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+4a^{4} \\\\cos{\\\\theta}^{4} r^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+8a^{4} \\\\cos{\\\\theta}^{4} r^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4a^{2} \\\\cos{\\\\theta}^{2} r^{7} \\\\partial_{r}\\\\left(r^{2}\\\\right) r_s \\\\sin{\\\\theta}^{2}-8a^{4} \\\\cos{\\\\theta}^{4} r^{5} \\\\partial_{r}\\\\left(r^{2}\\\\right) r_s \\\\sin{\\\\theta}^{2}-4a^{2} \\\\cos{\\\\theta}^{2} r^{7} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\sin{\\\\theta}^{2}%\\n-8a^{4} \\\\cos{\\\\theta}^{4} r^{5} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\sin{\\\\theta}^{2}+4a^{2} \\\\cos{\\\\theta}^{2} r^{8} \\\\partial_{r}\\\\left(r_s r\\\\right) \\\\sin{\\\\theta}^{2}+4a^{4} \\\\cos{\\\\theta}^{4} r^{6} \\\\partial_{r}\\\\left(r_s r\\\\right) \\\\sin{\\\\theta}^{2}-4a^{2} \\\\cos{\\\\theta}^{2} r^{8} \\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4a^{4} \\\\cos{\\\\theta}^{4} r^{6} \\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4a^{6} \\\\cos{\\\\theta}^{6} r^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4a^{6} \\\\cos{\\\\theta}^{6} r^{4} \\\\partial_{r}\\\\left(r_s r\\\\right) \\\\sin{\\\\theta}^{2}+4a^{6} \\\\cos{\\\\theta}^{6} r^{4} \\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2}+8a^{8} \\\\cos{\\\\theta}^{4} r^{3} \\\\sin{\\\\theta}^{6}+8a^{8} \\\\cos{\\\\theta}^{6} r^{3} \\\\sin{\\\\theta}^{4}-4a^{6} \\\\cos{\\\\theta}^{6} r^{5} \\\\sin{\\\\theta}^{2}-8a^{6} \\\\cos{\\\\theta}^{6} r^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4a^{6} \\\\cos{\\\\theta}^{6} r^{3} \\\\partial_{r}\\\\left(r^{2}\\\\right) r_s \\\\sin{\\\\theta}^{2}-4a^{6} \\\\cos{\\\\theta}^{6} r^{3} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\sin{\\\\theta}^{2}+4a^{8} \\\\cos{\\\\theta}^{8} r^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4a^{8} \\\\cos{\\\\theta}^{8} r^{2} \\\\partial_{r}\\\\left(r_s r\\\\right) \\\\sin{\\\\theta}^{2}+4a^{8} \\\\cos{\\\\theta}^{8} r^{2} \\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2}}{8r^{2} r_s^{2} a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4}-8r^{3} r_s a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4}-8r r_s a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4}+8r^{4} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4}-16r^{5} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4}-8r^{3} r_s a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4}-8r^{3} a^{2} r_s \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4}+8r^{4} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4}+8r^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4}+8r^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4}+8r^{4} a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4}-8a^{4} \\\\cos{\\\\theta}^{4} r r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4}+8a^{4} \\\\cos{\\\\theta}^{2} r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4}+8a^{6} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4}-8a^{2} \\\\cos{\\\\theta}^{2} r^{3} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4}+8a^{2} \\\\cos{\\\\theta}^{2} r^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4}+8a^{4} \\\\cos{\\\\theta}^{4} r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{r}= & \\\\frac{14r_s^{4} r^{8} a^{4} \\\\sin{\\\\theta}^{2}-2r_s^{5} r^{7} a^{4} \\\\sin{\\\\theta}^{2}+2r_s^{4} r^{6} a^{6} \\\\sin{\\\\theta}^{2}-20r_s^{3} r^{9} a^{4} \\\\sin{\\\\theta}^{2}-6r_s^{3} r^{7} a^{6} \\\\sin{\\\\theta}^{2}-24r_s^{3} r^{7} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+4r_s^{4} r^{6} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}-4r_s^{3} r^{5} a^{8} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+2r_s^{5} r^{5} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}-2r_s^{4} r^{4} a^{8} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+2r_s^{3} r^{5} a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-2r_s^{4} r^{4} a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+2r_s^{3} r^{3} a^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+16r_s^{4} r^{10} a^{2} \\\\sin{\\\\theta}^{2}-6r_s^{5} r^{9} a^{2} \\\\sin{\\\\theta}^{2}-14r_s^{3} r^{11} a^{2} \\\\sin{\\\\theta}^{2}-20r_s^{3} r^{9} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+14r_s^{4} r^{8} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}-2r_s^{5} r^{7} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}%\\n-4r_s^{3} r^{7} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+2r_s^{4} r^{6} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+8r_s^{2} r^{10} a^{4} \\\\sin{\\\\theta}^{2}+4r_s^{2} r^{8} a^{6} \\\\sin{\\\\theta}^{2}+16r_s^{2} r^{8} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+8r_s^{2} r^{6} a^{8} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}-2r_s^{2} r^{4} a^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+4r_s^{2} r^{12} a^{2} \\\\sin{\\\\theta}^{2}+8r_s^{2} r^{10} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+2r_s^{2} r^{8} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+8r_s^{2} r^{6} a^{8} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2}-4r_s^{3} r^{5} a^{8} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2}+4r_s^{2} r^{4} a^{10} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2}-2r_s^{4} r^{4} a^{8} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2}+2r_s^{3} r^{3} a^{10} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2}+2r_s^{3} r^{3} a^{6} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-2r_s^{2} r^{2} a^{8} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+4r_s^{2} r^{8} a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2}-6r_s^{3} r^{7} a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2}+2r_s^{4} r^{6} a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2}%\\n+2r_s^{2} r^{6} a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-2r_s^{3} r^{5} a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-2r_s^{2} r^{6} \\\\left(a^{2} r r_s-a^{2} r^{2}-a^{4} \\\\cos{\\\\theta}^{2}+r^{3} r_s-r^{4}-r^{2} a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+2r_s^{3} r^{5} \\\\left(a^{2} r r_s-a^{2} r^{2}-a^{4} \\\\cos{\\\\theta}^{2}+r^{3} r_s-r^{4}-r^{2} a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-2r_s^{2} r^{4} \\\\left(a^{2} r r_s-a^{2} r^{2}-a^{4} \\\\cos{\\\\theta}^{2}+r^{3} r_s-r^{4}-r^{2} a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2}+2r_s^{2} r^{4} a^{2} \\\\cos{\\\\theta}^{2} \\\\left(a^{2} r r_s-a^{2} r^{2}-a^{4} \\\\cos{\\\\theta}^{2}+r^{3} r_s-r^{4}-r^{2} a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-2r_s^{3} r^{3} a^{2} \\\\cos{\\\\theta}^{2} \\\\left(a^{2} r r_s-a^{2} r^{2}-a^{4} \\\\cos{\\\\theta}^{2}+r^{3} r_s-r^{4}-r^{2} a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+2r_s^{2} r^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\left(a^{2} r r_s-a^{2} r^{2}-a^{4} \\\\cos{\\\\theta}^{2}+r^{3} r_s-r^{4}-r^{2} a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-14r_s^{4} a^{6} \\\\cos{\\\\theta}^{2} r^{6} \\\\sin{\\\\theta}^{2}+2r_s^{5} a^{6} \\\\cos{\\\\theta}^{2} r^{5} \\\\sin{\\\\theta}^{2}-2r_s^{4} a^{8} \\\\cos{\\\\theta}^{2} r^{4} \\\\sin{\\\\theta}^{2}+20r_s^{3} a^{6} \\\\cos{\\\\theta}^{2} r^{7} \\\\sin{\\\\theta}^{2}+6r_s^{3} a^{8} \\\\cos{\\\\theta}^{2} r^{5} \\\\sin{\\\\theta}^{2}+24r_s^{3} a^{8} \\\\cos{\\\\theta}^{4} r^{5} \\\\sin{\\\\theta}^{2}-4r_s^{4} a^{8} \\\\cos{\\\\theta}^{4} r^{4} \\\\sin{\\\\theta}^{2}+4r_s^{3} a^{10} \\\\cos{\\\\theta}^{4} r^{3} \\\\sin{\\\\theta}^{2}-2r_s^{5} a^{8} \\\\cos{\\\\theta}^{4} r^{3} \\\\sin{\\\\theta}^{2}+2r_s^{4} a^{10} \\\\cos{\\\\theta}^{4} r^{2} \\\\sin{\\\\theta}^{2}-2r_s^{3} a^{6} \\\\cos{\\\\theta}^{2} r^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+2r_s^{4} a^{6} \\\\cos{\\\\theta}^{2} r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}%\\n-2r_s^{3} a^{8} \\\\cos{\\\\theta}^{2} r \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-16r_s^{4} a^{4} \\\\cos{\\\\theta}^{2} r^{8} \\\\sin{\\\\theta}^{2}+6r_s^{5} a^{4} \\\\cos{\\\\theta}^{2} r^{7} \\\\sin{\\\\theta}^{2}+14r_s^{3} a^{4} \\\\cos{\\\\theta}^{2} r^{9} \\\\sin{\\\\theta}^{2}+20r_s^{3} a^{6} \\\\cos{\\\\theta}^{4} r^{7} \\\\sin{\\\\theta}^{2}-14r_s^{4} a^{6} \\\\cos{\\\\theta}^{4} r^{6} \\\\sin{\\\\theta}^{2}+2r_s^{5} a^{6} \\\\cos{\\\\theta}^{4} r^{5} \\\\sin{\\\\theta}^{2}+4r_s^{3} a^{4} \\\\cos{\\\\theta}^{2} r^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-2r_s^{4} a^{4} \\\\cos{\\\\theta}^{2} r^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-8r_s^{2} a^{6} \\\\cos{\\\\theta}^{2} r^{8} \\\\sin{\\\\theta}^{2}-4r_s^{2} a^{8} \\\\cos{\\\\theta}^{2} r^{6} \\\\sin{\\\\theta}^{2}-16r_s^{2} a^{8} \\\\cos{\\\\theta}^{4} r^{6} \\\\sin{\\\\theta}^{2}-8r_s^{2} a^{10} \\\\cos{\\\\theta}^{4} r^{4} \\\\sin{\\\\theta}^{2}+2r_s^{2} a^{8} \\\\cos{\\\\theta}^{2} r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-4r_s^{2} a^{4} \\\\cos{\\\\theta}^{2} r^{10} \\\\sin{\\\\theta}^{2}-8r_s^{2} a^{6} \\\\cos{\\\\theta}^{4} r^{8} \\\\sin{\\\\theta}^{2}-2r_s^{2} a^{4} \\\\cos{\\\\theta}^{2} r^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-8r_s^{2} a^{10} \\\\cos{\\\\theta}^{6} r^{4} \\\\sin{\\\\theta}^{2}+4r_s^{3} a^{10} \\\\cos{\\\\theta}^{6} r^{3} \\\\sin{\\\\theta}^{2}-4r_s^{2} a^{12} \\\\cos{\\\\theta}^{6} r^{2} \\\\sin{\\\\theta}^{2}%\\n+2r_s^{4} a^{10} \\\\cos{\\\\theta}^{6} r^{2} \\\\sin{\\\\theta}^{2}-2r_s^{3} a^{12} \\\\cos{\\\\theta}^{6} r \\\\sin{\\\\theta}^{2}+2r_s^{2} a^{8} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2} r^{2}-2r_s^{3} a^{8} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2} r+2r_s^{2} a^{10} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-4r_s^{2} a^{8} \\\\cos{\\\\theta}^{6} r^{6} \\\\sin{\\\\theta}^{2}+6r_s^{3} a^{8} \\\\cos{\\\\theta}^{6} r^{5} \\\\sin{\\\\theta}^{2}-2r_s^{4} a^{8} \\\\cos{\\\\theta}^{6} r^{4} \\\\sin{\\\\theta}^{2}-2r_s^{2} a^{6} \\\\cos{\\\\theta}^{4} r^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+2r_s^{3} a^{6} \\\\cos{\\\\theta}^{4} r^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-2r_s^{2} a^{8} \\\\cos{\\\\theta}^{4} r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+2r_s^{2} a^{2} \\\\cos{\\\\theta}^{2} r^{4} \\\\left(a^{2} r r_s-a^{2} r^{2}-a^{4} \\\\cos{\\\\theta}^{2}+r^{3} r_s-r^{4}-r^{2} a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-2r_s^{3} a^{2} \\\\cos{\\\\theta}^{2} r^{3} \\\\left(a^{2} r r_s-a^{2} r^{2}-a^{4} \\\\cos{\\\\theta}^{2}+r^{3} r_s-r^{4}-r^{2} a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+2r_s^{2} a^{4} \\\\cos{\\\\theta}^{2} r^{2} \\\\left(a^{2} r r_s-a^{2} r^{2}-a^{4} \\\\cos{\\\\theta}^{2}+r^{3} r_s-r^{4}-r^{2} a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-2r_s^{2} a^{4} \\\\cos{\\\\theta}^{4} \\\\left(a^{2} r r_s-a^{2} r^{2}-a^{4} \\\\cos{\\\\theta}^{2}+r^{3} r_s-r^{4}-r^{2} a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r^{2}+2r_s^{3} a^{4} \\\\cos{\\\\theta}^{4} \\\\left(a^{2} r r_s-a^{2} r^{2}-a^{4} \\\\cos{\\\\theta}^{2}+r^{3} r_s-r^{4}-r^{2} a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r-2r_s^{2} a^{6} \\\\cos{\\\\theta}^{4} \\\\left(a^{2} r r_s-a^{2} r^{2}-a^{4} \\\\cos{\\\\theta}^{2}+r^{3} r_s-r^{4}-r^{2} a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-2r_s^{4} r^{4} a^{8} \\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{2}+r_s^{3} r^{5} a^{8} \\\\cos{4\\\\theta}+r_s^{3} r^{3} a^{10} \\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{2}%\\n-2r_s^{4} r^{6} a^{6} \\\\cos{4\\\\theta}+6r_s^{3} r^{7} a^{6} \\\\cos{4\\\\theta}+8r_s^{3} r^{5} a^{8} \\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{2}-2r_s^{2} r^{6} a^{8} \\\\cos{4\\\\theta}-3r_s^{2} r^{4} a^{10} \\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{2}-6r_s^{2} r^{8} a^{6} \\\\cos{4\\\\theta}-10r_s^{2} r^{6} a^{8} \\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{2}+2r_s^{3} r^{3} a^{10} \\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{4}-r_s^{2} r^{2} a^{12} \\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{4}-4r_s^{2} r^{4} a^{10} \\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{4}-5r_s^{4} r^{6} a^{6} \\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{2}-4r_s^{4} r^{8} a^{4} \\\\cos{4\\\\theta}+6r_s^{3} r^{9} a^{4} \\\\cos{4\\\\theta}+9r_s^{3} r^{7} a^{6} \\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{2}+r_s^{5} r^{5} a^{6} \\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{2}+r_s^{5} r^{7} a^{4} \\\\cos{4\\\\theta}-4r_s^{2} r^{10} a^{4} \\\\cos{4\\\\theta}-7r_s^{2} r^{8} a^{6} \\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{2}+3r_s^{3} r^{5} a^{8} \\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{4}-3r_s^{2} r^{6} a^{8} \\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{4}%\\n-r_s^{4} r^{4} a^{8} \\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{4}+2r_s^{4} r^{4} a^{8} \\\\cos{\\\\theta}^{2}-r_s^{3} r^{5} a^{8}-r_s^{3} r^{3} a^{10} \\\\cos{\\\\theta}^{2}+2r_s^{4} r^{6} a^{6}-18r_s^{3} r^{7} a^{6}-36r_s^{3} r^{5} a^{8} \\\\cos{\\\\theta}^{2}+2r_s^{2} r^{6} a^{8}+3r_s^{2} r^{4} a^{10} \\\\cos{\\\\theta}^{2}+30r_s^{2} r^{8} a^{6}+78r_s^{2} r^{6} a^{8} \\\\cos{\\\\theta}^{2}-14r_s^{3} r^{3} a^{10} \\\\cos{\\\\theta}^{4}+r_s^{2} r^{2} a^{12} \\\\cos{\\\\theta}^{4}+60r_s^{2} r^{4} a^{10} \\\\cos{\\\\theta}^{4}+47r_s^{4} r^{6} a^{6} \\\\cos{\\\\theta}^{2}+18r_s^{4} r^{8} a^{4}-74r_s^{3} r^{9} a^{4}-175r_s^{3} r^{7} a^{6} \\\\cos{\\\\theta}^{2}-r_s^{5} r^{5} a^{6} \\\\cos{\\\\theta}^{2}-r_s^{5} r^{7} a^{4}%\\n+98r_s^{2} r^{10} a^{4}+251r_s^{2} r^{8} a^{6} \\\\cos{\\\\theta}^{2}-89r_s^{3} r^{5} a^{8} \\\\cos{\\\\theta}^{4}+167r_s^{2} r^{6} a^{8} \\\\cos{\\\\theta}^{4}+19r_s^{4} r^{4} a^{8} \\\\cos{\\\\theta}^{4}+128r_s^{2} r^{12} a^{2}+292r_s^{2} r^{10} a^{4} \\\\cos{\\\\theta}^{2}-78r_s^{3} r^{13}+58r_s^{2} r^{14}+116r_s^{2} r^{12} a^{2} \\\\cos{\\\\theta}^{2}-14r_s^{5} r^{7} a^{4} \\\\cos{\\\\theta}^{2}-2r_s^{5} r^{9} a^{2}+44r_s^{4} r^{10} a^{2}+106r_s^{4} r^{8} a^{4} \\\\cos{\\\\theta}^{2}-126r_s^{3} r^{11} a^{2}-268r_s^{3} r^{9} a^{4} \\\\cos{\\\\theta}^{2}+22r_s^{4} r^{6} a^{6} \\\\cos{\\\\theta}^{4}-72r_s^{3} r^{7} a^{6} \\\\cos{\\\\theta}^{4}-22r_s^{5} r^{9} a^{2} \\\\cos{\\\\theta}^{2}-10r_s^{5} r^{11}%\\n+46r_s^{4} r^{12}+88r_s^{4} r^{10} a^{2} \\\\cos{\\\\theta}^{2}-146r_s^{3} r^{11} a^{2} \\\\cos{\\\\theta}^{2}-4r_s^{4} r^{8} a^{4} \\\\cos{\\\\theta}^{4}+2r_s^{3} r^{9} a^{4} \\\\cos{\\\\theta}^{4}+112r_s^{2} r^{8} a^{6} \\\\cos{\\\\theta}^{4}+100r_s^{3} r^{5} a^{8} \\\\cos{\\\\theta}^{6}-4r_s^{2} r^{4} a^{10} \\\\cos{\\\\theta}^{6}-116r_s^{2} r^{6} a^{8} \\\\cos{\\\\theta}^{6}+4r_s^{2} r^{10} a^{4} \\\\cos{\\\\theta}^{4}+106r_s^{3} r^{7} a^{6} \\\\cos{\\\\theta}^{6}-100r_s^{2} r^{8} a^{6} \\\\cos{\\\\theta}^{6}-6r_s^{5} r^{5} a^{6} \\\\cos{\\\\theta}^{4}-42r_s^{4} r^{4} a^{8} \\\\cos{\\\\theta}^{6}+14r_s^{3} r^{3} a^{10} \\\\cos{\\\\theta}^{6}+2r_s^{5} r^{7} a^{4} \\\\cos{\\\\theta}^{4}-56r_s^{4} r^{6} a^{6} \\\\cos{\\\\theta}^{6}+12r_s^{2} r^{2} a^{12} \\\\cos{\\\\theta}^{6}+30r_s^{3} r^{3} a^{10} \\\\cos{\\\\theta}^{8}-18r_s^{2} r^{2} a^{12} \\\\cos{\\\\theta}^{8}%\\n-64r_s^{2} r^{4} a^{10} \\\\cos{\\\\theta}^{8}+36r_s^{3} r^{5} a^{8} \\\\cos{\\\\theta}^{8}-46r_s^{2} r^{6} a^{8} \\\\cos{\\\\theta}^{8}+6r_s^{5} r^{3} a^{8} \\\\cos{\\\\theta}^{6}-10r_s^{4} r^{2} a^{10} \\\\cos{\\\\theta}^{6}-2r_s^{4} r^{2} a^{10} \\\\cos{\\\\theta}^{8}+2r_s^{3} r a^{12} \\\\cos{\\\\theta}^{8}+14r_s^{5} r^{5} a^{6} \\\\cos{\\\\theta}^{6}-10r_s^{4} r^{4} a^{8} \\\\cos{\\\\theta}^{8}+r_s r^{7} a^{8} \\\\cos{4\\\\theta}+2r_s r^{5} a^{10} \\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{2}+2r_s r^{9} a^{6} \\\\cos{4\\\\theta}+4r_s r^{7} a^{8} \\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{2}+r_s r^{3} a^{12} \\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{4}+2r_s r^{5} a^{10} \\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{4}+r_s r^{11} a^{4} \\\\cos{4\\\\theta}+2r_s r^{9} a^{6} \\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{2}+r_s r^{7} a^{8} \\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{4}-r_s r^{7} a^{8}-2r_s r^{5} a^{10} \\\\cos{\\\\theta}^{2}%\\n-14r_s r^{9} a^{6}-48r_s r^{7} a^{8} \\\\cos{\\\\theta}^{2}-r_s r^{3} a^{12} \\\\cos{\\\\theta}^{4}-54r_s r^{5} a^{10} \\\\cos{\\\\theta}^{4}-41r_s r^{11} a^{4}-126r_s r^{9} a^{6} \\\\cos{\\\\theta}^{2}-109r_s r^{7} a^{8} \\\\cos{\\\\theta}^{4}-44r_s r^{13} a^{2}-116r_s r^{11} a^{4} \\\\cos{\\\\theta}^{2}-16r_s r^{15}-36r_s r^{13} a^{2} \\\\cos{\\\\theta}^{2}-60r_s r^{9} a^{6} \\\\cos{\\\\theta}^{4}-4r_s r^{5} a^{10} \\\\cos{\\\\theta}^{6}+52r_s r^{7} a^{8} \\\\cos{\\\\theta}^{6}-4r_s r^{11} a^{4} \\\\cos{\\\\theta}^{4}+36r_s r^{9} a^{6} \\\\cos{\\\\theta}^{6}-20r_s r^{3} a^{12} \\\\cos{\\\\theta}^{6}+20r_s r^{3} a^{12} \\\\cos{\\\\theta}^{8}+40r_s r^{5} a^{10} \\\\cos{\\\\theta}^{8}+20r_s r^{7} a^{8} \\\\cos{\\\\theta}^{8}%\\n+2r_s^{3} a^{10} \\\\cos{\\\\theta}^{4} r^{3} \\\\cos{4\\\\theta}-r_s^{2} a^{10} \\\\cos{\\\\theta}^{2} r^{4} \\\\cos{4\\\\theta}-r_s^{2} a^{12} \\\\cos{\\\\theta}^{4} r^{2} \\\\cos{4\\\\theta}+2r_s^{3} a^{8} \\\\cos{\\\\theta}^{2} r^{5} \\\\cos{4\\\\theta}-4r_s^{2} a^{8} \\\\cos{\\\\theta}^{2} r^{6} \\\\cos{4\\\\theta}-6r_s^{2} a^{10} \\\\cos{\\\\theta}^{4} r^{4} \\\\cos{4\\\\theta}+r_s a^{10} \\\\cos{\\\\theta}^{2} r^{5} \\\\cos{4\\\\theta}+2r_s a^{12} \\\\cos{\\\\theta}^{4} r^{3} \\\\cos{4\\\\theta}+2r_s a^{8} \\\\cos{\\\\theta}^{2} r^{7} \\\\cos{4\\\\theta}+4r_s a^{10} \\\\cos{\\\\theta}^{4} r^{5} \\\\cos{4\\\\theta}-2r_s^{2} a^{12} \\\\cos{\\\\theta}^{6} r^{2} \\\\cos{4\\\\theta}+r_s a^{14} \\\\cos{\\\\theta}^{6} r \\\\cos{4\\\\theta}+2r_s a^{12} \\\\cos{\\\\theta}^{6} r^{3} \\\\cos{4\\\\theta}+4r_s^{3} a^{8} \\\\cos{\\\\theta}^{4} r^{5} \\\\cos{4\\\\theta}+3r_s^{3} a^{6} \\\\cos{\\\\theta}^{2} r^{7} \\\\cos{4\\\\theta}-3r_s^{2} a^{6} \\\\cos{\\\\theta}^{2} r^{8} \\\\cos{4\\\\theta}-5r_s^{2} a^{8} \\\\cos{\\\\theta}^{4} r^{6} \\\\cos{4\\\\theta}-r_s^{4} a^{8} \\\\cos{\\\\theta}^{4} r^{4} \\\\cos{4\\\\theta}-r_s^{4} a^{6} \\\\cos{\\\\theta}^{2} r^{6} \\\\cos{4\\\\theta}+r_s a^{6} \\\\cos{\\\\theta}^{2} r^{9} \\\\cos{4\\\\theta}%\\n+2r_s a^{8} \\\\cos{\\\\theta}^{4} r^{7} \\\\cos{4\\\\theta}-2r_s^{2} a^{10} \\\\cos{\\\\theta}^{6} r^{4} \\\\cos{4\\\\theta}+r_s a^{10} \\\\cos{\\\\theta}^{6} r^{5} \\\\cos{4\\\\theta}+r_s^{3} a^{10} \\\\cos{\\\\theta}^{6} r^{3} \\\\cos{4\\\\theta}-10r_s^{3} a^{10} \\\\cos{\\\\theta}^{4} r^{3}+r_s^{2} a^{10} \\\\cos{\\\\theta}^{2} r^{4}+r_s^{2} a^{12} \\\\cos{\\\\theta}^{4} r^{2}-6r_s^{3} a^{8} \\\\cos{\\\\theta}^{2} r^{5}+24r_s^{2} a^{8} \\\\cos{\\\\theta}^{2} r^{6}+54r_s^{2} a^{10} \\\\cos{\\\\theta}^{4} r^{4}-r_s a^{10} \\\\cos{\\\\theta}^{2} r^{5}-2r_s a^{12} \\\\cos{\\\\theta}^{4} r^{3}-14r_s a^{8} \\\\cos{\\\\theta}^{2} r^{7}-48r_s a^{10} \\\\cos{\\\\theta}^{4} r^{5}+30r_s^{2} a^{12} \\\\cos{\\\\theta}^{6} r^{2}-r_s a^{14} \\\\cos{\\\\theta}^{6} r-54r_s a^{12} \\\\cos{\\\\theta}^{6} r^{3}-198r_s^{3} a^{8} \\\\cos{\\\\theta}^{4} r^{5}-89r_s^{3} a^{6} \\\\cos{\\\\theta}^{2} r^{7}+129r_s^{2} a^{6} \\\\cos{\\\\theta}^{2} r^{8}%\\n+341r_s^{2} a^{8} \\\\cos{\\\\theta}^{4} r^{6}+33r_s^{4} a^{8} \\\\cos{\\\\theta}^{4} r^{4}+21r_s^{4} a^{6} \\\\cos{\\\\theta}^{2} r^{6}-57r_s a^{6} \\\\cos{\\\\theta}^{2} r^{9}-190r_s a^{8} \\\\cos{\\\\theta}^{4} r^{7}+274r_s^{2} a^{10} \\\\cos{\\\\theta}^{6} r^{4}-205r_s a^{10} \\\\cos{\\\\theta}^{6} r^{5}-115r_s^{3} a^{10} \\\\cos{\\\\theta}^{6} r^{3}-76r_s a^{4} \\\\cos{\\\\theta}^{2} r^{11}-244r_s a^{6} \\\\cos{\\\\theta}^{4} r^{9}+114r_s^{2} a^{2} \\\\cos{\\\\theta}^{2} r^{12}-32r_s a^{2} \\\\cos{\\\\theta}^{2} r^{13}-100r_s a^{4} \\\\cos{\\\\theta}^{4} r^{11}+186r_s^{4} a^{6} \\\\cos{\\\\theta}^{4} r^{6}+94r_s^{4} a^{4} \\\\cos{\\\\theta}^{2} r^{8}-222r_s^{3} a^{4} \\\\cos{\\\\theta}^{2} r^{9}-520r_s^{3} a^{6} \\\\cos{\\\\theta}^{4} r^{7}+220r_s^{2} a^{4} \\\\cos{\\\\theta}^{2} r^{10}+600r_s^{2} a^{6} \\\\cos{\\\\theta}^{4} r^{8}-344r_s^{3} a^{8} \\\\cos{\\\\theta}^{6} r^{5}%\\n+508r_s^{2} a^{8} \\\\cos{\\\\theta}^{6} r^{6}+162r_s^{4} a^{4} \\\\cos{\\\\theta}^{4} r^{8}+82r_s^{4} a^{2} \\\\cos{\\\\theta}^{2} r^{10}-148r_s^{3} a^{2} \\\\cos{\\\\theta}^{2} r^{11}-350r_s^{3} a^{4} \\\\cos{\\\\theta}^{4} r^{9}+312r_s^{2} a^{4} \\\\cos{\\\\theta}^{4} r^{10}-234r_s^{3} a^{6} \\\\cos{\\\\theta}^{6} r^{7}+264r_s^{2} a^{6} \\\\cos{\\\\theta}^{6} r^{8}-252r_s a^{8} \\\\cos{\\\\theta}^{6} r^{7}+120r_s^{2} a^{10} \\\\cos{\\\\theta}^{8} r^{4}-68r_s a^{12} \\\\cos{\\\\theta}^{8} r^{3}-76r_s a^{10} \\\\cos{\\\\theta}^{8} r^{5}-100r_s a^{6} \\\\cos{\\\\theta}^{6} r^{9}+56r_s^{2} a^{8} \\\\cos{\\\\theta}^{8} r^{6}-28r_s a^{8} \\\\cos{\\\\theta}^{8} r^{7}+98r_s^{4} a^{8} \\\\cos{\\\\theta}^{6} r^{4}-48r_s^{3} a^{10} \\\\cos{\\\\theta}^{8} r^{3}+64r_s^{2} a^{12} \\\\cos{\\\\theta}^{8} r^{2}+78r_s^{4} a^{6} \\\\cos{\\\\theta}^{6} r^{6}-26r_s^{3} a^{8} \\\\cos{\\\\theta}^{8} r^{5}%\\n-20r_s a^{14} \\\\cos{\\\\theta}^{8} r-8r_s^{2} a^{12} \\\\cos{\\\\theta}^{10} r^{2}+4r_s a^{14} \\\\cos{\\\\theta}^{10} r+8r_s a^{12} \\\\cos{\\\\theta}^{10} r^{3}-10r_s^{2} a^{10} \\\\cos{\\\\theta}^{10} r^{4}+4r_s a^{10} \\\\cos{\\\\theta}^{10} r^{5}+6r_s^{4} a^{10} \\\\cos{\\\\theta}^{8} r^{2}-6r_s^{3} a^{12} \\\\cos{\\\\theta}^{8} r-2r_s^{3} a^{12} \\\\cos{\\\\theta}^{10} r+2r_s^{2} a^{14} \\\\cos{\\\\theta}^{10}-2r_s^{4} a^{8} \\\\cos{\\\\theta}^{8} r^{4}+6r_s^{3} a^{10} \\\\cos{\\\\theta}^{10} r^{3}+148r_s^{3} r^{8} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{4} \\\\cos{\\\\theta}^{2}-60r_s^{4} r^{7} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{4} \\\\cos{\\\\theta}^{2}+80r_s^{3} r^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{6} \\\\cos{\\\\theta}^{2}+108r_s^{3} r^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{6} \\\\cos{\\\\theta}^{4}-36r_s^{4} r^{5} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{6} \\\\cos{\\\\theta}^{4}+52r_s^{3} r^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{8} \\\\cos{\\\\theta}^{4}-48r_s^{2} r^{9} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{4}+36r_s^{3} r^{8} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{4}%\\n-12r_s^{2} r^{7} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{6}-124r_s^{2} r^{7} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{6} \\\\cos{\\\\theta}^{2}-28r_s^{2} r^{5} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{8} \\\\cos{\\\\theta}^{2}-104r_s^{2} r^{5} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{8} \\\\cos{\\\\theta}^{4}-20r_s^{2} r^{3} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{10} \\\\cos{\\\\theta}^{4}+76r_s^{3} r^{10} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{2}-32r_s^{4} r^{9} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{2}-72r_s^{2} r^{11} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{2}-156r_s^{2} r^{9} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{4} \\\\cos{\\\\theta}^{2}-140r_s^{2} r^{7} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{6} \\\\cos{\\\\theta}^{4}+20r_s r^{10} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{4}+8r_s r^{8} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{6}+64r_s r^{8} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{6} \\\\cos{\\\\theta}^{2}+24r_s r^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{8} \\\\cos{\\\\theta}^{2}+68r_s r^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{8} \\\\cos{\\\\theta}^{4}+24r_s r^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{10} \\\\cos{\\\\theta}^{4}+24r_s r^{12} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{2}+60r_s r^{10} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{4} \\\\cos{\\\\theta}^{2}+64r_s r^{8} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{6} \\\\cos{\\\\theta}^{4}-44r_s^{2} r^{5} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{8} \\\\cos{\\\\theta}^{6}%\\n+24r_s^{3} r^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{8} \\\\cos{\\\\theta}^{6}-28r_s^{2} r^{3} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{10} \\\\cos{\\\\theta}^{6}+24r_s r^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{10} \\\\cos{\\\\theta}^{6}+8r_s r^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{12} \\\\cos{\\\\theta}^{6}+24r_s r^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{8} \\\\cos{\\\\theta}^{6}+76r_s^{3} r^{10} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{2} \\\\cos{\\\\theta}^{2}-40r_s^{4} r^{9} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{2} \\\\cos{\\\\theta}^{2}+56r_s^{3} r^{8} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{4} \\\\cos{\\\\theta}^{4}-24r_s^{4} r^{7} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{4} \\\\cos{\\\\theta}^{4}+60r_s^{3} r^{12} \\\\partial_{r}\\\\left(r^{2}\\\\right)-36r_s^{4} r^{11} \\\\partial_{r}\\\\left(r^{2}\\\\right)-44r_s^{2} r^{13} \\\\partial_{r}\\\\left(r^{2}\\\\right)-64r_s^{2} r^{11} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{2} \\\\cos{\\\\theta}^{2}-56r_s^{2} r^{9} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{4} \\\\cos{\\\\theta}^{4}+12r_s r^{14} \\\\partial_{r}\\\\left(r^{2}\\\\right)+20r_s r^{12} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{2} \\\\cos{\\\\theta}^{2}+20r_s r^{10} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{4} \\\\cos{\\\\theta}^{4}-20r_s^{2} r^{7} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{6} \\\\cos{\\\\theta}^{6}+16r_s^{3} r^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{6} \\\\cos{\\\\theta}^{6}+8r_s r^{8} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{6} \\\\cos{\\\\theta}^{6}%\\n+148r_s^{3} r^{8} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{4} \\\\cos{\\\\theta}^{2}-60r_s^{4} r^{7} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{4} \\\\cos{\\\\theta}^{2}+80r_s^{3} r^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{6} \\\\cos{\\\\theta}^{2}+108r_s^{3} r^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{6} \\\\cos{\\\\theta}^{4}-36r_s^{4} r^{5} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{6} \\\\cos{\\\\theta}^{4}+52r_s^{3} r^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{8} \\\\cos{\\\\theta}^{4}-48r_s^{2} r^{9} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{4}+36r_s^{3} r^{8} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{4}-12r_s^{2} r^{7} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{6}-124r_s^{2} r^{7} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{6} \\\\cos{\\\\theta}^{2}-28r_s^{2} r^{5} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{8} \\\\cos{\\\\theta}^{2}-104r_s^{2} r^{5} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{8} \\\\cos{\\\\theta}^{4}-20r_s^{2} r^{3} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{10} \\\\cos{\\\\theta}^{4}+76r_s^{3} r^{10} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{2}-32r_s^{4} r^{9} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{2}-72r_s^{2} r^{11} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{2}-156r_s^{2} r^{9} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{4} \\\\cos{\\\\theta}^{2}-140r_s^{2} r^{7} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{6} \\\\cos{\\\\theta}^{4}+20r_s r^{10} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{4}+8r_s r^{8} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{6}%\\n+64r_s r^{8} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{6} \\\\cos{\\\\theta}^{2}+24r_s r^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{8} \\\\cos{\\\\theta}^{2}+68r_s r^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{8} \\\\cos{\\\\theta}^{4}+24r_s r^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{10} \\\\cos{\\\\theta}^{4}+24r_s r^{12} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{2}+60r_s r^{10} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{4} \\\\cos{\\\\theta}^{2}+64r_s r^{8} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{6} \\\\cos{\\\\theta}^{4}-44r_s^{2} r^{5} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{8} \\\\cos{\\\\theta}^{6}+24r_s^{3} r^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{8} \\\\cos{\\\\theta}^{6}-28r_s^{2} r^{3} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{10} \\\\cos{\\\\theta}^{6}+24r_s r^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{10} \\\\cos{\\\\theta}^{6}+8r_s r^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{12} \\\\cos{\\\\theta}^{6}+24r_s r^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{8} \\\\cos{\\\\theta}^{6}+76r_s^{3} r^{10} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{2} \\\\cos{\\\\theta}^{2}-40r_s^{4} r^{9} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{2} \\\\cos{\\\\theta}^{2}+56r_s^{3} r^{8} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{4} \\\\cos{\\\\theta}^{4}-24r_s^{4} r^{7} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{4} \\\\cos{\\\\theta}^{4}+60r_s^{3} r^{12} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-36r_s^{4} r^{11} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-44r_s^{2} r^{13} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)%\\n-64r_s^{2} r^{11} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{2} \\\\cos{\\\\theta}^{2}-56r_s^{2} r^{9} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{4} \\\\cos{\\\\theta}^{4}+12r_s r^{14} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+20r_s r^{12} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{2} \\\\cos{\\\\theta}^{2}+20r_s r^{10} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{4} \\\\cos{\\\\theta}^{4}-20r_s^{2} r^{7} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{6} \\\\cos{\\\\theta}^{6}+16r_s^{3} r^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{6} \\\\cos{\\\\theta}^{6}+8r_s r^{8} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{6} \\\\cos{\\\\theta}^{6}-24r_s^{5} a^{6} \\\\cos{\\\\theta}^{4} r^{5}-8r_s^{5} a^{8} \\\\cos{\\\\theta}^{6} r^{3}+12r_s^{4} a^{10} \\\\cos{\\\\theta}^{6} r^{2}-4r_s^{3} a^{12} \\\\cos{\\\\theta}^{6} r-16r_s^{5} a^{4} \\\\cos{\\\\theta}^{2} r^{7}-24r_s^{5} a^{4} \\\\cos{\\\\theta}^{4} r^{7}-8r_s^{5} a^{6} \\\\cos{\\\\theta}^{6} r^{5}-16r_s^{5} a^{2} \\\\cos{\\\\theta}^{2} r^{9}-36r_s^{4} r^{7} a^{4} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+4r_s^{5} r^{6} a^{4} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-8r_s^{4} r^{5} a^{6} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-36r_s^{4} r^{7} a^{4} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)%\\n+4r_s^{5} r^{6} a^{4} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-8r_s^{4} r^{5} a^{6} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+40r_s^{3} r^{8} a^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)-12r_s^{4} r^{7} a^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)+8r_s^{3} r^{6} a^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right)+40r_s^{3} r^{8} a^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-12r_s^{4} r^{7} a^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+8r_s^{3} r^{6} a^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+60r_s^{3} r^{6} a^{6} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+4r_s^{3} r^{4} a^{8} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+60r_s^{3} r^{6} a^{6} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+4r_s^{3} r^{4} a^{8} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-24r_s^{4} r^{9} a^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+4r_s^{5} r^{8} a^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-24r_s^{4} r^{9} a^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+4r_s^{5} r^{8} a^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+48r_s^{3} r^{10} a^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+48r_s^{3} r^{10} a^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+124r_s^{3} r^{8} a^{4} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+124r_s^{3} r^{8} a^{4} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)%\\n-44r_s^{2} r^{9} a^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)-12r_s^{2} r^{7} a^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right)-44r_s^{2} r^{9} a^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-12r_s^{2} r^{7} a^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-124r_s^{2} r^{7} a^{6} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-28r_s^{2} r^{5} a^{8} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-124r_s^{2} r^{7} a^{6} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-28r_s^{2} r^{5} a^{8} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-40r_s^{2} r^{11} a^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-40r_s^{2} r^{11} a^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-164r_s^{2} r^{9} a^{4} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-164r_s^{2} r^{9} a^{4} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+100r_s^{3} r^{6} a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)-16r_s^{4} r^{5} a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)+40r_s^{3} r^{4} a^{8} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)+100r_s^{3} r^{6} a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-16r_s^{4} r^{5} a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+40r_s^{3} r^{4} a^{8} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-124r_s^{2} r^{5} a^{8} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)-24r_s^{2} r^{3} a^{10} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)%\\n-124r_s^{2} r^{5} a^{8} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-24r_s^{2} r^{3} a^{10} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-176r_s^{2} r^{7} a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)-176r_s^{2} r^{7} a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-28r_s^{4} r^{9} a^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+4r_s^{5} r^{8} a^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-28r_s^{4} r^{9} a^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+4r_s^{5} r^{8} a^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+8r_s^{5} r^{10} \\\\partial_{r}\\\\left(r^{2}\\\\right)+8r_s^{5} r^{10} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+68r_s^{3} r^{10} a^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+68r_s^{3} r^{10} a^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-68r_s^{2} r^{11} a^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-68r_s^{2} r^{11} a^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+60r_s^{3} r^{8} a^{4} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)-16r_s^{4} r^{7} a^{4} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)+60r_s^{3} r^{8} a^{4} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-16r_s^{4} r^{7} a^{4} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-76r_s^{2} r^{9} a^{4} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)-76r_s^{2} r^{9} a^{4} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)%\\n+16r_s r^{10} a^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)+4r_s r^{8} a^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right)+16r_s r^{10} a^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+4r_s r^{8} a^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+72r_s r^{8} a^{6} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+24r_s r^{6} a^{8} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+72r_s r^{8} a^{6} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+24r_s r^{6} a^{8} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+12r_s r^{12} a^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+12r_s r^{12} a^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+72r_s r^{10} a^{4} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+72r_s r^{10} a^{4} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+96r_s r^{6} a^{8} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)+32r_s r^{4} a^{10} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)+96r_s r^{6} a^{8} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+32r_s r^{4} a^{10} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+96r_s r^{8} a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)+96r_s r^{8} a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+24r_s r^{12} a^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+24r_s r^{12} a^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)%\\n+32r_s r^{10} a^{4} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)+32r_s r^{10} a^{4} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-52r_s^{2} r^{5} a^{8} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right)+24r_s^{3} r^{4} a^{8} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right)-32r_s^{2} r^{3} a^{10} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right)-52r_s^{2} r^{5} a^{8} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+24r_s^{3} r^{4} a^{8} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-32r_s^{2} r^{3} a^{10} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+36r_s r^{4} a^{10} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right)+12r_s r^{2} a^{12} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right)+36r_s r^{4} a^{10} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+12r_s r^{2} a^{12} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+36r_s r^{6} a^{8} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right)+36r_s r^{6} a^{8} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-24r_s^{2} r^{7} a^{6} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right)+16r_s^{3} r^{6} a^{6} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right)-24r_s^{2} r^{7} a^{6} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+16r_s^{3} r^{6} a^{6} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+12r_s r^{8} a^{6} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right)+12r_s r^{8} a^{6} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)%\\n+40r_s^{4} a^{6} \\\\cos{\\\\theta}^{4} r^{5} \\\\partial_{r}\\\\left(r^{2}\\\\right)-4r_s^{5} a^{6} \\\\cos{\\\\theta}^{4} r^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)+12r_s^{4} a^{8} \\\\cos{\\\\theta}^{4} r^{3} \\\\partial_{r}\\\\left(r^{2}\\\\right)+40r_s^{4} a^{6} \\\\cos{\\\\theta}^{4} r^{5} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-4r_s^{5} a^{6} \\\\cos{\\\\theta}^{4} r^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+12r_s^{4} a^{8} \\\\cos{\\\\theta}^{4} r^{3} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-48r_s^{3} a^{6} \\\\cos{\\\\theta}^{2} r^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right)+12r_s^{4} a^{6} \\\\cos{\\\\theta}^{2} r^{5} \\\\partial_{r}\\\\left(r^{2}\\\\right)-8r_s^{3} a^{8} \\\\cos{\\\\theta}^{2} r^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)-48r_s^{3} a^{6} \\\\cos{\\\\theta}^{2} r^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+12r_s^{4} a^{6} \\\\cos{\\\\theta}^{2} r^{5} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-8r_s^{3} a^{8} \\\\cos{\\\\theta}^{2} r^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-72r_s^{3} a^{8} \\\\cos{\\\\theta}^{4} r^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)-8r_s^{3} a^{10} \\\\cos{\\\\theta}^{4} r^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-72r_s^{3} a^{8} \\\\cos{\\\\theta}^{4} r^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-8r_s^{3} a^{10} \\\\cos{\\\\theta}^{4} r^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+32r_s^{4} a^{4} \\\\cos{\\\\theta}^{2} r^{7} \\\\partial_{r}\\\\left(r^{2}\\\\right)-4r_s^{5} a^{4} \\\\cos{\\\\theta}^{2} r^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right)+32r_s^{4} a^{4} \\\\cos{\\\\theta}^{2} r^{7} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-4r_s^{5} a^{4} \\\\cos{\\\\theta}^{2} r^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)%\\n-80r_s^{3} a^{4} \\\\cos{\\\\theta}^{2} r^{8} \\\\partial_{r}\\\\left(r^{2}\\\\right)-80r_s^{3} a^{4} \\\\cos{\\\\theta}^{2} r^{8} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-140r_s^{3} a^{6} \\\\cos{\\\\theta}^{4} r^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right)-140r_s^{3} a^{6} \\\\cos{\\\\theta}^{4} r^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+68r_s^{2} a^{6} \\\\cos{\\\\theta}^{2} r^{7} \\\\partial_{r}\\\\left(r^{2}\\\\right)+16r_s^{2} a^{8} \\\\cos{\\\\theta}^{2} r^{5} \\\\partial_{r}\\\\left(r^{2}\\\\right)+68r_s^{2} a^{6} \\\\cos{\\\\theta}^{2} r^{7} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+16r_s^{2} a^{8} \\\\cos{\\\\theta}^{2} r^{5} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+148r_s^{2} a^{8} \\\\cos{\\\\theta}^{4} r^{5} \\\\partial_{r}\\\\left(r^{2}\\\\right)+32r_s^{2} a^{10} \\\\cos{\\\\theta}^{4} r^{3} \\\\partial_{r}\\\\left(r^{2}\\\\right)+148r_s^{2} a^{8} \\\\cos{\\\\theta}^{4} r^{5} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+32r_s^{2} a^{10} \\\\cos{\\\\theta}^{4} r^{3} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+88r_s^{2} a^{4} \\\\cos{\\\\theta}^{2} r^{9} \\\\partial_{r}\\\\left(r^{2}\\\\right)+88r_s^{2} a^{4} \\\\cos{\\\\theta}^{2} r^{9} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+192r_s^{2} a^{6} \\\\cos{\\\\theta}^{4} r^{7} \\\\partial_{r}\\\\left(r^{2}\\\\right)+192r_s^{2} a^{6} \\\\cos{\\\\theta}^{4} r^{7} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-64r_s^{3} a^{8} \\\\cos{\\\\theta}^{6} r^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)+8r_s^{4} a^{8} \\\\cos{\\\\theta}^{6} r^{3} \\\\partial_{r}\\\\left(r^{2}\\\\right)-24r_s^{3} a^{10} \\\\cos{\\\\theta}^{6} r^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-64r_s^{3} a^{8} \\\\cos{\\\\theta}^{6} r^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)%\\n+8r_s^{4} a^{8} \\\\cos{\\\\theta}^{6} r^{3} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-24r_s^{3} a^{10} \\\\cos{\\\\theta}^{6} r^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+88r_s^{2} a^{10} \\\\cos{\\\\theta}^{6} r^{3} \\\\partial_{r}\\\\left(r^{2}\\\\right)+16r_s^{2} a^{12} \\\\cos{\\\\theta}^{6} r \\\\partial_{r}\\\\left(r^{2}\\\\right)+88r_s^{2} a^{10} \\\\cos{\\\\theta}^{6} r^{3} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+16r_s^{2} a^{12} \\\\cos{\\\\theta}^{6} r \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+120r_s^{2} a^{8} \\\\cos{\\\\theta}^{6} r^{5} \\\\partial_{r}\\\\left(r^{2}\\\\right)+120r_s^{2} a^{8} \\\\cos{\\\\theta}^{6} r^{5} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+28r_s^{4} a^{4} \\\\cos{\\\\theta}^{4} r^{7} \\\\partial_{r}\\\\left(r^{2}\\\\right)-4r_s^{5} a^{4} \\\\cos{\\\\theta}^{4} r^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right)+28r_s^{4} a^{4} \\\\cos{\\\\theta}^{4} r^{7} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-4r_s^{5} a^{4} \\\\cos{\\\\theta}^{4} r^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+20r_s^{4} a^{2} \\\\cos{\\\\theta}^{2} r^{9} \\\\partial_{r}\\\\left(r^{2}\\\\right)-4r_s^{5} a^{2} \\\\cos{\\\\theta}^{2} r^{8} \\\\partial_{r}\\\\left(r^{2}\\\\right)+20r_s^{4} a^{2} \\\\cos{\\\\theta}^{2} r^{9} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-4r_s^{5} a^{2} \\\\cos{\\\\theta}^{2} r^{8} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-40r_s^{3} a^{2} \\\\cos{\\\\theta}^{2} r^{10} \\\\partial_{r}\\\\left(r^{2}\\\\right)-40r_s^{3} a^{2} \\\\cos{\\\\theta}^{2} r^{10} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-72r_s^{3} a^{4} \\\\cos{\\\\theta}^{4} r^{8} \\\\partial_{r}\\\\left(r^{2}\\\\right)-72r_s^{3} a^{4} \\\\cos{\\\\theta}^{4} r^{8} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)%\\n+36r_s^{2} a^{2} \\\\cos{\\\\theta}^{2} r^{11} \\\\partial_{r}\\\\left(r^{2}\\\\right)+36r_s^{2} a^{2} \\\\cos{\\\\theta}^{2} r^{11} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+76r_s^{2} a^{4} \\\\cos{\\\\theta}^{4} r^{9} \\\\partial_{r}\\\\left(r^{2}\\\\right)+76r_s^{2} a^{4} \\\\cos{\\\\theta}^{4} r^{9} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-32r_s^{3} a^{6} \\\\cos{\\\\theta}^{6} r^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right)+8r_s^{4} a^{6} \\\\cos{\\\\theta}^{6} r^{5} \\\\partial_{r}\\\\left(r^{2}\\\\right)-32r_s^{3} a^{6} \\\\cos{\\\\theta}^{6} r^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+8r_s^{4} a^{6} \\\\cos{\\\\theta}^{6} r^{5} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+44r_s^{2} a^{6} \\\\cos{\\\\theta}^{6} r^{7} \\\\partial_{r}\\\\left(r^{2}\\\\right)+44r_s^{2} a^{6} \\\\cos{\\\\theta}^{6} r^{7} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-36r_s a^{6} \\\\cos{\\\\theta}^{2} r^{8} \\\\partial_{r}\\\\left(r^{2}\\\\right)-12r_s a^{8} \\\\cos{\\\\theta}^{2} r^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right)-36r_s a^{6} \\\\cos{\\\\theta}^{2} r^{8} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-12r_s a^{8} \\\\cos{\\\\theta}^{2} r^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-92r_s a^{8} \\\\cos{\\\\theta}^{4} r^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right)-32r_s a^{10} \\\\cos{\\\\theta}^{4} r^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)-92r_s a^{8} \\\\cos{\\\\theta}^{4} r^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-32r_s a^{10} \\\\cos{\\\\theta}^{4} r^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-36r_s a^{4} \\\\cos{\\\\theta}^{2} r^{10} \\\\partial_{r}\\\\left(r^{2}\\\\right)-36r_s a^{4} \\\\cos{\\\\theta}^{2} r^{10} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)%\\n-88r_s a^{6} \\\\cos{\\\\theta}^{4} r^{8} \\\\partial_{r}\\\\left(r^{2}\\\\right)-88r_s a^{6} \\\\cos{\\\\theta}^{4} r^{8} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-72r_s a^{10} \\\\cos{\\\\theta}^{6} r^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)-24r_s a^{12} \\\\cos{\\\\theta}^{6} r^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-72r_s a^{10} \\\\cos{\\\\theta}^{6} r^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-24r_s a^{12} \\\\cos{\\\\theta}^{6} r^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-68r_s a^{8} \\\\cos{\\\\theta}^{6} r^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right)-68r_s a^{8} \\\\cos{\\\\theta}^{6} r^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-12r_s a^{2} \\\\cos{\\\\theta}^{2} r^{12} \\\\partial_{r}\\\\left(r^{2}\\\\right)-12r_s a^{2} \\\\cos{\\\\theta}^{2} r^{12} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-28r_s a^{4} \\\\cos{\\\\theta}^{4} r^{10} \\\\partial_{r}\\\\left(r^{2}\\\\right)-28r_s a^{4} \\\\cos{\\\\theta}^{4} r^{10} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-20r_s a^{6} \\\\cos{\\\\theta}^{6} r^{8} \\\\partial_{r}\\\\left(r^{2}\\\\right)-20r_s a^{6} \\\\cos{\\\\theta}^{6} r^{8} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+16r_s^{2} a^{10} \\\\cos{\\\\theta}^{8} r^{3} \\\\partial_{r}\\\\left(r^{2}\\\\right)-4r_s^{3} a^{10} \\\\cos{\\\\theta}^{8} r^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+4r_s^{2} a^{12} \\\\cos{\\\\theta}^{8} r \\\\partial_{r}\\\\left(r^{2}\\\\right)+16r_s^{2} a^{10} \\\\cos{\\\\theta}^{8} r^{3} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-4r_s^{3} a^{10} \\\\cos{\\\\theta}^{8} r^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+4r_s^{2} a^{12} \\\\cos{\\\\theta}^{8} r \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)%\\n-4r_s a^{14} \\\\cos{\\\\theta}^{8} \\\\partial_{r}\\\\left(r^{2}\\\\right)-4r_s a^{14} \\\\cos{\\\\theta}^{8} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-16r_s a^{10} \\\\cos{\\\\theta}^{8} r^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)-12r_s a^{12} \\\\cos{\\\\theta}^{8} r^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-16r_s a^{10} \\\\cos{\\\\theta}^{8} r^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-12r_s a^{12} \\\\cos{\\\\theta}^{8} r^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+4r_s^{2} a^{8} \\\\cos{\\\\theta}^{8} r^{5} \\\\partial_{r}\\\\left(r^{2}\\\\right)+4r_s^{2} a^{8} \\\\cos{\\\\theta}^{8} r^{5} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-4r_s a^{8} \\\\cos{\\\\theta}^{8} r^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right)-4r_s a^{8} \\\\cos{\\\\theta}^{8} r^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+4r_s^{3} r^{6} a^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2}-4r_s^{4} r^{5} a^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2}+4r_s^{3} r^{4} a^{8} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2}+4r_s^{3} r^{6} a^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2}-4r_s^{4} r^{5} a^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2}+4r_s^{3} r^{4} a^{8} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2}+4r_s^{2} r^{7} a^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2}+4r_s^{2} r^{7} a^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2}-4r_s r^{8} a^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2}-4r_s r^{6} a^{8} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2}%\\n-4r_s r^{8} a^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2}-4r_s r^{6} a^{8} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2}+12r_s a^{10} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right) r^{4}-12r_s^{2} a^{10} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right) r^{3}+4r_s a^{12} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right) r^{2}+12r_s a^{10} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r^{4}-12r_s^{2} a^{10} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r^{3}+4r_s a^{12} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r^{2}+8r_s^{5} r^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{4} \\\\cos{\\\\theta}^{2}-16r_s^{4} r^{5} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{6} \\\\cos{\\\\theta}^{2}+4r_s^{5} r^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{6} \\\\cos{\\\\theta}^{4}-8r_s^{4} r^{3} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{8} \\\\cos{\\\\theta}^{4}-8r_s^{4} r^{7} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{4}+4r_s^{3} r^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{6}+8r_s^{3} r^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{8} \\\\cos{\\\\theta}^{2}+4r_s^{3} r^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{10} \\\\cos{\\\\theta}^{4}+4r_s^{5} r^{8} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{2}-4r_s^{4} r^{3} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{8} \\\\cos{\\\\theta}^{6}+8r_s^{3} r^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{10} \\\\cos{\\\\theta}^{6}-4r_s^{2} r \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{12} \\\\cos{\\\\theta}^{6}%\\n+8r_s^{5} r^{8} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{2} \\\\cos{\\\\theta}^{2}+4r_s^{5} r^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{4} \\\\cos{\\\\theta}^{4}-4r_s^{4} r^{5} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{6} \\\\cos{\\\\theta}^{6}+8r_s^{5} r^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{4} \\\\cos{\\\\theta}^{2}-16r_s^{4} r^{5} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{6} \\\\cos{\\\\theta}^{2}+4r_s^{5} r^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{6} \\\\cos{\\\\theta}^{4}-8r_s^{4} r^{3} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{8} \\\\cos{\\\\theta}^{4}-8r_s^{4} r^{7} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{4}+4r_s^{3} r^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{6}+8r_s^{3} r^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{8} \\\\cos{\\\\theta}^{2}+4r_s^{3} r^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{10} \\\\cos{\\\\theta}^{4}+4r_s^{5} r^{8} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{2}-4r_s^{4} r^{3} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{8} \\\\cos{\\\\theta}^{6}+8r_s^{3} r^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{10} \\\\cos{\\\\theta}^{6}-4r_s^{2} r \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{12} \\\\cos{\\\\theta}^{6}+8r_s^{5} r^{8} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{2} \\\\cos{\\\\theta}^{2}+4r_s^{5} r^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{4} \\\\cos{\\\\theta}^{4}-4r_s^{4} r^{5} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{6} \\\\cos{\\\\theta}^{6}-12r_s^{3} r^{6} a^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4}+4r_s^{4} r^{5} a^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4}%\\n-8r_s^{3} r^{4} a^{8} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4}+16r_s^{2} r^{5} a^{8} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4}+4r_s^{2} r^{3} a^{10} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4}+12r_s^{2} r^{7} a^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4}-12r_s^{3} r^{6} a^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{4}+4r_s^{4} r^{5} a^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{4}-8r_s^{3} r^{4} a^{8} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{4}+16r_s^{2} r^{5} a^{8} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{4}+4r_s^{2} r^{3} a^{10} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{4}+12r_s^{2} r^{7} a^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{4}+4r_s^{3} r a^{12} \\\\cos{\\\\theta}^{6}-4r_s^{4} r^{3} a^{8} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right)+8r_s^{3} r^{2} a^{10} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right)-4r_s^{2} r a^{12} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right)-4r_s^{4} r^{3} a^{8} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+8r_s^{3} r^{2} a^{10} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-4r_s^{2} r a^{12} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-4r_s^{4} r^{5} a^{6} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right)-4r_s^{4} r^{5} a^{6} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-8r_s r^{6} a^{8} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4}%\\n-4r_s r^{4} a^{10} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4}-4r_s r^{8} a^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4}-8r_s r^{6} a^{8} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{4}-4r_s r^{4} a^{10} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{4}-4r_s r^{8} a^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{4}-16r_s^{2} a^{8} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right) r^{5}+8r_s^{3} a^{8} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right) r^{4}-8r_s^{2} a^{10} \\\\cos{\\\\theta}^{8} \\\\partial_{r}\\\\left(r^{2}\\\\right) r^{3}+4r_s^{3} a^{10} \\\\cos{\\\\theta}^{8} \\\\partial_{r}\\\\left(r^{2}\\\\right) r^{2}+8r_s a^{8} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right) r^{6}-8r_s^{2} a^{8} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right) r^{5}+4r_s a^{10} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right) r^{4}-8r_s^{2} a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right) r^{7}+4r_s^{3} a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right) r^{6}+4r_s a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right) r^{8}+8r_s a^{8} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right) r^{6}+4r_s a^{10} \\\\cos{\\\\theta}^{8} \\\\partial_{r}\\\\left(r^{2}\\\\right) r^{4}-16r_s^{2} a^{8} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r^{5}+8r_s^{3} a^{8} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r^{4}-8r_s^{2} a^{10} \\\\cos{\\\\theta}^{8} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r^{3}%\\n+4r_s^{3} a^{10} \\\\cos{\\\\theta}^{8} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r^{2}+8r_s a^{8} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r^{6}-8r_s^{2} a^{8} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r^{5}+4r_s a^{10} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r^{4}-8r_s^{2} a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r^{7}+4r_s^{3} a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r^{6}+4r_s a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r^{8}+8r_s a^{8} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r^{6}+4r_s a^{10} \\\\cos{\\\\theta}^{8} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r^{4}+8\\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} r^{2}-a^{4} \\\\cos{\\\\theta}^{2}+r^{3} r_s-r^{4}-r^{2} a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} r^{2} \\\\cos{2\\\\theta}+8\\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} r^{2}-a^{4} \\\\cos{\\\\theta}^{2}+r^{3} r_s-r^{4}-r^{2} a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\cos{2\\\\theta}-4\\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} r^{2}-a^{4} \\\\cos{\\\\theta}^{2}+r^{3} r_s-r^{4}-r^{2} a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)-4\\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} r^{2}-a^{4} \\\\cos{\\\\theta}^{2}+r^{3} r_s-r^{4}-r^{2} a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-16\\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} r^{2}-a^{4} \\\\cos{\\\\theta}^{2}+r^{3} r_s-r^{4}-r^{2} a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r^{4}-16\\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} r^{2}-a^{4} \\\\cos{\\\\theta}^{2}+r^{3} r_s-r^{4}-r^{2} a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r^{2} a^{2} \\\\cos{\\\\theta}^{2}+4\\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} r^{2}-a^{4} \\\\cos{\\\\theta}^{2}+r^{3} r_s-r^{4}-r^{2} a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r^{3} r_s+4\\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} r^{2}-a^{4} \\\\cos{\\\\theta}^{2}+r^{3} r_s-r^{4}-r^{2} a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r r_s a^{2} \\\\cos{\\\\theta}^{2}+8\\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} r^{2}-a^{4} \\\\cos{\\\\theta}^{2}+r^{3} r_s-r^{4}-r^{2} a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r^{3} \\\\partial_{r}\\\\left(r^{2}\\\\right)+8\\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} r^{2}-a^{4} \\\\cos{\\\\theta}^{2}+r^{3} r_s-r^{4}-r^{2} a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r^{3} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-8\\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} r^{2}-a^{4} \\\\cos{\\\\theta}^{2}+r^{3} r_s-r^{4}-r^{2} a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r^{2} r_s \\\\partial_{r}\\\\left(r^{2}\\\\right)%\\n-8\\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} r^{2}-a^{4} \\\\cos{\\\\theta}^{2}+r^{3} r_s-r^{4}-r^{2} a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r^{2} r_s \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+8\\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} r^{2}-a^{4} \\\\cos{\\\\theta}^{2}+r^{3} r_s-r^{4}-r^{2} a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r a^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+8\\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} r^{2}-a^{4} \\\\cos{\\\\theta}^{2}+r^{3} r_s-r^{4}-r^{2} a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r a^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+8\\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} r^{2}-a^{4} \\\\cos{\\\\theta}^{2}+r^{3} r_s-r^{4}-r^{2} a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s r^{3}+8\\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} r^{2}-a^{4} \\\\cos{\\\\theta}^{2}+r^{3} r_s-r^{4}-r^{2} a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s r a^{2} \\\\cos{\\\\theta}^{2}-8\\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} r^{2}-a^{4} \\\\cos{\\\\theta}^{2}+r^{3} r_s-r^{4}-r^{2} a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} r^{2}-8\\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} r^{2}-a^{4} \\\\cos{\\\\theta}^{2}+r^{3} r_s-r^{4}-r^{2} a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{4} \\\\cos{\\\\theta}^{2}-8r^{4} r_s^{4} a^{8} \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}^{4}+8r^{5} r_s^{3} a^{8} \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}^{2}+8r^{3} r_s^{3} a^{10} \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}^{4}-8r^{6} r_s^{4} a^{6} \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}^{2}+24r^{7} r_s^{3} a^{6} \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}^{2}+24r^{5} r_s^{3} a^{8} \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}^{4}+4r^{5} r_s^{5} a^{6} \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{4}-18r^{6} r_s^{4} a^{6} \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{2}-4r^{4} r_s^{4} a^{8} \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{4}+6r^{7} r_s^{5} a^{4} \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{2}-34r^{8} r_s^{4} a^{4} \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{2}-20r^{6} r_s^{4} a^{6} \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{4}+64r^{7} r_s^{3} a^{6} \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{2}%\\n+16r^{5} r_s^{3} a^{8} \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{4}+74r^{9} r_s^{3} a^{4} \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{2}+32r^{7} r_s^{3} a^{6} \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{4}-64r^{4} r_s^{4} a^{8} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2}+254r^{5} r_s^{3} a^{8} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2}+82r^{3} r_s^{3} a^{10} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2}-194r^{6} r_s^{4} a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2}+300r^{7} r_s^{3} a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2}+156r^{5} r_s^{3} a^{8} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2}-36r^{6} r_s^{4} a^{6} \\\\cos{\\\\theta}^{4}+24r^{7} r_s^{3} a^{6} \\\\cos{\\\\theta}^{2}+24r^{5} r_s^{3} a^{8} \\\\cos{\\\\theta}^{4}-12r^{8} r_s^{4} a^{4} \\\\cos{\\\\theta}^{2}+44r^{9} r_s^{3} a^{4} \\\\cos{\\\\theta}^{2}+108r^{7} r_s^{3} a^{6} \\\\cos{\\\\theta}^{4}-20r^{4} r_s^{4} a^{8} \\\\cos{\\\\theta}^{6}+8r^{3} r_s^{3} a^{10} \\\\cos{\\\\theta}^{6}+84r^{5} r_s^{3} a^{8} \\\\cos{\\\\theta}^{6}-8r^{3} r_s^{3} a^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{4}+8r^{4} r_s^{2} a^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{2}%\\n+8r^{2} r_s^{2} a^{8} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{4}-8r^{5} r_s^{3} a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{2}+32r^{6} r_s^{2} a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{2}+32r^{4} r_s^{2} a^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{4}-24r^{8} r_s^{4} a^{4} \\\\cos{\\\\theta}^{4}+48r^{10} r_s^{4} a^{2} \\\\cos{\\\\theta}^{2}-64r^{11} r_s^{3} a^{2} \\\\cos{\\\\theta}^{2}-8r^{9} r_s^{3} a^{4} \\\\cos{\\\\theta}^{4}-48r^{6} r_s^{4} a^{6} \\\\cos{\\\\theta}^{6}+32r^{7} r_s^{3} a^{6} \\\\cos{\\\\theta}^{6}-8r^{5} r_s^{3} a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{4}-8r^{7} r_s^{3} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{2}+24r^{8} r_s^{2} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{2}+24r^{6} r_s^{2} a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{4}-2r^{8} r_s^{4} a^{4} \\\\sin{\\\\theta}^{2}-4r^{9} r_s^{5} a^{2} \\\\sin{\\\\theta}^{2}-4r^{10} r_s^{4} a^{2} \\\\sin{\\\\theta}^{2}+36r^{5} r_s^{5} a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2}-60r^{6} r_s^{4} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}-58r^{4} r_s^{4} a^{8} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2}%\\n+36r^{7} r_s^{5} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}-130r^{8} r_s^{4} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}-12r^{9} r_s^{5} a^{2} \\\\cos{\\\\theta}^{2}+4r^{10} r_s^{4} a^{2}-12r^{11} r_s^{5}+36r^{12} r_s^{4}+12r^{7} r_s^{5} a^{4} \\\\cos{\\\\theta}^{4}+28r^{6} r_s^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} \\\\cos{\\\\theta}^{2}-20r^{7} r_s^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2}-28r^{5} r_s^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{4} \\\\cos{\\\\theta}^{2}+20r^{8} r_s^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-68r^{9} r_s^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-108r^{7} r_s^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} \\\\cos{\\\\theta}^{2}+8r^{7} r_s^{3} a^{6} \\\\sin{\\\\theta}^{2}+12r^{5} r_s^{3} a^{8} \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{2}+40r^{9} r_s^{3} a^{4} \\\\sin{\\\\theta}^{2}+20r^{5} r_s^{3} a^{8} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+24r^{3} r_s^{3} a^{10} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2}+166r^{7} r_s^{3} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+8r^{9} r_s^{3} a^{4}%\\n+162r^{9} r_s^{3} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+36r^{5} r_s^{3} a^{4} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-44r^{6} r_s^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-48r^{4} r_s^{2} a^{6} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+32r^{7} r_s^{3} a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-48r^{8} r_s^{2} a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-44r^{6} r_s^{2} a^{4} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+2r^{3} r_s^{5} a^{8} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2}-2r^{2} r_s^{4} a^{10} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2}+12r^{5} r_s^{5} a^{6} \\\\cos{\\\\theta}^{6}-12r^{4} r_s^{4} a^{4} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+20r^{5} r_s^{3} a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+20r^{3} r_s^{3} a^{6} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-12r^{6} r_s^{4} a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+20r^{7} r_s^{4} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-4r^{6} r_s^{5} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+4r^{5} r_s^{4} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+20r^{7} r_s^{4} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-4r^{6} r_s^{5} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+4r^{5} r_s^{4} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)%\\n+4r^{5} r_s^{4} a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-4r^{3} r_s^{4} a^{8} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+4r^{5} r_s^{4} a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-4r^{3} r_s^{4} a^{8} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+8r^{9} r_s^{4} a^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-8r^{8} r_s^{5} a^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+24r^{7} r_s^{4} a^{4} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+8r^{9} r_s^{4} a^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-8r^{8} r_s^{5} a^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+24r^{7} r_s^{4} a^{4} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-40r^{7} r_s^{4} a^{4} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)+8r^{5} r_s^{4} a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)-40r^{7} r_s^{4} a^{4} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+8r^{5} r_s^{4} a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-40r^{6} r_s^{3} a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+8r^{5} r_s^{4} a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-16r^{4} r_s^{3} a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-40r^{6} r_s^{3} a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+8r^{5} r_s^{4} a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-16r^{4} r_s^{3} a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)%\\n-64r^{8} r_s^{3} a^{4} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+20r^{7} r_s^{4} a^{4} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-12r^{6} r_s^{3} a^{6} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-64r^{8} r_s^{3} a^{4} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+20r^{7} r_s^{4} a^{4} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-12r^{6} r_s^{3} a^{6} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-28r^{6} r_s^{3} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-28r^{6} r_s^{3} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-8r^{10} r_s^{3} a^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+8r^{9} r_s^{4} a^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-8r^{8} r_s^{3} a^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)-8r^{10} r_s^{3} a^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+8r^{9} r_s^{4} a^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-8r^{8} r_s^{3} a^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-24r^{8} r_s^{3} a^{4} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-16r^{6} r_s^{3} a^{6} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-24r^{8} r_s^{3} a^{4} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-16r^{6} r_s^{3} a^{6} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+24r^{7} r_s^{2} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-8r^{6} r_s^{3} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)%\\n+8r^{5} r_s^{2} a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+24r^{7} r_s^{2} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-8r^{6} r_s^{3} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+8r^{5} r_s^{2} a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+4r^{2} r_s^{3} a^{10} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+4r^{2} r_s^{3} a^{10} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+48r^{6} r_s^{3} a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)-8r^{4} r_s^{3} a^{8} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)+48r^{6} r_s^{3} a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-8r^{4} r_s^{3} a^{8} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+72r^{5} r_s^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+8r^{3} r_s^{2} a^{6} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+72r^{5} r_s^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+8r^{3} r_s^{2} a^{6} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+36r^{9} r_s^{4} a^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-8r^{8} r_s^{5} a^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+36r^{9} r_s^{4} a^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-8r^{8} r_s^{5} a^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-8r^{11} r_s^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)-8r^{11} r_s^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)%\\n-40r^{8} r_s^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+8r^{7} r_s^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-8r^{6} r_s^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{2}-40r^{8} r_s^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+8r^{7} r_s^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-8r^{6} r_s^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{2}-60r^{10} r_s^{3} a^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-60r^{10} r_s^{3} a^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-24r^{8} r_s^{3} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-24r^{8} r_s^{3} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+40r^{12} r_s^{3} \\\\partial_{r}\\\\left(r^{2}\\\\right)+8r^{10} r_s^{3} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{2}+40r^{12} r_s^{3} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+8r^{10} r_s^{3} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{2}+64r^{10} r_s^{3} a^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+64r^{10} r_s^{3} a^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+72r^{9} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+32r^{7} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{2}+72r^{9} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+32r^{7} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{2}%\\n-4r^{6} r_s^{3} a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-4r^{6} r_s^{3} a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+200r^{8} r_s^{3} a^{4} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)+200r^{8} r_s^{3} a^{4} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+64r^{7} r_s^{2} a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+64r^{7} r_s^{2} a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+104r^{6} r_s^{3} a^{6} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right)-16r^{5} r_s^{4} a^{6} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right)+24r^{4} r_s^{3} a^{8} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right)+104r^{6} r_s^{3} a^{6} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-16r^{5} r_s^{4} a^{6} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+24r^{4} r_s^{3} a^{8} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-40r^{6} r_s^{3} a^{6} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2}+12r^{5} r_s^{4} a^{6} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2}-8r^{4} r_s^{3} a^{8} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2}-40r^{6} r_s^{3} a^{6} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2}+12r^{5} r_s^{4} a^{6} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2}-8r^{4} r_s^{3} a^{8} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2}+16r^{8} r_s^{3} a^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2}+16r^{8} r_s^{3} a^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2}%\\n-24r^{11} r_s^{2} a^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-40r^{9} r_s^{2} a^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2}-16r^{7} r_s^{2} a^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2}-24r^{11} r_s^{2} a^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-40r^{9} r_s^{2} a^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2}-16r^{7} r_s^{2} a^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2}-128r^{9} r_s^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+8r^{7} r_s^{2} a^{6} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-312r^{7} r_s^{2} a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)-16r^{5} r_s^{2} a^{8} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)-128r^{9} r_s^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+8r^{7} r_s^{2} a^{6} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-312r^{7} r_s^{2} a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-16r^{5} r_s^{2} a^{8} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-176r^{5} r_s^{2} a^{8} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right)-8r^{3} r_s^{2} a^{10} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right)-176r^{5} r_s^{2} a^{8} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-8r^{3} r_s^{2} a^{10} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-8r^{4} r_s^{2} a^{6} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-8r^{2} r_s^{2} a^{8} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}%\\n+20r^{7} r_s^{4} a^{4} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2}-4r^{6} r_s^{5} a^{4} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2}+20r^{7} r_s^{4} a^{4} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2}-4r^{6} r_s^{5} a^{4} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2}-40r^{9} r_s^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{2} \\\\cos{\\\\theta}^{2}+8r^{8} r_s^{5} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{2} \\\\cos{\\\\theta}^{2}-8r^{7} r_s^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{4} \\\\cos{\\\\theta}^{2}-40r^{9} r_s^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{2} \\\\cos{\\\\theta}^{2}+8r^{8} r_s^{5} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{2} \\\\cos{\\\\theta}^{2}-8r^{7} r_s^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{4} \\\\cos{\\\\theta}^{2}+88r^{10} r_s^{3} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{2} \\\\cos{\\\\theta}^{2}+32r^{8} r_s^{3} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{4} \\\\cos{\\\\theta}^{2}+88r^{10} r_s^{3} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{2} \\\\cos{\\\\theta}^{2}+32r^{8} r_s^{3} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{4} \\\\cos{\\\\theta}^{2}+38r^{11} r_s^{3} a^{2} \\\\sin{\\\\theta}^{2}-36r^{8} r_s^{3} a^{4} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2}-36r^{8} r_s^{3} a^{4} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2}-36r^{13} r_s^{3}-72r^{13} r_s^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-32r^{11} r_s^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{2}%\\n-104r^{11} r_s^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{2} \\\\cos{\\\\theta}^{2}-56r^{9} r_s^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{4} \\\\cos{\\\\theta}^{2}-72r^{13} r_s^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-32r^{11} r_s^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{2}-104r^{11} r_s^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{2} \\\\cos{\\\\theta}^{2}-56r^{9} r_s^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{4} \\\\cos{\\\\theta}^{2}-144r^{11} r_s^{2} a^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-312r^{9} r_s^{2} a^{4} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)-144r^{11} r_s^{2} a^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-312r^{9} r_s^{2} a^{4} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+60r^{10} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+48r^{8} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2}+124r^{8} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} \\\\cos{\\\\theta}^{2}+80r^{6} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{4} \\\\cos{\\\\theta}^{2}-168r^{7} r_s^{2} a^{6} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right)-168r^{7} r_s^{2} a^{6} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-40r^{5} r_s^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{4} \\\\cos{\\\\theta}^{4}+8r^{4} r_s^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{4} \\\\cos{\\\\theta}^{4}-8r^{3} r_s^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{6} \\\\cos{\\\\theta}^{4}+24r^{7} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)%\\n-8r^{6} r_s^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+8r^{5} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)+24r^{5} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2}-8r^{4} r_s^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2}+8r^{3} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2}+24r^{7} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-8r^{6} r_s^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+8r^{5} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+24r^{5} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2}-8r^{4} r_s^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2}+8r^{3} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2}+24r^{7} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{2} \\\\cos{\\\\theta}^{2}-8r^{6} r_s^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{2} \\\\cos{\\\\theta}^{2}+8r^{5} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{4} \\\\cos{\\\\theta}^{2}+24r^{7} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{2} \\\\cos{\\\\theta}^{2}-8r^{6} r_s^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{2} \\\\cos{\\\\theta}^{2}+8r^{5} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{4} \\\\cos{\\\\theta}^{2}+64r^{6} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{4} \\\\cos{\\\\theta}^{4}+32r^{4} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{6} \\\\cos{\\\\theta}^{4}-16r^{6} r_s^{2} a^{8} \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}^{2}%\\n-16r^{4} r_s^{2} a^{10} \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}^{4}-16r^{8} r_s^{2} a^{6} \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}^{2}-16r^{6} r_s^{2} a^{8} \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}^{4}-70r^{8} r_s^{2} a^{6} \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{2}-16r^{6} r_s^{2} a^{8} \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{4}-46r^{10} r_s^{2} a^{4} \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{2}-16r^{8} r_s^{2} a^{6} \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{4}-214r^{6} r_s^{2} a^{8} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2}-114r^{4} r_s^{2} a^{10} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2}-142r^{8} r_s^{2} a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2}-94r^{6} r_s^{2} a^{8} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2}-56r^{8} r_s^{2} a^{6} \\\\cos{\\\\theta}^{2}-72r^{6} r_s^{2} a^{8} \\\\cos{\\\\theta}^{4}-28r^{10} r_s^{2} a^{4} \\\\cos{\\\\theta}^{2}-52r^{8} r_s^{2} a^{6} \\\\cos{\\\\theta}^{4}-40r^{4} r_s^{2} a^{10} \\\\cos{\\\\theta}^{6}-36r^{6} r_s^{2} a^{8} \\\\cos{\\\\theta}^{6}-16r^{5} r_s a^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{2}-16r^{3} r_s a^{8} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{4}-32r^{7} r_s a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{2}%\\n-32r^{5} r_s a^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{4}+44r^{12} r_s^{2} a^{2} \\\\cos{\\\\theta}^{2}+52r^{10} r_s^{2} a^{4} \\\\cos{\\\\theta}^{4}+20r^{8} r_s^{2} a^{6} \\\\cos{\\\\theta}^{6}-16r^{9} r_s a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{2}-16r^{7} r_s a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{4}-24r^{8} r_s^{2} a^{6} \\\\sin{\\\\theta}^{2}-24r^{6} r_s^{2} a^{8} \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{2}-54r^{10} r_s^{2} a^{4} \\\\sin{\\\\theta}^{2}-52r^{6} r_s^{2} a^{8} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}-72r^{4} r_s^{2} a^{10} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2}-120r^{8} r_s^{2} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}-16r^{10} r_s^{2} a^{4}-4r^{12} r_s^{2} a^{2}-68r^{10} r_s^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+44r^{7} r_s a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+36r^{5} r_s a^{6} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+28r^{9} r_s a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+20r^{7} r_s a^{4} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+56r^{9} r_s^{2} a^{4} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)%\\n+24r^{7} r_s^{2} a^{6} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+56r^{9} r_s^{2} a^{4} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+24r^{7} r_s^{2} a^{6} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+20r^{7} r_s^{2} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+12r^{5} r_s^{2} a^{8} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+20r^{7} r_s^{2} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+12r^{5} r_s^{2} a^{8} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-16r^{8} r_s a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-16r^{6} r_s a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-16r^{8} r_s a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-16r^{6} r_s a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-64r^{6} r_s a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-32r^{4} r_s a^{6} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-64r^{6} r_s a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-32r^{4} r_s a^{6} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+32r^{11} r_s^{2} a^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+32r^{11} r_s^{2} a^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+8r^{9} r_s^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+8r^{9} r_s^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-40r^{10} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)%\\n-40r^{8} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{2}-40r^{10} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-40r^{8} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{2}-32r^{8} r_s a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-32r^{8} r_s a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+36r^{7} r_s^{2} a^{6} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2}+16r^{5} r_s^{2} a^{8} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2}+36r^{7} r_s^{2} a^{6} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2}+16r^{5} r_s^{2} a^{8} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2}+24r^{12} r_s a^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+24r^{10} r_s a^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)+24r^{10} r_s a^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2}+24r^{8} r_s a^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2}+24r^{12} r_s a^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+24r^{10} r_s a^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+24r^{10} r_s a^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2}+24r^{8} r_s a^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2}+152r^{10} r_s a^{4} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+72r^{8} r_s a^{6} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+288r^{8} r_s a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)%\\n+136r^{6} r_s a^{8} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)+152r^{10} r_s a^{4} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+72r^{8} r_s a^{6} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+288r^{8} r_s a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+136r^{6} r_s a^{8} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+160r^{6} r_s a^{8} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right)+80r^{4} r_s a^{10} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right)+160r^{6} r_s a^{8} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+80r^{4} r_s a^{10} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+16r^{5} r_s a^{6} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+16r^{3} r_s a^{8} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-30r^{12} r_s^{2} a^{2} \\\\sin{\\\\theta}^{2}+20r^{9} r_s^{2} a^{4} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2}+20r^{9} r_s^{2} a^{4} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2}+12r^{14} r_s^{2}+40r^{14} r_s \\\\partial_{r}\\\\left(r^{2}\\\\right)+40r^{12} r_s \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{2}+48r^{12} r_s \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{2} \\\\cos{\\\\theta}^{2}+48r^{10} r_s \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{4} \\\\cos{\\\\theta}^{2}+40r^{14} r_s \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)%\\n+40r^{12} r_s \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{2}+48r^{12} r_s \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{2} \\\\cos{\\\\theta}^{2}+48r^{10} r_s \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{4} \\\\cos{\\\\theta}^{2}+80r^{12} r_s a^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+152r^{10} r_s a^{4} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)+80r^{12} r_s a^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+152r^{10} r_s a^{4} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-12r^{11} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-12r^{9} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2}-44r^{9} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} \\\\cos{\\\\theta}^{2}-44r^{7} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{4} \\\\cos{\\\\theta}^{2}+80r^{8} r_s a^{6} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right)+80r^{8} r_s a^{6} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-16r^{8} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-16r^{6} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)-16r^{6} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2}-16r^{4} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2}-16r^{8} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-16r^{6} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-16r^{6} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2}%\\n-16r^{4} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2}-16r^{8} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{2} \\\\cos{\\\\theta}^{2}-16r^{6} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{4} \\\\cos{\\\\theta}^{2}-16r^{8} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{2} \\\\cos{\\\\theta}^{2}-16r^{6} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{4} \\\\cos{\\\\theta}^{2}-32r^{7} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{4} \\\\cos{\\\\theta}^{4}-32r^{5} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{6} \\\\cos{\\\\theta}^{4}+8r^{3} r_s^{3} a^{10} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4}-8r^{4} r_s^{2} a^{10} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4}-8r^{2} r_s^{2} a^{12} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4}+8r^{5} r_s^{3} a^{8} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4}-8r^{6} r_s^{2} a^{8} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4}-8r^{4} r_s^{2} a^{10} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4}+22r^{3} r_s^{3} a^{10} \\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2}-20r^{2} r_s^{2} a^{12} \\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2}-20r^{4} r_s^{2} a^{10} \\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2}+20r^{3} r_s^{3} a^{10} \\\\cos{\\\\theta}^{8}-8r^{2} r_s^{2} a^{12} \\\\cos{\\\\theta}^{8}-8r^{4} r_s^{2} a^{10} \\\\cos{\\\\theta}^{8}-4r^{2} r_s^{2} a^{8} \\\\cos{\\\\theta}^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}%\\n-8r^{3} r_s a^{8} \\\\cos{\\\\theta}^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+12r^{5} r_s^{3} a^{8} \\\\cos{\\\\theta}^{8}+4r^{4} r_s^{2} a^{6} \\\\cos{\\\\theta}^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-8r^{5} r_s a^{6} \\\\cos{\\\\theta}^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-20r^{2} r_s^{2} a^{12} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2}-2r^{2} r_s^{4} a^{10} \\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2}+2r r_s^{3} a^{12} \\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2}-12r^{4} r_s^{4} a^{8} \\\\cos{\\\\theta}^{8}+4r^{3} r_s^{3} a^{6} \\\\cos{\\\\theta}^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+4r^{4} r_s^{3} a^{8} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+4r^{2} r_s^{3} a^{10} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+4r^{4} r_s^{3} a^{8} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+4r^{2} r_s^{3} a^{10} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+24r^{5} r_s^{2} a^{4} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-8r^{4} r_s^{3} a^{4} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+24r^{3} r_s^{2} a^{6} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+24r^{5} r_s^{2} a^{4} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-8r^{4} r_s^{3} a^{4} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+24r^{3} r_s^{2} a^{6} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-8r^{3} r_s^{2} a^{10} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)%\\n-4r r_s^{2} a^{12} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-8r^{3} r_s^{2} a^{10} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-4r r_s^{2} a^{12} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-32r^{4} r_s a^{6} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-16r^{2} r_s a^{8} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-32r^{4} r_s a^{6} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-16r^{2} r_s a^{8} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-4r^{5} r_s^{2} a^{8} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-4r^{5} r_s^{2} a^{8} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-16r^{6} r_s a^{4} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-16r^{6} r_s a^{4} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-32r^{5} r_s^{2} a^{8} \\\\cos{\\\\theta}^{8} \\\\partial_{r}\\\\left(r^{2}\\\\right)+16r^{4} r_s^{3} a^{8} \\\\cos{\\\\theta}^{8} \\\\partial_{r}\\\\left(r^{2}\\\\right)-32r^{3} r_s^{2} a^{10} \\\\cos{\\\\theta}^{8} \\\\partial_{r}\\\\left(r^{2}\\\\right)-32r^{5} r_s^{2} a^{8} \\\\cos{\\\\theta}^{8} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+16r^{4} r_s^{3} a^{8} \\\\cos{\\\\theta}^{8} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-32r^{3} r_s^{2} a^{10} \\\\cos{\\\\theta}^{8} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+32r^{4} r_s a^{10} \\\\cos{\\\\theta}^{8} \\\\partial_{r}\\\\left(r^{2}\\\\right)+16r^{2} r_s a^{12} \\\\cos{\\\\theta}^{8} \\\\partial_{r}\\\\left(r^{2}\\\\right)+32r^{4} r_s a^{10} \\\\cos{\\\\theta}^{8} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)%\\n+16r^{2} r_s a^{12} \\\\cos{\\\\theta}^{8} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+16r^{6} r_s a^{8} \\\\cos{\\\\theta}^{8} \\\\partial_{r}\\\\left(r^{2}\\\\right)+16r^{6} r_s a^{8} \\\\cos{\\\\theta}^{8} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-2r^{7} r_s^{5} a^{4} \\\\sin{\\\\theta}^{2}+2r^{6} r_s^{4} a^{6} \\\\sin{\\\\theta}^{2}+4r^{5} r_s^{5} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}-4r^{4} r_s^{4} a^{8} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}-2r^{4} r_s^{4} a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+2r^{3} r_s^{3} a^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-2r^{7} r_s^{3} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+2r^{6} r_s^{4} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-2r^{3} r_s^{5} a^{8} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2}+2r^{2} r_s^{4} a^{10} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2}+2r^{2} r_s^{4} a^{6} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-2r r_s^{3} a^{8} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+2r^{5} r_s^{3} a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-2r^{4} r_s^{4} a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-6r^{4} r_s^{2} \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s r^{2} \\\\sin{\\\\theta}^{2}-a^{4} r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+2r^{4} r_s+2r^{2} r_s a^{2} \\\\cos{\\\\theta}^{2}-2r \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}\\\\right)^{2}+2r^{3} r_s^{3} \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s r^{2} \\\\sin{\\\\theta}^{2}-a^{4} r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+2r^{4} r_s+2r^{2} r_s a^{2} \\\\cos{\\\\theta}^{2}-2r \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}\\\\right)^{2}-2r^{2} r_s^{2} \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s r^{2} \\\\sin{\\\\theta}^{2}-a^{4} r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+2r^{4} r_s+2r^{2} r_s a^{2} \\\\cos{\\\\theta}^{2}-2r \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}\\\\right)^{2} a^{2}%\\n+4r^{5} r_s \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s r^{2} \\\\sin{\\\\theta}^{2}-a^{4} r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+2r^{4} r_s+2r^{2} r_s a^{2} \\\\cos{\\\\theta}^{2}-2r \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}\\\\right)^{2}+4r^{3} r_s \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s r^{2} \\\\sin{\\\\theta}^{2}-a^{4} r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+2r^{4} r_s+2r^{2} r_s a^{2} \\\\cos{\\\\theta}^{2}-2r \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}\\\\right)^{2} a^{2}+2r^{3} r_s a^{2} \\\\cos{\\\\theta}^{2} \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s r^{2} \\\\sin{\\\\theta}^{2}-a^{4} r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+2r^{4} r_s+2r^{2} r_s a^{2} \\\\cos{\\\\theta}^{2}-2r \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}\\\\right)^{2}-2r^{2} r_s^{2} a^{2} \\\\cos{\\\\theta}^{2} \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s r^{2} \\\\sin{\\\\theta}^{2}-a^{4} r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+2r^{4} r_s+2r^{2} r_s a^{2} \\\\cos{\\\\theta}^{2}-2r \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}\\\\right)^{2}+2r r_s a^{4} \\\\cos{\\\\theta}^{2} \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s r^{2} \\\\sin{\\\\theta}^{2}-a^{4} r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+2r^{4} r_s+2r^{2} r_s a^{2} \\\\cos{\\\\theta}^{2}-2r \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}\\\\right)^{2}-8r^{6} a^{8} r_s^{2} \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}^{4}+8r^{7} a^{8} r_s \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}^{2}+8r^{5} a^{10} r_s \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}^{4}-8r^{8} a^{6} r_s^{2} \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}^{2}+8r^{9} a^{6} r_s \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}^{2}+8r^{7} a^{8} r_s \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}^{4}+4r^{7} a^{6} r_s^{3} \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{4}-4r^{8} a^{6} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{2}-4r^{6} a^{8} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{4}-8r^{9} a^{4} r_s^{3} \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{2}-8r^{10} a^{4} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{2}-12r^{8} a^{6} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{4}+28r^{9} a^{6} r_s \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{2}+8r^{7} a^{8} r_s \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{4}+16r^{11} a^{4} r_s \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{2}%\\n+8r^{9} a^{6} r_s \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{4}-28r^{6} a^{8} r_s^{2} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2}+36r^{7} a^{8} r_s \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2}+24r^{5} a^{10} r_s \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2}-68r^{8} a^{6} r_s^{2} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2}+32r^{9} a^{6} r_s \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2}+24r^{7} a^{8} r_s \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2}-24r^{8} a^{6} r_s^{2} \\\\cos{\\\\theta}^{4}+8r^{9} a^{6} r_s \\\\cos{\\\\theta}^{2}-8r^{7} a^{8} r_s \\\\cos{\\\\theta}^{4}-24r^{10} a^{4} r_s^{2} \\\\cos{\\\\theta}^{2}-24r^{9} a^{6} r_s \\\\cos{\\\\theta}^{4}-8r^{6} a^{8} r_s^{2} \\\\cos{\\\\theta}^{6}-8r^{5} a^{10} r_s \\\\cos{\\\\theta}^{6}-16r^{7} a^{8} r_s \\\\cos{\\\\theta}^{6}-8r^{5} a^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{4} r_s+8r^{6} a^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{2}+8r^{4} a^{8} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{4}+16r^{8} a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{2}+16r^{6} a^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{4}%\\n-16r^{10} a^{4} r_s^{2} \\\\cos{\\\\theta}^{4}-8r^{12} a^{2} r_s^{2} \\\\cos{\\\\theta}^{2}-8r^{13} a^{2} r_s \\\\cos{\\\\theta}^{2}-16r^{11} a^{4} r_s \\\\cos{\\\\theta}^{4}-8r^{8} a^{6} r_s^{2} \\\\cos{\\\\theta}^{6}-8r^{9} a^{6} r_s \\\\cos{\\\\theta}^{6}-8r^{7} a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{4} r_s-8r^{9} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{2} r_s+8r^{10} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{2}+8r^{8} a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{4}+12r^{9} a^{6} r_s \\\\sin{\\\\theta}^{2}+12r^{7} a^{8} r_s \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{2}+8r^{10} a^{4} r_s^{2} \\\\sin{\\\\theta}^{2}+20r^{11} a^{4} r_s \\\\sin{\\\\theta}^{2}-44r^{6} a^{8} r_s^{2} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2}+4r^{7} a^{8} r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+4r^{5} a^{10} r_s \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2}-32r^{8} a^{6} r_s^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+12r^{9} a^{6} r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+8r^{11} a^{4} r_s%\\n-8r^{12} a^{2} r_s^{2}+8r^{13} a^{2} r_s-8r^{7} a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s \\\\cos{\\\\theta}^{2}-98r^{8} a^{6} \\\\cos{\\\\theta}^{4} r_s^{2} \\\\sin{\\\\theta}^{2}+56r^{9} a^{6} \\\\cos{\\\\theta}^{2} r_s \\\\sin{\\\\theta}^{2}+108r^{7} a^{8} \\\\cos{\\\\theta}^{4} r_s \\\\sin{\\\\theta}^{2}-30r^{10} a^{4} \\\\cos{\\\\theta}^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+28r^{11} a^{4} \\\\cos{\\\\theta}^{2} r_s \\\\sin{\\\\theta}^{2}+60r^{9} a^{6} \\\\cos{\\\\theta}^{4} r_s \\\\sin{\\\\theta}^{2}-90r^{6} a^{8} \\\\cos{\\\\theta}^{6} r_s^{2} \\\\sin{\\\\theta}^{2}+72r^{5} a^{10} \\\\cos{\\\\theta}^{6} r_s \\\\sin{\\\\theta}^{2}+52r^{7} a^{8} \\\\cos{\\\\theta}^{6} r_s \\\\sin{\\\\theta}^{2}-36r^{10} a^{4} \\\\cos{\\\\theta}^{4} r_s^{2}+48r^{11} a^{4} \\\\cos{\\\\theta}^{2} r_s+104r^{9} a^{6} \\\\cos{\\\\theta}^{4} r_s-12r^{12} a^{2} \\\\cos{\\\\theta}^{2} r_s^{2}+24r^{13} a^{2} \\\\cos{\\\\theta}^{2} r_s+48r^{11} a^{4} \\\\cos{\\\\theta}^{4} r_s-36r^{8} a^{6} \\\\cos{\\\\theta}^{6} r_s^{2}+64r^{7} a^{8} \\\\cos{\\\\theta}^{6} r_s%\\n+24r^{9} a^{6} \\\\cos{\\\\theta}^{6} r_s-32r^{7} a^{4} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s-16r^{8} a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-8r^{6} a^{6} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-16r^{9} a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s-8r^{10} a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-8r^{8} a^{4} r_s^{3} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-8r^{8} a^{4} r_s^{3} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-4r^{7} a^{6} r_s^{2} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-4r^{5} a^{8} r_s^{2} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-4r^{7} a^{6} r_s^{2} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-4r^{5} a^{8} r_s^{2} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-16r^{11} a^{2} r_s^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+8r^{9} a^{4} r_s^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-16r^{11} a^{2} r_s^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+8r^{9} a^{4} r_s^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-32r^{9} a^{4} r_s^{2} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)-32r^{9} a^{4} r_s^{2} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-8r^{8} a^{2} r_s \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+8r^{7} a^{2} r_s^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)%\\n-8r^{6} a^{4} r_s \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-8r^{8} a^{2} r_s \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+8r^{7} a^{2} r_s^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-8r^{6} a^{4} r_s \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-24r^{10} a^{4} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+12r^{9} a^{4} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-12r^{8} a^{6} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-24r^{10} a^{4} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+12r^{9} a^{4} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-12r^{8} a^{6} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+16r^{8} a^{6} r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+8r^{6} a^{8} r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+16r^{8} a^{6} r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+8r^{6} a^{8} r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+8r^{10} a^{4} r_s \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-8r^{8} a^{6} r_s \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+8r^{10} a^{4} r_s \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-8r^{8} a^{6} r_s \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+8r^{9} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-8r^{8} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) r_s%\\n+8r^{7} a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+8r^{9} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-8r^{8} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s+8r^{7} a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-40r^{8} a^{6} \\\\cos{\\\\theta}^{2} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+28r^{7} a^{6} \\\\cos{\\\\theta}^{2} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-20r^{6} a^{8} \\\\cos{\\\\theta}^{2} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-40r^{8} a^{6} \\\\cos{\\\\theta}^{2} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+28r^{7} a^{6} \\\\cos{\\\\theta}^{2} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-20r^{6} a^{8} \\\\cos{\\\\theta}^{2} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-16r^{6} a^{8} \\\\cos{\\\\theta}^{4} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+16r^{5} a^{8} \\\\cos{\\\\theta}^{4} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-8r^{4} a^{10} \\\\cos{\\\\theta}^{4} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-16r^{6} a^{8} \\\\cos{\\\\theta}^{4} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+16r^{5} a^{8} \\\\cos{\\\\theta}^{4} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-8r^{4} a^{10} \\\\cos{\\\\theta}^{4} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+8r^{9} a^{4} \\\\cos{\\\\theta}^{2} r_s^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-8r^{8} a^{6} \\\\cos{\\\\theta}^{2} r_s \\\\partial_{r}\\\\left(r^{2}\\\\right)+8r^{9} a^{4} \\\\cos{\\\\theta}^{2} r_s^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-8r^{8} a^{6} \\\\cos{\\\\theta}^{2} r_s \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)%\\n+16r^{8} a^{6} \\\\cos{\\\\theta}^{4} r_s \\\\partial_{r}\\\\left(r^{2}\\\\right)+16r^{7} a^{6} \\\\cos{\\\\theta}^{4} r_s^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-16r^{6} a^{8} \\\\cos{\\\\theta}^{4} r_s \\\\partial_{r}\\\\left(r^{2}\\\\right)+16r^{8} a^{6} \\\\cos{\\\\theta}^{4} r_s \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+16r^{7} a^{6} \\\\cos{\\\\theta}^{4} r_s^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-16r^{6} a^{8} \\\\cos{\\\\theta}^{4} r_s \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+48r^{7} a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-24r^{6} a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) r_s+24r^{5} a^{6} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+48r^{7} a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-24r^{6} a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s+24r^{5} a^{6} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-12r^{12} a^{2} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+12r^{11} a^{2} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-12r^{12} a^{2} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+12r^{11} a^{2} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+8r^{10} a^{4} r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+8r^{10} a^{4} r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+16r^{11} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-16r^{10} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) r_s%\\n+16r^{9} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{2}+16r^{11} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-16r^{10} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s+16r^{9} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{2}-20r^{10} a^{4} \\\\cos{\\\\theta}^{2} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+28r^{9} a^{4} \\\\cos{\\\\theta}^{2} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-20r^{10} a^{4} \\\\cos{\\\\theta}^{2} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+28r^{9} a^{4} \\\\cos{\\\\theta}^{2} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-8r^{8} a^{6} \\\\cos{\\\\theta}^{4} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+16r^{7} a^{6} \\\\cos{\\\\theta}^{4} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-8r^{8} a^{6} \\\\cos{\\\\theta}^{4} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+16r^{7} a^{6} \\\\cos{\\\\theta}^{4} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+8r^{12} a^{2} \\\\cos{\\\\theta}^{2} r_s \\\\partial_{r}\\\\left(r^{2}\\\\right)-8r^{11} a^{2} \\\\cos{\\\\theta}^{2} r_s^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+8r^{12} a^{2} \\\\cos{\\\\theta}^{2} r_s \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-8r^{11} a^{2} \\\\cos{\\\\theta}^{2} r_s^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+32r^{10} a^{4} \\\\cos{\\\\theta}^{4} r_s \\\\partial_{r}\\\\left(r^{2}\\\\right)-32r^{9} a^{4} \\\\cos{\\\\theta}^{4} r_s^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+32r^{10} a^{4} \\\\cos{\\\\theta}^{4} r_s \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-32r^{9} a^{4} \\\\cos{\\\\theta}^{4} r_s^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)%\\n+24r^{9} a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-24r^{8} a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) r_s+24r^{9} a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-24r^{8} a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s-36r^{10} a^{4} r_s^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+32r^{9} a^{4} r_s^{3} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+38r^{7} a^{6} r_s^{3} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2}+16r^{11} a^{2} r_s^{3} \\\\cos{\\\\theta}^{2}+32r^{9} a^{4} r_s^{3} \\\\cos{\\\\theta}^{4}+16r^{7} a^{6} r_s^{3} \\\\cos{\\\\theta}^{6}+16r^{12} a^{2} r_s \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+32r^{10} a^{4} r_s \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)+32r^{8} a^{6} r_s \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)+16r^{12} a^{2} r_s \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+32r^{10} a^{4} r_s \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+32r^{8} a^{6} r_s \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+16r^{8} a^{6} r_s \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right)-16r^{7} a^{6} r_s^{2} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right)+16r^{6} a^{8} r_s \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right)+16r^{8} a^{6} r_s \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)%\\n-16r^{7} a^{6} r_s^{2} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+16r^{6} a^{8} r_s \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+8r^{9} a^{2} r_s \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-8r^{8} a^{2} r_s^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+8r^{7} a^{4} r_s \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+8r^{7} a^{4} r_s \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-8r^{6} a^{4} r_s^{2} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+8r^{5} a^{6} r_s \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-16r^{8} a^{6} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2}+8r^{7} a^{6} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2}-8r^{6} a^{8} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2}-16r^{8} a^{6} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2}+8r^{7} a^{6} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2}-8r^{6} a^{8} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2}+8r^{10} a^{4} r_s \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2}-8r^{9} a^{4} r_s^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2}+8r^{8} a^{6} r_s \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2}+8r^{10} a^{4} r_s \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2}-8r^{9} a^{4} r_s^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2}+8r^{8} a^{6} r_s \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2}%\\n-16r^{13} a^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+16r^{12} a^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) r_s-16r^{11} a^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)-16r^{11} a^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2}+16r^{10} a^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} r_s-16r^{9} a^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2}-16r^{13} a^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+16r^{12} a^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s-16r^{11} a^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-16r^{11} a^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2}+16r^{10} a^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2} r_s-16r^{9} a^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2}-96r^{11} a^{4} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+48r^{10} a^{4} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) r_s-48r^{9} a^{6} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-192r^{9} a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)+96r^{8} a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right) r_s-96r^{7} a^{8} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)-96r^{11} a^{4} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+48r^{10} a^{4} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s%\\n-48r^{9} a^{6} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-192r^{9} a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+96r^{8} a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s-96r^{7} a^{8} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-30r^{8} a^{6} \\\\cos{\\\\theta}^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+28r^{7} a^{8} \\\\cos{\\\\theta}^{2} r_s \\\\sin{\\\\theta}^{2}-86r^{6} a^{8} \\\\cos{\\\\theta}^{4} r_s^{2} \\\\sin{\\\\theta}^{2}+48r^{5} a^{10} \\\\cos{\\\\theta}^{4} r_s \\\\sin{\\\\theta}^{2}-12r^{10} a^{4} \\\\cos{\\\\theta}^{2} r_s^{2}+24r^{9} a^{6} \\\\cos{\\\\theta}^{2} r_s-44r^{8} a^{6} \\\\cos{\\\\theta}^{4} r_s^{2}+56r^{7} a^{8} \\\\cos{\\\\theta}^{4} r_s-52r^{6} a^{8} \\\\cos{\\\\theta}^{6} r_s^{2}+40r^{5} a^{10} \\\\cos{\\\\theta}^{6} r_s-128r^{7} a^{8} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right)+64r^{6} a^{8} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right) r_s-64r^{5} a^{10} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right)-128r^{7} a^{8} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+64r^{6} a^{8} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s-64r^{5} a^{10} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)%\\n-16r^{7} a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s-8r^{6} a^{6} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-24r^{5} a^{6} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s-8r^{4} a^{8} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+8r^{13} a^{2} r_s \\\\sin{\\\\theta}^{2}+8r^{12} a^{2} r_s^{2} \\\\sin{\\\\theta}^{2}-8r^{10} a^{4} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2}+8r^{9} a^{4} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2}-8r^{10} a^{4} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2}+8r^{9} a^{4} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2}-16r^{13} r_s a^{2} \\\\cos{\\\\theta}^{2}-16r^{11} r_s a^{4} \\\\cos{\\\\theta}^{2}-32r^{11} r_s a^{4} \\\\cos{\\\\theta}^{4}-32r^{9} r_s a^{6} \\\\cos{\\\\theta}^{4}-16r^{15} \\\\partial_{r}\\\\left(r^{2}\\\\right)+16r^{14} \\\\partial_{r}\\\\left(r^{2}\\\\right) r_s-16r^{13} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{2}-16r^{13} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{2} \\\\cos{\\\\theta}^{2}+16r^{12} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{2} \\\\cos{\\\\theta}^{2} r_s-16r^{11} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{4} \\\\cos{\\\\theta}^{2}%\\n-16r^{15} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+16r^{14} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s-16r^{13} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{2}-16r^{13} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{2} \\\\cos{\\\\theta}^{2}+16r^{12} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{2} \\\\cos{\\\\theta}^{2} r_s-16r^{11} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{4} \\\\cos{\\\\theta}^{2}-48r^{13} a^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+48r^{12} a^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) r_s-96r^{11} a^{4} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)+96r^{10} a^{4} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right) r_s-48r^{13} a^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+48r^{12} a^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s-96r^{11} a^{4} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+96r^{10} a^{4} \\\\cos{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s+8r^{12} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-32r^{11} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s+8r^{10} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2}+24r^{10} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} \\\\cos{\\\\theta}^{2}-24r^{9} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} \\\\cos{\\\\theta}^{2} r_s+24r^{8} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{4} \\\\cos{\\\\theta}^{2}%\\n-64r^{9} a^{6} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right)+64r^{8} a^{6} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right) r_s-64r^{9} a^{6} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+64r^{8} a^{6} \\\\cos{\\\\theta}^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s-22r^{11} a^{2} r_s^{3} \\\\sin{\\\\theta}^{2}+4r^{5} a^{8} r_s^{3} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2}-4r^{4} a^{10} r_s^{2} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2}+8r^{6} a^{8} r_s \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+4r^{4} a^{10} r_s \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+8r^{6} a^{8} r_s \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+4r^{4} a^{10} r_s \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+4r^{8} a^{6} r_s \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+4r^{8} a^{6} r_s \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+8r^{11} a^{4} r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}-16r^{9} r_s a^{6} \\\\cos{\\\\theta}^{6}-16r^{7} r_s a^{8} \\\\cos{\\\\theta}^{6}-8r^{9} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} r_s \\\\cos{\\\\theta}^{2}+8r^{8} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} r_s^{2} \\\\cos{\\\\theta}^{2}-8r^{7} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{4} r_s \\\\cos{\\\\theta}^{2}-8r^{7} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{4} r_s \\\\cos{\\\\theta}^{4}%\\n+8r^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{4} r_s^{2} \\\\cos{\\\\theta}^{4}-8r^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{6} r_s \\\\cos{\\\\theta}^{4}+8r^{9} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-8r^{8} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) r_s+8r^{7} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)+8r^{7} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2}-8r^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} r_s+8r^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2}+8r^{9} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-8r^{8} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s+8r^{7} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+8r^{7} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2}-8r^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2} r_s+8r^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2}+24r^{10} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s^{2}-24r^{9} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s a^{2}-24r^{9} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s a^{2} \\\\cos{\\\\theta}^{2}+24r^{8} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s^{2} a^{2} \\\\cos{\\\\theta}^{2}-24r^{7} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s a^{4} \\\\cos{\\\\theta}^{2}+8r^{9} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{2} \\\\cos{\\\\theta}^{2}%\\n-8r^{8} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{2} \\\\cos{\\\\theta}^{2} r_s+8r^{7} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) a^{4} \\\\cos{\\\\theta}^{2}+8r^{9} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{2} \\\\cos{\\\\theta}^{2}-8r^{8} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{2} \\\\cos{\\\\theta}^{2} r_s+8r^{7} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{4} \\\\cos{\\\\theta}^{2}+16r^{8} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{4} \\\\cos{\\\\theta}^{4}-16r^{7} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{4} \\\\cos{\\\\theta}^{4} r_s+16r^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{6} \\\\cos{\\\\theta}^{4}-8r^{4} a^{10} \\\\cos{\\\\theta}^{6} r_s^{2} \\\\sin{\\\\theta}^{4}+8r^{5} a^{10} \\\\cos{\\\\theta}^{4} r_s \\\\sin{\\\\theta}^{4}+8r^{3} a^{12} \\\\cos{\\\\theta}^{6} r_s \\\\sin{\\\\theta}^{4}-8r^{6} a^{8} \\\\cos{\\\\theta}^{4} r_s^{2} \\\\sin{\\\\theta}^{4}+8r^{7} a^{8} \\\\cos{\\\\theta}^{4} r_s \\\\sin{\\\\theta}^{4}+8r^{5} a^{10} \\\\cos{\\\\theta}^{6} r_s \\\\sin{\\\\theta}^{4}+38r^{5} a^{8} \\\\cos{\\\\theta}^{6} r_s^{3} \\\\sin{\\\\theta}^{2}-58r^{4} a^{10} \\\\cos{\\\\theta}^{6} r_s^{2} \\\\sin{\\\\theta}^{2}+38r^{7} a^{6} \\\\cos{\\\\theta}^{4} r_s^{3} \\\\sin{\\\\theta}^{2}-22r^{4} a^{10} \\\\cos{\\\\theta}^{8} r_s^{2} \\\\sin{\\\\theta}^{2}+20r^{3} a^{12} \\\\cos{\\\\theta}^{8} r_s \\\\sin{\\\\theta}^{2}+20r^{5} a^{10} \\\\cos{\\\\theta}^{8} r_s \\\\sin{\\\\theta}^{2}%\\n-20r^{4} a^{10} \\\\cos{\\\\theta}^{8} r_s^{2}+8r^{3} a^{12} \\\\cos{\\\\theta}^{8} r_s+8r^{5} a^{10} \\\\cos{\\\\theta}^{8} r_s-8r^{3} a^{8} \\\\cos{\\\\theta}^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s+8r^{4} a^{8} \\\\cos{\\\\theta}^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-12r^{6} a^{8} \\\\cos{\\\\theta}^{8} r_s^{2}-16r^{5} a^{6} \\\\cos{\\\\theta}^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s+8r^{6} a^{6} \\\\cos{\\\\theta}^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+2r^{9} a^{4} \\\\cos{\\\\theta}^{2} r_s^{3} \\\\sin{\\\\theta}^{2}-12r^{9} a^{4} \\\\cos{\\\\theta}^{4} r_s^{3}-12r^{11} a^{2} \\\\cos{\\\\theta}^{2} r_s^{3}+12r^{7} a^{6} \\\\cos{\\\\theta}^{6} r_s^{3}-16r^{6} a^{4} \\\\cos{\\\\theta}^{4} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+4r^{7} a^{4} \\\\cos{\\\\theta}^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+16r^{5} a^{6} \\\\cos{\\\\theta}^{4} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-4r^{8} a^{2} \\\\cos{\\\\theta}^{2} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+4r^{9} a^{2} \\\\cos{\\\\theta}^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+16r^{7} a^{4} \\\\cos{\\\\theta}^{4} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+20r^{3} a^{12} \\\\cos{\\\\theta}^{6} r_s \\\\sin{\\\\theta}^{2}+2r^{3} a^{10} \\\\cos{\\\\theta}^{8} r_s^{3} \\\\sin{\\\\theta}^{2}%\\n-2r^{2} a^{12} \\\\cos{\\\\theta}^{8} r_s^{2} \\\\sin{\\\\theta}^{2}+12r^{5} a^{8} \\\\cos{\\\\theta}^{8} r_s^{3}-12r^{4} a^{6} \\\\cos{\\\\theta}^{6} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+12r^{3} a^{8} \\\\cos{\\\\theta}^{6} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+12r^{5} a^{6} \\\\cos{\\\\theta}^{6} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-8r^{6} a^{6} \\\\cos{\\\\theta}^{4} r_s^{3} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-8r^{6} a^{6} \\\\cos{\\\\theta}^{4} r_s^{3} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-4r^{5} a^{8} \\\\cos{\\\\theta}^{6} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-4r^{3} a^{10} \\\\cos{\\\\theta}^{6} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-4r^{5} a^{8} \\\\cos{\\\\theta}^{6} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-4r^{3} a^{10} \\\\cos{\\\\theta}^{6} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-40r^{7} a^{6} \\\\cos{\\\\theta}^{6} r_s^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+8r^{5} a^{8} \\\\cos{\\\\theta}^{6} r_s^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-40r^{7} a^{6} \\\\cos{\\\\theta}^{6} r_s^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+8r^{5} a^{8} \\\\cos{\\\\theta}^{6} r_s^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-8r^{6} a^{4} \\\\cos{\\\\theta}^{4} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+8r^{5} a^{4} \\\\cos{\\\\theta}^{4} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-8r^{4} a^{6} \\\\cos{\\\\theta}^{4} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-8r^{6} a^{4} \\\\cos{\\\\theta}^{4} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+8r^{5} a^{4} \\\\cos{\\\\theta}^{4} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)%\\n-8r^{4} a^{6} \\\\cos{\\\\theta}^{4} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+8r^{4} a^{10} \\\\cos{\\\\theta}^{6} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+4r^{2} a^{12} \\\\cos{\\\\theta}^{6} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+8r^{4} a^{10} \\\\cos{\\\\theta}^{6} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+4r^{2} a^{12} \\\\cos{\\\\theta}^{6} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+32r^{6} a^{8} \\\\cos{\\\\theta}^{6} r_s \\\\partial_{r}\\\\left(r^{2}\\\\right)-8r^{4} a^{10} \\\\cos{\\\\theta}^{6} r_s \\\\partial_{r}\\\\left(r^{2}\\\\right)+32r^{6} a^{8} \\\\cos{\\\\theta}^{6} r_s \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-8r^{4} a^{10} \\\\cos{\\\\theta}^{6} r_s \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+32r^{5} a^{6} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-16r^{4} a^{6} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) r_s+16r^{3} a^{8} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+32r^{5} a^{6} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-16r^{4} a^{6} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s+16r^{3} a^{8} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-8r^{8} a^{4} \\\\cos{\\\\theta}^{2} r_s^{3} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-8r^{8} a^{4} \\\\cos{\\\\theta}^{2} r_s^{3} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-8r^{8} a^{2} \\\\cos{\\\\theta}^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+8r^{7} a^{2} \\\\cos{\\\\theta}^{2} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-8r^{6} a^{4} \\\\cos{\\\\theta}^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)%\\n-8r^{8} a^{2} \\\\cos{\\\\theta}^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+8r^{7} a^{2} \\\\cos{\\\\theta}^{2} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-8r^{6} a^{4} \\\\cos{\\\\theta}^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+4r^{6} a^{8} \\\\cos{\\\\theta}^{6} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+4r^{6} a^{8} \\\\cos{\\\\theta}^{6} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+40r^{8} a^{6} \\\\cos{\\\\theta}^{6} r_s \\\\partial_{r}\\\\left(r^{2}\\\\right)+40r^{8} a^{6} \\\\cos{\\\\theta}^{6} r_s \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+16r^{7} a^{4} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-16r^{6} a^{4} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) r_s+16r^{7} a^{4} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-16r^{6} a^{4} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s+16r^{6} a^{8} \\\\cos{\\\\theta}^{8} r_s \\\\partial_{r}\\\\left(r^{2}\\\\right)-16r^{5} a^{8} \\\\cos{\\\\theta}^{8} r_s^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+16r^{4} a^{10} \\\\cos{\\\\theta}^{8} r_s \\\\partial_{r}\\\\left(r^{2}\\\\right)+16r^{6} a^{8} \\\\cos{\\\\theta}^{8} r_s \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-16r^{5} a^{8} \\\\cos{\\\\theta}^{8} r_s^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+16r^{4} a^{10} \\\\cos{\\\\theta}^{8} r_s \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-32r^{5} a^{10} \\\\cos{\\\\theta}^{8} \\\\partial_{r}\\\\left(r^{2}\\\\right)+16r^{4} a^{10} \\\\cos{\\\\theta}^{8} \\\\partial_{r}\\\\left(r^{2}\\\\right) r_s-16r^{3} a^{12} \\\\cos{\\\\theta}^{8} \\\\partial_{r}\\\\left(r^{2}\\\\right)%\\n-32r^{5} a^{10} \\\\cos{\\\\theta}^{8} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+16r^{4} a^{10} \\\\cos{\\\\theta}^{8} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s-16r^{3} a^{12} \\\\cos{\\\\theta}^{8} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-16r^{7} a^{8} \\\\cos{\\\\theta}^{8} \\\\partial_{r}\\\\left(r^{2}\\\\right)+16r^{6} a^{8} \\\\cos{\\\\theta}^{8} \\\\partial_{r}\\\\left(r^{2}\\\\right) r_s-16r^{7} a^{8} \\\\cos{\\\\theta}^{8} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+16r^{6} a^{8} \\\\cos{\\\\theta}^{8} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s+32r^{6} a^{4} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s^{2}+8r^{4} a^{6} \\\\cos{\\\\theta}^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s^{2}+24r^{8} a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s^{2}-12r^{9} a^{4} r_s^{3} \\\\sin{\\\\theta}^{2}+2r^{8} a^{4} r_s^{4} \\\\sin{\\\\theta}^{2}-2r^{7} a^{6} r_s^{3} \\\\sin{\\\\theta}^{2}+4r^{8} a^{6} r_s^{2} \\\\sin{\\\\theta}^{2}+8r^{7} a^{6} r_s^{3} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}-4r^{6} a^{6} r_s^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+4r^{5} a^{8} r_s^{3} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+2r^{5} a^{4} r_s^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-2r^{4} a^{6} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+6r^{10} a^{2} r_s^{4} \\\\sin{\\\\theta}^{2}%\\n-4r^{8} a^{4} r_s^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+2r^{8} a^{2} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-2r^{7} a^{2} r_s^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+4r^{5} a^{8} r_s^{3} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2}-4r^{4} a^{10} r_s^{2} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2}+2r^{4} a^{8} r_s^{4} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2}-2r^{3} a^{10} r_s^{3} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2}-2r^{3} a^{6} r_s^{3} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+2r^{2} a^{8} r_s^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-2r^{6} a^{6} r_s^{4} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2}-2r^{6} a^{4} r_s^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+2r^{5} a^{4} r_s^{3} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-2r^{6} \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s r^{2} \\\\sin{\\\\theta}^{2}-a^{4} r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+2r^{4} r_s+2r^{2} r_s a^{2} \\\\cos{\\\\theta}^{2}-2r \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}\\\\right)^{2}+2r^{5} \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s r^{2} \\\\sin{\\\\theta}^{2}-a^{4} r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+2r^{4} r_s+2r^{2} r_s a^{2} \\\\cos{\\\\theta}^{2}-2r \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}\\\\right)^{2} r_s-2r^{4} \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s r^{2} \\\\sin{\\\\theta}^{2}-a^{4} r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+2r^{4} r_s+2r^{2} r_s a^{2} \\\\cos{\\\\theta}^{2}-2r \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}\\\\right)^{2} a^{2}-2r^{4} a^{2} \\\\cos{\\\\theta}^{2} \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s r^{2} \\\\sin{\\\\theta}^{2}-a^{4} r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+2r^{4} r_s+2r^{2} r_s a^{2} \\\\cos{\\\\theta}^{2}-2r \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}\\\\right)^{2}+2r^{3} a^{2} \\\\cos{\\\\theta}^{2} \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s r^{2} \\\\sin{\\\\theta}^{2}-a^{4} r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+2r^{4} r_s+2r^{2} r_s a^{2} \\\\cos{\\\\theta}^{2}-2r \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}\\\\right)^{2} r_s-2r^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s r^{2} \\\\sin{\\\\theta}^{2}-a^{4} r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+2r^{4} r_s+2r^{2} r_s a^{2} \\\\cos{\\\\theta}^{2}-2r \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}\\\\right)^{2}+8a^{10} \\\\cos{\\\\theta}^{6} r^{3} r_s^{3} \\\\sin{\\\\theta}^{4}-8a^{10} \\\\cos{\\\\theta}^{4} r^{4} r_s^{2} \\\\sin{\\\\theta}^{4}%\\n-8a^{12} \\\\cos{\\\\theta}^{6} r^{2} r_s^{2} \\\\sin{\\\\theta}^{4}+8a^{8} \\\\cos{\\\\theta}^{4} r^{5} r_s^{3} \\\\sin{\\\\theta}^{4}-16a^{8} \\\\cos{\\\\theta}^{4} r^{6} r_s^{2} \\\\sin{\\\\theta}^{4}-24a^{10} \\\\cos{\\\\theta}^{6} r^{4} r_s^{2} \\\\sin{\\\\theta}^{4}-38a^{8} \\\\cos{\\\\theta}^{6} r^{4} r_s^{4} \\\\sin{\\\\theta}^{2}+70a^{8} \\\\cos{\\\\theta}^{4} r^{5} r_s^{3} \\\\sin{\\\\theta}^{2}+58a^{10} \\\\cos{\\\\theta}^{6} r^{3} r_s^{3} \\\\sin{\\\\theta}^{2}-38a^{6} \\\\cos{\\\\theta}^{4} r^{6} r_s^{4} \\\\sin{\\\\theta}^{2}+108a^{6} \\\\cos{\\\\theta}^{4} r^{7} r_s^{3} \\\\sin{\\\\theta}^{2}+140a^{8} \\\\cos{\\\\theta}^{6} r^{5} r_s^{3} \\\\sin{\\\\theta}^{2}-146a^{8} \\\\cos{\\\\theta}^{4} r^{6} r_s^{2} \\\\sin{\\\\theta}^{2}-174a^{10} \\\\cos{\\\\theta}^{6} r^{4} r_s^{2} \\\\sin{\\\\theta}^{2}-114a^{6} \\\\cos{\\\\theta}^{4} r^{8} r_s^{2} \\\\sin{\\\\theta}^{2}-178a^{8} \\\\cos{\\\\theta}^{6} r^{6} r_s^{2} \\\\sin{\\\\theta}^{2}+44a^{10} \\\\cos{\\\\theta}^{8} r^{3} r_s^{3} \\\\sin{\\\\theta}^{2}-62a^{12} \\\\cos{\\\\theta}^{8} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}-94a^{10} \\\\cos{\\\\theta}^{8} r^{4} r_s^{2} \\\\sin{\\\\theta}^{2}+36a^{8} \\\\cos{\\\\theta}^{6} r^{5} r_s^{3}-24a^{8} \\\\cos{\\\\theta}^{4} r^{6} r_s^{2}-24a^{10} \\\\cos{\\\\theta}^{6} r^{4} r_s^{2}%\\n+12a^{6} \\\\cos{\\\\theta}^{4} r^{7} r_s^{3}-28a^{6} \\\\cos{\\\\theta}^{4} r^{8} r_s^{2}-60a^{8} \\\\cos{\\\\theta}^{6} r^{6} r_s^{2}+20a^{10} \\\\cos{\\\\theta}^{8} r^{3} r_s^{3}-8a^{12} \\\\cos{\\\\theta}^{8} r^{2} r_s^{2}-52a^{10} \\\\cos{\\\\theta}^{8} r^{4} r_s^{2}-4a^{8} \\\\cos{\\\\theta}^{6} r^{2} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+16a^{6} \\\\cos{\\\\theta}^{4} r^{4} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+12a^{8} \\\\cos{\\\\theta}^{6} r^{3} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-40a^{4} \\\\cos{\\\\theta}^{4} r^{9} r_s^{3}+28a^{4} \\\\cos{\\\\theta}^{4} r^{10} r_s^{2}+12a^{6} \\\\cos{\\\\theta}^{6} r^{8} r_s^{2}+24a^{8} \\\\cos{\\\\theta}^{8} r^{5} r_s^{3}-12a^{8} \\\\cos{\\\\theta}^{8} r^{6} r_s^{2}-16a^{6} \\\\cos{\\\\theta}^{6} r^{4} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+16a^{4} \\\\cos{\\\\theta}^{4} r^{6} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+12a^{6} \\\\cos{\\\\theta}^{6} r^{5} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+14a^{6} \\\\cos{\\\\theta}^{2} r^{7} r_s^{3} \\\\sin{\\\\theta}^{2}-2a^{4} \\\\cos{\\\\theta}^{2} r^{8} r_s^{4} \\\\sin{\\\\theta}^{2}+12a^{4} \\\\cos{\\\\theta}^{2} r^{9} r_s^{3} \\\\sin{\\\\theta}^{2}%\\n+12a^{4} \\\\cos{\\\\theta}^{4} r^{8} r_s^{4}-4a^{4} \\\\cos{\\\\theta}^{2} r^{9} r_s^{3}+12a^{2} \\\\cos{\\\\theta}^{2} r^{10} r_s^{4}-24a^{2} \\\\cos{\\\\theta}^{2} r^{11} r_s^{3}-12a^{6} \\\\cos{\\\\theta}^{6} r^{6} r_s^{4}-16a^{4} \\\\cos{\\\\theta}^{4} r^{5} r_s^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+20a^{4} \\\\cos{\\\\theta}^{2} r^{6} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-20a^{2} \\\\cos{\\\\theta}^{2} r^{7} r_s^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+24a^{2} \\\\cos{\\\\theta}^{2} r^{8} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-12a^{8} \\\\cos{\\\\theta}^{2} r^{6} r_s^{2} \\\\sin{\\\\theta}^{2}-32a^{10} \\\\cos{\\\\theta}^{4} r^{4} r_s^{2} \\\\sin{\\\\theta}^{2}-34a^{6} \\\\cos{\\\\theta}^{2} r^{8} r_s^{2} \\\\sin{\\\\theta}^{2}-20a^{12} \\\\cos{\\\\theta}^{6} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}-8a^{6} \\\\cos{\\\\theta}^{2} r^{8} r_s^{2}-4a^{4} \\\\cos{\\\\theta}^{2} r^{10} r_s^{2}-4a^{4} \\\\cos{\\\\theta}^{2} r^{7} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-2a^{10} \\\\cos{\\\\theta}^{8} r^{2} r_s^{4} \\\\sin{\\\\theta}^{2}+2a^{12} \\\\cos{\\\\theta}^{8} r r_s^{3} \\\\sin{\\\\theta}^{2}-12a^{8} \\\\cos{\\\\theta}^{8} r^{4} r_s^{4}+4a^{6} \\\\cos{\\\\theta}^{6} r^{3} r_s^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}%\\n-32a^{6} \\\\cos{\\\\theta}^{4} r^{6} r_s^{3} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+8a^{6} \\\\cos{\\\\theta}^{4} r^{5} r_s^{4} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-16a^{8} \\\\cos{\\\\theta}^{4} r^{4} r_s^{3} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-32a^{6} \\\\cos{\\\\theta}^{4} r^{6} r_s^{3} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+8a^{6} \\\\cos{\\\\theta}^{4} r^{5} r_s^{4} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-16a^{8} \\\\cos{\\\\theta}^{4} r^{4} r_s^{3} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-4a^{8} \\\\cos{\\\\theta}^{6} r^{4} r_s^{3} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+4a^{10} \\\\cos{\\\\theta}^{6} r^{2} r_s^{3} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-4a^{8} \\\\cos{\\\\theta}^{6} r^{4} r_s^{3} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+4a^{10} \\\\cos{\\\\theta}^{6} r^{2} r_s^{3} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+32a^{4} \\\\cos{\\\\theta}^{4} r^{8} r_s^{3} \\\\partial_{r}\\\\left(r^{2}\\\\right)-16a^{6} \\\\cos{\\\\theta}^{4} r^{6} r_s^{3} \\\\partial_{r}\\\\left(r^{2}\\\\right)+32a^{4} \\\\cos{\\\\theta}^{4} r^{8} r_s^{3} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-16a^{6} \\\\cos{\\\\theta}^{4} r^{6} r_s^{3} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+40a^{6} \\\\cos{\\\\theta}^{6} r^{6} r_s^{3} \\\\partial_{r}\\\\left(r^{2}\\\\right)-8a^{8} \\\\cos{\\\\theta}^{6} r^{4} r_s^{3} \\\\partial_{r}\\\\left(r^{2}\\\\right)+40a^{6} \\\\cos{\\\\theta}^{6} r^{6} r_s^{3} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-8a^{8} \\\\cos{\\\\theta}^{6} r^{4} r_s^{3} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+40a^{4} \\\\cos{\\\\theta}^{4} r^{5} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-8a^{4} \\\\cos{\\\\theta}^{4} r^{4} r_s^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)%\\n+24a^{6} \\\\cos{\\\\theta}^{4} r^{3} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+40a^{4} \\\\cos{\\\\theta}^{4} r^{5} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-8a^{4} \\\\cos{\\\\theta}^{4} r^{4} r_s^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+24a^{6} \\\\cos{\\\\theta}^{4} r^{3} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+44a^{6} \\\\cos{\\\\theta}^{2} r^{7} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-20a^{6} \\\\cos{\\\\theta}^{2} r^{6} r_s^{3} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+12a^{8} \\\\cos{\\\\theta}^{2} r^{5} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+44a^{6} \\\\cos{\\\\theta}^{2} r^{7} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-20a^{6} \\\\cos{\\\\theta}^{2} r^{6} r_s^{3} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+12a^{8} \\\\cos{\\\\theta}^{2} r^{5} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+56a^{8} \\\\cos{\\\\theta}^{4} r^{5} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+8a^{10} \\\\cos{\\\\theta}^{4} r^{3} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+56a^{8} \\\\cos{\\\\theta}^{4} r^{5} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+8a^{10} \\\\cos{\\\\theta}^{4} r^{3} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-8a^{4} \\\\cos{\\\\theta}^{2} r^{9} r_s^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-8a^{4} \\\\cos{\\\\theta}^{2} r^{8} r_s^{3} \\\\partial_{r}\\\\left(r^{2}\\\\right)+8a^{6} \\\\cos{\\\\theta}^{2} r^{7} r_s^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-8a^{4} \\\\cos{\\\\theta}^{2} r^{9} r_s^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-8a^{4} \\\\cos{\\\\theta}^{2} r^{8} r_s^{3} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+8a^{6} \\\\cos{\\\\theta}^{2} r^{7} r_s^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)%\\n-40a^{6} \\\\cos{\\\\theta}^{4} r^{7} r_s^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+16a^{8} \\\\cos{\\\\theta}^{4} r^{5} r_s^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-40a^{6} \\\\cos{\\\\theta}^{4} r^{7} r_s^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+16a^{8} \\\\cos{\\\\theta}^{4} r^{5} r_s^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-40a^{4} \\\\cos{\\\\theta}^{2} r^{6} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+24a^{4} \\\\cos{\\\\theta}^{2} r^{5} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-16a^{6} \\\\cos{\\\\theta}^{2} r^{4} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-40a^{4} \\\\cos{\\\\theta}^{2} r^{6} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+24a^{4} \\\\cos{\\\\theta}^{2} r^{5} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-16a^{6} \\\\cos{\\\\theta}^{2} r^{4} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+12a^{10} \\\\cos{\\\\theta}^{6} r^{3} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-4a^{12} \\\\cos{\\\\theta}^{6} r r_s^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+12a^{10} \\\\cos{\\\\theta}^{6} r^{3} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-4a^{12} \\\\cos{\\\\theta}^{6} r r_s^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-56a^{8} \\\\cos{\\\\theta}^{6} r^{5} r_s^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+8a^{10} \\\\cos{\\\\theta}^{6} r^{3} r_s^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-56a^{8} \\\\cos{\\\\theta}^{6} r^{5} r_s^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+8a^{10} \\\\cos{\\\\theta}^{6} r^{3} r_s^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-48a^{6} \\\\cos{\\\\theta}^{4} r^{4} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-16a^{8} \\\\cos{\\\\theta}^{4} r^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)%\\n-48a^{6} \\\\cos{\\\\theta}^{4} r^{4} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-16a^{8} \\\\cos{\\\\theta}^{4} r^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-28a^{4} \\\\cos{\\\\theta}^{2} r^{8} r_s^{3} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+8a^{4} \\\\cos{\\\\theta}^{2} r^{7} r_s^{4} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-28a^{4} \\\\cos{\\\\theta}^{2} r^{8} r_s^{3} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+8a^{4} \\\\cos{\\\\theta}^{2} r^{7} r_s^{4} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+8a^{2} \\\\cos{\\\\theta}^{2} r^{10} r_s^{3} \\\\partial_{r}\\\\left(r^{2}\\\\right)+8a^{2} \\\\cos{\\\\theta}^{2} r^{10} r_s^{3} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+32a^{2} \\\\cos{\\\\theta}^{2} r^{7} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-8a^{2} \\\\cos{\\\\theta}^{2} r^{6} r_s^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+32a^{2} \\\\cos{\\\\theta}^{2} r^{7} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-8a^{2} \\\\cos{\\\\theta}^{2} r^{6} r_s^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+32a^{4} \\\\cos{\\\\theta}^{2} r^{9} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+32a^{4} \\\\cos{\\\\theta}^{2} r^{9} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+48a^{6} \\\\cos{\\\\theta}^{4} r^{7} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+48a^{6} \\\\cos{\\\\theta}^{4} r^{7} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-32a^{2} \\\\cos{\\\\theta}^{2} r^{11} r_s^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-32a^{2} \\\\cos{\\\\theta}^{2} r^{11} r_s^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-120a^{4} \\\\cos{\\\\theta}^{4} r^{9} r_s^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-120a^{4} \\\\cos{\\\\theta}^{4} r^{9} r_s^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)%\\n-24a^{2} \\\\cos{\\\\theta}^{2} r^{8} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-24a^{2} \\\\cos{\\\\theta}^{2} r^{8} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+16a^{8} \\\\cos{\\\\theta}^{6} r^{5} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+16a^{8} \\\\cos{\\\\theta}^{6} r^{5} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-160a^{6} \\\\cos{\\\\theta}^{6} r^{7} r_s^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-160a^{6} \\\\cos{\\\\theta}^{6} r^{7} r_s^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-32a^{4} \\\\cos{\\\\theta}^{4} r^{6} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-32a^{4} \\\\cos{\\\\theta}^{4} r^{6} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-88a^{8} \\\\cos{\\\\theta}^{8} r^{5} r_s^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+16a^{8} \\\\cos{\\\\theta}^{8} r^{4} r_s^{3} \\\\partial_{r}\\\\left(r^{2}\\\\right)-24a^{10} \\\\cos{\\\\theta}^{8} r^{3} r_s^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-88a^{8} \\\\cos{\\\\theta}^{8} r^{5} r_s^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+16a^{8} \\\\cos{\\\\theta}^{8} r^{4} r_s^{3} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-24a^{10} \\\\cos{\\\\theta}^{8} r^{3} r_s^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+32a^{4} \\\\cos{\\\\theta}^{2} r^{10} r_s \\\\partial_{r}\\\\left(r^{2}\\\\right)+8a^{6} \\\\cos{\\\\theta}^{2} r^{8} r_s \\\\partial_{r}\\\\left(r^{2}\\\\right)+112a^{6} \\\\cos{\\\\theta}^{4} r^{8} r_s \\\\partial_{r}\\\\left(r^{2}\\\\right)+24a^{8} \\\\cos{\\\\theta}^{4} r^{6} r_s \\\\partial_{r}\\\\left(r^{2}\\\\right)+32a^{4} \\\\cos{\\\\theta}^{2} r^{10} r_s \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+8a^{6} \\\\cos{\\\\theta}^{2} r^{8} r_s \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)%\\n+112a^{6} \\\\cos{\\\\theta}^{4} r^{8} r_s \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+24a^{8} \\\\cos{\\\\theta}^{4} r^{6} r_s \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+144a^{8} \\\\cos{\\\\theta}^{6} r^{6} r_s \\\\partial_{r}\\\\left(r^{2}\\\\right)+24a^{10} \\\\cos{\\\\theta}^{6} r^{4} r_s \\\\partial_{r}\\\\left(r^{2}\\\\right)+144a^{8} \\\\cos{\\\\theta}^{6} r^{6} r_s \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+24a^{10} \\\\cos{\\\\theta}^{6} r^{4} r_s \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+80a^{10} \\\\cos{\\\\theta}^{8} r^{4} r_s \\\\partial_{r}\\\\left(r^{2}\\\\right)+8a^{12} \\\\cos{\\\\theta}^{8} r^{2} r_s \\\\partial_{r}\\\\left(r^{2}\\\\right)+80a^{10} \\\\cos{\\\\theta}^{8} r^{4} r_s \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+8a^{12} \\\\cos{\\\\theta}^{8} r^{2} r_s \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-18a^{4} \\\\cos{\\\\theta}^{2} r^{10} r_s^{2} \\\\sin{\\\\theta}^{2}+12a^{2} \\\\cos{\\\\theta}^{2} r^{12} r_s^{2}+24a^{2} \\\\cos{\\\\theta}^{2} r^{12} r_s \\\\partial_{r}\\\\left(r^{2}\\\\right)+88a^{4} \\\\cos{\\\\theta}^{4} r^{10} r_s \\\\partial_{r}\\\\left(r^{2}\\\\right)+24a^{2} \\\\cos{\\\\theta}^{2} r^{12} r_s \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+88a^{4} \\\\cos{\\\\theta}^{4} r^{10} r_s \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+120a^{6} \\\\cos{\\\\theta}^{6} r^{8} r_s \\\\partial_{r}\\\\left(r^{2}\\\\right)+120a^{6} \\\\cos{\\\\theta}^{6} r^{8} r_s \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-4a^{2} \\\\cos{\\\\theta}^{2} r^{9} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+72a^{8} \\\\cos{\\\\theta}^{8} r^{6} r_s \\\\partial_{r}\\\\left(r^{2}\\\\right)%\\n+72a^{8} \\\\cos{\\\\theta}^{8} r^{6} r_s \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+8a^{10} \\\\cos{\\\\theta}^{4} r^{5} r_s \\\\sin{\\\\theta}^{4}+16a^{12} \\\\cos{\\\\theta}^{6} r^{3} r_s \\\\sin{\\\\theta}^{4}+8a^{8} \\\\cos{\\\\theta}^{4} r^{7} r_s \\\\sin{\\\\theta}^{4}+16a^{10} \\\\cos{\\\\theta}^{6} r^{5} r_s \\\\sin{\\\\theta}^{4}+88a^{8} \\\\cos{\\\\theta}^{4} r^{7} r_s \\\\sin{\\\\theta}^{2}+128a^{10} \\\\cos{\\\\theta}^{6} r^{5} r_s \\\\sin{\\\\theta}^{2}+44a^{6} \\\\cos{\\\\theta}^{4} r^{9} r_s \\\\sin{\\\\theta}^{2}+76a^{8} \\\\cos{\\\\theta}^{6} r^{7} r_s \\\\sin{\\\\theta}^{2}+72a^{12} \\\\cos{\\\\theta}^{8} r^{3} r_s \\\\sin{\\\\theta}^{2}+52a^{10} \\\\cos{\\\\theta}^{8} r^{5} r_s \\\\sin{\\\\theta}^{2}+32a^{8} \\\\cos{\\\\theta}^{4} r^{7} r_s+48a^{10} \\\\cos{\\\\theta}^{6} r^{5} r_s+32a^{6} \\\\cos{\\\\theta}^{4} r^{9} r_s+48a^{8} \\\\cos{\\\\theta}^{6} r^{7} r_s+32a^{12} \\\\cos{\\\\theta}^{8} r^{3} r_s+32a^{10} \\\\cos{\\\\theta}^{8} r^{5} r_s-40a^{8} \\\\cos{\\\\theta}^{6} r^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s-56a^{6} \\\\cos{\\\\theta}^{4} r^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s+24a^{6} \\\\cos{\\\\theta}^{4} r^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}%\\n+24a^{8} \\\\cos{\\\\theta}^{6} r^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-64a^{6} \\\\cos{\\\\theta}^{6} r^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s-80a^{4} \\\\cos{\\\\theta}^{4} r^{7} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s+24a^{4} \\\\cos{\\\\theta}^{4} r^{8} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+24a^{6} \\\\cos{\\\\theta}^{6} r^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+12a^{8} \\\\cos{\\\\theta}^{2} r^{7} r_s \\\\sin{\\\\theta}^{2}+44a^{10} \\\\cos{\\\\theta}^{4} r^{5} r_s \\\\sin{\\\\theta}^{2}+20a^{6} \\\\cos{\\\\theta}^{2} r^{9} r_s \\\\sin{\\\\theta}^{2}+52a^{12} \\\\cos{\\\\theta}^{6} r^{3} r_s \\\\sin{\\\\theta}^{2}+8a^{6} \\\\cos{\\\\theta}^{2} r^{9} r_s+8a^{4} \\\\cos{\\\\theta}^{2} r^{11} r_s-24a^{4} \\\\cos{\\\\theta}^{2} r^{7} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s+8a^{4} \\\\cos{\\\\theta}^{2} r^{8} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-24a^{6} \\\\cos{\\\\theta}^{2} r^{8} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-12a^{8} \\\\cos{\\\\theta}^{2} r^{6} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-24a^{6} \\\\cos{\\\\theta}^{2} r^{8} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-12a^{8} \\\\cos{\\\\theta}^{2} r^{6} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-48a^{8} \\\\cos{\\\\theta}^{4} r^{6} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-24a^{10} \\\\cos{\\\\theta}^{4} r^{4} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-48a^{8} \\\\cos{\\\\theta}^{4} r^{6} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)%\\n-24a^{10} \\\\cos{\\\\theta}^{4} r^{4} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+32a^{4} \\\\cos{\\\\theta}^{2} r^{7} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-16a^{4} \\\\cos{\\\\theta}^{2} r^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) r_s+16a^{6} \\\\cos{\\\\theta}^{2} r^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+32a^{4} \\\\cos{\\\\theta}^{2} r^{7} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-16a^{4} \\\\cos{\\\\theta}^{2} r^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s+16a^{6} \\\\cos{\\\\theta}^{2} r^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-24a^{10} \\\\cos{\\\\theta}^{6} r^{4} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-12a^{12} \\\\cos{\\\\theta}^{6} r^{2} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-24a^{10} \\\\cos{\\\\theta}^{6} r^{4} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-12a^{12} \\\\cos{\\\\theta}^{6} r^{2} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+64a^{6} \\\\cos{\\\\theta}^{4} r^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-32a^{6} \\\\cos{\\\\theta}^{4} r^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) r_s+32a^{8} \\\\cos{\\\\theta}^{4} r^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+64a^{6} \\\\cos{\\\\theta}^{4} r^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-32a^{6} \\\\cos{\\\\theta}^{4} r^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s+32a^{8} \\\\cos{\\\\theta}^{4} r^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-12a^{4} \\\\cos{\\\\theta}^{2} r^{10} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-12a^{4} \\\\cos{\\\\theta}^{2} r^{10} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-24a^{6} \\\\cos{\\\\theta}^{4} r^{8} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)%\\n-24a^{6} \\\\cos{\\\\theta}^{4} r^{8} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+16a^{2} \\\\cos{\\\\theta}^{2} r^{9} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-16a^{2} \\\\cos{\\\\theta}^{2} r^{8} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) r_s+16a^{2} \\\\cos{\\\\theta}^{2} r^{9} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-16a^{2} \\\\cos{\\\\theta}^{2} r^{8} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s-12a^{8} \\\\cos{\\\\theta}^{6} r^{6} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-12a^{8} \\\\cos{\\\\theta}^{6} r^{6} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+32a^{4} \\\\cos{\\\\theta}^{4} r^{7} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-32a^{4} \\\\cos{\\\\theta}^{4} r^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) r_s+32a^{4} \\\\cos{\\\\theta}^{4} r^{7} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-32a^{4} \\\\cos{\\\\theta}^{4} r^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s-32a^{4} \\\\cos{\\\\theta}^{2} r^{11} \\\\partial_{r}\\\\left(r^{2}\\\\right)+16a^{4} \\\\cos{\\\\theta}^{2} r^{10} \\\\partial_{r}\\\\left(r^{2}\\\\right) r_s-16a^{6} \\\\cos{\\\\theta}^{2} r^{9} \\\\partial_{r}\\\\left(r^{2}\\\\right)-128a^{6} \\\\cos{\\\\theta}^{4} r^{9} \\\\partial_{r}\\\\left(r^{2}\\\\right)+64a^{6} \\\\cos{\\\\theta}^{4} r^{8} \\\\partial_{r}\\\\left(r^{2}\\\\right) r_s-64a^{8} \\\\cos{\\\\theta}^{4} r^{7} \\\\partial_{r}\\\\left(r^{2}\\\\right)-32a^{4} \\\\cos{\\\\theta}^{2} r^{11} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+16a^{4} \\\\cos{\\\\theta}^{2} r^{10} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s-16a^{6} \\\\cos{\\\\theta}^{2} r^{9} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)%\\n-128a^{6} \\\\cos{\\\\theta}^{4} r^{9} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+64a^{6} \\\\cos{\\\\theta}^{4} r^{8} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s-64a^{8} \\\\cos{\\\\theta}^{4} r^{7} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-192a^{8} \\\\cos{\\\\theta}^{6} r^{7} \\\\partial_{r}\\\\left(r^{2}\\\\right)+96a^{8} \\\\cos{\\\\theta}^{6} r^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right) r_s-96a^{10} \\\\cos{\\\\theta}^{6} r^{5} \\\\partial_{r}\\\\left(r^{2}\\\\right)-192a^{8} \\\\cos{\\\\theta}^{6} r^{7} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+96a^{8} \\\\cos{\\\\theta}^{6} r^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s-96a^{10} \\\\cos{\\\\theta}^{6} r^{5} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-128a^{10} \\\\cos{\\\\theta}^{8} r^{5} \\\\partial_{r}\\\\left(r^{2}\\\\right)+64a^{10} \\\\cos{\\\\theta}^{8} r^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right) r_s-64a^{12} \\\\cos{\\\\theta}^{8} r^{3} \\\\partial_{r}\\\\left(r^{2}\\\\right)-128a^{10} \\\\cos{\\\\theta}^{8} r^{5} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+64a^{10} \\\\cos{\\\\theta}^{8} r^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s-64a^{12} \\\\cos{\\\\theta}^{8} r^{3} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+8a^{4} \\\\cos{\\\\theta}^{2} r^{11} r_s \\\\sin{\\\\theta}^{2}-16a^{2} \\\\cos{\\\\theta}^{2} r^{13} \\\\partial_{r}\\\\left(r^{2}\\\\right)+16a^{2} \\\\cos{\\\\theta}^{2} r^{12} \\\\partial_{r}\\\\left(r^{2}\\\\right) r_s-64a^{4} \\\\cos{\\\\theta}^{4} r^{11} \\\\partial_{r}\\\\left(r^{2}\\\\right)+64a^{4} \\\\cos{\\\\theta}^{4} r^{10} \\\\partial_{r}\\\\left(r^{2}\\\\right) r_s%\\n-16a^{2} \\\\cos{\\\\theta}^{2} r^{13} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+16a^{2} \\\\cos{\\\\theta}^{2} r^{12} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s-64a^{4} \\\\cos{\\\\theta}^{4} r^{11} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+64a^{4} \\\\cos{\\\\theta}^{4} r^{10} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s-96a^{6} \\\\cos{\\\\theta}^{6} r^{9} \\\\partial_{r}\\\\left(r^{2}\\\\right)+96a^{6} \\\\cos{\\\\theta}^{6} r^{8} \\\\partial_{r}\\\\left(r^{2}\\\\right) r_s-96a^{6} \\\\cos{\\\\theta}^{6} r^{9} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+96a^{6} \\\\cos{\\\\theta}^{6} r^{8} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s+8a^{2} \\\\cos{\\\\theta}^{2} r^{10} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-32a^{2} \\\\cos{\\\\theta}^{2} r^{9} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s-64a^{8} \\\\cos{\\\\theta}^{8} r^{7} \\\\partial_{r}\\\\left(r^{2}\\\\right)+64a^{8} \\\\cos{\\\\theta}^{8} r^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right) r_s-64a^{8} \\\\cos{\\\\theta}^{8} r^{7} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+64a^{8} \\\\cos{\\\\theta}^{8} r^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s+56a^{4} \\\\cos{\\\\theta}^{4} r^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s^{2}+40a^{6} \\\\cos{\\\\theta}^{6} r^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s^{2}+24a^{2} \\\\cos{\\\\theta}^{2} r^{8} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s^{2}-8a^{12} \\\\cos{\\\\theta}^{8} r^{2} r_s^{2} \\\\sin{\\\\theta}^{4}+8a^{14} \\\\cos{\\\\theta}^{8} r r_s \\\\sin{\\\\theta}^{4}+8a^{12} \\\\cos{\\\\theta}^{8} r^{3} r_s \\\\sin{\\\\theta}^{4}%\\n-12a^{12} \\\\cos{\\\\theta}^{10} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+12a^{14} \\\\cos{\\\\theta}^{10} r r_s \\\\sin{\\\\theta}^{2}+12a^{12} \\\\cos{\\\\theta}^{10} r^{3} r_s \\\\sin{\\\\theta}^{2}-16a^{12} \\\\cos{\\\\theta}^{10} r^{2} r_s^{2}+8a^{14} \\\\cos{\\\\theta}^{10} r r_s+8a^{12} \\\\cos{\\\\theta}^{10} r^{3} r_s-8a^{10} \\\\cos{\\\\theta}^{8} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r r_s-8a^{10} \\\\cos{\\\\theta}^{10} r^{4} r_s^{2}-16a^{8} \\\\cos{\\\\theta}^{8} r^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s+8a^{10} \\\\cos{\\\\theta}^{8} r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+8a^{8} \\\\cos{\\\\theta}^{8} r^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+20a^{14} \\\\cos{\\\\theta}^{8} r r_s \\\\sin{\\\\theta}^{2}+24a^{8} \\\\cos{\\\\theta}^{6} r_s^{3} r^{5} \\\\sin{\\\\theta}^{2}-14a^{8} \\\\cos{\\\\theta}^{4} r_s^{2} r^{6} \\\\sin{\\\\theta}^{2}-26a^{10} \\\\cos{\\\\theta}^{6} r_s^{2} r^{4} \\\\sin{\\\\theta}^{2}+18a^{6} \\\\cos{\\\\theta}^{4} r_s^{3} r^{7} \\\\sin{\\\\theta}^{2}-22a^{6} \\\\cos{\\\\theta}^{4} r_s^{2} r^{8} \\\\sin{\\\\theta}^{2}-38a^{8} \\\\cos{\\\\theta}^{6} r_s^{2} r^{6} \\\\sin{\\\\theta}^{2}+4a^{10} \\\\cos{\\\\theta}^{8} r_s^{3} r^{3} \\\\sin{\\\\theta}^{2}-4a^{12} \\\\cos{\\\\theta}^{8} r_s^{2} r^{2} \\\\sin{\\\\theta}^{2}%\\n-12a^{10} \\\\cos{\\\\theta}^{8} r_s^{2} r^{4} \\\\sin{\\\\theta}^{2}+12a^{6} \\\\cos{\\\\theta}^{6} r_s^{3} r^{7}-4a^{6} \\\\cos{\\\\theta}^{4} r_s^{2} r^{8}-12a^{8} \\\\cos{\\\\theta}^{6} r_s^{2} r^{6}+4a^{4} \\\\cos{\\\\theta}^{4} r_s^{3} r^{9}-4a^{4} \\\\cos{\\\\theta}^{4} r_s^{2} r^{10}-12a^{6} \\\\cos{\\\\theta}^{6} r_s^{2} r^{8}+12a^{8} \\\\cos{\\\\theta}^{8} r_s^{3} r^{5}-12a^{10} \\\\cos{\\\\theta}^{8} r_s^{2} r^{4}-12a^{8} \\\\cos{\\\\theta}^{8} r_s^{2} r^{6}-8a^{6} \\\\cos{\\\\theta}^{6} r_s^{2} r^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+4a^{6} \\\\cos{\\\\theta}^{4} r_s r^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+8a^{8} \\\\cos{\\\\theta}^{6} r_s r^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-4a^{4} \\\\cos{\\\\theta}^{4} r_s^{2} r^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+4a^{4} \\\\cos{\\\\theta}^{4} r_s r^{7} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+8a^{6} \\\\cos{\\\\theta}^{6} r_s r^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+2a^{12} \\\\cos{\\\\theta}^{10} r_s^{3} \\\\sin{\\\\theta}^{2} r-14a^{12} \\\\cos{\\\\theta}^{8} r_s^{2} \\\\sin{\\\\theta}^{2} r^{2}-2a^{14} \\\\cos{\\\\theta}^{10} r_s^{2} \\\\sin{\\\\theta}^{2}+14a^{10} \\\\cos{\\\\theta}^{8} r_s^{3} \\\\sin{\\\\theta}^{2} r^{3}%\\n-30a^{10} \\\\cos{\\\\theta}^{8} r_s^{2} \\\\sin{\\\\theta}^{2} r^{4}-10a^{12} \\\\cos{\\\\theta}^{10} r_s^{2} \\\\sin{\\\\theta}^{2} r^{2}+4a^{10} \\\\cos{\\\\theta}^{10} r_s^{3} r^{3}-4a^{12} \\\\cos{\\\\theta}^{10} r_s^{2} r^{2}-4a^{10} \\\\cos{\\\\theta}^{10} r_s^{2} r^{4}-4a^{8} \\\\cos{\\\\theta}^{8} r_s^{2} r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+4a^{10} \\\\cos{\\\\theta}^{8} r_s r \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+4a^{8} \\\\cos{\\\\theta}^{8} r_s r^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-8a^{6} \\\\cos{\\\\theta}^{6} r^{4} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+8a^{6} \\\\cos{\\\\theta}^{6} r^{3} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-8a^{8} \\\\cos{\\\\theta}^{6} r^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-8a^{6} \\\\cos{\\\\theta}^{6} r^{4} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+8a^{6} \\\\cos{\\\\theta}^{6} r^{3} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-8a^{8} \\\\cos{\\\\theta}^{6} r^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+12a^{10} \\\\cos{\\\\theta}^{6} r_s r^{4} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-8a^{10} \\\\cos{\\\\theta}^{6} r_s^{2} r^{3} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+8a^{12} \\\\cos{\\\\theta}^{6} r_s r^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+12a^{10} \\\\cos{\\\\theta}^{6} r_s r^{4} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-8a^{10} \\\\cos{\\\\theta}^{6} r_s^{2} r^{3} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+8a^{12} \\\\cos{\\\\theta}^{6} r_s r^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)%\\n+4a^{12} \\\\cos{\\\\theta}^{8} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) r^{2}-4a^{12} \\\\cos{\\\\theta}^{8} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) r+4a^{14} \\\\cos{\\\\theta}^{8} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+4a^{12} \\\\cos{\\\\theta}^{8} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r^{2}-4a^{12} \\\\cos{\\\\theta}^{8} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r+4a^{14} \\\\cos{\\\\theta}^{8} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+32a^{8} \\\\cos{\\\\theta}^{6} r^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-16a^{8} \\\\cos{\\\\theta}^{6} r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) r_s+16a^{10} \\\\cos{\\\\theta}^{6} r \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+32a^{8} \\\\cos{\\\\theta}^{6} r^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-16a^{8} \\\\cos{\\\\theta}^{6} r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s+16a^{10} \\\\cos{\\\\theta}^{6} r \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+16a^{6} \\\\cos{\\\\theta}^{6} r^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-16a^{6} \\\\cos{\\\\theta}^{6} r^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) r_s+16a^{6} \\\\cos{\\\\theta}^{6} r^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-16a^{6} \\\\cos{\\\\theta}^{6} r^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s+8a^{10} \\\\cos{\\\\theta}^{10} r^{3} r_s^{3}+16a^{10} \\\\cos{\\\\theta}^{10} r^{4} r_s \\\\partial_{r}\\\\left(r^{2}\\\\right)-16a^{10} \\\\cos{\\\\theta}^{10} r^{3} r_s^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+16a^{12} \\\\cos{\\\\theta}^{10} r^{2} r_s \\\\partial_{r}\\\\left(r^{2}\\\\right)%\\n+16a^{10} \\\\cos{\\\\theta}^{10} r^{4} r_s \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-16a^{10} \\\\cos{\\\\theta}^{10} r^{3} r_s^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+16a^{12} \\\\cos{\\\\theta}^{10} r^{2} r_s \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+8a^{8} \\\\cos{\\\\theta}^{8} r^{3} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-8a^{8} \\\\cos{\\\\theta}^{8} r^{2} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+8a^{10} \\\\cos{\\\\theta}^{8} r r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-32a^{12} \\\\cos{\\\\theta}^{10} r^{3} \\\\partial_{r}\\\\left(r^{2}\\\\right)+16a^{12} \\\\cos{\\\\theta}^{10} r^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) r_s-16a^{14} \\\\cos{\\\\theta}^{10} r \\\\partial_{r}\\\\left(r^{2}\\\\right)-32a^{12} \\\\cos{\\\\theta}^{10} r^{3} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+16a^{12} \\\\cos{\\\\theta}^{10} r^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s-16a^{14} \\\\cos{\\\\theta}^{10} r \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+8a^{10} \\\\cos{\\\\theta}^{8} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s r-16a^{10} \\\\cos{\\\\theta}^{10} r^{5} \\\\partial_{r}\\\\left(r^{2}\\\\right)+16a^{10} \\\\cos{\\\\theta}^{10} r^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right) r_s-16a^{10} \\\\cos{\\\\theta}^{10} r^{5} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+16a^{10} \\\\cos{\\\\theta}^{10} r^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s+8a^{8} \\\\cos{\\\\theta}^{4} r_s r^{6} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-4a^{8} \\\\cos{\\\\theta}^{4} r_s^{2} r^{5} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+4a^{10} \\\\cos{\\\\theta}^{4} r_s r^{4} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)%\\n+8a^{8} \\\\cos{\\\\theta}^{4} r_s r^{6} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-4a^{8} \\\\cos{\\\\theta}^{4} r_s^{2} r^{5} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+4a^{10} \\\\cos{\\\\theta}^{4} r_s r^{4} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+4a^{6} \\\\cos{\\\\theta}^{4} r_s r^{8} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-4a^{6} \\\\cos{\\\\theta}^{4} r_s^{2} r^{7} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+4a^{8} \\\\cos{\\\\theta}^{6} r_s r^{6} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)-4a^{8} \\\\cos{\\\\theta}^{6} r_s^{2} r^{5} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+4a^{6} \\\\cos{\\\\theta}^{4} r_s r^{8} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-4a^{6} \\\\cos{\\\\theta}^{4} r_s^{2} r^{7} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+4a^{8} \\\\cos{\\\\theta}^{6} r_s r^{6} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-4a^{8} \\\\cos{\\\\theta}^{6} r_s^{2} r^{5} \\\\sin{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+8a^{6} \\\\cos{\\\\theta}^{4} r_s r^{9} \\\\sin{\\\\theta}^{2}+8a^{8} \\\\cos{\\\\theta}^{4} r_s r^{7} \\\\sin{\\\\theta}^{2}+16a^{8} \\\\cos{\\\\theta}^{6} r_s r^{7} \\\\sin{\\\\theta}^{2}+16a^{10} \\\\cos{\\\\theta}^{6} r_s r^{5} \\\\sin{\\\\theta}^{2}+8a^{10} \\\\cos{\\\\theta}^{8} r_s r^{5} \\\\sin{\\\\theta}^{2}+8a^{12} \\\\cos{\\\\theta}^{8} r_s r^{3} \\\\sin{\\\\theta}^{2}-20a^{8} \\\\cos{\\\\theta}^{6} r_s^{2} \\\\sin{\\\\theta}^{2} r^{6}+12a^{8} \\\\cos{\\\\theta}^{6} r_s^{3} \\\\sin{\\\\theta}^{2} r^{5}-12a^{10} \\\\cos{\\\\theta}^{6} r_s^{2} \\\\sin{\\\\theta}^{2} r^{4}%\\n+4a^{8} \\\\cos{\\\\theta}^{6} r_s \\\\sin{\\\\theta}^{2} r^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right)-4a^{8} \\\\cos{\\\\theta}^{6} r_s^{2} \\\\sin{\\\\theta}^{2} r^{5} \\\\partial_{r}\\\\left(r^{2}\\\\right)+4a^{10} \\\\cos{\\\\theta}^{6} r_s \\\\sin{\\\\theta}^{2} r^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)+4a^{10} \\\\cos{\\\\theta}^{8} r_s \\\\sin{\\\\theta}^{2} r^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)-4a^{10} \\\\cos{\\\\theta}^{8} r_s^{2} \\\\sin{\\\\theta}^{2} r^{3} \\\\partial_{r}\\\\left(r^{2}\\\\right)+4a^{12} \\\\cos{\\\\theta}^{8} r_s \\\\sin{\\\\theta}^{2} r^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right)+4a^{8} \\\\cos{\\\\theta}^{6} r_s \\\\sin{\\\\theta}^{2} r^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-4a^{8} \\\\cos{\\\\theta}^{6} r_s^{2} \\\\sin{\\\\theta}^{2} r^{5} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+4a^{10} \\\\cos{\\\\theta}^{6} r_s \\\\sin{\\\\theta}^{2} r^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+4a^{10} \\\\cos{\\\\theta}^{8} r_s \\\\sin{\\\\theta}^{2} r^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-4a^{10} \\\\cos{\\\\theta}^{8} r_s^{2} \\\\sin{\\\\theta}^{2} r^{3} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+4a^{12} \\\\cos{\\\\theta}^{8} r_s \\\\sin{\\\\theta}^{2} r^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+8a^{8} \\\\cos{\\\\theta}^{6} r_s \\\\sin{\\\\theta}^{2} r^{7}+8a^{10} \\\\cos{\\\\theta}^{6} r_s \\\\sin{\\\\theta}^{2} r^{5}+16a^{10} \\\\cos{\\\\theta}^{8} r_s \\\\sin{\\\\theta}^{2} r^{5}+16a^{12} \\\\cos{\\\\theta}^{8} r_s \\\\sin{\\\\theta}^{2} r^{3}+8a^{12} \\\\cos{\\\\theta}^{10} r_s \\\\sin{\\\\theta}^{2} r^{3}+8a^{14} \\\\cos{\\\\theta}^{10} r_s \\\\sin{\\\\theta}^{2} r+8a^{8} \\\\cos{\\\\theta}^{8} r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s^{2}-8a^{10} \\\\cos{\\\\theta}^{8} r \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s%\\n-12a^{6} \\\\cos{\\\\theta}^{2} r_s^{3} r^{7} \\\\sin{\\\\theta}^{2}+2a^{6} \\\\cos{\\\\theta}^{2} r_s^{4} r^{6} \\\\sin{\\\\theta}^{2}-2a^{8} \\\\cos{\\\\theta}^{2} r_s^{3} r^{5} \\\\sin{\\\\theta}^{2}+8a^{6} \\\\cos{\\\\theta}^{2} r_s^{2} r^{8} \\\\sin{\\\\theta}^{2}+4a^{8} \\\\cos{\\\\theta}^{2} r_s^{2} r^{6} \\\\sin{\\\\theta}^{2}+8a^{8} \\\\cos{\\\\theta}^{4} r_s^{3} r^{5} \\\\sin{\\\\theta}^{2}-4a^{8} \\\\cos{\\\\theta}^{4} r_s^{4} r^{4} \\\\sin{\\\\theta}^{2}+4a^{10} \\\\cos{\\\\theta}^{4} r_s^{3} r^{3} \\\\sin{\\\\theta}^{2}+2a^{6} \\\\cos{\\\\theta}^{2} r_s^{3} r^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-2a^{8} \\\\cos{\\\\theta}^{2} r_s^{2} r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-10a^{4} \\\\cos{\\\\theta}^{2} r_s^{3} r^{9} \\\\sin{\\\\theta}^{2}+6a^{4} \\\\cos{\\\\theta}^{2} r_s^{4} r^{8} \\\\sin{\\\\theta}^{2}+4a^{4} \\\\cos{\\\\theta}^{2} r_s^{2} r^{10} \\\\sin{\\\\theta}^{2}-4a^{6} \\\\cos{\\\\theta}^{4} r_s^{4} r^{6} \\\\sin{\\\\theta}^{2}+2a^{4} \\\\cos{\\\\theta}^{2} r_s^{2} r^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-2a^{4} \\\\cos{\\\\theta}^{2} r_s^{3} r^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+4a^{10} \\\\cos{\\\\theta}^{6} r_s^{3} r^{3} \\\\sin{\\\\theta}^{2}-4a^{12} \\\\cos{\\\\theta}^{6} r_s^{2} r^{2} \\\\sin{\\\\theta}^{2}+2a^{10} \\\\cos{\\\\theta}^{6} r_s^{4} r^{2} \\\\sin{\\\\theta}^{2}-2a^{12} \\\\cos{\\\\theta}^{6} r_s^{3} r \\\\sin{\\\\theta}^{2}%\\n+2a^{8} \\\\cos{\\\\theta}^{4} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2} r^{2}-2a^{8} \\\\cos{\\\\theta}^{4} r_s^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2} r+2a^{10} \\\\cos{\\\\theta}^{4} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-2a^{8} \\\\cos{\\\\theta}^{6} r_s^{4} r^{4} \\\\sin{\\\\theta}^{2}-2a^{6} \\\\cos{\\\\theta}^{4} r_s^{2} r^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+2a^{6} \\\\cos{\\\\theta}^{4} r_s^{3} r^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-2a^{8} \\\\cos{\\\\theta}^{4} r_s^{2} r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+2a^{2} \\\\cos{\\\\theta}^{2} r^{3} r_s \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s r^{2} \\\\sin{\\\\theta}^{2}-a^{4} r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+2r^{4} r_s+2r^{2} r_s a^{2} \\\\cos{\\\\theta}^{2}-2r \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}\\\\right)^{2}-2a^{2} \\\\cos{\\\\theta}^{2} r^{2} r_s^{2} \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s r^{2} \\\\sin{\\\\theta}^{2}-a^{4} r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+2r^{4} r_s+2r^{2} r_s a^{2} \\\\cos{\\\\theta}^{2}-2r \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}\\\\right)^{2}+2a^{4} \\\\cos{\\\\theta}^{2} r r_s \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s r^{2} \\\\sin{\\\\theta}^{2}-a^{4} r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+2r^{4} r_s+2r^{2} r_s a^{2} \\\\cos{\\\\theta}^{2}-2r \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}\\\\right)^{2}-2a^{2} \\\\cos{\\\\theta}^{2} r^{4} \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s r^{2} \\\\sin{\\\\theta}^{2}-a^{4} r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+2r^{4} r_s+2r^{2} r_s a^{2} \\\\cos{\\\\theta}^{2}-2r \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}\\\\right)^{2}+2a^{2} \\\\cos{\\\\theta}^{2} r^{3} \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s r^{2} \\\\sin{\\\\theta}^{2}-a^{4} r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+2r^{4} r_s+2r^{2} r_s a^{2} \\\\cos{\\\\theta}^{2}-2r \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}\\\\right)^{2} r_s-2a^{4} \\\\cos{\\\\theta}^{2} r^{2} \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s r^{2} \\\\sin{\\\\theta}^{2}-a^{4} r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+2r^{4} r_s+2r^{2} r_s a^{2} \\\\cos{\\\\theta}^{2}-2r \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}\\\\right)^{2}-2a^{4} \\\\cos{\\\\theta}^{4} \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s r^{2} \\\\sin{\\\\theta}^{2}-a^{4} r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+2r^{4} r_s+2r^{2} r_s a^{2} \\\\cos{\\\\theta}^{2}-2r \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}\\\\right)^{2} r^{2}+2a^{4} \\\\cos{\\\\theta}^{4} \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s r^{2} \\\\sin{\\\\theta}^{2}-a^{4} r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+2r^{4} r_s+2r^{2} r_s a^{2} \\\\cos{\\\\theta}^{2}-2r \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}\\\\right)^{2} r_s r-2a^{6} \\\\cos{\\\\theta}^{4} \\\\left(2a^{2} r^{2} r_s \\\\sin{\\\\theta}^{2}-a^{2} r_s r^{2} \\\\sin{\\\\theta}^{2}-a^{4} r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+2r^{4} r_s+2r^{2} r_s a^{2} \\\\cos{\\\\theta}^{2}-2r \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}\\\\right)^{2}}{8\\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} r^{2}-a^{4} \\\\cos{\\\\theta}^{2}+r^{3} r_s-r^{4}-r^{2} a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-8\\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} r^{2}-a^{4} \\\\cos{\\\\theta}^{2}+r^{3} r_s-r^{4}-r^{2} a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s r \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+8\\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} r^{2}-a^{4} \\\\cos{\\\\theta}^{2}+r^{3} r_s-r^{4}-r^{2} a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{\\\\theta}= & \\\\frac{-8r^{4} r_s^{4} a^{8} \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+20r^{5} r_s^{3} a^{8} \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-20r^{3} r_s^{3} a^{10} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}-24r^{6} r_s^{4} a^{6} \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8r^{5} r_s^{5} a^{6} \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8r^{4} r_s^{4} a^{8} \\\\sin{\\\\theta}^{6} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-24r^{5} r_s^{3} a^{8} \\\\sin{\\\\theta}^{6} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+24r^{3} r_s^{3} a^{10} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2}+8r^{4} r_s^{4} a^{8} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}-88r^{5} r_s^{3} a^{8} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}-40r^{3} r_s^{3} a^{10} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}-16r^{6} r_s^{2} a^{8} \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+120r^{4} r_s^{2} a^{10} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}+24r^{7} r_s^{3} a^{6} \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+24r^{6} r_s^{2} a^{8} \\\\sin{\\\\theta}^{6} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-136r^{4} r_s^{2} a^{10} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2}+160r^{6} r_s^{2} a^{8} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}+80r^{4} r_s^{2} a^{10} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}+28r^{2} r_s^{2} a^{12} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}%\\n-24r^{2} r_s^{2} a^{12} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2}+16r^{2} r_s^{2} a^{12} \\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}+16r^{8} r_s^{4} a^{4} \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-4r^{7} r_s^{5} a^{4} \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+32r^{6} r_s^{4} a^{6} \\\\sin{\\\\theta}^{6} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-48r^{7} r_s^{3} a^{6} \\\\sin{\\\\theta}^{6} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+160r^{5} r_s^{3} a^{8} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2}-64r^{6} r_s^{4} a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}+12r^{7} r_s^{3} a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}-64r^{5} r_s^{3} a^{8} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}-8r^{5} r_s^{5} a^{6} \\\\sin{\\\\theta}^{6} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-24r^{4} r_s^{4} a^{8} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2}+12r^{5} r_s^{5} a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}+12r^{4} r_s^{4} a^{8} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}-8r^{8} r_s^{2} a^{6} \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-20r^{9} r_s^{3} a^{4} \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+24r^{8} r_s^{2} a^{6} \\\\sin{\\\\theta}^{6} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-136r^{6} r_s^{2} a^{8} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2}+40r^{8} r_s^{2} a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}+52r^{6} r_s^{2} a^{8} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}%\\n-24r^{4} r_s^{2} a^{10} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2}+16r^{4} r_s^{2} a^{10} \\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}+24r^{3} r_s^{3} a^{10} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2}-16r^{3} r_s^{3} a^{10} \\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}-4r^{6} r_s^{4} a^{6} \\\\sin{2\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-4r^{4} r_s^{4} a^{8} \\\\sin{2\\\\theta}^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8r^{7} r_s^{3} a^{6} \\\\sin{2\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+12r^{5} r_s^{3} a^{8} \\\\sin{2\\\\theta}^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+4r^{3} r_s^{3} a^{10} \\\\sin{2\\\\theta}^{2} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-12r^{8} r_s^{4} a^{4} \\\\sin{2\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-16r^{6} r_s^{4} a^{6} \\\\sin{2\\\\theta}^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+4r^{7} r_s^{5} a^{4} \\\\sin{2\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+4r^{5} r_s^{5} a^{6} \\\\sin{2\\\\theta}^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+12r^{9} r_s^{3} a^{4} \\\\sin{2\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+20r^{7} r_s^{3} a^{6} \\\\sin{2\\\\theta}^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8r^{5} r_s^{3} a^{8} \\\\sin{2\\\\theta}^{2} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-4r^{4} r_s^{4} a^{8} \\\\sin{2\\\\theta}^{2} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-4r^{5} r_s^{3} a^{6} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-4r^{3} r_s^{3} a^{8} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8r^{6} r_s^{2} a^{6} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}%\\n+12r^{4} r_s^{2} a^{8} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+4r^{2} r_s^{2} a^{10} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-16r^{7} r_s^{3} a^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-20r^{5} r_s^{3} a^{6} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+4r^{6} r_s^{4} a^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+4r^{4} r_s^{4} a^{6} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+20r^{8} r_s^{2} a^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+32r^{6} r_s^{2} a^{6} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+12r^{4} r_s^{2} a^{8} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-4r^{3} r_s^{3} a^{8} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-4r^{5} r_s^{3} a^{6} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-4r^{3} r_s^{3} a^{8} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8r^{6} r_s^{2} a^{6} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+12r^{4} r_s^{2} a^{8} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+4r^{2} r_s^{2} a^{10} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-16r^{7} r_s^{3} a^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-20r^{5} r_s^{3} a^{6} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+4r^{6} r_s^{4} a^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+4r^{4} r_s^{4} a^{6} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+20r^{8} r_s^{2} a^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}%\\n+32r^{6} r_s^{2} a^{6} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+12r^{4} r_s^{2} a^{8} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-4r^{3} r_s^{3} a^{8} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-12r^{9} r_s^{3} a^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-16r^{7} r_s^{3} a^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+4r^{8} r_s^{4} a^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+4r^{6} r_s^{4} a^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+12r^{10} r_s^{2} a^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+20r^{8} r_s^{2} a^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8r^{6} r_s^{2} a^{6} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-4r^{5} r_s^{3} a^{6} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-12r^{9} r_s^{3} a^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-16r^{7} r_s^{3} a^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+4r^{8} r_s^{4} a^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+4r^{6} r_s^{4} a^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+12r^{10} r_s^{2} a^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+20r^{8} r_s^{2} a^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8r^{6} r_s^{2} a^{6} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-4r^{5} r_s^{3} a^{6} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-4r^{8} r_s^{2} a^{6} \\\\sin{2\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}%\\n-8r^{6} r_s^{2} a^{8} \\\\sin{2\\\\theta}^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-4r^{4} r_s^{2} a^{10} \\\\sin{2\\\\theta}^{2} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-4r^{10} r_s^{2} a^{4} \\\\sin{2\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-8r^{8} r_s^{2} a^{6} \\\\sin{2\\\\theta}^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-4r^{6} r_s^{2} a^{8} \\\\sin{2\\\\theta}^{2} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-4r^{7} r_s a^{6} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-8r^{5} r_s a^{8} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-4r^{3} r_s a^{10} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-8r^{9} r_s a^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-16r^{7} r_s a^{6} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-8r^{5} r_s a^{8} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-4r^{7} r_s a^{6} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-8r^{5} r_s a^{8} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-4r^{3} r_s a^{10} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-8r^{9} r_s a^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-16r^{7} r_s a^{6} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-8r^{5} r_s a^{8} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-4r^{11} r_s a^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-8r^{9} r_s a^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-4r^{7} r_s a^{6} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}%\\n-4r^{11} r_s a^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-8r^{9} r_s a^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-4r^{7} r_s a^{6} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+4r^{5} r_s^{3} a^{8} \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+4r^{3} r_s^{3} a^{10} \\\\cos{\\\\theta}^{4} \\\\sin{2\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-4r^{6} r_s^{2} a^{8} \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-8r^{4} r_s^{2} a^{10} \\\\cos{\\\\theta}^{4} \\\\sin{2\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-4r^{2} r_s^{2} a^{12} \\\\cos{\\\\theta}^{6} \\\\sin{2\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8r^{7} r_s^{3} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+12r^{5} r_s^{3} a^{8} \\\\cos{\\\\theta}^{4} \\\\sin{2\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-4r^{6} r_s^{4} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-4r^{4} r_s^{4} a^{8} \\\\cos{\\\\theta}^{4} \\\\sin{2\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-4r^{8} r_s^{2} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-8r^{6} r_s^{2} a^{8} \\\\cos{\\\\theta}^{4} \\\\sin{2\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-4r^{4} r_s^{2} a^{10} \\\\cos{\\\\theta}^{6} \\\\sin{2\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+4r^{3} r_s^{3} a^{10} \\\\cos{\\\\theta}^{6} \\\\sin{2\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+4r^{4} r_s^{2} a^{8} \\\\cos{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+4r^{2} r_s^{2} a^{10} \\\\cos{\\\\theta}^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-4r^{5} r_s a^{8} \\\\cos{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-8r^{3} r_s a^{10} \\\\cos{\\\\theta}^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}%\\n-4r r_s a^{12} \\\\cos{\\\\theta}^{6} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+12r^{6} r_s^{2} a^{6} \\\\cos{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+16r^{4} r_s^{2} a^{8} \\\\cos{\\\\theta}^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-4r^{5} r_s^{3} a^{6} \\\\cos{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-4r^{3} r_s^{3} a^{8} \\\\cos{\\\\theta}^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-8r^{7} r_s a^{6} \\\\cos{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-16r^{5} r_s a^{8} \\\\cos{\\\\theta}^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-8r^{3} r_s a^{10} \\\\cos{\\\\theta}^{6} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+4r^{2} r_s^{2} a^{10} \\\\cos{\\\\theta}^{6} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+4r^{4} r_s^{2} a^{8} \\\\cos{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+4r^{2} r_s^{2} a^{10} \\\\cos{\\\\theta}^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-4r^{5} r_s a^{8} \\\\cos{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-8r^{3} r_s a^{10} \\\\cos{\\\\theta}^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-4r r_s a^{12} \\\\cos{\\\\theta}^{6} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+12r^{6} r_s^{2} a^{6} \\\\cos{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+16r^{4} r_s^{2} a^{8} \\\\cos{\\\\theta}^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-4r^{5} r_s^{3} a^{6} \\\\cos{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-4r^{3} r_s^{3} a^{8} \\\\cos{\\\\theta}^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-8r^{7} r_s a^{6} \\\\cos{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-16r^{5} r_s a^{8} \\\\cos{\\\\theta}^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}%\\n-8r^{3} r_s a^{10} \\\\cos{\\\\theta}^{6} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+4r^{2} r_s^{2} a^{10} \\\\cos{\\\\theta}^{6} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8r^{8} r_s^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+12r^{6} r_s^{2} a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-4r^{7} r_s^{3} a^{4} \\\\cos{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-4r^{5} r_s^{3} a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-4r^{9} r_s a^{4} \\\\cos{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-8r^{7} r_s a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-4r^{5} r_s a^{8} \\\\cos{\\\\theta}^{6} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+4r^{4} r_s^{2} a^{8} \\\\cos{\\\\theta}^{6} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8r^{8} r_s^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+12r^{6} r_s^{2} a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-4r^{7} r_s^{3} a^{4} \\\\cos{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-4r^{5} r_s^{3} a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-4r^{9} r_s a^{4} \\\\cos{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-8r^{7} r_s a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-4r^{5} r_s a^{8} \\\\cos{\\\\theta}^{6} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+4r^{4} r_s^{2} a^{8} \\\\cos{\\\\theta}^{6} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8r^{4} r_s^{4} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8r^{4} r_s^{4} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}%\\n-48r^{5} r_s^{3} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-48r^{5} r_s^{3} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-16r^{3} r_s^{3} a^{8} \\\\cos{\\\\theta}^{4} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-16r^{3} r_s^{3} a^{8} \\\\cos{\\\\theta}^{4} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+28r^{6} r_s^{4} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+28r^{6} r_s^{4} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-4r^{5} r_s^{5} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-4r^{5} r_s^{5} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-60r^{7} r_s^{3} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-60r^{7} r_s^{3} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-28r^{5} r_s^{3} a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-28r^{5} r_s^{3} a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8r^{4} r_s^{4} a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8r^{4} r_s^{4} a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-4r^{5} r_s^{3} a^{6} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-4r^{5} r_s^{3} a^{6} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8r^{6} r_s^{2} a^{6} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8r^{6} r_s^{2} a^{6} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+20r^{4} r_s^{2} a^{8} \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+20r^{4} r_s^{2} a^{8} \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}%\\n-24r^{7} r_s^{3} a^{4} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-24r^{7} r_s^{3} a^{4} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8r^{6} r_s^{4} a^{4} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8r^{6} r_s^{4} a^{4} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+24r^{8} r_s^{2} a^{4} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+24r^{8} r_s^{2} a^{4} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+72r^{6} r_s^{2} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+72r^{6} r_s^{2} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-4r^{3} r_s^{3} a^{8} \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-4r^{3} r_s^{3} a^{8} \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8r^{2} r_s^{2} a^{10} \\\\cos{\\\\theta}^{4} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8r^{2} r_s^{2} a^{10} \\\\cos{\\\\theta}^{4} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+40r^{4} r_s^{2} a^{8} \\\\cos{\\\\theta}^{4} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+40r^{4} r_s^{2} a^{8} \\\\cos{\\\\theta}^{4} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+16r^{8} r_s^{4} a^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+16r^{8} r_s^{4} a^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-4r^{7} r_s^{5} a^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-4r^{7} r_s^{5} a^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-24r^{9} r_s^{3} a^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-24r^{9} r_s^{3} a^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}%\\n+16r^{10} r_s^{2} a^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+16r^{10} r_s^{2} a^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+52r^{8} r_s^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+52r^{8} r_s^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+32r^{6} r_s^{2} a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+32r^{6} r_s^{2} a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-4r^{7} r_s a^{6} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-4r^{7} r_s a^{6} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-16r^{5} r_s a^{8} \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-16r^{5} r_s a^{8} \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-8r^{9} r_s a^{4} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-8r^{9} r_s a^{4} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-32r^{7} r_s a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-32r^{7} r_s a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-12r^{3} r_s a^{10} \\\\cos{\\\\theta}^{4} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-12r^{3} r_s a^{10} \\\\cos{\\\\theta}^{4} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-24r^{5} r_s a^{8} \\\\cos{\\\\theta}^{4} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-24r^{5} r_s a^{8} \\\\cos{\\\\theta}^{4} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-4r^{11} r_s a^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-4r^{11} r_s a^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}%\\n-16r^{9} r_s a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-16r^{9} r_s a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-12r^{7} r_s a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-12r^{7} r_s a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8r^{2} r_s^{2} a^{10} \\\\cos{\\\\theta}^{6} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8r^{2} r_s^{2} a^{10} \\\\cos{\\\\theta}^{6} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8r^{4} r_s^{2} a^{8} \\\\cos{\\\\theta}^{6} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8r^{4} r_s^{2} a^{8} \\\\cos{\\\\theta}^{6} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-4r^{3} r_s^{3} a^{8} \\\\cos{\\\\theta}^{6} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-4r^{3} r_s^{3} a^{8} \\\\cos{\\\\theta}^{6} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-4r r_s a^{12} \\\\cos{\\\\theta}^{6} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-4r r_s a^{12} \\\\cos{\\\\theta}^{6} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-8r^{3} r_s a^{10} \\\\cos{\\\\theta}^{6} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-8r^{3} r_s a^{10} \\\\cos{\\\\theta}^{6} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-4r^{5} r_s a^{8} \\\\cos{\\\\theta}^{6} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-4r^{5} r_s a^{8} \\\\cos{\\\\theta}^{6} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-16r^{6} r_s^{4} a^{6} \\\\cos{\\\\theta}^{2} \\\\cos{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-16r^{4} r_s^{4} a^{8} \\\\cos{\\\\theta}^{4} \\\\cos{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+80r^{7} r_s^{3} a^{6} \\\\cos{\\\\theta}^{2} \\\\cos{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+112r^{5} r_s^{3} a^{8} \\\\cos{\\\\theta}^{4} \\\\cos{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}%\\n+32r^{3} r_s^{3} a^{10} \\\\cos{\\\\theta}^{6} \\\\cos{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-48r^{8} r_s^{4} a^{4} \\\\cos{\\\\theta}^{2} \\\\cos{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-64r^{6} r_s^{4} a^{6} \\\\cos{\\\\theta}^{4} \\\\cos{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8r^{7} r_s^{5} a^{4} \\\\cos{\\\\theta}^{2} \\\\cos{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8r^{5} r_s^{5} a^{6} \\\\cos{\\\\theta}^{4} \\\\cos{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+96r^{9} r_s^{3} a^{4} \\\\cos{\\\\theta}^{2} \\\\cos{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+152r^{7} r_s^{3} a^{6} \\\\cos{\\\\theta}^{4} \\\\cos{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+64r^{5} r_s^{3} a^{8} \\\\cos{\\\\theta}^{6} \\\\cos{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-16r^{4} r_s^{4} a^{8} \\\\cos{\\\\theta}^{6} \\\\cos{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8r^{7} r_s^{3} a^{6} \\\\cos{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8r^{5} r_s^{3} a^{8} \\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-16r^{8} r_s^{2} a^{6} \\\\cos{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-16r^{6} r_s^{2} a^{8} \\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-32r^{6} r_s^{2} a^{8} \\\\cos{\\\\theta}^{2} \\\\cos{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-48r^{4} r_s^{2} a^{10} \\\\cos{\\\\theta}^{4} \\\\cos{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-4r^{4} r_s^{2} a^{8} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-4r^{4} r_s^{2} a^{8} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+48r^{9} r_s^{3} a^{4} \\\\cos{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+48r^{7} r_s^{3} a^{6} \\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-16r^{8} r_s^{4} a^{4} \\\\cos{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}%\\n-16r^{6} r_s^{4} a^{6} \\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-48r^{10} r_s^{2} a^{4} \\\\cos{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-48r^{8} r_s^{2} a^{6} \\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-112r^{8} r_s^{2} a^{6} \\\\cos{\\\\theta}^{2} \\\\cos{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-192r^{6} r_s^{2} a^{8} \\\\cos{\\\\theta}^{4} \\\\cos{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-16r^{6} r_s^{2} a^{6} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-16r^{6} r_s^{2} a^{6} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8r^{5} r_s^{3} a^{6} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8r^{5} r_s^{3} a^{6} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8r^{5} r_s^{3} a^{8} \\\\cos{\\\\theta}^{2} \\\\cos{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8r^{3} r_s^{3} a^{10} \\\\cos{\\\\theta}^{4} \\\\cos{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-16r^{2} r_s^{2} a^{12} \\\\cos{\\\\theta}^{6} \\\\cos{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-96r^{4} r_s^{2} a^{10} \\\\cos{\\\\theta}^{6} \\\\cos{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-32r^{10} r_s^{4} a^{2} \\\\cos{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-32r^{8} r_s^{4} a^{4} \\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8r^{9} r_s^{5} a^{2} \\\\cos{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8r^{7} r_s^{5} a^{4} \\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+48r^{11} r_s^{3} a^{2} \\\\cos{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+48r^{9} r_s^{3} a^{4} \\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+12r^{7} r_s^{3} a^{4} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}%\\n+12r^{7} r_s^{3} a^{4} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-4r^{6} r_s^{4} a^{4} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-4r^{6} r_s^{4} a^{4} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-32r^{12} r_s^{2} a^{2} \\\\cos{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-32r^{10} r_s^{2} a^{4} \\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-80r^{10} r_s^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\cos{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-144r^{8} r_s^{2} a^{6} \\\\cos{\\\\theta}^{4} \\\\cos{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-12r^{8} r_s^{2} a^{4} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-12r^{8} r_s^{2} a^{4} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-80r^{6} r_s^{2} a^{8} \\\\cos{\\\\theta}^{6} \\\\cos{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8r^{9} r_s a^{6} \\\\cos{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8r^{7} r_s a^{8} \\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+24r^{7} r_s a^{8} \\\\cos{\\\\theta}^{2} \\\\cos{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+48r^{5} r_s a^{10} \\\\cos{\\\\theta}^{4} \\\\cos{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+4r^{5} r_s a^{8} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+4r^{5} r_s a^{8} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+16r^{11} r_s a^{4} \\\\cos{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+16r^{9} r_s a^{6} \\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+48r^{9} r_s a^{6} \\\\cos{\\\\theta}^{2} \\\\cos{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+96r^{7} r_s a^{8} \\\\cos{\\\\theta}^{4} \\\\cos{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}%\\n+8r^{7} r_s a^{6} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8r^{7} r_s a^{6} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+32r^{3} r_s a^{12} \\\\cos{\\\\theta}^{6} \\\\cos{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+64r^{5} r_s a^{10} \\\\cos{\\\\theta}^{6} \\\\cos{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8r^{13} r_s a^{2} \\\\cos{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8r^{11} r_s a^{4} \\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+24r^{11} r_s a^{4} \\\\cos{\\\\theta}^{2} \\\\cos{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+48r^{9} r_s a^{6} \\\\cos{\\\\theta}^{4} \\\\cos{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+4r^{9} r_s a^{4} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+4r^{9} r_s a^{4} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+32r^{7} r_s a^{8} \\\\cos{\\\\theta}^{6} \\\\cos{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-16r^{2} r_s^{2} a^{12} \\\\cos{\\\\theta}^{8} \\\\cos{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-16r^{4} r_s^{2} a^{10} \\\\cos{\\\\theta}^{8} \\\\cos{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8r^{3} r_s^{3} a^{10} \\\\cos{\\\\theta}^{8} \\\\cos{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8r r_s a^{14} \\\\cos{\\\\theta}^{8} \\\\cos{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+16r^{3} r_s a^{12} \\\\cos{\\\\theta}^{8} \\\\cos{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8r^{5} r_s a^{10} \\\\cos{\\\\theta}^{8} \\\\cos{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+2r^{2} r_s^{2} \\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{8} \\\\cos{\\\\theta}^{2} \\\\cos{4\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-2r^{2} r_s^{2} \\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{8} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+2r^{4} r_s^{2} \\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{6} \\\\cos{\\\\theta}^{2} \\\\cos{4\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}%\\n-2r^{4} r_s^{2} \\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-r^{3} r_s^{3} \\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{6} \\\\cos{\\\\theta}^{2} \\\\cos{4\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+r^{3} r_s^{3} \\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-16r^{4} r_s^{2} \\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+4r^{3} r_s^{3} \\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-8r^{2} r_s^{2} \\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{8} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-8r^{6} r_s^{2} \\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{4} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+4r^{5} r_s^{3} \\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{4} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-r^{3} r_s \\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{8} \\\\cos{4\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+r^{3} r_s \\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{8} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-2r^{5} r_s \\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{6} \\\\cos{4\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-2r^{5} r_s \\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{6} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+2r^{4} r_s^{2} \\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{6} \\\\cos{4\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-2r^{4} r_s^{2} \\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{6} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-11r^{7} r_s \\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+6r^{6} r_s^{2} \\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+r^{5} r_s \\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+2r^{3} r_s \\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{8} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-12r^{9} r_s \\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+16r^{8} r_s^{2} \\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}%\\n-r r_s \\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{10} \\\\cos{\\\\theta}^{2} \\\\cos{4\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+r r_s \\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{10} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-2r^{3} r_s \\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{8} \\\\cos{\\\\theta}^{2} \\\\cos{4\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+12r^{3} r_s \\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{8} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+4r r_s \\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{10} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+12r^{5} r_s \\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+2r^{6} r_s^{2} \\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{4} \\\\cos{4\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-r^{5} r_s^{3} \\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{4} \\\\cos{4\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+r^{5} r_s^{3} \\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-4r^{7} r_s^{3} \\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8r^{10} r_s^{2} \\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-4r^{9} r_s^{3} \\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-r^{7} r_s \\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{4} \\\\cos{4\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-4r^{11} r_s \\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-r^{5} r_s \\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{6} \\\\cos{\\\\theta}^{2} \\\\cos{4\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+4r^{7} r_s \\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{4} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8\\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} r^{2}-a^{4} \\\\cos{\\\\theta}^{2}+r^{3} r_s-r^{4}-r^{2} a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} r^{2} \\\\cos{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8\\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} r^{2}-a^{4} \\\\cos{\\\\theta}^{2}+r^{3} r_s-r^{4}-r^{2} a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\cos{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-4\\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} r^{2}-a^{4} \\\\cos{\\\\theta}^{2}+r^{3} r_s-r^{4}-r^{2} a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-4\\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} r^{2}-a^{4} \\\\cos{\\\\theta}^{2}+r^{3} r_s-r^{4}-r^{2} a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}%\\n-4\\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} r^{2}-a^{4} \\\\cos{\\\\theta}^{2}+r^{3} r_s-r^{4}-r^{2} a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r^{3} r_s \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-4\\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} r^{2}-a^{4} \\\\cos{\\\\theta}^{2}+r^{3} r_s-r^{4}-r^{2} a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r r_s a^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8\\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} r^{2}-a^{4} \\\\cos{\\\\theta}^{2}+r^{3} r_s-r^{4}-r^{2} a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r^{3} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-8\\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} r^{2}-a^{4} \\\\cos{\\\\theta}^{2}+r^{3} r_s-r^{4}-r^{2} a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r^{2} r_s \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-8\\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} r^{2}-a^{4} \\\\cos{\\\\theta}^{2}+r^{3} r_s-r^{4}-r^{2} a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r^{2} r_s \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8\\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} r^{2}-a^{4} \\\\cos{\\\\theta}^{2}+r^{3} r_s-r^{4}-r^{2} a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r a^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8\\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} r^{2}-a^{4} \\\\cos{\\\\theta}^{2}+r^{3} r_s-r^{4}-r^{2} a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r a^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8\\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} r^{2}-a^{4} \\\\cos{\\\\theta}^{2}+r^{3} r_s-r^{4}-r^{2} a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r^{3} \\\\partial_{r}\\\\left(r_s r\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-8\\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} r^{2}-a^{4} \\\\cos{\\\\theta}^{2}+r^{3} r_s-r^{4}-r^{2} a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r^{3} \\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-8\\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} r^{2}-a^{4} \\\\cos{\\\\theta}^{2}+r^{3} r_s-r^{4}-r^{2} a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r a^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8\\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} r^{2}-a^{4} \\\\cos{\\\\theta}^{2}+r^{3} r_s-r^{4}-r^{2} a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r a^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r_s r\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-8\\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} r^{2}-a^{4} \\\\cos{\\\\theta}^{2}+r^{3} r_s-r^{4}-r^{2} a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r a^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8\\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} r^{2}-a^{4} \\\\cos{\\\\theta}^{2}+r^{3} r_s-r^{4}-r^{2} a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s r^{3} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8\\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} r^{2}-a^{4} \\\\cos{\\\\theta}^{2}+r^{3} r_s-r^{4}-r^{2} a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s r a^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-8\\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} r^{2}-a^{4} \\\\cos{\\\\theta}^{2}+r^{3} r_s-r^{4}-r^{2} a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} r^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-8\\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} r^{2}-a^{4} \\\\cos{\\\\theta}^{2}+r^{3} r_s-r^{4}-r^{2} a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8r^{4} r_s^{4} a^{8} \\\\sin{\\\\theta}^{6} \\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}-8r^{3} r_s^{3} a^{10} \\\\sin{\\\\theta}^{6} \\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}-24r^{5} r_s^{3} a^{8} \\\\sin{\\\\theta}^{6} \\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}-8r^{5} r_s^{5} a^{6} \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}%\\n+8r^{4} r_s^{4} a^{8} \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}+32r^{6} r_s^{4} a^{6} \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}-24r^{5} r_s^{3} a^{8} \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}-40r^{7} r_s^{3} a^{6} \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}+40r^{6} r_s^{4} a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-56r^{7} r_s^{3} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-40r^{5} r_s^{3} a^{8} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+72r^{8} r_s^{4} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+48r^{9} r_s^{3} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+144r^{7} r_s^{3} a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-8r^{3} r_s^{3} a^{10} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+128r^{5} r_s^{3} a^{8} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8r^{3} r_s^{3} a^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-8r^{4} r_s^{2} a^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-8r^{2} r_s^{2} a^{8} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8r^{5} r_s^{3} a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-32r^{6} r_s^{2} a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-32r^{4} r_s^{2} a^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-128r^{8} r_s^{4} a^{4} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-80r^{10} r_s^{4} a^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}%\\n+136r^{11} r_s^{3} a^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+272r^{9} r_s^{3} a^{4} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-104r^{6} r_s^{4} a^{6} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+280r^{7} r_s^{3} a^{6} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8r^{5} r_s^{3} a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8r^{7} r_s^{3} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-24r^{8} r_s^{2} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-24r^{6} r_s^{2} a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-24r^{9} r_s^{3} a^{4} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}-88r^{10} r_s^{4} a^{2} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}+92r^{11} r_s^{3} a^{2} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}+28r^{9} r_s^{5} a^{2} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}-28r^{7} r_s^{3} a^{6} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}-120r^{7} r_s^{3} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}-156r^{8} r_s^{4} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}+132r^{9} r_s^{3} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}+24r^{6} r_s^{4} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}+44r^{7} r_s^{5} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}-68r^{5} r_s^{3} a^{8} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}-32r^{12} r_s^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}%\\n+48r^{13} r_s^{3} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+16r^{9} r_s^{5} a^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+32r^{10} r_s^{4} a^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8r^{11} r_s^{5} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-24r^{9} r_s^{3} a^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+16r^{7} r_s^{5} a^{4} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+32r^{7} r_s^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-48r^{8} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-48r^{6} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8r^{9} r_s^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-16r^{10} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-40r^{8} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-8r^{6} r_s^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+16r^{7} r_s^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+16r^{5} r_s^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-8r^{6} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-8r^{4} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8r^{6} r_s^{4} a^{6} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{5} \\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2}+8r^{4} r_s^{4} a^{8} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{5} \\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}-8r^{7} r_s^{5} a^{4} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{3} \\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2}%\\n-8r^{5} r_s^{5} a^{6} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{3} \\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}+32r^{8} r_s^{4} a^{4} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{3} \\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2}+32r^{6} r_s^{4} a^{6} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{3} \\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}+16r^{6} r_s^{4} a^{6} \\\\sin{2\\\\theta} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}+16r^{4} r_s^{4} a^{8} \\\\sin{2\\\\theta} \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}-8r^{8} r_s^{4} a^{4} \\\\sin{2\\\\theta} \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2}-16r^{6} r_s^{4} a^{6} \\\\sin{2\\\\theta} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8r^{4} r_s^{4} a^{8} \\\\sin{2\\\\theta} \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8r^{5} r_s^{3} a^{4} \\\\sin{2\\\\theta} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2}+8r^{3} r_s^{3} a^{6} \\\\sin{2\\\\theta} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8r^{10} r_s^{4} a^{2} \\\\sin{2\\\\theta} \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2}-16r^{8} r_s^{4} a^{4} \\\\sin{2\\\\theta} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8r^{6} r_s^{4} a^{6} \\\\sin{2\\\\theta} \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8r^{7} r_s^{3} a^{2} \\\\sin{2\\\\theta} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2}+8r^{5} r_s^{3} a^{4} \\\\sin{2\\\\theta} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8r^{5} r_s^{3} a^{6} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{5} \\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2}+8r^{3} r_s^{3} a^{8} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{5} \\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}-8r^{6} r_s^{4} a^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{3} \\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2}-8r^{4} r_s^{4} a^{6} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{3} \\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}+32r^{7} r_s^{3} a^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{3} \\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2}%\\n+32r^{5} r_s^{3} a^{6} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{3} \\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}+16r^{5} r_s^{3} a^{6} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}+16r^{3} r_s^{3} a^{8} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}-8r^{7} r_s^{3} a^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2}-16r^{5} r_s^{3} a^{6} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8r^{3} r_s^{3} a^{8} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8r^{4} r_s^{2} a^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2}+8r^{2} r_s^{2} a^{6} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8r^{9} r_s^{3} a^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2}-16r^{7} r_s^{3} a^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8r^{5} r_s^{3} a^{6} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8r^{6} r_s^{2} a^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2}+8r^{4} r_s^{2} a^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8r^{5} r_s^{3} a^{6} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{5} \\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2}+8r^{3} r_s^{3} a^{8} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{5} \\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}-8r^{6} r_s^{4} a^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{3} \\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2}-8r^{4} r_s^{4} a^{6} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{3} \\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}+32r^{7} r_s^{3} a^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{3} \\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2}+32r^{5} r_s^{3} a^{6} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{3} \\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}+16r^{5} r_s^{3} a^{6} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}%\\n+16r^{3} r_s^{3} a^{8} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}-8r^{7} r_s^{3} a^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2}-16r^{5} r_s^{3} a^{6} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8r^{3} r_s^{3} a^{8} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8r^{4} r_s^{2} a^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2}+8r^{2} r_s^{2} a^{6} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8r^{9} r_s^{3} a^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2}-16r^{7} r_s^{3} a^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8r^{5} r_s^{3} a^{6} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8r^{6} r_s^{2} a^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2}+8r^{4} r_s^{2} a^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8r^{7} r_s^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{4} \\\\sin{\\\\theta}^{5} \\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2}+8r^{5} r_s^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{6} \\\\sin{\\\\theta}^{5} \\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}-8r^{8} r_s^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{2} \\\\sin{\\\\theta}^{3} \\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2}-8r^{6} r_s^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{4} \\\\sin{\\\\theta}^{3} \\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}+32r^{9} r_s^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{2} \\\\sin{\\\\theta}^{3} \\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2}+32r^{7} r_s^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{4} \\\\sin{\\\\theta}^{3} \\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}+16r^{7} r_s^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{4} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}+16r^{5} r_s^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{6} \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}-8r^{9} r_s^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{2} \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2}%\\n-16r^{7} r_s^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{4} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8r^{5} r_s^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{6} \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8r^{6} r_s^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2}+8r^{4} r_s^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8r^{11} r_s^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2}-16r^{9} r_s^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{2} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8r^{7} r_s^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{4} \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8r^{8} r_s^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2}+8r^{6} r_s^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8r^{7} r_s^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{4} \\\\sin{\\\\theta}^{5} \\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2}+8r^{5} r_s^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{6} \\\\sin{\\\\theta}^{5} \\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}-8r^{8} r_s^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{2} \\\\sin{\\\\theta}^{3} \\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2}-8r^{6} r_s^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{4} \\\\sin{\\\\theta}^{3} \\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}+32r^{9} r_s^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{2} \\\\sin{\\\\theta}^{3} \\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2}+32r^{7} r_s^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{4} \\\\sin{\\\\theta}^{3} \\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}+16r^{7} r_s^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{4} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}+16r^{5} r_s^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{6} \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}-8r^{9} r_s^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{2} \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2}-16r^{7} r_s^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{4} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8r^{5} r_s^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{6} \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}%\\n+8r^{6} r_s^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2}+8r^{4} r_s^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8r^{11} r_s^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2}-16r^{9} r_s^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{2} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8r^{7} r_s^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{4} \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8r^{8} r_s^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2}+8r^{6} r_s^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8r^{5} r_s^{5} a^{6} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-24r^{4} r_s^{4} a^{8} \\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+24r^{8} r_s^{4} a^{4} \\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}+24r^{6} r_s^{4} a^{6} \\\\cos{\\\\theta}^{6} \\\\tan{\\\\theta}^{2}+8r^{4} r_s^{4} a^{8} \\\\cos{\\\\theta}^{8} \\\\tan{\\\\theta}^{2}-8r^{5} r_s^{3} a^{4} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2}-8r^{3} r_s^{3} a^{6} \\\\cos{\\\\theta}^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2}+24r^{10} r_s^{4} a^{2} \\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}+24r^{8} r_s^{4} a^{4} \\\\cos{\\\\theta}^{6} \\\\tan{\\\\theta}^{2}+8r^{6} r_s^{4} a^{6} \\\\cos{\\\\theta}^{8} \\\\tan{\\\\theta}^{2}-8r^{7} r_s^{3} a^{2} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2}-8r^{5} r_s^{3} a^{4} \\\\cos{\\\\theta}^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2}-8r^{8} r_s^{4} a^{4} \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}%\\n-8r^{6} r_s^{4} a^{6} \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}+32r^{9} r_s^{3} a^{4} \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+32r^{7} r_s^{3} a^{6} \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}-8r^{9} r_s^{3} a^{4} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-24r^{7} r_s^{3} a^{6} \\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}-24r^{5} r_s^{3} a^{8} \\\\cos{\\\\theta}^{6} \\\\tan{\\\\theta}^{2}+8r^{6} r_s^{2} a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8r^{4} r_s^{2} a^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}-32r^{11} r_s^{3} a^{2} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-104r^{9} r_s^{3} a^{4} \\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}-120r^{7} r_s^{3} a^{6} \\\\cos{\\\\theta}^{6} \\\\tan{\\\\theta}^{2}+32r^{8} r_s^{2} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+32r^{6} r_s^{2} a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}+32r^{3} r_s^{3} a^{10} \\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-8r^{3} r_s^{3} a^{10} \\\\cos{\\\\theta}^{8} \\\\tan{\\\\theta}^{2}+8r^{4} r_s^{2} a^{6} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2}+8r^{2} r_s^{2} a^{8} \\\\cos{\\\\theta}^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2}-56r^{5} r_s^{3} a^{8} \\\\cos{\\\\theta}^{8} \\\\tan{\\\\theta}^{2}+40r^{6} r_s^{2} a^{4} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2}+48r^{4} r_s^{2} a^{6} \\\\cos{\\\\theta}^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2}%\\n+8r^{9} r_s^{5} a^{2} \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8r^{7} r_s^{5} a^{4} \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}-40r^{10} r_s^{4} a^{2} \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-40r^{8} r_s^{4} a^{4} \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}+8r^{10} r_s^{4} a^{2} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-8r^{7} r_s^{3} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-8r^{5} r_s^{3} a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}+8r^{12} r_s^{4} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-8r^{9} r_s^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-8r^{7} r_s^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} \\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}+72r^{11} r_s^{3} a^{2} \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+72r^{9} r_s^{3} a^{4} \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}-24r^{13} r_s^{3} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-80r^{11} r_s^{3} a^{2} \\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}-96r^{9} r_s^{3} a^{4} \\\\cos{\\\\theta}^{6} \\\\tan{\\\\theta}^{2}+24r^{10} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+24r^{8} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} \\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}+112r^{5} r_s^{3} a^{8} \\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-48r^{7} r_s^{3} a^{6} \\\\cos{\\\\theta}^{8} \\\\tan{\\\\theta}^{2}+32r^{8} r_s^{2} a^{2} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2}%\\n+40r^{6} r_s^{2} a^{4} \\\\cos{\\\\theta}^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2}-8r^{4} r_s^{4} a^{6} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-8r^{4} r_s^{4} a^{6} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+16r^{5} r_s^{5} a^{4} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+16r^{5} r_s^{5} a^{4} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-128r^{6} r_s^{4} a^{4} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-128r^{6} r_s^{4} a^{4} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-48r^{4} r_s^{4} a^{6} \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-48r^{4} r_s^{4} a^{6} \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+32r^{6} r_s^{4} a^{4} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+32r^{6} r_s^{4} a^{4} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+16r^{4} r_s^{4} a^{6} \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+16r^{4} r_s^{4} a^{6} \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-16r^{3} r_s^{3} a^{4} \\\\cos{\\\\theta}^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-16r^{3} r_s^{3} a^{4} \\\\cos{\\\\theta}^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+32r^{8} r_s^{4} a^{2} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+32r^{8} r_s^{4} a^{2} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+16r^{6} r_s^{4} a^{4} \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+16r^{6} r_s^{4} a^{4} \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-16r^{5} r_s^{3} a^{2} \\\\cos{\\\\theta}^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}%\\n-16r^{5} r_s^{3} a^{2} \\\\cos{\\\\theta}^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+8r^{5} r_s^{3} a^{6} \\\\sin{\\\\theta}^{5} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+8r^{5} r_s^{3} a^{6} \\\\sin{\\\\theta}^{5} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-16r^{6} r_s^{4} a^{4} \\\\sin{\\\\theta}^{3} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-16r^{6} r_s^{4} a^{4} \\\\sin{\\\\theta}^{3} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+64r^{7} r_s^{3} a^{4} \\\\sin{\\\\theta}^{3} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+64r^{7} r_s^{3} a^{4} \\\\sin{\\\\theta}^{3} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+112r^{5} r_s^{3} a^{6} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+112r^{5} r_s^{3} a^{6} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-16r^{7} r_s^{3} a^{4} \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-16r^{7} r_s^{3} a^{4} \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-32r^{5} r_s^{3} a^{6} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-32r^{5} r_s^{3} a^{6} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+16r^{4} r_s^{2} a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+16r^{4} r_s^{2} a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-64r^{9} r_s^{3} a^{2} \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-64r^{9} r_s^{3} a^{2} \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-144r^{7} r_s^{3} a^{4} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-144r^{7} r_s^{3} a^{4} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+64r^{6} r_s^{2} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}%\\n+64r^{6} r_s^{2} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+8r^{3} r_s^{3} a^{8} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+8r^{3} r_s^{3} a^{8} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-16r^{4} r_s^{4} a^{6} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-16r^{4} r_s^{4} a^{6} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+48r^{3} r_s^{3} a^{8} \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+48r^{3} r_s^{3} a^{8} \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-16r^{3} r_s^{3} a^{8} \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-16r^{3} r_s^{3} a^{8} \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+16r^{2} r_s^{2} a^{6} \\\\cos{\\\\theta}^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+16r^{2} r_s^{2} a^{6} \\\\cos{\\\\theta}^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-96r^{5} r_s^{3} a^{6} \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-96r^{5} r_s^{3} a^{6} \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+80r^{4} r_s^{2} a^{4} \\\\cos{\\\\theta}^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+80r^{4} r_s^{2} a^{4} \\\\cos{\\\\theta}^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-8r^{6} r_s^{4} a^{4} \\\\sin{\\\\theta}^{5} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-8r^{6} r_s^{4} a^{4} \\\\sin{\\\\theta}^{5} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+16r^{7} r_s^{5} a^{2} \\\\sin{\\\\theta}^{3} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+16r^{7} r_s^{5} a^{2} \\\\sin{\\\\theta}^{3} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-80r^{8} r_s^{4} a^{2} \\\\sin{\\\\theta}^{3} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}%\\n-80r^{8} r_s^{4} a^{2} \\\\sin{\\\\theta}^{3} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+16r^{8} r_s^{4} a^{2} \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+16r^{8} r_s^{4} a^{2} \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-16r^{5} r_s^{3} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-16r^{5} r_s^{3} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+16r^{10} r_s^{4} \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+16r^{10} r_s^{4} \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-16r^{7} r_s^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-16r^{7} r_s^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+24r^{7} r_s^{3} a^{4} \\\\sin{\\\\theta}^{5} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+24r^{7} r_s^{3} a^{4} \\\\sin{\\\\theta}^{5} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+144r^{9} r_s^{3} a^{2} \\\\sin{\\\\theta}^{3} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+144r^{9} r_s^{3} a^{2} \\\\sin{\\\\theta}^{3} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+272r^{7} r_s^{3} a^{4} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+272r^{7} r_s^{3} a^{4} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-48r^{11} r_s^{3} \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-48r^{11} r_s^{3} \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-112r^{9} r_s^{3} a^{2} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-112r^{9} r_s^{3} a^{2} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+48r^{8} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}%\\n+48r^{8} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+32r^{5} r_s^{3} a^{6} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+32r^{5} r_s^{3} a^{6} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+176r^{5} r_s^{3} a^{6} \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+176r^{5} r_s^{3} a^{6} \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-80r^{7} r_s^{3} a^{4} \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-80r^{7} r_s^{3} a^{4} \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+64r^{6} r_s^{2} a^{2} \\\\cos{\\\\theta}^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+64r^{6} r_s^{2} a^{2} \\\\cos{\\\\theta}^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-80r^{6} r_s^{4} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2}-32r^{7} r_s^{5} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-16r^{5} r_s^{5} a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8r^{5} r_s^{5} a^{4} \\\\cos{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8r^{5} r_s^{5} a^{4} \\\\cos{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8r^{5} r_s^{5} a^{4} \\\\cos{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8r^{5} r_s^{5} a^{4} \\\\cos{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-48r^{4} r_s^{4} a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}+40r^{4} r_s^{4} a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-112r^{6} r_s^{4} a^{4} \\\\cos{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-112r^{6} r_s^{4} a^{4} \\\\cos{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}%\\n-40r^{4} r_s^{4} a^{6} \\\\cos{\\\\theta}^{7} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-40r^{4} r_s^{4} a^{6} \\\\cos{\\\\theta}^{7} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+56r^{6} r_s^{4} a^{4} \\\\cos{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+56r^{6} r_s^{4} a^{4} \\\\cos{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+16r^{4} r_s^{4} a^{6} \\\\cos{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+16r^{4} r_s^{4} a^{6} \\\\cos{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8r^{3} r_s^{3} a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+24r^{3} r_s^{3} a^{4} \\\\cos{\\\\theta}^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+24r^{3} r_s^{3} a^{4} \\\\cos{\\\\theta}^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8r^{6} r_s^{4} a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-88r^{8} r_s^{4} a^{2} \\\\cos{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-88r^{8} r_s^{4} a^{2} \\\\cos{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8r^{5} r_s^{3} a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+24r^{5} r_s^{3} a^{2} \\\\cos{\\\\theta}^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+24r^{5} r_s^{3} a^{2} \\\\cos{\\\\theta}^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+40r^{7} r_s^{3} a^{6} \\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2}+80r^{5} r_s^{3} a^{8} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2}+16r^{8} r_s^{4} a^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+32r^{6} r_s^{4} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8r^{6} r_s^{4} a^{4} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}%\\n+8r^{6} r_s^{4} a^{4} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+48r^{5} r_s^{3} a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}-40r^{5} r_s^{3} a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-56r^{7} r_s^{3} a^{4} \\\\cos{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-56r^{7} r_s^{3} a^{4} \\\\cos{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+16r^{5} r_s^{3} a^{6} \\\\cos{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+16r^{5} r_s^{3} a^{6} \\\\cos{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-32r^{7} r_s^{3} a^{4} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-32r^{7} r_s^{3} a^{4} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-56r^{5} r_s^{3} a^{6} \\\\cos{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-56r^{5} r_s^{3} a^{6} \\\\cos{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8r^{4} r_s^{2} a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-24r^{4} r_s^{2} a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-24r^{4} r_s^{2} a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-128r^{7} r_s^{3} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-56r^{9} r_s^{3} a^{2} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-56r^{9} r_s^{3} a^{2} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+32r^{6} r_s^{2} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-96r^{6} r_s^{2} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-96r^{6} r_s^{2} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}%\\n+16r^{4} r_s^{4} a^{8} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8r^{4} r_s^{4} a^{6} \\\\cos{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8r^{4} r_s^{4} a^{6} \\\\cos{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+48r^{3} r_s^{3} a^{6} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}-40r^{3} r_s^{3} a^{6} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+24r^{3} r_s^{3} a^{8} \\\\cos{\\\\theta}^{7} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+24r^{3} r_s^{3} a^{8} \\\\cos{\\\\theta}^{7} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-24r^{3} r_s^{3} a^{8} \\\\cos{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-24r^{3} r_s^{3} a^{8} \\\\cos{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8r^{2} r_s^{2} a^{6} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-24r^{2} r_s^{2} a^{6} \\\\cos{\\\\theta}^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-24r^{2} r_s^{2} a^{6} \\\\cos{\\\\theta}^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-168r^{5} r_s^{3} a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+40r^{4} r_s^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-120r^{4} r_s^{2} a^{4} \\\\cos{\\\\theta}^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-120r^{4} r_s^{2} a^{4} \\\\cos{\\\\theta}^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-40r^{8} r_s^{4} a^{4} \\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2}-16r^{9} r_s^{5} a^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8r^{7} r_s^{5} a^{2} \\\\cos{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8r^{7} r_s^{5} a^{2} \\\\cos{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}%\\n-8r^{7} r_s^{5} a^{2} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8r^{7} r_s^{5} a^{2} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-48r^{6} r_s^{4} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}+40r^{6} r_s^{4} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+40r^{8} r_s^{4} a^{2} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+40r^{8} r_s^{4} a^{2} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8r^{5} r_s^{3} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+24r^{5} r_s^{3} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+24r^{5} r_s^{3} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-16r^{10} r_s^{4} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-16r^{10} r_s^{4} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8r^{7} r_s^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+24r^{7} r_s^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+24r^{7} r_s^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+120r^{9} r_s^{3} a^{4} \\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2}+280r^{7} r_s^{3} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2}+144r^{7} r_s^{3} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}+232r^{9} r_s^{3} a^{2} \\\\cos{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+232r^{9} r_s^{3} a^{2} \\\\cos{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+328r^{7} r_s^{3} a^{4} \\\\cos{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}%\\n+328r^{7} r_s^{3} a^{4} \\\\cos{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+48r^{11} r_s^{3} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+48r^{11} r_s^{3} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+24r^{8} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-72r^{8} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-72r^{8} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+192r^{5} r_s^{3} a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}+184r^{5} r_s^{3} a^{6} \\\\cos{\\\\theta}^{7} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+184r^{5} r_s^{3} a^{6} \\\\cos{\\\\theta}^{7} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-24r^{7} r_s^{3} a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+32r^{6} r_s^{2} a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-96r^{6} r_s^{2} a^{2} \\\\cos{\\\\theta}^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-96r^{6} r_s^{2} a^{2} \\\\cos{\\\\theta}^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+16r^{4} r_s^{2} a^{10} \\\\sin{\\\\theta}^{6} \\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}+16r^{6} r_s^{2} a^{8} \\\\sin{\\\\theta}^{6} \\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}+16r^{6} r_s^{2} a^{8} \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}+8r^{8} r_s^{2} a^{6} \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}-56r^{8} r_s^{2} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-72r^{6} r_s^{2} a^{8} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-144r^{10} r_s^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}%\\n-240r^{8} r_s^{2} a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-40r^{4} r_s^{2} a^{10} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-224r^{6} r_s^{2} a^{8} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+16r^{5} r_s a^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+16r^{3} r_s a^{8} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+32r^{7} r_s a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+32r^{5} r_s a^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-88r^{12} r_s^{2} a^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-184r^{10} r_s^{2} a^{4} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-200r^{8} r_s^{2} a^{6} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+16r^{9} r_s a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+16r^{7} r_s a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+80r^{10} r_s^{2} a^{4} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}-8r^{12} r_s^{2} a^{2} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}+56r^{8} r_s^{2} a^{6} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}+200r^{8} r_s^{2} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}+4r^{10} r_s^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}+164r^{6} r_s^{2} a^{8} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}-48r^{12} r_s^{2} a^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-32r^{14} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}%\\n-16r^{10} r_s^{2} a^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+32r^{9} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+32r^{7} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8r^{11} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+16r^{9} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+16r^{7} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+16r^{5} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-16r^{7} r_s^{3} a^{6} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{5} \\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2}-16r^{5} r_s^{3} a^{8} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{5} \\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}-32r^{9} r_s^{3} a^{4} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{3} \\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2}-32r^{7} r_s^{3} a^{6} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{3} \\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}-32r^{7} r_s^{3} a^{6} \\\\sin{2\\\\theta} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}-32r^{5} r_s^{3} a^{8} \\\\sin{2\\\\theta} \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}+16r^{9} r_s^{3} a^{4} \\\\sin{2\\\\theta} \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2}+32r^{7} r_s^{3} a^{6} \\\\sin{2\\\\theta} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+16r^{5} r_s^{3} a^{8} \\\\sin{2\\\\theta} \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-16r^{6} r_s^{2} a^{4} \\\\sin{2\\\\theta} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2}-16r^{4} r_s^{2} a^{6} \\\\sin{2\\\\theta} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+16r^{11} r_s^{3} a^{2} \\\\sin{2\\\\theta} \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2}+32r^{9} r_s^{3} a^{4} \\\\sin{2\\\\theta} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}%\\n+16r^{7} r_s^{3} a^{6} \\\\sin{2\\\\theta} \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-16r^{8} r_s^{2} a^{2} \\\\sin{2\\\\theta} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2}-16r^{6} r_s^{2} a^{4} \\\\sin{2\\\\theta} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-16r^{6} r_s^{2} a^{6} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{5} \\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2}-16r^{4} r_s^{2} a^{8} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{5} \\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}-32r^{8} r_s^{2} a^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{3} \\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2}-32r^{6} r_s^{2} a^{6} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{3} \\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}-32r^{6} r_s^{2} a^{6} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}-32r^{4} r_s^{2} a^{8} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}+16r^{8} r_s^{2} a^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2}+32r^{6} r_s^{2} a^{6} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+16r^{4} r_s^{2} a^{8} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-16r^{5} r_s a^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2}-16r^{3} r_s a^{6} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+16r^{10} r_s^{2} a^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2}+32r^{8} r_s^{2} a^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+16r^{6} r_s^{2} a^{6} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-16r^{7} r_s a^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2}-16r^{5} r_s a^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-16r^{6} r_s^{2} a^{6} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{5} \\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2}%\\n-16r^{4} r_s^{2} a^{8} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{5} \\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}-32r^{8} r_s^{2} a^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{3} \\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2}-32r^{6} r_s^{2} a^{6} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{3} \\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}-32r^{6} r_s^{2} a^{6} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}-32r^{4} r_s^{2} a^{8} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}+16r^{8} r_s^{2} a^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2}+32r^{6} r_s^{2} a^{6} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+16r^{4} r_s^{2} a^{8} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-16r^{5} r_s a^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2}-16r^{3} r_s a^{6} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+16r^{10} r_s^{2} a^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2}+32r^{8} r_s^{2} a^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+16r^{6} r_s^{2} a^{6} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-16r^{7} r_s a^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2}-16r^{5} r_s a^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-16r^{8} r_s^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{4} \\\\sin{\\\\theta}^{5} \\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2}-16r^{6} r_s^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{6} \\\\sin{\\\\theta}^{5} \\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}-32r^{10} r_s^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{2} \\\\sin{\\\\theta}^{3} \\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2}-32r^{8} r_s^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{4} \\\\sin{\\\\theta}^{3} \\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}-32r^{8} r_s^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{4} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}%\\n-32r^{6} r_s^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{6} \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}+16r^{10} r_s^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{2} \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2}+32r^{8} r_s^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{4} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+16r^{6} r_s^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{6} \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-16r^{7} r_s \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2}-16r^{5} r_s \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+16r^{12} r_s^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2}+32r^{10} r_s^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{2} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+16r^{8} r_s^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{4} \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-16r^{9} r_s \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2}-16r^{7} r_s \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-16r^{8} r_s^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{4} \\\\sin{\\\\theta}^{5} \\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2}-16r^{6} r_s^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{6} \\\\sin{\\\\theta}^{5} \\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}-32r^{10} r_s^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{2} \\\\sin{\\\\theta}^{3} \\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2}-32r^{8} r_s^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{4} \\\\sin{\\\\theta}^{3} \\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}-32r^{8} r_s^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{4} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}-32r^{6} r_s^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{6} \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}+16r^{10} r_s^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{2} \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2}+32r^{8} r_s^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{4} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+16r^{6} r_s^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{6} \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}%\\n-16r^{7} r_s \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2}-16r^{5} r_s \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+16r^{12} r_s^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2}+32r^{10} r_s^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{2} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+16r^{8} r_s^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{4} \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-16r^{9} r_s \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2}-16r^{7} r_s \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-32r^{10} r_s^{2} a^{4} \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-32r^{8} r_s^{2} a^{6} \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}+16r^{10} r_s^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+56r^{8} r_s^{2} a^{6} \\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}+72r^{6} r_s^{2} a^{8} \\\\cos{\\\\theta}^{6} \\\\tan{\\\\theta}^{2}-16r^{7} r_s a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-16r^{5} r_s a^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}+40r^{12} r_s^{2} a^{2} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+128r^{10} r_s^{2} a^{4} \\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}+152r^{8} r_s^{2} a^{6} \\\\cos{\\\\theta}^{6} \\\\tan{\\\\theta}^{2}-40r^{9} r_s a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-40r^{7} r_s a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}-96r^{4} r_s^{2} a^{10} \\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}%\\n+40r^{4} r_s^{2} a^{10} \\\\cos{\\\\theta}^{8} \\\\tan{\\\\theta}^{2}-24r^{5} r_s a^{6} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2}-32r^{3} r_s a^{8} \\\\cos{\\\\theta}^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2}+80r^{6} r_s^{2} a^{8} \\\\cos{\\\\theta}^{8} \\\\tan{\\\\theta}^{2}-48r^{7} r_s a^{4} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2}-64r^{5} r_s a^{6} \\\\cos{\\\\theta}^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2}-48r^{12} r_s^{2} a^{2} \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-48r^{10} r_s^{2} a^{4} \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}+24r^{14} r_s^{2} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+72r^{12} r_s^{2} a^{2} \\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}+80r^{10} r_s^{2} a^{4} \\\\cos{\\\\theta}^{6} \\\\tan{\\\\theta}^{2}-24r^{11} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-24r^{9} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} \\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}-88r^{6} r_s^{2} a^{8} \\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+40r^{8} r_s^{2} a^{6} \\\\cos{\\\\theta}^{8} \\\\tan{\\\\theta}^{2}-24r^{9} r_s a^{2} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2}-32r^{7} r_s a^{4} \\\\cos{\\\\theta}^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2}-16r^{6} r_s^{2} a^{6} \\\\sin{\\\\theta}^{5} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-16r^{6} r_s^{2} a^{6} \\\\sin{\\\\theta}^{5} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-64r^{8} r_s^{2} a^{4} \\\\sin{\\\\theta}^{3} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}%\\n-64r^{8} r_s^{2} a^{4} \\\\sin{\\\\theta}^{3} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-160r^{6} r_s^{2} a^{6} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-160r^{6} r_s^{2} a^{6} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+32r^{8} r_s^{2} a^{4} \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+32r^{8} r_s^{2} a^{4} \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+80r^{6} r_s^{2} a^{6} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+80r^{6} r_s^{2} a^{6} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-32r^{5} r_s a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-32r^{5} r_s a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+80r^{10} r_s^{2} a^{2} \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+80r^{10} r_s^{2} a^{2} \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+176r^{8} r_s^{2} a^{4} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+176r^{8} r_s^{2} a^{4} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-80r^{7} r_s a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-80r^{7} r_s a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-24r^{4} r_s^{2} a^{8} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-24r^{4} r_s^{2} a^{8} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-128r^{4} r_s^{2} a^{8} \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-128r^{4} r_s^{2} a^{8} \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+64r^{4} r_s^{2} a^{8} \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}%\\n+64r^{4} r_s^{2} a^{8} \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-48r^{3} r_s a^{6} \\\\cos{\\\\theta}^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-48r^{3} r_s a^{6} \\\\cos{\\\\theta}^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+128r^{6} r_s^{2} a^{6} \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+128r^{6} r_s^{2} a^{6} \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-96r^{5} r_s a^{4} \\\\cos{\\\\theta}^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-96r^{5} r_s a^{4} \\\\cos{\\\\theta}^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-24r^{8} r_s^{2} a^{4} \\\\sin{\\\\theta}^{5} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-24r^{8} r_s^{2} a^{4} \\\\sin{\\\\theta}^{5} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-96r^{10} r_s^{2} a^{2} \\\\sin{\\\\theta}^{3} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-96r^{10} r_s^{2} a^{2} \\\\sin{\\\\theta}^{3} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-192r^{8} r_s^{2} a^{4} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-192r^{8} r_s^{2} a^{4} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+48r^{12} r_s^{2} \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+48r^{12} r_s^{2} \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+96r^{10} r_s^{2} a^{2} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+96r^{10} r_s^{2} a^{2} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-48r^{9} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-48r^{9} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-24r^{6} r_s^{2} a^{6} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}%\\n-24r^{6} r_s^{2} a^{6} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-128r^{6} r_s^{2} a^{6} \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-128r^{6} r_s^{2} a^{6} \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+64r^{8} r_s^{2} a^{4} \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+64r^{8} r_s^{2} a^{4} \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-48r^{7} r_s a^{2} \\\\cos{\\\\theta}^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-48r^{7} r_s a^{2} \\\\cos{\\\\theta}^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-80r^{8} r_s^{2} a^{6} \\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2}-200r^{6} r_s^{2} a^{8} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2}-96r^{6} r_s^{2} a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}+80r^{6} r_s^{2} a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-32r^{8} r_s^{2} a^{4} \\\\cos{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-32r^{8} r_s^{2} a^{4} \\\\cos{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-128r^{6} r_s^{2} a^{6} \\\\cos{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-128r^{6} r_s^{2} a^{6} \\\\cos{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+32r^{8} r_s^{2} a^{4} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+32r^{8} r_s^{2} a^{4} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+88r^{6} r_s^{2} a^{6} \\\\cos{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+88r^{6} r_s^{2} a^{6} \\\\cos{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-16r^{5} r_s a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}%\\n+48r^{5} r_s a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+48r^{5} r_s a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+136r^{8} r_s^{2} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+16r^{10} r_s^{2} a^{2} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+16r^{10} r_s^{2} a^{2} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-40r^{7} r_s a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+120r^{7} r_s a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+120r^{7} r_s a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-144r^{4} r_s^{2} a^{6} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}+120r^{4} r_s^{2} a^{6} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-112r^{4} r_s^{2} a^{8} \\\\cos{\\\\theta}^{7} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-112r^{4} r_s^{2} a^{8} \\\\cos{\\\\theta}^{7} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+80r^{4} r_s^{2} a^{8} \\\\cos{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+80r^{4} r_s^{2} a^{8} \\\\cos{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-24r^{3} r_s a^{6} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+72r^{3} r_s a^{6} \\\\cos{\\\\theta}^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+72r^{3} r_s a^{6} \\\\cos{\\\\theta}^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+128r^{6} r_s^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-48r^{5} r_s a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+144r^{5} r_s a^{4} \\\\cos{\\\\theta}^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}%\\n+144r^{5} r_s a^{4} \\\\cos{\\\\theta}^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-120r^{10} r_s^{2} a^{4} \\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2}-240r^{8} r_s^{2} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2}-144r^{8} r_s^{2} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}-184r^{10} r_s^{2} a^{2} \\\\cos{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-184r^{10} r_s^{2} a^{2} \\\\cos{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-240r^{8} r_s^{2} a^{4} \\\\cos{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-240r^{8} r_s^{2} a^{4} \\\\cos{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-48r^{12} r_s^{2} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-48r^{12} r_s^{2} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-24r^{9} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+72r^{9} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+72r^{9} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-144r^{6} r_s^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}-136r^{6} r_s^{2} a^{6} \\\\cos{\\\\theta}^{7} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-136r^{6} r_s^{2} a^{6} \\\\cos{\\\\theta}^{7} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8r^{8} r_s^{2} a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-24r^{7} r_s a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+72r^{7} r_s a^{2} \\\\cos{\\\\theta}^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+72r^{7} r_s a^{2} \\\\cos{\\\\theta}^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}%\\n-8r^{2} r_s^{2} a^{12} \\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-8r^{2} r_s^{2} a^{8} \\\\cos{\\\\theta}^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+16r^{3} r_s a^{8} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8r r_s a^{10} \\\\cos{\\\\theta}^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+24r^{4} r_s^{2} a^{6} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+32r^{5} r_s a^{6} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+16r^{3} r_s a^{8} \\\\cos{\\\\theta}^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-8r^{4} r_s^{2} a^{6} \\\\cos{\\\\theta}^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-16r^{6} r_s^{2} a^{4} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+16r^{7} r_s a^{4} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8r^{5} r_s a^{6} \\\\cos{\\\\theta}^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+16r^{7} r_s a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8r^{9} r_s a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8r^{5} r_s a^{6} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-8r^{5} r_s^{3} a^{8} \\\\cos{\\\\theta}^{3} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2}-8r^{3} r_s^{3} a^{10} \\\\cos{\\\\theta}^{5} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2}+8r^{6} r_s^{4} a^{6} \\\\cos{\\\\theta}^{3} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}+8r^{4} r_s^{4} a^{8} \\\\cos{\\\\theta}^{5} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}-16r^{7} r_s^{3} a^{6} \\\\cos{\\\\theta}^{3} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}-32r^{5} r_s^{3} a^{8} \\\\cos{\\\\theta}^{5} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}%\\n-16r^{3} r_s^{3} a^{10} \\\\cos{\\\\theta}^{7} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}+8r^{7} r_s^{3} a^{6} \\\\cos{\\\\theta}^{3} \\\\sin{2\\\\theta} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+16r^{5} r_s^{3} a^{8} \\\\cos{\\\\theta}^{5} \\\\sin{2\\\\theta} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8r^{3} r_s^{3} a^{10} \\\\cos{\\\\theta}^{7} \\\\sin{2\\\\theta} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8r^{4} r_s^{2} a^{6} \\\\cos{\\\\theta}^{3} \\\\sin{2\\\\theta} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8r^{2} r_s^{2} a^{8} \\\\cos{\\\\theta}^{5} \\\\sin{2\\\\theta} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8r^{9} r_s^{3} a^{4} \\\\cos{\\\\theta}^{3} \\\\sin{2\\\\theta} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+16r^{7} r_s^{3} a^{6} \\\\cos{\\\\theta}^{5} \\\\sin{2\\\\theta} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8r^{5} r_s^{3} a^{8} \\\\cos{\\\\theta}^{7} \\\\sin{2\\\\theta} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8r^{6} r_s^{2} a^{4} \\\\cos{\\\\theta}^{3} \\\\sin{2\\\\theta} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8r^{4} r_s^{2} a^{6} \\\\cos{\\\\theta}^{5} \\\\sin{2\\\\theta} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8r^{4} r_s^{2} a^{8} \\\\cos{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2}-8r^{2} r_s^{2} a^{10} \\\\cos{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2}+8r^{5} r_s^{3} a^{6} \\\\cos{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}+8r^{3} r_s^{3} a^{8} \\\\cos{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}-16r^{6} r_s^{2} a^{6} \\\\cos{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}-32r^{4} r_s^{2} a^{8} \\\\cos{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}-16r^{2} r_s^{2} a^{10} \\\\cos{\\\\theta}^{7} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}+24r^{2} r_s^{2} a^{10} \\\\cos{\\\\theta}^{7} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8r^{3} r_s a^{6} \\\\cos{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}%\\n-8r r_s a^{8} \\\\cos{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-16r^{5} r_s a^{4} \\\\cos{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-16r^{3} r_s a^{6} \\\\cos{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8r^{4} r_s^{2} a^{8} \\\\cos{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2}-8r^{2} r_s^{2} a^{10} \\\\cos{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2}+8r^{5} r_s^{3} a^{6} \\\\cos{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}+8r^{3} r_s^{3} a^{8} \\\\cos{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}-16r^{6} r_s^{2} a^{6} \\\\cos{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}-32r^{4} r_s^{2} a^{8} \\\\cos{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}-16r^{2} r_s^{2} a^{10} \\\\cos{\\\\theta}^{7} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}+24r^{2} r_s^{2} a^{10} \\\\cos{\\\\theta}^{7} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8r^{3} r_s a^{6} \\\\cos{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8r r_s a^{8} \\\\cos{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-16r^{5} r_s a^{4} \\\\cos{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-16r^{3} r_s a^{6} \\\\cos{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8r^{6} r_s^{2} a^{6} \\\\cos{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2}-8r^{4} r_s^{2} a^{8} \\\\cos{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2}+8r^{7} r_s^{3} a^{4} \\\\cos{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}+8r^{5} r_s^{3} a^{6} \\\\cos{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}-16r^{8} r_s^{2} a^{4} \\\\cos{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}%\\n-32r^{6} r_s^{2} a^{6} \\\\cos{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}-16r^{4} r_s^{2} a^{8} \\\\cos{\\\\theta}^{7} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}-8r^{7} r_s a^{2} \\\\cos{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8r^{5} r_s a^{4} \\\\cos{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8r^{6} r_s^{2} a^{6} \\\\cos{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2}-8r^{4} r_s^{2} a^{8} \\\\cos{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2}+8r^{7} r_s^{3} a^{4} \\\\cos{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}+8r^{5} r_s^{3} a^{6} \\\\cos{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}-16r^{8} r_s^{2} a^{4} \\\\cos{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}-32r^{6} r_s^{2} a^{6} \\\\cos{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}-16r^{4} r_s^{2} a^{8} \\\\cos{\\\\theta}^{7} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}-8r^{7} r_s a^{2} \\\\cos{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8r^{5} r_s a^{4} \\\\cos{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+16r^{3} r_s^{3} a^{10} \\\\cos{\\\\theta}^{10} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-8r^{3} r_s^{3} a^{10} \\\\cos{\\\\theta}^{10} \\\\tan{\\\\theta}^{2}+8r^{2} r_s^{2} a^{8} \\\\cos{\\\\theta}^{8} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2}-8r^{5} r_s^{3} a^{8} \\\\cos{\\\\theta}^{10} \\\\tan{\\\\theta}^{2}+8r^{4} r_s^{2} a^{6} \\\\cos{\\\\theta}^{8} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2}-16r^{2} r_s^{2} a^{12} \\\\cos{\\\\theta}^{10} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8r^{2} r_s^{2} a^{12} \\\\cos{\\\\theta}^{10} \\\\tan{\\\\theta}^{2}%\\n-8r r_s a^{10} \\\\cos{\\\\theta}^{8} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2}+16r^{4} r_s^{2} a^{10} \\\\cos{\\\\theta}^{10} \\\\tan{\\\\theta}^{2}-16r^{3} r_s a^{8} \\\\cos{\\\\theta}^{8} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2}-16r^{4} r_s^{2} a^{10} \\\\cos{\\\\theta}^{10} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8r^{6} r_s^{2} a^{8} \\\\cos{\\\\theta}^{10} \\\\tan{\\\\theta}^{2}-8r^{5} r_s a^{6} \\\\cos{\\\\theta}^{8} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2}+8r^{3} r_s^{3} a^{8} \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+8r^{3} r_s^{3} a^{8} \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+32r^{3} r_s^{3} a^{8} \\\\cos{\\\\theta}^{7} \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+32r^{3} r_s^{3} a^{8} \\\\cos{\\\\theta}^{7} \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-16r^{3} r_s^{3} a^{8} \\\\cos{\\\\theta}^{7} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-16r^{3} r_s^{3} a^{8} \\\\cos{\\\\theta}^{7} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+16r^{2} r_s^{2} a^{6} \\\\cos{\\\\theta}^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+16r^{2} r_s^{2} a^{6} \\\\cos{\\\\theta}^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-16r^{5} r_s^{3} a^{6} \\\\cos{\\\\theta}^{7} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-16r^{5} r_s^{3} a^{6} \\\\cos{\\\\theta}^{7} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+16r^{4} r_s^{2} a^{4} \\\\cos{\\\\theta}^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+16r^{4} r_s^{2} a^{4} \\\\cos{\\\\theta}^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-8r^{2} r_s^{2} a^{10} \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-8r^{2} r_s^{2} a^{10} \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}%\\n-32r^{2} r_s^{2} a^{10} \\\\cos{\\\\theta}^{7} \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-32r^{2} r_s^{2} a^{10} \\\\cos{\\\\theta}^{7} \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+16r^{2} r_s^{2} a^{10} \\\\cos{\\\\theta}^{7} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+16r^{2} r_s^{2} a^{10} \\\\cos{\\\\theta}^{7} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-16r r_s a^{8} \\\\cos{\\\\theta}^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-16r r_s a^{8} \\\\cos{\\\\theta}^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+32r^{4} r_s^{2} a^{8} \\\\cos{\\\\theta}^{7} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+32r^{4} r_s^{2} a^{8} \\\\cos{\\\\theta}^{7} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-32r^{3} r_s a^{6} \\\\cos{\\\\theta}^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-32r^{3} r_s a^{6} \\\\cos{\\\\theta}^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-8r^{4} r_s^{2} a^{8} \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-8r^{4} r_s^{2} a^{8} \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-32r^{4} r_s^{2} a^{8} \\\\cos{\\\\theta}^{7} \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-32r^{4} r_s^{2} a^{8} \\\\cos{\\\\theta}^{7} \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+16r^{6} r_s^{2} a^{6} \\\\cos{\\\\theta}^{7} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+16r^{6} r_s^{2} a^{6} \\\\cos{\\\\theta}^{7} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-16r^{5} r_s a^{4} \\\\cos{\\\\theta}^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-16r^{5} r_s a^{4} \\\\cos{\\\\theta}^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+48r^{3} r_s^{3} a^{6} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}-40r^{3} r_s^{3} a^{6} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}%\\n+32r^{3} r_s^{3} a^{8} \\\\cos{\\\\theta}^{9} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+32r^{3} r_s^{3} a^{8} \\\\cos{\\\\theta}^{9} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8r^{2} r_s^{2} a^{6} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-24r^{2} r_s^{2} a^{6} \\\\cos{\\\\theta}^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-24r^{2} r_s^{2} a^{6} \\\\cos{\\\\theta}^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8r^{4} r_s^{2} a^{4} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-24r^{4} r_s^{2} a^{4} \\\\cos{\\\\theta}^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-24r^{4} r_s^{2} a^{4} \\\\cos{\\\\theta}^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-48r^{2} r_s^{2} a^{8} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}+40r^{2} r_s^{2} a^{8} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-32r^{2} r_s^{2} a^{10} \\\\cos{\\\\theta}^{9} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-32r^{2} r_s^{2} a^{10} \\\\cos{\\\\theta}^{9} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8r r_s a^{8} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+24r r_s a^{8} \\\\cos{\\\\theta}^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+24r r_s a^{8} \\\\cos{\\\\theta}^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-16r^{3} r_s a^{6} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+48r^{3} r_s a^{6} \\\\cos{\\\\theta}^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+48r^{3} r_s a^{6} \\\\cos{\\\\theta}^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-48r^{4} r_s^{2} a^{6} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}-32r^{4} r_s^{2} a^{8} \\\\cos{\\\\theta}^{9} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}%\\n-32r^{4} r_s^{2} a^{8} \\\\cos{\\\\theta}^{9} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8r^{5} r_s a^{4} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+24r^{5} r_s a^{4} \\\\cos{\\\\theta}^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+24r^{5} r_s a^{4} \\\\cos{\\\\theta}^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8r^{4} r_s^{4} a^{8} \\\\sin{\\\\theta}^{8}-8r^{5} r_s^{3} a^{8} \\\\sin{\\\\theta}^{8}-8r^{3} r_s^{3} a^{10} \\\\sin{\\\\theta}^{8} \\\\cos{\\\\theta}^{2}+16r^{6} r_s^{4} a^{6} \\\\sin{\\\\theta}^{8}-8r^{5} r_s^{5} a^{6} \\\\sin{\\\\theta}^{8}-8r^{7} r_s^{3} a^{6} \\\\sin{\\\\theta}^{8}-8r^{5} r_s^{3} a^{8} \\\\sin{\\\\theta}^{8} \\\\cos{\\\\theta}^{2}+8r^{4} r_s^{4} a^{8} \\\\sin{\\\\theta}^{8} \\\\cos{\\\\theta}^{2}-8r^{5} r_s^{5} a^{6} \\\\sin{\\\\theta}^{6}+16r^{6} r_s^{4} a^{6} \\\\sin{\\\\theta}^{6}+16r^{4} r_s^{4} a^{8} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6}-24r^{7} r_s^{5} a^{4} \\\\sin{\\\\theta}^{6}+8r^{6} r_s^{6} a^{4} \\\\sin{\\\\theta}^{6}+24r^{8} r_s^{4} a^{4} \\\\sin{\\\\theta}^{6}+32r^{6} r_s^{4} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6}-16r^{5} r_s^{5} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6}%\\n-8r^{7} r_s^{3} a^{6} \\\\sin{\\\\theta}^{6}-16r^{5} r_s^{3} a^{8} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6}-8r^{9} r_s^{3} a^{4} \\\\sin{\\\\theta}^{6}-16r^{7} r_s^{3} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6}-8r^{3} r_s^{3} a^{10} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{6}-8r^{5} r_s^{3} a^{8} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{6}+8r^{4} r_s^{4} a^{8} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{6}-8r^{2} r_s^{2} \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r^{3} r_s \\\\sin{\\\\theta}^{2}+2a^{4} r r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}-a^{2} r^{3} r_s-a^{4} r r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-r^{5} r_s-r^{3} r_s a^{2} \\\\cos{\\\\theta}^{2}+r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+16r^{3} r_s \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r^{3} r_s \\\\sin{\\\\theta}^{2}+2a^{4} r r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}-a^{2} r^{3} r_s-a^{4} r r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-r^{5} r_s-r^{3} r_s a^{2} \\\\cos{\\\\theta}^{2}+r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+8r r_s a^{2} \\\\cos{\\\\theta}^{2} \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r^{3} r_s \\\\sin{\\\\theta}^{2}+2a^{4} r r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}-a^{2} r^{3} r_s-a^{4} r r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-r^{5} r_s-r^{3} r_s a^{2} \\\\cos{\\\\theta}^{2}+r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+8r^{6} a^{8} r_s^{2} \\\\sin{\\\\theta}^{6} \\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}-8r^{7} a^{8} r_s \\\\sin{\\\\theta}^{6} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-8r^{5} a^{10} r_s \\\\sin{\\\\theta}^{6} \\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}+8r^{8} a^{6} r_s^{2} \\\\sin{\\\\theta}^{6} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-8r^{9} a^{6} r_s \\\\sin{\\\\theta}^{6} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-8r^{7} a^{8} r_s \\\\sin{\\\\theta}^{6} \\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}-8r^{7} a^{6} r_s^{3} \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}+8r^{6} a^{8} r_s^{2} \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}-4r^{9} a^{4} r_s^{3} \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+16r^{10} a^{4} r_s^{2} \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}%\\n+24r^{8} a^{6} r_s^{2} \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}-8r^{7} a^{8} r_s \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}-4r^{11} a^{4} r_s \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-8r^{9} a^{6} r_s \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}+8r^{6} a^{8} r_s^{2} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}-24r^{7} a^{8} r_s \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}-16r^{5} a^{10} r_s \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}+16r^{8} a^{6} r_s^{2} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}-20r^{9} a^{6} r_s \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}-16r^{7} a^{8} r_s \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}-16r^{8} a^{6} r_s^{2} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8r^{9} a^{6} r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+16r^{7} a^{8} r_s \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8r^{10} a^{4} r_s^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+16r^{11} a^{4} r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+48r^{9} a^{6} r_s \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-8r^{6} a^{8} r_s^{2} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8r^{5} a^{10} r_s \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+32r^{7} a^{8} r_s \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8r^{5} a^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{4} r_s \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}%\\n-8r^{6} a^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-8r^{4} a^{8} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8r^{7} a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{2} r_s \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-16r^{8} a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-16r^{6} a^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-32r^{10} a^{4} r_s^{2} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-8r^{12} a^{2} r_s^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8r^{13} a^{2} r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+32r^{11} a^{4} r_s \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-40r^{8} a^{6} r_s^{2} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+24r^{9} a^{6} r_s \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8r^{7} a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{4} r_s \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8r^{9} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{2} r_s \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-8r^{10} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-8r^{8} a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-24r^{11} a^{4} r_s \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}-32r^{12} a^{2} r_s^{2} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}+4r^{13} a^{2} r_s \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}-32r^{10} a^{4} r_s^{2} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}+4r^{11} a^{2} r_s^{3} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}%\\n-28r^{9} a^{6} r_s \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}+4r^{7} a^{8} r_s \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-40r^{9} a^{6} r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}-16r^{10} a^{4} r_s^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}-4r^{11} a^{4} r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}+20r^{7} a^{6} r_s^{3} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}+16r^{8} a^{6} r_s^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}+40r^{6} a^{8} r_s^{2} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}+20r^{9} a^{4} r_s^{3} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}-36r^{7} a^{8} r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}-4r^{5} a^{10} r_s \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}+16r^{13} r_s a^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+32r^{11} r_s a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8r^{15} r_s \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+16r^{13} r_s a^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8r^{11} r_s a^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+16r^{9} r_s a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+16r^{9} r_s a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8r^{11} r_s a^{4} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8r^{7} r_s a^{8} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}%\\n+8r^{9} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-16r^{10} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-16r^{8} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+16r^{11} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-8r^{12} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-8r^{10} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-8r^{8} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s^{2} a^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8r^{9} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s a^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8r^{7} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-8r^{10} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8r^{9} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s a^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8r^{7} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{4} r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-8r^{8} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-8r^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8r^{9} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} r_s \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8r^{8} a^{6} r_s^{2} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{5} \\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2}+8r^{6} a^{8} r_s^{2} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{5} \\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}-8r^{9} a^{4} r_s^{3} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{3} \\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2}-8r^{7} a^{6} r_s^{3} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{3} \\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}+16r^{10} a^{4} r_s^{2} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{3} \\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2}%\\n+16r^{8} a^{6} r_s^{2} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{3} \\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}+16r^{8} a^{6} r_s^{2} \\\\sin{2\\\\theta} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}+16r^{6} a^{8} r_s^{2} \\\\sin{2\\\\theta} \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}-8r^{10} a^{4} r_s^{2} \\\\sin{2\\\\theta} \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2}-16r^{8} a^{6} r_s^{2} \\\\sin{2\\\\theta} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8r^{6} a^{8} r_s^{2} \\\\sin{2\\\\theta} \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8r^{7} a^{4} r_s \\\\sin{2\\\\theta} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2}+8r^{5} a^{6} r_s \\\\sin{2\\\\theta} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8r^{12} a^{2} r_s^{2} \\\\sin{2\\\\theta} \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2}-16r^{10} a^{4} r_s^{2} \\\\sin{2\\\\theta} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8r^{8} a^{6} r_s^{2} \\\\sin{2\\\\theta} \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8r^{9} a^{2} r_s \\\\sin{2\\\\theta} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2}+8r^{7} a^{4} r_s \\\\sin{2\\\\theta} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8r^{7} a^{6} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s \\\\sin{\\\\theta}^{5} \\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2}+8r^{5} a^{8} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s \\\\sin{\\\\theta}^{5} \\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}-8r^{8} a^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s^{2} \\\\sin{\\\\theta}^{3} \\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2}-8r^{6} a^{6} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s^{2} \\\\sin{\\\\theta}^{3} \\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}+16r^{9} a^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s \\\\sin{\\\\theta}^{3} \\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2}+16r^{7} a^{6} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s \\\\sin{\\\\theta}^{3} \\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}+16r^{7} a^{6} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}%\\n+16r^{5} a^{8} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}-8r^{9} a^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2}-16r^{7} a^{6} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8r^{5} a^{8} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8r^{6} a^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2}+8r^{4} a^{6} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8r^{11} a^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2}-16r^{9} a^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8r^{7} a^{6} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8r^{8} a^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2}+8r^{6} a^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8r^{7} a^{6} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\sin{\\\\theta}^{5} \\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2}+8r^{5} a^{8} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\sin{\\\\theta}^{5} \\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}-8r^{8} a^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s^{2} \\\\sin{\\\\theta}^{3} \\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2}-8r^{6} a^{6} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s^{2} \\\\sin{\\\\theta}^{3} \\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}+16r^{9} a^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\sin{\\\\theta}^{3} \\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2}+16r^{7} a^{6} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\sin{\\\\theta}^{3} \\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}+16r^{7} a^{6} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}+16r^{5} a^{8} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}-8r^{9} a^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2}%\\n-16r^{7} a^{6} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8r^{5} a^{8} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8r^{6} a^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2}+8r^{4} a^{6} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8r^{11} a^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2}-16r^{9} a^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8r^{7} a^{6} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8r^{8} a^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2}+8r^{6} a^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8r^{9} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{4} r_s \\\\sin{\\\\theta}^{5} \\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2}+8r^{7} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{6} r_s \\\\sin{\\\\theta}^{5} \\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}-8r^{10} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{2} r_s^{2} \\\\sin{\\\\theta}^{3} \\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2}-8r^{8} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{4} r_s^{2} \\\\sin{\\\\theta}^{3} \\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}+16r^{11} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{2} r_s \\\\sin{\\\\theta}^{3} \\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2}+16r^{9} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{4} r_s \\\\sin{\\\\theta}^{3} \\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}+16r^{9} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{4} r_s \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}+16r^{7} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{6} r_s \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}-8r^{11} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{2} r_s \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2}-16r^{9} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{4} r_s \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8r^{7} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{6} r_s \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}%\\n+8r^{8} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2}+8r^{6} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8r^{13} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2}-16r^{11} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s a^{2} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8r^{9} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s a^{4} \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8r^{10} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2}+8r^{8} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8r^{9} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{4} r_s \\\\sin{\\\\theta}^{5} \\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2}+8r^{7} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{6} r_s \\\\sin{\\\\theta}^{5} \\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}-8r^{10} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{2} r_s^{2} \\\\sin{\\\\theta}^{3} \\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2}-8r^{8} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{4} r_s^{2} \\\\sin{\\\\theta}^{3} \\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}+16r^{11} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{2} r_s \\\\sin{\\\\theta}^{3} \\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2}+16r^{9} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{4} r_s \\\\sin{\\\\theta}^{3} \\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}+16r^{9} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{4} r_s \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}+16r^{7} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{6} r_s \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}-8r^{11} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{2} r_s \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2}-16r^{9} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{4} r_s \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8r^{7} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{6} r_s \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8r^{8} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2}+8r^{6} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}%\\n-8r^{13} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2}-16r^{11} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s a^{2} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8r^{9} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s a^{4} \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8r^{10} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2}+8r^{8} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8r^{9} a^{4} r_s^{3} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8r^{7} a^{6} r_s^{3} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-16r^{6} a^{8} r_s^{2} \\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8r^{10} a^{4} r_s^{2} \\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}+16r^{8} a^{6} r_s^{2} \\\\cos{\\\\theta}^{6} \\\\tan{\\\\theta}^{2}+8r^{6} a^{8} r_s^{2} \\\\cos{\\\\theta}^{8} \\\\tan{\\\\theta}^{2}-8r^{7} a^{4} r_s \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2}-8r^{5} a^{6} r_s \\\\cos{\\\\theta}^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2}+8r^{12} a^{2} r_s^{2} \\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}+16r^{10} a^{4} r_s^{2} \\\\cos{\\\\theta}^{6} \\\\tan{\\\\theta}^{2}+8r^{8} a^{6} r_s^{2} \\\\cos{\\\\theta}^{8} \\\\tan{\\\\theta}^{2}-8r^{9} a^{2} r_s \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2}-8r^{7} a^{4} r_s \\\\cos{\\\\theta}^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2}-8r^{10} a^{4} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-8r^{8} a^{6} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}%\\n+16r^{11} a^{4} r_s \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+16r^{9} a^{6} r_s \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}-8r^{11} a^{4} r_s \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-16r^{9} a^{6} r_s \\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}-8r^{7} a^{8} r_s \\\\cos{\\\\theta}^{6} \\\\tan{\\\\theta}^{2}+8r^{8} a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8r^{6} a^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}-16r^{13} a^{2} r_s \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-32r^{11} a^{4} r_s \\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}-16r^{9} a^{6} r_s \\\\cos{\\\\theta}^{6} \\\\tan{\\\\theta}^{2}+16r^{10} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+16r^{8} a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}-96r^{7} a^{8} \\\\cos{\\\\theta}^{4} r_s \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}-48r^{5} a^{10} \\\\cos{\\\\theta}^{6} r_s \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}-8r^{8} a^{6} \\\\cos{\\\\theta}^{4} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-40r^{6} a^{8} \\\\cos{\\\\theta}^{6} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+80r^{9} a^{6} \\\\cos{\\\\theta}^{4} r_s \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+128r^{7} a^{8} \\\\cos{\\\\theta}^{6} r_s \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+80r^{5} a^{10} \\\\cos{\\\\theta}^{8} r_s \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-16r^{9} a^{6} \\\\cos{\\\\theta}^{4} r_s \\\\tan{\\\\theta}^{2}%\\n-40r^{7} a^{8} \\\\cos{\\\\theta}^{6} r_s \\\\tan{\\\\theta}^{2}-32r^{5} a^{10} \\\\cos{\\\\theta}^{8} r_s \\\\tan{\\\\theta}^{2}+16r^{6} a^{6} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2}+24r^{4} a^{8} \\\\cos{\\\\theta}^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2}-32r^{11} a^{4} \\\\cos{\\\\theta}^{4} r_s \\\\tan{\\\\theta}^{2}-80r^{9} a^{6} \\\\cos{\\\\theta}^{6} r_s \\\\tan{\\\\theta}^{2}-64r^{7} a^{8} \\\\cos{\\\\theta}^{8} r_s \\\\tan{\\\\theta}^{2}+32r^{8} a^{4} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2}+48r^{6} a^{6} \\\\cos{\\\\theta}^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2}-8r^{12} a^{2} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-8r^{10} a^{4} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}+16r^{13} a^{2} r_s \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+16r^{11} a^{4} r_s \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}-8r^{15} r_s \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-16r^{13} r_s a^{2} \\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}-8r^{11} r_s a^{4} \\\\cos{\\\\theta}^{6} \\\\tan{\\\\theta}^{2}+8r^{12} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8r^{10} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} \\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}-12r^{7} a^{8} \\\\cos{\\\\theta}^{6} r_s \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}-72r^{10} a^{4} \\\\cos{\\\\theta}^{4} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}%\\n-104r^{8} a^{6} \\\\cos{\\\\theta}^{6} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+56r^{11} a^{4} \\\\cos{\\\\theta}^{4} r_s \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+104r^{9} a^{6} \\\\cos{\\\\theta}^{6} r_s \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+72r^{7} a^{8} \\\\cos{\\\\theta}^{8} r_s \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-16r^{13} a^{2} \\\\cos{\\\\theta}^{4} r_s \\\\tan{\\\\theta}^{2}-40r^{11} a^{4} \\\\cos{\\\\theta}^{6} r_s \\\\tan{\\\\theta}^{2}-32r^{9} a^{6} \\\\cos{\\\\theta}^{8} r_s \\\\tan{\\\\theta}^{2}+16r^{10} a^{2} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2}+24r^{8} a^{4} \\\\cos{\\\\theta}^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2}-8r^{6} a^{6} r_s^{2} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-8r^{6} a^{6} r_s^{2} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+16r^{7} a^{4} r_s^{3} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+16r^{7} a^{4} r_s^{3} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-32r^{8} a^{4} r_s^{2} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-32r^{8} a^{4} r_s^{2} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-32r^{6} a^{6} r_s^{2} \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-32r^{6} a^{6} r_s^{2} \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+16r^{8} a^{4} r_s^{2} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+16r^{8} a^{4} r_s^{2} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+16r^{6} a^{6} r_s^{2} \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}%\\n+16r^{6} a^{6} r_s^{2} \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-16r^{5} a^{4} r_s \\\\cos{\\\\theta}^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-16r^{5} a^{4} r_s \\\\cos{\\\\theta}^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+16r^{10} a^{2} r_s^{2} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+16r^{10} a^{2} r_s^{2} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+16r^{8} a^{4} r_s^{2} \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+16r^{8} a^{4} r_s^{2} \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-16r^{7} a^{2} r_s \\\\cos{\\\\theta}^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-16r^{7} a^{2} r_s \\\\cos{\\\\theta}^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+8r^{7} a^{6} r_s \\\\sin{\\\\theta}^{5} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+8r^{7} a^{6} r_s \\\\sin{\\\\theta}^{5} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-16r^{8} a^{4} r_s^{2} \\\\sin{\\\\theta}^{3} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-16r^{8} a^{4} r_s^{2} \\\\sin{\\\\theta}^{3} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+32r^{9} a^{4} r_s \\\\sin{\\\\theta}^{3} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+32r^{9} a^{4} r_s \\\\sin{\\\\theta}^{3} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+32r^{7} a^{6} r_s \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+32r^{7} a^{6} r_s \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-16r^{9} a^{4} r_s \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-16r^{9} a^{4} r_s \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-16r^{7} a^{6} r_s \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}%\\n-16r^{7} a^{6} r_s \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+16r^{6} a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+16r^{6} a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-32r^{11} a^{2} r_s \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-32r^{11} a^{2} r_s \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-32r^{9} a^{4} r_s \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-32r^{9} a^{4} r_s \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+32r^{8} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+32r^{8} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+16r^{5} a^{8} \\\\cos{\\\\theta}^{3} r_s \\\\sin{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+16r^{5} a^{8} \\\\cos{\\\\theta}^{3} r_s \\\\sin{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-32r^{6} a^{6} \\\\cos{\\\\theta}^{3} r_s^{2} \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-32r^{6} a^{6} \\\\cos{\\\\theta}^{3} r_s^{2} \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+64r^{7} a^{6} \\\\cos{\\\\theta}^{3} r_s \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+64r^{7} a^{6} \\\\cos{\\\\theta}^{3} r_s \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+96r^{5} a^{8} \\\\cos{\\\\theta}^{5} r_s \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+96r^{5} a^{8} \\\\cos{\\\\theta}^{5} r_s \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-32r^{7} a^{6} \\\\cos{\\\\theta}^{3} r_s \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-32r^{7} a^{6} \\\\cos{\\\\theta}^{3} r_s \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-48r^{5} a^{8} \\\\cos{\\\\theta}^{5} r_s \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}%\\n-48r^{5} a^{8} \\\\cos{\\\\theta}^{5} r_s \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+32r^{4} a^{6} \\\\cos{\\\\theta}^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+32r^{4} a^{6} \\\\cos{\\\\theta}^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-64r^{9} a^{4} \\\\cos{\\\\theta}^{3} r_s \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-64r^{9} a^{4} \\\\cos{\\\\theta}^{3} r_s \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-96r^{7} a^{6} \\\\cos{\\\\theta}^{5} r_s \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-96r^{7} a^{6} \\\\cos{\\\\theta}^{5} r_s \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+64r^{6} a^{4} \\\\cos{\\\\theta}^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+64r^{6} a^{4} \\\\cos{\\\\theta}^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+8r^{9} a^{4} r_s \\\\sin{\\\\theta}^{5} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+8r^{9} a^{4} r_s \\\\sin{\\\\theta}^{5} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-16r^{10} a^{2} r_s^{2} \\\\sin{\\\\theta}^{3} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-16r^{10} a^{2} r_s^{2} \\\\sin{\\\\theta}^{3} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+32r^{11} a^{2} r_s \\\\sin{\\\\theta}^{3} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+32r^{11} a^{2} r_s \\\\sin{\\\\theta}^{3} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+32r^{9} a^{4} r_s \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+32r^{9} a^{4} r_s \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-16r^{13} r_s \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-16r^{13} r_s \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-16r^{11} r_s a^{2} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}%\\n-16r^{11} r_s a^{2} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+16r^{10} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+16r^{10} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+16r^{7} a^{6} \\\\cos{\\\\theta}^{3} r_s \\\\sin{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+16r^{7} a^{6} \\\\cos{\\\\theta}^{3} r_s \\\\sin{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-64r^{8} a^{4} \\\\cos{\\\\theta}^{3} r_s^{2} \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-64r^{8} a^{4} \\\\cos{\\\\theta}^{3} r_s^{2} \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+64r^{9} a^{4} \\\\cos{\\\\theta}^{3} r_s \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+64r^{9} a^{4} \\\\cos{\\\\theta}^{3} r_s \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+96r^{7} a^{6} \\\\cos{\\\\theta}^{5} r_s \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+96r^{7} a^{6} \\\\cos{\\\\theta}^{5} r_s \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-32r^{11} a^{2} \\\\cos{\\\\theta}^{3} r_s \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-32r^{11} a^{2} \\\\cos{\\\\theta}^{3} r_s \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-48r^{9} a^{4} \\\\cos{\\\\theta}^{5} r_s \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-48r^{9} a^{4} \\\\cos{\\\\theta}^{5} r_s \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+32r^{8} a^{2} \\\\cos{\\\\theta}^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+32r^{8} a^{2} \\\\cos{\\\\theta}^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-40r^{8} a^{6} r_s^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2}-40r^{6} a^{8} r_s^{2} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2}-16r^{9} a^{4} r_s^{3} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}%\\n-16r^{7} a^{6} r_s^{3} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8r^{7} a^{4} r_s^{3} \\\\cos{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8r^{7} a^{4} r_s^{3} \\\\cos{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8r^{7} a^{4} r_s^{3} \\\\cos{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8r^{7} a^{4} r_s^{3} \\\\cos{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-48r^{6} a^{4} r_s^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}+40r^{6} a^{4} r_s^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-48r^{8} a^{4} r_s^{2} \\\\cos{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-48r^{8} a^{4} r_s^{2} \\\\cos{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-32r^{6} a^{6} r_s^{2} \\\\cos{\\\\theta}^{7} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-32r^{6} a^{6} r_s^{2} \\\\cos{\\\\theta}^{7} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8r^{8} a^{4} r_s^{2} \\\\cos{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8r^{8} a^{4} r_s^{2} \\\\cos{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+16r^{6} a^{6} r_s^{2} \\\\cos{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+16r^{6} a^{6} r_s^{2} \\\\cos{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8r^{5} a^{4} r_s \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+24r^{5} a^{4} r_s \\\\cos{\\\\theta}^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+24r^{5} a^{4} r_s \\\\cos{\\\\theta}^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8r^{8} a^{2} r_s^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-24r^{10} a^{2} r_s^{2} \\\\cos{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}%\\n-24r^{10} a^{2} r_s^{2} \\\\cos{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8r^{7} a^{2} r_s \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+24r^{7} a^{2} r_s \\\\cos{\\\\theta}^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+24r^{7} a^{2} r_s \\\\cos{\\\\theta}^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+40r^{9} a^{6} r_s \\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2}+40r^{7} a^{8} r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2}+16r^{10} a^{4} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+16r^{8} a^{6} r_s^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8r^{8} a^{4} r_s^{2} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8r^{8} a^{4} r_s^{2} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+48r^{7} a^{4} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}-40r^{7} a^{4} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+32r^{9} a^{4} r_s \\\\cos{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+32r^{9} a^{4} r_s \\\\cos{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+32r^{7} a^{6} r_s \\\\cos{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+32r^{7} a^{6} r_s \\\\cos{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-16r^{9} a^{4} r_s \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-16r^{9} a^{4} r_s \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-16r^{7} a^{6} r_s \\\\cos{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-16r^{7} a^{6} r_s \\\\cos{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}%\\n+8r^{6} a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-24r^{6} a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-24r^{6} a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-48r^{9} a^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+16r^{8} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-48r^{8} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-48r^{8} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+80r^{7} a^{8} \\\\cos{\\\\theta}^{2} r_s \\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2}+112r^{5} a^{10} \\\\cos{\\\\theta}^{4} r_s \\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2}-60r^{7} a^{8} \\\\cos{\\\\theta}^{2} r_s \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}-96r^{5} a^{10} \\\\cos{\\\\theta}^{4} r_s \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}-24r^{8} a^{6} \\\\cos{\\\\theta}^{2} r_s^{2} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}+32r^{8} a^{6} \\\\cos{\\\\theta}^{2} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+48r^{6} a^{8} \\\\cos{\\\\theta}^{4} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+24r^{6} a^{6} \\\\cos{\\\\theta}^{5} r_s^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+24r^{6} a^{6} \\\\cos{\\\\theta}^{5} r_s^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+16r^{6} a^{6} \\\\cos{\\\\theta}^{3} r_s^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+16r^{6} a^{6} \\\\cos{\\\\theta}^{3} r_s^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+96r^{5} a^{6} \\\\cos{\\\\theta}^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}-80r^{5} a^{6} \\\\cos{\\\\theta}^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}%\\n+64r^{7} a^{6} \\\\cos{\\\\theta}^{5} r_s \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+64r^{7} a^{6} \\\\cos{\\\\theta}^{5} r_s \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+96r^{5} a^{8} \\\\cos{\\\\theta}^{7} r_s \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+96r^{5} a^{8} \\\\cos{\\\\theta}^{7} r_s \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-32r^{7} a^{6} \\\\cos{\\\\theta}^{3} r_s \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-32r^{7} a^{6} \\\\cos{\\\\theta}^{3} r_s \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-48r^{5} a^{8} \\\\cos{\\\\theta}^{5} r_s \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-48r^{5} a^{8} \\\\cos{\\\\theta}^{5} r_s \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+16r^{4} a^{6} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-48r^{4} a^{6} \\\\cos{\\\\theta}^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-48r^{4} a^{6} \\\\cos{\\\\theta}^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-96r^{7} a^{4} \\\\cos{\\\\theta}^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+32r^{6} a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-96r^{6} a^{4} \\\\cos{\\\\theta}^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-96r^{6} a^{4} \\\\cos{\\\\theta}^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+40r^{11} a^{4} r_s \\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2}+40r^{9} a^{6} r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2}+16r^{12} a^{2} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8r^{10} a^{2} r_s^{2} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8r^{10} a^{2} r_s^{2} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}%\\n+48r^{9} a^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}+32r^{11} a^{2} r_s \\\\cos{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+32r^{11} a^{2} r_s \\\\cos{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+32r^{9} a^{4} r_s \\\\cos{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+32r^{9} a^{4} r_s \\\\cos{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+16r^{13} r_s \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+16r^{13} r_s \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+16r^{11} r_s a^{2} \\\\cos{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+16r^{11} r_s a^{2} \\\\cos{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8r^{10} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-24r^{10} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-24r^{10} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+80r^{9} a^{6} \\\\cos{\\\\theta}^{2} r_s \\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2}+112r^{7} a^{8} \\\\cos{\\\\theta}^{4} r_s \\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2}-56r^{9} a^{6} \\\\cos{\\\\theta}^{2} r_s \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}-56r^{10} a^{4} \\\\cos{\\\\theta}^{2} r_s^{2} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}-56r^{8} a^{6} \\\\cos{\\\\theta}^{4} r_s^{2} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}+16r^{10} a^{4} \\\\cos{\\\\theta}^{2} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-80r^{8} a^{4} \\\\cos{\\\\theta}^{5} r_s^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-80r^{8} a^{4} \\\\cos{\\\\theta}^{5} r_s^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}%\\n+32r^{8} a^{4} \\\\cos{\\\\theta}^{3} r_s^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+32r^{8} a^{4} \\\\cos{\\\\theta}^{3} r_s^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+96r^{7} a^{4} \\\\cos{\\\\theta}^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}+112r^{9} a^{4} \\\\cos{\\\\theta}^{5} r_s \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+112r^{9} a^{4} \\\\cos{\\\\theta}^{5} r_s \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+112r^{7} a^{6} \\\\cos{\\\\theta}^{7} r_s \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+112r^{7} a^{6} \\\\cos{\\\\theta}^{7} r_s \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-16r^{9} a^{2} \\\\cos{\\\\theta}^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+32r^{11} a^{2} \\\\cos{\\\\theta}^{3} r_s \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+32r^{11} a^{2} \\\\cos{\\\\theta}^{3} r_s \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+16r^{8} a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-48r^{8} a^{2} \\\\cos{\\\\theta}^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-48r^{8} a^{2} \\\\cos{\\\\theta}^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-32r^{4} a^{10} \\\\cos{\\\\theta}^{6} r_s^{2} \\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2}+32r^{3} a^{12} \\\\cos{\\\\theta}^{6} r_s \\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2}-72r^{6} a^{8} \\\\cos{\\\\theta}^{4} r_s^{2} \\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2}+32r^{5} a^{10} \\\\cos{\\\\theta}^{6} r_s \\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2}+12r^{5} a^{8} \\\\cos{\\\\theta}^{6} r_s^{3} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}+24r^{4} a^{10} \\\\cos{\\\\theta}^{6} r_s^{2} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}+40r^{7} a^{6} \\\\cos{\\\\theta}^{4} r_s^{3} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}%\\n+8r^{6} a^{8} \\\\cos{\\\\theta}^{6} r_s^{2} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}+8r^{4} a^{10} \\\\cos{\\\\theta}^{8} r_s^{2} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}-8r^{3} a^{12} \\\\cos{\\\\theta}^{8} r_s \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}-8r^{5} a^{10} \\\\cos{\\\\theta}^{8} r_s \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}+24r^{7} a^{8} \\\\cos{\\\\theta}^{4} r_s \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+24r^{5} a^{10} \\\\cos{\\\\theta}^{6} r_s \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-16r^{4} a^{10} \\\\cos{\\\\theta}^{8} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8r^{3} a^{12} \\\\cos{\\\\theta}^{8} r_s \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8r^{3} a^{8} \\\\cos{\\\\theta}^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-16r^{4} a^{8} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-8r^{2} a^{10} \\\\cos{\\\\theta}^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+24r^{5} a^{6} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-32r^{6} a^{6} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-16r^{4} a^{8} \\\\cos{\\\\theta}^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-64r^{6} a^{8} \\\\cos{\\\\theta}^{8} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8r^{5} a^{6} \\\\cos{\\\\theta}^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+24r^{7} a^{4} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-16r^{8} a^{4} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-8r^{6} a^{6} \\\\cos{\\\\theta}^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+4r^{11} a^{4} \\\\cos{\\\\theta}^{2} r_s \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}%\\n+28r^{9} a^{4} \\\\cos{\\\\theta}^{2} r_s^{3} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}-36r^{3} a^{12} \\\\cos{\\\\theta}^{6} r_s \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}+16r^{11} a^{4} \\\\cos{\\\\theta}^{2} r_s \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-16r^{12} a^{2} \\\\cos{\\\\theta}^{2} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8r^{13} a^{2} \\\\cos{\\\\theta}^{2} r_s \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+24r^{9} a^{4} \\\\cos{\\\\theta}^{4} r_s^{3} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8r^{11} a^{2} \\\\cos{\\\\theta}^{2} r_s^{3} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8r^{9} a^{6} \\\\cos{\\\\theta}^{2} r_s \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+24r^{7} a^{6} \\\\cos{\\\\theta}^{6} r_s^{3} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-16r^{8} a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+16r^{9} a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-8r^{10} a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-8r^{6} a^{4} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+16r^{7} a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-8r^{8} a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-8r^{6} a^{6} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8r^{6} a^{8} \\\\cos{\\\\theta}^{3} r_s^{2} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2}+8r^{4} a^{10} \\\\cos{\\\\theta}^{5} r_s^{2} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2}-8r^{7} a^{6} \\\\cos{\\\\theta}^{3} r_s^{3} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}-8r^{5} a^{8} \\\\cos{\\\\theta}^{5} r_s^{3} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}%\\n+16r^{8} a^{6} \\\\cos{\\\\theta}^{3} r_s^{2} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}+32r^{6} a^{8} \\\\cos{\\\\theta}^{5} r_s^{2} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}+16r^{4} a^{10} \\\\cos{\\\\theta}^{7} r_s^{2} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}-8r^{8} a^{6} \\\\cos{\\\\theta}^{3} r_s^{2} \\\\sin{2\\\\theta} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-16r^{6} a^{8} \\\\cos{\\\\theta}^{5} r_s^{2} \\\\sin{2\\\\theta} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8r^{4} a^{10} \\\\cos{\\\\theta}^{7} r_s^{2} \\\\sin{2\\\\theta} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8r^{5} a^{6} \\\\cos{\\\\theta}^{3} r_s \\\\sin{2\\\\theta} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8r^{3} a^{8} \\\\cos{\\\\theta}^{5} r_s \\\\sin{2\\\\theta} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8r^{10} a^{4} \\\\cos{\\\\theta}^{3} r_s^{2} \\\\sin{2\\\\theta} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-16r^{8} a^{6} \\\\cos{\\\\theta}^{5} r_s^{2} \\\\sin{2\\\\theta} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8r^{6} a^{8} \\\\cos{\\\\theta}^{7} r_s^{2} \\\\sin{2\\\\theta} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8r^{7} a^{4} \\\\cos{\\\\theta}^{3} r_s \\\\sin{2\\\\theta} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8r^{5} a^{6} \\\\cos{\\\\theta}^{5} r_s \\\\sin{2\\\\theta} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8r^{5} a^{8} \\\\cos{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2}+8r^{3} a^{10} \\\\cos{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2}-8r^{6} a^{6} \\\\cos{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s^{2} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}-8r^{4} a^{8} \\\\cos{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s^{2} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}+16r^{7} a^{6} \\\\cos{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}+32r^{5} a^{8} \\\\cos{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}+16r^{3} a^{10} \\\\cos{\\\\theta}^{7} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}%\\n-8r^{7} a^{6} \\\\cos{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-16r^{5} a^{8} \\\\cos{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8r^{3} a^{10} \\\\cos{\\\\theta}^{7} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8r^{4} a^{6} \\\\cos{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8r^{2} a^{8} \\\\cos{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-16r^{9} a^{4} \\\\cos{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-32r^{7} a^{6} \\\\cos{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-16r^{5} a^{8} \\\\cos{\\\\theta}^{7} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+16r^{6} a^{4} \\\\cos{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+16r^{4} a^{6} \\\\cos{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8r^{5} a^{8} \\\\cos{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2}+8r^{3} a^{10} \\\\cos{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2}-8r^{6} a^{6} \\\\cos{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s^{2} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}-8r^{4} a^{8} \\\\cos{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s^{2} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}+16r^{7} a^{6} \\\\cos{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}+32r^{5} a^{8} \\\\cos{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}+16r^{3} a^{10} \\\\cos{\\\\theta}^{7} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}-8r^{7} a^{6} \\\\cos{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-16r^{5} a^{8} \\\\cos{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8r^{3} a^{10} \\\\cos{\\\\theta}^{7} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}%\\n+8r^{4} a^{6} \\\\cos{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8r^{2} a^{8} \\\\cos{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-16r^{9} a^{4} \\\\cos{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-32r^{7} a^{6} \\\\cos{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-16r^{5} a^{8} \\\\cos{\\\\theta}^{7} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+16r^{6} a^{4} \\\\cos{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+16r^{4} a^{6} \\\\cos{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8r^{7} a^{6} \\\\cos{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2}+8r^{5} a^{8} \\\\cos{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2}-8r^{8} a^{4} \\\\cos{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s^{2} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}-8r^{6} a^{6} \\\\cos{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s^{2} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}+16r^{9} a^{4} \\\\cos{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}+32r^{7} a^{6} \\\\cos{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}+16r^{5} a^{8} \\\\cos{\\\\theta}^{7} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}-8r^{11} a^{2} \\\\cos{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-16r^{9} a^{4} \\\\cos{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8r^{7} a^{6} \\\\cos{\\\\theta}^{7} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8r^{8} a^{2} \\\\cos{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8r^{6} a^{4} \\\\cos{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8r^{7} a^{6} \\\\cos{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2}%\\n+8r^{5} a^{8} \\\\cos{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2}-8r^{8} a^{4} \\\\cos{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s^{2} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}-8r^{6} a^{6} \\\\cos{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s^{2} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}+16r^{9} a^{4} \\\\cos{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}+32r^{7} a^{6} \\\\cos{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}+16r^{5} a^{8} \\\\cos{\\\\theta}^{7} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}-8r^{11} a^{2} \\\\cos{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-16r^{9} a^{4} \\\\cos{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8r^{7} a^{6} \\\\cos{\\\\theta}^{7} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8r^{8} a^{2} \\\\cos{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8r^{6} a^{4} \\\\cos{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8r^{5} a^{8} \\\\cos{\\\\theta}^{8} r_s^{3} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-16r^{4} a^{10} \\\\cos{\\\\theta}^{10} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+24r^{8} a^{6} \\\\cos{\\\\theta}^{6} r_s^{2} \\\\tan{\\\\theta}^{2}+24r^{6} a^{8} \\\\cos{\\\\theta}^{8} r_s^{2} \\\\tan{\\\\theta}^{2}+8r^{4} a^{10} \\\\cos{\\\\theta}^{10} r_s^{2} \\\\tan{\\\\theta}^{2}-16r^{5} a^{6} \\\\cos{\\\\theta}^{6} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2}-8r^{3} a^{8} \\\\cos{\\\\theta}^{8} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2}+24r^{10} a^{4} \\\\cos{\\\\theta}^{6} r_s^{2} \\\\tan{\\\\theta}^{2}+24r^{8} a^{6} \\\\cos{\\\\theta}^{8} r_s^{2} \\\\tan{\\\\theta}^{2}%\\n+8r^{6} a^{8} \\\\cos{\\\\theta}^{10} r_s^{2} \\\\tan{\\\\theta}^{2}-16r^{7} a^{4} \\\\cos{\\\\theta}^{6} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2}-8r^{5} a^{6} \\\\cos{\\\\theta}^{8} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2}+16r^{3} a^{12} \\\\cos{\\\\theta}^{10} r_s \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-8r^{3} a^{12} \\\\cos{\\\\theta}^{10} r_s \\\\tan{\\\\theta}^{2}+8r^{2} a^{10} \\\\cos{\\\\theta}^{8} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2}-16r^{5} a^{10} \\\\cos{\\\\theta}^{10} r_s \\\\tan{\\\\theta}^{2}+16r^{4} a^{8} \\\\cos{\\\\theta}^{8} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2}+8r^{10} a^{4} \\\\cos{\\\\theta}^{4} r_s^{2} \\\\tan{\\\\theta}^{2}-8r^{7} a^{4} \\\\cos{\\\\theta}^{4} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2}+8r^{12} a^{2} \\\\cos{\\\\theta}^{4} r_s^{2} \\\\tan{\\\\theta}^{2}-8r^{9} a^{2} \\\\cos{\\\\theta}^{4} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2}+16r^{5} a^{10} \\\\cos{\\\\theta}^{10} r_s \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-8r^{7} a^{8} \\\\cos{\\\\theta}^{10} r_s \\\\tan{\\\\theta}^{2}+8r^{6} a^{6} \\\\cos{\\\\theta}^{8} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2}-8r^{4} a^{8} \\\\cos{\\\\theta}^{5} r_s^{2} \\\\sin{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-8r^{4} a^{8} \\\\cos{\\\\theta}^{5} r_s^{2} \\\\sin{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+16r^{5} a^{6} \\\\cos{\\\\theta}^{5} r_s^{3} \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+16r^{5} a^{6} \\\\cos{\\\\theta}^{5} r_s^{3} \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-80r^{6} a^{6} \\\\cos{\\\\theta}^{5} r_s^{2} \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}%\\n-80r^{6} a^{6} \\\\cos{\\\\theta}^{5} r_s^{2} \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-32r^{4} a^{8} \\\\cos{\\\\theta}^{7} r_s^{2} \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-32r^{4} a^{8} \\\\cos{\\\\theta}^{7} r_s^{2} \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+32r^{6} a^{6} \\\\cos{\\\\theta}^{5} r_s^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+32r^{6} a^{6} \\\\cos{\\\\theta}^{5} r_s^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+16r^{4} a^{8} \\\\cos{\\\\theta}^{7} r_s^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+16r^{4} a^{8} \\\\cos{\\\\theta}^{7} r_s^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-16r^{3} a^{6} \\\\cos{\\\\theta}^{5} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-16r^{3} a^{6} \\\\cos{\\\\theta}^{5} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+32r^{8} a^{4} \\\\cos{\\\\theta}^{5} r_s^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+32r^{8} a^{4} \\\\cos{\\\\theta}^{5} r_s^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+16r^{6} a^{6} \\\\cos{\\\\theta}^{7} r_s^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+16r^{6} a^{6} \\\\cos{\\\\theta}^{7} r_s^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-16r^{5} a^{4} \\\\cos{\\\\theta}^{5} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-16r^{5} a^{4} \\\\cos{\\\\theta}^{5} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+8r^{3} a^{10} \\\\cos{\\\\theta}^{5} r_s \\\\sin{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+8r^{3} a^{10} \\\\cos{\\\\theta}^{5} r_s \\\\sin{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-16r^{4} a^{8} \\\\cos{\\\\theta}^{5} r_s^{2} \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-16r^{4} a^{8} \\\\cos{\\\\theta}^{5} r_s^{2} \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+32r^{3} a^{10} \\\\cos{\\\\theta}^{7} r_s \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}%\\n+32r^{3} a^{10} \\\\cos{\\\\theta}^{7} r_s \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-16r^{3} a^{10} \\\\cos{\\\\theta}^{7} r_s \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-16r^{3} a^{10} \\\\cos{\\\\theta}^{7} r_s \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+16r^{2} a^{8} \\\\cos{\\\\theta}^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+16r^{2} a^{8} \\\\cos{\\\\theta}^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-32r^{5} a^{8} \\\\cos{\\\\theta}^{7} r_s \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-32r^{5} a^{8} \\\\cos{\\\\theta}^{7} r_s \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+32r^{4} a^{6} \\\\cos{\\\\theta}^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+32r^{4} a^{6} \\\\cos{\\\\theta}^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-8r^{6} a^{6} \\\\cos{\\\\theta}^{3} r_s^{2} \\\\sin{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-8r^{6} a^{6} \\\\cos{\\\\theta}^{3} r_s^{2} \\\\sin{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+16r^{7} a^{4} \\\\cos{\\\\theta}^{3} r_s^{3} \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+16r^{7} a^{4} \\\\cos{\\\\theta}^{3} r_s^{3} \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+16r^{8} a^{4} \\\\cos{\\\\theta}^{3} r_s^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+16r^{8} a^{4} \\\\cos{\\\\theta}^{3} r_s^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-16r^{5} a^{4} \\\\cos{\\\\theta}^{3} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-16r^{5} a^{4} \\\\cos{\\\\theta}^{3} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+16r^{10} a^{2} \\\\cos{\\\\theta}^{3} r_s^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+16r^{10} a^{2} \\\\cos{\\\\theta}^{3} r_s^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-16r^{7} a^{2} \\\\cos{\\\\theta}^{3} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}%\\n-16r^{7} a^{2} \\\\cos{\\\\theta}^{3} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+8r^{5} a^{8} \\\\cos{\\\\theta}^{5} r_s \\\\sin{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+8r^{5} a^{8} \\\\cos{\\\\theta}^{5} r_s \\\\sin{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+32r^{5} a^{8} \\\\cos{\\\\theta}^{7} r_s \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+32r^{5} a^{8} \\\\cos{\\\\theta}^{7} r_s \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-16r^{7} a^{6} \\\\cos{\\\\theta}^{7} r_s \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-16r^{7} a^{6} \\\\cos{\\\\theta}^{7} r_s \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+16r^{6} a^{4} \\\\cos{\\\\theta}^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+16r^{6} a^{4} \\\\cos{\\\\theta}^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-32r^{7} a^{6} \\\\cos{\\\\theta}^{4} r_s^{3} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-16r^{5} a^{8} \\\\cos{\\\\theta}^{6} r_s^{3} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8r^{5} a^{6} \\\\cos{\\\\theta}^{7} r_s^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8r^{5} a^{6} \\\\cos{\\\\theta}^{7} r_s^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8r^{5} a^{6} \\\\cos{\\\\theta}^{5} r_s^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8r^{5} a^{6} \\\\cos{\\\\theta}^{5} r_s^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-48r^{4} a^{6} \\\\cos{\\\\theta}^{4} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}+40r^{4} a^{6} \\\\cos{\\\\theta}^{4} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-88r^{6} a^{6} \\\\cos{\\\\theta}^{7} r_s^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-88r^{6} a^{6} \\\\cos{\\\\theta}^{7} r_s^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-32r^{4} a^{8} \\\\cos{\\\\theta}^{9} r_s^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}%\\n-32r^{4} a^{8} \\\\cos{\\\\theta}^{9} r_s^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8r^{4} a^{8} \\\\cos{\\\\theta}^{7} r_s^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8r^{4} a^{8} \\\\cos{\\\\theta}^{7} r_s^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8r^{3} a^{6} \\\\cos{\\\\theta}^{4} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+24r^{3} a^{6} \\\\cos{\\\\theta}^{5} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+24r^{3} a^{6} \\\\cos{\\\\theta}^{5} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8r^{6} a^{4} \\\\cos{\\\\theta}^{4} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-8r^{5} a^{4} \\\\cos{\\\\theta}^{4} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+24r^{5} a^{4} \\\\cos{\\\\theta}^{5} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+24r^{5} a^{4} \\\\cos{\\\\theta}^{5} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+16r^{4} a^{10} \\\\cos{\\\\theta}^{6} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8r^{4} a^{8} \\\\cos{\\\\theta}^{5} r_s^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8r^{4} a^{8} \\\\cos{\\\\theta}^{5} r_s^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+48r^{3} a^{8} \\\\cos{\\\\theta}^{4} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}-40r^{3} a^{8} \\\\cos{\\\\theta}^{4} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+32r^{3} a^{10} \\\\cos{\\\\theta}^{9} r_s \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+32r^{3} a^{10} \\\\cos{\\\\theta}^{9} r_s \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-16r^{3} a^{10} \\\\cos{\\\\theta}^{7} r_s \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-16r^{3} a^{10} \\\\cos{\\\\theta}^{7} r_s \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8r^{2} a^{8} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}%\\n-24r^{2} a^{8} \\\\cos{\\\\theta}^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-24r^{2} a^{8} \\\\cos{\\\\theta}^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-48r^{5} a^{6} \\\\cos{\\\\theta}^{4} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+16r^{4} a^{6} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-48r^{4} a^{6} \\\\cos{\\\\theta}^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-48r^{4} a^{6} \\\\cos{\\\\theta}^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-40r^{8} a^{6} \\\\cos{\\\\theta}^{2} r_s^{2} \\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2}-16r^{9} a^{4} \\\\cos{\\\\theta}^{2} r_s^{3} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8r^{7} a^{4} \\\\cos{\\\\theta}^{5} r_s^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8r^{7} a^{4} \\\\cos{\\\\theta}^{5} r_s^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8r^{7} a^{4} \\\\cos{\\\\theta}^{3} r_s^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8r^{7} a^{4} \\\\cos{\\\\theta}^{3} r_s^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-48r^{6} a^{4} \\\\cos{\\\\theta}^{2} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}+40r^{6} a^{4} \\\\cos{\\\\theta}^{2} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-8r^{5} a^{4} \\\\cos{\\\\theta}^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+24r^{5} a^{4} \\\\cos{\\\\theta}^{3} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+24r^{5} a^{4} \\\\cos{\\\\theta}^{3} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8r^{8} a^{2} \\\\cos{\\\\theta}^{2} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-16r^{10} a^{2} \\\\cos{\\\\theta}^{3} r_s^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-16r^{10} a^{2} \\\\cos{\\\\theta}^{3} r_s^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}%\\n-8r^{7} a^{2} \\\\cos{\\\\theta}^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+24r^{7} a^{2} \\\\cos{\\\\theta}^{3} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+24r^{7} a^{2} \\\\cos{\\\\theta}^{3} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+48r^{5} a^{6} \\\\cos{\\\\theta}^{4} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}+32r^{5} a^{8} \\\\cos{\\\\theta}^{9} r_s \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+32r^{5} a^{8} \\\\cos{\\\\theta}^{9} r_s \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8r^{7} a^{4} \\\\cos{\\\\theta}^{4} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8r^{6} a^{4} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-24r^{6} a^{4} \\\\cos{\\\\theta}^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-24r^{6} a^{4} \\\\cos{\\\\theta}^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8r^{5} a^{8} r_s^{3} \\\\sin{\\\\theta}^{8}+8r^{6} a^{8} r_s^{2} \\\\sin{\\\\theta}^{8}+8r^{4} a^{10} r_s^{2} \\\\sin{\\\\theta}^{8} \\\\cos{\\\\theta}^{2}-16r^{7} a^{6} r_s^{3} \\\\sin{\\\\theta}^{8}+8r^{6} a^{6} r_s^{4} \\\\sin{\\\\theta}^{8}+8r^{8} a^{6} r_s^{2} \\\\sin{\\\\theta}^{8}+8r^{6} a^{8} r_s^{2} \\\\sin{\\\\theta}^{8} \\\\cos{\\\\theta}^{2}-8r^{5} a^{8} r_s^{3} \\\\sin{\\\\theta}^{8} \\\\cos{\\\\theta}^{2}+8r^{6} a^{6} r_s^{4} \\\\sin{\\\\theta}^{6}-16r^{7} a^{6} r_s^{3} \\\\sin{\\\\theta}^{6}%\\n-16r^{5} a^{8} r_s^{3} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6}+24r^{8} a^{4} r_s^{4} \\\\sin{\\\\theta}^{6}-8r^{7} a^{4} r_s^{5} \\\\sin{\\\\theta}^{6}-24r^{9} a^{4} r_s^{3} \\\\sin{\\\\theta}^{6}-32r^{7} a^{6} r_s^{3} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6}+16r^{6} a^{6} r_s^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6}+8r^{8} a^{6} r_s^{2} \\\\sin{\\\\theta}^{6}+16r^{6} a^{8} r_s^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6}+8r^{10} a^{4} r_s^{2} \\\\sin{\\\\theta}^{6}+16r^{8} a^{6} r_s^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6}+8r^{4} a^{10} r_s^{2} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{6}+8r^{6} a^{8} r_s^{2} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{6}-8r^{5} a^{8} r_s^{3} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{6}-8r^{4} \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r^{3} r_s \\\\sin{\\\\theta}^{2}+2a^{4} r r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}-a^{2} r^{3} r_s-a^{4} r r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-r^{5} r_s-r^{3} r_s a^{2} \\\\cos{\\\\theta}^{2}+r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-8r^{2} a^{2} \\\\cos{\\\\theta}^{2} \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r^{3} r_s \\\\sin{\\\\theta}^{2}+2a^{4} r r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}-a^{2} r^{3} r_s-a^{4} r r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-r^{5} r_s-r^{3} r_s a^{2} \\\\cos{\\\\theta}^{2}+r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+32a^{10} \\\\cos{\\\\theta}^{6} r^{3} r_s^{3} \\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2}-72a^{10} \\\\cos{\\\\theta}^{4} r^{4} r_s^{2} \\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2}-32a^{12} \\\\cos{\\\\theta}^{6} r^{2} r_s^{2} \\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2}+72a^{8} \\\\cos{\\\\theta}^{4} r^{5} r_s^{3} \\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2}-184a^{8} \\\\cos{\\\\theta}^{4} r^{6} r_s^{2} \\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2}%\\n-136a^{10} \\\\cos{\\\\theta}^{6} r^{4} r_s^{2} \\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2}-12a^{8} \\\\cos{\\\\theta}^{6} r^{4} r_s^{4} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}-24a^{8} \\\\cos{\\\\theta}^{4} r^{5} r_s^{3} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}-24a^{10} \\\\cos{\\\\theta}^{6} r^{3} r_s^{3} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}-40a^{6} \\\\cos{\\\\theta}^{4} r^{6} r_s^{4} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}+100a^{6} \\\\cos{\\\\theta}^{4} r^{7} r_s^{3} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}+44a^{8} \\\\cos{\\\\theta}^{6} r^{5} r_s^{3} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}+96a^{8} \\\\cos{\\\\theta}^{4} r^{6} r_s^{2} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}+104a^{10} \\\\cos{\\\\theta}^{6} r^{4} r_s^{2} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}-56a^{6} \\\\cos{\\\\theta}^{4} r^{8} r_s^{2} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}-4a^{8} \\\\cos{\\\\theta}^{6} r^{6} r_s^{2} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}+4a^{10} \\\\cos{\\\\theta}^{8} r^{3} r_s^{3} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}+32a^{12} \\\\cos{\\\\theta}^{8} r^{2} r_s^{2} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}+24a^{10} \\\\cos{\\\\theta}^{8} r^{4} r_s^{2} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}-16a^{8} \\\\cos{\\\\theta}^{6} r^{5} r_s^{3} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+24a^{8} \\\\cos{\\\\theta}^{4} r^{6} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+24a^{10} \\\\cos{\\\\theta}^{6} r^{4} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-32a^{6} \\\\cos{\\\\theta}^{4} r^{7} r_s^{3} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-80a^{6} \\\\cos{\\\\theta}^{4} r^{8} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-144a^{8} \\\\cos{\\\\theta}^{6} r^{6} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}%\\n+8a^{12} \\\\cos{\\\\theta}^{8} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-112a^{10} \\\\cos{\\\\theta}^{8} r^{4} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+32a^{8} \\\\cos{\\\\theta}^{6} r^{2} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-64a^{8} \\\\cos{\\\\theta}^{4} r^{3} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-32a^{10} \\\\cos{\\\\theta}^{6} r r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+104a^{6} \\\\cos{\\\\theta}^{4} r^{4} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-64a^{6} \\\\cos{\\\\theta}^{4} r^{5} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-32a^{8} \\\\cos{\\\\theta}^{6} r^{3} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+144a^{6} \\\\cos{\\\\theta}^{6} r^{7} r_s^{3} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+96a^{4} \\\\cos{\\\\theta}^{4} r^{9} r_s^{3} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-120a^{4} \\\\cos{\\\\theta}^{4} r^{10} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-232a^{6} \\\\cos{\\\\theta}^{6} r^{8} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+96a^{8} \\\\cos{\\\\theta}^{8} r^{5} r_s^{3} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-216a^{8} \\\\cos{\\\\theta}^{8} r^{6} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+24a^{6} \\\\cos{\\\\theta}^{2} r^{8} r_s^{2} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}+60a^{4} \\\\cos{\\\\theta}^{2} r^{9} r_s^{3} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}-36a^{4} \\\\cos{\\\\theta}^{2} r^{10} r_s^{2} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}-28a^{4} \\\\cos{\\\\theta}^{2} r^{8} r_s^{4} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}+28a^{8} \\\\cos{\\\\theta}^{2} r^{6} r_s^{2} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}+64a^{10} \\\\cos{\\\\theta}^{4} r^{4} r_s^{2} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}%\\n+36a^{12} \\\\cos{\\\\theta}^{6} r^{2} r_s^{2} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}-16a^{4} \\\\cos{\\\\theta}^{2} r^{10} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+24a^{2} \\\\cos{\\\\theta}^{2} r^{11} r_s^{3} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-24a^{2} \\\\cos{\\\\theta}^{2} r^{12} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-24a^{4} \\\\cos{\\\\theta}^{4} r^{8} r_s^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-16a^{4} \\\\cos{\\\\theta}^{2} r^{9} r_s^{3} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-8a^{2} \\\\cos{\\\\theta}^{2} r^{10} r_s^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8a^{6} \\\\cos{\\\\theta}^{2} r^{8} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-24a^{6} \\\\cos{\\\\theta}^{6} r^{6} r_s^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-32a^{4} \\\\cos{\\\\theta}^{2} r^{7} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+72a^{4} \\\\cos{\\\\theta}^{2} r^{6} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-32a^{6} \\\\cos{\\\\theta}^{2} r^{5} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-8a^{8} \\\\cos{\\\\theta}^{3} r^{5} r_s^{3} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2}-8a^{10} \\\\cos{\\\\theta}^{5} r^{3} r_s^{3} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2}+8a^{6} \\\\cos{\\\\theta}^{3} r^{6} r_s^{4} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}+8a^{8} \\\\cos{\\\\theta}^{5} r^{4} r_s^{4} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}-24a^{6} \\\\cos{\\\\theta}^{3} r^{7} r_s^{3} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}-48a^{8} \\\\cos{\\\\theta}^{5} r^{5} r_s^{3} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}-24a^{10} \\\\cos{\\\\theta}^{7} r^{3} r_s^{3} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}+8a^{6} \\\\cos{\\\\theta}^{3} r^{7} r_s^{3} \\\\sin{2\\\\theta} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}%\\n+16a^{8} \\\\cos{\\\\theta}^{5} r^{5} r_s^{3} \\\\sin{2\\\\theta} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8a^{10} \\\\cos{\\\\theta}^{7} r^{3} r_s^{3} \\\\sin{2\\\\theta} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8a^{6} \\\\cos{\\\\theta}^{3} r^{4} r_s^{2} \\\\sin{2\\\\theta} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8a^{8} \\\\cos{\\\\theta}^{5} r^{2} r_s^{2} \\\\sin{2\\\\theta} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8a^{4} \\\\cos{\\\\theta}^{3} r^{9} r_s^{3} \\\\sin{2\\\\theta} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+16a^{6} \\\\cos{\\\\theta}^{5} r^{7} r_s^{3} \\\\sin{2\\\\theta} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8a^{8} \\\\cos{\\\\theta}^{7} r^{5} r_s^{3} \\\\sin{2\\\\theta} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8a^{4} \\\\cos{\\\\theta}^{3} r^{6} r_s^{2} \\\\sin{2\\\\theta} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8a^{6} \\\\cos{\\\\theta}^{5} r^{4} r_s^{2} \\\\sin{2\\\\theta} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8a^{8} \\\\cos{\\\\theta}^{3} r^{4} r_s^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2}-8a^{10} \\\\cos{\\\\theta}^{5} r^{2} r_s^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2}+8a^{6} \\\\cos{\\\\theta}^{3} r^{5} r_s^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}+8a^{8} \\\\cos{\\\\theta}^{5} r^{3} r_s^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}-16a^{6} \\\\cos{\\\\theta}^{3} r^{6} r_s^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}-32a^{8} \\\\cos{\\\\theta}^{5} r^{4} r_s^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}-16a^{10} \\\\cos{\\\\theta}^{7} r^{2} r_s^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}+32a^{6} \\\\cos{\\\\theta}^{3} r^{6} r_s^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+64a^{8} \\\\cos{\\\\theta}^{5} r^{4} r_s^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+32a^{10} \\\\cos{\\\\theta}^{7} r^{2} r_s^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8a^{6} \\\\cos{\\\\theta}^{3} r^{3} r_s \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}%\\n-8a^{8} \\\\cos{\\\\theta}^{5} r r_s \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+40a^{4} \\\\cos{\\\\theta}^{3} r^{8} r_s^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+56a^{6} \\\\cos{\\\\theta}^{5} r^{6} r_s^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8a^{8} \\\\cos{\\\\theta}^{7} r^{4} r_s^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-16a^{4} \\\\cos{\\\\theta}^{3} r^{5} r_s \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-16a^{6} \\\\cos{\\\\theta}^{5} r^{3} r_s \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8a^{8} \\\\cos{\\\\theta}^{3} r^{4} r_s^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2}-8a^{10} \\\\cos{\\\\theta}^{5} r^{2} r_s^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2}+8a^{6} \\\\cos{\\\\theta}^{3} r^{5} r_s^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}+8a^{8} \\\\cos{\\\\theta}^{5} r^{3} r_s^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}-16a^{6} \\\\cos{\\\\theta}^{3} r^{6} r_s^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}-32a^{8} \\\\cos{\\\\theta}^{5} r^{4} r_s^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}-16a^{10} \\\\cos{\\\\theta}^{7} r^{2} r_s^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}+32a^{6} \\\\cos{\\\\theta}^{3} r^{6} r_s^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+64a^{8} \\\\cos{\\\\theta}^{5} r^{4} r_s^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+32a^{10} \\\\cos{\\\\theta}^{7} r^{2} r_s^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8a^{6} \\\\cos{\\\\theta}^{3} r^{3} r_s \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8a^{8} \\\\cos{\\\\theta}^{5} r r_s \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+40a^{4} \\\\cos{\\\\theta}^{3} r^{8} r_s^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+56a^{6} \\\\cos{\\\\theta}^{5} r^{6} r_s^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}%\\n-8a^{8} \\\\cos{\\\\theta}^{7} r^{4} r_s^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-16a^{4} \\\\cos{\\\\theta}^{3} r^{5} r_s \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-16a^{6} \\\\cos{\\\\theta}^{5} r^{3} r_s \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8a^{6} \\\\cos{\\\\theta}^{3} r^{6} r_s^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2}-8a^{8} \\\\cos{\\\\theta}^{5} r^{4} r_s^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2}+8a^{4} \\\\cos{\\\\theta}^{3} r^{7} r_s^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}+8a^{6} \\\\cos{\\\\theta}^{5} r^{5} r_s^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}-16a^{4} \\\\cos{\\\\theta}^{3} r^{8} r_s^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}-32a^{6} \\\\cos{\\\\theta}^{5} r^{6} r_s^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}-16a^{8} \\\\cos{\\\\theta}^{7} r^{4} r_s^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}-24a^{2} \\\\cos{\\\\theta}^{3} r^{10} r_s^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-136a^{4} \\\\cos{\\\\theta}^{5} r^{8} r_s^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-232a^{6} \\\\cos{\\\\theta}^{7} r^{6} r_s^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8a^{2} \\\\cos{\\\\theta}^{3} r^{7} r_s \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8a^{4} \\\\cos{\\\\theta}^{5} r^{5} r_s \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8a^{6} \\\\cos{\\\\theta}^{3} r^{6} r_s^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2}-8a^{8} \\\\cos{\\\\theta}^{5} r^{4} r_s^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2}+8a^{4} \\\\cos{\\\\theta}^{3} r^{7} r_s^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}+8a^{6} \\\\cos{\\\\theta}^{5} r^{5} r_s^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}-16a^{4} \\\\cos{\\\\theta}^{3} r^{8} r_s^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}%\\n-32a^{6} \\\\cos{\\\\theta}^{5} r^{6} r_s^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}-16a^{8} \\\\cos{\\\\theta}^{7} r^{4} r_s^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}-24a^{2} \\\\cos{\\\\theta}^{3} r^{10} r_s^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-136a^{4} \\\\cos{\\\\theta}^{5} r^{8} r_s^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-232a^{6} \\\\cos{\\\\theta}^{7} r^{6} r_s^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8a^{2} \\\\cos{\\\\theta}^{3} r^{7} r_s \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8a^{4} \\\\cos{\\\\theta}^{5} r^{5} r_s \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8a^{8} \\\\cos{\\\\theta}^{8} r^{4} r_s^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+24a^{10} \\\\cos{\\\\theta}^{10} r^{3} r_s^{3} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-24a^{6} \\\\cos{\\\\theta}^{6} r^{7} r_s^{3} \\\\tan{\\\\theta}^{2}-24a^{8} \\\\cos{\\\\theta}^{8} r^{5} r_s^{3} \\\\tan{\\\\theta}^{2}-8a^{10} \\\\cos{\\\\theta}^{10} r^{3} r_s^{3} \\\\tan{\\\\theta}^{2}+16a^{6} \\\\cos{\\\\theta}^{6} r^{4} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2}+8a^{8} \\\\cos{\\\\theta}^{8} r^{2} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2}-24a^{4} \\\\cos{\\\\theta}^{6} r^{9} r_s^{3} \\\\tan{\\\\theta}^{2}-24a^{6} \\\\cos{\\\\theta}^{8} r^{7} r_s^{3} \\\\tan{\\\\theta}^{2}-8a^{8} \\\\cos{\\\\theta}^{10} r^{5} r_s^{3} \\\\tan{\\\\theta}^{2}+16a^{4} \\\\cos{\\\\theta}^{6} r^{6} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2}+8a^{6} \\\\cos{\\\\theta}^{8} r^{4} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2}+8a^{6} \\\\cos{\\\\theta}^{4} r^{8} r_s^{2} \\\\tan{\\\\theta}^{2}%\\n+24a^{8} \\\\cos{\\\\theta}^{6} r^{6} r_s^{2} \\\\tan{\\\\theta}^{2}+24a^{10} \\\\cos{\\\\theta}^{8} r^{4} r_s^{2} \\\\tan{\\\\theta}^{2}-8a^{6} \\\\cos{\\\\theta}^{4} r^{5} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2}-16a^{8} \\\\cos{\\\\theta}^{6} r^{3} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2}+24a^{4} \\\\cos{\\\\theta}^{4} r^{10} r_s^{2} \\\\tan{\\\\theta}^{2}+80a^{6} \\\\cos{\\\\theta}^{6} r^{8} r_s^{2} \\\\tan{\\\\theta}^{2}+96a^{8} \\\\cos{\\\\theta}^{8} r^{6} r_s^{2} \\\\tan{\\\\theta}^{2}-24a^{4} \\\\cos{\\\\theta}^{4} r^{7} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2}-56a^{6} \\\\cos{\\\\theta}^{6} r^{5} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2}-32a^{12} \\\\cos{\\\\theta}^{10} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8a^{12} \\\\cos{\\\\theta}^{10} r^{2} r_s^{2} \\\\tan{\\\\theta}^{2}-8a^{10} \\\\cos{\\\\theta}^{8} r r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2}+48a^{10} \\\\cos{\\\\theta}^{10} r^{4} r_s^{2} \\\\tan{\\\\theta}^{2}-40a^{8} \\\\cos{\\\\theta}^{8} r^{3} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2}-8a^{4} \\\\cos{\\\\theta}^{4} r^{9} r_s^{3} \\\\tan{\\\\theta}^{2}+8a^{4} \\\\cos{\\\\theta}^{4} r^{6} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2}-8a^{2} \\\\cos{\\\\theta}^{4} r^{11} r_s^{3} \\\\tan{\\\\theta}^{2}+8a^{2} \\\\cos{\\\\theta}^{4} r^{8} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2}+16a^{2} \\\\cos{\\\\theta}^{4} r^{12} r_s^{2} \\\\tan{\\\\theta}^{2}+56a^{4} \\\\cos{\\\\theta}^{6} r^{10} r_s^{2} \\\\tan{\\\\theta}^{2}%\\n+72a^{6} \\\\cos{\\\\theta}^{8} r^{8} r_s^{2} \\\\tan{\\\\theta}^{2}-16a^{2} \\\\cos{\\\\theta}^{4} r^{9} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2}-40a^{4} \\\\cos{\\\\theta}^{6} r^{7} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2}-96a^{10} \\\\cos{\\\\theta}^{10} r^{4} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+40a^{8} \\\\cos{\\\\theta}^{10} r^{6} r_s^{2} \\\\tan{\\\\theta}^{2}-32a^{6} \\\\cos{\\\\theta}^{8} r^{5} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2}+8a^{8} \\\\cos{\\\\theta}^{5} r^{3} r_s^{3} \\\\sin{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+8a^{8} \\\\cos{\\\\theta}^{5} r^{3} r_s^{3} \\\\sin{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-16a^{6} \\\\cos{\\\\theta}^{5} r^{4} r_s^{4} \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-16a^{6} \\\\cos{\\\\theta}^{5} r^{4} r_s^{4} \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+112a^{6} \\\\cos{\\\\theta}^{5} r^{5} r_s^{3} \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+112a^{6} \\\\cos{\\\\theta}^{5} r^{5} r_s^{3} \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+48a^{8} \\\\cos{\\\\theta}^{7} r^{3} r_s^{3} \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+48a^{8} \\\\cos{\\\\theta}^{7} r^{3} r_s^{3} \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-32a^{6} \\\\cos{\\\\theta}^{5} r^{5} r_s^{3} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-32a^{6} \\\\cos{\\\\theta}^{5} r^{5} r_s^{3} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-16a^{8} \\\\cos{\\\\theta}^{7} r^{3} r_s^{3} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-16a^{8} \\\\cos{\\\\theta}^{7} r^{3} r_s^{3} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+16a^{6} \\\\cos{\\\\theta}^{5} r^{2} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+16a^{6} \\\\cos{\\\\theta}^{5} r^{2} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}%\\n-32a^{4} \\\\cos{\\\\theta}^{5} r^{7} r_s^{3} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-32a^{4} \\\\cos{\\\\theta}^{5} r^{7} r_s^{3} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-16a^{6} \\\\cos{\\\\theta}^{7} r^{5} r_s^{3} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-16a^{6} \\\\cos{\\\\theta}^{7} r^{5} r_s^{3} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+16a^{4} \\\\cos{\\\\theta}^{5} r^{4} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+16a^{4} \\\\cos{\\\\theta}^{5} r^{4} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-8a^{8} \\\\cos{\\\\theta}^{3} r^{4} r_s^{2} \\\\sin{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-8a^{8} \\\\cos{\\\\theta}^{3} r^{4} r_s^{2} \\\\sin{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+16a^{6} \\\\cos{\\\\theta}^{3} r^{5} r_s^{3} \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+16a^{6} \\\\cos{\\\\theta}^{3} r^{5} r_s^{3} \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-48a^{6} \\\\cos{\\\\theta}^{3} r^{6} r_s^{2} \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-48a^{6} \\\\cos{\\\\theta}^{3} r^{6} r_s^{2} \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-96a^{8} \\\\cos{\\\\theta}^{5} r^{4} r_s^{2} \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-96a^{8} \\\\cos{\\\\theta}^{5} r^{4} r_s^{2} \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+16a^{6} \\\\cos{\\\\theta}^{3} r^{6} r_s^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+16a^{6} \\\\cos{\\\\theta}^{3} r^{6} r_s^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+32a^{8} \\\\cos{\\\\theta}^{5} r^{4} r_s^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+32a^{8} \\\\cos{\\\\theta}^{5} r^{4} r_s^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-16a^{6} \\\\cos{\\\\theta}^{3} r^{3} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-16a^{6} \\\\cos{\\\\theta}^{3} r^{3} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}%\\n+48a^{4} \\\\cos{\\\\theta}^{3} r^{8} r_s^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+48a^{4} \\\\cos{\\\\theta}^{3} r^{8} r_s^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+112a^{6} \\\\cos{\\\\theta}^{5} r^{6} r_s^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+112a^{6} \\\\cos{\\\\theta}^{5} r^{6} r_s^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-48a^{4} \\\\cos{\\\\theta}^{3} r^{5} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-48a^{4} \\\\cos{\\\\theta}^{3} r^{5} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-8a^{10} \\\\cos{\\\\theta}^{5} r^{2} r_s^{2} \\\\sin{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-8a^{10} \\\\cos{\\\\theta}^{5} r^{2} r_s^{2} \\\\sin{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+16a^{8} \\\\cos{\\\\theta}^{5} r^{3} r_s^{3} \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+16a^{8} \\\\cos{\\\\theta}^{5} r^{3} r_s^{3} \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-48a^{10} \\\\cos{\\\\theta}^{7} r^{2} r_s^{2} \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-48a^{10} \\\\cos{\\\\theta}^{7} r^{2} r_s^{2} \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+16a^{10} \\\\cos{\\\\theta}^{7} r^{2} r_s^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+16a^{10} \\\\cos{\\\\theta}^{7} r^{2} r_s^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-16a^{8} \\\\cos{\\\\theta}^{5} r r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-16a^{8} \\\\cos{\\\\theta}^{5} r r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+80a^{8} \\\\cos{\\\\theta}^{7} r^{4} r_s^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+80a^{8} \\\\cos{\\\\theta}^{7} r^{4} r_s^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-64a^{6} \\\\cos{\\\\theta}^{5} r^{3} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-64a^{6} \\\\cos{\\\\theta}^{5} r^{3} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}%\\n+8a^{6} \\\\cos{\\\\theta}^{3} r^{5} r_s^{3} \\\\sin{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+8a^{6} \\\\cos{\\\\theta}^{3} r^{5} r_s^{3} \\\\sin{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-16a^{4} \\\\cos{\\\\theta}^{3} r^{6} r_s^{4} \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-16a^{4} \\\\cos{\\\\theta}^{3} r^{6} r_s^{4} \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+64a^{4} \\\\cos{\\\\theta}^{3} r^{7} r_s^{3} \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+64a^{4} \\\\cos{\\\\theta}^{3} r^{7} r_s^{3} \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-16a^{4} \\\\cos{\\\\theta}^{3} r^{7} r_s^{3} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-16a^{4} \\\\cos{\\\\theta}^{3} r^{7} r_s^{3} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+16a^{4} \\\\cos{\\\\theta}^{3} r^{4} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+16a^{4} \\\\cos{\\\\theta}^{3} r^{4} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-16a^{2} \\\\cos{\\\\theta}^{3} r^{9} r_s^{3} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-16a^{2} \\\\cos{\\\\theta}^{3} r^{9} r_s^{3} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+16a^{2} \\\\cos{\\\\theta}^{3} r^{6} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+16a^{2} \\\\cos{\\\\theta}^{3} r^{6} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-16a^{6} \\\\cos{\\\\theta}^{3} r^{6} r_s^{2} \\\\sin{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-16a^{6} \\\\cos{\\\\theta}^{3} r^{6} r_s^{2} \\\\sin{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-80a^{4} \\\\cos{\\\\theta}^{3} r^{8} r_s^{2} \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-80a^{4} \\\\cos{\\\\theta}^{3} r^{8} r_s^{2} \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-192a^{6} \\\\cos{\\\\theta}^{5} r^{6} r_s^{2} \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-192a^{6} \\\\cos{\\\\theta}^{5} r^{6} r_s^{2} \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}%\\n+32a^{2} \\\\cos{\\\\theta}^{3} r^{10} r_s^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+32a^{2} \\\\cos{\\\\theta}^{3} r^{10} r_s^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+80a^{4} \\\\cos{\\\\theta}^{5} r^{8} r_s^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+80a^{4} \\\\cos{\\\\theta}^{5} r^{8} r_s^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-32a^{2} \\\\cos{\\\\theta}^{3} r^{7} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-32a^{2} \\\\cos{\\\\theta}^{3} r^{7} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-24a^{8} \\\\cos{\\\\theta}^{5} r^{4} r_s^{2} \\\\sin{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-24a^{8} \\\\cos{\\\\theta}^{5} r^{4} r_s^{2} \\\\sin{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-144a^{8} \\\\cos{\\\\theta}^{7} r^{4} r_s^{2} \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-144a^{8} \\\\cos{\\\\theta}^{7} r^{4} r_s^{2} \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+64a^{6} \\\\cos{\\\\theta}^{7} r^{6} r_s^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+64a^{6} \\\\cos{\\\\theta}^{7} r^{6} r_s^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-48a^{4} \\\\cos{\\\\theta}^{5} r^{5} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-48a^{4} \\\\cos{\\\\theta}^{5} r^{5} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+32a^{6} \\\\cos{\\\\theta}^{4} r^{6} r_s^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+16a^{8} \\\\cos{\\\\theta}^{6} r^{4} r_s^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-8a^{6} \\\\cos{\\\\theta}^{7} r^{4} r_s^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8a^{6} \\\\cos{\\\\theta}^{7} r^{4} r_s^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8a^{6} \\\\cos{\\\\theta}^{5} r^{4} r_s^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8a^{6} \\\\cos{\\\\theta}^{5} r^{4} r_s^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}%\\n+48a^{6} \\\\cos{\\\\theta}^{4} r^{3} r_s^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}-40a^{6} \\\\cos{\\\\theta}^{4} r^{3} r_s^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+104a^{6} \\\\cos{\\\\theta}^{7} r^{5} r_s^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+104a^{6} \\\\cos{\\\\theta}^{7} r^{5} r_s^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+40a^{8} \\\\cos{\\\\theta}^{9} r^{3} r_s^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+40a^{8} \\\\cos{\\\\theta}^{9} r^{3} r_s^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-48a^{6} \\\\cos{\\\\theta}^{5} r^{5} r_s^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-48a^{6} \\\\cos{\\\\theta}^{5} r^{5} r_s^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-16a^{8} \\\\cos{\\\\theta}^{7} r^{3} r_s^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-16a^{8} \\\\cos{\\\\theta}^{7} r^{3} r_s^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8a^{6} \\\\cos{\\\\theta}^{4} r^{2} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-24a^{6} \\\\cos{\\\\theta}^{5} r^{2} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-24a^{6} \\\\cos{\\\\theta}^{5} r^{2} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+80a^{4} \\\\cos{\\\\theta}^{5} r^{7} r_s^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+80a^{4} \\\\cos{\\\\theta}^{5} r^{7} r_s^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8a^{4} \\\\cos{\\\\theta}^{4} r^{4} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-24a^{4} \\\\cos{\\\\theta}^{5} r^{4} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-24a^{4} \\\\cos{\\\\theta}^{5} r^{4} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-40a^{8} \\\\cos{\\\\theta}^{2} r^{6} r_s^{2} \\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2}-16a^{6} \\\\cos{\\\\theta}^{2} r^{7} r_s^{3} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}%\\n-32a^{8} \\\\cos{\\\\theta}^{4} r^{5} r_s^{3} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-8a^{6} \\\\cos{\\\\theta}^{3} r^{5} r_s^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8a^{6} \\\\cos{\\\\theta}^{3} r^{5} r_s^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-48a^{6} \\\\cos{\\\\theta}^{2} r^{4} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}+40a^{6} \\\\cos{\\\\theta}^{2} r^{4} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-8a^{6} \\\\cos{\\\\theta}^{2} r^{3} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+24a^{6} \\\\cos{\\\\theta}^{3} r^{3} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+24a^{6} \\\\cos{\\\\theta}^{3} r^{3} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-24a^{4} \\\\cos{\\\\theta}^{2} r^{5} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+72a^{4} \\\\cos{\\\\theta}^{3} r^{5} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+72a^{4} \\\\cos{\\\\theta}^{3} r^{5} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-16a^{10} \\\\cos{\\\\theta}^{6} r^{3} r_s^{3} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-8a^{8} \\\\cos{\\\\theta}^{5} r^{3} r_s^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8a^{8} \\\\cos{\\\\theta}^{5} r^{3} r_s^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-48a^{8} \\\\cos{\\\\theta}^{4} r^{2} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}+40a^{8} \\\\cos{\\\\theta}^{4} r^{2} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-24a^{10} \\\\cos{\\\\theta}^{9} r^{2} r_s^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-24a^{10} \\\\cos{\\\\theta}^{9} r^{2} r_s^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8a^{8} \\\\cos{\\\\theta}^{4} r r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+24a^{8} \\\\cos{\\\\theta}^{5} r r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}%\\n+24a^{8} \\\\cos{\\\\theta}^{5} r r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-32a^{6} \\\\cos{\\\\theta}^{4} r^{3} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+96a^{6} \\\\cos{\\\\theta}^{5} r^{3} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+96a^{6} \\\\cos{\\\\theta}^{5} r^{3} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+40a^{6} \\\\cos{\\\\theta}^{2} r^{7} r_s^{3} \\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2}+16a^{4} \\\\cos{\\\\theta}^{2} r^{8} r_s^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-8a^{4} \\\\cos{\\\\theta}^{5} r^{6} r_s^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8a^{4} \\\\cos{\\\\theta}^{5} r^{6} r_s^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8a^{4} \\\\cos{\\\\theta}^{3} r^{6} r_s^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8a^{4} \\\\cos{\\\\theta}^{3} r^{6} r_s^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+48a^{4} \\\\cos{\\\\theta}^{2} r^{5} r_s^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}-40a^{4} \\\\cos{\\\\theta}^{2} r^{5} r_s^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-32a^{4} \\\\cos{\\\\theta}^{3} r^{7} r_s^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-32a^{4} \\\\cos{\\\\theta}^{3} r^{7} r_s^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8a^{4} \\\\cos{\\\\theta}^{2} r^{4} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-24a^{4} \\\\cos{\\\\theta}^{3} r^{4} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-24a^{4} \\\\cos{\\\\theta}^{3} r^{4} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+16a^{2} \\\\cos{\\\\theta}^{3} r^{9} r_s^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+16a^{2} \\\\cos{\\\\theta}^{3} r^{9} r_s^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8a^{2} \\\\cos{\\\\theta}^{2} r^{6} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}%\\n-24a^{2} \\\\cos{\\\\theta}^{3} r^{6} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-24a^{2} \\\\cos{\\\\theta}^{3} r^{6} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-80a^{6} \\\\cos{\\\\theta}^{2} r^{8} r_s^{2} \\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2}-96a^{4} \\\\cos{\\\\theta}^{2} r^{6} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}-16a^{2} \\\\cos{\\\\theta}^{2} r^{7} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+48a^{2} \\\\cos{\\\\theta}^{3} r^{7} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+48a^{2} \\\\cos{\\\\theta}^{3} r^{7} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-144a^{6} \\\\cos{\\\\theta}^{4} r^{4} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}-152a^{8} \\\\cos{\\\\theta}^{9} r^{4} r_s^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-152a^{8} \\\\cos{\\\\theta}^{9} r^{4} r_s^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-24a^{4} \\\\cos{\\\\theta}^{4} r^{5} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+72a^{4} \\\\cos{\\\\theta}^{5} r^{5} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+72a^{4} \\\\cos{\\\\theta}^{5} r^{5} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+112a^{10} \\\\cos{\\\\theta}^{4} r^{5} r_s \\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2}+104a^{12} \\\\cos{\\\\theta}^{6} r^{3} r_s \\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2}+112a^{8} \\\\cos{\\\\theta}^{4} r^{7} r_s \\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2}+104a^{10} \\\\cos{\\\\theta}^{6} r^{5} r_s \\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2}-96a^{8} \\\\cos{\\\\theta}^{4} r^{7} r_s \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}-128a^{10} \\\\cos{\\\\theta}^{6} r^{5} r_s \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}-4a^{6} \\\\cos{\\\\theta}^{4} r^{9} r_s \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}%\\n-28a^{8} \\\\cos{\\\\theta}^{6} r^{7} r_s \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}-64a^{12} \\\\cos{\\\\theta}^{8} r^{3} r_s \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}-28a^{10} \\\\cos{\\\\theta}^{8} r^{5} r_s \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}+32a^{8} \\\\cos{\\\\theta}^{4} r^{7} r_s \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+48a^{10} \\\\cos{\\\\theta}^{6} r^{5} r_s \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+80a^{6} \\\\cos{\\\\theta}^{4} r^{9} r_s \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+160a^{8} \\\\cos{\\\\theta}^{6} r^{7} r_s \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+32a^{12} \\\\cos{\\\\theta}^{8} r^{3} r_s \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+160a^{10} \\\\cos{\\\\theta}^{8} r^{5} r_s \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+24a^{8} \\\\cos{\\\\theta}^{6} r^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-24a^{8} \\\\cos{\\\\theta}^{4} r^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-16a^{10} \\\\cos{\\\\theta}^{6} r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+40a^{6} \\\\cos{\\\\theta}^{4} r^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-48a^{6} \\\\cos{\\\\theta}^{4} r^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-40a^{8} \\\\cos{\\\\theta}^{6} r^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+48a^{4} \\\\cos{\\\\theta}^{4} r^{11} r_s \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+112a^{6} \\\\cos{\\\\theta}^{6} r^{9} r_s \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+128a^{8} \\\\cos{\\\\theta}^{8} r^{7} r_s \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+32a^{6} \\\\cos{\\\\theta}^{6} r^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+40a^{4} \\\\cos{\\\\theta}^{4} r^{7} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}%\\n-24a^{4} \\\\cos{\\\\theta}^{4} r^{8} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-24a^{6} \\\\cos{\\\\theta}^{6} r^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-24a^{6} \\\\cos{\\\\theta}^{2} r^{9} r_s \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}+4a^{4} \\\\cos{\\\\theta}^{2} r^{11} r_s \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}-28a^{8} \\\\cos{\\\\theta}^{2} r^{7} r_s \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}-92a^{10} \\\\cos{\\\\theta}^{4} r^{5} r_s \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}-100a^{12} \\\\cos{\\\\theta}^{6} r^{3} r_s \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}+16a^{4} \\\\cos{\\\\theta}^{2} r^{11} r_s \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8a^{2} \\\\cos{\\\\theta}^{2} r^{13} r_s \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8a^{6} \\\\cos{\\\\theta}^{2} r^{9} r_s \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-16a^{4} \\\\cos{\\\\theta}^{2} r^{8} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+16a^{2} \\\\cos{\\\\theta}^{2} r^{9} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-8a^{2} \\\\cos{\\\\theta}^{2} r^{10} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-16a^{4} \\\\cos{\\\\theta}^{4} r^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+16a^{4} \\\\cos{\\\\theta}^{2} r^{7} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-8a^{2} \\\\cos{\\\\theta}^{2} r^{8} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-8a^{6} \\\\cos{\\\\theta}^{2} r^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8a^{8} \\\\cos{\\\\theta}^{3} r^{6} r_s^{2} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2}+16a^{10} \\\\cos{\\\\theta}^{5} r^{4} r_s^{2} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2}+16a^{6} \\\\cos{\\\\theta}^{3} r^{8} r_s^{2} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}%\\n+48a^{8} \\\\cos{\\\\theta}^{5} r^{6} r_s^{2} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}+48a^{10} \\\\cos{\\\\theta}^{7} r^{4} r_s^{2} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}-8a^{6} \\\\cos{\\\\theta}^{3} r^{8} r_s^{2} \\\\sin{2\\\\theta} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-24a^{8} \\\\cos{\\\\theta}^{5} r^{6} r_s^{2} \\\\sin{2\\\\theta} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-24a^{10} \\\\cos{\\\\theta}^{7} r^{4} r_s^{2} \\\\sin{2\\\\theta} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8a^{6} \\\\cos{\\\\theta}^{3} r^{5} r_s \\\\sin{2\\\\theta} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+16a^{8} \\\\cos{\\\\theta}^{5} r^{3} r_s \\\\sin{2\\\\theta} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8a^{4} \\\\cos{\\\\theta}^{3} r^{10} r_s^{2} \\\\sin{2\\\\theta} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-24a^{6} \\\\cos{\\\\theta}^{5} r^{8} r_s^{2} \\\\sin{2\\\\theta} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-24a^{8} \\\\cos{\\\\theta}^{7} r^{6} r_s^{2} \\\\sin{2\\\\theta} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8a^{4} \\\\cos{\\\\theta}^{3} r^{7} r_s \\\\sin{2\\\\theta} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+16a^{6} \\\\cos{\\\\theta}^{5} r^{5} r_s \\\\sin{2\\\\theta} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8a^{8} \\\\cos{\\\\theta}^{3} r^{5} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2}+8a^{10} \\\\cos{\\\\theta}^{5} r^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2}-8a^{6} \\\\cos{\\\\theta}^{3} r^{6} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s^{2} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}-8a^{8} \\\\cos{\\\\theta}^{5} r^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s^{2} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}+16a^{6} \\\\cos{\\\\theta}^{3} r^{7} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}+32a^{8} \\\\cos{\\\\theta}^{5} r^{5} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}+16a^{10} \\\\cos{\\\\theta}^{7} r^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}-8a^{6} \\\\cos{\\\\theta}^{3} r^{7} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}%\\n-16a^{8} \\\\cos{\\\\theta}^{5} r^{5} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8a^{10} \\\\cos{\\\\theta}^{7} r^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8a^{6} \\\\cos{\\\\theta}^{3} r^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8a^{8} \\\\cos{\\\\theta}^{5} r^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-16a^{4} \\\\cos{\\\\theta}^{3} r^{9} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-40a^{6} \\\\cos{\\\\theta}^{5} r^{7} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-32a^{8} \\\\cos{\\\\theta}^{7} r^{5} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+16a^{4} \\\\cos{\\\\theta}^{3} r^{6} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+24a^{6} \\\\cos{\\\\theta}^{5} r^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8a^{8} \\\\cos{\\\\theta}^{3} r^{5} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2}+8a^{10} \\\\cos{\\\\theta}^{5} r^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2}-8a^{6} \\\\cos{\\\\theta}^{3} r^{6} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s^{2} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}-8a^{8} \\\\cos{\\\\theta}^{5} r^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s^{2} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}+16a^{6} \\\\cos{\\\\theta}^{3} r^{7} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}+32a^{8} \\\\cos{\\\\theta}^{5} r^{5} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}+16a^{10} \\\\cos{\\\\theta}^{7} r^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}-8a^{6} \\\\cos{\\\\theta}^{3} r^{7} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-16a^{8} \\\\cos{\\\\theta}^{5} r^{5} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8a^{10} \\\\cos{\\\\theta}^{7} r^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8a^{6} \\\\cos{\\\\theta}^{3} r^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}%\\n+8a^{8} \\\\cos{\\\\theta}^{5} r^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-16a^{4} \\\\cos{\\\\theta}^{3} r^{9} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-40a^{6} \\\\cos{\\\\theta}^{5} r^{7} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-32a^{8} \\\\cos{\\\\theta}^{7} r^{5} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+16a^{4} \\\\cos{\\\\theta}^{3} r^{6} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+24a^{6} \\\\cos{\\\\theta}^{5} r^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8a^{6} \\\\cos{\\\\theta}^{3} r^{7} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2}+16a^{8} \\\\cos{\\\\theta}^{5} r^{5} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2}-8a^{4} \\\\cos{\\\\theta}^{3} r^{8} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s^{2} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}-16a^{6} \\\\cos{\\\\theta}^{5} r^{6} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s^{2} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}+16a^{4} \\\\cos{\\\\theta}^{3} r^{9} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}+48a^{6} \\\\cos{\\\\theta}^{5} r^{7} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}+48a^{8} \\\\cos{\\\\theta}^{7} r^{5} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}-8a^{2} \\\\cos{\\\\theta}^{3} r^{11} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-24a^{4} \\\\cos{\\\\theta}^{5} r^{9} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-24a^{6} \\\\cos{\\\\theta}^{7} r^{7} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8a^{2} \\\\cos{\\\\theta}^{3} r^{8} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+16a^{4} \\\\cos{\\\\theta}^{5} r^{6} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8a^{6} \\\\cos{\\\\theta}^{3} r^{7} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2}+16a^{8} \\\\cos{\\\\theta}^{5} r^{5} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2}%\\n-8a^{4} \\\\cos{\\\\theta}^{3} r^{8} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s^{2} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}-16a^{6} \\\\cos{\\\\theta}^{5} r^{6} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s^{2} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}+16a^{4} \\\\cos{\\\\theta}^{3} r^{9} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}+48a^{6} \\\\cos{\\\\theta}^{5} r^{7} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}+48a^{8} \\\\cos{\\\\theta}^{7} r^{5} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}-8a^{2} \\\\cos{\\\\theta}^{3} r^{11} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-24a^{4} \\\\cos{\\\\theta}^{5} r^{9} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-24a^{6} \\\\cos{\\\\theta}^{7} r^{7} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8a^{2} \\\\cos{\\\\theta}^{3} r^{8} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+16a^{4} \\\\cos{\\\\theta}^{5} r^{6} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8a^{6} \\\\cos{\\\\theta}^{4} r^{9} r_s \\\\tan{\\\\theta}^{2}-32a^{8} \\\\cos{\\\\theta}^{6} r^{7} r_s \\\\tan{\\\\theta}^{2}-48a^{10} \\\\cos{\\\\theta}^{8} r^{5} r_s \\\\tan{\\\\theta}^{2}+8a^{6} \\\\cos{\\\\theta}^{4} r^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2}+24a^{8} \\\\cos{\\\\theta}^{6} r^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2}-16a^{4} \\\\cos{\\\\theta}^{4} r^{11} r_s \\\\tan{\\\\theta}^{2}-64a^{6} \\\\cos{\\\\theta}^{6} r^{9} r_s \\\\tan{\\\\theta}^{2}-96a^{8} \\\\cos{\\\\theta}^{8} r^{7} r_s \\\\tan{\\\\theta}^{2}+16a^{4} \\\\cos{\\\\theta}^{4} r^{8} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2}+48a^{6} \\\\cos{\\\\theta}^{6} r^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2}%\\n+80a^{12} \\\\cos{\\\\theta}^{10} r^{3} r_s \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-32a^{12} \\\\cos{\\\\theta}^{10} r^{3} r_s \\\\tan{\\\\theta}^{2}+16a^{10} \\\\cos{\\\\theta}^{8} r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2}-64a^{10} \\\\cos{\\\\theta}^{10} r^{5} r_s \\\\tan{\\\\theta}^{2}+48a^{8} \\\\cos{\\\\theta}^{8} r^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2}-8a^{2} \\\\cos{\\\\theta}^{4} r^{13} r_s \\\\tan{\\\\theta}^{2}-32a^{4} \\\\cos{\\\\theta}^{6} r^{11} r_s \\\\tan{\\\\theta}^{2}-48a^{6} \\\\cos{\\\\theta}^{8} r^{9} r_s \\\\tan{\\\\theta}^{2}+8a^{2} \\\\cos{\\\\theta}^{4} r^{10} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2}+24a^{4} \\\\cos{\\\\theta}^{6} r^{8} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2}+72a^{10} \\\\cos{\\\\theta}^{10} r^{5} r_s \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-32a^{8} \\\\cos{\\\\theta}^{10} r^{7} r_s \\\\tan{\\\\theta}^{2}+24a^{6} \\\\cos{\\\\theta}^{8} r^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2}+8a^{8} \\\\cos{\\\\theta}^{3} r^{5} r_s \\\\sin{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+8a^{8} \\\\cos{\\\\theta}^{3} r^{5} r_s \\\\sin{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+32a^{6} \\\\cos{\\\\theta}^{3} r^{7} r_s \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+32a^{6} \\\\cos{\\\\theta}^{3} r^{7} r_s \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+96a^{8} \\\\cos{\\\\theta}^{5} r^{5} r_s \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+96a^{8} \\\\cos{\\\\theta}^{5} r^{5} r_s \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-16a^{6} \\\\cos{\\\\theta}^{3} r^{7} r_s \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}%\\n-16a^{6} \\\\cos{\\\\theta}^{3} r^{7} r_s \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-48a^{8} \\\\cos{\\\\theta}^{5} r^{5} r_s \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-48a^{8} \\\\cos{\\\\theta}^{5} r^{5} r_s \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+16a^{6} \\\\cos{\\\\theta}^{3} r^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+16a^{6} \\\\cos{\\\\theta}^{3} r^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-32a^{4} \\\\cos{\\\\theta}^{3} r^{9} r_s \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-32a^{4} \\\\cos{\\\\theta}^{3} r^{9} r_s \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-96a^{6} \\\\cos{\\\\theta}^{5} r^{7} r_s \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-96a^{6} \\\\cos{\\\\theta}^{5} r^{7} r_s \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+32a^{4} \\\\cos{\\\\theta}^{3} r^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+32a^{4} \\\\cos{\\\\theta}^{3} r^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+16a^{10} \\\\cos{\\\\theta}^{5} r^{3} r_s \\\\sin{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+16a^{10} \\\\cos{\\\\theta}^{5} r^{3} r_s \\\\sin{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+96a^{10} \\\\cos{\\\\theta}^{7} r^{3} r_s \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+96a^{10} \\\\cos{\\\\theta}^{7} r^{3} r_s \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-48a^{10} \\\\cos{\\\\theta}^{7} r^{3} r_s \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-48a^{10} \\\\cos{\\\\theta}^{7} r^{3} r_s \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+32a^{8} \\\\cos{\\\\theta}^{5} r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+32a^{8} \\\\cos{\\\\theta}^{5} r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-96a^{8} \\\\cos{\\\\theta}^{7} r^{5} r_s \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}%\\n-96a^{8} \\\\cos{\\\\theta}^{7} r^{5} r_s \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+64a^{6} \\\\cos{\\\\theta}^{5} r^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+64a^{6} \\\\cos{\\\\theta}^{5} r^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+8a^{6} \\\\cos{\\\\theta}^{3} r^{7} r_s \\\\sin{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+8a^{6} \\\\cos{\\\\theta}^{3} r^{7} r_s \\\\sin{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+32a^{4} \\\\cos{\\\\theta}^{3} r^{9} r_s \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+32a^{4} \\\\cos{\\\\theta}^{3} r^{9} r_s \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+96a^{6} \\\\cos{\\\\theta}^{5} r^{7} r_s \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+96a^{6} \\\\cos{\\\\theta}^{5} r^{7} r_s \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-16a^{2} \\\\cos{\\\\theta}^{3} r^{11} r_s \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-16a^{2} \\\\cos{\\\\theta}^{3} r^{11} r_s \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-48a^{4} \\\\cos{\\\\theta}^{5} r^{9} r_s \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-48a^{4} \\\\cos{\\\\theta}^{5} r^{9} r_s \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+16a^{2} \\\\cos{\\\\theta}^{3} r^{8} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+16a^{2} \\\\cos{\\\\theta}^{3} r^{8} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+16a^{8} \\\\cos{\\\\theta}^{5} r^{5} r_s \\\\sin{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+16a^{8} \\\\cos{\\\\theta}^{5} r^{5} r_s \\\\sin{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+96a^{8} \\\\cos{\\\\theta}^{7} r^{5} r_s \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+96a^{8} \\\\cos{\\\\theta}^{7} r^{5} r_s \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-48a^{6} \\\\cos{\\\\theta}^{7} r^{7} r_s \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}%\\n-48a^{6} \\\\cos{\\\\theta}^{7} r^{7} r_s \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+32a^{4} \\\\cos{\\\\theta}^{5} r^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+32a^{4} \\\\cos{\\\\theta}^{5} r^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+40a^{8} \\\\cos{\\\\theta}^{2} r^{7} r_s \\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2}+48a^{6} \\\\cos{\\\\theta}^{2} r^{5} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}+32a^{6} \\\\cos{\\\\theta}^{5} r^{7} r_s \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+32a^{6} \\\\cos{\\\\theta}^{5} r^{7} r_s \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+96a^{8} \\\\cos{\\\\theta}^{7} r^{5} r_s \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+96a^{8} \\\\cos{\\\\theta}^{7} r^{5} r_s \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-16a^{6} \\\\cos{\\\\theta}^{3} r^{7} r_s \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-16a^{6} \\\\cos{\\\\theta}^{3} r^{7} r_s \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-48a^{8} \\\\cos{\\\\theta}^{5} r^{5} r_s \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-48a^{8} \\\\cos{\\\\theta}^{5} r^{5} r_s \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8a^{6} \\\\cos{\\\\theta}^{2} r^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-24a^{6} \\\\cos{\\\\theta}^{3} r^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-24a^{6} \\\\cos{\\\\theta}^{3} r^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+16a^{4} \\\\cos{\\\\theta}^{2} r^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-48a^{4} \\\\cos{\\\\theta}^{3} r^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-48a^{4} \\\\cos{\\\\theta}^{3} r^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+96a^{8} \\\\cos{\\\\theta}^{4} r^{3} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}%\\n+96a^{10} \\\\cos{\\\\theta}^{9} r^{3} r_s \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+96a^{10} \\\\cos{\\\\theta}^{9} r^{3} r_s \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-48a^{10} \\\\cos{\\\\theta}^{7} r^{3} r_s \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-48a^{10} \\\\cos{\\\\theta}^{7} r^{3} r_s \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+16a^{8} \\\\cos{\\\\theta}^{4} r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-48a^{8} \\\\cos{\\\\theta}^{5} r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-48a^{8} \\\\cos{\\\\theta}^{5} r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+32a^{6} \\\\cos{\\\\theta}^{4} r^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-96a^{6} \\\\cos{\\\\theta}^{5} r^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-96a^{6} \\\\cos{\\\\theta}^{5} r^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+40a^{6} \\\\cos{\\\\theta}^{2} r^{9} r_s \\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2}+48a^{4} \\\\cos{\\\\theta}^{2} r^{7} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}+80a^{4} \\\\cos{\\\\theta}^{5} r^{9} r_s \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+80a^{4} \\\\cos{\\\\theta}^{5} r^{9} r_s \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+144a^{6} \\\\cos{\\\\theta}^{7} r^{7} r_s \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+144a^{6} \\\\cos{\\\\theta}^{7} r^{7} r_s \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+16a^{2} \\\\cos{\\\\theta}^{3} r^{11} r_s \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+16a^{2} \\\\cos{\\\\theta}^{3} r^{11} r_s \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8a^{2} \\\\cos{\\\\theta}^{2} r^{8} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-24a^{2} \\\\cos{\\\\theta}^{3} r^{8} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}%\\n-24a^{2} \\\\cos{\\\\theta}^{3} r^{8} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+96a^{6} \\\\cos{\\\\theta}^{4} r^{5} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}+112a^{8} \\\\cos{\\\\theta}^{9} r^{5} r_s \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+112a^{8} \\\\cos{\\\\theta}^{9} r^{5} r_s \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+16a^{4} \\\\cos{\\\\theta}^{4} r^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-48a^{4} \\\\cos{\\\\theta}^{5} r^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-48a^{4} \\\\cos{\\\\theta}^{5} r^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-32a^{12} \\\\cos{\\\\theta}^{8} r^{2} r_s^{2} \\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2}+32a^{14} \\\\cos{\\\\theta}^{8} r r_s \\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2}+32a^{12} \\\\cos{\\\\theta}^{8} r^{3} r_s \\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2}+8a^{12} \\\\cos{\\\\theta}^{10} r^{2} r_s^{2} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}-8a^{14} \\\\cos{\\\\theta}^{10} r r_s \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}-8a^{12} \\\\cos{\\\\theta}^{10} r^{3} r_s \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}+8a^{14} \\\\cos{\\\\theta}^{10} r r_s \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8a^{10} \\\\cos{\\\\theta}^{8} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r r_s \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-8a^{10} \\\\cos{\\\\theta}^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-8a^{12} \\\\cos{\\\\theta}^{8} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8a^{8} \\\\cos{\\\\theta}^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r^{3} r_s \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-8a^{8} \\\\cos{\\\\theta}^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-8a^{10} \\\\cos{\\\\theta}^{8} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}%\\n+8a^{8} \\\\cos{\\\\theta}^{8} r^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-8a^{10} \\\\cos{\\\\theta}^{8} r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-8a^{8} \\\\cos{\\\\theta}^{8} r^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-36a^{14} \\\\cos{\\\\theta}^{8} r r_s \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}-8a^{6} \\\\cos{\\\\theta}^{6} r^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+8a^{12} \\\\cos{\\\\theta}^{7} r^{2} r_s^{2} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2}+16a^{12} \\\\cos{\\\\theta}^{9} r^{2} r_s^{2} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}-8a^{12} \\\\cos{\\\\theta}^{9} r^{2} r_s^{2} \\\\sin{2\\\\theta} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8a^{10} \\\\cos{\\\\theta}^{7} r r_s \\\\sin{2\\\\theta} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8a^{10} \\\\cos{\\\\theta}^{9} r^{4} r_s^{2} \\\\sin{2\\\\theta} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8a^{8} \\\\cos{\\\\theta}^{7} r^{3} r_s \\\\sin{2\\\\theta} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8a^{10} \\\\cos{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r^{3} r_s \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2}+8a^{12} \\\\cos{\\\\theta}^{7} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r r_s \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2}-8a^{8} \\\\cos{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r^{4} r_s^{2} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}-8a^{10} \\\\cos{\\\\theta}^{7} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r^{2} r_s^{2} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}+16a^{8} \\\\cos{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r^{5} r_s \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}+32a^{10} \\\\cos{\\\\theta}^{7} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r^{3} r_s \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}+16a^{12} \\\\cos{\\\\theta}^{9} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r r_s \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}-8a^{8} \\\\cos{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r^{5} r_s \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-16a^{10} \\\\cos{\\\\theta}^{7} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r^{3} r_s \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}%\\n-8a^{12} \\\\cos{\\\\theta}^{9} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r r_s \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8a^{8} \\\\cos{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r^{2} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8a^{10} \\\\cos{\\\\theta}^{7} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8a^{6} \\\\cos{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r^{7} r_s \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-16a^{8} \\\\cos{\\\\theta}^{7} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r^{5} r_s \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8a^{10} \\\\cos{\\\\theta}^{9} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r^{3} r_s \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8a^{6} \\\\cos{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8a^{8} \\\\cos{\\\\theta}^{7} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8a^{10} \\\\cos{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r^{3} r_s \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2}+8a^{12} \\\\cos{\\\\theta}^{7} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r r_s \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2}-8a^{8} \\\\cos{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r^{4} r_s^{2} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}-8a^{10} \\\\cos{\\\\theta}^{7} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r^{2} r_s^{2} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}+16a^{8} \\\\cos{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r^{5} r_s \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}+32a^{10} \\\\cos{\\\\theta}^{7} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r^{3} r_s \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}+16a^{12} \\\\cos{\\\\theta}^{9} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r r_s \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}-8a^{8} \\\\cos{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r^{5} r_s \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-16a^{10} \\\\cos{\\\\theta}^{7} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r^{3} r_s \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8a^{12} \\\\cos{\\\\theta}^{9} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r r_s \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8a^{8} \\\\cos{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r^{2} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8a^{10} \\\\cos{\\\\theta}^{7} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}%\\n-8a^{6} \\\\cos{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r^{7} r_s \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-16a^{8} \\\\cos{\\\\theta}^{7} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r^{5} r_s \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8a^{10} \\\\cos{\\\\theta}^{9} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r^{3} r_s \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8a^{6} \\\\cos{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8a^{8} \\\\cos{\\\\theta}^{7} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8a^{10} \\\\cos{\\\\theta}^{7} r^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2}-8a^{8} \\\\cos{\\\\theta}^{7} r^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s^{2} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}+16a^{10} \\\\cos{\\\\theta}^{9} r^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}-8a^{10} \\\\cos{\\\\theta}^{9} r^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8a^{8} \\\\cos{\\\\theta}^{7} r^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8a^{8} \\\\cos{\\\\theta}^{9} r^{5} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8a^{6} \\\\cos{\\\\theta}^{7} r^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8a^{10} \\\\cos{\\\\theta}^{7} r^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2}-8a^{8} \\\\cos{\\\\theta}^{7} r^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s^{2} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}+16a^{10} \\\\cos{\\\\theta}^{9} r^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2}-8a^{10} \\\\cos{\\\\theta}^{9} r^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8a^{8} \\\\cos{\\\\theta}^{7} r^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8a^{8} \\\\cos{\\\\theta}^{9} r^{5} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8a^{6} \\\\cos{\\\\theta}^{7} r^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-16a^{12} \\\\cos{\\\\theta}^{12} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}%\\n+8a^{12} \\\\cos{\\\\theta}^{12} r^{2} r_s^{2} \\\\tan{\\\\theta}^{2}-8a^{10} \\\\cos{\\\\theta}^{10} r r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2}+8a^{10} \\\\cos{\\\\theta}^{12} r^{4} r_s^{2} \\\\tan{\\\\theta}^{2}-8a^{8} \\\\cos{\\\\theta}^{10} r^{3} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2}+16a^{14} \\\\cos{\\\\theta}^{12} r r_s \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-8a^{14} \\\\cos{\\\\theta}^{12} r r_s \\\\tan{\\\\theta}^{2}+8a^{10} \\\\cos{\\\\theta}^{8} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r^{2} \\\\tan{\\\\theta}^{2}+8a^{12} \\\\cos{\\\\theta}^{10} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2}-16a^{12} \\\\cos{\\\\theta}^{12} r^{3} r_s \\\\tan{\\\\theta}^{2}+16a^{10} \\\\cos{\\\\theta}^{10} r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2}+16a^{12} \\\\cos{\\\\theta}^{12} r^{3} r_s \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-8a^{10} \\\\cos{\\\\theta}^{12} r^{5} r_s \\\\tan{\\\\theta}^{2}+8a^{8} \\\\cos{\\\\theta}^{10} r^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2}-8a^{10} \\\\cos{\\\\theta}^{7} r^{2} r_s^{2} \\\\sin{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-8a^{10} \\\\cos{\\\\theta}^{7} r^{2} r_s^{2} \\\\sin{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-32a^{10} \\\\cos{\\\\theta}^{9} r^{2} r_s^{2} \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-32a^{10} \\\\cos{\\\\theta}^{9} r^{2} r_s^{2} \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+16a^{10} \\\\cos{\\\\theta}^{9} r^{2} r_s^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+16a^{10} \\\\cos{\\\\theta}^{9} r^{2} r_s^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-16a^{8} \\\\cos{\\\\theta}^{7} r r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}%\\n-16a^{8} \\\\cos{\\\\theta}^{7} r r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+16a^{8} \\\\cos{\\\\theta}^{9} r^{4} r_s^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+16a^{8} \\\\cos{\\\\theta}^{9} r^{4} r_s^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-16a^{6} \\\\cos{\\\\theta}^{7} r^{3} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-16a^{6} \\\\cos{\\\\theta}^{7} r^{3} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+8a^{12} \\\\cos{\\\\theta}^{7} r r_s \\\\sin{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+8a^{12} \\\\cos{\\\\theta}^{7} r r_s \\\\sin{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+32a^{12} \\\\cos{\\\\theta}^{9} r r_s \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+32a^{12} \\\\cos{\\\\theta}^{9} r r_s \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-16a^{12} \\\\cos{\\\\theta}^{9} r r_s \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-16a^{12} \\\\cos{\\\\theta}^{9} r r_s \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+16a^{10} \\\\cos{\\\\theta}^{7} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+16a^{10} \\\\cos{\\\\theta}^{7} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-32a^{10} \\\\cos{\\\\theta}^{9} r^{3} r_s \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-32a^{10} \\\\cos{\\\\theta}^{9} r^{3} r_s \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+32a^{8} \\\\cos{\\\\theta}^{7} r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+32a^{8} \\\\cos{\\\\theta}^{7} r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+8a^{10} \\\\cos{\\\\theta}^{7} r^{3} r_s \\\\sin{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+8a^{10} \\\\cos{\\\\theta}^{7} r^{3} r_s \\\\sin{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+32a^{10} \\\\cos{\\\\theta}^{9} r^{3} r_s \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}%\\n+32a^{10} \\\\cos{\\\\theta}^{9} r^{3} r_s \\\\sin{\\\\theta}^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-16a^{8} \\\\cos{\\\\theta}^{9} r^{5} r_s \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}-16a^{8} \\\\cos{\\\\theta}^{9} r^{5} r_s \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}+16a^{6} \\\\cos{\\\\theta}^{7} r^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2}+16a^{6} \\\\cos{\\\\theta}^{7} r^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}^{2}-48a^{8} \\\\cos{\\\\theta}^{6} r^{2} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}-32a^{10} \\\\cos{\\\\theta}^{11} r^{2} r_s^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-32a^{10} \\\\cos{\\\\theta}^{11} r^{2} r_s^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8a^{8} \\\\cos{\\\\theta}^{6} r r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+24a^{8} \\\\cos{\\\\theta}^{7} r r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+24a^{8} \\\\cos{\\\\theta}^{7} r r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8a^{6} \\\\cos{\\\\theta}^{6} r^{3} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}+24a^{6} \\\\cos{\\\\theta}^{7} r^{3} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+24a^{6} \\\\cos{\\\\theta}^{7} r^{3} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+48a^{10} \\\\cos{\\\\theta}^{6} r r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}+32a^{12} \\\\cos{\\\\theta}^{11} r r_s \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+32a^{12} \\\\cos{\\\\theta}^{11} r r_s \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-16a^{12} \\\\cos{\\\\theta}^{9} r r_s \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-16a^{12} \\\\cos{\\\\theta}^{9} r r_s \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8a^{10} \\\\cos{\\\\theta}^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}%\\n-24a^{10} \\\\cos{\\\\theta}^{7} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-24a^{10} \\\\cos{\\\\theta}^{7} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+16a^{8} \\\\cos{\\\\theta}^{6} r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-48a^{8} \\\\cos{\\\\theta}^{7} r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-48a^{8} \\\\cos{\\\\theta}^{7} r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+48a^{8} \\\\cos{\\\\theta}^{6} r^{3} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2}+32a^{10} \\\\cos{\\\\theta}^{11} r^{3} r_s \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+32a^{10} \\\\cos{\\\\theta}^{11} r^{3} r_s \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}+8a^{6} \\\\cos{\\\\theta}^{6} r^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}-24a^{6} \\\\cos{\\\\theta}^{7} r^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-24a^{6} \\\\cos{\\\\theta}^{7} r^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta} \\\\tan{\\\\theta}^{2}-8a^{10} \\\\cos{\\\\theta}^{2} r^{3} r_s^{3} \\\\sin{\\\\theta}^{8}+8a^{10} \\\\cos{\\\\theta}^{2} r^{4} r_s^{2} \\\\sin{\\\\theta}^{8}+8a^{12} \\\\cos{\\\\theta}^{4} r^{2} r_s^{2} \\\\sin{\\\\theta}^{8}-16a^{8} \\\\cos{\\\\theta}^{2} r^{5} r_s^{3} \\\\sin{\\\\theta}^{8}+8a^{8} \\\\cos{\\\\theta}^{2} r^{4} r_s^{4} \\\\sin{\\\\theta}^{8}+8a^{8} \\\\cos{\\\\theta}^{2} r^{6} r_s^{2} \\\\sin{\\\\theta}^{8}+8a^{10} \\\\cos{\\\\theta}^{4} r^{4} r_s^{2} \\\\sin{\\\\theta}^{8}-8a^{10} \\\\cos{\\\\theta}^{4} r^{3} r_s^{3} \\\\sin{\\\\theta}^{8}+8a^{8} \\\\cos{\\\\theta}^{2} r^{4} r_s^{4} \\\\sin{\\\\theta}^{6}%\\n-16a^{8} \\\\cos{\\\\theta}^{2} r^{5} r_s^{3} \\\\sin{\\\\theta}^{6}-16a^{10} \\\\cos{\\\\theta}^{4} r^{3} r_s^{3} \\\\sin{\\\\theta}^{6}+24a^{6} \\\\cos{\\\\theta}^{2} r^{6} r_s^{4} \\\\sin{\\\\theta}^{6}-8a^{6} \\\\cos{\\\\theta}^{2} r^{5} r_s^{5} \\\\sin{\\\\theta}^{6}-24a^{6} \\\\cos{\\\\theta}^{2} r^{7} r_s^{3} \\\\sin{\\\\theta}^{6}-32a^{8} \\\\cos{\\\\theta}^{4} r^{5} r_s^{3} \\\\sin{\\\\theta}^{6}+16a^{8} \\\\cos{\\\\theta}^{4} r^{4} r_s^{4} \\\\sin{\\\\theta}^{6}+8a^{8} \\\\cos{\\\\theta}^{2} r^{6} r_s^{2} \\\\sin{\\\\theta}^{6}+16a^{10} \\\\cos{\\\\theta}^{4} r^{4} r_s^{2} \\\\sin{\\\\theta}^{6}+8a^{6} \\\\cos{\\\\theta}^{2} r^{8} r_s^{2} \\\\sin{\\\\theta}^{6}+16a^{8} \\\\cos{\\\\theta}^{4} r^{6} r_s^{2} \\\\sin{\\\\theta}^{6}+8a^{12} \\\\cos{\\\\theta}^{6} r^{2} r_s^{2} \\\\sin{\\\\theta}^{6}+8a^{10} \\\\cos{\\\\theta}^{6} r^{4} r_s^{2} \\\\sin{\\\\theta}^{6}-8a^{10} \\\\cos{\\\\theta}^{6} r^{3} r_s^{3} \\\\sin{\\\\theta}^{6}+8a^{2} \\\\cos{\\\\theta}^{2} r r_s \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r^{3} r_s \\\\sin{\\\\theta}^{2}+2a^{4} r r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}-a^{2} r^{3} r_s-a^{4} r r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-r^{5} r_s-r^{3} r_s a^{2} \\\\cos{\\\\theta}^{2}+r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-8a^{2} \\\\cos{\\\\theta}^{2} r^{2} \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r^{3} r_s \\\\sin{\\\\theta}^{2}+2a^{4} r r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}-a^{2} r^{3} r_s-a^{4} r r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-r^{5} r_s-r^{3} r_s a^{2} \\\\cos{\\\\theta}^{2}+r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-8a^{4} \\\\cos{\\\\theta}^{4} \\\\left(a^{4} r r_s \\\\sin{\\\\theta}^{4}-a^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{2} r^{3} r_s \\\\sin{\\\\theta}^{2}+2a^{4} r r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}-a^{2} r^{3} r_s-a^{4} r r_s \\\\cos{\\\\theta}^{2}+a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-r^{5} r_s-r^{3} r_s a^{2} \\\\cos{\\\\theta}^{2}+r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}}{8\\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} r^{2}-a^{4} \\\\cos{\\\\theta}^{2}+r^{3} r_s-r^{4}-r^{2} a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{\\\\phi}= & \\\\frac{49r^{5} r_s^{3} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6}+23r^{3} r_s^{3} a^{8} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{6}-7r^{5} r_s^{3} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4}-9r^{3} r_s^{3} a^{8} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4}+12r^{3} r_s^{3} a^{6} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+12r^{3} r_s^{3} a^{6} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+32r^{3} r_s^{3} a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4}+12r^{3} r_s^{3} a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{2\\\\theta}-12r^{3} r_s^{3} a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+8r^{5} r_s^{3} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+8r^{5} r_s^{3} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+4r^{3} r_s^{3} a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+4r^{3} r_s^{3} a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-4r^{5} r_s^{3} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)-4r^{5} r_s^{3} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-2r^{3} r_s^{3} a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)-2r^{3} r_s^{3} a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-4r^{2} r_s^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\cos{2\\\\theta}+2r^{2} r_s^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)%\\n+2r^{2} r_s^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-4r^{4} r_s^{2} a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\cos{2\\\\theta}+2r^{4} r_s^{2} a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+2r^{4} r_s^{2} a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+30r^{5} r_s^{3} a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4}+3r^{3} r_s^{3} a^{8} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4}+10r^{2} r_s^{2} a^{6} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+14r^{4} r_s^{2} a^{4} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+35r^{7} r_s^{3} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4}-17r^{6} r_s^{4} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4}+r^{4} r_s^{4} a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4}-2r^{6} r_s^{2} a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+4r^{5} r_s^{3} a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-12r^{4} r_s^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-24r^{6} r_s^{2} a^{6} \\\\sin{\\\\theta}^{6}-48r^{4} r_s^{2} a^{8} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6}+8r^{6} r_s^{2} a^{6} \\\\sin{\\\\theta}^{4}+24r^{4} r_s^{2} a^{8} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4}-12r^{4} r_s^{2} a^{6} \\\\sin{\\\\theta}^{5} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)-12r^{4} r_s^{2} a^{6} \\\\sin{\\\\theta}^{5} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)%\\n-32r^{4} r_s^{2} a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4}-12r^{4} r_s^{2} a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{2\\\\theta}+12r^{4} r_s^{2} a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-4r^{6} r_s^{2} a^{4} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)-4r^{6} r_s^{2} a^{4} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-8r^{4} r_s^{2} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)-8r^{4} r_s^{2} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+2r^{6} r_s^{2} a^{4} \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+2r^{6} r_s^{2} a^{4} \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+4r^{4} r_s^{2} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+4r^{4} r_s^{2} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+4r^{3} r_s a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\cos{2\\\\theta}-2r^{3} r_s a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)-2r^{3} r_s a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+12r^{5} r_s a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\cos{2\\\\theta}-6r^{5} r_s a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)-6r^{5} r_s a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-8r^{4} r_s^{2} a^{8} \\\\sin{\\\\theta}^{6} \\\\cos{\\\\theta}^{2}-16r^{6} r_s^{2} a^{6} \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}^{2}-22r^{4} r_s^{2} a^{8} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4}%\\n-8r^{3} r_s a^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}-24r^{5} r_s a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+6r^{8} r_s^{2} a^{4} \\\\sin{\\\\theta}^{4}+r^{7} r_s^{3} a^{4} \\\\sin{\\\\theta}^{4}+26r^{6} r_s^{2} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4}+12r^{7} r_s a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-10r^{6} r_s^{2} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+8r^{5} r_s a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-32r^{2} r_s^{2} a^{10} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{6}+16r^{2} r_s^{2} a^{10} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4}-12r^{2} r_s^{2} a^{8} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)-12r^{2} r_s^{2} a^{8} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-32r^{2} r_s^{2} a^{6} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4}-12r^{2} r_s^{2} a^{6} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{2\\\\theta}+12r^{2} r_s^{2} a^{6} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-4r^{2} r_s^{2} a^{8} \\\\cos{\\\\theta}^{4} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)-4r^{2} r_s^{2} a^{8} \\\\cos{\\\\theta}^{4} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+2r^{2} r_s^{2} a^{8} \\\\cos{\\\\theta}^{4} \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+2r^{2} r_s^{2} a^{8} \\\\cos{\\\\theta}^{4} \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+4r r_s a^{6} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\cos{2\\\\theta}%\\n-2r r_s a^{6} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)-2r r_s a^{6} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+8r^{3} r_s a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\cos{2\\\\theta}-4r^{3} r_s a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)-4r^{3} r_s a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-18r^{2} r_s^{2} a^{10} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4}-8r r_s a^{8} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-20r^{3} r_s a^{6} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+8r^{5} r_s a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+8r^{3} r_s a^{6} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+23r^{7} r_s^{3} a^{4} \\\\sin{\\\\theta}^{6}+12r^{5} r_s^{3} a^{4} \\\\sin{\\\\theta}^{5} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+12r^{5} r_s^{3} a^{4} \\\\sin{\\\\theta}^{5} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+32r^{5} r_s^{3} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4}+12r^{5} r_s^{3} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{2\\\\theta}-12r^{5} r_s^{3} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+4r^{7} r_s^{3} a^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+4r^{7} r_s^{3} a^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-2r^{7} r_s^{3} a^{2} \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)-2r^{7} r_s^{3} a^{2} \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)%\\n-4r^{4} r_s^{2} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\cos{2\\\\theta}+2r^{4} r_s^{2} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+2r^{4} r_s^{2} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-4r^{6} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\cos{2\\\\theta}+2r^{6} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+2r^{6} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-7r^{5} r_s^{3} a^{6} \\\\sin{\\\\theta}^{6} \\\\cos{\\\\theta}^{2}+2r^{7} r_s^{3} a^{4} \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}^{2}+8r^{4} r_s^{2} a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+8r^{6} r_s^{2} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+30r^{9} r_s^{3} a^{2} \\\\sin{\\\\theta}^{4}-9r^{8} r_s^{4} a^{2} \\\\sin{\\\\theta}^{4}-12r^{8} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+2r^{7} r_s^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-48r^{8} r_s^{2} a^{4} \\\\sin{\\\\theta}^{6}-72r^{6} r_s^{2} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6}-24r^{6} r_s^{2} a^{4} \\\\sin{\\\\theta}^{5} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)-24r^{6} r_s^{2} a^{4} \\\\sin{\\\\theta}^{5} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-64r^{6} r_s^{2} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4}-24r^{6} r_s^{2} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{2\\\\theta}%\\n+24r^{6} r_s^{2} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-8r^{8} r_s^{2} a^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)-8r^{8} r_s^{2} a^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-12r^{6} r_s^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)-12r^{6} r_s^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+4r^{8} r_s^{2} a^{2} \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+4r^{8} r_s^{2} a^{2} \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+6r^{6} r_s^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+6r^{6} r_s^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+8r^{7} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\cos{2\\\\theta}-4r^{7} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)-4r^{7} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-16r^{6} r_s^{2} a^{6} \\\\sin{\\\\theta}^{6} \\\\cos{\\\\theta}^{2}-32r^{8} r_s^{2} a^{4} \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}^{2}-57r^{6} r_s^{2} a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4}-16r^{7} r_s a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}-21r^{10} r_s^{2} a^{2} \\\\sin{\\\\theta}^{4}-16r^{8} r_s^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4}+10r^{9} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+8r^{7} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} \\\\sin{\\\\theta}^{2}%\\n-32r^{4} r_s^{2} a^{8} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{6}-12r^{4} r_s^{2} a^{6} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)-12r^{4} r_s^{2} a^{6} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-32r^{4} r_s^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4}-12r^{4} r_s^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{2\\\\theta}+12r^{4} r_s^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-4r^{4} r_s^{2} a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)-4r^{4} r_s^{2} a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+2r^{4} r_s^{2} a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+2r^{4} r_s^{2} a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+4r^{5} r_s a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\cos{2\\\\theta}-2r^{5} r_s a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)-2r^{5} r_s a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-18r^{4} r_s^{2} a^{8} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4}-12r^{5} r_s a^{4} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-6r^{7} r_s a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-25r^{6} a^{6} r_s^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6}-23r^{4} a^{8} r_s^{2} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{6}+2r^{6} a^{6} r_s^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4}+13r^{4} a^{8} r_s^{2} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4}%\\n-12r^{4} a^{6} r_s^{2} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)-12r^{4} a^{6} r_s^{2} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-32r^{4} a^{4} r_s^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4}-12r^{4} a^{4} r_s^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{2\\\\theta}+12r^{4} a^{4} r_s^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-4r^{6} a^{4} r_s^{2} \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)-4r^{6} a^{4} r_s^{2} \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-4r^{4} a^{6} r_s^{2} \\\\cos{\\\\theta}^{4} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)-4r^{4} a^{6} r_s^{2} \\\\cos{\\\\theta}^{4} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+2r^{6} a^{4} r_s^{2} \\\\cos{\\\\theta}^{2} \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+2r^{6} a^{4} r_s^{2} \\\\cos{\\\\theta}^{2} \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+2r^{4} a^{6} r_s^{2} \\\\cos{\\\\theta}^{4} \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+2r^{4} a^{6} r_s^{2} \\\\cos{\\\\theta}^{4} \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+4r^{3} a^{4} r_s \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\cos{2\\\\theta}-2r^{3} a^{4} r_s \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)-2r^{3} a^{4} r_s \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+4r^{5} a^{2} r_s \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\cos{2\\\\theta}-2r^{5} a^{2} r_s \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)-2r^{5} a^{2} r_s \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-6r^{6} a^{6} r_s^{2} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4}%\\n-2r^{4} a^{8} r_s^{2} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4}-8r^{3} a^{6} r_s \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-12r^{5} a^{4} r_s \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-18r^{8} a^{4} r_s^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4}+13r^{7} a^{4} r_s^{3} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4}-2r^{5} a^{6} r_s^{3} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4}+4r^{7} a^{2} r_s \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-6r^{6} a^{2} r_s^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+6r^{5} a^{4} r_s \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+24r^{7} a^{6} r_s \\\\sin{\\\\theta}^{6}+24r^{5} a^{8} r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6}-8r^{7} a^{6} r_s \\\\sin{\\\\theta}^{4}-16r^{5} a^{8} r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4}+12r^{5} a^{6} r_s \\\\sin{\\\\theta}^{5} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+12r^{5} a^{6} r_s \\\\sin{\\\\theta}^{5} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+32r^{5} a^{4} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4}+12r^{5} a^{4} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{2\\\\theta}-12r^{5} a^{4} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+4r^{7} a^{4} r_s \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+4r^{7} a^{4} r_s \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)%\\n+4r^{5} a^{6} r_s \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+4r^{5} a^{6} r_s \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-2r^{7} a^{4} r_s \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)-2r^{7} a^{4} r_s \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-2r^{5} a^{6} r_s \\\\cos{\\\\theta}^{2} \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)-2r^{5} a^{6} r_s \\\\cos{\\\\theta}^{2} \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-4r^{4} a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\cos{2\\\\theta}+2r^{4} a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+2r^{4} a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-8r^{6} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\cos{2\\\\theta}+4r^{6} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+4r^{6} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+8r^{5} a^{8} r_s \\\\sin{\\\\theta}^{6} \\\\cos{\\\\theta}^{2}+16r^{7} a^{6} r_s \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}^{2}+16r^{5} a^{8} r_s \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4}+8r^{4} a^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+16r^{6} a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+2r^{9} a^{4} r_s \\\\sin{\\\\theta}^{4}-9r^{8} a^{4} r_s^{2} \\\\sin{\\\\theta}^{4}-10r^{7} a^{6} r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4}%\\n-8r^{8} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+4r^{7} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s \\\\sin{\\\\theta}^{2}-8r^{6} a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+24r^{5} a^{8} \\\\cos{\\\\theta}^{2} r_s \\\\sin{\\\\theta}^{6}+32r^{3} a^{10} \\\\cos{\\\\theta}^{4} r_s \\\\sin{\\\\theta}^{6}-8r^{5} a^{8} \\\\cos{\\\\theta}^{2} r_s \\\\sin{\\\\theta}^{4}-16r^{3} a^{10} \\\\cos{\\\\theta}^{4} r_s \\\\sin{\\\\theta}^{4}+12r^{3} a^{8} \\\\cos{\\\\theta}^{3} r_s \\\\sin{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+12r^{3} a^{8} \\\\cos{\\\\theta}^{3} r_s \\\\sin{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+32r^{3} a^{6} \\\\cos{\\\\theta}^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4}+12r^{3} a^{6} \\\\cos{\\\\theta}^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{2\\\\theta}-12r^{3} a^{6} \\\\cos{\\\\theta}^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+4r^{5} a^{6} \\\\cos{\\\\theta}^{2} r_s \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+4r^{5} a^{6} \\\\cos{\\\\theta}^{2} r_s \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+4r^{3} a^{8} \\\\cos{\\\\theta}^{4} r_s \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+4r^{3} a^{8} \\\\cos{\\\\theta}^{4} r_s \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-2r^{5} a^{6} \\\\cos{\\\\theta}^{2} r_s \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)-2r^{5} a^{6} \\\\cos{\\\\theta}^{2} r_s \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-2r^{3} a^{8} \\\\cos{\\\\theta}^{4} r_s \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)-2r^{3} a^{8} \\\\cos{\\\\theta}^{4} r_s \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)%\\n-4r^{2} a^{6} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\cos{2\\\\theta}+2r^{2} a^{6} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+2r^{2} a^{6} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-8r^{4} a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\cos{2\\\\theta}+4r^{4} a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+4r^{4} a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+6r^{5} a^{8} \\\\cos{\\\\theta}^{4} r_s \\\\sin{\\\\theta}^{4}+18r^{3} a^{10} \\\\cos{\\\\theta}^{6} r_s \\\\sin{\\\\theta}^{4}+8r^{2} a^{8} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+20r^{4} a^{6} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-11r^{6} a^{6} \\\\cos{\\\\theta}^{2} r_s^{2} \\\\sin{\\\\theta}^{4}-4r^{4} a^{8} \\\\cos{\\\\theta}^{4} r_s^{2} \\\\sin{\\\\theta}^{4}-8r^{6} a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+4r^{5} a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s \\\\sin{\\\\theta}^{2}-8r^{4} a^{6} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+24r^{9} a^{4} r_s \\\\sin{\\\\theta}^{6}+24r^{7} a^{6} r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6}+12r^{7} a^{4} r_s \\\\sin{\\\\theta}^{5} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+12r^{7} a^{4} r_s \\\\sin{\\\\theta}^{5} \\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+32r^{7} a^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4}%\\n+12r^{7} a^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{2\\\\theta}-12r^{7} a^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+4r^{9} a^{2} r_s \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+4r^{9} a^{2} r_s \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+4r^{7} a^{4} r_s \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+4r^{7} a^{4} r_s \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-2r^{9} a^{2} r_s \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)-2r^{9} a^{2} r_s \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-2r^{7} a^{4} r_s \\\\cos{\\\\theta}^{2} \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)-2r^{7} a^{4} r_s \\\\cos{\\\\theta}^{2} \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-4r^{8} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\cos{2\\\\theta}+2r^{8} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+2r^{8} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+8r^{7} a^{6} r_s \\\\sin{\\\\theta}^{6} \\\\cos{\\\\theta}^{2}+16r^{9} a^{4} r_s \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}^{2}+16r^{7} a^{6} r_s \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4}+8r^{8} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+10r^{11} a^{2} r_s \\\\sin{\\\\theta}^{4}-8r^{10} a^{2} r_s^{2} \\\\sin{\\\\theta}^{4}+6r^{9} a^{4} r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4}%\\n-4r^{10} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-4r^{8} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} \\\\sin{\\\\theta}^{2}+24r^{7} a^{6} \\\\cos{\\\\theta}^{2} r_s \\\\sin{\\\\theta}^{6}+32r^{5} a^{8} \\\\cos{\\\\theta}^{4} r_s \\\\sin{\\\\theta}^{6}+12r^{5} a^{6} \\\\cos{\\\\theta}^{3} r_s \\\\sin{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+12r^{5} a^{6} \\\\cos{\\\\theta}^{3} r_s \\\\sin{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+32r^{5} a^{4} \\\\cos{\\\\theta}^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4}+12r^{5} a^{4} \\\\cos{\\\\theta}^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{2\\\\theta}-12r^{5} a^{4} \\\\cos{\\\\theta}^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+4r^{7} a^{4} \\\\cos{\\\\theta}^{2} r_s \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+4r^{7} a^{4} \\\\cos{\\\\theta}^{2} r_s \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+4r^{5} a^{6} \\\\cos{\\\\theta}^{4} r_s \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+4r^{5} a^{6} \\\\cos{\\\\theta}^{4} r_s \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-2r^{7} a^{4} \\\\cos{\\\\theta}^{2} r_s \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)-2r^{7} a^{4} \\\\cos{\\\\theta}^{2} r_s \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-2r^{5} a^{6} \\\\cos{\\\\theta}^{4} r_s \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)-2r^{5} a^{6} \\\\cos{\\\\theta}^{4} r_s \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-4r^{6} a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\cos{2\\\\theta}+2r^{6} a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+2r^{6} a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)%\\n+22r^{7} a^{6} \\\\cos{\\\\theta}^{4} r_s \\\\sin{\\\\theta}^{4}+18r^{5} a^{8} \\\\cos{\\\\theta}^{6} r_s \\\\sin{\\\\theta}^{4}+12r^{6} a^{4} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+8r^{9} a^{4} \\\\cos{\\\\theta}^{2} r_s \\\\sin{\\\\theta}^{4}-11r^{8} a^{4} \\\\cos{\\\\theta}^{2} r_s^{2} \\\\sin{\\\\theta}^{4}-4r^{6} a^{6} \\\\cos{\\\\theta}^{4} r_s^{2} \\\\sin{\\\\theta}^{4}+4r^{7} a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s \\\\sin{\\\\theta}^{2}-42a^{8} \\\\cos{\\\\theta}^{4} r^{4} r_s^{2} \\\\sin{\\\\theta}^{6}-16a^{10} \\\\cos{\\\\theta}^{6} r^{2} r_s^{2} \\\\sin{\\\\theta}^{6}+8a^{8} \\\\cos{\\\\theta}^{4} r^{4} r_s^{2} \\\\sin{\\\\theta}^{4}+7a^{10} \\\\cos{\\\\theta}^{6} r^{2} r_s^{2} \\\\sin{\\\\theta}^{4}-12a^{8} \\\\cos{\\\\theta}^{5} r^{2} r_s^{2} \\\\sin{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)-12a^{8} \\\\cos{\\\\theta}^{5} r^{2} r_s^{2} \\\\sin{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-32a^{6} \\\\cos{\\\\theta}^{4} r^{2} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4}-12a^{6} \\\\cos{\\\\theta}^{4} r^{2} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{2\\\\theta}+12a^{6} \\\\cos{\\\\theta}^{4} r^{2} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-8a^{6} \\\\cos{\\\\theta}^{4} r^{4} r_s^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)-8a^{6} \\\\cos{\\\\theta}^{4} r^{4} r_s^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-4a^{8} \\\\cos{\\\\theta}^{6} r^{2} r_s^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)-4a^{8} \\\\cos{\\\\theta}^{6} r^{2} r_s^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)%\\n+4a^{6} \\\\cos{\\\\theta}^{4} r^{4} r_s^{2} \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+4a^{6} \\\\cos{\\\\theta}^{4} r^{4} r_s^{2} \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+2a^{8} \\\\cos{\\\\theta}^{6} r^{2} r_s^{2} \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+2a^{8} \\\\cos{\\\\theta}^{6} r^{2} r_s^{2} \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+4a^{6} \\\\cos{\\\\theta}^{4} r r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\cos{2\\\\theta}-2a^{6} \\\\cos{\\\\theta}^{4} r r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)-2a^{6} \\\\cos{\\\\theta}^{4} r r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+4a^{4} \\\\cos{\\\\theta}^{4} r^{3} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\cos{2\\\\theta}-2a^{4} \\\\cos{\\\\theta}^{4} r^{3} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)-2a^{4} \\\\cos{\\\\theta}^{4} r^{3} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-15a^{8} \\\\cos{\\\\theta}^{6} r^{4} r_s^{2} \\\\sin{\\\\theta}^{4}-3a^{10} \\\\cos{\\\\theta}^{8} r^{2} r_s^{2} \\\\sin{\\\\theta}^{4}-8a^{8} \\\\cos{\\\\theta}^{6} r r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-14a^{6} \\\\cos{\\\\theta}^{6} r^{3} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-29a^{6} \\\\cos{\\\\theta}^{4} r^{6} r_s^{2} \\\\sin{\\\\theta}^{4}+3a^{6} \\\\cos{\\\\theta}^{4} r^{5} r_s^{3} \\\\sin{\\\\theta}^{4}-3a^{8} \\\\cos{\\\\theta}^{6} r^{3} r_s^{3} \\\\sin{\\\\theta}^{4}-8a^{4} \\\\cos{\\\\theta}^{4} r^{5} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-4a^{4} \\\\cos{\\\\theta}^{4} r^{4} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+2a^{6} \\\\cos{\\\\theta}^{4} r^{3} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}%\\n+24a^{8} \\\\cos{\\\\theta}^{2} r^{5} r_s \\\\sin{\\\\theta}^{6}+56a^{10} \\\\cos{\\\\theta}^{4} r^{3} r_s \\\\sin{\\\\theta}^{6}-8a^{8} \\\\cos{\\\\theta}^{2} r^{5} r_s \\\\sin{\\\\theta}^{4}-24a^{10} \\\\cos{\\\\theta}^{4} r^{3} r_s \\\\sin{\\\\theta}^{4}+12a^{8} \\\\cos{\\\\theta}^{3} r^{3} r_s \\\\sin{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+12a^{8} \\\\cos{\\\\theta}^{3} r^{3} r_s \\\\sin{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+32a^{6} \\\\cos{\\\\theta}^{2} r^{3} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4}+12a^{6} \\\\cos{\\\\theta}^{2} r^{3} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{2\\\\theta}-12a^{6} \\\\cos{\\\\theta}^{2} r^{3} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+4a^{6} \\\\cos{\\\\theta}^{2} r^{5} r_s \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+4a^{6} \\\\cos{\\\\theta}^{2} r^{5} r_s \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+8a^{8} \\\\cos{\\\\theta}^{4} r^{3} r_s \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+8a^{8} \\\\cos{\\\\theta}^{4} r^{3} r_s \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-2a^{6} \\\\cos{\\\\theta}^{2} r^{5} r_s \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)-2a^{6} \\\\cos{\\\\theta}^{2} r^{5} r_s \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-4a^{8} \\\\cos{\\\\theta}^{4} r^{3} r_s \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)-4a^{8} \\\\cos{\\\\theta}^{4} r^{3} r_s \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-4a^{6} \\\\cos{\\\\theta}^{2} r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\cos{2\\\\theta}+2a^{6} \\\\cos{\\\\theta}^{2} r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+2a^{6} \\\\cos{\\\\theta}^{2} r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)%\\n-8a^{4} \\\\cos{\\\\theta}^{2} r^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\cos{2\\\\theta}+4a^{4} \\\\cos{\\\\theta}^{2} r^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+4a^{4} \\\\cos{\\\\theta}^{2} r^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+6a^{8} \\\\cos{\\\\theta}^{4} r^{5} r_s \\\\sin{\\\\theta}^{4}+22a^{10} \\\\cos{\\\\theta}^{6} r^{3} r_s \\\\sin{\\\\theta}^{4}+8a^{6} \\\\cos{\\\\theta}^{4} r^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+2a^{6} \\\\cos{\\\\theta}^{2} r^{7} r_s \\\\sin{\\\\theta}^{4}+a^{6} \\\\cos{\\\\theta}^{2} r^{6} r_s^{2} \\\\sin{\\\\theta}^{4}-12a^{4} \\\\cos{\\\\theta}^{2} r^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-8a^{6} \\\\cos{\\\\theta}^{2} r^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+32a^{12} \\\\cos{\\\\theta}^{6} r r_s \\\\sin{\\\\theta}^{6}-16a^{12} \\\\cos{\\\\theta}^{6} r r_s \\\\sin{\\\\theta}^{4}+12a^{10} \\\\cos{\\\\theta}^{5} r r_s \\\\sin{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+12a^{10} \\\\cos{\\\\theta}^{5} r r_s \\\\sin{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+32a^{8} \\\\cos{\\\\theta}^{4} r r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4}+12a^{8} \\\\cos{\\\\theta}^{4} r r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{2\\\\theta}-12a^{8} \\\\cos{\\\\theta}^{4} r r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+4a^{10} \\\\cos{\\\\theta}^{6} r r_s \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+4a^{10} \\\\cos{\\\\theta}^{6} r r_s \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-2a^{10} \\\\cos{\\\\theta}^{6} r r_s \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)%\\n-2a^{10} \\\\cos{\\\\theta}^{6} r r_s \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-4a^{8} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\cos{2\\\\theta}+2a^{8} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+2a^{8} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-8a^{6} \\\\cos{\\\\theta}^{4} r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\cos{2\\\\theta}+4a^{6} \\\\cos{\\\\theta}^{4} r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+4a^{6} \\\\cos{\\\\theta}^{4} r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+18a^{12} \\\\cos{\\\\theta}^{8} r r_s \\\\sin{\\\\theta}^{4}+8a^{10} \\\\cos{\\\\theta}^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+20a^{8} \\\\cos{\\\\theta}^{6} r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-22a^{6} \\\\cos{\\\\theta}^{2} r^{6} r_s^{2} \\\\sin{\\\\theta}^{6}-12a^{6} \\\\cos{\\\\theta}^{3} r^{4} r_s^{2} \\\\sin{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)-12a^{6} \\\\cos{\\\\theta}^{3} r^{4} r_s^{2} \\\\sin{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-32a^{4} \\\\cos{\\\\theta}^{2} r^{4} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4}-12a^{4} \\\\cos{\\\\theta}^{2} r^{4} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{2\\\\theta}+12a^{4} \\\\cos{\\\\theta}^{2} r^{4} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-4a^{4} \\\\cos{\\\\theta}^{2} r^{6} r_s^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)-4a^{4} \\\\cos{\\\\theta}^{2} r^{6} r_s^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+2a^{4} \\\\cos{\\\\theta}^{2} r^{6} r_s^{2} \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+2a^{4} \\\\cos{\\\\theta}^{2} r^{6} r_s^{2} \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)%\\n+4a^{4} \\\\cos{\\\\theta}^{2} r^{3} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\cos{2\\\\theta}-2a^{4} \\\\cos{\\\\theta}^{2} r^{3} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)-2a^{4} \\\\cos{\\\\theta}^{2} r^{3} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+4a^{2} \\\\cos{\\\\theta}^{2} r^{5} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\cos{2\\\\theta}-2a^{2} \\\\cos{\\\\theta}^{2} r^{5} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)-2a^{2} \\\\cos{\\\\theta}^{2} r^{5} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-17a^{4} \\\\cos{\\\\theta}^{2} r^{8} r_s^{2} \\\\sin{\\\\theta}^{4}+7a^{4} \\\\cos{\\\\theta}^{2} r^{7} r_s^{3} \\\\sin{\\\\theta}^{4}+6a^{2} \\\\cos{\\\\theta}^{2} r^{7} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-6a^{2} \\\\cos{\\\\theta}^{2} r^{6} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+10a^{4} \\\\cos{\\\\theta}^{2} r^{5} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+24a^{6} \\\\cos{\\\\theta}^{2} r^{7} r_s \\\\sin{\\\\theta}^{6}+56a^{8} \\\\cos{\\\\theta}^{4} r^{5} r_s \\\\sin{\\\\theta}^{6}+12a^{6} \\\\cos{\\\\theta}^{3} r^{5} r_s \\\\sin{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+12a^{6} \\\\cos{\\\\theta}^{3} r^{5} r_s \\\\sin{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+32a^{4} \\\\cos{\\\\theta}^{2} r^{5} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4}+12a^{4} \\\\cos{\\\\theta}^{2} r^{5} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{2\\\\theta}-12a^{4} \\\\cos{\\\\theta}^{2} r^{5} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+4a^{4} \\\\cos{\\\\theta}^{2} r^{7} r_s \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+4a^{4} \\\\cos{\\\\theta}^{2} r^{7} r_s \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)%\\n+8a^{6} \\\\cos{\\\\theta}^{4} r^{5} r_s \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+8a^{6} \\\\cos{\\\\theta}^{4} r^{5} r_s \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-2a^{4} \\\\cos{\\\\theta}^{2} r^{7} r_s \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)-2a^{4} \\\\cos{\\\\theta}^{2} r^{7} r_s \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-4a^{6} \\\\cos{\\\\theta}^{4} r^{5} r_s \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)-4a^{6} \\\\cos{\\\\theta}^{4} r^{5} r_s \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-4a^{2} \\\\cos{\\\\theta}^{2} r^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\cos{2\\\\theta}+2a^{2} \\\\cos{\\\\theta}^{2} r^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+2a^{2} \\\\cos{\\\\theta}^{2} r^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+30a^{6} \\\\cos{\\\\theta}^{4} r^{7} r_s \\\\sin{\\\\theta}^{4}+38a^{8} \\\\cos{\\\\theta}^{6} r^{5} r_s \\\\sin{\\\\theta}^{4}+8a^{4} \\\\cos{\\\\theta}^{4} r^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+10a^{4} \\\\cos{\\\\theta}^{2} r^{9} r_s \\\\sin{\\\\theta}^{4}-4a^{2} \\\\cos{\\\\theta}^{2} r^{8} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+32a^{10} \\\\cos{\\\\theta}^{6} r^{3} r_s \\\\sin{\\\\theta}^{6}+12a^{8} \\\\cos{\\\\theta}^{5} r^{3} r_s \\\\sin{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+12a^{8} \\\\cos{\\\\theta}^{5} r^{3} r_s \\\\sin{\\\\theta}^{5} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+32a^{6} \\\\cos{\\\\theta}^{4} r^{3} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4}+12a^{6} \\\\cos{\\\\theta}^{4} r^{3} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{2\\\\theta}-12a^{6} \\\\cos{\\\\theta}^{4} r^{3} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}%\\n+4a^{8} \\\\cos{\\\\theta}^{6} r^{3} r_s \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+4a^{8} \\\\cos{\\\\theta}^{6} r^{3} r_s \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-2a^{8} \\\\cos{\\\\theta}^{6} r^{3} r_s \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)-2a^{8} \\\\cos{\\\\theta}^{6} r^{3} r_s \\\\sin{4\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-4a^{4} \\\\cos{\\\\theta}^{4} r^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\cos{2\\\\theta}+2a^{4} \\\\cos{\\\\theta}^{4} r^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right)+2a^{4} \\\\cos{\\\\theta}^{4} r^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{2\\\\theta} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+18a^{10} \\\\cos{\\\\theta}^{8} r^{3} r_s \\\\sin{\\\\theta}^{4}+12a^{6} \\\\cos{\\\\theta}^{6} r^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+8a^{4} \\\\cos{\\\\theta}^{4} r^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s \\\\sin{\\\\theta}^{2}-2r_s^{3} a^{8} r^{3} \\\\sin{\\\\theta}^{5} \\\\sin{2\\\\theta} \\\\cos{\\\\theta}+2r_s^{2} a^{8} r^{4} \\\\sin{\\\\theta}^{5} \\\\sin{2\\\\theta} \\\\cos{\\\\theta}+2r_s^{2} a^{10} r^{2} \\\\sin{\\\\theta}^{5} \\\\cos{\\\\theta}^{3} \\\\sin{2\\\\theta}-4r_s^{3} a^{6} r^{5} \\\\sin{\\\\theta}^{5} \\\\sin{2\\\\theta} \\\\cos{\\\\theta}+2r_s^{4} a^{6} r^{4} \\\\sin{\\\\theta}^{5} \\\\sin{2\\\\theta} \\\\cos{\\\\theta}+2r_s^{2} a^{6} r^{6} \\\\sin{\\\\theta}^{5} \\\\sin{2\\\\theta} \\\\cos{\\\\theta}+2r_s^{2} a^{8} r^{4} \\\\sin{\\\\theta}^{5} \\\\cos{\\\\theta}^{3} \\\\sin{2\\\\theta}-2r_s^{3} a^{8} r^{3} \\\\sin{\\\\theta}^{5} \\\\cos{\\\\theta}^{3} \\\\sin{2\\\\theta}-4r_s^{3} a^{6} r^{5} \\\\sin{\\\\theta}^{3} \\\\sin{2\\\\theta} \\\\cos{\\\\theta}+4r_s^{2} a^{6} r^{6} \\\\sin{\\\\theta}^{3} \\\\sin{2\\\\theta} \\\\cos{\\\\theta}%\\n+4r_s^{2} a^{8} r^{4} \\\\sin{\\\\theta}^{3} \\\\cos{\\\\theta}^{3} \\\\sin{2\\\\theta}-8r_s^{3} a^{4} r^{7} \\\\sin{\\\\theta}^{3} \\\\sin{2\\\\theta} \\\\cos{\\\\theta}+4r_s^{4} a^{4} r^{6} \\\\sin{\\\\theta}^{3} \\\\sin{2\\\\theta} \\\\cos{\\\\theta}+4r_s^{2} a^{4} r^{8} \\\\sin{\\\\theta}^{3} \\\\sin{2\\\\theta} \\\\cos{\\\\theta}+4r_s^{2} a^{6} r^{6} \\\\sin{\\\\theta}^{3} \\\\cos{\\\\theta}^{3} \\\\sin{2\\\\theta}-4r_s^{3} a^{6} r^{5} \\\\sin{\\\\theta}^{3} \\\\cos{\\\\theta}^{3} \\\\sin{2\\\\theta}-4r_s^{3} a^{8} r^{3} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{3} \\\\sin{2\\\\theta}+4r_s^{2} a^{8} r^{4} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{3} \\\\sin{2\\\\theta}+4r_s^{2} a^{10} r^{2} \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{3} \\\\sin{2\\\\theta}-8r_s^{3} a^{6} r^{5} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{3} \\\\sin{2\\\\theta}+4r_s^{4} a^{6} r^{4} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{3} \\\\sin{2\\\\theta}+4r_s^{2} a^{6} r^{6} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{3} \\\\sin{2\\\\theta}+4r_s^{2} a^{8} r^{4} \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{3} \\\\sin{2\\\\theta}-4r_s^{3} a^{8} r^{3} \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{3} \\\\sin{2\\\\theta}-2r_s^{2} a^{6} r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{2\\\\theta} \\\\cos{\\\\theta} \\\\sin{\\\\theta}+2r_s a^{6} r^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{2\\\\theta} \\\\cos{\\\\theta} \\\\sin{\\\\theta}+2r_s a^{8} r \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{3} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}-6r_s^{2} a^{4} r^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{2\\\\theta} \\\\cos{\\\\theta} \\\\sin{\\\\theta}+2r_s^{3} a^{4} r^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{2\\\\theta} \\\\cos{\\\\theta} \\\\sin{\\\\theta}+4r_s a^{4} r^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{2\\\\theta} \\\\cos{\\\\theta} \\\\sin{\\\\theta}%\\n+4r_s a^{6} r^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{3} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}-2r_s^{2} a^{6} r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{3} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}-4r_s^{2} a^{2} r^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{2\\\\theta} \\\\cos{\\\\theta} \\\\sin{\\\\theta}+2r_s^{3} a^{2} r^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{2\\\\theta} \\\\cos{\\\\theta} \\\\sin{\\\\theta}+2r_s a^{2} r^{7} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{2\\\\theta} \\\\cos{\\\\theta} \\\\sin{\\\\theta}+2r_s a^{4} r^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{3} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}-2r_s^{2} a^{4} r^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{3} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}+4r_s^{3} a^{8} r^{3} \\\\sin{\\\\theta}^{6} \\\\cos{\\\\theta}^{2}-4r_s^{2} a^{8} r^{4} \\\\sin{\\\\theta}^{6} \\\\cos{\\\\theta}^{2}-4r_s^{2} a^{10} r^{2} \\\\sin{\\\\theta}^{6} \\\\cos{\\\\theta}^{4}+8r_s^{3} a^{6} r^{5} \\\\sin{\\\\theta}^{6} \\\\cos{\\\\theta}^{2}-4r_s^{4} a^{6} r^{4} \\\\sin{\\\\theta}^{6} \\\\cos{\\\\theta}^{2}-4r_s^{2} a^{6} r^{6} \\\\sin{\\\\theta}^{6} \\\\cos{\\\\theta}^{2}-4r_s^{2} a^{8} r^{4} \\\\sin{\\\\theta}^{6} \\\\cos{\\\\theta}^{4}+4r_s^{3} a^{8} r^{3} \\\\sin{\\\\theta}^{6} \\\\cos{\\\\theta}^{4}+6r_s^{3} a^{6} r^{5} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4}-8r_s^{2} a^{6} r^{6} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4}-8r_s^{2} a^{8} r^{4} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4}+11r_s^{3} a^{4} r^{7} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4}-5r_s^{4} a^{4} r^{6} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4}%\\n-6r_s^{2} a^{4} r^{8} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4}-8r_s^{2} a^{6} r^{6} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4}+12r_s^{3} a^{6} r^{5} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4}+4r_s^{3} a^{8} r^{3} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4}-4r_s^{2} a^{10} r^{2} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4}-4r_s^{4} a^{6} r^{4} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4}-4r_s^{2} a^{8} r^{4} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4}+4r_s^{3} a^{8} r^{3} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4}+6r_s^{3} a^{4} r^{7} \\\\sin{\\\\theta}^{4}-r_s^{4} a^{4} r^{6} \\\\sin{\\\\theta}^{4}+r_s^{3} a^{6} r^{5} \\\\sin{\\\\theta}^{4}-4r_s^{2} a^{4} r^{8} \\\\sin{\\\\theta}^{4}-2r_s^{2} a^{6} r^{6} \\\\sin{\\\\theta}^{4}-2r_s^{2} a^{8} r^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4}+r_s^{4} a^{6} r^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4}-r_s^{3} a^{8} r^{3} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4}-r_s^{3} a^{4} r^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4}+r_s^{2} a^{6} r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4}+5r_s^{3} a^{2} r^{9} \\\\sin{\\\\theta}^{4}-3r_s^{4} a^{2} r^{8} \\\\sin{\\\\theta}^{4}%\\n-2r_s^{2} a^{2} r^{10} \\\\sin{\\\\theta}^{4}-r_s^{2} a^{2} r^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4}+r_s^{3} a^{2} r^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4}-3r_s^{3} a^{6} \\\\cos{\\\\theta}^{2} r^{5} \\\\sin{\\\\theta}^{4}+2r_s^{2} a^{6} \\\\cos{\\\\theta}^{2} r^{6} \\\\sin{\\\\theta}^{4}+r_s^{2} a^{8} \\\\cos{\\\\theta}^{2} r^{4} \\\\sin{\\\\theta}^{4}+2r_s^{2} a^{8} \\\\cos{\\\\theta}^{4} r^{4} \\\\sin{\\\\theta}^{4}-r_s^{3} a^{8} \\\\cos{\\\\theta}^{4} r^{3} \\\\sin{\\\\theta}^{4}+r_s^{2} a^{10} \\\\cos{\\\\theta}^{4} r^{2} \\\\sin{\\\\theta}^{4}-r_s^{4} a^{8} \\\\cos{\\\\theta}^{4} r^{2} \\\\sin{\\\\theta}^{4}+r_s^{3} a^{10} \\\\cos{\\\\theta}^{4} r \\\\sin{\\\\theta}^{4}-r_s^{2} a^{6} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r^{2} \\\\sin{\\\\theta}^{4}+r_s^{3} a^{6} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r \\\\sin{\\\\theta}^{4}-r_s^{2} a^{8} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4}-3r_s^{3} a^{4} \\\\cos{\\\\theta}^{2} r^{7} \\\\sin{\\\\theta}^{4}+2r_s^{4} a^{4} \\\\cos{\\\\theta}^{2} r^{6} \\\\sin{\\\\theta}^{4}+r_s^{2} a^{4} \\\\cos{\\\\theta}^{2} r^{8} \\\\sin{\\\\theta}^{4}+r_s^{2} a^{6} \\\\cos{\\\\theta}^{4} r^{6} \\\\sin{\\\\theta}^{4}-2r_s^{3} a^{6} \\\\cos{\\\\theta}^{4} r^{5} \\\\sin{\\\\theta}^{4}+r_s^{4} a^{6} \\\\cos{\\\\theta}^{4} r^{4} \\\\sin{\\\\theta}^{4}%\\n+r_s^{2} a^{4} \\\\cos{\\\\theta}^{2} r^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4}-r_s^{3} a^{4} \\\\cos{\\\\theta}^{2} r^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4}+r_s^{2} a^{6} \\\\cos{\\\\theta}^{2} r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4}-3r_s^{3} r^{7} a^{4} \\\\sin{\\\\theta}^{4}+r_s^{4} r^{6} a^{4} \\\\sin{\\\\theta}^{4}-r_s^{3} r^{5} a^{6} \\\\sin{\\\\theta}^{4}+2r_s^{2} r^{8} a^{4} \\\\sin{\\\\theta}^{4}+r_s^{2} r^{6} a^{6} \\\\sin{\\\\theta}^{4}+2r_s^{2} r^{6} a^{6} \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}^{2}-r_s^{3} r^{5} a^{6} \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}^{2}+r_s^{2} r^{4} a^{8} \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}^{2}-2r_s^{3} r^{9} a^{2} \\\\sin{\\\\theta}^{4}+r_s^{4} r^{8} a^{2} \\\\sin{\\\\theta}^{4}+r_s^{2} r^{10} a^{2} \\\\sin{\\\\theta}^{4}+r_s^{2} r^{8} a^{4} \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}^{2}-r_s^{3} r^{7} a^{4} \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}^{2}+3r_s^{3} r^{5} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4}-r_s^{4} r^{4} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4}+r_s^{3} r^{3} a^{8} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4}-2r_s^{2} r^{6} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4}%\\n-r_s^{2} r^{4} a^{8} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4}-2r_s^{2} r^{4} a^{8} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4}+r_s^{3} r^{3} a^{8} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4}-r_s^{2} r^{2} a^{10} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4}+2r_s^{3} r^{7} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4}-r_s^{4} r^{6} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4}-r_s^{2} r^{8} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4}-r_s^{2} r^{6} a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4}+r_s^{3} r^{5} a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4}+6r_s^{2} r^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} \\\\sin{\\\\theta}^{2}-2r_s^{3} r^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} \\\\sin{\\\\theta}^{2}+2r_s^{2} r^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{4} \\\\sin{\\\\theta}^{2}-4r_s r^{7} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} \\\\sin{\\\\theta}^{2}-2r_s r^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{4} \\\\sin{\\\\theta}^{2}-4r_s r^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+2r_s^{2} r^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}-2r_s r^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+4r_s^{2} r^{8} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-2r_s^{3} r^{7} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-2r_s r^{9} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}%\\n-2r_s r^{7} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+2r_s^{2} r^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}-3r_s^{3} a^{8} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} r^{3}+r_s^{4} a^{8} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} r^{2}-r_s^{3} a^{10} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} r+2r_s^{2} a^{8} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} r^{4}+r_s^{2} a^{10} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} r^{2}+2r_s^{2} a^{10} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} r^{2}-r_s^{3} a^{10} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} r+r_s^{2} a^{12} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4}-2r_s^{3} a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} r^{5}+r_s^{4} a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} r^{4}+r_s^{2} a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} r^{6}+r_s^{2} a^{8} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} r^{4}-r_s^{3} a^{8} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} r^{3}-6r_s^{2} a^{4} \\\\cos{\\\\theta}^{2} r^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+2r_s^{3} a^{4} \\\\cos{\\\\theta}^{2} r^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-2r_s^{2} a^{6} \\\\cos{\\\\theta}^{2} r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+4r_s a^{4} \\\\cos{\\\\theta}^{2} r^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+2r_s a^{6} \\\\cos{\\\\theta}^{2} r^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}%\\n+4r_s a^{6} \\\\cos{\\\\theta}^{4} r^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-2r_s^{2} a^{6} \\\\cos{\\\\theta}^{4} r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+2r_s a^{8} \\\\cos{\\\\theta}^{4} r \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-4r_s^{2} a^{2} \\\\cos{\\\\theta}^{2} r^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+2r_s^{3} a^{2} \\\\cos{\\\\theta}^{2} r^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+2r_s a^{2} \\\\cos{\\\\theta}^{2} r^{7} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+2r_s a^{4} \\\\cos{\\\\theta}^{4} r^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-2r_s^{2} a^{4} \\\\cos{\\\\theta}^{4} r^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+4r^{6} r_s^{3} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)-4r^{6} r_s^{3} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+4r^{5} r_s^{4} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)+4r^{5} r_s^{4} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-8r^{4} r_s^{3} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)-8r^{4} r_s^{3} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-8r^{6} r_s^{3} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r_s r\\\\right)+8r^{6} r_s^{3} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2}\\\\right)+12r^{4} r_s^{3} a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)-4r^{4} r_s^{3} a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r_s r\\\\right)+4r^{4} r_s^{3} a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2}\\\\right)+8r^{4} r_s^{3} a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)%\\n-4r^{3} r_s^{4} a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)-4r^{3} r_s^{4} a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+8r^{2} r_s^{3} a^{8} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)+8r^{2} r_s^{3} a^{8} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-2r^{2} r_s^{3} a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)+2r^{2} r_s^{3} a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r_s r\\\\right)-2r^{2} r_s^{3} a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2}\\\\right)+8r^{5} r_s^{2} a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+8r^{5} r_s^{2} a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4r^{4} r_s^{3} a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4r^{4} r_s^{3} a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+8r^{3} r_s^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+8r^{3} r_s^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4r^{3} r_s^{2} a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+4r^{3} r_s^{2} a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\partial_{r}\\\\left(r_s r\\\\right) \\\\sin{\\\\theta}^{2}-4r^{3} r_s^{2} a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2}-r^{2} r_s^{4} a^{8} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4}-2r^{3} r_s^{3} a^{4} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-8r^{4} r_s^{2} a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2}+4r^{3} r_s^{3} a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2}%\\n-8r^{2} r_s^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2}+20r^{7} r_s^{2} a^{4} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)+24r^{7} r_s^{2} a^{4} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-16r^{6} r_s^{3} a^{4} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)-16r^{6} r_s^{3} a^{4} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+8r^{5} r_s^{2} a^{6} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)+8r^{5} r_s^{2} a^{6} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+4r^{7} r_s^{2} a^{4} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r_s r\\\\right)-4r^{7} r_s^{2} a^{4} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2}\\\\right)-4r^{5} r_s^{2} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)+8r^{5} r_s^{2} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r_s r\\\\right)-8r^{5} r_s^{2} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2}\\\\right)+4r^{5} r_s^{2} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+4r^{3} r_s^{2} a^{8} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)+4r^{3} r_s^{2} a^{8} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+2r^{3} r_s^{2} a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)-2r^{3} r_s^{2} a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r_s r\\\\right)+2r^{3} r_s^{2} a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2}\\\\right)-12r^{6} r_s a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}-12r^{6} r_s a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}%\\n+8r^{5} r_s^{2} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+8r^{5} r_s^{2} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4r^{4} r_s a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4r^{4} r_s a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+4r^{4} r_s a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4r^{4} r_s a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\partial_{r}\\\\left(r_s r\\\\right) \\\\sin{\\\\theta}^{2}+4r^{4} r_s a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2}+12r^{5} r_s a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2}-8r^{4} r_s^{2} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2}+4r^{3} r_s a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2}-12r^{3} r_s^{2} a^{8} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)+4r^{3} r_s^{2} a^{8} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r_s r\\\\right)-4r^{3} r_s^{2} a^{8} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2}\\\\right)-8r^{3} r_s^{2} a^{8} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-4r r_s^{2} a^{10} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)-4r r_s^{2} a^{10} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+2r r_s^{2} a^{6} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)-2r r_s^{2} a^{6} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r_s r\\\\right)+2r r_s^{2} a^{6} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2}\\\\right)-8r^{4} r_s a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}%\\n-8r^{4} r_s a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4r^{2} r_s a^{6} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4r^{2} r_s a^{6} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+4r^{2} r_s a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4r^{2} r_s a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\partial_{r}\\\\left(r_s r\\\\right) \\\\sin{\\\\theta}^{2}+4r^{2} r_s a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2}+r r_s^{3} a^{10} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4}+8r^{3} r_s a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2}+4r r_s a^{6} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2}-20r^{8} r_s^{3} a^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)-24r^{8} r_s^{3} a^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+8r^{7} r_s^{4} a^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)+8r^{7} r_s^{4} a^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-4r^{8} r_s^{3} a^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r_s r\\\\right)+4r^{8} r_s^{3} a^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2}\\\\right)-2r^{4} r_s^{3} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)+2r^{4} r_s^{3} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r_s r\\\\right)-2r^{4} r_s^{3} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2}\\\\right)+12r^{7} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+12r^{7} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}%\\n-4r^{6} r_s^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4r^{6} r_s^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4r^{5} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+4r^{5} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\partial_{r}\\\\left(r_s r\\\\right) \\\\sin{\\\\theta}^{2}-4r^{5} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2}-12r^{6} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2}+4r^{5} r_s^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2}+8r^{9} r_s^{2} a^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)+16r^{9} r_s^{2} a^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+8r^{9} r_s^{2} a^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r_s r\\\\right)-8r^{9} r_s^{2} a^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2}\\\\right)-12r^{7} r_s^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)+12r^{7} r_s^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r_s r\\\\right)-12r^{7} r_s^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2}\\\\right)+4r^{5} r_s^{2} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)-4r^{5} r_s^{2} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r_s r\\\\right)+4r^{5} r_s^{2} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2}\\\\right)-12r^{8} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}-12r^{8} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+8r^{6} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}%\\n-8r^{6} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\partial_{r}\\\\left(r_s r\\\\right) \\\\sin{\\\\theta}^{2}+8r^{6} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2}+12r^{7} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2}-8r^{5} r_s^{2} a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)+4r^{5} r_s^{2} a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r_s r\\\\right)-4r^{5} r_s^{2} a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2}\\\\right)-4r^{5} r_s^{2} a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+2r^{3} r_s^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)-2r^{3} r_s^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r_s r\\\\right)+2r^{3} r_s^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2}\\\\right)-4r^{6} r_s a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4r^{6} r_s a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+4r^{4} r_s a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4r^{4} r_s a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\partial_{r}\\\\left(r_s r\\\\right) \\\\sin{\\\\theta}^{2}+4r^{4} r_s a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2}+4r^{5} r_s a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2}+4r^{7} a^{4} r_s^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-8r^{6} a^{4} r_s^{3} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)-8r^{6} a^{4} r_s^{3} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+4r^{5} a^{6} r_s^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)%\\n+4r^{5} a^{6} r_s^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+4r^{7} a^{4} r_s^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r_s r\\\\right)-4r^{7} a^{4} r_s^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2}\\\\right)-8r^{5} a^{6} r_s^{2} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)+4r^{5} a^{6} r_s^{2} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r_s r\\\\right)-4r^{5} a^{6} r_s^{2} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2}\\\\right)-4r^{5} a^{6} r_s^{2} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+4r^{4} a^{6} r_s^{3} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)+4r^{4} a^{6} r_s^{3} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-4r^{3} a^{8} r_s^{2} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)-4r^{3} a^{8} r_s^{2} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+2r^{3} a^{4} r_s^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)-2r^{3} a^{4} r_s^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r_s r\\\\right)+2r^{3} a^{4} r_s^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2}\\\\right)-4r^{6} a^{2} r_s \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4r^{6} a^{2} r_s \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+4r^{5} a^{2} r_s^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+4r^{5} a^{2} r_s^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4r^{4} a^{4} r_s \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4r^{4} a^{4} r_s \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}%\\n+4r^{4} a^{2} r_s \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4r^{4} a^{2} r_s \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\partial_{r}\\\\left(r_s r\\\\right) \\\\sin{\\\\theta}^{2}+4r^{4} a^{2} r_s \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2}+r^{3} a^{8} r_s^{3} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4}+2r^{4} a^{4} r_s^{2} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+4r^{5} a^{2} r_s \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2}-4r^{4} a^{2} r_s^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2}+4r^{3} a^{4} r_s \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2}-12r^{8} a^{4} r_s \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)-16r^{8} a^{4} r_s \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+8r^{7} a^{4} r_s^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)+8r^{7} a^{4} r_s^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-8r^{6} a^{6} r_s \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)-8r^{6} a^{6} r_s \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-4r^{8} a^{4} r_s \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r_s r\\\\right)+4r^{8} a^{4} r_s \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2}\\\\right)+12r^{6} a^{6} r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)-4r^{6} a^{6} r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r_s r\\\\right)+4r^{6} a^{6} r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2}\\\\right)+8r^{6} a^{6} r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)%\\n+4r^{4} a^{8} r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)+4r^{4} a^{8} r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-2r^{4} a^{4} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)+2r^{4} a^{4} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r_s r\\\\right)-2r^{4} a^{4} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2}\\\\right)+8r^{7} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+8r^{7} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4r^{6} a^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4r^{6} a^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+4r^{5} a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+4r^{5} a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4r^{5} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+4r^{5} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\partial_{r}\\\\left(r_s r\\\\right) \\\\sin{\\\\theta}^{2}-4r^{5} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2}+2r^{7} a^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-8r^{6} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2}+4r^{5} a^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2}-4r^{4} a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2}-12r^{6} a^{6} \\\\cos{\\\\theta}^{2} r_s \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)-16r^{6} a^{6} \\\\cos{\\\\theta}^{2} r_s \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)%\\n+8r^{5} a^{6} \\\\cos{\\\\theta}^{2} r_s^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)+8r^{5} a^{6} \\\\cos{\\\\theta}^{2} r_s^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-8r^{4} a^{8} \\\\cos{\\\\theta}^{2} r_s \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)-8r^{4} a^{8} \\\\cos{\\\\theta}^{2} r_s \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-4r^{6} a^{6} \\\\cos{\\\\theta}^{2} r_s \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r_s r\\\\right)+4r^{6} a^{6} \\\\cos{\\\\theta}^{2} r_s \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2}\\\\right)+12r^{4} a^{8} \\\\cos{\\\\theta}^{4} r_s \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)-4r^{4} a^{8} \\\\cos{\\\\theta}^{4} r_s \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r_s r\\\\right)+4r^{4} a^{8} \\\\cos{\\\\theta}^{4} r_s \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2}\\\\right)+8r^{4} a^{8} \\\\cos{\\\\theta}^{4} r_s \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-4r^{3} a^{8} \\\\cos{\\\\theta}^{4} r_s^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)-4r^{3} a^{8} \\\\cos{\\\\theta}^{4} r_s^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+4r^{2} a^{10} \\\\cos{\\\\theta}^{4} r_s \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)+4r^{2} a^{10} \\\\cos{\\\\theta}^{4} r_s \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-2r^{2} a^{6} \\\\cos{\\\\theta}^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)+2r^{2} a^{6} \\\\cos{\\\\theta}^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r_s r\\\\right)-2r^{2} a^{6} \\\\cos{\\\\theta}^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2}\\\\right)+8r^{5} a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+8r^{5} a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4r^{4} a^{4} \\\\cos{\\\\theta}^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}%\\n-4r^{4} a^{4} \\\\cos{\\\\theta}^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+4r^{3} a^{6} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+4r^{3} a^{6} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4r^{3} a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+4r^{3} a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\partial_{r}\\\\left(r_s r\\\\right) \\\\sin{\\\\theta}^{2}-4r^{3} a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2}+2r^{5} a^{4} \\\\cos{\\\\theta}^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-r^{2} a^{10} \\\\cos{\\\\theta}^{6} r_s^{2} \\\\sin{\\\\theta}^{4}-2r^{3} a^{6} \\\\cos{\\\\theta}^{4} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-8r^{4} a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2}+4r^{3} a^{4} \\\\cos{\\\\theta}^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2}-4r^{2} a^{6} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2}-4r^{10} a^{2} r_s \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)-8r^{10} a^{2} r_s \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+8r^{9} a^{2} r_s^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)+8r^{9} a^{2} r_s^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-4r^{10} a^{2} r_s \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r_s r\\\\right)+4r^{10} a^{2} r_s \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2}\\\\right)+8r^{8} a^{4} r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)-4r^{8} a^{4} r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r_s r\\\\right)%\\n+4r^{8} a^{4} r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2}\\\\right)+4r^{8} a^{4} r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-2r^{6} a^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)+2r^{6} a^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r_s r\\\\right)-2r^{6} a^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2}\\\\right)+4r^{9} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+4r^{9} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4r^{7} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+4r^{7} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\partial_{r}\\\\left(r_s r\\\\right) \\\\sin{\\\\theta}^{2}-4r^{7} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4r^{8} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2}-4r^{8} a^{4} \\\\cos{\\\\theta}^{2} r_s \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)-8r^{8} a^{4} \\\\cos{\\\\theta}^{2} r_s \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+8r^{7} a^{4} \\\\cos{\\\\theta}^{2} r_s^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)+8r^{7} a^{4} \\\\cos{\\\\theta}^{2} r_s^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-4r^{8} a^{4} \\\\cos{\\\\theta}^{2} r_s \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r_s r\\\\right)+4r^{8} a^{4} \\\\cos{\\\\theta}^{2} r_s \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2}\\\\right)+8r^{6} a^{6} \\\\cos{\\\\theta}^{4} r_s \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)-4r^{6} a^{6} \\\\cos{\\\\theta}^{4} r_s \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r_s r\\\\right)+4r^{6} a^{6} \\\\cos{\\\\theta}^{4} r_s \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2}\\\\right)%\\n+4r^{6} a^{6} \\\\cos{\\\\theta}^{4} r_s \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-4r^{5} a^{6} \\\\cos{\\\\theta}^{4} r_s^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)-4r^{5} a^{6} \\\\cos{\\\\theta}^{4} r_s^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-2r^{4} a^{4} \\\\cos{\\\\theta}^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)+2r^{4} a^{4} \\\\cos{\\\\theta}^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r_s r\\\\right)-2r^{4} a^{4} \\\\cos{\\\\theta}^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2}\\\\right)+4r^{7} a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+4r^{7} a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4r^{6} a^{2} \\\\cos{\\\\theta}^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4r^{6} a^{2} \\\\cos{\\\\theta}^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4r^{5} a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+4r^{5} a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\partial_{r}\\\\left(r_s r\\\\right) \\\\sin{\\\\theta}^{2}-4r^{5} a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2}+2r^{7} a^{2} \\\\cos{\\\\theta}^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-r^{4} a^{8} \\\\cos{\\\\theta}^{6} r_s^{2} \\\\sin{\\\\theta}^{4}-2r^{5} a^{4} \\\\cos{\\\\theta}^{4} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-4r^{6} a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2}+4r^{5} a^{2} \\\\cos{\\\\theta}^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2}+8a^{6} \\\\cos{\\\\theta}^{4} r^{5} r_s^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-4a^{6} \\\\cos{\\\\theta}^{4} r^{4} r_s^{3} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)%\\n-4a^{6} \\\\cos{\\\\theta}^{4} r^{4} r_s^{3} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+12a^{8} \\\\cos{\\\\theta}^{4} r^{3} r_s^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)+12a^{8} \\\\cos{\\\\theta}^{4} r^{3} r_s^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+8a^{6} \\\\cos{\\\\theta}^{4} r^{5} r_s^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r_s r\\\\right)-8a^{6} \\\\cos{\\\\theta}^{4} r^{5} r_s^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2}\\\\right)-12a^{8} \\\\cos{\\\\theta}^{6} r^{3} r_s^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)+4a^{8} \\\\cos{\\\\theta}^{6} r^{3} r_s^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r_s r\\\\right)-4a^{8} \\\\cos{\\\\theta}^{6} r^{3} r_s^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2}\\\\right)-8a^{8} \\\\cos{\\\\theta}^{6} r^{3} r_s^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+4a^{8} \\\\cos{\\\\theta}^{6} r^{2} r_s^{3} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)+4a^{8} \\\\cos{\\\\theta}^{6} r^{2} r_s^{3} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-4a^{10} \\\\cos{\\\\theta}^{6} r r_s^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)-4a^{10} \\\\cos{\\\\theta}^{6} r r_s^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+2a^{6} \\\\cos{\\\\theta}^{4} r r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)-2a^{6} \\\\cos{\\\\theta}^{4} r r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r_s r\\\\right)+2a^{6} \\\\cos{\\\\theta}^{4} r r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2}\\\\right)-8a^{4} \\\\cos{\\\\theta}^{4} r^{4} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}-8a^{4} \\\\cos{\\\\theta}^{4} r^{4} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+4a^{4} \\\\cos{\\\\theta}^{4} r^{3} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+4a^{4} \\\\cos{\\\\theta}^{4} r^{3} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}%\\n-8a^{6} \\\\cos{\\\\theta}^{4} r^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}-8a^{6} \\\\cos{\\\\theta}^{4} r^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+4a^{4} \\\\cos{\\\\theta}^{4} r^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4a^{4} \\\\cos{\\\\theta}^{4} r^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\partial_{r}\\\\left(r_s r\\\\right) \\\\sin{\\\\theta}^{2}+4a^{4} \\\\cos{\\\\theta}^{4} r^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2}+a^{10} \\\\cos{\\\\theta}^{8} r r_s^{3} \\\\sin{\\\\theta}^{4}+2a^{6} \\\\cos{\\\\theta}^{6} r^{2} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+8a^{4} \\\\cos{\\\\theta}^{4} r^{3} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2}-4a^{4} \\\\cos{\\\\theta}^{4} r^{2} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2}+4a^{6} \\\\cos{\\\\theta}^{4} r r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2}-12a^{6} \\\\cos{\\\\theta}^{2} r^{6} r_s \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)-16a^{6} \\\\cos{\\\\theta}^{2} r^{6} r_s \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+16a^{6} \\\\cos{\\\\theta}^{2} r^{5} r_s^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)+16a^{6} \\\\cos{\\\\theta}^{2} r^{5} r_s^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-8a^{8} \\\\cos{\\\\theta}^{2} r^{4} r_s \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)-8a^{8} \\\\cos{\\\\theta}^{2} r^{4} r_s \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-4a^{6} \\\\cos{\\\\theta}^{2} r^{6} r_s \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r_s r\\\\right)+4a^{6} \\\\cos{\\\\theta}^{2} r^{6} r_s \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2}\\\\right)-4a^{8} \\\\cos{\\\\theta}^{4} r^{4} r_s \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)-8a^{8} \\\\cos{\\\\theta}^{4} r^{4} r_s \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r_s r\\\\right)%\\n+8a^{8} \\\\cos{\\\\theta}^{4} r^{4} r_s \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2}\\\\right)-12a^{8} \\\\cos{\\\\theta}^{4} r^{4} r_s \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-8a^{10} \\\\cos{\\\\theta}^{4} r^{2} r_s \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)-8a^{10} \\\\cos{\\\\theta}^{4} r^{2} r_s \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-2a^{6} \\\\cos{\\\\theta}^{2} r^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)+2a^{6} \\\\cos{\\\\theta}^{2} r^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r_s r\\\\right)-2a^{6} \\\\cos{\\\\theta}^{2} r^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2}\\\\right)+8a^{4} \\\\cos{\\\\theta}^{2} r^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+8a^{4} \\\\cos{\\\\theta}^{2} r^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-8a^{4} \\\\cos{\\\\theta}^{2} r^{4} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}-8a^{4} \\\\cos{\\\\theta}^{2} r^{4} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+4a^{6} \\\\cos{\\\\theta}^{2} r^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+4a^{6} \\\\cos{\\\\theta}^{2} r^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4a^{4} \\\\cos{\\\\theta}^{2} r^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+4a^{4} \\\\cos{\\\\theta}^{2} r^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\partial_{r}\\\\left(r_s r\\\\right) \\\\sin{\\\\theta}^{2}-4a^{4} \\\\cos{\\\\theta}^{2} r^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2}-8a^{4} \\\\cos{\\\\theta}^{2} r^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2}+8a^{4} \\\\cos{\\\\theta}^{2} r^{3} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2}-4a^{6} \\\\cos{\\\\theta}^{2} r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2}+8a^{10} \\\\cos{\\\\theta}^{6} r^{2} r_s \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)%\\n-4a^{10} \\\\cos{\\\\theta}^{6} r^{2} r_s \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r_s r\\\\right)+4a^{10} \\\\cos{\\\\theta}^{6} r^{2} r_s \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2}\\\\right)+4a^{8} \\\\cos{\\\\theta}^{4} r_s r^{4} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)+4a^{8} \\\\cos{\\\\theta}^{4} r_s r^{4} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+4a^{10} \\\\cos{\\\\theta}^{6} r_s r^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)+4a^{10} \\\\cos{\\\\theta}^{6} r_s r^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-4a^{8} \\\\cos{\\\\theta}^{4} r_s^{2} r^{3} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)-4a^{8} \\\\cos{\\\\theta}^{4} r_s^{2} r^{3} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-4a^{10} \\\\cos{\\\\theta}^{6} r_s^{2} r \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)-4a^{10} \\\\cos{\\\\theta}^{6} r_s^{2} r \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+4a^{10} \\\\cos{\\\\theta}^{4} r_s r^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)+4a^{10} \\\\cos{\\\\theta}^{4} r_s r^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+4a^{12} \\\\cos{\\\\theta}^{6} r_s \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)+4a^{12} \\\\cos{\\\\theta}^{6} r_s \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-2a^{8} \\\\cos{\\\\theta}^{4} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)+2a^{8} \\\\cos{\\\\theta}^{4} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r_s r\\\\right)-2a^{8} \\\\cos{\\\\theta}^{4} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2}\\\\right)+8a^{6} \\\\cos{\\\\theta}^{4} r^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+8a^{6} \\\\cos{\\\\theta}^{4} r^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+4a^{8} \\\\cos{\\\\theta}^{4} r \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}%\\n+4a^{8} \\\\cos{\\\\theta}^{4} r \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4a^{6} \\\\cos{\\\\theta}^{4} r \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+4a^{6} \\\\cos{\\\\theta}^{4} r \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\partial_{r}\\\\left(r_s r\\\\right) \\\\sin{\\\\theta}^{2}-4a^{6} \\\\cos{\\\\theta}^{4} r \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2}-a^{8} \\\\cos{\\\\theta}^{4} r_s^{2} r^{4} \\\\sin{\\\\theta}^{4}-2a^{6} \\\\cos{\\\\theta}^{4} r_s r^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-a^{12} \\\\cos{\\\\theta}^{8} r_s^{2} \\\\sin{\\\\theta}^{4}-2a^{8} \\\\cos{\\\\theta}^{6} r_s r \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-8a^{6} \\\\cos{\\\\theta}^{4} r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2}+4a^{6} \\\\cos{\\\\theta}^{4} r_s r \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2}-4a^{8} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2}+12a^{4} \\\\cos{\\\\theta}^{2} r^{7} r_s^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)+16a^{4} \\\\cos{\\\\theta}^{2} r^{7} r_s^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-8a^{4} \\\\cos{\\\\theta}^{2} r^{6} r_s^{3} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)-8a^{4} \\\\cos{\\\\theta}^{2} r^{6} r_s^{3} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+4a^{4} \\\\cos{\\\\theta}^{2} r^{7} r_s^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r_s r\\\\right)-4a^{4} \\\\cos{\\\\theta}^{2} r^{7} r_s^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2}\\\\right)+2a^{4} \\\\cos{\\\\theta}^{2} r^{3} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)-2a^{4} \\\\cos{\\\\theta}^{2} r^{3} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r_s r\\\\right)+2a^{4} \\\\cos{\\\\theta}^{2} r^{3} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2}\\\\right)%\\n-8a^{2} \\\\cos{\\\\theta}^{2} r^{6} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}-8a^{2} \\\\cos{\\\\theta}^{2} r^{6} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+4a^{2} \\\\cos{\\\\theta}^{2} r^{5} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+4a^{2} \\\\cos{\\\\theta}^{2} r^{5} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+4a^{2} \\\\cos{\\\\theta}^{2} r^{4} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4a^{2} \\\\cos{\\\\theta}^{2} r^{4} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\partial_{r}\\\\left(r_s r\\\\right) \\\\sin{\\\\theta}^{2}+4a^{2} \\\\cos{\\\\theta}^{2} r^{4} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2}+8a^{2} \\\\cos{\\\\theta}^{2} r^{5} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2}-4a^{2} \\\\cos{\\\\theta}^{2} r^{4} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2}-4a^{4} \\\\cos{\\\\theta}^{2} r^{8} r_s \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)-8a^{4} \\\\cos{\\\\theta}^{2} r^{8} r_s \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-4a^{4} \\\\cos{\\\\theta}^{2} r^{8} r_s \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r_s r\\\\right)+4a^{4} \\\\cos{\\\\theta}^{2} r^{8} r_s \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2}\\\\right)+4a^{6} \\\\cos{\\\\theta}^{4} r^{6} r_s \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)-8a^{6} \\\\cos{\\\\theta}^{4} r^{6} r_s \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r_s r\\\\right)+8a^{6} \\\\cos{\\\\theta}^{4} r^{6} r_s \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2}\\\\right)-4a^{6} \\\\cos{\\\\theta}^{4} r^{6} r_s \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-2a^{4} \\\\cos{\\\\theta}^{2} r^{4} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)+2a^{4} \\\\cos{\\\\theta}^{2} r^{4} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r_s r\\\\right)-2a^{4} \\\\cos{\\\\theta}^{2} r^{4} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2}\\\\right)%\\n+4a^{2} \\\\cos{\\\\theta}^{2} r^{7} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+4a^{2} \\\\cos{\\\\theta}^{2} r^{7} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4a^{2} \\\\cos{\\\\theta}^{2} r^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+4a^{2} \\\\cos{\\\\theta}^{2} r^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\partial_{r}\\\\left(r_s r\\\\right) \\\\sin{\\\\theta}^{2}-4a^{2} \\\\cos{\\\\theta}^{2} r^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4a^{2} \\\\cos{\\\\theta}^{2} r^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2}+8a^{8} \\\\cos{\\\\theta}^{6} r^{4} r_s \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)-4a^{8} \\\\cos{\\\\theta}^{6} r^{4} r_s \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r_s r\\\\right)+4a^{8} \\\\cos{\\\\theta}^{6} r^{4} r_s \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2}\\\\right)+4a^{8} \\\\cos{\\\\theta}^{6} r^{4} r_s \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+4a^{10} \\\\cos{\\\\theta}^{6} r^{2} r_s \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-2a^{6} \\\\cos{\\\\theta}^{4} r^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)+2a^{6} \\\\cos{\\\\theta}^{4} r^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r_s r\\\\right)-2a^{6} \\\\cos{\\\\theta}^{4} r^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2}\\\\right)+4a^{4} \\\\cos{\\\\theta}^{4} r^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+4a^{4} \\\\cos{\\\\theta}^{4} r^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4a^{4} \\\\cos{\\\\theta}^{4} r^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+4a^{4} \\\\cos{\\\\theta}^{4} r^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\partial_{r}\\\\left(r_s r\\\\right) \\\\sin{\\\\theta}^{2}-4a^{4} \\\\cos{\\\\theta}^{4} r^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4a^{4} \\\\cos{\\\\theta}^{4} r^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2}%\\n+6a^{4} r_s^{3} r^{7} \\\\sin{\\\\theta}^{4}-a^{4} r_s^{4} r^{6} \\\\sin{\\\\theta}^{4}+a^{6} r_s^{3} r^{5} \\\\sin{\\\\theta}^{4}-4a^{4} r_s^{2} r^{8} \\\\sin{\\\\theta}^{4}-2a^{6} r_s^{2} r^{6} \\\\sin{\\\\theta}^{4}-4a^{6} r_s^{2} r^{6} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4}+2a^{6} r_s^{3} r^{5} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4}-2a^{8} r_s^{2} r^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4}+a^{6} r_s^{4} r^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4}-a^{8} r_s^{3} r^{3} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4}-a^{4} r_s^{3} r^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4}+a^{6} r_s^{2} r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4}+5a^{2} r_s^{3} r^{9} \\\\sin{\\\\theta}^{4}-3a^{2} r_s^{4} r^{8} \\\\sin{\\\\theta}^{4}-2a^{2} r_s^{2} r^{10} \\\\sin{\\\\theta}^{4}-2a^{4} r_s^{2} r^{8} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4}+3a^{4} r_s^{3} r^{7} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4}-a^{4} r_s^{4} r^{6} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4}-a^{2} r_s^{2} r^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4}+a^{2} r_s^{3} r^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4}%\\n-6a^{6} r_s^{3} \\\\cos{\\\\theta}^{2} r^{5} \\\\sin{\\\\theta}^{4}+a^{6} r_s^{4} \\\\cos{\\\\theta}^{2} r^{4} \\\\sin{\\\\theta}^{4}-a^{8} r_s^{3} \\\\cos{\\\\theta}^{2} r^{3} \\\\sin{\\\\theta}^{4}+4a^{6} r_s^{2} \\\\cos{\\\\theta}^{2} r^{6} \\\\sin{\\\\theta}^{4}+2a^{8} r_s^{2} \\\\cos{\\\\theta}^{2} r^{4} \\\\sin{\\\\theta}^{4}+4a^{8} r_s^{2} \\\\cos{\\\\theta}^{4} r^{4} \\\\sin{\\\\theta}^{4}-2a^{8} r_s^{3} \\\\cos{\\\\theta}^{4} r^{3} \\\\sin{\\\\theta}^{4}+2a^{10} r_s^{2} \\\\cos{\\\\theta}^{4} r^{2} \\\\sin{\\\\theta}^{4}-a^{8} r_s^{4} \\\\cos{\\\\theta}^{4} r^{2} \\\\sin{\\\\theta}^{4}+a^{10} r_s^{3} \\\\cos{\\\\theta}^{4} r \\\\sin{\\\\theta}^{4}-a^{6} r_s^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4} r^{2}+a^{6} r_s^{3} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4} r-a^{8} r_s^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4}-5a^{4} r_s^{3} \\\\cos{\\\\theta}^{2} r^{7} \\\\sin{\\\\theta}^{4}+3a^{4} r_s^{4} \\\\cos{\\\\theta}^{2} r^{6} \\\\sin{\\\\theta}^{4}+2a^{4} r_s^{2} \\\\cos{\\\\theta}^{2} r^{8} \\\\sin{\\\\theta}^{4}+2a^{6} r_s^{2} \\\\cos{\\\\theta}^{4} r^{6} \\\\sin{\\\\theta}^{4}-3a^{6} r_s^{3} \\\\cos{\\\\theta}^{4} r^{5} \\\\sin{\\\\theta}^{4}+a^{6} r_s^{4} \\\\cos{\\\\theta}^{4} r^{4} \\\\sin{\\\\theta}^{4}+a^{4} r_s^{2} \\\\cos{\\\\theta}^{2} r^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4}%\\n-a^{4} r_s^{3} \\\\cos{\\\\theta}^{2} r^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4}+a^{6} r_s^{2} \\\\cos{\\\\theta}^{2} r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4}+r^{6} r_s^{4} a^{4} \\\\sin{\\\\theta}^{6}-r^{5} r_s^{3} a^{6} \\\\sin{\\\\theta}^{6}+3r^{4} r_s^{4} a^{6} \\\\sin{\\\\theta}^{6} \\\\cos{\\\\theta}^{2}+r^{3} r_s^{3} a^{8} \\\\sin{\\\\theta}^{6} \\\\cos{\\\\theta}^{2}+10r^{6} r_s^{4} a^{4} \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}^{2}+2r^{5} r_s^{3} a^{6} \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}^{2}+2r^{6} r_s^{2} a^{2} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-2r^{5} r_s^{3} a^{2} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+2r^{4} r_s^{2} a^{4} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-r^{4} r_s^{4} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6}+r^{3} r_s^{3} a^{8} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6}+r^{2} r_s^{4} a^{8} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{6}-r r_s^{3} a^{10} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{6}-2r^{4} r_s^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+2r^{3} r_s^{3} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-2r^{2} r_s^{2} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+2r^{6} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} \\\\sin{\\\\theta}^{4}-2r^{5} r_s^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} \\\\sin{\\\\theta}^{4}%\\n+2r^{4} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{4} \\\\sin{\\\\theta}^{4}-2r^{4} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4}+2r^{3} r_s^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4}-2r^{2} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4}+4r^{6} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}-4r^{5} r_s^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+4r^{4} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}-4r^{5} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4} \\\\sin{\\\\theta}^{2}+4r^{4} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4} \\\\sin{\\\\theta}^{2}-4r^{3} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4} a^{2} \\\\sin{\\\\theta}^{2}+r^{8} a^{4} r_s^{2} \\\\sin{\\\\theta}^{6}-r^{7} a^{4} r_s^{3} \\\\sin{\\\\theta}^{6}+r^{6} a^{6} r_s^{2} \\\\sin{\\\\theta}^{6}+15r^{6} a^{6} r_s^{2} \\\\sin{\\\\theta}^{6} \\\\cos{\\\\theta}^{2}-3r^{5} a^{6} r_s^{3} \\\\sin{\\\\theta}^{6} \\\\cos{\\\\theta}^{2}-r^{4} a^{8} r_s^{2} \\\\sin{\\\\theta}^{6} \\\\cos{\\\\theta}^{2}-2r^{9} a^{2} r_s^{3} \\\\sin{\\\\theta}^{4}+14r^{8} a^{4} r_s^{2} \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}^{2}-10r^{7} a^{4} r_s^{3} \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}^{2}-2r^{6} a^{6} r_s^{2} \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}^{2}%\\n-2r^{7} a^{2} r_s \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+2r^{6} a^{2} r_s^{2} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-2r^{5} a^{4} r_s \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+r^{5} a^{6} r_s^{3} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6}-r^{4} a^{8} r_s^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6}-r^{3} a^{8} r_s^{3} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{6}+r^{2} a^{10} r_s^{2} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{6}+2r^{5} a^{4} r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-2r^{4} a^{4} r_s^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+2r^{3} a^{6} r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-2r^{7} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} r_s \\\\sin{\\\\theta}^{4}+2r^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} r_s^{2} \\\\sin{\\\\theta}^{4}-2r^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{4} r_s \\\\sin{\\\\theta}^{4}+2r^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{4} r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4}-2r^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{4} r_s^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4}+2r^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{6} r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4}+4r^{8} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s^{2} \\\\sin{\\\\theta}^{2}-4r^{7} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s a^{2} \\\\sin{\\\\theta}^{2}-4r^{7} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s a^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+4r^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s^{2} a^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}%\\n-4r^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+4r^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4} \\\\sin{\\\\theta}^{2}-4r^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4} r_s \\\\sin{\\\\theta}^{2}+4r^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4} a^{2} \\\\sin{\\\\theta}^{2}-2a^{6} \\\\cos{\\\\theta}^{2} r^{5} r_s^{3} \\\\sin{\\\\theta}^{6}+2a^{8} \\\\cos{\\\\theta}^{2} r^{4} r_s^{2} \\\\sin{\\\\theta}^{6}-2a^{8} \\\\cos{\\\\theta}^{4} r^{3} r_s^{3} \\\\sin{\\\\theta}^{6}-2a^{10} \\\\cos{\\\\theta}^{4} r^{2} r_s^{2} \\\\sin{\\\\theta}^{6}-4a^{4} \\\\cos{\\\\theta}^{2} r^{5} r_s \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+4a^{4} \\\\cos{\\\\theta}^{2} r^{4} r_s^{2} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-4a^{6} \\\\cos{\\\\theta}^{2} r^{3} r_s \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-a^{6} \\\\cos{\\\\theta}^{2} r_s^{2} r^{6} \\\\sin{\\\\theta}^{6}+a^{6} \\\\cos{\\\\theta}^{2} r_s^{3} r^{5} \\\\sin{\\\\theta}^{6}-a^{8} \\\\cos{\\\\theta}^{2} r_s^{2} r^{4} \\\\sin{\\\\theta}^{6}+a^{8} \\\\cos{\\\\theta}^{4} r_s^{2} r^{4} \\\\sin{\\\\theta}^{6}-a^{8} \\\\cos{\\\\theta}^{4} r_s^{3} r^{3} \\\\sin{\\\\theta}^{6}+a^{10} \\\\cos{\\\\theta}^{4} r_s^{2} r^{2} \\\\sin{\\\\theta}^{6}-2a^{4} \\\\cos{\\\\theta}^{2} r_s^{2} r^{8} \\\\sin{\\\\theta}^{4}+2a^{4} \\\\cos{\\\\theta}^{2} r_s^{3} r^{7} \\\\sin{\\\\theta}^{4}-2a^{6} \\\\cos{\\\\theta}^{2} r_s^{2} r^{6} \\\\sin{\\\\theta}^{4}%\\n-2a^{6} \\\\cos{\\\\theta}^{4} r_s^{2} r^{6} \\\\sin{\\\\theta}^{4}+2a^{6} \\\\cos{\\\\theta}^{4} r_s^{3} r^{5} \\\\sin{\\\\theta}^{4}+2a^{4} \\\\cos{\\\\theta}^{2} r_s r^{5} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-2a^{4} \\\\cos{\\\\theta}^{2} r_s^{2} r^{4} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+2a^{6} \\\\cos{\\\\theta}^{2} r_s r^{3} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-a^{8} \\\\cos{\\\\theta}^{4} r_s^{2} \\\\sin{\\\\theta}^{6} r^{4}+a^{8} \\\\cos{\\\\theta}^{4} r_s^{3} \\\\sin{\\\\theta}^{6} r^{3}-a^{10} \\\\cos{\\\\theta}^{4} r_s^{2} \\\\sin{\\\\theta}^{6} r^{2}+a^{10} \\\\cos{\\\\theta}^{6} r_s^{2} \\\\sin{\\\\theta}^{6} r^{2}-a^{10} \\\\cos{\\\\theta}^{6} r_s^{3} \\\\sin{\\\\theta}^{6} r+a^{12} \\\\cos{\\\\theta}^{6} r_s^{2} \\\\sin{\\\\theta}^{6}-2a^{6} \\\\cos{\\\\theta}^{4} r_s^{2} \\\\sin{\\\\theta}^{4} r^{6}+2a^{6} \\\\cos{\\\\theta}^{4} r_s^{3} \\\\sin{\\\\theta}^{4} r^{5}-2a^{8} \\\\cos{\\\\theta}^{4} r_s^{2} \\\\sin{\\\\theta}^{4} r^{4}-2a^{8} \\\\cos{\\\\theta}^{6} r_s^{2} \\\\sin{\\\\theta}^{4} r^{4}+2a^{8} \\\\cos{\\\\theta}^{6} r_s^{3} \\\\sin{\\\\theta}^{4} r^{3}-2a^{10} \\\\cos{\\\\theta}^{6} r_s^{2} \\\\sin{\\\\theta}^{4} r^{2}+2a^{6} \\\\cos{\\\\theta}^{4} r_s \\\\sin{\\\\theta}^{4} r^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-2a^{6} \\\\cos{\\\\theta}^{4} r_s^{2} \\\\sin{\\\\theta}^{4} r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+2a^{8} \\\\cos{\\\\theta}^{4} r_s \\\\sin{\\\\theta}^{4} r \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}%\\n-2a^{4} \\\\cos{\\\\theta}^{2} r^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s \\\\sin{\\\\theta}^{4}+2a^{4} \\\\cos{\\\\theta}^{2} r^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s^{2} \\\\sin{\\\\theta}^{4}-2a^{6} \\\\cos{\\\\theta}^{2} r^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s \\\\sin{\\\\theta}^{4}+6a^{6} \\\\cos{\\\\theta}^{4} r^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s \\\\sin{\\\\theta}^{4}-2a^{6} \\\\cos{\\\\theta}^{4} r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s^{2} \\\\sin{\\\\theta}^{4}+2a^{8} \\\\cos{\\\\theta}^{4} r \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s \\\\sin{\\\\theta}^{4}+4a^{2} \\\\cos{\\\\theta}^{2} r^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+4a^{2} \\\\cos{\\\\theta}^{2} r^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4} \\\\sin{\\\\theta}^{2}-4a^{2} \\\\cos{\\\\theta}^{2} r^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4} r_s \\\\sin{\\\\theta}^{2}+4a^{4} \\\\cos{\\\\theta}^{2} r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4} \\\\sin{\\\\theta}^{2}+4a^{8} r^{3} r_s^{3} \\\\sin{\\\\theta}^{6} \\\\cos{\\\\theta}^{2}-4a^{8} r^{4} r_s^{2} \\\\sin{\\\\theta}^{6} \\\\cos{\\\\theta}^{2}-4a^{10} r^{2} r_s^{2} \\\\sin{\\\\theta}^{6} \\\\cos{\\\\theta}^{4}+8a^{6} r^{5} r_s^{3} \\\\sin{\\\\theta}^{6} \\\\cos{\\\\theta}^{2}-4a^{6} r^{4} r_s^{4} \\\\sin{\\\\theta}^{6} \\\\cos{\\\\theta}^{2}-4a^{6} r^{6} r_s^{2} \\\\sin{\\\\theta}^{6} \\\\cos{\\\\theta}^{2}-4a^{8} r^{4} r_s^{2} \\\\sin{\\\\theta}^{6} \\\\cos{\\\\theta}^{4}+4a^{8} r^{3} r_s^{3} \\\\sin{\\\\theta}^{6} \\\\cos{\\\\theta}^{4}+4a^{6} r^{5} r_s^{3} \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}^{2}-4a^{6} r^{6} r_s^{2} \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}^{2}%\\n-8a^{8} r^{4} r_s^{2} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4}+8a^{4} r^{7} r_s^{3} \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}^{2}-4a^{4} r^{6} r_s^{4} \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}^{2}-4a^{4} r^{8} r_s^{2} \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}^{2}-8a^{6} r^{6} r_s^{2} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4}+12a^{6} r^{5} r_s^{3} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4}+4a^{8} r^{3} r_s^{3} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4}-4a^{10} r^{2} r_s^{2} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4}-4a^{6} r^{4} r_s^{4} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4}-4a^{8} r^{4} r_s^{2} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4}+4a^{8} r^{3} r_s^{3} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4}-4r^{3} r_s^{3} a^{8} \\\\sin{\\\\theta}^{8} \\\\cos{\\\\theta}^{2}-8r^{3} r_s^{3} a^{8} \\\\sin{\\\\theta}^{6} \\\\cos{\\\\theta}^{4}+4r^{3} r_s^{3} a^{8} \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}^{4}-4r^{2} r_s^{2} a^{6} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{2}-12r^{5} r_s^{3} a^{6} \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}^{4}-4r^{4} r_s^{2} a^{4} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{2}+8r^{7} r_s^{3} a^{4} \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{2}+8r^{5} r_s^{3} a^{6} \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{4}-8r^{4} r_s^{2} a^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{2}%\\n+8r^{9} r_s^{3} a^{2} \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{2}+8r^{7} r_s^{3} a^{4} \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{4}-8r^{6} r_s^{2} a^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{2}+8r^{5} r_s^{3} a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2}+8r^{3} r_s^{3} a^{8} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2}-8r^{2} r_s^{2} a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+8r^{7} r_s^{3} a^{4} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2}+8r^{5} r_s^{3} a^{6} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2}-8r^{4} r_s^{2} a^{4} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-4r^{2} r_s^{2} a^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}^{2}+4r^{3} r_s^{3} a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{2}-8r^{4} r_s^{2} a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{2}-8r^{2} r_s^{2} a^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2}+4r^{4} r_s^{2} a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{2}+4r^{2} r_s^{2} a^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{4}-4r r_s a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4} \\\\cos{\\\\theta}^{2}+4r^{6} r_s^{2} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{2}+4r^{4} r_s^{2} a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{4}-4r^{3} r_s a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4} \\\\cos{\\\\theta}^{2}-4r^{4} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{4} \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}^{2}%\\n+4r^{5} r_s^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{2}-8r^{6} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{2}-8r^{4} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{4} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2}+4r^{6} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} \\\\cos{\\\\theta}^{2}+4r^{4} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{4} \\\\cos{\\\\theta}^{4}-4r^{3} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4} a^{2} \\\\cos{\\\\theta}^{2}+4r^{8} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{2}+4r^{6} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} \\\\cos{\\\\theta}^{4}-4r^{5} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4} \\\\cos{\\\\theta}^{2}+4r^{4} a^{8} r_s^{2} \\\\sin{\\\\theta}^{8} \\\\cos{\\\\theta}^{2}+8r^{4} a^{8} r_s^{2} \\\\sin{\\\\theta}^{6} \\\\cos{\\\\theta}^{4}-4r^{4} a^{8} r_s^{2} \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}^{4}+4r^{3} a^{6} r_s \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{2}+12r^{6} a^{6} r_s^{2} \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}^{4}+4r^{5} a^{4} r_s \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{2}-8r^{8} a^{4} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{2}-8r^{6} a^{6} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{4}+8r^{5} a^{4} r_s \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{2}-8r^{10} a^{2} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{2}-8r^{8} a^{4} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{4}%\\n+8r^{7} a^{2} r_s \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{2}-8r^{6} a^{6} r_s^{2} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2}-8r^{4} a^{8} r_s^{2} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2}+8r^{3} a^{6} r_s \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-8r^{8} a^{4} r_s^{2} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2}-8r^{6} a^{6} r_s^{2} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2}+8r^{5} a^{4} r_s \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+4r^{3} a^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}^{2}-4r^{4} a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{2}+8r^{5} a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{2}+8r^{3} a^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2}-4r^{5} a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s \\\\cos{\\\\theta}^{2}-4r^{3} a^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s \\\\cos{\\\\theta}^{4}+4r^{2} a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4} \\\\cos{\\\\theta}^{2}-4r^{7} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s \\\\cos{\\\\theta}^{2}-4r^{5} a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s \\\\cos{\\\\theta}^{4}+4r^{4} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4} \\\\cos{\\\\theta}^{2}+4r^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{4} r_s \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}^{2}-4r^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{2}+8r^{7} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} r_s \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{2}%\\n+8r^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{4} r_s \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2}-4r^{7} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} r_s \\\\cos{\\\\theta}^{2}-4r^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{4} r_s \\\\cos{\\\\theta}^{4}+4r^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4} a^{2} \\\\cos{\\\\theta}^{2}-4r^{9} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s \\\\cos{\\\\theta}^{2}-4r^{7} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s a^{2} \\\\cos{\\\\theta}^{4}+4r^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4} \\\\cos{\\\\theta}^{2}+4a^{10} \\\\cos{\\\\theta}^{4} r^{2} r_s^{2} \\\\sin{\\\\theta}^{8}+4a^{8} \\\\cos{\\\\theta}^{4} r r_s \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+4a^{6} \\\\cos{\\\\theta}^{4} r^{3} r_s \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-8a^{6} \\\\cos{\\\\theta}^{4} r^{6} r_s^{2} \\\\sin{\\\\theta}^{2}-16a^{8} \\\\cos{\\\\theta}^{6} r^{4} r_s^{2} \\\\sin{\\\\theta}^{2}+8a^{6} \\\\cos{\\\\theta}^{4} r^{3} r_s \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-8a^{4} \\\\cos{\\\\theta}^{4} r^{8} r_s^{2} \\\\sin{\\\\theta}^{2}-16a^{6} \\\\cos{\\\\theta}^{6} r^{6} r_s^{2} \\\\sin{\\\\theta}^{2}+8a^{4} \\\\cos{\\\\theta}^{4} r^{5} r_s \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-8a^{10} \\\\cos{\\\\theta}^{8} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+8a^{8} \\\\cos{\\\\theta}^{6} r r_s \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-8a^{8} \\\\cos{\\\\theta}^{8} r^{4} r_s^{2} \\\\sin{\\\\theta}^{2}+8a^{6} \\\\cos{\\\\theta}^{6} r^{3} r_s \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}%\\n+4a^{8} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r r_s \\\\sin{\\\\theta}^{4}-4a^{6} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+8a^{6} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r^{3} r_s \\\\sin{\\\\theta}^{2}+8a^{8} \\\\cos{\\\\theta}^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r r_s \\\\sin{\\\\theta}^{2}-4a^{6} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r^{3} r_s-4a^{8} \\\\cos{\\\\theta}^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r r_s+4a^{6} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4}-4a^{4} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r^{5} r_s-4a^{6} \\\\cos{\\\\theta}^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r^{3} r_s+4a^{4} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4} r^{2}+8a^{6} \\\\cos{\\\\theta}^{6} r^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s \\\\sin{\\\\theta}^{2}-4a^{4} \\\\cos{\\\\theta}^{4} r^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s-4a^{6} \\\\cos{\\\\theta}^{6} r^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s+4a^{4} \\\\cos{\\\\theta}^{4} r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4}-4a^{2} \\\\cos{\\\\theta}^{4} r^{7} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s-4a^{4} \\\\cos{\\\\theta}^{6} r^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s+4a^{2} \\\\cos{\\\\theta}^{4} r^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4}}{4r^{2} r_s^{2} a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4}-4r^{3} r_s a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4}-4r r_s a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4}+4r^{4} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4}-8r^{5} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4}-4r^{3} r_s a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4}-4r^{3} a^{2} r_s \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4}+4r^{4} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4}+4r^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4}+4r^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4}+4r^{4} a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4}-4a^{4} \\\\cos{\\\\theta}^{4} r r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4}+4a^{4} \\\\cos{\\\\theta}^{2} r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4}+4a^{6} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4}-4a^{2} \\\\cos{\\\\theta}^{2} r^{3} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4}+4a^{2} \\\\cos{\\\\theta}^{2} r^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4}+4a^{4} \\\\cos{\\\\theta}^{4} r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{\\\\theta}= & \\\\frac{2r_s^{2} a^{6} r^{3} \\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta} \\\\tan{\\\\theta}+2r_s^{2} a^{4} r^{5} \\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta} \\\\tan{\\\\theta}+2r_s^{2} a^{4} r^{5} \\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\tan{\\\\theta}-2r_s^{3} a^{4} r^{4} \\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta} \\\\tan{\\\\theta}+2r_s^{2} a^{2} r^{7} \\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\tan{\\\\theta}-2r_s^{3} a^{2} r^{6} \\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\cos{\\\\theta} \\\\tan{\\\\theta}-2r_s^{2} a^{8} r \\\\cos{\\\\theta}^{5} \\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\tan{\\\\theta}-2r_s^{2} a^{6} r^{3} \\\\cos{\\\\theta}^{5} \\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\tan{\\\\theta}-2r_s^{2} a^{6} r^{3} \\\\cos{\\\\theta}^{3} \\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\tan{\\\\theta}+2r_s^{3} a^{6} r^{2} \\\\cos{\\\\theta}^{5} \\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\tan{\\\\theta}-2r_s^{2} a^{4} r^{5} \\\\cos{\\\\theta}^{3} \\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\tan{\\\\theta}+2r_s^{3} a^{4} r^{4} \\\\cos{\\\\theta}^{3} \\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta} \\\\tan{\\\\theta}+2r_s^{2} a^{6} \\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r^{3} \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-r_s^{2} a^{8} \\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r \\\\cos{\\\\theta}^{4} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+4r_s^{2} a^{4} \\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r^{5} \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-2r_s^{3} a^{4} \\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r^{4} \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-r_s^{2} a^{6} \\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r^{3} \\\\cos{\\\\theta}^{4} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-3r_s a^{6} \\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r^{4} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+r_s a^{8} \\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r^{2} \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}%\\n-6r_s a^{4} \\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r^{6} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+5r_s^{2} a^{4} \\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r^{5} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-r_s a^{6} \\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r^{4} \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-3r_s a^{8} \\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{2} r^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+r_s a^{10} \\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{4} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-3r_s a^{6} \\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{2} r^{4} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+2r_s^{2} a^{6} \\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{2} r^{3} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+r_s a^{8} \\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{4} r^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+5r_s^{2} a^{2} \\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r^{7} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-2r_s^{3} a^{2} \\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r^{6} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-3r_s a^{2} \\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r^{8} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-2r_s a^{4} \\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r^{6} \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+r_s a^{8} \\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r^{2} \\\\cos{\\\\theta}^{4} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+r_s a^{6} \\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r^{4} \\\\cos{\\\\theta}^{4} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+2r_s^{4} r^{7} a^{4} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+2r_s^{4} r^{5} a^{6} \\\\sin{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}-4r_s^{3} r^{8} a^{4} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-6r_s^{3} r^{6} a^{6} \\\\sin{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}-2r_s^{3} r^{4} a^{8} \\\\sin{2\\\\theta} \\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}+2r_s^{4} r^{9} a^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}%\\n+2r_s^{4} r^{7} a^{4} \\\\sin{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}-4r_s^{3} r^{10} a^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-6r_s^{3} r^{8} a^{4} \\\\sin{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}-2r_s^{3} r^{6} a^{6} \\\\sin{2\\\\theta} \\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}+6r_s^{3} r^{6} a^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+2r_s^{3} r^{4} a^{6} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}-12r_s^{2} r^{7} a^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-6r_s^{2} r^{5} a^{6} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}-2r_s^{2} r^{3} a^{8} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}+18r_s^{3} r^{8} a^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+2r_s^{3} r^{6} a^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}-24r_s^{2} r^{9} a^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-6r_s^{2} r^{7} a^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}-2r_s^{2} r^{5} a^{6} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}+6r_s^{3} r^{6} a^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}+2r_s^{3} r^{4} a^{6} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}-12r_s^{2} r^{7} a^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}-6r_s^{2} r^{5} a^{6} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}-2r_s^{2} r^{3} a^{8} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}+18r_s^{3} r^{8} a^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}%\\n+2r_s^{3} r^{6} a^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}-24r_s^{2} r^{9} a^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}-6r_s^{2} r^{7} a^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}-2r_s^{2} r^{5} a^{6} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}+2r_s^{3} r^{8} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{2} \\\\tan{\\\\theta}+2r_s^{3} r^{6} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{4} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}-4r_s^{2} r^{9} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{2} \\\\tan{\\\\theta}-6r_s^{2} r^{7} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{4} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}-2r_s^{2} r^{5} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{6} \\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}+14r_s^{3} r^{10} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+2r_s^{3} r^{8} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{2} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}-16r_s^{2} r^{11} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-6r_s^{2} r^{9} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{2} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}-2r_s^{2} r^{7} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{4} \\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}+2r_s^{3} r^{8} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{2} \\\\tan{\\\\theta}+2r_s^{3} r^{6} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{4} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}-4r_s^{2} r^{9} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{2} \\\\tan{\\\\theta}-6r_s^{2} r^{7} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{4} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}-2r_s^{2} r^{5} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{6} \\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}+14r_s^{3} r^{10} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}%\\n+2r_s^{3} r^{8} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{2} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}-16r_s^{2} r^{11} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}-6r_s^{2} r^{9} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{2} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}-2r_s^{2} r^{7} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{4} \\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}+2r_s^{2} r^{9} a^{4} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+4r_s^{2} r^{7} a^{6} \\\\sin{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}+2r_s^{2} r^{5} a^{8} \\\\sin{2\\\\theta} \\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}+2r_s^{2} r^{11} a^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+4r_s^{2} r^{9} a^{4} \\\\sin{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}+2r_s^{2} r^{7} a^{6} \\\\sin{2\\\\theta} \\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}+6r_s r^{8} a^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+4r_s r^{6} a^{6} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}+2r_s r^{4} a^{8} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}+10r_s r^{10} a^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+4r_s r^{8} a^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}+2r_s r^{6} a^{6} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}+6r_s r^{8} a^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}+4r_s r^{6} a^{6} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}+2r_s r^{4} a^{8} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}+10r_s r^{10} a^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}%\\n+4r_s r^{8} a^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}+2r_s r^{6} a^{6} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}+2r_s r^{10} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{2} \\\\tan{\\\\theta}+4r_s r^{8} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{4} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}+2r_s r^{6} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{6} \\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}+6r_s r^{12} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+4r_s r^{10} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{2} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}+2r_s r^{8} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{4} \\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}+2r_s r^{10} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{2} \\\\tan{\\\\theta}+4r_s r^{8} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{4} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}+2r_s r^{6} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{6} \\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}+6r_s r^{12} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}+4r_s r^{10} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{2} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}+2r_s r^{8} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{4} \\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}-2r_s^{3} r^{6} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-2r_s^{3} r^{4} a^{8} \\\\cos{\\\\theta}^{4} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+2r_s^{2} r^{7} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+4r_s^{2} r^{5} a^{8} \\\\cos{\\\\theta}^{4} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+2r_s^{2} r^{3} a^{10} \\\\cos{\\\\theta}^{6} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-2r_s^{3} r^{8} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}%\\n-2r_s^{3} r^{6} a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+2r_s^{2} r^{9} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+4r_s^{2} r^{7} a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+2r_s^{2} r^{5} a^{8} \\\\cos{\\\\theta}^{6} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-22r_s^{2} r^{5} a^{6} \\\\cos{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-18r_s^{2} r^{3} a^{8} \\\\cos{\\\\theta}^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+18r_s r^{6} a^{6} \\\\cos{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+24r_s r^{4} a^{8} \\\\cos{\\\\theta}^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+10r_s r^{2} a^{10} \\\\cos{\\\\theta}^{6} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-60r_s^{2} r^{7} a^{4} \\\\cos{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-56r_s^{2} r^{5} a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+36r_s r^{8} a^{4} \\\\cos{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+48r_s r^{6} a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+20r_s r^{4} a^{8} \\\\cos{\\\\theta}^{6} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-22r_s^{2} r^{5} a^{6} \\\\cos{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}-18r_s^{2} r^{3} a^{8} \\\\cos{\\\\theta}^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}+18r_s r^{6} a^{6} \\\\cos{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}+24r_s r^{4} a^{8} \\\\cos{\\\\theta}^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}+10r_s r^{2} a^{10} \\\\cos{\\\\theta}^{6} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}-60r_s^{2} r^{7} a^{4} \\\\cos{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}%\\n-56r_s^{2} r^{5} a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}+36r_s r^{8} a^{4} \\\\cos{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}+48r_s r^{6} a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}+20r_s r^{4} a^{8} \\\\cos{\\\\theta}^{6} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}-38r_s^{2} r^{9} a^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-38r_s^{2} r^{7} a^{4} \\\\cos{\\\\theta}^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+18r_s r^{10} a^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+24r_s r^{8} a^{4} \\\\cos{\\\\theta}^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+10r_s r^{6} a^{6} \\\\cos{\\\\theta}^{6} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-38r_s^{2} r^{9} a^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}-38r_s^{2} r^{7} a^{4} \\\\cos{\\\\theta}^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}+18r_s r^{10} a^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}+24r_s r^{8} a^{4} \\\\cos{\\\\theta}^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}+10r_s r^{6} a^{6} \\\\cos{\\\\theta}^{6} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}-2r_s^{4} a^{6} \\\\cos{\\\\theta}^{2} r^{5} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-2r_s^{4} a^{8} \\\\cos{\\\\theta}^{4} r^{3} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+4r_s^{3} a^{6} \\\\cos{\\\\theta}^{2} r^{6} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+8r_s^{3} a^{8} \\\\cos{\\\\theta}^{4} r^{4} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+4r_s^{3} a^{10} \\\\cos{\\\\theta}^{6} r^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-2r_s^{4} a^{4} \\\\cos{\\\\theta}^{2} r^{7} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}%\\n-2r_s^{4} a^{6} \\\\cos{\\\\theta}^{4} r^{5} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+4r_s^{3} a^{4} \\\\cos{\\\\theta}^{2} r^{8} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+8r_s^{3} a^{6} \\\\cos{\\\\theta}^{4} r^{6} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+4r_s^{3} a^{8} \\\\cos{\\\\theta}^{6} r^{4} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-4r_s^{3} a^{6} \\\\cos{\\\\theta}^{2} r^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-4r_s^{3} a^{8} \\\\cos{\\\\theta}^{4} r^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+8r_s^{2} a^{6} \\\\cos{\\\\theta}^{2} r^{5} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+14r_s^{2} a^{8} \\\\cos{\\\\theta}^{4} r^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+6r_s^{2} a^{10} \\\\cos{\\\\theta}^{6} r \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-12r_s^{3} a^{4} \\\\cos{\\\\theta}^{2} r^{6} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-16r_s^{3} a^{6} \\\\cos{\\\\theta}^{4} r^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+20r_s^{2} a^{4} \\\\cos{\\\\theta}^{2} r^{7} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+38r_s^{2} a^{6} \\\\cos{\\\\theta}^{4} r^{5} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+18r_s^{2} a^{8} \\\\cos{\\\\theta}^{6} r^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-4r_s^{3} a^{6} \\\\cos{\\\\theta}^{2} r^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}-4r_s^{3} a^{8} \\\\cos{\\\\theta}^{4} r^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}+8r_s^{2} a^{6} \\\\cos{\\\\theta}^{2} r^{5} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}+14r_s^{2} a^{8} \\\\cos{\\\\theta}^{4} r^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}+6r_s^{2} a^{10} \\\\cos{\\\\theta}^{6} r \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}-12r_s^{3} a^{4} \\\\cos{\\\\theta}^{2} r^{6} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}%\\n-16r_s^{3} a^{6} \\\\cos{\\\\theta}^{4} r^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}+20r_s^{2} a^{4} \\\\cos{\\\\theta}^{2} r^{7} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}+38r_s^{2} a^{6} \\\\cos{\\\\theta}^{4} r^{5} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}+18r_s^{2} a^{8} \\\\cos{\\\\theta}^{6} r^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}-8r_s^{3} a^{2} \\\\cos{\\\\theta}^{2} r^{8} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-12r_s^{3} a^{4} \\\\cos{\\\\theta}^{4} r^{6} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+12r_s^{2} a^{2} \\\\cos{\\\\theta}^{2} r^{9} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+24r_s^{2} a^{4} \\\\cos{\\\\theta}^{4} r^{7} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+12r_s^{2} a^{6} \\\\cos{\\\\theta}^{6} r^{5} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-8r_s^{3} a^{2} \\\\cos{\\\\theta}^{2} r^{8} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}-12r_s^{3} a^{4} \\\\cos{\\\\theta}^{4} r^{6} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}+12r_s^{2} a^{2} \\\\cos{\\\\theta}^{2} r^{9} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}+24r_s^{2} a^{4} \\\\cos{\\\\theta}^{4} r^{7} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}+12r_s^{2} a^{6} \\\\cos{\\\\theta}^{6} r^{5} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}-2r_s^{2} a^{6} \\\\cos{\\\\theta}^{2} r^{7} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-6r_s^{2} a^{8} \\\\cos{\\\\theta}^{4} r^{5} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-6r_s^{2} a^{10} \\\\cos{\\\\theta}^{6} r^{3} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-2r_s^{2} a^{4} \\\\cos{\\\\theta}^{2} r^{9} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-6r_s^{2} a^{6} \\\\cos{\\\\theta}^{4} r^{7} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-6r_s^{2} a^{8} \\\\cos{\\\\theta}^{6} r^{5} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}%\\n-6r_s a^{6} \\\\cos{\\\\theta}^{2} r^{6} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-12r_s a^{8} \\\\cos{\\\\theta}^{4} r^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-6r_s a^{10} \\\\cos{\\\\theta}^{6} r^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-12r_s a^{4} \\\\cos{\\\\theta}^{2} r^{8} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-26r_s a^{6} \\\\cos{\\\\theta}^{4} r^{6} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-16r_s a^{8} \\\\cos{\\\\theta}^{6} r^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-6r_s a^{6} \\\\cos{\\\\theta}^{2} r^{6} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}-12r_s a^{8} \\\\cos{\\\\theta}^{4} r^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}-6r_s a^{10} \\\\cos{\\\\theta}^{6} r^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}-12r_s a^{4} \\\\cos{\\\\theta}^{2} r^{8} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}-26r_s a^{6} \\\\cos{\\\\theta}^{4} r^{6} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}-16r_s a^{8} \\\\cos{\\\\theta}^{6} r^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}-6r_s a^{2} \\\\cos{\\\\theta}^{2} r^{10} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-14r_s a^{4} \\\\cos{\\\\theta}^{4} r^{8} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-10r_s a^{6} \\\\cos{\\\\theta}^{6} r^{6} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-6r_s a^{2} \\\\cos{\\\\theta}^{2} r^{10} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}-14r_s a^{4} \\\\cos{\\\\theta}^{4} r^{8} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}-10r_s a^{6} \\\\cos{\\\\theta}^{6} r^{6} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}-2r_s^{2} a^{12} \\\\cos{\\\\theta}^{8} r \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-2r_s^{2} a^{10} \\\\cos{\\\\theta}^{8} r^{3} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}%\\n+2r_s^{2} a^{8} \\\\cos{\\\\theta}^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r^{3} \\\\tan{\\\\theta}+2r_s^{2} a^{10} \\\\cos{\\\\theta}^{6} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r \\\\tan{\\\\theta}-2r_s a^{8} \\\\cos{\\\\theta}^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r^{4} \\\\tan{\\\\theta}-4r_s a^{10} \\\\cos{\\\\theta}^{6} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r^{2} \\\\tan{\\\\theta}-2r_s a^{12} \\\\cos{\\\\theta}^{8} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+2r_s^{2} a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r^{5} \\\\tan{\\\\theta}+2r_s^{2} a^{8} \\\\cos{\\\\theta}^{6} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r^{3} \\\\tan{\\\\theta}-2r_s a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r^{6} \\\\tan{\\\\theta}-4r_s a^{8} \\\\cos{\\\\theta}^{6} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r^{4} \\\\tan{\\\\theta}-2r_s a^{10} \\\\cos{\\\\theta}^{8} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r^{2} \\\\tan{\\\\theta}+2r_s^{2} a^{8} \\\\cos{\\\\theta}^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r^{3} \\\\tan{\\\\theta}+2r_s^{2} a^{10} \\\\cos{\\\\theta}^{6} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r \\\\tan{\\\\theta}-2r_s a^{8} \\\\cos{\\\\theta}^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r^{4} \\\\tan{\\\\theta}-4r_s a^{10} \\\\cos{\\\\theta}^{6} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r^{2} \\\\tan{\\\\theta}-2r_s a^{12} \\\\cos{\\\\theta}^{8} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}+2r_s^{2} a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r^{5} \\\\tan{\\\\theta}+2r_s^{2} a^{8} \\\\cos{\\\\theta}^{6} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r^{3} \\\\tan{\\\\theta}-2r_s a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r^{6} \\\\tan{\\\\theta}-4r_s a^{8} \\\\cos{\\\\theta}^{6} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r^{4} \\\\tan{\\\\theta}-2r_s a^{10} \\\\cos{\\\\theta}^{8} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r^{2} \\\\tan{\\\\theta}%\\n-2r_s a^{10} \\\\cos{\\\\theta}^{8} r^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-2r_s a^{8} \\\\cos{\\\\theta}^{8} r^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-2r_s a^{10} \\\\cos{\\\\theta}^{8} r^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}-2r_s a^{8} \\\\cos{\\\\theta}^{8} r^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}-6r_s^{4} r^{5} a^{4} \\\\cos{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-6r_s^{4} r^{5} a^{4} \\\\cos{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}+6r_s^{3} r^{4} a^{6} \\\\cos{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+6r_s^{3} r^{4} a^{6} \\\\cos{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}-4r_s^{4} r^{7} a^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-4r_s^{4} r^{7} a^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}+32r_s^{3} r^{6} a^{4} \\\\cos{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+32r_s^{3} r^{6} a^{4} \\\\cos{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}+20r_s^{3} r^{4} a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+20r_s^{3} r^{4} a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}-6r_s^{4} r^{7} a^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-6r_s^{4} r^{7} a^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}-4r_s^{4} r^{9} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-4r_s^{4} r^{9} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}+26r_s^{3} r^{8} a^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+26r_s^{3} r^{8} a^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}%\\n+18r_s^{3} r^{6} a^{4} \\\\cos{\\\\theta}^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+18r_s^{3} r^{6} a^{4} \\\\cos{\\\\theta}^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}-16r_s^{2} r^{3} a^{8} \\\\cos{\\\\theta}^{6} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-16r_s^{2} r^{3} a^{8} \\\\cos{\\\\theta}^{6} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}-12r_s^{2} r^{5} a^{6} \\\\cos{\\\\theta}^{6} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-12r_s^{2} r^{5} a^{6} \\\\cos{\\\\theta}^{6} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}+2r_s^{4} a^{6} \\\\cos{\\\\theta}^{4} r^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+2r_s^{4} a^{6} \\\\cos{\\\\theta}^{4} r^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}+2r_s^{4} a^{4} \\\\cos{\\\\theta}^{2} r^{5} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+2r_s^{4} a^{4} \\\\cos{\\\\theta}^{2} r^{5} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}-4r_s^{3} a^{8} \\\\cos{\\\\theta}^{6} r^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-4r_s^{3} a^{8} \\\\cos{\\\\theta}^{6} r^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}+2r_s^{4} a^{4} \\\\cos{\\\\theta}^{4} r^{5} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+2r_s^{4} a^{4} \\\\cos{\\\\theta}^{4} r^{5} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}+2r_s^{4} a^{2} \\\\cos{\\\\theta}^{2} r^{7} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+2r_s^{4} a^{2} \\\\cos{\\\\theta}^{2} r^{7} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}-4r_s^{3} a^{6} \\\\cos{\\\\theta}^{6} r^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-4r_s^{3} a^{6} \\\\cos{\\\\theta}^{6} r^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}-2r_s^{4} r^{3} a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-2r_s^{4} r^{3} a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}%\\n+4r_s^{3} r^{2} a^{8} \\\\cos{\\\\theta}^{6} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+4r_s^{3} r^{2} a^{8} \\\\cos{\\\\theta}^{6} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}-2r_s^{4} r^{5} a^{4} \\\\cos{\\\\theta}^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-2r_s^{4} r^{5} a^{4} \\\\cos{\\\\theta}^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}+4r_s^{3} r^{4} a^{6} \\\\cos{\\\\theta}^{6} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+4r_s^{3} r^{4} a^{6} \\\\cos{\\\\theta}^{6} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}+2r_s^{3} r^{2} a^{8} \\\\cos{\\\\theta}^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+2r_s^{3} r^{2} a^{8} \\\\cos{\\\\theta}^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}-4r_s^{2} r a^{10} \\\\cos{\\\\theta}^{6} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-4r_s^{2} r a^{10} \\\\cos{\\\\theta}^{6} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}+2\\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} \\\\sin{2\\\\theta} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} r^{2}-a^{4} \\\\cos{\\\\theta}^{2}+r^{3} r_s-r^{4}-r^{2} a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}+2\\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} \\\\sin{2\\\\theta} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} r^{2}-a^{4} \\\\cos{\\\\theta}^{2}+r^{3} r_s-r^{4}-r^{2} a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}+4\\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} r^{2}-a^{4} \\\\cos{\\\\theta}^{2}+r^{3} r_s-r^{4}-r^{2} a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}+4\\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} r^{2}-a^{4} \\\\cos{\\\\theta}^{2}+r^{3} r_s-r^{4}-r^{2} a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}-2r^{5} r_s^{4} a^{6} \\\\sin{\\\\theta}^{4}+10r^{6} r_s^{3} a^{6} \\\\sin{\\\\theta}^{4}+4r^{4} r_s^{3} a^{8} \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}^{2}+2r^{3} r_s^{4} a^{8} \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}^{2}-2r^{2} r_s^{3} a^{6} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+6r^{8} r_s^{3} a^{4} \\\\sin{\\\\theta}^{4}%\\n-4r^{6} r_s^{3} a^{6} \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}^{2}+2r^{5} r_s^{4} a^{6} \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}^{2}+2r^{4} r_s^{3} a^{4} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+2r^{6} r_s^{5} a^{4} \\\\sin{\\\\theta}^{2}-12r^{7} r_s^{4} a^{4} \\\\sin{\\\\theta}^{2}-6r^{5} r_s^{4} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}-2r^{4} r_s^{5} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+2r^{3} r_s^{4} a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+6r^{8} r_s^{5} a^{2} \\\\sin{\\\\theta}^{2}-20r^{9} r_s^{4} a^{2} \\\\sin{\\\\theta}^{2}-22r^{7} r_s^{4} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+2r^{6} r_s^{5} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}-2r^{5} r_s^{4} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+28r^{8} r_s^{3} a^{4} \\\\sin{\\\\theta}^{2}+42r^{6} r_s^{3} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}-2r^{4} r_s^{3} a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+36r^{10} r_s^{3} a^{2} \\\\sin{\\\\theta}^{2}+58r^{8} r_s^{3} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+6r^{6} r_s^{3} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+16r^{4} r_s^{3} a^{8} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2}%\\n+4r^{3} r_s^{4} a^{8} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2}-2r^{2} r_s^{3} a^{6} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+32r^{6} r_s^{3} a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2}-4r^{5} r_s^{4} a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2}+2r^{4} r_s^{3} a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-2r^{7} r_s^{4} a^{4} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}-2r^{5} r_s^{4} a^{6} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}+2r^{5} r_s^{4} a^{6} \\\\sin{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}+2r^{3} r_s^{4} a^{8} \\\\sin{2\\\\theta} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}-6r^{9} r_s^{4} a^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-10r^{7} r_s^{4} a^{4} \\\\sin{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}-4r^{5} r_s^{4} a^{6} \\\\sin{2\\\\theta} \\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}+4r^{6} r_s^{3} a^{2} \\\\sin{2\\\\theta} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}+4r^{4} r_s^{3} a^{4} \\\\sin{2\\\\theta} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}-2r^{6} r_s^{3} a^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}-2r^{4} r_s^{3} a^{6} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}+2r^{4} r_s^{3} a^{6} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}+2r^{2} r_s^{3} a^{8} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}-4r^{8} r_s^{3} a^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-4r^{6} r_s^{3} a^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}%\\n-4r^{4} r_s^{3} a^{6} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}+4r^{5} r_s^{2} a^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}+4r^{3} r_s^{2} a^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}-2r^{6} r_s^{3} a^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}-2r^{4} r_s^{3} a^{6} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}+2r^{4} r_s^{3} a^{6} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}+2r^{2} r_s^{3} a^{8} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}-4r^{8} r_s^{3} a^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}-4r^{6} r_s^{3} a^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}-4r^{4} r_s^{3} a^{6} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}+4r^{5} r_s^{2} a^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}+4r^{3} r_s^{2} a^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}-2r^{8} r_s^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}-2r^{6} r_s^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{4} \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}+2r^{6} r_s^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}+2r^{4} r_s^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}+4r^{10} r_s^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+12r^{8} r_s^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{2} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}-4r^{6} r_s^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{4} \\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}+4r^{7} r_s^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}%\\n+4r^{5} r_s^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}-2r^{8} r_s^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}-2r^{6} r_s^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{4} \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}+2r^{6} r_s^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}+2r^{4} r_s^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}+4r^{10} r_s^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}+12r^{8} r_s^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{2} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}-4r^{6} r_s^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{4} \\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}+4r^{7} r_s^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}+4r^{5} r_s^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}+2r^{5} r_s^{4} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+2r^{5} r_s^{4} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}+4r^{7} r_s^{4} a^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+4r^{7} r_s^{4} a^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}-4r^{4} r_s^{3} a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-4r^{4} r_s^{3} a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}-4r^{6} r_s^{3} a^{4} \\\\sin{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-4r^{6} r_s^{3} a^{4} \\\\sin{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}-2r^{4} r_s^{3} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-2r^{4} r_s^{3} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}%\\n-4r^{6} r_s^{3} a^{4} \\\\cos{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-4r^{6} r_s^{3} a^{4} \\\\cos{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}+4r^{5} r_s^{2} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+4r^{5} r_s^{2} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}+4r^{3} r_s^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+4r^{3} r_s^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}+4r^{7} r_s^{4} a^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+4r^{7} r_s^{4} a^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}-4r^{6} r_s^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-4r^{6} r_s^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}-12r^{8} r_s^{3} a^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-12r^{8} r_s^{3} a^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}-10r^{6} r_s^{3} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-10r^{6} r_s^{3} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}+4r^{8} r_s^{3} a^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+4r^{8} r_s^{3} a^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}+12r^{7} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+12r^{7} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}-4r^{4} r_s^{3} a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-4r^{4} r_s^{3} a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}%\\n+24r^{6} r_s^{3} a^{4} \\\\cos{\\\\theta}^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+24r^{6} r_s^{3} a^{4} \\\\cos{\\\\theta}^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}+16r^{5} r_s^{2} a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+16r^{5} r_s^{2} a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}+2r^{5} r_s^{4} a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+2r^{3} r_s^{4} a^{8} \\\\cos{\\\\theta}^{6} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+8r^{4} r_s^{3} a^{6} \\\\cos{\\\\theta}^{6} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+8r^{4} r_s^{3} a^{6} \\\\cos{\\\\theta}^{6} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}+2r^{8} r_s^{3} a^{4} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+2r^{6} r_s^{3} a^{6} \\\\sin{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}-2r^{4} r_s^{3} a^{8} \\\\cos{\\\\theta}^{4} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-2r^{4} r_s^{3} a^{6} \\\\sin{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}-2r^{4} r_s^{3} a^{6} \\\\sin{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}-4r^{7} r_s^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-16r^{5} r_s^{2} a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-4r^{7} r_s^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}-16r^{5} r_s^{2} a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}-2r^{2} r_s^{3} a^{10} \\\\cos{\\\\theta}^{6} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-4r^{3} r_s^{2} a^{8} \\\\cos{\\\\theta}^{6} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-4r^{3} r_s^{2} a^{8} \\\\cos{\\\\theta}^{6} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}%\\n+2r^{5} r_s^{4} a^{4} \\\\sin{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}+2r^{5} r_s^{4} a^{4} \\\\sin{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}-4r^{7} r_s^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{2} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}-4r^{7} r_s^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{2} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}+14r^{10} r_s^{3} a^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+22r^{8} r_s^{3} a^{4} \\\\sin{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}+6r^{8} r_s^{3} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+4r^{6} r_s^{3} a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-6r^{6} r_s^{3} a^{4} \\\\sin{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}-6r^{6} r_s^{3} a^{4} \\\\sin{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}-16r^{11} r_s^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-20r^{9} r_s^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{2} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}-16r^{11} r_s^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}-20r^{9} r_s^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{2} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}-40r^{9} r_s^{2} a^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-88r^{7} r_s^{2} a^{4} \\\\cos{\\\\theta}^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-40r^{9} r_s^{2} a^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}-88r^{7} r_s^{2} a^{4} \\\\cos{\\\\theta}^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}-4r^{4} r_s^{3} a^{8} \\\\cos{\\\\theta}^{6} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-44r^{5} r_s^{2} a^{6} \\\\cos{\\\\theta}^{6} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}%\\n-44r^{5} r_s^{2} a^{6} \\\\cos{\\\\theta}^{6} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}-6r^{5} r_s^{4} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4}-4r^{3} r_s^{4} a^{8} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4}+4r^{4} r_s^{3} a^{8} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4}-4r^{8} r_s^{3} a^{4}-8r^{6} r_s^{3} a^{6} \\\\cos{\\\\theta}^{2}-4r^{5} r_s^{2} a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+4r^{5} r_s^{2} a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-8r^{10} r_s^{3} a^{2}-16r^{8} r_s^{3} a^{4} \\\\cos{\\\\theta}^{2}+8r^{7} r_s^{2} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-2r^{2} r_s^{3} a^{10} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4}-4r^{4} r_s^{3} a^{8} \\\\cos{\\\\theta}^{4}-4r^{3} r_s^{2} a^{6} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+4r^{3} r_s^{2} a^{6} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-8r^{6} r_s^{3} a^{6} \\\\cos{\\\\theta}^{4}+4r^{5} r_s^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+4r^{8} r_s^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+10r^{6} r_s^{3} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4}-12r^{7} r_s^{2} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}%\\n-4r^{12} r_s^{3}-8r^{10} r_s^{3} a^{2} \\\\cos{\\\\theta}^{2}-4r^{9} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+2r^{4} r_s^{3} a^{8} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4}-8r^{5} r_s^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-4r^{8} r_s^{3} a^{4} \\\\cos{\\\\theta}^{4}+4r^{8} r_s^{3} a^{4} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}+4r^{6} r_s^{3} a^{6} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}-4r^{6} r_s^{3} a^{6} \\\\sin{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}-4r^{4} r_s^{3} a^{8} \\\\sin{2\\\\theta} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}+8r^{6} r_s^{3} a^{6} \\\\sin{2\\\\theta} \\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}-8r^{7} r_s^{2} a^{2} \\\\sin{2\\\\theta} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}-8r^{5} r_s^{2} a^{4} \\\\sin{2\\\\theta} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}+4r^{7} r_s^{2} a^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}+4r^{5} r_s^{2} a^{6} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}-4r^{5} r_s^{2} a^{6} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}-4r^{3} r_s^{2} a^{8} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}+8r^{5} r_s^{2} a^{6} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}-8r^{6} r_s a^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}-8r^{4} r_s a^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}%\\n+4r^{7} r_s^{2} a^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}+4r^{5} r_s^{2} a^{6} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}-4r^{5} r_s^{2} a^{6} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}-4r^{3} r_s^{2} a^{8} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}+8r^{5} r_s^{2} a^{6} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}-8r^{6} r_s a^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}-8r^{4} r_s a^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}+4r^{9} r_s^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}+4r^{7} r_s^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{4} \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}-4r^{7} r_s^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}-4r^{5} r_s^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}+8r^{7} r_s^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{4} \\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}-8r^{8} r_s \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}-8r^{6} r_s \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}+4r^{9} r_s^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}+4r^{7} r_s^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{4} \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}-4r^{7} r_s^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}-4r^{5} r_s^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}+8r^{7} r_s^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{4} \\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}-8r^{8} r_s \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}%\\n-8r^{6} r_s \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}+8r^{7} r_s^{2} a^{4} \\\\sin{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+8r^{7} r_s^{2} a^{4} \\\\sin{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}+8r^{5} r_s^{2} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+8r^{5} r_s^{2} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}-8r^{6} r_s a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-8r^{6} r_s a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}+4r^{3} r_s^{2} a^{8} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+4r^{3} r_s^{2} a^{8} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}-12r^{4} r_s a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-12r^{4} r_s a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}+12r^{9} r_s^{2} a^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+12r^{9} r_s^{2} a^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}+6r^{7} r_s^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+6r^{7} r_s^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}-12r^{8} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-12r^{8} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}+4r^{5} r_s^{2} a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+4r^{5} r_s^{2} a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}-12r^{6} r_s a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}%\\n-12r^{6} r_s a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}-4r^{9} r_s^{2} a^{4} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-4r^{7} r_s^{2} a^{6} \\\\sin{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}-2r^{7} r_s^{2} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+2r^{5} r_s^{2} a^{8} \\\\cos{\\\\theta}^{4} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+4r^{5} r_s^{2} a^{6} \\\\sin{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}+4r^{5} r_s^{2} a^{6} \\\\sin{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}+16r^{10} r_s a^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+16r^{8} r_s a^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}+16r^{10} r_s a^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}+16r^{8} r_s a^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}+40r^{8} r_s a^{4} \\\\cos{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+72r^{6} r_s a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+40r^{8} r_s a^{4} \\\\cos{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}+72r^{6} r_s a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}+6r^{3} r_s^{2} a^{10} \\\\cos{\\\\theta}^{6} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+40r^{4} r_s a^{8} \\\\cos{\\\\theta}^{6} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+40r^{4} r_s a^{8} \\\\cos{\\\\theta}^{6} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}-6r^{11} r_s^{2} a^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-6r^{9} r_s^{2} a^{4} \\\\sin{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}%\\n+4r^{7} r_s^{2} a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+6r^{7} r_s^{2} a^{4} \\\\sin{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}+6r^{7} r_s^{2} a^{4} \\\\sin{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}+24r^{12} r_s \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+28r^{10} r_s \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{2} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}+24r^{12} r_s \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}+28r^{10} r_s \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{2} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}+44r^{10} r_s a^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+80r^{8} r_s a^{4} \\\\cos{\\\\theta}^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+44r^{10} r_s a^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}+80r^{8} r_s a^{4} \\\\cos{\\\\theta}^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}+6r^{5} r_s^{2} a^{8} \\\\cos{\\\\theta}^{6} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+40r^{6} r_s a^{6} \\\\cos{\\\\theta}^{6} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+40r^{6} r_s a^{6} \\\\cos{\\\\theta}^{6} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}-12r^{7} r_s^{2} a^{6} \\\\sin{\\\\theta}^{4}-14r^{5} r_s^{2} a^{8} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4}-24r^{9} r_s^{2} a^{4} \\\\sin{\\\\theta}^{2}-60r^{7} r_s^{2} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+8r^{9} r_s^{2} a^{4}+20r^{7} r_s^{2} a^{6} \\\\cos{\\\\theta}^{2}%\\n+8r^{6} r_s a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-8r^{6} r_s a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+16r^{11} r_s^{2} a^{2}+36r^{9} r_s^{2} a^{4} \\\\cos{\\\\theta}^{2}-16r^{8} r_s a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-48r^{5} r_s^{2} a^{8} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2}+16r^{5} r_s^{2} a^{8} \\\\cos{\\\\theta}^{4}+12r^{4} r_s a^{6} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-12r^{4} r_s a^{6} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+28r^{7} r_s^{2} a^{6} \\\\cos{\\\\theta}^{4}-20r^{6} r_s a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-14r^{9} r_s^{2} a^{4} \\\\sin{\\\\theta}^{4}-8r^{7} r_s^{2} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4}-28r^{11} r_s^{2} a^{2} \\\\sin{\\\\theta}^{2}-56r^{9} r_s^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+12r^{8} r_s a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+8r^{13} r_s^{2}+16r^{11} r_s^{2} a^{2} \\\\cos{\\\\theta}^{2}-8r^{10} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-40r^{7} r_s^{2} a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2}%\\n+12r^{6} r_s a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+12r^{9} r_s^{2} a^{4} \\\\cos{\\\\theta}^{4}-8r^{8} r_s a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+2r^{6} r_s^{3} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}-2r^{2} r_s^{3} a^{10} \\\\cos{\\\\theta}^{6} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}-4r^{5} r_s^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}-4r^{3} r_s^{2} a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{2\\\\theta} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}+2r^{5} r_s^{2} a^{6} \\\\cos{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}-2r r_s^{2} a^{10} \\\\cos{\\\\theta}^{6} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}-4r^{4} r_s a^{4} \\\\cos{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}-4r^{2} r_s a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}+2r^{5} r_s^{2} a^{6} \\\\cos{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}-2r r_s^{2} a^{10} \\\\cos{\\\\theta}^{6} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}-4r^{4} r_s a^{4} \\\\cos{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}-4r^{2} r_s a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}+2r^{7} r_s^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}-2r^{3} r_s^{2} a^{8} \\\\cos{\\\\theta}^{6} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}-4r^{6} r_s a^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}-4r^{4} r_s a^{4} \\\\cos{\\\\theta}^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}+2r^{7} r_s^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}%\\n-2r^{3} r_s^{2} a^{8} \\\\cos{\\\\theta}^{6} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}-4r^{6} r_s a^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}-4r^{4} r_s a^{4} \\\\cos{\\\\theta}^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}+4r^{3} r_s^{2} a^{4} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+4r^{3} r_s^{2} a^{4} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}-4r^{2} r_s a^{6} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-4r^{2} r_s a^{6} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}-4r^{4} r_s a^{4} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-4r^{4} r_s a^{4} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}-2r^{2} r_s^{3} a^{10} \\\\cos{\\\\theta}^{8} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-8r^{3} r_s^{2} a^{8} \\\\cos{\\\\theta}^{8} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-8r^{3} r_s^{2} a^{8} \\\\cos{\\\\theta}^{8} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}+2r r_s^{2} a^{12} \\\\cos{\\\\theta}^{8} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+8r^{2} r_s a^{10} \\\\cos{\\\\theta}^{8} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+8r^{2} r_s a^{10} \\\\cos{\\\\theta}^{8} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}+2r^{3} r_s^{2} a^{10} \\\\cos{\\\\theta}^{8} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+8r^{4} r_s a^{8} \\\\cos{\\\\theta}^{8} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+8r^{4} r_s a^{8} \\\\cos{\\\\theta}^{8} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}+2r^{2} r_s^{3} a^{10} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4}+2r^{4} r_s^{3} a^{8} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2}%\\n+4r^{3} r_s^{2} a^{6} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-4r^{3} r_s^{2} a^{6} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-4r^{5} r_s^{2} a^{4} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+2r r_s^{2} a^{12} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4}-12r^{3} r_s^{2} a^{10} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2}+4r^{3} r_s^{2} a^{10} \\\\cos{\\\\theta}^{6}+4r^{2} r_s a^{8} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-4r^{2} r_s a^{8} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+8r^{5} r_s^{2} a^{8} \\\\cos{\\\\theta}^{6}-8r^{4} r_s a^{6} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+2r^{3} r_s^{2} a^{10} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4}-12r^{5} r_s^{2} a^{8} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2}+4r^{4} r_s a^{6} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+4r^{7} r_s^{2} a^{6} \\\\cos{\\\\theta}^{6}-4r^{6} r_s a^{4} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+2r^{5} r_s^{4} a^{6} \\\\sin{\\\\theta}^{6}-2r^{6} r_s^{5} a^{4} \\\\sin{\\\\theta}^{4}-2r^{5} r_s^{4} a^{6} \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{2}+2r^{4} r_s^{3} a^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-2r^{7} r_s^{4} a^{4} \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{2}%\\n+2r^{6} r_s^{3} a^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-2r^{3} r_s^{4} a^{8} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6}+2r^{4} r_s^{5} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4}-2r^{2} r_s^{3} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-2r^{4} r_s^{3} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-4r^{4} r_s^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{4} \\\\sin{\\\\theta}^{4}+4r^{5} r_s^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} \\\\sin{\\\\theta}^{2}-16r^{6} r_s^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} \\\\sin{\\\\theta}^{2}-8r^{4} r_s^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+4r^{6} r_s^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2}+4r^{4} r_s^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{4} \\\\cos{\\\\theta}^{2}-4r^{3} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4} a^{2}+4r^{6} r_s^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} \\\\cos{\\\\theta}^{2}-4r^{5} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4}-4r^{6} r_s^{3} a^{6} \\\\sin{\\\\theta}^{6}+4r^{6} r_s^{3} a^{6} \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{2}-4r^{5} r_s^{2} a^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+4r^{8} r_s^{3} a^{4} \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{2}-4r^{7} r_s^{2} a^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+2r^{4} r_s^{3} a^{8} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6}%\\n+2r^{3} r_s^{2} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+2r^{5} r_s^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+8r^{5} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{4} \\\\sin{\\\\theta}^{4}+16r^{7} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} \\\\sin{\\\\theta}^{2}+16r^{5} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}-8r^{7} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2}-8r^{5} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{4} \\\\cos{\\\\theta}^{2}+8r^{4} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4} a^{2}-8r^{7} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} \\\\cos{\\\\theta}^{2}+8r^{6} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4}+2r^{2} r_s^{3} a^{10} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{6}-2r^{2} r_s^{3} a^{10} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2}+2r r_s^{2} a^{8} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+2r^{3} r_s^{2} a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+4r^{3} r_s^{2} a^{6} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4}+4r^{2} r_s a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4}+4r^{4} r_s a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4}+2r^{6} a^{6} r_s^{3} \\\\sin{\\\\theta}^{4}-4r^{7} a^{6} r_s^{2} \\\\sin{\\\\theta}^{4}-4r^{5} a^{8} r_s^{2} \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}^{2}%\\n-2r^{4} a^{8} r_s^{3} \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}^{2}+2r^{3} a^{6} r_s^{2} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+4r^{8} a^{4} r_s^{3} \\\\sin{\\\\theta}^{4}+2r^{6} a^{6} r_s^{3} \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}^{2}-2r^{5} a^{4} r_s^{2} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-2r^{7} a^{4} r_s^{4} \\\\sin{\\\\theta}^{2}+6r^{8} a^{4} r_s^{3} \\\\sin{\\\\theta}^{2}+4r^{6} a^{6} r_s^{3} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+2r^{5} a^{6} r_s^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}-2r^{4} a^{4} r_s^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-6r^{9} a^{2} r_s^{4} \\\\sin{\\\\theta}^{2}+10r^{10} a^{2} r_s^{3} \\\\sin{\\\\theta}^{2}+16r^{8} a^{4} r_s^{3} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}-2r^{7} a^{4} r_s^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+2r^{6} a^{2} r_s^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-10r^{9} a^{4} r_s^{2} \\\\sin{\\\\theta}^{2}-6r^{7} a^{6} r_s^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+2r^{5} a^{4} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-10r^{11} a^{2} r_s^{2} \\\\sin{\\\\theta}^{2}-18r^{9} a^{4} r_s^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}%\\n-2r^{7} a^{2} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-2r^{5} a^{8} r_s^{2} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2}-2r^{4} a^{8} r_s^{3} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2}+2r^{3} a^{6} r_s^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-14r^{7} a^{6} r_s^{2} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2}+2r^{6} a^{6} r_s^{3} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2}-2r^{5} a^{4} r_s^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-2r^{9} a^{4} r_s^{2} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}-2r^{7} a^{6} r_s^{2} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}+2r^{7} a^{6} r_s^{2} \\\\sin{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}+2r^{5} a^{8} r_s^{2} \\\\sin{2\\\\theta} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}-4r^{11} a^{2} r_s^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-8r^{9} a^{4} r_s^{2} \\\\sin{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}-4r^{7} a^{6} r_s^{2} \\\\sin{2\\\\theta} \\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}+4r^{8} a^{2} r_s \\\\sin{2\\\\theta} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}+4r^{6} a^{4} r_s \\\\sin{2\\\\theta} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}-2r^{8} a^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}-2r^{6} a^{6} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}+2r^{6} a^{6} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}+2r^{4} a^{8} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}%\\n-4r^{10} a^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s \\\\tan{\\\\theta}-8r^{8} a^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}-4r^{6} a^{6} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s \\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}+4r^{7} a^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}+4r^{5} a^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}-2r^{8} a^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}-2r^{6} a^{6} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}+2r^{6} a^{6} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}+2r^{4} a^{8} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}-4r^{10} a^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\tan{\\\\theta}-8r^{8} a^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}-4r^{6} a^{6} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}+4r^{7} a^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}+4r^{5} a^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}-2r^{10} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{2} r_s \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}-2r^{8} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{4} r_s \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}+2r^{8} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{4} r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}+2r^{6} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{6} r_s \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}-4r^{12} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s \\\\tan{\\\\theta}-8r^{10} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s a^{2} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}%\\n-4r^{8} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s a^{4} \\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}+4r^{9} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}+4r^{7} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}-2r^{10} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{2} r_s \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}-2r^{8} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{4} r_s \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}+2r^{8} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{4} r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}+2r^{6} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{6} r_s \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}-4r^{12} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\tan{\\\\theta}-8r^{10} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s a^{2} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}-4r^{8} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s a^{4} \\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}+4r^{9} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}+4r^{7} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}+4r^{7} a^{4} r_s^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+4r^{7} a^{4} r_s^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}-4r^{6} a^{2} r_s \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-4r^{6} a^{2} r_s \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}-4r^{8} a^{4} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-4r^{8} a^{4} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}+2r^{6} a^{6} r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+2r^{6} a^{6} r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}%\\n-4r^{8} a^{4} r_s \\\\cos{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-4r^{8} a^{4} r_s \\\\cos{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}+4r^{7} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+4r^{7} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}-8r^{6} a^{6} \\\\cos{\\\\theta}^{2} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-8r^{6} a^{6} \\\\cos{\\\\theta}^{2} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}-4r^{4} a^{8} \\\\cos{\\\\theta}^{4} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-4r^{4} a^{8} \\\\cos{\\\\theta}^{4} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}+8r^{5} a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+8r^{5} a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}-4r^{10} a^{2} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-4r^{10} a^{2} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}+2r^{8} a^{4} r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+2r^{8} a^{4} r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}+4r^{9} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+4r^{9} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}-8r^{8} a^{4} \\\\cos{\\\\theta}^{2} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-8r^{8} a^{4} \\\\cos{\\\\theta}^{2} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}-4r^{6} a^{6} \\\\cos{\\\\theta}^{4} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-4r^{6} a^{6} \\\\cos{\\\\theta}^{4} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}%\\n+8r^{10} a^{2} \\\\cos{\\\\theta}^{2} r_s \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+8r^{10} a^{2} \\\\cos{\\\\theta}^{2} r_s \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}+24r^{8} a^{4} \\\\cos{\\\\theta}^{4} r_s \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+24r^{8} a^{4} \\\\cos{\\\\theta}^{4} r_s \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}+8r^{7} a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+8r^{7} a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}-2r^{9} a^{4} r_s^{2} \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+2r^{5} a^{8} r_s^{2} \\\\cos{\\\\theta}^{6} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+8r^{10} a^{2} r_s \\\\cos{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+16r^{8} a^{4} r_s \\\\cos{\\\\theta}^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+8r^{10} a^{2} r_s \\\\cos{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}+16r^{8} a^{4} r_s \\\\cos{\\\\theta}^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}+8r^{6} a^{6} r_s \\\\cos{\\\\theta}^{6} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+8r^{6} a^{6} r_s \\\\cos{\\\\theta}^{6} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}+2r^{10} a^{4} r_s \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+2r^{8} a^{6} r_s \\\\sin{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}-2r^{8} a^{6} r_s \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-2r^{6} a^{8} r_s \\\\cos{\\\\theta}^{4} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-2r^{6} a^{6} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}-2r^{6} a^{6} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}%\\n+4r^{8} a^{4} r_s \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}+4r^{8} a^{4} r_s \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}-8r^{11} a^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-8r^{9} a^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}-8r^{11} a^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}-8r^{9} a^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}-24r^{9} a^{4} \\\\cos{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-48r^{7} a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-24r^{9} a^{4} \\\\cos{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}-48r^{7} a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}+4r^{8} a^{6} \\\\cos{\\\\theta}^{2} r_s \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+2r^{6} a^{8} \\\\cos{\\\\theta}^{4} r_s \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-4r^{4} a^{10} \\\\cos{\\\\theta}^{6} r_s \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-32r^{5} a^{8} \\\\cos{\\\\theta}^{6} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-32r^{5} a^{8} \\\\cos{\\\\theta}^{6} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}+2r^{12} a^{2} r_s \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+2r^{10} a^{4} r_s \\\\sin{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}-2r^{10} a^{4} r_s \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-2r^{8} a^{6} r_s \\\\cos{\\\\theta}^{4} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-2r^{8} a^{4} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}%\\n-2r^{8} a^{4} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}-8r^{13} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-8r^{11} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{2} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}-8r^{13} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}-8r^{11} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) a^{2} \\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}-24r^{11} a^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-48r^{9} a^{4} \\\\cos{\\\\theta}^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-24r^{11} a^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}-48r^{9} a^{4} \\\\cos{\\\\theta}^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}+4r^{10} a^{4} \\\\cos{\\\\theta}^{2} r_s \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+2r^{8} a^{6} \\\\cos{\\\\theta}^{4} r_s \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-4r^{6} a^{8} \\\\cos{\\\\theta}^{6} r_s \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-32r^{7} a^{6} \\\\cos{\\\\theta}^{6} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-32r^{7} a^{6} \\\\cos{\\\\theta}^{6} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}-10r^{7} a^{6} r_s^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4}-2r^{5} a^{8} r_s^{2} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4}+4r^{9} a^{4} r_s^{2} \\\\cos{\\\\theta}^{2}+4r^{7} a^{6} r_s^{2} \\\\cos{\\\\theta}^{4}+4r^{6} a^{4} r_s \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-4r^{6} a^{4} r_s \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}%\\n+4r^{11} a^{2} r_s^{2} \\\\cos{\\\\theta}^{2}+4r^{9} a^{4} r_s^{2} \\\\cos{\\\\theta}^{4}-4r^{8} a^{2} r_s \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+6r^{8} a^{6} r_s \\\\sin{\\\\theta}^{4}-2r^{6} a^{8} r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4}+12r^{10} a^{4} r_s \\\\sin{\\\\theta}^{2}+12r^{8} a^{6} r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}-4r^{10} a^{4} r_s-4r^{8} a^{6} r_s \\\\cos{\\\\theta}^{2}-4r^{7} a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+4r^{7} a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-8r^{12} a^{2} r_s-8r^{10} a^{4} r_s \\\\cos{\\\\theta}^{2}+8r^{9} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+12r^{6} a^{8} \\\\cos{\\\\theta}^{2} r_s \\\\sin{\\\\theta}^{4}+2r^{4} a^{10} \\\\cos{\\\\theta}^{4} r_s \\\\sin{\\\\theta}^{4}-10r^{7} a^{6} \\\\cos{\\\\theta}^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+24r^{8} a^{6} \\\\cos{\\\\theta}^{2} r_s \\\\sin{\\\\theta}^{2}+36r^{6} a^{8} \\\\cos{\\\\theta}^{4} r_s \\\\sin{\\\\theta}^{2}-8r^{8} a^{6} \\\\cos{\\\\theta}^{2} r_s%\\n-12r^{6} a^{8} \\\\cos{\\\\theta}^{4} r_s-8r^{5} a^{6} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+8r^{5} a^{6} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-16r^{10} a^{4} \\\\cos{\\\\theta}^{2} r_s-24r^{8} a^{6} \\\\cos{\\\\theta}^{4} r_s+16r^{7} a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+6r^{10} a^{4} r_s \\\\sin{\\\\theta}^{4}-2r^{8} a^{6} r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4}+12r^{12} a^{2} r_s \\\\sin{\\\\theta}^{2}+12r^{10} a^{4} r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}-4r^{9} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-4r^{14} r_s-4r^{12} r_s a^{2} \\\\cos{\\\\theta}^{2}+4r^{11} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+12r^{8} a^{6} \\\\cos{\\\\theta}^{2} r_s \\\\sin{\\\\theta}^{4}+2r^{6} a^{8} \\\\cos{\\\\theta}^{4} r_s \\\\sin{\\\\theta}^{4}-14r^{9} a^{4} \\\\cos{\\\\theta}^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+24r^{10} a^{4} \\\\cos{\\\\theta}^{2} r_s \\\\sin{\\\\theta}^{2}+36r^{8} a^{6} \\\\cos{\\\\theta}^{4} r_s \\\\sin{\\\\theta}^{2}-8r^{7} a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}%\\n-8r^{12} a^{2} \\\\cos{\\\\theta}^{2} r_s-12r^{10} a^{4} \\\\cos{\\\\theta}^{4} r_s+8r^{9} a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-2r^{7} a^{6} \\\\cos{\\\\theta}^{2} r_s^{2} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}+2r^{3} a^{10} \\\\cos{\\\\theta}^{6} r_s^{2} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}-6r^{9} a^{4} \\\\cos{\\\\theta}^{2} r_s^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-10r^{7} a^{6} \\\\cos{\\\\theta}^{4} r_s^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-2r^{5} a^{8} \\\\cos{\\\\theta}^{6} r_s^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+4r^{6} a^{4} \\\\cos{\\\\theta}^{2} r_s \\\\sin{2\\\\theta} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}+4r^{4} a^{6} \\\\cos{\\\\theta}^{4} r_s \\\\sin{2\\\\theta} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}-2r^{6} a^{6} \\\\cos{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}+2r^{2} a^{10} \\\\cos{\\\\theta}^{6} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}-4r^{8} a^{4} \\\\cos{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s \\\\tan{\\\\theta}-8r^{6} a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s \\\\tan{\\\\theta}-4r^{4} a^{8} \\\\cos{\\\\theta}^{6} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s \\\\tan{\\\\theta}+4r^{5} a^{4} \\\\cos{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}+4r^{3} a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}-2r^{6} a^{6} \\\\cos{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}+2r^{2} a^{10} \\\\cos{\\\\theta}^{6} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}-4r^{8} a^{4} \\\\cos{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\tan{\\\\theta}%\\n-8r^{6} a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\tan{\\\\theta}-4r^{4} a^{8} \\\\cos{\\\\theta}^{6} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\tan{\\\\theta}+4r^{5} a^{4} \\\\cos{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}+4r^{3} a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}-2r^{8} a^{4} \\\\cos{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}+2r^{4} a^{8} \\\\cos{\\\\theta}^{6} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}-4r^{10} a^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s \\\\tan{\\\\theta}-8r^{8} a^{4} \\\\cos{\\\\theta}^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s \\\\tan{\\\\theta}-4r^{6} a^{6} \\\\cos{\\\\theta}^{6} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s \\\\tan{\\\\theta}+4r^{7} a^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}+4r^{5} a^{4} \\\\cos{\\\\theta}^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}-2r^{8} a^{4} \\\\cos{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}+2r^{4} a^{8} \\\\cos{\\\\theta}^{6} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}-4r^{10} a^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\tan{\\\\theta}-8r^{8} a^{4} \\\\cos{\\\\theta}^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\tan{\\\\theta}-4r^{6} a^{6} \\\\cos{\\\\theta}^{6} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\tan{\\\\theta}+4r^{7} a^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}+4r^{5} a^{4} \\\\cos{\\\\theta}^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}+4r^{5} a^{6} \\\\cos{\\\\theta}^{4} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+4r^{5} a^{6} \\\\cos{\\\\theta}^{4} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}%\\n-4r^{4} a^{4} \\\\cos{\\\\theta}^{4} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-4r^{4} a^{4} \\\\cos{\\\\theta}^{4} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}+4r^{3} a^{6} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+4r^{3} a^{6} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}+4r^{7} a^{4} \\\\cos{\\\\theta}^{2} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+4r^{7} a^{4} \\\\cos{\\\\theta}^{2} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}-4r^{6} a^{2} \\\\cos{\\\\theta}^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-4r^{6} a^{2} \\\\cos{\\\\theta}^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}+24r^{6} a^{6} \\\\cos{\\\\theta}^{6} r_s \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+24r^{6} a^{6} \\\\cos{\\\\theta}^{6} r_s \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}+4r^{5} a^{4} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+4r^{5} a^{4} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}+2r^{3} a^{10} \\\\cos{\\\\theta}^{8} r_s^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+8r^{4} a^{8} \\\\cos{\\\\theta}^{8} r_s \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+8r^{4} a^{8} \\\\cos{\\\\theta}^{8} r_s \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}-2r^{2} a^{12} \\\\cos{\\\\theta}^{8} r_s \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-8r^{3} a^{10} \\\\cos{\\\\theta}^{8} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-8r^{3} a^{10} \\\\cos{\\\\theta}^{8} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}-2r^{4} a^{10} \\\\cos{\\\\theta}^{8} r_s \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-8r^{5} a^{8} \\\\cos{\\\\theta}^{8} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}%\\n-8r^{5} a^{8} \\\\cos{\\\\theta}^{8} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}-2r^{3} a^{10} \\\\cos{\\\\theta}^{6} r_s^{2} \\\\sin{\\\\theta}^{4}-12r^{7} a^{6} \\\\cos{\\\\theta}^{4} r_s^{2} \\\\sin{\\\\theta}^{2}-2r^{5} a^{8} \\\\cos{\\\\theta}^{6} r_s^{2} \\\\sin{\\\\theta}^{2}+4r^{4} a^{6} \\\\cos{\\\\theta}^{4} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-2r^{2} a^{12} \\\\cos{\\\\theta}^{6} r_s \\\\sin{\\\\theta}^{4}-4r^{5} a^{8} \\\\cos{\\\\theta}^{4} r_s^{2} \\\\sin{\\\\theta}^{2}+12r^{4} a^{10} \\\\cos{\\\\theta}^{6} r_s \\\\sin{\\\\theta}^{2}-4r^{4} a^{10} \\\\cos{\\\\theta}^{6} r_s-4r^{3} a^{8} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+4r^{3} a^{8} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-8r^{6} a^{8} \\\\cos{\\\\theta}^{6} r_s+8r^{5} a^{6} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+2r^{7} a^{6} \\\\cos{\\\\theta}^{2} r_s^{2} \\\\sin{\\\\theta}^{4}+4r^{6} a^{4} \\\\cos{\\\\theta}^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-2r^{4} a^{10} \\\\cos{\\\\theta}^{6} r_s \\\\sin{\\\\theta}^{4}+12r^{6} a^{8} \\\\cos{\\\\theta}^{6} r_s \\\\sin{\\\\theta}^{2}-4r^{5} a^{6} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-4r^{8} a^{6} \\\\cos{\\\\theta}^{6} r_s+4r^{7} a^{4} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}%\\n+2r^{7} a^{6} r_s^{2} \\\\sin{\\\\theta}^{6}-2r^{7} a^{6} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{2}+2r^{6} a^{4} r_s \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-2r^{9} a^{4} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{2}+2r^{8} a^{2} r_s \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-2r^{5} a^{8} r_s^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6}+2r^{6} a^{6} r_s^{3} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4}-2r^{4} a^{6} r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-2r^{6} a^{4} r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-4r^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{4} r_s \\\\sin{\\\\theta}^{4}+4r^{7} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} r_s^{2} \\\\sin{\\\\theta}^{2}-8r^{8} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} r_s \\\\sin{\\\\theta}^{2}-8r^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{4} r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+4r^{8} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} r_s+4r^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{4} r_s \\\\cos{\\\\theta}^{2}-4r^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4} a^{2}+4r^{10} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s+4r^{8} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s a^{2} \\\\cos{\\\\theta}^{2}-4r^{7} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4}+2r^{5} a^{8} \\\\cos{\\\\theta}^{2} r_s^{2} \\\\sin{\\\\theta}^{6}%\\n-2r^{6} a^{6} \\\\cos{\\\\theta}^{2} r_s^{3} \\\\sin{\\\\theta}^{4}+2r^{4} a^{6} \\\\cos{\\\\theta}^{2} r_s \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+2r^{6} a^{4} \\\\cos{\\\\theta}^{2} r_s \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-2r^{3} a^{10} \\\\cos{\\\\theta}^{4} r_s^{2} \\\\sin{\\\\theta}^{6}+2r^{4} a^{8} \\\\cos{\\\\theta}^{4} r_s^{3} \\\\sin{\\\\theta}^{4}+2r^{3} a^{10} \\\\cos{\\\\theta}^{6} r_s^{2} \\\\sin{\\\\theta}^{2}-2r^{2} a^{8} \\\\cos{\\\\theta}^{4} r_s \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-2r^{4} a^{6} \\\\cos{\\\\theta}^{4} r_s \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-4r^{4} a^{6} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s \\\\sin{\\\\theta}^{4}+4r^{5} a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s^{2} \\\\sin{\\\\theta}^{2}-8r^{6} a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s \\\\sin{\\\\theta}^{2}-8r^{4} a^{6} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s \\\\sin{\\\\theta}^{2}+4r^{6} a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s+4r^{4} a^{6} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s-4r^{3} a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4}+4r^{8} a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s+4r^{6} a^{4} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s-4r^{5} a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4}+2a^{8} \\\\cos{\\\\theta}^{2} r^{4} r_s^{3} \\\\sin{\\\\theta}^{4}-10a^{8} \\\\cos{\\\\theta}^{2} r^{5} r_s^{2} \\\\sin{\\\\theta}^{4}%\\n-8a^{10} \\\\cos{\\\\theta}^{4} r^{3} r_s^{2} \\\\sin{\\\\theta}^{4}-2a^{10} \\\\cos{\\\\theta}^{4} r^{2} r_s^{3} \\\\sin{\\\\theta}^{4}+2a^{8} \\\\cos{\\\\theta}^{2} r r_s^{2} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+2a^{6} \\\\cos{\\\\theta}^{2} r^{6} r_s^{3} \\\\sin{\\\\theta}^{4}-8a^{6} \\\\cos{\\\\theta}^{2} r^{7} r_s^{2} \\\\sin{\\\\theta}^{4}-2a^{8} \\\\cos{\\\\theta}^{4} r^{5} r_s^{2} \\\\sin{\\\\theta}^{4}-2a^{6} \\\\cos{\\\\theta}^{2} r^{3} r_s^{2} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-2a^{6} \\\\cos{\\\\theta}^{2} r^{5} r_s^{4} \\\\sin{\\\\theta}^{2}+12a^{6} \\\\cos{\\\\theta}^{2} r^{6} r_s^{3} \\\\sin{\\\\theta}^{2}+8a^{8} \\\\cos{\\\\theta}^{4} r^{4} r_s^{3} \\\\sin{\\\\theta}^{2}+2a^{8} \\\\cos{\\\\theta}^{4} r^{3} r_s^{4} \\\\sin{\\\\theta}^{2}-2a^{6} \\\\cos{\\\\theta}^{2} r^{2} r_s^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-6a^{4} \\\\cos{\\\\theta}^{2} r^{7} r_s^{4} \\\\sin{\\\\theta}^{2}+20a^{4} \\\\cos{\\\\theta}^{2} r^{8} r_s^{3} \\\\sin{\\\\theta}^{2}+24a^{6} \\\\cos{\\\\theta}^{4} r^{6} r_s^{3} \\\\sin{\\\\theta}^{2}-2a^{6} \\\\cos{\\\\theta}^{4} r^{5} r_s^{4} \\\\sin{\\\\theta}^{2}-2a^{4} \\\\cos{\\\\theta}^{2} r^{4} r_s^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-22a^{6} \\\\cos{\\\\theta}^{2} r^{7} r_s^{2} \\\\sin{\\\\theta}^{2}-44a^{8} \\\\cos{\\\\theta}^{4} r^{5} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{6} \\\\cos{\\\\theta}^{2} r^{3} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}%\\n-26a^{4} \\\\cos{\\\\theta}^{2} r^{9} r_s^{2} \\\\sin{\\\\theta}^{2}-56a^{6} \\\\cos{\\\\theta}^{4} r^{7} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{4} \\\\cos{\\\\theta}^{2} r^{5} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-22a^{10} \\\\cos{\\\\theta}^{6} r^{3} r_s^{2} \\\\sin{\\\\theta}^{2}-4a^{10} \\\\cos{\\\\theta}^{6} r^{2} r_s^{3} \\\\sin{\\\\theta}^{2}+2a^{8} \\\\cos{\\\\theta}^{4} r r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-34a^{8} \\\\cos{\\\\theta}^{6} r^{5} r_s^{2} \\\\sin{\\\\theta}^{2}+4a^{8} \\\\cos{\\\\theta}^{6} r^{4} r_s^{3} \\\\sin{\\\\theta}^{2}+2a^{6} \\\\cos{\\\\theta}^{4} r^{3} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+2a^{6} \\\\cos{\\\\theta}^{2} r^{6} r_s^{3} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}-2a^{10} \\\\cos{\\\\theta}^{6} r^{2} r_s^{3} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}+6a^{4} \\\\cos{\\\\theta}^{2} r^{8} r_s^{3} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+10a^{6} \\\\cos{\\\\theta}^{4} r^{6} r_s^{3} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+2a^{8} \\\\cos{\\\\theta}^{6} r^{4} r_s^{3} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-4a^{4} \\\\cos{\\\\theta}^{2} r^{5} r_s^{2} \\\\sin{2\\\\theta} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}-4a^{6} \\\\cos{\\\\theta}^{4} r^{3} r_s^{2} \\\\sin{2\\\\theta} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}+2a^{6} \\\\cos{\\\\theta}^{2} r^{5} r_s^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}-2a^{10} \\\\cos{\\\\theta}^{6} r r_s^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}+4a^{4} \\\\cos{\\\\theta}^{2} r^{7} r_s^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+8a^{6} \\\\cos{\\\\theta}^{4} r^{5} r_s^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}%\\n+4a^{8} \\\\cos{\\\\theta}^{6} r^{3} r_s^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-4a^{4} \\\\cos{\\\\theta}^{2} r^{4} r_s \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}-4a^{6} \\\\cos{\\\\theta}^{4} r^{2} r_s \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}+2a^{6} \\\\cos{\\\\theta}^{2} r^{5} r_s^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}-2a^{10} \\\\cos{\\\\theta}^{6} r r_s^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}+4a^{4} \\\\cos{\\\\theta}^{2} r^{7} r_s^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}+8a^{6} \\\\cos{\\\\theta}^{4} r^{5} r_s^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}+4a^{8} \\\\cos{\\\\theta}^{6} r^{3} r_s^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}-4a^{4} \\\\cos{\\\\theta}^{2} r^{4} r_s \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}-4a^{6} \\\\cos{\\\\theta}^{4} r^{2} r_s \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}+2a^{4} \\\\cos{\\\\theta}^{2} r^{7} r_s^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}-2a^{8} \\\\cos{\\\\theta}^{6} r^{3} r_s^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}-4a^{2} \\\\cos{\\\\theta}^{2} r^{9} r_s^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-16a^{4} \\\\cos{\\\\theta}^{4} r^{7} r_s^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-20a^{6} \\\\cos{\\\\theta}^{6} r^{5} r_s^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-4a^{2} \\\\cos{\\\\theta}^{2} r^{6} r_s \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}-4a^{4} \\\\cos{\\\\theta}^{4} r^{4} r_s \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}+2a^{4} \\\\cos{\\\\theta}^{2} r^{7} r_s^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}-2a^{8} \\\\cos{\\\\theta}^{6} r^{3} r_s^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}-4a^{2} \\\\cos{\\\\theta}^{2} r^{9} r_s^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}%\\n-16a^{4} \\\\cos{\\\\theta}^{4} r^{7} r_s^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}-20a^{6} \\\\cos{\\\\theta}^{6} r^{5} r_s^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}-4a^{2} \\\\cos{\\\\theta}^{2} r^{6} r_s \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}-4a^{4} \\\\cos{\\\\theta}^{4} r^{4} r_s \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}-4a^{6} \\\\cos{\\\\theta}^{4} r^{4} r_s^{3} \\\\sin{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-4a^{6} \\\\cos{\\\\theta}^{4} r^{4} r_s^{3} \\\\sin{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}+4a^{4} \\\\cos{\\\\theta}^{4} r^{3} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+4a^{4} \\\\cos{\\\\theta}^{4} r^{3} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}+4a^{6} \\\\cos{\\\\theta}^{2} r^{5} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+4a^{6} \\\\cos{\\\\theta}^{2} r^{5} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}+4a^{8} \\\\cos{\\\\theta}^{4} r^{3} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+4a^{8} \\\\cos{\\\\theta}^{4} r^{3} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}-4a^{4} \\\\cos{\\\\theta}^{2} r^{4} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-4a^{4} \\\\cos{\\\\theta}^{2} r^{4} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}-4a^{6} \\\\cos{\\\\theta}^{4} r^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-4a^{6} \\\\cos{\\\\theta}^{4} r^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}-4a^{4} \\\\cos{\\\\theta}^{2} r^{6} r_s^{3} \\\\sin{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-4a^{4} \\\\cos{\\\\theta}^{2} r^{6} r_s^{3} \\\\sin{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}+4a^{2} \\\\cos{\\\\theta}^{2} r^{5} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+4a^{2} \\\\cos{\\\\theta}^{2} r^{5} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}%\\n+8a^{4} \\\\cos{\\\\theta}^{2} r^{7} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+8a^{4} \\\\cos{\\\\theta}^{2} r^{7} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}+12a^{6} \\\\cos{\\\\theta}^{4} r^{5} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+12a^{6} \\\\cos{\\\\theta}^{4} r^{5} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}-8a^{2} \\\\cos{\\\\theta}^{2} r^{6} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-8a^{2} \\\\cos{\\\\theta}^{2} r^{6} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}+4a^{8} \\\\cos{\\\\theta}^{6} r^{3} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+4a^{8} \\\\cos{\\\\theta}^{6} r^{3} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}-12a^{4} \\\\cos{\\\\theta}^{4} r^{4} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-12a^{4} \\\\cos{\\\\theta}^{4} r^{4} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}-2a^{10} \\\\cos{\\\\theta}^{8} r^{2} r_s^{3} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-8a^{8} \\\\cos{\\\\theta}^{8} r^{3} r_s^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-8a^{8} \\\\cos{\\\\theta}^{8} r^{3} r_s^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}-2a^{6} \\\\cos{\\\\theta}^{2} r^{7} r_s^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-2a^{8} \\\\cos{\\\\theta}^{4} r^{5} r_s^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+2a^{10} \\\\cos{\\\\theta}^{6} r^{3} r_s^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+8a^{4} \\\\cos{\\\\theta}^{2} r^{8} r_s \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+24a^{6} \\\\cos{\\\\theta}^{4} r^{6} r_s \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+8a^{4} \\\\cos{\\\\theta}^{2} r^{8} r_s \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}+24a^{6} \\\\cos{\\\\theta}^{4} r^{6} r_s \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}%\\n+24a^{8} \\\\cos{\\\\theta}^{6} r^{4} r_s \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+24a^{8} \\\\cos{\\\\theta}^{6} r^{4} r_s \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}+2a^{12} \\\\cos{\\\\theta}^{8} r r_s^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+8a^{10} \\\\cos{\\\\theta}^{8} r^{2} r_s \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+8a^{10} \\\\cos{\\\\theta}^{8} r^{2} r_s \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}-8a^{4} \\\\cos{\\\\theta}^{2} r^{9} r_s^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-18a^{6} \\\\cos{\\\\theta}^{4} r^{7} r_s^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-10a^{8} \\\\cos{\\\\theta}^{6} r^{5} r_s^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+16a^{2} \\\\cos{\\\\theta}^{2} r^{10} r_s \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+56a^{4} \\\\cos{\\\\theta}^{4} r^{8} r_s \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+16a^{2} \\\\cos{\\\\theta}^{2} r^{10} r_s \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}+56a^{4} \\\\cos{\\\\theta}^{4} r^{8} r_s \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}+72a^{6} \\\\cos{\\\\theta}^{6} r^{6} r_s \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+72a^{6} \\\\cos{\\\\theta}^{6} r^{6} r_s \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}+2a^{10} \\\\cos{\\\\theta}^{8} r^{3} r_s^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+40a^{8} \\\\cos{\\\\theta}^{8} r^{4} r_s \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+40a^{8} \\\\cos{\\\\theta}^{8} r^{4} r_s \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}+2a^{10} \\\\cos{\\\\theta}^{6} r^{2} r_s^{3} \\\\sin{\\\\theta}^{4}-4a^{6} \\\\cos{\\\\theta}^{4} r^{3} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-4a^{4} \\\\cos{\\\\theta}^{4} r^{5} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}%\\n+4a^{6} \\\\cos{\\\\theta}^{2} r^{7} r_s^{2}+8a^{8} \\\\cos{\\\\theta}^{4} r^{5} r_s^{2}+4a^{6} \\\\cos{\\\\theta}^{2} r^{4} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-4a^{6} \\\\cos{\\\\theta}^{2} r^{4} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+8a^{4} \\\\cos{\\\\theta}^{2} r^{9} r_s^{2}+16a^{6} \\\\cos{\\\\theta}^{4} r^{7} r_s^{2}-8a^{4} \\\\cos{\\\\theta}^{2} r^{6} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+2a^{12} \\\\cos{\\\\theta}^{6} r r_s^{2} \\\\sin{\\\\theta}^{4}+4a^{10} \\\\cos{\\\\theta}^{6} r^{3} r_s^{2}+4a^{8} \\\\cos{\\\\theta}^{4} r^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-4a^{8} \\\\cos{\\\\theta}^{4} r^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+8a^{8} \\\\cos{\\\\theta}^{6} r^{5} r_s^{2}-8a^{6} \\\\cos{\\\\theta}^{4} r^{4} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-4a^{4} \\\\cos{\\\\theta}^{2} r^{5} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-4a^{2} \\\\cos{\\\\theta}^{2} r^{7} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+8a^{4} \\\\cos{\\\\theta}^{2} r^{6} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+4a^{2} \\\\cos{\\\\theta}^{2} r^{11} r_s^{2}+8a^{4} \\\\cos{\\\\theta}^{4} r^{9} r_s^{2}-4a^{2} \\\\cos{\\\\theta}^{2} r^{8} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+8a^{10} \\\\cos{\\\\theta}^{6} r^{3} r_s^{2} \\\\sin{\\\\theta}^{4}%\\n+12a^{6} \\\\cos{\\\\theta}^{4} r^{4} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+4a^{6} \\\\cos{\\\\theta}^{6} r^{7} r_s^{2}-4a^{4} \\\\cos{\\\\theta}^{4} r^{6} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-2a^{6} \\\\cos{\\\\theta}^{2} r^{7} r_s^{2} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}-2a^{8} \\\\cos{\\\\theta}^{4} r^{5} r_s^{2} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}+2a^{10} \\\\cos{\\\\theta}^{6} r^{3} r_s^{2} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}+4a^{4} \\\\cos{\\\\theta}^{2} r^{6} r_s \\\\sin{2\\\\theta} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}+8a^{6} \\\\cos{\\\\theta}^{4} r^{4} r_s \\\\sin{2\\\\theta} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}-2a^{6} \\\\cos{\\\\theta}^{2} r^{6} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}+2a^{10} \\\\cos{\\\\theta}^{6} r^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}-4a^{4} \\\\cos{\\\\theta}^{2} r^{8} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s \\\\tan{\\\\theta}-8a^{6} \\\\cos{\\\\theta}^{4} r^{6} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s \\\\tan{\\\\theta}-4a^{8} \\\\cos{\\\\theta}^{6} r^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s \\\\tan{\\\\theta}+4a^{4} \\\\cos{\\\\theta}^{2} r^{5} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}+4a^{6} \\\\cos{\\\\theta}^{4} r^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}-2a^{6} \\\\cos{\\\\theta}^{2} r^{6} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}+2a^{10} \\\\cos{\\\\theta}^{6} r^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}-4a^{4} \\\\cos{\\\\theta}^{2} r^{8} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\tan{\\\\theta}-8a^{6} \\\\cos{\\\\theta}^{4} r^{6} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\tan{\\\\theta}-4a^{8} \\\\cos{\\\\theta}^{6} r^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\tan{\\\\theta}%\\n+4a^{4} \\\\cos{\\\\theta}^{2} r^{5} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}+4a^{6} \\\\cos{\\\\theta}^{4} r^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}-2a^{4} \\\\cos{\\\\theta}^{2} r^{8} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}-2a^{6} \\\\cos{\\\\theta}^{4} r^{6} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}+2a^{8} \\\\cos{\\\\theta}^{6} r^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}-4a^{2} \\\\cos{\\\\theta}^{2} r^{10} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s \\\\tan{\\\\theta}-12a^{4} \\\\cos{\\\\theta}^{4} r^{8} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s \\\\tan{\\\\theta}-12a^{6} \\\\cos{\\\\theta}^{6} r^{6} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s \\\\tan{\\\\theta}+4a^{2} \\\\cos{\\\\theta}^{2} r^{7} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}+8a^{4} \\\\cos{\\\\theta}^{4} r^{5} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}-2a^{4} \\\\cos{\\\\theta}^{2} r^{8} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}-2a^{6} \\\\cos{\\\\theta}^{4} r^{6} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}+2a^{8} \\\\cos{\\\\theta}^{6} r^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}-4a^{2} \\\\cos{\\\\theta}^{2} r^{10} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\tan{\\\\theta}-12a^{4} \\\\cos{\\\\theta}^{4} r^{8} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\tan{\\\\theta}-12a^{6} \\\\cos{\\\\theta}^{6} r^{6} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\tan{\\\\theta}+4a^{2} \\\\cos{\\\\theta}^{2} r^{7} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}+8a^{4} \\\\cos{\\\\theta}^{4} r^{5} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}-4a^{6} \\\\cos{\\\\theta}^{2} r^{6} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-4a^{6} \\\\cos{\\\\theta}^{2} r^{6} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}%\\n-8a^{8} \\\\cos{\\\\theta}^{4} r^{4} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-8a^{8} \\\\cos{\\\\theta}^{4} r^{4} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}+4a^{4} \\\\cos{\\\\theta}^{2} r^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+4a^{4} \\\\cos{\\\\theta}^{2} r^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}-4a^{10} \\\\cos{\\\\theta}^{6} r^{2} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-4a^{10} \\\\cos{\\\\theta}^{6} r^{2} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}+8a^{6} \\\\cos{\\\\theta}^{4} r^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+8a^{6} \\\\cos{\\\\theta}^{4} r^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}-4a^{4} \\\\cos{\\\\theta}^{2} r^{8} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-4a^{4} \\\\cos{\\\\theta}^{2} r^{8} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}-8a^{6} \\\\cos{\\\\theta}^{4} r^{6} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-8a^{6} \\\\cos{\\\\theta}^{4} r^{6} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}+4a^{2} \\\\cos{\\\\theta}^{2} r^{7} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+4a^{2} \\\\cos{\\\\theta}^{2} r^{7} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}-4a^{8} \\\\cos{\\\\theta}^{6} r^{4} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-4a^{8} \\\\cos{\\\\theta}^{6} r^{4} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}+8a^{4} \\\\cos{\\\\theta}^{4} r^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+8a^{4} \\\\cos{\\\\theta}^{4} r^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}+2a^{6} \\\\cos{\\\\theta}^{2} r^{8} r_s \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+4a^{8} \\\\cos{\\\\theta}^{4} r^{6} r_s \\\\sin{2\\\\theta} \\\\tan{\\\\theta}%\\n+2a^{10} \\\\cos{\\\\theta}^{6} r^{4} r_s \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-8a^{4} \\\\cos{\\\\theta}^{2} r^{9} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-32a^{6} \\\\cos{\\\\theta}^{4} r^{7} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-8a^{4} \\\\cos{\\\\theta}^{2} r^{9} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}-32a^{6} \\\\cos{\\\\theta}^{4} r^{7} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}-48a^{8} \\\\cos{\\\\theta}^{6} r^{5} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-48a^{8} \\\\cos{\\\\theta}^{6} r^{5} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}-32a^{10} \\\\cos{\\\\theta}^{8} r^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-32a^{10} \\\\cos{\\\\theta}^{8} r^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}+2a^{4} \\\\cos{\\\\theta}^{2} r^{10} r_s \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+4a^{6} \\\\cos{\\\\theta}^{4} r^{8} r_s \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-8a^{2} \\\\cos{\\\\theta}^{2} r^{11} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-32a^{4} \\\\cos{\\\\theta}^{4} r^{9} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-8a^{2} \\\\cos{\\\\theta}^{2} r^{11} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}-32a^{4} \\\\cos{\\\\theta}^{4} r^{9} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}-48a^{6} \\\\cos{\\\\theta}^{6} r^{7} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-48a^{6} \\\\cos{\\\\theta}^{6} r^{7} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}-4a^{10} \\\\cos{\\\\theta}^{8} r^{4} r_s \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-32a^{8} \\\\cos{\\\\theta}^{8} r^{5} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-32a^{8} \\\\cos{\\\\theta}^{8} r^{5} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}%\\n+6a^{8} \\\\cos{\\\\theta}^{2} r^{6} r_s \\\\sin{\\\\theta}^{4}+10a^{10} \\\\cos{\\\\theta}^{4} r^{4} r_s \\\\sin{\\\\theta}^{4}+12a^{6} \\\\cos{\\\\theta}^{2} r^{8} r_s \\\\sin{\\\\theta}^{2}+36a^{8} \\\\cos{\\\\theta}^{4} r^{6} r_s \\\\sin{\\\\theta}^{2}-4a^{6} \\\\cos{\\\\theta}^{2} r^{8} r_s-12a^{8} \\\\cos{\\\\theta}^{4} r^{6} r_s-4a^{6} \\\\cos{\\\\theta}^{2} r^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+4a^{6} \\\\cos{\\\\theta}^{2} r^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-8a^{4} \\\\cos{\\\\theta}^{2} r^{10} r_s-24a^{6} \\\\cos{\\\\theta}^{4} r^{8} r_s+8a^{4} \\\\cos{\\\\theta}^{2} r^{7} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+4a^{12} \\\\cos{\\\\theta}^{6} r^{2} r_s \\\\sin{\\\\theta}^{4}+36a^{10} \\\\cos{\\\\theta}^{6} r^{4} r_s \\\\sin{\\\\theta}^{2}-12a^{10} \\\\cos{\\\\theta}^{6} r^{4} r_s-8a^{8} \\\\cos{\\\\theta}^{4} r^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+8a^{8} \\\\cos{\\\\theta}^{4} r^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-24a^{8} \\\\cos{\\\\theta}^{6} r^{6} r_s+16a^{6} \\\\cos{\\\\theta}^{4} r^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+6a^{6} \\\\cos{\\\\theta}^{2} r^{8} r_s \\\\sin{\\\\theta}^{4}+10a^{8} \\\\cos{\\\\theta}^{4} r^{6} r_s \\\\sin{\\\\theta}^{4}%\\n+12a^{4} \\\\cos{\\\\theta}^{2} r^{10} r_s \\\\sin{\\\\theta}^{2}+36a^{6} \\\\cos{\\\\theta}^{4} r^{8} r_s \\\\sin{\\\\theta}^{2}-4a^{4} \\\\cos{\\\\theta}^{2} r^{7} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-4a^{2} \\\\cos{\\\\theta}^{2} r^{12} r_s-12a^{4} \\\\cos{\\\\theta}^{4} r^{10} r_s+4a^{2} \\\\cos{\\\\theta}^{2} r^{9} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+2a^{10} \\\\cos{\\\\theta}^{6} r^{4} r_s \\\\sin{\\\\theta}^{4}+36a^{8} \\\\cos{\\\\theta}^{6} r^{6} r_s \\\\sin{\\\\theta}^{2}-8a^{6} \\\\cos{\\\\theta}^{4} r^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-12a^{6} \\\\cos{\\\\theta}^{6} r^{8} r_s+8a^{4} \\\\cos{\\\\theta}^{4} r^{7} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+2a^{12} \\\\cos{\\\\theta}^{8} r r_s^{2} \\\\sin{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}+4a^{8} \\\\cos{\\\\theta}^{6} r^{2} r_s \\\\sin{2\\\\theta} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}-4a^{8} \\\\cos{\\\\theta}^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r^{4} r_s \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}-4a^{10} \\\\cos{\\\\theta}^{6} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r^{2} r_s \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}+2a^{8} \\\\cos{\\\\theta}^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s r^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}+2a^{10} \\\\cos{\\\\theta}^{6} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s r^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}+2a^{10} \\\\cos{\\\\theta}^{6} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s \\\\sin{\\\\theta}^{2} r^{2} \\\\tan{\\\\theta}+2a^{12} \\\\cos{\\\\theta}^{8} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}-4a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r^{6} r_s \\\\tan{\\\\theta}%\\n-8a^{8} \\\\cos{\\\\theta}^{6} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r^{4} r_s \\\\tan{\\\\theta}-4a^{10} \\\\cos{\\\\theta}^{8} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r^{2} r_s \\\\tan{\\\\theta}+4a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}+4a^{8} \\\\cos{\\\\theta}^{6} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}-4a^{8} \\\\cos{\\\\theta}^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r^{4} r_s \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}-4a^{10} \\\\cos{\\\\theta}^{6} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r^{2} r_s \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}+2a^{8} \\\\cos{\\\\theta}^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s r^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}+2a^{10} \\\\cos{\\\\theta}^{6} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s r^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}+2a^{10} \\\\cos{\\\\theta}^{6} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\sin{\\\\theta}^{2} r^{2} \\\\tan{\\\\theta}+2a^{12} \\\\cos{\\\\theta}^{8} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}-4a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r^{6} r_s \\\\tan{\\\\theta}-8a^{8} \\\\cos{\\\\theta}^{6} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r^{4} r_s \\\\tan{\\\\theta}-4a^{10} \\\\cos{\\\\theta}^{8} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r^{2} r_s \\\\tan{\\\\theta}+4a^{6} \\\\cos{\\\\theta}^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}+4a^{8} \\\\cos{\\\\theta}^{6} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}+2a^{10} \\\\cos{\\\\theta}^{8} r^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}-4a^{8} \\\\cos{\\\\theta}^{8} r^{4} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r_s \\\\tan{\\\\theta}+4a^{6} \\\\cos{\\\\theta}^{6} r^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}+2a^{10} \\\\cos{\\\\theta}^{8} r^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}-4a^{8} \\\\cos{\\\\theta}^{8} r^{4} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r_s \\\\tan{\\\\theta}%\\n+4a^{6} \\\\cos{\\\\theta}^{6} r^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}-4a^{6} \\\\cos{\\\\theta}^{6} r^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-4a^{6} \\\\cos{\\\\theta}^{6} r^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}+2a^{10} \\\\cos{\\\\theta}^{6} r_s r^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+2a^{10} \\\\cos{\\\\theta}^{6} r_s r^{2} \\\\sin{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}+4a^{8} \\\\cos{\\\\theta}^{6} r \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+4a^{8} \\\\cos{\\\\theta}^{6} r \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}+4a^{6} \\\\cos{\\\\theta}^{6} r^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+4a^{6} \\\\cos{\\\\theta}^{6} r^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}+2a^{12} \\\\cos{\\\\theta}^{10} r r_s^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+8a^{10} \\\\cos{\\\\theta}^{10} r^{2} r_s \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}+8a^{10} \\\\cos{\\\\theta}^{10} r^{2} r_s \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}-2a^{10} \\\\cos{\\\\theta}^{6} r_s r^{4} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-2a^{12} \\\\cos{\\\\theta}^{8} r_s r^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-2a^{12} \\\\cos{\\\\theta}^{8} r_s \\\\sin{2\\\\theta} r^{2} \\\\tan{\\\\theta}-2a^{14} \\\\cos{\\\\theta}^{10} r_s \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-2a^{10} \\\\cos{\\\\theta}^{6} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r^{2} \\\\tan{\\\\theta}-2a^{10} \\\\cos{\\\\theta}^{6} r_s \\\\sin{\\\\theta}^{2} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) r^{2} \\\\tan{\\\\theta}-8a^{12} \\\\cos{\\\\theta}^{10} r \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-8a^{12} \\\\cos{\\\\theta}^{10} r \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}%\\n-2a^{12} \\\\cos{\\\\theta}^{10} r^{2} r_s \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-8a^{10} \\\\cos{\\\\theta}^{10} r^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}-8a^{10} \\\\cos{\\\\theta}^{10} r^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\tan{\\\\theta}+2a^{12} \\\\cos{\\\\theta}^{8} r r_s^{2} \\\\sin{\\\\theta}^{4}-4a^{10} \\\\cos{\\\\theta}^{8} r^{3} r_s^{2} \\\\sin{\\\\theta}^{2}+4a^{8} \\\\cos{\\\\theta}^{6} r^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-2a^{12} \\\\cos{\\\\theta}^{6} r_s r^{2} \\\\sin{\\\\theta}^{4}-2a^{14} \\\\cos{\\\\theta}^{8} r_s \\\\sin{\\\\theta}^{4}+12a^{12} \\\\cos{\\\\theta}^{8} r^{2} r_s \\\\sin{\\\\theta}^{2}-4a^{12} \\\\cos{\\\\theta}^{8} r^{2} r_s-4a^{10} \\\\cos{\\\\theta}^{6} r \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+4a^{10} \\\\cos{\\\\theta}^{6} r \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-8a^{10} \\\\cos{\\\\theta}^{8} r^{4} r_s+8a^{8} \\\\cos{\\\\theta}^{6} r^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-2a^{12} \\\\cos{\\\\theta}^{8} r^{2} r_s \\\\sin{\\\\theta}^{4}+12a^{10} \\\\cos{\\\\theta}^{8} r^{4} r_s \\\\sin{\\\\theta}^{2}-4a^{8} \\\\cos{\\\\theta}^{6} r^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-4a^{8} \\\\cos{\\\\theta}^{8} r^{6} r_s+4a^{6} \\\\cos{\\\\theta}^{6} r^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-2a^{8} \\\\cos{\\\\theta}^{2} r^{4} r_s^{3} \\\\sin{\\\\theta}^{6}%\\n+2a^{6} \\\\cos{\\\\theta}^{2} r^{5} r_s^{4} \\\\sin{\\\\theta}^{4}-2a^{6} \\\\cos{\\\\theta}^{2} r^{3} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-2a^{4} \\\\cos{\\\\theta}^{2} r^{5} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+2a^{10} \\\\cos{\\\\theta}^{4} r^{2} r_s^{3} \\\\sin{\\\\theta}^{6}-2a^{8} \\\\cos{\\\\theta}^{4} r^{3} r_s^{4} \\\\sin{\\\\theta}^{4}+2a^{8} \\\\cos{\\\\theta}^{4} r r_s^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+2a^{6} \\\\cos{\\\\theta}^{4} r^{3} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+4a^{6} \\\\cos{\\\\theta}^{2} r^{3} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4}+4a^{4} \\\\cos{\\\\theta}^{2} r^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4}+4a^{2} \\\\cos{\\\\theta}^{2} r^{4} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4}+2a^{8} \\\\cos{\\\\theta}^{2} r^{5} r_s^{2} \\\\sin{\\\\theta}^{6}+2a^{6} \\\\cos{\\\\theta}^{2} r^{4} r_s \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+2a^{4} \\\\cos{\\\\theta}^{2} r^{6} r_s \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+2a^{10} \\\\cos{\\\\theta}^{4} r^{3} r_s^{2} \\\\sin{\\\\theta}^{6}+2a^{8} \\\\cos{\\\\theta}^{4} r^{2} r_s \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+2a^{6} \\\\cos{\\\\theta}^{4} r^{4} r_s \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-4a^{6} \\\\cos{\\\\theta}^{2} r^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s \\\\sin{\\\\theta}^{4}+4a^{4} \\\\cos{\\\\theta}^{2} r^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s^{2} \\\\sin{\\\\theta}^{2}-8a^{4} \\\\cos{\\\\theta}^{2} r^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s \\\\sin{\\\\theta}^{2}-16a^{6} \\\\cos{\\\\theta}^{4} r^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s \\\\sin{\\\\theta}^{2}%\\n+4a^{4} \\\\cos{\\\\theta}^{2} r^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s+8a^{6} \\\\cos{\\\\theta}^{4} r^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s-4a^{4} \\\\cos{\\\\theta}^{2} r^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4}+4a^{2} \\\\cos{\\\\theta}^{2} r^{8} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s+8a^{4} \\\\cos{\\\\theta}^{4} r^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s-4a^{2} \\\\cos{\\\\theta}^{2} r^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4}-2a^{10} \\\\cos{\\\\theta}^{4} r_s^{2} r^{3} \\\\sin{\\\\theta}^{6}+2a^{8} \\\\cos{\\\\theta}^{4} r_s^{3} r^{4} \\\\sin{\\\\theta}^{4}-4a^{8} \\\\cos{\\\\theta}^{4} r_s^{2} r^{5} \\\\sin{\\\\theta}^{4}-4a^{10} \\\\cos{\\\\theta}^{6} r_s^{2} r^{3} \\\\sin{\\\\theta}^{4}+2a^{8} \\\\cos{\\\\theta}^{4} r_s^{2} r^{5} \\\\sin{\\\\theta}^{2}+2a^{10} \\\\cos{\\\\theta}^{6} r_s^{2} r^{3} \\\\sin{\\\\theta}^{2}-2a^{8} \\\\cos{\\\\theta}^{4} r_s r^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+2a^{6} \\\\cos{\\\\theta}^{4} r_s^{2} r^{7} \\\\sin{\\\\theta}^{2}+2a^{8} \\\\cos{\\\\theta}^{6} r_s^{2} r^{5} \\\\sin{\\\\theta}^{2}-2a^{6} \\\\cos{\\\\theta}^{4} r_s r^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-2a^{12} \\\\cos{\\\\theta}^{6} r_s^{2} \\\\sin{\\\\theta}^{6} r+2a^{10} \\\\cos{\\\\theta}^{6} r_s^{3} \\\\sin{\\\\theta}^{4} r^{2}-4a^{10} \\\\cos{\\\\theta}^{6} r_s^{2} \\\\sin{\\\\theta}^{4} r^{3}-4a^{12} \\\\cos{\\\\theta}^{8} r_s^{2} \\\\sin{\\\\theta}^{4} r%\\n+2a^{10} \\\\cos{\\\\theta}^{6} r_s^{2} \\\\sin{\\\\theta}^{2} r^{3}+2a^{12} \\\\cos{\\\\theta}^{8} r_s^{2} \\\\sin{\\\\theta}^{2} r-2a^{10} \\\\cos{\\\\theta}^{6} r_s \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+2a^{8} \\\\cos{\\\\theta}^{6} r_s^{2} \\\\sin{\\\\theta}^{2} r^{5}+2a^{10} \\\\cos{\\\\theta}^{8} r_s^{2} \\\\sin{\\\\theta}^{2} r^{3}-2a^{8} \\\\cos{\\\\theta}^{6} r_s \\\\sin{\\\\theta}^{2} r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-4a^{8} \\\\cos{\\\\theta}^{4} r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s \\\\sin{\\\\theta}^{4}+4a^{6} \\\\cos{\\\\theta}^{4} r^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s^{2} \\\\sin{\\\\theta}^{2}-8a^{8} \\\\cos{\\\\theta}^{6} r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s \\\\sin{\\\\theta}^{2}+4a^{8} \\\\cos{\\\\theta}^{6} r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s-4a^{6} \\\\cos{\\\\theta}^{4} r \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4}+4a^{6} \\\\cos{\\\\theta}^{6} r^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s-4a^{4} \\\\cos{\\\\theta}^{4} r^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4}}{4\\\\left(r r_s-r^{2}-a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} r^{2}-a^{4} \\\\cos{\\\\theta}^{2}+r^{3} r_s-r^{4}-r^{2} a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{r}= & \\\\frac{-a^{6} r^{4} r_s^{3} \\\\sin{\\\\theta}^{4}+a^{6} r^{5} r_s^{2} \\\\sin{\\\\theta}^{4}-2a^{4} r^{6} r_s^{3} \\\\sin{\\\\theta}^{4}+a^{4} r^{5} r_s^{4} \\\\sin{\\\\theta}^{4}+a^{4} r^{7} r_s^{2} \\\\sin{\\\\theta}^{4}+a^{6} r^{4} r_s^{3} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4}+a^{8} r^{2} r_s^{3} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4}-a^{10} r r_s^{2} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4}-a^{6} r^{3} r_s^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4}-a^{8} r^{3} r_s^{2} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4}+a^{8} r^{2} r_s^{3} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4}+4a^{6} r_s^{3} r^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+6a^{6} r_s^{3} r^{3} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+6a^{6} r_s^{3} r^{3} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4a^{6} r_s^{2} r^{5} \\\\sin{\\\\theta}^{2}-4a^{8} r_s^{2} r^{3} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}-2a^{8} r_s^{3} r^{2} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2}-4a^{6} r_s^{2} r^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4a^{6} r_s^{2} r^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}%\\n-4a^{8} r_s^{2} r^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4a^{8} r_s^{2} r^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+3a^{6} r_s^{2} r \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+6a^{4} r_s^{3} r^{6} \\\\sin{\\\\theta}^{2}+8a^{4} r_s^{3} r^{5} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+8a^{4} r_s^{3} r^{5} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+6a^{4} r_s^{3} r^{5} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+6a^{4} r_s^{3} r^{5} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-14a^{4} r_s^{2} r^{7} \\\\sin{\\\\theta}^{2}-12a^{6} r_s^{2} r^{5} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}-2a^{4} r_s^{4} r^{4} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}-2a^{4} r_s^{4} r^{4} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-6a^{6} r_s^{3} r^{4} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2}-14a^{4} r_s^{2} r^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}-14a^{4} r_s^{2} r^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-14a^{6} r_s^{2} r^{4} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}-14a^{6} r_s^{2} r^{4} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+2a^{6} r_s^{4} r^{3} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2}+9a^{4} r_s^{2} r^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-3a^{4} r_s^{3} r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}%\\n+6a^{2} r_s^{3} r^{8} \\\\sin{\\\\theta}^{2}-2a^{2} r_s^{4} r^{7} \\\\sin{\\\\theta}^{2}+8a^{2} r_s^{3} r^{7} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+8a^{2} r_s^{3} r^{7} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-8a^{2} r_s^{2} r^{9} \\\\sin{\\\\theta}^{2}-4a^{4} r_s^{2} r^{7} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}-2a^{2} r_s^{4} r^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}-2a^{2} r_s^{4} r^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-10a^{2} r_s^{2} r^{8} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}-10a^{2} r_s^{2} r^{8} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-10a^{4} r_s^{2} r^{6} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}-10a^{4} r_s^{2} r^{6} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+4a^{2} r_s^{2} r^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-a^{2} r_s^{3} r^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+4a^{6} r_s r^{6} \\\\sin{\\\\theta}^{2}+4a^{8} r_s r^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+2a^{8} r_s^{2} r^{3} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2}+4a^{6} r_s r^{5} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+4a^{6} r_s r^{5} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+4a^{8} r_s r^{3} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}%\\n+4a^{8} r_s r^{3} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-3a^{6} r_s r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+8a^{4} r_s r^{8} \\\\sin{\\\\theta}^{2}+8a^{6} r_s r^{6} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+4a^{6} r_s^{2} r^{5} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2}+8a^{4} r_s r^{7} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+8a^{4} r_s r^{7} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+8a^{6} r_s r^{5} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+8a^{6} r_s r^{5} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-6a^{4} r_s r^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+4a^{2} r_s r^{10} \\\\sin{\\\\theta}^{2}+4a^{4} r_s r^{8} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+4a^{2} r_s r^{9} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+4a^{2} r_s r^{9} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+4a^{4} r_s r^{7} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+4a^{4} r_s r^{7} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-3a^{2} r_s r^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-4a^{8} r_s^{2} \\\\cos{\\\\theta}^{4} r^{3} \\\\sin{\\\\theta}^{2}-6a^{8} r_s^{2} \\\\cos{\\\\theta}^{4} r^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}-6a^{8} r_s^{2} \\\\cos{\\\\theta}^{4} r^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}%\\n+4a^{8} r_s \\\\cos{\\\\theta}^{2} r^{4} \\\\sin{\\\\theta}^{2}+4a^{10} r_s \\\\cos{\\\\theta}^{4} r^{2} \\\\sin{\\\\theta}^{2}+2a^{10} r_s^{2} \\\\cos{\\\\theta}^{6} r \\\\sin{\\\\theta}^{2}+4a^{8} r_s \\\\cos{\\\\theta}^{2} r^{3} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+4a^{8} r_s \\\\cos{\\\\theta}^{2} r^{3} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+4a^{10} r_s \\\\cos{\\\\theta}^{4} r \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+4a^{10} r_s \\\\cos{\\\\theta}^{4} r \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-3a^{8} r_s \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-6a^{6} r_s^{2} \\\\cos{\\\\theta}^{2} r^{5} \\\\sin{\\\\theta}^{2}-6a^{6} r_s^{2} \\\\cos{\\\\theta}^{4} r^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}-6a^{6} r_s^{2} \\\\cos{\\\\theta}^{4} r^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-6a^{6} r_s^{2} \\\\cos{\\\\theta}^{2} r^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}-6a^{6} r_s^{2} \\\\cos{\\\\theta}^{2} r^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+8a^{6} r_s \\\\cos{\\\\theta}^{2} r^{6} \\\\sin{\\\\theta}^{2}+8a^{8} r_s \\\\cos{\\\\theta}^{4} r^{4} \\\\sin{\\\\theta}^{2}+2a^{6} r_s^{3} \\\\cos{\\\\theta}^{4} r^{3} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+2a^{6} r_s^{3} \\\\cos{\\\\theta}^{4} r^{3} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+4a^{8} r_s^{2} \\\\cos{\\\\theta}^{6} r^{3} \\\\sin{\\\\theta}^{2}+8a^{6} r_s \\\\cos{\\\\theta}^{2} r^{5} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+8a^{6} r_s \\\\cos{\\\\theta}^{2} r^{5} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}%\\n+8a^{8} r_s \\\\cos{\\\\theta}^{4} r^{3} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+8a^{8} r_s \\\\cos{\\\\theta}^{4} r^{3} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-2a^{8} r_s^{3} \\\\cos{\\\\theta}^{6} r^{2} \\\\sin{\\\\theta}^{2}-6a^{6} r_s \\\\cos{\\\\theta}^{2} r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+3a^{6} r_s^{2} \\\\cos{\\\\theta}^{2} r \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-4a^{4} r_s^{2} \\\\cos{\\\\theta}^{2} r^{7} \\\\sin{\\\\theta}^{2}+2a^{4} r_s^{3} \\\\cos{\\\\theta}^{2} r^{6} \\\\sin{\\\\theta}^{2}-6a^{4} r_s^{2} \\\\cos{\\\\theta}^{2} r^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}-6a^{4} r_s^{2} \\\\cos{\\\\theta}^{2} r^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+4a^{4} r_s \\\\cos{\\\\theta}^{2} r^{8} \\\\sin{\\\\theta}^{2}+4a^{6} r_s \\\\cos{\\\\theta}^{4} r^{6} \\\\sin{\\\\theta}^{2}+2a^{4} r_s^{3} \\\\cos{\\\\theta}^{2} r^{5} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+2a^{4} r_s^{3} \\\\cos{\\\\theta}^{2} r^{5} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+4a^{4} r_s \\\\cos{\\\\theta}^{2} r^{7} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+4a^{4} r_s \\\\cos{\\\\theta}^{2} r^{7} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+4a^{6} r_s \\\\cos{\\\\theta}^{4} r^{5} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+4a^{6} r_s \\\\cos{\\\\theta}^{4} r^{5} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-3a^{4} r_s \\\\cos{\\\\theta}^{2} r^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+a^{4} r_s^{2} \\\\cos{\\\\theta}^{2} r^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-r r_s a^{2} \\\\sin{2\\\\theta} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} r^{2}-a^{4} \\\\cos{\\\\theta}^{2}+r^{3} r_s-r^{4}-r^{2} a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}%\\n-r r_s a^{2} \\\\sin{2\\\\theta} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} r^{2}-a^{4} \\\\cos{\\\\theta}^{2}+r^{3} r_s-r^{4}-r^{2} a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}-2r^{2} r_s \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} r^{2}-a^{4} \\\\cos{\\\\theta}^{2}+r^{3} r_s-r^{4}-r^{2} a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}-2r^{2} r_s \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} r^{2}-a^{4} \\\\cos{\\\\theta}^{2}+r^{3} r_s-r^{4}-r^{2} a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}+r^{2} a^{2} \\\\sin{2\\\\theta} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} r^{2}-a^{4} \\\\cos{\\\\theta}^{2}+r^{3} r_s-r^{4}-r^{2} a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}+r^{2} a^{2} \\\\sin{2\\\\theta} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} r^{2}-a^{4} \\\\cos{\\\\theta}^{2}+r^{3} r_s-r^{4}-r^{2} a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}+2r^{3} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} r^{2}-a^{4} \\\\cos{\\\\theta}^{2}+r^{3} r_s-r^{4}-r^{2} a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}+2r^{3} \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} r^{2}-a^{4} \\\\cos{\\\\theta}^{2}+r^{3} r_s-r^{4}-r^{2} a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}+a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} r^{2}-a^{4} \\\\cos{\\\\theta}^{2}+r^{3} r_s-r^{4}-r^{2} a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}+a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{2\\\\theta} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} r^{2}-a^{4} \\\\cos{\\\\theta}^{2}+r^{3} r_s-r^{4}-r^{2} a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}+2a^{2} \\\\cos{\\\\theta}^{2} r \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} r^{2}-a^{4} \\\\cos{\\\\theta}^{2}+r^{3} r_s-r^{4}-r^{2} a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}+2a^{2} \\\\cos{\\\\theta}^{2} r \\\\partial_{\\\\theta}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} r^{2}-a^{4} \\\\cos{\\\\theta}^{2}+r^{3} r_s-r^{4}-r^{2} a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}+2r^{3} r_s^{3} a^{6} \\\\sin{\\\\theta}^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right)+2r^{3} r_s^{3} a^{6} \\\\sin{\\\\theta}^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-2r^{3} r_s^{3} a^{6} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)-2r^{3} r_s^{3} a^{6} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+4r^{4} r_s^{2} a^{6} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)+4r^{4} r_s^{2} a^{6} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+4r^{2} r_s^{2} a^{8} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)+4r^{2} r_s^{2} a^{8} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-2r r_s^{2} a^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4}%\\n-2r^{5} r_s^{3} a^{4} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)-2r^{5} r_s^{3} a^{4} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-2r^{4} r_s^{4} a^{4} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)-2r^{4} r_s^{4} a^{4} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+2r^{4} r_s^{4} a^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+2r^{4} r_s^{4} a^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-3r^{6} r_s^{3} a^{4} \\\\sin{\\\\theta}^{4}-6r^{4} r_s^{3} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4}+4r^{6} r_s^{2} a^{4} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)+4r^{6} r_s^{2} a^{4} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+4r^{4} r_s^{2} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)+4r^{4} r_s^{2} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+r^{5} r_s^{4} a^{4} \\\\sin{\\\\theta}^{4}+3r^{3} r_s^{4} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4}-2r^{5} r_s^{4} a^{4} \\\\sin{\\\\theta}^{2}-2r^{3} r_s^{4} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}-4r^{5} r_s^{3} a^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4r^{5} r_s^{3} a^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4r^{3} r_s^{3} a^{6} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4r^{3} r_s^{3} a^{6} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}%\\n+2r^{3} r_s^{2} a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4}+4r^{2} r_s^{3} a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+2r^{2} r_s^{2} a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+2r^{2} r_s^{2} a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-2r r_s^{2} a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2}+2r^{6} r_s^{4} a^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+2r^{6} r_s^{4} a^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+2r^{7} r_s^{4} a^{2} \\\\sin{\\\\theta}^{2}+2r^{5} r_s^{4} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}-4r^{7} r_s^{3} a^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4r^{7} r_s^{3} a^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4r^{5} r_s^{3} a^{4} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4r^{5} r_s^{3} a^{4} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-4r^{4} r_s^{3} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+2r^{4} r_s^{2} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+2r^{4} r_s^{2} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+2r^{3} r_s^{2} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2}-r^{2} r_s^{3} a^{8} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4}-3r^{6} r_s^{3} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}-r^{4} r_s^{3} a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2}%\\n+2r^{3} r_s^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+3r^{5} r_s^{2} a^{6} \\\\sin{\\\\theta}^{4}+2r^{3} r_s^{2} a^{8} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4}-3r^{6} r_s^{3} a^{4} \\\\sin{\\\\theta}^{2}+6r^{7} r_s^{2} a^{4} \\\\sin{\\\\theta}^{2}+12r^{5} r_s^{2} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}-2r^{7} r_s^{2} a^{4}-4r^{5} r_s^{2} a^{6} \\\\cos{\\\\theta}^{2}-2r^{4} r_s a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+2r^{4} r_s a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-4r^{9} r_s^{2} a^{2}-6r^{7} r_s^{2} a^{4} \\\\cos{\\\\theta}^{2}+4r^{6} r_s a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-r r_s^{2} a^{10} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4}-r^{4} r_s^{3} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+6r^{3} r_s^{2} a^{8} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2}-2r^{3} r_s^{2} a^{8} \\\\cos{\\\\theta}^{4}-2r^{2} r_s a^{6} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+2r^{2} r_s a^{6} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-2r^{5} r_s^{2} a^{6} \\\\cos{\\\\theta}^{4}%\\n+2r^{4} r_s a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-5r^{8} r_s^{3} a^{2} \\\\sin{\\\\theta}^{2}+2r^{5} r_s^{2} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+2r^{7} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+4r^{7} r_s^{2} a^{4} \\\\sin{\\\\theta}^{4}-r^{5} r_s^{2} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4}+8r^{9} r_s^{2} a^{2} \\\\sin{\\\\theta}^{2}+10r^{7} r_s^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}-4r^{6} r_s a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-2r^{11} r_s^{2}-2r^{9} r_s^{2} a^{2} \\\\cos{\\\\theta}^{2}+2r^{8} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-r^{3} r_s^{2} a^{8} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4}+2r^{5} r_s^{2} a^{6} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2}-2r^{4} r_s a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-2r^{4} a^{6} r_s^{2} \\\\sin{\\\\theta}^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right)-2r^{4} a^{6} r_s^{2} \\\\sin{\\\\theta}^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+2r^{4} a^{6} r_s^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)+2r^{4} a^{6} r_s^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-4r^{5} a^{6} r_s \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)%\\n-4r^{5} a^{6} r_s \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-4r^{3} a^{8} r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)-4r^{3} a^{8} r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+2r^{2} a^{6} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4}+2r^{6} a^{4} r_s^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)+2r^{6} a^{4} r_s^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+2r^{5} a^{4} r_s^{3} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)+2r^{5} a^{4} r_s^{3} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-2r^{5} a^{4} r_s^{3} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}-2r^{5} a^{4} r_s^{3} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+2r^{7} a^{4} r_s^{2} \\\\sin{\\\\theta}^{4}+9r^{5} a^{6} r_s^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4}-4r^{7} a^{4} r_s \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)-4r^{7} a^{4} r_s \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-4r^{5} a^{6} r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)-4r^{5} a^{6} r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-r^{6} a^{4} r_s^{3} \\\\sin{\\\\theta}^{4}-3r^{4} a^{6} r_s^{3} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4}+2r^{6} a^{4} r_s^{3} \\\\sin{\\\\theta}^{2}+2r^{4} a^{6} r_s^{3} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}%\\n+4r^{6} a^{4} r_s^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+4r^{6} a^{4} r_s^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+4r^{4} a^{6} r_s^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+4r^{4} a^{6} r_s^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-2r^{4} a^{4} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4}-4r^{3} a^{4} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-2r^{3} a^{4} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}-2r^{3} a^{4} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+2r^{2} a^{4} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2}-2r^{7} a^{2} r_s^{3} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}-2r^{7} a^{2} r_s^{3} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-2r^{8} a^{2} r_s^{3} \\\\sin{\\\\theta}^{2}-4r^{6} a^{4} r_s^{3} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+4r^{8} a^{2} r_s^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+4r^{8} a^{2} r_s^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+4r^{6} a^{4} r_s^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+4r^{6} a^{4} r_s^{2} \\\\cos{\\\\theta}^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+4r^{5} a^{2} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-2r^{5} a^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}-2r^{5} a^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}%\\n-2r^{4} a^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2}+r^{3} a^{8} r_s^{2} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4}+5r^{7} a^{4} r_s^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+5r^{5} a^{6} r_s^{2} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2}-2r^{7} a^{4} r_s^{2} \\\\cos{\\\\theta}^{2}-2r^{5} a^{6} r_s^{2} \\\\cos{\\\\theta}^{4}-2r^{4} a^{4} r_s \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+2r^{4} a^{4} r_s \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-2r^{9} a^{2} r_s^{2} \\\\cos{\\\\theta}^{2}-2r^{7} a^{4} r_s^{2} \\\\cos{\\\\theta}^{4}+2r^{6} a^{2} r_s \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-3r^{6} a^{6} r_s \\\\sin{\\\\theta}^{4}+r^{4} a^{8} r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4}+3r^{7} a^{4} r_s^{2} \\\\sin{\\\\theta}^{2}-6r^{8} a^{4} r_s \\\\sin{\\\\theta}^{2}-6r^{6} a^{6} r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+2r^{8} a^{4} r_s+2r^{6} a^{6} r_s \\\\cos{\\\\theta}^{2}+2r^{5} a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-2r^{5} a^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}%\\n+4r^{10} a^{2} r_s+4r^{8} a^{4} r_s \\\\cos{\\\\theta}^{2}-4r^{7} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-3r^{4} a^{8} \\\\cos{\\\\theta}^{2} r_s \\\\sin{\\\\theta}^{4}+r^{2} a^{10} \\\\cos{\\\\theta}^{4} r_s \\\\sin{\\\\theta}^{4}+2r^{5} a^{6} \\\\cos{\\\\theta}^{2} r_s^{2} \\\\sin{\\\\theta}^{2}-6r^{6} a^{6} \\\\cos{\\\\theta}^{2} r_s \\\\sin{\\\\theta}^{2}-6r^{4} a^{8} \\\\cos{\\\\theta}^{4} r_s \\\\sin{\\\\theta}^{2}+2r^{6} a^{6} \\\\cos{\\\\theta}^{2} r_s+2r^{4} a^{8} \\\\cos{\\\\theta}^{4} r_s+2r^{3} a^{6} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-2r^{3} a^{6} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+4r^{8} a^{4} \\\\cos{\\\\theta}^{2} r_s+4r^{6} a^{6} \\\\cos{\\\\theta}^{4} r_s-4r^{5} a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-3r^{8} a^{4} r_s \\\\sin{\\\\theta}^{4}+r^{6} a^{6} r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4}+3r^{9} a^{2} r_s^{2} \\\\sin{\\\\theta}^{2}-6r^{10} a^{2} r_s \\\\sin{\\\\theta}^{2}-6r^{8} a^{4} r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}%\\n+2r^{7} a^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+2r^{12} r_s+2r^{10} r_s a^{2} \\\\cos{\\\\theta}^{2}-2r^{9} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-3r^{6} a^{6} \\\\cos{\\\\theta}^{2} r_s \\\\sin{\\\\theta}^{4}+r^{4} a^{8} \\\\cos{\\\\theta}^{4} r_s \\\\sin{\\\\theta}^{4}+2r^{7} a^{4} \\\\cos{\\\\theta}^{2} r_s^{2} \\\\sin{\\\\theta}^{2}-6r^{8} a^{4} \\\\cos{\\\\theta}^{2} r_s \\\\sin{\\\\theta}^{2}-6r^{6} a^{6} \\\\cos{\\\\theta}^{4} r_s \\\\sin{\\\\theta}^{2}+2r^{5} a^{4} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+2r^{10} a^{2} \\\\cos{\\\\theta}^{2} r_s+2r^{8} a^{4} \\\\cos{\\\\theta}^{4} r_s-2r^{7} a^{2} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-2a^{8} \\\\cos{\\\\theta}^{2} r_s^{2} r^{2} \\\\sin{\\\\theta}^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right)-2a^{8} \\\\cos{\\\\theta}^{2} r_s^{2} r^{2} \\\\sin{\\\\theta}^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+2a^{8} \\\\cos{\\\\theta}^{2} r_s^{2} r^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)+2a^{8} \\\\cos{\\\\theta}^{2} r_s^{2} r^{2} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-4a^{8} \\\\cos{\\\\theta}^{2} r_s r^{3} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)-4a^{8} \\\\cos{\\\\theta}^{2} r_s r^{3} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-4a^{10} \\\\cos{\\\\theta}^{4} r_s r \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)%\\n-4a^{10} \\\\cos{\\\\theta}^{4} r_s r \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+2a^{8} \\\\cos{\\\\theta}^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4}+2a^{6} \\\\cos{\\\\theta}^{2} r_s^{2} r^{4} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)+2a^{6} \\\\cos{\\\\theta}^{2} r_s^{2} r^{4} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)+2a^{6} \\\\cos{\\\\theta}^{2} r_s^{3} r^{3} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)+2a^{6} \\\\cos{\\\\theta}^{2} r_s^{3} r^{3} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-2a^{6} \\\\cos{\\\\theta}^{2} r_s^{3} r^{3} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}-2a^{6} \\\\cos{\\\\theta}^{2} r_s^{3} r^{3} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+6a^{6} \\\\cos{\\\\theta}^{2} r_s^{2} r^{5} \\\\sin{\\\\theta}^{4}+6a^{8} \\\\cos{\\\\theta}^{4} r_s^{2} r^{3} \\\\sin{\\\\theta}^{4}-4a^{6} \\\\cos{\\\\theta}^{2} r_s r^{5} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)-4a^{6} \\\\cos{\\\\theta}^{2} r_s r^{5} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-4a^{8} \\\\cos{\\\\theta}^{4} r_s r^{3} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right)-4a^{8} \\\\cos{\\\\theta}^{4} r_s r^{3} \\\\sin{\\\\theta}^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right)-3a^{6} \\\\cos{\\\\theta}^{2} r_s^{3} r^{4} \\\\sin{\\\\theta}^{4}-2a^{8} \\\\cos{\\\\theta}^{4} r_s^{3} r^{2} \\\\sin{\\\\theta}^{4}+2a^{6} \\\\cos{\\\\theta}^{2} r_s^{3} r^{4} \\\\sin{\\\\theta}^{2}+2a^{8} \\\\cos{\\\\theta}^{4} r_s^{3} r^{2} \\\\sin{\\\\theta}^{2}+4a^{6} \\\\cos{\\\\theta}^{2} r_s^{2} r^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+4a^{6} \\\\cos{\\\\theta}^{2} r_s^{2} r^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}%\\n+4a^{8} \\\\cos{\\\\theta}^{4} r_s^{2} r^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+4a^{8} \\\\cos{\\\\theta}^{4} r_s^{2} r^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-2a^{6} \\\\cos{\\\\theta}^{2} r_s r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{4}-4a^{6} \\\\cos{\\\\theta}^{2} r_s^{2} r \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-2a^{6} \\\\cos{\\\\theta}^{2} r_s r \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}-2a^{6} \\\\cos{\\\\theta}^{2} r_s r \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+2a^{6} \\\\cos{\\\\theta}^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2}-2a^{4} \\\\cos{\\\\theta}^{2} r_s^{3} r^{5} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}-2a^{4} \\\\cos{\\\\theta}^{2} r_s^{3} r^{5} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-2a^{4} \\\\cos{\\\\theta}^{2} r_s^{3} r^{6} \\\\sin{\\\\theta}^{2}-2a^{6} \\\\cos{\\\\theta}^{4} r_s^{3} r^{4} \\\\sin{\\\\theta}^{2}+4a^{4} \\\\cos{\\\\theta}^{2} r_s^{2} r^{6} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+4a^{4} \\\\cos{\\\\theta}^{2} r_s^{2} r^{6} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+4a^{6} \\\\cos{\\\\theta}^{4} r_s^{2} r^{4} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}+4a^{6} \\\\cos{\\\\theta}^{4} r_s^{2} r^{4} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}+4a^{4} \\\\cos{\\\\theta}^{2} r_s^{2} r^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-2a^{4} \\\\cos{\\\\theta}^{2} r_s r^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2}-2a^{4} \\\\cos{\\\\theta}^{2} r_s r^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\partial_{r}\\\\left(a^{2} \\\\cos{\\\\theta}^{2}\\\\right) \\\\sin{\\\\theta}^{2}-2a^{4} \\\\cos{\\\\theta}^{2} r_s r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{3} \\\\sin{\\\\theta}^{2}-4a^{8} \\\\cos{\\\\theta}^{4} r^{3} r_s^{2} \\\\sin{\\\\theta}^{4}%\\n-a^{10} \\\\cos{\\\\theta}^{6} r r_s^{2} \\\\sin{\\\\theta}^{4}+8a^{6} \\\\cos{\\\\theta}^{4} r^{5} r_s^{2} \\\\sin{\\\\theta}^{2}+2a^{8} \\\\cos{\\\\theta}^{6} r^{3} r_s^{2} \\\\sin{\\\\theta}^{2}-2a^{6} \\\\cos{\\\\theta}^{4} r^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-3a^{8} \\\\cos{\\\\theta}^{2} r^{4} r_s \\\\sin{\\\\theta}^{4}-3a^{10} \\\\cos{\\\\theta}^{4} r^{2} r_s \\\\sin{\\\\theta}^{4}+4a^{6} \\\\cos{\\\\theta}^{2} r^{5} r_s^{2} \\\\sin{\\\\theta}^{2}-6a^{6} \\\\cos{\\\\theta}^{2} r^{6} r_s \\\\sin{\\\\theta}^{2}-12a^{8} \\\\cos{\\\\theta}^{4} r^{4} r_s \\\\sin{\\\\theta}^{2}+2a^{6} \\\\cos{\\\\theta}^{2} r^{6} r_s+4a^{8} \\\\cos{\\\\theta}^{4} r^{4} r_s+2a^{6} \\\\cos{\\\\theta}^{2} r^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-2a^{6} \\\\cos{\\\\theta}^{2} r^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+4a^{4} \\\\cos{\\\\theta}^{2} r^{8} r_s+8a^{6} \\\\cos{\\\\theta}^{4} r^{6} r_s-4a^{4} \\\\cos{\\\\theta}^{2} r^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+a^{10} \\\\cos{\\\\theta}^{4} r_s r^{2} \\\\sin{\\\\theta}^{4}+a^{12} \\\\cos{\\\\theta}^{6} r_s \\\\sin{\\\\theta}^{4}+4a^{8} \\\\cos{\\\\theta}^{4} r^{3} r_s^{2} \\\\sin{\\\\theta}^{2}-6a^{10} \\\\cos{\\\\theta}^{6} r^{2} r_s \\\\sin{\\\\theta}^{2}%\\n+2a^{10} \\\\cos{\\\\theta}^{6} r^{2} r_s+2a^{8} \\\\cos{\\\\theta}^{4} r \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-2a^{8} \\\\cos{\\\\theta}^{4} r \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+4a^{8} \\\\cos{\\\\theta}^{6} r^{4} r_s-4a^{6} \\\\cos{\\\\theta}^{4} r^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-3a^{6} \\\\cos{\\\\theta}^{2} r^{5} r_s^{2} \\\\sin{\\\\theta}^{4}+6a^{4} \\\\cos{\\\\theta}^{2} r^{7} r_s^{2} \\\\sin{\\\\theta}^{2}-2a^{4} \\\\cos{\\\\theta}^{2} r^{4} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}-3a^{6} \\\\cos{\\\\theta}^{2} r^{6} r_s \\\\sin{\\\\theta}^{4}-2a^{8} \\\\cos{\\\\theta}^{4} r^{4} r_s \\\\sin{\\\\theta}^{4}-6a^{4} \\\\cos{\\\\theta}^{2} r^{8} r_s \\\\sin{\\\\theta}^{2}-12a^{6} \\\\cos{\\\\theta}^{4} r^{6} r_s \\\\sin{\\\\theta}^{2}+2a^{4} \\\\cos{\\\\theta}^{2} r^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+2a^{2} \\\\cos{\\\\theta}^{2} r^{10} r_s+4a^{4} \\\\cos{\\\\theta}^{4} r^{8} r_s-2a^{2} \\\\cos{\\\\theta}^{2} r^{7} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+a^{10} \\\\cos{\\\\theta}^{6} r^{2} r_s \\\\sin{\\\\theta}^{4}-6a^{8} \\\\cos{\\\\theta}^{6} r^{4} r_s \\\\sin{\\\\theta}^{2}+2a^{6} \\\\cos{\\\\theta}^{4} r^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\sin{\\\\theta}^{2}+2a^{6} \\\\cos{\\\\theta}^{6} r^{6} r_s%\\n-2a^{4} \\\\cos{\\\\theta}^{4} r^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+r^{4} r_s^{3} a^{6} \\\\sin{\\\\theta}^{6}+2r^{4} r_s^{3} a^{6} \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}^{2}-r^{4} r_s^{3} a^{6} \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{2}+r^{3} r_s^{2} a^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-r^{6} r_s^{3} a^{4} \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{2}+r^{5} r_s^{2} a^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-r^{2} r_s^{3} a^{8} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6}+r^{2} r_s^{3} a^{8} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2}-r r_s^{2} a^{6} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-r^{3} r_s^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-2r^{3} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{4} \\\\sin{\\\\theta}^{4}+2r^{4} r_s^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} \\\\sin{\\\\theta}^{2}-4r^{5} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} \\\\sin{\\\\theta}^{2}-4r^{3} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{4} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}+2r^{5} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2}+2r^{3} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{4} \\\\cos{\\\\theta}^{2}-2r^{2} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4} a^{2}+2r^{5} r_s^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} \\\\cos{\\\\theta}^{2}-2r^{4} r_s \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4}%\\n-r^{5} a^{6} r_s^{2} \\\\sin{\\\\theta}^{6}-2r^{5} a^{6} r_s^{2} \\\\sin{\\\\theta}^{4} \\\\cos{\\\\theta}^{2}+r^{5} a^{6} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{2}-r^{4} a^{4} r_s \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+r^{7} a^{4} r_s^{2} \\\\sin{\\\\theta}^{2} \\\\cos{\\\\theta}^{2}-r^{6} a^{2} r_s \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+r^{3} a^{8} r_s^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6}-r^{5} a^{6} r_s^{2} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}-r^{3} a^{8} r_s^{2} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2}+r^{2} a^{6} r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+r^{4} a^{4} r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+2r^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{4} r_s \\\\sin{\\\\theta}^{4}-2r^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+4r^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} r_s \\\\sin{\\\\theta}^{2}+4r^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{4} r_s \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2}-2r^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{2} r_s-2r^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} a^{4} r_s \\\\cos{\\\\theta}^{2}+2r^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4} a^{2}-2r^{8} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s-2r^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s a^{2} \\\\cos{\\\\theta}^{2}%\\n+2r^{5} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4}-2a^{8} \\\\cos{\\\\theta}^{2} r^{3} r_s^{2} \\\\sin{\\\\theta}^{6}+2a^{6} \\\\cos{\\\\theta}^{2} r^{4} r_s^{3} \\\\sin{\\\\theta}^{4}-2a^{6} \\\\cos{\\\\theta}^{2} r^{2} r_s \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-2a^{4} \\\\cos{\\\\theta}^{2} r^{4} r_s \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+a^{8} \\\\cos{\\\\theta}^{2} r_s^{2} r^{3} \\\\sin{\\\\theta}^{6}-a^{6} \\\\cos{\\\\theta}^{2} r_s^{2} r^{5} \\\\sin{\\\\theta}^{2}-a^{8} \\\\cos{\\\\theta}^{4} r_s^{2} r^{3} \\\\sin{\\\\theta}^{2}+a^{6} \\\\cos{\\\\theta}^{2} r_s r^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-a^{4} \\\\cos{\\\\theta}^{2} r_s^{2} r^{7} \\\\sin{\\\\theta}^{2}-a^{6} \\\\cos{\\\\theta}^{4} r_s^{2} r^{5} \\\\sin{\\\\theta}^{2}+a^{4} \\\\cos{\\\\theta}^{2} r_s r^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+a^{10} \\\\cos{\\\\theta}^{4} r_s^{2} \\\\sin{\\\\theta}^{6} r-a^{8} \\\\cos{\\\\theta}^{4} r_s^{3} \\\\sin{\\\\theta}^{4} r^{2}+2a^{8} \\\\cos{\\\\theta}^{4} r_s^{2} \\\\sin{\\\\theta}^{4} r^{3}+2a^{10} \\\\cos{\\\\theta}^{6} r_s^{2} \\\\sin{\\\\theta}^{4} r-a^{8} \\\\cos{\\\\theta}^{4} r_s^{2} \\\\sin{\\\\theta}^{2} r^{3}-a^{10} \\\\cos{\\\\theta}^{6} r_s^{2} \\\\sin{\\\\theta}^{2} r+a^{8} \\\\cos{\\\\theta}^{4} r_s \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}-a^{6} \\\\cos{\\\\theta}^{4} r_s^{2} \\\\sin{\\\\theta}^{2} r^{5}%\\n-a^{8} \\\\cos{\\\\theta}^{6} r_s^{2} \\\\sin{\\\\theta}^{2} r^{3}+a^{6} \\\\cos{\\\\theta}^{4} r_s \\\\sin{\\\\theta}^{2} r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2}+2a^{6} \\\\cos{\\\\theta}^{2} r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s \\\\sin{\\\\theta}^{4}-2a^{4} \\\\cos{\\\\theta}^{2} r^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s^{2} \\\\sin{\\\\theta}^{2}+4a^{4} \\\\cos{\\\\theta}^{2} r^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s \\\\sin{\\\\theta}^{2}+4a^{6} \\\\cos{\\\\theta}^{4} r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s \\\\sin{\\\\theta}^{2}-2a^{4} \\\\cos{\\\\theta}^{2} r^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s-2a^{6} \\\\cos{\\\\theta}^{4} r^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s+2a^{4} \\\\cos{\\\\theta}^{2} r \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4}-2a^{2} \\\\cos{\\\\theta}^{2} r^{6} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s-2a^{4} \\\\cos{\\\\theta}^{4} r^{4} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} r_s+2a^{2} \\\\cos{\\\\theta}^{2} r^{3} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{4}}{2r r_s \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} r^{2}-a^{4} \\\\cos{\\\\theta}^{2}+r^{3} r_s-r^{4}-r^{2} a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}-2r^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} r^{2}-a^{4} \\\\cos{\\\\theta}^{2}+r^{3} r_s-r^{4}-r^{2} a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}-2a^{2} \\\\cos{\\\\theta}^{2} \\\\left(a^{2} r r_s \\\\cos{\\\\theta}^{2}-a^{2} r^{2}-a^{4} \\\\cos{\\\\theta}^{2}+r^{3} r_s-r^{4}-r^{2} a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\left(r^{2}+a^{2} \\\\cos{\\\\theta}^{2}\\\\right)^{2} \\\\tan{\\\\theta}}\\\\\\\\[-.5ex]\\n\\\\end{aligned}\\\\right.\\n\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"distribute(_)\\ncollect_factors(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}R_{\\\\sigma \\\\nu} = \\\\left\\\\{\\\\begin{aligned}\\\\square{}_{t}{}_{t}= & \\\\frac{54\\\\cos{\\\\theta}^{2} a^{4} r^{5} r_s^{2}+6\\\\cos{\\\\theta}^{4} a^{6} r^{3} r_s^{2}-172\\\\cos{\\\\theta}^{2} a^{4} r^{6} r_s-72\\\\cos{\\\\theta}^{4} a^{6} r^{4} r_s-4\\\\cos{\\\\theta}^{6} a^{8} r^{2} r_s+90\\\\cos{\\\\theta}^{2} a^{2} r^{7} r_s^{2}-10\\\\cos{\\\\theta}^{4} a^{4} r^{5} r_s^{2}-14\\\\cos{\\\\theta}^{2} a^{2} r^{6} r_s^{3}+10\\\\cos{\\\\theta}^{4} a^{4} r^{4} r_s^{3}-140\\\\cos{\\\\theta}^{2} a^{2} r^{8} r_s-40\\\\cos{\\\\theta}^{4} a^{4} r^{6} r_s+28\\\\cos{\\\\theta}^{6} a^{6} r^{4} r_s-18\\\\cos{\\\\theta}^{6} a^{6} r^{3} r_s^{2}+80r^{9} r_s^{2}-26r^{8} r_s^{3}+50a^{2} r^{7} r_s^{2}-82r^{10} r_s-102a^{2} r^{8} r_s+8\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{6} r_s%\\n+12\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{4} r_s-4\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{5} r_s^{2}-4\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{3} r_s^{2}+4\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{4} r_s+4\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{2} r_s+120\\\\cos{\\\\theta}^{2} a^{4} r^{7}+80\\\\cos{\\\\theta}^{4} a^{6} r^{5}+8\\\\cos{\\\\theta}^{6} a^{8} r^{3}+64\\\\cos{\\\\theta}^{2} a^{2} r^{9}+40\\\\cos{\\\\theta}^{4} a^{4} r^{7}+28r^{11}+52a^{2} r^{9}-4\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{7}-8\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{5}-4\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{5}-8\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{3}-4\\\\cos{\\\\theta}^{8} a^{10} r-4\\\\cos{\\\\theta}^{8} a^{8} r^{3}+10\\\\cos{\\\\theta}^{8} a^{8} r^{2} r_s-4\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{3}%\\n+4\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{2} r_s-4\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r+8\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{6} r^{3} r_s^{2}-8\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{6} r^{4} r_s-8\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{8} r^{2} r_s-8\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{5} r_s^{2}+8\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{6} r_s+24\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{4} r_s-8\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{6} r^{3} r_s^{2}-16\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{3} r_s^{2}+8\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{6} r^{4} r_s+8\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{8} r^{2} r_s+16\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{8} r^{2} r_s-2\\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{2} a^{6} r^{3} r_s^{2}+2\\\\cos{4\\\\theta} a^{6} r^{4} r_s+2\\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{2} a^{8} r^{2} r_s-2\\\\cos{4\\\\theta} a^{4} r^{5} r_s^{2}+4\\\\cos{4\\\\theta} a^{4} r^{6} r_s+6\\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{2} a^{6} r^{4} r_s+2\\\\cos{\\\\theta}^{2} a^{6} r^{3} r_s^{2}%\\n-2a^{6} r^{4} r_s-2\\\\cos{\\\\theta}^{2} a^{8} r^{2} r_s+2a^{4} r^{5} r_s^{2}-28a^{4} r^{6} r_s-38\\\\cos{\\\\theta}^{2} a^{6} r^{4} r_s-16\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} a^{4} r^{5} r_s^{2}+8\\\\cos{2\\\\theta} a^{4} r^{6} r_s+16\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} a^{6} r^{4} r_s-8\\\\cos{2\\\\theta} a^{2} r^{7} r_s^{2}+16\\\\cos{2\\\\theta} a^{2} r^{8} r_s+40\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} a^{4} r^{6} r_s-8\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{4} a^{6} r^{3} r_s^{2}+8\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{4} a^{8} r^{2} r_s+32\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{4} a^{6} r^{4} r_s+12\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{3} r_s^{2} \\\\sin{2\\\\theta}-12\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{4} r^{4} \\\\sin{2\\\\theta} r_s-12\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{6} r^{2} \\\\sin{2\\\\theta} r_s+12\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{2} r^{5} r_s^{2} \\\\sin{2\\\\theta}-24\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{2} r^{6} \\\\sin{2\\\\theta} r_s-36\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{4} \\\\sin{2\\\\theta} r_s%\\n+12\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{3} r_s^{2} \\\\sin{2\\\\theta}-12\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{4} r^{4} \\\\sin{2\\\\theta} r_s-12\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{6} r^{2} \\\\sin{2\\\\theta} r_s+12\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{2} r^{5} r_s^{2} \\\\sin{2\\\\theta}-24\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{2} r^{6} \\\\sin{2\\\\theta} r_s-36\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{4} \\\\sin{2\\\\theta} r_s-10\\\\cos{\\\\theta}^{4} a^{8} r^{2} r_s-2\\\\cos{4\\\\theta} a^{6} r^{5}-4\\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{2} a^{8} r^{3}-2\\\\cos{4\\\\theta} a^{4} r^{7}-4\\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{2} a^{6} r^{5}+2a^{6} r^{5}+4\\\\cos{\\\\theta}^{2} a^{8} r^{3}+26a^{4} r^{7}+60\\\\cos{\\\\theta}^{2} a^{6} r^{5}-8\\\\cos{2\\\\theta} a^{4} r^{7}-24\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} a^{6} r^{5}-8\\\\cos{2\\\\theta} a^{2} r^{9}-24\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} a^{4} r^{7}-24\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{4} a^{8} r^{3}%\\n-24\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{4} a^{6} r^{5}+12\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{4} r^{5} \\\\sin{2\\\\theta}+24\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{6} r^{3} \\\\sin{2\\\\theta}+12\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{2} r^{7} \\\\sin{2\\\\theta}+24\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{5} \\\\sin{2\\\\theta}+12\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{4} r^{5} \\\\sin{2\\\\theta}+24\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{6} r^{3} \\\\sin{2\\\\theta}+12\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{2} r^{7} \\\\sin{2\\\\theta}+24\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{5} \\\\sin{2\\\\theta}+42\\\\cos{\\\\theta}^{4} a^{8} r^{3}+2\\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{4} a^{8} r^{2} r_s-2\\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{4} a^{10} r-2\\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{4} a^{8} r^{3}+2\\\\cos{\\\\theta}^{4} a^{10} r+8\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{6} a^{8} r^{2} r_s-8\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{6} a^{10} r-8\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{6} a^{8} r^{3}-12\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{2} \\\\sin{2\\\\theta} r_s+12\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{8} \\\\sin{2\\\\theta} r+12\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{3} \\\\sin{2\\\\theta}%\\n-12\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{2} \\\\sin{2\\\\theta} r_s+12\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{8} \\\\sin{2\\\\theta} r+12\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{3} \\\\sin{2\\\\theta}+8\\\\cos{\\\\theta}^{6} a^{10} r+6\\\\left(r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{3} r_s^{2}-2\\\\left(r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{2} r_s^{3}+2\\\\left(r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r_s^{2} r-4\\\\sin{\\\\theta}^{2} \\\\left(r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{3} r_s^{2}+2\\\\sin{\\\\theta}^{2} \\\\left(r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{2} r_s^{3}-2\\\\sin{\\\\theta}^{2} \\\\left(r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r_s^{2} r+2\\\\sin{\\\\theta}^{2} \\\\left(r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{4} r_s+2\\\\sin{\\\\theta}^{2} \\\\left(r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{2} r_s+2\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{2} r_s-2\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r_s^{2} r+2\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r_s-4\\\\left(r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{4} r_s-2\\\\left(r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{2} r_s-4\\\\cos{\\\\theta}^{2} \\\\left(r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{2} r_s+2\\\\cos{\\\\theta}^{2} \\\\left(r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r_s^{2} r-2\\\\cos{\\\\theta}^{2} \\\\left(r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r_s%\\n+4\\\\left(r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{5} r_s^{2}-2\\\\left(r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{4} r_s^{3}-2\\\\left(r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{6} r_s-2\\\\cos{\\\\theta}^{2} \\\\left(r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{4} r_s+2\\\\cos{\\\\theta}^{2} \\\\left(r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{3} r_s^{2}-2\\\\cos{\\\\theta}^{6} a^{6} r^{2} r_s^{3}+2\\\\cos{\\\\theta}^{6} a^{8} r_s^{2} r-36\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{2} r^{6} r_s^{2}+60\\\\partial_{r}\\\\left(r^{2}\\\\right) a^{2} r^{7} r_s+60\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{5} r_s-44\\\\partial_{r}\\\\left(r^{2}\\\\right) r^{8} r_s^{2}+40\\\\partial_{r}\\\\left(r^{2}\\\\right) r^{9} r_s+44\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{2} r^{7} r_s-40\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{2} r^{6} r_s^{2}+64\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{2} r^{7} r_s+64\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{5} r_s-48\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) r^{8} r_s^{2}+48\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) r^{9} r_s+56\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{2} r^{7} r_s+8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{2} r^{5} r_s^{3}%\\n-32\\\\partial_{r}\\\\left(r^{2}\\\\right) a^{2} r^{6} r_s^{2}-16\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{4} r_s^{2}+16\\\\partial_{r}\\\\left(r^{2}\\\\right) r^{7} r_s^{3}+8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{2} r^{5} r_s^{3}-32\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{2} r^{6} r_s^{2}-16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{4} r_s^{2}+16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) r^{7} r_s^{3}+16\\\\partial_{r}\\\\left(r^{2}\\\\right) a^{4} r^{5} r_s+8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{6} r^{3} r_s+16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{4} r^{5} r_s+8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{6} r^{3} r_s+12\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{4} r^{4} r_s^{2}-12\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{3} r_s-4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{4} r^{5} r_s+16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{4} r^{4} r_s^{2}-16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{3} r_s-8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{4} r^{5} r_s-8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{4} r^{3} r_s^{3}+16\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{2} r_s^{2}-8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{4} r^{3} r_s^{3}%\\n+16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{2} r_s^{2}-8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{8} r r_s-8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{8} r r_s-4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{2} a^{2} r^{6} r_s^{2}+4\\\\partial_{r}\\\\left(r r_s\\\\right) a^{2} r^{7} r_s+4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{5} r_s-4\\\\partial_{r}\\\\left(r r_s\\\\right) r^{8} r_s^{2}+8\\\\partial_{r}\\\\left(r r_s\\\\right) r^{9} r_s+12\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{2} a^{2} r^{7} r_s+4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{4} a^{4} r^{4} r_s^{2}-4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{3} r_s-4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{4} a^{4} r^{5} r_s+4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{2} r^{6} r_s^{2}-4\\\\partial_{r}\\\\left(a^{2}\\\\right) a^{2} r^{7} r_s-4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{5} r_s+4\\\\partial_{r}\\\\left(a^{2}\\\\right) r^{8} r_s^{2}-8\\\\partial_{r}\\\\left(a^{2}\\\\right) r^{9} r_s-12\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{2} r^{7} r_s-4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{4} r^{4} r_s^{2}+4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{3} r_s%\\n+4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{4} r^{5} r_s+4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{6} r^{2} r_s^{2}-12\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{8} r r_s-4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{6} r^{3} r_s+4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{6} a^{6} r^{2} r_s^{2}-4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{6} a^{8} r r_s-12\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{6} a^{6} r^{3} r_s-4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{6} r^{2} r_s^{2}+4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{8} r r_s+12\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{6} r^{3} r_s-28\\\\partial_{r}\\\\left(r^{2}\\\\right) a^{2} r^{8}-40\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{6}-12\\\\partial_{r}\\\\left(r^{2}\\\\right) r^{10}-16\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{2} r^{8}-32\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{2} r^{8}-48\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{6}-16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) r^{10}-24\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{2} r^{8}-16\\\\partial_{r}\\\\left(r^{2}\\\\right) a^{4} r^{6}-24\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{6} r^{4}%\\n-16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{4} r^{6}-24\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{6} r^{4}-4\\\\partial_{r}\\\\left(r r_s\\\\right) a^{2} r^{8}-8\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{6}-4\\\\partial_{r}\\\\left(r r_s\\\\right) r^{10}-8\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{2} a^{2} r^{8}+4\\\\partial_{r}\\\\left(a^{2}\\\\right) a^{2} r^{8}+8\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{6}+4\\\\partial_{r}\\\\left(a^{2}\\\\right) r^{10}+8\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{2} r^{8}+8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{8} r^{2}+8\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{6} a^{8} r^{2}+8\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{6} a^{6} r^{4}-8\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{8} r^{2}-8\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{6} r^{4}+2\\\\cos{\\\\theta}^{8} a^{8} r_s^{2} r-2\\\\cos{\\\\theta}^{8} a^{10} r_s-16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{6} r^{3} r_s+16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{8} r^{2}+8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{6} r^{4}%\\n+8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{6} r^{2} r_s^{2}-16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{8} r r_s+8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{10}+8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{10}+4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{8} a^{8} r r_s-4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{8} a^{10}-4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{8} a^{8} r^{2}-4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{8} a^{8} r r_s+4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{8} a^{10}+4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{8} a^{8} r^{2}+4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{8} a^{8} r r_s-4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{8} a^{10}-4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{8} a^{8} r^{2}}{8\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{2} r^{2} r_s^{2}-8\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{2} r^{3} r_s-8\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{4} r r_s+8\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} r^{4} r_s^{2}-16\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} r^{5} r_s-24\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{2} r^{3} r_s+8\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{2} r^{4}+16\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{4} r^{2}+8\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} r^{6}+16\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{2} r^{4}-8\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{4} r r_s+8\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{6}+8\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{4} r^{2}} r_s\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{t}= & \\\\frac{-64\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{5} r_s^{2}-16\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{3} r_s^{2}-36\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{2} r^{7} r_s^{2}+52\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{4} r^{5} r_s^{2}-20\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{4} r^{4} r_s^{3}-52\\\\sin{\\\\theta}^{2} r^{9} r_s^{2}+20\\\\sin{\\\\theta}^{2} r^{8} r_s^{3}-48\\\\sin{\\\\theta}^{2} a^{2} r^{7} r_s^{2}+176\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{6} r_s+104\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{4} r_s+64\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{2} r^{8} r_s-12\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{4} r^{6} r_s+44\\\\sin{\\\\theta}^{2} r^{10} r_s+88\\\\sin{\\\\theta}^{2} a^{2} r^{8} r_s+16\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{8} r^{2} r_s-48\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{6} r^{4} r_s+36\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{6} r^{3} r_s^{2}+24\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6} a^{6} r^{3} r_s^{2}-24\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{6} r^{3} r_s^{2}%\\n-16\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{4} r^{5} r_s^{2}+8\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{6} r^{3} r_s^{2}-16\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} a^{4} r^{5} r_s^{2}-12\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{4} a^{6} r^{3} r_s^{2}+16\\\\cos{\\\\theta}^{2} a^{4} r^{5} r_s^{2}+12\\\\cos{\\\\theta}^{4} a^{6} r^{3} r_s^{2}-6\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{3} r_s^{2} \\\\sin{2\\\\theta}-6\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{3} r_s^{2} \\\\sin{2\\\\theta}+3\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{3} r_s^{2} \\\\sin{4\\\\theta}+3\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{3} r_s^{2} \\\\sin{4\\\\theta}+2\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} a^{2} r^{7} r_s^{2}-10\\\\cos{\\\\theta}^{2} a^{2} r^{7} r_s^{2}-6\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{4} a^{4} r^{5} r_s^{2}+2\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{4} a^{4} r^{4} r_s^{3}-10\\\\cos{\\\\theta}^{4} a^{4} r^{5} r_s^{2}-2\\\\cos{\\\\theta}^{4} a^{4} r^{4} r_s^{3}+8\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{3} r_s^{2}-16\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{2} r^{5} r_s^{2} \\\\sin{2\\\\theta}-16\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{2} r^{5} r_s^{2} \\\\sin{2\\\\theta}-8\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{4} r^{3} r_s^{2} \\\\sin{2\\\\theta}%\\n-8\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{4} r^{3} r_s^{2} \\\\sin{2\\\\theta}-16\\\\sin{\\\\theta}^{6} a^{6} r^{4} r_s+16\\\\sin{\\\\theta}^{4} a^{6} r^{4} r_s+48\\\\sin{\\\\theta}^{4} a^{4} r^{6} r_s+88\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{6} r^{4} r_s+6\\\\cos{2\\\\theta} a^{4} r^{6} r_s+16\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} a^{6} r^{4} r_s-6a^{4} r^{6} r_s-16\\\\cos{\\\\theta}^{2} a^{6} r^{4} r_s+6\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{4} r^{4} \\\\sin{2\\\\theta} r_s+6\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{4} r^{4} \\\\sin{2\\\\theta} r_s-3\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{4} r^{4} \\\\sin{4\\\\theta} r_s-3\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{4} r^{4} \\\\sin{4\\\\theta} r_s+8\\\\cos{2\\\\theta} a^{2} r^{8} r_s-4\\\\cos{2\\\\theta} a^{2} r^{7} r_s^{2}-8a^{2} r^{8} r_s+4a^{2} r^{7} r_s^{2}+36\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} a^{4} r^{6} r_s-36\\\\cos{\\\\theta}^{2} a^{4} r^{6} r_s-8\\\\cos{2\\\\theta} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{4} r_s%\\n+20\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{2} r^{6} \\\\sin{2\\\\theta} r_s+20\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{2} r^{6} \\\\sin{2\\\\theta} r_s+34\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{4} \\\\sin{2\\\\theta} r_s+34\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{4} \\\\sin{2\\\\theta} r_s-16\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6} a^{8} r^{2} r_s+16\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{8} r^{2} r_s+40\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{8} r^{2} r_s+10\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{4} a^{8} r^{2} r_s-10\\\\cos{\\\\theta}^{4} a^{8} r^{2} r_s+6\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{6} r^{2} \\\\sin{2\\\\theta} r_s+6\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{6} r^{2} \\\\sin{2\\\\theta} r_s-3\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{6} r^{2} \\\\sin{4\\\\theta} r_s-3\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{6} r^{2} \\\\sin{4\\\\theta} r_s+40\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{4} a^{6} r^{4} r_s-40\\\\cos{\\\\theta}^{4} a^{6} r^{4} r_s-8\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{2} r_s+14\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{2} \\\\sin{2\\\\theta} r_s+14\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{2} \\\\sin{2\\\\theta} r_s+16\\\\sin{\\\\theta}^{6} a^{4} r^{5} r_s^{2}-16\\\\sin{\\\\theta}^{4} a^{4} r^{5} r_s^{2}%\\n-16\\\\sin{\\\\theta}^{4} a^{2} r^{7} r_s^{2}-6\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{2} r^{5} r_s^{2} \\\\sin{2\\\\theta}-6\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{2} r^{5} r_s^{2} \\\\sin{2\\\\theta}+3\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{2} r^{5} r_s^{2} \\\\sin{4\\\\theta}+3\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{2} r^{5} r_s^{2} \\\\sin{4\\\\theta}+6\\\\cos{2\\\\theta} r^{9} r_s^{2}-2\\\\cos{2\\\\theta} r^{8} r_s^{3}-6r^{9} r_s^{2}+2r^{8} r_s^{3}+8\\\\cos{2\\\\theta} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{5} r_s^{2}-8\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r^{7} r_s^{2} \\\\sin{2\\\\theta}-8\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) r^{7} r_s^{2} \\\\sin{2\\\\theta}-32\\\\sin{\\\\theta}^{6} a^{4} r^{6} r_s+32\\\\sin{\\\\theta}^{4} a^{2} r^{8} r_s+64\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{4} r^{6} r_s-6\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{2} r^{6} \\\\sin{4\\\\theta} r_s-6\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{2} r^{6} \\\\sin{4\\\\theta} r_s-6\\\\cos{2\\\\theta} r^{10} r_s+6r^{10} r_s-4\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} a^{2} r^{8} r_s%\\n+12\\\\cos{\\\\theta}^{2} a^{2} r^{8} r_s-16\\\\cos{2\\\\theta} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{6} r_s+16\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r^{8} \\\\sin{2\\\\theta} r_s+16\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) r^{8} \\\\sin{2\\\\theta} r_s+40\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{2} r^{6} \\\\sin{2\\\\theta} r_s+40\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{2} r^{6} \\\\sin{2\\\\theta} r_s-56\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6} a^{6} r^{4} r_s+24\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{6} r^{4} r_s-9\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{4} \\\\sin{4\\\\theta} r_s-9\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{4} \\\\sin{4\\\\theta} r_s+6\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{4} a^{4} r^{6} r_s+18\\\\cos{\\\\theta}^{4} a^{4} r^{6} r_s-24\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{4} r_s+32\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{4} r^{4} \\\\sin{2\\\\theta} r_s+32\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{4} r^{4} \\\\sin{2\\\\theta} r_s+16\\\\sin{\\\\theta}^{6} a^{6} r^{5}-16\\\\sin{\\\\theta}^{4} a^{6} r^{5}-32\\\\sin{\\\\theta}^{4} a^{4} r^{7}-80\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{6} r^{5}-6\\\\cos{2\\\\theta} a^{4} r^{7}%\\n-22\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} a^{6} r^{5}+6a^{4} r^{7}+22\\\\cos{\\\\theta}^{2} a^{6} r^{5}-6\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{4} r^{5} \\\\sin{2\\\\theta}-6\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{4} r^{5} \\\\sin{2\\\\theta}+3\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{4} r^{5} \\\\sin{4\\\\theta}+3\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{4} r^{5} \\\\sin{4\\\\theta}-4\\\\cos{2\\\\theta} a^{2} r^{9}+4a^{2} r^{9}-20\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} a^{4} r^{7}+20\\\\cos{\\\\theta}^{2} a^{4} r^{7}+8\\\\cos{2\\\\theta} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{5}-14\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{2} r^{7} \\\\sin{2\\\\theta}-14\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{2} r^{7} \\\\sin{2\\\\theta}-36\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{5} \\\\sin{2\\\\theta}-36\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{5} \\\\sin{2\\\\theta}+32\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6} a^{8} r^{3}-32\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{8} r^{3}-64\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{8} r^{3}-26\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{4} a^{8} r^{3}%\\n+26\\\\cos{\\\\theta}^{4} a^{8} r^{3}-12\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{6} r^{3} \\\\sin{2\\\\theta}-12\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{6} r^{3} \\\\sin{2\\\\theta}+6\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{6} r^{3} \\\\sin{4\\\\theta}+6\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{6} r^{3} \\\\sin{4\\\\theta}-28\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{4} a^{6} r^{5}+28\\\\cos{\\\\theta}^{4} a^{6} r^{5}+16\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{3}-30\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{3} \\\\sin{2\\\\theta}-30\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{3} \\\\sin{2\\\\theta}+16\\\\sin{\\\\theta}^{6} a^{4} r^{7}-16\\\\sin{\\\\theta}^{4} a^{2} r^{9}-48\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{4} r^{7}+3\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{2} r^{7} \\\\sin{4\\\\theta}+3\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{2} r^{7} \\\\sin{4\\\\theta}+2\\\\cos{2\\\\theta} r^{11}-2r^{11}+2\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} a^{2} r^{9}-2\\\\cos{\\\\theta}^{2} a^{2} r^{9}+8\\\\cos{2\\\\theta} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{7}%\\n-8\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r^{9} \\\\sin{2\\\\theta}-8\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) r^{9} \\\\sin{2\\\\theta}-24\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{2} r^{7} \\\\sin{2\\\\theta}-24\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{2} r^{7} \\\\sin{2\\\\theta}+32\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6} a^{6} r^{5}-48\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{6} r^{5}+6\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{5} \\\\sin{4\\\\theta}+6\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{5} \\\\sin{4\\\\theta}-2\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{4} a^{4} r^{7}+2\\\\cos{\\\\theta}^{4} a^{4} r^{7}+16\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{5}-24\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{4} r^{5} \\\\sin{2\\\\theta}-24\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{4} r^{5} \\\\sin{2\\\\theta}-24\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{6} a^{8} r^{2} r_s-8\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} a^{8} r^{2} r_s+12\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{6} a^{8} r^{2} r_s-12\\\\cos{\\\\theta}^{6} a^{8} r^{2} r_s-3\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{2} \\\\sin{4\\\\theta} r_s-3\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{2} \\\\sin{4\\\\theta} r_s+4\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{6} a^{6} r^{4} r_s%\\n-2\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{6} a^{6} r^{3} r_s^{2}+20\\\\cos{\\\\theta}^{6} a^{6} r^{4} r_s-6\\\\cos{\\\\theta}^{6} a^{6} r^{3} r_s^{2}-8\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{2} r_s+8\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{6} r^{2} \\\\sin{2\\\\theta} r_s+8\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{6} r^{2} \\\\sin{2\\\\theta} r_s+16\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{6} a^{10} r-16\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{10} r-16\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} a^{10} r-10\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{6} a^{10} r+10\\\\cos{\\\\theta}^{6} a^{10} r-6\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{8} \\\\sin{2\\\\theta} r-6\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{8} \\\\sin{2\\\\theta} r+3\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{8} \\\\sin{4\\\\theta} r+3\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{8} \\\\sin{4\\\\theta} r-12\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{6} a^{8} r^{3}+12\\\\cos{\\\\theta}^{6} a^{8} r^{3}+8\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r-8\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{8} \\\\sin{2\\\\theta} r-8\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{8} \\\\sin{2\\\\theta} r%\\n+16\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{6} a^{8} r^{3}-16\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} a^{8} r^{3}+3\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{3} \\\\sin{4\\\\theta}+3\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{3} \\\\sin{4\\\\theta}-2\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{6} a^{6} r^{5}+2\\\\cos{\\\\theta}^{6} a^{6} r^{5}+8\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{3}-8\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{6} r^{3} \\\\sin{2\\\\theta}-8\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{6} r^{3} \\\\sin{2\\\\theta}+20\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{2} r_s+20\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{4} r_s-8\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{3}-8\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{5}-12\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r-12\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{3}+8\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{4} r_s-8\\\\cos{\\\\theta}^{2} r^{9} r_s^{2}-16\\\\cos{\\\\theta}^{4} a^{2} r^{7} r_s^{2}+8\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{6} r_s-8\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{5}%\\n+8\\\\cos{\\\\theta}^{2} r^{10} r_s+24\\\\cos{\\\\theta}^{4} a^{2} r^{8} r_s-8\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{7}-16\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{3}+24\\\\cos{\\\\theta}^{6} a^{4} r^{6} r_s-16\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{5}+8\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{2} r_s-8\\\\cos{\\\\theta}^{6} a^{4} r^{5} r_s^{2}+8\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{4} r_s-16\\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} a^{8} r^{2} r_s+8\\\\cos{\\\\theta}^{8} a^{8} r^{2} r_s-8\\\\cos{\\\\theta}^{6} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r+8\\\\cos{\\\\theta}^{8} a^{6} r^{4} r_s-8\\\\cos{\\\\theta}^{6} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{3}-16\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{3} r_s^{2}+4\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{2} r_s^{3}+36\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{2} r^{6} r_s^{2}+40\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{2} r^{6} r_s^{2}-8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{2} r^{5} r_s^{3}-8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{2} r^{5} r_s^{3}%\\n+16\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{4} r_s^{2}+16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{4} r_s^{2}-12\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{4} r^{4} r_s^{2}-16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{4} r^{4} r_s^{2}+8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{4} r^{3} r_s^{3}+8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{4} r^{3} r_s^{3}-16\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{2} r_s^{2}-16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{2} r_s^{2}-4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{4} r^{4} r_s^{2}+4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{4} r^{4} r_s^{2}-4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{6} r^{2} r_s^{2}-4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{6} r^{2} r_s^{2}+4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{6} r^{2} r_s^{2}+28\\\\sin{\\\\theta}^{2} a^{4} r^{6} r_s+48\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{6} r^{4} r_s-4\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{3} r_s^{2}-60\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{2} r^{7} r_s-64\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{2} r^{7} r_s+32\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{2} r^{6} r_s^{2}+32\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{2} r^{6} r_s^{2}%\\n-16\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{4} r^{5} r_s-16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{4} r^{5} r_s-60\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{5} r_s-64\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{5} r_s-8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{6} r^{3} r_s-8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{6} r^{3} r_s-4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\sin{\\\\theta}^{2} a^{2} r^{7} r_s-4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{5} r_s+4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{2} r^{7} r_s+4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{5} r_s+12\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{3} r_s+4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{3} r_s-4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{3} r_s+20\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{8} r^{2} r_s-4\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r_s^{2} r+16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{3} r_s+8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{8} r r_s+8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{8} r r_s+12\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{8} r r_s+4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{8} r r_s%\\n-4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{8} r r_s-4\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{5} r_s^{2}+4\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{4} r_s^{3}+44\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} r^{8} r_s^{2}+48\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} r^{8} r_s^{2}-16\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} r^{7} r_s^{3}-16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} r^{7} r_s^{3}+4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\sin{\\\\theta}^{2} r^{8} r_s^{2}+4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{2} r^{6} r_s^{2}-4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2} r^{8} r_s^{2}-4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{2} r^{6} r_s^{2}-4\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{6} r_s-40\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} r^{9} r_s-48\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} r^{9} r_s-44\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{2} r^{7} r_s-56\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{2} r^{7} r_s-8\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\sin{\\\\theta}^{2} r^{9} r_s-12\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{2} r^{7} r_s+8\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2} r^{9} r_s+12\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{2} r^{7} r_s%\\n+4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{4} r^{5} r_s-4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{4} r^{5} r_s+8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{4} r^{5} r_s+4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{6} r^{3} r_s+12\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{6} r^{3} r_s-12\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{6} r^{3} r_s+8\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} r^{4} r_s-4\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} r^{3} r_s^{2}+4\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{2} r^{2} r_s+4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{4} r^{5} r_s-28\\\\sin{\\\\theta}^{2} a^{4} r^{7}-76\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{6} r^{5}-104\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{7}-40\\\\sin{\\\\theta}^{2} a^{2} r^{9}+4\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{5}+28\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{2} r^{8}+32\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{2} r^{8}+16\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{4} r^{6}+16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{4} r^{6}+40\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{6}%\\n+48\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{6}+24\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{6} r^{4}+24\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{6} r^{4}+4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\sin{\\\\theta}^{2} a^{2} r^{8}+8\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{6}-4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{2} r^{8}-8\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{6}-68\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{8} r^{3}-88\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{5}-8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{8} r^{2}-8\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{8} r^{2}+8\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{8} r^{2}-28\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{2} r^{9}-12\\\\sin{\\\\theta}^{2} r^{11}+4\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{7}+12\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} r^{10}+16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} r^{10}+16\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{2} r^{8}+24\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{2} r^{8}+4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\sin{\\\\theta}^{2} r^{10}%\\n+8\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{2} r^{8}-4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2} r^{10}-8\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{2} r^{8}-20\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{4} r^{7}-8\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{6} r^{4}+8\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{6} r^{4}-4\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} r^{5}-4\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{2} r^{3}+8\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{2} r_s-4\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r_s^{2} r+16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{6} r^{3} r_s-8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{6} r^{2} r_s^{2}+16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{8} r r_s-4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} a^{8} r r_s+4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} a^{8} r r_s-4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} a^{8} r r_s-20\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{10} r-24\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{8} r^{3}+4\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r_s-16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{8} r^{2}%\\n-8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{10}-8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{10}+4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} a^{10}-4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} a^{10}+4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} a^{10}-4\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{6} r^{5}-8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{6} r^{4}+4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} a^{8} r^{2}-4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} a^{8} r^{2}+4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} a^{8} r^{2}-4\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{2} r^{3}+4\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{2} r^{2} r_s-4\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{4} r}{8\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{2} r^{2} r_s^{2}-8\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{2} r^{3} r_s-8\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{4} r r_s+8\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} r^{4} r_s^{2}-16\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} r^{5} r_s-24\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{2} r^{3} r_s+8\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{2} r^{4}+16\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{4} r^{2}+8\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} r^{6}+16\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{2} r^{4}-8\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{4} r r_s+8\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{6}+8\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{4} r^{2}} a r_s\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}_{\\\\phi}= & \\\\frac{-62\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{5} r_s^{2}-26\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{3} r_s^{2}-46\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{2} r^{7} r_s^{2}+28\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{4} r^{5} r_s^{2}+4\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{2} r^{6} r_s^{3}-10\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{4} r^{4} r_s^{3}-56\\\\sin{\\\\theta}^{2} r^{9} r_s^{2}+22\\\\sin{\\\\theta}^{2} r^{8} r_s^{3}-54\\\\sin{\\\\theta}^{2} a^{2} r^{7} r_s^{2}+180\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{6} r_s+70\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{2} r^{8} r_s+2\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{4} r^{6} r_s+46\\\\sin{\\\\theta}^{2} r^{10} r_s+92\\\\sin{\\\\theta}^{2} a^{2} r^{8} r_s+28\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{8} r^{2} r_s-38\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{6} r^{4} r_s+26\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{6} r^{3} r_s^{2}+24\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6} a^{6} r^{3} r_s^{2}-28\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{6} r^{3} r_s^{2}%\\n-22\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{4} r^{5} r_s^{2}+8\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{6} r^{3} r_s^{2}-16\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} a^{4} r^{5} r_s^{2}-12\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{4} a^{6} r^{3} r_s^{2}+16\\\\cos{\\\\theta}^{2} a^{4} r^{5} r_s^{2}+12\\\\cos{\\\\theta}^{4} a^{6} r^{3} r_s^{2}-6\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{3} r_s^{2} \\\\sin{2\\\\theta}-6\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{3} r_s^{2} \\\\sin{2\\\\theta}+3\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{3} r_s^{2} \\\\sin{4\\\\theta}+3\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{3} r_s^{2} \\\\sin{4\\\\theta}+2\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} a^{2} r^{7} r_s^{2}-2\\\\cos{\\\\theta}^{2} a^{2} r^{7} r_s^{2}-6\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{4} a^{4} r^{5} r_s^{2}+2\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{4} a^{4} r^{4} r_s^{3}+6\\\\cos{\\\\theta}^{4} a^{4} r^{5} r_s^{2}-2\\\\cos{\\\\theta}^{4} a^{4} r^{4} r_s^{3}+8\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{3} r_s^{2}-16\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{2} r^{5} r_s^{2} \\\\sin{2\\\\theta}-16\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{2} r^{5} r_s^{2} \\\\sin{2\\\\theta}-8\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{4} r^{3} r_s^{2} \\\\sin{2\\\\theta}%\\n-8\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{4} r^{3} r_s^{2} \\\\sin{2\\\\theta}-16\\\\sin{\\\\theta}^{6} a^{6} r^{4} r_s+16\\\\sin{\\\\theta}^{4} a^{6} r^{4} r_s+46\\\\sin{\\\\theta}^{4} a^{4} r^{6} r_s+90\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{6} r^{4} r_s+6\\\\cos{2\\\\theta} a^{4} r^{6} r_s+16\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} a^{6} r^{4} r_s-6a^{4} r^{6} r_s-16\\\\cos{\\\\theta}^{2} a^{6} r^{4} r_s+6\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{4} r^{4} \\\\sin{2\\\\theta} r_s+6\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{4} r^{4} \\\\sin{2\\\\theta} r_s-3\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{4} r^{4} \\\\sin{4\\\\theta} r_s-3\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{4} r^{4} \\\\sin{4\\\\theta} r_s+8\\\\cos{2\\\\theta} a^{2} r^{8} r_s-4\\\\cos{2\\\\theta} a^{2} r^{7} r_s^{2}-8a^{2} r^{8} r_s+4a^{2} r^{7} r_s^{2}+36\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} a^{4} r^{6} r_s-36\\\\cos{\\\\theta}^{2} a^{4} r^{6} r_s-8\\\\cos{2\\\\theta} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{4} r_s%\\n+20\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{2} r^{6} \\\\sin{2\\\\theta} r_s+20\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{2} r^{6} \\\\sin{2\\\\theta} r_s+34\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{4} \\\\sin{2\\\\theta} r_s+34\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{4} \\\\sin{2\\\\theta} r_s-16\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6} a^{8} r^{2} r_s+16\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{8} r^{2} r_s+42\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{8} r^{2} r_s+10\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{4} a^{8} r^{2} r_s-10\\\\cos{\\\\theta}^{4} a^{8} r^{2} r_s+6\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{6} r^{2} \\\\sin{2\\\\theta} r_s+6\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{6} r^{2} \\\\sin{2\\\\theta} r_s-3\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{6} r^{2} \\\\sin{4\\\\theta} r_s-3\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{6} r^{2} \\\\sin{4\\\\theta} r_s+40\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{4} a^{6} r^{4} r_s-40\\\\cos{\\\\theta}^{4} a^{6} r^{4} r_s-8\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{2} r_s+14\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{2} \\\\sin{2\\\\theta} r_s+14\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{2} \\\\sin{2\\\\theta} r_s+16\\\\sin{\\\\theta}^{6} a^{4} r^{5} r_s^{2}-14\\\\sin{\\\\theta}^{4} a^{4} r^{5} r_s^{2}%\\n-12\\\\sin{\\\\theta}^{4} a^{2} r^{7} r_s^{2}-6\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{2} r^{5} r_s^{2} \\\\sin{2\\\\theta}-6\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{2} r^{5} r_s^{2} \\\\sin{2\\\\theta}+3\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{2} r^{5} r_s^{2} \\\\sin{4\\\\theta}+3\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{2} r^{5} r_s^{2} \\\\sin{4\\\\theta}+6\\\\cos{2\\\\theta} r^{9} r_s^{2}-2\\\\cos{2\\\\theta} r^{8} r_s^{3}-6r^{9} r_s^{2}+2r^{8} r_s^{3}+8\\\\cos{2\\\\theta} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{5} r_s^{2}-8\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r^{7} r_s^{2} \\\\sin{2\\\\theta}-8\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) r^{7} r_s^{2} \\\\sin{2\\\\theta}-32\\\\sin{\\\\theta}^{6} a^{4} r^{6} r_s+30\\\\sin{\\\\theta}^{4} a^{2} r^{8} r_s+66\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{4} r^{6} r_s-6\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{2} r^{6} \\\\sin{4\\\\theta} r_s-6\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{2} r^{6} \\\\sin{4\\\\theta} r_s-6\\\\cos{2\\\\theta} r^{10} r_s+6r^{10} r_s-4\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} a^{2} r^{8} r_s%\\n+4\\\\cos{\\\\theta}^{2} a^{2} r^{8} r_s-16\\\\cos{2\\\\theta} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{6} r_s+16\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r^{8} \\\\sin{2\\\\theta} r_s+16\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) r^{8} \\\\sin{2\\\\theta} r_s+40\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{2} r^{6} \\\\sin{2\\\\theta} r_s+40\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{2} r^{6} \\\\sin{2\\\\theta} r_s-56\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6} a^{6} r^{4} r_s+26\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{6} r^{4} r_s-9\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{4} \\\\sin{4\\\\theta} r_s-9\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{4} \\\\sin{4\\\\theta} r_s+6\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{4} a^{4} r^{6} r_s-6\\\\cos{\\\\theta}^{4} a^{4} r^{6} r_s-24\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{4} r_s+32\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{4} r^{4} \\\\sin{2\\\\theta} r_s+32\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{4} r^{4} \\\\sin{2\\\\theta} r_s+16\\\\sin{\\\\theta}^{6} a^{6} r^{5}-16\\\\sin{\\\\theta}^{4} a^{6} r^{5}-32\\\\sin{\\\\theta}^{4} a^{4} r^{7}-80\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{6} r^{5}-6\\\\cos{2\\\\theta} a^{4} r^{7}%\\n-22\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} a^{6} r^{5}+6a^{4} r^{7}+22\\\\cos{\\\\theta}^{2} a^{6} r^{5}-6\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{4} r^{5} \\\\sin{2\\\\theta}-6\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{4} r^{5} \\\\sin{2\\\\theta}+3\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{4} r^{5} \\\\sin{4\\\\theta}+3\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{4} r^{5} \\\\sin{4\\\\theta}-4\\\\cos{2\\\\theta} a^{2} r^{9}+4a^{2} r^{9}-20\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} a^{4} r^{7}+20\\\\cos{\\\\theta}^{2} a^{4} r^{7}+8\\\\cos{2\\\\theta} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{5}-14\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{2} r^{7} \\\\sin{2\\\\theta}-14\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{2} r^{7} \\\\sin{2\\\\theta}-36\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{5} \\\\sin{2\\\\theta}-36\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{5} \\\\sin{2\\\\theta}+32\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6} a^{8} r^{3}-32\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{8} r^{3}-64\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{8} r^{3}-26\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{4} a^{8} r^{3}%\\n+26\\\\cos{\\\\theta}^{4} a^{8} r^{3}-12\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{6} r^{3} \\\\sin{2\\\\theta}-12\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{6} r^{3} \\\\sin{2\\\\theta}+6\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{6} r^{3} \\\\sin{4\\\\theta}+6\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{6} r^{3} \\\\sin{4\\\\theta}-28\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{4} a^{6} r^{5}+28\\\\cos{\\\\theta}^{4} a^{6} r^{5}+16\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{3}-30\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{3} \\\\sin{2\\\\theta}-30\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{3} \\\\sin{2\\\\theta}+16\\\\sin{\\\\theta}^{6} a^{4} r^{7}-16\\\\sin{\\\\theta}^{4} a^{2} r^{9}-48\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{4} r^{7}+3\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{2} r^{7} \\\\sin{4\\\\theta}+3\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{2} r^{7} \\\\sin{4\\\\theta}+2\\\\cos{2\\\\theta} r^{11}-2r^{11}+2\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} a^{2} r^{9}-2\\\\cos{\\\\theta}^{2} a^{2} r^{9}+8\\\\cos{2\\\\theta} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{7}%\\n-8\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r^{9} \\\\sin{2\\\\theta}-8\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) r^{9} \\\\sin{2\\\\theta}-24\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{2} r^{7} \\\\sin{2\\\\theta}-24\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{2} r^{7} \\\\sin{2\\\\theta}+32\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6} a^{6} r^{5}-48\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{6} r^{5}+6\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{5} \\\\sin{4\\\\theta}+6\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{5} \\\\sin{4\\\\theta}-2\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{4} a^{4} r^{7}+2\\\\cos{\\\\theta}^{4} a^{4} r^{7}+16\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{5}-24\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{4} r^{5} \\\\sin{2\\\\theta}-24\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{4} r^{5} \\\\sin{2\\\\theta}-24\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{6} a^{8} r^{2} r_s-10\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} a^{8} r^{2} r_s+12\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{6} a^{8} r^{2} r_s-12\\\\cos{\\\\theta}^{6} a^{8} r^{2} r_s-3\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{2} \\\\sin{4\\\\theta} r_s-3\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{2} \\\\sin{4\\\\theta} r_s+4\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{6} a^{6} r^{4} r_s%\\n-2\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{6} a^{6} r^{3} r_s^{2}-4\\\\cos{\\\\theta}^{6} a^{6} r^{4} r_s+2\\\\cos{\\\\theta}^{6} a^{6} r^{3} r_s^{2}-8\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{2} r_s+8\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{6} r^{2} \\\\sin{2\\\\theta} r_s+8\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{6} r^{2} \\\\sin{2\\\\theta} r_s+16\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{6} a^{10} r-16\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{10} r-16\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} a^{10} r-10\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{6} a^{10} r+10\\\\cos{\\\\theta}^{6} a^{10} r-6\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{8} \\\\sin{2\\\\theta} r-6\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{8} \\\\sin{2\\\\theta} r+3\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{8} \\\\sin{4\\\\theta} r+3\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{8} \\\\sin{4\\\\theta} r-12\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{6} a^{8} r^{3}+12\\\\cos{\\\\theta}^{6} a^{8} r^{3}+8\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r-8\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{8} \\\\sin{2\\\\theta} r-8\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{8} \\\\sin{2\\\\theta} r%\\n+16\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{6} a^{8} r^{3}-16\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} a^{8} r^{3}+3\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{3} \\\\sin{4\\\\theta}+3\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{3} \\\\sin{4\\\\theta}-2\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{6} a^{6} r^{5}+2\\\\cos{\\\\theta}^{6} a^{6} r^{5}+8\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{3}-8\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{6} r^{3} \\\\sin{2\\\\theta}-8\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{6} r^{3} \\\\sin{2\\\\theta}+4\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{4} r^{4} r_s^{3}+116\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{4} r_s+20\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{2} r_s+28\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{4} r_s-8\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{3} r_s^{2}-8\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{5} r_s^{2}+16\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{4} r_s+16\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{6} r_s+16\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{2} r_s+16\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{4} r_s-16\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{3}%\\n-16\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{5}-8\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{5}-8\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{7}-16\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{3}-16\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{5}-16\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r-16\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{3}-16\\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} a^{8} r^{2} r_s-8\\\\cos{\\\\theta}^{6} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r-8\\\\cos{\\\\theta}^{6} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{3}+2\\\\sin{\\\\theta}^{2} a^{2} r^{6} r_s^{3}-2\\\\sin{\\\\theta}^{2} a^{4} r^{5} r_s^{2}+30\\\\sin{\\\\theta}^{2} a^{4} r^{6} r_s+46\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{6} r^{4} r_s-4\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{4} r_s^{3}+4\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{6} r^{3} r_s^{2}+18\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{8} r^{2} r_s-2\\\\sin{\\\\theta}^{4} a^{2} r^{6} r_s^{3}+2\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{6} r_s-4\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{5} r_s^{2}%\\n+2\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{4} r_s+2\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{2} r_s^{3}-2\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{8} r_s^{2} r-2\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{8} r_s^{2} r+2\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{10} r_s-2\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{6} r^{2} r_s^{3}+2\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{8} r_s^{2} r-14\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{3} r_s^{2}+2\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} a^{8} r_s^{2} r-2\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} a^{10} r_s+10\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{2} r_s+2\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{2} r_s^{3}+36\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{2} r^{6} r_s^{2}+40\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{2} r^{6} r_s^{2}-8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{2} r^{5} r_s^{3}-8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{2} r^{5} r_s^{3}+16\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{4} r_s^{2}+16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{4} r_s^{2}-12\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{4} r^{4} r_s^{2}-16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{4} r^{4} r_s^{2}%\\n+8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{4} r^{3} r_s^{3}+8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{4} r^{3} r_s^{3}-16\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{2} r_s^{2}-16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{2} r_s^{2}-4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{4} r^{4} r_s^{2}+4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{4} r^{4} r_s^{2}-4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{6} r^{2} r_s^{2}-4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{6} r^{2} r_s^{2}+4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{6} r^{2} r_s^{2}-2\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{3} r_s^{2}-60\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{2} r^{7} r_s-64\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{2} r^{7} r_s+32\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{2} r^{6} r_s^{2}+32\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{2} r^{6} r_s^{2}-16\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{4} r^{5} r_s-16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{4} r^{5} r_s-60\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{5} r_s-64\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{5} r_s-8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{6} r^{3} r_s-8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{6} r^{3} r_s%\\n-4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\sin{\\\\theta}^{2} a^{2} r^{7} r_s-4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{5} r_s+4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{2} r^{7} r_s+4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{5} r_s+12\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{3} r_s+4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{3} r_s-4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{3} r_s-2\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r_s^{2} r+16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{3} r_s+8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{8} r r_s+8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{8} r r_s+12\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{8} r r_s+4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{8} r r_s-4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{8} r r_s+2\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{4} r_s^{3}+44\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} r^{8} r_s^{2}+48\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} r^{8} r_s^{2}-16\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} r^{7} r_s^{3}-16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} r^{7} r_s^{3}+4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\sin{\\\\theta}^{2} r^{8} r_s^{2}%\\n+4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{2} r^{6} r_s^{2}-4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2} r^{8} r_s^{2}-4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{2} r^{6} r_s^{2}-40\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} r^{9} r_s-48\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} r^{9} r_s-44\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{2} r^{7} r_s-56\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{2} r^{7} r_s-8\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\sin{\\\\theta}^{2} r^{9} r_s-12\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{2} r^{7} r_s+8\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2} r^{9} r_s+12\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{2} r^{7} r_s+4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{4} r^{5} r_s-4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{4} r^{5} r_s+8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{4} r^{5} r_s+4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{6} r^{3} r_s+12\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{6} r^{3} r_s-12\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{6} r^{3} r_s+4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{4} r^{5} r_s-28\\\\sin{\\\\theta}^{2} a^{4} r^{7}-76\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{6} r^{5}%\\n-104\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{7}-40\\\\sin{\\\\theta}^{2} a^{2} r^{9}+28\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{2} r^{8}+32\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{2} r^{8}+16\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{4} r^{6}+16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{4} r^{6}+40\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{6}+48\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{6}+24\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{6} r^{4}+24\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{6} r^{4}+4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\sin{\\\\theta}^{2} a^{2} r^{8}+8\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{6}-4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{2} r^{8}-8\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{6}-68\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{8} r^{3}-88\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{5}-8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{8} r^{2}-8\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{8} r^{2}+8\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{8} r^{2}-28\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{2} r^{9}%\\n-12\\\\sin{\\\\theta}^{2} r^{11}+12\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} r^{10}+16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} r^{10}+16\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{2} r^{8}+24\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{2} r^{8}+4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\sin{\\\\theta}^{2} r^{10}+8\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{2} r^{8}-4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2} r^{10}-8\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{2} r^{8}-20\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{4} r^{7}-8\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{6} r^{4}+8\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{6} r^{4}-2\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r_s^{2} r+16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{6} r^{3} r_s-8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{6} r^{2} r_s^{2}+16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{8} r r_s-4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} a^{8} r r_s+4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} a^{8} r r_s-4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} a^{8} r r_s-20\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{10} r%\\n-24\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{8} r^{3}+2\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r_s-16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{8} r^{2}-8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{10}-8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{10}+4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} a^{10}-4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} a^{10}+4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} a^{10}-4\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{6} r^{5}-8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{6} r^{4}+4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} a^{8} r^{2}-4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} a^{8} r^{2}+4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} a^{8} r^{2}}{8\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{2} r^{2} r_s^{2}-8\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{2} r^{3} r_s-8\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{4} r r_s+8\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} r^{4} r_s^{2}-16\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} r^{5} r_s-24\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{2} r^{3} r_s+8\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{2} r^{4}+16\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{4} r^{2}+8\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} r^{6}+16\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{2} r^{4}-8\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{4} r r_s+8\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{6}+8\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{4} r^{2}} a r_s\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{r}= & \\\\frac{14\\\\sin{\\\\theta}^{2} a^{4} r^{8} r_s^{4}-4\\\\sin{\\\\theta}^{2} a^{4} r^{7} r_s^{5}+4\\\\sin{\\\\theta}^{2} a^{6} r^{6} r_s^{4}+8\\\\sin{\\\\theta}^{2} a^{4} r^{9} r_s^{3}+236\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{6} r^{7} r_s^{3}-90\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{6} r^{6} r_s^{4}+36\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{8} r^{5} r_s^{3}+8\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{6} r^{5} r_s^{5}-8\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{8} r^{4} r_s^{4}+4\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{5} r_s^{3}-4\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{4} r_s^{4}+4\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{3} r_s^{3}+18\\\\sin{\\\\theta}^{2} a^{2} r^{10} r_s^{4}-10\\\\sin{\\\\theta}^{2} a^{2} r^{9} r_s^{5}+2\\\\sin{\\\\theta}^{2} a^{2} r^{11} r_s^{3}+258\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{9} r_s^{3}-166\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{8} r_s^{4}+46\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{7} r_s^{5}-8\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{7} r_s^{3}%\\n+4\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{6} r_s^{4}-38\\\\sin{\\\\theta}^{2} a^{4} r^{10} r_s^{2}-16\\\\sin{\\\\theta}^{2} a^{6} r^{8} r_s^{2}-274\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{6} r^{8} r_s^{2}-80\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{8} r^{6} r_s^{2}-4\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{4} r_s^{2}-18\\\\sin{\\\\theta}^{2} a^{2} r^{12} r_s^{2}-198\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{10} r_s^{2}+4\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{8} r_s^{2}-532\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{8} r^{6} r_s^{2}+372\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{8} r^{5} r_s^{3}-112\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{10} r^{4} r_s^{2}-70\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{8} r^{4} r_s^{4}+32\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{10} r^{3} r_s^{3}-476\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{8} r_s^{2}+552\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{7} r_s^{3}-270\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{6} r_s^{4}+4\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{5} r_s^{3}-2\\\\left(a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} r^{6} r_s^{2}+2\\\\left(a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} r^{5} r_s^{3}%\\n-2\\\\left(a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} a^{2} r^{4} r_s^{2}+4\\\\cos{\\\\theta}^{2} \\\\left(a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} a^{2} r^{4} r_s^{2}-4\\\\cos{\\\\theta}^{2} \\\\left(a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} a^{2} r^{3} r_s^{3}+4\\\\cos{\\\\theta}^{2} \\\\left(a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} a^{4} r^{2} r_s^{2}-4\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{8} r^{3} r_s^{5}+4\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{10} r^{2} r_s^{4}+4\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{2} r_s^{4}-4\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} r_s^{3} r+42\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{5} r_s^{5}-4\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{4} r_s^{4}-396\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{10} r^{4} r_s^{2}+148\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{10} r^{3} r_s^{3}-48\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{12} r^{2} r_s^{2}+2\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{10} r^{2} r_s^{4}-4\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{12} r_s^{3} r-4\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} r_s^{3} r+4\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{10} r_s^{2}-452\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{8} r^{6} r_s^{2}+380\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{8} r^{5} r_s^{3}-106\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{8} r^{4} r_s^{4}%\\n-4\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{4} r_s^{2}+4\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{3} r_s^{3}-2\\\\cos{\\\\theta}^{4} \\\\left(a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} a^{4} r^{2} r_s^{2}+2\\\\cos{\\\\theta}^{4} \\\\left(a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} a^{4} r_s^{3} r-2\\\\cos{\\\\theta}^{4} \\\\left(a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} a^{6} r_s^{2}-2\\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{2} a^{8} r^{4} r_s^{4}+\\\\cos{4\\\\theta} a^{8} r^{5} r_s^{3}+\\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{2} a^{10} r^{3} r_s^{3}-2\\\\cos{4\\\\theta} a^{6} r^{6} r_s^{4}+6\\\\cos{4\\\\theta} a^{6} r^{7} r_s^{3}+10\\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{2} a^{8} r^{5} r_s^{3}-2\\\\cos{4\\\\theta} a^{8} r^{6} r_s^{2}-4\\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{2} a^{10} r^{4} r_s^{2}-6\\\\cos{4\\\\theta} a^{6} r^{8} r_s^{2}-14\\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{2} a^{8} r^{6} r_s^{2}+4\\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{4} a^{10} r^{3} r_s^{3}-2\\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{4} a^{12} r^{2} r_s^{2}-10\\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{4} a^{10} r^{4} r_s^{2}-6\\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{2} a^{6} r^{6} r_s^{4}-4\\\\cos{4\\\\theta} a^{4} r^{8} r_s^{4}%\\n+6\\\\cos{4\\\\theta} a^{4} r^{9} r_s^{3}+12\\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{2} a^{6} r^{7} r_s^{3}+\\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{2} a^{6} r^{5} r_s^{5}+\\\\cos{4\\\\theta} a^{4} r^{7} r_s^{5}-4\\\\cos{4\\\\theta} a^{4} r^{10} r_s^{2}-10\\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{2} a^{6} r^{8} r_s^{2}+7\\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{4} a^{8} r^{5} r_s^{3}-8\\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{4} a^{8} r^{6} r_s^{2}-2\\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{4} a^{8} r^{4} r_s^{4}+2\\\\cos{\\\\theta}^{2} a^{8} r^{4} r_s^{4}-a^{8} r^{5} r_s^{3}-\\\\cos{\\\\theta}^{2} a^{10} r^{3} r_s^{3}+2a^{6} r^{6} r_s^{4}-18a^{6} r^{7} r_s^{3}-42\\\\cos{\\\\theta}^{2} a^{8} r^{5} r_s^{3}+2a^{8} r^{6} r_s^{2}+4\\\\cos{\\\\theta}^{2} a^{10} r^{4} r_s^{2}+30a^{6} r^{8} r_s^{2}+102\\\\cos{\\\\theta}^{2} a^{8} r^{6} r_s^{2}-24\\\\cos{\\\\theta}^{4} a^{10} r^{3} r_s^{3}%\\n+2\\\\cos{\\\\theta}^{4} a^{12} r^{2} r_s^{2}+114\\\\cos{\\\\theta}^{4} a^{10} r^{4} r_s^{2}+68\\\\cos{\\\\theta}^{2} a^{6} r^{6} r_s^{4}+18a^{4} r^{8} r_s^{4}-66a^{4} r^{9} r_s^{3}-240\\\\cos{\\\\theta}^{2} a^{6} r^{7} r_s^{3}-\\\\cos{\\\\theta}^{2} a^{6} r^{5} r_s^{5}-a^{4} r^{7} r_s^{5}+82a^{4} r^{10} r_s^{2}+316\\\\cos{\\\\theta}^{2} a^{6} r^{8} r_s^{2}-263\\\\cos{\\\\theta}^{4} a^{8} r^{5} r_s^{3}+412\\\\cos{\\\\theta}^{4} a^{8} r^{6} r_s^{2}+52\\\\cos{\\\\theta}^{4} a^{8} r^{4} r_s^{4}+116a^{2} r^{12} r_s^{2}+444\\\\cos{\\\\theta}^{2} a^{4} r^{10} r_s^{2}-114r^{13} r_s^{3}+70r^{14} r_s^{2}+266\\\\cos{\\\\theta}^{2} a^{2} r^{12} r_s^{2}-30\\\\cos{\\\\theta}^{2} a^{4} r^{7} r_s^{5}-2a^{2} r^{9} r_s^{5}%\\n+48a^{2} r^{10} r_s^{4}+188\\\\cos{\\\\theta}^{2} a^{4} r^{8} r_s^{4}-126a^{2} r^{11} r_s^{3}-450\\\\cos{\\\\theta}^{2} a^{4} r^{9} r_s^{3}+172\\\\cos{\\\\theta}^{4} a^{6} r^{6} r_s^{4}-472\\\\cos{\\\\theta}^{4} a^{6} r^{7} r_s^{3}-50\\\\cos{\\\\theta}^{2} a^{2} r^{9} r_s^{5}-22r^{11} r_s^{5}+82r^{12} r_s^{4}+230\\\\cos{\\\\theta}^{2} a^{2} r^{10} r_s^{4}-378\\\\cos{\\\\theta}^{2} a^{2} r^{11} r_s^{3}+146\\\\cos{\\\\theta}^{4} a^{4} r^{8} r_s^{4}-372\\\\cos{\\\\theta}^{4} a^{4} r^{9} r_s^{3}+560\\\\cos{\\\\theta}^{4} a^{6} r^{8} r_s^{2}-124\\\\cos{\\\\theta}^{6} a^{8} r^{5} r_s^{3}+206\\\\cos{\\\\theta}^{6} a^{10} r^{4} r_s^{2}+224\\\\cos{\\\\theta}^{6} a^{8} r^{6} r_s^{2}+340\\\\cos{\\\\theta}^{4} a^{4} r^{10} r_s^{2}-56\\\\cos{\\\\theta}^{6} a^{6} r^{7} r_s^{3}+140\\\\cos{\\\\theta}^{6} a^{6} r^{8} r_s^{2}%\\n-30\\\\cos{\\\\theta}^{4} a^{6} r^{5} r_s^{5}+36\\\\cos{\\\\theta}^{6} a^{8} r^{4} r_s^{4}-93\\\\cos{\\\\theta}^{6} a^{10} r^{3} r_s^{3}-10\\\\cos{\\\\theta}^{4} a^{4} r^{7} r_s^{5}-38\\\\cos{\\\\theta}^{6} a^{6} r^{6} r_s^{4}+42\\\\cos{\\\\theta}^{6} a^{12} r^{2} r_s^{2}+22\\\\cos{\\\\theta}^{8} a^{10} r^{3} r_s^{3}+30\\\\cos{\\\\theta}^{8} a^{12} r^{2} r_s^{2}-36\\\\cos{\\\\theta}^{8} a^{10} r^{4} r_s^{2}+70\\\\cos{\\\\theta}^{8} a^{8} r^{5} r_s^{3}-26\\\\cos{\\\\theta}^{8} a^{8} r^{6} r_s^{2}-2\\\\cos{\\\\theta}^{6} a^{8} r^{3} r_s^{5}+2\\\\cos{\\\\theta}^{6} a^{10} r^{2} r_s^{4}+4\\\\cos{\\\\theta}^{8} a^{10} r^{2} r_s^{4}-4\\\\cos{\\\\theta}^{8} a^{12} r_s^{3} r+18\\\\cos{\\\\theta}^{6} a^{6} r^{5} r_s^{5}-36\\\\cos{\\\\theta}^{8} a^{8} r^{4} r_s^{4}+\\\\cos{4\\\\theta} a^{8} r^{7} r_s+3\\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{2} a^{10} r^{5} r_s+2\\\\cos{4\\\\theta} a^{6} r^{9} r_s%\\n+6\\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{2} a^{8} r^{7} r_s+3\\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{4} a^{12} r^{3} r_s+6\\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{4} a^{10} r^{5} r_s+\\\\cos{4\\\\theta} a^{4} r^{11} r_s+3\\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{2} a^{6} r^{9} r_s+3\\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{4} a^{8} r^{7} r_s-a^{8} r^{7} r_s-3\\\\cos{\\\\theta}^{2} a^{10} r^{5} r_s-14a^{6} r^{9} r_s-62\\\\cos{\\\\theta}^{2} a^{8} r^{7} r_s-3\\\\cos{\\\\theta}^{4} a^{12} r^{3} r_s-102\\\\cos{\\\\theta}^{4} a^{10} r^{5} r_s-33a^{4} r^{11} r_s-143\\\\cos{\\\\theta}^{2} a^{6} r^{9} r_s-219\\\\cos{\\\\theta}^{4} a^{8} r^{7} r_s-36a^{2} r^{13} r_s-152\\\\cos{\\\\theta}^{2} a^{4} r^{11} r_s-16r^{15} r_s-68\\\\cos{\\\\theta}^{2} a^{2} r^{13} r_s-224\\\\cos{\\\\theta}^{4} a^{6} r^{9} r_s%\\n-129\\\\cos{\\\\theta}^{6} a^{10} r^{5} r_s-120\\\\cos{\\\\theta}^{6} a^{8} r^{7} r_s-104\\\\cos{\\\\theta}^{4} a^{4} r^{11} r_s-64\\\\cos{\\\\theta}^{6} a^{6} r^{9} r_s-74\\\\cos{\\\\theta}^{6} a^{12} r^{3} r_s-8\\\\cos{\\\\theta}^{8} a^{12} r^{3} r_s+4\\\\cos{\\\\theta}^{8} a^{10} r^{5} r_s-8\\\\cos{\\\\theta}^{8} a^{8} r^{7} r_s-2\\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{6} a^{12} r^{2} r_s^{2}+\\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{6} a^{14} r r_s+2\\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{6} a^{12} r^{3} r_s-2\\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{6} a^{10} r^{4} r_s^{2}+\\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{6} a^{10} r^{5} r_s+\\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{6} a^{10} r^{3} r_s^{3}-\\\\cos{\\\\theta}^{6} a^{14} r r_s-20\\\\cos{\\\\theta}^{8} a^{14} r r_s-28\\\\cos{\\\\theta}^{10} a^{12} r^{2} r_s^{2}+12\\\\cos{\\\\theta}^{10} a^{14} r r_s+16\\\\cos{\\\\theta}^{10} a^{12} r^{3} r_s-22\\\\cos{\\\\theta}^{10} a^{10} r^{4} r_s^{2}%\\n+4\\\\cos{\\\\theta}^{10} a^{10} r^{5} r_s-2\\\\cos{\\\\theta}^{10} a^{12} r_s^{3} r+2\\\\cos{\\\\theta}^{10} a^{14} r_s^{2}+18\\\\cos{\\\\theta}^{10} a^{10} r^{3} r_s^{3}+208\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{8} r_s^{3}-48\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{7} r_s^{4}+80\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{6} r^{6} r_s^{3}+92\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{6} r_s^{3}+4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{8} r^{4} r_s^{3}-92\\\\partial_{r}\\\\left(r^{2}\\\\right) a^{4} r^{9} r_s^{2}+68\\\\partial_{r}\\\\left(r^{2}\\\\right) a^{4} r^{8} r_s^{3}-24\\\\partial_{r}\\\\left(r^{2}\\\\right) a^{6} r^{7} r_s^{2}-176\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{6} r^{7} r_s^{2}-40\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{8} r^{5} r_s^{2}-72\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{8} r^{5} r_s^{2}-8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{10} r^{3} r_s^{2}+124\\\\partial_{r}\\\\left(r^{2}\\\\right) a^{2} r^{10} r_s^{3}-48\\\\partial_{r}\\\\left(r^{2}\\\\right) a^{2} r^{9} r_s^{4}-168\\\\partial_{r}\\\\left(r^{2}\\\\right) a^{2} r^{11} r_s^{2}-456\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{9} r_s^{2}%\\n-456\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{7} r_s^{2}+60\\\\partial_{r}\\\\left(r^{2}\\\\right) a^{4} r^{10} r_s+12\\\\partial_{r}\\\\left(r^{2}\\\\right) a^{6} r^{8} r_s+192\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{6} r^{8} r_s+32\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{8} r^{6} r_s+216\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{8} r^{6} r_s+24\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{10} r^{4} r_s+116\\\\partial_{r}\\\\left(r^{2}\\\\right) a^{2} r^{12} r_s+448\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{10} r_s+680\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{8} r_s-216\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{8} r^{5} r_s^{2}+8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{8} r^{4} r_s^{3}+16\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{10} r^{3} r_s^{2}+96\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{10} r^{4} r_s+512\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{8} r^{6} r_s+264\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{2} r^{10} r_s^{3}-80\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{2} r^{9} r_s^{4}+276\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{4} r^{8} r_s^{3}-52\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{4} r^{7} r_s^{4}+100\\\\partial_{r}\\\\left(r^{2}\\\\right) r^{12} r_s^{3}%\\n-44\\\\partial_{r}\\\\left(r^{2}\\\\right) r^{11} r_s^{4}-116\\\\partial_{r}\\\\left(r^{2}\\\\right) r^{13} r_s^{2}-400\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{2} r^{11} r_s^{2}-552\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{4} r^{9} r_s^{2}+68\\\\partial_{r}\\\\left(r^{2}\\\\right) r^{14} r_s+288\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{2} r^{12} r_s+488\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{4} r^{10} r_s-384\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{6} r^{7} r_s^{2}+144\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{6} r^{6} r_s^{3}+416\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{6} r^{8} r_s+208\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{8} r_s^{3}-48\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{7} r_s^{4}+80\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{6} r^{6} r_s^{3}+92\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{6} r_s^{3}+4\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{8} r^{4} r_s^{3}-92\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{4} r^{9} r_s^{2}+68\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{4} r^{8} r_s^{3}-24\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{6} r^{7} r_s^{2}-176\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{6} r^{7} r_s^{2}-40\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{8} r^{5} r_s^{2}%\\n-72\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{8} r^{5} r_s^{2}-8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{10} r^{3} r_s^{2}+124\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{2} r^{10} r_s^{3}-48\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{2} r^{9} r_s^{4}-168\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{2} r^{11} r_s^{2}-456\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{9} r_s^{2}-456\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{7} r_s^{2}+60\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{4} r^{10} r_s+12\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{6} r^{8} r_s+192\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{6} r^{8} r_s+32\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{8} r^{6} r_s+216\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{8} r^{6} r_s+24\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{10} r^{4} r_s+116\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{2} r^{12} r_s+448\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{10} r_s+680\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{8} r_s-216\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{8} r^{5} r_s^{2}+8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{8} r^{4} r_s^{3}+16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{10} r^{3} r_s^{2}+96\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{10} r^{4} r_s%\\n+512\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{8} r^{6} r_s+264\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{2} r^{10} r_s^{3}-80\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{2} r^{9} r_s^{4}+276\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{4} r^{8} r_s^{3}-52\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{4} r^{7} r_s^{4}+100\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) r^{12} r_s^{3}-44\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) r^{11} r_s^{4}-116\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) r^{13} r_s^{2}-400\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{2} r^{11} r_s^{2}-552\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{4} r^{9} r_s^{2}+68\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) r^{14} r_s+288\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{2} r^{12} r_s+488\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{4} r^{10} r_s-384\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{6} r^{7} r_s^{2}+144\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{6} r^{6} r_s^{3}+416\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{6} r^{8} r_s+8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{6} r_s^{5}-16\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{6} r^{5} r_s^{4}+8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{6} r_s^{5}-16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{6} r^{5} r_s^{4}%\\n-20\\\\partial_{r}\\\\left(r^{2}\\\\right) a^{4} r^{7} r_s^{4}+12\\\\partial_{r}\\\\left(r^{2}\\\\right) a^{6} r^{6} r_s^{3}-20\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{4} r^{7} r_s^{4}+12\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{6} r^{6} r_s^{3}+8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{8} r^{4} r_s^{3}+8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{8} r^{4} r_s^{3}+8\\\\partial_{r}\\\\left(r^{2}\\\\right) a^{2} r^{8} r_s^{5}+8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{2} r^{8} r_s^{5}+8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{2} r^{8} r_s^{5}+8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{2} r^{8} r_s^{5}+8\\\\partial_{r}\\\\left(r^{2}\\\\right) r^{10} r_s^{5}+8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) r^{10} r_s^{5}+4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{8} r^{3} r_s^{4}+4\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{8} r^{3} r_s^{4}-4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{10} r^{2} r_s^{3}-4\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{10} r^{2} r_s^{3}-8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{10} r^{2} r_s^{3}-8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{10} r^{2} r_s^{3}+8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{12} r_s^{2} r+8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{12} r_s^{2} r%\\n-16\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{6} r^{5} r_s^{4}-16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{6} r^{5} r_s^{4}-48\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{8} a^{10} r^{3} r_s^{2}+4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{8} a^{12} r_s^{2} r-48\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{8} a^{10} r^{3} r_s^{2}+4\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{8} a^{12} r_s^{2} r-4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{8} a^{14} r_s-4\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{8} a^{14} r_s+196\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{8} a^{10} r^{4} r_s+12\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{8} a^{12} r^{2} r_s+196\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{8} a^{10} r^{4} r_s+12\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{8} a^{12} r^{2} r_s-132\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{8} a^{8} r^{5} r_s^{2}-132\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{8} a^{8} r^{5} r_s^{2}+180\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{8} a^{8} r^{6} r_s+180\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{8} a^{8} r^{6} r_s+8\\\\cos{2\\\\theta} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} a^{2} r^{2}+8\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} a^{4}-4\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} a^{2} \\\\sin{2\\\\theta}-4\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} a^{2} \\\\sin{2\\\\theta}%\\n-16\\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} r^{4}-16\\\\cos{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} a^{2} r^{2}+12\\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} r^{3} r_s+12\\\\cos{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} a^{2} r r_s+8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} r^{3}+8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} r^{3}-8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} r^{2} r_s-8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} r^{2} r_s+8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} a^{2} r+8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} a^{2} r-8\\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} a^{2} r^{2}-8\\\\cos{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} a^{4}-8\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{8} r^{4} r_s^{4}+8\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{8} r^{5} r_s^{3}+8\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{10} r^{3} r_s^{3}-8\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{6} r^{6} r_s^{4}+24\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{6} r^{7} r_s^{3}+40\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{8} r^{5} r_s^{3}+4\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{3} r_s^{3}-16\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{5} r_s^{3}%\\n+88\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{6} r_s^{2}+32\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{4} r_s^{2}-28\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{5} r_s^{3}-104\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{7} r_s^{3}+192\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{8} r_s^{2}+128\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{6} r_s^{2}+16\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{6} r_s^{4}-20\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{7} r_s^{3}+20\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{8} r_s^{4}-68\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{9} r_s^{3}+2\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{8} r^{3} r_s^{5}-4\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{4} r_s^{4}+48\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{7} r_s^{4}-8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{6} r_s^{5}+16\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{6} r^{5} r_s^{4}+48\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{7} r_s^{4}-8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{6} r_s^{5}+16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{6} r^{5} r_s^{4}+12\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{5} r_s^{4}-4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{8} r^{3} r_s^{4}%\\n+12\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{5} r_s^{4}-4\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{8} r^{3} r_s^{4}-56\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{6} r_s^{3}+8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{5} r_s^{4}-24\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{4} r_s^{3}-56\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{6} r_s^{3}+8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{5} r_s^{4}-24\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{4} r_s^{3}-64\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{4} r^{8} r_s^{3}+20\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{4} r^{7} r_s^{4}-12\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{6} r^{6} r_s^{3}-64\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{4} r^{8} r_s^{3}+20\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{4} r^{7} r_s^{4}-12\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{6} r^{6} r_s^{3}-88\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{6} r^{6} r_s^{3}-88\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{6} r^{6} r_s^{3}+80\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{7} r_s^{2}-24\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{6} r_s^{3}+16\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{5} r_s^{2}+80\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{7} r_s^{2}%\\n-24\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{6} r_s^{3}+16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{5} r_s^{2}+4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{10} r^{2} r_s^{3}+4\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{10} r^{2} r_s^{3}+128\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{5} r_s^{2}+16\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{3} r_s^{2}+128\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{5} r_s^{2}+16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{3} r_s^{2}+36\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{2} r^{9} r_s^{4}-8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{2} r^{8} r_s^{5}+36\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{2} r^{9} r_s^{4}-8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{2} r^{8} r_s^{5}-40\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{8} r_s^{3}+8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{7} r_s^{4}-40\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{8} r_s^{3}+8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{7} r_s^{4}-60\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{2} r^{10} r_s^{3}-60\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{2} r^{10} r_s^{3}-104\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{8} r_s^{3}-104\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{8} r_s^{3}%\\n+72\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{9} r_s^{2}+72\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{9} r_s^{2}-44\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{6} r_s^{3}-44\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{6} r_s^{3}+136\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{7} r_s^{2}+136\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{7} r_s^{2}-8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{8} r^{4} r_s^{3}-8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{8} r^{4} r_s^{3}+84\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{10} r_s^{2}+48\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{8} r_s^{2}-16\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{8} r^{6} r_s^{2}-32\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{10} r^{4} r_s^{2}-24\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{6} r^{8} r_s^{2}-56\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{8} r^{6} r_s^{2}-104\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{7} r_s-96\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{5} r_s-136\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{9} r_s-144\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{7} r_s+68\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{4} r^{9} r_s^{2}+24\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{6} r^{7} r_s^{2}%\\n+68\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{4} r^{9} r_s^{2}+24\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{6} r^{7} r_s^{2}+136\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{6} r^{7} r_s^{2}+40\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{8} r^{5} r_s^{2}+136\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{6} r^{7} r_s^{2}+40\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{8} r^{5} r_s^{2}-88\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{8} r_s-32\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{6} r_s-88\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{8} r_s-32\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{6} r_s-200\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{6} r_s-64\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{4} r_s-200\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{6} r_s-64\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{4} r_s+44\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{2} r^{11} r_s^{2}+44\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{2} r^{11} r_s^{2}+96\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{9} r_s^{2}+96\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{9} r_s^{2}-56\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{10} r_s-56\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{10} r_s%\\n-136\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{8} r_s-136\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{8} r_s-44\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{11} r_s-36\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{9} r_s+16\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} a^{10} r^{3} r_s^{3}-16\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} a^{12} r^{2} r_s^{2}-40\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} a^{10} r^{4} r_s^{2}+86\\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} a^{10} r^{3} r_s^{3}-102\\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} a^{12} r^{2} r_s^{2}-178\\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} a^{10} r^{4} r_s^{2}-8\\\\cos{\\\\theta}^{6} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} r^{2} r_s^{2}-24\\\\cos{\\\\theta}^{6} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} r^{3} r_s+16\\\\cos{\\\\theta}^{6} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{4} r_s^{2}-56\\\\cos{\\\\theta}^{6} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{5} r_s-4\\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} a^{10} r^{2} r_s^{4}+4\\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} a^{12} r_s^{3} r+8\\\\cos{\\\\theta}^{6} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{3} r_s^{3}+8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{10} r^{2} r_s^{3}+8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{10} r^{2} r_s^{3}+72\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{5} r_s^{2}%\\n-16\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{4} r_s^{3}+48\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{3} r_s^{2}+72\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{5} r_s^{2}-16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{4} r_s^{3}+48\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{3} r_s^{2}-8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{10} r^{3} r_s^{2}-8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{12} r_s^{2} r-8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{10} r^{3} r_s^{2}-8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{12} r_s^{2} r-136\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{4} r_s-32\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} r^{2} r_s-136\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{4} r_s-32\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} r^{2} r_s-104\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{6} r_s-104\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{6} r_s+32\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{8} a^{8} r^{4} r_s^{3}+32\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{8} a^{8} r^{4} r_s^{3}-6\\\\left(\\\\sin{\\\\theta}^{2} a^{2} r^{2} r_s-\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r_s+2r^{4} r_s+2\\\\cos{\\\\theta}^{2} a^{2} r^{2} r_s-2\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r\\\\right)^{2} r^{4} r_s^{2}+2\\\\left(\\\\sin{\\\\theta}^{2} a^{2} r^{2} r_s-\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r_s+2r^{4} r_s+2\\\\cos{\\\\theta}^{2} a^{2} r^{2} r_s-2\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r\\\\right)^{2} r^{3} r_s^{3}-2\\\\left(\\\\sin{\\\\theta}^{2} a^{2} r^{2} r_s-\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r_s+2r^{4} r_s+2\\\\cos{\\\\theta}^{2} a^{2} r^{2} r_s-2\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r\\\\right)^{2} a^{2} r^{2} r_s^{2}%\\n+6\\\\left(\\\\sin{\\\\theta}^{2} a^{2} r^{2} r_s-\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r_s+2r^{4} r_s+2\\\\cos{\\\\theta}^{2} a^{2} r^{2} r_s-2\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r\\\\right)^{2} r^{5} r_s+4\\\\left(\\\\sin{\\\\theta}^{2} a^{2} r^{2} r_s-\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r_s+2r^{4} r_s+2\\\\cos{\\\\theta}^{2} a^{2} r^{2} r_s-2\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r\\\\right)^{2} a^{2} r^{3} r_s+8\\\\cos{\\\\theta}^{2} \\\\left(\\\\sin{\\\\theta}^{2} a^{2} r^{2} r_s-\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r_s+2r^{4} r_s+2\\\\cos{\\\\theta}^{2} a^{2} r^{2} r_s-2\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r\\\\right)^{2} a^{2} r^{3} r_s-4\\\\cos{\\\\theta}^{2} \\\\left(\\\\sin{\\\\theta}^{2} a^{2} r^{2} r_s-\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r_s+2r^{4} r_s+2\\\\cos{\\\\theta}^{2} a^{2} r^{2} r_s-2\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r\\\\right)^{2} a^{2} r^{2} r_s^{2}+4\\\\cos{\\\\theta}^{2} \\\\left(\\\\sin{\\\\theta}^{2} a^{2} r^{2} r_s-\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r_s+2r^{4} r_s+2\\\\cos{\\\\theta}^{2} a^{2} r^{2} r_s-2\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r\\\\right)^{2} a^{4} r r_s+8\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{8} r^{7} r_s+24\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{10} r^{5} r_s+8\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{6} r^{9} r_s+24\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{8} r^{7} r_s+116\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{6} r^{9} r_s+248\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{8} r^{7} r_s+60\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{11} r_s+152\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{9} r_s+248\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{10} r^{5} r_s+176\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{8} r^{7} r_s+32\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{8}+48\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{6}+32\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{10}+48\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{8}+12\\\\sin{\\\\theta}^{2} a^{6} r^{9} r_s%\\n+56\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{8} r^{7} r_s+20\\\\sin{\\\\theta}^{2} a^{4} r^{11} r_s+96\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{10} r^{5} r_s+56\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{7} r_s^{2}+64\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{8} r^{5} r_s^{2}+56\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{7} r_s^{2}+64\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{8} r^{5} r_s^{2}-24\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{4} r^{10} r_s-12\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{6} r^{8} r_s-24\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{4} r^{10} r_s-12\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{6} r^{8} r_s-64\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{6} r^{8} r_s-32\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{8} r^{6} r_s-64\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{6} r^{8} r_s-32\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{8} r^{6} r_s+32\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{9}+16\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{7}+32\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{9}+16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{7}-48\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{8} r^{6} r_s%\\n-24\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{10} r^{4} r_s-48\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{8} r^{6} r_s-24\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{10} r^{4} r_s+96\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{7}+48\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{5}+96\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{7}+48\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{5}-12\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{2} r^{12} r_s-12\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{2} r^{12} r_s-32\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{10} r_s-32\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{10} r_s+16\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{11}+16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{11}-24\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{8} r_s-24\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{8} r_s+48\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{9}+48\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{9}-32\\\\partial_{r}\\\\left(r^{2}\\\\right) a^{2} r^{13}-16\\\\partial_{r}\\\\left(r^{2}\\\\right) a^{4} r^{11}-160\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{11}%\\n-80\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{6} r^{9}-32\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{2} r^{13}-16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{4} r^{11}-160\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{11}-80\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{6} r^{9}-320\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{9}-160\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{8} r^{7}-320\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{9}-160\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{8} r^{7}-320\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{8} r^{7}-160\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{10} r^{5}-320\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{8} r^{7}-160\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{10} r^{5}+8\\\\sin{\\\\theta}^{2} a^{2} r^{13} r_s-16\\\\partial_{r}\\\\left(r^{2}\\\\right) r^{15}-80\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{2} r^{13}-16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) r^{15}-80\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{2} r^{13}-160\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{4} r^{11}-160\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{4} r^{11}%\\n+8\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{12}+8\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{10}-160\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{6} r^{9}-160\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{6} r^{9}+24\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} a^{12} r^{3} r_s+24\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} a^{10} r^{5} r_s+116\\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} a^{12} r^{3} r_s+96\\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} a^{10} r^{5} r_s+32\\\\cos{\\\\theta}^{6} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} r^{4}+32\\\\cos{\\\\theta}^{6} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{6}+72\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{12} r^{3} r_s+96\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{5}+48\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} r^{3}+96\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{5}+48\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} r^{3}+48\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{7}+48\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{7}-160\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{8} a^{10} r^{5}-80\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{8} a^{12} r^{3}-160\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{8} a^{10} r^{5}%\\n-80\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{8} a^{12} r^{3}-80\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{8} a^{8} r^{7}-80\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{8} a^{8} r^{7}-2\\\\left(\\\\sin{\\\\theta}^{2} a^{2} r^{2} r_s-\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r_s+2r^{4} r_s+2\\\\cos{\\\\theta}^{2} a^{2} r^{2} r_s-2\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r\\\\right)^{2} r^{6}-2\\\\left(\\\\sin{\\\\theta}^{2} a^{2} r^{2} r_s-\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r_s+2r^{4} r_s+2\\\\cos{\\\\theta}^{2} a^{2} r^{2} r_s-2\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r\\\\right)^{2} a^{2} r^{4}-4\\\\cos{\\\\theta}^{2} \\\\left(\\\\sin{\\\\theta}^{2} a^{2} r^{2} r_s-\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r_s+2r^{4} r_s+2\\\\cos{\\\\theta}^{2} a^{2} r^{2} r_s-2\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r\\\\right)^{2} a^{2} r^{4}-4\\\\cos{\\\\theta}^{2} \\\\left(\\\\sin{\\\\theta}^{2} a^{2} r^{2} r_s-\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r_s+2r^{4} r_s+2\\\\cos{\\\\theta}^{2} a^{2} r^{2} r_s-2\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r\\\\right)^{2} a^{4} r^{2}-16\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{8} r^{4} r_s^{3}-16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{8} r^{4} r_s^{3}+8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{10} r^{3} r_s^{2}+8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{10} r^{3} r_s^{2}-8\\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{4} a^{12} r^{2} r_s^{2}+8\\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{4} a^{14} r r_s+8\\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{4} a^{12} r^{3} r_s-22\\\\cos{\\\\theta}^{10} \\\\sin{\\\\theta}^{2} a^{12} r^{2} r_s^{2}+20\\\\cos{\\\\theta}^{10} \\\\sin{\\\\theta}^{2} a^{14} r r_s+20\\\\cos{\\\\theta}^{10} \\\\sin{\\\\theta}^{2} a^{12} r^{3} r_s+4\\\\cos{\\\\theta}^{8} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{10} r r_s-4\\\\cos{\\\\theta}^{8} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} r^{3} r_s+8\\\\cos{\\\\theta}^{8} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{10} r^{2}%\\n+8\\\\cos{\\\\theta}^{8} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} r^{4}+20\\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} a^{14} r r_s+2\\\\cos{\\\\theta}^{10} \\\\sin{\\\\theta}^{2} a^{12} r_s^{3} r-2\\\\cos{\\\\theta}^{10} \\\\sin{\\\\theta}^{2} a^{14} r_s^{2}-4\\\\cos{\\\\theta}^{8} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} r^{2} r_s^{2}-24\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{4} r_s+8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{3} r_s^{2}-24\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} r^{2} r_s-24\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{4} r_s+8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{3} r_s^{2}-24\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} r^{2} r_s+8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} a^{12} r^{2} r_s-4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} a^{12} r_s^{2} r+4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} a^{14} r_s+8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} a^{12} r^{2} r_s-4\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} a^{12} r_s^{2} r+4\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} a^{14} r_s+32\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} r^{3}+16\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{10} r+32\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} r^{3}%\\n+16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{10} r+16\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{5}+16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{5}+32\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{10} a^{10} r^{4} r_s-16\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{10} a^{10} r^{3} r_s^{2}+32\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{10} a^{12} r^{2} r_s+32\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{10} a^{10} r^{4} r_s-16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{10} a^{10} r^{3} r_s^{2}+32\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{10} a^{12} r^{2} r_s-32\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{10} a^{12} r^{3}-16\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{10} a^{14} r-32\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{10} a^{12} r^{3}-16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{10} a^{14} r-16\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{10} a^{10} r^{5}-16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{10} a^{10} r^{5}+4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} a^{10} r^{4} r_s-4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} a^{10} r^{3} r_s^{2}+4\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} a^{10} r^{4} r_s-4\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} a^{10} r^{3} r_s^{2}-2\\\\cos{\\\\theta}^{4} \\\\left(\\\\sin{\\\\theta}^{2} a^{2} r^{2} r_s-\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r_s+2r^{4} r_s+2\\\\cos{\\\\theta}^{2} a^{2} r^{2} r_s-2\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r\\\\right)^{2} a^{4} r^{2}%\\n+2\\\\cos{\\\\theta}^{4} \\\\left(\\\\sin{\\\\theta}^{2} a^{2} r^{2} r_s-\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r_s+2r^{4} r_s+2\\\\cos{\\\\theta}^{2} a^{2} r^{2} r_s-2\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r\\\\right)^{2} a^{4} r r_s-2\\\\cos{\\\\theta}^{4} \\\\left(\\\\sin{\\\\theta}^{2} a^{2} r^{2} r_s-\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r_s+2r^{4} r_s+2\\\\cos{\\\\theta}^{2} a^{2} r^{2} r_s-2\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r\\\\right)^{2} a^{6}}{8\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} r^{2}-8\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} r r_s+8\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} a^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{\\\\theta}= & \\\\frac{-8\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{8} r^{4} r_s^{4}-48\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{8} r^{5} r_s^{3}-20\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{10} r^{3} r_s^{3}+8\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{6} r^{5} r_s^{5}+8\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2} a^{8} r^{4} r_s^{4}+56\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2} a^{8} r^{5} r_s^{3}+16\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2} a^{10} r^{3} r_s^{3}+16\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{8} r^{4} r_s^{4}-136\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{8} r^{5} r_s^{3}-64\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{10} r^{3} r_s^{3}+176\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{8} r^{6} r_s^{2}+184\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{10} r^{4} r_s^{2}-96\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{6} r^{7} r_s^{3}-216\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2} a^{8} r^{6} r_s^{2}-192\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2} a^{10} r^{4} r_s^{2}+320\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{8} r^{6} r_s^{2}+208\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{10} r^{4} r_s^{2}+64\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{12} r^{2} r_s^{2}-56\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2} a^{12} r^{2} r_s^{2}%\\n+48\\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{12} r^{2} r_s^{2}-168\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{4} r^{8} r_s^{4}+40\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{4} r^{7} r_s^{5}-48\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2} a^{6} r^{6} r_s^{4}+272\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2} a^{6} r^{7} r_s^{3}+208\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2} a^{8} r^{5} r_s^{3}-72\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{6} r^{6} r_s^{4}+124\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{6} r^{7} r_s^{3}-8\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{8} r^{5} r_s^{3}-8\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2} a^{6} r^{5} r_s^{5}-16\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2} a^{8} r^{4} r_s^{4}+4\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{6} r^{5} r_s^{5}+208\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{6} r^{8} r_s^{2}+216\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{4} r^{9} r_s^{3}-368\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2} a^{6} r^{8} r_s^{2}-408\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2} a^{8} r^{6} r_s^{2}-24\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{6} r^{8} r_s^{2}+64\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{8} r^{6} r_s^{2}-192\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2} a^{10} r^{4} r_s^{2}+48\\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{10} r^{4} r_s^{2}%\\n+56\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2} a^{10} r^{3} r_s^{3}-12\\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{10} r^{3} r_s^{3}-4\\\\sin{\\\\theta}^{2} \\\\sin{2\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{6} r_s^{4}-4\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\sin{2\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{4} r_s^{4}+8\\\\sin{\\\\theta}^{2} \\\\sin{2\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{7} r_s^{3}+16\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\sin{2\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{5} r_s^{3}+8\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\sin{2\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{10} r^{3} r_s^{3}-12\\\\sin{\\\\theta}^{2} \\\\sin{2\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{8} r_s^{4}-20\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\sin{2\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{6} r_s^{4}+4\\\\sin{\\\\theta}^{2} \\\\sin{2\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{7} r_s^{5}+4\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\sin{2\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{5} r_s^{5}+12\\\\sin{\\\\theta}^{2} \\\\sin{2\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{9} r_s^{3}+28\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\sin{2\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{7} r_s^{3}+20\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\sin{2\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{5} r_s^{3}-8\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\sin{2\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{4} r_s^{4}-8\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{5} r_s^{3} \\\\sin{2\\\\theta}-8\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{3} r_s^{3} \\\\sin{2\\\\theta}+16\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{6} r_s^{2} \\\\sin{2\\\\theta}+32\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{4} r_s^{2} \\\\sin{2\\\\theta}+16\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{10} r^{2} r_s^{2} \\\\sin{2\\\\theta}%\\n-40\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{7} r_s^{3} \\\\sin{2\\\\theta}-64\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{5} r_s^{3} \\\\sin{2\\\\theta}+12\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{6} r_s^{4} \\\\sin{2\\\\theta}+12\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{4} r_s^{4} \\\\sin{2\\\\theta}+44\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{8} r_s^{2} \\\\sin{2\\\\theta}+100\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{6} r_s^{2} \\\\sin{2\\\\theta}+68\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{4} r_s^{2} \\\\sin{2\\\\theta}-24\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{3} r_s^{3} \\\\sin{2\\\\theta}-8\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{5} r_s^{3} \\\\sin{2\\\\theta}-8\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{3} r_s^{3} \\\\sin{2\\\\theta}+16\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{6} r_s^{2} \\\\sin{2\\\\theta}+32\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{4} r_s^{2} \\\\sin{2\\\\theta}+16\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{10} r^{2} r_s^{2} \\\\sin{2\\\\theta}-40\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{7} r_s^{3} \\\\sin{2\\\\theta}-64\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{5} r_s^{3} \\\\sin{2\\\\theta}+12\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{6} r_s^{4} \\\\sin{2\\\\theta}+12\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{4} r_s^{4} \\\\sin{2\\\\theta}+44\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{8} r_s^{2} \\\\sin{2\\\\theta}+100\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{6} r_s^{2} \\\\sin{2\\\\theta}+68\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{4} r_s^{2} \\\\sin{2\\\\theta}%\\n-24\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{3} r_s^{3} \\\\sin{2\\\\theta}-36\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{9} r_s^{3} \\\\sin{2\\\\theta}-68\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{7} r_s^{3} \\\\sin{2\\\\theta}+20\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{8} r_s^{4} \\\\sin{2\\\\theta}+28\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{6} r_s^{4} \\\\sin{2\\\\theta}+28\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{10} r_s^{2} \\\\sin{2\\\\theta}+68\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{8} r_s^{2} \\\\sin{2\\\\theta}+52\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{6} r_s^{2} \\\\sin{2\\\\theta}-36\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{5} r_s^{3} \\\\sin{2\\\\theta}-36\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{9} r_s^{3} \\\\sin{2\\\\theta}-68\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{7} r_s^{3} \\\\sin{2\\\\theta}+20\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{8} r_s^{4} \\\\sin{2\\\\theta}+28\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{6} r_s^{4} \\\\sin{2\\\\theta}+28\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{10} r_s^{2} \\\\sin{2\\\\theta}+68\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{8} r_s^{2} \\\\sin{2\\\\theta}+52\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{6} r_s^{2} \\\\sin{2\\\\theta}-36\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{5} r_s^{3} \\\\sin{2\\\\theta}-4\\\\sin{\\\\theta}^{2} \\\\sin{2\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{8} r_s^{2}-12\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\sin{2\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{6} r_s^{2}-12\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\sin{2\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{10} r^{4} r_s^{2}%\\n-4\\\\sin{\\\\theta}^{2} \\\\sin{2\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{10} r_s^{2}-12\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\sin{2\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{8} r_s^{2}-12\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\sin{2\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{6} r_s^{2}-8\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{7} \\\\sin{2\\\\theta} r_s-24\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{5} \\\\sin{2\\\\theta} r_s-24\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{10} r^{3} \\\\sin{2\\\\theta} r_s-16\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{9} \\\\sin{2\\\\theta} r_s-48\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{7} \\\\sin{2\\\\theta} r_s-48\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{5} \\\\sin{2\\\\theta} r_s-8\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{7} \\\\sin{2\\\\theta} r_s-24\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{5} \\\\sin{2\\\\theta} r_s-24\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{10} r^{3} \\\\sin{2\\\\theta} r_s-16\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{9} \\\\sin{2\\\\theta} r_s-48\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{7} \\\\sin{2\\\\theta} r_s-48\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{5} \\\\sin{2\\\\theta} r_s-8\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{11} \\\\sin{2\\\\theta} r_s-24\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{9} \\\\sin{2\\\\theta} r_s-24\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{7} \\\\sin{2\\\\theta} r_s-8\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{11} \\\\sin{2\\\\theta} r_s-24\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{9} \\\\sin{2\\\\theta} r_s%\\n-24\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{7} \\\\sin{2\\\\theta} r_s-4\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\sin{2\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{12} r^{2} r_s^{2}-4\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\sin{2\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{10} r^{4} r_s^{2}+4\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\sin{2\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{10} r^{3} r_s^{3}-8\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{12} \\\\sin{2\\\\theta} r r_s-16\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{10} r^{3} \\\\sin{2\\\\theta} r_s+12\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{10} r^{2} r_s^{2} \\\\sin{2\\\\theta}-8\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{12} \\\\sin{2\\\\theta} r r_s-16\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{10} r^{3} \\\\sin{2\\\\theta} r_s+12\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{10} r^{2} r_s^{2} \\\\sin{2\\\\theta}-8\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{5} \\\\sin{2\\\\theta} r_s+12\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{4} r_s^{2} \\\\sin{2\\\\theta}-8\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{5} \\\\sin{2\\\\theta} r_s+12\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{4} r_s^{2} \\\\sin{2\\\\theta}-4\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{5} r_s^{5} \\\\sin{2\\\\theta}-4\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{5} r_s^{5} \\\\sin{2\\\\theta}+8\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{4} r_s^{4} \\\\sin{2\\\\theta}+8\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{4} r_s^{4} \\\\sin{2\\\\theta}-4\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{7} r_s^{5} \\\\sin{2\\\\theta}-4\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{7} r_s^{5} \\\\sin{2\\\\theta}%\\n-4\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{3} r_s^{3} \\\\sin{2\\\\theta}-4\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{3} r_s^{3} \\\\sin{2\\\\theta}-32\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{6} r_s^{4}-16\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{4} r_s^{4}+128\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{7} r_s^{3}+112\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{5} r_s^{3}+32\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{10} r^{3} r_s^{3}-80\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{8} r_s^{4}-64\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{6} r_s^{4}+16\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{7} r_s^{5}+8\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{5} r_s^{5}+144\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{9} r_s^{3}+152\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{7} r_s^{3}+64\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{5} r_s^{3}-16\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{4} r_s^{4}+8\\\\cos{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{7} r_s^{3}+16\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{5} r_s^{3}-16\\\\cos{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{8} r_s^{2}-48\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{6} r_s^{2}-48\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{10} r^{4} r_s^{2}%\\n+48\\\\cos{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{9} r_s^{3}-16\\\\cos{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{8} r_s^{4}-48\\\\cos{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{10} r_s^{2}-160\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{8} r_s^{2}-192\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{6} r_s^{2}+8\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{10} r^{3} r_s^{3}-16\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{12} r^{2} r_s^{2}-96\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{10} r^{4} r_s^{2}-32\\\\cos{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{10} r_s^{4}+8\\\\cos{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{9} r_s^{5}+48\\\\cos{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{11} r_s^{3}-32\\\\cos{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{12} r_s^{2}-112\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{10} r_s^{2}-144\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{8} r_s^{2}-80\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{6} r_s^{2}+8\\\\cos{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{9} r_s+32\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{7} r_s+48\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{10} r^{5} r_s+16\\\\cos{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{11} r_s+64\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{9} r_s%\\n+96\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{7} r_s+32\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{12} r^{3} r_s+64\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{10} r^{5} r_s+8\\\\cos{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{13} r_s+32\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{11} r_s+48\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{9} r_s+32\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{7} r_s-16\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{12} r^{2} r_s^{2}-16\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{10} r^{4} r_s^{2}+8\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{10} r^{3} r_s^{3}+8\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{14} r r_s+16\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{12} r^{3} r_s+8\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{10} r^{5} r_s+2\\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{2} r_s^{2}-2\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{2} r_s^{2}+2\\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{4} r_s^{2}-2\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{4} r_s^{2}-\\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{3} r_s^{3}+\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{3} r_s^{3}-16\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{4} r_s^{2}%\\n+4\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{3} r_s^{3}-8\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{2} r_s^{2}-8\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{6} r_s^{2}+4\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{5} r_s^{3}-\\\\cos{4\\\\theta} \\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{3} r_s+\\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{3} r_s-2\\\\cos{4\\\\theta} \\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{5} r_s-2\\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{5} r_s+2\\\\cos{4\\\\theta} \\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{4} r_s^{2}-2\\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{4} r_s^{2}-11\\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{7} r_s+6\\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{6} r_s^{2}+\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{5} r_s+2\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{3} r_s-12\\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{9} r_s+16\\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{8} r_s^{2}-\\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{10} r r_s+\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{10} r r_s-2\\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{3} r_s+12\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{3} r_s%\\n+4\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{10} r r_s+12\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{5} r_s+2\\\\cos{4\\\\theta} \\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{6} r_s^{2}-\\\\cos{4\\\\theta} \\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{5} r_s^{3}+\\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{5} r_s^{3}-4\\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{7} r_s^{3}+8\\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} r^{10} r_s^{2}-4\\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} r^{9} r_s^{3}-\\\\cos{4\\\\theta} \\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{7} r_s-4\\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} r^{11} r_s-\\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{5} r_s+4\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{7} r_s+8\\\\cos{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{2}+8\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4}-4\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{2} \\\\sin{2\\\\theta}-4\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{2} \\\\sin{2\\\\theta}+4\\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} r^{3} r_s+4\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{2} r r_s+8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} r^{3}-8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} r^{2} r_s%\\n-8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} r^{2} r_s+8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{2} r+8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{2} r+8\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} r^{3}-8\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} r^{3}-8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{2} r+8\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{2} r-8\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{2} r-8\\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{2}-8\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4}+64\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{6} r_s^{4}-72\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{7} r_s^{3}-72\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{5} r_s^{3}+80\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{8} r_s^{4}+32\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{9} r_s^{3}+96\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{7} r_s^{3}-24\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{10} r^{3} r_s^{3}+96\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{5} r_s^{3}-72\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{3} r_s^{3}+144\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{4} r_s^{2}%\\n+72\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{2} r_s^{2}-184\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{5} r_s^{3}+200\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{6} r_s^{2}+136\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{4} r_s^{2}-192\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{8} r_s^{4}-128\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{10} r_s^{4}+240\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{11} r_s^{3}+472\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{9} r_s^{3}-128\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{6} r_s^{4}+456\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{7} r_s^{3}+8\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{5} r_s^{3}+16\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{7} r_s^{3}-64\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{8} r_s^{2}-56\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{6} r_s^{2}-24\\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{4} r^{9} r_s^{3}-88\\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{2} r^{10} r_s^{4}+96\\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{2} r^{11} r_s^{3}+28\\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{2} r^{9} r_s^{5}-28\\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{6} r^{7} r_s^{3}-32\\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} r^{12} r_s^{4}%\\n+48\\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} r^{13} r_s^{3}+24\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{9} r_s^{5}+32\\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{10} r_s^{4}+8\\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} r^{11} r_s^{5}-24\\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{9} r_s^{3}+24\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{7} r_s^{5}+88\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{8} r_s^{2}+8\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} r^{9} r_s^{3}-24\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} r^{10} r_s^{2}-112\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{7} r_s^{3}+72\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{6} r_s^{2}+8\\\\cos{\\\\theta} \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{6} r^{6} r_s^{4} \\\\sin{2\\\\theta}+8\\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{8} r^{4} r_s^{4} \\\\sin{2\\\\theta}-8\\\\cos{\\\\theta} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{4} r^{7} r_s^{5} \\\\sin{2\\\\theta}-8\\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{6} r^{5} r_s^{5} \\\\sin{2\\\\theta}+32\\\\cos{\\\\theta} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{4} r^{8} r_s^{4} \\\\sin{2\\\\theta}+64\\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{6} r^{6} r_s^{4} \\\\sin{2\\\\theta}+32\\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{8} r^{4} r_s^{4} \\\\sin{2\\\\theta}-8\\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2} a^{4} r^{8} r_s^{4} \\\\sin{\\\\theta} \\\\sin{2\\\\theta}-16\\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{6} r^{6} r_s^{4} \\\\sin{\\\\theta} \\\\sin{2\\\\theta}%\\n-8\\\\cos{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{8} r^{4} r_s^{4} \\\\sin{\\\\theta} \\\\sin{2\\\\theta}+8\\\\cos{\\\\theta} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{5} r_s^{3} \\\\sin{\\\\theta} \\\\sin{2\\\\theta}+8\\\\cos{\\\\theta}^{3} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{3} r_s^{3} \\\\sin{\\\\theta} \\\\sin{2\\\\theta}-8\\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2} a^{2} r^{10} r_s^{4} \\\\sin{\\\\theta} \\\\sin{2\\\\theta}-16\\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{4} r^{8} r_s^{4} \\\\sin{\\\\theta} \\\\sin{2\\\\theta}-8\\\\cos{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{6} r^{6} r_s^{4} \\\\sin{\\\\theta} \\\\sin{2\\\\theta}+8\\\\cos{\\\\theta} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{7} r_s^{3} \\\\sin{\\\\theta} \\\\sin{2\\\\theta}+8\\\\cos{\\\\theta}^{3} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{5} r_s^{3} \\\\sin{\\\\theta} \\\\sin{2\\\\theta}+16\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{6} r^{5} r_s^{3}+16\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{8} r^{3} r_s^{3}-24\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{4} r^{6} r_s^{4}-24\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{6} r^{4} r_s^{4}+96\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{4} r^{7} r_s^{3}+192\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{6} r^{5} r_s^{3}+96\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{8} r^{3} r_s^{3}-56\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2} a^{4} r^{7} r_s^{3} \\\\sin{\\\\theta}-112\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{6} r^{5} r_s^{3} \\\\sin{\\\\theta}-56\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{8} r^{3} r_s^{3} \\\\sin{\\\\theta}-136\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2} a^{2} r^{9} r_s^{3} \\\\sin{\\\\theta}-296\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{4} r^{7} r_s^{3} \\\\sin{\\\\theta}%\\n-184\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{6} r^{5} r_s^{3} \\\\sin{\\\\theta}-16\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{6} r_s^{2} \\\\sin{\\\\theta}-32\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{4} r_s^{2} \\\\sin{\\\\theta}+16\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{6} r^{5} r_s^{3}+16\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{8} r^{3} r_s^{3}-24\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{4} r^{6} r_s^{4}-24\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{6} r^{4} r_s^{4}+96\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{4} r^{7} r_s^{3}+192\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{6} r^{5} r_s^{3}+96\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{8} r^{3} r_s^{3}-56\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\tan{\\\\theta}^{2} a^{4} r^{7} r_s^{3} \\\\sin{\\\\theta}-112\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{6} r^{5} r_s^{3} \\\\sin{\\\\theta}-56\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{8} r^{3} r_s^{3} \\\\sin{\\\\theta}-136\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\tan{\\\\theta}^{2} a^{2} r^{9} r_s^{3} \\\\sin{\\\\theta}-296\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{4} r^{7} r_s^{3} \\\\sin{\\\\theta}-184\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{6} r^{5} r_s^{3} \\\\sin{\\\\theta}-16\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{6} r_s^{2} \\\\sin{\\\\theta}-32\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{4} r_s^{2} \\\\sin{\\\\theta}+32\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{4} r^{7} r_s^{3}+48\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{6} r^{5} r_s^{3}%\\n-88\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{2} r^{8} r_s^{4}-152\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{4} r^{6} r_s^{4}+176\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{2} r^{9} r_s^{3}+432\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{4} r^{7} r_s^{3}+336\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{6} r^{5} r_s^{3}-8\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2} r^{11} r_s^{3} \\\\sin{\\\\theta}+104\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{2} r^{9} r_s^{3} \\\\sin{\\\\theta}+304\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{4} r^{7} r_s^{3} \\\\sin{\\\\theta}-16\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} r^{8} r_s^{2} \\\\sin{\\\\theta}-32\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{6} r_s^{2} \\\\sin{\\\\theta}+32\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{4} r^{7} r_s^{3}+48\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{6} r^{5} r_s^{3}-88\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{2} r^{8} r_s^{4}-152\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{4} r^{6} r_s^{4}+176\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{2} r^{9} r_s^{3}+432\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{4} r^{7} r_s^{3}+336\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{6} r^{5} r_s^{3}-8\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\tan{\\\\theta}^{2} r^{11} r_s^{3} \\\\sin{\\\\theta}+104\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{2} r^{9} r_s^{3} \\\\sin{\\\\theta}+304\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{4} r^{7} r_s^{3} \\\\sin{\\\\theta}%\\n-16\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} r^{8} r_s^{2} \\\\sin{\\\\theta}-32\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{6} r_s^{2} \\\\sin{\\\\theta}+8\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{5} r_s^{5}-32\\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{4} r_s^{4}+24\\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{4} r^{8} r_s^{4}+24\\\\cos{\\\\theta}^{6} \\\\tan{\\\\theta}^{2} a^{6} r^{6} r_s^{4}+8\\\\cos{\\\\theta}^{8} \\\\tan{\\\\theta}^{2} a^{8} r^{4} r_s^{4}-16\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{5} r_s^{3}-8\\\\cos{\\\\theta}^{6} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{3} r_s^{3}+24\\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{2} r^{10} r_s^{4}+24\\\\cos{\\\\theta}^{6} \\\\tan{\\\\theta}^{2} a^{4} r^{8} r_s^{4}+8\\\\cos{\\\\theta}^{8} \\\\tan{\\\\theta}^{2} a^{6} r^{6} r_s^{4}-16\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{7} r_s^{3}-8\\\\cos{\\\\theta}^{6} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{5} r_s^{3}-8\\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{9} r_s^{3}-24\\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{6} r^{7} r_s^{3}-24\\\\cos{\\\\theta}^{6} \\\\tan{\\\\theta}^{2} a^{8} r^{5} r_s^{3}+8\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{6} r_s^{2}+16\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{4} r_s^{2}-32\\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{11} r_s^{3}%\\n-112\\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{4} r^{9} r_s^{3}-144\\\\cos{\\\\theta}^{6} \\\\tan{\\\\theta}^{2} a^{6} r^{7} r_s^{3}+32\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{8} r_s^{2}+80\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{6} r_s^{2}+32\\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{10} r^{3} r_s^{3}-8\\\\cos{\\\\theta}^{8} \\\\tan{\\\\theta}^{2} a^{10} r^{3} r_s^{3}+8\\\\cos{\\\\theta}^{6} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{2} r_s^{2}-80\\\\cos{\\\\theta}^{8} \\\\tan{\\\\theta}^{2} a^{8} r^{5} r_s^{3}+64\\\\cos{\\\\theta}^{6} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{4} r_s^{2}+8\\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{10} r_s^{4}-8\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{7} r_s^{3}+8\\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} r^{12} r_s^{4}-8\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} r^{9} r_s^{3}-24\\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} r^{13} r_s^{3}-88\\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{2} r^{11} r_s^{3}-120\\\\cos{\\\\theta}^{6} \\\\tan{\\\\theta}^{2} a^{4} r^{9} r_s^{3}+24\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} r^{10} r_s^{2}+64\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{8} r_s^{2}+216\\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{5} r_s^{3}-72\\\\cos{\\\\theta}^{8} \\\\tan{\\\\theta}^{2} a^{6} r^{7} r_s^{3}%\\n+56\\\\cos{\\\\theta}^{6} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{6} r_s^{2}-8\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{6} r^{4} r_s^{4}-8\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{6} r^{4} r_s^{4}+16\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{4} r^{5} r_s^{5}+16\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{4} r^{5} r_s^{5}-64\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{6} r^{4} r_s^{4}-64\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{6} r^{4} r_s^{4}+96\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{4} r^{6} r_s^{4} \\\\sin{\\\\theta}+96\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{4} r^{6} r_s^{4} \\\\sin{\\\\theta}+40\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{6} r^{4} r_s^{4} \\\\sin{\\\\theta}+40\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{6} r^{4} r_s^{4} \\\\sin{\\\\theta}+8\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{3} r_s^{3} \\\\sin{\\\\theta}+8\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{3} r_s^{3} \\\\sin{\\\\theta}-56\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{2} r^{8} r_s^{4} \\\\sin{\\\\theta}-56\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{2} r^{8} r_s^{4} \\\\sin{\\\\theta}-104\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{4} r^{6} r_s^{4} \\\\sin{\\\\theta}-104\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{4} r^{6} r_s^{4} \\\\sin{\\\\theta}+8\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{5} r_s^{3} \\\\sin{\\\\theta}+8\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{5} r_s^{3} \\\\sin{\\\\theta}-8\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{4} r^{6} r_s^{4}%\\n-8\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{4} r^{6} r_s^{4}+16\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{2} r^{7} r_s^{5}+16\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{2} r^{7} r_s^{5}+56\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2} a^{2} r^{8} r_s^{4} \\\\sin{\\\\theta}+56\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\tan{\\\\theta}^{2} a^{2} r^{8} r_s^{4} \\\\sin{\\\\theta}+8\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{5} r_s^{3} \\\\sin{\\\\theta}+8\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{5} r_s^{3} \\\\sin{\\\\theta}+8\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} r^{7} r_s^{3} \\\\sin{\\\\theta}+8\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} r^{7} r_s^{3} \\\\sin{\\\\theta}-32\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{7} r_s^{5}-16\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{5} r_s^{5}+8\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{4} r^{5} r_s^{5} \\\\sin{\\\\theta}+8\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{4} r^{5} r_s^{5} \\\\sin{\\\\theta}-8\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{4} r^{5} r_s^{5} \\\\sin{\\\\theta}-8\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{4} r^{5} r_s^{5} \\\\sin{\\\\theta}-48\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{4} r_s^{4}+40\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{4} r_s^{4}-48\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{7} \\\\tan{\\\\theta}^{2} a^{6} r^{4} r_s^{4} \\\\sin{\\\\theta}-48\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{7} \\\\tan{\\\\theta}^{2} a^{6} r^{4} r_s^{4} \\\\sin{\\\\theta}-8\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} \\\\tan{\\\\theta}^{2} a^{4} r^{3} r_s^{3}%\\n-8\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} \\\\tan{\\\\theta}^{2} a^{2} r^{5} r_s^{3}+40\\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2} a^{6} r^{7} r_s^{3}+16\\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{8} r_s^{4}+32\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{6} r_s^{4}+8\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2} a^{4} r^{6} r_s^{4} \\\\sin{\\\\theta}+8\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\tan{\\\\theta}^{2} a^{4} r^{6} r_s^{4} \\\\sin{\\\\theta}+48\\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{5} r_s^{3}-40\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{5} r_s^{3}+8\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} \\\\tan{\\\\theta}^{2} a^{4} r^{4} r_s^{2}+32\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} \\\\tan{\\\\theta}^{2} a^{2} r^{6} r_s^{2}+16\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{4} r_s^{4}+8\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{6} r^{4} r_s^{4} \\\\sin{\\\\theta}+8\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{6} r^{4} r_s^{4} \\\\sin{\\\\theta}+48\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{3} r_s^{3}-40\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{3} r_s^{3}-24\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{7} \\\\tan{\\\\theta}^{2} a^{8} r^{3} r_s^{3} \\\\sin{\\\\theta}-24\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{7} \\\\tan{\\\\theta}^{2} a^{8} r^{3} r_s^{3} \\\\sin{\\\\theta}+8\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} \\\\tan{\\\\theta}^{2} a^{6} r^{2} r_s^{2}+48\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} \\\\tan{\\\\theta}^{2} a^{4} r^{4} r_s^{2}-40\\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2} a^{4} r^{8} r_s^{4}%\\n-16\\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{9} r_s^{5}+8\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{2} r^{7} r_s^{5} \\\\sin{\\\\theta}+8\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{2} r^{7} r_s^{5} \\\\sin{\\\\theta}-8\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2} a^{2} r^{7} r_s^{5} \\\\sin{\\\\theta}-8\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\tan{\\\\theta}^{2} a^{2} r^{7} r_s^{5} \\\\sin{\\\\theta}-48\\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{6} r_s^{4}+40\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{6} r_s^{4}-8\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} \\\\tan{\\\\theta}^{2} a^{2} r^{5} r_s^{3}-8\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} \\\\tan{\\\\theta}^{2} r^{7} r_s^{3}+120\\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2} a^{4} r^{9} r_s^{3}+144\\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{7} r_s^{3}+24\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} \\\\tan{\\\\theta}^{2} r^{8} r_s^{2}+240\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{5} r_s^{3}+264\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{7} \\\\tan{\\\\theta}^{2} a^{6} r^{5} r_s^{3} \\\\sin{\\\\theta}+264\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{7} \\\\tan{\\\\theta}^{2} a^{6} r^{5} r_s^{3} \\\\sin{\\\\theta}+40\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} \\\\tan{\\\\theta}^{2} a^{2} r^{6} r_s^{2}-176\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{10} r_s^{2}-384\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{8} r_s^{2}-416\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{6} r_s^{2}-72\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{5} r_s%\\n-72\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{3} r_s+8\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{7} r_s+24\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{5} r_s-192\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{12} r_s^{2}-464\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{10} r_s^{2}-576\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{8} r_s^{2}+80\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{9} r_s+96\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{7} r_s+48\\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{4} r^{10} r_s^{2}-40\\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{2} r^{12} r_s^{2}+56\\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{6} r^{8} r_s^{2}-88\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{4} r^{10} r_s^{2}-32\\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{12} r_s^{2}-32\\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} r^{14} r_s^{2}+24\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} r^{11} r_s-24\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{7} r_s-16\\\\cos{\\\\theta} \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{6} r^{7} r_s^{3} \\\\sin{2\\\\theta}-32\\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{8} r^{5} r_s^{3} \\\\sin{2\\\\theta}-40\\\\cos{\\\\theta} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{4} r^{9} r_s^{3} \\\\sin{2\\\\theta}-120\\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{6} r^{7} r_s^{3} \\\\sin{2\\\\theta}%\\n-120\\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{8} r^{5} r_s^{3} \\\\sin{2\\\\theta}+16\\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2} a^{4} r^{9} r_s^{3} \\\\sin{\\\\theta} \\\\sin{2\\\\theta}+48\\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{6} r^{7} r_s^{3} \\\\sin{\\\\theta} \\\\sin{2\\\\theta}+48\\\\cos{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{8} r^{5} r_s^{3} \\\\sin{\\\\theta} \\\\sin{2\\\\theta}-16\\\\cos{\\\\theta} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{6} r_s^{2} \\\\sin{\\\\theta} \\\\sin{2\\\\theta}-32\\\\cos{\\\\theta}^{3} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{4} r_s^{2} \\\\sin{\\\\theta} \\\\sin{2\\\\theta}+16\\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2} a^{2} r^{11} r_s^{3} \\\\sin{\\\\theta} \\\\sin{2\\\\theta}+48\\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{4} r^{9} r_s^{3} \\\\sin{\\\\theta} \\\\sin{2\\\\theta}+48\\\\cos{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{6} r^{7} r_s^{3} \\\\sin{\\\\theta} \\\\sin{2\\\\theta}-16\\\\cos{\\\\theta} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{8} r_s^{2} \\\\sin{\\\\theta} \\\\sin{2\\\\theta}-32\\\\cos{\\\\theta}^{3} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{6} r_s^{2} \\\\sin{\\\\theta} \\\\sin{2\\\\theta}-32\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{6} r^{6} r_s^{2}-64\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{8} r^{4} r_s^{2}-120\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{4} r^{8} r_s^{2}-360\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{6} r^{6} r_s^{2}-360\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{8} r^{4} r_s^{2}+88\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2} a^{4} r^{8} r_s^{2} \\\\sin{\\\\theta}+264\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{6} r^{6} r_s^{2} \\\\sin{\\\\theta}+264\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{8} r^{4} r_s^{2} \\\\sin{\\\\theta}+136\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2} a^{2} r^{10} r_s^{2} \\\\sin{\\\\theta}%\\n+368\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{4} r^{8} r_s^{2} \\\\sin{\\\\theta}+288\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{6} r^{6} r_s^{2} \\\\sin{\\\\theta}+8\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{7} \\\\sin{\\\\theta} r_s+24\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{5} \\\\sin{\\\\theta} r_s-32\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{6} r^{6} r_s^{2}-64\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{8} r^{4} r_s^{2}-120\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{4} r^{8} r_s^{2}-360\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{6} r^{6} r_s^{2}-360\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{8} r^{4} r_s^{2}+88\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\tan{\\\\theta}^{2} a^{4} r^{8} r_s^{2} \\\\sin{\\\\theta}+264\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{6} r^{6} r_s^{2} \\\\sin{\\\\theta}+264\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{8} r^{4} r_s^{2} \\\\sin{\\\\theta}+136\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\tan{\\\\theta}^{2} a^{2} r^{10} r_s^{2} \\\\sin{\\\\theta}+368\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{4} r^{8} r_s^{2} \\\\sin{\\\\theta}+288\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{6} r^{6} r_s^{2} \\\\sin{\\\\theta}+8\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{7} \\\\sin{\\\\theta} r_s+24\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{5} \\\\sin{\\\\theta} r_s-40\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{4} r^{8} r_s^{2}-88\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{6} r^{6} r_s^{2}-152\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{2} r^{10} r_s^{2}%\\n-488\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{4} r^{8} r_s^{2}-552\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{6} r^{6} r_s^{2}+16\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2} r^{12} r_s^{2} \\\\sin{\\\\theta}-56\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{2} r^{10} r_s^{2} \\\\sin{\\\\theta}-296\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{4} r^{8} r_s^{2} \\\\sin{\\\\theta}+8\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} r^{9} \\\\sin{\\\\theta} r_s+24\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{7} \\\\sin{\\\\theta} r_s-40\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{4} r^{8} r_s^{2}-88\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{6} r^{6} r_s^{2}-152\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{2} r^{10} r_s^{2}-488\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{4} r^{8} r_s^{2}-552\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{6} r^{6} r_s^{2}+16\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\tan{\\\\theta}^{2} r^{12} r_s^{2} \\\\sin{\\\\theta}-56\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{2} r^{10} r_s^{2} \\\\sin{\\\\theta}-296\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{4} r^{8} r_s^{2} \\\\sin{\\\\theta}+8\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} r^{9} \\\\sin{\\\\theta} r_s+24\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{7} \\\\sin{\\\\theta} r_s+16\\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{10} r_s^{2}+64\\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{6} r^{8} r_s^{2}+96\\\\cos{\\\\theta}^{6} \\\\tan{\\\\theta}^{2} a^{8} r^{6} r_s^{2}%\\n-16\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{7} r_s-48\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{5} r_s+40\\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{12} r_s^{2}+168\\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{4} r^{10} r_s^{2}+272\\\\cos{\\\\theta}^{6} \\\\tan{\\\\theta}^{2} a^{6} r^{8} r_s^{2}-40\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{9} r_s-128\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{7} r_s-224\\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{10} r^{4} r_s^{2}+64\\\\cos{\\\\theta}^{8} \\\\tan{\\\\theta}^{2} a^{10} r^{4} r_s^{2}-48\\\\cos{\\\\theta}^{6} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{3} r_s+208\\\\cos{\\\\theta}^{8} \\\\tan{\\\\theta}^{2} a^{8} r^{6} r_s^{2}-144\\\\cos{\\\\theta}^{6} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{5} r_s+24\\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} r^{14} r_s^{2}+104\\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{2} r^{12} r_s^{2}+176\\\\cos{\\\\theta}^{6} \\\\tan{\\\\theta}^{2} a^{4} r^{10} r_s^{2}-24\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} r^{11} r_s-80\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{9} r_s-384\\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{6} r_s^{2}+144\\\\cos{\\\\theta}^{8} \\\\tan{\\\\theta}^{2} a^{6} r^{8} r_s^{2}-96\\\\cos{\\\\theta}^{6} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{7} r_s%\\n-80\\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2} a^{6} r^{8} r_s^{2}-96\\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{6} r_s^{2}-16\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} \\\\tan{\\\\theta}^{2} a^{4} r^{5} r_s-40\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} \\\\tan{\\\\theta}^{2} a^{2} r^{7} r_s-192\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{4} r_s^{2}+16\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{7} \\\\tan{\\\\theta}^{2} a^{8} r^{4} r_s^{2} \\\\sin{\\\\theta}+16\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{7} \\\\tan{\\\\theta}^{2} a^{8} r^{4} r_s^{2} \\\\sin{\\\\theta}-32\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} \\\\tan{\\\\theta}^{2} a^{6} r^{3} r_s-88\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} \\\\tan{\\\\theta}^{2} a^{4} r^{5} r_s-120\\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2} a^{4} r^{10} r_s^{2}-144\\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{8} r_s^{2}-24\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} \\\\tan{\\\\theta}^{2} r^{9} r_s-336\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{6} r_s^{2}-392\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{7} \\\\tan{\\\\theta}^{2} a^{6} r^{6} r_s^{2} \\\\sin{\\\\theta}-392\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{7} \\\\tan{\\\\theta}^{2} a^{6} r^{6} r_s^{2} \\\\sin{\\\\theta}-56\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} \\\\tan{\\\\theta}^{2} a^{2} r^{7} r_s+24\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{2} r_s^{2}-24\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{10} r r_s+24\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{3} r_s-16\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{4} r_s^{2}%\\n+48\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{5} r_s-16\\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{10} r^{3} r_s^{3} \\\\sin{2\\\\theta}-40\\\\cos{\\\\theta}^{7} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{10} r^{3} r_s^{3} \\\\sin{2\\\\theta}+16\\\\cos{\\\\theta}^{7} \\\\tan{\\\\theta}^{2} a^{10} r^{3} r_s^{3} \\\\sin{\\\\theta} \\\\sin{2\\\\theta}-16\\\\cos{\\\\theta}^{5} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{2} r_s^{2} \\\\sin{\\\\theta} \\\\sin{2\\\\theta}+16\\\\cos{\\\\theta}^{7} \\\\tan{\\\\theta}^{2} a^{8} r^{5} r_s^{3} \\\\sin{\\\\theta} \\\\sin{2\\\\theta}-16\\\\cos{\\\\theta}^{5} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{4} r_s^{2} \\\\sin{\\\\theta} \\\\sin{2\\\\theta}-32\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{10} r^{2} r_s^{2}-120\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{7} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{10} r^{2} r_s^{2}+88\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{7} \\\\tan{\\\\theta}^{2} a^{10} r^{2} r_s^{2} \\\\sin{\\\\theta}+24\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{3} \\\\sin{\\\\theta} r_s-32\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{10} r^{2} r_s^{2}-120\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{7} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{10} r^{2} r_s^{2}+88\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{7} \\\\tan{\\\\theta}^{2} a^{10} r^{2} r_s^{2} \\\\sin{\\\\theta}+24\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{3} \\\\sin{\\\\theta} r_s-56\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{8} r^{4} r_s^{2}-248\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{7} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{8} r^{4} r_s^{2}+24\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{5} \\\\sin{\\\\theta} r_s-56\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{8} r^{4} r_s^{2}-248\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{7} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{8} r^{4} r_s^{2}%\\n+24\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{5} \\\\sin{\\\\theta} r_s+40\\\\cos{\\\\theta}^{10} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{10} r^{3} r_s^{3}-16\\\\cos{\\\\theta}^{10} \\\\tan{\\\\theta}^{2} a^{10} r^{3} r_s^{3}+16\\\\cos{\\\\theta}^{8} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{2} r_s^{2}-16\\\\cos{\\\\theta}^{10} \\\\tan{\\\\theta}^{2} a^{8} r^{5} r_s^{3}+16\\\\cos{\\\\theta}^{8} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{4} r_s^{2}-48\\\\cos{\\\\theta}^{10} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{12} r^{2} r_s^{2}+16\\\\cos{\\\\theta}^{10} \\\\tan{\\\\theta}^{2} a^{12} r^{2} r_s^{2}-16\\\\cos{\\\\theta}^{8} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{10} r r_s+72\\\\cos{\\\\theta}^{10} \\\\tan{\\\\theta}^{2} a^{10} r^{4} r_s^{2}-64\\\\cos{\\\\theta}^{8} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{3} r_s-128\\\\cos{\\\\theta}^{10} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{10} r^{4} r_s^{2}+56\\\\cos{\\\\theta}^{10} \\\\tan{\\\\theta}^{2} a^{8} r^{6} r_s^{2}-48\\\\cos{\\\\theta}^{8} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{5} r_s+16\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{8} r^{3} r_s^{3}+16\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{8} r^{3} r_s^{3}+80\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{7} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{8} r^{3} r_s^{3}+80\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{7} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{8} r^{3} r_s^{3}-16\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{2} r_s^{2} \\\\sin{\\\\theta}-16\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{2} r_s^{2} \\\\sin{\\\\theta}%\\n-16\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{4} r_s^{2} \\\\sin{\\\\theta}-16\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{4} r_s^{2} \\\\sin{\\\\theta}+96\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{3} r_s^{3}+72\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{9} \\\\tan{\\\\theta}^{2} a^{8} r^{3} r_s^{3} \\\\sin{\\\\theta}+72\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{9} \\\\tan{\\\\theta}^{2} a^{8} r^{3} r_s^{3} \\\\sin{\\\\theta}+16\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} \\\\tan{\\\\theta}^{2} a^{6} r^{2} r_s^{2}+16\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} \\\\tan{\\\\theta}^{2} a^{4} r^{4} r_s^{2}-96\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{2} r_s^{2}-40\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{9} \\\\tan{\\\\theta}^{2} a^{10} r^{2} r_s^{2} \\\\sin{\\\\theta}-40\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{9} \\\\tan{\\\\theta}^{2} a^{10} r^{2} r_s^{2} \\\\sin{\\\\theta}-16\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} \\\\tan{\\\\theta}^{2} a^{8} r r_s-56\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} \\\\tan{\\\\theta}^{2} a^{6} r^{3} r_s-240\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{4} r_s^{2}-200\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{9} \\\\tan{\\\\theta}^{2} a^{8} r^{4} r_s^{2} \\\\sin{\\\\theta}-200\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{9} \\\\tan{\\\\theta}^{2} a^{8} r^{4} r_s^{2} \\\\sin{\\\\theta}-40\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} \\\\tan{\\\\theta}^{2} a^{4} r^{5} r_s+8\\\\sin{\\\\theta}^{8} a^{8} r^{4} r_s^{4}-16\\\\sin{\\\\theta}^{8} a^{8} r^{5} r_s^{3}-16\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{8} a^{10} r^{3} r_s^{3}+24\\\\sin{\\\\theta}^{8} a^{6} r^{6} r_s^{4}%\\n-8\\\\sin{\\\\theta}^{8} a^{6} r^{5} r_s^{5}-24\\\\sin{\\\\theta}^{8} a^{6} r^{7} r_s^{3}-32\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{8} a^{8} r^{5} r_s^{3}+16\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{8} a^{8} r^{4} r_s^{4}-8\\\\sin{\\\\theta}^{6} a^{6} r^{5} r_s^{5}+24\\\\sin{\\\\theta}^{6} a^{6} r^{6} r_s^{4}+24\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6} a^{8} r^{4} r_s^{4}-32\\\\sin{\\\\theta}^{6} a^{4} r^{7} r_s^{5}+8\\\\sin{\\\\theta}^{6} a^{4} r^{6} r_s^{6}+48\\\\sin{\\\\theta}^{6} a^{4} r^{8} r_s^{4}+72\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6} a^{6} r^{6} r_s^{4}-24\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6} a^{6} r^{5} r_s^{5}-24\\\\sin{\\\\theta}^{6} a^{6} r^{7} r_s^{3}-48\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6} a^{8} r^{5} r_s^{3}-32\\\\sin{\\\\theta}^{6} a^{4} r^{9} r_s^{3}-72\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6} a^{6} r^{7} r_s^{3}-24\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{6} a^{10} r^{3} r_s^{3}-48\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{6} a^{8} r^{5} r_s^{3}+24\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{6} a^{8} r^{4} r_s^{4}-8\\\\sin{\\\\theta}^{2} \\\\left(\\\\sin{\\\\theta}^{4} a^{4} r r_s-\\\\sin{\\\\theta}^{2} a^{2} r^{2} r_s^{2}+2\\\\sin{\\\\theta}^{2} a^{2} r^{3} r_s+2\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r r_s-a^{2} r^{3} r_s-\\\\cos{\\\\theta}^{2} a^{4} r r_s+\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2}-r^{5} r_s-\\\\cos{\\\\theta}^{2} a^{2} r^{3} r_s+\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{2}\\\\right)^{2} r^{2} r_s^{2}%\\n+16\\\\sin{\\\\theta}^{2} \\\\left(\\\\sin{\\\\theta}^{4} a^{4} r r_s-\\\\sin{\\\\theta}^{2} a^{2} r^{2} r_s^{2}+2\\\\sin{\\\\theta}^{2} a^{2} r^{3} r_s+2\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r r_s-a^{2} r^{3} r_s-\\\\cos{\\\\theta}^{2} a^{4} r r_s+\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2}-r^{5} r_s-\\\\cos{\\\\theta}^{2} a^{2} r^{3} r_s+\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{2}\\\\right)^{2} r^{3} r_s+16\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(\\\\sin{\\\\theta}^{4} a^{4} r r_s-\\\\sin{\\\\theta}^{2} a^{2} r^{2} r_s^{2}+2\\\\sin{\\\\theta}^{2} a^{2} r^{3} r_s+2\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r r_s-a^{2} r^{3} r_s-\\\\cos{\\\\theta}^{2} a^{4} r r_s+\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2}-r^{5} r_s-\\\\cos{\\\\theta}^{2} a^{2} r^{3} r_s+\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{2}\\\\right)^{2} a^{2} r r_s+152\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2} a^{8} r^{7} r_s+216\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2} a^{10} r^{5} r_s+152\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2} a^{6} r^{9} r_s+216\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2} a^{8} r^{7} r_s-224\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{8} r^{7} r_s-32\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{6} r^{9} r_s-192\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{10} r^{5} r_s-56\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{8} r^{7} r_s+40\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{9} r_s+80\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{7} r_s+96\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{11} r_s+240\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{9} r_s+80\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{10} r^{5} r_s+320\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{7} r_s-32\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{6}-48\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{4}-64\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{8}-96\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{6}%\\n+56\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{13} r_s+160\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{11} r_s+240\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{9} r_s-32\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{10}-48\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{8}-24\\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{4} r^{11} r_s+4\\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{2} r^{13} r_s-28\\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{6} r^{9} r_s-120\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{8} r^{7} r_s-120\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{6} r^{9} r_s-192\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{10} r^{5} r_s+16\\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{13} r_s+8\\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} r^{15} r_s+8\\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{11} r_s-16\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{10}-8\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} r^{12}-8\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{8}+8\\\\cos{\\\\theta} \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{6} r^{8} r_s^{2} \\\\sin{2\\\\theta}+24\\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{8} r^{6} r_s^{2} \\\\sin{2\\\\theta}+16\\\\cos{\\\\theta} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{4} r^{10} r_s^{2} \\\\sin{2\\\\theta}%\\n+64\\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{6} r^{8} r_s^{2} \\\\sin{2\\\\theta}+96\\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{8} r^{6} r_s^{2} \\\\sin{2\\\\theta}-8\\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2} a^{4} r^{10} r_s^{2} \\\\sin{\\\\theta} \\\\sin{2\\\\theta}-32\\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{6} r^{8} r_s^{2} \\\\sin{\\\\theta} \\\\sin{2\\\\theta}-48\\\\cos{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{8} r^{6} r_s^{2} \\\\sin{\\\\theta} \\\\sin{2\\\\theta}+8\\\\cos{\\\\theta} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{7} \\\\sin{\\\\theta} \\\\sin{2\\\\theta} r_s+24\\\\cos{\\\\theta}^{3} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{5} \\\\sin{\\\\theta} \\\\sin{2\\\\theta} r_s-8\\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2} a^{2} r^{12} r_s^{2} \\\\sin{\\\\theta} \\\\sin{2\\\\theta}-32\\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{4} r^{10} r_s^{2} \\\\sin{\\\\theta} \\\\sin{2\\\\theta}-48\\\\cos{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{6} r^{8} r_s^{2} \\\\sin{\\\\theta} \\\\sin{2\\\\theta}+8\\\\cos{\\\\theta} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{9} \\\\sin{\\\\theta} \\\\sin{2\\\\theta} r_s+24\\\\cos{\\\\theta}^{3} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{7} \\\\sin{\\\\theta} \\\\sin{2\\\\theta} r_s+16\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{6} r^{7} r_s+48\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{8} r^{5} r_s+48\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{4} r^{9} r_s+192\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{6} r^{7} r_s+288\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{8} r^{5} r_s-40\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2} a^{4} r^{9} \\\\sin{\\\\theta} r_s-160\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{6} r^{7} \\\\sin{\\\\theta} r_s-240\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{8} r^{5} \\\\sin{\\\\theta} r_s%\\n-48\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2} a^{2} r^{11} \\\\sin{\\\\theta} r_s-160\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{4} r^{9} \\\\sin{\\\\theta} r_s-160\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{6} r^{7} \\\\sin{\\\\theta} r_s+16\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{6} r^{7} r_s+48\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{8} r^{5} r_s+48\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{4} r^{9} r_s+192\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{6} r^{7} r_s+288\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{8} r^{5} r_s-40\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\tan{\\\\theta}^{2} a^{4} r^{9} \\\\sin{\\\\theta} r_s-160\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{6} r^{7} \\\\sin{\\\\theta} r_s-240\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{8} r^{5} \\\\sin{\\\\theta} r_s-48\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\tan{\\\\theta}^{2} a^{2} r^{11} \\\\sin{\\\\theta} r_s-160\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{4} r^{9} \\\\sin{\\\\theta} r_s-160\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{6} r^{7} \\\\sin{\\\\theta} r_s+16\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{4} r^{9} r_s+48\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{6} r^{7} r_s+48\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{2} r^{11} r_s+192\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{4} r^{9} r_s+288\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{6} r^{7} r_s-8\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2} r^{13} \\\\sin{\\\\theta} r_s%\\n+80\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{4} r^{9} \\\\sin{\\\\theta} r_s+16\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{4} r^{9} r_s+48\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{6} r^{7} r_s+48\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{2} r^{11} r_s+192\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{4} r^{9} r_s+288\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{6} r^{7} r_s-8\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\tan{\\\\theta}^{2} r^{13} \\\\sin{\\\\theta} r_s+80\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{4} r^{9} \\\\sin{\\\\theta} r_s-8\\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{11} r_s-40\\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{6} r^{9} r_s-80\\\\cos{\\\\theta}^{6} \\\\tan{\\\\theta}^{2} a^{8} r^{7} r_s+8\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{8}+32\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{6}-16\\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{13} r_s-80\\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{4} r^{11} r_s-160\\\\cos{\\\\theta}^{6} \\\\tan{\\\\theta}^{2} a^{6} r^{9} r_s+16\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{10}+64\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{8}+240\\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{10} r^{5} r_s-80\\\\cos{\\\\theta}^{8} \\\\tan{\\\\theta}^{2} a^{10} r^{5} r_s%\\n+48\\\\cos{\\\\theta}^{6} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{4}-160\\\\cos{\\\\theta}^{8} \\\\tan{\\\\theta}^{2} a^{8} r^{7} r_s+96\\\\cos{\\\\theta}^{6} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{6}-8\\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} r^{15} r_s-40\\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{2} r^{13} r_s-80\\\\cos{\\\\theta}^{6} \\\\tan{\\\\theta}^{2} a^{4} r^{11} r_s+8\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} r^{12}+32\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{10}+200\\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{7} r_s-80\\\\cos{\\\\theta}^{8} \\\\tan{\\\\theta}^{2} a^{6} r^{9} r_s+48\\\\cos{\\\\theta}^{6} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{8}+40\\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2} a^{6} r^{9} r_s+48\\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{7} r_s+8\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} \\\\tan{\\\\theta}^{2} a^{4} r^{6}+16\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} \\\\tan{\\\\theta}^{2} a^{2} r^{8}+144\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{5} r_s+24\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} \\\\tan{\\\\theta}^{2} a^{6} r^{4}+48\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} \\\\tan{\\\\theta}^{2} a^{4} r^{6}+40\\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2} a^{4} r^{11} r_s+48\\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{9} r_s%\\n+8\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} \\\\tan{\\\\theta}^{2} r^{10}+144\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{7} r_s+160\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{7} \\\\tan{\\\\theta}^{2} a^{6} r^{7} \\\\sin{\\\\theta} r_s+160\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{7} \\\\tan{\\\\theta}^{2} a^{6} r^{7} \\\\sin{\\\\theta} r_s+24\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} \\\\tan{\\\\theta}^{2} a^{2} r^{8}+136\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2} a^{12} r^{3} r_s+136\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2} a^{10} r^{5} r_s-72\\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{12} r^{3} r_s-36\\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{10} r^{5} r_s+40\\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{12} r^{3} r_s-32\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{10} r^{2}-64\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{4}-32\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{6}-136\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{12} r^{3} r_s+24\\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{10} r^{4} r_s^{2} \\\\sin{2\\\\theta}+64\\\\cos{\\\\theta}^{7} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{10} r^{4} r_s^{2} \\\\sin{2\\\\theta}-32\\\\cos{\\\\theta}^{7} \\\\tan{\\\\theta}^{2} a^{10} r^{4} r_s^{2} \\\\sin{\\\\theta} \\\\sin{2\\\\theta}+24\\\\cos{\\\\theta}^{5} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{3} \\\\sin{\\\\theta} \\\\sin{2\\\\theta} r_s-32\\\\cos{\\\\theta}^{7} \\\\tan{\\\\theta}^{2} a^{8} r^{6} r_s^{2} \\\\sin{\\\\theta} \\\\sin{2\\\\theta}+24\\\\cos{\\\\theta}^{5} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{5} \\\\sin{\\\\theta} \\\\sin{2\\\\theta} r_s%\\n+48\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{10} r^{3} r_s+192\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{7} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{10} r^{3} r_s-160\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{7} \\\\tan{\\\\theta}^{2} a^{10} r^{3} \\\\sin{\\\\theta} r_s+48\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{10} r^{3} r_s+192\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{7} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{10} r^{3} r_s-160\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{7} \\\\tan{\\\\theta}^{2} a^{10} r^{3} \\\\sin{\\\\theta} r_s+48\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{8} r^{5} r_s+192\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{7} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{8} r^{5} r_s+48\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{8} r^{5} r_s+192\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{7} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{8} r^{5} r_s+96\\\\cos{\\\\theta}^{10} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{12} r^{3} r_s-40\\\\cos{\\\\theta}^{10} \\\\tan{\\\\theta}^{2} a^{12} r^{3} r_s+32\\\\cos{\\\\theta}^{8} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{10} r^{2}-80\\\\cos{\\\\theta}^{10} \\\\tan{\\\\theta}^{2} a^{10} r^{5} r_s+64\\\\cos{\\\\theta}^{8} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{4}+88\\\\cos{\\\\theta}^{10} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{10} r^{5} r_s-40\\\\cos{\\\\theta}^{10} \\\\tan{\\\\theta}^{2} a^{8} r^{7} r_s+32\\\\cos{\\\\theta}^{8} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{6}+144\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{3} r_s+80\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{9} \\\\tan{\\\\theta}^{2} a^{10} r^{3} \\\\sin{\\\\theta} r_s%\\n+80\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{9} \\\\tan{\\\\theta}^{2} a^{10} r^{3} \\\\sin{\\\\theta} r_s+24\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} \\\\tan{\\\\theta}^{2} a^{8} r^{2}+48\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} \\\\tan{\\\\theta}^{2} a^{6} r^{4}+144\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{5} r_s+120\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{9} \\\\tan{\\\\theta}^{2} a^{8} r^{5} \\\\sin{\\\\theta} r_s+120\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{9} \\\\tan{\\\\theta}^{2} a^{8} r^{5} \\\\sin{\\\\theta} r_s+24\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} \\\\tan{\\\\theta}^{2} a^{4} r^{6}+8\\\\sin{\\\\theta}^{8} a^{8} r^{6} r_s^{2}+16\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{8} a^{10} r^{4} r_s^{2}+8\\\\sin{\\\\theta}^{8} a^{6} r^{8} r_s^{2}+16\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{8} a^{8} r^{6} r_s^{2}+8\\\\sin{\\\\theta}^{6} a^{6} r^{8} r_s^{2}+24\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6} a^{8} r^{6} r_s^{2}+8\\\\sin{\\\\theta}^{6} a^{4} r^{10} r_s^{2}+24\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6} a^{6} r^{8} r_s^{2}+24\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{6} a^{10} r^{4} r_s^{2}+24\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{6} a^{8} r^{6} r_s^{2}-8\\\\sin{\\\\theta}^{2} \\\\left(\\\\sin{\\\\theta}^{4} a^{4} r r_s-\\\\sin{\\\\theta}^{2} a^{2} r^{2} r_s^{2}+2\\\\sin{\\\\theta}^{2} a^{2} r^{3} r_s+2\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r r_s-a^{2} r^{3} r_s-\\\\cos{\\\\theta}^{2} a^{4} r r_s+\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2}-r^{5} r_s-\\\\cos{\\\\theta}^{2} a^{2} r^{3} r_s+\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{2}\\\\right)^{2} r^{4}-16\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(\\\\sin{\\\\theta}^{4} a^{4} r r_s-\\\\sin{\\\\theta}^{2} a^{2} r^{2} r_s^{2}+2\\\\sin{\\\\theta}^{2} a^{2} r^{3} r_s+2\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r r_s-a^{2} r^{3} r_s-\\\\cos{\\\\theta}^{2} a^{4} r r_s+\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2}-r^{5} r_s-\\\\cos{\\\\theta}^{2} a^{2} r^{3} r_s+\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{2}\\\\right)^{2} a^{2} r^{2}+16\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{4} r_s^{4}%\\n-32\\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2} a^{12} r^{2} r_s^{2}+32\\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2} a^{14} r r_s+32\\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2} a^{12} r^{3} r_s+8\\\\cos{\\\\theta}^{10} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{12} r^{2} r_s^{2}-8\\\\cos{\\\\theta}^{10} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{14} r r_s-8\\\\cos{\\\\theta}^{10} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{12} r^{3} r_s+8\\\\cos{\\\\theta}^{10} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{14} r r_s+8\\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{10} r r_s-8\\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{12}-16\\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{10} r^{2}+8\\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{3} r_s-8\\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{4}-36\\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{14} r r_s+8\\\\cos{\\\\theta}^{7} \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{12} r^{2} r_s^{2} \\\\sin{2\\\\theta}+16\\\\cos{\\\\theta}^{9} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{12} r^{2} r_s^{2} \\\\sin{2\\\\theta}-8\\\\cos{\\\\theta}^{9} \\\\tan{\\\\theta}^{2} a^{12} r^{2} r_s^{2} \\\\sin{\\\\theta} \\\\sin{2\\\\theta}+8\\\\cos{\\\\theta}^{7} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{10} \\\\sin{\\\\theta} \\\\sin{2\\\\theta} r r_s-8\\\\cos{\\\\theta}^{9} \\\\tan{\\\\theta}^{2} a^{10} r^{4} r_s^{2} \\\\sin{\\\\theta} \\\\sin{2\\\\theta}+8\\\\cos{\\\\theta}^{7} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{3} \\\\sin{\\\\theta} \\\\sin{2\\\\theta} r_s+16\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{7} \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{12} r r_s%\\n+48\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{9} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{12} r r_s-40\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{9} \\\\tan{\\\\theta}^{2} a^{12} \\\\sin{\\\\theta} r r_s+16\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{7} \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{12} r r_s+48\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{9} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{12} r r_s-40\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{9} \\\\tan{\\\\theta}^{2} a^{12} \\\\sin{\\\\theta} r r_s+16\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{7} \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{10} r^{3} r_s+48\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{9} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{10} r^{3} r_s+16\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{7} \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{10} r^{3} r_s+48\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{9} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{10} r^{3} r_s-16\\\\cos{\\\\theta}^{12} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{12} r^{2} r_s^{2}+8\\\\cos{\\\\theta}^{12} \\\\tan{\\\\theta}^{2} a^{12} r^{2} r_s^{2}-8\\\\cos{\\\\theta}^{10} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{10} r r_s+8\\\\cos{\\\\theta}^{12} \\\\tan{\\\\theta}^{2} a^{10} r^{4} r_s^{2}-8\\\\cos{\\\\theta}^{10} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{3} r_s+16\\\\cos{\\\\theta}^{12} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{14} r r_s-8\\\\cos{\\\\theta}^{12} \\\\tan{\\\\theta}^{2} a^{14} r r_s+8\\\\cos{\\\\theta}^{10} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{12}-16\\\\cos{\\\\theta}^{12} \\\\tan{\\\\theta}^{2} a^{12} r^{3} r_s+16\\\\cos{\\\\theta}^{10} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{10} r^{2}+16\\\\cos{\\\\theta}^{12} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{12} r^{3} r_s%\\n-8\\\\cos{\\\\theta}^{12} \\\\tan{\\\\theta}^{2} a^{10} r^{5} r_s+8\\\\cos{\\\\theta}^{10} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{4}-8\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{7} \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{10} r^{2} r_s^{2}-8\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{7} \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{10} r^{2} r_s^{2}-32\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{9} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{10} r^{2} r_s^{2}-32\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{9} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{10} r^{2} r_s^{2}+8\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{7} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{8} \\\\sin{\\\\theta} r r_s+8\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{7} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{8} \\\\sin{\\\\theta} r r_s+8\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{7} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{3} \\\\sin{\\\\theta} r_s+8\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{7} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{3} \\\\sin{\\\\theta} r_s-48\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{2} r_s^{2}-32\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{11} \\\\tan{\\\\theta}^{2} a^{10} r^{2} r_s^{2} \\\\sin{\\\\theta}-32\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{11} \\\\tan{\\\\theta}^{2} a^{10} r^{2} r_s^{2} \\\\sin{\\\\theta}-8\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} \\\\tan{\\\\theta}^{2} a^{8} r r_s-8\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} \\\\tan{\\\\theta}^{2} a^{6} r^{3} r_s+48\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{10} r r_s+32\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{11} \\\\tan{\\\\theta}^{2} a^{12} \\\\sin{\\\\theta} r r_s+32\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{11} \\\\tan{\\\\theta}^{2} a^{12} \\\\sin{\\\\theta} r r_s+8\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} \\\\tan{\\\\theta}^{2} a^{10}+16\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} \\\\tan{\\\\theta}^{2} a^{8} r^{2}%\\n+48\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{3} r_s+32\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{11} \\\\tan{\\\\theta}^{2} a^{10} r^{3} \\\\sin{\\\\theta} r_s+32\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{11} \\\\tan{\\\\theta}^{2} a^{10} r^{3} \\\\sin{\\\\theta} r_s+8\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} \\\\tan{\\\\theta}^{2} a^{6} r^{4}+8\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{8} a^{12} r^{2} r_s^{2}+8\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{8} a^{10} r^{4} r_s^{2}-8\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{8} a^{10} r^{3} r_s^{3}+8\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{6} a^{12} r^{2} r_s^{2}+8\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{6} a^{10} r^{4} r_s^{2}-8\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{6} a^{10} r^{3} r_s^{3}-8\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(\\\\sin{\\\\theta}^{4} a^{4} r r_s-\\\\sin{\\\\theta}^{2} a^{2} r^{2} r_s^{2}+2\\\\sin{\\\\theta}^{2} a^{2} r^{3} r_s+2\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r r_s-a^{2} r^{3} r_s-\\\\cos{\\\\theta}^{2} a^{4} r r_s+\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2}-r^{5} r_s-\\\\cos{\\\\theta}^{2} a^{2} r^{3} r_s+\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{2}\\\\right)^{2} a^{4}}{8\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{\\\\phi}= & \\\\frac{55\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6} a^{6} r^{5} r_s^{3}+20\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{6} a^{8} r^{3} r_s^{3}-2\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{8} r^{3} r_s^{3}+12\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{5} a^{6} r^{3} r_s^{3}+12\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{5} a^{6} r^{3} r_s^{3}+34\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{3} r_s^{3}+12\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{3} r_s^{3}-12\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{3} r_s^{3}+8\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{5} r_s^{3} \\\\sin{2\\\\theta}+8\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{5} r_s^{3} \\\\sin{2\\\\theta}+4\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{3} r_s^{3} \\\\sin{2\\\\theta}+4\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{3} r_s^{3} \\\\sin{2\\\\theta}-4\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{5} r_s^{3} \\\\sin{4\\\\theta}-4\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{5} r_s^{3} \\\\sin{4\\\\theta}-2\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{3} r_s^{3} \\\\sin{4\\\\theta}-2\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{3} r_s^{3} \\\\sin{4\\\\theta}-4\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{4} r^{2} r_s^{2}+2\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{2} r_s^{2} \\\\sin{2\\\\theta}+2\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{2} r_s^{2} \\\\sin{2\\\\theta}%\\n-4\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{2} r^{4} r_s^{2}+2\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{4} r_s^{2} \\\\sin{2\\\\theta}+2\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{4} r_s^{2} \\\\sin{2\\\\theta}+41\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{6} r^{5} r_s^{3}+10\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} a^{8} r^{3} r_s^{3}-12\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{2} r_s^{2}-6\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{4} r_s^{2}+64\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{4} r^{7} r_s^{3}-13\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{4} r^{6} r_s^{4}-4\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{6} r^{4} r_s^{4}-16\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{6} r_s^{2}+6\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{5} r_s^{3}-24\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{4} r_s^{2}-23\\\\sin{\\\\theta}^{6} a^{6} r^{6} r_s^{2}-65\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6} a^{8} r^{4} r_s^{2}+5\\\\sin{\\\\theta}^{4} a^{6} r^{6} r_s^{2}+23\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{8} r^{4} r_s^{2}-12\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{5} a^{6} r^{4} r_s^{2}-12\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{5} a^{6} r^{4} r_s^{2}-28\\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{4} r_s^{2}%\\n-12\\\\cos{2\\\\theta} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{4} r_s^{2}+12\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{4} r_s^{2}-4\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{4} r^{6} r_s^{2} \\\\sin{2\\\\theta}-4\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{4} r^{6} r_s^{2} \\\\sin{2\\\\theta}-8\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{6} r^{4} r_s^{2} \\\\sin{2\\\\theta}-8\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{6} r^{4} r_s^{2} \\\\sin{2\\\\theta}+2\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{4} r^{6} r_s^{2} \\\\sin{4\\\\theta}+2\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{4} r^{6} r_s^{2} \\\\sin{4\\\\theta}+4\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{6} r^{4} r_s^{2} \\\\sin{4\\\\theta}+4\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{6} r^{4} r_s^{2} \\\\sin{4\\\\theta}+4\\\\cos{2\\\\theta} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{4} r^{3} r_s-2\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{3} \\\\sin{2\\\\theta} r_s-2\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{3} \\\\sin{2\\\\theta} r_s+12\\\\cos{2\\\\theta} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{2} r^{5} r_s-6\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{5} \\\\sin{2\\\\theta} r_s-6\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{5} \\\\sin{2\\\\theta} r_s-12\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{6} r^{6} r_s^{2}-22\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{8} r^{4} r_s^{2}+18\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{5} r_s-9\\\\sin{\\\\theta}^{4} a^{4} r^{8} r_s^{2}%\\n+10\\\\sin{\\\\theta}^{4} a^{4} r^{7} r_s^{3}+18\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{7} r_s-4\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{6} r_s^{2}+6\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{5} r_s-41\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{6} a^{10} r^{2} r_s^{2}+19\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{10} r^{2} r_s^{2}-12\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{5} a^{8} r^{2} r_s^{2}-12\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{5} a^{8} r^{2} r_s^{2}-44\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{2} r_s^{2}-12\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{2} r_s^{2}+12\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{2} r_s^{2}-4\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{8} r^{2} r_s^{2} \\\\sin{2\\\\theta}-4\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{8} r^{2} r_s^{2} \\\\sin{2\\\\theta}+2\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{8} r^{2} r_s^{2} \\\\sin{4\\\\theta}+2\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{8} r^{2} r_s^{2} \\\\sin{4\\\\theta}+4\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{6} r r_s-2\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} \\\\sin{2\\\\theta} r r_s-2\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} \\\\sin{2\\\\theta} r r_s+16\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{4} r^{3} r_s-8\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{3} \\\\sin{2\\\\theta} r_s%\\n-8\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{3} \\\\sin{2\\\\theta} r_s-20\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} a^{10} r^{2} r_s^{2}-6\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} r r_s+6\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{3} r_s+22\\\\sin{\\\\theta}^{6} a^{4} r^{7} r_s^{3}+12\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{5} a^{4} r^{5} r_s^{3}+12\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{5} a^{4} r^{5} r_s^{3}+30\\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{5} r_s^{3}+12\\\\cos{2\\\\theta} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{5} r_s^{3}-12\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{5} r_s^{3}+4\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{2} r^{7} r_s^{3} \\\\sin{2\\\\theta}+4\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{2} r^{7} r_s^{3} \\\\sin{2\\\\theta}-2\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{2} r^{7} r_s^{3} \\\\sin{4\\\\theta}-2\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{2} r^{7} r_s^{3} \\\\sin{4\\\\theta}-4\\\\cos{2\\\\theta} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{2} r^{4} r_s^{2}+2\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{4} r_s^{2} \\\\sin{2\\\\theta}+2\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{4} r_s^{2} \\\\sin{2\\\\theta}-4\\\\cos{2\\\\theta} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} r^{6} r_s^{2}+2\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{6} r_s^{2} \\\\sin{2\\\\theta}+2\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{6} r_s^{2} \\\\sin{2\\\\theta}%\\n+36\\\\sin{\\\\theta}^{4} a^{2} r^{9} r_s^{3}-14\\\\sin{\\\\theta}^{4} a^{2} r^{8} r_s^{4}-4\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{8} r_s^{2}-47\\\\sin{\\\\theta}^{6} a^{4} r^{8} r_s^{2}-129\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6} a^{6} r^{6} r_s^{2}-24\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{5} a^{4} r^{6} r_s^{2}-24\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{5} a^{4} r^{6} r_s^{2}-58\\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{6} r_s^{2}-24\\\\cos{2\\\\theta} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{6} r_s^{2}+24\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{6} r_s^{2}-8\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{2} r^{8} r_s^{2} \\\\sin{2\\\\theta}-8\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{2} r^{8} r_s^{2} \\\\sin{2\\\\theta}-20\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{6} r_s^{2} \\\\sin{2\\\\theta}-20\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{6} r_s^{2} \\\\sin{2\\\\theta}+4\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{2} r^{8} r_s^{2} \\\\sin{4\\\\theta}+4\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{2} r^{8} r_s^{2} \\\\sin{4\\\\theta}+10\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{6} r_s^{2} \\\\sin{4\\\\theta}+10\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{6} r_s^{2} \\\\sin{4\\\\theta}+8\\\\cos{2\\\\theta} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} r^{7} r_s-4\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{7} \\\\sin{2\\\\theta} r_s%\\n-4\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{7} \\\\sin{2\\\\theta} r_s-91\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{4} r^{8} r_s^{2}-101\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{6} r^{6} r_s^{2}+6\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{7} r_s-32\\\\sin{\\\\theta}^{4} a^{2} r^{10} r_s^{2}+8\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{9} r_s-97\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{6} a^{8} r^{4} r_s^{2}-36\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{5} a^{6} r^{4} r_s^{2}-36\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{5} a^{6} r^{4} r_s^{2}-106\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{4} r_s^{2}-36\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{4} r_s^{2}+40\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{4} r_s^{2}-16\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{4} r_s^{2} \\\\sin{2\\\\theta}-16\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{4} r_s^{2} \\\\sin{2\\\\theta}+8\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{4} r_s^{2} \\\\sin{4\\\\theta}+8\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{4} r_s^{2} \\\\sin{4\\\\theta}+12\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{2} r^{5} r_s-6\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{5} \\\\sin{2\\\\theta} r_s-6\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{5} \\\\sin{2\\\\theta} r_s-45\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} a^{8} r^{4} r_s^{2}%\\n+24\\\\sin{\\\\theta}^{6} a^{6} r^{7} r_s+80\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6} a^{8} r^{5} r_s-8\\\\sin{\\\\theta}^{4} a^{6} r^{7} r_s-32\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{8} r^{5} r_s+12\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{5} a^{6} r^{5} r_s+12\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{5} a^{6} r^{5} r_s+28\\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{5} r_s+12\\\\cos{2\\\\theta} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{5} r_s-12\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{5} r_s+4\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{4} r^{7} \\\\sin{2\\\\theta} r_s+4\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{4} r^{7} \\\\sin{2\\\\theta} r_s+12\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{6} r^{5} \\\\sin{2\\\\theta} r_s+12\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{6} r^{5} \\\\sin{2\\\\theta} r_s-2\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{4} r^{7} \\\\sin{4\\\\theta} r_s-2\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{4} r^{7} \\\\sin{4\\\\theta} r_s-6\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{6} r^{5} \\\\sin{4\\\\theta} r_s-6\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{6} r^{5} \\\\sin{4\\\\theta} r_s-4\\\\cos{2\\\\theta} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{4} r^{4}+2\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{4} \\\\sin{2\\\\theta}+2\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{4} \\\\sin{2\\\\theta}%\\n-8\\\\cos{2\\\\theta} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{2} r^{6}+4\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{6} \\\\sin{2\\\\theta}+4\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{6} \\\\sin{2\\\\theta}+8\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{6} r^{7} r_s+28\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{8} r^{5} r_s-8\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{4}-4\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{6}+2\\\\sin{\\\\theta}^{4} a^{4} r^{9} r_s-12\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{8}-8\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{6}+88\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{6} a^{10} r^{3} r_s-40\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{10} r^{3} r_s+24\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{5} a^{8} r^{3} r_s+24\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{5} a^{8} r^{3} r_s+72\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{3} r_s+24\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{3} r_s-24\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{3} r_s+12\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{8} r^{3} \\\\sin{2\\\\theta} r_s+12\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{8} r^{3} \\\\sin{2\\\\theta} r_s-6\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{8} r^{3} \\\\sin{4\\\\theta} r_s%\\n-6\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{8} r^{3} \\\\sin{4\\\\theta} r_s-8\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{6} r^{2}+4\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{2} \\\\sin{2\\\\theta}+4\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{2} \\\\sin{2\\\\theta}-16\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{4} r^{4}+8\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{4} \\\\sin{2\\\\theta}+8\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{4} \\\\sin{2\\\\theta}+40\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} a^{10} r^{3} r_s+8\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} r^{2}+28\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{4}+24\\\\sin{\\\\theta}^{6} a^{4} r^{9} r_s+80\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6} a^{6} r^{7} r_s+12\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{5} a^{4} r^{7} r_s+12\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{5} a^{4} r^{7} r_s+28\\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{7} r_s+12\\\\cos{2\\\\theta} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{7} r_s-12\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{7} r_s+4\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{2} r^{9} \\\\sin{2\\\\theta} r_s+4\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{2} r^{9} \\\\sin{2\\\\theta} r_s+12\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{7} \\\\sin{2\\\\theta} r_s%\\n+12\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{7} \\\\sin{2\\\\theta} r_s-2\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{2} r^{9} \\\\sin{4\\\\theta} r_s-2\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{2} r^{9} \\\\sin{4\\\\theta} r_s-6\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{7} \\\\sin{4\\\\theta} r_s-6\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{7} \\\\sin{4\\\\theta} r_s-4\\\\cos{2\\\\theta} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} r^{8}+2\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{8} \\\\sin{2\\\\theta}+2\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{8} \\\\sin{2\\\\theta}+40\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{4} r^{9} r_s+68\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{6} r^{7} r_s+4\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{8}+10\\\\sin{\\\\theta}^{4} a^{2} r^{11} r_s-4\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{10}+88\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{6} a^{8} r^{5} r_s+24\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{5} a^{6} r^{5} r_s+24\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{5} a^{6} r^{5} r_s+72\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{5} r_s+24\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{5} r_s-28\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{5} r_s+12\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{5} \\\\sin{2\\\\theta} r_s%\\n+12\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{5} \\\\sin{2\\\\theta} r_s-6\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{5} \\\\sin{4\\\\theta} r_s-6\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{5} \\\\sin{4\\\\theta} r_s-8\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{2} r^{6}+4\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{6} \\\\sin{2\\\\theta}+4\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{6} \\\\sin{2\\\\theta}+56\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} a^{8} r^{5} r_s+20\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{6}-15\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{6} a^{10} r^{2} r_s^{2}-12\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{5} a^{8} r^{2} r_s^{2}-12\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{5} a^{8} r^{2} r_s^{2}-36\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{2} r_s^{2}-12\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{2} r_s^{2}+16\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{2} r_s^{2}-4\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{8} r^{2} r_s^{2} \\\\sin{2\\\\theta}-4\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{8} r^{2} r_s^{2} \\\\sin{2\\\\theta}+2\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{8} r^{2} r_s^{2} \\\\sin{4\\\\theta}+2\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{8} r^{2} r_s^{2} \\\\sin{4\\\\theta}+4\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{6} r r_s-2\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} \\\\sin{2\\\\theta} r r_s%\\n-2\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} \\\\sin{2\\\\theta} r r_s+4\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{4} r^{3} r_s-2\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{3} \\\\sin{2\\\\theta} r_s-2\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{3} \\\\sin{2\\\\theta} r_s-3\\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{4} a^{10} r^{2} r_s^{2}+6\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} r r_s+2\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{3} r_s+32\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{6} a^{12} r r_s-16\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} a^{12} r r_s+12\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{5} a^{10} r r_s+12\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{5} a^{10} r r_s+44\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} r r_s+12\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} r r_s-12\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} r r_s+4\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{10} \\\\sin{2\\\\theta} r r_s+4\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{10} \\\\sin{2\\\\theta} r r_s-2\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{10} \\\\sin{4\\\\theta} r r_s-2\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{10} \\\\sin{4\\\\theta} r r_s-4\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{8}+2\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} \\\\sin{2\\\\theta}%\\n+2\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} \\\\sin{2\\\\theta}-8\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{6} r^{2}+4\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{2} \\\\sin{2\\\\theta}+4\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{2} \\\\sin{2\\\\theta}+18\\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{4} a^{12} r r_s+8\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{10}+20\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} r^{2}+32\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{6} a^{10} r^{3} r_s+12\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{5} a^{8} r^{3} r_s+12\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{5} a^{8} r^{3} r_s+44\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{3} r_s+12\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{3} r_s-20\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{3} r_s+4\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{8} r^{3} \\\\sin{2\\\\theta} r_s+4\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{8} r^{3} \\\\sin{2\\\\theta} r_s-2\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{8} r^{3} \\\\sin{4\\\\theta} r_s-2\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{8} r^{3} \\\\sin{4\\\\theta} r_s-4\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{4} r^{4}+2\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{4} \\\\sin{2\\\\theta}+2\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{4} \\\\sin{2\\\\theta}%\\n+18\\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{4} a^{10} r^{3} r_s+12\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{4}-2\\\\cos{\\\\theta} \\\\sin{\\\\theta}^{5} a^{8} r^{3} r_s^{3} \\\\sin{2\\\\theta}+2\\\\cos{\\\\theta} \\\\sin{\\\\theta}^{5} a^{8} r^{4} r_s^{2} \\\\sin{2\\\\theta}+2\\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{5} a^{10} r^{2} r_s^{2} \\\\sin{2\\\\theta}-4\\\\cos{\\\\theta} \\\\sin{\\\\theta}^{5} a^{6} r^{5} r_s^{3} \\\\sin{2\\\\theta}+2\\\\cos{\\\\theta} \\\\sin{\\\\theta}^{5} a^{6} r^{4} r_s^{4} \\\\sin{2\\\\theta}+2\\\\cos{\\\\theta} \\\\sin{\\\\theta}^{5} a^{6} r^{6} r_s^{2} \\\\sin{2\\\\theta}+2\\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{5} a^{8} r^{4} r_s^{2} \\\\sin{2\\\\theta}-2\\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{5} a^{8} r^{3} r_s^{3} \\\\sin{2\\\\theta}-4\\\\cos{\\\\theta} \\\\sin{\\\\theta}^{3} a^{6} r^{5} r_s^{3} \\\\sin{2\\\\theta}+4\\\\cos{\\\\theta} \\\\sin{\\\\theta}^{3} a^{6} r^{6} r_s^{2} \\\\sin{2\\\\theta}+8\\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{3} a^{8} r^{4} r_s^{2} \\\\sin{2\\\\theta}-8\\\\cos{\\\\theta} \\\\sin{\\\\theta}^{3} a^{4} r^{7} r_s^{3} \\\\sin{2\\\\theta}+4\\\\cos{\\\\theta} \\\\sin{\\\\theta}^{3} a^{4} r^{6} r_s^{4} \\\\sin{2\\\\theta}+4\\\\cos{\\\\theta} \\\\sin{\\\\theta}^{3} a^{4} r^{8} r_s^{2} \\\\sin{2\\\\theta}+8\\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{3} a^{6} r^{6} r_s^{2} \\\\sin{2\\\\theta}-12\\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{3} a^{6} r^{5} r_s^{3} \\\\sin{2\\\\theta}-4\\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{3} a^{8} r^{3} r_s^{3} \\\\sin{2\\\\theta}+4\\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{3} a^{10} r^{2} r_s^{2} \\\\sin{2\\\\theta}%\\n+4\\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{3} a^{6} r^{4} r_s^{4} \\\\sin{2\\\\theta}+4\\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{3} a^{8} r^{4} r_s^{2} \\\\sin{2\\\\theta}-4\\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{3} a^{8} r^{3} r_s^{3} \\\\sin{2\\\\theta}-2\\\\cos{\\\\theta} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{2} r_s^{2} \\\\sin{\\\\theta} \\\\sin{2\\\\theta}+2\\\\cos{\\\\theta} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{3} \\\\sin{\\\\theta} \\\\sin{2\\\\theta} r_s+2\\\\cos{\\\\theta}^{3} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} \\\\sin{\\\\theta} \\\\sin{2\\\\theta} r r_s-6\\\\cos{\\\\theta} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{4} r_s^{2} \\\\sin{\\\\theta} \\\\sin{2\\\\theta}+2\\\\cos{\\\\theta} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{3} r_s^{3} \\\\sin{\\\\theta} \\\\sin{2\\\\theta}+4\\\\cos{\\\\theta} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{5} \\\\sin{\\\\theta} \\\\sin{2\\\\theta} r_s+4\\\\cos{\\\\theta}^{3} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{3} \\\\sin{\\\\theta} \\\\sin{2\\\\theta} r_s-2\\\\cos{\\\\theta}^{3} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{2} r_s^{2} \\\\sin{\\\\theta} \\\\sin{2\\\\theta}-4\\\\cos{\\\\theta} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{6} r_s^{2} \\\\sin{\\\\theta} \\\\sin{2\\\\theta}+2\\\\cos{\\\\theta} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{5} r_s^{3} \\\\sin{\\\\theta} \\\\sin{2\\\\theta}+2\\\\cos{\\\\theta} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{7} \\\\sin{\\\\theta} \\\\sin{2\\\\theta} r_s+2\\\\cos{\\\\theta}^{3} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{5} \\\\sin{\\\\theta} \\\\sin{2\\\\theta} r_s-2\\\\cos{\\\\theta}^{3} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{4} r_s^{2} \\\\sin{\\\\theta} \\\\sin{2\\\\theta}+10\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6} a^{8} r^{3} r_s^{3}-6\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6} a^{6} r^{4} r_s^{4}-\\\\sin{\\\\theta}^{4} a^{4} r^{6} r_s^{4}+\\\\sin{\\\\theta}^{4} a^{6} r^{5} r_s^{3}%\\n+2\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{6} r^{4} r_s^{4}-2\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{8} r^{3} r_s^{3}-2\\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{3} r_s^{3}+2\\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{2} r_s^{2}-\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{8} r^{2} r_s^{4}+\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{10} r_s^{3} r+2\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r_s^{3} r-2\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} r_s^{2}-2\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{5} r_s^{3}+2\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{4} r_s^{2}+\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} a^{12} r_s^{2}+6\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{3} r_s^{3}-2\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{2} r_s^{2}-12\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{4} r^{6} r_s^{3}-20\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{4} r^{6} r_s^{3}+4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{4} r^{5} r_s^{4}+4\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{4} r^{5} r_s^{4}-8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{6} r^{4} r_s^{3}-8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{6} r^{4} r_s^{3}-8\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{4} r^{6} r_s^{3}%\\n+8\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{4} r^{6} r_s^{3}+12\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{6} r^{4} r_s^{3}-4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{6} r^{4} r_s^{3}+4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{6} r^{4} r_s^{3}+8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{6} r^{4} r_s^{3}-4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{6} r^{3} r_s^{4}-4\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{6} r^{3} r_s^{4}+8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{8} r^{2} r_s^{3}+8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{8} r^{2} r_s^{3}-2\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{2} r_s^{3}+2\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{2} r_s^{3}-2\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{2} r_s^{3}+16\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{5} r_s^{2}+16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{5} r_s^{2}-4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{4} r_s^{3}-4\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{4} r_s^{3}+8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{3} r_s^{2}+8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{3} r_s^{2}-4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{2} r^{3} r_s^{2}+4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{2} r^{3} r_s^{2}%\\n-4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{2} r^{3} r_s^{2}-\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} a^{8} r^{2} r_s^{4}-2\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{3} r_s^{3}-16\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{2} r^{4} r_s^{2}+4\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{2} r^{3} r_s^{3}-8\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{4} r^{2} r_s^{2}+28\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{4} a^{4} r^{7} r_s^{2}+32\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{4} a^{4} r^{7} r_s^{2}-16\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{4} a^{4} r^{6} r_s^{3}-16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{4} a^{4} r^{6} r_s^{3}+8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{4} a^{6} r^{5} r_s^{2}+8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{4} a^{6} r^{5} r_s^{2}+4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\sin{\\\\theta}^{4} a^{4} r^{7} r_s^{2}-4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{4} a^{4} r^{7} r_s^{2}+24\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{6} r^{5} r_s^{2}+8\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{6} r^{5} r_s^{2}-8\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{6} r^{5} r_s^{2}+32\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{6} r^{5} r_s^{2}+4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{8} r^{3} r_s^{2}+4\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{8} r^{3} r_s^{2}%\\n+2\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{3} r_s^{2}-2\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{3} r_s^{2}+2\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{3} r_s^{2}-16\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{6} r_s-16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{6} r_s+8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{5} r_s^{2}+8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{5} r_s^{2}-4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{4} r_s-4\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{4} r_s+4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{2} r^{4} r_s-4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{2} r^{4} r_s+4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{2} r^{4} r_s+16\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{2} r^{5} r_s-8\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{2} r^{4} r_s^{2}+4\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{4} r^{3} r_s-12\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{8} r^{3} r_s^{2}+4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{8} r^{3} r_s^{2}-4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{8} r^{3} r_s^{2}-8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{8} r^{3} r_s^{2}-4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{10} r_s^{2} r%\\n-4\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{10} r_s^{2} r+2\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r_s^{2} r-2\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r_s^{2} r+2\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r_s^{2} r-24\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{4} r_s-24\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{4} r_s-4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{2} r_s-4\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{2} r_s+4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{4} r^{2} r_s-4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{4} r^{2} r_s+4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{4} r^{2} r_s+24\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{4} r^{3} r_s+4\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{6} r r_s-20\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{4} a^{2} r^{8} r_s^{3}-24\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{4} a^{2} r^{8} r_s^{3}+8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{4} a^{2} r^{7} r_s^{4}+8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{4} a^{2} r^{7} r_s^{4}-4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\sin{\\\\theta}^{4} a^{2} r^{8} r_s^{3}+4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{4} a^{2} r^{8} r_s^{3}-2\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{4} r_s^{3}%\\n+2\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{4} r_s^{3}-2\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{4} r_s^{3}+12\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{7} r_s^{2}+12\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{7} r_s^{2}-4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{6} r_s^{3}-4\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{6} r_s^{3}-4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} r^{5} r_s^{2}+4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} r^{5} r_s^{2}-4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} r^{5} r_s^{2}-12\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} r^{6} r_s^{2}+4\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} r^{5} r_s^{3}+16\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{4} a^{2} r^{9} r_s^{2}+24\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{4} a^{2} r^{9} r_s^{2}+8\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\sin{\\\\theta}^{4} a^{2} r^{9} r_s^{2}-8\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{4} a^{2} r^{9} r_s^{2}+8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{4} r^{7} r_s^{2}+20\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{4} r^{7} r_s^{2}-20\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{4} r^{7} r_s^{2}+4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{5} r_s^{2}-4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{5} r_s^{2}%\\n+4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{5} r_s^{2}-12\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{8} r_s-12\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{8} r_s+8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} r^{6} r_s-8\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} r^{6} r_s+8\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} r^{6} r_s+12\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} r^{7} r_s-20\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{6} r^{5} r_s^{2}+16\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{6} r^{5} r_s^{2}-16\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{6} r^{5} r_s^{2}-4\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{6} r^{5} r_s^{2}+6\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{3} r_s^{2}-6\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{3} r_s^{2}+6\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{3} r_s^{2}-20\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{6} r_s-20\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{6} r_s+12\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{2} r^{4} r_s-12\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{2} r^{4} r_s+12\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{2} r^{4} r_s+20\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{2} r^{5} r_s%\\n+28\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{4} r^{7} r_s^{2}-12\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{4} a^{4} r^{8} r_s-16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{4} a^{4} r^{8} r_s-8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{4} a^{6} r^{6} r_s-8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{4} a^{6} r^{6} r_s-4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\sin{\\\\theta}^{4} a^{4} r^{8} r_s+4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{4} a^{4} r^{8} r_s-12\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{6} r^{6} r_s-12\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{6} r^{6} r_s+12\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{6} r^{6} r_s-24\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{6} r^{6} r_s-12\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{8} r^{4} r_s-12\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{8} r^{4} r_s-2\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{4} r_s+2\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{4} r_s-2\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{4} r_s+8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{7}+8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{7}+4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{5}+4\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{5}%\\n-4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{2} r^{5}+4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{2} r^{5}-4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{2} r^{5}-8\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{2} r^{6}-4\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{4} r^{4}+12\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{8} r^{4} r_s-12\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{8} r^{4} r_s+12\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{8} r^{4} r_s-4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{2} r_s+4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{2} r_s-4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{2} r_s+16\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{5}+16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{5}+8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{3}+8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{3}-8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{4} r^{3}+8\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{4} r^{3}-8\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{4} r^{3}-16\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{4} r^{4}-8\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{6} r^{2}%\\n-4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{4} a^{2} r^{10} r_s-8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{4} a^{2} r^{10} r_s-4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\sin{\\\\theta}^{4} a^{2} r^{10} r_s+4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{4} a^{2} r^{10} r_s-12\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{4} r^{8} r_s+12\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{4} r^{8} r_s-12\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{4} r^{8} r_s-2\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{6} r_s+2\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{6} r_s-2\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{6} r_s+4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{9}+4\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{9}-4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} r^{7}+4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} r^{7}-4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} r^{7}-4\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} r^{8}+12\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{6} r^{6} r_s-12\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{6} r^{6} r_s+12\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{6} r^{6} r_s-4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{4} r_s%\\n+4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{4} r_s-4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{4} r_s+8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{7}+8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{7}-8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{2} r^{5}+8\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{2} r^{5}-8\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{2} r^{5}-8\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{2} r^{6}-12\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} a^{8} r^{3} r_s^{2}+4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} a^{8} r^{3} r_s^{2}-4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} a^{8} r^{3} r_s^{2}-8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} a^{8} r^{3} r_s^{2}+4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} a^{8} r^{2} r_s^{3}+4\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} a^{8} r^{2} r_s^{3}-8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} a^{10} r_s^{2} r-8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} a^{10} r_s^{2} r+2\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r_s^{2} r-2\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r_s^{2} r+2\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r_s^{2} r-8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{4} r_s%\\n-8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{4} r_s+4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{3} r_s^{2}+4\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{3} r_s^{2}-8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{2} r_s-8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{2} r_s+4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{4} r^{2} r_s-4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{4} r^{2} r_s+4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{4} r^{2} r_s+\\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{4} a^{10} r_s^{3} r+2\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{2} r_s^{2}+8\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{4} r^{3} r_s-4\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{4} r^{2} r_s^{2}+8\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{6} r r_s+12\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} a^{10} r^{2} r_s-4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} a^{10} r^{2} r_s+4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} a^{10} r^{2} r_s+8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} a^{10} r^{2} r_s+4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} a^{12} r_s+4\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} a^{12} r_s-2\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} r_s%\\n+2\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} r_s-2\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} r_s+8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{3}+8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{3}+4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} r+4\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} r-4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{6} r+4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{6} r-4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{6} r-\\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{4} a^{12} r_s^{2}-8\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{6} r^{2}-4\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{8}+8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} a^{8} r^{4} r_s-4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} a^{8} r^{4} r_s+4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} a^{8} r^{4} r_s+4\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} a^{8} r^{4} r_s-2\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{2} r_s+2\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{2} r_s-2\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{2} r_s+4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{5}%\\n+4\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{5}-4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{4} r^{3}+4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{4} r^{3}-4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{4} r^{3}-4\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{4} r^{4}+\\\\sin{\\\\theta}^{6} a^{4} r^{6} r_s^{4}-\\\\sin{\\\\theta}^{6} a^{6} r^{5} r_s^{3}+\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{6} a^{8} r^{2} r_s^{4}-\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{6} a^{10} r_s^{3} r-8\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} r^{5} r_s+4\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} r^{4} r_s^{2}-4\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{2} r^{3} r_s+4\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} r^{6}+4\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{2} r^{4}-\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{6} a^{10} r_s^{3} r+\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{6} a^{12} r_s^{2}+4\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{2} r^{4}-4\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{2} r^{3} r_s+4\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{4} r^{2}-4\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{8} a^{8} r^{3} r_s^{3}%\\n+8\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{7} r_s^{3}+16\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{5} r_s^{3}+8\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{2} r^{9} r_s^{3}+16\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{4} r^{7} r_s^{3}+8\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{8} r^{3} r_s^{3}+8\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{6} r^{5} r_s^{3}-4\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{4} r r_s+8\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{6} r_s^{2}+8\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{4} r_s^{2}-8\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{2} r^{3} r_s+4\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{8} r_s^{2}+4\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{6} r_s^{2}-4\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} r^{5} r_s+4\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{8} a^{8} r^{4} r_s^{2}-8\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{8} r_s^{2}-24\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{6} r_s^{2}-8\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{2} r^{10} r_s^{2}-24\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{4} r^{8} r_s^{2}-24\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{8} r^{4} r_s^{2}-24\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{6} r^{6} r_s^{2}%\\n+4\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{4} r^{2}-8\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{7} r_s-16\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{5} r_s+8\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{2} r^{4}-4\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{9} r_s-8\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{7} r_s+4\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} r^{6}+4\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{8} a^{10} r^{2} r_s^{2}-8\\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} a^{10} r^{2} r_s^{2}-8\\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} a^{8} r^{4} r_s^{2}-4\\\\cos{\\\\theta}^{6} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} r r_s+4\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{6}-8\\\\cos{\\\\theta}^{6} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{3} r_s+8\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{4} r^{2}-4\\\\cos{\\\\theta}^{6} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{5} r_s+4\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{2} r^{4}}{4\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{2} r^{2} r_s^{2}-4\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{2} r^{3} r_s-4\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{4} r r_s+4\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} r^{4} r_s^{2}-8\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} r^{5} r_s-12\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{2} r^{3} r_s+4\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{2} r^{4}+8\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{4} r^{2}+4\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} r^{6}+8\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{2} r^{4}-4\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{4} r r_s+4\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{6}+4\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{4} r^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{\\\\theta}= & \\\\frac{2\\\\cos{\\\\theta} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{5} r_s^{2} \\\\sin{\\\\theta} \\\\tan{\\\\theta}+2\\\\cos{\\\\theta} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{7} r_s^{2} \\\\sin{\\\\theta} \\\\tan{\\\\theta}-2\\\\cos{\\\\theta} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{6} r_s^{3} \\\\sin{\\\\theta} \\\\tan{\\\\theta}-2\\\\cos{\\\\theta}^{5} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} r_s^{2} \\\\sin{\\\\theta} \\\\tan{\\\\theta} r-2\\\\cos{\\\\theta}^{5} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{3} r_s^{2} \\\\sin{\\\\theta} \\\\tan{\\\\theta}+2\\\\cos{\\\\theta}^{5} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{2} r_s^{3} \\\\sin{\\\\theta} \\\\tan{\\\\theta}+4\\\\cos{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{3} r_s^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-\\\\cos{\\\\theta}^{4} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} r_s^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta} r+4\\\\cos{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{5} r_s^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-2\\\\cos{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{4} r_s^{3} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-\\\\cos{\\\\theta}^{4} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{3} r_s^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-3\\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{4} \\\\sin{2\\\\theta} \\\\tan{\\\\theta} r_s-2\\\\cos{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} r^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta} r_s-6\\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{6} \\\\sin{2\\\\theta} \\\\tan{\\\\theta} r_s+5\\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{5} r_s^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-4\\\\cos{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{4} \\\\sin{2\\\\theta} \\\\tan{\\\\theta} r_s+\\\\cos{\\\\theta}^{4} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{10} \\\\sin{2\\\\theta} \\\\tan{\\\\theta} r_s+2\\\\cos{\\\\theta}^{4} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} r^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta} r_s+5\\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{7} r_s^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}%\\n-2\\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{6} r_s^{3} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-3\\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{8} \\\\sin{2\\\\theta} \\\\tan{\\\\theta} r_s-2\\\\cos{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{6} \\\\sin{2\\\\theta} \\\\tan{\\\\theta} r_s+\\\\cos{\\\\theta}^{4} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{4} \\\\sin{2\\\\theta} \\\\tan{\\\\theta} r_s+2a^{4} r^{7} r_s^{4} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-2a^{4} r^{8} r_s^{3} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-2\\\\cos{\\\\theta}^{2} a^{6} r^{6} r_s^{3} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+2\\\\cos{\\\\theta}^{4} a^{8} r^{4} r_s^{3} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-4a^{2} r^{9} r_s^{4} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-10\\\\cos{\\\\theta}^{2} a^{4} r^{7} r_s^{4} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+10a^{2} r^{10} r_s^{3} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+30\\\\cos{\\\\theta}^{2} a^{4} r^{8} r_s^{3} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+26\\\\cos{\\\\theta}^{4} a^{6} r^{6} r_s^{3} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+6\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{4} r^{6} r_s^{3} \\\\tan{\\\\theta}+4\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{6} r^{4} r_s^{3} \\\\tan{\\\\theta}-12\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{4} r^{7} r_s^{2} \\\\tan{\\\\theta}-20\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{6} r^{5} r_s^{2} \\\\tan{\\\\theta}-4\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{8} r^{3} r_s^{2} \\\\tan{\\\\theta}+16\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{2} r^{8} r_s^{3} \\\\tan{\\\\theta}+16\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{6} r_s^{3} \\\\tan{\\\\theta}%\\n-28\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{2} r^{9} r_s^{2} \\\\tan{\\\\theta}-52\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{7} r_s^{2} \\\\tan{\\\\theta}-20\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{5} r_s^{2} \\\\tan{\\\\theta}+6\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{4} r^{6} r_s^{3} \\\\tan{\\\\theta}+4\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{6} r^{4} r_s^{3} \\\\tan{\\\\theta}-12\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{4} r^{7} r_s^{2} \\\\tan{\\\\theta}-20\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{6} r^{5} r_s^{2} \\\\tan{\\\\theta}-4\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{8} r^{3} r_s^{2} \\\\tan{\\\\theta}+16\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{2} r^{8} r_s^{3} \\\\tan{\\\\theta}+16\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{6} r_s^{3} \\\\tan{\\\\theta}-28\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{2} r^{9} r_s^{2} \\\\tan{\\\\theta}-52\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{7} r_s^{2} \\\\tan{\\\\theta}-20\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{5} r_s^{2} \\\\tan{\\\\theta}+18\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r^{10} r_s^{3} \\\\tan{\\\\theta}+36\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{2} r^{8} r_s^{3} \\\\tan{\\\\theta}-32\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r^{11} r_s^{2} \\\\tan{\\\\theta}-96\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{2} r^{9} r_s^{2} \\\\tan{\\\\theta}-112\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{4} r^{7} r_s^{2} \\\\tan{\\\\theta}+18\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) r^{10} r_s^{3} \\\\tan{\\\\theta}+36\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{2} r^{8} r_s^{3} \\\\tan{\\\\theta}%\\n-32\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) r^{11} r_s^{2} \\\\tan{\\\\theta}-96\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{2} r^{9} r_s^{2} \\\\tan{\\\\theta}-112\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{4} r^{7} r_s^{2} \\\\tan{\\\\theta}-2a^{4} r^{9} r_s^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-4\\\\cos{\\\\theta}^{2} a^{6} r^{7} r_s^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-8a^{2} r^{11} r_s^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-26\\\\cos{\\\\theta}^{2} a^{4} r^{9} r_s^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-28\\\\cos{\\\\theta}^{4} a^{6} r^{7} r_s^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+6\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{4} r^{8} \\\\tan{\\\\theta} r_s+16\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{6} r^{6} \\\\tan{\\\\theta} r_s+12\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{8} r^{4} \\\\tan{\\\\theta} r_s+24\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{2} r^{10} \\\\tan{\\\\theta} r_s+80\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{8} \\\\tan{\\\\theta} r_s+96\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{6} \\\\tan{\\\\theta} r_s+6\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{4} r^{8} \\\\tan{\\\\theta} r_s+16\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{6} r^{6} \\\\tan{\\\\theta} r_s+12\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{8} r^{4} \\\\tan{\\\\theta} r_s+24\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{2} r^{10} \\\\tan{\\\\theta} r_s+80\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{8} \\\\tan{\\\\theta} r_s+96\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{6} \\\\tan{\\\\theta} r_s%\\n+26\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r^{12} \\\\tan{\\\\theta} r_s+104\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{2} r^{10} \\\\tan{\\\\theta} r_s+164\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{4} r^{8} \\\\tan{\\\\theta} r_s+26\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) r^{12} \\\\tan{\\\\theta} r_s+104\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{2} r^{10} \\\\tan{\\\\theta} r_s+164\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{4} r^{8} \\\\tan{\\\\theta} r_s+4\\\\cos{\\\\theta}^{6} a^{10} r^{3} r_s^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-8\\\\cos{\\\\theta}^{6} a^{8} r^{5} r_s^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+48\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{8} r^{4} \\\\tan{\\\\theta} r_s+48\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{8} r^{4} \\\\tan{\\\\theta} r_s+128\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{6} r^{6} \\\\tan{\\\\theta} r_s+128\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{6} r^{6} \\\\tan{\\\\theta} r_s-2\\\\cos{\\\\theta}^{4} a^{8} r^{3} r_s^{4} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+2\\\\cos{\\\\theta}^{6} a^{10} r^{2} r_s^{3} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-4\\\\cos{\\\\theta}^{4} a^{6} r^{5} r_s^{4} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+2\\\\cos{\\\\theta}^{6} a^{8} r^{4} r_s^{3} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-2\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{8} r^{2} r_s^{3} \\\\tan{\\\\theta}+4\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{10} r_s^{2} \\\\tan{\\\\theta} r+4\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{8} r^{3} r_s^{2} \\\\tan{\\\\theta}-2\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{8} r^{2} r_s^{3} \\\\tan{\\\\theta}%\\n+4\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{10} r_s^{2} \\\\tan{\\\\theta} r+4\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{8} r^{3} r_s^{2} \\\\tan{\\\\theta}+26\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{4} r^{6} r_s^{3} \\\\tan{\\\\theta}-64\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{6} r^{5} r_s^{2} \\\\tan{\\\\theta}+26\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{4} r^{6} r_s^{3} \\\\tan{\\\\theta}-64\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{6} r^{5} r_s^{2} \\\\tan{\\\\theta}+2\\\\cos{\\\\theta}^{8} a^{12} r_s^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta} r+4\\\\cos{\\\\theta}^{8} a^{10} r^{3} r_s^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-2\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{8} a^{12} \\\\tan{\\\\theta} r_s+8\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{8} a^{10} r^{2} \\\\tan{\\\\theta} r_s-2\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{8} a^{12} \\\\tan{\\\\theta} r_s+8\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{8} a^{10} r^{2} \\\\tan{\\\\theta} r_s+50\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{8} a^{8} r^{4} \\\\tan{\\\\theta} r_s+50\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{8} a^{8} r^{4} \\\\tan{\\\\theta} r_s-4\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{5} r_s^{4} \\\\tan{\\\\theta}-4\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{5} r_s^{4} \\\\tan{\\\\theta}-4\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{2} r^{7} r_s^{4} \\\\tan{\\\\theta}-4\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{2} r^{7} r_s^{4} \\\\tan{\\\\theta}-4\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{2} r^{7} r_s^{4} \\\\tan{\\\\theta}-4\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{2} r^{7} r_s^{4} \\\\tan{\\\\theta}%\\n-4\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r^{9} r_s^{4} \\\\tan{\\\\theta}-4\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) r^{9} r_s^{4} \\\\tan{\\\\theta}+8\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{6} r^{4} r_s^{3} \\\\tan{\\\\theta}+8\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{6} r^{4} r_s^{3} \\\\tan{\\\\theta}+2\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} a^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+2\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} a^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+4\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} \\\\tan{\\\\theta} r+4\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} \\\\tan{\\\\theta} r-2\\\\sin{\\\\theta}^{4} a^{6} r^{5} r_s^{4}+12\\\\sin{\\\\theta}^{4} a^{6} r^{6} r_s^{3}+8\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{8} r^{4} r_s^{3}+2\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{8} r^{3} r_s^{4}-2\\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{2} r_s^{3}+10\\\\sin{\\\\theta}^{4} a^{4} r^{8} r_s^{3}+10\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{6} r^{6} r_s^{3}-2\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{6} r^{5} r_s^{4}-2\\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{4} r_s^{3}+2\\\\sin{\\\\theta}^{2} a^{4} r^{6} r_s^{5}-14\\\\sin{\\\\theta}^{2} a^{4} r^{7} r_s^{4}-8\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{6} r^{5} r_s^{4}%\\n-2\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{6} r^{4} r_s^{5}+2\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{3} r_s^{4}+6\\\\sin{\\\\theta}^{2} a^{2} r^{8} r_s^{5}-26\\\\sin{\\\\theta}^{2} a^{2} r^{9} r_s^{4}-32\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{7} r_s^{4}+2\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{6} r_s^{5}+2\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{5} r_s^{4}+34\\\\sin{\\\\theta}^{2} a^{4} r^{8} r_s^{3}+62\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{6} r^{6} r_s^{3}-2\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{4} r_s^{3}+46\\\\sin{\\\\theta}^{2} a^{2} r^{10} r_s^{3}+98\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{8} r_s^{3}-6\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{6} r_s^{3}+22\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{8} r^{4} r_s^{3}+6\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{8} r^{3} r_s^{4}-6\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{2} r_s^{3}+58\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{6} r_s^{3}-6\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{5} r_s^{4}-10\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{4} r_s^{3}-2\\\\sin{\\\\theta}^{2} a^{4} r^{7} r_s^{4} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}%\\n+2\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{8} r^{3} r_s^{4} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+4\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{6} r_s^{3} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+4\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{4} r_s^{3} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-6\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{4} r^{6} r_s^{3} \\\\tan{\\\\theta}-4\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{6} r^{4} r_s^{3} \\\\tan{\\\\theta}+2\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{8} r^{2} r_s^{3} \\\\tan{\\\\theta}+8\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{5} r_s^{2} \\\\tan{\\\\theta}+8\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{3} r_s^{2} \\\\tan{\\\\theta}-6\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{4} r^{6} r_s^{3} \\\\tan{\\\\theta}-4\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{6} r^{4} r_s^{3} \\\\tan{\\\\theta}+2\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{8} r^{2} r_s^{3} \\\\tan{\\\\theta}+8\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{5} r_s^{2} \\\\tan{\\\\theta}+8\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{3} r_s^{2} \\\\tan{\\\\theta}-14\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{2} r^{8} r_s^{3} \\\\tan{\\\\theta}-20\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{6} r_s^{3} \\\\tan{\\\\theta}-6\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{4} r_s^{3} \\\\tan{\\\\theta}+16\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{7} r_s^{2} \\\\tan{\\\\theta}+24\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{5} r_s^{2} \\\\tan{\\\\theta}-14\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{2} r^{8} r_s^{3} \\\\tan{\\\\theta}-20\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{6} r_s^{3} \\\\tan{\\\\theta}%\\n-6\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{4} r_s^{3} \\\\tan{\\\\theta}+16\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{7} r_s^{2} \\\\tan{\\\\theta}+24\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{5} r_s^{2} \\\\tan{\\\\theta}+4\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{5} r_s^{4} \\\\tan{\\\\theta}+4\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{5} r_s^{4} \\\\tan{\\\\theta}-4\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{4} r_s^{3} \\\\tan{\\\\theta}-4\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{4} r_s^{3} \\\\tan{\\\\theta}+4\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{2} r^{7} r_s^{4} \\\\tan{\\\\theta}+4\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{2} r^{7} r_s^{4} \\\\tan{\\\\theta}-4\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{6} r_s^{3} \\\\tan{\\\\theta}-4\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{6} r_s^{3} \\\\tan{\\\\theta}+2\\\\cos{\\\\theta}^{6} a^{8} r^{3} r_s^{4} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-6\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{8} r^{3} r_s^{4}-4a^{4} r^{8} r_s^{3}-8\\\\cos{\\\\theta}^{2} a^{6} r^{6} r_s^{3}-6\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{5} r_s^{2}+4\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{5} r_s^{2}-8a^{2} r^{10} r_s^{3}-16\\\\cos{\\\\theta}^{2} a^{4} r^{8} r_s^{3}-4\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{10} r^{2} r_s^{3}%\\n-4\\\\cos{\\\\theta}^{4} a^{8} r^{4} r_s^{3}+4\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{3} r_s^{2}-8\\\\cos{\\\\theta}^{4} a^{6} r^{6} r_s^{3}-8\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{5} r_s^{2}+4\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{8} r_s^{3}+2\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{7} r_s^{2}-4r^{12} r_s^{3}-8\\\\cos{\\\\theta}^{2} a^{2} r^{10} r_s^{3}-4\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{9} r_s^{2}+6\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{8} r^{4} r_s^{3}+16\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{5} r_s^{2}-4\\\\cos{\\\\theta}^{4} a^{4} r^{8} r_s^{3}+4\\\\sin{\\\\theta}^{2} a^{4} r^{8} r_s^{3} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+4\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{6} r^{6} r_s^{3} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-4\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{8} r^{4} r_s^{3} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-8\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{7} r_s^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-16\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{5} r_s^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+12\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{4} r^{7} r_s^{2} \\\\tan{\\\\theta}+20\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{6} r^{5} r_s^{2} \\\\tan{\\\\theta}+4\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{8} r^{3} r_s^{2} \\\\tan{\\\\theta}%\\n-16\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{6} \\\\tan{\\\\theta} r_s-32\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{4} \\\\tan{\\\\theta} r_s+12\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{4} r^{7} r_s^{2} \\\\tan{\\\\theta}+20\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{6} r^{5} r_s^{2} \\\\tan{\\\\theta}+4\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{8} r^{3} r_s^{2} \\\\tan{\\\\theta}-16\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{6} \\\\tan{\\\\theta} r_s-32\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{4} \\\\tan{\\\\theta} r_s+16\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{2} r^{9} r_s^{2} \\\\tan{\\\\theta}+32\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{7} r_s^{2} \\\\tan{\\\\theta}+16\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{5} r_s^{2} \\\\tan{\\\\theta}-20\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{8} \\\\tan{\\\\theta} r_s-44\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{6} \\\\tan{\\\\theta} r_s+16\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{2} r^{9} r_s^{2} \\\\tan{\\\\theta}+32\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{7} r_s^{2} \\\\tan{\\\\theta}+16\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{5} r_s^{2} \\\\tan{\\\\theta}-20\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{8} \\\\tan{\\\\theta} r_s-44\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{6} \\\\tan{\\\\theta} r_s-16\\\\sin{\\\\theta}^{4} a^{6} r^{7} r_s^{2}-28\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{8} r^{5} r_s^{2}-34\\\\sin{\\\\theta}^{2} a^{4} r^{9} r_s^{2}%\\n-100\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{6} r^{7} r_s^{2}+8a^{4} r^{9} r_s^{2}+24\\\\cos{\\\\theta}^{2} a^{6} r^{7} r_s^{2}+10\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{6} r_s-8\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{6} r_s+16a^{2} r^{11} r_s^{2}+48\\\\cos{\\\\theta}^{2} a^{4} r^{9} r_s^{2}-12\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{8} r_s-96\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{8} r^{5} r_s^{2}+24\\\\cos{\\\\theta}^{4} a^{8} r^{5} r_s^{2}+18\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{4} r_s-16\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{4} r_s+48\\\\cos{\\\\theta}^{4} a^{6} r^{7} r_s^{2}-20\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{6} r_s-14\\\\sin{\\\\theta}^{4} a^{4} r^{9} r_s^{2}-24\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{6} r^{7} r_s^{2}-38\\\\sin{\\\\theta}^{2} a^{2} r^{11} r_s^{2}-116\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{9} r_s^{2}+6\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{8} r_s+8r^{13} r_s^{2}%\\n+24\\\\cos{\\\\theta}^{2} a^{2} r^{11} r_s^{2}-4\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{10} r_s-120\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{7} r_s^{2}+6\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{6} r_s+24\\\\cos{\\\\theta}^{4} a^{4} r^{9} r_s^{2}-4\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{8} r_s-4\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{10} r^{2} r_s^{3} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-8\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{3} r_s^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-4\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{10} r_s^{2} \\\\tan{\\\\theta} r-16\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{2} \\\\tan{\\\\theta} r_s-4\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{10} r_s^{2} \\\\tan{\\\\theta} r-16\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{2} \\\\tan{\\\\theta} r_s-28\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{4} \\\\tan{\\\\theta} r_s-28\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{4} \\\\tan{\\\\theta} r_s+8\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{3} r_s^{2} \\\\tan{\\\\theta}+8\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{3} r_s^{2} \\\\tan{\\\\theta}-4\\\\cos{\\\\theta}^{8} a^{10} r^{2} r_s^{3} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-16\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{8} a^{8} r^{3} r_s^{2} \\\\tan{\\\\theta}-16\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{8} a^{8} r^{3} r_s^{2} \\\\tan{\\\\theta}+6\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} a^{10} r^{2} r_s^{3}%\\n+6\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{8} r^{4} r_s^{3}+14\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{3} r_s^{2}-8\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{3} r_s^{2}-8\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{5} r_s^{2}+4\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} a^{12} r_s^{2} r-28\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{10} r^{3} r_s^{2}+8\\\\cos{\\\\theta}^{6} a^{10} r^{3} r_s^{2}+6\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} r^{2} r_s-8\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} r^{2} r_s+16\\\\cos{\\\\theta}^{6} a^{8} r^{5} r_s^{2}-4\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{4} r_s-44\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{8} r^{5} r_s^{2}-6\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{4} r_s+8\\\\cos{\\\\theta}^{6} a^{6} r^{7} r_s^{2}+4\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{6} r_s+2\\\\sin{\\\\theta}^{6} a^{6} r^{5} r_s^{4}-2\\\\sin{\\\\theta}^{4} a^{4} r^{6} r_s^{5}-2\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6} a^{8} r^{3} r_s^{4}+2\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{6} r^{4} r_s^{5}+4\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{6} r_s^{3}%\\n+4\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{4} r_s^{3}-4\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{2} r^{3} r_s^{2}+4\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{6} r_s^{3}-4\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} r^{5} r_s^{2}-4\\\\sin{\\\\theta}^{6} a^{6} r^{6} r_s^{3}+6\\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{5} r_s^{2}+8\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{2} r^{4} r_s-12\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{7} r_s^{2}+8\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} r^{6} r_s+4\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{6} a^{10} r^{2} r_s^{3}-6\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{10} r^{2} r_s^{3}+6\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} r_s^{2} r+6\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{3} r_s^{2}+8\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{4} r^{2} r_s+8\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{2} r^{4} r_s+2\\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{3} r_s^{2}-2\\\\sin{\\\\theta}^{2} a^{4} r^{9} r_s^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-4\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{6} r^{7} r_s^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+4\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{8} \\\\sin{2\\\\theta} \\\\tan{\\\\theta} r_s+12\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{6} \\\\sin{2\\\\theta} \\\\tan{\\\\theta} r_s%\\n-6\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{4} r^{8} \\\\tan{\\\\theta} r_s-16\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{6} r^{6} \\\\tan{\\\\theta} r_s-12\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{8} r^{4} \\\\tan{\\\\theta} r_s+8\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{7} \\\\tan{\\\\theta}+24\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{5} \\\\tan{\\\\theta}-6\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{4} r^{8} \\\\tan{\\\\theta} r_s-16\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{6} r^{6} \\\\tan{\\\\theta} r_s-12\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{8} r^{4} \\\\tan{\\\\theta} r_s+8\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{7} \\\\tan{\\\\theta}+24\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{5} \\\\tan{\\\\theta}-6\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{2} r^{10} \\\\tan{\\\\theta} r_s-16\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{8} \\\\tan{\\\\theta} r_s-12\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{6} \\\\tan{\\\\theta} r_s+8\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{9} \\\\tan{\\\\theta}+24\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{7} \\\\tan{\\\\theta}-6\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{2} r^{10} \\\\tan{\\\\theta} r_s-16\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{8} \\\\tan{\\\\theta} r_s-12\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{6} \\\\tan{\\\\theta} r_s+8\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{9} \\\\tan{\\\\theta}+24\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{7} \\\\tan{\\\\theta}%\\n+2a^{4} r^{10} \\\\sin{2\\\\theta} \\\\tan{\\\\theta} r_s+6\\\\cos{\\\\theta}^{2} a^{6} r^{8} \\\\sin{2\\\\theta} \\\\tan{\\\\theta} r_s+4\\\\cos{\\\\theta}^{4} a^{8} r^{6} \\\\sin{2\\\\theta} \\\\tan{\\\\theta} r_s-8\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{2} r^{11} \\\\tan{\\\\theta}-40\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{9} \\\\tan{\\\\theta}-8\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{2} r^{11} \\\\tan{\\\\theta}-40\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{9} \\\\tan{\\\\theta}-80\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{7} \\\\tan{\\\\theta}-80\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{7} \\\\tan{\\\\theta}-4\\\\cos{\\\\theta}^{6} a^{10} r^{4} \\\\sin{2\\\\theta} \\\\tan{\\\\theta} r_s-80\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{8} r^{5} \\\\tan{\\\\theta}-80\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{8} r^{5} \\\\tan{\\\\theta}+2a^{2} r^{12} \\\\sin{2\\\\theta} \\\\tan{\\\\theta} r_s+6\\\\cos{\\\\theta}^{2} a^{4} r^{10} \\\\sin{2\\\\theta} \\\\tan{\\\\theta} r_s+4\\\\cos{\\\\theta}^{4} a^{6} r^{8} \\\\sin{2\\\\theta} \\\\tan{\\\\theta} r_s-8\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r^{13} \\\\tan{\\\\theta}-40\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{2} r^{11} \\\\tan{\\\\theta}-8\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) r^{13} \\\\tan{\\\\theta}-40\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{2} r^{11} \\\\tan{\\\\theta}-80\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{4} r^{9} \\\\tan{\\\\theta}%\\n-80\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{4} r^{9} \\\\tan{\\\\theta}-4\\\\cos{\\\\theta}^{6} a^{8} r^{6} \\\\sin{2\\\\theta} \\\\tan{\\\\theta} r_s-80\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{6} r^{7} \\\\tan{\\\\theta}-80\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{6} r^{7} \\\\tan{\\\\theta}-8\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{8} r^{5} r_s^{2}+6\\\\sin{\\\\theta}^{4} a^{6} r^{8} r_s+16\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{8} r^{6} r_s+12\\\\sin{\\\\theta}^{2} a^{4} r^{10} r_s+48\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{6} r^{8} r_s-4a^{4} r^{10} r_s-16\\\\cos{\\\\theta}^{2} a^{6} r^{8} r_s-4\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{7}+4\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{7}-8a^{2} r^{12} r_s-32\\\\cos{\\\\theta}^{2} a^{4} r^{10} r_s+8\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{9}+12\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{10} r^{4} r_s+72\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{8} r^{6} r_s-24\\\\cos{\\\\theta}^{4} a^{8} r^{6} r_s-12\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{5}%\\n+12\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{5}-48\\\\cos{\\\\theta}^{4} a^{6} r^{8} r_s+24\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{7}+6\\\\sin{\\\\theta}^{4} a^{4} r^{10} r_s+16\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{6} r^{8} r_s+12\\\\sin{\\\\theta}^{2} a^{2} r^{12} r_s+48\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{10} r_s-4\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{9}-4r^{14} r_s-16\\\\cos{\\\\theta}^{2} a^{2} r^{12} r_s+4\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{11}+12\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{8} r^{6} r_s+72\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{8} r_s-12\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{7}-24\\\\cos{\\\\theta}^{4} a^{4} r^{10} r_s+12\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{9}+4\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{10} r^{3} r_s^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+12\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{4} \\\\sin{2\\\\theta} \\\\tan{\\\\theta} r_s+24\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{3} \\\\tan{\\\\theta}+24\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{3} \\\\tan{\\\\theta}%\\n+24\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{5} \\\\tan{\\\\theta}+24\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{5} \\\\tan{\\\\theta}-6\\\\cos{\\\\theta}^{8} a^{12} r^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta} r_s-40\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{8} a^{10} r^{3} \\\\tan{\\\\theta}-40\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{8} a^{10} r^{3} \\\\tan{\\\\theta}-6\\\\cos{\\\\theta}^{8} a^{10} r^{4} \\\\sin{2\\\\theta} \\\\tan{\\\\theta} r_s-40\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{8} a^{8} r^{5} \\\\tan{\\\\theta}-40\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{8} a^{8} r^{5} \\\\tan{\\\\theta}+48\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{10} r^{4} r_s-16\\\\cos{\\\\theta}^{6} a^{10} r^{4} r_s-12\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} r^{3}+12\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} r^{3}-32\\\\cos{\\\\theta}^{6} a^{8} r^{6} r_s+24\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{5}+48\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{8} r^{6} r_s-12\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{5}-16\\\\cos{\\\\theta}^{6} a^{6} r^{8} r_s+12\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{7}+2\\\\sin{\\\\theta}^{6} a^{6} r^{7} r_s^{2}+2\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6} a^{8} r^{5} r_s^{2}%\\n-4\\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{6} r_s-4\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{2} r^{5}-4\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} r^{7}-2\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{6} a^{10} r^{3} r_s^{2}-8\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{4} r_s-8\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{4} r^{3}-8\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{2} r^{5}-8\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{10} r^{3} r_s^{2}+2\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} r_s^{2} r+2\\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} a^{12} r_s^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta} r+4\\\\cos{\\\\theta}^{6} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} r^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta} r_s+2\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} a^{12} \\\\tan{\\\\theta} r_s+8\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} \\\\tan{\\\\theta} r+2\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} a^{12} \\\\tan{\\\\theta} r_s+8\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} \\\\tan{\\\\theta} r+2\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} a^{10} r^{2} \\\\tan{\\\\theta} r_s+8\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{3} \\\\tan{\\\\theta}+2\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} a^{10} r^{2} \\\\tan{\\\\theta} r_s+8\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{3} \\\\tan{\\\\theta}-4\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{2} \\\\tan{\\\\theta} r_s%\\n-4\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{2} \\\\tan{\\\\theta} r_s+2\\\\cos{\\\\theta}^{10} a^{12} r_s^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta} r+8\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{10} a^{10} r^{2} \\\\tan{\\\\theta} r_s+8\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{10} a^{10} r^{2} \\\\tan{\\\\theta} r_s-2\\\\cos{\\\\theta}^{10} a^{14} \\\\sin{2\\\\theta} \\\\tan{\\\\theta} r_s-8\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{10} a^{12} \\\\tan{\\\\theta} r-8\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{10} a^{12} \\\\tan{\\\\theta} r-2\\\\cos{\\\\theta}^{10} a^{12} r^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta} r_s-8\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{10} a^{10} r^{3} \\\\tan{\\\\theta}-8\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{10} a^{10} r^{3} \\\\tan{\\\\theta}-2\\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{4} a^{12} r_s^{2} r-2\\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} a^{10} r^{3} r_s^{2}-6\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} r^{2} r_s-2\\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{4} a^{14} r_s+12\\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} a^{12} r^{2} r_s-4\\\\cos{\\\\theta}^{8} a^{12} r^{2} r_s-4\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{10} r+4\\\\cos{\\\\theta}^{6} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{10} r-8\\\\cos{\\\\theta}^{8} a^{10} r^{4} r_s+8\\\\cos{\\\\theta}^{6} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} r^{3}%\\n-2\\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{4} a^{12} r^{2} r_s+12\\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} a^{10} r^{4} r_s-4\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} r^{3}-4\\\\cos{\\\\theta}^{8} a^{8} r^{6} r_s+4\\\\cos{\\\\theta}^{6} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{5}-2\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{6} a^{12} r_s^{2} r+2\\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} a^{12} r_s^{2} r-2\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{10} r_s-4\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} r^{2} r_s+4\\\\cos{\\\\theta}^{6} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} r^{2} r_s-4\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{6} r+4\\\\cos{\\\\theta}^{6} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{4} r_s-4\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{4} r^{3}}{4\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} \\\\tan{\\\\theta}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{r}= & \\\\frac{-\\\\sin{\\\\theta}^{4} a^{6} r^{4} r_s^{3}+4\\\\sin{\\\\theta}^{4} a^{6} r^{5} r_s^{2}-6\\\\sin{\\\\theta}^{4} a^{4} r^{6} r_s^{3}+2\\\\sin{\\\\theta}^{4} a^{4} r^{5} r_s^{4}+7\\\\sin{\\\\theta}^{4} a^{4} r^{7} r_s^{2}-7\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{6} r^{4} r_s^{3}+\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{8} r^{2} r_s^{3}-2\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{10} r_s^{2} r+2\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{6} r^{3} r_s^{4}+3\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{8} r^{3} r_s^{2}-3\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{8} r^{2} r_s^{3}+6\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{6} r^{4} r_s^{3}-4\\\\sin{\\\\theta}^{2} a^{6} r^{5} r_s^{2}-4\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{8} r^{3} r_s^{2}+\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{8} r^{2} r_s^{3}-4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{6} r^{4} r_s^{2}-4\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{6} r^{4} r_s^{2}-4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{8} r^{2} r_s^{2}-4\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{8} r^{2} r_s^{2}%\\n+3\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r_s^{2} r+5\\\\sin{\\\\theta}^{2} a^{4} r^{6} r_s^{3}+4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{5} r_s^{3}+4\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{5} r_s^{3}-5\\\\sin{\\\\theta}^{2} a^{4} r^{7} r_s^{2}-\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{6} r^{5} r_s^{2}-2\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{4} r_s^{4}-2\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{4} r_s^{4}-9\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{4} r_s^{3}-10\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{4} r^{6} r_s^{2}-10\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{4} r^{6} r_s^{2}-12\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{6} r^{4} r_s^{2}-12\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{6} r^{4} r_s^{2}+2\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{3} r_s^{4}+6\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{3} r_s^{2}+\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{2} r_s^{3}-\\\\sin{\\\\theta}^{2} a^{2} r^{8} r_s^{3}+2\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{2} r^{7} r_s^{3}+2\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{2} r^{7} r_s^{3}+3\\\\sin{\\\\theta}^{2} a^{2} r^{9} r_s^{2}%\\n+15\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{7} r_s^{2}-6\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{2} r^{8} r_s^{2}-6\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{2} r^{8} r_s^{2}-8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{6} r_s^{2}-8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{6} r_s^{2}+5\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{5} r_s^{2}-3\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{4} r_s^{3}+4\\\\sin{\\\\theta}^{2} a^{6} r^{6} r_s+8\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{8} r^{4} r_s+5\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{8} r^{3} r_s^{2}+4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{6} r^{5} r_s+4\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{6} r^{5} r_s+8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{8} r^{3} r_s+8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{8} r^{3} r_s-3\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{2} r_s+2\\\\sin{\\\\theta}^{2} a^{4} r^{8} r_s-2\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{6} r^{6} r_s+17\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{5} r_s^{2}+8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{4} r^{7} r_s+8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{4} r^{7} r_s%\\n+16\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{6} r^{5} r_s+16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{6} r^{5} r_s-9\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{4} r_s-2\\\\sin{\\\\theta}^{2} a^{2} r^{10} r_s-10\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{8} r_s+4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{2} r^{9} r_s+4\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{2} r^{9} r_s+8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{7} r_s+8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{7} r_s-4\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{6} r_s-2\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{8} r^{2} r_s^{2}-2\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{8} r^{2} r_s^{2}+4\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{10} r^{2} r_s+\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{10} r_s^{2} r+4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{10} r r_s+4\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{10} r r_s-3\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} r_s-2\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{4} r_s^{2}-2\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{4} r_s^{2}-10\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{8} r^{4} r_s%\\n+2\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{3} r_s^{3}+2\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{3} r_s^{3}+5\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{8} r^{3} r_s^{2}+8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{8} r^{3} r_s+8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{8} r^{3} r_s-2\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{8} r^{2} r_s^{3}-8\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{2} r_s-2\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r_s^{2} r-8\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{6} r_s^{3}-14\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{6} r_s+4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{5} r_s+4\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{5} r_s-\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{4} r_s-\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} a^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta} r r_s-\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} a^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta} r r_s-2\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} r^{2} \\\\tan{\\\\theta} r_s-2\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} r^{2} \\\\tan{\\\\theta} r_s+\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} a^{2} r^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} a^{2} r^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+2\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} r^{3} \\\\tan{\\\\theta}%\\n+2\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} r^{3} \\\\tan{\\\\theta}+\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} a^{4} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} a^{4} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+2\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} a^{2} \\\\tan{\\\\theta} r+2\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} a^{2} \\\\tan{\\\\theta} r+2\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{6} a^{6} r^{3} r_s^{3}+2\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{6} a^{6} r^{3} r_s^{3}-2\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{4} a^{6} r^{3} r_s^{3}-2\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{4} a^{6} r^{3} r_s^{3}+6\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{4} a^{6} r^{4} r_s^{2}+6\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{4} a^{6} r^{4} r_s^{2}+6\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{8} r^{2} r_s^{2}+6\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{8} r^{2} r_s^{2}-2\\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r_s^{2} r-2\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{4} a^{4} r^{4} r_s^{4}-2\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{4} a^{4} r^{4} r_s^{4}+2\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{4} r^{4} r_s^{4}+2\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{4} r^{4} r_s^{4}+6\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{4} a^{4} r^{6} r_s^{2}+6\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{4} a^{4} r^{6} r_s^{2}%\\n+6\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{6} r^{4} r_s^{2}+6\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{6} r^{4} r_s^{2}-2\\\\sin{\\\\theta}^{2} a^{4} r^{5} r_s^{4}-2\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{6} r^{3} r_s^{4}+2\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{2} r_s^{2}+2\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{2} r_s^{2}-2\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{4} r_s^{2} r+2\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{5} r_s^{4}+2\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{4} r_s^{2}+2\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{4} r_s^{2}+2\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{2} r^{3} r_s^{2}+2\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{8} r^{3} r_s^{2}-2a^{4} r^{7} r_s^{2}-4\\\\cos{\\\\theta}^{2} a^{6} r^{5} r_s^{2}+2\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{4} r_s-4a^{2} r^{9} r_s^{2}-8\\\\cos{\\\\theta}^{2} a^{4} r^{7} r_s^{2}+2\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{6} r_s-2\\\\cos{\\\\theta}^{4} a^{8} r^{3} r_s^{2}+2\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{2} r_s%\\n-4\\\\cos{\\\\theta}^{4} a^{6} r^{5} r_s^{2}+2\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{7} r_s^{2}+9\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{6} r^{5} r_s^{2}-2r^{11} r_s^{2}-4\\\\cos{\\\\theta}^{2} a^{2} r^{9} r_s^{2}-2\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{6} a^{6} r^{4} r_s^{2}-2\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{6} a^{6} r^{4} r_s^{2}-4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{4} a^{6} r^{5} r_s-4\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{4} a^{6} r^{5} r_s-8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{8} r^{3} r_s-8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{8} r^{3} r_s+2\\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{2} r_s-4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{4} a^{4} r^{7} r_s-4\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{4} a^{4} r^{7} r_s-8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{6} r^{5} r_s-8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{6} r^{5} r_s-2\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{3} r_s-2\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{3} r_s+2\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{4} r^{2} r_s-2\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{5} r_s%\\n-2\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{5} r_s-2\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{2} r^{4} r_s-2\\\\cos{\\\\theta}^{4} a^{4} r^{7} r_s^{2}-2\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{6} r_s-3\\\\sin{\\\\theta}^{4} a^{6} r^{6} r_s-5\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{8} r^{4} r_s+2a^{4} r^{8} r_s+6\\\\cos{\\\\theta}^{2} a^{6} r^{6} r_s+2\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{5}-2\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{5}+4a^{2} r^{10} r_s+12\\\\cos{\\\\theta}^{2} a^{4} r^{8} r_s-4\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{7}-\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{10} r^{2} r_s+6\\\\cos{\\\\theta}^{4} a^{8} r^{4} r_s+4\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{3}-4\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{3}+12\\\\cos{\\\\theta}^{4} a^{6} r^{6} r_s-8\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{5}-3\\\\sin{\\\\theta}^{4} a^{4} r^{8} r_s%\\n-5\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{6} r^{6} r_s+2\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{7}+2r^{12} r_s+6\\\\cos{\\\\theta}^{2} a^{2} r^{10} r_s-2\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{9}-\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{8} r^{4} r_s+4\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{5}+6\\\\cos{\\\\theta}^{4} a^{4} r^{8} r_s-4\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{7}-2\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6} a^{8} r^{2} r_s^{2}-2\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6} a^{8} r^{2} r_s^{2}-4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{10} r r_s-4\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{10} r r_s+2\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} r_s+2\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{6} r^{3} r_s^{3}+2\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{6} r^{3} r_s^{3}-4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{8} r^{3} r_s-4\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{8} r^{3} r_s-2\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r r_s-2\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r r_s%\\n+2\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{6} r_s-2\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{3} r_s-2\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{3} r_s-2\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{4} r^{2} r_s+\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} a^{10} r_s^{2} r+3\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{2} r_s+\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} a^{12} r_s-6\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{10} r^{2} r_s+2\\\\cos{\\\\theta}^{6} a^{10} r^{2} r_s+2\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} r-2\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} r+4\\\\cos{\\\\theta}^{6} a^{8} r^{4} r_s-4\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{3}+\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} a^{10} r^{2} r_s-6\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{8} r^{4} r_s+2\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{3}+2\\\\cos{\\\\theta}^{6} a^{6} r^{6} r_s-2\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{5}+\\\\sin{\\\\theta}^{6} a^{6} r^{4} r_s^{3}-\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6} a^{8} r^{2} r_s^{3}%\\n+2\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{5} r_s^{2}+2\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{3} r_s^{2}-2\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{2} r^{2} r_s+2\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{5} r_s^{2}-2\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} r^{4} r_s-\\\\sin{\\\\theta}^{6} a^{6} r^{5} r_s^{2}+2\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{2} r^{3}+2\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} r^{5}+\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{6} a^{10} r_s^{2} r+\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} r_s-2\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{2} r_s+2\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{4} r-2\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{4} r_s+2\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{2} r^{3}}{2\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} \\\\tan{\\\\theta} r r_s-2\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} r^{2} \\\\tan{\\\\theta}-2\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} a^{2} \\\\tan{\\\\theta}}\\\\\\\\[-.5ex]\\n\\\\end{aligned}\\\\right.\\n\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"sort_product(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}0 = \\\\left\\\\{\\\\begin{aligned}\\\\square{}_{t}{}_{t}= & \\\\frac{54\\\\cos{\\\\theta}^{2} a^{4} r^{5} r_s^{2}+6\\\\cos{\\\\theta}^{4} a^{6} r^{3} r_s^{2}-172\\\\cos{\\\\theta}^{2} a^{4} r^{6} r_s-72\\\\cos{\\\\theta}^{4} a^{6} r^{4} r_s-4\\\\cos{\\\\theta}^{6} a^{8} r^{2} r_s+90\\\\cos{\\\\theta}^{2} a^{2} r^{7} r_s^{2}-10\\\\cos{\\\\theta}^{4} a^{4} r^{5} r_s^{2}-14\\\\cos{\\\\theta}^{2} a^{2} r^{6} r_s^{3}+10\\\\cos{\\\\theta}^{4} a^{4} r^{4} r_s^{3}-140\\\\cos{\\\\theta}^{2} a^{2} r^{8} r_s-40\\\\cos{\\\\theta}^{4} a^{4} r^{6} r_s+28\\\\cos{\\\\theta}^{6} a^{6} r^{4} r_s-18\\\\cos{\\\\theta}^{6} a^{6} r^{3} r_s^{2}+80r^{9} r_s^{2}-26r^{8} r_s^{3}+50a^{2} r^{7} r_s^{2}-82r^{10} r_s-102a^{2} r^{8} r_s+8\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{6} r_s%\\n+12\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{4} r_s-4\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{5} r_s^{2}-4\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{3} r_s^{2}+4\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{4} r_s+4\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{2} r_s+120\\\\cos{\\\\theta}^{2} a^{4} r^{7}+80\\\\cos{\\\\theta}^{4} a^{6} r^{5}+8\\\\cos{\\\\theta}^{6} a^{8} r^{3}+64\\\\cos{\\\\theta}^{2} a^{2} r^{9}+40\\\\cos{\\\\theta}^{4} a^{4} r^{7}+28r^{11}+52a^{2} r^{9}-4\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{7}-8\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{5}-4\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{5}-8\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{3}-4\\\\cos{\\\\theta}^{8} a^{10} r-4\\\\cos{\\\\theta}^{8} a^{8} r^{3}+10\\\\cos{\\\\theta}^{8} a^{8} r^{2} r_s-4\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{3}%\\n+4\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{2} r_s-4\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r+8\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{6} r^{3} r_s^{2}-8\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{6} r^{4} r_s-8\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{8} r^{2} r_s-8\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{5} r_s^{2}+8\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{6} r_s+24\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{4} r_s-8\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{6} r^{3} r_s^{2}-16\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{3} r_s^{2}+8\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{6} r^{4} r_s+8\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{8} r^{2} r_s+16\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{8} r^{2} r_s-2\\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{2} a^{6} r^{3} r_s^{2}+2\\\\cos{4\\\\theta} a^{6} r^{4} r_s+2\\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{2} a^{8} r^{2} r_s-2\\\\cos{4\\\\theta} a^{4} r^{5} r_s^{2}+4\\\\cos{4\\\\theta} a^{4} r^{6} r_s+6\\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{2} a^{6} r^{4} r_s+2\\\\cos{\\\\theta}^{2} a^{6} r^{3} r_s^{2}%\\n-2a^{6} r^{4} r_s-2\\\\cos{\\\\theta}^{2} a^{8} r^{2} r_s+2a^{4} r^{5} r_s^{2}-28a^{4} r^{6} r_s-38\\\\cos{\\\\theta}^{2} a^{6} r^{4} r_s-16\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} a^{4} r^{5} r_s^{2}+8\\\\cos{2\\\\theta} a^{4} r^{6} r_s+16\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} a^{6} r^{4} r_s-8\\\\cos{2\\\\theta} a^{2} r^{7} r_s^{2}+16\\\\cos{2\\\\theta} a^{2} r^{8} r_s+40\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} a^{4} r^{6} r_s-8\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{4} a^{6} r^{3} r_s^{2}+8\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{4} a^{8} r^{2} r_s+32\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{4} a^{6} r^{4} r_s+12\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{3} r_s^{2} \\\\sin{2\\\\theta}-12\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{4} r^{4} \\\\sin{2\\\\theta} r_s-12\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{6} r^{2} \\\\sin{2\\\\theta} r_s+12\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{2} r^{5} r_s^{2} \\\\sin{2\\\\theta}-24\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{2} r^{6} \\\\sin{2\\\\theta} r_s-36\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{4} \\\\sin{2\\\\theta} r_s%\\n+12\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{3} r_s^{2} \\\\sin{2\\\\theta}-12\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{4} r^{4} \\\\sin{2\\\\theta} r_s-12\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{6} r^{2} \\\\sin{2\\\\theta} r_s+12\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{2} r^{5} r_s^{2} \\\\sin{2\\\\theta}-24\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{2} r^{6} \\\\sin{2\\\\theta} r_s-36\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{4} \\\\sin{2\\\\theta} r_s-10\\\\cos{\\\\theta}^{4} a^{8} r^{2} r_s-2\\\\cos{4\\\\theta} a^{6} r^{5}-4\\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{2} a^{8} r^{3}-2\\\\cos{4\\\\theta} a^{4} r^{7}-4\\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{2} a^{6} r^{5}+2a^{6} r^{5}+4\\\\cos{\\\\theta}^{2} a^{8} r^{3}+26a^{4} r^{7}+60\\\\cos{\\\\theta}^{2} a^{6} r^{5}-8\\\\cos{2\\\\theta} a^{4} r^{7}-24\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} a^{6} r^{5}-8\\\\cos{2\\\\theta} a^{2} r^{9}-24\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} a^{4} r^{7}-24\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{4} a^{8} r^{3}%\\n-24\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{4} a^{6} r^{5}+12\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{4} r^{5} \\\\sin{2\\\\theta}+24\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{6} r^{3} \\\\sin{2\\\\theta}+12\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{2} r^{7} \\\\sin{2\\\\theta}+24\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{5} \\\\sin{2\\\\theta}+12\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{4} r^{5} \\\\sin{2\\\\theta}+24\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{6} r^{3} \\\\sin{2\\\\theta}+12\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{2} r^{7} \\\\sin{2\\\\theta}+24\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{5} \\\\sin{2\\\\theta}+42\\\\cos{\\\\theta}^{4} a^{8} r^{3}+2\\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{4} a^{8} r^{2} r_s-2\\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{4} a^{10} r-2\\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{4} a^{8} r^{3}+2\\\\cos{\\\\theta}^{4} a^{10} r+8\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{6} a^{8} r^{2} r_s-8\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{6} a^{10} r-8\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{6} a^{8} r^{3}-12\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{2} \\\\sin{2\\\\theta} r_s+12\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{8} \\\\sin{2\\\\theta} r+12\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{3} \\\\sin{2\\\\theta}%\\n-12\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{2} \\\\sin{2\\\\theta} r_s+12\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{8} \\\\sin{2\\\\theta} r+12\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{3} \\\\sin{2\\\\theta}+8\\\\cos{\\\\theta}^{6} a^{10} r+6\\\\left(r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{3} r_s^{2}-2\\\\left(r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{2} r_s^{3}+2\\\\left(r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r_s^{2} r-4\\\\sin{\\\\theta}^{2} \\\\left(r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{3} r_s^{2}+2\\\\sin{\\\\theta}^{2} \\\\left(r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{2} r_s^{3}-2\\\\sin{\\\\theta}^{2} \\\\left(r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r_s^{2} r+2\\\\sin{\\\\theta}^{2} \\\\left(r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{4} r_s+2\\\\sin{\\\\theta}^{2} \\\\left(r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{2} r_s+2\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{2} r_s-2\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r_s^{2} r+2\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r_s-4\\\\left(r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{4} r_s-2\\\\left(r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{2} r_s-4\\\\cos{\\\\theta}^{2} \\\\left(r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{2} r_s+2\\\\cos{\\\\theta}^{2} \\\\left(r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r_s^{2} r-2\\\\cos{\\\\theta}^{2} \\\\left(r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r_s%\\n+4\\\\left(r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{5} r_s^{2}-2\\\\left(r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{4} r_s^{3}-2\\\\left(r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{6} r_s-2\\\\cos{\\\\theta}^{2} \\\\left(r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{4} r_s+2\\\\cos{\\\\theta}^{2} \\\\left(r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{3} r_s^{2}-2\\\\cos{\\\\theta}^{6} a^{6} r^{2} r_s^{3}+2\\\\cos{\\\\theta}^{6} a^{8} r_s^{2} r-36\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{2} r^{6} r_s^{2}+60\\\\partial_{r}\\\\left(r^{2}\\\\right) a^{2} r^{7} r_s+60\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{5} r_s-44\\\\partial_{r}\\\\left(r^{2}\\\\right) r^{8} r_s^{2}+40\\\\partial_{r}\\\\left(r^{2}\\\\right) r^{9} r_s+44\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{2} r^{7} r_s-40\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{2} r^{6} r_s^{2}+64\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{2} r^{7} r_s+64\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{5} r_s-48\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) r^{8} r_s^{2}+48\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) r^{9} r_s+56\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{2} r^{7} r_s+8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{2} r^{5} r_s^{3}%\\n-32\\\\partial_{r}\\\\left(r^{2}\\\\right) a^{2} r^{6} r_s^{2}-16\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{4} r_s^{2}+16\\\\partial_{r}\\\\left(r^{2}\\\\right) r^{7} r_s^{3}+8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{2} r^{5} r_s^{3}-32\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{2} r^{6} r_s^{2}-16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{4} r_s^{2}+16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) r^{7} r_s^{3}+16\\\\partial_{r}\\\\left(r^{2}\\\\right) a^{4} r^{5} r_s+8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{6} r^{3} r_s+16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{4} r^{5} r_s+8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{6} r^{3} r_s+12\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{4} r^{4} r_s^{2}-12\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{3} r_s-4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{4} r^{5} r_s+16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{4} r^{4} r_s^{2}-16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{3} r_s-8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{4} r^{5} r_s-8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{4} r^{3} r_s^{3}+16\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{2} r_s^{2}-8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{4} r^{3} r_s^{3}%\\n+16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{2} r_s^{2}-8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{8} r r_s-8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{8} r r_s-4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{2} a^{2} r^{6} r_s^{2}+4\\\\partial_{r}\\\\left(r r_s\\\\right) a^{2} r^{7} r_s+4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{5} r_s-4\\\\partial_{r}\\\\left(r r_s\\\\right) r^{8} r_s^{2}+8\\\\partial_{r}\\\\left(r r_s\\\\right) r^{9} r_s+12\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{2} a^{2} r^{7} r_s+4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{4} a^{4} r^{4} r_s^{2}-4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{3} r_s-4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{4} a^{4} r^{5} r_s+4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{2} r^{6} r_s^{2}-4\\\\partial_{r}\\\\left(a^{2}\\\\right) a^{2} r^{7} r_s-4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{5} r_s+4\\\\partial_{r}\\\\left(a^{2}\\\\right) r^{8} r_s^{2}-8\\\\partial_{r}\\\\left(a^{2}\\\\right) r^{9} r_s-12\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{2} r^{7} r_s-4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{4} r^{4} r_s^{2}+4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{3} r_s%\\n+4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{4} r^{5} r_s+4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{6} r^{2} r_s^{2}-12\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{8} r r_s-4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{6} r^{3} r_s+4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{6} a^{6} r^{2} r_s^{2}-4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{6} a^{8} r r_s-12\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{6} a^{6} r^{3} r_s-4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{6} r^{2} r_s^{2}+4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{8} r r_s+12\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{6} r^{3} r_s-28\\\\partial_{r}\\\\left(r^{2}\\\\right) a^{2} r^{8}-40\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{6}-12\\\\partial_{r}\\\\left(r^{2}\\\\right) r^{10}-16\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{2} r^{8}-32\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{2} r^{8}-48\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{6}-16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) r^{10}-24\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{2} r^{8}-16\\\\partial_{r}\\\\left(r^{2}\\\\right) a^{4} r^{6}-24\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{6} r^{4}%\\n-16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{4} r^{6}-24\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{6} r^{4}-4\\\\partial_{r}\\\\left(r r_s\\\\right) a^{2} r^{8}-8\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{6}-4\\\\partial_{r}\\\\left(r r_s\\\\right) r^{10}-8\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{2} a^{2} r^{8}+4\\\\partial_{r}\\\\left(a^{2}\\\\right) a^{2} r^{8}+8\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{6}+4\\\\partial_{r}\\\\left(a^{2}\\\\right) r^{10}+8\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{2} r^{8}+8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{8} r^{2}+8\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{6} a^{8} r^{2}+8\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{6} a^{6} r^{4}-8\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{8} r^{2}-8\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{6} r^{4}+2\\\\cos{\\\\theta}^{8} a^{8} r_s^{2} r-2\\\\cos{\\\\theta}^{8} a^{10} r_s-16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{6} r^{3} r_s+16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{8} r^{2}+8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{6} r^{4}%\\n+8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{6} r^{2} r_s^{2}-16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{8} r r_s+8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{10}+8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{10}+4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{8} a^{8} r r_s-4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{8} a^{10}-4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{8} a^{8} r^{2}-4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{8} a^{8} r r_s+4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{8} a^{10}+4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{8} a^{8} r^{2}+4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{8} a^{8} r r_s-4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{8} a^{10}-4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{8} a^{8} r^{2}}{8\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{2} r^{2} r_s^{2}-8\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{2} r^{3} r_s-8\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{4} r r_s+8\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} r^{4} r_s^{2}-16\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} r^{5} r_s-24\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{2} r^{3} r_s+8\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{2} r^{4}+16\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{4} r^{2}+8\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} r^{6}+16\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{2} r^{4}-8\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{4} r r_s+8\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{6}+8\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{4} r^{2}} r_s\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{t}= & \\\\frac{-64\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{5} r_s^{2}-16\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{3} r_s^{2}-36\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{2} r^{7} r_s^{2}+52\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{4} r^{5} r_s^{2}-20\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{4} r^{4} r_s^{3}-52\\\\sin{\\\\theta}^{2} r^{9} r_s^{2}+20\\\\sin{\\\\theta}^{2} r^{8} r_s^{3}-48\\\\sin{\\\\theta}^{2} a^{2} r^{7} r_s^{2}+176\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{6} r_s+104\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{4} r_s+64\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{2} r^{8} r_s-12\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{4} r^{6} r_s+44\\\\sin{\\\\theta}^{2} r^{10} r_s+88\\\\sin{\\\\theta}^{2} a^{2} r^{8} r_s+16\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{8} r^{2} r_s-48\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{6} r^{4} r_s+36\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{6} r^{3} r_s^{2}+24\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6} a^{6} r^{3} r_s^{2}-24\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{6} r^{3} r_s^{2}%\\n-16\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{4} r^{5} r_s^{2}+8\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{6} r^{3} r_s^{2}-16\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} a^{4} r^{5} r_s^{2}-12\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{4} a^{6} r^{3} r_s^{2}+16\\\\cos{\\\\theta}^{2} a^{4} r^{5} r_s^{2}+12\\\\cos{\\\\theta}^{4} a^{6} r^{3} r_s^{2}-6\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{3} r_s^{2} \\\\sin{2\\\\theta}-6\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{3} r_s^{2} \\\\sin{2\\\\theta}+3\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{3} r_s^{2} \\\\sin{4\\\\theta}+3\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{3} r_s^{2} \\\\sin{4\\\\theta}+2\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} a^{2} r^{7} r_s^{2}-10\\\\cos{\\\\theta}^{2} a^{2} r^{7} r_s^{2}-6\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{4} a^{4} r^{5} r_s^{2}+2\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{4} a^{4} r^{4} r_s^{3}-10\\\\cos{\\\\theta}^{4} a^{4} r^{5} r_s^{2}-2\\\\cos{\\\\theta}^{4} a^{4} r^{4} r_s^{3}+8\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{3} r_s^{2}-16\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{2} r^{5} r_s^{2} \\\\sin{2\\\\theta}-16\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{2} r^{5} r_s^{2} \\\\sin{2\\\\theta}-8\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{4} r^{3} r_s^{2} \\\\sin{2\\\\theta}%\\n-8\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{4} r^{3} r_s^{2} \\\\sin{2\\\\theta}-16\\\\sin{\\\\theta}^{6} a^{6} r^{4} r_s+16\\\\sin{\\\\theta}^{4} a^{6} r^{4} r_s+48\\\\sin{\\\\theta}^{4} a^{4} r^{6} r_s+88\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{6} r^{4} r_s+6\\\\cos{2\\\\theta} a^{4} r^{6} r_s+16\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} a^{6} r^{4} r_s-6a^{4} r^{6} r_s-16\\\\cos{\\\\theta}^{2} a^{6} r^{4} r_s+6\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{4} r^{4} \\\\sin{2\\\\theta} r_s+6\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{4} r^{4} \\\\sin{2\\\\theta} r_s-3\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{4} r^{4} \\\\sin{4\\\\theta} r_s-3\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{4} r^{4} \\\\sin{4\\\\theta} r_s+8\\\\cos{2\\\\theta} a^{2} r^{8} r_s-4\\\\cos{2\\\\theta} a^{2} r^{7} r_s^{2}-8a^{2} r^{8} r_s+4a^{2} r^{7} r_s^{2}+36\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} a^{4} r^{6} r_s-36\\\\cos{\\\\theta}^{2} a^{4} r^{6} r_s-8\\\\cos{2\\\\theta} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{4} r_s%\\n+20\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{2} r^{6} \\\\sin{2\\\\theta} r_s+20\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{2} r^{6} \\\\sin{2\\\\theta} r_s+34\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{4} \\\\sin{2\\\\theta} r_s+34\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{4} \\\\sin{2\\\\theta} r_s-16\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6} a^{8} r^{2} r_s+16\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{8} r^{2} r_s+40\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{8} r^{2} r_s+10\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{4} a^{8} r^{2} r_s-10\\\\cos{\\\\theta}^{4} a^{8} r^{2} r_s+6\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{6} r^{2} \\\\sin{2\\\\theta} r_s+6\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{6} r^{2} \\\\sin{2\\\\theta} r_s-3\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{6} r^{2} \\\\sin{4\\\\theta} r_s-3\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{6} r^{2} \\\\sin{4\\\\theta} r_s+40\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{4} a^{6} r^{4} r_s-40\\\\cos{\\\\theta}^{4} a^{6} r^{4} r_s-8\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{2} r_s+14\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{2} \\\\sin{2\\\\theta} r_s+14\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{2} \\\\sin{2\\\\theta} r_s+16\\\\sin{\\\\theta}^{6} a^{4} r^{5} r_s^{2}-16\\\\sin{\\\\theta}^{4} a^{4} r^{5} r_s^{2}%\\n-16\\\\sin{\\\\theta}^{4} a^{2} r^{7} r_s^{2}-6\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{2} r^{5} r_s^{2} \\\\sin{2\\\\theta}-6\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{2} r^{5} r_s^{2} \\\\sin{2\\\\theta}+3\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{2} r^{5} r_s^{2} \\\\sin{4\\\\theta}+3\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{2} r^{5} r_s^{2} \\\\sin{4\\\\theta}+6\\\\cos{2\\\\theta} r^{9} r_s^{2}-2\\\\cos{2\\\\theta} r^{8} r_s^{3}-6r^{9} r_s^{2}+2r^{8} r_s^{3}+8\\\\cos{2\\\\theta} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{5} r_s^{2}-8\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r^{7} r_s^{2} \\\\sin{2\\\\theta}-8\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) r^{7} r_s^{2} \\\\sin{2\\\\theta}-32\\\\sin{\\\\theta}^{6} a^{4} r^{6} r_s+32\\\\sin{\\\\theta}^{4} a^{2} r^{8} r_s+64\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{4} r^{6} r_s-6\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{2} r^{6} \\\\sin{4\\\\theta} r_s-6\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{2} r^{6} \\\\sin{4\\\\theta} r_s-6\\\\cos{2\\\\theta} r^{10} r_s+6r^{10} r_s-4\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} a^{2} r^{8} r_s%\\n+12\\\\cos{\\\\theta}^{2} a^{2} r^{8} r_s-16\\\\cos{2\\\\theta} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{6} r_s+16\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r^{8} \\\\sin{2\\\\theta} r_s+16\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) r^{8} \\\\sin{2\\\\theta} r_s+40\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{2} r^{6} \\\\sin{2\\\\theta} r_s+40\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{2} r^{6} \\\\sin{2\\\\theta} r_s-56\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6} a^{6} r^{4} r_s+24\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{6} r^{4} r_s-9\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{4} \\\\sin{4\\\\theta} r_s-9\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{4} \\\\sin{4\\\\theta} r_s+6\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{4} a^{4} r^{6} r_s+18\\\\cos{\\\\theta}^{4} a^{4} r^{6} r_s-24\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{4} r_s+32\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{4} r^{4} \\\\sin{2\\\\theta} r_s+32\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{4} r^{4} \\\\sin{2\\\\theta} r_s+16\\\\sin{\\\\theta}^{6} a^{6} r^{5}-16\\\\sin{\\\\theta}^{4} a^{6} r^{5}-32\\\\sin{\\\\theta}^{4} a^{4} r^{7}-80\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{6} r^{5}-6\\\\cos{2\\\\theta} a^{4} r^{7}%\\n-22\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} a^{6} r^{5}+6a^{4} r^{7}+22\\\\cos{\\\\theta}^{2} a^{6} r^{5}-6\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{4} r^{5} \\\\sin{2\\\\theta}-6\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{4} r^{5} \\\\sin{2\\\\theta}+3\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{4} r^{5} \\\\sin{4\\\\theta}+3\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{4} r^{5} \\\\sin{4\\\\theta}-4\\\\cos{2\\\\theta} a^{2} r^{9}+4a^{2} r^{9}-20\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} a^{4} r^{7}+20\\\\cos{\\\\theta}^{2} a^{4} r^{7}+8\\\\cos{2\\\\theta} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{5}-14\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{2} r^{7} \\\\sin{2\\\\theta}-14\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{2} r^{7} \\\\sin{2\\\\theta}-36\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{5} \\\\sin{2\\\\theta}-36\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{5} \\\\sin{2\\\\theta}+32\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6} a^{8} r^{3}-32\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{8} r^{3}-64\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{8} r^{3}-26\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{4} a^{8} r^{3}%\\n+26\\\\cos{\\\\theta}^{4} a^{8} r^{3}-12\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{6} r^{3} \\\\sin{2\\\\theta}-12\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{6} r^{3} \\\\sin{2\\\\theta}+6\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{6} r^{3} \\\\sin{4\\\\theta}+6\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{6} r^{3} \\\\sin{4\\\\theta}-28\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{4} a^{6} r^{5}+28\\\\cos{\\\\theta}^{4} a^{6} r^{5}+16\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{3}-30\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{3} \\\\sin{2\\\\theta}-30\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{3} \\\\sin{2\\\\theta}+16\\\\sin{\\\\theta}^{6} a^{4} r^{7}-16\\\\sin{\\\\theta}^{4} a^{2} r^{9}-48\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{4} r^{7}+3\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{2} r^{7} \\\\sin{4\\\\theta}+3\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{2} r^{7} \\\\sin{4\\\\theta}+2\\\\cos{2\\\\theta} r^{11}-2r^{11}+2\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} a^{2} r^{9}-2\\\\cos{\\\\theta}^{2} a^{2} r^{9}+8\\\\cos{2\\\\theta} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{7}%\\n-8\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r^{9} \\\\sin{2\\\\theta}-8\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) r^{9} \\\\sin{2\\\\theta}-24\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{2} r^{7} \\\\sin{2\\\\theta}-24\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{2} r^{7} \\\\sin{2\\\\theta}+32\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6} a^{6} r^{5}-48\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{6} r^{5}+6\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{5} \\\\sin{4\\\\theta}+6\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{5} \\\\sin{4\\\\theta}-2\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{4} a^{4} r^{7}+2\\\\cos{\\\\theta}^{4} a^{4} r^{7}+16\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{5}-24\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{4} r^{5} \\\\sin{2\\\\theta}-24\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{4} r^{5} \\\\sin{2\\\\theta}-24\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{6} a^{8} r^{2} r_s-8\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} a^{8} r^{2} r_s+12\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{6} a^{8} r^{2} r_s-12\\\\cos{\\\\theta}^{6} a^{8} r^{2} r_s-3\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{2} \\\\sin{4\\\\theta} r_s-3\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{2} \\\\sin{4\\\\theta} r_s+4\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{6} a^{6} r^{4} r_s%\\n-2\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{6} a^{6} r^{3} r_s^{2}+20\\\\cos{\\\\theta}^{6} a^{6} r^{4} r_s-6\\\\cos{\\\\theta}^{6} a^{6} r^{3} r_s^{2}-8\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{2} r_s+8\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{6} r^{2} \\\\sin{2\\\\theta} r_s+8\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{6} r^{2} \\\\sin{2\\\\theta} r_s+16\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{6} a^{10} r-16\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{10} r-16\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} a^{10} r-10\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{6} a^{10} r+10\\\\cos{\\\\theta}^{6} a^{10} r-6\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{8} \\\\sin{2\\\\theta} r-6\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{8} \\\\sin{2\\\\theta} r+3\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{8} \\\\sin{4\\\\theta} r+3\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{8} \\\\sin{4\\\\theta} r-12\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{6} a^{8} r^{3}+12\\\\cos{\\\\theta}^{6} a^{8} r^{3}+8\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r-8\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{8} \\\\sin{2\\\\theta} r-8\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{8} \\\\sin{2\\\\theta} r%\\n+16\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{6} a^{8} r^{3}-16\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} a^{8} r^{3}+3\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{3} \\\\sin{4\\\\theta}+3\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{3} \\\\sin{4\\\\theta}-2\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{6} a^{6} r^{5}+2\\\\cos{\\\\theta}^{6} a^{6} r^{5}+8\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{3}-8\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{6} r^{3} \\\\sin{2\\\\theta}-8\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{6} r^{3} \\\\sin{2\\\\theta}+20\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{2} r_s+20\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{4} r_s-8\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{3}-8\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{5}-12\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r-12\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{3}+8\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{4} r_s-8\\\\cos{\\\\theta}^{2} r^{9} r_s^{2}-16\\\\cos{\\\\theta}^{4} a^{2} r^{7} r_s^{2}+8\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{6} r_s-8\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{5}%\\n+8\\\\cos{\\\\theta}^{2} r^{10} r_s+24\\\\cos{\\\\theta}^{4} a^{2} r^{8} r_s-8\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{7}-16\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{3}+24\\\\cos{\\\\theta}^{6} a^{4} r^{6} r_s-16\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{5}+8\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{2} r_s-8\\\\cos{\\\\theta}^{6} a^{4} r^{5} r_s^{2}+8\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{4} r_s-16\\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} a^{8} r^{2} r_s+8\\\\cos{\\\\theta}^{8} a^{8} r^{2} r_s-8\\\\cos{\\\\theta}^{6} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r+8\\\\cos{\\\\theta}^{8} a^{6} r^{4} r_s-8\\\\cos{\\\\theta}^{6} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{3}-16\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{3} r_s^{2}+4\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{2} r_s^{3}+36\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{2} r^{6} r_s^{2}+40\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{2} r^{6} r_s^{2}-8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{2} r^{5} r_s^{3}-8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{2} r^{5} r_s^{3}%\\n+16\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{4} r_s^{2}+16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{4} r_s^{2}-12\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{4} r^{4} r_s^{2}-16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{4} r^{4} r_s^{2}+8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{4} r^{3} r_s^{3}+8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{4} r^{3} r_s^{3}-16\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{2} r_s^{2}-16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{2} r_s^{2}-4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{4} r^{4} r_s^{2}+4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{4} r^{4} r_s^{2}-4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{6} r^{2} r_s^{2}-4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{6} r^{2} r_s^{2}+4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{6} r^{2} r_s^{2}+28\\\\sin{\\\\theta}^{2} a^{4} r^{6} r_s+48\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{6} r^{4} r_s-4\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{3} r_s^{2}-60\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{2} r^{7} r_s-64\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{2} r^{7} r_s+32\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{2} r^{6} r_s^{2}+32\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{2} r^{6} r_s^{2}%\\n-16\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{4} r^{5} r_s-16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{4} r^{5} r_s-60\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{5} r_s-64\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{5} r_s-8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{6} r^{3} r_s-8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{6} r^{3} r_s-4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\sin{\\\\theta}^{2} a^{2} r^{7} r_s-4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{5} r_s+4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{2} r^{7} r_s+4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{5} r_s+12\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{3} r_s+4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{3} r_s-4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{3} r_s+20\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{8} r^{2} r_s-4\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r_s^{2} r+16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{3} r_s+8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{8} r r_s+8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{8} r r_s+12\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{8} r r_s+4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{8} r r_s%\\n-4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{8} r r_s-4\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{5} r_s^{2}+4\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{4} r_s^{3}+44\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} r^{8} r_s^{2}+48\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} r^{8} r_s^{2}-16\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} r^{7} r_s^{3}-16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} r^{7} r_s^{3}+4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\sin{\\\\theta}^{2} r^{8} r_s^{2}+4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{2} r^{6} r_s^{2}-4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2} r^{8} r_s^{2}-4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{2} r^{6} r_s^{2}-4\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{6} r_s-40\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} r^{9} r_s-48\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} r^{9} r_s-44\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{2} r^{7} r_s-56\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{2} r^{7} r_s-8\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\sin{\\\\theta}^{2} r^{9} r_s-12\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{2} r^{7} r_s+8\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2} r^{9} r_s+12\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{2} r^{7} r_s%\\n+4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{4} r^{5} r_s-4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{4} r^{5} r_s+8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{4} r^{5} r_s+4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{6} r^{3} r_s+12\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{6} r^{3} r_s-12\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{6} r^{3} r_s+8\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} r^{4} r_s-4\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} r^{3} r_s^{2}+4\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{2} r^{2} r_s+4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{4} r^{5} r_s-28\\\\sin{\\\\theta}^{2} a^{4} r^{7}-76\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{6} r^{5}-104\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{7}-40\\\\sin{\\\\theta}^{2} a^{2} r^{9}+4\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{5}+28\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{2} r^{8}+32\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{2} r^{8}+16\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{4} r^{6}+16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{4} r^{6}+40\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{6}%\\n+48\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{6}+24\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{6} r^{4}+24\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{6} r^{4}+4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\sin{\\\\theta}^{2} a^{2} r^{8}+8\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{6}-4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{2} r^{8}-8\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{6}-68\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{8} r^{3}-88\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{5}-8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{8} r^{2}-8\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{8} r^{2}+8\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{8} r^{2}-28\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{2} r^{9}-12\\\\sin{\\\\theta}^{2} r^{11}+4\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{7}+12\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} r^{10}+16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} r^{10}+16\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{2} r^{8}+24\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{2} r^{8}+4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\sin{\\\\theta}^{2} r^{10}%\\n+8\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{2} r^{8}-4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2} r^{10}-8\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{2} r^{8}-20\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{4} r^{7}-8\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{6} r^{4}+8\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{6} r^{4}-4\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} r^{5}-4\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{2} r^{3}+8\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{2} r_s-4\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r_s^{2} r+16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{6} r^{3} r_s-8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{6} r^{2} r_s^{2}+16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{8} r r_s-4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} a^{8} r r_s+4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} a^{8} r r_s-4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} a^{8} r r_s-20\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{10} r-24\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{8} r^{3}+4\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r_s-16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{8} r^{2}%\\n-8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{10}-8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{10}+4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} a^{10}-4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} a^{10}+4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} a^{10}-4\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{6} r^{5}-8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{6} r^{4}+4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} a^{8} r^{2}-4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} a^{8} r^{2}+4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} a^{8} r^{2}-4\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{2} r^{3}+4\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{2} r^{2} r_s-4\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{4} r}{8\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{2} r^{2} r_s^{2}-8\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{2} r^{3} r_s-8\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{4} r r_s+8\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} r^{4} r_s^{2}-16\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} r^{5} r_s-24\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{2} r^{3} r_s+8\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{2} r^{4}+16\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{4} r^{2}+8\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} r^{6}+16\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{2} r^{4}-8\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{4} r r_s+8\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{6}+8\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{4} r^{2}} a r_s\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}_{\\\\phi}= & \\\\frac{-62\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{5} r_s^{2}-26\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{3} r_s^{2}-46\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{2} r^{7} r_s^{2}+28\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{4} r^{5} r_s^{2}+4\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{2} r^{6} r_s^{3}-10\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{4} r^{4} r_s^{3}-56\\\\sin{\\\\theta}^{2} r^{9} r_s^{2}+22\\\\sin{\\\\theta}^{2} r^{8} r_s^{3}-54\\\\sin{\\\\theta}^{2} a^{2} r^{7} r_s^{2}+180\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{6} r_s+70\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{2} r^{8} r_s+2\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{4} r^{6} r_s+46\\\\sin{\\\\theta}^{2} r^{10} r_s+92\\\\sin{\\\\theta}^{2} a^{2} r^{8} r_s+28\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{8} r^{2} r_s-38\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{6} r^{4} r_s+26\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{6} r^{3} r_s^{2}+24\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6} a^{6} r^{3} r_s^{2}-28\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{6} r^{3} r_s^{2}%\\n-22\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{4} r^{5} r_s^{2}+8\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{6} r^{3} r_s^{2}-16\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} a^{4} r^{5} r_s^{2}-12\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{4} a^{6} r^{3} r_s^{2}+16\\\\cos{\\\\theta}^{2} a^{4} r^{5} r_s^{2}+12\\\\cos{\\\\theta}^{4} a^{6} r^{3} r_s^{2}-6\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{3} r_s^{2} \\\\sin{2\\\\theta}-6\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{3} r_s^{2} \\\\sin{2\\\\theta}+3\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{3} r_s^{2} \\\\sin{4\\\\theta}+3\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{3} r_s^{2} \\\\sin{4\\\\theta}+2\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} a^{2} r^{7} r_s^{2}-2\\\\cos{\\\\theta}^{2} a^{2} r^{7} r_s^{2}-6\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{4} a^{4} r^{5} r_s^{2}+2\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{4} a^{4} r^{4} r_s^{3}+6\\\\cos{\\\\theta}^{4} a^{4} r^{5} r_s^{2}-2\\\\cos{\\\\theta}^{4} a^{4} r^{4} r_s^{3}+8\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{3} r_s^{2}-16\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{2} r^{5} r_s^{2} \\\\sin{2\\\\theta}-16\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{2} r^{5} r_s^{2} \\\\sin{2\\\\theta}-8\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{4} r^{3} r_s^{2} \\\\sin{2\\\\theta}%\\n-8\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{4} r^{3} r_s^{2} \\\\sin{2\\\\theta}-16\\\\sin{\\\\theta}^{6} a^{6} r^{4} r_s+16\\\\sin{\\\\theta}^{4} a^{6} r^{4} r_s+46\\\\sin{\\\\theta}^{4} a^{4} r^{6} r_s+90\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{6} r^{4} r_s+6\\\\cos{2\\\\theta} a^{4} r^{6} r_s+16\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} a^{6} r^{4} r_s-6a^{4} r^{6} r_s-16\\\\cos{\\\\theta}^{2} a^{6} r^{4} r_s+6\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{4} r^{4} \\\\sin{2\\\\theta} r_s+6\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{4} r^{4} \\\\sin{2\\\\theta} r_s-3\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{4} r^{4} \\\\sin{4\\\\theta} r_s-3\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{4} r^{4} \\\\sin{4\\\\theta} r_s+8\\\\cos{2\\\\theta} a^{2} r^{8} r_s-4\\\\cos{2\\\\theta} a^{2} r^{7} r_s^{2}-8a^{2} r^{8} r_s+4a^{2} r^{7} r_s^{2}+36\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} a^{4} r^{6} r_s-36\\\\cos{\\\\theta}^{2} a^{4} r^{6} r_s-8\\\\cos{2\\\\theta} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{4} r_s%\\n+20\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{2} r^{6} \\\\sin{2\\\\theta} r_s+20\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{2} r^{6} \\\\sin{2\\\\theta} r_s+34\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{4} \\\\sin{2\\\\theta} r_s+34\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{4} \\\\sin{2\\\\theta} r_s-16\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6} a^{8} r^{2} r_s+16\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{8} r^{2} r_s+42\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{8} r^{2} r_s+10\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{4} a^{8} r^{2} r_s-10\\\\cos{\\\\theta}^{4} a^{8} r^{2} r_s+6\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{6} r^{2} \\\\sin{2\\\\theta} r_s+6\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{6} r^{2} \\\\sin{2\\\\theta} r_s-3\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{6} r^{2} \\\\sin{4\\\\theta} r_s-3\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{6} r^{2} \\\\sin{4\\\\theta} r_s+40\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{4} a^{6} r^{4} r_s-40\\\\cos{\\\\theta}^{4} a^{6} r^{4} r_s-8\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{2} r_s+14\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{2} \\\\sin{2\\\\theta} r_s+14\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{2} \\\\sin{2\\\\theta} r_s+16\\\\sin{\\\\theta}^{6} a^{4} r^{5} r_s^{2}-14\\\\sin{\\\\theta}^{4} a^{4} r^{5} r_s^{2}%\\n-12\\\\sin{\\\\theta}^{4} a^{2} r^{7} r_s^{2}-6\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{2} r^{5} r_s^{2} \\\\sin{2\\\\theta}-6\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{2} r^{5} r_s^{2} \\\\sin{2\\\\theta}+3\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{2} r^{5} r_s^{2} \\\\sin{4\\\\theta}+3\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{2} r^{5} r_s^{2} \\\\sin{4\\\\theta}+6\\\\cos{2\\\\theta} r^{9} r_s^{2}-2\\\\cos{2\\\\theta} r^{8} r_s^{3}-6r^{9} r_s^{2}+2r^{8} r_s^{3}+8\\\\cos{2\\\\theta} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{5} r_s^{2}-8\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r^{7} r_s^{2} \\\\sin{2\\\\theta}-8\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) r^{7} r_s^{2} \\\\sin{2\\\\theta}-32\\\\sin{\\\\theta}^{6} a^{4} r^{6} r_s+30\\\\sin{\\\\theta}^{4} a^{2} r^{8} r_s+66\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{4} r^{6} r_s-6\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{2} r^{6} \\\\sin{4\\\\theta} r_s-6\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{2} r^{6} \\\\sin{4\\\\theta} r_s-6\\\\cos{2\\\\theta} r^{10} r_s+6r^{10} r_s-4\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} a^{2} r^{8} r_s%\\n+4\\\\cos{\\\\theta}^{2} a^{2} r^{8} r_s-16\\\\cos{2\\\\theta} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{6} r_s+16\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r^{8} \\\\sin{2\\\\theta} r_s+16\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) r^{8} \\\\sin{2\\\\theta} r_s+40\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{2} r^{6} \\\\sin{2\\\\theta} r_s+40\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{2} r^{6} \\\\sin{2\\\\theta} r_s-56\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6} a^{6} r^{4} r_s+26\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{6} r^{4} r_s-9\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{4} \\\\sin{4\\\\theta} r_s-9\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{4} \\\\sin{4\\\\theta} r_s+6\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{4} a^{4} r^{6} r_s-6\\\\cos{\\\\theta}^{4} a^{4} r^{6} r_s-24\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{4} r_s+32\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{4} r^{4} \\\\sin{2\\\\theta} r_s+32\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{4} r^{4} \\\\sin{2\\\\theta} r_s+16\\\\sin{\\\\theta}^{6} a^{6} r^{5}-16\\\\sin{\\\\theta}^{4} a^{6} r^{5}-32\\\\sin{\\\\theta}^{4} a^{4} r^{7}-80\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{6} r^{5}-6\\\\cos{2\\\\theta} a^{4} r^{7}%\\n-22\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} a^{6} r^{5}+6a^{4} r^{7}+22\\\\cos{\\\\theta}^{2} a^{6} r^{5}-6\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{4} r^{5} \\\\sin{2\\\\theta}-6\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{4} r^{5} \\\\sin{2\\\\theta}+3\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{4} r^{5} \\\\sin{4\\\\theta}+3\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{4} r^{5} \\\\sin{4\\\\theta}-4\\\\cos{2\\\\theta} a^{2} r^{9}+4a^{2} r^{9}-20\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} a^{4} r^{7}+20\\\\cos{\\\\theta}^{2} a^{4} r^{7}+8\\\\cos{2\\\\theta} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{5}-14\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{2} r^{7} \\\\sin{2\\\\theta}-14\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{2} r^{7} \\\\sin{2\\\\theta}-36\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{5} \\\\sin{2\\\\theta}-36\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{5} \\\\sin{2\\\\theta}+32\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6} a^{8} r^{3}-32\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{8} r^{3}-64\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{8} r^{3}-26\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{4} a^{8} r^{3}%\\n+26\\\\cos{\\\\theta}^{4} a^{8} r^{3}-12\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{6} r^{3} \\\\sin{2\\\\theta}-12\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{6} r^{3} \\\\sin{2\\\\theta}+6\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{6} r^{3} \\\\sin{4\\\\theta}+6\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{6} r^{3} \\\\sin{4\\\\theta}-28\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{4} a^{6} r^{5}+28\\\\cos{\\\\theta}^{4} a^{6} r^{5}+16\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{3}-30\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{3} \\\\sin{2\\\\theta}-30\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{3} \\\\sin{2\\\\theta}+16\\\\sin{\\\\theta}^{6} a^{4} r^{7}-16\\\\sin{\\\\theta}^{4} a^{2} r^{9}-48\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{4} r^{7}+3\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{2} r^{7} \\\\sin{4\\\\theta}+3\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{2} r^{7} \\\\sin{4\\\\theta}+2\\\\cos{2\\\\theta} r^{11}-2r^{11}+2\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} a^{2} r^{9}-2\\\\cos{\\\\theta}^{2} a^{2} r^{9}+8\\\\cos{2\\\\theta} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{7}%\\n-8\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r^{9} \\\\sin{2\\\\theta}-8\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) r^{9} \\\\sin{2\\\\theta}-24\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{2} r^{7} \\\\sin{2\\\\theta}-24\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{2} r^{7} \\\\sin{2\\\\theta}+32\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6} a^{6} r^{5}-48\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{6} r^{5}+6\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{5} \\\\sin{4\\\\theta}+6\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{5} \\\\sin{4\\\\theta}-2\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{4} a^{4} r^{7}+2\\\\cos{\\\\theta}^{4} a^{4} r^{7}+16\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{5}-24\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{4} r^{5} \\\\sin{2\\\\theta}-24\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{4} r^{5} \\\\sin{2\\\\theta}-24\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{6} a^{8} r^{2} r_s-10\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} a^{8} r^{2} r_s+12\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{6} a^{8} r^{2} r_s-12\\\\cos{\\\\theta}^{6} a^{8} r^{2} r_s-3\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{2} \\\\sin{4\\\\theta} r_s-3\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{2} \\\\sin{4\\\\theta} r_s+4\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{6} a^{6} r^{4} r_s%\\n-2\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{6} a^{6} r^{3} r_s^{2}-4\\\\cos{\\\\theta}^{6} a^{6} r^{4} r_s+2\\\\cos{\\\\theta}^{6} a^{6} r^{3} r_s^{2}-8\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{2} r_s+8\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{6} r^{2} \\\\sin{2\\\\theta} r_s+8\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{6} r^{2} \\\\sin{2\\\\theta} r_s+16\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{6} a^{10} r-16\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{10} r-16\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} a^{10} r-10\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{6} a^{10} r+10\\\\cos{\\\\theta}^{6} a^{10} r-6\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{8} \\\\sin{2\\\\theta} r-6\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{8} \\\\sin{2\\\\theta} r+3\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{8} \\\\sin{4\\\\theta} r+3\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{8} \\\\sin{4\\\\theta} r-12\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{6} a^{8} r^{3}+12\\\\cos{\\\\theta}^{6} a^{8} r^{3}+8\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r-8\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{8} \\\\sin{2\\\\theta} r-8\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{8} \\\\sin{2\\\\theta} r%\\n+16\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{6} a^{8} r^{3}-16\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} a^{8} r^{3}+3\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{3} \\\\sin{4\\\\theta}+3\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{3} \\\\sin{4\\\\theta}-2\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{6} a^{6} r^{5}+2\\\\cos{\\\\theta}^{6} a^{6} r^{5}+8\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{3}-8\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{6} r^{3} \\\\sin{2\\\\theta}-8\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{6} r^{3} \\\\sin{2\\\\theta}+4\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{4} r^{4} r_s^{3}+116\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{4} r_s+20\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{2} r_s+28\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{4} r_s-8\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{3} r_s^{2}-8\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{5} r_s^{2}+16\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{4} r_s+16\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{6} r_s+16\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{2} r_s+16\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{4} r_s-16\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{3}%\\n-16\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{5}-8\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{5}-8\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{7}-16\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{3}-16\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{5}-16\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r-16\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{3}-16\\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} a^{8} r^{2} r_s-8\\\\cos{\\\\theta}^{6} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r-8\\\\cos{\\\\theta}^{6} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{3}+2\\\\sin{\\\\theta}^{2} a^{2} r^{6} r_s^{3}-2\\\\sin{\\\\theta}^{2} a^{4} r^{5} r_s^{2}+30\\\\sin{\\\\theta}^{2} a^{4} r^{6} r_s+46\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{6} r^{4} r_s-4\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{4} r_s^{3}+4\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{6} r^{3} r_s^{2}+18\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{8} r^{2} r_s-2\\\\sin{\\\\theta}^{4} a^{2} r^{6} r_s^{3}+2\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{6} r_s-4\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{5} r_s^{2}%\\n+2\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{4} r_s+2\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{2} r_s^{3}-2\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{8} r_s^{2} r-2\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{8} r_s^{2} r+2\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{10} r_s-2\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{6} r^{2} r_s^{3}+2\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{8} r_s^{2} r-14\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{3} r_s^{2}+2\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} a^{8} r_s^{2} r-2\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} a^{10} r_s+10\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{2} r_s+2\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{2} r_s^{3}+36\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{2} r^{6} r_s^{2}+40\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{2} r^{6} r_s^{2}-8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{2} r^{5} r_s^{3}-8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{2} r^{5} r_s^{3}+16\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{4} r_s^{2}+16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{4} r_s^{2}-12\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{4} r^{4} r_s^{2}-16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{4} r^{4} r_s^{2}%\\n+8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{4} r^{3} r_s^{3}+8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{4} r^{3} r_s^{3}-16\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{2} r_s^{2}-16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{2} r_s^{2}-4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{4} r^{4} r_s^{2}+4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{4} r^{4} r_s^{2}-4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{6} r^{2} r_s^{2}-4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{6} r^{2} r_s^{2}+4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{6} r^{2} r_s^{2}-2\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{3} r_s^{2}-60\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{2} r^{7} r_s-64\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{2} r^{7} r_s+32\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{2} r^{6} r_s^{2}+32\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{2} r^{6} r_s^{2}-16\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{4} r^{5} r_s-16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{4} r^{5} r_s-60\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{5} r_s-64\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{5} r_s-8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{6} r^{3} r_s-8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{6} r^{3} r_s%\\n-4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\sin{\\\\theta}^{2} a^{2} r^{7} r_s-4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{5} r_s+4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{2} r^{7} r_s+4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{5} r_s+12\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{3} r_s+4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{3} r_s-4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{3} r_s-2\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r_s^{2} r+16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{3} r_s+8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{8} r r_s+8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{8} r r_s+12\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{8} r r_s+4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{8} r r_s-4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{8} r r_s+2\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{4} r_s^{3}+44\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} r^{8} r_s^{2}+48\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} r^{8} r_s^{2}-16\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} r^{7} r_s^{3}-16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} r^{7} r_s^{3}+4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\sin{\\\\theta}^{2} r^{8} r_s^{2}%\\n+4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{2} r^{6} r_s^{2}-4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2} r^{8} r_s^{2}-4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{2} r^{6} r_s^{2}-40\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} r^{9} r_s-48\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} r^{9} r_s-44\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{2} r^{7} r_s-56\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{2} r^{7} r_s-8\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\sin{\\\\theta}^{2} r^{9} r_s-12\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{2} r^{7} r_s+8\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2} r^{9} r_s+12\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{2} r^{7} r_s+4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{4} r^{5} r_s-4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{4} r^{5} r_s+8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{4} r^{5} r_s+4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{6} r^{3} r_s+12\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{6} r^{3} r_s-12\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{6} r^{3} r_s+4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{4} r^{5} r_s-28\\\\sin{\\\\theta}^{2} a^{4} r^{7}-76\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{6} r^{5}%\\n-104\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{7}-40\\\\sin{\\\\theta}^{2} a^{2} r^{9}+28\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{2} r^{8}+32\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{2} r^{8}+16\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{4} r^{6}+16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{4} r^{6}+40\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{6}+48\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{6}+24\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{6} r^{4}+24\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{6} r^{4}+4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\sin{\\\\theta}^{2} a^{2} r^{8}+8\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{6}-4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{2} r^{8}-8\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{6}-68\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{8} r^{3}-88\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{5}-8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{8} r^{2}-8\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{8} r^{2}+8\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{8} r^{2}-28\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{2} r^{9}%\\n-12\\\\sin{\\\\theta}^{2} r^{11}+12\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} r^{10}+16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} r^{10}+16\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{2} r^{8}+24\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{2} r^{8}+4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\sin{\\\\theta}^{2} r^{10}+8\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{2} r^{8}-4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2} r^{10}-8\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{2} r^{8}-20\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{4} r^{7}-8\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{6} r^{4}+8\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{6} r^{4}-2\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r_s^{2} r+16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{6} r^{3} r_s-8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{6} r^{2} r_s^{2}+16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{8} r r_s-4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} a^{8} r r_s+4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} a^{8} r r_s-4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} a^{8} r r_s-20\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{10} r%\\n-24\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{8} r^{3}+2\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r_s-16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{8} r^{2}-8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{10}-8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{10}+4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} a^{10}-4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} a^{10}+4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} a^{10}-4\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{6} r^{5}-8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{6} r^{4}+4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} a^{8} r^{2}-4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} a^{8} r^{2}+4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} a^{8} r^{2}}{8\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{2} r^{2} r_s^{2}-8\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{2} r^{3} r_s-8\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{4} r r_s+8\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} r^{4} r_s^{2}-16\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} r^{5} r_s-24\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{2} r^{3} r_s+8\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{2} r^{4}+16\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{4} r^{2}+8\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} r^{6}+16\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{2} r^{4}-8\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{4} r r_s+8\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{6}+8\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{4} r^{2}} a r_s\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{r}= & \\\\frac{14\\\\sin{\\\\theta}^{2} a^{4} r^{8} r_s^{4}-4\\\\sin{\\\\theta}^{2} a^{4} r^{7} r_s^{5}+4\\\\sin{\\\\theta}^{2} a^{6} r^{6} r_s^{4}+8\\\\sin{\\\\theta}^{2} a^{4} r^{9} r_s^{3}+236\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{6} r^{7} r_s^{3}-90\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{6} r^{6} r_s^{4}+36\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{8} r^{5} r_s^{3}+8\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{6} r^{5} r_s^{5}-8\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{8} r^{4} r_s^{4}+4\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{5} r_s^{3}-4\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{4} r_s^{4}+4\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{3} r_s^{3}+18\\\\sin{\\\\theta}^{2} a^{2} r^{10} r_s^{4}-10\\\\sin{\\\\theta}^{2} a^{2} r^{9} r_s^{5}+2\\\\sin{\\\\theta}^{2} a^{2} r^{11} r_s^{3}+258\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{9} r_s^{3}-166\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{8} r_s^{4}+46\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{7} r_s^{5}-8\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{7} r_s^{3}%\\n+4\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{6} r_s^{4}-38\\\\sin{\\\\theta}^{2} a^{4} r^{10} r_s^{2}-16\\\\sin{\\\\theta}^{2} a^{6} r^{8} r_s^{2}-274\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{6} r^{8} r_s^{2}-80\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{8} r^{6} r_s^{2}-4\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{4} r_s^{2}-18\\\\sin{\\\\theta}^{2} a^{2} r^{12} r_s^{2}-198\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{10} r_s^{2}+4\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{8} r_s^{2}-532\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{8} r^{6} r_s^{2}+372\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{8} r^{5} r_s^{3}-112\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{10} r^{4} r_s^{2}-70\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{8} r^{4} r_s^{4}+32\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{10} r^{3} r_s^{3}-476\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{8} r_s^{2}+552\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{7} r_s^{3}-270\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{6} r_s^{4}+4\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{5} r_s^{3}-2\\\\left(a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} r^{6} r_s^{2}+2\\\\left(a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} r^{5} r_s^{3}%\\n-2\\\\left(a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} a^{2} r^{4} r_s^{2}+4\\\\cos{\\\\theta}^{2} \\\\left(a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} a^{2} r^{4} r_s^{2}-4\\\\cos{\\\\theta}^{2} \\\\left(a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} a^{2} r^{3} r_s^{3}+4\\\\cos{\\\\theta}^{2} \\\\left(a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} a^{4} r^{2} r_s^{2}-4\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{8} r^{3} r_s^{5}+4\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{10} r^{2} r_s^{4}+4\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{2} r_s^{4}-4\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} r_s^{3} r+42\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{5} r_s^{5}-4\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{4} r_s^{4}-396\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{10} r^{4} r_s^{2}+148\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{10} r^{3} r_s^{3}-48\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{12} r^{2} r_s^{2}+2\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{10} r^{2} r_s^{4}-4\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{12} r_s^{3} r-4\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} r_s^{3} r+4\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{10} r_s^{2}-452\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{8} r^{6} r_s^{2}+380\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{8} r^{5} r_s^{3}-106\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{8} r^{4} r_s^{4}%\\n-4\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{4} r_s^{2}+4\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{3} r_s^{3}-2\\\\cos{\\\\theta}^{4} \\\\left(a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} a^{4} r^{2} r_s^{2}+2\\\\cos{\\\\theta}^{4} \\\\left(a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} a^{4} r_s^{3} r-2\\\\cos{\\\\theta}^{4} \\\\left(a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} a^{6} r_s^{2}-2\\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{2} a^{8} r^{4} r_s^{4}+\\\\cos{4\\\\theta} a^{8} r^{5} r_s^{3}+\\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{2} a^{10} r^{3} r_s^{3}-2\\\\cos{4\\\\theta} a^{6} r^{6} r_s^{4}+6\\\\cos{4\\\\theta} a^{6} r^{7} r_s^{3}+10\\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{2} a^{8} r^{5} r_s^{3}-2\\\\cos{4\\\\theta} a^{8} r^{6} r_s^{2}-4\\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{2} a^{10} r^{4} r_s^{2}-6\\\\cos{4\\\\theta} a^{6} r^{8} r_s^{2}-14\\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{2} a^{8} r^{6} r_s^{2}+4\\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{4} a^{10} r^{3} r_s^{3}-2\\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{4} a^{12} r^{2} r_s^{2}-10\\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{4} a^{10} r^{4} r_s^{2}-6\\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{2} a^{6} r^{6} r_s^{4}-4\\\\cos{4\\\\theta} a^{4} r^{8} r_s^{4}%\\n+6\\\\cos{4\\\\theta} a^{4} r^{9} r_s^{3}+12\\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{2} a^{6} r^{7} r_s^{3}+\\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{2} a^{6} r^{5} r_s^{5}+\\\\cos{4\\\\theta} a^{4} r^{7} r_s^{5}-4\\\\cos{4\\\\theta} a^{4} r^{10} r_s^{2}-10\\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{2} a^{6} r^{8} r_s^{2}+7\\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{4} a^{8} r^{5} r_s^{3}-8\\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{4} a^{8} r^{6} r_s^{2}-2\\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{4} a^{8} r^{4} r_s^{4}+2\\\\cos{\\\\theta}^{2} a^{8} r^{4} r_s^{4}-a^{8} r^{5} r_s^{3}-\\\\cos{\\\\theta}^{2} a^{10} r^{3} r_s^{3}+2a^{6} r^{6} r_s^{4}-18a^{6} r^{7} r_s^{3}-42\\\\cos{\\\\theta}^{2} a^{8} r^{5} r_s^{3}+2a^{8} r^{6} r_s^{2}+4\\\\cos{\\\\theta}^{2} a^{10} r^{4} r_s^{2}+30a^{6} r^{8} r_s^{2}+102\\\\cos{\\\\theta}^{2} a^{8} r^{6} r_s^{2}-24\\\\cos{\\\\theta}^{4} a^{10} r^{3} r_s^{3}%\\n+2\\\\cos{\\\\theta}^{4} a^{12} r^{2} r_s^{2}+114\\\\cos{\\\\theta}^{4} a^{10} r^{4} r_s^{2}+68\\\\cos{\\\\theta}^{2} a^{6} r^{6} r_s^{4}+18a^{4} r^{8} r_s^{4}-66a^{4} r^{9} r_s^{3}-240\\\\cos{\\\\theta}^{2} a^{6} r^{7} r_s^{3}-\\\\cos{\\\\theta}^{2} a^{6} r^{5} r_s^{5}-a^{4} r^{7} r_s^{5}+82a^{4} r^{10} r_s^{2}+316\\\\cos{\\\\theta}^{2} a^{6} r^{8} r_s^{2}-263\\\\cos{\\\\theta}^{4} a^{8} r^{5} r_s^{3}+412\\\\cos{\\\\theta}^{4} a^{8} r^{6} r_s^{2}+52\\\\cos{\\\\theta}^{4} a^{8} r^{4} r_s^{4}+116a^{2} r^{12} r_s^{2}+444\\\\cos{\\\\theta}^{2} a^{4} r^{10} r_s^{2}-114r^{13} r_s^{3}+70r^{14} r_s^{2}+266\\\\cos{\\\\theta}^{2} a^{2} r^{12} r_s^{2}-30\\\\cos{\\\\theta}^{2} a^{4} r^{7} r_s^{5}-2a^{2} r^{9} r_s^{5}%\\n+48a^{2} r^{10} r_s^{4}+188\\\\cos{\\\\theta}^{2} a^{4} r^{8} r_s^{4}-126a^{2} r^{11} r_s^{3}-450\\\\cos{\\\\theta}^{2} a^{4} r^{9} r_s^{3}+172\\\\cos{\\\\theta}^{4} a^{6} r^{6} r_s^{4}-472\\\\cos{\\\\theta}^{4} a^{6} r^{7} r_s^{3}-50\\\\cos{\\\\theta}^{2} a^{2} r^{9} r_s^{5}-22r^{11} r_s^{5}+82r^{12} r_s^{4}+230\\\\cos{\\\\theta}^{2} a^{2} r^{10} r_s^{4}-378\\\\cos{\\\\theta}^{2} a^{2} r^{11} r_s^{3}+146\\\\cos{\\\\theta}^{4} a^{4} r^{8} r_s^{4}-372\\\\cos{\\\\theta}^{4} a^{4} r^{9} r_s^{3}+560\\\\cos{\\\\theta}^{4} a^{6} r^{8} r_s^{2}-124\\\\cos{\\\\theta}^{6} a^{8} r^{5} r_s^{3}+206\\\\cos{\\\\theta}^{6} a^{10} r^{4} r_s^{2}+224\\\\cos{\\\\theta}^{6} a^{8} r^{6} r_s^{2}+340\\\\cos{\\\\theta}^{4} a^{4} r^{10} r_s^{2}-56\\\\cos{\\\\theta}^{6} a^{6} r^{7} r_s^{3}+140\\\\cos{\\\\theta}^{6} a^{6} r^{8} r_s^{2}%\\n-30\\\\cos{\\\\theta}^{4} a^{6} r^{5} r_s^{5}+36\\\\cos{\\\\theta}^{6} a^{8} r^{4} r_s^{4}-93\\\\cos{\\\\theta}^{6} a^{10} r^{3} r_s^{3}-10\\\\cos{\\\\theta}^{4} a^{4} r^{7} r_s^{5}-38\\\\cos{\\\\theta}^{6} a^{6} r^{6} r_s^{4}+42\\\\cos{\\\\theta}^{6} a^{12} r^{2} r_s^{2}+22\\\\cos{\\\\theta}^{8} a^{10} r^{3} r_s^{3}+30\\\\cos{\\\\theta}^{8} a^{12} r^{2} r_s^{2}-36\\\\cos{\\\\theta}^{8} a^{10} r^{4} r_s^{2}+70\\\\cos{\\\\theta}^{8} a^{8} r^{5} r_s^{3}-26\\\\cos{\\\\theta}^{8} a^{8} r^{6} r_s^{2}-2\\\\cos{\\\\theta}^{6} a^{8} r^{3} r_s^{5}+2\\\\cos{\\\\theta}^{6} a^{10} r^{2} r_s^{4}+4\\\\cos{\\\\theta}^{8} a^{10} r^{2} r_s^{4}-4\\\\cos{\\\\theta}^{8} a^{12} r_s^{3} r+18\\\\cos{\\\\theta}^{6} a^{6} r^{5} r_s^{5}-36\\\\cos{\\\\theta}^{8} a^{8} r^{4} r_s^{4}+\\\\cos{4\\\\theta} a^{8} r^{7} r_s+3\\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{2} a^{10} r^{5} r_s+2\\\\cos{4\\\\theta} a^{6} r^{9} r_s%\\n+6\\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{2} a^{8} r^{7} r_s+3\\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{4} a^{12} r^{3} r_s+6\\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{4} a^{10} r^{5} r_s+\\\\cos{4\\\\theta} a^{4} r^{11} r_s+3\\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{2} a^{6} r^{9} r_s+3\\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{4} a^{8} r^{7} r_s-a^{8} r^{7} r_s-3\\\\cos{\\\\theta}^{2} a^{10} r^{5} r_s-14a^{6} r^{9} r_s-62\\\\cos{\\\\theta}^{2} a^{8} r^{7} r_s-3\\\\cos{\\\\theta}^{4} a^{12} r^{3} r_s-102\\\\cos{\\\\theta}^{4} a^{10} r^{5} r_s-33a^{4} r^{11} r_s-143\\\\cos{\\\\theta}^{2} a^{6} r^{9} r_s-219\\\\cos{\\\\theta}^{4} a^{8} r^{7} r_s-36a^{2} r^{13} r_s-152\\\\cos{\\\\theta}^{2} a^{4} r^{11} r_s-16r^{15} r_s-68\\\\cos{\\\\theta}^{2} a^{2} r^{13} r_s-224\\\\cos{\\\\theta}^{4} a^{6} r^{9} r_s%\\n-129\\\\cos{\\\\theta}^{6} a^{10} r^{5} r_s-120\\\\cos{\\\\theta}^{6} a^{8} r^{7} r_s-104\\\\cos{\\\\theta}^{4} a^{4} r^{11} r_s-64\\\\cos{\\\\theta}^{6} a^{6} r^{9} r_s-74\\\\cos{\\\\theta}^{6} a^{12} r^{3} r_s-8\\\\cos{\\\\theta}^{8} a^{12} r^{3} r_s+4\\\\cos{\\\\theta}^{8} a^{10} r^{5} r_s-8\\\\cos{\\\\theta}^{8} a^{8} r^{7} r_s-2\\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{6} a^{12} r^{2} r_s^{2}+\\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{6} a^{14} r r_s+2\\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{6} a^{12} r^{3} r_s-2\\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{6} a^{10} r^{4} r_s^{2}+\\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{6} a^{10} r^{5} r_s+\\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{6} a^{10} r^{3} r_s^{3}-\\\\cos{\\\\theta}^{6} a^{14} r r_s-20\\\\cos{\\\\theta}^{8} a^{14} r r_s-28\\\\cos{\\\\theta}^{10} a^{12} r^{2} r_s^{2}+12\\\\cos{\\\\theta}^{10} a^{14} r r_s+16\\\\cos{\\\\theta}^{10} a^{12} r^{3} r_s-22\\\\cos{\\\\theta}^{10} a^{10} r^{4} r_s^{2}%\\n+4\\\\cos{\\\\theta}^{10} a^{10} r^{5} r_s-2\\\\cos{\\\\theta}^{10} a^{12} r_s^{3} r+2\\\\cos{\\\\theta}^{10} a^{14} r_s^{2}+18\\\\cos{\\\\theta}^{10} a^{10} r^{3} r_s^{3}+208\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{8} r_s^{3}-48\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{7} r_s^{4}+80\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{6} r^{6} r_s^{3}+92\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{6} r_s^{3}+4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{8} r^{4} r_s^{3}-92\\\\partial_{r}\\\\left(r^{2}\\\\right) a^{4} r^{9} r_s^{2}+68\\\\partial_{r}\\\\left(r^{2}\\\\right) a^{4} r^{8} r_s^{3}-24\\\\partial_{r}\\\\left(r^{2}\\\\right) a^{6} r^{7} r_s^{2}-176\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{6} r^{7} r_s^{2}-40\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{8} r^{5} r_s^{2}-72\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{8} r^{5} r_s^{2}-8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{10} r^{3} r_s^{2}+124\\\\partial_{r}\\\\left(r^{2}\\\\right) a^{2} r^{10} r_s^{3}-48\\\\partial_{r}\\\\left(r^{2}\\\\right) a^{2} r^{9} r_s^{4}-168\\\\partial_{r}\\\\left(r^{2}\\\\right) a^{2} r^{11} r_s^{2}-456\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{9} r_s^{2}%\\n-456\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{7} r_s^{2}+60\\\\partial_{r}\\\\left(r^{2}\\\\right) a^{4} r^{10} r_s+12\\\\partial_{r}\\\\left(r^{2}\\\\right) a^{6} r^{8} r_s+192\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{6} r^{8} r_s+32\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{8} r^{6} r_s+216\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{8} r^{6} r_s+24\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{10} r^{4} r_s+116\\\\partial_{r}\\\\left(r^{2}\\\\right) a^{2} r^{12} r_s+448\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{10} r_s+680\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{8} r_s-216\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{8} r^{5} r_s^{2}+8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{8} r^{4} r_s^{3}+16\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{10} r^{3} r_s^{2}+96\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{10} r^{4} r_s+512\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{8} r^{6} r_s+264\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{2} r^{10} r_s^{3}-80\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{2} r^{9} r_s^{4}+276\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{4} r^{8} r_s^{3}-52\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{4} r^{7} r_s^{4}+100\\\\partial_{r}\\\\left(r^{2}\\\\right) r^{12} r_s^{3}%\\n-44\\\\partial_{r}\\\\left(r^{2}\\\\right) r^{11} r_s^{4}-116\\\\partial_{r}\\\\left(r^{2}\\\\right) r^{13} r_s^{2}-400\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{2} r^{11} r_s^{2}-552\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{4} r^{9} r_s^{2}+68\\\\partial_{r}\\\\left(r^{2}\\\\right) r^{14} r_s+288\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{2} r^{12} r_s+488\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{4} r^{10} r_s-384\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{6} r^{7} r_s^{2}+144\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{6} r^{6} r_s^{3}+416\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{6} r^{8} r_s+208\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{8} r_s^{3}-48\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{7} r_s^{4}+80\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{6} r^{6} r_s^{3}+92\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{6} r_s^{3}+4\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{8} r^{4} r_s^{3}-92\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{4} r^{9} r_s^{2}+68\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{4} r^{8} r_s^{3}-24\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{6} r^{7} r_s^{2}-176\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{6} r^{7} r_s^{2}-40\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{8} r^{5} r_s^{2}%\\n-72\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{8} r^{5} r_s^{2}-8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{10} r^{3} r_s^{2}+124\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{2} r^{10} r_s^{3}-48\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{2} r^{9} r_s^{4}-168\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{2} r^{11} r_s^{2}-456\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{9} r_s^{2}-456\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{7} r_s^{2}+60\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{4} r^{10} r_s+12\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{6} r^{8} r_s+192\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{6} r^{8} r_s+32\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{8} r^{6} r_s+216\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{8} r^{6} r_s+24\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{10} r^{4} r_s+116\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{2} r^{12} r_s+448\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{10} r_s+680\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{8} r_s-216\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{8} r^{5} r_s^{2}+8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{8} r^{4} r_s^{3}+16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{10} r^{3} r_s^{2}+96\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{10} r^{4} r_s%\\n+512\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{8} r^{6} r_s+264\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{2} r^{10} r_s^{3}-80\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{2} r^{9} r_s^{4}+276\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{4} r^{8} r_s^{3}-52\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{4} r^{7} r_s^{4}+100\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) r^{12} r_s^{3}-44\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) r^{11} r_s^{4}-116\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) r^{13} r_s^{2}-400\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{2} r^{11} r_s^{2}-552\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{4} r^{9} r_s^{2}+68\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) r^{14} r_s+288\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{2} r^{12} r_s+488\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{4} r^{10} r_s-384\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{6} r^{7} r_s^{2}+144\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{6} r^{6} r_s^{3}+416\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{6} r^{8} r_s+8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{6} r_s^{5}-16\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{6} r^{5} r_s^{4}+8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{6} r_s^{5}-16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{6} r^{5} r_s^{4}%\\n-20\\\\partial_{r}\\\\left(r^{2}\\\\right) a^{4} r^{7} r_s^{4}+12\\\\partial_{r}\\\\left(r^{2}\\\\right) a^{6} r^{6} r_s^{3}-20\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{4} r^{7} r_s^{4}+12\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{6} r^{6} r_s^{3}+8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{8} r^{4} r_s^{3}+8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{8} r^{4} r_s^{3}+8\\\\partial_{r}\\\\left(r^{2}\\\\right) a^{2} r^{8} r_s^{5}+8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{2} r^{8} r_s^{5}+8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{2} r^{8} r_s^{5}+8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{2} r^{8} r_s^{5}+8\\\\partial_{r}\\\\left(r^{2}\\\\right) r^{10} r_s^{5}+8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) r^{10} r_s^{5}+4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{8} r^{3} r_s^{4}+4\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{8} r^{3} r_s^{4}-4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{10} r^{2} r_s^{3}-4\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{10} r^{2} r_s^{3}-8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{10} r^{2} r_s^{3}-8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{10} r^{2} r_s^{3}+8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{12} r_s^{2} r+8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{12} r_s^{2} r%\\n-16\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{6} r^{5} r_s^{4}-16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{6} r^{5} r_s^{4}-48\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{8} a^{10} r^{3} r_s^{2}+4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{8} a^{12} r_s^{2} r-48\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{8} a^{10} r^{3} r_s^{2}+4\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{8} a^{12} r_s^{2} r-4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{8} a^{14} r_s-4\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{8} a^{14} r_s+196\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{8} a^{10} r^{4} r_s+12\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{8} a^{12} r^{2} r_s+196\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{8} a^{10} r^{4} r_s+12\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{8} a^{12} r^{2} r_s-132\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{8} a^{8} r^{5} r_s^{2}-132\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{8} a^{8} r^{5} r_s^{2}+180\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{8} a^{8} r^{6} r_s+180\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{8} a^{8} r^{6} r_s+8\\\\cos{2\\\\theta} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} a^{2} r^{2}+8\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} a^{4}-4\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} a^{2} \\\\sin{2\\\\theta}-4\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} a^{2} \\\\sin{2\\\\theta}%\\n-16\\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} r^{4}-16\\\\cos{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} a^{2} r^{2}+12\\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} r^{3} r_s+12\\\\cos{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} a^{2} r r_s+8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} r^{3}+8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} r^{3}-8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} r^{2} r_s-8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} r^{2} r_s+8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} a^{2} r+8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} a^{2} r-8\\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} a^{2} r^{2}-8\\\\cos{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} a^{4}-8\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{8} r^{4} r_s^{4}+8\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{8} r^{5} r_s^{3}+8\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{10} r^{3} r_s^{3}-8\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{6} r^{6} r_s^{4}+24\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{6} r^{7} r_s^{3}+40\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{8} r^{5} r_s^{3}+4\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{3} r_s^{3}-16\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{5} r_s^{3}%\\n+88\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{6} r_s^{2}+32\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{4} r_s^{2}-28\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{5} r_s^{3}-104\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{7} r_s^{3}+192\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{8} r_s^{2}+128\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{6} r_s^{2}+16\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{6} r_s^{4}-20\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{7} r_s^{3}+20\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{8} r_s^{4}-68\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{9} r_s^{3}+2\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{8} r^{3} r_s^{5}-4\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{4} r_s^{4}+48\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{7} r_s^{4}-8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{6} r_s^{5}+16\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{6} r^{5} r_s^{4}+48\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{7} r_s^{4}-8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{6} r_s^{5}+16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{6} r^{5} r_s^{4}+12\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{5} r_s^{4}-4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{8} r^{3} r_s^{4}%\\n+12\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{5} r_s^{4}-4\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{8} r^{3} r_s^{4}-56\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{6} r_s^{3}+8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{5} r_s^{4}-24\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{4} r_s^{3}-56\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{6} r_s^{3}+8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{5} r_s^{4}-24\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{4} r_s^{3}-64\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{4} r^{8} r_s^{3}+20\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{4} r^{7} r_s^{4}-12\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{6} r^{6} r_s^{3}-64\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{4} r^{8} r_s^{3}+20\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{4} r^{7} r_s^{4}-12\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{6} r^{6} r_s^{3}-88\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{6} r^{6} r_s^{3}-88\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{6} r^{6} r_s^{3}+80\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{7} r_s^{2}-24\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{6} r_s^{3}+16\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{5} r_s^{2}+80\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{7} r_s^{2}%\\n-24\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{6} r_s^{3}+16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{5} r_s^{2}+4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{10} r^{2} r_s^{3}+4\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{10} r^{2} r_s^{3}+128\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{5} r_s^{2}+16\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{3} r_s^{2}+128\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{5} r_s^{2}+16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{3} r_s^{2}+36\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{2} r^{9} r_s^{4}-8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{2} r^{8} r_s^{5}+36\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{2} r^{9} r_s^{4}-8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{2} r^{8} r_s^{5}-40\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{8} r_s^{3}+8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{7} r_s^{4}-40\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{8} r_s^{3}+8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{7} r_s^{4}-60\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{2} r^{10} r_s^{3}-60\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{2} r^{10} r_s^{3}-104\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{8} r_s^{3}-104\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{8} r_s^{3}%\\n+72\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{9} r_s^{2}+72\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{9} r_s^{2}-44\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{6} r_s^{3}-44\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{6} r_s^{3}+136\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{7} r_s^{2}+136\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{7} r_s^{2}-8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{8} r^{4} r_s^{3}-8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{8} r^{4} r_s^{3}+84\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{10} r_s^{2}+48\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{8} r_s^{2}-16\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{8} r^{6} r_s^{2}-32\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{10} r^{4} r_s^{2}-24\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{6} r^{8} r_s^{2}-56\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{8} r^{6} r_s^{2}-104\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{7} r_s-96\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{5} r_s-136\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{9} r_s-144\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{7} r_s+68\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{4} r^{9} r_s^{2}+24\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{6} r^{7} r_s^{2}%\\n+68\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{4} r^{9} r_s^{2}+24\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{6} r^{7} r_s^{2}+136\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{6} r^{7} r_s^{2}+40\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{8} r^{5} r_s^{2}+136\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{6} r^{7} r_s^{2}+40\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{8} r^{5} r_s^{2}-88\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{8} r_s-32\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{6} r_s-88\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{8} r_s-32\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{6} r_s-200\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{6} r_s-64\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{4} r_s-200\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{6} r_s-64\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{4} r_s+44\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{2} r^{11} r_s^{2}+44\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{2} r^{11} r_s^{2}+96\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{9} r_s^{2}+96\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{9} r_s^{2}-56\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{10} r_s-56\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{10} r_s%\\n-136\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{8} r_s-136\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{8} r_s-44\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{11} r_s-36\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{9} r_s+16\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} a^{10} r^{3} r_s^{3}-16\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} a^{12} r^{2} r_s^{2}-40\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} a^{10} r^{4} r_s^{2}+86\\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} a^{10} r^{3} r_s^{3}-102\\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} a^{12} r^{2} r_s^{2}-178\\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} a^{10} r^{4} r_s^{2}-8\\\\cos{\\\\theta}^{6} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} r^{2} r_s^{2}-24\\\\cos{\\\\theta}^{6} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} r^{3} r_s+16\\\\cos{\\\\theta}^{6} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{4} r_s^{2}-56\\\\cos{\\\\theta}^{6} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{5} r_s-4\\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} a^{10} r^{2} r_s^{4}+4\\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} a^{12} r_s^{3} r+8\\\\cos{\\\\theta}^{6} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{3} r_s^{3}+8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{10} r^{2} r_s^{3}+8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{10} r^{2} r_s^{3}+72\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{5} r_s^{2}%\\n-16\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{4} r_s^{3}+48\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{3} r_s^{2}+72\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{5} r_s^{2}-16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{4} r_s^{3}+48\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{3} r_s^{2}-8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{10} r^{3} r_s^{2}-8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{12} r_s^{2} r-8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{10} r^{3} r_s^{2}-8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{12} r_s^{2} r-136\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{4} r_s-32\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} r^{2} r_s-136\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{4} r_s-32\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} r^{2} r_s-104\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{6} r_s-104\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{6} r_s+32\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{8} a^{8} r^{4} r_s^{3}+32\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{8} a^{8} r^{4} r_s^{3}-6\\\\left(\\\\sin{\\\\theta}^{2} a^{2} r^{2} r_s-\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r_s+2r^{4} r_s+2\\\\cos{\\\\theta}^{2} a^{2} r^{2} r_s-2\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r\\\\right)^{2} r^{4} r_s^{2}+2\\\\left(\\\\sin{\\\\theta}^{2} a^{2} r^{2} r_s-\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r_s+2r^{4} r_s+2\\\\cos{\\\\theta}^{2} a^{2} r^{2} r_s-2\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r\\\\right)^{2} r^{3} r_s^{3}-2\\\\left(\\\\sin{\\\\theta}^{2} a^{2} r^{2} r_s-\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r_s+2r^{4} r_s+2\\\\cos{\\\\theta}^{2} a^{2} r^{2} r_s-2\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r\\\\right)^{2} a^{2} r^{2} r_s^{2}%\\n+6\\\\left(\\\\sin{\\\\theta}^{2} a^{2} r^{2} r_s-\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r_s+2r^{4} r_s+2\\\\cos{\\\\theta}^{2} a^{2} r^{2} r_s-2\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r\\\\right)^{2} r^{5} r_s+4\\\\left(\\\\sin{\\\\theta}^{2} a^{2} r^{2} r_s-\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r_s+2r^{4} r_s+2\\\\cos{\\\\theta}^{2} a^{2} r^{2} r_s-2\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r\\\\right)^{2} a^{2} r^{3} r_s+8\\\\cos{\\\\theta}^{2} \\\\left(\\\\sin{\\\\theta}^{2} a^{2} r^{2} r_s-\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r_s+2r^{4} r_s+2\\\\cos{\\\\theta}^{2} a^{2} r^{2} r_s-2\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r\\\\right)^{2} a^{2} r^{3} r_s-4\\\\cos{\\\\theta}^{2} \\\\left(\\\\sin{\\\\theta}^{2} a^{2} r^{2} r_s-\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r_s+2r^{4} r_s+2\\\\cos{\\\\theta}^{2} a^{2} r^{2} r_s-2\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r\\\\right)^{2} a^{2} r^{2} r_s^{2}+4\\\\cos{\\\\theta}^{2} \\\\left(\\\\sin{\\\\theta}^{2} a^{2} r^{2} r_s-\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r_s+2r^{4} r_s+2\\\\cos{\\\\theta}^{2} a^{2} r^{2} r_s-2\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r\\\\right)^{2} a^{4} r r_s+8\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{8} r^{7} r_s+24\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{10} r^{5} r_s+8\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{6} r^{9} r_s+24\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{8} r^{7} r_s+116\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{6} r^{9} r_s+248\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{8} r^{7} r_s+60\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{11} r_s+152\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{9} r_s+248\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{10} r^{5} r_s+176\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{8} r^{7} r_s+32\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{8}+48\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{6}+32\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{10}+48\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{8}+12\\\\sin{\\\\theta}^{2} a^{6} r^{9} r_s%\\n+56\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{8} r^{7} r_s+20\\\\sin{\\\\theta}^{2} a^{4} r^{11} r_s+96\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{10} r^{5} r_s+56\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{7} r_s^{2}+64\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{8} r^{5} r_s^{2}+56\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{7} r_s^{2}+64\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{8} r^{5} r_s^{2}-24\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{4} r^{10} r_s-12\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{6} r^{8} r_s-24\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{4} r^{10} r_s-12\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{6} r^{8} r_s-64\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{6} r^{8} r_s-32\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{8} r^{6} r_s-64\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{6} r^{8} r_s-32\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{8} r^{6} r_s+32\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{9}+16\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{7}+32\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{9}+16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{7}-48\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{8} r^{6} r_s%\\n-24\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{10} r^{4} r_s-48\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{8} r^{6} r_s-24\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{10} r^{4} r_s+96\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{7}+48\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{5}+96\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{7}+48\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{5}-12\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{2} r^{12} r_s-12\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{2} r^{12} r_s-32\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{10} r_s-32\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{10} r_s+16\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{11}+16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{11}-24\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{8} r_s-24\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{8} r_s+48\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{9}+48\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{9}-32\\\\partial_{r}\\\\left(r^{2}\\\\right) a^{2} r^{13}-16\\\\partial_{r}\\\\left(r^{2}\\\\right) a^{4} r^{11}-160\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{11}%\\n-80\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{6} r^{9}-32\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{2} r^{13}-16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{4} r^{11}-160\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{11}-80\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{6} r^{9}-320\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{9}-160\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{8} r^{7}-320\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{9}-160\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{8} r^{7}-320\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{8} r^{7}-160\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{10} r^{5}-320\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{8} r^{7}-160\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{10} r^{5}+8\\\\sin{\\\\theta}^{2} a^{2} r^{13} r_s-16\\\\partial_{r}\\\\left(r^{2}\\\\right) r^{15}-80\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{2} r^{13}-16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) r^{15}-80\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{2} r^{13}-160\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{4} r^{11}-160\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{4} r^{11}%\\n+8\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{12}+8\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{10}-160\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{6} r^{9}-160\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{6} r^{9}+24\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} a^{12} r^{3} r_s+24\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} a^{10} r^{5} r_s+116\\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} a^{12} r^{3} r_s+96\\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} a^{10} r^{5} r_s+32\\\\cos{\\\\theta}^{6} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} r^{4}+32\\\\cos{\\\\theta}^{6} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{6}+72\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{12} r^{3} r_s+96\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{5}+48\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} r^{3}+96\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{5}+48\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} r^{3}+48\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{7}+48\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{7}-160\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{8} a^{10} r^{5}-80\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{8} a^{12} r^{3}-160\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{8} a^{10} r^{5}%\\n-80\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{8} a^{12} r^{3}-80\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{8} a^{8} r^{7}-80\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{8} a^{8} r^{7}-2\\\\left(\\\\sin{\\\\theta}^{2} a^{2} r^{2} r_s-\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r_s+2r^{4} r_s+2\\\\cos{\\\\theta}^{2} a^{2} r^{2} r_s-2\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r\\\\right)^{2} r^{6}-2\\\\left(\\\\sin{\\\\theta}^{2} a^{2} r^{2} r_s-\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r_s+2r^{4} r_s+2\\\\cos{\\\\theta}^{2} a^{2} r^{2} r_s-2\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r\\\\right)^{2} a^{2} r^{4}-4\\\\cos{\\\\theta}^{2} \\\\left(\\\\sin{\\\\theta}^{2} a^{2} r^{2} r_s-\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r_s+2r^{4} r_s+2\\\\cos{\\\\theta}^{2} a^{2} r^{2} r_s-2\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r\\\\right)^{2} a^{2} r^{4}-4\\\\cos{\\\\theta}^{2} \\\\left(\\\\sin{\\\\theta}^{2} a^{2} r^{2} r_s-\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r_s+2r^{4} r_s+2\\\\cos{\\\\theta}^{2} a^{2} r^{2} r_s-2\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r\\\\right)^{2} a^{4} r^{2}-16\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{8} r^{4} r_s^{3}-16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{8} r^{4} r_s^{3}+8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{10} r^{3} r_s^{2}+8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{10} r^{3} r_s^{2}-8\\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{4} a^{12} r^{2} r_s^{2}+8\\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{4} a^{14} r r_s+8\\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{4} a^{12} r^{3} r_s-22\\\\cos{\\\\theta}^{10} \\\\sin{\\\\theta}^{2} a^{12} r^{2} r_s^{2}+20\\\\cos{\\\\theta}^{10} \\\\sin{\\\\theta}^{2} a^{14} r r_s+20\\\\cos{\\\\theta}^{10} \\\\sin{\\\\theta}^{2} a^{12} r^{3} r_s+4\\\\cos{\\\\theta}^{8} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{10} r r_s-4\\\\cos{\\\\theta}^{8} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} r^{3} r_s+8\\\\cos{\\\\theta}^{8} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{10} r^{2}%\\n+8\\\\cos{\\\\theta}^{8} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} r^{4}+20\\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} a^{14} r r_s+2\\\\cos{\\\\theta}^{10} \\\\sin{\\\\theta}^{2} a^{12} r_s^{3} r-2\\\\cos{\\\\theta}^{10} \\\\sin{\\\\theta}^{2} a^{14} r_s^{2}-4\\\\cos{\\\\theta}^{8} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} r^{2} r_s^{2}-24\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{4} r_s+8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{3} r_s^{2}-24\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} r^{2} r_s-24\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{4} r_s+8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{3} r_s^{2}-24\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} r^{2} r_s+8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} a^{12} r^{2} r_s-4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} a^{12} r_s^{2} r+4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} a^{14} r_s+8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} a^{12} r^{2} r_s-4\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} a^{12} r_s^{2} r+4\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} a^{14} r_s+32\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} r^{3}+16\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{10} r+32\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} r^{3}%\\n+16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{10} r+16\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{5}+16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{5}+32\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{10} a^{10} r^{4} r_s-16\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{10} a^{10} r^{3} r_s^{2}+32\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{10} a^{12} r^{2} r_s+32\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{10} a^{10} r^{4} r_s-16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{10} a^{10} r^{3} r_s^{2}+32\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{10} a^{12} r^{2} r_s-32\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{10} a^{12} r^{3}-16\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{10} a^{14} r-32\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{10} a^{12} r^{3}-16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{10} a^{14} r-16\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{10} a^{10} r^{5}-16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{10} a^{10} r^{5}+4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} a^{10} r^{4} r_s-4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} a^{10} r^{3} r_s^{2}+4\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} a^{10} r^{4} r_s-4\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} a^{10} r^{3} r_s^{2}-2\\\\cos{\\\\theta}^{4} \\\\left(\\\\sin{\\\\theta}^{2} a^{2} r^{2} r_s-\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r_s+2r^{4} r_s+2\\\\cos{\\\\theta}^{2} a^{2} r^{2} r_s-2\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r\\\\right)^{2} a^{4} r^{2}%\\n+2\\\\cos{\\\\theta}^{4} \\\\left(\\\\sin{\\\\theta}^{2} a^{2} r^{2} r_s-\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r_s+2r^{4} r_s+2\\\\cos{\\\\theta}^{2} a^{2} r^{2} r_s-2\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r\\\\right)^{2} a^{4} r r_s-2\\\\cos{\\\\theta}^{4} \\\\left(\\\\sin{\\\\theta}^{2} a^{2} r^{2} r_s-\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r_s+2r^{4} r_s+2\\\\cos{\\\\theta}^{2} a^{2} r^{2} r_s-2\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r\\\\right)^{2} a^{6}}{8\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} r^{2}-8\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} r r_s+8\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} a^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{\\\\theta}= & \\\\frac{-8\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{8} r^{4} r_s^{4}-48\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{8} r^{5} r_s^{3}-20\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{10} r^{3} r_s^{3}+8\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{6} r^{5} r_s^{5}+8\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2} a^{8} r^{4} r_s^{4}+56\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2} a^{8} r^{5} r_s^{3}+16\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2} a^{10} r^{3} r_s^{3}+16\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{8} r^{4} r_s^{4}-136\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{8} r^{5} r_s^{3}-64\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{10} r^{3} r_s^{3}+176\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{8} r^{6} r_s^{2}+184\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{10} r^{4} r_s^{2}-96\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{6} r^{7} r_s^{3}-216\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2} a^{8} r^{6} r_s^{2}-192\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2} a^{10} r^{4} r_s^{2}+320\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{8} r^{6} r_s^{2}+208\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{10} r^{4} r_s^{2}+64\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{12} r^{2} r_s^{2}-56\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2} a^{12} r^{2} r_s^{2}%\\n+48\\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{12} r^{2} r_s^{2}-168\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{4} r^{8} r_s^{4}+40\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{4} r^{7} r_s^{5}-48\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2} a^{6} r^{6} r_s^{4}+272\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2} a^{6} r^{7} r_s^{3}+208\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2} a^{8} r^{5} r_s^{3}-72\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{6} r^{6} r_s^{4}+124\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{6} r^{7} r_s^{3}-8\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{8} r^{5} r_s^{3}-8\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2} a^{6} r^{5} r_s^{5}-16\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2} a^{8} r^{4} r_s^{4}+4\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{6} r^{5} r_s^{5}+208\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{6} r^{8} r_s^{2}+216\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{4} r^{9} r_s^{3}-368\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2} a^{6} r^{8} r_s^{2}-408\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2} a^{8} r^{6} r_s^{2}-24\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{6} r^{8} r_s^{2}+64\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{8} r^{6} r_s^{2}-192\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2} a^{10} r^{4} r_s^{2}+48\\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{10} r^{4} r_s^{2}%\\n+56\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2} a^{10} r^{3} r_s^{3}-12\\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{10} r^{3} r_s^{3}-4\\\\sin{\\\\theta}^{2} \\\\sin{2\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{6} r_s^{4}-4\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\sin{2\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{4} r_s^{4}+8\\\\sin{\\\\theta}^{2} \\\\sin{2\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{7} r_s^{3}+16\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\sin{2\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{5} r_s^{3}+8\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\sin{2\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{10} r^{3} r_s^{3}-12\\\\sin{\\\\theta}^{2} \\\\sin{2\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{8} r_s^{4}-20\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\sin{2\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{6} r_s^{4}+4\\\\sin{\\\\theta}^{2} \\\\sin{2\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{7} r_s^{5}+4\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\sin{2\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{5} r_s^{5}+12\\\\sin{\\\\theta}^{2} \\\\sin{2\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{9} r_s^{3}+28\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\sin{2\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{7} r_s^{3}+20\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\sin{2\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{5} r_s^{3}-8\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\sin{2\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{4} r_s^{4}-8\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{5} r_s^{3} \\\\sin{2\\\\theta}-8\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{3} r_s^{3} \\\\sin{2\\\\theta}+16\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{6} r_s^{2} \\\\sin{2\\\\theta}+32\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{4} r_s^{2} \\\\sin{2\\\\theta}+16\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{10} r^{2} r_s^{2} \\\\sin{2\\\\theta}%\\n-40\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{7} r_s^{3} \\\\sin{2\\\\theta}-64\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{5} r_s^{3} \\\\sin{2\\\\theta}+12\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{6} r_s^{4} \\\\sin{2\\\\theta}+12\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{4} r_s^{4} \\\\sin{2\\\\theta}+44\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{8} r_s^{2} \\\\sin{2\\\\theta}+100\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{6} r_s^{2} \\\\sin{2\\\\theta}+68\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{4} r_s^{2} \\\\sin{2\\\\theta}-24\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{3} r_s^{3} \\\\sin{2\\\\theta}-8\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{5} r_s^{3} \\\\sin{2\\\\theta}-8\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{3} r_s^{3} \\\\sin{2\\\\theta}+16\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{6} r_s^{2} \\\\sin{2\\\\theta}+32\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{4} r_s^{2} \\\\sin{2\\\\theta}+16\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{10} r^{2} r_s^{2} \\\\sin{2\\\\theta}-40\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{7} r_s^{3} \\\\sin{2\\\\theta}-64\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{5} r_s^{3} \\\\sin{2\\\\theta}+12\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{6} r_s^{4} \\\\sin{2\\\\theta}+12\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{4} r_s^{4} \\\\sin{2\\\\theta}+44\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{8} r_s^{2} \\\\sin{2\\\\theta}+100\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{6} r_s^{2} \\\\sin{2\\\\theta}+68\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{4} r_s^{2} \\\\sin{2\\\\theta}%\\n-24\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{3} r_s^{3} \\\\sin{2\\\\theta}-36\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{9} r_s^{3} \\\\sin{2\\\\theta}-68\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{7} r_s^{3} \\\\sin{2\\\\theta}+20\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{8} r_s^{4} \\\\sin{2\\\\theta}+28\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{6} r_s^{4} \\\\sin{2\\\\theta}+28\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{10} r_s^{2} \\\\sin{2\\\\theta}+68\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{8} r_s^{2} \\\\sin{2\\\\theta}+52\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{6} r_s^{2} \\\\sin{2\\\\theta}-36\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{5} r_s^{3} \\\\sin{2\\\\theta}-36\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{9} r_s^{3} \\\\sin{2\\\\theta}-68\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{7} r_s^{3} \\\\sin{2\\\\theta}+20\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{8} r_s^{4} \\\\sin{2\\\\theta}+28\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{6} r_s^{4} \\\\sin{2\\\\theta}+28\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{10} r_s^{2} \\\\sin{2\\\\theta}+68\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{8} r_s^{2} \\\\sin{2\\\\theta}+52\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{6} r_s^{2} \\\\sin{2\\\\theta}-36\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{5} r_s^{3} \\\\sin{2\\\\theta}-4\\\\sin{\\\\theta}^{2} \\\\sin{2\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{8} r_s^{2}-12\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\sin{2\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{6} r_s^{2}-12\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\sin{2\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{10} r^{4} r_s^{2}%\\n-4\\\\sin{\\\\theta}^{2} \\\\sin{2\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{10} r_s^{2}-12\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\sin{2\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{8} r_s^{2}-12\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\sin{2\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{6} r_s^{2}-8\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{7} \\\\sin{2\\\\theta} r_s-24\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{5} \\\\sin{2\\\\theta} r_s-24\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{10} r^{3} \\\\sin{2\\\\theta} r_s-16\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{9} \\\\sin{2\\\\theta} r_s-48\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{7} \\\\sin{2\\\\theta} r_s-48\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{5} \\\\sin{2\\\\theta} r_s-8\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{7} \\\\sin{2\\\\theta} r_s-24\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{5} \\\\sin{2\\\\theta} r_s-24\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{10} r^{3} \\\\sin{2\\\\theta} r_s-16\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{9} \\\\sin{2\\\\theta} r_s-48\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{7} \\\\sin{2\\\\theta} r_s-48\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{5} \\\\sin{2\\\\theta} r_s-8\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{11} \\\\sin{2\\\\theta} r_s-24\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{9} \\\\sin{2\\\\theta} r_s-24\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{7} \\\\sin{2\\\\theta} r_s-8\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{11} \\\\sin{2\\\\theta} r_s-24\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{9} \\\\sin{2\\\\theta} r_s%\\n-24\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{7} \\\\sin{2\\\\theta} r_s-4\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\sin{2\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{12} r^{2} r_s^{2}-4\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\sin{2\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{10} r^{4} r_s^{2}+4\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\sin{2\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{10} r^{3} r_s^{3}-8\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{12} \\\\sin{2\\\\theta} r r_s-16\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{10} r^{3} \\\\sin{2\\\\theta} r_s+12\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{10} r^{2} r_s^{2} \\\\sin{2\\\\theta}-8\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{12} \\\\sin{2\\\\theta} r r_s-16\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{10} r^{3} \\\\sin{2\\\\theta} r_s+12\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{10} r^{2} r_s^{2} \\\\sin{2\\\\theta}-8\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{5} \\\\sin{2\\\\theta} r_s+12\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{4} r_s^{2} \\\\sin{2\\\\theta}-8\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{5} \\\\sin{2\\\\theta} r_s+12\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{4} r_s^{2} \\\\sin{2\\\\theta}-4\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{5} r_s^{5} \\\\sin{2\\\\theta}-4\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{5} r_s^{5} \\\\sin{2\\\\theta}+8\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{4} r_s^{4} \\\\sin{2\\\\theta}+8\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{4} r_s^{4} \\\\sin{2\\\\theta}-4\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{7} r_s^{5} \\\\sin{2\\\\theta}-4\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{7} r_s^{5} \\\\sin{2\\\\theta}%\\n-4\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{3} r_s^{3} \\\\sin{2\\\\theta}-4\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{3} r_s^{3} \\\\sin{2\\\\theta}-32\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{6} r_s^{4}-16\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{4} r_s^{4}+128\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{7} r_s^{3}+112\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{5} r_s^{3}+32\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{10} r^{3} r_s^{3}-80\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{8} r_s^{4}-64\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{6} r_s^{4}+16\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{7} r_s^{5}+8\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{5} r_s^{5}+144\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{9} r_s^{3}+152\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{7} r_s^{3}+64\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{5} r_s^{3}-16\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{4} r_s^{4}+8\\\\cos{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{7} r_s^{3}+16\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{5} r_s^{3}-16\\\\cos{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{8} r_s^{2}-48\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{6} r_s^{2}-48\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{10} r^{4} r_s^{2}%\\n+48\\\\cos{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{9} r_s^{3}-16\\\\cos{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{8} r_s^{4}-48\\\\cos{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{10} r_s^{2}-160\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{8} r_s^{2}-192\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{6} r_s^{2}+8\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{10} r^{3} r_s^{3}-16\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{12} r^{2} r_s^{2}-96\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{10} r^{4} r_s^{2}-32\\\\cos{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{10} r_s^{4}+8\\\\cos{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{9} r_s^{5}+48\\\\cos{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{11} r_s^{3}-32\\\\cos{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{12} r_s^{2}-112\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{10} r_s^{2}-144\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{8} r_s^{2}-80\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{6} r_s^{2}+8\\\\cos{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{9} r_s+32\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{7} r_s+48\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{10} r^{5} r_s+16\\\\cos{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{11} r_s+64\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{9} r_s%\\n+96\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{7} r_s+32\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{12} r^{3} r_s+64\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{10} r^{5} r_s+8\\\\cos{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{13} r_s+32\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{11} r_s+48\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{9} r_s+32\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{7} r_s-16\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{12} r^{2} r_s^{2}-16\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{10} r^{4} r_s^{2}+8\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{10} r^{3} r_s^{3}+8\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{14} r r_s+16\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{12} r^{3} r_s+8\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{10} r^{5} r_s+2\\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{2} r_s^{2}-2\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{2} r_s^{2}+2\\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{4} r_s^{2}-2\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{4} r_s^{2}-\\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{3} r_s^{3}+\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{3} r_s^{3}-16\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{4} r_s^{2}%\\n+4\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{3} r_s^{3}-8\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{2} r_s^{2}-8\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{6} r_s^{2}+4\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{5} r_s^{3}-\\\\cos{4\\\\theta} \\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{3} r_s+\\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{3} r_s-2\\\\cos{4\\\\theta} \\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{5} r_s-2\\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{5} r_s+2\\\\cos{4\\\\theta} \\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{4} r_s^{2}-2\\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{4} r_s^{2}-11\\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{7} r_s+6\\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{6} r_s^{2}+\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{5} r_s+2\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{3} r_s-12\\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{9} r_s+16\\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{8} r_s^{2}-\\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{10} r r_s+\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{10} r r_s-2\\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{3} r_s+12\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{3} r_s%\\n+4\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{10} r r_s+12\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{5} r_s+2\\\\cos{4\\\\theta} \\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{6} r_s^{2}-\\\\cos{4\\\\theta} \\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{5} r_s^{3}+\\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{5} r_s^{3}-4\\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{7} r_s^{3}+8\\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} r^{10} r_s^{2}-4\\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} r^{9} r_s^{3}-\\\\cos{4\\\\theta} \\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{7} r_s-4\\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} r^{11} r_s-\\\\cos{4\\\\theta} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{5} r_s+4\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{7} r_s+8\\\\cos{2\\\\theta} \\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{2}+8\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4}-4\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{2} \\\\sin{2\\\\theta}-4\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{2} \\\\sin{2\\\\theta}+4\\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} r^{3} r_s+4\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{2} r r_s+8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} r^{3}-8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} r^{2} r_s%\\n-8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} r^{2} r_s+8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{2} r+8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{2} r+8\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} r^{3}-8\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} r^{3}-8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{2} r+8\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{2} r-8\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{2} r-8\\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{2}-8\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4}+64\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{6} r_s^{4}-72\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{7} r_s^{3}-72\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{5} r_s^{3}+80\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{8} r_s^{4}+32\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{9} r_s^{3}+96\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{7} r_s^{3}-24\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{10} r^{3} r_s^{3}+96\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{5} r_s^{3}-72\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{3} r_s^{3}+144\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{4} r_s^{2}%\\n+72\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{2} r_s^{2}-184\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{5} r_s^{3}+200\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{6} r_s^{2}+136\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{4} r_s^{2}-192\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{8} r_s^{4}-128\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{10} r_s^{4}+240\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{11} r_s^{3}+472\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{9} r_s^{3}-128\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{6} r_s^{4}+456\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{7} r_s^{3}+8\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{5} r_s^{3}+16\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{7} r_s^{3}-64\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{8} r_s^{2}-56\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{6} r_s^{2}-24\\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{4} r^{9} r_s^{3}-88\\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{2} r^{10} r_s^{4}+96\\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{2} r^{11} r_s^{3}+28\\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{2} r^{9} r_s^{5}-28\\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{6} r^{7} r_s^{3}-32\\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} r^{12} r_s^{4}%\\n+48\\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} r^{13} r_s^{3}+24\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{9} r_s^{5}+32\\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{10} r_s^{4}+8\\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} r^{11} r_s^{5}-24\\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{9} r_s^{3}+24\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{7} r_s^{5}+88\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{8} r_s^{2}+8\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} r^{9} r_s^{3}-24\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} r^{10} r_s^{2}-112\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{7} r_s^{3}+72\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{6} r_s^{2}+8\\\\cos{\\\\theta} \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{6} r^{6} r_s^{4} \\\\sin{2\\\\theta}+8\\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{8} r^{4} r_s^{4} \\\\sin{2\\\\theta}-8\\\\cos{\\\\theta} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{4} r^{7} r_s^{5} \\\\sin{2\\\\theta}-8\\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{6} r^{5} r_s^{5} \\\\sin{2\\\\theta}+32\\\\cos{\\\\theta} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{4} r^{8} r_s^{4} \\\\sin{2\\\\theta}+64\\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{6} r^{6} r_s^{4} \\\\sin{2\\\\theta}+32\\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{8} r^{4} r_s^{4} \\\\sin{2\\\\theta}-8\\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2} a^{4} r^{8} r_s^{4} \\\\sin{\\\\theta} \\\\sin{2\\\\theta}-16\\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{6} r^{6} r_s^{4} \\\\sin{\\\\theta} \\\\sin{2\\\\theta}%\\n-8\\\\cos{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{8} r^{4} r_s^{4} \\\\sin{\\\\theta} \\\\sin{2\\\\theta}+8\\\\cos{\\\\theta} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{5} r_s^{3} \\\\sin{\\\\theta} \\\\sin{2\\\\theta}+8\\\\cos{\\\\theta}^{3} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{3} r_s^{3} \\\\sin{\\\\theta} \\\\sin{2\\\\theta}-8\\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2} a^{2} r^{10} r_s^{4} \\\\sin{\\\\theta} \\\\sin{2\\\\theta}-16\\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{4} r^{8} r_s^{4} \\\\sin{\\\\theta} \\\\sin{2\\\\theta}-8\\\\cos{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{6} r^{6} r_s^{4} \\\\sin{\\\\theta} \\\\sin{2\\\\theta}+8\\\\cos{\\\\theta} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{7} r_s^{3} \\\\sin{\\\\theta} \\\\sin{2\\\\theta}+8\\\\cos{\\\\theta}^{3} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{5} r_s^{3} \\\\sin{\\\\theta} \\\\sin{2\\\\theta}+16\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{6} r^{5} r_s^{3}+16\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{8} r^{3} r_s^{3}-24\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{4} r^{6} r_s^{4}-24\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{6} r^{4} r_s^{4}+96\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{4} r^{7} r_s^{3}+192\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{6} r^{5} r_s^{3}+96\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{8} r^{3} r_s^{3}-56\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2} a^{4} r^{7} r_s^{3} \\\\sin{\\\\theta}-112\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{6} r^{5} r_s^{3} \\\\sin{\\\\theta}-56\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{8} r^{3} r_s^{3} \\\\sin{\\\\theta}-136\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2} a^{2} r^{9} r_s^{3} \\\\sin{\\\\theta}-296\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{4} r^{7} r_s^{3} \\\\sin{\\\\theta}%\\n-184\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{6} r^{5} r_s^{3} \\\\sin{\\\\theta}-16\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{6} r_s^{2} \\\\sin{\\\\theta}-32\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{4} r_s^{2} \\\\sin{\\\\theta}+16\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{6} r^{5} r_s^{3}+16\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{8} r^{3} r_s^{3}-24\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{4} r^{6} r_s^{4}-24\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{6} r^{4} r_s^{4}+96\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{4} r^{7} r_s^{3}+192\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{6} r^{5} r_s^{3}+96\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{8} r^{3} r_s^{3}-56\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\tan{\\\\theta}^{2} a^{4} r^{7} r_s^{3} \\\\sin{\\\\theta}-112\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{6} r^{5} r_s^{3} \\\\sin{\\\\theta}-56\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{8} r^{3} r_s^{3} \\\\sin{\\\\theta}-136\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\tan{\\\\theta}^{2} a^{2} r^{9} r_s^{3} \\\\sin{\\\\theta}-296\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{4} r^{7} r_s^{3} \\\\sin{\\\\theta}-184\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{6} r^{5} r_s^{3} \\\\sin{\\\\theta}-16\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{6} r_s^{2} \\\\sin{\\\\theta}-32\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{4} r_s^{2} \\\\sin{\\\\theta}+32\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{4} r^{7} r_s^{3}+48\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{6} r^{5} r_s^{3}%\\n-88\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{2} r^{8} r_s^{4}-152\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{4} r^{6} r_s^{4}+176\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{2} r^{9} r_s^{3}+432\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{4} r^{7} r_s^{3}+336\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{6} r^{5} r_s^{3}-8\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2} r^{11} r_s^{3} \\\\sin{\\\\theta}+104\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{2} r^{9} r_s^{3} \\\\sin{\\\\theta}+304\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{4} r^{7} r_s^{3} \\\\sin{\\\\theta}-16\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} r^{8} r_s^{2} \\\\sin{\\\\theta}-32\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{6} r_s^{2} \\\\sin{\\\\theta}+32\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{4} r^{7} r_s^{3}+48\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{6} r^{5} r_s^{3}-88\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{2} r^{8} r_s^{4}-152\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{4} r^{6} r_s^{4}+176\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{2} r^{9} r_s^{3}+432\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{4} r^{7} r_s^{3}+336\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{6} r^{5} r_s^{3}-8\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\tan{\\\\theta}^{2} r^{11} r_s^{3} \\\\sin{\\\\theta}+104\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{2} r^{9} r_s^{3} \\\\sin{\\\\theta}+304\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{4} r^{7} r_s^{3} \\\\sin{\\\\theta}%\\n-16\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} r^{8} r_s^{2} \\\\sin{\\\\theta}-32\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{6} r_s^{2} \\\\sin{\\\\theta}+8\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{5} r_s^{5}-32\\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{4} r_s^{4}+24\\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{4} r^{8} r_s^{4}+24\\\\cos{\\\\theta}^{6} \\\\tan{\\\\theta}^{2} a^{6} r^{6} r_s^{4}+8\\\\cos{\\\\theta}^{8} \\\\tan{\\\\theta}^{2} a^{8} r^{4} r_s^{4}-16\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{5} r_s^{3}-8\\\\cos{\\\\theta}^{6} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{3} r_s^{3}+24\\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{2} r^{10} r_s^{4}+24\\\\cos{\\\\theta}^{6} \\\\tan{\\\\theta}^{2} a^{4} r^{8} r_s^{4}+8\\\\cos{\\\\theta}^{8} \\\\tan{\\\\theta}^{2} a^{6} r^{6} r_s^{4}-16\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{7} r_s^{3}-8\\\\cos{\\\\theta}^{6} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{5} r_s^{3}-8\\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{9} r_s^{3}-24\\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{6} r^{7} r_s^{3}-24\\\\cos{\\\\theta}^{6} \\\\tan{\\\\theta}^{2} a^{8} r^{5} r_s^{3}+8\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{6} r_s^{2}+16\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{4} r_s^{2}-32\\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{11} r_s^{3}%\\n-112\\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{4} r^{9} r_s^{3}-144\\\\cos{\\\\theta}^{6} \\\\tan{\\\\theta}^{2} a^{6} r^{7} r_s^{3}+32\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{8} r_s^{2}+80\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{6} r_s^{2}+32\\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{10} r^{3} r_s^{3}-8\\\\cos{\\\\theta}^{8} \\\\tan{\\\\theta}^{2} a^{10} r^{3} r_s^{3}+8\\\\cos{\\\\theta}^{6} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{2} r_s^{2}-80\\\\cos{\\\\theta}^{8} \\\\tan{\\\\theta}^{2} a^{8} r^{5} r_s^{3}+64\\\\cos{\\\\theta}^{6} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{4} r_s^{2}+8\\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{10} r_s^{4}-8\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{7} r_s^{3}+8\\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} r^{12} r_s^{4}-8\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} r^{9} r_s^{3}-24\\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} r^{13} r_s^{3}-88\\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{2} r^{11} r_s^{3}-120\\\\cos{\\\\theta}^{6} \\\\tan{\\\\theta}^{2} a^{4} r^{9} r_s^{3}+24\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} r^{10} r_s^{2}+64\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{8} r_s^{2}+216\\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{5} r_s^{3}-72\\\\cos{\\\\theta}^{8} \\\\tan{\\\\theta}^{2} a^{6} r^{7} r_s^{3}%\\n+56\\\\cos{\\\\theta}^{6} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{6} r_s^{2}-8\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{6} r^{4} r_s^{4}-8\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{6} r^{4} r_s^{4}+16\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{4} r^{5} r_s^{5}+16\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{4} r^{5} r_s^{5}-64\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{6} r^{4} r_s^{4}-64\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{6} r^{4} r_s^{4}+96\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{4} r^{6} r_s^{4} \\\\sin{\\\\theta}+96\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{4} r^{6} r_s^{4} \\\\sin{\\\\theta}+40\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{6} r^{4} r_s^{4} \\\\sin{\\\\theta}+40\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{6} r^{4} r_s^{4} \\\\sin{\\\\theta}+8\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{3} r_s^{3} \\\\sin{\\\\theta}+8\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{3} r_s^{3} \\\\sin{\\\\theta}-56\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{2} r^{8} r_s^{4} \\\\sin{\\\\theta}-56\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{2} r^{8} r_s^{4} \\\\sin{\\\\theta}-104\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{4} r^{6} r_s^{4} \\\\sin{\\\\theta}-104\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{4} r^{6} r_s^{4} \\\\sin{\\\\theta}+8\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{5} r_s^{3} \\\\sin{\\\\theta}+8\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{5} r_s^{3} \\\\sin{\\\\theta}-8\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{4} r^{6} r_s^{4}%\\n-8\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{4} r^{6} r_s^{4}+16\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{2} r^{7} r_s^{5}+16\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{2} r^{7} r_s^{5}+56\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2} a^{2} r^{8} r_s^{4} \\\\sin{\\\\theta}+56\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\tan{\\\\theta}^{2} a^{2} r^{8} r_s^{4} \\\\sin{\\\\theta}+8\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{5} r_s^{3} \\\\sin{\\\\theta}+8\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{5} r_s^{3} \\\\sin{\\\\theta}+8\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} r^{7} r_s^{3} \\\\sin{\\\\theta}+8\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} r^{7} r_s^{3} \\\\sin{\\\\theta}-32\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{7} r_s^{5}-16\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{5} r_s^{5}+8\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{4} r^{5} r_s^{5} \\\\sin{\\\\theta}+8\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{4} r^{5} r_s^{5} \\\\sin{\\\\theta}-8\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{4} r^{5} r_s^{5} \\\\sin{\\\\theta}-8\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{4} r^{5} r_s^{5} \\\\sin{\\\\theta}-48\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{4} r_s^{4}+40\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{4} r_s^{4}-48\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{7} \\\\tan{\\\\theta}^{2} a^{6} r^{4} r_s^{4} \\\\sin{\\\\theta}-48\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{7} \\\\tan{\\\\theta}^{2} a^{6} r^{4} r_s^{4} \\\\sin{\\\\theta}-8\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} \\\\tan{\\\\theta}^{2} a^{4} r^{3} r_s^{3}%\\n-8\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} \\\\tan{\\\\theta}^{2} a^{2} r^{5} r_s^{3}+40\\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2} a^{6} r^{7} r_s^{3}+16\\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{8} r_s^{4}+32\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{6} r_s^{4}+8\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2} a^{4} r^{6} r_s^{4} \\\\sin{\\\\theta}+8\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\tan{\\\\theta}^{2} a^{4} r^{6} r_s^{4} \\\\sin{\\\\theta}+48\\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{5} r_s^{3}-40\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{5} r_s^{3}+8\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} \\\\tan{\\\\theta}^{2} a^{4} r^{4} r_s^{2}+32\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} \\\\tan{\\\\theta}^{2} a^{2} r^{6} r_s^{2}+16\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{4} r_s^{4}+8\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{6} r^{4} r_s^{4} \\\\sin{\\\\theta}+8\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{6} r^{4} r_s^{4} \\\\sin{\\\\theta}+48\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{3} r_s^{3}-40\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{3} r_s^{3}-24\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{7} \\\\tan{\\\\theta}^{2} a^{8} r^{3} r_s^{3} \\\\sin{\\\\theta}-24\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{7} \\\\tan{\\\\theta}^{2} a^{8} r^{3} r_s^{3} \\\\sin{\\\\theta}+8\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} \\\\tan{\\\\theta}^{2} a^{6} r^{2} r_s^{2}+48\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} \\\\tan{\\\\theta}^{2} a^{4} r^{4} r_s^{2}-40\\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2} a^{4} r^{8} r_s^{4}%\\n-16\\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{9} r_s^{5}+8\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{2} r^{7} r_s^{5} \\\\sin{\\\\theta}+8\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{2} r^{7} r_s^{5} \\\\sin{\\\\theta}-8\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2} a^{2} r^{7} r_s^{5} \\\\sin{\\\\theta}-8\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\tan{\\\\theta}^{2} a^{2} r^{7} r_s^{5} \\\\sin{\\\\theta}-48\\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{6} r_s^{4}+40\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{6} r_s^{4}-8\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} \\\\tan{\\\\theta}^{2} a^{2} r^{5} r_s^{3}-8\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} \\\\tan{\\\\theta}^{2} r^{7} r_s^{3}+120\\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2} a^{4} r^{9} r_s^{3}+144\\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{7} r_s^{3}+24\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} \\\\tan{\\\\theta}^{2} r^{8} r_s^{2}+240\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{5} r_s^{3}+264\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{7} \\\\tan{\\\\theta}^{2} a^{6} r^{5} r_s^{3} \\\\sin{\\\\theta}+264\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{7} \\\\tan{\\\\theta}^{2} a^{6} r^{5} r_s^{3} \\\\sin{\\\\theta}+40\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} \\\\tan{\\\\theta}^{2} a^{2} r^{6} r_s^{2}-176\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{10} r_s^{2}-384\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{8} r_s^{2}-416\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{6} r_s^{2}-72\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{5} r_s%\\n-72\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{3} r_s+8\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{7} r_s+24\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{5} r_s-192\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{12} r_s^{2}-464\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{10} r_s^{2}-576\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{8} r_s^{2}+80\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{9} r_s+96\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{7} r_s+48\\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{4} r^{10} r_s^{2}-40\\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{2} r^{12} r_s^{2}+56\\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{6} r^{8} r_s^{2}-88\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{4} r^{10} r_s^{2}-32\\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{12} r_s^{2}-32\\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} r^{14} r_s^{2}+24\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} r^{11} r_s-24\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{7} r_s-16\\\\cos{\\\\theta} \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{6} r^{7} r_s^{3} \\\\sin{2\\\\theta}-32\\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{8} r^{5} r_s^{3} \\\\sin{2\\\\theta}-40\\\\cos{\\\\theta} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{4} r^{9} r_s^{3} \\\\sin{2\\\\theta}-120\\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{6} r^{7} r_s^{3} \\\\sin{2\\\\theta}%\\n-120\\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{8} r^{5} r_s^{3} \\\\sin{2\\\\theta}+16\\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2} a^{4} r^{9} r_s^{3} \\\\sin{\\\\theta} \\\\sin{2\\\\theta}+48\\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{6} r^{7} r_s^{3} \\\\sin{\\\\theta} \\\\sin{2\\\\theta}+48\\\\cos{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{8} r^{5} r_s^{3} \\\\sin{\\\\theta} \\\\sin{2\\\\theta}-16\\\\cos{\\\\theta} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{6} r_s^{2} \\\\sin{\\\\theta} \\\\sin{2\\\\theta}-32\\\\cos{\\\\theta}^{3} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{4} r_s^{2} \\\\sin{\\\\theta} \\\\sin{2\\\\theta}+16\\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2} a^{2} r^{11} r_s^{3} \\\\sin{\\\\theta} \\\\sin{2\\\\theta}+48\\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{4} r^{9} r_s^{3} \\\\sin{\\\\theta} \\\\sin{2\\\\theta}+48\\\\cos{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{6} r^{7} r_s^{3} \\\\sin{\\\\theta} \\\\sin{2\\\\theta}-16\\\\cos{\\\\theta} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{8} r_s^{2} \\\\sin{\\\\theta} \\\\sin{2\\\\theta}-32\\\\cos{\\\\theta}^{3} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{6} r_s^{2} \\\\sin{\\\\theta} \\\\sin{2\\\\theta}-32\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{6} r^{6} r_s^{2}-64\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{8} r^{4} r_s^{2}-120\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{4} r^{8} r_s^{2}-360\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{6} r^{6} r_s^{2}-360\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{8} r^{4} r_s^{2}+88\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2} a^{4} r^{8} r_s^{2} \\\\sin{\\\\theta}+264\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{6} r^{6} r_s^{2} \\\\sin{\\\\theta}+264\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{8} r^{4} r_s^{2} \\\\sin{\\\\theta}+136\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2} a^{2} r^{10} r_s^{2} \\\\sin{\\\\theta}%\\n+368\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{4} r^{8} r_s^{2} \\\\sin{\\\\theta}+288\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{6} r^{6} r_s^{2} \\\\sin{\\\\theta}+8\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{7} \\\\sin{\\\\theta} r_s+24\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{5} \\\\sin{\\\\theta} r_s-32\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{6} r^{6} r_s^{2}-64\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{8} r^{4} r_s^{2}-120\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{4} r^{8} r_s^{2}-360\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{6} r^{6} r_s^{2}-360\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{8} r^{4} r_s^{2}+88\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\tan{\\\\theta}^{2} a^{4} r^{8} r_s^{2} \\\\sin{\\\\theta}+264\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{6} r^{6} r_s^{2} \\\\sin{\\\\theta}+264\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{8} r^{4} r_s^{2} \\\\sin{\\\\theta}+136\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\tan{\\\\theta}^{2} a^{2} r^{10} r_s^{2} \\\\sin{\\\\theta}+368\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{4} r^{8} r_s^{2} \\\\sin{\\\\theta}+288\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{6} r^{6} r_s^{2} \\\\sin{\\\\theta}+8\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{7} \\\\sin{\\\\theta} r_s+24\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{5} \\\\sin{\\\\theta} r_s-40\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{4} r^{8} r_s^{2}-88\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{6} r^{6} r_s^{2}-152\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{2} r^{10} r_s^{2}%\\n-488\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{4} r^{8} r_s^{2}-552\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{6} r^{6} r_s^{2}+16\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2} r^{12} r_s^{2} \\\\sin{\\\\theta}-56\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{2} r^{10} r_s^{2} \\\\sin{\\\\theta}-296\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{4} r^{8} r_s^{2} \\\\sin{\\\\theta}+8\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} r^{9} \\\\sin{\\\\theta} r_s+24\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{7} \\\\sin{\\\\theta} r_s-40\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{4} r^{8} r_s^{2}-88\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{6} r^{6} r_s^{2}-152\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{2} r^{10} r_s^{2}-488\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{4} r^{8} r_s^{2}-552\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{6} r^{6} r_s^{2}+16\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\tan{\\\\theta}^{2} r^{12} r_s^{2} \\\\sin{\\\\theta}-56\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{2} r^{10} r_s^{2} \\\\sin{\\\\theta}-296\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{4} r^{8} r_s^{2} \\\\sin{\\\\theta}+8\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} r^{9} \\\\sin{\\\\theta} r_s+24\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{7} \\\\sin{\\\\theta} r_s+16\\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{10} r_s^{2}+64\\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{6} r^{8} r_s^{2}+96\\\\cos{\\\\theta}^{6} \\\\tan{\\\\theta}^{2} a^{8} r^{6} r_s^{2}%\\n-16\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{7} r_s-48\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{5} r_s+40\\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{12} r_s^{2}+168\\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{4} r^{10} r_s^{2}+272\\\\cos{\\\\theta}^{6} \\\\tan{\\\\theta}^{2} a^{6} r^{8} r_s^{2}-40\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{9} r_s-128\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{7} r_s-224\\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{10} r^{4} r_s^{2}+64\\\\cos{\\\\theta}^{8} \\\\tan{\\\\theta}^{2} a^{10} r^{4} r_s^{2}-48\\\\cos{\\\\theta}^{6} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{3} r_s+208\\\\cos{\\\\theta}^{8} \\\\tan{\\\\theta}^{2} a^{8} r^{6} r_s^{2}-144\\\\cos{\\\\theta}^{6} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{5} r_s+24\\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} r^{14} r_s^{2}+104\\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{2} r^{12} r_s^{2}+176\\\\cos{\\\\theta}^{6} \\\\tan{\\\\theta}^{2} a^{4} r^{10} r_s^{2}-24\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} r^{11} r_s-80\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{9} r_s-384\\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{6} r_s^{2}+144\\\\cos{\\\\theta}^{8} \\\\tan{\\\\theta}^{2} a^{6} r^{8} r_s^{2}-96\\\\cos{\\\\theta}^{6} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{7} r_s%\\n-80\\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2} a^{6} r^{8} r_s^{2}-96\\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{6} r_s^{2}-16\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} \\\\tan{\\\\theta}^{2} a^{4} r^{5} r_s-40\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} \\\\tan{\\\\theta}^{2} a^{2} r^{7} r_s-192\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{4} r_s^{2}+16\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{7} \\\\tan{\\\\theta}^{2} a^{8} r^{4} r_s^{2} \\\\sin{\\\\theta}+16\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{7} \\\\tan{\\\\theta}^{2} a^{8} r^{4} r_s^{2} \\\\sin{\\\\theta}-32\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} \\\\tan{\\\\theta}^{2} a^{6} r^{3} r_s-88\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} \\\\tan{\\\\theta}^{2} a^{4} r^{5} r_s-120\\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2} a^{4} r^{10} r_s^{2}-144\\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{8} r_s^{2}-24\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} \\\\tan{\\\\theta}^{2} r^{9} r_s-336\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{6} r_s^{2}-392\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{7} \\\\tan{\\\\theta}^{2} a^{6} r^{6} r_s^{2} \\\\sin{\\\\theta}-392\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{7} \\\\tan{\\\\theta}^{2} a^{6} r^{6} r_s^{2} \\\\sin{\\\\theta}-56\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} \\\\tan{\\\\theta}^{2} a^{2} r^{7} r_s+24\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{2} r_s^{2}-24\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{10} r r_s+24\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{3} r_s-16\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{4} r_s^{2}%\\n+48\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{5} r_s-16\\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{10} r^{3} r_s^{3} \\\\sin{2\\\\theta}-40\\\\cos{\\\\theta}^{7} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{10} r^{3} r_s^{3} \\\\sin{2\\\\theta}+16\\\\cos{\\\\theta}^{7} \\\\tan{\\\\theta}^{2} a^{10} r^{3} r_s^{3} \\\\sin{\\\\theta} \\\\sin{2\\\\theta}-16\\\\cos{\\\\theta}^{5} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{2} r_s^{2} \\\\sin{\\\\theta} \\\\sin{2\\\\theta}+16\\\\cos{\\\\theta}^{7} \\\\tan{\\\\theta}^{2} a^{8} r^{5} r_s^{3} \\\\sin{\\\\theta} \\\\sin{2\\\\theta}-16\\\\cos{\\\\theta}^{5} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{4} r_s^{2} \\\\sin{\\\\theta} \\\\sin{2\\\\theta}-32\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{10} r^{2} r_s^{2}-120\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{7} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{10} r^{2} r_s^{2}+88\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{7} \\\\tan{\\\\theta}^{2} a^{10} r^{2} r_s^{2} \\\\sin{\\\\theta}+24\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{3} \\\\sin{\\\\theta} r_s-32\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{10} r^{2} r_s^{2}-120\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{7} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{10} r^{2} r_s^{2}+88\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{7} \\\\tan{\\\\theta}^{2} a^{10} r^{2} r_s^{2} \\\\sin{\\\\theta}+24\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{3} \\\\sin{\\\\theta} r_s-56\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{8} r^{4} r_s^{2}-248\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{7} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{8} r^{4} r_s^{2}+24\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{5} \\\\sin{\\\\theta} r_s-56\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{8} r^{4} r_s^{2}-248\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{7} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{8} r^{4} r_s^{2}%\\n+24\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{5} \\\\sin{\\\\theta} r_s+40\\\\cos{\\\\theta}^{10} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{10} r^{3} r_s^{3}-16\\\\cos{\\\\theta}^{10} \\\\tan{\\\\theta}^{2} a^{10} r^{3} r_s^{3}+16\\\\cos{\\\\theta}^{8} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{2} r_s^{2}-16\\\\cos{\\\\theta}^{10} \\\\tan{\\\\theta}^{2} a^{8} r^{5} r_s^{3}+16\\\\cos{\\\\theta}^{8} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{4} r_s^{2}-48\\\\cos{\\\\theta}^{10} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{12} r^{2} r_s^{2}+16\\\\cos{\\\\theta}^{10} \\\\tan{\\\\theta}^{2} a^{12} r^{2} r_s^{2}-16\\\\cos{\\\\theta}^{8} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{10} r r_s+72\\\\cos{\\\\theta}^{10} \\\\tan{\\\\theta}^{2} a^{10} r^{4} r_s^{2}-64\\\\cos{\\\\theta}^{8} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{3} r_s-128\\\\cos{\\\\theta}^{10} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{10} r^{4} r_s^{2}+56\\\\cos{\\\\theta}^{10} \\\\tan{\\\\theta}^{2} a^{8} r^{6} r_s^{2}-48\\\\cos{\\\\theta}^{8} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{5} r_s+16\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{8} r^{3} r_s^{3}+16\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{8} r^{3} r_s^{3}+80\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{7} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{8} r^{3} r_s^{3}+80\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{7} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{8} r^{3} r_s^{3}-16\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{2} r_s^{2} \\\\sin{\\\\theta}-16\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{2} r_s^{2} \\\\sin{\\\\theta}%\\n-16\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{4} r_s^{2} \\\\sin{\\\\theta}-16\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{4} r_s^{2} \\\\sin{\\\\theta}+96\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{3} r_s^{3}+72\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{9} \\\\tan{\\\\theta}^{2} a^{8} r^{3} r_s^{3} \\\\sin{\\\\theta}+72\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{9} \\\\tan{\\\\theta}^{2} a^{8} r^{3} r_s^{3} \\\\sin{\\\\theta}+16\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} \\\\tan{\\\\theta}^{2} a^{6} r^{2} r_s^{2}+16\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} \\\\tan{\\\\theta}^{2} a^{4} r^{4} r_s^{2}-96\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{2} r_s^{2}-40\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{9} \\\\tan{\\\\theta}^{2} a^{10} r^{2} r_s^{2} \\\\sin{\\\\theta}-40\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{9} \\\\tan{\\\\theta}^{2} a^{10} r^{2} r_s^{2} \\\\sin{\\\\theta}-16\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} \\\\tan{\\\\theta}^{2} a^{8} r r_s-56\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} \\\\tan{\\\\theta}^{2} a^{6} r^{3} r_s-240\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{4} r_s^{2}-200\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{9} \\\\tan{\\\\theta}^{2} a^{8} r^{4} r_s^{2} \\\\sin{\\\\theta}-200\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{9} \\\\tan{\\\\theta}^{2} a^{8} r^{4} r_s^{2} \\\\sin{\\\\theta}-40\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} \\\\tan{\\\\theta}^{2} a^{4} r^{5} r_s+8\\\\sin{\\\\theta}^{8} a^{8} r^{4} r_s^{4}-16\\\\sin{\\\\theta}^{8} a^{8} r^{5} r_s^{3}-16\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{8} a^{10} r^{3} r_s^{3}+24\\\\sin{\\\\theta}^{8} a^{6} r^{6} r_s^{4}%\\n-8\\\\sin{\\\\theta}^{8} a^{6} r^{5} r_s^{5}-24\\\\sin{\\\\theta}^{8} a^{6} r^{7} r_s^{3}-32\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{8} a^{8} r^{5} r_s^{3}+16\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{8} a^{8} r^{4} r_s^{4}-8\\\\sin{\\\\theta}^{6} a^{6} r^{5} r_s^{5}+24\\\\sin{\\\\theta}^{6} a^{6} r^{6} r_s^{4}+24\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6} a^{8} r^{4} r_s^{4}-32\\\\sin{\\\\theta}^{6} a^{4} r^{7} r_s^{5}+8\\\\sin{\\\\theta}^{6} a^{4} r^{6} r_s^{6}+48\\\\sin{\\\\theta}^{6} a^{4} r^{8} r_s^{4}+72\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6} a^{6} r^{6} r_s^{4}-24\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6} a^{6} r^{5} r_s^{5}-24\\\\sin{\\\\theta}^{6} a^{6} r^{7} r_s^{3}-48\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6} a^{8} r^{5} r_s^{3}-32\\\\sin{\\\\theta}^{6} a^{4} r^{9} r_s^{3}-72\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6} a^{6} r^{7} r_s^{3}-24\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{6} a^{10} r^{3} r_s^{3}-48\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{6} a^{8} r^{5} r_s^{3}+24\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{6} a^{8} r^{4} r_s^{4}-8\\\\sin{\\\\theta}^{2} \\\\left(\\\\sin{\\\\theta}^{4} a^{4} r r_s-\\\\sin{\\\\theta}^{2} a^{2} r^{2} r_s^{2}+2\\\\sin{\\\\theta}^{2} a^{2} r^{3} r_s+2\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r r_s-a^{2} r^{3} r_s-\\\\cos{\\\\theta}^{2} a^{4} r r_s+\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2}-r^{5} r_s-\\\\cos{\\\\theta}^{2} a^{2} r^{3} r_s+\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{2}\\\\right)^{2} r^{2} r_s^{2}%\\n+16\\\\sin{\\\\theta}^{2} \\\\left(\\\\sin{\\\\theta}^{4} a^{4} r r_s-\\\\sin{\\\\theta}^{2} a^{2} r^{2} r_s^{2}+2\\\\sin{\\\\theta}^{2} a^{2} r^{3} r_s+2\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r r_s-a^{2} r^{3} r_s-\\\\cos{\\\\theta}^{2} a^{4} r r_s+\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2}-r^{5} r_s-\\\\cos{\\\\theta}^{2} a^{2} r^{3} r_s+\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{2}\\\\right)^{2} r^{3} r_s+16\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(\\\\sin{\\\\theta}^{4} a^{4} r r_s-\\\\sin{\\\\theta}^{2} a^{2} r^{2} r_s^{2}+2\\\\sin{\\\\theta}^{2} a^{2} r^{3} r_s+2\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r r_s-a^{2} r^{3} r_s-\\\\cos{\\\\theta}^{2} a^{4} r r_s+\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2}-r^{5} r_s-\\\\cos{\\\\theta}^{2} a^{2} r^{3} r_s+\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{2}\\\\right)^{2} a^{2} r r_s+152\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2} a^{8} r^{7} r_s+216\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2} a^{10} r^{5} r_s+152\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2} a^{6} r^{9} r_s+216\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2} a^{8} r^{7} r_s-224\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{8} r^{7} r_s-32\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{6} r^{9} r_s-192\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{10} r^{5} r_s-56\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{8} r^{7} r_s+40\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{9} r_s+80\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{7} r_s+96\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{11} r_s+240\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{9} r_s+80\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{10} r^{5} r_s+320\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{7} r_s-32\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{6}-48\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{4}-64\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{8}-96\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{6}%\\n+56\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{13} r_s+160\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{11} r_s+240\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{9} r_s-32\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{10}-48\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{8}-24\\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{4} r^{11} r_s+4\\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{2} r^{13} r_s-28\\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{6} r^{9} r_s-120\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{8} r^{7} r_s-120\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{6} r^{9} r_s-192\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{10} r^{5} r_s+16\\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{13} r_s+8\\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} r^{15} r_s+8\\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{11} r_s-16\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{10}-8\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} r^{12}-8\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{8}+8\\\\cos{\\\\theta} \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{6} r^{8} r_s^{2} \\\\sin{2\\\\theta}+24\\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{8} r^{6} r_s^{2} \\\\sin{2\\\\theta}+16\\\\cos{\\\\theta} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{4} r^{10} r_s^{2} \\\\sin{2\\\\theta}%\\n+64\\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{6} r^{8} r_s^{2} \\\\sin{2\\\\theta}+96\\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{8} r^{6} r_s^{2} \\\\sin{2\\\\theta}-8\\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2} a^{4} r^{10} r_s^{2} \\\\sin{\\\\theta} \\\\sin{2\\\\theta}-32\\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{6} r^{8} r_s^{2} \\\\sin{\\\\theta} \\\\sin{2\\\\theta}-48\\\\cos{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{8} r^{6} r_s^{2} \\\\sin{\\\\theta} \\\\sin{2\\\\theta}+8\\\\cos{\\\\theta} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{7} \\\\sin{\\\\theta} \\\\sin{2\\\\theta} r_s+24\\\\cos{\\\\theta}^{3} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{5} \\\\sin{\\\\theta} \\\\sin{2\\\\theta} r_s-8\\\\cos{\\\\theta} \\\\tan{\\\\theta}^{2} a^{2} r^{12} r_s^{2} \\\\sin{\\\\theta} \\\\sin{2\\\\theta}-32\\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{4} r^{10} r_s^{2} \\\\sin{\\\\theta} \\\\sin{2\\\\theta}-48\\\\cos{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{6} r^{8} r_s^{2} \\\\sin{\\\\theta} \\\\sin{2\\\\theta}+8\\\\cos{\\\\theta} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{9} \\\\sin{\\\\theta} \\\\sin{2\\\\theta} r_s+24\\\\cos{\\\\theta}^{3} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{7} \\\\sin{\\\\theta} \\\\sin{2\\\\theta} r_s+16\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{6} r^{7} r_s+48\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{8} r^{5} r_s+48\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{4} r^{9} r_s+192\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{6} r^{7} r_s+288\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{8} r^{5} r_s-40\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2} a^{4} r^{9} \\\\sin{\\\\theta} r_s-160\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{6} r^{7} \\\\sin{\\\\theta} r_s-240\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{8} r^{5} \\\\sin{\\\\theta} r_s%\\n-48\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2} a^{2} r^{11} \\\\sin{\\\\theta} r_s-160\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{4} r^{9} \\\\sin{\\\\theta} r_s-160\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{6} r^{7} \\\\sin{\\\\theta} r_s+16\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{6} r^{7} r_s+48\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{8} r^{5} r_s+48\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{4} r^{9} r_s+192\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{6} r^{7} r_s+288\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{8} r^{5} r_s-40\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\tan{\\\\theta}^{2} a^{4} r^{9} \\\\sin{\\\\theta} r_s-160\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{6} r^{7} \\\\sin{\\\\theta} r_s-240\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{8} r^{5} \\\\sin{\\\\theta} r_s-48\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\tan{\\\\theta}^{2} a^{2} r^{11} \\\\sin{\\\\theta} r_s-160\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{4} r^{9} \\\\sin{\\\\theta} r_s-160\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{6} r^{7} \\\\sin{\\\\theta} r_s+16\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{4} r^{9} r_s+48\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{6} r^{7} r_s+48\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{2} r^{11} r_s+192\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{4} r^{9} r_s+288\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{6} r^{7} r_s-8\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\tan{\\\\theta}^{2} r^{13} \\\\sin{\\\\theta} r_s%\\n+80\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{4} r^{9} \\\\sin{\\\\theta} r_s+16\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{4} r^{9} r_s+48\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{6} r^{7} r_s+48\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{2} r^{11} r_s+192\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{4} r^{9} r_s+288\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{6} r^{7} r_s-8\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\tan{\\\\theta}^{2} r^{13} \\\\sin{\\\\theta} r_s+80\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{4} r^{9} \\\\sin{\\\\theta} r_s-8\\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{11} r_s-40\\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{6} r^{9} r_s-80\\\\cos{\\\\theta}^{6} \\\\tan{\\\\theta}^{2} a^{8} r^{7} r_s+8\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{8}+32\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{6}-16\\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{13} r_s-80\\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{4} r^{11} r_s-160\\\\cos{\\\\theta}^{6} \\\\tan{\\\\theta}^{2} a^{6} r^{9} r_s+16\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{10}+64\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{8}+240\\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{10} r^{5} r_s-80\\\\cos{\\\\theta}^{8} \\\\tan{\\\\theta}^{2} a^{10} r^{5} r_s%\\n+48\\\\cos{\\\\theta}^{6} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{4}-160\\\\cos{\\\\theta}^{8} \\\\tan{\\\\theta}^{2} a^{8} r^{7} r_s+96\\\\cos{\\\\theta}^{6} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{6}-8\\\\cos{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} r^{15} r_s-40\\\\cos{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{2} r^{13} r_s-80\\\\cos{\\\\theta}^{6} \\\\tan{\\\\theta}^{2} a^{4} r^{11} r_s+8\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} r^{12}+32\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{10}+200\\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{7} r_s-80\\\\cos{\\\\theta}^{8} \\\\tan{\\\\theta}^{2} a^{6} r^{9} r_s+48\\\\cos{\\\\theta}^{6} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{8}+40\\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2} a^{6} r^{9} r_s+48\\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{7} r_s+8\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} \\\\tan{\\\\theta}^{2} a^{4} r^{6}+16\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} \\\\tan{\\\\theta}^{2} a^{2} r^{8}+144\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{5} r_s+24\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} \\\\tan{\\\\theta}^{2} a^{6} r^{4}+48\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} \\\\tan{\\\\theta}^{2} a^{4} r^{6}+40\\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2} a^{4} r^{11} r_s+48\\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{2} r^{9} r_s%\\n+8\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} \\\\tan{\\\\theta}^{2} r^{10}+144\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{4} r^{7} r_s+160\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{7} \\\\tan{\\\\theta}^{2} a^{6} r^{7} \\\\sin{\\\\theta} r_s+160\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{7} \\\\tan{\\\\theta}^{2} a^{6} r^{7} \\\\sin{\\\\theta} r_s+24\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} \\\\tan{\\\\theta}^{2} a^{2} r^{8}+136\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2} a^{12} r^{3} r_s+136\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2} a^{10} r^{5} r_s-72\\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{12} r^{3} r_s-36\\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{10} r^{5} r_s+40\\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{12} r^{3} r_s-32\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{10} r^{2}-64\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{4}-32\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{6}-136\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{12} r^{3} r_s+24\\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{10} r^{4} r_s^{2} \\\\sin{2\\\\theta}+64\\\\cos{\\\\theta}^{7} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{10} r^{4} r_s^{2} \\\\sin{2\\\\theta}-32\\\\cos{\\\\theta}^{7} \\\\tan{\\\\theta}^{2} a^{10} r^{4} r_s^{2} \\\\sin{\\\\theta} \\\\sin{2\\\\theta}+24\\\\cos{\\\\theta}^{5} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{3} \\\\sin{\\\\theta} \\\\sin{2\\\\theta} r_s-32\\\\cos{\\\\theta}^{7} \\\\tan{\\\\theta}^{2} a^{8} r^{6} r_s^{2} \\\\sin{\\\\theta} \\\\sin{2\\\\theta}+24\\\\cos{\\\\theta}^{5} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{5} \\\\sin{\\\\theta} \\\\sin{2\\\\theta} r_s%\\n+48\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{10} r^{3} r_s+192\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{7} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{10} r^{3} r_s-160\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{7} \\\\tan{\\\\theta}^{2} a^{10} r^{3} \\\\sin{\\\\theta} r_s+48\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{10} r^{3} r_s+192\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{7} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{10} r^{3} r_s-160\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{7} \\\\tan{\\\\theta}^{2} a^{10} r^{3} \\\\sin{\\\\theta} r_s+48\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{8} r^{5} r_s+192\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{7} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{8} r^{5} r_s+48\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{8} r^{5} r_s+192\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{7} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{8} r^{5} r_s+96\\\\cos{\\\\theta}^{10} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{12} r^{3} r_s-40\\\\cos{\\\\theta}^{10} \\\\tan{\\\\theta}^{2} a^{12} r^{3} r_s+32\\\\cos{\\\\theta}^{8} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{10} r^{2}-80\\\\cos{\\\\theta}^{10} \\\\tan{\\\\theta}^{2} a^{10} r^{5} r_s+64\\\\cos{\\\\theta}^{8} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{4}+88\\\\cos{\\\\theta}^{10} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{10} r^{5} r_s-40\\\\cos{\\\\theta}^{10} \\\\tan{\\\\theta}^{2} a^{8} r^{7} r_s+32\\\\cos{\\\\theta}^{8} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{6}+144\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{3} r_s+80\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{9} \\\\tan{\\\\theta}^{2} a^{10} r^{3} \\\\sin{\\\\theta} r_s%\\n+80\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{9} \\\\tan{\\\\theta}^{2} a^{10} r^{3} \\\\sin{\\\\theta} r_s+24\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} \\\\tan{\\\\theta}^{2} a^{8} r^{2}+48\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} \\\\tan{\\\\theta}^{2} a^{6} r^{4}+144\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{5} r_s+120\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{9} \\\\tan{\\\\theta}^{2} a^{8} r^{5} \\\\sin{\\\\theta} r_s+120\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{9} \\\\tan{\\\\theta}^{2} a^{8} r^{5} \\\\sin{\\\\theta} r_s+24\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} \\\\tan{\\\\theta}^{2} a^{4} r^{6}+8\\\\sin{\\\\theta}^{8} a^{8} r^{6} r_s^{2}+16\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{8} a^{10} r^{4} r_s^{2}+8\\\\sin{\\\\theta}^{8} a^{6} r^{8} r_s^{2}+16\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{8} a^{8} r^{6} r_s^{2}+8\\\\sin{\\\\theta}^{6} a^{6} r^{8} r_s^{2}+24\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6} a^{8} r^{6} r_s^{2}+8\\\\sin{\\\\theta}^{6} a^{4} r^{10} r_s^{2}+24\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6} a^{6} r^{8} r_s^{2}+24\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{6} a^{10} r^{4} r_s^{2}+24\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{6} a^{8} r^{6} r_s^{2}-8\\\\sin{\\\\theta}^{2} \\\\left(\\\\sin{\\\\theta}^{4} a^{4} r r_s-\\\\sin{\\\\theta}^{2} a^{2} r^{2} r_s^{2}+2\\\\sin{\\\\theta}^{2} a^{2} r^{3} r_s+2\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r r_s-a^{2} r^{3} r_s-\\\\cos{\\\\theta}^{2} a^{4} r r_s+\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2}-r^{5} r_s-\\\\cos{\\\\theta}^{2} a^{2} r^{3} r_s+\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{2}\\\\right)^{2} r^{4}-16\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(\\\\sin{\\\\theta}^{4} a^{4} r r_s-\\\\sin{\\\\theta}^{2} a^{2} r^{2} r_s^{2}+2\\\\sin{\\\\theta}^{2} a^{2} r^{3} r_s+2\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r r_s-a^{2} r^{3} r_s-\\\\cos{\\\\theta}^{2} a^{4} r r_s+\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2}-r^{5} r_s-\\\\cos{\\\\theta}^{2} a^{2} r^{3} r_s+\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{2}\\\\right)^{2} a^{2} r^{2}+16\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{4} r_s^{4}%\\n-32\\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2} a^{12} r^{2} r_s^{2}+32\\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2} a^{14} r r_s+32\\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{6} \\\\tan{\\\\theta}^{2} a^{12} r^{3} r_s+8\\\\cos{\\\\theta}^{10} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{12} r^{2} r_s^{2}-8\\\\cos{\\\\theta}^{10} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{14} r r_s-8\\\\cos{\\\\theta}^{10} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{12} r^{3} r_s+8\\\\cos{\\\\theta}^{10} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{14} r r_s+8\\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{10} r r_s-8\\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{12}-16\\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{10} r^{2}+8\\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{3} r_s-8\\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{4}-36\\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{4} \\\\tan{\\\\theta}^{2} a^{14} r r_s+8\\\\cos{\\\\theta}^{7} \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{12} r^{2} r_s^{2} \\\\sin{2\\\\theta}+16\\\\cos{\\\\theta}^{9} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{12} r^{2} r_s^{2} \\\\sin{2\\\\theta}-8\\\\cos{\\\\theta}^{9} \\\\tan{\\\\theta}^{2} a^{12} r^{2} r_s^{2} \\\\sin{\\\\theta} \\\\sin{2\\\\theta}+8\\\\cos{\\\\theta}^{7} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{10} \\\\sin{\\\\theta} \\\\sin{2\\\\theta} r r_s-8\\\\cos{\\\\theta}^{9} \\\\tan{\\\\theta}^{2} a^{10} r^{4} r_s^{2} \\\\sin{\\\\theta} \\\\sin{2\\\\theta}+8\\\\cos{\\\\theta}^{7} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{3} \\\\sin{\\\\theta} \\\\sin{2\\\\theta} r_s+16\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{7} \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{12} r r_s%\\n+48\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{9} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{12} r r_s-40\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{9} \\\\tan{\\\\theta}^{2} a^{12} \\\\sin{\\\\theta} r r_s+16\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{7} \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{12} r r_s+48\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{9} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{12} r r_s-40\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{9} \\\\tan{\\\\theta}^{2} a^{12} \\\\sin{\\\\theta} r r_s+16\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{7} \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{10} r^{3} r_s+48\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{9} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{10} r^{3} r_s+16\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{7} \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{10} r^{3} r_s+48\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{9} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{10} r^{3} r_s-16\\\\cos{\\\\theta}^{12} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{12} r^{2} r_s^{2}+8\\\\cos{\\\\theta}^{12} \\\\tan{\\\\theta}^{2} a^{12} r^{2} r_s^{2}-8\\\\cos{\\\\theta}^{10} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{10} r r_s+8\\\\cos{\\\\theta}^{12} \\\\tan{\\\\theta}^{2} a^{10} r^{4} r_s^{2}-8\\\\cos{\\\\theta}^{10} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{3} r_s+16\\\\cos{\\\\theta}^{12} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{14} r r_s-8\\\\cos{\\\\theta}^{12} \\\\tan{\\\\theta}^{2} a^{14} r r_s+8\\\\cos{\\\\theta}^{10} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{12}-16\\\\cos{\\\\theta}^{12} \\\\tan{\\\\theta}^{2} a^{12} r^{3} r_s+16\\\\cos{\\\\theta}^{10} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{10} r^{2}+16\\\\cos{\\\\theta}^{12} \\\\sin{\\\\theta}^{2} \\\\tan{\\\\theta}^{2} a^{12} r^{3} r_s%\\n-8\\\\cos{\\\\theta}^{12} \\\\tan{\\\\theta}^{2} a^{10} r^{5} r_s+8\\\\cos{\\\\theta}^{10} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{4}-8\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{7} \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{10} r^{2} r_s^{2}-8\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{7} \\\\sin{\\\\theta}^{5} \\\\tan{\\\\theta}^{2} a^{10} r^{2} r_s^{2}-32\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{9} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{10} r^{2} r_s^{2}-32\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{9} \\\\sin{\\\\theta}^{3} \\\\tan{\\\\theta}^{2} a^{10} r^{2} r_s^{2}+8\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{7} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{8} \\\\sin{\\\\theta} r r_s+8\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{7} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{8} \\\\sin{\\\\theta} r r_s+8\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{7} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{3} \\\\sin{\\\\theta} r_s+8\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{7} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{6} r^{3} \\\\sin{\\\\theta} r_s-48\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{2} r_s^{2}-32\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{11} \\\\tan{\\\\theta}^{2} a^{10} r^{2} r_s^{2} \\\\sin{\\\\theta}-32\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{11} \\\\tan{\\\\theta}^{2} a^{10} r^{2} r_s^{2} \\\\sin{\\\\theta}-8\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} \\\\tan{\\\\theta}^{2} a^{8} r r_s-8\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} \\\\tan{\\\\theta}^{2} a^{6} r^{3} r_s+48\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{10} r r_s+32\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{11} \\\\tan{\\\\theta}^{2} a^{12} \\\\sin{\\\\theta} r r_s+32\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{11} \\\\tan{\\\\theta}^{2} a^{12} \\\\sin{\\\\theta} r r_s+8\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} \\\\tan{\\\\theta}^{2} a^{10}+16\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} \\\\tan{\\\\theta}^{2} a^{8} r^{2}%\\n+48\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2} a^{8} r^{3} r_s+32\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{11} \\\\tan{\\\\theta}^{2} a^{10} r^{3} \\\\sin{\\\\theta} r_s+32\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{11} \\\\tan{\\\\theta}^{2} a^{10} r^{3} \\\\sin{\\\\theta} r_s+8\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} \\\\tan{\\\\theta}^{2} a^{6} r^{4}+8\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{8} a^{12} r^{2} r_s^{2}+8\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{8} a^{10} r^{4} r_s^{2}-8\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{8} a^{10} r^{3} r_s^{3}+8\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{6} a^{12} r^{2} r_s^{2}+8\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{6} a^{10} r^{4} r_s^{2}-8\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{6} a^{10} r^{3} r_s^{3}-8\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(\\\\sin{\\\\theta}^{4} a^{4} r r_s-\\\\sin{\\\\theta}^{2} a^{2} r^{2} r_s^{2}+2\\\\sin{\\\\theta}^{2} a^{2} r^{3} r_s+2\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r r_s-a^{2} r^{3} r_s-\\\\cos{\\\\theta}^{2} a^{4} r r_s+\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2}-r^{5} r_s-\\\\cos{\\\\theta}^{2} a^{2} r^{3} r_s+\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{2}\\\\right)^{2} a^{4}}{8\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} \\\\tan{\\\\theta}^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{\\\\phi}= & \\\\frac{55\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6} a^{6} r^{5} r_s^{3}+20\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{6} a^{8} r^{3} r_s^{3}-2\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{8} r^{3} r_s^{3}+12\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{5} a^{6} r^{3} r_s^{3}+12\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{5} a^{6} r^{3} r_s^{3}+34\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{3} r_s^{3}+12\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{3} r_s^{3}-12\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{3} r_s^{3}+8\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{5} r_s^{3} \\\\sin{2\\\\theta}+8\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{5} r_s^{3} \\\\sin{2\\\\theta}+4\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{3} r_s^{3} \\\\sin{2\\\\theta}+4\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{3} r_s^{3} \\\\sin{2\\\\theta}-4\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{5} r_s^{3} \\\\sin{4\\\\theta}-4\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{5} r_s^{3} \\\\sin{4\\\\theta}-2\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{3} r_s^{3} \\\\sin{4\\\\theta}-2\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{3} r_s^{3} \\\\sin{4\\\\theta}-4\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{4} r^{2} r_s^{2}+2\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{2} r_s^{2} \\\\sin{2\\\\theta}+2\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{2} r_s^{2} \\\\sin{2\\\\theta}%\\n-4\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{2} r^{4} r_s^{2}+2\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{4} r_s^{2} \\\\sin{2\\\\theta}+2\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{4} r_s^{2} \\\\sin{2\\\\theta}+41\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{6} r^{5} r_s^{3}+10\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} a^{8} r^{3} r_s^{3}-12\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{2} r_s^{2}-6\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{4} r_s^{2}+64\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{4} r^{7} r_s^{3}-13\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{4} r^{6} r_s^{4}-4\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{6} r^{4} r_s^{4}-16\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{6} r_s^{2}+6\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{5} r_s^{3}-24\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{4} r_s^{2}-23\\\\sin{\\\\theta}^{6} a^{6} r^{6} r_s^{2}-65\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6} a^{8} r^{4} r_s^{2}+5\\\\sin{\\\\theta}^{4} a^{6} r^{6} r_s^{2}+23\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{8} r^{4} r_s^{2}-12\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{5} a^{6} r^{4} r_s^{2}-12\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{5} a^{6} r^{4} r_s^{2}-28\\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{4} r_s^{2}%\\n-12\\\\cos{2\\\\theta} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{4} r_s^{2}+12\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{4} r_s^{2}-4\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{4} r^{6} r_s^{2} \\\\sin{2\\\\theta}-4\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{4} r^{6} r_s^{2} \\\\sin{2\\\\theta}-8\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{6} r^{4} r_s^{2} \\\\sin{2\\\\theta}-8\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{6} r^{4} r_s^{2} \\\\sin{2\\\\theta}+2\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{4} r^{6} r_s^{2} \\\\sin{4\\\\theta}+2\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{4} r^{6} r_s^{2} \\\\sin{4\\\\theta}+4\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{6} r^{4} r_s^{2} \\\\sin{4\\\\theta}+4\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{6} r^{4} r_s^{2} \\\\sin{4\\\\theta}+4\\\\cos{2\\\\theta} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{4} r^{3} r_s-2\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{3} \\\\sin{2\\\\theta} r_s-2\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{3} \\\\sin{2\\\\theta} r_s+12\\\\cos{2\\\\theta} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{2} r^{5} r_s-6\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{5} \\\\sin{2\\\\theta} r_s-6\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{5} \\\\sin{2\\\\theta} r_s-12\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{6} r^{6} r_s^{2}-22\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{8} r^{4} r_s^{2}+18\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{5} r_s-9\\\\sin{\\\\theta}^{4} a^{4} r^{8} r_s^{2}%\\n+10\\\\sin{\\\\theta}^{4} a^{4} r^{7} r_s^{3}+18\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{7} r_s-4\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{6} r_s^{2}+6\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{5} r_s-41\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{6} a^{10} r^{2} r_s^{2}+19\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{10} r^{2} r_s^{2}-12\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{5} a^{8} r^{2} r_s^{2}-12\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{5} a^{8} r^{2} r_s^{2}-44\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{2} r_s^{2}-12\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{2} r_s^{2}+12\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{2} r_s^{2}-4\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{8} r^{2} r_s^{2} \\\\sin{2\\\\theta}-4\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{8} r^{2} r_s^{2} \\\\sin{2\\\\theta}+2\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{8} r^{2} r_s^{2} \\\\sin{4\\\\theta}+2\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{8} r^{2} r_s^{2} \\\\sin{4\\\\theta}+4\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{6} r r_s-2\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} \\\\sin{2\\\\theta} r r_s-2\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} \\\\sin{2\\\\theta} r r_s+16\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{4} r^{3} r_s-8\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{3} \\\\sin{2\\\\theta} r_s%\\n-8\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{3} \\\\sin{2\\\\theta} r_s-20\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} a^{10} r^{2} r_s^{2}-6\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} r r_s+6\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{3} r_s+22\\\\sin{\\\\theta}^{6} a^{4} r^{7} r_s^{3}+12\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{5} a^{4} r^{5} r_s^{3}+12\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{5} a^{4} r^{5} r_s^{3}+30\\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{5} r_s^{3}+12\\\\cos{2\\\\theta} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{5} r_s^{3}-12\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{5} r_s^{3}+4\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{2} r^{7} r_s^{3} \\\\sin{2\\\\theta}+4\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{2} r^{7} r_s^{3} \\\\sin{2\\\\theta}-2\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{2} r^{7} r_s^{3} \\\\sin{4\\\\theta}-2\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{2} r^{7} r_s^{3} \\\\sin{4\\\\theta}-4\\\\cos{2\\\\theta} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{2} r^{4} r_s^{2}+2\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{4} r_s^{2} \\\\sin{2\\\\theta}+2\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{4} r_s^{2} \\\\sin{2\\\\theta}-4\\\\cos{2\\\\theta} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} r^{6} r_s^{2}+2\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{6} r_s^{2} \\\\sin{2\\\\theta}+2\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{6} r_s^{2} \\\\sin{2\\\\theta}%\\n+36\\\\sin{\\\\theta}^{4} a^{2} r^{9} r_s^{3}-14\\\\sin{\\\\theta}^{4} a^{2} r^{8} r_s^{4}-4\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{8} r_s^{2}-47\\\\sin{\\\\theta}^{6} a^{4} r^{8} r_s^{2}-129\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6} a^{6} r^{6} r_s^{2}-24\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{5} a^{4} r^{6} r_s^{2}-24\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{5} a^{4} r^{6} r_s^{2}-58\\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{6} r_s^{2}-24\\\\cos{2\\\\theta} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{6} r_s^{2}+24\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{6} r_s^{2}-8\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{2} r^{8} r_s^{2} \\\\sin{2\\\\theta}-8\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{2} r^{8} r_s^{2} \\\\sin{2\\\\theta}-20\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{6} r_s^{2} \\\\sin{2\\\\theta}-20\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{6} r_s^{2} \\\\sin{2\\\\theta}+4\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{2} r^{8} r_s^{2} \\\\sin{4\\\\theta}+4\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{2} r^{8} r_s^{2} \\\\sin{4\\\\theta}+10\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{6} r_s^{2} \\\\sin{4\\\\theta}+10\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{6} r_s^{2} \\\\sin{4\\\\theta}+8\\\\cos{2\\\\theta} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} r^{7} r_s-4\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{7} \\\\sin{2\\\\theta} r_s%\\n-4\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{7} \\\\sin{2\\\\theta} r_s-91\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{4} r^{8} r_s^{2}-101\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{6} r^{6} r_s^{2}+6\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{7} r_s-32\\\\sin{\\\\theta}^{4} a^{2} r^{10} r_s^{2}+8\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{9} r_s-97\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{6} a^{8} r^{4} r_s^{2}-36\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{5} a^{6} r^{4} r_s^{2}-36\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{5} a^{6} r^{4} r_s^{2}-106\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{4} r_s^{2}-36\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{4} r_s^{2}+40\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{4} r_s^{2}-16\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{4} r_s^{2} \\\\sin{2\\\\theta}-16\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{4} r_s^{2} \\\\sin{2\\\\theta}+8\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{4} r_s^{2} \\\\sin{4\\\\theta}+8\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{4} r_s^{2} \\\\sin{4\\\\theta}+12\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{2} r^{5} r_s-6\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{5} \\\\sin{2\\\\theta} r_s-6\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{5} \\\\sin{2\\\\theta} r_s-45\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} a^{8} r^{4} r_s^{2}%\\n+24\\\\sin{\\\\theta}^{6} a^{6} r^{7} r_s+80\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6} a^{8} r^{5} r_s-8\\\\sin{\\\\theta}^{4} a^{6} r^{7} r_s-32\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{8} r^{5} r_s+12\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{5} a^{6} r^{5} r_s+12\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{5} a^{6} r^{5} r_s+28\\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{5} r_s+12\\\\cos{2\\\\theta} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{5} r_s-12\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{5} r_s+4\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{4} r^{7} \\\\sin{2\\\\theta} r_s+4\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{4} r^{7} \\\\sin{2\\\\theta} r_s+12\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{6} r^{5} \\\\sin{2\\\\theta} r_s+12\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{6} r^{5} \\\\sin{2\\\\theta} r_s-2\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{4} r^{7} \\\\sin{4\\\\theta} r_s-2\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{4} r^{7} \\\\sin{4\\\\theta} r_s-6\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{6} r^{5} \\\\sin{4\\\\theta} r_s-6\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{6} r^{5} \\\\sin{4\\\\theta} r_s-4\\\\cos{2\\\\theta} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{4} r^{4}+2\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{4} \\\\sin{2\\\\theta}+2\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{4} \\\\sin{2\\\\theta}%\\n-8\\\\cos{2\\\\theta} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{2} r^{6}+4\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{6} \\\\sin{2\\\\theta}+4\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{6} \\\\sin{2\\\\theta}+8\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{6} r^{7} r_s+28\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{8} r^{5} r_s-8\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{4}-4\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{6}+2\\\\sin{\\\\theta}^{4} a^{4} r^{9} r_s-12\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{8}-8\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{6}+88\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{6} a^{10} r^{3} r_s-40\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{10} r^{3} r_s+24\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{5} a^{8} r^{3} r_s+24\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{5} a^{8} r^{3} r_s+72\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{3} r_s+24\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{3} r_s-24\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{3} r_s+12\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{8} r^{3} \\\\sin{2\\\\theta} r_s+12\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{8} r^{3} \\\\sin{2\\\\theta} r_s-6\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{8} r^{3} \\\\sin{4\\\\theta} r_s%\\n-6\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{8} r^{3} \\\\sin{4\\\\theta} r_s-8\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{6} r^{2}+4\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{2} \\\\sin{2\\\\theta}+4\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{2} \\\\sin{2\\\\theta}-16\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{4} r^{4}+8\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{4} \\\\sin{2\\\\theta}+8\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{4} \\\\sin{2\\\\theta}+40\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} a^{10} r^{3} r_s+8\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} r^{2}+28\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{4}+24\\\\sin{\\\\theta}^{6} a^{4} r^{9} r_s+80\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6} a^{6} r^{7} r_s+12\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{5} a^{4} r^{7} r_s+12\\\\cos{\\\\theta} \\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{5} a^{4} r^{7} r_s+28\\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{7} r_s+12\\\\cos{2\\\\theta} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{7} r_s-12\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{7} r_s+4\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{2} r^{9} \\\\sin{2\\\\theta} r_s+4\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{2} r^{9} \\\\sin{2\\\\theta} r_s+12\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{7} \\\\sin{2\\\\theta} r_s%\\n+12\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{7} \\\\sin{2\\\\theta} r_s-2\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{2} r^{9} \\\\sin{4\\\\theta} r_s-2\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{2} r^{9} \\\\sin{4\\\\theta} r_s-6\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{7} \\\\sin{4\\\\theta} r_s-6\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{7} \\\\sin{4\\\\theta} r_s-4\\\\cos{2\\\\theta} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} r^{8}+2\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{8} \\\\sin{2\\\\theta}+2\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{8} \\\\sin{2\\\\theta}+40\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{4} r^{9} r_s+68\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{6} r^{7} r_s+4\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{8}+10\\\\sin{\\\\theta}^{4} a^{2} r^{11} r_s-4\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{10}+88\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{6} a^{8} r^{5} r_s+24\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{5} a^{6} r^{5} r_s+24\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{5} a^{6} r^{5} r_s+72\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{5} r_s+24\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{5} r_s-28\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{5} r_s+12\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{5} \\\\sin{2\\\\theta} r_s%\\n+12\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{5} \\\\sin{2\\\\theta} r_s-6\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{5} \\\\sin{4\\\\theta} r_s-6\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{5} \\\\sin{4\\\\theta} r_s-8\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{2} r^{6}+4\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{6} \\\\sin{2\\\\theta}+4\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{6} \\\\sin{2\\\\theta}+56\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} a^{8} r^{5} r_s+20\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{6}-15\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{6} a^{10} r^{2} r_s^{2}-12\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{5} a^{8} r^{2} r_s^{2}-12\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{5} a^{8} r^{2} r_s^{2}-36\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{2} r_s^{2}-12\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{2} r_s^{2}+16\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{2} r_s^{2}-4\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{8} r^{2} r_s^{2} \\\\sin{2\\\\theta}-4\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{8} r^{2} r_s^{2} \\\\sin{2\\\\theta}+2\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{8} r^{2} r_s^{2} \\\\sin{4\\\\theta}+2\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{8} r^{2} r_s^{2} \\\\sin{4\\\\theta}+4\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{6} r r_s-2\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} \\\\sin{2\\\\theta} r r_s%\\n-2\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} \\\\sin{2\\\\theta} r r_s+4\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{4} r^{3} r_s-2\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{3} \\\\sin{2\\\\theta} r_s-2\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{3} \\\\sin{2\\\\theta} r_s-3\\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{4} a^{10} r^{2} r_s^{2}+6\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} r r_s+2\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{3} r_s+32\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{6} a^{12} r r_s-16\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} a^{12} r r_s+12\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{5} a^{10} r r_s+12\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{5} a^{10} r r_s+44\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} r r_s+12\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} r r_s-12\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} r r_s+4\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{10} \\\\sin{2\\\\theta} r r_s+4\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{10} \\\\sin{2\\\\theta} r r_s-2\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{10} \\\\sin{4\\\\theta} r r_s-2\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{10} \\\\sin{4\\\\theta} r r_s-4\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{8}+2\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} \\\\sin{2\\\\theta}%\\n+2\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} \\\\sin{2\\\\theta}-8\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{6} r^{2}+4\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{2} \\\\sin{2\\\\theta}+4\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{2} \\\\sin{2\\\\theta}+18\\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{4} a^{12} r r_s+8\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{10}+20\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} r^{2}+32\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{6} a^{10} r^{3} r_s+12\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{5} a^{8} r^{3} r_s+12\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{5} a^{8} r^{3} r_s+44\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{3} r_s+12\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{3} r_s-20\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{3} r_s+4\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{8} r^{3} \\\\sin{2\\\\theta} r_s+4\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{8} r^{3} \\\\sin{2\\\\theta} r_s-2\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{8} r^{3} \\\\sin{4\\\\theta} r_s-2\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{8} r^{3} \\\\sin{4\\\\theta} r_s-4\\\\cos{2\\\\theta} \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{4} r^{4}+2\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{4} \\\\sin{2\\\\theta}+2\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{4} \\\\sin{2\\\\theta}%\\n+18\\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{4} a^{10} r^{3} r_s+12\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{4}-2\\\\cos{\\\\theta} \\\\sin{\\\\theta}^{5} a^{8} r^{3} r_s^{3} \\\\sin{2\\\\theta}+2\\\\cos{\\\\theta} \\\\sin{\\\\theta}^{5} a^{8} r^{4} r_s^{2} \\\\sin{2\\\\theta}+2\\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{5} a^{10} r^{2} r_s^{2} \\\\sin{2\\\\theta}-4\\\\cos{\\\\theta} \\\\sin{\\\\theta}^{5} a^{6} r^{5} r_s^{3} \\\\sin{2\\\\theta}+2\\\\cos{\\\\theta} \\\\sin{\\\\theta}^{5} a^{6} r^{4} r_s^{4} \\\\sin{2\\\\theta}+2\\\\cos{\\\\theta} \\\\sin{\\\\theta}^{5} a^{6} r^{6} r_s^{2} \\\\sin{2\\\\theta}+2\\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{5} a^{8} r^{4} r_s^{2} \\\\sin{2\\\\theta}-2\\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{5} a^{8} r^{3} r_s^{3} \\\\sin{2\\\\theta}-4\\\\cos{\\\\theta} \\\\sin{\\\\theta}^{3} a^{6} r^{5} r_s^{3} \\\\sin{2\\\\theta}+4\\\\cos{\\\\theta} \\\\sin{\\\\theta}^{3} a^{6} r^{6} r_s^{2} \\\\sin{2\\\\theta}+8\\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{3} a^{8} r^{4} r_s^{2} \\\\sin{2\\\\theta}-8\\\\cos{\\\\theta} \\\\sin{\\\\theta}^{3} a^{4} r^{7} r_s^{3} \\\\sin{2\\\\theta}+4\\\\cos{\\\\theta} \\\\sin{\\\\theta}^{3} a^{4} r^{6} r_s^{4} \\\\sin{2\\\\theta}+4\\\\cos{\\\\theta} \\\\sin{\\\\theta}^{3} a^{4} r^{8} r_s^{2} \\\\sin{2\\\\theta}+8\\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{3} a^{6} r^{6} r_s^{2} \\\\sin{2\\\\theta}-12\\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{3} a^{6} r^{5} r_s^{3} \\\\sin{2\\\\theta}-4\\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{3} a^{8} r^{3} r_s^{3} \\\\sin{2\\\\theta}+4\\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{3} a^{10} r^{2} r_s^{2} \\\\sin{2\\\\theta}%\\n+4\\\\cos{\\\\theta}^{3} \\\\sin{\\\\theta}^{3} a^{6} r^{4} r_s^{4} \\\\sin{2\\\\theta}+4\\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{3} a^{8} r^{4} r_s^{2} \\\\sin{2\\\\theta}-4\\\\cos{\\\\theta}^{5} \\\\sin{\\\\theta}^{3} a^{8} r^{3} r_s^{3} \\\\sin{2\\\\theta}-2\\\\cos{\\\\theta} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{2} r_s^{2} \\\\sin{\\\\theta} \\\\sin{2\\\\theta}+2\\\\cos{\\\\theta} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{3} \\\\sin{\\\\theta} \\\\sin{2\\\\theta} r_s+2\\\\cos{\\\\theta}^{3} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} \\\\sin{\\\\theta} \\\\sin{2\\\\theta} r r_s-6\\\\cos{\\\\theta} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{4} r_s^{2} \\\\sin{\\\\theta} \\\\sin{2\\\\theta}+2\\\\cos{\\\\theta} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{3} r_s^{3} \\\\sin{\\\\theta} \\\\sin{2\\\\theta}+4\\\\cos{\\\\theta} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{5} \\\\sin{\\\\theta} \\\\sin{2\\\\theta} r_s+4\\\\cos{\\\\theta}^{3} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{3} \\\\sin{\\\\theta} \\\\sin{2\\\\theta} r_s-2\\\\cos{\\\\theta}^{3} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{2} r_s^{2} \\\\sin{\\\\theta} \\\\sin{2\\\\theta}-4\\\\cos{\\\\theta} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{6} r_s^{2} \\\\sin{\\\\theta} \\\\sin{2\\\\theta}+2\\\\cos{\\\\theta} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{5} r_s^{3} \\\\sin{\\\\theta} \\\\sin{2\\\\theta}+2\\\\cos{\\\\theta} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{7} \\\\sin{\\\\theta} \\\\sin{2\\\\theta} r_s+2\\\\cos{\\\\theta}^{3} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{5} \\\\sin{\\\\theta} \\\\sin{2\\\\theta} r_s-2\\\\cos{\\\\theta}^{3} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{4} r_s^{2} \\\\sin{\\\\theta} \\\\sin{2\\\\theta}+10\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6} a^{8} r^{3} r_s^{3}-6\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6} a^{6} r^{4} r_s^{4}-\\\\sin{\\\\theta}^{4} a^{4} r^{6} r_s^{4}+\\\\sin{\\\\theta}^{4} a^{6} r^{5} r_s^{3}%\\n+2\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{6} r^{4} r_s^{4}-2\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{8} r^{3} r_s^{3}-2\\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{3} r_s^{3}+2\\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{2} r_s^{2}-\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{8} r^{2} r_s^{4}+\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{10} r_s^{3} r+2\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r_s^{3} r-2\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} r_s^{2}-2\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{5} r_s^{3}+2\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{4} r_s^{2}+\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} a^{12} r_s^{2}+6\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{3} r_s^{3}-2\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{2} r_s^{2}-12\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{4} r^{6} r_s^{3}-20\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{4} r^{6} r_s^{3}+4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{4} r^{5} r_s^{4}+4\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{4} r^{5} r_s^{4}-8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{6} r^{4} r_s^{3}-8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{6} r^{4} r_s^{3}-8\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{4} r^{6} r_s^{3}%\\n+8\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{4} r^{6} r_s^{3}+12\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{6} r^{4} r_s^{3}-4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{6} r^{4} r_s^{3}+4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{6} r^{4} r_s^{3}+8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{6} r^{4} r_s^{3}-4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{6} r^{3} r_s^{4}-4\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{6} r^{3} r_s^{4}+8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{8} r^{2} r_s^{3}+8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{8} r^{2} r_s^{3}-2\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{2} r_s^{3}+2\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{2} r_s^{3}-2\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{2} r_s^{3}+16\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{5} r_s^{2}+16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{5} r_s^{2}-4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{4} r_s^{3}-4\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{4} r_s^{3}+8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{3} r_s^{2}+8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{3} r_s^{2}-4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{2} r^{3} r_s^{2}+4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{2} r^{3} r_s^{2}%\\n-4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{2} r^{3} r_s^{2}-\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} a^{8} r^{2} r_s^{4}-2\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{3} r_s^{3}-16\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{2} r^{4} r_s^{2}+4\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{2} r^{3} r_s^{3}-8\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{4} r^{2} r_s^{2}+28\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{4} a^{4} r^{7} r_s^{2}+32\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{4} a^{4} r^{7} r_s^{2}-16\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{4} a^{4} r^{6} r_s^{3}-16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{4} a^{4} r^{6} r_s^{3}+8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{4} a^{6} r^{5} r_s^{2}+8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{4} a^{6} r^{5} r_s^{2}+4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\sin{\\\\theta}^{4} a^{4} r^{7} r_s^{2}-4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{4} a^{4} r^{7} r_s^{2}+24\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{6} r^{5} r_s^{2}+8\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{6} r^{5} r_s^{2}-8\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{6} r^{5} r_s^{2}+32\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{6} r^{5} r_s^{2}+4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{8} r^{3} r_s^{2}+4\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{8} r^{3} r_s^{2}%\\n+2\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{3} r_s^{2}-2\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{3} r_s^{2}+2\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{3} r_s^{2}-16\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{6} r_s-16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{6} r_s+8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{5} r_s^{2}+8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{5} r_s^{2}-4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{4} r_s-4\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{4} r_s+4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{2} r^{4} r_s-4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{2} r^{4} r_s+4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{2} r^{4} r_s+16\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{2} r^{5} r_s-8\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{2} r^{4} r_s^{2}+4\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{4} r^{3} r_s-12\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{8} r^{3} r_s^{2}+4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{8} r^{3} r_s^{2}-4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{8} r^{3} r_s^{2}-8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{8} r^{3} r_s^{2}-4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{10} r_s^{2} r%\\n-4\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{10} r_s^{2} r+2\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r_s^{2} r-2\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r_s^{2} r+2\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r_s^{2} r-24\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{4} r_s-24\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{4} r_s-4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{2} r_s-4\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{2} r_s+4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{4} r^{2} r_s-4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{4} r^{2} r_s+4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{4} r^{2} r_s+24\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{4} r^{3} r_s+4\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{6} r r_s-20\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{4} a^{2} r^{8} r_s^{3}-24\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{4} a^{2} r^{8} r_s^{3}+8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{4} a^{2} r^{7} r_s^{4}+8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{4} a^{2} r^{7} r_s^{4}-4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\sin{\\\\theta}^{4} a^{2} r^{8} r_s^{3}+4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{4} a^{2} r^{8} r_s^{3}-2\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{4} r_s^{3}%\\n+2\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{4} r_s^{3}-2\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{4} r_s^{3}+12\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{7} r_s^{2}+12\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{7} r_s^{2}-4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{6} r_s^{3}-4\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{6} r_s^{3}-4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} r^{5} r_s^{2}+4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} r^{5} r_s^{2}-4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} r^{5} r_s^{2}-12\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} r^{6} r_s^{2}+4\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} r^{5} r_s^{3}+16\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{4} a^{2} r^{9} r_s^{2}+24\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{4} a^{2} r^{9} r_s^{2}+8\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\sin{\\\\theta}^{4} a^{2} r^{9} r_s^{2}-8\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{4} a^{2} r^{9} r_s^{2}+8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{4} r^{7} r_s^{2}+20\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{4} r^{7} r_s^{2}-20\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{4} r^{7} r_s^{2}+4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{5} r_s^{2}-4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{5} r_s^{2}%\\n+4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{5} r_s^{2}-12\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{8} r_s-12\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{8} r_s+8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} r^{6} r_s-8\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} r^{6} r_s+8\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} r^{6} r_s+12\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} r^{7} r_s-20\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{6} r^{5} r_s^{2}+16\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{6} r^{5} r_s^{2}-16\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{6} r^{5} r_s^{2}-4\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{6} r^{5} r_s^{2}+6\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{3} r_s^{2}-6\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{3} r_s^{2}+6\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{3} r_s^{2}-20\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{6} r_s-20\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{6} r_s+12\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{2} r^{4} r_s-12\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{2} r^{4} r_s+12\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{2} r^{4} r_s+20\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{2} r^{5} r_s%\\n+28\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{4} r^{7} r_s^{2}-12\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{4} a^{4} r^{8} r_s-16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{4} a^{4} r^{8} r_s-8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{4} a^{6} r^{6} r_s-8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{4} a^{6} r^{6} r_s-4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\sin{\\\\theta}^{4} a^{4} r^{8} r_s+4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{4} a^{4} r^{8} r_s-12\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{6} r^{6} r_s-12\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{6} r^{6} r_s+12\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{6} r^{6} r_s-24\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{6} r^{6} r_s-12\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{8} r^{4} r_s-12\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{8} r^{4} r_s-2\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{4} r_s+2\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{4} r_s-2\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{4} r_s+8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{7}+8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{7}+4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{5}+4\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{5}%\\n-4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{2} r^{5}+4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{2} r^{5}-4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{2} r^{5}-8\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{2} r^{6}-4\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{4} r^{4}+12\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{8} r^{4} r_s-12\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{8} r^{4} r_s+12\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{8} r^{4} r_s-4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{2} r_s+4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{2} r_s-4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{2} r_s+16\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{5}+16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{5}+8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{3}+8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{3}-8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{4} r^{3}+8\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{4} r^{3}-8\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{4} r^{3}-16\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{4} r^{4}-8\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{6} r^{2}%\\n-4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{4} a^{2} r^{10} r_s-8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{4} a^{2} r^{10} r_s-4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\sin{\\\\theta}^{4} a^{2} r^{10} r_s+4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{4} a^{2} r^{10} r_s-12\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{4} r^{8} r_s+12\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{4} r^{8} r_s-12\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{4} r^{8} r_s-2\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{6} r_s+2\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{6} r_s-2\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{6} r_s+4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{9}+4\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{9}-4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} r^{7}+4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} r^{7}-4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} r^{7}-4\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} r^{8}+12\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{6} r^{6} r_s-12\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{6} r^{6} r_s+12\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{6} r^{6} r_s-4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{4} r_s%\\n+4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{4} r_s-4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{4} r_s+8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{7}+8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{7}-8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{2} r^{5}+8\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{2} r^{5}-8\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{2} r^{5}-8\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{2} r^{6}-12\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} a^{8} r^{3} r_s^{2}+4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} a^{8} r^{3} r_s^{2}-4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} a^{8} r^{3} r_s^{2}-8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} a^{8} r^{3} r_s^{2}+4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} a^{8} r^{2} r_s^{3}+4\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} a^{8} r^{2} r_s^{3}-8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} a^{10} r_s^{2} r-8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} a^{10} r_s^{2} r+2\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r_s^{2} r-2\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r_s^{2} r+2\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r_s^{2} r-8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{4} r_s%\\n-8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{4} r_s+4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{3} r_s^{2}+4\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{3} r_s^{2}-8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{2} r_s-8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{2} r_s+4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{4} r^{2} r_s-4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{4} r^{2} r_s+4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{4} r^{2} r_s+\\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{4} a^{10} r_s^{3} r+2\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{2} r_s^{2}+8\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{4} r^{3} r_s-4\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{4} r^{2} r_s^{2}+8\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{6} r r_s+12\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} a^{10} r^{2} r_s-4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} a^{10} r^{2} r_s+4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} a^{10} r^{2} r_s+8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} a^{10} r^{2} r_s+4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} a^{12} r_s+4\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} a^{12} r_s-2\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} r_s%\\n+2\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} r_s-2\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} r_s+8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{3}+8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{3}+4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} r+4\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} r-4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{6} r+4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{6} r-4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{6} r-\\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{4} a^{12} r_s^{2}-8\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{6} r^{2}-4\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{8}+8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} a^{8} r^{4} r_s-4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} a^{8} r^{4} r_s+4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} a^{8} r^{4} r_s+4\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} a^{8} r^{4} r_s-2\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{2} r_s+2\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{2} r_s-2\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{2} r_s+4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{5}%\\n+4\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{5}-4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{4} r^{3}+4\\\\partial_{r}\\\\left(r r_s\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{4} r^{3}-4\\\\partial_{r}\\\\left(a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{4} r^{3}-4\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{4} r^{4}+\\\\sin{\\\\theta}^{6} a^{4} r^{6} r_s^{4}-\\\\sin{\\\\theta}^{6} a^{6} r^{5} r_s^{3}+\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{6} a^{8} r^{2} r_s^{4}-\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{6} a^{10} r_s^{3} r-8\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} r^{5} r_s+4\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} r^{4} r_s^{2}-4\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{2} r^{3} r_s+4\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} r^{6}+4\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{2} r^{4}-\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{6} a^{10} r_s^{3} r+\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{6} a^{12} r_s^{2}+4\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{2} r^{4}-4\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{2} r^{3} r_s+4\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{4} r^{2}-4\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{8} a^{8} r^{3} r_s^{3}%\\n+8\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{7} r_s^{3}+16\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{5} r_s^{3}+8\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{2} r^{9} r_s^{3}+16\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{4} r^{7} r_s^{3}+8\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{8} r^{3} r_s^{3}+8\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{6} r^{5} r_s^{3}-4\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{4} r r_s+8\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{6} r_s^{2}+8\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{4} r_s^{2}-8\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{2} r^{3} r_s+4\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{8} r_s^{2}+4\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{6} r_s^{2}-4\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} r^{5} r_s+4\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{8} a^{8} r^{4} r_s^{2}-8\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{8} r_s^{2}-24\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{6} r_s^{2}-8\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{2} r^{10} r_s^{2}-24\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{4} r^{8} r_s^{2}-24\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{8} r^{4} r_s^{2}-24\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{6} r^{6} r_s^{2}%\\n+4\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{4} r^{2}-8\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{7} r_s-16\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{5} r_s+8\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{2} r^{4}-4\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{9} r_s-8\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{7} r_s+4\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} r^{6}+4\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{8} a^{10} r^{2} r_s^{2}-8\\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} a^{10} r^{2} r_s^{2}-8\\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} a^{8} r^{4} r_s^{2}-4\\\\cos{\\\\theta}^{6} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} r r_s+4\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{6}-8\\\\cos{\\\\theta}^{6} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{3} r_s+8\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{4} r^{2}-4\\\\cos{\\\\theta}^{6} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{5} r_s+4\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{2} r^{4}}{4\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{2} r^{2} r_s^{2}-4\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{2} r^{3} r_s-4\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{4} r r_s+4\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} r^{4} r_s^{2}-8\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} r^{5} r_s-12\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{2} r^{3} r_s+4\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{2} r^{4}+8\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{4} r^{2}+4\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} r^{6}+8\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{2} r^{4}-4\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{4} r r_s+4\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{6}+4\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{4} r^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{\\\\theta}= & \\\\frac{2\\\\cos{\\\\theta} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{5} r_s^{2} \\\\sin{\\\\theta} \\\\tan{\\\\theta}+2\\\\cos{\\\\theta} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{7} r_s^{2} \\\\sin{\\\\theta} \\\\tan{\\\\theta}-2\\\\cos{\\\\theta} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{6} r_s^{3} \\\\sin{\\\\theta} \\\\tan{\\\\theta}-2\\\\cos{\\\\theta}^{5} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} r_s^{2} \\\\sin{\\\\theta} \\\\tan{\\\\theta} r-2\\\\cos{\\\\theta}^{5} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{3} r_s^{2} \\\\sin{\\\\theta} \\\\tan{\\\\theta}+2\\\\cos{\\\\theta}^{5} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{2} r_s^{3} \\\\sin{\\\\theta} \\\\tan{\\\\theta}+4\\\\cos{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{3} r_s^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-\\\\cos{\\\\theta}^{4} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} r_s^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta} r+4\\\\cos{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{5} r_s^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-2\\\\cos{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{4} r_s^{3} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-\\\\cos{\\\\theta}^{4} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{3} r_s^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-3\\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{4} \\\\sin{2\\\\theta} \\\\tan{\\\\theta} r_s-2\\\\cos{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} r^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta} r_s-6\\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{6} \\\\sin{2\\\\theta} \\\\tan{\\\\theta} r_s+5\\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{5} r_s^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-4\\\\cos{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{4} \\\\sin{2\\\\theta} \\\\tan{\\\\theta} r_s+\\\\cos{\\\\theta}^{4} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{10} \\\\sin{2\\\\theta} \\\\tan{\\\\theta} r_s+2\\\\cos{\\\\theta}^{4} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} r^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta} r_s+5\\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{7} r_s^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}%\\n-2\\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{6} r_s^{3} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-3\\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{8} \\\\sin{2\\\\theta} \\\\tan{\\\\theta} r_s-2\\\\cos{\\\\theta}^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{6} \\\\sin{2\\\\theta} \\\\tan{\\\\theta} r_s+\\\\cos{\\\\theta}^{4} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{4} \\\\sin{2\\\\theta} \\\\tan{\\\\theta} r_s+2a^{4} r^{7} r_s^{4} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-2a^{4} r^{8} r_s^{3} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-2\\\\cos{\\\\theta}^{2} a^{6} r^{6} r_s^{3} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+2\\\\cos{\\\\theta}^{4} a^{8} r^{4} r_s^{3} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-4a^{2} r^{9} r_s^{4} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-10\\\\cos{\\\\theta}^{2} a^{4} r^{7} r_s^{4} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+10a^{2} r^{10} r_s^{3} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+30\\\\cos{\\\\theta}^{2} a^{4} r^{8} r_s^{3} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+26\\\\cos{\\\\theta}^{4} a^{6} r^{6} r_s^{3} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+6\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{4} r^{6} r_s^{3} \\\\tan{\\\\theta}+4\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{6} r^{4} r_s^{3} \\\\tan{\\\\theta}-12\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{4} r^{7} r_s^{2} \\\\tan{\\\\theta}-20\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{6} r^{5} r_s^{2} \\\\tan{\\\\theta}-4\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{8} r^{3} r_s^{2} \\\\tan{\\\\theta}+16\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{2} r^{8} r_s^{3} \\\\tan{\\\\theta}+16\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{6} r_s^{3} \\\\tan{\\\\theta}%\\n-28\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{2} r^{9} r_s^{2} \\\\tan{\\\\theta}-52\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{7} r_s^{2} \\\\tan{\\\\theta}-20\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{5} r_s^{2} \\\\tan{\\\\theta}+6\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{4} r^{6} r_s^{3} \\\\tan{\\\\theta}+4\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{6} r^{4} r_s^{3} \\\\tan{\\\\theta}-12\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{4} r^{7} r_s^{2} \\\\tan{\\\\theta}-20\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{6} r^{5} r_s^{2} \\\\tan{\\\\theta}-4\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{8} r^{3} r_s^{2} \\\\tan{\\\\theta}+16\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{2} r^{8} r_s^{3} \\\\tan{\\\\theta}+16\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{6} r_s^{3} \\\\tan{\\\\theta}-28\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{2} r^{9} r_s^{2} \\\\tan{\\\\theta}-52\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{7} r_s^{2} \\\\tan{\\\\theta}-20\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{5} r_s^{2} \\\\tan{\\\\theta}+18\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r^{10} r_s^{3} \\\\tan{\\\\theta}+36\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{2} r^{8} r_s^{3} \\\\tan{\\\\theta}-32\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r^{11} r_s^{2} \\\\tan{\\\\theta}-96\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{2} r^{9} r_s^{2} \\\\tan{\\\\theta}-112\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{4} r^{7} r_s^{2} \\\\tan{\\\\theta}+18\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) r^{10} r_s^{3} \\\\tan{\\\\theta}+36\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{2} r^{8} r_s^{3} \\\\tan{\\\\theta}%\\n-32\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) r^{11} r_s^{2} \\\\tan{\\\\theta}-96\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{2} r^{9} r_s^{2} \\\\tan{\\\\theta}-112\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{4} r^{7} r_s^{2} \\\\tan{\\\\theta}-2a^{4} r^{9} r_s^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-4\\\\cos{\\\\theta}^{2} a^{6} r^{7} r_s^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-8a^{2} r^{11} r_s^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-26\\\\cos{\\\\theta}^{2} a^{4} r^{9} r_s^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-28\\\\cos{\\\\theta}^{4} a^{6} r^{7} r_s^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+6\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{4} r^{8} \\\\tan{\\\\theta} r_s+16\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{6} r^{6} \\\\tan{\\\\theta} r_s+12\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{8} r^{4} \\\\tan{\\\\theta} r_s+24\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{2} r^{10} \\\\tan{\\\\theta} r_s+80\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{8} \\\\tan{\\\\theta} r_s+96\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{6} \\\\tan{\\\\theta} r_s+6\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{4} r^{8} \\\\tan{\\\\theta} r_s+16\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{6} r^{6} \\\\tan{\\\\theta} r_s+12\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{8} r^{4} \\\\tan{\\\\theta} r_s+24\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{2} r^{10} \\\\tan{\\\\theta} r_s+80\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{8} \\\\tan{\\\\theta} r_s+96\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{6} \\\\tan{\\\\theta} r_s%\\n+26\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r^{12} \\\\tan{\\\\theta} r_s+104\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{2} r^{10} \\\\tan{\\\\theta} r_s+164\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{4} r^{8} \\\\tan{\\\\theta} r_s+26\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) r^{12} \\\\tan{\\\\theta} r_s+104\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{2} r^{10} \\\\tan{\\\\theta} r_s+164\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{4} r^{8} \\\\tan{\\\\theta} r_s+4\\\\cos{\\\\theta}^{6} a^{10} r^{3} r_s^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-8\\\\cos{\\\\theta}^{6} a^{8} r^{5} r_s^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+48\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{8} r^{4} \\\\tan{\\\\theta} r_s+48\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{8} r^{4} \\\\tan{\\\\theta} r_s+128\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{6} r^{6} \\\\tan{\\\\theta} r_s+128\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{6} r^{6} \\\\tan{\\\\theta} r_s-2\\\\cos{\\\\theta}^{4} a^{8} r^{3} r_s^{4} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+2\\\\cos{\\\\theta}^{6} a^{10} r^{2} r_s^{3} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-4\\\\cos{\\\\theta}^{4} a^{6} r^{5} r_s^{4} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+2\\\\cos{\\\\theta}^{6} a^{8} r^{4} r_s^{3} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-2\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{8} r^{2} r_s^{3} \\\\tan{\\\\theta}+4\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{10} r_s^{2} \\\\tan{\\\\theta} r+4\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{8} r^{3} r_s^{2} \\\\tan{\\\\theta}-2\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{8} r^{2} r_s^{3} \\\\tan{\\\\theta}%\\n+4\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{10} r_s^{2} \\\\tan{\\\\theta} r+4\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{8} r^{3} r_s^{2} \\\\tan{\\\\theta}+26\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{4} r^{6} r_s^{3} \\\\tan{\\\\theta}-64\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{6} r^{5} r_s^{2} \\\\tan{\\\\theta}+26\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{4} r^{6} r_s^{3} \\\\tan{\\\\theta}-64\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{6} r^{5} r_s^{2} \\\\tan{\\\\theta}+2\\\\cos{\\\\theta}^{8} a^{12} r_s^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta} r+4\\\\cos{\\\\theta}^{8} a^{10} r^{3} r_s^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-2\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{8} a^{12} \\\\tan{\\\\theta} r_s+8\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{8} a^{10} r^{2} \\\\tan{\\\\theta} r_s-2\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{8} a^{12} \\\\tan{\\\\theta} r_s+8\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{8} a^{10} r^{2} \\\\tan{\\\\theta} r_s+50\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{8} a^{8} r^{4} \\\\tan{\\\\theta} r_s+50\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{8} a^{8} r^{4} \\\\tan{\\\\theta} r_s-4\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{5} r_s^{4} \\\\tan{\\\\theta}-4\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{5} r_s^{4} \\\\tan{\\\\theta}-4\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{2} r^{7} r_s^{4} \\\\tan{\\\\theta}-4\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{2} r^{7} r_s^{4} \\\\tan{\\\\theta}-4\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{2} r^{7} r_s^{4} \\\\tan{\\\\theta}-4\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{2} r^{7} r_s^{4} \\\\tan{\\\\theta}%\\n-4\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r^{9} r_s^{4} \\\\tan{\\\\theta}-4\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) r^{9} r_s^{4} \\\\tan{\\\\theta}+8\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{6} r^{4} r_s^{3} \\\\tan{\\\\theta}+8\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{6} r^{4} r_s^{3} \\\\tan{\\\\theta}+2\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} a^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+2\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} a^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+4\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} \\\\tan{\\\\theta} r+4\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} \\\\tan{\\\\theta} r-2\\\\sin{\\\\theta}^{4} a^{6} r^{5} r_s^{4}+12\\\\sin{\\\\theta}^{4} a^{6} r^{6} r_s^{3}+8\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{8} r^{4} r_s^{3}+2\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{8} r^{3} r_s^{4}-2\\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{2} r_s^{3}+10\\\\sin{\\\\theta}^{4} a^{4} r^{8} r_s^{3}+10\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{6} r^{6} r_s^{3}-2\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{6} r^{5} r_s^{4}-2\\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{4} r_s^{3}+2\\\\sin{\\\\theta}^{2} a^{4} r^{6} r_s^{5}-14\\\\sin{\\\\theta}^{2} a^{4} r^{7} r_s^{4}-8\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{6} r^{5} r_s^{4}%\\n-2\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{6} r^{4} r_s^{5}+2\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{3} r_s^{4}+6\\\\sin{\\\\theta}^{2} a^{2} r^{8} r_s^{5}-26\\\\sin{\\\\theta}^{2} a^{2} r^{9} r_s^{4}-32\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{7} r_s^{4}+2\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{6} r_s^{5}+2\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{5} r_s^{4}+34\\\\sin{\\\\theta}^{2} a^{4} r^{8} r_s^{3}+62\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{6} r^{6} r_s^{3}-2\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{4} r_s^{3}+46\\\\sin{\\\\theta}^{2} a^{2} r^{10} r_s^{3}+98\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{8} r_s^{3}-6\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{6} r_s^{3}+22\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{8} r^{4} r_s^{3}+6\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{8} r^{3} r_s^{4}-6\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{2} r_s^{3}+58\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{6} r_s^{3}-6\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{5} r_s^{4}-10\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{4} r_s^{3}-2\\\\sin{\\\\theta}^{2} a^{4} r^{7} r_s^{4} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}%\\n+2\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{8} r^{3} r_s^{4} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+4\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{6} r_s^{3} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+4\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{4} r_s^{3} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-6\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{4} r^{6} r_s^{3} \\\\tan{\\\\theta}-4\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{6} r^{4} r_s^{3} \\\\tan{\\\\theta}+2\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{8} r^{2} r_s^{3} \\\\tan{\\\\theta}+8\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{5} r_s^{2} \\\\tan{\\\\theta}+8\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{3} r_s^{2} \\\\tan{\\\\theta}-6\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{4} r^{6} r_s^{3} \\\\tan{\\\\theta}-4\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{6} r^{4} r_s^{3} \\\\tan{\\\\theta}+2\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{8} r^{2} r_s^{3} \\\\tan{\\\\theta}+8\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{5} r_s^{2} \\\\tan{\\\\theta}+8\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{3} r_s^{2} \\\\tan{\\\\theta}-14\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{2} r^{8} r_s^{3} \\\\tan{\\\\theta}-20\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{6} r_s^{3} \\\\tan{\\\\theta}-6\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{4} r_s^{3} \\\\tan{\\\\theta}+16\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{7} r_s^{2} \\\\tan{\\\\theta}+24\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{5} r_s^{2} \\\\tan{\\\\theta}-14\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{2} r^{8} r_s^{3} \\\\tan{\\\\theta}-20\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{6} r_s^{3} \\\\tan{\\\\theta}%\\n-6\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{4} r_s^{3} \\\\tan{\\\\theta}+16\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{7} r_s^{2} \\\\tan{\\\\theta}+24\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{5} r_s^{2} \\\\tan{\\\\theta}+4\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{5} r_s^{4} \\\\tan{\\\\theta}+4\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{5} r_s^{4} \\\\tan{\\\\theta}-4\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{4} r_s^{3} \\\\tan{\\\\theta}-4\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{4} r_s^{3} \\\\tan{\\\\theta}+4\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{2} r^{7} r_s^{4} \\\\tan{\\\\theta}+4\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{2} r^{7} r_s^{4} \\\\tan{\\\\theta}-4\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{6} r_s^{3} \\\\tan{\\\\theta}-4\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{6} r_s^{3} \\\\tan{\\\\theta}+2\\\\cos{\\\\theta}^{6} a^{8} r^{3} r_s^{4} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-6\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{8} r^{3} r_s^{4}-4a^{4} r^{8} r_s^{3}-8\\\\cos{\\\\theta}^{2} a^{6} r^{6} r_s^{3}-6\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{5} r_s^{2}+4\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{5} r_s^{2}-8a^{2} r^{10} r_s^{3}-16\\\\cos{\\\\theta}^{2} a^{4} r^{8} r_s^{3}-4\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{10} r^{2} r_s^{3}%\\n-4\\\\cos{\\\\theta}^{4} a^{8} r^{4} r_s^{3}+4\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{3} r_s^{2}-8\\\\cos{\\\\theta}^{4} a^{6} r^{6} r_s^{3}-8\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{5} r_s^{2}+4\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{8} r_s^{3}+2\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{7} r_s^{2}-4r^{12} r_s^{3}-8\\\\cos{\\\\theta}^{2} a^{2} r^{10} r_s^{3}-4\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{9} r_s^{2}+6\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{8} r^{4} r_s^{3}+16\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{5} r_s^{2}-4\\\\cos{\\\\theta}^{4} a^{4} r^{8} r_s^{3}+4\\\\sin{\\\\theta}^{2} a^{4} r^{8} r_s^{3} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+4\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{6} r^{6} r_s^{3} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-4\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{8} r^{4} r_s^{3} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-8\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{7} r_s^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-16\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{5} r_s^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+12\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{4} r^{7} r_s^{2} \\\\tan{\\\\theta}+20\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{6} r^{5} r_s^{2} \\\\tan{\\\\theta}+4\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{8} r^{3} r_s^{2} \\\\tan{\\\\theta}%\\n-16\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{6} \\\\tan{\\\\theta} r_s-32\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{4} \\\\tan{\\\\theta} r_s+12\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{4} r^{7} r_s^{2} \\\\tan{\\\\theta}+20\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{6} r^{5} r_s^{2} \\\\tan{\\\\theta}+4\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{8} r^{3} r_s^{2} \\\\tan{\\\\theta}-16\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{6} \\\\tan{\\\\theta} r_s-32\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{4} \\\\tan{\\\\theta} r_s+16\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{2} r^{9} r_s^{2} \\\\tan{\\\\theta}+32\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{7} r_s^{2} \\\\tan{\\\\theta}+16\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{5} r_s^{2} \\\\tan{\\\\theta}-20\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{8} \\\\tan{\\\\theta} r_s-44\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{6} \\\\tan{\\\\theta} r_s+16\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{2} r^{9} r_s^{2} \\\\tan{\\\\theta}+32\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{7} r_s^{2} \\\\tan{\\\\theta}+16\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{5} r_s^{2} \\\\tan{\\\\theta}-20\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{8} \\\\tan{\\\\theta} r_s-44\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{6} \\\\tan{\\\\theta} r_s-16\\\\sin{\\\\theta}^{4} a^{6} r^{7} r_s^{2}-28\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{8} r^{5} r_s^{2}-34\\\\sin{\\\\theta}^{2} a^{4} r^{9} r_s^{2}%\\n-100\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{6} r^{7} r_s^{2}+8a^{4} r^{9} r_s^{2}+24\\\\cos{\\\\theta}^{2} a^{6} r^{7} r_s^{2}+10\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{6} r_s-8\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{6} r_s+16a^{2} r^{11} r_s^{2}+48\\\\cos{\\\\theta}^{2} a^{4} r^{9} r_s^{2}-12\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{8} r_s-96\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{8} r^{5} r_s^{2}+24\\\\cos{\\\\theta}^{4} a^{8} r^{5} r_s^{2}+18\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{4} r_s-16\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{4} r_s+48\\\\cos{\\\\theta}^{4} a^{6} r^{7} r_s^{2}-20\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{6} r_s-14\\\\sin{\\\\theta}^{4} a^{4} r^{9} r_s^{2}-24\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{6} r^{7} r_s^{2}-38\\\\sin{\\\\theta}^{2} a^{2} r^{11} r_s^{2}-116\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{9} r_s^{2}+6\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{8} r_s+8r^{13} r_s^{2}%\\n+24\\\\cos{\\\\theta}^{2} a^{2} r^{11} r_s^{2}-4\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{10} r_s-120\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{7} r_s^{2}+6\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{6} r_s+24\\\\cos{\\\\theta}^{4} a^{4} r^{9} r_s^{2}-4\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{8} r_s-4\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{10} r^{2} r_s^{3} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-8\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{3} r_s^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-4\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{10} r_s^{2} \\\\tan{\\\\theta} r-16\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{2} \\\\tan{\\\\theta} r_s-4\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{10} r_s^{2} \\\\tan{\\\\theta} r-16\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{2} \\\\tan{\\\\theta} r_s-28\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{4} \\\\tan{\\\\theta} r_s-28\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{4} \\\\tan{\\\\theta} r_s+8\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{3} r_s^{2} \\\\tan{\\\\theta}+8\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{3} r_s^{2} \\\\tan{\\\\theta}-4\\\\cos{\\\\theta}^{8} a^{10} r^{2} r_s^{3} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-16\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{8} a^{8} r^{3} r_s^{2} \\\\tan{\\\\theta}-16\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{8} a^{8} r^{3} r_s^{2} \\\\tan{\\\\theta}+6\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} a^{10} r^{2} r_s^{3}%\\n+6\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{8} r^{4} r_s^{3}+14\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{3} r_s^{2}-8\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{3} r_s^{2}-8\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{5} r_s^{2}+4\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} a^{12} r_s^{2} r-28\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{10} r^{3} r_s^{2}+8\\\\cos{\\\\theta}^{6} a^{10} r^{3} r_s^{2}+6\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} r^{2} r_s-8\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} r^{2} r_s+16\\\\cos{\\\\theta}^{6} a^{8} r^{5} r_s^{2}-4\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{4} r_s-44\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{8} r^{5} r_s^{2}-6\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{4} r_s+8\\\\cos{\\\\theta}^{6} a^{6} r^{7} r_s^{2}+4\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{6} r_s+2\\\\sin{\\\\theta}^{6} a^{6} r^{5} r_s^{4}-2\\\\sin{\\\\theta}^{4} a^{4} r^{6} r_s^{5}-2\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6} a^{8} r^{3} r_s^{4}+2\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{6} r^{4} r_s^{5}+4\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{6} r_s^{3}%\\n+4\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{4} r_s^{3}-4\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{2} r^{3} r_s^{2}+4\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{6} r_s^{3}-4\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} r^{5} r_s^{2}-4\\\\sin{\\\\theta}^{6} a^{6} r^{6} r_s^{3}+6\\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{5} r_s^{2}+8\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{2} r^{4} r_s-12\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{7} r_s^{2}+8\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} r^{6} r_s+4\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{6} a^{10} r^{2} r_s^{3}-6\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{10} r^{2} r_s^{3}+6\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} r_s^{2} r+6\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{3} r_s^{2}+8\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{4} r^{2} r_s+8\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{2} r^{4} r_s+2\\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{3} r_s^{2}-2\\\\sin{\\\\theta}^{2} a^{4} r^{9} r_s^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}-4\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{6} r^{7} r_s^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+4\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{8} \\\\sin{2\\\\theta} \\\\tan{\\\\theta} r_s+12\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{6} \\\\sin{2\\\\theta} \\\\tan{\\\\theta} r_s%\\n-6\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{4} r^{8} \\\\tan{\\\\theta} r_s-16\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{6} r^{6} \\\\tan{\\\\theta} r_s-12\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{8} r^{4} \\\\tan{\\\\theta} r_s+8\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{7} \\\\tan{\\\\theta}+24\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{5} \\\\tan{\\\\theta}-6\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{4} r^{8} \\\\tan{\\\\theta} r_s-16\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{6} r^{6} \\\\tan{\\\\theta} r_s-12\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{8} r^{4} \\\\tan{\\\\theta} r_s+8\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{7} \\\\tan{\\\\theta}+24\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{5} \\\\tan{\\\\theta}-6\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{2} r^{10} \\\\tan{\\\\theta} r_s-16\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{8} \\\\tan{\\\\theta} r_s-12\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{6} \\\\tan{\\\\theta} r_s+8\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{9} \\\\tan{\\\\theta}+24\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{7} \\\\tan{\\\\theta}-6\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{2} r^{10} \\\\tan{\\\\theta} r_s-16\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{8} \\\\tan{\\\\theta} r_s-12\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{6} \\\\tan{\\\\theta} r_s+8\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{9} \\\\tan{\\\\theta}+24\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{7} \\\\tan{\\\\theta}%\\n+2a^{4} r^{10} \\\\sin{2\\\\theta} \\\\tan{\\\\theta} r_s+6\\\\cos{\\\\theta}^{2} a^{6} r^{8} \\\\sin{2\\\\theta} \\\\tan{\\\\theta} r_s+4\\\\cos{\\\\theta}^{4} a^{8} r^{6} \\\\sin{2\\\\theta} \\\\tan{\\\\theta} r_s-8\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) a^{2} r^{11} \\\\tan{\\\\theta}-40\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{9} \\\\tan{\\\\theta}-8\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) a^{2} r^{11} \\\\tan{\\\\theta}-40\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{4} r^{9} \\\\tan{\\\\theta}-80\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{7} \\\\tan{\\\\theta}-80\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{6} r^{7} \\\\tan{\\\\theta}-4\\\\cos{\\\\theta}^{6} a^{10} r^{4} \\\\sin{2\\\\theta} \\\\tan{\\\\theta} r_s-80\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{8} r^{5} \\\\tan{\\\\theta}-80\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{8} r^{5} \\\\tan{\\\\theta}+2a^{2} r^{12} \\\\sin{2\\\\theta} \\\\tan{\\\\theta} r_s+6\\\\cos{\\\\theta}^{2} a^{4} r^{10} \\\\sin{2\\\\theta} \\\\tan{\\\\theta} r_s+4\\\\cos{\\\\theta}^{4} a^{6} r^{8} \\\\sin{2\\\\theta} \\\\tan{\\\\theta} r_s-8\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) r^{13} \\\\tan{\\\\theta}-40\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{2} r^{11} \\\\tan{\\\\theta}-8\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) r^{13} \\\\tan{\\\\theta}-40\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} a^{2} r^{11} \\\\tan{\\\\theta}-80\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{4} r^{9} \\\\tan{\\\\theta}%\\n-80\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} a^{4} r^{9} \\\\tan{\\\\theta}-4\\\\cos{\\\\theta}^{6} a^{8} r^{6} \\\\sin{2\\\\theta} \\\\tan{\\\\theta} r_s-80\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{6} r^{7} \\\\tan{\\\\theta}-80\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} a^{6} r^{7} \\\\tan{\\\\theta}-8\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{8} r^{5} r_s^{2}+6\\\\sin{\\\\theta}^{4} a^{6} r^{8} r_s+16\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{8} r^{6} r_s+12\\\\sin{\\\\theta}^{2} a^{4} r^{10} r_s+48\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{6} r^{8} r_s-4a^{4} r^{10} r_s-16\\\\cos{\\\\theta}^{2} a^{6} r^{8} r_s-4\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{7}+4\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{7}-8a^{2} r^{12} r_s-32\\\\cos{\\\\theta}^{2} a^{4} r^{10} r_s+8\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{9}+12\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{10} r^{4} r_s+72\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{8} r^{6} r_s-24\\\\cos{\\\\theta}^{4} a^{8} r^{6} r_s-12\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{5}%\\n+12\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{5}-48\\\\cos{\\\\theta}^{4} a^{6} r^{8} r_s+24\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{7}+6\\\\sin{\\\\theta}^{4} a^{4} r^{10} r_s+16\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{6} r^{8} r_s+12\\\\sin{\\\\theta}^{2} a^{2} r^{12} r_s+48\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{10} r_s-4\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{9}-4r^{14} r_s-16\\\\cos{\\\\theta}^{2} a^{2} r^{12} r_s+4\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{11}+12\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{8} r^{6} r_s+72\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{8} r_s-12\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{7}-24\\\\cos{\\\\theta}^{4} a^{4} r^{10} r_s+12\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{9}+4\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{10} r^{3} r_s^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+12\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{4} \\\\sin{2\\\\theta} \\\\tan{\\\\theta} r_s+24\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{3} \\\\tan{\\\\theta}+24\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{3} \\\\tan{\\\\theta}%\\n+24\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{5} \\\\tan{\\\\theta}+24\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{5} \\\\tan{\\\\theta}-6\\\\cos{\\\\theta}^{8} a^{12} r^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta} r_s-40\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{8} a^{10} r^{3} \\\\tan{\\\\theta}-40\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{8} a^{10} r^{3} \\\\tan{\\\\theta}-6\\\\cos{\\\\theta}^{8} a^{10} r^{4} \\\\sin{2\\\\theta} \\\\tan{\\\\theta} r_s-40\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{8} a^{8} r^{5} \\\\tan{\\\\theta}-40\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{8} a^{8} r^{5} \\\\tan{\\\\theta}+48\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{10} r^{4} r_s-16\\\\cos{\\\\theta}^{6} a^{10} r^{4} r_s-12\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} r^{3}+12\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} r^{3}-32\\\\cos{\\\\theta}^{6} a^{8} r^{6} r_s+24\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{5}+48\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{8} r^{6} r_s-12\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{5}-16\\\\cos{\\\\theta}^{6} a^{6} r^{8} r_s+12\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{7}+2\\\\sin{\\\\theta}^{6} a^{6} r^{7} r_s^{2}+2\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6} a^{8} r^{5} r_s^{2}%\\n-4\\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{6} r_s-4\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{2} r^{5}-4\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} r^{7}-2\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{6} a^{10} r^{3} r_s^{2}-8\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{4} r_s-8\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{4} r^{3}-8\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{2} r^{5}-8\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{10} r^{3} r_s^{2}+2\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} r_s^{2} r+2\\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} a^{12} r_s^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta} r+4\\\\cos{\\\\theta}^{6} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} r^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta} r_s+2\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} a^{12} \\\\tan{\\\\theta} r_s+8\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} \\\\tan{\\\\theta} r+2\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} a^{12} \\\\tan{\\\\theta} r_s+8\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} \\\\tan{\\\\theta} r+2\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} a^{10} r^{2} \\\\tan{\\\\theta} r_s+8\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{3} \\\\tan{\\\\theta}+2\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} a^{10} r^{2} \\\\tan{\\\\theta} r_s+8\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{3} \\\\tan{\\\\theta}-4\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{2} \\\\tan{\\\\theta} r_s%\\n-4\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{6} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{2} \\\\tan{\\\\theta} r_s+2\\\\cos{\\\\theta}^{10} a^{12} r_s^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta} r+8\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{10} a^{10} r^{2} \\\\tan{\\\\theta} r_s+8\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{10} a^{10} r^{2} \\\\tan{\\\\theta} r_s-2\\\\cos{\\\\theta}^{10} a^{14} \\\\sin{2\\\\theta} \\\\tan{\\\\theta} r_s-8\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{10} a^{12} \\\\tan{\\\\theta} r-8\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{10} a^{12} \\\\tan{\\\\theta} r-2\\\\cos{\\\\theta}^{10} a^{12} r^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta} r_s-8\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{10} a^{10} r^{3} \\\\tan{\\\\theta}-8\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{10} a^{10} r^{3} \\\\tan{\\\\theta}-2\\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{4} a^{12} r_s^{2} r-2\\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} a^{10} r^{3} r_s^{2}-6\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} r^{2} r_s-2\\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{4} a^{14} r_s+12\\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} a^{12} r^{2} r_s-4\\\\cos{\\\\theta}^{8} a^{12} r^{2} r_s-4\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{10} r+4\\\\cos{\\\\theta}^{6} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{10} r-8\\\\cos{\\\\theta}^{8} a^{10} r^{4} r_s+8\\\\cos{\\\\theta}^{6} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} r^{3}%\\n-2\\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{4} a^{12} r^{2} r_s+12\\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} a^{10} r^{4} r_s-4\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} r^{3}-4\\\\cos{\\\\theta}^{8} a^{8} r^{6} r_s+4\\\\cos{\\\\theta}^{6} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{5}-2\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{6} a^{12} r_s^{2} r+2\\\\cos{\\\\theta}^{8} \\\\sin{\\\\theta}^{2} a^{12} r_s^{2} r-2\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{10} r_s-4\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} r^{2} r_s+4\\\\cos{\\\\theta}^{6} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} r^{2} r_s-4\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{6} r+4\\\\cos{\\\\theta}^{6} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{4} r_s-4\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{4} r^{3}}{4\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\left(r r_s-r^{2}-\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} \\\\tan{\\\\theta}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{r}= & \\\\frac{-\\\\sin{\\\\theta}^{4} a^{6} r^{4} r_s^{3}+4\\\\sin{\\\\theta}^{4} a^{6} r^{5} r_s^{2}-6\\\\sin{\\\\theta}^{4} a^{4} r^{6} r_s^{3}+2\\\\sin{\\\\theta}^{4} a^{4} r^{5} r_s^{4}+7\\\\sin{\\\\theta}^{4} a^{4} r^{7} r_s^{2}-7\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{6} r^{4} r_s^{3}+\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{8} r^{2} r_s^{3}-2\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{10} r_s^{2} r+2\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{6} r^{3} r_s^{4}+3\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{8} r^{3} r_s^{2}-3\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{8} r^{2} r_s^{3}+6\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{6} r^{4} r_s^{3}-4\\\\sin{\\\\theta}^{2} a^{6} r^{5} r_s^{2}-4\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{8} r^{3} r_s^{2}+\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{8} r^{2} r_s^{3}-4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{6} r^{4} r_s^{2}-4\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{6} r^{4} r_s^{2}-4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{8} r^{2} r_s^{2}-4\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{8} r^{2} r_s^{2}%\\n+3\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r_s^{2} r+5\\\\sin{\\\\theta}^{2} a^{4} r^{6} r_s^{3}+4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{5} r_s^{3}+4\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{5} r_s^{3}-5\\\\sin{\\\\theta}^{2} a^{4} r^{7} r_s^{2}-\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{6} r^{5} r_s^{2}-2\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{4} r_s^{4}-2\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{4} r_s^{4}-9\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{4} r_s^{3}-10\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{4} r^{6} r_s^{2}-10\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{4} r^{6} r_s^{2}-12\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{6} r^{4} r_s^{2}-12\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{6} r^{4} r_s^{2}+2\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{3} r_s^{4}+6\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{3} r_s^{2}+\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{2} r_s^{3}-\\\\sin{\\\\theta}^{2} a^{2} r^{8} r_s^{3}+2\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{2} r^{7} r_s^{3}+2\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{2} r^{7} r_s^{3}+3\\\\sin{\\\\theta}^{2} a^{2} r^{9} r_s^{2}%\\n+15\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{7} r_s^{2}-6\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{2} r^{8} r_s^{2}-6\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{2} r^{8} r_s^{2}-8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{6} r_s^{2}-8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{6} r_s^{2}+5\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{5} r_s^{2}-3\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{4} r_s^{3}+4\\\\sin{\\\\theta}^{2} a^{6} r^{6} r_s+8\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{8} r^{4} r_s+5\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{8} r^{3} r_s^{2}+4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{6} r^{5} r_s+4\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{6} r^{5} r_s+8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{8} r^{3} r_s+8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{8} r^{3} r_s-3\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{2} r_s+2\\\\sin{\\\\theta}^{2} a^{4} r^{8} r_s-2\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{6} r^{6} r_s+17\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{5} r_s^{2}+8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{4} r^{7} r_s+8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{4} r^{7} r_s%\\n+16\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{6} r^{5} r_s+16\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{6} r^{5} r_s-9\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{4} r_s-2\\\\sin{\\\\theta}^{2} a^{2} r^{10} r_s-10\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{8} r_s+4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{2} r^{9} r_s+4\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{2} r^{9} r_s+8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{7} r_s+8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{7} r_s-4\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{6} r_s-2\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{8} r^{2} r_s^{2}-2\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{8} r^{2} r_s^{2}+4\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{10} r^{2} r_s+\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{10} r_s^{2} r+4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{10} r r_s+4\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{10} r r_s-3\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} r_s-2\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{4} r_s^{2}-2\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{4} r_s^{2}-10\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{8} r^{4} r_s%\\n+2\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{3} r_s^{3}+2\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{3} r_s^{3}+5\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{8} r^{3} r_s^{2}+8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{8} r^{3} r_s+8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{8} r^{3} r_s-2\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{8} r^{2} r_s^{3}-8\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{2} r_s-2\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r_s^{2} r-8\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{6} r_s^{3}-14\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{6} r_s+4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{5} r_s+4\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} a^{6} r^{5} r_s-\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{4} r_s-\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} a^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta} r r_s-\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} a^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta} r r_s-2\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} r^{2} \\\\tan{\\\\theta} r_s-2\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} r^{2} \\\\tan{\\\\theta} r_s+\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} a^{2} r^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} a^{2} r^{2} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+2\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} r^{3} \\\\tan{\\\\theta}%\\n+2\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} r^{3} \\\\tan{\\\\theta}+\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} a^{4} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} a^{4} \\\\sin{2\\\\theta} \\\\tan{\\\\theta}+2\\\\partial_{\\\\theta}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} a^{2} \\\\tan{\\\\theta} r+2\\\\partial_{\\\\theta}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} a^{2} \\\\tan{\\\\theta} r+2\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{6} a^{6} r^{3} r_s^{3}+2\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{6} a^{6} r^{3} r_s^{3}-2\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{4} a^{6} r^{3} r_s^{3}-2\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{4} a^{6} r^{3} r_s^{3}+6\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{4} a^{6} r^{4} r_s^{2}+6\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{4} a^{6} r^{4} r_s^{2}+6\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{8} r^{2} r_s^{2}+6\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{8} r^{2} r_s^{2}-2\\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r_s^{2} r-2\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{4} a^{4} r^{4} r_s^{4}-2\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{4} a^{4} r^{4} r_s^{4}+2\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{4} r^{4} r_s^{4}+2\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} a^{4} r^{4} r_s^{4}+6\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{4} a^{4} r^{6} r_s^{2}+6\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{4} a^{4} r^{6} r_s^{2}%\\n+6\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{6} r^{4} r_s^{2}+6\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{6} r^{4} r_s^{2}-2\\\\sin{\\\\theta}^{2} a^{4} r^{5} r_s^{4}-2\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{6} r^{3} r_s^{4}+2\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{2} r_s^{2}+2\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{2} r_s^{2}-2\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{4} r_s^{2} r+2\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} a^{4} r^{5} r_s^{4}+2\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{4} r_s^{2}+2\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{4} r_s^{2}+2\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{2} r^{3} r_s^{2}+2\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{8} r^{3} r_s^{2}-2a^{4} r^{7} r_s^{2}-4\\\\cos{\\\\theta}^{2} a^{6} r^{5} r_s^{2}+2\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{4} r_s-4a^{2} r^{9} r_s^{2}-8\\\\cos{\\\\theta}^{2} a^{4} r^{7} r_s^{2}+2\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{6} r_s-2\\\\cos{\\\\theta}^{4} a^{8} r^{3} r_s^{2}+2\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{2} r_s%\\n-4\\\\cos{\\\\theta}^{4} a^{6} r^{5} r_s^{2}+2\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{7} r_s^{2}+9\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{6} r^{5} r_s^{2}-2r^{11} r_s^{2}-4\\\\cos{\\\\theta}^{2} a^{2} r^{9} r_s^{2}-2\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{6} a^{6} r^{4} r_s^{2}-2\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{6} a^{6} r^{4} r_s^{2}-4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{4} a^{6} r^{5} r_s-4\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{4} a^{6} r^{5} r_s-8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{8} r^{3} r_s-8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{8} r^{3} r_s+2\\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{2} r_s-4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{4} a^{4} r^{7} r_s-4\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{4} a^{4} r^{7} r_s-8\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{6} r^{5} r_s-8\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{6} r^{5} r_s-2\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{3} r_s-2\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{3} r_s+2\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{4} r^{2} r_s-2\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{5} r_s%\\n-2\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{5} r_s-2\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{2} r^{4} r_s-2\\\\cos{\\\\theta}^{4} a^{4} r^{7} r_s^{2}-2\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{6} r_s-3\\\\sin{\\\\theta}^{4} a^{6} r^{6} r_s-5\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{8} r^{4} r_s+2a^{4} r^{8} r_s+6\\\\cos{\\\\theta}^{2} a^{6} r^{6} r_s+2\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{5}-2\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{5}+4a^{2} r^{10} r_s+12\\\\cos{\\\\theta}^{2} a^{4} r^{8} r_s-4\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{7}-\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{10} r^{2} r_s+6\\\\cos{\\\\theta}^{4} a^{8} r^{4} r_s+4\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{3}-4\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{3}+12\\\\cos{\\\\theta}^{4} a^{6} r^{6} r_s-8\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{5}-3\\\\sin{\\\\theta}^{4} a^{4} r^{8} r_s%\\n-5\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{6} r^{6} r_s+2\\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{7}+2r^{12} r_s+6\\\\cos{\\\\theta}^{2} a^{2} r^{10} r_s-2\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} r^{9}-\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{8} r^{4} r_s+4\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{5}+6\\\\cos{\\\\theta}^{4} a^{4} r^{8} r_s-4\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{7}-2\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6} a^{8} r^{2} r_s^{2}-2\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6} a^{8} r^{2} r_s^{2}-4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{10} r r_s-4\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{10} r r_s+2\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} r_s+2\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{6} r^{3} r_s^{3}+2\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{4} a^{6} r^{3} r_s^{3}-4\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{8} r^{3} r_s-4\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{4} a^{8} r^{3} r_s-2\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r r_s-2\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r r_s%\\n+2\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{6} r_s-2\\\\partial_{r}\\\\left(r^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{3} r_s-2\\\\partial_{r}\\\\left(\\\\cos{\\\\theta}^{2} a^{2}\\\\right) \\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{3} r_s-2\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{3} a^{4} r^{2} r_s+\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} a^{10} r_s^{2} r+3\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{2} r_s+\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} a^{12} r_s-6\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{10} r^{2} r_s+2\\\\cos{\\\\theta}^{6} a^{10} r^{2} r_s+2\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} r-2\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} r+4\\\\cos{\\\\theta}^{6} a^{8} r^{4} r_s-4\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{3}+\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{4} a^{10} r^{2} r_s-6\\\\cos{\\\\theta}^{6} \\\\sin{\\\\theta}^{2} a^{8} r^{4} r_s+2\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{3}+2\\\\cos{\\\\theta}^{6} a^{6} r^{6} r_s-2\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{5}+\\\\sin{\\\\theta}^{6} a^{6} r^{4} r_s^{3}-\\\\cos{\\\\theta}^{2} \\\\sin{\\\\theta}^{6} a^{8} r^{2} r_s^{3}%\\n+2\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{5} r_s^{2}+2\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{3} r_s^{2}-2\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{2} r^{2} r_s+2\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{2} r^{5} r_s^{2}-2\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} r^{4} r_s-\\\\sin{\\\\theta}^{6} a^{6} r^{5} r_s^{2}+2\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{2} r^{3}+2\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} r^{5}+\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{6} a^{10} r_s^{2} r+\\\\cos{\\\\theta}^{4} \\\\sin{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{8} r_s-2\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{6} r^{2} r_s+2\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{4} r-2\\\\cos{\\\\theta}^{4} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} a^{4} r^{4} r_s+2\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{4} a^{2} r^{3}}{2\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} \\\\tan{\\\\theta} r r_s-2\\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} r^{2} \\\\tan{\\\\theta}-2\\\\cos{\\\\theta}^{2} \\\\left(r^{2}+\\\\cos{\\\\theta}^{2} a^{2}\\\\right)^{2} \\\\left(\\\\cos{\\\\theta}^{2} a^{2} r r_s-a^{2} r^{2}-\\\\cos{\\\\theta}^{2} a^{4}+r^{3} r_s-r^{4}-\\\\cos{\\\\theta}^{2} a^{2} r^{2}\\\\right)^{2} a^{2} \\\\tan{\\\\theta}}\\\\\\\\[-.5ex]\\n\\\\end{aligned}\\\\right.\\n\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"evaluate(_,kerr);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1\n}\n"
  },
  {
    "path": "examples/library.cnb",
    "content": "{\n\t\"cells\" : \n\t[\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Indices(position=free) to~}\\\\left[m,~\\\\discretionary{}{}{} n,~\\\\discretionary{}{}{} p,~\\\\discretionary{}{}{} q,~\\\\discretionary{}{}{} r\\\\right].\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"A_{q r} A_{q r}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}A_{q r} A_{q r}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"{m,n,p,q,r}::Indices;\\nex:=A_{q r} A_{q r};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1\n}\n"
  },
  {
    "path": "examples/lovelock.cnb",
    "content": "{\n\t\"cells\" : \n\t[\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property TableauSymmetry to~}R_{a b c d}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Symmetric to~}R_{a b}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property EpsilonTensor to~}\\\\epsilon_{a b c d}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property KroneckerDelta to~}\\\\delta\\\\left(\\\\#\\\\right).\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"R_{a b c d}::RiemannTensor;\\nR_{a b}::Symmetric;\\n\\\\epsilon_{a b c d}::EpsilonTensor(delta=\\\\delta);\\n\\\\delta{#}::KroneckerDelta;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Indices(position=free) to~}\\\\left(a, \\\\linebreak[0] b, \\\\linebreak[0] c, \\\\linebreak[0] d, \\\\linebreak[0] e, \\\\linebreak[0] f, \\\\linebreak[0] g, \\\\linebreak[0] h, \\\\linebreak[0] i, \\\\linebreak[0] j, \\\\linebreak[0] l\\\\right).\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Integer to~}\\\\left(a, \\\\linebreak[0] b, \\\\linebreak[0] c, \\\\linebreak[0] d, \\\\linebreak[0] e, \\\\linebreak[0] f, \\\\linebreak[0] g, \\\\linebreak[0] h, \\\\linebreak[0] i, \\\\linebreak[0] j, \\\\linebreak[0] l\\\\right).\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"{a,b,c,d,e,f,g,h,i,j,l}::Indices;\\n{a,b,c,d,e,f,g,h,i,j,l}::Integer(0..3);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"import cdb.relativity as rel\\n\\ndef post_process(ex):\\n    sort_product(ex)\\n    rel.riemann_to_ricci(ex)\\n    collect_terms(ex)\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}R_{a b}\\\\,^{c d} \\\\epsilon_{i c d e} \\\\epsilon^{i f g h}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex:=R_{a b}^{c d} \\\\epsilon_{i c d e} \\\\epsilon^{i f g h};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\frac{1}{120}R_{a b}\\\\,^{c d} \\\\epsilon_{i c d e} \\\\epsilon^{i f g h} - \\\\frac{1}{120}R_{a b}\\\\,^{c d} \\\\epsilon_{i c e d} \\\\epsilon^{i f g h} - \\\\frac{1}{120}R_{a b}\\\\,^{c d} \\\\epsilon_{i d c e} \\\\epsilon^{i f g h}+\\\\frac{1}{120}R_{a b}\\\\,^{c d} \\\\epsilon_{i d e c} \\\\epsilon^{i f g h}+\\\\frac{1}{120}R_{a b}\\\\,^{c d} \\\\epsilon_{i e c d} \\\\epsilon^{i f g h} - \\\\frac{1}{120}R_{a b}\\\\,^{c d} \\\\epsilon_{i e d c} \\\\epsilon^{i f g h}+\\\\frac{1}{60}R_{a}\\\\,^{d} \\\\epsilon_{i b d e} \\\\epsilon^{i f g h} - \\\\frac{1}{60}R_{a}\\\\,^{d} \\\\epsilon_{i b e d} \\\\epsilon^{i f g h} - \\\\frac{1}{60}R_{a}\\\\,^{d} \\\\epsilon_{i d b e} \\\\epsilon^{i f g h}+\\\\frac{1}{60}R_{a}\\\\,^{d} \\\\epsilon_{i d e b} \\\\epsilon^{i f g h}+\\\\frac{1}{60}R_{a}\\\\,^{d} \\\\epsilon_{i e b d} \\\\epsilon^{i f g h} - \\\\frac{1}{60}R_{a}\\\\,^{d} \\\\epsilon_{i e d b} \\\\epsilon^{i f g h}+\\\\frac{1}{60}R_{a}\\\\,^{c} \\\\epsilon_{i b c e} \\\\epsilon^{i f g h} - \\\\frac{1}{60}R_{a}\\\\,^{c} \\\\epsilon_{i b e c} \\\\epsilon^{i f g h} - \\\\frac{1}{60}R_{a}\\\\,^{c} \\\\epsilon_{i c b e} \\\\epsilon^{i f g h}+\\\\frac{1}{60}R_{a}\\\\,^{c} \\\\epsilon_{i c e b} \\\\epsilon^{i f g h}+\\\\frac{1}{60}R_{a}\\\\,^{c} \\\\epsilon_{i e b c} \\\\epsilon^{i f g h} - \\\\frac{1}{60}R_{a}\\\\,^{c} \\\\epsilon_{i e c b} \\\\epsilon^{i f g h} - \\\\frac{1}{120}R_{a e}\\\\,^{c d} \\\\epsilon_{i b c d} \\\\epsilon^{i f g h}%\\n+\\\\frac{1}{120}R_{a e}\\\\,^{c d} \\\\epsilon_{i b d c} \\\\epsilon^{i f g h}+\\\\frac{1}{120}R_{a e}\\\\,^{c d} \\\\epsilon_{i c b d} \\\\epsilon^{i f g h} - \\\\frac{1}{120}R_{a e}\\\\,^{c d} \\\\epsilon_{i c d b} \\\\epsilon^{i f g h} - \\\\frac{1}{120}R_{a e}\\\\,^{c d} \\\\epsilon_{i d b c} \\\\epsilon^{i f g h}+\\\\frac{1}{120}R_{a e}\\\\,^{c d} \\\\epsilon_{i d c b} \\\\epsilon^{i f g h} - \\\\frac{1}{120}R_{b a}\\\\,^{c d} \\\\epsilon_{i c d e} \\\\epsilon^{i f g h}+\\\\frac{1}{120}R_{b a}\\\\,^{c d} \\\\epsilon_{i c e d} \\\\epsilon^{i f g h}+\\\\frac{1}{120}R_{b a}\\\\,^{c d} \\\\epsilon_{i d c e} \\\\epsilon^{i f g h} - \\\\frac{1}{120}R_{b a}\\\\,^{c d} \\\\epsilon_{i d e c} \\\\epsilon^{i f g h} - \\\\frac{1}{120}R_{b a}\\\\,^{c d} \\\\epsilon_{i e c d} \\\\epsilon^{i f g h}+\\\\frac{1}{120}R_{b a}\\\\,^{c d} \\\\epsilon_{i e d c} \\\\epsilon^{i f g h} - \\\\frac{1}{60}R_{b}\\\\,^{d} \\\\epsilon_{i a d e} \\\\epsilon^{i f g h}+\\\\frac{1}{60}R_{b}\\\\,^{d} \\\\epsilon_{i a e d} \\\\epsilon^{i f g h}+\\\\frac{1}{60}R_{b}\\\\,^{d} \\\\epsilon_{i d a e} \\\\epsilon^{i f g h} - \\\\frac{1}{60}R_{b}\\\\,^{d} \\\\epsilon_{i d e a} \\\\epsilon^{i f g h} - \\\\frac{1}{60}R_{b}\\\\,^{d} \\\\epsilon_{i e a d} \\\\epsilon^{i f g h}+\\\\frac{1}{60}R_{b}\\\\,^{d} \\\\epsilon_{i e d a} \\\\epsilon^{i f g h} - \\\\frac{1}{60}R_{b}\\\\,^{c} \\\\epsilon_{i a c e} \\\\epsilon^{i f g h}+\\\\frac{1}{60}R_{b}\\\\,^{c} \\\\epsilon_{i a e c} \\\\epsilon^{i f g h}+\\\\frac{1}{60}R_{b}\\\\,^{c} \\\\epsilon_{i c a e} \\\\epsilon^{i f g h}%\\n - \\\\frac{1}{60}R_{b}\\\\,^{c} \\\\epsilon_{i c e a} \\\\epsilon^{i f g h} - \\\\frac{1}{60}R_{b}\\\\,^{c} \\\\epsilon_{i e a c} \\\\epsilon^{i f g h}+\\\\frac{1}{60}R_{b}\\\\,^{c} \\\\epsilon_{i e c a} \\\\epsilon^{i f g h}+\\\\frac{1}{120}R_{b e}\\\\,^{c d} \\\\epsilon_{i a c d} \\\\epsilon^{i f g h} - \\\\frac{1}{120}R_{b e}\\\\,^{c d} \\\\epsilon_{i a d c} \\\\epsilon^{i f g h} - \\\\frac{1}{120}R_{b e}\\\\,^{c d} \\\\epsilon_{i c a d} \\\\epsilon^{i f g h}+\\\\frac{1}{120}R_{b e}\\\\,^{c d} \\\\epsilon_{i c d a} \\\\epsilon^{i f g h}+\\\\frac{1}{120}R_{b e}\\\\,^{c d} \\\\epsilon_{i d a c} \\\\epsilon^{i f g h} - \\\\frac{1}{120}R_{b e}\\\\,^{c d} \\\\epsilon_{i d c a} \\\\epsilon^{i f g h}+\\\\frac{1}{120}R_{d}\\\\,^{d} \\\\epsilon_{i a b e} \\\\epsilon^{i f g h} - \\\\frac{1}{120}R_{d}\\\\,^{d} \\\\epsilon_{i a e b} \\\\epsilon^{i f g h} - \\\\frac{1}{120}R_{d}\\\\,^{d} \\\\epsilon_{i b a e} \\\\epsilon^{i f g h}+\\\\frac{1}{120}R_{d}\\\\,^{d} \\\\epsilon_{i b e a} \\\\epsilon^{i f g h}+\\\\frac{1}{120}R_{d}\\\\,^{d} \\\\epsilon_{i e a b} \\\\epsilon^{i f g h} - \\\\frac{1}{120}R_{d}\\\\,^{d} \\\\epsilon_{i e b a} \\\\epsilon^{i f g h} - \\\\frac{1}{60}R_{e}\\\\,^{d} \\\\epsilon_{i a b d} \\\\epsilon^{i f g h}+\\\\frac{1}{60}R_{e}\\\\,^{d} \\\\epsilon_{i a d b} \\\\epsilon^{i f g h}+\\\\frac{1}{60}R_{e}\\\\,^{d} \\\\epsilon_{i b a d} \\\\epsilon^{i f g h} - \\\\frac{1}{60}R_{e}\\\\,^{d} \\\\epsilon_{i b d a} \\\\epsilon^{i f g h} - \\\\frac{1}{60}R_{e}\\\\,^{d} \\\\epsilon_{i d a b} \\\\epsilon^{i f g h}%\\n+\\\\frac{1}{60}R_{e}\\\\,^{d} \\\\epsilon_{i d b a} \\\\epsilon^{i f g h}+\\\\frac{1}{120}R_{c}\\\\,^{c} \\\\epsilon_{i a b e} \\\\epsilon^{i f g h} - \\\\frac{1}{120}R_{c}\\\\,^{c} \\\\epsilon_{i a e b} \\\\epsilon^{i f g h} - \\\\frac{1}{120}R_{c}\\\\,^{c} \\\\epsilon_{i b a e} \\\\epsilon^{i f g h}+\\\\frac{1}{120}R_{c}\\\\,^{c} \\\\epsilon_{i b e a} \\\\epsilon^{i f g h}+\\\\frac{1}{120}R_{c}\\\\,^{c} \\\\epsilon_{i e a b} \\\\epsilon^{i f g h} - \\\\frac{1}{120}R_{c}\\\\,^{c} \\\\epsilon_{i e b a} \\\\epsilon^{i f g h} - \\\\frac{1}{60}R_{e}\\\\,^{c} \\\\epsilon_{i a b c} \\\\epsilon^{i f g h}+\\\\frac{1}{60}R_{e}\\\\,^{c} \\\\epsilon_{i a c b} \\\\epsilon^{i f g h}+\\\\frac{1}{60}R_{e}\\\\,^{c} \\\\epsilon_{i b a c} \\\\epsilon^{i f g h} - \\\\frac{1}{60}R_{e}\\\\,^{c} \\\\epsilon_{i b c a} \\\\epsilon^{i f g h} - \\\\frac{1}{60}R_{e}\\\\,^{c} \\\\epsilon_{i c a b} \\\\epsilon^{i f g h}+\\\\frac{1}{60}R_{e}\\\\,^{c} \\\\epsilon_{i c b a} \\\\epsilon^{i f g h}+\\\\frac{1}{120}R_{e a}\\\\,^{c d} \\\\epsilon_{i b c d} \\\\epsilon^{i f g h} - \\\\frac{1}{120}R_{e a}\\\\,^{c d} \\\\epsilon_{i b d c} \\\\epsilon^{i f g h} - \\\\frac{1}{120}R_{e a}\\\\,^{c d} \\\\epsilon_{i c b d} \\\\epsilon^{i f g h}+\\\\frac{1}{120}R_{e a}\\\\,^{c d} \\\\epsilon_{i c d b} \\\\epsilon^{i f g h}+\\\\frac{1}{120}R_{e a}\\\\,^{c d} \\\\epsilon_{i d b c} \\\\epsilon^{i f g h} - \\\\frac{1}{120}R_{e a}\\\\,^{c d} \\\\epsilon_{i d c b} \\\\epsilon^{i f g h} - \\\\frac{1}{120}R_{e b}\\\\,^{c d} \\\\epsilon_{i a c d} \\\\epsilon^{i f g h}%\\n+\\\\frac{1}{120}R_{e b}\\\\,^{c d} \\\\epsilon_{i a d c} \\\\epsilon^{i f g h}+\\\\frac{1}{120}R_{e b}\\\\,^{c d} \\\\epsilon_{i c a d} \\\\epsilon^{i f g h} - \\\\frac{1}{120}R_{e b}\\\\,^{c d} \\\\epsilon_{i c d a} \\\\epsilon^{i f g h} - \\\\frac{1}{120}R_{e b}\\\\,^{c d} \\\\epsilon_{i d a c} \\\\epsilon^{i f g h}+\\\\frac{1}{120}R_{e b}\\\\,^{c d} \\\\epsilon_{i d c a} \\\\epsilon^{i f g h}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"asym(_, $_{a}, _{b}, _{c}, _{d}, _{e}$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\frac{1}{20}R_{a b}\\\\,^{c d} \\\\delta_{c}\\\\,^{f}\\\\,_{d}\\\\,^{g}\\\\,_{e}\\\\,^{h} - \\\\frac{1}{20}R_{a b}\\\\,^{c d} \\\\delta_{c}\\\\,^{f}\\\\,_{e}\\\\,^{g}\\\\,_{d}\\\\,^{h} - \\\\frac{1}{20}R_{a b}\\\\,^{c d} \\\\delta_{d}\\\\,^{f}\\\\,_{c}\\\\,^{g}\\\\,_{e}\\\\,^{h}+\\\\frac{1}{20}R_{a b}\\\\,^{c d} \\\\delta_{d}\\\\,^{f}\\\\,_{e}\\\\,^{g}\\\\,_{c}\\\\,^{h}+\\\\frac{1}{20}R_{a b}\\\\,^{c d} \\\\delta_{e}\\\\,^{f}\\\\,_{c}\\\\,^{g}\\\\,_{d}\\\\,^{h} - \\\\frac{1}{20}R_{a b}\\\\,^{c d} \\\\delta_{e}\\\\,^{f}\\\\,_{d}\\\\,^{g}\\\\,_{c}\\\\,^{h}+\\\\frac{1}{10}R_{a}\\\\,^{d} \\\\delta_{b}\\\\,^{f}\\\\,_{d}\\\\,^{g}\\\\,_{e}\\\\,^{h} - \\\\frac{1}{10}R_{a}\\\\,^{d} \\\\delta_{b}\\\\,^{f}\\\\,_{e}\\\\,^{g}\\\\,_{d}\\\\,^{h} - \\\\frac{1}{10}R_{a}\\\\,^{d} \\\\delta_{d}\\\\,^{f}\\\\,_{b}\\\\,^{g}\\\\,_{e}\\\\,^{h}+\\\\frac{1}{10}R_{a}\\\\,^{d} \\\\delta_{d}\\\\,^{f}\\\\,_{e}\\\\,^{g}\\\\,_{b}\\\\,^{h}+\\\\frac{1}{10}R_{a}\\\\,^{d} \\\\delta_{e}\\\\,^{f}\\\\,_{b}\\\\,^{g}\\\\,_{d}\\\\,^{h} - \\\\frac{1}{10}R_{a}\\\\,^{d} \\\\delta_{e}\\\\,^{f}\\\\,_{d}\\\\,^{g}\\\\,_{b}\\\\,^{h}+\\\\frac{1}{10}R_{a}\\\\,^{c} \\\\delta_{b}\\\\,^{f}\\\\,_{c}\\\\,^{g}\\\\,_{e}\\\\,^{h} - \\\\frac{1}{10}R_{a}\\\\,^{c} \\\\delta_{b}\\\\,^{f}\\\\,_{e}\\\\,^{g}\\\\,_{c}\\\\,^{h} - \\\\frac{1}{10}R_{a}\\\\,^{c} \\\\delta_{c}\\\\,^{f}\\\\,_{b}\\\\,^{g}\\\\,_{e}\\\\,^{h}+\\\\frac{1}{10}R_{a}\\\\,^{c} \\\\delta_{c}\\\\,^{f}\\\\,_{e}\\\\,^{g}\\\\,_{b}\\\\,^{h}+\\\\frac{1}{10}R_{a}\\\\,^{c} \\\\delta_{e}\\\\,^{f}\\\\,_{b}\\\\,^{g}\\\\,_{c}\\\\,^{h} - \\\\frac{1}{10}R_{a}\\\\,^{c} \\\\delta_{e}\\\\,^{f}\\\\,_{c}\\\\,^{g}\\\\,_{b}\\\\,^{h} - \\\\frac{1}{20}R_{a e}\\\\,^{c d} \\\\delta_{b}\\\\,^{f}\\\\,_{c}\\\\,^{g}\\\\,_{d}\\\\,^{h}%\\n+\\\\frac{1}{20}R_{a e}\\\\,^{c d} \\\\delta_{b}\\\\,^{f}\\\\,_{d}\\\\,^{g}\\\\,_{c}\\\\,^{h}+\\\\frac{1}{20}R_{a e}\\\\,^{c d} \\\\delta_{c}\\\\,^{f}\\\\,_{b}\\\\,^{g}\\\\,_{d}\\\\,^{h} - \\\\frac{1}{20}R_{a e}\\\\,^{c d} \\\\delta_{c}\\\\,^{f}\\\\,_{d}\\\\,^{g}\\\\,_{b}\\\\,^{h} - \\\\frac{1}{20}R_{a e}\\\\,^{c d} \\\\delta_{d}\\\\,^{f}\\\\,_{b}\\\\,^{g}\\\\,_{c}\\\\,^{h}+\\\\frac{1}{20}R_{a e}\\\\,^{c d} \\\\delta_{d}\\\\,^{f}\\\\,_{c}\\\\,^{g}\\\\,_{b}\\\\,^{h} - \\\\frac{1}{20}R_{b a}\\\\,^{c d} \\\\delta_{c}\\\\,^{f}\\\\,_{d}\\\\,^{g}\\\\,_{e}\\\\,^{h}+\\\\frac{1}{20}R_{b a}\\\\,^{c d} \\\\delta_{c}\\\\,^{f}\\\\,_{e}\\\\,^{g}\\\\,_{d}\\\\,^{h}+\\\\frac{1}{20}R_{b a}\\\\,^{c d} \\\\delta_{d}\\\\,^{f}\\\\,_{c}\\\\,^{g}\\\\,_{e}\\\\,^{h} - \\\\frac{1}{20}R_{b a}\\\\,^{c d} \\\\delta_{d}\\\\,^{f}\\\\,_{e}\\\\,^{g}\\\\,_{c}\\\\,^{h} - \\\\frac{1}{20}R_{b a}\\\\,^{c d} \\\\delta_{e}\\\\,^{f}\\\\,_{c}\\\\,^{g}\\\\,_{d}\\\\,^{h}+\\\\frac{1}{20}R_{b a}\\\\,^{c d} \\\\delta_{e}\\\\,^{f}\\\\,_{d}\\\\,^{g}\\\\,_{c}\\\\,^{h} - \\\\frac{1}{10}R_{b}\\\\,^{d} \\\\delta_{a}\\\\,^{f}\\\\,_{d}\\\\,^{g}\\\\,_{e}\\\\,^{h}+\\\\frac{1}{10}R_{b}\\\\,^{d} \\\\delta_{a}\\\\,^{f}\\\\,_{e}\\\\,^{g}\\\\,_{d}\\\\,^{h}+\\\\frac{1}{10}R_{b}\\\\,^{d} \\\\delta_{d}\\\\,^{f}\\\\,_{a}\\\\,^{g}\\\\,_{e}\\\\,^{h} - \\\\frac{1}{10}R_{b}\\\\,^{d} \\\\delta_{d}\\\\,^{f}\\\\,_{e}\\\\,^{g}\\\\,_{a}\\\\,^{h} - \\\\frac{1}{10}R_{b}\\\\,^{d} \\\\delta_{e}\\\\,^{f}\\\\,_{a}\\\\,^{g}\\\\,_{d}\\\\,^{h}+\\\\frac{1}{10}R_{b}\\\\,^{d} \\\\delta_{e}\\\\,^{f}\\\\,_{d}\\\\,^{g}\\\\,_{a}\\\\,^{h} - \\\\frac{1}{10}R_{b}\\\\,^{c} \\\\delta_{a}\\\\,^{f}\\\\,_{c}\\\\,^{g}\\\\,_{e}\\\\,^{h}+\\\\frac{1}{10}R_{b}\\\\,^{c} \\\\delta_{a}\\\\,^{f}\\\\,_{e}\\\\,^{g}\\\\,_{c}\\\\,^{h}+\\\\frac{1}{10}R_{b}\\\\,^{c} \\\\delta_{c}\\\\,^{f}\\\\,_{a}\\\\,^{g}\\\\,_{e}\\\\,^{h}%\\n - \\\\frac{1}{10}R_{b}\\\\,^{c} \\\\delta_{c}\\\\,^{f}\\\\,_{e}\\\\,^{g}\\\\,_{a}\\\\,^{h} - \\\\frac{1}{10}R_{b}\\\\,^{c} \\\\delta_{e}\\\\,^{f}\\\\,_{a}\\\\,^{g}\\\\,_{c}\\\\,^{h}+\\\\frac{1}{10}R_{b}\\\\,^{c} \\\\delta_{e}\\\\,^{f}\\\\,_{c}\\\\,^{g}\\\\,_{a}\\\\,^{h}+\\\\frac{1}{20}R_{b e}\\\\,^{c d} \\\\delta_{a}\\\\,^{f}\\\\,_{c}\\\\,^{g}\\\\,_{d}\\\\,^{h} - \\\\frac{1}{20}R_{b e}\\\\,^{c d} \\\\delta_{a}\\\\,^{f}\\\\,_{d}\\\\,^{g}\\\\,_{c}\\\\,^{h} - \\\\frac{1}{20}R_{b e}\\\\,^{c d} \\\\delta_{c}\\\\,^{f}\\\\,_{a}\\\\,^{g}\\\\,_{d}\\\\,^{h}+\\\\frac{1}{20}R_{b e}\\\\,^{c d} \\\\delta_{c}\\\\,^{f}\\\\,_{d}\\\\,^{g}\\\\,_{a}\\\\,^{h}+\\\\frac{1}{20}R_{b e}\\\\,^{c d} \\\\delta_{d}\\\\,^{f}\\\\,_{a}\\\\,^{g}\\\\,_{c}\\\\,^{h} - \\\\frac{1}{20}R_{b e}\\\\,^{c d} \\\\delta_{d}\\\\,^{f}\\\\,_{c}\\\\,^{g}\\\\,_{a}\\\\,^{h}+\\\\frac{1}{10}R \\\\delta_{a}\\\\,^{f}\\\\,_{b}\\\\,^{g}\\\\,_{e}\\\\,^{h} - \\\\frac{1}{10}R \\\\delta_{a}\\\\,^{f}\\\\,_{e}\\\\,^{g}\\\\,_{b}\\\\,^{h} - \\\\frac{1}{10}R \\\\delta_{b}\\\\,^{f}\\\\,_{a}\\\\,^{g}\\\\,_{e}\\\\,^{h}+\\\\frac{1}{10}R \\\\delta_{b}\\\\,^{f}\\\\,_{e}\\\\,^{g}\\\\,_{a}\\\\,^{h}+\\\\frac{1}{10}R \\\\delta_{e}\\\\,^{f}\\\\,_{a}\\\\,^{g}\\\\,_{b}\\\\,^{h} - \\\\frac{1}{10}R \\\\delta_{e}\\\\,^{f}\\\\,_{b}\\\\,^{g}\\\\,_{a}\\\\,^{h} - \\\\frac{1}{10}R_{e}\\\\,^{d} \\\\delta_{a}\\\\,^{f}\\\\,_{b}\\\\,^{g}\\\\,_{d}\\\\,^{h}+\\\\frac{1}{10}R_{e}\\\\,^{d} \\\\delta_{a}\\\\,^{f}\\\\,_{d}\\\\,^{g}\\\\,_{b}\\\\,^{h}+\\\\frac{1}{10}R_{e}\\\\,^{d} \\\\delta_{b}\\\\,^{f}\\\\,_{a}\\\\,^{g}\\\\,_{d}\\\\,^{h} - \\\\frac{1}{10}R_{e}\\\\,^{d} \\\\delta_{b}\\\\,^{f}\\\\,_{d}\\\\,^{g}\\\\,_{a}\\\\,^{h} - \\\\frac{1}{10}R_{e}\\\\,^{d} \\\\delta_{d}\\\\,^{f}\\\\,_{a}\\\\,^{g}\\\\,_{b}\\\\,^{h}%\\n+\\\\frac{1}{10}R_{e}\\\\,^{d} \\\\delta_{d}\\\\,^{f}\\\\,_{b}\\\\,^{g}\\\\,_{a}\\\\,^{h} - \\\\frac{1}{10}R_{e}\\\\,^{c} \\\\delta_{a}\\\\,^{f}\\\\,_{b}\\\\,^{g}\\\\,_{c}\\\\,^{h}+\\\\frac{1}{10}R_{e}\\\\,^{c} \\\\delta_{a}\\\\,^{f}\\\\,_{c}\\\\,^{g}\\\\,_{b}\\\\,^{h}+\\\\frac{1}{10}R_{e}\\\\,^{c} \\\\delta_{b}\\\\,^{f}\\\\,_{a}\\\\,^{g}\\\\,_{c}\\\\,^{h} - \\\\frac{1}{10}R_{e}\\\\,^{c} \\\\delta_{b}\\\\,^{f}\\\\,_{c}\\\\,^{g}\\\\,_{a}\\\\,^{h} - \\\\frac{1}{10}R_{e}\\\\,^{c} \\\\delta_{c}\\\\,^{f}\\\\,_{a}\\\\,^{g}\\\\,_{b}\\\\,^{h}+\\\\frac{1}{10}R_{e}\\\\,^{c} \\\\delta_{c}\\\\,^{f}\\\\,_{b}\\\\,^{g}\\\\,_{a}\\\\,^{h}+\\\\frac{1}{20}R_{e a}\\\\,^{c d} \\\\delta_{b}\\\\,^{f}\\\\,_{c}\\\\,^{g}\\\\,_{d}\\\\,^{h} - \\\\frac{1}{20}R_{e a}\\\\,^{c d} \\\\delta_{b}\\\\,^{f}\\\\,_{d}\\\\,^{g}\\\\,_{c}\\\\,^{h} - \\\\frac{1}{20}R_{e a}\\\\,^{c d} \\\\delta_{c}\\\\,^{f}\\\\,_{b}\\\\,^{g}\\\\,_{d}\\\\,^{h}+\\\\frac{1}{20}R_{e a}\\\\,^{c d} \\\\delta_{c}\\\\,^{f}\\\\,_{d}\\\\,^{g}\\\\,_{b}\\\\,^{h}+\\\\frac{1}{20}R_{e a}\\\\,^{c d} \\\\delta_{d}\\\\,^{f}\\\\,_{b}\\\\,^{g}\\\\,_{c}\\\\,^{h} - \\\\frac{1}{20}R_{e a}\\\\,^{c d} \\\\delta_{d}\\\\,^{f}\\\\,_{c}\\\\,^{g}\\\\,_{b}\\\\,^{h} - \\\\frac{1}{20}R_{e b}\\\\,^{c d} \\\\delta_{a}\\\\,^{f}\\\\,_{c}\\\\,^{g}\\\\,_{d}\\\\,^{h}+\\\\frac{1}{20}R_{e b}\\\\,^{c d} \\\\delta_{a}\\\\,^{f}\\\\,_{d}\\\\,^{g}\\\\,_{c}\\\\,^{h}+\\\\frac{1}{20}R_{e b}\\\\,^{c d} \\\\delta_{c}\\\\,^{f}\\\\,_{a}\\\\,^{g}\\\\,_{d}\\\\,^{h} - \\\\frac{1}{20}R_{e b}\\\\,^{c d} \\\\delta_{c}\\\\,^{f}\\\\,_{d}\\\\,^{g}\\\\,_{a}\\\\,^{h} - \\\\frac{1}{20}R_{e b}\\\\,^{c d} \\\\delta_{d}\\\\,^{f}\\\\,_{a}\\\\,^{g}\\\\,_{c}\\\\,^{h}+\\\\frac{1}{20}R_{e b}\\\\,^{c d} \\\\delta_{d}\\\\,^{f}\\\\,_{c}\\\\,^{g}\\\\,_{a}\\\\,^{h}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"epsilon_to_delta(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\frac{1}{20}R_{a b}\\\\,^{c d} \\\\left(\\\\frac{1}{6}\\\\delta_{c}\\\\,^{f} \\\\delta_{d}\\\\,^{g} \\\\delta_{e}\\\\,^{h} - \\\\frac{1}{6}\\\\delta_{c}\\\\,^{f} \\\\delta_{d}\\\\,^{h} \\\\delta_{e}\\\\,^{g} - \\\\frac{1}{6}\\\\delta_{c}\\\\,^{g} \\\\delta_{d}\\\\,^{f} \\\\delta_{e}\\\\,^{h}+\\\\frac{1}{6}\\\\delta_{c}\\\\,^{h} \\\\delta_{d}\\\\,^{f} \\\\delta_{e}\\\\,^{g}+\\\\frac{1}{6}\\\\delta_{c}\\\\,^{g} \\\\delta_{d}\\\\,^{h} \\\\delta_{e}\\\\,^{f} - \\\\frac{1}{6}\\\\delta_{c}\\\\,^{h} \\\\delta_{d}\\\\,^{g} \\\\delta_{e}\\\\,^{f}\\\\right) - \\\\frac{1}{20}R_{a b}\\\\,^{c d} \\\\left(\\\\frac{1}{6}\\\\delta_{c}\\\\,^{f} \\\\delta_{d}\\\\,^{h} \\\\delta_{e}\\\\,^{g} - \\\\frac{1}{6}\\\\delta_{c}\\\\,^{f} \\\\delta_{d}\\\\,^{g} \\\\delta_{e}\\\\,^{h} - \\\\frac{1}{6}\\\\delta_{c}\\\\,^{g} \\\\delta_{d}\\\\,^{h} \\\\delta_{e}\\\\,^{f}+\\\\frac{1}{6}\\\\delta_{c}\\\\,^{h} \\\\delta_{d}\\\\,^{g} \\\\delta_{e}\\\\,^{f}+\\\\frac{1}{6}\\\\delta_{c}\\\\,^{g} \\\\delta_{d}\\\\,^{f} \\\\delta_{e}\\\\,^{h} - \\\\frac{1}{6}\\\\delta_{c}\\\\,^{h} \\\\delta_{d}\\\\,^{f} \\\\delta_{e}\\\\,^{g}\\\\right) - \\\\frac{1}{20}R_{a b}\\\\,^{c d} \\\\left(\\\\frac{1}{6}\\\\delta_{c}\\\\,^{g} \\\\delta_{d}\\\\,^{f} \\\\delta_{e}\\\\,^{h} - \\\\frac{1}{6}\\\\delta_{c}\\\\,^{h} \\\\delta_{d}\\\\,^{f} \\\\delta_{e}\\\\,^{g} - \\\\frac{1}{6}\\\\delta_{c}\\\\,^{f} \\\\delta_{d}\\\\,^{g} \\\\delta_{e}\\\\,^{h}+\\\\frac{1}{6}\\\\delta_{c}\\\\,^{f} \\\\delta_{d}\\\\,^{h} \\\\delta_{e}\\\\,^{g}+\\\\frac{1}{6}\\\\delta_{c}\\\\,^{h} \\\\delta_{d}\\\\,^{g} \\\\delta_{e}\\\\,^{f} - \\\\frac{1}{6}\\\\delta_{c}\\\\,^{g} \\\\delta_{d}\\\\,^{h} \\\\delta_{e}\\\\,^{f}\\\\right)+\\\\frac{1}{20}R_{a b}\\\\,^{c d} \\\\left(\\\\frac{1}{6}\\\\delta_{c}\\\\,^{h} \\\\delta_{d}\\\\,^{f} \\\\delta_{e}\\\\,^{g} - \\\\frac{1}{6}\\\\delta_{c}\\\\,^{g} \\\\delta_{d}\\\\,^{f} \\\\delta_{e}\\\\,^{h} - \\\\frac{1}{6}\\\\delta_{c}\\\\,^{h} \\\\delta_{d}\\\\,^{g} \\\\delta_{e}\\\\,^{f}+\\\\frac{1}{6}\\\\delta_{c}\\\\,^{g} \\\\delta_{d}\\\\,^{h} \\\\delta_{e}\\\\,^{f}+\\\\frac{1}{6}\\\\delta_{c}\\\\,^{f} \\\\delta_{d}\\\\,^{g} \\\\delta_{e}\\\\,^{h} - \\\\frac{1}{6}\\\\delta_{c}\\\\,^{f} \\\\delta_{d}\\\\,^{h} \\\\delta_{e}\\\\,^{g}\\\\right)+\\\\frac{1}{20}R_{a b}\\\\,^{c d} \\\\left(\\\\frac{1}{6}\\\\delta_{c}\\\\,^{g} \\\\delta_{d}\\\\,^{h} \\\\delta_{e}\\\\,^{f} - \\\\frac{1}{6}\\\\delta_{c}\\\\,^{h} \\\\delta_{d}\\\\,^{g} \\\\delta_{e}\\\\,^{f} - \\\\frac{1}{6}\\\\delta_{c}\\\\,^{f} \\\\delta_{d}\\\\,^{h} \\\\delta_{e}\\\\,^{g}+\\\\frac{1}{6}\\\\delta_{c}\\\\,^{f} \\\\delta_{d}\\\\,^{g} \\\\delta_{e}\\\\,^{h}+\\\\frac{1}{6}\\\\delta_{c}\\\\,^{h} \\\\delta_{d}\\\\,^{f} \\\\delta_{e}\\\\,^{g} - \\\\frac{1}{6}\\\\delta_{c}\\\\,^{g} \\\\delta_{d}\\\\,^{f} \\\\delta_{e}\\\\,^{h}\\\\right) - \\\\frac{1}{20}R_{a b}\\\\,^{c d} \\\\left(\\\\frac{1}{6}\\\\delta_{c}\\\\,^{h} \\\\delta_{d}\\\\,^{g} \\\\delta_{e}\\\\,^{f} - \\\\frac{1}{6}\\\\delta_{c}\\\\,^{g} \\\\delta_{d}\\\\,^{h} \\\\delta_{e}\\\\,^{f} - \\\\frac{1}{6}\\\\delta_{c}\\\\,^{h} \\\\delta_{d}\\\\,^{f} \\\\delta_{e}\\\\,^{g}+\\\\frac{1}{6}\\\\delta_{c}\\\\,^{g} \\\\delta_{d}\\\\,^{f} \\\\delta_{e}\\\\,^{h}+\\\\frac{1}{6}\\\\delta_{c}\\\\,^{f} \\\\delta_{d}\\\\,^{h} \\\\delta_{e}\\\\,^{g} - \\\\frac{1}{6}\\\\delta_{c}\\\\,^{f} \\\\delta_{d}\\\\,^{g} \\\\delta_{e}\\\\,^{h}\\\\right)+\\\\frac{1}{10}R_{a}\\\\,^{d} \\\\left(\\\\frac{1}{6}\\\\delta_{b}\\\\,^{f} \\\\delta_{d}\\\\,^{g} \\\\delta_{e}\\\\,^{h} - \\\\frac{1}{6}\\\\delta_{b}\\\\,^{f} \\\\delta_{d}\\\\,^{h} \\\\delta_{e}\\\\,^{g} - \\\\frac{1}{6}\\\\delta_{b}\\\\,^{g} \\\\delta_{d}\\\\,^{f} \\\\delta_{e}\\\\,^{h}+\\\\frac{1}{6}\\\\delta_{b}\\\\,^{h} \\\\delta_{d}\\\\,^{f} \\\\delta_{e}\\\\,^{g}+\\\\frac{1}{6}\\\\delta_{b}\\\\,^{g} \\\\delta_{d}\\\\,^{h} \\\\delta_{e}\\\\,^{f} - \\\\frac{1}{6}\\\\delta_{b}\\\\,^{h} \\\\delta_{d}\\\\,^{g} \\\\delta_{e}\\\\,^{f}\\\\right) - \\\\frac{1}{10}R_{a}\\\\,^{d} \\\\left(\\\\frac{1}{6}\\\\delta_{b}\\\\,^{f} \\\\delta_{d}\\\\,^{h} \\\\delta_{e}\\\\,^{g} - \\\\frac{1}{6}\\\\delta_{b}\\\\,^{f} \\\\delta_{d}\\\\,^{g} \\\\delta_{e}\\\\,^{h} - \\\\frac{1}{6}\\\\delta_{b}\\\\,^{g} \\\\delta_{d}\\\\,^{h} \\\\delta_{e}\\\\,^{f}+\\\\frac{1}{6}\\\\delta_{b}\\\\,^{h} \\\\delta_{d}\\\\,^{g} \\\\delta_{e}\\\\,^{f}+\\\\frac{1}{6}\\\\delta_{b}\\\\,^{g} \\\\delta_{d}\\\\,^{f} \\\\delta_{e}\\\\,^{h} - \\\\frac{1}{6}\\\\delta_{b}\\\\,^{h} \\\\delta_{d}\\\\,^{f} \\\\delta_{e}\\\\,^{g}\\\\right) - \\\\frac{1}{10}R_{a}\\\\,^{d} \\\\left(\\\\frac{1}{6}\\\\delta_{b}\\\\,^{g} \\\\delta_{d}\\\\,^{f} \\\\delta_{e}\\\\,^{h} - \\\\frac{1}{6}\\\\delta_{b}\\\\,^{h} \\\\delta_{d}\\\\,^{f} \\\\delta_{e}\\\\,^{g} - \\\\frac{1}{6}\\\\delta_{b}\\\\,^{f} \\\\delta_{d}\\\\,^{g} \\\\delta_{e}\\\\,^{h}+\\\\frac{1}{6}\\\\delta_{b}\\\\,^{f} \\\\delta_{d}\\\\,^{h} \\\\delta_{e}\\\\,^{g}+\\\\frac{1}{6}\\\\delta_{b}\\\\,^{h} \\\\delta_{d}\\\\,^{g} \\\\delta_{e}\\\\,^{f} - \\\\frac{1}{6}\\\\delta_{b}\\\\,^{g} \\\\delta_{d}\\\\,^{h} \\\\delta_{e}\\\\,^{f}\\\\right)+\\\\frac{1}{10}R_{a}\\\\,^{d} \\\\left(\\\\frac{1}{6}\\\\delta_{b}\\\\,^{h} \\\\delta_{d}\\\\,^{f} \\\\delta_{e}\\\\,^{g} - \\\\frac{1}{6}\\\\delta_{b}\\\\,^{g} \\\\delta_{d}\\\\,^{f} \\\\delta_{e}\\\\,^{h} - \\\\frac{1}{6}\\\\delta_{b}\\\\,^{h} \\\\delta_{d}\\\\,^{g} \\\\delta_{e}\\\\,^{f}+\\\\frac{1}{6}\\\\delta_{b}\\\\,^{g} \\\\delta_{d}\\\\,^{h} \\\\delta_{e}\\\\,^{f}+\\\\frac{1}{6}\\\\delta_{b}\\\\,^{f} \\\\delta_{d}\\\\,^{g} \\\\delta_{e}\\\\,^{h} - \\\\frac{1}{6}\\\\delta_{b}\\\\,^{f} \\\\delta_{d}\\\\,^{h} \\\\delta_{e}\\\\,^{g}\\\\right)+\\\\frac{1}{10}R_{a}\\\\,^{d} \\\\left(\\\\frac{1}{6}\\\\delta_{b}\\\\,^{g} \\\\delta_{d}\\\\,^{h} \\\\delta_{e}\\\\,^{f} - \\\\frac{1}{6}\\\\delta_{b}\\\\,^{h} \\\\delta_{d}\\\\,^{g} \\\\delta_{e}\\\\,^{f} - \\\\frac{1}{6}\\\\delta_{b}\\\\,^{f} \\\\delta_{d}\\\\,^{h} \\\\delta_{e}\\\\,^{g}+\\\\frac{1}{6}\\\\delta_{b}\\\\,^{f} \\\\delta_{d}\\\\,^{g} \\\\delta_{e}\\\\,^{h}+\\\\frac{1}{6}\\\\delta_{b}\\\\,^{h} \\\\delta_{d}\\\\,^{f} \\\\delta_{e}\\\\,^{g} - \\\\frac{1}{6}\\\\delta_{b}\\\\,^{g} \\\\delta_{d}\\\\,^{f} \\\\delta_{e}\\\\,^{h}\\\\right) - \\\\frac{1}{10}R_{a}\\\\,^{d} \\\\left(\\\\frac{1}{6}\\\\delta_{b}\\\\,^{h} \\\\delta_{d}\\\\,^{g} \\\\delta_{e}\\\\,^{f} - \\\\frac{1}{6}\\\\delta_{b}\\\\,^{g} \\\\delta_{d}\\\\,^{h} \\\\delta_{e}\\\\,^{f} - \\\\frac{1}{6}\\\\delta_{b}\\\\,^{h} \\\\delta_{d}\\\\,^{f} \\\\delta_{e}\\\\,^{g}+\\\\frac{1}{6}\\\\delta_{b}\\\\,^{g} \\\\delta_{d}\\\\,^{f} \\\\delta_{e}\\\\,^{h}+\\\\frac{1}{6}\\\\delta_{b}\\\\,^{f} \\\\delta_{d}\\\\,^{h} \\\\delta_{e}\\\\,^{g} - \\\\frac{1}{6}\\\\delta_{b}\\\\,^{f} \\\\delta_{d}\\\\,^{g} \\\\delta_{e}\\\\,^{h}\\\\right)+\\\\frac{1}{10}R_{a}\\\\,^{c} \\\\left(\\\\frac{1}{6}\\\\delta_{b}\\\\,^{f} \\\\delta_{c}\\\\,^{g} \\\\delta_{e}\\\\,^{h} - \\\\frac{1}{6}\\\\delta_{b}\\\\,^{f} \\\\delta_{c}\\\\,^{h} \\\\delta_{e}\\\\,^{g} - \\\\frac{1}{6}\\\\delta_{b}\\\\,^{g} \\\\delta_{c}\\\\,^{f} \\\\delta_{e}\\\\,^{h}+\\\\frac{1}{6}\\\\delta_{b}\\\\,^{h} \\\\delta_{c}\\\\,^{f} \\\\delta_{e}\\\\,^{g}+\\\\frac{1}{6}\\\\delta_{b}\\\\,^{g} \\\\delta_{c}\\\\,^{h} \\\\delta_{e}\\\\,^{f} - \\\\frac{1}{6}\\\\delta_{b}\\\\,^{h} \\\\delta_{c}\\\\,^{g} \\\\delta_{e}\\\\,^{f}\\\\right) - \\\\frac{1}{10}R_{a}\\\\,^{c} \\\\left(\\\\frac{1}{6}\\\\delta_{b}\\\\,^{f} \\\\delta_{c}\\\\,^{h} \\\\delta_{e}\\\\,^{g} - \\\\frac{1}{6}\\\\delta_{b}\\\\,^{f} \\\\delta_{c}\\\\,^{g} \\\\delta_{e}\\\\,^{h} - \\\\frac{1}{6}\\\\delta_{b}\\\\,^{g} \\\\delta_{c}\\\\,^{h} \\\\delta_{e}\\\\,^{f}+\\\\frac{1}{6}\\\\delta_{b}\\\\,^{h} \\\\delta_{c}\\\\,^{g} \\\\delta_{e}\\\\,^{f}+\\\\frac{1}{6}\\\\delta_{b}\\\\,^{g} \\\\delta_{c}\\\\,^{f} \\\\delta_{e}\\\\,^{h} - \\\\frac{1}{6}\\\\delta_{b}\\\\,^{h} \\\\delta_{c}\\\\,^{f} \\\\delta_{e}\\\\,^{g}\\\\right) - \\\\frac{1}{10}R_{a}\\\\,^{c} \\\\left(\\\\frac{1}{6}\\\\delta_{b}\\\\,^{g} \\\\delta_{c}\\\\,^{f} \\\\delta_{e}\\\\,^{h} - \\\\frac{1}{6}\\\\delta_{b}\\\\,^{h} \\\\delta_{c}\\\\,^{f} \\\\delta_{e}\\\\,^{g} - \\\\frac{1}{6}\\\\delta_{b}\\\\,^{f} \\\\delta_{c}\\\\,^{g} \\\\delta_{e}\\\\,^{h}+\\\\frac{1}{6}\\\\delta_{b}\\\\,^{f} \\\\delta_{c}\\\\,^{h} \\\\delta_{e}\\\\,^{g}+\\\\frac{1}{6}\\\\delta_{b}\\\\,^{h} \\\\delta_{c}\\\\,^{g} \\\\delta_{e}\\\\,^{f} - \\\\frac{1}{6}\\\\delta_{b}\\\\,^{g} \\\\delta_{c}\\\\,^{h} \\\\delta_{e}\\\\,^{f}\\\\right)+\\\\frac{1}{10}R_{a}\\\\,^{c} \\\\left(\\\\frac{1}{6}\\\\delta_{b}\\\\,^{h} \\\\delta_{c}\\\\,^{f} \\\\delta_{e}\\\\,^{g} - \\\\frac{1}{6}\\\\delta_{b}\\\\,^{g} \\\\delta_{c}\\\\,^{f} \\\\delta_{e}\\\\,^{h} - \\\\frac{1}{6}\\\\delta_{b}\\\\,^{h} \\\\delta_{c}\\\\,^{g} \\\\delta_{e}\\\\,^{f}+\\\\frac{1}{6}\\\\delta_{b}\\\\,^{g} \\\\delta_{c}\\\\,^{h} \\\\delta_{e}\\\\,^{f}+\\\\frac{1}{6}\\\\delta_{b}\\\\,^{f} \\\\delta_{c}\\\\,^{g} \\\\delta_{e}\\\\,^{h} - \\\\frac{1}{6}\\\\delta_{b}\\\\,^{f} \\\\delta_{c}\\\\,^{h} \\\\delta_{e}\\\\,^{g}\\\\right)+\\\\frac{1}{10}R_{a}\\\\,^{c} \\\\left(\\\\frac{1}{6}\\\\delta_{b}\\\\,^{g} \\\\delta_{c}\\\\,^{h} \\\\delta_{e}\\\\,^{f} - \\\\frac{1}{6}\\\\delta_{b}\\\\,^{h} \\\\delta_{c}\\\\,^{g} \\\\delta_{e}\\\\,^{f} - \\\\frac{1}{6}\\\\delta_{b}\\\\,^{f} \\\\delta_{c}\\\\,^{h} \\\\delta_{e}\\\\,^{g}+\\\\frac{1}{6}\\\\delta_{b}\\\\,^{f} \\\\delta_{c}\\\\,^{g} \\\\delta_{e}\\\\,^{h}+\\\\frac{1}{6}\\\\delta_{b}\\\\,^{h} \\\\delta_{c}\\\\,^{f} \\\\delta_{e}\\\\,^{g} - \\\\frac{1}{6}\\\\delta_{b}\\\\,^{g} \\\\delta_{c}\\\\,^{f} \\\\delta_{e}\\\\,^{h}\\\\right) - \\\\frac{1}{10}R_{a}\\\\,^{c} \\\\left(\\\\frac{1}{6}\\\\delta_{b}\\\\,^{h} \\\\delta_{c}\\\\,^{g} \\\\delta_{e}\\\\,^{f} - \\\\frac{1}{6}\\\\delta_{b}\\\\,^{g} \\\\delta_{c}\\\\,^{h} \\\\delta_{e}\\\\,^{f} - \\\\frac{1}{6}\\\\delta_{b}\\\\,^{h} \\\\delta_{c}\\\\,^{f} \\\\delta_{e}\\\\,^{g}+\\\\frac{1}{6}\\\\delta_{b}\\\\,^{g} \\\\delta_{c}\\\\,^{f} \\\\delta_{e}\\\\,^{h}+\\\\frac{1}{6}\\\\delta_{b}\\\\,^{f} \\\\delta_{c}\\\\,^{h} \\\\delta_{e}\\\\,^{g} - \\\\frac{1}{6}\\\\delta_{b}\\\\,^{f} \\\\delta_{c}\\\\,^{g} \\\\delta_{e}\\\\,^{h}\\\\right) - \\\\frac{1}{20}R_{a e}\\\\,^{c d} \\\\left(\\\\frac{1}{6}\\\\delta_{b}\\\\,^{f} \\\\delta_{c}\\\\,^{g} \\\\delta_{d}\\\\,^{h} - \\\\frac{1}{6}\\\\delta_{b}\\\\,^{f} \\\\delta_{c}\\\\,^{h} \\\\delta_{d}\\\\,^{g} - \\\\frac{1}{6}\\\\delta_{b}\\\\,^{g} \\\\delta_{c}\\\\,^{f} \\\\delta_{d}\\\\,^{h}+\\\\frac{1}{6}\\\\delta_{b}\\\\,^{h} \\\\delta_{c}\\\\,^{f} \\\\delta_{d}\\\\,^{g}+\\\\frac{1}{6}\\\\delta_{b}\\\\,^{g} \\\\delta_{c}\\\\,^{h} \\\\delta_{d}\\\\,^{f} - \\\\frac{1}{6}\\\\delta_{b}\\\\,^{h} \\\\delta_{c}\\\\,^{g} \\\\delta_{d}\\\\,^{f}\\\\right)%\\n+\\\\frac{1}{20}R_{a e}\\\\,^{c d} \\\\left(\\\\frac{1}{6}\\\\delta_{b}\\\\,^{f} \\\\delta_{c}\\\\,^{h} \\\\delta_{d}\\\\,^{g} - \\\\frac{1}{6}\\\\delta_{b}\\\\,^{f} \\\\delta_{c}\\\\,^{g} \\\\delta_{d}\\\\,^{h} - \\\\frac{1}{6}\\\\delta_{b}\\\\,^{g} \\\\delta_{c}\\\\,^{h} \\\\delta_{d}\\\\,^{f}+\\\\frac{1}{6}\\\\delta_{b}\\\\,^{h} \\\\delta_{c}\\\\,^{g} \\\\delta_{d}\\\\,^{f}+\\\\frac{1}{6}\\\\delta_{b}\\\\,^{g} \\\\delta_{c}\\\\,^{f} \\\\delta_{d}\\\\,^{h} - \\\\frac{1}{6}\\\\delta_{b}\\\\,^{h} \\\\delta_{c}\\\\,^{f} \\\\delta_{d}\\\\,^{g}\\\\right)+\\\\frac{1}{20}R_{a e}\\\\,^{c d} \\\\left(\\\\frac{1}{6}\\\\delta_{b}\\\\,^{g} \\\\delta_{c}\\\\,^{f} \\\\delta_{d}\\\\,^{h} - \\\\frac{1}{6}\\\\delta_{b}\\\\,^{h} \\\\delta_{c}\\\\,^{f} \\\\delta_{d}\\\\,^{g} - \\\\frac{1}{6}\\\\delta_{b}\\\\,^{f} \\\\delta_{c}\\\\,^{g} \\\\delta_{d}\\\\,^{h}+\\\\frac{1}{6}\\\\delta_{b}\\\\,^{f} \\\\delta_{c}\\\\,^{h} \\\\delta_{d}\\\\,^{g}+\\\\frac{1}{6}\\\\delta_{b}\\\\,^{h} \\\\delta_{c}\\\\,^{g} \\\\delta_{d}\\\\,^{f} - \\\\frac{1}{6}\\\\delta_{b}\\\\,^{g} \\\\delta_{c}\\\\,^{h} \\\\delta_{d}\\\\,^{f}\\\\right) - \\\\frac{1}{20}R_{a e}\\\\,^{c d} \\\\left(\\\\frac{1}{6}\\\\delta_{b}\\\\,^{h} \\\\delta_{c}\\\\,^{f} \\\\delta_{d}\\\\,^{g} - \\\\frac{1}{6}\\\\delta_{b}\\\\,^{g} \\\\delta_{c}\\\\,^{f} \\\\delta_{d}\\\\,^{h} - \\\\frac{1}{6}\\\\delta_{b}\\\\,^{h} \\\\delta_{c}\\\\,^{g} \\\\delta_{d}\\\\,^{f}+\\\\frac{1}{6}\\\\delta_{b}\\\\,^{g} \\\\delta_{c}\\\\,^{h} \\\\delta_{d}\\\\,^{f}+\\\\frac{1}{6}\\\\delta_{b}\\\\,^{f} \\\\delta_{c}\\\\,^{g} \\\\delta_{d}\\\\,^{h} - \\\\frac{1}{6}\\\\delta_{b}\\\\,^{f} \\\\delta_{c}\\\\,^{h} \\\\delta_{d}\\\\,^{g}\\\\right) - \\\\frac{1}{20}R_{a e}\\\\,^{c d} \\\\left(\\\\frac{1}{6}\\\\delta_{b}\\\\,^{g} \\\\delta_{c}\\\\,^{h} \\\\delta_{d}\\\\,^{f} - \\\\frac{1}{6}\\\\delta_{b}\\\\,^{h} \\\\delta_{c}\\\\,^{g} \\\\delta_{d}\\\\,^{f} - \\\\frac{1}{6}\\\\delta_{b}\\\\,^{f} \\\\delta_{c}\\\\,^{h} \\\\delta_{d}\\\\,^{g}+\\\\frac{1}{6}\\\\delta_{b}\\\\,^{f} \\\\delta_{c}\\\\,^{g} \\\\delta_{d}\\\\,^{h}+\\\\frac{1}{6}\\\\delta_{b}\\\\,^{h} \\\\delta_{c}\\\\,^{f} \\\\delta_{d}\\\\,^{g} - \\\\frac{1}{6}\\\\delta_{b}\\\\,^{g} \\\\delta_{c}\\\\,^{f} \\\\delta_{d}\\\\,^{h}\\\\right)+\\\\frac{1}{20}R_{a e}\\\\,^{c d} \\\\left(\\\\frac{1}{6}\\\\delta_{b}\\\\,^{h} \\\\delta_{c}\\\\,^{g} \\\\delta_{d}\\\\,^{f} - \\\\frac{1}{6}\\\\delta_{b}\\\\,^{g} \\\\delta_{c}\\\\,^{h} \\\\delta_{d}\\\\,^{f} - \\\\frac{1}{6}\\\\delta_{b}\\\\,^{h} \\\\delta_{c}\\\\,^{f} \\\\delta_{d}\\\\,^{g}+\\\\frac{1}{6}\\\\delta_{b}\\\\,^{g} \\\\delta_{c}\\\\,^{f} \\\\delta_{d}\\\\,^{h}+\\\\frac{1}{6}\\\\delta_{b}\\\\,^{f} \\\\delta_{c}\\\\,^{h} \\\\delta_{d}\\\\,^{g} - \\\\frac{1}{6}\\\\delta_{b}\\\\,^{f} \\\\delta_{c}\\\\,^{g} \\\\delta_{d}\\\\,^{h}\\\\right) - \\\\frac{1}{20}R_{b a}\\\\,^{c d} \\\\left(\\\\frac{1}{6}\\\\delta_{c}\\\\,^{f} \\\\delta_{d}\\\\,^{g} \\\\delta_{e}\\\\,^{h} - \\\\frac{1}{6}\\\\delta_{c}\\\\,^{f} \\\\delta_{d}\\\\,^{h} \\\\delta_{e}\\\\,^{g} - \\\\frac{1}{6}\\\\delta_{c}\\\\,^{g} \\\\delta_{d}\\\\,^{f} \\\\delta_{e}\\\\,^{h}+\\\\frac{1}{6}\\\\delta_{c}\\\\,^{h} \\\\delta_{d}\\\\,^{f} \\\\delta_{e}\\\\,^{g}+\\\\frac{1}{6}\\\\delta_{c}\\\\,^{g} \\\\delta_{d}\\\\,^{h} \\\\delta_{e}\\\\,^{f} - \\\\frac{1}{6}\\\\delta_{c}\\\\,^{h} \\\\delta_{d}\\\\,^{g} \\\\delta_{e}\\\\,^{f}\\\\right)+\\\\frac{1}{20}R_{b a}\\\\,^{c d} \\\\left(\\\\frac{1}{6}\\\\delta_{c}\\\\,^{f} \\\\delta_{d}\\\\,^{h} \\\\delta_{e}\\\\,^{g} - \\\\frac{1}{6}\\\\delta_{c}\\\\,^{f} \\\\delta_{d}\\\\,^{g} \\\\delta_{e}\\\\,^{h} - \\\\frac{1}{6}\\\\delta_{c}\\\\,^{g} \\\\delta_{d}\\\\,^{h} \\\\delta_{e}\\\\,^{f}+\\\\frac{1}{6}\\\\delta_{c}\\\\,^{h} \\\\delta_{d}\\\\,^{g} \\\\delta_{e}\\\\,^{f}+\\\\frac{1}{6}\\\\delta_{c}\\\\,^{g} \\\\delta_{d}\\\\,^{f} \\\\delta_{e}\\\\,^{h} - \\\\frac{1}{6}\\\\delta_{c}\\\\,^{h} \\\\delta_{d}\\\\,^{f} \\\\delta_{e}\\\\,^{g}\\\\right)+\\\\frac{1}{20}R_{b a}\\\\,^{c d} \\\\left(\\\\frac{1}{6}\\\\delta_{c}\\\\,^{g} \\\\delta_{d}\\\\,^{f} \\\\delta_{e}\\\\,^{h} - \\\\frac{1}{6}\\\\delta_{c}\\\\,^{h} \\\\delta_{d}\\\\,^{f} \\\\delta_{e}\\\\,^{g} - \\\\frac{1}{6}\\\\delta_{c}\\\\,^{f} \\\\delta_{d}\\\\,^{g} \\\\delta_{e}\\\\,^{h}+\\\\frac{1}{6}\\\\delta_{c}\\\\,^{f} \\\\delta_{d}\\\\,^{h} \\\\delta_{e}\\\\,^{g}+\\\\frac{1}{6}\\\\delta_{c}\\\\,^{h} \\\\delta_{d}\\\\,^{g} \\\\delta_{e}\\\\,^{f} - \\\\frac{1}{6}\\\\delta_{c}\\\\,^{g} \\\\delta_{d}\\\\,^{h} \\\\delta_{e}\\\\,^{f}\\\\right) - \\\\frac{1}{20}R_{b a}\\\\,^{c d} \\\\left(\\\\frac{1}{6}\\\\delta_{c}\\\\,^{h} \\\\delta_{d}\\\\,^{f} \\\\delta_{e}\\\\,^{g} - \\\\frac{1}{6}\\\\delta_{c}\\\\,^{g} \\\\delta_{d}\\\\,^{f} \\\\delta_{e}\\\\,^{h} - \\\\frac{1}{6}\\\\delta_{c}\\\\,^{h} \\\\delta_{d}\\\\,^{g} \\\\delta_{e}\\\\,^{f}+\\\\frac{1}{6}\\\\delta_{c}\\\\,^{g} \\\\delta_{d}\\\\,^{h} \\\\delta_{e}\\\\,^{f}+\\\\frac{1}{6}\\\\delta_{c}\\\\,^{f} \\\\delta_{d}\\\\,^{g} \\\\delta_{e}\\\\,^{h} - \\\\frac{1}{6}\\\\delta_{c}\\\\,^{f} \\\\delta_{d}\\\\,^{h} \\\\delta_{e}\\\\,^{g}\\\\right) - \\\\frac{1}{20}R_{b a}\\\\,^{c d} \\\\left(\\\\frac{1}{6}\\\\delta_{c}\\\\,^{g} \\\\delta_{d}\\\\,^{h} \\\\delta_{e}\\\\,^{f} - \\\\frac{1}{6}\\\\delta_{c}\\\\,^{h} \\\\delta_{d}\\\\,^{g} \\\\delta_{e}\\\\,^{f} - \\\\frac{1}{6}\\\\delta_{c}\\\\,^{f} \\\\delta_{d}\\\\,^{h} \\\\delta_{e}\\\\,^{g}+\\\\frac{1}{6}\\\\delta_{c}\\\\,^{f} \\\\delta_{d}\\\\,^{g} \\\\delta_{e}\\\\,^{h}+\\\\frac{1}{6}\\\\delta_{c}\\\\,^{h} \\\\delta_{d}\\\\,^{f} \\\\delta_{e}\\\\,^{g} - \\\\frac{1}{6}\\\\delta_{c}\\\\,^{g} \\\\delta_{d}\\\\,^{f} \\\\delta_{e}\\\\,^{h}\\\\right)+\\\\frac{1}{20}R_{b a}\\\\,^{c d} \\\\left(\\\\frac{1}{6}\\\\delta_{c}\\\\,^{h} \\\\delta_{d}\\\\,^{g} \\\\delta_{e}\\\\,^{f} - \\\\frac{1}{6}\\\\delta_{c}\\\\,^{g} \\\\delta_{d}\\\\,^{h} \\\\delta_{e}\\\\,^{f} - \\\\frac{1}{6}\\\\delta_{c}\\\\,^{h} \\\\delta_{d}\\\\,^{f} \\\\delta_{e}\\\\,^{g}+\\\\frac{1}{6}\\\\delta_{c}\\\\,^{g} \\\\delta_{d}\\\\,^{f} \\\\delta_{e}\\\\,^{h}+\\\\frac{1}{6}\\\\delta_{c}\\\\,^{f} \\\\delta_{d}\\\\,^{h} \\\\delta_{e}\\\\,^{g} - \\\\frac{1}{6}\\\\delta_{c}\\\\,^{f} \\\\delta_{d}\\\\,^{g} \\\\delta_{e}\\\\,^{h}\\\\right) - \\\\frac{1}{10}R_{b}\\\\,^{d} \\\\left(\\\\frac{1}{6}\\\\delta_{a}\\\\,^{f} \\\\delta_{d}\\\\,^{g} \\\\delta_{e}\\\\,^{h} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{f} \\\\delta_{d}\\\\,^{h} \\\\delta_{e}\\\\,^{g} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{g} \\\\delta_{d}\\\\,^{f} \\\\delta_{e}\\\\,^{h}+\\\\frac{1}{6}\\\\delta_{a}\\\\,^{h} \\\\delta_{d}\\\\,^{f} \\\\delta_{e}\\\\,^{g}+\\\\frac{1}{6}\\\\delta_{a}\\\\,^{g} \\\\delta_{d}\\\\,^{h} \\\\delta_{e}\\\\,^{f} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{h} \\\\delta_{d}\\\\,^{g} \\\\delta_{e}\\\\,^{f}\\\\right)+\\\\frac{1}{10}R_{b}\\\\,^{d} \\\\left(\\\\frac{1}{6}\\\\delta_{a}\\\\,^{f} \\\\delta_{d}\\\\,^{h} \\\\delta_{e}\\\\,^{g} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{f} \\\\delta_{d}\\\\,^{g} \\\\delta_{e}\\\\,^{h} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{g} \\\\delta_{d}\\\\,^{h} \\\\delta_{e}\\\\,^{f}+\\\\frac{1}{6}\\\\delta_{a}\\\\,^{h} \\\\delta_{d}\\\\,^{g} \\\\delta_{e}\\\\,^{f}+\\\\frac{1}{6}\\\\delta_{a}\\\\,^{g} \\\\delta_{d}\\\\,^{f} \\\\delta_{e}\\\\,^{h} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{h} \\\\delta_{d}\\\\,^{f} \\\\delta_{e}\\\\,^{g}\\\\right)+\\\\frac{1}{10}R_{b}\\\\,^{d} \\\\left(\\\\frac{1}{6}\\\\delta_{a}\\\\,^{g} \\\\delta_{d}\\\\,^{f} \\\\delta_{e}\\\\,^{h} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{h} \\\\delta_{d}\\\\,^{f} \\\\delta_{e}\\\\,^{g} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{f} \\\\delta_{d}\\\\,^{g} \\\\delta_{e}\\\\,^{h}+\\\\frac{1}{6}\\\\delta_{a}\\\\,^{f} \\\\delta_{d}\\\\,^{h} \\\\delta_{e}\\\\,^{g}+\\\\frac{1}{6}\\\\delta_{a}\\\\,^{h} \\\\delta_{d}\\\\,^{g} \\\\delta_{e}\\\\,^{f} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{g} \\\\delta_{d}\\\\,^{h} \\\\delta_{e}\\\\,^{f}\\\\right) - \\\\frac{1}{10}R_{b}\\\\,^{d} \\\\left(\\\\frac{1}{6}\\\\delta_{a}\\\\,^{h} \\\\delta_{d}\\\\,^{f} \\\\delta_{e}\\\\,^{g} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{g} \\\\delta_{d}\\\\,^{f} \\\\delta_{e}\\\\,^{h} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{h} \\\\delta_{d}\\\\,^{g} \\\\delta_{e}\\\\,^{f}+\\\\frac{1}{6}\\\\delta_{a}\\\\,^{g} \\\\delta_{d}\\\\,^{h} \\\\delta_{e}\\\\,^{f}+\\\\frac{1}{6}\\\\delta_{a}\\\\,^{f} \\\\delta_{d}\\\\,^{g} \\\\delta_{e}\\\\,^{h} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{f} \\\\delta_{d}\\\\,^{h} \\\\delta_{e}\\\\,^{g}\\\\right) - \\\\frac{1}{10}R_{b}\\\\,^{d} \\\\left(\\\\frac{1}{6}\\\\delta_{a}\\\\,^{g} \\\\delta_{d}\\\\,^{h} \\\\delta_{e}\\\\,^{f} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{h} \\\\delta_{d}\\\\,^{g} \\\\delta_{e}\\\\,^{f} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{f} \\\\delta_{d}\\\\,^{h} \\\\delta_{e}\\\\,^{g}+\\\\frac{1}{6}\\\\delta_{a}\\\\,^{f} \\\\delta_{d}\\\\,^{g} \\\\delta_{e}\\\\,^{h}+\\\\frac{1}{6}\\\\delta_{a}\\\\,^{h} \\\\delta_{d}\\\\,^{f} \\\\delta_{e}\\\\,^{g} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{g} \\\\delta_{d}\\\\,^{f} \\\\delta_{e}\\\\,^{h}\\\\right)+\\\\frac{1}{10}R_{b}\\\\,^{d} \\\\left(\\\\frac{1}{6}\\\\delta_{a}\\\\,^{h} \\\\delta_{d}\\\\,^{g} \\\\delta_{e}\\\\,^{f} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{g} \\\\delta_{d}\\\\,^{h} \\\\delta_{e}\\\\,^{f} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{h} \\\\delta_{d}\\\\,^{f} \\\\delta_{e}\\\\,^{g}+\\\\frac{1}{6}\\\\delta_{a}\\\\,^{g} \\\\delta_{d}\\\\,^{f} \\\\delta_{e}\\\\,^{h}+\\\\frac{1}{6}\\\\delta_{a}\\\\,^{f} \\\\delta_{d}\\\\,^{h} \\\\delta_{e}\\\\,^{g} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{f} \\\\delta_{d}\\\\,^{g} \\\\delta_{e}\\\\,^{h}\\\\right) - \\\\frac{1}{10}R_{b}\\\\,^{c} \\\\left(\\\\frac{1}{6}\\\\delta_{a}\\\\,^{f} \\\\delta_{c}\\\\,^{g} \\\\delta_{e}\\\\,^{h} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{f} \\\\delta_{c}\\\\,^{h} \\\\delta_{e}\\\\,^{g} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{g} \\\\delta_{c}\\\\,^{f} \\\\delta_{e}\\\\,^{h}+\\\\frac{1}{6}\\\\delta_{a}\\\\,^{h} \\\\delta_{c}\\\\,^{f} \\\\delta_{e}\\\\,^{g}+\\\\frac{1}{6}\\\\delta_{a}\\\\,^{g} \\\\delta_{c}\\\\,^{h} \\\\delta_{e}\\\\,^{f} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{h} \\\\delta_{c}\\\\,^{g} \\\\delta_{e}\\\\,^{f}\\\\right)+\\\\frac{1}{10}R_{b}\\\\,^{c} \\\\left(\\\\frac{1}{6}\\\\delta_{a}\\\\,^{f} \\\\delta_{c}\\\\,^{h} \\\\delta_{e}\\\\,^{g} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{f} \\\\delta_{c}\\\\,^{g} \\\\delta_{e}\\\\,^{h} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{g} \\\\delta_{c}\\\\,^{h} \\\\delta_{e}\\\\,^{f}+\\\\frac{1}{6}\\\\delta_{a}\\\\,^{h} \\\\delta_{c}\\\\,^{g} \\\\delta_{e}\\\\,^{f}+\\\\frac{1}{6}\\\\delta_{a}\\\\,^{g} \\\\delta_{c}\\\\,^{f} \\\\delta_{e}\\\\,^{h} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{h} \\\\delta_{c}\\\\,^{f} \\\\delta_{e}\\\\,^{g}\\\\right)+\\\\frac{1}{10}R_{b}\\\\,^{c} \\\\left(\\\\frac{1}{6}\\\\delta_{a}\\\\,^{g} \\\\delta_{c}\\\\,^{f} \\\\delta_{e}\\\\,^{h} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{h} \\\\delta_{c}\\\\,^{f} \\\\delta_{e}\\\\,^{g} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{f} \\\\delta_{c}\\\\,^{g} \\\\delta_{e}\\\\,^{h}+\\\\frac{1}{6}\\\\delta_{a}\\\\,^{f} \\\\delta_{c}\\\\,^{h} \\\\delta_{e}\\\\,^{g}+\\\\frac{1}{6}\\\\delta_{a}\\\\,^{h} \\\\delta_{c}\\\\,^{g} \\\\delta_{e}\\\\,^{f} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{g} \\\\delta_{c}\\\\,^{h} \\\\delta_{e}\\\\,^{f}\\\\right)%\\n - \\\\frac{1}{10}R_{b}\\\\,^{c} \\\\left(\\\\frac{1}{6}\\\\delta_{a}\\\\,^{h} \\\\delta_{c}\\\\,^{f} \\\\delta_{e}\\\\,^{g} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{g} \\\\delta_{c}\\\\,^{f} \\\\delta_{e}\\\\,^{h} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{h} \\\\delta_{c}\\\\,^{g} \\\\delta_{e}\\\\,^{f}+\\\\frac{1}{6}\\\\delta_{a}\\\\,^{g} \\\\delta_{c}\\\\,^{h} \\\\delta_{e}\\\\,^{f}+\\\\frac{1}{6}\\\\delta_{a}\\\\,^{f} \\\\delta_{c}\\\\,^{g} \\\\delta_{e}\\\\,^{h} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{f} \\\\delta_{c}\\\\,^{h} \\\\delta_{e}\\\\,^{g}\\\\right) - \\\\frac{1}{10}R_{b}\\\\,^{c} \\\\left(\\\\frac{1}{6}\\\\delta_{a}\\\\,^{g} \\\\delta_{c}\\\\,^{h} \\\\delta_{e}\\\\,^{f} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{h} \\\\delta_{c}\\\\,^{g} \\\\delta_{e}\\\\,^{f} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{f} \\\\delta_{c}\\\\,^{h} \\\\delta_{e}\\\\,^{g}+\\\\frac{1}{6}\\\\delta_{a}\\\\,^{f} \\\\delta_{c}\\\\,^{g} \\\\delta_{e}\\\\,^{h}+\\\\frac{1}{6}\\\\delta_{a}\\\\,^{h} \\\\delta_{c}\\\\,^{f} \\\\delta_{e}\\\\,^{g} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{g} \\\\delta_{c}\\\\,^{f} \\\\delta_{e}\\\\,^{h}\\\\right)+\\\\frac{1}{10}R_{b}\\\\,^{c} \\\\left(\\\\frac{1}{6}\\\\delta_{a}\\\\,^{h} \\\\delta_{c}\\\\,^{g} \\\\delta_{e}\\\\,^{f} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{g} \\\\delta_{c}\\\\,^{h} \\\\delta_{e}\\\\,^{f} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{h} \\\\delta_{c}\\\\,^{f} \\\\delta_{e}\\\\,^{g}+\\\\frac{1}{6}\\\\delta_{a}\\\\,^{g} \\\\delta_{c}\\\\,^{f} \\\\delta_{e}\\\\,^{h}+\\\\frac{1}{6}\\\\delta_{a}\\\\,^{f} \\\\delta_{c}\\\\,^{h} \\\\delta_{e}\\\\,^{g} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{f} \\\\delta_{c}\\\\,^{g} \\\\delta_{e}\\\\,^{h}\\\\right)+\\\\frac{1}{20}R_{b e}\\\\,^{c d} \\\\left(\\\\frac{1}{6}\\\\delta_{a}\\\\,^{f} \\\\delta_{c}\\\\,^{g} \\\\delta_{d}\\\\,^{h} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{f} \\\\delta_{c}\\\\,^{h} \\\\delta_{d}\\\\,^{g} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{g} \\\\delta_{c}\\\\,^{f} \\\\delta_{d}\\\\,^{h}+\\\\frac{1}{6}\\\\delta_{a}\\\\,^{h} \\\\delta_{c}\\\\,^{f} \\\\delta_{d}\\\\,^{g}+\\\\frac{1}{6}\\\\delta_{a}\\\\,^{g} \\\\delta_{c}\\\\,^{h} \\\\delta_{d}\\\\,^{f} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{h} \\\\delta_{c}\\\\,^{g} \\\\delta_{d}\\\\,^{f}\\\\right) - \\\\frac{1}{20}R_{b e}\\\\,^{c d} \\\\left(\\\\frac{1}{6}\\\\delta_{a}\\\\,^{f} \\\\delta_{c}\\\\,^{h} \\\\delta_{d}\\\\,^{g} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{f} \\\\delta_{c}\\\\,^{g} \\\\delta_{d}\\\\,^{h} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{g} \\\\delta_{c}\\\\,^{h} \\\\delta_{d}\\\\,^{f}+\\\\frac{1}{6}\\\\delta_{a}\\\\,^{h} \\\\delta_{c}\\\\,^{g} \\\\delta_{d}\\\\,^{f}+\\\\frac{1}{6}\\\\delta_{a}\\\\,^{g} \\\\delta_{c}\\\\,^{f} \\\\delta_{d}\\\\,^{h} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{h} \\\\delta_{c}\\\\,^{f} \\\\delta_{d}\\\\,^{g}\\\\right) - \\\\frac{1}{20}R_{b e}\\\\,^{c d} \\\\left(\\\\frac{1}{6}\\\\delta_{a}\\\\,^{g} \\\\delta_{c}\\\\,^{f} \\\\delta_{d}\\\\,^{h} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{h} \\\\delta_{c}\\\\,^{f} \\\\delta_{d}\\\\,^{g} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{f} \\\\delta_{c}\\\\,^{g} \\\\delta_{d}\\\\,^{h}+\\\\frac{1}{6}\\\\delta_{a}\\\\,^{f} \\\\delta_{c}\\\\,^{h} \\\\delta_{d}\\\\,^{g}+\\\\frac{1}{6}\\\\delta_{a}\\\\,^{h} \\\\delta_{c}\\\\,^{g} \\\\delta_{d}\\\\,^{f} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{g} \\\\delta_{c}\\\\,^{h} \\\\delta_{d}\\\\,^{f}\\\\right)+\\\\frac{1}{20}R_{b e}\\\\,^{c d} \\\\left(\\\\frac{1}{6}\\\\delta_{a}\\\\,^{h} \\\\delta_{c}\\\\,^{f} \\\\delta_{d}\\\\,^{g} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{g} \\\\delta_{c}\\\\,^{f} \\\\delta_{d}\\\\,^{h} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{h} \\\\delta_{c}\\\\,^{g} \\\\delta_{d}\\\\,^{f}+\\\\frac{1}{6}\\\\delta_{a}\\\\,^{g} \\\\delta_{c}\\\\,^{h} \\\\delta_{d}\\\\,^{f}+\\\\frac{1}{6}\\\\delta_{a}\\\\,^{f} \\\\delta_{c}\\\\,^{g} \\\\delta_{d}\\\\,^{h} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{f} \\\\delta_{c}\\\\,^{h} \\\\delta_{d}\\\\,^{g}\\\\right)+\\\\frac{1}{20}R_{b e}\\\\,^{c d} \\\\left(\\\\frac{1}{6}\\\\delta_{a}\\\\,^{g} \\\\delta_{c}\\\\,^{h} \\\\delta_{d}\\\\,^{f} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{h} \\\\delta_{c}\\\\,^{g} \\\\delta_{d}\\\\,^{f} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{f} \\\\delta_{c}\\\\,^{h} \\\\delta_{d}\\\\,^{g}+\\\\frac{1}{6}\\\\delta_{a}\\\\,^{f} \\\\delta_{c}\\\\,^{g} \\\\delta_{d}\\\\,^{h}+\\\\frac{1}{6}\\\\delta_{a}\\\\,^{h} \\\\delta_{c}\\\\,^{f} \\\\delta_{d}\\\\,^{g} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{g} \\\\delta_{c}\\\\,^{f} \\\\delta_{d}\\\\,^{h}\\\\right) - \\\\frac{1}{20}R_{b e}\\\\,^{c d} \\\\left(\\\\frac{1}{6}\\\\delta_{a}\\\\,^{h} \\\\delta_{c}\\\\,^{g} \\\\delta_{d}\\\\,^{f} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{g} \\\\delta_{c}\\\\,^{h} \\\\delta_{d}\\\\,^{f} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{h} \\\\delta_{c}\\\\,^{f} \\\\delta_{d}\\\\,^{g}+\\\\frac{1}{6}\\\\delta_{a}\\\\,^{g} \\\\delta_{c}\\\\,^{f} \\\\delta_{d}\\\\,^{h}+\\\\frac{1}{6}\\\\delta_{a}\\\\,^{f} \\\\delta_{c}\\\\,^{h} \\\\delta_{d}\\\\,^{g} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{f} \\\\delta_{c}\\\\,^{g} \\\\delta_{d}\\\\,^{h}\\\\right)+\\\\frac{1}{10}R \\\\left(\\\\frac{1}{6}\\\\delta_{a}\\\\,^{f} \\\\delta_{b}\\\\,^{g} \\\\delta_{e}\\\\,^{h} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{f} \\\\delta_{b}\\\\,^{h} \\\\delta_{e}\\\\,^{g} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{g} \\\\delta_{b}\\\\,^{f} \\\\delta_{e}\\\\,^{h}+\\\\frac{1}{6}\\\\delta_{a}\\\\,^{h} \\\\delta_{b}\\\\,^{f} \\\\delta_{e}\\\\,^{g}+\\\\frac{1}{6}\\\\delta_{a}\\\\,^{g} \\\\delta_{b}\\\\,^{h} \\\\delta_{e}\\\\,^{f} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{h} \\\\delta_{b}\\\\,^{g} \\\\delta_{e}\\\\,^{f}\\\\right) - \\\\frac{1}{10}R \\\\left(\\\\frac{1}{6}\\\\delta_{a}\\\\,^{f} \\\\delta_{b}\\\\,^{h} \\\\delta_{e}\\\\,^{g} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{f} \\\\delta_{b}\\\\,^{g} \\\\delta_{e}\\\\,^{h} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{g} \\\\delta_{b}\\\\,^{h} \\\\delta_{e}\\\\,^{f}+\\\\frac{1}{6}\\\\delta_{a}\\\\,^{h} \\\\delta_{b}\\\\,^{g} \\\\delta_{e}\\\\,^{f}+\\\\frac{1}{6}\\\\delta_{a}\\\\,^{g} \\\\delta_{b}\\\\,^{f} \\\\delta_{e}\\\\,^{h} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{h} \\\\delta_{b}\\\\,^{f} \\\\delta_{e}\\\\,^{g}\\\\right) - \\\\frac{1}{10}R \\\\left(\\\\frac{1}{6}\\\\delta_{a}\\\\,^{g} \\\\delta_{b}\\\\,^{f} \\\\delta_{e}\\\\,^{h} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{h} \\\\delta_{b}\\\\,^{f} \\\\delta_{e}\\\\,^{g} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{f} \\\\delta_{b}\\\\,^{g} \\\\delta_{e}\\\\,^{h}+\\\\frac{1}{6}\\\\delta_{a}\\\\,^{f} \\\\delta_{b}\\\\,^{h} \\\\delta_{e}\\\\,^{g}+\\\\frac{1}{6}\\\\delta_{a}\\\\,^{h} \\\\delta_{b}\\\\,^{g} \\\\delta_{e}\\\\,^{f} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{g} \\\\delta_{b}\\\\,^{h} \\\\delta_{e}\\\\,^{f}\\\\right)+\\\\frac{1}{10}R \\\\left(\\\\frac{1}{6}\\\\delta_{a}\\\\,^{h} \\\\delta_{b}\\\\,^{f} \\\\delta_{e}\\\\,^{g} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{g} \\\\delta_{b}\\\\,^{f} \\\\delta_{e}\\\\,^{h} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{h} \\\\delta_{b}\\\\,^{g} \\\\delta_{e}\\\\,^{f}+\\\\frac{1}{6}\\\\delta_{a}\\\\,^{g} \\\\delta_{b}\\\\,^{h} \\\\delta_{e}\\\\,^{f}+\\\\frac{1}{6}\\\\delta_{a}\\\\,^{f} \\\\delta_{b}\\\\,^{g} \\\\delta_{e}\\\\,^{h} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{f} \\\\delta_{b}\\\\,^{h} \\\\delta_{e}\\\\,^{g}\\\\right)+\\\\frac{1}{10}R \\\\left(\\\\frac{1}{6}\\\\delta_{a}\\\\,^{g} \\\\delta_{b}\\\\,^{h} \\\\delta_{e}\\\\,^{f} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{h} \\\\delta_{b}\\\\,^{g} \\\\delta_{e}\\\\,^{f} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{f} \\\\delta_{b}\\\\,^{h} \\\\delta_{e}\\\\,^{g}+\\\\frac{1}{6}\\\\delta_{a}\\\\,^{f} \\\\delta_{b}\\\\,^{g} \\\\delta_{e}\\\\,^{h}+\\\\frac{1}{6}\\\\delta_{a}\\\\,^{h} \\\\delta_{b}\\\\,^{f} \\\\delta_{e}\\\\,^{g} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{g} \\\\delta_{b}\\\\,^{f} \\\\delta_{e}\\\\,^{h}\\\\right) - \\\\frac{1}{10}R \\\\left(\\\\frac{1}{6}\\\\delta_{a}\\\\,^{h} \\\\delta_{b}\\\\,^{g} \\\\delta_{e}\\\\,^{f} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{g} \\\\delta_{b}\\\\,^{h} \\\\delta_{e}\\\\,^{f} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{h} \\\\delta_{b}\\\\,^{f} \\\\delta_{e}\\\\,^{g}+\\\\frac{1}{6}\\\\delta_{a}\\\\,^{g} \\\\delta_{b}\\\\,^{f} \\\\delta_{e}\\\\,^{h}+\\\\frac{1}{6}\\\\delta_{a}\\\\,^{f} \\\\delta_{b}\\\\,^{h} \\\\delta_{e}\\\\,^{g} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{f} \\\\delta_{b}\\\\,^{g} \\\\delta_{e}\\\\,^{h}\\\\right) - \\\\frac{1}{10}R_{e}\\\\,^{d} \\\\left(\\\\frac{1}{6}\\\\delta_{a}\\\\,^{f} \\\\delta_{b}\\\\,^{g} \\\\delta_{d}\\\\,^{h} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{f} \\\\delta_{b}\\\\,^{h} \\\\delta_{d}\\\\,^{g} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{g} \\\\delta_{b}\\\\,^{f} \\\\delta_{d}\\\\,^{h}+\\\\frac{1}{6}\\\\delta_{a}\\\\,^{h} \\\\delta_{b}\\\\,^{f} \\\\delta_{d}\\\\,^{g}+\\\\frac{1}{6}\\\\delta_{a}\\\\,^{g} \\\\delta_{b}\\\\,^{h} \\\\delta_{d}\\\\,^{f} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{h} \\\\delta_{b}\\\\,^{g} \\\\delta_{d}\\\\,^{f}\\\\right)+\\\\frac{1}{10}R_{e}\\\\,^{d} \\\\left(\\\\frac{1}{6}\\\\delta_{a}\\\\,^{f} \\\\delta_{b}\\\\,^{h} \\\\delta_{d}\\\\,^{g} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{f} \\\\delta_{b}\\\\,^{g} \\\\delta_{d}\\\\,^{h} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{g} \\\\delta_{b}\\\\,^{h} \\\\delta_{d}\\\\,^{f}+\\\\frac{1}{6}\\\\delta_{a}\\\\,^{h} \\\\delta_{b}\\\\,^{g} \\\\delta_{d}\\\\,^{f}+\\\\frac{1}{6}\\\\delta_{a}\\\\,^{g} \\\\delta_{b}\\\\,^{f} \\\\delta_{d}\\\\,^{h} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{h} \\\\delta_{b}\\\\,^{f} \\\\delta_{d}\\\\,^{g}\\\\right)+\\\\frac{1}{10}R_{e}\\\\,^{d} \\\\left(\\\\frac{1}{6}\\\\delta_{a}\\\\,^{g} \\\\delta_{b}\\\\,^{f} \\\\delta_{d}\\\\,^{h} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{h} \\\\delta_{b}\\\\,^{f} \\\\delta_{d}\\\\,^{g} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{f} \\\\delta_{b}\\\\,^{g} \\\\delta_{d}\\\\,^{h}+\\\\frac{1}{6}\\\\delta_{a}\\\\,^{f} \\\\delta_{b}\\\\,^{h} \\\\delta_{d}\\\\,^{g}+\\\\frac{1}{6}\\\\delta_{a}\\\\,^{h} \\\\delta_{b}\\\\,^{g} \\\\delta_{d}\\\\,^{f} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{g} \\\\delta_{b}\\\\,^{h} \\\\delta_{d}\\\\,^{f}\\\\right) - \\\\frac{1}{10}R_{e}\\\\,^{d} \\\\left(\\\\frac{1}{6}\\\\delta_{a}\\\\,^{h} \\\\delta_{b}\\\\,^{f} \\\\delta_{d}\\\\,^{g} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{g} \\\\delta_{b}\\\\,^{f} \\\\delta_{d}\\\\,^{h} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{h} \\\\delta_{b}\\\\,^{g} \\\\delta_{d}\\\\,^{f}+\\\\frac{1}{6}\\\\delta_{a}\\\\,^{g} \\\\delta_{b}\\\\,^{h} \\\\delta_{d}\\\\,^{f}+\\\\frac{1}{6}\\\\delta_{a}\\\\,^{f} \\\\delta_{b}\\\\,^{g} \\\\delta_{d}\\\\,^{h} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{f} \\\\delta_{b}\\\\,^{h} \\\\delta_{d}\\\\,^{g}\\\\right) - \\\\frac{1}{10}R_{e}\\\\,^{d} \\\\left(\\\\frac{1}{6}\\\\delta_{a}\\\\,^{g} \\\\delta_{b}\\\\,^{h} \\\\delta_{d}\\\\,^{f} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{h} \\\\delta_{b}\\\\,^{g} \\\\delta_{d}\\\\,^{f} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{f} \\\\delta_{b}\\\\,^{h} \\\\delta_{d}\\\\,^{g}+\\\\frac{1}{6}\\\\delta_{a}\\\\,^{f} \\\\delta_{b}\\\\,^{g} \\\\delta_{d}\\\\,^{h}+\\\\frac{1}{6}\\\\delta_{a}\\\\,^{h} \\\\delta_{b}\\\\,^{f} \\\\delta_{d}\\\\,^{g} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{g} \\\\delta_{b}\\\\,^{f} \\\\delta_{d}\\\\,^{h}\\\\right)%\\n+\\\\frac{1}{10}R_{e}\\\\,^{d} \\\\left(\\\\frac{1}{6}\\\\delta_{a}\\\\,^{h} \\\\delta_{b}\\\\,^{g} \\\\delta_{d}\\\\,^{f} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{g} \\\\delta_{b}\\\\,^{h} \\\\delta_{d}\\\\,^{f} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{h} \\\\delta_{b}\\\\,^{f} \\\\delta_{d}\\\\,^{g}+\\\\frac{1}{6}\\\\delta_{a}\\\\,^{g} \\\\delta_{b}\\\\,^{f} \\\\delta_{d}\\\\,^{h}+\\\\frac{1}{6}\\\\delta_{a}\\\\,^{f} \\\\delta_{b}\\\\,^{h} \\\\delta_{d}\\\\,^{g} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{f} \\\\delta_{b}\\\\,^{g} \\\\delta_{d}\\\\,^{h}\\\\right) - \\\\frac{1}{10}R_{e}\\\\,^{c} \\\\left(\\\\frac{1}{6}\\\\delta_{a}\\\\,^{f} \\\\delta_{b}\\\\,^{g} \\\\delta_{c}\\\\,^{h} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{f} \\\\delta_{b}\\\\,^{h} \\\\delta_{c}\\\\,^{g} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{g} \\\\delta_{b}\\\\,^{f} \\\\delta_{c}\\\\,^{h}+\\\\frac{1}{6}\\\\delta_{a}\\\\,^{h} \\\\delta_{b}\\\\,^{f} \\\\delta_{c}\\\\,^{g}+\\\\frac{1}{6}\\\\delta_{a}\\\\,^{g} \\\\delta_{b}\\\\,^{h} \\\\delta_{c}\\\\,^{f} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{h} \\\\delta_{b}\\\\,^{g} \\\\delta_{c}\\\\,^{f}\\\\right)+\\\\frac{1}{10}R_{e}\\\\,^{c} \\\\left(\\\\frac{1}{6}\\\\delta_{a}\\\\,^{f} \\\\delta_{b}\\\\,^{h} \\\\delta_{c}\\\\,^{g} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{f} \\\\delta_{b}\\\\,^{g} \\\\delta_{c}\\\\,^{h} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{g} \\\\delta_{b}\\\\,^{h} \\\\delta_{c}\\\\,^{f}+\\\\frac{1}{6}\\\\delta_{a}\\\\,^{h} \\\\delta_{b}\\\\,^{g} \\\\delta_{c}\\\\,^{f}+\\\\frac{1}{6}\\\\delta_{a}\\\\,^{g} \\\\delta_{b}\\\\,^{f} \\\\delta_{c}\\\\,^{h} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{h} \\\\delta_{b}\\\\,^{f} \\\\delta_{c}\\\\,^{g}\\\\right)+\\\\frac{1}{10}R_{e}\\\\,^{c} \\\\left(\\\\frac{1}{6}\\\\delta_{a}\\\\,^{g} \\\\delta_{b}\\\\,^{f} \\\\delta_{c}\\\\,^{h} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{h} \\\\delta_{b}\\\\,^{f} \\\\delta_{c}\\\\,^{g} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{f} \\\\delta_{b}\\\\,^{g} \\\\delta_{c}\\\\,^{h}+\\\\frac{1}{6}\\\\delta_{a}\\\\,^{f} \\\\delta_{b}\\\\,^{h} \\\\delta_{c}\\\\,^{g}+\\\\frac{1}{6}\\\\delta_{a}\\\\,^{h} \\\\delta_{b}\\\\,^{g} \\\\delta_{c}\\\\,^{f} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{g} \\\\delta_{b}\\\\,^{h} \\\\delta_{c}\\\\,^{f}\\\\right) - \\\\frac{1}{10}R_{e}\\\\,^{c} \\\\left(\\\\frac{1}{6}\\\\delta_{a}\\\\,^{h} \\\\delta_{b}\\\\,^{f} \\\\delta_{c}\\\\,^{g} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{g} \\\\delta_{b}\\\\,^{f} \\\\delta_{c}\\\\,^{h} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{h} \\\\delta_{b}\\\\,^{g} \\\\delta_{c}\\\\,^{f}+\\\\frac{1}{6}\\\\delta_{a}\\\\,^{g} \\\\delta_{b}\\\\,^{h} \\\\delta_{c}\\\\,^{f}+\\\\frac{1}{6}\\\\delta_{a}\\\\,^{f} \\\\delta_{b}\\\\,^{g} \\\\delta_{c}\\\\,^{h} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{f} \\\\delta_{b}\\\\,^{h} \\\\delta_{c}\\\\,^{g}\\\\right) - \\\\frac{1}{10}R_{e}\\\\,^{c} \\\\left(\\\\frac{1}{6}\\\\delta_{a}\\\\,^{g} \\\\delta_{b}\\\\,^{h} \\\\delta_{c}\\\\,^{f} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{h} \\\\delta_{b}\\\\,^{g} \\\\delta_{c}\\\\,^{f} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{f} \\\\delta_{b}\\\\,^{h} \\\\delta_{c}\\\\,^{g}+\\\\frac{1}{6}\\\\delta_{a}\\\\,^{f} \\\\delta_{b}\\\\,^{g} \\\\delta_{c}\\\\,^{h}+\\\\frac{1}{6}\\\\delta_{a}\\\\,^{h} \\\\delta_{b}\\\\,^{f} \\\\delta_{c}\\\\,^{g} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{g} \\\\delta_{b}\\\\,^{f} \\\\delta_{c}\\\\,^{h}\\\\right)+\\\\frac{1}{10}R_{e}\\\\,^{c} \\\\left(\\\\frac{1}{6}\\\\delta_{a}\\\\,^{h} \\\\delta_{b}\\\\,^{g} \\\\delta_{c}\\\\,^{f} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{g} \\\\delta_{b}\\\\,^{h} \\\\delta_{c}\\\\,^{f} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{h} \\\\delta_{b}\\\\,^{f} \\\\delta_{c}\\\\,^{g}+\\\\frac{1}{6}\\\\delta_{a}\\\\,^{g} \\\\delta_{b}\\\\,^{f} \\\\delta_{c}\\\\,^{h}+\\\\frac{1}{6}\\\\delta_{a}\\\\,^{f} \\\\delta_{b}\\\\,^{h} \\\\delta_{c}\\\\,^{g} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{f} \\\\delta_{b}\\\\,^{g} \\\\delta_{c}\\\\,^{h}\\\\right)+\\\\frac{1}{20}R_{e a}\\\\,^{c d} \\\\left(\\\\frac{1}{6}\\\\delta_{b}\\\\,^{f} \\\\delta_{c}\\\\,^{g} \\\\delta_{d}\\\\,^{h} - \\\\frac{1}{6}\\\\delta_{b}\\\\,^{f} \\\\delta_{c}\\\\,^{h} \\\\delta_{d}\\\\,^{g} - \\\\frac{1}{6}\\\\delta_{b}\\\\,^{g} \\\\delta_{c}\\\\,^{f} \\\\delta_{d}\\\\,^{h}+\\\\frac{1}{6}\\\\delta_{b}\\\\,^{h} \\\\delta_{c}\\\\,^{f} \\\\delta_{d}\\\\,^{g}+\\\\frac{1}{6}\\\\delta_{b}\\\\,^{g} \\\\delta_{c}\\\\,^{h} \\\\delta_{d}\\\\,^{f} - \\\\frac{1}{6}\\\\delta_{b}\\\\,^{h} \\\\delta_{c}\\\\,^{g} \\\\delta_{d}\\\\,^{f}\\\\right) - \\\\frac{1}{20}R_{e a}\\\\,^{c d} \\\\left(\\\\frac{1}{6}\\\\delta_{b}\\\\,^{f} \\\\delta_{c}\\\\,^{h} \\\\delta_{d}\\\\,^{g} - \\\\frac{1}{6}\\\\delta_{b}\\\\,^{f} \\\\delta_{c}\\\\,^{g} \\\\delta_{d}\\\\,^{h} - \\\\frac{1}{6}\\\\delta_{b}\\\\,^{g} \\\\delta_{c}\\\\,^{h} \\\\delta_{d}\\\\,^{f}+\\\\frac{1}{6}\\\\delta_{b}\\\\,^{h} \\\\delta_{c}\\\\,^{g} \\\\delta_{d}\\\\,^{f}+\\\\frac{1}{6}\\\\delta_{b}\\\\,^{g} \\\\delta_{c}\\\\,^{f} \\\\delta_{d}\\\\,^{h} - \\\\frac{1}{6}\\\\delta_{b}\\\\,^{h} \\\\delta_{c}\\\\,^{f} \\\\delta_{d}\\\\,^{g}\\\\right) - \\\\frac{1}{20}R_{e a}\\\\,^{c d} \\\\left(\\\\frac{1}{6}\\\\delta_{b}\\\\,^{g} \\\\delta_{c}\\\\,^{f} \\\\delta_{d}\\\\,^{h} - \\\\frac{1}{6}\\\\delta_{b}\\\\,^{h} \\\\delta_{c}\\\\,^{f} \\\\delta_{d}\\\\,^{g} - \\\\frac{1}{6}\\\\delta_{b}\\\\,^{f} \\\\delta_{c}\\\\,^{g} \\\\delta_{d}\\\\,^{h}+\\\\frac{1}{6}\\\\delta_{b}\\\\,^{f} \\\\delta_{c}\\\\,^{h} \\\\delta_{d}\\\\,^{g}+\\\\frac{1}{6}\\\\delta_{b}\\\\,^{h} \\\\delta_{c}\\\\,^{g} \\\\delta_{d}\\\\,^{f} - \\\\frac{1}{6}\\\\delta_{b}\\\\,^{g} \\\\delta_{c}\\\\,^{h} \\\\delta_{d}\\\\,^{f}\\\\right)+\\\\frac{1}{20}R_{e a}\\\\,^{c d} \\\\left(\\\\frac{1}{6}\\\\delta_{b}\\\\,^{h} \\\\delta_{c}\\\\,^{f} \\\\delta_{d}\\\\,^{g} - \\\\frac{1}{6}\\\\delta_{b}\\\\,^{g} \\\\delta_{c}\\\\,^{f} \\\\delta_{d}\\\\,^{h} - \\\\frac{1}{6}\\\\delta_{b}\\\\,^{h} \\\\delta_{c}\\\\,^{g} \\\\delta_{d}\\\\,^{f}+\\\\frac{1}{6}\\\\delta_{b}\\\\,^{g} \\\\delta_{c}\\\\,^{h} \\\\delta_{d}\\\\,^{f}+\\\\frac{1}{6}\\\\delta_{b}\\\\,^{f} \\\\delta_{c}\\\\,^{g} \\\\delta_{d}\\\\,^{h} - \\\\frac{1}{6}\\\\delta_{b}\\\\,^{f} \\\\delta_{c}\\\\,^{h} \\\\delta_{d}\\\\,^{g}\\\\right)+\\\\frac{1}{20}R_{e a}\\\\,^{c d} \\\\left(\\\\frac{1}{6}\\\\delta_{b}\\\\,^{g} \\\\delta_{c}\\\\,^{h} \\\\delta_{d}\\\\,^{f} - \\\\frac{1}{6}\\\\delta_{b}\\\\,^{h} \\\\delta_{c}\\\\,^{g} \\\\delta_{d}\\\\,^{f} - \\\\frac{1}{6}\\\\delta_{b}\\\\,^{f} \\\\delta_{c}\\\\,^{h} \\\\delta_{d}\\\\,^{g}+\\\\frac{1}{6}\\\\delta_{b}\\\\,^{f} \\\\delta_{c}\\\\,^{g} \\\\delta_{d}\\\\,^{h}+\\\\frac{1}{6}\\\\delta_{b}\\\\,^{h} \\\\delta_{c}\\\\,^{f} \\\\delta_{d}\\\\,^{g} - \\\\frac{1}{6}\\\\delta_{b}\\\\,^{g} \\\\delta_{c}\\\\,^{f} \\\\delta_{d}\\\\,^{h}\\\\right) - \\\\frac{1}{20}R_{e a}\\\\,^{c d} \\\\left(\\\\frac{1}{6}\\\\delta_{b}\\\\,^{h} \\\\delta_{c}\\\\,^{g} \\\\delta_{d}\\\\,^{f} - \\\\frac{1}{6}\\\\delta_{b}\\\\,^{g} \\\\delta_{c}\\\\,^{h} \\\\delta_{d}\\\\,^{f} - \\\\frac{1}{6}\\\\delta_{b}\\\\,^{h} \\\\delta_{c}\\\\,^{f} \\\\delta_{d}\\\\,^{g}+\\\\frac{1}{6}\\\\delta_{b}\\\\,^{g} \\\\delta_{c}\\\\,^{f} \\\\delta_{d}\\\\,^{h}+\\\\frac{1}{6}\\\\delta_{b}\\\\,^{f} \\\\delta_{c}\\\\,^{h} \\\\delta_{d}\\\\,^{g} - \\\\frac{1}{6}\\\\delta_{b}\\\\,^{f} \\\\delta_{c}\\\\,^{g} \\\\delta_{d}\\\\,^{h}\\\\right) - \\\\frac{1}{20}R_{e b}\\\\,^{c d} \\\\left(\\\\frac{1}{6}\\\\delta_{a}\\\\,^{f} \\\\delta_{c}\\\\,^{g} \\\\delta_{d}\\\\,^{h} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{f} \\\\delta_{c}\\\\,^{h} \\\\delta_{d}\\\\,^{g} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{g} \\\\delta_{c}\\\\,^{f} \\\\delta_{d}\\\\,^{h}+\\\\frac{1}{6}\\\\delta_{a}\\\\,^{h} \\\\delta_{c}\\\\,^{f} \\\\delta_{d}\\\\,^{g}+\\\\frac{1}{6}\\\\delta_{a}\\\\,^{g} \\\\delta_{c}\\\\,^{h} \\\\delta_{d}\\\\,^{f} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{h} \\\\delta_{c}\\\\,^{g} \\\\delta_{d}\\\\,^{f}\\\\right)+\\\\frac{1}{20}R_{e b}\\\\,^{c d} \\\\left(\\\\frac{1}{6}\\\\delta_{a}\\\\,^{f} \\\\delta_{c}\\\\,^{h} \\\\delta_{d}\\\\,^{g} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{f} \\\\delta_{c}\\\\,^{g} \\\\delta_{d}\\\\,^{h} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{g} \\\\delta_{c}\\\\,^{h} \\\\delta_{d}\\\\,^{f}+\\\\frac{1}{6}\\\\delta_{a}\\\\,^{h} \\\\delta_{c}\\\\,^{g} \\\\delta_{d}\\\\,^{f}+\\\\frac{1}{6}\\\\delta_{a}\\\\,^{g} \\\\delta_{c}\\\\,^{f} \\\\delta_{d}\\\\,^{h} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{h} \\\\delta_{c}\\\\,^{f} \\\\delta_{d}\\\\,^{g}\\\\right)+\\\\frac{1}{20}R_{e b}\\\\,^{c d} \\\\left(\\\\frac{1}{6}\\\\delta_{a}\\\\,^{g} \\\\delta_{c}\\\\,^{f} \\\\delta_{d}\\\\,^{h} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{h} \\\\delta_{c}\\\\,^{f} \\\\delta_{d}\\\\,^{g} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{f} \\\\delta_{c}\\\\,^{g} \\\\delta_{d}\\\\,^{h}+\\\\frac{1}{6}\\\\delta_{a}\\\\,^{f} \\\\delta_{c}\\\\,^{h} \\\\delta_{d}\\\\,^{g}+\\\\frac{1}{6}\\\\delta_{a}\\\\,^{h} \\\\delta_{c}\\\\,^{g} \\\\delta_{d}\\\\,^{f} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{g} \\\\delta_{c}\\\\,^{h} \\\\delta_{d}\\\\,^{f}\\\\right) - \\\\frac{1}{20}R_{e b}\\\\,^{c d} \\\\left(\\\\frac{1}{6}\\\\delta_{a}\\\\,^{h} \\\\delta_{c}\\\\,^{f} \\\\delta_{d}\\\\,^{g} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{g} \\\\delta_{c}\\\\,^{f} \\\\delta_{d}\\\\,^{h} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{h} \\\\delta_{c}\\\\,^{g} \\\\delta_{d}\\\\,^{f}+\\\\frac{1}{6}\\\\delta_{a}\\\\,^{g} \\\\delta_{c}\\\\,^{h} \\\\delta_{d}\\\\,^{f}+\\\\frac{1}{6}\\\\delta_{a}\\\\,^{f} \\\\delta_{c}\\\\,^{g} \\\\delta_{d}\\\\,^{h} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{f} \\\\delta_{c}\\\\,^{h} \\\\delta_{d}\\\\,^{g}\\\\right) - \\\\frac{1}{20}R_{e b}\\\\,^{c d} \\\\left(\\\\frac{1}{6}\\\\delta_{a}\\\\,^{g} \\\\delta_{c}\\\\,^{h} \\\\delta_{d}\\\\,^{f} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{h} \\\\delta_{c}\\\\,^{g} \\\\delta_{d}\\\\,^{f} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{f} \\\\delta_{c}\\\\,^{h} \\\\delta_{d}\\\\,^{g}+\\\\frac{1}{6}\\\\delta_{a}\\\\,^{f} \\\\delta_{c}\\\\,^{g} \\\\delta_{d}\\\\,^{h}+\\\\frac{1}{6}\\\\delta_{a}\\\\,^{h} \\\\delta_{c}\\\\,^{f} \\\\delta_{d}\\\\,^{g} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{g} \\\\delta_{c}\\\\,^{f} \\\\delta_{d}\\\\,^{h}\\\\right)+\\\\frac{1}{20}R_{e b}\\\\,^{c d} \\\\left(\\\\frac{1}{6}\\\\delta_{a}\\\\,^{h} \\\\delta_{c}\\\\,^{g} \\\\delta_{d}\\\\,^{f} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{g} \\\\delta_{c}\\\\,^{h} \\\\delta_{d}\\\\,^{f} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{h} \\\\delta_{c}\\\\,^{f} \\\\delta_{d}\\\\,^{g}+\\\\frac{1}{6}\\\\delta_{a}\\\\,^{g} \\\\delta_{c}\\\\,^{f} \\\\delta_{d}\\\\,^{h}+\\\\frac{1}{6}\\\\delta_{a}\\\\,^{f} \\\\delta_{c}\\\\,^{h} \\\\delta_{d}\\\\,^{g} - \\\\frac{1}{6}\\\\delta_{a}\\\\,^{f} \\\\delta_{c}\\\\,^{g} \\\\delta_{d}\\\\,^{h}\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"expand_delta(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\frac{1}{20}R_{a b}\\\\,^{c d} \\\\delta_{c}\\\\,^{f} \\\\delta_{d}\\\\,^{g} \\\\delta_{e}\\\\,^{h} - \\\\frac{1}{20}R_{a b}\\\\,^{c d} \\\\delta_{c}\\\\,^{f} \\\\delta_{d}\\\\,^{h} \\\\delta_{e}\\\\,^{g} - \\\\frac{1}{20}R_{a b}\\\\,^{c d} \\\\delta_{c}\\\\,^{g} \\\\delta_{d}\\\\,^{f} \\\\delta_{e}\\\\,^{h}+\\\\frac{1}{20}R_{a b}\\\\,^{c d} \\\\delta_{c}\\\\,^{h} \\\\delta_{d}\\\\,^{f} \\\\delta_{e}\\\\,^{g}+\\\\frac{1}{20}R_{a b}\\\\,^{c d} \\\\delta_{c}\\\\,^{g} \\\\delta_{d}\\\\,^{h} \\\\delta_{e}\\\\,^{f} - \\\\frac{1}{20}R_{a b}\\\\,^{c d} \\\\delta_{c}\\\\,^{h} \\\\delta_{d}\\\\,^{g} \\\\delta_{e}\\\\,^{f}+\\\\frac{1}{10}R_{a}\\\\,^{d} \\\\delta_{b}\\\\,^{f} \\\\delta_{d}\\\\,^{g} \\\\delta_{e}\\\\,^{h} - \\\\frac{1}{10}R_{a}\\\\,^{d} \\\\delta_{b}\\\\,^{f} \\\\delta_{d}\\\\,^{h} \\\\delta_{e}\\\\,^{g} - \\\\frac{1}{10}R_{a}\\\\,^{d} \\\\delta_{b}\\\\,^{g} \\\\delta_{d}\\\\,^{f} \\\\delta_{e}\\\\,^{h}+\\\\frac{1}{10}R_{a}\\\\,^{d} \\\\delta_{b}\\\\,^{h} \\\\delta_{d}\\\\,^{f} \\\\delta_{e}\\\\,^{g}+\\\\frac{1}{10}R_{a}\\\\,^{d} \\\\delta_{b}\\\\,^{g} \\\\delta_{d}\\\\,^{h} \\\\delta_{e}\\\\,^{f} - \\\\frac{1}{10}R_{a}\\\\,^{d} \\\\delta_{b}\\\\,^{h} \\\\delta_{d}\\\\,^{g} \\\\delta_{e}\\\\,^{f}+\\\\frac{1}{10}R_{a}\\\\,^{c} \\\\delta_{b}\\\\,^{f} \\\\delta_{c}\\\\,^{g} \\\\delta_{e}\\\\,^{h} - \\\\frac{1}{10}R_{a}\\\\,^{c} \\\\delta_{b}\\\\,^{f} \\\\delta_{c}\\\\,^{h} \\\\delta_{e}\\\\,^{g} - \\\\frac{1}{10}R_{a}\\\\,^{c} \\\\delta_{b}\\\\,^{g} \\\\delta_{c}\\\\,^{f} \\\\delta_{e}\\\\,^{h}+\\\\frac{1}{10}R_{a}\\\\,^{c} \\\\delta_{b}\\\\,^{h} \\\\delta_{c}\\\\,^{f} \\\\delta_{e}\\\\,^{g}+\\\\frac{1}{10}R_{a}\\\\,^{c} \\\\delta_{b}\\\\,^{g} \\\\delta_{c}\\\\,^{h} \\\\delta_{e}\\\\,^{f} - \\\\frac{1}{10}R_{a}\\\\,^{c} \\\\delta_{b}\\\\,^{h} \\\\delta_{c}\\\\,^{g} \\\\delta_{e}\\\\,^{f} - \\\\frac{1}{20}R_{a e}\\\\,^{c d} \\\\delta_{b}\\\\,^{f} \\\\delta_{c}\\\\,^{g} \\\\delta_{d}\\\\,^{h}%\\n+\\\\frac{1}{20}R_{a e}\\\\,^{c d} \\\\delta_{b}\\\\,^{f} \\\\delta_{c}\\\\,^{h} \\\\delta_{d}\\\\,^{g}+\\\\frac{1}{20}R_{a e}\\\\,^{c d} \\\\delta_{b}\\\\,^{g} \\\\delta_{c}\\\\,^{f} \\\\delta_{d}\\\\,^{h} - \\\\frac{1}{20}R_{a e}\\\\,^{c d} \\\\delta_{b}\\\\,^{h} \\\\delta_{c}\\\\,^{f} \\\\delta_{d}\\\\,^{g} - \\\\frac{1}{20}R_{a e}\\\\,^{c d} \\\\delta_{b}\\\\,^{g} \\\\delta_{c}\\\\,^{h} \\\\delta_{d}\\\\,^{f}+\\\\frac{1}{20}R_{a e}\\\\,^{c d} \\\\delta_{b}\\\\,^{h} \\\\delta_{c}\\\\,^{g} \\\\delta_{d}\\\\,^{f} - \\\\frac{1}{20}R_{b a}\\\\,^{c d} \\\\delta_{c}\\\\,^{f} \\\\delta_{d}\\\\,^{g} \\\\delta_{e}\\\\,^{h}+\\\\frac{1}{20}R_{b a}\\\\,^{c d} \\\\delta_{c}\\\\,^{f} \\\\delta_{d}\\\\,^{h} \\\\delta_{e}\\\\,^{g}+\\\\frac{1}{20}R_{b a}\\\\,^{c d} \\\\delta_{c}\\\\,^{g} \\\\delta_{d}\\\\,^{f} \\\\delta_{e}\\\\,^{h} - \\\\frac{1}{20}R_{b a}\\\\,^{c d} \\\\delta_{c}\\\\,^{h} \\\\delta_{d}\\\\,^{f} \\\\delta_{e}\\\\,^{g} - \\\\frac{1}{20}R_{b a}\\\\,^{c d} \\\\delta_{c}\\\\,^{g} \\\\delta_{d}\\\\,^{h} \\\\delta_{e}\\\\,^{f}+\\\\frac{1}{20}R_{b a}\\\\,^{c d} \\\\delta_{c}\\\\,^{h} \\\\delta_{d}\\\\,^{g} \\\\delta_{e}\\\\,^{f} - \\\\frac{1}{10}R_{b}\\\\,^{d} \\\\delta_{a}\\\\,^{f} \\\\delta_{d}\\\\,^{g} \\\\delta_{e}\\\\,^{h}+\\\\frac{1}{10}R_{b}\\\\,^{d} \\\\delta_{a}\\\\,^{f} \\\\delta_{d}\\\\,^{h} \\\\delta_{e}\\\\,^{g}+\\\\frac{1}{10}R_{b}\\\\,^{d} \\\\delta_{a}\\\\,^{g} \\\\delta_{d}\\\\,^{f} \\\\delta_{e}\\\\,^{h} - \\\\frac{1}{10}R_{b}\\\\,^{d} \\\\delta_{a}\\\\,^{h} \\\\delta_{d}\\\\,^{f} \\\\delta_{e}\\\\,^{g} - \\\\frac{1}{10}R_{b}\\\\,^{d} \\\\delta_{a}\\\\,^{g} \\\\delta_{d}\\\\,^{h} \\\\delta_{e}\\\\,^{f}+\\\\frac{1}{10}R_{b}\\\\,^{d} \\\\delta_{a}\\\\,^{h} \\\\delta_{d}\\\\,^{g} \\\\delta_{e}\\\\,^{f} - \\\\frac{1}{10}R_{b}\\\\,^{c} \\\\delta_{a}\\\\,^{f} \\\\delta_{c}\\\\,^{g} \\\\delta_{e}\\\\,^{h}+\\\\frac{1}{10}R_{b}\\\\,^{c} \\\\delta_{a}\\\\,^{f} \\\\delta_{c}\\\\,^{h} \\\\delta_{e}\\\\,^{g}+\\\\frac{1}{10}R_{b}\\\\,^{c} \\\\delta_{a}\\\\,^{g} \\\\delta_{c}\\\\,^{f} \\\\delta_{e}\\\\,^{h}%\\n - \\\\frac{1}{10}R_{b}\\\\,^{c} \\\\delta_{a}\\\\,^{h} \\\\delta_{c}\\\\,^{f} \\\\delta_{e}\\\\,^{g} - \\\\frac{1}{10}R_{b}\\\\,^{c} \\\\delta_{a}\\\\,^{g} \\\\delta_{c}\\\\,^{h} \\\\delta_{e}\\\\,^{f}+\\\\frac{1}{10}R_{b}\\\\,^{c} \\\\delta_{a}\\\\,^{h} \\\\delta_{c}\\\\,^{g} \\\\delta_{e}\\\\,^{f}+\\\\frac{1}{20}R_{b e}\\\\,^{c d} \\\\delta_{a}\\\\,^{f} \\\\delta_{c}\\\\,^{g} \\\\delta_{d}\\\\,^{h} - \\\\frac{1}{20}R_{b e}\\\\,^{c d} \\\\delta_{a}\\\\,^{f} \\\\delta_{c}\\\\,^{h} \\\\delta_{d}\\\\,^{g} - \\\\frac{1}{20}R_{b e}\\\\,^{c d} \\\\delta_{a}\\\\,^{g} \\\\delta_{c}\\\\,^{f} \\\\delta_{d}\\\\,^{h}+\\\\frac{1}{20}R_{b e}\\\\,^{c d} \\\\delta_{a}\\\\,^{h} \\\\delta_{c}\\\\,^{f} \\\\delta_{d}\\\\,^{g}+\\\\frac{1}{20}R_{b e}\\\\,^{c d} \\\\delta_{a}\\\\,^{g} \\\\delta_{c}\\\\,^{h} \\\\delta_{d}\\\\,^{f} - \\\\frac{1}{20}R_{b e}\\\\,^{c d} \\\\delta_{a}\\\\,^{h} \\\\delta_{c}\\\\,^{g} \\\\delta_{d}\\\\,^{f}+\\\\frac{1}{10}R \\\\delta_{a}\\\\,^{f} \\\\delta_{b}\\\\,^{g} \\\\delta_{e}\\\\,^{h} - \\\\frac{1}{10}R \\\\delta_{a}\\\\,^{f} \\\\delta_{b}\\\\,^{h} \\\\delta_{e}\\\\,^{g} - \\\\frac{1}{10}R \\\\delta_{a}\\\\,^{g} \\\\delta_{b}\\\\,^{f} \\\\delta_{e}\\\\,^{h}+\\\\frac{1}{10}R \\\\delta_{a}\\\\,^{h} \\\\delta_{b}\\\\,^{f} \\\\delta_{e}\\\\,^{g}+\\\\frac{1}{10}R \\\\delta_{a}\\\\,^{g} \\\\delta_{b}\\\\,^{h} \\\\delta_{e}\\\\,^{f} - \\\\frac{1}{10}R \\\\delta_{a}\\\\,^{h} \\\\delta_{b}\\\\,^{g} \\\\delta_{e}\\\\,^{f} - \\\\frac{1}{10}R_{e}\\\\,^{d} \\\\delta_{a}\\\\,^{f} \\\\delta_{b}\\\\,^{g} \\\\delta_{d}\\\\,^{h}+\\\\frac{1}{10}R_{e}\\\\,^{d} \\\\delta_{a}\\\\,^{f} \\\\delta_{b}\\\\,^{h} \\\\delta_{d}\\\\,^{g}+\\\\frac{1}{10}R_{e}\\\\,^{d} \\\\delta_{a}\\\\,^{g} \\\\delta_{b}\\\\,^{f} \\\\delta_{d}\\\\,^{h} - \\\\frac{1}{10}R_{e}\\\\,^{d} \\\\delta_{a}\\\\,^{h} \\\\delta_{b}\\\\,^{f} \\\\delta_{d}\\\\,^{g} - \\\\frac{1}{10}R_{e}\\\\,^{d} \\\\delta_{a}\\\\,^{g} \\\\delta_{b}\\\\,^{h} \\\\delta_{d}\\\\,^{f}%\\n+\\\\frac{1}{10}R_{e}\\\\,^{d} \\\\delta_{a}\\\\,^{h} \\\\delta_{b}\\\\,^{g} \\\\delta_{d}\\\\,^{f} - \\\\frac{1}{10}R_{e}\\\\,^{c} \\\\delta_{a}\\\\,^{f} \\\\delta_{b}\\\\,^{g} \\\\delta_{c}\\\\,^{h}+\\\\frac{1}{10}R_{e}\\\\,^{c} \\\\delta_{a}\\\\,^{f} \\\\delta_{b}\\\\,^{h} \\\\delta_{c}\\\\,^{g}+\\\\frac{1}{10}R_{e}\\\\,^{c} \\\\delta_{a}\\\\,^{g} \\\\delta_{b}\\\\,^{f} \\\\delta_{c}\\\\,^{h} - \\\\frac{1}{10}R_{e}\\\\,^{c} \\\\delta_{a}\\\\,^{h} \\\\delta_{b}\\\\,^{f} \\\\delta_{c}\\\\,^{g} - \\\\frac{1}{10}R_{e}\\\\,^{c} \\\\delta_{a}\\\\,^{g} \\\\delta_{b}\\\\,^{h} \\\\delta_{c}\\\\,^{f}+\\\\frac{1}{10}R_{e}\\\\,^{c} \\\\delta_{a}\\\\,^{h} \\\\delta_{b}\\\\,^{g} \\\\delta_{c}\\\\,^{f}+\\\\frac{1}{20}R_{e a}\\\\,^{c d} \\\\delta_{b}\\\\,^{f} \\\\delta_{c}\\\\,^{g} \\\\delta_{d}\\\\,^{h} - \\\\frac{1}{20}R_{e a}\\\\,^{c d} \\\\delta_{b}\\\\,^{f} \\\\delta_{c}\\\\,^{h} \\\\delta_{d}\\\\,^{g} - \\\\frac{1}{20}R_{e a}\\\\,^{c d} \\\\delta_{b}\\\\,^{g} \\\\delta_{c}\\\\,^{f} \\\\delta_{d}\\\\,^{h}+\\\\frac{1}{20}R_{e a}\\\\,^{c d} \\\\delta_{b}\\\\,^{h} \\\\delta_{c}\\\\,^{f} \\\\delta_{d}\\\\,^{g}+\\\\frac{1}{20}R_{e a}\\\\,^{c d} \\\\delta_{b}\\\\,^{g} \\\\delta_{c}\\\\,^{h} \\\\delta_{d}\\\\,^{f} - \\\\frac{1}{20}R_{e a}\\\\,^{c d} \\\\delta_{b}\\\\,^{h} \\\\delta_{c}\\\\,^{g} \\\\delta_{d}\\\\,^{f} - \\\\frac{1}{20}R_{e b}\\\\,^{c d} \\\\delta_{a}\\\\,^{f} \\\\delta_{c}\\\\,^{g} \\\\delta_{d}\\\\,^{h}+\\\\frac{1}{20}R_{e b}\\\\,^{c d} \\\\delta_{a}\\\\,^{f} \\\\delta_{c}\\\\,^{h} \\\\delta_{d}\\\\,^{g}+\\\\frac{1}{20}R_{e b}\\\\,^{c d} \\\\delta_{a}\\\\,^{g} \\\\delta_{c}\\\\,^{f} \\\\delta_{d}\\\\,^{h} - \\\\frac{1}{20}R_{e b}\\\\,^{c d} \\\\delta_{a}\\\\,^{h} \\\\delta_{c}\\\\,^{f} \\\\delta_{d}\\\\,^{g} - \\\\frac{1}{20}R_{e b}\\\\,^{c d} \\\\delta_{a}\\\\,^{g} \\\\delta_{c}\\\\,^{h} \\\\delta_{d}\\\\,^{f}+\\\\frac{1}{20}R_{e b}\\\\,^{c d} \\\\delta_{a}\\\\,^{h} \\\\delta_{c}\\\\,^{g} \\\\delta_{d}\\\\,^{f}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"distribute(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\frac{1}{20}R_{a b}\\\\,^{f g} \\\\delta_{e}\\\\,^{h} - \\\\frac{1}{20}R_{a b}\\\\,^{f h} \\\\delta_{e}\\\\,^{g} - \\\\frac{1}{20}R_{a b}\\\\,^{g f} \\\\delta_{e}\\\\,^{h}+\\\\frac{1}{20}R_{a b}\\\\,^{h f} \\\\delta_{e}\\\\,^{g}+\\\\frac{1}{20}R_{a b}\\\\,^{g h} \\\\delta_{e}\\\\,^{f} - \\\\frac{1}{20}R_{a b}\\\\,^{h g} \\\\delta_{e}\\\\,^{f}+\\\\frac{1}{5}R_{a}\\\\,^{g} \\\\delta_{b}\\\\,^{f} \\\\delta_{e}\\\\,^{h} - \\\\frac{1}{5}R_{a}\\\\,^{h} \\\\delta_{b}\\\\,^{f} \\\\delta_{e}\\\\,^{g} - \\\\frac{1}{5}R_{a}\\\\,^{f} \\\\delta_{b}\\\\,^{g} \\\\delta_{e}\\\\,^{h}+\\\\frac{1}{5}R_{a}\\\\,^{f} \\\\delta_{b}\\\\,^{h} \\\\delta_{e}\\\\,^{g}+\\\\frac{1}{5}R_{a}\\\\,^{h} \\\\delta_{b}\\\\,^{g} \\\\delta_{e}\\\\,^{f} - \\\\frac{1}{5}R_{a}\\\\,^{g} \\\\delta_{b}\\\\,^{h} \\\\delta_{e}\\\\,^{f} - \\\\frac{1}{20}R_{a e}\\\\,^{g h} \\\\delta_{b}\\\\,^{f}+\\\\frac{1}{20}R_{a e}\\\\,^{h g} \\\\delta_{b}\\\\,^{f}+\\\\frac{1}{20}R_{a e}\\\\,^{f h} \\\\delta_{b}\\\\,^{g} - \\\\frac{1}{20}R_{a e}\\\\,^{f g} \\\\delta_{b}\\\\,^{h} - \\\\frac{1}{20}R_{a e}\\\\,^{h f} \\\\delta_{b}\\\\,^{g}+\\\\frac{1}{20}R_{a e}\\\\,^{g f} \\\\delta_{b}\\\\,^{h} - \\\\frac{1}{20}R_{b a}\\\\,^{f g} \\\\delta_{e}\\\\,^{h}%\\n+\\\\frac{1}{20}R_{b a}\\\\,^{f h} \\\\delta_{e}\\\\,^{g}+\\\\frac{1}{20}R_{b a}\\\\,^{g f} \\\\delta_{e}\\\\,^{h} - \\\\frac{1}{20}R_{b a}\\\\,^{h f} \\\\delta_{e}\\\\,^{g} - \\\\frac{1}{20}R_{b a}\\\\,^{g h} \\\\delta_{e}\\\\,^{f}+\\\\frac{1}{20}R_{b a}\\\\,^{h g} \\\\delta_{e}\\\\,^{f} - \\\\frac{1}{5}R_{b}\\\\,^{g} \\\\delta_{a}\\\\,^{f} \\\\delta_{e}\\\\,^{h}+\\\\frac{1}{5}R_{b}\\\\,^{h} \\\\delta_{a}\\\\,^{f} \\\\delta_{e}\\\\,^{g}+\\\\frac{1}{5}R_{b}\\\\,^{f} \\\\delta_{a}\\\\,^{g} \\\\delta_{e}\\\\,^{h} - \\\\frac{1}{5}R_{b}\\\\,^{f} \\\\delta_{a}\\\\,^{h} \\\\delta_{e}\\\\,^{g} - \\\\frac{1}{5}R_{b}\\\\,^{h} \\\\delta_{a}\\\\,^{g} \\\\delta_{e}\\\\,^{f}+\\\\frac{1}{5}R_{b}\\\\,^{g} \\\\delta_{a}\\\\,^{h} \\\\delta_{e}\\\\,^{f}+\\\\frac{1}{20}R_{b e}\\\\,^{g h} \\\\delta_{a}\\\\,^{f} - \\\\frac{1}{20}R_{b e}\\\\,^{h g} \\\\delta_{a}\\\\,^{f} - \\\\frac{1}{20}R_{b e}\\\\,^{f h} \\\\delta_{a}\\\\,^{g}+\\\\frac{1}{20}R_{b e}\\\\,^{f g} \\\\delta_{a}\\\\,^{h}+\\\\frac{1}{20}R_{b e}\\\\,^{h f} \\\\delta_{a}\\\\,^{g} - \\\\frac{1}{20}R_{b e}\\\\,^{g f} \\\\delta_{a}\\\\,^{h}+\\\\frac{1}{10}R \\\\delta_{a}\\\\,^{f} \\\\delta_{b}\\\\,^{g} \\\\delta_{e}\\\\,^{h} - \\\\frac{1}{10}R \\\\delta_{a}\\\\,^{f} \\\\delta_{b}\\\\,^{h} \\\\delta_{e}\\\\,^{g} - \\\\frac{1}{10}R \\\\delta_{a}\\\\,^{g} \\\\delta_{b}\\\\,^{f} \\\\delta_{e}\\\\,^{h}%\\n+\\\\frac{1}{10}R \\\\delta_{a}\\\\,^{h} \\\\delta_{b}\\\\,^{f} \\\\delta_{e}\\\\,^{g}+\\\\frac{1}{10}R \\\\delta_{a}\\\\,^{g} \\\\delta_{b}\\\\,^{h} \\\\delta_{e}\\\\,^{f} - \\\\frac{1}{10}R \\\\delta_{a}\\\\,^{h} \\\\delta_{b}\\\\,^{g} \\\\delta_{e}\\\\,^{f} - \\\\frac{1}{5}R_{e}\\\\,^{h} \\\\delta_{a}\\\\,^{f} \\\\delta_{b}\\\\,^{g}+\\\\frac{1}{5}R_{e}\\\\,^{g} \\\\delta_{a}\\\\,^{f} \\\\delta_{b}\\\\,^{h}+\\\\frac{1}{5}R_{e}\\\\,^{h} \\\\delta_{a}\\\\,^{g} \\\\delta_{b}\\\\,^{f} - \\\\frac{1}{5}R_{e}\\\\,^{g} \\\\delta_{a}\\\\,^{h} \\\\delta_{b}\\\\,^{f} - \\\\frac{1}{5}R_{e}\\\\,^{f} \\\\delta_{a}\\\\,^{g} \\\\delta_{b}\\\\,^{h}+\\\\frac{1}{5}R_{e}\\\\,^{f} \\\\delta_{a}\\\\,^{h} \\\\delta_{b}\\\\,^{g}+\\\\frac{1}{20}R_{e a}\\\\,^{g h} \\\\delta_{b}\\\\,^{f} - \\\\frac{1}{20}R_{e a}\\\\,^{h g} \\\\delta_{b}\\\\,^{f} - \\\\frac{1}{20}R_{e a}\\\\,^{f h} \\\\delta_{b}\\\\,^{g}+\\\\frac{1}{20}R_{e a}\\\\,^{f g} \\\\delta_{b}\\\\,^{h}+\\\\frac{1}{20}R_{e a}\\\\,^{h f} \\\\delta_{b}\\\\,^{g} - \\\\frac{1}{20}R_{e a}\\\\,^{g f} \\\\delta_{b}\\\\,^{h} - \\\\frac{1}{20}R_{e b}\\\\,^{g h} \\\\delta_{a}\\\\,^{f}+\\\\frac{1}{20}R_{e b}\\\\,^{h g} \\\\delta_{a}\\\\,^{f}+\\\\frac{1}{20}R_{e b}\\\\,^{f h} \\\\delta_{a}\\\\,^{g} - \\\\frac{1}{20}R_{e b}\\\\,^{f g} \\\\delta_{a}\\\\,^{h} - \\\\frac{1}{20}R_{e b}\\\\,^{h f} \\\\delta_{a}\\\\,^{g}%\\n+\\\\frac{1}{20}R_{e b}\\\\,^{g f} \\\\delta_{a}\\\\,^{h}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"eliminate_kronecker(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\frac{1}{5}R_{a b}\\\\,^{f g} \\\\delta_{e}\\\\,^{h} - \\\\frac{1}{5}R_{a b}\\\\,^{f h} \\\\delta_{e}\\\\,^{g}+\\\\frac{1}{5}R_{a b}\\\\,^{g h} \\\\delta_{e}\\\\,^{f}+\\\\frac{1}{5}R_{a}\\\\,^{g} \\\\delta_{b}\\\\,^{f} \\\\delta_{e}\\\\,^{h} - \\\\frac{1}{5}R_{a}\\\\,^{h} \\\\delta_{b}\\\\,^{f} \\\\delta_{e}\\\\,^{g} - \\\\frac{1}{5}R_{a}\\\\,^{f} \\\\delta_{b}\\\\,^{g} \\\\delta_{e}\\\\,^{h}+\\\\frac{1}{5}R_{a}\\\\,^{f} \\\\delta_{b}\\\\,^{h} \\\\delta_{e}\\\\,^{g}+\\\\frac{1}{5}R_{a}\\\\,^{h} \\\\delta_{b}\\\\,^{g} \\\\delta_{e}\\\\,^{f} - \\\\frac{1}{5}R_{a}\\\\,^{g} \\\\delta_{b}\\\\,^{h} \\\\delta_{e}\\\\,^{f} - \\\\frac{1}{5}R_{a e}\\\\,^{g h} \\\\delta_{b}\\\\,^{f}+\\\\frac{1}{5}R_{a e}\\\\,^{f h} \\\\delta_{b}\\\\,^{g} - \\\\frac{1}{5}R_{a e}\\\\,^{f g} \\\\delta_{b}\\\\,^{h} - \\\\frac{1}{5}R_{b}\\\\,^{g} \\\\delta_{a}\\\\,^{f} \\\\delta_{e}\\\\,^{h}+\\\\frac{1}{5}R_{b}\\\\,^{h} \\\\delta_{a}\\\\,^{f} \\\\delta_{e}\\\\,^{g}+\\\\frac{1}{5}R_{b}\\\\,^{f} \\\\delta_{a}\\\\,^{g} \\\\delta_{e}\\\\,^{h} - \\\\frac{1}{5}R_{b}\\\\,^{f} \\\\delta_{a}\\\\,^{h} \\\\delta_{e}\\\\,^{g} - \\\\frac{1}{5}R_{b}\\\\,^{h} \\\\delta_{a}\\\\,^{g} \\\\delta_{e}\\\\,^{f}+\\\\frac{1}{5}R_{b}\\\\,^{g} \\\\delta_{a}\\\\,^{h} \\\\delta_{e}\\\\,^{f}+\\\\frac{1}{5}R_{b e}\\\\,^{g h} \\\\delta_{a}\\\\,^{f}%\\n - \\\\frac{1}{5}R_{b e}\\\\,^{f h} \\\\delta_{a}\\\\,^{g}+\\\\frac{1}{5}R_{b e}\\\\,^{f g} \\\\delta_{a}\\\\,^{h}+\\\\frac{1}{10}R \\\\delta_{a}\\\\,^{f} \\\\delta_{b}\\\\,^{g} \\\\delta_{e}\\\\,^{h} - \\\\frac{1}{10}R \\\\delta_{a}\\\\,^{f} \\\\delta_{b}\\\\,^{h} \\\\delta_{e}\\\\,^{g} - \\\\frac{1}{10}R \\\\delta_{a}\\\\,^{g} \\\\delta_{b}\\\\,^{f} \\\\delta_{e}\\\\,^{h}+\\\\frac{1}{10}R \\\\delta_{a}\\\\,^{h} \\\\delta_{b}\\\\,^{f} \\\\delta_{e}\\\\,^{g}+\\\\frac{1}{10}R \\\\delta_{a}\\\\,^{g} \\\\delta_{b}\\\\,^{h} \\\\delta_{e}\\\\,^{f} - \\\\frac{1}{10}R \\\\delta_{a}\\\\,^{h} \\\\delta_{b}\\\\,^{g} \\\\delta_{e}\\\\,^{f} - \\\\frac{1}{5}R_{e}\\\\,^{h} \\\\delta_{a}\\\\,^{f} \\\\delta_{b}\\\\,^{g}+\\\\frac{1}{5}R_{e}\\\\,^{g} \\\\delta_{a}\\\\,^{f} \\\\delta_{b}\\\\,^{h}+\\\\frac{1}{5}R_{e}\\\\,^{h} \\\\delta_{a}\\\\,^{g} \\\\delta_{b}\\\\,^{f} - \\\\frac{1}{5}R_{e}\\\\,^{g} \\\\delta_{a}\\\\,^{h} \\\\delta_{b}\\\\,^{f} - \\\\frac{1}{5}R_{e}\\\\,^{f} \\\\delta_{a}\\\\,^{g} \\\\delta_{b}\\\\,^{h}+\\\\frac{1}{5}R_{e}\\\\,^{f} \\\\delta_{a}\\\\,^{h} \\\\delta_{b}\\\\,^{g}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"canonicalise(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\frac{5}{2}R_{f g}\\\\,^{e a} \\\\delta_{h l} \\\\left(\\\\frac{1}{5}R_{a b}\\\\,^{f g} \\\\delta_{e}\\\\,^{h} - \\\\frac{1}{5}R_{a b}\\\\,^{f h} \\\\delta_{e}\\\\,^{g}+\\\\frac{1}{5}R_{a b}\\\\,^{g h} \\\\delta_{e}\\\\,^{f}+\\\\frac{1}{5}R_{a}\\\\,^{g} \\\\delta_{b}\\\\,^{f} \\\\delta_{e}\\\\,^{h} - \\\\frac{1}{5}R_{a}\\\\,^{h} \\\\delta_{b}\\\\,^{f} \\\\delta_{e}\\\\,^{g} - \\\\frac{1}{5}R_{a}\\\\,^{f} \\\\delta_{b}\\\\,^{g} \\\\delta_{e}\\\\,^{h}+\\\\frac{1}{5}R_{a}\\\\,^{f} \\\\delta_{b}\\\\,^{h} \\\\delta_{e}\\\\,^{g}+\\\\frac{1}{5}R_{a}\\\\,^{h} \\\\delta_{b}\\\\,^{g} \\\\delta_{e}\\\\,^{f} - \\\\frac{1}{5}R_{a}\\\\,^{g} \\\\delta_{b}\\\\,^{h} \\\\delta_{e}\\\\,^{f} - \\\\frac{1}{5}R_{a e}\\\\,^{g h} \\\\delta_{b}\\\\,^{f}+\\\\frac{1}{5}R_{a e}\\\\,^{f h} \\\\delta_{b}\\\\,^{g} - \\\\frac{1}{5}R_{a e}\\\\,^{f g} \\\\delta_{b}\\\\,^{h} - \\\\frac{1}{5}R_{b}\\\\,^{g} \\\\delta_{a}\\\\,^{f} \\\\delta_{e}\\\\,^{h}+\\\\frac{1}{5}R_{b}\\\\,^{h} \\\\delta_{a}\\\\,^{f} \\\\delta_{e}\\\\,^{g}+\\\\frac{1}{5}R_{b}\\\\,^{f} \\\\delta_{a}\\\\,^{g} \\\\delta_{e}\\\\,^{h} - \\\\frac{1}{5}R_{b}\\\\,^{f} \\\\delta_{a}\\\\,^{h} \\\\delta_{e}\\\\,^{g} - \\\\frac{1}{5}R_{b}\\\\,^{h} \\\\delta_{a}\\\\,^{g} \\\\delta_{e}\\\\,^{f}+\\\\frac{1}{5}R_{b}\\\\,^{g} \\\\delta_{a}\\\\,^{h} \\\\delta_{e}\\\\,^{f}+\\\\frac{1}{5}R_{b e}\\\\,^{g h} \\\\delta_{a}\\\\,^{f}%\\n - \\\\frac{1}{5}R_{b e}\\\\,^{f h} \\\\delta_{a}\\\\,^{g}+\\\\frac{1}{5}R_{b e}\\\\,^{f g} \\\\delta_{a}\\\\,^{h}+\\\\frac{1}{10}R \\\\delta_{a}\\\\,^{f} \\\\delta_{b}\\\\,^{g} \\\\delta_{e}\\\\,^{h} - \\\\frac{1}{10}R \\\\delta_{a}\\\\,^{f} \\\\delta_{b}\\\\,^{h} \\\\delta_{e}\\\\,^{g} - \\\\frac{1}{10}R \\\\delta_{a}\\\\,^{g} \\\\delta_{b}\\\\,^{f} \\\\delta_{e}\\\\,^{h}+\\\\frac{1}{10}R \\\\delta_{a}\\\\,^{h} \\\\delta_{b}\\\\,^{f} \\\\delta_{e}\\\\,^{g}+\\\\frac{1}{10}R \\\\delta_{a}\\\\,^{g} \\\\delta_{b}\\\\,^{h} \\\\delta_{e}\\\\,^{f} - \\\\frac{1}{10}R \\\\delta_{a}\\\\,^{h} \\\\delta_{b}\\\\,^{g} \\\\delta_{e}\\\\,^{f} - \\\\frac{1}{5}R_{e}\\\\,^{h} \\\\delta_{a}\\\\,^{f} \\\\delta_{b}\\\\,^{g}+\\\\frac{1}{5}R_{e}\\\\,^{g} \\\\delta_{a}\\\\,^{f} \\\\delta_{b}\\\\,^{h}+\\\\frac{1}{5}R_{e}\\\\,^{h} \\\\delta_{a}\\\\,^{g} \\\\delta_{b}\\\\,^{f} - \\\\frac{1}{5}R_{e}\\\\,^{g} \\\\delta_{a}\\\\,^{h} \\\\delta_{b}\\\\,^{f} - \\\\frac{1}{5}R_{e}\\\\,^{f} \\\\delta_{a}\\\\,^{g} \\\\delta_{b}\\\\,^{h}+\\\\frac{1}{5}R_{e}\\\\,^{f} \\\\delta_{a}\\\\,^{h} \\\\delta_{b}\\\\,^{g}\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex2:= 5/2 @(ex) \\\\delta_{h l} R_{f g}^{e a};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\frac{1}{2}R_{a b}\\\\,^{f g} R_{f g}\\\\,^{e a} \\\\delta_{e}\\\\,^{h} \\\\delta_{h l} - \\\\frac{1}{2}R_{a b}\\\\,^{f h} R_{f g}\\\\,^{e a} \\\\delta_{e}\\\\,^{g} \\\\delta_{h l}+\\\\frac{1}{2}R_{a b}\\\\,^{g h} R_{f g}\\\\,^{e a} \\\\delta_{e}\\\\,^{f} \\\\delta_{h l}+\\\\frac{1}{2}R_{a}\\\\,^{g} R_{f g}\\\\,^{e a} \\\\delta_{b}\\\\,^{f} \\\\delta_{e}\\\\,^{h} \\\\delta_{h l} - \\\\frac{1}{2}R_{a}\\\\,^{h} R_{f g}\\\\,^{e a} \\\\delta_{b}\\\\,^{f} \\\\delta_{e}\\\\,^{g} \\\\delta_{h l} - \\\\frac{1}{2}R_{a}\\\\,^{f} R_{f g}\\\\,^{e a} \\\\delta_{b}\\\\,^{g} \\\\delta_{e}\\\\,^{h} \\\\delta_{h l}+\\\\frac{1}{2}R_{a}\\\\,^{f} R_{f g}\\\\,^{e a} \\\\delta_{b}\\\\,^{h} \\\\delta_{e}\\\\,^{g} \\\\delta_{h l}+\\\\frac{1}{2}R_{a}\\\\,^{h} R_{f g}\\\\,^{e a} \\\\delta_{b}\\\\,^{g} \\\\delta_{e}\\\\,^{f} \\\\delta_{h l} - \\\\frac{1}{2}R_{a}\\\\,^{g} R_{f g}\\\\,^{e a} \\\\delta_{b}\\\\,^{h} \\\\delta_{e}\\\\,^{f} \\\\delta_{h l} - \\\\frac{1}{2}R_{a e}\\\\,^{g h} R_{f g}\\\\,^{e a} \\\\delta_{b}\\\\,^{f} \\\\delta_{h l}+\\\\frac{1}{2}R_{a e}\\\\,^{f h} R_{f g}\\\\,^{e a} \\\\delta_{b}\\\\,^{g} \\\\delta_{h l} - \\\\frac{1}{2}R_{a e}\\\\,^{f g} R_{f g}\\\\,^{e a} \\\\delta_{b}\\\\,^{h} \\\\delta_{h l} - \\\\frac{1}{2}R_{b}\\\\,^{g} R_{f g}\\\\,^{e a} \\\\delta_{a}\\\\,^{f} \\\\delta_{e}\\\\,^{h} \\\\delta_{h l}+\\\\frac{1}{2}R_{b}\\\\,^{h} R_{f g}\\\\,^{e a} \\\\delta_{a}\\\\,^{f} \\\\delta_{e}\\\\,^{g} \\\\delta_{h l}+\\\\frac{1}{2}R_{b}\\\\,^{f} R_{f g}\\\\,^{e a} \\\\delta_{a}\\\\,^{g} \\\\delta_{e}\\\\,^{h} \\\\delta_{h l} - \\\\frac{1}{2}R_{b}\\\\,^{f} R_{f g}\\\\,^{e a} \\\\delta_{a}\\\\,^{h} \\\\delta_{e}\\\\,^{g} \\\\delta_{h l} - \\\\frac{1}{2}R_{b}\\\\,^{h} R_{f g}\\\\,^{e a} \\\\delta_{a}\\\\,^{g} \\\\delta_{e}\\\\,^{f} \\\\delta_{h l}+\\\\frac{1}{2}R_{b}\\\\,^{g} R_{f g}\\\\,^{e a} \\\\delta_{a}\\\\,^{h} \\\\delta_{e}\\\\,^{f} \\\\delta_{h l}+\\\\frac{1}{2}R_{b e}\\\\,^{g h} R_{f g}\\\\,^{e a} \\\\delta_{a}\\\\,^{f} \\\\delta_{h l}%\\n - \\\\frac{1}{2}R_{b e}\\\\,^{f h} R_{f g}\\\\,^{e a} \\\\delta_{a}\\\\,^{g} \\\\delta_{h l}+\\\\frac{1}{2}R_{b e}\\\\,^{f g} R_{f g}\\\\,^{e a} \\\\delta_{a}\\\\,^{h} \\\\delta_{h l}+\\\\frac{1}{4}R R_{f g}\\\\,^{e a} \\\\delta_{a}\\\\,^{f} \\\\delta_{b}\\\\,^{g} \\\\delta_{e}\\\\,^{h} \\\\delta_{h l} - \\\\frac{1}{4}R R_{f g}\\\\,^{e a} \\\\delta_{a}\\\\,^{f} \\\\delta_{b}\\\\,^{h} \\\\delta_{e}\\\\,^{g} \\\\delta_{h l} - \\\\frac{1}{4}R R_{f g}\\\\,^{e a} \\\\delta_{a}\\\\,^{g} \\\\delta_{b}\\\\,^{f} \\\\delta_{e}\\\\,^{h} \\\\delta_{h l}+\\\\frac{1}{4}R R_{f g}\\\\,^{e a} \\\\delta_{a}\\\\,^{h} \\\\delta_{b}\\\\,^{f} \\\\delta_{e}\\\\,^{g} \\\\delta_{h l}+\\\\frac{1}{4}R R_{f g}\\\\,^{e a} \\\\delta_{a}\\\\,^{g} \\\\delta_{b}\\\\,^{h} \\\\delta_{e}\\\\,^{f} \\\\delta_{h l} - \\\\frac{1}{4}R R_{f g}\\\\,^{e a} \\\\delta_{a}\\\\,^{h} \\\\delta_{b}\\\\,^{g} \\\\delta_{e}\\\\,^{f} \\\\delta_{h l} - \\\\frac{1}{2}R_{e}\\\\,^{h} R_{f g}\\\\,^{e a} \\\\delta_{a}\\\\,^{f} \\\\delta_{b}\\\\,^{g} \\\\delta_{h l}+\\\\frac{1}{2}R_{e}\\\\,^{g} R_{f g}\\\\,^{e a} \\\\delta_{a}\\\\,^{f} \\\\delta_{b}\\\\,^{h} \\\\delta_{h l}+\\\\frac{1}{2}R_{e}\\\\,^{h} R_{f g}\\\\,^{e a} \\\\delta_{a}\\\\,^{g} \\\\delta_{b}\\\\,^{f} \\\\delta_{h l} - \\\\frac{1}{2}R_{e}\\\\,^{g} R_{f g}\\\\,^{e a} \\\\delta_{a}\\\\,^{h} \\\\delta_{b}\\\\,^{f} \\\\delta_{h l} - \\\\frac{1}{2}R_{e}\\\\,^{f} R_{f g}\\\\,^{e a} \\\\delta_{a}\\\\,^{g} \\\\delta_{b}\\\\,^{h} \\\\delta_{h l}+\\\\frac{1}{2}R_{e}\\\\,^{f} R_{f g}\\\\,^{e a} \\\\delta_{a}\\\\,^{h} \\\\delta_{b}\\\\,^{g} \\\\delta_{h l}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"distribute(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\frac{1}{2}R_{a b}\\\\,^{f g} R_{f g l}\\\\,^{a}+\\\\frac{1}{2}R_{a b}\\\\,^{f}\\\\,_{l} R_{f}\\\\,^{a}+\\\\frac{1}{2}R_{a b}\\\\,^{g}\\\\,_{l} R_{g}\\\\,^{a}+\\\\frac{1}{2}R_{a}\\\\,^{g} R_{b g l}\\\\,^{a}+R_{a l} R_{b}\\\\,^{a} - \\\\frac{1}{2}R_{a}\\\\,^{f} R_{f b l}\\\\,^{a} - \\\\frac{1}{2}R_{a}\\\\,^{f} R_{f}\\\\,^{a} \\\\delta_{b l} - \\\\frac{1}{2}R_{a}\\\\,^{g} R_{g}\\\\,^{a} \\\\delta_{b l} - \\\\frac{1}{2}R_{a e}\\\\,^{g}\\\\,_{l} R_{b g}\\\\,^{e a}+\\\\frac{1}{2}R_{a e}\\\\,^{f}\\\\,_{l} R_{f b}\\\\,^{e a} - \\\\frac{1}{2}R_{a e}\\\\,^{f g} R_{f g}\\\\,^{e a} \\\\delta_{b l}+R_{b}\\\\,^{g} R_{g l} - \\\\frac{1}{2}R_{b l} R_{e}\\\\,^{e}+R_{b}\\\\,^{f} R_{f l} - \\\\frac{1}{2}R_{b l} R_{a}\\\\,^{a} - \\\\frac{1}{2}R_{g}\\\\,^{e} R_{b e}\\\\,^{g}\\\\,_{l} - \\\\frac{1}{2}R_{b e}\\\\,^{f}\\\\,_{l} R_{f}\\\\,^{e}+\\\\frac{1}{2}R_{b e}\\\\,^{f g} R_{f g}\\\\,^{e}\\\\,_{l}-R R_{b l}%\\n+\\\\frac{1}{4}R R_{e}\\\\,^{e} \\\\delta_{b l}+\\\\frac{1}{4}R R_{a}\\\\,^{a} \\\\delta_{b l}+R_{e l} R_{b}\\\\,^{e} - \\\\frac{1}{2}R_{e}\\\\,^{g} R_{g}\\\\,^{e} \\\\delta_{b l} - \\\\frac{1}{2}R_{e}\\\\,^{g} R_{b g}\\\\,^{e}\\\\,_{l} - \\\\frac{1}{2}R_{e}\\\\,^{f} R_{f}\\\\,^{e} \\\\delta_{b l}+\\\\frac{1}{2}R_{e}\\\\,^{f} R_{f b}\\\\,^{e}\\\\,_{l}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"eliminate_kronecker(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{} - \\\\frac{1}{2}R_{b}\\\\,^{a f g} R_{l a f g}+\\\\frac{1}{2}R_{a f} R_{b}\\\\,^{a}\\\\,_{l}\\\\,^{f}+\\\\frac{1}{2}R_{a g} R_{b}\\\\,^{a}\\\\,_{l}\\\\,^{g}+\\\\frac{1}{2}R^{a g} R_{b a l g}+R_{b}\\\\,^{a} R_{l a}+\\\\frac{1}{2}R^{a f} R_{b a l f} - \\\\frac{1}{2}R_{a f} R^{a f} \\\\delta_{b l} - \\\\frac{1}{2}R_{a g} R^{a g} \\\\delta_{b l} - \\\\frac{1}{2}R_{b}\\\\,^{a e g} R_{l a e g} - \\\\frac{1}{2}R_{b}\\\\,^{a e f} R_{l a e f}+\\\\frac{1}{2}R_{a e f g} R^{a e f g} \\\\delta_{b l}+R_{b}\\\\,^{g} R_{l g} - \\\\frac{1}{2}R_{b l} R+R_{b}\\\\,^{f} R_{l f} - \\\\frac{3}{2}R R_{b l}+R^{e g} R_{b e l g}+\\\\frac{1}{2}R_{e f} R_{b}\\\\,^{e}\\\\,_{l}\\\\,^{f} - \\\\frac{1}{2}R_{b}\\\\,^{e f g} R_{l e f g}+\\\\frac{1}{2}R R \\\\delta_{b l}%\\n+R_{b}\\\\,^{e} R_{l e} - \\\\frac{1}{2}R_{e g} R^{e g} \\\\delta_{b l} - \\\\frac{1}{2}R_{e f} R^{e f} \\\\delta_{b l}+\\\\frac{1}{2}R^{e f} R_{b e l f}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"canonicalise(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}-2R_{b}\\\\,^{a c d} R_{l a c d}+\\\\frac{3}{2}R_{a c} R_{b}\\\\,^{a}\\\\,_{l}\\\\,^{c}+\\\\frac{5}{2}R^{a c} R_{b a l c}+4R_{b}\\\\,^{a} R_{l a}-2R_{a c} R^{a c} \\\\delta_{b l}+\\\\frac{1}{2}R_{a c d e} R^{a c d e} \\\\delta_{b l}-2R R_{b l}+\\\\frac{1}{2}R R \\\\delta_{b l}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"rename_dummies(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}-2R_{b}\\\\,^{a c d} R_{l a c d}+4R^{a c} R_{b a l c}+4R_{b}\\\\,^{a} R_{l a}-2R_{a c} R^{a c} \\\\delta_{b l}+\\\\frac{1}{2}R_{a c d e} R^{a c d e} \\\\delta_{b l}-2R R_{b l}+\\\\frac{1}{2}R R \\\\delta_{b l}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"canonicalise(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}-2R_{b}\\\\,^{a c d} R_{l a c d}+4R^{a c} R_{b a l c}+4R_{b}\\\\,^{a} R_{l a}-2R R_{b l}+\\\\delta_{b l} \\\\left(-2R_{a c} R^{a c}+\\\\frac{1}{2}R_{a c d e} R^{a c d e}+\\\\frac{1}{2}R R\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"factor_out(_, $\\\\delta_{b l}$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1\n}\n"
  },
  {
    "path": "examples/nintegrate.cnb",
    "content": "{\n\t\"cell_id\": 8051754127212445684,\n\t\"cells\": [\n\t\t{\n\t\t\t\"cell_id\": 2931391241472840946,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"from cdb.graphics.plot import plot\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 13975185716264529983,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 18118323855584737614,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 6043849711601370921,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"A + \\\\int{(\\\\sin(x))**2 \\\\cos(\\\\pi x)}{{x, 0,  2/3 \\\\pi}} + B\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}A\\\\discretionary{}{}{}+\\\\int_{0\\\\,}^{\\\\frac{2}{3}\\\\,\\\\pi} {\\\\left(\\\\sin{x}\\\\right)}^{2\\\\,} \\\\cos\\\\left(\\\\pi x\\\\right)\\\\,\\\\,{\\\\rm d}x\\\\discretionary{}{}{}+B\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex:=A + \\\\int{\\\\sin(x)**2 \\\\cos(\\\\pi x)}{x,0,2/3\\\\pi} + B;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 14546848392773906838,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 17342733029827741368,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 12709660310964246116,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"A-0.0554932 + B\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}A\\\\discretionary{}{}{}-0.0554932\\\\,\\\\discretionary{}{}{}+B\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"nval(ex.copy());\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 16440894535807297616,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 2740567749694519304,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 17803805087820925012,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"(\\\\pi (4-(\\\\pi)**2) (A + B) -  3/4 (\\\\pi)**2 \\\\sin( 2/3 (\\\\pi)**2) + 2\\\\sin( 2/3 (\\\\pi)**2) +  1/2 \\\\sqrt(3) \\\\pi \\\\cos( 2/3 (\\\\pi)**2)) (\\\\pi (4-(\\\\pi)**2))**(-1)\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\left(\\\\pi \\\\left(4\\\\,\\\\discretionary{}{}{}-\\\\,{\\\\pi}^{2\\\\,}\\\\right) \\\\left(A\\\\discretionary{}{}{}+B\\\\right)\\\\discretionary{}{}{} - \\\\frac{3}{4}\\\\,{\\\\pi}^{2\\\\,} \\\\sin\\\\left(\\\\frac{2}{3}\\\\,{\\\\pi}^{2\\\\,}\\\\right)\\\\discretionary{}{}{}+2\\\\,\\\\sin\\\\left(\\\\frac{2}{3}\\\\,{\\\\pi}^{2\\\\,}\\\\right)\\\\discretionary{}{}{}+\\\\frac{1}{2}\\\\,\\\\sqrt{3\\\\,} \\\\pi \\\\cos\\\\left(\\\\frac{2}{3}\\\\,{\\\\pi}^{2\\\\,}\\\\right)\\\\right) {\\\\left(\\\\pi \\\\left(4\\\\,\\\\discretionary{}{}{}-\\\\,{\\\\pi}^{2\\\\,}\\\\right)\\\\right)}^{-\\\\,1}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"simplify(ex.copy());\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 1675088285994927682,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 5332288531556171852,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"verbatim\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}2.3463563791336464\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"nintegrate($\\\\abs(\\\\sin(x))$, {$x$: (0, 4)});\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 4936177558051148034,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 1610547645856147127,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 8905612121600026423,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 3283797457482985993,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"858**( 1/2 ) x (x-1)**5\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\sqrt{858\\\\,} x {\\\\left(x\\\\discretionary{}{}{}-\\\\,1\\\\right)}^{5\\\\,}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"phi(n):= \\\\sqrt{2} \\\\sin(x @(n) \\\\pi));\\nex    := \\\\sqrt{858} x (x-1)**5;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 11321697640771047903,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 18037986334033764963,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"$\\\\big[$$\\\\verb|-0.6224866550154421|$,\\\\discretionary{}{}{} $\\\\verb|-0.6547656078293627|$,\\\\discretionary{}{}{} $\\\\verb|-0.3701537588217539|$,\\\\discretionary{}{}{} $\\\\verb|-0.17702485011865277|$$\\\\big]$\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"cn = [nintegrate(phi(n) * ex, {$x$: (0, 1)}) for n in range(1,5)];\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 14374908308221553272,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 6283696119366076931,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"verbatim\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}0.9845592395978734\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"sum(c**2 for c in cn);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 15876348162803326487,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 155723929641301087,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"$\\\\big[$$-0.622487 \\\\sqrt{2\\\\,} \\\\sin\\\\left(x \\\\pi\\\\right)$,\\\\discretionary{}{}{} $-0.654766 \\\\sqrt{2\\\\,} \\\\sin\\\\left(2\\\\,x \\\\pi\\\\right)$,\\\\discretionary{}{}{} $-0.370154 \\\\sqrt{2\\\\,} \\\\sin\\\\left(3\\\\,x \\\\pi\\\\right)$,\\\\discretionary{}{}{} $-0.177025 \\\\sqrt{2\\\\,} \\\\sin\\\\left(4\\\\,x \\\\pi\\\\right)$$\\\\big]$\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"[Ex(cn[i-1]) * phi(i) for i in range(1,5)];\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 6126845228435655555,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"approx = Ex(0)\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 17831969859550202078,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 17237419944192970188,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 7392635822037708650,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"-0.622487 2**( 1/2 ) \\\\sin(x \\\\pi) + -0.654766 2**( 1/2 ) \\\\sin(2x \\\\pi) + -0.370154 2**( 1/2 ) \\\\sin(3x \\\\pi) + -0.177025 2**( 1/2 ) \\\\sin(4x \\\\pi)\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}-0.622487 \\\\sqrt{2\\\\,} \\\\sin\\\\left(x \\\\pi\\\\right)\\\\discretionary{}{}{}+-0.654766 \\\\sqrt{2\\\\,} \\\\sin\\\\left(2\\\\,x \\\\pi\\\\right)\\\\discretionary{}{}{}+-0.370154 \\\\sqrt{2\\\\,} \\\\sin\\\\left(3\\\\,x \\\\pi\\\\right)\\\\discretionary{}{}{}+-0.177025 \\\\sqrt{2\\\\,} \\\\sin\\\\left(4\\\\,x \\\\pi\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"for i in range(1,5):\\n   approx += Ex(cn[i-1]) * phi(i)\\napprox;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 5759033717931581555,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 16412685053038420359,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\section*{Basic evaluate}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\section*{Basic evaluate}\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 5492019440282277894,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 16539683725511946601,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 14520806591865121796,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"(-x)**( 1/2 )\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\sqrt{-x}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 2648626369669508240,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 5914944422784917035,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"1\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}[1.93634e-17 - 0.316228i, 2.73839e-17 - 0.447214i, 3.35383e-17 - 0.547723i]\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex:= \\\\sqrt(-x);\\nnevaluate(ex, {$x$: [0.1, 0.2, 0.3]});\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 17450870577901381309,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 3843471659787676211,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 6290463412817069437,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"1\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}[1.93634e-17 - 0.316228i, 2.73839e-17 - 0.447214i, 3.35383e-17 - 0.547723i]\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 2038738571753114116,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 3777555118990169184,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"output\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}{1}\\n\\n\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"print(tree(ex))\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 18054555599642648051,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 3442092987853239677,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 7489206703373326878,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"1\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}1\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex.copy();\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 6854314875014069650,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9714453434200925488,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"output\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}{1}\\n\\n\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"print(tree(ex))\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 9094128843997226060,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 15897755206676774417,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 13830739368032708840,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\sin(x) (-y)**( 1/2 )\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\sin{x} \\\\sqrt{-y}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 12823481624565641501,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 15542552330907628331,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"1\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}1\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex:= \\\\sin(x) \\\\sqrt(-y);\\nnevaluate(ex, {$x$: [0.1, 0.2, 0.3], $y$: [-0.2, -0.4]});\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 9564013552617521835,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 4218581402320880132,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 13334898660421544104,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"(-y)**( 1/2 )\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\sqrt{-y}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 15237353373470505432,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"verbatim\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}[[2.73839e-17 - 0.447214i, 3.87267e-17 - 0.632456i], [2.73839e-17 - 0.447214i, 3.87267e-17 - 0.632456i], [2.73839e-17 - 0.447214i, 3.87267e-17 - 0.632456i]]\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex:= \\\\sqrt(-y);\\nnevaluate(ex, {$x$: [0.1, 0.2, 0.3], $y$: [0.2, 0.4]});\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 8999525424784193788,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 15059727915456861206,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"The above should display the values.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"The above should display the values.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 5449713691475908791,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 10262884598638735702,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\subsection*{Basic integral}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\subsection*{Basic integral}\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 5162087654464530656,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 10979637231354350328,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 16044464667978039478,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"D E F + \\\\int{(\\\\sin(x))**2}{{x, 0, a}} + A B C\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}D E F\\\\discretionary{}{}{}+\\\\int_{0}^{a} {\\\\left(\\\\sin{x}\\\\right)}^{2}\\\\,\\\\,{\\\\rm d}x\\\\discretionary{}{}{}+A B C\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex:= D E F + \\\\int{ \\\\sin(x)**2 }{x, 0, a} + A B C;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 12014490083622660223,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 17418234012875626772,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 15105335754397677590,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \" ...  + \\\\int{(\\\\sin(x))**2}{{x, 0, a}} +  ... \"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{} \\\\ldots \\\\discretionary{}{}{}+\\\\int_{0}^{a} {\\\\left(\\\\sin{x}\\\\right)}^{2}\\\\,\\\\,{\\\\rm d}x\\\\discretionary{}{}{}+ \\\\ldots \\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"zoom(ex, $\\\\int{#}$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 1384911713275376326,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 11154618271273819641,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"Should the call below turn the expression into \\\\verb|DEF + NTensor(a) + ABC|? \"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"Should the call below turn the expression into \\\\verb|DEF + NTensor(a) + ABC|? \"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 18326899318170345646,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 13227009998421462577,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"error\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}RuntimeError: Value unknown for subtree with head D.\\n\\nAt:\\n  Notebook Cell (Line 1): _ = nevaluate(ex, {Ex('a', False): [1, 2, 3]})\\n\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"nevaluate(ex, {$a$: [1,2,3]});\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 9873173291472633947,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 16125733197646685804,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 1055904793355604851,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"c_{a} + \\\\int{(\\\\sin(x))**2}{{x, 0, a}} + d_{a}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}c_{a}\\\\discretionary{}{}{}+\\\\int_{0}^{a} {\\\\left(\\\\sin{x}\\\\right)}^{2}\\\\,\\\\,{\\\\rm d}x\\\\discretionary{}{}{}+d_{a}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"a::Symbol.\\nex:= c_{a} + \\\\int{ \\\\sin(x)**2 }{x, 0, a} + d_{a};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 4717554382451427067,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 4836667551544584392,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 3952429860820889302,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \" ...  + \\\\int{(\\\\sin(x))**2}{{x, 0, a}} +  ... \"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{} \\\\ldots \\\\discretionary{}{}{}+\\\\int_{0}^{a} {\\\\left(\\\\sin{x}\\\\right)}^{2}\\\\,\\\\,{\\\\rm d}x\\\\discretionary{}{}{}+ \\\\ldots \\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"zoom(ex, $\\\\int{#}$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 9963184012515097042,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 13521403040521131803,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"error\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}AttributeError: 'cadabra2.Ex' object has no attribute 'eval'\\n\\nAt:\\n  Notebook Cell (Line 1): _ = ex.eval()\\n\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex.eval();\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 3113154890928877587,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9216572187257208273,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 2185256517892902042,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"(A)**2 + (B)**2\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}{A}^{2}\\\\discretionary{}{}{}+{B}^{2}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 4234060308304748590,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 17499194072528103119,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"1 + (B)**2\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}1\\\\discretionary{}{}{}+{B}^{2}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9301435958211735584,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 7233973149586856348,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"1 + 2**2\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}1\\\\discretionary{}{}{}+{2}^{2}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"$A**2+B**2$;\\nsubstitute(_, $A=1$);\\nsubstitute(_, $B=2$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 6471804076682425243,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 8021868355304705738,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 13905799246688778147,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\subsection*{QM example}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\subsection*{QM example}\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 16863211061719007360,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 3347434996613403651,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property Symbol attached to~}n.\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"n::Symbol;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 17475731012768243081,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 6603658260302536190,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 8214933418196057274,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"c_{n} = \\\\int{\\\\phi_{n}(x) f(x)}{{x, 0, 1}}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}c_{n} = \\\\int_{0\\\\,}^{1} \\\\phi_{n}\\\\!\\\\left(x\\\\right) f\\\\left(x\\\\right)\\\\,\\\\,{\\\\rm d}x\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"coeffs := c_{n} = \\\\int{ \\\\phi_{n}(x) f(x) }{x, 0, 1};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 9430347704188686098,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 7260870698752645800,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 10269791103366778364,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\phi_{n}(x) = 2**( 1/2 ) \\\\sin(x n \\\\pi)\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\phi_{n}\\\\!\\\\left(x\\\\right) = \\\\sqrt{2\\\\,} \\\\sin\\\\left(x n \\\\pi\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"phin := \\\\phi_{n}(x) = \\\\sqrt{2} \\\\sin( x n \\\\pi );\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 6799162622394040722,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 16313872455528434491,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 4798693946065070146,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"f(x) = 858**( 1/2 ) x (x-1)**5\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}f\\\\left(x\\\\right) = \\\\sqrt{858\\\\,} x {\\\\left(x\\\\discretionary{}{}{}-\\\\,1\\\\right)}^{5\\\\,}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"f := f(x) = \\\\sqrt{858} x (x-1)**5;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 7239102288921320512,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 13033196473356063198,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 6274067749712215252,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"c_{n} = \\\\int{2**( 1/2 ) \\\\sin(x n \\\\pi) 858**( 1/2 ) x (x-1)**5}{{x, 0, 1}}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}c_{n} = \\\\int_{0\\\\,}^{1} \\\\sqrt{2\\\\,} \\\\sin\\\\left(x n \\\\pi\\\\right) \\\\sqrt{858\\\\,} x {\\\\left(x\\\\discretionary{}{}{}-\\\\,1\\\\right)}^{5\\\\,}\\\\,\\\\,{\\\\rm d}x\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"substitute(coeffs, join(phin, f));\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 16285999519670065508,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 595186206859359349,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 9802077612790741496,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"c_{1} = [-0.622487 + 3.81163e-16i]\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}c_{1} = -0.622487 + 3.81163 \\\\times 10^{-16}i\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 10053171280746494707,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 1455889606261866616,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"c_{2} = [-0.654766 + 4.00928e-16i]\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}c_{2\\\\,} = -0.654766 + 4.00928 \\\\times 10^{-16}i\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 1966914798927873315,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 214873960592455937,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"c_{3} = [-0.370154 + 2.26654e-16i]\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}c_{3\\\\,} = -0.370154 + 2.26654 \\\\times 10^{-16}i\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 7836603269911416148,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 13116965666178155284,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"c_{4} = -0.177025\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}c_{4\\\\,} = -0.177025\\\\,\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"for n in range(1,5):\\n   nval( substitute(coeffs.copy(), $n -> @(n), _{n} -> _{@(n)}$), {} );\\n   # nval(coeffs.copy(), {$n$: n});\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 10515578753319076783,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 14145725797530272103,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"The above would be shorter if we could do the lot with nval, and it would be faster, but does it make sense to make nval act on sub-expressions that do not fully evaluate, like the left-hand sides above?\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"The above would be shorter if we could do the lot with nval, and it would be faster, but does it make sense to make nval act on sub-expressions that do not fully evaluate, like the left-hand sides above?\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 12231632011440604227,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 4465267799687256926,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 8894142618069097779,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\Sigma_{i = 1}^{4} c_{i} \\\\phi_{i}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\Sigma_{i = 1}\\\\,^{4\\\\,} c_{i} \\\\phi_{i}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"approx := \\\\Sigma_{i=1}^{4} c_{i} \\\\phi_{i};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 11902034280760350495,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 15106911912947859857,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"image_svg\",\n\t\t\t\t\t\"source\": \"<?xml version="1.0" encoding="utf-8" standalone="no"?>
<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
  "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="460.8pt" height="345.6pt" viewBox="0 0 460.8 345.6" xmlns="http://www.w3.org/2000/svg" version="1.1">
 <metadata>
  <rdf:RDF xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:cc="http://creativecommons.org/ns#" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
   <cc:Work>
    <dc:type rdf:resource="http://purl.org/dc/dcmitype/StillImage"/>
    <dc:date>2025-03-10T19:43:49.845978</dc:date>
    <dc:format>image/svg+xml</dc:format>
    <dc:creator>
     <cc:Agent>
      <dc:title>Matplotlib v3.6.3, https://matplotlib.org/</dc:title>
     </cc:Agent>
    </dc:creator>
   </cc:Work>
  </rdf:RDF>
 </metadata>
 <defs>
  <style type="text/css">*{stroke-linejoin: round; stroke-linecap: butt}</style>
 </defs>
 <g id="figure_1">
  <g id="patch_1">
   <path d="M 0 345.6 
L 460.8 345.6 
L 460.8 0 
L 0 0 
z
" style="fill: #ffffff"/>
  </g>
  <g id="axes_1">
   <g id="patch_2">
    <path d="M 57.6 307.584 
L 414.72 307.584 
L 414.72 41.472 
L 57.6 41.472 
z
" style="fill: #ffffff"/>
   </g>
   <g id="matplotlib.axis_1">
    <g id="xtick_1">
     <g id="line2d_1">
      <defs>
       <path id="mf7a9ace6f6" d="M 0 0 
L 0 3.5 
" style="stroke: #000000; stroke-width: 0.8"/>
      </defs>
      <g>
       <use xlink:href="#mf7a9ace6f6" x="73.832727" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_1">
      <!-- 0.0 -->
      <g transform="translate(65.881165 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-30" d="M 2034 4250 
Q 1547 4250 1301 3770 
Q 1056 3291 1056 2328 
Q 1056 1369 1301 889 
Q 1547 409 2034 409 
Q 2525 409 2770 889 
Q 3016 1369 3016 2328 
Q 3016 3291 2770 3770 
Q 2525 4250 2034 4250 
z
M 2034 4750 
Q 2819 4750 3233 4129 
Q 3647 3509 3647 2328 
Q 3647 1150 3233 529 
Q 2819 -91 2034 -91 
Q 1250 -91 836 529 
Q 422 1150 422 2328 
Q 422 3509 836 4129 
Q 1250 4750 2034 4750 
z
" transform="scale(0.015625)"/>
        <path id="DejaVuSans-2e" d="M 684 794 
L 1344 794 
L 1344 0 
L 684 0 
L 684 794 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-30"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-30" x="95.410156"/>
      </g>
     </g>
    </g>
    <g id="xtick_2">
     <g id="line2d_2">
      <g>
       <use xlink:href="#mf7a9ace6f6" x="138.763636" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_2">
      <!-- 0.2 -->
      <g transform="translate(130.812074 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-32" d="M 1228 531 
L 3431 531 
L 3431 0 
L 469 0 
L 469 531 
Q 828 903 1448 1529 
Q 2069 2156 2228 2338 
Q 2531 2678 2651 2914 
Q 2772 3150 2772 3378 
Q 2772 3750 2511 3984 
Q 2250 4219 1831 4219 
Q 1534 4219 1204 4116 
Q 875 4013 500 3803 
L 500 4441 
Q 881 4594 1212 4672 
Q 1544 4750 1819 4750 
Q 2544 4750 2975 4387 
Q 3406 4025 3406 3419 
Q 3406 3131 3298 2873 
Q 3191 2616 2906 2266 
Q 2828 2175 2409 1742 
Q 1991 1309 1228 531 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-30"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-32" x="95.410156"/>
      </g>
     </g>
    </g>
    <g id="xtick_3">
     <g id="line2d_3">
      <g>
       <use xlink:href="#mf7a9ace6f6" x="203.694545" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_3">
      <!-- 0.4 -->
      <g transform="translate(195.742983 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-34" d="M 2419 4116 
L 825 1625 
L 2419 1625 
L 2419 4116 
z
M 2253 4666 
L 3047 4666 
L 3047 1625 
L 3713 1625 
L 3713 1100 
L 3047 1100 
L 3047 0 
L 2419 0 
L 2419 1100 
L 313 1100 
L 313 1709 
L 2253 4666 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-30"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-34" x="95.410156"/>
      </g>
     </g>
    </g>
    <g id="xtick_4">
     <g id="line2d_4">
      <g>
       <use xlink:href="#mf7a9ace6f6" x="268.625455" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_4">
      <!-- 0.6 -->
      <g transform="translate(260.673892 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-36" d="M 2113 2584 
Q 1688 2584 1439 2293 
Q 1191 2003 1191 1497 
Q 1191 994 1439 701 
Q 1688 409 2113 409 
Q 2538 409 2786 701 
Q 3034 994 3034 1497 
Q 3034 2003 2786 2293 
Q 2538 2584 2113 2584 
z
M 3366 4563 
L 3366 3988 
Q 3128 4100 2886 4159 
Q 2644 4219 2406 4219 
Q 1781 4219 1451 3797 
Q 1122 3375 1075 2522 
Q 1259 2794 1537 2939 
Q 1816 3084 2150 3084 
Q 2853 3084 3261 2657 
Q 3669 2231 3669 1497 
Q 3669 778 3244 343 
Q 2819 -91 2113 -91 
Q 1303 -91 875 529 
Q 447 1150 447 2328 
Q 447 3434 972 4092 
Q 1497 4750 2381 4750 
Q 2619 4750 2861 4703 
Q 3103 4656 3366 4563 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-30"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-36" x="95.410156"/>
      </g>
     </g>
    </g>
    <g id="xtick_5">
     <g id="line2d_5">
      <g>
       <use xlink:href="#mf7a9ace6f6" x="333.556364" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_5">
      <!-- 0.8 -->
      <g transform="translate(325.604801 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-38" d="M 2034 2216 
Q 1584 2216 1326 1975 
Q 1069 1734 1069 1313 
Q 1069 891 1326 650 
Q 1584 409 2034 409 
Q 2484 409 2743 651 
Q 3003 894 3003 1313 
Q 3003 1734 2745 1975 
Q 2488 2216 2034 2216 
z
M 1403 2484 
Q 997 2584 770 2862 
Q 544 3141 544 3541 
Q 544 4100 942 4425 
Q 1341 4750 2034 4750 
Q 2731 4750 3128 4425 
Q 3525 4100 3525 3541 
Q 3525 3141 3298 2862 
Q 3072 2584 2669 2484 
Q 3125 2378 3379 2068 
Q 3634 1759 3634 1313 
Q 3634 634 3220 271 
Q 2806 -91 2034 -91 
Q 1263 -91 848 271 
Q 434 634 434 1313 
Q 434 1759 690 2068 
Q 947 2378 1403 2484 
z
M 1172 3481 
Q 1172 3119 1398 2916 
Q 1625 2713 2034 2713 
Q 2441 2713 2670 2916 
Q 2900 3119 2900 3481 
Q 2900 3844 2670 4047 
Q 2441 4250 2034 4250 
Q 1625 4250 1398 4047 
Q 1172 3844 1172 3481 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-30"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-38" x="95.410156"/>
      </g>
     </g>
    </g>
    <g id="xtick_6">
     <g id="line2d_6">
      <g>
       <use xlink:href="#mf7a9ace6f6" x="398.487273" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_6">
      <!-- 1.0 -->
      <g transform="translate(390.53571 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-31" d="M 794 531 
L 1825 531 
L 1825 4091 
L 703 3866 
L 703 4441 
L 1819 4666 
L 2450 4666 
L 2450 531 
L 3481 531 
L 3481 0 
L 794 0 
L 794 531 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-31"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-30" x="95.410156"/>
      </g>
     </g>
    </g>
   </g>
   <g id="matplotlib.axis_2">
    <g id="ytick_1">
     <g id="line2d_7">
      <defs>
       <path id="mcebb79ac0a" d="M 0 0 
L -3.5 0 
" style="stroke: #000000; stroke-width: 0.8"/>
      </defs>
      <g>
       <use xlink:href="#mcebb79ac0a" x="57.6" y="290.624501" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_7">
      <!-- −2.0 -->
      <g transform="translate(26.317187 294.42372) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-2212" d="M 678 2272 
L 4684 2272 
L 4684 1741 
L 678 1741 
L 678 2272 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-2212"/>
       <use xlink:href="#DejaVuSans-32" x="83.789062"/>
       <use xlink:href="#DejaVuSans-2e" x="147.412109"/>
       <use xlink:href="#DejaVuSans-30" x="179.199219"/>
      </g>
     </g>
    </g>
    <g id="ytick_2">
     <g id="line2d_8">
      <g>
       <use xlink:href="#mcebb79ac0a" x="57.6" y="233.83963" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_8">
      <!-- −1.5 -->
      <g transform="translate(26.317187 237.638849) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-35" d="M 691 4666 
L 3169 4666 
L 3169 4134 
L 1269 4134 
L 1269 2991 
Q 1406 3038 1543 3061 
Q 1681 3084 1819 3084 
Q 2600 3084 3056 2656 
Q 3513 2228 3513 1497 
Q 3513 744 3044 326 
Q 2575 -91 1722 -91 
Q 1428 -91 1123 -41 
Q 819 9 494 109 
L 494 744 
Q 775 591 1075 516 
Q 1375 441 1709 441 
Q 2250 441 2565 725 
Q 2881 1009 2881 1497 
Q 2881 1984 2565 2268 
Q 2250 2553 1709 2553 
Q 1456 2553 1204 2497 
Q 953 2441 691 2322 
L 691 4666 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-2212"/>
       <use xlink:href="#DejaVuSans-31" x="83.789062"/>
       <use xlink:href="#DejaVuSans-2e" x="147.412109"/>
       <use xlink:href="#DejaVuSans-35" x="179.199219"/>
      </g>
     </g>
    </g>
    <g id="ytick_3">
     <g id="line2d_9">
      <g>
       <use xlink:href="#mcebb79ac0a" x="57.6" y="177.054759" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_9">
      <!-- −1.0 -->
      <g transform="translate(26.317187 180.853978) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-2212"/>
       <use xlink:href="#DejaVuSans-31" x="83.789062"/>
       <use xlink:href="#DejaVuSans-2e" x="147.412109"/>
       <use xlink:href="#DejaVuSans-30" x="179.199219"/>
      </g>
     </g>
    </g>
    <g id="ytick_4">
     <g id="line2d_10">
      <g>
       <use xlink:href="#mcebb79ac0a" x="57.6" y="120.269888" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_10">
      <!-- −0.5 -->
      <g transform="translate(26.317187 124.069106) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-2212"/>
       <use xlink:href="#DejaVuSans-30" x="83.789062"/>
       <use xlink:href="#DejaVuSans-2e" x="147.412109"/>
       <use xlink:href="#DejaVuSans-35" x="179.199219"/>
      </g>
     </g>
    </g>
    <g id="ytick_5">
     <g id="line2d_11">
      <g>
       <use xlink:href="#mcebb79ac0a" x="57.6" y="63.485016" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_11">
      <!-- 0.0 -->
      <g transform="translate(34.696875 67.284235) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-30"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-30" x="95.410156"/>
      </g>
     </g>
    </g>
   </g>
   <g id="line2d_12">
    <path d="M 73.832727 63.485016 
L 77.112066 95.424324 
L 80.391405 124.170356 
L 83.670744 149.916613 
L 86.950083 172.848701 
L 90.229421 193.14453 
L 93.50876 210.974519 
L 96.788099 226.50179 
L 100.067438 239.88237 
L 103.346777 251.265379 
L 106.626116 260.793224 
L 109.905455 268.601784 
L 113.184793 274.8206 
L 116.464132 279.573054 
L 119.743471 282.976554 
L 123.02281 285.142708 
L 126.302149 286.177502 
L 129.581488 286.18147 
L 132.860826 285.249869 
L 136.140165 283.472845 
L 139.419504 280.935596 
L 142.698843 277.718537 
L 145.978182 273.897462 
L 149.257521 269.543697 
L 152.53686 264.72426 
L 155.816198 259.50201 
L 159.095537 253.935801 
L 162.374876 248.080624 
L 165.654215 241.987759 
L 168.933554 235.704909 
L 172.212893 229.27635 
L 175.492231 222.743059 
L 178.77157 216.142855 
L 182.050909 209.510527 
L 185.330248 202.877969 
L 188.609587 196.274301 
L 191.888926 189.725999 
L 195.168264 183.257013 
L 198.447603 176.88889 
L 201.726942 170.640889 
L 205.006281 164.530095 
L 208.28562 158.571534 
L 211.564959 152.778278 
L 214.844298 147.161555 
L 218.123636 141.730854 
L 221.402975 136.494021 
L 224.682314 131.457368 
L 227.961653 126.62576 
L 231.240992 122.002715 
L 234.520331 117.590492 
L 237.799669 113.390184 
L 241.079008 109.401802 
L 244.358347 105.624358 
L 247.637686 102.055949 
L 250.917025 98.693834 
L 254.196364 95.534511 
L 257.475702 92.573791 
L 260.755041 89.806867 
L 264.03438 87.228388 
L 267.313719 84.83252 
L 270.593058 82.613009 
L 273.872397 80.563249 
L 277.151736 78.676333 
L 280.431074 76.945113 
L 283.710413 75.36225 
L 286.989752 73.920271 
L 290.269091 72.611611 
L 293.54843 71.428661 
L 296.827769 70.363813 
L 300.107107 69.4095 
L 303.386446 68.55823 
L 306.665785 67.802628 
L 309.945124 67.135467 
L 313.224463 66.549693 
L 316.503802 66.038464 
L 319.78314 65.595163 
L 323.062479 65.213431 
L 326.341818 64.887182 
L 329.621157 64.610622 
L 332.900496 64.378265 
L 336.179835 64.184944 
L 339.459174 64.025824 
L 342.738512 63.896406 
L 346.017851 63.792536 
L 349.29719 63.710404 
L 352.576529 63.646547 
L 355.855868 63.597843 
L 359.135207 63.561509 
L 362.414545 63.535094 
L 365.693884 63.516464 
L 368.973223 63.503794 
L 372.252562 63.495553 
L 375.531901 63.49048 
L 378.81124 63.487572 
L 382.090579 63.486054 
L 385.369917 63.48536 
L 388.649256 63.485099 
L 391.928595 63.485027 
L 395.207934 63.485017 
L 398.487273 63.485016 
" clip-path="url(#pc4eb40fb86)" style="fill: none; stroke: #1f77b4; stroke-width: 1.5; stroke-linecap: square"/>
   </g>
   <g id="line2d_13">
    <path d="M 73.832727 63.485016 
L 77.112066 82.577505 
L 80.391405 101.530849 
L 83.670744 120.207414 
L 86.950083 138.472554 
L 90.229421 156.19607 
L 93.50876 173.253591 
L 96.788099 189.527896 
L 100.067438 204.91013 
L 103.346777 219.300924 
L 106.626116 232.611379 
L 109.905455 244.763931 
L 113.184793 255.693056 
L 116.464132 265.345836 
L 119.743471 273.682352 
L 123.02281 280.675927 
L 126.302149 286.313192 
L 129.581488 290.593997 
L 132.860826 293.531155 
L 136.140165 295.150035 
L 139.419504 295.488 
L 142.698843 294.593709 
L 145.978182 292.526292 
L 149.257521 289.354407 
L 152.53686 285.155197 
L 155.816198 280.01316 
L 159.095537 274.018951 
L 162.374876 267.268135 
L 165.654215 259.859902 
L 168.933554 251.895766 
L 172.212893 243.478276 
L 175.492231 234.709731 
L 178.77157 225.690951 
L 182.050909 216.520089 
L 185.330248 207.291516 
L 188.609587 198.094794 
L 191.888926 189.01374 
L 195.168264 180.125601 
L 198.447603 171.500347 
L 201.726942 163.200081 
L 205.006281 155.278591 
L 208.28562 147.781022 
L 211.564959 140.743694 
L 214.844298 134.194048 
L 218.123636 128.150722 
L 221.402975 122.623758 
L 224.682314 117.614928 
L 227.961653 113.11817 
L 231.240992 109.120124 
L 234.520331 105.600769 
L 237.799669 102.534125 
L 241.079008 99.889033 
L 244.358347 97.629974 
L 247.637686 95.71794 
L 250.917025 94.111309 
L 254.196364 92.766742 
L 257.475702 91.640064 
L 260.755041 90.687127 
L 264.03438 89.864633 
L 267.313719 89.130913 
L 270.593058 88.446642 
L 273.872397 87.77549 
L 277.151736 87.084685 
L 280.431074 86.345494 
L 283.710413 85.53361 
L 286.989752 84.629443 
L 290.269091 83.618309 
L 293.54843 82.490521 
L 296.827769 81.241375 
L 300.107107 79.871049 
L 303.386446 78.384401 
L 306.665785 76.790684 
L 309.945124 75.103182 
L 313.224463 73.338775 
L 316.503802 71.51744 
L 319.78314 69.661707 
L 323.062479 67.796072 
L 326.341818 65.946381 
L 329.621157 64.139205 
L 332.900496 62.401206 
L 336.179835 60.758512 
L 339.459174 59.236117 
L 342.738512 57.857312 
L 346.017851 56.64315 
L 349.29719 55.611981 
L 352.576529 54.779024 
L 355.855868 54.156031 
L 359.135207 53.751002 
L 362.414545 53.568 
L 365.693884 53.607028 
L 368.973223 53.864001 
L 372.252562 54.3308 
L 375.531901 54.995398 
L 378.81124 55.842077 
L 382.090579 56.851709 
L 385.369917 58.002105 
L 388.649256 59.268433 
L 391.928595 60.623677 
L 395.207934 62.039147 
L 398.487273 63.485016 
" clip-path="url(#pc4eb40fb86)" style="fill: none; stroke: #ff7f0e; stroke-width: 1.5; stroke-linecap: square"/>
   </g>
   <g id="patch_3">
    <path d="M 57.6 307.584 
L 57.6 41.472 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
   <g id="patch_4">
    <path d="M 414.72 307.584 
L 414.72 41.472 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
   <g id="patch_5">
    <path d="M 57.6 307.584 
L 414.72 307.584 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
   <g id="patch_6">
    <path d="M 57.6 41.472 
L 414.72 41.472 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
  </g>
 </g>
 <defs>
  <clipPath id="pc4eb40fb86">
   <rect x="57.6" y="41.472" width="357.12" height="266.112"/>
  </clipPath>
 </defs>
</svg>
\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"plot([Re(ex), Re(approx)], {$x$: (0,1)});\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 6638988550985815943,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 6417084589674135123,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"error\",\n\t\t\t\t\t\"source\": \"{\\\\color{red}{\\\\begin{verbatim}TypeError: unsupported operand type(s) for +: 'int' and 'cadabra2.Ex'\\n\\nAt:\\n  Notebook Cell (Line 1): approx = sum((Ex(cn[i - 1]) * ex for i in range(1, 4)))\\n\\\\end{verbatim}}}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"approx = sum(Ex(cn[i-1]) * ex for i in range(1,4))\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 15386486392948455785,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9365916491336435565,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 6825797584138565871,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"-0.622487 2**( 1/2 ) \\\\sin(x \\\\pi) 858**( 1/2 ) x (x-1)**5\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}-0.622487 \\\\sqrt{2} \\\\sin\\\\left(x \\\\pi\\\\right) \\\\sqrt{858} x {\\\\left(x\\\\discretionary{}{}{}-1\\\\right)}^{5}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"sol = Ex(cn[0]) * ex(1);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 3298289353320551968,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 5524457616137074309,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"verbatim\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}4.5\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"nintegrate($x**2 y$, {$y$: 1/2, $x$: (0, 3)});\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 13275781745521193411,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"\"\n\t\t}\n\t],\n\t\"description\": \"Cadabra JSON notebook format\",\n\t\"flags\": {\n\t\t\"hide_input_cells\": false\n\t},\n\t\"version\": 1.0\n}\n"
  },
  {
    "path": "examples/numerics.cnb",
    "content": "{\n\t\"cell_id\": 751520650258365731,\n\t\"cells\": [\n\t\t{\n\t\t\t\"cell_id\": 18032559207565559019,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"import numpy as np\\nimport matplotlib.pyplot as plt\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 1287114047286213846,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 692672026591266146,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 17543236372422490929,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"(x)**( 1/2 ) \\\\cos(3x)\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\sqrt{x} \\\\cos\\\\left(3\\\\,x\\\\right)\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 4196114612645572766,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 630039793602204380,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"10\\\\exp(-(x)**2)\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}10\\\\,\\\\exp\\\\left(-\\\\,{x}^{2\\\\,}\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex := x**(1/2) \\\\cos(3 x) ;\\nex2:= 10\\\\exp(-x**2);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 222680480077732576,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"xv  = np.linspace(0, np.pi*2, 100)\\nexv = np.array( nevaluate(ex,  {$x$: xv} ) )\\nexv2= np.array( nevaluate(ex2, {$x$: xv} ))\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 13031088175072566041,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 15191098792231308563,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"image_svg\",\n\t\t\t\t\t\"source\": \"<?xml version="1.0" encoding="utf-8" standalone="no"?>
<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
  "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="460.8pt" height="345.6pt" viewBox="0 0 460.8 345.6" xmlns="http://www.w3.org/2000/svg" version="1.1">
 <metadata>
  <rdf:RDF xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:cc="http://creativecommons.org/ns#" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
   <cc:Work>
    <dc:type rdf:resource="http://purl.org/dc/dcmitype/StillImage"/>
    <dc:date>2025-03-17T10:07:09.018016</dc:date>
    <dc:format>image/svg+xml</dc:format>
    <dc:creator>
     <cc:Agent>
      <dc:title>Matplotlib v3.6.3, https://matplotlib.org/</dc:title>
     </cc:Agent>
    </dc:creator>
   </cc:Work>
  </rdf:RDF>
 </metadata>
 <defs>
  <style type="text/css">*{stroke-linejoin: round; stroke-linecap: butt}</style>
 </defs>
 <g id="figure_1">
  <g id="patch_1">
   <path d="M 0 345.6 
L 460.8 345.6 
L 460.8 0 
L 0 0 
z
" style="fill: #ffffff"/>
  </g>
  <g id="axes_1">
   <g id="patch_2">
    <path d="M 57.6 307.584 
L 414.72 307.584 
L 414.72 41.472 
L 57.6 41.472 
z
" style="fill: #ffffff"/>
   </g>
   <g id="matplotlib.axis_1">
    <g id="xtick_1">
     <g id="line2d_1">
      <defs>
       <path id="m354e9c3c6d" d="M 0 0 
L 0 3.5 
" style="stroke: #000000; stroke-width: 0.8"/>
      </defs>
      <g>
       <use xlink:href="#m354e9c3c6d" x="73.832727" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_1">
      <!-- 0 -->
      <g transform="translate(70.651477 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-30" d="M 2034 4250 
Q 1547 4250 1301 3770 
Q 1056 3291 1056 2328 
Q 1056 1369 1301 889 
Q 1547 409 2034 409 
Q 2525 409 2770 889 
Q 3016 1369 3016 2328 
Q 3016 3291 2770 3770 
Q 2525 4250 2034 4250 
z
M 2034 4750 
Q 2819 4750 3233 4129 
Q 3647 3509 3647 2328 
Q 3647 1150 3233 529 
Q 2819 -91 2034 -91 
Q 1250 -91 836 529 
Q 422 1150 422 2328 
Q 422 3509 836 4129 
Q 1250 4750 2034 4750 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-30"/>
      </g>
     </g>
    </g>
    <g id="xtick_2">
     <g id="line2d_2">
      <g>
       <use xlink:href="#m354e9c3c6d" x="125.503103" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_2">
      <!-- 1 -->
      <g transform="translate(122.321853 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-31" d="M 794 531 
L 1825 531 
L 1825 4091 
L 703 3866 
L 703 4441 
L 1819 4666 
L 2450 4666 
L 2450 531 
L 3481 531 
L 3481 0 
L 794 0 
L 794 531 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-31"/>
      </g>
     </g>
    </g>
    <g id="xtick_3">
     <g id="line2d_3">
      <g>
       <use xlink:href="#m354e9c3c6d" x="177.173479" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_3">
      <!-- 2 -->
      <g transform="translate(173.992229 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-32" d="M 1228 531 
L 3431 531 
L 3431 0 
L 469 0 
L 469 531 
Q 828 903 1448 1529 
Q 2069 2156 2228 2338 
Q 2531 2678 2651 2914 
Q 2772 3150 2772 3378 
Q 2772 3750 2511 3984 
Q 2250 4219 1831 4219 
Q 1534 4219 1204 4116 
Q 875 4013 500 3803 
L 500 4441 
Q 881 4594 1212 4672 
Q 1544 4750 1819 4750 
Q 2544 4750 2975 4387 
Q 3406 4025 3406 3419 
Q 3406 3131 3298 2873 
Q 3191 2616 2906 2266 
Q 2828 2175 2409 1742 
Q 1991 1309 1228 531 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-32"/>
      </g>
     </g>
    </g>
    <g id="xtick_4">
     <g id="line2d_4">
      <g>
       <use xlink:href="#m354e9c3c6d" x="228.843854" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_4">
      <!-- 3 -->
      <g transform="translate(225.662604 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-33" d="M 2597 2516 
Q 3050 2419 3304 2112 
Q 3559 1806 3559 1356 
Q 3559 666 3084 287 
Q 2609 -91 1734 -91 
Q 1441 -91 1130 -33 
Q 819 25 488 141 
L 488 750 
Q 750 597 1062 519 
Q 1375 441 1716 441 
Q 2309 441 2620 675 
Q 2931 909 2931 1356 
Q 2931 1769 2642 2001 
Q 2353 2234 1838 2234 
L 1294 2234 
L 1294 2753 
L 1863 2753 
Q 2328 2753 2575 2939 
Q 2822 3125 2822 3475 
Q 2822 3834 2567 4026 
Q 2313 4219 1838 4219 
Q 1578 4219 1281 4162 
Q 984 4106 628 3988 
L 628 4550 
Q 988 4650 1302 4700 
Q 1616 4750 1894 4750 
Q 2613 4750 3031 4423 
Q 3450 4097 3450 3541 
Q 3450 3153 3228 2886 
Q 3006 2619 2597 2516 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-33"/>
      </g>
     </g>
    </g>
    <g id="xtick_5">
     <g id="line2d_5">
      <g>
       <use xlink:href="#m354e9c3c6d" x="280.51423" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_5">
      <!-- 4 -->
      <g transform="translate(277.33298 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-34" d="M 2419 4116 
L 825 1625 
L 2419 1625 
L 2419 4116 
z
M 2253 4666 
L 3047 4666 
L 3047 1625 
L 3713 1625 
L 3713 1100 
L 3047 1100 
L 3047 0 
L 2419 0 
L 2419 1100 
L 313 1100 
L 313 1709 
L 2253 4666 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-34"/>
      </g>
     </g>
    </g>
    <g id="xtick_6">
     <g id="line2d_6">
      <g>
       <use xlink:href="#m354e9c3c6d" x="332.184606" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_6">
      <!-- 5 -->
      <g transform="translate(329.003356 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-35" d="M 691 4666 
L 3169 4666 
L 3169 4134 
L 1269 4134 
L 1269 2991 
Q 1406 3038 1543 3061 
Q 1681 3084 1819 3084 
Q 2600 3084 3056 2656 
Q 3513 2228 3513 1497 
Q 3513 744 3044 326 
Q 2575 -91 1722 -91 
Q 1428 -91 1123 -41 
Q 819 9 494 109 
L 494 744 
Q 775 591 1075 516 
Q 1375 441 1709 441 
Q 2250 441 2565 725 
Q 2881 1009 2881 1497 
Q 2881 1984 2565 2268 
Q 2250 2553 1709 2553 
Q 1456 2553 1204 2497 
Q 953 2441 691 2322 
L 691 4666 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-35"/>
      </g>
     </g>
    </g>
    <g id="xtick_7">
     <g id="line2d_7">
      <g>
       <use xlink:href="#m354e9c3c6d" x="383.854982" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_7">
      <!-- 6 -->
      <g transform="translate(380.673732 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-36" d="M 2113 2584 
Q 1688 2584 1439 2293 
Q 1191 2003 1191 1497 
Q 1191 994 1439 701 
Q 1688 409 2113 409 
Q 2538 409 2786 701 
Q 3034 994 3034 1497 
Q 3034 2003 2786 2293 
Q 2538 2584 2113 2584 
z
M 3366 4563 
L 3366 3988 
Q 3128 4100 2886 4159 
Q 2644 4219 2406 4219 
Q 1781 4219 1451 3797 
Q 1122 3375 1075 2522 
Q 1259 2794 1537 2939 
Q 1816 3084 2150 3084 
Q 2853 3084 3261 2657 
Q 3669 2231 3669 1497 
Q 3669 778 3244 343 
Q 2819 -91 2113 -91 
Q 1303 -91 875 529 
Q 447 1150 447 2328 
Q 447 3434 972 4092 
Q 1497 4750 2381 4750 
Q 2619 4750 2861 4703 
Q 3103 4656 3366 4563 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-36"/>
      </g>
     </g>
    </g>
   </g>
   <g id="matplotlib.axis_2">
    <g id="ytick_1">
     <g id="line2d_8">
      <defs>
       <path id="m9b4d5303df" d="M 0 0 
L -3.5 0 
" style="stroke: #000000; stroke-width: 0.8"/>
      </defs>
      <g>
       <use xlink:href="#m9b4d5303df" x="57.6" y="289.880328" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_8">
      <!-- −2 -->
      <g transform="translate(35.857813 293.679547) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-2212" d="M 678 2272 
L 4684 2272 
L 4684 1741 
L 678 1741 
L 678 2272 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-2212"/>
       <use xlink:href="#DejaVuSans-32" x="83.789062"/>
      </g>
     </g>
    </g>
    <g id="ytick_2">
     <g id="line2d_9">
      <g>
       <use xlink:href="#m9b4d5303df" x="57.6" y="250.49494" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_9">
      <!-- 0 -->
      <g transform="translate(44.2375 254.294159) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-30"/>
      </g>
     </g>
    </g>
    <g id="ytick_3">
     <g id="line2d_10">
      <g>
       <use xlink:href="#m9b4d5303df" x="57.6" y="211.109552" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_10">
      <!-- 2 -->
      <g transform="translate(44.2375 214.908771) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-32"/>
      </g>
     </g>
    </g>
    <g id="ytick_4">
     <g id="line2d_11">
      <g>
       <use xlink:href="#m9b4d5303df" x="57.6" y="171.724164" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_11">
      <!-- 4 -->
      <g transform="translate(44.2375 175.523383) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-34"/>
      </g>
     </g>
    </g>
    <g id="ytick_5">
     <g id="line2d_12">
      <g>
       <use xlink:href="#m9b4d5303df" x="57.6" y="132.338776" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_12">
      <!-- 6 -->
      <g transform="translate(44.2375 136.137995) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-36"/>
      </g>
     </g>
    </g>
    <g id="ytick_6">
     <g id="line2d_13">
      <g>
       <use xlink:href="#m9b4d5303df" x="57.6" y="92.953388" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_13">
      <!-- 8 -->
      <g transform="translate(44.2375 96.752607) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-38" d="M 2034 2216 
Q 1584 2216 1326 1975 
Q 1069 1734 1069 1313 
Q 1069 891 1326 650 
Q 1584 409 2034 409 
Q 2484 409 2743 651 
Q 3003 894 3003 1313 
Q 3003 1734 2745 1975 
Q 2488 2216 2034 2216 
z
M 1403 2484 
Q 997 2584 770 2862 
Q 544 3141 544 3541 
Q 544 4100 942 4425 
Q 1341 4750 2034 4750 
Q 2731 4750 3128 4425 
Q 3525 4100 3525 3541 
Q 3525 3141 3298 2862 
Q 3072 2584 2669 2484 
Q 3125 2378 3379 2068 
Q 3634 1759 3634 1313 
Q 3634 634 3220 271 
Q 2806 -91 2034 -91 
Q 1263 -91 848 271 
Q 434 634 434 1313 
Q 434 1759 690 2068 
Q 947 2378 1403 2484 
z
M 1172 3481 
Q 1172 3119 1398 2916 
Q 1625 2713 2034 2713 
Q 2441 2713 2670 2916 
Q 2900 3119 2900 3481 
Q 2900 3844 2670 4047 
Q 2441 4250 2034 4250 
Q 1625 4250 1398 4047 
Q 1172 3844 1172 3481 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-38"/>
      </g>
     </g>
    </g>
    <g id="ytick_7">
     <g id="line2d_14">
      <g>
       <use xlink:href="#m9b4d5303df" x="57.6" y="53.568" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_14">
      <!-- 10 -->
      <g transform="translate(37.875 57.367219) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-31"/>
       <use xlink:href="#DejaVuSans-30" x="63.623047"/>
      </g>
     </g>
    </g>
   </g>
   <g id="line2d_15">
    <path d="M 73.832727 250.49494 
L 77.112066 245.623499 
L 80.391405 243.981467 
L 83.670744 243.26616 
L 86.950083 243.313915 
L 90.229421 244.060169 
L 93.50876 245.446755 
L 96.788099 247.40041 
L 100.067438 249.827266 
L 103.346777 252.613052 
L 106.626116 255.626099 
L 109.905455 258.721984 
L 113.184793 261.749203 
L 116.464132 264.555448 
L 119.743471 266.994139 
L 123.02281 268.930864 
L 126.302149 270.24946 
L 129.581488 270.857433 
L 132.860826 270.690482 
L 136.140165 269.715925 
L 139.419504 267.934854 
L 142.698843 265.38293 
L 145.978182 262.129737 
L 149.257521 258.276728 
L 152.53686 253.953802 
L 155.816198 249.314648 
L 159.095537 244.531013 
L 162.374876 239.786122 
L 165.654215 235.267493 
L 168.933554 231.159437 
L 172.212893 227.635531 
L 175.492231 224.851372 
L 178.77157 222.93791 
L 182.050909 221.995624 
L 185.330248 222.089803 
L 188.609587 223.247129 
L 191.888926 225.453712 
L 195.168264 228.654704 
L 198.447603 232.755501 
L 201.726942 237.624542 
L 205.006281 243.097599 
L 208.28562 248.983429 
L 211.564959 255.070585 
L 214.844298 261.135138 
L 218.123636 266.949028 
L 221.402975 272.288726 
L 224.682314 276.94388 
L 227.961653 280.725609 
L 231.240992 283.474123 
L 234.520331 285.06535 
L 237.799669 285.416327 
L 241.079008 284.489103 
L 244.358347 282.292991 
L 247.637686 278.885064 
L 250.917025 274.368836 
L 254.196364 268.891169 
L 257.475702 262.637479 
L 260.755041 255.825405 
L 264.03438 248.697173 
L 267.313719 241.510901 
L 270.593058 234.531177 
L 273.872397 228.019252 
L 277.151736 222.223215 
L 280.431074 217.368509 
L 283.710413 213.649174 
L 286.989752 211.220129 
L 290.269091 210.190821 
L 293.54843 210.620479 
L 296.827769 212.515194 
L 300.107107 215.82693 
L 303.386446 220.454555 
L 306.665785 226.246866 
L 309.945124 233.007513 
L 313.224463 240.501683 
L 316.503802 248.464289 
L 319.78314 256.609402 
L 323.062479 264.640569 
L 326.341818 272.261652 
L 329.621157 279.187792 
L 332.900496 285.156084 
L 336.179835 289.935569 
L 339.459174 293.336155 
L 342.738512 295.216136 
L 346.017851 295.488 
L 349.29719 294.122298 
L 352.576529 291.14941 
L 355.855868 286.659116 
L 359.135207 280.797969 
L 362.414545 273.764534 
L 365.693884 265.802659 
L 368.973223 257.192998 
L 372.252562 248.243087 
L 375.531901 239.276317 
L 378.81124 230.620215 
L 382.090579 222.594439 
L 385.369917 215.498951 
L 388.649256 209.602786 
L 391.928595 205.133851 
L 395.207934 202.270137 
L 398.487273 201.132676 
" clip-path="url(#p4f07d1849e)" style="fill: none; stroke: #1f77b4; stroke-width: 1.5; stroke-linecap: square"/>
   </g>
   <g id="line2d_16">
    <path d="M 73.832727 53.568 
L 77.112066 54.359626 
L 80.391405 56.715462 
L 83.670744 60.579142 
L 86.950083 65.859218 
L 90.229421 72.432759 
L 93.50876 80.150103 
L 96.788099 88.84052 
L 100.067438 98.318465 
L 103.346777 108.39013 
L 106.626116 118.859945 
L 109.905455 129.536753 
L 113.184793 140.239379 
L 116.464132 150.80139 
L 119.743471 161.074883 
L 123.02281 170.933223 
L 126.302149 180.2727 
L 129.581488 189.013146 
L 132.860826 197.097589 
L 136.140165 204.491086 
L 139.419504 211.178875 
L 142.698843 217.164028 
L 145.978182 222.464773 
L 149.257521 227.111657 
L 152.53686 231.144689 
L 155.816198 234.610604 
L 159.095537 237.560345 
L 162.374876 240.046825 
L 165.654215 242.123034 
L 168.933554 243.840491 
L 172.212893 245.248059 
L 175.492231 246.391089 
L 178.77157 247.310865 
L 182.050909 248.044318 
L 185.330248 248.623953 
L 188.609587 249.077951 
L 191.888926 249.430396 
L 195.168264 249.701596 
L 198.447603 249.908449 
L 201.726942 250.064847 
L 205.006281 250.182069 
L 208.28562 250.269169 
L 211.564959 250.333328 
L 214.844298 250.380183 
L 218.123636 250.414107 
L 221.402975 250.43846 
L 224.682314 250.455792 
L 227.961653 250.468024 
L 231.240992 250.476582 
L 234.520331 250.482519 
L 237.799669 250.486604 
L 241.079008 250.48939 
L 244.358347 250.491275 
L 247.637686 250.492539 
L 250.917025 250.49338 
L 254.196364 250.493934 
L 257.475702 250.494297 
L 260.755041 250.494532 
L 264.03438 250.494683 
L 267.313719 250.49478 
L 270.593058 250.494841 
L 273.872397 250.494879 
L 277.151736 250.494903 
L 280.431074 250.494918 
L 283.710413 250.494927 
L 286.989752 250.494932 
L 290.269091 250.494935 
L 293.54843 250.494937 
L 296.827769 250.494938 
L 300.107107 250.494939 
L 303.386446 250.494939 
L 306.665785 250.49494 
L 309.945124 250.49494 
L 313.224463 250.49494 
L 316.503802 250.49494 
L 319.78314 250.49494 
L 323.062479 250.49494 
L 326.341818 250.49494 
L 329.621157 250.49494 
L 332.900496 250.49494 
L 336.179835 250.49494 
L 339.459174 250.49494 
L 342.738512 250.49494 
L 346.017851 250.49494 
L 349.29719 250.49494 
L 352.576529 250.49494 
L 355.855868 250.49494 
L 359.135207 250.49494 
L 362.414545 250.49494 
L 365.693884 250.49494 
L 368.973223 250.49494 
L 372.252562 250.49494 
L 375.531901 250.49494 
L 378.81124 250.49494 
L 382.090579 250.49494 
L 385.369917 250.49494 
L 388.649256 250.49494 
L 391.928595 250.49494 
L 395.207934 250.49494 
L 398.487273 250.49494 
" clip-path="url(#p4f07d1849e)" style="fill: none; stroke: #ff7f0e; stroke-width: 1.5; stroke-linecap: square"/>
   </g>
   <g id="patch_3">
    <path d="M 57.6 307.584 
L 57.6 41.472 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
   <g id="patch_4">
    <path d="M 414.72 307.584 
L 414.72 41.472 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
   <g id="patch_5">
    <path d="M 57.6 307.584 
L 414.72 307.584 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
   <g id="patch_6">
    <path d="M 57.6 41.472 
L 414.72 41.472 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
  </g>
 </g>
 <defs>
  <clipPath id="p4f07d1849e">
   <rect x="57.6" y="41.472" width="357.12" height="266.112"/>
  </clipPath>
 </defs>
</svg>
\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"plt.cla()\\nplt.plot(xv, exv)\\nplt.plot(xv, exv2);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 10264276499275938942,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 3439996290039193888,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"verbatim\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}[1.8369702e-16]\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"np.array(nevaluate( $3\\\\cos(3 x + \\\\pi/4)$, {$x$: np.pi/12}));\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 5431556865949466370,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 17353068500484059474,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"verbatim\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}[]\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"np.array(nevaluate( $3\\\\cos(3 x + \\\\pi/4)$, {$x$: $\\\\pi/12$}));\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 16084743544579086385,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 14530765317592913267,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"verbatim\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}{y: 0, x: 3}\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"q={$y$: 0, $x$: 3};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 17469630515750232834,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 3369315314932196031,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 7216021993827968852,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"3b + 2.5\\\\int{\\\\sin(x)}{{x, 0, a \\\\pi}}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}3\\\\,b\\\\discretionary{}{}{}+2.5\\\\,\\\\int_{0\\\\,}^{a \\\\pi} \\\\sin{x}\\\\,\\\\,{\\\\rm d}x\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex:= 3b + 2.5\\\\int{ \\\\sin(x) }{x, 0, a \\\\pi};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 8920520732984220007,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 1555889857808735268,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 17650964429344617564,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"3b + [5]\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}3\\\\,b\\\\discretionary{}{}{}+5\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"nval(ex.copy(), {$a$: 1});\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 1383841293063583168,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 11394148258473291931,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"output\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}{\\\\sum}\\n  1:{b}  3\\n  2:{1}\\n\\n\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"print(tree(_))\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 4588849812975869004,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 16335796475391127635,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 1157272491380028082,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"3.5x\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}3.5\\\\,x\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex:= 3.5 x;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 10258327774597512801,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 13635830073316767128,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"output\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}{x}  3.5\\n\\n\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"print(tree(ex))\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 6932843571784960699,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 12728653852762897373,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 8813911481504474581,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\int{(x)**( 1/2 )}{{x, -1, 1}}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\int_{-\\\\,1}^{1} \\\\sqrt{x}\\\\,\\\\,{\\\\rm d}x\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex:= \\\\int{ \\\\sqrt{x} }{x, -1, 1};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 12360389547161657605,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 15877422970854931052,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 9090660271777075552,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"[0.666667 + 0.666667i]\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}0.666667 + 0.666667i\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"nval(ex.copy(), {});\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 565533511902576155,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 13389254535508917371,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"output\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}{1}\\n\\n\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"print(tree(_))\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 13026458770356487205,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"\"\n\t\t}\n\t],\n\t\"description\": \"Cadabra JSON notebook format\",\n\t\"flags\": {\n\t\t\"hide_input_cells\": false\n\t},\n\t\"version\": 1.0\n}\n"
  },
  {
    "path": "examples/packages.cnb",
    "content": "{\n\t\"cells\" : \n\t[\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"import cdb.gr as gr\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"output\",\n\t\t\t\t\t\"source\" : \"\\\\begin{verbatim}Help on function RiemannFromChristoffel in module cdb.gr:\\n\\nRiemannFromChristoffel(R, c)\\n    @param R: Riemann tensor.\\n    @param c: Christoffel symbol.\\n\\n\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"help(gr.RiemannFromChristoffel)\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}@\\\\left(R\\\\right)\\\\,^{\\\\rho}\\\\,_{\\\\sigma \\\\mu \\\\nu} = \\\\partial_{\\\\mu}\\\\left(@\\\\left(c\\\\right)\\\\,^{\\\\rho}\\\\,_{\\\\nu \\\\sigma}\\\\right)-\\\\partial_{\\\\nu}\\\\left(@\\\\left(c\\\\right)\\\\,^{\\\\rho}\\\\,_{\\\\mu \\\\sigma}\\\\right)+@\\\\left(c\\\\right)\\\\,^{\\\\rho}\\\\,_{\\\\mu \\\\lambda} @\\\\left(c\\\\right)\\\\,^{\\\\lambda}\\\\,_{\\\\nu \\\\sigma}-@\\\\left(c\\\\right)\\\\,^{\\\\rho}\\\\,_{\\\\nu \\\\lambda} @\\\\left(c\\\\right)\\\\,^{\\\\lambda}\\\\,_{\\\\mu \\\\sigma}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex=gr.RiemannFromChristoffel($R$, $\\\\Gamma$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"verbatim\",\n\t\t\t\t\t\"source\" : \"\\\\begin{verbatim}<class 'cadabra2.Ex'>\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"type(ex);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"verbatim\",\n\t\t\t\t\t\"source\" : \"\\\\begin{verbatim}<class 'cadabra2.Ex'>\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex.____;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1\n}\n"
  },
  {
    "path": "examples/packages2.cnb",
    "content": "{\n\t\"cells\" : \n\t[\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"import cdb.relativity as gr\\nimport cdb.relativity.schwarzschild as ss\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\left(g_{t t} = -1+\\\\frac{2M}{r}, \\\\linebreak[0] g_{r r} = \\\\frac{1}{1 - \\\\frac{2M}{r}}, \\\\linebreak[0] g_{\\\\theta \\\\theta} = r^{2}, \\\\linebreak[0] g_{\\\\phi \\\\phi} = r^{2} \\\\sin\\\\left(\\\\theta\\\\right)^{2}\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"rl=ss.metric();\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\left(g_{t t} = -1+\\\\frac{2M}{r}, \\\\linebreak[0] g_{r r} = \\\\frac{1}{1 - \\\\frac{2M}{r}}, \\\\linebreak[0] g_{\\\\theta \\\\theta} = r^{2}, \\\\linebreak[0] g_{\\\\phi \\\\phi} = r^{2} \\\\sin\\\\left(\\\\theta\\\\right)^{2}, \\\\linebreak[0] g^{r r} = \\\\frac{-2M+r}{r}, \\\\linebreak[0] g^{t t} = \\\\frac{r}{2M-r}, \\\\linebreak[0] g^{\\\\theta \\\\theta} = r^{-2}, \\\\linebreak[0] g^{\\\\phi \\\\phi} = \\\\frac{1}{r^{2} \\\\sin\\\\left(\\\\theta\\\\right)^{2}}\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"complete(_,$g^{\\\\mu\\\\nu}$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\Gamma^{\\\\lambda}\\\\,_{\\\\mu \\\\nu} = \\\\frac{1}{2}g^{\\\\lambda \\\\kappa} \\\\left(\\\\partial_{\\\\mu}{g_{\\\\kappa \\\\nu}}+\\\\partial_{\\\\nu}{g_{\\\\kappa \\\\mu}}-\\\\partial_{\\\\kappa}{g_{\\\\mu \\\\nu}}\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ch=gr.christoffel_from_metric();\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\Gamma^{\\\\lambda}\\\\,_{\\\\mu \\\\nu} = \\\\left\\\\{\\\\begin{aligned}\\\\square{}_{\\\\phi}{}_{r}{}^{\\\\phi}= & \\\\frac{1}{r}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{\\\\theta}{}^{\\\\phi}= & \\\\frac{1}{\\\\tan\\\\left(\\\\theta\\\\right)}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{r}{}^{\\\\theta}= & \\\\frac{1}{r}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{r}{}^{r}= & \\\\frac{M}{r \\\\left(2M-r\\\\right)}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}_{r}{}^{t}= & \\\\frac{M}{r \\\\left(-2M+r\\\\right)}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{\\\\phi}{}^{\\\\phi}= & \\\\frac{1}{r}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{\\\\phi}{}^{\\\\phi}= & \\\\frac{1}{\\\\tan\\\\left(\\\\theta\\\\right)}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{\\\\theta}{}^{\\\\theta}= & \\\\frac{1}{r}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{t}{}^{t}= & \\\\frac{M}{r \\\\left(-2M+r\\\\right)}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{\\\\phi}{}^{r}= & \\\\left(2M-r\\\\right) \\\\sin\\\\left(\\\\theta\\\\right)^{2}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{\\\\phi}{}^{\\\\theta}= &  - \\\\frac{1}{2}\\\\sin\\\\left(2\\\\theta\\\\right)\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{\\\\theta}{}^{r}= & 2M-r\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}_{t}{}^{r}= & M \\\\frac{-2M+r}{r^{3}}\\\\\\\\[-.5ex]\\n\\\\end{aligned}\\\\right.\\n\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"evaluate(ch, rl, rhsonly=True);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Derivative to~}\\\\nabla{\\\\#}.\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"\\\\nabla{#}::Derivative;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}K^{\\\\mu} \\\\nabla_{\\\\mu}{K^{\\\\nu}} = \\\\kappa K^{\\\\nu}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"sg:= K^{\\\\mu} \\\\nabla_{\\\\mu}{K^\\\\nu} = \\\\kappa K^{\\\\nu};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}K^{\\\\mu} \\\\left(\\\\partial_{\\\\mu}{K^{\\\\nu}}+\\\\Gamma^{\\\\nu}\\\\,_{\\\\mu \\\\rho} K^{\\\\rho}\\\\right) = \\\\kappa K^{\\\\nu}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"substitute(sg, gr.expand_covariant_derivative());\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}K^{t} = \\\\frac{1}{\\\\sqrt{1 - \\\\frac{2M}{r}}}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"rl2:= K^{t}=1/\\\\sqrt{1- 2 M/r};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}K^{\\\\mu} \\\\left(\\\\partial_{\\\\mu}{K^{\\\\nu}}+\\\\left\\\\{\\\\begin{aligned}\\\\square{}_{\\\\phi}{}_{r}{}^{\\\\phi}= & \\\\frac{1}{r}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{\\\\theta}{}^{\\\\phi}= & \\\\frac{1}{\\\\tan\\\\left(\\\\theta\\\\right)}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{r}{}^{\\\\theta}= & \\\\frac{1}{r}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{r}{}^{r}= & \\\\frac{M}{r \\\\left(2M-r\\\\right)}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}_{r}{}^{t}= & \\\\frac{M}{r \\\\left(-2M+r\\\\right)}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{\\\\phi}{}^{\\\\phi}= & \\\\frac{1}{r}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{\\\\phi}{}^{\\\\phi}= & \\\\frac{1}{\\\\tan\\\\left(\\\\theta\\\\right)}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{\\\\theta}{}^{\\\\theta}= & \\\\frac{1}{r}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{t}{}^{t}= & \\\\frac{M}{r \\\\left(-2M+r\\\\right)}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{\\\\phi}{}^{r}= & \\\\left(2M-r\\\\right) \\\\sin\\\\left(\\\\theta\\\\right)^{2}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{\\\\phi}{}^{\\\\theta}= &  - \\\\frac{1}{2}\\\\sin\\\\left(2\\\\theta\\\\right)\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{\\\\theta}{}^{r}= & 2M-r\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}_{t}{}^{r}= & M \\\\frac{-2M+r}{r^{3}}\\\\\\\\[-.5ex]\\n\\\\end{aligned}\\\\right.\\n K^{\\\\rho}\\\\right) = \\\\kappa K^{\\\\nu}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"substitute(sg, ch);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\left\\\\{\\\\begin{aligned}\\\\square{}^{r}= & \\\\frac{M}{r^{2}}\\\\\\\\[-.5ex]\\n\\\\end{aligned}\\\\right.\\n = \\\\left\\\\{\\\\begin{aligned}\\\\square{}^{t}= & \\\\frac{\\\\kappa}{\\\\sqrt{\\\\frac{-2M+r}{r}}}\\\\\\\\[-.5ex]\\n\\\\end{aligned}\\\\right.\\n\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"evaluate(sg, rl2);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}g^{\\\\mu \\\\lambda} \\\\nabla_{\\\\lambda}{K^{\\\\nu}}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"nK:= g^{\\\\mu\\\\lambda}\\\\nabla_{\\\\lambda}{K^{\\\\nu}};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}g^{\\\\mu \\\\lambda} \\\\left(\\\\partial_{\\\\lambda}{K^{\\\\nu}}+\\\\Gamma^{\\\\nu}\\\\,_{\\\\lambda \\\\rho} K^{\\\\rho}\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"substitute(_, gr.expand_covariant_derivative());\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}g^{\\\\mu \\\\lambda} \\\\left(\\\\partial_{\\\\lambda}{K^{\\\\nu}}+\\\\left\\\\{\\\\begin{aligned}\\\\square{}_{\\\\phi}{}_{r}{}^{\\\\phi}= & \\\\frac{1}{r}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{\\\\theta}{}^{\\\\phi}= & \\\\frac{1}{\\\\tan\\\\left(\\\\theta\\\\right)}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{r}{}^{\\\\theta}= & \\\\frac{1}{r}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{r}{}^{r}= & \\\\frac{M}{r \\\\left(2M-r\\\\right)}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}_{r}{}^{t}= & \\\\frac{M}{r \\\\left(-2M+r\\\\right)}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{\\\\phi}{}^{\\\\phi}= & \\\\frac{1}{r}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{\\\\phi}{}^{\\\\phi}= & \\\\frac{1}{\\\\tan\\\\left(\\\\theta\\\\right)}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{\\\\theta}{}^{\\\\theta}= & \\\\frac{1}{r}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{t}{}^{t}= & \\\\frac{M}{r \\\\left(-2M+r\\\\right)}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{\\\\phi}{}^{r}= & \\\\left(2M-r\\\\right) \\\\sin\\\\left(\\\\theta\\\\right)^{2}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{\\\\phi}{}^{\\\\theta}= &  - \\\\frac{1}{2}\\\\sin\\\\left(2\\\\theta\\\\right)\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{\\\\theta}{}^{r}= & 2M-r\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}_{t}{}^{r}= & M \\\\frac{-2M+r}{r^{3}}\\\\\\\\[-.5ex]\\n\\\\end{aligned}\\\\right.\\n K^{\\\\rho}\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"substitute(_, ch);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}K^{t} = 1\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"rl3:= K^{t}=1;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\left\\\\{\\\\begin{aligned}\\\\square{}^{t}{}^{r}= & \\\\frac{M}{r^{2}}\\\\\\\\[-.5ex]\\n\\\\square{}^{r}{}^{t}= &  - \\\\frac{M}{r^{2}}\\\\\\\\[-.5ex]\\n\\\\end{aligned}\\\\right.\\n\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"evaluate(nK, rl+rl3);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1\n}\n"
  },
  {
    "path": "examples/plotting.cnb",
    "content": "{\n\t\"cell_id\": 8855944566024926689,\n\t\"cells\": [\n\t\t{\n\t\t\t\"cell_id\": 2976888846447930228,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 16717438647011792960,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\section*{Plotting data and functions}\\n\\nThis notebook shows how to make plots of data and functions. Cadabra notebooks can display \\nplots which are generated by matplotlib, so you have the full machinery of that library\\nat your disposal to visualise your maths.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\section*{Plotting data and functions}\\n\\nThis notebook shows how to make plots of data and functions. Cadabra notebooks can display \\nplots which are generated by matplotlib, so you have the full machinery of that library\\nat your disposal to visualise your maths.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 8761523474901702761,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 11700403708075191958,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\subsection*{Basic plotting with matplotlib}\\n\\nThe first example that we will show is a basic matplotlib plot of a number of data points.\\nYou can find examples of this on any matplotlib tutorial. The only difference is how you make\\nthe plot appear in your Cadabra notebook.\\n\\nWe start by generating the plot and storing it in a variable $p$.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\subsection*{Basic plotting with matplotlib}\\n\\nThe first example that we will show is a basic matplotlib plot of a number of data points.\\nYou can find examples of this on any matplotlib tutorial. The only difference is how you make\\nthe plot appear in your Cadabra notebook.\\n\\nWe start by generating the plot and storing it in a variable $p$.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 3524910430355576331,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"import matplotlib.pyplot as plt\\nimport numpy as np\\np=plt.plot([1,2,3,4,5],[1,2,5,3,2],'-o')\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 4051443736501369881,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 12066997917657158100,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"We then make it appear in the notebook using the \\\\verb|display| command. This command figures\\nout the type of the object which you hand it, and sends the appropriate data to the notebook\\ninterface.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"We then make it appear in the notebook using the \\\\verb|display| command. This command figures\\nout the type of the object which you hand it, and sends the appropriate data to the notebook\\ninterface.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 2311842112467759032,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9223372036854775810,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"image_png\",\n\t\t\t\t\t\"source\": \"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\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"display(p[0])\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 83377570136931709,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 5599987191402776889,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\subsection*{3D plotting with matplotlib}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\subsection*{3D plotting with matplotlib}\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 16771518769536471597,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"from mpl_toolkits.mplot3d import axes3d\\nimport matplotlib.pyplot as plt\\nfig=plt.figure()\\nax=fig.add_subplot(111,projection='3d')\\nX,Y,Z = axes3d.get_test_data(0.05)\\ncset = ax.contour(X,Y,Z)\\nax.clabel(cset,fontsize=9,inline=1)\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 3589770310753153079,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9223372036854775813,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"image_png\",\n\t\t\t\t\t\"source\": \"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\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"display(fig)\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 16870455449402682855,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9868180105062890100,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\subsection*{Plotting functions with sympy}\\n\\nIn order to plot symbolic functions, rather than numerical data, use sympy. This library can\\ngenerate both two-dimensional and three-dimensional plots.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\subsection*{Plotting functions with sympy}\\n\\nIn order to plot symbolic functions, rather than numerical data, use sympy. This library can\\ngenerate both two-dimensional and three-dimensional plots.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 16432830887788007622,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"from sympy.plotting import plot, plot3d\\nx,y=symbols('x y')\\np1=plot3d(sin(x)*y)\\np2=plot(sin(x)*x**2)\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 18220392128932635794,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9223372036854775816,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"image_png\",\n\t\t\t\t\t\"source\": \"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\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9223372036854775817,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"image_png\",\n\t\t\t\t\t\"source\": \"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\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"display(p1)\\ndisplay(p2)\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 9864811625027922680,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9223372036854775819,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"output\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}cartesian surface: y*sin(x) for y over (-10.0, 10.0) and x over (-10.0, 10.0)\\n\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"print(p1[0])\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 8575285083676239171,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9223372036854775820,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"output\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}<matplotlib.figure.Figure object at 0x7f4e59637e80>\\n\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"print(repr(p1._backend.fig))\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 12533899187916108365,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"\"\n\t\t}\n\t],\n\t\"description\": \"Cadabra JSON notebook format\",\n\t\"version\": 1.0\n}\n"
  },
  {
    "path": "examples/poincare_algebra.cnb",
    "content": "{\n\t\"cell_id\": 11106613021756569334,\n\t\"cells\": [\n\t\t{\n\t\t\t\"cell_id\": 9315766075641420399,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 17343772776960357109,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\section*{Commutator algebra}\\n\\nAn often asked question is how to handle commutator algebra with Cadabra. This requires a few steps which are perhaps not entirely transparent to a new user, hence the following simple example. \"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\section*{Commutator algebra}\\n\\nAn often asked question is how to handle commutator algebra with Cadabra. This requires a few steps which are perhaps not entirely transparent to a new user, hence the following simple example. \"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 7023131363295410827,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 7396292867082315560,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"In this notebook, we will verify the invariance of the two quadratic Casimirs of the  Poincar\\\\'e algebra. That is, we will verify that \\n\\\\begin{equation}\\n[ J_{\\\\mu\\\\nu}, P^2 ] = 0\\\\,,\\\\quad{\\\\rm and}\\\\quad\\n[ J_{\\\\mu\\\\nu}, W^2 ] = 0\\\\,,\\n\\\\end{equation}\\nwhere~$P^2 = P_\\\\mu P_\\\\mu$ is the momentum squared and $W^2 = W_\\\\mu W_\\\\mu$ is the square of \\n\\\\begin{equation}\\nW_\\\\mu = \\\\epsilon_{\\\\mu\\\\nu\\\\rho\\\\sigma} P_{\\\\nu} J_{\\\\rho\\\\sigma}\\\\,.\\n\\\\end{equation}\\n\\nWe first make some straightforward property assignments: declaration of indices, declaration \\nof the operators~$P_\\\\mu$ and $J_{\\\\mu\\\\nu}$ and the fact that they do not commute, and so on.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"In this notebook, we will verify the invariance of the two quadratic Casimirs of the  Poincar\\\\'e algebra. That is, we will verify that \\n\\\\begin{equation}\\n[ J_{\\\\mu\\\\nu}, P^2 ] = 0\\\\,,\\\\quad{\\\\rm and}\\\\quad\\n[ J_{\\\\mu\\\\nu}, W^2 ] = 0\\\\,,\\n\\\\end{equation}\\nwhere~$P^2 = P_\\\\mu P_\\\\mu$ is the momentum squared and $W^2 = W_\\\\mu W_\\\\mu$ is the square of \\n\\\\begin{equation}\\nW_\\\\mu = \\\\epsilon_{\\\\mu\\\\nu\\\\rho\\\\sigma} P_{\\\\nu} J_{\\\\rho\\\\sigma}\\\\,.\\n\\\\end{equation}\\n\\nWe first make some straightforward property assignments: declaration of indices, declaration \\nof the operators~$P_\\\\mu$ and $J_{\\\\mu\\\\nu}$ and the fact that they do not commute, and so on.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 9370404668174603973,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"{\\\\mu,\\\\nu,\\\\rho,\\\\sigma,\\\\lambda,\\\\kappa,\\\\alpha,\\\\beta,\\\\gamma,\\\\xi}::Indices.\\n{\\\\mu,\\\\nu,\\\\rho,\\\\sigma,\\\\lambda,\\\\kappa,\\\\alpha,\\\\beta,\\\\gamma,\\\\xi}::Integer(0..3).\\n\\\\eta_{\\\\mu\\\\nu}::KroneckerDelta.\\n\\\\delta{#}::KroneckerDelta.\\ne_{\\\\mu\\\\nu\\\\lambda\\\\rho}::EpsilonTensor(delta=\\\\delta).\\nJ_{\\\\mu\\\\nu}::AntiSymmetric.\\nJ_{\\\\mu\\\\nu}::SelfNonCommuting.\\n{ J_{\\\\mu\\\\nu}, P_{\\\\mu}, W_{\\\\mu} }::NonCommuting.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 14191442662655080844,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"{J_{\\\\mu\\\\nu}, P_{\\\\mu}, W_{\\\\mu} }::Depends(\\\\commutator{#}).\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 18322109326161563221,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 4515515517754441930,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"For computations involving algebras like the one in this notebook, the following set of post processing\\nrules is useful. They move all objects out of commutators and anti-commutators which commute with\\neverything else, and then reorder and relabel indices to obtain a simple form.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"For computations involving algebras like the one in this notebook, the following set of post processing\\nrules is useful. They move all objects out of commutators and anti-commutators which commute with\\neverything else, and then reorder and relabel indices to obtain a simple form.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 7703209800365975813,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"def post_process(ex):\\n   unwrap(ex)\\n   eliminate_kronecker(ex)\\n   canonicalise(ex)\\n   rename_dummies(ex)\\n   collect_terms(ex)\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 721481446680713510,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 13750334956568318436,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\subsection*{The Poincar\\\\'e algebra}\\n\\nWe now input the rules which define the Poincar\\\\'e algebra. These are simply substitution rules,\\nto be used later in explicit substition commands.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\subsection*{The Poincar\\\\'e algebra}\\n\\nWe now input the rules which define the Poincar\\\\'e algebra. These are simply substitution rules,\\nto be used later in explicit substition commands.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 14678525790528458483,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 7515470650463038223,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 14718562114636147143,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"{[J_{\\\\mu \\\\nu}, P_{\\\\rho}] -> \\\\eta_{\\\\mu \\\\rho} P_{\\\\nu}-\\\\eta_{\\\\nu \\\\rho} P_{\\\\mu}, [J_{\\\\mu \\\\nu}, J_{\\\\rho \\\\sigma}] -> \\\\eta_{\\\\mu \\\\rho} J_{\\\\nu \\\\sigma}-\\\\eta_{\\\\mu \\\\sigma} J_{\\\\nu \\\\rho}-\\\\eta_{\\\\nu \\\\rho} J_{\\\\mu \\\\sigma} + \\\\eta_{\\\\nu \\\\sigma} J_{\\\\mu \\\\rho}}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\left[{}\\\\left[J_{\\\\mu \\\\nu}, \\\\discretionary{}{}{}P_{\\\\rho}\\\\right]{} \\\\rightarrow \\\\eta_{\\\\mu \\\\rho} P_{\\\\nu}\\\\discretionary{}{}{}-\\\\,\\\\eta_{\\\\nu \\\\rho} P_{\\\\mu}, \\\\discretionary{}{}{}{}\\\\left[J_{\\\\mu \\\\nu}, \\\\discretionary{}{}{}J_{\\\\rho \\\\sigma}\\\\right]{} \\\\rightarrow \\\\eta_{\\\\mu \\\\rho} J_{\\\\nu \\\\sigma}\\\\discretionary{}{}{}-\\\\,\\\\eta_{\\\\mu \\\\sigma} J_{\\\\nu \\\\rho}\\\\discretionary{}{}{}-\\\\,\\\\eta_{\\\\nu \\\\rho} J_{\\\\mu \\\\sigma}\\\\discretionary{}{}{}+\\\\eta_{\\\\nu \\\\sigma} J_{\\\\mu \\\\rho}\\\\right]\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"poincare:= { \\\\commutator{J_{\\\\mu\\\\nu}}{P_{\\\\rho}} -> \\\\eta_{\\\\mu\\\\rho} P_{\\\\nu} - \\\\eta_{\\\\nu\\\\rho} P_{\\\\mu},\\n             \\\\commutator{J_{\\\\mu\\\\nu}}{J_{\\\\rho\\\\sigma}} -> \\\\eta_{\\\\mu\\\\rho} J_{\\\\nu\\\\sigma} \\n                                                      - \\\\eta_{\\\\mu\\\\sigma} J_{\\\\nu\\\\rho}\\n                                                      - \\\\eta_{\\\\nu\\\\rho} J_{\\\\mu\\\\sigma}\\n                                                      + \\\\eta_{\\\\nu\\\\sigma} J_{\\\\mu\\\\rho} };\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 6528359529597968728,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 6400228875885604255,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\subsection*{The $P^2$ Casimir}\\n\\nWe know that $P^2$ is a Casimir, so the following should vanish:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\subsection*{The $P^2$ Casimir}\\n\\nWe know that $P^2$ is a Casimir, so the following should vanish:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 14173868040898864651,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9994139315106144986,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 14062550396190429241,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"[J_{\\\\mu \\\\nu}, P_{\\\\rho} P_{\\\\rho}]\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}{}\\\\left[J_{\\\\mu \\\\nu}, \\\\discretionary{}{}{}P_{\\\\rho} P_{\\\\rho}\\\\right]{}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"Psq:= \\\\commutator{J_{\\\\mu\\\\nu}}{ P_{\\\\rho}P_{\\\\rho} };\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 18192389058298689521,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9681807010676353903,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 10427584475320492806,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"[J_{\\\\mu \\\\nu}, P_{\\\\rho}] P_{\\\\rho} + P_{\\\\rho} [J_{\\\\mu \\\\nu}, P_{\\\\rho}]\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}{}\\\\left[J_{\\\\mu \\\\nu}, \\\\discretionary{}{}{}P_{\\\\rho}\\\\right]{} P_{\\\\rho}\\\\discretionary{}{}{}+P_{\\\\rho} {}\\\\left[J_{\\\\mu \\\\nu}, \\\\discretionary{}{}{}P_{\\\\rho}\\\\right]{}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"product_rule(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 9743743344113656599,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 18257736613168707616,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 2761812607044190089,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"(\\\\eta_{\\\\mu \\\\rho} P_{\\\\nu}-\\\\eta_{\\\\nu \\\\rho} P_{\\\\mu}) P_{\\\\rho} + P_{\\\\rho} (\\\\eta_{\\\\mu \\\\rho} P_{\\\\nu}-\\\\eta_{\\\\nu \\\\rho} P_{\\\\mu})\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\left(\\\\eta_{\\\\mu \\\\rho} P_{\\\\nu}\\\\discretionary{}{}{}-\\\\,\\\\eta_{\\\\nu \\\\rho} P_{\\\\mu}\\\\right) P_{\\\\rho}\\\\discretionary{}{}{}+P_{\\\\rho} \\\\left(\\\\eta_{\\\\mu \\\\rho} P_{\\\\nu}\\\\discretionary{}{}{}-\\\\,\\\\eta_{\\\\nu \\\\rho} P_{\\\\mu}\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"substitute(_, poincare);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 7283064845850749409,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 15115716107954714884,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 3084005768199014968,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"0\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}0\\\\,\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"distribute(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 5886591640803187846,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 2221975938778038510,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\subsection*{The $W^2$ Casimir}\\n\\nNext we do the same thing with $W^2$, the other Poincar\\\\'e Casimir...\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\subsection*{The $W^2$ Casimir}\\n\\nNext we do the same thing with $W^2$, the other Poincar\\\\'e Casimir...\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 1128160442213401089,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 11404982420601735035,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 8691224832353392546,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"[J_{\\\\mu \\\\nu}, W_{\\\\rho} W_{\\\\rho}]\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}{}\\\\left[J_{\\\\mu \\\\nu}, \\\\discretionary{}{}{}W_{\\\\rho} W_{\\\\rho}\\\\right]{}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"Wsq:=\\\\commutator{J_{\\\\mu\\\\nu}}{W_\\\\mu W_\\\\mu};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 4673163097987323507,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 5646178958541389047,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 7420054074567340915,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"e_{\\\\gamma \\\\alpha \\\\lambda \\\\kappa} e_{\\\\gamma \\\\rho \\\\sigma \\\\beta} [J_{\\\\mu \\\\nu}, P_{\\\\alpha} J_{\\\\rho \\\\sigma} P_{\\\\beta} J_{\\\\lambda \\\\kappa}]\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}e_{\\\\gamma \\\\alpha \\\\lambda \\\\kappa} e_{\\\\gamma \\\\rho \\\\sigma \\\\beta} {}\\\\left[J_{\\\\mu \\\\nu}, \\\\discretionary{}{}{}P_{\\\\alpha} J_{\\\\rho \\\\sigma} P_{\\\\beta} J_{\\\\lambda \\\\kappa}\\\\right]{}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"substitute(_, $W_\\\\mu -> e_{\\\\mu\\\\nu\\\\lambda\\\\rho} P_\\\\nu J_{\\\\lambda\\\\rho}$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 14540991334474653221,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 6644535209949996862,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 13940562148982541503,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"6\\\\delta_{\\\\alpha \\\\rho \\\\lambda \\\\sigma \\\\kappa \\\\beta} [J_{\\\\mu \\\\nu}, P_{\\\\alpha} J_{\\\\rho \\\\sigma} P_{\\\\beta} J_{\\\\lambda \\\\kappa}]\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}6\\\\,\\\\delta_{\\\\alpha \\\\rho \\\\lambda \\\\sigma \\\\kappa \\\\beta} {}\\\\left[J_{\\\\mu \\\\nu}, \\\\discretionary{}{}{}P_{\\\\alpha} J_{\\\\rho \\\\sigma} P_{\\\\beta} J_{\\\\lambda \\\\kappa}\\\\right]{}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"epsilon_to_delta(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 18197240252079900808,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 10809178207384550003,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 4056238156539035162,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"-6( 1/6 \\\\delta_{\\\\alpha \\\\rho} \\\\delta_{\\\\beta \\\\lambda} \\\\delta_{\\\\kappa \\\\sigma} -  1/6 \\\\delta_{\\\\alpha \\\\rho} \\\\delta_{\\\\beta \\\\kappa} \\\\delta_{\\\\lambda \\\\sigma} -  1/6 \\\\delta_{\\\\alpha \\\\sigma} \\\\delta_{\\\\beta \\\\lambda} \\\\delta_{\\\\kappa \\\\rho} +  1/6 \\\\delta_{\\\\alpha \\\\beta} \\\\delta_{\\\\lambda \\\\sigma} \\\\delta_{\\\\kappa \\\\rho} +  1/6 \\\\delta_{\\\\alpha \\\\sigma} \\\\delta_{\\\\beta \\\\kappa} \\\\delta_{\\\\lambda \\\\rho} -  1/6 \\\\delta_{\\\\alpha \\\\beta} \\\\delta_{\\\\lambda \\\\rho} \\\\delta_{\\\\kappa \\\\sigma}) [J_{\\\\mu \\\\nu}, P_{\\\\alpha} J_{\\\\rho \\\\sigma} P_{\\\\beta} J_{\\\\lambda \\\\kappa}]\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}-6\\\\,\\\\left(\\\\frac{1}{6}\\\\,\\\\delta_{\\\\alpha \\\\rho} \\\\delta_{\\\\beta \\\\lambda} \\\\delta_{\\\\kappa \\\\sigma}\\\\discretionary{}{}{} - \\\\frac{1}{6}\\\\,\\\\delta_{\\\\alpha \\\\rho} \\\\delta_{\\\\beta \\\\kappa} \\\\delta_{\\\\lambda \\\\sigma}\\\\discretionary{}{}{} - \\\\frac{1}{6}\\\\,\\\\delta_{\\\\alpha \\\\sigma} \\\\delta_{\\\\beta \\\\lambda} \\\\delta_{\\\\kappa \\\\rho}\\\\discretionary{}{}{}+\\\\frac{1}{6}\\\\,\\\\delta_{\\\\alpha \\\\beta} \\\\delta_{\\\\lambda \\\\sigma} \\\\delta_{\\\\kappa \\\\rho}\\\\discretionary{}{}{}+\\\\frac{1}{6}\\\\,\\\\delta_{\\\\alpha \\\\sigma} \\\\delta_{\\\\beta \\\\kappa} \\\\delta_{\\\\lambda \\\\rho}\\\\discretionary{}{}{} - \\\\frac{1}{6}\\\\,\\\\delta_{\\\\alpha \\\\beta} \\\\delta_{\\\\lambda \\\\rho} \\\\delta_{\\\\kappa \\\\sigma}\\\\right) {}\\\\left[J_{\\\\mu \\\\nu}, \\\\discretionary{}{}{}P_{\\\\alpha} J_{\\\\rho \\\\sigma} P_{\\\\beta} J_{\\\\lambda \\\\kappa}\\\\right]{}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"expand_delta(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 12879772976132515189,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9667107681200747915,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 10879618064370296532,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"-6( 1/6 \\\\delta_{\\\\alpha \\\\rho} \\\\delta_{\\\\beta \\\\kappa} \\\\delta_{\\\\lambda \\\\sigma} -  1/6 \\\\delta_{\\\\alpha \\\\rho} \\\\delta_{\\\\beta \\\\lambda} \\\\delta_{\\\\kappa \\\\sigma} -  1/6 \\\\delta_{\\\\alpha \\\\sigma} \\\\delta_{\\\\beta \\\\kappa} \\\\delta_{\\\\lambda \\\\rho} +  1/6 \\\\delta_{\\\\alpha \\\\beta} \\\\delta_{\\\\lambda \\\\rho} \\\\delta_{\\\\kappa \\\\sigma} +  1/6 \\\\delta_{\\\\alpha \\\\sigma} \\\\delta_{\\\\beta \\\\lambda} \\\\delta_{\\\\kappa \\\\rho} -  1/6 \\\\delta_{\\\\alpha \\\\beta} \\\\delta_{\\\\lambda \\\\sigma} \\\\delta_{\\\\kappa \\\\rho}) (-[J_{\\\\mu \\\\nu}, P_{\\\\alpha}] J_{\\\\rho \\\\sigma} P_{\\\\beta} J_{\\\\lambda \\\\kappa}-P_{\\\\alpha} [J_{\\\\mu \\\\nu}, J_{\\\\rho \\\\sigma}] P_{\\\\beta} J_{\\\\lambda \\\\kappa}-P_{\\\\alpha} J_{\\\\rho \\\\sigma} [J_{\\\\mu \\\\nu}, P_{\\\\beta}] J_{\\\\lambda \\\\kappa}-P_{\\\\alpha} J_{\\\\rho \\\\sigma} P_{\\\\beta} [J_{\\\\mu \\\\nu}, J_{\\\\lambda \\\\kappa}])\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}-6\\\\,\\\\left(\\\\frac{1}{6}\\\\,\\\\delta_{\\\\alpha \\\\rho} \\\\delta_{\\\\beta \\\\kappa} \\\\delta_{\\\\lambda \\\\sigma}\\\\discretionary{}{}{} - \\\\frac{1}{6}\\\\,\\\\delta_{\\\\alpha \\\\rho} \\\\delta_{\\\\beta \\\\lambda} \\\\delta_{\\\\kappa \\\\sigma}\\\\discretionary{}{}{} - \\\\frac{1}{6}\\\\,\\\\delta_{\\\\alpha \\\\sigma} \\\\delta_{\\\\beta \\\\kappa} \\\\delta_{\\\\lambda \\\\rho}\\\\discretionary{}{}{}+\\\\frac{1}{6}\\\\,\\\\delta_{\\\\alpha \\\\beta} \\\\delta_{\\\\lambda \\\\rho} \\\\delta_{\\\\kappa \\\\sigma}\\\\discretionary{}{}{}+\\\\frac{1}{6}\\\\,\\\\delta_{\\\\alpha \\\\sigma} \\\\delta_{\\\\beta \\\\lambda} \\\\delta_{\\\\kappa \\\\rho}\\\\discretionary{}{}{} - \\\\frac{1}{6}\\\\,\\\\delta_{\\\\alpha \\\\beta} \\\\delta_{\\\\lambda \\\\sigma} \\\\delta_{\\\\kappa \\\\rho}\\\\right) \\\\left(-\\\\,{}\\\\left[J_{\\\\mu \\\\nu}, \\\\discretionary{}{}{}P_{\\\\alpha}\\\\right]{} J_{\\\\rho \\\\sigma} P_{\\\\beta} J_{\\\\lambda \\\\kappa}\\\\discretionary{}{}{}-\\\\,P_{\\\\alpha} {}\\\\left[J_{\\\\mu \\\\nu}, \\\\discretionary{}{}{}J_{\\\\rho \\\\sigma}\\\\right]{} P_{\\\\beta} J_{\\\\lambda \\\\kappa}\\\\discretionary{}{}{}-\\\\,P_{\\\\alpha} J_{\\\\rho \\\\sigma} {}\\\\left[J_{\\\\mu \\\\nu}, \\\\discretionary{}{}{}P_{\\\\beta}\\\\right]{} J_{\\\\lambda \\\\kappa}\\\\discretionary{}{}{}-\\\\,P_{\\\\alpha} J_{\\\\rho \\\\sigma} P_{\\\\beta} {}\\\\left[J_{\\\\mu \\\\nu}, \\\\discretionary{}{}{}J_{\\\\lambda \\\\kappa}\\\\right]{}\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"product_rule(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 12517975367971533918,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 1974543218799396855,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 13611940801069841760,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"-6( 1/6 \\\\delta_{\\\\beta \\\\rho} \\\\delta_{\\\\alpha \\\\kappa} \\\\delta_{\\\\lambda \\\\sigma} -  1/6 \\\\delta_{\\\\beta \\\\rho} \\\\delta_{\\\\alpha \\\\lambda} \\\\delta_{\\\\kappa \\\\sigma} -  1/6 \\\\delta_{\\\\beta \\\\sigma} \\\\delta_{\\\\alpha \\\\kappa} \\\\delta_{\\\\lambda \\\\rho} +  1/6 \\\\delta_{\\\\beta \\\\alpha} \\\\delta_{\\\\kappa \\\\sigma} \\\\delta_{\\\\lambda \\\\rho} +  1/6 \\\\delta_{\\\\beta \\\\sigma} \\\\delta_{\\\\alpha \\\\lambda} \\\\delta_{\\\\kappa \\\\rho} -  1/6 \\\\delta_{\\\\beta \\\\alpha} \\\\delta_{\\\\kappa \\\\rho} \\\\delta_{\\\\lambda \\\\sigma}) (-(\\\\eta_{\\\\beta \\\\mu} P_{\\\\nu}-\\\\eta_{\\\\beta \\\\nu} P_{\\\\mu}) J_{\\\\rho \\\\sigma} P_{\\\\alpha} J_{\\\\lambda \\\\kappa}-P_{\\\\beta} (\\\\eta_{\\\\mu \\\\rho} J_{\\\\nu \\\\sigma}-\\\\eta_{\\\\mu \\\\sigma} J_{\\\\nu \\\\rho}-\\\\eta_{\\\\nu \\\\rho} J_{\\\\mu \\\\sigma} + \\\\eta_{\\\\nu \\\\sigma} J_{\\\\mu \\\\rho}) P_{\\\\alpha} J_{\\\\lambda \\\\kappa}-P_{\\\\beta} J_{\\\\rho \\\\sigma} (\\\\eta_{\\\\alpha \\\\mu} P_{\\\\nu}-\\\\eta_{\\\\alpha \\\\nu} P_{\\\\mu}) J_{\\\\lambda \\\\kappa}-P_{\\\\beta} J_{\\\\rho \\\\sigma} P_{\\\\alpha} (-\\\\eta_{\\\\lambda \\\\mu} J_{\\\\kappa \\\\nu} + \\\\eta_{\\\\kappa \\\\mu} J_{\\\\lambda \\\\nu} + \\\\eta_{\\\\lambda \\\\nu} J_{\\\\kappa \\\\mu}-\\\\eta_{\\\\kappa \\\\nu} J_{\\\\lambda \\\\mu}))\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}-6\\\\,\\\\left(\\\\frac{1}{6}\\\\,\\\\delta_{\\\\beta \\\\rho} \\\\delta_{\\\\alpha \\\\kappa} \\\\delta_{\\\\lambda \\\\sigma}\\\\discretionary{}{}{} - \\\\frac{1}{6}\\\\,\\\\delta_{\\\\beta \\\\rho} \\\\delta_{\\\\alpha \\\\lambda} \\\\delta_{\\\\kappa \\\\sigma}\\\\discretionary{}{}{} - \\\\frac{1}{6}\\\\,\\\\delta_{\\\\beta \\\\sigma} \\\\delta_{\\\\alpha \\\\kappa} \\\\delta_{\\\\lambda \\\\rho}\\\\discretionary{}{}{}+\\\\frac{1}{6}\\\\,\\\\delta_{\\\\beta \\\\alpha} \\\\delta_{\\\\kappa \\\\sigma} \\\\delta_{\\\\lambda \\\\rho}\\\\discretionary{}{}{}+\\\\frac{1}{6}\\\\,\\\\delta_{\\\\beta \\\\sigma} \\\\delta_{\\\\alpha \\\\lambda} \\\\delta_{\\\\kappa \\\\rho}\\\\discretionary{}{}{} - \\\\frac{1}{6}\\\\,\\\\delta_{\\\\beta \\\\alpha} \\\\delta_{\\\\kappa \\\\rho} \\\\delta_{\\\\lambda \\\\sigma}\\\\right) \\\\left(-\\\\,\\\\left(\\\\eta_{\\\\beta \\\\mu} P_{\\\\nu}\\\\discretionary{}{}{}-\\\\,\\\\eta_{\\\\beta \\\\nu} P_{\\\\mu}\\\\right) J_{\\\\rho \\\\sigma} P_{\\\\alpha} J_{\\\\lambda \\\\kappa}\\\\discretionary{}{}{}-\\\\,P_{\\\\beta} \\\\left(\\\\eta_{\\\\mu \\\\rho} J_{\\\\nu \\\\sigma}\\\\discretionary{}{}{}-\\\\,\\\\eta_{\\\\mu \\\\sigma} J_{\\\\nu \\\\rho}\\\\discretionary{}{}{}-\\\\,\\\\eta_{\\\\nu \\\\rho} J_{\\\\mu \\\\sigma}\\\\discretionary{}{}{}+\\\\eta_{\\\\nu \\\\sigma} J_{\\\\mu \\\\rho}\\\\right) P_{\\\\alpha} J_{\\\\lambda \\\\kappa}\\\\discretionary{}{}{}-\\\\,P_{\\\\beta} J_{\\\\rho \\\\sigma} \\\\left(\\\\eta_{\\\\alpha \\\\mu} P_{\\\\nu}\\\\discretionary{}{}{}-\\\\,\\\\eta_{\\\\alpha \\\\nu} P_{\\\\mu}\\\\right) J_{\\\\lambda \\\\kappa}\\\\discretionary{}{}{}-\\\\,P_{\\\\beta} J_{\\\\rho \\\\sigma} P_{\\\\alpha} \\\\left(-\\\\,\\\\eta_{\\\\lambda \\\\mu} J_{\\\\kappa \\\\nu}\\\\discretionary{}{}{}+\\\\eta_{\\\\kappa \\\\mu} J_{\\\\lambda \\\\nu}\\\\discretionary{}{}{}+\\\\eta_{\\\\lambda \\\\nu} J_{\\\\kappa \\\\mu}\\\\discretionary{}{}{}-\\\\,\\\\eta_{\\\\kappa \\\\nu} J_{\\\\lambda \\\\mu}\\\\right)\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"substitute(_, poincare);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 6318297901614041256,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 17408127201849635253,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 10783874335149056130,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"0\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}0\\\\,\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"distribute(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 11573777653020638176,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"\"\n\t\t}\n\t],\n\t\"description\": \"Cadabra JSON notebook format\",\n\t\"flags\": {\n\t\t\"hide_input_cells\": false\n\t},\n\t\"version\": 1.0\n}\n"
  },
  {
    "path": "examples/post_processing.cnb",
    "content": "\n{\n\t\"cells\" : \n\t[\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\subsection*{Post-processing expressions}\\n\\nIn the old Cadabra, one could use the property \\\\verb|::PostDefaultRules| to automatically call\\na number of algorithms to clean up expressions after each processing step. In the new Cadabra,\\nthis is more flexible. If you define a function \\\\verb|post_process| which takes an \\\\verb|Ex| \\nobject as argument, this function will be called as a cleanup function after every algorithm\\nhas finished. \\n\\nThis is much more flexible, because you can now decide to e.g. call a cleanup function only\\nwhen an expression reaches a certain size. \\n\\nThe basics are shown in the example below.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\subsection*{Post-processing expressions}\\n\\nIn the old Cadabra, one could use the property \\\\verb|::PostDefaultRules| to automatically call\\na number of algorithms to clean up expressions after each processing step. In the new Cadabra,\\nthis is more flexible. If you define a function \\\\verb|post_process| which takes an \\\\verb|Ex| \\nobject as argument, this function will be called as a cleanup function after every algorithm\\nhas finished. \\n\\nThis is much more flexible, because you can now decide to e.g. call a cleanup function only\\nwhen an expression reaches a certain size. \\n\\nThe basics are shown in the example below.\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"def post_process(ex):\\n\\tsubstitute(ex, $A->B$)\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}B+C+D\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex:=B+C+D;\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}2B+D\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"substitute(ex,$C->A$);\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"When writing a \\\\verb|post_process| function, remember that all Cadabra algorithms change expressions in-place. That is \\nthe reason why you do not have to do \\\\verb|ex = substitute(ex, $A->B$)| in the example above, and why you do not\\nneed to \\\\verb|return ex| at the end of that function.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"When writing a \\\\verb|post_process| function, remember that all Cadabra algorithms change expressions in-place. That is \\nthe reason why you do not have to do \\\\verb|ex = substitute(ex, $A->B$)| in the example above, and why you do not\\nneed to \\\\verb|return ex| at the end of that function.\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1.0\n}\n\n"
  },
  {
    "path": "examples/quickstart.cnb",
    "content": "{\n\t\"cell_id\" : 5716356280111729715,\n\t\"cells\" : \n\t[\n\t\t{\n\t\t\t\"cell_id\" : 7757173625391423646,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 11255716305935146302,\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\section*{Cadabra quick start}\\n\\nThis is a quick start introduction to Cadabra. For more in-depth\\ndiscussion of its features, consult the various\\n\\\\href{http://cadabra.science/tutorials.html}{tutorials}.\\n\\nAfter installation, Cadabra can be started with \\\\verb|cadabra2-gtk| from the command line, \\nor by picking it from the `Education' menu.\\n\\n\\\\subsection*{Bosonic basics}\\n\\nBefore discussing actual calculations, let us start with a few words\\nconcerning notation. This discussion can be short because \\nmathematical expressions are entered\\nessentially as one would enter them in TeX (with a few restrictions\\nto avoid ambiguities, which we will discuss as we go along). In order\\nto manipulate expressions, Cadabra often needs to know a bit more about\\nproperties of tensors or other symbols. Such properties are entered\\nusing the `\\\\verb|::|' symbol. A simple example is the declaration of\\nindex sets, useful for automatic dummy index relabelling. An example\\nwill clarify this,\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\section*{Cadabra quick start}\\n\\nThis is a quick start introduction to Cadabra. For more in-depth\\ndiscussion of its features, consult the various\\n\\\\href{http://cadabra.science/tutorials.html}{tutorials}.\\n\\nAfter installation, Cadabra can be started with \\\\verb|cadabra2-gtk| from the command line, \\nor by picking it from the `Education' menu.\\n\\n\\\\subsection*{Bosonic basics}\\n\\nBefore discussing actual calculations, let us start with a few words\\nconcerning notation. This discussion can be short because \\nmathematical expressions are entered\\nessentially as one would enter them in TeX (with a few restrictions\\nto avoid ambiguities, which we will discuss as we go along). In order\\nto manipulate expressions, Cadabra often needs to know a bit more about\\nproperties of tensors or other symbols. Such properties are entered\\nusing the `\\\\verb|::|' symbol. A simple example is the declaration of\\nindex sets, useful for automatic dummy index relabelling. An example\\nwill clarify this,\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 103293113963716287,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 9223372036854775809,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Indices(position=free) to~}\\\\left[a,~\\\\discretionary{}{}{} b,~\\\\discretionary{}{}{} c,~\\\\discretionary{}{}{} d\\\\right].\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 9223372036854775810,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\" : 9223372036854775811,\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"A_{a b} B_{b c}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}A_{a b} B_{b c}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"{ a, b, c, d }::Indices;\\nex:= A_{a b} B_{b c};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 6206707828745205786,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 9223372036854775813,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\" : 9223372036854775814,\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"A_{a b} C_{b c d} D_{d}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}A_{a b} C_{b c d} D_{d}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"substitute(_, $B_{a b} ->  C_{a b c} D_{c}$ );\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 7045409746205840896,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 3700100225770046834,\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"The automatic index relabelling which has taken place in this\\nsubstitute command was clearly only possible because of the property\\ndeclaration in the first line. Note how the substitute command has\\nalso figured out that \\\\verb|B_{a b}| on the left-hand side is\\nequivalent to \\\\verb|B_{b c}|, without any explicit wildcards or\\npatterns. We will see more of this type of field-theory motivated\\nlogic throughout the paper.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"The automatic index relabelling which has taken place in this\\nsubstitute command was clearly only possible because of the property\\ndeclaration in the first line. Note how the substitute command has\\nalso figured out that \\\\verb|B_{a b}| on the left-hand side is\\nequivalent to \\\\verb|B_{b c}|, without any explicit wildcards or\\npatterns. We will see more of this type of field-theory motivated\\nlogic throughout the paper.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 3939233137557893239,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 8995867847458487530,\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"Indices can be simple letters, as in the example above, but it is also\\nperfectly possible to put accents on them. This can be useful for\\ne.g.~notations involving chiral spinors. The following example\\nillustrates the use of accents on indices.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"Indices can be simple letters, as in the example above, but it is also\\nperfectly possible to put accents on them. This can be useful for\\ne.g.~notations involving chiral spinors. The following example\\nillustrates the use of accents on indices.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 18272292102993358173,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\\\\dot{#}::Accent;\\nA_{\\\\dot{a} \\\\dot{b}}::AntiSymmetric;\\nex:= A_{\\\\dot{b} \\\\dot{a}};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 8726009276796452632,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 10191742109424542640,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}-A_{\\\\dot{a} \\\\dot{b}}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"canonicalise(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 17301188597788460065,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 12380391792656256536,\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"Here we also see a second usage of property declarations: the\\nconstruction in the first line declares that the $A_{\\\\dot{a} \\\\dot{b}}$\\ntensor is antisymmetric in its indices. The canonicalise command\\nsubsequently writes the input in a canonical form, which in this\\ntrivial example simply means that the indices gets sorted in\\nalphabetical order.  Continuing the example above, one can also use\\nsubscripts or superscripts on indices, as in the example below.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"Here we also see a second usage of property declarations: the\\nconstruction in the first line declares that the $A_{\\\\dot{a} \\\\dot{b}}$\\ntensor is antisymmetric in its indices. The canonicalise command\\nsubsequently writes the input in a canonical form, which in this\\ntrivial example simply means that the indices gets sorted in\\nalphabetical order.  Continuing the example above, one can also use\\nsubscripts or superscripts on indices, as in the example below.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 11192134437285109843,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 6608670350216599249,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Indices(position=free) to~}\\\\left\\\\{a_{1}, \\\\linebreak[0] a_{2}, \\\\linebreak[0] a_{3}, \\\\linebreak[0] a_{4}\\\\right\\\\}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 11894732657201129903,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}V_{a_{1}} W_{a_{1}}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 193345049390931887,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}M_{a_{1} a} N_{a} W_{a_{1}}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"{ a_{1}, a_{2}, a_{3}, a_{4} }::Indices(vector);\\nex:= V_{a_{1}} W_{a_{1}};\\nsubstitute(_, $V_{a_{2}} -> M_{a_{2} a_{1}} N_{a_{1}}$ );\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 14955216728724290107,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 4273410186771757488,\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"The input format is a mixture of Cadabra's own LaTeX-like language for\\nthe description of mathematical expressions, and Python. The\\nunderscore symbol `\\\\verb|_|' always refers to the last-used expression.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"The input format is a mixture of Cadabra's own LaTeX-like language for\\nthe description of mathematical expressions, and Python. The\\nunderscore symbol `\\\\verb|_|' always refers to the last-used expression.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 10649798021102149437,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 7873409660672401713,\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"A guiding principle in Cadabra is that nothing ever has to be declared\\nunless this is absolutely needed. This is in contrast to many other\\nsystems, where for instance one has to declare manifolds and index\\nsets and so on before one can even enter a tensor expression. This\\nmakes code hard to read, but more importantly, such additional\\ndeclarations are hard to remember. As an example of how Cadabra works,\\none can e.g.~input tensor expressions and perform substitution on them,\\nwithout ever declaring the symbols used for indices. Only when the\\nprogram needs to generate new dummy indices does one need to declare\\nindex sets, so that dummy indices can be taken out of the right\\nset. The general guideline is that ``one only\\nneeds to tell the program about the meaning of symbols when this is\\nactually required to do the manipulation correctly''.\\n\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"A guiding principle in Cadabra is that nothing ever has to be declared\\nunless this is absolutely needed. This is in contrast to many other\\nsystems, where for instance one has to declare manifolds and index\\nsets and so on before one can even enter a tensor expression. This\\nmakes code hard to read, but more importantly, such additional\\ndeclarations are hard to remember. As an example of how Cadabra works,\\none can e.g.~input tensor expressions and perform substitution on them,\\nwithout ever declaring the symbols used for indices. Only when the\\nprogram needs to generate new dummy indices does one need to declare\\nindex sets, so that dummy indices can be taken out of the right\\nset. The general guideline is that ``one only\\nneeds to tell the program about the meaning of symbols when this is\\nactually required to do the manipulation correctly''.\\n\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 4928880447376698898,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 7710784338868361327,\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"In order to declare symmetries of tensors, it is possible to use\\nsimple shorthands like the \\\\prop{AntiSymmetric} in the example above. \\nMore generally, symmetries can be declared using  a generic Young\\ntableau notation. An object with the symmetries of a Riemann tensor,\\nfor example, can be declared as in the following example.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"In order to declare symmetries of tensors, it is possible to use\\nsimple shorthands like the \\\\prop{AntiSymmetric} in the example above. \\nMore generally, symmetries can be declared using  a generic Young\\ntableau notation. An object with the symmetries of a Riemann tensor,\\nfor example, can be declared as in the following example.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 11042877764109095134,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 1402957615224784829,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}R_{a b c d} R_{d c a b}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 8694570044256099378,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}-R_{a b c d} R_{a b c d}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"R_{a b c d}::TableauSymmetry(shape={2,2}, indices={0,2,1,3}).\\nex:=R_{a b c d} R_{d c a b};\\ncanonicalise(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 17179130787021300618,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 19485351281891507,\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"The first line indicates that the tensor has the symmetries of the\\n$2\\\\times 2$ Young tableau. The \\\\algo{canonicalise} command writes\\nthe input in canonical form with respect to mono-term symmetries\\n(anti-symmetry in the two index pairs and symmetry under pair\\nexchange). The Ricci symmetry is also encoded in the Young tableau and\\nwill be discussed later. Many tensor symmetries have shorthand\\nnotations, so one often does not have spell out the tableau (e.g.~\\\\prop{RiemannTensor} or \\\\prop{SatisfiesBianchi}).\\n\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"The first line indicates that the tensor has the symmetries of the\\n$2\\\\times 2$ Young tableau. The \\\\algo{canonicalise} command writes\\nthe input in canonical form with respect to mono-term symmetries\\n(anti-symmetry in the two index pairs and symmetry under pair\\nexchange). The Ricci symmetry is also encoded in the Young tableau and\\nwill be discussed later. Many tensor symmetries have shorthand\\nnotations, so one often does not have spell out the tableau (e.g.~\\\\prop{RiemannTensor} or \\\\prop{SatisfiesBianchi}).\\n\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 13295413574068657490,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 18067534547552251550,\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\subsection*{Derivatives and dependencies}\\n\\nThere are relatively few surprises when it comes to derivatives.\\nIt is possible to write derivatives with respect to coordinates,\\ni.e.~write~$\\\\partial_x$ where~$x$ is a coordinate, but\\nit is also possible to use indices, as in~$\\\\partial_i$ with $i$ being\\na vector index. It is also possible to make objects implicitly\\ndependent on a derivative operator, so that one can write~$\\\\partial\\nA$ without an explicit specification of the coordinate which is\\ninvolved here. \"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\subsection*{Derivatives and dependencies}\\n\\nThere are relatively few surprises when it comes to derivatives.\\nIt is possible to write derivatives with respect to coordinates,\\ni.e.~write~$\\\\partial_x$ where~$x$ is a coordinate, but\\nit is also possible to use indices, as in~$\\\\partial_i$ with $i$ being\\na vector index. It is also possible to make objects implicitly\\ndependent on a derivative operator, so that one can write~$\\\\partial\\nA$ without an explicit specification of the coordinate which is\\ninvolved here. \"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 15605589921123687497,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 508266178189537151,\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"In order to make this possible, however, derivative objects have to be\\ndeclared just like indices, otherwise the system does not know which\\nsymbol ($\\\\partial$, $D$, $d$, $\\\\nabla$, \\\\ldots) one wants to use for\\nthem. Implicit dependencies of objects on coordinates associated to\\nderivatives is indicated through a \\\\prop{Depends} property. Here is an\\nexample to illustrate all this:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"In order to make this possible, however, derivative objects have to be\\ndeclared just like indices, otherwise the system does not know which\\nsymbol ($\\\\partial$, $D$, $d$, $\\\\nabla$, \\\\ldots) one wants to use for\\nthem. Implicit dependencies of objects on coordinates associated to\\nderivatives is indicated through a \\\\prop{Depends} property. Here is an\\nexample to illustrate all this:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 11942606738048787455,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 6117908760502214353,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Indices(position=free) to~}\\\\left\\\\{m, \\\\linebreak[0] n, \\\\linebreak[0] p, \\\\linebreak[0] q, \\\\linebreak[0] r\\\\right\\\\}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 1202969890068169255,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Derivative to~}\\\\nabla{\\\\#}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 16962655093109485107,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property PartialDerivative to~}\\\\partial{\\\\#}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 11000508826222965474,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property AntiSymmetric to~}A_{m n}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 10050122667762509553,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Depends to~}V_{m}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 6920800992316428716,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\partial_{m p}\\\\left(A_{q r} V_{n}\\\\right) A^{p m}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"{m,n,p,q,r}::Indices(position=free);\\n\\\\nabla{#}::Derivative;\\n\\\\partial{#}::PartialDerivative;\\nA_{m n}::AntiSymmetric;\\nV_{m}::Depends(\\\\nabla{#});\\n\\nex:= \\\\partial_{m p}( A_{q r} V_{n} ) A^{p m};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 3136840608177541058,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 4897756282813376460,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}0\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"canonicalise(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 10994095467781940960,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 15342546519721877711,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\nabla_{m p}\\\\left(A_{q r} V_{n}\\\\right) A^{p m}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 9104149497242645041,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}-\\\\nabla^{m p}\\\\left(A_{q r} V_{n}\\\\right) A_{m p}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex:=\\\\nabla_{m p}( A_{q r} V_{n} ) A^{p m};\\ncanonicalise(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 17765294794886716645,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 18213103545406437598,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}-A_{q r} \\\\nabla^{m p}{V_{n}} A_{m p}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"unwrap(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 16161961747209770793,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 910392170269658202,\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"Note how the symmetry of a double partial derivative has automatically\\nbeen taken into account (it\\nis part of the \\\\prop{PartialDerivative} property). This is called\\n``property inheritance''.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"Note how the symmetry of a double partial derivative has automatically\\nbeen taken into account (it\\nis part of the \\\\prop{PartialDerivative} property). This is called\\n``property inheritance''.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 3935600940570551980,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 12617856564588563850,\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\section*{More to follow ...}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\section*{More to follow ...}\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 5559244724204550377,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1\n}\n"
  },
  {
    "path": "examples/ref_accents.cnb",
    "content": "{\n\t\"cell_id\": 15346339992211116796,\n\t\"cells\": [\n\t\t{\n\t\t\t\"cell_id\": 16459148063967060997,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 6792806555766337768,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\section*{Accents}\\n\\nIt often occurs that you want to put a hat or tilde or some other\\naccent on top of a symbol, as a means to indicate a slightly different\\nobject. In most of these cases, the properties of the normal symbol\\nand the accented symbol are identical. Such accents are declared using\\nthe \\\\prop{Accent} property, as in\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\section*{Accents}\\n\\nIt often occurs that you want to put a hat or tilde or some other\\naccent on top of a symbol, as a means to indicate a slightly different\\nobject. In most of these cases, the properties of the normal symbol\\nand the accented symbol are identical. Such accents are declared using\\nthe \\\\prop{Accent} property, as in\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 16057021908384386123,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 11553527963445813639,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property Accent attached to~}\\\\backslash\\\\texttt{hat}\\\\{\\\\#\\\\}.\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"\\\\hat{#}::Accent;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 16972251731688036769,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 12965346805565846436,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"This automatically makes all symbols with hats inherit the properties\\nof the unhatted symbols,\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"This automatically makes all symbols with hats inherit the properties\\nof the unhatted symbols,\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 17676320454094676305,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 15299440598427965471,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 4840539522801871562,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\hat{\\\\chi} \\\\psi\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\widehat{\\\\chi} \\\\psi\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 11746078301643897089,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 14275938498403721147,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"-\\\\psi \\\\hat{\\\\chi}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}-\\\\psi \\\\widehat{\\\\chi}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"\\\\hat{#}::Accent.\\n{\\\\psi, \\\\chi}::AntiCommuting.\\n{\\\\psi, \\\\chi}::SortOrder.\\nex:= \\\\hat{\\\\chi} \\\\psi;\\nsort_product(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 16254242404429757988,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 2296267821247394715,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"If you want to put an accent on an object with indices, wrap the\\naccent around the entire object, do not leave the indices outside.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"If you want to put an accent on an object with indices, wrap the\\naccent around the entire object, do not leave the indices outside.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 4078046895693549704,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 14719176952547821212,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"Note that it is also possible to mark objects by attaching sub- or\\nsuperscripted symbols to them, as in e.g.~$A^\\\\dagger$. This can be\\ndone by declaring these symbols explicitly using the \\\\prop{Symbol}\\nproperty,\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"Note that it is also possible to mark objects by attaching sub- or\\nsuperscripted symbols to them, as in e.g.~$A^\\\\dagger$. This can be\\ndone by declaring these symbols explicitly using the \\\\prop{Symbol}\\nproperty,\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 7750888541147789542,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 7392594223693586359,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property Symbol attached to~}\\\\dagger.\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"\\\\dagger::Symbol;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 865666516606114027,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 8568844144367393656,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"If you do not do this, the dagger symbol will be seen as an index\\nand an error will be reported if it appears more than twice.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"If you do not do this, the dagger symbol will be seen as an index\\nand an error will be reported if it appears more than twice.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 17791353427878308235,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"\"\n\t\t}\n\t],\n\t\"description\": \"Cadabra JSON notebook format\",\n\t\"version\": 1.0\n}\n"
  },
  {
    "path": "examples/ref_c++_library.cnb",
    "content": "{\n\t\"cell_id\": 1142308909871904320,\n\t\"cells\": [\n\t\t{\n\t\t\t\"cell_id\": 17497369068236213474,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 2932484825110357390,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\section*{Using Cadabra directly from C++}\\n\\nIt is possible to use the functionality of Cadabra directly from C++ code,\\nwithout dealing with the Python layer on top of it, and without using the\\nnotebook interface. The library is called \\\\verb|cadabra2++| and building \\nand installation instructions are provided in the project's \\\\verb|README|.\\nHere we describe how to use this library.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\section*{Using Cadabra directly from C++}\\n\\nIt is possible to use the functionality of Cadabra directly from C++ code,\\nwithout dealing with the Python layer on top of it, and without using the\\nnotebook interface. The library is called \\\\verb|cadabra2++| and building \\nand installation instructions are provided in the project's \\\\verb|README|.\\nHere we describe how to use this library.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 1136201673028859752,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 1610651877957794132,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\subsection*{Simple example}\\n\\nBasic use of the Cadabra C++ library consists of five parts: creating a kernel,\\ninserting object properties into the kernel, defining expressions, acting with\\nalgorithms on those expressions, and displaying the result. A minimal example \\nis as follows:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\subsection*{Simple example}\\n\\nBasic use of the Cadabra C++ library consists of five parts: creating a kernel,\\ninserting object properties into the kernel, defining expressions, acting with\\nalgorithms on those expressions, and displaying the result. A minimal example \\nis as follows:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 13937482186812407628,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"#include \\\"cadabra2++.hh\\\"\\n#include <iostream>\\n\\nusing namespace cadabra;\\nusing namespace cadabra::cpplib;\\n\\nint main() {\\n   Kernel k(true);\\n   inject_property<AntiCommuting>(k, \\\"{A,B}\\\");\\n   auto ex = \\\"A B - B A\\\"_ex(k);\\n   sort_product sp(k, *ex);\\n   sp.apply_generic();\\n   collect_terms(k, *ex);\\n   sp.apply_generic();\\n   std::cout << pprint(k, ex) << std::endl;   \\n}\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 2190494406404461834,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 5966978324235453015,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"The output of this program is \\\\verb|2 A B|.\\n\\nMost of the above should be fairly easy to understand for anyone who has worked with the\\nPython interface to Cadabra before. Note how properties are attached to objects using\\nthe \\\\verb|inject_property| function call. This takes the kernel as argument, as well\\nas a textual expression of what you would use in the Python interface.\\n\\nAlgorithms are C++ objects, which you need to instantiate, and then run explicitly\\nby calling the \\\\verb|apply_generic| function. As in the Python version, algorithms act \\nin-place (mostly), and the \\\\verb|ex| expression above thus changes as the code\\nprogresses. \\n\\nFinally, the expression is printed by using the `pprint` function. This is necessary\\nbecause printing requires information stored in the Cadabra kernel.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"The output of this program is \\\\verb|2 A B|.\\n\\nMost of the above should be fairly easy to understand for anyone who has worked with the\\nPython interface to Cadabra before. Note how properties are attached to objects using\\nthe \\\\verb|inject_property| function call. This takes the kernel as argument, as well\\nas a textual expression of what you would use in the Python interface.\\n\\nAlgorithms are C++ objects, which you need to instantiate, and then run explicitly\\nby calling the \\\\verb|apply_generic| function. As in the Python version, algorithms act \\nin-place (mostly), and the \\\\verb|ex| expression above thus changes as the code\\nprogresses. \\n\\nFinally, the expression is printed by using the `pprint` function. This is necessary\\nbecause printing requires information stored in the Cadabra kernel.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 4292845191419390817,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"\"\n\t\t}\n\t],\n\t\"description\": \"Cadabra JSON notebook format\",\n\t\"version\": 1.0\n}\n"
  },
  {
    "path": "examples/ref_core_package.cnb",
    "content": "{\n\t\"cells\" : \n\t[\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\section*{Elementary operations on expressions}\\n\\nThe package \\\\verb|cdb.core| and its various sub-packages contain a number of useful\\nhelper functions to manipulate expressions in elementary ways. This includes things\\nlike moving terms from one side of an equation or inequality to the other side, or multiplying\\nboth sides of an equation by the same factor. \"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\section*{Elementary operations on expressions}\\n\\nThe package \\\\verb|cdb.core| and its various sub-packages contain a number of useful\\nhelper functions to manipulate expressions in elementary ways. This includes things\\nlike moving terms from one side of an equation or inequality to the other side, or multiplying\\nboth sides of an equation by the same factor. \"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1\n}\n"
  },
  {
    "path": "examples/ref_default_simplification.cnb",
    "content": "{\n\t\"cells\" : \n\t[\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\section*{Default simplification}\\n\\nBy default, Cadabra does very few things ``by itself'' with your\\nexpressions. It only collects equal terms, but even that can be turned\\noff if you want to. The logic is that all simplification steps are contained\\nin a function \\\\verb|post_process|, which is executed on every new input and on every completion of\\nan algorithm. It can contain arbitrary code, but by default it reads\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\section*{Default simplification}\\n\\nBy default, Cadabra does very few things ``by itself'' with your\\nexpressions. It only collects equal terms, but even that can be turned\\noff if you want to. The logic is that all simplification steps are contained\\nin a function \\\\verb|post_process|, which is executed on every new input and on every completion of\\nan algorithm. It can contain arbitrary code, but by default it reads\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"def post_process(ex):\\n    collect_terms(ex)\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"which simply collects equal terms. You can for instance apply a substitution on every input automatically,\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"which simply collects equal terms. You can for instance apply a substitution on every input automatically,\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"def post_process(ex):\\n    distribute(ex)\\n    substitute(ex, $A_{m n} -> B_{m q} B_{q n}$)\\n    collect_terms(ex)\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Indices(position=free) to~}\\\\left[m,~\\\\discretionary{}{}{} n,~\\\\discretionary{}{}{} p,~\\\\discretionary{}{}{} q\\\\right].\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Symmetric to~}B_{m q} B_{q n}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"B_{m q} B_{q n} B_{n p} B_{p m} + B_{m q} B_{q n} C_{n m}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}B_{m q} B_{q n} B_{n p} B_{p m}+B_{m q} B_{q n} C_{n m}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"{m,n,p,q}::Indices(vector);\\nA_{m n}::Symmetric;\\nex:=A_{m n} ( A_{n m} + C_{n m});\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"As usual dummy indices have been relabelled appropriately.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"As usual dummy indices have been relabelled appropriately.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"The \\\\verb|post_process| function can be redefined on-the-fly in the middle of a notebook.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"The \\\\verb|post_process| function can be redefined on-the-fly in the middle of a notebook.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1\n}\n"
  },
  {
    "path": "examples/ref_derivatives.cnb",
    "content": "{\n\t\"cell_id\": 1122815849851778574,\n\t\"cells\": [\n\t\t{\n\t\t\t\"cell_id\": 5978568215711204063,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9163289818544044159,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\section*{Derivatives and implicit dependence on coordinates}\\n\\nThere is no fixed notation for derivatives; as with all other objects\\nyou have to declare derivatives by associating a property to them, in\\nthis case the \\\\prop{Derivative} property. \"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\section*{Derivatives and implicit dependence on coordinates}\\n\\nThere is no fixed notation for derivatives; as with all other objects\\nyou have to declare derivatives by associating a property to them, in\\nthis case the \\\\prop{Derivative} property. \"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 3121771876375322580,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 17189132776906135827,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property Derivative attached to~}\\\\backslash\\\\texttt{nabla}\\\\{\\\\#\\\\}.\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"\\\\nabla{#}::Derivative;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 13092358405604264614,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 13903985434684835252,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"Derivative objects can be used in various ways. You can just write the\\nderivative symbol, as in\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"Derivative objects can be used in various ways. You can just write the\\nderivative symbol, as in\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 18151900650212757933,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 13634587081560003361,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 17401122873979242133,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\nabla(A_{\\\\mu})\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\nabla{A_{\\\\mu}}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex:=\\\\nabla{ A_{\\\\mu} };\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 2535925725272172629,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 2703885803720580789,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"Or you can write the coordinate with\\nrespect to which the derivative is taken,\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"Or you can write the coordinate with\\nrespect to which the derivative is taken,\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 16893005691693910276,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 6265159977008670288,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property Coordinate attached to~}s.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 2508463848585078013,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property Depends attached to~}A_{\\\\mu}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9585809248094876254,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 14661015508918667345,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\nabla_{s}(A_{\\\\mu})\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\nabla_{s}{A_{\\\\mu}}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"s::Coordinate;\\nA_{\\\\mu}::Depends(s);\\nex:=\\\\nabla_{s}{ A_{\\\\mu} };\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 10153963060502655636,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 10916447968963342696,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"Finally, you can use an index as the subscript argument, as in\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"Finally, you can use an index as the subscript argument, as in\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 13561250281933297262,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 2893963764896938419,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property Indices(position=free) attached to~}\\\\left[\\\\mu, \\\\discretionary{}{}{}\\\\nu\\\\right].\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 10286893870653739756,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 8500921658553144632,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\nabla_{\\\\nu}(A_{\\\\mu})\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\nabla_{\\\\nu}{A_{\\\\mu}}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"{ \\\\mu, \\\\nu }::Indices(vector);\\nex:=\\\\nabla_{\\\\nu}{ A_{\\\\mu} };\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 10444583949408313065,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 4530724075209643387,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"(in which case the first line is, for the purpose of using the\\nderivative operator, actually unnecessary). \"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"(in which case the first line is, for the purpose of using the\\nderivative operator, actually unnecessary). \"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 13397161166768324625,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 17715485633604521333,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"The main point of associating the \\\\prop{Derivative} property to an\\nobject is to make the object obey the Leibnitz or product rule, as\\nillustrated by the following example,\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"The main point of associating the \\\\prop{Derivative} property to an\\nobject is to make the object obey the Leibnitz or product rule, as\\nillustrated by the following example,\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 4282409426609146563,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 17039843437785172514,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property Derivative attached to~}\\\\backslash\\\\texttt{nabla}\\\\{\\\\#\\\\}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 12960000548412277736,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 535790888793878903,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\nabla(A_{\\\\mu} B_{\\\\nu})\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\nabla\\\\left(A_{\\\\mu} B_{\\\\nu}\\\\right)\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 12457032370277415749,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 3795438018106939319,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\nabla(A_{\\\\mu}) B_{\\\\nu} + A_{\\\\mu} \\\\nabla(B_{\\\\nu})\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\nabla{A_{\\\\mu}} B_{\\\\nu}\\\\discretionary{}{}{}+A_{\\\\mu} \\\\nabla{B_{\\\\nu}}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"\\\\nabla{#}::Derivative;\\nex:= \\\\nabla{ A_{\\\\mu} * B_{\\\\nu} };\\nproduct_rule(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 8677916216204324123,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 17244218890176750790,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"This behaviour is a consequence of the fact that \\\\prop{Derivative}\\nderives from \\\\prop{Distributable}. Note that the\\n\\\\prop{Derivative} property does not automatically give you \\ncommuting derivatives, so that you can e.g.~use it to write covariant\\nderivatives. \"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"This behaviour is a consequence of the fact that \\\\prop{Derivative}\\nderives from \\\\prop{Distributable}. Note that the\\n\\\\prop{Derivative} property does not automatically give you \\ncommuting derivatives, so that you can e.g.~use it to write covariant\\nderivatives. \"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 4266922430318706841,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 7753763602494058227,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"More specific derivative types exist too. An example are partial\\nderivatives, declared using the \\\\prop{PartialDerivative} property.\\nPartial derivatives are commuting and therefore automatically\\nsymmetric in their indices,\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"More specific derivative types exist too. An example are partial\\nderivatives, declared using the \\\\prop{PartialDerivative} property.\\nPartial derivatives are commuting and therefore automatically\\nsymmetric in their indices,\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 1000836246543036704,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 7592315176139174518,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property PartialDerivative attached to~}\\\\backslash\\\\texttt{partial}\\\\{\\\\#\\\\}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 1289170573850456116,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property Indices(position=free) attached to~}\\\\left[a, \\\\discretionary{}{}{}b, \\\\discretionary{}{}{}m, \\\\discretionary{}{}{}n\\\\right].\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 11151070317708428483,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property Symmetric attached to~}C_{m n}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 15420425853360909320,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 16823369671527784028,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"T^{b a} \\\\partial_{a b}(C_{m n} D_{n m})\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}T^{b a} \\\\partial_{a b}\\\\left(C_{m n} D_{n m}\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"\\\\partial{#}::PartialDerivative;\\n{a,b,m,n}::Indices(vector);\\nC_{m n}::Symmetric;\\nex:=T^{b a} \\\\partial_{a b}( C_{m n} D_{n m} );\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 17184423938730932951,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 14011557080814126640,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 7167017290773373763,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"T^{a b} \\\\partial_{a b}(C_{m n} D_{m n})\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}T^{a b} \\\\partial_{a b}\\\\left(C_{m n} D_{m n}\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"canonicalise(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 17585485201075769805,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"\"\n\t\t}\n\t],\n\t\"description\": \"Cadabra JSON notebook format\",\n\t\"version\": 1.0\n}\n"
  },
  {
    "path": "examples/ref_dynamical_updates.cnb",
    "content": "{\n\t\"cell_id\": 15099524443234900231,\n\t\"cells\": [\n\t\t{\n\t\t\t\"cell_id\": 18224201033722515016,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 288377247472214505,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\section*{Dynamic cell updates}\\n\\nBy default the output generated by \\\\verb|display| will generate a new output cell.\\nHowever, it is possible to put the output into an existing cell. In order to do this,\\nuse the \\\\verb|cell_id| parameter of the \\\\verb|display| call, passing it the ID of\\nthe cell you want to use for output. To obtain that cell, note that all \\\\verb|display|\\ncalls return the ID of the cell generated or re-used. \\n\\nThe following example shows how to use this. On the first iteration of the loop\\nwe pass the ID '0', which leads to generation of a new cell. The call returns the\\nID of the newly generated cell, which is then used for any subsequent iterations of\\nthe loop.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\section*{Dynamic cell updates}\\n\\nBy default the output generated by \\\\verb|display| will generate a new output cell.\\nHowever, it is possible to put the output into an existing cell. In order to do this,\\nuse the \\\\verb|cell_id| parameter of the \\\\verb|display| call, passing it the ID of\\nthe cell you want to use for output. To obtain that cell, note that all \\\\verb|display|\\ncalls return the ID of the cell generated or re-used. \\n\\nThe following example shows how to use this. On the first iteration of the loop\\nwe pass the ID '0', which leads to generation of a new cell. The call returns the\\nID of the newly generated cell, which is then used for any subsequent iterations of\\nthe loop.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 13251744526743992062,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"from time import time, sleep\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 2146353832374992238,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 6012879893807672433,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"verbatim\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}100\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"out=0\\nfor i in range(100):\\n   if i!=0:\\n      sleep(0.02)\\n   out=display(i+1, cell_id=out)\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 9892886858352650674,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 3080659676924590408,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"You do not necessarily have to refer to an output cell generated by the current input\\ncell, as the following example shows. The first input cell generates output, which is\\nthen changed by the following output cell.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"You do not necessarily have to refer to an output cell generated by the current input\\ncell, as the following example shows. The first input cell generates output, which is\\nthen changed by the following output cell.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 105907711687349616,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 10796302101274432061,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"verbatim\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}🍅\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"out=0\\nfor i in range(40):\\n   out=display(\\\"🍅\\\"*i, cell_id=out)\\n   sleep(0.01)\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 7666176074787439841,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"for i in range(40):\\n   out=display(\\\"🍅\\\"*(40-i), cell_id=out)\\n   sleep(0.01)\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 17146903837014280937,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 3727440420867125456,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"Note that while the updates are reasonably fast, there is of course some overhead;\\nthe following cell is a modified version of the first example, timing the total \\nrun.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"Note that while the updates are reasonably fast, there is of course some overhead;\\nthe following cell is a modified version of the first example, timing the total \\nrun.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 9488396359116664289,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 4340157784515055137,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"verbatim\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}1000\\\\end{verbatim}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 5804908784821541658,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"verbatim\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}time taken 1.34 sec\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"start=time()\\nout=0\\nfor i in range(1000):\\n   if i!=0:\\n      sleep(0.001)\\n   out=display(i+1, cell_id=out)\\nend=time()\\ndisplay(f\\\"time taken {(end-start):.2f} sec\\\")\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 12976171920402918008,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 6406072888083276979,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"You can also use this mechanism to generate simple animations of functions. If you use \\\\verb|display|\\nto put a plot into an existing output cell, the plot will be replaced.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"You can also use this mechanism to generate simple animations of functions. If you use \\\\verb|display|\\nto put a plot into an existing output cell, the plot will be replaced.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 16316670679203193483,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"from cdb.graphics.plot import plot\\nimport numpy as np\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 4578427611787586049,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 1856423342358845881,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"image_svg\",\n\t\t\t\t\t\"source\": \"<?xml version="1.0" encoding="utf-8" standalone="no"?>
<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
  "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="460.8pt" height="345.6pt" viewBox="0 0 460.8 345.6" xmlns="http://www.w3.org/2000/svg" version="1.1">
 <metadata>
  <rdf:RDF xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:cc="http://creativecommons.org/ns#" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
   <cc:Work>
    <dc:type rdf:resource="http://purl.org/dc/dcmitype/StillImage"/>
    <dc:date>2025-06-22T17:00:12.065438</dc:date>
    <dc:format>image/svg+xml</dc:format>
    <dc:creator>
     <cc:Agent>
      <dc:title>Matplotlib v3.6.3, https://matplotlib.org/</dc:title>
     </cc:Agent>
    </dc:creator>
   </cc:Work>
  </rdf:RDF>
 </metadata>
 <defs>
  <style type="text/css">*{stroke-linejoin: round; stroke-linecap: butt}</style>
 </defs>
 <g id="figure_1">
  <g id="patch_1">
   <path d="M 0 345.6 
L 460.8 345.6 
L 460.8 0 
L 0 0 
z
" style="fill: #ffffff"/>
  </g>
  <g id="axes_1">
   <g id="patch_2">
    <path d="M 57.6 307.584 
L 414.72 307.584 
L 414.72 41.472 
L 57.6 41.472 
z
" style="fill: #ffffff"/>
   </g>
   <g id="matplotlib.axis_1">
    <g id="xtick_1">
     <g id="line2d_1">
      <defs>
       <path id="mfe36c1baae" d="M 0 0 
L 0 3.5 
" style="stroke: #000000; stroke-width: 0.8"/>
      </defs>
      <g>
       <use xlink:href="#mfe36c1baae" x="73.832727" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_1">
      <!-- 0 -->
      <g transform="translate(70.651477 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-30" d="M 2034 4250 
Q 1547 4250 1301 3770 
Q 1056 3291 1056 2328 
Q 1056 1369 1301 889 
Q 1547 409 2034 409 
Q 2525 409 2770 889 
Q 3016 1369 3016 2328 
Q 3016 3291 2770 3770 
Q 2525 4250 2034 4250 
z
M 2034 4750 
Q 2819 4750 3233 4129 
Q 3647 3509 3647 2328 
Q 3647 1150 3233 529 
Q 2819 -91 2034 -91 
Q 1250 -91 836 529 
Q 422 1150 422 2328 
Q 422 3509 836 4129 
Q 1250 4750 2034 4750 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-30"/>
      </g>
     </g>
    </g>
    <g id="xtick_2">
     <g id="line2d_2">
      <g>
       <use xlink:href="#mfe36c1baae" x="125.529311" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_2">
      <!-- 1 -->
      <g transform="translate(122.348061 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-31" d="M 794 531 
L 1825 531 
L 1825 4091 
L 703 3866 
L 703 4441 
L 1819 4666 
L 2450 4666 
L 2450 531 
L 3481 531 
L 3481 0 
L 794 0 
L 794 531 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-31"/>
      </g>
     </g>
    </g>
    <g id="xtick_3">
     <g id="line2d_3">
      <g>
       <use xlink:href="#mfe36c1baae" x="177.225895" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_3">
      <!-- 2 -->
      <g transform="translate(174.044645 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-32" d="M 1228 531 
L 3431 531 
L 3431 0 
L 469 0 
L 469 531 
Q 828 903 1448 1529 
Q 2069 2156 2228 2338 
Q 2531 2678 2651 2914 
Q 2772 3150 2772 3378 
Q 2772 3750 2511 3984 
Q 2250 4219 1831 4219 
Q 1534 4219 1204 4116 
Q 875 4013 500 3803 
L 500 4441 
Q 881 4594 1212 4672 
Q 1544 4750 1819 4750 
Q 2544 4750 2975 4387 
Q 3406 4025 3406 3419 
Q 3406 3131 3298 2873 
Q 3191 2616 2906 2266 
Q 2828 2175 2409 1742 
Q 1991 1309 1228 531 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-32"/>
      </g>
     </g>
    </g>
    <g id="xtick_4">
     <g id="line2d_4">
      <g>
       <use xlink:href="#mfe36c1baae" x="228.922478" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_4">
      <!-- 3 -->
      <g transform="translate(225.741228 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-33" d="M 2597 2516 
Q 3050 2419 3304 2112 
Q 3559 1806 3559 1356 
Q 3559 666 3084 287 
Q 2609 -91 1734 -91 
Q 1441 -91 1130 -33 
Q 819 25 488 141 
L 488 750 
Q 750 597 1062 519 
Q 1375 441 1716 441 
Q 2309 441 2620 675 
Q 2931 909 2931 1356 
Q 2931 1769 2642 2001 
Q 2353 2234 1838 2234 
L 1294 2234 
L 1294 2753 
L 1863 2753 
Q 2328 2753 2575 2939 
Q 2822 3125 2822 3475 
Q 2822 3834 2567 4026 
Q 2313 4219 1838 4219 
Q 1578 4219 1281 4162 
Q 984 4106 628 3988 
L 628 4550 
Q 988 4650 1302 4700 
Q 1616 4750 1894 4750 
Q 2613 4750 3031 4423 
Q 3450 4097 3450 3541 
Q 3450 3153 3228 2886 
Q 3006 2619 2597 2516 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-33"/>
      </g>
     </g>
    </g>
    <g id="xtick_5">
     <g id="line2d_5">
      <g>
       <use xlink:href="#mfe36c1baae" x="280.619062" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_5">
      <!-- 4 -->
      <g transform="translate(277.437812 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-34" d="M 2419 4116 
L 825 1625 
L 2419 1625 
L 2419 4116 
z
M 2253 4666 
L 3047 4666 
L 3047 1625 
L 3713 1625 
L 3713 1100 
L 3047 1100 
L 3047 0 
L 2419 0 
L 2419 1100 
L 313 1100 
L 313 1709 
L 2253 4666 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-34"/>
      </g>
     </g>
    </g>
    <g id="xtick_6">
     <g id="line2d_6">
      <g>
       <use xlink:href="#mfe36c1baae" x="332.315646" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_6">
      <!-- 5 -->
      <g transform="translate(329.134396 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-35" d="M 691 4666 
L 3169 4666 
L 3169 4134 
L 1269 4134 
L 1269 2991 
Q 1406 3038 1543 3061 
Q 1681 3084 1819 3084 
Q 2600 3084 3056 2656 
Q 3513 2228 3513 1497 
Q 3513 744 3044 326 
Q 2575 -91 1722 -91 
Q 1428 -91 1123 -41 
Q 819 9 494 109 
L 494 744 
Q 775 591 1075 516 
Q 1375 441 1709 441 
Q 2250 441 2565 725 
Q 2881 1009 2881 1497 
Q 2881 1984 2565 2268 
Q 2250 2553 1709 2553 
Q 1456 2553 1204 2497 
Q 953 2441 691 2322 
L 691 4666 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-35"/>
      </g>
     </g>
    </g>
    <g id="xtick_7">
     <g id="line2d_7">
      <g>
       <use xlink:href="#mfe36c1baae" x="384.012229" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_7">
      <!-- 6 -->
      <g transform="translate(380.830979 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-36" d="M 2113 2584 
Q 1688 2584 1439 2293 
Q 1191 2003 1191 1497 
Q 1191 994 1439 701 
Q 1688 409 2113 409 
Q 2538 409 2786 701 
Q 3034 994 3034 1497 
Q 3034 2003 2786 2293 
Q 2538 2584 2113 2584 
z
M 3366 4563 
L 3366 3988 
Q 3128 4100 2886 4159 
Q 2644 4219 2406 4219 
Q 1781 4219 1451 3797 
Q 1122 3375 1075 2522 
Q 1259 2794 1537 2939 
Q 1816 3084 2150 3084 
Q 2853 3084 3261 2657 
Q 3669 2231 3669 1497 
Q 3669 778 3244 343 
Q 2819 -91 2113 -91 
Q 1303 -91 875 529 
Q 447 1150 447 2328 
Q 447 3434 972 4092 
Q 1497 4750 2381 4750 
Q 2619 4750 2861 4703 
Q 3103 4656 3366 4563 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-36"/>
      </g>
     </g>
    </g>
   </g>
   <g id="matplotlib.axis_2">
    <g id="ytick_1">
     <g id="line2d_8">
      <defs>
       <path id="m9e4f5722fa" d="M 0 0 
L -3.5 0 
" style="stroke: #000000; stroke-width: 0.8"/>
      </defs>
      <g>
       <use xlink:href="#m9e4f5722fa" x="57.6" y="295.193979" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_8">
      <!-- 0 -->
      <g transform="translate(44.2375 298.993197) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-30"/>
      </g>
     </g>
    </g>
    <g id="ytick_2">
     <g id="line2d_9">
      <g>
       <use xlink:href="#m9e4f5722fa" x="57.6" y="262.003574" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_9">
      <!-- 1 -->
      <g transform="translate(44.2375 265.802793) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-31"/>
      </g>
     </g>
    </g>
    <g id="ytick_3">
     <g id="line2d_10">
      <g>
       <use xlink:href="#m9e4f5722fa" x="57.6" y="228.813169" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_10">
      <!-- 2 -->
      <g transform="translate(44.2375 232.612388) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-32"/>
      </g>
     </g>
    </g>
    <g id="ytick_4">
     <g id="line2d_11">
      <g>
       <use xlink:href="#m9e4f5722fa" x="57.6" y="195.622764" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_11">
      <!-- 3 -->
      <g transform="translate(44.2375 199.421983) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-33"/>
      </g>
     </g>
    </g>
    <g id="ytick_5">
     <g id="line2d_12">
      <g>
       <use xlink:href="#m9e4f5722fa" x="57.6" y="162.432359" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_12">
      <!-- 4 -->
      <g transform="translate(44.2375 166.231578) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-34"/>
      </g>
     </g>
    </g>
    <g id="ytick_6">
     <g id="line2d_13">
      <g>
       <use xlink:href="#m9e4f5722fa" x="57.6" y="129.241955" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_13">
      <!-- 5 -->
      <g transform="translate(44.2375 133.041173) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-35"/>
      </g>
     </g>
    </g>
    <g id="ytick_7">
     <g id="line2d_14">
      <g>
       <use xlink:href="#m9e4f5722fa" x="57.6" y="96.05155" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_14">
      <!-- 6 -->
      <g transform="translate(44.2375 99.850769) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-36"/>
      </g>
     </g>
    </g>
    <g id="ytick_8">
     <g id="line2d_15">
      <g>
       <use xlink:href="#m9e4f5722fa" x="57.6" y="62.861145" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_15">
      <!-- 7 -->
      <g transform="translate(44.2375 66.660364) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-37" d="M 525 4666 
L 3525 4666 
L 3525 4397 
L 1831 0 
L 1172 0 
L 2766 4134 
L 525 4134 
L 525 4666 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-37"/>
      </g>
     </g>
    </g>
   </g>
   <g id="line2d_16">
    <path d="M 73.832727 262.003574 
L 78.382441 259.211006 
L 82.932154 256.674352 
L 87.481867 254.390635 
L 92.031581 252.354923 
L 96.581294 250.560364 
L 101.131007 248.998237 
L 106.0057 247.570475 
L 110.880393 246.382315 
L 115.755086 245.41651 
L 120.954758 244.609704 
L 126.47941 243.977021 
L 132.654021 243.503437 
L 139.478591 243.208736 
L 148.253038 243.071105 
L 172.626503 242.842 
L 179.451073 242.482478 
L 185.625684 241.932634 
L 191.150336 241.218446 
L 196.350008 240.324341 
L 201.224701 239.268164 
L 206.099394 237.9822 
L 210.649107 236.560167 
L 215.198821 234.912071 
L 219.748534 233.02806 
L 224.298247 230.900107 
L 228.847961 228.522072 
L 233.397674 225.889754 
L 237.947387 223.000918 
L 242.497101 219.855313 
L 247.371794 216.202104 
L 252.246486 212.260812 
L 257.121179 208.038647 
L 262.320852 203.236403 
L 267.845504 197.812603 
L 273.370156 192.078696 
L 279.219787 185.697279 
L 285.719378 178.27289 
L 292.868927 169.759661 
L 301.318395 159.330763 
L 312.367699 145.304872 
L 335.441245 115.914479 
L 343.890713 105.563829 
L 351.040262 97.138871 
L 357.539853 89.810793 
L 363.714464 83.188179 
L 369.239115 77.574426 
L 374.763767 72.279707 
L 379.96344 67.605788 
L 384.838133 63.508773 
L 389.712826 59.696185 
L 394.587518 56.17409 
L 398.487273 53.568 
L 398.487273 53.568 
" clip-path="url(#p8443255817)" style="fill: none; stroke: #1f77b4; stroke-width: 1.5; stroke-linecap: square"/>
   </g>
   <g id="patch_3">
    <path d="M 57.6 307.584 
L 57.6 41.472 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
   <g id="patch_4">
    <path d="M 414.72 307.584 
L 414.72 41.472 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
   <g id="patch_5">
    <path d="M 57.6 307.584 
L 414.72 307.584 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
   <g id="patch_6">
    <path d="M 57.6 41.472 
L 414.72 41.472 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
  </g>
 </g>
 <defs>
  <clipPath id="p8443255817">
   <rect x="57.6" y="41.472" width="357.12" height="266.112"/>
  </clipPath>
 </defs>
</svg>
\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"out=None\\nfig=None\\nfor i in range(3):\\n   for v in np.concatenate([np.linspace(1.0, 3.0, 50), np.linspace(3.0, 1.0, 50)]):\\n      ex := \\\\cos(v x) + x:\\n      substitute(ex, $v -> @(v)$)\\n      fig = plot(ex, ($x$, 0, 6.28), fig=fig)\\n      out = display(fig, out)\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 8706864135545547608,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"\"\n\t\t}\n\t],\n\t\"description\": \"Cadabra JSON notebook format\",\n\t\"flags\": {\n\t\t\"hide_input_cells\": false\n\t},\n\t\"version\": 1.0\n}\n"
  },
  {
    "path": "examples/ref_exponents.cnb",
    "content": "{\n\t\"cell_id\": 14480591988213317330,\n\t\"cells\": [\n\t\t{\n\t\t\t\"cell_id\": 2472153521307117009,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 5058811582632187013,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\section*{Exponents, indices and labels}\\n\\nExponents, indices and labels are traditionally all placed using\\nsuper- or subscript notation, making these slightly ambiguous for a\\ncomputer algebra system. Since this situation can become quite complex\\n(how do you represent the third power of the first element of a\\nvector?), Cadabra requires all powers to be entered with a double-star\\n``$**$'' notation:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\section*{Exponents, indices and labels}\\n\\nExponents, indices and labels are traditionally all placed using\\nsuper- or subscript notation, making these slightly ambiguous for a\\ncomputer algebra system. Since this situation can become quite complex\\n(how do you represent the third power of the first element of a\\nvector?), Cadabra requires all powers to be entered with a double-star\\n``$**$'' notation:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 18294238673793497418,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 17667427082762968149,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 10490233587446114323,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"(a)**2\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}{a}^{2}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 12288615719137532703,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 7800622082703522619,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"(a)**(2 + 3b)\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}{a}^{\\\\left(2\\\\discretionary{}{}{}+3b\\\\right)}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex1:= a**2;\\nex2:= a**(2 + 3b);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 1344652704977985610,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 8432529926233722226,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"In addition, all sub- or superscripts with \\\\emph{curly} braces\\nindicate indices, to which the summation convention applies. In\\nparticular, there are not allowed to be more than two identical\\nindices in a single product. The summation convention does not apply\\nto arguments with any other bracket types. In particular, sub- or\\nsuperscripts with \\\\emph{square} or \\\\emph{pointy} brackets have (as of\\nyet) no fixed meaning.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"In addition, all sub- or superscripts with \\\\emph{curly} braces\\nindicate indices, to which the summation convention applies. In\\nparticular, there are not allowed to be more than two identical\\nindices in a single product. The summation convention does not apply\\nto arguments with any other bracket types. In particular, sub- or\\nsuperscripts with \\\\emph{square} or \\\\emph{pointy} brackets have (as of\\nyet) no fixed meaning.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 8007425223672013941,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"\"\n\t\t}\n\t],\n\t\"description\": \"Cadabra JSON notebook format\",\n\t\"version\": 1.0\n}\n"
  },
  {
    "path": "examples/ref_flags_variables.cnb",
    "content": "{\n\t\"cell_id\": 4427753813546749341,\n\t\"cells\": [\n\t\t{\n\t\t\t\"cell_id\": 4499672568827372488,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 13183467289063702239,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\section*{Startup flags and environment variables}\\n\\nThe behaviour of Cadabra can be tuned at startup by using startup flags as well as environment variables.\\nMost of these are for debugging purposes and should normally left unchanged from their defaults.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\section*{Startup flags and environment variables}\\n\\nThe behaviour of Cadabra can be tuned at startup by using startup flags as well as environment variables.\\nMost of these are for debugging purposes and should normally left unchanged from their defaults.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 4610613234485604057,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 11074161799911474457,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\subsection*{Environment variables}\\n\\nEach of the following environment variables\\n can be set to a non-empty value to trigger the behaviour listed in the right-hand column.\\n\\\\begin{tabular}{ll}\\n\\\\verb|CADABRA_SHOW_RECV|    & \\\\text{Show all messages which the notebook receives from the kernel on stdout.}\\\\\\\\\\n\\\\verb|CADABRA_SHOW_SENT|    & \\\\text{Show all messages which the notebook sends to the kernel on stdout.}\\\\\\\\\\n\\\\verb|CADABRA_NO_UNICODE|   & \\\\text{Do not use unicode when displaying expressions in the terminal.}\\\\\\\\\\n\\\\verb|CADABRA_LOG_OUTPUT|   & \\\\text{Windows only: store stdout and stderr in a log file.}\\n\\\\end{tabular}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\subsection*{Environment variables}\\n\\nEach of the following environment variables\\n can be set to a non-empty value to trigger the behaviour listed in the right-hand column.\\n\\\\begin{tabular}{ll}\\n\\\\verb|CADABRA_SHOW_RECV|    & \\\\text{Show all messages which the notebook receives from the kernel on stdout.}\\\\\\\\\\n\\\\verb|CADABRA_SHOW_SENT|    & \\\\text{Show all messages which the notebook sends to the kernel on stdout.}\\\\\\\\\\n\\\\verb|CADABRA_NO_UNICODE|   & \\\\text{Do not use unicode when displaying expressions in the terminal.}\\\\\\\\\\n\\\\verb|CADABRA_LOG_OUTPUT|   & \\\\text{Windows only: store stdout and stderr in a log file.}\\n\\\\end{tabular}\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 3401637449413597037,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 16519983505863779635,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\subsection*{Startup flags}\\n\\nThe notebook interface normally starts a new Cadabra kernel (\\\\verb|cadabra-server|) when it opens, but\\nit is possible to start the kernel manually and then instruct the notebook interface to connect to that\\nalready running kernel. The following flags achieve that:\\n\\n\\\\begin{tabular}{ll}\\n\\\\verb|--server-port|, \\\\verb|-s| & \\\\text{Connect to a running server on a given port.} \\\\\\\\\\n\\\\verb|--server-ip-address|, \\\\verb|-a| & \\\\text{Connect to a running server on the given IP address.}\\\\\\\\\\n\\\\verb|--token|, \\\\verb|-t| & \\\\text{Use the given authentication token to connect to the server.}\\n\\\\end{tabular}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\subsection*{Startup flags}\\n\\nThe notebook interface normally starts a new Cadabra kernel (\\\\verb|cadabra-server|) when it opens, but\\nit is possible to start the kernel manually and then instruct the notebook interface to connect to that\\nalready running kernel. The following flags achieve that:\\n\\n\\\\begin{tabular}{ll}\\n\\\\verb|--server-port|, \\\\verb|-s| & \\\\text{Connect to a running server on a given port.} \\\\\\\\\\n\\\\verb|--server-ip-address|, \\\\verb|-a| & \\\\text{Connect to a running server on the given IP address.}\\\\\\\\\\n\\\\verb|--token|, \\\\verb|-t| & \\\\text{Use the given authentication token to connect to the server.}\\n\\\\end{tabular}\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 14749822792221338951,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9930842036444179435,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"The server itself can be started as \\\\verb|cadabra-server [port] [exit-on-disconnect]|, where \\\\verb|port|\\nis the port on which the server will listen (use $0$ to let it pick a random free port) and \\\\verb|exit-on-disconnect|\\n(if non-empty) instructs the server to exit as soon as the notebook disconnects.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"The server itself can be started as \\\\verb|cadabra-server [port] [exit-on-disconnect]|, where \\\\verb|port|\\nis the port on which the server will listen (use $0$ to let it pick a random free port) and \\\\verb|exit-on-disconnect|\\n(if non-empty) instructs the server to exit as soon as the notebook disconnects.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 5548489942229082877,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 13181529303942452978,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"Finally the command-line client \\\\verb|cadabra2| accepts a single flag \\\\verb|-d| which will run Cadabra under \\ncontrol of the debugger.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"Finally the command-line client \\\\verb|cadabra2| accepts a single flag \\\\verb|-d| which will run Cadabra under \\ncontrol of the debugger.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 13846612080819932419,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"\"\n\t\t}\n\t],\n\t\"description\": \"Cadabra JSON notebook format\",\n\t\"version\": 1.0\n}\n"
  },
  {
    "path": "examples/ref_implicit_versus_explicit.cnb",
    "content": "{\n\t\"cells\" : \n\t[\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\section*{Implicit versus explicit indices}\\n\\nWhen writing expressions which involves vectors, spinors and matrices,\\none often employs an implicit notation in which some or all of the\\nindices are suppressed. Examples are\\n$$ a = M b\\\\,, \\\\quad \\\\bar{\\\\psi}\\\\gamma^{m}\\\\chi\\\\,,$$\\nwhere $a$ and $b$  are vectors, $\\\\psi$ and~$\\\\chi$ are spinors and~$M$\\nand~$\\\\gamma^{m}$ are matrices. Clearly, the computer cannot know this\\nwithout some further information. In Cadabra objects can carry implicit\\nindices, through the \\\\prop{ImplicitIndex} property. There are\\nderived forms of this, e.g.~\\\\prop{Matrix} and~\\\\prop{Spinor}.\\nThe following example shows how implicit indices ensure that objects\\ndo not get moved through each other when sorting expressions.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\section*{Implicit versus explicit indices}\\n\\nWhen writing expressions which involves vectors, spinors and matrices,\\none often employs an implicit notation in which some or all of the\\nindices are suppressed. Examples are\\n$$ a = M b\\\\,, \\\\quad \\\\bar{\\\\psi}\\\\gamma^{m}\\\\chi\\\\,,$$\\nwhere $a$ and $b$  are vectors, $\\\\psi$ and~$\\\\chi$ are spinors and~$M$\\nand~$\\\\gamma^{m}$ are matrices. Clearly, the computer cannot know this\\nwithout some further information. In Cadabra objects can carry implicit\\nindices, through the \\\\prop{ImplicitIndex} property. There are\\nderived forms of this, e.g.~\\\\prop{Matrix} and~\\\\prop{Spinor}.\\nThe following example shows how implicit indices ensure that objects\\ndo not get moved through each other when sorting expressions.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property ImplicitIndex to~}\\\\left[a,~\\\\discretionary{}{}{} b\\\\right].\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Matrix to~}M.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"a = M b\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}a = M b\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"a = M b\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}a = M b\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"{a,b}::ImplicitIndex;\\nM::Matrix;\\nex:= a = M b;\\nsort_product(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"If you had not made the property assignment in the first two lines,\\nthe \\\\algo{sort_product} would have incorrectly swapped the matrix\\nand vector, leading to a meaningless expression.\\n\\nIf you have more than one set of implicit indices, it is best to use a \\nform of \\\\prop{ImplicitIndex} which makes explicit which indices are suppressed.\\nIn the following example, we write consider the expression $M c b$ in which $M$ is a matrix\\nacting on the vector $b$, while $c$ is a different matrix which does not act on the\\nsame vector space. In other words, we consider $ M^{i}{}_{j} c^{m}{}_{n} b^{j}$.\\nClearly we can also write this as $M b c$, which is indeed what \\\\algo{sort_product} converts it to.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"If you had not made the property assignment in the first two lines,\\nthe \\\\algo{sort_product} would have incorrectly swapped the matrix\\nand vector, leading to a meaningless expression.\\n\\nIf you have more than one set of implicit indices, it is best to use a \\nform of \\\\prop{ImplicitIndex} which makes explicit which indices are suppressed.\\nIn the following example, we write consider the expression $M c b$ in which $M$ is a matrix\\nacting on the vector $b$, while $c$ is a different matrix which does not act on the\\nsame vector space. In other words, we consider $ M^{i}{}_{j} c^{m}{}_{n} b^{j}$.\\nClearly we can also write this as $M b c$, which is indeed what \\\\algo{sort_product} converts it to.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Indices(position=free) to~}\\\\left[i,~\\\\discretionary{}{}{} j\\\\right].\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Indices(position=free) to~}\\\\left[m,~\\\\discretionary{}{}{} n\\\\right].\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property ImplicitIndex to~}M.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property ImplicitIndex to~}b.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property ImplicitIndex to~}c.\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"{i,j}::Indices(vector);\\n{m,n}::Indices(spinor);\\nM::ImplicitIndex(M^{i}_{j});\\nb::ImplicitIndex(b^{i});\\nc::ImplicitIndex(c^{m}_{n});\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"M c b\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}M c b\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex:= M c b;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"M b c\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}M b c\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"sort_product(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"Such explicit property information is also respected by operators like \\\\prop{Trace}.\\nThe following example shows how to remove objects from traces when they do not\\ncarry any indices on which the trace acts.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"Such explicit property information is also respected by operators like \\\\prop{Trace}.\\nThe following example shows how to remove objects from traces when they do not\\ncarry any indices on which the trace acts.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Trace to~}Tr\\\\left(\\\\#\\\\right).\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"Tr(M c M)\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}Tr\\\\left(M c M\\\\right)\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"c Tr(M M)\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}c Tr\\\\left(M M\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"Tr{#}::Trace(indices=vector);\\nex:= Tr( M c M );\\nuntrace(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\subsection*{Converting between implicit and explicit}\\n\\nIt is possible to convert from implicit indices to explicit indices, that is, make Cadabra write out all implicit indices explicitly.\\nFor this to work you need to have declared an \\\\prop{ImplicitIndex} property which lists the explicit indices of the object.\\nCadabra will then take care of creating index lines.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\subsection*{Converting between implicit and explicit}\\n\\nIt is possible to convert from implicit indices to explicit indices, that is, make Cadabra write out all implicit indices explicitly.\\nFor this to work you need to have declared an \\\\prop{ImplicitIndex} property which lists the explicit indices of the object.\\nCadabra will then take care of creating index lines.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Indices(position=free) to~}\\\\left[i,~\\\\discretionary{}{}{} j,~\\\\discretionary{}{}{} k\\\\right].\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property ImplicitIndex to~}a.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property ImplicitIndex to~}M.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"M a\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}M a\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"{i,j,k}::Indices;\\na::ImplicitIndex(a^{i});\\nM::ImplicitIndex(M^{i}_{j});\\nex:= M a;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"M^{i}_{j} a^{j}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}M^{i}\\\\,_{j} a^{j}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"explicit_indices(ex);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"Note how dummy indices were introduced automatically.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"Note how dummy indices were introduced automatically.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1\n}\n"
  },
  {
    "path": "examples/ref_import.cnb",
    "content": "{\n\t\"cell_id\" : 8589337354142072464,\n\t\"cells\" : \n\t[\n\t\t{\n\t\t\t\"cell_id\" : 18335642165121633802,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 18438625418858246260,\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\section*{Using multiple files and notebooks}\\n\\nAt some point, you will encounter computations which are best separated out into their\\nown notebook. Or you will do a computation which takes a long time, and you want to write\\nan intermediate result into a file so that you can read it back later easily. There are \\ntwo options for this in Cadabra: importing notebooks into other notebooks, or writing \\nindividual expressions to a file and reading them back.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\section*{Using multiple files and notebooks}\\n\\nAt some point, you will encounter computations which are best separated out into their\\nown notebook. Or you will do a computation which takes a long time, and you want to write\\nan intermediate result into a file so that you can read it back later easily. There are \\ntwo options for this in Cadabra: importing notebooks into other notebooks, or writing \\nindividual expressions to a file and reading them back.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 8213440041221983394,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 7789347635294861682,\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\subsection*{Importing a notebook into another one}\\n\\nThe simplest way to separate functionality is to simply write a separate notebook with the\\nproperties and expressions which you want to re-use elsewhere. In this way, writing a \\n`package' for Cadabra is nothing else but writing a separate notebook. You can import any \\nnotebook into another one by using the standard Python import logic.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\subsection*{Importing a notebook into another one}\\n\\nThe simplest way to separate functionality is to simply write a separate notebook with the\\nproperties and expressions which you want to re-use elsewhere. In this way, writing a \\n`package' for Cadabra is nothing else but writing a separate notebook. You can import any \\nnotebook into another one by using the standard Python import logic.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 1942692638989080526,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 11079700572726959640,\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\subsubsection*{Example}\\n\\nLet us say we have a notebook \\\\verb|library.cnb|, which contains a single cell with the following \\ncontent:\\n\\\\begin{verbatim}\\n   {m,n,p,q,r}::Indices;\\n   ex:=A_{q r} A_{q r};\\n\\\\end{verbatim}\\nYou can now import this into another notebook by simply using\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\subsubsection*{Example}\\n\\nLet us say we have a notebook \\\\verb|library.cnb|, which contains a single cell with the following \\ncontent:\\n\\\\begin{verbatim}\\n   {m,n,p,q,r}::Indices;\\n   ex:=A_{q r} A_{q r};\\n\\\\end{verbatim}\\nYou can now import this into another notebook by simply using\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 3561489114726530089,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"from library import *\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 1316256212347283961,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 11518391810218108451,\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"Cadabra looks for the \\\\verb|library.cnb| notebook in your \\\\verb|PYTHONPATH| (just as in ordinary Python programs),\\n as well as in the current directory. You can see that this worked by e.g. the following:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"Cadabra looks for the \\\\verb|library.cnb| notebook in your \\\\verb|PYTHONPATH| (just as in ordinary Python programs),\\n as well as in the current directory. You can see that this worked by e.g. the following:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 37268896913279161,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 16774845059730372451,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\" : 15291342196228748438,\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"A_{q r} A_{q r}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}A_{q r} A_{q r}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 10215936131369656133,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\" : 2008929433626558299,\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"A_{m n} A_{m n}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}A_{m n} A_{m n}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex;\\nrename_dummies(ex);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 8355013287855316724,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 5820656270542915781,\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"Note that the import has thus not only imported the \\\\verb|ex| expression, but also the property \\ninformation about the index set, which enabled the \\\\verb|rename_dummies| to work.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"Note that the import has thus not only imported the \\\\verb|ex| expression, but also the property \\ninformation about the index set, which enabled the \\\\verb|rename_dummies| to work.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 14481788688662175832,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 3233447126429706603,\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"Behind the scenes, what happens is that the import statement looks for a file \\\\verb|library.cnb|. If it\\nfinds this, it will first convert that file to a proper Python file (remember the \\\\verb|library.cnb| file is a \\nCadabra notebook, not a Python file). It then uses the standard Python logic to do the import.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"Behind the scenes, what happens is that the import statement looks for a file \\\\verb|library.cnb|. If it\\nfinds this, it will first convert that file to a proper Python file (remember the \\\\verb|library.cnb| file is a \\nCadabra notebook, not a Python file). It then uses the standard Python logic to do the import.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 13398410042259813666,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 15901214011191945668,\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\subsection*{Writing expressions to a file and reading them back}\\n\\nA somewhat more difficult way to re-use expressions is to write them to a file\\nusing standard Python methods, and then read them back elsewhere. This method is best\\nused for long computations of which you want to write an intermediate result out to \\ndisk, to be read in later (instead of doing a re-computation). Be aware that if you \\nwrite an expression to disk, you do not write the property information of any of the\\nsymbols in that expression to disk. \"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\subsection*{Writing expressions to a file and reading them back}\\n\\nA somewhat more difficult way to re-use expressions is to write them to a file\\nusing standard Python methods, and then read them back elsewhere. This method is best\\nused for long computations of which you want to write an intermediate result out to \\ndisk, to be read in later (instead of doing a re-computation). Be aware that if you \\nwrite an expression to disk, you do not write the property information of any of the\\nsymbols in that expression to disk. \"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 11444201106378708990,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 12988076038731780414,\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\subsubsection*{Example}\\n\\nThe following example declares two expressions and writes them to disk. It then reads the\\nexpressions back in again and assigns them to different Python names.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\subsubsection*{Example}\\n\\nThe following example declares two expressions and writes them to disk. It then reads the\\nexpressions back in again and assigns them to different Python names.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 11792617782253406692,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 74831037821067521,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\" : 15970060422258541493,\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"A_{m n} \\\\sin(x)\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}A_{m n} \\\\sin{x}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 6535555148371619996,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\" : 8248852654806885795,\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"B_{m n}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}B_{m n}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex1:= A_{m n} \\\\sin{x};\\nex2:= B_{m n};\\nwith open(\\\"output.cdb\\\", \\\"w\\\") as file:\\n   file.write( ex1.input_form()+\\\"\\\\n\\\" )\\n   file.write( ex2.input_form()+\\\"\\\\n\\\" )\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 12958713239442749254,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"with open(\\\"output.cdb\\\", \\\"r\\\") as file:\\n   ex3=Ex( file.readline() )\\n   ex4=Ex( file.readline() )\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 2842740079552019795,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 3025403952431302262,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\" : 1436721049922411551,\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"A_{m n} \\\\sin(x)\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}A_{m n} \\\\sin{x}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 11419665305986047774,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\" : 5706079747164185254,\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"B_{m n}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}B_{m n}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex3;\\nex4;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 4528355418093952061,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 2572353665904379176,\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"Note that when written in this way, the file \\\\verb|output.cdb| only contains the expressions, not their names \\n(\\\\verb|ex1| and \\\\verb|ex2| in the example above).\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"Note that when written in this way, the file \\\\verb|output.cdb| only contains the expressions, not their names \\n(\\\\verb|ex1| and \\\\verb|ex2| in the example above).\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 18362525774477466829,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 5471488843845048840,\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"Cadabra's expressions can also be written to disk using Python's pickle functionality. This makes the code slightly less\\nmessy, but note that the file will no longer be human-readable. If you use the pickle module, the example above would read:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"Cadabra's expressions can also be written to disk using Python's pickle functionality. This makes the code slightly less\\nmessy, but note that the file will no longer be human-readable. If you use the pickle module, the example above would read:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 3330220280430081959,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 17984593104865150603,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\" : 5159751946892680671,\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"A_{m n} \\\\sin(x)\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}A_{m n} \\\\sin{x}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 3227544683490869462,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\" : 9174965331626861211,\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"B_{m n}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}B_{m n}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"import pickle\\n\\nex1:= A_{m n} \\\\sin{x};\\nex2:= B_{m n};\\nwith open(\\\"output.pkl\\\", \\\"wb\\\") as file:\\n   pickle.dump(ex1, file)\\n   pickle.dump(ex2, file)\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 8396342817603552752,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"with open(\\\"output.pkl\\\", \\\"rb\\\") as file:\\n   ex3=pickle.load(file)\\n   ex4=pickle.load(file)\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 13954138713009803288,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 5156660075745956210,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\" : 11648319486263924817,\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"A_{m n} \\\\sin(x)\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}A_{m n} \\\\sin{x}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 16686590355822369460,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\" : 8221793975087585259,\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"B_{m n}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}B_{m n}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex3;\\nex4;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 4146470860102493543,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1\n}\n"
  },
  {
    "path": "examples/ref_indexbrackets.cnb",
    "content": "{\n\t\"cell_id\": 15015813501029528490,\n\t\"cells\": [\n\t\t{\n\t\t\t\"cell_id\": 7579096609771855197,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9721816120441887067,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\section*{Index brackets}\\n\\nIndices can be associated to tensors, as in~$T_{\\\\mu\\\\nu}$, but it often\\nalso happens that we want to associate indices to a sum or product of\\ntensors, without writing all indices out explicitly. Examples are\\n\\\\begin{equation*}\\n(A + B + C)_{\\\\alpha\\\\beta}\\\\,,\\\\quad\\\\text{or}\\\\quad\\n(\\\\psi \\\\Gamma_{m n} \\\\Gamma_{p})_{\\\\beta}\\\\,.\\n\\\\end{equation*}\\nHere the objects $A$, $B$, $C$ and~$\\\\Gamma$ are matrices, while~$\\\\psi$\\nis a vector. Their explicit components are labelled with~$\\\\alpha$\\nand~$\\\\beta$ indices, but the notation above keeps most of these vector\\nindices implicit.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\section*{Index brackets}\\n\\nIndices can be associated to tensors, as in~$T_{\\\\mu\\\\nu}$, but it often\\nalso happens that we want to associate indices to a sum or product of\\ntensors, without writing all indices out explicitly. Examples are\\n\\\\begin{equation*}\\n(A + B + C)_{\\\\alpha\\\\beta}\\\\,,\\\\quad\\\\text{or}\\\\quad\\n(\\\\psi \\\\Gamma_{m n} \\\\Gamma_{p})_{\\\\beta}\\\\,.\\n\\\\end{equation*}\\nHere the objects $A$, $B$, $C$ and~$\\\\Gamma$ are matrices, while~$\\\\psi$\\nis a vector. Their explicit components are labelled with~$\\\\alpha$\\nand~$\\\\beta$ indices, but the notation above keeps most of these vector\\nindices implicit.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 3747593314381049400,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 15377235912404650595,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"Cadabra can deal with such expressions through a construction which is\\ncalled the ``indexbracket''. It is possible to convert from one form\\nto the other by using the \\\\algo{combine} and\\n\\\\algo{expand} algorithms. Combining terms goes like this:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"Cadabra can deal with such expressions through a construction which is\\ncalled the ``indexbracket''. It is possible to convert from one form\\nto the other by using the \\\\algo{combine} and\\n\\\\algo{expand} algorithms. Combining terms goes like this:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 3639762061202278259,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 4445289936618923500,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 5271033377246372260,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\indexbracket(\\\\Gamma_{r})_{\\\\alpha \\\\beta} \\\\indexbracket(\\\\Gamma_{s t u})_{\\\\beta \\\\gamma}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\left(\\\\Gamma_{r}\\\\right)\\\\,_{\\\\alpha \\\\beta} \\\\left(\\\\Gamma_{s t u}\\\\right)\\\\,_{\\\\beta \\\\gamma}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 2579952125931719981,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 9890904167601362925,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\indexbracket(\\\\Gamma_{r} \\\\Gamma_{s t u})_{\\\\alpha \\\\gamma}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\left(\\\\Gamma_{r} \\\\Gamma_{s t u}\\\\right)\\\\,_{\\\\alpha \\\\gamma}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex:= (\\\\Gamma_r)_{\\\\alpha\\\\beta} (\\\\Gamma_{s t u})_{\\\\beta\\\\gamma};\\ncombine(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 2045427073752557899,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 15309898336879391955,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 5134532710074123407,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\indexbracket(\\\\Gamma_{r})_{\\\\alpha \\\\beta} Q_{\\\\beta}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\left(\\\\Gamma_{r}\\\\right)\\\\,_{\\\\alpha \\\\beta} Q_{\\\\beta}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 11166369338585191579,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 11097134341779913894,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\indexbracket(\\\\Gamma_{r} Q)_{\\\\alpha}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\left(\\\\Gamma_{r} Q\\\\right)\\\\,_{\\\\alpha}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex:= (\\\\Gamma_r)_{\\\\alpha\\\\beta} Q_\\\\beta;\\ncombine(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 15195548963049034984,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 3902786993697460889,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"If the index bracket has only one index, either the first or the last\\nargument should be a matrix, but not both:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"If the index bracket has only one index, either the first or the last\\nargument should be a matrix, but not both:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 7854483963016823975,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9055389825227335019,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 8276388607940852606,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\indexbracket(A B)_{m}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\left(A B\\\\right)\\\\,_{m}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9463496701081442497,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 3741645233334530940,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\indexbracket(A B)_{m}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\left(A B\\\\right)\\\\,_{m}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"A::Matrix.\\n{m,n,p}::Indices(vector).\\nex:= (A B)_{m};\\nexpand(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 12418331311729001079,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 3827274058311932496,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"If the index bracket has two indices, all arguments should be matrices,\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"If the index bracket has two indices, all arguments should be matrices,\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 17229919566251876524,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 12992989275292965348,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 766899928363640140,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\indexbracket(A B)_{m n}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\left(A B\\\\right)\\\\,_{m n}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 2382938984798027775,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 14435010680306336547,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"A_{m p} B_{p n}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}A_{m p} B_{p n}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"{A,B}::Matrix.\\n{m,n,p}::Indices(vector).\\nex:= (A B)_{m n};\\nexpand(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 5630921792772693475,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 13278504945955909698,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"If there are more arguments inside the bracket, these of course all\\nneed to be matrices (and are assumed to be so by default).\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"If there are more arguments inside the bracket, these of course all\\nneed to be matrices (and are assumed to be so by default).\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 5783698868778637130,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"\"\n\t\t}\n\t],\n\t\"description\": \"Cadabra JSON notebook format\",\n\t\"version\": 1.0\n}\n"
  },
  {
    "path": "examples/ref_indices.cnb",
    "content": "{\n\t\"cell_id\": 12664457255956679119,\n\t\"cells\": [\n\t\t{\n\t\t\t\"cell_id\": 2603007457225824030,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 16398884988095052806,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\section*{Indices, dummy indices and automatic index renaming}\\n\\nIn Cadabra, all objects which occur as subscripts or superscripts\\nare considered to be ``indices''. The names of indices are understood\\nto be irrelevant when they occur in a pair, and automatic relabelling\\nwill take place whenever necessary in order to avoid index clashes. \\n\\nCadabra knows about the differences between free and dummy indices. It \\nchecks the input for consistency and displays a warning when the\\nindex structure does not make sense. Thus, the input\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\section*{Indices, dummy indices and automatic index renaming}\\n\\nIn Cadabra, all objects which occur as subscripts or superscripts\\nare considered to be ``indices''. The names of indices are understood\\nto be irrelevant when they occur in a pair, and automatic relabelling\\nwill take place whenever necessary in order to avoid index clashes. \\n\\nCadabra knows about the differences between free and dummy indices. It \\nchecks the input for consistency and displays a warning when the\\nindex structure does not make sense. Thus, the input\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 15901390708985939557,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"ex:= A_{m n} + B_{m} = 0;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 3601763275766639027,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 210781383732853346,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"will result in an error message.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"will result in an error message.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 8873963798221486951,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 2795464499727936181,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"The location of indices is, by default, not considered to be\\nrelevant. That is, you can write\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"The location of indices is, by default, not considered to be\\nrelevant. That is, you can write\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 2820740517798032455,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 3779065371905443791,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Attached property Indices(position=free) to~}\\\\left[m,~\\\\discretionary{}{}{} n\\\\right].\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 12237235239697771748,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 9414779593694940232,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"A_{m} + A^{m}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}A_{m}+A^{m}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"{m, n}::Indices(name=\\\"free\\\");\\nex:=A_{m} + A^{m};|\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 14542057507706825743,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9760096887462824147,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"as input and these are considered to be consistent expressions. You can collect such terms\\nby using \\\\algo{lower_free_indices} or \\\\algo{raise_free_indices},\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"as input and these are considered to be consistent expressions. You can collect such terms\\nby using \\\\algo{lower_free_indices} or \\\\algo{raise_free_indices},\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 2736816848492249371,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 16332006585139489656,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 12543664447024095469,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"2A_{m}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}2A_{m}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"lower_free_indices(ex);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 3420150786956556315,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 16332361616390480422,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"If,\\nhowever, the position of an index means something (like in general\\nrelativity, where index lowering and raising implies contraction with\\na metric), then you can declare index positions to be ``fixed''. This\\nis done using\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"If,\\nhowever, the position of an index means something (like in general\\nrelativity, where index lowering and raising implies contraction with\\na metric), then you can declare index positions to be ``fixed''. This\\nis done using\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 9248052594616249299,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 1143495560860578432,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Attached property Indices(position=fixed) to~}\\\\left[a,~\\\\discretionary{}{}{} b,~\\\\discretionary{}{}{} c,~\\\\discretionary{}{}{} d,~\\\\discretionary{}{}{} e,~\\\\discretionary{}{}{} f\\\\right].\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"{a,b,c,d,e,f}::Indices(name=\\\"fixed\\\", position=fixed);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 6840758994246203573,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9044396775528022498,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"Cadabra will raise or lower indices on such expressions to a canonical form when the\\n\\\\algo{canonicalise} algorithm is used,\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"Cadabra will raise or lower indices on such expressions to a canonical form when the\\n\\\\algo{canonicalise} algorithm is used,\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 2081072977466570259,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 14219870068814531026,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 9556788623881644461,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"G_{a b} F^{a b} + G^{a b} F_{a b}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}G_{a b} F^{a b}+G^{a b} F_{a b}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 1394139579612278374,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 2525156888606985620,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"2G^{a b} F_{a b}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}2G^{a b} F_{a b}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex:= G_{a b} F^{a b} + G^{a b} F_{a b};\\ncanonicalise(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 14302869922211230433,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 15592543561493567160,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"If upper and lower indices should remain untouched at all times, there is a third index position type,\\ncalled `independent',\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"If upper and lower indices should remain untouched at all times, there is a third index position type,\\ncalled `independent',\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 5062804308848888743,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 8544846990947287991,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Attached property Indices(position=independent) to~}\\\\left[q,~\\\\discretionary{}{}{} r,~\\\\discretionary{}{}{} s\\\\right].\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 17148728148626256032,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 10987261822505544553,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"G_{q r} F^{q r} + G^{q r} F_{q r}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}G_{q r} F^{q r}+G^{q r} F_{q r}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 5705016383598053748,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 13029846229228925610,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"G_{q r} F^{q r} + G^{q r} F_{q r}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}G_{q r} F^{q r}+G^{q r} F_{q r}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"{q,r,s}::Indices(name=\\\"independent\\\", position=independent);\\nex:= G_{q r} F^{q r} + G^{q r} F_{q r};\\ncanonicalise(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 8471289050708003734,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 12293302538623812488,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"As the last line shows, the index positions have remained unchanged.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"As the last line shows, the index positions have remained unchanged.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 1923640147759365874,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 18361553095233638011,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"When substituting an expression into another one, dummy indices will\\nautomatically be relabelled when necessary. To see this in action,\\nconsider the following example:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"When substituting an expression into another one, dummy indices will\\nautomatically be relabelled when necessary. To see this in action,\\nconsider the following example:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 15697062427148001098,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 17002631327703913227,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 16011245533710997120,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"G_{a b} Q\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}G_{a b} Q\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 2713391754974550285,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 8078697658186934777,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"Q → F_{a b} F^{a b}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}Q \\\\rightarrow F_{a b} F^{a b}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 10205932028176583645,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 9371390078094034135,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"G_{a b} F_{c d} F^{c d}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}G_{a b} F_{c d} F^{c d}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex:= G_{a b} Q;\\nrl:= Q-> F_{a b} F^{a b};\\nsubstitute(ex, rl);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 18060735432401029226,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 3512684296452765657,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"The $a$ and $b$ indices have automatically been relabelled to $c$ and $d$\\nin order to avoid a conflict with the free indices on the $G_{a b}$ object.\\nCadabra figured out that it could use these names as we attached $a$-$f$ to\\nthe same \\\\prop{Indices} list property a few cells ago. If you do not declare\\nsuch an index sets, Cadabra will complain that it does not know how to relabel\\ndummy indices.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"The $a$ and $b$ indices have automatically been relabelled to $c$ and $d$\\nin order to avoid a conflict with the free indices on the $G_{a b}$ object.\\nCadabra figured out that it could use these names as we attached $a$-$f$ to\\nthe same \\\\prop{Indices} list property a few cells ago. If you do not declare\\nsuch an index sets, Cadabra will complain that it does not know how to relabel\\ndummy indices.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 14522048402832550635,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 17201415940783896500,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"You may have noticed that when you write \\\\verb|T_{a b}| the `\\\\verb|a b|' in the subscript is\\nnot interpreted as a product, but rather as two different indices to the tensor~$T$. If you really\\ndo want to write a product inside a sub- or super-script, you need to write a multiplication '*' \\nexplicitly.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"You may have noticed that when you write \\\\verb|T_{a b}| the `\\\\verb|a b|' in the subscript is\\nnot interpreted as a product, but rather as two different indices to the tensor~$T$. If you really\\ndo want to write a product inside a sub- or super-script, you need to write a multiplication '*' \\nexplicitly.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 16546289900809526296,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"\"\n\t\t}\n\t],\n\t\"description\": \"Cadabra JSON notebook format\",\n\t\"version\": 1.0\n}\n"
  },
  {
    "path": "examples/ref_kernel.cnb",
    "content": "{\n\t\"cell_id\": 13629045816255798702,\n\t\"cells\": [\n\t\t{\n\t\t\t\"cell_id\": 8849555755772786534,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 12370158924790282502,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\section*{The kernel and other internals}\\n\\nBecause Cadabra stores mathematical expressions in a separate expression tree in \\\\verb|Ex| objects,\\nit behaves somewhat differently from systems in which expressions are stored as a Python expression\\ntree. In Cadabra, the meaning of a particular symbol in a mathematical expression is determined by\\nthe properties which you have attached to it, not by the Python type of that symbol (it does not have\\na Python type). To see what the above means, consider the following example:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"\\\\section*{The kernel and other internals}\\n\\nBecause Cadabra stores mathematical expressions in a separate expression tree in \\\\verb|Ex| objects,\\nit behaves somewhat differently from systems in which expressions are stored as a Python expression\\ntree. In Cadabra, the meaning of a particular symbol in a mathematical expression is determined by\\nthe properties which you have attached to it, not by the Python type of that symbol (it does not have\\na Python type). To see what the above means, consider the following example:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 12042551384764104111,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 13672040626640859045,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property Symmetric attached to~}A_{m n}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9851969310638711740,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 6574861475250942513,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"A_{m n} + A_{n m}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}A_{m n}\\\\discretionary{}{}{}+A_{n m}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 16263284384910359364,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 4397616846171026227,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"2A_{m n}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}2A_{m n}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"A_{m n}::Symmetric;\\nex:= A_{m n} + A_{n m};\\ncanonicalise(ex);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 9306146065819952695,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 3013271056476369623,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"Here, the symbol \\\\verb|A_{m n}| is not a Python object, but rather a string which can appear in a mathematical\\nexpression. If you look under the hood, the above cell can be written in pure Python as\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"Here, the symbol \\\\verb|A_{m n}| is not a Python object, but rather a string which can appear in a mathematical\\nexpression. If you look under the hood, the above cell can be written in pure Python as\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 6972904807946610316,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 16462270235232285755,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property Symmetric attached to~}A_{m n}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 2462848695655197614,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 8384194984997684422,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"A_{m n} + A_{n m}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}A_{m n}\\\\discretionary{}{}{}+A_{n m}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 15823427100863555800,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 8859566742968700959,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"2A_{m n}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}2A_{m n}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"Symmetric( Ex(r\\\" A_{m n} \\\") );\\nex = Ex(r\\\" A_{m n} + A_{n m} \\\" );\\ncanonicalise(ex);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 10585184257996959815,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 11136225035560683399,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"From this example, it should hopefully be clear that the only Python object is \\\\verb|ex|, and the mathematics\\nis not stored as Python functions/objects.\\n\\nSo how does Cadabra now know that \\\\verb|A_{m n}| is symmetric in its indices? Where did that property get stored?\\nIt is not because \\\\verb|A_{m n}| is of Python type \\\\verb|Symmetric| (it cannot be, because \\\\verb|A_{m n}| is not even\\na valid Python identifier name). Rather, the first line in the example above makes this information go into \\nthe Cadabra \\\\emph{kernel}. \\n\\nThe kernel is a global object which automatically gets created when you start Cadabra\\n(or when you \\\\verb|import cadabra2| if you use it from pure Python). It has the name \\\\verb|__cdbkernel__|:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"From this example, it should hopefully be clear that the only Python object is \\\\verb|ex|, and the mathematics\\nis not stored as Python functions/objects.\\n\\nSo how does Cadabra now know that \\\\verb|A_{m n}| is symmetric in its indices? Where did that property get stored?\\nIt is not because \\\\verb|A_{m n}| is of Python type \\\\verb|Symmetric| (it cannot be, because \\\\verb|A_{m n}| is not even\\na valid Python identifier name). Rather, the first line in the example above makes this information go into \\nthe Cadabra \\\\emph{kernel}. \\n\\nThe kernel is a global object which automatically gets created when you start Cadabra\\n(or when you \\\\verb|import cadabra2| if you use it from pure Python). It has the name \\\\verb|__cdbkernel__|:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 45856600362238896,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 16294516257136820305,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"verbatim\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}<cadabra2.Kernel object at 0xffffaa9d1a30>\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"__cdbkernel__;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 7025123213090975220,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 288800776347470677,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"All Cadabra algorithms look for this object and use it to extract or store property information about the symbols\\nwhich appear in mathematical expressions. \"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"All Cadabra algorithms look for this object and use it to extract or store property information about the symbols\\nwhich appear in mathematical expressions. \"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 4539756454185987543,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 7809667929969088196,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"For most situations, having just this single global kernel object is sufficient, as you will want the properties\\nof mathematical symbols to be shared between all expressions, whether they get created at global scope or in some\\nlocal context inside a function. However, there are situations where you might want to \\\"start with a clean slate\\\" inside\\na function. In that case, you can create a new local kernel scope by doing\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"For most situations, having just this single global kernel object is sufficient, as you will want the properties\\nof mathematical symbols to be shared between all expressions, whether they get created at global scope or in some\\nlocal context inside a function. However, there are situations where you might want to \\\"start with a clean slate\\\" inside\\na function. In that case, you can create a new local kernel scope by doing\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 12205210069457161110,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 14069236159961730214,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"verbatim\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}<cadabra2.Kernel object at 0xffffaa3fea70>\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"__cdbkernel__ = create_scope();\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 4201856381823193209,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 17402143550802271243,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"You will see this used in the test programs in the \\\\verb|test/| folder of the Cadabra source code.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"You will see this used in the test programs in the \\\\verb|test/| folder of the Cadabra source code.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 2671523501922209461,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 18163868036366986479,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\subsection*{Kernel parameters and options}\\n\\nVarious global Cadabra settings can be queried and configured by setting options in the current kernel.\\nIn order to determine the current version and build, there are some read-only options:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\subsection*{Kernel parameters and options}\\n\\nVarious global Cadabra settings can be queried and configured by setting options in the current kernel.\\nIn order to determine the current version and build, there are some read-only options:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 18377425193476512512,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 3851195423111399157,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"verbatim\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}2.5.9\\\\end{verbatim}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 5979562681690966676,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"verbatim\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}3436.a19d6939e3\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"__cdbkernel__.version;\\n__cdbkernel__.build;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 9830875065386943985,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 12204927870060801580,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"To switch between the display of fractions in two-dimensional form or using the $(...)^{-1}$ notation,\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"To switch between the display of fractions in two-dimensional form or using the $(...)^{-1}$ notation,\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 1725968702659204153,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 15511308279008711323,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 16277940918531804827,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"a (b)**(-1)\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\frac{a}{b}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"__cdbkernel__.display_fractions=True\\nex:= a/b;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 2573922325839279496,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 14940346752126201661,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 5681444561252168539,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"a (b)**(-1)\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}a {b}^{-1}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"__cdbkernel__.display_fractions=False\\nex:= a/b;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 9355373558063200252,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 8079701494229551055,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"To switch the scalar backend used for simplification of scalar expressions using \\\\algo{simplify}, there\\nare currently two options: \\\\verb|scalar_backend_t.mathematica| and \\\\verb|scalar_backend_t.sympy|. \"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"To switch the scalar backend used for simplification of scalar expressions using \\\\algo{simplify}, there\\nare currently two options: \\\\verb|scalar_backend_t.mathematica| and \\\\verb|scalar_backend_t.sympy|. \"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 11177374336733547393,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"__cdbkernel__.scalar_backend = scalar_backend_t.mathematica\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 17735255867559487334,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 4323940300054202230,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"Unless you have built Cadabra with Mathematica support, the expression below will remain\\nunsimplified:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"Unless you have built Cadabra with Mathematica support, the expression below will remain\\nunsimplified:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 3157742344791853514,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 11166821269592507071,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 13660063936394300196,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"(\\\\sin(x))**2 + (\\\\cos(x))**2\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}{\\\\left(\\\\sin{x}\\\\right)}^{2}\\\\discretionary{}{}{}+{\\\\left(\\\\cos{x}\\\\right)}^{2}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"simplify($\\\\sin(x)**2 + \\\\cos(x)**2$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 15117942814232253837,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"__cdbkernel__.scalar_backend=scalar_backend_t.sympy\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 2060847852779222105,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 95816655246225054,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 6329887174223332697,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"1\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}1\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"simplify($\\\\sin(x)**2 + \\\\cos(x)**2$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 15783455992243902484,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 2164321970993920001,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"If you want to be able to write mathematical expressions which contain Python functions acting on\\nsub-expressions, use\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"If you want to be able to write mathematical expressions which contain Python functions acting on\\nsub-expressions, use\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 13702456694274505585,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"__cdbkernel__.call_embedded_python_functions=True\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 9873818455953374450,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9662591733689155128,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 15675228372636278967,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"A C + A D + B C + B D\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}A C\\\\discretionary{}{}{}+A D\\\\discretionary{}{}{}+B C\\\\discretionary{}{}{}+B D\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex:= distribute( (A+B)*(C+D) );\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 4886129485221259673,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 11045096235463665163,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"Compare the above to what happens when this functionality is turned off (the default):\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"Compare the above to what happens when this functionality is turned off (the default):\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 4871737881202628813,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"__cdbkernel__.call_embedded_python_functions=False\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 10895627135241426619,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 45042463627634647,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 14172362488317087161,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"distribute((A + B) (C + D))\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}distribute\\\\left(\\\\left(A\\\\discretionary{}{}{}+B\\\\right) \\\\left(C\\\\discretionary{}{}{}+D\\\\right)\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex:= distribute( (A+B)*(C+D) );\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 7505202705468877718,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"\"\n\t\t}\n\t],\n\t\"description\": \"Cadabra JSON notebook format\",\n\t\"version\": 1.0\n}\n"
  },
  {
    "path": "examples/ref_ndsolve.cnb",
    "content": "{\n\t\"cell_id\": 2972420482671957517,\n\t\"cells\": [\n\t\t{\n\t\t\t\"cell_id\": 4398375992092886125,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 18334240841561318432,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\section*{Numerical solution of differential equations}\\n\\nCadabra has functionality to determine numerical solutions to ordinary differential equations. The equations themselves are written as standard Cadabra expressions, and the result is (one or more) interpolating function objects. These can then be used for further analysis, e.g. plotting. To see how this works, it is best to look at some concrete examples.\\n\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\section*{Numerical solution of differential equations}\\n\\nCadabra has functionality to determine numerical solutions to ordinary differential equations. The equations themselves are written as standard Cadabra expressions, and the result is (one or more) interpolating function objects. These can then be used for further analysis, e.g. plotting. To see how this works, it is best to look at some concrete examples.\\n\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 15405320483067930519,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 6989876134854896662,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\subsection*{Damped coupled harmonic oscillators}\\n\\nThe system we look at here contains two functions $x(\\\\tau)$ and $y(\\\\tau)$, which satisfy two differential equations. In order to enter these into Cadabra, we first have to declare these two functions and the variable on which they depend.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\subsection*{Damped coupled harmonic oscillators}\\n\\nThe system we look at here contains two functions $x(\\\\tau)$ and $y(\\\\tau)$, which satisfy two differential equations. In order to enter these into Cadabra, we first have to declare these two functions and the variable on which they depend.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 8957379084239617579,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 12499243394216302136,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property Coordinate attached to~}\\\\tau.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 17734446434737046431,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property Derivative attached to~}\\\\backslash\\\\texttt{dot}\\\\{\\\\#\\\\}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 7475243283182554295,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property Depends attached to~}\\\\left[x, \\\\discretionary{}{}{}y\\\\right].\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"\\\\tau::Coordinate;\\n\\\\dot{#}::Derivative(\\\\tau);\\n{x,y}::Depends(\\\\tau);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 18020433852883809783,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 3342451081423976315,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"The differential equations are given below. There is one parameter $\\\\gamma$ which describes the damping rate.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"The differential equations are given below. There is one parameter $\\\\gamma$ which describes the damping rate.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 12150018836439156169,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 5673587788063414972,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 15781141266903332796,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"{\\\\dot(x) = y, \\\\dot(y) = -x + \\\\gamma y}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\left[\\\\dot{x} = y, \\\\discretionary{}{}{}\\\\dot{y} = -\\\\,x\\\\discretionary{}{}{}+\\\\gamma y\\\\right]\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ho:= [  \\\\dot{x} = y, \\\\dot{y} = -x + \\\\gamma y ];\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 3382617899479622935,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 18056129744192343529,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"Note how, by virtue of the property that $x$ and $y$ depend on $\\\\tau$, we do not have to write that dependence explicitly anymore (so you do not have to write $x(\\\\tau)$ ). Let us specialise to a particular value of the damping,\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"Note how, by virtue of the property that $x$ and $y$ depend on $\\\\tau$, we do not have to write that dependence explicitly anymore (so you do not have to write $x(\\\\tau)$ ). Let us specialise to a particular value of the damping,\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 305896598762222459,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 11953990094748602761,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 10218502941338733202,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"{\\\\dot(x) = y, \\\\dot(y) = -x-0.2y}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\left[\\\\dot{x} = y, \\\\discretionary{}{}{}\\\\dot{y} = -\\\\,x\\\\discretionary{}{}{}-0.2\\\\,y\\\\right]\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"substitute(ho, $\\\\gamma->-0.2$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 13867069946604679431,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 3388709292250503775,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"We can now solve this system with a call to \\\\algo{ndsolve} which sets the initial values of $x$ and $y$, and the range of $\\\\tau$ for which we want to solve for the functions.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"We can now solve this system with a call to \\\\algo{ndsolve} which sets the initial values of $x$ and $y$, and the range of $\\\\tau$ for which we want to solve for the functions.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 11426231981637334556,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 2834339595878778940,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 398832428626914661,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"{x =  (NInterpolatingFunction), y =  (NInterpolatingFunction)}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\left[x = \\\\square{}\\n(\\\\tau), \\\\discretionary{}{}{}y = \\\\square{}\\n(\\\\tau)\\\\right]\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"sol = ndsolve(ho, {$x$: 0, $y$: 1}, ($\\\\tau$, 0, 10));\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 746203457875801198,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 5678411129077973675,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"The result is a list of two equations, one for $x$ and one for $y$, expressing them both in terms of 'anonymous functions'. These are interpolating functions which can be evaluated numerically. If we want to plot the result, do the following:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"The result is a list of two equations, one for $x$ and one for $y$, expressing them both in terms of 'anonymous functions'. These are interpolating functions which can be evaluated numerically. If we want to plot the result, do the following:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 4444740050407976925,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 5060251045193030899,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"image_svg\",\n\t\t\t\t\t\"source\": \"<?xml version="1.0" encoding="utf-8" standalone="no"?>
<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
  "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="460.8pt" height="345.6pt" viewBox="0 0 460.8 345.6" xmlns="http://www.w3.org/2000/svg" version="1.1">
 <metadata>
  <rdf:RDF xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:cc="http://creativecommons.org/ns#" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
   <cc:Work>
    <dc:type rdf:resource="http://purl.org/dc/dcmitype/StillImage"/>
    <dc:date>2025-05-29T12:23:50.277821</dc:date>
    <dc:format>image/svg+xml</dc:format>
    <dc:creator>
     <cc:Agent>
      <dc:title>Matplotlib v3.6.3, https://matplotlib.org/</dc:title>
     </cc:Agent>
    </dc:creator>
   </cc:Work>
  </rdf:RDF>
 </metadata>
 <defs>
  <style type="text/css">*{stroke-linejoin: round; stroke-linecap: butt}</style>
 </defs>
 <g id="figure_1">
  <g id="patch_1">
   <path d="M 0 345.6 
L 460.8 345.6 
L 460.8 0 
L 0 0 
z
" style="fill: #ffffff"/>
  </g>
  <g id="axes_1">
   <g id="patch_2">
    <path d="M 57.6 307.584 
L 414.72 307.584 
L 414.72 41.472 
L 57.6 41.472 
z
" style="fill: #ffffff"/>
   </g>
   <g id="matplotlib.axis_1">
    <g id="xtick_1">
     <g id="line2d_1">
      <defs>
       <path id="m8615db906f" d="M 0 0 
L 0 3.5 
" style="stroke: #000000; stroke-width: 0.8"/>
      </defs>
      <g>
       <use xlink:href="#m8615db906f" x="73.832727" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_1">
      <!-- 0 -->
      <g transform="translate(70.651477 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-30" d="M 2034 4250 
Q 1547 4250 1301 3770 
Q 1056 3291 1056 2328 
Q 1056 1369 1301 889 
Q 1547 409 2034 409 
Q 2525 409 2770 889 
Q 3016 1369 3016 2328 
Q 3016 3291 2770 3770 
Q 2525 4250 2034 4250 
z
M 2034 4750 
Q 2819 4750 3233 4129 
Q 3647 3509 3647 2328 
Q 3647 1150 3233 529 
Q 2819 -91 2034 -91 
Q 1250 -91 836 529 
Q 422 1150 422 2328 
Q 422 3509 836 4129 
Q 1250 4750 2034 4750 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-30"/>
      </g>
     </g>
    </g>
    <g id="xtick_2">
     <g id="line2d_2">
      <g>
       <use xlink:href="#m8615db906f" x="138.763636" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_2">
      <!-- 2 -->
      <g transform="translate(135.582386 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-32" d="M 1228 531 
L 3431 531 
L 3431 0 
L 469 0 
L 469 531 
Q 828 903 1448 1529 
Q 2069 2156 2228 2338 
Q 2531 2678 2651 2914 
Q 2772 3150 2772 3378 
Q 2772 3750 2511 3984 
Q 2250 4219 1831 4219 
Q 1534 4219 1204 4116 
Q 875 4013 500 3803 
L 500 4441 
Q 881 4594 1212 4672 
Q 1544 4750 1819 4750 
Q 2544 4750 2975 4387 
Q 3406 4025 3406 3419 
Q 3406 3131 3298 2873 
Q 3191 2616 2906 2266 
Q 2828 2175 2409 1742 
Q 1991 1309 1228 531 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-32"/>
      </g>
     </g>
    </g>
    <g id="xtick_3">
     <g id="line2d_3">
      <g>
       <use xlink:href="#m8615db906f" x="203.694545" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_3">
      <!-- 4 -->
      <g transform="translate(200.513295 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-34" d="M 2419 4116 
L 825 1625 
L 2419 1625 
L 2419 4116 
z
M 2253 4666 
L 3047 4666 
L 3047 1625 
L 3713 1625 
L 3713 1100 
L 3047 1100 
L 3047 0 
L 2419 0 
L 2419 1100 
L 313 1100 
L 313 1709 
L 2253 4666 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-34"/>
      </g>
     </g>
    </g>
    <g id="xtick_4">
     <g id="line2d_4">
      <g>
       <use xlink:href="#m8615db906f" x="268.625455" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_4">
      <!-- 6 -->
      <g transform="translate(265.444205 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-36" d="M 2113 2584 
Q 1688 2584 1439 2293 
Q 1191 2003 1191 1497 
Q 1191 994 1439 701 
Q 1688 409 2113 409 
Q 2538 409 2786 701 
Q 3034 994 3034 1497 
Q 3034 2003 2786 2293 
Q 2538 2584 2113 2584 
z
M 3366 4563 
L 3366 3988 
Q 3128 4100 2886 4159 
Q 2644 4219 2406 4219 
Q 1781 4219 1451 3797 
Q 1122 3375 1075 2522 
Q 1259 2794 1537 2939 
Q 1816 3084 2150 3084 
Q 2853 3084 3261 2657 
Q 3669 2231 3669 1497 
Q 3669 778 3244 343 
Q 2819 -91 2113 -91 
Q 1303 -91 875 529 
Q 447 1150 447 2328 
Q 447 3434 972 4092 
Q 1497 4750 2381 4750 
Q 2619 4750 2861 4703 
Q 3103 4656 3366 4563 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-36"/>
      </g>
     </g>
    </g>
    <g id="xtick_5">
     <g id="line2d_5">
      <g>
       <use xlink:href="#m8615db906f" x="333.556364" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_5">
      <!-- 8 -->
      <g transform="translate(330.375114 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-38" d="M 2034 2216 
Q 1584 2216 1326 1975 
Q 1069 1734 1069 1313 
Q 1069 891 1326 650 
Q 1584 409 2034 409 
Q 2484 409 2743 651 
Q 3003 894 3003 1313 
Q 3003 1734 2745 1975 
Q 2488 2216 2034 2216 
z
M 1403 2484 
Q 997 2584 770 2862 
Q 544 3141 544 3541 
Q 544 4100 942 4425 
Q 1341 4750 2034 4750 
Q 2731 4750 3128 4425 
Q 3525 4100 3525 3541 
Q 3525 3141 3298 2862 
Q 3072 2584 2669 2484 
Q 3125 2378 3379 2068 
Q 3634 1759 3634 1313 
Q 3634 634 3220 271 
Q 2806 -91 2034 -91 
Q 1263 -91 848 271 
Q 434 634 434 1313 
Q 434 1759 690 2068 
Q 947 2378 1403 2484 
z
M 1172 3481 
Q 1172 3119 1398 2916 
Q 1625 2713 2034 2713 
Q 2441 2713 2670 2916 
Q 2900 3119 2900 3481 
Q 2900 3844 2670 4047 
Q 2441 4250 2034 4250 
Q 1625 4250 1398 4047 
Q 1172 3844 1172 3481 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-38"/>
      </g>
     </g>
    </g>
    <g id="xtick_6">
     <g id="line2d_6">
      <g>
       <use xlink:href="#m8615db906f" x="398.487273" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_6">
      <!-- 10 -->
      <g transform="translate(392.124773 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-31" d="M 794 531 
L 1825 531 
L 1825 4091 
L 703 3866 
L 703 4441 
L 1819 4666 
L 2450 4666 
L 2450 531 
L 3481 531 
L 3481 0 
L 794 0 
L 794 531 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-31"/>
       <use xlink:href="#DejaVuSans-30" x="63.623047"/>
      </g>
     </g>
    </g>
   </g>
   <g id="matplotlib.axis_2">
    <g id="ytick_1">
     <g id="line2d_7">
      <defs>
       <path id="med7b2961fa" d="M 0 0 
L -3.5 0 
" style="stroke: #000000; stroke-width: 0.8"/>
      </defs>
      <g>
       <use xlink:href="#med7b2961fa" x="57.6" y="296.670276" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_7">
      <!-- −0.75 -->
      <g transform="translate(19.954687 300.469495) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-2212" d="M 678 2272 
L 4684 2272 
L 4684 1741 
L 678 1741 
L 678 2272 
z
" transform="scale(0.015625)"/>
        <path id="DejaVuSans-2e" d="M 684 794 
L 1344 794 
L 1344 0 
L 684 0 
L 684 794 
z
" transform="scale(0.015625)"/>
        <path id="DejaVuSans-37" d="M 525 4666 
L 3525 4666 
L 3525 4397 
L 1831 0 
L 1172 0 
L 2766 4134 
L 525 4134 
L 525 4666 
z
" transform="scale(0.015625)"/>
        <path id="DejaVuSans-35" d="M 691 4666 
L 3169 4666 
L 3169 4134 
L 1269 4134 
L 1269 2991 
Q 1406 3038 1543 3061 
Q 1681 3084 1819 3084 
Q 2600 3084 3056 2656 
Q 3513 2228 3513 1497 
Q 3513 744 3044 326 
Q 2575 -91 1722 -91 
Q 1428 -91 1123 -41 
Q 819 9 494 109 
L 494 744 
Q 775 591 1075 516 
Q 1375 441 1709 441 
Q 2250 441 2565 725 
Q 2881 1009 2881 1497 
Q 2881 1984 2565 2268 
Q 2250 2553 1709 2553 
Q 1456 2553 1204 2497 
Q 953 2441 691 2322 
L 691 4666 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-2212"/>
       <use xlink:href="#DejaVuSans-30" x="83.789062"/>
       <use xlink:href="#DejaVuSans-2e" x="147.412109"/>
       <use xlink:href="#DejaVuSans-37" x="179.199219"/>
       <use xlink:href="#DejaVuSans-35" x="242.822266"/>
      </g>
     </g>
    </g>
    <g id="ytick_2">
     <g id="line2d_8">
      <g>
       <use xlink:href="#med7b2961fa" x="57.6" y="261.941379" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_8">
      <!-- −0.50 -->
      <g transform="translate(19.954687 265.740598) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-2212"/>
       <use xlink:href="#DejaVuSans-30" x="83.789062"/>
       <use xlink:href="#DejaVuSans-2e" x="147.412109"/>
       <use xlink:href="#DejaVuSans-35" x="179.199219"/>
       <use xlink:href="#DejaVuSans-30" x="242.822266"/>
      </g>
     </g>
    </g>
    <g id="ytick_3">
     <g id="line2d_9">
      <g>
       <use xlink:href="#med7b2961fa" x="57.6" y="227.212483" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_9">
      <!-- −0.25 -->
      <g transform="translate(19.954687 231.011701) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-2212"/>
       <use xlink:href="#DejaVuSans-30" x="83.789062"/>
       <use xlink:href="#DejaVuSans-2e" x="147.412109"/>
       <use xlink:href="#DejaVuSans-32" x="179.199219"/>
       <use xlink:href="#DejaVuSans-35" x="242.822266"/>
      </g>
     </g>
    </g>
    <g id="ytick_4">
     <g id="line2d_10">
      <g>
       <use xlink:href="#med7b2961fa" x="57.6" y="192.483586" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_10">
      <!-- 0.00 -->
      <g transform="translate(28.334375 196.282805) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-30"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-30" x="95.410156"/>
       <use xlink:href="#DejaVuSans-30" x="159.033203"/>
      </g>
     </g>
    </g>
    <g id="ytick_5">
     <g id="line2d_11">
      <g>
       <use xlink:href="#med7b2961fa" x="57.6" y="157.75469" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_11">
      <!-- 0.25 -->
      <g transform="translate(28.334375 161.553908) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-30"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-32" x="95.410156"/>
       <use xlink:href="#DejaVuSans-35" x="159.033203"/>
      </g>
     </g>
    </g>
    <g id="ytick_6">
     <g id="line2d_12">
      <g>
       <use xlink:href="#med7b2961fa" x="57.6" y="123.025793" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_12">
      <!-- 0.50 -->
      <g transform="translate(28.334375 126.825012) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-30"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-35" x="95.410156"/>
       <use xlink:href="#DejaVuSans-30" x="159.033203"/>
      </g>
     </g>
    </g>
    <g id="ytick_7">
     <g id="line2d_13">
      <g>
       <use xlink:href="#med7b2961fa" x="57.6" y="88.296897" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_13">
      <!-- 0.75 -->
      <g transform="translate(28.334375 92.096115) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-30"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-37" x="95.410156"/>
       <use xlink:href="#DejaVuSans-35" x="159.033203"/>
      </g>
     </g>
    </g>
    <g id="ytick_8">
     <g id="line2d_14">
      <g>
       <use xlink:href="#med7b2961fa" x="57.6" y="53.568" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_14">
      <!-- 1.00 -->
      <g transform="translate(28.334375 57.367219) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-31"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-30" x="95.410156"/>
       <use xlink:href="#DejaVuSans-30" x="159.033203"/>
      </g>
     </g>
    </g>
   </g>
   <g id="line2d_15">
    <path d="M 73.832727 192.483586 
L 77.112066 178.78001 
L 80.391405 165.368557 
L 83.670744 152.594018 
L 86.950083 140.595575 
L 90.229421 128.597133 
L 93.50876 118.75511 
L 96.788099 109.018473 
L 100.067438 100.173278 
L 103.346777 93.383958 
L 106.626116 86.594638 
L 109.905455 81.559204 
L 113.184793 78.132189 
L 116.464132 74.705174 
L 119.743471 73.826408 
L 123.02281 73.839228 
L 126.302149 73.852049 
L 129.581488 76.985703 
L 132.860826 80.249465 
L 136.140165 84.019255 
L 139.419504 90.10759 
L 142.698843 96.195926 
L 145.978182 103.163048 
L 149.257521 111.457589 
L 152.53686 119.75213 
L 155.816198 128.944178 
L 159.095537 138.692176 
L 162.374876 148.440174 
L 165.654215 158.716151 
L 168.933554 169.095196 
L 172.212893 179.463377 
L 175.492231 189.647887 
L 178.77157 199.832397 
L 182.050909 209.752838 
L 185.330248 218.97716 
L 188.609587 228.201483 
L 191.888926 236.629748 
L 195.168264 244.243245 
L 198.447603 251.856742 
L 201.726942 257.931561 
L 205.006281 263.38813 
L 208.28562 268.8447 
L 211.564959 272.267466 
L 214.844298 275.197229 
L 218.123636 278.126992 
L 221.402975 278.702376 
L 224.682314 279.005703 
L 227.961653 279.309029 
L 231.240992 277.140722 
L 234.520331 274.942246 
L 237.799669 272.570844 
L 241.079008 268.196291 
L 244.358347 263.821737 
L 247.637686 259.158576 
L 250.917025 253.096181 
L 254.196364 247.033786 
L 257.475702 240.686035 
L 260.755041 233.536638 
L 264.03438 226.387242 
L 267.313719 219.085612 
L 270.593058 211.506231 
L 273.872397 203.926849 
L 277.151736 196.447864 
L 280.431074 189.093805 
L 283.710413 181.739746 
L 286.989752 174.828511 
L 290.269091 168.298936 
L 293.54843 161.769361 
L 296.827769 156.070089 
L 300.107107 150.861353 
L 303.386446 145.652617 
L 306.665785 141.676273 
L 309.945124 138.178851 
L 313.224463 134.68143 
L 316.503802 132.5644 
L 319.78314 131.012888 
L 323.062479 129.461376 
L 326.341818 129.285605 
L 329.621157 129.703321 
L 332.900496 130.121037 
L 336.179835 131.787783 
L 339.459174 134.021327 
L 342.738512 136.254871 
L 346.017851 139.510689 
L 349.29719 143.254029 
L 352.576529 146.997369 
L 355.855868 151.478534 
L 359.135207 156.329167 
L 362.414545 161.1798 
L 365.693884 166.326468 
L 368.973223 171.772679 
L 372.252562 177.21889 
L 375.531901 182.672506 
L 378.81124 188.14131 
L 382.090579 193.610113 
L 385.369917 198.996959 
L 388.649256 203.948681 
L 391.928595 208.900404 
L 395.207934 213.852127 
L 398.487273 218.230799 
" clip-path="url(#p3192fabcf0)" style="fill: none; stroke: #1f77b4; stroke-width: 1.5; stroke-linecap: square"/>
   </g>
   <g id="line2d_16">
    <path d="M 73.832727 53.568 
L 77.112066 57.49348 
L 80.391405 62.31732 
L 83.670744 68.318355 
L 86.950083 75.753831 
L 90.229421 83.189308 
L 93.50876 92.897569 
L 96.788099 102.716903 
L 100.067438 113.045778 
L 103.346777 124.549774 
L 106.626116 136.05377 
L 109.905455 147.958079 
L 113.184793 160.2295 
L 116.464132 172.500921 
L 119.743471 184.616886 
L 123.02281 196.67846 
L 126.302149 208.740034 
L 129.581488 219.728605 
L 132.860826 230.672443 
L 136.140165 241.277534 
L 139.419504 250.33054 
L 142.698843 259.383546 
L 145.978182 267.449672 
L 149.257521 274.025107 
L 152.53686 280.600541 
L 155.816198 285.420173 
L 159.095537 289.152195 
L 162.374876 292.884217 
L 165.654215 294.129199 
L 168.933554 294.888683 
L 172.212893 295.488 
L 175.492231 293.379445 
L 178.77157 291.27089 
L 182.050909 288.460861 
L 185.330248 283.801665 
L 188.609587 279.142469 
L 191.888926 273.467131 
L 195.168264 266.751766 
L 198.447603 260.036401 
L 201.726942 252.283764 
L 205.006281 244.114343 
L 208.28562 235.944921 
L 211.564959 227.186487 
L 214.844298 218.285273 
L 218.123636 209.384059 
L 221.402975 200.528331 
L 224.682314 191.67786 
L 227.961653 182.827388 
L 231.240992 174.751859 
L 234.520331 166.685788 
L 237.799669 158.731837 
L 241.079008 152.07668 
L 244.358347 145.421522 
L 247.637686 139.088557 
L 250.917025 134.317655 
L 254.196364 129.546753 
L 257.475702 125.346504 
L 260.755041 122.749377 
L 264.03438 120.15225 
L 267.313719 118.357336 
L 270.593058 118.026077 
L 273.872397 117.694817 
L 277.151736 118.327826 
L 280.431074 120.160702 
L 283.710413 121.993577 
L 286.989752 124.84054 
L 290.269091 128.56152 
L 293.54843 132.282499 
L 296.827769 136.927983 
L 300.107107 142.119656 
L 303.386446 147.311328 
L 306.665785 153.197795 
L 309.945124 159.354268 
L 313.224463 165.51074 
L 316.503802 171.937835 
L 319.78314 178.475798 
L 323.062479 185.013762 
L 326.341818 191.395814 
L 329.621157 197.710606 
L 332.900496 204.025398 
L 336.179835 209.808973 
L 339.459174 215.351486 
L 342.738512 220.893998 
L 346.017851 225.610307 
L 349.29719 229.9326 
L 352.576529 234.254893 
L 355.855868 237.526403 
L 359.135207 240.271731 
L 362.414545 243.017058 
L 365.693884 244.876372 
L 368.973223 245.839173 
L 372.252562 246.801975 
L 375.531901 247.185679 
L 378.81124 246.381743 
L 382.090579 245.577806 
L 385.369917 244.523749 
L 388.649256 242.141776 
L 391.928595 239.759802 
L 395.207934 237.377828 
L 398.487273 234.127807 
" clip-path="url(#p3192fabcf0)" style="fill: none; stroke: #ff7f0e; stroke-width: 1.5; stroke-linecap: square"/>
   </g>
   <g id="patch_3">
    <path d="M 57.6 307.584 
L 57.6 41.472 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
   <g id="patch_4">
    <path d="M 414.72 307.584 
L 414.72 41.472 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
   <g id="patch_5">
    <path d="M 57.6 307.584 
L 414.72 307.584 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
   <g id="patch_6">
    <path d="M 57.6 41.472 
L 414.72 41.472 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
   <g id="legend_1">
    <g id="patch_7">
     <path d="M 369.92 78.848563 
L 407.72 78.848563 
Q 409.72 78.848563 409.72 76.848563 
L 409.72 48.472 
Q 409.72 46.472 407.72 46.472 
L 369.92 46.472 
Q 367.92 46.472 367.92 48.472 
L 367.92 76.848563 
Q 367.92 78.848563 369.92 78.848563 
z
" style="fill: #ffffff; opacity: 0.8; stroke: #cccccc; stroke-linejoin: miter"/>
    </g>
    <g id="line2d_17">
     <path d="M 371.92 54.570438 
L 381.92 54.570438 
L 391.92 54.570438 
" style="fill: none; stroke: #1f77b4; stroke-width: 1.5; stroke-linecap: square"/>
    </g>
    <g id="text_15">
     <!-- $x$ -->
     <g transform="translate(399.92 58.070438) scale(0.1 -0.1)">
      <defs>
       <path id="Cmmi10-78" d="M 500 184 
Q 613 97 819 97 
Q 1019 97 1172 289 
Q 1325 481 1381 709 
L 1672 1844 
Q 1741 2153 1741 2266 
Q 1741 2425 1652 2544 
Q 1563 2663 1403 2663 
Q 1200 2663 1022 2536 
Q 844 2409 722 2214 
Q 600 2019 550 1819 
Q 538 1778 500 1778 
L 422 1778 
Q 372 1778 372 1838 
L 372 1856 
Q 434 2094 584 2320 
Q 734 2547 951 2687 
Q 1169 2828 1416 2828 
Q 1650 2828 1839 2703 
Q 2028 2578 2106 2363 
Q 2216 2559 2386 2693 
Q 2556 2828 2759 2828 
Q 2897 2828 3040 2779 
Q 3184 2731 3275 2631 
Q 3366 2531 3366 2381 
Q 3366 2219 3261 2101 
Q 3156 1984 2994 1984 
Q 2891 1984 2822 2050 
Q 2753 2116 2753 2216 
Q 2753 2350 2845 2451 
Q 2938 2553 3066 2572 
Q 2950 2663 2747 2663 
Q 2541 2663 2389 2472 
Q 2238 2281 2175 2047 
L 1894 916 
Q 1825 659 1825 494 
Q 1825 331 1917 214 
Q 2009 97 2163 97 
Q 2463 97 2698 361 
Q 2934 625 3009 941 
Q 3022 978 3059 978 
L 3138 978 
Q 3163 978 3178 961 
Q 3194 944 3194 922 
Q 3194 916 3188 903 
Q 3097 522 2806 225 
Q 2516 -72 2150 -72 
Q 1916 -72 1727 54 
Q 1538 181 1459 397 
Q 1359 209 1182 68 
Q 1006 -72 806 -72 
Q 669 -72 523 -23 
Q 378 25 287 125 
Q 197 225 197 378 
Q 197 528 301 651 
Q 406 775 563 775 
Q 669 775 741 711 
Q 813 647 813 544 
Q 813 409 723 309 
Q 634 209 500 184 
z
" transform="scale(0.015625)"/>
      </defs>
      <use xlink:href="#Cmmi10-78" transform="translate(0 0.8125)"/>
     </g>
    </g>
    <g id="line2d_18">
     <path d="M 371.92 69.248563 
L 381.92 69.248563 
L 391.92 69.248563 
" style="fill: none; stroke: #ff7f0e; stroke-width: 1.5; stroke-linecap: square"/>
    </g>
    <g id="text_16">
     <!-- $y$ -->
     <g transform="translate(399.92 72.748563) scale(0.1 -0.1)">
      <defs>
       <path id="Cmmi10-79" d="M 538 -916 
Q 672 -1147 1006 -1147 
Q 1309 -1147 1531 -934 
Q 1753 -722 1889 -420 
Q 2025 -119 2100 197 
Q 1816 -72 1484 -72 
Q 1231 -72 1053 15 
Q 875 103 776 276 
Q 678 450 678 697 
Q 678 906 734 1126 
Q 791 1347 892 1617 
Q 994 1888 1069 2088 
Q 1153 2322 1153 2472 
Q 1153 2663 1013 2663 
Q 759 2663 595 2402 
Q 431 2141 353 1819 
Q 341 1778 300 1778 
L 225 1778 
Q 172 1778 172 1838 
L 172 1856 
Q 275 2238 487 2533 
Q 700 2828 1025 2828 
Q 1253 2828 1411 2678 
Q 1569 2528 1569 2297 
Q 1569 2178 1516 2047 
Q 1488 1969 1388 1706 
Q 1288 1444 1234 1272 
Q 1181 1100 1147 934 
Q 1113 769 1113 603 
Q 1113 391 1203 244 
Q 1294 97 1491 97 
Q 1888 97 2203 581 
L 2688 2553 
Q 2709 2638 2787 2698 
Q 2866 2759 2956 2759 
Q 3034 2759 3092 2709 
Q 3150 2659 3150 2578 
Q 3150 2541 3144 2528 
L 2509 -19 
Q 2425 -347 2200 -647 
Q 1975 -947 1658 -1130 
Q 1341 -1313 997 -1313 
Q 831 -1313 668 -1248 
Q 506 -1184 406 -1056 
Q 306 -928 306 -756 
Q 306 -581 409 -453 
Q 513 -325 684 -325 
Q 788 -325 858 -389 
Q 928 -453 928 -556 
Q 928 -703 818 -812 
Q 709 -922 563 -922 
Q 556 -919 550 -917 
Q 544 -916 538 -916 
z
" transform="scale(0.015625)"/>
      </defs>
      <use xlink:href="#Cmmi10-79" transform="translate(0 0.8125)"/>
     </g>
    </g>
   </g>
  </g>
  <g id="text_17">
   <!-- Damped coupled oscillators -->
   <g transform="translate(122.505469 26.314313) scale(0.18 -0.18)">
    <defs>
     <path id="Cmr10-44" d="M 213 0 
L 213 225 
Q 872 225 872 428 
L 872 3944 
Q 872 4147 213 4147 
L 213 4372 
L 2572 4372 
Q 3009 4372 3371 4183 
Q 3734 3994 3990 3678 
Q 4247 3363 4386 2963 
Q 4525 2563 4525 2144 
Q 4525 1738 4384 1355 
Q 4244 972 3980 664 
Q 3716 356 3355 178 
Q 2994 0 2572 0 
L 213 0 
z
M 1447 428 
Q 1447 291 1525 258 
Q 1603 225 1772 225 
L 2406 225 
Q 2734 225 3029 367 
Q 3325 509 3519 763 
Q 3722 1031 3790 1364 
Q 3859 1697 3859 2144 
Q 3859 2609 3790 2959 
Q 3722 3309 3519 3584 
Q 3328 3856 3034 4001 
Q 2741 4147 2406 4147 
L 1772 4147 
Q 1656 4147 1592 4137 
Q 1528 4128 1487 4083 
Q 1447 4038 1447 3944 
L 1447 428 
z
" transform="scale(0.015625)"/>
     <path id="Cmr10-61" d="M 256 628 
Q 256 1009 556 1248 
Q 856 1488 1276 1586 
Q 1697 1684 2075 1684 
L 2075 1947 
Q 2075 2131 1994 2304 
Q 1913 2478 1759 2589 
Q 1606 2700 1422 2700 
Q 997 2700 775 2509 
Q 897 2509 976 2417 
Q 1056 2325 1056 2203 
Q 1056 2075 965 1984 
Q 875 1894 750 1894 
Q 622 1894 531 1984 
Q 441 2075 441 2203 
Q 441 2541 747 2705 
Q 1053 2869 1422 2869 
Q 1681 2869 1943 2758 
Q 2206 2647 2373 2440 
Q 2541 2234 2541 1959 
L 2541 519 
Q 2541 394 2594 289 
Q 2647 184 2759 184 
Q 2866 184 2917 290 
Q 2969 397 2969 519 
L 2969 928 
L 3156 928 
L 3156 519 
Q 3156 375 3081 245 
Q 3006 116 2879 39 
Q 2753 -38 2606 -38 
Q 2419 -38 2283 107 
Q 2147 253 2131 453 
Q 2013 213 1781 70 
Q 1550 -72 1288 -72 
Q 1044 -72 808 0 
Q 572 72 414 226 
Q 256 381 256 628 
z
M 775 628 
Q 775 403 940 250 
Q 1106 97 1331 97 
Q 1538 97 1706 200 
Q 1875 303 1975 481 
Q 2075 659 2075 856 
L 2075 1522 
Q 1784 1522 1479 1426 
Q 1175 1331 975 1128 
Q 775 925 775 628 
z
" transform="scale(0.015625)"/>
     <path id="Cmr10-6d" d="M 191 0 
L 191 225 
Q 409 225 550 259 
Q 691 294 691 428 
L 691 2175 
Q 691 2347 639 2423 
Q 588 2500 491 2517 
Q 394 2534 191 2534 
L 191 2759 
L 1119 2828 
L 1119 2203 
Q 1247 2478 1498 2653 
Q 1750 2828 2047 2828 
Q 2784 2828 2913 2228 
Q 3041 2497 3287 2662 
Q 3534 2828 3828 2828 
Q 4119 2828 4317 2734 
Q 4516 2641 4616 2448 
Q 4716 2256 4716 1966 
L 4716 428 
Q 4716 294 4858 259 
Q 5000 225 5216 225 
L 5216 0 
L 3750 0 
L 3750 225 
Q 3969 225 4109 259 
Q 4250 294 4250 428 
L 4250 1947 
Q 4250 2269 4159 2466 
Q 4069 2663 3788 2663 
Q 3419 2663 3178 2366 
Q 2938 2069 2938 1691 
L 2938 428 
Q 2938 294 3078 259 
Q 3219 225 3438 225 
L 3438 0 
L 1972 0 
L 1972 225 
Q 2191 225 2331 259 
Q 2472 294 2472 428 
L 2472 1947 
Q 2472 2259 2381 2461 
Q 2291 2663 2009 2663 
Q 1638 2663 1398 2366 
Q 1159 2069 1159 1691 
L 1159 428 
Q 1159 294 1300 259 
Q 1441 225 1656 225 
L 1656 0 
L 191 0 
z
" transform="scale(0.015625)"/>
     <path id="Cmr10-70" d="M 166 -1241 
L 166 -1019 
Q 384 -1019 525 -981 
Q 666 -944 666 -813 
L 666 2272 
Q 666 2447 541 2490 
Q 416 2534 166 2534 
L 166 2759 
L 1113 2828 
L 1113 2431 
Q 1288 2625 1520 2726 
Q 1753 2828 2016 2828 
Q 2394 2828 2697 2623 
Q 3000 2419 3170 2086 
Q 3341 1753 3341 1381 
Q 3341 994 3152 659 
Q 2963 325 2636 126 
Q 2309 -72 1919 -72 
Q 1453 -72 1131 306 
L 1131 -813 
Q 1131 -944 1273 -981 
Q 1416 -1019 1631 -1019 
L 1631 -1241 
L 166 -1241 
z
M 1131 622 
Q 1244 394 1444 245 
Q 1644 97 1881 97 
Q 2103 97 2273 215 
Q 2444 334 2559 534 
Q 2675 734 2729 954 
Q 2784 1175 2784 1381 
Q 2784 1638 2692 1936 
Q 2600 2234 2411 2439 
Q 2222 2644 1953 2644 
Q 1694 2644 1476 2511 
Q 1259 2378 1131 2150 
L 1131 622 
z
" transform="scale(0.015625)"/>
     <path id="Cmr10-65" d="M 1594 -72 
Q 1203 -72 876 133 
Q 550 338 364 680 
Q 178 1022 178 1403 
Q 178 1778 348 2115 
Q 519 2453 823 2661 
Q 1128 2869 1503 2869 
Q 1797 2869 2014 2770 
Q 2231 2672 2372 2497 
Q 2513 2322 2584 2084 
Q 2656 1847 2656 1563 
Q 2656 1478 2591 1478 
L 738 1478 
L 738 1409 
Q 738 878 952 497 
Q 1166 116 1650 116 
Q 1847 116 2014 203 
Q 2181 291 2304 447 
Q 2428 603 2472 781 
Q 2478 803 2495 820 
Q 2513 838 2534 838 
L 2591 838 
Q 2656 838 2656 756 
Q 2566 394 2266 161 
Q 1966 -72 1594 -72 
z
M 744 1638 
L 2203 1638 
Q 2203 1878 2136 2125 
Q 2069 2372 1912 2536 
Q 1756 2700 1503 2700 
Q 1141 2700 942 2361 
Q 744 2022 744 1638 
z
" transform="scale(0.015625)"/>
     <path id="Cmr10-64" d="M 1563 -72 
Q 1184 -72 871 133 
Q 559 338 386 672 
Q 213 1006 213 1381 
Q 213 1769 402 2101 
Q 591 2434 916 2631 
Q 1241 2828 1631 2828 
Q 1866 2828 2075 2729 
Q 2284 2631 2438 2456 
L 2438 3788 
Q 2438 3959 2386 4036 
Q 2334 4113 2239 4130 
Q 2144 4147 1941 4147 
L 1941 4372 
L 2888 4441 
L 2888 581 
Q 2888 413 2939 336 
Q 2991 259 3086 242 
Q 3181 225 3384 225 
L 3384 0 
L 2419 -72 
L 2419 331 
Q 2253 141 2025 34 
Q 1797 -72 1563 -72 
z
M 909 556 
Q 1019 347 1201 222 
Q 1384 97 1600 97 
Q 1866 97 2087 250 
Q 2309 403 2419 647 
L 2419 2181 
Q 2344 2322 2230 2433 
Q 2116 2544 1973 2603 
Q 1831 2663 1672 2663 
Q 1338 2663 1134 2473 
Q 931 2284 850 1990 
Q 769 1697 769 1375 
Q 769 1119 795 928 
Q 822 738 909 556 
z
" transform="scale(0.015625)"/>
     <path id="Cmr10-20" transform="scale(0.015625)"/>
     <path id="Cmr10-63" d="M 1594 -72 
Q 1206 -72 890 129 
Q 575 331 394 667 
Q 213 1003 213 1381 
Q 213 1759 392 2106 
Q 572 2453 889 2661 
Q 1206 2869 1594 2869 
Q 1969 2869 2276 2722 
Q 2584 2575 2584 2241 
Q 2584 2116 2495 2023 
Q 2406 1931 2278 1931 
Q 2150 1931 2061 2023 
Q 1972 2116 1972 2241 
Q 1972 2353 2044 2436 
Q 2116 2519 2222 2541 
Q 2000 2681 1600 2681 
Q 1294 2681 1106 2478 
Q 919 2275 844 1975 
Q 769 1675 769 1381 
Q 769 1072 861 783 
Q 953 494 1158 305 
Q 1363 116 1672 116 
Q 1975 116 2187 302 
Q 2400 488 2478 788 
Q 2478 825 2528 825 
L 2606 825 
Q 2625 825 2640 808 
Q 2656 791 2656 769 
L 2656 750 
Q 2559 372 2271 150 
Q 1984 -72 1594 -72 
z
" transform="scale(0.015625)"/>
     <path id="Cmr10-6f" d="M 1600 -72 
Q 1216 -72 887 123 
Q 559 319 368 647 
Q 178 975 178 1363 
Q 178 1656 283 1928 
Q 388 2200 583 2414 
Q 778 2628 1037 2748 
Q 1297 2869 1600 2869 
Q 1994 2869 2317 2661 
Q 2641 2453 2828 2104 
Q 3016 1756 3016 1363 
Q 3016 978 2825 648 
Q 2634 319 2307 123 
Q 1981 -72 1600 -72 
z
M 1600 116 
Q 2113 116 2284 487 
Q 2456 859 2456 1434 
Q 2456 1756 2422 1967 
Q 2388 2178 2272 2350 
Q 2200 2456 2089 2536 
Q 1978 2616 1854 2658 
Q 1731 2700 1600 2700 
Q 1400 2700 1220 2609 
Q 1041 2519 922 2350 
Q 803 2169 770 1951 
Q 738 1734 738 1434 
Q 738 1075 800 789 
Q 863 503 1052 309 
Q 1241 116 1600 116 
z
" transform="scale(0.015625)"/>
     <path id="Cmr10-75" d="M 691 763 
L 691 2175 
Q 691 2347 639 2423 
Q 588 2500 491 2517 
Q 394 2534 191 2534 
L 191 2759 
L 1159 2828 
L 1159 763 
Q 1159 513 1195 373 
Q 1231 234 1348 165 
Q 1466 97 1722 97 
Q 2066 97 2269 384 
Q 2472 672 2472 1038 
L 2472 2175 
Q 2472 2347 2419 2423 
Q 2366 2500 2270 2517 
Q 2175 2534 1972 2534 
L 1972 2759 
L 2938 2828 
L 2938 581 
Q 2938 413 2989 336 
Q 3041 259 3137 242 
Q 3234 225 3438 225 
L 3438 0 
L 2491 -72 
L 2491 469 
Q 2372 228 2159 78 
Q 1947 -72 1691 -72 
Q 1231 -72 961 123 
Q 691 319 691 763 
z
" transform="scale(0.015625)"/>
     <path id="Cmr10-6c" d="M 197 0 
L 197 225 
Q 416 225 556 259 
Q 697 294 697 428 
L 697 3788 
Q 697 3959 645 4036 
Q 594 4113 497 4130 
Q 400 4147 197 4147 
L 197 4372 
L 1147 4441 
L 1147 428 
Q 1147 294 1287 259 
Q 1428 225 1644 225 
L 1644 0 
L 197 0 
z
" transform="scale(0.015625)"/>
     <path id="Cmr10-73" d="M 213 -19 
L 213 1025 
Q 213 1075 269 1075 
L 347 1075 
Q 384 1075 397 1025 
Q 575 97 1259 97 
Q 1563 97 1767 234 
Q 1972 372 1972 659 
Q 1972 866 1812 1011 
Q 1653 1156 1434 1209 
L 1006 1294 
Q 791 1341 614 1437 
Q 438 1534 325 1695 
Q 213 1856 213 2069 
Q 213 2350 361 2529 
Q 509 2709 746 2789 
Q 984 2869 1259 2869 
Q 1588 2869 1831 2694 
L 2016 2853 
Q 2016 2869 2047 2869 
L 2094 2869 
Q 2113 2869 2128 2851 
Q 2144 2834 2144 2816 
L 2144 1978 
Q 2144 1919 2094 1919 
L 2016 1919 
Q 1959 1919 1959 1978 
Q 1959 2313 1773 2516 
Q 1588 2719 1253 2719 
Q 966 2719 755 2612 
Q 544 2506 544 2247 
Q 544 2069 695 1955 
Q 847 1841 1050 1791 
L 1484 1709 
Q 1703 1659 1892 1540 
Q 2081 1422 2192 1240 
Q 2303 1059 2303 831 
Q 2303 600 2223 429 
Q 2144 259 2001 146 
Q 1859 34 1665 -19 
Q 1472 -72 1259 -72 
Q 859 -72 575 197 
L 341 -56 
Q 341 -72 306 -72 
L 269 -72 
Q 213 -72 213 -19 
z
" transform="scale(0.015625)"/>
     <path id="Cmr10-69" d="M 197 0 
L 197 225 
Q 416 225 556 259 
Q 697 294 697 428 
L 697 2175 
Q 697 2422 601 2478 
Q 506 2534 225 2534 
L 225 2759 
L 1147 2828 
L 1147 428 
Q 1147 294 1269 259 
Q 1391 225 1594 225 
L 1594 0 
L 197 0 
z
M 469 3928 
Q 469 4069 575 4175 
Q 681 4281 819 4281 
Q 909 4281 993 4234 
Q 1078 4188 1125 4103 
Q 1172 4019 1172 3928 
Q 1172 3791 1065 3684 
Q 959 3578 819 3578 
Q 681 3578 575 3684 
Q 469 3791 469 3928 
z
" transform="scale(0.015625)"/>
     <path id="Cmr10-74" d="M 653 769 
L 653 2534 
L 122 2534 
L 122 2700 
Q 541 2700 737 3090 
Q 934 3481 934 3938 
L 1119 3938 
L 1119 2759 
L 2022 2759 
L 2022 2534 
L 1119 2534 
L 1119 781 
Q 1119 516 1208 316 
Q 1297 116 1528 116 
Q 1747 116 1844 327 
Q 1941 538 1941 781 
L 1941 1159 
L 2125 1159 
L 2125 769 
Q 2125 569 2051 373 
Q 1978 178 1834 53 
Q 1691 -72 1484 -72 
Q 1100 -72 876 158 
Q 653 388 653 769 
z
" transform="scale(0.015625)"/>
     <path id="Cmr10-72" d="M 166 0 
L 166 225 
Q 384 225 525 259 
Q 666 294 666 428 
L 666 2175 
Q 666 2347 614 2423 
Q 563 2500 466 2517 
Q 369 2534 166 2534 
L 166 2759 
L 1081 2828 
L 1081 2203 
Q 1184 2481 1375 2654 
Q 1566 2828 1838 2828 
Q 2028 2828 2178 2715 
Q 2328 2603 2328 2419 
Q 2328 2303 2245 2217 
Q 2163 2131 2041 2131 
Q 1922 2131 1837 2215 
Q 1753 2300 1753 2419 
Q 1753 2591 1875 2663 
L 1838 2663 
Q 1578 2663 1414 2475 
Q 1250 2288 1181 2009 
Q 1113 1731 1113 1478 
L 1113 428 
Q 1113 225 1734 225 
L 1734 0 
L 166 0 
z
" transform="scale(0.015625)"/>
    </defs>
    <use xlink:href="#Cmr10-44"/>
    <use xlink:href="#Cmr10-61" x="76.318359"/>
    <use xlink:href="#Cmr10-6d" x="126.318359"/>
    <use xlink:href="#Cmr10-70" x="209.619141"/>
    <use xlink:href="#Cmr10-65" x="265.136719"/>
    <use xlink:href="#Cmr10-64" x="309.521484"/>
    <use xlink:href="#Cmr10-20" x="365.039062"/>
    <use xlink:href="#Cmr10-63" x="398.339844"/>
    <use xlink:href="#Cmr10-6f" x="442.724609"/>
    <use xlink:href="#Cmr10-75" x="492.724609"/>
    <use xlink:href="#Cmr10-70" x="548.242188"/>
    <use xlink:href="#Cmr10-6c" x="603.759766"/>
    <use xlink:href="#Cmr10-65" x="631.445312"/>
    <use xlink:href="#Cmr10-64" x="675.830078"/>
    <use xlink:href="#Cmr10-20" x="731.347656"/>
    <use xlink:href="#Cmr10-6f" x="764.648438"/>
    <use xlink:href="#Cmr10-73" x="814.648438"/>
    <use xlink:href="#Cmr10-63" x="854.052734"/>
    <use xlink:href="#Cmr10-69" x="898.4375"/>
    <use xlink:href="#Cmr10-6c" x="926.123047"/>
    <use xlink:href="#Cmr10-6c" x="953.808594"/>
    <use xlink:href="#Cmr10-61" x="981.494141"/>
    <use xlink:href="#Cmr10-74" x="1031.494141"/>
    <use xlink:href="#Cmr10-6f" x="1070.3125"/>
    <use xlink:href="#Cmr10-72" x="1120.3125"/>
    <use xlink:href="#Cmr10-73" x="1159.423828"/>
   </g>
  </g>
 </g>
 <defs>
  <clipPath id="p3192fabcf0">
   <rect x="57.6" y="41.472" width="357.12" height="266.112"/>
  </clipPath>
 </defs>
</svg>
\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"from cdb.graphics.plot import *\\nplot(sol, title=\\\"Damped coupled oscillators\\\");\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 14649026388562681645,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 15810749854545181619,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"Note how we did not have to specify the range of the variable $\\\\tau$ for plotting, as the \\\\algo{plot} command has automatically figured out the range for which the interpolating functions are defined (if you want, you can of course specify the range by hand).\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"Note how we did not have to specify the range of the variable $\\\\tau$ for plotting, as the \\\\algo{plot} command has automatically figured out the range for which the interpolating functions are defined (if you want, you can of course specify the range by hand).\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 5433039321472049200,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 11408622105792591178,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\subsection*{Lotka-Volterra equations}\\n\\nThe following example is a little bit more complicated. It shows how to numerically solve a system of two ODEs, and then adds a slider so you can interact with the value of the constant which appears in the equations.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\subsection*{Lotka-Volterra equations}\\n\\nThe following example is a little bit more complicated. It shows how to numerically solve a system of two ODEs, and then adds a slider so you can interact with the value of the constant which appears in the equations.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 6427470927468349618,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"from cdb.interact.slider import *\\nfrom cdb.graphics.plot import *\\nfig=None\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 14420855019088504514,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"t::Coordinate.\\n{x, y}::Depends(t).\\n\\\\dot{#}::Derivative(t).\\nK = 0.45\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 15970746748854718218,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 14788814495096219627,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"The equations themselves describe a very simple predator-prey system, in which $x$ are the number of prey and $y$ are the number of predators.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"The equations themselves describe a very simple predator-prey system, in which $x$ are the number of prey and $y$ are the number of predators.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 4083308006389521999,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 6615307240543804167,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 383779447477266097,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"{\\\\dot(x) = x (1-y), \\\\dot(y) = -0.69y (1-x)}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\left[\\\\dot{x} = x \\\\left(1\\\\discretionary{}{}{}-\\\\,y\\\\right), \\\\discretionary{}{}{}\\\\dot{y} = -0.69\\\\,y \\\\left(1\\\\discretionary{}{}{}-\\\\,x\\\\right)\\\\right]\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"lotka_volterra := [ \\\\dot{x} = x*(1-y), \\\\dot{y} = - @(K) y*(1-x) ];\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 552980910531781488,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 1272125326665430932,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"We solve these numerically with some initial conditions, and then feed the solutions of \\\\verb|ndsolve| straight into \\\\verb|plot| to visualise them.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"We solve these numerically with some initial conditions, and then feed the solutions of \\\\verb|ndsolve| straight into \\\\verb|plot| to visualise them.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 3770567865522131118,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 15403245634330416740,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"image_svg\",\n\t\t\t\t\t\"source\": \"<?xml version="1.0" encoding="utf-8" standalone="no"?>
<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
  "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="460.8pt" height="345.6pt" viewBox="0 0 460.8 345.6" xmlns="http://www.w3.org/2000/svg" version="1.1">
 <metadata>
  <rdf:RDF xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:cc="http://creativecommons.org/ns#" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
   <cc:Work>
    <dc:type rdf:resource="http://purl.org/dc/dcmitype/StillImage"/>
    <dc:date>2025-05-29T12:28:28.508966</dc:date>
    <dc:format>image/svg+xml</dc:format>
    <dc:creator>
     <cc:Agent>
      <dc:title>Matplotlib v3.6.3, https://matplotlib.org/</dc:title>
     </cc:Agent>
    </dc:creator>
   </cc:Work>
  </rdf:RDF>
 </metadata>
 <defs>
  <style type="text/css">*{stroke-linejoin: round; stroke-linecap: butt}</style>
 </defs>
 <g id="figure_1">
  <g id="patch_1">
   <path d="M 0 345.6 
L 460.8 345.6 
L 460.8 0 
L 0 0 
z
" style="fill: #ffffff"/>
  </g>
  <g id="axes_1">
   <g id="patch_2">
    <path d="M 57.6 307.584 
L 414.72 307.584 
L 414.72 41.472 
L 57.6 41.472 
z
" style="fill: #ffffff"/>
   </g>
   <g id="matplotlib.axis_1">
    <g id="xtick_1">
     <g id="line2d_1">
      <defs>
       <path id="m9129fa4e7c" d="M 0 0 
L 0 3.5 
" style="stroke: #000000; stroke-width: 0.8"/>
      </defs>
      <g>
       <use xlink:href="#m9129fa4e7c" x="73.832727" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_1">
      <!-- 0 -->
      <g transform="translate(70.651477 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-30" d="M 2034 4250 
Q 1547 4250 1301 3770 
Q 1056 3291 1056 2328 
Q 1056 1369 1301 889 
Q 1547 409 2034 409 
Q 2525 409 2770 889 
Q 3016 1369 3016 2328 
Q 3016 3291 2770 3770 
Q 2525 4250 2034 4250 
z
M 2034 4750 
Q 2819 4750 3233 4129 
Q 3647 3509 3647 2328 
Q 3647 1150 3233 529 
Q 2819 -91 2034 -91 
Q 1250 -91 836 529 
Q 422 1150 422 2328 
Q 422 3509 836 4129 
Q 1250 4750 2034 4750 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-30"/>
      </g>
     </g>
    </g>
    <g id="xtick_2">
     <g id="line2d_2">
      <g>
       <use xlink:href="#m9129fa4e7c" x="127.941818" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_2">
      <!-- 5 -->
      <g transform="translate(124.760568 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-35" d="M 691 4666 
L 3169 4666 
L 3169 4134 
L 1269 4134 
L 1269 2991 
Q 1406 3038 1543 3061 
Q 1681 3084 1819 3084 
Q 2600 3084 3056 2656 
Q 3513 2228 3513 1497 
Q 3513 744 3044 326 
Q 2575 -91 1722 -91 
Q 1428 -91 1123 -41 
Q 819 9 494 109 
L 494 744 
Q 775 591 1075 516 
Q 1375 441 1709 441 
Q 2250 441 2565 725 
Q 2881 1009 2881 1497 
Q 2881 1984 2565 2268 
Q 2250 2553 1709 2553 
Q 1456 2553 1204 2497 
Q 953 2441 691 2322 
L 691 4666 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-35"/>
      </g>
     </g>
    </g>
    <g id="xtick_3">
     <g id="line2d_3">
      <g>
       <use xlink:href="#m9129fa4e7c" x="182.050909" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_3">
      <!-- 10 -->
      <g transform="translate(175.688409 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-31" d="M 794 531 
L 1825 531 
L 1825 4091 
L 703 3866 
L 703 4441 
L 1819 4666 
L 2450 4666 
L 2450 531 
L 3481 531 
L 3481 0 
L 794 0 
L 794 531 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-31"/>
       <use xlink:href="#DejaVuSans-30" x="63.623047"/>
      </g>
     </g>
    </g>
    <g id="xtick_4">
     <g id="line2d_4">
      <g>
       <use xlink:href="#m9129fa4e7c" x="236.16" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_4">
      <!-- 15 -->
      <g transform="translate(229.7975 322.182437) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-31"/>
       <use xlink:href="#DejaVuSans-35" x="63.623047"/>
      </g>
     </g>
    </g>
    <g id="xtick_5">
     <g id="line2d_5">
      <g>
       <use xlink:href="#m9129fa4e7c" x="290.269091" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_5">
      <!-- 20 -->
      <g transform="translate(283.906591 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-32" d="M 1228 531 
L 3431 531 
L 3431 0 
L 469 0 
L 469 531 
Q 828 903 1448 1529 
Q 2069 2156 2228 2338 
Q 2531 2678 2651 2914 
Q 2772 3150 2772 3378 
Q 2772 3750 2511 3984 
Q 2250 4219 1831 4219 
Q 1534 4219 1204 4116 
Q 875 4013 500 3803 
L 500 4441 
Q 881 4594 1212 4672 
Q 1544 4750 1819 4750 
Q 2544 4750 2975 4387 
Q 3406 4025 3406 3419 
Q 3406 3131 3298 2873 
Q 3191 2616 2906 2266 
Q 2828 2175 2409 1742 
Q 1991 1309 1228 531 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-32"/>
       <use xlink:href="#DejaVuSans-30" x="63.623047"/>
      </g>
     </g>
    </g>
    <g id="xtick_6">
     <g id="line2d_6">
      <g>
       <use xlink:href="#m9129fa4e7c" x="344.378182" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_6">
      <!-- 25 -->
      <g transform="translate(338.015682 322.182437) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-32"/>
       <use xlink:href="#DejaVuSans-35" x="63.623047"/>
      </g>
     </g>
    </g>
    <g id="xtick_7">
     <g id="line2d_7">
      <g>
       <use xlink:href="#m9129fa4e7c" x="398.487273" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_7">
      <!-- 30 -->
      <g transform="translate(392.124773 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-33" d="M 2597 2516 
Q 3050 2419 3304 2112 
Q 3559 1806 3559 1356 
Q 3559 666 3084 287 
Q 2609 -91 1734 -91 
Q 1441 -91 1130 -33 
Q 819 25 488 141 
L 488 750 
Q 750 597 1062 519 
Q 1375 441 1716 441 
Q 2309 441 2620 675 
Q 2931 909 2931 1356 
Q 2931 1769 2642 2001 
Q 2353 2234 1838 2234 
L 1294 2234 
L 1294 2753 
L 1863 2753 
Q 2328 2753 2575 2939 
Q 2822 3125 2822 3475 
Q 2822 3834 2567 4026 
Q 2313 4219 1838 4219 
Q 1578 4219 1281 4162 
Q 984 4106 628 3988 
L 628 4550 
Q 988 4650 1302 4700 
Q 1616 4750 1894 4750 
Q 2613 4750 3031 4423 
Q 3450 4097 3450 3541 
Q 3450 3153 3228 2886 
Q 3006 2619 2597 2516 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-33"/>
       <use xlink:href="#DejaVuSans-30" x="63.623047"/>
      </g>
     </g>
    </g>
   </g>
   <g id="matplotlib.axis_2">
    <g id="ytick_1">
     <g id="line2d_8">
      <defs>
       <path id="maf8a7b5146" d="M 0 0 
L -3.5 0 
" style="stroke: #000000; stroke-width: 0.8"/>
      </defs>
      <g>
       <use xlink:href="#maf8a7b5146" x="57.6" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_8">
      <!-- 0 -->
      <g transform="translate(44.2375 311.383219) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-30"/>
      </g>
     </g>
    </g>
    <g id="ytick_2">
     <g id="line2d_9">
      <g>
       <use xlink:href="#maf8a7b5146" x="57.6" y="254.3616" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_9">
      <!-- 1 -->
      <g transform="translate(44.2375 258.160819) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-31"/>
      </g>
     </g>
    </g>
    <g id="ytick_3">
     <g id="line2d_10">
      <g>
       <use xlink:href="#maf8a7b5146" x="57.6" y="201.1392" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_10">
      <!-- 2 -->
      <g transform="translate(44.2375 204.938419) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-32"/>
      </g>
     </g>
    </g>
    <g id="ytick_4">
     <g id="line2d_11">
      <g>
       <use xlink:href="#maf8a7b5146" x="57.6" y="147.9168" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_11">
      <!-- 3 -->
      <g transform="translate(44.2375 151.716019) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-33"/>
      </g>
     </g>
    </g>
    <g id="ytick_5">
     <g id="line2d_12">
      <g>
       <use xlink:href="#maf8a7b5146" x="57.6" y="94.6944" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_12">
      <!-- 4 -->
      <g transform="translate(44.2375 98.493619) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-34" d="M 2419 4116 
L 825 1625 
L 2419 1625 
L 2419 4116 
z
M 2253 4666 
L 3047 4666 
L 3047 1625 
L 3713 1625 
L 3713 1100 
L 3047 1100 
L 3047 0 
L 2419 0 
L 2419 1100 
L 313 1100 
L 313 1709 
L 2253 4666 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-34"/>
      </g>
     </g>
    </g>
    <g id="ytick_6">
     <g id="line2d_13">
      <g>
       <use xlink:href="#maf8a7b5146" x="57.6" y="41.472" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_13">
      <!-- 5 -->
      <g transform="translate(44.2375 45.271219) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-35"/>
      </g>
     </g>
    </g>
   </g>
   <g id="line2d_14">
    <path d="M 73.832727 275.65056 
L 77.112066 266.566878 
L 80.391405 255.145485 
L 83.670744 240.038362 
L 86.950083 221.523637 
L 90.229421 199.101451 
L 93.50876 172.728356 
L 96.788099 145.235812 
L 100.067438 124.16841 
L 103.346777 121.760791 
L 106.626116 153.524449 
L 109.905455 205.805414 
L 113.184793 249.754919 
L 116.464132 275.068173 
L 119.743471 288.351061 
L 123.02281 294.932111 
L 126.302149 298.420932 
L 129.581488 300.174754 
L 132.860826 301.099197 
L 136.140165 301.441609 
L 139.419504 301.376108 
L 142.698843 301.026381 
L 145.978182 300.409944 
L 149.257521 299.33271 
L 152.53686 298.028176 
L 155.816198 295.958713 
L 159.095537 293.523022 
L 162.374876 290.218698 
L 165.654215 285.645056 
L 168.933554 279.932772 
L 172.212893 272.654825 
L 175.492231 262.442557 
L 178.77157 249.834313 
L 182.050909 234.664705 
L 185.330248 214.29885 
L 188.609587 190.459609 
L 191.888926 162.983023 
L 195.168264 136.414918 
L 198.447603 120.052766 
L 201.726942 129.600514 
L 205.006281 171.402626 
L 208.28562 222.871306 
L 211.564959 260.060687 
L 214.844298 280.954862 
L 218.123636 291.181572 
L 221.402975 296.405321 
L 224.682314 299.07247 
L 227.961653 300.511199 
L 231.240992 301.22283 
L 234.520331 301.470922 
L 237.799669 301.320899 
L 241.079008 300.811631 
L 244.358347 300.13115 
L 247.637686 298.904178 
L 250.917025 297.31359 
L 254.196364 295.214033 
L 257.475702 292.380257 
L 260.755041 288.875067 
L 264.03438 283.898344 
L 267.313719 277.382395 
L 270.593058 269.359866 
L 273.872397 258.688737 
L 277.151736 244.508637 
L 280.431074 227.596267 
L 283.710413 206.477075 
L 286.989752 180.900577 
L 290.269091 153.159342 
L 293.54843 128.926143 
L 296.827769 120.802092 
L 300.107107 141.516453 
L 303.386446 189.791224 
L 306.665785 238.281368 
L 309.945124 269.456774 
L 313.224463 285.275911 
L 316.503802 293.397452 
L 319.78314 297.501961 
L 323.062479 299.702508 
L 326.341818 300.833296 
L 329.621157 301.33566 
L 332.900496 301.419917 
L 336.179835 301.230211 
L 339.459174 300.587711 
L 342.738512 299.706224 
L 346.017851 298.467258 
L 349.29719 296.57882 
L 352.576529 294.460473 
L 355.855868 291.214364 
L 359.135207 287.135333 
L 362.414545 282.141441 
L 365.693884 274.807375 
L 368.973223 265.627022 
L 372.252562 254.473095 
L 375.531901 239.128648 
L 378.81124 220.438621 
L 382.090579 197.847598 
L 385.369917 171.325483 
L 388.649256 143.934362 
L 391.928595 123.435484 
L 395.207934 122.727872 
L 398.487273 155.733856 
" clip-path="url(#pec1b61d189)" style="fill: none; stroke: #1f77b4; stroke-width: 1.5; stroke-linecap: square"/>
   </g>
   <g id="line2d_15">
    <path d="M 73.832727 296.93952 
L 77.112066 297.592597 
L 80.391405 297.865125 
L 83.670744 297.554087 
L 86.950083 296.585089 
L 90.229421 294.598495 
L 93.50876 290.695445 
L 96.788099 282.792791 
L 100.067438 267.508551 
L 103.346777 240.774811 
L 106.626116 200.767328 
L 109.905455 164.378381 
L 113.184793 149.565934 
L 116.464132 155.713748 
L 119.743471 171.489192 
L 123.02281 190.193055 
L 126.302149 208.265802 
L 129.581488 224.29095 
L 132.860826 238.200056 
L 136.140165 249.783949 
L 139.419504 259.277717 
L 142.698843 267.377599 
L 145.978182 274.188338 
L 149.257521 279.496886 
L 152.53686 284.213463 
L 155.816198 287.612829 
L 159.095537 290.696854 
L 162.374876 293.032945 
L 165.654215 294.801406 
L 168.933554 296.202902 
L 172.212893 297.196 
L 175.492231 297.667128 
L 178.77157 297.752482 
L 182.050909 297.433741 
L 185.330248 296.093984 
L 188.609587 293.634953 
L 191.888926 288.4191 
L 195.168264 278.576167 
L 198.447603 259.935213 
L 201.726942 227.560445 
L 205.006281 186.765955 
L 208.28562 156.816417 
L 211.564959 150.373957 
L 214.844298 160.424635 
L 218.123636 177.984265 
L 221.402975 196.648514 
L 224.682314 213.96568 
L 227.961653 229.207614 
L 231.240992 242.272596 
L 234.520331 253.378159 
L 237.799669 262.436552 
L 241.079008 269.771545 
L 244.358347 276.361293 
L 247.637686 281.197646 
L 250.917025 285.420253 
L 254.196364 288.78377 
L 257.475702 291.52539 
L 260.755041 293.766731 
L 264.03438 295.35811 
L 267.313719 296.550875 
L 270.593058 297.410725 
L 273.872397 297.801619 
L 277.151736 297.63823 
L 280.431074 296.978272 
L 283.710413 295.405651 
L 286.989752 292.042885 
L 290.269091 285.788906 
L 293.54843 273.307183 
L 296.827769 249.677401 
L 300.107107 213.364743 
L 303.386446 173.648275 
L 306.665785 151.700989 
L 309.945124 152.085714 
L 313.224463 166.235932 
L 316.503802 184.543703 
L 319.78314 202.926023 
L 323.062479 219.625998 
L 326.341818 234.077871 
L 329.621157 246.294382 
L 332.900496 256.558832 
L 336.179835 265.423187 
L 339.459174 272.125692 
L 342.738512 278.06895 
L 346.017851 282.876522 
L 349.29719 286.601324 
L 352.576529 289.942832 
L 355.855868 292.33876 
L 359.135207 294.325469 
L 362.414545 295.911172 
L 365.693884 296.893518 
L 368.973223 297.548432 
L 372.252562 297.862983 
L 375.531901 297.515042 
L 378.81124 296.503028 
L 382.090579 294.455671 
L 385.369917 290.432362 
L 388.649256 282.218501 
L 391.928595 266.488641 
L 395.207934 238.924782 
L 398.487273 198.63352 
" clip-path="url(#pec1b61d189)" style="fill: none; stroke: #ff7f0e; stroke-width: 1.5; stroke-linecap: square"/>
   </g>
   <g id="patch_3">
    <path d="M 57.6 307.584 
L 57.6 41.472 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
   <g id="patch_4">
    <path d="M 414.72 307.584 
L 414.72 41.472 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
   <g id="patch_5">
    <path d="M 57.6 307.584 
L 414.72 307.584 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
   <g id="patch_6">
    <path d="M 57.6 41.472 
L 414.72 41.472 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
   <g id="legend_1">
    <g id="patch_7">
     <path d="M 369.92 78.848563 
L 407.72 78.848563 
Q 409.72 78.848563 409.72 76.848563 
L 409.72 48.472 
Q 409.72 46.472 407.72 46.472 
L 369.92 46.472 
Q 367.92 46.472 367.92 48.472 
L 367.92 76.848563 
Q 367.92 78.848563 369.92 78.848563 
z
" style="fill: #ffffff; opacity: 0.8; stroke: #cccccc; stroke-linejoin: miter"/>
    </g>
    <g id="line2d_16">
     <path d="M 371.92 54.570438 
L 381.92 54.570438 
L 391.92 54.570438 
" style="fill: none; stroke: #1f77b4; stroke-width: 1.5; stroke-linecap: square"/>
    </g>
    <g id="text_14">
     <!-- $x$ -->
     <g transform="translate(399.92 58.070438) scale(0.1 -0.1)">
      <defs>
       <path id="Cmmi10-78" d="M 500 184 
Q 613 97 819 97 
Q 1019 97 1172 289 
Q 1325 481 1381 709 
L 1672 1844 
Q 1741 2153 1741 2266 
Q 1741 2425 1652 2544 
Q 1563 2663 1403 2663 
Q 1200 2663 1022 2536 
Q 844 2409 722 2214 
Q 600 2019 550 1819 
Q 538 1778 500 1778 
L 422 1778 
Q 372 1778 372 1838 
L 372 1856 
Q 434 2094 584 2320 
Q 734 2547 951 2687 
Q 1169 2828 1416 2828 
Q 1650 2828 1839 2703 
Q 2028 2578 2106 2363 
Q 2216 2559 2386 2693 
Q 2556 2828 2759 2828 
Q 2897 2828 3040 2779 
Q 3184 2731 3275 2631 
Q 3366 2531 3366 2381 
Q 3366 2219 3261 2101 
Q 3156 1984 2994 1984 
Q 2891 1984 2822 2050 
Q 2753 2116 2753 2216 
Q 2753 2350 2845 2451 
Q 2938 2553 3066 2572 
Q 2950 2663 2747 2663 
Q 2541 2663 2389 2472 
Q 2238 2281 2175 2047 
L 1894 916 
Q 1825 659 1825 494 
Q 1825 331 1917 214 
Q 2009 97 2163 97 
Q 2463 97 2698 361 
Q 2934 625 3009 941 
Q 3022 978 3059 978 
L 3138 978 
Q 3163 978 3178 961 
Q 3194 944 3194 922 
Q 3194 916 3188 903 
Q 3097 522 2806 225 
Q 2516 -72 2150 -72 
Q 1916 -72 1727 54 
Q 1538 181 1459 397 
Q 1359 209 1182 68 
Q 1006 -72 806 -72 
Q 669 -72 523 -23 
Q 378 25 287 125 
Q 197 225 197 378 
Q 197 528 301 651 
Q 406 775 563 775 
Q 669 775 741 711 
Q 813 647 813 544 
Q 813 409 723 309 
Q 634 209 500 184 
z
" transform="scale(0.015625)"/>
      </defs>
      <use xlink:href="#Cmmi10-78" transform="translate(0 0.8125)"/>
     </g>
    </g>
    <g id="line2d_17">
     <path d="M 371.92 69.248563 
L 381.92 69.248563 
L 391.92 69.248563 
" style="fill: none; stroke: #ff7f0e; stroke-width: 1.5; stroke-linecap: square"/>
    </g>
    <g id="text_15">
     <!-- $y$ -->
     <g transform="translate(399.92 72.748563) scale(0.1 -0.1)">
      <defs>
       <path id="Cmmi10-79" d="M 538 -916 
Q 672 -1147 1006 -1147 
Q 1309 -1147 1531 -934 
Q 1753 -722 1889 -420 
Q 2025 -119 2100 197 
Q 1816 -72 1484 -72 
Q 1231 -72 1053 15 
Q 875 103 776 276 
Q 678 450 678 697 
Q 678 906 734 1126 
Q 791 1347 892 1617 
Q 994 1888 1069 2088 
Q 1153 2322 1153 2472 
Q 1153 2663 1013 2663 
Q 759 2663 595 2402 
Q 431 2141 353 1819 
Q 341 1778 300 1778 
L 225 1778 
Q 172 1778 172 1838 
L 172 1856 
Q 275 2238 487 2533 
Q 700 2828 1025 2828 
Q 1253 2828 1411 2678 
Q 1569 2528 1569 2297 
Q 1569 2178 1516 2047 
Q 1488 1969 1388 1706 
Q 1288 1444 1234 1272 
Q 1181 1100 1147 934 
Q 1113 769 1113 603 
Q 1113 391 1203 244 
Q 1294 97 1491 97 
Q 1888 97 2203 581 
L 2688 2553 
Q 2709 2638 2787 2698 
Q 2866 2759 2956 2759 
Q 3034 2759 3092 2709 
Q 3150 2659 3150 2578 
Q 3150 2541 3144 2528 
L 2509 -19 
Q 2425 -347 2200 -647 
Q 1975 -947 1658 -1130 
Q 1341 -1313 997 -1313 
Q 831 -1313 668 -1248 
Q 506 -1184 406 -1056 
Q 306 -928 306 -756 
Q 306 -581 409 -453 
Q 513 -325 684 -325 
Q 788 -325 858 -389 
Q 928 -453 928 -556 
Q 928 -703 818 -812 
Q 709 -922 563 -922 
Q 556 -919 550 -917 
Q 544 -916 538 -916 
z
" transform="scale(0.015625)"/>
      </defs>
      <use xlink:href="#Cmmi10-79" transform="translate(0 0.8125)"/>
     </g>
    </g>
   </g>
  </g>
  <g id="text_16">
   <!-- Lotka-Volterra with K=0.69 -->
   <g transform="translate(118.323281 26.314313) scale(0.18 -0.18)">
    <defs>
     <path id="Cmr10-4c" d="M 197 0 
L 197 225 
Q 856 225 856 428 
L 856 3944 
Q 856 4147 197 4147 
L 197 4372 
L 2272 4372 
L 2272 4147 
Q 1453 4147 1453 3944 
L 1453 428 
Q 1453 291 1531 258 
Q 1609 225 1778 225 
L 2272 225 
Q 2750 225 3009 400 
Q 3269 575 3376 876 
Q 3484 1178 3541 1678 
L 3725 1678 
L 3547 0 
L 197 0 
z
" transform="scale(0.015625)"/>
     <path id="Cmr10-6f" d="M 1600 -72 
Q 1216 -72 887 123 
Q 559 319 368 647 
Q 178 975 178 1363 
Q 178 1656 283 1928 
Q 388 2200 583 2414 
Q 778 2628 1037 2748 
Q 1297 2869 1600 2869 
Q 1994 2869 2317 2661 
Q 2641 2453 2828 2104 
Q 3016 1756 3016 1363 
Q 3016 978 2825 648 
Q 2634 319 2307 123 
Q 1981 -72 1600 -72 
z
M 1600 116 
Q 2113 116 2284 487 
Q 2456 859 2456 1434 
Q 2456 1756 2422 1967 
Q 2388 2178 2272 2350 
Q 2200 2456 2089 2536 
Q 1978 2616 1854 2658 
Q 1731 2700 1600 2700 
Q 1400 2700 1220 2609 
Q 1041 2519 922 2350 
Q 803 2169 770 1951 
Q 738 1734 738 1434 
Q 738 1075 800 789 
Q 863 503 1052 309 
Q 1241 116 1600 116 
z
" transform="scale(0.015625)"/>
     <path id="Cmr10-74" d="M 653 769 
L 653 2534 
L 122 2534 
L 122 2700 
Q 541 2700 737 3090 
Q 934 3481 934 3938 
L 1119 3938 
L 1119 2759 
L 2022 2759 
L 2022 2534 
L 1119 2534 
L 1119 781 
Q 1119 516 1208 316 
Q 1297 116 1528 116 
Q 1747 116 1844 327 
Q 1941 538 1941 781 
L 1941 1159 
L 2125 1159 
L 2125 769 
Q 2125 569 2051 373 
Q 1978 178 1834 53 
Q 1691 -72 1484 -72 
Q 1100 -72 876 158 
Q 653 388 653 769 
z
" transform="scale(0.015625)"/>
     <path id="Cmr10-6b" d="M 166 0 
L 166 225 
Q 384 225 525 259 
Q 666 294 666 428 
L 666 3788 
Q 666 3959 614 4036 
Q 563 4113 466 4130 
Q 369 4147 166 4147 
L 166 4372 
L 1113 4441 
L 1113 1403 
L 1972 2156 
Q 2100 2278 2100 2381 
Q 2100 2456 2047 2495 
Q 1994 2534 1919 2534 
L 1919 2759 
L 3122 2759 
L 3122 2534 
Q 2688 2534 2253 2156 
L 1797 1759 
L 2613 603 
Q 2781 363 2895 294 
Q 3009 225 3272 225 
L 3272 0 
L 1997 0 
L 1997 225 
Q 2216 225 2216 359 
Q 2216 456 2100 603 
L 1484 1478 
L 1094 1141 
L 1094 428 
Q 1094 294 1236 259 
Q 1378 225 1594 225 
L 1594 0 
L 166 0 
z
" transform="scale(0.015625)"/>
     <path id="Cmr10-61" d="M 256 628 
Q 256 1009 556 1248 
Q 856 1488 1276 1586 
Q 1697 1684 2075 1684 
L 2075 1947 
Q 2075 2131 1994 2304 
Q 1913 2478 1759 2589 
Q 1606 2700 1422 2700 
Q 997 2700 775 2509 
Q 897 2509 976 2417 
Q 1056 2325 1056 2203 
Q 1056 2075 965 1984 
Q 875 1894 750 1894 
Q 622 1894 531 1984 
Q 441 2075 441 2203 
Q 441 2541 747 2705 
Q 1053 2869 1422 2869 
Q 1681 2869 1943 2758 
Q 2206 2647 2373 2440 
Q 2541 2234 2541 1959 
L 2541 519 
Q 2541 394 2594 289 
Q 2647 184 2759 184 
Q 2866 184 2917 290 
Q 2969 397 2969 519 
L 2969 928 
L 3156 928 
L 3156 519 
Q 3156 375 3081 245 
Q 3006 116 2879 39 
Q 2753 -38 2606 -38 
Q 2419 -38 2283 107 
Q 2147 253 2131 453 
Q 2013 213 1781 70 
Q 1550 -72 1288 -72 
Q 1044 -72 808 0 
Q 572 72 414 226 
Q 256 381 256 628 
z
M 775 628 
Q 775 403 940 250 
Q 1106 97 1331 97 
Q 1538 97 1706 200 
Q 1875 303 1975 481 
Q 2075 659 2075 856 
L 2075 1522 
Q 1784 1522 1479 1426 
Q 1175 1331 975 1128 
Q 775 925 775 628 
z
" transform="scale(0.015625)"/>
     <path id="Cmr10-2d" d="M 72 1184 
L 72 1581 
L 1766 1581 
L 1766 1184 
L 72 1184 
z
" transform="scale(0.015625)"/>
     <path id="Cmr10-56" d="M 2253 -72 
L 744 3944 
Q 688 4078 528 4112 
Q 369 4147 122 4147 
L 122 4372 
L 1881 4372 
L 1881 4147 
Q 1350 4147 1350 3981 
Q 1353 3972 1354 3964 
Q 1356 3956 1356 3944 
L 2584 678 
L 3744 3769 
Q 3756 3794 3756 3847 
Q 3756 4003 3612 4075 
Q 3469 4147 3291 4147 
L 3291 4372 
L 4672 4372 
L 4672 4147 
Q 4431 4147 4248 4058 
Q 4066 3969 3988 3769 
L 2541 -72 
Q 2522 -141 2438 -141 
L 2356 -141 
Q 2272 -141 2253 -72 
z
" transform="scale(0.015625)"/>
     <path id="Cmr10-6c" d="M 197 0 
L 197 225 
Q 416 225 556 259 
Q 697 294 697 428 
L 697 3788 
Q 697 3959 645 4036 
Q 594 4113 497 4130 
Q 400 4147 197 4147 
L 197 4372 
L 1147 4441 
L 1147 428 
Q 1147 294 1287 259 
Q 1428 225 1644 225 
L 1644 0 
L 197 0 
z
" transform="scale(0.015625)"/>
     <path id="Cmr10-65" d="M 1594 -72 
Q 1203 -72 876 133 
Q 550 338 364 680 
Q 178 1022 178 1403 
Q 178 1778 348 2115 
Q 519 2453 823 2661 
Q 1128 2869 1503 2869 
Q 1797 2869 2014 2770 
Q 2231 2672 2372 2497 
Q 2513 2322 2584 2084 
Q 2656 1847 2656 1563 
Q 2656 1478 2591 1478 
L 738 1478 
L 738 1409 
Q 738 878 952 497 
Q 1166 116 1650 116 
Q 1847 116 2014 203 
Q 2181 291 2304 447 
Q 2428 603 2472 781 
Q 2478 803 2495 820 
Q 2513 838 2534 838 
L 2591 838 
Q 2656 838 2656 756 
Q 2566 394 2266 161 
Q 1966 -72 1594 -72 
z
M 744 1638 
L 2203 1638 
Q 2203 1878 2136 2125 
Q 2069 2372 1912 2536 
Q 1756 2700 1503 2700 
Q 1141 2700 942 2361 
Q 744 2022 744 1638 
z
" transform="scale(0.015625)"/>
     <path id="Cmr10-72" d="M 166 0 
L 166 225 
Q 384 225 525 259 
Q 666 294 666 428 
L 666 2175 
Q 666 2347 614 2423 
Q 563 2500 466 2517 
Q 369 2534 166 2534 
L 166 2759 
L 1081 2828 
L 1081 2203 
Q 1184 2481 1375 2654 
Q 1566 2828 1838 2828 
Q 2028 2828 2178 2715 
Q 2328 2603 2328 2419 
Q 2328 2303 2245 2217 
Q 2163 2131 2041 2131 
Q 1922 2131 1837 2215 
Q 1753 2300 1753 2419 
Q 1753 2591 1875 2663 
L 1838 2663 
Q 1578 2663 1414 2475 
Q 1250 2288 1181 2009 
Q 1113 1731 1113 1478 
L 1113 428 
Q 1113 225 1734 225 
L 1734 0 
L 166 0 
z
" transform="scale(0.015625)"/>
     <path id="Cmr10-20" transform="scale(0.015625)"/>
     <path id="Cmr10-77" d="M 1416 0 
L 588 2328 
Q 531 2469 425 2501 
Q 319 2534 116 2534 
L 116 2759 
L 1434 2759 
L 1434 2534 
Q 1056 2534 1056 2375 
Q 1059 2366 1061 2356 
Q 1063 2347 1063 2328 
L 1678 603 
L 2209 2106 
L 2125 2328 
Q 2075 2469 1965 2501 
Q 1856 2534 1656 2534 
L 1656 2759 
L 2919 2759 
L 2919 2534 
Q 2541 2534 2541 2375 
Q 2541 2350 2547 2328 
L 3188 525 
L 3769 2156 
Q 3781 2206 3781 2247 
Q 3781 2381 3667 2457 
Q 3553 2534 3413 2534 
L 3413 2759 
L 4500 2759 
L 4500 2534 
Q 4306 2534 4167 2432 
Q 4028 2331 3963 2156 
L 3200 0 
Q 3178 -72 3103 -72 
L 3053 -72 
Q 2978 -72 2956 0 
L 2309 1825 
L 1663 0 
Q 1631 -72 1563 -72 
L 1516 -72 
Q 1438 -72 1416 0 
z
" transform="scale(0.015625)"/>
     <path id="Cmr10-69" d="M 197 0 
L 197 225 
Q 416 225 556 259 
Q 697 294 697 428 
L 697 2175 
Q 697 2422 601 2478 
Q 506 2534 225 2534 
L 225 2759 
L 1147 2828 
L 1147 428 
Q 1147 294 1269 259 
Q 1391 225 1594 225 
L 1594 0 
L 197 0 
z
M 469 3928 
Q 469 4069 575 4175 
Q 681 4281 819 4281 
Q 909 4281 993 4234 
Q 1078 4188 1125 4103 
Q 1172 4019 1172 3928 
Q 1172 3791 1065 3684 
Q 959 3578 819 3578 
Q 681 3578 575 3684 
Q 469 3791 469 3928 
z
" transform="scale(0.015625)"/>
     <path id="Cmr10-68" d="M 191 0 
L 191 225 
Q 409 225 550 259 
Q 691 294 691 428 
L 691 3788 
Q 691 3959 639 4036 
Q 588 4113 491 4130 
Q 394 4147 191 4147 
L 191 4372 
L 1141 4441 
L 1141 2241 
Q 1275 2506 1515 2667 
Q 1756 2828 2047 2828 
Q 2491 2828 2714 2615 
Q 2938 2403 2938 1966 
L 2938 428 
Q 2938 294 3078 259 
Q 3219 225 3438 225 
L 3438 0 
L 1972 0 
L 1972 225 
Q 2191 225 2331 259 
Q 2472 294 2472 428 
L 2472 1947 
Q 2472 2259 2381 2461 
Q 2291 2663 2009 2663 
Q 1638 2663 1398 2366 
Q 1159 2069 1159 1691 
L 1159 428 
Q 1159 294 1300 259 
Q 1441 225 1656 225 
L 1656 0 
L 191 0 
z
" transform="scale(0.015625)"/>
     <path id="Cmr10-4b" d="M 197 0 
L 197 225 
Q 856 225 856 428 
L 856 3944 
Q 856 4147 197 4147 
L 197 4372 
L 2113 4372 
L 2113 4147 
Q 1453 4147 1453 3944 
L 1453 1869 
L 3431 3769 
Q 3513 3856 3513 3944 
Q 3513 4044 3427 4095 
Q 3341 4147 3231 4147 
L 3231 4372 
L 4622 4372 
L 4622 4147 
Q 4097 4147 3700 3769 
L 2566 2681 
L 3969 603 
Q 4141 350 4270 287 
Q 4400 225 4709 225 
L 4709 0 
L 3034 0 
L 3034 225 
Q 3188 225 3292 256 
Q 3397 288 3397 403 
Q 3397 481 3316 603 
L 2169 2303 
L 1453 1613 
L 1453 428 
Q 1453 225 2113 225 
L 2113 0 
L 197 0 
z
" transform="scale(0.015625)"/>
     <path id="Cmr10-3d" d="M 481 850 
Q 428 850 393 890 
Q 359 931 359 978 
Q 359 1031 393 1068 
Q 428 1106 481 1106 
L 4500 1106 
Q 4547 1106 4581 1068 
Q 4616 1031 4616 978 
Q 4616 931 4581 890 
Q 4547 850 4500 850 
L 481 850 
z
M 481 2094 
Q 428 2094 393 2131 
Q 359 2169 359 2222 
Q 359 2269 393 2309 
Q 428 2350 481 2350 
L 4500 2350 
Q 4547 2350 4581 2309 
Q 4616 2269 4616 2222 
Q 4616 2169 4581 2131 
Q 4547 2094 4500 2094 
L 481 2094 
z
" transform="scale(0.015625)"/>
     <path id="Cmr10-30" d="M 1600 -141 
Q 816 -141 533 504 
Q 250 1150 250 2041 
Q 250 2597 351 3087 
Q 453 3578 754 3920 
Q 1056 4263 1600 4263 
Q 2022 4263 2290 4056 
Q 2559 3850 2700 3523 
Q 2841 3197 2892 2823 
Q 2944 2450 2944 2041 
Q 2944 1491 2842 1011 
Q 2741 531 2444 195 
Q 2147 -141 1600 -141 
z
M 1600 25 
Q 1956 25 2131 390 
Q 2306 756 2347 1200 
Q 2388 1644 2388 2144 
Q 2388 2625 2347 3031 
Q 2306 3438 2132 3767 
Q 1959 4097 1600 4097 
Q 1238 4097 1063 3765 
Q 888 3434 847 3029 
Q 806 2625 806 2144 
Q 806 1788 823 1472 
Q 841 1156 916 820 
Q 991 484 1158 254 
Q 1325 25 1600 25 
z
" transform="scale(0.015625)"/>
     <path id="Cmr10-2e" d="M 538 353 
Q 538 497 644 600 
Q 750 703 891 703 
Q 978 703 1062 656 
Q 1147 609 1194 525 
Q 1241 441 1241 353 
Q 1241 213 1137 106 
Q 1034 0 891 0 
Q 750 0 644 106 
Q 538 213 538 353 
z
" transform="scale(0.015625)"/>
     <path id="Cmr10-36" d="M 1600 -141 
Q 1203 -141 937 70 
Q 672 281 526 617 
Q 381 953 325 1322 
Q 269 1691 269 2069 
Q 269 2575 466 3084 
Q 663 3594 1045 3928 
Q 1428 4263 1953 4263 
Q 2172 4263 2361 4180 
Q 2550 4097 2658 3936 
Q 2766 3775 2766 3547 
Q 2766 3416 2677 3327 
Q 2588 3238 2456 3238 
Q 2331 3238 2240 3328 
Q 2150 3419 2150 3547 
Q 2150 3672 2240 3762 
Q 2331 3853 2456 3853 
L 2491 3853 
Q 2409 3969 2261 4023 
Q 2113 4078 1953 4078 
Q 1759 4078 1595 3993 
Q 1431 3909 1300 3765 
Q 1169 3622 1081 3448 
Q 994 3275 945 3053 
Q 897 2831 884 2637 
Q 872 2444 872 2150 
Q 984 2413 1190 2580 
Q 1397 2747 1656 2747 
Q 1941 2747 2175 2631 
Q 2409 2516 2578 2311 
Q 2747 2106 2836 1843 
Q 2925 1581 2925 1313 
Q 2925 938 2758 598 
Q 2591 259 2287 59 
Q 1984 -141 1600 -141 
z
M 1600 63 
Q 1847 63 1997 175 
Q 2147 288 2217 473 
Q 2288 659 2305 848 
Q 2322 1038 2322 1313 
Q 2322 1675 2287 1931 
Q 2253 2188 2100 2383 
Q 1947 2578 1631 2578 
Q 1372 2578 1205 2403 
Q 1038 2228 961 1961 
Q 884 1694 884 1447 
Q 884 1363 891 1319 
Q 891 1309 889 1303 
Q 888 1297 884 1288 
Q 884 1013 940 731 
Q 997 450 1156 256 
Q 1316 63 1600 63 
z
" transform="scale(0.015625)"/>
     <path id="Cmr10-39" d="M 722 269 
Q 897 63 1331 63 
Q 1575 63 1786 228 
Q 1997 394 2113 634 
Q 2247 906 2284 1214 
Q 2322 1522 2322 1978 
Q 2213 1719 2008 1553 
Q 1803 1388 1538 1388 
Q 1166 1388 873 1589 
Q 581 1791 425 2120 
Q 269 2450 269 2822 
Q 269 3206 444 3539 
Q 619 3872 928 4067 
Q 1238 4263 1631 4263 
Q 2019 4263 2280 4052 
Q 2541 3841 2678 3508 
Q 2816 3175 2870 2803 
Q 2925 2431 2925 2069 
Q 2925 1575 2744 1061 
Q 2563 547 2202 203 
Q 1841 -141 1331 -141 
Q 953 -141 690 37 
Q 428 216 428 575 
Q 428 706 517 795 
Q 606 884 738 884 
Q 866 884 955 795 
Q 1044 706 1044 575 
Q 1044 450 953 359 
Q 863 269 738 269 
L 722 269 
z
M 1563 1556 
Q 1825 1556 1992 1732 
Q 2159 1909 2234 2171 
Q 2309 2434 2309 2694 
L 2309 2816 
L 2309 2841 
Q 2309 3322 2168 3700 
Q 2028 4078 1631 4078 
Q 1378 4078 1220 3967 
Q 1063 3856 988 3672 
Q 913 3488 892 3278 
Q 872 3069 872 2822 
Q 872 2459 906 2203 
Q 941 1947 1094 1751 
Q 1247 1556 1563 1556 
z
" transform="scale(0.015625)"/>
    </defs>
    <use xlink:href="#Cmr10-4c"/>
    <use xlink:href="#Cmr10-6f" x="62.5"/>
    <use xlink:href="#Cmr10-74" x="112.5"/>
    <use xlink:href="#Cmr10-6b" x="151.318359"/>
    <use xlink:href="#Cmr10-61" x="204.003906"/>
    <use xlink:href="#Cmr10-2d" x="254.003906"/>
    <use xlink:href="#Cmr10-56" x="287.304688"/>
    <use xlink:href="#Cmr10-6f" x="362.304688"/>
    <use xlink:href="#Cmr10-6c" x="412.304688"/>
    <use xlink:href="#Cmr10-74" x="439.990234"/>
    <use xlink:href="#Cmr10-65" x="478.808594"/>
    <use xlink:href="#Cmr10-72" x="523.193359"/>
    <use xlink:href="#Cmr10-72" x="562.304688"/>
    <use xlink:href="#Cmr10-61" x="601.416016"/>
    <use xlink:href="#Cmr10-20" x="651.416016"/>
    <use xlink:href="#Cmr10-77" x="684.716797"/>
    <use xlink:href="#Cmr10-69" x="756.933594"/>
    <use xlink:href="#Cmr10-74" x="784.619141"/>
    <use xlink:href="#Cmr10-68" x="823.4375"/>
    <use xlink:href="#Cmr10-20" x="878.955078"/>
    <use xlink:href="#Cmr10-4b" x="912.255859"/>
    <use xlink:href="#Cmr10-3d" x="989.941406"/>
    <use xlink:href="#Cmr10-30" x="1067.626953"/>
    <use xlink:href="#Cmr10-2e" x="1117.626953"/>
    <use xlink:href="#Cmr10-36" x="1145.3125"/>
    <use xlink:href="#Cmr10-39" x="1195.3125"/>
   </g>
  </g>
 </g>
 <defs>
  <clipPath id="pec1b61d189">
   <rect x="57.6" y="41.472" width="357.12" height="266.112"/>
  </clipPath>
 </defs>
</svg>
\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"solution = ndsolve( lotka_volterra, {$x$: 0.6, $y$: 0.2}, ($t$, 0, 30) ) \\nfig = plot(solution, {$t$: (0,30)}, title=f\\\"Lotka-Volterra with K={K}\\\", fig=fig, yrange=[0, 5]);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 8228301184857714505,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 1931241143117165399,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"By adding a slider for the variable $K$, we can create a dynamical plot which updates automatically when the slider is changed:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"By adding a slider for the variable $K$, we can create a dynamical plot which updates automatically when the slider is changed:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 13899966688441089158,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 12897363280863513893,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"slider\",\n\t\t\t\t\t\"source\": \"{\\\"value\\\": 0.45, \\\"variable\\\": \\\"K\\\", \\\"min_value\\\": 0.1, \\\"max_value\\\": 1.5, \\\"step_size\\\": 0.05}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"slider(\\\"K\\\", K, 0.1, 1.5, 0.05);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 4077477699969684728,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 6831851033388957520,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"If you drag the slider above, the numerical solution to the ODEs will be re-computed and then re-plotted.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"If you drag the slider above, the numerical solution to the ODEs will be re-computed and then re-plotted.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 18034799362745794265,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 10861953489905871051,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\subsection*{Stopping conditions}\\n\\nSometimes you do not know the range of the independent variable, but you only know that you want to stop the numerical integration when a particular condition is satisfied (e.g. when the function reaches a particular value). You can pass conditions like these into \\\\algo{ndsolve} using the \\\\verb|stop| parameter.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\subsection*{Stopping conditions}\\n\\nSometimes you do not know the range of the independent variable, but you only know that you want to stop the numerical integration when a particular condition is satisfied (e.g. when the function reaches a particular value). You can pass conditions like these into \\\\algo{ndsolve} using the \\\\verb|stop| parameter.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 15329001784365153030,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"from cdb.graphics.plot import plot\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 17866117841199405266,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 13657783030752724038,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property Coordinate attached to~}t.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9915881245855287819,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property Depends attached to~}x.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 5416506983560291736,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property Derivative attached to~}\\\\backslash\\\\texttt{dot}\\\\{\\\\#\\\\}.\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"t::Coordinate;\\nx::Depends(t);\\n\\\\dot{#}::Derivative(t);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 8388271973071423304,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 3192134833992478620,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 16848357627619611845,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\dot(x) =  1/5 x +  1/10 \"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\dot{x} = \\\\frac{1}{5}\\\\,x\\\\discretionary{}{}{}+\\\\frac{1}{10}\\\\,\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"eq:= \\\\dot{x} = x/5+1/10;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 12822642894572882480,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 15167624275054694128,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"We want to evaluate this until $x$ gets larger than $2$, so we do\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"We want to evaluate this until $x$ gets larger than $2$, so we do\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 18181499287998800953,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 14732579770309537544,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 18184242644711691837,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"{x =  (NInterpolatingFunction)}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\left[x = \\\\square{}\\n(t)\\\\right]\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"sol2 = ndsolve(eq, {$x$: 0}, ($t$, 0, 100), stop=$x > 2$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 4034316680154962355,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 474345600885128069,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"As above, we can now plot this by simply passing the solution to the \\\\algo{plot} function, which will figure out the maximal range of $t$ for which the numerical solution has been obtained.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"As above, we can now plot this by simply passing the solution to the \\\\algo{plot} function, which will figure out the maximal range of $t$ for which the numerical solution has been obtained.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 4219094034245341581,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 5167795040383456585,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"image_svg\",\n\t\t\t\t\t\"source\": \"<?xml version="1.0" encoding="utf-8" standalone="no"?>
<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
  "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="460.8pt" height="345.6pt" viewBox="0 0 460.8 345.6" xmlns="http://www.w3.org/2000/svg" version="1.1">
 <metadata>
  <rdf:RDF xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:cc="http://creativecommons.org/ns#" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
   <cc:Work>
    <dc:type rdf:resource="http://purl.org/dc/dcmitype/StillImage"/>
    <dc:date>2025-05-29T12:30:46.141793</dc:date>
    <dc:format>image/svg+xml</dc:format>
    <dc:creator>
     <cc:Agent>
      <dc:title>Matplotlib v3.6.3, https://matplotlib.org/</dc:title>
     </cc:Agent>
    </dc:creator>
   </cc:Work>
  </rdf:RDF>
 </metadata>
 <defs>
  <style type="text/css">*{stroke-linejoin: round; stroke-linecap: butt}</style>
 </defs>
 <g id="figure_1">
  <g id="patch_1">
   <path d="M 0 345.6 
L 460.8 345.6 
L 460.8 0 
L 0 0 
z
" style="fill: #ffffff"/>
  </g>
  <g id="axes_1">
   <g id="patch_2">
    <path d="M 57.6 307.584 
L 414.72 307.584 
L 414.72 41.472 
L 57.6 41.472 
z
" style="fill: #ffffff"/>
   </g>
   <g id="matplotlib.axis_1">
    <g id="xtick_1">
     <g id="line2d_1">
      <defs>
       <path id="mce0665bb2c" d="M 0 0 
L 0 3.5 
" style="stroke: #000000; stroke-width: 0.8"/>
      </defs>
      <g>
       <use xlink:href="#mce0665bb2c" x="73.832727" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_1">
      <!-- 0 -->
      <g transform="translate(70.651477 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-30" d="M 2034 4250 
Q 1547 4250 1301 3770 
Q 1056 3291 1056 2328 
Q 1056 1369 1301 889 
Q 1547 409 2034 409 
Q 2525 409 2770 889 
Q 3016 1369 3016 2328 
Q 3016 3291 2770 3770 
Q 2525 4250 2034 4250 
z
M 2034 4750 
Q 2819 4750 3233 4129 
Q 3647 3509 3647 2328 
Q 3647 1150 3233 529 
Q 2819 -91 2034 -91 
Q 1250 -91 836 529 
Q 422 1150 422 2328 
Q 422 3509 836 4129 
Q 1250 4750 2034 4750 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-30"/>
      </g>
     </g>
    </g>
    <g id="xtick_2">
     <g id="line2d_2">
      <g>
       <use xlink:href="#mce0665bb2c" x="113.750963" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_2">
      <!-- 1 -->
      <g transform="translate(110.569713 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-31" d="M 794 531 
L 1825 531 
L 1825 4091 
L 703 3866 
L 703 4441 
L 1819 4666 
L 2450 4666 
L 2450 531 
L 3481 531 
L 3481 0 
L 794 0 
L 794 531 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-31"/>
      </g>
     </g>
    </g>
    <g id="xtick_3">
     <g id="line2d_3">
      <g>
       <use xlink:href="#mce0665bb2c" x="153.6692" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_3">
      <!-- 2 -->
      <g transform="translate(150.48795 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-32" d="M 1228 531 
L 3431 531 
L 3431 0 
L 469 0 
L 469 531 
Q 828 903 1448 1529 
Q 2069 2156 2228 2338 
Q 2531 2678 2651 2914 
Q 2772 3150 2772 3378 
Q 2772 3750 2511 3984 
Q 2250 4219 1831 4219 
Q 1534 4219 1204 4116 
Q 875 4013 500 3803 
L 500 4441 
Q 881 4594 1212 4672 
Q 1544 4750 1819 4750 
Q 2544 4750 2975 4387 
Q 3406 4025 3406 3419 
Q 3406 3131 3298 2873 
Q 3191 2616 2906 2266 
Q 2828 2175 2409 1742 
Q 1991 1309 1228 531 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-32"/>
      </g>
     </g>
    </g>
    <g id="xtick_4">
     <g id="line2d_4">
      <g>
       <use xlink:href="#mce0665bb2c" x="193.587436" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_4">
      <!-- 3 -->
      <g transform="translate(190.406186 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-33" d="M 2597 2516 
Q 3050 2419 3304 2112 
Q 3559 1806 3559 1356 
Q 3559 666 3084 287 
Q 2609 -91 1734 -91 
Q 1441 -91 1130 -33 
Q 819 25 488 141 
L 488 750 
Q 750 597 1062 519 
Q 1375 441 1716 441 
Q 2309 441 2620 675 
Q 2931 909 2931 1356 
Q 2931 1769 2642 2001 
Q 2353 2234 1838 2234 
L 1294 2234 
L 1294 2753 
L 1863 2753 
Q 2328 2753 2575 2939 
Q 2822 3125 2822 3475 
Q 2822 3834 2567 4026 
Q 2313 4219 1838 4219 
Q 1578 4219 1281 4162 
Q 984 4106 628 3988 
L 628 4550 
Q 988 4650 1302 4700 
Q 1616 4750 1894 4750 
Q 2613 4750 3031 4423 
Q 3450 4097 3450 3541 
Q 3450 3153 3228 2886 
Q 3006 2619 2597 2516 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-33"/>
      </g>
     </g>
    </g>
    <g id="xtick_5">
     <g id="line2d_5">
      <g>
       <use xlink:href="#mce0665bb2c" x="233.505672" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_5">
      <!-- 4 -->
      <g transform="translate(230.324422 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-34" d="M 2419 4116 
L 825 1625 
L 2419 1625 
L 2419 4116 
z
M 2253 4666 
L 3047 4666 
L 3047 1625 
L 3713 1625 
L 3713 1100 
L 3047 1100 
L 3047 0 
L 2419 0 
L 2419 1100 
L 313 1100 
L 313 1709 
L 2253 4666 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-34"/>
      </g>
     </g>
    </g>
    <g id="xtick_6">
     <g id="line2d_6">
      <g>
       <use xlink:href="#mce0665bb2c" x="273.423908" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_6">
      <!-- 5 -->
      <g transform="translate(270.242658 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-35" d="M 691 4666 
L 3169 4666 
L 3169 4134 
L 1269 4134 
L 1269 2991 
Q 1406 3038 1543 3061 
Q 1681 3084 1819 3084 
Q 2600 3084 3056 2656 
Q 3513 2228 3513 1497 
Q 3513 744 3044 326 
Q 2575 -91 1722 -91 
Q 1428 -91 1123 -41 
Q 819 9 494 109 
L 494 744 
Q 775 591 1075 516 
Q 1375 441 1709 441 
Q 2250 441 2565 725 
Q 2881 1009 2881 1497 
Q 2881 1984 2565 2268 
Q 2250 2553 1709 2553 
Q 1456 2553 1204 2497 
Q 953 2441 691 2322 
L 691 4666 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-35"/>
      </g>
     </g>
    </g>
    <g id="xtick_7">
     <g id="line2d_7">
      <g>
       <use xlink:href="#mce0665bb2c" x="313.342144" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_7">
      <!-- 6 -->
      <g transform="translate(310.160894 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-36" d="M 2113 2584 
Q 1688 2584 1439 2293 
Q 1191 2003 1191 1497 
Q 1191 994 1439 701 
Q 1688 409 2113 409 
Q 2538 409 2786 701 
Q 3034 994 3034 1497 
Q 3034 2003 2786 2293 
Q 2538 2584 2113 2584 
z
M 3366 4563 
L 3366 3988 
Q 3128 4100 2886 4159 
Q 2644 4219 2406 4219 
Q 1781 4219 1451 3797 
Q 1122 3375 1075 2522 
Q 1259 2794 1537 2939 
Q 1816 3084 2150 3084 
Q 2853 3084 3261 2657 
Q 3669 2231 3669 1497 
Q 3669 778 3244 343 
Q 2819 -91 2113 -91 
Q 1303 -91 875 529 
Q 447 1150 447 2328 
Q 447 3434 972 4092 
Q 1497 4750 2381 4750 
Q 2619 4750 2861 4703 
Q 3103 4656 3366 4563 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-36"/>
      </g>
     </g>
    </g>
    <g id="xtick_8">
     <g id="line2d_8">
      <g>
       <use xlink:href="#mce0665bb2c" x="353.26038" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_8">
      <!-- 7 -->
      <g transform="translate(350.07913 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-37" d="M 525 4666 
L 3525 4666 
L 3525 4397 
L 1831 0 
L 1172 0 
L 2766 4134 
L 525 4134 
L 525 4666 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-37"/>
      </g>
     </g>
    </g>
    <g id="xtick_9">
     <g id="line2d_9">
      <g>
       <use xlink:href="#mce0665bb2c" x="393.178617" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_9">
      <!-- 8 -->
      <g transform="translate(389.997367 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-38" d="M 2034 2216 
Q 1584 2216 1326 1975 
Q 1069 1734 1069 1313 
Q 1069 891 1326 650 
Q 1584 409 2034 409 
Q 2484 409 2743 651 
Q 3003 894 3003 1313 
Q 3003 1734 2745 1975 
Q 2488 2216 2034 2216 
z
M 1403 2484 
Q 997 2584 770 2862 
Q 544 3141 544 3541 
Q 544 4100 942 4425 
Q 1341 4750 2034 4750 
Q 2731 4750 3128 4425 
Q 3525 4100 3525 3541 
Q 3525 3141 3298 2862 
Q 3072 2584 2669 2484 
Q 3125 2378 3379 2068 
Q 3634 1759 3634 1313 
Q 3634 634 3220 271 
Q 2806 -91 2034 -91 
Q 1263 -91 848 271 
Q 434 634 434 1313 
Q 434 1759 690 2068 
Q 947 2378 1403 2484 
z
M 1172 3481 
Q 1172 3119 1398 2916 
Q 1625 2713 2034 2713 
Q 2441 2713 2670 2916 
Q 2900 3119 2900 3481 
Q 2900 3844 2670 4047 
Q 2441 4250 2034 4250 
Q 1625 4250 1398 4047 
Q 1172 3844 1172 3481 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-38"/>
      </g>
     </g>
    </g>
   </g>
   <g id="matplotlib.axis_2">
    <g id="ytick_1">
     <g id="line2d_10">
      <defs>
       <path id="m402c5f1a32" d="M 0 0 
L -3.5 0 
" style="stroke: #000000; stroke-width: 0.8"/>
      </defs>
      <g>
       <use xlink:href="#m402c5f1a32" x="57.6" y="295.488" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_10">
      <!-- 0.00 -->
      <g transform="translate(28.334375 299.287219) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-2e" d="M 684 794 
L 1344 794 
L 1344 0 
L 684 0 
L 684 794 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-30"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-30" x="95.410156"/>
       <use xlink:href="#DejaVuSans-30" x="159.033203"/>
      </g>
     </g>
    </g>
    <g id="ytick_2">
     <g id="line2d_11">
      <g>
       <use xlink:href="#m402c5f1a32" x="57.6" y="265.888395" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_11">
      <!-- 0.25 -->
      <g transform="translate(28.334375 269.687614) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-30"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-32" x="95.410156"/>
       <use xlink:href="#DejaVuSans-35" x="159.033203"/>
      </g>
     </g>
    </g>
    <g id="ytick_3">
     <g id="line2d_12">
      <g>
       <use xlink:href="#m402c5f1a32" x="57.6" y="236.288791" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_12">
      <!-- 0.50 -->
      <g transform="translate(28.334375 240.08801) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-30"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-35" x="95.410156"/>
       <use xlink:href="#DejaVuSans-30" x="159.033203"/>
      </g>
     </g>
    </g>
    <g id="ytick_4">
     <g id="line2d_13">
      <g>
       <use xlink:href="#m402c5f1a32" x="57.6" y="206.689186" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_13">
      <!-- 0.75 -->
      <g transform="translate(28.334375 210.488405) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-30"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-37" x="95.410156"/>
       <use xlink:href="#DejaVuSans-35" x="159.033203"/>
      </g>
     </g>
    </g>
    <g id="ytick_5">
     <g id="line2d_14">
      <g>
       <use xlink:href="#m402c5f1a32" x="57.6" y="177.089582" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_14">
      <!-- 1.00 -->
      <g transform="translate(28.334375 180.8888) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-31"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-30" x="95.410156"/>
       <use xlink:href="#DejaVuSans-30" x="159.033203"/>
      </g>
     </g>
    </g>
    <g id="ytick_6">
     <g id="line2d_15">
      <g>
       <use xlink:href="#m402c5f1a32" x="57.6" y="147.489977" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_15">
      <!-- 1.25 -->
      <g transform="translate(28.334375 151.289196) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-31"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-32" x="95.410156"/>
       <use xlink:href="#DejaVuSans-35" x="159.033203"/>
      </g>
     </g>
    </g>
    <g id="ytick_7">
     <g id="line2d_16">
      <g>
       <use xlink:href="#m402c5f1a32" x="57.6" y="117.890372" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_16">
      <!-- 1.50 -->
      <g transform="translate(28.334375 121.689591) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-31"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-35" x="95.410156"/>
       <use xlink:href="#DejaVuSans-30" x="159.033203"/>
      </g>
     </g>
    </g>
    <g id="ytick_8">
     <g id="line2d_17">
      <g>
       <use xlink:href="#m402c5f1a32" x="57.6" y="88.290768" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_17">
      <!-- 1.75 -->
      <g transform="translate(28.334375 92.089986) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-31"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-37" x="95.410156"/>
       <use xlink:href="#DejaVuSans-35" x="159.033203"/>
      </g>
     </g>
    </g>
    <g id="ytick_9">
     <g id="line2d_18">
      <g>
       <use xlink:href="#m402c5f1a32" x="57.6" y="58.691163" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_18">
      <!-- 2.00 -->
      <g transform="translate(28.334375 62.490382) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-32"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-30" x="95.410156"/>
       <use xlink:href="#DejaVuSans-30" x="159.033203"/>
      </g>
     </g>
    </g>
   </g>
   <g id="line2d_19">
    <path d="M 73.832727 295.488 
L 77.112066 294.501519 
L 80.391405 293.497915 
L 83.670744 292.494311 
L 86.950083 291.387089 
L 90.229421 290.26377 
L 93.50876 289.140452 
L 96.788099 288.017133 
L 100.067438 286.893814 
L 103.346777 285.770495 
L 106.626116 284.647177 
L 109.905455 283.523858 
L 113.184793 282.400539 
L 116.464132 281.27722 
L 119.743471 280.153902 
L 123.02281 278.8035 
L 126.302149 277.386495 
L 129.581488 275.969491 
L 132.860826 274.552486 
L 136.140165 273.135481 
L 139.419504 271.718477 
L 142.698843 270.301472 
L 145.978182 268.884467 
L 149.257521 267.467463 
L 152.53686 266.050458 
L 155.816198 264.633454 
L 159.095537 263.216449 
L 162.374876 261.799444 
L 165.654215 260.38244 
L 168.933554 258.965435 
L 172.212893 257.548431 
L 175.492231 256.131426 
L 178.77157 254.341809 
L 182.050909 252.469608 
L 185.330248 250.597407 
L 188.609587 248.725206 
L 191.888926 246.853005 
L 195.168264 244.980803 
L 198.447603 243.108602 
L 201.726942 241.236401 
L 205.006281 239.3642 
L 208.28562 237.491999 
L 211.564959 235.619798 
L 214.844298 233.747596 
L 218.123636 231.875395 
L 221.402975 230.003194 
L 224.682314 228.130993 
L 227.961653 226.258792 
L 231.240992 224.386591 
L 234.520331 221.994802 
L 237.799669 219.521177 
L 241.079008 217.047553 
L 244.358347 214.573928 
L 247.637686 212.100304 
L 250.917025 209.62668 
L 254.196364 207.153055 
L 257.475702 204.679431 
L 260.755041 202.205807 
L 264.03438 199.732182 
L 267.313719 197.258558 
L 270.593058 194.784934 
L 273.872397 192.311309 
L 277.151736 189.837685 
L 280.431074 187.36406 
L 283.710413 184.890436 
L 286.989752 182.416812 
L 290.269091 179.220646 
L 293.54843 175.952398 
L 296.827769 172.68415 
L 300.107107 169.415903 
L 303.386446 166.147655 
L 306.665785 162.879407 
L 309.945124 159.611159 
L 313.224463 156.342911 
L 316.503802 153.074663 
L 319.78314 149.806415 
L 323.062479 146.538167 
L 326.341818 143.269919 
L 329.621157 140.001671 
L 332.900496 136.733423 
L 336.179835 133.465175 
L 339.459174 130.196927 
L 342.738512 126.92868 
L 346.017851 122.658163 
L 349.29719 118.340028 
L 352.576529 114.021893 
L 355.855868 109.703758 
L 359.135207 105.385623 
L 362.414545 101.067487 
L 365.693884 96.749352 
L 368.973223 92.431217 
L 372.252562 88.113082 
L 375.531901 83.794946 
L 378.81124 79.476811 
L 382.090579 75.158676 
L 385.369917 70.840541 
L 388.649256 66.522406 
L 391.928595 62.20427 
L 395.207934 57.886135 
L 398.487273 53.568 
" clip-path="url(#p1d8d004351)" style="fill: none; stroke: #1f77b4; stroke-width: 1.5; stroke-linecap: square"/>
   </g>
   <g id="patch_3">
    <path d="M 57.6 307.584 
L 57.6 41.472 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
   <g id="patch_4">
    <path d="M 414.72 307.584 
L 414.72 41.472 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
   <g id="patch_5">
    <path d="M 57.6 307.584 
L 414.72 307.584 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
   <g id="patch_6">
    <path d="M 57.6 41.472 
L 414.72 41.472 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
   <g id="legend_1">
    <g id="patch_7">
     <path d="M 64.6 64.150125 
L 102.4 64.150125 
Q 104.4 64.150125 104.4 62.150125 
L 104.4 48.472 
Q 104.4 46.472 102.4 46.472 
L 64.6 46.472 
Q 62.6 46.472 62.6 48.472 
L 62.6 62.150125 
Q 62.6 64.150125 64.6 64.150125 
z
" style="fill: #ffffff; opacity: 0.8; stroke: #cccccc; stroke-linejoin: miter"/>
    </g>
    <g id="line2d_20">
     <path d="M 66.6 54.570438 
L 76.6 54.570438 
L 86.6 54.570438 
" style="fill: none; stroke: #1f77b4; stroke-width: 1.5; stroke-linecap: square"/>
    </g>
    <g id="text_19">
     <!-- $x$ -->
     <g transform="translate(94.6 58.070438) scale(0.1 -0.1)">
      <defs>
       <path id="Cmmi10-78" d="M 500 184 
Q 613 97 819 97 
Q 1019 97 1172 289 
Q 1325 481 1381 709 
L 1672 1844 
Q 1741 2153 1741 2266 
Q 1741 2425 1652 2544 
Q 1563 2663 1403 2663 
Q 1200 2663 1022 2536 
Q 844 2409 722 2214 
Q 600 2019 550 1819 
Q 538 1778 500 1778 
L 422 1778 
Q 372 1778 372 1838 
L 372 1856 
Q 434 2094 584 2320 
Q 734 2547 951 2687 
Q 1169 2828 1416 2828 
Q 1650 2828 1839 2703 
Q 2028 2578 2106 2363 
Q 2216 2559 2386 2693 
Q 2556 2828 2759 2828 
Q 2897 2828 3040 2779 
Q 3184 2731 3275 2631 
Q 3366 2531 3366 2381 
Q 3366 2219 3261 2101 
Q 3156 1984 2994 1984 
Q 2891 1984 2822 2050 
Q 2753 2116 2753 2216 
Q 2753 2350 2845 2451 
Q 2938 2553 3066 2572 
Q 2950 2663 2747 2663 
Q 2541 2663 2389 2472 
Q 2238 2281 2175 2047 
L 1894 916 
Q 1825 659 1825 494 
Q 1825 331 1917 214 
Q 2009 97 2163 97 
Q 2463 97 2698 361 
Q 2934 625 3009 941 
Q 3022 978 3059 978 
L 3138 978 
Q 3163 978 3178 961 
Q 3194 944 3194 922 
Q 3194 916 3188 903 
Q 3097 522 2806 225 
Q 2516 -72 2150 -72 
Q 1916 -72 1727 54 
Q 1538 181 1459 397 
Q 1359 209 1182 68 
Q 1006 -72 806 -72 
Q 669 -72 523 -23 
Q 378 25 287 125 
Q 197 225 197 378 
Q 197 528 301 651 
Q 406 775 563 775 
Q 669 775 741 711 
Q 813 647 813 544 
Q 813 409 723 309 
Q 634 209 500 184 
z
" transform="scale(0.015625)"/>
      </defs>
      <use xlink:href="#Cmmi10-78" transform="translate(0 0.8125)"/>
     </g>
    </g>
   </g>
  </g>
 </g>
 <defs>
  <clipPath id="p1d8d004351">
   <rect x="57.6" y="41.472" width="357.12" height="266.112"/>
  </clipPath>
 </defs>
</svg>
\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"plot(sol2);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 5612812522896293433,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"\"\n\t\t}\n\t],\n\t\"description\": \"Cadabra JSON notebook format\",\n\t\"flags\": {\n\t\t\"hide_input_cells\": false\n\t},\n\t\"version\": 1.0\n}\n"
  },
  {
    "path": "examples/ref_numerical.cnb",
    "content": "{\n\t\"cell_id\": 55098764045313374,\n\t\"cells\": [\n\t\t{\n\t\t\t\"cell_id\": 11153443340774785722,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 3683726891078164525,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\section*{Numerical evaluation of expressions}\\n\\nCadabra is primarily a symbolic computer algebra system, in the sense that \\nit focuses on symbolic expressions, not the numerical value they take when\\nall symbols in them are replaced with values. However, Cadabra does have\\nfunctionality to evaluate expressions numerically as well, using either\\na call through SymPy, or using its own internal expression \\nevaluator. We will here focus on the latter, as it is by far the fastest.\\n\\nLet us start with a simple example to understand the basics. The following\\ncode creates a Cadabra expression containing just $\\\\cos(x)$, and then\\nnumerically evaluates that expression for 100 values of $x$ in the range\\n$[0, 2\\\\pi]$. \"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\section*{Numerical evaluation of expressions}\\n\\nCadabra is primarily a symbolic computer algebra system, in the sense that \\nit focuses on symbolic expressions, not the numerical value they take when\\nall symbols in them are replaced with values. However, Cadabra does have\\nfunctionality to evaluate expressions numerically as well, using either\\na call through SymPy, or using its own internal expression \\nevaluator. We will here focus on the latter, as it is by far the fastest.\\n\\nLet us start with a simple example to understand the basics. The following\\ncode creates a Cadabra expression containing just $\\\\cos(x)$, and then\\nnumerically evaluates that expression for 100 values of $x$ in the range\\n$[0, 2\\\\pi]$. \"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 1786627167757323955,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"import numpy as np\\nimport matplotlib.pyplot as plt\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 6954937305566758514,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 305992300014101782,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 16654053675824919366,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"2\\\\cos(2x)\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}2\\\\cos\\\\left(2x\\\\right)\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 1613724672150468322,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"verbatim\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}<cadabra2.NTensor object at 0xf5e5162c7270>\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex := 2\\\\cos(2 x);\\nxv  = np.linspace(0, np.pi*2, 100)\\nexv = nevaluate(ex, {$x$: xv, $y$: np.linspace(0,1,100)} );\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 17813844956869416932,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 18054204918676316375,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"The \\\\algo{nevaluate} function returns an \\\\verb|NTensor|, which is Cadabra's\\nobject to store numerical values of tensors. It can be converted to a numpy\\narray by wrapping it in `np.array`, after which you can plot it:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"The \\\\algo{nevaluate} function returns an \\\\verb|NTensor|, which is Cadabra's\\nobject to store numerical values of tensors. It can be converted to a numpy\\narray by wrapping it in `np.array`, after which you can plot it:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 5634273073315875314,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 3913448749670155735,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"image_svg\",\n\t\t\t\t\t\"source\": \"<?xml version="1.0" encoding="utf-8" standalone="no"?>
<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
  "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="460.8pt" height="345.6pt" viewBox="0 0 460.8 345.6" xmlns="http://www.w3.org/2000/svg" version="1.1">
 <metadata>
  <rdf:RDF xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:cc="http://creativecommons.org/ns#" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
   <cc:Work>
    <dc:type rdf:resource="http://purl.org/dc/dcmitype/StillImage"/>
    <dc:date>2025-03-06T14:10:33.670853</dc:date>
    <dc:format>image/svg+xml</dc:format>
    <dc:creator>
     <cc:Agent>
      <dc:title>Matplotlib v3.6.3, https://matplotlib.org/</dc:title>
     </cc:Agent>
    </dc:creator>
   </cc:Work>
  </rdf:RDF>
 </metadata>
 <defs>
  <style type="text/css">*{stroke-linejoin: round; stroke-linecap: butt}</style>
 </defs>
 <g id="figure_1">
  <g id="patch_1">
   <path d="M 0 345.6 
L 460.8 345.6 
L 460.8 0 
L 0 0 
z
" style="fill: #ffffff"/>
  </g>
  <g id="axes_1">
   <g id="patch_2">
    <path d="M 57.6 307.584 
L 414.72 307.584 
L 414.72 41.472 
L 57.6 41.472 
z
" style="fill: #ffffff"/>
   </g>
   <g id="matplotlib.axis_1">
    <g id="xtick_1">
     <g id="line2d_1">
      <defs>
       <path id="md14801f7b8" d="M 0 0 
L 0 3.5 
" style="stroke: #000000; stroke-width: 0.8"/>
      </defs>
      <g>
       <use xlink:href="#md14801f7b8" x="73.832727" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_1">
      <!-- 0 -->
      <g transform="translate(70.651477 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-30" d="M 2034 4250 
Q 1547 4250 1301 3770 
Q 1056 3291 1056 2328 
Q 1056 1369 1301 889 
Q 1547 409 2034 409 
Q 2525 409 2770 889 
Q 3016 1369 3016 2328 
Q 3016 3291 2770 3770 
Q 2525 4250 2034 4250 
z
M 2034 4750 
Q 2819 4750 3233 4129 
Q 3647 3509 3647 2328 
Q 3647 1150 3233 529 
Q 2819 -91 2034 -91 
Q 1250 -91 836 529 
Q 422 1150 422 2328 
Q 422 3509 836 4129 
Q 1250 4750 2034 4750 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-30"/>
      </g>
     </g>
    </g>
    <g id="xtick_2">
     <g id="line2d_2">
      <g>
       <use xlink:href="#md14801f7b8" x="125.503103" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_2">
      <!-- 1 -->
      <g transform="translate(122.321853 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-31" d="M 794 531 
L 1825 531 
L 1825 4091 
L 703 3866 
L 703 4441 
L 1819 4666 
L 2450 4666 
L 2450 531 
L 3481 531 
L 3481 0 
L 794 0 
L 794 531 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-31"/>
      </g>
     </g>
    </g>
    <g id="xtick_3">
     <g id="line2d_3">
      <g>
       <use xlink:href="#md14801f7b8" x="177.173479" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_3">
      <!-- 2 -->
      <g transform="translate(173.992229 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-32" d="M 1228 531 
L 3431 531 
L 3431 0 
L 469 0 
L 469 531 
Q 828 903 1448 1529 
Q 2069 2156 2228 2338 
Q 2531 2678 2651 2914 
Q 2772 3150 2772 3378 
Q 2772 3750 2511 3984 
Q 2250 4219 1831 4219 
Q 1534 4219 1204 4116 
Q 875 4013 500 3803 
L 500 4441 
Q 881 4594 1212 4672 
Q 1544 4750 1819 4750 
Q 2544 4750 2975 4387 
Q 3406 4025 3406 3419 
Q 3406 3131 3298 2873 
Q 3191 2616 2906 2266 
Q 2828 2175 2409 1742 
Q 1991 1309 1228 531 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-32"/>
      </g>
     </g>
    </g>
    <g id="xtick_4">
     <g id="line2d_4">
      <g>
       <use xlink:href="#md14801f7b8" x="228.843854" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_4">
      <!-- 3 -->
      <g transform="translate(225.662604 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-33" d="M 2597 2516 
Q 3050 2419 3304 2112 
Q 3559 1806 3559 1356 
Q 3559 666 3084 287 
Q 2609 -91 1734 -91 
Q 1441 -91 1130 -33 
Q 819 25 488 141 
L 488 750 
Q 750 597 1062 519 
Q 1375 441 1716 441 
Q 2309 441 2620 675 
Q 2931 909 2931 1356 
Q 2931 1769 2642 2001 
Q 2353 2234 1838 2234 
L 1294 2234 
L 1294 2753 
L 1863 2753 
Q 2328 2753 2575 2939 
Q 2822 3125 2822 3475 
Q 2822 3834 2567 4026 
Q 2313 4219 1838 4219 
Q 1578 4219 1281 4162 
Q 984 4106 628 3988 
L 628 4550 
Q 988 4650 1302 4700 
Q 1616 4750 1894 4750 
Q 2613 4750 3031 4423 
Q 3450 4097 3450 3541 
Q 3450 3153 3228 2886 
Q 3006 2619 2597 2516 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-33"/>
      </g>
     </g>
    </g>
    <g id="xtick_5">
     <g id="line2d_5">
      <g>
       <use xlink:href="#md14801f7b8" x="280.51423" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_5">
      <!-- 4 -->
      <g transform="translate(277.33298 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-34" d="M 2419 4116 
L 825 1625 
L 2419 1625 
L 2419 4116 
z
M 2253 4666 
L 3047 4666 
L 3047 1625 
L 3713 1625 
L 3713 1100 
L 3047 1100 
L 3047 0 
L 2419 0 
L 2419 1100 
L 313 1100 
L 313 1709 
L 2253 4666 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-34"/>
      </g>
     </g>
    </g>
    <g id="xtick_6">
     <g id="line2d_6">
      <g>
       <use xlink:href="#md14801f7b8" x="332.184606" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_6">
      <!-- 5 -->
      <g transform="translate(329.003356 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-35" d="M 691 4666 
L 3169 4666 
L 3169 4134 
L 1269 4134 
L 1269 2991 
Q 1406 3038 1543 3061 
Q 1681 3084 1819 3084 
Q 2600 3084 3056 2656 
Q 3513 2228 3513 1497 
Q 3513 744 3044 326 
Q 2575 -91 1722 -91 
Q 1428 -91 1123 -41 
Q 819 9 494 109 
L 494 744 
Q 775 591 1075 516 
Q 1375 441 1709 441 
Q 2250 441 2565 725 
Q 2881 1009 2881 1497 
Q 2881 1984 2565 2268 
Q 2250 2553 1709 2553 
Q 1456 2553 1204 2497 
Q 953 2441 691 2322 
L 691 4666 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-35"/>
      </g>
     </g>
    </g>
    <g id="xtick_7">
     <g id="line2d_7">
      <g>
       <use xlink:href="#md14801f7b8" x="383.854982" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_7">
      <!-- 6 -->
      <g transform="translate(380.673732 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-36" d="M 2113 2584 
Q 1688 2584 1439 2293 
Q 1191 2003 1191 1497 
Q 1191 994 1439 701 
Q 1688 409 2113 409 
Q 2538 409 2786 701 
Q 3034 994 3034 1497 
Q 3034 2003 2786 2293 
Q 2538 2584 2113 2584 
z
M 3366 4563 
L 3366 3988 
Q 3128 4100 2886 4159 
Q 2644 4219 2406 4219 
Q 1781 4219 1451 3797 
Q 1122 3375 1075 2522 
Q 1259 2794 1537 2939 
Q 1816 3084 2150 3084 
Q 2853 3084 3261 2657 
Q 3669 2231 3669 1497 
Q 3669 778 3244 343 
Q 2819 -91 2113 -91 
Q 1303 -91 875 529 
Q 447 1150 447 2328 
Q 447 3434 972 4092 
Q 1497 4750 2381 4750 
Q 2619 4750 2861 4703 
Q 3103 4656 3366 4563 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-36"/>
      </g>
     </g>
    </g>
   </g>
   <g id="matplotlib.axis_2">
    <g id="ytick_1">
     <g id="line2d_8">
      <defs>
       <path id="m2949dd50e3" d="M 0 0 
L -3.5 0 
" style="stroke: #000000; stroke-width: 0.8"/>
      </defs>
      <g>
       <use xlink:href="#m2949dd50e3" x="57.6" y="295.548914" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_8">
      <!-- −2.0 -->
      <g transform="translate(26.317187 299.348132) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-2212" d="M 678 2272 
L 4684 2272 
L 4684 1741 
L 678 1741 
L 678 2272 
z
" transform="scale(0.015625)"/>
        <path id="DejaVuSans-2e" d="M 684 794 
L 1344 794 
L 1344 0 
L 684 0 
L 684 794 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-2212"/>
       <use xlink:href="#DejaVuSans-32" x="83.789062"/>
       <use xlink:href="#DejaVuSans-2e" x="147.412109"/>
       <use xlink:href="#DejaVuSans-30" x="179.199219"/>
      </g>
     </g>
    </g>
    <g id="ytick_2">
     <g id="line2d_9">
      <g>
       <use xlink:href="#m2949dd50e3" x="57.6" y="265.301299" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_9">
      <!-- −1.5 -->
      <g transform="translate(26.317187 269.100518) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-2212"/>
       <use xlink:href="#DejaVuSans-31" x="83.789062"/>
       <use xlink:href="#DejaVuSans-2e" x="147.412109"/>
       <use xlink:href="#DejaVuSans-35" x="179.199219"/>
      </g>
     </g>
    </g>
    <g id="ytick_3">
     <g id="line2d_10">
      <g>
       <use xlink:href="#m2949dd50e3" x="57.6" y="235.053685" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_10">
      <!-- −1.0 -->
      <g transform="translate(26.317187 238.852904) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-2212"/>
       <use xlink:href="#DejaVuSans-31" x="83.789062"/>
       <use xlink:href="#DejaVuSans-2e" x="147.412109"/>
       <use xlink:href="#DejaVuSans-30" x="179.199219"/>
      </g>
     </g>
    </g>
    <g id="ytick_4">
     <g id="line2d_11">
      <g>
       <use xlink:href="#m2949dd50e3" x="57.6" y="204.806071" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_11">
      <!-- −0.5 -->
      <g transform="translate(26.317187 208.60529) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-2212"/>
       <use xlink:href="#DejaVuSans-30" x="83.789062"/>
       <use xlink:href="#DejaVuSans-2e" x="147.412109"/>
       <use xlink:href="#DejaVuSans-35" x="179.199219"/>
      </g>
     </g>
    </g>
    <g id="ytick_5">
     <g id="line2d_12">
      <g>
       <use xlink:href="#m2949dd50e3" x="57.6" y="174.558457" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_12">
      <!-- 0.0 -->
      <g transform="translate(34.696875 178.357676) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-30"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-30" x="95.410156"/>
      </g>
     </g>
    </g>
    <g id="ytick_6">
     <g id="line2d_13">
      <g>
       <use xlink:href="#m2949dd50e3" x="57.6" y="144.310843" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_13">
      <!-- 0.5 -->
      <g transform="translate(34.696875 148.110061) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-30"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-35" x="95.410156"/>
      </g>
     </g>
    </g>
    <g id="ytick_7">
     <g id="line2d_14">
      <g>
       <use xlink:href="#m2949dd50e3" x="57.6" y="114.063228" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_14">
      <!-- 1.0 -->
      <g transform="translate(34.696875 117.862447) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-31"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-30" x="95.410156"/>
      </g>
     </g>
    </g>
    <g id="ytick_8">
     <g id="line2d_15">
      <g>
       <use xlink:href="#m2949dd50e3" x="57.6" y="83.815614" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_15">
      <!-- 1.5 -->
      <g transform="translate(34.696875 87.614833) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-31"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-35" x="95.410156"/>
      </g>
     </g>
    </g>
    <g id="ytick_9">
     <g id="line2d_16">
      <g>
       <use xlink:href="#m2949dd50e3" x="57.6" y="53.568" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_16">
      <!-- 2.0 -->
      <g transform="translate(34.696875 57.367219) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-32"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-30" x="95.410156"/>
      </g>
     </g>
    </g>
   </g>
   <g id="line2d_17">
    <path d="M 73.832727 53.568 
L 77.112066 54.541391 
L 80.391405 57.445901 
L 83.670744 62.234797 
L 86.950083 68.831021 
L 90.229421 77.12844 
L 93.50876 86.993545 
L 96.788099 98.267602 
L 100.067438 110.769207 
L 103.346777 124.297205 
L 106.626116 138.633925 
L 109.905455 153.548684 
L 113.184793 168.801499 
L 116.464132 184.146945 
L 119.743471 199.338109 
L 123.02281 214.130559 
L 126.302149 228.286279 
L 129.581488 241.577498 
L 132.860826 253.790356 
L 136.140165 264.728343 
L 139.419504 274.215463 
L 142.698843 282.099064 
L 145.978182 288.252296 
L 149.257521 292.576152 
L 152.53686 295.001059 
L 155.816198 295.488 
L 159.095537 294.029139 
L 162.374876 290.64795 
L 165.654215 285.398838 
L 168.933554 278.366262 
L 172.212893 269.66338 
L 175.492231 259.430224 
L 178.77157 247.831449 
L 182.050909 235.053685 
L 185.330248 221.30253 
L 188.609587 206.799245 
L 191.888926 191.777194 
L 195.168264 176.478087 
L 198.447603 161.148092 
L 201.726942 146.033875 
L 205.006281 131.37863 
L 208.28562 117.418164 
L 211.564959 104.377106 
L 214.844298 92.465293 
L 218.123636 81.87439 
L 221.402975 72.774808 
L 224.682314 65.312962 
L 227.961653 59.608918 
L 231.240992 55.754455 
L 234.520331 53.811593 
L 237.799669 53.811593 
L 241.079008 55.754455 
L 244.358347 59.608918 
L 247.637686 65.312962 
L 250.917025 72.774808 
L 254.196364 81.87439 
L 257.475702 92.465293 
L 260.755041 104.377106 
L 264.03438 117.418164 
L 267.313719 131.37863 
L 270.593058 146.033875 
L 273.872397 161.148092 
L 277.151736 176.478087 
L 280.431074 191.777194 
L 283.710413 206.799245 
L 286.989752 221.30253 
L 290.269091 235.053685 
L 293.54843 247.831449 
L 296.827769 259.430224 
L 300.107107 269.66338 
L 303.386446 278.366262 
L 306.665785 285.398838 
L 309.945124 290.64795 
L 313.224463 294.029139 
L 316.503802 295.488 
L 319.78314 295.001059 
L 323.062479 292.576152 
L 326.341818 288.252296 
L 329.621157 282.099064 
L 332.900496 274.215463 
L 336.179835 264.728343 
L 339.459174 253.790356 
L 342.738512 241.577498 
L 346.017851 228.286279 
L 349.29719 214.130559 
L 352.576529 199.338109 
L 355.855868 184.146945 
L 359.135207 168.801499 
L 362.414545 153.548684 
L 365.693884 138.633925 
L 368.973223 124.297205 
L 372.252562 110.769207 
L 375.531901 98.267602 
L 378.81124 86.993545 
L 382.090579 77.12844 
L 385.369917 68.831021 
L 388.649256 62.234797 
L 391.928595 57.445901 
L 395.207934 54.541391 
L 398.487273 53.568 
" clip-path="url(#p983b030a50)" style="fill: none; stroke: #1f77b4; stroke-width: 1.5; stroke-linecap: square"/>
   </g>
   <g id="patch_3">
    <path d="M 57.6 307.584 
L 57.6 41.472 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
   <g id="patch_4">
    <path d="M 414.72 307.584 
L 414.72 41.472 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
   <g id="patch_5">
    <path d="M 57.6 307.584 
L 414.72 307.584 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
   <g id="patch_6">
    <path d="M 57.6 41.472 
L 414.72 41.472 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
  </g>
 </g>
 <defs>
  <clipPath id="p983b030a50">
   <rect x="57.6" y="41.472" width="357.12" height="266.112"/>
  </clipPath>
 </defs>
</svg>
\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"plt.plot( xv, np.array(exv) );\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 8775842585223173737,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 10488429707702954358,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"To understand \\\\algo{nevaluate}, take a close look at the arguments. The first argument\\nis the expression we want to evaluate. The second argument is a dictionary, in wich\\nwe list the symbols appearing in the expression (here just $x$) and the values that\\neach such symbol takes (here it's the values in the array \\\\verb|xv|).\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"To understand \\\\algo{nevaluate}, take a close look at the arguments. The first argument\\nis the expression we want to evaluate. The second argument is a dictionary, in wich\\nwe list the symbols appearing in the expression (here just $x$) and the values that\\neach such symbol takes (here it's the values in the array \\\\verb|xv|).\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 9144309306588434351,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 11117129739894336245,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\subsection*{More complicated examples}\\n\\nThe example above evaluated a function of a single variable over a range of values\\nof that variable. We can also use this to evaluate functions of multiple variables.\\nThe example below shows this.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\subsection*{More complicated examples}\\n\\nThe example above evaluated a function of a single variable over a range of values\\nof that variable. We can also use this to evaluate functions of multiple variables.\\nThe example below shows this.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 12217825775307860772,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 3881865514960249820,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 13876229443538253978,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\cos(x) \\\\sin(y)\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\cos{x} \\\\sin{y}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex:= \\\\cos(x) \\\\sin(y);\\nxv = np.linspace(0, np.pi, 100)\\nyv = np.linspace(0, np.pi, 100)\\nz = np.array( nevaluate(ex, {$x$: xv, $y$: yv} ) )\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 1982156798941009245,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 1782089119232902477,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"The \\\\verb|z| variable is now a two-dimensional array, the first axis of which is the\\n$x$-axis and the second the $y$-axis (more on this order below). We can plot such a\\ndata set by creating a meshgrid from the $x$ and $y$ values, and then feeding the lot\\ninto \\\\verb|plot_surface|:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"The \\\\verb|z| variable is now a two-dimensional array, the first axis of which is the\\n$x$-axis and the second the $y$-axis (more on this order below). We can plot such a\\ndata set by creating a meshgrid from the $x$ and $y$ values, and then feeding the lot\\ninto \\\\verb|plot_surface|:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 16848152364733261862,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 18159325734197832024,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"image_svg\",\n\t\t\t\t\t\"source\": \"<?xml version="1.0" encoding="utf-8" standalone="no"?>
<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
  "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1440pt" height="720pt" viewBox="0 0 1440 720" xmlns="http://www.w3.org/2000/svg" version="1.1">
 <metadata>
  <rdf:RDF xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:cc="http://creativecommons.org/ns#" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
   <cc:Work>
    <dc:type rdf:resource="http://purl.org/dc/dcmitype/StillImage"/>
    <dc:date>2025-03-06T14:10:35.126553</dc:date>
    <dc:format>image/svg+xml</dc:format>
    <dc:creator>
     <cc:Agent>
      <dc:title>Matplotlib v3.6.3, https://matplotlib.org/</dc:title>
     </cc:Agent>
    </dc:creator>
   </cc:Work>
  </rdf:RDF>
 </metadata>
 <defs>
  <style type="text/css">*{stroke-linejoin: round; stroke-linecap: butt}</style>
 </defs>
 <g id="figure_1">
  <g id="patch_1">
   <path d="M 0 720 
L 1440 720 
L 1440 0 
L 0 0 
z
" style="fill: #ffffff"/>
  </g>
  <g id="patch_2">
   <path d="M 460.8 640.8 
L 1015.2 640.8 
L 1015.2 86.4 
L 460.8 86.4 
z
" style="fill: #ffffff"/>
  </g>
  <g id="pane3d_1">
   <g id="patch_3">
    <path d="M 502.661023 504.102727 
L 685.742009 350.640614 
L 683.197008 129.320814 
L 491.354653 269.318627 
" style="fill: #f2f2f2; opacity: 0.5; stroke: #f2f2f2; stroke-linejoin: miter"/>
   </g>
  </g>
  <g id="pane3d_2">
   <g id="patch_4">
    <path d="M 685.742009 350.640614 
L 979.521668 436.030763 
L 990.005628 207.087856 
L 683.197008 129.320814 
" style="fill: #e6e6e6; opacity: 0.5; stroke: #e6e6e6; stroke-linejoin: miter"/>
   </g>
  </g>
  <g id="pane3d_3">
   <g id="patch_5">
    <path d="M 502.661023 504.102727 
L 814.08181 605.812756 
L 979.521668 436.030763 
L 685.742009 350.640614 
" style="fill: #ececec; opacity: 0.5; stroke: #ececec; stroke-linejoin: miter"/>
   </g>
  </g>
  <g id="axis3d_1">
   <g id="line2d_1">
    <path d="M 502.661023 504.102727 
L 814.08181 605.812756 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linecap: square"/>
   </g>
   <g id="Line3DCollection_1">
    <path d="M 521.5223 510.26282 
L 703.608789 355.833782 
L 701.819208 134.040999 
" style="fill: none; stroke: #b0b0b0; stroke-width: 0.8"/>
    <path d="M 563.123585 523.8498 
L 742.982739 367.278235 
L 742.874789 144.447392 
" style="fill: none; stroke: #b0b0b0; stroke-width: 0.8"/>
    <path d="M 605.329159 537.63414 
L 782.881129 378.875121 
L 784.500896 154.998397 
" style="fill: none; stroke: #b0b0b0; stroke-width: 0.8"/>
    <path d="M 648.152286 551.620173 
L 823.314505 390.627508 
L 826.709506 165.697049 
" style="fill: none; stroke: #b0b0b0; stroke-width: 0.8"/>
    <path d="M 691.606618 565.812358 
L 864.293701 402.538542 
L 869.512931 176.54647 
" style="fill: none; stroke: #b0b0b0; stroke-width: 0.8"/>
    <path d="M 735.706216 580.215287 
L 905.829844 414.611459 
L 912.923836 187.549869 
" style="fill: none; stroke: #b0b0b0; stroke-width: 0.8"/>
    <path d="M 780.46556 594.833688 
L 947.934365 426.849581 
L 956.955243 198.710547 
" style="fill: none; stroke: #b0b0b0; stroke-width: 0.8"/>
   </g>
   <g id="xtick_1">
    <g id="line2d_2">
     <path d="M 523.107899 508.918061 
L 518.344299 512.958109 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linecap: square"/>
    </g>
    <g id="text_1">
     <!-- 0.0 -->
     <g transform="translate(506.056214 533.541659) scale(0.1 -0.1)">
      <defs>
       <path id="DejaVuSans-30" d="M 2034 4250 
Q 1547 4250 1301 3770 
Q 1056 3291 1056 2328 
Q 1056 1369 1301 889 
Q 1547 409 2034 409 
Q 2525 409 2770 889 
Q 3016 1369 3016 2328 
Q 3016 3291 2770 3770 
Q 2525 4250 2034 4250 
z
M 2034 4750 
Q 2819 4750 3233 4129 
Q 3647 3509 3647 2328 
Q 3647 1150 3233 529 
Q 2819 -91 2034 -91 
Q 1250 -91 836 529 
Q 422 1150 422 2328 
Q 422 3509 836 4129 
Q 1250 4750 2034 4750 
z
" transform="scale(0.015625)"/>
       <path id="DejaVuSans-2e" d="M 684 794 
L 1344 794 
L 1344 0 
L 684 0 
L 684 794 
z
" transform="scale(0.015625)"/>
      </defs>
      <use xlink:href="#DejaVuSans-30"/>
      <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
      <use xlink:href="#DejaVuSans-30" x="95.410156"/>
     </g>
    </g>
   </g>
   <g id="xtick_2">
    <g id="line2d_3">
     <path d="M 564.690706 522.485585 
L 559.98257 526.584126 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linecap: square"/>
    </g>
    <g id="text_2">
     <!-- 0.5 -->
     <g transform="translate(547.677839 547.266276) scale(0.1 -0.1)">
      <defs>
       <path id="DejaVuSans-35" d="M 691 4666 
L 3169 4666 
L 3169 4134 
L 1269 4134 
L 1269 2991 
Q 1406 3038 1543 3061 
Q 1681 3084 1819 3084 
Q 2600 3084 3056 2656 
Q 3513 2228 3513 1497 
Q 3513 744 3044 326 
Q 2575 -91 1722 -91 
Q 1428 -91 1123 -41 
Q 819 9 494 109 
L 494 744 
Q 775 591 1075 516 
Q 1375 441 1709 441 
Q 2250 441 2565 725 
Q 2881 1009 2881 1497 
Q 2881 1984 2565 2268 
Q 2250 2553 1709 2553 
Q 1456 2553 1204 2497 
Q 953 2441 691 2322 
L 691 4666 
z
" transform="scale(0.015625)"/>
      </defs>
      <use xlink:href="#DejaVuSans-30"/>
      <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
      <use xlink:href="#DejaVuSans-35" x="95.410156"/>
     </g>
    </g>
   </g>
   <g id="xtick_3">
    <g id="line2d_4">
     <path d="M 606.877097 536.250044 
L 602.226546 540.408358 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linecap: square"/>
    </g>
    <g id="text_3">
     <!-- 1.0 -->
     <g transform="translate(589.90514 561.190614) scale(0.1 -0.1)">
      <defs>
       <path id="DejaVuSans-31" d="M 794 531 
L 1825 531 
L 1825 4091 
L 703 3866 
L 703 4441 
L 1819 4666 
L 2450 4666 
L 2450 531 
L 3481 531 
L 3481 0 
L 794 0 
L 794 531 
z
" transform="scale(0.015625)"/>
      </defs>
      <use xlink:href="#DejaVuSans-31"/>
      <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
      <use xlink:href="#DejaVuSans-30" x="95.410156"/>
     </g>
    </g>
   </g>
   <g id="xtick_4">
    <g id="line2d_5">
     <path d="M 649.680308 550.215758 
L 645.08954 554.435162 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linecap: square"/>
    </g>
    <g id="text_4">
     <!-- 1.5 -->
     <g transform="translate(632.751437 575.319063) scale(0.1 -0.1)">
      <use xlink:href="#DejaVuSans-31"/>
      <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
      <use xlink:href="#DejaVuSans-35" x="95.410156"/>
     </g>
    </g>
   </g>
   <g id="xtick_5">
    <g id="line2d_6">
     <path d="M 693.113969 564.387174 
L 688.585258 568.669023 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linecap: square"/>
    </g>
    <g id="text_5">
     <!-- 2.0 -->
     <g transform="translate(676.230439 589.656145) scale(0.1 -0.1)">
      <defs>
       <path id="DejaVuSans-32" d="M 1228 531 
L 3431 531 
L 3431 0 
L 469 0 
L 469 531 
Q 828 903 1448 1529 
Q 2069 2156 2228 2338 
Q 2531 2678 2651 2914 
Q 2772 3150 2772 3378 
Q 2772 3750 2511 3984 
Q 2250 4219 1831 4219 
Q 1534 4219 1204 4116 
Q 875 4013 500 3803 
L 500 4441 
Q 881 4594 1212 4672 
Q 1544 4750 1819 4750 
Q 2544 4750 2975 4387 
Q 3406 4025 3406 3419 
Q 3406 3131 3298 2873 
Q 3191 2616 2906 2266 
Q 2828 2175 2409 1742 
Q 1991 1309 1228 531 
z
" transform="scale(0.015625)"/>
      </defs>
      <use xlink:href="#DejaVuSans-32"/>
      <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
      <use xlink:href="#DejaVuSans-30" x="95.410156"/>
     </g>
    </g>
   </g>
   <g id="xtick_6">
    <g id="line2d_7">
     <path d="M 737.192111 578.768869 
L 732.727814 583.11456 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linecap: square"/>
    </g>
    <g id="text_6">
     <!-- 2.5 -->
     <g transform="translate(720.356265 604.206515) scale(0.1 -0.1)">
      <use xlink:href="#DejaVuSans-32"/>
      <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
      <use xlink:href="#DejaVuSans-35" x="95.410156"/>
     </g>
    </g>
   </g>
   <g id="xtick_7">
    <g id="line2d_8">
     <path d="M 781.929186 593.365559 
L 777.531745 597.77653 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linecap: square"/>
    </g>
    <g id="text_7">
     <!-- 3.0 -->
     <g transform="translate(765.143458 618.974969) scale(0.1 -0.1)">
      <defs>
       <path id="DejaVuSans-33" d="M 2597 2516 
Q 3050 2419 3304 2112 
Q 3559 1806 3559 1356 
Q 3559 666 3084 287 
Q 2609 -91 1734 -91 
Q 1441 -91 1130 -33 
Q 819 25 488 141 
L 488 750 
Q 750 597 1062 519 
Q 1375 441 1716 441 
Q 2309 441 2620 675 
Q 2931 909 2931 1356 
Q 2931 1769 2642 2001 
Q 2353 2234 1838 2234 
L 1294 2234 
L 1294 2753 
L 1863 2753 
Q 2328 2753 2575 2939 
Q 2822 3125 2822 3475 
Q 2822 3834 2567 4026 
Q 2313 4219 1838 4219 
Q 1578 4219 1281 4162 
Q 984 4106 628 3988 
L 628 4550 
Q 988 4650 1302 4700 
Q 1616 4750 1894 4750 
Q 2613 4750 3031 4423 
Q 3450 4097 3450 3541 
Q 3450 3153 3228 2886 
Q 3006 2619 2597 2516 
z
" transform="scale(0.015625)"/>
      </defs>
      <use xlink:href="#DejaVuSans-33"/>
      <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
      <use xlink:href="#DejaVuSans-30" x="95.410156"/>
     </g>
    </g>
   </g>
  </g>
  <g id="axis3d_2">
   <g id="line2d_9">
    <path d="M 979.521668 436.030763 
L 814.08181 605.812756 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linecap: square"/>
   </g>
   <g id="Line3DCollection_2">
    <path d="M 504.621027 259.637432 
L 515.27685 493.527891 
L 825.528968 594.065156 
" style="fill: none; stroke: #b0b0b0; stroke-width: 0.8"/>
    <path d="M 533.041474 238.897484 
L 542.325912 470.854831 
L 850.048829 568.901746 
" style="fill: none; stroke: #b0b0b0; stroke-width: 0.8"/>
    <path d="M 560.74937 218.677523 
L 568.726088 448.72568 
L 873.949612 544.373663 
" style="fill: none; stroke: #b0b0b0; stroke-width: 0.8"/>
    <path d="M 587.771182 198.958236 
L 594.500451 427.121098 
L 897.254472 520.457144 
" style="fill: none; stroke: #b0b0b0; stroke-width: 0.8"/>
    <path d="M 614.13208 179.721253 
L 619.670992 406.022651 
L 919.98542 497.1296 
" style="fill: none; stroke: #b0b0b0; stroke-width: 0.8"/>
    <path d="M 639.856018 160.949095 
L 644.258685 385.412759 
L 942.163399 474.369537 
" style="fill: none; stroke: #b0b0b0; stroke-width: 0.8"/>
    <path d="M 664.965808 142.625114 
L 668.283543 365.274647 
L 963.808344 452.156498 
" style="fill: none; stroke: #b0b0b0; stroke-width: 0.8"/>
   </g>
   <g id="xtick_8">
    <g id="line2d_10">
     <path d="M 822.914464 593.217925 
L 830.764737 595.761808 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linecap: square"/>
    </g>
    <g id="text_8">
     <!-- 0.0 -->
     <g transform="translate(830.45403 615.082707) scale(0.1 -0.1)">
      <use xlink:href="#DejaVuSans-30"/>
      <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
      <use xlink:href="#DejaVuSans-30" x="95.410156"/>
     </g>
    </g>
   </g>
   <g id="xtick_9">
    <g id="line2d_11">
     <path d="M 847.457318 568.076037 
L 855.238467 570.555273 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linecap: square"/>
    </g>
    <g id="text_9">
     <!-- 0.5 -->
     <g transform="translate(854.816167 589.740543) scale(0.1 -0.1)">
      <use xlink:href="#DejaVuSans-30"/>
      <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
      <use xlink:href="#DejaVuSans-35" x="95.410156"/>
     </g>
    </g>
   </g>
   <g id="xtick_10">
    <g id="line2d_12">
     <path d="M 871.380774 543.568665 
L 879.093765 545.985687 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linecap: square"/>
    </g>
    <g id="text_10">
     <!-- 1.0 -->
     <g transform="translate(878.563035 565.038397) scale(0.1 -0.1)">
      <use xlink:href="#DejaVuSans-31"/>
      <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
      <use xlink:href="#DejaVuSans-30" x="95.410156"/>
     </g>
    </g>
   </g>
   <g id="xtick_11">
    <g id="line2d_13">
     <path d="M 894.707988 519.672089 
L 902.353779 522.02921 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linecap: square"/>
    </g>
    <g id="text_11">
     <!-- 1.5 -->
     <g transform="translate(901.717654 540.952326) scale(0.1 -0.1)">
      <use xlink:href="#DejaVuSans-31"/>
      <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
      <use xlink:href="#DejaVuSans-35" x="95.410156"/>
     </g>
    </g>
   </g>
   <g id="xtick_12">
    <g id="line2d_14">
     <path d="M 917.460975 496.363754 
L 925.040517 498.663174 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linecap: square"/>
    </g>
    <g id="text_12">
     <!-- 2.0 -->
     <g transform="translate(924.301905 517.459567) scale(0.1 -0.1)">
      <use xlink:href="#DejaVuSans-32"/>
      <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
      <use xlink:href="#DejaVuSans-30" x="95.410156"/>
     </g>
    </g>
   </g>
   <g id="xtick_13">
    <g id="line2d_15">
     <path d="M 939.660681 473.622205 
L 947.174914 475.866016 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linecap: square"/>
    </g>
    <g id="text_13">
     <!-- 2.5 -->
     <g transform="translate(946.336608 494.538463) scale(0.1 -0.1)">
      <use xlink:href="#DejaVuSans-32"/>
      <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
      <use xlink:href="#DejaVuSans-35" x="95.410156"/>
     </g>
    </g>
   </g>
   <g id="xtick_14">
    <g id="line2d_16">
     <path d="M 961.327043 451.427017 
L 968.7769 453.617213 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linecap: square"/>
    </g>
    <g id="text_14">
     <!-- 3.0 -->
     <g transform="translate(967.841579 472.1684) scale(0.1 -0.1)">
      <use xlink:href="#DejaVuSans-33"/>
      <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
      <use xlink:href="#DejaVuSans-30" x="95.410156"/>
     </g>
    </g>
   </g>
  </g>
  <g id="axis3d_3">
   <g id="line2d_17">
    <path d="M 979.521668 436.030763 
L 990.005628 207.087856 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linecap: square"/>
   </g>
   <g id="Line3DCollection_3">
    <path d="M 980.934513 405.177831 
L 685.398411 320.760471 
L 501.139569 472.508752 
" style="fill: none; stroke: #b0b0b0; stroke-width: 0.8"/>
    <path d="M 982.159725 378.422332 
L 685.100604 294.862342 
L 499.819613 445.099005 
" style="fill: none; stroke: #b0b0b0; stroke-width: 0.8"/>
    <path d="M 983.397755 351.386913 
L 684.799829 268.706245 
L 498.485319 417.391523 
" style="fill: none; stroke: #b0b0b0; stroke-width: 0.8"/>
    <path d="M 984.648806 324.067157 
L 684.496044 242.288307 
L 497.136452 389.381428 
" style="fill: none; stroke: #b0b0b0; stroke-width: 0.8"/>
    <path d="M 985.913084 296.458555 
L 684.189203 215.604576 
L 495.772772 361.063735 
" style="fill: none; stroke: #b0b0b0; stroke-width: 0.8"/>
    <path d="M 987.190801 268.556502 
L 683.879258 188.651021 
L 494.394034 332.433349 
" style="fill: none; stroke: #b0b0b0; stroke-width: 0.8"/>
    <path d="M 988.48217 240.356293 
L 683.566164 161.423529 
L 492.999988 303.485063 
" style="fill: none; stroke: #b0b0b0; stroke-width: 0.8"/>
   </g>
   <g id="xtick_15">
    <g id="line2d_18">
     <path d="M 978.453451 404.469137 
L 985.902574 406.596915 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linecap: square"/>
    </g>
    <g id="text_15">
     <!-- −0.75 -->
     <g transform="translate(983.997123 410.196214) scale(0.1 -0.1)">
      <defs>
       <path id="DejaVuSans-2212" d="M 678 2272 
L 4684 2272 
L 4684 1741 
L 678 1741 
L 678 2272 
z
" transform="scale(0.015625)"/>
       <path id="DejaVuSans-37" d="M 525 4666 
L 3525 4666 
L 3525 4397 
L 1831 0 
L 1172 0 
L 2766 4134 
L 525 4134 
L 525 4666 
z
" transform="scale(0.015625)"/>
      </defs>
      <use xlink:href="#DejaVuSans-2212"/>
      <use xlink:href="#DejaVuSans-30" x="83.789062"/>
      <use xlink:href="#DejaVuSans-2e" x="147.412109"/>
      <use xlink:href="#DejaVuSans-37" x="179.199219"/>
      <use xlink:href="#DejaVuSans-35" x="242.822266"/>
     </g>
    </g>
   </g>
   <g id="xtick_16">
    <g id="line2d_19">
     <path d="M 979.665266 377.720664 
L 987.154643 379.827357 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linecap: square"/>
    </g>
    <g id="text_16">
     <!-- −0.50 -->
     <g transform="translate(985.316084 383.466308) scale(0.1 -0.1)">
      <use xlink:href="#DejaVuSans-2212"/>
      <use xlink:href="#DejaVuSans-30" x="83.789062"/>
      <use xlink:href="#DejaVuSans-2e" x="147.412109"/>
      <use xlink:href="#DejaVuSans-35" x="179.199219"/>
      <use xlink:href="#DejaVuSans-30" x="242.822266"/>
     </g>
    </g>
   </g>
   <g id="xtick_17">
    <g id="line2d_20">
     <path d="M 980.889755 350.692457 
L 988.419821 352.777504 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linecap: square"/>
    </g>
    <g id="text_17">
     <!-- −0.25 -->
     <g transform="translate(986.648824 356.457159) scale(0.1 -0.1)">
      <use xlink:href="#DejaVuSans-2212"/>
      <use xlink:href="#DejaVuSans-30" x="83.789062"/>
      <use xlink:href="#DejaVuSans-2e" x="147.412109"/>
      <use xlink:href="#DejaVuSans-32" x="179.199219"/>
      <use xlink:href="#DejaVuSans-35" x="242.822266"/>
     </g>
    </g>
   </g>
   <g id="xtick_18">
    <g id="line2d_21">
     <path d="M 982.127116 323.380104 
L 989.698316 325.442933 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linecap: square"/>
    </g>
    <g id="text_18">
     <!-- 0.00 -->
     <g transform="translate(992.185404 329.164368) scale(0.1 -0.1)">
      <use xlink:href="#DejaVuSans-30"/>
      <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
      <use xlink:href="#DejaVuSans-30" x="95.410156"/>
      <use xlink:href="#DejaVuSans-30" x="159.033203"/>
     </g>
    </g>
   </g>
   <g id="xtick_19">
    <g id="line2d_22">
     <path d="M 983.377555 295.7791 
L 990.990339 297.819124 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linecap: square"/>
    </g>
    <g id="text_19">
     <!-- 0.25 -->
     <g transform="translate(993.546357 301.583443) scale(0.1 -0.1)">
      <use xlink:href="#DejaVuSans-30"/>
      <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
      <use xlink:href="#DejaVuSans-32" x="95.410156"/>
      <use xlink:href="#DejaVuSans-35" x="159.033203"/>
     </g>
    </g>
   </g>
   <g id="xtick_20">
    <g id="line2d_23">
     <path d="M 984.641279 267.884846 
L 992.296106 269.901462 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linecap: square"/>
    </g>
    <g id="text_20">
     <!-- 0.50 -->
     <g transform="translate(994.921755 273.709797) scale(0.1 -0.1)">
      <use xlink:href="#DejaVuSans-30"/>
      <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
      <use xlink:href="#DejaVuSans-35" x="95.410156"/>
      <use xlink:href="#DejaVuSans-30" x="159.033203"/>
     </g>
    </g>
   </g>
   <g id="xtick_21">
    <g id="line2d_24">
     <path d="M 985.918501 239.692643 
L 993.615838 241.685232 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linecap: square"/>
    </g>
    <g id="text_21">
     <!-- 0.75 -->
     <g transform="translate(996.311828 245.538746) scale(0.1 -0.1)">
      <use xlink:href="#DejaVuSans-30"/>
      <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
      <use xlink:href="#DejaVuSans-37" x="95.410156"/>
      <use xlink:href="#DejaVuSans-35" x="159.033203"/>
     </g>
    </g>
   </g>
  </g>
  <g id="axes_1">
   <g id="Poly3DCollection_1">
    <path d="M 690.251903 253.752187 
L 692.798809 254.45206 
L 694.353726 256.633889 
L 691.80969 255.935756 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #faf996"/>
    <path d="M 692.798809 254.45206 
L 695.347932 255.155953 
L 696.899941 257.332621 
L 694.353726 256.633889 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #faf996"/>
    <path d="M 695.347932 255.155953 
L 697.899269 255.863863 
L 699.448339 258.031951 
L 696.899941 257.332621 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #faf996"/>
    <path d="M 697.899269 255.863863 
L 700.452819 256.575786 
L 701.998923 258.731881 
L 699.448339 258.031951 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #faf996"/>
    <path d="M 688.689833 251.56599 
L 691.239617 252.267606 
L 692.798809 254.45206 
L 690.251903 253.752187 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f2ee92"/>
    <path d="M 700.452819 256.575786 
L 703.008578 257.291714 
L 704.551696 259.432412 
L 701.998923 258.731881 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #faf996"/>
    <path d="M 691.239617 252.267606 
L 693.791655 252.976672 
L 695.347932 255.155953 
L 692.798809 254.45206 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f2ee92"/>
    <path d="M 703.008578 257.291714 
L 705.566545 258.011636 
L 707.10666 260.133544 
L 704.551696 259.432412 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #faf996"/>
    <path d="M 693.791655 252.976672 
L 696.345941 253.693182 
L 697.899269 255.863863 
L 695.347932 255.155953 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f2ee92"/>
    <path d="M 705.566545 258.011636 
L 708.126717 258.735535 
L 709.663818 260.835279 
L 707.10666 260.133544 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fcfb97"/>
    <path d="M 696.345941 253.693182 
L 698.902467 254.417128 
L 700.452819 256.575786 
L 697.899269 255.863863 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f2ee92"/>
    <path d="M 687.123506 249.380587 
L 689.67617 250.083948 
L 691.239617 252.267606 
L 688.689833 251.56599 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eae48e"/>
    <path d="M 708.126717 258.735535 
L 710.689093 259.463393 
L 712.223174 261.537616 
L 709.663818 260.835279 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fcfb97"/>
    <path d="M 698.902467 254.417128 
L 701.461227 255.148492 
L 703.008578 257.291714 
L 700.452819 256.575786 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f2ee92"/>
    <path d="M 689.67617 250.083948 
L 692.23113 250.798194 
L 693.791655 252.976672 
L 691.239617 252.267606 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eae48e"/>
    <path d="M 710.689093 259.463393 
L 713.25367 260.195189 
L 714.784729 262.240557 
L 712.223174 261.537616 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fcfb97"/>
    <path d="M 701.461227 255.148492 
L 704.022212 255.887248 
L 705.566545 258.011636 
L 703.008578 257.291714 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f4f193"/>
    <path d="M 692.23113 250.798194 
L 694.788372 251.523318 
L 696.345941 253.693182 
L 693.791655 252.976672 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eae48e"/>
    <path d="M 713.25367 260.195189 
L 715.820445 260.930897 
L 717.348487 262.944102 
L 714.784729 262.240557 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fcfb97"/>
    <path d="M 704.022212 255.887248 
L 706.585416 256.633367 
L 708.126717 258.735535 
L 705.566545 258.011636 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f4f193"/>
    <path d="M 694.788372 251.523318 
L 697.347885 252.259304 
L 698.902467 254.417128 
L 696.345941 253.693182 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eae48e"/>
    <path d="M 685.552947 247.199415 
L 688.108494 247.904523 
L 689.67617 250.083948 
L 687.123506 249.380587 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e2da89"/>
    <path d="M 715.820445 260.930897 
L 718.389417 261.670488 
L 719.91445 263.648253 
L 717.348487 262.944102 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fcfb97"/>
    <path d="M 706.585416 256.633367 
L 709.150832 257.38681 
L 710.689093 259.463393 
L 708.126717 258.735535 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f4f193"/>
    <path d="M 697.347885 252.259304 
L 699.909657 253.006127 
L 701.461227 255.148492 
L 698.902467 254.417128 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eae48e"/>
    <path d="M 688.108494 247.904523 
L 690.666379 248.623953 
L 692.23113 250.798194 
L 689.67617 250.083948 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e2da89"/>
    <path d="M 718.389417 261.670488 
L 720.960584 262.413931 
L 722.482622 264.353009 
L 719.91445 263.648253 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fcfb97"/>
    <path d="M 709.150832 257.38681 
L 711.718451 258.147531 
L 713.25367 260.195189 
L 710.689093 259.463393 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f4f193"/>
    <path d="M 699.909657 253.006127 
L 702.473675 253.763748 
L 704.022212 255.887248 
L 701.461227 255.148492 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ece78f"/>
    <path d="M 690.666379 248.623953 
L 693.226584 249.357696 
L 694.788372 251.523318 
L 692.23113 250.798194 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e2da89"/>
    <path d="M 720.960584 262.413931 
L 723.533943 263.161189 
L 725.053006 265.058373 
L 722.482622 264.353009 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fcfb97"/>
    <path d="M 711.718451 258.147531 
L 714.288267 258.91548 
L 715.820445 260.930897 
L 713.25367 260.195189 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f4f193"/>
    <path d="M 702.473675 253.763748 
L 705.039926 254.53212 
L 706.585416 256.633367 
L 704.022212 255.887248 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ece78f"/>
    <path d="M 693.226584 249.357696 
L 695.789092 250.105731 
L 697.347885 252.259304 
L 694.788372 251.523318 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e2da89"/>
    <path d="M 683.978189 245.025929 
L 686.536619 245.732784 
L 688.108494 247.904523 
L 685.552947 247.199415 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dad085"/>
    <path d="M 723.533943 263.161189 
L 726.109493 263.912225 
L 727.625603 265.764344 
L 725.053006 265.058373 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fcfb97"/>
    <path d="M 714.288267 258.91548 
L 716.860273 259.690598 
L 718.389417 261.670488 
L 715.820445 260.930897 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f4f193"/>
    <path d="M 705.039926 254.53212 
L 707.608399 255.311185 
L 709.150832 257.38681 
L 706.585416 256.633367 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ece78f"/>
    <path d="M 695.789092 250.105731 
L 698.353887 250.868021 
L 699.909657 253.006127 
L 697.347885 252.259304 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e2da89"/>
    <path d="M 686.536619 245.732784 
L 689.097432 246.457397 
L 690.666379 248.623953 
L 688.108494 247.904523 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dad085"/>
    <path d="M 726.109493 263.912225 
L 728.687231 264.666996 
L 730.200417 266.470923 
L 727.625603 265.764344 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fcfb97"/>
    <path d="M 716.860273 259.690598 
L 719.434462 260.472819 
L 720.960584 262.413931 
L 718.389417 261.670488 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f4f193"/>
    <path d="M 707.608399 255.311185 
L 710.179081 256.100876 
L 711.718451 258.147531 
L 709.150832 257.38681 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ece78f"/>
    <path d="M 698.353887 250.868021 
L 700.920949 251.644517 
L 702.473675 253.763748 
L 699.909657 253.006127 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e4dc8a"/>
    <path d="M 689.097432 246.457397 
L 691.660604 247.199757 
L 693.226584 249.357696 
L 690.666379 248.623953 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dad085"/>
    <path d="M 728.687231 264.666996 
L 731.267156 265.425458 
L 732.777451 267.178112 
L 730.200417 266.470923 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fcfb97"/>
    <path d="M 719.434462 260.472819 
L 722.010826 261.262072 
L 723.533943 263.161189 
L 720.960584 262.413931 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f4f193"/>
    <path d="M 710.179081 256.100876 
L 712.75196 256.901113 
L 714.288267 258.91548 
L 711.718451 258.147531 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ece78f"/>
    <path d="M 700.920949 251.644517 
L 703.490262 252.435154 
L 705.039926 254.53212 
L 702.473675 253.763748 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e4dc8a"/>
    <path d="M 691.660604 247.199757 
L 694.226114 247.959835 
L 695.789092 250.105731 
L 693.226584 249.357696 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dad085"/>
    <path d="M 731.267156 265.425458 
L 733.849265 266.187563 
L 735.356708 267.88591 
L 732.777451 267.178112 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fcfb97"/>
    <path d="M 722.010826 261.262072 
L 724.589358 262.058279 
L 726.109493 263.912225 
L 723.533943 263.161189 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f4f193"/>
    <path d="M 682.399265 242.863591 
L 684.960578 243.572194 
L 686.536619 245.732784 
L 683.978189 245.025929 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d2c581"/>
    <path d="M 712.75196 256.901113 
L 715.327023 257.711808 
L 716.860273 259.690598 
L 714.288267 258.91548 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ece78f"/>
    <path d="M 703.490262 252.435154 
L 706.061809 253.239856 
L 707.608399 255.311185 
L 705.039926 254.53212 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e4dc8a"/>
    <path d="M 694.226114 247.959835 
L 696.793939 248.737588 
L 698.353887 250.868021 
L 695.789092 250.105731 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dad085"/>
    <path d="M 733.849265 266.187563 
L 736.433558 266.953259 
L 737.938191 268.59432 
L 735.356708 267.88591 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fcfb97"/>
    <path d="M 724.589358 262.058279 
L 727.170052 262.861354 
L 728.687231 264.666996 
L 726.109493 263.912225 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f4f193"/>
    <path d="M 684.960578 243.572194 
L 687.524319 244.301985 
L 689.097432 246.457397 
L 686.536619 245.732784 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d2c581"/>
    <path d="M 715.327023 257.711808 
L 717.904259 258.532863 
L 719.434462 260.472819 
L 716.860273 259.690598 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ece78f"/>
    <path d="M 706.061809 253.239856 
L 708.635572 254.05853 
L 710.179081 256.100876 
L 707.608399 255.311185 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e4dc8a"/>
    <path d="M 696.793939 248.737588 
L 699.364057 249.532951 
L 700.920949 251.644517 
L 698.353887 250.868021 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dcd286"/>
    <path d="M 736.433558 266.953259 
L 739.020032 267.722491 
L 740.521902 269.303341 
L 737.938191 268.59432 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fcfb97"/>
    <path d="M 727.170052 262.861354 
L 729.752901 263.671206 
L 731.267156 265.425458 
L 728.687231 264.666996 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f4f193"/>
    <path d="M 687.524319 244.301985 
L 690.090462 245.052951 
L 691.660604 247.199757 
L 689.097432 246.457397 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d2c581"/>
    <path d="M 717.904259 258.532863 
L 720.483654 259.364169 
L 722.010826 261.262072 
L 719.434462 260.472819 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ece78f"/>
    <path d="M 708.635572 254.05853 
L 711.211533 254.891071 
L 712.75196 256.901113 
L 710.179081 256.100876 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e4dc8a"/>
    <path d="M 699.364057 249.532951 
L 701.936444 250.345845 
L 703.490262 252.435154 
L 700.920949 251.644517 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dcd286"/>
    <path d="M 739.020032 267.722491 
L 741.608686 268.495204 
L 743.107844 270.012974 
L 740.521902 269.303341 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fcfb97"/>
    <path d="M 729.752901 263.671206 
L 732.337898 264.487738 
L 733.849265 266.187563 
L 731.267156 265.425458 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f4f193"/>
    <path d="M 690.090462 245.052951 
L 692.658978 245.825059 
L 694.226114 247.959835 
L 691.660604 247.199757 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d2c581"/>
    <path d="M 720.483654 259.364169 
L 723.065198 260.205608 
L 724.589358 262.058279 
L 722.010826 261.262072 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ece78f"/>
    <path d="M 680.816217 240.715873 
L 683.38041 241.426223 
L 684.960578 243.572194 
L 682.399265 242.863591 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cabb7c"/>
    <path d="M 711.211533 254.891071 
L 713.789675 255.737361 
L 715.327023 257.711808 
L 712.75196 256.901113 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e4dc8a"/>
    <path d="M 701.936444 250.345845 
L 704.511079 251.176172 
L 706.061809 253.239856 
L 703.490262 252.435154 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dcd286"/>
    <path d="M 741.608686 268.495204 
L 744.199518 269.271336 
L 745.696021 270.72322 
L 743.107844 270.012974 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fcfb97"/>
    <path d="M 732.337898 264.487738 
L 734.925038 265.310847 
L 736.433558 266.953259 
L 733.849265 266.187563 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f4f193"/>
    <path d="M 692.658978 245.825059 
L 695.229841 246.618253 
L 696.793939 248.737588 
L 694.226114 247.959835 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d2c581"/>
    <path d="M 723.065198 260.205608 
L 725.648878 261.057051 
L 727.170052 262.861354 
L 724.589358 262.058279 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ece78f"/>
    <path d="M 683.38041 241.426223 
L 685.947078 242.161183 
L 687.524319 244.301985 
L 684.960578 243.572194 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cabb7c"/>
    <path d="M 713.789675 255.737361 
L 716.369981 256.597267 
L 717.904259 258.532863 
L 715.327023 257.711808 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e4dc8a"/>
    <path d="M 704.511079 251.176172 
L 707.087938 252.023816 
L 708.635572 254.05853 
L 706.061809 253.239856 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dcd286"/>
    <path d="M 744.199518 269.271336 
L 746.792527 270.050825 
L 748.286434 271.43408 
L 745.696021 270.72322 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fcfb97"/>
    <path d="M 734.925038 265.310847 
L 737.514313 266.140422 
L 739.020032 267.722491 
L 736.433558 266.953259 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f4f193"/>
    <path d="M 695.229841 246.618253 
L 697.803022 247.432458 
L 699.364057 249.532951 
L 696.793939 248.737588 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d4c882"/>
    <path d="M 725.648878 261.057051 
L 728.234684 261.91836 
L 729.752901 263.671206 
L 727.170052 262.861354 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eee990"/>
    <path d="M 716.369981 256.597267 
L 718.952434 257.470642 
L 720.483654 259.364169 
L 717.904259 258.532863 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e4dc8a"/>
    <path d="M 685.947078 242.161183 
L 688.516192 242.920738 
L 690.090462 245.052951 
L 687.524319 244.301985 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cabb7c"/>
    <path d="M 707.087938 252.023816 
L 709.667 252.888645 
L 711.211533 254.891071 
L 708.635572 254.05853 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dcd286"/>
    <path d="M 737.514313 266.140422 
L 740.105718 266.976347 
L 741.608686 268.495204 
L 739.020032 267.722491 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f6f394"/>
    <path d="M 746.792527 270.050825 
L 749.387712 270.833604 
L 750.879088 272.145555 
L 748.286434 271.43408 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fcfb97"/>
    <path d="M 697.803022 247.432458 
L 700.378494 248.267577 
L 701.936444 250.345845 
L 699.364057 249.532951 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d4c882"/>
    <path d="M 728.234684 261.91836 
L 730.822603 262.789388 
L 732.337898 264.487738 
L 729.752901 263.671206 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eee990"/>
    <path d="M 718.952434 257.470642 
L 721.537016 258.35733 
L 723.065198 260.205608 
L 720.483654 259.364169 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e6df8b"/>
    <path d="M 688.516192 242.920738 
L 691.087717 243.704848 
L 692.658978 245.825059 
L 690.090462 245.052951 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cabb7c"/>
    <path d="M 679.229088 238.58625 
L 681.796155 239.298346 
L 683.38041 241.426223 
L 680.816217 240.715873 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c2b178"/>
    <path d="M 709.667 252.888645 
L 712.248241 253.77051 
L 713.789675 255.737361 
L 711.211533 254.891071 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dcd286"/>
    <path d="M 740.105718 266.976347 
L 742.699247 267.818502 
L 744.199518 269.271336 
L 741.608686 268.495204 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f6f394"/>
    <path d="M 749.387712 270.833604 
L 751.985072 271.619606 
L 753.473985 272.857646 
L 750.879088 272.145555 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fcfb97"/>
    <path d="M 700.378494 248.267577 
L 702.95623 249.123492 
L 704.511079 251.176172 
L 701.936444 250.345845 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d4c882"/>
    <path d="M 730.822603 262.789388 
L 733.412624 263.669979 
L 734.925038 265.310847 
L 732.337898 264.487738 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eee990"/>
    <path d="M 721.537016 258.35733 
L 724.123712 259.257157 
L 725.648878 261.057051 
L 723.065198 260.205608 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e6df8b"/>
    <path d="M 691.087717 243.704848 
L 693.661622 244.513449 
L 695.229841 246.618253 
L 692.658978 245.825059 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ccbe7d"/>
    <path d="M 712.248241 253.77051 
L 714.831639 254.669244 
L 716.369981 256.597267 
L 713.789675 255.737361 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dcd286"/>
    <path d="M 681.796155 239.298346 
L 684.365749 240.038461 
L 685.947078 242.161183 
L 683.38041 241.426223 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c2b178"/>
    <path d="M 742.699247 267.818502 
L 745.294894 268.666758 
L 746.792527 270.050825 
L 744.199518 269.271336 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f6f394"/>
    <path d="M 751.985072 271.619606 
L 754.584606 272.408758 
L 756.071128 273.570353 
L 753.473985 272.857646 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fcfb97"/>
    <path d="M 702.95623 249.123492 
L 705.5362 250.000063 
L 707.087938 252.023816 
L 704.511079 251.176172 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d4c882"/>
    <path d="M 733.412624 263.669979 
L 736.004737 264.559967 
L 737.514313 266.140422 
L 734.925038 265.310847 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eee990"/>
    <path d="M 724.123712 259.257157 
L 726.712504 260.169938 
L 728.234684 261.91836 
L 725.648878 261.057051 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e6df8b"/>
    <path d="M 693.661622 244.513449 
L 696.237874 245.346451 
L 697.803022 247.432458 
L 695.229841 246.618253 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ccbe7d"/>
    <path d="M 714.831639 254.669244 
L 717.417173 255.584665 
L 718.952434 257.470642 
L 716.369981 256.597267 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ded587"/>
    <path d="M 684.365749 240.038461 
L 686.937832 240.806579 
L 688.516192 242.920738 
L 685.947078 242.161183 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c2b178"/>
    <path d="M 745.294894 268.666758 
L 747.892654 269.520983 
L 749.387712 270.833604 
L 746.792527 270.050825 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f6f394"/>
    <path d="M 705.5362 250.000063 
L 708.118379 250.897132 
L 709.667 252.888645 
L 707.087938 252.023816 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d4c882"/>
    <path d="M 736.004737 264.559967 
L 738.598932 265.459177 
L 740.105718 266.976347 
L 737.514313 266.140422 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eee990"/>
    <path d="M 754.584606 272.408758 
L 757.186314 273.200988 
L 758.670519 274.283676 
L 756.071128 273.570353 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fcfb97"/>
    <path d="M 726.712504 260.169938 
L 729.303377 261.095477 
L 730.822603 262.789388 
L 728.234684 261.91836 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e6df8b"/>
    <path d="M 696.237874 245.346451 
L 698.81644 246.203742 
L 700.378494 248.267577 
L 697.803022 247.432458 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ccbe7d"/>
    <path d="M 717.417173 255.584665 
L 720.004819 256.516573 
L 721.537016 258.35733 
L 718.952434 257.470642 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ded587"/>
    <path d="M 686.937832 240.806579 
L 689.512368 241.602653 
L 691.087717 243.704848 
L 688.516192 242.920738 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c4b379"/>
    <path d="M 747.892654 269.520983 
L 750.492523 270.381038 
L 751.985072 271.619606 
L 749.387712 270.833604 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f6f394"/>
    <path d="M 708.118379 250.897132 
L 710.702737 251.814518 
L 712.248241 253.77051 
L 709.667 252.888645 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d4c882"/>
    <path d="M 677.637925 236.478197 
L 680.20786 237.192036 
L 681.796155 239.298346 
L 679.229088 238.58625 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #baa774"/>
    <path d="M 738.598932 265.459177 
L 741.195198 266.367426 
L 742.699247 267.818502 
L 740.105718 266.976347 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eee990"/>
    <path d="M 757.186314 273.200988 
L 759.790193 273.996219 
L 761.272162 274.997618 
L 758.670519 274.283676 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fcfb97"/>
    <path d="M 729.303377 261.095477 
L 731.896315 262.033564 
L 733.412624 263.669979 
L 730.822603 262.789388 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e6df8b"/>
    <path d="M 698.81644 246.203742 
L 701.397286 247.085183 
L 702.95623 249.123492 
L 700.378494 248.267577 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ccbe7d"/>
    <path d="M 720.004819 256.516573 
L 722.594558 257.464752 
L 724.123712 259.257157 
L 721.537016 258.35733 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ded587"/>
    <path d="M 689.512368 241.602653 
L 692.089319 242.42661 
L 693.661622 244.513449 
L 691.087717 243.704848 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c4b379"/>
    <path d="M 710.702737 251.814518 
L 713.289248 252.752021 
L 714.831639 254.669244 
L 712.248241 253.77051 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d6cb83"/>
    <path d="M 750.492523 270.381038 
L 753.094494 271.246779 
L 754.584606 272.408758 
L 751.985072 271.619606 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f6f394"/>
    <path d="M 741.195198 266.367426 
L 743.793524 267.284521 
L 745.294894 268.666758 
L 742.699247 267.818502 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f0ec91"/>
    <path d="M 680.20786 237.192036 
L 682.780375 237.937289 
L 684.365749 240.038461 
L 681.796155 239.298346 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #baa774"/>
    <path d="M 759.790193 273.996219 
L 762.396245 274.794371 
L 763.87606 275.712179 
L 761.272162 274.997618 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fcfb97"/>
    <path d="M 731.896315 262.033564 
L 734.491302 262.983975 
L 736.004737 264.559967 
L 733.412624 263.669979 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e8e28d"/>
    <path d="M 701.397286 247.085183 
L 703.980381 247.99061 
L 705.5362 250.000063 
L 702.95623 249.123492 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ccbe7d"/>
    <path d="M 722.594558 257.464752 
L 725.186366 258.42897 
L 726.712504 260.169938 
L 724.123712 259.257157 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ded587"/>
    <path d="M 692.089319 242.42661 
L 694.668646 243.278347 
L 696.237874 245.346451 
L 693.661622 244.513449 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c4b379"/>
    <path d="M 713.289248 252.752021 
L 715.877884 253.70942 
L 717.417173 255.584665 
L 714.831639 254.669244 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d6cb83"/>
    <path d="M 753.094494 271.246779 
L 755.698564 272.118058 
L 757.186314 273.200988 
L 754.584606 272.408758 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f6f394"/>
    <path d="M 743.793524 267.284521 
L 746.393902 268.210261 
L 747.892654 269.520983 
L 745.294894 268.666758 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f0ec91"/>
    <path d="M 682.780375 237.937289 
L 685.355426 238.713936 
L 686.937832 240.806579 
L 684.365749 240.038461 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #baa774"/>
    <path d="M 734.491302 262.983975 
L 737.088323 263.946478 
L 738.598932 265.459177 
L 736.004737 264.559967 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e8e28d"/>
    <path d="M 762.396245 274.794371 
L 765.004468 275.595365 
L 766.482215 276.427359 
L 763.87606 275.712179 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fcfb97"/>
    <path d="M 703.980381 247.99061 
L 706.56569 248.919838 
L 708.118379 250.897132 
L 705.5362 250.000063 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ccbe7d"/>
    <path d="M 725.186366 258.42897 
L 727.780224 259.40898 
L 729.303377 261.095477 
L 726.712504 260.169938 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e0d788"/>
    <path d="M 694.668646 243.278347 
L 697.250312 244.157735 
L 698.81644 246.203742 
L 696.237874 245.346451 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c4b379"/>
    <path d="M 715.877884 253.70942 
L 718.468618 254.686475 
L 720.004819 256.516573 
L 717.417173 255.584665 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d6cb83"/>
    <path d="M 746.393902 268.210261 
L 748.996323 269.144438 
L 750.492523 270.381038 
L 747.892654 269.520983 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f0ec91"/>
    <path d="M 755.698564 272.118058 
L 758.304729 272.99472 
L 759.790193 273.996219 
L 757.186314 273.200988 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f6f394"/>
    <path d="M 685.355426 238.713936 
L 687.932972 239.521924 
L 689.512368 241.602653 
L 686.937832 240.806579 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bca975"/>
    <path d="M 737.088323 263.946478 
L 739.687364 264.920827 
L 741.195198 266.367426 
L 738.598932 265.459177 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e8e28d"/>
    <path d="M 765.004468 275.595365 
L 767.614863 276.399116 
L 769.090631 277.143159 
L 766.482215 276.427359 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fcfb97"/>
    <path d="M 706.56569 248.919838 
L 709.153182 249.872655 
L 710.702737 251.814518 
L 708.118379 250.897132 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cec07f"/>
    <path d="M 676.04278 234.395184 
L 678.615576 235.110764 
L 680.20786 237.192036 
L 677.637925 236.478197 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b29c6f"/>
    <path d="M 727.780224 259.40898 
L 730.37611 260.404517 
L 731.896315 262.033564 
L 729.303377 261.095477 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e0d788"/>
    <path d="M 697.250312 244.157735 
L 699.834279 245.064614 
L 701.397286 247.085183 
L 698.81644 246.203742 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c4b379"/>
    <path d="M 718.468618 254.686475 
L 721.061425 255.682926 
L 722.594558 257.464752 
L 720.004819 256.516573 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d8cd84"/>
    <path d="M 748.996323 269.144438 
L 751.600777 270.086835 
L 753.094494 271.246779 
L 750.492523 270.381038 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f0ec91"/>
    <path d="M 758.304729 272.99472 
L 760.912984 273.876606 
L 762.396245 274.794371 
L 759.790193 273.996219 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f8f695"/>
    <path d="M 739.687364 264.920827 
L 742.28841 265.906762 
L 743.793524 267.284521 
L 741.195198 266.367426 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e8e28d"/>
    <path d="M 687.932972 239.521924 
L 690.512969 240.361172 
L 692.089319 242.42661 
L 689.512368 241.602653 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bca975"/>
    <path d="M 709.153182 249.872655 
L 711.742824 250.848827 
L 713.289248 252.752021 
L 710.702737 251.814518 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cec07f"/>
    <path d="M 767.614863 276.399116 
L 770.22743 277.205539 
L 771.701311 277.859581 
L 769.090631 277.143159 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fcfb97"/>
    <path d="M 730.37611 260.404517 
L 732.974004 261.415303 
L 734.491302 262.983975 
L 731.896315 262.033564 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e0d788"/>
    <path d="M 678.615576 235.110764 
L 681.191005 235.861132 
L 682.780375 237.937289 
L 680.20786 237.192036 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b49f70"/>
    <path d="M 699.834279 245.064614 
L 702.420508 245.998797 
L 703.980381 247.99061 
L 701.397286 247.085183 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c4b379"/>
    <path d="M 721.061425 255.682926 
L 723.656276 256.698493 
L 725.186366 258.42897 
L 722.594558 257.464752 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d8cd84"/>
    <path d="M 751.600777 270.086835 
L 754.207257 271.037228 
L 755.698564 272.118058 
L 753.094494 271.246779 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f0ec91"/>
    <path d="M 760.912984 273.876606 
L 763.523326 274.763553 
L 765.004468 275.595365 
L 762.396245 274.794371 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f8f695"/>
    <path d="M 742.28841 265.906762 
L 744.891447 266.904018 
L 746.393902 268.210261 
L 743.793524 267.284521 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eae48e"/>
    <path d="M 690.512969 240.361172 
L 693.095375 241.231563 
L 694.668646 243.278347 
L 692.089319 242.42661 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bca975"/>
    <path d="M 711.742824 250.848827 
L 714.334583 251.848095 
L 715.877884 253.70942 
L 713.289248 252.752021 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cec07f"/>
    <path d="M 732.974004 261.415303 
L 735.573888 262.441044 
L 737.088323 263.946478 
L 734.491302 262.983975 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e2da89"/>
    <path d="M 770.22743 277.205539 
L 772.842168 278.014546 
L 774.314257 278.576624 
L 771.701311 277.859581 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fcfb97"/>
    <path d="M 681.191005 235.861132 
L 683.76902 236.646266 
L 685.355426 238.713936 
L 682.780375 237.937289 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b49f70"/>
    <path d="M 702.420508 245.998797 
L 705.008961 246.960071 
L 706.56569 248.919838 
L 703.980381 247.99061 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c6b67a"/>
    <path d="M 723.656276 256.698493 
L 726.253148 257.732878 
L 727.780224 259.40898 
L 725.186366 258.42897 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d8cd84"/>
    <path d="M 754.207257 271.037228 
L 756.815754 271.995383 
L 758.304729 272.99472 
L 755.698564 272.118058 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f2ee92"/>
    <path d="M 744.891447 266.904018 
L 747.496463 267.912312 
L 748.996323 269.144438 
L 746.393902 268.210261 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eae48e"/>
    <path d="M 763.523326 274.763553 
L 766.135751 275.655393 
L 767.614863 276.399116 
L 765.004468 275.595365 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f8f695"/>
    <path d="M 693.095375 241.231563 
L 695.680146 242.13295 
L 697.250312 244.157735 
L 694.668646 243.278347 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bca975"/>
    <path d="M 714.334583 251.848095 
L 716.928427 252.870178 
L 718.468618 254.686475 
L 715.877884 253.70942 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d0c380"/>
    <path d="M 735.573888 262.441044 
L 738.175741 263.481431 
L 739.687364 264.920827 
L 737.088323 263.946478 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e2da89"/>
    <path d="M 772.842168 278.014546 
L 775.459079 278.826047 
L 776.929472 279.29429 
L 774.314257 278.576624 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fcfb97"/>
    <path d="M 683.76902 236.646266 
L 686.349572 237.466109 
L 687.932972 239.521924 
L 685.355426 238.713936 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b49f70"/>
    <path d="M 726.253148 257.732878 
L 728.852013 258.785763 
L 730.37611 260.404517 
L 727.780224 259.40898 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dad085"/>
    <path d="M 705.008961 246.960071 
L 707.599601 247.948194 
L 709.153182 249.872655 
L 706.56569 248.919838 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c6b67a"/>
    <path d="M 674.443709 232.340675 
L 677.019357 233.057992 
L 678.615576 235.110764 
L 676.04278 234.395184 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ac956c"/>
    <path d="M 756.815754 271.995383 
L 759.426262 272.961061 
L 760.912984 273.876606 
L 758.304729 272.99472 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f2ee92"/>
    <path d="M 747.496463 267.912312 
L 750.103445 268.931355 
L 751.600777 270.086835 
L 748.996323 269.144438 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eae48e"/>
    <path d="M 766.135751 275.655393 
L 768.750258 276.551952 
L 770.22743 277.205539 
L 767.614863 276.399116 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f8f695"/>
    <path d="M 716.928427 252.870178 
L 719.524326 253.914772 
L 721.061425 255.682926 
L 718.468618 254.686475 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d0c380"/>
    <path d="M 695.680146 242.13295 
L 698.267239 243.065153 
L 699.834279 245.064614 
L 697.250312 244.157735 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bca975"/>
    <path d="M 738.175741 263.481431 
L 740.779546 264.536142 
L 742.28841 265.906762 
L 739.687364 264.920827 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e2da89"/>
    <path d="M 775.459079 278.826047 
L 778.078162 279.639951 
L 779.546959 280.01258 
L 776.929472 279.29429 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 686.349572 237.466109 
L 688.932616 238.320566 
L 690.512969 240.361172 
L 687.932972 239.521924 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b49f70"/>
    <path d="M 728.852013 258.785763 
L 731.452848 259.856813 
L 732.974004 261.415303 
L 730.37611 260.404517 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dad085"/>
    <path d="M 707.599601 247.948194 
L 710.19239 248.962896 
L 711.742824 250.848827 
L 709.153182 249.872655 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c6b67a"/>
    <path d="M 677.019357 233.057992 
L 679.597692 233.813449 
L 681.191005 235.861132 
L 678.615576 235.110764 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ac956c"/>
    <path d="M 759.426262 272.961061 
L 762.038772 273.934017 
L 763.523326 274.763553 
L 760.912984 273.876606 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f2ee92"/>
    <path d="M 750.103445 268.931355 
L 752.71238 269.960847 
L 754.207257 271.037228 
L 751.600777 270.086835 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ece78f"/>
    <path d="M 719.524326 253.914772 
L 722.122246 254.981549 
L 723.656276 256.698493 
L 721.061425 255.682926 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d0c380"/>
    <path d="M 768.750258 276.551952 
L 771.366842 277.453055 
L 772.842168 278.014546 
L 770.22743 277.205539 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f8f695"/>
    <path d="M 698.267239 243.065153 
L 700.856612 244.027963 
L 702.420508 245.998797 
L 699.834279 245.064614 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #beac76"/>
    <path d="M 740.779546 264.536142 
L 743.385283 265.604839 
L 744.891447 266.904018 
L 742.28841 265.906762 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e4dc8a"/>
    <path d="M 731.452848 259.856813 
L 734.055629 260.945673 
L 735.573888 262.441044 
L 732.974004 261.415303 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dad085"/>
    <path d="M 778.078162 279.639951 
L 780.699419 280.456164 
L 782.166722 280.731494 
L 779.546959 280.01258 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 688.932616 238.320566 
L 691.518101 239.209511 
L 693.095375 241.231563 
L 690.512969 240.361172 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b49f70"/>
    <path d="M 710.19239 248.962896 
L 712.78729 250.003881 
L 714.334583 251.848095 
L 711.742824 250.848827 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c8b97b"/>
    <path d="M 762.038772 273.934017 
L 764.653279 274.913995 
L 766.135751 275.655393 
L 763.523326 274.763553 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f2ee92"/>
    <path d="M 752.71238 269.960847 
L 755.323257 271.000476 
L 756.815754 271.995383 
L 754.207257 271.037228 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ece78f"/>
    <path d="M 679.597692 233.813449 
L 682.178664 234.607021 
L 683.76902 236.646266 
L 681.191005 235.861132 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ac956c"/>
    <path d="M 722.122246 254.981549 
L 724.722159 256.070159 
L 726.253148 257.732878 
L 723.656276 256.698493 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d2c581"/>
    <path d="M 700.856612 244.027963 
L 703.44822 245.021138 
L 705.008961 246.960071 
L 702.420508 245.998797 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #beac76"/>
    <path d="M 743.385283 265.604839 
L 745.992936 266.687171 
L 747.496463 267.912312 
L 744.891447 266.904018 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e4dc8a"/>
    <path d="M 771.366842 277.453055 
L 773.985502 278.35852 
L 775.459079 278.826047 
L 772.842168 278.014546 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f8f695"/>
    <path d="M 734.055629 260.945673 
L 736.66033 262.051973 
L 738.175741 263.481431 
L 735.573888 262.441044 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dcd286"/>
    <path d="M 712.78729 250.003881 
L 715.384264 251.070827 
L 716.928427 252.870178 
L 714.334583 251.848095 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c8b97b"/>
    <path d="M 691.518101 239.209511 
L 694.105981 240.132777 
L 695.680146 242.13295 
L 693.095375 241.231563 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b49f70"/>
    <path d="M 780.699419 280.456164 
L 783.32285 281.274592 
L 784.788763 281.451034 
L 782.166722 280.731494 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 755.323257 271.000476 
L 757.936064 272.049922 
L 759.426262 272.961061 
L 756.815754 271.995383 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ece78f"/>
    <path d="M 764.653279 274.913995 
L 767.269777 275.900737 
L 768.750258 276.551952 
L 766.135751 275.655393 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f4f193"/>
    <path d="M 724.722159 256.070159 
L 727.324033 257.180231 
L 728.852013 258.785763 
L 726.253148 257.732878 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d2c581"/>
    <path d="M 682.178664 234.607021 
L 684.762219 235.438644 
L 686.349572 237.466109 
L 683.76902 236.646266 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ac956c"/>
    <path d="M 745.992936 266.687171 
L 748.602488 267.782775 
L 750.103445 268.931355 
L 747.496463 267.912312 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e6df8b"/>
    <path d="M 703.44822 245.021138 
L 706.04202 246.044404 
L 707.599601 247.948194 
L 705.008961 246.960071 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #beac76"/>
    <path d="M 773.985502 278.35852 
L 776.606236 279.268163 
L 778.078162 279.639951 
L 775.459079 278.826047 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #faf996"/>
    <path d="M 672.840773 230.318121 
L 675.419259 231.037172 
L 677.019357 233.057992 
L 674.443709 232.340675 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a48b68"/>
    <path d="M 736.66033 262.051973 
L 739.26693 263.175322 
L 740.779546 264.536142 
L 738.175741 263.481431 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dcd286"/>
    <path d="M 715.384264 251.070827 
L 717.983276 252.163385 
L 719.524326 253.914772 
L 716.928427 252.870178 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c8b97b"/>
    <path d="M 694.105981 240.132777 
L 696.696206 241.090167 
L 698.267239 243.065153 
L 695.680146 242.13295 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b6a272"/>
    <path d="M 783.32285 281.274592 
L 785.948458 282.095136 
L 787.413085 282.171199 
L 784.788763 281.451034 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 757.936064 272.049922 
L 760.550793 273.108854 
L 762.038772 273.934017 
L 759.426262 272.961061 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eee990"/>
    <path d="M 727.324033 257.180231 
L 729.927839 258.311373 
L 731.452848 259.856813 
L 728.852013 258.785763 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d4c882"/>
    <path d="M 767.269777 275.900737 
L 769.88826 276.893976 
L 771.366842 277.453055 
L 768.750258 276.551952 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f4f193"/>
    <path d="M 748.602488 267.782775 
L 751.213923 268.891272 
L 752.71238 269.960847 
L 750.103445 268.931355 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e6df8b"/>
    <path d="M 684.762219 235.438644 
L 687.348306 236.308217 
L 688.932616 238.320566 
L 686.349572 237.466109 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ac956c"/>
    <path d="M 706.04202 246.044404 
L 708.63797 247.097458 
L 710.19239 248.962896 
L 707.599601 247.948194 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c0ae77"/>
    <path d="M 776.606236 279.268163 
L 779.229043 280.181794 
L 780.699419 280.456164 
L 778.078162 279.639951 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #faf996"/>
    <path d="M 739.26693 263.175322 
L 741.875406 264.315316 
L 743.385283 265.604839 
L 740.779546 264.536142 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ded587"/>
    <path d="M 675.419259 231.037172 
L 678.000492 231.797687 
L 679.597692 233.813449 
L 677.019357 233.057992 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a48b68"/>
    <path d="M 717.983276 252.163385 
L 720.58429 253.281179 
L 722.122246 254.981549 
L 719.524326 253.914772 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cabb7c"/>
    <path d="M 696.696206 241.090167 
L 699.288728 242.081444 
L 700.856612 244.027963 
L 698.267239 243.065153 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b6a272"/>
    <path d="M 729.927839 258.311373 
L 732.533549 259.46317 
L 734.055629 260.945673 
L 731.452848 259.856813 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d4c882"/>
    <path d="M 785.948458 282.095136 
L 788.576242 282.917699 
L 790.039691 282.891991 
L 787.413085 282.171199 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 760.550793 273.108854 
L 763.167432 274.176934 
L 764.653279 274.913995 
L 762.038772 273.934017 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eee990"/>
    <path d="M 769.88826 276.893976 
L 772.508724 277.89344 
L 773.985502 278.35852 
L 771.366842 277.453055 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f4f193"/>
    <path d="M 751.213923 268.891272 
L 753.827225 270.012273 
L 755.323257 271.000476 
L 752.71238 269.960847 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e6df8b"/>
    <path d="M 708.63797 247.097458 
L 711.236028 248.179966 
L 712.78729 250.003881 
L 710.19239 248.962896 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c0ae77"/>
    <path d="M 687.348306 236.308217 
L 689.93687 237.215595 
L 691.518101 239.209511 
L 688.932616 238.320566 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ac956c"/>
    <path d="M 741.875406 264.315316 
L 744.485737 265.471532 
L 745.992936 266.687171 
L 743.385283 265.604839 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ded587"/>
    <path d="M 779.229043 280.181794 
L 781.853921 281.099224 
L 783.32285 281.274592 
L 780.699419 280.456164 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #faf996"/>
    <path d="M 720.58429 253.281179 
L 723.187269 254.423809 
L 724.722159 256.070159 
L 722.122246 254.981549 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cabb7c"/>
    <path d="M 678.000492 231.797687 
L 680.584412 232.599639 
L 682.178664 234.607021 
L 679.597692 233.813449 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a48b68"/>
    <path d="M 699.288728 242.081444 
L 701.883499 243.106341 
L 703.44822 245.021138 
L 700.856612 244.027963 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b6a272"/>
    <path d="M 732.533549 259.46317 
L 735.141133 260.635187 
L 736.66033 262.051973 
L 734.055629 260.945673 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d6cb83"/>
    <path d="M 763.167432 274.176934 
L 765.785973 275.253814 
L 767.269777 275.900737 
L 764.653279 274.913995 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eee990"/>
    <path d="M 753.827225 270.012273 
L 756.442381 271.145377 
L 757.936064 272.049922 
L 755.323257 271.000476 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e8e28d"/>
    <path d="M 788.576242 282.917699 
L 791.206205 283.74218 
L 792.668585 283.613411 
L 790.039691 282.891991 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 772.508724 277.89344 
L 775.131164 278.89885 
L 776.606236 279.268163 
L 773.985502 278.35852 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f6f394"/>
    <path d="M 711.236028 248.179966 
L 713.836151 249.291564 
L 715.384264 251.070827 
L 712.78729 250.003881 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c0ae77"/>
    <path d="M 689.93687 237.215595 
L 692.527859 238.1606 
L 694.105981 240.132777 
L 691.518101 239.209511 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ae976d"/>
    <path d="M 744.485737 265.471532 
L 747.097901 266.643532 
L 748.602488 267.782775 
L 745.992936 266.687171 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e0d788"/>
    <path d="M 723.187269 254.423809 
L 725.792179 255.59085 
L 727.324033 257.180231 
L 724.722159 256.070159 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ccbe7d"/>
    <path d="M 781.853921 281.099224 
L 784.480871 282.020255 
L 785.948458 282.095136 
L 783.32285 281.274592 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #faf996"/>
    <path d="M 680.584412 232.599639 
L 683.170964 233.442959 
L 684.762219 235.438644 
L 682.178664 234.607021 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a48b68"/>
    <path d="M 701.883499 243.106341 
L 704.480471 244.164552 
L 706.04202 246.044404 
L 703.44822 245.021138 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b8a473"/>
    <path d="M 735.141133 260.635187 
L 737.750564 261.82697 
L 739.26693 263.175322 
L 736.66033 262.051973 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d6cb83"/>
    <path d="M 671.234034 228.33096 
L 673.815347 229.051739 
L 675.419259 231.037172 
L 672.840773 230.318121 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9c8064"/>
    <path d="M 765.785973 275.253814 
L 768.406408 276.339138 
L 769.88826 276.893976 
L 767.269777 275.900737 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f0ec91"/>
    <path d="M 756.442381 271.145377 
L 759.059376 272.290169 
L 760.550793 273.108854 
L 757.936064 272.049922 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e8e28d"/>
    <path d="M 713.836151 249.291564 
L 716.438296 250.431858 
L 717.983276 252.163385 
L 715.384264 251.070827 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c2b178"/>
    <path d="M 775.131164 278.89885 
L 777.755576 279.909922 
L 779.229043 280.181794 
L 776.606236 279.268163 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f6f394"/>
    <path d="M 791.206205 283.74218 
L 793.838349 284.568479 
L 795.299769 284.335459 
L 792.668585 283.613411 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 692.527859 238.1606 
L 695.121218 239.14301 
L 696.696206 241.090167 
L 694.105981 240.132777 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ae976d"/>
    <path d="M 747.097901 266.643532 
L 749.71188 267.830862 
L 751.213923 268.891272 
L 748.602488 267.782775 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e0d788"/>
    <path d="M 725.792179 255.59085 
L 728.398986 256.78185 
L 729.927839 258.311373 
L 727.324033 257.180231 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ccbe7d"/>
    <path d="M 784.480871 282.020255 
L 787.10989 282.944691 
L 788.576242 282.917699 
L 785.948458 282.095136 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #faf996"/>
    <path d="M 704.480471 244.164552 
L 707.079595 245.255741 
L 708.63797 247.097458 
L 706.04202 246.044404 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b8a473"/>
    <path d="M 737.750564 261.82697 
L 740.361817 263.038044 
L 741.875406 264.315316 
L 739.26693 263.175322 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d8cd84"/>
    <path d="M 683.170964 233.442959 
L 685.76009 234.327535 
L 687.348306 236.308217 
L 684.762219 235.438644 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a48b68"/>
    <path d="M 768.406408 276.339138 
L 771.028729 277.432541 
L 772.508724 277.89344 
L 769.88826 276.893976 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f0ec91"/>
    <path d="M 759.059376 272.290169 
L 761.678197 273.446225 
L 763.167432 274.176934 
L 760.550793 273.108854 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eae48e"/>
    <path d="M 716.438296 250.431858 
L 719.042425 251.600425 
L 720.58429 253.281179 
L 717.983276 252.163385 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c2b178"/>
    <path d="M 673.815347 229.051739 
L 676.399465 229.817276 
L 678.000492 231.797687 
L 675.419259 231.037172 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9c8064"/>
    <path d="M 777.755576 279.909922 
L 780.381958 280.926369 
L 781.853921 281.099224 
L 779.229043 280.181794 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f6f394"/>
    <path d="M 749.71188 267.830862 
L 752.327653 269.033052 
L 753.827225 270.012273 
L 751.213923 268.891272 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e2da89"/>
    <path d="M 728.398986 256.78185 
L 731.007655 257.996337 
L 732.533549 259.46317 
L 729.927839 258.311373 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cec07f"/>
    <path d="M 695.121218 239.14301 
L 697.716895 240.162568 
L 699.288728 242.081444 
L 696.696206 241.090167 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ae976d"/>
    <path d="M 793.838349 284.568479 
L 796.472675 285.396493 
L 797.933246 285.058137 
L 795.299769 284.335459 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 740.361817 263.038044 
L 742.974864 264.267914 
L 744.485737 265.471532 
L 741.875406 264.315316 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d8cd84"/>
    <path d="M 787.10989 282.944691 
L 789.740981 283.87233 
L 791.206205 283.74218 
L 788.576242 282.917699 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #faf996"/>
    <path d="M 707.079595 245.255741 
L 709.680824 246.379534 
L 711.236028 248.179966 
L 708.63797 247.097458 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b8a473"/>
    <path d="M 685.76009 234.327535 
L 688.35173 235.253211 
L 689.93687 237.215595 
L 687.348306 236.308217 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a68d69"/>
    <path d="M 761.678197 273.446225 
L 764.298833 274.613108 
L 765.785973 275.253814 
L 763.167432 274.176934 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eae48e"/>
    <path d="M 771.028729 277.432541 
L 773.652929 278.533651 
L 775.131164 278.89885 
L 772.508724 277.89344 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f2ee92"/>
    <path d="M 719.042425 251.600425 
L 721.648495 252.796814 
L 723.187269 254.423809 
L 720.58429 253.281179 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c4b379"/>
    <path d="M 752.327653 269.033052 
L 754.945202 270.24962 
L 756.442381 271.145377 
L 753.827225 270.012273 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e2da89"/>
    <path d="M 676.399465 229.817276 
L 678.986325 230.627544 
L 680.584412 232.599639 
L 678.000492 231.797687 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9c8064"/>
    <path d="M 780.381958 280.926369 
L 783.010307 281.947897 
L 784.480871 282.020255 
L 781.853921 281.099224 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f6f394"/>
    <path d="M 731.007655 257.996337 
L 733.618155 259.233811 
L 735.141133 260.635187 
L 732.533549 259.46317 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cec07f"/>
    <path d="M 697.716895 240.162568 
L 700.314836 241.218975 
L 701.883499 243.106341 
L 699.288728 242.081444 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b09a6e"/>
    <path d="M 796.472675 285.396493 
L 799.109186 286.226118 
L 800.569019 285.781445 
L 797.933246 285.058137 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 742.974864 264.267914 
L 745.589682 265.516069 
L 747.097901 266.643532 
L 744.485737 265.471532 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dad085"/>
    <path d="M 709.680824 246.379534 
L 712.284111 247.535526 
L 713.836151 249.291564 
L 711.236028 248.179966 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #baa774"/>
    <path d="M 789.740981 283.87233 
L 792.374144 284.802968 
L 793.838349 284.568479 
L 791.206205 283.74218 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fcfb97"/>
    <path d="M 688.35173 235.253211 
L 690.945827 236.219789 
L 692.527859 238.1606 
L 689.93687 237.215595 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a68d69"/>
    <path d="M 721.648495 252.796814 
L 724.256466 254.020545 
L 725.792179 255.59085 
L 723.187269 254.423809 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c6b67a"/>
    <path d="M 764.298833 274.613108 
L 766.921271 275.790372 
L 768.406408 276.339138 
L 765.785973 275.253814 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ece78f"/>
    <path d="M 773.652929 278.533651 
L 776.279003 279.64209 
L 777.755576 279.909922 
L 775.131164 278.89885 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f2ee92"/>
    <path d="M 754.945202 270.24962 
L 757.564512 271.480068 
L 759.059376 272.290169 
L 756.442381 271.145377 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e4dc8a"/>
    <path d="M 733.618155 259.233811 
L 736.230453 260.493751 
L 737.750564 261.82697 
L 735.141133 260.635187 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d0c380"/>
    <path d="M 783.010307 281.947897 
L 785.64062 282.974206 
L 787.10989 282.944691 
L 784.480871 282.020255 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f8f695"/>
    <path d="M 678.986325 230.627544 
L 681.575865 231.482465 
L 683.170964 233.442959 
L 680.584412 232.599639 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9c8064"/>
    <path d="M 700.314836 241.218975 
L 702.914988 242.311898 
L 704.480471 244.164552 
L 701.883499 243.106341 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b09a6e"/>
    <path d="M 745.589682 265.516069 
L 748.206246 266.781978 
L 749.71188 267.830862 
L 747.097901 266.643532 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dad085"/>
    <path d="M 669.62356 226.382608 
L 672.207685 227.10511 
L 673.815347 229.051739 
L 671.234034 228.33096 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #94765f"/>
    <path d="M 712.284111 247.535526 
L 714.889409 248.72328 
L 716.438296 250.431858 
L 713.836151 249.291564 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #baa774"/>
    <path d="M 799.109186 286.226118 
L 801.747885 287.057249 
L 803.207091 286.505383 
L 800.569019 285.781445 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 724.256466 254.020545 
L 726.866301 255.27111 
L 728.398986 256.78185 
L 725.792179 255.59085 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c6b67a"/>
    <path d="M 792.374144 284.802968 
L 795.009378 285.7364 
L 796.472675 285.396493 
L 793.838349 284.568479 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fcfb97"/>
    <path d="M 766.921271 275.790372 
L 769.545503 276.977561 
L 771.028729 277.432541 
L 768.406408 276.339138 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ece78f"/>
    <path d="M 690.945827 236.219789 
L 693.542323 237.227029 
L 695.121218 239.14301 
L 692.527859 238.1606 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a68d69"/>
    <path d="M 776.279003 279.64209 
L 778.906945 280.757471 
L 780.381958 280.926369 
L 777.755576 279.909922 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f2ee92"/>
    <path d="M 757.564512 271.480068 
L 760.185564 272.723884 
L 761.678197 273.446225 
L 759.059376 272.290169 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e4dc8a"/>
    <path d="M 736.230453 260.493751 
L 738.844518 261.775615 
L 740.361817 263.038044 
L 737.750564 261.82697 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d2c581"/>
    <path d="M 702.914988 242.311898 
L 705.517296 243.440963 
L 707.079595 245.255741 
L 704.480471 244.164552 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b09a6e"/>
    <path d="M 785.64062 282.974206 
L 788.272897 284.004996 
L 789.740981 283.87233 
L 787.10989 282.944691 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f8f695"/>
    <path d="M 681.575865 231.482465 
L 684.168023 232.381918 
L 685.76009 234.327535 
L 683.170964 233.442959 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9e8365"/>
    <path d="M 748.206246 266.781978 
L 750.824534 268.065091 
L 752.327653 269.033052 
L 749.71188 267.830862 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dcd286"/>
    <path d="M 714.889409 248.72328 
L 717.496672 249.942323 
L 719.042425 251.600425 
L 716.438296 250.431858 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bca975"/>
    <path d="M 672.207685 227.10511 
L 674.794675 227.875631 
L 676.399465 229.817276 
L 673.815347 229.051739 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #94765f"/>
    <path d="M 726.866301 255.27111 
L 729.47796 256.547974 
L 731.007655 257.996337 
L 728.398986 256.78185 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c8b97b"/>
    <path d="M 801.747885 287.057249 
L 804.388773 287.889782 
L 805.847465 287.229954 
L 803.207091 286.505383 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 769.545503 276.977561 
L 772.171518 278.174209 
L 773.652929 278.533651 
L 771.028729 277.432541 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eee990"/>
    <path d="M 693.542323 237.227029 
L 696.141157 238.274649 
L 697.716895 240.162568 
L 695.121218 239.14301 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a68d69"/>
    <path d="M 738.844518 261.775615 
L 741.46032 263.078835 
L 742.974864 264.267914 
L 740.361817 263.038044 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d2c581"/>
    <path d="M 778.906945 280.757471 
L 781.53675 281.879402 
L 783.010307 281.947897 
L 780.381958 280.926369 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f4f193"/>
    <path d="M 795.009378 285.7364 
L 797.646687 286.672417 
L 799.109186 286.226118 
L 796.472675 285.396493 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fcfb97"/>
    <path d="M 760.185564 272.723884 
L 762.808345 273.980544 
L 764.298833 274.613108 
L 761.678197 273.446225 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e6df8b"/>
    <path d="M 705.517296 243.440963 
L 708.121709 244.60576 
L 709.680824 246.379534 
L 707.079595 245.255741 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b29c6f"/>
    <path d="M 750.824534 268.065091 
L 753.444523 269.364844 
L 754.945202 270.24962 
L 752.327653 269.033052 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ded587"/>
    <path d="M 788.272897 284.004996 
L 790.907137 285.039959 
L 792.374144 284.802968 
L 789.740981 283.87233 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f8f695"/>
    <path d="M 717.496672 249.942323 
L 720.105854 251.192155 
L 721.648495 252.796814 
L 719.042425 251.600425 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #beac76"/>
    <path d="M 684.168023 232.381918 
L 686.762735 233.325735 
L 688.35173 235.253211 
L 685.76009 234.327535 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9e8365"/>
    <path d="M 729.47796 256.547974 
L 732.091406 257.850576 
L 733.618155 259.233811 
L 731.007655 257.996337 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c8b97b"/>
    <path d="M 772.171518 278.174209 
L 774.799309 279.379841 
L 776.279003 279.64209 
L 773.652929 278.533651 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eee990"/>
    <path d="M 674.794675 227.875631 
L 677.384463 228.694139 
L 678.986325 230.627544 
L 676.399465 229.817276 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #94765f"/>
    <path d="M 741.46032 263.078835 
L 744.07783 264.402825 
L 745.589682 265.516069 
L 742.974864 264.267914 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d4c882"/>
    <path d="M 762.808345 273.980544 
L 765.432839 275.249512 
L 766.921271 275.790372 
L 764.298833 274.613108 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e6df8b"/>
    <path d="M 804.388773 287.889782 
L 807.031855 288.723609 
L 808.490145 287.955157 
L 805.847465 287.229954 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 696.141157 238.274649 
L 698.742272 239.362323 
L 700.314836 241.218975 
L 697.716895 240.162568 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a8906a"/>
    <path d="M 781.53675 281.879402 
L 784.168415 283.007485 
L 785.64062 282.974206 
L 783.010307 281.947897 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f4f193"/>
    <path d="M 797.646687 286.672417 
L 800.286072 287.610807 
L 801.747885 287.057249 
L 799.109186 286.226118 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fcfb97"/>
    <path d="M 708.121709 244.60576 
L 710.728175 245.805844 
L 712.284111 247.535526 
L 709.680824 246.379534 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b29c6f"/>
    <path d="M 753.444523 269.364844 
L 756.066194 270.680656 
L 757.564512 271.480068 
L 754.945202 270.24962 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ded587"/>
    <path d="M 720.105854 251.192155 
L 722.716911 252.472239 
L 724.256466 254.020545 
L 721.648495 252.796814 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #beac76"/>
    <path d="M 790.907137 285.039959 
L 793.54334 286.078785 
L 795.009378 285.7364 
L 792.374144 284.802968 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #faf996"/>
    <path d="M 732.091406 257.850576 
L 734.706602 259.178328 
L 736.230453 260.493751 
L 733.618155 259.233811 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cabb7c"/>
    <path d="M 686.762735 233.325735 
L 689.359937 234.3137 
L 690.945827 236.219789 
L 688.35173 235.253211 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9e8365"/>
    <path d="M 744.07783 264.402825 
L 746.697021 265.746979 
L 748.206246 266.781978 
L 745.589682 265.516069 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d6cb83"/>
    <path d="M 774.799309 279.379841 
L 777.428867 280.593973 
L 778.906945 280.757471 
L 776.279003 279.64209 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f0ec91"/>
    <path d="M 765.432839 275.249512 
L 768.059034 276.530239 
L 769.545503 276.977561 
L 766.921271 275.790372 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e8e28d"/>
    <path d="M 698.742272 239.362323 
L 701.345609 240.489687 
L 702.914988 242.311898 
L 700.314836 241.218975 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a8906a"/>
    <path d="M 677.384463 228.694139 
L 679.976981 229.560554 
L 681.575865 231.482465 
L 678.986325 230.627544 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #967960"/>
    <path d="M 784.168415 283.007485 
L 786.801938 284.141315 
L 788.272897 284.004996 
L 785.64062 282.974206 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f6f394"/>
    <path d="M 807.031855 288.723609 
L 809.677132 289.558624 
L 811.135133 288.680993 
L 808.490145 287.955157 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 756.066194 270.680656 
L 758.689525 272.011929 
L 760.185564 272.723884 
L 757.564512 271.480068 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e0d788"/>
    <path d="M 710.728175 245.805844 
L 713.336641 247.04073 
L 714.889409 248.72328 
L 712.284111 247.535526 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b49f70"/>
    <path d="M 800.286072 287.610807 
L 802.927535 288.55136 
L 804.388773 287.889782 
L 801.747885 287.057249 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fcfb97"/>
    <path d="M 668.009423 224.47646 
L 670.596344 225.200678 
L 672.207685 227.10511 
L 669.62356 226.382608 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8e6e5c"/>
    <path d="M 722.716911 252.472239 
L 725.329799 253.782011 
L 726.866301 255.27111 
L 724.256466 254.020545 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c0ae77"/>
    <path d="M 734.706602 259.178328 
L 737.323514 260.530618 
L 738.844518 261.775615 
L 736.230453 260.493751 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ccbe7d"/>
    <path d="M 793.54334 286.078785 
L 796.181507 287.121161 
L 797.646687 286.672417 
L 795.009378 285.7364 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #faf996"/>
    <path d="M 689.359937 234.3137 
L 691.959566 235.345554 
L 693.542323 237.227029 
L 690.945827 236.219789 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9e8365"/>
    <path d="M 746.697021 265.746979 
L 749.317866 267.110666 
L 750.824534 268.065091 
L 748.206246 266.781978 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d6cb83"/>
    <path d="M 777.428867 280.593973 
L 780.060186 281.816116 
L 781.53675 281.879402 
L 778.906945 280.757471 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f0ec91"/>
    <path d="M 768.059034 276.530239 
L 770.686918 277.822165 
L 772.171518 278.174209 
L 769.545503 276.977561 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eae48e"/>
    <path d="M 701.345609 240.489687 
L 703.951111 241.656332 
L 705.517296 243.440963 
L 702.914988 242.311898 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #aa926b"/>
    <path d="M 786.801938 284.141315 
L 789.437315 285.280483 
L 790.907137 285.039959 
L 788.272897 284.004996 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f6f394"/>
    <path d="M 758.689525 272.011929 
L 761.3145 273.358049 
L 762.808345 273.980544 
L 760.185564 272.723884 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e2da89"/>
    <path d="M 679.976981 229.560554 
L 682.572163 230.474744 
L 684.168023 232.381918 
L 681.575865 231.482465 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #967960"/>
    <path d="M 713.336641 247.04073 
L 715.947057 248.309901 
L 717.496672 249.942323 
L 714.889409 248.72328 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b6a272"/>
    <path d="M 725.329799 253.782011 
L 727.944475 255.120877 
L 729.47796 256.547974 
L 726.866301 255.27111 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c2b178"/>
    <path d="M 809.677132 289.558624 
L 812.32461 290.394718 
L 813.782432 289.407464 
L 811.135133 288.680993 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 737.323514 260.530618 
L 739.942108 261.906808 
L 741.46032 263.078835 
L 738.844518 261.775615 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ccbe7d"/>
    <path d="M 802.927535 288.55136 
L 805.571078 289.493861 
L 807.031855 288.723609 
L 804.388773 287.889782 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 670.596344 225.200678 
L 673.186191 225.976138 
L 674.794675 227.875631 
L 672.207685 227.10511 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8e6e5c"/>
    <path d="M 749.317866 267.110666 
L 751.940339 268.493242 
L 753.444523 269.364844 
L 750.824534 268.065091 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d8cd84"/>
    <path d="M 796.181507 287.121161 
L 798.821638 288.166771 
L 800.286072 287.610807 
L 797.646687 286.672417 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #faf996"/>
    <path d="M 691.959566 235.345554 
L 694.561559 236.420989 
L 696.141157 238.274649 
L 693.542323 237.227029 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a08566"/>
    <path d="M 770.686918 277.822165 
L 773.316481 279.124719 
L 774.799309 279.379841 
L 772.171518 278.174209 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eae48e"/>
    <path d="M 780.060186 281.816116 
L 782.693261 283.045768 
L 784.168415 283.007485 
L 781.53675 281.879402 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f2ee92"/>
    <path d="M 703.951111 241.656332 
L 706.558718 242.861811 
L 708.121709 244.60576 
L 705.517296 243.440963 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #aa926b"/>
    <path d="M 761.3145 273.358049 
L 763.941101 274.718391 
L 765.432839 275.249512 
L 762.808345 273.980544 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e2da89"/>
    <path d="M 789.437315 285.280483 
L 792.074547 286.424576 
L 793.54334 286.078785 
L 790.907137 285.039959 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f8f695"/>
    <path d="M 715.947057 248.309901 
L 718.559371 249.612802 
L 720.105854 251.192155 
L 717.496672 249.942323 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b6a272"/>
    <path d="M 727.944475 255.120877 
L 730.560897 256.48821 
L 732.091406 257.850576 
L 729.47796 256.547974 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c2b178"/>
    <path d="M 682.572163 230.474744 
L 685.169939 231.436526 
L 686.762735 233.325735 
L 684.168023 232.381918 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #967960"/>
    <path d="M 739.942108 261.906808 
L 742.562349 263.306237 
L 744.07783 264.402825 
L 741.46032 263.078835 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cec07f"/>
    <path d="M 751.940339 268.493242 
L 754.564417 269.894039 
L 756.066194 270.680656 
L 753.444523 269.364844 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dad085"/>
    <path d="M 805.571078 289.493861 
L 808.216707 290.438095 
L 809.677132 289.558624 
L 807.031855 288.723609 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 812.32461 290.394718 
L 814.97429 291.231784 
L 816.432045 290.13457 
L 813.782432 289.407464 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 673.186191 225.976138 
L 675.778892 226.802807 
L 677.384463 228.694139 
L 674.794675 227.875631 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8e6e5c"/>
    <path d="M 798.821638 288.166771 
L 801.463737 289.215294 
L 802.927535 288.55136 
L 800.286072 287.610807 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fcfb97"/>
    <path d="M 773.316481 279.124719 
L 775.947711 280.437321 
L 777.428867 280.593973 
L 774.799309 279.379841 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ece78f"/>
    <path d="M 694.561559 236.420989 
L 697.165851 237.539654 
L 698.742272 239.362323 
L 696.141157 238.274649 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a08566"/>
    <path d="M 782.693261 283.045768 
L 785.328088 284.282426 
L 786.801938 284.141315 
L 784.168415 283.007485 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f2ee92"/>
    <path d="M 763.941101 274.718391 
L 766.569312 276.092313 
L 768.059034 276.530239 
L 765.432839 275.249512 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e4dc8a"/>
    <path d="M 706.558718 242.861811 
L 709.168374 244.105636 
L 710.728175 245.805844 
L 708.121709 244.60576 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ac956c"/>
    <path d="M 718.559371 249.612802 
L 721.173535 250.948844 
L 722.716911 252.472239 
L 720.105854 251.192155 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b8a473"/>
    <path d="M 730.560897 256.48821 
L 733.179023 257.883358 
L 734.706602 259.178328 
L 732.091406 257.850576 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c4b379"/>
    <path d="M 792.074547 286.424576 
L 794.713632 287.573173 
L 796.181507 287.121161 
L 793.54334 286.078785 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f8f695"/>
    <path d="M 742.562349 263.306237 
L 745.184207 264.72822 
L 746.697021 265.746979 
L 744.07783 264.402825 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d0c380"/>
    <path d="M 685.169939 231.436526 
L 687.770242 232.445671 
L 689.359937 234.3137 
L 686.762735 233.325735 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #967960"/>
    <path d="M 754.564417 269.894039 
L 757.190075 271.312374 
L 758.689525 272.011929 
L 756.066194 270.680656 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dcd286"/>
    <path d="M 775.947711 280.437321 
L 778.580602 281.75938 
L 780.060186 281.816116 
L 777.428867 280.593973 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eee990"/>
    <path d="M 808.216707 290.438095 
L 810.864423 291.383846 
L 812.32461 290.394718 
L 809.677132 289.558624 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 697.165851 237.539654 
L 699.772379 238.701151 
L 701.345609 240.489687 
L 698.742272 239.362323 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a28867"/>
    <path d="M 785.328088 284.282426 
L 787.964663 285.525575 
L 789.437315 285.280483 
L 786.801938 284.141315 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f4f193"/>
    <path d="M 814.97429 291.231784 
L 817.626177 292.069712 
L 819.083976 290.862311 
L 816.432045 290.13457 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 801.463737 289.215294 
L 804.107805 290.266411 
L 805.571078 289.493861 
L 802.927535 288.55136 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fcfb97"/>
    <path d="M 675.778892 226.802807 
L 678.374377 227.680597 
L 679.976981 229.560554 
L 677.384463 228.694139 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8e6e5c"/>
    <path d="M 766.569312 276.092313 
L 769.199119 277.479161 
L 770.686918 277.822165 
L 768.059034 276.530239 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e6df8b"/>
    <path d="M 709.168374 244.105636 
L 711.780023 245.387279 
L 713.336641 247.04073 
L 710.728175 245.805844 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ae976d"/>
    <path d="M 721.173535 250.948844 
L 723.7895 252.317406 
L 725.329799 253.782011 
L 722.716911 252.472239 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #baa774"/>
    <path d="M 733.179023 257.883358 
L 735.798816 259.305638 
L 737.323514 260.530618 
L 734.706602 259.178328 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c6b67a"/>
    <path d="M 745.184207 264.72822 
L 747.80765 266.172051 
L 749.317866 267.110666 
L 746.697021 265.746979 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d2c581"/>
    <path d="M 666.391698 222.615882 
L 668.981396 223.34181 
L 670.596344 225.200678 
L 668.009423 224.47646 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #866458"/>
    <path d="M 794.713632 287.573173 
L 797.354572 288.725853 
L 798.821638 288.166771 
L 796.181507 287.121161 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f8f695"/>
    <path d="M 757.190075 271.312374 
L 759.817293 272.747547 
L 761.3145 273.358049 
L 758.689525 272.011929 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dcd286"/>
    <path d="M 687.770242 232.445671 
L 690.373003 233.501895 
L 691.959566 235.345554 
L 689.359937 234.3137 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #987b61"/>
    <path d="M 778.580602 281.75938 
L 781.215146 283.090298 
L 782.693261 283.045768 
L 780.060186 281.816116 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eee990"/>
    <path d="M 699.772379 238.701151 
L 702.381079 239.905039 
L 703.951111 241.656332 
L 701.345609 240.489687 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a28867"/>
    <path d="M 769.199119 277.479161 
L 771.830508 278.878269 
L 773.316481 279.124719 
L 770.686918 277.822165 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e6df8b"/>
    <path d="M 787.964663 285.525575 
L 790.602984 286.774699 
L 792.074547 286.424576 
L 789.437315 285.280483 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f4f193"/>
    <path d="M 735.798816 259.305638 
L 738.420234 260.754343 
L 739.942108 261.906808 
L 737.323514 260.530618 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c8b97b"/>
    <path d="M 810.864423 291.383846 
L 813.514231 292.330895 
L 814.97429 291.231784 
L 812.32461 290.394718 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 723.7895 252.317406 
L 726.407219 253.717831 
L 727.944475 255.120877 
L 725.329799 253.782011 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #baa774"/>
    <path d="M 711.780023 245.387279 
L 714.393607 246.706174 
L 715.947057 248.309901 
L 713.336641 247.04073 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ae976d"/>
    <path d="M 747.80765 266.172051 
L 750.43265 267.637 
L 751.940339 268.493242 
L 749.317866 267.110666 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d4c882"/>
    <path d="M 804.107805 290.266411 
L 806.753845 291.319796 
L 808.216707 290.438095 
L 805.571078 289.493861 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fcfb97"/>
    <path d="M 678.374377 227.680597 
L 680.972573 228.609367 
L 682.572163 230.474744 
L 679.976981 229.560554 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8e6e5c"/>
    <path d="M 817.626177 292.069712 
L 820.280276 292.908394 
L 821.738227 291.59069 
L 819.083976 290.862311 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 759.817293 272.747547 
L 762.446051 274.19884 
L 763.941101 274.718391 
L 761.3145 273.358049 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ded587"/>
    <path d="M 797.354572 288.725853 
L 799.997368 289.88219 
L 801.463737 289.215294 
L 798.821638 288.166771 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #faf996"/>
    <path d="M 668.981396 223.34181 
L 671.574083 224.122161 
L 673.186191 225.976138 
L 670.596344 225.200678 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #866458"/>
    <path d="M 690.373003 233.501895 
L 692.978152 234.60487 
L 694.561559 236.420989 
L 691.959566 235.345554 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #987b61"/>
    <path d="M 781.215146 283.090298 
L 783.851336 284.429465 
L 785.328088 284.282426 
L 782.693261 283.045768 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f0ec91"/>
    <path d="M 771.830508 278.878269 
L 774.463467 280.288958 
L 775.947711 280.437321 
L 773.316481 279.124719 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e8e28d"/>
    <path d="M 738.420234 260.754343 
L 741.043243 262.228735 
L 742.562349 263.306237 
L 739.942108 261.906808 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c8b97b"/>
    <path d="M 702.381079 239.905039 
L 704.991889 241.150833 
L 706.558718 242.861811 
L 703.951111 241.656332 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a48b68"/>
    <path d="M 726.407219 253.717831 
L 729.026643 255.149432 
L 730.560897 256.48821 
L 727.944475 255.120877 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bca975"/>
    <path d="M 790.602984 286.774699 
L 793.24305 288.029273 
L 794.713632 287.573173 
L 792.074547 286.424576 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f6f394"/>
    <path d="M 750.43265 267.637 
L 753.059179 269.122317 
L 754.564417 269.894039 
L 751.940339 268.493242 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d4c882"/>
    <path d="M 714.393607 246.706174 
L 717.009072 248.061715 
L 718.559371 249.612802 
L 715.947057 248.309901 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b09a6e"/>
    <path d="M 813.514231 292.330895 
L 816.166136 293.279025 
L 817.626177 292.069712 
L 814.97429 291.231784 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 806.753845 291.319796 
L 809.401862 292.375126 
L 810.864423 291.383846 
L 808.216707 290.438095 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 762.446051 274.19884 
L 765.076329 275.665519 
L 766.569312 276.092313 
L 763.941101 274.718391 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e0d788"/>
    <path d="M 680.972573 228.609367 
L 683.573405 229.588922 
L 685.169939 231.436526 
L 682.572163 230.474744 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #90715d"/>
    <path d="M 820.280276 292.908394 
L 822.936589 293.747721 
L 824.394801 292.319706 
L 821.738227 291.59069 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fdff99"/>
    <path d="M 799.997368 289.88219 
L 802.642022 291.041755 
L 804.107805 290.266411 
L 801.463737 289.215294 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #faf996"/>
    <path d="M 671.574083 224.122161 
L 674.169684 224.956901 
L 675.778892 226.802807 
L 673.186191 225.976138 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #866458"/>
    <path d="M 783.851336 284.429465 
L 786.489169 285.776268 
L 787.964663 285.525575 
L 785.328088 284.282426 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f2ee92"/>
    <path d="M 692.978152 234.60487 
L 695.585621 235.754215 
L 697.165851 237.539654 
L 694.561559 236.420989 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9a7e62"/>
    <path d="M 741.043243 262.228735 
L 743.667806 263.728053 
L 745.184207 264.72822 
L 742.562349 263.306237 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cabb7c"/>
    <path d="M 774.463467 280.288958 
L 777.097987 281.710539 
L 778.580602 281.75938 
L 775.947711 280.437321 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eae48e"/>
    <path d="M 729.026643 255.149432 
L 731.64773 256.611489 
L 733.179023 257.883358 
L 730.560897 256.48821 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #beac76"/>
    <path d="M 753.059179 269.122317 
L 755.68721 270.627232 
L 757.190075 271.312374 
L 754.564417 269.894039 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d6cb83"/>
    <path d="M 717.009072 248.061715 
L 719.626363 249.453261 
L 721.173535 250.948844 
L 718.559371 249.612802 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b29c6f"/>
    <path d="M 704.991889 241.150833 
L 707.604745 242.438003 
L 709.168374 244.105636 
L 706.558718 242.861811 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a68d69"/>
    <path d="M 793.24305 288.029273 
L 795.88486 289.288769 
L 797.354572 288.725853 
L 794.713632 287.573173 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f6f394"/>
    <path d="M 765.076329 275.665519 
L 767.708111 277.146836 
L 769.199119 277.479161 
L 766.569312 276.092313 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e2da89"/>
    <path d="M 809.401862 292.375126 
L 812.051861 293.432072 
L 813.514231 292.330895 
L 810.864423 291.383846 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 816.166136 293.279025 
L 818.820143 294.228016 
L 820.280276 292.908394 
L 817.626177 292.069712 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 683.573405 229.588922 
L 686.176801 230.619013 
L 687.770242 232.445671 
L 685.169939 231.436526 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #90715d"/>
    <path d="M 802.642022 291.041755 
L 805.288538 292.204116 
L 806.753845 291.319796 
L 804.107805 290.266411 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fcfb97"/>
    <path d="M 743.667806 263.728053 
L 746.293887 265.251511 
L 747.80765 266.172051 
L 745.184207 264.72822 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ccbe7d"/>
    <path d="M 822.936589 293.747721 
L 825.595123 294.587584 
L 827.053702 293.04936 
L 824.394801 292.319706 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fdff99"/>
    <path d="M 786.489169 285.776268 
L 789.128641 287.130083 
L 790.602984 286.774699 
L 787.964663 285.525575 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f2ee92"/>
    <path d="M 731.64773 256.611489 
L 734.270433 258.103251 
L 735.798816 259.305638 
L 733.179023 257.883358 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c0ae77"/>
    <path d="M 755.68721 270.627232 
L 758.316719 272.150957 
L 759.817293 272.747547 
L 757.190075 271.312374 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d8cd84"/>
    <path d="M 777.097987 281.710539 
L 779.734057 283.142313 
L 781.215146 283.090298 
L 778.580602 281.75938 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ece78f"/>
    <path d="M 695.585621 235.754215 
L 698.195341 236.949504 
L 699.772379 238.701151 
L 697.165851 237.539654 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9a7e62"/>
    <path d="M 719.626363 249.453261 
L 722.245427 250.880132 
L 723.7895 252.317406 
L 721.173535 250.948844 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b29c6f"/>
    <path d="M 707.604745 242.438003 
L 710.219588 243.765978 
L 711.780023 245.387279 
L 709.168374 244.105636 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a68d69"/>
    <path d="M 674.169684 224.956901 
L 676.768122 225.845936 
L 678.374377 227.680597 
L 675.778892 226.802807 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #866458"/>
    <path d="M 795.88486 289.288769 
L 798.528417 290.552654 
L 799.997368 289.88219 
L 797.354572 288.725853 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f8f695"/>
    <path d="M 767.708111 277.146836 
L 770.341381 278.64203 
L 771.830508 278.878269 
L 769.199119 277.479161 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e4dc8a"/>
    <path d="M 664.770464 220.804211 
L 667.36292 221.53184 
L 668.981396 223.34181 
L 666.391698 222.615882 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #805c54"/>
    <path d="M 812.051861 293.432072 
L 814.703846 294.490308 
L 816.166136 293.279025 
L 813.514231 292.330895 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 746.293887 265.251511 
L 748.921456 266.798299 
L 750.43265 267.637 
L 747.80765 266.172051 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cec07f"/>
    <path d="M 686.176801 230.619013 
L 688.782688 231.699341 
L 690.373003 233.501895 
L 687.770242 232.445671 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #90715d"/>
    <path d="M 734.270433 258.103251 
L 736.894711 259.623938 
L 738.420234 260.754343 
L 735.798816 259.305638 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c2b178"/>
    <path d="M 758.316719 272.150957 
L 760.947682 273.692684 
L 762.446051 274.19884 
L 759.817293 272.747547 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dad085"/>
    <path d="M 818.820143 294.228016 
L 821.476257 295.177651 
L 822.936589 293.747721 
L 820.280276 292.908394 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fdff99"/>
    <path d="M 805.288538 292.204116 
L 807.93692 293.368838 
L 809.401862 292.375126 
L 806.753845 291.319796 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fcfb97"/>
    <path d="M 779.734057 283.142313 
L 782.371671 284.58357 
L 783.851336 284.429465 
L 781.215146 283.090298 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eee990"/>
    <path d="M 789.128641 287.130083 
L 791.769749 288.490283 
L 793.24305 288.029273 
L 790.602984 286.774699 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f4f193"/>
    <path d="M 722.245427 250.880132 
L 724.866211 252.341611 
L 726.407219 253.717831 
L 723.7895 252.317406 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b49f70"/>
    <path d="M 698.195341 236.949504 
L 700.807244 238.190259 
L 702.381079 239.905039 
L 699.772379 238.701151 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9c8064"/>
    <path d="M 710.219588 243.765978 
L 712.836354 245.134142 
L 714.393607 246.706174 
L 711.780023 245.387279 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a8906a"/>
    <path d="M 770.341381 278.64203 
L 772.976125 280.150324 
L 774.463467 280.288958 
L 771.830508 278.878269 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e6df8b"/>
    <path d="M 825.595123 294.587584 
L 828.255881 295.427874 
L 829.714932 293.779654 
L 827.053702 293.04936 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fdff99"/>
    <path d="M 798.528417 290.552654 
L 801.173721 291.820391 
L 802.642022 291.041755 
L 799.997368 289.88219 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #faf996"/>
    <path d="M 676.768122 225.845936 
L 679.369318 226.789114 
L 680.972573 228.609367 
L 678.374377 227.680597 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #886759"/>
    <path d="M 748.921456 266.798299 
L 751.550479 268.367583 
L 753.059179 269.122317 
L 750.43265 267.637 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d0c380"/>
    <path d="M 667.36292 221.53184 
L 669.958429 222.317031 
L 671.574083 224.122161 
L 668.981396 223.34181 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #805c54"/>
    <path d="M 760.947682 273.692684 
L 763.580079 275.251587 
L 765.076329 275.665519 
L 762.446051 274.19884 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dcd286"/>
    <path d="M 736.894711 259.623938 
L 739.520521 261.172739 
L 741.043243 262.228735 
L 738.420234 260.754343 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c4b379"/>
    <path d="M 782.371671 284.58357 
L 785.010821 286.033593 
L 786.489169 285.776268 
L 783.851336 284.429465 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eee990"/>
    <path d="M 688.782688 231.699341 
L 691.39099 232.82955 
L 692.978152 234.60487 
L 690.373003 233.501895 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #92735e"/>
    <path d="M 724.866211 252.341611 
L 727.488664 253.836948 
L 729.026643 255.149432 
L 726.407219 253.717831 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b6a272"/>
    <path d="M 814.703846 294.490308 
L 817.357824 295.549505 
L 818.820143 294.228016 
L 816.166136 293.279025 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 791.769749 288.490283 
L 794.412493 289.856232 
L 795.88486 289.288769 
L 793.24305 288.029273 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f6f394"/>
    <path d="M 807.93692 293.368838 
L 810.587172 294.535486 
L 812.051861 293.432072 
L 809.401862 292.375126 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 712.836354 245.134142 
L 715.454985 246.541841 
L 717.009072 248.061715 
L 714.393607 246.706174 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #aa926b"/>
    <path d="M 772.976125 280.150324 
L 775.612329 281.670932 
L 777.097987 281.710539 
L 774.463467 280.288958 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e6df8b"/>
    <path d="M 700.807244 238.190259 
L 703.421262 239.475958 
L 704.991889 241.150833 
L 702.381079 239.905039 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9c8064"/>
    <path d="M 821.476257 295.177651 
L 824.134484 296.12771 
L 825.595123 294.587584 
L 822.936589 293.747721 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fdff99"/>
    <path d="M 801.173721 291.820391 
L 803.820776 293.091441 
L 805.288538 292.204116 
L 802.642022 291.041755 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #faf996"/>
    <path d="M 751.550479 268.367583 
L 754.180929 269.958507 
L 755.68721 270.627232 
L 753.059179 269.122317 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d2c581"/>
    <path d="M 828.255881 295.427874 
L 830.918869 296.268481 
L 832.378495 294.510588 
L 829.714932 293.779654 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fdff99"/>
    <path d="M 679.369318 226.789114 
L 681.973196 227.786229 
L 683.573405 229.588922 
L 680.972573 228.609367 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #886759"/>
    <path d="M 739.520521 261.172739 
L 742.147825 262.748817 
L 743.667806 263.728053 
L 741.043243 262.228735 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c6b67a"/>
    <path d="M 763.580079 275.251587 
L 766.213889 276.826825 
L 767.708111 277.146836 
L 765.076329 275.665519 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ded587"/>
    <path d="M 785.010821 286.033593 
L 787.651505 287.491654 
L 789.128641 287.130083 
L 786.489169 285.776268 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f0ec91"/>
    <path d="M 727.488664 253.836948 
L 730.112737 255.365357 
L 731.64773 256.611489 
L 729.026643 255.149432 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b8a473"/>
    <path d="M 794.412493 289.856232 
L 797.056873 291.227291 
L 798.528417 290.552654 
L 795.88486 289.288769 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f6f394"/>
    <path d="M 669.958429 222.317031 
L 672.556911 223.159745 
L 674.169684 224.956901 
L 671.574083 224.122161 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #805c54"/>
    <path d="M 691.39099 232.82955 
L 694.001634 234.009234 
L 695.585621 235.754215 
L 692.978152 234.60487 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #92735e"/>
    <path d="M 775.612329 281.670932 
L 778.249984 283.203052 
L 779.734057 283.142313 
L 777.097987 281.710539 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e8e28d"/>
    <path d="M 715.454985 246.541841 
L 718.075421 247.988377 
L 719.626363 249.453261 
L 717.009072 248.061715 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #aa926b"/>
    <path d="M 703.421262 239.475958 
L 706.037328 240.806031 
L 707.604745 242.438003 
L 704.991889 241.150833 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9e8365"/>
    <path d="M 817.357824 295.549505 
L 820.013801 296.609334 
L 821.476257 295.177651 
L 818.820143 294.228016 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fdff99"/>
    <path d="M 810.587172 294.535486 
L 813.239302 295.703623 
L 814.703846 294.490308 
L 812.051861 293.432072 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 824.134484 296.12771 
L 826.794832 297.077973 
L 828.255881 295.427874 
L 825.595123 294.587584 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fdff99"/>
    <path d="M 754.180929 269.958507 
L 756.812775 271.570193 
L 758.316719 272.150957 
L 755.68721 270.627232 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d4c882"/>
    <path d="M 803.820776 293.091441 
L 806.469587 294.36526 
L 807.93692 293.368838 
L 805.288538 292.204116 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fcfb97"/>
    <path d="M 742.147825 262.748817 
L 744.776584 264.351306 
L 746.293887 265.251511 
L 743.667806 263.728053 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c8b97b"/>
    <path d="M 766.213889 276.826825 
L 768.849093 278.417539 
L 770.341381 278.64203 
L 767.708111 277.146836 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e0d788"/>
    <path d="M 730.112737 255.365357 
L 732.738381 256.926019 
L 734.270433 258.103251 
L 731.64773 256.611489 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #baa774"/>
    <path d="M 681.973196 227.786229 
L 684.579676 228.837016 
L 686.176801 230.619013 
L 683.573405 229.588922 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #886759"/>
    <path d="M 787.651505 287.491654 
L 790.293717 288.957021 
L 791.769749 288.490283 
L 789.128641 287.130083 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f2ee92"/>
    <path d="M 830.918869 296.268481 
L 833.584092 297.109297 
L 835.044394 295.242162 
L 832.378495 294.510588 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fdff99"/>
    <path d="M 778.249984 283.203052 
L 780.88908 284.745874 
L 782.371671 284.58357 
L 779.734057 283.142313 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eae48e"/>
    <path d="M 718.075421 247.988377 
L 720.697603 249.473015 
L 722.245427 250.880132 
L 719.626363 249.453261 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ac956c"/>
    <path d="M 797.056873 291.227291 
L 799.702891 292.602817 
L 801.173721 291.820391 
L 798.528417 290.552654 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f8f695"/>
    <path d="M 694.001634 234.009234 
L 696.614547 235.237934 
L 698.195341 236.949504 
L 695.585621 235.754215 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #94765f"/>
    <path d="M 706.037328 240.806031 
L 708.655374 242.179862 
L 710.219588 243.765978 
L 707.604745 242.438003 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a08566"/>
    <path d="M 672.556911 223.159745 
L 675.158286 224.059882 
L 676.768122 225.845936 
L 674.169684 224.956901 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #805c54"/>
    <path d="M 756.812775 271.570193 
L 759.445993 273.201745 
L 760.947682 273.692684 
L 758.316719 272.150957 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d6cb83"/>
    <path d="M 813.239302 295.703623 
L 815.893315 296.872811 
L 817.357824 295.549505 
L 814.703846 294.490308 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 820.013801 296.609334 
L 822.671786 297.669467 
L 824.134484 296.12771 
L 821.476257 295.177651 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fdff99"/>
    <path d="M 744.776584 264.351306 
L 747.406761 265.979314 
L 748.921456 266.798299 
L 746.293887 265.251511 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cabb7c"/>
    <path d="M 768.849093 278.417539 
L 771.485676 280.022857 
L 772.976125 280.150324 
L 770.341381 278.64203 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e2da89"/>
    <path d="M 663.145804 219.044746 
L 665.740995 219.774069 
L 667.36292 221.53184 
L 664.770464 220.804211 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #87655e"/>
    <path d="M 806.469587 294.36526 
L 809.120158 295.641304 
L 810.587172 294.535486 
L 807.93692 293.368838 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fcfb97"/>
    <path d="M 732.738381 256.926019 
L 735.365549 258.518081 
L 736.894711 259.623938 
L 734.270433 258.103251 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bca975"/>
    <path d="M 826.794832 297.077973 
L 829.457305 298.028223 
L 830.918869 296.268481 
L 828.255881 295.427874 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fdff99"/>
    <path d="M 790.293717 288.957021 
L 792.937458 290.428954 
L 794.412493 289.856232 
L 791.769749 288.490283 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f4f193"/>
    <path d="M 780.88908 284.745874 
L 783.52961 286.298579 
L 785.010821 286.033593 
L 782.371671 284.58357 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ece78f"/>
    <path d="M 684.579676 228.837016 
L 687.188681 229.941152 
L 688.782688 231.699341 
L 686.176801 230.619013 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8a695a"/>
    <path d="M 720.697603 249.473015 
L 723.321475 250.994977 
L 724.866211 252.341611 
L 722.245427 250.880132 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ae976d"/>
    <path d="M 799.702891 292.602817 
L 802.35055 293.982161 
L 803.820776 293.091441 
L 801.173721 291.820391 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #faf996"/>
    <path d="M 759.445993 273.201745 
L 762.080558 274.852244 
L 763.580079 275.251587 
L 760.947682 273.692684 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d8cd84"/>
    <path d="M 708.655374 242.179862 
L 711.275334 243.596788 
L 712.836354 245.134142 
L 710.219588 243.765978 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a28867"/>
    <path d="M 696.614547 235.237934 
L 699.229655 236.515141 
L 700.807244 238.190259 
L 698.195341 236.949504 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #94765f"/>
    <path d="M 747.406761 265.979314 
L 750.038322 267.631924 
L 751.550479 268.367583 
L 748.921456 266.798299 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ccbe7d"/>
    <path d="M 833.584092 297.109297 
L 836.251555 297.950213 
L 837.712631 295.974379 
L 835.044394 295.242162 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fdff99"/>
    <path d="M 771.485676 280.022857 
L 774.123622 281.641893 
L 775.612329 281.670932 
L 772.976125 280.150324 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e4dc8a"/>
    <path d="M 815.893315 296.872811 
L 818.54922 298.042611 
L 820.013801 296.609334 
L 817.357824 295.549505 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fdff99"/>
    <path d="M 735.365549 258.518081 
L 737.994195 260.14066 
L 739.520521 261.172739 
L 736.894711 259.623938 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #beac76"/>
    <path d="M 675.158286 224.059882 
L 677.762469 225.017283 
L 679.369318 226.789114 
L 676.768122 225.845936 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #805c54"/>
    <path d="M 822.671786 297.669467 
L 825.331784 298.729573 
L 826.794832 297.077973 
L 824.134484 296.12771 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fdff99"/>
    <path d="M 809.120158 295.641304 
L 811.772497 296.919027 
L 813.239302 295.703623 
L 810.587172 294.535486 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 792.937458 290.428954 
L 795.582726 291.906706 
L 797.056873 291.227291 
L 794.412493 289.856232 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f6f394"/>
    <path d="M 783.52961 286.298579 
L 786.171566 287.860335 
L 787.651505 287.491654 
L 785.010821 286.033593 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eee990"/>
    <path d="M 665.740995 219.774069 
L 668.339306 220.564042 
L 669.958429 222.317031 
L 667.36292 221.53184 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #87655e"/>
    <path d="M 723.321475 250.994977 
L 725.946981 252.553452 
L 727.488664 253.836948 
L 724.866211 252.341611 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b09a6e"/>
    <path d="M 829.457305 298.028223 
L 832.121913 298.978241 
L 833.584092 297.109297 
L 830.918869 296.268481 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fdff99"/>
    <path d="M 762.080558 274.852244 
L 764.716446 276.520756 
L 766.213889 276.826825 
L 763.580079 275.251587 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dad085"/>
    <path d="M 802.35055 293.982161 
L 804.999855 295.364672 
L 806.469587 294.36526 
L 803.820776 293.091441 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #faf996"/>
    <path d="M 687.188681 229.941152 
L 689.80013 231.098261 
L 691.39099 232.82955 
L 688.782688 231.699341 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8a695a"/>
    <path d="M 750.038322 267.631924 
L 752.671232 269.308195 
L 754.180929 269.958507 
L 751.550479 268.367583 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cec07f"/>
    <path d="M 711.275334 243.596788 
L 713.897145 245.056104 
L 715.454985 246.541841 
L 712.836354 245.134142 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a28867"/>
    <path d="M 774.123622 281.641893 
L 776.76292 283.273747 
L 778.249984 283.203052 
L 775.612329 281.670932 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e6df8b"/>
    <path d="M 699.229655 236.515141 
L 701.846884 237.840293 
L 703.421262 239.475958 
L 700.807244 238.190259 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #967960"/>
    <path d="M 737.994195 260.14066 
L 740.624275 261.792842 
L 742.147825 262.748817 
L 739.520521 261.172739 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c0ae77"/>
    <path d="M 836.251555 297.950213 
L 838.921264 298.791123 
L 840.38321 296.707238 
L 837.712631 295.974379 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fdff99"/>
    <path d="M 818.54922 298.042611 
L 821.207026 299.212584 
L 822.671786 297.669467 
L 820.013801 296.609334 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fdff99"/>
    <path d="M 786.171566 287.860335 
L 788.814946 289.430306 
L 790.293717 288.957021 
L 787.651505 287.491654 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f0ec91"/>
    <path d="M 795.582726 291.906706 
L 798.229523 293.389527 
L 799.702891 292.602817 
L 797.056873 291.227291 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f6f394"/>
    <path d="M 725.946981 252.553452 
L 728.574066 254.147586 
L 730.112737 255.365357 
L 727.488664 253.836948 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b29c6f"/>
    <path d="M 811.772497 296.919027 
L 814.426612 298.197882 
L 815.893315 296.872811 
L 813.239302 295.703623 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 677.762469 225.017283 
L 680.369379 226.031727 
L 681.973196 227.786229 
L 679.369318 226.789114 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #805c54"/>
    <path d="M 825.331784 298.729573 
L 827.993807 299.789327 
L 829.457305 298.028223 
L 826.794832 297.077973 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9fe98"/>
    <path d="M 764.716446 276.520756 
L 767.353638 278.206327 
L 768.849093 278.417539 
L 766.213889 276.826825 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dcd286"/>
    <path d="M 752.671232 269.308195 
L 755.305462 271.00716 
L 756.812775 271.570193 
L 754.180929 269.958507 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d0c380"/>
    <path d="M 776.76292 283.273747 
L 779.403557 284.917508 
L 780.88908 284.745874 
L 778.249984 283.203052 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e8e28d"/>
    <path d="M 713.897145 245.056104 
L 716.52074 246.557059 
L 718.075421 247.988377 
L 715.454985 246.541841 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a48b68"/>
    <path d="M 804.999855 295.364672 
L 807.650812 296.749697 
L 809.120158 295.641304 
L 806.469587 294.36526 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fcfb97"/>
    <path d="M 668.339306 220.564042 
L 670.940651 221.414625 
L 672.556911 223.159745 
L 669.958429 222.317031 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #87655e"/>
    <path d="M 689.80013 231.098261 
L 692.413946 232.307908 
L 694.001634 234.009234 
L 691.39099 232.82955 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8c6c5b"/>
    <path d="M 740.624275 261.792842 
L 743.255748 263.473681 
L 744.776584 264.351306 
L 742.147825 262.748817 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c2b178"/>
    <path d="M 701.846884 237.840293 
L 704.466164 239.212781 
L 706.037328 240.806031 
L 703.421262 239.475958 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #987b61"/>
    <path d="M 832.121913 298.978241 
L 834.788662 299.927811 
L 836.251555 297.950213 
L 833.584092 297.109297 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9fe98"/>
    <path d="M 728.574066 254.147586 
L 731.202678 255.776492 
L 732.738381 256.926019 
L 730.112737 255.365357 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b49f70"/>
    <path d="M 788.814946 289.430306 
L 791.459746 291.007645 
L 792.937458 290.428954 
L 790.293717 288.957021 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f2ee92"/>
    <path d="M 767.353638 278.206327 
L 769.992115 279.907988 
L 771.485676 280.022857 
L 768.849093 278.417539 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ded587"/>
    <path d="M 798.229523 293.389527 
L 800.877852 294.876661 
L 802.35055 293.982161 
L 799.702891 292.602817 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f8f695"/>
    <path d="M 755.305462 271.00716 
L 757.940981 272.727834 
L 759.445993 273.201745 
L 756.812775 271.570193 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d2c581"/>
    <path d="M 821.207026 299.212584 
L 823.866741 300.382294 
L 825.331784 298.729573 
L 822.671786 297.669467 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9fe98"/>
    <path d="M 814.426612 298.197882 
L 817.08251 299.477319 
L 818.54922 298.042611 
L 815.893315 296.872811 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fdff99"/>
    <path d="M 779.403557 284.917508 
L 782.045525 286.572252 
L 783.52961 286.298579 
L 780.88908 284.745874 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eae48e"/>
    <path d="M 680.369379 226.031727 
L 682.978933 227.102933 
L 684.579676 228.837016 
L 681.973196 227.786229 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #825f56"/>
    <path d="M 838.921264 298.791123 
L 841.593225 299.631919 
L 843.056134 297.440741 
L 840.38321 296.707238 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fdff99"/>
    <path d="M 716.52074 246.557059 
L 719.146059 248.09886 
L 720.697603 249.473015 
L 718.075421 247.988377 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a68d69"/>
    <path d="M 743.255748 263.473681 
L 745.888573 265.182206 
L 747.406761 265.979314 
L 744.776584 264.351306 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c4b379"/>
    <path d="M 827.993807 299.789327 
L 830.657862 300.848399 
L 832.121913 298.978241 
L 829.457305 298.028223 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9fe98"/>
    <path d="M 807.650812 296.749697 
L 810.303427 298.136581 
L 811.772497 296.919027 
L 809.120158 295.641304 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 704.466164 239.212781 
L 707.087421 240.631944 
L 708.655374 242.179862 
L 706.037328 240.806031 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9a7e62"/>
    <path d="M 692.413946 232.307908 
L 695.030049 233.569606 
L 696.614547 235.237934 
L 694.001634 234.009234 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8c6c5b"/>
    <path d="M 670.940651 221.414625 
L 673.544945 222.325712 
L 675.158286 224.059882 
L 672.556911 223.159745 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #87655e"/>
    <path d="M 731.202678 255.776492 
L 733.832765 257.439247 
L 735.365549 258.518081 
L 732.738381 256.926019 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b6a272"/>
    <path d="M 769.992115 279.907988 
L 772.631859 281.624755 
L 774.123622 281.641893 
L 771.485676 280.022857 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e0d788"/>
    <path d="M 791.459746 291.007645 
L 794.105967 292.591501 
L 795.582726 291.906706 
L 792.937458 290.428954 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f4f193"/>
    <path d="M 834.788662 299.927811 
L 837.457561 300.876715 
L 838.921264 298.791123 
L 836.251555 297.950213 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9fe98"/>
    <path d="M 757.940981 272.727834 
L 760.577763 274.469207 
L 762.080558 274.852244 
L 759.445993 273.201745 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d4c882"/>
    <path d="M 661.517802 217.340749 
L 664.115707 218.071757 
L 665.740995 219.774069 
L 663.145804 219.044746 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8d6d66"/>
    <path d="M 800.877852 294.876661 
L 803.527718 296.36735 
L 804.999855 295.364672 
L 802.35055 293.982161 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #faf996"/>
    <path d="M 782.045525 286.572252 
L 784.688816 288.237046 
L 786.171566 287.860335 
L 783.52961 286.298579 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ece78f"/>
    <path d="M 745.888573 265.182206 
L 748.522711 266.917415 
L 750.038322 267.631924 
L 747.406761 265.979314 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c6b67a"/>
    <path d="M 719.146059 248.09886 
L 721.773038 249.680671 
L 723.321475 250.994977 
L 720.697603 249.473015 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a8906a"/>
    <path d="M 817.08251 299.477319 
L 819.740203 300.756793 
L 821.207026 299.212584 
L 818.54922 298.042611 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9fe98"/>
    <path d="M 823.866741 300.382294 
L 826.528376 301.551301 
L 827.993807 299.789327 
L 825.331784 298.729573 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9fe98"/>
    <path d="M 682.978933 227.102933 
L 685.591046 228.230559 
L 687.188681 229.941152 
L 684.579676 228.837016 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #825f56"/>
    <path d="M 810.303427 298.136581 
L 812.957709 299.524668 
L 814.426612 298.197882 
L 811.772497 296.919027 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 707.087421 240.631944 
L 709.710585 242.097073 
L 711.275334 243.596788 
L 708.655374 242.179862 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9a7e62"/>
    <path d="M 830.657862 300.848399 
L 833.32396 301.906465 
L 834.788662 299.927811 
L 832.121913 298.978241 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9fe98"/>
    <path d="M 733.832765 257.439247 
L 736.464278 259.134895 
L 737.994195 260.14066 
L 735.365549 258.518081 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b8a473"/>
    <path d="M 695.030049 233.569606 
L 697.648361 234.882809 
L 699.229655 236.515141 
L 696.614547 235.237934 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8e6e5c"/>
    <path d="M 841.593225 299.631919 
L 844.267444 300.472494 
L 845.731405 298.174888 
L 843.056134 297.440741 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fdff99"/>
    <path d="M 772.631859 281.624755 
L 775.272856 283.355628 
L 776.76292 283.273747 
L 774.123622 281.641893 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e2da89"/>
    <path d="M 760.577763 274.469207 
L 763.215781 276.23025 
L 764.716446 276.520756 
L 762.080558 274.852244 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d6cb83"/>
    <path d="M 794.105967 292.591501 
L 796.753608 294.181016 
L 798.229523 293.389527 
L 795.582726 291.906706 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f6f394"/>
    <path d="M 803.527718 296.36735 
L 806.179126 297.860832 
L 807.650812 296.749697 
L 804.999855 295.364672 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fcfb97"/>
    <path d="M 784.688816 288.237046 
L 787.333426 289.91095 
L 788.814946 289.430306 
L 786.171566 287.860335 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eee990"/>
    <path d="M 748.522711 266.917415 
L 751.158125 268.678281 
L 752.671232 269.308195 
L 750.038322 267.631924 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c8b97b"/>
    <path d="M 673.544945 222.325712 
L 676.152099 223.297135 
L 677.762469 225.017283 
L 675.158286 224.059882 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #85635c"/>
    <path d="M 721.773038 249.680671 
L 724.401617 251.301616 
L 725.946981 252.553452 
L 723.321475 250.994977 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #aa926b"/>
    <path d="M 837.457561 300.876715 
L 840.128619 301.824739 
L 841.593225 299.631919 
L 838.921264 298.791123 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9fe98"/>
    <path d="M 664.115707 218.071757 
L 666.716797 218.866451 
L 668.339306 220.564042 
L 665.740995 219.774069 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8d6d66"/>
    <path d="M 819.740203 300.756793 
L 822.399701 302.035755 
L 823.866741 300.382294 
L 821.207026 299.212584 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9fe98"/>
    <path d="M 736.464278 259.134895 
L 739.097168 260.862443 
L 740.624275 261.792842 
L 737.994195 260.14066 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #baa774"/>
    <path d="M 826.528376 301.551301 
L 829.191944 302.719172 
L 830.657862 300.848399 
L 827.993807 299.789327 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f5fd97"/>
    <path d="M 775.272856 283.355628 
L 777.915093 285.099595 
L 779.403557 284.917508 
L 776.76292 283.273747 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e4dc8a"/>
    <path d="M 709.710585 242.097073 
L 712.335586 243.60741 
L 713.897145 245.056104 
L 711.275334 243.596788 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9c8064"/>
    <path d="M 763.215781 276.23025 
L 765.855012 278.009916 
L 767.353638 278.206327 
L 764.716446 276.520756 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d8cd84"/>
    <path d="M 812.957709 299.524668 
L 815.613669 300.913301 
L 817.08251 299.477319 
L 814.426612 298.197882 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fdff99"/>
    <path d="M 685.591046 228.230559 
L 688.205634 229.414205 
L 689.80013 231.098261 
L 687.188681 229.941152 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #846257"/>
    <path d="M 697.648361 234.882809 
L 700.268804 236.246921 
L 701.846884 237.840293 
L 699.229655 236.515141 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #90715d"/>
    <path d="M 796.753608 294.181016 
L 799.402673 295.775329 
L 800.877852 294.876661 
L 798.229523 293.389527 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f8f695"/>
    <path d="M 751.158125 268.678281 
L 753.794782 270.463753 
L 755.305462 271.00716 
L 752.671232 269.308195 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ccbe7d"/>
    <path d="M 787.333426 289.91095 
L 789.97935 291.593012 
L 791.459746 291.007645 
L 788.814946 289.430306 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f0ec91"/>
    <path d="M 833.32396 301.906465 
L 835.992111 302.9632 
L 837.457561 300.876715 
L 834.788662 299.927811 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f5fd97"/>
    <path d="M 806.179126 297.860832 
L 808.832085 299.356343 
L 810.303427 298.136581 
L 807.650812 296.749697 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 724.401617 251.301616 
L 727.031738 252.960778 
L 728.574066 254.147586 
L 725.946981 252.553452 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ac956c"/>
    <path d="M 844.267444 300.472494 
L 846.943927 301.312743 
L 848.409028 298.90968 
L 845.731405 298.174888 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fdff99"/>
    <path d="M 676.152099 223.297135 
L 678.762027 224.328659 
L 680.369379 226.031727 
L 677.762469 225.017283 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #85635c"/>
    <path d="M 739.097168 260.862443 
L 741.73139 262.62087 
L 743.255748 263.473681 
L 740.624275 261.792842 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #beac76"/>
    <path d="M 765.855012 278.009916 
L 768.495436 279.80714 
L 769.992115 279.907988 
L 767.353638 278.206327 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dcd286"/>
    <path d="M 777.915093 285.099595 
L 780.558559 286.855632 
L 782.045525 286.572252 
L 779.403557 284.917508 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e8e28d"/>
    <path d="M 712.335586 243.60741 
L 714.962356 245.162154 
L 716.52074 246.557059 
L 713.897145 245.056104 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9e8365"/>
    <path d="M 822.399701 302.035755 
L 825.061016 303.31366 
L 826.528376 301.551301 
L 823.866741 300.382294 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f5fd97"/>
    <path d="M 840.128619 301.824739 
L 842.801844 302.77167 
L 844.267444 300.472494 
L 841.593225 299.631919 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9fe98"/>
    <path d="M 815.613669 300.913301 
L 818.271317 302.301823 
L 819.740203 300.756793 
L 817.08251 299.477319 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9fe98"/>
    <path d="M 753.794782 270.463753 
L 756.432649 272.272753 
L 757.940981 272.727834 
L 755.305462 271.00716 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cec07f"/>
    <path d="M 799.402673 295.775329 
L 802.053167 297.373572 
L 803.527718 296.36735 
L 800.877852 294.876661 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #faf996"/>
    <path d="M 829.191944 302.719172 
L 831.857455 303.88547 
L 833.32396 301.906465 
L 830.657862 300.848399 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f5fd97"/>
    <path d="M 666.716797 218.866451 
L 669.320985 219.724791 
L 670.940651 221.414625 
L 668.339306 220.564042 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8d6d66"/>
    <path d="M 688.205634 229.414205 
L 690.822615 230.653409 
L 692.413946 232.307908 
L 689.80013 231.098261 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #846257"/>
    <path d="M 789.97935 291.593012 
L 792.626587 293.282276 
L 794.105967 292.591501 
L 791.459746 291.007645 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f2ee92"/>
    <path d="M 700.268804 236.246921 
L 702.891301 237.661289 
L 704.466164 239.212781 
L 701.846884 237.840293 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #92735e"/>
    <path d="M 727.031738 252.960778 
L 729.663344 254.657202 
L 731.202678 255.776492 
L 728.574066 254.147586 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ae976d"/>
    <path d="M 808.832085 299.356343 
L 811.486604 300.853119 
L 812.957709 299.524668 
L 810.303427 298.136581 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 741.73139 262.62087 
L 744.366899 264.409123 
L 745.888573 265.182206 
L 743.255748 263.473681 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c0ae77"/>
    <path d="M 768.495436 279.80714 
L 771.137033 281.620839 
L 772.631859 281.624755 
L 769.992115 279.907988 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ded587"/>
    <path d="M 835.992111 302.9632 
L 838.662328 304.018282 
L 840.128619 301.824739 
L 837.457561 300.876715 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f5fd97"/>
    <path d="M 780.558559 286.855632 
L 783.203246 288.622704 
L 784.688816 288.237046 
L 782.045525 286.572252 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eae48e"/>
    <path d="M 714.962356 245.162154 
L 717.590825 246.760453 
L 719.146059 248.09886 
L 716.52074 246.557059 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a08566"/>
    <path d="M 756.432649 272.272753 
L 759.071694 274.104182 
L 760.577763 274.469207 
L 757.940981 272.727834 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d0c380"/>
    <path d="M 846.943927 301.312743 
L 849.622681 302.15256 
L 851.089005 299.645118 
L 848.409028 298.90968 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fdff99"/>
    <path d="M 678.762027 224.328659 
L 681.37464 225.419988 
L 682.978933 227.102933 
L 680.369379 226.031727 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #85635c"/>
    <path d="M 802.053167 297.373572 
L 804.705095 298.974877 
L 806.179126 297.860832 
L 803.527718 296.36735 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fcfb97"/>
    <path d="M 792.626587 293.282276 
L 795.275138 294.977777 
L 796.753608 294.181016 
L 794.105967 292.591501 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f4f193"/>
    <path d="M 825.061016 303.31366 
L 827.724163 304.589963 
L 829.191944 302.719172 
L 826.528376 301.551301 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f5fd97"/>
    <path d="M 818.271317 302.301823 
L 820.930666 303.689579 
L 822.399701 302.035755 
L 819.740203 300.756793 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f5fd97"/>
    <path d="M 729.663344 254.657202 
L 732.296378 256.389893 
L 733.832765 257.439247 
L 731.202678 255.776492 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b09a6e"/>
    <path d="M 702.891301 237.661289 
L 705.515774 239.125211 
L 707.087421 240.631944 
L 704.466164 239.212781 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #92735e"/>
    <path d="M 690.822615 230.653409 
L 693.441904 231.947652 
L 695.030049 233.569606 
L 692.413946 232.307908 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #866458"/>
    <path d="M 842.801844 302.77167 
L 845.477246 303.717296 
L 846.943927 301.312743 
L 844.267444 300.472494 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9fe98"/>
    <path d="M 831.857455 303.88547 
L 834.524923 305.049765 
L 835.992111 302.9632 
L 833.32396 301.906465 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1fc96"/>
    <path d="M 744.366899 264.409123 
L 747.003653 266.226116 
L 748.522711 266.917415 
L 745.888573 265.182206 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c2b178"/>
    <path d="M 771.137033 281.620839 
L 773.779786 283.449915 
L 775.272856 283.355628 
L 772.631859 281.624755 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e0d788"/>
    <path d="M 811.486604 300.853119 
L 814.142693 302.350395 
L 815.613669 300.913301 
L 812.957709 299.524668 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fdff99"/>
    <path d="M 783.203246 288.622704 
L 785.849148 290.399764 
L 787.333426 289.91095 
L 784.688816 288.237046 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ece78f"/>
    <path d="M 669.320985 219.724791 
L 671.928177 220.646664 
L 673.544945 222.325712 
L 670.940651 221.414625 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8d6d66"/>
    <path d="M 759.071694 274.104182 
L 761.711891 275.956919 
L 763.215781 276.23025 
L 760.577763 274.469207 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d2c581"/>
    <path d="M 659.88655 215.695438 
L 662.487142 216.42812 
L 664.115707 218.071757 
L 661.517802 217.340749 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #957771"/>
    <path d="M 717.590825 246.760453 
L 720.220929 248.401413 
L 721.773038 249.680671 
L 719.146059 248.09886 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a28867"/>
    <path d="M 838.662328 304.018282 
L 841.334621 305.071391 
L 842.801844 302.77167 
L 840.128619 301.824739 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f5fd97"/>
    <path d="M 795.275138 294.977777 
L 797.925006 296.678547 
L 799.402673 295.775329 
L 796.753608 294.181016 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f6f394"/>
    <path d="M 732.296378 256.389893 
L 734.930786 258.157821 
L 736.464278 259.134895 
L 733.832765 257.439247 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b49f70"/>
    <path d="M 804.705095 298.974877 
L 807.358466 300.578372 
L 808.832085 299.356343 
L 806.179126 297.860832 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 747.003653 266.226116 
L 749.641613 268.07074 
L 751.158125 268.678281 
L 748.522711 266.917415 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c4b379"/>
    <path d="M 773.779786 283.449915 
L 776.423681 285.293255 
L 777.915093 285.099595 
L 775.272856 283.355628 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e2da89"/>
    <path d="M 681.37464 225.419988 
L 683.98985 226.570759 
L 685.591046 228.230559 
L 682.978933 227.102933 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #836059"/>
    <path d="M 705.515774 239.125211 
L 708.142149 240.63793 
L 709.710585 242.097073 
L 707.087421 240.631944 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #94765f"/>
    <path d="M 820.930666 303.689579 
L 823.591729 305.075914 
L 825.061016 303.31366 
L 822.399701 302.035755 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f5fd97"/>
    <path d="M 827.724163 304.589963 
L 830.389154 305.864122 
L 831.857455 303.88547 
L 829.191944 302.719172 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1fc96"/>
    <path d="M 785.849148 290.399764 
L 788.496259 292.185759 
L 789.97935 291.593012 
L 787.333426 289.91095 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eee990"/>
    <path d="M 849.622681 302.15256 
L 852.303713 302.991844 
L 853.77134 300.381203 
L 851.089005 299.645118 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fdff99"/>
    <path d="M 693.441904 231.947652 
L 696.063417 233.296359 
L 697.648361 234.882809 
L 695.030049 233.569606 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #886759"/>
    <path d="M 761.711891 275.956919 
L 764.353214 277.829822 
L 765.855012 278.009916 
L 763.215781 276.23025 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d6cb83"/>
    <path d="M 814.142693 302.350395 
L 816.800365 303.847406 
L 818.271317 302.301823 
L 815.613669 300.913301 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9fe98"/>
    <path d="M 834.524923 305.049765 
L 837.194362 306.211627 
L 838.662328 304.018282 
L 835.992111 302.9632 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1fc96"/>
    <path d="M 720.220929 248.401413 
L 722.852601 250.084096 
L 724.401617 251.301616 
L 721.773038 249.680671 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a48b68"/>
    <path d="M 845.477246 303.717296 
L 848.154835 304.661406 
L 849.622681 302.15256 
L 846.943927 301.312743 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f5fd97"/>
    <path d="M 671.928177 220.646664 
L 674.538284 221.631892 
L 676.152099 223.297135 
L 673.544945 222.325712 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8d6d66"/>
    <path d="M 734.930786 258.157821 
L 737.566518 259.959921 
L 739.097168 260.862443 
L 736.464278 259.134895 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b6a272"/>
    <path d="M 797.925006 296.678547 
L 800.576195 298.383613 
L 802.053167 297.373572 
L 799.402673 295.775329 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f8f695"/>
    <path d="M 749.641613 268.07074 
L 752.280739 269.941854 
L 753.794782 270.463753 
L 751.158125 268.678281 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c6b67a"/>
    <path d="M 807.358466 300.578372 
L 810.01329 302.183186 
L 811.486604 300.853119 
L 808.832085 299.356343 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 776.423681 285.293255 
L 779.068706 287.149736 
L 780.558559 286.855632 
L 777.915093 285.099595 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e4dc8a"/>
    <path d="M 662.487142 216.42812 
L 665.090989 217.227472 
L 666.716797 218.866451 
L 664.115707 218.071757 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #957771"/>
    <path d="M 788.496259 292.185759 
L 791.144579 293.979627 
L 792.626587 293.282276 
L 789.97935 291.593012 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f0ec91"/>
    <path d="M 708.142149 240.63793 
L 710.77035 242.198639 
L 712.335586 243.60741 
L 709.710585 242.097073 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #967960"/>
    <path d="M 764.353214 277.829822 
L 766.995637 279.721729 
L 768.495436 279.80714 
L 765.855012 278.009916 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d8cd84"/>
    <path d="M 841.334621 305.071391 
L 844.009003 306.122209 
L 845.477246 303.717296 
L 842.801844 302.77167 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1fc96"/>
    <path d="M 823.591729 305.075914 
L 826.254522 306.460178 
L 827.724163 304.589963 
L 825.061016 303.31366 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1fc96"/>
    <path d="M 683.98985 226.570759 
L 686.607567 227.780549 
L 688.205634 229.414205 
L 685.591046 228.230559 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #836059"/>
    <path d="M 830.389154 305.864122 
L 833.056005 307.135599 
L 834.524923 305.049765 
L 831.857455 303.88547 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #edfb95"/>
    <path d="M 696.063417 233.296359 
L 698.687073 234.698892 
L 700.268804 236.246921 
L 697.648361 234.882809 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #886759"/>
    <path d="M 816.800365 303.847406 
L 819.459634 305.343389 
L 820.930666 303.689579 
L 818.271317 302.301823 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f5fd97"/>
    <path d="M 722.852601 250.084096 
L 725.48578 251.807519 
L 727.031738 252.960778 
L 724.401617 251.301616 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a68d69"/>
    <path d="M 737.566518 259.959921 
L 740.203522 261.795091 
L 741.73139 262.62087 
L 739.097168 260.862443 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b8a473"/>
    <path d="M 752.280739 269.941854 
L 754.920998 271.838293 
L 756.432649 272.272753 
L 753.794782 270.463753 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cabb7c"/>
    <path d="M 800.576195 298.383613 
L 803.228711 300.091999 
L 804.705095 298.974877 
L 802.053167 297.373572 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #faf996"/>
    <path d="M 779.068706 287.149736 
L 781.71485 289.018218 
L 783.203246 288.622704 
L 780.558559 286.855632 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e8e28d"/>
    <path d="M 852.303713 302.991844 
L 854.987028 303.83049 
L 856.456034 301.117936 
L 853.77134 300.381203 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fdff99"/>
    <path d="M 837.194362 306.211627 
L 839.865788 307.37063 
L 841.334621 305.071391 
L 838.662328 304.018282 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1fc96"/>
    <path d="M 810.01329 302.183186 
L 812.669578 303.788444 
L 814.142693 302.350395 
L 811.486604 300.853119 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fdff99"/>
    <path d="M 766.995637 279.721729 
L 769.639141 281.631461 
L 771.137033 281.620839 
L 768.495436 279.80714 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dad085"/>
    <path d="M 791.144579 293.979627 
L 793.794106 295.780298 
L 795.275138 294.977777 
L 792.626587 293.282276 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f2ee92"/>
    <path d="M 674.538284 221.631892 
L 677.151213 222.680229 
L 678.762027 224.328659 
L 676.152099 223.297135 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8b6b64"/>
    <path d="M 848.154835 304.661406 
L 850.834621 305.603794 
L 852.303713 302.991844 
L 849.622681 302.15256 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f5fd97"/>
    <path d="M 710.77035 242.198639 
L 713.400304 243.806483 
L 714.962356 245.162154 
L 712.335586 243.60741 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #987b61"/>
    <path d="M 725.48578 251.807519 
L 728.120402 253.57066 
L 729.663344 254.657202 
L 727.031738 252.960778 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #aa926b"/>
    <path d="M 740.203522 261.795091 
L 742.841751 263.662198 
L 744.366899 264.409123 
L 741.73139 262.62087 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #baa774"/>
    <path d="M 826.254522 306.460178 
L 828.919062 307.841719 
L 830.389154 305.864122 
L 827.724163 304.589963 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #edfb95"/>
    <path d="M 754.920998 271.838293 
L 757.562355 273.758867 
L 759.071694 274.104182 
L 756.432649 272.272753 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ccbe7d"/>
    <path d="M 698.687073 234.698892 
L 701.312788 236.154562 
L 702.891301 237.661289 
L 700.268804 236.246921 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8a695a"/>
    <path d="M 819.459634 305.343389 
L 822.120515 306.837581 
L 823.591729 305.075914 
L 820.930666 303.689579 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1fc96"/>
    <path d="M 665.090989 217.227472 
L 667.697995 218.093448 
L 669.320985 219.724791 
L 666.716797 218.866451 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #957771"/>
    <path d="M 686.607567 227.780549 
L 689.227705 229.04887 
L 690.822615 230.653409 
L 688.205634 229.414205 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #815e56"/>
    <path d="M 844.009003 306.122209 
L 846.685488 307.170421 
L 848.154835 304.661406 
L 845.477246 303.717296 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1fc96"/>
    <path d="M 781.71485 289.018218 
L 784.362106 290.897554 
L 785.849148 290.399764 
L 783.203246 288.622704 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eae48e"/>
    <path d="M 833.056005 307.135599 
L 835.724734 308.403858 
L 837.194362 306.211627 
L 834.524923 305.049765 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #edfb95"/>
    <path d="M 803.228711 300.091999 
L 805.882564 301.802727 
L 807.358466 300.578372 
L 804.705095 298.974877 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fcfb97"/>
    <path d="M 769.639141 281.631461 
L 772.283707 283.557822 
L 773.779786 283.449915 
L 771.137033 281.620839 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ded587"/>
    <path d="M 793.794106 295.780298 
L 796.444844 297.586698 
L 797.925006 296.678547 
L 795.275138 294.977777 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f6f394"/>
    <path d="M 812.669578 303.788444 
L 815.327345 305.393276 
L 816.800365 303.847406 
L 814.142693 302.350395 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9fe98"/>
    <path d="M 713.400304 243.806483 
L 716.031938 245.460554 
L 717.590825 246.760453 
L 714.962356 245.162154 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9a7e62"/>
    <path d="M 839.865788 307.37063 
L 842.539214 308.526351 
L 844.009003 306.122209 
L 841.334621 305.071391 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #edfb95"/>
    <path d="M 742.841751 263.662198 
L 745.481159 265.560076 
L 747.003653 266.226116 
L 744.366899 264.409123 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #beac76"/>
    <path d="M 728.120402 253.57066 
L 730.756408 255.372455 
L 732.296378 256.389893 
L 729.663344 254.657202 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ac956c"/>
    <path d="M 757.562355 273.758867 
L 760.204779 275.702364 
L 761.711891 275.956919 
L 759.071694 274.104182 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cec07f"/>
    <path d="M 854.987028 303.83049 
L 857.672635 304.668398 
L 859.143092 301.855317 
L 856.456034 301.117936 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fdff99"/>
    <path d="M 784.362106 290.897554 
L 787.010469 292.786586 
L 788.496259 292.185759 
L 785.849148 290.399764 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ece78f"/>
    <path d="M 677.151213 222.680229 
L 679.76687 223.791361 
L 681.37464 225.419988 
L 678.762027 224.328659 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8b6b64"/>
    <path d="M 772.283707 283.557822 
L 774.929318 285.4996 
L 776.423681 285.293255 
L 773.779786 283.449915 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e0d788"/>
    <path d="M 850.834621 305.603794 
L 853.516615 306.544253 
L 854.987028 303.83049 
L 852.303713 302.991844 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f5fd97"/>
    <path d="M 701.312788 236.154562 
L 703.940481 237.662621 
L 705.515774 239.125211 
L 702.891301 237.661289 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8c6c5b"/>
    <path d="M 828.919062 307.841719 
L 831.585366 309.219894 
L 833.056005 307.135599 
L 830.389154 305.864122 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #edfb95"/>
    <path d="M 805.882564 301.802727 
L 808.537763 303.514817 
L 810.01329 302.183186 
L 807.358466 300.578372 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 822.120515 306.837581 
L 824.783025 308.329224 
L 826.254522 306.460178 
L 823.591729 305.075914 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #edfb95"/>
    <path d="M 796.444844 297.586698 
L 799.096796 299.397748 
L 800.576195 298.383613 
L 797.925006 296.678547 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f8f695"/>
    <path d="M 689.227705 229.04887 
L 691.850172 230.375174 
L 693.441904 231.947652 
L 690.822615 230.653409 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #805c54"/>
    <path d="M 835.724734 308.403858 
L 838.395358 309.668366 
L 839.865788 307.37063 
L 837.194362 306.211627 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e9fb95"/>
    <path d="M 815.327345 305.393276 
L 817.986605 306.996809 
L 819.459634 305.343389 
L 816.800365 303.847406 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f5fd97"/>
    <path d="M 846.685488 307.170421 
L 849.364089 308.215716 
L 850.834621 305.603794 
L 848.154835 304.661406 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1fc96"/>
    <path d="M 667.697995 218.093448 
L 670.308066 219.025931 
L 671.928177 220.646664 
L 669.320985 219.724791 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #93756e"/>
    <path d="M 716.031938 245.460554 
L 718.665181 247.1599 
L 720.220929 248.401413 
L 717.590825 246.760453 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9c8064"/>
    <path d="M 745.481159 265.560076 
L 748.121703 267.487528 
L 749.641613 268.07074 
L 747.003653 266.226116 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c0ae77"/>
    <path d="M 760.204779 275.702364 
L 762.848242 277.667546 
L 764.353214 277.829822 
L 761.711891 275.956919 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d2c581"/>
    <path d="M 730.756408 255.372455 
L 733.39374 257.2118 
L 734.930786 258.157821 
L 732.296378 256.389893 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ae976d"/>
    <path d="M 658.252138 214.111984 
L 660.855392 214.84633 
L 662.487142 216.42812 
L 659.88655 215.695438 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9b7f79"/>
    <path d="M 787.010469 292.786586 
L 789.659935 294.684148 
L 791.144579 293.979627 
L 788.496259 292.185759 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f0ec91"/>
    <path d="M 774.929318 285.4996 
L 777.57596 287.455571 
L 779.068706 287.149736 
L 776.423681 285.293255 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e2da89"/>
    <path d="M 842.539214 308.526351 
L 845.214658 309.678371 
L 846.685488 307.170421 
L 844.009003 306.122209 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #edfb95"/>
    <path d="M 808.537763 303.514817 
L 811.194322 305.22729 
L 812.669578 303.788444 
L 810.01329 302.183186 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9fe98"/>
    <path d="M 799.096796 299.397748 
L 801.74997 301.212366 
L 803.228711 300.091999 
L 800.576195 298.383613 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #faf996"/>
    <path d="M 703.940481 237.662621 
L 706.570071 239.222266 
L 708.142149 240.63793 
L 705.515774 239.125211 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8e6e5c"/>
    <path d="M 679.76687 223.791361 
L 682.385163 224.964908 
L 683.98985 226.570759 
L 681.37464 225.419988 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #896861"/>
    <path d="M 824.783025 308.329224 
L 827.447184 309.817562 
L 828.919062 307.841719 
L 826.254522 306.460178 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #edfb95"/>
    <path d="M 831.585366 309.219894 
L 834.253453 310.594059 
L 835.724734 308.403858 
L 833.056005 307.135599 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e9fb95"/>
    <path d="M 762.848242 277.667546 
L 765.492717 279.653159 
L 766.995637 279.721729 
L 764.353214 277.829822 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d4c882"/>
    <path d="M 748.121703 267.487528 
L 750.763341 269.443331 
L 752.280739 269.941854 
L 749.641613 268.07074 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c2b178"/>
    <path d="M 857.672635 304.668398 
L 860.360542 305.505468 
L 861.832517 302.593348 
L 859.143092 301.855317 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fdff99"/>
    <path d="M 691.850172 230.375174 
L 694.474882 231.75885 
L 696.063417 233.296359 
L 693.441904 231.947652 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #805c54"/>
    <path d="M 733.39374 257.2118 
L 736.032342 259.087555 
L 737.566518 259.959921 
L 734.930786 258.157821 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b09a6e"/>
    <path d="M 718.665181 247.1599 
L 721.299964 248.903521 
L 722.852601 250.084096 
L 720.220929 248.401413 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9e8365"/>
    <path d="M 817.986605 306.996809 
L 820.647375 308.598176 
L 822.120515 306.837581 
L 819.459634 305.343389 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1fc96"/>
    <path d="M 789.659935 294.684148 
L 792.310504 296.589066 
L 793.794106 295.780298 
L 791.144579 293.979627 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f2ee92"/>
    <path d="M 853.516615 306.544253 
L 856.200828 307.482581 
L 857.672635 304.668398 
L 854.987028 303.83049 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f5fd97"/>
    <path d="M 777.57596 287.455571 
L 780.223621 289.424494 
L 781.71485 289.018218 
L 779.068706 287.149736 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e6df8b"/>
    <path d="M 838.395358 309.668366 
L 841.067895 310.928596 
L 842.539214 308.526351 
L 839.865788 307.37063 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e9fb95"/>
    <path d="M 849.364089 308.215716 
L 852.044821 309.257786 
L 853.516615 306.544253 
L 850.834621 305.603794 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #edfb95"/>
    <path d="M 670.308066 219.025931 
L 672.921105 220.024734 
L 674.538284 221.631892 
L 671.928177 220.646664 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #93756e"/>
    <path d="M 801.74997 301.212366 
L 804.404374 303.029467 
L 805.882564 301.802727 
L 803.228711 300.091999 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fcfb97"/>
    <path d="M 811.194322 305.22729 
L 813.852254 306.939165 
L 815.327345 305.393276 
L 812.669578 303.788444 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f5fd97"/>
    <path d="M 765.492717 279.653159 
L 768.138182 281.657926 
L 769.639141 281.631461 
L 766.995637 279.721729 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d8cd84"/>
    <path d="M 750.763341 269.443331 
L 753.406034 271.426229 
L 754.920998 271.838293 
L 752.280739 269.941854 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c6b67a"/>
    <path d="M 706.570071 239.222266 
L 709.201479 240.832642 
L 710.77035 242.198639 
L 708.142149 240.63793 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #90715d"/>
    <path d="M 660.855392 214.84633 
L 663.46197 215.650269 
L 665.090989 217.227472 
L 662.487142 216.42812 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9b7f79"/>
    <path d="M 736.032342 259.087555 
L 738.672161 260.998541 
L 740.203522 261.795091 
L 737.566518 259.959921 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b49f70"/>
    <path d="M 845.214658 309.678371 
L 847.892138 310.826275 
L 849.364089 308.215716 
L 846.685488 307.170421 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e9fb95"/>
    <path d="M 721.299964 248.903521 
L 723.936219 250.690369 
L 725.48578 251.807519 
L 722.852601 250.084096 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a28867"/>
    <path d="M 827.447184 309.817562 
L 830.11301 311.301843 
L 831.585366 309.219894 
L 828.919062 307.841719 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e9fb95"/>
    <path d="M 792.310504 296.589066 
L 794.962179 298.500161 
L 796.444844 297.586698 
L 793.794106 295.780298 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f4f193"/>
    <path d="M 780.223621 289.424494 
L 782.872294 291.40512 
L 784.362106 290.897554 
L 781.71485 289.018218 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e8e28d"/>
    <path d="M 682.385163 224.964908 
L 685.005997 226.200422 
L 686.607567 227.780549 
L 683.98985 226.570759 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #896861"/>
    <path d="M 834.253453 310.594059 
L 836.923343 311.963579 
L 838.395358 309.668366 
L 835.724734 308.403858 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e5fa94"/>
    <path d="M 820.647375 308.598176 
L 823.309674 310.196512 
L 824.783025 308.329224 
L 822.120515 306.837581 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #edfb95"/>
    <path d="M 694.474882 231.75885 
L 697.101747 233.199227 
L 698.687073 234.698892 
L 696.063417 233.296359 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #825f56"/>
    <path d="M 768.138182 281.657926 
L 770.784615 283.680554 
L 772.283707 283.557822 
L 769.639141 281.631461 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dad085"/>
    <path d="M 753.406034 271.426229 
L 756.049747 273.434944 
L 757.562355 273.758867 
L 754.920998 271.838293 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c8b97b"/>
    <path d="M 804.404374 303.029467 
L 807.060019 304.847965 
L 808.537763 303.514817 
L 805.882564 301.802727 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 841.067895 310.928596 
L 843.742364 312.184026 
L 845.214658 309.678371 
L 842.539214 308.526351 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e5fa94"/>
    <path d="M 860.360542 305.505468 
L 863.050754 306.341601 
L 864.524312 303.332029 
L 861.832517 302.593348 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fdff99"/>
    <path d="M 813.852254 306.939165 
L 816.511577 308.649467 
L 817.986605 306.996809 
L 815.327345 305.393276 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1fc96"/>
    <path d="M 856.200828 307.482581 
L 858.887271 308.418577 
L 860.360542 305.505468 
L 857.672635 304.668398 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f5fd97"/>
    <path d="M 738.672161 260.998541 
L 741.313143 262.943546 
L 742.841751 263.662198 
L 740.203522 261.795091 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b6a272"/>
    <path d="M 709.201479 240.832642 
L 711.834626 242.492839 
L 713.400304 243.806483 
L 710.77035 242.198639 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #92735e"/>
    <path d="M 782.872294 291.40512 
L 785.521971 293.396188 
L 787.010469 292.786586 
L 784.362106 290.897554 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eae48e"/>
    <path d="M 794.962179 298.500161 
L 797.614963 300.416248 
L 799.096796 299.397748 
L 796.444844 297.586698 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f8f695"/>
    <path d="M 723.936219 250.690369 
L 726.573879 252.519356 
L 728.120402 253.57066 
L 725.48578 251.807519 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a48b68"/>
    <path d="M 672.921105 220.024734 
L 675.537016 221.089599 
L 677.151213 222.680229 
L 674.538284 221.631892 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #93756e"/>
    <path d="M 852.044821 309.257786 
L 854.727699 310.296327 
L 856.200828 307.482581 
L 853.516615 306.544253 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #edfb95"/>
    <path d="M 830.11301 311.301843 
L 832.780526 312.781322 
L 834.253453 310.594059 
L 831.585366 309.219894 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e5fa94"/>
    <path d="M 770.784615 283.680554 
L 773.431998 285.719733 
L 774.929318 285.4996 
L 772.283707 283.557822 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ded587"/>
    <path d="M 823.309674 310.196512 
L 825.973523 311.790954 
L 827.447184 309.817562 
L 824.783025 308.329224 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e9fb95"/>
    <path d="M 756.049747 273.434944 
L 758.694445 275.468171 
L 760.204779 275.702364 
L 757.562355 273.758867 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ccbe7d"/>
    <path d="M 697.101747 233.199227 
L 699.730679 234.695573 
L 701.312788 236.154562 
L 698.687073 234.698892 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #846257"/>
    <path d="M 847.892138 310.826275 
L 850.571671 311.969653 
L 852.044821 309.257786 
L 849.364089 308.215716 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e9fb95"/>
    <path d="M 836.923343 311.963579 
L 839.595059 313.327822 
L 841.067895 310.928596 
L 838.395358 309.668366 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e5fa94"/>
    <path d="M 663.46197 215.650269 
L 666.071771 216.523753 
L 667.697995 218.093448 
L 665.090989 217.227472 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9b7f79"/>
    <path d="M 685.005997 226.200422 
L 687.62928 227.49739 
L 689.227705 229.04887 
L 686.607567 227.780549 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #87655e"/>
    <path d="M 807.060019 304.847965 
L 809.71692 306.666775 
L 811.194322 305.22729 
L 808.537763 303.514817 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9fe98"/>
    <path d="M 741.313143 262.943546 
L 743.955241 264.921321 
L 745.481159 265.560076 
L 742.841751 263.662198 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b8a473"/>
    <path d="M 785.521971 293.396188 
L 788.172649 295.396428 
L 789.659935 294.684148 
L 787.010469 292.786586 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eee990"/>
    <path d="M 816.511577 308.649467 
L 819.172309 310.357221 
L 820.647375 308.598176 
L 817.986605 306.996809 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #edfb95"/>
    <path d="M 797.614963 300.416248 
L 800.268864 302.336141 
L 801.74997 301.212366 
L 799.096796 299.397748 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #faf996"/>
    <path d="M 726.573879 252.519356 
L 729.212881 254.389348 
L 730.756408 255.372455 
L 728.120402 253.57066 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a68d69"/>
    <path d="M 711.834626 242.492839 
L 714.469436 244.201896 
L 716.031938 245.460554 
L 713.400304 243.806483 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #94765f"/>
    <path d="M 843.742364 312.184026 
L 846.418788 313.434139 
L 847.892138 310.826275 
L 845.214658 309.678371 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e5fa94"/>
    <path d="M 773.431998 285.719733 
L 776.080316 287.774137 
L 777.57596 287.455571 
L 774.929318 285.4996 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e0d788"/>
    <path d="M 758.694445 275.468171 
L 761.340098 277.524581 
L 762.848242 277.667546 
L 760.204779 275.702364 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cec07f"/>
    <path d="M 863.050754 306.341601 
L 865.74328 307.1767 
L 867.218479 304.071361 
L 864.524312 303.332029 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9fe98"/>
    <path d="M 858.887271 308.418577 
L 861.575956 309.352044 
L 863.050754 306.341601 
L 860.360542 305.505468 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f5fd97"/>
    <path d="M 743.955241 264.921321 
L 746.598406 266.930588 
L 748.121703 267.487528 
L 745.481159 265.560076 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bca975"/>
    <path d="M 832.780526 312.781322 
L 835.449754 314.255256 
L 836.923343 311.963579 
L 834.253453 310.594059 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e1f993"/>
    <path d="M 825.973523 311.790954 
L 828.638944 313.380647 
L 830.11301 311.301843 
L 827.447184 309.817562 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e5fa94"/>
    <path d="M 675.537016 221.089599 
L 678.1557 222.220195 
L 679.76687 223.791361 
L 677.151213 222.680229 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #91726c"/>
    <path d="M 809.71692 306.666775 
L 812.37509 308.484812 
L 813.852254 306.939165 
L 811.194322 305.22729 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f5fd97"/>
    <path d="M 788.172649 295.396428 
L 790.824327 297.404564 
L 792.310504 296.589066 
L 789.659935 294.684148 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f0ec91"/>
    <path d="M 699.730679 234.695573 
L 702.361592 236.247099 
L 703.940481 237.662621 
L 701.312788 236.154562 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #866458"/>
    <path d="M 854.727699 310.296327 
L 857.412737 311.331039 
L 858.887271 308.418577 
L 856.200828 307.482581 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #edfb95"/>
    <path d="M 800.268864 302.336141 
L 802.92389 304.258648 
L 804.404374 303.029467 
L 801.74997 301.212366 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fcfb97"/>
    <path d="M 729.212881 254.389348 
L 731.853162 256.299169 
L 733.39374 257.2118 
L 730.756408 255.372455 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a8906a"/>
    <path d="M 687.62928 227.49739 
L 690.254918 228.855233 
L 691.850172 230.375174 
L 689.227705 229.04887 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #87655e"/>
    <path d="M 839.595059 313.327822 
L 842.268622 314.686163 
L 843.742364 312.184026 
L 841.067895 310.928596 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e1f993"/>
    <path d="M 819.172309 310.357221 
L 821.83447 312.061456 
L 823.309674 310.196512 
L 820.647375 308.598176 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e9fb95"/>
    <path d="M 714.469436 244.201896 
L 717.105831 245.958802 
L 718.665181 247.1599 
L 716.031938 245.460554 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #967960"/>
    <path d="M 776.080316 287.774137 
L 778.729555 289.842428 
L 780.223621 289.424494 
L 777.57596 287.455571 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e4dc8a"/>
    <path d="M 761.340098 277.524581 
L 763.986676 279.602824 
L 765.492717 279.653159 
L 762.848242 277.667546 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d2c581"/>
    <path d="M 850.571671 311.969653 
L 853.253275 313.108101 
L 854.727699 310.296327 
L 852.044821 309.257786 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e5fa94"/>
    <path d="M 666.071771 216.523753 
L 668.684697 217.466661 
L 670.308066 219.025931 
L 667.697995 218.093448 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9b7f79"/>
    <path d="M 656.614663 212.593504 
L 659.220551 213.329504 
L 660.855392 214.84633 
L 658.252138 214.111984 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a18781"/>
    <path d="M 746.598406 266.930588 
L 749.242595 268.970035 
L 750.763341 269.443331 
L 748.121703 267.487528 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #beac76"/>
    <path d="M 790.824327 297.404564 
L 793.477006 299.419312 
L 794.962179 298.500161 
L 792.310504 296.589066 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f4f193"/>
    <path d="M 846.418788 313.434139 
L 849.097186 314.678423 
L 850.571671 311.969653 
L 847.892138 310.826275 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e1f993"/>
    <path d="M 812.37509 308.484812 
L 815.034549 310.300993 
L 816.511577 308.649467 
L 813.852254 306.939165 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1fc96"/>
    <path d="M 802.92389 304.258648 
L 805.580053 306.18258 
L 807.060019 304.847965 
L 804.404374 303.029467 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 828.638944 313.380647 
L 831.305961 314.96474 
L 832.780526 312.781322 
L 830.11301 311.301843 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e1f993"/>
    <path d="M 731.853162 256.299169 
L 734.494662 258.247604 
L 736.032342 259.087555 
L 733.39374 257.2118 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ac956c"/>
    <path d="M 702.361592 236.247099 
L 704.9944 237.852955 
L 706.570071 239.222266 
L 703.940481 237.662621 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #886759"/>
    <path d="M 778.729555 289.842428 
L 781.379706 291.923254 
L 782.872294 291.40512 
L 780.223621 289.424494 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e6df8b"/>
    <path d="M 763.986676 279.602824 
L 766.634154 281.70153 
L 768.138182 281.657926 
L 765.492717 279.653159 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d4c882"/>
    <path d="M 835.449754 314.255256 
L 838.120718 315.722912 
L 839.595059 313.327822 
L 836.923343 311.963579 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ddf892"/>
    <path d="M 717.105831 245.958802 
L 719.743739 247.762494 
L 721.299964 248.903521 
L 718.665181 247.1599 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9a7e62"/>
    <path d="M 821.83447 312.061456 
L 824.498083 313.761205 
L 825.973523 311.790954 
L 823.309674 310.196512 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e5fa94"/>
    <path d="M 678.1557 222.220195 
L 680.777059 223.416122 
L 682.385163 224.964908 
L 679.76687 223.791361 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #91726c"/>
    <path d="M 749.242595 268.970035 
L 751.887766 271.038322 
L 753.406034 271.426229 
L 750.763341 269.443331 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c2b178"/>
    <path d="M 690.254918 228.855233 
L 692.882817 230.273307 
L 694.474882 231.75885 
L 691.850172 230.375174 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #85635c"/>
    <path d="M 861.575956 309.352044 
L 864.266896 310.282788 
L 865.74328 307.1767 
L 863.050754 306.341601 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1fc96"/>
    <path d="M 865.74328 307.1767 
L 868.438128 308.01067 
L 869.915022 304.811345 
L 867.218479 304.071361 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9fe98"/>
    <path d="M 842.268622 314.686163 
L 844.944057 316.037983 
L 846.418788 313.434139 
L 843.742364 312.184026 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ddf892"/>
    <path d="M 857.412737 311.331039 
L 860.099953 312.361625 
L 861.575956 309.352044 
L 858.887271 308.418577 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #edfb95"/>
    <path d="M 793.477006 299.419312 
L 796.130691 301.439384 
L 797.614963 300.416248 
L 794.962179 298.500161 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f6f394"/>
    <path d="M 766.634154 281.70153 
L 769.282508 283.819306 
L 770.784615 283.680554 
L 768.138182 281.657926 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d8cd84"/>
    <path d="M 781.379706 291.923254 
L 784.03076 294.015252 
L 785.521971 293.396188 
L 782.872294 291.40512 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eae48e"/>
    <path d="M 853.253275 313.108101 
L 855.936971 314.24122 
L 857.412737 311.331039 
L 854.727699 310.296327 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e5fa94"/>
    <path d="M 815.034549 310.300993 
L 817.695316 312.114238 
L 819.172309 310.357221 
L 816.511577 308.649467 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #edfb95"/>
    <path d="M 734.494662 258.247604 
L 737.137324 260.233399 
L 738.672161 260.998541 
L 736.032342 259.087555 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ae976d"/>
    <path d="M 805.580053 306.18258 
L 808.237368 308.106744 
L 809.71692 306.666775 
L 807.060019 304.847965 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9fe98"/>
    <path d="M 668.684697 217.466661 
L 671.300646 218.478794 
L 672.921105 220.024734 
L 670.308066 219.025931 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #997c76"/>
    <path d="M 704.9944 237.852955 
L 707.629019 239.512238 
L 709.201479 240.832642 
L 706.570071 239.222266 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8a695a"/>
    <path d="M 831.305961 314.96474 
L 833.974599 316.542388 
L 835.449754 314.255256 
L 832.780526 312.781322 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ddf892"/>
    <path d="M 751.887766 271.038322 
L 754.533878 273.13408 
L 756.049747 273.434944 
L 753.406034 271.426229 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c4b379"/>
    <path d="M 719.743739 247.762494 
L 722.383087 249.611863 
L 723.936219 250.690369 
L 721.299964 248.903521 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9c8064"/>
    <path d="M 849.097186 314.678423 
L 851.777582 315.916373 
L 853.253275 313.108101 
L 850.571671 311.969653 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e1f993"/>
    <path d="M 659.220551 213.329504 
L 661.829832 214.137958 
L 663.46197 215.650269 
L 660.855392 214.84633 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a18781"/>
    <path d="M 824.498083 313.761205 
L 827.163172 315.455509 
L 828.638944 313.380647 
L 825.973523 311.790954 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e1f993"/>
    <path d="M 838.120718 315.722912 
L 840.793446 317.183563 
L 842.268622 314.686163 
L 839.595059 313.327822 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ddf892"/>
    <path d="M 796.130691 301.439384 
L 798.785388 303.463488 
L 800.268864 302.336141 
L 797.614963 300.416248 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #faf996"/>
    <path d="M 769.282508 283.819306 
L 771.93172 285.954747 
L 773.431998 285.719733 
L 770.784615 283.680554 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dad085"/>
    <path d="M 784.03076 294.015252 
L 786.682715 296.117051 
L 788.172649 295.396428 
L 785.521971 293.396188 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ece78f"/>
    <path d="M 692.882817 230.273307 
L 695.512886 231.750906 
L 697.101747 233.199227 
L 694.474882 231.75885 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #836059"/>
    <path d="M 680.777059 223.416122 
L 683.400996 224.676911 
L 685.005997 226.200422 
L 682.385163 224.964908 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8f7069"/>
    <path d="M 737.137324 260.233399 
L 739.781092 262.255261 
L 741.313143 262.943546 
L 738.672161 260.998541 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b29c6f"/>
    <path d="M 808.237368 308.106744 
L 810.89585 310.029953 
L 812.37509 308.484812 
L 809.71692 306.666775 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f5fd97"/>
    <path d="M 817.695316 312.114238 
L 820.357414 313.923474 
L 821.83447 312.061456 
L 819.172309 310.357221 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e5fa94"/>
    <path d="M 844.944057 316.037983 
L 847.621389 317.382669 
L 849.097186 314.678423 
L 846.418788 313.434139 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ddf892"/>
    <path d="M 754.533878 273.13408 
L 757.180896 275.255914 
L 758.694445 275.468171 
L 756.049747 273.434944 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c8b97b"/>
    <path d="M 864.266896 310.282788 
L 866.960102 311.210617 
L 868.438128 308.01067 
L 865.74328 307.1767 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1fc96"/>
    <path d="M 722.383087 249.611863 
L 725.023804 251.505753 
L 726.573879 252.519356 
L 723.936219 250.690369 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9e8365"/>
    <path d="M 860.099953 312.361625 
L 862.789363 313.387796 
L 864.266896 310.282788 
L 861.575956 309.352044 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e9fb95"/>
    <path d="M 707.629019 239.512238 
L 710.265366 241.223985 
L 711.834626 242.492839 
L 709.201479 240.832642 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8c6c5b"/>
    <path d="M 868.438128 308.01067 
L 871.135306 308.843418 
L 872.613945 305.551983 
L 869.915022 304.811345 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9fe98"/>
    <path d="M 798.785388 303.463488 
L 801.441107 305.490329 
L 802.92389 304.258648 
L 800.268864 302.336141 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fcfb97"/>
    <path d="M 771.93172 285.954747 
L 774.581771 288.106428 
L 776.080316 287.774137 
L 773.431998 285.719733 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ded587"/>
    <path d="M 855.936971 314.24122 
L 858.622779 315.368616 
L 860.099953 312.361625 
L 857.412737 311.331039 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e5fa94"/>
    <path d="M 833.974599 316.542388 
L 836.644885 318.112755 
L 838.120718 315.722912 
L 835.449754 314.255256 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d9f791"/>
    <path d="M 786.682715 296.117051 
L 789.335567 298.227271 
L 790.824327 297.404564 
L 788.172649 295.396428 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f0ec91"/>
    <path d="M 827.163172 315.455509 
L 829.829764 317.143414 
L 831.305961 314.96474 
L 828.638944 313.380647 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ddf892"/>
    <path d="M 739.781092 262.255261 
L 742.425913 264.311863 
L 743.955241 264.921321 
L 741.313143 262.943546 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b49f70"/>
    <path d="M 671.300646 218.478794 
L 673.919517 219.559883 
L 675.537016 221.089599 
L 672.921105 220.024734 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #997c76"/>
    <path d="M 840.793446 317.183563 
L 843.467963 318.636487 
L 844.944057 316.037983 
L 842.268622 314.686163 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d9f791"/>
    <path d="M 757.180896 275.255914 
L 759.828785 277.402404 
L 761.340098 277.524581 
L 758.694445 275.468171 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cabb7c"/>
    <path d="M 851.777582 315.916373 
L 854.46 317.147493 
L 855.936971 314.24122 
L 853.253275 313.108101 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ddf892"/>
    <path d="M 810.89585 310.029953 
L 813.555519 311.951018 
L 815.034549 310.300993 
L 812.37509 308.484812 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1fc96"/>
    <path d="M 695.512886 231.750906 
L 698.145031 233.287259 
L 699.730679 234.695573 
L 697.101747 233.199227 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #815e56"/>
    <path d="M 820.357414 313.923474 
L 823.020866 315.727629 
L 824.498083 313.761205 
L 821.83447 312.061456 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e1f993"/>
    <path d="M 661.829832 214.137958 
L 664.442402 215.018815 
L 666.071771 216.523753 
L 663.46197 215.650269 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a18781"/>
    <path d="M 683.400996 224.676911 
L 686.027412 226.002023 
L 687.62928 227.49739 
L 685.005997 226.200422 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8d6d66"/>
    <path d="M 725.023804 251.505753 
L 727.665823 253.442961 
L 729.212881 254.389348 
L 726.573879 252.519356 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a08566"/>
    <path d="M 774.581771 288.106428 
L 777.232647 290.27291 
L 778.729555 289.842428 
L 776.080316 287.774137 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e2da89"/>
    <path d="M 801.441107 305.490329 
L 804.09786 307.518613 
L 805.580053 306.18258 
L 802.92389 304.258648 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 789.335567 298.227271 
L 791.989318 300.344526 
L 793.477006 299.419312 
L 790.824327 297.404564 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f2ee92"/>
    <path d="M 847.621389 317.382669 
L 850.300644 318.71962 
L 851.777582 315.916373 
L 849.097186 314.678423 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d9f791"/>
    <path d="M 710.265366 241.223985 
L 712.903359 242.987181 
L 714.469436 244.201896 
L 711.834626 242.492839 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8e6e5c"/>
    <path d="M 742.425913 264.311863 
L 745.071736 266.401841 
L 746.598406 266.930588 
L 743.955241 264.921321 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b8a473"/>
    <path d="M 759.828785 277.402404 
L 762.477515 279.572105 
L 763.986676 279.602824 
L 761.340098 277.524581 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cec07f"/>
    <path d="M 829.829764 317.143414 
L 832.497886 318.823973 
L 833.974599 316.542388 
L 831.305961 314.96474 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d9f791"/>
    <path d="M 836.644885 318.112755 
L 839.316849 319.675013 
L 840.793446 317.183563 
L 838.120718 315.722912 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d5f791"/>
    <path d="M 813.555519 311.951018 
L 816.216396 313.868756 
L 817.695316 312.114238 
L 815.034549 310.300993 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e9fb95"/>
    <path d="M 777.232647 290.27291 
L 779.884337 292.452743 
L 781.379706 291.923254 
L 778.729555 289.842428 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e4dc8a"/>
    <path d="M 862.789363 313.387796 
L 865.480984 314.409265 
L 866.960102 311.210617 
L 864.266896 310.282788 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e9fb95"/>
    <path d="M 866.960102 311.210617 
L 869.655588 312.135345 
L 871.135306 308.843418 
L 868.438128 308.01067 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1fc96"/>
    <path d="M 823.020866 315.727629 
L 825.685699 317.52564 
L 827.163172 315.455509 
L 824.498083 313.761205 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ddf892"/>
    <path d="M 858.622779 315.368616 
L 861.310719 316.489901 
L 862.789363 313.387796 
L 860.099953 312.361625 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e1f993"/>
    <path d="M 727.665823 253.442961 
L 730.309076 255.422241 
L 731.853162 256.299169 
L 729.212881 254.389348 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a48b68"/>
    <path d="M 791.989318 300.344526 
L 794.643972 302.467424 
L 796.130691 301.439384 
L 793.477006 299.419312 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f6f394"/>
    <path d="M 804.09786 307.518613 
L 806.755661 309.547044 
L 808.237368 308.106744 
L 805.580053 306.18258 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9fe98"/>
    <path d="M 843.467963 318.636487 
L 846.144298 320.080975 
L 847.621389 317.382669 
L 844.944057 316.037983 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d5f791"/>
    <path d="M 871.135306 308.843418 
L 873.834822 309.674852 
L 875.31525 306.293274 
L 872.613945 305.551983 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9fe98"/>
    <path d="M 698.145031 233.287259 
L 700.779161 234.881534 
L 702.361592 236.247099 
L 699.730679 234.695573 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #805c54"/>
    <path d="M 673.919517 219.559883 
L 676.541208 220.709582 
L 678.1557 222.220195 
L 675.537016 221.089599 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #977a74"/>
    <path d="M 745.071736 266.401841 
L 747.718514 268.523801 
L 749.242595 268.970035 
L 746.598406 266.930588 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #baa774"/>
    <path d="M 762.477515 279.572105 
L 765.127058 281.763553 
L 766.634154 281.70153 
L 763.986676 279.602824 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d2c581"/>
    <path d="M 854.46 317.147493 
L 857.144463 318.371292 
L 858.622779 315.368616 
L 855.936971 314.24122 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ddf892"/>
    <path d="M 712.903359 242.987181 
L 715.542917 244.800756 
L 717.105831 245.958802 
L 714.469436 244.201896 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #92735e"/>
    <path d="M 686.027412 226.002023 
L 688.656208 227.390848 
L 690.254918 228.855233 
L 687.62928 227.49739 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8d6d66"/>
    <path d="M 779.884337 292.452743 
L 782.536832 294.644462 
L 784.03076 294.015252 
L 781.379706 291.923254 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e8e28d"/>
    <path d="M 816.216396 313.868756 
L 818.878505 315.781988 
L 820.357414 313.923474 
L 817.695316 312.114238 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e5fa94"/>
    <path d="M 850.300644 318.71962 
L 852.98185 320.048238 
L 854.46 317.147493 
L 851.777582 315.916373 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d5f791"/>
    <path d="M 664.442402 215.018815 
L 667.058157 215.971949 
L 668.684697 217.466661 
L 666.071771 216.523753 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a18781"/>
    <path d="M 832.497886 318.823973 
L 835.167569 320.496248 
L 836.644885 318.112755 
L 833.974599 316.542388 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d5f791"/>
    <path d="M 794.643972 302.467424 
L 797.299536 304.59457 
L 798.785388 303.463488 
L 796.130691 301.439384 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f8f695"/>
    <path d="M 654.974223 211.143064 
L 657.582716 211.880706 
L 659.220551 213.329504 
L 656.614663 212.593504 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a78e89"/>
    <path d="M 730.309076 255.422241 
L 732.953501 257.442304 
L 734.494662 258.247604 
L 731.853162 256.299169 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a68d69"/>
    <path d="M 806.755661 309.547044 
L 809.414529 311.574329 
L 810.89585 310.029953 
L 808.237368 308.106744 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f5fd97"/>
    <path d="M 839.316849 319.675013 
L 841.990521 321.228341 
L 843.467963 318.636487 
L 840.793446 317.183563 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d1f690"/>
    <path d="M 747.718514 268.523801 
L 750.366201 270.676314 
L 751.887766 271.038322 
L 749.242595 268.970035 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #beac76"/>
    <path d="M 765.127058 281.763553 
L 767.777387 283.975261 
L 769.282508 283.819306 
L 766.634154 281.70153 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d4c882"/>
    <path d="M 825.685699 317.52564 
L 828.351941 319.316452 
L 829.829764 317.143414 
L 827.163172 315.455509 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d9f791"/>
    <path d="M 700.779161 234.881534 
L 703.415188 236.532836 
L 704.9944 237.852955 
L 702.361592 236.247099 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #825f56"/>
    <path d="M 782.536832 294.644462 
L 785.190127 296.846595 
L 786.682715 296.117051 
L 784.03076 294.015252 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eae48e"/>
    <path d="M 715.542917 244.800756 
L 718.183963 246.663589 
L 719.743739 247.762494 
L 717.105831 245.958802 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #94765f"/>
    <path d="M 846.144298 320.080975 
L 848.822482 321.516325 
L 850.300644 318.71962 
L 847.621389 317.382669 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d1f690"/>
    <path d="M 865.480984 314.409265 
L 868.174833 315.425751 
L 869.655588 312.135345 
L 866.960102 311.210617 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e9fb95"/>
    <path d="M 797.299536 304.59457 
L 799.956019 306.724567 
L 801.441107 305.490329 
L 798.785388 303.463488 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fcfb97"/>
    <path d="M 861.310719 316.489901 
L 864.000813 317.604697 
L 865.480984 314.409265 
L 862.789363 313.387796 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e1f993"/>
    <path d="M 676.541208 220.709582 
L 679.165616 221.927471 
L 680.777059 223.416122 
L 678.1557 222.220195 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #977a74"/>
    <path d="M 869.655588 312.135345 
L 872.353366 313.056788 
L 873.834822 309.674852 
L 871.135306 308.843418 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1fc96"/>
    <path d="M 818.878505 315.781988 
L 821.541872 317.689543 
L 823.020866 315.727629 
L 820.357414 313.923474 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e1f993"/>
    <path d="M 767.777387 283.975261 
L 770.428483 286.205725 
L 771.93172 285.954747 
L 769.282508 283.819306 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d8cd84"/>
    <path d="M 750.366201 270.676314 
L 753.014755 272.857926 
L 754.533878 273.13408 
L 751.887766 271.038322 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c0ae77"/>
    <path d="M 732.953501 257.442304 
L 735.599034 259.501818 
L 737.137324 260.233399 
L 734.494662 258.247604 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #aa926b"/>
    <path d="M 809.414529 311.574329 
L 812.074483 313.599178 
L 813.555519 311.951018 
L 810.89585 310.029953 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #edfb95"/>
    <path d="M 688.656208 227.390848 
L 691.287287 228.842713 
L 692.882817 230.273307 
L 690.254918 228.855233 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8b6b64"/>
    <path d="M 857.144463 318.371292 
L 859.830996 319.587287 
L 861.310719 316.489901 
L 858.622779 315.368616 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d9f791"/>
    <path d="M 873.834822 309.674852 
L 876.536685 310.504882 
L 878.01894 307.035219 
L 875.31525 306.293274 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9fe98"/>
    <path d="M 835.167569 320.496248 
L 837.838844 322.159311 
L 839.316849 319.675013 
L 836.644885 318.112755 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d1f690"/>
    <path d="M 785.190127 296.846595 
L 787.84422 299.057661 
L 789.335567 298.227271 
L 786.682715 296.117051 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eee990"/>
    <path d="M 828.351941 319.316452 
L 831.019623 321.099016 
L 832.497886 318.823973 
L 829.829764 317.143414 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d5f791"/>
    <path d="M 841.990521 321.228341 
L 844.665932 322.771931 
L 846.144298 320.080975 
L 843.467963 318.636487 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cdf58f"/>
    <path d="M 852.98185 320.048238 
L 855.665034 321.367939 
L 857.144463 318.371292 
L 854.46 317.147493 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d5f791"/>
    <path d="M 718.183963 246.663589 
L 720.826419 248.574506 
L 722.383087 249.611863 
L 719.743739 247.762494 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #967960"/>
    <path d="M 770.428483 286.205725 
L 773.080324 288.453424 
L 774.581771 288.106428 
L 771.93172 285.954747 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dcd286"/>
    <path d="M 799.956019 306.724567 
L 802.613434 308.856017 
L 804.09786 307.518613 
L 801.441107 305.490329 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 703.415188 236.532836 
L 706.05302 238.240212 
L 707.629019 239.512238 
L 704.9944 237.852955 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #846257"/>
    <path d="M 667.058157 215.971949 
L 669.676993 216.997154 
L 671.300646 218.478794 
L 668.684697 217.466661 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9f847e"/>
    <path d="M 753.014755 272.857926 
L 755.664136 275.06715 
L 757.180896 275.255914 
L 754.533878 273.13408 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c4b379"/>
    <path d="M 735.599034 259.501818 
L 738.245616 261.599415 
L 739.781092 262.255261 
L 737.137324 260.233399 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ac956c"/>
    <path d="M 812.074483 313.599178 
L 814.735546 315.620304 
L 816.216396 313.868756 
L 813.555519 311.951018 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e9fb95"/>
    <path d="M 821.541872 317.689543 
L 824.206525 319.590255 
L 825.685699 317.52564 
L 823.020866 315.727629 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d9f791"/>
    <path d="M 657.582716 211.880706 
L 660.194672 212.693597 
L 661.829832 214.137958 
L 659.220551 213.329504 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a78e89"/>
    <path d="M 848.822482 321.516325 
L 851.502546 322.941844 
L 852.98185 320.048238 
L 850.300644 318.71962 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cdf58f"/>
    <path d="M 787.84422 299.057661 
L 790.49911 301.276172 
L 791.989318 300.344526 
L 789.335567 298.227271 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f2ee92"/>
    <path d="M 691.287287 228.842713 
L 693.920551 230.356872 
L 695.512886 231.750906 
L 692.882817 230.273307 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #896861"/>
    <path d="M 773.080324 288.453424 
L 775.732896 290.716821 
L 777.232647 290.27291 
L 774.581771 288.106428 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ded587"/>
    <path d="M 679.165616 221.927471 
L 681.792639 223.213058 
L 683.400996 224.676911 
L 680.777059 223.416122 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #957771"/>
    <path d="M 755.664136 275.06715 
L 758.314309 277.302476 
L 759.828785 277.402404 
L 757.180896 275.255914 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c8b97b"/>
    <path d="M 837.838844 322.159311 
L 840.511744 323.812243 
L 841.990521 321.228341 
L 839.316849 319.675013 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cdf58f"/>
    <path d="M 802.613434 308.856017 
L 805.271796 310.98752 
L 806.755661 309.547044 
L 804.09786 307.518613 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9fe98"/>
    <path d="M 831.019623 321.099016 
L 833.688778 322.872295 
L 835.167569 320.496248 
L 832.497886 318.823973 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d1f690"/>
    <path d="M 720.826419 248.574506 
L 723.47021 250.532285 
L 725.023804 251.505753 
L 722.383087 249.611863 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #987b61"/>
    <path d="M 864.000813 317.604697 
L 866.693084 318.712629 
L 868.174833 315.425751 
L 865.480984 314.409265 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ddf892"/>
    <path d="M 868.174833 315.425751 
L 870.870928 316.43698 
L 872.353366 313.056788 
L 869.655588 312.135345 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e5fa94"/>
    <path d="M 738.245616 261.599415 
L 740.893192 263.733687 
L 742.425913 264.311863 
L 739.781092 262.255261 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b09a6e"/>
    <path d="M 859.830996 319.587287 
L 862.519627 320.795005 
L 864.000813 317.604697 
L 861.310719 316.489901 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d9f791"/>
    <path d="M 872.353366 313.056788 
L 875.053451 313.974766 
L 876.536685 310.504882 
L 873.834822 309.674852 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1fc96"/>
    <path d="M 844.665932 322.771931 
L 847.343117 324.304984 
L 848.822482 321.516325 
L 846.144298 320.080975 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cdf58f"/>
    <path d="M 706.05302 238.240212 
L 708.69257 240.002649 
L 710.265366 241.223985 
L 707.629019 239.512238 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #866458"/>
    <path d="M 790.49911 301.276172 
L 793.154802 303.500633 
L 794.643972 302.467424 
L 791.989318 300.344526 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f4f193"/>
    <path d="M 814.735546 315.620304 
L 817.397743 317.636428 
L 818.878505 315.781988 
L 816.216396 313.868756 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e1f993"/>
    <path d="M 824.206525 319.590255 
L 826.872495 321.482968 
L 828.351941 319.316452 
L 825.685699 317.52564 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d5f791"/>
    <path d="M 855.665034 321.367939 
L 858.350227 322.678145 
L 859.830996 319.587287 
L 857.144463 318.371292 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d1f690"/>
    <path d="M 775.732896 290.716821 
L 778.386186 292.994364 
L 779.884337 292.452743 
L 777.232647 290.27291 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e2da89"/>
    <path d="M 876.536685 310.504882 
L 879.240902 311.33342 
L 880.725019 307.77782 
L 878.01894 307.035219 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9fe98"/>
    <path d="M 758.314309 277.302476 
L 760.965239 279.562367 
L 762.477515 279.572105 
L 759.828785 277.402404 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ccbe7d"/>
    <path d="M 805.271796 310.98752 
L 807.931124 313.117683 
L 809.414529 311.574329 
L 806.755661 309.547044 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1fc96"/>
    <path d="M 669.676993 216.997154 
L 672.298802 218.094146 
L 673.919517 219.559883 
L 671.300646 218.478794 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9f847e"/>
    <path d="M 740.893192 263.733687 
L 743.541707 265.903188 
L 745.071736 266.401841 
L 742.425913 264.311863 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b49f70"/>
    <path d="M 851.502546 322.941844 
L 854.184521 324.356852 
L 855.665034 321.367939 
L 852.98185 320.048238 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cdf58f"/>
    <path d="M 723.47021 250.532285 
L 726.115264 252.535656 
L 727.665823 253.442961 
L 725.023804 251.505753 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9c8064"/>
    <path d="M 793.154802 303.500633 
L 795.811302 305.729549 
L 797.299536 304.59457 
L 794.643972 302.467424 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f8f695"/>
    <path d="M 693.920551 230.356872 
L 696.555903 231.932518 
L 698.145031 233.287259 
L 695.512886 231.750906 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #87655e"/>
    <path d="M 833.688778 322.872295 
L 836.35944 324.635262 
L 837.838844 322.159311 
L 835.167569 320.496248 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c9f48e"/>
    <path d="M 840.511744 323.812243 
L 843.186306 325.454138 
L 844.665932 322.771931 
L 841.990521 321.228341 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c9f48e"/>
    <path d="M 778.386186 292.994364 
L 781.040183 295.284493 
L 782.536832 294.644462 
L 779.884337 292.452743 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e6df8b"/>
    <path d="M 817.397743 317.636428 
L 820.061102 319.646275 
L 821.541872 317.689543 
L 818.878505 315.781988 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ddf892"/>
    <path d="M 660.194672 212.693597 
L 662.809982 213.581685 
L 664.442402 215.018815 
L 661.829832 214.137958 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a78e89"/>
    <path d="M 681.792639 223.213058 
L 684.422171 224.565779 
L 686.027412 226.002023 
L 683.400996 224.676911 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #957771"/>
    <path d="M 760.965239 279.562367 
L 763.616896 281.845265 
L 765.127058 281.763553 
L 762.477515 279.572105 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cec07f"/>
    <path d="M 708.69257 240.002649 
L 711.333753 241.819077 
L 712.903359 242.987181 
L 710.265366 241.223985 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #886759"/>
    <path d="M 826.872495 321.482968 
L 829.539815 323.366532 
L 831.019623 321.099016 
L 828.351941 319.316452 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d1f690"/>
    <path d="M 847.343117 324.304984 
L 850.022109 325.82671 
L 851.502546 322.941844 
L 848.822482 321.516325 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c9f48e"/>
    <path d="M 807.931124 313.117683 
L 810.591439 315.245112 
L 812.074483 313.599178 
L 809.414529 311.574329 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #edfb95"/>
    <path d="M 743.541707 265.903188 
L 746.19111 268.106439 
L 747.718514 268.523801 
L 745.071736 266.401841 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b6a272"/>
    <path d="M 866.693084 318.712629 
L 869.387555 319.813332 
L 870.870928 316.43698 
L 868.174833 315.425751 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ddf892"/>
    <path d="M 862.519627 320.795005 
L 865.210381 321.993981 
L 866.693084 318.712629 
L 864.000813 317.604697 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d5f791"/>
    <path d="M 795.811302 305.729549 
L 798.468621 307.961419 
L 799.956019 306.724567 
L 797.299536 304.59457 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fcfb97"/>
    <path d="M 870.870928 316.43698 
L 873.569289 317.442682 
L 875.053451 313.974766 
L 872.353366 313.056788 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e5fa94"/>
    <path d="M 726.115264 252.535656 
L 728.761511 254.583302 
L 730.309076 255.422241 
L 727.665823 253.442961 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9e8365"/>
    <path d="M 781.040183 295.284493 
L 783.694882 297.585633 
L 785.190127 296.846595 
L 782.536832 294.644462 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eae48e"/>
    <path d="M 858.350227 322.678145 
L 861.037459 323.97829 
L 862.519627 320.795005 
L 859.830996 319.587287 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cdf58f"/>
    <path d="M 763.616896 281.845265 
L 766.269253 284.149589 
L 767.777387 283.975261 
L 765.127058 281.763553 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d2c581"/>
    <path d="M 875.053451 313.974766 
L 877.755855 314.889102 
L 879.240902 311.33342 
L 876.536685 310.504882 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1fc96"/>
    <path d="M 820.061102 319.646275 
L 822.725653 321.64858 
L 824.206525 319.590255 
L 821.541872 317.689543 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d5f791"/>
    <path d="M 836.35944 324.635262 
L 839.031646 326.386901 
L 840.511744 323.812243 
L 837.838844 322.159311 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c5f38d"/>
    <path d="M 696.555903 231.932518 
L 699.193247 233.568775 
L 700.779161 234.881534 
L 698.145031 233.287259 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #85635c"/>
    <path d="M 854.184521 324.356852 
L 856.868441 325.760677 
L 858.350227 322.678145 
L 855.665034 321.367939 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c9f48e"/>
    <path d="M 711.333753 241.819077 
L 713.976482 243.68837 
L 715.542917 244.800756 
L 712.903359 242.987181 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8c6c5b"/>
    <path d="M 843.186306 325.454138 
L 845.862565 327.0841 
L 847.343117 324.304984 
L 844.665932 322.771931 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c5f38d"/>
    <path d="M 746.19111 268.106439 
L 748.841352 270.341928 
L 750.366201 270.676314 
L 747.718514 268.523801 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #baa774"/>
    <path d="M 672.298802 218.094146 
L 674.923478 219.262565 
L 676.541208 220.709582 
L 673.919517 219.559883 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9f847e"/>
    <path d="M 810.591439 315.245112 
L 813.252764 317.368421 
L 814.735546 315.620304 
L 812.074483 313.599178 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e5fa94"/>
    <path d="M 879.240902 311.33342 
L 881.947482 312.160381 
L 883.43349 308.521077 
L 880.725019 307.77782 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9fe98"/>
    <path d="M 829.539815 323.366532 
L 832.208519 325.239813 
L 833.688778 322.872295 
L 831.019623 321.099016 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c9f48e"/>
    <path d="M 798.468621 307.961419 
L 801.126771 310.194743 
L 802.613434 308.856017 
L 799.956019 306.724567 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 783.694882 297.585633 
L 786.35028 299.896203 
L 787.84422 299.057661 
L 785.190127 296.846595 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eee990"/>
    <path d="M 766.269253 284.149589 
L 768.922286 286.473739 
L 770.428483 286.205725 
L 767.777387 283.975261 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d6cb83"/>
    <path d="M 728.761511 254.583302 
L 731.408882 256.673861 
L 732.953501 257.442304 
L 730.309076 255.422241 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a28867"/>
    <path d="M 684.422171 224.565779 
L 687.054112 225.984997 
L 688.656208 227.390848 
L 686.027412 226.002023 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #93756e"/>
    <path d="M 850.022109 325.82671 
L 852.702946 327.336336 
L 854.184521 324.356852 
L 851.502546 322.941844 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c5f38d"/>
    <path d="M 662.809982 213.581685 
L 665.42854 214.544838 
L 667.058157 215.971949 
L 664.442402 215.018815 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a78e89"/>
    <path d="M 748.841352 270.341928 
L 751.492388 272.608112 
L 753.014755 272.857926 
L 750.366201 270.676314 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #beac76"/>
    <path d="M 653.330921 209.763667 
L 655.941987 210.502938 
L 657.582716 211.880706 
L 654.974223 211.143064 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ad9691"/>
    <path d="M 822.725653 321.64858 
L 825.391429 323.642085 
L 826.872495 321.482968 
L 824.206525 319.590255 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d1f690"/>
    <path d="M 801.126771 310.194743 
L 803.785768 312.428023 
L 805.271796 310.98752 
L 802.613434 308.856017 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9fe98"/>
    <path d="M 786.35028 299.896203 
L 789.006377 302.214615 
L 790.49911 301.276172 
L 787.84422 299.057661 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f0ec91"/>
    <path d="M 813.252764 317.368421 
L 815.915127 319.486227 
L 817.397743 317.636428 
L 814.735546 315.620304 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e1f993"/>
    <path d="M 768.922286 286.473739 
L 771.575974 288.816097 
L 773.080324 288.453424 
L 770.428483 286.205725 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dad085"/>
    <path d="M 865.210381 321.993981 
L 867.903288 323.183759 
L 869.387555 319.813332 
L 866.693084 318.712629 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d5f791"/>
    <path d="M 713.976482 243.68837 
L 716.620675 245.609346 
L 718.183963 246.663589 
L 715.542917 244.800756 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8e6e5c"/>
    <path d="M 869.387555 319.813332 
L 872.084248 320.906448 
L 873.569289 317.442682 
L 870.870928 316.43698 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ddf892"/>
    <path d="M 839.031646 326.386901 
L 841.705434 328.126208 
L 843.186306 325.454138 
L 840.511744 323.812243 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c1f38d"/>
    <path d="M 699.193247 233.568775 
L 701.832488 235.264706 
L 703.415188 236.532836 
L 700.779161 234.881534 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #836059"/>
    <path d="M 861.037459 323.97829 
L 863.726762 325.267817 
L 865.210381 321.993981 
L 862.519627 320.795005 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cdf58f"/>
    <path d="M 731.408882 256.673861 
L 734.057312 258.805928 
L 735.599034 259.501818 
L 732.953501 257.442304 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a48b68"/>
    <path d="M 832.208519 325.239813 
L 834.878646 327.101685 
L 836.35944 324.635262 
L 833.688778 322.872295 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c5f38d"/>
    <path d="M 873.569289 317.442682 
L 876.269934 318.442594 
L 877.755855 314.889102 
L 875.053451 313.974766 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e5fa94"/>
    <path d="M 845.862565 327.0841 
L 848.540561 328.701247 
L 850.022109 325.82671 
L 847.343117 324.304984 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c1f38d"/>
    <path d="M 856.868441 325.760677 
L 859.554343 327.152663 
L 861.037459 323.97829 
L 858.350227 322.678145 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c5f38d"/>
    <path d="M 751.492388 272.608112 
L 754.144176 274.903417 
L 755.664136 275.06715 
L 753.014755 272.857926 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c0ae77"/>
    <path d="M 877.755855 314.889102 
L 880.460594 315.799627 
L 881.947482 312.160381 
L 879.240902 311.33342 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #edfb95"/>
    <path d="M 789.006377 302.214615 
L 791.663175 304.539273 
L 793.154802 303.500633 
L 790.49911 301.276172 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f4f193"/>
    <path d="M 771.575974 288.816097 
L 774.230299 291.175029 
L 775.732896 290.716821 
L 773.080324 288.453424 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dcd286"/>
    <path d="M 674.923478 219.262565 
L 677.550914 220.501972 
L 679.165616 221.927471 
L 676.541208 220.709582 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9d827c"/>
    <path d="M 803.785768 312.428023 
L 806.445631 314.659761 
L 807.931124 313.117683 
L 805.271796 310.98752 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1fc96"/>
    <path d="M 825.391429 323.642085 
L 828.058465 325.625546 
L 829.539815 323.366532 
L 826.872495 321.482968 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cdf58f"/>
    <path d="M 687.054112 225.984997 
L 689.688358 227.470004 
L 691.287287 228.842713 
L 688.656208 227.390848 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #91726c"/>
    <path d="M 815.915127 319.486227 
L 818.578555 321.597156 
L 820.061102 319.646275 
L 817.397743 317.636428 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d9f791"/>
    <path d="M 852.702946 327.336336 
L 855.385666 328.833099 
L 856.868441 325.760677 
L 854.184521 324.356852 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c1f38d"/>
    <path d="M 734.057312 258.805928 
L 736.706737 260.978055 
L 738.245616 261.599415 
L 735.599034 259.501818 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a8906a"/>
    <path d="M 716.620675 245.609346 
L 719.266251 247.58077 
L 720.826419 248.574506 
L 718.183963 246.663589 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #90715d"/>
    <path d="M 881.947482 312.160381 
L 884.656435 312.985681 
L 886.144355 309.264992 
L 883.43349 308.521077 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9fe98"/>
    <path d="M 754.144176 274.903417 
L 756.796676 277.226242 
L 758.314309 277.302476 
L 755.664136 275.06715 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c4b379"/>
    <path d="M 841.705434 328.126208 
L 844.380844 329.852192 
L 845.862565 327.0841 
L 843.186306 325.454138 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bdf28c"/>
    <path d="M 774.230299 291.175029 
L 776.885248 293.548888 
L 778.386186 292.994364 
L 775.732896 290.716821 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e0d788"/>
    <path d="M 791.663175 304.539273 
L 794.320683 306.868582 
L 795.811302 305.729549 
L 793.154802 303.500633 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f8f695"/>
    <path d="M 834.878646 327.101685 
L 837.550235 328.951035 
L 839.031646 326.386901 
L 836.35944 324.635262 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c1f38d"/>
    <path d="M 701.832488 235.264706 
L 704.473533 237.019309 
L 706.05302 238.240212 
L 703.415188 236.532836 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #815e56"/>
    <path d="M 806.445631 314.659761 
L 809.106383 316.888465 
L 810.591439 315.245112 
L 807.931124 313.117683 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e9fb95"/>
    <path d="M 665.42854 214.544838 
L 668.050235 215.582841 
L 669.676993 216.997154 
L 667.058157 215.971949 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a58c86"/>
    <path d="M 848.540561 328.701247 
L 851.220334 330.304711 
L 852.702946 327.336336 
L 850.022109 325.82671 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bdf28c"/>
    <path d="M 818.578555 321.597156 
L 821.243083 323.699845 
L 822.725653 321.64858 
L 820.061102 319.646275 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d5f791"/>
    <path d="M 867.903288 323.183759 
L 870.598374 324.363893 
L 872.084248 320.906448 
L 869.387555 319.813332 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d1f690"/>
    <path d="M 655.941987 210.502938 
L 658.556587 211.320186 
L 660.194672 212.693597 
L 657.582716 211.880706 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ad9691"/>
    <path d="M 828.058465 325.625546 
L 830.726798 327.597727 
L 832.208519 325.239813 
L 829.539815 323.366532 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c5f38d"/>
    <path d="M 863.726762 325.267817 
L 866.418167 326.546183 
L 867.903288 323.183759 
L 865.210381 321.993981 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c9f48e"/>
    <path d="M 736.706737 260.978055 
L 739.357098 263.188756 
L 740.893192 263.733687 
L 738.245616 261.599415 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ac956c"/>
    <path d="M 872.084248 320.906448 
L 874.783189 321.991627 
L 876.269934 318.442594 
L 873.569289 317.442682 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d9f791"/>
    <path d="M 756.796676 277.226242 
L 759.449853 279.574959 
L 760.965239 279.562367 
L 758.314309 277.302476 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c8b97b"/>
    <path d="M 776.885248 293.548888 
L 779.54081 295.936012 
L 781.040183 295.284493 
L 778.386186 292.994364 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e4dc8a"/>
    <path d="M 794.320683 306.868582 
L 796.978908 309.200939 
L 798.468621 307.961419 
L 795.811302 305.729549 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fcfb97"/>
    <path d="M 719.266251 247.58077 
L 721.913131 249.601355 
L 723.47021 250.532285 
L 720.826419 248.574506 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #94765f"/>
    <path d="M 859.554343 327.152663 
L 862.24226 328.532162 
L 863.726762 325.267817 
L 861.037459 323.97829 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c5f38d"/>
    <path d="M 876.269934 318.442594 
L 878.972882 319.436459 
L 880.460594 315.799627 
L 877.755855 314.889102 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e5fa94"/>
    <path d="M 689.688358 227.470004 
L 692.324807 229.020021 
L 693.920551 230.356872 
L 691.287287 228.842713 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8f7069"/>
    <path d="M 677.550914 220.501972 
L 680.181003 221.811854 
L 681.792639 223.213058 
L 679.165616 221.927471 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9b7f79"/>
    <path d="M 809.106383 316.888465 
L 811.768047 319.112646 
L 813.252764 317.368421 
L 810.591439 315.245112 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e5fa94"/>
    <path d="M 855.385666 328.833099 
L 858.070306 330.316249 
L 859.554343 327.152663 
L 856.868441 325.760677 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bdf28c"/>
    <path d="M 837.550235 328.951035 
L 840.223328 330.786765 
L 841.705434 328.126208 
L 839.031646 326.386901 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bdf28c"/>
    <path d="M 704.473533 237.019309 
L 707.116289 238.831519 
L 708.69257 240.002649 
L 706.05302 238.240212 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #805c54"/>
    <path d="M 759.449853 279.574959 
L 762.103673 281.947918 
L 763.616896 281.845265 
L 760.965239 279.562367 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ccbe7d"/>
    <path d="M 844.380844 329.852192 
L 847.05792 331.563879 
L 848.540561 328.701247 
L 845.862565 327.0841 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b9f18b"/>
    <path d="M 880.460594 315.799627 
L 883.167681 316.706172 
L 884.656435 312.985681 
L 881.947482 312.160381 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #edfb95"/>
    <path d="M 739.357098 263.188756 
L 742.008336 265.436505 
L 743.541707 265.903188 
L 740.893192 263.733687 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ae976d"/>
    <path d="M 779.54081 295.936012 
L 782.196976 298.33473 
L 783.694882 297.585633 
L 781.040183 295.284493 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e8e28d"/>
    <path d="M 821.243083 323.699845 
L 823.908744 325.792937 
L 825.391429 323.642085 
L 822.725653 321.64858 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cdf58f"/>
    <path d="M 796.978908 309.200939 
L 799.637866 311.534746 
L 801.126771 310.194743 
L 798.468621 307.961419 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 830.726798 327.597727 
L 833.39647 329.557407 
L 834.878646 327.101685 
L 832.208519 325.239813 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c1f38d"/>
    <path d="M 721.913131 249.601355 
L 724.561238 251.669763 
L 726.115264 252.535656 
L 723.47021 250.532285 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #967960"/>
    <path d="M 851.220334 330.304711 
L 853.901925 331.893637 
L 855.385666 328.833099 
L 852.702946 327.336336 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b9f18b"/>
    <path d="M 811.768047 319.112646 
L 814.430653 321.330824 
L 815.915127 319.486227 
L 813.252764 317.368421 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ddf892"/>
    <path d="M 884.656435 312.985681 
L 887.367769 313.80924 
L 888.857619 310.009565 
L 886.144355 309.264992 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9fe98"/>
    <path d="M 762.103673 281.947918 
L 764.758108 284.343444 
L 766.269253 284.149589 
L 763.616896 281.845265 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d0c380"/>
    <path d="M 782.196976 298.33473 
L 784.853745 300.743361 
L 786.35028 299.896203 
L 783.694882 297.585633 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ece78f"/>
    <path d="M 668.050235 215.582841 
L 670.674957 216.695398 
L 672.298802 218.094146 
L 669.676993 216.997154 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a58c86"/>
    <path d="M 742.008336 265.436505 
L 744.660398 267.71974 
L 746.19111 268.106439 
L 743.541707 265.903188 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b29c6f"/>
    <path d="M 799.637866 311.534746 
L 802.297572 313.868402 
L 803.785768 312.428023 
L 801.126771 310.194743 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9fe98"/>
    <path d="M 866.418167 326.546183 
L 869.111709 327.812854 
L 870.598374 324.363893 
L 867.903288 323.183759 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c9f48e"/>
    <path d="M 870.598374 324.363893 
L 873.295669 325.533947 
L 874.783189 321.991627 
L 872.084248 320.906448 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d1f690"/>
    <path d="M 692.324807 229.020021 
L 694.963358 230.634202 
L 696.555903 231.932518 
L 693.920551 230.356872 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8d6d66"/>
    <path d="M 823.908744 325.792937 
L 826.575576 327.87509 
L 828.058465 325.625546 
L 825.391429 323.642085 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c9f48e"/>
    <path d="M 862.24226 328.532162 
L 864.932231 329.898542 
L 866.418167 326.546183 
L 863.726762 325.267817 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c1f38d"/>
    <path d="M 707.116289 238.831519 
L 709.760664 240.700215 
L 711.333753 241.819077 
L 708.69257 240.002649 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #846257"/>
    <path d="M 840.223328 330.786765 
L 842.897968 332.607792 
L 844.380844 329.852192 
L 841.705434 328.126208 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b9f18b"/>
    <path d="M 874.783189 321.991627 
L 877.484402 323.068528 
L 878.972882 319.436459 
L 876.269934 318.442594 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d9f791"/>
    <path d="M 658.556587 211.320186 
L 661.174609 212.215355 
L 662.809982 213.581685 
L 660.194672 212.693597 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ad9691"/>
    <path d="M 680.181003 221.811854 
L 682.813635 223.19162 
L 684.422171 224.565779 
L 681.792639 223.213058 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9b7f79"/>
    <path d="M 764.758108 284.343444 
L 767.413131 286.759844 
L 768.922286 286.473739 
L 766.269253 284.149589 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d4c882"/>
    <path d="M 847.05792 331.563879 
L 849.736704 333.260309 
L 851.220334 330.304711 
L 848.540561 328.701247 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b5f08a"/>
    <path d="M 724.561238 251.669763 
L 727.210497 253.784608 
L 728.761511 254.583302 
L 726.115264 252.535656 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9a7e62"/>
    <path d="M 833.39647 329.557407 
L 836.067522 331.503379 
L 837.550235 328.951035 
L 834.878646 327.101685 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bdf28c"/>
    <path d="M 784.853745 300.743361 
L 787.511114 303.160217 
L 789.006377 302.214615 
L 786.35028 299.896203 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f0ec91"/>
    <path d="M 814.430653 321.330824 
L 817.094231 323.541527 
L 818.578555 321.597156 
L 815.915127 319.486227 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d5f791"/>
    <path d="M 858.070306 330.316249 
L 860.756909 331.785051 
L 862.24226 328.532162 
L 859.554343 327.152663 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b9f18b"/>
    <path d="M 744.660398 267.71974 
L 747.313232 270.036865 
L 748.841352 270.341928 
L 746.19111 268.106439 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b6a272"/>
    <path d="M 878.972882 319.436459 
L 881.678154 320.424027 
L 883.167681 316.706172 
L 880.460594 315.799627 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e1f993"/>
    <path d="M 802.297572 313.868402 
L 804.958045 316.200312 
L 806.445631 314.659761 
L 803.785768 312.428023 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1fc96"/>
    <path d="M 853.901925 331.893637 
L 856.585378 333.467188 
L 858.070306 330.316249 
L 855.385666 328.833099 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b5f08a"/>
    <path d="M 767.413131 286.759844 
L 770.06872 289.195405 
L 771.575974 288.816097 
L 768.922286 286.473739 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d8cd84"/>
    <path d="M 787.511114 303.160217 
L 790.169087 305.583604 
L 791.663175 304.539273 
L 789.006377 302.214615 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f4f193"/>
    <path d="M 826.575576 327.87509 
L 829.243619 329.944974 
L 830.726798 327.597727 
L 828.058465 325.625546 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c1f38d"/>
    <path d="M 883.167681 316.706172 
L 885.877131 317.608575 
L 887.367769 313.80924 
L 884.656435 312.985681 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #edfb95"/>
    <path d="M 709.760664 240.700215 
L 712.40657 242.624212 
L 713.976482 243.68837 
L 711.333753 241.819077 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #866458"/>
    <path d="M 727.210497 253.784608 
L 729.860835 255.944456 
L 731.408882 256.673861 
L 728.761511 254.583302 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9e8365"/>
    <path d="M 817.094231 323.541527 
L 819.758814 325.743292 
L 821.243083 323.699845 
L 818.578555 321.597156 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d1f690"/>
    <path d="M 747.313232 270.036865 
L 749.966788 272.38625 
L 751.492388 272.608112 
L 748.841352 270.341928 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #baa774"/>
    <path d="M 694.963358 230.634202 
L 697.603909 232.31163 
L 699.193247 233.568775 
L 696.555903 231.932518 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8b6b64"/>
    <path d="M 842.897968 332.607792 
L 845.574201 334.413047 
L 847.05792 331.563879 
L 844.380844 329.852192 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b1ef89"/>
    <path d="M 804.958045 316.200312 
L 807.61931 318.528882 
L 809.106383 316.888465 
L 806.445631 314.659761 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e9fb95"/>
    <path d="M 836.067522 331.503379 
L 838.739999 333.434451 
L 840.223328 330.786765 
L 837.550235 328.951035 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b5f08a"/>
    <path d="M 670.674957 216.695398 
L 673.302595 217.882134 
L 674.923478 219.262565 
L 672.298802 218.094146 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a58c86"/>
    <path d="M 770.06872 289.195405 
L 772.724856 291.648396 
L 774.230299 291.175029 
L 771.575974 288.816097 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dad085"/>
    <path d="M 790.169087 305.583604 
L 792.827671 308.011827 
L 794.320683 306.868582 
L 791.663175 304.539273 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f8f695"/>
    <path d="M 849.736704 333.260309 
L 852.417242 334.940537 
L 853.901925 331.893637 
L 851.220334 330.304711 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b1ef89"/>
    <path d="M 869.111709 327.812854 
L 871.807421 329.06731 
L 873.295669 325.533947 
L 870.598374 324.363893 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c5f38d"/>
    <path d="M 864.932231 329.898542 
L 867.624294 331.251185 
L 869.111709 327.812854 
L 866.418167 326.546183 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bdf28c"/>
    <path d="M 887.367769 313.80924 
L 890.081493 314.630978 
L 891.573284 310.754796 
L 888.857619 310.009565 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9fe98"/>
    <path d="M 873.295669 325.533947 
L 875.995204 326.693498 
L 877.484402 323.068528 
L 874.783189 321.991627 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cdf58f"/>
    <path d="M 682.813635 223.19162 
L 685.448705 224.640606 
L 687.054112 225.984997 
L 684.422171 224.565779 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #997c76"/>
    <path d="M 749.966788 272.38625 
L 752.621023 274.766234 
L 754.144176 274.903417 
L 751.492388 272.608112 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #beac76"/>
    <path d="M 860.756909 331.785051 
L 863.445514 333.238787 
L 864.932231 329.898542 
L 862.24226 328.532162 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b9f18b"/>
    <path d="M 829.243619 329.944974 
L 831.912917 332.001271 
L 833.39647 329.557407 
L 830.726798 327.597727 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bdf28c"/>
    <path d="M 877.484402 323.068528 
L 880.187911 324.136818 
L 881.678154 320.424027 
L 878.972882 319.436459 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d9f791"/>
    <path d="M 729.860835 255.944456 
L 732.512185 258.147827 
L 734.057312 258.805928 
L 731.408882 256.673861 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a08566"/>
    <path d="M 819.758814 325.743292 
L 822.424441 327.934667 
L 823.908744 325.792937 
L 821.243083 323.699845 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c9f48e"/>
    <path d="M 807.61931 318.528882 
L 810.281391 320.852527 
L 811.768047 319.112646 
L 809.106383 316.888465 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e1f993"/>
    <path d="M 661.174609 212.215355 
L 663.79594 213.188308 
L 665.42854 214.544838 
L 662.809982 213.581685 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ad9691"/>
    <path d="M 772.724856 291.648396 
L 775.381523 294.117074 
L 776.885248 293.548888 
L 774.230299 291.175029 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ded587"/>
    <path d="M 651.684859 208.458254 
L 654.298467 209.199143 
L 655.941987 210.502938 
L 653.330921 209.763667 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b39e99"/>
    <path d="M 712.40657 242.624212 
L 715.053919 244.602271 
L 716.620675 245.609346 
L 713.976482 243.68837 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #886759"/>
    <path d="M 792.827671 308.011827 
L 795.486875 310.443185 
L 796.978908 309.200939 
L 794.320683 306.868582 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fcfb97"/>
    <path d="M 856.585378 333.467188 
L 859.270737 335.02454 
L 860.756909 331.785051 
L 858.070306 330.316249 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b1ef89"/>
    <path d="M 881.678154 320.424027 
L 884.385769 321.405055 
L 885.877131 317.608575 
L 883.167681 316.706172 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e1f993"/>
    <path d="M 697.603909 232.31163 
L 700.246361 234.051324 
L 701.832488 235.264706 
L 699.193247 233.568775 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #896861"/>
    <path d="M 838.739999 333.434451 
L 841.413948 335.349446 
L 842.897968 332.607792 
L 840.223328 330.786765 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b1ef89"/>
    <path d="M 845.574201 334.413047 
L 848.252074 336.20148 
L 849.736704 333.260309 
L 847.05792 331.563879 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #adef89"/>
    <path d="M 752.621023 274.766234 
L 755.275894 277.175127 
L 756.796676 277.226242 
L 754.144176 274.903417 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c2b178"/>
    <path d="M 775.381523 294.117074 
L 778.038709 296.599679 
L 779.54081 295.936012 
L 776.885248 293.548888 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e2da89"/>
    <path d="M 810.281391 320.852527 
L 812.944319 323.169669 
L 814.430653 321.330824 
L 811.768047 319.112646 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ddf892"/>
    <path d="M 732.512185 258.147827 
L 735.164478 260.393199 
L 736.706737 260.978055 
L 734.057312 258.805928 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a48b68"/>
    <path d="M 795.486875 310.443185 
L 798.146713 312.875979 
L 799.637866 311.534746 
L 796.978908 309.200939 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 822.424441 327.934667 
L 825.091151 330.114212 
L 826.575576 327.87509 
L 823.908744 325.792937 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c5f38d"/>
    <path d="M 831.912917 332.001271 
L 834.583513 334.04268 
L 836.067522 331.503379 
L 833.39647 329.557407 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b5f08a"/>
    <path d="M 852.417242 334.940537 
L 855.099582 336.603635 
L 856.585378 333.467188 
L 853.901925 331.893637 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #adef89"/>
    <path d="M 885.877131 317.608575 
L 888.588958 318.506678 
L 890.081493 314.630978 
L 887.367769 313.80924 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #edfb95"/>
    <path d="M 673.302595 217.882134 
L 675.933036 219.142592 
L 677.550914 220.501972 
L 674.923478 219.262565 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a38984"/>
    <path d="M 755.275894 277.175127 
L 757.931363 279.611213 
L 759.449853 279.574959 
L 756.796676 277.226242 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c4b379"/>
    <path d="M 715.053919 244.602271 
L 717.702625 246.633094 
L 719.266251 247.58077 
L 716.620675 245.609346 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8c6c5b"/>
    <path d="M 685.448705 224.640606 
L 688.086104 226.158071 
L 689.688358 227.470004 
L 687.054112 225.984997 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #977a74"/>
    <path d="M 778.038709 296.599679 
L 780.696406 299.094445 
L 782.196976 298.33473 
L 779.54081 295.936012 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e6df8b"/>
    <path d="M 867.624294 331.251185 
L 870.318487 332.589485 
L 871.807421 329.06731 
L 869.111709 327.812854 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bdf28c"/>
    <path d="M 871.807421 329.06731 
L 874.505338 330.309043 
L 875.995204 326.693498 
L 873.295669 325.533947 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c5f38d"/>
    <path d="M 863.445514 333.238787 
L 866.136166 334.676753 
L 867.624294 331.251185 
L 864.932231 329.898542 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b5f08a"/>
    <path d="M 798.146713 312.875979 
L 800.807201 315.308511 
L 802.297572 313.868402 
L 799.637866 311.534746 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9fe98"/>
    <path d="M 812.944319 323.169669 
L 815.608125 325.478736 
L 817.094231 323.541527 
L 814.430653 321.330824 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d5f791"/>
    <path d="M 875.995204 326.693498 
L 878.697008 327.842129 
L 880.187911 324.136818 
L 877.484402 323.068528 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cdf58f"/>
    <path d="M 735.164478 260.393199 
L 737.817651 262.679007 
L 739.357098 263.188756 
L 736.706737 260.978055 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a8906a"/>
    <path d="M 841.413948 335.349446 
L 844.089418 337.247206 
L 845.574201 334.413047 
L 842.897968 332.607792 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #adef89"/>
    <path d="M 700.246361 234.051324 
L 702.890615 235.852233 
L 704.473533 237.019309 
L 701.832488 235.264706 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #87655e"/>
    <path d="M 848.252074 336.20148 
L 850.931637 337.972058 
L 852.417242 334.940537 
L 849.736704 333.260309 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a9ee88"/>
    <path d="M 825.091151 330.114212 
L 827.758985 332.280504 
L 829.243619 329.944974 
L 826.575576 327.87509 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bdf28c"/>
    <path d="M 859.270737 335.02454 
L 861.958049 336.564888 
L 863.445514 333.238787 
L 860.756909 331.785051 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #adef89"/>
    <path d="M 757.931363 279.611213 
L 760.587394 282.072749 
L 762.103673 281.947918 
L 759.449853 279.574959 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c8b97b"/>
    <path d="M 890.081493 314.630978 
L 892.797616 315.450819 
L 894.291354 311.500688 
L 891.573284 310.754796 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9fe98"/>
    <path d="M 780.696406 299.094445 
L 783.354609 301.599592 
L 784.853745 300.743361 
L 782.196976 298.33473 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eae48e"/>
    <path d="M 880.187911 324.136818 
L 882.893743 325.196174 
L 884.385769 321.405055 
L 881.678154 320.424027 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d5f791"/>
    <path d="M 834.583513 334.04268 
L 837.255456 336.067918 
L 838.739999 333.434451 
L 836.067522 331.503379 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b1ef89"/>
    <path d="M 663.79594 213.188308 
L 666.420467 214.238822 
L 668.050235 215.582841 
L 665.42854 214.544838 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ab938e"/>
    <path d="M 800.807201 315.308511 
L 803.468361 317.739088 
L 804.958045 316.200312 
L 802.297572 313.868402 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1fc96"/>
    <path d="M 717.702625 246.633094 
L 720.352605 248.715332 
L 721.913131 249.601355 
L 719.266251 247.58077 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8e6e5c"/>
    <path d="M 654.298467 209.199143 
L 656.915679 210.020662 
L 658.556587 211.320186 
L 655.941987 210.502938 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b39e99"/>
    <path d="M 815.608125 325.478736 
L 818.272846 327.778171 
L 819.758814 325.743292 
L 817.094231 323.541527 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cdf58f"/>
    <path d="M 855.099582 336.603635 
L 857.783773 338.248697 
L 859.270737 335.02454 
L 856.585378 333.467188 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a9ee88"/>
    <path d="M 737.817651 262.679007 
L 740.471644 265.003645 
L 742.008336 265.436505 
L 739.357098 263.188756 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #aa926b"/>
    <path d="M 760.587394 282.072749 
L 763.243957 284.557969 
L 764.758108 284.343444 
L 762.103673 281.947918 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ccbe7d"/>
    <path d="M 783.354609 301.599592 
L 786.013317 304.113334 
L 787.511114 303.160217 
L 784.853745 300.743361 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eee990"/>
    <path d="M 884.385769 321.405055 
L 887.095747 322.379306 
L 888.588958 318.506678 
L 885.877131 317.608575 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e1f993"/>
    <path d="M 688.086104 226.158071 
L 690.725725 227.743203 
L 692.324807 229.020021 
L 689.688358 227.470004 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #957771"/>
    <path d="M 827.758985 332.280504 
L 830.42799 334.432131 
L 831.912917 332.001271 
L 829.243619 329.944974 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b5f08a"/>
    <path d="M 803.468361 317.739088 
L 806.130215 320.166018 
L 807.61931 318.528882 
L 804.958045 316.200312 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e9fb95"/>
    <path d="M 675.933036 219.142592 
L 678.56617 220.476236 
L 680.181003 221.811854 
L 677.550914 220.501972 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a18781"/>
    <path d="M 844.089418 337.247206 
L 846.76646 339.126591 
L 848.252074 336.20148 
L 845.574201 334.413047 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a5ed87"/>
    <path d="M 702.890615 235.852233 
L 705.536575 237.713245 
L 707.116289 238.831519 
L 704.473533 237.019309 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #836059"/>
    <path d="M 763.243957 284.557969 
L 765.901022 287.065086 
L 767.413131 286.759844 
L 764.758108 284.343444 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d0c380"/>
    <path d="M 870.318487 332.589485 
L 873.014851 333.912854 
L 874.505338 330.309043 
L 871.807421 329.06731 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b9f18b"/>
    <path d="M 786.013317 304.113334 
L 788.672533 306.633882 
L 790.169087 305.583604 
L 787.511114 303.160217 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f2ee92"/>
    <path d="M 837.255456 336.067918 
L 839.928795 338.075717 
L 841.413948 335.349446 
L 838.739999 333.434451 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a9ee88"/>
    <path d="M 866.136166 334.676753 
L 868.828908 336.09826 
L 870.318487 332.589485 
L 867.624294 331.251185 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b1ef89"/>
    <path d="M 850.931637 337.972058 
L 853.612942 339.723767 
L 855.099582 336.603635 
L 852.417242 334.940537 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a5ed87"/>
    <path d="M 740.471644 265.003645 
L 743.126397 267.36547 
L 744.660398 267.71974 
L 742.008336 265.436505 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ae976d"/>
    <path d="M 818.272846 327.778171 
L 820.93852 330.066427 
L 822.424441 327.934667 
L 819.758814 325.743292 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c5f38d"/>
    <path d="M 720.352605 248.715332 
L 723.003778 250.847579 
L 724.561238 251.669763 
L 721.913131 249.601355 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #92735e"/>
    <path d="M 874.505338 330.309043 
L 877.205497 331.537558 
L 878.697008 327.842129 
L 875.995204 326.693498 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c1f38d"/>
    <path d="M 888.588958 318.506678 
L 891.303178 319.400328 
L 892.797616 315.450819 
L 890.081493 314.630978 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #edfb95"/>
    <path d="M 861.958049 336.564888 
L 864.647361 338.087444 
L 866.136166 334.676753 
L 863.445514 333.238787 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a9ee88"/>
    <path d="M 878.697008 327.842129 
L 881.401113 328.97944 
L 882.893743 325.196174 
L 880.187911 324.136818 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cdf58f"/>
    <path d="M 806.130215 320.166018 
L 808.792792 322.587618 
L 810.281391 320.852527 
L 807.61931 318.528882 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e1f993"/>
    <path d="M 765.901022 287.065086 
L 768.558566 289.592294 
L 770.06872 289.195405 
L 767.413131 286.759844 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d4c882"/>
    <path d="M 788.672533 306.633882 
L 791.332263 309.159439 
L 792.827671 308.011827 
L 790.169087 305.583604 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f6f394"/>
    <path d="M 830.42799 334.432131 
L 833.098213 336.567701 
L 834.583513 334.04268 
L 831.912917 332.001271 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b1ef89"/>
    <path d="M 857.783773 338.248697 
L 860.469865 339.87483 
L 861.958049 336.564888 
L 859.270737 335.02454 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a5ed87"/>
    <path d="M 743.126397 267.36547 
L 745.781856 269.762802 
L 747.313232 270.036865 
L 744.660398 267.71974 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b29c6f"/>
    <path d="M 666.420467 214.238822 
L 669.048074 215.366589 
L 670.674957 216.695398 
L 668.050235 215.582841 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ab938e"/>
    <path d="M 820.93852 330.066427 
L 823.605189 332.34197 
L 825.091151 330.114212 
L 822.424441 327.934667 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bdf28c"/>
    <path d="M 882.893743 325.196174 
L 885.601924 326.246282 
L 887.095747 322.379306 
L 884.385769 321.405055 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d5f791"/>
    <path d="M 723.003778 250.847579 
L 725.656065 253.028382 
L 727.210497 253.784608 
L 724.561238 251.669763 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #967960"/>
    <path d="M 846.76646 339.126591 
L 849.445128 340.986481 
L 850.931637 337.972058 
L 848.252074 336.20148 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a1ec86"/>
    <path d="M 705.536575 237.713245 
L 708.184144 239.633184 
L 709.760664 240.700215 
L 707.116289 238.831519 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #815e56"/>
    <path d="M 690.725725 227.743203 
L 693.367462 229.395118 
L 694.963358 230.634202 
L 692.324807 229.020021 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #93756e"/>
    <path d="M 892.797616 315.450819 
L 895.516148 316.26869 
L 897.011831 312.24724 
L 894.291354 311.500688 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9fe98"/>
    <path d="M 839.928795 338.075717 
L 842.603584 340.06483 
L 844.089418 337.247206 
L 841.413948 335.349446 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a5ed87"/>
    <path d="M 768.558566 289.592294 
L 771.216568 292.137768 
L 772.724856 291.648396 
L 770.06872 289.195405 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d8cd84"/>
    <path d="M 791.332263 309.159439 
L 793.992516 311.68821 
L 795.486875 310.443185 
L 792.827671 308.011827 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #faf996"/>
    <path d="M 808.792792 322.587618 
L 811.45612 325.002214 
L 812.944319 323.169669 
L 810.281391 320.852527 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d9f791"/>
    <path d="M 656.915679 210.020662 
L 659.53638 210.922755 
L 661.174609 212.215355 
L 658.556587 211.320186 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b39e99"/>
    <path d="M 853.612942 339.723767 
L 856.296041 341.455613 
L 857.783773 338.248697 
L 855.099582 336.603635 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a1ec86"/>
    <path d="M 678.56617 220.476236 
L 681.201882 221.882453 
L 682.813635 223.19162 
L 680.181003 221.811854 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a18781"/>
    <path d="M 745.781856 269.762802 
L 748.437971 272.193927 
L 749.966788 272.38625 
L 747.313232 270.036865 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b6a272"/>
    <path d="M 887.095747 322.379306 
L 889.808111 323.346552 
L 891.303178 319.400328 
L 888.588958 318.506678 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e1f993"/>
    <path d="M 833.098213 336.567701 
L 835.769704 338.685839 
L 837.255456 336.067918 
L 834.583513 334.04268 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a9ee88"/>
    <path d="M 771.216568 292.137768 
L 773.87501 294.699669 
L 775.381523 294.117074 
L 772.724856 291.648396 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ded587"/>
    <path d="M 868.828908 336.09826 
L 871.523785 337.502639 
L 873.014851 333.912854 
L 870.318487 332.589485 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #adef89"/>
    <path d="M 793.992516 311.68821 
L 796.653307 314.218396 
L 798.146713 312.875979 
L 795.486875 310.443185 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 823.605189 332.34197 
L 826.272897 334.603281 
L 827.758985 332.280504 
L 825.091151 330.114212 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b9f18b"/>
    <path d="M 873.014851 333.912854 
L 875.713427 335.220716 
L 877.205497 331.537558 
L 874.505338 330.309043 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b5f08a"/>
    <path d="M 811.45612 325.002214 
L 814.120236 327.408141 
L 815.608125 325.478736 
L 812.944319 323.169669 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d1f690"/>
    <path d="M 864.647361 338.087444 
L 867.338721 339.59144 
L 868.828908 336.09826 
L 866.136166 334.676753 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a9ee88"/>
    <path d="M 725.656065 253.028382 
L 728.309391 255.256235 
L 729.860835 255.944456 
L 727.210497 253.784608 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #987b61"/>
    <path d="M 877.205497 331.537558 
L 879.907934 332.752374 
L 881.401113 328.97944 
L 878.697008 327.842129 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c1f38d"/>
    <path d="M 748.437971 272.193927 
L 751.094692 274.657098 
L 752.621023 274.766234 
L 749.966788 272.38625 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #baa774"/>
    <path d="M 708.184144 239.633184 
L 710.83323 241.610811 
L 712.40657 242.624212 
L 709.760664 240.700215 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #805c54"/>
    <path d="M 773.87501 294.699669 
L 776.533881 297.276144 
L 778.038709 296.599679 
L 775.381523 294.117074 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e2da89"/>
    <path d="M 842.603584 340.06483 
L 845.279877 342.034029 
L 846.76646 339.126591 
L 844.089418 337.247206 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9deb85"/>
    <path d="M 860.469865 339.87483 
L 863.15791 341.481165 
L 864.647361 338.087444 
L 861.958049 336.564888 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a1ec86"/>
    <path d="M 849.445128 340.986481 
L 852.125476 342.825777 
L 853.612942 339.723767 
L 850.931637 337.972058 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9deb85"/>
    <path d="M 796.653307 314.218396 
L 799.314653 316.748205 
L 800.807201 315.308511 
L 798.146713 312.875979 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f5fd97"/>
    <path d="M 891.303178 319.400328 
L 894.019806 320.289378 
L 895.516148 316.26869 
L 892.797616 315.450819 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #edfb95"/>
    <path d="M 881.401113 328.97944 
L 884.107551 330.10504 
L 885.601924 326.246282 
L 882.893743 325.196174 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c9f48e"/>
    <path d="M 693.367462 229.395118 
L 696.011211 231.112858 
L 697.603909 232.31163 
L 694.963358 230.634202 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #91726c"/>
    <path d="M 814.120236 327.408141 
L 816.785175 329.803744 
L 818.272846 327.778171 
L 815.608125 325.478736 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c9f48e"/>
    <path d="M 826.272897 334.603281 
L 828.941692 336.84886 
L 830.42799 334.432131 
L 827.758985 332.280504 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b1ef89"/>
    <path d="M 835.769704 338.685839 
L 838.442517 340.785188 
L 839.928795 338.075717 
L 837.255456 336.067918 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a5ed87"/>
    <path d="M 751.094692 274.657098 
L 753.751975 277.150538 
L 755.275894 277.175127 
L 752.621023 274.766234 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #beac76"/>
    <path d="M 728.309391 255.256235 
L 730.963681 257.529586 
L 732.512185 258.147827 
L 729.860835 255.944456 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9c8064"/>
    <path d="M 776.533881 297.276144 
L 779.193169 299.865328 
L 780.696406 299.094445 
L 778.038709 296.599679 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e6df8b"/>
    <path d="M 669.048074 215.366589 
L 671.678647 216.571219 
L 673.302595 217.882134 
L 670.674957 216.695398 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ab938e"/>
    <path d="M 856.296041 341.455613 
L 858.980989 343.166622 
L 860.469865 339.87483 
L 857.783773 338.248697 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9deb85"/>
    <path d="M 799.314653 316.748205 
L 801.976574 319.275844 
L 803.468361 317.739088 
L 800.807201 315.308511 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #edfb95"/>
    <path d="M 885.601924 326.246282 
L 888.312481 327.286839 
L 889.808111 323.346552 
L 887.095747 322.379306 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d5f791"/>
    <path d="M 681.201882 221.882453 
L 683.840062 223.360548 
L 685.448705 224.640606 
L 682.813635 223.19162 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9f847e"/>
    <path d="M 710.83323 241.610811 
L 713.483739 243.644828 
L 715.053919 244.602271 
L 712.40657 242.624212 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #846257"/>
    <path d="M 779.193169 299.865328 
L 781.852871 302.465347 
L 783.354609 301.599592 
L 780.696406 299.094445 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eae48e"/>
    <path d="M 816.785175 329.803744 
L 819.450978 332.187384 
L 820.93852 330.066427 
L 818.272846 327.778171 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c1f38d"/>
    <path d="M 753.751975 277.150538 
L 756.409779 279.672441 
L 757.931363 279.611213 
L 755.275894 277.175127 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c2b178"/>
    <path d="M 895.516148 316.26869 
L 898.237098 317.084519 
L 899.734719 312.994454 
L 897.011831 312.24724 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9fe98"/>
    <path d="M 650.036146 207.2297 
L 652.652261 207.972192 
L 654.298467 209.199143 
L 651.684859 208.458254 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b9a5a1"/>
    <path d="M 845.279877 342.034029 
L 847.95773 343.982107 
L 849.445128 340.986481 
L 846.76646 339.126591 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #99eb85"/>
    <path d="M 659.53638 210.922755 
L 662.160454 211.90528 
L 663.79594 213.188308 
L 661.174609 212.215355 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b39e99"/>
    <path d="M 871.523785 337.502639 
L 874.220844 338.889236 
L 875.713427 335.220716 
L 873.014851 333.912854 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #adef89"/>
    <path d="M 828.941692 336.84886 
L 831.611626 339.077222 
L 833.098213 336.567701 
L 830.42799 334.432131 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a9ee88"/>
    <path d="M 801.976574 319.275844 
L 804.639095 321.799528 
L 806.130215 320.166018 
L 803.468361 317.739088 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e5fa94"/>
    <path d="M 867.338721 339.59144 
L 870.032181 341.076125 
L 871.523785 337.502639 
L 868.828908 336.09826 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a5ed87"/>
    <path d="M 730.963681 257.529586 
L 733.618866 259.846837 
L 735.164478 260.393199 
L 732.512185 258.147827 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a08566"/>
    <path d="M 875.713427 335.220716 
L 878.414257 336.512514 
L 879.907934 332.752374 
L 877.205497 331.537558 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b5f08a"/>
    <path d="M 852.125476 342.825777 
L 854.807562 344.643399 
L 856.296041 341.455613 
L 853.612942 339.723767 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #99eb85"/>
    <path d="M 838.442517 340.785188 
L 841.116708 342.864413 
L 842.603584 340.06483 
L 839.928795 338.075717 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9deb85"/>
    <path d="M 889.808111 323.346552 
L 892.52288 324.306572 
L 894.019806 320.289378 
L 891.303178 319.400328 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e1f993"/>
    <path d="M 696.011211 231.112858 
L 698.656866 232.895398 
L 700.246361 234.051324 
L 697.603909 232.31163 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8f7069"/>
    <path d="M 863.15791 341.481165 
L 865.847962 343.066852 
L 867.338721 339.59144 
L 864.647361 338.087444 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9deb85"/>
    <path d="M 781.852871 302.465347 
L 784.512983 305.07432 
L 786.013317 304.113334 
L 783.354609 301.599592 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eee990"/>
    <path d="M 879.907934 332.752374 
L 882.612685 333.953026 
L 884.107551 330.10504 
L 881.401113 328.97944 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bdf28c"/>
    <path d="M 756.409779 279.672441 
L 759.068067 282.220976 
L 760.587394 282.072749 
L 757.931363 279.611213 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c6b67a"/>
    <path d="M 819.450978 332.187384 
L 822.117689 334.557434 
L 823.605189 332.34197 
L 820.93852 330.066427 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b9f18b"/>
    <path d="M 804.639095 321.799528 
L 807.302244 324.317478 
L 808.792792 322.587618 
L 806.130215 320.166018 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ddf892"/>
    <path d="M 858.980989 343.166622 
L 861.667843 344.855842 
L 863.15791 341.481165 
L 860.469865 339.87483 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #99eb85"/>
    <path d="M 713.483739 243.644828 
L 716.135582 245.733878 
L 717.702625 246.633094 
L 715.053919 244.602271 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #866458"/>
    <path d="M 784.512983 305.07432 
L 787.173509 307.690358 
L 788.672533 306.633882 
L 786.013317 304.113334 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f2ee92"/>
    <path d="M 733.618866 259.846837 
L 736.274877 262.206347 
L 737.817651 262.679007 
L 735.164478 260.393199 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a48b68"/>
    <path d="M 831.611626 339.077222 
L 834.28275 341.286903 
L 835.769704 338.685839 
L 833.098213 336.567701 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a5ed87"/>
    <path d="M 884.107551 330.10504 
L 886.816353 331.218549 
L 888.312481 327.286839 
L 885.601924 326.246282 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c9f48e"/>
    <path d="M 759.068067 282.220976 
L 761.726804 284.794286 
L 763.243957 284.557969 
L 760.587394 282.072749 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cabb7c"/>
    <path d="M 671.678647 216.571219 
L 674.312069 217.852237 
L 675.933036 219.142592 
L 673.302595 217.882134 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a9918c"/>
    <path d="M 847.95773 343.982107 
L 850.637203 345.907881 
L 852.125476 342.825777 
L 849.445128 340.986481 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #95ea84"/>
    <path d="M 894.019806 320.289378 
L 896.738857 321.173685 
L 898.237098 317.084519 
L 895.516148 316.26869 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #edfb95"/>
    <path d="M 683.840062 223.360548 
L 686.480596 224.909751 
L 688.086104 226.158071 
L 685.448705 224.640606 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9d827c"/>
    <path d="M 807.302244 324.317478 
L 809.966054 326.827924 
L 811.45612 325.002214 
L 808.792792 322.587618 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d5f791"/>
    <path d="M 841.116708 342.864413 
L 843.792335 344.9222 
L 845.279877 342.034029 
L 842.603584 340.06483 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #99eb85"/>
    <path d="M 787.173509 307.690358 
L 789.834453 310.311571 
L 791.332263 309.159439 
L 788.672533 306.633882 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f6f394"/>
    <path d="M 822.117689 334.557434 
L 824.785354 336.912285 
L 826.272897 334.603281 
L 823.605189 332.34197 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b5f08a"/>
    <path d="M 854.807562 344.643399 
L 857.491446 346.438293 
L 858.980989 343.166622 
L 856.296041 341.455613 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #91e983"/>
    <path d="M 761.726804 284.794286 
L 764.385962 287.390492 
L 765.901022 287.065086 
L 763.243957 284.557969 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cec07f"/>
    <path d="M 698.656866 232.895398 
L 701.304324 234.741643 
L 702.890615 235.852233 
L 700.246361 234.051324 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8b6b64"/>
    <path d="M 736.274877 262.206347 
L 738.931651 264.606431 
L 740.471644 265.003645 
L 737.817651 262.679007 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a68d69"/>
    <path d="M 888.312481 327.286839 
L 891.02544 328.317549 
L 892.52288 324.306572 
L 889.808111 323.346552 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d1f690"/>
    <path d="M 870.032181 341.076125 
L 872.72779 342.540769 
L 874.220844 338.889236 
L 871.523785 337.502639 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a1ec86"/>
    <path d="M 874.220844 338.889236 
L 876.920131 340.257417 
L 878.414257 336.512514 
L 875.713427 335.220716 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a9ee88"/>
    <path d="M 716.135582 245.733878 
L 718.788672 247.876546 
L 720.352605 248.715332 
L 717.702625 246.633094 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8a695a"/>
    <path d="M 789.834453 310.311571 
L 792.495827 312.936068 
L 793.992516 311.68821 
L 791.332263 309.159439 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #faf996"/>
    <path d="M 834.28275 341.286903 
L 836.955121 343.47646 
L 838.442517 340.785188 
L 835.769704 338.685839 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9deb85"/>
    <path d="M 809.966054 326.827924 
L 812.630558 329.329108 
L 814.120236 327.408141 
L 811.45612 325.002214 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cdf58f"/>
    <path d="M 865.847962 343.066852 
L 868.540075 344.631062 
L 870.032181 341.076125 
L 867.338721 339.59144 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #99eb85"/>
    <path d="M 878.414257 336.512514 
L 881.117383 337.787706 
L 882.612685 333.953026 
L 879.907934 332.752374 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b1ef89"/>
    <path d="M 662.160454 211.90528 
L 664.787783 212.968004 
L 666.420467 214.238822 
L 663.79594 213.188308 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b19b96"/>
    <path d="M 764.385962 287.390492 
L 767.045513 290.007696 
L 768.558566 289.592294 
L 765.901022 287.065086 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d2c581"/>
    <path d="M 824.785354 336.912285 
L 827.454025 339.250344 
L 828.941692 336.84886 
L 826.272897 334.603281 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #adef89"/>
    <path d="M 652.652261 207.972192 
L 655.272051 208.797894 
L 656.915679 210.020662 
L 654.298467 209.199143 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b9a5a1"/>
    <path d="M 898.237098 317.084519 
L 900.960474 317.898238 
L 902.460022 313.74233 
L 899.734719 312.994454 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9fe98"/>
    <path d="M 861.667843 344.855842 
L 864.356661 346.522345 
L 865.847962 343.066852 
L 863.15791 341.481165 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #95ea84"/>
    <path d="M 738.931651 264.606431 
L 741.589125 267.045366 
L 743.126397 267.36547 
L 740.471644 265.003645 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #aa926b"/>
    <path d="M 792.495827 312.936068 
L 795.157643 315.561954 
L 796.653307 314.218396 
L 793.992516 311.68821 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 850.637203 345.907881 
L 853.318358 347.81019 
L 854.807562 344.643399 
L 852.125476 342.825777 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8de882"/>
    <path d="M 843.792335 344.9222 
L 846.469457 346.957258 
L 847.95773 343.982107 
L 845.279877 342.034029 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #91e983"/>
    <path d="M 882.612685 333.953026 
L 885.31979 335.139061 
L 886.816353 331.218549 
L 884.107551 330.10504 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bdf28c"/>
    <path d="M 892.52288 324.306572 
L 895.240076 325.259152 
L 896.738857 321.173685 
L 894.019806 320.289378 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ddf892"/>
    <path d="M 812.630558 329.329108 
L 815.295797 331.819283 
L 816.785175 329.803744 
L 814.120236 327.408141 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c5f38d"/>
    <path d="M 767.045513 290.007696 
L 769.705435 292.643981 
L 771.216568 292.137768 
L 768.558566 289.592294 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d8cd84"/>
    <path d="M 686.480596 224.909751 
L 689.123375 226.529216 
L 690.725725 227.743203 
L 688.086104 226.158071 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9b7f79"/>
    <path d="M 718.788672 247.876546 
L 721.442924 250.071365 
L 723.003778 250.847579 
L 720.352605 248.715332 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8e6e5c"/>
    <path d="M 701.304324 234.741643 
L 703.953484 236.65043 
L 705.536575 237.713245 
L 702.890615 235.852233 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #896861"/>
    <path d="M 857.491446 346.438293 
L 860.177187 348.209426 
L 861.667843 344.855842 
L 858.980989 343.166622 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8de882"/>
    <path d="M 836.955121 343.47646 
L 839.628799 345.644469 
L 841.116708 342.864413 
L 838.442517 340.785188 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #95ea84"/>
    <path d="M 795.157643 315.561954 
L 797.819919 318.18734 
L 799.314653 316.748205 
L 796.653307 314.218396 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f5fd97"/>
    <path d="M 674.312069 217.852237 
L 676.948224 219.209086 
L 678.56617 220.476236 
L 675.933036 219.142592 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a78e89"/>
    <path d="M 741.589125 267.045366 
L 744.247243 269.521391 
L 745.781856 269.762802 
L 743.126397 267.36547 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ae976d"/>
    <path d="M 827.454025 339.250344 
L 830.123753 341.57004 
L 831.611626 339.077222 
L 828.941692 336.84886 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a5ed87"/>
    <path d="M 886.816353 331.218549 
L 889.527554 332.319603 
L 891.02544 328.317549 
L 888.312481 327.286839 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c5f38d"/>
    <path d="M 769.705435 292.643981 
L 772.36571 295.297413 
L 773.87501 294.699669 
L 771.216568 292.137768 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dcd286"/>
    <path d="M 815.295797 331.819283 
L 817.961812 334.296716 
L 819.450978 332.187384 
L 816.785175 329.803744 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bdf28c"/>
    <path d="M 797.819919 318.18734 
L 800.482677 320.810341 
L 801.976574 319.275844 
L 799.314653 316.748205 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #edfb95"/>
    <path d="M 872.72779 342.540769 
L 875.425602 343.984661 
L 876.920131 340.257417 
L 874.220844 338.889236 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9deb85"/>
    <path d="M 896.738857 321.173685 
L 899.460347 322.053111 
L 900.960474 317.898238 
L 898.237098 317.084519 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #edfb95"/>
    <path d="M 846.469457 346.957258 
L 849.148138 348.96832 
L 850.637203 345.907881 
L 847.95773 343.982107 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8de882"/>
    <path d="M 868.540075 344.631062 
L 871.234306 346.172989 
L 872.72779 342.540769 
L 870.032181 341.076125 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #95ea84"/>
    <path d="M 772.36571 295.297413 
L 775.026323 297.966047 
L 776.533881 297.276144 
L 773.87501 294.699669 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e0d788"/>
    <path d="M 744.247243 269.521391 
L 746.90595 272.032707 
L 748.437971 272.193927 
L 745.781856 269.762802 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b29c6f"/>
    <path d="M 876.920131 340.257417 
L 879.621694 341.606566 
L 881.117383 337.787706 
L 878.414257 336.512514 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a5ed87"/>
    <path d="M 853.318358 347.81019 
L 856.001256 349.687897 
L 857.491446 346.438293 
L 854.807562 344.643399 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #89e781"/>
    <path d="M 721.442924 250.071365 
L 724.098253 252.316811 
L 725.656065 253.028382 
L 723.003778 250.847579 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #90715d"/>
    <path d="M 891.02544 328.317549 
L 893.740828 329.338131 
L 895.240076 325.259152 
L 892.52288 324.306572 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d1f690"/>
    <path d="M 864.356661 346.522345 
L 867.047503 348.165224 
L 868.540075 344.631062 
L 865.847962 343.066852 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #91e983"/>
    <path d="M 830.123753 341.57004 
L 832.794596 343.86982 
L 834.28275 341.286903 
L 831.611626 339.077222 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9deb85"/>
    <path d="M 839.628799 345.644469 
L 842.303844 347.789534 
L 843.792335 344.9222 
L 841.116708 342.864413 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #91e983"/>
    <path d="M 817.961812 334.296716 
L 820.628648 336.759691 
L 822.117689 334.557434 
L 819.450978 332.187384 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b5f08a"/>
    <path d="M 800.482677 320.810341 
L 803.145942 323.429076 
L 804.639095 321.799528 
L 801.976574 319.275844 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e5fa94"/>
    <path d="M 881.117383 337.787706 
L 883.822848 339.045768 
L 885.31979 335.139061 
L 882.612685 333.953026 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b1ef89"/>
    <path d="M 775.026323 297.966047 
L 777.687264 300.647922 
L 779.193169 299.865328 
L 776.533881 297.276144 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e4dc8a"/>
    <path d="M 703.953484 236.65043 
L 706.604246 238.62053 
L 708.184144 239.633184 
L 705.536575 237.713245 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #87655e"/>
    <path d="M 664.787783 212.968004 
L 667.418247 214.110609 
L 669.048074 215.366589 
L 666.420467 214.238822 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b19b96"/>
    <path d="M 689.123375 226.529216 
L 691.768286 228.21802 
L 693.367462 229.395118 
L 690.725725 227.743203 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #997c76"/>
    <path d="M 746.90595 272.032707 
L 749.565194 274.577484 
L 751.094692 274.657098 
L 748.437971 272.193927 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b6a272"/>
    <path d="M 860.177187 348.209426 
L 862.864848 349.955792 
L 864.356661 346.522345 
L 861.667843 344.855842 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #89e781"/>
    <path d="M 803.145942 323.429076 
L 805.809743 326.041673 
L 807.302244 324.317478 
L 804.639095 321.799528 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ddf892"/>
    <path d="M 777.687264 300.647922 
L 780.348527 303.341071 
L 781.852871 302.465347 
L 779.193169 299.865328 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e8e28d"/>
    <path d="M 885.31979 335.139061 
L 888.029286 336.310041 
L 889.527554 332.319603 
L 886.816353 331.218549 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b9f18b"/>
    <path d="M 655.272051 208.797894 
L 657.895399 209.706748 
L 659.53638 210.922755 
L 656.915679 210.020662 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b9a5a1"/>
    <path d="M 724.098253 252.316811 
L 726.754582 254.61131 
L 728.309391 255.256235 
L 725.656065 253.028382 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #94765f"/>
    <path d="M 820.628648 336.759691 
L 823.296356 339.206509 
L 824.785354 336.912285 
L 822.117689 334.557434 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b1ef89"/>
    <path d="M 900.960474 317.898238 
L 903.686288 318.709781 
L 905.187742 314.49087 
L 902.460022 313.74233 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9fe98"/>
    <path d="M 676.948224 219.209086 
L 679.586994 220.641128 
L 681.201882 221.882453 
L 678.56617 220.476236 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a58c86"/>
    <path d="M 849.148138 348.96832 
L 851.828444 350.954144 
L 853.318358 347.81019 
L 850.637203 345.907881 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #85e781"/>
    <path d="M 832.794596 343.86982 
L 835.466611 346.148154 
L 836.955121 343.47646 
L 834.28275 341.286903 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #99eb85"/>
    <path d="M 895.240076 325.259152 
L 897.959721 326.204086 
L 899.460347 322.053111 
L 896.738857 321.173685 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ddf892"/>
    <path d="M 749.565194 274.577484 
L 752.224929 277.153858 
L 753.751975 277.150538 
L 751.094692 274.657098 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #baa774"/>
    <path d="M 780.348527 303.341071 
L 783.010108 306.043518 
L 784.512983 305.07432 
L 781.852871 302.465347 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eee990"/>
    <path d="M 842.303844 347.789534 
L 844.98032 349.910279 
L 846.469457 346.957258 
L 843.792335 344.9222 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #89e781"/>
    <path d="M 805.809743 326.041673 
L 808.474113 328.646269 
L 809.966054 326.827924 
L 807.302244 324.317478 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d5f791"/>
    <path d="M 856.001256 349.687897 
L 858.685964 351.539893 
L 860.177187 348.209426 
L 857.491446 346.438293 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #85e781"/>
    <path d="M 889.527554 332.319603 
L 892.241184 333.407848 
L 893.740828 329.338131 
L 891.02544 328.317549 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c5f38d"/>
    <path d="M 706.604246 238.62053 
L 709.256511 240.650652 
L 710.83323 241.610811 
L 708.184144 239.633184 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #836059"/>
    <path d="M 871.234306 346.172989 
L 873.930712 347.691849 
L 875.425602 343.984661 
L 872.72779 342.540769 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #91e983"/>
    <path d="M 875.425602 343.984661 
L 878.125669 345.407114 
L 879.621694 341.606566 
L 876.920131 340.257417 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #99eb85"/>
    <path d="M 823.296356 339.206509 
L 825.964987 341.635489 
L 827.454025 339.250344 
L 824.785354 336.912285 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a9ee88"/>
    <path d="M 783.010108 306.043518 
L 785.67201 308.753281 
L 787.173509 307.690358 
L 784.512983 305.07432 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f2ee92"/>
    <path d="M 752.224929 277.153858 
L 754.88511 279.759936 
L 756.409779 279.672441 
L 753.751975 277.150538 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c0ae77"/>
    <path d="M 867.047503 348.165224 
L 869.740428 349.783597 
L 871.234306 346.172989 
L 868.540075 344.631062 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8de882"/>
    <path d="M 726.754582 254.61131 
L 729.411831 256.953239 
L 730.963681 257.529586 
L 728.309391 255.256235 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #987b61"/>
    <path d="M 879.621694 341.606566 
L 882.325583 342.936088 
L 883.822848 339.045768 
L 881.117383 337.787706 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a5ed87"/>
    <path d="M 808.474113 328.646269 
L 811.139087 331.241014 
L 812.630558 329.329108 
L 809.966054 326.827924 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cdf58f"/>
    <path d="M 691.768286 228.21802 
L 694.415219 229.975169 
L 696.011211 231.112858 
L 693.367462 229.395118 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #977a74"/>
    <path d="M 835.466611 346.148154 
L 838.139861 348.403535 
L 839.628799 345.644469 
L 836.955121 343.47646 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #91e983"/>
    <path d="M 862.864848 349.955792 
L 865.554494 351.676408 
L 867.047503 348.165224 
L 864.356661 346.522345 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #85e781"/>
    <path d="M 785.67201 308.753281 
L 788.334238 311.468374 
L 789.834453 310.311571 
L 787.173509 307.690358 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f6f394"/>
    <path d="M 899.460347 322.053111 
L 902.184291 322.927526 
L 903.686288 318.709781 
L 900.960474 317.898238 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e9fb95"/>
    <path d="M 754.88511 279.759936 
L 757.545699 282.393799 
L 759.068067 282.220976 
L 756.409779 279.672441 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c4b379"/>
    <path d="M 883.822848 339.045768 
L 886.530698 340.286192 
L 888.029286 336.310041 
L 885.31979 335.139061 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #adef89"/>
    <path d="M 851.828444 350.954144 
L 854.51044 352.913516 
L 856.001256 349.687897 
L 853.318358 347.81019 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #81e680"/>
    <path d="M 844.98032 349.910279 
L 847.658294 352.005357 
L 849.148138 348.96832 
L 846.469457 346.957258 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #85e781"/>
    <path d="M 893.740828 329.338131 
L 896.458674 330.34831 
L 897.959721 326.204086 
L 895.240076 325.259152 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d1f690"/>
    <path d="M 667.418247 214.110609 
L 670.051727 215.332689 
L 671.678647 216.571219 
L 669.048074 215.366589 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #af9994"/>
    <path d="M 825.964987 341.635489 
L 828.634596 344.044971 
L 830.123753 341.57004 
L 827.454025 339.250344 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a1ec86"/>
    <path d="M 811.139087 331.241014 
L 813.804708 333.82407 
L 815.295797 331.819283 
L 812.630558 329.329108 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c5f38d"/>
    <path d="M 729.411831 256.953239 
L 732.069928 259.340925 
L 733.618866 259.846837 
L 730.963681 257.529586 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9c8064"/>
    <path d="M 788.334238 311.468374 
L 790.996801 314.186812 
L 792.495827 312.936068 
L 789.834453 310.311571 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #faf996"/>
    <path d="M 709.256511 240.650652 
L 711.910184 242.739441 
L 713.483739 243.644828 
L 710.83323 241.610811 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #815e56"/>
    <path d="M 679.586994 220.641128 
L 682.228262 222.147641 
L 683.840062 223.360548 
L 681.201882 221.882453 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a58c86"/>
    <path d="M 757.545699 282.393799 
L 760.206658 285.053501 
L 761.726804 284.794286 
L 759.068067 282.220976 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c8b97b"/>
    <path d="M 858.685964 351.539893 
L 861.372548 353.365094 
L 862.864848 349.955792 
L 860.177187 348.209426 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #81e680"/>
    <path d="M 888.029286 336.310041 
L 890.741213 337.465547 
L 892.241184 333.407848 
L 889.527554 332.319603 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b9f18b"/>
    <path d="M 838.139861 348.403535 
L 840.81441 350.634484 
L 842.303844 347.789534 
L 839.628799 345.644469 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #89e781"/>
    <path d="M 648.38489 206.080806 
L 651.003476 206.824888 
L 652.652261 207.972192 
L 650.036146 207.2297 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bfada9"/>
    <path d="M 790.996801 314.186812 
L 793.659715 316.906607 
L 795.157643 315.561954 
L 792.495827 312.936068 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 813.804708 333.82407 
L 816.471018 336.393615 
L 817.961812 334.296716 
L 815.295797 331.819283 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bdf28c"/>
    <path d="M 657.895399 209.706748 
L 660.522183 210.698605 
L 662.160454 211.90528 
L 659.53638 210.922755 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b9a5a1"/>
    <path d="M 828.634596 344.044971 
L 831.305243 346.433317 
L 832.794596 343.86982 
L 830.123753 341.57004 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #99eb85"/>
    <path d="M 760.206658 285.053501 
L 762.867956 287.737074 
L 764.385962 287.390492 
L 761.726804 284.794286 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ccbe7d"/>
    <path d="M 732.069928 259.340925 
L 734.7288 261.772651 
L 736.274877 262.206347 
L 733.618866 259.846837 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a08566"/>
    <path d="M 873.930712 347.691849 
L 876.629351 349.186881 
L 878.125669 345.407114 
L 875.425602 343.984661 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #91e983"/>
    <path d="M 694.415219 229.975169 
L 697.064067 231.799591 
L 698.656866 232.895398 
L 696.011211 231.112858 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #93756e"/>
    <path d="M 869.740428 349.783597 
L 872.4355 351.376609 
L 873.930712 347.691849 
L 871.234306 346.172989 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #89e781"/>
    <path d="M 793.659715 316.906607 
L 796.322996 319.625777 
L 797.819919 318.18734 
L 795.157643 315.561954 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f5fd97"/>
    <path d="M 897.959721 326.204086 
L 900.681837 327.141178 
L 902.184291 322.927526 
L 899.460347 322.053111 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ddf892"/>
    <path d="M 878.125669 345.407114 
L 880.828045 346.80746 
L 882.325583 342.936088 
L 879.621694 341.606566 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #99eb85"/>
    <path d="M 903.686288 318.709781 
L 906.414547 319.519085 
L 907.917882 315.240074 
L 905.187742 314.49087 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9fe98"/>
    <path d="M 847.658294 352.005357 
L 850.337834 354.073448 
L 851.828444 350.954144 
L 849.148138 348.96832 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #7de57f"/>
    <path d="M 854.51044 352.913516 
L 857.194196 354.845248 
L 858.685964 351.539893 
L 856.001256 349.687897 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #7de57f"/>
    <path d="M 865.554494 351.676408 
L 868.24619 353.370319 
L 869.740428 349.783597 
L 867.047503 348.165224 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #81e680"/>
    <path d="M 816.471018 336.393615 
L 819.138064 338.947842 
L 820.628648 336.759691 
L 817.961812 334.296716 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b1ef89"/>
    <path d="M 762.867956 287.737074 
L 765.529565 290.442528 
L 767.045513 290.007696 
L 764.385962 287.390492 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d0c380"/>
    <path d="M 711.910184 242.739441 
L 714.565169 244.885478 
L 716.135582 245.733878 
L 713.483739 243.644828 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #825f56"/>
    <path d="M 892.241184 333.407848 
L 894.95728 334.482944 
L 896.458674 330.34831 
L 893.740828 329.338131 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c5f38d"/>
    <path d="M 882.325583 342.936088 
L 885.031847 344.245406 
L 886.530698 340.286192 
L 883.822848 339.045768 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a1ec86"/>
    <path d="M 796.322996 319.625777 
L 798.986666 322.342342 
L 800.482677 320.810341 
L 797.819919 318.18734 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #edfb95"/>
    <path d="M 840.81441 350.634484 
L 843.490326 352.839543 
L 844.98032 349.910279 
L 842.303844 347.789534 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #81e680"/>
    <path d="M 734.7288 261.772651 
L 737.388381 264.246657 
L 738.931651 264.606431 
L 736.274877 262.206347 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a48b68"/>
    <path d="M 831.305243 346.433317 
L 833.976988 348.798914 
L 835.466611 346.148154 
L 832.794596 343.86982 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #91e983"/>
    <path d="M 765.529565 290.442528 
L 768.191461 293.167855 
L 769.705435 292.643981 
L 767.045513 290.007696 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d6cb83"/>
    <path d="M 861.372548 353.365094 
L 864.061077 355.162442 
L 865.554494 351.676408 
L 862.864848 349.955792 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #7de57f"/>
    <path d="M 819.138064 338.947842 
L 821.805899 341.484965 
L 823.296356 339.206509 
L 820.628648 336.759691 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a9ee88"/>
    <path d="M 798.986666 322.342342 
L 801.650751 325.05433 
L 803.145942 323.429076 
L 800.482677 320.810341 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e5fa94"/>
    <path d="M 886.530698 340.286192 
L 889.240976 341.50849 
L 890.741213 337.465547 
L 888.029286 336.310041 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #adef89"/>
    <path d="M 670.051727 215.332689 
L 672.688102 216.633753 
L 674.312069 217.852237 
L 671.678647 216.571219 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #af9994"/>
    <path d="M 682.228262 222.147641 
L 684.871913 223.727826 
L 686.480596 224.909751 
L 683.840062 223.360548 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a38984"/>
    <path d="M 768.191461 293.167855 
L 770.853623 295.911031 
L 772.36571 295.297413 
L 769.705435 292.643981 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dad085"/>
    <path d="M 902.184291 322.927526 
L 904.910706 323.796801 
L 906.414547 319.519085 
L 903.686288 318.709781 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e9fb95"/>
    <path d="M 737.388381 264.246657 
L 740.048605 266.761139 
L 741.589125 267.045366 
L 738.931651 264.606431 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a8906a"/>
    <path d="M 850.337834 354.073448 
L 853.019012 356.113257 
L 854.51044 352.913516 
L 851.828444 350.954144 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #79e47e"/>
    <path d="M 714.565169 244.885478 
L 717.221376 247.08729 
L 718.788672 247.876546 
L 716.135582 245.733878 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #846257"/>
    <path d="M 896.458674 330.34831 
L 899.179005 331.347824 
L 900.681837 327.141178 
L 897.959721 326.204086 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d1f690"/>
    <path d="M 697.064067 231.799591 
L 699.714721 233.690148 
L 701.304324 234.741643 
L 698.656866 232.895398 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #91726c"/>
    <path d="M 801.650751 325.05433 
L 804.315282 327.759778 
L 805.809743 326.041673 
L 803.145942 323.429076 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ddf892"/>
    <path d="M 833.976988 348.798914 
L 836.649898 351.140171 
L 838.139861 348.403535 
L 835.466611 346.148154 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #89e781"/>
    <path d="M 857.194196 354.845248 
L 859.879784 356.74818 
L 861.372548 353.365094 
L 858.685964 351.539893 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #75e37d"/>
    <path d="M 770.853623 295.911031 
L 773.516037 298.670016 
L 775.026323 297.966047 
L 772.36571 295.297413 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ded587"/>
    <path d="M 843.490326 352.839543 
L 846.167679 355.017286 
L 847.658294 352.005357 
L 844.98032 349.910279 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #7de57f"/>
    <path d="M 821.805899 341.484965 
L 824.474575 344.003216 
L 825.964987 341.635489 
L 823.296356 339.206509 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a1ec86"/>
    <path d="M 890.741213 337.465547 
L 893.455609 338.605171 
L 894.95728 334.482944 
L 892.241184 333.407848 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b5f08a"/>
    <path d="M 872.4355 351.376609 
L 875.132782 352.943427 
L 876.629351 349.186881 
L 873.930712 347.691849 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #85e781"/>
    <path d="M 876.629351 349.186881 
L 879.330283 350.657349 
L 880.828045 346.80746 
L 878.125669 345.407114 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8de882"/>
    <path d="M 804.315282 327.759778 
L 806.980291 330.456731 
L 808.474113 328.646269 
L 805.809743 326.041673 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d1f690"/>
    <path d="M 868.24619 353.370319 
L 870.940003 355.036597 
L 872.4355 351.376609 
L 869.740428 349.783597 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #7de57f"/>
    <path d="M 660.522183 210.698605 
L 663.152281 211.773225 
L 664.787783 212.968004 
L 662.160454 211.90528 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b7a39f"/>
    <path d="M 740.048605 266.761139 
L 742.709412 269.314256 
L 744.247243 269.521391 
L 741.589125 267.045366 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ac956c"/>
    <path d="M 773.516037 298.670016 
L 776.17869 301.442759 
L 777.687264 300.647922 
L 775.026323 297.966047 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e2da89"/>
    <path d="M 880.828045 346.80746 
L 883.532787 348.185056 
L 885.031847 344.245406 
L 882.325583 342.936088 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #95ea84"/>
    <path d="M 651.003476 206.824888 
L 653.62581 207.654681 
L 655.272051 208.797894 
L 652.652261 207.972192 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bfada9"/>
    <path d="M 824.474575 344.003216 
L 827.144152 346.500851 
L 828.634596 344.044971 
L 825.964987 341.635489 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #99eb85"/>
    <path d="M 717.221376 247.08729 
L 719.878715 249.343342 
L 721.442924 250.071365 
L 718.788672 247.876546 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #886759"/>
    <path d="M 864.061077 355.162442 
L 866.751621 356.930911 
L 868.24619 353.370319 
L 865.554494 351.676408 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #75e37d"/>
    <path d="M 776.17869 301.442759 
L 778.841575 304.227201 
L 780.348527 303.341071 
L 777.687264 300.647922 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e8e28d"/>
    <path d="M 806.980291 330.456731 
L 809.645818 333.143248 
L 811.139087 331.241014 
L 808.474113 328.646269 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c9f48e"/>
    <path d="M 836.649898 351.140171 
L 839.324039 353.455527 
L 840.81441 350.634484 
L 838.139861 348.403535 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #81e680"/>
    <path d="M 885.031847 344.245406 
L 887.740536 345.533964 
L 889.240976 341.50849 
L 886.530698 340.286192 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9deb85"/>
    <path d="M 900.681837 327.141178 
L 903.406446 328.070239 
L 904.910706 323.796801 
L 902.184291 322.927526 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ddf892"/>
    <path d="M 853.019012 356.113257 
L 855.701901 358.123522 
L 857.194196 354.845248 
L 854.51044 352.913516 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #71e37d"/>
    <path d="M 742.709412 269.314256 
L 745.370744 271.904128 
L 746.90595 272.032707 
L 744.247243 269.521391 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b09a6e"/>
    <path d="M 894.95728 334.482944 
L 897.675874 335.544567 
L 899.179005 331.347824 
L 896.458674 330.34831 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c1f38d"/>
    <path d="M 699.714721 233.690148 
L 702.367076 235.645629 
L 703.953484 236.65043 
L 701.304324 234.741643 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8f7069"/>
    <path d="M 684.871913 223.727826 
L 687.517831 225.380802 
L 689.123375 226.529216 
L 686.480596 224.909751 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a18781"/>
    <path d="M 906.414547 319.519085 
L 909.145263 320.32609 
L 910.650446 315.989943 
L 907.917882 315.240074 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9fe98"/>
    <path d="M 846.167679 355.017286 
L 848.846541 357.166313 
L 850.337834 354.073448 
L 847.658294 352.005357 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #75e37d"/>
    <path d="M 778.841575 304.227201 
L 781.504689 307.02127 
L 783.010108 306.043518 
L 780.348527 303.341071 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ece78f"/>
    <path d="M 809.645818 333.143248 
L 812.311902 335.817404 
L 813.804708 333.82407 
L 811.139087 331.241014 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c1f38d"/>
    <path d="M 672.688102 216.633753 
L 675.327252 218.013223 
L 676.948224 219.209086 
L 674.312069 217.852237 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ad9691"/>
    <path d="M 859.879784 356.74818 
L 862.567277 358.621183 
L 864.061077 355.162442 
L 861.372548 353.365094 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #71e37d"/>
    <path d="M 827.144152 346.500851 
L 829.81469 348.976146 
L 831.305243 346.433317 
L 828.634596 344.044971 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #91e983"/>
    <path d="M 781.504689 307.02127 
L 784.168033 309.822895 
L 785.67201 308.753281 
L 783.010108 306.043518 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f0ec91"/>
    <path d="M 745.370744 271.904128 
L 748.032546 274.528841 
L 749.565194 274.577484 
L 746.90595 272.032707 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b49f70"/>
    <path d="M 889.240976 341.50849 
L 891.953729 342.712191 
L 893.455609 338.605171 
L 890.741213 337.465547 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a9ee88"/>
    <path d="M 719.878715 249.343342 
L 722.537098 251.652046 
L 724.098253 252.316811 
L 721.442924 250.071365 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8c6c5b"/>
    <path d="M 839.324039 353.455527 
L 841.999483 355.743447 
L 843.490326 352.839543 
L 840.81441 350.634484 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #7de57f"/>
    <path d="M 812.311902 335.817404 
L 814.97859 338.477287 
L 816.471018 336.393615 
L 813.804708 333.82407 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b9f18b"/>
    <path d="M 784.168033 309.822895 
L 786.831612 312.629996 
L 788.334238 311.468374 
L 785.67201 308.753281 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f6f394"/>
    <path d="M 875.132782 352.943427 
L 877.832339 354.483247 
L 879.330283 350.657349 
L 876.629351 349.186881 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #81e680"/>
    <path d="M 870.940003 355.036597 
L 873.636001 356.674341 
L 875.132782 352.943427 
L 872.4355 351.376609 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #79e47e"/>
    <path d="M 879.330283 350.657349 
L 882.033568 352.102542 
L 883.532787 348.185056 
L 880.828045 346.80746 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #89e781"/>
    <path d="M 748.032546 274.528841 
L 750.69477 277.186447 
L 752.224929 277.153858 
L 749.565194 274.577484 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b8a473"/>
    <path d="M 899.179005 331.347824 
L 901.90185 332.336424 
L 903.406446 328.070239 
L 900.681837 327.141178 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cdf58f"/>
    <path d="M 829.81469 348.976146 
L 832.486255 351.427407 
L 833.976988 348.798914 
L 831.305243 346.433317 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #89e781"/>
    <path d="M 786.831612 312.629996 
L 789.495435 315.440495 
L 790.996801 314.186812 
L 788.334238 311.468374 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #faf996"/>
    <path d="M 848.846541 357.166313 
L 851.526986 359.285257 
L 853.019012 356.113257 
L 850.337834 354.073448 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #71e37d"/>
    <path d="M 904.910706 323.796801 
L 907.639607 324.660818 
L 909.145263 320.32609 
L 906.414547 319.519085 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e9fb95"/>
    <path d="M 855.701901 358.123522 
L 858.386576 360.10301 
L 859.879784 356.74818 
L 857.194196 354.845248 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #6de27c"/>
    <path d="M 866.751621 356.930911 
L 869.444251 358.6695 
L 870.940003 355.036597 
L 868.24619 353.370319 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #71e37d"/>
    <path d="M 702.367076 235.645629 
L 705.021026 237.664754 
L 706.604246 238.62053 
L 703.953484 236.65043 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8b6b64"/>
    <path d="M 814.97859 338.477287 
L 817.645931 341.121004 
L 819.138064 338.947842 
L 816.471018 336.393615 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b1ef89"/>
    <path d="M 893.455609 338.605171 
L 896.172516 339.728526 
L 897.675874 335.544567 
L 894.95728 334.482944 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b5f08a"/>
    <path d="M 883.532787 348.185056 
L 886.239949 349.539279 
L 887.740536 345.533964 
L 885.031847 344.245406 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #91e983"/>
    <path d="M 722.537098 251.652046 
L 725.196443 254.011759 
L 726.754582 254.61131 
L 724.098253 252.316811 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #90715d"/>
    <path d="M 663.152281 211.773225 
L 665.785571 212.93028 
L 667.418247 214.110609 
L 664.787783 212.968004 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b7a39f"/>
    <path d="M 789.495435 315.440495 
L 792.159517 318.252314 
L 793.659715 316.906607 
L 790.996801 314.186812 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 750.69477 277.186447 
L 753.357369 279.874968 
L 754.88511 279.759936 
L 752.224929 277.153858 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bca975"/>
    <path d="M 687.517831 225.380802 
L 690.165899 227.10561 
L 691.768286 228.21802 
L 689.123375 226.529216 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9f847e"/>
    <path d="M 841.999483 355.743447 
L 844.676302 358.002424 
L 846.167679 355.017286 
L 843.490326 352.839543 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #75e37d"/>
    <path d="M 862.567277 358.621183 
L 865.256748 360.463158 
L 866.751621 356.930911 
L 864.061077 355.162442 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #6de27c"/>
    <path d="M 817.645931 341.121004 
L 820.313978 343.746682 
L 821.805899 341.484965 
L 819.138064 338.947842 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a5ed87"/>
    <path d="M 792.159517 318.252314 
L 794.823876 321.063377 
L 796.322996 319.625777 
L 793.659715 316.906607 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f5fd97"/>
    <path d="M 832.486255 351.427407 
L 835.158912 353.852962 
L 836.649898 351.140171 
L 833.976988 348.798914 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #85e781"/>
    <path d="M 653.62581 207.654681 
L 656.251769 208.570124 
L 657.895399 209.706748 
L 655.272051 208.797894 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bfada9"/>
    <path d="M 887.740536 345.533964 
L 890.451702 346.801228 
L 891.953729 342.712191 
L 889.240976 341.50849 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9deb85"/>
    <path d="M 753.357369 279.874968 
L 756.0203 282.592397 
L 757.545699 282.393799 
L 754.88511 279.759936 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c0ae77"/>
    <path d="M 675.327252 218.013223 
L 677.969055 219.470435 
L 679.586994 220.641128 
L 676.948224 219.209086 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ab938e"/>
    <path d="M 794.823876 321.063377 
L 797.488533 323.871616 
L 798.986666 322.342342 
L 796.322996 319.625777 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #edfb95"/>
    <path d="M 725.196443 254.011759 
L 727.856668 256.420786 
L 729.411831 256.953239 
L 726.754582 254.61131 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #94765f"/>
    <path d="M 851.526986 359.285257 
L 854.209093 361.372779 
L 855.701901 358.123522 
L 853.019012 356.113257 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #69e17b"/>
    <path d="M 897.675874 335.544567 
L 900.397 336.592403 
L 901.90185 332.336424 
L 899.179005 331.347824 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c1f38d"/>
    <path d="M 903.406446 328.070239 
L 906.133569 328.991088 
L 907.639607 324.660818 
L 904.910706 323.796801 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ddf892"/>
    <path d="M 820.313978 343.746682 
L 822.982787 346.352469 
L 824.474575 344.003216 
L 821.805899 341.484965 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9deb85"/>
    <path d="M 756.0203 282.592397 
L 758.683525 285.336702 
L 760.206658 285.053501 
L 757.545699 282.393799 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c6b67a"/>
    <path d="M 705.021026 237.664754 
L 707.676469 239.746178 
L 709.256511 240.650652 
L 706.604246 238.62053 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #896861"/>
    <path d="M 858.386576 360.10301 
L 861.073114 362.050519 
L 862.567277 358.621183 
L 859.879784 356.74818 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #69e17b"/>
    <path d="M 797.488533 323.871616 
L 800.153516 326.674966 
L 801.650751 325.05433 
L 798.986666 322.342342 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e1f993"/>
    <path d="M 873.636001 356.674341 
L 876.334256 358.28268 
L 877.832339 354.483247 
L 875.132782 352.943427 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #75e37d"/>
    <path d="M 909.145263 320.32609 
L 911.878444 321.130739 
L 913.385437 316.740478 
L 910.650446 315.989943 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9fe98"/>
    <path d="M 844.676302 358.002424 
L 847.354572 360.230985 
L 848.846541 357.166313 
L 846.167679 355.017286 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #6de27c"/>
    <path d="M 877.832339 354.483247 
L 880.534237 355.995293 
L 882.033568 352.102542 
L 879.330283 350.657349 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #7de57f"/>
    <path d="M 891.953729 342.712191 
L 894.669001 343.896843 
L 896.172516 339.728526 
L 893.455609 338.605171 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a9ee88"/>
    <path d="M 835.158912 353.852962 
L 837.832734 356.25117 
L 839.324039 353.455527 
L 836.649898 351.140171 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #7de57f"/>
    <path d="M 869.444251 358.6695 
L 872.139043 360.377243 
L 873.636001 356.674341 
L 870.940003 355.036597 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #6de27c"/>
    <path d="M 758.683525 285.336702 
L 761.347011 288.105826 
L 762.867956 287.737074 
L 760.206658 285.053501 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cabb7c"/>
    <path d="M 800.153516 326.674966 
L 802.818854 329.471374 
L 804.315282 327.759778 
L 801.650751 325.05433 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d9f791"/>
    <path d="M 882.033568 352.102542 
L 884.739268 353.521774 
L 886.239949 349.539279 
L 883.532787 348.185056 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #85e781"/>
    <path d="M 822.982787 346.352469 
L 825.652419 348.936537 
L 827.144152 346.500851 
L 824.474575 344.003216 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #95ea84"/>
    <path d="M 727.856668 256.420786 
L 730.517695 258.877385 
L 732.069928 259.340925 
L 729.411831 256.953239 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #987b61"/>
    <path d="M 690.165899 227.10561 
L 692.816004 228.901217 
L 694.415219 229.975169 
L 691.768286 228.21802 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9b7f79"/>
    <path d="M 761.347011 288.105826 
L 764.010728 290.89769 
L 765.529565 290.442528 
L 762.867956 287.737074 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cec07f"/>
    <path d="M 865.256748 360.463158 
L 867.948276 362.273037 
L 869.444251 358.6695 
L 866.751621 356.930911 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #69e17b"/>
    <path d="M 802.818854 329.471374 
L 805.484583 332.258799 
L 806.980291 330.456731 
L 804.315282 327.759778 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d1f690"/>
    <path d="M 886.239949 349.539279 
L 888.949589 350.869534 
L 890.451702 346.801228 
L 887.740536 345.533964 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #91e983"/>
    <path d="M 854.209093 361.372779 
L 856.89294 363.427575 
L 858.386576 360.10301 
L 855.701901 358.123522 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #65e07a"/>
    <path d="M 901.90185 332.336424 
L 904.627237 333.31387 
L 906.133569 328.991088 
L 903.406446 328.070239 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cdf58f"/>
    <path d="M 837.832734 356.25117 
L 840.507793 358.620417 
L 841.999483 355.743447 
L 839.324039 353.455527 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #75e37d"/>
    <path d="M 707.676469 239.746178 
L 710.333304 241.888488 
L 711.910184 242.739441 
L 709.256511 240.650652 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #85635c"/>
    <path d="M 764.010728 290.89769 
L 766.674649 293.710198 
L 768.191461 293.167855 
L 765.529565 290.442528 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d4c882"/>
    <path d="M 665.785571 212.93028 
L 668.421928 214.169348 
L 670.051727 215.332689 
L 667.418247 214.110609 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b5a09c"/>
    <path d="M 896.172516 339.728526 
L 898.891973 340.835238 
L 900.397 336.592403 
L 897.675874 335.544567 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b5f08a"/>
    <path d="M 825.652419 348.936537 
L 828.322936 351.497081 
L 829.81469 348.976146 
L 827.144152 346.500851 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8de882"/>
    <path d="M 805.484583 332.258799 
L 808.150742 335.03521 
L 809.645818 333.143248 
L 806.980291 330.456731 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c5f38d"/>
    <path d="M 847.354572 360.230985 
L 850.034372 362.427685 
L 851.526986 359.285257 
L 848.846541 357.166313 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #69e17b"/>
    <path d="M 730.517695 258.877385 
L 733.17945 261.379763 
L 734.7288 261.772651 
L 732.069928 259.340925 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9c8064"/>
    <path d="M 907.639607 324.660818 
L 910.37101 325.519462 
L 911.878444 321.130739 
L 909.145263 320.32609 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e9fb95"/>
    <path d="M 861.073114 362.050519 
L 863.761596 363.964882 
L 865.256748 360.463158 
L 862.567277 358.621183 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #61df79"/>
    <path d="M 766.674649 293.710198 
L 769.338753 296.541234 
L 770.853623 295.911031 
L 768.191461 293.167855 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d8cd84"/>
    <path d="M 677.969055 219.470435 
L 680.613389 221.004644 
L 682.228262 222.147641 
L 679.586994 220.641128 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a9918c"/>
    <path d="M 890.451702 346.801228 
L 893.165397 348.046686 
L 894.669001 343.896843 
L 891.953729 342.712191 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #99eb85"/>
    <path d="M 646.731204 205.014301 
L 649.352224 205.759958 
L 651.003476 206.824888 
L 648.38489 206.080806 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c5b5b1"/>
    <path d="M 808.150742 335.03521 
L 810.817373 337.798593 
L 812.311902 335.817404 
L 809.645818 333.143248 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bdf28c"/>
    <path d="M 769.338753 296.541234 
L 772.003023 299.38867 
L 773.516037 298.670016 
L 770.853623 295.911031 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dcd286"/>
    <path d="M 828.322936 351.497081 
L 830.994407 354.032325 
L 832.486255 351.427407 
L 829.81469 348.976146 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #85e781"/>
    <path d="M 656.251769 208.570124 
L 658.881229 209.571065 
L 660.522183 210.698605 
L 657.895399 209.706748 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bdaba7"/>
    <path d="M 876.334256 358.28268 
L 879.034836 359.860771 
L 880.534237 355.995293 
L 877.832339 354.483247 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #71e37d"/>
    <path d="M 733.17945 261.379763 
L 735.841861 263.926084 
L 737.388381 264.246657 
L 734.7288 261.772651 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a08566"/>
    <path d="M 840.507793 358.620417 
L 843.184167 360.959122 
L 844.676302 358.002424 
L 841.999483 355.743447 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #6de27c"/>
    <path d="M 872.139043 360.377243 
L 874.836069 362.053201 
L 876.334256 358.28268 
L 873.636001 356.674341 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #69e17b"/>
    <path d="M 692.816004 228.901217 
L 695.468032 230.766511 
L 697.064067 231.799591 
L 694.415219 229.975169 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #997c76"/>
    <path d="M 810.817373 337.798593 
L 813.484523 340.546952 
L 814.97859 338.477287 
L 812.311902 335.817404 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b5f08a"/>
    <path d="M 772.003023 299.38867 
L 774.667446 302.250364 
L 776.17869 301.442759 
L 773.516037 298.670016 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e2da89"/>
    <path d="M 880.534237 355.995293 
L 883.238541 357.478815 
L 884.739268 353.521774 
L 882.033568 352.102542 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #79e47e"/>
    <path d="M 710.333304 241.888488 
L 712.991434 244.090211 
L 714.565169 244.885478 
L 711.910184 242.739441 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #836059"/>
    <path d="M 900.397 336.592403 
L 903.120695 337.626155 
L 904.627237 333.31387 
L 901.90185 332.336424 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c1f38d"/>
    <path d="M 867.948276 362.273037 
L 870.641937 364.049786 
L 872.139043 360.377243 
L 869.444251 358.6695 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #61df79"/>
    <path d="M 856.89294 363.427575 
L 859.578609 365.448373 
L 861.073114 362.050519 
L 858.386576 360.10301 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #5ddf79"/>
    <path d="M 850.034372 362.427685 
L 852.715784 364.591116 
L 854.209093 361.372779 
L 851.526986 359.285257 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #61df79"/>
    <path d="M 774.667446 302.250364 
L 777.332015 305.124164 
L 778.841575 304.227201 
L 776.17869 301.442759 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e6df8b"/>
    <path d="M 906.133569 328.991088 
L 908.86323 329.903554 
L 910.37101 325.519462 
L 907.639607 324.660818 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ddf892"/>
    <path d="M 884.739268 353.521774 
L 887.447445 354.914385 
L 888.949589 350.869534 
L 886.239949 349.539279 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #85e781"/>
    <path d="M 894.669001 343.896843 
L 897.38684 345.062015 
L 898.891973 340.835238 
L 896.172516 339.728526 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a5ed87"/>
    <path d="M 813.484523 340.546952 
L 816.152243 343.278309 
L 817.645931 341.121004 
L 814.97859 338.477287 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #adef89"/>
    <path d="M 830.994407 354.032325 
L 833.666902 356.540519 
L 835.158912 353.852962 
L 832.486255 351.427407 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #7de57f"/>
    <path d="M 735.841861 263.926084 
L 738.504861 266.514467 
L 740.048605 266.761139 
L 737.388381 264.246657 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a48b68"/>
    <path d="M 777.332015 305.124164 
L 779.996724 308.007911 
L 781.504689 307.02127 
L 778.841575 304.227201 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ece78f"/>
    <path d="M 863.761596 363.964882 
L 866.452101 365.844962 
L 867.948276 362.273037 
L 865.256748 360.463158 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #5ddf79"/>
    <path d="M 911.878444 321.130739 
L 914.6141 321.932978 
L 916.122858 317.49168 
L 913.385437 316.740478 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9fe98"/>
    <path d="M 843.184167 360.959122 
L 845.861935 363.265737 
L 847.354572 360.230985 
L 844.676302 358.002424 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #65e07a"/>
    <path d="M 779.996724 308.007911 
L 782.661574 310.899439 
L 784.168033 309.822895 
L 781.504689 307.02127 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f0ec91"/>
    <path d="M 816.152243 343.278309 
L 818.820588 345.990707 
L 820.313978 343.746682 
L 817.645931 341.121004 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a1ec86"/>
    <path d="M 888.949589 350.869534 
L 891.661764 352.175245 
L 893.165397 348.046686 
L 890.451702 346.801228 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8de882"/>
    <path d="M 712.991434 244.090211 
L 715.650762 246.349811 
L 717.221376 247.08729 
L 714.565169 244.885478 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #805c54"/>
    <path d="M 738.504861 266.514467 
L 741.168384 269.142992 
L 742.709412 269.314256 
L 740.048605 266.761139 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a8906a"/>
    <path d="M 782.661574 310.899439 
L 785.326571 313.796582 
L 786.831612 312.629996 
L 784.168033 309.822895 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f6f394"/>
    <path d="M 668.421928 214.169348 
L 671.061228 215.489921 
L 672.688102 216.633753 
L 670.051727 215.332689 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b5a09c"/>
    <path d="M 680.613389 221.004644 
L 683.260135 222.615018 
L 684.871913 223.727826 
L 682.228262 222.147641 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a78e89"/>
    <path d="M 833.666902 356.540519 
L 836.340493 359.019943 
L 837.832734 356.25117 
L 835.158912 353.852962 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #75e37d"/>
    <path d="M 695.468032 230.766511 
L 698.121871 232.700308 
L 699.714721 233.690148 
L 697.064067 231.799591 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #977a74"/>
    <path d="M 785.326571 313.796582 
L 787.991723 316.697168 
L 789.495435 315.440495 
L 786.831612 312.629996 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #faf996"/>
    <path d="M 818.820588 345.990707 
L 821.489616 348.68221 
L 822.982787 346.352469 
L 820.313978 343.746682 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #99eb85"/>
    <path d="M 852.715784 364.591116 
L 855.398889 366.719901 
L 856.89294 363.427575 
L 854.209093 361.372779 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #59de78"/>
    <path d="M 898.891973 340.835238 
L 901.614021 341.924952 
L 903.120695 337.626155 
L 900.397 336.592403 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b1ef89"/>
    <path d="M 904.627237 333.31387 
L 907.355195 334.279933 
L 908.86323 329.903554 
L 906.133569 328.991088 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cdf58f"/>
    <path d="M 859.578609 365.448373 
L 862.266184 367.433936 
L 863.761596 363.964882 
L 861.073114 362.050519 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #59de78"/>
    <path d="M 787.991723 316.697168 
L 790.657045 319.599031 
L 792.159517 318.252314 
L 789.495435 315.440495 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 741.168384 269.142992 
L 743.832371 271.809699 
L 745.370744 271.904128 
L 742.709412 269.314256 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ac956c"/>
    <path d="M 874.836069 362.053201 
L 877.535406 363.69647 
L 879.034836 359.860771 
L 876.334256 358.28268 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #65e07a"/>
    <path d="M 879.034836 359.860771 
L 881.737815 361.407804 
L 883.238541 357.478815 
L 880.534237 355.995293 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #6de27c"/>
    <path d="M 893.165397 348.046686 
L 895.881671 349.269845 
L 897.38684 345.062015 
L 894.669001 343.896843 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #99eb85"/>
    <path d="M 845.861935 363.265737 
L 848.541179 365.538744 
L 850.034372 362.427685 
L 847.354572 360.230985 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #5ddf79"/>
    <path d="M 870.641937 364.049786 
L 873.337812 365.792402 
L 874.836069 362.053201 
L 872.139043 360.377243 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #5ddf79"/>
    <path d="M 910.37101 325.519462 
L 913.104932 326.372624 
L 914.6141 321.932978 
L 911.878444 321.130739 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e9fb95"/>
    <path d="M 790.657045 319.599031 
L 793.322554 322.500006 
L 794.823876 321.063377 
L 792.159517 318.252314 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f5fd97"/>
    <path d="M 821.489616 348.68221 
L 824.159391 351.350909 
L 825.652419 348.936537 
L 822.982787 346.352469 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #91e983"/>
    <path d="M 883.238541 357.478815 
L 885.945321 358.933092 
L 887.447445 354.914385 
L 884.739268 353.521774 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #75e37d"/>
    <path d="M 836.340493 359.019943 
L 839.015258 361.468909 
L 840.507793 358.620417 
L 837.832734 356.25117 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #6de27c"/>
    <path d="M 715.650762 246.349811 
L 718.311194 248.66569 
L 719.878715 249.343342 
L 717.221376 247.08729 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #846257"/>
    <path d="M 658.881229 209.571065 
L 661.514064 210.657255 
L 663.152281 211.773225 
L 660.522183 210.698605 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bdaba7"/>
    <path d="M 743.832371 271.809699 
L 746.496766 274.512592 
L 748.032546 274.528841 
L 745.370744 271.904128 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b09a6e"/>
    <path d="M 793.322554 322.500006 
L 795.988273 325.397934 
L 797.488533 323.871616 
L 794.823876 321.063377 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #edfb95"/>
    <path d="M 649.352224 205.759958 
L 651.977065 206.593746 
L 653.62581 207.654681 
L 651.003476 206.824888 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c3b2af"/>
    <path d="M 866.452101 365.844962 
L 869.144713 367.68966 
L 870.641937 364.049786 
L 867.948276 362.273037 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #59de78"/>
    <path d="M 795.988273 325.397934 
L 798.654228 328.290663 
L 800.153516 326.674966 
L 797.488533 323.871616 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e1f993"/>
    <path d="M 887.447445 354.914385 
L 890.158162 356.279743 
L 891.661764 352.175245 
L 888.949589 350.869534 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #81e680"/>
    <path d="M 824.159391 351.350909 
L 826.829976 353.994919 
L 828.322936 351.497081 
L 825.652419 348.936537 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #89e781"/>
    <path d="M 855.398889 366.719901 
L 858.083775 368.812701 
L 859.578609 365.448373 
L 856.89294 363.427575 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #55dd77"/>
    <path d="M 746.496766 274.512592 
L 749.161514 277.24964 
L 750.69477 277.186447 
L 748.032546 274.528841 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b6a272"/>
    <path d="M 903.120695 337.626155 
L 905.846991 338.64554 
L 907.355195 334.279933 
L 904.627237 333.31387 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bdf28c"/>
    <path d="M 698.121871 232.700308 
L 700.77741 234.701348 
L 702.367076 235.645629 
L 699.714721 233.690148 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #93756e"/>
    <path d="M 798.654228 328.290663 
L 801.320452 331.176053 
L 802.818854 329.471374 
L 800.153516 326.674966 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d9f791"/>
    <path d="M 897.38684 345.062015 
L 900.107291 346.207294 
L 901.614021 341.924952 
L 898.891973 340.835238 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a5ed87"/>
    <path d="M 839.015258 361.468909 
L 841.691277 363.88576 
L 843.184167 360.959122 
L 840.507793 358.620417 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #65e07a"/>
    <path d="M 683.260135 222.615018 
L 685.909171 224.300645 
L 687.517831 225.380802 
L 684.871913 223.727826 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a58c86"/>
    <path d="M 848.541179 365.538744 
L 851.221983 367.776663 
L 852.715784 364.591116 
L 850.034372 362.427685 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #59de78"/>
    <path d="M 718.311194 248.66569 
L 720.972641 251.036195 
L 722.537098 251.652046 
L 719.878715 249.343342 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #886759"/>
    <path d="M 862.266184 367.433936 
L 864.955749 369.383063 
L 866.452101 365.844962 
L 863.761596 363.964882 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #51dc76"/>
    <path d="M 908.86323 329.903554 
L 911.595451 330.807474 
L 913.104932 326.372624 
L 910.37101 325.519462 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d9f791"/>
    <path d="M 801.320452 331.176053 
L 803.98698 334.051973 
L 805.484583 332.258799 
L 802.818854 329.471374 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cdf58f"/>
    <path d="M 749.161514 277.24964 
L 751.826568 280.018782 
L 753.357369 279.874968 
L 750.69477 277.186447 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #baa774"/>
    <path d="M 826.829976 353.994919 
L 829.501443 356.612385 
L 830.994407 354.032325 
L 828.322936 351.497081 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #81e680"/>
    <path d="M 891.661764 352.175245 
L 894.376532 353.455864 
L 895.881671 349.269845 
L 893.165397 348.046686 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8de882"/>
    <path d="M 671.061228 215.489921 
L 673.703344 216.891401 
L 675.327252 218.013223 
L 672.688102 216.633753 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b39e99"/>
    <path d="M 803.98698 334.051973 
L 806.653852 336.916309 
L 808.150742 335.03521 
L 805.484583 332.258799 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c5f38d"/>
    <path d="M 877.535406 363.69647 
L 880.237132 365.306176 
L 881.737815 361.407804 
L 879.034836 359.860771 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #61df79"/>
    <path d="M 751.826568 280.018782 
L 754.491882 282.817926 
L 756.0203 282.592397 
L 753.357369 279.874968 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #beac76"/>
    <path d="M 873.337812 365.792402 
L 876.035982 367.499919 
L 877.535406 363.69647 
L 874.836069 362.053201 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #59de78"/>
    <path d="M 914.6141 321.932978 
L 917.352241 322.732756 
L 918.862713 318.24355 
L 916.122858 317.49168 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9fe98"/>
    <path d="M 881.737815 361.407804 
L 884.443266 362.922998 
L 885.945321 358.933092 
L 883.238541 357.478815 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #69e17b"/>
    <path d="M 806.653852 336.916309 
L 809.321112 339.766961 
L 810.817373 337.798593 
L 808.150742 335.03521 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b9f18b"/>
    <path d="M 841.691277 363.88576 
L 844.368632 366.268875 
L 845.861935 363.265737 
L 843.184167 360.959122 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #5ddf79"/>
    <path d="M 829.501443 356.612385 
L 832.173864 359.201481 
L 833.666902 356.540519 
L 830.994407 354.032325 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #75e37d"/>
    <path d="M 720.972641 251.036195 
L 723.635013 253.459616 
L 725.196443 254.011759 
L 722.537098 251.652046 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8c6c5b"/>
    <path d="M 754.491882 282.817926 
L 757.157417 285.644953 
L 758.683525 285.336702 
L 756.0203 282.592397 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c2b178"/>
    <path d="M 869.144713 367.68966 
L 871.839516 369.49791 
L 873.337812 365.792402 
L 870.641937 364.049786 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #55dd77"/>
    <path d="M 901.614021 341.924952 
L 904.338701 342.997331 
L 905.846991 338.64554 
L 903.120695 337.626155 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b1ef89"/>
    <path d="M 858.083775 368.812701 
L 860.770529 370.868212 
L 862.266184 367.433936 
L 859.578609 365.448373 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #4ddb75"/>
    <path d="M 851.221983 367.776663 
L 853.904436 369.978051 
L 855.398889 366.719901 
L 852.715784 364.591116 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #51dc76"/>
    <path d="M 809.321112 339.766961 
L 811.988807 342.601849 
L 813.484523 340.546952 
L 810.817373 337.798593 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b1ef89"/>
    <path d="M 700.77741 234.701348 
L 703.434542 236.768304 
L 705.021026 237.664754 
L 702.367076 235.645629 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #91726c"/>
    <path d="M 885.945321 358.933092 
L 888.654644 360.357434 
L 890.158162 356.279743 
L 887.447445 354.914385 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #75e37d"/>
    <path d="M 895.881671 349.269845 
L 898.600579 350.470238 
L 900.107291 346.207294 
L 897.38684 345.062015 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #95ea84"/>
    <path d="M 907.355195 334.279933 
L 910.085753 335.234399 
L 911.595451 330.807474 
L 908.86323 329.903554 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cdf58f"/>
    <path d="M 757.157417 285.644953 
L 759.823136 288.497722 
L 761.347011 288.105826 
L 758.683525 285.336702 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c8b97b"/>
    <path d="M 811.988807 342.601849 
L 814.656992 345.41891 
L 816.152243 343.278309 
L 813.484523 340.546952 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a9ee88"/>
    <path d="M 832.173864 359.201481 
L 834.847316 361.760409 
L 836.340493 359.019943 
L 833.666902 356.540519 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #6de27c"/>
    <path d="M 864.955749 369.383063 
L 867.647394 371.294591 
L 869.144713 367.68966 
L 866.452101 365.844962 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #4ddb75"/>
    <path d="M 661.514064 210.657255 
L 664.150146 211.828354 
L 665.785571 212.93028 
L 663.152281 211.773225 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bba8a4"/>
    <path d="M 759.823136 288.497722 
L 762.489007 291.374066 
L 764.010728 290.89769 
L 761.347011 288.105826 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ccbe7d"/>
    <path d="M 685.909171 224.300645 
L 688.560378 226.060531 
L 690.165899 227.10561 
L 687.517831 225.380802 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a38984"/>
    <path d="M 913.104932 326.372624 
L 915.841388 327.220202 
L 917.352241 322.732756 
L 914.6141 321.932978 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e9fb95"/>
    <path d="M 844.368632 366.268875 
L 847.04741 368.616667 
L 848.541179 365.538744 
L 845.861935 363.265737 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #55dd77"/>
    <path d="M 890.158162 356.279743 
L 892.871483 357.617242 
L 894.376532 353.455864 
L 891.661764 352.175245 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #7de57f"/>
    <path d="M 723.635013 253.459616 
L 726.298227 255.934191 
L 727.856668 256.420786 
L 725.196443 254.011759 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #90715d"/>
    <path d="M 814.656992 345.41891 
L 817.325721 348.216107 
L 818.820588 345.990707 
L 816.152243 343.278309 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9deb85"/>
    <path d="M 762.489007 291.374066 
L 765.155003 294.271801 
L 766.674649 293.710198 
L 764.010728 290.89769 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d2c581"/>
    <path d="M 651.977065 206.593746 
L 654.605599 207.515602 
L 656.251769 208.570124 
L 653.62581 207.654681 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c3b2af"/>
    <path d="M 765.155003 294.271801 
L 767.821101 297.188723 
L 769.338753 296.541234 
L 766.674649 293.710198 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d6cb83"/>
    <path d="M 834.847316 361.760409 
L 837.521877 364.287409 
L 839.015258 361.468909 
L 836.340493 359.019943 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #65e07a"/>
    <path d="M 853.904436 369.978051 
L 856.588626 372.141499 
L 858.083775 368.812701 
L 855.398889 366.719901 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #49db75"/>
    <path d="M 817.325721 348.216107 
L 819.995056 350.991423 
L 821.489616 348.68221 
L 818.820588 345.990707 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #95ea84"/>
    <path d="M 900.107291 346.207294 
L 902.830403 347.332288 
L 904.338701 342.997331 
L 901.614021 341.924952 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a1ec86"/>
    <path d="M 673.703344 216.891401 
L 676.348153 218.373102 
L 677.969055 219.470435 
L 675.327252 218.013223 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b19b96"/>
    <path d="M 703.434542 236.768304 
L 706.093158 238.899777 
L 707.676469 239.746178 
L 705.021026 237.664754 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8d6d66"/>
    <path d="M 860.770529 370.868212 
L 863.45924 372.885169 
L 864.955749 369.383063 
L 862.266184 367.433936 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #49db75"/>
    <path d="M 905.846991 338.64554 
L 908.575925 339.650289 
L 910.085753 335.234399 
L 907.355195 334.279933 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bdf28c"/>
    <path d="M 767.821101 297.188723 
L 770.487283 300.122616 
L 772.003023 299.38867 
L 769.338753 296.541234 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dcd286"/>
    <path d="M 876.035982 367.499919 
L 878.736529 369.171403 
L 880.237132 365.306176 
L 877.535406 363.69647 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #55dd77"/>
    <path d="M 880.237132 365.306176 
L 882.941324 366.881481 
L 884.443266 362.922998 
L 881.737815 361.407804 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #5ddf79"/>
    <path d="M 726.298227 255.934191 
L 728.962201 258.458103 
L 730.517695 258.877385 
L 727.856668 256.420786 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #94765f"/>
    <path d="M 894.376532 353.455864 
L 897.093951 354.710869 
L 898.600579 350.470238 
L 895.881671 349.269845 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #89e781"/>
    <path d="M 871.839516 369.49791 
L 874.536596 371.268686 
L 876.035982 367.499919 
L 873.337812 365.792402 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #4ddb75"/>
    <path d="M 770.487283 300.122616 
L 773.153534 303.071249 
L 774.667446 302.250364 
L 772.003023 299.38867 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e0d788"/>
    <path d="M 819.995056 350.991423 
L 822.665061 353.742869 
L 824.159391 351.350909 
L 821.489616 348.68221 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8de882"/>
    <path d="M 847.04741 368.616667 
L 849.727697 370.927587 
L 851.221983 367.776663 
L 848.541179 365.538744 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #51dc76"/>
    <path d="M 884.443266 362.922998 
L 887.151263 364.405605 
L 888.654644 360.357434 
L 885.945321 358.933092 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #65e07a"/>
    <path d="M 911.595451 330.807474 
L 914.330255 331.702696 
L 915.841388 327.220202 
L 913.104932 326.372624 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d9f791"/>
    <path d="M 773.153534 303.071249 
L 775.819845 306.032381 
L 777.332015 305.124164 
L 774.667446 302.250364 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e6df8b"/>
    <path d="M 837.521877 364.287409 
L 840.197632 366.780751 
L 841.691277 363.88576 
L 839.015258 361.468909 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #5ddf79"/>
    <path d="M 775.819845 306.032381 
L 778.486211 309.003766 
L 779.996724 308.007911 
L 777.332015 305.124164 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eae48e"/>
    <path d="M 867.647394 371.294591 
L 870.341206 373.167392 
L 871.839516 369.49791 
L 869.144713 367.68966 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #49db75"/>
    <path d="M 728.962201 258.458103 
L 731.626857 261.02949 
L 733.17945 261.379763 
L 730.517695 258.877385 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #987b61"/>
    <path d="M 822.665061 353.742869 
L 825.335804 356.468483 
L 826.829976 353.994919 
L 824.159391 351.350909 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #81e680"/>
    <path d="M 778.486211 309.003766 
L 781.152632 311.983149 
L 782.661574 310.899439 
L 779.996724 308.007911 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f0ec91"/>
    <path d="M 688.560378 226.060531 
L 691.213637 227.893604 
L 692.816004 228.901217 
L 690.165899 227.10561 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a18781"/>
    <path d="M 888.654644 360.357434 
L 891.366581 361.751178 
L 892.871483 357.617242 
L 890.158162 356.279743 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #71e37d"/>
    <path d="M 781.152632 311.983149 
L 783.819112 314.968274 
L 785.326571 313.796582 
L 782.661574 310.899439 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f4f193"/>
    <path d="M 856.588626 372.141499 
L 859.274645 374.26564 
L 860.770529 370.868212 
L 858.083775 368.812701 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #45da74"/>
    <path d="M 706.093158 238.899777 
L 708.753154 241.094301 
L 710.333304 241.888488 
L 707.676469 239.746178 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8b6b64"/>
    <path d="M 917.352241 322.732756 
L 920.092876 323.530025 
L 921.605004 318.996088 
L 918.862713 318.24355 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9fe98"/>
    <path d="M 783.819112 314.968274 
L 786.485661 317.956882 
L 787.991723 316.697168 
L 785.326571 313.796582 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #faf996"/>
    <path d="M 904.338701 342.997331 
L 907.066054 344.052052 
L 908.575925 339.650289 
L 905.846991 338.64554 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b1ef89"/>
    <path d="M 898.600579 350.470238 
L 901.322173 351.647419 
L 902.830403 347.332288 
L 900.107291 346.207294 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #95ea84"/>
    <path d="M 825.335804 356.468483 
L 828.007357 359.166331 
L 829.501443 356.612385 
L 826.829976 353.994919 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #79e47e"/>
    <path d="M 786.485661 317.956882 
L 789.152292 320.946719 
L 790.657045 319.599031 
L 787.991723 316.697168 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 849.727697 370.927587 
L 852.409586 373.200122 
L 853.904436 369.978051 
L 851.221983 367.776663 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #49db75"/>
    <path d="M 863.45924 372.885169 
L 866.150001 374.862344 
L 867.647394 371.294591 
L 864.955749 369.383063 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #41d973"/>
    <path d="M 840.197632 366.780751 
L 842.874666 369.238742 
L 844.368632 366.268875 
L 841.691277 363.88576 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #55dd77"/>
    <path d="M 731.626857 261.02949 
L 734.292119 263.64644 
L 735.841861 263.926084 
L 733.17945 261.379763 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9c8064"/>
    <path d="M 664.150146 211.828354 
L 666.789347 213.083928 
L 668.421928 214.169348 
L 665.785571 212.93028 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bba8a4"/>
    <path d="M 789.152292 320.946719 
L 791.819023 323.935531 
L 793.322554 322.500006 
L 790.657045 319.599031 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f5fd97"/>
    <path d="M 910.085753 335.234399 
L 912.818939 336.177064 
L 914.330255 331.702696 
L 911.595451 330.807474 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cdf58f"/>
    <path d="M 892.871483 357.617242 
L 895.587472 358.926304 
L 897.093951 354.710869 
L 894.376532 353.455864 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #7de57f"/>
    <path d="M 791.819023 323.935531 
L 794.485877 326.921075 
L 795.988273 325.397934 
L 793.322554 322.500006 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e9fb95"/>
    <path d="M 794.485877 326.921075 
L 797.152881 329.90111 
L 798.654228 328.290663 
L 795.988273 325.397934 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e1f993"/>
    <path d="M 676.348153 218.373102 
L 678.995528 219.93425 
L 680.613389 221.004644 
L 677.969055 219.470435 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #af9994"/>
    <path d="M 645.0752 204.032834 
L 647.698617 204.780051 
L 649.352224 205.759958 
L 646.731204 205.014301 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c9bab7"/>
    <path d="M 828.007357 359.166331 
L 830.679795 361.834514 
L 832.173864 359.201481 
L 829.501443 356.612385 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #71e37d"/>
    <path d="M 878.736529 369.171403 
L 881.439536 370.805958 
L 882.941324 366.881481 
L 880.237132 365.306176 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #51dc76"/>
    <path d="M 874.536596 371.268686 
L 877.23604 373.000994 
L 878.736529 369.171403 
L 876.035982 367.499919 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #49db75"/>
    <path d="M 797.152881 329.90111 
L 799.820069 332.873412 
L 801.320452 331.176053 
L 798.654228 328.290663 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d5f791"/>
    <path d="M 734.292119 263.64644 
L 736.957917 266.306997 
L 738.504861 266.514467 
L 735.841861 263.926084 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a08566"/>
    <path d="M 882.941324 366.881481 
L 885.648063 368.42158 
L 887.151263 364.405605 
L 884.443266 362.922998 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #59de78"/>
    <path d="M 654.605599 207.515602 
L 657.237698 208.525368 
L 658.881229 209.571065 
L 656.251769 208.570124 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c3b2af"/>
    <path d="M 915.841388 327.220202 
L 918.580395 328.062099 
L 920.092876 323.530025 
L 917.352241 322.732756 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e9fb95"/>
    <path d="M 708.753154 241.094301 
L 711.414427 243.350345 
L 712.991434 244.090211 
L 710.333304 241.888488 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #87655e"/>
    <path d="M 799.820069 332.873412 
L 802.487474 335.835765 
L 803.98698 334.051973 
L 801.320452 331.176053 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cdf58f"/>
    <path d="M 842.874666 369.238742 
L 845.553068 371.659728 
L 847.04741 368.616667 
L 844.368632 366.268875 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #4ddb75"/>
    <path d="M 870.341206 373.167392 
L 873.037275 375.000379 
L 874.536596 371.268686 
L 871.839516 369.49791 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #45da74"/>
    <path d="M 691.213637 227.893604 
L 693.868829 229.798711 
L 695.468032 230.766511 
L 692.816004 228.901217 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9f847e"/>
    <path d="M 859.274645 374.26564 
L 861.962588 376.349146 
L 863.45924 372.885169 
L 860.770529 370.868212 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #3dd872"/>
    <path d="M 902.830403 347.332288 
L 905.556222 348.436625 
L 907.066054 344.052052 
L 904.338701 342.997331 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a1ec86"/>
    <path d="M 802.487474 335.835765 
L 805.15514 338.785971 
L 806.653852 336.916309 
L 803.98698 334.051973 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c1f38d"/>
    <path d="M 887.151263 364.405605 
L 889.86188 365.854907 
L 891.366581 361.751178 
L 888.654644 360.357434 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #65e07a"/>
    <path d="M 830.679795 361.834514 
L 833.353197 364.47116 
L 834.847316 361.760409 
L 832.173864 359.201481 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #69e17b"/>
    <path d="M 852.409586 373.200122 
L 855.093169 375.432801 
L 856.588626 372.141499 
L 853.904436 369.978051 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #41d973"/>
    <path d="M 897.093951 354.710869 
L 899.814081 355.93976 
L 901.322173 351.647419 
L 898.600579 350.470238 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #85e781"/>
    <path d="M 736.957917 266.306997 
L 739.624183 269.009163 
L 741.168384 269.142992 
L 738.504861 266.514467 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a48b68"/>
    <path d="M 805.15514 338.785971 
L 807.823111 341.721846 
L 809.321112 339.766961 
L 806.653852 336.916309 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b9f18b"/>
    <path d="M 908.575925 339.650289 
L 911.307532 340.640148 
L 912.818939 336.177064 
L 910.085753 335.234399 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bdf28c"/>
    <path d="M 866.150001 374.862344 
L 868.842904 376.798553 
L 870.341206 373.167392 
L 867.647394 371.294591 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #3dd872"/>
    <path d="M 807.823111 341.721846 
L 810.491436 344.641229 
L 811.988807 342.601849 
L 809.321112 339.766961 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #adef89"/>
    <path d="M 891.366581 361.751178 
L 894.0812 363.113693 
L 895.587472 358.926304 
L 892.871483 357.617242 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #6de27c"/>
    <path d="M 739.624183 269.009163 
L 742.290855 271.7509 
L 743.832371 271.809699 
L 741.168384 269.142992 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a8906a"/>
    <path d="M 833.353197 364.47116 
L 836.027647 367.074435 
L 837.521877 364.287409 
L 834.847316 361.760409 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #61df79"/>
    <path d="M 810.491436 344.641229 
L 813.160169 347.541976 
L 814.656992 345.41891 
L 811.988807 342.601849 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a5ed87"/>
    <path d="M 845.553068 371.659728 
L 848.232929 374.042091 
L 849.727697 370.927587 
L 847.04741 368.616667 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #49db75"/>
    <path d="M 711.414427 243.350345 
L 714.076878 245.666311 
L 715.650762 246.349811 
L 712.991434 244.090211 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #836059"/>
    <path d="M 914.330255 331.702696 
L 917.067664 332.589075 
L 918.580395 328.062099 
L 915.841388 327.220202 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d9f791"/>
    <path d="M 813.160169 347.541976 
L 815.829369 350.421969 
L 817.325721 348.216107 
L 814.656992 345.41891 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #99eb85"/>
    <path d="M 742.290855 271.7509 
L 744.957871 274.530131 
L 746.496766 274.512592 
L 743.832371 271.809699 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ae976d"/>
    <path d="M 855.093169 375.432801 
L 857.778543 377.624192 
L 859.274645 374.26564 
L 856.588626 372.141499 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #3dd872"/>
    <path d="M 901.322173 351.647419 
L 904.046507 352.800966 
L 905.556222 348.436625 
L 902.830403 347.332288 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #91e983"/>
    <path d="M 678.995528 219.93425 
L 681.645343 221.573987 
L 683.260135 222.615018 
L 680.613389 221.004644 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ad9691"/>
    <path d="M 666.789347 213.083928 
L 669.43154 214.423452 
L 671.061228 215.489921 
L 668.421928 214.169348 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b9a5a1"/>
    <path d="M 861.962588 376.349146 
L 864.65255 378.390729 
L 866.150001 374.862344 
L 863.45924 372.885169 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #39d771"/>
    <path d="M 877.23604 373.000994 
L 879.937936 374.693884 
L 881.439536 370.805958 
L 878.736529 369.171403 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #45da74"/>
    <path d="M 836.027647 367.074435 
L 838.703229 369.642541 
L 840.197632 366.780751 
L 837.521877 364.287409 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #59de78"/>
    <path d="M 815.829369 350.421969 
L 818.499098 353.279114 
L 819.995056 350.991423 
L 817.325721 348.216107 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #91e983"/>
    <path d="M 881.439536 370.805958 
L 884.145088 372.402724 
L 885.648063 368.42158 
L 882.941324 366.881481 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #4ddb75"/>
    <path d="M 907.066054 344.052052 
L 909.796123 345.088815 
L 911.307532 340.640148 
L 908.575925 339.650289 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #adef89"/>
    <path d="M 693.868829 229.798711 
L 696.52584 231.774624 
L 698.121871 232.700308 
L 695.468032 230.766511 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9b7f79"/>
    <path d="M 895.587472 358.926304 
L 898.306193 360.20638 
L 899.814081 355.93976 
L 897.093951 354.710869 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #79e47e"/>
    <path d="M 744.957871 274.530131 
L 747.625177 277.344746 
L 749.161514 277.24964 
L 746.496766 274.512592 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b29c6f"/>
    <path d="M 873.037275 375.000379 
L 875.735695 376.792504 
L 877.23604 373.000994 
L 874.536596 371.268686 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #3dd872"/>
    <path d="M 920.092876 323.530025 
L 922.836017 324.324741 
L 924.349736 319.749296 
L 921.605004 318.996088 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9fe98"/>
    <path d="M 885.648063 368.42158 
L 888.357428 369.925703 
L 889.86188 365.854907 
L 887.151263 364.405605 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #55dd77"/>
    <path d="M 818.499098 353.279114 
L 821.169422 356.111344 
L 822.665061 353.742869 
L 819.995056 350.991423 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #85e781"/>
    <path d="M 848.232929 374.042091 
L 850.914345 376.384254 
L 852.409586 373.200122 
L 849.727697 370.927587 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #41d973"/>
    <path d="M 714.076878 245.666311 
L 716.740408 248.040544 
L 718.311194 248.66569 
L 715.650762 246.349811 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #805c54"/>
    <path d="M 747.625177 277.344746 
L 750.292722 280.1926 
L 751.826568 280.018782 
L 749.161514 277.24964 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b6a272"/>
    <path d="M 912.818939 336.177064 
L 915.554782 337.107735 
L 917.067664 332.589075 
L 914.330255 331.702696 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c9f48e"/>
    <path d="M 868.842904 376.798553 
L 871.538045 378.692648 
L 873.037275 375.000379 
L 870.341206 373.167392 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #39d771"/>
    <path d="M 838.703229 369.642541 
L 841.380033 372.173715 
L 842.874666 369.238742 
L 840.197632 366.780751 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #51dc76"/>
    <path d="M 821.169422 356.111344 
L 823.840411 358.91662 
L 825.335804 356.468483 
L 822.665061 353.742869 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #7de57f"/>
    <path d="M 889.86188 365.854907 
L 892.575192 367.270222 
L 894.0812 363.113693 
L 891.366581 361.751178 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #61df79"/>
    <path d="M 750.292722 280.1926 
L 752.960458 283.071519 
L 754.491882 282.817926 
L 751.826568 280.018782 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bca975"/>
    <path d="M 657.237698 208.525368 
L 659.873233 209.622788 
L 661.514064 210.657255 
L 658.881229 209.571065 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c3b2af"/>
    <path d="M 647.698617 204.780051 
L 650.325925 205.617734 
L 651.977065 206.593746 
L 649.352224 205.759958 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c9bab7"/>
    <path d="M 857.778543 377.624192 
L 860.465805 379.772906 
L 861.962588 376.349146 
L 859.274645 374.26564 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #35d771"/>
    <path d="M 752.960458 283.071519 
L 755.628343 285.979301 
L 757.157417 285.644953 
L 754.491882 282.817926 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c0ae77"/>
    <path d="M 823.840411 358.91662 
L 826.51214 361.692936 
L 828.007357 359.166331 
L 825.335804 356.468483 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #75e37d"/>
    <path d="M 899.814081 355.93976 
L 902.536981 357.142066 
L 904.046507 352.800966 
L 901.322173 351.647419 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #85e781"/>
    <path d="M 905.556222 348.436625 
L 908.284797 349.519954 
L 909.796123 345.088815 
L 907.066054 344.052052 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a1ec86"/>
    <path d="M 918.580395 328.062099 
L 921.321969 328.898225 
L 922.836017 324.324741 
L 920.092876 323.530025 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e9fb95"/>
    <path d="M 716.740408 248.040544 
L 719.404923 250.471324 
L 720.972641 251.036195 
L 718.311194 248.66569 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #846257"/>
    <path d="M 864.65255 378.390729 
L 867.34463 380.389144 
L 868.842904 376.798553 
L 866.150001 374.862344 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #31d670"/>
    <path d="M 755.628343 285.979301 
L 758.296338 288.913719 
L 759.823136 288.497722 
L 757.157417 285.644953 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c6b67a"/>
    <path d="M 850.914345 376.384254 
L 853.597412 378.684681 
L 855.093169 375.432801 
L 852.409586 373.200122 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #39d771"/>
    <path d="M 696.52584 231.774624 
L 699.184553 233.820038 
L 700.77741 234.701348 
L 698.121871 232.700308 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #997c76"/>
    <path d="M 841.380033 372.173715 
L 844.058152 374.666235 
L 845.553068 371.659728 
L 842.874666 369.238742 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #49db75"/>
    <path d="M 894.0812 363.113693 
L 896.798573 364.44438 
L 898.306193 360.20638 
L 895.587472 358.926304 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #6de27c"/>
    <path d="M 911.307532 340.640148 
L 914.041846 341.614881 
L 915.554782 337.107735 
L 912.818939 336.177064 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bdf28c"/>
    <path d="M 758.296338 288.913719 
L 760.964411 291.872521 
L 762.489007 291.374066 
L 759.823136 288.497722 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cabb7c"/>
    <path d="M 826.51214 361.692936 
L 829.184686 364.438316 
L 830.679795 361.834514 
L 828.007357 359.166331 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #6de27c"/>
    <path d="M 681.645343 221.573987 
L 684.297475 223.291367 
L 685.909171 224.300645 
L 683.260135 222.615018 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ab938e"/>
    <path d="M 760.964411 291.872521 
L 763.63253 294.853438 
L 765.155003 294.271801 
L 762.489007 291.374066 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d0c380"/>
    <path d="M 879.937936 374.693884 
L 882.642375 376.346441 
L 884.145088 372.402724 
L 881.439536 370.805958 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #41d973"/>
    <path d="M 875.735695 376.792504 
L 878.436559 378.542759 
L 879.937936 374.693884 
L 877.23604 373.000994 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #39d771"/>
    <path d="M 763.63253 294.853438 
L 766.300673 297.854181 
L 767.821101 297.188723 
L 765.155003 294.271801 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d4c882"/>
    <path d="M 884.145088 372.402724 
L 886.85327 373.96088 
L 888.357428 369.925703 
L 885.648063 368.42158 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #49db75"/>
    <path d="M 669.43154 214.423452 
L 672.076593 215.846307 
L 673.703344 216.891401 
L 671.061228 215.489921 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b7a39f"/>
    <path d="M 766.300673 297.854181 
L 768.968819 300.872446 
L 770.487283 300.122616 
L 767.821101 297.188723 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dad085"/>
    <path d="M 719.404923 250.471324 
L 722.070332 252.956877 
L 723.635013 253.459616 
L 720.972641 251.036195 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #886759"/>
    <path d="M 829.184686 364.438316 
L 831.858132 367.150819 
L 833.353197 364.47116 
L 830.679795 361.834514 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #61df79"/>
    <path d="M 768.968819 300.872446 
L 771.636953 303.905916 
L 773.153534 303.071249 
L 770.487283 300.122616 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e0d788"/>
    <path d="M 871.538045 378.692648 
L 874.235522 380.543526 
L 875.735695 376.792504 
L 873.037275 375.000379 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #35d771"/>
    <path d="M 917.067664 332.589075 
L 919.8077 333.466476 
L 921.321969 328.898225 
L 918.580395 328.062099 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d9f791"/>
    <path d="M 771.636953 303.905916 
L 774.305064 306.952265 
L 775.819845 306.032381 
L 773.153534 303.071249 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e4dc8a"/>
    <path d="M 844.058152 374.666235 
L 846.737679 377.118418 
L 848.232929 374.042091 
L 845.553068 371.659728 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #41d973"/>
    <path d="M 860.465805 379.772906 
L 863.155056 381.877596 
L 864.65255 378.390729 
L 861.962588 376.349146 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2dd56f"/>
    <path d="M 888.357428 369.925703 
L 891.0695 371.393116 
L 892.575192 367.270222 
L 889.86188 365.854907 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #55dd77"/>
    <path d="M 904.046507 352.800966 
L 906.773634 353.930481 
L 908.284797 349.519954 
L 905.556222 348.436625 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #91e983"/>
    <path d="M 774.305064 306.952265 
L 776.973147 310.009158 
L 778.486211 309.003766 
L 775.819845 306.032381 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eae48e"/>
    <path d="M 853.597412 378.684681 
L 856.28223 380.94188 
L 857.778543 377.624192 
L 855.093169 375.432801 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #31d670"/>
    <path d="M 776.973147 310.009158 
L 779.641201 313.074255 
L 781.152632 311.983149 
L 778.486211 309.003766 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f0ec91"/>
    <path d="M 898.306193 360.20638 
L 901.027713 361.456949 
L 902.536981 357.142066 
L 899.814081 355.93976 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #75e37d"/>
    <path d="M 779.641201 313.074255 
L 782.30923 316.145212 
L 783.819112 314.968274 
L 781.152632 311.983149 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f4f193"/>
    <path d="M 782.30923 316.145212 
L 784.977242 319.219686 
L 786.485661 317.956882 
L 783.819112 314.968274 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #faf996"/>
    <path d="M 831.858132 367.150819 
L 834.532561 369.828541 
L 836.027647 367.074435 
L 833.353197 364.47116 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #59de78"/>
    <path d="M 784.977242 319.219686 
L 787.645252 322.295336 
L 789.152292 320.946719 
L 786.485661 317.956882 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 699.184553 233.820038 
L 701.844856 235.933577 
L 703.434542 236.768304 
L 700.77741 234.701348 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #957771"/>
    <path d="M 909.796123 345.088815 
L 912.528948 346.107335 
L 914.041846 341.614881 
L 911.307532 340.640148 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #adef89"/>
    <path d="M 787.645252 322.295336 
L 790.313276 325.369824 
L 791.819023 323.935531 
L 789.152292 320.946719 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f5fd97"/>
    <path d="M 790.313276 325.369824 
L 792.981339 328.44082 
L 794.485877 326.921075 
L 791.819023 323.935531 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e9fb95"/>
    <path d="M 867.34463 380.389144 
L 870.038926 382.343188 
L 871.538045 378.692648 
L 868.842904 376.798553 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2dd56f"/>
    <path d="M 722.070332 252.956877 
L 724.736546 255.495373 
L 726.298227 255.934191 
L 723.635013 253.459616 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8c6c5b"/>
    <path d="M 792.981339 328.44082 
L 795.649467 331.506002 
L 797.152881 329.90111 
L 794.485877 326.921075 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e1f993"/>
    <path d="M 795.649467 331.506002 
L 798.317694 334.56306 
L 799.820069 332.873412 
L 797.152881 329.90111 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d5f791"/>
    <path d="M 892.575192 367.270222 
L 895.291277 368.650901 
L 896.798573 364.44438 
L 894.0812 363.113693 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #5ddf79"/>
    <path d="M 798.317694 334.56306 
L 800.986056 337.609697 
L 802.487474 335.835765 
L 799.820069 332.873412 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c9f48e"/>
    <path d="M 800.986056 337.609697 
L 803.654596 340.643632 
L 805.15514 338.785971 
L 802.487474 335.835765 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c1f38d"/>
    <path d="M 846.737679 377.118418 
L 849.418713 379.528624 
L 850.914345 376.384254 
L 848.232929 374.042091 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #39d771"/>
    <path d="M 922.836017 324.324741 
L 925.581671 325.116861 
L 927.09691 320.503175 
L 924.349736 319.749296 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9fe98"/>
    <path d="M 834.532561 369.828541 
L 837.208064 372.469613 
L 838.703229 369.642541 
L 836.027647 367.074435 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #51dc76"/>
    <path d="M 803.654596 340.643632 
L 806.32336 343.662602 
L 807.823111 341.721846 
L 805.15514 338.785971 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b5f08a"/>
    <path d="M 915.554782 337.107735 
L 918.293313 338.026235 
L 919.8077 333.466476 
L 917.067664 332.589075 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c9f48e"/>
    <path d="M 659.873233 209.622788 
L 662.512072 210.807511 
L 664.150146 211.828354 
L 661.514064 210.657255 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c1b0ac"/>
    <path d="M 684.297475 223.291367 
L 686.951799 225.085364 
L 688.560378 226.060531 
L 685.909171 224.300645 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a9918c"/>
    <path d="M 806.32336 343.662602 
L 808.992397 346.664363 
L 810.491436 344.641229 
L 807.823111 341.721846 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a9ee88"/>
    <path d="M 724.736546 255.495373 
L 727.40348 258.084926 
L 728.962201 258.458103 
L 726.298227 255.934191 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #90715d"/>
    <path d="M 808.992397 346.664363 
L 811.661765 349.646696 
L 813.160169 347.541976 
L 810.491436 344.641229 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a1ec86"/>
    <path d="M 856.28223 380.94188 
L 858.968901 383.154401 
L 860.465805 379.772906 
L 857.778543 377.624192 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2dd56f"/>
    <path d="M 902.536981 357.142066 
L 905.26271 358.317343 
L 906.773634 353.930481 
L 904.046507 352.800966 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #81e680"/>
    <path d="M 863.155056 381.877596 
L 865.846398 383.936959 
L 867.34463 380.389144 
L 864.65255 378.390729 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #29d46e"/>
    <path d="M 878.436559 378.542759 
L 881.13996 380.250179 
L 882.642375 376.346441 
L 879.937936 374.693884 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #35d771"/>
    <path d="M 650.325925 205.617734 
L 652.956996 206.545819 
L 654.605599 207.515602 
L 651.977065 206.593746 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c9bab7"/>
    <path d="M 882.642375 376.346441 
L 885.349447 377.957791 
L 886.85327 373.96088 
L 884.145088 372.402724 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #3dd872"/>
    <path d="M 811.661765 349.646696 
L 814.331522 352.607402 
L 815.829369 350.421969 
L 813.160169 347.541976 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #95ea84"/>
    <path d="M 908.284797 349.519954 
L 911.016174 350.581946 
L 912.528948 346.107335 
L 909.796123 345.088815 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9deb85"/>
    <path d="M 896.798573 364.44438 
L 899.51877 365.742671 
L 901.027713 361.456949 
L 898.306193 360.20638 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #69e17b"/>
    <path d="M 874.235522 380.543526 
L 876.935431 382.350126 
L 878.436559 378.542759 
L 875.735695 376.792504 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2dd56f"/>
    <path d="M 701.844856 235.933577 
L 704.506637 238.113791 
L 706.093158 238.899777 
L 703.434542 236.768304 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #93756e"/>
    <path d="M 837.208064 372.469613 
L 839.884731 375.072207 
L 841.380033 372.173715 
L 838.703229 369.642541 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #49db75"/>
    <path d="M 814.331522 352.607402 
L 817.001732 355.544313 
L 818.499098 353.279114 
L 815.829369 350.421969 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8de882"/>
    <path d="M 886.85327 373.96088 
L 889.564169 375.47964 
L 891.0695 371.393116 
L 888.357428 369.925703 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #45da74"/>
    <path d="M 672.076593 215.846307 
L 674.724378 217.351784 
L 676.348153 218.373102 
L 673.703344 216.891401 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b7a39f"/>
    <path d="M 849.418713 379.528624 
L 852.101355 381.895256 
L 853.597412 378.684681 
L 850.914345 376.384254 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #31d670"/>
    <path d="M 921.321969 328.898225 
L 924.066127 329.728498 
L 925.581671 325.116861 
L 922.836017 324.324741 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e9fb95"/>
    <path d="M 727.40348 258.084926 
L 730.071052 260.723602 
L 731.626857 261.02949 
L 728.962201 258.458103 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #94765f"/>
    <path d="M 817.001732 355.544313 
L 819.672464 358.455285 
L 821.169422 356.111344 
L 818.499098 353.279114 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #81e680"/>
    <path d="M 914.041846 341.614881 
L 916.778905 342.574264 
L 918.293313 338.026235 
L 915.554782 337.107735 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b9f18b"/>
    <path d="M 870.038926 382.343188 
L 872.735541 384.251703 
L 874.235522 380.543526 
L 871.538045 378.692648 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #29d46e"/>
    <path d="M 819.672464 358.455285 
L 822.343789 361.338208 
L 823.840411 358.91662 
L 821.169422 356.111344 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #79e47e"/>
    <path d="M 891.0695 371.393116 
L 893.784361 372.82312 
L 895.291277 368.650901 
L 892.575192 367.270222 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #51dc76"/>
    <path d="M 839.884731 375.072207 
L 842.562658 377.634536 
L 844.058152 374.666235 
L 841.380033 372.173715 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #41d973"/>
    <path d="M 730.071052 260.723602 
L 732.739184 263.409417 
L 734.292119 263.64644 
L 731.626857 261.02949 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #987b61"/>
    <path d="M 858.968901 383.154401 
L 861.657529 385.32084 
L 863.155056 381.877596 
L 860.465805 379.772906 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #25d36d"/>
    <path d="M 822.343789 361.338208 
L 825.015784 364.190999 
L 826.51214 361.692936 
L 823.840411 358.91662 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #6de27c"/>
    <path d="M 901.027713 361.456949 
L 903.752097 362.67752 
L 905.26271 358.317343 
L 902.536981 357.142066 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #75e37d"/>
    <path d="M 906.773634 353.930481 
L 909.503608 355.035589 
L 911.016174 350.581946 
L 908.284797 349.519954 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #91e983"/>
    <path d="M 686.951799 225.085364 
L 689.608192 226.954866 
L 691.213637 227.893604 
L 688.560378 226.060531 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a78e89"/>
    <path d="M 704.506637 238.113791 
L 707.169788 240.35916 
L 708.753154 241.094301 
L 706.093158 238.899777 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8f7069"/>
    <path d="M 865.846398 383.936959 
L 868.539935 385.949737 
L 870.038926 382.343188 
L 867.34463 380.389144 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #21d36d"/>
    <path d="M 919.8077 333.466476 
L 922.550388 334.334774 
L 924.066127 329.728498 
L 921.321969 328.898225 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d9f791"/>
    <path d="M 852.101355 381.895256 
L 854.785709 384.216761 
L 856.28223 380.94188 
L 853.597412 378.684681 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #29d46e"/>
    <path d="M 825.015784 364.190999 
L 827.68853 367.011615 
L 829.184686 364.438316 
L 826.51214 361.692936 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #65e07a"/>
    <path d="M 895.291277 368.650901 
L 898.010211 369.996327 
L 899.51877 365.742671 
L 896.798573 364.44438 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #5ddf79"/>
    <path d="M 732.739184 263.409417 
L 735.407802 266.140341 
L 736.957917 266.306997 
L 734.292119 263.64644 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9c8064"/>
    <path d="M 842.562658 377.634536 
L 845.241944 380.154853 
L 846.737679 377.118418 
L 844.058152 374.666235 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #39d771"/>
    <path d="M 912.528948 346.107335 
L 915.264571 347.107347 
L 916.778905 342.574264 
L 914.041846 341.614881 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #adef89"/>
    <path d="M 881.13996 380.250179 
L 883.845996 381.913838 
L 885.349447 377.957791 
L 882.642375 376.346441 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #31d670"/>
    <path d="M 876.935431 382.350126 
L 879.637873 384.11143 
L 881.13996 380.250179 
L 878.436559 378.542759 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #29d46e"/>
    <path d="M 827.68853 367.011615 
L 830.36211 369.798043 
L 831.858132 367.150819 
L 829.184686 364.438316 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #5ddf79"/>
    <path d="M 885.349447 377.957791 
L 888.059243 379.527102 
L 889.564169 375.47964 
L 886.85327 373.96088 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #39d771"/>
    <path d="M 662.512072 210.807511 
L 665.154084 212.079091 
L 666.789347 213.083928 
L 664.150146 211.828354 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bfada9"/>
    <path d="M 735.407802 266.140341 
L 738.076835 268.9143 
L 739.624183 269.009163 
L 736.957917 266.306997 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a28867"/>
    <path d="M 643.416995 203.138972 
L 646.042768 203.887734 
L 647.698617 204.780051 
L 645.0752 204.032834 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cfc2bf"/>
    <path d="M 872.735541 384.251703 
L 875.434577 386.113575 
L 876.935431 382.350126 
L 874.235522 380.543526 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #25d36d"/>
    <path d="M 861.657529 385.32084 
L 864.348221 387.439838 
L 865.846398 383.936959 
L 863.155056 381.877596 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1dd26c"/>
    <path d="M 674.724378 217.351784 
L 677.374765 218.939087 
L 678.995528 219.93425 
L 676.348153 218.373102 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b5a09c"/>
    <path d="M 707.169788 240.35916 
L 709.834202 242.668096 
L 711.414427 243.350345 
L 708.753154 241.094301 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8b6b64"/>
    <path d="M 830.36211 369.798043 
L 833.036612 372.548312 
L 834.532561 369.828541 
L 831.858132 367.150819 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #51dc76"/>
    <path d="M 889.564169 375.47964 
L 892.277872 376.958258 
L 893.784361 372.82312 
L 891.0695 371.393116 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #45da74"/>
    <path d="M 918.293313 338.026235 
L 921.034559 338.932397 
L 922.550388 334.334774 
L 919.8077 333.466476 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c9f48e"/>
    <path d="M 845.241944 380.154853 
L 847.92269 382.631456 
L 849.418713 379.528624 
L 846.737679 377.118418 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #31d670"/>
    <path d="M 905.26271 358.317343 
L 907.991328 359.465171 
L 909.503608 355.035589 
L 906.773634 353.930481 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #81e680"/>
    <path d="M 738.076835 268.9143 
L 740.746216 271.729179 
L 742.290855 271.7509 
L 739.624183 269.009163 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a68d69"/>
    <path d="M 925.581671 325.116861 
L 928.32985 325.906348 
L 929.846531 321.257725 
L 927.09691 320.503175 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9fe98"/>
    <path d="M 854.785709 384.216761 
L 857.471879 386.49163 
L 858.968901 383.154401 
L 856.28223 380.94188 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #21d36d"/>
    <path d="M 899.51877 365.742671 
L 902.241863 367.008028 
L 903.752097 362.67752 
L 901.027713 361.456949 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #65e07a"/>
    <path d="M 652.956996 206.545819 
L 655.591697 207.564142 
L 657.237698 208.525368 
L 654.605599 207.515602 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c9bab7"/>
    <path d="M 911.016174 350.581946 
L 913.750402 351.622293 
L 915.264571 347.107347 
L 912.528948 346.107335 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9deb85"/>
    <path d="M 689.608192 226.954866 
L 692.266532 228.898682 
L 693.868829 229.798711 
L 691.213637 227.893604 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a38984"/>
    <path d="M 740.746216 271.729179 
L 743.415883 274.582825 
L 744.957871 274.530131 
L 742.290855 271.7509 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #aa926b"/>
    <path d="M 868.539935 385.949737 
L 871.235772 387.914721 
L 872.735541 384.251703 
L 870.038926 382.343188 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1dd26c"/>
    <path d="M 833.036612 372.548312 
L 835.712127 375.260486 
L 837.208064 372.469613 
L 834.532561 369.828541 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #49db75"/>
    <path d="M 893.784361 372.82312 
L 896.502092 374.215054 
L 898.010211 369.996327 
L 895.291277 368.650901 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #4ddb75"/>
    <path d="M 743.415883 274.582825 
L 746.085779 277.473046 
L 747.625177 277.344746 
L 744.957871 274.530131 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b09a6e"/>
    <path d="M 847.92269 382.631456 
L 850.605 385.062687 
L 852.101355 381.895256 
L 849.418713 379.528624 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #29d46e"/>
    <path d="M 709.834202 242.668096 
L 712.499774 245.038946 
L 714.076878 245.666311 
L 711.414427 243.350345 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #87655e"/>
    <path d="M 916.778905 342.574264 
L 919.518742 343.51809 
L 921.034559 338.932397 
L 918.293313 338.026235 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b9f18b"/>
    <path d="M 746.085779 277.473046 
L 748.755848 280.397618 
L 750.292722 280.1926 
L 747.625177 277.344746 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b49f70"/>
    <path d="M 924.066127 329.728498 
L 926.812884 330.552839 
L 928.32985 325.906348 
L 925.581671 325.116861 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e9fb95"/>
    <path d="M 835.712127 375.260486 
L 838.388751 377.932672 
L 839.884731 375.072207 
L 837.208064 372.469613 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #41d973"/>
    <path d="M 748.755848 280.397618 
L 751.426042 283.354287 
L 752.960458 283.071519 
L 750.292722 280.1926 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #baa774"/>
    <path d="M 857.471879 386.49163 
L 860.159975 388.718405 
L 861.657529 385.32084 
L 858.968901 383.154401 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1dd26c"/>
    <path d="M 903.752097 362.67752 
L 906.47941 363.867632 
L 907.991328 359.465171 
L 905.26271 358.317343 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #71e37d"/>
    <path d="M 879.637873 384.11143 
L 882.342947 385.826466 
L 883.845996 381.913838 
L 881.13996 380.250179 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #25d36d"/>
    <path d="M 864.348221 387.439838 
L 867.041085 389.510085 
L 868.539935 385.949737 
L 865.846398 383.936959 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #19d16b"/>
    <path d="M 883.845996 381.913838 
L 886.554761 383.532856 
L 888.059243 379.527102 
L 885.349447 377.957791 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2dd56f"/>
    <path d="M 751.426042 283.354287 
L 754.096316 286.340767 
L 755.628343 285.979301 
L 752.960458 283.071519 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #beac76"/>
    <path d="M 909.503608 355.035589 
L 912.236483 356.115941 
L 913.750402 351.622293 
L 911.016174 350.581946 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8de882"/>
    <path d="M 898.010211 369.996327 
L 900.73207 371.305921 
L 902.241863 367.008028 
L 899.51877 365.742671 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #59de78"/>
    <path d="M 875.434577 386.113575 
L 878.136139 387.927738 
L 879.637873 384.11143 
L 876.935431 382.350126 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1dd26c"/>
    <path d="M 754.096316 286.340767 
L 756.76663 289.354751 
L 758.296338 288.913719 
L 755.628343 285.979301 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c4b379"/>
    <path d="M 796.813319 336.244615 
L 799.482717 339.373302 
L 800.986056 337.609697 
L 798.317694 334.56306 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c9f48e"/>
    <path d="M 799.482717 339.373302 
L 802.15221 342.488743 
L 803.654596 340.643632 
L 800.986056 337.609697 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bdf28c"/>
    <path d="M 794.143977 333.105041 
L 796.813319 336.244615 
L 798.317694 334.56306 
L 795.649467 331.506002 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d5f791"/>
    <path d="M 802.15221 342.488743 
L 804.821848 345.588596 
L 806.32336 343.662602 
L 803.654596 340.643632 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b1ef89"/>
    <path d="M 888.059243 379.527102 
L 890.771856 381.05358 
L 892.277872 376.958258 
L 889.564169 375.47964 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #35d771"/>
    <path d="M 791.47465 329.956958 
L 794.143977 333.105041 
L 795.649467 331.506002 
L 792.981339 328.44082 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ddf892"/>
    <path d="M 838.388751 377.932672 
L 841.066582 380.563019 
L 842.562658 377.634536 
L 839.884731 375.072207 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #39d771"/>
    <path d="M 804.821848 345.588596 
L 807.491681 348.67054 
L 808.992397 346.664363 
L 806.32336 343.662602 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a9ee88"/>
    <path d="M 788.805307 326.802758 
L 791.47465 329.956958 
L 792.981339 328.44082 
L 790.313276 325.369824 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e9fb95"/>
    <path d="M 756.76663 289.354751 
L 759.436947 292.393903 
L 760.964411 291.872521 
L 758.296338 288.913719 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c8b97b"/>
    <path d="M 786.135919 323.644844 
L 788.805307 326.802758 
L 790.313276 325.369824 
L 787.645252 322.295336 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f5fd97"/>
    <path d="M 807.491681 348.67054 
L 810.161768 351.732278 
L 811.661765 349.646696 
L 808.992397 346.664363 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9deb85"/>
    <path d="M 783.466464 320.485628 
L 786.135919 323.644844 
L 787.645252 322.295336 
L 784.977242 319.219686 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 759.436947 292.393903 
L 762.107237 295.455869 
L 763.63253 294.853438 
L 760.964411 291.872521 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cec07f"/>
    <path d="M 780.796922 317.327532 
L 783.466464 320.485628 
L 784.977242 319.219686 
L 782.30923 316.145212 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #faf996"/>
    <path d="M 692.266532 228.898682 
L 694.926698 230.915541 
L 696.52584 231.774624 
L 693.868829 229.798711 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a18781"/>
    <path d="M 810.161768 351.732278 
L 812.832167 354.771537 
L 814.331522 352.607402 
L 811.661765 349.646696 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #91e983"/>
    <path d="M 850.605 385.062687 
L 853.288981 387.446936 
L 854.785709 384.216761 
L 852.101355 381.895256 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #21d36d"/>
    <path d="M 677.374765 218.939087 
L 680.027624 220.607326 
L 681.645343 221.573987 
L 678.995528 219.93425 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b39e99"/>
    <path d="M 712.499774 245.038946 
L 715.166404 247.469992 
L 716.740408 248.040544 
L 714.076878 245.666311 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #836059"/>
    <path d="M 665.154084 212.079091 
L 667.799135 213.436984 
L 669.43154 214.423452 
L 666.789347 213.083928 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bfada9"/>
    <path d="M 778.127282 314.17298 
L 780.796922 317.327532 
L 782.30923 316.145212 
L 779.641201 313.074255 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f4f193"/>
    <path d="M 762.107237 295.455869 
L 764.777473 298.538278 
L 766.300673 297.854181 
L 763.63253 294.853438 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d4c882"/>
    <path d="M 775.457534 311.0244 
L 778.127282 314.17298 
L 779.641201 313.074255 
L 776.973147 310.009158 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eee990"/>
    <path d="M 764.777473 298.538278 
L 767.447635 301.638742 
L 768.968819 300.872446 
L 766.300673 297.854181 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d8cd84"/>
    <path d="M 772.787674 307.884218 
L 775.457534 311.0244 
L 776.973147 310.009158 
L 774.305064 306.952265 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eae48e"/>
    <path d="M 767.447635 301.638742 
L 770.117706 304.754859 
L 771.636953 303.905916 
L 768.968819 300.872446 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ded587"/>
    <path d="M 770.117706 304.754859 
L 772.787674 307.884218 
L 774.305064 306.952265 
L 771.636953 303.905916 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e4dc8a"/>
    <path d="M 812.832167 354.771537 
L 815.502946 357.786074 
L 817.001732 355.544313 
L 814.331522 352.607402 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #89e781"/>
    <path d="M 922.550388 334.334774 
L 925.295748 335.193855 
L 926.812884 330.552839 
L 924.066127 329.728498 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d9f791"/>
    <path d="M 871.235772 387.914721 
L 873.934018 389.830744 
L 875.434577 386.113575 
L 872.735541 384.251703 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #19d16b"/>
    <path d="M 915.264571 347.107347 
L 918.003034 348.088602 
L 919.518742 343.51809 
L 916.778905 342.574264 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a9ee88"/>
    <path d="M 815.502946 357.786074 
L 818.174174 360.773672 
L 819.672464 358.455285 
L 817.001732 355.544313 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #7de57f"/>
    <path d="M 892.277872 376.958258 
L 894.994466 378.396029 
L 896.502092 374.215054 
L 893.784361 372.82312 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #41d973"/>
    <path d="M 818.174174 360.773672 
L 820.845925 363.732149 
L 822.343789 361.338208 
L 819.672464 358.455285 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #75e37d"/>
    <path d="M 841.066582 380.563019 
L 843.74572 383.14972 
L 845.241944 380.154853 
L 842.562658 377.634536 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #31d670"/>
    <path d="M 860.159975 388.718405 
L 862.850106 390.895672 
L 864.348221 387.439838 
L 861.657529 385.32084 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #15d06a"/>
    <path d="M 820.845925 363.732149 
L 823.518277 366.659354 
L 825.015784 364.190999 
L 822.343789 361.338208 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #69e17b"/>
    <path d="M 902.241863 367.008028 
L 904.967923 368.239949 
L 906.47941 363.867632 
L 903.752097 362.67752 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #65e07a"/>
    <path d="M 907.991328 359.465171 
L 910.722896 360.58516 
L 912.236483 356.115941 
L 909.503608 355.035589 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #81e680"/>
    <path d="M 715.166404 247.469992 
L 717.833992 249.959454 
L 719.404923 250.471324 
L 716.740408 248.040544 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #805c54"/>
    <path d="M 867.041085 389.510085 
L 869.73623 391.530317 
L 871.235772 387.914721 
L 868.539935 385.949737 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #11cf69"/>
    <path d="M 646.042768 203.887734 
L 648.672505 204.729209 
L 650.325925 205.617734 
L 647.698617 204.780051 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cdbfbc"/>
    <path d="M 823.518277 366.659354 
L 826.191314 369.553171 
L 827.68853 367.011615 
L 825.015784 364.190999 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #61df79"/>
    <path d="M 655.591697 207.564142 
L 658.229895 208.67244 
L 659.873233 209.622788 
L 657.237698 208.525368 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c7b7b4"/>
    <path d="M 853.288981 387.446936 
L 855.974743 389.782639 
L 857.471879 386.49163 
L 854.785709 384.216761 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #19d16b"/>
    <path d="M 921.034559 338.932397 
L 923.77855 339.826067 
L 925.295748 335.193855 
L 922.550388 334.334774 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c9f48e"/>
    <path d="M 896.502092 374.215054 
L 899.222778 375.568295 
L 900.73207 371.305921 
L 898.010211 369.996327 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #4ddb75"/>
    <path d="M 843.74572 383.14972 
L 846.426271 385.691012 
L 847.92269 382.631456 
L 845.241944 380.154853 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #29d46e"/>
    <path d="M 913.750402 351.622293 
L 916.487528 352.640708 
L 918.003034 348.088602 
L 915.264571 347.107347 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9deb85"/>
    <path d="M 928.32985 325.906348 
L 931.080562 326.693166 
L 932.598602 322.012947 
L 929.846531 321.257725 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9fe98"/>
    <path d="M 826.191314 369.553171 
L 828.865121 372.411524 
L 830.36211 369.798043 
L 827.68853 367.011615 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #55dd77"/>
    <path d="M 882.342947 385.826466 
L 885.050757 387.494304 
L 886.554761 383.532856 
L 883.845996 381.913838 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #21d36d"/>
    <path d="M 694.926698 230.915541 
L 697.58857 233.004093 
L 699.184553 233.820038 
L 696.52584 231.774624 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9d827c"/>
    <path d="M 878.136139 387.927738 
L 880.840331 389.69317 
L 882.342947 385.826466 
L 879.637873 384.11143 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #19d16b"/>
    <path d="M 886.554761 383.532856 
L 889.266355 385.106396 
L 890.771856 381.05358 
L 888.059243 379.527102 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #29d46e"/>
    <path d="M 717.833992 249.959454 
L 720.502443 252.505493 
L 722.070332 252.956877 
L 719.404923 250.471324 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #846257"/>
    <path d="M 828.865121 372.411524 
L 831.539788 375.232371 
L 833.036612 372.548312 
L 830.36211 369.798043 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #4ddb75"/>
    <path d="M 873.934018 389.830744 
L 876.63478 391.696692 
L 878.136139 387.927738 
L 875.434577 386.113575 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #11cf69"/>
    <path d="M 680.027624 220.607326 
L 682.682826 222.355526 
L 684.297475 223.291367 
L 681.645343 221.573987 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #af9994"/>
    <path d="M 862.850106 390.895672 
L 865.542384 393.022068 
L 867.041085 389.510085 
L 864.348221 387.439838 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0dcf69"/>
    <path d="M 890.771856 381.05358 
L 893.487379 382.536476 
L 894.994466 378.396029 
L 892.277872 376.958258 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #35d771"/>
    <path d="M 906.47941 363.867632 
L 909.209719 365.026853 
L 910.722896 360.58516 
L 907.991328 359.465171 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #71e37d"/>
    <path d="M 846.426271 385.691012 
L 849.108343 388.185179 
L 850.605 385.062687 
L 847.92269 382.631456 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #21d36d"/>
    <path d="M 919.518742 343.51809 
L 922.261393 344.446169 
L 923.77855 339.826067 
L 921.034559 338.932397 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b9f18b"/>
    <path d="M 900.73207 371.305921 
L 903.456933 372.579138 
L 904.967923 368.239949 
L 902.241863 367.008028 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #55dd77"/>
    <path d="M 855.974743 389.782639 
L 858.662396 392.068281 
L 860.159975 388.718405 
L 857.471879 386.49163 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #11cf69"/>
    <path d="M 831.539788 375.232371 
L 834.215411 378.013716 
L 835.712127 375.260486 
L 833.036612 372.548312 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #45da74"/>
    <path d="M 926.812884 330.552839 
L 929.562258 331.371179 
L 931.080562 326.693166 
L 928.32985 325.906348 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e9fb95"/>
    <path d="M 667.799135 213.436984 
L 670.447093 214.880554 
L 672.076593 215.846307 
L 669.43154 214.423452 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bdaba7"/>
    <path d="M 912.236483 356.115941 
L 914.972313 357.171211 
L 916.487528 352.640708 
L 913.750402 351.622293 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8de882"/>
    <path d="M 720.502443 252.505493 
L 723.171666 255.106211 
L 724.736546 255.495373 
L 722.070332 252.956877 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #886759"/>
    <path d="M 869.73623 391.530317 
L 872.433769 393.499322 
L 873.934018 389.830744 
L 871.235772 387.914721 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0dcf69"/>
    <path d="M 834.215411 378.013716 
L 836.892085 380.753601 
L 838.388751 377.932672 
L 835.712127 375.260486 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #39d771"/>
    <path d="M 894.994466 378.396029 
L 897.71404 379.792287 
L 899.222778 375.568295 
L 896.502092 374.215054 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #3dd872"/>
    <path d="M 697.58857 233.004093 
L 700.252033 235.162913 
L 701.844856 235.933577 
L 699.184553 233.820038 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9b7f79"/>
    <path d="M 849.108343 388.185179 
L 851.792044 390.630555 
L 853.288981 387.446936 
L 850.605 385.062687 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #19d16b"/>
    <path d="M 723.171666 255.106211 
L 725.84157 257.759658 
L 727.40348 258.084926 
L 724.736546 255.495373 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8c6c5b"/>
    <path d="M 918.003034 348.088602 
L 920.744378 349.050875 
L 922.261393 344.446169 
L 919.518742 343.51809 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a9ee88"/>
    <path d="M 925.295748 335.193855 
L 928.043805 336.043612 
L 929.562258 331.371179 
L 926.812884 330.552839 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d9f791"/>
    <path d="M 836.892085 380.753601 
L 839.569913 383.450114 
L 841.066582 380.563019 
L 838.388751 377.932672 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #31d670"/>
    <path d="M 858.662396 392.068281 
L 861.352057 394.302398 
L 862.850106 390.895672 
L 860.159975 388.718405 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #09ce68"/>
    <path d="M 904.967923 368.239949 
L 907.697023 369.437962 
L 909.209719 365.026853 
L 906.47941 363.867632 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #61df79"/>
    <path d="M 880.840331 389.69317 
L 883.54726 391.408898 
L 885.050757 387.494304 
L 882.342947 385.826466 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #15d06a"/>
    <path d="M 865.542384 393.022068 
L 868.236925 395.096281 
L 869.73623 391.530317 
L 867.041085 389.510085 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #09ce68"/>
    <path d="M 885.050757 387.494304 
L 887.761404 389.114065 
L 889.266355 385.106396 
L 886.554761 383.532856 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1dd26c"/>
    <path d="M 899.222778 375.568295 
L 901.9465 376.882256 
L 903.456933 372.579138 
L 900.73207 371.305921 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #49db75"/>
    <path d="M 910.722896 360.58516 
L 913.457474 361.676946 
L 914.972313 357.171211 
L 912.236483 356.115941 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #7de57f"/>
    <path d="M 876.63478 391.696692 
L 879.33817 393.511497 
L 880.840331 389.69317 
L 878.136139 387.927738 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0dcf69"/>
    <path d="M 658.229895 208.67244 
L 660.871454 209.870353 
L 662.512072 210.807511 
L 659.873233 209.622788 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c7b7b4"/>
    <path d="M 682.682826 222.355526 
L 685.340243 224.182627 
L 686.951799 225.085364 
L 684.297475 223.291367 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ad9691"/>
    <path d="M 725.84157 257.759658 
L 728.512072 260.463828 
L 730.071052 260.723602 
L 727.40348 258.084926 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #90715d"/>
    <path d="M 889.266355 385.106396 
L 891.980875 386.633663 
L 893.487379 382.536476 
L 890.771856 381.05358 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #25d36d"/>
    <path d="M 839.569913 383.450114 
L 842.248998 386.101388 
L 843.74572 383.14972 
L 841.066582 380.563019 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #29d46e"/>
    <path d="M 648.672505 204.729209 
L 651.306073 205.663333 
L 652.956996 206.545819 
L 650.325925 205.617734 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cdbfbc"/>
    <path d="M 700.252033 235.162913 
L 702.916969 237.390503 
L 704.506637 238.113791 
L 701.844856 235.933577 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #977a74"/>
    <path d="M 851.792044 390.630555 
L 854.47749 393.025522 
L 855.974743 389.782639 
L 853.288981 387.446936 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #11cf69"/>
    <path d="M 872.433769 393.499322 
L 875.133816 395.415935 
L 876.63478 391.696692 
L 873.934018 389.830744 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #09ce68"/>
    <path d="M 923.77855 339.826067 
L 926.525314 340.707106 
L 928.043805 336.043612 
L 925.295748 335.193855 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c9f48e"/>
    <path d="M 916.487528 352.640708 
L 919.227601 353.636929 
L 920.744378 349.050875 
L 918.003034 348.088602 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #99eb85"/>
    <path d="M 728.512072 260.463828 
L 731.18309 263.216668 
L 732.739184 263.409417 
L 730.071052 260.723602 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #94765f"/>
    <path d="M 893.487379 382.536476 
L 896.205905 383.975081 
L 897.71404 379.792287 
L 894.994466 378.396029 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #31d670"/>
    <path d="M 808.660165 353.797952 
L 811.331293 356.913527 
L 812.832167 354.771537 
L 810.161768 351.732278 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8de882"/>
    <path d="M 805.989276 350.659066 
L 808.660165 353.797952 
L 810.161768 351.732278 
L 807.491681 348.67054 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #99eb85"/>
    <path d="M 670.447093 214.880554 
L 673.097823 216.409071 
L 674.724378 217.351784 
L 672.076593 215.846307 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bba8a4"/>
    <path d="M 811.331293 356.913527 
L 814.002727 360.003475 
L 815.502946 357.786074 
L 812.832167 354.771537 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #85e781"/>
    <path d="M 803.318564 347.499215 
L 805.989276 350.659066 
L 807.491681 348.67054 
L 804.821848 345.588596 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a5ed87"/>
    <path d="M 931.080562 326.693166 
L 933.833818 327.477284 
L 935.353126 322.768842 
L 932.598602 322.012947 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9fe98"/>
    <path d="M 842.248998 386.101388 
L 844.929449 388.705603 
L 846.426271 385.691012 
L 843.74572 383.14972 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #21d36d"/>
    <path d="M 814.002727 360.003475 
L 816.674539 363.065509 
L 818.174174 360.773672 
L 815.502946 357.786074 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #79e47e"/>
    <path d="M 800.647971 344.32077 
L 803.318564 347.499215 
L 804.821848 345.588596 
L 802.15221 342.488743 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b1ef89"/>
    <path d="M 861.352057 394.302398 
L 864.04384 396.483575 
L 865.542384 393.022068 
L 862.850106 390.895672 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #05cd67"/>
    <path d="M 816.674539 363.065509 
L 819.346806 366.097378 
L 820.845925 363.732149 
L 818.174174 360.773672 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #6de27c"/>
    <path d="M 797.977444 341.126126 
L 800.647971 344.32077 
L 802.15221 342.488743 
L 799.482717 339.373302 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bdf28c"/>
    <path d="M 731.18309 263.216668 
L 733.854545 266.016074 
L 735.407802 266.140341 
L 732.739184 263.409417 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9a7e62"/>
    <path d="M 903.456933 372.579138 
L 906.184876 373.815466 
L 907.697023 369.437962 
L 904.967923 368.239949 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #55dd77"/>
    <path d="M 795.306935 337.917703 
L 797.977444 341.126126 
L 799.482717 339.373302 
L 796.813319 336.244615 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c5f38d"/>
    <path d="M 819.346806 366.097378 
L 822.019606 369.096861 
L 823.518277 366.659354 
L 820.845925 363.732149 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #65e07a"/>
    <path d="M 909.209719 365.026853 
L 911.943089 366.154783 
L 913.457474 361.676946 
L 910.722896 360.58516 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #71e37d"/>
    <path d="M 868.236925 395.096281 
L 870.933844 397.117049 
L 872.433769 393.499322 
L 869.73623 391.530317 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #01cc66"/>
    <path d="M 792.636401 334.697936 
L 795.306935 337.917703 
L 796.813319 336.244615 
L 794.143977 333.105041 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d1f690"/>
    <path d="M 822.019606 369.096861 
L 824.693025 372.061779 
L 826.191314 369.553171 
L 823.518277 366.659354 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #59de78"/>
    <path d="M 854.47749 393.025522 
L 857.164794 395.368511 
L 858.662396 392.068281 
L 855.974743 389.782639 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #09ce68"/>
    <path d="M 789.965803 331.469282 
L 792.636401 334.697936 
L 794.143977 333.105041 
L 791.47465 329.956958 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ddf892"/>
    <path d="M 733.854545 266.016074 
L 736.526365 268.859899 
L 738.076835 268.9143 
L 735.407802 266.140341 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9e8365"/>
    <path d="M 897.71404 379.792287 
L 900.436682 381.146404 
L 901.9465 376.882256 
L 899.222778 375.568295 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #39d771"/>
    <path d="M 702.916969 237.390503 
L 705.583267 239.68529 
L 707.169788 240.35916 
L 704.506637 238.113791 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #93756e"/>
    <path d="M 922.261393 344.446169 
L 925.006894 345.358326 
L 926.525314 340.707106 
L 923.77855 339.826067 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b9f18b"/>
    <path d="M 787.295109 328.23421 
L 789.965803 331.469282 
L 791.47465 329.956958 
L 788.805307 326.802758 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e9fb95"/>
    <path d="M 824.693025 372.061779 
L 827.367152 374.989986 
L 828.865121 372.411524 
L 826.191314 369.553171 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #51dc76"/>
    <path d="M 844.929449 388.705603 
L 847.611376 391.260986 
L 849.108343 388.185179 
L 846.426271 385.691012 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #19d16b"/>
    <path d="M 914.972313 357.171211 
L 917.711153 358.201101 
L 919.227601 353.636929 
L 916.487528 352.640708 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8de882"/>
    <path d="M 685.340243 224.182627 
L 687.999748 226.08748 
L 689.608192 226.954866 
L 686.951799 225.085364 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ab938e"/>
    <path d="M 784.624289 324.995204 
L 787.295109 328.23421 
L 788.805307 326.802758 
L 786.135919 323.644844 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f5fd97"/>
    <path d="M 883.54726 391.408898 
L 886.257035 393.073998 
L 887.761404 389.114065 
L 885.050757 387.494304 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #11cf69"/>
    <path d="M 929.562258 331.371179 
L 932.314263 332.183454 
L 933.833818 327.477284 
L 931.080562 326.693166 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e9fb95"/>
    <path d="M 736.526365 268.859899 
L 739.19848 271.745953 
L 740.746216 271.729179 
L 738.076835 268.9143 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a28867"/>
    <path d="M 879.33817 393.511497 
L 882.044297 395.274141 
L 883.54726 391.408898 
L 880.840331 389.69317 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #09ce68"/>
    <path d="M 781.95332 321.754757 
L 784.624289 324.995204 
L 786.135919 323.644844 
L 783.466464 320.485628 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 827.367152 374.989986 
L 830.042078 377.87938 
L 831.539788 375.232371 
L 828.865121 372.411524 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #45da74"/>
    <path d="M 887.761404 389.114065 
L 890.474991 390.684912 
L 891.980875 386.633663 
L 889.266355 385.106396 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #19d16b"/>
    <path d="M 779.282185 318.515369 
L 781.95332 321.754757 
L 783.466464 320.485628 
L 780.796922 317.327532 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #faf996"/>
    <path d="M 739.19848 271.745953 
L 741.870825 274.672006 
L 743.415883 274.582825 
L 740.746216 271.729179 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a8906a"/>
    <path d="M 776.61087 315.279546 
L 779.282185 318.515369 
L 780.796922 317.327532 
L 778.127282 314.17298 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f4f193"/>
    <path d="M 875.133816 395.415935 
L 877.836483 397.279044 
L 879.33817 393.511497 
L 876.63478 391.696692 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #01cc66"/>
    <path d="M 830.042078 377.87938 
L 832.717901 380.7279 
L 834.215411 378.013716 
L 831.539788 375.232371 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #3dd872"/>
    <path d="M 773.939368 312.049797 
L 776.61087 315.279546 
L 778.127282 314.17298 
L 775.457534 311.0244 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eee990"/>
    <path d="M 864.04384 396.483575 
L 866.737864 398.610452 
L 868.236925 395.096281 
L 865.542384 393.022068 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00cb6b"/>
    <path d="M 741.870825 274.672006 
L 744.543338 277.63579 
L 746.085779 277.473046 
L 743.415883 274.582825 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ac956c"/>
    <path d="M 891.980875 386.633663 
L 894.69842 388.113911 
L 896.205905 383.975081 
L 893.487379 382.536476 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #25d36d"/>
    <path d="M 907.697023 369.437962 
L 910.429233 370.60163 
L 911.943089 366.154783 
L 909.209719 365.026853 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #61df79"/>
    <path d="M 771.267675 308.828632 
L 773.939368 312.049797 
L 775.457534 311.0244 
L 772.787674 307.884218 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e8e28d"/>
    <path d="M 847.611376 391.260986 
L 850.294892 393.765816 
L 851.792044 390.630555 
L 849.108343 388.185179 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #11cf69"/>
    <path d="M 901.9465 376.882256 
L 904.673343 378.156389 
L 906.184876 373.815466 
L 903.456933 372.579138 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #45da74"/>
    <path d="M 920.744378 349.050875 
L 923.488645 349.993956 
L 925.006894 345.358326 
L 922.261393 344.446169 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a9ee88"/>
    <path d="M 857.164794 395.368511 
L 859.854075 397.658007 
L 861.352057 394.302398 
L 858.662396 392.068281 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #01cc66"/>
    <path d="M 660.871454 209.870353 
L 663.51624 211.157419 
L 665.154084 212.079091 
L 662.512072 210.807511 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c5b5b1"/>
    <path d="M 744.543338 277.63579 
L 747.215964 280.635003 
L 748.755848 280.397618 
L 746.085779 277.473046 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b29c6f"/>
    <path d="M 705.583267 239.68529 
L 708.250815 242.045632 
L 709.834202 242.668096 
L 707.169788 240.35916 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8f7069"/>
    <path d="M 641.756706 202.335196 
L 644.384795 203.085486 
L 646.042768 203.887734 
L 643.416995 203.138972 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d3c7c4"/>
    <path d="M 768.595795 305.618555 
L 771.267675 308.828632 
L 772.787674 307.884218 
L 770.117706 304.754859 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e2da89"/>
    <path d="M 832.717901 380.7279 
L 835.39472 383.533529 
L 836.892085 380.753601 
L 834.215411 378.013716 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #35d771"/>
    <path d="M 765.923735 302.42207 
L 768.595795 305.618555 
L 770.117706 304.754859 
L 767.447635 301.638742 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ded587"/>
    <path d="M 747.215964 280.635003 
L 749.88865 283.667311 
L 751.426042 283.354287 
L 748.755848 280.397618 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b6a272"/>
    <path d="M 928.043805 336.043612 
L 930.794579 336.883949 
L 932.314263 332.183454 
L 929.562258 331.371179 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d9f791"/>
    <path d="M 763.251507 299.241668 
L 765.923735 302.42207 
L 767.447635 301.638742 
L 764.777473 298.538278 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d8cd84"/>
    <path d="M 913.457474 361.676946 
L 916.195121 362.740196 
L 917.711153 358.201101 
L 914.972313 357.171211 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #7de57f"/>
    <path d="M 749.88865 283.667311 
L 752.56135 286.73035 
L 754.096316 286.340767 
L 751.426042 283.354287 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bca975"/>
    <path d="M 870.933844 397.117049 
L 873.633259 399.083163 
L 875.133816 395.415935 
L 872.433769 393.499322 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00cb6b"/>
    <path d="M 760.579129 296.079834 
L 763.251507 299.241668 
L 764.777473 298.538278 
L 762.107237 295.455869 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d2c581"/>
    <path d="M 752.56135 286.73035 
L 755.23402 289.82173 
L 756.76663 289.354751 
L 754.096316 286.340767 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c2b178"/>
    <path d="M 757.906625 292.939036 
L 760.579129 296.079834 
L 762.107237 295.455869 
L 759.436947 292.393903 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ccbe7d"/>
    <path d="M 755.23402 289.82173 
L 757.906625 292.939036 
L 759.436947 292.393903 
L 756.76663 289.354751 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c6b67a"/>
    <path d="M 673.097823 216.409071 
L 675.751191 218.02171 
L 677.374765 218.939087 
L 674.724378 217.351784 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b9a5a1"/>
    <path d="M 896.205905 383.975081 
L 898.927529 385.368732 
L 900.436682 381.146404 
L 897.71404 379.792287 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2dd56f"/>
    <path d="M 835.39472 383.533529 
L 838.07264 386.294294 
L 839.569913 383.450114 
L 836.892085 380.753601 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #29d46e"/>
    <path d="M 651.306073 205.663333 
L 653.943336 206.689935 
L 655.591697 207.564142 
L 652.956996 206.545819 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cdbfbc"/>
    <path d="M 687.999748 226.08748 
L 690.661214 228.068856 
L 692.266532 228.898682 
L 689.608192 226.954866 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a9918c"/>
    <path d="M 850.294892 393.765816 
L 852.980115 396.218422 
L 854.47749 393.025522 
L 851.792044 390.630555 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #09ce68"/>
    <path d="M 919.227601 353.636929 
L 921.970668 354.610712 
L 923.488645 349.993956 
L 920.744378 349.050875 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #99eb85"/>
    <path d="M 708.250815 242.045632 
L 710.919505 244.469818 
L 712.499774 245.038946 
L 709.834202 242.668096 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8d6d66"/>
    <path d="M 926.525314 340.707106 
L 929.274882 341.575387 
L 930.794579 336.883949 
L 928.043805 336.043612 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c9f48e"/>
    <path d="M 838.07264 386.294294 
L 840.751767 389.008272 
L 842.248998 386.101388 
L 839.569913 383.450114 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #21d36d"/>
    <path d="M 859.854075 397.658007 
L 862.545453 399.892548 
L 864.04384 396.483575 
L 861.352057 394.302398 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c970"/>
    <path d="M 906.184876 373.815466 
L 908.915978 375.014434 
L 910.429233 370.60163 
L 907.697023 369.437962 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #51dc76"/>
    <path d="M 866.737864 398.610452 
L 869.43425 400.68172 
L 870.933844 397.117049 
L 868.236925 395.096281 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c970"/>
    <path d="M 882.044297 395.274141 
L 884.753275 396.983659 
L 886.257035 393.073998 
L 883.54726 391.408898 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #05cd67"/>
    <path d="M 886.257035 393.073998 
L 888.969762 394.687594 
L 890.474991 390.684912 
L 887.761404 389.114065 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0dcf69"/>
    <path d="M 900.436682 381.146404 
L 903.162481 382.457798 
L 904.673343 378.156389 
L 901.9465 376.882256 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #39d771"/>
    <path d="M 911.943089 366.154783 
L 914.679586 367.251053 
L 916.195121 362.740196 
L 913.457474 361.676946 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #6de27c"/>
    <path d="M 877.836483 397.279044 
L 880.541889 399.08759 
L 882.044297 395.274141 
L 879.33817 393.511497 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00cb6b"/>
    <path d="M 933.833818 327.477284 
L 936.589627 328.258674 
L 938.110106 323.525411 
L 935.353126 322.768842 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9fe98"/>
    <path d="M 890.474991 390.684912 
L 893.191623 392.206058 
L 894.69842 388.113911 
L 891.980875 386.633663 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #15d06a"/>
    <path d="M 840.751767 389.008272 
L 843.432213 391.673585 
L 844.929449 388.705603 
L 842.248998 386.101388 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #19d16b"/>
    <path d="M 852.980115 396.218422 
L 855.667163 398.617186 
L 857.164794 395.368511 
L 854.47749 393.025522 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #01cc66"/>
    <path d="M 710.919505 244.469818 
L 713.589232 246.956073 
L 715.166404 247.469992 
L 712.499774 245.038946 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #896861"/>
    <path d="M 873.633259 399.083163 
L 876.335288 400.993466 
L 877.836483 397.279044 
L 875.133816 395.415935 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c970"/>
    <path d="M 925.006894 345.358326 
L 927.755279 346.254402 
L 929.274882 341.575387 
L 926.525314 340.707106 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b9f18b"/>
    <path d="M 917.711153 358.201101 
L 920.453056 359.205334 
L 921.970668 354.610712 
L 919.227601 353.636929 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #89e781"/>
    <path d="M 894.69842 388.113911 
L 897.419089 389.546436 
L 898.927529 385.368732 
L 896.205905 383.975081 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #21d36d"/>
    <path d="M 690.661214 228.068856 
L 693.324516 230.125442 
L 694.926698 230.915541 
L 692.266532 228.898682 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a58c86"/>
    <path d="M 675.751191 218.02171 
L 678.407064 219.717558 
L 680.027624 220.607326 
L 677.374765 218.939087 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b7a39f"/>
    <path d="M 663.51624 211.157419 
L 666.164115 212.533081 
L 667.799135 213.436984 
L 665.154084 212.079091 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c3b2af"/>
    <path d="M 843.432213 391.673585 
L 846.11409 394.288408 
L 847.611376 391.260986 
L 844.929449 388.705603 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #11cf69"/>
    <path d="M 862.545453 399.892548 
L 865.239051 402.070726 
L 866.737864 398.610452 
L 864.04384 396.483575 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c677"/>
    <path d="M 932.314263 332.183454 
L 935.068916 332.989605 
L 936.589627 328.258674 
L 933.833818 327.477284 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e9fb95"/>
    <path d="M 904.673343 378.156389 
L 907.403388 379.390187 
L 908.915978 375.014434 
L 906.184876 373.815466 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #45da74"/>
    <path d="M 910.429233 370.60163 
L 913.164627 371.73055 
L 914.679586 367.251053 
L 911.943089 366.154783 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #61df79"/>
    <path d="M 812.501061 362.19562 
L 815.173546 365.329829 
L 816.674539 363.065509 
L 814.002727 360.003475 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #75e37d"/>
    <path d="M 815.173546 365.329829 
L 817.846417 368.432857 
L 819.346806 366.097378 
L 816.674539 363.065509 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #69e17b"/>
    <path d="M 869.43425 400.68172 
L 872.133119 402.696126 
L 873.633259 399.083163 
L 870.933844 397.117049 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c47d"/>
    <path d="M 713.589232 246.956073 
L 716.259893 249.502556 
L 717.833992 249.959454 
L 715.166404 247.469992 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #85635c"/>
    <path d="M 809.828884 359.032548 
L 812.501061 362.19562 
L 814.002727 360.003475 
L 811.331293 356.913527 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #81e680"/>
    <path d="M 817.846417 368.432857 
L 820.519756 371.502417 
L 822.019606 369.096861 
L 819.346806 366.097378 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #61df79"/>
    <path d="M 807.156942 355.842969 
L 809.828884 359.032548 
L 811.331293 356.913527 
L 808.660165 353.797952 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8de882"/>
    <path d="M 855.667163 398.617186 
L 858.356158 400.960543 
L 859.854075 397.658007 
L 857.164794 395.368511 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c970"/>
    <path d="M 820.519756 371.502417 
L 823.193649 374.536264 
L 824.693025 372.061779 
L 822.019606 369.096861 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #55dd77"/>
    <path d="M 804.485167 352.629268 
L 807.156942 355.842969 
L 808.660165 353.797952 
L 805.989276 350.659066 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #95ea84"/>
    <path d="M 898.927529 385.368732 
L 901.652344 386.716808 
L 903.162481 382.457798 
L 900.436682 381.146404 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #29d46e"/>
    <path d="M 923.488645 349.993956 
L 926.235877 350.917657 
L 927.755279 346.254402 
L 925.006894 345.358326 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a9ee88"/>
    <path d="M 823.193649 374.536264 
L 825.868188 377.532192 
L 827.367152 374.989986 
L 824.693025 372.061779 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #49db75"/>
    <path d="M 801.813495 349.393861 
L 804.485167 352.629268 
L 805.989276 350.659066 
L 803.318564 347.499215 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a1ec86"/>
    <path d="M 846.11409 394.288408 
L 848.797516 396.850966 
L 850.294892 393.765816 
L 847.611376 391.260986 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #09ce68"/>
    <path d="M 916.195121 362.740196 
L 918.935897 363.774601 
L 920.453056 359.205334 
L 917.711153 358.201101 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #7de57f"/>
    <path d="M 644.384795 203.085486 
L 647.016919 203.930648 
L 648.672505 204.729209 
L 646.042768 203.887734 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d3c7c4"/>
    <path d="M 825.868188 377.532192 
L 828.543466 380.488036 
L 830.042078 377.87938 
L 827.367152 374.989986 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #41d973"/>
    <path d="M 884.753275 396.983659 
L 887.465217 398.639134 
L 888.969762 394.687594 
L 886.257035 393.073998 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #01cc66"/>
    <path d="M 799.141866 346.139191 
L 801.813495 349.393861 
L 803.318564 347.499215 
L 800.647971 344.32077 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #adef89"/>
    <path d="M 880.541889 399.08759 
L 883.250148 400.840564 
L 884.753275 396.983659 
L 882.044297 395.274141 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c970"/>
    <path d="M 930.794579 336.883949 
L 933.548095 337.714781 
L 935.068916 332.989605 
L 932.314263 332.183454 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d9f791"/>
    <path d="M 653.943336 206.689935 
L 656.584157 207.808748 
L 658.229895 208.67244 
L 655.591697 207.564142 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cdbfbc"/>
    <path d="M 888.969762 394.687594 
L 891.685551 396.248859 
L 893.191623 392.206058 
L 890.474991 390.684912 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #09ce68"/>
    <path d="M 796.470228 342.867727 
L 799.141866 346.139191 
L 800.647971 344.32077 
L 797.977444 341.126126 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b9f18b"/>
    <path d="M 716.259893 249.502556 
L 718.93139 252.107366 
L 720.502443 252.505493 
L 717.833992 249.959454 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #805c54"/>
    <path d="M 828.543466 380.488036 
L 831.219583 383.401674 
L 832.717901 380.7279 
L 830.042078 377.87938 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #35d771"/>
    <path d="M 693.324516 230.125442 
L 695.989531 232.255845 
L 697.58857 233.004093 
L 694.926698 230.915541 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a38984"/>
    <path d="M 793.798531 339.581962 
L 796.470228 342.867727 
L 797.977444 341.126126 
L 795.306935 337.917703 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c5f38d"/>
    <path d="M 876.335288 400.993466 
L 879.040052 402.846857 
L 880.541889 399.08759 
L 877.836483 397.279044 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c47d"/>
    <path d="M 831.219583 383.401674 
L 833.896642 386.27103 
L 835.39472 383.533529 
L 832.717901 380.7279 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2dd56f"/>
    <path d="M 865.239051 402.070726 
L 867.934992 404.191187 
L 869.43425 400.68172 
L 866.737864 398.610452 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c382"/>
    <path d="M 893.191623 392.206058 
L 895.911404 393.676764 
L 897.419089 389.546436 
L 894.69842 388.113911 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #11cf69"/>
    <path d="M 791.126731 336.284406 
L 793.798531 339.581962 
L 795.306935 337.917703 
L 792.636401 334.697936 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d1f690"/>
    <path d="M 908.915978 375.014434 
L 911.650316 376.175605 
L 913.164627 371.73055 
L 910.429233 370.60163 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #51dc76"/>
    <path d="M 848.797516 396.850966 
L 851.482611 399.359537 
L 852.980115 396.218422 
L 850.294892 393.765816 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #01cc66"/>
    <path d="M 858.356158 400.960543 
L 861.047223 403.246983 
L 862.545453 399.892548 
L 859.854075 397.658007 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c47d"/>
    <path d="M 903.162481 382.457798 
L 905.891525 383.725924 
L 907.403388 379.390187 
L 904.673343 378.156389 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #35d771"/>
    <path d="M 921.970668 354.610712 
L 924.716777 355.561838 
L 926.235877 350.917657 
L 923.488645 349.993956 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #99eb85"/>
    <path d="M 718.93139 252.107366 
L 721.603627 254.76854 
L 723.171666 255.106211 
L 720.502443 252.505493 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #846257"/>
    <path d="M 788.45479 332.97759 
L 791.126731 336.284406 
L 792.636401 334.697936 
L 789.965803 331.469282 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ddf892"/>
    <path d="M 833.896642 386.27103 
L 836.574749 389.094075 
L 838.07264 386.294294 
L 835.39472 383.533529 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #25d36d"/>
    <path d="M 678.407064 219.717558 
L 681.065309 221.495609 
L 682.682826 222.355526 
L 680.027624 220.607326 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b5a09c"/>
    <path d="M 929.274882 341.575387 
L 932.02728 342.430794 
L 933.548095 337.714781 
L 930.794579 336.883949 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c9f48e"/>
    <path d="M 914.679586 367.251053 
L 917.419277 368.315324 
L 918.935897 363.774601 
L 916.195121 362.740196 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #6de27c"/>
    <path d="M 872.133119 402.696126 
L 874.834594 404.652472 
L 876.335288 400.993466 
L 873.633259 399.083163 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c382"/>
    <path d="M 785.782674 329.664062 
L 788.45479 332.97759 
L 789.965803 331.469282 
L 787.295109 328.23421 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e9fb95"/>
    <path d="M 897.419089 389.546436 
L 900.142982 390.930582 
L 901.652344 386.716808 
L 898.927529 385.368732 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1dd26c"/>
    <path d="M 836.574749 389.094075 
L 839.254013 391.86883 
L 840.751767 389.008272 
L 838.07264 386.294294 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #19d16b"/>
    <path d="M 783.110353 326.346381 
L 785.782674 329.664062 
L 787.295109 328.23421 
L 784.624289 324.995204 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f5fd97"/>
    <path d="M 666.164115 212.533081 
L 668.814941 213.996682 
L 670.447093 214.880554 
L 667.799135 213.436984 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c1b0ac"/>
    <path d="M 721.603627 254.76854 
L 724.27651 257.484061 
L 725.84157 257.759658 
L 723.171666 255.106211 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #886759"/>
    <path d="M 936.589627 328.258674 
L 939.347999 329.03731 
L 940.869546 324.282656 
L 938.110106 323.525411 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f5fd97"/>
    <path d="M 851.482611 399.359537 
L 854.169497 401.812454 
L 855.667163 398.617186 
L 852.980115 396.218422 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c970"/>
    <path d="M 695.989531 232.255845 
L 698.656138 234.458593 
L 700.252033 235.162913 
L 697.58857 233.004093 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9f847e"/>
    <path d="M 780.437806 323.027118 
L 783.110353 326.346381 
L 784.624289 324.995204 
L 781.95332 321.754757 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 920.453056 359.205334 
L 923.198075 360.183664 
L 924.716777 355.561838 
L 921.970668 354.610712 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #89e781"/>
    <path d="M 927.755279 346.254402 
L 930.506584 347.134257 
L 932.02728 342.430794 
L 929.274882 341.575387 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b9f18b"/>
    <path d="M 839.254013 391.86883 
L 841.934549 394.593363 
L 843.432213 391.673585 
L 840.751767 389.008272 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #11cf69"/>
    <path d="M 861.047223 403.246983 
L 863.740484 405.475053 
L 865.239051 402.070726 
L 862.545453 399.892548 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c088"/>
    <path d="M 777.765014 319.708851 
L 780.437806 323.027118 
L 781.95332 321.754757 
L 779.282185 318.515369 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #faf996"/>
    <path d="M 907.403388 379.390187 
L 910.13672 380.58318 
L 911.650316 376.175605 
L 908.915978 375.014434 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #41d973"/>
    <path d="M 724.27651 257.484061 
L 726.949953 260.251858 
L 728.512072 260.463828 
L 725.84157 257.759658 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8c6c5b"/>
    <path d="M 867.934992 404.191187 
L 870.633402 406.252634 
L 872.133119 402.696126 
L 869.43425 400.68172 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c088"/>
    <path d="M 883.250148 400.840564 
L 885.96138 402.537013 
L 887.465217 398.639134 
L 884.753275 396.983659 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c677"/>
    <path d="M 887.465217 398.639134 
L 890.180236 400.239703 
L 891.685551 396.248859 
L 888.969762 394.687594 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00cb6b"/>
    <path d="M 913.164627 371.73055 
L 915.903275 372.824352 
L 917.419277 368.315324 
L 914.679586 367.251053 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #5ddf79"/>
    <path d="M 901.652344 386.716808 
L 904.380445 388.01873 
L 905.891525 383.725924 
L 903.162481 382.457798 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #29d46e"/>
    <path d="M 775.091964 316.394165 
L 777.765014 319.708851 
L 779.282185 318.515369 
L 776.61087 315.279546 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f4f193"/>
    <path d="M 879.040052 402.846857 
L 881.747673 404.64229 
L 883.250148 400.840564 
L 880.541889 399.08759 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c382"/>
    <path d="M 891.685551 396.248859 
L 894.404512 397.757019 
L 895.911404 393.676764 
L 893.191623 392.206058 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #05cd67"/>
    <path d="M 935.068916 332.989605 
L 937.826234 333.789584 
L 939.347999 329.03731 
L 936.589627 328.258674 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e9fb95"/>
    <path d="M 726.949953 260.251858 
L 729.623869 263.069806 
L 731.18309 263.216668 
L 728.512072 260.463828 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #92735e"/>
    <path d="M 772.41865 313.085649 
L 775.091964 316.394165 
L 776.61087 315.279546 
L 773.939368 312.049797 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eee990"/>
    <path d="M 841.934549 394.593363 
L 844.616473 397.265796 
L 846.11409 394.288408 
L 843.432213 391.673585 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #09ce68"/>
    <path d="M 854.169497 401.812454 
L 856.858298 404.208105 
L 858.356158 400.960543 
L 855.667163 398.617186 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c47d"/>
    <path d="M 681.065309 221.495609 
L 683.725793 223.354768 
L 685.340243 224.182627 
L 682.682826 222.355526 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b39e99"/>
    <path d="M 656.584157 207.808748 
L 659.228398 209.019399 
L 660.871454 209.870353 
L 658.229895 208.67244 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cbbcb9"/>
    <path d="M 769.745069 309.785889 
L 772.41865 313.085649 
L 773.939368 312.049797 
L 771.267675 308.828632 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e8e28d"/>
    <path d="M 874.834594 404.652472 
L 877.5388 406.549614 
L 879.040052 402.846857 
L 876.335288 400.993466 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c088"/>
    <path d="M 926.235877 350.917657 
L 928.986114 351.821808 
L 930.506584 347.134257 
L 927.755279 346.254402 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a9ee88"/>
    <path d="M 918.935897 363.774601 
L 921.679862 364.779885 
L 923.198075 360.183664 
L 920.453056 359.205334 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #79e47e"/>
    <path d="M 729.623869 263.069806 
L 732.298178 265.935732 
L 733.854545 266.016074 
L 731.18309 263.216668 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #967960"/>
    <path d="M 698.656138 234.458593 
L 701.324216 236.732139 
L 702.916969 237.390503 
L 700.252033 235.162913 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9b7f79"/>
    <path d="M 647.016919 203.930648 
L 649.652942 204.870614 
L 651.306073 205.663333 
L 648.672505 204.729209 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d3c7c4"/>
    <path d="M 895.911404 393.676764 
L 898.634439 395.096339 
L 900.142982 390.930582 
L 897.419089 389.546436 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #11cf69"/>
    <path d="M 767.071223 306.497473 
L 769.745069 309.785889 
L 771.267675 308.828632 
L 768.595795 305.618555 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e2da89"/>
    <path d="M 732.298178 265.935732 
L 734.972804 268.847419 
L 736.526365 268.859899 
L 733.854545 266.016074 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9a7e62"/>
    <path d="M 844.616473 397.265796 
L 847.299904 399.884303 
L 848.797516 396.850966 
L 846.11409 394.288408 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #01cc66"/>
    <path d="M 764.397123 303.222982 
L 767.071223 306.497473 
L 768.595795 305.618555 
L 765.923735 302.42207 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dcd286"/>
    <path d="M 863.740484 405.475053 
L 866.43607 407.643356 
L 867.934992 404.191187 
L 865.239051 402.070726 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00be8f"/>
    <path d="M 933.548095 337.714781 
L 936.304374 338.536033 
L 937.826234 333.789584 
L 935.068916 332.989605 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d9f791"/>
    <path d="M 905.891525 383.725924 
L 908.623904 384.950282 
L 910.13672 380.58318 
L 907.403388 379.390187 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #35d771"/>
    <path d="M 761.722781 299.964987 
L 764.397123 303.222982 
L 765.923735 302.42207 
L 763.251507 299.241668 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d6cb83"/>
    <path d="M 734.972804 268.847419 
L 737.647674 271.802601 
L 739.19848 271.745953 
L 736.526365 268.859899 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a08566"/>
    <path d="M 911.650316 376.175605 
L 914.387967 377.298578 
L 915.903275 372.824352 
L 913.164627 371.73055 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #4ddb75"/>
    <path d="M 870.633402 406.252634 
L 873.334409 408.253829 
L 874.834594 404.652472 
L 872.133119 402.696126 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00bc94"/>
    <path d="M 759.048217 296.726053 
L 761.722781 299.964987 
L 763.251507 299.241668 
L 760.579129 296.079834 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d0c380"/>
    <path d="M 668.814941 213.996682 
L 671.468582 215.547472 
L 673.097823 216.409071 
L 670.447093 214.880554 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c1b0ac"/>
    <path d="M 737.647674 271.802601 
L 740.322719 274.798975 
L 741.870825 274.672006 
L 739.19848 271.745953 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a48b68"/>
    <path d="M 856.858298 404.208105 
L 859.549143 406.544933 
L 861.047223 403.246983 
L 858.356158 400.960543 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c088"/>
    <path d="M 756.373455 293.508728 
L 759.048217 296.726053 
L 760.579129 296.079834 
L 757.906625 292.939036 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cabb7c"/>
    <path d="M 816.344741 370.73758 
L 819.018709 373.874949 
L 820.519756 371.502417 
L 817.846417 368.432857 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #59de78"/>
    <path d="M 819.018709 373.874949 
L 821.693168 376.975492 
L 823.193649 374.536264 
L 820.519756 371.502417 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #51dc76"/>
    <path d="M 740.322719 274.798975 
L 742.997877 277.834199 
L 744.543338 277.63579 
L 741.870825 274.672006 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #aa926b"/>
    <path d="M 900.142982 390.930582 
L 902.870198 392.26574 
L 904.380445 388.01873 
L 901.652344 386.716808 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #19d16b"/>
    <path d="M 924.716777 355.561838 
L 927.465975 356.490112 
L 928.986114 351.821808 
L 926.235877 350.917657 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #99eb85"/>
    <path d="M 813.671176 367.565695 
L 816.344741 370.73758 
L 817.846417 368.432857 
L 815.173546 365.329829 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #65e07a"/>
    <path d="M 821.693168 376.975492 
L 824.368211 380.036943 
L 825.868188 377.532192 
L 823.193649 374.536264 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #45da74"/>
    <path d="M 753.698524 290.315546 
L 756.373455 293.508728 
L 757.906625 292.939036 
L 755.23402 289.82173 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c6b67a"/>
    <path d="M 742.997877 277.834199 
L 745.673088 280.905894 
L 747.215964 280.635003 
L 744.543338 277.63579 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b09a6e"/>
    <path d="M 751.023458 287.149022 
L 753.698524 290.315546 
L 755.23402 289.82173 
L 752.56135 286.73035 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c0ae77"/>
    <path d="M 810.997931 364.361641 
L 813.671176 367.565695 
L 815.173546 365.329829 
L 812.501061 362.19562 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #71e37d"/>
    <path d="M 847.299904 399.884303 
L 849.984966 402.447115 
L 851.482611 399.359537 
L 848.797516 396.850966 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c677"/>
    <path d="M 745.673088 280.905894 
L 748.348298 284.011649 
L 749.88865 283.667311 
L 747.215964 280.635003 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b49f70"/>
    <path d="M 824.368211 380.036943 
L 827.043935 383.057077 
L 828.543466 380.488036 
L 825.868188 377.532192 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #39d771"/>
    <path d="M 917.419277 368.315324 
L 920.162226 369.347289 
L 921.679862 364.779885 
L 918.935897 363.774601 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #6de27c"/>
    <path d="M 748.348298 284.011649 
L 751.023458 287.149022 
L 752.56135 286.73035 
L 749.88865 283.667311 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #baa774"/>
    <path d="M 701.324216 236.732139 
L 703.993649 239.07486 
L 705.583267 239.68529 
L 702.916969 237.390503 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #977a74"/>
    <path d="M 808.324925 361.127803 
L 810.997931 364.361641 
L 812.501061 362.19562 
L 809.828884 359.032548 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #7de57f"/>
    <path d="M 885.96138 402.537013 
L 888.675703 404.176038 
L 890.180236 400.239703 
L 887.465217 398.639134 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c47d"/>
    <path d="M 827.043935 383.057077 
L 829.720441 386.033715 
L 831.219583 383.401674 
L 828.543466 380.488036 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #31d670"/>
    <path d="M 932.02728 342.430794 
L 934.782539 343.273228 
L 936.304374 338.536033 
L 933.548095 337.714781 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c9f48e"/>
    <path d="M 881.747673 404.64229 
L 884.458273 406.378772 
L 885.96138 402.537013 
L 883.250148 400.840564 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c088"/>
    <path d="M 805.652085 357.866602 
L 808.324925 361.127803 
L 809.828884 359.032548 
L 807.156942 355.842969 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #89e781"/>
    <path d="M 890.180236 400.239703 
L 892.898447 401.784557 
L 894.404512 397.757019 
L 891.685551 396.248859 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c970"/>
    <path d="M 829.720441 386.033715 
L 832.397834 388.964724 
L 833.896642 386.27103 
L 831.219583 383.401674 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #25d36d"/>
    <path d="M 683.725793 223.354768 
L 686.388384 225.293853 
L 687.999748 226.08748 
L 685.340243 224.182627 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #af9994"/>
    <path d="M 802.97934 354.580491 
L 805.652085 357.866602 
L 807.156942 355.842969 
L 804.485167 352.629268 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #95ea84"/>
    <path d="M 877.5388 406.549614 
L 880.245864 408.386469 
L 881.747673 404.64229 
L 879.040052 402.846857 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00bc94"/>
    <path d="M 832.397834 388.964724 
L 835.076223 391.84802 
L 836.574749 389.094075 
L 833.896642 386.27103 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1dd26c"/>
    <path d="M 866.43607 407.643356 
L 869.134111 409.750553 
L 870.633402 406.252634 
L 867.934992 404.191187 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00bb9b"/>
    <path d="M 800.306627 351.271953 
L 802.97934 354.580491 
L 804.485167 352.629268 
L 801.813495 349.393861 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a1ec86"/>
    <path d="M 894.404512 397.757019 
L 897.126755 399.211348 
L 898.634439 395.096339 
L 895.911404 393.676764 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #01cc66"/>
    <path d="M 910.13672 380.58318 
L 912.873422 381.734938 
L 914.387967 377.298578 
L 911.650316 376.175605 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #41d973"/>
    <path d="M 849.984966 402.447115 
L 852.671784 404.952515 
L 854.169497 401.812454 
L 851.482611 399.359537 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c382"/>
    <path d="M 923.198075 360.183664 
L 925.946264 361.135865 
L 927.465975 356.490112 
L 924.716777 355.561838 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #89e781"/>
    <path d="M 859.549143 406.544933 
L 862.24216 408.821443 
L 863.740484 405.475053 
L 861.047223 403.246983 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00bc94"/>
    <path d="M 904.380445 388.01873 
L 907.111926 389.273969 
L 908.623904 384.950282 
L 905.891525 383.725924 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #25d36d"/>
    <path d="M 939.347999 329.03731 
L 942.108943 329.813172 
L 943.631449 325.040576 
L 940.869546 324.282656 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f5fd97"/>
    <path d="M 797.633884 347.943502 
L 800.306627 351.271953 
L 801.813495 349.393861 
L 799.141866 346.139191 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a9ee88"/>
    <path d="M 703.993649 239.07486 
L 706.664323 241.485061 
L 708.250815 242.045632 
L 705.583267 239.68529 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #957771"/>
    <path d="M 835.076223 391.84802 
L 837.75572 394.68157 
L 839.254013 391.86883 
L 836.574749 389.094075 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #15d06a"/>
    <path d="M 930.506584 347.134257 
L 933.260844 347.997764 
L 934.782539 343.273228 
L 932.02728 342.430794 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b9f18b"/>
    <path d="M 915.903275 372.824352 
L 918.64525 373.882701 
L 920.162226 369.347289 
L 917.419277 368.315324 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #5ddf79"/>
    <path d="M 640.094452 201.623897 
L 642.724814 202.375699 
L 644.384795 203.085486 
L 641.756706 202.335196 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d7ccc9"/>
    <path d="M 873.334409 408.253829 
L 876.038142 410.19359 
L 877.5388 406.549614 
L 874.834594 404.652472 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00bb9b"/>
    <path d="M 794.961057 344.597677 
L 797.633884 347.943502 
L 799.141866 346.139191 
L 796.470228 342.867727 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b5f08a"/>
    <path d="M 659.228398 209.019399 
L 661.875919 210.321415 
L 663.51624 211.157419 
L 660.871454 209.870353 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c9bab7"/>
    <path d="M 898.634439 395.096339 
L 901.360832 396.464141 
L 902.870198 392.26574 
L 900.142982 390.930582 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0dcf69"/>
    <path d="M 837.75572 394.68157 
L 840.436442 397.46339 
L 841.934549 394.593363 
L 839.254013 391.86883 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #09ce68"/>
    <path d="M 792.288096 341.23704 
L 794.961057 344.597677 
L 796.470228 342.867727 
L 793.798531 339.581962 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c1f38d"/>
    <path d="M 937.826234 333.789584 
L 940.586231 334.583347 
L 942.108943 329.813172 
L 939.347999 329.03731 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e5fa94"/>
    <path d="M 852.671784 404.952515 
L 855.360486 407.398846 
L 856.858298 404.208105 
L 854.169497 401.812454 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00be8f"/>
    <path d="M 671.468582 215.547472 
L 674.124898 217.184603 
L 675.751191 218.02171 
L 673.097823 216.409071 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bfada9"/>
    <path d="M 649.652942 204.870614 
L 652.292726 205.905211 
L 653.943336 206.689935 
L 651.306073 205.663333 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d1c4c1"/>
    <path d="M 921.679862 364.779885 
L 924.427076 365.755797 
L 925.946264 361.135865 
L 923.198075 360.183664 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #79e47e"/>
    <path d="M 789.614957 337.864176 
L 792.288096 341.23704 
L 793.798531 339.581962 
L 791.126731 336.284406 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cdf58f"/>
    <path d="M 706.664323 241.485061 
L 709.336124 243.960977 
L 710.919505 244.469818 
L 708.250815 242.045632 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #91726c"/>
    <path d="M 928.986114 351.821808 
L 931.739398 352.70626 
L 933.260844 347.997764 
L 930.506584 347.134257 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a9ee88"/>
    <path d="M 686.388384 225.293853 
L 689.052953 227.311597 
L 690.661214 228.068856 
L 687.999748 226.08748 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ad9691"/>
    <path d="M 840.436442 397.46339 
L 843.118508 400.191551 
L 844.616473 397.265796 
L 841.934549 394.593363 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #01cc66"/>
    <path d="M 862.24216 408.821443 
L 864.937482 411.036195 
L 866.43607 407.643356 
L 863.740484 405.475053 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b8a0"/>
    <path d="M 908.623904 384.950282 
L 911.359707 386.130413 
L 912.873422 381.734938 
L 910.13672 380.58318 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #31d670"/>
    <path d="M 869.134111 409.750553 
L 871.834737 411.795367 
L 873.334409 408.253829 
L 870.633402 406.252634 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b8a0"/>
    <path d="M 884.458273 406.378772 
L 887.171975 408.055369 
L 888.675703 404.176038 
L 885.96138 402.537013 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00be8f"/>
    <path d="M 888.675703 404.176038 
L 891.393236 405.756793 
L 892.898447 401.784557 
L 890.180236 400.239703 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c382"/>
    <path d="M 786.941602 334.481688 
L 789.614957 337.864176 
L 791.126731 336.284406 
L 788.45479 332.97759 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d9f791"/>
    <path d="M 914.387967 377.298578 
L 917.129009 378.382992 
L 918.64525 373.882701 
L 915.903275 372.824352 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #4ddb75"/>
    <path d="M 902.870198 392.26574 
L 905.600838 393.551347 
L 907.111926 389.273969 
L 904.380445 388.01873 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #19d16b"/>
    <path d="M 880.245864 408.386469 
L 882.955911 410.162007 
L 884.458273 406.378772 
L 881.747673 404.64229 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00bb9b"/>
    <path d="M 936.304374 338.536033 
L 939.063438 339.347638 
L 940.586231 334.583347 
L 937.826234 333.789584 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d5f791"/>
    <path d="M 892.898447 401.784557 
L 895.619965 403.272937 
L 897.126755 399.211348 
L 894.404512 397.757019 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c677"/>
    <path d="M 843.118508 400.191551 
L 845.80204 402.86418 
L 847.299904 399.884303 
L 844.616473 397.265796 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c970"/>
    <path d="M 784.267994 331.092198 
L 786.941602 334.481688 
L 788.45479 332.97759 
L 785.782674 329.664062 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e5fa94"/>
    <path d="M 855.360486 407.398846 
L 858.051204 409.784509 
L 859.549143 406.544933 
L 856.858298 404.208105 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00bc94"/>
    <path d="M 709.336124 243.960977 
L 712.008944 246.500774 
L 713.589232 246.956073 
L 710.919505 244.469818 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8d6d66"/>
    <path d="M 927.465975 356.490112 
L 930.218309 357.39536 
L 931.739398 352.70626 
L 928.986114 351.821808 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #99eb85"/>
    <path d="M 920.162226 369.347289 
L 922.9085 370.346673 
L 924.427076 365.755797 
L 921.679862 364.779885 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #69e17b"/>
    <path d="M 876.038142 410.19359 
L 878.74473 412.070795 
L 880.245864 408.386469 
L 877.5388 406.549614 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b8a0"/>
    <path d="M 781.594107 327.698338 
L 784.267994 331.092198 
L 785.782674 329.664062 
L 783.110353 326.346381 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1fc96"/>
    <path d="M 897.126755 399.211348 
L 899.852389 400.611174 
L 901.360832 396.464141 
L 898.634439 395.096339 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #01cc66"/>
    <path d="M 845.80204 402.86418 
L 848.487165 405.479459 
L 849.984966 402.447115 
L 847.299904 399.884303 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c47d"/>
    <path d="M 934.782539 343.273228 
L 937.540686 344.102602 
L 939.063438 339.347638 
L 936.304374 338.536033 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c5f38d"/>
    <path d="M 864.937482 411.036195 
L 867.635242 413.187811 
L 869.134111 409.750553 
L 866.43607 407.643356 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b6a7"/>
    <path d="M 778.919918 324.302756 
L 781.594107 327.698338 
L 783.110353 326.346381 
L 780.437806 323.027118 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 689.052953 227.311597 
L 691.71937 229.406645 
L 693.324516 230.125442 
L 690.661214 228.068856 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a9918c"/>
    <path d="M 907.111926 389.273969 
L 909.846881 390.482035 
L 911.359707 386.130413 
L 908.623904 384.950282 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #25d36d"/>
    <path d="M 712.008944 246.500774 
L 714.682677 249.102553 
L 716.259893 249.502556 
L 713.589232 246.956073 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #87655e"/>
    <path d="M 912.873422 381.734938 
L 915.613577 382.845072 
L 917.129009 378.382992 
L 914.387967 377.298578 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #3dd872"/>
    <path d="M 674.124898 217.184603 
L 676.783754 218.907134 
L 678.407064 219.717558 
L 675.751191 218.02171 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bdaba7"/>
    <path d="M 661.875919 210.321415 
L 664.526579 211.714223 
L 666.164115 212.533081 
L 663.51624 211.157419 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c9bab7"/>
    <path d="M 871.834737 411.795367 
L 874.538081 413.776577 
L 876.038142 410.19359 
L 873.334409 408.253829 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b4ac"/>
    <path d="M 858.051204 409.784509 
L 860.74407 412.107964 
L 862.24216 408.821443 
L 859.549143 406.544933 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b8a0"/>
    <path d="M 776.245407 320.908105 
L 778.919918 324.302756 
L 780.437806 323.027118 
L 777.765014 319.708851 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f8f695"/>
    <path d="M 925.946264 361.135865 
L 928.697676 362.061743 
L 930.218309 357.39536 
L 927.465975 356.490112 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #89e781"/>
    <path d="M 901.360832 396.464141 
L 904.090689 397.779577 
L 905.600838 393.551347 
L 902.870198 392.26574 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #09ce68"/>
    <path d="M 820.191563 379.378361 
L 822.867203 382.503076 
L 824.368211 380.036943 
L 821.693168 376.975492 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #41d973"/>
    <path d="M 822.867203 382.503076 
L 825.543465 385.585282 
L 827.043935 383.057077 
L 824.368211 380.036943 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #35d771"/>
    <path d="M 817.516447 376.213418 
L 820.191563 379.378361 
L 821.693168 376.975492 
L 819.018709 373.874949 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #4ddb75"/>
    <path d="M 848.487165 405.479459 
L 851.174011 408.035626 
L 852.671784 404.952515 
L 849.984966 402.447115 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00be8f"/>
    <path d="M 918.64525 373.882701 
L 921.390621 374.905298 
L 922.9085 370.346673 
L 920.162226 369.347289 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #5ddf79"/>
    <path d="M 825.543465 385.585282 
L 828.220454 388.622744 
L 829.720441 386.033715 
L 827.043935 383.057077 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #29d46e"/>
    <path d="M 814.84176 373.010574 
L 817.516447 376.213418 
L 819.018709 373.874949 
L 816.344741 370.73758 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #55dd77"/>
    <path d="M 942.108943 329.813172 
L 944.87247 330.586241 
L 946.395818 325.799173 
L 943.631449 325.040576 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f5fd97"/>
    <path d="M 773.570563 317.517046 
L 776.245407 320.908105 
L 777.765014 319.708851 
L 775.091964 316.394165 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f2ee92"/>
    <path d="M 714.682677 249.102553 
L 717.35722 251.764351 
L 718.93139 252.107366 
L 716.259893 249.502556 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #836059"/>
    <path d="M 828.220454 388.622744 
L 830.898276 391.613275 
L 832.397834 388.964724 
L 829.720441 386.033715 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #21d36d"/>
    <path d="M 812.167413 369.772197 
L 814.84176 373.010574 
L 816.344741 370.73758 
L 813.671176 367.565695 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #61df79"/>
    <path d="M 933.260844 347.997764 
L 936.018092 348.844816 
L 937.540686 344.102602 
L 934.782539 343.273228 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b5f08a"/>
    <path d="M 887.171975 408.055369 
L 889.888903 409.671204 
L 891.393236 405.756793 
L 888.675703 404.176038 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00bc94"/>
    <path d="M 642.724814 202.375699 
L 645.359283 203.224438 
L 647.016919 203.930648 
L 644.384795 203.085486 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d7ccc9"/>
    <path d="M 882.955911 410.162007 
L 885.66907 411.875262 
L 887.171975 408.055369 
L 884.458273 406.378772 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b8a0"/>
    <path d="M 809.49332 366.500696 
L 812.167413 369.772197 
L 813.671176 367.565695 
L 810.997931 364.361641 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #6de27c"/>
    <path d="M 830.898276 391.613275 
L 833.577043 394.554738 
L 835.076223 391.84802 
L 832.397834 388.964724 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #15d06a"/>
    <path d="M 891.393236 405.756793 
L 894.114098 407.278491 
L 895.619965 403.272937 
L 892.898447 401.784557 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c088"/>
    <path d="M 770.89538 314.132244 
L 773.570563 317.517046 
L 775.091964 316.394165 
L 772.41865 313.085649 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ece78f"/>
    <path d="M 652.292726 205.905211 
L 654.936129 207.034162 
L 656.584157 207.808748 
L 653.943336 206.689935 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d1c4c1"/>
    <path d="M 806.8194 363.198518 
L 809.49332 366.500696 
L 810.997931 364.361641 
L 808.324925 361.127803 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #79e47e"/>
    <path d="M 833.577043 394.554738 
L 836.256869 397.445047 
L 837.75572 394.68157 
L 835.076223 391.84802 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0dcf69"/>
    <path d="M 878.74473 412.070795 
L 881.454305 413.884381 
L 882.955911 410.162007 
L 880.245864 408.386469 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b4ac"/>
    <path d="M 691.71937 229.406645 
L 694.387508 231.577563 
L 695.989531 232.255845 
L 693.324516 230.125442 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a78e89"/>
    <path d="M 717.35722 251.764351 
L 720.032474 254.484144 
L 721.603627 254.76854 
L 718.93139 252.107366 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #805c54"/>
    <path d="M 867.635242 413.187811 
L 870.335575 415.274973 
L 871.834737 411.795367 
L 869.134111 409.750553 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b2b2"/>
    <path d="M 851.174011 408.035626 
L 853.862709 410.53098 
L 855.360486 407.398846 
L 852.671784 404.952515 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00bb9b"/>
    <path d="M 768.219856 310.756363 
L 770.89538 314.132244 
L 772.41865 313.085649 
L 769.745069 309.785889 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e6df8b"/>
    <path d="M 911.359707 386.130413 
L 914.099022 387.265901 
L 915.613577 382.845072 
L 912.873422 381.734938 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #31d670"/>
    <path d="M 924.427076 365.755797 
L 927.177597 366.702118 
L 928.697676 362.061743 
L 925.946264 361.135865 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #79e47e"/>
    <path d="M 804.145577 359.868147 
L 806.8194 363.198518 
L 808.324925 361.127803 
L 805.652085 357.866602 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #85e781"/>
    <path d="M 895.619965 403.272937 
L 898.344904 404.704141 
L 899.852389 400.611174 
L 897.126755 399.211348 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c47d"/>
    <path d="M 940.586231 334.583347 
L 943.348924 335.370856 
L 944.87247 330.586241 
L 942.108943 329.813172 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e5fa94"/>
    <path d="M 860.74407 412.107964 
L 863.439219 414.367732 
L 864.937482 411.036195 
L 862.24216 408.821443 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b4ac"/>
    <path d="M 905.600838 393.551347 
L 908.335 394.786888 
L 909.846881 390.482035 
L 907.111926 389.273969 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #15d06a"/>
    <path d="M 836.256869 397.445047 
L 838.937873 400.282169 
L 840.436442 397.46339 
L 837.75572 394.68157 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #01cc66"/>
    <path d="M 931.739398 352.70626 
L 934.495769 353.570883 
L 936.018092 348.844816 
L 933.260844 347.997764 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a5ed87"/>
    <path d="M 917.129009 378.382992 
L 919.873519 379.428521 
L 921.390621 374.905298 
L 918.64525 373.882701 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #4ddb75"/>
    <path d="M 765.543994 307.392068 
L 768.219856 310.756363 
L 769.745069 309.785889 
L 767.071223 306.497473 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e0d788"/>
    <path d="M 801.471781 356.512101 
L 804.145577 359.868147 
L 805.652085 357.866602 
L 802.97934 354.580491 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #91e983"/>
    <path d="M 720.032474 254.484144 
L 722.708342 257.259851 
L 724.27651 257.484061 
L 721.603627 254.76854 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #846257"/>
    <path d="M 874.538081 413.776577 
L 877.244278 415.693025 
L 878.74473 412.070795 
L 876.038142 410.19359 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b2b2"/>
    <path d="M 676.783754 218.907134 
L 679.445011 220.71403 
L 681.065309 221.495609 
L 678.407064 219.717558 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b9a5a1"/>
    <path d="M 838.937873 400.282169 
L 841.620177 403.064128 
L 843.118508 400.191551 
L 840.436442 397.46339 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c970"/>
    <path d="M 762.867805 304.042015 
L 765.543994 307.392068 
L 767.071223 306.497473 
L 764.397123 303.222982 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dad085"/>
    <path d="M 798.797945 353.13293 
L 801.471781 356.512101 
L 802.97934 354.580491 
L 800.306627 351.271953 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9deb85"/>
    <path d="M 899.852389 400.611174 
L 902.581524 401.955877 
L 904.090689 397.779577 
L 901.360832 396.464141 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00cb6b"/>
    <path d="M 939.063438 339.347638 
L 941.825309 340.149542 
L 943.348924 335.370856 
L 940.586231 334.583347 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d5f791"/>
    <path d="M 722.708342 257.259851 
L 725.384733 260.089334 
L 726.949953 260.251858 
L 724.27651 257.484061 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8a695a"/>
    <path d="M 853.862709 410.53098 
L 856.553394 412.963879 
L 858.051204 409.784509 
L 855.360486 407.398846 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b6a7"/>
    <path d="M 760.191304 300.708855 
L 762.867805 304.042015 
L 764.397123 303.222982 
L 761.722781 299.964987 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d4c882"/>
    <path d="M 922.9085 370.346673 
L 925.658163 371.313234 
L 927.177597 366.702118 
L 924.427076 365.755797 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #69e17b"/>
    <path d="M 796.124009 349.733214 
L 798.797945 353.13293 
L 800.306627 351.271953 
L 797.633884 347.943502 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a9ee88"/>
    <path d="M 664.526579 211.714223 
L 667.180237 213.19715 
L 668.814941 213.996682 
L 666.164115 212.533081 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c7b7b4"/>
    <path d="M 930.218309 357.39536 
L 932.973826 358.277432 
L 934.495769 353.570883 
L 931.739398 352.70626 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #99eb85"/>
    <path d="M 694.387508 231.577563 
L 697.05724 233.822835 
L 698.656138 234.458593 
L 695.989531 232.255845 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a38984"/>
    <path d="M 841.620177 403.064128 
L 844.303906 405.789002 
L 845.80204 402.86418 
L 843.118508 400.191551 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c47d"/>
    <path d="M 757.51451 297.395229 
L 760.191304 300.708855 
L 761.722781 299.964987 
L 759.048217 296.726053 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d0c380"/>
    <path d="M 725.384733 260.089334 
L 728.061559 262.970402 
L 729.623869 263.069806 
L 726.949953 260.251858 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8e6e5c"/>
    <path d="M 863.439219 414.367732 
L 866.136789 416.562396 
L 867.635242 413.187811 
L 864.937482 411.036195 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b0b9"/>
    <path d="M 909.846881 390.482035 
L 912.585405 391.642489 
L 914.099022 387.265901 
L 911.359707 386.130413 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #21d36d"/>
    <path d="M 870.335575 415.274973 
L 873.038618 417.296427 
L 874.538081 413.776577 
L 871.834737 411.795367 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b0b9"/>
    <path d="M 793.449917 346.315559 
L 796.124009 349.733214 
L 797.633884 347.943502 
L 794.961057 344.597677 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b5f08a"/>
    <path d="M 754.837449 294.103762 
L 757.51451 297.395229 
L 759.048217 296.726053 
L 756.373455 293.508728 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cabb7c"/>
    <path d="M 885.66907 411.875262 
L 888.385468 413.525323 
L 889.888903 409.671204 
L 887.171975 408.055369 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b6a7"/>
    <path d="M 915.613577 382.845072 
L 918.357267 383.913233 
L 919.873519 379.428521 
L 917.129009 378.382992 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #3dd872"/>
    <path d="M 728.061559 262.970402 
L 730.738735 265.900814 
L 732.298178 265.935732 
L 729.623869 263.069806 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #92735e"/>
    <path d="M 889.888903 409.671204 
L 892.609182 411.225456 
L 894.114098 407.278491 
L 891.393236 405.756793 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00bb9b"/>
    <path d="M 904.090689 397.779577 
L 906.824115 399.042108 
L 908.335 394.786888 
L 905.600838 393.551347 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #09ce68"/>
    <path d="M 752.160154 290.837066 
L 754.837449 294.103762 
L 756.373455 293.508728 
L 753.698524 290.315546 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c4b379"/>
    <path d="M 937.540686 344.102602 
L 940.30175 344.918842 
L 941.825309 340.149542 
L 939.063438 339.347638 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c5f38d"/>
    <path d="M 881.454305 413.884381 
L 884.166999 415.633347 
L 885.66907 411.875262 
L 882.955911 410.162007 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b2b2"/>
    <path d="M 844.303906 405.789002 
L 846.98919 408.454928 
L 848.487165 405.479459 
L 845.80204 402.86418 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c088"/>
    <path d="M 730.738735 265.900814 
L 733.416182 268.87828 
L 734.972804 268.847419 
L 732.298178 265.935732 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #987b61"/>
    <path d="M 749.482658 287.597731 
L 752.160154 290.837066 
L 753.698524 290.315546 
L 751.023458 287.149022 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #beac76"/>
    <path d="M 790.775619 342.882596 
L 793.449917 346.315559 
L 794.961057 344.597677 
L 792.288096 341.23704 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c1f38d"/>
    <path d="M 894.114098 407.278491 
L 896.838411 408.740398 
L 898.344904 404.704141 
L 895.619965 403.272937 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00be8f"/>
    <path d="M 856.553394 412.963879 
L 859.246202 415.332743 
L 860.74407 412.107964 
L 858.051204 409.784509 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b4ac"/>
    <path d="M 733.416182 268.87828 
L 736.093825 271.900468 
L 737.647674 271.802601 
L 734.972804 268.847419 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9c8064"/>
    <path d="M 746.805006 284.388327 
L 749.482658 287.597731 
L 751.023458 287.149022 
L 748.348298 284.011649 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b8a473"/>
    <path d="M 736.093825 271.900468 
L 738.771592 274.965 
L 740.322719 274.798975 
L 737.647674 271.802601 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a28867"/>
    <path d="M 928.697676 362.061743 
L 931.452365 362.961125 
L 932.973826 358.277432 
L 930.218309 357.39536 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #89e781"/>
    <path d="M 744.127242 281.211398 
L 746.805006 284.388327 
L 748.348298 284.011649 
L 745.673088 280.905894 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b29c6f"/>
    <path d="M 921.390621 374.905298 
L 924.139461 375.891877 
L 925.658163 371.313234 
L 922.9085 370.346673 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #59de78"/>
    <path d="M 738.771592 274.965 
L 741.449419 278.06946 
L 742.997877 277.834199 
L 740.322719 274.798975 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a8906a"/>
    <path d="M 741.449419 278.06946 
L 744.127242 281.211398 
L 745.673088 280.905894 
L 742.997877 277.834199 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ac956c"/>
    <path d="M 877.244278 415.693025 
L 879.953463 417.543616 
L 881.454305 413.884381 
L 878.74473 412.070795 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b0b9"/>
    <path d="M 697.05724 233.822835 
L 699.728445 236.140865 
L 701.324216 236.732139 
L 698.656138 234.458593 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9f847e"/>
    <path d="M 788.101069 339.436981 
L 790.775619 342.882596 
L 792.288096 341.23704 
L 789.614957 337.864176 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cdf58f"/>
    <path d="M 654.936129 207.034162 
L 657.58301 208.257087 
L 659.228398 209.019399 
L 656.584157 207.808748 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cfc2bf"/>
    <path d="M 679.445011 220.71403 
L 682.108532 222.604166 
L 683.725793 223.354768 
L 681.065309 221.495609 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b7a39f"/>
    <path d="M 846.98919 408.454928 
L 849.67616 411.060101 
L 851.174011 408.035626 
L 848.487165 405.479459 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00bb9b"/>
    <path d="M 645.359283 203.224438 
L 647.997719 204.170044 
L 649.652942 204.870614 
L 647.016919 203.930648 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d7ccc9"/>
    <path d="M 898.344904 404.704141 
L 901.07338 406.077519 
L 902.581524 401.955877 
L 899.852389 400.611174 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c47d"/>
    <path d="M 944.87247 330.586241 
L 947.638588 331.356503 
L 949.162656 326.558447 
L 946.395818 325.799173 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f5fd97"/>
    <path d="M 936.018092 348.844816 
L 938.778364 349.67532 
L 940.30175 344.918842 
L 937.540686 344.102602 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b5f08a"/>
    <path d="M 866.136789 416.562396 
L 868.836918 418.690601 
L 870.335575 415.274973 
L 867.635242 413.187811 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00aebf"/>
    <path d="M 785.426229 335.981387 
L 788.101069 339.436981 
L 789.614957 337.864176 
L 786.941602 334.481688 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d9f791"/>
    <path d="M 908.335 394.786888 
L 911.072785 395.971897 
L 912.585405 391.642489 
L 909.846881 390.482035 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #15d06a"/>
    <path d="M 914.099022 387.265901 
L 916.841937 388.356374 
L 918.357267 383.913233 
L 915.613577 382.845072 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2dd56f"/>
    <path d="M 859.246202 415.332743 
L 861.941271 417.636055 
L 863.439219 414.367732 
L 860.74407 412.107964 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b0b9"/>
    <path d="M 873.038618 417.296427 
L 875.744509 419.250979 
L 877.244278 415.693025 
L 874.538081 413.776577 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00acc4"/>
    <path d="M 927.177597 366.702118 
L 929.931485 367.618657 
L 931.452365 362.961125 
L 928.697676 362.061743 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #79e47e"/>
    <path d="M 821.365141 384.92947 
L 824.042035 388.071472 
L 825.543465 385.585282 
L 822.867203 382.503076 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #31d670"/>
    <path d="M 824.042035 388.071472 
L 826.719601 391.167526 
L 828.220454 388.622744 
L 825.543465 385.585282 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #25d36d"/>
    <path d="M 849.67616 411.060101 
L 852.36495 413.602777 
L 853.862709 410.53098 
L 851.174011 408.035626 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b6a7"/>
    <path d="M 782.751063 332.518505 
L 785.426229 335.981387 
L 786.941602 334.481688 
L 784.267994 331.092198 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e5fa94"/>
    <path d="M 818.688812 381.743808 
L 821.365141 384.92947 
L 822.867203 382.503076 
L 820.191563 379.378361 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #3dd872"/>
    <path d="M 826.719601 391.167526 
L 829.397947 394.215393 
L 830.898276 391.613275 
L 828.220454 388.622744 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #19d16b"/>
    <path d="M 919.873519 379.428521 
L 922.621573 380.434879 
L 924.139461 375.891877 
L 921.390621 374.905298 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #4ddb75"/>
    <path d="M 902.581524 401.955877 
L 905.314271 403.244888 
L 906.824115 399.042108 
L 904.090689 397.779577 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c970"/>
    <path d="M 667.180237 213.19715 
L 669.836752 214.769422 
L 671.468582 215.547472 
L 668.814941 213.996682 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c5b5b1"/>
    <path d="M 943.348924 335.370856 
L 946.114329 336.152082 
L 947.638588 331.356503 
L 944.87247 330.586241 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e5fa94"/>
    <path d="M 699.728445 236.140865 
L 702.401 238.529982 
L 703.993649 239.07486 
L 701.324216 236.732139 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9d827c"/>
    <path d="M 816.012949 378.516824 
L 818.688812 381.743808 
L 820.191563 379.378361 
L 817.516447 376.213418 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #45da74"/>
    <path d="M 829.397947 394.215393 
L 832.077186 397.212885 
L 833.577043 394.554738 
L 830.898276 391.613275 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #11cf69"/>
    <path d="M 934.495769 353.570883 
L 937.255268 354.415568 
L 938.778364 349.67532 
L 936.018092 348.844816 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a5ed87"/>
    <path d="M 813.337454 375.250899 
L 816.012949 378.516824 
L 817.516447 376.213418 
L 814.84176 373.010574 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #51dc76"/>
    <path d="M 832.077186 397.212885 
L 834.757436 400.157866 
L 836.256869 397.445047 
L 833.577043 394.554738 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #05cd67"/>
    <path d="M 888.385468 413.525323 
L 891.105235 415.111342 
L 892.609182 411.225456 
L 889.888903 409.671204 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b4ac"/>
    <path d="M 780.075545 329.051042 
L 782.751063 332.518505 
L 784.267994 331.092198 
L 781.594107 327.698338 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1fc96"/>
    <path d="M 884.166999 415.633347 
L 886.882945 417.316752 
L 888.385468 413.525323 
L 885.66907 411.875262 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b0b9"/>
    <path d="M 810.662236 371.948459 
L 813.337454 375.250899 
L 814.84176 373.010574 
L 812.167413 369.772197 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #5ddf79"/>
    <path d="M 892.609182 411.225456 
L 895.332935 412.717366 
L 896.838411 408.740398 
L 894.114098 407.278491 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b8a0"/>
    <path d="M 834.757436 400.157866 
L 837.438819 403.048257 
L 838.937873 400.282169 
L 836.256869 397.445047 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00cb6b"/>
    <path d="M 682.108532 222.604166 
L 684.774183 224.576323 
L 686.388384 225.293853 
L 683.725793 223.354768 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b5a09c"/>
    <path d="M 807.987209 368.611972 
L 810.662236 371.948459 
L 812.167413 369.772197 
L 809.49332 366.500696 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #69e17b"/>
    <path d="M 925.658163 371.313234 
L 928.41128 372.246761 
L 929.931485 367.618657 
L 927.177597 366.702118 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #69e17b"/>
    <path d="M 852.36495 413.602777 
L 855.055697 416.081274 
L 856.553394 412.963879 
L 853.862709 410.53098 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b2b2"/>
    <path d="M 879.953463 417.543616 
L 882.665773 419.327316 
L 884.166999 415.633347 
L 881.454305 413.884381 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00acc4"/>
    <path d="M 941.825309 340.149542 
L 944.59001 340.941699 
L 946.114329 336.152082 
L 943.348924 335.370856 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d5f791"/>
    <path d="M 868.836918 418.690601 
L 871.539748 420.751059 
L 873.038618 417.296427 
L 870.335575 415.274973 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00aacb"/>
    <path d="M 912.585405 391.642489 
L 915.327591 392.754934 
L 916.841937 388.356374 
L 914.099022 387.265901 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #21d36d"/>
    <path d="M 777.39965 325.581715 
L 780.075545 329.051042 
L 781.594107 327.698338 
L 778.919918 324.302756 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 861.941271 417.636055 
L 864.638743 419.87236 
L 866.136789 416.562396 
L 863.439219 414.367732 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00acc4"/>
    <path d="M 837.438819 403.048257 
L 840.121458 405.882034 
L 841.620177 403.064128 
L 838.937873 400.282169 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c47d"/>
    <path d="M 896.838411 408.740398 
L 899.566292 410.141839 
L 901.07338 406.077519 
L 898.344904 404.704141 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00be8f"/>
    <path d="M 932.973826 358.277432 
L 935.732572 359.1362 
L 937.255268 354.415568 
L 934.495769 353.570883 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #95ea84"/>
    <path d="M 702.401 238.529982 
L 705.074787 240.988438 
L 706.664323 241.485061 
L 703.993649 239.07486 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #997c76"/>
    <path d="M 906.824115 399.042108 
L 909.561214 400.25124 
L 911.072785 395.971897 
L 908.335 394.786888 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #05cd67"/>
    <path d="M 805.31229 365.243945 
L 807.987209 368.611972 
L 809.49332 366.500696 
L 806.8194 363.198518 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #75e37d"/>
    <path d="M 918.357267 383.913233 
L 921.104575 384.939113 
L 922.621573 380.434879 
L 919.873519 379.428521 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #3dd872"/>
    <path d="M 638.430353 201.007374 
L 641.062945 201.760672 
L 642.724814 202.375699 
L 640.094452 201.623897 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dbd1cf"/>
    <path d="M 774.723361 322.113253 
L 777.39965 325.581715 
L 778.919918 324.302756 
L 776.245407 320.908105 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f8f695"/>
    <path d="M 840.121458 405.882034 
L 842.805481 408.65723 
L 844.303906 405.789002 
L 841.620177 403.064128 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c088"/>
    <path d="M 802.637402 361.846924 
L 805.31229 365.243945 
L 806.8194 363.198518 
L 804.145577 359.868147 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #81e680"/>
    <path d="M 875.744509 419.250979 
L 878.453387 421.137501 
L 879.953463 417.543616 
L 877.244278 415.693025 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00aacb"/>
    <path d="M 657.58301 208.257087 
L 660.233225 209.5735 
L 661.875919 210.321415 
L 659.228398 209.019399 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cfc2bf"/>
    <path d="M 940.30175 344.918842 
L 943.065757 345.721888 
L 944.59001 340.941699 
L 941.825309 340.149542 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c5f38d"/>
    <path d="M 901.07338 406.077519 
L 903.805508 407.392479 
L 905.314271 403.244888 
L 902.581524 401.955877 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c382"/>
    <path d="M 855.055697 416.081274 
L 857.748541 418.493973 
L 859.246202 415.332743 
L 856.553394 412.963879 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00aebf"/>
    <path d="M 799.962472 358.423487 
L 802.637402 361.846924 
L 804.145577 359.868147 
L 801.471781 356.512101 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8de882"/>
    <path d="M 772.046666 318.64839 
L 774.723361 322.113253 
L 776.245407 320.908105 
L 773.570563 317.517046 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f2ee92"/>
    <path d="M 924.139461 375.891877 
L 926.89184 376.842209 
L 928.41128 372.246761 
L 925.658163 371.313234 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #59de78"/>
    <path d="M 705.074787 240.988438 
L 707.74969 243.514416 
L 709.336124 243.960977 
L 706.664323 241.485061 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #957771"/>
    <path d="M 931.452365 362.961125 
L 934.210381 363.833868 
L 935.732572 359.1362 
L 932.973826 358.277432 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #89e781"/>
    <path d="M 842.805481 408.65723 
L 845.49102 411.371938 
L 846.98919 408.454928 
L 844.303906 405.789002 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00bc94"/>
    <path d="M 669.836752 214.769422 
L 672.495982 216.430171 
L 674.124898 217.184603 
L 671.468582 215.547472 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c3b2af"/>
    <path d="M 647.997719 204.170044 
L 650.63998 205.212341 
L 652.292726 205.905211 
L 649.652942 204.870614 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d7ccc9"/>
    <path d="M 684.774183 224.576323 
L 687.441829 226.629199 
L 689.052953 227.311597 
L 686.388384 225.293853 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b19b96"/>
    <path d="M 864.638743 419.87236 
L 867.338759 422.040269 
L 868.836918 418.690601 
L 866.136789 416.562396 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a8d0"/>
    <path d="M 911.072785 395.971897 
L 913.814291 397.105955 
L 915.327591 392.754934 
L 912.585405 391.642489 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #11cf69"/>
    <path d="M 797.287435 354.976249 
L 799.962472 358.423487 
L 801.471781 356.512101 
L 798.797945 353.13293 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #99eb85"/>
    <path d="M 769.369559 315.189865 
L 772.046666 318.64839 
L 773.570563 317.517046 
L 770.89538 314.132244 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ece78f"/>
    <path d="M 871.539748 420.751059 
L 874.245419 422.742542 
L 875.744509 419.250979 
L 873.038618 417.296427 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a8d0"/>
    <path d="M 916.841937 388.356374 
L 919.58854 389.401502 
L 921.104575 384.939113 
L 918.357267 383.913233 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2dd56f"/>
    <path d="M 938.778364 349.67532 
L 941.541693 350.489203 
L 943.065757 345.721888 
L 940.30175 344.918842 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b5f08a"/>
    <path d="M 947.638588 331.356503 
L 950.407306 332.123947 
L 951.931968 327.318401 
L 949.162656 326.558447 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f5fd97"/>
    <path d="M 886.882945 417.316752 
L 889.602275 418.933719 
L 891.105235 415.111342 
L 888.385468 413.525323 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00aebf"/>
    <path d="M 845.49102 411.371938 
L 848.17821 414.024312 
L 849.67616 411.060101 
L 846.98919 408.454928 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b8a0"/>
    <path d="M 891.105235 415.111342 
L 893.828501 416.632528 
L 895.332935 412.717366 
L 892.609182 411.225456 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b2b2"/>
    <path d="M 905.314271 403.244888 
L 908.050739 404.477692 
L 909.561214 400.25124 
L 906.824115 399.042108 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c970"/>
    <path d="M 707.74969 243.514416 
L 710.425597 246.106026 
L 712.008944 246.500774 
L 709.336124 243.960977 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #91726c"/>
    <path d="M 882.665773 419.327316 
L 885.381343 421.043155 
L 886.882945 417.316752 
L 884.166999 415.633347 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00aacb"/>
    <path d="M 794.612228 351.507853 
L 797.287435 354.976249 
L 798.797945 353.13293 
L 796.124009 349.733214 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a5ed87"/>
    <path d="M 766.692039 311.740415 
L 769.369559 315.189865 
L 770.89538 314.132244 
L 768.219856 310.756363 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e6df8b"/>
    <path d="M 857.748541 418.493973 
L 860.443623 420.839318 
L 861.941271 417.636055 
L 859.246202 415.332743 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00acc4"/>
    <path d="M 929.931485 367.618657 
L 932.688797 368.505253 
L 934.210381 363.833868 
L 931.452365 362.961125 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #79e47e"/>
    <path d="M 895.332935 412.717366 
L 898.060289 414.146231 
L 899.566292 410.141839 
L 896.838411 408.740398 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b6a7"/>
    <path d="M 922.621573 380.434879 
L 925.373248 381.401817 
L 926.89184 376.842209 
L 924.139461 375.891877 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #49db75"/>
    <path d="M 764.014112 308.302779 
L 766.692039 311.740415 
L 768.219856 310.756363 
L 765.543994 307.392068 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e0d788"/>
    <path d="M 791.936796 348.020971 
L 794.612228 351.507853 
L 796.124009 349.733214 
L 793.449917 346.315559 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b1ef89"/>
    <path d="M 878.453387 421.137501 
L 881.165393 422.954929 
L 882.665773 419.327316 
L 879.953463 417.543616 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a8d0"/>
    <path d="M 848.17821 414.024312 
L 850.867187 416.612568 
L 852.36495 413.602777 
L 849.67616 411.060101 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b2b2"/>
    <path d="M 946.114329 336.152082 
L 948.88246 336.927002 
L 950.407306 332.123947 
L 947.638588 331.356503 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e5fa94"/>
    <path d="M 937.255268 354.415568 
L 940.017934 355.240225 
L 941.541693 350.489203 
L 938.778364 349.67532 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a5ed87"/>
    <path d="M 710.425597 246.106026 
L 713.102396 248.761311 
L 714.682677 249.102553 
L 712.008944 246.500774 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8b6b64"/>
    <path d="M 899.566292 410.141839 
L 902.297863 411.482195 
L 903.805508 407.392479 
L 901.07338 406.077519 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00bc94"/>
    <path d="M 687.441829 226.629199 
L 690.111336 228.761401 
L 691.71937 229.406645 
L 689.052953 227.311597 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #af9994"/>
    <path d="M 761.335787 304.87969 
L 764.014112 308.302779 
L 765.543994 307.392068 
L 762.867805 304.042015 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dad085"/>
    <path d="M 867.338759 422.040269 
L 870.041463 424.138457 
L 871.539748 420.751059 
L 868.836918 418.690601 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a6d7"/>
    <path d="M 915.327591 392.754934 
L 918.073533 393.81902 
L 919.58854 389.401502 
L 916.841937 388.356374 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #21d36d"/>
    <path d="M 909.561214 400.25124 
L 912.30209 401.406535 
L 913.814291 397.105955 
L 911.072785 395.971897 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #05cd67"/>
    <path d="M 789.261087 344.518301 
L 791.936796 348.020971 
L 793.449917 346.315559 
L 790.775619 342.882596 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c1f38d"/>
    <path d="M 928.41128 372.246761 
L 931.167915 373.147077 
L 932.688797 368.505253 
L 929.931485 367.618657 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #69e17b"/>
    <path d="M 713.102396 248.761311 
L 715.779983 251.478251 
L 717.35722 251.764351 
L 714.682677 249.102553 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #87655e"/>
    <path d="M 860.443623 420.839318 
L 863.141089 423.115821 
L 864.638743 419.87236 
L 861.941271 417.636055 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a8d0"/>
    <path d="M 672.495982 216.430171 
L 675.157785 218.178428 
L 676.783754 218.907134 
L 674.124898 217.184603 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c1b0ac"/>
    <path d="M 825.217857 393.666869 
L 827.896821 396.769833 
L 829.397947 394.215393 
L 826.719601 391.167526 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #15d06a"/>
    <path d="M 822.539621 390.514508 
L 825.217857 393.666869 
L 826.719601 391.167526 
L 824.042035 388.071472 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #21d36d"/>
    <path d="M 660.233225 209.5735 
L 662.886631 210.982812 
L 664.526579 211.714223 
L 661.875919 210.321415 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cdbfbc"/>
    <path d="M 827.896821 396.769833 
L 830.576629 399.821166 
L 832.077186 397.212885 
L 829.397947 394.215393 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #09ce68"/>
    <path d="M 758.657082 301.473873 
L 761.335787 304.87969 
L 762.867805 304.042015 
L 760.191304 300.708855 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d4c882"/>
    <path d="M 819.862002 387.315041 
L 822.539621 390.514508 
L 824.042035 388.071472 
L 821.365141 384.92947 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2dd56f"/>
    <path d="M 874.245419 422.742542 
L 876.954076 424.663891 
L 878.453387 421.137501 
L 875.744509 419.250979 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a4dc"/>
    <path d="M 944.59001 340.941699 
L 947.35756 341.724075 
L 948.88246 336.927002 
L 946.114329 336.152082 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d5f791"/>
    <path d="M 850.867187 416.612568 
L 853.558092 419.134985 
L 855.055697 416.081274 
L 852.36495 413.602777 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00aebf"/>
    <path d="M 921.104575 384.939113 
L 923.855582 385.922444 
L 925.373248 381.401817 
L 922.621573 380.434879 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #3dd872"/>
    <path d="M 830.576629 399.821166 
L 833.257399 402.818684 
L 834.757436 400.157866 
L 832.077186 397.212885 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #01cc66"/>
    <path d="M 935.732572 359.1362 
L 938.494592 359.971562 
L 940.017934 355.240225 
L 937.255268 354.415568 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #95ea84"/>
    <path d="M 817.184894 384.070808 
L 819.862002 387.315041 
L 821.365141 384.92947 
L 818.688812 381.743808 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #35d771"/>
    <path d="M 903.805508 407.392479 
L 906.541403 408.648483 
L 908.050739 404.477692 
L 905.314271 403.244888 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c382"/>
    <path d="M 786.585055 341.002564 
L 789.261087 344.518301 
L 790.775619 342.882596 
L 788.101069 339.436981 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cdf58f"/>
    <path d="M 833.257399 402.818684 
L 835.939256 405.760262 
L 837.438819 403.048257 
L 834.757436 400.157866 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c677"/>
    <path d="M 814.508192 380.784198 
L 817.184894 384.070808 
L 818.688812 381.743808 
L 816.012949 378.516824 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #41d973"/>
    <path d="M 641.062945 201.760672 
L 643.699714 202.612876 
L 645.359283 203.224438 
L 642.724814 202.375699 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dbd1cf"/>
    <path d="M 755.978017 298.088042 
L 758.657082 301.473873 
L 760.191304 300.708855 
L 757.51451 297.395229 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cec07f"/>
    <path d="M 715.779983 251.478251 
L 718.458253 254.25476 
L 720.032474 254.484144 
L 717.35722 251.764351 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #836059"/>
    <path d="M 811.8318 377.457646 
L 814.508192 380.784198 
L 816.012949 378.516824 
L 813.337454 375.250899 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #4ddb75"/>
    <path d="M 835.939256 405.760262 
L 838.622326 408.64383 
L 840.121458 405.882034 
L 837.438819 403.048257 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c382"/>
    <path d="M 889.602275 418.933719 
L 892.325124 420.483432 
L 893.828501 416.632528 
L 891.105235 415.111342 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00acc4"/>
    <path d="M 753.29862 294.724899 
L 755.978017 298.088042 
L 757.51451 297.395229 
L 754.837449 294.103762 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c8b97b"/>
    <path d="M 885.381343 421.043155 
L 888.100313 422.690228 
L 889.602275 418.933719 
L 886.882945 417.316752 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a8d0"/>
    <path d="M 650.63998 205.212341 
L 653.285923 206.351044 
L 654.936129 207.034162 
L 652.292726 205.905211 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d5c9c7"/>
    <path d="M 783.908662 337.476502 
L 786.585055 341.002564 
L 788.101069 339.436981 
L 785.426229 335.981387 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d9f791"/>
    <path d="M 943.065757 345.721888 
L 945.832736 346.511694 
L 947.35756 341.724075 
L 944.59001 340.941699 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c5f38d"/>
    <path d="M 718.458253 254.25476 
L 721.137108 257.088695 
L 722.708342 257.259851 
L 720.032474 254.484144 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #805c54"/>
    <path d="M 893.828501 416.632528 
L 896.555394 418.088156 
L 898.060289 414.146231 
L 895.332935 412.717366 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b0b9"/>
    <path d="M 690.111336 228.761401 
L 692.782573 230.971452 
L 694.387508 231.577563 
L 691.71937 229.406645 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ab938e"/>
    <path d="M 926.89184 376.842209 
L 929.647826 377.7561 
L 931.167915 373.147077 
L 928.41128 372.246761 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #59de78"/>
    <path d="M 853.558092 419.134985 
L 856.251067 421.589905 
L 857.748541 418.493973 
L 855.055697 416.081274 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00aacb"/>
    <path d="M 809.155625 374.093633 
L 811.8318 377.457646 
L 813.337454 375.250899 
L 810.662236 371.948459 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #59de78"/>
    <path d="M 838.622326 408.64383 
L 841.30674 411.46738 
L 842.805481 408.65723 
L 840.121458 405.882034 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00bc94"/>
    <path d="M 750.618924 291.387129 
L 753.29862 294.724899 
L 754.837449 294.103762 
L 752.160154 290.837066 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c2b178"/>
    <path d="M 934.210381 363.833868 
L 936.971777 364.679854 
L 938.494592 359.971562 
L 935.732572 359.1362 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #85e781"/>
    <path d="M 913.814291 397.105955 
L 916.559617 398.188694 
L 918.073533 393.81902 
L 915.327591 392.754934 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #11cf69"/>
    <path d="M 870.041463 424.138457 
L 872.747002 426.165667 
L 874.245419 422.742542 
L 871.539748 420.751059 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a2e2"/>
    <path d="M 881.165393 422.954929 
L 883.880669 424.702264 
L 885.381343 421.043155 
L 882.665773 419.327316 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a6d7"/>
    <path d="M 863.141089 423.115821 
L 865.841083 425.322058 
L 867.338759 422.040269 
L 864.638743 419.87236 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a4dc"/>
    <path d="M 721.137108 257.088695 
L 723.816453 259.977855 
L 725.384733 260.089334 
L 722.708342 257.259851 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #866458"/>
    <path d="M 908.050739 404.477692 
L 910.791038 405.653828 
L 912.30209 401.406535 
L 909.561214 400.25124 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c677"/>
    <path d="M 806.479578 370.694684 
L 809.155625 374.093633 
L 810.662236 371.948459 
L 807.987209 368.611972 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #65e07a"/>
    <path d="M 747.938967 288.077397 
L 750.618924 291.387129 
L 752.160154 290.837066 
L 749.482658 287.597731 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bca975"/>
    <path d="M 898.060289 414.146231 
L 900.791366 415.511408 
L 902.297863 411.482195 
L 899.566292 410.141839 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b6a7"/>
    <path d="M 919.58854 389.401502 
L 922.338918 390.401001 
L 923.855582 385.922444 
L 921.104575 384.939113 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2dd56f"/>
    <path d="M 781.231873 333.942875 
L 783.908662 337.476502 
L 785.426229 335.981387 
L 782.751063 332.518505 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e5fa94"/>
    <path d="M 841.30674 411.46738 
L 843.992632 414.228964 
L 845.49102 411.371938 
L 842.805481 408.65723 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b8a0"/>
    <path d="M 723.816453 259.977855 
L 726.496196 262.919983 
L 728.061559 262.970402 
L 725.384733 260.089334 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8a695a"/>
    <path d="M 745.258792 284.798345 
L 747.938967 288.077397 
L 749.482658 287.597731 
L 746.805006 284.388327 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b6a272"/>
    <path d="M 941.541693 350.489203 
L 944.308112 351.286406 
L 945.832736 346.511694 
L 943.065757 345.721888 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b5f08a"/>
    <path d="M 803.803575 367.263364 
L 806.479578 370.694684 
L 807.987209 368.611972 
L 805.31229 365.243945 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #71e37d"/>
    <path d="M 742.578447 281.552593 
L 745.258792 284.798345 
L 746.805006 284.388327 
L 744.127242 281.211398 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b09a6e"/>
    <path d="M 726.496196 262.919983 
L 729.176249 265.912772 
L 730.738735 265.900814 
L 728.061559 262.970402 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #90715d"/>
    <path d="M 675.157785 218.178428 
L 677.822021 220.013131 
L 679.445011 220.71403 
L 676.783754 218.907134 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bfada9"/>
    <path d="M 950.407306 332.123947 
L 953.178635 332.888564 
L 954.703755 328.079033 
L 951.931968 327.318401 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f5fd97"/>
    <path d="M 876.954076 424.663891 
L 879.665861 426.514012 
L 881.165393 422.954929 
L 878.453387 421.137501 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a2e2"/>
    <path d="M 739.897988 278.342728 
L 742.578447 281.552593 
L 744.127242 281.211398 
L 741.449419 278.06946 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #aa926b"/>
    <path d="M 729.176249 265.912772 
L 731.856531 268.953865 
L 733.416182 268.87828 
L 730.738735 265.900814 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #94765f"/>
    <path d="M 856.251067 421.589905 
L 858.946257 423.975739 
L 860.443623 420.839318 
L 857.748541 418.493973 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a8d0"/>
    <path d="M 737.217472 275.171309 
L 739.897988 278.342728 
L 741.449419 278.06946 
L 738.771592 274.965 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a68d69"/>
    <path d="M 731.856531 268.953865 
L 734.536963 272.040859 
L 736.093825 271.900468 
L 733.416182 268.87828 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9a7e62"/>
    <path d="M 778.554659 330.404458 
L 781.231873 333.942875 
L 782.751063 332.518505 
L 780.075545 329.051042 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1fc96"/>
    <path d="M 734.536963 272.040859 
L 737.217472 275.171309 
L 738.771592 274.965 
L 736.093825 271.900468 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a08566"/>
    <path d="M 925.373248 381.401817 
L 928.128618 382.329125 
L 929.647826 377.7561 
L 926.89184 376.842209 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #49db75"/>
    <path d="M 902.297863 411.482195 
L 905.033244 412.760906 
L 906.541403 408.648483 
L 903.805508 407.392479 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00bb9b"/>
    <path d="M 932.688797 368.505253 
L 935.44959 369.361775 
L 936.971777 364.679854 
L 934.210381 363.833868 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #75e37d"/>
    <path d="M 843.992632 414.228964 
L 846.680138 416.926694 
L 848.17821 414.024312 
L 845.49102 411.371938 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b4ac"/>
    <path d="M 692.782573 230.971452 
L 695.455412 233.257793 
L 697.05724 233.822835 
L 694.387508 231.577563 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a78e89"/>
    <path d="M 801.127539 363.802275 
L 803.803575 367.263364 
L 805.31229 365.243945 
L 802.637402 361.846924 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #7de57f"/>
    <path d="M 662.886631 210.982812 
L 665.543082 212.484334 
L 667.180237 213.19715 
L 664.526579 211.714223 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cbbcb9"/>
    <path d="M 940.017934 355.240225 
L 942.783806 356.044787 
L 944.308112 351.286406 
L 941.541693 350.489203 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a5ed87"/>
    <path d="M 865.841083 425.322058 
L 868.543752 427.456671 
L 870.041463 424.138457 
L 867.338759 422.040269 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a2e2"/>
    <path d="M 948.88246 336.927002 
L 951.653333 337.6956 
L 953.178635 332.888564 
L 950.407306 332.123947 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e5fa94"/>
    <path d="M 912.30209 401.406535 
L 915.046848 402.507603 
L 916.559617 398.188694 
L 913.814291 397.105955 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #01cc66"/>
    <path d="M 775.876998 326.864039 
L 778.554659 330.404458 
L 780.075545 329.051042 
L 777.39965 325.581715 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 918.073533 393.81902 
L 920.823323 394.834446 
L 922.338918 390.401001 
L 919.58854 389.401502 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1dd26c"/>
    <path d="M 798.451397 360.314058 
L 801.127539 363.802275 
L 802.637402 361.846924 
L 799.962472 358.423487 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #89e781"/>
    <path d="M 846.680138 416.926694 
L 849.369399 419.558747 
L 850.867187 416.612568 
L 848.17821 414.024312 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b0b9"/>
    <path d="M 872.747002 426.165667 
L 875.455523 428.120708 
L 876.954076 424.663891 
L 874.245419 422.742542 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a0e8"/>
    <path d="M 888.100313 422.690228 
L 890.822819 424.267693 
L 892.325124 420.483432 
L 889.602275 418.933719 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a6d7"/>
    <path d="M 906.541403 408.648483 
L 909.28118 409.845048 
L 910.791038 405.653828 
L 908.050739 404.477692 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c088"/>
    <path d="M 892.325124 420.483432 
L 895.051626 421.965139 
L 896.555394 418.088156 
L 893.828501 416.632528 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00aacb"/>
    <path d="M 931.167915 373.147077 
L 933.92813 374.014037 
L 935.44959 369.361775 
L 932.688797 368.505253 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #69e17b"/>
    <path d="M 858.946257 423.975739 
L 861.643809 426.290963 
L 863.141089 423.115821 
L 860.443623 420.839318 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a4dc"/>
    <path d="M 883.880669 424.702264 
L 886.599354 426.378574 
L 888.100313 422.690228 
L 885.381343 421.043155 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a4dc"/>
    <path d="M 773.198872 323.324416 
L 775.876998 326.864039 
L 777.39965 325.581715 
L 774.723361 322.113253 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f8f695"/>
    <path d="M 923.855582 385.922444 
L 926.610369 386.863002 
L 928.128618 382.329125 
L 925.373248 381.401817 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #39d771"/>
    <path d="M 695.455412 233.257793 
L 698.129724 235.618783 
L 699.728445 236.140865 
L 697.05724 233.822835 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a38984"/>
    <path d="M 795.77508 356.801385 
L 798.451397 360.314058 
L 799.962472 358.423487 
L 797.287435 354.976249 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #99eb85"/>
    <path d="M 896.555394 418.088156 
L 899.286043 419.477559 
L 900.791366 415.511408 
L 898.060289 414.146231 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b0b9"/>
    <path d="M 947.35756 341.724075 
L 950.127982 342.496646 
L 951.653333 337.6956 
L 948.88246 336.927002 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d5f791"/>
    <path d="M 938.494592 359.971562 
L 941.259933 360.783438 
L 942.783806 356.044787 
L 940.017934 355.240225 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #95ea84"/>
    <path d="M 643.699714 202.612876 
L 646.340519 203.563915 
L 647.997719 204.170044 
L 645.359283 203.224438 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dbd1cf"/>
    <path d="M 653.285923 206.351044 
L 655.935401 207.585764 
L 657.58301 208.257087 
L 654.936129 207.034162 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d5c9c7"/>
    <path d="M 849.369399 419.558747 
L 852.060557 422.123367 
L 853.558092 419.134985 
L 850.867187 416.612568 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00aacb"/>
    <path d="M 677.822021 220.013131 
L 680.488549 221.933123 
L 682.108532 222.604166 
L 679.445011 220.71403 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bba8a4"/>
    <path d="M 879.665861 426.514012 
L 882.380922 428.291879 
L 883.880669 424.702264 
L 881.165393 422.954929 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a0e8"/>
    <path d="M 770.52027 319.788394 
L 773.198872 323.324416 
L 774.723361 322.113253 
L 772.046666 318.64839 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f2ee92"/>
    <path d="M 793.098526 353.266964 
L 795.77508 356.801385 
L 797.287435 354.976249 
L 794.612228 351.507853 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a5ed87"/>
    <path d="M 900.791366 415.511408 
L 903.526293 416.812316 
L 905.033244 412.760906 
L 902.297863 411.482195 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b4ac"/>
    <path d="M 868.543752 427.456671 
L 871.249247 429.518374 
L 872.747002 426.165667 
L 870.041463 424.138457 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #009eef"/>
    <path d="M 826.394873 399.275401 
L 829.075343 402.378337 
L 830.576629 399.821166 
L 827.896821 396.769833 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #05cd67"/>
    <path d="M 823.715196 396.119627 
L 826.394873 399.275401 
L 827.896821 396.769833 
L 825.217857 393.666869 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #11cf69"/>
    <path d="M 916.559617 398.188694 
L 919.308861 399.219792 
L 920.823323 394.834446 
L 918.073533 393.81902 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #11cf69"/>
    <path d="M 929.647826 377.7561 
L 932.40749 378.63339 
L 933.92813 374.014037 
L 931.167915 373.147077 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #59de78"/>
    <path d="M 829.075343 402.378337 
L 831.75673 405.426208 
L 833.257399 402.818684 
L 830.576629 399.821166 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c970"/>
    <path d="M 910.791038 405.653828 
L 913.535278 406.772889 
L 915.046848 402.507603 
L 912.30209 401.406535 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c677"/>
    <path d="M 821.036197 392.913298 
L 823.715196 396.119627 
L 825.217857 393.666869 
L 822.539621 390.514508 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #19d16b"/>
    <path d="M 945.832736 346.511694 
L 948.602714 347.288227 
L 950.127982 342.496646 
L 947.35756 341.724075 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c5f38d"/>
    <path d="M 698.129724 235.618783 
L 700.805384 238.052702 
L 702.401 238.529982 
L 699.728445 236.140865 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a18781"/>
    <path d="M 831.75673 405.426208 
L 834.439157 408.416844 
L 835.939256 405.760262 
L 833.257399 402.818684 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c47d"/>
    <path d="M 861.643809 426.290963 
L 864.343873 428.534119 
L 865.841083 425.322058 
L 863.141089 423.115821 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a0e8"/>
    <path d="M 818.357762 389.658751 
L 821.036197 392.913298 
L 822.539621 390.514508 
L 819.862002 387.315041 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #25d36d"/>
    <path d="M 852.060557 422.123367 
L 854.753758 424.618859 
L 856.251067 421.589905 
L 853.558092 419.134985 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a6d7"/>
    <path d="M 767.841186 316.258784 
L 770.52027 319.788394 
L 772.046666 318.64839 
L 769.369559 315.189865 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ece78f"/>
    <path d="M 936.971777 364.679854 
L 939.736603 365.498993 
L 941.259933 360.783438 
L 938.494592 359.971562 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #85e781"/>
    <path d="M 790.421679 349.713527 
L 793.098526 353.266964 
L 794.612228 351.507853 
L 791.936796 348.020971 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b1ef89"/>
    <path d="M 665.543082 212.484334 
L 668.202433 214.077273 
L 669.836752 214.769422 
L 667.180237 213.19715 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c9bab7"/>
    <path d="M 922.338918 390.401001 
L 925.093157 391.354629 
L 926.610369 386.863002 
L 923.855582 385.922444 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2dd56f"/>
    <path d="M 834.439157 408.416844 
L 837.122755 411.348135 
L 838.622326 408.64383 
L 835.939256 405.760262 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00be8f"/>
    <path d="M 875.455523 428.120708 
L 878.167172 430.00246 
L 879.665861 426.514012 
L 876.954076 424.663891 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #009eef"/>
    <path d="M 815.679782 386.358375 
L 818.357762 389.658751 
L 819.862002 387.315041 
L 817.184894 384.070808 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #31d670"/>
    <path d="M 905.033244 412.760906 
L 907.772553 413.97747 
L 909.28118 409.845048 
L 906.541403 408.648483 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00bb9b"/>
    <path d="M 837.122755 411.348135 
L 839.807656 414.218028 
L 841.30674 411.46738 
L 838.622326 408.64383 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00bb9b"/>
    <path d="M 813.002153 383.01461 
L 815.679782 386.358375 
L 817.184894 384.070808 
L 814.508192 380.784198 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #3dd872"/>
    <path d="M 765.161621 312.738395 
L 767.841186 316.258784 
L 769.369559 315.189865 
L 766.692039 311.740415 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e6df8b"/>
    <path d="M 944.308112 351.286406 
L 947.077654 352.066889 
L 948.602714 347.288227 
L 945.832736 346.511694 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b5f08a"/>
    <path d="M 787.744488 346.143837 
L 790.421679 349.713527 
L 791.936796 348.020971 
L 789.261087 344.518301 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bdf28c"/>
    <path d="M 680.488549 221.933123 
L 683.157228 223.937155 
L 684.774183 224.576323 
L 682.108532 222.604166 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b9a5a1"/>
    <path d="M 700.805384 238.052702 
L 703.48227 240.557754 
L 705.074787 240.988438 
L 702.401 238.529982 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9d827c"/>
    <path d="M 810.324776 379.629942 
L 813.002153 383.01461 
L 814.508192 380.784198 
L 811.8318 377.457646 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #49db75"/>
    <path d="M 928.128618 382.329125 
L 930.887758 383.216632 
L 932.40749 378.63339 
L 929.647826 377.7561 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #49db75"/>
    <path d="M 839.807656 414.218028 
L 842.493997 417.024538 
L 843.992632 414.228964 
L 841.30674 411.46738 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b4ac"/>
    <path d="M 890.822819 424.267693 
L 893.549 425.774773 
L 895.051626 421.965139 
L 892.325124 420.483432 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a6d7"/>
    <path d="M 854.753758 424.618859 
L 857.44915 427.043601 
L 858.946257 423.975739 
L 856.251067 421.589905 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a4dc"/>
    <path d="M 935.44959 369.361775 
L 938.213922 370.188121 
L 939.736603 365.498993 
L 936.971777 364.679854 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #75e37d"/>
    <path d="M 886.599354 426.378574 
L 889.321593 427.982993 
L 890.822819 424.267693 
L 888.100313 422.690228 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a2e2"/>
    <path d="M 895.051626 421.965139 
L 897.781914 423.378152 
L 899.286043 419.477559 
L 896.555394 418.088156 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00aacb"/>
    <path d="M 762.481581 309.230036 
L 765.161621 312.738395 
L 766.692039 311.740415 
L 764.014112 308.302779 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e0d788"/>
    <path d="M 636.764531 200.48783 
L 639.399308 201.242606 
L 641.062945 201.760672 
L 638.430353 201.007374 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dfd6d4"/>
    <path d="M 915.046848 402.507603 
L 917.795591 403.554109 
L 919.308861 399.219792 
L 916.559617 398.188694 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #01cc66"/>
    <path d="M 807.647556 376.206906 
L 810.324776 379.629942 
L 811.8318 377.457646 
L 809.155625 374.093633 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #55dd77"/>
    <path d="M 864.343873 428.534119 
L 867.046598 430.703823 
L 868.543752 427.456671 
L 865.841083 425.322058 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #009cf4"/>
    <path d="M 871.249247 429.518374 
L 873.957717 431.505947 
L 875.455523 428.120708 
L 872.747002 426.165667 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #009cf4"/>
    <path d="M 785.066905 342.560679 
L 787.744488 346.143837 
L 789.261087 344.518301 
L 786.585055 341.002564 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c9f48e"/>
    <path d="M 882.380922 428.291879 
L 885.099402 429.996533 
L 886.599354 426.378574 
L 883.880669 424.702264 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #009eef"/>
    <path d="M 842.493997 417.024538 
L 845.181916 419.765738 
L 846.680138 416.926694 
L 843.992632 414.228964 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b0b9"/>
    <path d="M 920.823323 394.834446 
L 923.577052 395.800955 
L 925.093157 391.354629 
L 922.338918 390.401001 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1dd26c"/>
    <path d="M 909.28118 409.845048 
L 912.024951 410.981748 
L 913.535278 406.772889 
L 910.791038 405.653828 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c088"/>
    <path d="M 942.783806 356.044787 
L 945.552923 356.829204 
L 947.077654 352.066889 
L 944.308112 351.286406 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a5ed87"/>
    <path d="M 899.286043 419.477559 
L 902.020578 420.800134 
L 903.526293 416.812316 
L 900.791366 415.511408 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00aebf"/>
    <path d="M 703.48227 240.557754 
L 706.160263 243.132068 
L 707.74969 243.514416 
L 705.074787 240.988438 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #997c76"/>
    <path d="M 759.801076 305.736514 
L 762.481581 309.230036 
L 764.014112 308.302779 
L 761.335787 304.87969 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d8cd84"/>
    <path d="M 655.935401 207.585764 
L 658.588268 208.916003 
L 660.233225 209.5735 
L 657.58301 208.257087 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d3c7c4"/>
    <path d="M 804.970404 372.748079 
L 807.647556 376.206906 
L 809.155625 374.093633 
L 806.479578 370.694684 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #61df79"/>
    <path d="M 933.92813 374.014037 
L 936.691989 374.847527 
L 938.213922 370.188121 
L 935.44959 369.361775 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #69e17b"/>
    <path d="M 845.181916 419.765738 
L 847.871557 422.43977 
L 849.369399 419.558747 
L 846.680138 416.926694 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00acc4"/>
    <path d="M 857.44915 427.043601 
L 860.146882 429.396034 
L 861.643809 426.290963 
L 858.946257 423.975739 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a0e8"/>
    <path d="M 782.388892 338.966859 
L 785.066905 342.560679 
L 786.585055 341.002564 
L 783.908662 337.476502 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d9f791"/>
    <path d="M 878.167172 430.00246 
L 880.882099 431.809869 
L 882.380922 428.291879 
L 879.665861 426.514012 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #009cf4"/>
    <path d="M 926.610369 386.863002 
L 929.369017 387.760602 
L 930.887758 383.216632 
L 928.128618 382.329125 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #39d771"/>
    <path d="M 646.340519 203.563915 
L 648.985213 204.613608 
L 650.63998 205.212341 
L 647.997719 204.170044 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dbd1cf"/>
    <path d="M 668.202433 214.077273 
L 670.864538 215.760736 
L 672.495982 216.430171 
L 669.836752 214.769422 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c7b7b4"/>
    <path d="M 757.120125 302.260624 
L 759.801076 305.736514 
L 761.335787 304.87969 
L 758.657082 301.473873 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d2c581"/>
    <path d="M 802.293235 369.25608 
L 804.970404 372.748079 
L 806.479578 370.694684 
L 803.803575 367.263364 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #6de27c"/>
    <path d="M 903.526293 416.812316 
L 906.265193 418.048433 
L 907.772553 413.97747 
L 905.033244 412.760906 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b4ac"/>
    <path d="M 683.157228 223.937155 
L 685.827922 226.023887 
L 687.441829 226.629199 
L 684.774183 224.576323 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b5a09c"/>
    <path d="M 706.160263 243.132068 
L 708.839245 245.773702 
L 710.425597 246.106026 
L 707.74969 243.514416 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #93756e"/>
    <path d="M 941.259933 360.783438 
L 944.028638 361.57177 
L 945.552923 356.829204 
L 942.783806 356.044787 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #95ea84"/>
    <path d="M 754.438751 298.805154 
L 757.120125 302.260624 
L 758.657082 301.473873 
L 755.978017 298.088042 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ccbe7d"/>
    <path d="M 847.871557 422.43977 
L 850.563065 425.044839 
L 852.060557 422.123367 
L 849.369399 419.558747 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a8d0"/>
    <path d="M 779.710415 335.365204 
L 782.388892 338.966859 
L 783.908662 337.476502 
L 781.231873 333.942875 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e5fa94"/>
    <path d="M 867.046598 430.703823 
L 869.752138 432.798755 
L 871.249247 429.518374 
L 868.543752 427.456671 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #009afa"/>
    <path d="M 913.535278 406.772889 
L 916.283565 407.834521 
L 917.795591 403.554109 
L 915.046848 402.507603 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c677"/>
    <path d="M 799.61597 365.73357 
L 802.293235 369.25608 
L 803.803575 367.263364 
L 801.127539 363.802275 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #7de57f"/>
    <path d="M 919.308861 399.219792 
L 922.06212 400.198981 
L 923.577052 395.800955 
L 920.823323 394.834446 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0dcf69"/>
    <path d="M 873.957717 431.505947 
L 876.669315 433.418241 
L 878.167172 430.00246 
L 875.455523 428.120708 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0098fe"/>
    <path d="M 708.839245 245.773702 
L 711.519103 248.480644 
L 713.102396 248.761311 
L 710.425597 246.106026 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8f7069"/>
    <path d="M 932.40749 378.63339 
L 935.170899 379.473959 
L 936.691989 374.847527 
L 933.92813 374.014037 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #59de78"/>
    <path d="M 751.756982 295.372878 
L 754.438751 298.805154 
L 755.978017 298.088042 
L 753.29862 294.724899 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c6b67a"/>
    <path d="M 860.146882 429.396034 
L 862.847108 431.674673 
L 864.343873 428.534119 
L 861.643809 426.290963 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #009cf4"/>
    <path d="M 907.772553 413.97747 
L 910.51591 415.131443 
L 912.024951 410.981748 
L 909.28118 409.845048 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b8a0"/>
    <path d="M 889.321593 427.982993 
L 892.047526 429.514721 
L 893.549 425.774773 
L 890.822819 424.267693 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a0e8"/>
    <path d="M 925.093157 391.354629 
L 927.851344 392.26219 
L 929.369017 387.760602 
L 926.610369 386.863002 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #29d46e"/>
    <path d="M 893.549 425.774773 
L 896.278995 427.210761 
L 897.781914 423.378152 
L 895.051626 421.965139 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a4dc"/>
    <path d="M 939.736603 365.498993 
L 942.504911 366.29122 
L 944.028638 361.57177 
L 941.259933 360.783438 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #85e781"/>
    <path d="M 796.938535 362.183244 
L 799.61597 365.73357 
L 801.127539 363.802275 
L 798.451397 360.314058 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #89e781"/>
    <path d="M 777.031444 331.758555 
L 779.710415 335.365204 
L 781.231873 333.942875 
L 778.554659 330.404458 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1fc96"/>
    <path d="M 885.099402 429.996533 
L 887.821448 431.627086 
L 889.321593 427.982993 
L 886.599354 426.378574 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #009cf4"/>
    <path d="M 850.563065 425.044839 
L 853.256588 427.57922 
L 854.753758 424.618859 
L 852.060557 422.123367 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a4dc"/>
    <path d="M 749.074852 291.966551 
L 751.756982 295.372878 
L 753.29862 294.724899 
L 750.618924 291.387129 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c0ae77"/>
    <path d="M 711.519103 248.480644 
L 714.199728 251.250815 
L 715.779983 251.478251 
L 713.102396 248.761311 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8b6b64"/>
    <path d="M 897.781914 423.378152 
L 900.516122 424.721847 
L 902.020578 420.800134 
L 899.286043 419.477559 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a8d0"/>
    <path d="M 685.827922 226.023887 
L 688.500493 228.191889 
L 690.111336 228.761401 
L 687.441829 226.629199 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b39e99"/>
    <path d="M 746.392402 288.58891 
L 749.074852 291.966551 
L 750.618924 291.387129 
L 747.938967 288.077397 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #baa774"/>
    <path d="M 827.573301 404.883204 
L 830.255398 407.9792 
L 831.75673 405.426208 
L 829.075343 402.378337 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c677"/>
    <path d="M 824.892073 401.730949 
L 827.573301 404.883204 
L 829.075343 402.378337 
L 826.394873 399.275401 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #01cc66"/>
    <path d="M 830.255398 407.9792 
L 832.938492 411.016722 
L 834.439157 408.416844 
L 831.75673 405.426208 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c088"/>
    <path d="M 822.21159 398.524702 
L 824.892073 401.730949 
L 826.394873 399.275401 
L 823.715196 396.119627 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #09ce68"/>
    <path d="M 794.260862 358.607834 
L 796.938535 362.183244 
L 798.451397 360.314058 
L 795.77508 356.801385 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #95ea84"/>
    <path d="M 880.882099 431.809869 
L 883.600453 433.541953 
L 885.099402 429.996533 
L 882.380922 428.291879 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0098fe"/>
    <path d="M 714.199728 251.250815 
L 716.881013 254.082073 
L 718.458253 254.25476 
L 715.779983 251.478251 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #87655e"/>
    <path d="M 774.351957 328.149768 
L 777.031444 331.758555 
L 778.554659 330.404458 
L 775.876998 326.864039 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 670.864538 215.760736 
L 673.529253 217.533732 
L 675.157785 218.178428 
L 672.495982 216.430171 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c5b5b1"/>
    <path d="M 658.588268 208.916003 
L 661.244377 210.34116 
L 662.886631 210.982812 
L 660.233225 209.5735 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d1c4c1"/>
    <path d="M 930.887758 383.216632 
L 933.650742 384.064204 
L 935.170899 379.473959 
L 932.40749 378.63339 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #49db75"/>
    <path d="M 832.938492 411.016722 
L 835.622714 413.993621 
L 837.122755 411.348135 
L 834.439157 408.416844 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00bc94"/>
    <path d="M 819.531735 395.266792 
L 822.21159 398.524702 
L 823.715196 396.119627 
L 821.036197 392.913298 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #15d06a"/>
    <path d="M 743.709677 285.242671 
L 746.392402 288.58891 
L 747.938967 288.077397 
L 745.258792 284.798345 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b49f70"/>
    <path d="M 902.020578 420.800134 
L 904.759129 422.055341 
L 906.265193 418.048433 
L 903.526293 416.812316 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00acc4"/>
    <path d="M 917.795591 403.554109 
L 920.54842 404.545765 
L 922.06212 400.198981 
L 919.308861 399.219792 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #01cc66"/>
    <path d="M 869.752138 432.798755 
L 872.460645 434.817669 
L 873.957717 431.505947 
L 871.249247 429.518374 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0296fc"/>
    <path d="M 938.213922 370.188121 
L 940.981848 370.984219 
L 942.504911 366.29122 
L 939.736603 365.498993 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #75e37d"/>
    <path d="M 639.399308 201.242606 
L 642.038333 202.098159 
L 643.699714 202.612876 
L 641.062945 201.760672 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dfd6d4"/>
    <path d="M 816.852392 391.959601 
L 819.531735 395.266792 
L 821.036197 392.913298 
L 818.357762 389.658751 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #21d36d"/>
    <path d="M 716.881013 254.082073 
L 719.562855 256.972213 
L 721.137108 257.088695 
L 718.458253 254.25476 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #815e56"/>
    <path d="M 835.622714 413.993621 
L 838.308199 416.907807 
L 839.807656 414.218028 
L 837.122755 411.348135 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b6a7"/>
    <path d="M 912.024951 410.981748 
L 914.772831 412.058215 
L 916.283565 407.834521 
L 913.535278 406.772889 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00be8f"/>
    <path d="M 853.256588 427.57922 
L 855.952276 430.041255 
L 857.44915 427.043601 
L 854.753758 424.618859 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a0e8"/>
    <path d="M 862.847108 431.674673 
L 865.54998 433.8781 
L 867.046598 430.703823 
L 864.343873 428.534119 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0098fe"/>
    <path d="M 741.026728 281.930521 
L 743.709677 285.242671 
L 745.258792 284.798345 
L 742.578447 281.552593 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ae976d"/>
    <path d="M 923.577052 395.800955 
L 926.334813 396.718337 
L 927.851344 392.26219 
L 925.093157 391.354629 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1dd26c"/>
    <path d="M 791.582887 355.010106 
L 794.260862 358.607834 
L 795.77508 356.801385 
L 793.098526 353.266964 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a1ec86"/>
    <path d="M 719.562855 256.972213 
L 722.245155 259.918972 
L 723.816453 259.977855 
L 721.137108 257.088695 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #825f56"/>
    <path d="M 814.173451 388.605564 
L 816.852392 391.959601 
L 818.357762 389.658751 
L 815.679782 386.358375 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2dd56f"/>
    <path d="M 838.308199 416.907807 
L 840.995086 419.757255 
L 842.493997 417.024538 
L 839.807656 414.218028 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b2b2"/>
    <path d="M 738.34361 278.655121 
L 741.026728 281.930521 
L 742.578447 281.552593 
L 739.897988 278.342728 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a8906a"/>
    <path d="M 771.671938 324.541707 
L 774.351957 328.149768 
L 775.876998 326.864039 
L 773.198872 323.324416 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f8f695"/>
    <path d="M 876.669315 433.418241 
L 879.384191 435.254178 
L 880.882099 431.809869 
L 878.167172 430.00246 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0296fc"/>
    <path d="M 648.985213 204.613608 
L 651.63365 205.761666 
L 653.285923 206.351044 
L 650.63998 205.212341 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d9cecc"/>
    <path d="M 722.245155 259.918972 
L 724.92782 262.920031 
L 726.496196 262.919983 
L 723.816453 259.977855 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #886759"/>
    <path d="M 735.660385 275.419097 
L 738.34361 278.655121 
L 739.897988 278.342728 
L 737.217472 275.171309 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a28867"/>
    <path d="M 688.500493 228.191889 
L 691.174805 230.439645 
L 692.782573 230.971452 
L 690.111336 228.761401 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #af9994"/>
    <path d="M 724.92782 262.920031 
L 727.610759 265.973018 
L 729.176249 265.912772 
L 726.496196 262.919983 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8c6c5b"/>
    <path d="M 732.97712 272.225042 
L 735.660385 275.419097 
L 737.217472 275.171309 
L 734.536963 272.040859 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9e8365"/>
    <path d="M 811.494806 385.207169 
L 814.173451 388.605564 
L 815.679782 386.358375 
L 813.002153 383.01461 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #39d771"/>
    <path d="M 906.265193 418.048433 
L 909.00819 419.219297 
L 910.51591 415.131443 
L 907.772553 413.97747 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b2b2"/>
    <path d="M 727.610759 265.973018 
L 730.293886 269.075512 
L 731.856531 268.953865 
L 729.176249 265.912772 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #92735e"/>
    <path d="M 730.293886 269.075512 
L 732.97712 272.225042 
L 734.536963 272.040859 
L 731.856531 268.953865 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #987b61"/>
    <path d="M 840.995086 419.757255 
L 843.683515 422.540002 
L 845.181916 419.765738 
L 842.493997 417.024538 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00acc4"/>
    <path d="M 929.369017 387.760602 
L 932.131603 388.6151 
L 933.650742 384.064204 
L 930.887758 383.216632 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #39d771"/>
    <path d="M 936.691989 374.847527 
L 939.459552 375.64747 
L 940.981848 370.984219 
L 938.213922 370.188121 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #65e07a"/>
    <path d="M 788.904553 351.392853 
L 791.582887 355.010106 
L 793.098526 353.266964 
L 790.421679 349.713527 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b1ef89"/>
    <path d="M 855.952276 430.041255 
L 858.650283 432.429356 
L 860.146882 429.396034 
L 857.44915 427.043601 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #009cf4"/>
    <path d="M 768.991375 320.937247 
L 771.671938 324.541707 
L 773.198872 323.324416 
L 770.52027 319.788394 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f2ee92"/>
    <path d="M 808.816356 381.766951 
L 811.494806 385.207169 
L 813.002153 383.01461 
L 810.324776 379.629942 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #45da74"/>
    <path d="M 892.047526 429.514721 
L 894.777297 430.973029 
L 896.278995 427.210761 
L 893.549 425.774773 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #009eef"/>
    <path d="M 887.821448 431.627086 
L 890.547207 433.182715 
L 892.047526 429.514721 
L 889.321593 427.982993 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #009afa"/>
    <path d="M 843.683515 422.540002 
L 846.373633 425.254155 
L 847.871557 422.43977 
L 845.181916 419.765738 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a8d0"/>
    <path d="M 916.283565 407.834521 
L 919.036007 408.838425 
L 920.54842 404.545765 
L 917.795591 403.554109 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c47d"/>
    <path d="M 896.278995 427.210761 
L 899.012941 428.575011 
L 900.516122 424.721847 
L 897.781914 423.378152 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a2e2"/>
    <path d="M 865.54998 433.8781 
L 868.255654 436.004971 
L 869.752138 432.798755 
L 867.046598 430.703823 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0296fc"/>
    <path d="M 673.529253 217.533732 
L 676.196432 219.395171 
L 677.822021 220.013131 
L 675.157785 218.178428 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c3b2af"/>
    <path d="M 922.06212 400.198981 
L 924.81949 401.126037 
L 926.334813 396.718337 
L 923.577052 395.800955 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0dcf69"/>
    <path d="M 872.460645 434.817669 
L 875.172277 436.759391 
L 876.669315 433.418241 
L 873.957717 431.505947 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0393f9"/>
    <path d="M 806.138007 378.287496 
L 808.816356 381.766951 
L 810.324776 379.629942 
L 807.647556 376.206906 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #51dc76"/>
    <path d="M 786.225808 347.758897 
L 788.904553 351.392853 
L 790.421679 349.713527 
L 787.744488 346.143837 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bdf28c"/>
    <path d="M 883.600453 433.541953 
L 886.322385 435.197797 
L 887.821448 431.627086 
L 885.099402 429.996533 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0296fc"/>
    <path d="M 910.51591 415.131443 
L 913.263432 416.22244 
L 914.772831 412.058215 
L 912.024951 410.981748 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b8a0"/>
    <path d="M 766.310264 317.339265 
L 768.991375 320.937247 
L 770.52027 319.788394 
L 767.841186 316.258784 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ece78f"/>
    <path d="M 691.174805 230.439645 
L 693.850725 232.765553 
L 695.455412 233.257793 
L 692.782573 230.971452 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ab938e"/>
    <path d="M 900.516122 424.721847 
L 903.254383 425.995666 
L 904.759129 422.055341 
L 902.020578 420.800134 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a6d7"/>
    <path d="M 935.170899 379.473959 
L 937.93812 380.277718 
L 939.459552 375.64747 
L 936.691989 374.847527 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #59de78"/>
    <path d="M 846.373633 425.254155 
L 849.065586 427.897886 
L 850.563065 425.044839 
L 847.871557 422.43977 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a4dc"/>
    <path d="M 661.244377 210.34116 
L 663.903579 211.860526 
L 665.543082 212.484334 
L 662.886631 210.982812 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cfc2bf"/>
    <path d="M 803.459666 374.771431 
L 806.138007 378.287496 
L 807.647556 376.206906 
L 804.970404 372.748079 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #5ddf79"/>
    <path d="M 927.851344 392.26219 
L 930.613562 393.123531 
L 932.131603 388.6151 
L 929.369017 387.760602 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #29d46e"/>
    <path d="M 858.650283 432.429356 
L 861.350763 434.742008 
L 862.847108 431.674673 
L 860.146882 429.396034 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0098fe"/>
    <path d="M 879.384191 435.254178 
L 882.102501 437.01275 
L 883.600453 433.541953 
L 880.882099 431.809869 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0393f9"/>
    <path d="M 763.628606 313.75064 
L 766.310264 317.339265 
L 767.841186 316.258784 
L 765.161621 312.738395 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e4dc8a"/>
    <path d="M 783.546607 344.111085 
L 786.225808 347.758897 
L 787.744488 346.143837 
L 785.066905 342.560679 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c9f48e"/>
    <path d="M 904.759129 422.055341 
L 907.501822 423.242701 
L 909.00819 419.219297 
L 906.265193 418.048433 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00acc4"/>
    <path d="M 800.781249 371.221428 
L 803.459666 374.771431 
L 804.970404 372.748079 
L 802.293235 369.25608 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #6de27c"/>
    <path d="M 849.065586 427.897886 
L 851.759526 430.469437 
L 853.256588 427.57922 
L 850.563065 425.044839 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a0e8"/>
    <path d="M 693.850725 232.765553 
L 696.528123 235.167928 
L 698.129724 235.618783 
L 695.455412 233.257793 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a78e89"/>
    <path d="M 868.255654 436.004971 
L 870.964288 438.054012 
L 872.460645 434.817669 
L 869.752138 432.798755 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0490f6"/>
    <path d="M 920.54842 404.545765 
L 923.305437 405.482342 
L 924.81949 401.126037 
L 922.06212 400.198981 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #01cc66"/>
    <path d="M 914.772831 412.058215 
L 917.524932 413.074136 
L 919.036007 408.838425 
L 916.283565 407.834521 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00be8f"/>
    <path d="M 933.650742 384.064204 
L 936.417643 384.871749 
L 937.93812 380.277718 
L 935.170899 379.473959 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #49db75"/>
    <path d="M 760.946407 310.174252 
L 763.628606 313.75064 
L 765.161621 312.738395 
L 762.481581 309.230036 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ded587"/>
    <path d="M 642.038333 202.098159 
L 644.68146 203.054418 
L 646.340519 203.563915 
L 643.699714 202.612876 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dfd6d4"/>
    <path d="M 651.63365 205.761666 
L 654.285681 207.007688 
L 655.935401 207.585764 
L 653.285923 206.351044 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d9cecc"/>
    <path d="M 780.86691 340.452287 
L 783.546607 344.111085 
L 785.066905 342.560679 
L 782.388892 338.966859 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d5f791"/>
    <path d="M 676.196432 219.395171 
L 678.865931 221.343866 
L 680.488549 221.933123 
L 677.822021 220.013131 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bfada9"/>
    <path d="M 875.172277 436.759391 
L 877.887187 438.622818 
L 879.384191 435.254178 
L 876.669315 433.418241 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0490f6"/>
    <path d="M 798.102675 367.640201 
L 800.781249 371.221428 
L 802.293235 369.25608 
L 799.61597 365.73357 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #79e47e"/>
    <path d="M 861.350763 434.742008 
L 864.053874 436.977766 
L 865.54998 433.8781 
L 862.847108 431.674673 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0393f9"/>
    <path d="M 926.334813 396.718337 
L 929.096693 397.586432 
L 930.613562 393.123531 
L 927.851344 392.26219 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1dd26c"/>
    <path d="M 909.00819 419.219297 
L 911.755406 420.324509 
L 913.263432 416.22244 
L 910.51591 415.131443 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b2b2"/>
    <path d="M 851.759526 430.469437 
L 854.455607 432.96712 
L 855.952276 430.041255 
L 853.256588 427.57922 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #009cf4"/>
    <path d="M 890.547207 433.182715 
L 893.276825 434.66267 
L 894.777297 430.973029 
L 892.047526 429.514721 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0098fe"/>
    <path d="M 758.26368 306.612973 
L 760.946407 310.174252 
L 762.481581 309.230036 
L 759.801076 305.736514 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d8cd84"/>
    <path d="M 826.070469 407.334626 
L 828.753372 410.476472 
L 830.255398 407.9792 
L 827.573301 404.883204 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c47d"/>
    <path d="M 828.753372 410.476472 
L 831.437228 413.558668 
L 832.938492 411.016722 
L 830.255398 407.9792 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00be8f"/>
    <path d="M 894.777297 430.973029 
L 897.511047 432.357253 
L 899.012941 428.575011 
L 896.278995 427.210761 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #009cf4"/>
    <path d="M 823.388389 404.135379 
L 826.070469 407.334626 
L 827.573301 404.883204 
L 824.892073 401.730949 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c970"/>
    <path d="M 696.528123 235.167928 
L 699.206868 237.645004 
L 700.805384 238.052702 
L 698.129724 235.618783 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a58c86"/>
    <path d="M 831.437228 413.558668 
L 834.122171 416.579023 
L 835.622714 413.993621 
L 832.938492 411.016722 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b8a0"/>
    <path d="M 886.322385 435.197797 
L 889.048044 436.77656 
L 890.547207 433.182715 
L 887.821448 431.627086 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0393f9"/>
    <path d="M 820.707008 400.881042 
L 823.388389 404.135379 
L 824.892073 401.730949 
L 822.21159 398.524702 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #05cd67"/>
    <path d="M 778.186681 336.785391 
L 780.86691 340.452287 
L 782.388892 338.966859 
L 779.710415 335.365204 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e5fa94"/>
    <path d="M 834.122171 416.579023 
L 836.808336 419.53541 
L 838.308199 416.907807 
L 835.622714 413.993621 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b4ac"/>
    <path d="M 795.423869 364.0305 
L 798.102675 367.640201 
L 799.61597 365.73357 
L 796.938535 362.183244 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #85e781"/>
    <path d="M 899.012941 428.575011 
L 901.750975 429.866948 
L 903.254383 425.995666 
L 900.516122 424.721847 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a0e8"/>
    <path d="M 818.026205 397.573986 
L 820.707008 400.881042 
L 822.21159 398.524702 
L 819.531735 395.266792 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #11cf69"/>
    <path d="M 663.903579 211.860526 
L 666.565725 213.47329 
L 668.202433 214.077273 
L 665.543082 212.484334 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cdbfbc"/>
    <path d="M 932.131603 388.6151 
L 934.898207 389.426397 
L 936.417643 384.871749 
L 933.650742 384.064204 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #39d771"/>
    <path d="M 755.580444 303.069672 
L 758.26368 306.612973 
L 759.801076 305.736514 
L 757.120125 302.260624 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d2c581"/>
    <path d="M 836.808336 419.53541 
L 839.495864 422.425769 
L 840.995086 419.757255 
L 838.308199 416.907807 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00aebf"/>
    <path d="M 882.102501 437.01275 
L 884.824396 438.693024 
L 886.322385 435.197797 
L 883.600453 433.541953 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0490f6"/>
    <path d="M 815.345863 394.216634 
L 818.026205 397.573986 
L 819.531735 395.266792 
L 816.852392 391.959601 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1dd26c"/>
    <path d="M 919.036007 408.838425 
L 921.792711 409.784358 
L 923.305437 405.482342 
L 920.54842 404.545765 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c47d"/>
    <path d="M 854.455607 432.96712 
L 857.153982 435.389318 
L 858.650283 432.429356 
L 855.952276 430.041255 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0098fe"/>
    <path d="M 870.964288 438.054012 
L 873.67604 440.024023 
L 875.172277 436.759391 
L 872.460645 434.817669 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #068ef4"/>
    <path d="M 903.254383 425.995666 
L 905.99683 427.199114 
L 907.501822 423.242701 
L 904.759129 422.055341 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a6d7"/>
    <path d="M 699.206868 237.645004 
L 701.886836 240.194937 
L 703.48227 240.557754 
L 700.805384 238.052702 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a18781"/>
    <path d="M 839.495864 422.425769 
L 842.184901 425.248104 
L 843.683515 422.540002 
L 840.995086 419.757255 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00aacb"/>
    <path d="M 913.263432 416.22244 
L 916.015238 417.250137 
L 917.524932 413.074136 
L 914.772831 412.058215 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b8a0"/>
    <path d="M 775.505893 333.113303 
L 778.186681 336.785391 
L 779.710415 335.365204 
L 777.031444 331.758555 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1fc96"/>
    <path d="M 864.053874 436.977766 
L 866.759774 439.135257 
L 868.255654 436.004971 
L 865.54998 433.8781 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0490f6"/>
    <path d="M 792.744764 360.395112 
L 795.423869 364.0305 
L 796.938535 362.183244 
L 794.260862 358.607834 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #91e983"/>
    <path d="M 924.81949 401.126037 
L 927.581065 402.000792 
L 929.096693 397.586432 
L 926.334813 396.718337 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0dcf69"/>
    <path d="M 812.665872 390.811468 
L 815.345863 394.216634 
L 816.852392 391.959601 
L 814.173451 388.605564 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #29d46e"/>
    <path d="M 678.865931 221.343866 
L 681.537607 223.378537 
L 683.157228 223.937155 
L 680.488549 221.933123 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bdaba7"/>
    <path d="M 752.896723 299.547203 
L 755.580444 303.069672 
L 757.120125 302.260624 
L 754.438751 298.805154 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ccbe7d"/>
    <path d="M 635.097108 200.067368 
L 637.734025 200.823604 
L 639.399308 201.242606 
L 636.764531 200.48783 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e3dbd9"/>
    <path d="M 842.184901 425.248104 
L 844.875591 428.000487 
L 846.373633 425.254155 
L 843.683515 422.540002 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a4dc"/>
    <path d="M 877.887187 438.622818 
L 880.605533 440.40692 
L 882.102501 437.01275 
L 879.384191 435.254178 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #078bf1"/>
    <path d="M 809.986123 387.361019 
L 812.665872 390.811468 
L 814.173451 388.605564 
L 811.494806 385.207169 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #35d771"/>
    <path d="M 701.886836 240.194937 
L 704.567903 242.815806 
L 706.160263 243.132068 
L 703.48227 240.557754 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9b7f79"/>
    <path d="M 750.212548 296.04841 
L 752.896723 299.547203 
L 754.438751 298.805154 
L 751.756982 295.372878 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c4b379"/>
    <path d="M 930.613562 393.123531 
L 933.379896 393.938544 
L 934.898207 389.426397 
L 932.131603 388.6151 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #29d46e"/>
    <path d="M 907.501822 423.242701 
L 910.248785 424.361801 
L 911.755406 420.324509 
L 909.00819 419.219297 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00acc4"/>
    <path d="M 790.065294 356.736859 
L 792.744764 360.395112 
L 794.260862 358.607834 
L 791.582887 355.010106 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a1ec86"/>
    <path d="M 772.824524 329.438942 
L 775.505893 333.113303 
L 777.031444 331.758555 
L 774.351957 328.149768 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 857.153982 435.389318 
L 859.854811 437.734485 
L 861.350763 434.742008 
L 858.650283 432.429356 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0393f9"/>
    <path d="M 654.285681 207.007688 
L 656.941156 208.351168 
L 658.588268 208.916003 
L 655.935401 207.585764 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d7ccc9"/>
    <path d="M 844.875591 428.000487 
L 847.568087 430.681059 
L 849.065586 427.897886 
L 846.373633 425.254155 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a0e8"/>
    <path d="M 807.306514 383.867871 
L 809.986123 387.361019 
L 811.494806 385.207169 
L 808.816356 381.766951 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #41d973"/>
    <path d="M 747.527954 292.576118 
L 750.212548 296.04841 
L 751.756982 295.372878 
L 749.074852 291.966551 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #beac76"/>
    <path d="M 644.68146 203.054418 
L 647.328541 204.111197 
L 648.985213 204.613608 
L 646.340519 203.563915 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dfd6d4"/>
    <path d="M 704.567903 242.815806 
L 707.249948 245.505618 
L 708.839245 245.773702 
L 706.160263 243.132068 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #977a74"/>
    <path d="M 893.276825 434.66267 
L 896.010449 436.066271 
L 897.511047 432.357253 
L 894.777297 430.973029 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0296fc"/>
    <path d="M 917.524932 413.074136 
L 920.281364 414.029256 
L 921.792711 409.784358 
L 919.036007 408.838425 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00be8f"/>
    <path d="M 923.305437 405.482342 
L 926.066742 406.363657 
L 927.581065 402.000792 
L 924.81949 401.126037 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #01cc66"/>
    <path d="M 866.759774 439.135257 
L 869.468623 441.213184 
L 870.964288 438.054012 
L 868.255654 436.004971 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #078bf1"/>
    <path d="M 889.048044 436.77656 
L 891.777582 438.277473 
L 893.276825 434.66267 
L 890.547207 433.182715 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0393f9"/>
    <path d="M 666.565725 213.47329 
L 669.230666 215.17854 
L 670.864538 215.760736 
L 668.202433 214.077273 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cbbcb9"/>
    <path d="M 787.385402 353.05859 
L 790.065294 356.736859 
L 791.582887 355.010106 
L 788.904553 351.392853 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #adef89"/>
    <path d="M 681.537607 223.378537 
L 684.211317 225.497808 
L 685.827922 226.023887 
L 683.157228 223.937155 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b9a5a1"/>
    <path d="M 770.142557 325.765238 
L 772.824524 329.438942 
L 774.351957 328.149768 
L 771.671938 324.541707 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f8f695"/>
    <path d="M 897.511047 432.357253 
L 900.248919 433.666801 
L 901.750975 429.866948 
L 899.012941 428.575011 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #009cf4"/>
    <path d="M 804.62695 380.334654 
L 807.306514 383.867871 
L 808.816356 381.766951 
L 806.138007 378.287496 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #4ddb75"/>
    <path d="M 873.67604 440.024023 
L 876.391068 441.913879 
L 877.887187 438.622818 
L 875.172277 436.759391 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0888ee"/>
    <path d="M 744.842984 289.133134 
L 747.527954 292.576118 
L 749.074852 291.966551 
L 746.392402 288.58891 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b8a473"/>
    <path d="M 847.568087 430.681059 
L 850.262541 433.288031 
L 851.759526 430.469437 
L 849.065586 427.897886 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #009cf4"/>
    <path d="M 911.755406 420.324509 
L 914.506964 421.363732 
L 916.015238 417.250137 
L 913.263432 416.22244 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b0b9"/>
    <path d="M 884.824396 438.693024 
L 887.550032 440.294137 
L 889.048044 436.77656 
L 886.322385 435.197797 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #068ef4"/>
    <path d="M 707.249948 245.505618 
L 709.932855 248.262306 
L 711.519103 248.480644 
L 708.839245 245.773702 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #93756e"/>
    <path d="M 929.096693 397.586432 
L 931.862783 398.405124 
L 933.379896 393.938544 
L 930.613562 393.123531 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1dd26c"/>
    <path d="M 901.750975 429.866948 
L 904.493236 431.086063 
L 905.99683 427.199114 
L 903.254383 425.995666 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a0e8"/>
    <path d="M 742.157684 285.72224 
L 744.842984 289.133134 
L 746.392402 288.58891 
L 743.709677 285.242671 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b29c6f"/>
    <path d="M 859.854811 437.734485 
L 862.558253 440.001152 
L 864.053874 436.977766 
L 861.350763 434.742008 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #068ef4"/>
    <path d="M 801.947338 376.764047 
L 804.62695 380.334654 
L 806.138007 378.287496 
L 803.459666 374.771431 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #5ddf79"/>
    <path d="M 767.459981 322.09513 
L 770.142557 325.765238 
L 771.671938 324.541707 
L 768.991375 320.937247 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f2ee92"/>
    <path d="M 784.705036 349.363188 
L 787.385402 353.05859 
L 788.904553 351.392853 
L 786.225808 347.758897 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b9f18b"/>
    <path d="M 709.932855 248.262306 
L 712.616509 251.083737 
L 714.199728 251.250815 
L 711.519103 248.480644 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8f7069"/>
    <path d="M 739.472107 282.346193 
L 742.157684 285.72224 
L 743.709677 285.242671 
L 741.026728 281.930521 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ac956c"/>
    <path d="M 850.262541 433.288031 
L 852.959108 435.819685 
L 854.455607 432.96712 
L 851.759526 430.469437 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0098fe"/>
    <path d="M 880.605533 440.40692 
L 883.327472 442.110741 
L 884.824396 438.693024 
L 882.102501 437.01275 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0888ee"/>
    <path d="M 905.99683 427.199114 
L 908.743595 428.331764 
L 910.248785 424.361801 
L 907.501822 423.242701 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a6d7"/>
    <path d="M 712.616509 251.083737 
L 715.300803 253.967712 
L 716.881013 254.082073 
L 714.199728 251.250815 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #896861"/>
    <path d="M 736.786313 279.00772 
L 739.472107 282.346193 
L 741.026728 281.930521 
L 738.34361 278.655121 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a68d69"/>
    <path d="M 799.267592 373.15877 
L 801.947338 376.764047 
L 803.459666 374.771431 
L 800.781249 371.221428 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #69e17b"/>
    <path d="M 684.211317 225.497808 
L 686.886921 227.700215 
L 688.500493 228.191889 
L 685.827922 226.023887 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b7a39f"/>
    <path d="M 921.792711 409.784358 
L 924.553783 410.67213 
L 926.066742 406.363657 
L 923.305437 405.482342 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c47d"/>
    <path d="M 734.100363 275.709517 
L 736.786313 279.00772 
L 738.34361 278.655121 
L 735.660385 275.419097 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a08566"/>
    <path d="M 715.300803 253.967712 
L 717.985628 256.911969 
L 719.562855 256.972213 
L 716.881013 254.082073 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #85635c"/>
    <path d="M 869.468623 441.213184 
L 872.180582 443.210322 
L 873.67604 440.024023 
L 870.964288 438.054012 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0888ee"/>
    <path d="M 916.015238 417.250137 
L 918.771442 418.214268 
L 920.281364 414.029256 
L 917.524932 413.074136 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b6a7"/>
    <path d="M 764.776794 318.431562 
L 767.459981 322.09513 
L 768.991375 320.937247 
L 766.310264 317.339265 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eae48e"/>
    <path d="M 782.02415 345.653556 
L 784.705036 349.363188 
L 786.225808 347.758897 
L 783.546607 344.111085 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c9f48e"/>
    <path d="M 827.250618 412.916896 
L 829.935331 416.041511 
L 831.437228 413.558668 
L 828.753372 410.476472 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00bc94"/>
    <path d="M 829.935331 416.041511 
L 832.621089 419.103129 
L 834.122171 416.579023 
L 831.437228 413.558668 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b6a7"/>
    <path d="M 824.566814 409.731512 
L 827.250618 412.916896 
L 828.753372 410.476472 
L 826.070469 407.334626 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c088"/>
    <path d="M 731.414328 272.454242 
L 734.100363 275.709517 
L 735.660385 275.419097 
L 732.97712 272.225042 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9a7e62"/>
    <path d="M 717.985628 256.911969 
L 720.670884 259.914183 
L 722.245155 259.918972 
L 719.562855 256.972213 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #805c54"/>
    <path d="M 927.581065 402.000792 
L 930.346941 402.823122 
L 931.862783 398.405124 
L 929.096693 397.586432 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0dcf69"/>
    <path d="M 832.621089 419.103129 
L 835.30803 422.099591 
L 836.808336 419.53541 
L 834.122171 416.579023 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b0b9"/>
    <path d="M 821.88379 406.487645 
L 824.566814 409.731512 
L 826.070469 407.334626 
L 823.388389 404.135379 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c677"/>
    <path d="M 862.558253 440.001152 
L 865.264469 442.18792 
L 866.759774 439.135257 
L 864.053874 436.977766 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #078bf1"/>
    <path d="M 728.728281 269.244516 
L 731.414328 272.454242 
L 732.97712 272.225042 
L 730.293886 269.075512 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #967960"/>
    <path d="M 656.941156 208.351168 
L 659.599924 209.791488 
L 661.244377 210.34116 
L 658.588268 208.916003 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d5c9c7"/>
    <path d="M 720.670884 259.914183 
L 723.356473 262.971977 
L 724.92782 262.920031 
L 722.245155 259.918972 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #846257"/>
    <path d="M 852.959108 435.819685 
L 855.657947 438.274378 
L 857.153982 435.389318 
L 854.455607 432.96712 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0393f9"/>
    <path d="M 669.230666 215.17854 
L 671.898253 216.975258 
L 673.529253 217.533732 
L 670.864538 215.760736 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c9bab7"/>
    <path d="M 637.734025 200.823604 
L 640.375258 201.682389 
L 642.038333 202.098159 
L 639.399308 201.242606 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e3dbd9"/>
    <path d="M 726.042301 266.082917 
L 728.728281 269.244516 
L 730.293886 269.075512 
L 727.610759 265.973018 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #90715d"/>
    <path d="M 723.356473 262.971977 
L 726.042301 266.082917 
L 727.610759 265.973018 
L 724.92782 262.920031 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8a695a"/>
    <path d="M 876.391068 441.913879 
L 879.109533 443.722528 
L 880.605533 440.40692 
L 877.887187 438.622818 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0a86ec"/>
    <path d="M 835.30803 422.099591 
L 837.996297 425.0288 
L 839.495864 422.425769 
L 836.808336 419.53541 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00acc4"/>
    <path d="M 819.201418 403.187646 
L 821.88379 406.487645 
L 823.388389 404.135379 
L 820.707008 400.881042 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #01cc66"/>
    <path d="M 796.58763 369.521588 
L 799.267592 373.15877 
L 800.781249 371.221428 
L 798.102675 367.640201 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #75e37d"/>
    <path d="M 910.248785 424.361801 
L 913.000145 425.412292 
L 914.506964 421.363732 
L 911.755406 420.324509 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00aacb"/>
    <path d="M 762.092996 314.777478 
L 764.776794 318.431562 
L 766.310264 317.339265 
L 763.628606 313.75064 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e4dc8a"/>
    <path d="M 816.519575 399.833922 
L 819.201418 403.187646 
L 820.707008 400.881042 
L 818.026205 397.573986 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0dcf69"/>
    <path d="M 891.777582 438.277473 
L 894.511147 439.699838 
L 896.010449 436.066271 
L 893.276825 434.66267 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0490f6"/>
    <path d="M 837.996297 425.0288 
L 840.686037 427.888728 
L 842.184901 425.248104 
L 839.495864 422.425769 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a6d7"/>
    <path d="M 896.010449 436.066271 
L 898.748223 437.392908 
L 900.248919 433.666801 
L 897.511047 432.357253 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0296fc"/>
    <path d="M 779.342703 341.932624 
L 782.02415 345.653556 
L 783.546607 344.111085 
L 780.86691 340.452287 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d5f791"/>
    <path d="M 647.328541 204.111197 
L 649.979426 205.268201 
L 651.63365 205.761666 
L 648.985213 204.613608 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ddd3d1"/>
    <path d="M 887.550032 440.294137 
L 890.279562 441.815301 
L 891.777582 438.277473 
L 889.048044 436.77656 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #078bf1"/>
    <path d="M 686.886921 227.700215 
L 689.56428 229.984203 
L 691.174805 230.439645 
L 688.500493 228.191889 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b39e99"/>
    <path d="M 813.838145 396.428941 
L 816.519575 399.833922 
L 818.026205 397.573986 
L 815.345863 394.216634 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #19d16b"/>
    <path d="M 900.248919 433.666801 
L 902.991054 434.901148 
L 904.493236 431.086063 
L 901.750975 429.866948 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #009afa"/>
    <path d="M 840.686037 427.888728 
L 843.377397 430.677416 
L 844.875591 428.000487 
L 842.184901 425.248104 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a2e2"/>
    <path d="M 793.907378 365.855303 
L 796.58763 369.521588 
L 798.102675 367.640201 
L 795.423869 364.0305 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #85e781"/>
    <path d="M 855.657947 438.274378 
L 858.359218 440.650537 
L 859.854811 437.734485 
L 857.153982 435.389318 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #068ef4"/>
    <path d="M 920.281364 414.029256 
L 923.042239 414.923378 
L 924.553783 410.67213 
L 921.792711 409.784358 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00be8f"/>
    <path d="M 759.408595 311.135824 
L 762.092996 314.777478 
L 763.628606 313.75064 
L 760.946407 310.174252 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ded587"/>
    <path d="M 883.327472 442.110741 
L 886.053161 443.7334 
L 887.550032 440.294137 
L 884.824396 438.693024 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0a86ec"/>
    <path d="M 811.157014 392.975225 
L 813.838145 396.428941 
L 815.345863 394.216634 
L 812.665872 390.811468 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #25d36d"/>
    <path d="M 926.066742 406.363657 
L 928.832435 407.189583 
L 930.346941 402.823122 
L 927.581065 402.000792 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #01cc66"/>
    <path d="M 872.180582 443.210322 
L 874.895814 445.125525 
L 876.391068 441.913879 
L 873.67604 440.024023 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0b83e9"/>
    <path d="M 865.264469 442.18792 
L 867.973622 444.293469 
L 869.468623 441.213184 
L 866.759774 439.135257 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0a86ec"/>
    <path d="M 904.493236 431.086063 
L 907.239859 432.231914 
L 908.743595 428.331764 
L 905.99683 427.199114 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a0e8"/>
    <path d="M 914.506964 421.363732 
L 917.262985 422.33669 
L 918.771442 418.214268 
L 916.015238 417.250137 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b0b9"/>
    <path d="M 776.660663 338.203341 
L 779.342703 341.932624 
L 780.86691 340.452287 
L 778.186681 336.785391 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e5fa94"/>
    <path d="M 843.377397 430.677416 
L 846.070531 433.392976 
L 847.568087 430.681059 
L 844.875591 428.000487 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #009eef"/>
    <path d="M 791.226766 362.162755 
L 793.907378 365.855303 
L 795.423869 364.0305 
L 792.744764 360.395112 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #91e983"/>
    <path d="M 808.476074 389.475347 
L 811.157014 392.975225 
L 812.665872 390.811468 
L 809.986123 387.361019 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #31d670"/>
    <path d="M 671.898253 216.975258 
L 674.568337 218.862329 
L 676.196432 219.395171 
L 673.529253 217.533732 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c7b7b4"/>
    <path d="M 689.56428 229.984203 
L 692.243256 232.348129 
L 693.850725 232.765553 
L 691.174805 230.439645 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #af9994"/>
    <path d="M 756.723606 307.509541 
L 759.408595 311.135824 
L 760.946407 310.174252 
L 758.26368 306.612973 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d8cd84"/>
    <path d="M 879.109533 443.722528 
L 881.831596 445.448995 
L 883.327472 442.110741 
L 880.605533 440.40692 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0b83e9"/>
    <path d="M 846.070531 433.392976 
L 848.765594 436.033589 
L 850.262541 433.288031 
L 847.568087 430.681059 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0098fe"/>
    <path d="M 858.359218 440.650537 
L 861.063083 442.946666 
L 862.558253 440.001152 
L 859.854811 437.734485 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0888ee"/>
    <path d="M 659.599924 209.791488 
L 662.261833 211.327927 
L 663.903579 211.860526 
L 661.244377 210.34116 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d3c7c4"/>
    <path d="M 908.743595 428.331764 
L 911.494809 429.393254 
L 913.000145 425.412292 
L 910.248785 424.361801 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a4dc"/>
    <path d="M 773.978 334.468673 
L 776.660663 338.203341 
L 778.186681 336.785391 
L 775.505893 333.113303 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1fc96"/>
    <path d="M 805.795222 385.931936 
L 808.476074 389.475347 
L 809.986123 387.361019 
L 807.306514 383.867871 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #3dd872"/>
    <path d="M 788.545729 358.446818 
L 791.226766 362.162755 
L 792.744764 360.395112 
L 790.065294 356.736859 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9deb85"/>
    <path d="M 754.038048 303.90156 
L 756.723606 307.509541 
L 758.26368 306.612973 
L 755.580444 303.069672 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d0c380"/>
    <path d="M 924.553783 410.67213 
L 927.319325 411.501609 
L 928.832435 407.189583 
L 926.066742 406.363657 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c47d"/>
    <path d="M 918.771442 418.214268 
L 921.53216 419.114626 
L 923.042239 414.923378 
L 920.281364 414.029256 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b6a7"/>
    <path d="M 848.765594 436.033589 
L 851.462744 438.597511 
L 852.959108 435.819685 
L 850.262541 433.288031 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0393f9"/>
    <path d="M 692.243256 232.348129 
L 694.923714 234.790266 
L 696.528123 235.167928 
L 693.850725 232.765553 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ab938e"/>
    <path d="M 867.973622 444.293469 
L 870.685877 446.316551 
L 872.180582 443.210322 
L 869.468623 441.213184 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0b83e9"/>
    <path d="M 803.11436 382.347668 
L 805.795222 385.931936 
L 807.306514 383.867871 
L 804.62695 380.334654 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #4ddb75"/>
    <path d="M 894.511147 439.699838 
L 897.248891 441.043028 
L 898.748223 437.392908 
L 896.010449 436.066271 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #068ef4"/>
    <path d="M 890.279562 441.815301 
L 893.013141 443.2558 
L 894.511147 439.699838 
L 891.777582 438.277473 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0888ee"/>
    <path d="M 640.375258 201.682389 
L 643.020661 202.643649 
L 644.68146 203.054418 
L 642.038333 202.098159 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e3dbd9"/>
    <path d="M 874.895814 445.125525 
L 877.614482 446.957721 
L 879.109533 443.722528 
L 876.391068 441.913879 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0c80e6"/>
    <path d="M 771.294692 330.7316 
L 773.978 334.468673 
L 775.505893 333.113303 
L 772.824524 329.438942 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 898.748223 437.392908 
L 901.490295 438.642042 
L 902.991054 434.901148 
L 900.248919 433.666801 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0393f9"/>
    <path d="M 751.351946 300.314805 
L 754.038048 303.90156 
L 755.580444 303.069672 
L 752.896723 299.547203 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cabb7c"/>
    <path d="M 649.979426 205.268201 
L 652.633964 206.525022 
L 654.285681 207.007688 
L 651.63365 205.761666 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ddd3d1"/>
    <path d="M 913.000145 425.412292 
L 915.756028 426.393885 
L 917.262985 422.33669 
L 914.506964 421.363732 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00aacb"/>
    <path d="M 861.063083 442.946666 
L 863.769707 445.161344 
L 865.264469 442.18792 
L 862.558253 440.001152 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0a86ec"/>
    <path d="M 785.864209 354.710397 
L 788.545729 358.446818 
L 790.065294 356.736859 
L 787.385402 353.05859 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #adef89"/>
    <path d="M 674.568337 218.862329 
L 677.240771 220.838539 
L 678.865931 221.343866 
L 676.196432 219.395171 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c3b2af"/>
    <path d="M 886.053161 443.7334 
L 888.782759 445.274091 
L 890.279562 441.815301 
L 887.550032 440.294137 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0a86ec"/>
    <path d="M 902.991054 434.901148 
L 905.737592 436.05984 
L 907.239859 432.231914 
L 904.493236 431.086063 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #009afa"/>
    <path d="M 800.433395 378.725266 
L 803.11436 382.347668 
L 804.62695 380.334654 
L 801.947338 376.764047 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #59de78"/>
    <path d="M 851.462744 438.597511 
L 854.162141 441.08307 
L 855.657947 438.274378 
L 852.959108 435.819685 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #068ef4"/>
    <path d="M 694.923714 234.790266 
L 697.605523 237.308803 
L 699.206868 237.645004 
L 696.528123 235.167928 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a78e89"/>
    <path d="M 748.665334 296.752185 
L 751.351946 300.314805 
L 752.896723 299.547203 
L 750.212548 296.04841 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c4b379"/>
    <path d="M 828.432762 418.464139 
L 831.11943 421.564792 
L 832.621089 419.103129 
L 829.935331 416.041511 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b4ac"/>
    <path d="M 825.747097 415.299397 
L 828.432762 418.464139 
L 829.935331 416.041511 
L 827.250618 412.916896 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b8a0"/>
    <path d="M 768.610725 326.995116 
L 771.294692 330.7316 
L 772.824524 329.438942 
L 770.142557 325.765238 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f8f695"/>
    <path d="M 831.11943 421.564792 
L 833.807243 424.599164 
L 835.30803 422.099591 
L 832.621089 419.103129 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00aebf"/>
    <path d="M 881.831596 445.448995 
L 884.557417 447.09238 
L 886.053161 443.7334 
L 883.327472 442.110741 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0c80e6"/>
    <path d="M 823.0623 412.072827 
L 825.747097 415.299397 
L 827.250618 412.916896 
L 824.566814 409.731512 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00be8f"/>
    <path d="M 833.807243 424.599164 
L 836.496345 427.565127 
L 837.996297 425.0288 
L 835.30803 422.099591 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a8d0"/>
    <path d="M 783.182155 350.956427 
L 785.864209 354.710397 
L 787.385402 353.05859 
L 784.705036 349.363188 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b9f18b"/>
    <path d="M 820.378238 408.786752 
L 823.0623 412.072827 
L 824.566814 409.731512 
L 821.88379 406.487645 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c47d"/>
    <path d="M 907.239859 432.231914 
L 909.99098 433.304127 
L 911.494809 429.393254 
L 908.743595 428.331764 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #009eef"/>
    <path d="M 662.261833 211.327927 
L 664.926731 212.959653 
L 666.565725 213.47329 
L 663.903579 211.860526 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d1c4c1"/>
    <path d="M 923.042239 414.923378 
L 925.807665 415.756361 
L 927.319325 411.501609 
L 924.553783 410.67213 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00be8f"/>
    <path d="M 797.752241 375.067499 
L 800.433395 378.725266 
L 801.947338 376.764047 
L 799.267592 373.15877 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #65e07a"/>
    <path d="M 745.978248 293.216593 
L 748.665334 296.752185 
L 750.212548 296.04841 
L 747.527954 292.576118 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #beac76"/>
    <path d="M 697.605523 237.308803 
L 700.288552 239.901851 
L 701.886836 240.194937 
L 699.206868 237.645004 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a38984"/>
    <path d="M 836.496345 427.565127 
L 839.186884 430.460622 
L 840.686037 427.888728 
L 837.996297 425.0288 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a4dc"/>
    <path d="M 870.685877 446.316551 
L 873.401398 448.255998 
L 874.895814 445.125525 
L 872.180582 443.210322 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0e7ee4"/>
    <path d="M 917.262985 422.33669 
L 920.023587 423.243167 
L 921.53216 419.114626 
L 918.771442 418.214268 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b0b9"/>
    <path d="M 817.694783 405.443558 
L 820.378238 408.786752 
L 821.88379 406.487645 
L 819.201418 403.187646 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00cb6b"/>
    <path d="M 854.162141 441.08307 
L 856.863948 443.488669 
L 858.359218 440.650537 
L 855.657947 438.274378 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0888ee"/>
    <path d="M 863.769707 445.161344 
L 866.479255 447.293227 
L 867.973622 444.293469 
L 865.264469 442.18792 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0c80e6"/>
    <path d="M 633.428208 199.74799 
L 636.067217 200.505668 
L 637.734025 200.823604 
L 635.097108 200.067368 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e7e0df"/>
    <path d="M 765.926088 323.26222 
L 768.610725 326.995116 
L 770.142557 325.765238 
L 767.459981 322.09513 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f2ee92"/>
    <path d="M 839.186884 430.460622 
L 841.879011 433.28366 
L 843.377397 430.677416 
L 840.686037 427.888728 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a0e8"/>
    <path d="M 815.011811 402.045691 
L 817.694783 405.443558 
L 819.201418 403.187646 
L 816.519575 399.833922 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #09ce68"/>
    <path d="M 677.240771 220.838539 
L 679.915407 222.902576 
L 681.537607 223.378537 
L 678.865931 221.343866 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c1b0ac"/>
    <path d="M 743.290732 289.7109 
L 745.978248 293.216593 
L 747.527954 292.576118 
L 744.842984 289.133134 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b6a272"/>
    <path d="M 877.614482 446.957721 
L 880.33675 448.705914 
L 881.831596 445.448995 
L 879.109533 443.722528 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0e7ee4"/>
    <path d="M 795.070814 371.377178 
L 797.752241 375.067499 
L 799.267592 373.15877 
L 796.58763 369.521588 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #75e37d"/>
    <path d="M 780.49952 347.187871 
L 783.182155 350.956427 
L 784.705036 349.363188 
L 782.02415 345.653556 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c9f48e"/>
    <path d="M 700.288552 239.901851 
L 702.972675 242.56744 
L 704.567903 242.815806 
L 701.886836 240.194937 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9f847e"/>
    <path d="M 911.494809 429.393254 
L 914.250603 430.383287 
L 915.756028 426.393885 
L 913.000145 425.412292 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a4dc"/>
    <path d="M 812.329204 398.595655 
L 815.011811 402.045691 
L 816.519575 399.833922 
L 813.838145 396.428941 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #15d06a"/>
    <path d="M 841.879011 433.28366 
L 844.572879 436.032325 
L 846.070531 433.392976 
L 843.377397 430.677416 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #009afa"/>
    <path d="M 740.602835 286.237956 
L 743.290732 289.7109 
L 744.842984 289.133134 
L 742.157684 285.72224 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b09a6e"/>
    <path d="M 893.013141 443.2558 
L 895.750922 444.614995 
L 897.248891 441.043028 
L 894.511147 439.699838 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0888ee"/>
    <path d="M 897.248891 441.043028 
L 899.990963 442.306491 
L 901.490295 438.642042 
L 898.748223 437.392908 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #068ef4"/>
    <path d="M 763.240777 319.53592 
L 765.926088 323.26222 
L 767.459981 322.09513 
L 764.776794 318.431562 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eae48e"/>
    <path d="M 856.863948 443.488669 
L 859.56833 445.81279 
L 861.063083 442.946666 
L 858.359218 440.650537 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0a86ec"/>
    <path d="M 888.782759 445.274091 
L 891.516423 446.732083 
L 893.013141 443.2558 
L 890.279562 441.815301 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0b83e9"/>
    <path d="M 652.633964 206.525022 
L 655.292 207.881141 
L 656.941156 208.351168 
L 654.285681 207.007688 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dbd1cf"/>
    <path d="M 702.972675 242.56744 
L 705.657767 245.303526 
L 707.249948 245.505618 
L 704.567903 242.815806 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9b7f79"/>
    <path d="M 809.646847 395.096012 
L 812.329204 398.595655 
L 813.838145 396.428941 
L 811.157014 392.975225 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #21d36d"/>
    <path d="M 901.490295 438.642042 
L 904.236808 439.813206 
L 905.737592 436.05984 
L 902.991054 434.901148 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0393f9"/>
    <path d="M 737.914613 282.800582 
L 740.602835 286.237956 
L 742.157684 285.72224 
L 739.472107 282.346193 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #aa926b"/>
    <path d="M 643.020661 202.643649 
L 645.670081 203.707197 
L 647.328541 204.111197 
L 644.68146 203.054418 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e3dbd9"/>
    <path d="M 844.572879 436.032325 
L 847.268648 438.704771 
L 848.765594 436.033589 
L 846.070531 433.392976 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0296fc"/>
    <path d="M 792.38904 367.657156 
L 795.070814 371.377178 
L 796.58763 369.521588 
L 793.907378 365.855303 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #81e680"/>
    <path d="M 921.53216 419.114626 
L 924.297506 419.951066 
L 925.807665 415.756361 
L 923.042239 414.923378 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b6a7"/>
    <path d="M 777.816263 343.407714 
L 780.49952 347.187871 
L 782.02415 345.653556 
L 779.342703 341.932624 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d5f791"/>
    <path d="M 866.479255 447.293227 
L 869.191894 449.341047 
L 870.685877 446.316551 
L 867.973622 444.293469 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0e7ee4"/>
    <path d="M 884.557417 447.09238 
L 887.287158 448.651859 
L 888.782759 445.274091 
L 886.053161 443.7334 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0e7ee4"/>
    <path d="M 705.657767 245.303526 
L 708.343708 248.107992 
L 709.932855 248.262306 
L 707.249948 245.505618 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #977a74"/>
    <path d="M 873.401398 448.255998 
L 876.120353 450.110719 
L 877.614482 446.957721 
L 874.895814 445.125525 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0f7be1"/>
    <path d="M 735.226125 279.401571 
L 737.914613 282.800582 
L 739.472107 282.346193 
L 736.786313 279.00772 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a48b68"/>
    <path d="M 664.926731 212.959653 
L 667.594465 214.685734 
L 669.230666 215.17854 
L 666.565725 213.47329 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cfc2bf"/>
    <path d="M 679.915407 222.902576 
L 682.5921 225.053033 
L 684.211317 225.497808 
L 681.537607 223.378537 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bdaba7"/>
    <path d="M 915.756028 426.393885 
L 918.516558 427.306361 
L 920.023587 423.243167 
L 917.262985 422.33669 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00aacb"/>
    <path d="M 806.96463 391.549377 
L 809.646847 395.096012 
L 811.157014 392.975225 
L 808.476074 389.475347 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2dd56f"/>
    <path d="M 905.737592 436.05984 
L 908.488674 437.142493 
L 909.99098 433.304127 
L 907.239859 432.231914 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0098fe"/>
    <path d="M 760.554796 315.819223 
L 763.240777 319.53592 
L 764.776794 318.431562 
L 762.092996 314.777478 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e4dc8a"/>
    <path d="M 847.268648 438.704771 
L 849.966475 441.299227 
L 851.462744 438.597511 
L 848.765594 436.033589 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0490f6"/>
    <path d="M 732.537437 276.043684 
L 735.226125 279.401571 
L 736.786313 279.00772 
L 734.100363 275.709517 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9e8365"/>
    <path d="M 708.343708 248.107992 
L 711.030382 250.978653 
L 712.616509 251.083737 
L 709.932855 248.262306 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #91726c"/>
    <path d="M 789.706848 363.910321 
L 792.38904 367.657156 
L 793.907378 365.855303 
L 791.226766 362.162755 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8de882"/>
    <path d="M 859.56833 445.81279 
L 862.275453 448.053987 
L 863.769707 445.161344 
L 861.063083 442.946666 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0c80e6"/>
    <path d="M 729.848621 272.729641 
L 732.537437 276.043684 
L 734.100363 275.709517 
L 731.414328 272.454242 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #987b61"/>
    <path d="M 711.030382 250.978653 
L 713.717674 253.913253 
L 715.300803 253.967712 
L 712.616509 251.083737 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8d6d66"/>
    <path d="M 775.132352 339.618961 
L 777.816263 343.407714 
L 779.342703 341.932624 
L 776.660663 338.203341 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e5fa94"/>
    <path d="M 880.33675 448.705914 
L 883.062782 450.369187 
L 884.557417 447.09238 
L 881.831596 445.448995 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0f7be1"/>
    <path d="M 804.28245 387.958419 
L 806.96463 391.549377 
L 808.476074 389.475347 
L 805.795222 385.931936 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #3dd872"/>
    <path d="M 727.159754 269.462128 
L 729.848621 272.729641 
L 731.414328 272.454242 
L 728.728281 269.244516 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #92735e"/>
    <path d="M 713.717674 253.913253 
L 716.405477 256.909475 
L 717.985628 256.911969 
L 715.300803 253.967712 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #87655e"/>
    <path d="M 909.99098 433.304127 
L 912.746733 434.302398 
L 914.250603 430.383287 
L 911.494809 429.393254 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #009eef"/>
    <path d="M 724.470917 266.243785 
L 727.159754 269.462128 
L 728.728281 269.244516 
L 726.042301 266.082917 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8c6c5b"/>
    <path d="M 757.868153 312.115138 
L 760.554796 315.819223 
L 762.092996 314.777478 
L 759.408595 311.135824 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dcd286"/>
    <path d="M 716.405477 256.909475 
L 719.093685 259.964939 
L 720.670884 259.914183 
L 717.985628 256.911969 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #836059"/>
    <path d="M 721.782197 263.077207 
L 724.470917 266.243785 
L 726.042301 266.082917 
L 723.356473 262.971977 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #886759"/>
    <path d="M 719.093685 259.964939 
L 721.782197 263.077207 
L 723.356473 262.971977 
L 720.670884 259.914183 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #825f56"/>
    <path d="M 849.966475 441.299227 
L 852.666526 443.813998 
L 854.162141 441.08307 
L 851.462744 438.597511 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #078bf1"/>
    <path d="M 682.5921 225.053033 
L 685.270704 227.288409 
L 686.886921 227.700215 
L 684.211317 225.497808 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bba8a4"/>
    <path d="M 787.024174 360.139598 
L 789.706848 363.910321 
L 791.226766 362.162755 
L 788.545729 358.446818 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9deb85"/>
    <path d="M 801.600208 384.325857 
L 804.28245 387.958419 
L 805.795222 385.931936 
L 803.11436 382.347668 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #49db75"/>
    <path d="M 920.023587 423.243167 
L 922.78889 424.083014 
L 924.297506 419.951066 
L 921.53216 419.114626 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b0b9"/>
    <path d="M 869.191894 449.341047 
L 871.907792 451.303616 
L 873.401398 448.255998 
L 870.685877 446.316551 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1078de"/>
    <path d="M 772.447758 335.824637 
L 775.132352 339.618961 
L 776.660663 338.203341 
L 773.978 334.468673 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1fc96"/>
    <path d="M 636.067217 200.505668 
L 638.710612 201.367563 
L 640.375258 201.682389 
L 637.734025 200.823604 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e7e0df"/>
    <path d="M 895.750922 444.614995 
L 898.493059 445.892319 
L 899.990963 442.306491 
L 897.248891 441.043028 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0a86ec"/>
    <path d="M 655.292 207.881141 
L 657.953381 209.335928 
L 659.599924 209.791488 
L 656.941156 208.351168 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d9cecc"/>
    <path d="M 755.180863 308.426668 
L 757.868153 312.115138 
L 759.408595 311.135824 
L 756.723606 307.509541 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d6cb83"/>
    <path d="M 876.120353 450.110719 
L 878.842909 451.879701 
L 880.33675 448.705914 
L 877.614482 446.957721 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1078de"/>
    <path d="M 667.594465 214.685734 
L 670.264882 216.50513 
L 671.898253 216.975258 
L 669.230666 215.17854 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cdbfbc"/>
    <path d="M 891.516423 446.732083 
L 894.25431 448.10672 
L 895.750922 444.614995 
L 893.013141 443.2558 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0c80e6"/>
    <path d="M 826.929481 420.825497 
L 829.617155 423.962923 
L 831.11943 421.564792 
L 828.432762 418.464139 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b0b9"/>
    <path d="M 862.275453 448.053987 
L 864.985486 450.210896 
L 866.479255 447.293227 
L 863.769707 445.161344 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0f7be1"/>
    <path d="M 829.617155 423.962923 
L 832.305935 427.033009 
L 833.807243 424.599164 
L 831.11943 421.564792 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00acc4"/>
    <path d="M 899.990963 442.306491 
L 902.737511 443.489749 
L 904.236808 439.813206 
L 901.490295 438.642042 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #078bf1"/>
    <path d="M 824.242771 417.622955 
L 826.929481 420.825497 
L 828.432762 418.464139 
L 825.747097 415.299397 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b6a7"/>
    <path d="M 914.250603 430.383287 
L 917.011104 431.301636 
L 918.516558 427.306361 
L 915.756028 426.393885 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a4dc"/>
    <path d="M 852.666526 443.813998 
L 855.368963 446.247463 
L 856.863948 443.488669 
L 854.162141 441.08307 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0a86ec"/>
    <path d="M 832.305935 427.033009 
L 834.995967 430.033597 
L 836.496345 427.565127 
L 833.807243 424.599164 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a6d7"/>
    <path d="M 821.556888 414.357589 
L 824.242771 417.622955 
L 825.747097 415.299397 
L 823.0623 412.072827 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00bc94"/>
    <path d="M 798.917811 380.654458 
L 801.600208 384.325857 
L 803.11436 382.347668 
L 800.433395 378.725266 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #55dd77"/>
    <path d="M 887.287158 448.651859 
L 890.02098 450.126687 
L 891.516423 446.732083 
L 888.782759 445.274091 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0f7be1"/>
    <path d="M 834.995967 430.033597 
L 837.687401 432.962601 
L 839.186884 430.460622 
L 836.496345 427.565127 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a2e2"/>
    <path d="M 784.340959 356.347944 
L 787.024174 360.139598 
L 788.545729 358.446818 
L 785.864209 354.710397 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a9ee88"/>
    <path d="M 645.670081 203.707197 
L 648.323367 204.872729 
L 649.979426 205.268201 
L 647.328541 204.111197 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e1d9d7"/>
    <path d="M 818.871697 411.031756 
L 821.556888 414.357589 
L 823.0623 412.072827 
L 820.378238 408.786752 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c382"/>
    <path d="M 904.236808 439.813206 
L 906.987906 440.906006 
L 908.488674 437.142493 
L 905.737592 436.05984 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0490f6"/>
    <path d="M 685.270704 227.288409 
L 687.951078 229.607113 
L 689.56428 229.984203 
L 686.886921 227.700215 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b7a39f"/>
    <path d="M 769.762459 332.027781 
L 772.447758 335.824637 
L 773.978 334.468673 
L 771.294692 330.7316 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 752.492948 304.756811 
L 755.180863 308.426668 
L 756.723606 307.509541 
L 754.038048 303.90156 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d0c380"/>
    <path d="M 837.687401 432.962601 
L 840.380389 435.818004 
L 841.879011 433.28366 
L 839.186884 430.460622 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #009cf4"/>
    <path d="M 816.187068 407.647876 
L 818.871697 411.031756 
L 820.378238 408.786752 
L 817.694783 405.443558 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c970"/>
    <path d="M 883.062782 450.369187 
L 885.792742 451.946701 
L 887.287158 448.651859 
L 884.557417 447.09238 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1078de"/>
    <path d="M 796.23517 376.947034 
L 798.917811 380.654458 
L 800.433395 378.725266 
L 797.752241 375.067499 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #65e07a"/>
    <path d="M 840.380389 435.818004 
L 843.075088 438.597862 
L 844.572879 436.032325 
L 841.879011 433.28366 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0098fe"/>
    <path d="M 855.368963 446.247463 
L 858.073954 448.59808 
L 859.56833 445.81279 
L 856.863948 443.488669 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0c80e6"/>
    <path d="M 908.488674 437.142493 
L 911.244438 438.148792 
L 912.746733 434.302398 
L 909.99098 433.304127 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0098fe"/>
    <path d="M 813.502878 404.208428 
L 816.187068 407.647876 
L 817.694783 405.443558 
L 815.011811 402.045691 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #05cd67"/>
    <path d="M 871.907792 451.303616 
L 874.627119 453.179824 
L 876.120353 450.110719 
L 873.401398 448.255998 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1276dc"/>
    <path d="M 918.516558 427.306361 
L 921.281857 428.149562 
L 922.78889 424.083014 
L 920.023587 423.243167 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00aacb"/>
    <path d="M 781.657152 352.538348 
L 784.340959 356.347944 
L 785.864209 354.710397 
L 783.182155 350.956427 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b9f18b"/>
    <path d="M 749.804435 301.108552 
L 752.492948 304.756811 
L 754.038048 303.90156 
L 751.351946 300.314805 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c8b97b"/>
    <path d="M 864.985486 450.210896 
L 867.698599 452.282228 
L 869.191894 449.341047 
L 866.479255 447.293227 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1078de"/>
    <path d="M 767.076441 328.231444 
L 769.762459 332.027781 
L 771.294692 330.7316 
L 768.610725 326.995116 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f8f695"/>
    <path d="M 687.951078 229.607113 
L 690.63308 232.007463 
L 692.243256 232.348129 
L 689.56428 229.984203 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b39e99"/>
    <path d="M 670.264882 216.50513 
L 672.937831 218.416701 
L 674.568337 218.862329 
L 671.898253 216.975258 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cbbcb9"/>
    <path d="M 843.075088 438.597862 
L 845.771658 441.300305 
L 847.268648 438.704771 
L 844.572879 436.032325 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0393f9"/>
    <path d="M 810.819006 400.715954 
L 813.502878 404.208428 
L 815.011811 402.045691 
L 812.329204 398.595655 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #11cf69"/>
    <path d="M 793.552203 373.206443 
L 796.23517 376.947034 
L 797.752241 375.067499 
L 795.070814 371.377178 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #71e37d"/>
    <path d="M 878.842909 451.879701 
L 881.569231 453.56201 
L 883.062782 450.369187 
L 880.33675 448.705914 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1276dc"/>
    <path d="M 747.115357 297.484865 
L 749.804435 301.108552 
L 751.351946 300.314805 
L 748.665334 296.752185 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c2b178"/>
    <path d="M 657.953381 209.335928 
L 660.617951 210.888647 
L 662.261833 211.327927 
L 659.599924 209.791488 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d7ccc9"/>
    <path d="M 912.746733 434.302398 
L 915.507251 435.226489 
L 917.011104 431.301636 
L 914.250603 430.383287 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #009eef"/>
    <path d="M 808.135336 397.173052 
L 810.819006 400.715954 
L 812.329204 398.595655 
L 809.646847 395.096012 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1dd26c"/>
    <path d="M 778.972705 348.713822 
L 781.657152 352.538348 
L 783.182155 350.956427 
L 780.49952 347.187871 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c5f38d"/>
    <path d="M 845.771658 441.300305 
L 848.470259 443.923538 
L 849.966475 441.299227 
L 847.268648 438.704771 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #078bf1"/>
    <path d="M 858.073954 448.59808 
L 860.781669 450.864384 
L 862.275453 448.053987 
L 859.56833 445.81279 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0f7be1"/>
    <path d="M 764.389694 324.438686 
L 767.076441 328.231444 
L 768.610725 326.995116 
L 765.926088 323.26222 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f2ee92"/>
    <path d="M 894.25431 448.10672 
L 896.996577 449.397426 
L 898.493059 445.892319 
L 895.750922 444.614995 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0e7ee4"/>
    <path d="M 690.63308 232.007463 
L 693.316573 234.487692 
L 694.923714 234.790266 
L 692.243256 232.348129 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #af9994"/>
    <path d="M 898.493059 445.892319 
L 901.239703 447.087282 
L 902.737511 443.489749 
L 899.990963 442.306491 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0b83e9"/>
    <path d="M 638.710612 201.367563 
L 641.358241 202.333602 
L 643.020661 202.643649 
L 640.375258 201.682389 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e7e0df"/>
    <path d="M 890.02098 450.126687 
L 892.759043 451.516195 
L 894.25431 448.10672 
L 891.516423 446.732083 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0f7be1"/>
    <path d="M 744.425753 293.888706 
L 747.115357 297.484865 
L 748.665334 296.752185 
L 745.978248 293.216593 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bca975"/>
    <path d="M 790.868833 369.435582 
L 793.552203 373.206443 
L 795.070814 371.377178 
L 792.38904 367.657156 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #7de57f"/>
    <path d="M 902.737511 443.489749 
L 905.488682 444.592396 
L 906.987906 440.906006 
L 904.236808 439.813206 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #078bf1"/>
    <path d="M 805.451758 393.582375 
L 808.135336 397.173052 
L 809.646847 395.096012 
L 806.96463 391.549377 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2dd56f"/>
    <path d="M 867.698599 452.282228 
L 870.414961 454.266778 
L 871.907792 451.303616 
L 869.191894 449.341047 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1373d9"/>
    <path d="M 648.323367 204.872729 
L 650.980362 206.13983 
L 652.633964 206.525022 
L 649.979426 205.268201 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e1d9d7"/>
    <path d="M 848.470259 443.923538 
L 851.171057 446.465842 
L 852.666526 443.813998 
L 849.966475 441.299227 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0a86ec"/>
    <path d="M 874.627119 453.179824 
L 877.350044 454.968641 
L 878.842909 451.879701 
L 876.120353 450.110719 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1373d9"/>
    <path d="M 885.792742 451.946701 
L 888.526796 453.437695 
L 890.02098 450.126687 
L 887.287158 448.651859 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1276dc"/>
    <path d="M 672.937831 218.416701 
L 675.61316 220.419205 
L 677.240771 220.838539 
L 674.568337 218.862329 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c7b7b4"/>
    <path d="M 917.011104 431.301636 
L 919.77644 432.148137 
L 921.281857 428.149562 
L 918.516558 427.306361 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a4dc"/>
    <path d="M 776.287579 344.877407 
L 778.972705 348.713822 
L 780.49952 347.187871 
L 777.816263 343.407714 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d5f791"/>
    <path d="M 693.316573 234.487692 
L 696.001419 237.045946 
L 697.605523 237.308803 
L 694.923714 234.790266 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ab938e"/>
    <path d="M 741.735669 290.323009 
L 744.425753 293.888706 
L 745.978248 293.216593 
L 743.290732 289.7109 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b6a272"/>
    <path d="M 761.702216 320.652574 
L 764.389694 324.438686 
L 765.926088 323.26222 
L 763.240777 319.53592 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eae48e"/>
    <path d="M 906.987906 440.906006 
L 909.743732 441.920118 
L 911.244438 438.148792 
L 908.488674 437.142493 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0490f6"/>
    <path d="M 802.768168 389.946631 
L 805.451758 393.582375 
L 806.96463 391.549377 
L 804.28245 387.958419 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #39d771"/>
    <path d="M 860.781669 450.864384 
L 863.492278 453.044989 
L 864.985486 450.210896 
L 862.275453 448.053987 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1078de"/>
    <path d="M 788.184991 365.637388 
L 790.868833 369.435582 
L 792.38904 367.657156 
L 789.706848 363.910321 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8de882"/>
    <path d="M 739.045156 286.790687 
L 741.735669 290.323009 
L 743.290732 289.7109 
L 740.602835 286.237956 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ae976d"/>
    <path d="M 851.171057 446.465842 
L 853.874218 448.925574 
L 855.368963 446.247463 
L 852.666526 443.813998 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0c80e6"/>
    <path d="M 881.569231 453.56201 
L 884.299489 455.15679 
L 885.792742 451.946701 
L 883.062782 450.369187 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1373d9"/>
    <path d="M 696.001419 237.045946 
L 698.687486 239.68029 
L 700.288552 239.901851 
L 697.605523 237.308803 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a78e89"/>
    <path d="M 660.617951 210.888647 
L 663.285555 212.538449 
L 664.926731 212.959653 
L 662.261833 211.327927 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d5c9c7"/>
    <path d="M 911.244438 438.148792 
L 914.00502 439.078493 
L 915.507251 435.226489 
L 912.746733 434.302398 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0098fe"/>
    <path d="M 631.757955 199.531591 
L 634.399009 200.290692 
L 636.067217 200.505668 
L 633.428208 199.74799 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ebe5e4"/>
    <path d="M 773.60174 341.032163 
L 776.287579 344.877407 
L 777.816263 343.407714 
L 775.132352 339.618961 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e1f993"/>
    <path d="M 828.114219 426.296493 
L 830.80406 429.400065 
L 832.305935 427.033009 
L 829.617155 423.962923 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00aacb"/>
    <path d="M 759.01401 316.876176 
L 761.702216 320.652574 
L 763.240777 319.53592 
L 760.554796 315.819223 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e4dc8a"/>
    <path d="M 800.084465 386.268579 
L 802.768168 389.946631 
L 804.28245 387.958419 
L 801.600208 384.325857 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #45da74"/>
    <path d="M 825.425446 423.12459 
L 828.114219 426.296493 
L 829.617155 423.962923 
L 826.929481 420.825497 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00aebf"/>
    <path d="M 830.80406 429.400065 
L 833.495118 432.433121 
L 834.995967 430.033597 
L 832.305935 427.033009 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a4dc"/>
    <path d="M 822.737599 419.88661 
L 825.425446 423.12459 
L 826.929481 420.825497 
L 824.242771 417.622955 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b4ac"/>
    <path d="M 736.35427 283.294626 
L 739.045156 286.790687 
L 740.602835 286.237956 
L 737.914613 282.800582 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a8906a"/>
    <path d="M 833.495118 432.433121 
L 836.187542 435.393547 
L 837.687401 432.962601 
L 834.995967 430.033597 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #009eef"/>
    <path d="M 820.050537 416.584874 
L 822.737599 419.88661 
L 824.242771 417.622955 
L 821.556888 414.357589 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00bb9b"/>
    <path d="M 785.500611 361.814832 
L 788.184991 365.637388 
L 789.706848 363.910321 
L 787.024174 360.139598 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #99eb85"/>
    <path d="M 870.414961 454.266778 
L 873.134745 456.163417 
L 874.627119 453.179824 
L 871.907792 451.303616 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1470d6"/>
    <path d="M 698.687486 239.68029 
L 701.374643 242.38871 
L 702.972675 242.56744 
L 700.288552 239.901851 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a38984"/>
    <path d="M 675.61316 220.419205 
L 678.290719 222.511301 
L 679.915407 222.902576 
L 677.240771 220.838539 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c5b5b1"/>
    <path d="M 836.187542 435.393547 
L 838.881488 438.279301 
L 840.380389 435.818004 
L 837.687401 432.962601 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #009afa"/>
    <path d="M 733.663076 279.837679 
L 736.35427 283.294626 
L 737.914613 282.800582 
L 735.226125 279.401571 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a28867"/>
    <path d="M 817.364126 413.221769 
L 820.050537 416.584874 
L 821.556888 414.357589 
L 818.871697 411.031756 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c088"/>
    <path d="M 853.874218 448.925574 
L 856.579913 451.301172 
L 858.073954 448.59808 
L 855.368963 446.247463 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0f7be1"/>
    <path d="M 863.492278 453.044989 
L 866.205953 455.13859 
L 867.698599 452.282228 
L 864.985486 450.210896 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1373d9"/>
    <path d="M 877.350044 454.968641 
L 880.076738 456.669117 
L 881.569231 453.56201 
L 878.842909 451.879701 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1470d6"/>
    <path d="M 797.400556 382.551027 
L 800.084465 386.268579 
L 801.600208 384.325857 
L 798.917811 380.654458 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #55dd77"/>
    <path d="M 896.996577 449.397426 
L 899.743381 450.603698 
L 901.239703 447.087282 
L 898.493059 445.892319 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0e7ee4"/>
    <path d="M 756.325087 313.11256 
L 759.01401 316.876176 
L 760.554796 315.819223 
L 757.868153 312.115138 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dcd286"/>
    <path d="M 838.881488 438.279301 
L 841.577113 441.088415 
L 843.075088 438.597862 
L 840.380389 435.818004 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0393f9"/>
    <path d="M 701.374643 242.38871 
L 704.062763 245.169114 
L 705.657767 245.303526 
L 702.972675 242.56744 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9f847e"/>
    <path d="M 892.759043 451.516195 
L 895.501508 452.819792 
L 896.996577 449.397426 
L 894.25431 448.10672 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1078de"/>
    <path d="M 915.507251 435.226489 
L 918.272665 436.076234 
L 919.77644 432.148137 
L 917.011104 431.301636 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #009eef"/>
    <path d="M 770.91516 337.181168 
L 773.60174 341.032163 
L 775.132352 339.618961 
L 772.447758 335.824637 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1fc96"/>
    <path d="M 814.678235 409.799746 
L 817.364126 413.221769 
L 818.871697 411.031756 
L 816.187068 407.647876 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c677"/>
    <path d="M 730.97164 276.422669 
L 733.663076 279.837679 
L 735.226125 279.401571 
L 732.537437 276.043684 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9c8064"/>
    <path d="M 901.239703 447.087282 
L 903.991006 448.19947 
L 905.488682 444.592396 
L 902.737511 443.489749 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0b83e9"/>
    <path d="M 650.980362 206.13983 
L 653.640911 207.507972 
L 655.292 207.881141 
L 652.633964 206.525022 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dfd6d4"/>
    <path d="M 641.358241 202.333602 
L 644.009952 203.403592 
L 645.670081 203.707197 
L 643.020661 202.643649 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e5dedc"/>
    <path d="M 888.526796 453.437695 
L 891.265106 454.841488 
L 892.759043 451.516195 
L 890.02098 450.126687 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1373d9"/>
    <path d="M 782.815635 357.970922 
L 785.500611 361.814832 
L 787.024174 360.139598 
L 784.340959 356.347944 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a9ee88"/>
    <path d="M 704.062763 245.169114 
L 706.751722 248.019335 
L 708.343708 248.107992 
L 705.657767 245.303526 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #997c76"/>
    <path d="M 728.280036 273.052378 
L 730.97164 276.422669 
L 732.537437 276.043684 
L 729.848621 272.729641 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #967960"/>
    <path d="M 841.577113 441.088415 
L 844.274578 443.818994 
L 845.771658 441.300305 
L 843.075088 438.597862 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #068ef4"/>
    <path d="M 811.992737 406.321319 
L 814.678235 409.799746 
L 816.187068 407.647876 
L 813.502878 404.208428 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #01cc66"/>
    <path d="M 905.488682 444.592396 
L 908.244625 445.614101 
L 909.743732 441.920118 
L 906.987906 440.906006 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0888ee"/>
    <path d="M 794.716352 378.796829 
L 797.400556 382.551027 
L 798.917811 380.654458 
L 796.23517 376.947034 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #61df79"/>
    <path d="M 706.751722 248.019335 
L 709.441401 250.937136 
L 711.030382 250.978653 
L 708.343708 248.107992 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #957771"/>
    <path d="M 725.588344 269.729553 
L 728.280036 273.052378 
L 729.848621 272.729641 
L 727.159754 269.462128 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #90715d"/>
    <path d="M 753.635462 309.364791 
L 756.325087 313.11256 
L 757.868153 312.115138 
L 755.180863 308.426668 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d6cb83"/>
    <path d="M 678.290719 222.511301 
L 680.970357 224.69155 
L 682.5921 225.053033 
L 679.915407 222.902576 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c1b0ac"/>
    <path d="M 663.285555 212.538449 
L 665.956038 214.284382 
L 667.594465 214.685734 
L 664.926731 212.959653 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d3c7c4"/>
    <path d="M 856.579913 451.301172 
L 859.288312 453.591149 
L 860.781669 450.864384 
L 858.073954 448.59808 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1078de"/>
    <path d="M 722.896648 266.456893 
L 725.588344 269.729553 
L 727.159754 269.462128 
L 724.470917 266.243785 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8a695a"/>
    <path d="M 709.441401 250.937136 
L 712.131681 253.920212 
L 713.717674 253.913253 
L 711.030382 250.978653 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8f7069"/>
    <path d="M 884.299489 455.15679 
L 887.033849 456.663269 
L 888.526796 453.437695 
L 885.792742 451.946701 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1470d6"/>
    <path d="M 768.227819 333.327518 
L 770.91516 337.181168 
L 772.447758 335.824637 
L 769.762459 332.027781 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 809.307513 402.789062 
L 811.992737 406.321319 
L 813.502878 404.208428 
L 810.819006 400.715954 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0dcf69"/>
    <path d="M 844.274578 443.818994 
L 846.974048 446.469222 
L 848.470259 443.923538 
L 845.771658 441.300305 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0888ee"/>
    <path d="M 720.205037 263.237052 
L 722.896648 266.456893 
L 724.470917 266.243785 
L 721.782197 263.077207 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #846257"/>
    <path d="M 712.131681 253.920212 
L 714.822452 256.966189 
L 716.405477 256.909475 
L 713.717674 253.913253 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8b6b64"/>
    <path d="M 717.513605 260.072634 
L 720.205037 263.237052 
L 721.782197 263.077207 
L 719.093685 259.964939 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #805c54"/>
    <path d="M 714.822452 256.966189 
L 717.513605 260.072634 
L 719.093685 259.964939 
L 716.405477 256.909475 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #85635c"/>
    <path d="M 909.743732 441.920118 
L 912.504427 442.855293 
L 914.00502 439.078493 
L 911.244438 438.148792 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0490f6"/>
    <path d="M 873.134745 456.163417 
L 875.858124 457.971099 
L 877.350044 454.968641 
L 874.627119 453.179824 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #166ed4"/>
    <path d="M 866.205953 455.13859 
L 868.922867 457.143961 
L 870.414961 454.266778 
L 867.698599 452.282228 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1470d6"/>
    <path d="M 780.130011 354.108693 
L 782.815635 357.970922 
L 784.340959 356.347944 
L 781.657152 352.538348 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b9f18b"/>
    <path d="M 792.031771 375.008884 
L 794.716352 378.796829 
L 796.23517 376.947034 
L 793.552203 373.206443 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #6de27c"/>
    <path d="M 750.945157 305.635927 
L 753.635462 309.364791 
L 755.180863 308.426668 
L 752.492948 304.756811 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cec07f"/>
    <path d="M 806.622446 399.205609 
L 809.307513 402.789062 
L 810.819006 400.715954 
L 808.135336 397.173052 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #19d16b"/>
    <path d="M 846.974048 446.469222 
L 849.675688 449.037356 
L 851.171057 446.465842 
L 848.470259 443.923538 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0b83e9"/>
    <path d="M 880.076738 456.669117 
L 882.807371 458.280383 
L 884.299489 455.15679 
L 881.569231 453.56201 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #166ed4"/>
    <path d="M 680.970357 224.69155 
L 683.651926 226.95842 
L 685.270704 227.288409 
L 682.5921 225.053033 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bfada9"/>
    <path d="M 765.539702 329.474319 
L 768.227819 333.327518 
L 769.762459 332.027781 
L 767.076441 328.231444 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f8f695"/>
    <path d="M 859.288312 453.591149 
L 861.999587 455.794102 
L 863.492278 453.044989 
L 860.781669 450.864384 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1373d9"/>
    <path d="M 634.399009 200.290692 
L 637.044516 201.155575 
L 638.710612 201.367563 
L 636.067217 200.505668 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ebe5e4"/>
    <path d="M 914.00502 439.078493 
L 916.770557 439.931425 
L 918.272665 436.076234 
L 915.507251 435.226489 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0098fe"/>
    <path d="M 803.937424 395.573647 
L 806.622446 399.205609 
L 808.135336 397.173052 
L 805.451758 393.582375 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #29d46e"/>
    <path d="M 777.443692 350.231211 
L 780.130011 354.108693 
L 781.657152 352.538348 
L 778.972705 348.713822 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c5f38d"/>
    <path d="M 748.254203 301.929013 
L 750.945157 305.635927 
L 752.492948 304.756811 
L 749.804435 301.108552 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c8b97b"/>
    <path d="M 653.640911 207.507972 
L 656.304857 208.976513 
L 657.953381 209.335928 
L 655.292 207.881141 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ddd3d1"/>
    <path d="M 789.346734 371.190133 
L 792.031771 375.008884 
L 793.552203 373.206443 
L 790.868833 369.435582 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #7de57f"/>
    <path d="M 665.956038 214.284382 
L 668.629242 216.125384 
L 670.264882 216.50513 
L 667.594465 214.685734 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d1c4c1"/>
    <path d="M 895.501508 452.819792 
L 898.248535 454.036967 
L 899.743381 450.603698 
L 896.996577 449.397426 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1276dc"/>
    <path d="M 849.675688 449.037356 
L 852.379668 451.521735 
L 853.874218 448.925574 
L 851.171057 446.465842 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0e7ee4"/>
    <path d="M 899.743381 450.603698 
L 902.494876 451.725111 
L 903.991006 448.19947 
L 901.239703 447.087282 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0f7be1"/>
    <path d="M 891.265106 454.841488 
L 894.007838 456.157478 
L 895.501508 452.819792 
L 892.759043 451.516195 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1373d9"/>
    <path d="M 868.922867 457.143961 
L 871.643194 459.059959 
L 873.134745 456.163417 
L 870.414961 454.266778 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #176bd1"/>
    <path d="M 903.991006 448.19947 
L 906.74712 449.228542 
L 908.244625 445.614101 
L 905.488682 444.592396 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0b83e9"/>
    <path d="M 644.009952 203.403592 
L 646.665587 204.577225 
L 648.323367 204.872729 
L 645.670081 203.707197 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e5dedc"/>
    <path d="M 762.850801 325.624689 
L 765.539702 329.474319 
L 767.076441 328.231444 
L 764.389694 324.438686 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f0ec91"/>
    <path d="M 801.252342 391.895921 
L 803.937424 395.573647 
L 805.451758 393.582375 
L 802.768168 389.946631 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #35d771"/>
    <path d="M 683.651926 226.95842 
L 686.335282 229.310283 
L 687.951078 229.607113 
L 685.270704 227.288409 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bba8a4"/>
    <path d="M 875.858124 457.971099 
L 878.58527 459.68886 
L 880.076738 456.669117 
L 877.350044 454.968641 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #176bd1"/>
    <path d="M 745.562633 298.247085 
L 748.254203 301.929013 
L 749.804435 301.108552 
L 747.115357 297.484865 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c2b178"/>
    <path d="M 887.033849 456.663269 
L 889.772479 458.080751 
L 891.265106 454.841488 
L 888.526796 453.437695 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #166ed4"/>
    <path d="M 826.610578 428.564538 
L 829.301574 431.699338 
L 830.80406 429.400065 
L 828.114219 426.296493 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a6d7"/>
    <path d="M 829.301574 431.699338 
L 831.99375 434.762674 
L 833.495118 432.433121 
L 830.80406 429.400065 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a2e2"/>
    <path d="M 861.999587 455.794102 
L 864.713914 457.908708 
L 866.205953 455.13859 
L 863.492278 453.044989 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #166ed4"/>
    <path d="M 823.920613 425.360485 
L 826.610578 428.564538 
L 828.114219 426.296493 
L 825.425446 423.12459 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00acc4"/>
    <path d="M 774.756638 346.341564 
L 777.443692 350.231211 
L 778.972705 348.713822 
L 776.287579 344.877407 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d5f791"/>
    <path d="M 786.661173 367.343557 
L 789.346734 371.190133 
L 790.868833 369.435582 
L 788.184991 365.637388 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #89e781"/>
    <path d="M 831.99375 434.762674 
L 834.68726 437.752408 
L 836.187542 435.393547 
L 833.495118 432.433121 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #009cf4"/>
    <path d="M 908.244625 445.614101 
L 911.005483 446.554608 
L 912.504427 442.855293 
L 909.743732 441.920118 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0888ee"/>
    <path d="M 852.379668 451.521735 
L 855.086159 453.920775 
L 856.579913 451.301172 
L 853.874218 448.925574 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1078de"/>
    <path d="M 821.231536 422.08946 
L 823.920613 425.360485 
L 825.425446 423.12459 
L 822.737599 419.88661 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b2b2"/>
    <path d="M 834.68726 437.752408 
L 837.382258 440.666474 
L 838.881488 438.279301 
L 836.187542 435.393547 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0098fe"/>
    <path d="M 818.543204 418.75381 
L 821.231536 422.08946 
L 822.737599 419.88661 
L 820.050537 416.584874 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b8a0"/>
    <path d="M 798.5671 388.175226 
L 801.252342 391.895921 
L 802.768168 389.946631 
L 800.084465 386.268579 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #41d973"/>
    <path d="M 742.870488 294.593158 
L 745.562633 298.247085 
L 747.115357 297.484865 
L 744.425753 293.888706 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #baa774"/>
    <path d="M 760.161113 321.781748 
L 762.850801 325.624689 
L 764.389694 324.438686 
L 761.702216 320.652574 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eae48e"/>
    <path d="M 686.335282 229.310283 
L 689.020279 231.74542 
L 690.63308 232.007463 
L 687.951078 229.607113 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b7a39f"/>
    <path d="M 837.382258 440.666474 
L 840.078904 443.502881 
L 841.577113 441.088415 
L 838.881488 438.279301 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0490f6"/>
    <path d="M 882.807371 458.280383 
L 885.542113 459.801651 
L 887.033849 456.663269 
L 884.299489 455.15679 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #176bd1"/>
    <path d="M 815.855483 415.355953 
L 818.543204 418.75381 
L 820.050537 416.584874 
L 817.364126 413.221769 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00be8f"/>
    <path d="M 668.629242 216.125384 
L 671.305012 218.060291 
L 672.937831 218.416701 
L 670.264882 216.50513 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cfc2bf"/>
    <path d="M 912.504427 442.855293 
L 915.270131 443.711352 
L 916.770557 439.931425 
L 914.00502 439.078493 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0490f6"/>
    <path d="M 772.068817 342.442864 
L 774.756638 346.341564 
L 776.287579 344.877407 
L 773.60174 341.032163 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e1f993"/>
    <path d="M 783.975021 363.472174 
L 786.661173 367.343557 
L 788.184991 365.637388 
L 785.500611 361.814832 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #99eb85"/>
    <path d="M 840.078904 443.502881 
L 842.777361 446.259711 
L 844.274578 443.818994 
L 841.577113 441.088415 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #078bf1"/>
    <path d="M 740.177817 290.970229 
L 742.870488 294.593158 
L 744.425753 293.888706 
L 741.735669 290.323009 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b49f70"/>
    <path d="M 813.168241 411.898368 
L 815.855483 415.355953 
L 817.364126 413.221769 
L 814.678235 409.799746 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c47d"/>
    <path d="M 855.086159 453.920775 
L 857.795334 456.232974 
L 859.288312 453.591149 
L 856.579913 451.301172 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1373d9"/>
    <path d="M 656.304857 208.976513 
L 658.97204 210.5447 
L 660.617951 210.888647 
L 657.953381 209.335928 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dbd1cf"/>
    <path d="M 871.643194 459.059959 
L 874.367111 460.885522 
L 875.858124 457.971099 
L 873.134745 456.163417 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1868ce"/>
    <path d="M 795.881603 384.41441 
L 798.5671 388.175226 
L 800.084465 386.268579 
L 797.400556 382.551027 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #51dc76"/>
    <path d="M 864.713914 457.908708 
L 867.431468 459.933725 
L 868.922867 457.143961 
L 866.205953 455.13859 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #176bd1"/>
    <path d="M 757.470644 317.948625 
L 760.161113 321.781748 
L 761.702216 320.652574 
L 759.01401 316.876176 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e2da89"/>
    <path d="M 689.020279 231.74542 
L 691.706774 234.262025 
L 693.316573 234.487692 
L 690.63308 232.007463 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b39e99"/>
    <path d="M 637.044516 201.155575 
L 639.694322 202.126164 
L 641.358241 202.333602 
L 638.710612 201.367563 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e9e3e2"/>
    <path d="M 810.48135 408.383599 
L 813.168241 411.898368 
L 814.678235 409.799746 
L 811.992737 406.321319 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00cb6b"/>
    <path d="M 842.777361 446.259711 
L 845.477794 448.935128 
L 846.974048 446.469222 
L 844.274578 443.818994 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0a86ec"/>
    <path d="M 878.58527 459.68886 
L 881.316357 461.315816 
L 882.807371 458.280383 
L 880.076738 456.669117 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1868ce"/>
    <path d="M 737.48467 287.381269 
L 740.177817 290.970229 
L 741.735669 290.323009 
L 739.045156 286.790687 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ae976d"/>
    <path d="M 898.248535 454.036967 
L 901.000282 455.167286 
L 902.494876 451.725111 
L 899.743381 450.603698 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1276dc"/>
    <path d="M 894.007838 456.157478 
L 896.755153 457.385142 
L 898.248535 454.036967 
L 895.501508 452.819792 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1470d6"/>
    <path d="M 646.665587 204.577225 
L 649.324991 205.854078 
L 650.980362 206.13983 
L 648.323367 204.872729 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e3dbd9"/>
    <path d="M 902.494876 451.725111 
L 905.251216 452.761321 
L 906.74712 449.228542 
L 903.991006 448.19947 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0f7be1"/>
    <path d="M 769.3802 338.538243 
L 772.068817 342.442864 
L 773.60174 341.032163 
L 770.91516 337.181168 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1fc96"/>
    <path d="M 781.28822 359.579035 
L 783.975021 363.472174 
L 785.500611 361.814832 
L 782.815635 357.970922 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a9ee88"/>
    <path d="M 793.195761 380.616364 
L 795.881603 384.41441 
L 797.400556 382.551027 
L 794.716352 378.796829 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #5ddf79"/>
    <path d="M 807.794689 404.814253 
L 810.48135 408.383599 
L 811.992737 406.321319 
L 809.307513 402.789062 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #09ce68"/>
    <path d="M 691.706774 234.262025 
L 694.39463 236.858204 
L 696.001419 237.045946 
L 693.316573 234.487692 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #af9994"/>
    <path d="M 889.772479 458.080751 
L 892.515545 459.408624 
L 894.007838 456.157478 
L 891.265106 454.841488 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #176bd1"/>
    <path d="M 671.305012 218.060291 
L 673.983194 220.087837 
L 675.61316 220.419205 
L 672.937831 218.416701 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cbbcb9"/>
    <path d="M 845.477794 448.935128 
L 848.180371 451.52737 
L 849.675688 449.037356 
L 846.974048 446.469222 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0c80e6"/>
    <path d="M 734.791109 283.829224 
L 737.48467 287.381269 
L 739.045156 286.790687 
L 736.35427 283.294626 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a68d69"/>
    <path d="M 857.795334 456.232974 
L 860.507367 458.456908 
L 861.999587 455.794102 
L 859.288312 453.591149 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #166ed4"/>
    <path d="M 754.779404 314.128443 
L 757.470644 317.948625 
L 759.01401 316.876176 
L 756.325087 313.11256 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dcd286"/>
    <path d="M 906.74712 449.228542 
L 909.508192 450.174237 
L 911.005483 446.554608 
L 908.244625 445.614101 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0b83e9"/>
    <path d="M 805.108141 401.192993 
L 807.794689 404.814253 
L 809.307513 402.789062 
L 806.622446 399.205609 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #19d16b"/>
    <path d="M 732.097197 280.317008 
L 734.791109 283.829224 
L 736.35427 283.294626 
L 733.663076 279.837679 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a08566"/>
    <path d="M 694.39463 236.858204 
L 697.083708 239.531978 
L 698.687486 239.68029 
L 696.001419 237.045946 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ab938e"/>
    <path d="M 885.542113 459.801651 
L 888.281136 461.232216 
L 889.772479 458.080751 
L 887.033849 456.663269 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1868ce"/>
    <path d="M 630.086473 199.419958 
L 632.729523 200.180464 
L 634.399009 200.290692 
L 631.757955 199.531591 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ede8e7"/>
    <path d="M 867.431468 459.933725 
L 870.152425 461.867993 
L 871.643194 459.059959 
L 868.922867 457.143961 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1868ce"/>
    <path d="M 874.367111 460.885522 
L 877.094791 462.619671 
L 878.58527 459.68886 
L 875.858124 457.971099 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1a66cc"/>
    <path d="M 790.509493 376.784028 
L 793.195761 380.616364 
L 794.716352 378.796829 
L 792.031771 375.008884 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #6de27c"/>
    <path d="M 766.690768 334.630848 
L 769.3802 338.538243 
L 770.91516 337.181168 
L 768.227819 333.327518 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 848.180371 451.52737 
L 850.885263 454.034754 
L 852.379668 451.521735 
L 849.675688 449.037356 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0f7be1"/>
    <path d="M 778.600717 355.667222 
L 781.28822 359.579035 
L 782.815635 357.970922 
L 780.130011 354.108693 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b5f08a"/>
    <path d="M 911.005483 446.554608 
L 913.7714 447.413733 
L 915.270131 443.711352 
L 912.504427 442.855293 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0888ee"/>
    <path d="M 658.97204 210.5447 
L 661.642303 212.211671 
L 663.285555 212.538449 
L 660.617951 210.888647 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d9cecc"/>
    <path d="M 752.087411 310.324326 
L 754.779404 314.128443 
L 756.325087 313.11256 
L 753.635462 309.364791 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d4c882"/>
    <path d="M 729.403005 276.847501 
L 732.097197 280.317008 
L 733.663076 279.837679 
L 730.97164 276.422669 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9a7e62"/>
    <path d="M 697.083708 239.531978 
L 699.773876 242.281291 
L 701.374643 242.38871 
L 698.687486 239.68029 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a78e89"/>
    <path d="M 802.421593 397.522541 
L 805.108141 401.192993 
L 806.622446 399.205609 
L 803.937424 395.573647 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #25d36d"/>
    <path d="M 860.507367 458.456908 
L 863.222436 460.591239 
L 864.713914 457.908708 
L 861.999587 455.794102 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #176bd1"/>
    <path d="M 673.983194 220.087837 
L 676.663634 222.206651 
L 678.290719 222.511301 
L 675.61316 220.419205 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c9bab7"/>
    <path d="M 726.708609 273.423547 
L 729.403005 276.847501 
L 730.97164 276.422669 
L 728.280036 273.052378 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #94765f"/>
    <path d="M 881.316357 461.315816 
L 884.051558 462.851168 
L 885.542113 459.801651 
L 882.807371 458.280383 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1a66cc"/>
    <path d="M 699.773876 242.281291 
L 702.465002 245.104003 
L 704.062763 245.169114 
L 701.374643 242.38871 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a18781"/>
    <path d="M 850.885263 454.034754 
L 853.592643 456.455681 
L 855.086159 453.920775 
L 852.379668 451.521735 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1276dc"/>
    <path d="M 787.82272 372.920384 
L 790.509493 376.784028 
L 792.031771 375.008884 
L 789.346734 371.190133 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #79e47e"/>
    <path d="M 724.01409 270.047946 
L 726.708609 273.423547 
L 728.280036 273.052378 
L 725.588344 269.729553 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8e6e5c"/>
    <path d="M 764.000507 330.723837 
L 766.690768 334.630848 
L 768.227819 333.327518 
L 765.539702 329.474319 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f8f695"/>
    <path d="M 775.912468 351.739848 
L 778.600717 355.667222 
L 780.130011 354.108693 
L 777.443692 350.231211 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c5f38d"/>
    <path d="M 749.394688 306.539387 
L 752.087411 310.324326 
L 753.635462 309.364791 
L 750.945157 305.635927 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cec07f"/>
    <path d="M 827.798426 433.929898 
L 830.491815 437.021302 
L 831.99375 434.762674 
L 829.301574 431.699338 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a0e8"/>
    <path d="M 825.106182 430.766156 
L 827.798426 433.929898 
L 829.301574 431.699338 
L 826.610578 428.564538 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a4dc"/>
    <path d="M 702.465002 245.104003 
L 705.156959 247.997902 
L 706.751722 248.019335 
L 704.062763 245.169114 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9d827c"/>
    <path d="M 830.491815 437.021302 
L 833.186504 440.038204 
L 834.68726 437.752408 
L 831.99375 434.762674 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #009afa"/>
    <path d="M 799.73494 393.805676 
L 802.421593 397.522541 
L 803.937424 395.573647 
L 801.252342 391.895921 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #31d670"/>
    <path d="M 822.414934 427.532308 
L 825.106182 430.766156 
L 826.610578 428.564538 
L 823.920613 425.360485 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00aacb"/>
    <path d="M 639.694322 202.126164 
L 642.348272 203.202264 
L 644.009952 203.403592 
L 641.358241 202.333602 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e9e3e2"/>
    <path d="M 649.324991 205.854078 
L 651.988003 207.233613 
L 653.640911 207.507972 
L 650.980362 206.13983 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e3dbd9"/>
    <path d="M 721.319536 266.723458 
L 724.01409 270.047946 
L 725.588344 269.729553 
L 722.896648 266.456893 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #886759"/>
    <path d="M 833.186504 440.038204 
L 835.882648 442.978518 
L 837.382258 440.666474 
L 834.68726 437.752408 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0296fc"/>
    <path d="M 819.724536 424.230659 
L 822.414934 427.532308 
L 823.920613 425.360485 
L 821.231536 422.08946 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b0b9"/>
    <path d="M 705.156959 247.997902 
L 707.849625 250.960701 
L 709.441401 250.937136 
L 706.751722 248.019335 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #977a74"/>
    <path d="M 896.755153 457.385142 
L 899.507214 458.52404 
L 901.000282 455.167286 
L 898.248535 454.036967 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1470d6"/>
    <path d="M 718.625039 263.452791 
L 721.319536 266.723458 
L 722.896648 266.456893 
L 720.205037 263.237052 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #825f56"/>
    <path d="M 901.000282 455.167286 
L 903.756907 456.210396 
L 905.251216 452.761321 
L 902.494876 451.725111 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1276dc"/>
    <path d="M 870.152425 461.867993 
L 872.876964 463.710438 
L 874.367111 460.885522 
L 871.643194 459.059959 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1b63c9"/>
    <path d="M 707.849625 250.960701 
L 710.542879 253.990044 
L 712.131681 253.920212 
L 709.441401 250.937136 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #93756e"/>
    <path d="M 715.930694 260.238606 
L 718.625039 263.452791 
L 720.205037 263.237052 
L 717.513605 260.072634 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #836059"/>
    <path d="M 710.542879 253.990044 
L 713.236606 257.083508 
L 714.822452 256.966189 
L 712.131681 253.920212 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8d6d66"/>
    <path d="M 817.034845 420.863585 
L 819.724536 424.230659 
L 821.231536 422.08946 
L 818.543204 418.75381 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b6a7"/>
    <path d="M 835.882648 442.978518 
L 838.58041 445.84023 
L 840.078904 443.502881 
L 837.382258 440.666474 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #068ef4"/>
    <path d="M 713.236606 257.083508 
L 715.930694 260.238606 
L 717.513605 260.072634 
L 714.822452 256.966189 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #87655e"/>
    <path d="M 892.515545 459.408624 
L 895.263215 460.646356 
L 896.755153 457.385142 
L 894.007838 456.157478 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #176bd1"/>
    <path d="M 676.663634 222.206651 
L 679.346177 224.415266 
L 680.970357 224.69155 
L 678.290719 222.511301 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c5b5b1"/>
    <path d="M 905.251216 452.761321 
L 908.012555 453.712056 
L 909.508192 450.174237 
L 906.74712 449.228542 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0f7be1"/>
    <path d="M 661.642303 212.211671 
L 664.315487 213.976452 
L 665.956038 214.284382 
L 663.285555 212.538449 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d7ccc9"/>
    <path d="M 877.094791 462.619671 
L 879.826412 464.261511 
L 881.316357 461.315816 
L 878.58527 459.68886 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1b63c9"/>
    <path d="M 853.592643 456.455681 
L 856.302686 458.788629 
L 857.795334 456.232974 
L 855.086159 453.920775 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1470d6"/>
    <path d="M 746.701266 302.776733 
L 749.394688 306.539387 
L 750.945157 305.635927 
L 748.254203 301.929013 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c6b67a"/>
    <path d="M 785.135371 369.028453 
L 787.82272 372.920384 
L 789.346734 371.190133 
L 786.661173 367.343557 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #89e781"/>
    <path d="M 863.222436 460.591239 
L 865.940718 462.63471 
L 867.431468 459.933725 
L 864.713914 457.908708 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1a66cc"/>
    <path d="M 797.048081 390.045227 
L 799.73494 393.805676 
L 801.252342 391.895921 
L 798.5671 388.175226 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #41d973"/>
    <path d="M 761.309408 326.820382 
L 764.000507 330.723837 
L 765.539702 329.474319 
L 762.850801 325.624689 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f0ec91"/>
    <path d="M 814.345726 417.433527 
L 817.034845 420.863585 
L 818.543204 418.75381 
L 815.855483 415.355953 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00bc94"/>
    <path d="M 838.58041 445.84023 
L 841.279953 448.621405 
L 842.777361 446.259711 
L 840.078904 443.502881 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0888ee"/>
    <path d="M 773.223431 347.800049 
L 775.912468 351.739848 
L 777.443692 350.231211 
L 774.756638 346.341564 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d5f791"/>
    <path d="M 888.281136 461.232216 
L 891.024608 462.571455 
L 892.515545 459.408624 
L 889.772479 458.080751 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1a66cc"/>
    <path d="M 909.508192 450.174237 
L 912.27437 451.036367 
L 913.7714 447.413733 
L 911.005483 446.554608 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0c80e6"/>
    <path d="M 811.657045 413.942992 
L 814.345726 417.433527 
L 815.855483 415.355953 
L 813.168241 411.898368 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c382"/>
    <path d="M 841.279953 448.621405 
L 843.981443 451.320184 
L 845.477794 448.935128 
L 842.777361 446.259711 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0b83e9"/>
    <path d="M 744.007181 299.039453 
L 746.701266 302.776733 
L 748.254203 301.929013 
L 745.562633 298.247085 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c0ae77"/>
    <path d="M 632.729523 200.180464 
L 635.377091 201.048209 
L 637.044516 201.155575 
L 634.399009 200.290692 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ede8e7"/>
    <path d="M 794.36092 386.244076 
L 797.048081 390.045227 
L 798.5671 388.175226 
L 795.881603 384.41441 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #4ddb75"/>
    <path d="M 884.051558 462.851168 
L 886.791047 464.2942 
L 888.281136 461.232216 
L 885.542113 459.801651 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1b63c9"/>
    <path d="M 782.447382 365.111295 
L 785.135371 369.028453 
L 786.661173 367.343557 
L 783.975021 363.472174 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #99eb85"/>
    <path d="M 679.346177 224.415266 
L 682.030674 226.712116 
L 683.651926 226.95842 
L 680.970357 224.69155 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c1b0ac"/>
    <path d="M 808.968676 410.394553 
L 811.657045 413.942992 
L 813.168241 411.898368 
L 810.48135 408.383599 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c970"/>
    <path d="M 856.302686 458.788629 
L 859.015569 461.032162 
L 860.507367 458.456908 
L 857.795334 456.232974 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #176bd1"/>
    <path d="M 758.617471 322.923658 
L 761.309408 326.820382 
L 762.850801 325.624689 
L 760.161113 321.781748 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eae48e"/>
    <path d="M 770.533575 343.850986 
L 773.223431 347.800049 
L 774.756638 346.341564 
L 772.068817 342.442864 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e1f993"/>
    <path d="M 843.981443 451.320184 
L 846.685051 453.934789 
L 848.180371 451.52737 
L 845.477794 448.935128 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0f7be1"/>
    <path d="M 872.876964 463.710438 
L 875.605261 465.460067 
L 877.094791 462.619671 
L 874.367111 460.885522 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1c60c6"/>
    <path d="M 651.988003 207.233613 
L 654.654463 208.715177 
L 656.304857 208.976513 
L 653.640911 207.507972 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e1d9d7"/>
    <path d="M 865.940718 462.63471 
L 868.662392 464.586147 
L 870.152425 461.867993 
L 867.431468 459.933725 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1b63c9"/>
    <path d="M 741.312475 295.330623 
L 744.007181 299.039453 
L 745.562633 298.247085 
L 742.870488 294.593158 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #baa774"/>
    <path d="M 664.315487 213.976452 
L 666.991431 215.837963 
L 668.629242 216.125384 
L 665.956038 214.284382 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d5c9c7"/>
    <path d="M 806.280494 406.790843 
L 808.968676 410.394553 
L 810.48135 408.383599 
L 807.794689 404.814253 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #09ce68"/>
    <path d="M 642.348272 203.202264 
L 645.006206 204.383561 
L 646.665587 204.577225 
L 644.009952 203.403592 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e9e3e2"/>
    <path d="M 791.673368 382.405153 
L 794.36092 386.244076 
L 795.881603 384.41441 
L 793.195761 380.616364 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #5ddf79"/>
    <path d="M 879.826412 464.261511 
L 882.56215 465.810231 
L 884.051558 462.851168 
L 881.316357 461.315816 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1c60c6"/>
    <path d="M 682.030674 226.712116 
L 684.716975 229.095541 
L 686.335282 229.310283 
L 683.651926 226.95842 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bfada9"/>
    <path d="M 846.685051 453.934789 
L 849.390949 456.463519 
L 850.885263 454.034754 
L 848.180371 451.52737 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1276dc"/>
    <path d="M 779.758694 361.172003 
L 782.447382 365.111295 
L 783.975021 363.472174 
L 781.28822 359.579035 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a5ed87"/>
    <path d="M 755.924702 319.036845 
L 758.617471 322.923658 
L 760.161113 321.781748 
L 757.470644 317.948625 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e2da89"/>
    <path d="M 899.507214 458.52404 
L 902.264181 459.57381 
L 903.756907 456.210396 
L 901.000282 455.167286 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #166ed4"/>
    <path d="M 738.617199 291.653295 
L 741.312475 295.330623 
L 742.870488 294.593158 
L 740.177817 290.970229 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b29c6f"/>
    <path d="M 859.015569 461.032162 
L 861.73147 463.184923 
L 863.222436 460.591239 
L 860.507367 458.456908 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1a66cc"/>
    <path d="M 767.842872 339.895838 
L 770.533575 343.850986 
L 772.068817 342.442864 
L 769.3802 338.538243 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1fc96"/>
    <path d="M 895.263215 460.646356 
L 898.015653 461.793499 
L 899.507214 458.52404 
L 896.755153 457.385142 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1868ce"/>
    <path d="M 803.592382 403.134558 
L 806.280494 406.790843 
L 807.794689 404.814253 
L 805.108141 401.192993 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #15d06a"/>
    <path d="M 903.756907 456.210396 
L 906.518566 457.166022 
L 908.012555 453.712056 
L 905.251216 452.761321 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1276dc"/>
    <path d="M 891.024608 462.571455 
L 893.772699 463.818827 
L 895.263215 460.646356 
L 892.515545 459.408624 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1a66cc"/>
    <path d="M 788.985342 378.531433 
L 791.673368 382.405153 
L 793.195761 380.616364 
L 790.509493 376.784028 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #69e17b"/>
    <path d="M 908.012555 453.712056 
L 910.779042 454.577127 
L 912.27437 451.036367 
L 909.508192 450.174237 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0f7be1"/>
    <path d="M 849.390949 456.463519 
L 852.099312 458.904758 
L 853.592643 456.455681 
L 850.885263 454.034754 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1470d6"/>
    <path d="M 684.716975 229.095541 
L 687.404931 231.563787 
L 689.020279 231.74542 
L 686.335282 229.310283 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bba8a4"/>
    <path d="M 735.921406 288.0105 
L 738.617199 291.653295 
L 740.177817 290.970229 
L 737.48467 287.381269 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ac956c"/>
    <path d="M 753.231112 315.163123 
L 755.924702 319.036845 
L 757.470644 317.948625 
L 754.779404 314.128443 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dcd286"/>
    <path d="M 800.904229 399.428449 
L 803.592382 403.134558 
L 805.108141 401.192993 
L 802.421593 397.522541 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #21d36d"/>
    <path d="M 777.069255 357.213705 
L 779.758694 361.172003 
L 781.28822 359.579035 
L 778.600717 355.667222 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b5f08a"/>
    <path d="M 868.662392 464.586147 
L 871.387637 466.444462 
L 872.876964 463.710438 
L 870.152425 461.867993 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1c60c6"/>
    <path d="M 666.991431 215.837963 
L 669.669978 217.795016 
L 671.305012 218.060291 
L 668.629242 216.125384 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d1c4c1"/>
    <path d="M 886.791047 464.2942 
L 889.534996 465.644278 
L 891.024608 462.571455 
L 888.281136 461.232216 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1c60c6"/>
    <path d="M 875.605261 465.460067 
L 878.337496 467.115973 
L 879.826412 464.261511 
L 877.094791 462.619671 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1e5ec4"/>
    <path d="M 765.151302 335.937802 
L 767.842872 339.895838 
L 769.3802 338.538243 
L 766.690768 334.630848 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 826.294566 436.090882 
L 828.989261 439.208114 
L 830.491815 437.021302 
L 827.798426 433.929898 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #009eef"/>
    <path d="M 823.600983 432.900507 
L 826.294566 436.090882 
L 827.798426 433.929898 
L 825.106182 430.766156 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a4dc"/>
    <path d="M 828.989261 439.208114 
L 831.685221 442.250022 
L 833.186504 440.038204 
L 830.491815 437.021302 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0098fe"/>
    <path d="M 654.654463 208.715177 
L 657.32421 210.298004 
L 658.97204 210.5447 
L 656.304857 208.976513 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dfd6d4"/>
    <path d="M 733.225158 284.405238 
L 735.921406 288.0105 
L 737.48467 287.381269 
L 734.791109 283.829224 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a68d69"/>
    <path d="M 820.90836 429.639245 
L 823.600983 432.900507 
L 825.106182 430.766156 
L 822.414934 427.532308 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a8d0"/>
    <path d="M 831.685221 442.250022 
L 834.382606 445.214496 
L 835.882648 442.978518 
L 833.186504 440.038204 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0393f9"/>
    <path d="M 861.73147 463.184923 
L 864.450568 465.245641 
L 865.940718 462.63471 
L 863.222436 460.591239 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1b63c9"/>
    <path d="M 687.404931 231.563787 
L 690.094397 234.115009 
L 691.706774 234.262025 
L 689.020279 231.74542 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b7a39f"/>
    <path d="M 635.377091 201.048209 
L 638.029023 202.023116 
L 639.694322 202.126164 
L 637.044516 201.155575 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ede8e7"/>
    <path d="M 786.296764 374.625935 
L 788.985342 378.531433 
L 790.509493 376.784028 
L 787.82272 372.920384 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #79e47e"/>
    <path d="M 818.216551 426.309424 
L 820.90836 429.639245 
L 822.414934 427.532308 
L 819.724536 424.230659 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00aebf"/>
    <path d="M 852.099312 458.904758 
L 854.810315 461.256969 
L 856.302686 458.788629 
L 853.592643 456.455681 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #176bd1"/>
    <path d="M 798.215926 395.675325 
L 800.904229 399.428449 
L 802.421593 397.522541 
L 799.73494 393.805676 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #31d670"/>
    <path d="M 834.382606 445.214496 
L 837.081577 448.099506 
L 838.58041 445.84023 
L 835.882648 442.978518 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #078bf1"/>
    <path d="M 750.536721 311.305669 
L 753.231112 315.163123 
L 754.779404 314.128443 
L 752.087411 310.324326 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d4c882"/>
    <path d="M 815.525413 422.913442 
L 818.216551 426.309424 
L 819.724536 424.230659 
L 817.034845 420.863585 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b4ac"/>
    <path d="M 730.528521 280.840482 
L 733.225158 284.405238 
L 734.791109 283.829224 
L 732.097197 280.317008 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9e8365"/>
    <path d="M 882.56215 465.810231 
L 885.302179 467.265103 
L 886.791047 464.2942 
L 884.051558 462.851168 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1e5ec4"/>
    <path d="M 774.379019 353.239556 
L 777.069255 357.213705 
L 778.600717 355.667222 
L 775.912468 351.739848 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c5f38d"/>
    <path d="M 645.006206 204.383561 
L 647.667966 205.669627 
L 649.324991 205.854078 
L 646.665587 204.577225 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e7e0df"/>
    <path d="M 837.081577 448.099506 
L 839.782299 450.903097 
L 841.279953 448.621405 
L 838.58041 445.84023 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0a86ec"/>
    <path d="M 690.094397 234.115009 
L 692.78523 236.747275 
L 694.39463 236.858204 
L 691.706774 234.262025 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b39e99"/>
    <path d="M 762.458853 331.980087 
L 765.151302 335.937802 
L 766.690768 334.630848 
L 764.000507 330.723837 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f8f695"/>
    <path d="M 812.834808 419.453763 
L 815.525413 422.913442 
L 817.034845 420.863585 
L 814.345726 417.433527 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00bb9b"/>
    <path d="M 669.669978 217.795016 
L 672.350968 219.84632 
L 673.983194 220.087837 
L 671.305012 218.060291 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cfc2bf"/>
    <path d="M 727.831568 277.319167 
L 730.528521 280.840482 
L 732.097197 280.317008 
L 729.403005 276.847501 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #987b61"/>
    <path d="M 795.527374 391.878048 
L 798.215926 395.675325 
L 799.73494 393.805676 
L 797.048081 390.045227 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #3dd872"/>
    <path d="M 839.782299 450.903097 
L 842.484941 453.623393 
L 843.981443 451.320184 
L 841.279953 448.621405 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0e7ee4"/>
    <path d="M 783.607563 370.69172 
L 786.296764 374.625935 
L 787.82272 372.920384 
L 785.135371 369.028453 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #89e781"/>
    <path d="M 871.387637 466.444462 
L 874.116635 468.20865 
L 875.605261 465.460067 
L 872.876964 463.710438 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1e5ec4"/>
    <path d="M 628.413887 199.414769 
L 631.058882 200.176659 
L 632.729523 200.180464 
L 630.086473 199.419958 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1edec"/>
    <path d="M 854.810315 461.256969 
L 857.524138 463.518699 
L 859.015569 461.032162 
L 856.302686 458.788629 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1868ce"/>
    <path d="M 747.841553 307.467651 
L 750.536721 311.305669 
L 752.087411 310.324326 
L 749.394688 306.539387 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ccbe7d"/>
    <path d="M 692.78523 236.747275 
L 695.477291 239.458568 
L 697.083708 239.531978 
L 694.39463 236.858204 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ad9691"/>
    <path d="M 810.144604 415.932922 
L 812.834808 419.453763 
L 814.345726 417.433527 
L 811.657045 413.942992 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c382"/>
    <path d="M 898.015653 461.793499 
L 900.773023 462.849684 
L 902.264181 459.57381 
L 899.507214 458.52404 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1868ce"/>
    <path d="M 902.264181 459.57381 
L 905.026215 460.534172 
L 906.518566 457.166022 
L 903.756907 456.210396 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #166ed4"/>
    <path d="M 725.134378 273.844192 
L 727.831568 277.319167 
L 729.403005 276.847501 
L 726.708609 273.423547 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #92735e"/>
    <path d="M 864.450568 465.245641 
L 867.173045 467.213131 
L 868.662392 464.586147 
L 865.940718 462.63471 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1e5ec4"/>
    <path d="M 893.772699 463.818827 
L 896.525577 464.973875 
L 898.015653 461.793499 
L 895.263215 460.646356 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1b63c9"/>
    <path d="M 771.687946 349.252737 
L 774.379019 353.239556 
L 775.912468 351.739848 
L 773.223431 347.800049 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d1f690"/>
    <path d="M 878.337496 467.115973 
L 881.073847 468.677334 
L 882.56215 465.810231 
L 879.826412 464.261511 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1f5bc1"/>
    <path d="M 842.484941 453.623393 
L 845.189674 456.258598 
L 846.685051 453.934789 
L 843.981443 451.320184 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1078de"/>
    <path d="M 906.518566 457.166022 
L 909.285413 458.033968 
L 910.779042 454.577127 
L 908.012555 453.712056 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1373d9"/>
    <path d="M 657.32421 210.298004 
L 659.997082 211.981214 
L 661.642303 212.211671 
L 658.97204 210.5447 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ddd3d1"/>
    <path d="M 695.477291 239.458568 
L 698.170441 242.246785 
L 699.773876 242.281291 
L 697.083708 239.531978 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a9918c"/>
    <path d="M 759.765517 328.025913 
L 762.458853 331.980087 
L 764.000507 330.723837 
L 761.309408 326.820382 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f0ec91"/>
    <path d="M 722.437034 270.418414 
L 725.134378 273.844192 
L 726.708609 273.423547 
L 724.01409 270.047946 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8c6c5b"/>
    <path d="M 807.454671 412.353514 
L 810.144604 415.932922 
L 811.657045 413.942992 
L 808.968676 410.394553 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c970"/>
    <path d="M 792.838476 388.039532 
L 795.527374 391.878048 
L 797.048081 390.045227 
L 794.36092 386.244076 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #4ddb75"/>
    <path d="M 889.534996 465.644278 
L 892.283576 466.900854 
L 893.772699 463.818827 
L 891.024608 462.571455 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1c60c6"/>
    <path d="M 745.145639 303.652229 
L 747.841553 307.467651 
L 749.394688 306.539387 
L 746.701266 302.776733 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c6b67a"/>
    <path d="M 698.170441 242.246785 
L 700.864548 245.109746 
L 702.465002 245.104003 
L 699.773876 242.281291 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a58c86"/>
    <path d="M 719.739627 267.044645 
L 722.437034 270.418414 
L 724.01409 270.047946 
L 721.319536 266.723458 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #866458"/>
    <path d="M 672.350968 219.84632 
L 675.034245 221.99048 
L 676.663634 222.206651 
L 673.983194 220.087837 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cbbcb9"/>
    <path d="M 780.917675 366.731886 
L 783.607563 370.69172 
L 785.135371 369.028453 
L 782.447382 365.111295 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #95ea84"/>
    <path d="M 845.189674 456.258598 
L 847.896671 458.806996 
L 849.390949 456.463519 
L 846.685051 453.934789 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1373d9"/>
    <path d="M 857.524138 463.518699 
L 860.240961 465.688579 
L 861.73147 463.184923 
L 859.015569 461.032162 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1b63c9"/>
    <path d="M 717.042249 263.72565 
L 719.739627 267.044645 
L 721.319536 266.723458 
L 718.625039 263.452791 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #805c54"/>
    <path d="M 700.864548 245.109746 
L 703.559481 248.045194 
L 705.156959 247.997902 
L 702.465002 245.104003 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9f847e"/>
    <path d="M 804.764886 408.718201 
L 807.454671 412.353514 
L 808.968676 410.394553 
L 806.280494 406.790843 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #05cd67"/>
    <path d="M 714.345002 260.464139 
L 717.042249 263.72565 
L 718.625039 263.452791 
L 715.930694 260.238606 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #85635c"/>
    <path d="M 638.029023 202.023116 
L 640.68516 203.104987 
L 642.348272 203.202264 
L 639.694322 202.126164 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ede8e7"/>
    <path d="M 703.559481 248.045194 
L 706.255114 251.050794 
L 707.849625 250.960701 
L 705.156959 247.997902 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9b7f79"/>
    <path d="M 768.996004 345.256454 
L 771.687946 349.252737 
L 773.223431 347.800049 
L 770.533575 343.850986 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e1f993"/>
    <path d="M 885.302179 467.265103 
L 888.046676 468.625487 
L 889.534996 465.644278 
L 886.791047 464.2942 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1f5bc1"/>
    <path d="M 711.64799 257.262771 
L 714.345002 260.464139 
L 715.930694 260.238606 
L 713.236606 257.083508 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8b6b64"/>
    <path d="M 706.255114 251.050794 
L 708.951323 254.124144 
L 710.542879 253.990044 
L 707.849625 250.960701 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #957771"/>
    <path d="M 647.667966 205.669627 
L 650.333388 207.059912 
L 651.988003 207.233613 
L 649.324991 205.854078 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e5dedc"/>
    <path d="M 708.951323 254.124144 
L 711.64799 257.262771 
L 713.236606 257.083508 
L 710.542879 253.990044 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8f7069"/>
    <path d="M 790.149143 384.162741 
L 792.838476 388.039532 
L 794.36092 386.244076 
L 791.673368 382.405153 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #59de78"/>
    <path d="M 757.071294 324.078506 
L 759.765517 328.025913 
L 761.309408 326.820382 
L 758.617471 322.923658 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eae48e"/>
    <path d="M 742.449019 299.862549 
L 745.145639 303.652229 
L 746.701266 302.776733 
L 744.007181 299.039453 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #beac76"/>
    <path d="M 867.173045 467.213131 
L 869.899083 469.086291 
L 871.387637 466.444462 
L 868.662392 464.586147 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1f5bc1"/>
    <path d="M 874.116635 468.20865 
L 876.849564 469.877792 
L 878.337496 467.115973 
L 875.605261 465.460067 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2058be"/>
    <path d="M 847.896671 458.806996 
L 850.606109 461.266955 
L 852.099312 458.904758 
L 849.390949 456.463519 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #166ed4"/>
    <path d="M 802.075131 405.029704 
L 804.764886 408.718201 
L 806.280494 406.790843 
L 803.592382 403.134558 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #11cf69"/>
    <path d="M 778.22704 362.749566 
L 780.917675 366.731886 
L 782.447382 365.111295 
L 779.758694 361.172003 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a5ed87"/>
    <path d="M 675.034245 221.99048 
L 677.719652 224.225998 
L 679.346177 224.415266 
L 676.663634 222.206651 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c9bab7"/>
    <path d="M 659.997082 211.981214 
L 662.672917 213.763818 
L 664.315487 213.976452 
L 661.642303 212.211671 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dbd1cf"/>
    <path d="M 881.073847 468.677334 
L 883.814492 470.143413 
L 885.302179 467.265103 
L 882.56215 465.810231 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2058be"/>
    <path d="M 860.240961 465.688579 
L 862.960965 467.765325 
L 864.450568 465.245641 
L 861.73147 463.184923 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1c60c6"/>
    <path d="M 739.751736 296.10174 
L 742.449019 299.862549 
L 744.007181 299.039453 
L 741.312475 295.330623 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b8a473"/>
    <path d="M 766.303167 341.253932 
L 768.996004 345.256454 
L 770.533575 343.850986 
L 767.842872 339.895838 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1fc96"/>
    <path d="M 787.45929 380.250683 
L 790.149143 384.162741 
L 791.673368 382.405153 
L 788.985342 378.531433 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #69e17b"/>
    <path d="M 754.376191 320.141098 
L 757.071294 324.078506 
L 758.617471 322.923658 
L 755.924702 319.036845 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e2da89"/>
    <path d="M 799.385293 401.290803 
L 802.075131 405.029704 
L 803.592382 403.134558 
L 800.904229 399.428449 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #21d36d"/>
    <path d="M 824.78994 438.18149 
L 827.486032 441.322291 
L 828.989261 439.208114 
L 826.294566 436.090882 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #009cf4"/>
    <path d="M 827.486032 441.322291 
L 830.183356 444.387018 
L 831.685221 442.250022 
L 828.989261 439.208114 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0296fc"/>
    <path d="M 822.094927 434.966817 
L 824.78994 438.18149 
L 826.294566 436.090882 
L 823.600983 432.900507 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a2e2"/>
    <path d="M 850.606109 461.266955 
L 853.318164 463.636924 
L 854.810315 461.256969 
L 852.099312 458.904758 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1868ce"/>
    <path d="M 631.058882 200.176659 
L 633.708461 201.047139 
L 635.377091 201.048209 
L 632.729523 200.180464 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1edec"/>
    <path d="M 900.773023 462.849684 
L 903.535488 463.814626 
L 905.026215 460.534172 
L 902.264181 459.57381 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1868ce"/>
    <path d="M 830.183356 444.387018 
L 832.882074 447.373546 
L 834.382606 445.214496 
L 831.685221 442.250022 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0490f6"/>
    <path d="M 896.525577 464.973875 
L 899.28341 466.036225 
L 900.773023 462.849684 
L 898.015653 461.793499 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1b63c9"/>
    <path d="M 819.40084 431.680548 
L 822.094927 434.966817 
L 823.600983 432.900507 
L 820.90836 429.639245 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a8d0"/>
    <path d="M 905.026215 460.534172 
L 907.793473 461.404927 
L 909.285413 458.033968 
L 906.518566 457.166022 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #166ed4"/>
    <path d="M 832.882074 447.373546 
L 835.582347 450.279825 
L 837.081577 448.099506 
L 834.382606 445.214496 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0888ee"/>
    <path d="M 775.535607 358.747928 
L 778.22704 362.749566 
L 779.758694 361.172003 
L 777.069255 357.213705 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b5f08a"/>
    <path d="M 677.719652 224.225998 
L 680.407036 226.55128 
L 682.030674 226.712116 
L 679.346177 224.415266 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c5b5b1"/>
    <path d="M 816.707532 428.32503 
L 819.40084 431.680548 
L 820.90836 429.639245 
L 818.216551 426.309424 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00aebf"/>
    <path d="M 892.283576 466.900854 
L 895.03696 468.063463 
L 896.525577 464.973875 
L 893.772699 463.818827 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1e5ec4"/>
    <path d="M 737.05384 292.372909 
L 739.751736 296.10174 
L 741.312475 295.330623 
L 738.617199 291.653295 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b29c6f"/>
    <path d="M 835.582347 450.279825 
L 838.284343 453.103885 
L 839.782299 450.903097 
L 837.081577 448.099506 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0b83e9"/>
    <path d="M 869.899083 469.086291 
L 872.628863 470.864105 
L 874.116635 468.20865 
L 871.387637 466.444462 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2058be"/>
    <path d="M 796.695265 397.504336 
L 799.385293 401.290803 
L 800.904229 399.428449 
L 798.215926 395.675325 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2dd56f"/>
    <path d="M 814.014859 424.902682 
L 816.707532 428.32503 
L 818.216551 426.309424 
L 815.525413 422.913442 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b4ac"/>
    <path d="M 650.333388 207.059912 
L 653.002311 208.553753 
L 654.654463 208.715177 
L 651.988003 207.233613 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e3dbd9"/>
    <path d="M 784.768842 376.306414 
L 787.45929 380.250683 
L 788.985342 378.531433 
L 786.296764 374.625935 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #79e47e"/>
    <path d="M 751.680221 316.216919 
L 754.376191 320.141098 
L 755.924702 319.036845 
L 753.231112 315.163123 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dad085"/>
    <path d="M 763.609416 337.248413 
L 766.303167 341.253932 
L 767.842872 339.895838 
L 765.151302 335.937802 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 876.849564 469.877792 
L 879.586608 471.451058 
L 881.073847 468.677334 
L 878.337496 467.115973 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2058be"/>
    <path d="M 662.672917 213.763818 
L 665.351553 215.644715 
L 666.991431 215.837963 
L 664.315487 213.976452 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d7ccc9"/>
    <path d="M 888.046676 468.625487 
L 890.795815 469.890824 
L 892.283576 466.900854 
L 889.534996 465.644278 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1f5bc1"/>
    <path d="M 640.68516 203.104987 
L 643.345341 204.293504 
L 645.006206 204.383561 
L 642.348272 203.202264 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ebe5e4"/>
    <path d="M 853.318164 463.636924 
L 856.033019 465.915437 
L 857.524138 463.518699 
L 854.810315 461.256969 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1a66cc"/>
    <path d="M 862.960965 467.765325 
L 865.684332 469.747739 
L 867.173045 467.213131 
L 864.450568 465.245641 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1f5bc1"/>
    <path d="M 838.284343 453.103885 
L 840.98823 455.843833 
L 842.484941 453.623393 
L 839.782299 450.903097 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0f7be1"/>
    <path d="M 811.322683 421.415992 
L 814.014859 424.902682 
L 815.525413 422.913442 
L 812.834808 419.453763 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00bb9b"/>
    <path d="M 734.35539 288.67914 
L 737.05384 292.372909 
L 738.617199 291.653295 
L 735.921406 288.0105 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #aa926b"/>
    <path d="M 680.407036 226.55128 
L 683.096241 228.964632 
L 684.716975 229.095541 
L 682.030674 226.712116 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c1b0ac"/>
    <path d="M 772.84333 354.730168 
L 775.535607 358.747928 
L 777.069255 357.213705 
L 774.379019 353.239556 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c1f38d"/>
    <path d="M 794.004946 393.673192 
L 796.695265 397.504336 
L 798.215926 395.675325 
L 795.527374 391.878048 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #3dd872"/>
    <path d="M 840.98823 455.843833 
L 843.69418 458.497857 
L 845.189674 456.258598 
L 842.484941 453.623393 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1276dc"/>
    <path d="M 808.63087 417.867514 
L 811.322683 421.415992 
L 812.834808 419.453763 
L 810.144604 415.932922 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c088"/>
    <path d="M 748.983404 312.309197 
L 751.680221 316.216919 
L 753.231112 315.163123 
L 750.536721 311.305669 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d4c882"/>
    <path d="M 782.077726 372.333027 
L 784.768842 376.306414 
L 786.296764 374.625935 
L 783.607563 370.69172 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #85e781"/>
    <path d="M 731.656447 285.023489 
L 734.35539 288.67914 
L 735.921406 288.0105 
L 733.225158 284.405238 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a48b68"/>
    <path d="M 883.814492 470.143413 
L 886.55961 471.513559 
L 888.046676 468.625487 
L 885.302179 467.265103 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2058be"/>
    <path d="M 760.914738 333.243153 
L 763.609416 337.248413 
L 765.151302 335.937802 
L 762.458853 331.980087 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f8f695"/>
    <path d="M 683.096241 228.964632 
L 685.787118 231.464268 
L 687.404931 231.563787 
L 684.716975 229.095541 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bdaba7"/>
    <path d="M 856.033019 465.915437 
L 858.750853 468.101113 
L 860.240961 465.688579 
L 857.524138 463.518699 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1c60c6"/>
    <path d="M 805.939291 414.259869 
L 808.63087 417.867514 
L 810.144604 415.932922 
L 807.454671 412.353514 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c677"/>
    <path d="M 843.69418 458.497857 
L 846.402369 461.06423 
L 847.896671 458.806996 
L 845.189674 456.258598 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1470d6"/>
    <path d="M 665.351553 215.644715 
L 668.032827 217.622697 
L 669.669978 217.795016 
L 666.991431 215.837963 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d5c9c7"/>
    <path d="M 872.628863 470.864105 
L 875.362569 472.545645 
L 876.849564 469.877792 
L 874.116635 468.20865 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2256bc"/>
    <path d="M 791.314239 389.800318 
L 794.004946 393.673192 
L 795.527374 391.878048 
L 792.838476 388.039532 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #49db75"/>
    <path d="M 728.95708 281.408981 
L 731.656447 285.023489 
L 733.225158 284.405238 
L 730.528521 280.840482 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9e8365"/>
    <path d="M 770.15017 350.699509 
L 772.84333 354.730168 
L 774.379019 353.239556 
L 771.687946 349.252737 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d1f690"/>
    <path d="M 865.684332 469.747739 
L 868.411247 471.634708 
L 869.899083 469.086291 
L 867.173045 467.213131 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2058be"/>
    <path d="M 633.708461 201.047139 
L 636.362466 202.026128 
L 638.029023 202.023116 
L 635.377091 201.048209 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #efebea"/>
    <path d="M 653.002311 208.553753 
L 655.674569 210.150372 
L 657.32421 210.298004 
L 654.654463 208.715177 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e3dbd9"/>
    <path d="M 746.285766 308.421151 
L 748.983404 312.309197 
L 750.536721 311.305669 
L 747.841553 307.467651 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ccbe7d"/>
    <path d="M 899.28341 466.036225 
L 902.046363 467.005588 
L 903.535488 463.814626 
L 900.773023 462.849684 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1b63c9"/>
    <path d="M 685.787118 231.464268 
L 688.479519 234.048308 
L 690.094397 234.115009 
L 687.404931 231.563787 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b9a5a1"/>
    <path d="M 903.535488 463.814626 
L 906.303209 464.688122 
L 907.793473 461.404927 
L 905.026215 460.534172 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1868ce"/>
    <path d="M 803.247822 410.595741 
L 805.939291 414.259869 
L 807.454671 412.353514 
L 804.764886 408.718201 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #01cc66"/>
    <path d="M 779.385878 368.333659 
L 782.077726 372.333027 
L 783.607563 370.69172 
L 780.917675 366.731886 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #95ea84"/>
    <path d="M 879.586608 471.451058 
L 882.327945 472.9277 
L 883.814492 470.143413 
L 881.073847 468.677334 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2256bc"/>
    <path d="M 895.03696 468.063463 
L 897.795317 469.131726 
L 899.28341 466.036225 
L 896.525577 464.973875 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1e5ec4"/>
    <path d="M 726.257365 277.838605 
L 728.95708 281.408981 
L 730.528521 280.840482 
L 727.831568 277.319167 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #967960"/>
    <path d="M 758.219127 329.241419 
L 760.914738 333.243153 
L 762.458853 331.980087 
L 759.765517 328.025913 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f0ec91"/>
    <path d="M 846.402369 461.06423 
L 849.112974 463.541302 
L 850.606109 461.266955 
L 847.896671 458.806996 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #176bd1"/>
    <path d="M 643.345341 204.293504 
L 646.009404 205.588231 
L 647.667966 205.669627 
L 645.006206 204.383561 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ebe5e4"/>
    <path d="M 788.623055 385.888705 
L 791.314239 389.800318 
L 792.838476 388.039532 
L 790.149143 384.162741 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #59de78"/>
    <path d="M 858.750853 468.101113 
L 861.471851 470.192654 
L 862.960965 467.765325 
L 860.240961 465.688579 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1f5bc1"/>
    <path d="M 688.479519 234.048308 
L 691.173296 236.714782 
L 692.78523 236.747275 
L 690.094397 234.115009 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b5a09c"/>
    <path d="M 890.795815 469.890824 
L 893.54977 471.060644 
L 895.03696 468.063463 
L 892.283576 466.900854 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2058be"/>
    <path d="M 723.557383 274.315312 
L 726.257365 277.838605 
L 727.831568 277.319167 
L 725.134378 273.844192 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #90715d"/>
    <path d="M 800.556345 406.877877 
L 803.247822 410.595741 
L 804.764886 408.718201 
L 802.075131 405.029704 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #11cf69"/>
    <path d="M 767.456096 346.659198 
L 770.15017 350.699509 
L 771.687946 349.252737 
L 768.996004 345.256454 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e1f993"/>
    <path d="M 743.58734 304.555995 
L 746.285766 308.421151 
L 747.841553 307.467651 
L 745.145639 303.652229 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c4b379"/>
    <path d="M 626.740321 199.517586 
L 629.38721 200.280843 
L 631.058882 200.176659 
L 628.413887 199.414769 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f3f0ef"/>
    <path d="M 668.032827 217.622697 
L 670.716579 219.696449 
L 672.350968 219.84632 
L 669.669978 217.795016 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d3c7c4"/>
    <path d="M 849.112974 463.541302 
L 851.826174 465.927512 
L 853.318164 463.636924 
L 850.606109 461.266955 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1a66cc"/>
    <path d="M 691.173296 236.714782 
L 693.868306 239.461633 
L 695.477291 239.458568 
L 692.78523 236.747275 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b19b96"/>
    <path d="M 720.857218 270.842012 
L 723.557383 274.315312 
L 725.134378 273.844192 
L 722.437034 270.418414 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8a695a"/>
    <path d="M 776.693239 364.311479 
L 779.385878 368.333659 
L 780.917675 366.731886 
L 778.22704 362.749566 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a5ed87"/>
    <path d="M 755.522583 325.246486 
L 758.219127 329.241419 
L 759.765517 328.025913 
L 757.071294 324.078506 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e8e28d"/>
    <path d="M 886.55961 471.513559 
L 889.309377 472.787209 
L 890.795815 469.890824 
L 888.046676 468.625487 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2256bc"/>
    <path d="M 823.284493 440.200991 
L 825.982072 443.363079 
L 827.486032 441.322291 
L 824.78994 438.18149 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #009afa"/>
    <path d="M 825.982072 443.363079 
L 828.680852 446.448421 
L 830.183356 444.387018 
L 827.486032 441.322291 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0393f9"/>
    <path d="M 868.411247 471.634708 
L 871.141894 473.425206 
L 872.628863 470.864105 
L 869.899083 469.086291 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2256bc"/>
    <path d="M 820.587961 436.964377 
L 823.284493 440.200991 
L 824.78994 438.18149 
L 822.094927 434.966817 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a0e8"/>
    <path d="M 828.680852 446.448421 
L 831.380994 449.454875 
L 832.882074 447.373546 
L 830.183356 444.387018 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #068ef4"/>
    <path d="M 718.156964 267.421568 
L 720.857218 270.842012 
L 722.437034 270.418414 
L 719.739627 267.044645 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #846257"/>
    <path d="M 875.362569 472.545645 
L 878.100383 474.13007 
L 879.586608 471.451058 
L 876.849564 469.877792 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2353b9"/>
    <path d="M 797.864747 403.109081 
L 800.556345 406.877877 
L 802.075131 405.029704 
L 799.385293 401.290803 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1dd26c"/>
    <path d="M 693.868306 239.461633 
L 696.56441 242.286722 
L 698.170441 242.246785 
L 695.477291 239.458568 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ab938e"/>
    <path d="M 785.93131 381.941395 
L 788.623055 385.888705 
L 790.149143 384.162741 
L 787.45929 380.250683 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #69e17b"/>
    <path d="M 817.892321 433.655529 
L 820.587961 436.964377 
L 822.094927 434.966817 
L 819.40084 431.680548 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a6d7"/>
    <path d="M 831.380994 449.454875 
L 834.082662 452.380377 
L 835.582347 450.279825 
L 832.882074 447.373546 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0a86ec"/>
    <path d="M 655.674569 210.150372 
L 658.349999 211.848874 
L 659.997082 211.981214 
L 657.32421 210.298004 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dfd6d4"/>
    <path d="M 740.888167 300.716924 
L 743.58734 304.555995 
L 745.145639 303.652229 
L 742.449019 299.862549 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #beac76"/>
    <path d="M 715.456718 264.056796 
L 718.156964 267.421568 
L 719.739627 267.044645 
L 717.042249 263.72565 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #815e56"/>
    <path d="M 696.56441 242.286722 
L 699.26147 245.187826 
L 700.864548 245.109746 
L 698.170441 242.246785 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a78e89"/>
    <path d="M 815.197426 430.276813 
L 817.892321 433.655529 
L 819.40084 431.680548 
L 816.707532 428.32503 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00acc4"/>
    <path d="M 834.082662 452.380377 
L 836.786023 455.222941 
L 838.284343 453.103885 
L 835.582347 450.279825 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0c80e6"/>
    <path d="M 764.761081 342.612503 
L 767.456096 346.659198 
L 768.996004 345.256454 
L 766.303167 341.253932 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1fc96"/>
    <path d="M 861.471851 470.192654 
L 864.196196 472.188851 
L 865.684332 469.747739 
L 862.960965 467.765325 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2058be"/>
    <path d="M 712.756581 260.750456 
L 715.456718 264.056796 
L 717.042249 263.72565 
L 714.345002 260.464139 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #87655e"/>
    <path d="M 851.826174 465.927512 
L 854.54215 468.22138 
L 856.033019 465.915437 
L 853.318164 463.636924 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1c60c6"/>
    <path d="M 699.26147 245.187826 
L 701.959352 248.162644 
L 703.559481 248.045194 
L 700.864548 245.109746 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a38984"/>
    <path d="M 670.716579 219.696449 
L 673.402648 221.86455 
L 675.034245 221.99048 
L 672.350968 219.84632 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cfc2bf"/>
    <path d="M 710.056662 257.505256 
L 712.756581 260.750456 
L 714.345002 260.464139 
L 711.64799 257.262771 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8d6d66"/>
    <path d="M 812.503132 426.830667 
L 815.197426 430.276813 
L 816.707532 428.32503 
L 814.014859 424.902682 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b2b2"/>
    <path d="M 701.959352 248.162644 
L 704.657928 251.208799 
L 706.255114 251.050794 
L 703.559481 248.045194 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9d827c"/>
    <path d="M 882.327945 472.9277 
L 885.073756 474.307061 
L 886.55961 471.513559 
L 883.814492 470.143413 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2353b9"/>
    <path d="M 773.999757 360.269691 
L 776.693239 364.311479 
L 778.22704 362.749566 
L 775.535607 358.747928 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b1ef89"/>
    <path d="M 752.825115 321.261631 
L 755.522583 325.246486 
L 757.071294 324.078506 
L 754.376191 320.141098 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e2da89"/>
    <path d="M 707.357072 254.323842 
L 710.056662 257.505256 
L 711.64799 257.262771 
L 708.951323 254.124144 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #93756e"/>
    <path d="M 704.657928 251.208799 
L 707.357072 254.323842 
L 708.951323 254.124144 
L 706.255114 251.050794 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #977a74"/>
    <path d="M 795.172919 399.292217 
L 797.864747 403.109081 
L 799.385293 401.290803 
L 796.695265 397.504336 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2dd56f"/>
    <path d="M 836.786023 455.222941 
L 839.491247 457.980659 
L 840.98823 455.843833 
L 838.284343 453.103885 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0f7be1"/>
    <path d="M 636.362466 202.026128 
L 639.020737 203.113425 
L 640.68516 203.104987 
L 638.029023 202.023116 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #efebea"/>
    <path d="M 738.188291 296.907118 
L 740.888167 300.716924 
L 742.449019 299.862549 
L 739.751736 296.10174 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b6a272"/>
    <path d="M 783.238927 377.961473 
L 785.93131 381.941395 
L 787.45929 380.250683 
L 784.768842 376.306414 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #75e37d"/>
    <path d="M 646.009404 205.588231 
L 648.677183 206.98861 
L 650.333388 207.059912 
L 647.667966 205.669627 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e9e3e2"/>
    <path d="M 809.809301 423.319597 
L 812.503132 426.830667 
L 814.014859 424.902682 
L 811.322683 421.415992 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b8a0"/>
    <path d="M 902.046363 467.005588 
L 904.8146 467.881757 
L 906.303209 464.688122 
L 903.535488 463.814626 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1b63c9"/>
    <path d="M 897.795317 469.131726 
L 900.558816 470.105347 
L 902.046363 467.005588 
L 899.28341 466.036225 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1e5ec4"/>
    <path d="M 839.491247 457.980659 
L 842.198508 460.651708 
L 843.69418 458.497857 
L 840.98823 455.843833 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1373d9"/>
    <path d="M 762.065106 338.562709 
L 764.761081 342.612503 
L 766.303167 341.253932 
L 763.609416 337.248413 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 893.54977 471.060644 
L 896.308714 472.134561 
L 897.795317 469.131726 
L 895.03696 468.063463 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2058be"/>
    <path d="M 871.141894 473.425206 
L 873.876457 475.118295 
L 875.362569 472.545645 
L 872.628863 470.864105 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2353b9"/>
    <path d="M 854.54215 468.22138 
L 857.261086 470.421513 
L 858.750853 468.101113 
L 856.033019 465.915437 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1e5ec4"/>
    <path d="M 807.115797 419.746179 
L 809.809301 423.319597 
L 811.322683 421.415992 
L 808.63087 417.867514 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00be8f"/>
    <path d="M 792.48076 395.430202 
L 795.172919 399.292217 
L 796.695265 397.504336 
L 794.004946 393.673192 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #39d771"/>
    <path d="M 673.402648 221.86455 
L 676.090874 224.125478 
L 677.719652 224.225998 
L 675.034245 221.99048 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cbbcb9"/>
    <path d="M 658.349999 211.848874 
L 661.028434 213.648254 
L 662.672917 213.763818 
L 659.997082 211.981214 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ddd3d1"/>
    <path d="M 750.126737 317.290133 
L 752.825115 321.261631 
L 754.376191 320.141098 
L 751.680221 316.216919 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dad085"/>
    <path d="M 735.487766 293.129736 
L 738.188291 296.907118 
L 739.751736 296.10174 
L 737.05384 292.372909 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b09a6e"/>
    <path d="M 771.305388 356.211529 
L 773.999757 360.269691 
L 775.535607 358.747928 
L 772.84333 354.730168 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c1f38d"/>
    <path d="M 864.196196 472.188851 
L 866.924074 474.088582 
L 868.411247 471.634708 
L 865.684332 469.747739 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2256bc"/>
    <path d="M 842.198508 460.651708 
L 844.907981 463.234345 
L 846.402369 461.06423 
L 843.69418 458.497857 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #166ed4"/>
    <path d="M 878.100383 474.13007 
L 880.842488 475.616625 
L 882.327945 472.9277 
L 879.586608 471.451058 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2450b6"/>
    <path d="M 629.38721 200.280843 
L 632.038748 201.153926 
L 633.708461 201.047139 
L 631.058882 200.176659 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f3f0ef"/>
    <path d="M 780.545835 373.952068 
L 783.238927 377.961473 
L 784.768842 376.306414 
L 782.077726 372.333027 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #85e781"/>
    <path d="M 889.309377 472.787209 
L 892.063969 473.963885 
L 893.54977 471.060644 
L 890.795815 469.890824 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2256bc"/>
    <path d="M 804.422491 416.113054 
L 807.115797 419.746179 
L 808.63087 417.867514 
L 805.939291 414.259869 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c677"/>
    <path d="M 732.78665 289.387914 
L 735.487766 293.129736 
L 737.05384 292.372909 
L 734.35539 288.67914 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #aa926b"/>
    <path d="M 789.788175 391.526007 
L 792.48076 395.430202 
L 794.004946 393.673192 
L 791.314239 389.800318 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #49db75"/>
    <path d="M 759.368161 334.513116 
L 762.065106 338.562709 
L 763.609416 337.248413 
L 760.914738 333.243153 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f8f695"/>
    <path d="M 844.907981 463.234345 
L 847.619845 465.72691 
L 849.112974 463.541302 
L 846.402369 461.06423 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1868ce"/>
    <path d="M 676.090874 224.125478 
L 678.781099 226.477608 
L 680.407036 226.55128 
L 677.719652 224.225998 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c9bab7"/>
    <path d="M 747.42747 313.335266 
L 750.126737 317.290133 
L 751.680221 316.216919 
L 748.983404 312.309197 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d2c581"/>
    <path d="M 857.261086 470.421513 
L 859.983166 472.526604 
L 861.471851 470.192654 
L 858.750853 468.101113 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2058be"/>
    <path d="M 801.729259 412.422928 
L 804.422491 416.113054 
L 805.939291 414.259869 
L 803.247822 410.595741 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #01cc66"/>
    <path d="M 885.073756 474.307061 
L 887.824221 475.588569 
L 889.309377 472.787209 
L 886.55961 471.513559 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2450b6"/>
    <path d="M 768.610093 352.140255 
L 771.305388 356.211529 
L 772.84333 354.730168 
L 770.15017 350.699509 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d1f690"/>
    <path d="M 648.677183 206.98861 
L 651.348514 208.49397 
L 653.002311 208.553753 
L 650.333388 207.059912 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e7e0df"/>
    <path d="M 639.020737 203.113425 
L 641.68311 204.308709 
L 643.345341 204.293504 
L 640.68516 203.104987 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #efebea"/>
    <path d="M 777.851969 369.916347 
L 780.545835 373.952068 
L 782.077726 372.333027 
L 779.385878 368.333659 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #95ea84"/>
    <path d="M 730.085008 285.684758 
L 732.78665 289.387914 
L 734.35539 288.67914 
L 731.656447 285.023489 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a28867"/>
    <path d="M 661.028434 213.648254 
L 663.70971 215.547392 
L 665.351553 215.644715 
L 662.672917 213.763818 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dbd1cf"/>
    <path d="M 873.876457 475.118295 
L 876.615122 476.713125 
L 878.100383 474.13007 
L 875.362569 472.545645 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2450b6"/>
    <path d="M 866.924074 474.088582 
L 869.655671 475.890811 
L 871.141894 473.425206 
L 868.411247 471.634708 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2450b6"/>
    <path d="M 847.619845 465.72691 
L 850.33428 468.127828 
L 851.826174 465.927512 
L 849.112974 463.541302 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1b63c9"/>
    <path d="M 678.781099 226.477608 
L 681.473168 228.919217 
L 683.096241 228.964632 
L 680.407036 226.55128 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c5b5b1"/>
    <path d="M 787.095074 387.582654 
L 789.788175 391.526007 
L 791.314239 389.800318 
L 788.623055 385.888705 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #55dd77"/>
    <path d="M 799.035983 408.678569 
L 801.729259 412.422928 
L 803.247822 410.595741 
L 800.556345 406.877877 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0dcf69"/>
    <path d="M 756.67024 330.467033 
L 759.368161 334.513116 
L 760.914738 333.243153 
L 758.219127 329.241419 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f0ec91"/>
    <path d="M 744.727342 309.400302 
L 747.42747 313.335266 
L 748.983404 312.309197 
L 746.285766 308.421151 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ccbe7d"/>
    <path d="M 727.38291 282.023343 
L 730.085008 285.684758 
L 731.656447 285.023489 
L 728.95708 281.408981 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9c8064"/>
    <path d="M 900.558816 470.105347 
L 903.327624 470.984118 
L 904.8146 467.881757 
L 902.046363 467.005588 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1e5ec4"/>
    <path d="M 824.477322 445.329796 
L 827.177648 448.433529 
L 828.680852 446.448421 
L 825.982072 443.363079 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0393f9"/>
    <path d="M 821.778167 442.148722 
L 824.477322 445.329796 
L 825.982072 443.363079 
L 823.284493 440.200991 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #009afa"/>
    <path d="M 880.842488 475.616625 
L 883.589067 477.004644 
L 885.073756 474.307061 
L 882.327945 472.9277 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #264eb4"/>
    <path d="M 827.177648 448.433529 
L 829.879305 451.457765 
L 831.380994 449.454875 
L 828.680852 446.448421 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #078bf1"/>
    <path d="M 765.91384 348.059155 
L 768.610093 352.140255 
L 770.15017 350.699509 
L 767.456096 346.659198 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e1f993"/>
    <path d="M 819.080026 438.892543 
L 821.778167 442.148722 
L 823.284493 440.200991 
L 820.587961 436.964377 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #009eef"/>
    <path d="M 859.983166 472.526604 
L 862.708576 474.535434 
L 864.196196 472.188851 
L 861.471851 470.192654 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2256bc"/>
    <path d="M 896.308714 472.134561 
L 899.072818 473.112278 
L 900.558816 470.105347 
L 897.795317 469.131726 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2058be"/>
    <path d="M 829.879305 451.457765 
L 832.582459 454.400427 
L 834.082662 452.380377 
L 831.380994 449.454875 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0a86ec"/>
    <path d="M 681.473168 228.919217 
L 684.166926 231.448486 
L 685.787118 231.464268 
L 683.096241 228.964632 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c1b0ac"/>
    <path d="M 775.15727 365.857514 
L 777.851969 369.916347 
L 779.385878 368.333659 
L 776.693239 364.311479 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a1ec86"/>
    <path d="M 816.382747 435.563565 
L 819.080026 438.892543 
L 820.587961 436.964377 
L 817.892321 433.655529 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a4dc"/>
    <path d="M 796.342549 404.882804 
L 799.035983 408.678569 
L 800.556345 406.877877 
L 797.864747 403.109081 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1dd26c"/>
    <path d="M 850.33428 468.127828 
L 853.051468 470.435611 
L 854.54215 468.22138 
L 851.826174 465.927512 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1e5ec4"/>
    <path d="M 724.680434 278.406709 
L 727.38291 282.023343 
L 728.95708 281.408981 
L 726.257365 277.838605 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #967960"/>
    <path d="M 832.582459 454.400427 
L 835.287277 457.259513 
L 836.786023 455.222941 
L 834.082662 452.380377 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0e7ee4"/>
    <path d="M 784.401372 383.603211 
L 787.095074 387.582654 
L 788.623055 385.888705 
L 785.93131 381.941395 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #65e07a"/>
    <path d="M 892.063969 473.963885 
L 894.823563 475.043196 
L 896.308714 472.134561 
L 893.54977 471.060644 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2353b9"/>
    <path d="M 813.68618 432.164171 
L 816.382747 435.563565 
L 817.892321 433.655529 
L 815.197426 430.276813 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00aacb"/>
    <path d="M 663.70971 215.547392 
L 666.393662 217.54506 
L 668.032827 217.622697 
L 665.351553 215.644715 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d9cecc"/>
    <path d="M 742.026386 305.488497 
L 744.727342 309.400302 
L 746.285766 308.421151 
L 743.58734 304.555995 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c4b379"/>
    <path d="M 632.038748 201.153926 
L 634.694773 202.136756 
L 636.362466 202.026128 
L 633.708461 201.047139 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f3f0ef"/>
    <path d="M 753.971344 326.427779 
L 756.67024 330.467033 
L 758.219127 329.241419 
L 755.522583 325.246486 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e8e28d"/>
    <path d="M 651.348514 208.49397 
L 654.02323 210.103517 
L 655.674569 210.150372 
L 653.002311 208.553753 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e5dedc"/>
    <path d="M 835.287277 457.259513 
L 837.99393 460.033107 
L 839.491247 457.980659 
L 836.786023 455.222941 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1078de"/>
    <path d="M 684.166926 231.448486 
L 686.862221 234.063503 
L 688.479519 234.048308 
L 685.787118 231.464268 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bdaba7"/>
    <path d="M 810.990181 428.696815 
L 813.68618 432.164171 
L 815.197426 430.276813 
L 812.503132 426.830667 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b0b9"/>
    <path d="M 721.977664 274.837856 
L 724.680434 278.406709 
L 726.257365 277.838605 
L 723.557383 274.315312 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8e6e5c"/>
    <path d="M 869.655671 475.890811 
L 872.391173 477.594592 
L 873.876457 475.118295 
L 871.141894 473.425206 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #264eb4"/>
    <path d="M 793.648849 401.038519 
L 796.342549 404.882804 
L 797.864747 403.109081 
L 795.172919 399.292217 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #29d46e"/>
    <path d="M 763.216604 343.971535 
L 765.91384 348.059155 
L 767.456096 346.659198 
L 764.761081 342.612503 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1fc96"/>
    <path d="M 887.824221 475.588569 
L 890.579519 476.771741 
L 892.063969 473.963885 
L 889.309377 472.787209 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2450b6"/>
    <path d="M 641.68311 204.308709 
L 644.349421 205.611536 
L 646.009404 205.588231 
L 643.345341 204.293504 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ede8e7"/>
    <path d="M 876.615122 476.713125 
L 879.358072 478.208934 
L 880.842488 475.616625 
L 878.100383 474.13007 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #264eb4"/>
    <path d="M 837.99393 460.033107 
L 840.702593 462.719369 
L 842.198508 460.651708 
L 839.491247 457.980659 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1373d9"/>
    <path d="M 772.461688 361.778806 
L 775.15727 365.857514 
L 776.693239 364.311479 
L 773.999757 360.269691 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b1ef89"/>
    <path d="M 808.294611 425.164021 
L 810.990181 428.696815 
L 812.503132 426.830667 
L 809.809301 423.319597 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b6a7"/>
    <path d="M 719.274686 271.319744 
L 721.977664 274.837856 
L 723.557383 274.315312 
L 720.857218 270.842012 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #886759"/>
    <path d="M 686.862221 234.063503 
L 689.558904 236.762264 
L 691.173296 236.714782 
L 688.479519 234.048308 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b7a39f"/>
    <path d="M 853.051468 470.435611 
L 855.771595 472.648853 
L 857.261086 470.421513 
L 854.54215 468.22138 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1f5bc1"/>
    <path d="M 625.065898 199.729858 
L 627.714631 200.49446 
L 629.38721 200.280843 
L 626.740321 199.517586 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f5f2f2"/>
    <path d="M 739.324645 301.603098 
L 742.026386 305.488497 
L 743.58734 304.555995 
L 740.888167 300.716924 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bca975"/>
    <path d="M 862.708576 474.535434 
L 865.437503 476.44687 
L 866.924074 474.088582 
L 864.196196 472.188851 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2450b6"/>
    <path d="M 781.706993 379.590793 
L 784.401372 383.603211 
L 785.93131 381.941395 
L 783.238927 377.961473 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #75e37d"/>
    <path d="M 751.271483 322.398677 
L 753.971344 326.427779 
L 755.522583 325.246486 
L 752.825115 321.261631 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e0d788"/>
    <path d="M 716.571596 267.855284 
L 719.274686 271.319744 
L 720.857218 270.842012 
L 718.156964 267.421568 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #825f56"/>
    <path d="M 666.393662 217.54506 
L 669.080126 219.639921 
L 670.716579 219.696449 
L 668.032827 217.622697 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d5c9c7"/>
    <path d="M 689.558904 236.762264 
L 692.256829 239.542674 
L 693.868306 239.461633 
L 691.173296 236.714782 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b39e99"/>
    <path d="M 840.702593 462.719369 
L 843.413442 465.316548 
L 844.907981 463.234345 
L 842.198508 460.651708 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #176bd1"/>
    <path d="M 805.599335 421.568382 
L 808.294611 425.164021 
L 809.809301 423.319597 
L 807.115797 419.746179 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00be8f"/>
    <path d="M 790.954782 397.148657 
L 793.648849 401.038519 
L 795.172919 399.292217 
L 792.48076 395.430202 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #39d771"/>
    <path d="M 883.589067 477.004644 
L 886.340301 478.29355 
L 887.824221 475.588569 
L 885.073756 474.307061 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #264eb4"/>
    <path d="M 713.868494 264.44734 
L 716.571596 267.855284 
L 718.156964 267.421568 
L 715.456718 264.056796 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #836059"/>
    <path d="M 692.256829 239.542674 
L 694.955853 242.402557 
L 696.56441 242.286722 
L 693.868306 239.461633 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #af9994"/>
    <path d="M 760.518368 339.88072 
L 763.216604 343.971535 
L 764.761081 342.612503 
L 762.065106 338.562709 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 736.622166 297.747332 
L 739.324645 301.603098 
L 740.888167 300.716924 
L 738.188291 296.907118 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b6a272"/>
    <path d="M 711.165484 261.098719 
L 713.868494 264.44734 
L 715.456718 264.056796 
L 712.756581 260.750456 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #896861"/>
    <path d="M 769.765177 357.683494 
L 772.461688 361.778806 
L 773.999757 360.269691 
L 771.305388 356.211529 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c1f38d"/>
    <path d="M 802.904223 417.912559 
L 805.599335 421.568382 
L 807.115797 419.746179 
L 804.422491 416.113054 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c47d"/>
    <path d="M 654.02323 210.103517 
L 656.701163 211.816346 
L 658.349999 211.848874 
L 655.674569 210.150372 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e3dbd9"/>
    <path d="M 694.955853 242.402557 
L 697.655834 245.339651 
L 699.26147 245.187826 
L 696.56441 242.286722 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a9918c"/>
    <path d="M 843.413442 465.316548 
L 846.126656 467.822971 
L 847.619845 465.72691 
L 844.907981 463.234345 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1a66cc"/>
    <path d="M 855.771595 472.648853 
L 858.494846 474.766239 
L 859.983166 472.526604 
L 857.261086 470.421513 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2256bc"/>
    <path d="M 779.011866 375.548557 
L 781.706993 379.590793 
L 783.238927 377.961473 
L 780.545835 373.952068 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #85e781"/>
    <path d="M 708.462676 257.812176 
L 711.165484 261.098719 
L 712.756581 260.750456 
L 710.056662 257.505256 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8f7069"/>
    <path d="M 697.655834 245.339651 
L 700.356638 248.351614 
L 701.959352 248.162644 
L 699.26147 245.187826 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a58c86"/>
    <path d="M 705.760185 254.590403 
L 708.462676 257.812176 
L 710.056662 257.505256 
L 707.357072 254.323842 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #957771"/>
    <path d="M 899.072818 473.112278 
L 901.842252 473.99358 
L 903.327624 470.984118 
L 900.558816 470.105347 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2058be"/>
    <path d="M 700.356638 248.351614 
L 703.058131 251.436028 
L 704.657928 251.208799 
L 701.959352 248.162644 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9f847e"/>
    <path d="M 748.570672 318.383048 
L 751.271483 322.398677 
L 752.825115 321.261631 
L 750.126737 317.290133 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dad085"/>
    <path d="M 703.058131 251.436028 
L 705.760185 254.590403 
L 707.357072 254.323842 
L 704.657928 251.208799 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9b7f79"/>
    <path d="M 872.391173 477.594592 
L 875.130767 479.199066 
L 876.615122 476.713125 
L 873.876457 475.118295 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #274bb1"/>
    <path d="M 788.260251 393.216211 
L 790.954782 397.148657 
L 792.48076 395.430202 
L 789.788175 391.526007 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #45da74"/>
    <path d="M 669.080126 219.639921 
L 671.768937 221.830532 
L 673.402648 221.86455 
L 670.716579 219.696449 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d3c7c4"/>
    <path d="M 634.694773 202.136756 
L 637.355123 203.22913 
L 639.020737 203.113425 
L 636.362466 202.026128 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1edec"/>
    <path d="M 865.437503 476.44687 
L 868.170134 478.259868 
L 869.655671 475.890811 
L 866.924074 474.088582 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #264eb4"/>
    <path d="M 894.823563 475.043196 
L 897.588333 476.02484 
L 899.072818 473.112278 
L 896.308714 472.134561 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2353b9"/>
    <path d="M 800.209152 414.199275 
L 802.904223 417.912559 
L 804.422491 416.113054 
L 801.729259 412.422928 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00cb6b"/>
    <path d="M 733.919003 293.924408 
L 736.622166 297.747332 
L 738.188291 296.907118 
L 735.487766 293.129736 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ae976d"/>
    <path d="M 644.349421 205.611536 
L 647.019502 207.021343 
L 648.677183 206.98861 
L 646.009404 205.588231 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ebe5e4"/>
    <path d="M 879.358072 478.208934 
L 882.105493 479.60505 
L 883.589067 477.004644 
L 880.842488 475.616625 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #274bb1"/>
    <path d="M 846.126656 467.822971 
L 848.842416 470.237055 
L 850.33428 468.127828 
L 847.619845 465.72691 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1c60c6"/>
    <path d="M 757.81912 335.790051 
L 760.518368 339.88072 
L 762.065106 338.562709 
L 759.368161 334.513116 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f8f695"/>
    <path d="M 767.067701 353.574872 
L 769.765177 357.683494 
L 771.305388 356.211529 
L 768.610093 352.140255 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d1f690"/>
    <path d="M 890.579519 476.771741 
L 893.339827 477.856181 
L 894.823563 475.043196 
L 892.063969 473.963885 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2450b6"/>
    <path d="M 776.315925 371.479702 
L 779.011866 375.548557 
L 780.545835 373.952068 
L 777.851969 369.916347 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #91e983"/>
    <path d="M 745.868933 314.384214 
L 748.570672 318.383048 
L 750.126737 317.290133 
L 747.42747 313.335266 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d2c581"/>
    <path d="M 858.494846 474.766239 
L 861.221408 476.78654 
L 862.708576 474.535434 
L 859.983166 472.526604 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2353b9"/>
    <path d="M 797.514001 410.431318 
L 800.209152 414.199275 
L 801.729259 412.422928 
L 799.035983 408.678569 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0dcf69"/>
    <path d="M 785.565167 389.244229 
L 788.260251 393.216211 
L 789.788175 391.526007 
L 787.095074 387.582654 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #55dd77"/>
    <path d="M 731.215216 290.137506 
L 733.919003 293.924408 
L 735.487766 293.129736 
L 732.78665 289.387914 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a8906a"/>
    <path d="M 671.768937 221.830532 
L 674.459934 224.115343 
L 676.090874 224.125478 
L 673.402648 221.86455 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cfc2bf"/>
    <path d="M 656.701163 211.816346 
L 659.382144 213.631433 
L 661.028434 213.648254 
L 658.349999 211.848874 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e1d9d7"/>
    <path d="M 822.971721 447.221828 
L 825.673681 450.341713 
L 827.177648 448.433529 
L 824.477322 445.329796 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0490f6"/>
    <path d="M 627.714631 200.49446 
L 630.368074 201.370016 
L 632.038748 201.153926 
L 629.38721 200.280843 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f5f2f2"/>
    <path d="M 820.270902 444.024087 
L 822.971721 447.221828 
L 824.477322 445.329796 
L 821.778167 442.148722 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0098fe"/>
    <path d="M 825.673681 450.341713 
L 828.376944 453.381572 
L 829.879305 451.457765 
L 827.177648 448.433529 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #078bf1"/>
    <path d="M 817.571066 440.750735 
L 820.270902 444.024087 
L 821.778167 442.148722 
L 819.080026 438.892543 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #009eef"/>
    <path d="M 848.842416 470.237055 
L 851.560907 472.557299 
L 853.051468 470.435611 
L 850.33428 468.127828 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1e5ec4"/>
    <path d="M 828.376944 453.381572 
L 831.081673 456.339314 
L 832.582459 454.400427 
L 829.879305 451.457765 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0b83e9"/>
    <path d="M 886.340301 478.29355 
L 889.096372 479.482854 
L 890.579519 476.771741 
L 887.824221 475.588569 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #274bb1"/>
    <path d="M 814.872061 437.404094 
L 817.571066 440.750735 
L 819.080026 438.892543 
L 816.382747 435.563565 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a4dc"/>
    <path d="M 755.118856 331.702876 
L 757.81912 335.790051 
L 759.368161 334.513116 
L 756.67024 330.467033 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f0ec91"/>
    <path d="M 831.081673 456.339314 
L 833.788039 459.212929 
L 835.287277 457.259513 
L 832.582459 454.400427 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0f7be1"/>
    <path d="M 728.510872 286.389783 
L 731.215216 290.137506 
L 732.78665 289.387914 
L 730.085008 285.684758 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a08566"/>
    <path d="M 794.818659 406.611535 
L 797.514001 410.431318 
L 799.035983 408.678569 
L 796.342549 404.882804 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #19d16b"/>
    <path d="M 868.170134 478.259868 
L 870.906657 479.973475 
L 872.391173 477.594592 
L 869.655671 475.890811 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #274bb1"/>
    <path d="M 875.130767 479.199066 
L 877.87464 480.703464 
L 879.358072 478.208934 
L 876.615122 476.713125 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2848ae"/>
    <path d="M 764.369227 349.456263 
L 767.067701 353.574872 
L 768.610093 352.140255 
L 765.91384 348.059155 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e1f993"/>
    <path d="M 812.173738 433.986561 
L 814.872061 437.404094 
L 816.382747 435.563565 
L 813.68618 432.164171 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00aacb"/>
    <path d="M 773.619114 367.387461 
L 776.315925 371.479702 
L 777.851969 369.916347 
L 775.15727 365.857514 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a1ec86"/>
    <path d="M 743.166295 310.405489 
L 745.868933 314.384214 
L 747.42747 313.335266 
L 744.727342 309.400302 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cabb7c"/>
    <path d="M 674.459934 224.115343 
L 677.152956 226.492705 
L 678.781099 226.477608 
L 676.090874 224.125478 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cbbcb9"/>
    <path d="M 833.788039 459.212929 
L 836.496212 462.000487 
L 837.99393 460.033107 
L 835.287277 457.259513 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1276dc"/>
    <path d="M 782.869446 385.235805 
L 785.565167 389.244229 
L 787.095074 387.582654 
L 784.401372 383.603211 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #65e07a"/>
    <path d="M 809.475951 430.500604 
L 812.173738 433.986561 
L 813.68618 432.164171 
L 810.990181 428.696815 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b0b9"/>
    <path d="M 647.019502 207.021343 
L 649.693186 208.537447 
L 651.348514 208.49397 
L 648.677183 206.98861 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e9e3e2"/>
    <path d="M 861.221408 476.78654 
L 863.951469 478.708615 
L 865.437503 476.44687 
L 862.708576 474.535434 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #264eb4"/>
    <path d="M 637.355123 203.22913 
L 640.019632 204.43072 
L 641.68311 204.308709 
L 639.020737 203.113425 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1edec"/>
    <path d="M 851.560907 472.557299 
L 854.282314 474.782292 
L 855.771595 472.648853 
L 853.051468 470.435611 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2058be"/>
    <path d="M 725.806045 282.684359 
L 728.510872 286.389783 
L 730.085008 285.684758 
L 727.38291 282.023343 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9a7e62"/>
    <path d="M 836.496212 462.000487 
L 839.206368 464.70014 
L 840.702593 462.719369 
L 837.99393 460.033107 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1470d6"/>
    <path d="M 882.105493 479.60505 
L 884.857568 480.900889 
L 886.340301 478.29355 
L 883.589067 477.004644 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2848ae"/>
    <path d="M 659.382144 213.631433 
L 662.066008 215.547644 
L 663.70971 215.547392 
L 661.028434 213.648254 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dfd6d4"/>
    <path d="M 792.123016 402.742834 
L 794.818659 406.611535 
L 796.342549 404.882804 
L 793.648849 401.038519 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #29d46e"/>
    <path d="M 806.778561 426.948762 
L 809.475951 430.500604 
L 810.990181 428.696815 
L 808.294611 425.164021 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b6a7"/>
    <path d="M 752.41758 327.622557 
L 755.118856 331.702876 
L 756.67024 330.467033 
L 753.971344 326.427779 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e8e28d"/>
    <path d="M 897.588333 476.02484 
L 900.358449 476.908601 
L 901.842252 473.99358 
L 899.072818 473.112278 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2353b9"/>
    <path d="M 677.152956 226.492705 
L 679.847842 228.960866 
L 681.473168 228.919217 
L 678.781099 226.477608 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c7b7b4"/>
    <path d="M 740.462795 306.450175 
L 743.166295 310.405489 
L 744.727342 309.400302 
L 742.026386 305.488497 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c4b379"/>
    <path d="M 761.669731 345.33101 
L 764.369227 349.456263 
L 765.91384 348.059155 
L 763.216604 343.971535 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1fc96"/>
    <path d="M 770.921382 363.275103 
L 773.619114 367.387461 
L 775.15727 365.857514 
L 772.461688 361.778806 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b1ef89"/>
    <path d="M 839.206368 464.70014 
L 841.918683 467.310125 
L 843.413442 465.316548 
L 840.702593 462.719369 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #176bd1"/>
    <path d="M 723.100814 279.024323 
L 725.806045 282.684359 
L 727.38291 282.023343 
L 724.680434 278.406709 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #94765f"/>
    <path d="M 780.173011 381.194079 
L 782.869446 385.235805 
L 784.401372 383.603211 
L 781.706993 379.590793 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #75e37d"/>
    <path d="M 893.339827 477.856181 
L 896.105322 478.841584 
L 897.588333 476.02484 
L 894.823563 475.043196 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #264eb4"/>
    <path d="M 804.081434 423.333644 
L 806.778561 426.948762 
L 808.294611 425.164021 
L 805.599335 421.568382 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00bc94"/>
    <path d="M 789.426972 398.828176 
L 792.123016 402.742834 
L 793.648849 401.038519 
L 790.954782 397.148657 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #35d771"/>
    <path d="M 679.847842 228.960866 
L 682.544437 231.517977 
L 684.166926 231.448486 
L 681.473168 228.919217 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c3b2af"/>
    <path d="M 870.906657 479.973475 
L 873.647261 481.586824 
L 875.130767 479.199066 
L 872.391173 477.594592 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2848ae"/>
    <path d="M 854.282314 474.782292 
L 857.006824 476.910707 
L 858.494846 474.766239 
L 855.771595 472.648853 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2353b9"/>
    <path d="M 720.395262 275.412721 
L 723.100814 279.024323 
L 724.680434 278.406709 
L 721.977664 274.837856 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8c6c5b"/>
    <path d="M 630.368074 201.370016 
L 633.026064 202.356444 
L 634.694773 202.136756 
L 632.038748 201.153926 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f5f2f2"/>
    <path d="M 841.918683 467.310125 
L 844.633338 469.828761 
L 846.126656 467.822971 
L 843.413442 465.316548 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1a66cc"/>
    <path d="M 737.758474 302.521563 
L 740.462795 306.450175 
L 742.026386 305.488497 
L 739.324645 301.603098 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bca975"/>
    <path d="M 749.7153 323.552454 
L 752.41758 327.622557 
L 753.971344 326.427779 
L 751.271483 322.398677 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e0d788"/>
    <path d="M 863.951469 478.708615 
L 866.685218 480.531413 
L 868.170134 478.259868 
L 865.437503 476.44687 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #274bb1"/>
    <path d="M 877.87464 480.703464 
L 880.622977 482.107109 
L 882.105493 479.60505 
L 879.358072 478.208934 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2848ae"/>
    <path d="M 801.384439 419.657925 
L 804.081434 423.333644 
L 805.599335 421.568382 
L 802.904223 417.912559 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c47d"/>
    <path d="M 889.096372 479.482854 
L 891.857459 480.572156 
L 893.339827 477.856181 
L 890.579519 476.771741 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #274bb1"/>
    <path d="M 662.066008 215.547644 
L 664.752584 217.563732 
L 666.393662 217.54506 
L 663.70971 215.547392 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dbd1cf"/>
    <path d="M 649.693186 208.537447 
L 652.370302 210.159044 
L 654.02323 210.103517 
L 651.348514 208.49397 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e7e0df"/>
    <path d="M 682.544437 231.517977 
L 685.242586 234.162095 
L 686.862221 234.063503 
L 684.166926 231.448486 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bfada9"/>
    <path d="M 717.689482 271.852559 
L 720.395262 275.412721 
L 721.977664 274.837856 
L 719.274686 271.319744 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #866458"/>
    <path d="M 758.969197 341.202473 
L 761.669731 345.33101 
L 763.216604 343.971535 
L 760.518368 339.88072 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 777.475792 377.122236 
L 780.173011 381.194079 
L 781.706993 379.590793 
L 779.011866 375.548557 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #81e680"/>
    <path d="M 768.222684 359.145929 
L 770.921382 363.275103 
L 772.461688 361.778806 
L 769.765177 357.683494 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c1f38d"/>
    <path d="M 623.390743 200.052913 
L 626.041267 200.818842 
L 627.714631 200.49446 
L 625.065898 199.729858 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f7f5f4"/>
    <path d="M 786.73043 394.870578 
L 789.426972 398.828176 
L 790.954782 397.148657 
L 788.260251 393.216211 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #45da74"/>
    <path d="M 640.019632 204.43072 
L 642.688135 205.741079 
L 644.349421 205.611536 
L 641.68311 204.308709 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #efebea"/>
    <path d="M 844.633338 469.828761 
L 847.350514 472.254455 
L 848.842416 470.237055 
L 846.126656 467.822971 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1c60c6"/>
    <path d="M 798.687453 415.924346 
L 801.384439 419.657925 
L 802.904223 417.912559 
L 800.209152 414.199275 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00cb6b"/>
    <path d="M 714.983571 268.346794 
L 717.689482 271.852559 
L 719.274686 271.319744 
L 716.571596 267.855284 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #805c54"/>
    <path d="M 685.242586 234.162095 
L 687.942135 236.891181 
L 689.558904 236.762264 
L 686.862221 234.063503 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bba8a4"/>
    <path d="M 735.053383 298.622927 
L 737.758474 302.521563 
L 739.324645 301.603098 
L 736.622166 297.747332 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b49f70"/>
    <path d="M 857.006824 476.910707 
L 859.734625 478.941308 
L 861.221408 476.78654 
L 858.494846 474.766239 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2450b6"/>
    <path d="M 884.857568 480.900889 
L 887.61448 482.095957 
L 889.096372 479.482854 
L 886.340301 478.29355 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2848ae"/>
    <path d="M 747.012033 319.495934 
L 749.7153 323.552454 
L 751.271483 322.398677 
L 748.570672 318.383048 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d8cd84"/>
    <path d="M 712.277629 264.898333 
L 714.983571 268.346794 
L 716.571596 267.855284 
L 713.868494 264.44734 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #85635c"/>
    <path d="M 687.942135 236.891181 
L 690.642936 239.70311 
L 692.256829 239.542674 
L 689.558904 236.762264 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b7a39f"/>
    <path d="M 664.752584 217.563732 
L 667.441707 219.678338 
L 669.080126 219.639921 
L 666.393662 217.54506 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d9cecc"/>
    <path d="M 774.777725 373.023498 
L 777.475792 377.122236 
L 779.011866 375.548557 
L 776.315925 371.479702 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #91e983"/>
    <path d="M 709.571764 261.51003 
L 712.277629 264.898333 
L 713.868494 264.44734 
L 711.165484 261.098719 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8b6b64"/>
    <path d="M 795.990355 412.135711 
L 798.687453 415.924346 
L 800.209152 414.199275 
L 797.514001 410.431318 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #09ce68"/>
    <path d="M 756.267614 337.074028 
L 758.969197 341.202473 
L 760.518368 339.88072 
L 757.81912 335.790051 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f8f695"/>
    <path d="M 765.522982 355.003266 
L 768.222684 359.145929 
L 769.765177 357.683494 
L 767.067701 353.574872 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d1f690"/>
    <path d="M 847.350514 472.254455 
L 850.070398 474.5857 
L 851.560907 472.557299 
L 848.842416 470.237055 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1f5bc1"/>
    <path d="M 690.642936 239.70311 
L 693.344843 242.595667 
L 694.955853 242.402557 
L 692.256829 239.542674 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b19b96"/>
    <path d="M 873.647261 481.586824 
L 876.392133 483.099141 
L 877.87464 480.703464 
L 875.130767 479.199066 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2a46ac"/>
    <path d="M 821.465205 449.038634 
L 824.168888 452.172416 
L 825.673681 450.341713 
L 822.971721 447.221828 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0490f6"/>
    <path d="M 784.033301 390.873108 
L 786.73043 394.870578 
L 788.260251 393.216211 
L 785.565167 389.244229 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #55dd77"/>
    <path d="M 824.168888 452.172416 
L 826.873843 455.225723 
L 828.376944 453.381572 
L 825.673681 450.341713 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0888ee"/>
    <path d="M 866.685218 480.531413 
L 869.422844 482.253972 
L 870.906657 479.973475 
L 868.170134 478.259868 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2848ae"/>
    <path d="M 818.762635 445.826557 
L 821.465205 449.038634 
L 822.971721 447.221828 
L 820.270902 444.024087 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0296fc"/>
    <path d="M 706.866089 258.184683 
L 709.571764 261.51003 
L 711.165484 261.098719 
L 708.462676 257.812176 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #91726c"/>
    <path d="M 732.347577 294.757517 
L 735.053383 298.622927 
L 736.622166 297.747332 
L 733.919003 293.924408 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ae976d"/>
    <path d="M 826.873843 455.225723 
L 829.580238 458.196454 
L 831.081673 456.339314 
L 828.376944 453.381572 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0c80e6"/>
    <path d="M 816.06102 442.538442 
L 818.762635 445.826557 
L 820.270902 444.024087 
L 817.571066 440.750735 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #009cf4"/>
    <path d="M 693.344843 242.595667 
L 696.047712 245.566554 
L 697.655834 245.339651 
L 694.955853 242.402557 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ad9691"/>
    <path d="M 704.160722 254.925025 
L 706.866089 258.184683 
L 708.462676 257.812176 
L 705.760185 254.590403 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #977a74"/>
    <path d="M 652.370302 210.159044 
L 655.050682 211.885216 
L 656.701163 211.816346 
L 654.02323 210.103517 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e5dedc"/>
    <path d="M 696.047712 245.566554 
L 698.751405 248.613394 
L 700.356638 248.351614 
L 697.655834 245.339651 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a78e89"/>
    <path d="M 701.455785 251.733728 
L 704.160722 254.925025 
L 705.760185 254.590403 
L 703.058131 251.436028 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9d827c"/>
    <path d="M 698.751405 248.613394 
L 701.455785 251.733728 
L 703.058131 251.436028 
L 700.356638 248.351614 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a18781"/>
    <path d="M 829.580238 458.196454 
L 832.288241 461.08259 
L 833.788039 459.212929 
L 831.081673 456.339314 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0f7be1"/>
    <path d="M 896.105322 478.841584 
L 898.876178 479.727731 
L 900.358449 476.908601 
L 897.588333 476.02484 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #264eb4"/>
    <path d="M 813.360205 439.176622 
L 816.06102 442.538442 
L 817.571066 440.750735 
L 814.872061 437.404094 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a2e2"/>
    <path d="M 744.307804 315.456356 
L 747.012033 319.495934 
L 748.570672 318.383048 
L 745.868933 314.384214 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d2c581"/>
    <path d="M 880.622977 482.107109 
L 883.375965 483.40941 
L 884.857568 480.900889 
L 882.105493 479.60505 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2a46ac"/>
    <path d="M 633.026064 202.356444 
L 635.688437 203.453537 
L 637.355123 203.22913 
L 634.694773 202.136756 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f5f2f2"/>
    <path d="M 793.293033 408.294886 
L 795.990355 412.135711 
L 797.514001 410.431318 
L 794.818659 406.611535 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #19d16b"/>
    <path d="M 810.660042 435.743506 
L 813.360205 439.176622 
L 814.872061 437.404094 
L 812.173738 433.986561 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a8d0"/>
    <path d="M 859.734625 478.941308 
L 862.465905 480.872948 
L 863.951469 478.708615 
L 861.221408 476.78654 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #274bb1"/>
    <path d="M 832.288241 461.08259 
L 834.998024 463.88219 
L 836.496212 462.000487 
L 833.788039 459.212929 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1276dc"/>
    <path d="M 667.441707 219.678338 
L 670.13321 221.889998 
L 671.768937 221.830532 
L 669.080126 219.639921 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d5c9c7"/>
    <path d="M 729.641118 290.928562 
L 732.347577 294.757517 
L 733.919003 293.924408 
L 731.215216 290.137506 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a68d69"/>
    <path d="M 891.857459 480.572156 
L 894.623742 481.561147 
L 896.105322 478.841584 
L 893.339827 477.856181 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #274bb1"/>
    <path d="M 850.070398 474.5857 
L 852.793173 476.821073 
L 854.282314 474.782292 
L 851.560907 472.557299 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2256bc"/>
    <path d="M 772.078751 368.901128 
L 774.777725 373.023498 
L 776.315925 371.479702 
L 773.619114 367.387461 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a1ec86"/>
    <path d="M 753.564978 332.949065 
L 756.267614 337.074028 
L 757.81912 335.790051 
L 755.118856 331.702876 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f0ec91"/>
    <path d="M 781.335501 386.838883 
L 784.033301 390.873108 
L 785.565167 389.244229 
L 782.869446 385.235805 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #65e07a"/>
    <path d="M 642.688135 205.741079 
L 645.36046 207.159635 
L 647.019502 207.021343 
L 644.349421 205.611536 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #efebea"/>
    <path d="M 762.822247 350.850469 
L 765.522982 355.003266 
L 767.067701 353.574872 
L 764.369227 349.456263 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e1f993"/>
    <path d="M 807.960387 432.241573 
L 810.660042 435.743506 
L 812.173738 433.986561 
L 809.475951 430.500604 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00aebf"/>
    <path d="M 834.998024 463.88219 
L 837.709763 466.593399 
L 839.206368 464.70014 
L 836.496212 462.000487 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #166ed4"/>
    <path d="M 741.602641 311.437076 
L 744.307804 315.456356 
L 745.868933 314.384214 
L 743.166295 310.405489 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cabb7c"/>
    <path d="M 790.59538 404.404794 
L 793.293033 408.294886 
L 794.818659 406.611535 
L 792.123016 402.742834 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #25d36d"/>
    <path d="M 626.041267 200.818842 
L 628.696561 201.696736 
L 630.368074 201.370016 
L 627.714631 200.49446 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f7f5f4"/>
    <path d="M 805.261098 428.673377 
L 807.960387 432.241573 
L 809.475951 430.500604 
L 806.778561 426.948762 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b6a7"/>
    <path d="M 726.934074 287.13926 
L 729.641118 290.928562 
L 731.215216 290.137506 
L 728.510872 286.389783 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a08566"/>
    <path d="M 837.709763 466.593399 
L 840.423634 469.214444 
L 841.918683 467.310125 
L 839.206368 464.70014 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1868ce"/>
    <path d="M 887.61448 482.095957 
L 890.376412 483.18985 
L 891.857459 480.572156 
L 889.096372 479.482854 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2848ae"/>
    <path d="M 869.422844 482.253972 
L 872.164537 483.875421 
L 873.647261 481.586824 
L 870.906657 479.973475 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2a46ac"/>
    <path d="M 670.13321 221.889998 
L 672.826928 224.19714 
L 674.459934 224.115343 
L 671.768937 221.830532 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d1c4c1"/>
    <path d="M 655.050682 211.885216 
L 657.734155 213.714925 
L 659.382144 213.631433 
L 656.701163 211.816346 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e3dbd9"/>
    <path d="M 876.392133 483.099141 
L 879.141462 484.509741 
L 880.622977 482.107109 
L 877.87464 480.703464 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2a46ac"/>
    <path d="M 852.793173 476.821073 
L 855.51903 478.959244 
L 857.006824 476.910707 
L 854.282314 474.782292 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2353b9"/>
    <path d="M 778.636954 382.771067 
L 781.335501 386.838883 
L 782.869446 385.235805 
L 780.173011 381.194079 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #71e37d"/>
    <path d="M 769.378821 364.758424 
L 772.078751 368.901128 
L 773.619114 367.387461 
L 770.921382 363.275103 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b1ef89"/>
    <path d="M 750.861294 328.830977 
L 753.564978 332.949065 
L 755.118856 331.702876 
L 752.41758 327.622557 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e8e28d"/>
    <path d="M 802.562042 425.041538 
L 805.261098 428.673377 
L 806.778561 426.948762 
L 804.081434 423.333644 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00bc94"/>
    <path d="M 862.465905 480.872948 
L 865.200856 482.704568 
L 866.685218 480.531413 
L 863.951469 478.708615 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2848ae"/>
    <path d="M 760.120455 346.690912 
L 762.822247 350.850469 
L 764.369227 349.456263 
L 761.669731 345.33101 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1fc96"/>
    <path d="M 840.423634 469.214444 
L 843.13982 471.743638 
L 844.633338 469.828761 
L 841.918683 467.310125 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1b63c9"/>
    <path d="M 724.226522 283.392777 
L 726.934074 287.13926 
L 728.510872 286.389783 
L 725.806045 282.684359 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #987b61"/>
    <path d="M 787.897293 400.468417 
L 790.59538 404.404794 
L 792.123016 402.742834 
L 789.426972 398.828176 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #35d771"/>
    <path d="M 738.896584 307.441441 
L 741.602641 311.437076 
L 743.166295 310.405489 
L 740.462795 306.450175 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c2b178"/>
    <path d="M 672.826928 224.19714 
L 675.522696 226.598087 
L 677.152956 226.492705 
L 674.459934 224.115343 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cdbfbc"/>
    <path d="M 883.375965 483.40941 
L 886.133788 484.60987 
L 887.61448 482.095957 
L 884.857568 480.900889 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2a46ac"/>
    <path d="M 799.863089 421.348745 
L 802.562042 425.041538 
L 804.081434 423.333644 
L 801.384439 419.657925 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c382"/>
    <path d="M 635.688437 203.453537 
L 638.355026 204.660967 
L 640.019632 204.43072 
L 637.355123 203.22913 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f3f0ef"/>
    <path d="M 645.36046 207.159635 
L 648.036439 208.685696 
L 649.693186 208.537447 
L 647.019502 207.021343 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ede8e7"/>
    <path d="M 721.518542 279.692245 
L 724.226522 283.392777 
L 725.806045 282.684359 
L 723.100814 279.024323 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #92735e"/>
    <path d="M 843.13982 471.743638 
L 845.858502 474.179379 
L 847.350514 472.254455 
L 844.633338 469.828761 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1e5ec4"/>
    <path d="M 775.93759 378.672867 
L 778.636954 382.771067 
L 780.173011 381.194079 
L 777.475792 377.122236 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #81e680"/>
    <path d="M 657.734155 213.714925 
L 660.42055 215.647021 
L 662.066008 215.547644 
L 659.382144 213.631433 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e1d9d7"/>
    <path d="M 748.156573 324.723167 
L 750.861294 328.830977 
L 752.41758 327.622557 
L 749.7153 323.552454 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e0d788"/>
    <path d="M 855.51903 478.959244 
L 858.248155 480.998968 
L 859.734625 478.941308 
L 857.006824 476.910707 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #264eb4"/>
    <path d="M 766.677891 360.598712 
L 769.378821 364.758424 
L 770.921382 363.275103 
L 768.222684 359.145929 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c1f38d"/>
    <path d="M 785.198676 396.488789 
L 787.897293 400.468417 
L 789.426972 398.828176 
L 786.73043 394.870578 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #45da74"/>
    <path d="M 675.522696 226.598087 
L 678.220353 229.091062 
L 679.847842 228.960866 
L 677.152956 226.492705 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c9bab7"/>
    <path d="M 757.417589 342.527991 
L 760.120455 346.690912 
L 761.669731 345.33101 
L 758.969197 341.202473 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 797.164114 417.597754 
L 799.863089 421.348745 
L 801.384439 419.657925 
L 798.687453 415.924346 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00cb6b"/>
    <path d="M 736.189676 303.47278 
L 738.896584 307.441441 
L 740.462795 306.450175 
L 737.758474 302.521563 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bca975"/>
    <path d="M 894.623742 481.561147 
L 897.395396 482.449606 
L 898.876178 479.727731 
L 896.105322 478.841584 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #274bb1"/>
    <path d="M 872.164537 483.875421 
L 874.910487 485.39498 
L 876.392133 483.099141 
L 873.647261 481.586824 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2b43a9"/>
    <path d="M 718.810221 276.040754 
L 721.518542 279.692245 
L 723.100814 279.024323 
L 720.395262 275.412721 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8c6c5b"/>
    <path d="M 865.200856 482.704568 
L 867.939667 484.435201 
L 869.422844 482.253972 
L 866.685218 480.531413 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2a46ac"/>
    <path d="M 845.858502 474.179379 
L 848.579866 476.520151 
L 850.070398 474.5857 
L 847.350514 472.254455 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2058be"/>
    <path d="M 879.141462 484.509741 
L 881.895435 485.818031 
L 883.375965 483.40941 
L 880.622977 482.107109 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2b43a9"/>
    <path d="M 628.696561 201.696736 
L 631.35646 202.686514 
L 633.026064 202.356444 
L 630.368074 201.370016 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f7f5f4"/>
    <path d="M 678.220353 229.091062 
L 680.919739 231.674189 
L 682.544437 231.517977 
L 679.847842 228.960866 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c5b5b1"/>
    <path d="M 890.376412 483.18985 
L 893.143543 484.182256 
L 894.623742 481.561147 
L 891.857459 480.572156 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2a46ac"/>
    <path d="M 716.101653 272.441352 
L 718.810221 276.040754 
L 720.395262 275.412721 
L 717.689482 271.852559 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #846257"/>
    <path d="M 794.464998 413.791382 
L 797.164114 417.597754 
L 798.687453 415.924346 
L 795.990355 412.135711 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #09ce68"/>
    <path d="M 819.95771 450.77974 
L 822.663201 453.925153 
L 824.168888 452.172416 
L 821.465205 449.038634 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #068ef4"/>
    <path d="M 822.663201 453.925153 
L 825.369937 456.989722 
L 826.873843 455.225723 
L 824.168888 452.172416 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0888ee"/>
    <path d="M 817.253304 447.555673 
L 819.95771 450.77974 
L 821.465205 449.038634 
L 818.762635 445.826557 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0296fc"/>
    <path d="M 773.237344 374.54753 
L 775.93759 378.672867 
L 777.475792 377.122236 
L 774.777725 373.023498 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #91e983"/>
    <path d="M 745.450832 320.629037 
L 748.156573 324.723167 
L 749.7153 323.552454 
L 747.012033 319.495934 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d8cd84"/>
    <path d="M 825.369937 456.989722 
L 828.078085 459.971339 
L 829.580238 458.196454 
L 826.873843 455.225723 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0c80e6"/>
    <path d="M 733.481967 299.534409 
L 736.189676 303.47278 
L 737.758474 302.521563 
L 735.053383 298.622927 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b49f70"/>
    <path d="M 782.499442 392.468997 
L 785.198676 396.488789 
L 786.73043 394.870578 
L 784.033301 390.873108 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #55dd77"/>
    <path d="M 814.549825 444.255218 
L 817.253304 447.555673 
L 818.762635 445.826557 
L 816.06102 442.538442 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #009cf4"/>
    <path d="M 763.975924 356.42535 
L 766.677891 360.598712 
L 768.222684 359.145929 
L 765.522982 355.003266 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d1f690"/>
    <path d="M 660.42055 215.647021 
L 663.109696 217.680239 
L 664.752584 217.563732 
L 662.066008 215.547644 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ddd3d1"/>
    <path d="M 754.71364 338.365114 
L 757.417589 342.527991 
L 758.969197 341.202473 
L 756.267614 337.074028 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f8f695"/>
    <path d="M 828.078085 459.971339 
L 830.787813 462.867976 
L 832.288241 461.08259 
L 829.580238 458.196454 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1078de"/>
    <path d="M 648.036439 208.685696 
L 650.715899 210.31845 
L 652.370302 210.159044 
L 649.693186 208.537447 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ebe5e4"/>
    <path d="M 858.248155 480.998968 
L 860.980741 482.93909 
L 862.465905 480.872948 
L 859.734625 478.941308 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #274bb1"/>
    <path d="M 621.714979 200.487962 
L 624.367241 201.255197 
L 626.041267 200.818842 
L 623.390743 200.052913 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9f7f7"/>
    <path d="M 680.919739 231.674189 
L 683.620696 234.345494 
L 685.242586 234.162095 
L 682.544437 231.517977 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c1b0ac"/>
    <path d="M 713.392936 268.89704 
L 716.101653 272.441352 
L 717.689482 271.852559 
L 714.983571 268.346794 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #815e56"/>
    <path d="M 811.847118 440.880717 
L 814.549825 444.255218 
L 816.06102 442.538442 
L 813.360205 439.176622 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a2e2"/>
    <path d="M 638.355026 204.660967 
L 641.025662 205.978279 
L 642.688135 205.741079 
L 640.019632 204.43072 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1edec"/>
    <path d="M 830.787813 462.867976 
L 833.499295 465.677687 
L 834.998024 463.88219 
L 832.288241 461.08259 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1373d9"/>
    <path d="M 848.579866 476.520151 
L 851.304099 478.764529 
L 852.793173 476.821073 
L 850.070398 474.5857 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2256bc"/>
    <path d="M 791.765629 409.93251 
L 794.464998 413.791382 
L 795.990355 412.135711 
L 793.293033 408.294886 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #19d16b"/>
    <path d="M 809.145035 437.434588 
L 811.847118 440.880717 
L 813.360205 439.176622 
L 810.660042 435.743506 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a8d0"/>
    <path d="M 886.133788 484.60987 
L 888.896631 485.708082 
L 890.376412 483.18985 
L 887.61448 482.095957 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2b43a9"/>
    <path d="M 710.684174 265.410766 
L 713.392936 268.89704 
L 714.983571 268.346794 
L 712.277629 264.898333 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #87655e"/>
    <path d="M 683.620696 234.345494 
L 686.323068 237.10291 
L 687.942135 236.891181 
L 685.242586 234.162095 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bdaba7"/>
    <path d="M 730.773516 295.629622 
L 733.481967 299.534409 
L 735.053383 298.622927 
L 732.347577 294.757517 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ac956c"/>
    <path d="M 833.499295 465.677687 
L 836.212705 468.398606 
L 837.709763 466.593399 
L 834.998024 463.88219 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #166ed4"/>
    <path d="M 742.744096 316.551984 
L 745.450832 320.629037 
L 747.012033 319.495934 
L 744.307804 315.456356 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d0c380"/>
    <path d="M 806.443431 433.919321 
L 809.145035 437.434588 
L 810.660042 435.743506 
L 807.960387 432.241573 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00aebf"/>
    <path d="M 779.799506 388.412179 
L 782.499442 392.468997 
L 784.033301 390.873108 
L 781.335501 386.838883 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #61df79"/>
    <path d="M 707.975477 261.985427 
L 710.684174 265.410766 
L 712.277629 264.898333 
L 709.571764 261.51003 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8d6d66"/>
    <path d="M 770.53616 370.398342 
L 773.237344 374.54753 
L 774.777725 373.023498 
L 772.078751 368.901128 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a1ec86"/>
    <path d="M 867.939667 484.435201 
L 870.682531 486.063969 
L 872.164537 483.875421 
L 869.422844 482.253972 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2b43a9"/>
    <path d="M 686.323068 237.10291 
L 689.026704 239.944277 
L 690.642936 239.70311 
L 687.942135 236.891181 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b9a5a1"/>
    <path d="M 874.910487 485.39498 
L 877.660884 486.811958 
L 879.141462 484.509741 
L 876.392133 483.099141 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2c40a6"/>
    <path d="M 761.272891 352.241721 
L 763.975924 356.42535 
L 765.522982 355.003266 
L 762.822247 350.850469 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e1f993"/>
    <path d="M 663.109696 217.680239 
L 665.801424 219.813203 
L 667.441707 219.678338 
L 664.752584 217.563732 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dbd1cf"/>
    <path d="M 705.266962 258.623858 
L 707.975477 261.985427 
L 709.571764 261.51003 
L 706.866089 258.184683 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #93756e"/>
    <path d="M 752.008606 334.205704 
L 754.71364 338.365114 
L 756.267614 337.074028 
L 753.564978 332.949065 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f0ec91"/>
    <path d="M 689.026704 239.944277 
L 691.731455 242.867349 
L 693.344843 242.595667 
L 690.642936 239.70311 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b39e99"/>
    <path d="M 789.065898 406.024076 
L 791.765629 409.93251 
L 793.293033 408.294886 
L 790.59538 404.404794 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #25d36d"/>
    <path d="M 836.212705 468.398606 
L 838.928222 471.028956 
L 840.423634 469.214444 
L 837.709763 466.593399 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1868ce"/>
    <path d="M 803.742166 430.33748 
L 806.443431 433.919321 
L 807.960387 432.241573 
L 805.261098 428.673377 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b4ac"/>
    <path d="M 702.558746 255.328836 
L 705.266962 258.623858 
L 706.866089 258.184683 
L 704.160722 254.925025 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #997c76"/>
    <path d="M 691.731455 242.867349 
L 694.437174 245.869795 
L 696.047712 245.566554 
L 693.344843 242.595667 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #af9994"/>
    <path d="M 851.304099 478.764529 
L 854.031389 480.911173 
L 855.51903 478.959244 
L 852.793173 476.821073 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2450b6"/>
    <path d="M 860.980741 482.93909 
L 863.716977 484.778548 
L 865.200856 482.704568 
L 862.465905 480.872948 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2a46ac"/>
    <path d="M 699.850956 252.103069 
L 702.558746 255.328836 
L 704.160722 254.925025 
L 701.455785 251.733728 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9f847e"/>
    <path d="M 694.437174 245.869795 
L 697.143721 248.949199 
L 698.751405 248.613394 
L 696.047712 245.566554 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a9918c"/>
    <path d="M 728.064386 291.761686 
L 730.773516 295.629622 
L 732.347577 294.757517 
L 729.641118 290.928562 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a68d69"/>
    <path d="M 697.143721 248.949199 
L 699.850956 252.103069 
L 701.455785 251.733728 
L 698.751405 248.613394 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a58c86"/>
    <path d="M 881.895435 485.818031 
L 884.654239 487.023508 
L 886.133788 484.60987 
L 883.375965 483.40941 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2c40a6"/>
    <path d="M 650.715899 210.31845 
L 653.398668 212.056966 
L 655.050682 211.885216 
L 652.370302 210.159044 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e9e3e2"/>
    <path d="M 631.35646 202.686514 
L 634.0208 203.787967 
L 635.688437 203.453537 
L 633.026064 202.356444 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f7f5f4"/>
    <path d="M 740.036397 312.495404 
L 742.744096 316.551984 
L 744.307804 315.456356 
L 741.602641 311.437076 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cabb7c"/>
    <path d="M 801.041106 426.691695 
L 803.742166 430.33748 
L 805.261098 428.673377 
L 802.562042 425.041538 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00bb9b"/>
    <path d="M 777.098792 384.321517 
L 779.799506 388.412179 
L 781.335501 386.838883 
L 778.636954 382.771067 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #71e37d"/>
    <path d="M 838.928222 471.028956 
L 841.646028 473.567043 
L 843.13982 471.743638 
L 840.423634 469.214444 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1b63c9"/>
    <path d="M 767.833988 366.228626 
L 770.53616 370.398342 
L 772.078751 368.901128 
L 769.378821 364.758424 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b1ef89"/>
    <path d="M 665.801424 219.813203 
L 668.495564 222.044427 
L 670.13321 221.889998 
L 667.441707 219.678338 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d7ccc9"/>
    <path d="M 893.143543 484.182256 
L 895.916054 485.072951 
L 897.395396 482.449606 
L 894.623742 481.561147 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2a46ac"/>
    <path d="M 786.365705 402.069077 
L 789.065898 406.024076 
L 790.59538 404.404794 
L 787.897293 400.468417 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #35d771"/>
    <path d="M 641.025662 205.978279 
L 643.700173 207.404896 
L 645.36046 207.159635 
L 642.688135 205.741079 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1edec"/>
    <path d="M 758.568768 348.051229 
L 761.272891 352.241721 
L 762.822247 350.850469 
L 760.120455 346.690912 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1fc96"/>
    <path d="M 725.354648 287.933841 
L 728.064386 291.761686 
L 729.641118 290.928562 
L 726.934074 287.13926 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9e8365"/>
    <path d="M 749.302492 330.053189 
L 752.008606 334.205704 
L 753.564978 332.949065 
L 750.861294 328.830977 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e8e28d"/>
    <path d="M 798.340121 422.984668 
L 801.041106 426.691695 
L 802.562042 425.041538 
L 799.863089 421.348745 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c382"/>
    <path d="M 624.367241 201.255197 
L 627.02433 202.135295 
L 628.696561 201.696736 
L 626.041267 200.818842 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9f7f7"/>
    <path d="M 841.646028 473.567043 
L 844.366304 476.011257 
L 845.858502 474.179379 
L 843.13982 471.743638 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1e5ec4"/>
    <path d="M 854.031389 480.911173 
L 856.761926 482.958833 
L 858.248155 480.998968 
L 855.51903 478.959244 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #274bb1"/>
    <path d="M 870.682531 486.063969 
L 873.429636 487.590086 
L 874.910487 485.39498 
L 872.164537 483.875421 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2c40a6"/>
    <path d="M 737.327774 308.462678 
L 740.036397 312.495404 
L 741.602641 311.437076 
L 738.896584 307.441441 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c2b178"/>
    <path d="M 888.896631 485.708082 
L 891.664675 486.703728 
L 893.143543 484.182256 
L 890.376412 483.18985 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2b43a9"/>
    <path d="M 877.660884 486.811958 
L 880.415915 488.125757 
L 881.895435 485.818031 
L 879.141462 484.509741 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2c40a6"/>
    <path d="M 774.397231 380.200239 
L 777.098792 384.321517 
L 778.636954 382.771067 
L 775.93759 378.672867 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #81e680"/>
    <path d="M 863.716977 484.778548 
L 866.457056 486.516368 
L 867.939667 484.435201 
L 865.200856 482.704568 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2b43a9"/>
    <path d="M 722.644378 284.149296 
L 725.354648 287.933841 
L 726.934074 287.13926 
L 724.226522 283.392777 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #987b61"/>
    <path d="M 668.495564 222.044427 
L 671.19195 224.372316 
L 672.826928 224.19714 
L 670.13321 221.889998 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d5c9c7"/>
    <path d="M 653.398668 212.056966 
L 656.084573 213.900193 
L 657.734155 213.714925 
L 655.050682 211.885216 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e5dedc"/>
    <path d="M 783.664954 398.070564 
L 786.365705 402.069077 
L 787.897293 400.468417 
L 785.198676 396.488789 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #45da74"/>
    <path d="M 795.639086 419.219164 
L 798.340121 422.984668 
L 799.863089 421.348745 
L 797.164114 417.597754 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c970"/>
    <path d="M 765.130785 362.041733 
L 767.833988 366.228626 
L 769.378821 364.758424 
L 766.677891 360.598712 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c1f38d"/>
    <path d="M 746.59531 325.911005 
L 749.302492 330.053189 
L 750.861294 328.830977 
L 748.156573 324.723167 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e0d788"/>
    <path d="M 755.86354 343.857299 
L 758.568768 348.051229 
L 760.120455 346.690912 
L 757.417589 342.527991 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 844.366304 476.011257 
L 847.089237 478.360079 
L 848.579866 476.520151 
L 845.858502 474.179379 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2058be"/>
    <path d="M 719.933661 280.411221 
L 722.644378 284.149296 
L 724.226522 283.392777 
L 721.518542 279.692245 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #90715d"/>
    <path d="M 734.618272 304.457177 
L 737.327774 308.462678 
L 738.896584 307.441441 
L 736.189676 303.47278 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #baa774"/>
    <path d="M 884.654239 487.023508 
L 887.418059 488.125761 
L 888.896631 485.708082 
L 886.133788 484.60987 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2c40a6"/>
    <path d="M 634.0208 203.787967 
L 636.68941 205.000763 
L 638.355026 204.660967 
L 635.688437 203.453537 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f5f2f2"/>
    <path d="M 671.19195 224.372316 
L 673.890413 226.795173 
L 675.522696 226.598087 
L 672.826928 224.19714 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d1c4c1"/>
    <path d="M 818.449169 452.444746 
L 821.156552 455.599511 
L 822.663201 453.925153 
L 819.95771 450.77974 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #068ef4"/>
    <path d="M 821.156552 455.599511 
L 823.865154 458.673147 
L 825.369937 456.989722 
L 822.663201 453.925153 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0a86ec"/>
    <path d="M 792.937883 415.398013 
L 795.639086 419.219164 
L 797.164114 417.597754 
L 794.464998 413.791382 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #09ce68"/>
    <path d="M 856.761926 482.958833 
L 859.495902 484.906351 
L 860.980741 482.93909 
L 858.248155 480.998968 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2848ae"/>
    <path d="M 815.742843 449.211047 
L 818.449169 452.444746 
L 819.95771 450.77974 
L 817.253304 447.555673 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0296fc"/>
    <path d="M 823.865154 458.673147 
L 826.575141 461.663537 
L 828.078085 459.971339 
L 825.369937 456.989722 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0c80e6"/>
    <path d="M 643.700173 207.404896 
L 646.378387 208.940117 
L 648.036439 208.685696 
L 645.36046 207.159635 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #efebea"/>
    <path d="M 771.694759 376.051613 
L 774.397231 380.200239 
L 775.93759 378.672867 
L 773.237344 374.54753 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #91e983"/>
    <path d="M 813.037417 445.900686 
L 815.742843 449.211047 
L 817.253304 447.555673 
L 814.549825 444.255218 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #009cf4"/>
    <path d="M 780.963556 394.03164 
L 783.664954 398.070564 
L 785.198676 396.488789 
L 782.499442 392.468997 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #51dc76"/>
    <path d="M 826.575141 461.663537 
L 829.286682 464.568647 
L 830.787813 462.867976 
L 828.078085 459.971339 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1078de"/>
    <path d="M 717.222584 276.722747 
L 719.933661 280.411221 
L 721.518542 279.692245 
L 718.810221 276.040754 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8a695a"/>
    <path d="M 762.426514 357.841047 
L 765.130785 362.041733 
L 766.677891 360.598712 
L 763.975924 356.42535 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d1f690"/>
    <path d="M 810.332738 442.516013 
L 813.037417 445.900686 
L 814.549825 444.255218 
L 811.847118 440.880717 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a2e2"/>
    <path d="M 656.084573 213.900193 
L 658.773441 215.846966 
L 660.42055 215.647021 
L 657.734155 213.714925 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e3dbd9"/>
    <path d="M 847.089237 478.360079 
L 849.815015 480.612076 
L 851.304099 478.764529 
L 848.579866 476.520151 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2353b9"/>
    <path d="M 743.887078 321.782588 
L 746.59531 325.911005 
L 748.156573 324.723167 
L 745.450832 320.629037 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d8cd84"/>
    <path d="M 829.286682 464.568647 
L 831.99995 467.386526 
L 833.499295 465.677687 
L 830.787813 462.867976 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1373d9"/>
    <path d="M 873.429636 487.590086 
L 876.181175 489.01286 
L 877.660884 486.811958 
L 874.910487 485.39498 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2c40a6"/>
    <path d="M 753.157198 339.66337 
L 755.86354 343.857299 
L 757.417589 342.527991 
L 754.71364 338.365114 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f8f695"/>
    <path d="M 673.890413 226.795173 
L 676.59079 229.311195 
L 678.220353 229.091062 
L 675.522696 226.598087 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cdbfbc"/>
    <path d="M 866.457056 486.516368 
L 869.201169 488.151668 
L 870.682531 486.063969 
L 867.939667 484.435201 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2c40a6"/>
    <path d="M 807.628655 439.059455 
L 810.332738 442.516013 
L 811.847118 440.880717 
L 809.145035 437.434588 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a8d0"/>
    <path d="M 790.2364 411.524107 
L 792.937883 415.398013 
L 794.464998 413.791382 
L 791.765629 409.93251 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #15d06a"/>
    <path d="M 731.907944 300.482254 
L 734.618272 304.457177 
L 736.189676 303.47278 
L 733.481967 299.534409 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b49f70"/>
    <path d="M 714.511244 273.086963 
L 717.222584 276.722747 
L 718.810221 276.040754 
L 716.101653 272.441352 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #846257"/>
    <path d="M 627.02433 202.135295 
L 629.686082 203.128172 
L 631.35646 202.686514 
L 628.696561 201.696736 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9f7f7"/>
    <path d="M 831.99995 467.386526 
L 834.715121 470.115303 
L 836.212705 468.398606 
L 833.499295 465.677687 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #176bd1"/>
    <path d="M 880.415915 488.125757 
L 883.175769 489.335872 
L 884.654239 487.023508 
L 881.895435 485.818031 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2e3ea4"/>
    <path d="M 804.925026 435.533508 
L 807.628655 439.059455 
L 809.145035 437.434588 
L 806.443431 433.919321 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00aebf"/>
    <path d="M 778.261429 389.955458 
L 780.963556 394.03164 
L 782.499442 392.468997 
L 779.799506 388.412179 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #61df79"/>
    <path d="M 676.59079 229.311195 
L 679.292917 231.91848 
L 680.919739 231.674189 
L 678.220353 229.091062 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c9bab7"/>
    <path d="M 768.991319 371.878946 
L 771.694759 376.051613 
L 773.237344 374.54753 
L 770.53616 370.398342 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a1ec86"/>
    <path d="M 859.495902 484.906351 
L 862.233507 486.752657 
L 863.716977 484.778548 
L 860.980741 482.93909 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2a46ac"/>
    <path d="M 891.664675 486.703728 
L 894.438102 487.596584 
L 895.916054 485.072951 
L 893.143543 484.182256 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2b43a9"/>
    <path d="M 620.038728 201.036093 
L 622.692673 201.804613 
L 624.367241 201.255197 
L 621.714979 200.487962 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fbfafa"/>
    <path d="M 711.799741 269.506907 
L 714.511244 273.086963 
L 716.101653 272.441352 
L 713.392936 268.89704 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #836059"/>
    <path d="M 834.715121 470.115303 
L 837.432372 472.753194 
L 838.928222 471.028956 
L 836.212705 468.398606 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1a66cc"/>
    <path d="M 849.815015 480.612076 
L 852.543826 482.765905 
L 854.031389 480.911173 
L 851.304099 478.764529 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #264eb4"/>
    <path d="M 759.721148 353.629975 
L 762.426514 357.841047 
L 763.975924 356.42535 
L 761.272891 352.241721 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e1f993"/>
    <path d="M 787.534528 407.600398 
L 790.2364 411.524107 
L 791.765629 409.93251 
L 789.065898 406.024076 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #25d36d"/>
    <path d="M 741.177823 317.671372 
L 743.887078 321.782588 
L 745.450832 320.629037 
L 742.744096 316.551984 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d0c380"/>
    <path d="M 802.221709 431.940744 
L 804.925026 435.533508 
L 806.443431 433.919321 
L 803.742166 430.33748 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b4ac"/>
    <path d="M 658.773441 215.846966 
L 661.4651 217.896005 
L 663.109696 217.680239 
L 660.42055 215.647021 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e1d9d7"/>
    <path d="M 729.196848 296.54124 
L 731.907944 300.482254 
L 733.481967 299.534409 
L 730.773516 295.629622 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ac956c"/>
    <path d="M 646.378387 208.940117 
L 649.060131 210.583121 
L 650.715899 210.31845 
L 648.036439 208.685696 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ede8e7"/>
    <path d="M 679.292917 231.91848 
L 681.996634 234.615027 
L 683.620696 234.345494 
L 680.919739 231.674189 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c3b2af"/>
    <path d="M 750.449742 335.472892 
L 753.157198 339.66337 
L 754.71364 338.365114 
L 752.008606 334.205704 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f0ec91"/>
    <path d="M 709.088183 265.985569 
L 711.799741 269.506907 
L 713.392936 268.89704 
L 710.684174 265.410766 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #896861"/>
    <path d="M 636.68941 205.000763 
L 639.36212 206.324442 
L 641.025662 205.978279 
L 638.355026 204.660967 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f5f2f2"/>
    <path d="M 837.432372 472.753194 
L 840.151885 475.298501 
L 841.646028 473.567043 
L 838.928222 471.028956 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1c60c6"/>
    <path d="M 799.518571 428.283803 
L 802.221709 431.940744 
L 803.742166 430.33748 
L 801.041106 426.691695 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00bb9b"/>
    <path d="M 681.996634 234.615027 
L 684.701784 237.39874 
L 686.323068 237.10291 
L 683.620696 234.345494 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bfada9"/>
    <path d="M 706.37668 262.525881 
L 709.088183 265.985569 
L 710.684174 265.410766 
L 707.975477 261.985427 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8f7069"/>
    <path d="M 775.558496 385.845219 
L 778.261429 389.955458 
L 779.799506 388.412179 
L 777.098792 384.321517 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #71e37d"/>
    <path d="M 887.418059 488.125761 
L 890.187079 489.124471 
L 891.664675 486.703728 
L 888.896631 485.708082 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2c40a6"/>
    <path d="M 869.201169 488.151668 
L 871.949509 489.683658 
L 873.429636 487.590086 
L 870.682531 486.063969 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2e3ea4"/>
    <path d="M 766.286863 367.685581 
L 768.991319 371.878946 
L 770.53616 370.398342 
L 767.833988 366.228626 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b1ef89"/>
    <path d="M 784.832168 403.629895 
L 787.534528 407.600398 
L 789.065898 406.024076 
L 786.365705 402.069077 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #35d771"/>
    <path d="M 726.485052 292.637441 
L 729.196848 296.54124 
L 730.773516 295.629622 
L 728.064386 291.761686 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a48b68"/>
    <path d="M 684.701784 237.39874 
L 687.408211 240.267431 
L 689.026704 239.944277 
L 686.323068 237.10291 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bba8a4"/>
    <path d="M 703.665351 259.130719 
L 706.37668 262.525881 
L 707.975477 261.985427 
L 705.266962 258.623858 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #957771"/>
    <path d="M 876.181175 489.01286 
L 878.937338 490.331686 
L 880.415915 488.125757 
L 877.660884 486.811958 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2e3ea4"/>
    <path d="M 738.467577 313.580784 
L 741.177823 317.671372 
L 742.744096 316.551984 
L 740.036397 312.495404 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c8b97b"/>
    <path d="M 852.543826 482.765905 
L 855.275861 484.82031 
L 856.761926 482.958833 
L 854.031389 480.911173 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #274bb1"/>
    <path d="M 757.014663 349.411949 
L 759.721148 353.629975 
L 761.272891 352.241721 
L 758.568768 348.051229 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1fc96"/>
    <path d="M 661.4651 217.896005 
L 664.159376 220.045915 
L 665.801424 219.813203 
L 663.109696 217.680239 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ddd3d1"/>
    <path d="M 700.954318 255.802894 
L 703.665351 259.130719 
L 705.266962 258.623858 
L 702.558746 255.328836 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9b7f79"/>
    <path d="M 796.815483 424.565393 
L 799.518571 428.283803 
L 801.041106 426.691695 
L 798.340121 422.984668 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c382"/>
    <path d="M 687.408211 240.267431 
L 690.115763 243.218823 
L 691.731455 242.867349 
L 689.026704 239.944277 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b5a09c"/>
    <path d="M 840.151885 475.298501 
L 842.873843 477.749609 
L 844.366304 476.011257 
L 841.646028 473.567043 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1f5bc1"/>
    <path d="M 862.233507 486.752657 
L 864.974935 488.496773 
L 866.457056 486.516368 
L 863.716977 484.778548 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2b43a9"/>
    <path d="M 747.741178 331.289328 
L 750.449742 335.472892 
L 752.008606 334.205704 
L 749.302492 330.053189 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e8e28d"/>
    <path d="M 698.243709 252.545152 
L 700.954318 255.802894 
L 702.558746 255.328836 
L 699.850956 252.103069 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a18781"/>
    <path d="M 690.115763 243.218823 
L 692.824292 246.250551 
L 694.437174 245.869795 
L 691.731455 242.867349 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b19b96"/>
    <path d="M 695.533655 249.36017 
L 698.243709 252.545152 
L 699.850956 252.103069 
L 697.143721 248.949199 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a78e89"/>
    <path d="M 692.824292 246.250551 
L 695.533655 249.36017 
L 697.143721 248.949199 
L 694.437174 245.869795 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ab938e"/>
    <path d="M 629.686082 203.128172 
L 632.35233 204.233621 
L 634.0208 203.787967 
L 631.35646 202.686514 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9f7f7"/>
    <path d="M 649.060131 210.583121 
L 651.745229 212.332967 
L 653.398668 212.056966 
L 650.715899 210.31845 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ebe5e4"/>
    <path d="M 723.772626 288.774135 
L 726.485052 292.637441 
L 728.064386 291.761686 
L 725.354648 287.933841 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9e8365"/>
    <path d="M 772.854689 381.704166 
L 775.558496 385.845219 
L 777.098792 384.321517 
L 774.397231 380.200239 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #81e680"/>
    <path d="M 883.175769 489.335872 
L 885.940634 490.441888 
L 887.418059 488.125761 
L 884.654239 487.023508 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2e3ea4"/>
    <path d="M 782.129224 399.615661 
L 784.832168 403.629895 
L 786.365705 402.069077 
L 783.664954 398.070564 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #41d973"/>
    <path d="M 794.112319 420.788291 
L 796.815483 424.565393 
L 798.340121 422.984668 
L 795.639086 419.219164 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c970"/>
    <path d="M 763.581348 363.474893 
L 766.286863 367.685581 
L 767.833988 366.228626 
L 765.130785 362.041733 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c1f38d"/>
    <path d="M 842.873843 477.749609 
L 845.598433 480.104995 
L 847.089237 478.360079 
L 844.366304 476.011257 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2256bc"/>
    <path d="M 735.756382 309.514243 
L 738.467577 313.580784 
L 740.036397 312.495404 
L 737.327774 308.462678 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c2b178"/>
    <path d="M 639.36212 206.324442 
L 642.038756 207.758422 
L 643.700173 207.404896 
L 641.025662 205.978279 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f3f0ef"/>
    <path d="M 664.159376 220.045915 
L 666.856098 222.295192 
L 668.495564 222.044427 
L 665.801424 219.813203 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d9cecc"/>
    <path d="M 622.692673 201.804613 
L 625.351503 202.686777 
L 627.02433 202.135295 
L 624.367241 201.255197 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fbfafa"/>
    <path d="M 855.275861 484.82031 
L 858.011311 486.774128 
L 859.495902 484.906351 
L 856.761926 482.958833 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2a46ac"/>
    <path d="M 754.307045 345.190418 
L 757.014663 349.411949 
L 758.568768 348.051229 
L 755.86354 343.857299 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 745.031517 327.116142 
L 747.741178 331.289328 
L 749.302492 330.053189 
L 746.59531 325.911005 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e0d788"/>
    <path d="M 721.059651 284.954567 
L 723.772626 288.774135 
L 725.354648 287.933841 
L 722.644378 284.149296 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #967960"/>
    <path d="M 816.939511 454.033322 
L 819.64887 457.195153 
L 821.156552 455.599511 
L 818.449169 452.444746 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #068ef4"/>
    <path d="M 819.64887 457.195153 
L 822.359423 460.27565 
L 823.865154 458.673147 
L 821.156552 455.599511 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0a86ec"/>
    <path d="M 791.408963 416.955334 
L 794.112319 420.788291 
L 795.639086 419.219164 
L 792.937883 415.398013 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #09ce68"/>
    <path d="M 814.231184 450.792356 
L 816.939511 454.033322 
L 818.449169 452.444746 
L 815.742843 449.211047 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0393f9"/>
    <path d="M 871.949509 489.683658 
L 874.702267 491.11164 
L 876.181175 489.01286 
L 873.429636 487.590086 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2e3ea4"/>
    <path d="M 822.359423 460.27565 
L 825.071335 463.272692 
L 826.575141 461.663537 
L 823.865154 458.673147 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0e7ee4"/>
    <path d="M 811.523732 447.474534 
L 814.231184 450.792356 
L 815.742843 449.211047 
L 813.037417 445.900686 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #009afa"/>
    <path d="M 779.425607 395.560813 
L 782.129224 399.615661 
L 783.664954 398.070564 
L 780.963556 394.03164 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #51dc76"/>
    <path d="M 770.149945 377.535585 
L 772.854689 381.704166 
L 774.397231 380.200239 
L 771.694759 376.051613 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #91e983"/>
    <path d="M 825.071335 463.272692 
L 827.784774 466.18424 
L 829.286682 464.568647 
L 826.575141 461.663537 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1078de"/>
    <path d="M 864.974935 488.496773 
L 867.720379 490.137813 
L 869.201169 488.151668 
L 866.457056 486.516368 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2c40a6"/>
    <path d="M 845.598433 480.104995 
L 848.325843 482.363221 
L 849.815015 480.612076 
L 847.089237 478.360079 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2353b9"/>
    <path d="M 733.044285 305.475153 
L 735.756382 309.514243 
L 737.327774 308.462678 
L 734.618272 304.457177 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #baa774"/>
    <path d="M 808.817001 444.08221 
L 811.523732 447.474534 
L 813.037417 445.900686 
L 810.332738 442.516013 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a0e8"/>
    <path d="M 651.745229 212.332967 
L 654.433507 214.188591 
L 656.084573 213.900193 
L 653.398668 212.056966 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e9e3e2"/>
    <path d="M 666.856098 222.295192 
L 669.555095 224.642223 
L 671.19195 224.372316 
L 668.495564 222.044427 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d7ccc9"/>
    <path d="M 878.937338 490.331686 
L 881.698314 491.546058 
L 883.175769 489.335872 
L 880.415915 488.125757 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2f3ba1"/>
    <path d="M 890.187079 489.124471 
L 892.961483 490.019412 
L 894.438102 487.596584 
L 891.664675 486.703728 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2c40a6"/>
    <path d="M 718.34621 281.181946 
L 721.059651 284.954567 
L 722.644378 284.149296 
L 719.933661 280.411221 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #90715d"/>
    <path d="M 827.784774 466.18424 
L 830.499915 469.008337 
L 831.99995 467.386526 
L 829.286682 464.568647 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1470d6"/>
    <path d="M 760.874739 359.250287 
L 763.581348 363.474893 
L 765.130785 362.041733 
L 762.426514 357.841047 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d1f690"/>
    <path d="M 806.110842 440.617815 
L 808.817001 444.08221 
L 810.332738 442.516013 
L 807.628655 439.059455 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a6d7"/>
    <path d="M 788.705301 413.069424 
L 791.408963 416.955334 
L 792.937883 415.398013 
L 790.2364 411.524107 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #15d06a"/>
    <path d="M 751.598287 340.968849 
L 754.307045 345.190418 
L 755.86354 343.857299 
L 753.157198 339.66337 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f8f695"/>
    <path d="M 742.320782 322.956801 
L 745.031517 327.116142 
L 746.59531 325.911005 
L 743.887078 321.782588 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d8cd84"/>
    <path d="M 830.499915 469.008337 
L 833.216932 471.743111 
L 834.715121 470.115303 
L 831.99995 467.386526 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #176bd1"/>
    <path d="M 632.35233 204.233621 
L 635.022901 205.451303 
L 636.68941 205.000763 
L 634.0208 203.787967 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f7f5f4"/>
    <path d="M 858.011311 486.774128 
L 860.750369 488.626286 
L 862.233507 486.752657 
L 859.495902 484.906351 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2b43a9"/>
    <path d="M 803.405111 437.083852 
L 806.110842 440.617815 
L 807.628655 439.059455 
L 804.925026 435.533508 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00aebf"/>
    <path d="M 715.632395 277.45944 
L 718.34621 281.181946 
L 719.933661 280.411221 
L 717.222584 276.722747 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #886759"/>
    <path d="M 669.555095 224.642223 
L 672.256199 227.085288 
L 673.890413 226.795173 
L 671.19195 224.372316 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d3c7c4"/>
    <path d="M 776.721236 391.468518 
L 779.425607 395.560813 
L 780.963556 394.03164 
L 778.261429 389.955458 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #61df79"/>
    <path d="M 642.038756 207.758422 
L 644.719145 209.301995 
L 646.378387 208.940117 
L 643.700173 207.404896 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1edec"/>
    <path d="M 848.325843 482.363221 
L 851.056261 484.522939 
L 852.543826 482.765905 
L 849.815015 480.612076 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #264eb4"/>
    <path d="M 730.331338 301.466901 
L 733.044285 305.475153 
L 734.618272 304.457177 
L 731.907944 300.482254 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b29c6f"/>
    <path d="M 767.444207 373.342803 
L 770.149945 377.535585 
L 771.694759 376.051613 
L 768.991319 371.878946 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a1ec86"/>
    <path d="M 833.216932 471.743111 
L 835.936004 474.386774 
L 837.432372 472.753194 
L 834.715121 470.115303 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1a66cc"/>
    <path d="M 885.940634 490.441888 
L 888.710695 491.443485 
L 890.187079 489.124471 
L 887.418059 488.125761 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2e3ea4"/>
    <path d="M 786.001228 409.133522 
L 788.705301 413.069424 
L 790.2364 411.524107 
L 787.534528 407.600398 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #25d36d"/>
    <path d="M 800.699669 433.4829 
L 803.405111 437.083852 
L 804.925026 435.533508 
L 802.221709 431.940744 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b4ac"/>
    <path d="M 758.167008 355.015192 
L 760.874739 359.250287 
L 762.426514 357.841047 
L 759.721148 353.629975 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e1f993"/>
    <path d="M 654.433507 214.188591 
L 657.124789 216.148816 
L 658.773441 215.846966 
L 656.084573 213.900193 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e5dedc"/>
    <path d="M 712.918304 273.790172 
L 715.632395 277.45944 
L 717.222584 276.722747 
L 714.511244 273.086963 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #825f56"/>
    <path d="M 672.256199 227.085288 
L 674.959242 229.62256 
L 676.59079 229.311195 
L 673.890413 226.795173 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cfc2bf"/>
    <path d="M 625.351503 202.686777 
L 628.01505 203.682502 
L 629.686082 203.128172 
L 627.02433 202.135295 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fbfafa"/>
    <path d="M 867.720379 490.137813 
L 870.47003 491.674985 
L 871.949509 489.683658 
L 869.201169 488.151668 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2e3ea4"/>
    <path d="M 739.608998 318.814769 
L 742.320782 322.956801 
L 743.887078 321.782588 
L 741.177823 317.671372 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d0c380"/>
    <path d="M 874.702267 491.11164 
L 877.459634 492.435009 
L 878.937338 490.331686 
L 876.181175 489.01286 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2f3ba1"/>
    <path d="M 835.936004 474.386774 
L 838.657312 476.937621 
L 840.151885 475.298501 
L 837.432372 472.753194 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1c60c6"/>
    <path d="M 748.888388 336.75072 
L 751.598287 340.968849 
L 753.157198 339.66337 
L 750.449742 335.472892 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f0ec91"/>
    <path d="M 797.994382 429.817602 
L 800.699669 433.4829 
L 802.221709 431.940744 
L 799.518571 428.283803 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00bb9b"/>
    <path d="M 727.617603 297.492853 
L 730.331338 301.466901 
L 731.907944 300.482254 
L 729.196848 296.54124 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #aa926b"/>
    <path d="M 618.362109 201.698268 
L 621.017684 202.468054 
L 622.692673 201.804613 
L 620.038728 201.036093 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fdfcfc"/>
    <path d="M 774.016036 387.341989 
L 776.721236 391.468518 
L 778.261429 389.955458 
L 775.558496 385.845219 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #71e37d"/>
    <path d="M 710.204039 270.17722 
L 712.918304 273.790172 
L 714.511244 273.086963 
L 711.799741 269.506907 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #836059"/>
    <path d="M 851.056261 484.522939 
L 853.789878 486.582891 
L 855.275861 484.82031 
L 852.543826 482.765905 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2848ae"/>
    <path d="M 674.959242 229.62256 
L 677.664059 232.252115 
L 679.292917 231.91848 
L 676.59079 229.311195 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cbbcb9"/>
    <path d="M 764.737428 369.129179 
L 767.444207 373.342803 
L 768.991319 371.878946 
L 766.286863 367.685581 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b1ef89"/>
    <path d="M 783.296641 405.150647 
L 786.001228 409.133522 
L 787.534528 407.600398 
L 784.832168 403.629895 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #31d670"/>
    <path d="M 860.750369 488.626286 
L 863.493228 490.375803 
L 864.974935 488.496773 
L 862.233507 486.752657 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2c40a6"/>
    <path d="M 881.698314 491.546058 
L 884.464291 492.655557 
L 885.940634 490.441888 
L 883.175769 489.335872 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2f3ba1"/>
    <path d="M 838.657312 476.937621 
L 841.38104 479.394038 
L 842.873843 477.749609 
L 840.151885 475.298501 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1f5bc1"/>
    <path d="M 707.489709 266.623606 
L 710.204039 270.17722 
L 711.799741 269.506907 
L 709.088183 265.985569 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #896861"/>
    <path d="M 795.289121 426.090676 
L 797.994382 429.817602 
L 799.518571 428.283803 
L 796.815483 424.565393 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c088"/>
    <path d="M 644.719145 209.301995 
L 647.403111 210.954331 
L 649.060131 210.583121 
L 646.378387 208.940117 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #efebea"/>
    <path d="M 657.124789 216.148816 
L 659.818899 218.212346 
L 661.4651 217.896005 
L 658.773441 215.846966 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e3dbd9"/>
    <path d="M 755.458133 350.773061 
L 758.167008 355.015192 
L 759.721148 353.629975 
L 757.014663 349.411949 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1fc96"/>
    <path d="M 635.022901 205.451303 
L 637.697624 206.780757 
L 639.36212 206.324442 
L 636.68941 205.000763 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f5f2f2"/>
    <path d="M 677.664059 232.252115 
L 680.370487 234.971927 
L 681.996634 234.615027 
L 679.292917 231.91848 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c7b7b4"/>
    <path d="M 736.8962 314.693507 
L 739.608998 318.814769 
L 741.177823 317.671372 
L 738.467577 313.580784 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c8b97b"/>
    <path d="M 724.903148 293.55635 
L 727.617603 297.492853 
L 729.196848 296.54124 
L 726.485052 292.637441 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a48b68"/>
    <path d="M 704.775429 263.1323 
L 707.489709 266.623606 
L 709.088183 265.985569 
L 706.37668 262.525881 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #91726c"/>
    <path d="M 746.177356 332.539518 
L 748.888388 336.75072 
L 750.449742 335.472892 
L 747.741178 331.289328 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e8e28d"/>
    <path d="M 771.309937 383.184485 
L 774.016036 387.341989 
L 775.558496 385.845219 
L 772.854689 381.704166 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #81e680"/>
    <path d="M 680.370487 234.971927 
L 683.078364 237.779874 
L 684.701784 237.39874 
L 681.996634 234.615027 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c1b0ac"/>
    <path d="M 780.591448 401.123873 
L 783.296641 405.150647 
L 784.832168 403.629895 
L 782.129224 399.615661 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #41d973"/>
    <path d="M 792.583762 422.3049 
L 795.289121 426.090676 
L 796.815483 424.565393 
L 794.112319 420.788291 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c970"/>
    <path d="M 702.061319 259.706211 
L 704.775429 263.1323 
L 706.37668 262.525881 
L 703.665351 259.130719 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #977a74"/>
    <path d="M 841.38104 479.394038 
L 844.107373 481.754496 
L 845.598433 480.104995 
L 842.873843 477.749609 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2256bc"/>
    <path d="M 762.029566 364.898106 
L 764.737428 369.129179 
L 766.286863 367.685581 
L 763.581348 363.474893 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bdf28c"/>
    <path d="M 683.078364 237.779874 
L 685.787534 240.67374 
L 687.408211 240.267431 
L 684.701784 237.39874 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bdaba7"/>
    <path d="M 853.789878 486.582891 
L 856.526887 488.541911 
L 858.011311 486.774128 
L 855.275861 484.82031 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2a46ac"/>
    <path d="M 699.347502 256.348185 
L 702.061319 259.706211 
L 703.665351 259.130719 
L 700.954318 255.802894 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9d827c"/>
    <path d="M 870.47003 491.674985 
L 873.224083 493.107586 
L 874.702267 491.11164 
L 871.949509 489.683658 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2f3ba1"/>
    <path d="M 888.710695 491.443485 
L 891.486137 492.340433 
L 892.961483 490.019412 
L 890.187079 489.124471 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2e3ea4"/>
    <path d="M 685.787534 240.67374 
L 688.497843 243.651221 
L 690.115763 243.218823 
L 687.408211 240.267431 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b7a39f"/>
    <path d="M 696.63411 253.061001 
L 699.347502 256.348185 
L 700.954318 255.802894 
L 698.243709 252.545152 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a38984"/>
    <path d="M 722.188046 289.660705 
L 724.903148 293.55635 
L 726.485052 292.637441 
L 723.772626 288.774135 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9c8064"/>
    <path d="M 659.818899 218.212346 
L 662.515664 220.377771 
L 664.159376 220.045915 
L 661.4651 217.896005 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dfd6d4"/>
    <path d="M 688.497843 243.651221 
L 691.209139 246.709923 
L 692.824292 246.250551 
L 690.115763 243.218823 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b39e99"/>
    <path d="M 693.921276 249.847369 
L 696.63411 253.061001 
L 698.243709 252.545152 
L 695.533655 249.36017 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a78e89"/>
    <path d="M 877.459634 492.435009 
L 880.221802 493.653253 
L 881.698314 491.546058 
L 878.937338 490.331686 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2f3ba1"/>
    <path d="M 691.209139 246.709923 
L 693.921276 249.847369 
L 695.533655 249.36017 
L 692.824292 246.250551 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ad9691"/>
    <path d="M 734.182431 310.596462 
L 736.8962 314.693507 
L 738.467577 313.580784 
L 735.756382 309.514243 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c0ae77"/>
    <path d="M 752.748101 346.527369 
L 755.458133 350.773061 
L 757.014663 349.411949 
L 754.307045 345.190418 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 628.01505 203.682502 
L 630.683146 204.791576 
L 632.35233 204.233621 
L 629.686082 203.128172 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9f7f7"/>
    <path d="M 863.493228 490.375803 
L 866.240081 492.021789 
L 867.720379 490.137813 
L 864.974935 488.496773 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2e3ea4"/>
    <path d="M 815.428668 455.54521 
L 818.140084 458.711814 
L 819.64887 457.195153 
L 816.939511 454.033322 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #068ef4"/>
    <path d="M 818.140084 458.711814 
L 820.85267 461.79696 
L 822.359423 460.27565 
L 819.64887 457.195153 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0a86ec"/>
    <path d="M 789.878188 418.463123 
L 792.583762 422.3049 
L 794.112319 420.788291 
L 791.408963 416.955334 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #05cd67"/>
    <path d="M 812.71826 452.299352 
L 815.428668 455.54521 
L 816.939511 454.033322 
L 814.231184 450.792356 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0393f9"/>
    <path d="M 820.85267 461.79696 
L 823.566589 464.798525 
L 825.071335 463.272692 
L 822.359423 460.27565 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0e7ee4"/>
    <path d="M 743.465204 328.338735 
L 746.177356 332.539518 
L 747.741178 331.289328 
L 745.031517 327.116142 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e0d788"/>
    <path d="M 647.403111 210.954331 
L 650.090476 212.714478 
L 651.745229 212.332967 
L 649.060131 210.583121 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ede8e7"/>
    <path d="M 844.107373 481.754496 
L 846.8365 484.017554 
L 848.325843 482.363221 
L 845.598433 480.104995 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2450b6"/>
    <path d="M 810.008702 448.976519 
L 812.71826 452.299352 
L 814.231184 450.792356 
L 811.523732 447.474534 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #009afa"/>
    <path d="M 777.88556 397.056326 
L 780.591448 401.123873 
L 782.129224 399.615661 
L 779.425607 395.560813 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #51dc76"/>
    <path d="M 823.566589 464.798525 
L 826.282012 467.714468 
L 827.784774 466.18424 
L 825.071335 463.272692 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1078de"/>
    <path d="M 768.602877 378.999306 
L 771.309937 383.184485 
L 772.854689 381.704166 
L 770.149945 377.535585 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #91e983"/>
    <path d="M 621.017684 202.468054 
L 623.678198 203.352146 
L 625.351503 202.686777 
L 622.692673 201.804613 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fdfcfc"/>
    <path d="M 807.299842 445.579071 
L 810.008702 448.976519 
L 811.523732 447.474534 
L 808.817001 444.08221 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a0e8"/>
    <path d="M 719.472378 285.809196 
L 722.188046 289.660705 
L 723.772626 288.774135 
L 721.059651 284.954567 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #967960"/>
    <path d="M 826.282012 467.714468 
L 828.999111 470.54283 
L 830.499915 469.008337 
L 827.784774 466.18424 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1470d6"/>
    <path d="M 637.697624 206.780757 
L 640.376325 208.221393 
L 642.038756 207.758422 
L 639.36212 206.324442 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f5f2f2"/>
    <path d="M 759.320586 360.653009 
L 762.029566 364.898106 
L 763.581348 363.474893 
L 760.874739 359.250287 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cdf58f"/>
    <path d="M 884.464291 492.655557 
L 887.235457 493.659861 
L 888.710695 491.443485 
L 885.940634 490.441888 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2f3ba1"/>
    <path d="M 662.515664 220.377771 
L 665.214909 222.643571 
L 666.856098 222.295192 
L 664.159376 220.045915 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ddd3d1"/>
    <path d="M 787.172287 414.56825 
L 789.878188 418.463123 
L 791.408963 416.955334 
L 788.705301 413.069424 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #15d06a"/>
    <path d="M 804.591531 442.109441 
L 807.299842 445.579071 
L 808.817001 444.08221 
L 806.110842 440.617815 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a6d7"/>
    <path d="M 856.526887 488.541911 
L 859.267481 490.398922 
L 860.750369 488.626286 
L 858.011311 486.774128 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2b43a9"/>
    <path d="M 731.467738 306.527071 
L 734.182431 310.596462 
L 735.756382 309.514243 
L 733.044285 305.475153 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #baa774"/>
    <path d="M 828.999111 470.54283 
L 831.71806 473.281735 
L 833.216932 471.743111 
L 830.499915 469.008337 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #176bd1"/>
    <path d="M 750.036904 342.281604 
L 752.748101 346.527369 
L 754.307045 345.190418 
L 751.598287 340.968849 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f8f695"/>
    <path d="M 846.8365 484.017554 
L 849.568611 486.181863 
L 851.056261 484.522939 
L 848.325843 482.363221 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #264eb4"/>
    <path d="M 801.883626 438.570137 
L 804.591531 442.109441 
L 806.110842 440.617815 
L 803.405111 437.083852 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00acc4"/>
    <path d="M 716.756232 282.005066 
L 719.472378 285.809196 
L 721.059651 284.954567 
L 718.34621 281.181946 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8e6e5c"/>
    <path d="M 740.751954 324.151866 
L 743.465204 328.338735 
L 745.031517 327.116142 
L 742.320782 322.956801 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d8cd84"/>
    <path d="M 775.178896 392.951185 
L 777.88556 397.056326 
L 779.425607 395.560813 
L 776.721236 391.468518 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #61df79"/>
    <path d="M 765.894802 374.789793 
L 768.602877 378.999306 
L 770.149945 377.535585 
L 767.444207 373.342803 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9deb85"/>
    <path d="M 831.71806 473.281735 
L 834.439038 475.929393 
L 835.936004 474.386774 
L 833.216932 471.743111 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1a66cc"/>
    <path d="M 873.224083 493.107586 
L 875.982729 494.435008 
L 877.459634 492.435009 
L 874.702267 491.11164 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #30389e"/>
    <path d="M 650.090476 212.714478 
L 652.781064 214.581364 
L 654.433507 214.188591 
L 651.745229 212.332967 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ebe5e4"/>
    <path d="M 665.214909 222.643571 
L 667.916461 225.008112 
L 669.555095 224.642223 
L 666.856098 222.295192 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d9cecc"/>
    <path d="M 866.240081 492.021789 
L 868.991123 493.563447 
L 870.47003 491.674985 
L 867.720379 490.137813 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2f3ba1"/>
    <path d="M 784.465952 410.623251 
L 787.172287 414.56825 
L 788.705301 413.069424 
L 786.001228 409.133522 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #25d36d"/>
    <path d="M 799.175987 434.963738 
L 801.883626 438.570137 
L 803.405111 437.083852 
L 800.699669 433.4829 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b4ac"/>
    <path d="M 728.752177 302.488752 
L 731.467738 306.527071 
L 733.044285 305.475153 
L 730.331338 301.466901 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b29c6f"/>
    <path d="M 756.610461 356.397335 
L 759.320586 360.653009 
L 760.874739 359.250287 
L 758.167008 355.015192 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ddf892"/>
    <path d="M 714.039699 278.251516 
L 716.756232 282.005066 
L 718.34621 281.181946 
L 715.632395 277.45944 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #886759"/>
    <path d="M 630.683146 204.791576 
L 633.355618 206.013661 
L 635.022901 205.451303 
L 632.35233 204.233621 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9f7f7"/>
    <path d="M 834.439038 475.929393 
L 837.162227 478.484098 
L 838.657312 476.937621 
L 835.936004 474.386774 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1c60c6"/>
    <path d="M 880.221802 493.653253 
L 882.98896 494.765953 
L 884.464291 492.655557 
L 881.698314 491.546058 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #30389e"/>
    <path d="M 747.324545 338.039267 
L 750.036904 342.281604 
L 751.598287 340.968849 
L 748.888388 336.75072 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f0ec91"/>
    <path d="M 796.468482 431.292894 
L 799.175987 434.963738 
L 800.699669 433.4829 
L 797.994382 429.817602 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00bb9b"/>
    <path d="M 859.267481 490.398922 
L 862.011852 492.152939 
L 863.493228 490.375803 
L 860.750369 488.626286 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2c40a6"/>
    <path d="M 640.376325 208.221393 
L 643.058826 209.772499 
L 644.719145 209.301995 
L 642.038756 207.758422 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f3f0ef"/>
    <path d="M 738.037635 319.982404 
L 740.751954 324.151866 
L 742.320782 322.956801 
L 739.608998 318.814769 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d0c380"/>
    <path d="M 849.568611 486.181863 
L 852.303896 488.246161 
L 853.789878 486.582891 
L 851.056261 484.522939 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2848ae"/>
    <path d="M 772.47138 388.811673 
L 775.178896 392.951185 
L 776.721236 391.468518 
L 774.016036 387.341989 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #71e37d"/>
    <path d="M 667.916461 225.008112 
L 670.620149 227.469656 
L 672.256199 227.085288 
L 669.555095 224.642223 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d5c9c7"/>
    <path d="M 711.32288 274.551705 
L 714.039699 278.251516 
L 715.632395 277.45944 
L 712.918304 273.790172 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #805c54"/>
    <path d="M 781.759083 406.631151 
L 784.465952 410.623251 
L 786.001228 409.133522 
L 783.296641 405.150647 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #31d670"/>
    <path d="M 763.185664 370.55932 
L 765.894802 374.789793 
L 767.444207 373.342803 
L 764.737428 369.129179 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #adef89"/>
    <path d="M 837.162227 478.484098 
L 839.88781 480.944233 
L 841.38104 479.394038 
L 838.657312 476.937621 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1f5bc1"/>
    <path d="M 623.678198 203.352146 
L 626.343481 204.350463 
L 628.01505 203.682502 
L 625.351503 202.686777 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fdfcfc"/>
    <path d="M 726.03581 298.484902 
L 728.752177 302.488752 
L 730.331338 301.466901 
L 727.617603 297.492853 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #aa926b"/>
    <path d="M 652.781064 214.581364 
L 655.474698 216.553798 
L 657.124789 216.148816 
L 654.433507 214.188591 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e7e0df"/>
    <path d="M 793.760981 427.560323 
L 796.468482 431.292894 
L 797.994382 429.817602 
L 795.289121 426.090676 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c088"/>
    <path d="M 616.685244 202.475328 
L 619.342393 203.246357 
L 621.017684 202.468054 
L 618.362109 201.698268 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fdfcfc"/>
    <path d="M 670.620149 227.469656 
L 673.325802 230.026357 
L 674.959242 229.62256 
L 672.256199 227.085288 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d1c4c1"/>
    <path d="M 753.899171 352.134558 
L 756.610461 356.397335 
L 758.167008 355.015192 
L 755.458133 350.773061 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #edfb95"/>
    <path d="M 708.605879 270.90874 
L 711.32288 274.551705 
L 712.918304 273.790172 
L 710.204039 270.17722 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #85635c"/>
    <path d="M 887.235457 493.659861 
L 890.011998 494.558738 
L 891.486137 492.340433 
L 888.710695 491.443485 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2f3ba1"/>
    <path d="M 735.322282 315.833834 
L 738.037635 319.982404 
L 739.608998 318.814769 
L 736.8962 314.693507 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c8b97b"/>
    <path d="M 744.611031 333.80387 
L 747.324545 338.039267 
L 748.888388 336.75072 
L 746.177356 332.539518 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e8e28d"/>
    <path d="M 868.991123 493.563447 
L 871.746547 495.000074 
L 873.224083 493.107586 
L 870.47003 491.674985 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #30389e"/>
    <path d="M 769.762946 384.64106 
L 772.47138 388.811673 
L 774.016036 387.341989 
L 771.309937 383.184485 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #7de57f"/>
    <path d="M 839.88781 480.944233 
L 842.615973 483.308266 
L 844.107373 481.754496 
L 841.38104 479.394038 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2256bc"/>
    <path d="M 779.051588 402.595031 
L 781.759083 406.631151 
L 783.296641 405.150647 
L 780.591448 401.123873 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #41d973"/>
    <path d="M 791.053363 423.768811 
L 793.760981 427.560323 
L 795.289121 426.090676 
L 792.583762 422.3049 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c970"/>
    <path d="M 705.888808 267.32568 
L 708.605879 270.90874 
L 710.204039 270.17722 
L 707.489709 266.623606 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8b6b64"/>
    <path d="M 852.303896 488.246161 
L 855.042548 490.209279 
L 856.526887 488.541911 
L 853.789878 486.582891 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2a46ac"/>
    <path d="M 875.982729 494.435008 
L 878.74616 495.656738 
L 880.221802 493.653253 
L 877.459634 492.435009 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #30389e"/>
    <path d="M 673.325802 230.026357 
L 676.033254 232.676267 
L 677.664059 232.252115 
L 674.959242 229.62256 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cdbfbc"/>
    <path d="M 723.318707 294.518892 
L 726.03581 298.484902 
L 727.617603 297.492853 
L 724.903148 293.55635 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a28867"/>
    <path d="M 760.475422 366.311297 
L 763.185664 370.55932 
L 764.737428 369.129179 
L 762.029566 364.898106 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bdf28c"/>
    <path d="M 862.011852 492.152939 
L 864.760196 493.803071 
L 866.240081 492.021789 
L 863.493228 490.375803 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2e3ea4"/>
    <path d="M 633.355618 206.013661 
L 636.032292 207.348289 
L 637.697624 206.780757 
L 635.022901 205.451303 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f7f5f4"/>
    <path d="M 643.058826 209.772499 
L 645.74495 211.433236 
L 647.403111 210.954331 
L 644.719145 209.301995 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1edec"/>
    <path d="M 703.171783 263.805524 
L 705.888808 267.32568 
L 707.489709 266.623606 
L 704.775429 263.1323 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #91726c"/>
    <path d="M 655.474698 216.553798 
L 658.171199 218.630472 
L 659.818899 218.212346 
L 657.124789 216.148816 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e5dedc"/>
    <path d="M 676.033254 232.676267 
L 678.742338 235.417339 
L 680.370487 234.971927 
L 677.664059 232.252115 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c9bab7"/>
    <path d="M 751.186702 347.86817 
L 753.899171 352.134558 
L 755.458133 350.773061 
L 752.748101 346.527369 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 788.345509 419.921208 
L 791.053363 423.768811 
L 792.583762 422.3049 
L 789.878188 418.463123 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #05cd67"/>
    <path d="M 882.98896 494.765953 
L 885.761296 495.772783 
L 887.235457 493.659861 
L 884.464291 492.655557 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #30389e"/>
    <path d="M 813.916567 456.980224 
L 816.63012 460.149301 
L 818.140084 458.711814 
L 815.428668 455.54521 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #078bf1"/>
    <path d="M 816.63012 460.149301 
L 819.344819 463.23688 
L 820.85267 461.79696 
L 818.140084 458.711814 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0a86ec"/>
    <path d="M 700.454925 260.351213 
L 703.171783 263.805524 
L 704.775429 263.1323 
L 702.061319 259.706211 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #977a74"/>
    <path d="M 811.203998 453.731852 
L 813.916567 456.980224 
L 815.428668 455.54521 
L 812.71826 452.299352 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0393f9"/>
    <path d="M 842.615973 483.308266 
L 845.346904 485.574757 
L 846.8365 484.017554 
L 844.107373 481.754496 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2450b6"/>
    <path d="M 819.344819 463.23688 
L 822.060829 466.240836 
L 823.566589 464.798525 
L 820.85267 461.79696 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0e7ee4"/>
    <path d="M 678.742338 235.417339 
L 681.452892 238.247426 
L 683.078364 237.779874 
L 680.370487 234.971927 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c3b2af"/>
    <path d="M 732.605939 311.709633 
L 735.322282 315.833834 
L 736.8962 314.693507 
L 734.182431 310.596462 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c0ae77"/>
    <path d="M 720.600943 290.594067 
L 723.318707 294.518892 
L 724.903148 293.55635 
L 722.188046 289.660705 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9c8064"/>
    <path d="M 776.343378 398.518025 
L 779.051588 402.595031 
L 780.591448 401.123873 
L 777.88556 397.056326 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #51dc76"/>
    <path d="M 808.492258 450.406467 
L 811.203998 453.731852 
L 812.71826 452.299352 
L 810.008702 448.976519 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #009afa"/>
    <path d="M 767.053531 380.442657 
L 769.762946 384.64106 
L 771.309937 383.184485 
L 768.602877 378.999306 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8de882"/>
    <path d="M 741.896378 329.578928 
L 744.611031 333.80387 
L 746.177356 332.539518 
L 743.465204 328.338735 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e0d788"/>
    <path d="M 822.060829 466.240836 
L 824.778318 469.159128 
L 826.282012 467.714468 
L 823.566589 464.798525 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1078de"/>
    <path d="M 697.738363 256.965623 
L 700.454925 260.351213 
L 702.061319 259.706211 
L 699.347502 256.348185 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9d827c"/>
    <path d="M 681.452892 238.247426 
L 684.164755 241.164288 
L 685.787534 240.67374 
L 683.078364 237.779874 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bfada9"/>
    <path d="M 805.781194 447.006428 
L 808.492258 450.406467 
L 810.008702 448.976519 
L 807.299842 445.579071 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a0e8"/>
    <path d="M 695.022227 253.651566 
L 697.738363 256.965623 
L 699.347502 256.348185 
L 696.63411 253.061001 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a38984"/>
    <path d="M 824.778318 469.159128 
L 827.497457 471.989795 
L 828.999111 470.54283 
L 826.282012 467.714468 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1470d6"/>
    <path d="M 684.164755 241.164288 
L 686.877772 244.165595 
L 688.497843 243.651221 
L 685.787534 240.67374 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b9a5a1"/>
    <path d="M 855.042548 490.209279 
L 857.784759 492.070139 
L 859.267481 490.398922 
L 856.526887 488.541911 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2b43a9"/>
    <path d="M 626.343481 204.350463 
L 629.013365 205.462791 
L 630.683146 204.791576 
L 628.01505 203.682502 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fbfafa"/>
    <path d="M 757.764042 362.04916 
L 760.475422 366.311297 
L 762.029566 364.898106 
L 759.320586 360.653009 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cdf58f"/>
    <path d="M 692.306656 250.411779 
L 695.022227 253.651566 
L 696.63411 253.061001 
L 693.921276 249.847369 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a9918c"/>
    <path d="M 686.877772 244.165595 
L 689.591789 247.248927 
L 691.209139 246.709923 
L 688.497843 243.651221 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b5a09c"/>
    <path d="M 689.591789 247.248927 
L 692.306656 250.411779 
L 693.921276 249.847369 
L 691.209139 246.709923 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #af9994"/>
    <path d="M 658.171199 218.630472 
L 660.870391 220.809962 
L 662.515664 220.377771 
L 659.818899 218.212346 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e1d9d7"/>
    <path d="M 785.637308 416.020424 
L 788.345509 419.921208 
L 789.878188 418.463123 
L 787.172287 414.56825 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #15d06a"/>
    <path d="M 803.070658 443.534171 
L 805.781194 447.006428 
L 807.299842 445.579071 
L 804.591531 442.109441 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a6d7"/>
    <path d="M 827.497457 471.989795 
L 830.218423 474.730961 
L 831.71806 473.281735 
L 828.999111 470.54283 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #176bd1"/>
    <path d="M 717.8826 286.713735 
L 720.600943 290.594067 
L 722.188046 289.660705 
L 719.472378 285.809196 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #94765f"/>
    <path d="M 871.746547 495.000074 
L 874.506545 496.331059 
L 875.982729 494.435008 
L 873.224083 493.107586 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #30389e"/>
    <path d="M 619.342393 203.246357 
L 622.004533 204.13224 
L 623.678198 203.352146 
L 621.017684 202.468054 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fdfcfc"/>
    <path d="M 645.74495 211.433236 
L 648.434519 213.202645 
L 650.090476 212.714478 
L 647.403111 210.954331 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #efebea"/>
    <path d="M 845.346904 485.574757 
L 848.080792 487.742353 
L 849.568611 486.181863 
L 846.8365 484.017554 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #274bb1"/>
    <path d="M 748.47305 343.601679 
L 751.186702 347.86817 
L 752.748101 346.527369 
L 750.036904 342.281604 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f6f394"/>
    <path d="M 729.888654 307.613265 
L 732.605939 311.709633 
L 734.182431 310.596462 
L 731.467738 306.527071 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b8a473"/>
    <path d="M 773.634373 394.403319 
L 776.343378 398.518025 
L 777.88556 397.056326 
L 775.178896 392.951185 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #61df79"/>
    <path d="M 800.360507 439.992204 
L 803.070658 443.534171 
L 804.591531 442.109441 
L 801.883626 438.570137 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00acc4"/>
    <path d="M 864.760196 493.803071 
L 867.512706 495.348518 
L 868.991123 493.563447 
L 866.240081 492.021789 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2f3ba1"/>
    <path d="M 764.343082 376.219817 
L 767.053531 380.442657 
L 768.602877 378.999306 
L 765.894802 374.789793 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9deb85"/>
    <path d="M 739.180607 325.36796 
L 741.896378 329.578928 
L 743.465204 328.338735 
L 740.751954 324.151866 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d8cd84"/>
    <path d="M 636.032292 207.348289 
L 638.712993 208.794869 
L 640.376325 208.221393 
L 637.697624 206.780757 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f7f5f4"/>
    <path d="M 878.74616 495.656738 
L 881.514567 496.772354 
L 882.98896 494.765953 
L 880.221802 493.653253 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #32369c"/>
    <path d="M 830.218423 474.730961 
L 832.941393 477.380835 
L 834.439038 475.929393 
L 831.71806 473.281735 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1a66cc"/>
    <path d="M 782.928656 412.069433 
L 785.637308 416.020424 
L 787.172287 414.56825 
L 784.465952 410.623251 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #25d36d"/>
    <path d="M 660.870391 220.809962 
L 663.572097 223.090731 
L 665.214909 222.643571 
L 662.515664 220.377771 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dfd6d4"/>
    <path d="M 797.650603 436.383107 
L 800.360507 439.992204 
L 801.883626 438.570137 
L 799.175987 434.963738 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b4ac"/>
    <path d="M 715.163768 282.881171 
L 717.8826 286.713735 
L 719.472378 285.809196 
L 716.756232 282.005066 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8e6e5c"/>
    <path d="M 755.051497 357.776376 
L 757.764042 362.04916 
L 759.320586 360.653009 
L 756.610461 356.397335 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ddf892"/>
    <path d="M 832.941393 477.380835 
L 835.666548 479.93771 
L 837.162227 478.484098 
L 834.439038 475.929393 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1c60c6"/>
    <path d="M 857.784759 492.070139 
L 860.530724 493.827753 
L 862.011852 492.152939 
L 859.267481 490.398922 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2e3ea4"/>
    <path d="M 727.170486 303.548175 
L 729.888654 307.613265 
L 731.467738 306.527071 
L 728.752177 302.488752 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b29c6f"/>
    <path d="M 848.080792 487.742353 
L 850.817829 489.809792 
L 852.303896 488.246161 
L 849.568611 486.181863 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2848ae"/>
    <path d="M 794.940812 432.709532 
L 797.650603 436.383107 
L 799.175987 434.963738 
L 796.468482 431.292894 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00bb9b"/>
    <path d="M 770.924499 390.254144 
L 773.634373 394.403319 
L 775.178896 392.951185 
L 772.47138 388.811673 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #71e37d"/>
    <path d="M 745.758216 339.338607 
L 748.47305 343.601679 
L 750.036904 342.281604 
L 747.324545 338.039267 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eee990"/>
    <path d="M 885.761296 495.772783 
L 888.538998 496.673512 
L 890.011998 494.558738 
L 887.235457 493.659861 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #30389e"/>
    <path d="M 712.444541 279.099605 
L 715.163768 282.881171 
L 716.756232 282.005066 
L 714.039699 278.251516 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #866458"/>
    <path d="M 648.434519 213.202645 
L 651.127354 215.079644 
L 652.781064 214.581364 
L 650.090476 212.714478 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ede8e7"/>
    <path d="M 736.463749 321.174481 
L 739.180607 325.36796 
L 740.751954 324.151866 
L 738.037635 319.982404 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d0c380"/>
    <path d="M 663.572097 223.090731 
L 666.276143 225.471131 
L 667.916461 225.008112 
L 665.214909 222.643571 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dbd1cf"/>
    <path d="M 780.219452 408.071265 
L 782.928656 412.069433 
L 784.465952 410.623251 
L 781.759083 406.631151 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #31d670"/>
    <path d="M 761.631552 371.975925 
L 764.343082 376.219817 
L 765.894802 374.789793 
L 763.185664 370.55932 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #adef89"/>
    <path d="M 629.013365 205.462791 
L 631.687676 206.688789 
L 633.355618 206.013661 
L 630.683146 204.791576 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fbfafa"/>
    <path d="M 835.666548 479.93771 
L 838.394071 482.399968 
L 839.88781 480.944233 
L 837.162227 478.484098 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1f5bc1"/>
    <path d="M 792.231008 428.974198 
L 794.940812 432.709532 
L 796.468482 431.292894 
L 793.760981 427.560323 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c088"/>
    <path d="M 867.512706 495.348518 
L 870.269577 496.788575 
L 871.746547 495.000074 
L 868.991123 493.563447 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #30389e"/>
    <path d="M 709.725021 275.372225 
L 712.444541 279.099605 
L 714.039699 278.251516 
L 711.32288 274.551705 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #805c54"/>
    <path d="M 752.337769 353.496432 
L 755.051497 357.776376 
L 756.610461 356.397335 
L 753.899171 352.134558 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #edfb95"/>
    <path d="M 874.506545 496.331059 
L 877.271311 497.555886 
L 878.74616 495.656738 
L 875.982729 494.435008 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #32369c"/>
    <path d="M 638.712993 208.794869 
L 641.397542 210.35268 
L 643.058826 209.772499 
L 640.376325 208.221393 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f5f2f2"/>
    <path d="M 724.451499 299.517788 
L 727.170486 303.548175 
L 728.752177 302.488752 
L 726.03581 298.484902 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #aa926b"/>
    <path d="M 666.276143 225.471131 
L 668.982355 227.949404 
L 670.620149 227.469656 
L 667.916461 225.008112 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d7ccc9"/>
    <path d="M 622.004533 204.13224 
L 624.671494 205.132891 
L 626.343481 204.350463 
L 623.678198 203.352146 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fdfcfc"/>
    <path d="M 768.213689 386.073778 
L 770.924499 390.254144 
L 772.47138 388.811673 
L 769.762946 384.64106 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #7de57f"/>
    <path d="M 615.008248 203.367983 
L 617.666917 204.140236 
L 619.342393 203.246357 
L 616.685244 202.475328 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ffffff"/>
    <path d="M 850.817829 489.809792 
L 853.558206 491.775902 
L 855.042548 490.209279 
L 852.303896 488.246161 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2a46ac"/>
    <path d="M 777.509604 404.029004 
L 780.219452 408.071265 
L 781.759083 406.631151 
L 779.051588 402.595031 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #41d973"/>
    <path d="M 838.394071 482.399968 
L 841.124148 484.766079 
L 842.615973 483.308266 
L 839.88781 480.944233 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2256bc"/>
    <path d="M 743.042209 335.082485 
L 745.758216 339.338607 
L 747.324545 338.039267 
L 744.611031 333.80387 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e6df8b"/>
    <path d="M 789.521067 425.179892 
L 792.231008 428.974198 
L 793.760981 427.560323 
L 791.053363 423.768811 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c970"/>
    <path d="M 733.745841 317.002002 
L 736.463749 321.174481 
L 738.037635 319.982404 
L 735.322282 315.833834 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c8b97b"/>
    <path d="M 860.530724 493.827753 
L 863.280638 495.481229 
L 864.760196 493.803071 
L 862.011852 492.152939 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2f3ba1"/>
    <path d="M 707.005314 271.70217 
L 709.725021 275.372225 
L 711.32288 274.551705 
L 708.605879 270.90874 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #85635c"/>
    <path d="M 881.514567 496.772354 
L 884.28814 497.781529 
L 885.761296 495.772783 
L 882.98896 494.765953 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #32369c"/>
    <path d="M 651.127354 215.079644 
L 653.823274 217.06303 
L 655.474698 216.553798 
L 652.781064 214.581364 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e9e3e2"/>
    <path d="M 758.918899 367.714402 
L 761.631552 371.975925 
L 763.185664 370.55932 
L 760.475422 366.311297 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bdf28c"/>
    <path d="M 668.982355 227.949404 
L 671.69056 230.523687 
L 673.325802 230.026357 
L 670.620149 227.469656 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d3c7c4"/>
    <path d="M 721.731762 295.525504 
L 724.451499 299.517788 
L 726.03581 298.484902 
L 723.318707 294.518892 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a28867"/>
    <path d="M 704.285534 268.092526 
L 707.005314 271.70217 
L 708.605879 270.90874 
L 705.888808 267.32568 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8d6d66"/>
    <path d="M 749.622846 349.212837 
L 752.337769 353.496432 
L 753.899171 352.134558 
L 751.186702 347.86817 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 786.810874 421.329465 
L 789.521067 425.179892 
L 791.053363 423.768811 
L 788.345509 419.921208 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #05cd67"/>
    <path d="M 841.124148 484.766079 
L 843.856967 487.034599 
L 845.346904 485.574757 
L 842.615973 483.308266 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2450b6"/>
    <path d="M 812.403133 458.338249 
L 815.118901 461.507498 
L 816.63012 460.149301 
L 813.916567 456.980224 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #068ef4"/>
    <path d="M 815.118901 461.507498 
L 817.835794 464.59529 
L 819.344819 463.23688 
L 816.63012 460.149301 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0a86ec"/>
    <path d="M 671.69056 230.523687 
L 674.400589 233.192013 
L 676.033254 232.676267 
L 673.325802 230.026357 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cfc2bf"/>
    <path d="M 809.688329 455.089746 
L 812.403133 458.338249 
L 813.916567 456.980224 
L 811.203998 453.731852 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0393f9"/>
    <path d="M 774.799025 399.945789 
L 777.509604 404.029004 
L 779.051588 402.595031 
L 776.343378 398.518025 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #51dc76"/>
    <path d="M 817.835794 464.59529 
L 820.553974 467.599502 
L 822.060829 466.240836 
L 819.344819 463.23688 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0e7ee4"/>
    <path d="M 765.501882 381.865541 
L 768.213689 386.073778 
L 769.762946 384.64106 
L 767.053531 380.442657 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8de882"/>
    <path d="M 631.687676 206.688789 
L 634.366239 208.027987 
L 636.032292 207.348289 
L 633.355618 206.013661 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9f7f7"/>
    <path d="M 701.565799 264.546322 
L 704.285534 268.092526 
L 705.888808 267.32568 
L 703.171783 263.805524 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #93756e"/>
    <path d="M 806.974332 451.764269 
L 809.688329 455.089746 
L 811.203998 453.731852 
L 808.492258 450.406467 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #009afa"/>
    <path d="M 641.397542 210.35268 
L 644.08576 212.020879 
L 645.74495 211.433236 
L 643.058826 209.772499 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f3f0ef"/>
    <path d="M 820.553974 467.599502 
L 823.27361 470.518092 
L 824.778318 469.159128 
L 822.060829 466.240836 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1078de"/>
    <path d="M 740.325046 330.836848 
L 743.042209 335.082485 
L 744.611031 333.80387 
L 741.896378 329.578928 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ded587"/>
    <path d="M 731.026927 312.854023 
L 733.745841 317.002002 
L 735.322282 315.833834 
L 732.605939 311.709633 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c0ae77"/>
    <path d="M 853.558206 491.775902 
L 856.302118 493.639604 
L 857.784759 492.070139 
L 855.042548 490.209279 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2c40a6"/>
    <path d="M 653.823274 217.06303 
L 656.522102 219.151485 
L 658.171199 218.630472 
L 655.474698 216.553798 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e7e0df"/>
    <path d="M 804.26099 448.364178 
L 806.974332 451.764269 
L 808.492258 450.406467 
L 805.781194 447.006428 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a0e8"/>
    <path d="M 719.011353 291.574692 
L 721.731762 295.525504 
L 723.318707 294.518892 
L 720.600943 290.594067 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9a7e62"/>
    <path d="M 674.400589 233.192013 
L 677.112274 235.952312 
L 678.742338 235.417339 
L 676.033254 232.676267 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c9bab7"/>
    <path d="M 756.205093 363.438698 
L 758.918899 367.714402 
L 760.475422 366.311297 
L 757.764042 362.04916 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cdf58f"/>
    <path d="M 823.27361 470.518092 
L 825.994874 473.349102 
L 827.497457 471.989795 
L 824.778318 469.159128 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1470d6"/>
    <path d="M 870.269577 496.788575 
L 873.031001 498.12263 
L 874.506545 496.331059 
L 871.746547 495.000074 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #32369c"/>
    <path d="M 698.846233 261.066528 
L 701.565799 264.546322 
L 703.171783 263.805524 
L 700.454925 260.351213 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #997c76"/>
    <path d="M 784.100318 417.42583 
L 786.810874 421.329465 
L 788.345509 419.921208 
L 785.637308 416.020424 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #15d06a"/>
    <path d="M 801.548158 444.891904 
L 804.26099 448.364178 
L 805.781194 447.006428 
L 803.070658 443.534171 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a6d7"/>
    <path d="M 877.271311 497.555886 
L 880.041036 498.674133 
L 881.514567 496.772354 
L 878.74616 495.656738 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #32369c"/>
    <path d="M 677.112274 235.952312 
L 679.825449 238.802418 
L 681.452892 238.247426 
L 678.742338 235.417339 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c5b5b1"/>
    <path d="M 863.280638 495.481229 
L 866.034694 497.029765 
L 867.512706 495.348518 
L 864.760196 493.803071 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #30389e"/>
    <path d="M 696.126965 257.656047 
L 698.846233 261.066528 
L 700.454925 260.351213 
L 697.738363 256.965623 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9f847e"/>
    <path d="M 825.994874 473.349102 
L 828.717939 476.090656 
L 830.218423 474.730961 
L 827.497457 471.989795 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #176bd1"/>
    <path d="M 843.856967 487.034599 
L 846.592717 489.204176 
L 848.080792 487.742353 
L 845.346904 485.574757 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #274bb1"/>
    <path d="M 624.671494 205.132891 
L 627.343105 206.248097 
L 629.013365 205.462791 
L 626.343481 204.350463 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fdfcfc"/>
    <path d="M 746.906722 344.929115 
L 749.622846 349.212837 
L 751.186702 347.86817 
L 748.47305 343.601679 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f6f394"/>
    <path d="M 772.087635 395.824811 
L 774.799025 399.945789 
L 776.343378 398.518025 
L 773.634373 394.403319 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #61df79"/>
    <path d="M 679.825449 238.802418 
L 682.539953 241.740069 
L 684.164755 241.164288 
L 681.452892 238.247426 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c1b0ac"/>
    <path d="M 693.408129 254.317718 
L 696.126965 257.656047 
L 697.738363 256.965623 
L 695.022227 253.651566 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a58c86"/>
    <path d="M 798.835692 441.349957 
L 801.548158 444.891904 
L 803.070658 443.534171 
L 800.360507 439.992204 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00acc4"/>
    <path d="M 762.789025 377.632791 
L 765.501882 381.865541 
L 767.053531 380.442657 
L 764.343082 376.219817 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9deb85"/>
    <path d="M 682.539953 241.740069 
L 685.255627 244.76291 
L 686.877772 244.165595 
L 684.164755 241.164288 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bba8a4"/>
    <path d="M 690.689864 251.054305 
L 693.408129 254.317718 
L 695.022227 253.651566 
L 692.306656 250.411779 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ab938e"/>
    <path d="M 716.290357 287.668691 
L 719.011353 291.574692 
L 720.600943 290.594067 
L 717.8826 286.713735 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #94765f"/>
    <path d="M 728.307059 308.734032 
L 731.026927 312.854023 
L 732.605939 311.709633 
L 729.888654 307.613265 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b8a473"/>
    <path d="M 685.255627 244.76291 
L 687.972314 247.868499 
L 689.591789 247.248927 
L 686.877772 244.165595 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b7a39f"/>
    <path d="M 687.972314 247.868499 
L 690.689864 251.054305 
L 692.306656 250.411779 
L 689.591789 247.248927 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b19b96"/>
    <path d="M 617.666917 204.140236 
L 620.330625 205.027768 
L 622.004533 204.13224 
L 619.342393 203.246357 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ffffff"/>
    <path d="M 828.717939 476.090656 
L 831.442983 478.740964 
L 832.941393 477.380835 
L 830.218423 474.730961 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1a66cc"/>
    <path d="M 737.60675 326.605235 
L 740.325046 330.836848 
L 741.896378 329.578928 
L 739.180607 325.36796 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d8cd84"/>
    <path d="M 656.522102 219.151485 
L 659.223657 221.343572 
L 660.870391 220.809962 
L 658.171199 218.630472 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e3dbd9"/>
    <path d="M 781.389294 413.47196 
L 784.100318 417.42583 
L 785.637308 416.020424 
L 782.928656 412.069433 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #21d36d"/>
    <path d="M 884.28814 497.781529 
L 887.067065 498.684031 
L 888.538998 496.673512 
L 885.761296 495.772783 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #32369c"/>
    <path d="M 796.123455 437.740916 
L 798.835692 441.349957 
L 800.360507 439.992204 
L 797.650603 436.383107 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b4ac"/>
    <path d="M 644.08576 212.020879 
L 646.777467 213.798499 
L 648.434519 213.202645 
L 645.74495 211.433236 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1edec"/>
    <path d="M 753.490106 359.15229 
L 756.205093 363.438698 
L 757.764042 362.04916 
L 755.051497 357.776376 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ddf892"/>
    <path d="M 856.302118 493.639604 
L 859.049758 495.39991 
L 860.530724 493.827753 
L 857.784759 492.070139 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2e3ea4"/>
    <path d="M 634.366239 208.027987 
L 637.048875 209.479789 
L 638.712993 208.794869 
L 636.032292 207.348289 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f7f5f4"/>
    <path d="M 831.442983 478.740964 
L 834.170188 481.298319 
L 835.666548 479.93771 
L 832.941393 477.380835 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1c60c6"/>
    <path d="M 713.568863 283.8108 
L 716.290357 287.668691 
L 717.8826 286.713735 
L 715.163768 282.881171 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8c6c5b"/>
    <path d="M 846.592717 489.204176 
L 849.331588 491.273547 
L 850.817829 489.809792 
L 848.080792 487.742353 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2848ae"/>
    <path d="M 769.375361 391.669305 
L 772.087635 395.824811 
L 773.634373 394.403319 
L 770.924499 390.254144 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #6de27c"/>
    <path d="M 793.411315 434.06743 
L 796.123455 437.740916 
L 797.650603 436.383107 
L 794.940812 432.709532 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00bb9b"/>
    <path d="M 744.189402 340.648803 
L 746.906722 344.929115 
L 748.47305 343.601679 
L 745.758216 339.338607 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eee990"/>
    <path d="M 725.586294 304.6455 
L 728.307059 308.734032 
L 729.888654 307.613265 
L 727.170486 303.548175 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b09a6e"/>
    <path d="M 659.223657 221.343572 
L 661.927761 223.637739 
L 663.572097 223.090731 
L 660.870391 220.809962 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dfd6d4"/>
    <path d="M 778.677703 409.470887 
L 781.389294 413.47196 
L 782.928656 412.069433 
L 780.219452 408.071265 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #31d670"/>
    <path d="M 760.075071 373.378925 
L 762.789025 377.632791 
L 764.343082 376.219817 
L 761.631552 371.975925 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #adef89"/>
    <path d="M 734.887354 322.391183 
L 737.60675 326.605235 
L 739.180607 325.36796 
L 736.463749 321.174481 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d0c380"/>
    <path d="M 873.031001 498.12263 
L 875.797174 499.350165 
L 877.271311 497.555886 
L 874.506545 496.331059 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #32369c"/>
    <path d="M 834.170188 481.298319 
L 836.899735 483.761105 
L 838.394071 482.399968 
L 835.666548 479.93771 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1f5bc1"/>
    <path d="M 866.034694 497.029765 
L 868.793088 498.472655 
L 870.269577 496.788575 
L 867.512706 495.348518 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #30389e"/>
    <path d="M 710.846969 280.004277 
L 713.568863 283.8108 
L 715.163768 282.881171 
L 712.444541 279.099605 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #866458"/>
    <path d="M 790.699144 430.332218 
L 793.411315 434.06743 
L 794.940812 432.709532 
L 792.231008 428.974198 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c088"/>
    <path d="M 750.773921 354.858679 
L 753.490106 359.15229 
L 755.051497 357.776376 
L 752.337769 353.496432 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #edfb95"/>
    <path d="M 880.041036 498.674133 
L 882.81591 499.685471 
L 884.28814 497.781529 
L 881.514567 496.772354 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #32369c"/>
    <path d="M 646.777467 213.798499 
L 649.472482 215.684448 
L 651.127354 215.079644 
L 648.434519 213.202645 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ede8e7"/>
    <path d="M 627.343105 206.248097 
L 630.019191 207.477515 
L 631.687676 206.688789 
L 629.013365 205.462791 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fbfafa"/>
    <path d="M 661.927761 223.637739 
L 664.634239 226.032325 
L 666.276143 225.471131 
L 663.572097 223.090731 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ddd3d1"/>
    <path d="M 766.662137 387.482554 
L 769.375361 391.669305 
L 770.924499 390.254144 
L 768.213689 386.073778 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #7de57f"/>
    <path d="M 722.864699 300.591873 
L 725.586294 304.6455 
L 727.170486 303.548175 
L 724.451499 299.517788 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #aa926b"/>
    <path d="M 849.331588 491.273547 
L 852.073774 493.24154 
L 853.558206 491.775902 
L 850.817829 489.809792 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2a46ac"/>
    <path d="M 859.049758 495.39991 
L 861.801321 497.055926 
L 863.280638 495.481229 
L 860.530724 493.827753 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2f3ba1"/>
    <path d="M 775.965455 405.425698 
L 778.677703 409.470887 
L 780.219452 408.071265 
L 777.509604 404.029004 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #41d973"/>
    <path d="M 708.124777 276.252338 
L 710.846969 280.004277 
L 712.444541 279.099605 
L 709.725021 275.372225 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #815e56"/>
    <path d="M 836.899735 483.761105 
L 839.63181 486.127791 
L 841.124148 484.766079 
L 838.394071 482.399968 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2256bc"/>
    <path d="M 741.470894 336.37545 
L 744.189402 340.648803 
L 745.758216 339.338607 
L 743.042209 335.082485 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e6df8b"/>
    <path d="M 787.986822 426.538065 
L 790.699144 430.332218 
L 792.231008 428.974198 
L 789.521067 425.179892 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c970"/>
    <path d="M 757.359982 369.10737 
L 760.075071 373.378925 
L 761.631552 371.975925 
L 758.918899 367.714402 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bdf28c"/>
    <path d="M 613.331239 204.376819 
L 615.991372 205.150274 
L 617.666917 204.140236 
L 615.008248 203.367983 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ffffff"/>
    <path d="M 637.048875 209.479789 
L 639.735406 211.043471 
L 641.397542 210.35268 
L 638.712993 208.794869 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f5f2f2"/>
    <path d="M 620.330625 205.027768 
L 622.999203 206.030495 
L 624.671494 205.132891 
L 622.004533 204.13224 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ffffff"/>
    <path d="M 732.166894 318.198221 
L 734.887354 322.391183 
L 736.463749 321.174481 
L 733.745841 317.002002 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c8b97b"/>
    <path d="M 664.634239 226.032325 
L 667.342912 228.525557 
L 668.982355 227.949404 
L 666.276143 225.471131 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d9cecc"/>
    <path d="M 705.402397 272.558146 
L 708.124777 276.252338 
L 709.725021 275.372225 
L 707.005314 271.70217 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #87655e"/>
    <path d="M 748.056527 350.561385 
L 750.773921 354.858679 
L 752.337769 353.496432 
L 749.622846 349.212837 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 720.142346 296.576577 
L 722.864699 300.591873 
L 724.451499 299.517788 
L 721.731762 295.525504 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a28867"/>
    <path d="M 785.274233 422.687821 
L 787.986822 426.538065 
L 789.521067 425.179892 
L 786.810874 421.329465 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #05cd67"/>
    <path d="M 649.472482 215.684448 
L 652.170624 217.677517 
L 653.823274 217.06303 
L 651.127354 215.079644 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ebe5e4"/>
    <path d="M 839.63181 486.127791 
L 842.3666 488.396935 
L 843.856967 487.034599 
L 841.124148 484.766079 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2450b6"/>
    <path d="M 773.252462 401.339533 
L 775.965455 405.425698 
L 777.509604 404.029004 
L 774.799025 399.945789 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #51dc76"/>
    <path d="M 763.947903 383.267883 
L 766.662137 387.482554 
L 768.213689 386.073778 
L 765.501882 381.865541 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8de882"/>
    <path d="M 810.888293 459.619245 
L 813.606352 462.786362 
L 815.118901 461.507498 
L 812.403133 458.338249 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #068ef4"/>
    <path d="M 813.606352 462.786362 
L 816.325515 465.872145 
L 817.835794 464.59529 
L 815.118901 461.507498 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0a86ec"/>
    <path d="M 808.171178 456.372994 
L 810.888293 459.619245 
L 812.403133 458.338249 
L 809.688329 455.089746 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0393f9"/>
    <path d="M 816.325515 465.872145 
L 819.045944 468.874476 
L 820.553974 467.599502 
L 817.835794 464.59529 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0e7ee4"/>
    <path d="M 702.679944 268.924814 
L 705.402397 272.558146 
L 707.005314 271.70217 
L 704.285534 268.092526 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8d6d66"/>
    <path d="M 667.342912 228.525557 
L 670.053608 231.115553 
L 671.69056 230.523687 
L 668.982355 227.949404 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d5c9c7"/>
    <path d="M 868.793088 498.472655 
L 871.556013 499.809284 
L 873.031001 498.12263 
L 870.269577 496.788575 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #32369c"/>
    <path d="M 852.073774 493.24154 
L 854.819468 495.107076 
L 856.302118 493.639604 
L 853.558206 491.775902 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2c40a6"/>
    <path d="M 738.751218 332.112607 
L 741.470894 336.37545 
L 743.042209 335.082485 
L 740.325046 330.836848 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ded587"/>
    <path d="M 805.454851 453.049888 
L 808.171178 456.372994 
L 809.688329 455.089746 
L 806.974332 451.764269 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #009afa"/>
    <path d="M 875.797174 499.350165 
L 878.568285 500.470755 
L 880.041036 498.674133 
L 877.271311 497.555886 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #333399"/>
    <path d="M 819.045944 468.874476 
L 821.767808 471.791314 
L 823.27361 470.518092 
L 820.553974 467.599502 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1078de"/>
    <path d="M 729.445416 314.029871 
L 732.166894 318.198221 
L 733.745841 317.002002 
L 731.026927 312.854023 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c0ae77"/>
    <path d="M 754.643725 364.821586 
L 757.359982 369.10737 
L 758.918899 367.714402 
L 756.205093 363.438698 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cdf58f"/>
    <path d="M 802.739162 449.652282 
L 805.454851 453.049888 
L 806.974332 451.764269 
L 804.26099 448.364178 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a0e8"/>
    <path d="M 630.019191 207.477515 
L 632.699577 208.820674 
L 634.366239 208.027987 
L 631.687676 206.688789 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fbfafa"/>
    <path d="M 821.767808 471.791314 
L 824.491275 474.620704 
L 825.994874 473.349102 
L 823.27361 470.518092 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1470d6"/>
    <path d="M 782.561267 418.784397 
L 785.274233 422.687821 
L 786.810874 421.329465 
L 784.100318 417.42583 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #15d06a"/>
    <path d="M 861.801321 497.055926 
L 864.557001 498.606849 
L 866.034694 497.029765 
L 863.280638 495.481229 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #30389e"/>
    <path d="M 699.957537 265.355397 
L 702.679944 268.924814 
L 704.285534 268.092526 
L 701.565799 264.546322 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #957771"/>
    <path d="M 670.053608 231.115553 
L 672.766154 233.800331 
L 674.400589 233.192013 
L 671.69056 230.523687 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cfc2bf"/>
    <path d="M 717.419313 292.603004 
L 720.142346 296.576577 
L 721.731762 295.525504 
L 719.011353 291.574692 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9a7e62"/>
    <path d="M 639.735406 211.043471 
L 642.425651 212.718183 
L 644.08576 212.020879 
L 641.397542 210.35268 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f3f0ef"/>
    <path d="M 800.023964 446.182606 
L 802.739162 449.652282 
L 804.26099 448.364178 
L 801.548158 444.891904 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a6d7"/>
    <path d="M 842.3666 488.396935 
L 845.104295 490.567186 
L 846.592717 489.204176 
L 843.856967 487.034599 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #274bb1"/>
    <path d="M 770.538645 397.215583 
L 773.252462 401.339533 
L 774.799025 399.945789 
L 772.087635 395.824811 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #61df79"/>
    <path d="M 824.491275 474.620704 
L 827.216521 477.360772 
L 828.717939 476.090656 
L 825.994874 473.349102 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #176bd1"/>
    <path d="M 745.33792 346.263946 
L 748.056527 350.561385 
L 749.622846 349.212837 
L 746.906722 344.929115 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f6f394"/>
    <path d="M 697.235303 261.852889 
L 699.957537 265.355397 
L 701.565799 264.546322 
L 698.846233 261.066528 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9b7f79"/>
    <path d="M 882.81591 499.685471 
L 885.596123 500.589666 
L 887.067065 498.684031 
L 884.28814 497.781529 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #32369c"/>
    <path d="M 652.170624 217.677517 
L 654.871711 219.776374 
L 656.522102 219.151485 
L 653.823274 217.06303 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e7e0df"/>
    <path d="M 672.766154 233.800331 
L 675.480381 236.577802 
L 677.112274 235.952312 
L 674.400589 233.192013 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cbbcb9"/>
    <path d="M 761.232607 379.028655 
L 763.947903 383.267883 
L 765.501882 381.865541 
L 762.789025 377.632791 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9deb85"/>
    <path d="M 797.309116 442.643364 
L 800.023964 446.182606 
L 801.548158 444.891904 
L 798.835692 441.349957 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00aebf"/>
    <path d="M 694.513373 258.420219 
L 697.235303 261.852889 
L 698.846233 261.066528 
L 696.126965 257.656047 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a18781"/>
    <path d="M 622.999203 206.030495 
L 625.672479 207.148201 
L 627.343105 206.248097 
L 624.671494 205.132891 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fdfcfc"/>
    <path d="M 726.722974 309.88964 
L 729.445416 314.029871 
L 731.026927 312.854023 
L 728.307059 308.734032 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b8a473"/>
    <path d="M 736.030397 327.863829 
L 738.751218 332.112607 
L 740.325046 330.836848 
L 737.60675 326.605235 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d6cb83"/>
    <path d="M 675.480381 236.577802 
L 678.19612 239.445782 
L 679.825449 238.802418 
L 677.112274 235.952312 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c7b7b4"/>
    <path d="M 779.84782 414.830766 
L 782.561267 418.784397 
L 784.100318 417.42583 
L 781.389294 413.47196 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #25d36d"/>
    <path d="M 827.216521 477.360772 
L 829.943723 480.00973 
L 831.442983 478.740964 
L 828.717939 476.090656 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1a66cc"/>
    <path d="M 714.695687 288.674516 
L 717.419313 292.603004 
L 719.011353 291.574692 
L 716.290357 287.668691 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #92735e"/>
    <path d="M 615.991372 205.150274 
L 618.65659 206.039315 
L 620.330625 205.027768 
L 617.666917 204.140236 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ffffff"/>
    <path d="M 691.791883 255.060249 
L 694.513373 258.420219 
L 696.126965 257.656047 
L 693.408129 254.317718 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a78e89"/>
    <path d="M 751.926277 360.525058 
L 754.643725 364.821586 
L 756.205093 363.438698 
L 753.490106 359.15229 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ddf892"/>
    <path d="M 854.819468 495.107076 
L 857.568863 496.869166 
L 859.049758 495.39991 
L 856.302118 493.639604 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2e3ea4"/>
    <path d="M 794.594482 439.037132 
L 797.309116 442.643364 
L 798.835692 441.349957 
L 796.123455 437.740916 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b4ac"/>
    <path d="M 678.19612 239.445782 
L 680.913208 242.401987 
L 682.539953 241.740069 
L 679.825449 238.802418 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c1b0ac"/>
    <path d="M 689.070973 251.775767 
L 691.791883 255.060249 
L 693.408129 254.317718 
L 690.689864 251.054305 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ad9691"/>
    <path d="M 680.913208 242.401987 
L 683.631485 245.444044 
L 685.255627 244.76291 
L 682.539953 241.740069 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bdaba7"/>
    <path d="M 686.350791 248.569488 
L 689.070973 251.775767 
L 690.689864 251.054305 
L 687.972314 247.868499 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b19b96"/>
    <path d="M 683.631485 245.444044 
L 686.350791 248.569488 
L 687.972314 247.868499 
L 685.255627 244.76291 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b7a39f"/>
    <path d="M 845.104295 490.567186 
L 847.845084 492.637279 
L 849.331588 491.273547 
L 846.592717 489.204176 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2848ae"/>
    <path d="M 829.943723 480.00973 
L 832.673059 482.565875 
L 834.170188 481.298319 
L 831.442983 478.740964 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1c60c6"/>
    <path d="M 767.823934 393.057086 
L 770.538645 397.215583 
L 772.087635 395.824811 
L 769.375361 391.669305 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #6de27c"/>
    <path d="M 654.871711 219.776374 
L 657.575564 221.979574 
L 659.223657 221.343572 
L 656.522102 219.151485 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e5dedc"/>
    <path d="M 871.556013 499.809284 
L 874.323663 501.039135 
L 875.797174 499.350165 
L 873.031001 498.12263 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #32369c"/>
    <path d="M 742.618105 341.969911 
L 745.33792 346.263946 
L 746.906722 344.929115 
L 744.189402 340.648803 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eee990"/>
    <path d="M 791.87993 435.366557 
L 794.594482 439.037132 
L 796.123455 437.740916 
L 793.411315 434.06743 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00bb9b"/>
    <path d="M 642.425651 212.718183 
L 645.119429 214.502952 
L 646.777467 213.798499 
L 644.08576 212.020879 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1edec"/>
    <path d="M 758.516203 374.768271 
L 761.232607 379.028655 
L 762.789025 377.632791 
L 760.075071 373.378925 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #adef89"/>
    <path d="M 711.971559 284.794437 
L 714.695687 288.674516 
L 716.290357 287.668691 
L 713.568863 283.8108 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8c6c5b"/>
    <path d="M 777.133795 410.829958 
L 779.84782 414.830766 
L 781.389294 413.47196 
L 778.677703 409.470887 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #31d670"/>
    <path d="M 632.699577 208.820674 
L 635.384083 210.276972 
L 637.048875 209.479789 
L 634.366239 208.027987 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9f7f7"/>
    <path d="M 864.557001 498.606849 
L 867.316993 500.051971 
L 868.793088 498.472655 
L 866.034694 497.029765 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #32369c"/>
    <path d="M 723.999628 305.78102 
L 726.722974 309.88964 
L 728.307059 308.734032 
L 725.586294 304.6455 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b09a6e"/>
    <path d="M 878.568285 500.470755 
L 881.344528 501.484072 
L 882.81591 499.685471 
L 880.041036 498.674133 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #333399"/>
    <path d="M 733.308464 323.632669 
L 736.030397 327.863829 
L 737.60675 326.605235 
L 734.887354 322.391183 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cec07f"/>
    <path d="M 832.673059 482.565875 
L 835.404713 485.027591 
L 836.899735 483.761105 
L 834.170188 481.298319 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1f5bc1"/>
    <path d="M 789.165334 431.634353 
L 791.87993 435.366557 
L 793.411315 434.06743 
L 790.699144 430.332218 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c088"/>
    <path d="M 749.207619 356.221295 
L 751.926277 360.525058 
L 753.490106 359.15229 
L 750.773921 354.858679 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #edfb95"/>
    <path d="M 657.575564 221.979574 
L 660.282001 224.285552 
L 661.927761 223.637739 
L 659.223657 221.343572 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e1d9d7"/>
    <path d="M 709.247028 280.966048 
L 711.971559 284.794437 
L 713.568863 283.8108 
L 710.846969 280.004277 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #846257"/>
    <path d="M 765.108261 388.867326 
L 767.823934 393.057086 
L 769.375361 391.669305 
L 766.662137 387.482554 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #7de57f"/>
    <path d="M 857.568863 496.869166 
L 860.322153 498.526915 
L 861.801321 497.055926 
L 859.049758 495.39991 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2f3ba1"/>
    <path d="M 847.845084 492.637279 
L 850.58916 494.606046 
L 852.073774 493.24154 
L 849.331588 491.273547 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2a46ac"/>
    <path d="M 774.4191 406.785058 
L 777.133795 410.829958 
L 778.677703 409.470887 
L 775.965455 405.425698 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #41d973"/>
    <path d="M 625.672479 207.148201 
L 628.350278 208.380544 
L 630.019191 207.477515 
L 627.343105 206.248097 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fdfcfc"/>
    <path d="M 721.275443 301.707478 
L 723.999628 305.78102 
L 725.586294 304.6455 
L 722.864699 300.591873 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a8906a"/>
    <path d="M 739.897092 337.68284 
L 742.618105 341.969911 
L 744.189402 340.648803 
L 741.470894 336.37545 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e6df8b"/>
    <path d="M 786.450573 427.843302 
L 789.165334 431.634353 
L 790.699144 430.332218 
L 787.986822 426.538065 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c970"/>
    <path d="M 755.798653 370.490164 
L 758.516203 374.768271 
L 760.075071 373.378925 
L 757.359982 369.10737 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bdf28c"/>
    <path d="M 835.404713 485.027591 
L 838.138868 487.393351 
L 839.63181 486.127791 
L 836.899735 483.761105 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2256bc"/>
    <path d="M 645.119429 214.502952 
L 647.816557 216.396679 
L 649.472482 215.684448 
L 646.777467 213.798499 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #efebea"/>
    <path d="M 730.585459 319.422674 
L 733.308464 323.632669 
L 734.887354 322.391183 
L 732.166894 318.198221 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c8b97b"/>
    <path d="M 611.65433 205.50229 
L 614.31587 206.276927 
L 615.991372 205.150274 
L 613.331239 204.376819 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ffffff"/>
    <path d="M 706.522198 277.192588 
L 709.247028 280.966048 
L 710.846969 280.004277 
L 708.124777 276.252338 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #815e56"/>
    <path d="M 660.282001 224.285552 
L 662.990844 226.692635 
L 664.634239 226.032325 
L 661.927761 223.637739 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ddd3d1"/>
    <path d="M 618.65659 206.039315 
L 621.326724 207.043857 
L 622.999203 206.030495 
L 620.330625 205.027768 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ffffff"/>
    <path d="M 635.384083 210.276972 
L 638.07253 211.845682 
L 639.735406 211.043471 
L 637.048875 209.479789 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f7f5f4"/>
    <path d="M 746.487741 351.913828 
L 749.207619 356.221295 
L 750.773921 354.858679 
L 748.056527 350.561385 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 783.735533 423.996249 
L 786.450573 427.843302 
L 787.986822 426.538065 
L 785.274233 422.687821 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #05cd67"/>
    <path d="M 762.391569 384.64963 
L 765.108261 388.867326 
L 766.662137 387.482554 
L 763.947903 383.267883 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8de882"/>
    <path d="M 771.703651 402.699206 
L 774.4191 406.785058 
L 775.965455 405.425698 
L 773.252462 401.339533 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #51dc76"/>
    <path d="M 867.316993 500.051971 
L 870.081492 501.390679 
L 871.556013 499.809284 
L 868.793088 498.472655 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #32369c"/>
    <path d="M 874.323663 501.039135 
L 877.096231 502.161781 
L 878.568285 500.470755 
L 875.797174 499.350165 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #333399"/>
    <path d="M 703.797181 273.477243 
L 706.522198 277.192588 
L 708.124777 276.252338 
L 705.402397 272.558146 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #87655e"/>
    <path d="M 718.550494 297.672459 
L 721.275443 301.707478 
L 722.864699 300.591873 
L 720.142346 296.576577 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a28867"/>
    <path d="M 838.138868 487.393351 
L 840.875712 489.661713 
L 842.3666 488.396935 
L 839.63181 486.127791 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2450b6"/>
    <path d="M 662.990844 226.692635 
L 665.701915 229.199034 
L 667.342912 228.525557 
L 664.634239 226.032325 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d9cecc"/>
    <path d="M 809.37197 460.823241 
L 812.092394 463.985923 
L 813.606352 462.786362 
L 810.888293 459.619245 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #068ef4"/>
    <path d="M 812.092394 463.985923 
L 814.813903 467.067478 
L 816.325515 465.872145 
L 813.606352 462.786362 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0a86ec"/>
    <path d="M 850.58916 494.606046 
L 853.336716 496.472406 
L 854.819468 495.107076 
L 852.073774 493.24154 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2c40a6"/>
    <path d="M 806.652471 457.581627 
L 809.37197 460.823241 
L 810.888293 459.619245 
L 808.171178 456.372994 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0296fc"/>
    <path d="M 737.174901 333.406299 
L 739.897092 337.68284 
L 741.470894 336.37545 
L 738.751218 332.112607 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ded587"/>
    <path d="M 814.813903 467.067478 
L 817.536658 470.065791 
L 819.045944 468.874476 
L 816.325515 465.872145 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0c80e6"/>
    <path d="M 753.079926 366.197799 
L 755.798653 370.490164 
L 757.359982 369.10737 
L 754.643725 364.821586 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cdf58f"/>
    <path d="M 803.933744 454.263353 
L 806.652471 457.581627 
L 808.171178 456.372994 
L 805.454851 453.049888 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #009cf4"/>
    <path d="M 727.861428 315.237383 
L 730.585459 319.422674 
L 732.166894 318.198221 
L 729.445416 314.029871 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c0ae77"/>
    <path d="M 647.816557 216.396679 
L 650.516851 218.398148 
L 652.170624 217.677517 
L 649.472482 215.684448 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ede8e7"/>
    <path d="M 817.536658 470.065791 
L 820.260826 472.978826 
L 821.767808 471.791314 
L 819.045944 468.874476 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1078de"/>
    <path d="M 860.322153 498.526915 
L 863.079535 500.079521 
L 864.557001 498.606849 
L 861.801321 497.055926 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #30389e"/>
    <path d="M 701.072093 269.823147 
L 703.797181 273.477243 
L 705.402397 272.558146 
L 702.679944 268.924814 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8f7069"/>
    <path d="M 881.344528 501.484072 
L 884.12609 502.389882 
L 885.596123 500.589666 
L 882.81591 499.685471 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #333399"/>
    <path d="M 801.215638 450.870771 
L 803.933744 454.263353 
L 805.454851 453.049888 
L 802.739162 449.652282 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a2e2"/>
    <path d="M 781.020106 420.096102 
L 783.735533 423.996249 
L 785.274233 422.687821 
L 782.561267 418.784397 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #15d06a"/>
    <path d="M 665.701915 229.199034 
L 668.415037 231.802857 
L 670.053608 231.115553 
L 667.342912 228.525557 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d5c9c7"/>
    <path d="M 820.260826 472.978826 
L 822.986577 475.804633 
L 824.491275 474.620704 
L 821.767808 471.791314 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1373d9"/>
    <path d="M 715.824861 293.679378 
L 718.550494 297.672459 
L 720.142346 296.576577 
L 717.419313 292.603004 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9a7e62"/>
    <path d="M 798.498008 447.406304 
L 801.215638 450.870771 
L 802.739162 449.652282 
L 800.023964 446.182606 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a8d0"/>
    <path d="M 628.350278 208.380544 
L 631.032421 209.727048 
L 632.699577 208.820674 
L 630.019191 207.477515 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fbfafa"/>
    <path d="M 768.98737 398.57559 
L 771.703651 402.699206 
L 773.252462 401.339533 
L 770.538645 397.215583 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #61df79"/>
    <path d="M 743.766643 347.606201 
L 746.487741 351.913828 
L 748.056527 350.561385 
L 745.33792 346.263946 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f6f394"/>
    <path d="M 698.347056 266.23338 
L 701.072093 269.823147 
L 702.679944 268.924814 
L 699.957537 265.355397 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #957771"/>
    <path d="M 840.875712 489.661713 
L 843.615434 491.831327 
L 845.104295 490.567186 
L 842.3666 488.396935 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #264eb4"/>
    <path d="M 759.673805 380.407363 
L 762.391569 384.64963 
L 763.947903 383.267883 
L 761.232607 379.028655 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9deb85"/>
    <path d="M 822.986577 475.804633 
L 825.714084 478.541341 
L 827.216521 477.360772 
L 824.491275 474.620704 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #176bd1"/>
    <path d="M 638.07253 211.845682 
L 640.764734 213.525951 
L 642.425651 212.718183 
L 639.735406 211.043471 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f5f2f2"/>
    <path d="M 668.415037 231.802857 
L 671.130038 234.502102 
L 672.766154 233.800331 
L 670.053608 231.115553 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d1c4c1"/>
    <path d="M 795.780714 443.872451 
L 798.498008 447.406304 
L 800.023964 446.182606 
L 797.309116 442.643364 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00aebf"/>
    <path d="M 734.451558 329.143856 
L 737.174901 333.406299 
L 738.751218 332.112607 
L 736.030397 327.863829 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d6cb83"/>
    <path d="M 695.622199 262.710955 
L 698.347056 266.23338 
L 699.957537 265.355397 
L 697.235303 261.852889 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9b7f79"/>
    <path d="M 778.304188 416.14583 
L 781.020106 420.096102 
L 782.561267 418.784397 
L 779.84782 414.830766 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #25d36d"/>
    <path d="M 725.136427 311.08032 
L 727.861428 315.237383 
L 729.445416 314.029871 
L 726.722974 309.88964 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b8a473"/>
    <path d="M 750.359999 361.894666 
L 753.079926 366.197799 
L 754.643725 364.821586 
L 751.926277 360.525058 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ddf892"/>
    <path d="M 650.516851 218.398148 
L 653.220131 220.506017 
L 654.871711 219.776374 
L 652.170624 217.677517 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e9e3e2"/>
    <path d="M 621.326724 207.043857 
L 624.001602 208.163684 
L 625.672479 207.148201 
L 622.999203 206.030495 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fdfcfc"/>
    <path d="M 853.336716 496.472406 
L 856.087946 498.23537 
L 857.568863 496.869166 
L 854.819468 495.107076 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2e3ea4"/>
    <path d="M 825.714084 478.541341 
L 828.443522 481.187167 
L 829.943723 480.00973 
L 827.216521 477.360772 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1a66cc"/>
    <path d="M 671.130038 234.502102 
L 673.846745 237.294669 
L 675.480381 236.577802 
L 672.766154 233.800331 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cdbfbc"/>
    <path d="M 614.31587 206.276927 
L 616.98254 207.167336 
L 618.65659 206.039315 
L 615.991372 205.150274 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ffffff"/>
    <path d="M 713.098632 289.731614 
L 715.824861 293.679378 
L 717.419313 292.603004 
L 714.695687 288.674516 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #92735e"/>
    <path d="M 692.897653 259.258825 
L 695.622199 262.710955 
L 697.235303 261.852889 
L 694.513373 258.420219 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a18781"/>
    <path d="M 793.063621 440.271783 
L 795.780714 443.872451 
L 797.309116 442.643364 
L 794.594482 439.037132 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b4ac"/>
    <path d="M 870.081492 501.390679 
L 872.850692 502.622452 
L 874.323663 501.039135 
L 871.556013 499.809284 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #333399"/>
    <path d="M 673.846745 237.294669 
L 676.564988 240.178353 
L 678.19612 239.445782 
L 675.480381 236.577802 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c9bab7"/>
    <path d="M 766.270185 394.417447 
L 768.98737 398.57559 
L 770.538645 397.215583 
L 767.823934 393.057086 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #6de27c"/>
    <path d="M 690.173558 255.879872 
L 692.897653 259.258825 
L 694.513373 258.420219 
L 691.791883 255.060249 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a78e89"/>
    <path d="M 843.615434 491.831327 
L 846.358223 493.900934 
L 847.845084 492.637279 
L 845.104295 490.567186 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2848ae"/>
    <path d="M 741.044328 343.301975 
L 743.766643 347.606201 
L 745.33792 346.263946 
L 742.618105 341.969911 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eee990"/>
    <path d="M 877.096231 502.161781 
L 879.873908 503.176893 
L 881.344528 501.484072 
L 878.568285 500.470755 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #333399"/>
    <path d="M 676.564988 240.178353 
L 679.284602 243.150856 
L 680.913208 242.401987 
L 678.19612 239.445782 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c3b2af"/>
    <path d="M 828.443522 481.187167 
L 831.175072 483.740411 
L 832.673059 482.565875 
L 829.943723 480.00973 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1c60c6"/>
    <path d="M 756.954927 376.143926 
L 759.673805 380.407363 
L 761.232607 379.028655 
L 758.516203 374.768271 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #adef89"/>
    <path d="M 687.450055 252.576906 
L 690.173558 255.879872 
L 691.791883 255.060249 
L 689.070973 251.775767 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ad9691"/>
    <path d="M 863.079535 500.079521 
L 865.841202 501.526275 
L 867.316993 500.051971 
L 864.557001 498.606849 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #32369c"/>
    <path d="M 790.346597 436.606939 
L 793.063621 440.271783 
L 794.594482 439.037132 
L 791.87993 435.366557 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00bb9b"/>
    <path d="M 679.284602 243.150856 
L 682.005424 246.209786 
L 683.631485 245.444044 
L 680.913208 242.401987 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bdaba7"/>
    <path d="M 775.587682 412.148458 
L 778.304188 416.14583 
L 779.84782 414.830766 
L 777.133795 410.829958 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #31d670"/>
    <path d="M 684.727293 249.352659 
L 687.450055 252.576906 
L 689.070973 251.775767 
L 686.350791 248.569488 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b39e99"/>
    <path d="M 682.005424 246.209786 
L 684.727293 249.352659 
L 686.350791 248.569488 
L 683.631485 245.444044 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b9a5a1"/>
    <path d="M 722.410515 306.954991 
L 725.136427 311.08032 
L 726.722974 309.88964 
L 723.999628 305.78102 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b09a6e"/>
    <path d="M 710.3719 285.832512 
L 713.098632 289.731614 
L 714.695687 288.674516 
L 711.971559 284.794437 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8c6c5b"/>
    <path d="M 731.727095 324.899076 
L 734.451558 329.143856 
L 736.030397 327.863829 
L 733.308464 323.632669 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cec07f"/>
    <path d="M 653.220131 220.506017 
L 655.926212 222.718832 
L 657.575564 221.979574 
L 654.871711 219.776374 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e5dedc"/>
    <path d="M 640.764734 213.525951 
L 643.460513 215.316799 
L 645.119429 214.502952 
L 642.425651 212.718183 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f3f0ef"/>
    <path d="M 631.032421 209.727048 
L 633.71873 211.187111 
L 635.384083 210.276972 
L 632.699577 208.820674 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9f7f7"/>
    <path d="M 747.638855 357.58428 
L 750.359999 361.894666 
L 751.926277 360.525058 
L 749.207619 356.221295 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #edfb95"/>
    <path d="M 787.629517 432.880629 
L 790.346597 436.606939 
L 791.87993 435.366557 
L 789.165334 431.634353 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c382"/>
    <path d="M 831.175072 483.740411 
L 833.908913 486.19946 
L 835.404713 485.027591 
L 832.673059 482.565875 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1f5bc1"/>
    <path d="M 763.552032 390.228059 
L 766.270185 394.417447 
L 767.823934 393.057086 
L 765.108261 388.867326 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #7de57f"/>
    <path d="M 856.087946 498.23537 
L 858.843043 499.894046 
L 860.322153 498.526915 
L 857.568863 496.869166 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2f3ba1"/>
    <path d="M 707.644765 281.985374 
L 710.3719 285.832512 
L 711.971559 284.794437 
L 709.247028 280.966048 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #846257"/>
    <path d="M 772.870499 408.107067 
L 775.587682 412.148458 
L 777.133795 410.829958 
L 774.4191 406.785058 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #41d973"/>
    <path d="M 846.358223 493.900934 
L 849.10427 495.869362 
L 850.58916 494.606046 
L 847.845084 492.637279 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2a46ac"/>
    <path d="M 738.320808 339.004718 
L 741.044328 343.301975 
L 742.618105 341.969911 
L 739.897092 337.68284 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e6df8b"/>
    <path d="M 754.234895 371.862756 
L 756.954927 376.143926 
L 758.516203 374.768271 
L 755.798653 370.490164 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bdf28c"/>
    <path d="M 655.926212 222.718832 
L 658.634914 225.035019 
L 660.282001 224.285552 
L 657.575564 221.979574 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e3dbd9"/>
    <path d="M 719.683761 302.864883 
L 722.410515 306.954991 
L 723.999628 305.78102 
L 721.275443 301.707478 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a8906a"/>
    <path d="M 784.912264 429.095628 
L 787.629517 432.880629 
L 789.165334 431.634353 
L 786.450573 427.843302 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c970"/>
    <path d="M 624.001602 208.163684 
L 626.681047 209.398452 
L 628.350278 208.380544 
L 625.672479 207.148201 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fdfcfc"/>
    <path d="M 833.908913 486.19946 
L 836.645231 488.562791 
L 838.138868 487.393351 
L 835.404713 485.027591 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2256bc"/>
    <path d="M 609.977633 206.744724 
L 612.640523 207.520521 
L 614.31587 206.276927 
L 611.65433 205.50229 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ffffff"/>
    <path d="M 729.001555 320.675519 
L 731.727095 324.899076 
L 733.308464 323.632669 
L 730.585459 319.422674 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c6b67a"/>
    <path d="M 616.98254 207.167336 
L 619.654169 208.173431 
L 621.326724 207.043857 
L 618.65659 206.039315 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ffffff"/>
    <path d="M 704.917334 278.193457 
L 707.644765 281.985374 
L 709.247028 280.966048 
L 706.522198 277.192588 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #815e56"/>
    <path d="M 744.916485 353.270176 
L 747.638855 357.58428 
L 749.207619 356.221295 
L 746.487741 351.913828 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 643.460513 215.316799 
L 646.159684 217.217123 
L 647.816557 216.396679 
L 645.119429 214.502952 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1edec"/>
    <path d="M 872.850692 502.622452 
L 875.624785 503.746865 
L 877.096231 502.161781 
L 874.323663 501.039135 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #333399"/>
    <path d="M 865.841202 501.526275 
L 868.607349 502.866563 
L 870.081492 501.390679 
L 867.316993 500.051971 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #32369c"/>
    <path d="M 760.832853 386.010753 
L 763.552032 390.228059 
L 765.108261 388.867326 
L 762.391569 384.64963 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8de882"/>
    <path d="M 770.152556 404.024792 
L 772.870499 408.107067 
L 774.4191 406.785058 
L 771.703651 402.699206 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #51dc76"/>
    <path d="M 782.194722 425.254774 
L 784.912264 429.095628 
L 786.450573 427.843302 
L 783.735533 423.996249 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #09ce68"/>
    <path d="M 658.634914 225.035019 
L 661.346055 227.452892 
L 662.990844 226.692635 
L 660.282001 224.285552 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dfd6d4"/>
    <path d="M 633.71873 211.187111 
L 636.409023 212.760003 
L 638.07253 211.845682 
L 635.384083 210.276972 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f7f5f4"/>
    <path d="M 716.95624 298.813456 
L 719.683761 302.864883 
L 721.275443 301.707478 
L 718.550494 297.672459 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a08566"/>
    <path d="M 879.873908 503.176893 
L 882.656884 504.084237 
L 884.12609 502.389882 
L 881.344528 501.484072 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #333399"/>
    <path d="M 735.596105 334.718005 
L 738.320808 339.004718 
L 739.897092 337.68284 
L 737.174901 333.406299 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ded587"/>
    <path d="M 836.645231 488.562791 
L 839.38421 490.828965 
L 840.875712 489.661713 
L 838.138868 487.393351 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2353b9"/>
    <path d="M 702.189719 274.459967 
L 704.917334 278.193457 
L 706.522198 277.192588 
L 703.797181 273.477243 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #896861"/>
    <path d="M 751.513681 367.567318 
L 754.234895 371.862756 
L 755.798653 370.490164 
L 753.079926 366.197799 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cdf58f"/>
    <path d="M 849.10427 495.869362 
L 851.853769 497.735535 
L 853.336716 496.472406 
L 850.58916 494.606046 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2b43a9"/>
    <path d="M 807.854086 461.950341 
L 810.576948 465.106288 
L 812.092394 463.985923 
L 809.37197 460.823241 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #068ef4"/>
    <path d="M 810.576948 465.106288 
L 813.300876 468.181395 
L 814.813903 467.067478 
L 812.092394 463.985923 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0888ee"/>
    <path d="M 726.274984 316.476738 
L 729.001555 320.675519 
L 730.585459 319.422674 
L 727.861428 315.237383 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #beac76"/>
    <path d="M 805.132134 458.715744 
L 807.854086 461.950341 
L 809.37197 460.823241 
L 806.652471 457.581627 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0296fc"/>
    <path d="M 858.843043 499.894046 
L 861.602203 501.44763 
L 863.079535 500.079521 
L 860.322153 498.526915 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #30389e"/>
    <path d="M 813.300876 468.181395 
L 816.026032 471.173555 
L 817.536658 470.065791 
L 814.813903 467.067478 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0c80e6"/>
    <path d="M 802.410938 455.404763 
L 805.132134 458.715744 
L 806.652471 457.581627 
L 803.933744 454.263353 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #009cf4"/>
    <path d="M 661.346055 227.452892 
L 664.059456 229.970653 
L 665.701915 229.199034 
L 662.990844 226.692635 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dbd1cf"/>
    <path d="M 779.476784 421.360969 
L 782.194722 425.254774 
L 783.735533 423.996249 
L 781.020106 420.096102 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #15d06a"/>
    <path d="M 816.026032 471.173555 
L 818.752582 474.08074 
L 820.260826 472.978826 
L 817.536658 470.065791 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1078de"/>
    <path d="M 699.462039 270.788059 
L 702.189719 274.459967 
L 703.797181 273.477243 
L 701.072093 269.823147 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8f7069"/>
    <path d="M 799.690349 452.019739 
L 802.410938 455.404763 
L 803.933744 454.263353 
L 801.215638 450.870771 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a2e2"/>
    <path d="M 646.159684 217.217123 
L 648.862062 219.225698 
L 650.516851 218.398148 
L 647.816557 216.396679 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ede8e7"/>
    <path d="M 742.192889 348.955906 
L 744.916485 353.270176 
L 746.487741 351.913828 
L 743.766643 347.606201 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f6f394"/>
    <path d="M 767.433774 399.904817 
L 770.152556 404.024792 
L 771.703651 402.699206 
L 768.98737 398.57559 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #61df79"/>
    <path d="M 758.112598 381.76889 
L 760.832853 386.010753 
L 762.391569 384.64963 
L 759.673805 380.407363 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9deb85"/>
    <path d="M 714.228035 294.804141 
L 716.95624 298.813456 
L 718.550494 297.672459 
L 715.824861 293.679378 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9a7e62"/>
    <path d="M 818.752582 474.08074 
L 821.480693 476.901002 
L 822.986577 475.804633 
L 820.260826 472.978826 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1373d9"/>
    <path d="M 796.970223 448.563091 
L 799.690349 452.019739 
L 801.215638 450.870771 
L 798.498008 447.406304 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a8d0"/>
    <path d="M 626.681047 209.398452 
L 629.364882 210.747684 
L 631.032421 209.727048 
L 628.350278 208.380544 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fbfafa"/>
    <path d="M 664.059456 229.970653 
L 666.77494 232.586396 
L 668.415037 231.802857 
L 665.701915 229.199034 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d7ccc9"/>
    <path d="M 839.38421 490.828965 
L 842.12604 492.996635 
L 843.615434 491.831327 
L 840.875712 489.661713 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #264eb4"/>
    <path d="M 696.734417 267.180829 
L 699.462039 270.788059 
L 701.072093 269.823147 
L 698.347056 266.23338 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #957771"/>
    <path d="M 732.870245 330.445412 
L 735.596105 334.718005 
L 737.174901 333.406299 
L 734.451558 329.143856 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d6cb83"/>
    <path d="M 821.480693 476.901002 
L 824.210538 479.632479 
L 825.714084 478.541341 
L 822.986577 475.804633 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #166ed4"/>
    <path d="M 748.791261 363.261106 
L 751.513681 367.567318 
L 753.079926 366.197799 
L 750.359999 361.894666 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ddf892"/>
    <path d="M 794.25042 445.037309 
L 796.970223 448.563091 
L 798.498008 447.406304 
L 795.780714 443.872451 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00aebf"/>
    <path d="M 776.758349 417.417173 
L 779.476784 421.360969 
L 781.020106 420.096102 
L 778.304188 416.14583 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #25d36d"/>
    <path d="M 723.54744 312.306268 
L 726.274984 316.476738 
L 727.861428 315.237383 
L 725.136427 311.08032 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b8a473"/>
    <path d="M 636.409023 212.760003 
L 639.103117 214.444865 
L 640.764734 213.525951 
L 638.07253 211.845682 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f5f2f2"/>
    <path d="M 612.640523 207.520521 
L 615.308585 208.412156 
L 616.98254 207.167336 
L 614.31587 206.276927 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ffffff"/>
    <path d="M 666.77494 232.586396 
L 669.492329 235.298108 
L 671.130038 234.502102 
L 668.415037 231.802857 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d3c7c4"/>
    <path d="M 619.654169 208.173431 
L 622.330585 209.294998 
L 624.001602 208.163684 
L 621.326724 207.043857 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ffffff"/>
    <path d="M 851.853769 497.735535 
L 854.606913 499.498465 
L 856.087946 498.23537 
L 853.336716 496.472406 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2e3ea4"/>
    <path d="M 694.006983 263.641311 
L 696.734417 267.180829 
L 698.347056 266.23338 
L 695.622199 262.710955 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9d827c"/>
    <path d="M 868.607349 502.866563 
L 871.378169 504.099866 
L 872.850692 502.622452 
L 870.081492 501.390679 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #333399"/>
    <path d="M 711.499233 290.840335 
L 714.228035 294.804141 
L 715.824861 293.679378 
L 713.098632 289.731614 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #92735e"/>
    <path d="M 824.210538 479.632479 
L 826.942293 482.273391 
L 828.443522 481.187167 
L 825.714084 478.541341 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1868ce"/>
    <path d="M 875.624785 503.746865 
L 878.403963 504.763588 
L 879.873908 503.176893 
L 877.096231 502.161781 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #333399"/>
    <path d="M 791.530807 441.444955 
L 794.25042 445.037309 
L 795.780714 443.872451 
L 793.063621 440.271783 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b4ac"/>
    <path d="M 764.714083 395.750375 
L 767.433774 399.904817 
L 768.98737 398.57559 
L 766.270185 394.417447 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #71e37d"/>
    <path d="M 648.862062 219.225698 
L 651.567463 221.341178 
L 653.220131 220.506017 
L 650.516851 218.398148 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ebe5e4"/>
    <path d="M 739.468072 344.645033 
L 742.192889 348.955906 
L 743.766643 347.606201 
L 741.044328 343.301975 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eee990"/>
    <path d="M 669.492329 235.298108 
L 672.211452 238.103673 
L 673.846745 237.294669 
L 671.130038 234.502102 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cdbfbc"/>
    <path d="M 691.279872 260.172475 
L 694.006983 263.641311 
L 695.622199 262.710955 
L 692.897653 259.258825 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a38984"/>
    <path d="M 755.391223 377.505872 
L 758.112598 381.76889 
L 759.673805 380.407363 
L 756.954927 376.143926 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #adef89"/>
    <path d="M 861.602203 501.44763 
L 864.36562 502.895414 
L 865.841202 501.526275 
L 863.079535 500.079521 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #32369c"/>
    <path d="M 842.12604 492.996635 
L 844.870909 495.064544 
L 846.358223 493.900934 
L 843.615434 491.831327 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2848ae"/>
    <path d="M 774.039321 413.426407 
L 776.758349 417.417173 
L 778.304188 416.14583 
L 775.587682 412.148458 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #31d670"/>
    <path d="M 688.553223 256.777221 
L 691.279872 260.172475 
L 692.897653 259.258825 
L 690.173558 255.879872 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a9918c"/>
    <path d="M 672.211452 238.103673 
L 674.932137 241.000874 
L 676.564988 240.178353 
L 673.846745 237.294669 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c9bab7"/>
    <path d="M 788.811254 437.788661 
L 791.530807 441.444955 
L 793.063621 440.271783 
L 790.346597 436.606939 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00bb9b"/>
    <path d="M 826.942293 482.273391 
L 829.676135 484.822045 
L 831.175072 483.740411 
L 828.443522 481.187167 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1b63c9"/>
    <path d="M 730.143262 326.190516 
L 732.870245 330.445412 
L 734.451558 329.143856 
L 731.727095 324.899076 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cec07f"/>
    <path d="M 720.818983 308.167631 
L 723.54744 312.306268 
L 725.136427 311.08032 
L 722.410515 306.954991 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b09a6e"/>
    <path d="M 685.827182 253.458376 
L 688.553223 256.777221 
L 690.173558 255.879872 
L 687.450055 252.576906 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #af9994"/>
    <path d="M 674.932137 241.000874 
L 677.654215 243.987398 
L 679.284602 243.150856 
L 676.564988 240.178353 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c5b5b1"/>
    <path d="M 708.769931 286.9254 
L 711.499233 290.840335 
L 713.098632 289.731614 
L 710.3719 285.832512 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8a695a"/>
    <path d="M 746.067622 358.947634 
L 748.791261 363.261106 
L 750.359999 361.894666 
L 747.638855 357.58428 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #edfb95"/>
    <path d="M 683.101897 250.218691 
L 685.827182 253.458376 
L 687.450055 252.576906 
L 684.727293 249.352659 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b5a09c"/>
    <path d="M 677.654215 243.987398 
L 680.377522 247.060836 
L 682.005424 246.209786 
L 679.284602 243.150856 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bfada9"/>
    <path d="M 680.377522 247.060836 
L 683.101897 250.218691 
L 684.727293 249.352659 
L 682.005424 246.209786 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b9a5a1"/>
    <path d="M 629.364882 210.747684 
L 632.052925 212.210777 
L 633.71873 211.187111 
L 631.032421 209.727048 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fbfafa"/>
    <path d="M 651.567463 221.341178 
L 654.275703 223.562098 
L 655.926212 222.718832 
L 653.220131 220.506017 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e7e0df"/>
    <path d="M 639.103117 214.444865 
L 641.800827 216.240715 
L 643.460513 215.316799 
L 640.764734 213.525951 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f3f0ef"/>
    <path d="M 786.091637 434.071127 
L 788.811254 437.788661 
L 790.346597 436.606939 
L 787.629517 432.880629 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c382"/>
    <path d="M 761.99342 391.564743 
L 764.714083 395.750375 
L 766.270185 394.417447 
L 763.552032 390.228059 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #7de57f"/>
    <path d="M 829.676135 484.822045 
L 832.412244 487.276832 
L 833.908913 486.19946 
L 831.175072 483.740411 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1e5ec4"/>
    <path d="M 854.606913 499.498465 
L 857.363895 501.157259 
L 858.843043 499.894046 
L 856.087946 498.23537 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2f3ba1"/>
    <path d="M 736.742048 340.341133 
L 739.468072 344.645033 
L 741.044328 343.301975 
L 738.320808 339.004718 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e6df8b"/>
    <path d="M 771.319611 409.391743 
L 774.039321 413.426407 
L 775.587682 412.148458 
L 772.870499 408.107067 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #41d973"/>
    <path d="M 752.668692 373.225133 
L 755.391223 377.505872 
L 756.954927 376.143926 
L 754.234895 371.862756 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bdf28c"/>
    <path d="M 706.040229 283.062652 
L 708.769931 286.9254 
L 710.3719 285.832512 
L 707.644765 281.985374 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #846257"/>
    <path d="M 844.870909 495.064544 
L 847.619008 497.031524 
L 849.10427 495.869362 
L 846.358223 493.900934 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2a46ac"/>
    <path d="M 608.301257 208.104315 
L 610.965441 208.881252 
L 612.640523 207.520521 
L 609.977633 206.744724 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ffffff"/>
    <path d="M 718.089684 304.064326 
L 720.818983 308.167631 
L 722.410515 306.954991 
L 719.683761 302.864883 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a8906a"/>
    <path d="M 727.415199 321.956885 
L 730.143262 326.190516 
L 731.727095 324.899076 
L 729.001555 320.675519 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c6b67a"/>
    <path d="M 783.371839 430.29512 
L 786.091637 434.071127 
L 787.629517 432.880629 
L 784.912264 429.095628 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c970"/>
    <path d="M 622.330585 209.294998 
L 625.011612 210.531689 
L 626.681047 209.398452 
L 624.001602 208.163684 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fdfcfc"/>
    <path d="M 654.275703 223.562098 
L 656.986599 225.886879 
L 658.634914 225.035019 
L 655.926212 222.718832 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e3dbd9"/>
    <path d="M 871.378169 504.099866 
L 874.153857 505.225757 
L 875.624785 503.746865 
L 872.850692 502.622452 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #333399"/>
    <path d="M 743.342754 354.63044 
L 746.067622 358.947634 
L 747.638855 357.58428 
L 744.916485 353.270176 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 615.308585 208.412156 
L 617.981648 209.419542 
L 619.654169 208.173431 
L 616.98254 207.167336 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ffffff"/>
    <path d="M 832.412244 487.276832 
L 835.150803 489.636233 
L 836.645231 488.562791 
L 833.908913 486.19946 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2058be"/>
    <path d="M 864.36562 502.895414 
L 867.133488 504.236785 
L 868.607349 502.866563 
L 865.841202 501.526275 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #32369c"/>
    <path d="M 703.310236 279.255366 
L 706.040229 283.062652 
L 707.644765 281.985374 
L 704.917334 278.193457 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #836059"/>
    <path d="M 759.271729 387.351242 
L 761.99342 391.564743 
L 763.552032 390.228059 
L 760.832853 386.010753 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8de882"/>
    <path d="M 768.599136 405.316309 
L 771.319611 409.391743 
L 772.870499 408.107067 
L 770.152556 404.024792 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #51dc76"/>
    <path d="M 878.403963 504.763588 
L 881.188418 505.672387 
L 882.656884 504.084237 
L 879.873908 503.176893 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #333399"/>
    <path d="M 641.800827 216.240715 
L 644.50197 218.146446 
L 646.159684 217.217123 
L 643.460513 215.316799 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1edec"/>
    <path d="M 780.651746 426.463469 
L 783.371839 430.29512 
L 784.912264 429.095628 
L 782.194722 425.254774 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #09ce68"/>
    <path d="M 734.014838 336.047786 
L 736.742048 340.341133 
L 738.320808 339.004718 
L 735.596105 334.718005 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ded587"/>
    <path d="M 715.359618 299.999825 
L 718.089684 304.064326 
L 719.683761 302.864883 
L 716.95624 298.813456 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a08566"/>
    <path d="M 749.944976 368.930136 
L 752.668692 373.225133 
L 754.234895 371.862756 
L 751.513681 367.567318 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cdf58f"/>
    <path d="M 632.052925 212.210777 
L 634.744995 213.786997 
L 636.409023 212.760003 
L 633.71873 211.187111 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9f7f7"/>
    <path d="M 656.986599 225.886879 
L 659.699969 228.313823 
L 661.346055 227.452892 
L 658.634914 225.035019 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dfd6d4"/>
    <path d="M 724.686106 317.748081 
L 727.415199 321.956885 
L 729.001555 320.675519 
L 726.274984 316.476738 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #beac76"/>
    <path d="M 700.580066 275.506764 
L 703.310236 279.255366 
L 704.917334 278.193457 
L 702.189719 274.459967 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #896861"/>
    <path d="M 847.619008 497.031524 
L 850.370529 498.896499 
L 851.853769 497.735535 
L 849.10427 495.869362 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2b43a9"/>
    <path d="M 835.150803 489.636233 
L 837.891999 491.898815 
L 839.38421 490.828965 
L 836.645231 488.562791 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2353b9"/>
    <path d="M 857.363895 501.157259 
L 860.124909 502.711115 
L 861.602203 501.44763 
L 858.843043 499.894046 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #30389e"/>
    <path d="M 806.334563 463.000721 
L 809.059932 466.147635 
L 810.576948 465.106288 
L 807.854086 461.950341 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0490f6"/>
    <path d="M 809.059932 466.147635 
L 811.786351 469.214081 
L 813.300876 468.181395 
L 810.576948 465.106288 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0888ee"/>
    <path d="M 803.610089 459.775518 
L 806.334563 463.000721 
L 807.854086 461.950341 
L 805.132134 458.715744 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0296fc"/>
    <path d="M 740.616658 350.313078 
L 743.342754 354.63044 
L 744.916485 353.270176 
L 742.192889 348.955906 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f6f394"/>
    <path d="M 777.931252 422.579066 
L 780.651746 426.463469 
L 782.194722 425.254774 
L 779.476784 421.360969 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #15d06a"/>
    <path d="M 811.786351 469.214081 
L 814.513981 472.197958 
L 816.026032 471.173555 
L 813.300876 468.181395 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0c80e6"/>
    <path d="M 800.886358 456.474283 
L 803.610089 459.775518 
L 805.132134 458.715744 
L 802.410938 455.404763 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #009cf4"/>
    <path d="M 765.87782 401.203282 
L 768.599136 405.316309 
L 770.152556 404.024792 
L 767.433774 399.904817 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #61df79"/>
    <path d="M 756.54896 383.113231 
L 759.271729 387.351242 
L 760.832853 386.010753 
L 758.112598 381.76889 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9deb85"/>
    <path d="M 659.699969 228.313823 
L 662.415631 230.841125 
L 664.059456 229.970653 
L 661.346055 227.452892 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dbd1cf"/>
    <path d="M 697.849838 271.820015 
L 700.580066 275.506764 
L 702.189719 274.459967 
L 699.462039 270.788059 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #91726c"/>
    <path d="M 814.513981 472.197958 
L 817.242986 475.097246 
L 818.752582 474.08074 
L 816.026032 471.173555 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0f7be1"/>
    <path d="M 798.163221 453.099349 
L 800.886358 456.474283 
L 802.410938 455.404763 
L 799.690349 452.019739 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a2e2"/>
    <path d="M 712.628871 295.977572 
L 715.359618 299.999825 
L 716.95624 298.813456 
L 714.228035 294.804141 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #987b61"/>
    <path d="M 644.50197 218.146446 
L 647.206359 220.160826 
L 648.862062 219.225698 
L 646.159684 217.217123 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #efebea"/>
    <path d="M 625.011612 210.531689 
L 627.697069 211.88303 
L 629.364882 210.747684 
L 626.681047 209.398452 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fdfcfc"/>
    <path d="M 731.28647 331.768574 
L 734.014838 336.047786 
L 735.596105 334.718005 
L 732.870245 330.445412 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d6cb83"/>
    <path d="M 795.440537 449.653124 
L 798.163221 453.099349 
L 799.690349 452.019739 
L 796.970223 448.563091 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a8d0"/>
    <path d="M 817.242986 475.097246 
L 819.973534 477.910007 
L 821.480693 476.901002 
L 818.752582 474.08074 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1276dc"/>
    <path d="M 747.220055 364.624373 
L 749.944976 368.930136 
L 751.513681 367.567318 
L 748.791261 363.261106 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ddf892"/>
    <path d="M 837.891999 491.898815 
L 840.636016 494.063234 
L 842.12604 492.996635 
L 839.38421 490.828965 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #264eb4"/>
    <path d="M 721.956039 313.56765 
L 724.686106 317.748081 
L 726.274984 316.476738 
L 723.54744 312.306268 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b8a473"/>
    <path d="M 695.119679 268.198232 
L 697.849838 271.820015 
L 699.462039 270.788059 
L 696.734417 267.180829 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #977a74"/>
    <path d="M 610.965441 208.881252 
L 613.634835 209.773971 
L 615.308585 208.412156 
L 612.640523 207.520521 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ffffff"/>
    <path d="M 662.415631 230.841125 
L 665.133406 233.466867 
L 666.77494 232.586396 
L 664.059456 229.970653 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d7ccc9"/>
    <path d="M 775.210257 418.644863 
L 777.931252 422.579066 
L 779.476784 421.360969 
L 776.758349 417.417173 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #25d36d"/>
    <path d="M 617.981648 209.419542 
L 620.659538 210.542465 
L 622.330585 209.294998 
L 619.654169 208.173431 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ffffff"/>
    <path d="M 792.718167 446.138088 
L 795.440537 449.653124 
L 796.970223 448.563091 
L 794.25042 445.037309 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00aebf"/>
    <path d="M 634.744995 213.786997 
L 637.440907 215.475485 
L 639.103117 214.444865 
L 636.409023 212.760003 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f7f5f4"/>
    <path d="M 867.133488 504.236785 
L 869.906001 505.471222 
L 871.378169 504.099866 
L 868.607349 502.866563 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #333399"/>
    <path d="M 819.973534 477.910007 
L 822.705795 480.634383 
L 824.210538 479.632479 
L 821.480693 476.901002 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #166ed4"/>
    <path d="M 874.153857 505.225757 
L 876.934604 506.243906 
L 878.403963 504.763588 
L 875.624785 503.746865 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #333399"/>
    <path d="M 850.370529 498.896499 
L 853.125665 500.658485 
L 854.606913 499.498465 
L 851.853769 497.735535 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2c40a6"/>
    <path d="M 763.155594 397.055887 
L 765.87782 401.203282 
L 767.433774 399.904817 
L 764.714083 395.750375 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #71e37d"/>
    <path d="M 709.897531 292.000979 
L 712.628871 295.977572 
L 714.228035 294.804141 
L 711.499233 290.840335 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #92735e"/>
    <path d="M 692.389719 264.644465 
L 695.119679 268.198232 
L 696.734417 267.180829 
L 694.006983 263.641311 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9d827c"/>
    <path d="M 737.88934 345.999114 
L 740.616658 350.313078 
L 742.192889 348.955906 
L 739.468072 344.645033 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eee990"/>
    <path d="M 665.133406 233.466867 
L 667.853118 236.189027 
L 669.492329 235.298108 
L 666.77494 232.586396 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d3c7c4"/>
    <path d="M 753.825071 378.854104 
L 756.54896 383.113231 
L 758.112598 381.76889 
L 755.391223 377.505872 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #adef89"/>
    <path d="M 789.995977 442.556794 
L 792.718167 446.138088 
L 794.25042 445.037309 
L 791.530807 441.444955 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b6a7"/>
    <path d="M 647.206359 220.160826 
L 649.91381 222.282504 
L 651.567463 221.341178 
L 648.862062 219.225698 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ebe5e4"/>
    <path d="M 822.705795 480.634383 
L 825.439943 483.268604 
L 826.942293 482.273391 
L 824.210538 479.632479 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1868ce"/>
    <path d="M 860.124909 502.711115 
L 862.890151 504.159328 
L 864.36562 502.895414 
L 861.602203 501.44763 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #30389e"/>
    <path d="M 689.660095 261.161697 
L 692.389719 264.644465 
L 694.006983 263.641311 
L 691.279872 260.172475 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a38984"/>
    <path d="M 667.853118 236.189027 
L 670.574589 239.005477 
L 672.211452 238.103673 
L 669.492329 235.298108 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cfc2bf"/>
    <path d="M 772.488666 414.663868 
L 775.210257 418.644863 
L 776.758349 417.417173 
L 774.039321 413.426407 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #35d771"/>
    <path d="M 728.55698 327.507079 
L 731.28647 331.768574 
L 732.870245 330.445412 
L 730.143262 326.190516 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cec07f"/>
    <path d="M 719.225061 309.419121 
L 721.956039 313.56765 
L 723.54744 312.306268 
L 720.818983 308.167631 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b09a6e"/>
    <path d="M 744.493912 360.311359 
L 747.220055 364.624373 
L 748.791261 363.261106 
L 746.067622 358.947634 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #edfb95"/>
    <path d="M 840.636016 494.063234 
L 843.383045 496.128236 
L 844.870909 495.064544 
L 842.12604 492.996635 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #274bb1"/>
    <path d="M 686.930948 257.752844 
L 689.660095 261.161697 
L 691.279872 260.172475 
L 688.553223 256.777221 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a9918c"/>
    <path d="M 787.27384 438.911862 
L 789.995977 442.556794 
L 791.530807 441.444955 
L 788.811254 437.788661 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00bc94"/>
    <path d="M 670.574589 239.005477 
L 673.297649 241.91399 
L 674.932137 241.000874 
L 672.211452 238.103673 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cbbcb9"/>
    <path d="M 707.165695 288.073418 
L 709.897531 292.000979 
L 711.499233 290.840335 
L 708.769931 286.9254 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8a695a"/>
    <path d="M 825.439943 483.268604 
L 828.176154 485.810981 
L 829.676135 484.822045 
L 826.942293 482.273391 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1b63c9"/>
    <path d="M 684.202425 254.420748 
L 686.930948 257.752844 
L 688.553223 256.777221 
L 685.827182 253.458376 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #af9994"/>
    <path d="M 673.297649 241.91399 
L 676.022128 244.912239 
L 677.654215 243.987398 
L 674.932137 241.000874 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c5b5b1"/>
    <path d="M 627.697069 211.88303 
L 630.386778 213.348414 
L 632.052925 212.210777 
L 629.364882 210.747684 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fbfafa"/>
    <path d="M 681.474677 251.168174 
L 684.202425 254.420748 
L 685.827182 253.458376 
L 683.101897 250.218691 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b5a09c"/>
    <path d="M 760.432397 392.877394 
L 763.155594 397.055887 
L 764.714083 395.750375 
L 761.99342 391.564743 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #7de57f"/>
    <path d="M 676.022128 244.912239 
L 678.747858 247.997804 
L 680.377522 247.060836 
L 677.654215 243.987398 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bfada9"/>
    <path d="M 678.747858 247.997804 
L 681.474677 251.168174 
L 683.101897 250.218691 
L 680.377522 247.060836 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bba8a4"/>
    <path d="M 637.440907 215.475485 
L 640.140477 217.275254 
L 641.800827 216.240715 
L 639.103117 214.444865 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f3f0ef"/>
    <path d="M 735.160817 341.692124 
L 737.88934 345.999114 
L 739.468072 344.645033 
L 736.742048 340.341133 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e6df8b"/>
    <path d="M 784.551634 435.205982 
L 787.27384 438.911862 
L 788.811254 437.788661 
L 786.091637 434.071127 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c382"/>
    <path d="M 649.91381 222.282504 
L 652.624136 224.510011 
L 654.275703 223.562098 
L 651.567463 221.341178 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e7e0df"/>
    <path d="M 751.100026 374.577292 
L 753.825071 378.854104 
L 755.391223 377.505872 
L 752.668692 373.225133 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bdf28c"/>
    <path d="M 606.625307 209.581129 
L 609.290729 210.359185 
L 610.965441 208.881252 
L 608.301257 208.104315 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ffffff"/>
    <path d="M 769.766392 410.639146 
L 772.488666 414.663868 
L 774.039321 413.426407 
L 771.319611 409.391743 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #41d973"/>
    <path d="M 853.125665 500.658485 
L 855.884609 502.316589 
L 857.363895 501.157259 
L 854.606913 499.498465 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2e3ea4"/>
    <path d="M 828.176154 485.810981 
L 830.91461 488.259914 
L 832.412244 487.276832 
L 829.676135 484.822045 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1e5ec4"/>
    <path d="M 704.433466 284.198221 
L 707.165695 288.073418 
L 708.769931 286.9254 
L 706.040229 283.062652 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #846257"/>
    <path d="M 716.493243 305.306003 
L 719.225061 309.419121 
L 720.818983 308.167631 
L 718.089684 304.064326 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a8906a"/>
    <path d="M 725.826412 323.266875 
L 728.55698 327.507079 
L 730.143262 326.190516 
L 727.415199 321.956885 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c6b67a"/>
    <path d="M 620.659538 210.542465 
L 623.342079 211.780578 
L 625.011612 210.531689 
L 622.330585 209.294998 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fdfcfc"/>
    <path d="M 613.634835 209.773971 
L 616.309269 210.782386 
L 617.981648 209.419542 
L 615.308585 208.412156 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ffffff"/>
    <path d="M 843.383045 496.128236 
L 846.133275 498.092657 
L 847.619008 497.031524 
L 844.870909 495.064544 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2a46ac"/>
    <path d="M 741.766543 355.994628 
L 744.493912 360.311359 
L 746.067622 358.947634 
L 743.342754 354.63044 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 781.829242 431.441907 
L 784.551634 435.205982 
L 786.091637 434.071127 
L 783.371839 430.29512 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00cb6b"/>
    <path d="M 869.906001 505.471222 
L 872.683353 506.598301 
L 874.153857 505.225757 
L 871.378169 504.099866 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #333399"/>
    <path d="M 757.708171 388.671114 
L 760.432397 392.877394 
L 761.99342 391.564743 
L 759.271729 387.351242 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8de882"/>
    <path d="M 876.934604 506.243906 
L 879.7206 507.154078 
L 881.188418 505.672387 
L 878.403963 504.763588 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #333399"/>
    <path d="M 652.624136 224.510011 
L 655.337155 226.841758 
L 656.986599 225.886879 
L 654.275703 223.562098 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e5dedc"/>
    <path d="M 862.890151 504.159328 
L 865.659814 505.501283 
L 867.133488 504.236785 
L 864.36562 502.895414 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #32369c"/>
    <path d="M 701.700954 280.378672 
L 704.433466 284.198221 
L 706.040229 283.062652 
L 703.310236 279.255366 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #836059"/>
    <path d="M 767.043353 406.573814 
L 769.766392 410.639146 
L 771.319611 409.391743 
L 768.599136 405.316309 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #51dc76"/>
    <path d="M 830.91461 488.259914 
L 833.65549 490.613887 
L 835.150803 489.636233 
L 832.412244 487.276832 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2058be"/>
    <path d="M 732.431108 337.39569 
L 735.160817 341.692124 
L 736.742048 340.341133 
L 734.014838 336.047786 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ded587"/>
    <path d="M 748.373798 370.286252 
L 751.100026 374.577292 
L 752.668692 373.225133 
L 749.944976 368.930136 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cdf58f"/>
    <path d="M 640.140477 217.275254 
L 642.843519 219.185195 
L 644.50197 218.146446 
L 641.800827 216.240715 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1edec"/>
    <path d="M 713.760664 301.231779 
L 716.493243 305.306003 
L 718.089684 304.064326 
L 715.359618 299.999825 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a08566"/>
    <path d="M 779.106552 427.622457 
L 781.829242 431.441907 
L 783.371839 430.29512 
L 780.651746 426.463469 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #09ce68"/>
    <path d="M 630.386778 213.348414 
L 633.080553 214.927107 
L 634.744995 213.786997 
L 632.052925 212.210777 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9f7f7"/>
    <path d="M 723.094815 319.051528 
L 725.826412 323.266875 
L 727.415199 321.956885 
L 724.686106 317.748081 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #beac76"/>
    <path d="M 655.337155 226.841758 
L 658.052681 229.276043 
L 659.699969 228.313823 
L 656.986599 225.886879 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e1d9d7"/>
    <path d="M 698.968274 276.618009 
L 701.700954 280.378672 
L 703.310236 279.255366 
L 700.580066 275.506764 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #896861"/>
    <path d="M 739.037948 351.677732 
L 741.766543 355.994628 
L 743.342754 354.63044 
L 740.616658 350.313078 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f6f394"/>
    <path d="M 855.884609 502.316589 
L 858.647555 503.870014 
L 860.124909 502.711115 
L 857.363895 501.157259 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2f3ba1"/>
    <path d="M 846.133275 498.092657 
L 848.886897 499.955424 
L 850.370529 498.896499 
L 847.619008 497.031524 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2b43a9"/>
    <path d="M 833.65549 490.613887 
L 836.39898 492.871474 
L 837.891999 491.898815 
L 835.150803 489.636233 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2256bc"/>
    <path d="M 754.982869 384.440398 
L 757.708171 388.671114 
L 759.271729 387.351242 
L 756.54896 383.113231 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9deb85"/>
    <path d="M 776.383459 423.750511 
L 779.106552 427.622457 
L 780.651746 426.463469 
L 777.931252 422.579066 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #19d16b"/>
    <path d="M 764.319474 402.471037 
L 767.043353 406.573814 
L 768.599136 405.316309 
L 765.87782 401.203282 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #61df79"/>
    <path d="M 804.813322 463.974628 
L 807.541265 467.11022 
L 809.059932 466.147635 
L 806.334563 463.000721 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0490f6"/>
    <path d="M 802.08626 460.761189 
L 804.813322 463.974628 
L 806.334563 463.000721 
L 803.610089 459.775518 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0098fe"/>
    <path d="M 711.027408 297.199902 
L 713.760664 301.231779 
L 715.359618 299.999825 
L 712.628871 295.977572 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #987b61"/>
    <path d="M 807.541265 467.11022 
L 810.270245 470.165795 
L 811.786351 469.214081 
L 809.059932 466.147635 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #078bf1"/>
    <path d="M 696.235548 272.919411 
L 698.968274 276.618009 
L 700.580066 275.506764 
L 697.849838 271.820015 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #91726c"/>
    <path d="M 623.342079 211.780578 
L 626.029092 213.133405 
L 627.697069 211.88303 
L 625.011612 210.531689 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fdfcfc"/>
    <path d="M 799.35993 457.472148 
L 802.08626 460.761189 
L 803.610089 459.775518 
L 800.886358 456.474283 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #009eef"/>
    <path d="M 729.700245 333.113398 
L 732.431108 337.39569 
L 734.014838 336.047786 
L 731.28647 331.768574 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d6cb83"/>
    <path d="M 658.052681 229.276043 
L 660.770532 231.811053 
L 662.415631 230.841125 
L 659.699969 228.313823 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ddd3d1"/>
    <path d="M 810.270245 470.165795 
L 813.00042 473.139264 
L 814.513981 472.197958 
L 811.786351 469.214081 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0b83e9"/>
    <path d="M 609.290729 210.359185 
L 611.961395 211.252845 
L 613.634835 209.773971 
L 610.965441 208.881252 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ffffff"/>
    <path d="M 745.646367 365.984471 
L 748.373798 370.286252 
L 749.944976 368.930136 
L 747.220055 364.624373 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ddf892"/>
    <path d="M 642.843519 219.185195 
L 645.549846 221.204071 
L 647.206359 220.160826 
L 644.50197 218.146446 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #efebea"/>
    <path d="M 796.634184 454.109828 
L 799.35993 457.472148 
L 800.886358 456.474283 
L 798.163221 453.099349 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a4dc"/>
    <path d="M 720.362248 314.864592 
L 723.094815 319.051528 
L 724.686106 317.748081 
L 721.956039 313.56765 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b6a272"/>
    <path d="M 813.00042 473.139264 
L 815.731954 476.028617 
L 817.242986 475.097246 
L 814.513981 472.197958 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0f7be1"/>
    <path d="M 616.309269 210.782386 
L 618.988568 211.906282 
L 620.659538 210.542465 
L 617.981648 209.419542 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ffffff"/>
    <path d="M 693.502903 269.286004 
L 696.235548 272.919411 
L 697.849838 271.820015 
L 695.119679 268.198232 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #977a74"/>
    <path d="M 793.908882 450.676624 
L 796.634184 454.109828 
L 798.163221 453.099349 
L 795.440537 449.653124 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00aacb"/>
    <path d="M 773.659863 419.829008 
L 776.383459 423.750511 
L 777.931252 422.579066 
L 775.210257 418.644863 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #25d36d"/>
    <path d="M 872.683353 506.598301 
L 875.465735 507.617691 
L 876.934604 506.243906 
L 874.153857 505.225757 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #333399"/>
    <path d="M 815.731954 476.028617 
L 818.465011 478.831922 
L 819.973534 477.910007 
L 817.242986 475.097246 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1276dc"/>
    <path d="M 660.770532 231.811053 
L 663.490528 234.444861 
L 665.133406 233.466867 
L 662.415631 230.841125 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d9cecc"/>
    <path d="M 633.080553 214.927107 
L 635.778212 216.618248 
L 637.440907 215.475485 
L 634.744995 213.786997 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f7f5f4"/>
    <path d="M 865.659814 505.501283 
L 868.434091 506.736461 
L 869.906001 505.471222 
L 867.133488 504.236785 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #32369c"/>
    <path d="M 836.39898 492.871474 
L 839.145265 495.031336 
L 840.636016 494.063234 
L 837.891999 491.898815 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2450b6"/>
    <path d="M 736.308135 347.364236 
L 739.037948 351.677732 
L 740.616658 350.313078 
L 737.88934 345.999114 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eee990"/>
    <path d="M 761.594687 398.33403 
L 764.319474 402.471037 
L 765.87782 401.203282 
L 763.155594 397.055887 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #71e37d"/>
    <path d="M 708.293566 293.213792 
L 711.027408 297.199902 
L 712.628871 295.977572 
L 709.897531 292.000979 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #92735e"/>
    <path d="M 791.183886 447.175003 
L 793.908882 450.676624 
L 795.440537 449.653124 
L 792.718167 446.138088 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b0b9"/>
    <path d="M 752.256451 380.188634 
L 754.982869 384.440398 
L 756.54896 383.113231 
L 753.825071 378.854104 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #adef89"/>
    <path d="M 690.77047 265.720849 
L 693.502903 269.286004 
L 695.119679 268.198232 
L 692.389719 264.644465 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9d827c"/>
    <path d="M 818.465011 478.831922 
L 821.199761 481.547335 
L 822.705795 480.634383 
L 819.973534 477.910007 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1470d6"/>
    <path d="M 848.886897 499.955424 
L 851.644104 501.715557 
L 853.125665 500.658485 
L 850.370529 498.896499 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2c40a6"/>
    <path d="M 663.490528 234.444861 
L 666.212491 237.175438 
L 667.853118 236.189027 
L 665.133406 233.466867 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d5c9c7"/>
    <path d="M 726.968264 328.848829 
L 729.700245 333.113398 
L 731.28647 331.768574 
L 728.55698 327.507079 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cec07f"/>
    <path d="M 645.549846 221.204071 
L 648.259272 223.330529 
L 649.91381 222.282504 
L 647.206359 220.160826 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ebe5e4"/>
    <path d="M 788.459065 443.607506 
L 791.183886 447.175003 
L 792.718167 446.138088 
L 789.995977 442.556794 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b6a7"/>
    <path d="M 742.917719 361.675459 
L 745.646367 365.984471 
L 747.220055 364.624373 
L 744.493912 360.311359 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #edfb95"/>
    <path d="M 717.628776 310.709601 
L 720.362248 314.864592 
L 721.956039 313.56765 
L 719.225061 309.419121 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b09a6e"/>
    <path d="M 688.03839 262.226943 
L 690.77047 265.720849 
L 692.389719 264.644465 
L 689.660095 261.161697 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a38984"/>
    <path d="M 858.647555 503.870014 
L 861.414696 505.318052 
L 862.890151 504.159328 
L 860.124909 502.711115 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #30389e"/>
    <path d="M 770.935673 415.860945 
L 773.659863 419.829008 
L 775.210257 418.644863 
L 772.488666 414.663868 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #35d771"/>
    <path d="M 666.212491 237.175438 
L 668.936242 240.000646 
L 670.574589 239.005477 
L 667.853118 236.189027 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cfc2bf"/>
    <path d="M 821.199761 481.547335 
L 823.936378 484.17309 
L 825.439943 483.268604 
L 822.705795 480.634383 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #176bd1"/>
    <path d="M 705.559237 289.27683 
L 708.293566 293.213792 
L 709.897531 292.000979 
L 707.165695 288.073418 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8a695a"/>
    <path d="M 685.306803 258.807211 
L 688.03839 262.226943 
L 689.660095 261.161697 
L 686.930948 257.752844 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a9918c"/>
    <path d="M 604.949888 211.1751 
L 607.61649 211.954253 
L 609.290729 210.359185 
L 606.625307 209.581129 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ffffff"/>
    <path d="M 785.734293 439.976741 
L 788.459065 443.607506 
L 789.995977 442.556794 
L 787.27384 438.911862 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00bc94"/>
    <path d="M 626.029092 213.133405 
L 628.720394 214.600339 
L 630.386778 213.348414 
L 627.697069 211.88303 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fbfafa"/>
    <path d="M 668.936242 240.000646 
L 671.661609 242.91825 
L 673.297649 241.91399 
L 670.574589 239.005477 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cbbcb9"/>
    <path d="M 839.145265 495.031336 
L 841.894533 497.092224 
L 843.383045 496.128236 
L 840.636016 494.063234 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #274bb1"/>
    <path d="M 758.868931 394.166052 
L 761.594687 398.33403 
L 763.155594 397.055887 
L 760.432397 392.877394 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #81e680"/>
    <path d="M 682.575858 255.464508 
L 685.306803 258.807211 
L 686.930948 257.752844 
L 684.202425 254.420748 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #af9994"/>
    <path d="M 733.57712 343.057714 
L 736.308135 347.364236 
L 737.88934 345.999114 
L 735.160817 341.692124 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e6df8b"/>
    <path d="M 671.661609 242.91825 
L 674.388421 245.925913 
L 676.022128 244.912239 
L 673.297649 241.91399 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c5b5b1"/>
    <path d="M 749.528881 375.919243 
L 752.256451 380.188634 
L 753.825071 378.854104 
L 751.100026 374.577292 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bdf28c"/>
    <path d="M 679.845708 252.201608 
L 682.575858 255.464508 
L 684.202425 254.420748 
L 681.474677 251.168174 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b5a09c"/>
    <path d="M 635.778212 216.618248 
L 638.479568 218.420849 
L 640.140477 217.275254 
L 637.440907 215.475485 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f5f2f2"/>
    <path d="M 674.388421 245.925913 
L 677.116508 249.021207 
L 678.747858 247.997804 
L 676.022128 244.912239 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c1b0ac"/>
    <path d="M 677.116508 249.021207 
L 679.845708 252.201608 
L 681.474677 251.168174 
L 678.747858 247.997804 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bba8a4"/>
    <path d="M 823.936378 484.17309 
L 826.675037 486.707509 
L 828.176154 485.810981 
L 825.439943 483.268604 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1a66cc"/>
    <path d="M 648.259272 223.330529 
L 650.971611 225.563094 
L 652.624136 224.510011 
L 649.91381 222.282504 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e9e3e2"/>
    <path d="M 768.210801 411.849372 
L 770.935673 415.860945 
L 772.488666 414.663868 
L 769.766392 410.639146 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #45da74"/>
    <path d="M 783.009448 436.285382 
L 785.734293 439.976741 
L 787.27384 438.911862 
L 784.551634 435.205982 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c47d"/>
    <path d="M 611.961395 211.252845 
L 614.637137 212.262026 
L 616.309269 210.782386 
L 613.634835 209.773971 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ffffff"/>
    <path d="M 618.988568 211.906282 
L 621.672556 213.145313 
L 623.342079 211.780578 
L 620.659538 210.542465 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fdfcfc"/>
    <path d="M 714.894471 306.59007 
L 717.628776 310.709601 
L 719.225061 309.419121 
L 716.493243 305.306003 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a8906a"/>
    <path d="M 724.23521 324.605562 
L 726.968264 328.848829 
L 728.55698 327.507079 
L 725.826412 323.266875 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c6b67a"/>
    <path d="M 702.824524 285.392359 
L 705.559237 289.27683 
L 707.165695 288.073418 
L 704.433466 284.198221 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #825f56"/>
    <path d="M 740.187849 357.362744 
L 742.917719 361.675459 
L 744.493912 360.311359 
L 741.766543 355.994628 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 851.644104 501.715557 
L 854.405087 503.372165 
L 855.884609 502.316589 
L 853.125665 500.658485 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2e3ea4"/>
    <path d="M 868.434091 506.736461 
L 871.213176 507.864437 
L 872.683353 506.598301 
L 869.906001 505.471222 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #333399"/>
    <path d="M 826.675037 486.707509 
L 829.415915 489.148998 
L 830.91461 488.259914 
L 828.176154 485.810981 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1c60c6"/>
    <path d="M 780.284416 432.53617 
L 783.009448 436.285382 
L 784.551634 435.205982 
L 781.829242 431.441907 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00cb6b"/>
    <path d="M 875.465735 507.617691 
L 878.253337 508.529157 
L 879.7206 507.154078 
L 876.934604 506.243906 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #333399"/>
    <path d="M 756.142151 389.970403 
L 758.868931 394.166052 
L 760.432397 392.877394 
L 757.708171 388.671114 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #91e983"/>
    <path d="M 841.894533 497.092224 
L 844.646972 499.052979 
L 846.133275 498.092657 
L 843.383045 496.128236 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2848ae"/>
    <path d="M 650.971611 225.563094 
L 653.686677 227.900173 
L 655.337155 226.841758 
L 652.624136 224.510011 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e5dedc"/>
    <path d="M 730.844925 338.761748 
L 733.57712 343.057714 
L 735.160817 341.692124 
L 732.431108 337.39569 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ded587"/>
    <path d="M 700.08954 281.563671 
L 702.824524 285.392359 
L 704.433466 284.198221 
L 701.700954 280.378672 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #836059"/>
    <path d="M 746.800133 371.635675 
L 749.528881 375.919243 
L 751.100026 374.577292 
L 748.373798 370.286252 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cdf58f"/>
    <path d="M 765.485167 407.797393 
L 768.210801 411.849372 
L 769.766392 410.639146 
L 767.043353 406.573814 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #51dc76"/>
    <path d="M 861.414696 505.318052 
L 864.186227 506.660092 
L 865.659814 505.501283 
L 862.890151 504.159328 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #32369c"/>
    <path d="M 712.159412 302.509486 
L 714.894471 306.59007 
L 716.493243 305.306003 
L 713.760664 301.231779 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a08566"/>
    <path d="M 638.479568 218.420849 
L 641.184434 220.333797 
L 642.843519 219.185195 
L 640.140477 217.275254 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1edec"/>
    <path d="M 628.720394 214.600339 
L 631.415804 216.180647 
L 633.080553 214.927107 
L 630.386778 213.348414 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9f7f7"/>
    <path d="M 721.501133 320.387163 
L 724.23521 324.605562 
L 725.826412 323.266875 
L 723.094815 319.051528 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #beac76"/>
    <path d="M 777.559085 428.73191 
L 780.284416 432.53617 
L 781.829242 431.441907 
L 779.106552 427.622457 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #09ce68"/>
    <path d="M 829.415915 489.148998 
L 832.159194 491.49605 
L 833.65549 490.613887 
L 830.91461 488.259914 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1f5bc1"/>
    <path d="M 737.456759 353.049875 
L 740.187849 357.362744 
L 741.766543 355.994628 
L 739.037948 351.677732 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f6f394"/>
    <path d="M 697.354399 277.794012 
L 700.08954 281.563671 
L 701.700954 280.378672 
L 698.968274 276.618009 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8b6b64"/>
    <path d="M 653.686677 227.900173 
L 656.404285 230.340059 
L 658.052681 229.276043 
L 655.337155 226.841758 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e1d9d7"/>
    <path d="M 753.414302 385.750424 
L 756.142151 389.970403 
L 757.708171 388.671114 
L 754.982869 384.440398 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9deb85"/>
    <path d="M 607.61649 211.954253 
L 610.288369 212.848715 
L 611.961395 211.252845 
L 609.290729 210.359185 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ffffff"/>
    <path d="M 762.758698 403.708161 
L 765.485167 407.797393 
L 767.043353 406.573814 
L 764.319474 402.471037 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #61df79"/>
    <path d="M 621.672556 213.145313 
L 624.361054 214.499003 
L 626.029092 213.133405 
L 623.342079 211.780578 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fdfcfc"/>
    <path d="M 854.405087 503.372165 
L 857.170039 504.924453 
L 858.647555 503.870014 
L 855.884609 502.316589 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2f3ba1"/>
    <path d="M 709.423684 298.47131 
L 712.159412 302.509486 
L 713.760664 301.231779 
L 711.027408 297.199902 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #987b61"/>
    <path d="M 774.833352 424.875466 
L 777.559085 428.73191 
L 779.106552 427.622457 
L 776.383459 423.750511 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #19d16b"/>
    <path d="M 728.111583 334.47992 
L 730.844925 338.761748 
L 732.431108 337.39569 
L 729.700245 333.113398 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d6cb83"/>
    <path d="M 844.646972 499.052979 
L 847.402773 500.912531 
L 848.886897 499.955424 
L 846.133275 498.092657 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2a46ac"/>
    <path d="M 694.619226 274.086572 
L 697.354399 277.794012 
L 698.968274 276.618009 
L 696.235548 272.919411 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #91726c"/>
    <path d="M 744.070189 367.341407 
L 746.800133 371.635675 
L 748.373798 370.286252 
L 745.646367 365.984471 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ddf892"/>
    <path d="M 614.637137 212.262026 
L 617.31778 213.386512 
L 618.988568 211.906282 
L 616.309269 210.782386 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fdfcfc"/>
    <path d="M 832.159194 491.49605 
L 834.905056 493.747243 
L 836.39898 492.871474 
L 833.65549 490.613887 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2256bc"/>
    <path d="M 718.766094 316.197189 
L 721.501133 320.387163 
L 723.094815 319.051528 
L 720.362248 314.864592 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b6a272"/>
    <path d="M 656.404285 230.340059 
L 659.124252 232.880932 
L 660.770532 231.811053 
L 658.052681 229.276043 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ddd3d1"/>
    <path d="M 641.184434 220.333797 
L 643.892624 222.355856 
L 645.549846 221.204071 
L 642.843519 219.185195 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #efebea"/>
    <path d="M 803.290282 464.872383 
L 806.020866 467.99437 
L 807.541265 467.11022 
L 804.813322 463.974628 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0393f9"/>
    <path d="M 800.560569 461.67307 
L 803.290282 464.872383 
L 804.813322 463.974628 
L 802.08626 460.761189 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #009afa"/>
    <path d="M 806.020866 467.99437 
L 808.752473 471.036874 
L 810.270245 470.165795 
L 807.541265 467.11022 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #078bf1"/>
    <path d="M 797.831578 458.398663 
L 800.560569 461.67307 
L 802.08626 460.761189 
L 799.35993 457.472148 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #009eef"/>
    <path d="M 808.752473 471.036874 
L 811.485262 473.997817 
L 813.00042 473.139264 
L 810.270245 470.165795 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0a86ec"/>
    <path d="M 691.884148 270.444485 
L 694.619226 274.086572 
L 696.235548 272.919411 
L 693.502903 269.286004 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #977a74"/>
    <path d="M 631.415804 216.180647 
L 634.115135 217.873466 
L 635.778212 216.618248 
L 633.080553 214.927107 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f7f5f4"/>
    <path d="M 734.724458 348.740409 
L 737.456759 353.049875 
L 739.037948 351.677732 
L 736.308135 347.364236 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eee990"/>
    <path d="M 795.103163 455.051471 
L 797.831578 458.398663 
L 799.35993 457.472148 
L 796.634184 454.109828 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a4dc"/>
    <path d="M 871.213176 507.864437 
L 873.99726 508.884883 
L 875.465735 507.617691 
L 872.683353 506.598301 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #333399"/>
    <path d="M 772.10712 420.969763 
L 774.833352 424.875466 
L 776.383459 423.750511 
L 773.659863 419.829008 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #25d36d"/>
    <path d="M 659.124252 232.880932 
L 661.846396 235.520863 
L 663.490528 234.444861 
L 660.770532 231.811053 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d9cecc"/>
    <path d="M 706.687381 294.478966 
L 709.423684 298.47131 
L 711.027408 297.199902 
L 708.293566 293.213792 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #92735e"/>
    <path d="M 811.485262 473.997817 
L 814.219394 476.875201 
L 815.731954 476.028617 
L 813.00042 473.139264 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0e7ee4"/>
    <path d="M 750.685342 381.50949 
L 753.414302 385.750424 
L 754.982869 384.440398 
L 752.256451 380.188634 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #adef89"/>
    <path d="M 760.031326 399.584877 
L 762.758698 403.708161 
L 764.319474 402.471037 
L 761.594687 398.33403 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #71e37d"/>
    <path d="M 864.186227 506.660092 
L 866.962339 507.895617 
L 868.434091 506.736461 
L 865.659814 505.501283 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #32369c"/>
    <path d="M 792.375186 451.633875 
L 795.103163 455.051471 
L 796.634184 454.109828 
L 793.908882 450.676624 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00aacb"/>
    <path d="M 689.1493 266.87082 
L 691.884148 270.444485 
L 693.502903 269.286004 
L 690.77047 265.720849 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9d827c"/>
    <path d="M 725.37713 330.21581 
L 728.111583 334.47992 
L 729.700245 333.113398 
L 726.968264 328.848829 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cec07f"/>
    <path d="M 814.219394 476.875201 
L 816.955032 479.667106 
L 818.465011 478.831922 
L 815.731954 476.028617 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1078de"/>
    <path d="M 834.905056 493.747243 
L 837.653686 495.901247 
L 839.145265 495.031336 
L 836.39898 492.871474 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2353b9"/>
    <path d="M 603.2751 212.886031 
L 605.942825 213.666262 
L 607.61649 211.954253 
L 604.949888 211.1751 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fdfcfc"/>
    <path d="M 789.647511 448.148329 
L 792.375186 451.633875 
L 793.908882 450.676624 
L 791.183886 447.175003 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b0b9"/>
    <path d="M 741.339035 363.03994 
L 744.070189 367.341407 
L 745.646367 365.984471 
L 742.917719 361.675459 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #edfb95"/>
    <path d="M 661.846396 235.520863 
L 664.570537 238.257813 
L 666.212491 237.175438 
L 663.490528 234.444861 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d5c9c7"/>
    <path d="M 716.030159 312.039175 
L 718.766094 316.197189 
L 720.362248 314.864592 
L 717.628776 310.709601 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b09a6e"/>
    <path d="M 643.892624 222.355856 
L 646.60395 224.485668 
L 648.259272 223.330529 
L 645.549846 221.204071 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ede8e7"/>
    <path d="M 686.414821 263.368582 
L 689.1493 266.87082 
L 690.77047 265.720849 
L 688.03839 262.226943 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a58c86"/>
    <path d="M 847.402773 500.912531 
L 850.162126 502.669903 
L 851.644104 501.715557 
L 848.886897 499.955424 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2b43a9"/>
    <path d="M 769.380296 417.01778 
L 772.10712 420.969763 
L 773.659863 419.829008 
L 770.935673 415.860945 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #35d771"/>
    <path d="M 816.955032 479.667106 
L 819.692346 482.371697 
L 821.199761 481.547335 
L 818.465011 478.831922 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1373d9"/>
    <path d="M 786.920007 444.597357 
L 789.647511 448.148329 
L 791.183886 447.175003 
L 788.459065 443.607506 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b6a7"/>
    <path d="M 624.361054 214.499003 
L 627.05388 215.966746 
L 628.720394 214.600339 
L 626.029092 213.133405 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fbfafa"/>
    <path d="M 703.950602 290.535842 
L 706.687381 294.478966 
L 708.293566 293.213792 
L 705.559237 289.27683 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8a695a"/>
    <path d="M 664.570537 238.257813 
L 667.296497 241.089642 
L 668.936242 240.000646 
L 666.212491 237.175438 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d1c4c1"/>
    <path d="M 857.170039 504.924453 
L 859.939154 506.371716 
L 861.414696 505.318052 
L 858.647555 503.870014 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #30389e"/>
    <path d="M 683.680855 259.940706 
L 686.414821 263.368582 
L 688.03839 262.226943 
L 685.306803 258.807211 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ab938e"/>
    <path d="M 731.990963 344.437917 
L 734.724458 348.740409 
L 736.308135 347.364236 
L 733.57712 343.057714 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e6df8b"/>
    <path d="M 757.302993 395.430785 
L 760.031326 399.584877 
L 761.594687 398.33403 
L 758.868931 394.166052 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #81e680"/>
    <path d="M 667.296497 241.089642 
L 670.0241 244.014105 
L 671.661609 242.91825 
L 668.936242 240.000646 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cbbcb9"/>
    <path d="M 610.288369 212.848715 
L 612.965356 213.858399 
L 614.637137 212.262026 
L 611.961395 211.252845 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ffffff"/>
    <path d="M 680.947552 256.590054 
L 683.680855 259.940706 
L 685.306803 258.807211 
L 682.575858 255.464508 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b19b96"/>
    <path d="M 747.955239 377.25101 
L 750.685342 381.50949 
L 752.256451 380.188634 
L 749.528881 375.919243 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bdf28c"/>
    <path d="M 634.115135 217.873466 
L 636.818202 219.677808 
L 638.479568 218.420849 
L 635.778212 216.618248 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f5f2f2"/>
    <path d="M 617.31778 213.386512 
L 620.003148 214.625958 
L 621.672556 213.145313 
L 618.988568 211.906282 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fdfcfc"/>
    <path d="M 784.19255 440.983551 
L 786.920007 444.597357 
L 788.459065 443.607506 
L 785.734293 439.976741 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00be8f"/>
    <path d="M 819.692346 482.371697 
L 822.431506 484.98722 
L 823.936378 484.17309 
L 821.199761 481.547335 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #176bd1"/>
    <path d="M 670.0241 244.014105 
L 672.753175 247.02886 
L 674.388421 245.925913 
L 671.661609 242.91825 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c7b7b4"/>
    <path d="M 678.215065 253.319408 
L 680.947552 256.590054 
L 682.575858 255.464508 
L 679.845708 252.201608 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b7a39f"/>
    <path d="M 672.753175 247.02886 
L 675.483552 250.131471 
L 677.116508 249.021207 
L 674.388421 245.925913 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c1b0ac"/>
    <path d="M 675.483552 250.131471 
L 678.215065 253.319408 
L 679.845708 252.201608 
L 677.116508 249.021207 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bba8a4"/>
    <path d="M 722.641612 325.972995 
L 725.37713 330.21581 
L 726.968264 328.848829 
L 724.23521 324.605562 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c6b67a"/>
    <path d="M 713.293399 307.916638 
L 716.030159 312.039175 
L 717.628776 310.709601 
L 714.894471 306.59007 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a8906a"/>
    <path d="M 646.60395 224.485668 
L 649.318225 226.721756 
L 650.971611 225.563094 
L 648.259272 223.330529 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e9e3e2"/>
    <path d="M 837.653686 495.901247 
L 840.405269 497.956816 
L 841.894533 497.092224 
L 839.145265 495.031336 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #264eb4"/>
    <path d="M 701.213452 286.645284 
L 703.950602 290.535842 
L 705.559237 289.27683 
L 702.824524 285.392359 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #825f56"/>
    <path d="M 766.652796 413.022555 
L 769.380296 417.01778 
L 770.935673 415.860945 
L 768.210801 411.849372 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #45da74"/>
    <path d="M 738.606667 358.734795 
L 741.339035 363.03994 
L 742.917719 361.675459 
L 740.187849 357.362744 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 781.46502 437.309571 
L 784.19255 440.983551 
L 785.734293 439.976741 
L 783.009448 436.285382 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c47d"/>
    <path d="M 822.431506 484.98722 
L 825.172686 487.512004 
L 826.675037 486.707509 
L 823.936378 484.17309 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1a66cc"/>
    <path d="M 754.573644 391.249171 
L 757.302993 395.430785 
L 758.868931 394.166052 
L 756.142151 389.970403 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #91e983"/>
    <path d="M 866.962339 507.895617 
L 869.743226 509.024201 
L 871.213176 507.864437 
L 868.434091 506.736461 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #333399"/>
    <path d="M 850.162126 502.669903 
L 852.925224 504.32421 
L 854.405087 503.372165 
L 851.644104 501.715557 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2c40a6"/>
    <path d="M 873.99726 508.884883 
L 876.786533 509.797562 
L 878.253337 508.529157 
L 875.465735 507.617691 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #333399"/>
    <path d="M 729.256298 340.145973 
L 731.990963 344.437917 
L 733.57712 343.057714 
L 730.844925 338.761748 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ded587"/>
    <path d="M 698.476043 282.810593 
L 701.213452 286.645284 
L 702.824524 285.392359 
L 700.08954 281.563671 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #836059"/>
    <path d="M 745.223967 372.978422 
L 747.955239 377.25101 
L 749.528881 375.919243 
L 746.800133 371.635675 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cdf58f"/>
    <path d="M 649.318225 226.721756 
L 652.035262 229.062525 
L 653.686677 227.900173 
L 650.971611 225.563094 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e5dedc"/>
    <path d="M 778.737303 433.578142 
L 781.46502 437.309571 
L 783.009448 436.285382 
L 780.284416 432.53617 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00cb6b"/>
    <path d="M 710.555897 303.833068 
L 713.293399 307.916638 
L 714.894471 306.59007 
L 712.159412 302.509486 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a08566"/>
    <path d="M 627.05388 215.966746 
L 629.75085 217.547808 
L 631.415804 216.180647 
L 628.720394 214.600339 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9f7f7"/>
    <path d="M 636.818202 219.677808 
L 639.524817 221.592559 
L 641.184434 220.333797 
L 638.479568 218.420849 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1edec"/>
    <path d="M 763.92454 408.987172 
L 766.652796 413.022555 
L 768.210801 411.849372 
L 765.485167 407.797393 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #55dd77"/>
    <path d="M 719.905083 321.75504 
L 722.641612 325.972995 
L 724.23521 324.605562 
L 721.501133 320.387163 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #beac76"/>
    <path d="M 825.172686 487.512004 
L 827.916062 489.944466 
L 829.415915 489.148998 
L 826.675037 486.707509 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1c60c6"/>
    <path d="M 859.939154 506.371716 
L 862.712625 507.713344 
L 864.186227 506.660092 
L 861.414696 505.318052 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #30389e"/>
    <path d="M 840.405269 497.956816 
L 843.159995 499.912799 
L 844.646972 499.052979 
L 841.894533 497.092224 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #274bb1"/>
    <path d="M 605.942825 213.666262 
L 608.615856 214.561382 
L 610.288369 212.848715 
L 607.61649 211.954253 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fdfcfc"/>
    <path d="M 735.87309 354.42951 
L 738.606667 358.734795 
L 740.187849 357.362744 
L 737.456759 353.049875 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f6f394"/>
    <path d="M 695.738494 279.035018 
L 698.476043 282.810593 
L 700.08954 281.563671 
L 697.354399 277.794012 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8b6b64"/>
    <path d="M 776.009291 429.792049 
L 778.737303 433.578142 
L 780.284416 432.53617 
L 777.559085 428.73191 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0dcf69"/>
    <path d="M 620.003148 214.625958 
L 622.693061 215.979887 
L 624.361054 214.499003 
L 621.672556 213.145313 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fbfafa"/>
    <path d="M 652.035262 229.062525 
L 654.754877 231.506264 
L 656.404285 230.340059 
L 653.686677 227.900173 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e1d9d7"/>
    <path d="M 612.965356 213.858399 
L 615.647277 214.983091 
L 617.31778 213.386512 
L 614.637137 212.262026 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fdfcfc"/>
    <path d="M 751.843234 387.04336 
L 754.573644 391.249171 
L 756.142151 389.970403 
L 753.414302 385.750424 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a1ec86"/>
    <path d="M 726.520495 335.868155 
L 729.256298 340.145973 
L 730.844925 338.761748 
L 728.111583 334.47992 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d6cb83"/>
    <path d="M 707.817738 299.791927 
L 710.555897 303.833068 
L 712.159412 302.509486 
L 709.423684 298.47131 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #987b61"/>
    <path d="M 827.916062 489.944466 
L 830.661815 492.283106 
L 832.159194 491.49605 
L 829.415915 489.148998 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1e5ec4"/>
    <path d="M 761.195457 404.91477 
L 763.92454 408.987172 
L 765.485167 407.797393 
L 762.758698 403.708161 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #61df79"/>
    <path d="M 742.491508 368.695192 
L 745.223967 372.978422 
L 746.800133 371.635675 
L 744.070189 367.341407 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ddf892"/>
    <path d="M 693.000928 275.321755 
L 695.738494 279.035018 
L 697.354399 277.794012 
L 694.619226 274.086572 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #91726c"/>
    <path d="M 717.167602 317.565499 
L 719.905083 321.75504 
L 721.501133 320.387163 
L 718.766094 316.197189 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b6a272"/>
    <path d="M 639.524817 221.592559 
L 642.234793 223.616482 
L 643.892624 222.355856 
L 641.184434 220.333797 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #efebea"/>
    <path d="M 773.280881 425.954141 
L 776.009291 429.792049 
L 777.559085 428.73191 
L 774.833352 424.875466 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #19d16b"/>
    <path d="M 654.754877 231.506264 
L 657.476883 234.051151 
L 659.124252 232.880932 
L 656.404285 230.340059 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ddd3d1"/>
    <path d="M 852.925224 504.32421 
L 855.692258 505.874657 
L 857.170039 504.924453 
L 854.405087 503.372165 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2e3ea4"/>
    <path d="M 629.75085 217.547808 
L 632.45178 219.241328 
L 634.115135 217.873466 
L 631.415804 216.180647 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f7f5f4"/>
    <path d="M 733.138312 350.127635 
L 735.87309 354.42951 
L 737.456759 353.049875 
L 734.724458 348.740409 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eee990"/>
    <path d="M 843.159995 499.912799 
L 845.918051 501.76813 
L 847.402773 500.912531 
L 844.646972 499.052979 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2a46ac"/>
    <path d="M 690.263475 271.673942 
L 693.000928 275.321755 
L 694.619226 274.086572 
L 691.884148 270.444485 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #977a74"/>
    <path d="M 601.601039 214.713596 
L 604.26983 215.494883 
L 605.942825 213.666262 
L 603.2751 212.886031 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fdfcfc"/>
    <path d="M 705.079017 295.796642 
L 707.817738 299.791927 
L 709.423684 298.47131 
L 706.687381 294.478966 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #90715d"/>
    <path d="M 830.661815 492.283106 
L 833.410126 494.526511 
L 834.905056 493.747243 
L 832.159194 491.49605 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2058be"/>
    <path d="M 749.111724 382.816714 
L 751.843234 387.04336 
L 753.414302 385.750424 
L 750.685342 381.50949 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b1ef89"/>
    <path d="M 657.476883 234.051151 
L 660.201099 236.695251 
L 661.846396 235.520863 
L 659.124252 232.880932 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d9cecc"/>
    <path d="M 869.743226 509.024201 
L 872.529079 510.045516 
L 873.99726 508.884883 
L 871.213176 507.864437 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #333399"/>
    <path d="M 799.032936 462.511543 
L 801.765362 465.694379 
L 803.290282 464.872383 
L 800.560569 461.67307 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #009afa"/>
    <path d="M 801.765362 465.694379 
L 804.498649 468.800488 
L 806.020866 467.99437 
L 803.290282 464.872383 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0393f9"/>
    <path d="M 758.465481 400.808532 
L 761.195457 404.91477 
L 762.758698 403.708161 
L 760.031326 399.584877 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #71e37d"/>
    <path d="M 770.551977 422.067324 
L 773.280881 425.954141 
L 774.833352 424.875466 
L 772.10712 420.969763 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #29d46e"/>
    <path d="M 796.301225 459.254199 
L 799.032936 462.511543 
L 800.560569 461.67307 
L 797.831578 458.398663 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a0e8"/>
    <path d="M 804.498649 468.800488 
L 807.23295 471.827729 
L 808.752473 471.036874 
L 806.020866 467.99437 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #068ef4"/>
    <path d="M 723.783593 331.608038 
L 726.520495 335.868155 
L 728.111583 334.47992 
L 725.37713 330.21581 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cec07f"/>
    <path d="M 687.526271 268.094656 
L 690.263475 271.673942 
L 691.884148 270.444485 
L 689.1493 266.87082 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9f847e"/>
    <path d="M 793.570085 455.924638 
L 796.301225 459.254199 
L 797.831578 458.398663 
L 795.103163 455.051471 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a6d7"/>
    <path d="M 807.23295 471.827729 
L 809.968419 474.774038 
L 811.485262 473.997817 
L 808.752473 471.036874 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0a86ec"/>
    <path d="M 714.429236 313.407907 
L 717.167602 317.565499 
L 718.766094 316.197189 
L 716.030159 312.039175 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b09a6e"/>
    <path d="M 739.757851 364.404809 
L 742.491508 368.695192 
L 744.070189 367.341407 
L 741.339035 363.03994 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #edfb95"/>
    <path d="M 862.712625 507.713344 
L 865.490643 508.94882 
L 866.962339 507.895617 
L 864.186227 506.660092 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #32369c"/>
    <path d="M 642.234793 223.616482 
L 644.947941 225.748218 
L 646.60395 224.485668 
L 643.892624 222.355856 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ede8e7"/>
    <path d="M 660.201099 236.695251 
L 662.927343 239.436525 
L 664.570537 238.257813 
L 661.846396 235.520863 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d5c9c7"/>
    <path d="M 622.693061 215.979887 
L 625.387338 217.447697 
L 627.05388 215.966746 
L 624.361054 214.499003 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fbfafa"/>
    <path d="M 790.839379 452.525227 
L 793.570085 455.924638 
L 795.103163 455.051471 
L 792.375186 451.633875 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00acc4"/>
    <path d="M 809.968419 474.774038 
L 812.705218 477.637429 
L 814.219394 476.875201 
L 811.485262 473.997817 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0c80e6"/>
    <path d="M 608.615856 214.561382 
L 611.294025 215.571308 
L 612.965356 213.858399 
L 610.288369 212.848715 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fdfcfc"/>
    <path d="M 684.789456 264.586905 
L 687.526271 268.094656 
L 689.1493 266.87082 
L 686.414821 263.368582 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a58c86"/>
    <path d="M 702.339834 291.850602 
L 705.079017 295.796642 
L 706.687381 294.478966 
L 703.950602 290.535842 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8a695a"/>
    <path d="M 788.108972 449.058402 
L 790.839379 452.525227 
L 792.375186 451.633875 
L 789.647511 448.148329 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b2b2"/>
    <path d="M 615.647277 214.983091 
L 618.333955 216.222448 
L 620.003148 214.625958 
L 617.31778 213.386512 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fdfcfc"/>
    <path d="M 662.927343 239.436525 
L 665.655437 242.272826 
L 667.296497 241.089642 
L 664.570537 238.257813 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d1c4c1"/>
    <path d="M 730.402351 345.832731 
L 733.138312 350.127635 
L 734.724458 348.740409 
L 731.990963 344.437917 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e6df8b"/>
    <path d="M 812.705218 477.637429 
L 815.443507 480.415996 
L 816.955032 479.667106 
L 814.219394 476.875201 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0f7be1"/>
    <path d="M 767.82249 418.13456 
L 770.551977 422.067324 
L 772.10712 420.969763 
L 769.380296 417.01778 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #35d771"/>
    <path d="M 682.053175 261.15363 
L 684.789456 264.586905 
L 686.414821 263.368582 
L 683.680855 259.940706 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ab938e"/>
    <path d="M 833.410126 494.526511 
L 836.161176 496.673358 
L 837.653686 495.901247 
L 834.905056 493.747243 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2353b9"/>
    <path d="M 632.45178 219.241328 
L 635.156482 221.046318 
L 636.818202 219.677808 
L 634.115135 217.873466 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f5f2f2"/>
    <path d="M 755.734553 396.671684 
L 758.465481 400.808532 
L 760.031326 399.584877 
L 757.302993 395.430785 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #81e680"/>
    <path d="M 746.379082 378.572627 
L 749.111724 382.816714 
L 750.685342 381.50949 
L 747.955239 377.25101 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bdf28c"/>
    <path d="M 665.655437 242.272826 
L 668.385204 245.201907 
L 670.0241 244.014105 
L 667.296497 241.089642 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cbbcb9"/>
    <path d="M 845.918051 501.76813 
L 848.679628 503.521837 
L 850.162126 502.669903 
L 847.402773 500.912531 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2b43a9"/>
    <path d="M 679.317579 257.797697 
L 682.053175 261.15363 
L 683.680855 259.940706 
L 680.947552 256.590054 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b19b96"/>
    <path d="M 785.378735 445.52667 
L 788.108972 449.058402 
L 789.647511 448.148329 
L 786.920007 444.597357 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b8a0"/>
    <path d="M 855.692258 505.874657 
L 858.46342 507.320544 
L 859.939154 506.371716 
L 857.170039 504.924453 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2f3ba1"/>
    <path d="M 721.045638 327.369193 
L 723.783593 331.608038 
L 725.37713 330.21581 
L 722.641612 325.972995 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c6b67a"/>
    <path d="M 668.385204 245.201907 
L 671.11647 248.221421 
L 672.753175 247.02886 
L 670.0241 244.014105 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c7b7b4"/>
    <path d="M 711.690059 309.285778 
L 714.429236 313.407907 
L 716.030159 312.039175 
L 713.293399 307.916638 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a8906a"/>
    <path d="M 676.582822 254.521894 
L 679.317579 257.797697 
L 680.947552 256.590054 
L 678.215065 253.319408 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b7a39f"/>
    <path d="M 815.443507 480.415996 
L 818.183455 483.107916 
L 819.692346 482.371697 
L 816.955032 479.667106 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1373d9"/>
    <path d="M 671.11647 248.221421 
L 673.849065 251.328928 
L 675.483552 250.131471 
L 672.753175 247.02886 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c1b0ac"/>
    <path d="M 673.849065 251.328928 
L 676.582822 254.521894 
L 678.215065 253.319408 
L 675.483552 250.131471 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bba8a4"/>
    <path d="M 644.947941 225.748218 
L 647.664075 227.986291 
L 649.318225 226.721756 
L 646.60395 224.485668 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e9e3e2"/>
    <path d="M 699.600296 287.957155 
L 702.339834 291.850602 
L 703.950602 290.535842 
L 701.213452 286.645284 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #825f56"/>
    <path d="M 737.022994 360.110782 
L 739.757851 364.404809 
L 741.339035 363.03994 
L 738.606667 358.734795 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 782.648547 441.932605 
L 785.378735 445.52667 
L 786.920007 444.597357 
L 784.19255 440.983551 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00be8f"/>
    <path d="M 765.092334 414.158866 
L 767.82249 418.13456 
L 769.380296 417.01778 
L 766.652796 413.022555 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #45da74"/>
    <path d="M 818.183455 483.107916 
L 820.925229 485.711445 
L 822.431506 484.98722 
L 819.692346 482.371697 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #166ed4"/>
    <path d="M 727.665234 341.548363 
L 730.402351 345.832731 
L 731.990963 344.437917 
L 729.256298 340.145973 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ded587"/>
    <path d="M 836.161176 496.673358 
L 838.915152 498.72241 
L 840.405269 497.956816 
L 837.653686 495.901247 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2450b6"/>
    <path d="M 604.26983 215.494883 
L 606.943954 216.390521 
L 608.615856 214.561382 
L 605.942825 213.666262 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fdfcfc"/>
    <path d="M 779.918288 438.278849 
L 782.648547 441.932605 
L 784.19255 440.983551 
L 781.46502 437.309571 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c677"/>
    <path d="M 625.387338 217.447697 
L 628.085795 219.028653 
L 629.75085 217.547808 
L 627.05388 215.966746 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9f7f7"/>
    <path d="M 753.002621 392.507497 
L 755.734553 396.671684 
L 757.302993 395.430785 
L 754.573644 391.249171 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #91e983"/>
    <path d="M 696.860516 284.119604 
L 699.600296 287.957155 
L 701.213452 286.645284 
L 698.476043 282.810593 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #836059"/>
    <path d="M 743.645285 374.314521 
L 746.379082 378.572627 
L 747.955239 377.25101 
L 745.223967 372.978422 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cdf58f"/>
    <path d="M 647.664075 227.986291 
L 650.383006 230.329102 
L 652.035262 229.062525 
L 649.318225 226.721756 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e5dedc"/>
    <path d="M 708.950154 305.202601 
L 711.690059 309.285778 
L 713.293399 307.916638 
L 710.555897 303.833068 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a08566"/>
    <path d="M 635.156482 221.046318 
L 637.864768 222.961664 
L 639.524817 221.592559 
L 636.818202 219.677808 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1edec"/>
    <path d="M 872.529079 510.045516 
L 875.320088 510.959329 
L 876.786533 509.797562 
L 873.99726 508.884883 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #333399"/>
    <path d="M 718.306686 323.15518 
L 721.045638 327.369193 
L 722.641612 325.972995 
L 719.905083 321.75504 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #beac76"/>
    <path d="M 865.490643 508.94882 
L 868.273401 510.077723 
L 869.743226 509.024201 
L 866.962339 507.895617 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #32369c"/>
    <path d="M 820.925229 485.711445 
L 823.669004 488.224926 
L 825.172686 487.512004 
L 822.431506 484.98722 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1868ce"/>
    <path d="M 762.361432 410.14331 
L 765.092334 414.158866 
L 766.652796 413.022555 
L 763.92454 408.987172 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #55dd77"/>
    <path d="M 848.679628 503.521837 
L 851.444916 505.173038 
L 852.925224 504.32421 
L 850.162126 502.669903 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2c40a6"/>
    <path d="M 611.294025 215.571308 
L 613.977157 216.695825 
L 615.647277 214.983091 
L 612.965356 213.858399 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fdfcfc"/>
    <path d="M 734.286939 355.816634 
L 737.022994 360.110782 
L 738.606667 358.734795 
L 735.87309 354.42951 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f6f394"/>
    <path d="M 777.187847 434.568106 
L 779.918288 438.278849 
L 781.46502 437.309571 
L 778.737303 433.578142 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #01cc66"/>
    <path d="M 618.333955 216.222448 
L 621.025213 217.575995 
L 622.693061 215.979887 
L 620.003148 214.625958 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fbfafa"/>
    <path d="M 694.120613 280.3412 
L 696.860516 284.119604 
L 698.476043 282.810593 
L 695.738494 279.035018 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8b6b64"/>
    <path d="M 650.383006 230.329102 
L 653.104548 232.774942 
L 654.754877 231.506264 
L 652.035262 229.062525 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e1d9d7"/>
    <path d="M 858.46342 507.320544 
L 861.238903 508.661262 
L 862.712625 507.713344 
L 859.939154 506.371716 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #30389e"/>
    <path d="M 724.926993 337.2781 
L 727.665234 341.548363 
L 729.256298 340.145973 
L 726.520495 335.868155 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d6cb83"/>
    <path d="M 706.209608 301.161835 
L 708.950154 305.202601 
L 710.555897 303.833068 
L 707.817738 299.791927 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #987b61"/>
    <path d="M 823.669004 488.224926 
L 826.414953 490.646783 
L 827.916062 489.944466 
L 825.172686 487.512004 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1b63c9"/>
    <path d="M 750.269642 388.319276 
L 753.002621 392.507497 
L 754.573644 391.249171 
L 751.843234 387.04336 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a1ec86"/>
    <path d="M 838.915152 498.72241 
L 841.67224 500.672518 
L 843.159995 499.912799 
L 840.405269 497.956816 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #274bb1"/>
    <path d="M 774.457116 430.803145 
L 777.187847 434.568106 
L 778.737303 433.578142 
L 776.009291 429.792049 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0dcf69"/>
    <path d="M 599.9278 216.657336 
L 602.5976 217.43966 
L 604.26983 215.494883 
L 601.601039 214.713596 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fbfafa"/>
    <path d="M 740.910315 370.045847 
L 743.645285 374.314521 
L 745.223967 372.978422 
L 742.491508 368.695192 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ddf892"/>
    <path d="M 715.566795 318.969546 
L 718.306686 323.15518 
L 719.905083 321.75504 
L 717.167602 317.565499 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b8a473"/>
    <path d="M 691.380712 276.625141 
L 694.120613 280.3412 
L 695.738494 279.035018 
L 693.000928 275.321755 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #91726c"/>
    <path d="M 637.864768 222.961664 
L 640.576452 224.986131 
L 642.234793 223.616482 
L 639.524817 221.592559 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #efebea"/>
    <path d="M 759.629715 406.091009 
L 762.361432 410.14331 
L 763.92454 408.987172 
L 761.195457 404.91477 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #65e07a"/>
    <path d="M 628.085795 219.028653 
L 630.788246 220.721897 
L 632.45178 219.241328 
L 629.75085 217.547808 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f7f5f4"/>
    <path d="M 653.104548 232.774942 
L 655.828516 235.321986 
L 657.476883 234.051151 
L 654.754877 231.506264 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ddd3d1"/>
    <path d="M 731.549698 351.525905 
L 734.286939 355.816634 
L 735.87309 354.42951 
L 733.138312 350.127635 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eee990"/>
    <path d="M 771.725994 426.986792 
L 774.457116 430.803145 
L 776.009291 429.792049 
L 773.280881 425.954141 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1dd26c"/>
    <path d="M 688.640944 272.974568 
L 691.380712 276.625141 
L 693.000928 275.321755 
L 690.263475 271.673942 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #977a74"/>
    <path d="M 826.414953 490.646783 
L 829.163254 492.975527 
L 830.661815 492.283106 
L 827.916062 489.944466 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1e5ec4"/>
    <path d="M 703.468515 297.166906 
L 706.209608 301.161835 
L 707.817738 299.791927 
L 705.079017 295.796642 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #92735e"/>
    <path d="M 655.828516 235.321986 
L 658.554726 237.968298 
L 660.201099 236.695251 
L 657.476883 234.051151 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d9cecc"/>
    <path d="M 606.943954 216.390521 
L 609.62324 217.400427 
L 611.294025 215.571308 
L 608.615856 214.561382 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fdfcfc"/>
    <path d="M 851.444916 505.173038 
L 854.214106 506.720943 
L 855.692258 505.874657 
L 852.925224 504.32421 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2e3ea4"/>
    <path d="M 747.535576 384.110366 
L 750.269642 388.319276 
L 751.843234 387.04336 
L 749.111724 382.816714 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b1ef89"/>
    <path d="M 722.187668 333.025509 
L 724.926993 337.2781 
L 726.520495 335.868155 
L 723.783593 331.608038 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cec07f"/>
    <path d="M 621.025213 217.575995 
L 623.720868 219.043129 
L 625.387338 217.447697 
L 622.693061 215.979887 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9f7f7"/>
    <path d="M 685.901446 269.392557 
L 688.640944 272.974568 
L 690.263475 271.673942 
L 687.526271 268.094656 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9f847e"/>
    <path d="M 712.826036 314.815822 
L 715.566795 318.969546 
L 717.167602 317.565499 
L 714.429236 313.407907 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b09a6e"/>
    <path d="M 756.897117 402.005127 
L 759.629715 406.091009 
L 761.195457 404.91477 
L 758.465481 400.808532 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #71e37d"/>
    <path d="M 738.174161 365.770077 
L 740.910315 370.045847 
L 742.491508 368.695192 
L 739.757851 364.404809 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #edfb95"/>
    <path d="M 640.576452 224.986131 
L 643.291344 227.11836 
L 644.947941 225.748218 
L 642.234793 223.616482 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ede8e7"/>
    <path d="M 841.67224 500.672518 
L 844.432628 502.522626 
L 845.918051 501.76813 
L 843.159995 499.912799 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2848ae"/>
    <path d="M 868.273401 510.077723 
L 871.06109 511.099723 
L 872.529079 510.045516 
L 869.743226 509.024201 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #32369c"/>
    <path d="M 613.977157 216.695825 
L 616.665078 217.93459 
L 618.333955 216.222448 
L 615.647277 214.983091 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fbfafa"/>
    <path d="M 768.994388 423.121933 
L 771.725994 426.986792 
L 773.280881 425.954141 
L 770.551977 422.067324 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #29d46e"/>
    <path d="M 658.554726 237.968298 
L 661.282996 240.711838 
L 662.927343 239.436525 
L 660.201099 236.695251 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d5c9c7"/>
    <path d="M 683.162359 265.882121 
L 685.901446 269.392557 
L 687.526271 268.094656 
L 684.789456 264.586905 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a58c86"/>
    <path d="M 700.726978 293.221202 
L 703.468515 297.166906 
L 705.079017 295.796642 
L 702.339834 291.850602 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8a695a"/>
    <path d="M 829.163254 492.975527 
L 831.914087 495.209757 
L 833.410126 494.526511 
L 830.661815 492.283106 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1f5bc1"/>
    <path d="M 797.503283 463.277061 
L 800.23848 466.441079 
L 801.765362 465.694379 
L 799.032936 462.511543 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #009cf4"/>
    <path d="M 800.23848 466.441079 
L 802.974532 469.529051 
L 804.498649 468.800488 
L 801.765362 465.694379 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0296fc"/>
    <path d="M 794.768795 460.039194 
L 797.503283 463.277061 
L 799.032936 462.511543 
L 796.301225 459.254199 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a2e2"/>
    <path d="M 728.811291 347.242143 
L 731.549698 351.525905 
L 733.138312 350.127635 
L 730.402351 345.832731 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e6df8b"/>
    <path d="M 861.238903 508.661262 
L 864.018898 509.896297 
L 865.490643 508.94882 
L 862.712625 507.713344 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #30389e"/>
    <path d="M 630.788246 220.721897 
L 633.494506 222.526441 
L 635.156482 221.046318 
L 632.45178 219.241328 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f3f0ef"/>
    <path d="M 802.974532 469.529051 
L 805.711588 472.538849 
L 807.23295 471.827729 
L 804.498649 468.800488 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0490f6"/>
    <path d="M 661.282996 240.711838 
L 664.013147 243.550458 
L 665.655437 242.272826 
L 662.927343 239.436525 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d1c4c1"/>
    <path d="M 792.034876 456.729756 
L 794.768795 460.039194 
L 796.301225 459.254199 
L 793.570085 455.924638 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a8d0"/>
    <path d="M 680.42383 262.4462 
L 683.162359 265.882121 
L 684.789456 264.586905 
L 682.053175 261.15363 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ab938e"/>
    <path d="M 805.711588 472.538849 
L 808.449803 475.468425 
L 809.968419 474.774038 
L 807.23295 471.827729 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0888ee"/>
    <path d="M 789.301388 453.351092 
L 792.034876 456.729756 
L 793.570085 455.924638 
L 790.839379 452.525227 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00aebf"/>
    <path d="M 664.013147 243.550458 
L 666.745002 246.481909 
L 668.385204 245.201907 
L 665.655437 242.272826 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cbbcb9"/>
    <path d="M 744.800395 379.884141 
L 747.535576 384.110366 
L 749.111724 382.816714 
L 746.379082 378.572627 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c1f38d"/>
    <path d="M 719.447306 328.794149 
L 722.187668 333.025509 
L 723.783593 331.608038 
L 721.045638 327.369193 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c6b67a"/>
    <path d="M 677.68601 259.087663 
L 680.42383 262.4462 
L 682.053175 261.15363 
L 679.317579 257.797697 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b19b96"/>
    <path d="M 710.084482 310.697517 
L 712.826036 314.815822 
L 714.429236 313.407907 
L 711.690059 309.285778 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a8906a"/>
    <path d="M 766.262208 419.21151 
L 768.994388 423.121933 
L 770.551977 422.067324 
L 767.82249 418.13456 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #39d771"/>
    <path d="M 754.163581 397.888869 
L 756.897117 402.005127 
L 758.465481 400.808532 
L 755.734553 396.671684 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #81e680"/>
    <path d="M 808.449803 475.468425 
L 811.189334 478.315809 
L 812.705218 477.637429 
L 809.968419 474.774038 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0b83e9"/>
    <path d="M 666.745002 246.481909 
L 669.478384 249.503843 
L 671.11647 248.221421 
L 668.385204 245.201907 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c7b7b4"/>
    <path d="M 643.291344 227.11836 
L 646.009256 229.356875 
L 647.664075 227.986291 
L 644.947941 225.748218 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e9e3e2"/>
    <path d="M 674.949055 255.8093 
L 677.68601 259.087663 
L 679.317579 257.797697 
L 676.582822 254.521894 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b7a39f"/>
    <path d="M 786.5682 449.905621 
L 789.301388 453.351092 
L 790.839379 452.525227 
L 788.108972 449.058402 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b4ac"/>
    <path d="M 669.478384 249.503843 
L 672.213125 252.613819 
L 673.849065 251.328928 
L 671.11647 248.221421 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c1b0ac"/>
    <path d="M 672.213125 252.613819 
L 674.949055 255.8093 
L 676.582822 254.521894 
L 673.849065 251.328928 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bdaba7"/>
    <path d="M 602.5976 217.43966 
L 605.272755 218.335676 
L 606.943954 216.390521 
L 604.26983 215.494883 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fbfafa"/>
    <path d="M 697.985104 289.328069 
L 700.726978 293.221202 
L 702.339834 291.850602 
L 699.600296 287.957155 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #825f56"/>
    <path d="M 735.436823 361.490705 
L 738.174161 365.770077 
L 739.757851 364.404809 
L 737.022994 360.110782 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 811.189334 478.315809 
L 813.930342 481.079111 
L 815.443507 480.415996 
L 812.705218 477.637429 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0f7be1"/>
    <path d="M 831.914087 495.209757 
L 834.667634 497.348154 
L 836.161176 496.673358 
L 833.410126 494.526511 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2256bc"/>
    <path d="M 783.835185 446.395829 
L 786.5682 449.905621 
L 788.108972 449.058402 
L 785.378735 445.52667 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00bb9b"/>
    <path d="M 844.432628 502.522626 
L 847.196503 504.271765 
L 848.679628 503.521837 
L 845.918051 501.76813 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2a46ac"/>
    <path d="M 854.214106 506.720943 
L 856.987388 508.164854 
L 858.46342 507.320544 
L 855.692258 505.874657 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2e3ea4"/>
    <path d="M 623.720868 219.043129 
L 626.420736 220.62312 
L 628.085795 219.028653 
L 625.387338 217.447697 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f7f5f4"/>
    <path d="M 726.071744 342.968899 
L 728.811291 347.242143 
L 730.402351 345.832731 
L 727.665234 341.548363 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ded587"/>
    <path d="M 763.529372 415.258517 
L 766.262208 419.21151 
L 767.82249 418.13456 
L 765.092334 414.158866 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #45da74"/>
    <path d="M 813.930342 481.079111 
L 816.672993 483.756518 
L 818.183455 483.107916 
L 815.443507 480.415996 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1276dc"/>
    <path d="M 609.62324 217.400427 
L 612.307518 218.524387 
L 613.977157 216.695825 
L 611.294025 215.571308 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fbfafa"/>
    <path d="M 633.494506 222.526441 
L 636.204385 224.441175 
L 637.864768 222.961664 
L 635.156482 221.046318 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1edec"/>
    <path d="M 781.102221 442.824271 
L 783.835185 446.395829 
L 785.378735 445.52667 
L 782.648547 441.932605 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c088"/>
    <path d="M 695.243008 285.490807 
L 697.985104 289.328069 
L 699.600296 287.957155 
L 696.860516 284.119604 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #836059"/>
    <path d="M 707.342218 306.618113 
L 710.084482 310.697517 
L 711.690059 309.285778 
L 708.950154 305.202601 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a08566"/>
    <path d="M 646.009256 229.356875 
L 648.73 231.70008 
L 650.383006 230.329102 
L 647.664075 227.986291 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e5dedc"/>
    <path d="M 716.705963 324.587574 
L 719.447306 328.794149 
L 721.045638 327.369193 
L 718.306686 323.15518 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #beac76"/>
    <path d="M 616.665078 217.93459 
L 619.357609 219.287132 
L 621.025213 217.575995 
L 618.333955 216.222448 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fbfafa"/>
    <path d="M 742.064074 375.644006 
L 744.800395 379.884141 
L 746.379082 378.572627 
L 743.645285 374.314521 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d1f690"/>
    <path d="M 751.429057 393.745486 
L 754.163581 397.888869 
L 755.734553 396.671684 
L 753.002621 392.507497 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #91e983"/>
    <path d="M 598.25547 218.716665 
L 600.926223 219.500004 
L 602.5976 217.43966 
L 599.9278 216.657336 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9f7f7"/>
    <path d="M 778.369192 439.193567 
L 781.102221 442.824271 
L 782.648547 441.932605 
L 779.918288 438.278849 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c677"/>
    <path d="M 732.698305 357.21124 
L 735.436823 361.490705 
L 737.022994 360.110782 
L 734.286939 355.816634 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f6f394"/>
    <path d="M 816.672993 483.756518 
L 819.417452 486.346302 
L 820.925229 485.711445 
L 818.183455 483.107916 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1470d6"/>
    <path d="M 871.06109 511.099723 
L 873.853898 512.014588 
L 875.320088 510.959329 
L 872.529079 510.045516 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #32369c"/>
    <path d="M 692.500809 281.712667 
L 695.243008 285.490807 
L 696.860516 284.119604 
L 694.120613 280.3412 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8b6b64"/>
    <path d="M 834.667634 497.348154 
L 837.424077 499.389492 
L 838.915152 498.72241 
L 836.161176 496.673358 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2353b9"/>
    <path d="M 760.795803 411.266001 
L 763.529372 415.258517 
L 765.092334 414.158866 
L 762.361432 410.14331 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #55dd77"/>
    <path d="M 864.018898 509.896297 
L 866.803596 511.025228 
L 868.273401 510.077723 
L 865.490643 508.94882 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #32369c"/>
    <path d="M 648.73 231.70008 
L 651.45339 234.146264 
L 653.104548 232.774942 
L 650.383006 230.329102 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e1d9d7"/>
    <path d="M 723.33109 338.709731 
L 726.071744 342.968899 
L 727.665234 341.548363 
L 724.926993 337.2781 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d6cb83"/>
    <path d="M 704.59933 302.581064 
L 707.342218 306.618113 
L 708.950154 305.202601 
L 706.209608 301.161835 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #987b61"/>
    <path d="M 775.635988 435.5064 
L 778.369192 439.193567 
L 779.918288 438.278849 
L 777.187847 434.568106 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #01cc66"/>
    <path d="M 819.417452 486.346302 
L 822.163892 488.846817 
L 823.669004 488.224926 
L 820.925229 485.711445 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #176bd1"/>
    <path d="M 713.9637 320.40932 
L 716.705963 324.587574 
L 718.306686 323.15518 
L 715.566795 318.969546 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b8a473"/>
    <path d="M 636.204385 224.441175 
L 638.917697 226.464864 
L 640.576452 224.986131 
L 637.864768 222.961664 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #efebea"/>
    <path d="M 748.693502 389.578262 
L 751.429057 393.745486 
L 753.002621 392.507497 
L 750.269642 388.319276 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a1ec86"/>
    <path d="M 847.196503 504.271765 
L 849.964055 505.91906 
L 851.444916 505.173038 
L 848.679628 503.521837 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2b43a9"/>
    <path d="M 626.420736 220.62312 
L 629.124633 222.315111 
L 630.788246 220.721897 
L 628.085795 219.028653 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f5f2f2"/>
    <path d="M 689.758634 277.996845 
L 692.500809 281.712667 
L 694.120613 280.3412 
L 691.380712 276.625141 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #91726c"/>
    <path d="M 739.326598 371.393393 
L 742.064074 375.644006 
L 743.645285 374.314521 
L 740.910315 370.045847 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e1f993"/>
    <path d="M 605.272755 218.335676 
L 607.953096 219.345301 
L 609.62324 217.400427 
L 606.943954 216.390521 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fbfafa"/>
    <path d="M 651.45339 234.146264 
L 654.17924 236.693605 
L 655.828516 235.321986 
L 653.104548 232.774942 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ddd3d1"/>
    <path d="M 856.987388 508.164854 
L 859.764955 509.504167 
L 861.238903 508.661262 
L 858.46342 507.320544 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2f3ba1"/>
    <path d="M 772.902504 431.765516 
L 775.635988 435.5064 
L 777.187847 434.568106 
L 774.457116 430.803145 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #11cf69"/>
    <path d="M 729.95862 352.935203 
L 732.698305 357.21124 
L 734.286939 355.816634 
L 731.549698 351.525905 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eee990"/>
    <path d="M 758.061434 407.237056 
L 760.795803 411.266001 
L 762.361432 410.14331 
L 759.629715 406.091009 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #65e07a"/>
    <path d="M 687.016615 274.34648 
L 689.758634 277.996845 
L 691.380712 276.625141 
L 688.640944 272.974568 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #977a74"/>
    <path d="M 701.855916 298.589791 
L 704.59933 302.581064 
L 706.209608 301.161835 
L 703.468515 297.166906 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #92735e"/>
    <path d="M 619.357609 219.287132 
L 622.054568 220.752852 
L 623.720868 219.043129 
L 621.025213 217.575995 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9f7f7"/>
    <path d="M 822.163892 488.846817 
L 824.912485 491.256501 
L 826.414953 490.646783 
L 823.669004 488.224926 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1a66cc"/>
    <path d="M 837.424077 499.389492 
L 840.183603 501.332629 
L 841.67224 500.672518 
L 838.915152 498.72241 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #264eb4"/>
    <path d="M 612.307518 218.524387 
L 614.996612 219.762061 
L 616.665078 217.93459 
L 613.977157 216.695825 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fbfafa"/>
    <path d="M 654.17924 236.693605 
L 656.907364 239.340169 
L 658.554726 237.968298 
L 655.828516 235.321986 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d9cecc"/>
    <path d="M 720.589371 334.468191 
L 723.33109 338.709731 
L 724.926993 337.2781 
L 722.187668 333.025509 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cec07f"/>
    <path d="M 711.220587 316.262909 
L 713.9637 320.40932 
L 715.566795 318.969546 
L 712.826036 314.815822 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b09a6e"/>
    <path d="M 745.956879 385.39052 
L 748.693502 389.578262 
L 750.269642 388.319276 
L 747.535576 384.110366 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b1ef89"/>
    <path d="M 770.16864 427.97372 
L 772.902504 431.765516 
L 774.457116 430.803145 
L 771.725994 426.986792 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1dd26c"/>
    <path d="M 684.274888 270.764647 
L 687.016615 274.34648 
L 688.640944 272.974568 
L 685.901446 269.392557 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9f847e"/>
    <path d="M 638.917697 226.464864 
L 641.634252 228.596154 
L 643.291344 227.11836 
L 640.576452 224.986131 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ebe5e4"/>
    <path d="M 736.587958 367.135755 
L 739.326598 371.393393 
L 740.910315 370.045847 
L 738.174161 365.770077 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1fc96"/>
    <path d="M 656.907364 239.340169 
L 659.637582 242.083914 
L 661.282996 240.711838 
L 658.554726 237.968298 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d5c9c7"/>
    <path d="M 755.3262 403.174822 
L 758.061434 407.237056 
L 759.629715 406.091009 
L 756.897117 402.005127 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #75e37d"/>
    <path d="M 629.124633 222.315111 
L 631.832372 224.118117 
L 633.494506 222.526441 
L 630.788246 220.721897 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f3f0ef"/>
    <path d="M 681.533597 267.254356 
L 684.274888 270.764647 
L 685.901446 269.392557 
L 683.162359 265.882121 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a58c86"/>
    <path d="M 699.112078 294.647677 
L 701.855916 298.589791 
L 703.468515 297.166906 
L 700.726978 293.221202 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8a695a"/>
    <path d="M 824.912485 491.256501 
L 827.663408 493.573874 
L 829.163254 492.975527 
L 826.414953 490.646783 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1c60c6"/>
    <path d="M 600.926223 219.500004 
L 603.602349 220.396258 
L 605.272755 218.335676 
L 602.5976 217.43966 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9f7f7"/>
    <path d="M 727.217788 348.666126 
L 729.95862 352.935203 
L 731.549698 351.525905 
L 728.811291 347.242143 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e6df8b"/>
    <path d="M 849.964055 505.91906 
L 852.735475 507.463723 
L 854.214106 506.720943 
L 851.444916 505.173038 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2c40a6"/>
    <path d="M 659.637582 242.083914 
L 662.369711 244.922695 
L 664.013147 243.550458 
L 661.282996 240.711838 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d1c4c1"/>
    <path d="M 767.434302 424.133874 
L 770.16864 427.97372 
L 771.725994 426.986792 
L 768.994388 423.121933 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2dd56f"/>
    <path d="M 678.792889 263.818547 
L 681.533597 267.254356 
L 683.162359 265.882121 
L 680.42383 262.4462 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ab938e"/>
    <path d="M 866.803596 511.025228 
L 869.593187 512.047729 
L 871.06109 511.099723 
L 868.273401 510.077723 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #32369c"/>
    <path d="M 717.846635 330.247828 
L 720.589371 334.468191 
L 722.187668 333.025509 
L 719.447306 328.794149 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c8b97b"/>
    <path d="M 662.369711 244.922695 
L 665.103575 247.854265 
L 666.745002 246.481909 
L 664.013147 243.550458 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cbbcb9"/>
    <path d="M 708.4767 312.15184 
L 711.220587 316.262909 
L 712.826036 314.815822 
L 710.084482 310.697517 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a8906a"/>
    <path d="M 676.052916 260.460088 
L 678.792889 263.818547 
L 680.42383 262.4462 
L 677.68601 259.087663 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b19b96"/>
    <path d="M 641.634252 228.596154 
L 644.353862 230.833569 
L 646.009256 229.356875 
L 643.291344 227.11836 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e9e3e2"/>
    <path d="M 840.183603 501.332629 
L 842.946396 503.176515 
L 844.432628 502.522626 
L 841.67224 500.672518 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #274bb1"/>
    <path d="M 743.219158 381.185613 
L 745.956879 385.39052 
L 747.535576 384.110366 
L 744.800395 379.884141 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c1f38d"/>
    <path d="M 665.103575 247.854265 
L 667.838997 250.876276 
L 669.478384 249.503843 
L 666.745002 246.481909 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c7b7b4"/>
    <path d="M 673.313835 257.181765 
L 676.052916 260.460088 
L 677.68601 259.087663 
L 674.949055 255.8093 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b7a39f"/>
    <path d="M 696.367924 290.758061 
L 699.112078 294.647677 
L 700.726978 293.221202 
L 697.985104 289.328069 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #825f56"/>
    <path d="M 667.838997 250.876276 
L 670.575807 253.986287 
L 672.213125 252.613819 
L 669.478384 249.503843 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c1b0ac"/>
    <path d="M 670.575807 253.986287 
L 673.313835 257.181765 
L 674.949055 255.8093 
L 672.213125 252.613819 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bba8a4"/>
    <path d="M 622.054568 220.752852 
L 624.755772 222.33102 
L 626.420736 220.62312 
L 623.720868 219.043129 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f7f5f4"/>
    <path d="M 859.764955 509.504167 
L 862.546997 510.738368 
L 864.018898 509.896297 
L 861.238903 508.661262 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2f3ba1"/>
    <path d="M 733.848153 362.874565 
L 736.587958 367.135755 
L 738.174161 365.770077 
L 735.436823 361.490705 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 752.590047 399.082483 
L 755.3262 403.174822 
L 756.897117 402.005127 
L 754.163581 397.888869 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #81e680"/>
    <path d="M 795.971529 463.970145 
L 798.709554 467.113022 
L 800.23848 466.441079 
L 797.503283 463.277061 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #009eef"/>
    <path d="M 607.953096 219.345301 
L 610.638452 220.468326 
L 612.307518 218.524387 
L 609.62324 217.400427 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9f7f7"/>
    <path d="M 793.234211 460.754158 
L 795.971529 463.970145 
L 797.503283 463.277061 
L 794.768795 460.039194 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a4dc"/>
    <path d="M 798.709554 467.113022 
L 801.448429 470.180608 
L 802.974532 469.529051 
L 800.23848 466.441079 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0098fe"/>
    <path d="M 827.663408 493.573874 
L 830.416837 495.797545 
L 831.914087 495.209757 
L 829.163254 492.975527 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1e5ec4"/>
    <path d="M 764.699405 420.248895 
L 767.434302 424.133874 
L 768.994388 423.121933 
L 766.262208 419.21151 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #39d771"/>
    <path d="M 790.49746 457.467316 
L 793.234211 460.754158 
L 794.768795 460.039194 
L 792.034876 456.729756 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a8d0"/>
    <path d="M 801.448429 470.180608 
L 804.188301 473.170796 
L 805.711588 472.538849 
L 802.974532 469.529051 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0393f9"/>
    <path d="M 596.584137 220.890865 
L 599.255786 221.6752 
L 600.926223 219.500004 
L 598.25547 218.716665 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f7f5f4"/>
    <path d="M 614.996612 219.762061 
L 617.690343 221.11298 
L 619.357609 219.287132 
L 616.665078 217.93459 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9f7f7"/>
    <path d="M 787.761142 454.111946 
L 790.49746 457.467316 
L 792.034876 456.729756 
L 789.301388 453.351092 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00aebf"/>
    <path d="M 631.832372 224.118117 
L 634.543765 226.031032 
L 636.204385 224.441175 
L 633.494506 222.526441 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1edec"/>
    <path d="M 804.188301 473.170796 
L 806.929324 476.081554 
L 808.449803 475.468425 
L 805.711588 472.538849 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #078bf1"/>
    <path d="M 724.475835 344.407547 
L 727.217788 348.666126 
L 728.811291 347.242143 
L 726.071744 342.968899 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ded587"/>
    <path d="M 644.353862 230.833569 
L 647.076338 233.175516 
L 648.73 231.70008 
L 646.009256 229.356875 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e5dedc"/>
    <path d="M 785.025126 450.690444 
L 787.761142 454.111946 
L 789.301388 453.351092 
L 786.5682 449.905621 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b4ac"/>
    <path d="M 693.62357 286.92424 
L 696.367924 290.758061 
L 697.985104 289.328069 
L 695.243008 285.490807 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #836059"/>
    <path d="M 705.732123 308.079587 
L 708.4767 312.15184 
L 710.084482 310.697517 
L 707.342218 306.618113 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a08566"/>
    <path d="M 715.102937 326.05218 
L 717.846635 330.247828 
L 719.447306 328.794149 
L 716.705963 324.587574 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c0ae77"/>
    <path d="M 806.929324 476.081554 
L 809.671652 478.91093 
L 811.189334 478.315809 
L 808.449803 475.468425 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0a86ec"/>
    <path d="M 740.480319 376.966923 
L 743.219158 381.185613 
L 744.800395 379.884141 
L 742.064074 375.644006 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d1f690"/>
    <path d="M 782.289288 447.205276 
L 785.025126 450.690444 
L 786.5682 449.905621 
L 783.835185 446.395829 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00bb9b"/>
    <path d="M 761.963867 416.321754 
L 764.699405 420.248895 
L 766.262208 419.21151 
L 763.529372 415.258517 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #49db75"/>
    <path d="M 749.852924 394.963264 
L 752.590047 399.082483 
L 754.163581 397.888869 
L 751.429057 393.745486 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #91e983"/>
    <path d="M 809.671652 478.91093 
L 812.415445 481.657048 
L 813.930342 481.079111 
L 811.189334 478.315809 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0e7ee4"/>
    <path d="M 852.735475 507.463723 
L 855.51095 508.905062 
L 856.987388 508.164854 
L 854.214106 506.720943 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2c40a6"/>
    <path d="M 731.107189 358.613313 
L 733.848153 362.874565 
L 735.436823 361.490705 
L 732.698305 357.21124 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f8f695"/>
    <path d="M 830.416837 495.797545 
L 833.172953 497.926207 
L 834.667634 497.348154 
L 831.914087 495.209757 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2058be"/>
    <path d="M 842.946396 503.176515 
L 845.712644 504.920188 
L 847.196503 504.271765 
L 844.432628 502.522626 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2848ae"/>
    <path d="M 690.879136 283.149459 
L 693.62357 286.92424 
L 695.243008 285.490807 
L 692.500809 281.712667 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8b6b64"/>
    <path d="M 779.553508 443.658973 
L 782.289288 447.205276 
L 783.835185 446.395829 
L 781.102221 442.824271 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c382"/>
    <path d="M 647.076338 233.175516 
L 649.801494 235.620289 
L 651.45339 234.146264 
L 648.73 231.70008 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e1d9d7"/>
    <path d="M 603.602349 220.396258 
L 606.283681 221.405346 
L 607.953096 219.345301 
L 605.272755 218.335676 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9f7f7"/>
    <path d="M 624.755772 222.33102 
L 627.461037 224.020782 
L 629.124633 222.315111 
L 626.420736 220.62312 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f5f2f2"/>
    <path d="M 702.986944 304.049596 
L 705.732123 308.079587 
L 707.342218 306.618113 
L 704.59933 302.581064 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #987b61"/>
    <path d="M 721.732797 340.163003 
L 724.475835 344.407547 
L 726.071744 342.968899 
L 723.33109 338.709731 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d8cd84"/>
    <path d="M 812.415445 481.657048 
L 815.160865 484.318113 
L 816.672993 483.756518 
L 813.930342 481.079111 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1078de"/>
    <path d="M 634.543765 226.031032 
L 637.258624 228.052624 
L 638.917697 226.464864 
L 636.204385 224.441175 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #efebea"/>
    <path d="M 776.817672 440.054131 
L 779.553508 443.658973 
L 781.102221 442.824271 
L 778.369192 439.193567 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c970"/>
    <path d="M 712.358342 321.884772 
L 715.102937 326.05218 
L 716.705963 324.587574 
L 713.9637 320.40932 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b8a473"/>
    <path d="M 869.593187 512.047729 
L 872.38786 512.963566 
L 873.853898 512.014588 
L 871.06109 511.099723 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #32369c"/>
    <path d="M 759.227614 412.355473 
L 761.963867 416.321754 
L 763.529372 415.258517 
L 760.795803 411.266001 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #55dd77"/>
    <path d="M 688.134751 279.436908 
L 690.879136 283.149459 
L 692.500809 281.712667 
L 689.758634 277.996845 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #91726c"/>
    <path d="M 737.740346 372.73786 
L 740.480319 376.966923 
L 742.064074 375.644006 
L 739.326598 371.393393 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e1f993"/>
    <path d="M 649.801494 235.620289 
L 652.529143 238.166067 
L 654.17924 236.693605 
L 651.45339 234.146264 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ddd3d1"/>
    <path d="M 610.638452 220.468326 
L 613.328649 221.704411 
L 614.996612 219.762061 
L 612.307518 218.524387 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9f7f7"/>
    <path d="M 747.11479 390.820426 
L 749.852924 394.963264 
L 751.429057 393.745486 
L 748.693502 389.578262 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a1ec86"/>
    <path d="M 617.690343 221.11298 
L 620.388532 222.576546 
L 622.054568 220.752852 
L 619.357609 219.287132 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f7f5f4"/>
    <path d="M 862.546997 510.738368 
L 865.333703 511.86704 
L 866.803596 511.025228 
L 864.018898 509.896297 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #30389e"/>
    <path d="M 815.160865 484.318113 
L 817.908078 486.892411 
L 819.417452 486.346302 
L 816.672993 483.756518 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1373d9"/>
    <path d="M 774.081671 436.39341 
L 776.817672 440.054131 
L 778.369192 439.193567 
L 775.635988 435.5064 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #05cd67"/>
    <path d="M 833.172953 497.926207 
L 835.931938 499.958641 
L 837.424077 499.389492 
L 834.667634 497.348154 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2256bc"/>
    <path d="M 728.365079 354.355502 
L 731.107189 358.613313 
L 732.698305 357.21124 
L 729.95862 352.935203 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f0ec91"/>
    <path d="M 685.390545 275.789721 
L 688.134751 279.436908 
L 689.758634 277.996845 
L 687.016615 274.34648 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #977a74"/>
    <path d="M 700.241261 300.065276 
L 702.986944 304.049596 
L 704.59933 302.581064 
L 701.855916 298.589791 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #92735e"/>
    <path d="M 599.255786 221.6752 
L 601.932824 222.571554 
L 603.602349 220.396258 
L 600.926223 219.500004 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f7f5f4"/>
    <path d="M 652.529143 238.166067 
L 655.2591 240.810919 
L 656.907364 239.340169 
L 654.17924 236.693605 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d9cecc"/>
    <path d="M 718.988716 335.936033 
L 721.732797 340.163003 
L 723.33109 338.709731 
L 720.589371 334.468191 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d0c380"/>
    <path d="M 756.490579 408.353119 
L 759.227614 412.355473 
L 760.795803 411.266001 
L 758.061434 407.237056 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #65e07a"/>
    <path d="M 637.258624 228.052624 
L 639.97676 230.181542 
L 641.634252 228.596154 
L 638.917697 226.464864 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ebe5e4"/>
    <path d="M 845.712644 504.920188 
L 848.482534 506.562777 
L 849.964055 505.91906 
L 847.196503 504.271765 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2a46ac"/>
    <path d="M 709.612919 317.749113 
L 712.358342 321.884772 
L 713.9637 320.40932 
L 711.220587 316.262909 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b09a6e"/>
    <path d="M 817.908078 486.892411 
L 820.657252 489.37831 
L 822.163892 488.846817 
L 819.417452 486.346302 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #166ed4"/>
    <path d="M 771.345401 432.679532 
L 774.081671 436.39341 
L 775.635988 435.5064 
L 772.902504 431.765516 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #11cf69"/>
    <path d="M 682.646658 272.210968 
L 685.390545 275.789721 
L 687.016615 274.34648 
L 684.274888 270.764647 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9d827c"/>
    <path d="M 627.461037 224.020782 
L 630.170175 225.821161 
L 631.832372 224.118117 
L 629.124633 222.315111 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f3f0ef"/>
    <path d="M 855.51095 508.905062 
L 858.290672 510.242474 
L 859.764955 509.504167 
L 856.987388 508.164854 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2e3ea4"/>
    <path d="M 655.2591 240.810919 
L 657.991183 243.552808 
L 659.637582 242.083914 
L 656.907364 239.340169 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d5c9c7"/>
    <path d="M 744.37561 386.657266 
L 747.11479 390.820426 
L 748.693502 389.578262 
L 745.956879 385.39052 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b1ef89"/>
    <path d="M 734.999232 368.501855 
L 737.740346 372.73786 
L 739.326598 371.393393 
L 736.587958 367.135755 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1fc96"/>
    <path d="M 697.495177 296.130003 
L 700.241261 300.065276 
L 701.855916 298.589791 
L 699.112078 294.647677 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8a695a"/>
    <path d="M 679.903233 268.703656 
L 682.646658 272.210968 
L 684.274888 270.764647 
L 681.533597 267.254356 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a58c86"/>
    <path d="M 725.621846 350.104643 
L 728.365079 354.355502 
L 729.95862 352.935203 
L 727.217788 348.666126 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e8e28d"/>
    <path d="M 657.991183 243.552808 
L 660.72521 246.389592 
L 662.369711 244.922695 
L 659.637582 242.083914 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d1c4c1"/>
    <path d="M 768.608765 428.915274 
L 771.345401 432.679532 
L 772.902504 431.765516 
L 770.16864 427.97372 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #21d36d"/>
    <path d="M 594.913882 223.179093 
L 597.586371 223.964403 
L 599.255786 221.6752 
L 596.584137 220.890865 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f5f2f2"/>
    <path d="M 606.283681 221.405346 
L 608.970049 222.527058 
L 610.638452 220.468326 
L 607.953096 219.345301 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9f7f7"/>
    <path d="M 820.657252 489.37831 
L 823.40856 491.774259 
L 824.912485 491.256501 
L 822.163892 488.846817 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1868ce"/>
    <path d="M 835.931938 499.958641 
L 838.693974 501.893714 
L 840.183603 501.332629 
L 837.424077 499.389492 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2450b6"/>
    <path d="M 677.160418 265.270719 
L 679.903233 268.703656 
L 681.533597 267.254356 
L 678.792889 263.818547 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ab938e"/>
    <path d="M 753.752699 404.317807 
L 756.490579 408.353119 
L 758.061434 407.237056 
L 755.3262 403.174822 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #75e37d"/>
    <path d="M 639.97676 230.181542 
L 642.697984 232.416315 
L 644.353862 230.833569 
L 641.634252 228.596154 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e7e0df"/>
    <path d="M 620.388532 222.576546 
L 623.090996 224.152036 
L 624.755772 222.33102 
L 622.054568 220.752852 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f5f2f2"/>
    <path d="M 660.72521 246.389592 
L 663.461003 249.319027 
L 665.103575 247.854265 
L 662.369711 244.922695 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cbbcb9"/>
    <path d="M 716.243642 331.730166 
L 718.988716 335.936033 
L 720.589371 334.468191 
L 717.846635 330.247828 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c8b97b"/>
    <path d="M 706.866745 313.648688 
L 709.612919 317.749113 
L 711.220587 316.262909 
L 708.4767 312.15184 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a8906a"/>
    <path d="M 674.418366 261.915019 
L 677.160418 265.270719 
L 678.792889 263.818547 
L 676.052916 260.460088 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b19b96"/>
    <path d="M 663.461003 249.319027 
L 666.198386 252.33877 
L 667.838997 250.876276 
L 665.103575 247.854265 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c7b7b4"/>
    <path d="M 613.328649 221.704411 
L 616.02351 223.053089 
L 617.690343 221.11298 
L 614.996612 219.762061 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f7f5f4"/>
    <path d="M 671.677235 258.63934 
L 674.418366 261.915019 
L 676.052916 260.460088 
L 673.313835 257.181765 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b7a39f"/>
    <path d="M 694.748802 292.247108 
L 697.495177 296.130003 
L 699.112078 294.647677 
L 696.367924 290.758061 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #846257"/>
    <path d="M 666.198386 252.33877 
L 668.937186 255.446384 
L 670.575807 253.986287 
L 667.838997 250.876276 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c1b0ac"/>
    <path d="M 668.937186 255.446384 
L 671.677235 258.63934 
L 673.313835 257.181765 
L 670.575807 253.986287 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bba8a4"/>
    <path d="M 765.871672 425.103475 
L 768.608765 428.915274 
L 770.16864 427.97372 
L 767.434302 424.133874 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2dd56f"/>
    <path d="M 741.635356 382.477113 
L 744.37561 386.657266 
L 745.956879 385.39052 
L 743.219158 381.185613 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c1f38d"/>
    <path d="M 732.256977 364.262358 
L 734.999232 368.501855 
L 736.587958 367.135755 
L 733.848153 362.874565 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 630.170175 225.821161 
L 632.883001 227.731052 
L 634.543765 226.031032 
L 631.832372 224.118117 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1edec"/>
    <path d="M 865.333703 511.86704 
L 868.125263 512.889856 
L 869.593187 512.047729 
L 866.803596 511.025228 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #30389e"/>
    <path d="M 823.40856 491.774259 
L 826.162174 494.078793 
L 827.663408 493.573874 
L 824.912485 491.256501 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1a66cc"/>
    <path d="M 848.482534 506.562777 
L 851.256255 508.103502 
L 852.735475 507.463723 
L 849.964055 505.91906 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2b43a9"/>
    <path d="M 751.01392 400.252694 
L 753.752699 404.317807 
L 755.3262 403.174822 
L 752.590047 399.082483 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #85e781"/>
    <path d="M 642.697984 232.416315 
L 645.42211 234.755356 
L 647.076338 233.175516 
L 644.353862 230.833569 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e5dedc"/>
    <path d="M 722.877517 345.864254 
L 725.621846 350.104643 
L 727.217788 348.666126 
L 724.475835 344.407547 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e0d788"/>
    <path d="M 692.002251 288.419876 
L 694.748802 292.247108 
L 696.367924 290.758061 
L 693.62357 286.92424 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #836059"/>
    <path d="M 704.119903 309.58696 
L 706.866745 313.648688 
L 708.4767 312.15184 
L 705.732123 308.079587 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a08566"/>
    <path d="M 601.932824 222.571554 
L 604.615083 223.579848 
L 606.283681 221.405346 
L 603.602349 220.396258 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f7f5f4"/>
    <path d="M 713.49763 327.548927 
L 716.243642 331.730166 
L 717.846635 330.247828 
L 715.102937 326.05218 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c0ae77"/>
    <path d="M 763.134036 421.247023 
L 765.871672 425.103475 
L 767.434302 424.133874 
L 764.699405 420.248895 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #3dd872"/>
    <path d="M 838.693974 501.893714 
L 841.459247 503.730384 
L 842.946396 503.176515 
L 840.183603 501.332629 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #264eb4"/>
    <path d="M 858.290672 510.242474 
L 861.07483 511.47545 
L 862.546997 510.738368 
L 859.764955 509.504167 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2f3ba1"/>
    <path d="M 794.437595 464.591388 
L 797.178502 467.710815 
L 798.709554 467.113022 
L 795.971529 463.970145 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a0e8"/>
    <path d="M 791.697395 461.399665 
L 794.437595 464.591388 
L 795.971529 463.970145 
L 793.234211 460.754158 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a4dc"/>
    <path d="M 797.178502 467.710815 
L 799.920255 470.755784 
L 801.448429 470.180608 
L 798.709554 467.113022 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #009afa"/>
    <path d="M 788.957764 458.137877 
L 791.697395 461.399665 
L 793.234211 460.754158 
L 790.49746 457.467316 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00aacb"/>
    <path d="M 738.894007 378.283323 
L 741.635356 382.477113 
L 743.219158 381.185613 
L 740.480319 376.966923 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d1f690"/>
    <path d="M 623.090996 224.152036 
L 625.79755 225.8386 
L 627.461037 224.020782 
L 624.755772 222.33102 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f3f0ef"/>
    <path d="M 645.42211 234.755356 
L 648.148948 237.196962 
L 649.801494 235.620289 
L 647.076338 233.175516 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e1d9d7"/>
    <path d="M 799.920255 470.755784 
L 802.663002 473.724209 
L 804.188301 473.170796 
L 801.448429 470.180608 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0296fc"/>
    <path d="M 689.255647 284.651546 
L 692.002251 288.419876 
L 693.62357 286.92424 
L 690.879136 283.149459 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #896861"/>
    <path d="M 786.218568 454.808329 
L 788.957764 458.137877 
L 790.49746 457.467316 
L 787.761142 454.111946 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b0b9"/>
    <path d="M 826.162174 494.078793 
L 828.918271 496.290532 
L 830.416837 495.797545 
L 827.663408 493.573874 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1c60c6"/>
    <path d="M 729.513587 360.022836 
L 732.256977 364.262358 
L 733.848153 362.874565 
L 731.107189 358.613313 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f8f695"/>
    <path d="M 632.883001 227.731052 
L 635.599325 229.749229 
L 637.258624 228.052624 
L 634.543765 226.031032 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ede8e7"/>
    <path d="M 748.274195 396.160978 
L 751.01392 400.252694 
L 752.590047 399.082483 
L 749.852924 394.963264 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #91e983"/>
    <path d="M 608.970049 222.527058 
L 611.66128 223.761058 
L 613.328649 221.704411 
L 610.638452 220.468326 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f7f5f4"/>
    <path d="M 783.479681 451.413394 
L 786.218568 454.808329 
L 787.761142 454.111946 
L 785.025126 450.690444 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b6a7"/>
    <path d="M 802.663002 473.724209 
L 805.406892 476.614078 
L 806.929324 476.081554 
L 804.188301 473.170796 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #068ef4"/>
    <path d="M 760.395778 417.348864 
L 763.134036 421.247023 
L 764.699405 420.248895 
L 761.963867 416.321754 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #49db75"/>
    <path d="M 701.372486 305.56736 
L 704.119903 309.58696 
L 705.732123 308.079587 
L 702.986944 304.049596 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9a7e62"/>
    <path d="M 720.132127 341.637852 
L 722.877517 345.864254 
L 724.475835 344.407547 
L 721.732797 340.163003 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d8cd84"/>
    <path d="M 616.02351 223.053089 
L 618.722854 224.513768 
L 620.388532 222.576546 
L 617.690343 221.11298 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f7f5f4"/>
    <path d="M 597.586371 223.964403 
L 600.264259 224.86072 
L 601.932824 222.571554 
L 599.255786 221.6752 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f5f2f2"/>
    <path d="M 710.750745 323.395822 
L 713.49763 327.548927 
L 715.102937 326.05218 
L 712.358342 321.884772 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b8a473"/>
    <path d="M 780.74098 447.955513 
L 783.479681 451.413394 
L 785.025126 450.690444 
L 782.289288 447.205276 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00bc94"/>
    <path d="M 805.406892 476.614078 
L 808.152079 479.423457 
L 809.671652 478.91093 
L 806.929324 476.081554 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0888ee"/>
    <path d="M 686.509117 280.945298 
L 689.255647 284.651546 
L 690.879136 283.149459 
L 688.134751 279.436908 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #91726c"/>
    <path d="M 648.148948 237.196962 
L 650.878312 239.739317 
L 652.529143 238.166067 
L 649.801494 235.620289 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ddd3d1"/>
    <path d="M 851.256255 508.103502 
L 854.033996 509.541673 
L 855.51095 508.905062 
L 852.735475 507.463723 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2c40a6"/>
    <path d="M 778.002346 444.437192 
L 780.74098 447.955513 
L 782.289288 447.205276 
L 779.553508 443.658973 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c382"/>
    <path d="M 736.15155 374.079281 
L 738.894007 378.283323 
L 740.480319 376.966923 
L 737.740346 372.73786 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e1f993"/>
    <path d="M 808.152079 479.423457 
L 810.89872 482.150489 
L 812.415445 481.657048 
L 809.671652 478.91093 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0b83e9"/>
    <path d="M 841.459247 503.730384 
L 844.22794 505.467697 
L 845.712644 504.920188 
L 842.946396 503.176515 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #274bb1"/>
    <path d="M 757.656826 413.411989 
L 760.395778 417.348864 
L 761.963867 416.321754 
L 759.227614 412.355473 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #59de78"/>
    <path d="M 828.918271 496.290532 
L 831.677029 498.408179 
L 833.172953 497.926207 
L 830.416837 495.797545 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1f5bc1"/>
    <path d="M 683.762794 277.304258 
L 686.509117 280.945298 
L 688.134751 279.436908 
L 685.390545 275.789721 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #977a74"/>
    <path d="M 745.533483 392.045894 
L 748.274195 396.160978 
L 749.852924 394.963264 
L 747.11479 390.820426 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a1ec86"/>
    <path d="M 698.62459 301.593287 
L 701.372486 305.56736 
L 702.986944 304.049596 
L 700.241261 300.065276 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #92735e"/>
    <path d="M 726.769078 355.786768 
L 729.513587 360.022836 
L 731.107189 358.613313 
L 728.365079 354.355502 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f0ec91"/>
    <path d="M 635.599325 229.749229 
L 638.318958 231.874347 
L 639.97676 230.181542 
L 637.258624 228.052624 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ebe5e4"/>
    <path d="M 650.878312 239.739317 
L 653.610019 242.380497 
L 655.2591 240.810919 
L 652.529143 238.166067 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d9cecc"/>
    <path d="M 775.263667 440.861002 
L 778.002346 444.437192 
L 779.553508 443.658973 
L 776.817672 440.054131 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c970"/>
    <path d="M 868.125263 512.889856 
L 870.921864 513.806585 
L 872.38786 512.963566 
L 869.593187 512.047729 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #30389e"/>
    <path d="M 593.244782 225.580377 
L 595.918055 226.366642 
L 597.586371 223.964403 
L 594.913882 223.179093 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f3f0ef"/>
    <path d="M 625.79755 225.8386 
L 628.508008 227.635264 
L 630.170175 225.821161 
L 627.461037 224.020782 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1edec"/>
    <path d="M 717.38572 337.428955 
L 720.132127 341.637852 
L 721.732797 340.163003 
L 718.988716 335.936033 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d0c380"/>
    <path d="M 810.89872 482.150489 
L 813.646974 484.793394 
L 815.160865 484.318113 
L 812.415445 481.657048 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0f7be1"/>
    <path d="M 708.003058 319.274344 
L 710.750745 323.395822 
L 712.358342 321.884772 
L 709.612919 317.749113 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b09a6e"/>
    <path d="M 681.016818 273.731488 
L 683.762794 277.304258 
L 685.390545 275.789721 
L 682.646658 272.210968 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9d827c"/>
    <path d="M 604.615083 223.579848 
L 607.302396 224.699873 
L 608.970049 222.527058 
L 606.283681 221.405346 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f7f5f4"/>
    <path d="M 653.610019 242.380497 
L 656.343883 245.118471 
L 657.991183 243.552808 
L 655.2591 240.810919 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d5c9c7"/>
    <path d="M 861.07483 511.47545 
L 863.863613 512.603574 
L 865.333703 511.86704 
L 862.546997 510.738368 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2f3ba1"/>
    <path d="M 772.524836 437.229576 
L 775.263667 440.861002 
L 776.817672 440.054131 
L 774.081671 436.39341 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #09ce68"/>
    <path d="M 754.917112 409.439438 
L 757.656826 413.411989 
L 759.227614 412.355473 
L 756.490579 408.353119 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #69e17b"/>
    <path d="M 695.87632 297.668101 
L 698.62459 301.593287 
L 700.241261 300.065276 
L 697.495177 296.130003 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8a695a"/>
    <path d="M 678.271332 270.229986 
L 681.016818 273.731488 
L 682.646658 272.210968 
L 679.903233 268.703656 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a38984"/>
    <path d="M 618.722854 224.513768 
L 621.426499 226.085729 
L 623.090996 224.152036 
L 620.388532 222.576546 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f5f2f2"/>
    <path d="M 813.646974 484.793394 
L 816.397007 487.350476 
L 817.908078 486.892411 
L 815.160865 484.318113 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1276dc"/>
    <path d="M 733.407977 369.868392 
L 736.15155 374.079281 
L 737.740346 372.73786 
L 734.999232 368.501855 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1fc96"/>
    <path d="M 611.66128 223.761058 
L 614.357196 225.106883 
L 616.02351 223.053089 
L 613.328649 221.704411 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f5f2f2"/>
    <path d="M 656.343883 245.118471 
L 659.079725 247.951101 
L 660.72521 246.389592 
L 657.991183 243.552808 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cfc2bf"/>
    <path d="M 742.79175 387.910709 
L 745.533483 392.045894 
L 747.11479 390.820426 
L 744.37561 386.657266 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b1ef89"/>
    <path d="M 638.318958 231.874347 
L 641.041714 234.104941 
L 642.697984 232.416315 
L 639.97676 230.181542 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e7e0df"/>
    <path d="M 831.677029 498.408179 
L 834.438627 500.430525 
L 835.931938 499.958641 
L 833.172953 497.926207 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2058be"/>
    <path d="M 675.526485 266.802678 
L 678.271332 270.229986 
L 679.903233 268.703656 
L 677.160418 265.270719 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a9918c"/>
    <path d="M 724.023472 351.557642 
L 726.769078 355.786768 
L 728.365079 354.355502 
L 725.621846 350.104643 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e8e28d"/>
    <path d="M 769.785752 433.545608 
L 772.524836 437.229576 
L 774.081671 436.39341 
L 771.345401 432.679532 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #15d06a"/>
    <path d="M 659.079725 247.951101 
L 661.817364 250.87615 
L 663.461003 249.319027 
L 660.72521 246.389592 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cbbcb9"/>
    <path d="M 705.254646 315.187963 
L 708.003058 319.274344 
L 709.612919 317.749113 
L 706.866745 313.648688 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a8906a"/>
    <path d="M 672.782431 263.452418 
L 675.526485 266.802678 
L 677.160418 265.270719 
L 674.418366 261.915019 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #af9994"/>
    <path d="M 714.638346 333.241074 
L 717.38572 337.428955 
L 718.988716 335.936033 
L 716.243642 331.730166 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c8b97b"/>
    <path d="M 844.22794 505.467697 
L 847.000241 507.104787 
L 848.482534 506.562777 
L 845.712644 504.920188 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2848ae"/>
    <path d="M 661.817364 250.87615 
L 664.556626 253.891282 
L 666.198386 252.33877 
L 663.461003 249.319027 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c5b5b1"/>
    <path d="M 670.039328 260.181983 
L 672.782431 263.452418 
L 674.418366 261.915019 
L 671.677235 258.63934 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b5a09c"/>
    <path d="M 628.508008 227.635264 
L 631.222184 229.54093 
L 632.883001 227.731052 
L 630.170175 225.821161 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #efebea"/>
    <path d="M 693.127785 293.795122 
L 695.87632 297.668101 
L 697.495177 296.130003 
L 694.748802 292.247108 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #846257"/>
    <path d="M 664.556626 253.891282 
L 667.297337 256.994067 
L 668.937186 255.446384 
L 666.198386 252.33877 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c1b0ac"/>
    <path d="M 667.297337 256.994067 
L 670.039328 260.181983 
L 671.677235 258.63934 
L 668.937186 255.446384 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bba8a4"/>
    <path d="M 816.397007 487.350476 
L 819.148984 489.820116 
L 820.657252 489.37831 
L 817.908078 486.892411 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1470d6"/>
    <path d="M 854.033996 509.541673 
L 856.815943 510.876692 
L 858.290672 510.242474 
L 855.51095 508.905062 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2c40a6"/>
    <path d="M 600.264259 224.86072 
L 602.947383 225.867965 
L 604.615083 223.579848 
L 601.932824 222.571554 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f5f2f2"/>
    <path d="M 752.176578 405.434299 
L 754.917112 409.439438 
L 756.490579 408.353119 
L 753.752699 404.317807 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #75e37d"/>
    <path d="M 767.046319 429.811849 
L 769.785752 433.545608 
L 771.345401 432.679532 
L 768.608765 428.915274 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #21d36d"/>
    <path d="M 641.041714 234.104941 
L 643.767403 236.439429 
L 645.42211 234.755356 
L 642.697984 232.416315 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e3dbd9"/>
    <path d="M 730.663291 365.654079 
L 733.407977 369.868392 
L 734.999232 368.501855 
L 732.256977 364.262358 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 740.04897 383.758725 
L 742.79175 387.910709 
L 744.37561 386.657266 
L 741.635356 382.477113 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c1f38d"/>
    <path d="M 721.276797 347.338952 
L 724.023472 351.557642 
L 725.621846 350.104643 
L 722.877517 345.864254 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e0d788"/>
    <path d="M 690.379102 289.977624 
L 693.127785 293.795122 
L 694.748802 292.247108 
L 692.002251 288.419876 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #836059"/>
    <path d="M 702.505594 311.140123 
L 705.254646 315.187963 
L 706.866745 313.648688 
L 704.119903 309.58696 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a28867"/>
    <path d="M 834.438627 500.430525 
L 837.203247 502.356449 
L 838.693974 501.893714 
L 835.931938 499.958641 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2256bc"/>
    <path d="M 819.148984 489.820116 
L 821.903074 492.200781 
L 823.40856 491.774259 
L 820.657252 489.37831 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #176bd1"/>
    <path d="M 764.306447 426.031106 
L 767.046319 429.811849 
L 768.608765 428.915274 
L 765.871672 425.103475 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #31d670"/>
    <path d="M 621.426499 226.085729 
L 624.134263 227.768127 
L 625.79755 225.8386 
L 623.090996 224.152036 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f3f0ef"/>
    <path d="M 711.890062 329.077711 
L 714.638346 333.241074 
L 716.243642 331.730166 
L 713.49763 327.548927 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c0ae77"/>
    <path d="M 607.302396 224.699873 
L 609.99459 225.931296 
L 611.66128 223.761058 
L 608.970049 222.527058 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f5f2f2"/>
    <path d="M 595.918055 226.366642 
L 598.596735 227.262787 
L 600.264259 224.86072 
L 597.586371 223.964403 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f3f0ef"/>
    <path d="M 749.435171 401.399697 
L 752.176578 405.434299 
L 753.752699 404.317807 
L 751.01392 400.252694 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #85e781"/>
    <path d="M 614.357196 225.106883 
L 617.05762 226.563945 
L 618.722854 224.513768 
L 616.02351 223.053089 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f5f2f2"/>
    <path d="M 631.222184 229.54093 
L 633.93989 231.55438 
L 635.599325 229.749229 
L 632.883001 227.731052 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ede8e7"/>
    <path d="M 643.767403 236.439429 
L 646.495838 238.876116 
L 648.148948 237.196962 
L 645.42211 234.755356 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dfd6d4"/>
    <path d="M 863.863613 512.603574 
L 866.657207 513.626522 
L 868.125263 512.889856 
L 865.333703 511.86704 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2f3ba1"/>
    <path d="M 687.630394 286.218831 
L 690.379102 289.977624 
L 692.002251 288.419876 
L 689.255647 284.651546 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #896861"/>
    <path d="M 737.305123 379.59327 
L 740.04897 383.758725 
L 741.635356 382.477113 
L 738.894007 378.283323 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d1f690"/>
    <path d="M 761.566054 422.206241 
L 764.306447 426.031106 
L 765.871672 425.103475 
L 763.134036 421.247023 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #3dd872"/>
    <path d="M 727.9175 361.439783 
L 730.663291 365.654079 
L 732.256977 364.262358 
L 729.513587 360.022836 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f8f695"/>
    <path d="M 847.000241 507.104787 
L 849.776336 508.64088 
L 851.256255 508.103502 
L 848.482534 506.562777 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2a46ac"/>
    <path d="M 699.755994 307.134239 
L 702.505594 311.140123 
L 704.119903 309.58696 
L 701.372486 305.56736 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9a7e62"/>
    <path d="M 591.576909 228.093619 
L 594.250911 228.880821 
L 595.918055 226.366642 
L 593.244782 225.580377 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1edec"/>
    <path d="M 821.903074 492.200781 
L 824.659449 494.491018 
L 826.162174 494.078793 
L 823.40856 491.774259 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1868ce"/>
    <path d="M 718.529091 343.134193 
L 721.276797 347.338952 
L 722.877517 345.864254 
L 720.132127 341.637852 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d8cd84"/>
    <path d="M 646.495838 238.876116 
L 649.226833 241.413194 
L 650.878312 239.739317 
L 648.148948 237.196962 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dbd1cf"/>
    <path d="M 709.140933 324.942354 
L 711.890062 329.077711 
L 713.49763 327.548927 
L 710.750745 323.395822 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b8a473"/>
    <path d="M 684.881788 282.521913 
L 687.630394 286.218831 
L 689.255647 284.651546 
L 686.509117 280.945298 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #91726c"/>
    <path d="M 746.692843 397.338801 
L 749.435171 401.399697 
L 751.01392 400.252694 
L 748.274195 396.160978 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #95ea84"/>
    <path d="M 856.815943 510.876692 
L 859.602286 512.108054 
L 861.07483 511.47545 
L 858.290672 510.242474 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2e3ea4"/>
    <path d="M 837.203247 502.356449 
L 839.97107 504.184915 
L 841.459247 503.730384 
L 838.693974 501.893714 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2450b6"/>
    <path d="M 602.947383 225.867965 
L 605.635573 226.985933 
L 607.302396 224.699873 
L 604.615083 223.579848 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f5f2f2"/>
    <path d="M 790.158269 461.976357 
L 792.901401 465.141452 
L 794.437595 464.591388 
L 791.697395 461.399665 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a6d7"/>
    <path d="M 758.825061 418.340167 
L 761.566054 422.206241 
L 763.134036 421.247023 
L 760.395778 417.348864 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #4ddb75"/>
    <path d="M 792.901401 465.141452 
L 795.64524 468.235137 
L 797.178502 467.710815 
L 794.437595 464.591388 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a2e2"/>
    <path d="M 787.415711 458.742061 
L 790.158269 461.976357 
L 791.697395 461.399665 
L 788.957764 458.137877 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00acc4"/>
    <path d="M 624.134263 227.768127 
L 626.84596 229.559995 
L 628.508008 227.635264 
L 625.79755 225.8386 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1edec"/>
    <path d="M 633.93989 231.55438 
L 636.660937 233.674274 
L 638.318958 231.874347 
L 635.599325 229.749229 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e9e3e2"/>
    <path d="M 795.64524 468.235137 
L 798.389926 471.255276 
L 799.920255 470.755784 
L 797.178502 467.710815 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #009cf4"/>
    <path d="M 784.673595 455.440843 
L 787.415711 458.742061 
L 788.957764 458.137877 
L 786.218568 454.808329 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b2b2"/>
    <path d="M 682.13342 278.889984 
L 684.881788 282.521913 
L 686.509117 280.945298 
L 683.762794 277.304258 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #977a74"/>
    <path d="M 649.226833 241.413194 
L 651.960203 244.048745 
L 653.610019 242.380497 
L 650.878312 239.739317 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d7ccc9"/>
    <path d="M 697.005944 303.173694 
L 699.755994 307.134239 
L 701.372486 305.56736 
L 698.62459 301.593287 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #92735e"/>
    <path d="M 798.389926 471.255276 
L 801.135603 474.199802 
L 802.663002 473.724209 
L 799.920255 470.755784 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0098fe"/>
    <path d="M 734.560197 375.417697 
L 737.305123 379.59327 
L 738.894007 378.283323 
L 736.15155 374.079281 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e1f993"/>
    <path d="M 781.931796 452.075051 
L 784.673595 455.440843 
L 786.218568 454.808329 
L 783.479681 451.413394 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b8a0"/>
    <path d="M 824.659449 494.491018 
L 827.418284 496.689459 
L 828.918271 496.290532 
L 826.162174 494.078793 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1b63c9"/>
    <path d="M 725.170619 357.228956 
L 727.9175 361.439783 
L 729.513587 360.022836 
L 726.769078 355.786768 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f0ec91"/>
    <path d="M 609.99459 225.931296 
L 612.691489 227.27366 
L 614.357196 225.106883 
L 611.66128 223.761058 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f5f2f2"/>
    <path d="M 801.135603 474.199802 
L 803.882418 477.066727 
L 805.406892 476.614078 
L 802.663002 473.724209 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0490f6"/>
    <path d="M 617.05762 226.563945 
L 619.762371 228.131531 
L 621.426499 226.085729 
L 618.722854 224.513768 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f3f0ef"/>
    <path d="M 715.780396 338.946857 
L 718.529091 343.134193 
L 720.132127 341.637852 
L 717.38572 337.428955 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d0c380"/>
    <path d="M 779.190192 448.647098 
L 781.931796 452.075051 
L 783.479681 451.413394 
L 780.74098 447.955513 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00be8f"/>
    <path d="M 706.391031 320.838474 
L 709.140933 324.942354 
L 710.750745 323.395822 
L 708.003058 319.274344 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b09a6e"/>
    <path d="M 679.385428 275.326093 
L 682.13342 278.889984 
L 683.762794 277.304258 
L 681.016818 273.731488 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9d827c"/>
    <path d="M 743.949557 393.254813 
L 746.692843 397.338801 
L 748.274195 396.160978 
L 745.533483 392.045894 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a1ec86"/>
    <path d="M 651.960203 244.048745 
L 654.695764 246.780746 
L 656.343883 245.118471 
L 653.610019 242.380497 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d3c7c4"/>
    <path d="M 756.083397 414.435846 
L 758.825061 418.340167 
L 760.395778 417.348864 
L 757.656826 413.411989 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #59de78"/>
    <path d="M 803.882418 477.066727 
L 806.630523 479.854136 
L 808.152079 479.423457 
L 805.406892 476.614078 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #078bf1"/>
    <path d="M 776.448668 445.159465 
L 779.190192 448.647098 
L 780.74098 447.955513 
L 778.002346 444.437192 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c47d"/>
    <path d="M 598.596735 227.262787 
L 601.280659 228.268732 
L 602.947383 225.867965 
L 600.264259 224.86072 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f3f0ef"/>
    <path d="M 676.637956 271.833226 
L 679.385428 275.326093 
L 681.016818 273.731488 
L 678.271332 270.229986 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a38984"/>
    <path d="M 694.255548 299.261833 
L 697.005944 303.173694 
L 698.62459 301.593287 
L 695.87632 297.668101 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8c6c5b"/>
    <path d="M 636.660937 233.674274 
L 639.385138 235.899155 
L 641.041714 234.104941 
L 638.318958 231.874347 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e5dedc"/>
    <path d="M 654.695764 246.780746 
L 657.433335 249.607069 
L 659.079725 247.951101 
L 656.343883 245.118471 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cfc2bf"/>
    <path d="M 849.776336 508.64088 
L 852.556412 510.075291 
L 854.033996 509.541673 
L 851.256255 508.103502 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2a46ac"/>
    <path d="M 673.891155 268.4143 
L 676.637956 271.833226 
L 678.271332 270.229986 
L 675.526485 266.802678 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a9918c"/>
    <path d="M 773.707115 441.614693 
L 776.448668 445.159465 
L 778.002346 444.437192 
L 775.263667 440.861002 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00cb6b"/>
    <path d="M 806.630523 479.854136 
L 809.380072 482.560191 
L 810.89872 482.150489 
L 808.152079 479.423457 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0a86ec"/>
    <path d="M 866.657207 513.626522 
L 869.455802 514.544064 
L 870.921864 513.806585 
L 868.125263 512.889856 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2f3ba1"/>
    <path d="M 626.84596 229.559995 
L 629.561404 231.460242 
L 631.222184 229.54093 
L 628.508008 227.635264 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ede8e7"/>
    <path d="M 839.97107 504.184915 
L 842.742282 505.914978 
L 844.22794 505.467697 
L 841.459247 503.730384 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #264eb4"/>
    <path d="M 657.433335 249.607069 
L 660.172737 252.525486 
L 661.817364 250.87615 
L 659.079725 247.951101 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cbbcb9"/>
    <path d="M 731.814186 371.235383 
L 734.560197 375.417697 
L 736.15155 374.079281 
L 733.407977 369.868392 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1fc96"/>
    <path d="M 827.418284 496.689459 
L 830.179753 498.79482 
L 831.677029 498.408179 
L 828.918271 496.290532 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1c60c6"/>
    <path d="M 722.42267 353.025059 
L 725.170619 357.228956 
L 726.769078 355.786768 
L 724.023472 351.557642 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e8e28d"/>
    <path d="M 671.145177 265.072156 
L 673.891155 268.4143 
L 675.526485 266.802678 
L 672.782431 263.452418 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #af9994"/>
    <path d="M 703.640434 316.76952 
L 706.391031 320.838474 
L 708.003058 319.274344 
L 705.254646 315.187963 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #aa926b"/>
    <path d="M 753.340999 410.496287 
L 756.083397 414.435846 
L 757.656826 413.411989 
L 754.917112 409.439438 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #69e17b"/>
    <path d="M 660.172737 252.525486 
L 662.913794 255.533669 
L 664.556626 253.891282 
L 661.817364 250.87615 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c5b5b1"/>
    <path d="M 741.205279 389.150972 
L 743.949557 393.254813 
L 745.533483 392.045894 
L 742.79175 387.910709 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b1ef89"/>
    <path d="M 713.030765 334.780432 
L 715.780396 338.946857 
L 717.38572 337.428955 
L 714.638346 333.241074 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c8b97b"/>
    <path d="M 668.400182 261.809561 
L 671.145177 265.072156 
L 672.782431 263.452418 
L 670.039328 260.181983 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b5a09c"/>
    <path d="M 662.913794 255.533669 
L 665.656332 258.629198 
L 667.297337 256.994067 
L 664.556626 253.891282 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bfada9"/>
    <path d="M 665.656332 258.629198 
L 668.400182 261.809561 
L 670.039328 260.181983 
L 667.297337 256.994067 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bba8a4"/>
    <path d="M 691.504918 295.401958 
L 694.255548 299.261833 
L 695.87632 297.668101 
L 693.127785 293.795122 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #846257"/>
    <path d="M 770.965425 438.015387 
L 773.707115 441.614693 
L 775.263667 440.861002 
L 772.524836 437.229576 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #09ce68"/>
    <path d="M 594.250911 228.880821 
L 596.930323 229.776659 
L 598.596735 227.262787 
L 595.918055 226.366642 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1edec"/>
    <path d="M 809.380072 482.560191 
L 812.131224 485.183133 
L 813.646974 484.793394 
L 810.89872 482.150489 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0c80e6"/>
    <path d="M 859.602286 512.108054 
L 862.393212 513.235344 
L 863.863613 512.603574 
L 861.07483 511.47545 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2e3ea4"/>
    <path d="M 605.635573 226.985933 
L 608.328661 228.214293 
L 609.99459 225.931296 
L 607.302396 224.699873 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f3f0ef"/>
    <path d="M 639.385138 235.899155 
L 642.112305 238.22745 
L 643.767403 236.439429 
L 641.041714 234.104941 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e3dbd9"/>
    <path d="M 619.762371 228.131531 
L 622.471265 229.808802 
L 624.134263 227.768127 
L 621.426499 226.085729 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1edec"/>
    <path d="M 768.223502 434.36421 
L 770.965425 438.015387 
L 772.524836 437.229576 
L 769.785752 433.545608 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #19d16b"/>
    <path d="M 612.691489 227.27366 
L 615.392918 228.726381 
L 617.05762 226.563945 
L 614.357196 225.106883 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f3f0ef"/>
    <path d="M 589.910332 230.717599 
L 592.585008 231.505718 
L 594.250911 228.880821 
L 591.576909 228.093619 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ede8e7"/>
    <path d="M 750.597806 406.524544 
L 753.340999 410.496287 
L 754.917112 409.439438 
L 752.176578 405.434299 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #79e47e"/>
    <path d="M 688.75417 291.597328 
L 691.504918 295.401958 
L 693.127785 293.795122 
L 690.379102 289.977624 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #815e56"/>
    <path d="M 729.067093 367.049723 
L 731.814186 371.235383 
L 733.407977 369.868392 
L 730.663291 365.654079 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 812.131224 485.183133 
L 814.88414 487.721281 
L 816.397007 487.350476 
L 813.646974 484.793394 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0f7be1"/>
    <path d="M 700.889228 312.738919 
L 703.640434 316.76952 
L 705.254646 315.187963 
L 702.505594 311.140123 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a28867"/>
    <path d="M 719.673685 348.831558 
L 722.42267 353.025059 
L 724.023472 351.557642 
L 721.276797 347.338952 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e0d788"/>
    <path d="M 629.561404 231.460242 
L 632.280407 233.467657 
L 633.93989 231.55438 
L 631.222184 229.54093 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ebe5e4"/>
    <path d="M 738.459984 385.030546 
L 741.205279 389.150972 
L 742.79175 387.910709 
L 740.04897 383.758725 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c1f38d"/>
    <path d="M 830.179753 498.79482 
L 832.944036 500.805904 
L 834.438627 500.430525 
L 831.677029 498.408179 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1f5bc1"/>
    <path d="M 710.280255 330.638397 
L 713.030765 334.780432 
L 714.638346 333.241074 
L 711.890062 329.077711 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c0ae77"/>
    <path d="M 642.112305 238.22745 
L 644.84225 240.657472 
L 646.495838 238.876116 
L 643.767403 236.439429 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dfd6d4"/>
    <path d="M 765.481249 430.663883 
L 768.223502 434.36421 
L 769.785752 433.545608 
L 767.046319 429.811849 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #25d36d"/>
    <path d="M 842.742282 505.914978 
L 845.517064 507.545779 
L 847.000241 507.104787 
L 844.22794 505.467697 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #274bb1"/>
    <path d="M 852.556412 510.075291 
L 855.340655 511.407427 
L 856.815943 510.876692 
L 854.033996 509.541673 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2b43a9"/>
    <path d="M 686.003428 287.851151 
L 688.75417 291.597328 
L 690.379102 289.977624 
L 687.630394 286.218831 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #896861"/>
    <path d="M 601.280659 228.268732 
L 603.969661 229.384274 
L 605.635573 226.985933 
L 602.947383 225.867965 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1edec"/>
    <path d="M 814.88414 487.721281 
L 817.638985 490.173035 
L 819.148984 489.820116 
L 816.397007 487.350476 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1276dc"/>
    <path d="M 747.853769 402.523711 
L 750.597806 406.524544 
L 752.176578 405.434299 
L 749.435171 401.399697 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #85e781"/>
    <path d="M 698.137504 308.750063 
L 700.889228 312.738919 
L 702.505594 311.140123 
L 699.755994 307.134239 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9a7e62"/>
    <path d="M 762.738581 426.917182 
L 765.481249 430.663883 
L 767.046319 429.811849 
L 764.306447 426.031106 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #31d670"/>
    <path d="M 644.84225 240.657472 
L 647.574788 243.187422 
L 649.226833 241.413194 
L 646.495838 238.876116 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dbd1cf"/>
    <path d="M 726.318926 362.864125 
L 729.067093 367.049723 
L 730.663291 365.654079 
L 727.9175 361.439783 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f8f695"/>
    <path d="M 622.471265 229.808802 
L 625.184118 231.594798 
L 626.84596 229.559995 
L 624.134263 227.768127 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #efebea"/>
    <path d="M 683.252819 284.166581 
L 686.003428 287.851151 
L 687.630394 286.218831 
L 684.881788 282.521913 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8f7069"/>
    <path d="M 735.713654 380.896832 
L 738.459984 385.030546 
L 740.04897 383.758725 
L 737.305123 379.59327 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d1f690"/>
    <path d="M 716.9237 344.651921 
L 719.673685 348.831558 
L 721.276797 347.338952 
L 718.529091 343.134193 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d8cd84"/>
    <path d="M 707.528932 326.524214 
L 710.280255 330.638397 
L 711.890062 329.077711 
L 709.140933 324.942354 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b8a473"/>
    <path d="M 632.280407 233.467657 
L 635.002782 235.580909 
L 636.660937 233.674274 
L 633.93989 231.55438 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e7e0df"/>
    <path d="M 608.328661 228.214293 
L 611.026471 229.552591 
L 612.691489 227.27366 
L 609.99459 225.931296 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1edec"/>
    <path d="M 832.944036 500.805904 
L 835.711309 502.721599 
L 837.203247 502.356449 
L 834.438627 500.430525 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2058be"/>
    <path d="M 817.638985 490.173035 
L 820.395924 492.536877 
L 821.903074 492.200781 
L 819.148984 489.820116 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1470d6"/>
    <path d="M 615.392918 228.726381 
L 618.098694 230.288751 
L 619.762371 228.131531 
L 617.05762 226.563945 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1edec"/>
    <path d="M 596.930323 229.776659 
L 599.614985 230.781055 
L 601.280659 228.268732 
L 598.596735 227.262787 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #efebea"/>
    <path d="M 647.574788 243.187422 
L 650.309734 245.815394 
L 651.960203 244.048745 
L 649.226833 241.413194 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d7ccc9"/>
    <path d="M 759.995414 423.126935 
L 762.738581 426.917182 
L 764.306447 426.031106 
L 761.566054 422.206241 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #41d973"/>
    <path d="M 680.502479 280.546715 
L 683.252819 284.166581 
L 684.881788 282.521913 
L 682.13342 278.889984 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #957771"/>
    <path d="M 862.393212 513.235344 
L 865.188908 514.25824 
L 866.657207 513.626522 
L 863.863613 512.603574 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2e3ea4"/>
    <path d="M 695.385362 304.806317 
L 698.137504 308.750063 
L 699.755994 307.134239 
L 697.005944 303.173694 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #92735e"/>
    <path d="M 745.108843 398.496922 
L 747.853769 402.523711 
L 749.435171 401.399697 
L 746.692843 397.338801 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #95ea84"/>
    <path d="M 650.309734 245.815394 
L 653.046904 248.539373 
L 654.695764 246.780746 
L 651.960203 244.048745 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d3c7c4"/>
    <path d="M 677.752548 276.994591 
L 680.502479 280.546715 
L 682.13342 278.889984 
L 679.385428 275.326093 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9d827c"/>
    <path d="M 723.569703 358.682013 
L 726.318926 362.864125 
L 727.9175 361.439783 
L 725.170619 357.228956 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f0ec91"/>
    <path d="M 704.776868 322.441332 
L 707.528932 326.524214 
L 709.140933 324.942354 
L 706.391031 320.838474 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b29c6f"/>
    <path d="M 845.517064 507.545779 
L 848.295604 509.07655 
L 849.776336 508.64088 
L 847.000241 507.104787 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2848ae"/>
    <path d="M 732.966277 376.753151 
L 735.713654 380.896832 
L 737.305123 379.59327 
L 734.560197 375.417697 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e1f993"/>
    <path d="M 714.17276 340.489614 
L 716.9237 344.651921 
L 718.529091 343.134193 
L 715.780396 338.946857 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d0c380"/>
    <path d="M 635.002782 235.580909 
L 637.728342 237.798551 
L 639.385138 235.899155 
L 636.660937 233.674274 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e5dedc"/>
    <path d="M 592.585008 231.505718 
L 595.265094 232.401117 
L 596.930323 229.776659 
L 594.250911 228.880821 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ede8e7"/>
    <path d="M 757.251674 419.296024 
L 759.995414 423.126935 
L 761.566054 422.206241 
L 758.825061 418.340167 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #4ddb75"/>
    <path d="M 820.395924 492.536877 
L 823.155128 494.811369 
L 824.659449 494.491018 
L 821.903074 492.200781 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #176bd1"/>
    <path d="M 653.046904 248.539373 
L 655.786118 251.357244 
L 657.433335 249.607069 
L 654.695764 246.780746 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cdbfbc"/>
    <path d="M 625.184118 231.594798 
L 627.900746 233.488438 
L 629.561404 231.460242 
L 626.84596 229.559995 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ede8e7"/>
    <path d="M 675.003169 273.513178 
L 677.752548 276.994591 
L 679.385428 275.326093 
L 676.637956 271.833226 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a38984"/>
    <path d="M 692.632906 300.911004 
L 695.385362 304.806317 
L 697.005944 303.173694 
L 694.255548 299.261833 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8c6c5b"/>
    <path d="M 855.340655 511.407427 
L 858.129252 512.636786 
L 859.602286 512.108054 
L 856.815943 510.876692 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2c40a6"/>
    <path d="M 603.969661 229.384274 
L 606.663571 230.609088 
L 608.328661 228.214293 
L 605.635573 226.985933 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1edec"/>
    <path d="M 742.362988 394.447347 
L 745.108843 398.496922 
L 746.692843 397.338801 
L 743.949557 393.254813 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a5ed87"/>
    <path d="M 672.254492 270.105377 
L 675.003169 273.513178 
L 676.637956 271.833226 
L 673.891155 268.4143 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a9918c"/>
    <path d="M 588.245115 233.450973 
L 590.92041 234.23999 
L 592.585008 231.505718 
L 589.910332 230.717599 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ebe5e4"/>
    <path d="M 655.786118 251.357244 
L 658.527196 254.266788 
L 660.172737 252.525486 
L 657.433335 249.607069 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c9bab7"/>
    <path d="M 788.616756 462.484944 
L 791.362864 465.621066 
L 792.901401 465.141452 
L 790.158269 461.976357 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00aacb"/>
    <path d="M 785.871227 459.280555 
L 788.616756 462.484944 
L 790.158269 461.976357 
L 787.415711 458.742061 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00aebf"/>
    <path d="M 791.362864 465.621066 
L 794.109685 468.68674 
L 795.64524 468.235137 
L 792.901401 465.141452 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a4dc"/>
    <path d="M 835.711309 502.721599 
L 838.481755 504.540879 
L 839.97107 504.184915 
L 837.203247 502.356449 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2256bc"/>
    <path d="M 783.126149 456.010153 
L 785.871227 459.280555 
L 787.415711 458.742061 
L 784.673595 455.440843 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b4ac"/>
    <path d="M 794.109685 468.68674 
L 796.857354 471.679853 
L 798.389926 471.255276 
L 795.64524 468.235137 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #009eef"/>
    <path d="M 669.506673 266.774017 
L 672.254492 270.105377 
L 673.891155 268.4143 
L 671.145177 265.072156 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #af9994"/>
    <path d="M 658.527196 254.266788 
L 661.269962 257.265691 
L 662.913794 255.533669 
L 660.172737 252.525486 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c5b5b1"/>
    <path d="M 754.507291 415.427377 
L 757.251674 419.296024 
L 758.825061 418.340167 
L 756.083397 414.435846 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #5ddf79"/>
    <path d="M 780.3814 452.676056 
L 783.126149 456.010153 
L 784.673595 455.440843 
L 781.931796 452.075051 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00bb9b"/>
    <path d="M 666.759869 263.521849 
L 669.506673 266.774017 
L 671.145177 265.072156 
L 668.400182 261.809561 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b5a09c"/>
    <path d="M 618.098694 230.288751 
L 620.808638 231.95994 
L 622.471265 229.808802 
L 619.762371 228.131531 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #efebea"/>
    <path d="M 661.269962 257.265691 
L 664.014243 260.351545 
L 665.656332 258.629198 
L 662.913794 255.533669 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bfada9"/>
    <path d="M 702.024141 318.393175 
L 704.776868 322.441332 
L 706.391031 320.838474 
L 703.640434 316.76952 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #aa926b"/>
    <path d="M 664.014243 260.351545 
L 666.759869 263.521849 
L 668.400182 261.809561 
L 665.656332 258.629198 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b9a5a1"/>
    <path d="M 611.026471 229.552591 
L 613.728827 231.000252 
L 615.392918 228.726381 
L 612.691489 227.27366 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1edec"/>
    <path d="M 796.857354 471.679853 
L 799.606014 474.598364 
L 801.135603 474.199802 
L 798.389926 471.255276 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #009afa"/>
    <path d="M 637.728342 237.798551 
L 640.456899 240.119019 
L 642.112305 238.22745 
L 639.385138 235.899155 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e1d9d7"/>
    <path d="M 720.819446 354.506816 
L 723.569703 358.682013 
L 725.170619 357.228956 
L 722.42267 353.025059 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e8e28d"/>
    <path d="M 730.21785 372.602847 
L 732.966277 376.753151 
L 734.560197 375.417697 
L 731.814186 371.235383 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1fc96"/>
    <path d="M 689.880247 297.067408 
L 692.632906 300.911004 
L 694.255548 299.261833 
L 691.504918 295.401958 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #846257"/>
    <path d="M 777.636859 449.28065 
L 780.3814 452.676056 
L 781.931796 452.075051 
L 779.190192 448.647098 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c088"/>
    <path d="M 711.420917 336.348097 
L 714.17276 340.489614 
L 715.780396 338.946857 
L 713.030765 334.780432 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c8b97b"/>
    <path d="M 823.155128 494.811369 
L 825.916769 496.995157 
L 827.418284 496.689459 
L 824.659449 494.491018 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1a66cc"/>
    <path d="M 799.606014 474.598364 
L 802.35581 477.440307 
L 803.882418 477.066727 
L 801.135603 474.199802 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0393f9"/>
    <path d="M 774.892414 445.826385 
L 777.636859 449.28065 
L 779.190192 448.647098 
L 776.448668 445.159465 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c677"/>
    <path d="M 739.616176 390.37819 
L 742.362988 394.447347 
L 743.949557 393.254813 
L 741.205279 389.150972 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b1ef89"/>
    <path d="M 599.614985 230.781055 
L 602.304731 231.893809 
L 603.969661 229.384274 
L 601.280659 228.268732 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #efebea"/>
    <path d="M 627.900746 233.488438 
L 630.620961 235.488518 
L 632.280407 233.467657 
L 629.561404 231.460242 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e9e3e2"/>
    <path d="M 751.762201 411.523969 
L 754.507291 415.427377 
L 756.083397 414.435846 
L 753.340999 410.496287 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #69e17b"/>
    <path d="M 802.35581 477.440307 
L 805.10689 480.203789 
L 806.630523 479.854136 
L 803.882418 477.066727 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #068ef4"/>
    <path d="M 772.147956 442.315771 
L 774.892414 445.826385 
L 776.448668 445.159465 
L 773.707115 441.614693 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #01cc66"/>
    <path d="M 687.127504 293.278767 
L 689.880247 297.067408 
L 691.504918 295.401958 
L 688.75417 291.597328 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #815e56"/>
    <path d="M 640.456899 240.119019 
L 643.188266 242.540638 
L 644.84225 240.657472 
L 642.112305 238.22745 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ddd3d1"/>
    <path d="M 848.295604 509.07655 
L 851.078085 510.506613 
L 852.556412 510.075291 
L 849.776336 508.64088 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2848ae"/>
    <path d="M 699.270839 314.383146 
L 702.024141 318.393175 
L 703.640434 316.76952 
L 700.889228 312.738919 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a28867"/>
    <path d="M 865.188908 514.25824 
L 867.989559 515.176515 
L 869.455802 514.544064 
L 866.657207 513.626522 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2e3ea4"/>
    <path d="M 718.068188 350.341971 
L 720.819446 354.506816 
L 722.42267 353.025059 
L 719.673685 348.831558 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e0d788"/>
    <path d="M 708.66823 332.230819 
L 711.420917 336.348097 
L 713.030765 334.780432 
L 710.280255 330.638397 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c0ae77"/>
    <path d="M 727.468375 368.44928 
L 730.21785 372.602847 
L 731.814186 371.235383 
L 729.067093 367.049723 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 769.403382 438.751383 
L 772.147956 442.315771 
L 773.707115 441.614693 
L 770.965425 438.015387 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0dcf69"/>
    <path d="M 805.10689 480.203789 
L 807.859408 482.886995 
L 809.380072 482.560191 
L 806.630523 479.854136 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0888ee"/>
    <path d="M 838.481755 504.540879 
L 841.255555 506.262808 
L 842.742282 505.914978 
L 839.97107 504.184915 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2353b9"/>
    <path d="M 825.916769 496.995157 
L 828.681019 499.086971 
L 830.179753 498.79482 
L 827.418284 496.689459 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1b63c9"/>
    <path d="M 595.265094 232.401117 
L 597.95043 233.403718 
L 599.614985 230.781055 
L 596.930323 229.776659 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ede8e7"/>
    <path d="M 684.3748 289.548271 
L 687.127504 293.278767 
L 688.75417 291.597328 
L 686.003428 287.851151 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #87655e"/>
    <path d="M 606.663571 230.609088 
L 609.362218 231.942724 
L 611.026471 229.552591 
L 608.328661 228.214293 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #efebea"/>
    <path d="M 620.808638 231.95994 
L 623.522566 233.738998 
L 625.184118 231.594798 
L 622.471265 229.808802 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ede8e7"/>
    <path d="M 736.86838 386.292684 
L 739.616176 390.37819 
L 741.205279 389.150972 
L 738.459984 385.030546 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c1f38d"/>
    <path d="M 749.01635 407.588816 
L 751.762201 411.523969 
L 753.340999 410.496287 
L 750.597806 406.524544 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #79e47e"/>
    <path d="M 643.188266 242.540638 
L 645.922259 245.061619 
L 647.574788 243.187422 
L 644.84225 240.657472 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d9cecc"/>
    <path d="M 858.129252 512.636786 
L 860.922389 513.762956 
L 862.393212 513.235344 
L 859.602286 512.108054 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2c40a6"/>
    <path d="M 766.658596 435.135851 
L 769.403382 438.751383 
L 770.965425 438.015387 
L 768.223502 434.36421 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #19d16b"/>
    <path d="M 630.620961 235.488518 
L 633.344577 237.59372 
L 635.002782 235.580909 
L 632.280407 233.467657 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e7e0df"/>
    <path d="M 613.728827 231.000252 
L 616.435552 232.556574 
L 618.098694 230.288751 
L 615.392918 228.726381 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #efebea"/>
    <path d="M 807.859408 482.886995 
L 810.613517 485.488184 
L 812.131224 485.183133 
L 809.380072 482.560191 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0b83e9"/>
    <path d="M 696.517053 310.414614 
L 699.270839 314.383146 
L 700.889228 312.738919 
L 698.137504 308.750063 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9a7e62"/>
    <path d="M 681.622263 285.879054 
L 684.3748 289.548271 
L 686.003428 287.851151 
L 683.252819 284.166581 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8f7069"/>
    <path d="M 590.92041 234.23999 
L 593.601111 235.134819 
L 595.265094 232.401117 
L 592.585008 231.505718 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ebe5e4"/>
    <path d="M 705.914764 328.141218 
L 708.66823 332.230819 
L 710.280255 330.638397 
L 707.528932 326.524214 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #baa774"/>
    <path d="M 763.913504 431.471861 
L 766.658596 435.135851 
L 768.223502 434.36421 
L 765.481249 430.663883 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #29d46e"/>
    <path d="M 645.922259 245.061619 
L 648.658692 247.680069 
L 650.309734 245.815394 
L 647.574788 243.187422 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d5c9c7"/>
    <path d="M 715.315966 346.190913 
L 718.068188 350.341971 
L 719.673685 348.831558 
L 716.9237 344.651921 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d8cd84"/>
    <path d="M 724.717864 364.295828 
L 727.468375 368.44928 
L 729.067093 367.049723 
L 726.318926 362.864125 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f8f695"/>
    <path d="M 746.269686 403.62498 
L 749.01635 407.588816 
L 750.597806 406.524544 
L 747.853769 402.523711 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #89e781"/>
    <path d="M 810.613517 485.488184 
L 813.369379 488.005696 
L 814.88414 487.721281 
L 812.131224 485.183133 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0e7ee4"/>
    <path d="M 586.581314 236.292277 
L 589.257176 237.082174 
L 590.92041 234.23999 
L 588.245115 233.450973 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e7e0df"/>
    <path d="M 734.119585 382.19409 
L 736.86838 386.292684 
L 738.459984 385.030546 
L 735.713654 380.896832 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d1f690"/>
    <path d="M 678.870028 282.274196 
L 681.622263 285.879054 
L 683.252819 284.166581 
L 680.502479 280.546715 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #957771"/>
    <path d="M 693.762883 306.490919 
L 696.517053 310.414614 
L 698.137504 308.750063 
L 695.385362 304.806317 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #94765f"/>
    <path d="M 828.681019 499.086971 
L 831.448054 501.085625 
L 832.944036 500.805904 
L 830.179753 498.79482 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1e5ec4"/>
    <path d="M 602.304731 231.893809 
L 604.999395 233.114599 
L 606.663571 230.609088 
L 603.969661 229.384274 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #efebea"/>
    <path d="M 648.658692 247.680069 
L 651.397382 250.393986 
L 653.046904 248.539373 
L 650.309734 245.815394 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d1c4c1"/>
    <path d="M 761.168023 427.762157 
L 763.913504 431.471861 
L 765.481249 430.663883 
L 762.738581 426.917182 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #35d771"/>
    <path d="M 633.344577 237.59372 
L 636.071408 239.802605 
L 637.728342 237.798551 
L 635.002782 235.580909 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e3dbd9"/>
    <path d="M 851.078085 510.506613 
L 853.864692 511.835378 
L 855.340655 511.407427 
L 852.556412 510.075291 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2a46ac"/>
    <path d="M 623.522566 233.738998 
L 626.240293 235.62485 
L 627.900746 233.488438 
L 625.184118 231.594798 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ebe5e4"/>
    <path d="M 841.255555 506.262808 
L 844.03289 507.886535 
L 845.517064 507.545779 
L 842.742282 505.914978 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2450b6"/>
    <path d="M 676.118235 278.736713 
L 678.870028 282.274196 
L 680.502479 280.546715 
L 677.752548 276.994591 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9b7f79"/>
    <path d="M 703.160593 324.082712 
L 705.914764 328.141218 
L 707.528932 326.524214 
L 704.776868 322.441332 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b29c6f"/>
    <path d="M 651.397382 250.393986 
L 654.13815 253.201268 
L 655.786118 251.357244 
L 653.046904 248.539373 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cdbfbc"/>
    <path d="M 813.369379 488.005696 
L 816.127154 490.437949 
L 817.638985 490.173035 
L 814.88414 487.721281 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1078de"/>
    <path d="M 743.522166 399.635557 
L 746.269686 403.62498 
L 747.853769 402.523711 
L 745.108843 398.496922 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #95ea84"/>
    <path d="M 712.562826 342.057078 
L 715.315966 346.190913 
L 716.9237 344.651921 
L 714.17276 340.489614 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d0c380"/>
    <path d="M 673.367029 275.269559 
L 676.118235 278.736713 
L 677.752548 276.994591 
L 675.003169 273.513178 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a18781"/>
    <path d="M 721.966332 360.145877 
L 724.717864 364.295828 
L 726.318926 362.864125 
L 723.569703 358.682013 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f0ec91"/>
    <path d="M 609.362218 231.942724 
L 612.065427 233.384613 
L 613.728827 231.000252 
L 611.026471 229.552591 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #efebea"/>
    <path d="M 616.435552 232.556574 
L 619.146465 234.220736 
L 620.808638 231.95994 
L 618.098694 230.288751 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ede8e7"/>
    <path d="M 691.008434 302.615362 
L 693.762883 306.490919 
L 695.385362 304.806317 
L 692.632906 300.911004 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8c6c5b"/>
    <path d="M 758.422071 424.009533 
L 761.168023 427.762157 
L 762.738581 426.917182 
L 759.995414 423.126935 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #41d973"/>
    <path d="M 654.13815 253.201268 
L 656.880815 256.099709 
L 658.527196 254.266788 
L 655.786118 251.357244 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c9bab7"/>
    <path d="M 731.36978 378.085694 
L 734.119585 382.19409 
L 735.713654 380.896832 
L 732.966277 376.753151 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e1f993"/>
    <path d="M 670.616561 271.875616 
L 673.367029 275.269559 
L 675.003169 273.513178 
L 672.254492 270.105377 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a78e89"/>
    <path d="M 597.95043 233.403718 
L 600.640855 234.513326 
L 602.304731 231.893809 
L 599.614985 230.781055 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ede8e7"/>
    <path d="M 656.880815 256.099709 
L 659.625203 259.087011 
L 661.269962 257.265691 
L 658.527196 254.266788 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c3b2af"/>
    <path d="M 636.071408 239.802605 
L 638.801266 242.113623 
L 640.456899 240.119019 
L 637.728342 237.798551 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dfd6d4"/>
    <path d="M 667.866983 268.557696 
L 670.616561 271.875616 
L 672.254492 270.105377 
L 669.506673 266.774017 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ad9691"/>
    <path d="M 659.625203 259.087011 
L 662.371139 262.160781 
L 664.014243 260.351545 
L 661.269962 257.265691 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bdaba7"/>
    <path d="M 665.118455 265.318532 
L 667.866983 268.557696 
L 669.506673 266.774017 
L 666.759869 263.521849 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b39e99"/>
    <path d="M 860.922389 513.762956 
L 863.720251 514.785619 
L 865.188908 514.25824 
L 862.393212 513.235344 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2c40a6"/>
    <path d="M 662.371139 262.160781 
L 665.118455 265.318532 
L 666.759869 263.521849 
L 664.014243 260.351545 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b9a5a1"/>
    <path d="M 831.448054 501.085625 
L 834.218052 502.99002 
L 835.711309 502.721599 
L 832.944036 500.805904 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1f5bc1"/>
    <path d="M 816.127154 490.437949 
L 818.887008 492.783441 
L 820.395924 492.536877 
L 817.638985 490.173035 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1373d9"/>
    <path d="M 755.675574 420.216832 
L 758.422071 424.009533 
L 759.995414 423.126935 
L 757.251674 419.296024 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #51dc76"/>
    <path d="M 700.405796 320.0587 
L 703.160593 324.082712 
L 704.776868 322.441332 
L 702.024141 318.393175 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #aa926b"/>
    <path d="M 688.253817 298.791203 
L 691.008434 302.615362 
L 692.632906 300.911004 
L 689.880247 297.067408 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #866458"/>
    <path d="M 626.240293 235.62485 
L 628.961634 237.616306 
L 630.620961 235.488518 
L 627.900746 233.488438 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e7e0df"/>
    <path d="M 740.773754 395.62368 
L 743.522166 399.635557 
L 745.108843 398.496922 
L 742.362988 394.447347 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a5ed87"/>
    <path d="M 709.80882 337.943894 
L 712.562826 342.057078 
L 714.17276 340.489614 
L 711.420917 336.348097 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c8b97b"/>
    <path d="M 593.601111 235.134819 
L 596.28706 236.135384 
L 597.95043 233.403718 
L 595.265094 232.401117 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e9e3e2"/>
    <path d="M 719.213805 356.002826 
L 721.966332 360.145877 
L 723.569703 358.682013 
L 720.819446 354.506816 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e8e28d"/>
    <path d="M 728.618962 373.970804 
L 731.36978 378.085694 
L 732.966277 376.753151 
L 730.21785 372.602847 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1fc96"/>
    <path d="M 638.801266 242.113623 
L 641.533967 244.525109 
L 643.188266 242.540638 
L 640.456899 240.119019 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ddd3d1"/>
    <path d="M 604.999395 233.114599 
L 607.698806 234.442983 
L 609.362218 231.942724 
L 606.663571 230.609088 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ede8e7"/>
    <path d="M 844.03289 507.886535 
L 846.813944 509.411299 
L 848.295604 509.07655 
L 845.517064 507.545779 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #264eb4"/>
    <path d="M 752.928466 416.386948 
L 755.675574 420.216832 
L 757.251674 419.296024 
L 754.507291 415.427377 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #5ddf79"/>
    <path d="M 685.499152 295.021657 
L 688.253817 298.791203 
L 689.880247 297.067408 
L 687.127504 293.278767 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #815e56"/>
    <path d="M 589.257176 237.082174 
L 591.938434 237.976305 
L 593.601111 235.134819 
L 590.92041 234.23999 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e7e0df"/>
    <path d="M 619.146465 234.220736 
L 621.861383 235.991795 
L 623.522566 233.738998 
L 620.808638 231.95994 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ebe5e4"/>
    <path d="M 853.864692 511.835378 
L 856.655611 513.062348 
L 858.129252 512.636786 
L 855.340655 511.407427 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2a46ac"/>
    <path d="M 818.887008 492.783441 
L 821.649106 495.040752 
L 823.155128 494.811369 
L 820.395924 492.536877 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #166ed4"/>
    <path d="M 697.650459 316.072556 
L 700.405796 320.0587 
L 702.024141 318.393175 
L 699.270839 314.383146 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a28867"/>
    <path d="M 612.065427 233.384613 
L 614.773021 234.934063 
L 616.435552 232.556574 
L 613.728827 231.000252 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ede8e7"/>
    <path d="M 784.324237 459.754113 
L 787.072777 462.926202 
L 788.616756 462.484944 
L 785.871227 459.280555 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b0b9"/>
    <path d="M 738.02442 391.592515 
L 740.773754 395.62368 
L 742.362988 394.447347 
L 739.616176 390.37819 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b5f08a"/>
    <path d="M 787.072777 462.926202 
L 789.821906 466.03103 
L 791.362864 465.621066 
L 788.616756 462.484944 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00acc4"/>
    <path d="M 584.918985 239.239928 
L 587.59536 240.030687 
L 589.257176 237.082174 
L 586.581314 236.292277 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e3dbd9"/>
    <path d="M 781.576159 456.516986 
L 784.324237 459.754113 
L 785.871227 459.280555 
L 783.126149 456.010153 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b6a7"/>
    <path d="M 789.821906 466.03103 
L 792.571754 469.066444 
L 794.109685 468.68674 
L 791.362864 465.621066 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a6d7"/>
    <path d="M 778.828424 453.217112 
L 781.576159 456.516986 
L 783.126149 456.010153 
L 780.3814 452.676056 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00bc94"/>
    <path d="M 707.054007 333.854781 
L 709.80882 337.943894 
L 711.420917 336.348097 
L 708.66823 332.230819 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c2b178"/>
    <path d="M 628.961634 237.616306 
L 631.686404 239.712057 
L 633.344577 237.59372 
L 630.620961 235.488518 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e5dedc"/>
    <path d="M 641.533967 244.525109 
L 644.269324 247.035292 
L 645.922259 245.061619 
L 643.188266 242.540638 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d9cecc"/>
    <path d="M 792.571754 469.066444 
L 795.322455 472.030357 
L 796.857354 471.679853 
L 794.109685 468.68674 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a2e2"/>
    <path d="M 834.218052 502.99002 
L 836.991189 504.799139 
L 838.481755 504.540879 
L 835.711309 502.721599 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2058be"/>
    <path d="M 682.74456 291.309891 
L 685.499152 295.021657 
L 687.127504 293.278767 
L 684.3748 289.548271 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #87655e"/>
    <path d="M 716.460315 351.870074 
L 719.213805 356.002826 
L 720.819446 354.506816 
L 718.068188 350.341971 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e0d788"/>
    <path d="M 776.080913 449.856843 
L 778.828424 453.217112 
L 780.3814 452.676056 
L 777.636859 449.28065 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c382"/>
    <path d="M 750.180685 412.522816 
L 752.928466 416.386948 
L 754.507291 415.427377 
L 751.762201 411.523969 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #6de27c"/>
    <path d="M 725.867136 369.852743 
L 728.618962 373.970804 
L 730.21785 372.602847 
L 727.468375 368.44928 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 795.322455 472.030357 
L 798.074149 474.920756 
L 799.606014 474.598364 
L 796.857354 471.679853 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #009cf4"/>
    <path d="M 773.333517 446.438599 
L 776.080913 449.856843 
L 777.636859 449.28065 
L 774.892414 445.826385 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c970"/>
    <path d="M 600.640855 234.513326 
L 603.336203 235.729621 
L 604.999395 233.114599 
L 602.304731 231.893809 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ebe5e4"/>
    <path d="M 694.894676 312.127623 
L 697.650459 316.072556 
L 699.270839 314.383146 
L 696.517053 310.414614 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9c8064"/>
    <path d="M 644.269324 247.035292 
L 647.007153 249.642289 
L 648.658692 247.680069 
L 645.922259 245.061619 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d5c9c7"/>
    <path d="M 679.990171 287.659017 
L 682.74456 291.309891 
L 684.3748 289.548271 
L 681.622263 285.879054 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8d6d66"/>
    <path d="M 798.074149 474.920756 
L 800.826978 477.735699 
L 802.35581 477.440307 
L 799.606014 474.598364 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0098fe"/>
    <path d="M 821.649106 495.040752 
L 824.413618 497.208543 
L 825.916769 496.995157 
L 823.155128 494.811369 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #176bd1"/>
    <path d="M 770.586129 442.964857 
L 773.333517 446.438599 
L 774.892414 445.826385 
L 772.147956 442.315771 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #05cd67"/>
    <path d="M 735.274142 387.545258 
L 738.02442 391.592515 
L 739.616176 390.37819 
L 736.86838 386.292684 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c1f38d"/>
    <path d="M 704.298454 329.793143 
L 707.054007 333.854781 
L 708.66823 332.230819 
L 705.914764 328.141218 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #baa774"/>
    <path d="M 621.861383 235.991795 
L 624.580125 237.868691 
L 626.240293 235.62485 
L 623.522566 233.738998 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e9e3e2"/>
    <path d="M 747.432176 408.627418 
L 750.180685 412.522816 
L 751.762201 411.523969 
L 749.01635 407.588816 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #79e47e"/>
    <path d="M 863.720251 514.785619 
L 866.523022 515.704547 
L 867.989559 515.176515 
L 865.188908 514.25824 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2c40a6"/>
    <path d="M 631.686404 239.712057 
L 634.414417 241.910679 
L 636.071408 239.802605 
L 633.344577 237.59372 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e1d9d7"/>
    <path d="M 800.826978 477.735699 
L 803.581088 480.473317 
L 805.10689 480.203789 
L 802.35581 477.440307 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0393f9"/>
    <path d="M 767.838648 439.438155 
L 770.586129 442.964857 
L 772.147956 442.315771 
L 769.403382 438.751383 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #11cf69"/>
    <path d="M 677.236121 284.072092 
L 679.990171 287.659017 
L 681.622263 285.879054 
L 678.870028 282.274196 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #957771"/>
    <path d="M 713.705901 347.751024 
L 716.460315 351.870074 
L 718.068188 350.341971 
L 715.315966 346.190913 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d8cd84"/>
    <path d="M 647.007153 249.642289 
L 649.747274 252.344115 
L 651.397382 250.393986 
L 648.658692 247.680069 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cfc2bf"/>
    <path d="M 607.698806 234.442983 
L 610.402792 235.878397 
L 612.065427 233.384613 
L 609.362218 231.942724 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ebe5e4"/>
    <path d="M 846.813944 509.411299 
L 849.5989 510.836428 
L 851.078085 510.506613 
L 848.295604 509.07655 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #274bb1"/>
    <path d="M 596.28706 236.135384 
L 598.978097 237.241491 
L 600.640855 234.513326 
L 597.95043 233.403718 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e9e3e2"/>
    <path d="M 723.114312 365.734851 
L 725.867136 369.852743 
L 727.468375 368.44928 
L 724.717864 364.295828 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f8f695"/>
    <path d="M 692.138545 308.227212 
L 694.894676 312.127623 
L 696.517053 310.414614 
L 693.762883 306.490919 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #94765f"/>
    <path d="M 614.773021 234.934063 
L 617.484822 236.59026 
L 619.146465 234.220736 
L 616.435552 232.556574 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ebe5e4"/>
    <path d="M 765.09098 435.861091 
L 767.838648 439.438155 
L 769.403382 438.751383 
L 766.658596 435.135851 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1dd26c"/>
    <path d="M 674.482548 280.552112 
L 677.236121 284.072092 
L 678.870028 282.274196 
L 676.118235 278.736713 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9b7f79"/>
    <path d="M 803.581088 480.473317 
L 806.33663 483.131817 
L 807.859408 482.886995 
L 805.10689 480.203789 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #078bf1"/>
    <path d="M 649.747274 252.344115 
L 652.489505 255.138682 
L 654.13815 253.201268 
L 651.397382 250.393986 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cbbcb9"/>
    <path d="M 836.991189 504.799139 
L 839.767647 506.512057 
L 841.255555 506.262808 
L 838.481755 504.540879 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2256bc"/>
    <path d="M 732.522903 383.485131 
L 735.274142 387.545258 
L 736.86838 386.292684 
L 734.119585 382.19409 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d1f690"/>
    <path d="M 856.655611 513.062348 
L 859.451026 514.187115 
L 860.922389 513.762956 
L 858.129252 512.636786 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2b43a9"/>
    <path d="M 744.68289 404.703773 
L 747.432176 408.627418 
L 749.01635 407.588816 
L 746.269686 403.62498 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #89e781"/>
    <path d="M 824.413618 497.208543 
L 827.180716 499.285559 
L 828.681019 499.086971 
L 825.916769 496.995157 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1a66cc"/>
    <path d="M 671.729599 277.102007 
L 674.482548 280.552112 
L 676.118235 278.736713 
L 673.367029 275.269559 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a18781"/>
    <path d="M 591.938434 237.976305 
L 594.624934 238.974595 
L 596.28706 236.135384 
L 593.601111 235.134819 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e7e0df"/>
    <path d="M 701.542234 325.762369 
L 704.298454 329.793143 
L 705.914764 328.141218 
L 703.160593 324.082712 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b29c6f"/>
    <path d="M 652.489505 255.138682 
L 655.233667 258.023804 
L 656.880815 256.099709 
L 654.13815 253.201268 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c7b7b4"/>
    <path d="M 762.343033 432.236315 
L 765.09098 435.861091 
L 766.658596 435.135851 
L 763.913504 431.471861 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2dd56f"/>
    <path d="M 634.414417 241.910679 
L 637.145487 244.210633 
L 638.801266 242.113623 
L 636.071408 239.802605 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dfd6d4"/>
    <path d="M 689.382173 304.374598 
L 692.138545 308.227212 
L 693.762883 306.490919 
L 691.008434 302.615362 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8e6e5c"/>
    <path d="M 668.977422 273.72464 
L 671.729599 277.102007 
L 673.367029 275.269559 
L 670.616561 271.875616 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a78e89"/>
    <path d="M 710.950608 343.649077 
L 713.705901 347.751024 
L 715.315966 346.190913 
L 712.562826 342.057078 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d0c380"/>
    <path d="M 806.33663 483.131817 
L 809.093756 485.709482 
L 810.613517 485.488184 
L 807.859408 482.886995 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0a86ec"/>
    <path d="M 655.233667 258.023804 
L 657.979587 260.997197 
L 659.625203 259.087011 
L 656.880815 256.099709 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c1b0ac"/>
    <path d="M 587.59536 240.030687 
L 590.277117 240.923993 
L 591.938434 237.976305 
L 589.257176 237.082174 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e3dbd9"/>
    <path d="M 624.580125 237.868691 
L 627.302506 239.850243 
L 628.961634 237.616306 
L 626.240293 235.62485 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e5dedc"/>
    <path d="M 666.226172 270.422801 
L 668.977422 273.72464 
L 670.616561 271.875616 
L 667.866983 268.557696 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ad9691"/>
    <path d="M 720.360509 361.620479 
L 723.114312 365.734851 
L 724.717864 364.295828 
L 721.966332 360.145877 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f0ec91"/>
    <path d="M 657.979587 260.997197 
L 660.72709 264.056486 
L 662.371139 262.160781 
L 659.625203 259.087011 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bdaba7"/>
    <path d="M 603.336203 235.729621 
L 606.036305 237.052169 
L 607.698806 234.442983 
L 604.999395 233.114599 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ebe5e4"/>
    <path d="M 663.476007 267.199204 
L 666.226172 270.422801 
L 667.866983 268.557696 
L 665.118455 265.318532 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b19b96"/>
    <path d="M 660.72709 264.056486 
L 663.476007 267.199204 
L 665.118455 265.318532 
L 662.371139 262.160781 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b7a39f"/>
    <path d="M 583.258175 242.292226 
L 585.93501 243.08383 
L 587.59536 240.030687 
L 584.918985 239.239928 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dfd6d4"/>
    <path d="M 759.594726 428.566532 
L 762.343033 432.236315 
L 763.913504 431.471861 
L 761.168023 427.762157 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #39d771"/>
    <path d="M 741.932787 400.75494 
L 744.68289 404.703773 
L 746.269686 403.62498 
L 743.522166 399.635557 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #99eb85"/>
    <path d="M 729.770694 379.415381 
L 732.522903 383.485131 
L 734.119585 382.19409 
L 731.36978 378.085694 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e1f993"/>
    <path d="M 686.625672 300.573014 
L 689.382173 304.374598 
L 691.008434 302.615362 
L 688.253817 298.791203 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #866458"/>
    <path d="M 698.785428 321.765826 
L 701.542234 325.762369 
L 703.160593 324.082712 
L 700.405796 320.0587 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #aa926b"/>
    <path d="M 809.093756 485.709482 
L 811.852623 488.204671 
L 813.369379 488.005696 
L 810.613517 485.488184 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0c80e6"/>
    <path d="M 637.145487 244.210633 
L 639.879429 246.610272 
L 641.533967 244.525109 
L 638.801266 242.113623 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dbd1cf"/>
    <path d="M 617.484822 236.59026 
L 620.200648 238.352273 
L 621.861383 235.991795 
L 619.146465 234.220736 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e9e3e2"/>
    <path d="M 610.402792 235.878397 
L 613.111176 237.420157 
L 614.773021 234.934063 
L 612.065427 233.384613 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e9e3e2"/>
    <path d="M 827.180716 499.285559 
L 829.950572 501.270626 
L 831.448054 501.085625 
L 828.681019 499.086971 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1b63c9"/>
    <path d="M 756.845979 424.8545 
L 759.594726 428.566532 
L 761.168023 427.762157 
L 758.422071 424.009533 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #45da74"/>
    <path d="M 708.19449 339.567626 
L 710.950608 343.649077 
L 712.562826 342.057078 
L 709.80882 337.943894 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cabb7c"/>
    <path d="M 849.5989 510.836428 
L 852.38794 512.161338 
L 853.864692 511.835378 
L 851.078085 510.506613 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2848ae"/>
    <path d="M 839.767647 506.512057 
L 842.547604 508.12793 
L 844.03289 507.886535 
L 841.255555 506.262808 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2353b9"/>
    <path d="M 717.605752 357.512986 
L 720.360509 361.620479 
L 721.966332 360.145877 
L 719.213805 356.002826 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e8e28d"/>
    <path d="M 598.978097 237.241491 
L 601.674059 238.452828 
L 603.336203 235.729621 
L 600.640855 234.513326 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e9e3e2"/>
    <path d="M 683.869158 296.825649 
L 686.625672 300.573014 
L 688.253817 298.791203 
L 685.499152 295.021657 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #805c54"/>
    <path d="M 627.302506 239.850243 
L 630.028341 241.935156 
L 631.686404 239.712057 
L 628.961634 237.616306 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e3dbd9"/>
    <path d="M 739.18183 396.784012 
L 741.932787 400.75494 
L 743.522166 399.635557 
L 740.773754 395.62368 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a5ed87"/>
    <path d="M 639.879429 246.610272 
L 642.616059 249.107837 
L 644.269324 247.035292 
L 641.533967 244.525109 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d7ccc9"/>
    <path d="M 811.852623 488.204671 
L 814.61339 490.615823 
L 816.127154 490.437949 
L 813.369379 488.005696 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0f7be1"/>
    <path d="M 727.017515 375.339275 
L 729.770694 379.415381 
L 731.36978 378.085694 
L 728.618962 373.970804 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1fc96"/>
    <path d="M 696.028121 317.806856 
L 698.785428 321.765826 
L 700.405796 320.0587 
L 697.650459 316.072556 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a48b68"/>
    <path d="M 754.09672 421.103024 
L 756.845979 424.8545 
L 758.422071 424.009533 
L 755.675574 420.216832 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #55dd77"/>
    <path d="M 681.112757 293.135642 
L 683.869158 296.825649 
L 685.499152 295.021657 
L 682.74456 291.309891 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #85635c"/>
    <path d="M 594.624934 238.974595 
L 597.316518 240.076853 
L 598.978097 237.241491 
L 596.28706 236.135384 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e5dedc"/>
    <path d="M 705.437606 335.510055 
L 708.19449 339.567626 
L 709.80882 337.943894 
L 707.054007 333.854781 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c2b178"/>
    <path d="M 859.451026 514.187115 
L 862.251119 515.209363 
L 863.720251 514.785619 
L 860.922389 513.762956 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2b43a9"/>
    <path d="M 606.036305 237.052169 
L 608.74099 238.480413 
L 610.402792 235.878397 
L 607.698806 234.442983 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e9e3e2"/>
    <path d="M 642.616059 249.107837 
L 645.355194 251.701464 
L 647.007153 249.642289 
L 644.269324 247.035292 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d3c7c4"/>
    <path d="M 620.200648 238.352273 
L 622.920319 240.219053 
L 624.580125 237.868691 
L 621.861383 235.991795 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e5dedc"/>
    <path d="M 714.850074 353.415735 
L 717.605752 357.512986 
L 719.213805 356.002826 
L 716.460315 351.870074 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e0d788"/>
    <path d="M 751.346885 417.314956 
L 754.09672 421.103024 
L 755.675574 420.216832 
L 752.928466 416.386948 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #61df79"/>
    <path d="M 736.429992 392.794114 
L 739.18183 396.784012 
L 740.773754 395.62368 
L 738.02442 391.592515 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b5f08a"/>
    <path d="M 829.950572 501.270626 
L 832.723361 503.162658 
L 834.218052 502.99002 
L 831.448054 501.085625 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1c60c6"/>
    <path d="M 814.61339 490.615823 
L 817.37622 492.941454 
L 818.887008 492.783441 
L 816.127154 490.437949 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1078de"/>
    <path d="M 693.270407 313.888772 
L 696.028121 317.806856 
L 697.650459 316.072556 
L 694.894676 312.127623 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9c8064"/>
    <path d="M 678.356596 289.506082 
L 681.112757 293.135642 
L 682.74456 291.309891 
L 679.990171 287.659017 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8d6d66"/>
    <path d="M 630.028341 241.935156 
L 632.757446 244.122019 
L 634.414417 241.910679 
L 631.686404 239.712057 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dfd6d4"/>
    <path d="M 613.111176 237.420157 
L 615.823783 239.067463 
L 617.484822 236.59026 
L 614.773021 234.934063 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e7e0df"/>
    <path d="M 590.277117 240.923993 
L 592.964107 241.919774 
L 594.624934 238.974595 
L 591.938434 237.976305 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e3dbd9"/>
    <path d="M 724.263369 371.260098 
L 727.017515 375.339275 
L 728.618962 373.970804 
L 725.867136 369.852743 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 645.355194 251.701464 
L 648.096652 254.389184 
L 649.747274 252.344115 
L 647.007153 249.642289 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cfc2bf"/>
    <path d="M 585.93501 243.08383 
L 588.617211 243.976188 
L 590.277117 240.923993 
L 587.59536 240.030687 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dfd6d4"/>
    <path d="M 581.598926 245.44736 
L 584.27617 246.23979 
L 585.93501 243.08383 
L 583.258175 242.292226 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dbd1cf"/>
    <path d="M 675.600812 285.939998 
L 678.356596 289.506082 
L 679.990171 287.659017 
L 677.236121 284.072092 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #93756e"/>
    <path d="M 702.680024 331.479735 
L 705.437606 335.510055 
L 707.054007 333.854781 
L 704.298454 329.793143 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #baa774"/>
    <path d="M 842.547604 508.12793 
L 845.331241 509.646007 
L 846.813944 509.411299 
L 844.03289 507.886535 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2450b6"/>
    <path d="M 748.596413 413.493194 
L 751.346885 417.314956 
L 752.928466 416.386948 
L 750.180685 412.522816 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #6de27c"/>
    <path d="M 852.38794 512.161338 
L 855.181248 513.385535 
L 856.655611 513.062348 
L 853.864692 511.835378 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2848ae"/>
    <path d="M 648.096652 254.389184 
L 650.840255 257.168927 
L 652.489505 255.138682 
L 649.747274 252.344115 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c9bab7"/>
    <path d="M 690.512387 310.014854 
L 693.270407 313.888772 
L 694.894676 312.127623 
L 692.138545 308.227212 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #967960"/>
    <path d="M 782.774665 460.163549 
L 785.526255 463.300972 
L 787.072777 462.926202 
L 784.324237 459.754113 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b4ac"/>
    <path d="M 780.023553 456.962132 
L 782.774665 460.163549 
L 784.324237 459.754113 
L 781.576159 456.516986 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b8a0"/>
    <path d="M 733.677252 388.7884 
L 736.429992 392.794114 
L 738.02442 391.592515 
L 735.274142 387.545258 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c5f38d"/>
    <path d="M 712.093515 349.332091 
L 714.850074 353.415735 
L 716.460315 351.870074 
L 713.705901 347.751024 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d8cd84"/>
    <path d="M 601.674059 238.452828 
L 604.374779 239.768964 
L 606.036305 237.052169 
L 603.336203 235.729621 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e7e0df"/>
    <path d="M 785.526255 463.300972 
L 788.278445 466.372211 
L 789.821906 466.03103 
L 787.072777 462.926202 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00aebf"/>
    <path d="M 672.845543 282.440361 
L 675.600812 285.939998 
L 677.236121 284.072092 
L 674.482548 280.552112 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #997c76"/>
    <path d="M 777.272799 453.698979 
L 780.023553 456.962132 
L 781.576159 456.516986 
L 778.828424 453.217112 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00be8f"/>
    <path d="M 817.37622 492.941454 
L 820.141276 495.180162 
L 821.649106 495.040752 
L 818.887008 492.783441 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1373d9"/>
    <path d="M 788.278445 466.372211 
L 791.031364 469.37514 
L 792.571754 469.066444 
L 789.821906 466.03103 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a8d0"/>
    <path d="M 632.757446 244.122019 
L 635.489637 246.409312 
L 637.145487 244.210633 
L 634.414417 241.910679 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ddd3d1"/>
    <path d="M 774.52229 450.376411 
L 777.272799 453.698979 
L 778.828424 453.217112 
L 776.080913 449.856843 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c47d"/>
    <path d="M 622.920319 240.219053 
L 625.643651 242.189434 
L 627.302506 239.850243 
L 624.580125 237.868691 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e3dbd9"/>
    <path d="M 650.840255 257.168927 
L 653.585823 260.038527 
L 655.233667 258.023804 
L 652.489505 255.138682 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c5b5b1"/>
    <path d="M 721.508269 367.181148 
L 724.263369 371.260098 
L 725.867136 369.852743 
L 723.114312 365.734851 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f8f695"/>
    <path d="M 670.090935 279.010078 
L 672.845543 282.440361 
L 674.482548 280.552112 
L 671.729599 277.102007 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9f847e"/>
    <path d="M 791.031364 469.37514 
L 793.785143 472.307704 
L 795.322455 472.030357 
L 792.571754 469.066444 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a4dc"/>
    <path d="M 771.771916 446.99681 
L 774.52229 450.376411 
L 776.080913 449.856843 
L 773.333517 446.438599 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00cb6b"/>
    <path d="M 745.845252 409.640677 
L 748.596413 413.493194 
L 750.180685 412.522816 
L 747.432176 408.627418 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #7de57f"/>
    <path d="M 832.723361 503.162658 
L 835.499259 504.96065 
L 836.991189 504.799139 
L 834.218052 502.99002 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1e5ec4"/>
    <path d="M 653.585823 260.038527 
L 656.333182 262.995719 
L 657.979587 260.997197 
L 655.233667 258.023804 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c1b0ac"/>
    <path d="M 667.337136 275.651986 
L 670.090935 279.010078 
L 671.729599 277.102007 
L 668.977422 273.72464 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a58c86"/>
    <path d="M 699.921817 327.48002 
L 702.680024 331.479735 
L 704.298454 329.793143 
L 701.542234 325.762369 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b49f70"/>
    <path d="M 793.785143 472.307704 
L 796.539918 475.167916 
L 798.074149 474.920756 
L 795.322455 472.030357 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a0e8"/>
    <path d="M 687.754164 306.188347 
L 690.512387 310.014854 
L 692.138545 308.227212 
L 689.382173 304.374598 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8e6e5c"/>
    <path d="M 608.74099 238.480413 
L 611.450086 240.01368 
L 613.111176 237.420157 
L 610.402792 235.878397 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e7e0df"/>
    <path d="M 769.021575 443.56262 
L 771.771916 446.99681 
L 773.333517 446.438599 
L 770.586129 442.964857 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #09ce68"/>
    <path d="M 656.333182 262.995719 
L 659.082161 266.038148 
L 660.72709 264.056486 
L 657.979587 260.997197 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bba8a4"/>
    <path d="M 664.584302 272.368853 
L 667.337136 275.651986 
L 668.977422 273.72464 
L 666.226172 270.422801 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ab938e"/>
    <path d="M 615.823783 239.067463 
L 618.540433 240.819394 
L 620.200648 238.352273 
L 617.484822 236.59026 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e5dedc"/>
    <path d="M 659.082161 266.038148 
L 661.832589 269.163369 
L 663.476007 267.199204 
L 660.72709 264.056486 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b7a39f"/>
    <path d="M 661.832589 269.163369 
L 664.584302 272.368853 
L 666.226172 270.422801 
L 663.476007 267.199204 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b19b96"/>
    <path d="M 597.316518 240.076853 
L 600.013024 241.282773 
L 601.674059 238.452828 
L 598.978097 237.241491 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e5dedc"/>
    <path d="M 730.923593 384.770051 
L 733.677252 388.7884 
L 735.274142 387.545258 
L 732.522903 383.485131 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d1f690"/>
    <path d="M 709.33612 345.265416 
L 712.093515 349.332091 
L 713.705901 347.751024 
L 710.950608 343.649077 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d2c581"/>
    <path d="M 766.271167 440.076343 
L 769.021575 443.56262 
L 770.586129 442.964857 
L 767.838648 439.438155 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #15d06a"/>
    <path d="M 796.539918 475.167916 
L 799.29583 477.953862 
L 800.826978 477.735699 
L 798.074149 474.920756 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #009afa"/>
    <path d="M 635.489637 246.409312 
L 638.224729 248.795401 
L 639.879429 246.610272 
L 637.145487 244.210633 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d9cecc"/>
    <path d="M 820.141276 495.180162 
L 822.908725 497.330624 
L 824.413618 497.208543 
L 821.649106 495.040752 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #166ed4"/>
    <path d="M 862.251119 515.209363 
L 865.056074 516.128866 
L 866.523022 515.704547 
L 863.720251 514.785619 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2b43a9"/>
    <path d="M 743.093354 405.760384 
L 745.845252 409.640677 
L 747.432176 408.627418 
L 744.68289 404.703773 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #89e781"/>
    <path d="M 718.752234 363.105737 
L 721.508269 367.181148 
L 723.114312 365.734851 
L 720.360509 361.620479 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f0ec91"/>
    <path d="M 684.995853 302.412453 
L 687.754164 306.188347 
L 689.382173 304.374598 
L 686.625672 300.573014 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #886759"/>
    <path d="M 763.520599 436.540538 
L 766.271167 440.076343 
L 767.838648 439.438155 
L 765.09098 435.861091 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #21d36d"/>
    <path d="M 592.964107 241.919774 
L 595.656172 243.017841 
L 597.316518 240.076853 
L 594.624934 238.974595 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e3dbd9"/>
    <path d="M 799.29583 477.953862 
L 802.053023 480.663698 
L 803.581088 480.473317 
L 800.826978 477.735699 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0296fc"/>
    <path d="M 625.643651 242.189434 
L 628.370462 244.262134 
L 630.028341 241.935156 
L 627.302506 239.850243 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e1d9d7"/>
    <path d="M 697.163065 323.514241 
L 699.921817 327.48002 
L 701.542234 325.762369 
L 698.785428 321.765826 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ac956c"/>
    <path d="M 845.331241 509.646007 
L 848.118739 511.06562 
L 849.5989 510.836428 
L 846.813944 509.411299 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #264eb4"/>
    <path d="M 638.224729 248.795401 
L 640.96254 251.278545 
L 642.616059 249.107837 
L 639.879429 246.610272 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d5c9c7"/>
    <path d="M 728.16901 380.742271 
L 730.923593 384.770051 
L 732.522903 383.485131 
L 729.770694 379.415381 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e1f993"/>
    <path d="M 760.769785 432.957817 
L 763.520599 436.540538 
L 765.09098 435.861091 
L 762.343033 432.236315 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2dd56f"/>
    <path d="M 588.617211 243.976188 
L 591.30463 244.969229 
L 592.964107 241.919774 
L 590.277117 240.923993 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dfd6d4"/>
    <path d="M 604.374779 239.768964 
L 607.080089 241.189353 
L 608.74099 238.480413 
L 606.036305 237.052169 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e5dedc"/>
    <path d="M 706.577944 341.219064 
L 709.33612 345.265416 
L 710.950608 343.649077 
L 708.19449 339.567626 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cabb7c"/>
    <path d="M 682.23757 298.690331 
L 684.995853 302.412453 
L 686.625672 300.573014 
L 683.869158 296.825649 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #805c54"/>
    <path d="M 579.941276 248.703405 
L 582.618879 249.496645 
L 584.27617 246.23979 
L 581.598926 245.44736 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d7ccc9"/>
    <path d="M 802.053023 480.663698 
L 804.811643 483.295656 
L 806.33663 483.131817 
L 803.581088 480.473317 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0490f6"/>
    <path d="M 584.27617 246.23979 
L 586.958759 247.131079 
L 588.617211 243.976188 
L 585.93501 243.08383 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dbd1cf"/>
    <path d="M 740.340679 401.85533 
L 743.093354 405.760384 
L 744.68289 404.703773 
L 741.932787 400.75494 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #99eb85"/>
    <path d="M 835.499259 504.96065 
L 838.278442 506.663685 
L 839.767647 506.512057 
L 836.991189 504.799139 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2058be"/>
    <path d="M 855.181248 513.385535 
L 857.979005 514.508617 
L 859.451026 514.187115 
L 856.655611 513.062348 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2848ae"/>
    <path d="M 618.540433 240.819394 
L 621.260946 242.674913 
L 622.920319 240.219053 
L 620.200648 238.352273 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e3dbd9"/>
    <path d="M 715.995291 359.037182 
L 718.752234 363.105737 
L 720.360509 361.620479 
L 717.605752 357.512986 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e8e28d"/>
    <path d="M 694.403856 319.585706 
L 697.163065 323.514241 
L 698.785428 321.765826 
L 696.028121 317.806856 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a48b68"/>
    <path d="M 758.018641 429.330846 
L 760.769785 432.957817 
L 762.343033 432.236315 
L 759.594726 428.566532 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #3dd872"/>
    <path d="M 611.450086 240.01368 
L 614.163417 241.651179 
L 615.823783 239.067463 
L 613.111176 237.420157 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e5dedc"/>
    <path d="M 822.908725 497.330624 
L 825.678735 499.391601 
L 827.180716 499.285559 
L 824.413618 497.208543 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #176bd1"/>
    <path d="M 640.96254 251.278545 
L 643.702887 253.8569 
L 645.355194 251.701464 
L 642.616059 249.107837 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d1c4c1"/>
    <path d="M 679.479438 295.025091 
L 682.23757 298.690331 
L 683.869158 296.825649 
L 681.112757 293.135642 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #85635c"/>
    <path d="M 628.370462 244.262134 
L 631.100569 246.43576 
L 632.757446 244.122019 
L 630.028341 241.935156 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ddd3d1"/>
    <path d="M 804.811643 483.295656 
L 807.571841 485.848042 
L 809.093756 485.709482 
L 806.33663 483.131817 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #078bf1"/>
    <path d="M 725.4135 376.708284 
L 728.16901 380.742271 
L 729.770694 379.415381 
L 727.017515 375.339275 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1fc96"/>
    <path d="M 600.013024 241.282773 
L 602.71429 242.591932 
L 604.374779 239.768964 
L 601.674059 238.452828 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e3dbd9"/>
    <path d="M 755.267093 425.662341 
L 758.018641 429.330846 
L 759.594726 428.566532 
L 756.845979 424.8545 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #49db75"/>
    <path d="M 703.819048 337.196383 
L 706.577944 341.219064 
L 708.19449 339.567626 
L 705.437606 335.510055 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c2b178"/>
    <path d="M 737.587194 397.928564 
L 740.340679 401.85533 
L 741.932787 400.75494 
L 739.18183 396.784012 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a9ee88"/>
    <path d="M 676.721588 291.419791 
L 679.479438 295.025091 
L 681.112757 293.135642 
L 678.356596 289.506082 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8b6b64"/>
    <path d="M 643.702887 253.8569 
L 646.445589 256.528515 
L 648.096652 254.389184 
L 645.355194 251.701464 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cdbfbc"/>
    <path d="M 691.644282 315.697694 
L 694.403856 319.585706 
L 696.028121 317.806856 
L 693.270407 313.888772 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9e8365"/>
    <path d="M 713.237472 354.978806 
L 715.995291 359.037182 
L 717.605752 357.512986 
L 714.850074 353.415735 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e0d788"/>
    <path d="M 807.571841 485.848042 
L 810.333772 488.319239 
L 811.852623 488.204671 
L 809.093756 485.709482 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0a86ec"/>
    <path d="M 752.51507 421.955068 
L 755.267093 425.662341 
L 756.845979 424.8545 
L 754.09672 421.103024 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #55dd77"/>
    <path d="M 673.964154 287.877433 
L 676.721588 291.419791 
L 678.356596 289.506082 
L 675.600812 285.939998 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #91726c"/>
    <path d="M 646.445589 256.528515 
L 649.190469 259.291342 
L 650.840255 257.168927 
L 648.096652 254.389184 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c9bab7"/>
    <path d="M 621.260946 242.674913 
L 623.985143 244.632869 
L 625.643651 242.189434 
L 622.920319 240.219053 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e1d9d7"/>
    <path d="M 631.100569 246.43576 
L 633.833789 248.708807 
L 635.489637 246.409312 
L 632.757446 244.122019 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d9cecc"/>
    <path d="M 848.118739 511.06562 
L 850.910279 512.386194 
L 852.38794 512.161338 
L 849.5989 510.836428 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #264eb4"/>
    <path d="M 595.656172 243.017841 
L 598.353156 244.217895 
L 600.013024 241.282773 
L 597.316518 240.076853 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e1d9d7"/>
    <path d="M 825.678735 499.391601 
L 828.451478 501.361934 
L 829.950572 501.270626 
L 827.180716 499.285559 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1868ce"/>
    <path d="M 607.080089 241.189353 
L 609.789817 242.713332 
L 611.450086 240.01368 
L 608.74099 238.480413 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e3dbd9"/>
    <path d="M 722.65707 372.671332 
L 725.4135 376.708284 
L 727.017515 375.339275 
L 724.263369 371.260098 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 734.832872 393.983169 
L 737.587194 397.928564 
L 739.18183 396.784012 
L 736.429992 392.794114 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b5f08a"/>
    <path d="M 701.059497 333.200704 
L 703.819048 337.196383 
L 705.437606 335.510055 
L 702.680024 331.479735 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bca975"/>
    <path d="M 838.278442 506.663685 
L 841.061089 508.270933 
L 842.547604 508.12793 
L 839.767647 506.512057 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2058be"/>
    <path d="M 671.207275 284.40096 
L 673.964154 287.877433 
L 675.600812 285.939998 
L 672.845543 282.440361 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #977a74"/>
    <path d="M 688.884444 311.853451 
L 691.644282 315.697694 
L 693.270407 313.888772 
L 690.512387 310.014854 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #967960"/>
    <path d="M 614.163417 241.651179 
L 616.880807 243.392002 
L 618.540433 240.819394 
L 615.823783 239.067463 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e3dbd9"/>
    <path d="M 649.190469 259.291342 
L 651.93735 262.143235 
L 653.585823 260.038527 
L 650.840255 257.168927 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c3b2af"/>
    <path d="M 749.762509 418.211835 
L 752.51507 421.955068 
L 754.09672 421.103024 
L 751.346885 417.314956 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #65e07a"/>
    <path d="M 591.30463 244.969229 
L 593.997112 246.06277 
L 595.656172 243.017841 
L 592.964107 241.919774 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dfd6d4"/>
    <path d="M 668.451095 280.993249 
L 671.207275 284.40096 
L 672.845543 282.440361 
L 670.090935 279.010078 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9d827c"/>
    <path d="M 810.333772 488.319239 
L 813.09759 490.707706 
L 814.61339 490.615823 
L 811.852623 488.204671 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0c80e6"/>
    <path d="M 710.478818 350.93393 
L 713.237472 354.978806 
L 714.850074 353.415735 
L 712.093515 349.332091 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dad085"/>
    <path d="M 651.93735 262.143235 
L 654.686056 265.081951 
L 656.333182 262.995719 
L 653.585823 260.038527 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bfada9"/>
    <path d="M 578.285257 252.058327 
L 580.963168 252.85236 
L 582.618879 249.496645 
L 579.941276 248.703405 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d3c7c4"/>
    <path d="M 665.695764 277.657111 
L 668.451095 280.993249 
L 670.090935 279.010078 
L 667.337136 275.651986 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a38984"/>
    <path d="M 586.958759 247.131079 
L 589.646547 248.121155 
L 591.30463 244.969229 
L 588.617211 243.976188 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dbd1cf"/>
    <path d="M 654.686056 265.081951 
L 657.436418 268.10516 
L 659.082161 266.038148 
L 656.333182 262.995719 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b9a5a1"/>
    <path d="M 582.618879 249.496645 
L 585.3018 250.386745 
L 586.958759 247.131079 
L 584.27617 246.23979 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d7ccc9"/>
    <path d="M 857.979005 514.508617 
L 860.781395 515.53027 
L 862.251119 515.209363 
L 859.451026 514.187115 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2a46ac"/>
    <path d="M 633.833789 248.708807 
L 636.569938 251.07966 
L 638.224729 248.795401 
L 635.489637 246.409312 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d7ccc9"/>
    <path d="M 662.941435 274.395286 
L 665.695764 277.657111 
L 667.337136 275.651986 
L 664.584302 272.368853 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a9918c"/>
    <path d="M 657.436418 268.10516 
L 660.188266 271.21044 
L 661.832589 269.163369 
L 659.082161 266.038148 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b5a09c"/>
    <path d="M 660.188266 271.21044 
L 662.941435 274.395286 
L 664.584302 272.368853 
L 661.832589 269.163369 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #af9994"/>
    <path d="M 686.124447 308.056187 
L 688.884444 311.853451 
L 690.512387 310.014854 
L 687.754164 306.188347 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #90715d"/>
    <path d="M 732.077693 390.022254 
L 734.832872 393.983169 
L 736.429992 392.794114 
L 733.677252 388.7884 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c5f38d"/>
    <path d="M 698.299366 329.235343 
L 701.059497 333.200704 
L 702.680024 331.479735 
L 699.921817 327.48002 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b49f70"/>
    <path d="M 719.899734 368.634671 
L 722.65707 372.671332 
L 724.263369 371.260098 
L 721.508269 367.181148 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f8f695"/>
    <path d="M 747.009351 414.435498 
L 749.762509 418.211835 
L 751.346885 417.314956 
L 748.596413 413.493194 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #71e37d"/>
    <path d="M 623.985143 244.632869 
L 626.71284 246.691998 
L 628.370462 244.262134 
L 625.643651 242.189434 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ddd3d1"/>
    <path d="M 602.71429 242.591932 
L 605.420149 244.003791 
L 607.080089 241.189353 
L 604.374779 239.768964 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e3dbd9"/>
    <path d="M 828.451478 501.361934 
L 831.227125 503.240549 
L 832.723361 503.162658 
L 829.950572 501.270626 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1b63c9"/>
    <path d="M 813.09759 490.707706 
L 815.863456 493.011979 
L 817.37622 492.941454 
L 814.61339 490.615823 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0f7be1"/>
    <path d="M 707.719376 346.905876 
L 710.478818 350.93393 
L 712.093515 349.332091 
L 709.33612 345.265416 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d2c581"/>
    <path d="M 683.364403 304.309071 
L 686.124447 308.056187 
L 687.754164 306.188347 
L 684.995853 302.412453 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #886759"/>
    <path d="M 636.569938 251.07966 
L 639.308836 253.546598 
L 640.96254 251.278545 
L 638.224729 248.795401 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d3c7c4"/>
    <path d="M 609.789817 242.713332 
L 612.503792 244.340122 
L 614.163417 241.651179 
L 611.450086 240.01368 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e3dbd9"/>
    <path d="M 616.880807 243.392002 
L 619.602077 245.235129 
L 621.260946 242.674913 
L 618.540433 240.819394 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e1d9d7"/>
    <path d="M 744.255545 410.628952 
L 747.009351 414.435498 
L 748.596413 413.493194 
L 745.845252 409.640677 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #7de57f"/>
    <path d="M 729.321643 386.048955 
L 732.077693 390.022254 
L 733.677252 388.7884 
L 730.923593 384.770051 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d5f791"/>
    <path d="M 695.538736 325.303593 
L 698.299366 329.235343 
L 699.921817 327.48002 
L 697.163065 323.514241 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ac956c"/>
    <path d="M 778.468258 457.346441 
L 781.222438 460.509744 
L 782.774665 460.163549 
L 780.023553 456.962132 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00bc94"/>
    <path d="M 841.061089 508.270933 
L 843.847377 509.781646 
L 845.331241 509.646007 
L 842.547604 508.12793 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2256bc"/>
    <path d="M 781.222438 460.509744 
L 783.977112 463.610164 
L 785.526255 463.300972 
L 782.774665 460.163549 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b6a7"/>
    <path d="M 775.714456 454.122479 
L 778.468258 457.346441 
L 780.023553 456.962132 
L 777.272799 453.698979 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c088"/>
    <path d="M 598.353156 244.217895 
L 601.054895 245.519519 
L 602.71429 242.591932 
L 600.013024 241.282773 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e1d9d7"/>
    <path d="M 717.14151 364.601565 
L 719.899734 368.634671 
L 721.508269 367.181148 
L 718.752234 363.105737 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f0ec91"/>
    <path d="M 783.977112 463.610164 
L 786.732401 466.645544 
L 788.278445 466.372211 
L 785.526255 463.300972 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b0b9"/>
    <path d="M 850.910279 512.386194 
L 853.706043 513.607239 
L 855.181248 513.385535 
L 852.38794 512.161338 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #274bb1"/>
    <path d="M 772.960922 450.840142 
L 775.714456 454.122479 
L 777.272799 453.698979 
L 774.52229 450.376411 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c677"/>
    <path d="M 680.60443 300.615227 
L 683.364403 304.309071 
L 684.995853 302.412453 
L 682.23757 298.690331 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #825f56"/>
    <path d="M 786.732401 466.645544 
L 789.488431 469.61379 
L 791.031364 469.37514 
L 788.278445 466.372211 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00acc4"/>
    <path d="M 770.207547 447.501776 
L 772.960922 450.840142 
L 774.52229 450.376411 
L 771.771916 446.99681 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #01cc66"/>
    <path d="M 626.71284 246.691998 
L 629.443858 248.850922 
L 631.100569 246.43576 
L 628.370462 244.262134 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dbd1cf"/>
    <path d="M 639.308836 253.546598 
L 642.050301 256.107796 
L 643.702887 253.8569 
L 640.96254 251.278545 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cfc2bf"/>
    <path d="M 704.9592 342.897957 
L 707.719376 346.905876 
L 709.33612 345.265416 
L 706.577944 341.219064 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cabb7c"/>
    <path d="M 815.863456 493.011979 
L 818.631531 495.230675 
L 820.141276 495.180162 
L 817.37622 492.941454 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1078de"/>
    <path d="M 767.454232 444.109787 
L 770.207547 447.501776 
L 771.771916 446.99681 
L 769.021575 443.56262 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0dcf69"/>
    <path d="M 789.488431 469.61379 
L 792.245331 472.512879 
L 793.785143 472.307704 
L 791.031364 469.37514 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a6d7"/>
    <path d="M 741.501047 406.79513 
L 744.255545 410.628952 
L 745.845252 409.640677 
L 743.093354 405.760384 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8de882"/>
    <path d="M 593.997112 246.06277 
L 596.694504 247.256516 
L 598.353156 244.217895 
L 595.656172 243.017841 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ddd3d1"/>
    <path d="M 692.777694 321.408724 
L 695.538736 325.303593 
L 697.163065 323.514241 
L 694.403856 319.585706 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a68d69"/>
    <path d="M 677.844652 296.977734 
L 680.60443 300.615227 
L 682.23757 298.690331 
L 679.479438 295.025091 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #836059"/>
    <path d="M 726.564715 382.06643 
L 729.321643 386.048955 
L 730.923593 384.770051 
L 728.16901 380.742271 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e1f993"/>
    <path d="M 764.70088 440.666638 
L 767.454232 444.109787 
L 769.021575 443.56262 
L 766.271167 440.076343 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #19d16b"/>
    <path d="M 792.245331 472.512879 
L 795.003234 475.340853 
L 796.539918 475.167916 
L 793.785143 472.307704 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a2e2"/>
    <path d="M 831.227125 503.240549 
L 834.00585 505.026456 
L 835.499259 504.96065 
L 832.723361 503.162658 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1c60c6"/>
    <path d="M 576.630894 255.509987 
L 579.309064 256.304798 
L 580.963168 252.85236 
L 578.285257 252.058327 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cfc2bf"/>
    <path d="M 642.050301 256.107796 
L 644.794153 258.761327 
L 646.445589 256.528515 
L 643.702887 253.8569 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cbbcb9"/>
    <path d="M 605.420149 244.003791 
L 608.130431 245.5177 
L 609.789817 242.713332 
L 607.080089 241.189353 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e1d9d7"/>
    <path d="M 714.382427 360.57529 
L 717.14151 364.601565 
L 718.752234 363.105737 
L 715.995291 359.037182 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e8e28d"/>
    <path d="M 589.646547 248.121155 
L 592.339383 249.20984 
L 593.997112 246.06277 
L 591.30463 244.969229 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dbd1cf"/>
    <path d="M 619.602077 245.235129 
L 622.327049 247.179424 
L 623.985143 244.632869 
L 621.260946 242.674913 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dfd6d4"/>
    <path d="M 761.947401 437.174847 
L 764.70088 440.666638 
L 766.271167 440.076343 
L 763.520599 436.540538 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #25d36d"/>
    <path d="M 580.963168 252.85236 
L 583.646368 253.741156 
L 585.3018 250.386745 
L 582.618879 249.496645 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d3c7c4"/>
    <path d="M 585.3018 250.386745 
L 587.989898 251.373636 
L 589.646547 248.121155 
L 586.958759 247.131079 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d7ccc9"/>
    <path d="M 675.085196 293.399616 
L 677.844652 296.977734 
L 679.479438 295.025091 
L 676.721588 291.419791 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #896861"/>
    <path d="M 795.003234 475.340853 
L 797.762277 478.095827 
L 799.29583 477.953862 
L 796.539918 475.167916 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #009eef"/>
    <path d="M 738.745816 402.937003 
L 741.501047 406.79513 
L 743.093354 405.760384 
L 740.340679 401.85533 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #99eb85"/>
    <path d="M 629.443858 248.850922 
L 632.178014 251.108156 
L 633.833789 248.708807 
L 631.100569 246.43576 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d7ccc9"/>
    <path d="M 860.781395 515.53027 
L 863.588597 516.450269 
L 865.056074 516.128866 
L 862.251119 515.209363 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2a46ac"/>
    <path d="M 612.503792 244.340122 
L 615.221837 246.068829 
L 616.880807 243.392002 
L 614.163417 241.651179 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dfd6d4"/>
    <path d="M 702.19835 338.913477 
L 704.9592 342.897957 
L 706.577944 341.219064 
L 703.819048 337.196383 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c4b379"/>
    <path d="M 644.794153 258.761327 
L 647.540216 261.505165 
L 649.190469 259.291342 
L 646.445589 256.528515 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c7b7b4"/>
    <path d="M 690.016333 317.553976 
L 692.777694 321.408724 
L 694.403856 319.585706 
L 691.644282 315.697694 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9e8365"/>
    <path d="M 759.193708 433.636987 
L 761.947401 437.174847 
L 763.520599 436.540538 
L 760.769785 432.957817 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #31d670"/>
    <path d="M 818.631531 495.230675 
L 821.40198 497.362491 
L 822.908725 497.330624 
L 820.141276 495.180162 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1373d9"/>
    <path d="M 672.326198 289.883844 
L 675.085196 293.399616 
L 676.721588 291.419791 
L 673.964154 287.877433 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #91726c"/>
    <path d="M 723.806911 378.077857 
L 726.564715 382.06643 
L 728.16901 380.742271 
L 725.4135 376.708284 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1fc96"/>
    <path d="M 797.762277 478.095827 
L 800.522602 480.775985 
L 802.053023 480.663698 
L 799.29583 477.953862 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0098fe"/>
    <path d="M 647.540216 261.505165 
L 650.288313 264.337186 
L 651.93735 262.143235 
L 649.190469 259.291342 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c1b0ac"/>
    <path d="M 843.847377 509.781646 
L 846.637485 511.195168 
L 848.118739 511.06562 
L 845.331241 509.646007 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2353b9"/>
    <path d="M 711.622517 356.559122 
L 714.382427 360.57529 
L 715.995291 359.037182 
L 713.237472 354.978806 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e2da89"/>
    <path d="M 601.054895 245.519519 
L 603.761227 246.922186 
L 605.420149 244.003791 
L 602.71429 242.591932 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dfd6d4"/>
    <path d="M 756.439722 430.055681 
L 759.193708 433.636987 
L 760.769785 432.957817 
L 758.018641 429.330846 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #3dd872"/>
    <path d="M 669.567796 286.433328 
L 672.326198 289.883844 
L 673.964154 287.877433 
L 671.207275 284.40096 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #977a74"/>
    <path d="M 735.989823 399.057574 
L 738.745816 402.937003 
L 740.340679 401.85533 
L 737.587194 397.928564 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a9ee88"/>
    <path d="M 650.288313 264.337186 
L 653.038273 267.255175 
L 654.686056 265.081951 
L 651.93735 262.143235 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bdaba7"/>
    <path d="M 687.254753 313.742558 
L 690.016333 317.553976 
L 691.644282 315.697694 
L 688.884444 311.853451 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #987b61"/>
    <path d="M 632.178014 251.108156 
L 634.915127 253.462106 
L 636.569938 251.07966 
L 633.833789 248.708807 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d5c9c7"/>
    <path d="M 666.810134 283.050914 
L 669.567796 286.433328 
L 671.207275 284.40096 
L 668.451095 280.993249 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9d827c"/>
    <path d="M 699.436895 334.955727 
L 702.19835 338.913477 
L 703.819048 337.196383 
L 701.059497 333.200704 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bca975"/>
    <path d="M 853.706043 513.607239 
L 856.506209 514.728355 
L 857.979005 514.508617 
L 855.181248 513.385535 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #274bb1"/>
    <path d="M 800.522602 480.775985 
L 803.284352 483.379586 
L 804.811643 483.295656 
L 802.053023 480.663698 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0393f9"/>
    <path d="M 622.327049 247.179424 
L 625.055543 249.223638 
L 626.71284 246.691998 
L 623.985143 244.632869 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dbd1cf"/>
    <path d="M 653.038273 267.255175 
L 655.789923 270.256825 
L 657.436418 268.10516 
L 654.686056 265.081951 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b7a39f"/>
    <path d="M 664.053361 279.739385 
L 666.810134 283.050914 
L 668.451095 280.993249 
L 665.695764 277.657111 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a38984"/>
    <path d="M 753.685369 426.433601 
L 756.439722 430.055681 
L 758.018641 429.330846 
L 755.267093 425.662341 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #4ddb75"/>
    <path d="M 834.00585 505.026456 
L 836.787825 506.718747 
L 838.278442 506.663685 
L 835.499259 504.96065 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1e5ec4"/>
    <path d="M 655.789923 270.256825 
L 658.543096 273.339743 
L 660.188266 271.21044 
L 657.436418 268.10516 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b39e99"/>
    <path d="M 661.297629 276.501449 
L 664.053361 279.739385 
L 665.695764 277.657111 
L 662.941435 274.395286 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a78e89"/>
    <path d="M 658.543096 273.339743 
L 661.297629 276.501449 
L 662.941435 274.395286 
L 660.188266 271.21044 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ad9691"/>
    <path d="M 721.048236 374.086431 
L 723.806911 378.077857 
L 725.4135 376.708284 
L 722.65707 372.671332 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 608.130431 245.5177 
L 610.844967 247.132892 
L 612.503792 244.340122 
L 609.789817 242.713332 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dfd6d4"/>
    <path d="M 596.694504 247.256516 
L 599.396645 248.550059 
L 601.054895 245.519519 
L 598.353156 244.217895 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ddd3d1"/>
    <path d="M 821.40198 497.362491 
L 824.174967 499.406201 
L 825.678735 499.391601 
L 822.908725 497.330624 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1470d6"/>
    <path d="M 615.221837 246.068829 
L 617.943777 247.898448 
L 619.602077 245.235129 
L 616.880807 243.392002 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ddd3d1"/>
    <path d="M 708.861822 352.556339 
L 711.622517 356.559122 
L 713.237472 354.978806 
L 710.478818 350.93393 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dad085"/>
    <path d="M 684.493059 309.977642 
L 687.254753 313.742558 
L 688.884444 311.853451 
L 686.124447 308.056187 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #90715d"/>
    <path d="M 733.23304 395.159877 
L 735.989823 399.057574 
L 737.587194 397.928564 
L 734.832872 393.983169 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b9f18b"/>
    <path d="M 750.930582 422.77347 
L 753.685369 426.433601 
L 755.267093 425.662341 
L 752.51507 421.955068 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #59de78"/>
    <path d="M 803.284352 483.379586 
L 806.047676 485.90496 
L 807.571841 485.848042 
L 804.811643 483.295656 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #068ef4"/>
    <path d="M 634.915127 253.462106 
L 637.655017 255.911071 
L 639.308836 253.546598 
L 636.569938 251.07966 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d1c4c1"/>
    <path d="M 574.978207 259.056143 
L 577.65659 259.851717 
L 579.309064 256.304798 
L 576.630894 255.509987 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c9bab7"/>
    <path d="M 696.674907 331.02798 
L 699.436895 334.955727 
L 701.059497 333.200704 
L 698.299366 329.235343 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b49f70"/>
    <path d="M 592.339383 249.20984 
L 595.037115 250.396846 
L 596.694504 247.256516 
L 593.997112 246.06277 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d9cecc"/>
    <path d="M 579.309064 256.304798 
L 581.99249 257.192176 
L 583.646368 253.741156 
L 580.963168 252.85236 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cdbfbc"/>
    <path d="M 681.731363 306.26236 
L 684.493059 309.977642 
L 686.124447 308.056187 
L 683.364403 304.309071 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8a695a"/>
    <path d="M 587.989898 251.373636 
L 590.683025 252.457143 
L 592.339383 249.20984 
L 589.646547 248.121155 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d7ccc9"/>
    <path d="M 718.288704 370.095362 
L 721.048236 374.086431 
L 722.65707 372.671332 
L 719.899734 368.634671 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f8f695"/>
    <path d="M 625.055543 249.223638 
L 627.78738 251.366415 
L 629.443858 248.850922 
L 626.71284 246.691998 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d9cecc"/>
    <path d="M 748.175299 419.078051 
L 750.930582 422.77347 
L 752.51507 421.955068 
L 749.762509 418.211835 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #65e07a"/>
    <path d="M 583.646368 253.741156 
L 586.334718 254.724647 
L 587.989898 251.373636 
L 585.3018 250.386745 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d3c7c4"/>
    <path d="M 730.475449 391.246975 
L 733.23304 395.159877 
L 734.832872 393.983169 
L 732.077693 390.022254 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c5f38d"/>
    <path d="M 706.100389 348.570217 
L 708.861822 352.556339 
L 710.478818 350.93393 
L 707.719376 346.905876 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d2c581"/>
    <path d="M 637.655017 255.911071 
L 640.397504 258.453249 
L 642.050301 256.107796 
L 639.308836 253.546598 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cdbfbc"/>
    <path d="M 806.047676 485.90496 
L 808.812725 488.350514 
L 810.333772 488.319239 
L 807.571841 485.848042 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0888ee"/>
    <path d="M 603.761227 246.922186 
L 606.471984 248.425256 
L 608.130431 245.5177 
L 605.420149 244.003791 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ddd3d1"/>
    <path d="M 693.912469 327.133488 
L 696.674907 331.02798 
L 698.299366 329.235343 
L 695.538736 325.303593 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ae976d"/>
    <path d="M 846.637485 511.195168 
L 849.431592 512.510928 
L 850.910279 512.386194 
L 848.118739 511.06562 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2450b6"/>
    <path d="M 678.969783 302.599801 
L 681.731363 306.26236 
L 683.364403 304.309071 
L 680.60443 300.615227 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #846257"/>
    <path d="M 824.174967 499.406201 
L 826.950661 501.360664 
L 828.451478 501.361934 
L 825.678735 499.391601 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #176bd1"/>
    <path d="M 745.419463 415.350154 
L 748.175299 419.078051 
L 749.762509 418.211835 
L 747.009351 414.435498 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #75e37d"/>
    <path d="M 617.943777 247.898448 
L 620.669436 249.827859 
L 622.327049 247.179424 
L 619.602077 245.235129 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dbd1cf"/>
    <path d="M 836.787825 506.718747 
L 839.573228 508.316601 
L 841.061089 508.270933 
L 838.278442 506.663685 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1f5bc1"/>
    <path d="M 610.844967 247.132892 
L 613.563583 248.848489 
L 615.221837 246.068829 
L 612.503792 244.340122 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ddd3d1"/>
    <path d="M 640.397504 258.453249 
L 643.14241 261.086738 
L 644.794153 258.761327 
L 642.050301 256.107796 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c9bab7"/>
    <path d="M 715.528338 366.107866 
L 718.288704 370.095362 
L 719.899734 368.634671 
L 717.14151 364.601565 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f0ec91"/>
    <path d="M 727.717038 387.321956 
L 730.475449 391.246975 
L 732.077693 390.022254 
L 729.321643 386.048955 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d5f791"/>
    <path d="M 627.78738 251.366415 
L 630.522379 253.606289 
L 632.178014 251.108156 
L 629.443858 248.850922 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d5c9c7"/>
    <path d="M 676.208441 298.993004 
L 678.969783 302.599801 
L 680.60443 300.615227 
L 677.844652 296.977734 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #836059"/>
    <path d="M 808.812725 488.350514 
L 811.579651 490.714729 
L 813.09759 490.707706 
L 810.333772 488.319239 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0a86ec"/>
    <path d="M 703.338272 344.604024 
L 706.100389 348.570217 
L 707.719376 346.905876 
L 704.9592 342.897957 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ccbe7d"/>
    <path d="M 599.396645 248.550059 
L 602.103375 249.942882 
L 603.761227 246.922186 
L 601.054895 245.519519 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dbd1cf"/>
    <path d="M 691.149666 323.27548 
L 693.912469 327.133488 
L 695.538736 325.303593 
L 692.777694 321.408724 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a68d69"/>
    <path d="M 856.506209 514.728355 
L 859.310958 515.749233 
L 860.781395 515.53027 
L 857.979005 514.508617 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #274bb1"/>
    <path d="M 742.663024 411.592626 
L 745.419463 415.350154 
L 747.009351 414.435498 
L 744.255545 410.628952 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #81e680"/>
    <path d="M 643.14241 261.086738 
L 645.88956 263.809535 
L 647.540216 261.505165 
L 644.794153 258.761327 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c3b2af"/>
    <path d="M 673.447467 295.444961 
L 676.208441 298.993004 
L 677.844652 296.977734 
L 675.085196 293.399616 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #896861"/>
    <path d="M 573.327211 262.694454 
L 576.00576 263.490775 
L 577.65659 259.851717 
L 574.978207 259.056143 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c5b5b1"/>
    <path d="M 595.037115 250.396846 
L 597.739587 251.681772 
L 599.396645 248.550059 
L 596.694504 247.256516 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d9cecc"/>
    <path d="M 712.767163 362.12717 
L 715.528338 366.107866 
L 717.14151 364.601565 
L 714.382427 360.57529 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eae48e"/>
    <path d="M 645.88956 263.809535 
L 648.638778 266.619545 
L 650.288313 264.337186 
L 647.540216 261.505165 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bfada9"/>
    <path d="M 670.686993 291.958605 
L 673.447467 295.444961 
L 675.085196 293.399616 
L 672.326198 289.883844 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8f7069"/>
    <path d="M 724.9578 383.387928 
L 727.717038 387.321956 
L 729.321643 386.048955 
L 726.564715 382.06643 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e1f993"/>
    <path d="M 688.386593 319.457153 
L 691.149666 323.27548 
L 692.777694 321.408724 
L 690.016333 317.553976 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a08566"/>
    <path d="M 620.669436 249.827859 
L 623.398636 251.855835 
L 625.055543 249.223638 
L 622.327049 247.179424 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d9cecc"/>
    <path d="M 700.575533 340.661019 
L 703.338272 344.604024 
L 704.9592 342.897957 
L 702.19835 338.913477 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c4b379"/>
    <path d="M 739.90594 407.808354 
L 742.663024 411.592626 
L 744.255545 410.628952 
L 741.501047 406.79513 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8de882"/>
    <path d="M 630.522379 253.606289 
L 633.260361 255.941688 
L 634.915127 253.462106 
L 632.178014 251.108156 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d1c4c1"/>
    <path d="M 606.471984 248.425256 
L 609.187 250.027976 
L 610.844967 247.132892 
L 608.130431 245.5177 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dbd1cf"/>
    <path d="M 826.950661 501.360664 
L 829.72923 503.22482 
L 831.227125 503.240549 
L 828.451478 501.361934 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1868ce"/>
    <path d="M 577.65659 259.851717 
L 580.340189 260.737568 
L 581.99249 257.192176 
L 579.309064 256.304798 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c9bab7"/>
    <path d="M 811.579651 490.714729 
L 814.348612 492.996164 
L 815.863456 493.011979 
L 813.09759 490.707706 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0c80e6"/>
    <path d="M 590.683025 252.457143 
L 593.38103 253.636985 
L 595.037115 250.396846 
L 592.339383 249.20984 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d5c9c7"/>
    <path d="M 774.153327 454.48849 
L 776.910203 457.670825 
L 778.468258 457.346441 
L 775.714456 454.122479 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c47d"/>
    <path d="M 648.638778 266.619545 
L 651.389894 269.514577 
L 653.038273 267.255175 
L 650.288313 264.337186 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bba8a4"/>
    <path d="M 667.927158 288.536811 
L 670.686993 291.958605 
L 672.326198 289.883844 
L 669.567796 286.433328 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #957771"/>
    <path d="M 776.910203 457.670825 
L 779.66748 460.793641 
L 781.222438 460.509744 
L 778.468258 457.346441 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00be8f"/>
    <path d="M 771.396744 451.248881 
L 774.153327 454.48849 
L 775.714456 454.122479 
L 772.960922 450.840142 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c970"/>
    <path d="M 779.66748 460.793641 
L 782.425271 463.85475 
L 783.977112 463.610164 
L 781.222438 460.509744 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b8a0"/>
    <path d="M 613.563583 248.848489 
L 616.286107 250.6635 
L 617.943777 247.898448 
L 615.221837 246.068829 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dbd1cf"/>
    <path d="M 581.99249 257.192176 
L 584.681035 258.172057 
L 586.334718 254.724647 
L 583.646368 253.741156 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cdbfbc"/>
    <path d="M 586.334718 254.724647 
L 589.028072 255.802662 
L 590.683025 252.457143 
L 587.989898 251.373636 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d1c4c1"/>
    <path d="M 768.640349 447.954307 
L 771.396744 451.248881 
L 772.960922 450.840142 
L 770.207547 447.501776 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #05cd67"/>
    <path d="M 782.425271 463.85475 
L 785.183695 466.85203 
L 786.732401 466.645544 
L 783.977112 463.610164 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b4ac"/>
    <path d="M 665.168106 285.182393 
L 667.927158 288.536811 
L 669.567796 286.433328 
L 666.810134 283.050914 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9b7f79"/>
    <path d="M 651.389894 269.514577 
L 654.142737 272.492355 
L 655.789923 270.256825 
L 653.038273 267.255175 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b5a09c"/>
    <path d="M 765.884043 444.607132 
L 768.640349 447.954307 
L 770.207547 447.501776 
L 767.454232 444.109787 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #11cf69"/>
    <path d="M 839.573228 508.316601 
L 842.362234 509.819283 
L 843.847377 509.781646 
L 841.061089 508.270933 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2058be"/>
    <path d="M 849.431592 512.510928 
L 852.229876 513.728442 
L 853.706043 513.607239 
L 850.910279 512.386194 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2450b6"/>
    <path d="M 662.409983 281.898098 
L 665.168106 285.182393 
L 666.810134 283.050914 
L 664.053361 279.739385 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a18781"/>
    <path d="M 685.623348 315.681676 
L 688.386593 319.457153 
L 690.016333 317.553976 
L 687.254753 313.742558 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #987b61"/>
    <path d="M 654.142737 272.492355 
L 656.897141 275.550513 
L 658.543096 273.339743 
L 655.789923 270.256825 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b19b96"/>
    <path d="M 785.183695 466.85203 
L 787.942874 469.783424 
L 789.488431 469.61379 
L 786.732401 466.645544 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00aebf"/>
    <path d="M 659.652943 278.686603 
L 662.409983 281.898098 
L 664.053361 279.739385 
L 661.297629 276.501449 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a78e89"/>
    <path d="M 656.897141 275.550513 
L 659.652943 278.686603 
L 661.297629 276.501449 
L 658.543096 273.339743 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ab938e"/>
    <path d="M 737.148174 404.000259 
L 739.90594 407.808354 
L 741.501047 406.79513 
L 738.745816 402.937003 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9deb85"/>
    <path d="M 710.005215 358.156504 
L 712.767163 362.12717 
L 714.382427 360.57529 
L 711.622517 356.559122 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e2da89"/>
    <path d="M 722.197739 379.448021 
L 724.9578 383.387928 
L 726.564715 382.06643 
L 723.806911 378.077857 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1fc96"/>
    <path d="M 763.127733 441.209777 
L 765.884043 444.607132 
L 767.454232 444.109787 
L 764.70088 440.666638 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1dd26c"/>
    <path d="M 697.812239 336.744447 
L 700.575533 340.661019 
L 702.19835 338.913477 
L 699.436895 334.955727 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bca975"/>
    <path d="M 633.260361 255.941688 
L 636.001147 258.370935 
L 637.655017 255.911071 
L 634.915127 253.462106 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cdbfbc"/>
    <path d="M 787.942874 469.783424 
L 790.702934 472.646939 
L 792.245331 472.512879 
L 789.488431 469.61379 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00aacb"/>
    <path d="M 602.103375 249.942882 
L 604.814529 251.434358 
L 606.471984 248.425256 
L 603.761227 246.922186 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d9cecc"/>
    <path d="M 760.37133 437.76472 
L 763.127733 441.209777 
L 764.70088 440.666638 
L 761.947401 437.174847 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #29d46e"/>
    <path d="M 814.348612 492.996164 
L 817.119766 495.193456 
L 818.631531 495.230675 
L 815.863456 493.011979 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0f7be1"/>
    <path d="M 623.398636 251.855835 
L 626.131199 253.981039 
L 627.78738 251.366415 
L 625.055543 249.223638 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d5c9c7"/>
    <path d="M 682.860037 311.952179 
L 685.623348 315.681676 
L 687.254753 313.742558 
L 684.493059 309.977642 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #92735e"/>
    <path d="M 790.702934 472.646939 
L 793.464007 475.44065 
L 795.003234 475.340853 
L 792.245331 472.512879 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a4dc"/>
    <path d="M 757.614752 434.274487 
L 760.37133 437.76472 
L 761.947401 437.174847 
L 759.193708 433.636987 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #35d771"/>
    <path d="M 734.389694 400.171297 
L 737.148174 404.000259 
L 738.745816 402.937003 
L 735.989823 399.057574 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a9ee88"/>
    <path d="M 829.72923 503.22482 
L 832.510846 504.997691 
L 834.00585 505.026456 
L 831.227125 503.240549 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1a66cc"/>
    <path d="M 571.677914 266.422479 
L 574.356583 267.219533 
L 576.00576 263.490775 
L 573.327211 262.694454 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bfada9"/>
    <path d="M 707.242535 354.199097 
L 710.005215 358.156504 
L 711.622517 356.559122 
L 708.861822 352.556339 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dad085"/>
    <path d="M 636.001147 258.370935 
L 638.74456 260.892253 
L 640.397504 258.453249 
L 637.655017 255.911071 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c9bab7"/>
    <path d="M 719.43686 375.505379 
L 722.197739 379.448021 
L 723.806911 378.077857 
L 721.048236 374.086431 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 695.048464 332.857536 
L 697.812239 336.744447 
L 699.436895 334.955727 
L 696.674907 331.02798 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b6a272"/>
    <path d="M 609.187 250.027976 
L 611.906104 251.729484 
L 613.563583 248.848489 
L 610.844967 247.132892 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d9cecc"/>
    <path d="M 616.286107 250.6635 
L 619.012364 252.576827 
L 620.669436 249.827859 
L 617.943777 247.898448 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d7ccc9"/>
    <path d="M 859.310958 515.749233 
L 862.120469 516.669652 
L 863.588597 516.450269 
L 860.781395 515.53027 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #274bb1"/>
    <path d="M 597.739587 251.681772 
L 600.44664 253.064114 
L 602.103375 249.942882 
L 599.396645 248.550059 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d7ccc9"/>
    <path d="M 793.464007 475.44065 
L 796.226226 478.162703 
L 797.762277 478.095827 
L 795.003234 475.340853 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a0e8"/>
    <path d="M 754.85792 430.741659 
L 757.614752 434.274487 
L 759.193708 433.636987 
L 756.439722 430.055681 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #41d973"/>
    <path d="M 680.096772 308.271755 
L 682.860037 311.952179 
L 684.493059 309.977642 
L 681.731363 306.26236 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8c6c5b"/>
    <path d="M 576.00576 263.490775 
L 578.689482 264.374992 
L 580.340189 260.737568 
L 577.65659 259.851717 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c3b2af"/>
    <path d="M 731.630476 396.32445 
L 734.389694 400.171297 
L 735.989823 399.057574 
L 733.23304 395.159877 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b9f18b"/>
    <path d="M 626.131199 253.981039 
L 628.866947 256.202027 
L 630.522379 253.606289 
L 627.78738 251.366415 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d3c7c4"/>
    <path d="M 752.100764 427.168862 
L 754.85792 430.741659 
L 756.439722 430.055681 
L 753.685369 426.433601 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #4ddb75"/>
    <path d="M 638.74456 260.892253 
L 641.490424 263.503764 
L 643.14241 261.086738 
L 640.397504 258.453249 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c5b5b1"/>
    <path d="M 817.119766 495.193456 
L 819.893274 497.30532 
L 821.40198 497.362491 
L 818.631531 495.230675 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1078de"/>
    <path d="M 593.38103 253.636985 
L 596.083762 254.91277 
L 597.739587 251.681772 
L 595.037115 250.396846 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d5c9c7"/>
    <path d="M 796.226226 478.162703 
L 798.98973 480.811311 
L 800.522602 480.775985 
L 797.762277 478.095827 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #009cf4"/>
    <path d="M 677.33367 304.643451 
L 680.096772 308.271755 
L 681.731363 306.26236 
L 678.969783 302.599801 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #846257"/>
    <path d="M 692.284289 329.003494 
L 695.048464 332.857536 
L 696.674907 331.02798 
L 693.912469 327.133488 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ae976d"/>
    <path d="M 704.47917 350.258176 
L 707.242535 354.199097 
L 708.861822 352.556339 
L 706.100389 348.570217 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d4c882"/>
    <path d="M 716.67518 371.563161 
L 719.43686 375.505379 
L 721.048236 374.086431 
L 718.288704 370.095362 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f8f695"/>
    <path d="M 580.340189 260.737568 
L 583.028872 261.713633 
L 584.681035 258.172057 
L 581.99249 257.192176 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c9bab7"/>
    <path d="M 842.362234 509.819283 
L 845.155017 511.226142 
L 846.637485 511.195168 
L 843.847377 509.781646 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2058be"/>
    <path d="M 589.028072 255.802662 
L 591.726286 256.974925 
L 593.38103 253.636985 
L 590.683025 252.457143 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d1c4c1"/>
    <path d="M 584.681035 258.172057 
L 587.374556 259.244272 
L 589.028072 255.802662 
L 586.334718 254.724647 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cdbfbc"/>
    <path d="M 749.343216 423.558771 
L 752.100764 427.168862 
L 753.685369 426.433601 
L 750.930582 422.77347 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #5ddf79"/>
    <path d="M 604.814529 251.434358 
L 607.529944 253.023748 
L 609.187 250.027976 
L 606.471984 248.425256 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d7ccc9"/>
    <path d="M 641.490424 263.503764 
L 644.238563 266.203495 
L 645.88956 263.809535 
L 643.14241 261.086738 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c1b0ac"/>
    <path d="M 674.570852 301.070269 
L 677.33367 304.643451 
L 678.969783 302.599801 
L 676.208441 298.993004 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #815e56"/>
    <path d="M 852.229876 513.728442 
L 855.032515 514.847316 
L 856.506209 514.728355 
L 853.706043 513.607239 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2450b6"/>
    <path d="M 798.98973 480.811311 
L 801.754661 483.384761 
L 803.284352 483.379586 
L 800.522602 480.775985 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0098fe"/>
    <path d="M 728.870503 392.462731 
L 731.630476 396.32445 
L 733.23304 395.159877 
L 730.475449 391.246975 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c5f38d"/>
    <path d="M 619.012364 252.576827 
L 621.742179 254.587261 
L 623.398636 251.855835 
L 620.669436 249.827859 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d5c9c7"/>
    <path d="M 689.519801 325.185502 
L 692.284289 329.003494 
L 693.912469 327.133488 
L 691.149666 323.27548 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a8906a"/>
    <path d="M 611.906104 251.729484 
L 614.629125 253.528808 
L 616.286107 250.6635 
L 613.563583 248.848489 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d7ccc9"/>
    <path d="M 832.510846 504.997691 
L 835.29568 506.678384 
L 836.787825 506.718747 
L 834.00585 505.026456 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1b63c9"/>
    <path d="M 628.866947 256.202027 
L 631.605703 258.51725 
L 633.260361 255.941688 
L 630.522379 253.606289 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cfc2bf"/>
    <path d="M 671.808447 297.555159 
L 674.570852 301.070269 
L 676.208441 298.993004 
L 673.447467 295.444961 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #87655e"/>
    <path d="M 746.585218 419.914102 
L 749.343216 423.558771 
L 750.930582 422.77347 
L 748.175299 419.078051 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #69e17b"/>
    <path d="M 644.238563 266.203495 
L 646.988805 268.989377 
L 648.638778 266.619545 
L 645.88956 263.809535 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bdaba7"/>
    <path d="M 701.715176 346.336961 
L 704.47917 350.258176 
L 706.100389 348.570217 
L 703.338272 344.604024 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ccbe7d"/>
    <path d="M 713.912719 367.624534 
L 716.67518 371.563161 
L 718.288704 370.095362 
L 715.528338 366.107866 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f0ec91"/>
    <path d="M 570.030319 270.237687 
L 572.709063 271.035461 
L 574.356583 267.219533 
L 571.677914 266.422479 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b9a5a1"/>
    <path d="M 819.893274 497.30532 
L 822.6693 499.330549 
L 824.174967 499.406201 
L 821.40198 497.362491 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1373d9"/>
    <path d="M 669.046588 294.101016 
L 671.808447 297.555159 
L 673.447467 295.444961 
L 670.686993 291.958605 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8d6d66"/>
    <path d="M 600.44664 253.064114 
L 603.158114 254.543255 
L 604.814529 251.434358 
L 602.103375 249.942882 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d5c9c7"/>
    <path d="M 646.988805 268.989377 
L 649.740979 271.859251 
L 651.389894 269.514577 
L 648.638778 266.619545 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b9a5a1"/>
    <path d="M 801.754661 483.384761 
L 804.521162 485.881409 
L 806.047676 485.90496 
L 803.284352 483.379586 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0393f9"/>
    <path d="M 726.109764 388.589175 
L 728.870503 392.462731 
L 730.475449 391.246975 
L 727.717038 387.321956 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d5f791"/>
    <path d="M 743.826714 416.237616 
L 746.585218 419.914102 
L 748.175299 419.078051 
L 745.419463 415.350154 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #75e37d"/>
    <path d="M 686.755093 321.406715 
L 689.519801 325.185502 
L 691.149666 323.27548 
L 688.386593 319.457153 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a08566"/>
    <path d="M 666.285412 290.710679 
L 669.046588 294.101016 
L 670.686993 291.958605 
L 667.927158 288.536811 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #93756e"/>
    <path d="M 649.740979 271.859251 
L 652.494918 274.81087 
L 654.142737 272.492355 
L 651.389894 269.514577 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b39e99"/>
    <path d="M 663.525062 287.386923 
L 666.285412 290.710679 
L 667.927158 288.536811 
L 665.168106 285.182393 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #997c76"/>
    <path d="M 631.605703 258.51725 
L 634.34729 260.925058 
L 636.001147 258.370935 
L 633.260361 255.941688 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cbbcb9"/>
    <path d="M 574.356583 267.219533 
L 577.040377 268.102013 
L 578.689482 264.374992 
L 576.00576 263.490775 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bfada9"/>
    <path d="M 652.494918 274.81087 
L 655.250456 277.841901 
L 656.897141 275.550513 
L 654.142737 272.492355 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #af9994"/>
    <path d="M 698.950613 342.438661 
L 701.715176 346.336961 
L 703.338272 344.604024 
L 700.575533 340.661019 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c4b379"/>
    <path d="M 711.149505 363.692674 
L 713.912719 367.624534 
L 715.528338 366.107866 
L 712.767163 362.12717 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eae48e"/>
    <path d="M 660.765685 284.132459 
L 663.525062 287.386923 
L 665.168106 285.182393 
L 662.409983 281.898098 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9f847e"/>
    <path d="M 621.742179 254.587261 
L 624.475375 256.693487 
L 626.131199 253.981039 
L 623.398636 251.855835 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d3c7c4"/>
    <path d="M 655.250456 277.841901 
L 658.007431 280.949928 
L 659.652943 278.686603 
L 656.897141 275.550513 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a9918c"/>
    <path d="M 658.007431 280.949928 
L 660.765685 284.132459 
L 662.409983 281.898098 
L 659.652943 278.686603 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a58c86"/>
    <path d="M 596.083762 254.91277 
L 598.791065 256.284005 
L 600.44664 253.064114 
L 597.739587 251.681772 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d3c7c4"/>
    <path d="M 741.067657 412.53211 
L 743.826714 416.237616 
L 745.419463 415.350154 
L 742.663024 411.592626 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #85e781"/>
    <path d="M 607.529944 253.023748 
L 610.249451 254.710207 
L 611.906104 251.729484 
L 609.187 250.027976 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d5c9c7"/>
    <path d="M 804.521162 485.881409 
L 807.289381 488.299689 
L 808.812725 488.350514 
L 806.047676 485.90496 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #068ef4"/>
    <path d="M 683.990264 317.670257 
L 686.755093 321.406715 
L 688.386593 319.457153 
L 685.623348 315.681676 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9a7e62"/>
    <path d="M 723.348255 384.706841 
L 726.109764 388.589175 
L 727.717038 387.321956 
L 724.9578 383.387928 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e1f993"/>
    <path d="M 578.689482 264.374992 
L 581.378247 265.347044 
L 583.028872 261.713633 
L 580.340189 260.737568 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c3b2af"/>
    <path d="M 845.155017 511.226142 
L 847.951756 512.536615 
L 849.431592 512.510928 
L 846.637485 511.195168 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2256bc"/>
    <path d="M 614.629125 253.528808 
L 617.355891 255.424867 
L 619.012364 252.576827 
L 616.286107 250.6635 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d5c9c7"/>
    <path d="M 591.726286 256.974925 
L 594.429208 258.241058 
L 596.083762 254.91277 
L 593.38103 253.636985 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cfc2bf"/>
    <path d="M 583.028872 261.713633 
L 585.7225 262.779751 
L 587.374556 259.244272 
L 584.681035 258.172057 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c9bab7"/>
    <path d="M 634.34729 260.925058 
L 637.091532 263.423699 
L 638.74456 260.892253 
L 636.001147 258.370935 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c7b7b4"/>
    <path d="M 587.374556 259.244272 
L 590.072912 260.408555 
L 591.726286 256.974925 
L 589.028072 255.802662 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cdbfbc"/>
    <path d="M 822.6693 499.330549 
L 825.448007 501.268019 
L 826.950661 501.360664 
L 824.174967 499.406201 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1470d6"/>
    <path d="M 696.185549 338.566474 
L 698.950613 342.438661 
L 700.575533 340.661019 
L 697.812239 336.744447 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #beac76"/>
    <path d="M 835.29568 506.678384 
L 838.083904 508.266087 
L 839.573228 508.316601 
L 836.787825 506.718747 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1c60c6"/>
    <path d="M 738.308006 408.800421 
L 741.067657 412.53211 
L 742.663024 411.592626 
L 739.90594 407.808354 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #91e983"/>
    <path d="M 708.385575 359.770757 
L 711.149505 363.692674 
L 712.767163 362.12717 
L 710.005215 358.156504 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e2da89"/>
    <path d="M 681.225419 313.979213 
L 683.990264 317.670257 
L 685.623348 315.681676 
L 682.860037 311.952179 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #94765f"/>
    <path d="M 568.384421 274.137456 
L 571.063198 274.935936 
L 572.709063 271.035461 
L 570.030319 270.237687 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b39e99"/>
    <path d="M 855.032515 514.847316 
L 857.839688 515.867242 
L 859.310958 515.749233 
L 856.506209 514.728355 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #264eb4"/>
    <path d="M 624.475375 256.693487 
L 627.211778 258.894085 
L 628.866947 256.202027 
L 626.131199 253.981039 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cfc2bf"/>
    <path d="M 720.585977 380.818804 
L 723.348255 384.706841 
L 724.9578 383.387928 
L 722.197739 379.448021 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1fc96"/>
    <path d="M 807.289381 488.299689 
L 810.059471 490.638105 
L 811.579651 490.714729 
L 808.812725 488.350514 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0888ee"/>
    <path d="M 603.158114 254.543255 
L 605.873847 256.118475 
L 607.529944 253.023748 
L 604.814529 251.434358 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d3c7c4"/>
    <path d="M 637.091532 263.423699 
L 639.838254 266.011325 
L 641.490424 263.503764 
L 638.74456 260.892253 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c3b2af"/>
    <path d="M 678.460669 310.336632 
L 681.225419 313.979213 
L 682.860037 311.952179 
L 680.096772 308.271755 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8c6c5b"/>
    <path d="M 693.420059 334.723579 
L 696.185549 338.566474 
L 697.812239 336.744447 
L 695.048464 332.857536 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b6a272"/>
    <path d="M 735.547725 405.045419 
L 738.308006 408.800421 
L 739.90594 407.808354 
L 737.148174 404.000259 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9deb85"/>
    <path d="M 705.620968 355.861963 
L 708.385575 359.770757 
L 710.005215 358.156504 
L 707.242535 354.199097 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dcd286"/>
    <path d="M 617.355891 255.424867 
L 620.086229 257.416476 
L 621.742179 254.587261 
L 619.012364 252.576827 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d1c4c1"/>
    <path d="M 610.249451 254.710207 
L 612.972882 256.492782 
L 614.629125 253.528808 
L 611.906104 251.729484 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d3c7c4"/>
    <path d="M 572.709063 271.035461 
L 575.392882 271.916103 
L 577.040377 268.102013 
L 574.356583 267.219533 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b9a5a1"/>
    <path d="M 772.589344 454.797949 
L 775.349317 457.936256 
L 776.910203 457.670825 
L 774.153327 454.48849 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c677"/>
    <path d="M 769.829691 451.603531 
L 772.589344 454.797949 
L 774.153327 454.48849 
L 771.396744 451.248881 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #01cc66"/>
    <path d="M 775.349317 457.936256 
L 778.109717 461.016244 
L 779.66748 460.793641 
L 776.910203 457.670825 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c088"/>
    <path d="M 767.070257 448.355268 
L 769.829691 451.603531 
L 771.396744 451.248881 
L 768.640349 447.954307 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #09ce68"/>
    <path d="M 639.838254 266.011325 
L 642.587285 268.685989 
L 644.238563 266.203495 
L 641.490424 263.503764 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bfada9"/>
    <path d="M 675.696131 306.745518 
L 678.460669 310.336632 
L 680.096772 308.271755 
L 677.33367 304.643451 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #866458"/>
    <path d="M 717.822939 376.928156 
L 720.585977 380.818804 
L 722.197739 379.448021 
L 719.43686 375.505379 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 598.791065 256.284005 
L 601.502781 257.750088 
L 603.158114 254.543255 
L 600.44664 253.064114 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d1c4c1"/>
    <path d="M 778.109717 461.016244 
L 780.870655 464.035766 
L 782.425271 463.85475 
L 779.66748 460.793641 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00bc94"/>
    <path d="M 764.310947 445.055481 
L 767.070257 448.355268 
L 768.640349 447.954307 
L 765.884043 444.607132 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #15d06a"/>
    <path d="M 627.211778 258.894085 
L 629.951212 261.187532 
L 631.605703 258.51725 
L 628.866947 256.202027 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cbbcb9"/>
    <path d="M 825.448007 501.268019 
L 828.229562 503.116685 
L 829.72923 503.22482 
L 826.950661 501.360664 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #166ed4"/>
    <path d="M 810.059471 490.638105 
L 812.831583 492.89524 
L 814.348612 492.996164 
L 811.579651 490.714729 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0a86ec"/>
    <path d="M 732.786784 401.270006 
L 735.547725 405.045419 
L 737.148174 404.000259 
L 734.389694 400.171297 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #adef89"/>
    <path d="M 761.551669 441.706549 
L 764.310947 445.055481 
L 765.884043 444.607132 
L 763.127733 441.209777 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #21d36d"/>
    <path d="M 780.870655 464.035766 
L 783.632246 466.992739 
L 785.183695 466.85203 
L 782.425271 463.85475 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b6a7"/>
    <path d="M 690.654222 330.913134 
L 693.420059 334.723579 
L 695.048464 332.857536 
L 692.284289 329.003494 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b09a6e"/>
    <path d="M 577.040377 268.102013 
L 579.729171 269.069859 
L 581.378247 265.347044 
L 578.689482 264.374992 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bfada9"/>
    <path d="M 672.931926 303.20883 
L 675.696131 306.745518 
L 677.33367 304.643451 
L 674.570852 301.070269 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #805c54"/>
    <path d="M 642.587285 268.685989 
L 645.338452 271.445657 
L 646.988805 268.989377 
L 644.238563 266.203495 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bba8a4"/>
    <path d="M 758.792336 438.310903 
L 761.551669 441.706549 
L 763.127733 441.209777 
L 760.37133 437.76472 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2dd56f"/>
    <path d="M 783.632246 466.992739 
L 786.394609 469.885139 
L 787.942874 469.783424 
L 785.183695 466.85203 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b2b2"/>
    <path d="M 702.855734 351.969467 
L 705.620968 355.861963 
L 707.242535 354.199097 
L 704.47917 350.258176 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d4c882"/>
    <path d="M 594.429208 258.241058 
L 597.136687 259.600576 
L 598.791065 256.284005 
L 596.083762 254.91277 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cfc2bf"/>
    <path d="M 847.951756 512.536615 
L 850.752626 513.750224 
L 852.229876 513.728442 
L 849.431592 512.510928 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2256bc"/>
    <path d="M 838.083904 508.266087 
L 840.875692 509.760074 
L 842.362234 509.819283 
L 839.573228 508.316601 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1e5ec4"/>
    <path d="M 581.378247 265.347044 
L 584.071921 266.406773 
L 585.7225 262.779751 
L 583.028872 261.713633 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c3b2af"/>
    <path d="M 756.032868 434.871024 
L 758.792336 438.310903 
L 760.37133 437.76472 
L 757.614752 434.274487 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #39d771"/>
    <path d="M 670.168181 299.729476 
L 672.931926 303.20883 
L 674.570852 301.070269 
L 671.808447 297.555159 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #85635c"/>
    <path d="M 715.059157 373.038002 
L 717.822939 376.928156 
L 719.43686 375.505379 
L 716.67518 371.563161 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f8f695"/>
    <path d="M 566.740211 278.119078 
L 569.418979 278.918251 
L 571.063198 274.935936 
L 568.384421 274.137456 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ad9691"/>
    <path d="M 590.072912 260.408555 
L 592.775955 261.664535 
L 594.429208 258.241058 
L 591.726286 256.974925 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cbbcb9"/>
    <path d="M 786.394609 469.885139 
L 789.157868 472.71101 
L 790.702934 472.646939 
L 787.942874 469.783424 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00acc4"/>
    <path d="M 645.338452 271.445657 
L 648.091587 274.2882 
L 649.740979 271.859251 
L 646.988805 268.989377 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b7a39f"/>
    <path d="M 730.025161 397.477113 
L 732.786784 401.270006 
L 734.389694 400.171297 
L 731.630476 396.32445 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b9f18b"/>
    <path d="M 585.7225 262.779751 
L 588.420933 263.93566 
L 590.072912 260.408555 
L 587.374556 259.244272 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c7b7b4"/>
    <path d="M 687.888126 327.138274 
L 690.654222 330.913134 
L 692.284289 329.003494 
L 689.519801 325.185502 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #aa926b"/>
    <path d="M 605.873847 256.118475 
L 608.593673 257.788944 
L 610.249451 254.710207 
L 607.529944 253.023748 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d1c4c1"/>
    <path d="M 620.086229 257.416476 
L 622.819966 259.502343 
L 624.475375 256.693487 
L 621.742179 254.587261 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cfc2bf"/>
    <path d="M 629.951212 261.187532 
L 632.693503 263.572205 
L 634.34729 260.925058 
L 631.605703 258.51725 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c9bab7"/>
    <path d="M 667.405029 296.31031 
L 670.168181 299.729476 
L 671.808447 297.555159 
L 669.046588 294.101016 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8b6b64"/>
    <path d="M 753.27319 431.389445 
L 756.032868 434.871024 
L 757.614752 434.274487 
L 754.85792 430.741659 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #45da74"/>
    <path d="M 648.091587 274.2882 
L 650.846523 277.211403 
L 652.494918 274.81087 
L 649.740979 271.859251 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b19b96"/>
    <path d="M 812.831583 492.89524 
L 815.605873 495.069752 
L 817.119766 495.193456 
L 814.348612 492.996164 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0c80e6"/>
    <path d="M 612.972882 256.492782 
L 615.700068 258.370414 
L 617.355891 255.424867 
L 614.629125 253.528808 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d1c4c1"/>
    <path d="M 789.157868 472.71101 
L 791.922151 475.468462 
L 793.464007 475.44065 
L 790.702934 472.646939 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a8d0"/>
    <path d="M 700.089927 348.096435 
L 702.855734 351.969467 
L 704.47917 350.258176 
L 701.715176 346.336961 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ccbe7d"/>
    <path d="M 664.642606 292.954128 
L 667.405029 296.31031 
L 669.046588 294.101016 
L 666.285412 290.710679 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #91726c"/>
    <path d="M 650.846523 277.211403 
L 653.603096 280.21297 
L 655.250456 277.841901 
L 652.494918 274.81087 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ad9691"/>
    <path d="M 750.513232 427.868745 
L 753.27319 431.389445 
L 754.85792 430.741659 
L 752.100764 427.168862 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #51dc76"/>
    <path d="M 661.881053 289.663667 
L 664.642606 292.954128 
L 666.285412 290.710679 
L 663.525062 287.386923 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #977a74"/>
    <path d="M 653.603096 280.21297 
L 656.361147 283.29052 
L 658.007431 280.949928 
L 655.250456 277.841901 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a78e89"/>
    <path d="M 659.120517 286.441596 
L 661.881053 289.663667 
L 663.525062 287.386923 
L 660.765685 284.132459 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9d827c"/>
    <path d="M 685.121863 323.402104 
L 687.888126 327.138274 
L 689.519801 325.185502 
L 686.755093 321.406715 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a28867"/>
    <path d="M 656.361147 283.29052 
L 659.120517 286.441596 
L 660.765685 284.132459 
L 658.007431 280.949928 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a18781"/>
    <path d="M 727.262839 393.669698 
L 730.025161 397.477113 
L 731.630476 396.32445 
L 728.870503 392.462731 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c9f48e"/>
    <path d="M 712.294653 369.151456 
L 715.059157 373.038002 
L 716.67518 371.563161 
L 713.912719 367.624534 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f0ec91"/>
    <path d="M 857.839688 515.867242 
L 860.65157 516.788003 
L 862.120469 516.669652 
L 859.310958 515.749233 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #264eb4"/>
    <path d="M 571.063198 274.935936 
L 573.746993 275.814645 
L 575.392882 271.916103 
L 572.709063 271.035461 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b39e99"/>
    <path d="M 828.229562 503.116685 
L 831.014133 504.875582 
L 832.510846 504.997691 
L 829.72923 503.22482 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #176bd1"/>
    <path d="M 791.922151 475.468462 
L 794.687589 478.15567 
L 796.226226 478.162703 
L 793.464007 475.44065 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a4dc"/>
    <path d="M 601.502781 257.750088 
L 604.218751 259.310314 
L 605.873847 256.118475 
L 603.158114 254.543255 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cfc2bf"/>
    <path d="M 632.693503 263.572205 
L 635.438476 266.04638 
L 637.091532 263.423699 
L 634.34729 260.925058 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c5b5b1"/>
    <path d="M 747.752931 424.311547 
L 750.513232 427.868745 
L 752.100764 427.168862 
L 749.343216 423.558771 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #5ddf79"/>
    <path d="M 697.323609 344.246027 
L 700.089927 348.096435 
L 701.715176 346.336961 
L 698.950613 342.438661 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c6b67a"/>
    <path d="M 622.819966 259.502343 
L 625.55693 261.681072 
L 627.211778 258.894085 
L 624.475375 256.693487 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cbbcb9"/>
    <path d="M 682.355532 319.707701 
L 685.121863 323.402104 
L 686.755093 321.406715 
L 683.990264 317.670257 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9c8064"/>
    <path d="M 575.392882 271.916103 
L 578.081651 272.879558 
L 579.729171 269.069859 
L 577.040377 268.102013 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b9a5a1"/>
    <path d="M 724.499809 389.850742 
L 727.262839 393.669698 
L 728.870503 392.462731 
L 726.109764 388.589175 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d5f791"/>
    <path d="M 744.992228 420.720519 
L 747.752931 424.311547 
L 749.343216 423.558771 
L 746.585218 419.914102 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #6de27c"/>
    <path d="M 794.687589 478.15567 
L 797.454317 480.770881 
L 798.98973 480.811311 
L 796.226226 478.162703 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a0e8"/>
    <path d="M 709.529456 365.271638 
L 712.294653 369.151456 
L 713.912719 367.624534 
L 711.149505 363.692674 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eae48e"/>
    <path d="M 565.097673 282.17976 
L 567.776391 282.979614 
L 569.418979 278.918251 
L 566.740211 278.119078 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a78e89"/>
    <path d="M 815.605873 495.069752 
L 818.3825 497.160375 
L 819.893274 497.30532 
L 817.119766 495.193456 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0e7ee4"/>
    <path d="M 597.136687 259.600576 
L 599.848568 261.052893 
L 601.502781 257.750088 
L 598.791065 256.284005 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cdbfbc"/>
    <path d="M 608.593673 257.788944 
L 611.317429 259.55373 
L 612.972882 256.492782 
L 610.249451 254.710207 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cfc2bf"/>
    <path d="M 635.438476 266.04638 
L 638.18596 268.608238 
L 639.838254 266.011325 
L 637.091532 263.423699 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c1b0ac"/>
    <path d="M 840.875692 509.760074 
L 843.671217 511.159705 
L 845.155017 511.226142 
L 842.362234 509.819283 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1f5bc1"/>
    <path d="M 615.700068 258.370414 
L 618.430839 260.341938 
L 620.086229 257.416476 
L 617.355891 255.424867 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cfc2bf"/>
    <path d="M 679.589238 316.058102 
L 682.355532 319.707701 
L 683.990264 317.670257 
L 681.225419 313.979213 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #967960"/>
    <path d="M 579.729171 269.069859 
L 582.422834 270.12292 
L 584.071921 266.406773 
L 581.378247 265.347044 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bdaba7"/>
    <path d="M 694.556847 340.421386 
L 697.323609 344.246027 
L 698.950613 342.438661 
L 696.185549 338.566474 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #beac76"/>
    <path d="M 742.231071 417.098368 
L 744.992228 420.720519 
L 746.585218 419.914102 
L 743.826714 416.237616 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #79e47e"/>
    <path d="M 592.775955 261.664535 
L 595.483538 263.011741 
L 597.136687 259.600576 
L 594.429208 258.241058 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c9bab7"/>
    <path d="M 850.752626 513.750224 
L 853.557803 514.866579 
L 855.032515 514.847316 
L 852.229876 513.728442 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2353b9"/>
    <path d="M 584.071921 266.406773 
L 586.77037 267.553928 
L 588.420933 263.93566 
L 585.7225 262.779751 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c3b2af"/>
    <path d="M 797.454317 480.770881 
L 800.222473 483.31241 
L 801.754661 483.384761 
L 798.98973 480.811311 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #009cf4"/>
    <path d="M 588.420933 263.93566 
L 591.12403 265.181002 
L 592.775955 261.664535 
L 590.072912 260.408555 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c7b7b4"/>
    <path d="M 721.736068 386.023248 
L 724.499809 389.850742 
L 726.109764 388.589175 
L 723.348255 384.706841 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e5fa94"/>
    <path d="M 625.55693 261.681072 
L 628.296946 263.951169 
L 629.951212 261.187532 
L 627.211778 258.894085 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c9bab7"/>
    <path d="M 638.18596 268.608238 
L 640.935782 271.255868 
L 642.587285 268.685989 
L 639.838254 266.011325 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bdaba7"/>
    <path d="M 706.763601 361.401671 
L 709.529456 365.271638 
L 711.149505 363.692674 
L 708.385575 359.770757 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e2da89"/>
    <path d="M 676.823091 312.456309 
L 679.589238 316.058102 
L 681.225419 313.979213 
L 678.460669 310.336632 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8e6e5c"/>
    <path d="M 569.418979 278.918251 
L 572.102704 279.794933 
L 573.746993 275.814645 
L 571.063198 274.935936 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ad9691"/>
    <path d="M 831.014133 504.875582 
L 833.801889 506.543831 
L 835.29568 506.678384 
L 832.510846 504.997691 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1868ce"/>
    <path d="M 739.469414 413.447841 
L 742.231071 417.098368 
L 743.826714 416.237616 
L 741.067657 412.53211 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #85e781"/>
    <path d="M 604.218751 259.310314 
L 606.938814 260.963872 
L 608.593673 257.788944 
L 605.873847 256.118475 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cdbfbc"/>
    <path d="M 691.789715 336.62564 
L 694.556847 340.421386 
L 696.185549 338.566474 
L 693.420059 334.723579 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b8a473"/>
    <path d="M 674.057206 308.90528 
L 676.823091 312.456309 
L 678.460669 310.336632 
L 675.696131 306.745518 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #886759"/>
    <path d="M 640.935782 271.255868 
L 643.687775 273.987264 
L 645.338452 271.445657 
L 642.587285 268.685989 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b7a39f"/>
    <path d="M 818.3825 497.160375 
L 821.161623 499.165924 
L 822.6693 499.330549 
L 819.893274 497.30532 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1078de"/>
    <path d="M 800.222473 483.31241 
L 802.9922 485.778643 
L 804.521162 485.881409 
L 801.754661 483.384761 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0098fe"/>
    <path d="M 718.971617 382.190237 
L 721.736068 386.023248 
L 723.348255 384.706841 
L 720.585977 380.818804 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1fc96"/>
    <path d="M 618.430839 260.341938 
L 621.165025 262.406089 
L 622.819966 259.502343 
L 620.086229 257.416476 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cbbcb9"/>
    <path d="M 736.707216 409.771721 
L 739.469414 413.447841 
L 741.067657 412.53211 
L 738.308006 408.800421 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #91e983"/>
    <path d="M 703.99713 357.544679 
L 706.763601 361.401671 
L 708.385575 359.770757 
L 705.620968 355.861963 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dcd286"/>
    <path d="M 563.456784 286.316631 
L 566.135414 287.117156 
L 567.776391 282.979614 
L 565.097673 282.17976 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a18781"/>
    <path d="M 611.317429 259.55373 
L 614.044946 261.411795 
L 615.700068 258.370414 
L 612.972882 256.492782 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cdbfbc"/>
    <path d="M 671.291704 305.407927 
L 674.057206 308.90528 
L 675.696131 306.745518 
L 672.931926 303.20883 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #825f56"/>
    <path d="M 573.746993 275.814645 
L 576.435686 276.773528 
L 578.081651 272.879558 
L 575.392882 271.916103 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b39e99"/>
    <path d="M 628.296946 263.951169 
L 631.039843 266.311039 
L 632.693503 263.572205 
L 629.951212 261.187532 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c5b5b1"/>
    <path d="M 643.687775 273.987264 
L 646.44177 276.800334 
L 648.091587 274.2882 
L 645.338452 271.445657 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b39e99"/>
    <path d="M 689.022294 332.861897 
L 691.789715 336.62564 
L 693.420059 334.723579 
L 690.654222 330.913134 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b29c6f"/>
    <path d="M 599.848568 261.052893 
L 602.564696 262.59732 
L 604.218751 259.310314 
L 601.502781 257.750088 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cbbcb9"/>
    <path d="M 668.526712 301.967113 
L 671.291704 305.407927 
L 672.931926 303.20883 
L 670.168181 299.729476 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #836059"/>
    <path d="M 646.44177 276.800334 
L 649.197604 279.692899 
L 650.846523 277.211403 
L 648.091587 274.2882 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #af9994"/>
    <path d="M 733.944445 406.072822 
L 736.707216 409.771721 
L 738.308006 408.800421 
L 735.547725 405.045419 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a1ec86"/>
    <path d="M 716.206467 378.354743 
L 718.971617 382.190237 
L 720.585977 380.818804 
L 717.822939 376.928156 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 802.9922 485.778643 
L 805.763642 488.168039 
L 807.289381 488.299689 
L 804.521162 485.881409 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0393f9"/>
    <path d="M 578.081651 272.879558 
L 580.775246 273.925677 
L 582.422834 270.12292 
L 579.729171 269.069859 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b9a5a1"/>
    <path d="M 665.762361 298.585647 
L 668.526712 301.967113 
L 670.168181 299.729476 
L 667.405029 296.31031 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #896861"/>
    <path d="M 843.671217 511.159705 
L 846.470652 512.464422 
L 847.951756 512.536615 
L 845.155017 511.226142 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1f5bc1"/>
    <path d="M 701.230091 353.703781 
L 703.99713 357.544679 
L 705.620968 355.861963 
L 702.855734 351.969467 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d4c882"/>
    <path d="M 649.197604 279.692899 
L 651.955113 282.662699 
L 653.603096 280.21297 
L 650.846523 277.211403 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a9918c"/>
    <path d="M 595.483538 263.011741 
L 598.195509 264.449602 
L 599.848568 261.052893 
L 597.136687 259.600576 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c9bab7"/>
    <path d="M 686.254669 329.133237 
L 689.022294 332.861897 
L 690.654222 330.913134 
L 687.888126 327.138274 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #aa926b"/>
    <path d="M 662.998785 295.266282 
L 665.762361 298.585647 
L 667.405029 296.31031 
L 664.642606 292.954128 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8f7069"/>
    <path d="M 651.955113 282.662699 
L 654.71414 285.707391 
L 656.361147 283.29052 
L 653.603096 280.21297 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a58c86"/>
    <path d="M 631.039843 266.311039 
L 633.785449 268.758988 
L 635.438476 266.04638 
L 632.693503 263.572205 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c1b0ac"/>
    <path d="M 567.776391 282.979614 
L 570.460001 283.854181 
L 572.102704 279.794933 
L 569.418979 278.918251 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a78e89"/>
    <path d="M 660.236127 292.011709 
L 662.998785 295.266282 
L 664.642606 292.954128 
L 661.881053 289.663667 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #957771"/>
    <path d="M 582.422834 270.12292 
L 585.121235 271.26095 
L 586.77037 267.553928 
L 584.071921 266.406773 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bdaba7"/>
    <path d="M 654.71414 285.707391 
L 657.474529 288.824558 
L 659.120517 286.441596 
L 656.361147 283.29052 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9f847e"/>
    <path d="M 621.165025 262.406089 
L 623.902453 264.561498 
L 625.55693 261.681072 
L 622.819966 259.502343 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c9bab7"/>
    <path d="M 657.474529 288.824558 
L 660.236127 292.011709 
L 661.881053 289.663667 
L 659.120517 286.441596 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9b7f79"/>
    <path d="M 591.12403 265.181002 
L 593.831644 266.515317 
L 595.483538 263.011741 
L 592.775955 261.664535 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c5b5b1"/>
    <path d="M 821.161623 499.165924 
L 823.943404 501.08529 
L 825.448007 501.268019 
L 822.6693 499.330549 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1276dc"/>
    <path d="M 606.938814 260.963872 
L 609.662808 262.70985 
L 611.317429 259.55373 
L 608.593673 257.788944 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cbbcb9"/>
    <path d="M 731.181072 402.353993 
L 733.944445 406.072822 
L 735.547725 405.045419 
L 732.786784 401.270006 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #adef89"/>
    <path d="M 833.801889 506.543831 
L 836.592998 508.120632 
L 838.083904 508.266087 
L 835.29568 506.678384 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1a66cc"/>
    <path d="M 586.77037 267.553928 
L 589.473452 268.788158 
L 591.12403 265.181002 
L 588.420933 263.93566 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c1b0ac"/>
    <path d="M 853.557803 514.866579 
L 856.367462 515.885378 
L 857.839688 515.867242 
L 855.032515 514.847316 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2353b9"/>
    <path d="M 713.440635 374.519816 
L 716.206467 378.354743 
L 717.822939 376.928156 
L 715.059157 373.038002 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f8f695"/>
    <path d="M 614.044946 261.411795 
L 616.776059 263.362 
L 618.430839 260.341938 
L 615.700068 258.370414 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cbbcb9"/>
    <path d="M 561.817516 290.526747 
L 564.49602 291.327932 
L 566.135414 287.117156 
L 563.456784 286.316631 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9b7f79"/>
    <path d="M 683.486934 325.442717 
L 686.254669 329.133237 
L 687.888126 327.138274 
L 685.121863 323.402104 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a48b68"/>
    <path d="M 698.46254 349.882091 
L 701.230091 353.703781 
L 702.855734 351.969467 
L 700.089927 348.096435 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cec07f"/>
    <path d="M 805.763642 488.168039 
L 808.536946 490.479129 
L 810.059471 490.638105 
L 807.289381 488.299689 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #068ef4"/>
    <path d="M 633.785449 268.758988 
L 636.533594 271.29323 
L 638.18596 268.608238 
L 635.438476 266.04638 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bdaba7"/>
    <path d="M 768.259699 451.905048 
L 771.022438 455.051851 
L 772.589344 454.797949 
L 769.829691 451.603531 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #05cd67"/>
    <path d="M 765.497213 448.705576 
L 768.259699 451.905048 
L 769.829691 451.603531 
L 767.070257 448.355268 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #11cf69"/>
    <path d="M 771.022438 455.051851 
L 773.78553 458.143764 
L 775.349317 457.936256 
L 772.589344 454.797949 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c970"/>
    <path d="M 728.417076 398.618107 
L 731.181072 402.353993 
L 732.786784 401.270006 
L 730.025161 397.477113 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b9f18b"/>
    <path d="M 762.734887 445.455712 
L 765.497213 448.705576 
L 767.070257 448.355268 
L 764.310947 445.055481 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #19d16b"/>
    <path d="M 572.102704 279.794933 
L 574.791271 280.749072 
L 576.435686 276.773528 
L 573.746993 275.814645 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ad9691"/>
    <path d="M 773.78553 458.143764 
L 776.549078 461.178621 
L 778.109717 461.016244 
L 775.349317 457.936256 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c47d"/>
    <path d="M 759.972632 442.157789 
L 762.734887 445.455712 
L 764.310947 445.055481 
L 761.551669 441.706549 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #25d36d"/>
    <path d="M 680.719185 321.793359 
L 683.486934 325.442717 
L 685.121863 323.402104 
L 682.355532 319.707701 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9e8365"/>
    <path d="M 602.564696 262.59732 
L 605.284913 264.233067 
L 606.938814 260.963872 
L 604.218751 259.310314 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c9bab7"/>
    <path d="M 710.674143 370.68851 
L 713.440635 374.519816 
L 715.059157 373.038002 
L 712.294653 369.151456 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f2ee92"/>
    <path d="M 776.549078 461.178621 
L 779.313189 464.154316 
L 780.870655 464.035766 
L 778.109717 461.016244 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00be8f"/>
    <path d="M 757.210365 438.814189 
L 759.972632 442.157789 
L 761.551669 441.706549 
L 758.792336 438.310903 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #31d670"/>
    <path d="M 623.902453 264.561498 
L 626.642956 266.806699 
L 628.296946 263.951169 
L 625.55693 261.681072 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c5b5b1"/>
    <path d="M 695.694537 346.08271 
L 698.46254 349.882091 
L 700.089927 348.096435 
L 697.323609 344.246027 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c6b67a"/>
    <path d="M 779.313189 464.154316 
L 782.077975 467.068804 
L 783.632246 466.992739 
L 780.870655 464.035766 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00bb9b"/>
    <path d="M 754.448007 435.427346 
L 757.210365 438.814189 
L 758.792336 438.310903 
L 756.032868 434.871024 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #3dd872"/>
    <path d="M 636.533594 271.29323 
L 639.284109 273.911886 
L 640.935782 271.255868 
L 638.18596 268.608238 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b9a5a1"/>
    <path d="M 725.652441 394.868066 
L 728.417076 398.618107 
L 730.025161 397.477113 
L 727.262839 393.669698 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c9f48e"/>
    <path d="M 576.435686 276.773528 
L 579.129157 277.812444 
L 580.775246 273.925677 
L 578.081651 272.879558 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b39e99"/>
    <path d="M 677.951528 318.188154 
L 680.719185 321.793359 
L 682.355532 319.707701 
L 679.589238 316.058102 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #967960"/>
    <path d="M 566.135414 287.117156 
L 568.818866 287.989522 
L 570.460001 283.854181 
L 567.776391 282.979614 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a18781"/>
    <path d="M 808.536946 490.479129 
L 811.312263 492.710521 
L 812.831583 492.89524 
L 810.059471 490.638105 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #078bf1"/>
    <path d="M 823.943404 501.08529 
L 826.728006 502.917446 
L 828.229562 503.116685 
L 825.448007 501.268019 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1373d9"/>
    <path d="M 751.685485 431.999742 
L 754.448007 435.427346 
L 756.032868 434.871024 
L 753.27319 431.389445 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #49db75"/>
    <path d="M 609.662808 262.70985 
L 612.390569 264.547235 
L 614.044946 261.411795 
L 611.317429 259.55373 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c9bab7"/>
    <path d="M 782.077975 467.068804 
L 784.843555 469.920103 
L 786.394609 469.885139 
L 783.632246 466.992739 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b4ac"/>
    <path d="M 598.195509 264.449602 
L 600.911716 265.977447 
L 602.564696 262.59732 
L 599.848568 261.052893 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c7b7b4"/>
    <path d="M 616.776059 263.362 
L 619.510599 265.403105 
L 621.165025 262.406089 
L 618.430839 260.341938 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c7b7b4"/>
    <path d="M 707.907019 366.86389 
L 710.674143 370.68851 
L 712.294653 369.151456 
L 709.529456 365.271638 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eae48e"/>
    <path d="M 560.179835 294.80709 
L 562.858176 295.608924 
L 564.49602 291.327932 
L 561.817516 290.526747 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #957771"/>
    <path d="M 692.926151 342.308728 
L 695.694537 346.08271 
L 697.323609 344.246027 
L 694.556847 340.421386 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c0ae77"/>
    <path d="M 639.284109 273.911886 
L 642.036826 276.612987 
L 643.687775 273.987264 
L 640.935782 271.255868 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b5a09c"/>
    <path d="M 846.470652 512.464422 
L 849.274172 513.673755 
L 850.752626 513.750224 
L 847.951756 512.536615 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2058be"/>
    <path d="M 748.922732 428.533906 
L 751.685485 431.999742 
L 753.27319 431.389445 
L 750.513232 427.868745 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #55dd77"/>
    <path d="M 580.775246 273.925677 
L 583.473538 275.054225 
L 585.121235 271.26095 
L 582.422834 270.12292 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b7a39f"/>
    <path d="M 675.184072 314.63005 
L 677.951528 318.188154 
L 679.589238 316.058102 
L 676.823091 312.456309 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #90715d"/>
    <path d="M 784.843555 469.920103 
L 787.610047 472.706291 
L 789.157868 472.71101 
L 786.394609 469.885139 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b0b9"/>
    <path d="M 836.592998 508.120632 
L 839.387633 509.605269 
L 840.875692 509.760074 
L 838.083904 508.266087 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1b63c9"/>
    <path d="M 593.831644 266.515317 
L 596.54363 267.938049 
L 598.195509 264.449602 
L 595.483538 263.011741 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c3b2af"/>
    <path d="M 626.642956 266.806699 
L 629.386361 269.140126 
L 631.039843 266.311039 
L 628.296946 263.951169 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c1b0ac"/>
    <path d="M 722.88716 391.106794 
L 725.652441 394.868066 
L 727.262839 393.669698 
L 724.499809 389.850742 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d5f791"/>
    <path d="M 585.121235 271.26095 
L 587.824238 272.483611 
L 589.473452 268.788158 
L 586.77037 267.553928 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bba8a4"/>
    <path d="M 589.473452 268.788158 
L 592.181028 270.109019 
L 593.831644 266.515317 
L 591.12403 265.181002 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bfada9"/>
    <path d="M 746.159687 425.032408 
L 748.922732 428.533906 
L 750.513232 427.868745 
L 747.752931 424.311547 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #61df79"/>
    <path d="M 642.036826 276.612987 
L 644.791581 279.394478 
L 646.44177 276.800334 
L 643.687775 273.987264 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b19b96"/>
    <path d="M 672.416931 311.121956 
L 675.184072 314.63005 
L 676.823091 312.456309 
L 674.057206 308.90528 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8a695a"/>
    <path d="M 570.460001 283.854181 
L 573.148393 284.80341 
L 574.791271 280.749072 
L 572.102704 279.794933 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a78e89"/>
    <path d="M 787.610047 472.706291 
L 790.377577 475.425514 
L 791.922151 475.468462 
L 789.157868 472.71101 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00acc4"/>
    <path d="M 705.139301 363.049021 
L 707.907019 366.86389 
L 709.529456 365.271638 
L 706.763601 361.401671 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e4dc8a"/>
    <path d="M 690.157454 338.563217 
L 692.926151 342.308728 
L 694.556847 340.421386 
L 691.789715 336.62564 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #baa774"/>
    <path d="M 605.284913 264.233067 
L 608.009059 265.959243 
L 609.662808 262.70985 
L 606.938814 260.963872 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c7b7b4"/>
    <path d="M 743.396292 421.497863 
L 746.159687 425.032408 
L 747.752931 424.311547 
L 744.992228 420.720519 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #6de27c"/>
    <path d="M 669.650226 307.666736 
L 672.416931 311.121956 
L 674.057206 308.90528 
L 671.291704 305.407927 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #846257"/>
    <path d="M 811.312263 492.710521 
L 814.089745 494.860894 
L 815.605873 495.069752 
L 812.831583 492.89524 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0a86ec"/>
    <path d="M 644.791581 279.394478 
L 647.548212 282.254216 
L 649.197604 279.692899 
L 646.44177 276.800334 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ab938e"/>
    <path d="M 720.121229 387.337235 
L 722.88716 391.106794 
L 724.499809 389.850742 
L 721.736068 386.023248 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e5fa94"/>
    <path d="M 856.367462 515.885378 
L 859.181776 516.806404 
L 860.65157 516.788003 
L 857.839688 515.867242 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2353b9"/>
    <path d="M 619.510599 265.403105 
L 622.248399 267.533769 
L 623.902453 264.561498 
L 621.165025 262.406089 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c5b5b1"/>
    <path d="M 629.386361 269.140126 
L 632.132501 271.56012 
L 633.785449 268.758988 
L 631.039843 266.311039 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bfada9"/>
    <path d="M 666.88408 304.267203 
L 669.650226 307.666736 
L 671.291704 305.407927 
L 668.526712 301.967113 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #815e56"/>
    <path d="M 564.49602 291.327932 
L 567.179272 292.198016 
L 568.818866 287.989522 
L 566.135414 287.117156 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9b7f79"/>
    <path d="M 612.390569 264.547235 
L 615.121932 266.474912 
L 616.776059 263.362 
L 614.044946 261.411795 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c7b7b4"/>
    <path d="M 647.548212 282.254216 
L 650.306557 285.189982 
L 651.955113 282.662699 
L 649.197604 279.692899 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a78e89"/>
    <path d="M 790.377577 475.425514 
L 793.146273 478.075983 
L 794.687589 478.15567 
L 791.922151 475.468462 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a8d0"/>
    <path d="M 740.632499 417.932925 
L 743.396292 421.497863 
L 744.992228 420.720519 
L 742.231071 417.098368 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #7de57f"/>
    <path d="M 687.388527 334.849228 
L 690.157454 338.563217 
L 691.789715 336.62564 
L 689.022294 332.861897 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b29c6f"/>
    <path d="M 558.543699 299.154574 
L 561.221843 299.957048 
L 562.858176 295.608924 
L 560.179835 294.80709 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8d6d66"/>
    <path d="M 826.728006 502.917446 
L 829.515594 504.661442 
L 831.014133 504.875582 
L 828.229562 503.116685 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1470d6"/>
    <path d="M 574.791271 280.749072 
L 577.484562 281.780531 
L 579.129157 277.812444 
L 576.435686 276.773528 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ad9691"/>
    <path d="M 664.118625 300.926119 
L 666.88408 304.267203 
L 668.526712 301.967113 
L 665.762361 298.585647 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #87655e"/>
    <path d="M 702.371029 359.246968 
L 705.139301 363.049021 
L 706.763601 361.401671 
L 703.99713 357.544679 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dcd286"/>
    <path d="M 650.306557 285.189982 
L 653.066461 288.199474 
L 654.71414 285.707391 
L 651.955113 282.662699 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a38984"/>
    <path d="M 661.353995 297.64619 
L 664.118625 300.926119 
L 665.762361 298.585647 
L 662.998785 295.266282 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8d6d66"/>
    <path d="M 600.911716 265.977447 
L 603.632004 267.594504 
L 605.284913 264.233067 
L 602.564696 262.59732 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c5b5b1"/>
    <path d="M 653.066461 288.199474 
L 655.827768 291.280316 
L 657.474529 288.824558 
L 654.71414 285.707391 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9d827c"/>
    <path d="M 658.590328 294.430061 
L 661.353995 297.64619 
L 662.998785 295.266282 
L 660.236127 292.011709 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #93756e"/>
    <path d="M 717.354652 383.562351 
L 720.121229 387.337235 
L 721.736068 386.023248 
L 718.971617 382.190237 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1fc96"/>
    <path d="M 655.827768 291.280316 
L 658.590328 294.430061 
L 660.236127 292.011709 
L 657.474529 288.824558 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #977a74"/>
    <path d="M 737.868262 414.340283 
L 740.632499 417.932925 
L 742.231071 417.098368 
L 739.469414 413.447841 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #89e781"/>
    <path d="M 793.146273 478.075983 
L 795.916267 480.655976 
L 797.454317 480.770881 
L 794.687589 478.15567 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a4dc"/>
    <path d="M 632.132501 271.56012 
L 634.881208 274.064929 
L 636.533594 271.29323 
L 633.785449 268.758988 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bba8a4"/>
    <path d="M 684.619456 331.16979 
L 687.388527 334.849228 
L 689.022294 332.861897 
L 686.254669 329.133237 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ac956c"/>
    <path d="M 579.129157 277.812444 
L 581.82728 278.931163 
L 583.473538 275.054225 
L 580.775246 273.925677 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b19b96"/>
    <path d="M 596.54363 267.938049 
L 599.259837 269.448547 
L 600.911716 265.977447 
L 598.195509 264.449602 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c1b0ac"/>
    <path d="M 814.089745 494.860894 
L 816.869547 496.929005 
L 818.3825 497.160375 
L 815.605873 495.069752 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0b83e9"/>
    <path d="M 699.602253 355.460791 
L 702.371029 359.246968 
L 703.99713 357.544679 
L 701.230091 353.703781 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d6cb83"/>
    <path d="M 622.248399 267.533769 
L 624.98929 269.752557 
L 626.642956 266.806699 
L 623.902453 264.561498 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c1b0ac"/>
    <path d="M 568.818866 287.989522 
L 571.507034 288.933682 
L 573.148393 284.80341 
L 570.460001 283.854181 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a18781"/>
    <path d="M 839.387633 509.605269 
L 842.185962 510.997111 
L 843.671217 511.159705 
L 840.875692 509.760074 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1c60c6"/>
    <path d="M 735.103543 410.722666 
L 737.868262 414.340283 
L 739.469414 413.447841 
L 736.707216 409.771721 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #95ea84"/>
    <path d="M 583.473538 275.054225 
L 586.176395 276.264873 
L 587.824238 272.483611 
L 585.121235 271.26095 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b7a39f"/>
    <path d="M 714.587441 379.785119 
L 717.354652 383.562351 
L 718.971617 382.190237 
L 716.206467 378.354743 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 608.009059 265.959243 
L 610.736975 267.774859 
L 612.390569 264.547235 
L 609.662808 262.70985 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c5b5b1"/>
    <path d="M 592.181028 270.109019 
L 594.892954 271.515971 
L 596.54363 267.938049 
L 593.831644 266.515317 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bfada9"/>
    <path d="M 849.274172 513.673755 
L 852.081949 514.78732 
L 853.557803 514.866579 
L 850.752626 513.750224 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2058be"/>
    <path d="M 587.824238 272.483611 
L 590.531705 273.790471 
L 592.181028 270.109019 
L 589.473452 268.788158 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bba8a4"/>
    <path d="M 681.850332 327.527903 
L 684.619456 331.16979 
L 686.254669 329.133237 
L 683.486934 325.442717 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a68d69"/>
    <path d="M 615.121932 266.474912 
L 617.856734 268.491669 
L 619.510599 265.403105 
L 616.776059 263.362 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c3b2af"/>
    <path d="M 634.881208 274.064929 
L 637.632314 276.652708 
L 639.284109 273.911886 
L 636.533594 271.29323 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b7a39f"/>
    <path d="M 795.916267 480.655976 
L 798.687695 483.16384 
L 800.222473 483.31241 
L 797.454317 480.770881 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a0e8"/>
    <path d="M 562.858176 295.608924 
L 565.541187 296.476648 
L 567.179272 292.198016 
L 564.49602 291.327932 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #957771"/>
    <path d="M 556.909062 303.566052 
L 559.586975 304.369156 
L 561.221843 299.957048 
L 558.543699 299.154574 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #87655e"/>
    <path d="M 732.33831 407.08283 
L 735.103543 410.722666 
L 736.707216 409.771721 
L 733.944445 406.072822 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a1ec86"/>
    <path d="M 696.833028 351.693546 
L 699.602253 355.460791 
L 701.230091 353.703781 
L 698.46254 349.882091 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cec07f"/>
    <path d="M 679.081253 323.926535 
L 681.850332 327.527903 
L 683.486934 325.442717 
L 680.719185 321.793359 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9e8365"/>
    <path d="M 711.819612 376.008525 
L 714.587441 379.785119 
L 716.206467 378.354743 
L 713.440635 374.519816 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f8f695"/>
    <path d="M 573.148393 284.80341 
L 575.841452 285.827169 
L 577.484562 281.780531 
L 574.791271 280.749072 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a78e89"/>
    <path d="M 829.515594 504.661442 
L 832.306334 506.316412 
L 833.801889 506.543831 
L 831.014133 504.875582 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #166ed4"/>
    <path d="M 624.98929 269.752557 
L 627.733106 272.057936 
L 629.386361 269.140126 
L 626.642956 266.806699 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bfada9"/>
    <path d="M 637.632314 276.652708 
L 640.385656 279.321526 
L 642.036826 276.612987 
L 639.284109 273.911886 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b39e99"/>
    <path d="M 603.632004 267.594504 
L 606.356218 269.299908 
L 608.009059 265.959243 
L 605.284913 264.233067 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c3b2af"/>
    <path d="M 729.572536 403.423564 
L 732.33831 407.08283 
L 733.944445 406.072822 
L 731.181072 402.353993 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b1ef89"/>
    <path d="M 798.687695 483.16384 
L 801.460693 485.597991 
L 802.9922 485.778643 
L 800.222473 483.31241 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #009cf4"/>
    <path d="M 676.312322 320.368622 
L 679.081253 323.926535 
L 680.719185 321.793359 
L 677.951528 318.188154 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #987b61"/>
    <path d="M 816.869547 496.929005 
L 819.651825 498.913689 
L 821.161623 499.165924 
L 818.3825 497.160375 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0e7ee4"/>
    <path d="M 694.063414 347.948276 
L 696.833028 351.693546 
L 698.46254 349.882091 
L 695.694537 346.08271 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c8b97b"/>
    <path d="M 640.385656 279.321526 
L 643.14107 282.069366 
L 644.791581 279.394478 
L 642.036826 276.612987 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ad9691"/>
    <path d="M 709.051187 372.235567 
L 711.819612 376.008525 
L 713.440635 374.519816 
L 710.674143 370.68851 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f2ee92"/>
    <path d="M 567.179272 292.198016 
L 569.86717 293.136954 
L 571.507034 288.933682 
L 568.818866 287.989522 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9b7f79"/>
    <path d="M 577.484562 281.780531 
L 580.182458 282.88909 
L 581.82728 278.931163 
L 579.129157 277.812444 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ab938e"/>
    <path d="M 617.856734 268.491669 
L 620.59481 270.596195 
L 622.248399 267.533769 
L 619.510599 265.403105 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c1b0ac"/>
    <path d="M 610.736975 267.774859 
L 613.468499 269.678827 
L 615.121932 266.474912 
L 612.390569 264.547235 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c3b2af"/>
    <path d="M 555.27587 308.038314 
L 557.953521 308.842041 
L 559.586975 304.369156 
L 556.909062 303.566052 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #815e56"/>
    <path d="M 673.543648 316.857061 
L 676.312322 320.368622 
L 677.951528 318.188154 
L 675.184072 314.63005 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #92735e"/>
    <path d="M 599.259837 269.448547 
L 601.980115 271.046061 
L 603.632004 267.594504 
L 600.911716 265.977447 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c1b0ac"/>
    <path d="M 726.806202 399.747686 
L 729.572536 403.423564 
L 731.181072 402.353993 
L 728.417076 398.618107 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bdf28c"/>
    <path d="M 561.221843 299.957048 
L 563.904575 300.82234 
L 565.541187 296.476648 
L 562.858176 295.608924 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8d6d66"/>
    <path d="M 627.733106 272.057936 
L 630.479681 274.448279 
L 632.132501 271.56012 
L 629.386361 269.140126 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bba8a4"/>
    <path d="M 691.293479 344.228013 
L 694.063414 347.948276 
L 695.694537 346.08271 
L 692.926151 342.308728 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c2b178"/>
    <path d="M 643.14107 282.069366 
L 645.898395 284.894128 
L 647.548212 282.254216 
L 644.791581 279.394478 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a9918c"/>
    <path d="M 581.82728 278.931163 
L 584.529929 280.129371 
L 586.176395 276.264873 
L 583.473538 275.054225 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b19b96"/>
    <path d="M 670.775343 313.394706 
L 673.543648 316.857061 
L 675.184072 314.63005 
L 672.416931 311.121956 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8c6c5b"/>
    <path d="M 801.460693 485.597991 
L 804.235405 487.956917 
L 805.763642 488.168039 
L 802.9922 485.778643 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0098fe"/>
    <path d="M 594.892954 271.515971 
L 597.609084 273.00838 
L 599.259837 269.448547 
L 596.54363 267.938049 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bdaba7"/>
    <path d="M 842.185962 510.997111 
L 844.988157 512.295609 
L 846.470652 512.464422 
L 843.671217 511.159705 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1c60c6"/>
    <path d="M 706.282198 368.469246 
L 709.051187 372.235567 
L 710.674143 370.68851 
L 707.907019 366.86389 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eae48e"/>
    <path d="M 586.176395 276.264873 
L 588.883686 277.557206 
L 590.531705 273.790471 
L 587.824238 272.483611 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b5a09c"/>
    <path d="M 645.898395 284.894128 
L 648.657475 287.793633 
L 650.306557 285.189982 
L 647.548212 282.254216 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a58c86"/>
    <path d="M 590.531705 273.790471 
L 593.243498 275.181009 
L 594.892954 271.515971 
L 592.181028 270.109019 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b9a5a1"/>
    <path d="M 668.007528 309.98437 
L 670.775343 313.394706 
L 672.416931 311.121956 
L 669.650226 307.666736 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #866458"/>
    <path d="M 724.039293 396.058035 
L 726.806202 399.747686 
L 728.417076 398.618107 
L 725.652441 394.868066 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c9f48e"/>
    <path d="M 571.507034 288.933682 
L 574.199809 289.94951 
L 575.841452 285.827169 
L 573.148393 284.80341 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a18781"/>
    <path d="M 688.523297 340.535769 
L 691.293479 344.228013 
L 692.926151 342.308728 
L 690.157454 338.563217 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #baa774"/>
    <path d="M 665.240325 306.628814 
L 668.007528 309.98437 
L 669.650226 307.666736 
L 666.88408 304.267203 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #805c54"/>
    <path d="M 648.657475 287.793633 
L 651.418153 290.765622 
L 653.066461 288.199474 
L 650.306557 285.189982 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9f847e"/>
    <path d="M 606.356218 269.299908 
L 609.084201 271.092692 
L 610.736975 267.774859 
L 608.009059 265.959243 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c1b0ac"/>
    <path d="M 763.921154 449.0062 
L 766.686703 452.154443 
L 768.259699 451.905048 
L 765.497213 448.705576 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #15d06a"/>
    <path d="M 761.155804 445.808751 
L 763.921154 449.0062 
L 765.497213 448.705576 
L 762.734887 445.455712 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #21d36d"/>
    <path d="M 852.081949 514.78732 
L 854.894155 515.804816 
L 856.367462 515.885378 
L 853.557803 514.866579 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2058be"/>
    <path d="M 630.479681 274.448279 
L 633.228849 276.921871 
L 634.881208 274.064929 
L 632.132501 271.56012 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b7a39f"/>
    <path d="M 819.651825 498.913689 
L 822.436738 500.813856 
L 823.943404 501.08529 
L 821.161623 499.165924 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0f7be1"/>
    <path d="M 766.686703 452.154443 
L 769.452544 455.251248 
L 771.022438 455.051851 
L 768.259699 451.905048 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #09ce68"/>
    <path d="M 832.306334 506.316412 
L 835.100391 507.881568 
L 836.592998 508.120632 
L 833.801889 506.543831 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #176bd1"/>
    <path d="M 758.390568 442.564378 
L 761.155804 445.808751 
L 762.734887 445.455712 
L 759.972632 442.157789 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2dd56f"/>
    <path d="M 620.59481 270.596195 
L 623.335994 272.787085 
L 624.98929 269.752557 
L 622.248399 267.533769 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bdaba7"/>
    <path d="M 662.473864 303.330749 
L 665.240325 306.628814 
L 666.88408 304.267203 
L 664.118625 300.926119 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #85635c"/>
    <path d="M 651.418153 290.765622 
L 654.180278 293.807765 
L 655.827768 291.280316 
L 653.066461 288.199474 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9b7f79"/>
    <path d="M 553.644063 312.568098 
L 556.321423 313.37244 
L 557.953521 308.842041 
L 555.27587 308.038314 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #866458"/>
    <path d="M 769.452544 455.251248 
L 772.218772 458.29444 
L 773.78553 458.143764 
L 771.022438 455.051851 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #01cc66"/>
    <path d="M 755.625365 439.275415 
L 758.390568 442.564378 
L 759.972632 442.157789 
L 757.210365 438.814189 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #35d771"/>
    <path d="M 659.708277 300.092832 
L 662.473864 303.330749 
L 664.118625 300.926119 
L 661.353995 297.64619 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8b6b64"/>
    <path d="M 654.180278 293.807765 
L 656.943701 296.917658 
L 658.590328 294.430061 
L 655.827768 291.280316 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #957771"/>
    <path d="M 656.943701 296.917658 
L 659.708277 300.092832 
L 661.353995 297.64619 
L 658.590328 294.430061 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8f7069"/>
    <path d="M 703.51268 364.712567 
L 706.282198 368.469246 
L 707.907019 366.86389 
L 705.139301 363.049021 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e4dc8a"/>
    <path d="M 721.271802 392.357476 
L 724.039293 396.058035 
L 725.652441 394.868066 
L 722.88716 391.106794 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d5f791"/>
    <path d="M 565.541187 296.476648 
L 568.228772 297.410222 
L 569.86717 293.136954 
L 567.179272 292.198016 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #957771"/>
    <path d="M 613.468499 269.678827 
L 616.20347 271.669962 
L 617.856734 268.491669 
L 615.121932 266.474912 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bfada9"/>
    <path d="M 772.218772 458.29444 
L 774.985488 461.281899 
L 776.549078 461.178621 
L 773.78553 458.143764 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c677"/>
    <path d="M 752.860119 435.944244 
L 755.625365 439.275415 
L 757.210365 438.814189 
L 754.448007 435.427346 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #41d973"/>
    <path d="M 559.586975 304.369156 
L 562.26939 305.231947 
L 563.904575 300.82234 
L 561.221843 299.957048 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #87655e"/>
    <path d="M 804.235405 487.956917 
L 807.011975 490.239177 
L 808.536946 490.479129 
L 805.763642 488.168039 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0393f9"/>
    <path d="M 685.752946 336.874538 
L 688.523297 340.535769 
L 690.157454 338.563217 
L 687.388527 334.849228 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b49f70"/>
    <path d="M 750.09476 432.573294 
L 752.860119 435.944244 
L 754.448007 435.427346 
L 751.685485 431.999742 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #4ddb75"/>
    <path d="M 774.985488 461.281899 
L 777.752795 464.211562 
L 779.313189 464.154316 
L 776.549078 461.178621 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c382"/>
    <path d="M 575.841452 285.827169 
L 578.539064 286.925249 
L 580.182458 282.88909 
L 577.484562 281.780531 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a58c86"/>
    <path d="M 601.980115 271.046061 
L 604.704313 272.729746 
L 606.356218 269.299908 
L 603.632004 267.594504 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bfada9"/>
    <path d="M 633.228849 276.921871 
L 635.980446 279.476905 
L 637.632314 276.652708 
L 634.881208 274.064929 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b39e99"/>
    <path d="M 747.329221 429.16504 
L 750.09476 432.573294 
L 751.685485 431.999742 
L 748.922732 428.533906 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #59de78"/>
    <path d="M 777.752795 464.211562 
L 780.520805 467.081426 
L 782.077975 467.068804 
L 779.313189 464.154316 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00bc94"/>
    <path d="M 700.742674 360.968533 
L 703.51268 364.712567 
L 705.139301 363.049021 
L 702.371029 359.246968 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dcd286"/>
    <path d="M 718.503728 388.648892 
L 721.271802 392.357476 
L 722.88716 391.106794 
L 720.121229 387.337235 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e5fa94"/>
    <path d="M 682.982512 333.247291 
L 685.752946 336.874538 
L 687.388527 334.849228 
L 684.619456 331.16979 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ae976d"/>
    <path d="M 623.335994 272.787085 
L 626.080123 275.062841 
L 627.733106 272.057936 
L 624.98929 269.752557 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bba8a4"/>
    <path d="M 744.563444 425.721999 
L 747.329221 429.16504 
L 748.922732 428.533906 
L 746.159687 425.032408 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #65e07a"/>
    <path d="M 580.182458 282.88909 
L 582.884836 284.074446 
L 584.529929 280.129371 
L 581.82728 278.931163 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ab938e"/>
    <path d="M 552.013577 317.152087 
L 554.690616 317.957038 
L 556.321423 313.37244 
L 553.644063 312.568098 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8e6e5c"/>
    <path d="M 780.520805 467.081426 
L 783.28963 469.889548 
L 784.843555 469.920103 
L 782.077975 467.068804 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b8a0"/>
    <path d="M 597.609084 273.00838 
L 600.329272 274.585519 
L 601.980115 271.046061 
L 599.259837 269.448547 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bba8a4"/>
    <path d="M 569.86717 293.136954 
L 572.559612 294.144628 
L 574.199809 289.94951 
L 571.507034 288.933682 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9b7f79"/>
    <path d="M 635.980446 279.476905 
L 638.73431 282.11149 
L 640.385656 279.321526 
L 637.632314 276.652708 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #af9994"/>
    <path d="M 741.797375 422.246729 
L 744.563444 425.721999 
L 746.159687 425.032408 
L 743.396292 421.497863 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #71e37d"/>
    <path d="M 609.084201 271.092692 
L 611.815795 272.971798 
L 613.468499 269.678827 
L 610.736975 267.774859 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bfada9"/>
    <path d="M 680.212086 329.656968 
L 682.982512 333.247291 
L 684.619456 331.16979 
L 681.850332 327.527903 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a68d69"/>
    <path d="M 584.529929 280.129371 
L 587.236975 281.406666 
L 588.883686 277.557206 
L 586.176395 276.264873 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #af9994"/>
    <path d="M 715.735075 384.935182 
L 718.503728 388.648892 
L 720.121229 387.337235 
L 717.354652 383.562351 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1fc96"/>
    <path d="M 807.011975 490.239177 
L 809.790548 492.443402 
L 811.312263 492.710521 
L 808.536946 490.479129 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0490f6"/>
    <path d="M 697.972231 357.240145 
L 700.742674 360.968533 
L 702.371029 359.246968 
L 699.602253 355.460791 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d6cb83"/>
    <path d="M 822.436738 500.813856 
L 825.224447 502.628495 
L 826.728006 502.917446 
L 823.943404 501.08529 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1078de"/>
    <path d="M 593.243498 275.181009 
L 595.959474 276.654609 
L 597.609084 273.00838 
L 594.892954 271.515971 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b7a39f"/>
    <path d="M 616.20347 271.669962 
L 618.941727 273.746986 
L 620.59481 270.596195 
L 617.856734 268.491669 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bdaba7"/>
    <path d="M 557.953521 308.842041 
L 560.635584 309.702266 
L 562.26939 305.231947 
L 559.586975 304.369156 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #805c54"/>
    <path d="M 563.904575 300.82234 
L 566.591802 301.750411 
L 568.228772 297.410222 
L 565.541187 296.476648 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8d6d66"/>
    <path d="M 588.883686 277.557206 
L 591.595273 278.930717 
L 593.243498 275.181009 
L 590.531705 273.790471 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b5a09c"/>
    <path d="M 783.28963 469.889548 
L 786.059387 472.634046 
L 787.610047 472.706291 
L 784.843555 469.920103 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b4ac"/>
    <path d="M 844.988157 512.295609 
L 847.794389 513.5003 
L 849.274172 513.673755 
L 846.470652 512.464422 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1e5ec4"/>
    <path d="M 739.030965 418.741827 
L 741.797375 422.246729 
L 743.396292 421.497863 
L 740.632499 417.932925 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #7de57f"/>
    <path d="M 677.441765 326.106482 
L 680.212086 329.656968 
L 681.850332 327.527903 
L 679.081253 323.926535 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a08566"/>
    <path d="M 638.73431 282.11149 
L 641.49028 284.823649 
L 643.14107 282.069366 
L 640.385656 279.321526 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ab938e"/>
    <path d="M 835.100391 507.881568 
L 837.897935 509.356208 
L 839.387633 509.605269 
L 836.592998 508.120632 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1868ce"/>
    <path d="M 626.080123 275.062841 
L 628.827033 277.421874 
L 630.479681 274.448279 
L 627.733106 272.057936 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b7a39f"/>
    <path d="M 712.965855 381.21926 
L 715.735075 384.935182 
L 717.354652 383.562351 
L 714.587441 379.785119 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 695.201404 353.530394 
L 697.972231 357.240145 
L 699.602253 355.460791 
L 696.833028 351.693546 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d0c380"/>
    <path d="M 574.199809 289.94951 
L 576.897081 291.036803 
L 578.539064 286.925249 
L 575.841452 285.827169 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9f847e"/>
    <path d="M 550.384339 321.786919 
L 553.061031 322.592473 
L 554.690616 317.957038 
L 552.013577 317.152087 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #94765f"/>
    <path d="M 736.264172 415.209925 
L 739.030965 418.741827 
L 740.632499 417.932925 
L 737.868262 414.340283 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #89e781"/>
    <path d="M 786.059387 472.634046 
L 788.830199 475.313104 
L 790.377577 475.425514 
L 787.610047 472.706291 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b0b9"/>
    <path d="M 674.67165 322.598711 
L 677.441765 326.106482 
L 679.081253 323.926535 
L 676.312322 320.368622 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9a7e62"/>
    <path d="M 604.704313 272.729746 
L 607.432276 274.498665 
L 609.084201 271.092692 
L 606.356218 269.299908 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bdaba7"/>
    <path d="M 641.49028 284.823649 
L 644.248199 287.611326 
L 645.898395 284.894128 
L 643.14107 282.069366 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a78e89"/>
    <path d="M 854.894155 515.804816 
L 857.710963 516.726033 
L 859.181776 516.806404 
L 856.367462 515.885378 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2058be"/>
    <path d="M 733.496958 411.653691 
L 736.264172 415.209925 
L 737.868262 414.340283 
L 735.103543 410.722666 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #99eb85"/>
    <path d="M 809.790548 492.443402 
L 812.571275 494.568297 
L 814.089745 494.860894 
L 811.312263 492.710521 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #078bf1"/>
    <path d="M 671.90185 319.136495 
L 674.67165 322.598711 
L 676.312322 320.368622 
L 673.543648 316.857061 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #94765f"/>
    <path d="M 556.321423 313.37244 
L 559.003099 314.230038 
L 560.635584 309.702266 
L 557.953521 308.842041 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #866458"/>
    <path d="M 692.430255 349.842264 
L 695.201404 353.530394 
L 696.833028 351.693546 
L 694.063414 347.948276 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c8b97b"/>
    <path d="M 618.941727 273.746986 
L 621.683107 275.908528 
L 623.335994 272.787085 
L 620.59481 270.596195 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b9a5a1"/>
    <path d="M 710.196084 377.504051 
L 712.965855 381.21926 
L 714.587441 379.785119 
L 711.819612 376.008525 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f8f695"/>
    <path d="M 568.228772 297.410222 
L 570.92083 298.40953 
L 572.559612 294.144628 
L 569.86717 293.136954 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #93756e"/>
    <path d="M 644.248199 287.611326 
L 647.007911 290.472383 
L 648.657475 287.793633 
L 645.898395 284.894128 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a18781"/>
    <path d="M 578.539064 286.925249 
L 581.24111 288.097356 
L 582.884836 284.074446 
L 580.182458 282.88909 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a58c86"/>
    <path d="M 788.830199 475.313104 
L 791.602191 477.924968 
L 793.146273 478.075983 
L 790.377577 475.425514 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00aacb"/>
    <path d="M 611.815795 272.971798 
L 614.550843 274.93607 
L 616.20347 271.669962 
L 613.468499 269.678827 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bba8a4"/>
    <path d="M 628.827033 277.421874 
L 631.576561 279.862503 
L 633.228849 276.921871 
L 630.479681 274.448279 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b39e99"/>
    <path d="M 562.26939 305.231947 
L 564.956219 306.154387 
L 566.591802 301.750411 
L 563.904575 300.82234 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #87655e"/>
    <path d="M 669.132476 315.722634 
L 671.90185 319.136495 
L 673.543648 316.857061 
L 670.775343 313.394706 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8e6e5c"/>
    <path d="M 600.329272 274.585519 
L 603.053369 276.246568 
L 604.704313 272.729746 
L 601.980115 271.046061 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b9a5a1"/>
    <path d="M 647.007911 290.472383 
L 649.769262 293.40461 
L 651.418153 290.765622 
L 648.657475 287.793633 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9d827c"/>
    <path d="M 730.729294 408.075822 
L 733.496958 411.653691 
L 735.103543 410.722666 
L 732.33831 407.08283 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a5ed87"/>
    <path d="M 548.756272 326.46919 
L 551.432592 327.27534 
L 553.061031 322.592473 
L 550.384339 321.786919 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9c8064"/>
    <path d="M 825.224447 502.628495 
L 828.015112 504.356673 
L 829.515594 504.661442 
L 826.728006 502.917446 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1276dc"/>
    <path d="M 666.363647 312.359883 
L 669.132476 315.722634 
L 670.775343 313.394706 
L 668.007528 309.98437 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #886759"/>
    <path d="M 582.884836 284.074446 
L 585.591571 285.336211 
L 587.236975 281.406666 
L 584.529929 280.129371 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ab938e"/>
    <path d="M 689.65885 346.178723 
L 692.430255 349.842264 
L 694.063414 347.948276 
L 691.293479 344.228013 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c2b178"/>
    <path d="M 649.769262 293.40461 
L 652.532103 296.405723 
L 654.180278 293.807765 
L 651.418153 290.765622 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #977a74"/>
    <path d="M 707.425788 373.792488 
L 710.196084 377.504051 
L 711.819612 376.008525 
L 709.051187 372.235567 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f2ee92"/>
    <path d="M 663.595484 309.050952 
L 666.363647 312.359883 
L 668.007528 309.98437 
L 665.240325 306.628814 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #825f56"/>
    <path d="M 595.959474 276.654609 
L 598.679492 278.210568 
L 600.329272 274.585519 
L 597.609084 273.00838 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b7a39f"/>
    <path d="M 652.532103 296.405723 
L 655.296287 299.473366 
L 656.943701 296.917658 
L 654.180278 293.807765 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #93756e"/>
    <path d="M 791.602191 477.924968 
L 794.375491 480.467951 
L 795.916267 480.655976 
L 793.146273 478.075983 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a6d7"/>
    <path d="M 660.828115 305.798496 
L 663.595484 309.050952 
L 665.240325 306.628814 
L 662.473864 303.330749 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #836059"/>
    <path d="M 587.236975 281.406666 
L 589.948286 282.762558 
L 591.595273 278.930717 
L 588.883686 277.557206 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #af9994"/>
    <path d="M 655.296287 299.473366 
L 658.061671 302.605118 
L 659.708277 300.092832 
L 656.943701 296.917658 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8d6d66"/>
    <path d="M 658.061671 302.605118 
L 660.828115 305.798496 
L 662.473864 303.330749 
L 659.708277 300.092832 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #87655e"/>
    <path d="M 727.961154 404.479047 
L 730.729294 408.075822 
L 732.33831 407.08283 
L 729.572536 403.423564 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b1ef89"/>
    <path d="M 591.595273 278.930717 
L 594.31102 280.384812 
L 595.959474 276.654609 
L 593.243498 275.181009 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b39e99"/>
    <path d="M 631.576561 279.862503 
L 634.328548 282.382964 
L 635.980446 279.476905 
L 633.228849 276.921871 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #af9994"/>
    <path d="M 572.559612 294.144628 
L 575.256489 295.220843 
L 576.897081 291.036803 
L 574.199809 289.94951 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #997c76"/>
    <path d="M 554.690616 317.957038 
L 557.371873 318.811952 
L 559.003099 314.230038 
L 556.321423 313.37244 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8e6e5c"/>
    <path d="M 621.683107 275.908528 
L 624.427451 278.153124 
L 626.080123 275.062841 
L 623.335994 272.787085 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b7a39f"/>
    <path d="M 686.887262 342.542724 
L 689.65885 346.178723 
L 691.293479 344.228013 
L 688.523297 340.535769 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bca975"/>
    <path d="M 607.432276 274.498665 
L 610.163851 276.351786 
L 611.815795 272.971798 
L 609.084201 271.092692 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b9a5a1"/>
    <path d="M 812.571275 494.568297 
L 815.354306 496.612642 
L 816.869547 496.929005 
L 814.089745 494.860894 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0888ee"/>
    <path d="M 704.654996 370.087509 
L 707.425788 373.792488 
L 709.051187 372.235567 
L 706.282198 368.469246 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eae48e"/>
    <path d="M 837.897935 509.356208 
L 840.699131 510.739708 
L 842.185962 510.997111 
L 839.387633 509.605269 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1a66cc"/>
    <path d="M 847.794389 513.5003 
L 850.604828 514.610804 
L 852.081949 514.78732 
L 849.274172 513.673755 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1e5ec4"/>
    <path d="M 725.19252 400.866119 
L 727.961154 404.479047 
L 729.572536 403.423564 
L 726.806202 399.747686 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bdf28c"/>
    <path d="M 547.129291 331.195452 
L 549.805216 332.002195 
L 551.432592 327.27534 
L 548.756272 326.46919 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a48b68"/>
    <path d="M 566.591802 301.750411 
L 569.283431 302.741153 
L 570.92083 298.40953 
L 568.228772 297.410222 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8d6d66"/>
    <path d="M 560.635584 309.702266 
L 563.321974 310.618952 
L 564.956219 306.154387 
L 562.26939 305.231947 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #805c54"/>
    <path d="M 614.550843 274.93607 
L 617.289187 276.984263 
L 618.941727 273.746986 
L 616.20347 271.669962 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b9a5a1"/>
    <path d="M 794.375491 480.467951 
L 797.15023 482.940434 
L 798.687695 483.16384 
L 795.916267 480.655976 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a4dc"/>
    <path d="M 634.328548 282.382964 
L 637.082832 284.981405 
L 638.73431 282.11149 
L 635.980446 279.476905 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ab938e"/>
    <path d="M 684.115571 338.937198 
L 686.887262 342.542724 
L 688.523297 340.535769 
L 685.752946 336.874538 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b6a272"/>
    <path d="M 576.897081 291.036803 
L 579.598735 292.195282 
L 581.24111 288.097356 
L 578.539064 286.925249 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9f847e"/>
    <path d="M 701.883743 366.392054 
L 704.654996 370.087509 
L 706.282198 368.469246 
L 703.51268 364.712567 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e4dc8a"/>
    <path d="M 722.423378 397.239818 
L 725.19252 400.866119 
L 726.806202 399.747686 
L 724.039293 396.058035 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c9f48e"/>
    <path d="M 603.053369 276.246568 
L 605.781226 277.990615 
L 607.432276 274.498665 
L 604.704313 272.729746 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b7a39f"/>
    <path d="M 624.427451 278.153124 
L 627.174597 280.479222 
L 628.827033 277.421874 
L 626.080123 275.062841 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b39e99"/>
    <path d="M 553.061031 322.592473 
L 555.741839 323.444652 
L 557.371873 318.811952 
L 554.690616 317.957038 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #94765f"/>
    <path d="M 681.34386 335.365054 
L 684.115571 338.937198 
L 685.752946 336.874538 
L 682.982512 333.247291 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ae976d"/>
    <path d="M 828.015112 504.356673 
L 830.808897 505.997539 
L 832.306334 506.316412 
L 829.515594 504.661442 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1373d9"/>
    <path d="M 637.082832 284.981405 
L 639.839256 287.655893 
L 641.49028 284.823649 
L 638.73431 282.11149 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a78e89"/>
    <path d="M 545.503308 335.962227 
L 548.178816 336.769559 
L 549.805216 332.002195 
L 547.129291 331.195452 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ac956c"/>
    <path d="M 581.24111 288.097356 
L 583.947469 289.343119 
L 585.591571 285.336211 
L 582.884836 284.074446 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a58c86"/>
    <path d="M 797.15023 482.940434 
L 799.926545 485.340863 
L 801.460693 485.597991 
L 798.687695 483.16384 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a0e8"/>
    <path d="M 719.653723 393.602942 
L 722.423378 397.239818 
L 724.039293 396.058035 
L 721.271802 392.357476 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d9f791"/>
    <path d="M 570.92083 298.40953 
L 573.617261 299.474388 
L 575.256489 295.220843 
L 572.559612 294.144628 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #93756e"/>
    <path d="M 598.679492 278.210568 
L 601.403406 279.848089 
L 603.053369 276.246568 
L 600.329272 274.585519 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b5a09c"/>
    <path d="M 699.112073 362.709063 
L 701.883743 366.392054 
L 703.51268 364.712567 
L 700.742674 360.968533 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ded587"/>
    <path d="M 678.57222 331.829173 
L 681.34386 335.365054 
L 682.982512 333.247291 
L 680.212086 329.656968 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a8906a"/>
    <path d="M 610.163851 276.351786 
L 612.898884 278.287986 
L 614.550843 274.93607 
L 611.815795 272.971798 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b7a39f"/>
    <path d="M 559.003099 314.230038 
L 561.689013 315.140857 
L 563.321974 310.618952 
L 560.635584 309.702266 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #866458"/>
    <path d="M 815.354306 496.612642 
L 818.139796 498.575293 
L 819.651825 498.913689 
L 816.869547 496.929005 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0b83e9"/>
    <path d="M 617.289187 276.984263 
L 620.030667 279.11504 
L 621.683107 275.908528 
L 618.941727 273.746986 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b5a09c"/>
    <path d="M 585.591571 285.336211 
L 588.302537 286.673915 
L 589.948286 282.762558 
L 587.236975 281.406666 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a9918c"/>
    <path d="M 564.956219 306.154387 
L 567.647372 307.136373 
L 569.283431 302.741153 
L 566.591802 301.750411 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #87655e"/>
    <path d="M 639.839256 287.655893 
L 642.597665 290.404417 
L 644.248199 287.611326 
L 641.49028 284.823649 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a38984"/>
    <path d="M 594.31102 280.384812 
L 597.030789 281.918809 
L 598.679492 278.210568 
L 595.959474 276.654609 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b19b96"/>
    <path d="M 589.948286 282.762558 
L 592.66373 284.196475 
L 594.31102 280.384812 
L 591.595273 278.930717 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ad9691"/>
    <path d="M 675.800747 328.332406 
L 678.57222 331.829173 
L 680.212086 329.656968 
L 677.441765 326.106482 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a28867"/>
    <path d="M 716.883554 389.958313 
L 719.653723 393.602942 
L 721.271802 392.357476 
L 718.503728 388.648892 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e5fa94"/>
    <path d="M 627.174597 280.479222 
L 629.924386 282.885182 
L 631.576561 279.862503 
L 628.827033 277.421874 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #af9994"/>
    <path d="M 696.340034 359.041471 
L 699.112073 362.709063 
L 700.742674 360.968533 
L 697.972231 357.240145 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d8cd84"/>
    <path d="M 543.878227 340.766004 
L 546.553299 341.573921 
L 548.178816 336.769559 
L 545.503308 335.962227 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b29c6f"/>
    <path d="M 551.432592 327.27534 
L 554.112921 328.124737 
L 555.741839 323.444652 
L 553.061031 322.592473 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9c8064"/>
    <path d="M 642.597665 290.404417 
L 645.357906 293.224886 
L 647.007911 290.472383 
L 644.248199 287.611326 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9f847e"/>
    <path d="M 756.805424 442.927247 
L 759.573642 446.115574 
L 761.155804 445.808751 
L 758.390568 442.564378 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #31d670"/>
    <path d="M 759.573642 446.115574 
L 762.34202 449.258162 
L 763.921154 449.0062 
L 761.155804 445.808751 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #25d36d"/>
    <path d="M 575.256489 295.220843 
L 577.957693 296.365332 
L 579.598735 292.195282 
L 576.897081 291.036803 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #997c76"/>
    <path d="M 673.029541 324.877572 
L 675.800747 328.332406 
L 677.441765 326.106482 
L 674.67165 322.598711 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9c8064"/>
    <path d="M 754.037287 439.695463 
L 756.805424 442.927247 
L 758.390568 442.564378 
L 755.625365 439.275415 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #3dd872"/>
    <path d="M 762.34202 449.258162 
L 765.110642 452.35278 
L 766.686703 452.154443 
L 763.921154 449.0062 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #19d16b"/>
    <path d="M 799.926545 485.340863 
L 802.704573 487.667757 
L 804.235405 487.956917 
L 801.460693 485.597991 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #009cf4"/>
    <path d="M 751.269158 436.42255 
L 754.037287 439.695463 
L 755.625365 439.275415 
L 752.860119 435.944244 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #45da74"/>
    <path d="M 765.110642 452.35278 
L 767.879596 455.397246 
L 769.452544 455.251248 
L 766.686703 452.154443 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #11cf69"/>
    <path d="M 840.699131 510.739708 
L 843.504148 512.031529 
L 844.988157 512.295609 
L 842.185962 510.997111 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1a66cc"/>
    <path d="M 605.781226 277.990615 
L 608.512694 279.816661 
L 610.163851 276.351786 
L 607.432276 274.498665 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b5a09c"/>
    <path d="M 714.112877 386.308763 
L 716.883554 389.958313 
L 718.503728 388.648892 
L 715.735075 384.935182 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1fc96"/>
    <path d="M 748.500969 433.110882 
L 751.269158 436.42255 
L 752.860119 435.944244 
L 750.09476 432.573294 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #51dc76"/>
    <path d="M 645.357906 293.224886 
L 648.119827 296.115137 
L 649.769262 293.40461 
L 647.007911 290.472383 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #997c76"/>
    <path d="M 670.25871 321.467451 
L 673.029541 324.877572 
L 674.67165 322.598711 
L 671.90185 319.136495 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #967960"/>
    <path d="M 767.879596 455.397246 
L 770.648974 458.389433 
L 772.218772 458.29444 
L 769.452544 455.251248 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #05cd67"/>
    <path d="M 693.567681 355.392205 
L 696.340034 359.041471 
L 697.972231 357.240145 
L 695.201404 353.530394 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d0c380"/>
    <path d="M 557.371873 318.811952 
L 560.057275 319.716799 
L 561.689013 315.140857 
L 559.003099 314.230038 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8e6e5c"/>
    <path d="M 745.732658 429.762879 
L 748.500969 433.110882 
L 750.09476 432.573294 
L 747.329221 429.16504 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #5ddf79"/>
    <path d="M 620.030667 279.11504 
L 622.775127 281.326975 
L 624.427451 278.153124 
L 621.683107 275.908528 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b39e99"/>
    <path d="M 629.924386 282.885182 
L 632.67666 285.369281 
L 634.328548 282.382964 
L 631.576561 279.862503 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ab938e"/>
    <path d="M 569.283431 302.741153 
L 571.979363 303.794391 
L 573.617261 299.474388 
L 570.92083 298.40953 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8d6d66"/>
    <path d="M 648.119827 296.115137 
L 650.883281 299.072935 
L 652.532103 296.405723 
L 649.769262 293.40461 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #957771"/>
    <path d="M 770.648974 458.389433 
L 773.418875 461.327268 
L 774.985488 461.281899 
L 772.218772 458.29444 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00cb6b"/>
    <path d="M 667.488363 318.104784 
L 670.25871 321.467451 
L 671.90185 319.136495 
L 669.132476 315.722634 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #90715d"/>
    <path d="M 850.604828 514.610804 
L 853.419644 515.626826 
L 854.894155 515.804816 
L 852.081949 514.78732 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1e5ec4"/>
    <path d="M 542.253946 345.603245 
L 544.928563 346.411746 
L 546.553299 341.573921 
L 543.878227 340.766004 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #baa774"/>
    <path d="M 612.898884 278.287986 
L 615.637221 280.306053 
L 617.289187 276.984263 
L 614.550843 274.93607 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b5a09c"/>
    <path d="M 563.321974 310.618952 
L 566.012608 311.592005 
L 567.647372 307.136373 
L 564.956219 306.154387 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #805c54"/>
    <path d="M 579.598735 292.195282 
L 582.304656 293.424592 
L 583.947469 289.343119 
L 581.24111 288.097356 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9f847e"/>
    <path d="M 742.964165 426.380999 
L 745.732658 429.762879 
L 747.329221 429.16504 
L 744.563444 425.721999 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #69e17b"/>
    <path d="M 664.718617 314.79227 
L 667.488363 318.104784 
L 669.132476 315.722634 
L 666.363647 312.359883 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8a695a"/>
    <path d="M 650.883281 299.072935 
L 653.648124 302.095976 
L 655.296287 299.473366 
L 652.532103 296.405723 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8f7069"/>
    <path d="M 549.805216 332.002195 
L 552.48504 332.848766 
L 554.112921 328.124737 
L 551.432592 327.27534 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a48b68"/>
    <path d="M 830.808897 505.997539 
L 833.605964 507.55032 
L 835.100391 507.881568 
L 832.306334 506.316412 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1470d6"/>
    <path d="M 818.139796 498.575293 
L 820.927898 500.455179 
L 822.436738 500.813856 
L 819.651825 498.913689 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0c80e6"/>
    <path d="M 711.341703 382.657141 
L 714.112877 386.308763 
L 715.735075 384.935182 
L 712.965855 381.21926 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 601.403406 279.848089 
L 604.131072 281.566291 
L 605.781226 277.990615 
L 603.053369 276.246568 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b39e99"/>
    <path d="M 773.418875 461.327268 
L 776.189401 464.208733 
L 777.752795 464.211562 
L 774.985488 461.281899 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c47d"/>
    <path d="M 690.795073 351.764184 
L 693.567681 355.392205 
L 695.201404 353.530394 
L 692.430255 349.842264 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cabb7c"/>
    <path d="M 661.949592 311.532557 
L 664.718617 314.79227 
L 666.363647 312.359883 
L 663.595484 309.050952 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #846257"/>
    <path d="M 653.648124 302.095976 
L 656.414214 305.181891 
L 658.061671 302.605118 
L 655.296287 299.473366 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8b6b64"/>
    <path d="M 659.181415 308.328249 
L 661.949592 311.532557 
L 663.595484 309.050952 
L 660.828115 305.798496 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #805c54"/>
    <path d="M 656.414214 305.181891 
L 659.181415 308.328249 
L 660.828115 305.798496 
L 658.061671 302.605118 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #85635c"/>
    <path d="M 740.195441 422.967743 
L 742.964165 426.380999 
L 744.563444 425.721999 
L 741.797375 422.246729 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #75e37d"/>
    <path d="M 802.704573 487.667757 
L 805.484455 489.919703 
L 807.011975 490.239177 
L 804.235405 487.956917 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0098fe"/>
    <path d="M 583.947469 289.343119 
L 586.658021 290.662087 
L 588.302537 286.673915 
L 585.591571 285.336211 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a38984"/>
    <path d="M 776.189401 464.208733 
L 778.960656 467.031869 
L 780.520805 467.081426 
L 777.752795 464.211562 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c088"/>
    <path d="M 737.426437 419.525646 
L 740.195441 422.967743 
L 741.797375 422.246729 
L 739.030965 418.741827 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #81e680"/>
    <path d="M 632.67666 285.369281 
L 635.431262 287.929709 
L 637.082832 284.981405 
L 634.328548 282.382964 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a78e89"/>
    <path d="M 597.030789 281.918809 
L 599.754439 283.531941 
L 601.403406 279.848089 
L 598.679492 278.210568 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #af9994"/>
    <path d="M 708.570051 379.006307 
L 711.341703 382.657141 
L 712.965855 381.21926 
L 710.196084 377.504051 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f8f695"/>
    <path d="M 688.022279 348.160312 
L 690.795073 351.764184 
L 692.430255 349.842264 
L 689.65885 346.178723 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c4b379"/>
    <path d="M 540.630359 350.47039 
L 543.304505 351.279472 
L 544.928563 346.411746 
L 542.253946 345.603245 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c2b178"/>
    <path d="M 588.302537 286.673915 
L 591.017605 288.087006 
L 592.66373 284.196475 
L 589.948286 282.762558 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a78e89"/>
    <path d="M 555.741839 323.444652 
L 558.426693 324.343429 
L 560.057275 319.716799 
L 557.371873 318.811952 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #94765f"/>
    <path d="M 592.66373 284.196475 
L 595.383172 285.707759 
L 597.030789 281.918809 
L 594.31102 280.384812 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ab938e"/>
    <path d="M 573.617261 299.474388 
L 576.317959 300.604543 
L 577.957693 296.365332 
L 575.256489 295.220843 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #93756e"/>
    <path d="M 622.775127 281.326975 
L 625.52241 283.618554 
L 627.174597 280.479222 
L 624.427451 278.153124 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #af9994"/>
    <path d="M 734.657114 416.057282 
L 737.426437 419.525646 
L 739.030965 418.741827 
L 736.264172 415.209925 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8de882"/>
    <path d="M 548.178816 336.769559 
L 550.858109 337.613265 
L 552.48504 332.848766 
L 549.805216 332.002195 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ac956c"/>
    <path d="M 608.512694 279.816661 
L 611.247621 281.723613 
L 612.898884 278.287986 
L 610.163851 276.351786 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b39e99"/>
    <path d="M 778.960656 467.031869 
L 781.732753 469.794775 
L 783.28963 469.889548 
L 780.520805 467.081426 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00bc94"/>
    <path d="M 561.689013 315.140857 
L 564.379086 316.104809 
L 566.012608 311.592005 
L 563.321974 310.618952 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #866458"/>
    <path d="M 685.249369 344.583475 
L 688.022279 348.160312 
L 689.65885 346.178723 
L 686.887262 342.542724 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #beac76"/>
    <path d="M 567.647372 307.136373 
L 570.342758 308.17774 
L 571.979363 303.794391 
L 569.283431 302.741153 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #85635c"/>
    <path d="M 615.637221 280.306053 
L 618.378706 282.404686 
L 620.030667 279.11504 
L 617.289187 276.984263 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b19b96"/>
    <path d="M 705.797945 375.359127 
L 708.570051 379.006307 
L 710.196084 377.504051 
L 707.425788 373.792488 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f2ee92"/>
    <path d="M 635.431262 287.929709 
L 638.188037 290.564581 
L 639.839256 287.655893 
L 637.082832 284.981405 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a38984"/>
    <path d="M 731.887436 412.565254 
L 734.657114 416.057282 
L 736.264172 415.209925 
L 733.496958 411.653691 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #99eb85"/>
    <path d="M 539.007353 355.36386 
L 541.681014 356.173522 
L 543.304505 351.279472 
L 540.630359 350.47039 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cabb7c"/>
    <path d="M 781.732753 469.794775 
L 784.505806 472.495611 
L 786.059387 472.634046 
L 783.28963 469.889548 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b8a0"/>
    <path d="M 805.484455 489.919703 
L 808.266334 492.09536 
L 809.790548 492.443402 
L 807.011975 490.239177 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0296fc"/>
    <path d="M 577.957693 296.365332 
L 580.663114 297.577756 
L 582.304656 293.424592 
L 579.598735 292.195282 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #977a74"/>
    <path d="M 682.476423 341.036542 
L 685.249369 344.583475 
L 686.887262 342.542724 
L 684.115571 338.937198 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b6a272"/>
    <path d="M 729.117374 409.052199 
L 731.887436 412.565254 
L 733.496958 411.653691 
L 730.729294 408.075822 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a5ed87"/>
    <path d="M 820.927898 500.455179 
L 823.718771 502.251309 
L 825.224447 502.628495 
L 822.436738 500.813856 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0e7ee4"/>
    <path d="M 843.504148 512.031529 
L 846.313154 513.231215 
L 847.794389 513.5003 
L 844.988157 512.295609 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1b63c9"/>
    <path d="M 554.112921 328.124737 
L 556.797196 329.017353 
L 558.426693 324.343429 
L 555.741839 323.444652 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9c8064"/>
    <path d="M 604.131072 281.566291 
L 606.862344 283.364202 
L 608.512694 279.816661 
L 605.781226 277.990615 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #af9994"/>
    <path d="M 703.025414 371.718472 
L 705.797945 375.359127 
L 707.425788 373.792488 
L 704.654996 370.087509 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ece78f"/>
    <path d="M 625.52241 283.618554 
L 628.272359 285.988179 
L 629.924386 282.885182 
L 627.174597 280.479222 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ab938e"/>
    <path d="M 638.188037 290.564581 
L 640.946833 293.27193 
L 642.597665 290.404417 
L 639.839256 287.655893 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9f847e"/>
    <path d="M 546.553299 341.573921 
L 549.232038 342.414729 
L 550.858109 337.613265 
L 548.178816 336.769559 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b49f70"/>
    <path d="M 679.703523 337.522356 
L 682.476423 341.036542 
L 684.115571 338.937198 
L 681.34386 335.365054 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b09a6e"/>
    <path d="M 833.605964 507.55032 
L 836.406477 509.014322 
L 837.897935 509.356208 
L 835.100391 507.881568 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #166ed4"/>
    <path d="M 726.346905 405.52078 
L 729.117374 409.052199 
L 730.729294 408.075822 
L 727.961154 404.479047 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b1ef89"/>
    <path d="M 784.505806 472.495611 
L 787.279932 475.1326 
L 788.830199 475.313104 
L 786.059387 472.634046 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b2b2"/>
    <path d="M 582.304656 293.424592 
L 585.014727 294.724299 
L 586.658021 290.662087 
L 583.947469 289.343119 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9d827c"/>
    <path d="M 537.384809 360.280061 
L 540.057973 361.090303 
L 541.681014 356.173522 
L 539.007353 355.36386 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d2c581"/>
    <path d="M 571.979363 303.794391 
L 574.679501 304.909883 
L 576.317959 300.604543 
L 573.617261 299.474388 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8b6b64"/>
    <path d="M 560.057275 319.716799 
L 562.746747 320.671495 
L 564.379086 316.104809 
L 561.689013 315.140857 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8e6e5c"/>
    <path d="M 640.946833 293.27193 
L 643.707498 296.049716 
L 645.357906 293.224886 
L 642.597665 290.404417 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9b7f79"/>
    <path d="M 599.754439 283.531941 
L 602.481829 285.223353 
L 604.131072 281.566291 
L 601.403406 279.848089 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ad9691"/>
    <path d="M 700.252496 368.087215 
L 703.025414 371.718472 
L 704.654996 370.087509 
L 701.883743 366.392054 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e4dc8a"/>
    <path d="M 611.247621 281.723613 
L 613.985856 283.710295 
L 615.637221 280.306053 
L 612.898884 278.287986 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #af9994"/>
    <path d="M 618.378706 282.404686 
L 621.123185 284.582497 
L 622.775127 281.326975 
L 620.030667 279.11504 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #af9994"/>
    <path d="M 676.93076 334.043735 
L 679.703523 337.522356 
L 681.34386 335.365054 
L 678.57222 331.829173 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #aa926b"/>
    <path d="M 566.012608 311.592005 
L 568.707399 312.621267 
L 570.342758 308.17774 
L 567.647372 307.136373 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #805c54"/>
    <path d="M 853.419644 515.626826 
L 856.239005 516.548157 
L 857.710963 516.726033 
L 854.894155 515.804816 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1e5ec4"/>
    <path d="M 723.576012 401.973688 
L 726.346905 405.52078 
L 727.961154 404.479047 
L 725.19252 400.866119 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c1f38d"/>
    <path d="M 586.658021 290.662087 
L 589.37264 292.05373 
L 591.017605 288.087006 
L 588.302537 286.673915 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a18781"/>
    <path d="M 595.383172 285.707759 
L 598.106477 287.295669 
L 599.754439 283.531941 
L 597.030789 281.918809 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a9918c"/>
    <path d="M 544.928563 346.411746 
L 547.606727 347.249625 
L 549.232038 342.414729 
L 546.553299 341.573921 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #baa774"/>
    <path d="M 628.272359 285.988179 
L 631.024818 288.434169 
L 632.67666 285.369281 
L 629.924386 282.885182 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a78e89"/>
    <path d="M 591.017605 288.087006 
L 593.736644 289.574851 
L 595.383172 285.707759 
L 592.66373 284.196475 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a58c86"/>
    <path d="M 643.707498 296.049716 
L 646.469885 298.895825 
L 648.119827 296.115137 
L 645.357906 293.224886 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #977a74"/>
    <path d="M 552.48504 332.848766 
L 555.168705 333.73514 
L 556.797196 329.017353 
L 554.112921 328.124737 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a48b68"/>
    <path d="M 674.158226 330.603468 
L 676.93076 334.043735 
L 678.57222 331.829173 
L 675.800747 328.332406 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a48b68"/>
    <path d="M 787.279932 475.1326 
L 790.055253 477.704025 
L 791.602191 477.924968 
L 788.830199 475.313104 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00aebf"/>
    <path d="M 808.266334 492.09536 
L 811.050356 494.193459 
L 812.571275 494.568297 
L 809.790548 492.443402 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0490f6"/>
    <path d="M 697.479233 364.468227 
L 700.252496 368.087215 
L 701.883743 366.392054 
L 699.112073 362.709063 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ded587"/>
    <path d="M 535.762606 365.215389 
L 538.435261 366.026212 
L 540.057973 361.090303 
L 537.384809 360.280061 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dad085"/>
    <path d="M 720.804682 398.413634 
L 723.576012 401.973688 
L 725.19252 400.866119 
L 722.423378 397.239818 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cdf58f"/>
    <path d="M 671.386023 327.204308 
L 674.158226 330.603468 
L 675.800747 328.332406 
L 673.029541 324.877572 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9e8365"/>
    <path d="M 646.469885 298.895825 
L 649.233849 301.808074 
L 650.883281 299.072935 
L 648.119827 296.115137 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #91726c"/>
    <path d="M 576.317959 300.604543 
L 579.022819 301.79967 
L 580.663114 297.577756 
L 577.957693 296.365332 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #91726c"/>
    <path d="M 668.614255 323.848975 
L 671.386023 327.204308 
L 673.029541 324.877572 
L 670.25871 321.467451 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #987b61"/>
    <path d="M 606.862344 283.364202 
L 609.597074 285.240766 
L 611.247621 281.723613 
L 608.512694 279.816661 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ad9691"/>
    <path d="M 649.233849 301.808074 
L 651.999248 304.784212 
L 653.648124 302.095976 
L 650.883281 299.072935 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8d6d66"/>
    <path d="M 558.426693 324.343429 
L 561.115526 325.288725 
L 562.746747 320.671495 
L 560.057275 319.716799 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #967960"/>
    <path d="M 823.718771 502.251309 
L 826.512572 503.962767 
L 828.015112 504.356673 
L 825.224447 502.628495 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0f7be1"/>
    <path d="M 694.705672 360.864378 
L 697.479233 364.468227 
L 699.112073 362.709063 
L 696.340034 359.041471 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d8cd84"/>
    <path d="M 543.304505 351.279472 
L 545.982074 352.114397 
L 547.606727 347.249625 
L 544.928563 346.411746 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c2b178"/>
    <path d="M 718.032911 394.843353 
L 720.804682 398.413634 
L 722.423378 397.239818 
L 719.653723 393.602942 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d9f791"/>
    <path d="M 631.024818 288.434169 
L 633.779635 290.954762 
L 635.431262 287.929709 
L 632.67666 285.369281 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a58c86"/>
    <path d="M 665.843032 320.540148 
L 668.614255 323.848975 
L 670.25871 321.467451 
L 667.488363 318.104784 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #92735e"/>
    <path d="M 621.123185 284.582497 
L 623.870505 286.838013 
L 625.52241 283.618554 
L 622.775127 281.326975 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ab938e"/>
    <path d="M 651.999248 304.784212 
L 654.765943 307.821925 
L 656.414214 305.181891 
L 653.648124 302.095976 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #87655e"/>
    <path d="M 790.055253 477.704025 
L 792.831895 480.208236 
L 794.375491 480.467951 
L 791.602191 477.924968 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00aacb"/>
    <path d="M 534.140613 370.166234 
L 536.812752 370.977638 
L 538.435261 366.026212 
L 535.762606 365.215389 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e2da89"/>
    <path d="M 663.072468 317.280464 
L 665.843032 320.540148 
L 667.488363 318.104784 
L 664.718617 314.79227 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8c6c5b"/>
    <path d="M 570.342758 308.17774 
L 573.042281 309.278261 
L 574.679501 304.909883 
L 571.979363 303.794391 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #85635c"/>
    <path d="M 654.765943 307.821925 
L 657.533798 310.918837 
L 659.181415 308.328249 
L 656.414214 305.181891 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #836059"/>
    <path d="M 550.858109 337.613265 
L 553.541135 338.493324 
L 555.168705 333.73514 
L 552.48504 332.848766 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ac956c"/>
    <path d="M 564.379086 316.104809 
L 567.073236 317.121747 
L 568.707399 312.621267 
L 566.012608 311.592005 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #886759"/>
    <path d="M 660.302682 314.072513 
L 663.072468 317.280464 
L 664.718617 314.79227 
L 661.949592 311.532557 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #886759"/>
    <path d="M 657.533798 310.918837 
L 660.302682 314.072513 
L 661.949592 311.532557 
L 659.181415 308.328249 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #825f56"/>
    <path d="M 613.985856 283.710295 
L 616.72725 285.775442 
L 618.378706 282.404686 
L 615.637221 280.306053 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ad9691"/>
    <path d="M 580.663114 297.577756 
L 583.372639 298.857702 
L 585.014727 294.724299 
L 582.304656 293.424592 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #977a74"/>
    <path d="M 691.93187 357.278525 
L 694.705672 360.864378 
L 696.340034 359.041471 
L 693.567681 355.392205 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d2c581"/>
    <path d="M 715.260699 391.265597 
L 718.032911 394.843353 
L 719.653723 393.602942 
L 716.883554 389.958313 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e5fa94"/>
    <path d="M 602.481829 285.223353 
L 605.212818 286.992105 
L 606.862344 283.364202 
L 604.131072 281.566291 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ab938e"/>
    <path d="M 811.050356 494.193459 
L 813.836669 496.212802 
L 815.354306 496.612642 
L 812.571275 494.568297 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #068ef4"/>
    <path d="M 633.779635 290.954762 
L 636.536658 293.548117 
L 638.188037 290.564581 
L 635.431262 287.929709 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a18781"/>
    <path d="M 836.406477 509.014322 
L 839.210601 510.388934 
L 840.699131 510.739708 
L 837.897935 509.356208 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #176bd1"/>
    <path d="M 846.313154 513.231215 
L 849.126316 514.338391 
L 850.604828 514.610804 
L 847.794389 513.5003 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1b63c9"/>
    <path d="M 541.681014 356.173522 
L 544.35797 357.005472 
L 545.982074 352.114397 
L 543.304505 351.279472 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cabb7c"/>
    <path d="M 532.518698 375.128981 
L 535.190312 375.94097 
L 536.812752 370.977638 
L 534.140613 370.166234 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eae48e"/>
    <path d="M 585.014727 294.724299 
L 587.728828 296.093896 
L 589.37264 292.05373 
L 586.658021 290.662087 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9b7f79"/>
    <path d="M 689.157884 353.71352 
L 691.93187 357.278525 
L 693.567681 355.392205 
L 690.795073 351.764184 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ccbe7d"/>
    <path d="M 792.831895 480.208236 
L 795.609986 482.643648 
L 797.15023 482.940434 
L 794.375491 480.467951 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a8d0"/>
    <path d="M 556.797196 329.017353 
L 559.485354 329.953117 
L 561.115526 325.288725 
L 558.426693 324.343429 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9c8064"/>
    <path d="M 598.106477 287.295669 
L 600.833508 288.959378 
L 602.481829 285.223353 
L 599.754439 283.531941 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a78e89"/>
    <path d="M 712.488052 387.683132 
L 715.260699 391.265597 
L 716.883554 389.958313 
L 714.112877 386.308763 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1fc96"/>
    <path d="M 623.870505 286.838013 
L 626.620512 289.16968 
L 628.272359 285.988179 
L 625.52241 283.618554 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a78e89"/>
    <path d="M 549.232038 342.414729 
L 551.914398 343.288407 
L 553.541135 338.493324 
L 550.858109 337.613265 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b49f70"/>
    <path d="M 589.37264 292.05373 
L 592.091203 293.517438 
L 593.736644 289.574851 
L 591.017605 288.087006 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a18781"/>
    <path d="M 574.679501 304.909883 
L 577.383742 306.087323 
L 579.022819 301.79967 
L 576.317959 300.604543 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8b6b64"/>
    <path d="M 593.736644 289.574851 
L 596.459525 291.136735 
L 598.106477 287.295669 
L 595.383172 285.707759 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a58c86"/>
    <path d="M 609.597074 285.240766 
L 612.335117 287.19484 
L 613.985856 283.710295 
L 611.247621 281.723613 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ab938e"/>
    <path d="M 636.536658 293.548117 
L 639.295737 296.212318 
L 640.946833 293.27193 
L 638.188037 290.564581 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9b7f79"/>
    <path d="M 686.383783 350.172199 
L 689.157884 353.71352 
L 690.795073 351.764184 
L 688.022279 348.160312 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c4b379"/>
    <path d="M 562.746747 320.671495 
L 565.440213 321.675903 
L 567.073236 317.121747 
L 564.379086 316.104809 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8e6e5c"/>
    <path d="M 709.714982 384.098738 
L 712.488052 387.683132 
L 714.112877 386.308763 
L 711.341703 382.657141 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 568.707399 312.621267 
L 571.406257 313.706525 
L 573.042281 309.278261 
L 570.342758 308.17774 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #805c54"/>
    <path d="M 530.896722 380.100019 
L 533.567806 380.912594 
L 535.190312 375.94097 
L 532.518698 375.128981 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f2ee92"/>
    <path d="M 616.72725 285.775442 
L 619.471651 287.917707 
L 621.123185 284.582497 
L 618.378706 282.404686 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a9918c"/>
    <path d="M 540.057973 361.090303 
L 542.734301 361.919262 
L 544.35797 357.005472 
L 541.681014 356.173522 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d2c581"/>
    <path d="M 826.512572 503.962767 
L 829.30946 505.588716 
L 830.808897 505.997539 
L 828.015112 504.356673 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1078de"/>
    <path d="M 683.609636 346.657382 
L 686.383783 350.172199 
L 688.022279 348.160312 
L 685.249369 344.583475 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #beac76"/>
    <path d="M 795.609986 482.643648 
L 798.389657 485.008743 
L 799.926545 485.340863 
L 797.15023 482.940434 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a4dc"/>
    <path d="M 639.295737 296.212318 
L 642.056723 298.945374 
L 643.707498 296.049716 
L 640.946833 293.27193 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #977a74"/>
    <path d="M 547.606727 347.249625 
L 550.288396 348.116865 
L 551.914398 343.288407 
L 549.232038 342.414729 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #baa774"/>
    <path d="M 579.022819 301.79967 
L 581.731734 303.059375 
L 583.372639 298.857702 
L 580.663114 297.577756 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #91726c"/>
    <path d="M 555.168705 333.73514 
L 557.856152 334.661253 
L 559.485354 329.953117 
L 556.797196 329.017353 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a48b68"/>
    <path d="M 752.446079 440.075258 
L 755.217145 443.247371 
L 756.805424 442.927247 
L 754.037287 439.695463 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #41d973"/>
    <path d="M 706.941509 380.515206 
L 709.714982 384.098738 
L 711.341703 382.657141 
L 708.570051 379.006307 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f8f695"/>
    <path d="M 755.217145 443.247371 
L 757.988345 446.377205 
L 759.573642 446.115574 
L 756.805424 442.927247 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #35d771"/>
    <path d="M 749.675076 436.863138 
L 752.446079 440.075258 
L 754.037287 439.695463 
L 751.269158 436.42255 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #4ddb75"/>
    <path d="M 626.620512 289.16968 
L 629.373056 291.57586 
L 631.024818 288.434169 
L 628.272359 285.988179 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a38984"/>
    <path d="M 757.988345 446.377205 
L 760.759754 449.462534 
L 762.34202 449.258162 
L 759.573642 446.115574 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #29d46e"/>
    <path d="M 746.90407 433.613329 
L 749.675076 436.863138 
L 751.269158 436.42255 
L 748.500969 433.110882 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #55dd77"/>
    <path d="M 605.212818 286.992105 
L 607.947262 288.837176 
L 609.597074 285.240766 
L 606.862344 283.364202 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a9918c"/>
    <path d="M 529.27454 385.075741 
L 531.945092 385.888905 
L 533.567806 380.912594 
L 530.896722 380.100019 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #faf996"/>
    <path d="M 813.836669 496.212802 
L 816.625424 498.152269 
L 818.139796 498.575293 
L 815.354306 496.612642 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0888ee"/>
    <path d="M 760.759754 449.462534 
L 763.531453 452.501178 
L 765.110642 452.35278 
L 762.34202 449.258162 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #21d36d"/>
    <path d="M 744.133 430.32819 
L 746.90407 433.613329 
L 748.500969 433.110882 
L 745.732658 429.762879 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #61df79"/>
    <path d="M 680.835522 343.171868 
L 683.609636 346.657382 
L 685.249369 344.583475 
L 682.476423 341.036542 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b8a473"/>
    <path d="M 538.435261 366.026212 
L 541.110948 366.852169 
L 542.734301 361.919262 
L 540.057973 361.090303 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dad085"/>
    <path d="M 741.361811 427.01012 
L 744.133 430.32819 
L 745.732658 429.762879 
L 742.964165 426.380999 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #6de27c"/>
    <path d="M 763.531453 452.501178 
L 766.303528 455.491009 
L 767.879596 455.397246 
L 765.110642 452.35278 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #15d06a"/>
    <path d="M 642.056723 298.945374 
L 644.819473 301.745225 
L 646.469885 298.895825 
L 643.707498 296.049716 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #93756e"/>
    <path d="M 704.167657 376.935332 
L 706.941509 380.515206 
L 708.570051 379.006307 
L 705.797945 375.359127 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f2ee92"/>
    <path d="M 561.115526 325.288725 
L 563.808266 326.280414 
L 565.440213 321.675903 
L 562.746747 320.671495 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #967960"/>
    <path d="M 583.372639 298.857702 
L 586.086153 300.204683 
L 587.728828 296.093896 
L 585.014727 294.724299 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #957771"/>
    <path d="M 738.590453 423.661559 
L 741.361811 427.01012 
L 742.964165 426.380999 
L 740.195441 422.967743 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #79e47e"/>
    <path d="M 678.061523 339.718434 
L 680.835522 343.171868 
L 682.476423 341.036542 
L 679.703523 337.522356 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b29c6f"/>
    <path d="M 573.042281 309.278261 
L 575.745847 310.437644 
L 577.383742 306.087323 
L 574.679501 304.909883 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #85635c"/>
    <path d="M 766.303528 455.491009 
L 769.076069 458.42995 
L 770.648974 458.389433 
L 767.879596 455.397246 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0dcf69"/>
    <path d="M 619.471651 287.917707 
L 622.21891 290.135659 
L 623.870505 286.838013 
L 621.123185 284.582497 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a78e89"/>
    <path d="M 600.833508 288.959378 
L 603.564127 290.697982 
L 605.212818 286.992105 
L 602.481829 285.223353 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a58c86"/>
    <path d="M 612.335117 287.19484 
L 615.076324 289.225201 
L 616.72725 285.775442 
L 613.985856 283.710295 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a9918c"/>
    <path d="M 567.073236 317.121747 
L 569.77138 318.191469 
L 571.406257 313.706525 
L 568.707399 312.621267 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #886759"/>
    <path d="M 545.982074 352.114397 
L 548.66303 352.975151 
L 550.288396 348.116865 
L 547.606727 347.249625 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c2b178"/>
    <path d="M 735.818882 420.28498 
L 738.590453 423.661559 
L 740.195441 422.967743 
L 737.426437 419.525646 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #85e781"/>
    <path d="M 644.819473 301.745225 
L 647.583842 304.609742 
L 649.233849 301.808074 
L 646.469885 298.895825 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8f7069"/>
    <path d="M 675.287727 336.299832 
L 678.061523 339.718434 
L 679.703523 337.522356 
L 676.93076 334.043735 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ac956c"/>
    <path d="M 629.373056 291.57586 
L 632.127986 294.054839 
L 633.779635 290.954762 
L 631.024818 288.434169 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a18781"/>
    <path d="M 553.541135 338.493324 
L 556.227841 339.409677 
L 557.856152 334.661253 
L 555.168705 333.73514 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ac956c"/>
    <path d="M 798.389657 485.008743 
L 801.171044 487.302068 
L 802.704573 487.667757 
L 799.926545 485.340863 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a0e8"/>
    <path d="M 587.728828 296.093896 
L 590.446839 297.532799 
L 592.091203 293.517438 
L 589.37264 292.05373 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9b7f79"/>
    <path d="M 769.076069 458.42995 
L 771.84917 461.315976 
L 773.418875 461.327268 
L 770.648974 458.389433 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #01cc66"/>
    <path d="M 536.812752 370.977638 
L 539.487785 371.800585 
L 541.110948 366.852169 
L 538.435261 366.026212 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e2da89"/>
    <path d="M 701.393456 373.361918 
L 704.167657 376.935332 
L 705.797945 375.359127 
L 703.025414 371.718472 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ece78f"/>
    <path d="M 839.210601 510.388934 
L 842.018502 511.673625 
L 843.504148 512.031529 
L 840.699131 510.739708 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #176bd1"/>
    <path d="M 596.459525 291.136735 
L 599.186114 292.771864 
L 600.833508 288.959378 
L 598.106477 287.295669 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a38984"/>
    <path d="M 733.047059 416.882892 
L 735.818882 420.28498 
L 737.426437 419.525646 
L 734.657114 416.057282 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #91e983"/>
    <path d="M 592.091203 293.517438 
L 594.813581 295.052525 
L 596.459525 291.136735 
L 593.736644 289.574851 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9f847e"/>
    <path d="M 647.583842 304.609742 
L 650.349693 307.536729 
L 651.999248 304.784212 
L 649.233849 301.808074 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #896861"/>
    <path d="M 672.514227 332.918783 
L 675.287727 336.299832 
L 676.93076 334.043735 
L 674.158226 330.603468 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a68d69"/>
    <path d="M 771.84917 461.315976 
L 774.62293 464.147117 
L 776.189401 464.208733 
L 773.418875 461.327268 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c970"/>
    <path d="M 730.274949 413.457835 
L 733.047059 416.882892 
L 734.657114 416.057282 
L 731.887436 412.565254 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9deb85"/>
    <path d="M 849.126316 514.338391 
L 851.943801 515.352768 
L 853.419644 515.626826 
L 850.604828 514.610804 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1b63c9"/>
    <path d="M 669.741122 329.577975 
L 672.514227 332.918783 
L 674.158226 330.603468 
L 671.386023 327.204308 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a08566"/>
    <path d="M 650.349693 307.536729 
L 653.116888 310.523929 
L 654.765943 307.821925 
L 651.999248 304.784212 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #85635c"/>
    <path d="M 698.618943 369.797766 
L 701.393456 373.361918 
L 703.025414 371.718472 
L 700.252496 368.087215 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e6df8b"/>
    <path d="M 577.383742 306.087323 
L 580.091985 307.326335 
L 581.731734 303.059375 
L 579.022819 301.79967 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #896861"/>
    <path d="M 666.968515 326.280064 
L 669.741122 329.577975 
L 671.386023 327.204308 
L 668.614255 323.848975 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9a7e62"/>
    <path d="M 544.35797 357.005472 
L 547.038192 357.859699 
L 548.66303 352.975151 
L 545.982074 352.114397 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cabb7c"/>
    <path d="M 653.116888 310.523929 
L 655.885295 313.569024 
L 657.533798 310.918837 
L 654.765943 307.821925 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #805c54"/>
    <path d="M 559.485354 329.953117 
L 562.177328 330.931913 
L 563.808266 326.280414 
L 561.115526 325.288725 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9e8365"/>
    <path d="M 632.127986 294.054839 
L 634.885153 296.604825 
L 636.536658 293.548117 
L 633.779635 290.954762 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9d827c"/>
    <path d="M 535.190312 375.94097 
L 537.864682 376.760903 
L 539.487785 371.800585 
L 536.812752 370.977638 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eae48e"/>
    <path d="M 607.947262 288.837176 
L 610.685019 290.75746 
L 612.335117 287.19484 
L 609.597074 285.240766 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a78e89"/>
    <path d="M 664.196514 323.027663 
L 666.968515 326.280064 
L 668.614255 323.848975 
L 665.843032 320.540148 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #967960"/>
    <path d="M 727.502527 410.01238 
L 730.274949 413.457835 
L 731.887436 412.565254 
L 729.117374 409.052199 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a9ee88"/>
    <path d="M 655.885295 313.569024 
L 658.654785 316.669639 
L 660.302682 314.072513 
L 657.533798 310.918837 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #846257"/>
    <path d="M 661.425231 319.823345 
L 664.196514 323.027663 
L 665.843032 320.540148 
L 663.072468 317.280464 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #90715d"/>
    <path d="M 829.30946 505.588716 
L 832.109595 507.128397 
L 833.605964 507.55032 
L 830.808897 505.997539 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1276dc"/>
    <path d="M 658.654785 316.669639 
L 661.425231 319.823345 
L 663.072468 317.280464 
L 660.302682 314.072513 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8a695a"/>
    <path d="M 816.625424 498.152269 
L 819.416771 500.01081 
L 820.927898 500.455179 
L 818.139796 498.575293 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0a86ec"/>
    <path d="M 622.21891 290.135659 
L 624.968876 292.427788 
L 626.620512 289.16968 
L 623.870505 286.838013 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a38984"/>
    <path d="M 774.62293 464.147117 
L 777.397453 466.92146 
L 778.960656 467.031869 
L 776.189401 464.208733 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c47d"/>
    <path d="M 551.914398 343.288407 
L 554.600331 344.194903 
L 556.227841 339.409677 
L 553.541135 338.493324 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b49f70"/>
    <path d="M 695.84416 366.245679 
L 698.618943 369.797766 
L 700.252496 368.087215 
L 697.479233 364.468227 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e0d788"/>
    <path d="M 571.406257 313.706525 
L 574.109092 314.847504 
L 575.745847 310.437644 
L 573.042281 309.278261 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #825f56"/>
    <path d="M 565.440213 321.675903 
L 568.137594 322.729836 
L 569.77138 318.191469 
L 567.073236 317.121747 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #90715d"/>
    <path d="M 615.076324 289.225201 
L 617.820551 291.33054 
L 619.471651 287.917707 
L 616.72725 285.775442 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a58c86"/>
    <path d="M 724.729769 406.549124 
L 727.502527 410.01238 
L 729.117374 409.052199 
L 726.346905 405.52078 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b5f08a"/>
    <path d="M 801.171044 487.302068 
L 803.954284 489.522243 
L 805.484455 489.919703 
L 802.704573 487.667757 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #009cf4"/>
    <path d="M 581.731734 303.059375 
L 584.444594 304.383197 
L 586.086153 300.204683 
L 583.372639 298.857702 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8f7069"/>
    <path d="M 777.397453 466.92146 
L 780.172846 469.63715 
L 781.732753 469.794775 
L 778.960656 467.031869 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c088"/>
    <path d="M 542.734301 361.919262 
L 545.41377 362.766929 
L 547.038192 357.859699 
L 544.35797 357.005472 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d2c581"/>
    <path d="M 533.567806 380.912594 
L 536.241505 381.729516 
L 537.864682 376.760903 
L 535.190312 375.94097 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f2ee92"/>
    <path d="M 634.885153 296.604825 
L 637.64441 299.223954 
L 639.295737 296.212318 
L 636.536658 293.548117 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #997c76"/>
    <path d="M 603.564127 290.697982 
L 606.298197 292.510492 
L 607.947262 288.837176 
L 605.212818 286.992105 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a38984"/>
    <path d="M 693.069155 362.708452 
L 695.84416 366.245679 
L 697.479233 364.468227 
L 694.705672 360.864378 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d8cd84"/>
    <path d="M 721.95666 403.070688 
L 724.729769 406.549124 
L 726.346905 405.52078 
L 723.576012 401.973688 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c1f38d"/>
    <path d="M 557.856152 334.661253 
L 560.547323 335.626997 
L 562.177328 330.931913 
L 559.485354 329.953117 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a48b68"/>
    <path d="M 586.086153 300.204683 
L 588.803541 301.618142 
L 590.446839 297.532799 
L 587.728828 296.093896 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #957771"/>
    <path d="M 550.288396 348.116865 
L 552.973529 349.01342 
L 554.600331 344.194903 
L 551.914398 343.288407 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bca975"/>
    <path d="M 624.968876 292.427788 
L 627.721403 294.792504 
L 629.373056 291.57586 
L 626.620512 289.16968 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9f847e"/>
    <path d="M 719.183189 399.579718 
L 721.95666 403.070688 
L 723.576012 401.973688 
L 720.804682 398.413634 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cdf58f"/>
    <path d="M 690.293982 359.188876 
L 693.069155 362.708452 
L 694.705672 360.864378 
L 691.93187 357.278525 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d2c581"/>
    <path d="M 599.186114 292.771864 
L 601.916279 294.479364 
L 603.564127 290.697982 
L 600.833508 288.959378 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a18781"/>
    <path d="M 780.172846 469.63715 
L 782.949219 472.292387 
L 784.505806 472.495611 
L 781.732753 469.794775 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00bb9b"/>
    <path d="M 575.745847 310.437644 
L 578.453357 311.655535 
L 580.091985 307.326335 
L 577.383742 306.087323 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #836059"/>
    <path d="M 590.446839 297.532799 
L 593.168638 299.040351 
L 594.813581 295.052525 
L 592.091203 293.517438 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #997c76"/>
    <path d="M 637.64441 299.223954 
L 640.405614 301.910286 
L 642.056723 298.945374 
L 639.295737 296.212318 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #93756e"/>
    <path d="M 594.813581 295.052525 
L 597.539647 296.658229 
L 599.186114 292.771864 
L 596.459525 291.136735 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9d827c"/>
    <path d="M 531.945092 385.888905 
L 534.618114 386.702821 
L 536.241505 381.729516 
L 533.567806 380.912594 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #faf996"/>
    <path d="M 541.110948 366.852169 
L 543.789646 367.693252 
L 545.41377 362.766929 
L 542.734301 361.919262 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dad085"/>
    <path d="M 563.808266 326.280414 
L 566.50484 327.318322 
L 568.137594 322.729836 
L 565.440213 321.675903 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #967960"/>
    <path d="M 610.685019 290.75746 
L 613.425947 292.751773 
L 615.076324 289.225201 
L 612.335117 287.19484 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a38984"/>
    <path d="M 716.409352 396.078877 
L 719.183189 399.579718 
L 720.804682 398.413634 
L 718.032911 394.843353 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d9f791"/>
    <path d="M 687.5187 355.68973 
L 690.293982 359.188876 
L 691.93187 357.278525 
L 689.157884 353.71352 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ccbe7d"/>
    <path d="M 569.77138 318.191469 
L 572.473432 319.313719 
L 574.109092 314.847504 
L 571.406257 313.706525 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #886759"/>
    <path d="M 617.820551 291.33054 
L 620.567649 293.509471 
L 622.21891 290.135659 
L 619.471651 287.917707 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a38984"/>
    <path d="M 803.954284 489.522243 
L 806.739516 491.667953 
L 808.266334 492.09536 
L 805.484455 489.919703 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #009afa"/>
    <path d="M 842.018502 511.673625 
L 844.830342 512.867947 
L 846.313154 513.231215 
L 843.504148 512.031529 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1868ce"/>
    <path d="M 819.416771 500.01081 
L 822.210863 501.787453 
L 823.718771 502.251309 
L 820.927898 500.455179 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0b83e9"/>
    <path d="M 640.405614 301.910286 
L 643.168621 304.661817 
L 644.819473 301.745225 
L 642.056723 298.945374 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8f7069"/>
    <path d="M 548.66303 352.975151 
L 551.347336 353.861692 
L 552.973529 349.01342 
L 550.288396 348.116865 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c4b379"/>
    <path d="M 782.949219 472.292387 
L 785.726688 474.885437 
L 787.279932 475.1326 
L 784.505806 472.495611 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b6a7"/>
    <path d="M 556.227841 339.409677 
L 558.918171 340.362226 
L 560.547323 335.626997 
L 557.856152 334.661253 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ac956c"/>
    <path d="M 713.635151 392.570847 
L 716.409352 396.078877 
L 718.032911 394.843353 
L 715.260699 391.265597 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e5fa94"/>
    <path d="M 684.743375 352.213778 
L 687.5187 355.68973 
L 689.157884 353.71352 
L 686.383783 350.172199 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c6b67a"/>
    <path d="M 627.721403 294.792504 
L 630.476343 297.22814 
L 632.127986 294.054839 
L 629.373056 291.57586 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9d827c"/>
    <path d="M 580.091985 307.326335 
L 582.804125 308.626482 
L 584.444594 304.383197 
L 581.731734 303.059375 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #896861"/>
    <path d="M 539.487785 371.800585 
L 542.165699 372.635068 
L 543.789646 367.693252 
L 541.110948 366.852169 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e2da89"/>
    <path d="M 832.109595 507.128397 
L 834.913138 508.581131 
L 836.406477 509.014322 
L 833.605964 507.55032 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1373d9"/>
    <path d="M 606.298197 292.510492 
L 609.035578 294.395843 
L 610.685019 290.75746 
L 607.947262 288.837176 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a18781"/>
    <path d="M 681.968079 348.763771 
L 684.743375 352.213778 
L 686.383783 350.172199 
L 683.609636 346.657382 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c0ae77"/>
    <path d="M 643.168621 304.661817 
L 645.933291 307.476473 
L 647.583842 304.609742 
L 644.819473 301.745225 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8b6b64"/>
    <path d="M 710.860591 389.058326 
L 713.635151 392.570847 
L 715.260699 391.265597 
L 712.488052 387.683132 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1fc96"/>
    <path d="M 851.943801 515.352768 
L 854.765776 516.274141 
L 856.239005 516.548157 
L 853.419644 515.626826 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1b63c9"/>
    <path d="M 562.177328 330.931913 
L 564.873051 331.95358 
L 566.50484 327.318322 
L 563.808266 326.280414 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9e8365"/>
    <path d="M 679.192885 345.342438 
L 681.968079 348.763771 
L 683.609636 346.657382 
L 680.835522 343.171868 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #baa774"/>
    <path d="M 574.109092 314.847504 
L 576.815813 316.043871 
L 578.453357 311.655535 
L 575.745847 310.437644 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #825f56"/>
    <path d="M 785.726688 474.885437 
L 788.505371 477.414622 
L 790.055253 477.704025 
L 787.279932 475.1326 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b2b2"/>
    <path d="M 547.038192 357.859699 
L 549.721647 358.736167 
L 551.347336 353.861692 
L 548.66303 352.975151 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cabb7c"/>
    <path d="M 584.444594 304.383197 
L 587.161288 305.770604 
L 588.803541 301.618142 
L 586.086153 300.204683 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8d6d66"/>
    <path d="M 645.933291 307.476473 
L 648.69949 310.352116 
L 650.349693 307.536729 
L 647.583842 304.609742 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #87655e"/>
    <path d="M 620.567649 293.509471 
L 623.317475 295.76053 
L 624.968876 292.427788 
L 622.21891 290.135659 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9f847e"/>
    <path d="M 708.085687 385.544021 
L 710.860591 389.058326 
L 712.488052 387.683132 
L 709.714982 384.098738 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 568.137594 322.729836 
L 570.838812 323.833053 
L 572.473432 319.313719 
L 569.77138 318.191469 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #90715d"/>
    <path d="M 613.425947 292.751773 
L 616.169902 294.81885 
L 617.820551 291.33054 
L 615.076324 289.225201 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a18781"/>
    <path d="M 537.864682 376.760903 
L 540.5418 377.588779 
L 542.165699 372.635068 
L 539.487785 371.800585 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eae48e"/>
    <path d="M 601.916279 294.479364 
L 604.649886 296.258287 
L 606.298197 292.510492 
L 603.564127 290.697982 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9f847e"/>
    <path d="M 630.476343 297.22814 
L 633.23355 299.732956 
L 634.885153 296.604825 
L 632.127986 294.054839 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #997c76"/>
    <path d="M 554.600331 344.194903 
L 557.289788 345.13413 
L 558.918171 340.362226 
L 556.227841 339.409677 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b49f70"/>
    <path d="M 676.417878 341.952486 
L 679.192885 345.342438 
L 680.835522 343.171868 
L 678.061523 339.718434 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b49f70"/>
    <path d="M 806.739516 491.667953 
L 809.526883 493.737957 
L 811.050356 494.193459 
L 808.266334 492.09536 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0296fc"/>
    <path d="M 648.69949 310.352116 
L 651.467082 313.286549 
L 653.116888 310.523929 
L 650.349693 307.536729 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #815e56"/>
    <path d="M 588.803541 301.618142 
L 591.524686 303.097451 
L 593.168638 299.040351 
L 590.446839 297.532799 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #93756e"/>
    <path d="M 673.643143 338.596596 
L 676.417878 341.952486 
L 678.061523 339.718434 
L 675.287727 336.299832 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ae976d"/>
    <path d="M 597.539647 296.658229 
L 600.269274 298.33371 
L 601.916279 294.479364 
L 599.186114 292.771864 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9b7f79"/>
    <path d="M 705.310457 382.030651 
L 708.085687 385.544021 
L 709.714982 384.098738 
L 706.941509 380.515206 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f8f695"/>
    <path d="M 593.168638 299.040351 
L 595.894103 300.615819 
L 597.539647 296.658229 
L 594.813581 295.052525 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #977a74"/>
    <path d="M 651.467082 313.286549 
L 654.235937 316.277514 
L 655.885295 313.569024 
L 653.116888 310.523929 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #825f56"/>
    <path d="M 670.868771 335.277421 
L 673.643143 338.596596 
L 675.287727 336.299832 
L 672.514227 332.918783 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a8906a"/>
    <path d="M 545.41377 362.766929 
L 548.096353 363.633275 
L 549.721647 358.736167 
L 547.038192 357.859699 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d2c581"/>
    <path d="M 654.235937 316.277514 
L 657.005929 319.322697 
L 658.654785 316.669639 
L 655.885295 313.569024 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #886759"/>
    <path d="M 668.094861 331.99758 
L 670.868771 335.277421 
L 672.514227 332.918783 
L 669.741122 329.577975 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a28867"/>
    <path d="M 788.505371 477.414622 
L 791.285389 479.878332 
L 792.831895 480.208236 
L 790.055253 477.704025 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00aebf"/>
    <path d="M 536.241505 381.729516 
L 538.917816 382.550785 
L 540.5418 377.588779 
L 537.864682 376.760903 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f2ee92"/>
    <path d="M 578.453357 311.655535 
L 581.164714 312.93152 
L 582.804125 308.626482 
L 580.091985 307.326335 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #836059"/>
    <path d="M 822.210863 501.787453 
L 825.007856 503.481301 
L 826.512572 503.962767 
L 823.718771 502.251309 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0c80e6"/>
    <path d="M 560.547323 335.626997 
L 563.242154 336.632226 
L 564.873051 331.95358 
L 562.177328 330.931913 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a68d69"/>
    <path d="M 657.005929 319.322697 
L 659.776934 322.419735 
L 661.425231 319.823345 
L 658.654785 316.669639 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8c6c5b"/>
    <path d="M 665.321513 328.759661 
L 668.094861 331.99758 
L 669.741122 329.577975 
L 666.968515 326.280064 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9e8365"/>
    <path d="M 702.534925 378.52094 
L 705.310457 382.030651 
L 706.941509 380.515206 
L 704.167657 376.935332 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f2ee92"/>
    <path d="M 633.23355 299.732956 
L 635.992882 302.305139 
L 637.64441 299.223954 
L 634.885153 296.604825 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #957771"/>
    <path d="M 659.776934 322.419735 
L 662.548834 325.56621 
L 664.196514 323.027663 
L 661.425231 319.823345 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #92735e"/>
    <path d="M 662.548834 325.56621 
L 665.321513 328.759661 
L 666.968515 326.280064 
L 664.196514 323.027663 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #987b61"/>
    <path d="M 552.973529 349.01342 
L 555.662082 349.939213 
L 557.289788 345.13413 
L 554.600331 344.194903 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bca975"/>
    <path d="M 609.035578 294.395843 
L 611.776132 296.352891 
L 613.425947 292.751773 
L 610.685019 290.75746 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9f847e"/>
    <path d="M 623.317475 295.76053 
L 626.069883 298.082174 
L 627.721403 294.792504 
L 624.968876 292.427788 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9b7f79"/>
    <path d="M 566.50484 327.318322 
L 569.205174 328.402225 
L 570.838812 323.833053 
L 568.137594 322.729836 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #967960"/>
    <path d="M 572.473432 319.313719 
L 575.179305 320.488183 
L 576.815813 316.043871 
L 574.109092 314.847504 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8a695a"/>
    <path d="M 699.759124 375.017617 
L 702.534925 378.52094 
L 704.167657 376.935332 
L 701.393456 373.361918 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ece78f"/>
    <path d="M 616.169902 294.81885 
L 618.916743 296.957349 
L 620.567649 293.509471 
L 617.820551 291.33054 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9d827c"/>
    <path d="M 543.789646 367.693252 
L 546.471338 368.549438 
L 548.096353 363.633275 
L 545.41377 362.766929 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dad085"/>
    <path d="M 534.618114 386.702821 
L 537.29361 387.517491 
L 538.917816 382.550785 
L 536.241505 381.729516 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #faf996"/>
    <path d="M 582.804125 308.626482 
L 585.520057 309.987259 
L 587.161288 305.770604 
L 584.444594 304.383197 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #87655e"/>
    <path d="M 635.992882 302.305139 
L 638.754198 304.942807 
L 640.405614 301.910286 
L 637.64441 299.223954 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #91726c"/>
    <path d="M 844.830342 512.867947 
L 847.646288 513.971533 
L 849.126316 514.338391 
L 846.313154 513.231215 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1868ce"/>
    <path d="M 809.526883 493.737957 
L 812.316528 495.731084 
L 813.836669 496.212802 
L 811.050356 494.193459 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0393f9"/>
    <path d="M 834.913138 508.581131 
L 837.720251 509.946316 
L 839.210601 510.388934 
L 836.406477 509.014322 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1373d9"/>
    <path d="M 696.983089 371.523412 
L 699.759124 375.017617 
L 701.393456 373.361918 
L 698.618943 369.797766 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e6df8b"/>
    <path d="M 791.285389 479.878332 
L 794.066868 482.275016 
L 795.609986 482.643648 
L 792.831895 480.208236 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00acc4"/>
    <path d="M 604.649886 296.258287 
L 607.386801 298.107603 
L 609.035578 294.395843 
L 606.298197 292.510492 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9b7f79"/>
    <path d="M 745.304019 434.081492 
L 748.077828 437.266922 
L 749.675076 436.863138 
L 746.90407 433.613329 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #59de78"/>
    <path d="M 748.077828 437.266922 
L 750.851694 440.415768 
L 752.446079 440.075258 
L 749.675076 436.863138 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #51dc76"/>
    <path d="M 558.918171 340.362226 
L 561.612071 341.350838 
L 563.242154 336.632226 
L 560.547323 335.626997 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ac956c"/>
    <path d="M 551.347336 353.861692 
L 554.034955 354.773955 
L 555.662082 349.939213 
L 552.973529 349.01342 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c4b379"/>
    <path d="M 742.530209 430.861773 
L 745.304019 434.081492 
L 746.90407 433.613329 
L 744.133 430.32819 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #65e07a"/>
    <path d="M 750.851694 440.415768 
L 753.625681 443.52577 
L 755.217145 443.247371 
L 752.446079 440.075258 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #45da74"/>
    <path d="M 739.756345 427.610106 
L 742.530209 430.861773 
L 744.133 430.32819 
L 741.361811 427.01012 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #71e37d"/>
    <path d="M 753.625681 443.52577 
L 756.399857 446.594716 
L 757.988345 446.377205 
L 755.217145 443.247371 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #39d771"/>
    <path d="M 626.069883 298.082174 
L 628.82473 300.472788 
L 630.476343 297.22814 
L 627.721403 294.792504 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #977a74"/>
    <path d="M 587.161288 305.770604 
L 589.881705 307.220997 
L 591.524686 303.097451 
L 588.803541 301.618142 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8d6d66"/>
    <path d="M 694.206861 368.041053 
L 696.983089 371.523412 
L 698.618943 369.797766 
L 695.84416 366.245679 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e0d788"/>
    <path d="M 736.98238 424.328862 
L 739.756345 427.610106 
L 741.361811 427.01012 
L 738.590453 423.661559 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #7de57f"/>
    <path d="M 756.399857 446.594716 
L 759.174296 449.620436 
L 760.759754 449.462534 
L 757.988345 446.377205 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #31d670"/>
    <path d="M 638.754198 304.942807 
L 641.517357 307.64401 
L 643.168621 304.661817 
L 640.405614 301.910286 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8b6b64"/>
    <path d="M 600.269274 298.33371 
L 603.002332 300.078055 
L 604.649886 296.258287 
L 601.916279 294.479364 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #997c76"/>
    <path d="M 542.165699 372.635068 
L 544.846481 373.481072 
L 546.471338 368.549438 
L 543.789646 367.693252 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e2da89"/>
    <path d="M 734.208269 421.020453 
L 736.98238 424.328862 
L 738.590453 423.661559 
L 735.818882 420.28498 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #89e781"/>
    <path d="M 576.815813 316.043871 
L 579.526325 317.295234 
L 581.164714 312.93152 
L 578.453357 311.655535 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #846257"/>
    <path d="M 591.524686 303.097451 
L 594.24947 304.64191 
L 595.894103 300.615819 
L 593.168638 299.040351 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #91726c"/>
    <path d="M 759.174296 449.620436 
L 761.949075 452.600807 
L 763.531453 452.501178 
L 760.759754 449.462534 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #25d36d"/>
    <path d="M 564.873051 331.95358 
L 567.572455 333.017912 
L 569.205174 328.402225 
L 566.50484 327.318322 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9e8365"/>
    <path d="M 595.894103 300.615819 
L 598.623109 302.258401 
L 600.269274 298.33371 
L 597.539647 296.658229 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #957771"/>
    <path d="M 731.433978 417.68732 
L 734.208269 421.020453 
L 735.818882 420.28498 
L 733.047059 416.882892 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #95ea84"/>
    <path d="M 691.430489 364.573263 
L 694.206861 368.041053 
L 695.84416 366.245679 
L 693.069155 362.708452 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dad085"/>
    <path d="M 611.776132 296.352891 
L 614.519721 298.380414 
L 616.169902 294.81885 
L 613.425947 292.751773 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9b7f79"/>
    <path d="M 570.838812 323.833053 
L 573.543784 324.985262 
L 575.179305 320.488183 
L 572.473432 319.313719 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #90715d"/>
    <path d="M 618.916743 296.957349 
L 621.666328 299.165852 
L 623.317475 295.76053 
L 620.567649 293.509471 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9b7f79"/>
    <path d="M 761.949075 452.600807 
L 764.724276 455.533754 
L 766.303528 455.491009 
L 763.531453 452.501178 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1dd26c"/>
    <path d="M 728.659473 414.331936 
L 731.433978 417.68732 
L 733.047059 416.882892 
L 730.274949 413.457835 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a1ec86"/>
    <path d="M 641.517357 307.64401 
L 644.282225 310.406733 
L 645.933291 307.476473 
L 643.168621 304.661817 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #87655e"/>
    <path d="M 794.066868 482.275016 
L 796.849935 484.603191 
L 798.389657 485.008743 
L 795.609986 482.643648 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a8d0"/>
    <path d="M 549.721647 358.736167 
L 552.408305 359.634819 
L 554.034955 354.773955 
L 551.347336 353.861692 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ccbe7d"/>
    <path d="M 825.007856 503.481301 
L 827.807905 505.091532 
L 829.30946 505.588716 
L 826.512572 503.962767 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0e7ee4"/>
    <path d="M 688.654027 361.122758 
L 691.430489 364.573263 
L 693.069155 362.708452 
L 690.293982 359.188876 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d4c882"/>
    <path d="M 557.289788 345.13413 
L 559.98272 346.105968 
L 561.612071 341.350838 
L 558.918171 340.362226 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b49f70"/>
    <path d="M 725.884729 410.956804 
L 728.659473 414.331936 
L 730.274949 413.457835 
L 727.502527 410.01238 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a9ee88"/>
    <path d="M 628.82473 300.472788 
L 631.581875 302.930684 
L 633.23355 299.732956 
L 630.476343 297.22814 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #957771"/>
    <path d="M 764.724276 455.533754 
L 767.499988 458.417252 
L 769.076069 458.42995 
L 766.303528 455.491009 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #15d06a"/>
    <path d="M 540.5418 377.588779 
L 543.221657 378.424586 
L 544.846481 373.481072 
L 542.165699 372.635068 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eae48e"/>
    <path d="M 581.164714 312.93152 
L 583.879817 314.265121 
L 585.520057 309.987259 
L 582.804125 308.626482 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #815e56"/>
    <path d="M 685.877533 357.692244 
L 688.654027 361.122758 
L 690.293982 359.188876 
L 687.5187 355.68973 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cec07f"/>
    <path d="M 723.109726 407.564451 
L 725.884729 410.956804 
L 727.502527 410.01238 
L 724.729769 406.549124 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b5f08a"/>
    <path d="M 644.282225 310.406733 
L 647.048665 313.228898 
L 648.69949 310.352116 
L 645.933291 307.476473 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #836059"/>
    <path d="M 812.316528 495.731084 
L 815.108599 497.646235 
L 816.625424 498.152269 
L 813.836669 496.212802 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0490f6"/>
    <path d="M 607.386801 298.107603 
L 610.12689 300.026211 
L 611.776132 296.352891 
L 609.035578 294.395843 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #997c76"/>
    <path d="M 767.499988 458.417252 
L 770.276301 461.249329 
L 771.84917 461.315976 
L 769.076069 458.42995 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #09ce68"/>
    <path d="M 683.101071 354.284412 
L 685.877533 357.692244 
L 687.5187 355.68973 
L 684.743375 352.213778 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c8b97b"/>
    <path d="M 720.334447 404.157428 
L 723.109726 407.564451 
L 724.729769 406.549124 
L 721.95666 403.070688 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c1f38d"/>
    <path d="M 563.242154 336.632226 
L 565.940583 337.67675 
L 567.572455 333.017912 
L 564.873051 331.95358 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a68d69"/>
    <path d="M 548.096353 363.633275 
L 550.782025 364.518252 
L 552.408305 359.634819 
L 549.721647 358.736167 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d2c581"/>
    <path d="M 647.048665 313.228898 
L 649.816549 316.108368 
L 651.467082 313.286549 
L 648.69949 310.352116 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #805c54"/>
    <path d="M 575.179305 320.488183 
L 577.888912 321.714494 
L 579.526325 317.295234 
L 576.815813 316.043871 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8a695a"/>
    <path d="M 621.666328 299.165852 
L 624.418517 301.442869 
L 626.069883 298.082174 
L 623.317475 295.76053 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #977a74"/>
    <path d="M 538.917816 382.550785 
L 541.596736 383.376395 
L 543.221657 378.424586 
L 540.5418 377.588779 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f2ee92"/>
    <path d="M 585.520057 309.987259 
L 588.239675 311.408097 
L 589.881705 307.220997 
L 587.161288 305.770604 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #87655e"/>
    <path d="M 680.324712 350.901939 
L 683.101071 354.284412 
L 684.743375 352.213778 
L 681.968079 348.763771 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c2b178"/>
    <path d="M 555.662082 349.939213 
L 558.35401 350.894137 
L 559.98272 346.105968 
L 557.289788 345.13413 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bca975"/>
    <path d="M 569.205174 328.402225 
L 571.909193 329.531853 
L 573.543784 324.985262 
L 570.838812 323.833053 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #987b61"/>
    <path d="M 717.558885 400.73831 
L 720.334447 404.157428 
L 721.95666 403.070688 
L 719.183189 399.579718 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cdf58f"/>
    <path d="M 631.581875 302.930684 
L 634.341179 305.454104 
L 635.992882 302.305139 
L 633.23355 299.732956 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #91726c"/>
    <path d="M 614.519721 298.380414 
L 617.266208 300.477116 
L 618.916743 296.957349 
L 616.169902 294.81885 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #997c76"/>
    <path d="M 770.276301 461.249329 
L 773.053312 464.028064 
L 774.62293 464.147117 
L 771.84917 461.315976 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #01cc66"/>
    <path d="M 796.849935 484.603191 
L 799.634722 486.861439 
L 801.171044 487.302068 
L 798.389657 485.008743 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a4dc"/>
    <path d="M 603.002332 300.078055 
L 605.738692 301.890276 
L 607.386801 298.107603 
L 604.649886 296.258287 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #977a74"/>
    <path d="M 649.816549 316.108368 
L 652.585749 319.04295 
L 654.235937 316.277514 
L 651.467082 313.286549 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #866458"/>
    <path d="M 677.548531 347.547481 
L 680.324712 350.901939 
L 681.968079 348.763771 
L 679.192885 345.342438 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bca975"/>
    <path d="M 837.720251 509.946316 
L 840.531093 511.223431 
L 842.018502 511.673625 
L 839.210601 510.388934 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1470d6"/>
    <path d="M 714.783035 397.309689 
L 717.558885 400.73831 
L 719.183189 399.579718 
L 716.409352 396.078877 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d9f791"/>
    <path d="M 589.881705 307.220997 
L 592.605733 308.73371 
L 594.24947 304.64191 
L 591.524686 303.097451 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8b6b64"/>
    <path d="M 652.585749 319.04295 
L 655.35614 322.030395 
L 657.005929 319.322697 
L 654.235937 316.277514 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8a695a"/>
    <path d="M 674.772608 344.223672 
L 677.548531 347.547481 
L 679.192885 345.342438 
L 676.417878 341.952486 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b6a272"/>
    <path d="M 598.623109 302.258401 
L 601.355533 303.967221 
L 603.002332 300.078055 
L 600.269274 298.33371 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #93756e"/>
    <path d="M 847.646288 513.971533 
L 850.466502 514.984097 
L 851.943801 515.352768 
L 849.126316 514.338391 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1868ce"/>
    <path d="M 594.24947 304.64191 
L 596.977775 306.250753 
L 598.623109 302.258401 
L 595.894103 300.615819 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8f7069"/>
    <path d="M 546.471338 368.549438 
L 549.156001 369.420692 
L 550.782025 364.518252 
L 548.096353 363.633275 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dad085"/>
    <path d="M 671.997027 340.933121 
L 674.772608 344.223672 
L 676.417878 341.952486 
L 673.643143 338.596596 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b09a6e"/>
    <path d="M 655.35614 322.030395 
L 658.127601 325.068402 
L 659.776934 322.419735 
L 657.005929 319.322697 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #90715d"/>
    <path d="M 773.053312 464.028064 
L 775.83112 466.751591 
L 777.397453 466.92146 
L 774.62293 464.147117 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c970"/>
    <path d="M 712.0069 393.874173 
L 714.783035 397.309689 
L 716.409352 396.078877 
L 713.635151 392.570847 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e5fa94"/>
    <path d="M 537.29361 387.517491 
L 539.971582 388.332915 
L 541.596736 383.376395 
L 538.917816 382.550785 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #faf996"/>
    <path d="M 669.221881 337.678409 
L 671.997027 340.933121 
L 673.643143 338.596596 
L 670.868771 335.277421 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #aa926b"/>
    <path d="M 658.127601 325.068402 
L 660.900017 328.154623 
L 662.548834 325.56621 
L 659.776934 322.419735 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #94765f"/>
    <path d="M 561.612071 341.350838 
L 564.309483 342.375343 
L 565.940583 337.67675 
L 563.242154 336.632226 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ae976d"/>
    <path d="M 634.341179 305.454104 
L 637.102502 308.041222 
L 638.754198 304.942807 
L 635.992882 302.305139 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8d6d66"/>
    <path d="M 666.447263 334.462084 
L 669.221881 337.678409 
L 670.868771 335.277421 
L 668.094861 331.99758 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a68d69"/>
    <path d="M 660.900017 328.154623 
L 663.673274 331.286663 
L 665.321513 328.759661 
L 662.548834 325.56621 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9a7e62"/>
    <path d="M 663.673274 331.286663 
L 666.447263 334.462084 
L 668.094861 331.99758 
L 665.321513 328.759661 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a08566"/>
    <path d="M 579.526325 317.295234 
L 582.240534 318.601144 
L 583.879817 314.265121 
L 581.164714 312.93152 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #846257"/>
    <path d="M 554.034955 354.773955 
L 556.725847 355.711846 
L 558.35401 350.894137 
L 555.662082 349.939213 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c4b379"/>
    <path d="M 709.230487 390.434386 
L 712.0069 393.874173 
L 713.635151 392.570847 
L 710.860591 389.058326 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1fc96"/>
    <path d="M 624.418517 301.442869 
L 627.173171 303.786834 
L 628.82473 300.472788 
L 626.069883 298.082174 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #93756e"/>
    <path d="M 610.12689 300.026211 
L 612.870019 302.012934 
L 614.519721 298.380414 
L 611.776132 296.352891 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #977a74"/>
    <path d="M 827.807905 505.091532 
L 830.611166 506.617402 
L 832.109595 507.128397 
L 829.30946 505.588716 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0f7be1"/>
    <path d="M 815.108599 497.646235 
L 817.903242 499.482384 
L 819.416771 500.01081 
L 816.625424 498.152269 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #078bf1"/>
    <path d="M 567.572455 333.017912 
L 570.27547 334.124659 
L 571.909193 329.531853 
L 569.205174 328.402225 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9e8365"/>
    <path d="M 775.83112 466.751591 
L 778.609829 469.418102 
L 780.172846 469.63715 
L 777.397453 466.92146 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c47d"/>
    <path d="M 573.543784 324.985262 
L 576.252429 326.186121 
L 577.888912 321.714494 
L 575.179305 320.488183 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #92735e"/>
    <path d="M 799.634722 486.861439 
L 802.421362 489.048409 
L 803.954284 489.522243 
L 801.171044 487.302068 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a2e2"/>
    <path d="M 706.453811 386.992963 
L 709.230487 390.434386 
L 710.860591 389.058326 
L 708.085687 385.544021 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 617.266208 300.477116 
L 620.015454 302.64163 
L 621.666328 299.165852 
L 618.916743 296.957349 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #957771"/>
    <path d="M 544.846481 373.481072 
L 547.530116 374.338568 
L 549.156001 369.420692 
L 546.471338 368.549438 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e2da89"/>
    <path d="M 637.102502 308.041222 
L 639.865709 310.690146 
L 641.517357 307.64401 
L 638.754198 304.942807 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #87655e"/>
    <path d="M 583.879817 314.265121 
L 586.598565 315.655799 
L 588.239675 311.408097 
L 585.520057 309.987259 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #805c54"/>
    <path d="M 703.67689 383.552545 
L 706.453811 386.992963 
L 708.085687 385.544021 
L 705.310457 382.030651 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f8f695"/>
    <path d="M 605.738692 301.890276 
L 608.478224 303.769316 
L 610.12689 300.026211 
L 607.386801 298.107603 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #93756e"/>
    <path d="M 559.98272 346.105968 
L 562.679074 347.110264 
L 564.309483 342.375343 
L 561.612071 341.350838 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b49f70"/>
    <path d="M 552.408305 359.634819 
L 555.098132 360.555577 
L 556.725847 355.711846 
L 554.034955 354.773955 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ccbe7d"/>
    <path d="M 778.609829 469.418102 
L 781.389547 472.025843 
L 782.949219 472.292387 
L 780.172846 469.63715 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00be8f"/>
    <path d="M 627.173171 303.786834 
L 629.93015 306.196114 
L 631.581875 302.930684 
L 628.82473 300.472788 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8f7069"/>
    <path d="M 700.899749 380.115784 
L 703.67689 383.552545 
L 705.310457 382.030651 
L 702.534925 378.52094 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f2ee92"/>
    <path d="M 639.865709 310.690146 
L 642.630667 313.398922 
L 644.282225 310.406733 
L 641.517357 307.64401 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #836059"/>
    <path d="M 588.239675 311.408097 
L 590.96287 312.888364 
L 592.605733 308.73371 
L 589.881705 307.220997 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #85635c"/>
    <path d="M 543.221657 378.424586 
L 545.904246 379.268307 
L 547.530116 374.338568 
L 544.846481 373.481072 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eae48e"/>
    <path d="M 601.355533 303.967221 
L 604.09125 305.741332 
L 605.738692 301.890276 
L 603.002332 300.078055 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #91726c"/>
    <path d="M 577.888912 321.714494 
L 580.602164 322.992231 
L 582.240534 318.601144 
L 579.526325 317.295234 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8c6c5b"/>
    <path d="M 565.940583 337.67675 
L 568.642546 338.760342 
L 570.27547 334.124659 
L 567.572455 333.017912 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a68d69"/>
    <path d="M 698.122419 376.685333 
L 700.899749 380.115784 
L 702.534925 378.52094 
L 699.759124 375.017617 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ece78f"/>
    <path d="M 592.605733 308.73371 
L 595.333257 310.308012 
L 596.977775 306.250753 
L 594.24947 304.64191 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #896861"/>
    <path d="M 596.977775 306.250753 
L 599.709481 307.923141 
L 601.355533 303.967221 
L 598.623109 302.258401 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8d6d66"/>
    <path d="M 612.870019 302.012934 
L 615.616054 304.066525 
L 617.266208 300.477116 
L 614.519721 298.380414 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #93756e"/>
    <path d="M 571.909193 329.531853 
L 574.61682 330.706888 
L 576.252429 326.186121 
L 573.543784 324.985262 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #987b61"/>
    <path d="M 620.015454 302.64163 
L 622.767324 304.872513 
L 624.418517 301.442869 
L 621.666328 299.165852 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #93756e"/>
    <path d="M 642.630667 313.398922 
L 645.397246 316.165534 
L 647.048665 313.228898 
L 644.282225 310.406733 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #805c54"/>
    <path d="M 802.421362 489.048409 
L 805.209992 491.162819 
L 806.739516 491.667953 
L 803.954284 489.522243 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #009eef"/>
    <path d="M 550.782025 364.518252 
L 553.470759 365.421796 
L 555.098132 360.555577 
L 552.408305 359.634819 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d4c882"/>
    <path d="M 781.389547 472.025843 
L 784.170385 474.57312 
L 785.726688 474.885437 
L 782.949219 472.292387 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00bb9b"/>
    <path d="M 695.344936 373.263844 
L 698.122419 376.685333 
L 699.759124 375.017617 
L 696.983089 371.523412 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e6df8b"/>
    <path d="M 558.35401 350.894137 
L 561.049269 351.878057 
L 562.679074 347.110264 
L 559.98272 346.105968 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bca975"/>
    <path d="M 840.531093 511.223431 
L 843.345828 512.412037 
L 844.830342 512.867947 
L 842.018502 511.673625 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1470d6"/>
    <path d="M 817.903242 499.482384 
L 820.700608 501.238578 
L 822.210863 501.787453 
L 819.416771 500.01081 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0888ee"/>
    <path d="M 629.93015 306.196114 
L 632.689321 308.669008 
L 634.341179 305.454104 
L 631.581875 302.930684 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8d6d66"/>
    <path d="M 541.596736 383.376395 
L 544.278264 384.206338 
L 545.904246 379.268307 
L 543.221657 378.424586 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f2ee92"/>
    <path d="M 692.567342 369.85397 
L 695.344936 373.263844 
L 696.983089 371.523412 
L 694.206861 368.041053 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e0d788"/>
    <path d="M 645.397246 316.165534 
L 648.165317 318.98791 
L 649.816549 316.108368 
L 647.048665 313.228898 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #846257"/>
    <path d="M 582.240534 318.601144 
L 584.958344 319.961093 
L 586.598565 315.655799 
L 583.879817 314.265121 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #866458"/>
    <path d="M 830.611166 506.617402 
L 833.417797 508.058245 
L 834.913138 508.581131 
L 832.109595 507.128397 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0f7be1"/>
    <path d="M 689.789684 366.458359 
L 692.567342 369.85397 
L 694.206861 368.041053 
L 691.430489 364.573263 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dad085"/>
    <path d="M 608.478224 303.769316 
L 611.2208 305.714042 
L 612.870019 302.012934 
L 610.12689 300.026211 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #91726c"/>
    <path d="M 850.466502 514.984097 
L 853.291148 515.905437 
L 854.765776 516.274141 
L 851.943801 515.352768 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1868ce"/>
    <path d="M 564.309483 342.375343 
L 567.010349 343.435533 
L 568.642546 338.760342 
L 565.940583 337.67675 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ae976d"/>
    <path d="M 549.156001 369.420692 
L 551.843617 370.306959 
L 553.470759 365.421796 
L 550.782025 364.518252 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dcd286"/>
    <path d="M 648.165317 318.98791 
L 650.934756 321.863919 
L 652.585749 319.04295 
L 649.816549 316.108368 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8a695a"/>
    <path d="M 784.170385 474.57312 
L 786.952458 477.0583 
L 788.505371 477.414622 
L 785.726688 474.885437 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b6a7"/>
    <path d="M 687.012015 363.079649 
L 689.789684 366.458359 
L 691.430489 364.573263 
L 688.654027 361.122758 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d4c882"/>
    <path d="M 539.971582 388.332915 
L 542.652035 389.149094 
L 544.278264 384.206338 
L 541.596736 383.376395 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #faf996"/>
    <path d="M 576.252429 326.186121 
L 578.964663 327.435235 
L 580.602164 322.992231 
L 577.888912 321.714494 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #92735e"/>
    <path d="M 622.767324 304.872513 
L 625.521681 307.168256 
L 627.173171 303.786834 
L 624.418517 301.442869 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8f7069"/>
    <path d="M 556.725847 355.711846 
L 559.419975 356.675247 
L 561.049269 351.878057 
L 558.35401 350.894137 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c4b379"/>
    <path d="M 632.689321 308.669008 
L 635.450547 311.203748 
L 637.102502 308.041222 
L 634.341179 305.454104 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #896861"/>
    <path d="M 570.27547 334.124659 
L 572.982025 335.273527 
L 574.61682 330.706888 
L 571.909193 329.531853 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a08566"/>
    <path d="M 586.598565 315.655799 
L 589.320856 317.102956 
L 590.96287 312.888364 
L 588.239675 311.408097 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #805c54"/>
    <path d="M 684.234394 359.72047 
L 687.012015 363.079649 
L 688.654027 361.122758 
L 685.877533 357.692244 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d0c380"/>
    <path d="M 615.616054 304.066525 
L 618.364864 306.185664 
L 620.015454 302.64163 
L 617.266208 300.477116 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #91726c"/>
    <path d="M 650.934756 321.863919 
L 653.705441 324.79138 
L 655.35614 322.030395 
L 652.585749 319.04295 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8e6e5c"/>
    <path d="M 604.09125 305.741332 
L 606.830136 307.579719 
L 608.478224 303.769316 
L 605.738692 301.890276 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8f7069"/>
    <path d="M 681.456883 356.383437 
L 684.234394 359.72047 
L 685.877533 357.692244 
L 683.101071 354.284412 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cabb7c"/>
    <path d="M 805.209992 491.162819 
L 808.000749 493.203454 
L 809.526883 493.737957 
L 806.739516 491.667953 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #009cf4"/>
    <path d="M 653.705441 324.79138 
L 656.477256 327.768061 
L 658.127601 325.068402 
L 655.35614 322.030395 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #92735e"/>
    <path d="M 590.96287 312.888364 
L 593.689536 314.427364 
L 595.333257 310.308012 
L 592.605733 308.73371 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #836059"/>
    <path d="M 678.679552 353.071151 
L 681.456883 356.383437 
L 683.101071 354.284412 
L 680.324712 350.901939 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c4b379"/>
    <path d="M 599.709481 307.923141 
L 602.44447 309.65817 
L 604.09125 305.741332 
L 601.355533 303.967221 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8b6b64"/>
    <path d="M 547.530116 374.338568 
L 550.21659 375.207517 
L 551.843617 370.306959 
L 549.156001 369.420692 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e4dc8a"/>
    <path d="M 656.477256 327.768061 
L 659.250085 330.791682 
L 660.900017 328.154623 
L 658.127601 325.068402 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #987b61"/>
    <path d="M 595.333257 310.308012 
L 598.064163 311.943104 
L 599.709481 307.923141 
L 596.977775 306.250753 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #87655e"/>
    <path d="M 675.902474 349.786191 
L 678.679552 353.071151 
L 680.324712 350.901939 
L 677.548531 347.547481 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #beac76"/>
    <path d="M 786.952458 477.0583 
L 789.735883 479.479811 
L 791.285389 479.878332 
L 788.505371 477.414622 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b4ac"/>
    <path d="M 562.679074 347.110264 
L 565.378799 348.146831 
L 567.010349 343.435533 
L 564.309483 342.375343 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b6a272"/>
    <path d="M 659.250085 330.791682 
L 662.023818 333.859919 
L 663.673274 331.286663 
L 660.900017 328.154623 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9c8064"/>
    <path d="M 738.147731 428.181732 
L 740.924245 431.364468 
L 742.530209 430.861773 
L 739.756345 427.610106 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #75e37d"/>
    <path d="M 740.924245 431.364468 
L 743.700773 434.516267 
L 745.304019 434.081492 
L 742.530209 430.861773 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #69e17b"/>
    <path d="M 635.450547 311.203748 
L 638.213697 313.798502 
L 639.865709 310.690146 
L 637.102502 308.041222 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #85635c"/>
    <path d="M 673.125729 346.531117 
L 675.902474 349.786191 
L 677.548531 347.547481 
L 674.772608 344.223672 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b8a473"/>
    <path d="M 735.371185 424.970368 
L 738.147731 428.181732 
L 739.756345 427.610106 
L 736.98238 424.328862 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #81e680"/>
    <path d="M 743.700773 434.516267 
L 746.477367 437.634857 
L 748.077828 437.266922 
L 745.304019 434.081492 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #61df79"/>
    <path d="M 662.023818 333.859919 
L 664.798348 336.970404 
L 666.447263 334.462084 
L 663.673274 331.286663 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a28867"/>
    <path d="M 732.594568 421.732717 
L 735.371185 424.970368 
L 736.98238 424.328862 
L 734.208269 421.020453 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8de882"/>
    <path d="M 670.349399 343.308462 
L 673.125729 346.531117 
L 674.772608 344.223672 
L 671.997027 340.933121 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b29c6f"/>
    <path d="M 555.098132 360.555577 
L 557.791096 361.498339 
L 559.419975 356.675247 
L 556.725847 355.711846 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ccbe7d"/>
    <path d="M 580.602164 322.992231 
L 583.318971 324.320917 
L 584.958344 319.961093 
L 582.240534 318.601144 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8c6c5b"/>
    <path d="M 746.477367 437.634857 
L 749.254082 440.718003 
L 750.851694 440.415768 
L 748.077828 437.266922 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #55dd77"/>
    <path d="M 664.798348 336.970404 
L 667.573575 340.120733 
L 669.221881 337.678409 
L 666.447263 334.462084 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a8906a"/>
    <path d="M 667.573575 340.120733 
L 670.349399 343.308462 
L 671.997027 340.933121 
L 669.221881 337.678409 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ac956c"/>
    <path d="M 729.817844 418.471153 
L 732.594568 421.732717 
L 734.208269 421.020453 
L 731.433978 417.68732 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #95ea84"/>
    <path d="M 625.521681 307.168256 
L 628.278393 309.527281 
L 629.93015 306.196114 
L 627.173171 303.786834 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8b6b64"/>
    <path d="M 749.254082 440.718003 
L 752.03098 443.763511 
L 753.625681 443.52577 
L 750.851694 440.415768 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #49db75"/>
    <path d="M 820.700608 501.238578 
L 823.500848 502.913939 
L 825.007856 503.481301 
L 822.210863 501.787453 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0a86ec"/>
    <path d="M 727.040982 415.188079 
L 729.817844 418.471153 
L 731.433978 417.68732 
L 728.659473 414.331936 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a1ec86"/>
    <path d="M 611.2208 305.714042 
L 613.966289 307.723255 
L 615.616054 304.066525 
L 612.870019 302.012934 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8f7069"/>
    <path d="M 568.642546 338.760342 
L 571.347978 339.882732 
L 572.982025 335.273527 
L 570.27547 334.124659 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a68d69"/>
    <path d="M 752.03098 443.763511 
L 754.808125 446.769227 
L 756.399857 446.594716 
L 753.625681 443.52577 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #41d973"/>
    <path d="M 724.263959 411.885927 
L 727.040982 415.188079 
L 728.659473 414.331936 
L 725.884729 410.956804 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #adef89"/>
    <path d="M 574.61682 330.706888 
L 577.327977 331.926962 
L 578.964663 327.435235 
L 576.252429 326.186121 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9a7e62"/>
    <path d="M 545.904246 379.268307 
L 548.589558 380.119916 
L 550.21659 375.207517 
L 547.530116 374.338568 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ece78f"/>
    <path d="M 618.364864 306.185664 
L 621.116314 308.368962 
L 622.767324 304.872513 
L 620.015454 302.64163 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8d6d66"/>
    <path d="M 721.486755 408.567151 
L 724.263959 411.885927 
L 725.884729 410.956804 
L 723.109726 407.564451 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b9f18b"/>
    <path d="M 638.213697 313.798502 
L 640.978641 316.451379 
L 642.630667 313.398922 
L 639.865709 310.690146 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #805c54"/>
    <path d="M 754.808125 446.769227 
L 757.585589 449.733041 
L 759.174296 449.620436 
L 756.399857 446.594716 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #35d771"/>
    <path d="M 718.709356 405.23423 
L 721.486755 408.567151 
L 723.109726 407.564451 
L 720.334447 404.157428 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c5f38d"/>
    <path d="M 584.958344 319.961093 
L 587.679659 321.374517 
L 589.320856 317.102956 
L 586.598565 315.655799 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #886759"/>
    <path d="M 843.345828 512.412037 
L 846.164616 513.511772 
L 847.646288 513.971533 
L 844.830342 512.867947 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #166ed4"/>
    <path d="M 789.735883 479.479811 
L 792.520784 481.83614 
L 794.066868 482.275016 
L 791.285389 479.878332 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b0b9"/>
    <path d="M 757.585589 449.733041 
L 760.363447 452.652889 
L 761.949075 452.600807 
L 759.174296 449.620436 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2dd56f"/>
    <path d="M 561.049269 351.878057 
L 563.747812 352.890808 
L 565.378799 348.146831 
L 562.679074 347.110264 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bca975"/>
    <path d="M 553.470759 365.421796 
L 556.162528 366.343822 
L 557.791096 361.498339 
L 555.098132 360.555577 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d4c882"/>
    <path d="M 606.830136 307.579719 
L 609.572066 309.481299 
L 611.2208 305.714042 
L 608.478224 303.769316 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8b6b64"/>
    <path d="M 715.931754 401.889665 
L 718.709356 405.23423 
L 720.334447 404.157428 
L 717.558885 400.73831 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d1f690"/>
    <path d="M 833.417797 508.058245 
L 836.227956 509.413471 
L 837.720251 509.946316 
L 834.913138 508.581131 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1078de"/>
    <path d="M 808.000749 493.203454 
L 810.793774 495.169169 
L 812.316528 495.731084 
L 809.526883 493.737957 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0098fe"/>
    <path d="M 628.278393 309.527281 
L 631.037327 311.947944 
L 632.689321 308.669008 
L 629.93015 306.196114 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #87655e"/>
    <path d="M 640.978641 316.451379 
L 643.745252 319.160427 
L 645.397246 316.165534 
L 642.630667 313.398922 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #846257"/>
    <path d="M 713.153947 398.535973 
L 715.931754 401.889665 
L 717.558885 400.73831 
L 714.783035 397.309689 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ddf892"/>
    <path d="M 760.363447 452.652889 
L 763.141778 455.526751 
L 764.724276 455.533754 
L 761.949075 452.600807 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #25d36d"/>
    <path d="M 544.278264 384.206338 
L 546.962396 385.040603 
L 548.589558 380.119916 
L 545.904246 379.268307 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f4f193"/>
    <path d="M 589.320856 317.102956 
L 592.046588 318.605935 
L 593.689536 314.427364 
L 590.96287 312.888364 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #825f56"/>
    <path d="M 602.44447 309.65817 
L 605.18262 311.454869 
L 606.830136 307.579719 
L 604.09125 305.741332 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #896861"/>
    <path d="M 710.375938 395.175687 
L 713.153947 398.535973 
L 714.783035 397.309689 
L 712.0069 393.874173 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e9fb95"/>
    <path d="M 578.964663 327.435235 
L 581.680401 328.732159 
L 583.318971 324.320917 
L 580.602164 322.992231 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #94765f"/>
    <path d="M 567.010349 343.435533 
L 569.714609 344.531163 
L 571.347978 339.882732 
L 568.642546 338.760342 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ae976d"/>
    <path d="M 593.689536 314.427364 
L 596.419563 316.024339 
L 598.064163 311.943104 
L 595.333257 310.308012 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #815e56"/>
    <path d="M 598.064163 311.943104 
L 600.798339 313.638125 
L 602.44447 309.65817 
L 599.709481 307.923141 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #85635c"/>
    <path d="M 613.966289 307.723255 
L 616.714565 309.795688 
L 618.364864 306.185664 
L 615.616054 304.066525 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8b6b64"/>
    <path d="M 763.141778 455.526751 
L 765.920666 458.352659 
L 767.499988 458.417252 
L 764.724276 455.533754 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #19d16b"/>
    <path d="M 572.982025 335.273527 
L 575.692048 336.464179 
L 577.327977 331.926962 
L 574.61682 330.706888 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a08566"/>
    <path d="M 707.597734 391.811354 
L 710.375938 395.175687 
L 712.0069 393.874173 
L 709.230487 390.434386 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f5fd97"/>
    <path d="M 621.116314 308.368962 
L 623.870276 310.614966 
L 625.521681 307.168256 
L 622.767324 304.872513 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8b6b64"/>
    <path d="M 643.745252 319.160427 
L 646.513405 321.923638 
L 648.165317 318.98791 
L 645.397246 316.165534 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #886759"/>
    <path d="M 551.843617 370.306959 
L 554.534163 371.208175 
L 556.162528 366.343822 
L 553.470759 365.421796 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dcd286"/>
    <path d="M 559.419975 356.675247 
L 562.117298 357.664015 
L 563.747812 352.890808 
L 561.049269 351.878057 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c4b379"/>
    <path d="M 704.81935 388.445531 
L 707.597734 391.811354 
L 709.230487 390.434386 
L 706.453811 386.992963 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 792.520784 481.83614 
L 795.307283 484.125841 
L 796.849935 484.603191 
L 794.066868 482.275016 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00acc4"/>
    <path d="M 631.037327 311.947944 
L 633.798353 314.428538 
L 635.450547 311.203748 
L 632.689321 308.669008 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #836059"/>
    <path d="M 542.652035 389.149094 
L 545.334972 389.966029 
L 546.962396 385.040603 
L 544.278264 384.206338 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #faf996"/>
    <path d="M 765.920666 458.352659 
L 768.700201 461.128693 
L 770.276301 461.249329 
L 767.499988 458.417252 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #11cf69"/>
    <path d="M 702.040806 385.080786 
L 704.81935 388.445531 
L 706.453811 386.992963 
L 703.67689 383.552545 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #faf996"/>
    <path d="M 823.500848 502.913939 
L 826.304113 504.507663 
L 827.807905 505.091532 
L 825.007856 503.481301 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0a86ec"/>
    <path d="M 646.513405 321.923638 
L 649.282979 324.73895 
L 650.934756 321.863919 
L 648.165317 318.98791 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8c6c5b"/>
    <path d="M 583.318971 324.320917 
L 586.039241 325.700022 
L 587.679659 321.374517 
L 584.958344 319.961093 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8e6e5c"/>
    <path d="M 699.262126 381.719688 
L 702.040806 385.080786 
L 703.67689 383.552545 
L 700.899749 380.115784 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f4f193"/>
    <path d="M 609.572066 309.481299 
L 612.316916 311.444921 
L 613.966289 307.723255 
L 611.2208 305.714042 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #896861"/>
    <path d="M 565.378799 348.146831 
L 568.081841 349.21545 
L 569.714609 344.531163 
L 567.010349 343.435533 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b6a272"/>
    <path d="M 550.21659 375.207517 
L 552.905888 376.087872 
L 554.534163 371.208175 
L 551.843617 370.306959 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e4dc8a"/>
    <path d="M 810.793774 495.169169 
L 813.58921 497.058892 
L 815.108599 497.646235 
L 812.316528 495.731084 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0296fc"/>
    <path d="M 649.282979 324.73895 
L 652.053855 327.60425 
L 653.705441 324.79138 
L 650.934756 321.863919 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #92735e"/>
    <path d="M 696.483341 378.364814 
L 699.262126 381.719688 
L 700.899749 380.115784 
L 698.122419 376.685333 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eee990"/>
    <path d="M 768.700201 461.128693 
L 771.480473 463.852983 
L 773.053312 464.028064 
L 770.276301 461.249329 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #09ce68"/>
    <path d="M 557.791096 361.498339 
L 560.487162 362.462982 
L 562.117298 357.664015 
L 559.419975 356.675247 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ccbe7d"/>
    <path d="M 577.327977 331.926962 
L 580.042585 333.191664 
L 581.680401 328.732159 
L 578.964663 327.435235 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9a7e62"/>
    <path d="M 623.870276 310.614966 
L 626.626618 312.922153 
L 628.278393 309.527281 
L 625.521681 307.168256 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #87655e"/>
    <path d="M 633.798353 314.428538 
L 636.561341 316.967293 
L 638.213697 313.798502 
L 635.450547 311.203748 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #815e56"/>
    <path d="M 571.347978 339.882732 
L 574.056814 341.043611 
L 575.692048 336.464179 
L 572.982025 335.273527 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a8906a"/>
    <path d="M 693.704488 375.018739 
L 696.483341 378.364814 
L 698.122419 376.685333 
L 695.344936 373.263844 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e8e28d"/>
    <path d="M 587.679659 321.374517 
L 590.404382 322.840795 
L 592.046588 318.605935 
L 589.320856 317.102956 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #886759"/>
    <path d="M 616.714565 309.795688 
L 619.465499 311.930005 
L 621.116314 308.368962 
L 618.364864 306.185664 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #896861"/>
    <path d="M 652.053855 327.60425 
L 654.825918 330.517376 
L 656.477256 327.768061 
L 653.705441 324.79138 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #967960"/>
    <path d="M 605.18262 311.454869 
L 607.923814 313.312203 
L 609.572066 309.481299 
L 606.830136 307.579719 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #87655e"/>
    <path d="M 690.925607 371.684034 
L 693.704488 375.018739 
L 695.344936 373.263844 
L 692.567342 369.85397 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e2da89"/>
    <path d="M 795.307283 484.125841 
L 798.095508 486.347531 
L 799.634722 486.861439 
L 796.849935 484.603191 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a8d0"/>
    <path d="M 654.825918 330.517376 
L 657.599057 333.47612 
L 659.250085 330.791682 
L 656.477256 327.768061 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9a7e62"/>
    <path d="M 771.480473 463.852983 
L 774.261581 466.523714 
L 775.83112 466.751591 
L 773.053312 464.028064 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #01cc66"/>
    <path d="M 688.146745 368.36327 
L 690.925607 371.684034 
L 692.567342 369.85397 
L 689.789684 366.458359 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dcd286"/>
    <path d="M 592.046588 318.605935 
L 594.775656 320.164017 
L 596.419563 316.024339 
L 593.689536 314.427364 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #846257"/>
    <path d="M 836.227956 509.413471 
L 839.0418 510.682571 
L 840.531093 511.223431 
L 837.720251 509.946316 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1276dc"/>
    <path d="M 548.589558 380.119916 
L 551.277584 380.979381 
L 552.905888 376.087872 
L 550.21659 375.207517 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ece78f"/>
    <path d="M 600.798339 313.638125 
L 603.535667 315.392149 
L 605.18262 311.454869 
L 602.44447 309.65817 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #836059"/>
    <path d="M 685.367954 365.059005 
L 688.146745 368.36327 
L 689.789684 366.458359 
L 687.012015 363.079649 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d6cb83"/>
    <path d="M 596.419563 316.024339 
L 599.152841 317.678472 
L 600.798339 313.638125 
L 598.064163 311.943104 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #805c54"/>
    <path d="M 657.599057 333.47612 
L 660.373164 336.47823 
L 662.023818 333.859919 
L 659.250085 330.791682 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a08566"/>
    <path d="M 846.164616 513.511772 
L 848.987618 514.522356 
L 850.466502 514.984097 
L 847.646288 513.971533 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #166ed4"/>
    <path d="M 563.747812 352.890808 
L 566.449592 353.932195 
L 568.081841 349.21545 
L 565.378799 348.146831 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #beac76"/>
    <path d="M 636.561341 316.967293 
L 639.326166 319.562381 
L 640.978641 316.451379 
L 638.213697 313.798502 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #846257"/>
    <path d="M 682.589292 361.773789 
L 685.367954 365.059005 
L 687.012015 363.079649 
L 684.234394 359.72047 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d0c380"/>
    <path d="M 660.373164 336.47823 
L 663.148135 339.521412 
L 664.798348 336.970404 
L 662.023818 333.859919 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a48b68"/>
    <path d="M 556.162528 366.343822 
L 558.857304 367.284228 
L 560.487162 362.462982 
L 557.791096 361.498339 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d4c882"/>
    <path d="M 581.680401 328.732159 
L 584.399559 330.0764 
L 586.039241 325.700022 
L 583.318971 324.320917 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #94765f"/>
    <path d="M 679.810821 358.510161 
L 682.589292 361.773789 
L 684.234394 359.72047 
L 681.456883 356.383437 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cabb7c"/>
    <path d="M 663.148135 339.521412 
L 665.923871 342.603335 
L 667.573575 340.120733 
L 664.798348 336.970404 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #aa926b"/>
    <path d="M 626.626618 312.922153 
L 629.385213 315.28894 
L 631.037327 311.947944 
L 628.278393 309.527281 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #836059"/>
    <path d="M 677.032609 355.27064 
L 679.810821 358.510161 
L 681.456883 356.383437 
L 678.679552 353.071151 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c6b67a"/>
    <path d="M 665.923871 342.603335 
L 668.700275 345.721634 
L 670.349399 343.308462 
L 667.573575 340.120733 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b09a6e"/>
    <path d="M 674.254729 352.057729 
L 677.032609 355.27064 
L 678.679552 353.071151 
L 675.902474 349.786191 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c0ae77"/>
    <path d="M 612.316916 311.444921 
L 615.064562 313.469369 
L 616.714565 309.795688 
L 613.966289 307.723255 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #87655e"/>
    <path d="M 774.261581 466.523714 
L 777.043625 469.139126 
L 778.609829 469.418102 
L 775.83112 466.751591 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c677"/>
    <path d="M 668.700275 345.721634 
L 671.477256 348.873908 
L 673.125729 346.531117 
L 670.349399 343.308462 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b49f70"/>
    <path d="M 671.477256 348.873908 
L 674.254729 352.057729 
L 675.902474 349.786191 
L 673.125729 346.531117 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #baa774"/>
    <path d="M 569.714609 344.531163 
L 572.422205 345.661954 
L 574.056814 341.043611 
L 571.347978 339.882732 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b09a6e"/>
    <path d="M 575.692048 336.464179 
L 578.405467 337.696233 
L 580.042585 333.191664 
L 577.327977 331.926962 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a28867"/>
    <path d="M 546.962396 385.040603 
L 549.64913 385.879173 
L 551.277584 380.979381 
L 548.589558 380.119916 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f4f193"/>
    <path d="M 619.465499 311.930005 
L 622.218964 314.124808 
L 623.870276 310.614966 
L 621.116314 308.368962 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #85635c"/>
    <path d="M 639.326166 319.562381 
L 642.092704 322.211917 
L 643.745252 319.160427 
L 640.978641 316.451379 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #886759"/>
    <path d="M 826.304113 504.507663 
L 829.110557 506.019021 
L 830.611166 506.617402 
L 827.807905 505.091532 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0b83e9"/>
    <path d="M 813.58921 497.058892 
L 816.387201 498.871618 
L 817.903242 499.482384 
L 815.108599 497.646235 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0393f9"/>
    <path d="M 798.095508 486.347531 
L 800.885589 488.499892 
L 802.421362 489.048409 
L 799.634722 486.861439 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a6d7"/>
    <path d="M 586.039241 325.700022 
L 588.762883 327.128964 
L 590.404382 322.840795 
L 587.679659 321.374517 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #90715d"/>
    <path d="M 562.117298 357.664015 
L 564.817775 358.677978 
L 566.449592 353.932195 
L 563.747812 352.890808 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c4b379"/>
    <path d="M 554.534163 371.208175 
L 557.227618 372.124258 
L 558.857304 367.284228 
L 556.162528 366.343822 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dcd286"/>
    <path d="M 607.923814 313.312203 
L 610.667931 315.229072 
L 612.316916 311.444921 
L 609.572066 309.481299 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #836059"/>
    <path d="M 777.043625 469.139126 
L 779.826707 471.697511 
L 781.389547 472.025843 
L 778.609829 469.418102 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c382"/>
    <path d="M 629.385213 315.28894 
L 632.145934 317.713681 
L 633.798353 314.428538 
L 631.037327 311.947944 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #805c54"/>
    <path d="M 642.092704 322.211917 
L 644.860834 324.91396 
L 646.513405 321.923638 
L 643.745252 319.160427 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8c6c5b"/>
    <path d="M 590.404382 322.840795 
L 593.132414 324.359252 
L 594.775656 320.164017 
L 592.046588 318.605935 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8a695a"/>
    <path d="M 545.334972 389.966029 
L 548.020396 390.783722 
L 549.64913 385.879173 
L 546.962396 385.040603 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fcfb97"/>
    <path d="M 603.535667 315.392149 
L 606.276035 317.204189 
L 607.923814 313.312203 
L 605.18262 311.454869 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #815e56"/>
    <path d="M 568.081841 349.21545 
L 570.788148 350.315869 
L 572.422205 345.661954 
L 569.714609 344.531163 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b6a272"/>
    <path d="M 580.042585 333.191664 
L 582.760566 334.500534 
L 584.399559 330.0764 
L 581.680401 328.732159 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9c8064"/>
    <path d="M 594.775656 320.164017 
L 597.507957 321.776428 
L 599.152841 317.678472 
L 596.419563 316.024339 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #866458"/>
    <path d="M 599.152841 317.678472 
L 601.889263 319.388882 
L 603.535667 315.392149 
L 600.798339 313.638125 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #825f56"/>
    <path d="M 615.064562 313.469369 
L 617.814881 315.553364 
L 619.465499 311.930005 
L 616.714565 309.795688 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #836059"/>
    <path d="M 574.056814 341.043611 
L 576.768986 342.24263 
L 578.405467 337.696233 
L 575.692048 336.464179 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a8906a"/>
    <path d="M 622.218964 314.124808 
L 624.974835 316.378634 
L 626.626618 312.922153 
L 623.870276 310.614966 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #836059"/>
    <path d="M 644.860834 324.91396 
L 647.630437 327.666518 
L 649.282979 324.73895 
L 646.513405 321.923638 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #90715d"/>
    <path d="M 552.905888 376.087872 
L 555.597994 376.979571 
L 557.227618 372.124258 
L 554.534163 371.208175 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e4dc8a"/>
    <path d="M 779.826707 471.697511 
L 782.610938 474.197222 
L 784.170385 474.57312 
L 781.389547 472.025843 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00be8f"/>
    <path d="M 560.487162 362.462982 
L 563.186296 363.449362 
L 564.817775 358.677978 
L 562.117298 357.664015 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ccbe7d"/>
    <path d="M 632.145934 317.713681 
L 634.908656 320.19467 
L 636.561341 316.967293 
L 633.798353 314.428538 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #846257"/>
    <path d="M 800.885589 488.499892 
L 803.677658 490.581672 
L 805.209992 491.162819 
L 802.421362 489.048409 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a2e2"/>
    <path d="M 839.0418 510.682571 
L 841.859487 511.865112 
L 843.345828 512.412037 
L 840.531093 511.223431 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1276dc"/>
    <path d="M 647.630437 327.666518 
L 650.401399 330.467549 
L 652.053855 327.60425 
L 649.282979 324.73895 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #94765f"/>
    <path d="M 584.399559 330.0764 
L 587.122051 331.467413 
L 588.762883 327.128964 
L 586.039241 325.700022 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #967960"/>
    <path d="M 816.387201 498.871618 
L 819.187893 500.606418 
L 820.700608 501.238578 
L 817.903242 499.482384 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0490f6"/>
    <path d="M 730.977748 422.422451 
L 733.756838 425.58682 
L 735.371185 424.970368 
L 732.594568 421.732717 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8de882"/>
    <path d="M 728.198629 419.235004 
L 730.977748 422.422451 
L 732.594568 421.732717 
L 729.817844 418.471153 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #99eb85"/>
    <path d="M 733.756838 425.58682 
L 736.535932 428.725808 
L 738.147731 428.181732 
L 735.371185 424.970368 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #85e781"/>
    <path d="M 725.419451 416.026809 
L 728.198629 419.235004 
L 729.817844 418.471153 
L 727.040982 415.188079 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a5ed87"/>
    <path d="M 610.667931 315.229072 
L 613.414853 317.204313 
L 615.064562 313.469369 
L 612.316916 311.444921 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #815e56"/>
    <path d="M 736.535932 428.725808 
L 739.315069 431.837143 
L 740.924245 431.364468 
L 738.147731 428.181732 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #79e47e"/>
    <path d="M 566.449592 353.932195 
L 569.154562 355.001993 
L 570.788148 350.315869 
L 568.081841 349.21545 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #beac76"/>
    <path d="M 722.640193 412.800223 
L 725.419451 416.026809 
L 727.040982 415.188079 
L 724.263959 411.885927 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b1ef89"/>
    <path d="M 551.277584 380.979381 
L 553.968315 381.846662 
L 555.597994 376.979571 
L 552.905888 376.087872 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ece78f"/>
    <path d="M 739.315069 431.837143 
L 742.094292 434.918587 
L 743.700773 434.516267 
L 740.924245 431.364468 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #6de27c"/>
    <path d="M 719.860837 409.557629 
L 722.640193 412.800223 
L 724.263959 411.885927 
L 721.486755 408.567151 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bdf28c"/>
    <path d="M 650.401399 330.467549 
L 653.173607 333.314962 
L 654.825918 330.517376 
L 652.053855 327.60425 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9a7e62"/>
    <path d="M 717.081369 406.301428 
L 719.860837 409.557629 
L 721.486755 408.567151 
L 718.709356 405.23423 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c5f38d"/>
    <path d="M 848.987618 514.522356 
L 851.814994 515.443592 
L 853.291148 515.905437 
L 850.466502 514.984097 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #166ed4"/>
    <path d="M 782.610938 474.197222 
L 785.396427 476.636668 
L 786.952458 477.0583 
L 784.170385 474.57312 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00bc94"/>
    <path d="M 742.094292 434.918587 
L 744.87365 437.967933 
L 746.477367 437.634857 
L 743.700773 434.516267 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #65e07a"/>
    <path d="M 829.110557 506.019021 
L 831.920332 507.447362 
L 833.417797 508.058245 
L 830.611166 506.617402 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0c80e6"/>
    <path d="M 624.974835 316.378634 
L 627.732989 318.689961 
L 629.385213 315.28894 
L 626.626618 312.922153 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #805c54"/>
    <path d="M 558.857304 367.284228 
L 561.555059 368.242895 
L 563.186296 363.449362 
L 560.487162 362.462982 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d4c882"/>
    <path d="M 578.405467 337.696233 
L 581.122209 338.969266 
L 582.760566 334.500534 
L 580.042585 333.191664 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a28867"/>
    <path d="M 634.908656 320.19467 
L 637.673257 322.730145 
L 639.326166 319.562381 
L 636.561341 316.967293 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #886759"/>
    <path d="M 714.301783 403.034045 
L 717.081369 406.301428 
L 718.709356 405.23423 
L 715.931754 401.889665 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d1f690"/>
    <path d="M 572.422205 345.661954 
L 575.133076 346.827587 
L 576.768986 342.24263 
L 574.056814 341.043611 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b09a6e"/>
    <path d="M 588.762883 327.128964 
L 591.489805 328.607109 
L 593.132414 324.359252 
L 590.404382 322.840795 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #92735e"/>
    <path d="M 744.87365 437.967933 
L 747.653197 440.983014 
L 749.254082 440.718003 
L 746.477367 437.634857 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #59de78"/>
    <path d="M 617.814881 315.553364 
L 620.567751 317.695565 
L 622.218964 314.124808 
L 619.465499 311.930005 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #815e56"/>
    <path d="M 711.522076 399.757918 
L 714.301783 403.034045 
L 715.931754 401.889665 
L 713.153947 398.535973 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ddf892"/>
    <path d="M 653.173607 333.314962 
L 655.946953 336.206622 
L 657.599057 333.47612 
L 654.825918 330.517376 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9e8365"/>
    <path d="M 606.276035 317.204189 
L 609.019328 319.073197 
L 610.667931 315.229072 
L 607.923814 313.312203 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #805c54"/>
    <path d="M 708.742253 396.475504 
L 711.522076 399.757918 
L 713.153947 398.535973 
L 710.375938 395.175687 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e9fb95"/>
    <path d="M 747.653197 440.983014 
L 750.432991 443.9617 
L 752.03098 443.763511 
L 749.254082 440.718003 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #51dc76"/>
    <path d="M 705.962323 393.189271 
L 708.742253 396.475504 
L 710.375938 395.175687 
L 707.597734 391.811354 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f5fd97"/>
    <path d="M 593.132414 324.359252 
L 595.863658 325.929157 
L 597.507957 321.776428 
L 594.775656 320.164017 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8c6c5b"/>
    <path d="M 655.946953 336.206622 
L 658.721331 339.140353 
L 660.373164 336.47823 
L 657.599057 333.47612 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a28867"/>
    <path d="M 703.182299 389.901695 
L 705.962323 393.189271 
L 707.597734 391.811354 
L 704.81935 388.445531 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 601.889263 319.388882 
L 604.628717 321.154632 
L 606.276035 317.204189 
L 603.535667 315.392149 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #846257"/>
    <path d="M 750.432991 443.9617 
L 753.213096 446.901901 
L 754.808125 446.769227 
L 752.03098 443.763511 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #45da74"/>
    <path d="M 549.64913 385.879173 
L 552.338463 386.72203 
L 553.968315 381.846662 
L 551.277584 380.979381 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f4f193"/>
    <path d="M 597.507957 321.776428 
L 600.243387 323.442336 
L 601.889263 319.388882 
L 599.152841 317.678472 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #886759"/>
    <path d="M 700.402202 386.615265 
L 703.182299 389.901695 
L 704.81935 388.445531 
L 702.040806 385.080786 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #faf996"/>
    <path d="M 803.677658 490.581672 
L 806.471849 492.591687 
L 808.000749 493.203454 
L 805.209992 491.162819 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a0e8"/>
    <path d="M 564.817775 358.677978 
L 567.521364 359.716943 
L 569.154562 355.001993 
L 566.449592 353.932195 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c6b67a"/>
    <path d="M 637.673257 322.730145 
L 640.439617 325.318289 
L 642.092704 322.211917 
L 639.326166 319.562381 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8c6c5b"/>
    <path d="M 658.721331 339.140353 
L 661.496641 342.113938 
L 663.148135 339.521412 
L 660.373164 336.47823 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a8906a"/>
    <path d="M 697.622057 383.33247 
L 700.402202 386.615265 
L 702.040806 385.080786 
L 699.262126 381.719688 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f4f193"/>
    <path d="M 557.227618 372.124258 
L 559.92396 373.055112 
L 561.555059 368.242895 
L 558.857304 367.284228 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dcd286"/>
    <path d="M 785.396427 476.636668 
L 788.183289 479.014317 
L 789.735883 479.479811 
L 786.952458 477.0583 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b8a0"/>
    <path d="M 582.760566 334.500534 
L 585.48184 335.853067 
L 587.122051 331.467413 
L 584.399559 330.0764 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9c8064"/>
    <path d="M 753.213096 446.901901 
L 755.993578 449.801568 
L 757.585589 449.733041 
L 754.808125 446.769227 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #3dd872"/>
    <path d="M 694.841893 380.055804 
L 697.622057 383.33247 
L 699.262126 381.719688 
L 696.483341 378.364814 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eee990"/>
    <path d="M 627.732989 318.689961 
L 630.493302 321.057206 
L 632.145934 317.713681 
L 629.385213 315.28894 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #846257"/>
    <path d="M 661.496641 342.113938 
L 664.272784 345.125121 
L 665.923871 342.603335 
L 663.148135 339.521412 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ac956c"/>
    <path d="M 692.061747 376.787761 
L 694.841893 380.055804 
L 696.483341 378.364814 
L 693.704488 375.018739 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e8e28d"/>
    <path d="M 613.414853 317.204313 
L 616.164461 319.236703 
L 617.814881 315.553364 
L 615.064562 313.469369 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #805c54"/>
    <path d="M 570.788148 350.315869 
L 573.497664 351.447802 
L 575.133076 346.827587 
L 572.422205 345.661954 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b8a473"/>
    <path d="M 664.272784 345.125121 
L 667.049669 348.171615 
L 668.700275 345.721634 
L 665.923871 342.603335 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b29c6f"/>
    <path d="M 689.28166 373.530834 
L 692.061747 376.787761 
L 693.704488 375.018739 
L 690.925607 371.684034 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e2da89"/>
    <path d="M 576.768986 342.24263 
L 579.484428 343.479401 
L 581.122209 338.969266 
L 578.405467 337.696233 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #aa926b"/>
    <path d="M 755.993578 449.801568 
L 758.774511 452.658696 
L 760.363447 452.652889 
L 757.585589 449.733041 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #35d771"/>
    <path d="M 686.501678 370.287507 
L 689.28166 373.530834 
L 690.925607 371.684034 
L 688.146745 368.36327 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ded587"/>
    <path d="M 667.049669 348.171615 
L 669.827205 351.2511 
L 671.477256 348.873908 
L 668.700275 345.721634 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b6a272"/>
    <path d="M 620.567751 317.695565 
L 623.323051 319.894568 
L 624.974835 316.378634 
L 622.218964 314.124808 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #825f56"/>
    <path d="M 683.721852 367.06026 
L 686.501678 370.287507 
L 688.146745 368.36327 
L 685.367954 365.059005 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d8cd84"/>
    <path d="M 669.827205 351.2511 
L 672.605308 354.361224 
L 674.254729 352.057729 
L 671.477256 348.873908 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bca975"/>
    <path d="M 640.439617 325.318289 
L 643.207619 327.95723 
L 644.860834 324.91396 
L 642.092704 322.211917 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #90715d"/>
    <path d="M 548.020396 390.783722 
L 550.708311 391.602173 
L 552.338463 386.72203 
L 549.64913 385.879173 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fcfb97"/>
    <path d="M 680.942238 363.851561 
L 683.721852 367.06026 
L 685.367954 365.059005 
L 682.589292 361.773789 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d2c581"/>
    <path d="M 672.605308 354.361224 
L 675.383897 357.499613 
L 677.032609 355.27064 
L 674.254729 352.057729 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c2b178"/>
    <path d="M 819.187893 500.606418 
L 821.991432 502.262431 
L 823.500848 502.913939 
L 820.700608 501.238578 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #068ef4"/>
    <path d="M 678.162897 360.663865 
L 680.942238 363.851561 
L 682.589292 361.773789 
L 679.810821 358.510161 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ccbe7d"/>
    <path d="M 675.383897 357.499613 
L 678.162897 360.663865 
L 679.810821 358.510161 
L 677.032609 355.27064 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c6b67a"/>
    <path d="M 587.122051 331.467413 
L 589.84779 332.904605 
L 591.489805 328.607109 
L 588.762883 327.128964 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #987b61"/>
    <path d="M 758.774511 452.658696 
L 761.555971 455.471326 
L 763.141778 455.526751 
L 760.363447 452.652889 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #29d46e"/>
    <path d="M 563.186296 363.449362 
L 565.888463 364.457312 
L 567.521364 359.716943 
L 564.817775 358.677978 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ccbe7d"/>
    <path d="M 555.597994 376.979571 
L 558.292892 377.882542 
L 559.92396 373.055112 
L 557.227618 372.124258 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e4dc8a"/>
    <path d="M 609.019328 319.073197 
L 611.765432 320.998064 
L 613.414853 317.204313 
L 610.667931 315.229072 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #846257"/>
    <path d="M 630.493302 321.057206 
L 633.255654 323.478728 
L 634.908656 320.19467 
L 632.145934 317.713681 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #886759"/>
    <path d="M 788.183289 479.014317 
L 790.971642 481.328699 
L 792.520784 481.83614 
L 789.735883 479.479811 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b4ac"/>
    <path d="M 841.859487 511.865112 
L 844.681175 512.96074 
L 846.164616 513.511772 
L 843.345828 512.412037 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1276dc"/>
    <path d="M 643.207619 327.95723 
L 645.977147 330.645046 
L 647.630437 327.666518 
L 644.860834 324.91396 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #94765f"/>
    <path d="M 591.489805 328.607109 
L 594.219915 330.133771 
L 595.863658 325.929157 
L 593.132414 324.359252 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #92735e"/>
    <path d="M 761.555971 455.471326 
L 764.338039 458.237545 
L 765.920666 458.352659 
L 763.141778 455.526751 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #21d36d"/>
    <path d="M 806.471849 492.591687 
L 809.2683 494.528819 
L 810.793774 495.169169 
L 808.000749 493.203454 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #009eef"/>
    <path d="M 831.920332 507.447362 
L 834.733594 508.792108 
L 836.227956 509.413471 
L 833.417797 508.058245 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0e7ee4"/>
    <path d="M 604.628717 321.154632 
L 607.371097 322.974725 
L 609.019328 319.073197 
L 606.276035 317.204189 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #866458"/>
    <path d="M 569.154562 355.001993 
L 571.862674 356.099952 
L 573.497664 351.447802 
L 570.788148 350.315869 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #beac76"/>
    <path d="M 581.122209 338.969266 
L 583.842199 340.282812 
L 585.48184 335.853067 
L 582.760566 334.500534 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a48b68"/>
    <path d="M 595.863658 325.929157 
L 598.598015 327.549724 
L 600.243387 323.442336 
L 597.507957 321.776428 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8e6e5c"/>
    <path d="M 616.164461 319.236703 
L 618.916637 321.324959 
L 620.567751 317.695565 
L 617.814881 315.553364 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #846257"/>
    <path d="M 600.243387 323.442336 
L 602.981842 325.160852 
L 604.628717 321.154632 
L 601.889263 319.388882 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8a695a"/>
    <path d="M 575.133076 346.827587 
L 577.847159 348.02771 
L 579.484428 343.479401 
L 576.768986 342.24263 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b09a6e"/>
    <path d="M 623.323051 319.894568 
L 626.080661 322.148914 
L 627.732989 318.689961 
L 624.974835 316.378634 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #846257"/>
    <path d="M 645.977147 330.645046 
L 648.748089 333.379769 
L 650.401399 330.467549 
L 647.630437 327.666518 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #987b61"/>
    <path d="M 553.968315 381.846662 
L 556.661742 382.721713 
L 558.292892 377.882542 
L 555.597994 376.979571 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ece78f"/>
    <path d="M 561.555059 368.242895 
L 564.255764 369.219683 
L 565.888463 364.457312 
L 563.186296 363.449362 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d4c882"/>
    <path d="M 764.338039 458.237545 
L 767.1208 460.955489 
L 768.700201 461.128693 
L 765.920666 458.352659 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #19d16b"/>
    <path d="M 633.255654 323.478728 
L 636.019927 325.952833 
L 637.673257 322.730145 
L 634.908656 320.19467 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8c6c5b"/>
    <path d="M 790.971642 481.328699 
L 793.761606 483.578404 
L 795.307283 484.125841 
L 792.520784 481.83614 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b0b9"/>
    <path d="M 585.48184 335.853067 
L 588.206325 337.248711 
L 589.84779 332.904605 
L 587.122051 331.467413 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9e8365"/>
    <path d="M 648.748089 333.379769 
L 651.520338 336.159383 
L 653.173607 333.314962 
L 650.401399 330.467549 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9c8064"/>
    <path d="M 611.765432 320.998064 
L 614.514234 322.977624 
L 616.164461 319.236703 
L 613.414853 317.204313 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #866458"/>
    <path d="M 767.1208 460.955489 
L 769.904344 463.623343 
L 771.480473 463.852983 
L 768.700201 461.128693 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #11cf69"/>
    <path d="M 567.521364 359.716943 
L 570.228025 360.780688 
L 571.862674 356.099952 
L 569.154562 355.001993 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c6b67a"/>
    <path d="M 821.991432 502.262431 
L 824.797967 503.838873 
L 826.304113 504.507663 
L 823.500848 502.913939 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #078bf1"/>
    <path d="M 552.338463 386.72203 
L 555.030392 387.56915 
L 556.661742 382.721713 
L 553.968315 381.846662 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f4f193"/>
    <path d="M 651.520338 336.159383 
L 654.293786 338.981828 
L 655.946953 336.206622 
L 653.173607 333.314962 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a28867"/>
    <path d="M 626.080661 322.148914 
L 628.840464 324.457084 
L 630.493302 321.057206 
L 627.732989 318.689961 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #886759"/>
    <path d="M 579.484428 343.479401 
L 582.203071 344.753496 
L 583.842199 340.282812 
L 581.122209 338.969266 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #aa926b"/>
    <path d="M 559.92396 373.055112 
L 562.623167 374.000627 
L 564.255764 369.219683 
L 561.555059 368.242895 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dcd286"/>
    <path d="M 636.019927 325.952833 
L 638.786005 328.477773 
L 640.439617 325.318289 
L 637.673257 322.730145 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #90715d"/>
    <path d="M 573.497664 351.447802 
L 576.210335 352.610934 
L 577.847159 348.02771 
L 575.133076 346.827587 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b8a473"/>
    <path d="M 589.84779 332.904605 
L 592.57669 334.387335 
L 594.219915 330.133771 
L 591.489805 328.607109 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9a7e62"/>
    <path d="M 618.916637 321.324959 
L 621.671267 323.467739 
L 623.323051 319.894568 
L 620.567751 317.695565 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #866458"/>
    <path d="M 809.2683 494.528819 
L 812.067149 496.392021 
L 813.58921 497.058892 
L 810.793774 495.169169 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #009cf4"/>
    <path d="M 607.371097 322.974725 
L 610.116291 324.84811 
L 611.765432 320.998064 
L 609.019328 319.073197 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #886759"/>
    <path d="M 654.293786 338.981828 
L 657.068332 341.845003 
L 658.721331 339.140353 
L 655.946953 336.206622 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a68d69"/>
    <path d="M 769.904344 463.623343 
L 772.688764 466.239343 
L 774.261581 466.523714 
L 771.480473 463.852983 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #09ce68"/>
    <path d="M 594.219915 330.133771 
L 596.953119 331.708212 
L 598.598015 327.549724 
L 595.863658 325.929157 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #94765f"/>
    <path d="M 602.981842 325.160852 
L 605.723219 326.931034 
L 607.371097 322.974725 
L 604.628717 321.154632 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8c6c5b"/>
    <path d="M 598.598015 327.549724 
L 601.335387 329.220118 
L 602.981842 325.160852 
L 600.243387 323.442336 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #90715d"/>
    <path d="M 793.761606 483.578404 
L 796.553305 485.762085 
L 798.095508 486.347531 
L 795.307283 484.125841 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00aebf"/>
    <path d="M 657.068332 341.845003 
L 659.843878 344.746771 
L 661.496641 342.113938 
L 658.721331 339.140353 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #aa926b"/>
    <path d="M 550.708311 391.602173 
L 553.39872 392.421383 
L 555.030392 387.56915 
L 552.338463 386.72203 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fcfb97"/>
    <path d="M 565.888463 364.457312 
L 568.593627 365.486644 
L 570.228025 360.780688 
L 567.521364 359.716943 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cec07f"/>
    <path d="M 638.786005 328.477773 
L 641.553773 331.051746 
L 643.207619 327.95723 
L 640.439617 325.318289 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #94765f"/>
    <path d="M 583.842199 340.282812 
L 586.565362 341.636361 
L 588.206325 337.248711 
L 585.48184 335.853067 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a68d69"/>
    <path d="M 558.292892 377.882542 
L 560.990567 378.796705 
L 562.623167 374.000627 
L 559.92396 373.055112 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e4dc8a"/>
    <path d="M 628.840464 324.457084 
L 631.602344 326.817506 
L 633.255654 323.478728 
L 630.493302 321.057206 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8c6c5b"/>
    <path d="M 834.733594 508.792108 
L 837.550496 510.052759 
L 839.0418 510.682571 
L 836.227956 509.413471 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0e7ee4"/>
    <path d="M 659.843878 344.746771 
L 662.620329 347.684956 
L 664.272784 345.125121 
L 661.496641 342.113938 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b09a6e"/>
    <path d="M 844.681175 512.96074 
L 847.507022 513.969182 
L 848.987618 514.522356 
L 846.164616 513.511772 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1276dc"/>
    <path d="M 614.514234 322.977624 
L 617.265621 325.010654 
L 618.916637 321.324959 
L 616.164461 319.236703 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #886759"/>
    <path d="M 772.688764 466.239343 
L 775.474156 468.801778 
L 777.043625 469.139126 
L 774.261581 466.523714 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00cb6b"/>
    <path d="M 571.862674 356.099952 
L 574.573879 357.22579 
L 576.210335 352.610934 
L 573.497664 351.447802 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c0ae77"/>
    <path d="M 577.847159 348.02771 
L 580.564395 349.261936 
L 582.203071 344.753496 
L 579.484428 343.479401 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b29c6f"/>
    <path d="M 662.620329 347.684956 
L 665.397594 350.657349 
L 667.049669 348.171615 
L 664.272784 345.125121 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b49f70"/>
    <path d="M 621.671267 323.467739 
L 624.428234 325.663647 
L 626.080661 322.148914 
L 623.323051 319.894568 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8a695a"/>
    <path d="M 641.553773 331.051746 
L 644.32312 333.672906 
L 645.977147 330.645046 
L 643.207619 327.95723 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #987b61"/>
    <path d="M 665.397594 350.657349 
L 668.175586 353.661712 
L 669.827205 351.2511 
L 667.049669 348.171615 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #baa774"/>
    <path d="M 588.206325 337.248711 
L 590.933942 338.686873 
L 592.57669 334.387335 
L 589.84779 332.904605 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a08566"/>
    <path d="M 668.175586 353.661712 
L 670.954222 356.695775 
L 672.605308 354.361224 
L 669.827205 351.2511 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #beac76"/>
    <path d="M 564.255764 369.219683 
L 566.95939 370.214438 
L 568.593627 365.486644 
L 565.888463 364.457312 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d4c882"/>
    <path d="M 610.116291 324.84811 
L 612.864193 326.773676 
L 614.514234 322.977624 
L 611.765432 320.998064 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8c6c5b"/>
    <path d="M 556.661742 382.721713 
L 559.357854 383.604479 
L 560.990567 378.796705 
L 558.292892 377.882542 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ece78f"/>
    <path d="M 670.954222 356.695775 
L 673.733425 359.757246 
L 675.383897 357.499613 
L 672.605308 354.361224 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c4b379"/>
    <path d="M 715.45047 407.359368 
L 718.231953 410.536305 
L 719.860837 409.557629 
L 717.081369 406.301428 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c9f48e"/>
    <path d="M 718.231953 410.536305 
L 721.013412 413.700187 
L 722.640193 412.800223 
L 719.860837 409.557629 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bdf28c"/>
    <path d="M 712.668956 404.171721 
L 715.45047 407.359368 
L 717.081369 406.301428 
L 714.301783 403.034045 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d5f791"/>
    <path d="M 721.013412 413.700187 
L 723.794857 416.848688 
L 725.419451 416.026809 
L 722.640193 412.800223 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b1ef89"/>
    <path d="M 709.887411 400.975722 
L 712.668956 404.171721 
L 714.301783 403.034045 
L 711.522076 399.757918 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ddf892"/>
    <path d="M 723.794857 416.848688 
L 726.576306 419.979506 
L 728.198629 419.235004 
L 725.419451 416.026809 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a9ee88"/>
    <path d="M 707.105838 397.773746 
L 709.887411 400.975722 
L 711.522076 399.757918 
L 708.742253 396.475504 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e9fb95"/>
    <path d="M 824.797967 503.838873 
L 827.607647 505.335031 
L 829.110557 506.019021 
L 826.304113 504.507663 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0888ee"/>
    <path d="M 775.474156 468.801778 
L 778.260622 471.308992 
L 779.826707 471.697511 
L 777.043625 469.139126 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c970"/>
    <path d="M 812.067149 496.392021 
L 814.868535 498.180315 
L 816.387201 498.871618 
L 813.58921 497.058892 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0098fe"/>
    <path d="M 631.602344 326.817506 
L 634.366185 329.228552 
L 636.019927 325.952833 
L 633.255654 323.478728 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #90715d"/>
    <path d="M 673.733425 359.757246 
L 676.51312 362.843806 
L 678.162897 360.663865 
L 675.383897 357.499613 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c8b97b"/>
    <path d="M 796.553305 485.762085 
L 799.346864 487.878459 
L 800.885589 488.499892 
L 798.095508 486.347531 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00aacb"/>
    <path d="M 704.324247 394.568181 
L 707.105838 397.773746 
L 708.742253 396.475504 
L 705.962323 393.189271 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f5fd97"/>
    <path d="M 726.576306 419.979506 
L 729.35778 423.090358 
L 730.977748 422.422451 
L 728.198629 419.235004 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9deb85"/>
    <path d="M 701.542653 391.361422 
L 704.324247 394.568181 
L 705.962323 393.189271 
L 703.182299 389.901695 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 676.51312 362.843806 
L 679.293238 365.953119 
L 680.942238 363.851561 
L 678.162897 360.663865 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cec07f"/>
    <path d="M 698.761075 388.155872 
L 701.542653 391.361422 
L 703.182299 389.901695 
L 700.402202 386.615265 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #faf996"/>
    <path d="M 729.35778 423.090358 
L 732.139306 426.178989 
L 733.756838 425.58682 
L 730.977748 422.422451 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #91e983"/>
    <path d="M 695.979539 384.953939 
L 698.761075 388.155872 
L 700.402202 386.615265 
L 697.622057 383.33247 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f4f193"/>
    <path d="M 679.293238 365.953119 
L 682.073714 369.082829 
L 683.721852 367.06026 
L 680.942238 363.851561 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d4c882"/>
    <path d="M 644.32312 333.672906 
L 647.093939 336.339357 
L 648.748089 333.379769 
L 645.977147 330.645046 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9c8064"/>
    <path d="M 693.198074 381.758033 
L 695.979539 384.953939 
L 697.622057 383.33247 
L 694.841893 380.055804 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eee990"/>
    <path d="M 592.57669 334.387335 
L 595.308663 335.914916 
L 596.953119 331.708212 
L 594.219915 330.133771 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9a7e62"/>
    <path d="M 682.073714 369.082829 
L 684.854489 372.230565 
L 686.501678 370.287507 
L 683.721852 367.06026 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d8cd84"/>
    <path d="M 690.416717 378.570565 
L 693.198074 381.758033 
L 694.841893 380.055804 
L 692.061747 376.787761 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eae48e"/>
    <path d="M 684.854489 372.230565 
L 687.635506 375.393941 
L 689.28166 373.530834 
L 686.501678 370.287507 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ded587"/>
    <path d="M 687.635506 375.393941 
L 690.416717 378.570565 
L 692.061747 376.787761 
L 689.28166 373.530834 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e4dc8a"/>
    <path d="M 732.139306 426.178989 
L 734.920915 429.243171 
L 736.535932 428.725808 
L 733.756838 425.58682 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #89e781"/>
    <path d="M 605.723219 326.931034 
L 608.467414 328.751885 
L 610.116291 324.84811 
L 607.371097 322.974725 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8e6e5c"/>
    <path d="M 582.203071 344.753496 
L 584.924847 346.06445 
L 586.565362 341.636361 
L 583.842199 340.282812 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ac956c"/>
    <path d="M 570.228025 360.780688 
L 572.937714 361.868969 
L 574.573879 357.22579 
L 571.862674 356.099952 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c6b67a"/>
    <path d="M 734.920915 429.243171 
L 737.702644 432.280704 
L 739.315069 431.837143 
L 736.535932 428.725808 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #7de57f"/>
    <path d="M 596.953119 331.708212 
L 599.689325 333.329647 
L 601.335387 329.220118 
L 598.598015 327.549724 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #967960"/>
    <path d="M 617.265621 325.010654 
L 620.019483 327.095875 
L 621.671267 323.467739 
L 618.916637 321.324959 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8c6c5b"/>
    <path d="M 601.335387 329.220118 
L 604.075676 330.939447 
L 605.723219 326.931034 
L 602.981842 325.160852 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #92735e"/>
    <path d="M 576.210335 352.610934 
L 578.926105 353.804916 
L 580.564395 349.261936 
L 577.847159 348.02771 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b8a473"/>
    <path d="M 624.428234 325.663647 
L 627.187426 327.911231 
L 628.840464 324.457084 
L 626.080661 322.148914 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8e6e5c"/>
    <path d="M 737.702644 432.280704 
L 740.484535 435.289419 
L 742.094292 434.918587 
L 739.315069 431.837143 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #75e37d"/>
    <path d="M 647.093939 336.339357 
L 649.866123 339.049159 
L 651.520338 336.159383 
L 648.748089 333.379769 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a08566"/>
    <path d="M 555.030392 387.56915 
L 557.724914 388.420507 
L 559.357854 383.604479 
L 556.661742 382.721713 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f4f193"/>
    <path d="M 562.623167 374.000627 
L 565.325216 374.960679 
L 566.95939 370.214438 
L 564.255764 369.219683 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dcd286"/>
    <path d="M 740.484535 435.289419 
L 743.266635 438.267183 
L 744.87365 437.967933 
L 742.094292 434.918587 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #69e17b"/>
    <path d="M 778.260622 471.308992 
L 781.048265 473.759382 
L 782.610938 474.197222 
L 779.826707 471.697511 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c47d"/>
    <path d="M 634.366185 329.228552 
L 637.131876 331.688545 
L 638.786005 328.477773 
L 636.019927 325.952833 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #94765f"/>
    <path d="M 743.266635 438.267183 
L 746.048993 441.211895 
L 747.653197 440.983014 
L 744.87365 437.967933 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #61df79"/>
    <path d="M 586.565362 341.636361 
L 589.291625 343.029366 
L 590.933942 338.686873 
L 588.206325 337.248711 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a68d69"/>
    <path d="M 649.866123 339.049159 
L 652.63957 341.800331 
L 654.293786 338.981828 
L 651.520338 336.159383 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a48b68"/>
    <path d="M 612.864193 326.773676 
L 615.614696 328.750262 
L 617.265621 325.010654 
L 614.514234 322.977624 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8e6e5c"/>
    <path d="M 746.048993 441.211895 
L 748.831667 444.121492 
L 750.432991 443.9617 
L 747.653197 440.983014 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #55dd77"/>
    <path d="M 799.346864 487.878459 
L 802.142412 489.926307 
L 803.677658 490.581672 
L 800.885589 488.499892 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a8d0"/>
    <path d="M 568.593627 365.486644 
L 571.301753 366.537147 
L 572.937714 361.868969 
L 570.228025 360.780688 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cec07f"/>
    <path d="M 837.550496 510.052759 
L 840.371193 511.228892 
L 841.859487 511.865112 
L 839.0418 510.682571 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0f7be1"/>
    <path d="M 580.564395 349.261936 
L 583.28472 350.529841 
L 584.924847 346.06445 
L 582.203071 344.753496 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b29c6f"/>
    <path d="M 627.187426 327.911231 
L 629.94873 330.208985 
L 631.602344 326.817506 
L 628.840464 324.457084 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #90715d"/>
    <path d="M 553.39872 392.421383 
L 556.091626 393.241354 
L 557.724914 388.420507 
L 555.030392 387.56915 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fcfb97"/>
    <path d="M 748.831667 444.121492 
L 751.614717 446.993949 
L 753.213096 446.901901 
L 750.432991 443.9617 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #4ddb75"/>
    <path d="M 574.573879 357.22579 
L 577.288128 358.379197 
L 578.926105 353.804916 
L 576.210335 352.610934 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c0ae77"/>
    <path d="M 637.131876 331.688545 
L 639.899306 334.19576 
L 641.553773 331.051746 
L 638.786005 328.477773 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #987b61"/>
    <path d="M 560.990567 378.796705 
L 563.691003 379.721967 
L 565.325216 374.960679 
L 562.623167 374.000627 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e4dc8a"/>
    <path d="M 590.933942 338.686873 
L 593.664609 340.166912 
L 595.308663 335.914916 
L 592.57669 334.387335 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a28867"/>
    <path d="M 652.63957 341.800331 
L 655.414181 344.590852 
L 657.068332 341.845003 
L 654.293786 338.981828 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a8906a"/>
    <path d="M 620.019483 327.095875 
L 622.775707 329.231955 
L 624.428234 325.663647 
L 621.671267 323.467739 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8e6e5c"/>
    <path d="M 781.048265 473.759382 
L 783.837194 476.151402 
L 785.396427 476.636668 
L 782.610938 474.197222 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c088"/>
    <path d="M 814.868535 498.180315 
L 817.672602 499.892791 
L 819.187893 500.606418 
L 816.387201 498.871618 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0296fc"/>
    <path d="M 608.467414 328.751885 
L 611.214325 330.622354 
L 612.864193 326.773676 
L 610.116291 324.84811 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #92735e"/>
    <path d="M 847.507022 513.969182 
L 850.337185 514.890243 
L 851.814994 515.443592 
L 848.987618 514.522356 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1373d9"/>
    <path d="M 751.614717 446.993949 
L 754.398208 449.827283 
L 755.993578 449.801568 
L 753.213096 446.901901 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #45da74"/>
    <path d="M 827.607647 505.335031 
L 830.420622 506.750267 
L 831.920332 507.447362 
L 829.110557 506.019021 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0888ee"/>
    <path d="M 595.308663 335.914916 
L 598.043623 337.486613 
L 599.689325 333.329647 
L 596.953119 331.708212 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9c8064"/>
    <path d="M 655.414181 344.590852 
L 658.189861 347.418662 
L 659.843878 344.746771 
L 657.068332 341.845003 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ae976d"/>
    <path d="M 604.075676 330.939447 
L 606.818783 332.706772 
L 608.467414 328.751885 
L 605.723219 326.931034 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #94765f"/>
    <path d="M 599.689325 333.329647 
L 602.42844 334.99724 
L 604.075676 330.939447 
L 601.335387 329.220118 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #987b61"/>
    <path d="M 566.95939 370.214438 
L 569.665908 371.226984 
L 571.301753 366.537147 
L 568.593627 365.486644 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d6cb83"/>
    <path d="M 639.899306 334.19576 
L 642.668368 336.748421 
L 644.32312 333.672906 
L 641.553773 331.051746 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9c8064"/>
    <path d="M 754.398208 449.827283 
L 757.182209 452.61955 
L 758.774511 452.658696 
L 755.993578 449.801568 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #39d771"/>
    <path d="M 584.924847 346.06445 
L 587.649687 347.41176 
L 589.291625 343.029366 
L 586.565362 341.636361 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ae976d"/>
    <path d="M 658.189861 347.418662 
L 660.966517 350.281668 
L 662.620329 347.684956 
L 659.843878 344.746771 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b29c6f"/>
    <path d="M 629.94873 330.208985 
L 632.712036 332.555355 
L 634.366185 329.228552 
L 631.602344 326.817506 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #94765f"/>
    <path d="M 559.357854 383.604479 
L 562.056644 384.494899 
L 563.691003 379.721967 
L 560.990567 378.796705 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ece78f"/>
    <path d="M 615.614696 328.750262 
L 618.367691 330.776652 
L 620.019483 327.095875 
L 617.265621 325.010654 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #90715d"/>
    <path d="M 783.837194 476.151402 
L 786.627518 478.483565 
L 788.183289 479.014317 
L 785.396427 476.636668 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00bc94"/>
    <path d="M 802.142412 489.926307 
L 804.94008 491.904475 
L 806.471849 492.591687 
L 803.677658 490.581672 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a4dc"/>
    <path d="M 572.937714 361.868969 
L 575.650388 362.981516 
L 577.288128 358.379197 
L 574.573879 357.22579 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c8b97b"/>
    <path d="M 578.926105 353.804916 
L 581.644918 355.029368 
L 583.28472 350.529841 
L 580.564395 349.261936 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #baa774"/>
    <path d="M 660.966517 350.281668 
L 663.744062 353.177743 
L 665.397594 350.657349 
L 662.620329 347.684956 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b6a272"/>
    <path d="M 622.775707 329.231955 
L 625.534187 331.417508 
L 627.187426 327.911231 
L 624.428234 325.663647 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #92735e"/>
    <path d="M 757.182209 452.61955 
L 759.966795 455.368853 
L 761.555971 455.471326 
L 758.774511 452.658696 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #31d670"/>
    <path d="M 642.668368 336.748421 
L 645.438958 339.34471 
L 647.093939 336.339357 
L 644.32312 333.672906 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a08566"/>
    <path d="M 589.291625 343.029366 
L 592.020912 344.461235 
L 593.664609 340.166912 
L 590.933942 338.686873 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a8906a"/>
    <path d="M 663.744062 353.177743 
L 666.52241 356.104732 
L 668.175586 353.661712 
L 665.397594 350.657349 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bca975"/>
    <path d="M 611.214325 330.622354 
L 613.963848 332.541341 
L 615.614696 328.750262 
L 612.864193 326.773676 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #94765f"/>
    <path d="M 565.325216 374.960679 
L 568.030085 375.935129 
L 569.665908 371.226984 
L 566.95939 370.214438 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dcd286"/>
    <path d="M 666.52241 356.104732 
L 669.301483 359.06045 
L 670.954222 356.695775 
L 668.175586 353.661712 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c0ae77"/>
    <path d="M 759.966795 455.368853 
L 762.752042 458.073337 
L 764.338039 458.237545 
L 761.555971 455.471326 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #29d46e"/>
    <path d="M 557.724914 388.420507 
L 560.422026 389.276072 
L 562.056644 384.494899 
L 559.357854 383.604479 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f4f193"/>
    <path d="M 632.712036 332.555355 
L 635.477236 334.948733 
L 637.131876 331.688545 
L 634.366185 329.228552 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #987b61"/>
    <path d="M 817.672602 499.892791 
L 820.479492 501.528612 
L 821.991432 502.262431 
L 819.187893 500.606418 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0393f9"/>
    <path d="M 593.664609 340.166912 
L 596.398245 341.688146 
L 598.043623 337.486613 
L 595.308663 335.914916 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a28867"/>
    <path d="M 669.301483 359.06045 
L 672.081202 362.042688 
L 673.733425 359.757246 
L 670.954222 356.695775 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c6b67a"/>
    <path d="M 645.438958 339.34471 
L 648.210974 341.982766 
L 649.866123 339.049159 
L 647.093939 336.339357 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a48b68"/>
    <path d="M 786.627518 478.483565 
L 789.419352 480.754441 
L 790.971642 481.328699 
L 788.183289 479.014317 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b8a0"/>
    <path d="M 606.818783 332.706772 
L 609.564611 334.521103 
L 611.214325 330.622354 
L 608.467414 328.751885 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #967960"/>
    <path d="M 583.28472 350.529841 
L 586.008072 351.830969 
L 587.649687 347.41176 
L 584.924847 346.06445 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b49f70"/>
    <path d="M 571.301753 366.537147 
L 574.012804 367.608593 
L 575.650388 362.981516 
L 572.937714 361.868969 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cec07f"/>
    <path d="M 672.081202 362.042688 
L 674.861497 365.049215 
L 676.51312 362.843806 
L 673.733425 359.757246 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cabb7c"/>
    <path d="M 598.043623 337.486613 
L 600.781483 339.101644 
L 602.42844 334.99724 
L 599.689325 333.329647 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9e8365"/>
    <path d="M 602.42844 334.99724 
L 605.170373 336.710108 
L 606.818783 332.706772 
L 604.075676 330.939447 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9a7e62"/>
    <path d="M 840.371193 511.228892 
L 843.195838 512.320162 
L 844.681175 512.96074 
L 841.859487 511.865112 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0f7be1"/>
    <path d="M 618.367691 330.776652 
L 621.123075 332.85158 
L 622.775707 329.231955 
L 620.019483 327.095875 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #94765f"/>
    <path d="M 577.288128 358.379197 
L 580.005371 359.559837 
L 581.644918 355.029368 
L 578.926105 353.804916 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c0ae77"/>
    <path d="M 625.534187 331.417508 
L 628.294814 333.6511 
L 629.94873 330.208985 
L 627.187426 327.911231 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #967960"/>
    <path d="M 674.861497 365.049215 
L 677.6423 368.077778 
L 679.293238 365.953119 
L 676.51312 362.843806 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d0c380"/>
    <path d="M 762.752042 458.073337 
L 765.538033 460.731196 
L 767.1208 460.955489 
L 764.338039 458.237545 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #21d36d"/>
    <path d="M 677.6423 368.077778 
L 680.423548 371.126108 
L 682.073714 369.082829 
L 679.293238 365.953119 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d4c882"/>
    <path d="M 804.94008 491.904475 
L 807.739999 493.811876 
L 809.2683 494.528819 
L 806.471849 492.591687 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a2e2"/>
    <path d="M 830.420622 506.750267 
L 833.237042 508.084019 
L 834.733594 508.792108 
L 831.920332 507.447362 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0a86ec"/>
    <path d="M 563.691003 379.721967 
L 566.394183 380.658224 
L 568.030085 375.935129 
L 565.325216 374.960679 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e4dc8a"/>
    <path d="M 680.423548 371.126108 
L 683.205182 374.19192 
L 684.854489 372.230565 
L 682.073714 369.082829 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dad085"/>
    <path d="M 648.210974 341.982766 
L 650.984315 344.660686 
L 652.63957 341.800331 
L 649.866123 339.049159 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a8906a"/>
    <path d="M 556.091626 393.241354 
L 558.787034 394.062087 
L 560.422026 389.276072 
L 557.724914 388.420507 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fcfb97"/>
    <path d="M 635.477236 334.948733 
L 638.244224 337.38747 
L 639.899306 334.19576 
L 637.131876 331.688545 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9c8064"/>
    <path d="M 683.205182 374.19192 
L 685.987148 377.272916 
L 687.635506 375.393941 
L 684.854489 372.230565 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e0d788"/>
    <path d="M 685.987148 377.272916 
L 688.769397 380.366789 
L 690.416717 378.570565 
L 687.635506 375.393941 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e4dc8a"/>
    <path d="M 587.649687 347.41176 
L 590.377523 348.794884 
L 592.020912 344.461235 
L 589.291625 343.029366 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ae976d"/>
    <path d="M 688.769397 380.366789 
L 691.551884 383.471224 
L 693.198074 381.758033 
L 690.416717 378.570565 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eae48e"/>
    <path d="M 691.551884 383.471224 
L 694.334571 386.583899 
L 695.979539 384.953939 
L 693.198074 381.758033 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f0ec91"/>
    <path d="M 765.538033 460.731196 
L 768.324854 463.340671 
L 769.904344 463.623343 
L 767.1208 460.955489 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #19d16b"/>
    <path d="M 613.963848 332.541341 
L 616.715883 334.507694 
L 618.367691 330.776652 
L 615.614696 328.750262 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #967960"/>
    <path d="M 694.334571 386.583899 
L 697.117421 389.702491 
L 698.761075 388.155872 
L 695.979539 384.953939 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f4f193"/>
    <path d="M 697.117421 389.702491 
L 699.900405 392.824676 
L 701.542653 391.361422 
L 698.761075 388.155872 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #faf996"/>
    <path d="M 569.665908 371.226984 
L 572.375288 372.257132 
L 574.012804 367.608593 
L 571.301753 366.537147 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d6cb83"/>
    <path d="M 789.419352 480.754441 
L 792.212812 482.96266 
L 793.761606 483.578404 
L 790.971642 481.328699 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b6a7"/>
    <path d="M 699.900405 392.824676 
L 702.683499 395.948131 
L 704.324247 394.568181 
L 701.542653 391.361422 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 650.984315 344.660686 
L 653.758888 347.37653 
L 655.414181 344.590852 
L 652.63957 341.800331 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ac956c"/>
    <path d="M 702.683499 395.948131 
L 705.466682 399.070539 
L 707.105838 397.773746 
L 704.324247 394.568181 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f5fd97"/>
    <path d="M 705.466682 399.070539 
L 708.249939 402.189587 
L 709.887411 400.975722 
L 707.105838 397.773746 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e9fb95"/>
    <path d="M 581.644918 355.029368 
L 584.366718 356.283878 
L 586.008072 351.830969 
L 583.28472 350.529841 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #baa774"/>
    <path d="M 708.249939 402.189587 
L 711.033262 405.302975 
L 712.668956 404.171721 
L 709.887411 400.975722 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e1f993"/>
    <path d="M 628.294814 333.6511 
L 631.057482 335.931246 
L 632.712036 332.555355 
L 629.94873 330.208985 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #987b61"/>
    <path d="M 711.033262 405.302975 
L 713.816644 408.40841 
L 715.45047 407.359368 
L 712.668956 404.171721 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d5f791"/>
    <path d="M 575.650388 362.981516 
L 578.366006 364.118034 
L 580.005371 359.559837 
L 577.288128 358.379197 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c8b97b"/>
    <path d="M 592.020912 344.461235 
L 594.753148 345.931338 
L 596.398245 341.688146 
L 593.664609 340.166912 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #aa926b"/>
    <path d="M 621.123075 332.85158 
L 623.880743 334.973728 
L 625.534187 331.417508 
L 622.775707 329.231955 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #967960"/>
    <path d="M 638.244224 337.38747 
L 641.012898 339.869866 
L 642.668368 336.748421 
L 639.899306 334.19576 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a08566"/>
    <path d="M 713.816644 408.40841 
L 716.600086 411.503614 
L 718.231953 410.536305 
L 715.45047 407.359368 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c9f48e"/>
    <path d="M 562.056644 384.494899 
L 564.758099 385.392905 
L 566.394183 380.658224 
L 563.691003 379.721967 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ece78f"/>
    <path d="M 609.564611 334.521103 
L 612.313063 336.3814 
L 613.963848 332.541341 
L 611.214325 330.622354 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9a7e62"/>
    <path d="M 716.600086 411.503614 
L 719.383594 414.586327 
L 721.013412 413.700187 
L 718.231953 410.536305 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c1f38d"/>
    <path d="M 653.758888 347.37653 
L 656.534599 350.128321 
L 658.189861 347.418662 
L 655.414181 344.590852 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b09a6e"/>
    <path d="M 768.324854 463.340671 
L 771.112594 465.900051 
L 772.688764 466.239343 
L 769.904344 463.623343 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #11cf69"/>
    <path d="M 719.383594 414.586327 
L 722.167177 417.654302 
L 723.794857 416.848688 
L 721.013412 413.700187 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b5f08a"/>
    <path d="M 820.479492 501.528612 
L 823.289349 503.087011 
L 824.797967 503.838873 
L 821.991432 502.262431 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0393f9"/>
    <path d="M 596.398245 341.688146 
L 599.134769 343.249849 
L 600.781483 339.101644 
L 598.043623 337.486613 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a48b68"/>
    <path d="M 722.167177 417.654302 
L 724.950851 420.705316 
L 726.576306 419.979506 
L 723.794857 416.848688 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a9ee88"/>
    <path d="M 605.170373 336.710108 
L 607.91503 338.467322 
L 609.564611 334.521103 
L 606.818783 332.706772 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9c8064"/>
    <path d="M 600.781483 339.101644 
L 603.522156 340.759186 
L 605.170373 336.710108 
L 602.42844 334.99724 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a08566"/>
    <path d="M 724.950851 420.705316 
L 727.734637 423.737167 
L 729.35778 423.090358 
L 726.576306 419.979506 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a1ec86"/>
    <path d="M 807.739999 493.811876 
L 810.542306 495.647488 
L 812.067149 496.392021 
L 809.2683 494.528819 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a0e8"/>
    <path d="M 656.534599 350.128321 
L 659.311359 352.914048 
L 660.966517 350.281668 
L 658.189861 347.418662 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b6a272"/>
    <path d="M 568.030085 375.935129 
L 570.737749 376.923826 
L 572.375288 372.257132 
L 569.665908 371.226984 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ded587"/>
    <path d="M 727.734637 423.737167 
L 730.518558 426.747676 
L 732.139306 426.178989 
L 729.35778 423.090358 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #95ea84"/>
    <path d="M 586.008072 351.830969 
L 588.734389 353.164828 
L 590.377523 348.794884 
L 587.649687 347.41176 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b6a272"/>
    <path d="M 641.012898 339.869866 
L 643.783155 342.394181 
L 645.438958 339.34471 
L 642.668368 336.748421 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a48b68"/>
    <path d="M 631.057482 335.931246 
L 633.822089 338.256415 
L 635.477236 334.948733 
L 632.712036 332.555355 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9c8064"/>
    <path d="M 792.212812 482.96266 
L 795.008017 485.106914 
L 796.553305 485.762085 
L 793.761606 483.578404 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b2b2"/>
    <path d="M 730.518558 426.747676 
L 733.302646 429.73469 
L 734.920915 429.243171 
L 732.139306 426.178989 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8de882"/>
    <path d="M 616.715883 334.507694 
L 619.47033 336.520215 
L 621.123075 332.85158 
L 618.367691 330.776652 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #987b61"/>
    <path d="M 771.112594 465.900051 
L 773.901348 468.407679 
L 775.474156 468.801778 
L 772.688764 466.239343 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #09ce68"/>
    <path d="M 560.422026 389.276072 
L 563.121725 390.135811 
L 564.758099 385.392905 
L 562.056644 384.494899 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f4f193"/>
    <path d="M 574.012804 367.608593 
L 576.726744 368.700728 
L 578.366006 364.118034 
L 575.650388 362.981516 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d0c380"/>
    <path d="M 580.005371 359.559837 
L 582.725559 360.767344 
L 584.366718 356.283878 
L 581.644918 355.029368 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c2b178"/>
    <path d="M 659.311359 352.914048 
L 662.089082 355.731671 
L 663.744062 353.177743 
L 660.966517 350.281668 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #baa774"/>
    <path d="M 733.302646 429.73469 
L 736.086934 432.696085 
L 737.702644 432.280704 
L 734.920915 429.243171 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #81e680"/>
    <path d="M 623.880743 334.973728 
L 626.640593 337.141734 
L 628.294814 333.6511 
L 625.534187 331.417508 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9a7e62"/>
    <path d="M 843.195838 512.320162 
L 846.024587 513.3263 
L 847.507022 513.969182 
L 844.681175 512.96074 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0f7be1"/>
    <path d="M 833.237042 508.084019 
L 836.057058 509.335796 
L 837.550496 510.052759 
L 834.733594 508.792108 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0b83e9"/>
    <path d="M 736.086934 432.696085 
L 738.871464 435.629768 
L 740.484535 435.289419 
L 737.702644 432.280704 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #79e47e"/>
    <path d="M 590.377523 348.794884 
L 593.108286 350.213245 
L 594.753148 345.931338 
L 592.020912 344.461235 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b09a6e"/>
    <path d="M 662.089082 355.731671 
L 664.867687 358.579117 
L 666.52241 356.104732 
L 663.744062 353.177743 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #beac76"/>
    <path d="M 643.783155 342.394181 
L 646.554897 344.958634 
L 648.210974 341.982766 
L 645.438958 339.34471 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a8906a"/>
    <path d="M 612.313063 336.3814 
L 615.064044 338.286579 
L 616.715883 334.507694 
L 613.963848 332.541341 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9c8064"/>
    <path d="M 566.394183 380.658224 
L 569.100091 381.605362 
L 570.737749 376.923826 
L 568.030085 375.935129 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e4dc8a"/>
    <path d="M 738.871464 435.629768 
L 741.656278 438.533674 
L 743.266635 438.267183 
L 740.484535 435.289419 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #6de27c"/>
    <path d="M 773.901348 468.407679 
L 776.691212 470.861947 
L 778.260622 471.308992 
L 775.474156 468.801778 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #01cc66"/>
    <path d="M 633.822089 338.256415 
L 636.588533 340.625031 
L 638.244224 337.38747 
L 635.477236 334.948733 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a08566"/>
    <path d="M 664.867687 358.579117 
L 667.647097 361.454288 
L 669.301483 359.06045 
L 666.52241 356.104732 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c2b178"/>
    <path d="M 594.753148 345.931338 
L 597.488258 347.439005 
L 599.134769 343.249849 
L 596.398245 341.688146 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #aa926b"/>
    <path d="M 558.787034 394.062087 
L 561.484947 394.883582 
L 563.121725 390.135811 
L 560.422026 389.276072 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fcfb97"/>
    <path d="M 607.91503 338.467322 
L 610.662321 340.267906 
L 612.313063 336.3814 
L 609.564611 334.521103 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9e8365"/>
    <path d="M 741.656278 438.533674 
L 744.441425 441.405776 
L 746.048993 441.211895 
L 743.266635 438.267183 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #65e07a"/>
    <path d="M 584.366718 356.283878 
L 587.091449 357.568005 
L 588.734389 353.164828 
L 586.008072 351.830969 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bca975"/>
    <path d="M 572.375288 372.257132 
L 575.0875 373.30467 
L 576.726744 368.700728 
L 574.012804 367.608593 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d6cb83"/>
    <path d="M 795.008017 485.106914 
L 797.80509 487.185954 
L 799.346864 487.878459 
L 796.553305 485.762085 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b0b9"/>
    <path d="M 599.134769 343.249849 
L 601.8741 344.851255 
L 603.522156 340.759186 
L 600.781483 339.101644 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a68d69"/>
    <path d="M 667.647097 361.454288 
L 670.427236 364.355063 
L 672.081202 362.042688 
L 669.301483 359.06045 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c8b97b"/>
    <path d="M 646.554897 344.958634 
L 649.32803 347.561403 
L 650.984315 344.660686 
L 648.210974 341.982766 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ac956c"/>
    <path d="M 603.522156 340.759186 
L 606.265556 342.458368 
L 607.91503 338.467322 
L 605.170373 336.710108 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a28867"/>
    <path d="M 619.47033 336.520215 
L 622.227088 338.577655 
L 623.880743 334.973728 
L 621.123075 332.85158 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9c8064"/>
    <path d="M 823.289349 503.087011 
L 826.102318 504.567292 
L 827.607647 505.335031 
L 824.797967 503.838873 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0490f6"/>
    <path d="M 810.542306 495.647488 
L 813.347134 497.410358 
L 814.868535 498.180315 
L 812.067149 496.392021 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #009eef"/>
    <path d="M 578.366006 364.118034 
L 581.084523 365.278206 
L 582.725559 360.767344 
L 580.005371 359.559837 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c8b97b"/>
    <path d="M 626.640593 337.141734 
L 629.402523 339.354184 
L 631.057482 335.931246 
L 628.294814 333.6511 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9e8365"/>
    <path d="M 744.441425 441.405776 
L 747.22696 444.244079 
L 748.831667 444.121492 
L 746.048993 441.211895 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #5ddf79"/>
    <path d="M 670.427236 364.355063 
L 673.208036 367.279298 
L 674.861497 365.049215 
L 672.081202 362.042688 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ccbe7d"/>
    <path d="M 564.758099 385.392905 
L 567.462212 386.298422 
L 569.100091 381.605362 
L 566.394183 380.658224 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ece78f"/>
    <path d="M 776.691212 470.861947 
L 779.482286 473.261302 
L 781.048265 473.759382 
L 778.260622 471.308992 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c970"/>
    <path d="M 636.588533 340.625031 
L 639.356713 343.035474 
L 641.012898 339.869866 
L 638.244224 337.38747 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a48b68"/>
    <path d="M 673.208036 367.279298 
L 675.98943 370.224827 
L 677.6423 368.077778 
L 674.861497 365.049215 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d2c581"/>
    <path d="M 649.32803 347.561403 
L 652.10246 350.20063 
L 653.758888 347.37653 
L 650.984315 344.660686 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b09a6e"/>
    <path d="M 588.734389 353.164828 
L 591.463607 354.530893 
L 593.108286 350.213245 
L 590.377523 348.794884 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b6a272"/>
    <path d="M 747.22696 444.244079 
L 750.012939 447.046627 
L 751.614717 446.993949 
L 748.831667 444.121492 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #51dc76"/>
    <path d="M 675.98943 370.224827 
L 678.771357 373.189471 
L 680.423548 371.126108 
L 677.6423 368.077778 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d6cb83"/>
    <path d="M 615.064044 338.286579 
L 617.817458 340.235507 
L 619.47033 336.520215 
L 616.715883 334.507694 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9e8365"/>
    <path d="M 570.737749 376.923826 
L 573.448186 377.926603 
L 575.0875 373.30467 
L 572.375288 372.257132 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ded587"/>
    <path d="M 678.771357 373.189471 
L 681.553761 376.171032 
L 683.205182 374.19192 
L 680.423548 371.126108 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dcd286"/>
    <path d="M 750.012939 447.046627 
L 752.799425 449.811501 
L 754.398208 449.827283 
L 751.614717 446.993949 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #49db75"/>
    <path d="M 582.725559 360.767344 
L 585.448641 362.001328 
L 587.091449 357.568005 
L 584.366718 356.283878 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c2b178"/>
    <path d="M 629.402523 339.354184 
L 632.166435 341.609624 
L 633.822089 338.256415 
L 631.057482 335.931246 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a08566"/>
    <path d="M 652.10246 350.20063 
L 654.878099 352.874423 
L 656.534599 350.128321 
L 653.758888 347.37653 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b49f70"/>
    <path d="M 593.108286 350.213245 
L 595.841906 351.66623 
L 597.488258 347.439005 
L 594.753148 345.931338 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b29c6f"/>
    <path d="M 681.553761 376.171032 
L 684.336587 379.167303 
L 685.987148 377.272916 
L 683.205182 374.19192 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e0d788"/>
    <path d="M 576.726744 368.700728 
L 579.443535 369.813281 
L 581.084523 365.278206 
L 578.366006 364.118034 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d0c380"/>
    <path d="M 622.227088 338.577655 
L 624.986062 340.678722 
L 626.640593 337.141734 
L 623.880743 334.973728 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9e8365"/>
    <path d="M 797.80509 487.185954 
L 800.604155 489.198595 
L 802.142412 489.926307 
L 799.346864 487.878459 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00acc4"/>
    <path d="M 610.662321 340.267906 
L 613.412155 342.11084 
L 615.064044 338.286579 
L 612.313063 336.3814 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a28867"/>
    <path d="M 639.356713 343.035474 
L 642.126533 345.486082 
L 643.783155 342.394181 
L 641.012898 339.869866 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a68d69"/>
    <path d="M 684.336587 379.167303 
L 687.11979 382.176065 
L 688.769397 380.366789 
L 685.987148 377.272916 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e6df8b"/>
    <path d="M 779.482286 473.261302 
L 782.274675 475.604247 
L 783.837194 476.151402 
L 781.048265 473.759382 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c47d"/>
    <path d="M 563.121725 390.135811 
L 565.824008 390.999687 
L 567.462212 386.298422 
L 564.758099 385.392905 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f4f193"/>
    <path d="M 836.057058 509.335796 
L 838.88082 510.505185 
L 840.371193 511.228892 
L 837.550496 510.052759 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0b83e9"/>
    <path d="M 597.488258 347.439005 
L 600.226167 348.98353 
L 601.8741 344.851255 
L 599.134769 343.249849 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ac956c"/>
    <path d="M 752.799425 449.811501 
L 755.586485 452.536824 
L 757.182209 452.61955 
L 754.398208 449.827283 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #41d973"/>
    <path d="M 687.11979 382.176065 
L 689.903323 385.19509 
L 691.551884 383.471224 
L 688.769397 380.366789 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eae48e"/>
    <path d="M 606.265556 342.458368 
L 609.011598 344.19828 
L 610.662321 340.267906 
L 607.91503 338.467322 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a48b68"/>
    <path d="M 601.8741 344.851255 
L 604.616159 346.491556 
L 606.265556 342.458368 
L 603.522156 340.759186 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a8906a"/>
    <path d="M 654.878099 352.874423 
L 657.654861 355.580856 
L 659.311359 352.914048 
L 656.534599 350.128321 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b8a473"/>
    <path d="M 846.024587 513.3263 
L 848.857592 514.247115 
L 850.337185 514.890243 
L 847.507022 513.969182 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0f7be1"/>
    <path d="M 813.347134 497.410358 
L 816.154624 499.099601 
L 817.672602 499.892791 
L 814.868535 498.180315 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #009cf4"/>
    <path d="M 689.903323 385.19509 
L 692.68715 388.222149 
L 694.334571 386.583899 
L 691.551884 383.471224 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f0ec91"/>
    <path d="M 692.68715 388.222149 
L 695.471236 391.255004 
L 697.117421 389.702491 
L 694.334571 386.583899 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f4f193"/>
    <path d="M 587.091449 357.568005 
L 589.819055 358.881277 
L 591.463607 354.530893 
L 588.734389 353.164828 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #beac76"/>
    <path d="M 569.100091 381.605362 
L 571.808709 382.563258 
L 573.448186 377.926603 
L 570.737749 376.923826 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e6df8b"/>
    <path d="M 695.471236 391.255004 
L 698.255551 394.291422 
L 699.900405 392.824676 
L 697.117421 389.702491 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #faf996"/>
    <path d="M 826.102318 504.567292 
L 828.918546 505.968834 
L 830.420622 506.750267 
L 827.607647 505.335031 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #068ef4"/>
    <path d="M 755.586485 452.536824 
L 758.37419 455.22076 
L 759.966795 455.368853 
L 757.182209 452.61955 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #39d771"/>
    <path d="M 642.126533 345.486082 
L 644.897899 347.975155 
L 646.554897 344.958634 
L 643.783155 342.394181 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #aa926b"/>
    <path d="M 617.817458 340.235507 
L 620.57321 342.227007 
L 622.227088 338.577655 
L 619.47033 336.520215 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a08566"/>
    <path d="M 632.166435 341.609624 
L 634.93223 343.906553 
L 636.588533 340.625031 
L 633.822089 338.256415 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a48b68"/>
    <path d="M 698.255551 394.291422 
L 701.040071 397.329167 
L 702.683499 395.948131 
L 699.900405 392.824676 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 657.654861 355.580856 
L 660.432662 358.317974 
L 662.089082 355.731671 
L 659.311359 352.914048 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bca975"/>
    <path d="M 581.084523 365.278206 
L 583.805897 366.461688 
L 585.448641 362.001328 
L 582.725559 360.767344 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cabb7c"/>
    <path d="M 575.0875 373.30467 
L 577.802513 374.369375 
L 579.443535 369.813281 
L 576.726744 368.700728 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d8cd84"/>
    <path d="M 701.040071 397.329167 
L 703.824776 400.366009 
L 705.466682 399.070539 
L 702.683499 395.948131 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f5fd97"/>
    <path d="M 561.484947 394.883582 
L 564.185367 395.705841 
L 565.824008 390.999687 
L 563.121725 390.135811 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fcfb97"/>
    <path d="M 782.274675 475.604247 
L 785.068484 477.889336 
L 786.627518 478.483565 
L 783.837194 476.151402 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c088"/>
    <path d="M 624.986062 340.678722 
L 627.747153 342.82208 
L 629.402523 339.354184 
L 626.640593 337.141734 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a28867"/>
    <path d="M 703.824776 400.366009 
L 706.609651 403.399725 
L 708.249939 402.189587 
L 705.466682 399.070539 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e9fb95"/>
    <path d="M 591.463607 354.530893 
L 594.195664 355.928607 
L 595.841906 351.66623 
L 593.108286 350.213245 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b8a473"/>
    <path d="M 800.604155 489.198595 
L 803.405337 491.143717 
L 804.94008 491.904475 
L 802.142412 489.926307 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00aacb"/>
    <path d="M 706.609651 403.399725 
L 709.394685 406.428097 
L 711.033262 405.302975 
L 708.249939 402.189587 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e1f993"/>
    <path d="M 660.432662 358.317974 
L 663.211424 361.083792 
L 664.867687 358.579117 
L 662.089082 355.731671 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c0ae77"/>
    <path d="M 758.37419 455.22076 
L 761.162613 457.861517 
L 762.752042 458.073337 
L 759.966795 455.368853 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #31d670"/>
    <path d="M 613.412155 342.11084 
L 616.164443 343.99506 
L 617.817458 340.235507 
L 615.064044 338.286579 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a48b68"/>
    <path d="M 709.394685 406.428097 
L 712.179874 409.448922 
L 713.816644 408.40841 
L 711.033262 405.302975 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d5f791"/>
    <path d="M 644.897899 347.975155 
L 647.670719 350.500955 
L 649.32803 347.561403 
L 646.554897 344.958634 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ae976d"/>
    <path d="M 712.179874 409.448922 
L 714.965217 412.460005 
L 716.600086 411.503614 
L 713.816644 408.40841 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cdf58f"/>
    <path d="M 567.462212 386.298422 
L 570.168972 387.211368 
L 571.808709 382.563258 
L 569.100091 381.605362 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ece78f"/>
    <path d="M 595.841906 351.66623 
L 598.578315 353.153189 
L 600.226167 348.98353 
L 597.488258 347.439005 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b29c6f"/>
    <path d="M 634.93223 343.906553 
L 637.699815 346.243432 
L 639.356713 343.035474 
L 636.588533 340.625031 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a8906a"/>
    <path d="M 663.211424 361.083792 
L 665.991071 363.876301 
L 667.647097 361.454288 
L 664.867687 358.579117 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c6b67a"/>
    <path d="M 714.965217 412.460005 
L 717.750719 415.459169 
L 719.383594 414.586327 
L 716.600086 411.503614 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c1f38d"/>
    <path d="M 609.011598 344.19828 
L 611.760195 345.977968 
L 613.412155 342.11084 
L 610.662321 340.267906 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a68d69"/>
    <path d="M 585.448641 362.001328 
L 588.174569 363.261369 
L 589.819055 358.881277 
L 587.091449 357.568005 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c4b379"/>
    <path d="M 761.162613 457.861517 
L 763.951834 460.457347 
L 765.538033 460.731196 
L 762.752042 458.073337 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #29d46e"/>
    <path d="M 600.226167 348.98353 
L 602.966801 350.564165 
L 604.616159 346.491556 
L 601.8741 344.851255 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ae976d"/>
    <path d="M 604.616159 346.491556 
L 607.360864 348.169905 
L 609.011598 344.19828 
L 606.265556 342.458368 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #aa926b"/>
    <path d="M 717.750719 415.459169 
L 720.536388 418.444253 
L 722.167177 417.654302 
L 719.383594 414.586327 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b9f18b"/>
    <path d="M 573.448186 377.926603 
L 576.161372 378.943279 
L 577.802513 374.369375 
L 575.0875 373.30467 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ded587"/>
    <path d="M 620.57321 342.227007 
L 623.33121 344.25986 
L 624.986062 340.678722 
L 622.227088 338.577655 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a48b68"/>
    <path d="M 785.068484 477.889336 
L 787.863824 480.115185 
L 789.419352 480.754441 
L 786.627518 478.483565 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00be8f"/>
    <path d="M 816.154624 499.099601 
L 818.964913 500.7144 
L 820.479492 501.528612 
L 817.672602 499.892791 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #009afa"/>
    <path d="M 579.443535 369.813281 
L 582.163141 370.94596 
L 583.805897 366.461688 
L 581.084523 365.278206 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d0c380"/>
    <path d="M 665.991071 363.876301 
L 668.771533 366.693468 
L 670.427236 364.355063 
L 667.647097 361.454288 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cabb7c"/>
    <path d="M 627.747153 342.82208 
L 630.510268 345.006347 
L 632.166435 341.609624 
L 629.402523 339.354184 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a48b68"/>
    <path d="M 647.670719 350.500955 
L 650.444904 353.061708 
L 652.10246 350.20063 
L 649.32803 347.561403 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b29c6f"/>
    <path d="M 720.536388 418.444253 
L 723.322238 421.413114 
L 724.950851 420.705316 
L 722.167177 417.654302 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #adef89"/>
    <path d="M 838.88082 510.505185 
L 841.708478 511.591849 
L 843.195838 512.320162 
L 840.371193 511.228892 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0b83e9"/>
    <path d="M 723.322238 421.413114 
L 726.108289 424.363631 
L 727.734637 423.737167 
L 724.950851 420.705316 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a5ed87"/>
    <path d="M 668.771533 366.693468 
L 671.552741 369.533239 
L 673.208036 367.279298 
L 670.427236 364.355063 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cec07f"/>
    <path d="M 589.819055 358.881277 
L 592.549478 360.223194 
L 594.195664 355.928607 
L 591.463607 354.530893 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #beac76"/>
    <path d="M 637.699815 346.243432 
L 640.469096 348.618681 
L 642.126533 345.486082 
L 639.356713 343.035474 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #aa926b"/>
    <path d="M 763.951834 460.457347 
L 766.741935 463.00655 
L 768.324854 463.340671 
L 765.538033 460.731196 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #21d36d"/>
    <path d="M 565.824008 390.999687 
L 568.528871 391.867659 
L 570.168972 387.211368 
L 567.462212 386.298422 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f4f193"/>
    <path d="M 803.405337 491.143717 
L 806.208767 493.020261 
L 807.739999 493.811876 
L 804.94008 491.904475 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a8d0"/>
    <path d="M 726.108289 424.363631 
L 728.894564 427.293705 
L 730.518558 426.747676 
L 727.734637 423.737167 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #99eb85"/>
    <path d="M 828.918546 505.968834 
L 831.738178 507.291086 
L 833.237042 508.084019 
L 830.420622 506.750267 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #068ef4"/>
    <path d="M 616.164443 343.99506 
L 618.919095 345.919462 
L 620.57321 342.227007 
L 617.817458 340.235507 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a68d69"/>
    <path d="M 650.444904 353.061708 
L 653.220369 355.655608 
L 654.878099 352.874423 
L 652.10246 350.20063 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b6a272"/>
    <path d="M 671.552741 369.533239 
L 674.334632 372.393538 
L 675.98943 370.224827 
L 673.208036 367.279298 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d4c882"/>
    <path d="M 728.894564 427.293705 
L 731.681092 430.201263 
L 733.302646 429.73469 
L 730.518558 426.747676 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #91e983"/>
    <path d="M 571.808709 382.563258 
L 574.520022 383.531778 
L 576.161372 378.943279 
L 573.448186 377.926603 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e6df8b"/>
    <path d="M 583.805897 366.461688 
L 586.530082 367.668117 
L 588.174569 363.261369 
L 585.448641 362.001328 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cabb7c"/>
    <path d="M 594.195664 355.928607 
L 596.930498 357.357381 
L 598.578315 353.153189 
L 595.841906 351.66623 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #baa774"/>
    <path d="M 787.863824 480.115185 
L 790.660808 482.280463 
L 792.212812 482.96266 
L 789.419352 480.754441 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00bb9b"/>
    <path d="M 674.334632 372.393538 
L 677.117146 375.272275 
L 678.771357 373.189471 
L 675.98943 370.224827 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d8cd84"/>
    <path d="M 630.510268 345.006347 
L 633.275315 347.230104 
L 634.93223 343.906553 
L 632.166435 341.609624 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a8906a"/>
    <path d="M 623.33121 344.25986 
L 626.091364 346.332803 
L 627.747153 342.82208 
L 624.986062 340.678722 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a68d69"/>
    <path d="M 577.802513 374.369375 
L 580.520298 375.451002 
L 582.163141 370.94596 
L 579.443535 369.813281 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d8cd84"/>
    <path d="M 611.760195 345.977968 
L 614.511264 347.796437 
L 616.164443 343.99506 
L 613.412155 342.11084 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #aa926b"/>
    <path d="M 731.681092 430.201263 
L 734.467904 433.084257 
L 736.086934 432.696085 
L 733.302646 429.73469 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #85e781"/>
    <path d="M 766.741935 463.00655 
L 769.533003 465.507471 
L 771.112594 465.900051 
L 768.324854 463.340671 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #19d16b"/>
    <path d="M 653.220369 355.655608 
L 655.997029 358.280815 
L 657.654861 355.580856 
L 654.878099 352.874423 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #baa774"/>
    <path d="M 640.469096 348.618681 
L 643.239982 351.03068 
L 644.897899 347.975155 
L 642.126533 345.486082 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ae976d"/>
    <path d="M 677.117146 375.272275 
L 679.900228 378.167346 
L 681.553761 376.171032 
L 678.771357 373.189471 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dcd286"/>
    <path d="M 598.578315 353.153189 
L 601.317445 354.673439 
L 602.966801 350.564165 
L 600.226167 348.98353 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b49f70"/>
    <path d="M 564.185367 395.705841 
L 566.888299 396.528865 
L 568.528871 391.867659 
L 565.824008 390.999687 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fcfb97"/>
    <path d="M 607.360864 348.169905 
L 610.108136 349.885416 
L 611.760195 345.977968 
L 609.011598 344.19828 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ac956c"/>
    <path d="M 734.467904 433.084257 
L 737.255039 435.940669 
L 738.871464 435.629768 
L 736.086934 432.696085 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #7de57f"/>
    <path d="M 602.966801 350.564165 
L 605.710086 352.180128 
L 607.360864 348.169905 
L 604.616159 346.491556 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b09a6e"/>
    <path d="M 679.900228 378.167346 
L 682.683826 381.076633 
L 684.336587 379.167303 
L 681.553761 376.171032 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e2da89"/>
    <path d="M 818.964913 500.7144 
L 821.778142 502.25401 
L 823.289349 503.087011 
L 820.479492 501.528612 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0098fe"/>
    <path d="M 588.174569 363.261369 
L 590.90329 364.547022 
L 592.549478 360.223194 
L 589.819055 358.881277 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c6b67a"/>
    <path d="M 655.997029 358.280815 
L 658.774807 360.935462 
L 660.432662 358.317974 
L 657.654861 355.580856 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c0ae77"/>
    <path d="M 737.255039 435.940669 
L 740.042539 438.768512 
L 741.656278 438.533674 
L 738.871464 435.629768 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #75e37d"/>
    <path d="M 682.683826 381.076633 
L 685.467894 383.998008 
L 687.11979 382.176065 
L 684.336587 379.167303 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e6df8b"/>
    <path d="M 570.168972 387.211368 
L 572.878368 388.131654 
L 574.520022 383.531778 
L 571.808709 382.563258 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ece78f"/>
    <path d="M 618.919095 345.919462 
L 621.676023 347.882897 
L 623.33121 344.25986 
L 620.57321 342.227007 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a8906a"/>
    <path d="M 769.533003 465.507471 
L 772.325127 467.958506 
L 773.901348 468.407679 
L 771.112594 465.900051 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #11cf69"/>
    <path d="M 633.275315 347.230104 
L 636.042202 349.491891 
L 637.699815 346.243432 
L 634.93223 343.906553 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ac956c"/>
    <path d="M 806.208767 493.020261 
L 809.014573 494.827234 
L 810.542306 495.647488 
L 807.739999 493.811876 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a6d7"/>
    <path d="M 643.239982 351.03068 
L 646.012386 353.477777 
L 647.670719 350.500955 
L 644.897899 347.975155 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b29c6f"/>
    <path d="M 582.163141 370.94596 
L 584.885526 372.098453 
L 586.530082 367.668117 
L 583.805897 366.461688 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d2c581"/>
    <path d="M 685.467894 383.998008 
L 688.25239 386.929337 
L 689.903323 385.19509 
L 687.11979 382.176065 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ece78f"/>
    <path d="M 790.660808 482.280463 
L 793.459551 484.383903 
L 795.008017 485.106914 
L 792.212812 482.96266 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b8a0"/>
    <path d="M 576.161372 378.943279 
L 578.877284 379.973661 
L 580.520298 375.451002 
L 577.802513 374.369375 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ded587"/>
    <path d="M 740.042539 438.768512 
L 742.830449 441.565828 
L 744.441425 441.405776 
L 741.656278 438.533674 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #6de27c"/>
    <path d="M 626.091364 346.332803 
L 628.853583 348.444534 
L 630.510268 345.006347 
L 627.747153 342.82208 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #aa926b"/>
    <path d="M 658.774807 360.935462 
L 661.553625 363.617655 
L 663.211424 361.083792 
L 660.432662 358.317974 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c4b379"/>
    <path d="M 592.549478 360.223194 
L 595.282664 361.593225 
L 596.930498 357.357381 
L 594.195664 355.928607 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c0ae77"/>
    <path d="M 688.25239 386.929337 
L 691.037275 389.868478 
L 692.68715 388.222149 
L 689.903323 385.19509 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f0ec91"/>
    <path d="M 614.511264 347.796437 
L 617.264722 349.652655 
L 618.919095 345.919462 
L 616.164443 343.99506 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ac956c"/>
    <path d="M 841.708478 511.591849 
L 844.540184 512.595524 
L 846.024587 513.3263 
L 843.195838 512.320162 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0b83e9"/>
    <path d="M 691.037275 389.868478 
L 693.822517 392.813288 
L 695.471236 391.255004 
L 692.68715 388.222149 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f6f394"/>
    <path d="M 742.830449 441.565828 
L 745.618822 444.330697 
L 747.22696 444.244079 
L 744.441425 441.405776 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #61df79"/>
    <path d="M 831.738178 507.291086 
L 834.561361 508.533571 
L 836.057058 509.335796 
L 833.237042 508.084019 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #078bf1"/>
    <path d="M 772.325127 467.958506 
L 775.118401 470.358101 
L 776.691212 470.861947 
L 773.901348 468.407679 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #09ce68"/>
    <path d="M 646.012386 353.477777 
L 648.786223 355.958284 
L 650.444904 353.061708 
L 647.670719 350.500955 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b6a272"/>
    <path d="M 596.930498 357.357381 
L 599.668046 358.816592 
L 601.317445 354.673439 
L 598.578315 353.153189 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #baa774"/>
    <path d="M 661.553625 363.617655 
L 664.333412 366.325474 
L 665.991071 363.876301 
L 663.211424 361.083792 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c8b97b"/>
    <path d="M 693.822517 392.813288 
L 696.608085 395.761622 
L 698.255551 394.291422 
L 695.471236 391.255004 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #faf996"/>
    <path d="M 568.528871 391.867659 
L 571.236311 392.739685 
L 572.878368 388.131654 
L 570.168972 387.211368 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f4f193"/>
    <path d="M 610.108136 349.885416 
L 612.857897 351.637164 
L 614.511264 347.796437 
L 611.760195 345.977968 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ae976d"/>
    <path d="M 636.042202 349.491891 
L 638.81084 351.790208 
L 640.469096 348.618681 
L 637.699815 346.243432 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ae976d"/>
    <path d="M 586.530082 367.668117 
L 589.257037 368.897102 
L 590.90329 364.547022 
L 588.174569 363.261369 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ccbe7d"/>
    <path d="M 601.317445 354.673439 
L 604.059227 356.226261 
L 605.710086 352.180128 
L 602.966801 350.564165 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b6a272"/>
    <path d="M 605.710086 352.180128 
L 608.455947 353.830601 
L 610.108136 349.885416 
L 607.360864 348.169905 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b29c6f"/>
    <path d="M 745.618822 444.330697 
L 748.407712 447.061231 
L 750.012939 447.046627 
L 747.22696 444.244079 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #59de78"/>
    <path d="M 696.608085 395.761622 
L 699.393956 398.711336 
L 701.040071 397.329167 
L 698.255551 394.291422 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 621.676023 347.882897 
L 624.435143 349.884182 
L 626.091364 346.332803 
L 623.33121 344.25986 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ac956c"/>
    <path d="M 574.520022 383.531778 
L 577.234012 384.510777 
L 578.877284 379.973661 
L 576.161372 378.943279 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e6df8b"/>
    <path d="M 580.520298 375.451002 
L 583.240824 376.549293 
L 584.885526 372.098453 
L 582.163141 370.94596 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d8cd84"/>
    <path d="M 628.853583 348.444534 
L 631.61778 350.593712 
L 633.275315 347.230104 
L 630.510268 345.006347 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ac956c"/>
    <path d="M 664.333412 366.325474 
L 667.114098 369.056976 
L 668.771533 366.693468 
L 665.991071 363.876301 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ccbe7d"/>
    <path d="M 699.393956 398.711336 
L 702.180111 401.660291 
L 703.824776 400.366009 
L 701.040071 397.329167 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f5fd97"/>
    <path d="M 793.459551 484.383903 
L 796.26017 486.424292 
L 797.80509 487.185954 
L 795.008017 485.106914 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b4ac"/>
    <path d="M 648.786223 355.958284 
L 651.56141 358.470481 
L 653.220369 355.655608 
L 650.444904 353.061708 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #baa774"/>
    <path d="M 809.014573 494.827234 
L 811.822888 496.563711 
L 813.347134 497.410358 
L 810.542306 495.647488 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a4dc"/>
    <path d="M 821.778142 502.25401 
L 824.594451 503.717752 
L 826.102318 504.567292 
L 823.289349 503.087011 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0296fc"/>
    <path d="M 702.180111 401.660291 
L 704.966534 404.60635 
L 706.609651 403.399725 
L 703.824776 400.366009 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #edfb95"/>
    <path d="M 748.407712 447.061231 
L 751.197178 449.75558 
L 752.799425 449.811501 
L 750.012939 447.046627 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #51dc76"/>
    <path d="M 775.118401 470.358101 
L 777.912921 472.704753 
L 779.482286 473.261302 
L 776.691212 470.861947 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #01cc66"/>
    <path d="M 590.90329 364.547022 
L 593.634757 365.857818 
L 595.282664 361.593225 
L 592.549478 360.223194 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c6b67a"/>
    <path d="M 667.114098 369.056976 
L 669.895617 371.810199 
L 671.552741 369.533239 
L 668.771533 366.693468 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d0c380"/>
    <path d="M 704.966534 404.60635 
L 707.753214 407.547388 
L 709.394685 406.428097 
L 706.609651 403.399725 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e1f993"/>
    <path d="M 638.81084 351.790208 
L 641.581145 354.123524 
L 643.239982 351.03068 
L 640.469096 348.618681 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b29c6f"/>
    <path d="M 566.888299 396.528865 
L 569.593746 397.352655 
L 571.236311 392.739685 
L 568.528871 391.867659 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fcfb97"/>
    <path d="M 617.264722 349.652655 
L 620.020486 351.545549 
L 621.676023 347.882897 
L 618.919095 345.919462 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ae976d"/>
    <path d="M 707.753214 407.547388 
L 710.540146 410.481287 
L 712.179874 409.448922 
L 709.394685 406.428097 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d9f791"/>
    <path d="M 751.197178 449.75558 
L 753.987285 452.411934 
L 755.586485 452.536824 
L 752.799425 449.811501 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #49db75"/>
    <path d="M 651.56141 358.470481 
L 654.337868 361.012618 
L 655.997029 358.280815 
L 653.220369 355.655608 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #beac76"/>
    <path d="M 669.895617 371.810199 
L 672.677909 374.583159 
L 674.334632 372.393538 
L 671.552741 369.533239 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d6cb83"/>
    <path d="M 584.885526 372.098453 
L 587.610652 373.270426 
L 589.257037 368.897102 
L 586.530082 367.668117 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d2c581"/>
    <path d="M 595.282664 361.593225 
L 598.018555 362.990811 
L 599.668046 358.816592 
L 596.930498 357.357381 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c2b178"/>
    <path d="M 572.878368 388.131654 
L 575.590391 389.059184 
L 577.234012 384.510777 
L 574.520022 383.531778 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eee990"/>
    <path d="M 710.540146 410.481287 
L 713.32733 413.405941 
L 714.965217 412.460005 
L 712.179874 409.448922 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cdf58f"/>
    <path d="M 631.61778 350.593712 
L 634.383869 352.778958 
L 636.042202 349.491891 
L 633.275315 347.230104 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b09a6e"/>
    <path d="M 624.435143 349.884182 
L 627.196369 351.922092 
L 628.853583 348.444534 
L 626.091364 346.332803 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ae976d"/>
    <path d="M 612.857897 351.637164 
L 615.610069 353.424188 
L 617.264722 349.652655 
L 614.511264 347.796437 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b09a6e"/>
    <path d="M 578.877284 379.973661 
L 581.595898 381.017543 
L 583.240824 376.549293 
L 580.520298 375.451002 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e0d788"/>
    <path d="M 777.912921 472.704753 
L 780.708787 474.997012 
L 782.274675 475.604247 
L 779.482286 473.261302 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c970"/>
    <path d="M 599.668046 358.816592 
L 602.408246 360.305589 
L 604.059227 356.226261 
L 601.317445 354.673439 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bca975"/>
    <path d="M 713.32733 413.405941 
L 716.114767 416.319258 
L 717.750719 415.459169 
L 714.965217 412.460005 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c5f38d"/>
    <path d="M 672.677909 374.583159 
L 675.460916 377.373861 
L 677.117146 375.272275 
L 674.334632 372.393538 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dad085"/>
    <path d="M 796.26017 486.424292 
L 799.062785 488.400482 
L 800.604155 489.198595 
L 797.80509 487.185954 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b2b2"/>
    <path d="M 608.455947 353.830601 
L 611.204313 355.514729 
L 612.857897 351.637164 
L 610.108136 349.885416 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b49f70"/>
    <path d="M 641.581145 354.123524 
L 644.353031 356.490269 
L 646.012386 353.477777 
L 643.239982 351.03068 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b6a272"/>
    <path d="M 753.987285 452.411934 
L 756.778099 455.028523 
L 758.37419 455.22076 
L 755.586485 452.536824 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #41d973"/>
    <path d="M 604.059227 356.226261 
L 606.803594 357.810907 
L 608.455947 353.830601 
L 605.710086 352.180128 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b8a473"/>
    <path d="M 834.561361 508.533571 
L 837.388243 509.695886 
L 838.88082 510.505185 
L 836.057058 509.335796 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #078bf1"/>
    <path d="M 654.337868 361.012618 
L 657.115521 363.582918 
L 658.774807 360.935462 
L 655.997029 358.280815 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c2b178"/>
    <path d="M 716.114767 416.319258 
L 718.902468 419.219164 
L 720.536388 418.444253 
L 717.750719 415.459169 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b9f18b"/>
    <path d="M 675.460916 377.373861 
L 678.244585 380.18029 
L 679.900228 378.167346 
L 677.117146 375.272275 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ded587"/>
    <path d="M 844.540184 512.595524 
L 847.376086 513.516025 
L 848.857592 514.247115 
L 846.024587 513.3263 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0c80e6"/>
    <path d="M 589.257037 368.897102 
L 591.986718 370.148234 
L 593.634757 365.857818 
L 590.90329 364.547022 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ccbe7d"/>
    <path d="M 811.822888 496.563711 
L 814.633846 498.22883 
L 816.154624 499.099601 
L 813.347134 497.410358 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a2e2"/>
    <path d="M 718.902468 419.219164 
L 721.690443 422.103599 
L 723.322238 421.413114 
L 720.536388 418.444253 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b1ef89"/>
    <path d="M 620.020486 351.545549 
L 622.778475 353.47401 
L 624.435143 349.884182 
L 621.676023 347.882897 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b09a6e"/>
    <path d="M 571.236311 392.739685 
L 573.946325 393.615717 
L 575.590391 389.059184 
L 572.878368 388.131654 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f4f193"/>
    <path d="M 756.778099 455.028523 
L 759.569692 457.603616 
L 761.162613 457.861517 
L 758.37419 455.22076 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #39d771"/>
    <path d="M 634.383869 352.778958 
L 637.151764 354.998859 
L 638.81084 351.790208 
L 636.042202 349.491891 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b49f70"/>
    <path d="M 678.244585 380.18029 
L 681.028865 383.000424 
L 682.683826 381.076633 
L 679.900228 378.167346 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e2da89"/>
    <path d="M 657.115521 363.582918 
L 659.894295 366.179577 
L 661.553625 363.617655 
L 658.774807 360.935462 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c6b67a"/>
    <path d="M 583.240824 376.549293 
L 585.964061 377.663972 
L 587.610652 373.270426 
L 584.885526 372.098453 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dad085"/>
    <path d="M 824.594451 503.717752 
L 827.413983 505.10502 
L 828.918546 505.968834 
L 826.102318 504.567292 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0296fc"/>
    <path d="M 721.690443 422.103599 
L 724.478712 424.970527 
L 726.108289 424.363631 
L 723.322238 421.413114 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a9ee88"/>
    <path d="M 644.353031 356.490269 
L 647.126417 358.888843 
L 648.786223 355.958284 
L 646.012386 353.477777 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #baa774"/>
    <path d="M 780.708787 474.997012 
L 783.506102 477.233481 
L 785.068484 477.889336 
L 782.274675 475.604247 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c677"/>
    <path d="M 577.234012 384.510777 
L 579.950663 385.500101 
L 581.595898 381.017543 
L 578.877284 379.973661 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e6df8b"/>
    <path d="M 627.196369 351.922092 
L 629.959617 353.995366 
L 631.61778 350.593712 
L 628.853583 348.444534 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b29c6f"/>
    <path d="M 593.634757 365.857818 
L 596.368919 367.19326 
L 598.018555 362.990811 
L 595.282664 361.593225 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c8b97b"/>
    <path d="M 681.028865 383.000424 
L 683.813711 385.832227 
L 685.467894 383.998008 
L 682.683826 381.076633 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e8e28d"/>
    <path d="M 615.610069 353.424188 
L 618.364576 355.245491 
L 620.020486 351.545549 
L 617.264722 349.652655 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b49f70"/>
    <path d="M 724.478712 424.970527 
L 727.267296 427.81793 
L 728.894564 427.293705 
L 726.108289 424.363631 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9deb85"/>
    <path d="M 799.062785 488.400482 
L 801.86752 490.311384 
L 803.405337 491.143717 
L 800.604155 489.198595 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b0b9"/>
    <path d="M 759.569692 457.603616 
L 762.36214 460.135529 
L 763.951834 460.457347 
L 761.162613 457.861517 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #31d670"/>
    <path d="M 659.894295 366.179577 
L 662.674121 368.800766 
L 664.333412 366.325474 
L 661.553625 363.617655 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cabb7c"/>
    <path d="M 598.018555 362.990811 
L 600.757095 364.415367 
L 602.408246 360.305589 
L 599.668046 358.816592 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c2b178"/>
    <path d="M 683.813711 385.832227 
L 686.599083 388.673659 
L 688.25239 386.929337 
L 685.467894 383.998008 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ece78f"/>
    <path d="M 727.267296 427.81793 
L 730.056221 430.643816 
L 731.681092 430.201263 
L 728.894564 427.293705 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #95ea84"/>
    <path d="M 611.204313 355.514729 
L 613.95511 357.231625 
L 615.610069 353.424188 
L 612.857897 351.637164 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b6a272"/>
    <path d="M 647.126417 358.888843 
L 649.901225 361.317616 
L 651.56141 358.470481 
L 648.786223 355.958284 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #beac76"/>
    <path d="M 587.610652 373.270426 
L 590.338481 374.461529 
L 591.986718 370.148234 
L 589.257037 368.897102 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d4c882"/>
    <path d="M 602.408246 360.305589 
L 605.151036 361.82369 
L 606.803594 357.810907 
L 604.059227 356.226261 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #beac76"/>
    <path d="M 637.151764 354.998859 
L 639.921384 357.251965 
L 641.581145 354.123524 
L 638.81084 351.790208 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b6a272"/>
    <path d="M 569.593746 397.352655 
L 572.301712 398.177211 
L 573.946325 393.615717 
L 571.236311 392.739685 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fcfb97"/>
    <path d="M 606.803594 357.810907 
L 609.550478 359.426592 
L 611.204313 355.514729 
L 608.455947 353.830601 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #baa774"/>
    <path d="M 686.599083 388.673659 
L 689.384943 391.522672 
L 691.037275 389.868478 
L 688.25239 386.929337 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f0ec91"/>
    <path d="M 622.778475 353.47401 
L 625.53861 355.436894 
L 627.196369 351.922092 
L 624.435143 349.884182 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b49f70"/>
    <path d="M 783.506102 477.233481 
L 786.304972 479.412818 
L 787.863824 480.115185 
L 785.068484 477.889336 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c382"/>
    <path d="M 730.056221 430.643816 
L 732.845519 433.446218 
L 734.467904 433.084257 
L 731.681092 430.201263 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8de882"/>
    <path d="M 662.674121 368.800766 
L 665.454933 371.444636 
L 667.114098 369.056976 
L 664.333412 366.325474 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cec07f"/>
    <path d="M 575.590391 389.059184 
L 578.305031 389.993857 
L 579.950663 385.500101 
L 577.234012 384.510777 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eee990"/>
    <path d="M 581.595898 381.017543 
L 584.31719 382.074705 
L 585.964061 377.663972 
L 583.240824 376.549293 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e0d788"/>
    <path d="M 629.959617 353.995366 
L 632.724807 356.102709 
L 634.383869 352.778958 
L 631.61778 350.593712 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b49f70"/>
    <path d="M 762.36214 460.135529 
L 765.155522 462.62262 
L 766.741935 463.00655 
L 763.951834 460.457347 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #29d46e"/>
    <path d="M 689.384943 391.522672 
L 692.171259 394.377216 
L 693.822517 392.813288 
L 691.037275 389.868478 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f6f394"/>
    <path d="M 814.633846 498.22883 
L 817.447581 499.821798 
L 818.964913 500.7144 
L 816.154624 499.099601 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a0e8"/>
    <path d="M 732.845519 433.446218 
L 735.635225 436.223195 
L 737.255039 435.940669 
L 734.467904 433.084257 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #81e680"/>
    <path d="M 591.986718 370.148234 
L 594.71908 371.421078 
L 596.368919 367.19326 
L 593.634757 365.857818 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cec07f"/>
    <path d="M 837.388243 509.695886 
L 840.218969 510.7777 
L 841.708478 511.591849 
L 838.88082 510.505185 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0888ee"/>
    <path d="M 649.901225 361.317616 
L 652.677378 363.774928 
L 654.337868 361.012618 
L 651.56141 358.470481 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c2b178"/>
    <path d="M 692.171259 394.377216 
L 694.958002 397.235239 
L 696.608085 395.761622 
L 693.822517 392.813288 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #faf996"/>
    <path d="M 665.454933 371.444636 
L 668.236667 374.109318 
L 669.895617 371.810199 
L 667.114098 369.056976 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d2c581"/>
    <path d="M 618.364576 355.245491 
L 621.121341 357.100044 
L 622.778475 353.47401 
L 620.020486 351.545549 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b6a272"/>
    <path d="M 639.921384 357.251965 
L 642.69265 359.536796 
L 644.353031 356.490269 
L 641.581145 354.123524 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #baa774"/>
    <path d="M 801.86752 490.311384 
L 804.674497 492.155973 
L 806.208767 493.020261 
L 803.405337 491.143717 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00acc4"/>
    <path d="M 735.635225 436.223195 
L 738.425379 438.972836 
L 740.042539 438.768512 
L 737.255039 435.940669 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #79e47e"/>
    <path d="M 694.958002 397.235239 
L 697.745148 400.094689 
L 699.393956 398.711336 
L 696.608085 395.761622 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 827.413983 505.10502 
L 830.236879 506.415278 
L 831.738178 507.291086 
L 828.918546 505.968834 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0393f9"/>
    <path d="M 765.155522 462.62262 
L 767.94992 465.063294 
L 769.533003 465.507471 
L 766.741935 463.00655 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #21d36d"/>
    <path d="M 596.368919 367.19326 
L 599.105726 368.552827 
L 600.757095 364.415367 
L 598.018555 362.990811 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c8b97b"/>
    <path d="M 585.964061 377.663972 
L 588.689979 378.794745 
L 590.338481 374.461529 
L 587.610652 373.270426 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dad085"/>
    <path d="M 668.236667 374.109318 
L 671.019265 376.792923 
L 672.677909 374.583159 
L 669.895617 371.810199 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d8cd84"/>
    <path d="M 786.304972 479.412818 
L 789.105504 481.533737 
L 790.660808 482.280463 
L 787.863824 480.115185 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c088"/>
    <path d="M 613.95511 357.231625 
L 616.708268 358.980369 
L 618.364576 355.245491 
L 615.610069 353.424188 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b8a473"/>
    <path d="M 625.53861 355.436894 
L 628.300812 357.433022 
L 629.959617 353.995366 
L 627.196369 351.922092 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b6a272"/>
    <path d="M 573.946325 393.615717 
L 576.658909 394.495705 
L 578.305031 389.993857 
L 575.590391 389.059184 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f4f193"/>
    <path d="M 632.724807 356.102709 
L 635.491859 358.24279 
L 637.151764 354.998859 
L 634.383869 352.778958 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b8a473"/>
    <path d="M 697.745148 400.094689 
L 700.532678 402.95352 
L 702.180111 401.660291 
L 699.393956 398.711336 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f5fd97"/>
    <path d="M 652.677378 363.774928 
L 655.454805 366.259093 
L 657.115521 363.582918 
L 654.337868 361.012618 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c4b379"/>
    <path d="M 579.950663 385.500101 
L 582.669957 386.499585 
L 584.31719 382.074705 
L 581.595898 381.017543 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e6df8b"/>
    <path d="M 738.425379 438.972836 
L 741.216024 441.693261 
L 742.830449 441.565828 
L 740.042539 438.768512 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #71e37d"/>
    <path d="M 600.757095 364.415367 
L 603.49823 365.866277 
L 605.151036 361.82369 
L 602.408246 360.305589 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c4b379"/>
    <path d="M 609.550478 359.426592 
L 612.299813 361.072503 
L 613.95511 357.231625 
L 611.204313 355.514729 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bca975"/>
    <path d="M 605.151036 361.82369 
L 607.896355 363.370183 
L 609.550478 359.426592 
L 606.803594 357.810907 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c0ae77"/>
    <path d="M 700.532678 402.95352 
L 703.320578 405.809687 
L 704.966534 404.60635 
L 702.180111 401.660291 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #edfb95"/>
    <path d="M 671.019265 376.792923 
L 673.802671 379.493549 
L 675.460916 377.373861 
L 672.677909 374.583159 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dcd286"/>
    <path d="M 642.69265 359.536796 
L 645.465484 361.85184 
L 647.126417 358.888843 
L 644.353031 356.490269 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #beac76"/>
    <path d="M 767.94992 465.063294 
L 770.745421 467.456001 
L 772.325127 467.958506 
L 769.533003 465.507471 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #19d16b"/>
    <path d="M 590.338481 374.461529 
L 593.068978 375.671391 
L 594.71908 371.421078 
L 591.986718 370.148234 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d4c882"/>
    <path d="M 741.216024 441.693261 
L 744.00721 444.382621 
L 745.618822 444.330697 
L 742.830449 441.565828 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #69e17b"/>
    <path d="M 703.320578 405.809687 
L 706.108836 408.661155 
L 707.753214 407.547388 
L 704.966534 404.60635 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e1f993"/>
    <path d="M 655.454805 366.259093 
L 658.233435 368.768398 
L 659.894295 366.179577 
L 657.115521 363.582918 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c8b97b"/>
    <path d="M 621.121341 357.100044 
L 623.88029 358.98678 
L 625.53861 355.436894 
L 622.778475 353.47401 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b8a473"/>
    <path d="M 817.447581 499.821798 
L 820.264229 501.341887 
L 821.778142 502.25401 
L 818.964913 500.7144 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #009eef"/>
    <path d="M 673.802671 379.493549 
L 676.586833 382.209277 
L 678.244585 380.18029 
L 675.460916 377.373861 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e0d788"/>
    <path d="M 706.108836 408.661155 
L 708.897446 411.505897 
L 710.540146 410.481287 
L 707.753214 407.547388 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d9f791"/>
    <path d="M 635.491859 358.24279 
L 638.260695 360.414248 
L 639.921384 357.251965 
L 637.151764 354.998859 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #baa774"/>
    <path d="M 572.301712 398.177211 
L 575.012201 399.002536 
L 576.658909 394.495705 
L 573.946325 393.615717 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fcfb97"/>
    <path d="M 804.674497 492.155973 
L 807.483844 493.933285 
L 809.014573 494.827234 
L 806.208767 493.020261 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00aacb"/>
    <path d="M 584.31719 382.074705 
L 587.041136 383.144914 
L 588.689979 378.794745 
L 585.964061 377.663972 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e0d788"/>
    <path d="M 789.105504 481.533737 
L 791.907812 483.59501 
L 793.459551 484.383903 
L 790.660808 482.280463 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00bc94"/>
    <path d="M 744.00721 444.382621 
L 746.798988 447.039102 
L 748.407712 447.061231 
L 745.618822 444.330697 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #61df79"/>
    <path d="M 628.300812 357.433022 
L 631.065006 359.461182 
L 632.724807 356.102709 
L 629.959617 353.995366 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b8a473"/>
    <path d="M 578.305031 389.993857 
L 581.022277 390.935564 
L 582.669957 386.499585 
L 579.950663 385.500101 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eee990"/>
    <path d="M 594.71908 371.421078 
L 597.454082 372.715181 
L 599.105726 368.552827 
L 596.368919 367.19326 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cec07f"/>
    <path d="M 645.465484 361.85184 
L 648.239811 364.195557 
L 649.901225 361.317616 
L 647.126417 358.888843 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c0ae77"/>
    <path d="M 676.586833 382.209277 
L 679.371704 384.93818 
L 681.028865 383.000424 
L 678.244585 380.18029 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e4dc8a"/>
    <path d="M 708.897446 411.505897 
L 711.686407 414.341897 
L 713.32733 413.405941 
L 710.540146 410.481287 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d1f690"/>
    <path d="M 616.708268 358.980369 
L 619.463717 360.760007 
L 621.121341 357.100044 
L 618.364576 355.245491 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #baa774"/>
    <path d="M 770.745421 467.456001 
L 773.542114 469.799242 
L 775.118401 470.358101 
L 772.325127 467.958506 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #11cf69"/>
    <path d="M 658.233435 368.768398 
L 661.013201 371.301111 
L 662.674121 368.800766 
L 659.894295 366.179577 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ccbe7d"/>
    <path d="M 840.218969 510.7777 
L 843.053686 511.778758 
L 844.540184 512.595524 
L 841.708478 511.591849 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0888ee"/>
    <path d="M 599.105726 368.552827 
L 601.845129 369.935975 
L 603.49823 365.866277 
L 600.757095 364.415367 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cabb7c"/>
    <path d="M 711.686407 414.341897 
L 714.475721 417.167152 
L 716.114767 416.319258 
L 713.32733 413.405941 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c5f38d"/>
    <path d="M 746.798988 447.039102 
L 749.591415 449.660925 
L 751.197178 449.75558 
L 748.407712 447.061231 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #59de78"/>
    <path d="M 830.236879 506.415278 
L 833.063283 507.648061 
L 834.561361 508.533571 
L 831.738178 507.291086 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0393f9"/>
    <path d="M 612.299813 361.072503 
L 615.051534 362.747796 
L 616.708268 358.980369 
L 613.95511 357.231625 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #beac76"/>
    <path d="M 679.371704 384.93818 
L 682.15724 387.678318 
L 683.813711 385.832227 
L 681.028865 383.000424 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e8e28d"/>
    <path d="M 603.49823 365.866277 
L 606.241904 367.342904 
L 607.896355 363.370183 
L 605.151036 361.82369 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c6b67a"/>
    <path d="M 607.896355 363.370183 
L 610.644144 364.944328 
L 612.299813 361.072503 
L 609.550478 359.426592 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c2b178"/>
    <path d="M 588.689979 378.794745 
L 591.418546 379.941307 
L 593.068978 375.671391 
L 590.338481 374.461529 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dad085"/>
    <path d="M 661.013201 371.301111 
L 663.79404 373.855475 
L 665.454933 371.444636 
L 662.674121 368.800766 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d0c380"/>
    <path d="M 638.260695 360.414248 
L 641.03124 362.615692 
L 642.69265 359.536796 
L 639.921384 357.251965 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #beac76"/>
    <path d="M 714.475721 417.167152 
L 717.265396 419.979674 
L 718.902468 419.219164 
L 716.114767 416.319258 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bdf28c"/>
    <path d="M 623.88029 358.98678 
L 626.64135 360.904603 
L 628.300812 357.433022 
L 625.53861 355.436894 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #baa774"/>
    <path d="M 648.239811 364.195557 
L 651.01556 366.566379 
L 652.677378 363.774928 
L 649.901225 361.317616 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c4b379"/>
    <path d="M 682.15724 387.678318 
L 684.9434 390.427746 
L 686.599083 388.673659 
L 683.813711 385.832227 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eee990"/>
    <path d="M 582.669957 386.499585 
L 585.391877 387.509056 
L 587.041136 383.144914 
L 584.31719 382.074705 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e8e28d"/>
    <path d="M 791.907812 483.59501 
L 794.712007 485.595465 
L 796.26017 486.424292 
L 793.459551 484.383903 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00bb9b"/>
    <path d="M 773.542114 469.799242 
L 776.340091 472.091566 
L 777.912921 472.704753 
L 775.118401 470.358101 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #09ce68"/>
    <path d="M 631.065006 359.461182 
L 633.831115 361.520129 
L 635.491859 358.24279 
L 632.724807 356.102709 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bca975"/>
    <path d="M 749.591415 449.660925 
L 752.384553 452.246348 
L 753.987285 452.411934 
L 751.197178 449.75558 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #51dc76"/>
    <path d="M 576.658909 394.495705 
L 579.37406 395.379594 
L 581.022277 390.935564 
L 578.305031 389.993857 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f4f193"/>
    <path d="M 717.265396 419.979674 
L 720.055444 422.777492 
L 721.690443 422.103599 
L 718.902468 419.219164 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b5f08a"/>
    <path d="M 807.483844 493.933285 
L 810.295687 495.64242 
L 811.822888 496.563711 
L 809.014573 494.827234 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a8d0"/>
    <path d="M 820.264229 501.341887 
L 823.083927 502.78844 
L 824.594451 503.717752 
L 821.778142 502.25401 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #009cf4"/>
    <path d="M 593.068978 375.671391 
L 595.802106 376.899623 
L 597.454082 372.715181 
L 594.71908 371.421078 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d6cb83"/>
    <path d="M 684.9434 390.427746 
L 687.73015 393.184511 
L 689.384943 391.522672 
L 686.599083 388.673659 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f2ee92"/>
    <path d="M 663.79404 373.855475 
L 666.575891 376.429716 
L 668.236667 374.109318 
L 665.454933 371.444636 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d4c882"/>
    <path d="M 619.463717 360.760007 
L 622.221387 362.569555 
L 623.88029 358.98678 
L 621.121341 357.100044 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #beac76"/>
    <path d="M 720.055444 422.777492 
L 722.84588 425.558654 
L 724.478712 424.970527 
L 721.690443 422.103599 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #adef89"/>
    <path d="M 651.01556 366.566379 
L 653.79266 368.962712 
L 655.454805 366.259093 
L 652.677378 363.774928 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c8b97b"/>
    <path d="M 752.384553 452.246348 
L 755.178465 454.793667 
L 756.778099 455.028523 
L 753.987285 452.411934 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #49db75"/>
    <path d="M 641.03124 362.615692 
L 643.803421 364.845698 
L 645.465484 361.85184 
L 642.69265 359.536796 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c0ae77"/>
    <path d="M 687.73015 393.184511 
L 690.517457 395.946659 
L 692.171259 394.377216 
L 689.384943 391.522672 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f6f394"/>
    <path d="M 597.454082 372.715181 
L 600.19168 374.030066 
L 601.845129 369.935975 
L 599.105726 368.552827 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d0c380"/>
    <path d="M 587.041136 383.144914 
L 589.767714 384.227924 
L 591.418546 379.941307 
L 588.689979 378.794745 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e2da89"/>
    <path d="M 776.340091 472.091566 
L 779.13945 474.331573 
L 780.708787 474.997012 
L 777.912921 472.704753 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #05cd67"/>
    <path d="M 722.84588 425.558654 
L 725.636725 428.321228 
L 727.267296 427.81793 
L 724.478712 424.970527 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a1ec86"/>
    <path d="M 666.575891 376.429716 
L 669.358699 379.022042 
L 671.019265 376.792923 
L 668.236667 374.109318 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d8cd84"/>
    <path d="M 615.051534 362.747796 
L 617.805577 364.451595 
L 619.463717 360.760007 
L 616.708268 358.980369 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c0ae77"/>
    <path d="M 626.64135 360.904603 
L 629.40445 362.852386 
L 631.065006 359.461182 
L 628.300812 357.433022 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #beac76"/>
    <path d="M 633.831115 361.520129 
L 636.599067 363.608589 
L 638.260695 360.414248 
L 635.491859 358.24279 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #beac76"/>
    <path d="M 575.012201 399.002536 
L 577.725214 399.828629 
L 579.37406 395.379594 
L 576.658909 394.495705 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fcfb97"/>
    <path d="M 601.845129 369.935975 
L 604.587079 371.342135 
L 606.241904 367.342904 
L 603.49823 365.866277 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ccbe7d"/>
    <path d="M 581.022277 390.935564 
L 583.742119 391.88419 
L 585.391877 387.509056 
L 582.669957 386.499585 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eee990"/>
    <path d="M 690.517457 395.946659 
L 693.305295 398.712232 
L 694.958002 397.235239 
L 692.171259 394.377216 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #faf996"/>
    <path d="M 610.644144 364.944328 
L 613.394341 366.545357 
L 615.051534 362.747796 
L 612.299813 361.072503 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c4b379"/>
    <path d="M 794.712007 485.595465 
L 797.518205 487.533988 
L 799.062785 488.400482 
L 796.26017 486.424292 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b8a0"/>
    <path d="M 606.241904 367.342904 
L 608.988063 368.844579 
L 610.644144 364.944328 
L 607.896355 363.370183 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c8b97b"/>
    <path d="M 755.178465 454.793667 
L 757.97322 457.301219 
L 759.569692 457.603616 
L 756.778099 455.028523 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #41d973"/>
    <path d="M 725.636725 428.321228 
L 728.428004 431.063304 
L 730.056221 430.643816 
L 727.267296 427.81793 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #99eb85"/>
    <path d="M 653.79266 368.962712 
L 656.571045 371.382939 
L 658.233435 368.768398 
L 655.454805 366.259093 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ccbe7d"/>
    <path d="M 833.063283 507.648061 
L 835.893336 508.802977 
L 837.388243 509.695886 
L 834.561361 508.533571 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0490f6"/>
    <path d="M 669.358699 379.022042 
L 672.142409 381.630646 
L 673.802671 379.493549 
L 671.019265 376.792923 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ded587"/>
    <path d="M 693.305295 398.712232 
L 696.093638 401.479276 
L 697.745148 400.094689 
L 694.958002 397.235239 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 843.053686 511.778758 
L 845.892539 512.698877 
L 847.376086 513.516025 
L 844.540184 512.595524 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0888ee"/>
    <path d="M 643.803421 364.845698 
L 646.577167 367.102818 
L 648.239811 364.195557 
L 645.465484 361.85184 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c4b379"/>
    <path d="M 591.418546 379.941307 
L 594.149734 381.103333 
L 595.802106 376.899623 
L 593.068978 375.671391 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dcd286"/>
    <path d="M 622.221387 362.569555 
L 624.981211 364.408 
L 626.64135 360.904603 
L 623.88029 358.98678 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c0ae77"/>
    <path d="M 728.428004 431.063304 
L 731.219747 433.782997 
L 732.845519 433.446218 
L 730.056221 430.643816 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #91e983"/>
    <path d="M 810.295687 495.64242 
L 813.110156 497.282544 
L 814.633846 498.22883 
L 811.822888 496.563711 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a6d7"/>
    <path d="M 779.13945 474.331573 
L 781.940288 476.517915 
L 783.506102 477.233481 
L 780.708787 474.997012 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00cb6b"/>
    <path d="M 696.093638 401.479276 
L 698.882469 404.245836 
L 700.532678 402.95352 
L 697.745148 400.094689 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f5fd97"/>
    <path d="M 757.97322 457.301219 
L 760.768889 459.767382 
L 762.36214 460.135529 
L 759.569692 457.603616 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #39d771"/>
    <path d="M 672.142409 381.630646 
L 674.926972 384.253708 
L 676.586833 382.209277 
L 673.802671 379.493549 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e2da89"/>
    <path d="M 656.571045 371.382939 
L 659.350652 373.82542 
L 661.013201 371.301111 
L 658.233435 368.768398 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d0c380"/>
    <path d="M 823.083927 502.78844 
L 825.906813 504.160868 
L 827.413983 505.10502 
L 824.594451 503.717752 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #009cf4"/>
    <path d="M 585.391877 387.509056 
L 588.116407 388.528331 
L 589.767714 384.227924 
L 587.041136 383.144914 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e8e28d"/>
    <path d="M 636.599067 363.608589 
L 639.368792 365.72526 
L 641.03124 362.615692 
L 638.260695 360.414248 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c2b178"/>
    <path d="M 629.40445 362.852386 
L 632.169519 364.828971 
L 633.831115 361.520129 
L 631.065006 359.461182 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c0ae77"/>
    <path d="M 595.802106 376.899623 
L 598.537828 378.145819 
L 600.19168 374.030066 
L 597.454082 372.715181 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d6cb83"/>
    <path d="M 731.219747 433.782997 
L 734.011986 436.478447 
L 735.635225 436.223195 
L 732.845519 433.446218 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #89e781"/>
    <path d="M 579.37406 395.379594 
L 582.091776 396.26733 
L 583.742119 391.88419 
L 581.022277 390.935564 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f4f193"/>
    <path d="M 698.882469 404.245836 
L 701.671773 407.009963 
L 703.320578 405.809687 
L 700.532678 402.95352 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #edfb95"/>
    <path d="M 617.805577 364.451595 
L 620.561876 366.182999 
L 622.221387 362.569555 
L 619.463717 360.760007 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c2b178"/>
    <path d="M 646.577167 367.102818 
L 649.352409 369.385577 
L 651.01556 366.566379 
L 648.239811 364.195557 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c8b97b"/>
    <path d="M 797.518205 487.533988 
L 800.326526 489.409527 
L 801.86752 490.311384 
L 799.062785 488.400482 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b4ac"/>
    <path d="M 674.926972 384.253708 
L 677.712342 386.889395 
L 679.371704 384.93818 
L 676.586833 382.209277 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e6df8b"/>
    <path d="M 600.19168 374.030066 
L 602.931831 375.365237 
L 604.587079 371.342135 
L 601.845129 369.935975 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d2c581"/>
    <path d="M 760.768889 459.767382 
L 763.565548 462.190576 
L 765.155522 462.62262 
L 762.36214 460.135529 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #31d670"/>
    <path d="M 613.394341 366.545357 
L 616.14689 368.172476 
L 617.805577 364.451595 
L 615.051534 362.747796 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c6b67a"/>
    <path d="M 734.011986 436.478447 
L 736.804759 439.147822 
L 738.425379 438.972836 
L 735.635225 436.223195 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #81e680"/>
    <path d="M 701.671773 407.009963 
L 704.461538 409.769714 
L 706.108836 408.661155 
L 703.320578 405.809687 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e5fa94"/>
    <path d="M 659.350652 373.82542 
L 662.131419 376.288497 
L 663.79404 373.855475 
L 661.013201 371.301111 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d4c882"/>
    <path d="M 604.587079 371.342135 
L 607.331529 372.770716 
L 608.988063 368.844579 
L 606.241904 367.342904 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ccbe7d"/>
    <path d="M 608.988063 368.844579 
L 611.736654 370.370614 
L 613.394341 366.545357 
L 610.644144 364.944328 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c8b97b"/>
    <path d="M 781.940288 476.517915 
L 784.742707 478.649296 
L 786.304972 479.412818 
L 783.506102 477.233481 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c970"/>
    <path d="M 589.767714 384.227924 
L 592.496899 385.323477 
L 594.149734 381.103333 
L 591.418546 379.941307 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e2da89"/>
    <path d="M 624.981211 364.408 
L 627.743122 366.274299 
L 629.40445 362.852386 
L 626.64135 360.904603 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c2b178"/>
    <path d="M 677.712342 386.889395 
L 680.498478 389.535868 
L 682.15724 387.678318 
L 679.371704 384.93818 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eae48e"/>
    <path d="M 639.368792 365.72526 
L 642.14022 367.868811 
L 643.803421 364.845698 
L 641.03124 362.615692 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c4b379"/>
    <path d="M 704.461538 409.769714 
L 707.251758 412.523155 
L 708.897446 411.505897 
L 706.108836 408.661155 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ddf892"/>
    <path d="M 736.804759 439.147822 
L 739.598108 441.789319 
L 741.216024 441.693261 
L 738.425379 438.972836 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #75e37d"/>
    <path d="M 583.742119 391.88419 
L 586.464547 392.839612 
L 588.116407 388.528331 
L 585.391877 387.509056 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eee990"/>
    <path d="M 649.352409 369.385577 
L 652.129082 371.692475 
L 653.79266 368.962712 
L 651.01556 366.566379 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ccbe7d"/>
    <path d="M 632.169519 364.828971 
L 634.93649 366.833172 
L 636.599067 363.608589 
L 633.831115 361.520129 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c2b178"/>
    <path d="M 813.110156 497.282544 
L 815.927382 498.852886 
L 817.447581 499.821798 
L 814.633846 498.22883 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a6d7"/>
    <path d="M 577.725214 399.828629 
L 580.440757 400.655493 
L 582.091776 396.26733 
L 579.37406 395.379594 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fcfb97"/>
    <path d="M 662.131419 376.288497 
L 664.913291 378.770492 
L 666.575891 376.429716 
L 663.79404 373.855475 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d8cd84"/>
    <path d="M 763.565548 462.190576 
L 766.363277 464.569266 
L 767.94992 465.063294 
L 765.155522 462.62262 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #29d46e"/>
    <path d="M 835.893336 508.802977 
L 838.727183 509.879703 
L 840.218969 510.7777 
L 837.388243 509.695886 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0490f6"/>
    <path d="M 594.149734 381.103333 
L 596.883512 382.280485 
L 598.537828 378.145819 
L 595.802106 376.899623 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dcd286"/>
    <path d="M 707.251758 412.523155 
L 710.042432 415.268363 
L 711.686407 414.341897 
L 708.897446 411.505897 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d1f690"/>
    <path d="M 680.498478 389.535868 
L 683.28534 392.191277 
L 684.9434 390.427746 
L 682.15724 387.678318 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eee990"/>
    <path d="M 620.561876 366.182999 
L 623.320372 367.941077 
L 624.981211 364.408 
L 622.221387 362.569555 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c4b379"/>
    <path d="M 739.598108 441.789319 
L 742.392079 444.401166 
L 744.00721 444.382621 
L 741.216024 441.693261 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #6de27c"/>
    <path d="M 800.326526 489.409527 
L 803.137087 491.221088 
L 804.674497 492.155973 
L 801.86752 490.311384 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b2b2"/>
    <path d="M 825.906813 504.160868 
L 828.733024 505.458647 
L 830.236879 506.415278 
L 827.413983 505.10502 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #009afa"/>
    <path d="M 784.742707 478.649296 
L 787.546811 480.724475 
L 789.105504 481.533737 
L 786.304972 479.412818 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c47d"/>
    <path d="M 710.042432 415.268363 
L 712.833562 418.003424 
L 714.475721 417.167152 
L 711.686407 414.341897 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c9f48e"/>
    <path d="M 598.537828 378.145819 
L 601.276107 379.409553 
L 602.931831 375.365237 
L 600.19168 374.030066 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d8cd84"/>
    <path d="M 683.28534 392.191277 
L 686.072894 394.853767 
L 687.73015 393.184511 
L 684.9434 390.427746 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f2ee92"/>
    <path d="M 664.913291 378.770492 
L 667.696211 381.269709 
L 669.358699 379.022042 
L 666.575891 376.429716 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dad085"/>
    <path d="M 642.14022 367.868811 
L 644.913284 370.037886 
L 646.577167 367.102818 
L 643.803421 364.845698 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c8b97b"/>
    <path d="M 652.129082 371.692475 
L 654.907123 374.021991 
L 656.571045 371.382939 
L 653.79266 368.962712 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cec07f"/>
    <path d="M 616.14689 368.172476 
L 618.90173 369.824863 
L 620.561876 366.182999 
L 617.805577 364.451595 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c8b97b"/>
    <path d="M 588.116407 388.528331 
L 590.84353 389.557217 
L 592.496899 385.323477 
L 589.767714 384.227924 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e8e28d"/>
    <path d="M 766.363277 464.569266 
L 769.162158 466.90196 
L 770.745421 467.456001 
L 767.94992 465.063294 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #21d36d"/>
    <path d="M 627.743122 366.274299 
L 630.507055 368.167383 
L 632.169519 364.828971 
L 629.40445 362.852386 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c4b379"/>
    <path d="M 602.931831 375.365237 
L 605.674495 376.720177 
L 607.331529 372.770716 
L 604.587079 371.342135 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d2c581"/>
    <path d="M 742.392079 444.401166 
L 745.186721 446.981622 
L 746.798988 447.039102 
L 744.00721 444.382621 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #65e07a"/>
    <path d="M 712.833562 418.003424 
L 715.625153 420.726442 
L 717.265396 419.979674 
L 714.475721 417.167152 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c1f38d"/>
    <path d="M 611.736654 370.370614 
L 614.487622 371.920292 
L 616.14689 368.172476 
L 613.394341 366.545357 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cabb7c"/>
    <path d="M 634.93649 366.833172 
L 637.705296 368.863778 
L 639.368792 365.72526 
L 636.599067 363.608589 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c6b67a"/>
    <path d="M 582.091776 396.26733 
L 584.812051 397.15885 
L 586.464547 392.839612 
L 583.742119 391.88419 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f6f394"/>
    <path d="M 607.331529 372.770716 
L 610.07843 374.221105 
L 611.736654 370.370614 
L 608.988063 368.844579 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cec07f"/>
    <path d="M 686.072894 394.853767 
L 688.861109 397.521482 
L 690.517457 395.946659 
L 687.73015 393.184511 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f6f394"/>
    <path d="M 667.696211 381.269709 
L 670.480131 383.784442 
L 672.142409 381.630646 
L 669.358699 379.022042 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ded587"/>
    <path d="M 715.625153 420.726442 
L 718.417216 423.435534 
L 720.055444 422.777492 
L 717.265396 419.979674 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b9f18b"/>
    <path d="M 592.496899 385.323477 
L 595.228668 386.431305 
L 596.883512 382.280485 
L 594.149734 381.103333 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e2da89"/>
    <path d="M 654.907123 374.021991 
L 657.686471 376.372583 
L 659.350652 373.82542 
L 656.571045 371.382939 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d2c581"/>
    <path d="M 745.186721 446.981622 
L 747.982089 449.528982 
L 749.591415 449.660925 
L 746.798988 447.039102 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #5ddf79"/>
    <path d="M 815.927382 498.852886 
L 818.747496 500.352742 
L 820.264229 501.341887 
L 817.447581 499.821798 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a4dc"/>
    <path d="M 688.861109 397.521482 
L 691.649959 400.192562 
L 693.305295 398.712232 
L 690.517457 395.946659 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #faf996"/>
    <path d="M 644.913284 370.037886 
L 647.687921 372.231103 
L 649.352409 369.385577 
L 646.577167 367.102818 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cabb7c"/>
    <path d="M 623.320372 367.941077 
L 626.081001 369.724874 
L 627.743122 366.274299 
L 624.981211 364.408 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c6b67a"/>
    <path d="M 787.546811 480.724475 
L 790.352708 482.742265 
L 791.907812 483.59501 
L 789.105504 481.533737 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c382"/>
    <path d="M 769.162158 466.90196 
L 771.962276 469.187214 
L 773.542114 469.799242 
L 770.745421 467.456001 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1dd26c"/>
    <path d="M 803.137087 491.221088 
L 805.950012 492.967739 
L 807.483844 493.933285 
L 804.674497 492.155973 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b0b9"/>
    <path d="M 718.417216 423.435534 
L 721.209767 426.128835 
L 722.84588 425.558654 
L 720.055444 422.777492 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b1ef89"/>
    <path d="M 670.480131 383.784442 
L 673.265001 386.312967 
L 674.926972 384.253708 
L 672.142409 381.630646 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e2da89"/>
    <path d="M 586.464547 392.839612 
L 589.189552 393.801705 
L 590.84353 389.557217 
L 588.116407 388.528331 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eee990"/>
    <path d="M 596.883512 382.280485 
L 599.61985 383.472409 
L 601.276107 379.409553 
L 598.537828 378.145819 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ded587"/>
    <path d="M 637.705296 368.863778 
L 640.475872 370.919549 
L 642.14022 367.868811 
L 639.368792 365.72526 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c8b97b"/>
    <path d="M 630.507055 368.167383 
L 633.272948 370.086155 
L 634.93649 366.833172 
L 632.169519 364.828971 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c6b67a"/>
    <path d="M 691.649959 400.192562 
L 694.43942 402.865148 
L 696.093638 401.479276 
L 693.305295 398.712232 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 747.982089 449.528982 
L 750.778239 452.041575 
L 752.384553 452.246348 
L 749.591415 449.660925 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #55dd77"/>
    <path d="M 618.90173 369.824863 
L 621.658806 371.501673 
L 623.320372 367.941077 
L 620.561876 366.182999 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cabb7c"/>
    <path d="M 580.440757 400.655493 
L 583.158833 401.483128 
L 584.812051 397.15885 
L 582.091776 396.26733 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fcfb97"/>
    <path d="M 838.727183 509.879703 
L 841.564964 510.87799 
L 843.053686 511.778758 
L 840.218969 510.7777 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0490f6"/>
    <path d="M 657.686471 376.372583 
L 660.46707 378.742688 
L 662.131419 376.288497 
L 659.350652 373.82542 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d6cb83"/>
    <path d="M 721.209767 426.128835 
L 724.002825 428.804501 
L 725.636725 428.321228 
L 722.84588 425.558654 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a5ed87"/>
    <path d="M 828.733024 505.458647 
L 831.562699 506.681327 
L 833.063283 507.648061 
L 830.236879 506.415278 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #009afa"/>
    <path d="M 601.276107 379.409553 
L 604.01691 380.690382 
L 605.674495 376.720177 
L 602.931831 375.365237 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d8cd84"/>
    <path d="M 614.487622 371.920292 
L 617.240916 373.492875 
L 618.90173 369.824863 
L 616.14689 368.172476 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ccbe7d"/>
    <path d="M 673.265001 386.312967 
L 676.050779 388.853551 
L 677.712342 386.889395 
L 674.926972 384.253708 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e6df8b"/>
    <path d="M 647.687921 372.231103 
L 650.464068 374.447058 
L 652.129082 371.692475 
L 649.352409 369.385577 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cec07f"/>
    <path d="M 694.43942 402.865148 
L 697.229475 405.537382 
L 698.882469 404.245836 
L 696.093638 401.479276 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f5fd97"/>
    <path d="M 771.962276 469.187214 
L 774.763721 471.423633 
L 776.340091 472.091566 
L 773.542114 469.799242 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #15d06a"/>
    <path d="M 605.674495 376.720177 
L 608.419628 378.09435 
L 610.07843 374.221105 
L 607.331529 372.770716 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d4c882"/>
    <path d="M 610.07843 374.221105 
L 612.827736 375.692666 
L 614.487622 371.920292 
L 611.736654 370.370614 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d0c380"/>
    <path d="M 590.84353 389.557217 
L 593.573229 390.595512 
L 595.228668 386.431305 
L 592.496899 385.323477 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e8e28d"/>
    <path d="M 750.778239 452.041575 
L 753.575234 454.517766 
L 755.178465 454.793667 
L 752.384553 452.246348 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #4ddb75"/>
    <path d="M 790.352708 482.742265 
L 793.160507 484.701535 
L 794.712007 485.595465 
L 791.907812 483.59501 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c088"/>
    <path d="M 724.002825 428.804501 
L 726.796411 431.460707 
L 728.428004 431.063304 
L 725.636725 428.321228 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9deb85"/>
    <path d="M 626.081001 369.724874 
L 628.843704 371.533406 
L 630.507055 368.167383 
L 627.743122 366.274299 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c8b97b"/>
    <path d="M 660.46707 378.742688 
L 663.248863 381.130727 
L 664.913291 378.770492 
L 662.131419 376.288497 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dad085"/>
    <path d="M 697.229475 405.537382 
L 700.020108 408.207411 
L 701.671773 407.009963 
L 698.882469 404.245836 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #edfb95"/>
    <path d="M 640.475872 370.919549 
L 643.248156 372.999222 
L 644.913284 370.037886 
L 642.14022 367.868811 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ccbe7d"/>
    <path d="M 676.050779 388.853551 
L 678.837423 391.404454 
L 680.498478 389.535868 
L 677.712342 386.889395 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eae48e"/>
    <path d="M 805.950012 492.967739 
L 808.765423 494.648608 
L 810.295687 495.64242 
L 807.483844 493.933285 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00aebf"/>
    <path d="M 584.812051 397.15885 
L 587.534884 398.054093 
L 589.189552 393.801705 
L 586.464547 392.839612 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f6f394"/>
    <path d="M 633.272948 370.086155 
L 636.040738 372.029493 
L 637.705296 368.863778 
L 634.93649 366.833172 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cabb7c"/>
    <path d="M 818.747496 500.352742 
L 821.57063 501.781471 
L 823.083927 502.78844 
L 820.264229 501.341887 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a2e2"/>
    <path d="M 726.796411 431.460707 
L 729.590555 434.095652 
L 731.219747 433.782997 
L 728.428004 431.063304 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #95ea84"/>
    <path d="M 595.228668 386.431305 
L 597.962998 387.551125 
L 599.61985 383.472409 
L 596.883512 382.280485 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e4dc8a"/>
    <path d="M 650.464068 374.447058 
L 653.241665 376.684328 
L 654.907123 374.021991 
L 652.129082 371.692475 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d2c581"/>
    <path d="M 753.575234 454.517766 
L 756.373138 456.955959 
L 757.97322 457.301219 
L 755.178465 454.793667 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #49db75"/>
    <path d="M 700.020108 408.207411 
L 702.811309 410.873389 
L 704.461538 409.769714 
L 701.671773 407.009963 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e5fa94"/>
    <path d="M 774.763721 471.423633 
L 777.566584 473.609867 
L 779.13945 474.331573 
L 776.340091 472.091566 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0dcf69"/>
    <path d="M 621.658806 371.501673 
L 624.418062 373.202036 
L 626.081001 369.724874 
L 623.320372 367.941077 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ccbe7d"/>
    <path d="M 678.837423 391.404454 
L 681.624898 393.963925 
L 683.28534 392.191277 
L 680.498478 389.535868 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eee990"/>
    <path d="M 663.248863 381.130727 
L 666.031801 383.535104 
L 667.696211 381.269709 
L 664.913291 378.770492 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dcd286"/>
    <path d="M 729.590555 434.095652 
L 732.385287 436.70756 
L 734.011986 436.478447 
L 731.219747 433.782997 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8de882"/>
    <path d="M 599.61985 383.472409 
L 602.35872 384.67874 
L 604.01691 380.690382 
L 601.276107 379.409553 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ded587"/>
    <path d="M 702.811309 410.873389 
L 705.603071 413.533475 
L 707.251758 412.523155 
L 704.461538 409.769714 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ddf892"/>
    <path d="M 617.240916 373.492875 
L 619.996485 375.087602 
L 621.658806 371.501673 
L 618.90173 369.824863 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cec07f"/>
    <path d="M 793.160507 484.701535 
L 795.970318 486.601209 
L 797.518205 487.533988 
L 794.712007 485.595465 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00bc94"/>
    <path d="M 589.189552 393.801705 
L 591.917122 394.770334 
L 593.573229 390.595512 
L 590.84353 389.557217 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f0ec91"/>
    <path d="M 643.248156 372.999222 
L 646.022088 375.101513 
L 647.687921 372.231103 
L 644.913284 370.037886 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cec07f"/>
    <path d="M 628.843704 371.533406 
L 631.608424 373.365669 
L 633.272948 370.086155 
L 630.507055 368.167383 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ccbe7d"/>
    <path d="M 604.01691 380.690382 
L 606.760199 381.98785 
L 608.419628 378.09435 
L 605.674495 376.720177 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dad085"/>
    <path d="M 756.373138 456.955959 
L 759.17202 459.354597 
L 760.768889 459.767382 
L 757.97322 457.301219 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #41d973"/>
    <path d="M 612.827736 375.692666 
L 615.579399 377.184743 
L 617.240916 373.492875 
L 614.487622 371.920292 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d2c581"/>
    <path d="M 681.624898 393.963925 
L 684.413169 396.53021 
L 686.072894 394.853767 
L 683.28534 392.191277 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f2ee92"/>
    <path d="M 653.241665 376.684328 
L 656.020657 378.941467 
L 657.686471 376.372583 
L 654.907123 374.021991 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d4c882"/>
    <path d="M 608.419628 378.09435 
L 611.16719 379.4872 
L 612.827736 375.692666 
L 610.07843 374.221105 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d6cb83"/>
    <path d="M 831.562699 506.681327 
L 834.395977 507.828526 
L 835.893336 508.802977 
L 833.063283 507.648061 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0098fe"/>
    <path d="M 636.040738 372.029493 
L 638.810365 373.996253 
L 640.475872 370.919549 
L 637.705296 368.863778 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ccbe7d"/>
    <path d="M 841.564964 510.87799 
L 844.406822 511.797662 
L 845.892539 512.698877 
L 843.053686 511.778758 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0490f6"/>
    <path d="M 583.158833 401.483128 
L 585.879445 402.311535 
L 587.534884 398.054093 
L 584.812051 397.15885 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fcfb97"/>
    <path d="M 732.385287 436.70756 
L 735.180643 439.294678 
L 736.804759 439.147822 
L 734.011986 436.478447 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #85e781"/>
    <path d="M 666.031801 383.535104 
L 668.815834 385.954211 
L 670.480131 383.784442 
L 667.696211 381.269709 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e0d788"/>
    <path d="M 705.603071 413.533475 
L 708.395392 416.18584 
L 710.042432 415.268363 
L 707.251758 412.523155 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d5f791"/>
    <path d="M 777.566584 473.609867 
L 780.370959 475.74462 
L 781.940288 476.517915 
L 779.13945 474.331573 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #09ce68"/>
    <path d="M 808.765423 494.648608 
L 811.583445 496.262887 
L 813.110156 497.282544 
L 810.295687 495.64242 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00acc4"/>
    <path d="M 593.573229 390.595512 
L 596.305487 391.643007 
L 597.962998 387.551125 
L 595.228668 386.431305 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eae48e"/>
    <path d="M 684.413169 396.53021 
L 687.202208 399.101551 
L 688.861109 397.521482 
L 686.072894 394.853767 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f6f394"/>
    <path d="M 624.418062 373.202036 
L 627.179443 374.925058 
L 628.843704 371.533406 
L 626.081001 369.724874 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cec07f"/>
    <path d="M 821.57063 501.781471 
L 824.396917 503.138503 
L 825.906813 504.160868 
L 823.083927 502.78844 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a0e8"/>
    <path d="M 708.395392 416.18584 
L 711.188272 418.828665 
L 712.833562 418.003424 
L 710.042432 415.268363 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cdf58f"/>
    <path d="M 759.17202 459.354597 
L 761.971952 461.712166 
L 763.565548 462.190576 
L 760.768889 459.767382 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #39d771"/>
    <path d="M 735.180643 439.294678 
L 737.976662 441.855284 
L 739.598108 441.789319 
L 736.804759 439.147822 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #7de57f"/>
    <path d="M 646.022088 375.101513 
L 648.79761 377.225115 
L 650.464068 374.447058 
L 647.687921 372.231103 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d2c581"/>
    <path d="M 656.020657 378.941467 
L 658.800987 381.217012 
L 660.46707 378.742688 
L 657.686471 376.372583 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d8cd84"/>
    <path d="M 668.815834 385.954211 
L 671.600918 388.386427 
L 673.265001 386.312967 
L 670.480131 383.784442 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e4dc8a"/>
    <path d="M 795.970318 486.601209 
L 798.782256 488.44027 
L 800.326526 489.409527 
L 797.518205 487.533988 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00bb9b"/>
    <path d="M 597.962998 387.551125 
L 600.699867 388.682644 
L 602.35872 384.67874 
L 599.61985 383.472409 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e4dc8a"/>
    <path d="M 587.534884 398.054093 
L 590.260271 398.952993 
L 591.917122 394.770334 
L 589.189552 393.801705 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f6f394"/>
    <path d="M 687.202208 399.101551 
L 689.991987 401.676187 
L 691.649959 400.192562 
L 688.861109 397.521482 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #faf996"/>
    <path d="M 631.608424 373.365669 
L 634.375102 375.220632 
L 636.040738 372.029493 
L 633.272948 370.086155 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cec07f"/>
    <path d="M 619.996485 375.087602 
L 622.754278 376.70369 
L 624.418062 373.202036 
L 621.658806 371.501673 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d0c380"/>
    <path d="M 638.810365 373.996253 
L 641.581771 375.985266 
L 643.248156 372.999222 
L 640.475872 370.919549 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cec07f"/>
    <path d="M 711.188272 418.828665 
L 713.981719 421.460143 
L 715.625153 420.726442 
L 712.833562 418.003424 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c5f38d"/>
    <path d="M 780.370959 475.74462 
L 783.176945 477.826642 
L 784.742707 478.649296 
L 781.940288 476.517915 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #01cc66"/>
    <path d="M 737.976662 441.855284 
L 740.773387 444.387683 
L 742.392079 444.401166 
L 739.598108 441.789319 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #75e37d"/>
    <path d="M 602.35872 384.67874 
L 605.100091 385.899093 
L 606.760199 381.98785 
L 604.01691 380.690382 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e0d788"/>
    <path d="M 761.971952 461.712166 
L 764.773009 464.027189 
L 766.363277 464.569266 
L 763.565548 462.190576 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #31d670"/>
    <path d="M 615.579399 377.184743 
L 618.333375 378.696659 
L 619.996485 375.087602 
L 617.240916 373.492875 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d4c882"/>
    <path d="M 671.600918 388.386427 
L 674.387011 390.830118 
L 676.050779 388.853551 
L 673.265001 386.312967 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e8e28d"/>
    <path d="M 606.760199 381.98785 
L 609.50594 383.301479 
L 611.16719 379.4872 
L 608.419628 378.09435 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dad085"/>
    <path d="M 658.800987 381.217012 
L 661.582606 383.509484 
L 663.248863 381.130727 
L 660.46707 378.742688 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dcd286"/>
    <path d="M 611.16719 379.4872 
L 613.917141 380.898154 
L 615.579399 377.184743 
L 612.827736 375.692666 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d6cb83"/>
    <path d="M 689.991987 401.676187 
L 692.782487 404.252358 
L 694.43942 402.865148 
L 691.649959 400.192562 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 713.981719 421.460143 
L 716.775741 424.078485 
L 718.417216 423.435534 
L 715.625153 420.726442 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bdf28c"/>
    <path d="M 648.79761 377.225115 
L 651.574666 379.368699 
L 653.241665 376.684328 
L 650.464068 374.447058 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d4c882"/>
    <path d="M 591.917122 394.770334 
L 594.647248 395.745359 
L 596.305487 391.643007 
L 593.573229 390.595512 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f0ec91"/>
    <path d="M 740.773387 444.387683 
L 743.570866 446.890213 
L 745.186721 446.981622 
L 742.392079 444.401166 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #6de27c"/>
    <path d="M 811.583445 496.262887 
L 814.404205 497.80983 
L 815.927382 498.852886 
L 813.110156 497.282544 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00aacb"/>
    <path d="M 627.179443 374.925058 
L 629.942896 376.669824 
L 631.608424 373.365669 
L 628.843704 371.533406 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d0c380"/>
    <path d="M 834.395977 507.828526 
L 837.232995 508.89993 
L 838.727183 509.879703 
L 835.893336 508.802977 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0098fe"/>
    <path d="M 674.387011 390.830118 
L 677.174074 393.283644 
L 678.837423 391.404454 
L 676.050779 388.853551 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ece78f"/>
    <path d="M 692.782487 404.252358 
L 695.573687 406.828305 
L 697.229475 405.537382 
L 694.43942 402.865148 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f5fd97"/>
    <path d="M 716.775741 424.078485 
L 719.570352 426.681915 
L 721.209767 426.128835 
L 718.417216 423.435534 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b1ef89"/>
    <path d="M 641.581771 375.985266 
L 644.354901 377.995344 
L 646.022088 375.101513 
L 643.248156 372.999222 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d2c581"/>
    <path d="M 585.879445 402.311535 
L 588.602597 403.140716 
L 590.260271 398.952993 
L 587.534884 398.054093 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fcfb97"/>
    <path d="M 798.782256 488.44027 
L 801.596436 490.217759 
L 803.137087 491.221088 
L 800.326526 489.409527 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b8a0"/>
    <path d="M 783.176945 477.826642 
L 785.984642 479.854739 
L 787.546811 480.724475 
L 784.742707 478.649296 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00cb6b"/>
    <path d="M 634.375102 375.220632 
L 637.143684 377.097245 
L 638.810365 373.996253 
L 636.040738 372.029493 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d0c380"/>
    <path d="M 764.773009 464.027189 
L 767.57527 466.298238 
L 769.162158 466.90196 
L 766.363277 464.569266 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2dd56f"/>
    <path d="M 596.305487 391.643007 
L 599.040289 392.699482 
L 600.699867 388.682644 
L 597.962998 387.551125 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eae48e"/>
    <path d="M 661.582606 383.509484 
L 664.365465 385.817388 
L 666.031801 383.535104 
L 663.248863 381.130727 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ded587"/>
    <path d="M 824.396917 503.138503 
L 827.226492 504.42333 
L 828.733024 505.458647 
L 825.906813 504.160868 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a0e8"/>
    <path d="M 743.570866 446.890213 
L 746.36915 449.361242 
L 747.982089 449.528982 
L 745.186721 446.981622 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #65e07a"/>
    <path d="M 622.754278 376.70369 
L 625.514247 378.340333 
L 627.179443 374.925058 
L 624.418062 373.202036 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d2c581"/>
    <path d="M 651.574666 379.368699 
L 654.353202 381.530922 
L 656.020657 378.941467 
L 653.241665 376.684328 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d8cd84"/>
    <path d="M 695.573687 406.828305 
L 698.365574 409.402273 
L 700.020108 408.207411 
L 697.229475 405.537382 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #edfb95"/>
    <path d="M 719.570352 426.681915 
L 722.365569 429.268677 
L 724.002825 428.804501 
L 721.209767 426.128835 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a9ee88"/>
    <path d="M 677.174074 393.283644 
L 679.962072 395.745357 
L 681.624898 393.963925 
L 678.837423 391.404454 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f0ec91"/>
    <path d="M 600.699867 388.682644 
L 603.43925 389.825557 
L 605.100091 385.899093 
L 602.35872 384.67874 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e6df8b"/>
    <path d="M 618.333375 378.696659 
L 621.089619 380.227719 
L 622.754278 376.70369 
L 619.996485 375.087602 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d4c882"/>
    <path d="M 590.260271 398.952993 
L 592.988209 399.85548 
L 594.647248 395.745359 
L 591.917122 394.770334 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f6f394"/>
    <path d="M 605.100091 385.899093 
L 607.843936 387.133076 
L 609.50594 383.301479 
L 606.760199 381.98785 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e0d788"/>
    <path d="M 767.57527 466.298238 
L 770.378818 468.523925 
L 771.962276 469.187214 
L 769.162158 466.90196 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #25d36d"/>
    <path d="M 664.365465 385.817388 
L 667.149517 388.139216 
L 668.815834 385.954211 
L 666.031801 383.535104 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e2da89"/>
    <path d="M 746.36915 449.361242 
L 749.168292 451.799171 
L 750.778239 452.041575 
L 747.982089 449.528982 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #5ddf79"/>
    <path d="M 629.942896 376.669824 
L 632.70837 378.435398 
L 634.375102 375.220632 
L 631.608424 373.365669 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d2c581"/>
    <path d="M 613.917141 380.898154 
L 616.66944 382.32662 
L 618.333375 378.696659 
L 615.579399 377.184743 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d8cd84"/>
    <path d="M 644.354901 377.995344 
L 647.1297 380.025276 
L 648.79761 377.225115 
L 646.022088 375.101513 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d4c882"/>
    <path d="M 609.50594 383.301479 
L 612.254098 384.630779 
L 613.917141 380.898154 
L 611.16719 379.4872 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dcd286"/>
    <path d="M 698.365574 409.402273 
L 701.158138 411.972512 
L 702.811309 410.873389 
L 700.020108 408.207411 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e5fa94"/>
    <path d="M 722.365569 429.268677 
L 725.161415 431.837034 
L 726.796411 431.460707 
L 724.002825 428.804501 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a1ec86"/>
    <path d="M 785.984642 479.854739 
L 788.794151 481.827766 
L 790.352708 482.742265 
L 787.546811 480.724475 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c970"/>
    <path d="M 637.143684 377.097245 
L 639.914117 378.994434 
L 641.581771 375.985266 
L 638.810365 373.996253 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d2c581"/>
    <path d="M 814.404205 497.80983 
L 817.227828 499.288754 
L 818.747496 500.352742 
L 815.927382 498.852886 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00aacb"/>
    <path d="M 679.962072 395.745357 
L 682.750973 398.213603 
L 684.413169 396.53021 
L 681.624898 393.963925 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f4f193"/>
    <path d="M 654.353202 381.530922 
L 657.133168 383.710418 
L 658.800987 381.217012 
L 656.020657 378.941467 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dad085"/>
    <path d="M 801.596436 490.217759 
L 804.412974 491.932775 
L 805.950012 492.967739 
L 803.137087 491.221088 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b6a7"/>
    <path d="M 594.647248 395.745359 
L 597.379921 396.726636 
L 599.040289 392.699482 
L 596.305487 391.643007 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f0ec91"/>
    <path d="M 701.158138 411.972512 
L 703.95137 414.53728 
L 705.603071 413.533475 
L 702.811309 410.873389 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ddf892"/>
    <path d="M 725.161415 431.837034 
L 727.957914 434.385272 
L 729.590555 434.095652 
L 726.796411 431.460707 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #99eb85"/>
    <path d="M 749.168292 451.799171 
L 751.968352 454.202438 
L 753.575234 454.517766 
L 750.778239 452.041575 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #55dd77"/>
    <path d="M 625.514247 378.340333 
L 628.276343 379.996709 
L 629.942896 376.669824 
L 627.179443 374.925058 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d4c882"/>
    <path d="M 667.149517 388.139216 
L 669.934721 390.473448 
L 671.600918 388.386427 
L 668.815834 385.954211 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e6df8b"/>
    <path d="M 837.232995 508.89993 
L 840.073892 509.895298 
L 841.564964 510.87799 
L 838.727183 509.879703 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0098fe"/>
    <path d="M 770.378818 468.523925 
L 773.183735 470.702909 
L 774.763721 471.423633 
L 771.962276 469.187214 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1dd26c"/>
    <path d="M 682.750973 398.213603 
L 685.540749 400.686725 
L 687.202208 399.101551 
L 684.413169 396.53021 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f8f695"/>
    <path d="M 827.226492 504.42333 
L 830.059488 505.635515 
L 831.562699 506.681327 
L 828.733024 505.458647 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a0e8"/>
    <path d="M 647.1297 380.025276 
L 649.906117 382.073835 
L 651.574666 379.368699 
L 648.79761 377.225115 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d8cd84"/>
    <path d="M 599.040289 392.699482 
L 601.777618 393.76471 
L 603.43925 389.825557 
L 600.699867 388.682644 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eae48e"/>
    <path d="M 703.95137 414.53728 
L 706.74527 417.094843 
L 708.395392 416.18584 
L 705.603071 413.533475 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d5f791"/>
    <path d="M 588.602597 403.140716 
L 591.328292 403.970671 
L 592.988209 399.85548 
L 590.260271 398.952993 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fcfb97"/>
    <path d="M 727.957914 434.385272 
L 730.755097 436.911699 
L 732.385287 436.70756 
L 729.590555 434.095652 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #91e983"/>
    <path d="M 621.089619 380.227719 
L 623.848087 381.777207 
L 625.514247 378.340333 
L 622.754278 376.70369 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d6cb83"/>
    <path d="M 657.133168 383.710418 
L 659.914516 385.905812 
L 661.582606 383.509484 
L 658.800987 381.217012 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ded587"/>
    <path d="M 632.70837 378.435398 
L 635.475812 380.220822 
L 637.143684 377.097245 
L 634.375102 375.220632 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d4c882"/>
    <path d="M 788.794151 481.827766 
L 791.605577 483.744635 
L 793.160507 484.701535 
L 790.352708 482.742265 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c47d"/>
    <path d="M 639.914117 378.994434 
L 642.686348 380.911107 
L 644.354901 377.995344 
L 641.581771 375.985266 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d6cb83"/>
    <path d="M 751.968352 454.202438 
L 754.769391 456.569516 
L 756.373138 456.955959 
L 753.575234 454.517766 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #51dc76"/>
    <path d="M 603.43925 389.825557 
L 606.181127 390.97955 
L 607.843936 387.133076 
L 605.100091 385.899093 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e6df8b"/>
    <path d="M 669.934721 390.473448 
L 672.721036 392.818555 
L 674.387011 390.830118 
L 671.600918 388.386427 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eae48e"/>
    <path d="M 685.540749 400.686725 
L 688.331375 403.163064 
L 689.991987 401.676187 
L 687.202208 399.101551 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fcfb97"/>
    <path d="M 616.66944 382.32662 
L 619.42405 383.77199 
L 621.089619 380.227719 
L 618.333375 378.696659 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dad085"/>
    <path d="M 607.843936 387.133076 
L 610.590226 388.380278 
L 612.254098 384.630779 
L 609.50594 383.301479 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e2da89"/>
    <path d="M 612.254098 384.630779 
L 615.004641 385.975245 
L 616.66944 382.32662 
L 613.917141 380.898154 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ded587"/>
    <path d="M 706.74527 417.094843 
L 709.539837 419.643476 
L 711.188272 418.828665 
L 708.395392 416.18584 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cdf58f"/>
    <path d="M 804.412974 491.932775 
L 807.23199 493.584476 
L 808.765423 494.648608 
L 805.950012 492.967739 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b4ac"/>
    <path d="M 773.183735 470.702909 
L 775.990112 472.833897 
L 777.566584 473.609867 
L 774.763721 471.423633 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #19d16b"/>
    <path d="M 730.755097 436.911699 
L 733.552996 439.414646 
L 735.180643 439.294678 
L 732.385287 436.70756 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #89e781"/>
    <path d="M 817.227828 499.288754 
L 820.054442 500.69904 
L 821.57063 501.781471 
L 818.747496 500.352742 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a8d0"/>
    <path d="M 592.988209 399.85548 
L 595.718694 400.761483 
L 597.379921 396.726636 
L 594.647248 395.745359 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f6f394"/>
    <path d="M 628.276343 379.996709 
L 631.040519 381.671973 
L 632.70837 378.435398 
L 629.942896 376.669824 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d6cb83"/>
    <path d="M 649.906117 382.073835 
L 652.684101 384.139776 
L 654.353202 381.530922 
L 651.574666 379.368699 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dad085"/>
    <path d="M 659.914516 385.905812 
L 662.697199 388.115708 
L 664.365465 385.817388 
L 661.582606 383.509484 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e2da89"/>
    <path d="M 688.331375 403.163064 
L 691.122831 405.640959 
L 692.782487 404.252358 
L 689.991987 401.676187 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 754.769391 456.569516 
L 757.571475 458.898917 
L 759.17202 459.354597 
L 756.373138 456.955959 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #49db75"/>
    <path d="M 672.721036 392.818555 
L 675.508426 395.172997 
L 677.174074 393.283644 
L 674.387011 390.830118 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eee990"/>
    <path d="M 709.539837 419.643476 
L 712.335076 422.181469 
L 713.981719 421.460143 
L 711.188272 418.828665 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c5f38d"/>
    <path d="M 733.552996 439.414646 
L 736.351648 441.892472 
L 737.976662 441.855284 
L 735.180643 439.294678 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #85e781"/>
    <path d="M 635.475812 380.220822 
L 638.245176 382.02512 
L 639.914117 378.994434 
L 637.143684 377.097245 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d6cb83"/>
    <path d="M 642.686348 380.911107 
L 645.460328 382.846154 
L 647.1297 380.025276 
L 644.354901 377.995344 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d8cd84"/>
    <path d="M 791.605577 483.744635 
L 794.419028 485.60431 
L 795.970318 486.601209 
L 793.160507 484.701535 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c382"/>
    <path d="M 597.379921 396.726636 
L 600.115131 397.714014 
L 601.777618 393.76471 
L 599.040289 392.699482 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f0ec91"/>
    <path d="M 623.848087 381.777207 
L 626.608736 383.344392 
L 628.276343 379.996709 
L 625.514247 378.340333 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d8cd84"/>
    <path d="M 691.122831 405.640959 
L 693.915098 408.118754 
L 695.573687 406.828305 
L 692.782487 404.252358 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9fe98"/>
    <path d="M 775.990112 472.833897 
L 778.798037 474.915641 
L 780.370959 475.74462 
L 777.566584 473.609867 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #11cf69"/>
    <path d="M 840.073892 509.895298 
L 842.918806 510.814457 
L 844.406822 511.797662 
L 841.564964 510.87799 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0098fe"/>
    <path d="M 712.335076 422.181469 
L 715.130996 424.707123 
L 716.775741 424.078485 
L 713.981719 421.460143 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bdf28c"/>
    <path d="M 830.059488 505.635515 
L 832.896039 506.774687 
L 834.395977 507.828526 
L 831.562699 506.681327 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #009eef"/>
    <path d="M 675.508426 395.172997 
L 678.296857 397.535231 
L 679.962072 395.745357 
L 677.174074 393.283644 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f0ec91"/>
    <path d="M 662.697199 388.115708 
L 665.481175 390.338703 
L 667.149517 388.139216 
L 664.365465 385.817388 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e4dc8a"/>
    <path d="M 757.571475 458.898917 
L 760.37467 461.189188 
L 761.971952 461.712166 
L 759.17202 459.354597 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #41d973"/>
    <path d="M 601.777618 393.76471 
L 604.517457 394.838455 
L 606.181127 390.97955 
L 603.43925 389.825557 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ece78f"/>
    <path d="M 652.684101 384.139776 
L 655.463605 386.221836 
L 657.133168 383.710418 
L 654.353202 381.530922 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ded587"/>
    <path d="M 619.42405 383.77199 
L 622.180931 385.233639 
L 623.848087 381.777207 
L 621.089619 380.227719 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dcd286"/>
    <path d="M 736.351648 441.892472 
L 739.151095 444.343564 
L 740.773387 444.387683 
L 737.976662 441.855284 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #7de57f"/>
    <path d="M 807.23199 493.584476 
L 810.053604 495.172082 
L 811.583445 496.262887 
L 808.765423 494.648608 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b2b2"/>
    <path d="M 606.181127 390.97955 
L 608.925475 392.144297 
L 610.590226 388.380278 
L 607.843936 387.133076 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e6df8b"/>
    <path d="M 591.328292 403.970671 
L 594.056535 404.801401 
L 595.718694 400.761483 
L 592.988209 399.85548 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fcfb97"/>
    <path d="M 615.004641 385.975245 
L 617.757534 387.334353 
L 619.42405 383.77199 
L 616.66944 382.32662 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ded587"/>
    <path d="M 610.590226 388.380278 
L 613.338933 389.640279 
L 615.004641 385.975245 
L 612.254098 384.630779 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e2da89"/>
    <path d="M 631.040519 381.671973 
L 633.80673 383.365264 
L 635.475812 380.220822 
L 632.70837 378.435398 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d8cd84"/>
    <path d="M 693.915098 408.118754 
L 696.708162 410.594792 
L 698.365574 409.402273 
L 695.573687 406.828305 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1fc96"/>
    <path d="M 715.130996 424.707123 
L 717.92761 427.218757 
L 719.570352 426.681915 
L 716.775741 424.078485 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b5f08a"/>
    <path d="M 820.054442 500.69904 
L 822.884178 502.040135 
L 824.396917 503.138503 
L 821.57063 501.781471 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a6d7"/>
    <path d="M 645.460328 382.846154 
L 648.236008 384.798448 
L 649.906117 382.073835 
L 647.1297 380.025276 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dad085"/>
    <path d="M 678.296857 397.535231 
L 681.0863 399.903703 
L 682.750973 398.213603 
L 679.962072 395.745357 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f4f193"/>
    <path d="M 638.245176 382.02512 
L 641.016414 383.847297 
L 642.686348 380.911107 
L 639.914117 378.994434 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d8cd84"/>
    <path d="M 794.419028 485.60431 
L 797.234613 487.40581 
L 798.782256 488.44027 
L 795.970318 486.601209 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c088"/>
    <path d="M 739.151095 444.343564 
L 741.951381 446.766336 
L 743.570866 446.890213 
L 740.773387 444.387683 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #75e37d"/>
    <path d="M 665.481175 390.338703 
L 668.266405 392.57338 
L 669.934721 390.473448 
L 667.149517 388.139216 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e8e28d"/>
    <path d="M 760.37467 461.189188 
L 763.179051 463.438921 
L 764.773009 464.027189 
L 761.971952 461.712166 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #3dd872"/>
    <path d="M 778.798037 474.915641 
L 781.607604 476.946943 
L 783.176945 477.826642 
L 780.370959 475.74462 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0dcf69"/>
    <path d="M 595.718694 400.761483 
L 598.451724 401.670927 
L 600.115131 397.714014 
L 597.379921 396.726636 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f6f394"/>
    <path d="M 655.463605 386.221836 
L 658.244585 388.31874 
L 659.914516 385.905812 
L 657.133168 383.710418 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e0d788"/>
    <path d="M 696.708162 410.594792 
L 699.502013 413.067423 
L 701.158138 411.972512 
L 698.365574 409.402273 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e9fb95"/>
    <path d="M 717.92761 427.218757 
L 720.724934 429.714703 
L 722.365569 429.268677 
L 719.570352 426.681915 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b1ef89"/>
    <path d="M 626.608736 383.344392 
L 629.371525 384.928522 
L 631.040519 381.671973 
L 628.276343 379.996709 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dad085"/>
    <path d="M 681.0863 399.903703 
L 683.876728 402.276862 
L 685.540749 400.686725 
L 682.750973 398.213603 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f8f695"/>
    <path d="M 600.115131 397.714014 
L 602.852868 398.707335 
L 604.517457 394.838455 
L 601.777618 393.76471 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f0ec91"/>
    <path d="M 741.951381 446.766336 
L 744.752554 449.159234 
L 746.36915 449.361242 
L 743.570866 446.890213 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #6de27c"/>
    <path d="M 622.180931 385.233639 
L 624.940048 386.710926 
L 626.608736 383.344392 
L 623.848087 381.777207 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dcd286"/>
    <path d="M 668.266405 392.57338 
L 671.052849 394.818312 
L 672.721036 392.818555 
L 669.934721 390.473448 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eae48e"/>
    <path d="M 699.502013 413.067423 
L 702.296644 415.535003 
L 703.95137 414.53728 
L 701.158138 411.972512 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e1f993"/>
    <path d="M 648.236008 384.798448 
L 651.013344 386.766842 
L 652.684101 384.139776 
L 649.906117 382.073835 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ded587"/>
    <path d="M 763.179051 463.438921 
L 765.98469 465.646746 
L 767.57527 466.298238 
L 764.773009 464.027189 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #35d771"/>
    <path d="M 633.80673 383.365264 
L 636.574932 385.075702 
L 638.245176 382.02512 
L 635.475812 380.220822 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dad085"/>
    <path d="M 720.724934 429.714703 
L 723.522987 432.193317 
L 725.161415 431.837034 
L 722.365569 429.268677 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a9ee88"/>
    <path d="M 810.053604 495.172082 
L 812.877937 496.694871 
L 814.404205 497.80983 
L 811.583445 496.262887 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b0b9"/>
    <path d="M 832.896039 506.774687 
L 835.736279 507.840541 
L 837.232995 508.89993 
L 834.395977 507.828526 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #009eef"/>
    <path d="M 604.517457 394.838455 
L 607.259792 395.920473 
L 608.925475 392.144297 
L 606.181127 390.97955 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ece78f"/>
    <path d="M 641.016414 383.847297 
L 643.789479 385.686344 
L 645.460328 382.846154 
L 642.686348 380.911107 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dcd286"/>
    <path d="M 781.607604 476.946943 
L 784.418909 478.926656 
L 785.984642 479.854739 
L 783.176945 477.826642 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #09ce68"/>
    <path d="M 617.757534 387.334353 
L 620.512746 388.707571 
L 622.180931 385.233639 
L 619.42405 383.77199 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e0d788"/>
    <path d="M 658.244585 388.31874 
L 661.026998 390.429198 
L 662.697199 388.115708 
L 659.914516 385.905812 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e4dc8a"/>
    <path d="M 608.925475 392.144297 
L 611.672272 393.31946 
L 613.338933 389.640279 
L 610.590226 388.380278 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e8e28d"/>
    <path d="M 797.234613 487.40581 
L 800.052442 489.148211 
L 801.596436 490.217759 
L 798.782256 488.44027 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00be8f"/>
    <path d="M 613.338933 389.640279 
L 616.090031 390.912646 
L 617.757534 387.334353 
L 615.004641 385.975245 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e4dc8a"/>
    <path d="M 683.876728 402.276862 
L 686.668116 404.653149 
L 688.331375 403.163064 
L 685.540749 400.686725 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fcfb97"/>
    <path d="M 744.752554 449.159234 
L 747.554665 451.520735 
L 749.168292 451.799171 
L 746.36915 449.361242 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #65e07a"/>
    <path d="M 822.884178 502.040135 
L 825.717163 503.311548 
L 827.226492 504.42333 
L 824.396917 503.138503 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a6d7"/>
    <path d="M 702.296644 415.535003 
L 705.092052 417.995897 
L 706.74527 417.094843 
L 703.95137 414.53728 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d9f791"/>
    <path d="M 723.522987 432.193317 
L 726.321794 434.652971 
L 727.957914 434.385272 
L 725.161415 431.837034 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a1ec86"/>
    <path d="M 594.056535 404.801401 
L 596.787328 405.632908 
L 598.451724 401.670927 
L 595.718694 400.761483 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fcfb97"/>
    <path d="M 671.052849 394.818312 
L 673.840475 397.072066 
L 675.508426 395.172997 
L 672.721036 392.818555 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eee990"/>
    <path d="M 629.371525 384.928522 
L 632.136414 386.528833 
L 633.80673 383.365264 
L 631.040519 381.671973 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dcd286"/>
    <path d="M 765.98469 465.646746 
L 768.791667 467.811336 
L 770.378818 468.523925 
L 767.57527 466.298238 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2dd56f"/>
    <path d="M 651.013344 386.766842 
L 653.792291 388.750179 
L 655.463605 386.221836 
L 652.684101 384.139776 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e0d788"/>
    <path d="M 686.668116 404.653149 
L 689.460445 407.031007 
L 691.122831 405.640959 
L 688.331375 403.163064 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 661.026998 390.429198 
L 663.810804 392.551909 
L 665.481175 390.338703 
L 662.697199 388.115708 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e6df8b"/>
    <path d="M 705.092052 417.995897 
L 707.888238 420.448477 
L 709.539837 419.643476 
L 706.74527 417.094843 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d1f690"/>
    <path d="M 598.451724 401.670927 
L 601.187295 402.583734 
L 602.852868 398.707335 
L 600.115131 397.714014 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f6f394"/>
    <path d="M 747.554665 451.520735 
L 750.357769 453.849349 
L 751.968352 454.202438 
L 749.168292 451.799171 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #5ddf79"/>
    <path d="M 636.574932 385.075702 
L 639.345082 386.802391 
L 641.016414 383.847297 
L 638.245176 382.02512 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #dcd286"/>
    <path d="M 726.321794 434.652971 
L 729.121382 437.092059 
L 730.755097 436.911699 
L 727.957914 434.385272 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #99eb85"/>
    <path d="M 784.418909 478.926656 
L 787.23205 480.85368 
L 788.794151 481.827766 
L 785.984642 479.854739 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #01cc66"/>
    <path d="M 643.789479 385.686344 
L 646.564329 387.541231 
L 648.236008 384.798448 
L 645.460328 382.846154 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ded587"/>
    <path d="M 624.940048 386.710926 
L 627.701362 388.203194 
L 629.371525 384.928522 
L 626.608736 383.344392 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ded587"/>
    <path d="M 673.840475 397.072066 
L 676.62925 399.333199 
L 678.296857 397.535231 
L 675.508426 395.172997 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f2ee92"/>
    <path d="M 812.877937 496.694871 
L 815.705111 498.152184 
L 817.227828 499.288754 
L 814.404205 497.80983 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b0b9"/>
    <path d="M 800.052442 489.148211 
L 802.872627 490.830645 
L 804.412974 491.932775 
L 801.596436 490.217759 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00bc94"/>
    <path d="M 602.852868 398.707335 
L 605.593122 399.70644 
L 607.259792 395.920473 
L 604.517457 394.838455 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f2ee92"/>
    <path d="M 620.512746 388.707571 
L 623.270244 390.094348 
L 624.940048 386.710926 
L 622.180931 385.233639 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e2da89"/>
    <path d="M 768.791667 467.811336 
L 771.600062 469.931408 
L 773.183735 470.702909 
L 770.378818 468.523925 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #29d46e"/>
    <path d="M 689.460445 407.031007 
L 692.253698 409.408882 
L 693.915098 408.118754 
L 691.122831 405.640959 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9fe98"/>
    <path d="M 707.888238 420.448477 
L 710.685206 422.891127 
L 712.335076 422.181469 
L 709.539837 419.643476 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c9f48e"/>
    <path d="M 729.121382 437.092059 
L 731.921783 439.509 
L 733.552996 439.414646 
L 730.755097 436.911699 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #91e983"/>
    <path d="M 607.259792 395.920473 
L 610.004607 397.010514 
L 611.672272 393.31946 
L 608.925475 392.144297 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ece78f"/>
    <path d="M 750.357769 453.849349 
L 753.161926 456.143621 
L 754.769391 456.569516 
L 751.968352 454.202438 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #59de78"/>
    <path d="M 616.090031 390.912646 
L 618.843492 392.196933 
L 620.512746 388.707571 
L 617.757534 387.334353 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e4dc8a"/>
    <path d="M 653.792291 388.750179 
L 656.572808 390.747286 
L 658.244585 388.31874 
L 655.463605 386.221836 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e2da89"/>
    <path d="M 835.736279 507.840541 
L 838.580343 508.832843 
L 840.073892 509.895298 
L 837.232995 508.89993 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #009eef"/>
    <path d="M 611.672272 393.31946 
L 614.421497 394.504695 
L 616.090031 390.912646 
L 613.338933 389.640279 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e8e28d"/>
    <path d="M 663.810804 392.551909 
L 666.595965 394.68556 
L 668.266405 392.57338 
L 665.481175 390.338703 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eae48e"/>
    <path d="M 632.136414 386.528833 
L 634.903363 388.14454 
L 636.574932 385.075702 
L 633.80673 383.365264 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ded587"/>
    <path d="M 825.717163 503.311548 
L 828.553527 504.512854 
L 830.059488 505.635515 
L 827.226492 504.42333 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a6d7"/>
    <path d="M 676.62925 399.333199 
L 679.419146 401.600266 
L 681.0863 399.903703 
L 678.296857 397.535231 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f4f193"/>
    <path d="M 787.23205 480.85368 
L 790.047127 482.726969 
L 791.605577 483.744635 
L 788.794151 481.827766 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00cb6b"/>
    <path d="M 646.564329 387.541231 
L 649.340921 389.410918 
L 651.013344 386.766842 
L 648.236008 384.798448 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e0d788"/>
    <path d="M 692.253698 409.408882 
L 695.047861 411.785218 
L 696.708162 410.594792 
L 693.915098 408.118754 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1fc96"/>
    <path d="M 710.685206 422.891127 
L 713.482963 425.322247 
L 715.130996 424.707123 
L 712.335076 422.181469 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c1f38d"/>
    <path d="M 639.345082 386.802391 
L 642.117139 388.544421 
L 643.789479 385.686344 
L 641.016414 383.847297 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ded587"/>
    <path d="M 731.921783 439.509 
L 734.723031 441.902235 
L 736.351648 441.892472 
L 733.552996 439.414646 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #89e781"/>
    <path d="M 596.787328 405.632908 
L 599.520675 406.465193 
L 601.187295 402.583734 
L 598.451724 401.670927 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fcfb97"/>
    <path d="M 771.600062 469.931408 
L 774.409958 472.005722 
L 775.990112 472.833897 
L 773.183735 470.702909 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #21d36d"/>
    <path d="M 753.161926 456.143621 
L 755.967196 458.402131 
L 757.571475 458.898917 
L 754.769391 456.569516 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #51dc76"/>
    <path d="M 627.701362 388.203194 
L 630.46484 389.709774 
L 632.136414 386.528833 
L 629.371525 384.928522 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e0d788"/>
    <path d="M 666.595965 394.68556 
L 669.382446 396.828831 
L 671.052849 394.818312 
L 668.266405 392.57338 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ece78f"/>
    <path d="M 802.872627 490.830645 
L 805.695283 492.452302 
L 807.23199 493.584476 
L 804.412974 491.932775 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00bb9b"/>
    <path d="M 656.572808 390.747286 
L 659.354855 392.756976 
L 661.026998 390.429198 
L 658.244585 388.31874 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e6df8b"/>
    <path d="M 679.419146 401.600266 
L 682.210139 403.871816 
L 683.876728 402.276862 
L 681.0863 399.903703 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f8f695"/>
    <path d="M 815.705111 498.152184 
L 818.53525 499.543423 
L 820.054442 500.69904 
L 817.227828 499.288754 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00aebf"/>
    <path d="M 713.482963 425.322247 
L 716.281521 427.740246 
L 717.92761 427.218757 
L 715.130996 424.707123 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b9f18b"/>
    <path d="M 695.047861 411.785218 
L 697.842924 414.158467 
L 699.502013 413.067423 
L 696.708162 410.594792 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e9fb95"/>
    <path d="M 601.187295 402.583734 
L 603.925405 403.499826 
L 605.593122 399.70644 
L 602.852868 398.707335 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f6f394"/>
    <path d="M 734.723031 441.902235 
L 737.525163 444.270234 
L 739.151095 444.343564 
L 736.351648 441.892472 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #81e680"/>
    <path d="M 623.270244 390.094348 
L 626.029999 391.494123 
L 627.701362 388.203194 
L 624.940048 386.710926 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e2da89"/>
    <path d="M 634.903363 388.14454 
L 637.672334 389.774849 
L 639.345082 386.802391 
L 636.574932 385.075702 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e0d788"/>
    <path d="M 605.593122 399.70644 
L 608.335885 400.711161 
L 610.004607 397.010514 
L 607.259792 395.920473 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f2ee92"/>
    <path d="M 649.340921 389.410918 
L 652.119216 391.294348 
L 653.792291 388.750179 
L 651.013344 386.766842 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e2da89"/>
    <path d="M 755.967196 458.402131 
L 758.773645 460.623496 
L 760.37467 461.189188 
L 757.571475 458.898917 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #49db75"/>
    <path d="M 618.843492 392.196933 
L 621.599291 393.492683 
L 623.270244 390.094348 
L 620.512746 388.707571 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e6df8b"/>
    <path d="M 790.047127 482.726969 
L 792.864242 484.545528 
L 794.419028 485.60431 
L 791.605577 483.744635 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c970"/>
    <path d="M 642.117139 388.544421 
L 644.891064 390.300865 
L 646.564329 387.541231 
L 643.789479 385.686344 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e0d788"/>
    <path d="M 610.004607 397.010514 
L 612.751886 398.108317 
L 614.421497 394.504695 
L 611.672272 393.31946 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eee990"/>
    <path d="M 774.409958 472.005722 
L 777.221442 474.033086 
L 778.798037 474.915641 
L 775.990112 472.833897 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1dd26c"/>
    <path d="M 614.421497 394.504695 
L 617.17313 395.699645 
L 618.843492 392.196933 
L 616.090031 390.912646 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eae48e"/>
    <path d="M 716.281521 427.740246 
L 719.080895 430.143554 
L 720.724934 429.714703 
L 717.92761 427.218757 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b5f08a"/>
    <path d="M 669.382446 396.828831 
L 672.170216 398.980392 
L 673.840475 397.072066 
L 671.052849 394.818312 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f0ec91"/>
    <path d="M 697.842924 414.158467 
L 700.63888 416.527086 
L 702.296644 415.535003 
L 699.502013 413.067423 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e1f993"/>
    <path d="M 682.210139 403.871816 
L 685.002204 406.146398 
L 686.668116 404.653149 
L 683.876728 402.276862 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fcfb97"/>
    <path d="M 659.354855 392.756976 
L 662.138396 394.778055 
L 663.810804 392.551909 
L 661.026998 390.429198 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e8e28d"/>
    <path d="M 838.580343 508.832843 
L 841.428364 509.751425 
L 842.918806 510.814457 
L 840.073892 509.895298 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #009eef"/>
    <path d="M 737.525163 444.270234 
L 740.328224 446.611491 
L 741.951381 446.766336 
L 739.151095 444.343564 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #7de57f"/>
    <path d="M 828.553527 504.512854 
L 831.3934 505.643695 
L 832.896039 506.774687 
L 830.059488 505.635515 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a4dc"/>
    <path d="M 630.46484 389.709774 
L 633.230446 391.229981 
L 634.903363 388.14454 
L 632.136414 386.528833 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e2da89"/>
    <path d="M 805.695283 492.452302 
L 808.520525 494.012428 
L 810.053604 495.172082 
L 807.23199 493.584476 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b8a0"/>
    <path d="M 758.773645 460.623496 
L 761.58134 462.806371 
L 763.179051 463.438921 
L 760.37467 461.189188 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #45da74"/>
    <path d="M 719.080895 430.143554 
L 721.881103 432.530613 
L 723.522987 432.193317 
L 720.724934 429.714703 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #adef89"/>
    <path d="M 700.63888 416.527086 
L 703.435727 418.889538 
L 705.092052 417.995897 
L 702.296644 415.535003 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ddf892"/>
    <path d="M 685.002204 406.146398 
L 687.795324 408.422558 
L 689.460445 407.031007 
L 686.668116 404.653149 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 652.119216 391.294348 
L 654.899175 393.190452 
L 656.572808 390.747286 
L 653.792291 388.750179 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e4dc8a"/>
    <path d="M 599.520675 406.465193 
L 602.256579 407.298257 
L 603.925405 403.499826 
L 601.187295 402.583734 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fcfb97"/>
    <path d="M 672.170216 398.980392 
L 674.959245 401.138908 
L 676.62925 399.333199 
L 673.840475 397.072066 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f2ee92"/>
    <path d="M 818.53525 499.543423 
L 821.368477 500.868053 
L 822.884178 502.040135 
L 820.054442 500.69904 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00acc4"/>
    <path d="M 740.328224 446.611491 
L 743.132256 448.924531 
L 744.752554 449.159234 
L 741.951381 446.766336 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #75e37d"/>
    <path d="M 637.672334 389.774849 
L 640.443291 391.418949 
L 642.117139 388.544421 
L 639.345082 386.802391 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e2da89"/>
    <path d="M 777.221442 474.033086 
L 780.034602 476.012352 
L 781.607604 476.946943 
L 778.798037 474.915641 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #19d16b"/>
    <path d="M 626.029999 391.494123 
L 628.791979 392.906321 
L 630.46484 389.709774 
L 627.701362 388.203194 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e4dc8a"/>
    <path d="M 792.864242 484.545528 
L 795.6835 486.308415 
L 797.234613 487.40581 
L 794.419028 485.60431 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c677"/>
    <path d="M 644.891064 390.300865 
L 647.666819 392.070785 
L 649.340921 389.410918 
L 646.564329 387.541231 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e2da89"/>
    <path d="M 662.138396 394.778055 
L 664.923395 396.809315 
L 666.595965 394.68556 
L 663.810804 392.551909 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eae48e"/>
    <path d="M 603.925405 403.499826 
L 606.666051 404.419118 
L 608.335885 400.711161 
L 605.593122 399.70644 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f8f695"/>
    <path d="M 721.881103 432.530613 
L 724.682168 434.899888 
L 726.321794 434.652971 
L 723.522987 432.193317 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a5ed87"/>
    <path d="M 621.599291 393.492683 
L 624.357403 394.799429 
L 626.029999 391.494123 
L 623.270244 390.094348 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e6df8b"/>
    <path d="M 703.435727 418.889538 
L 706.233463 421.244295 
L 707.888238 420.448477 
L 705.092052 417.995897 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d5f791"/>
    <path d="M 761.58134 462.806371 
L 764.390353 464.94945 
L 765.98469 465.646746 
L 763.179051 463.438921 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #3dd872"/>
    <path d="M 608.335885 400.711161 
L 611.081148 401.721325 
L 612.751886 398.108317 
L 610.004607 397.010514 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f2ee92"/>
    <path d="M 687.795324 408.422558 
L 690.589481 410.698844 
L 692.253698 409.408882 
L 689.460445 407.031007 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9fe98"/>
    <path d="M 617.17313 395.699645 
L 619.927151 396.903947 
L 621.599291 393.492683 
L 618.843492 392.196933 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eae48e"/>
    <path d="M 612.751886 398.108317 
L 615.501616 399.213619 
L 617.17313 395.699645 
L 614.421497 394.504695 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eee990"/>
    <path d="M 743.132256 448.924531 
L 745.937309 451.207908 
L 747.554665 451.520735 
L 744.752554 449.159234 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #6de27c"/>
    <path d="M 674.959245 401.138908 
L 677.749506 403.303039 
L 679.419146 401.600266 
L 676.62925 399.333199 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f6f394"/>
    <path d="M 633.230446 391.229981 
L 635.998149 392.763118 
L 637.672334 389.774849 
L 634.903363 388.14454 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e4dc8a"/>
    <path d="M 654.899175 393.190452 
L 657.680762 395.098152 
L 659.354855 392.756976 
L 656.572808 390.747286 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e8e28d"/>
    <path d="M 780.034602 476.012352 
L 782.84953 477.94242 
L 784.418909 478.926656 
L 781.607604 476.946943 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #11cf69"/>
    <path d="M 724.682168 434.899888 
L 727.484115 437.249863 
L 729.121382 437.092059 
L 726.321794 434.652971 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9deb85"/>
    <path d="M 808.520525 494.012428 
L 811.348469 495.51033 
L 812.877937 496.694871 
L 810.053604 495.172082 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b6a7"/>
    <path d="M 831.3934 505.643695 
L 834.236911 506.703776 
L 835.736279 507.840541 
L 832.896039 506.774687 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a4dc"/>
    <path d="M 664.923395 396.809315 
L 667.709821 398.849542 
L 669.382446 396.828831 
L 666.595965 394.68556 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eee990"/>
    <path d="M 706.233463 421.244295 
L 709.032093 423.589841 
L 710.685206 422.891127 
L 707.888238 420.448477 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cdf58f"/>
    <path d="M 640.443291 391.418949 
L 643.216199 393.076015 
L 644.891064 390.300865 
L 642.117139 388.544421 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e4dc8a"/>
    <path d="M 647.666819 392.070785 
L 650.444367 393.853228 
L 652.119216 391.294348 
L 649.340921 389.410918 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e4dc8a"/>
    <path d="M 795.6835 486.308415 
L 798.505006 488.014743 
L 800.052442 489.148211 
L 797.234613 487.40581 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c47d"/>
    <path d="M 690.589481 410.698844 
L 693.384664 412.973806 
L 695.047861 411.785218 
L 692.253698 409.408882 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1fc96"/>
    <path d="M 764.390353 464.94945 
L 767.200757 467.051468 
L 768.791667 467.811336 
L 765.98469 465.646746 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #39d771"/>
    <path d="M 628.791979 392.906321 
L 631.556156 394.330356 
L 633.230446 391.229981 
L 630.46484 389.709774 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e6df8b"/>
    <path d="M 745.937309 451.207908 
L 748.743435 453.460208 
L 750.357769 453.849349 
L 747.554665 451.520735 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #69e17b"/>
    <path d="M 821.368477 500.868053 
L 824.204918 502.125601 
L 825.717163 503.311548 
L 822.884178 502.040135 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00acc4"/>
    <path d="M 677.749506 403.303039 
L 680.540975 405.47144 
L 682.210139 403.871816 
L 679.419146 401.600266 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f8f695"/>
    <path d="M 727.484115 437.249863 
L 730.286973 439.579043 
L 731.921783 439.509 
L 729.121382 437.092059 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #99eb85"/>
    <path d="M 602.256579 407.298257 
L 604.995045 408.132101 
L 606.666051 404.419118 
L 603.925405 403.499826 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fcfb97"/>
    <path d="M 709.032093 423.589841 
L 711.831624 425.92467 
L 713.482963 425.322247 
L 710.685206 422.891127 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c5f38d"/>
    <path d="M 624.357403 394.799429 
L 627.117802 396.116692 
L 628.791979 392.906321 
L 626.029999 391.494123 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e8e28d"/>
    <path d="M 657.680762 395.098152 
L 660.463945 397.016355 
L 662.138396 394.778055 
L 659.354855 392.756976 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eae48e"/>
    <path d="M 667.709821 398.849542 
L 670.497644 400.897513 
L 672.170216 398.980392 
L 669.382446 396.828831 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f0ec91"/>
    <path d="M 693.384664 412.973806 
L 696.180862 415.245999 
L 697.842924 414.158467 
L 695.047861 411.785218 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e9fb95"/>
    <path d="M 782.84953 477.94242 
L 785.66632 479.822239 
L 787.23205 480.85368 
L 784.418909 478.926656 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0dcf69"/>
    <path d="M 635.998149 392.763118 
L 638.767915 394.308475 
L 640.443291 391.418949 
L 637.672334 389.774849 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e6df8b"/>
    <path d="M 606.666051 404.419118 
L 609.40923 405.341526 
L 611.081148 401.721325 
L 608.335885 400.711161 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f8f695"/>
    <path d="M 619.927151 396.903947 
L 622.683539 398.117226 
L 624.357403 394.799429 
L 621.599291 393.492683 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ece78f"/>
    <path d="M 748.743435 453.460208 
L 751.550689 455.680047 
L 753.161926 456.143621 
L 750.357769 453.849349 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #61df79"/>
    <path d="M 611.081148 401.721325 
L 613.828902 402.736757 
L 615.501616 399.213619 
L 612.751886 398.108317 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f2ee92"/>
    <path d="M 615.501616 399.213619 
L 618.253781 400.326145 
L 619.927151 396.903947 
L 617.17313 395.699645 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eee990"/>
    <path d="M 767.200757 467.051468 
L 770.012629 469.1112 
L 771.600062 469.931408 
L 768.791667 467.811336 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #31d670"/>
    <path d="M 650.444367 393.853228 
L 653.223675 395.647231 
L 654.899175 393.190452 
L 652.119216 391.294348 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e8e28d"/>
    <path d="M 680.540975 405.47144 
L 683.333632 407.642765 
L 685.002204 406.146398 
L 682.210139 403.871816 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fcfb97"/>
    <path d="M 643.216199 393.076015 
L 645.991024 394.745212 
L 647.666819 392.070785 
L 644.891064 390.300865 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e6df8b"/>
    <path d="M 730.286973 439.579043 
L 733.090774 441.885955 
L 734.723031 441.902235 
L 731.921783 439.509 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #91e983"/>
    <path d="M 811.348469 495.51033 
L 814.179234 496.945371 
L 815.705111 498.152184 
L 812.877937 496.694871 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b6a7"/>
    <path d="M 711.831624 425.92467 
L 714.632065 428.247289 
L 716.281521 427.740246 
L 713.482963 425.322247 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bdf28c"/>
    <path d="M 798.505006 488.014743 
L 801.328869 489.663676 
L 802.872627 490.830645 
L 800.052442 489.148211 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c382"/>
    <path d="M 696.180862 415.245999 
L 698.978068 417.513979 
L 700.63888 416.527086 
L 697.842924 414.158467 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e5fa94"/>
    <path d="M 631.556156 394.330356 
L 634.322502 395.76563 
L 635.998149 392.763118 
L 633.230446 391.229981 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e6df8b"/>
    <path d="M 834.236911 506.703776 
L 837.084191 507.692869 
L 838.580343 508.832843 
L 835.736279 507.840541 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a4dc"/>
    <path d="M 660.463945 397.016355 
L 663.24869 398.943964 
L 664.923395 396.809315 
L 662.138396 394.778055 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ece78f"/>
    <path d="M 670.497644 400.897513 
L 673.286836 402.952 
L 674.959245 401.138908 
L 672.170216 398.980392 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f4f193"/>
    <path d="M 751.550689 455.680047 
L 754.35913 457.866079 
L 755.967196 458.402131 
L 753.161926 456.143621 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #59de78"/>
    <path d="M 733.090774 441.885955 
L 735.895555 444.169152 
L 737.525163 444.270234 
L 734.723031 441.902235 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #89e781"/>
    <path d="M 824.204918 502.125601 
L 827.044696 503.315655 
L 828.553527 504.512854 
L 825.717163 503.311548 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00acc4"/>
    <path d="M 785.66632 479.822239 
L 788.485066 481.650806 
L 790.047127 482.726969 
L 787.23205 480.85368 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #09ce68"/>
    <path d="M 683.333632 407.642765 
L 686.127459 409.815667 
L 687.795324 408.422558 
L 685.002204 406.146398 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 714.632065 428.247289 
L 717.433432 430.55622 
L 719.080895 430.143554 
L 716.281521 427.740246 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b9f18b"/>
    <path d="M 770.012629 469.1112 
L 772.826049 471.127465 
L 774.409958 472.005722 
L 771.600062 469.931408 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2dd56f"/>
    <path d="M 627.117802 396.116692 
L 629.880465 397.443985 
L 631.556156 394.330356 
L 628.791979 392.906321 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eae48e"/>
    <path d="M 638.767915 394.308475 
L 641.539715 395.865332 
L 643.216199 393.076015 
L 640.443291 391.418949 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e6df8b"/>
    <path d="M 653.223675 395.647231 
L 656.00471 397.45182 
L 657.680762 395.098152 
L 654.899175 393.190452 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eae48e"/>
    <path d="M 698.978068 417.513979 
L 701.77628 419.776314 
L 703.435727 418.889538 
L 700.63888 416.527086 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ddf892"/>
    <path d="M 645.991024 394.745212 
L 648.767734 396.425693 
L 650.444367 393.853228 
L 647.666819 392.070785 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e8e28d"/>
    <path d="M 604.995045 408.132101 
L 607.736076 408.966725 
L 609.40923 405.341526 
L 606.666051 404.419118 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fcfb97"/>
    <path d="M 622.683539 398.117226 
L 625.442275 399.3391 
L 627.117802 396.116692 
L 624.357403 394.799429 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ece78f"/>
    <path d="M 801.328869 489.663676 
L 804.155197 491.254438 
L 805.695283 492.452302 
L 802.872627 490.830645 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c088"/>
    <path d="M 673.286836 402.952 
L 676.077373 405.011769 
L 677.749506 403.303039 
L 674.959245 401.138908 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f6f394"/>
    <path d="M 754.35913 457.866079 
L 757.168817 460.016988 
L 758.773645 460.623496 
L 755.967196 458.402131 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #55dd77"/>
    <path d="M 735.895555 444.169152 
L 738.701354 446.427212 
L 740.328224 446.611491 
L 737.525163 444.270234 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #81e680"/>
    <path d="M 717.433432 430.55622 
L 720.235739 432.850003 
L 721.881103 432.530613 
L 719.080895 430.143554 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b1ef89"/>
    <path d="M 663.24869 398.943964 
L 666.034968 400.879869 
L 667.709821 398.849542 
L 664.923395 396.809315 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f0ec91"/>
    <path d="M 609.40923 405.341526 
L 612.15494 406.266962 
L 613.828902 402.736757 
L 611.081148 401.721325 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f8f695"/>
    <path d="M 814.179234 496.945371 
L 817.012938 498.316976 
L 818.53525 499.543423 
L 815.705111 498.152184 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b4ac"/>
    <path d="M 618.253781 400.326145 
L 621.008368 401.445616 
L 622.683539 398.117226 
L 619.927151 396.903947 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f0ec91"/>
    <path d="M 686.127459 409.815667 
L 688.922439 411.988799 
L 690.589481 410.698844 
L 687.795324 408.422558 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9fe98"/>
    <path d="M 613.828902 402.736757 
L 616.579139 403.757276 
L 618.253781 400.326145 
L 615.501616 399.213619 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f4f193"/>
    <path d="M 634.322502 395.76563 
L 637.09099 397.211537 
L 638.767915 394.308475 
L 635.998149 392.763118 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e8e28d"/>
    <path d="M 772.826049 471.127465 
L 775.641097 473.099124 
L 777.221442 474.033086 
L 774.409958 472.005722 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #29d46e"/>
    <path d="M 701.77628 419.776314 
L 704.575497 422.031576 
L 706.233463 421.244295 
L 703.435727 418.889538 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d5f791"/>
    <path d="M 788.485066 481.650806 
L 791.305867 483.427169 
L 792.864242 484.545528 
L 790.047127 482.726969 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #05cd67"/>
    <path d="M 656.00471 397.45182 
L 658.787441 399.266012 
L 660.463945 397.016355 
L 657.680762 395.098152 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ece78f"/>
    <path d="M 720.235739 432.850003 
L 723.039009 435.127192 
L 724.682168 434.899888 
L 721.881103 432.530613 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a9ee88"/>
    <path d="M 738.701354 446.427212 
L 741.508214 448.658741 
L 743.132256 448.924531 
L 740.328224 446.611491 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #7de57f"/>
    <path d="M 641.539715 395.865332 
L 644.313519 397.432956 
L 645.991024 394.745212 
L 643.216199 393.076015 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e8e28d"/>
    <path d="M 676.077373 405.011769 
L 678.869232 407.075584 
L 680.540975 405.47144 
L 677.749506 403.303039 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #faf996"/>
    <path d="M 757.168817 460.016988 
L 759.979816 462.131498 
L 761.58134 462.806371 
L 758.773645 460.623496 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #4ddb75"/>
    <path d="M 837.084191 507.692869 
L 839.935367 508.610814 
L 841.428364 509.751425 
L 838.580343 508.832843 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00a4dc"/>
    <path d="M 688.922439 411.988799 
L 691.718561 414.160816 
L 693.384664 412.973806 
L 690.589481 410.698844 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1fc96"/>
    <path d="M 648.767734 396.425693 
L 651.546298 398.1166 
L 653.223675 395.647231 
L 650.444367 393.853228 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eae48e"/>
    <path d="M 827.044696 503.315655 
L 829.887938 504.437869 
L 831.3934 505.643695 
L 828.553527 504.512854 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00aacb"/>
    <path d="M 629.880465 397.443985 
L 632.645369 398.78081 
L 634.322502 395.76563 
L 631.556156 394.330356 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eae48e"/>
    <path d="M 666.034968 400.879869 
L 668.822753 402.822958 
L 670.497644 400.897513 
L 667.709821 398.849542 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f2ee92"/>
    <path d="M 704.575497 422.031576 
L 707.375722 424.278347 
L 709.032093 423.589841 
L 706.233463 421.244295 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d1f690"/>
    <path d="M 804.155197 491.254438 
L 806.984102 492.786302 
L 808.520525 494.012428 
L 805.695283 492.452302 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00be8f"/>
    <path d="M 775.641097 473.099124 
L 778.45786 475.025082 
L 780.034602 476.012352 
L 777.221442 474.033086 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #25d36d"/>
    <path d="M 625.442275 399.3391 
L 628.203341 400.56918 
L 629.880465 397.443985 
L 627.117802 396.116692 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eee990"/>
    <path d="M 723.039009 435.127192 
L 725.843265 437.386363 
L 727.484115 437.249863 
L 724.682168 434.899888 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a5ed87"/>
    <path d="M 741.508214 448.658741 
L 744.316181 450.862371 
L 745.937309 451.207908 
L 743.132256 448.924531 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #75e37d"/>
    <path d="M 817.012938 498.316976 
L 819.849699 499.624628 
L 821.368477 500.868053 
L 818.53525 499.543423 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b4ac"/>
    <path d="M 791.305867 483.427169 
L 794.128822 485.150425 
L 795.6835 486.308415 
L 792.864242 484.545528 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #01cc66"/>
    <path d="M 607.736076 408.966725 
L 610.479676 409.802132 
L 612.15494 406.266962 
L 609.40923 405.341526 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fcfb97"/>
    <path d="M 637.09099 397.211537 
L 639.861593 398.667456 
L 641.539715 395.865332 
L 638.767915 394.308475 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eae48e"/>
    <path d="M 678.869232 407.075584 
L 681.662395 409.142205 
L 683.333632 407.642765 
L 680.540975 405.47144 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fcfb97"/>
    <path d="M 691.718561 414.160816 
L 694.515816 416.330376 
L 696.180862 415.245999 
L 693.384664 412.973806 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #edfb95"/>
    <path d="M 759.979816 462.131498 
L 762.792194 464.208368 
L 764.390353 464.94945 
L 761.58134 462.806371 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #49db75"/>
    <path d="M 621.008368 401.445616 
L 623.765363 402.571746 
L 625.442275 399.3391 
L 622.683539 398.117226 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f0ec91"/>
    <path d="M 658.787441 399.266012 
L 661.57184 401.088815 
L 663.24869 398.943964 
L 660.463945 397.016355 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eee990"/>
    <path d="M 612.15494 406.266962 
L 614.903178 407.195337 
L 616.579139 403.757276 
L 613.828902 402.736757 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f8f695"/>
    <path d="M 616.579139 403.757276 
L 619.33185 404.782696 
L 621.008368 401.445616 
L 618.253781 400.326145 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f4f193"/>
    <path d="M 707.375722 424.278347 
L 710.176961 426.515222 
L 711.831624 425.92467 
L 709.032093 423.589841 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c9f48e"/>
    <path d="M 668.822753 402.822958 
L 671.612018 404.772108 
L 673.286836 402.952 
L 670.497644 400.897513 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f4f193"/>
    <path d="M 644.313519 397.432956 
L 647.089299 399.010605 
L 648.767734 396.425693 
L 645.991024 394.745212 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eae48e"/>
    <path d="M 651.546298 398.1166 
L 654.326688 399.817067 
L 656.00471 397.45182 
L 653.223675 395.647231 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ece78f"/>
    <path d="M 725.843265 437.386363 
L 728.648534 439.626108 
L 730.286973 439.579043 
L 727.484115 437.249863 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9deb85"/>
    <path d="M 744.316181 450.862371 
L 747.125303 453.036764 
L 748.743435 453.460208 
L 745.937309 451.207908 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #71e37d"/>
    <path d="M 632.645369 398.78081 
L 635.412491 400.126659 
L 637.09099 397.211537 
L 634.322502 395.76563 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ece78f"/>
    <path d="M 778.45786 475.025082 
L 781.276423 476.904289 
L 782.84953 477.94242 
L 780.034602 476.012352 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1dd26c"/>
    <path d="M 694.515816 416.330376 
L 697.314197 418.496141 
L 698.978068 417.513979 
L 696.180862 415.245999 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e5fa94"/>
    <path d="M 681.662395 409.142205 
L 684.456843 411.210393 
L 686.127459 409.815667 
L 683.333632 407.642765 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 710.176961 426.515222 
L 712.979223 428.740806 
L 714.632065 428.247289 
L 711.831624 425.92467 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c5f38d"/>
    <path d="M 762.792194 464.208368 
L 765.606021 466.246394 
L 767.200757 467.051468 
L 764.390353 464.94945 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #41d973"/>
    <path d="M 806.984102 492.786302 
L 809.815694 494.258604 
L 811.348469 495.51033 
L 808.520525 494.012428 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00be8f"/>
    <path d="M 829.887938 504.437869 
L 832.734767 505.49196 
L 834.236911 506.703776 
L 831.3934 505.643695 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00aacb"/>
    <path d="M 661.57184 401.088815 
L 664.357879 402.919229 
L 666.034968 400.879869 
L 663.24869 398.943964 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f0ec91"/>
    <path d="M 794.128822 485.150425 
L 796.954032 486.819725 
L 798.505006 488.014743 
L 795.6835 486.308415 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00cb6b"/>
    <path d="M 671.612018 404.772108 
L 674.402742 406.726197 
L 676.077373 405.011769 
L 673.286836 402.952 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f8f695"/>
    <path d="M 628.203341 400.56918 
L 630.96672 401.807069 
L 632.645369 398.78081 
L 629.880465 397.443985 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eee990"/>
    <path d="M 728.648534 439.626108 
L 731.454846 441.845046 
L 733.090774 441.885955 
L 730.286973 439.579043 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #95ea84"/>
    <path d="M 639.861593 398.667456 
L 642.634287 400.132762 
L 644.313519 397.432956 
L 641.539715 395.865332 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ece78f"/>
    <path d="M 819.849699 499.624628 
L 822.689639 500.867871 
L 824.204918 502.125601 
L 821.368477 500.868053 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b2b2"/>
    <path d="M 747.125303 453.036764 
L 749.935632 455.180614 
L 751.550689 455.680047 
L 748.743435 453.460208 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #69e17b"/>
    <path d="M 654.326688 399.817067 
L 657.108875 401.526217 
L 658.787441 399.266012 
L 656.00471 397.45182 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eee990"/>
    <path d="M 697.314197 418.496141 
L 700.1137 420.656782 
L 701.77628 419.776314 
L 698.978068 417.513979 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e1f993"/>
    <path d="M 647.089299 399.010605 
L 649.867029 400.59753 
L 651.546298 398.1166 
L 648.767734 396.425693 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ece78f"/>
    <path d="M 623.765363 402.571746 
L 626.524753 403.704245 
L 628.203341 400.56918 
L 625.442275 399.3391 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f2ee92"/>
    <path d="M 712.979223 428.740806 
L 715.782522 430.953717 
L 717.433432 430.55622 
L 714.632065 428.247289 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bdf28c"/>
    <path d="M 684.456843 411.210393 
L 687.252564 413.278907 
L 688.922439 411.988799 
L 686.127459 409.815667 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9fe98"/>
    <path d="M 610.479676 409.802132 
L 613.225847 410.638322 
L 614.903178 407.195337 
L 612.15494 406.266962 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fcfb97"/>
    <path d="M 781.276423 476.904289 
L 784.096875 478.735742 
L 785.66632 479.822239 
L 782.84953 477.94242 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #19d16b"/>
    <path d="M 619.33185 404.782696 
L 622.087028 405.812827 
L 623.765363 402.571746 
L 621.008368 401.445616 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f4f193"/>
    <path d="M 765.606021 466.246394 
L 768.421368 468.244414 
L 770.012629 469.1112 
L 767.200757 467.051468 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #3dd872"/>
    <path d="M 614.903178 407.195337 
L 617.653941 408.126559 
L 619.33185 404.782696 
L 616.579139 403.757276 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f8f695"/>
    <path d="M 731.454846 441.845046 
L 734.262234 444.041813 
L 735.895555 444.169152 
L 733.090774 441.885955 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #91e983"/>
    <path d="M 635.412491 400.126659 
L 638.181811 401.48102 
L 639.861593 398.667456 
L 637.09099 397.211537 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eee990"/>
    <path d="M 664.357879 402.919229 
L 667.145534 404.75625 
L 668.822753 402.822958 
L 666.034968 400.879869 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f2ee92"/>
    <path d="M 674.402742 406.726197 
L 677.194903 408.684094 
L 678.869232 407.075584 
L 676.077373 405.011769 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #faf996"/>
    <path d="M 749.935632 455.180614 
L 752.747222 457.292645 
L 754.35913 457.866079 
L 751.550689 455.680047 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #65e07a"/>
    <path d="M 809.815694 494.258604 
L 812.650087 495.670731 
L 814.179234 496.945371 
L 811.348469 495.51033 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00bc94"/>
    <path d="M 796.954032 486.819725 
L 799.7816 488.434268 
L 801.328869 489.663676 
L 798.505006 488.014743 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c970"/>
    <path d="M 700.1137 420.656782 
L 702.914326 422.810973 
L 704.575497 422.031576 
L 701.77628 419.776314 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d9f791"/>
    <path d="M 715.782522 430.953717 
L 718.586873 433.15259 
L 720.235739 432.850003 
L 717.433432 430.55622 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b5f08a"/>
    <path d="M 687.252564 413.278907 
L 690.049545 415.346509 
L 691.718561 414.160816 
L 688.922439 411.988799 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f5fd97"/>
    <path d="M 642.634287 400.132762 
L 645.409048 401.606818 
L 647.089299 399.010605 
L 644.313519 397.432956 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eee990"/>
    <path d="M 657.108875 401.526217 
L 659.892836 403.243168 
L 661.57184 401.088815 
L 658.787441 399.266012 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f0ec91"/>
    <path d="M 832.734767 505.49196 
L 835.58531 506.477706 
L 837.084191 507.692869 
L 834.236911 506.703776 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00aacb"/>
    <path d="M 630.96672 401.807069 
L 633.732393 403.05236 
L 635.412491 400.126659 
L 632.645369 398.78081 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f0ec91"/>
    <path d="M 768.421368 468.244414 
L 771.238312 470.201305 
L 772.826049 471.127465 
L 770.012629 469.1112 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #39d771"/>
    <path d="M 734.262234 444.041813 
L 737.070735 446.215072 
L 738.701354 446.427212 
L 735.895555 444.169152 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #89e781"/>
    <path d="M 649.867029 400.59753 
L 652.646683 402.192969 
L 654.326688 399.817067 
L 651.546298 398.1166 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eee990"/>
    <path d="M 784.096875 478.735742 
L 786.919308 480.518485 
L 788.485066 481.650806 
L 785.66632 479.822239 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #15d06a"/>
    <path d="M 822.689639 500.867871 
L 825.532876 502.04631 
L 827.044696 503.315655 
L 824.204918 502.125601 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b2b2"/>
    <path d="M 677.194903 408.684094 
L 679.988485 410.64467 
L 681.662395 409.142205 
L 678.869232 407.075584 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fcfb97"/>
    <path d="M 752.747222 457.292645 
L 755.560132 459.371615 
L 757.168817 460.016988 
L 754.35913 457.866079 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #5ddf79"/>
    <path d="M 667.145534 404.75625 
L 669.934783 406.598865 
L 671.612018 404.772108 
L 668.822753 402.822958 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f6f394"/>
    <path d="M 626.524753 403.704245 
L 629.286525 404.842813 
L 630.96672 401.807069 
L 628.203341 400.56918 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f2ee92"/>
    <path d="M 702.914326 422.810973 
L 705.716077 424.957398 
L 707.375722 424.278347 
L 704.575497 422.031576 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d5f791"/>
    <path d="M 718.586873 433.15259 
L 721.392294 435.336073 
L 723.039009 435.127192 
L 720.235739 432.850003 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b1ef89"/>
    <path d="M 690.049545 415.346509 
L 692.847778 417.411964 
L 694.515816 416.330376 
L 691.718561 414.160816 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #edfb95"/>
    <path d="M 622.087028 405.812827 
L 624.844664 406.847475 
L 626.524753 403.704245 
L 623.765363 402.571746 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f6f394"/>
    <path d="M 638.181811 401.48102 
L 640.953308 402.843368 
L 642.634287 400.132762 
L 639.861593 398.667456 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eee990"/>
    <path d="M 613.225847 410.638322 
L 615.974595 411.475296 
L 617.653941 408.126559 
L 614.903178 407.195337 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fcfb97"/>
    <path d="M 617.653941 408.126559 
L 620.407228 409.060533 
L 622.087028 405.812827 
L 619.33185 404.782696 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f8f695"/>
    <path d="M 799.7816 488.434268 
L 802.611631 489.993309 
L 804.155197 491.254438 
L 801.328869 489.663676 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c677"/>
    <path d="M 737.070735 446.215072 
L 739.880389 448.363511 
L 741.508214 448.658741 
L 738.701354 446.427212 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #85e781"/>
    <path d="M 812.650087 495.670731 
L 815.487394 497.022131 
L 817.012938 498.316976 
L 814.179234 496.945371 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00bb9b"/>
    <path d="M 659.892836 403.243168 
L 662.678546 404.96703 
L 664.357879 402.919229 
L 661.57184 401.088815 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f2ee92"/>
    <path d="M 771.238312 470.201305 
L 774.05693 472.115982 
L 775.641097 473.099124 
L 772.826049 471.127465 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #35d771"/>
    <path d="M 645.409048 401.606818 
L 648.185854 403.088979 
L 649.867029 400.59753 
L 647.089299 399.010605 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #eee990"/>
    <path d="M 721.392294 435.336073 
L 724.198807 437.502835 
L 725.843265 437.386363 
L 723.039009 435.127192 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a9ee88"/>
    <path d="M 705.716077 424.957398 
L 708.518958 427.094752 
L 710.176961 426.515222 
L 707.375722 424.278347 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cdf58f"/>
    <path d="M 786.919308 480.518485 
L 789.743813 482.251608 
L 791.305867 483.427169 
L 788.485066 481.650806 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #11cf69"/>
    <path d="M 755.560132 459.371615 
L 758.374422 461.416314 
L 759.979816 462.131498 
L 757.168817 460.016988 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #59de78"/>
    <path d="M 652.646683 402.192969 
L 655.428237 403.796157 
L 657.108875 401.526217 
L 654.326688 399.817067 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f0ec91"/>
    <path d="M 679.988485 410.64467 
L 682.783471 412.606793 
L 684.456843 411.210393 
L 681.662395 409.142205 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 669.934783 406.598865 
L 672.725605 408.44606 
L 674.402742 406.726197 
L 671.612018 404.772108 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f8f695"/>
    <path d="M 633.732393 403.05236 
L 636.500345 404.304644 
L 638.181811 401.48102 
L 635.412491 400.126659 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f0ec91"/>
    <path d="M 692.847778 417.411964 
L 695.647256 419.474039 
L 697.314197 418.496141 
L 694.515816 416.330376 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e9fb95"/>
    <path d="M 739.880389 448.363511 
L 742.691238 450.485844 
L 744.316181 450.862371 
L 741.508214 448.658741 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #7de57f"/>
    <path d="M 835.58531 506.477706 
L 838.43969 507.394953 
L 839.935367 508.610814 
L 837.084191 507.692869 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00aacb"/>
    <path d="M 825.532876 502.04631 
L 828.379531 503.15961 
L 829.887938 504.437869 
L 827.044696 503.315655 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b0b9"/>
    <path d="M 629.286525 404.842813 
L 632.050668 405.987149 
L 633.732393 403.05236 
L 630.96672 401.807069 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f2ee92"/>
    <path d="M 724.198807 437.502835 
L 727.006438 439.65156 
L 728.648534 439.626108 
L 725.843265 437.386363 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a5ed87"/>
    <path d="M 708.518958 427.094752 
L 711.322977 429.221739 
L 712.979223 428.740806 
L 710.176961 426.515222 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c9f48e"/>
    <path d="M 774.05693 472.115982 
L 776.877301 473.987408 
L 778.45786 475.025082 
L 775.641097 473.099124 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2dd56f"/>
    <path d="M 662.678546 404.96703 
L 665.465982 406.696906 
L 667.145534 404.75625 
L 664.357879 402.919229 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f4f193"/>
    <path d="M 640.953308 402.843368 
L 643.726962 404.213173 
L 645.409048 401.606818 
L 642.634287 400.132762 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f0ec91"/>
    <path d="M 802.611631 489.993309 
L 805.44423 491.496154 
L 806.984102 492.786302 
L 804.155197 491.254438 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c47d"/>
    <path d="M 758.374422 461.416314 
L 761.190154 463.425569 
L 762.792194 464.208368 
L 759.979816 462.131498 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #51dc76"/>
    <path d="M 682.783471 412.606793 
L 685.579849 414.569332 
L 687.252564 413.278907 
L 684.456843 411.210393 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9fe98"/>
    <path d="M 624.844664 406.847475 
L 627.604752 407.886443 
L 629.286525 404.842813 
L 626.524753 403.704245 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f6f394"/>
    <path d="M 789.743813 482.251608 
L 792.570487 483.934249 
L 794.128822 485.150425 
L 791.305867 483.427169 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0dcf69"/>
    <path d="M 695.647256 419.474039 
L 698.447976 421.531509 
L 700.1137 420.656782 
L 697.314197 418.496141 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e1f993"/>
    <path d="M 672.725605 408.44606 
L 675.517982 410.296816 
L 677.194903 408.684094 
L 674.402742 406.726197 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #faf996"/>
    <path d="M 815.487394 497.022131 
L 818.32773 498.312306 
L 819.849699 499.624628 
L 817.012938 498.316976 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00bb9b"/>
    <path d="M 655.428237 403.796157 
L 658.211669 405.406318 
L 659.892836 403.243168 
L 657.108875 401.526217 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f2ee92"/>
    <path d="M 648.185854 403.088979 
L 650.964682 404.578595 
L 652.646683 402.192969 
L 649.867029 400.59753 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f0ec91"/>
    <path d="M 742.691238 450.485844 
L 745.503327 452.580812 
L 747.125303 453.036764 
L 744.316181 450.862371 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #79e47e"/>
    <path d="M 620.407228 409.060533 
L 623.163037 409.997164 
L 624.844664 406.847475 
L 622.087028 405.812827 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #faf996"/>
    <path d="M 615.974595 411.475296 
L 618.725921 412.313056 
L 620.407228 409.060533 
L 617.653941 408.126559 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fcfb97"/>
    <path d="M 727.006438 439.65156 
L 729.815215 441.780954 
L 731.454846 441.845046 
L 728.648534 439.626108 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9deb85"/>
    <path d="M 711.322977 429.221739 
L 714.128147 431.337078 
L 715.782522 430.953717 
L 712.979223 428.740806 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c1f38d"/>
    <path d="M 636.500345 404.304644 
L 639.270559 405.563501 
L 640.953308 402.843368 
L 638.181811 401.48102 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f2ee92"/>
    <path d="M 776.877301 473.987408 
L 779.699507 475.814582 
L 781.276423 476.904289 
L 778.45786 475.025082 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #29d46e"/>
    <path d="M 761.190154 463.425569 
L 764.007395 465.398242 
L 765.606021 466.246394 
L 762.792194 464.208368 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #4ddb75"/>
    <path d="M 685.579849 414.569332 
L 688.377607 416.531155 
L 690.049545 415.346509 
L 687.252564 413.278907 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f5fd97"/>
    <path d="M 665.465982 406.696906 
L 668.255125 408.431895 
L 669.934783 406.598865 
L 667.145534 404.75625 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f6f394"/>
    <path d="M 698.447976 421.531509 
L 701.249939 423.583152 
L 702.914326 422.810973 
L 700.1137 420.656782 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ddf892"/>
    <path d="M 745.503327 452.580812 
L 748.316705 454.647184 
L 749.935632 455.180614 
L 747.125303 453.036764 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #71e37d"/>
    <path d="M 675.517982 410.296816 
L 678.311897 412.150113 
L 679.988485 410.64467 
L 677.194903 408.684094 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fcfb97"/>
    <path d="M 805.44423 491.496154 
L 808.279504 492.942165 
L 809.815694 494.258604 
L 806.984102 492.786302 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c47d"/>
    <path d="M 643.726962 404.213173 
L 646.502755 405.5899 
L 648.185854 403.088979 
L 645.409048 401.606818 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f2ee92"/>
    <path d="M 828.379531 503.15961 
L 831.229724 504.207498 
L 832.734767 505.49196 
L 829.887938 504.437869 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b0b9"/>
    <path d="M 632.050668 405.987149 
L 634.817169 407.136943 
L 636.500345 404.304644 
L 633.732393 403.05236 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f4f193"/>
    <path d="M 792.570487 483.934249 
L 795.399424 485.565597 
L 796.954032 486.819725 
L 794.128822 485.150425 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #09ce68"/>
    <path d="M 729.815215 441.780954 
L 732.625168 443.889743 
L 734.262234 444.041813 
L 731.454846 441.845046 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #99eb85"/>
    <path d="M 658.211669 405.406318 
L 660.996959 407.022674 
L 662.678546 404.96703 
L 659.892836 403.243168 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f4f193"/>
    <path d="M 714.128147 431.337078 
L 716.934481 433.439498 
L 718.586873 433.15259 
L 715.782522 430.953717 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bdf28c"/>
    <path d="M 650.964682 404.578595 
L 653.745513 406.075007 
L 655.428237 403.796157 
L 652.646683 402.192969 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f2ee92"/>
    <path d="M 627.604752 407.886443 
L 630.367285 408.929529 
L 632.050668 405.987149 
L 629.286525 404.842813 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f6f394"/>
    <path d="M 818.32773 498.312306 
L 821.17121 499.540819 
L 822.689639 500.867871 
L 819.849699 499.624628 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b8a0"/>
    <path d="M 764.007395 465.398242 
L 766.826213 467.333232 
L 768.421368 468.244414 
L 765.606021 466.246394 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #49db75"/>
    <path d="M 688.377607 416.531155 
L 691.176738 418.491135 
L 692.847778 417.411964 
L 690.049545 415.346509 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1fc96"/>
    <path d="M 701.249939 423.583152 
L 704.053145 425.627757 
L 705.716077 424.957398 
L 702.914326 422.810973 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d5f791"/>
    <path d="M 779.699507 475.814582 
L 782.523634 477.596552 
L 784.096875 478.735742 
L 781.276423 476.904289 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #25d36d"/>
    <path d="M 748.316705 454.647184 
L 751.131424 456.68376 
L 752.747222 457.292645 
L 749.935632 455.180614 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #6de27c"/>
    <path d="M 623.163037 409.997164 
L 625.921365 410.936353 
L 627.604752 407.886443 
L 624.844664 406.847475 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #faf996"/>
    <path d="M 668.255125 408.431895 
L 671.045957 410.171094 
L 672.725605 408.44606 
L 669.934783 406.598865 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f8f695"/>
    <path d="M 618.725921 412.313056 
L 621.479831 413.151602 
L 623.163037 409.997164 
L 620.407228 409.060533 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 639.270559 405.563501 
L 642.043021 406.828509 
L 643.726962 404.213173 
L 640.953308 402.843368 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f2ee92"/>
    <path d="M 678.311897 412.150113 
L 681.107336 414.004928 
L 682.783471 412.606793 
L 679.988485 410.64467 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 732.625168 443.889743 
L 735.436331 445.976676 
L 737.070735 446.215072 
L 734.262234 444.041813 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #91e983"/>
    <path d="M 716.934481 433.439498 
L 719.741998 435.527745 
L 721.392294 435.336073 
L 718.586873 433.15259 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b5f08a"/>
    <path d="M 795.399424 485.565597 
L 798.230724 487.144889 
L 799.7816 488.434268 
L 796.954032 486.819725 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #05cd67"/>
    <path d="M 660.996959 407.022674 
L 663.784087 408.644438 
L 665.465982 406.696906 
L 662.678546 404.96703 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f6f394"/>
    <path d="M 646.502755 405.5899 
L 649.28067 406.973005 
L 650.964682 404.578595 
L 648.185854 403.088979 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f2ee92"/>
    <path d="M 808.279504 492.942165 
L 811.117561 494.330757 
L 812.650087 495.670731 
L 809.815694 494.258604 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c382"/>
    <path d="M 704.053145 425.627757 
L 706.8576 427.66412 
L 708.518958 427.094752 
L 705.716077 424.957398 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d1f690"/>
    <path d="M 691.176738 418.491135 
L 693.977236 420.448147 
L 695.647256 419.474039 
L 692.847778 417.411964 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e9fb95"/>
    <path d="M 653.745513 406.075007 
L 656.528327 407.577552 
L 658.211669 405.406318 
L 655.428237 403.796157 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f4f193"/>
    <path d="M 766.826213 467.333232 
L 769.646679 469.229475 
L 771.238312 470.201305 
L 768.421368 468.244414 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #45da74"/>
    <path d="M 634.817169 407.136943 
L 637.586018 408.291884 
L 639.270559 405.563501 
L 636.500345 404.304644 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f4f193"/>
    <path d="M 751.131424 456.68376 
L 753.947536 458.68937 
L 755.560132 459.371615 
L 752.747222 457.292645 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #69e17b"/>
    <path d="M 831.229724 504.207498 
L 834.083576 505.189762 
L 835.58531 506.477706 
L 832.734767 505.49196 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b0b9"/>
    <path d="M 782.523634 477.596552 
L 785.349767 479.332408 
L 786.919308 480.518485 
L 784.096875 478.735742 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #21d36d"/>
    <path d="M 735.436331 445.976676 
L 738.248741 448.040525 
L 739.880389 448.363511 
L 737.070735 446.215072 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8de882"/>
    <path d="M 719.741998 435.527745 
L 722.550716 437.600582 
L 724.198807 437.502835 
L 721.392294 435.336073 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b1ef89"/>
    <path d="M 671.045957 410.171094 
L 673.838461 411.913594 
L 675.517982 410.296816 
L 672.725605 408.44606 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #faf996"/>
    <path d="M 681.107336 414.004928 
L 683.904287 415.860239 
L 685.579849 414.569332 
L 682.783471 412.606793 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9fe98"/>
    <path d="M 821.17121 499.540819 
L 824.017948 500.70729 
L 825.532876 502.04631 
L 822.689639 500.867871 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b8a0"/>
    <path d="M 630.367285 408.929529 
L 633.132256 409.976528 
L 634.817169 407.136943 
L 632.050668 405.987149 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f6f394"/>
    <path d="M 642.043021 406.828509 
L 644.817716 408.099238 
L 646.502755 405.5899 
L 643.726962 404.213173 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f4f193"/>
    <path d="M 706.8576 427.66412 
L 709.663311 429.691046 
L 711.322977 429.221739 
L 708.518958 427.094752 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cdf58f"/>
    <path d="M 625.921365 410.936353 
L 628.682212 411.877999 
L 630.367285 408.929529 
L 627.604752 407.886443 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #faf996"/>
    <path d="M 693.977236 420.448147 
L 696.779098 422.401071 
L 698.447976 421.531509 
L 695.647256 419.474039 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e5fa94"/>
    <path d="M 663.784087 408.644438 
L 666.573036 410.270821 
L 668.255125 408.431895 
L 665.465982 406.696906 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f8f695"/>
    <path d="M 769.646679 469.229475 
L 772.468866 471.085948 
L 774.05693 472.115982 
L 771.238312 470.201305 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #3dd872"/>
    <path d="M 753.947536 458.68937 
L 756.7651 460.662877 
L 758.374422 461.416314 
L 755.560132 459.371615 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #61df79"/>
    <path d="M 798.230724 487.144889 
L 801.064485 488.671413 
L 802.611631 489.993309 
L 799.7816 488.434268 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #01cc66"/>
    <path d="M 621.479831 413.151602 
L 624.236328 413.990935 
L 625.921365 410.936353 
L 623.163037 409.997164 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 738.248741 448.040525 
L 741.062438 450.080087 
L 742.691238 450.485844 
L 739.880389 448.363511 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #85e781"/>
    <path d="M 722.550716 437.600582 
L 725.360658 439.656785 
L 727.006438 439.65156 
L 724.198807 437.502835 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a9ee88"/>
    <path d="M 649.28067 406.973005 
L 652.06069 408.361939 
L 653.745513 406.075007 
L 650.964682 404.578595 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f4f193"/>
    <path d="M 656.528327 407.577552 
L 659.313109 409.085559 
L 660.996959 407.022674 
L 658.211669 405.406318 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f6f394"/>
    <path d="M 811.117561 494.330757 
L 813.958508 495.661398 
L 815.487394 497.022131 
L 812.650087 495.670731 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c382"/>
    <path d="M 785.349767 479.332408 
L 788.177993 481.021284 
L 789.743813 482.251608 
L 786.919308 480.518485 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1dd26c"/>
    <path d="M 683.904287 415.860239 
L 686.702741 417.715024 
L 688.377607 416.531155 
L 685.579849 414.569332 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f5fd97"/>
    <path d="M 673.838461 411.913594 
L 676.632623 413.658485 
L 678.311897 412.150113 
L 675.517982 410.296816 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fcfb97"/>
    <path d="M 637.586018 408.291884 
L 640.357204 409.451653 
L 642.043021 406.828509 
L 639.270559 405.563501 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f6f394"/>
    <path d="M 709.663311 429.691046 
L 712.470289 431.707354 
L 714.128147 431.337078 
L 711.322977 429.221739 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c5f38d"/>
    <path d="M 696.779098 422.401071 
L 699.582323 424.348792 
L 701.249939 423.583152 
L 698.447976 421.531509 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e1f993"/>
    <path d="M 834.083576 505.189762 
L 836.941207 506.106252 
L 838.43969 507.394953 
L 835.58531 506.477706 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b0b9"/>
    <path d="M 756.7651 460.662877 
L 759.584174 462.603174 
L 761.190154 463.425569 
L 758.374422 461.416314 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #5ddf79"/>
    <path d="M 725.360658 439.656785 
L 728.171852 441.695152 
L 729.815215 441.780954 
L 727.006438 439.65156 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a5ed87"/>
    <path d="M 741.062438 450.080087 
L 743.877464 452.094182 
L 745.503327 452.580812 
L 742.691238 450.485844 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #81e680"/>
    <path d="M 772.468866 471.085948 
L 775.292849 472.901664 
L 776.877301 473.987408 
L 774.05693 472.115982 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #39d771"/>
    <path d="M 824.017948 500.70729 
L 826.86806 501.811397 
L 828.379531 503.15961 
L 825.532876 502.04631 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b8a0"/>
    <path d="M 633.132256 409.976528 
L 635.899658 411.027233 
L 637.586018 408.291884 
L 634.817169 407.136943 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f8f695"/>
    <path d="M 666.573036 410.270821 
L 669.36379 411.90103 
L 671.045957 410.171094 
L 668.255125 408.431895 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #faf996"/>
    <path d="M 644.817716 408.099238 
L 647.594631 409.375253 
L 649.28067 406.973005 
L 646.502755 405.5899 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f4f193"/>
    <path d="M 801.064485 488.671413 
L 803.900808 490.144507 
L 805.44423 491.496154 
L 802.611631 489.993309 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #01cc66"/>
    <path d="M 686.702741 417.715024 
L 689.50269 419.568265 
L 691.176738 418.491135 
L 688.377607 416.531155 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1fc96"/>
    <path d="M 659.313109 409.085559 
L 662.09984 410.598354 
L 663.784087 408.644438 
L 660.996959 407.022674 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f6f394"/>
    <path d="M 652.06069 408.361939 
L 654.842799 409.756149 
L 656.528327 407.577552 
L 653.745513 406.075007 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f6f394"/>
    <path d="M 676.632623 413.658485 
L 679.428429 415.404856 
L 681.107336 414.004928 
L 678.311897 412.150113 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 788.177993 481.021284 
L 791.008404 482.662362 
L 792.570487 483.934249 
L 789.743813 482.251608 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #19d16b"/>
    <path d="M 628.682212 411.877999 
L 631.445575 412.822003 
L 633.132256 409.976528 
L 630.367285 408.929529 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #faf996"/>
    <path d="M 712.470289 431.707354 
L 715.278546 433.711873 
L 716.934481 433.439498 
L 714.128147 431.337078 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c1f38d"/>
    <path d="M 813.958508 495.661398 
L 816.802457 496.933613 
L 818.32773 498.312306 
L 815.487394 497.022131 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c088"/>
    <path d="M 699.582323 424.348792 
L 702.386913 426.290202 
L 704.053145 425.627757 
L 701.249939 423.583152 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d9f791"/>
    <path d="M 624.236328 413.990935 
L 626.995414 414.831058 
L 628.682212 411.877999 
L 625.921365 410.936353 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 728.171852 441.695152 
L 730.984324 443.714499 
L 732.625168 443.889743 
L 729.815215 441.780954 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9deb85"/>
    <path d="M 759.584174 462.603174 
L 762.404819 464.50919 
L 764.007395 465.398242 
L 761.190154 463.425569 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #59de78"/>
    <path d="M 743.877464 452.094182 
L 746.693863 454.08166 
L 748.316705 454.647184 
L 745.503327 452.580812 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #7de57f"/>
    <path d="M 640.357204 409.451653 
L 643.130716 410.61593 
L 644.817716 408.099238 
L 642.043021 406.828509 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f6f394"/>
    <path d="M 775.292849 472.901664 
L 778.118706 474.67568 
L 779.699507 475.814582 
L 776.877301 473.987408 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #35d771"/>
    <path d="M 669.36379 411.90103 
L 672.156334 413.534268 
L 673.838461 411.913594 
L 671.045957 410.171094 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fcfb97"/>
    <path d="M 689.50269 419.568265 
L 692.30413 421.418946 
L 693.977236 420.448147 
L 691.176738 418.491135 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #edfb95"/>
    <path d="M 715.278546 433.711873 
L 718.088099 435.703446 
L 719.741998 435.527745 
L 716.934481 433.439498 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bdf28c"/>
    <path d="M 679.428429 415.404856 
L 682.225871 417.151795 
L 683.904287 415.860239 
L 681.107336 414.004928 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9fe98"/>
    <path d="M 647.594631 409.375253 
L 650.373753 410.656117 
L 652.06069 408.361939 
L 649.28067 406.973005 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f6f394"/>
    <path d="M 702.386913 426.290202 
L 705.192873 428.224202 
L 706.8576 427.66412 
L 704.053145 425.627757 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d5f791"/>
    <path d="M 635.899658 411.027233 
L 638.669486 412.081431 
L 640.357204 409.451653 
L 637.586018 408.291884 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f8f695"/>
    <path d="M 803.900808 490.144507 
L 806.739795 491.56356 
L 808.279504 492.942165 
L 805.44423 491.496154 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00cb6b"/>
    <path d="M 826.86806 501.811397 
L 829.721661 502.852877 
L 831.229724 504.207498 
L 828.379531 503.15961 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b6a7"/>
    <path d="M 662.09984 410.598354 
L 664.888507 412.115261 
L 666.573036 410.270821 
L 663.784087 408.644438 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f8f695"/>
    <path d="M 791.008404 482.662362 
L 793.84109 484.254869 
L 795.399424 485.565597 
L 792.570487 483.934249 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #15d06a"/>
    <path d="M 730.984324 443.714499 
L 733.798107 445.713663 
L 735.436331 445.976676 
L 732.625168 443.889743 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #99eb85"/>
    <path d="M 654.842799 409.756149 
L 657.626984 411.155075 
L 659.313109 409.085559 
L 656.528327 407.577552 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f6f394"/>
    <path d="M 746.693863 454.08166 
L 749.511685 456.041396 
L 751.131424 456.68376 
L 748.316705 454.647184 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #75e37d"/>
    <path d="M 762.404819 464.50919 
L 765.2271 466.379889 
L 766.826213 467.333232 
L 764.007395 465.398242 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #55dd77"/>
    <path d="M 778.118706 474.67568 
L 780.946515 476.407092 
L 782.523634 477.596552 
L 779.699507 475.814582 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #31d670"/>
    <path d="M 631.445575 412.822003 
L 634.211453 413.768259 
L 635.899658 411.027233 
L 633.132256 409.976528 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #faf996"/>
    <path d="M 816.802457 496.933613 
L 819.649516 498.146983 
L 821.17121 499.540819 
L 818.32773 498.312306 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c088"/>
    <path d="M 692.30413 421.418946 
L 695.107056 423.266053 
L 696.779098 422.401071 
L 693.977236 420.448147 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e5fa94"/>
    <path d="M 718.088099 435.703446 
L 720.898966 437.680931 
L 722.550716 437.600582 
L 719.741998 435.527745 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b5f08a"/>
    <path d="M 672.156334 413.534268 
L 674.950657 415.169737 
L 676.632623 413.658485 
L 673.838461 411.913594 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 643.130716 410.61593 
L 645.906547 411.784388 
L 647.594631 409.375253 
L 644.817716 408.099238 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f8f695"/>
    <path d="M 626.995414 414.831058 
L 629.757095 415.67197 
L 631.445575 412.822003 
L 628.682212 411.877999 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 705.192873 428.224202 
L 708.000209 430.149701 
L 709.663311 429.691046 
L 706.8576 427.66412 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d1f690"/>
    <path d="M 682.225871 417.151795 
L 685.024938 418.898391 
L 686.702741 417.715024 
L 683.904287 415.860239 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f5fd97"/>
    <path d="M 733.798107 445.713663 
L 736.613235 447.691501 
L 738.248741 448.040525 
L 735.436331 445.976676 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #95ea84"/>
    <path d="M 749.511685 456.041396 
L 752.330979 457.972295 
L 753.947536 458.68937 
L 751.131424 456.68376 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #71e37d"/>
    <path d="M 765.2271 466.379889 
L 768.051083 468.214268 
L 769.646679 469.229475 
L 766.826213 467.333232 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #4ddb75"/>
    <path d="M 664.888507 412.115261 
L 667.679095 413.635597 
L 669.36379 411.90103 
L 666.573036 410.270821 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #faf996"/>
    <path d="M 793.84109 484.254869 
L 796.676144 485.798081 
L 798.230724 487.144889 
L 795.399424 485.565597 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #11cf69"/>
    <path d="M 650.373753 410.656117 
L 653.155071 411.941385 
L 654.842799 409.756149 
L 652.06069 408.361939 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f6f394"/>
    <path d="M 806.739795 491.56356 
L 809.581548 492.928014 
L 811.117561 494.330757 
L 808.279504 492.942165 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c970"/>
    <path d="M 657.626984 411.155075 
L 660.413231 412.558157 
L 662.09984 410.598354 
L 659.313109 409.085559 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f8f695"/>
    <path d="M 638.669486 412.081431 
L 641.441735 413.138911 
L 643.130716 410.61593 
L 640.357204 409.451653 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f8f695"/>
    <path d="M 720.898966 437.680931 
L 723.711168 439.6432 
L 725.360658 439.656785 
L 722.550716 437.600582 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b1ef89"/>
    <path d="M 780.946515 476.407092 
L 783.776359 478.095039 
L 785.349767 479.332408 
L 782.523634 477.596552 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2dd56f"/>
    <path d="M 695.107056 423.266053 
L 697.91147 425.108579 
L 699.582323 424.348792 
L 696.779098 422.401071 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e1f993"/>
    <path d="M 829.721661 502.852877 
L 832.578867 503.831528 
L 834.083576 505.189762 
L 831.229724 504.207498 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b6a7"/>
    <path d="M 708.000209 430.149701 
L 710.80893 432.065617 
L 712.470289 431.707354 
L 709.663311 429.691046 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c9f48e"/>
    <path d="M 674.950657 415.169737 
L 677.746746 416.806638 
L 679.428429 415.404856 
L 676.632623 413.658485 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 736.613235 447.691501 
L 739.429743 449.646894 
L 741.062438 450.080087 
L 738.248741 448.040525 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8de882"/>
    <path d="M 685.024938 418.898391 
L 687.825625 420.643736 
L 689.50269 419.568265 
L 686.702741 417.715024 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1fc96"/>
    <path d="M 752.330979 457.972295 
L 755.151797 459.873292 
L 756.7651 460.662877 
L 753.947536 458.68937 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #6de27c"/>
    <path d="M 819.649516 498.146983 
L 822.499795 499.301144 
L 824.017948 500.70729 
L 821.17121 499.540819 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00be8f"/>
    <path d="M 634.211453 413.768259 
L 636.979845 414.716664 
L 638.669486 412.081431 
L 635.899658 411.027233 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #faf996"/>
    <path d="M 768.051083 468.214268 
L 770.876837 470.011362 
L 772.468866 471.085948 
L 769.646679 469.229475 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #49db75"/>
    <path d="M 645.906547 411.784388 
L 648.684687 412.956699 
L 650.373753 410.656117 
L 647.594631 409.375253 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f8f695"/>
    <path d="M 667.679095 413.635597 
L 670.471594 415.158678 
L 672.156334 413.534268 
L 669.36379 411.90103 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fcfb97"/>
    <path d="M 723.711168 439.6432 
L 726.524729 441.589143 
L 728.171852 441.695152 
L 725.360658 439.656785 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #adef89"/>
    <path d="M 796.676144 485.798081 
L 799.51366 487.291319 
L 801.064485 488.671413 
L 798.230724 487.144889 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #11cf69"/>
    <path d="M 629.757095 415.67197 
L 632.521373 416.513673 
L 634.211453 413.768259 
L 631.445575 412.822003 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 697.91147 425.108579 
L 700.717371 426.945522 
L 702.386913 426.290202 
L 699.582323 424.348792 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ddf892"/>
    <path d="M 653.155071 411.941385 
L 655.938573 413.230611 
L 657.626984 411.155075 
L 654.842799 409.756149 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f8f695"/>
    <path d="M 660.413231 412.558157 
L 663.201529 413.964828 
L 664.888507 412.115261 
L 662.09984 410.598354 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #faf996"/>
    <path d="M 783.776359 478.095039 
L 786.608321 479.738702 
L 788.177993 481.021284 
L 785.349767 479.332408 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #29d46e"/>
    <path d="M 809.581548 492.928014 
L 812.426171 494.237362 
L 813.958508 495.661398 
L 811.117561 494.330757 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c970"/>
    <path d="M 710.80893 432.065617 
L 713.619049 433.97088 
L 715.278546 433.711873 
L 712.470289 431.707354 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c5f38d"/>
    <path d="M 739.429743 449.646894 
L 742.247672 451.578746 
L 743.877464 452.094182 
L 741.062438 450.080087 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #89e781"/>
    <path d="M 677.746746 416.806638 
L 680.544594 418.44417 
L 682.225871 417.151795 
L 679.428429 415.404856 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fdff99"/>
    <path d="M 755.151797 459.873292 
L 757.974196 461.743351 
L 759.584174 462.603174 
L 756.7651 460.662877 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #69e17b"/>
    <path d="M 687.825625 420.643736 
L 690.627927 422.386923 
L 692.30413 421.418946 
L 689.50269 419.568265 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #edfb95"/>
    <path d="M 641.441735 413.138911 
L 644.2164 414.199454 
L 645.906547 411.784388 
L 643.130716 410.61593 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #faf996"/>
    <path d="M 770.876837 470.011362 
L 773.704433 471.770244 
L 775.292849 472.901664 
L 772.468866 471.085948 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #45da74"/>
    <path d="M 832.578867 503.831528 
L 835.439793 504.747203 
L 836.941207 506.106252 
L 834.083576 505.189762 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00b6a7"/>
    <path d="M 726.524729 441.589143 
L 729.339674 443.517669 
L 730.984324 443.714499 
L 728.171852 441.695152 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a5ed87"/>
    <path d="M 822.499795 499.301144 
L 825.353405 500.395787 
L 826.86806 501.811397 
L 824.017948 500.70729 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00be8f"/>
    <path d="M 700.717371 426.945522 
L 703.524765 428.775888 
L 705.192873 428.224202 
L 702.386913 426.290202 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d9f791"/>
    <path d="M 670.471594 415.158678 
L 673.265992 416.68382 
L 674.950657 415.169737 
L 672.156334 413.534268 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 713.619049 433.97088 
L 716.430579 435.864434 
L 718.088099 435.703446 
L 715.278546 433.711873 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c1f38d"/>
    <path d="M 648.684687 412.956699 
L 651.465128 414.132531 
L 653.155071 411.941385 
L 650.373753 410.656117 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f8f695"/>
    <path d="M 742.247672 451.578746 
L 745.067063 453.485986 
L 746.693863 454.08166 
L 743.877464 452.094182 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #85e781"/>
    <path d="M 636.979845 414.716664 
L 639.75075 415.667111 
L 641.441735 413.138911 
L 638.669486 412.081431 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fcfb97"/>
    <path d="M 799.51366 487.291319 
L 802.353735 488.733954 
L 803.900808 490.144507 
L 801.064485 488.671413 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0dcf69"/>
    <path d="M 786.608321 479.738702 
L 789.442485 481.337304 
L 791.008404 482.662362 
L 788.177993 481.021284 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #25d36d"/>
    <path d="M 757.974196 461.743351 
L 760.798232 463.581468 
L 762.404819 464.50919 
L 759.584174 462.603174 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #61df79"/>
    <path d="M 663.201529 413.964828 
L 665.991866 415.37452 
L 667.679095 413.635597 
L 664.888507 412.115261 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #faf996"/>
    <path d="M 655.938573 413.230611 
L 658.72425 414.523346 
L 660.413231 412.558157 
L 657.626984 411.155075 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #faf996"/>
    <path d="M 690.627927 422.386923 
L 693.431841 424.127047 
L 695.107056 423.266053 
L 692.30413 421.418946 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e9fb95"/>
    <path d="M 680.544594 418.44417 
L 683.344193 420.081535 
L 685.024938 418.898391 
L 682.225871 417.151795 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9fe98"/>
    <path d="M 812.426171 494.237362 
L 815.273768 495.49115 
L 816.802457 496.933613 
L 813.958508 495.661398 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c677"/>
    <path d="M 632.521373 416.513673 
L 635.288252 417.356169 
L 636.979845 414.716664 
L 634.211453 413.768259 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 729.339674 443.517669 
L 732.156033 445.427702 
L 733.798107 445.713663 
L 730.984324 443.714499 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a1ec86"/>
    <path d="M 773.704433 471.770244 
L 776.533943 473.490023 
L 778.118706 474.67568 
L 775.292849 472.901664 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #41d973"/>
    <path d="M 703.524765 428.775888 
L 706.333657 430.598691 
L 708.000209 430.149701 
L 705.192873 428.224202 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d5f791"/>
    <path d="M 644.2164 414.199454 
L 646.993475 415.262843 
L 648.684687 412.956699 
L 645.906547 411.784388 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #faf996"/>
    <path d="M 716.430579 435.864434 
L 719.243538 437.745232 
L 720.898966 437.680931 
L 718.088099 435.703446 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bdf28c"/>
    <path d="M 745.067063 453.485986 
L 747.88796 455.367569 
L 749.511685 456.041396 
L 746.693863 454.08166 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #81e680"/>
    <path d="M 673.265992 416.68382 
L 676.06228 418.210335 
L 677.746746 416.806638 
L 674.950657 415.169737 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 760.798232 463.581468 
L 763.623966 465.386672 
L 765.2271 466.379889 
L 762.404819 464.50919 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #5ddf79"/>
    <path d="M 789.442485 481.337304 
L 792.278938 482.890116 
L 793.84109 484.254869 
L 791.008404 482.662362 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #25d36d"/>
    <path d="M 693.431841 424.127047 
L 696.237368 425.863209 
L 697.91147 425.108579 
L 695.107056 423.266053 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e5fa94"/>
    <path d="M 802.353735 488.733954 
L 805.196463 490.125405 
L 806.739795 491.56356 
L 803.900808 490.144507 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #09ce68"/>
    <path d="M 825.353405 500.395787 
L 828.210457 501.43066 
L 829.721661 502.852877 
L 826.86806 501.811397 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00be8f"/>
    <path d="M 651.465128 414.132531 
L 654.247863 415.311549 
L 655.938573 413.230611 
L 653.155071 411.941385 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #faf996"/>
    <path d="M 683.344193 420.081535 
L 686.145537 421.717934 
L 687.825625 420.643736 
L 685.024938 418.898391 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f5fd97"/>
    <path d="M 732.156033 445.427702 
L 734.973836 447.318189 
L 736.613235 447.691501 
L 733.798107 445.713663 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9deb85"/>
    <path d="M 665.991866 415.37452 
L 668.784232 416.786663 
L 670.471594 415.158678 
L 667.679095 413.635597 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fcfb97"/>
    <path d="M 639.75075 415.667111 
L 642.524168 416.619492 
L 644.2164 414.199454 
L 641.441735 413.138911 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fcfb97"/>
    <path d="M 658.72425 414.523346 
L 661.512092 415.819135 
L 663.201529 413.964828 
L 660.413231 412.558157 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #faf996"/>
    <path d="M 776.533943 473.490023 
L 779.365442 475.169848 
L 780.946515 476.407092 
L 778.118706 474.67568 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #3dd872"/>
    <path d="M 706.333657 430.598691 
L 709.144055 432.412951 
L 710.80893 432.065617 
L 708.000209 430.149701 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d1f690"/>
    <path d="M 719.243538 437.745232 
L 722.057944 439.612245 
L 723.711168 439.6432 
L 720.898966 437.680931 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b9f18b"/>
    <path d="M 747.88796 455.367569 
L 750.71041 457.222474 
L 752.330979 457.972295 
L 749.511685 456.041396 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #7de57f"/>
    <path d="M 815.273768 495.49115 
L 818.124444 496.688977 
L 819.649516 498.146983 
L 816.802457 496.933613 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c677"/>
    <path d="M 635.288252 417.356169 
L 638.057737 418.199457 
L 639.75075 415.667111 
L 636.979845 414.716664 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 763.623966 465.386672 
L 766.451459 467.158025 
L 768.051083 468.214268 
L 765.2271 466.379889 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #59de78"/>
    <path d="M 676.06228 418.210335 
L 678.860451 419.737536 
L 680.544594 418.44417 
L 677.746746 416.806638 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fdff99"/>
    <path d="M 646.993475 415.262843 
L 649.772956 416.328856 
L 651.465128 414.132531 
L 648.684687 412.956699 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #faf996"/>
    <path d="M 696.237368 425.863209 
L 699.044507 427.594517 
L 700.717371 426.945522 
L 697.91147 425.108579 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e1f993"/>
    <path d="M 734.973836 447.318189 
L 737.793118 449.188095 
L 739.429743 449.646894 
L 736.613235 447.691501 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #99eb85"/>
    <path d="M 686.145537 421.717934 
L 688.948622 423.352571 
L 690.627927 422.386923 
L 687.825625 420.643736 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1fc96"/>
    <path d="M 792.278938 482.890116 
L 795.117767 484.396449 
L 796.676144 485.798081 
L 793.84109 484.254869 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #21d36d"/>
    <path d="M 805.196463 490.125405 
L 808.041944 491.465141 
L 809.581548 492.928014 
L 806.739795 491.56356 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #09ce68"/>
    <path d="M 668.784232 416.786663 
L 671.578621 418.200683 
L 673.265992 416.68382 
L 670.471594 415.158678 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 722.057944 439.612245 
L 724.87382 441.464456 
L 726.524729 441.589143 
L 723.711168 439.6432 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b1ef89"/>
    <path d="M 779.365442 475.169848 
L 782.199006 476.808907 
L 783.776359 478.095039 
L 780.946515 476.407092 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #39d771"/>
    <path d="M 709.144055 432.412951 
L 711.955972 434.217702 
L 713.619049 433.97088 
L 710.80893 432.065617 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c9f48e"/>
    <path d="M 654.247863 415.311549 
L 657.032885 416.493416 
L 658.72425 414.523346 
L 655.938573 413.230611 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #faf996"/>
    <path d="M 750.71041 457.222474 
L 753.534462 459.049711 
L 755.151797 459.873292 
L 752.330979 457.972295 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #75e37d"/>
    <path d="M 661.512092 415.819135 
L 664.302092 417.117525 
L 665.991866 415.37452 
L 663.201529 413.964828 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fcfb97"/>
    <path d="M 828.210457 501.43066 
L 831.071061 502.40557 
L 832.578867 503.831528 
L 829.721661 502.852877 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00be8f"/>
    <path d="M 642.524168 416.619492 
L 645.300097 417.573699 
L 646.993475 415.262843 
L 644.2164 414.199454 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fcfb97"/>
    <path d="M 766.451459 467.158025 
L 769.280776 468.894622 
L 770.876837 470.011362 
L 768.051083 468.214268 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #55dd77"/>
    <path d="M 818.124444 496.688977 
L 820.978303 497.830497 
L 822.499795 499.301144 
L 819.649516 498.146983 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c677"/>
    <path d="M 737.793118 449.188095 
L 740.613914 451.036411 
L 742.247672 451.578746 
L 739.429743 449.646894 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #91e983"/>
    <path d="M 699.044507 427.594517 
L 701.853264 429.320081 
L 703.524765 428.775888 
L 700.717371 426.945522 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ddf892"/>
    <path d="M 678.860451 419.737536 
L 681.660498 421.264736 
L 683.344193 420.081535 
L 680.544594 418.44417 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9fe98"/>
    <path d="M 688.948622 423.352571 
L 691.753446 424.984653 
L 693.431841 424.127047 
L 690.627927 422.386923 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #edfb95"/>
    <path d="M 724.87382 441.464456 
L 727.691189 443.300867 
L 729.339674 443.517669 
L 726.524729 441.589143 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #adef89"/>
    <path d="M 711.955972 434.217702 
L 714.769418 436.011986 
L 716.430579 435.864434 
L 713.619049 433.97088 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c5f38d"/>
    <path d="M 638.057737 418.199457 
L 640.82983 419.04354 
L 642.524168 416.619492 
L 639.75075 415.667111 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 795.117767 484.396449 
L 797.959062 485.855661 
L 799.51366 487.291319 
L 796.676144 485.798081 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1dd26c"/>
    <path d="M 753.534462 459.049711 
L 756.360167 460.848315 
L 757.974196 461.743351 
L 755.151797 459.873292 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #71e37d"/>
    <path d="M 649.772956 416.328856 
L 652.55484 417.39727 
L 654.247863 415.311549 
L 651.465128 414.132531 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fcfb97"/>
    <path d="M 782.199006 476.808907 
L 785.034713 478.406428 
L 786.608321 479.738702 
L 783.776359 478.095039 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #35d771"/>
    <path d="M 671.578621 418.200683 
L 674.375023 419.616008 
L 676.06228 418.210335 
L 673.265992 416.68382 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 808.041944 491.465141 
L 810.890274 492.75268 
L 812.426171 494.237362 
L 809.581548 492.928014 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #05cd67"/>
    <path d="M 657.032885 416.493416 
L 659.820188 417.677791 
L 661.512092 415.819135 
L 658.72425 414.523346 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fcfb97"/>
    <path d="M 664.302092 417.117525 
L 667.094242 418.418059 
L 668.784232 416.786663 
L 665.991866 415.37452 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fcfb97"/>
    <path d="M 769.280776 468.894622 
L 772.111982 470.595594 
L 773.704433 471.770244 
L 770.876837 470.011362 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #51dc76"/>
    <path d="M 740.613914 451.036411 
L 743.436263 452.862145 
L 745.067063 453.485986 
L 742.247672 451.578746 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8de882"/>
    <path d="M 701.853264 429.320081 
L 704.663642 431.03902 
L 706.333657 430.598691 
L 703.524765 428.775888 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d9f791"/>
    <path d="M 681.660498 421.264736 
L 684.462418 422.791249 
L 686.145537 421.717934 
L 683.344193 420.081535 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f5fd97"/>
    <path d="M 831.071061 502.40557 
L 833.935326 503.320376 
L 835.439793 504.747203 
L 832.578867 503.831528 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00be8f"/>
    <path d="M 727.691189 443.300867 
L 730.510077 445.120493 
L 732.156033 445.427702 
L 729.339674 443.517669 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a9ee88"/>
    <path d="M 645.300097 417.573699 
L 648.078538 418.529622 
L 649.772956 416.328856 
L 646.993475 415.262843 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fcfb97"/>
    <path d="M 691.753446 424.984653 
L 694.560009 426.61339 
L 696.237368 425.863209 
L 693.431841 424.127047 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e9fb95"/>
    <path d="M 714.769418 436.011986 
L 717.58441 437.794858 
L 719.243538 437.745232 
L 716.430579 435.864434 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c1f38d"/>
    <path d="M 756.360167 460.848315 
L 759.187578 462.617353 
L 760.798232 463.581468 
L 757.974196 461.743351 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #6de27c"/>
    <path d="M 820.978303 497.830497 
L 823.835451 498.915414 
L 825.353405 500.395787 
L 822.499795 499.301144 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c47d"/>
    <path d="M 797.959062 485.855661 
L 800.802912 487.267158 
L 802.353735 488.733954 
L 799.51366 487.291319 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #19d16b"/>
    <path d="M 785.034713 478.406428 
L 787.872644 479.961682 
L 789.442485 481.337304 
L 786.608321 479.738702 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #35d771"/>
    <path d="M 674.375023 419.616008 
L 677.173434 421.032064 
L 678.860451 419.737536 
L 676.06228 418.210335 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fdff99"/>
    <path d="M 652.55484 417.39727 
L 655.339124 418.46786 
L 657.032885 416.493416 
L 654.247863 415.311549 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fcfb97"/>
    <path d="M 743.436263 452.862145 
L 746.260206 454.664332 
L 747.88796 455.367569 
L 745.067063 453.485986 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #89e781"/>
    <path d="M 772.111982 470.595594 
L 774.945146 472.260106 
L 776.533943 473.490023 
L 773.704433 471.770244 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #4ddb75"/>
    <path d="M 640.82983 419.04354 
L 643.604535 419.888418 
L 645.300097 417.573699 
L 642.524168 416.619492 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 810.890274 492.75268 
L 813.741554 493.98759 
L 815.273768 495.49115 
L 812.426171 494.237362 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #05cd67"/>
    <path d="M 704.663642 431.03902 
L 707.475652 432.750461 
L 709.144055 432.412951 
L 706.333657 430.598691 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d5f791"/>
    <path d="M 667.094242 418.418059 
L 669.888537 419.720277 
L 671.578621 418.200683 
L 668.784232 416.786663 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 659.820188 417.677791 
L 662.609766 418.864334 
L 664.302092 417.117525 
L 661.512092 415.819135 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fcfb97"/>
    <path d="M 730.510077 445.120493 
L 733.330512 446.922371 
L 734.973836 447.318189 
L 732.156033 445.427702 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a5ed87"/>
    <path d="M 684.462418 422.791249 
L 687.266206 424.31639 
L 688.948622 423.352571 
L 686.145537 421.717934 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1fc96"/>
    <path d="M 717.58441 437.794858 
L 720.400965 439.565383 
L 722.057944 439.612245 
L 719.243538 437.745232 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bdf28c"/>
    <path d="M 694.560009 426.61339 
L 697.368312 428.237997 
L 699.044507 427.594517 
L 696.237368 425.863209 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e5fa94"/>
    <path d="M 759.187578 462.617353 
L 762.016752 464.355919 
L 763.623966 465.386672 
L 760.798232 463.581468 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #69e17b"/>
    <path d="M 648.078538 418.529622 
L 650.85949 419.48715 
L 652.55484 417.39727 
L 649.772956 416.328856 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fcfb97"/>
    <path d="M 787.872644 479.961682 
L 790.71288 481.473977 
L 792.278938 482.890116 
L 789.442485 481.337304 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #31d670"/>
    <path d="M 746.260206 454.664332 
L 749.085785 456.442032 
L 750.71041 457.222474 
L 747.88796 455.367569 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #85e781"/>
    <path d="M 800.802912 487.267158 
L 803.649409 488.630388 
L 805.196463 490.125405 
L 802.353735 488.733954 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #19d16b"/>
    <path d="M 823.835451 498.915414 
L 826.695994 499.943488 
L 828.210457 501.43066 
L 825.353405 500.395787 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c47d"/>
    <path d="M 677.173434 421.032064 
L 679.973848 422.448278 
L 681.660498 421.264736 
L 678.860451 419.737536 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9fe98"/>
    <path d="M 774.945146 472.260106 
L 777.780337 473.887361 
L 779.365442 475.169848 
L 776.533943 473.490023 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #49db75"/>
    <path d="M 707.475652 432.750461 
L 710.2893 434.45354 
L 711.955972 434.217702 
L 709.144055 432.412951 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d1f690"/>
    <path d="M 733.330512 446.922371 
L 736.152526 448.705555 
L 737.793118 449.188095 
L 734.973836 447.318189 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a1ec86"/>
    <path d="M 720.400965 439.565383 
L 723.219102 441.322644 
L 724.87382 441.464456 
L 722.057944 439.612245 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b9f18b"/>
    <path d="M 655.339124 418.46786 
L 658.125804 419.540402 
L 659.820188 417.677791 
L 657.032885 416.493416 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fcfb97"/>
    <path d="M 813.741554 493.98759 
L 816.595882 495.16949 
L 818.124444 496.688977 
L 815.273768 495.49115 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #01cc66"/>
    <path d="M 669.888537 419.720277 
L 672.68497 421.023721 
L 674.375023 419.616008 
L 671.578621 418.200683 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 762.016752 464.355919 
L 764.847744 466.063141 
L 766.451459 467.158025 
L 763.623966 465.386672 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #65e07a"/>
    <path d="M 687.266206 424.31639 
L 690.071862 425.839479 
L 691.753446 424.984653 
L 688.948622 423.352571 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #edfb95"/>
    <path d="M 697.368312 428.237997 
L 700.178359 429.857693 
L 701.853264 429.320081 
L 699.044507 427.594517 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e1f993"/>
    <path d="M 662.609766 418.864334 
L 665.401616 420.052701 
L 667.094242 418.418059 
L 664.302092 417.117525 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 643.604535 419.888418 
L 646.381856 420.734093 
L 648.078538 418.529622 
L 645.300097 417.573699 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 749.085785 456.442032 
L 751.913046 458.194326 
L 753.534462 459.049711 
L 750.71041 457.222474 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #81e680"/>
    <path d="M 790.71288 481.473977 
L 793.555502 482.942666 
L 795.117767 484.396449 
L 792.278938 482.890116 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2dd56f"/>
    <path d="M 710.2893 434.45354 
L 713.1046 436.147401 
L 714.769418 436.011986 
L 711.955972 434.217702 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cdf58f"/>
    <path d="M 777.780337 473.887361 
L 780.617627 475.476597 
L 782.199006 476.808907 
L 779.365442 475.169848 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #45da74"/>
    <path d="M 736.152526 448.705555 
L 738.976152 450.469118 
L 740.613914 451.036411 
L 737.793118 449.188095 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9deb85"/>
    <path d="M 803.649409 488.630388 
L 806.498646 489.944848 
L 808.041944 491.465141 
L 805.196463 490.125405 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #15d06a"/>
    <path d="M 679.973848 422.448278 
L 682.776263 423.864075 
L 684.462418 422.791249 
L 681.660498 421.264736 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f5fd97"/>
    <path d="M 723.219102 441.322644 
L 726.038843 443.065735 
L 727.691189 443.300867 
L 724.87382 441.464456 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b5f08a"/>
    <path d="M 650.85949 419.48715 
L 653.642954 420.446171 
L 655.339124 418.46786 
L 652.55484 417.39727 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 764.847744 466.063141 
L 767.680616 467.738177 
L 769.280776 468.894622 
L 766.451459 467.158025 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #61df79"/>
    <path d="M 826.695994 499.943488 
L 829.560036 500.914533 
L 831.071061 502.40557 
L 828.210457 501.43066 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c47d"/>
    <path d="M 700.178359 429.857693 
L 702.990155 431.471704 
L 704.663642 431.03902 
L 701.853264 429.320081 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ddf892"/>
    <path d="M 690.071862 425.839479 
L 692.879386 427.359834 
L 694.560009 426.61339 
L 691.753446 424.984653 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #edfb95"/>
    <path d="M 672.68497 421.023721 
L 675.483538 422.327931 
L 677.173434 421.032064 
L 674.375023 419.616008 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fdff99"/>
    <path d="M 658.125804 419.540402 
L 660.914878 420.614666 
L 662.609766 418.864334 
L 659.820188 417.677791 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 816.595882 495.16949 
L 819.453358 496.298049 
L 820.978303 497.830497 
L 818.124444 496.688977 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #01cc66"/>
    <path d="M 751.913046 458.194326 
L 754.742036 459.920326 
L 756.360167 460.848315 
L 753.534462 459.049711 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #7de57f"/>
    <path d="M 665.401616 420.052701 
L 668.195733 421.24255 
L 669.888537 419.720277 
L 667.094242 418.418059 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 713.1046 436.147401 
L 715.921565 437.8312 
L 717.58441 437.794858 
L 714.769418 436.011986 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c9f48e"/>
    <path d="M 646.381856 420.734093 
L 649.161797 421.580565 
L 650.85949 419.48715 
L 648.078538 418.529622 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 738.976152 450.469118 
L 741.801424 452.212155 
L 743.436263 452.862145 
L 740.613914 451.036411 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #99eb85"/>
    <path d="M 793.555502 482.942666 
L 796.400595 484.367145 
L 797.959062 485.855661 
L 795.117767 484.396449 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #29d46e"/>
    <path d="M 780.617627 475.476597 
L 783.457089 477.027092 
L 785.034713 478.406428 
L 782.199006 476.808907 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #45da74"/>
    <path d="M 726.038843 443.065735 
L 728.860212 444.793766 
L 730.510077 445.120493 
L 727.691189 443.300867 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b1ef89"/>
    <path d="M 682.776263 423.864075 
L 685.580675 425.278885 
L 687.266206 424.31639 
L 684.462418 422.791249 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f5fd97"/>
    <path d="M 767.680616 467.738177 
L 770.515429 469.380216 
L 772.111982 470.595594 
L 769.280776 468.894622 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #5ddf79"/>
    <path d="M 806.498646 489.944848 
L 809.350714 491.210081 
L 810.890274 492.75268 
L 808.041944 491.465141 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #15d06a"/>
    <path d="M 702.990155 431.471704 
L 705.803706 433.079264 
L 707.475652 432.750461 
L 704.663642 431.03902 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d9f791"/>
    <path d="M 692.879386 427.359834 
L 695.688778 428.876782 
L 697.368312 428.237997 
L 694.560009 426.61339 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e9fb95"/>
    <path d="M 653.642954 420.446171 
L 656.42893 421.406573 
L 658.125804 419.540402 
L 655.339124 418.46786 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 754.742036 459.920326 
L 757.572804 461.619167 
L 759.187578 462.617353 
L 756.360167 460.848315 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #79e47e"/>
    <path d="M 675.483538 422.327931 
L 678.284237 423.632447 
L 679.973848 422.448278 
L 677.173434 421.032064 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9fe98"/>
    <path d="M 829.560036 500.914533 
L 832.427683 501.828417 
L 833.935326 503.320376 
L 831.071061 502.40557 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #00c47d"/>
    <path d="M 715.921565 437.8312 
L 718.740211 439.504102 
L 720.400965 439.565383 
L 717.58441 437.794858 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c5f38d"/>
    <path d="M 741.801424 452.212155 
L 744.62838 453.933781 
L 746.260206 454.664332 
L 743.436263 452.862145 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #95ea84"/>
    <path d="M 660.914878 420.614666 
L 663.706344 421.690426 
L 665.401616 420.052701 
L 662.609766 418.864334 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 668.195733 421.24255 
L 670.992114 422.433535 
L 672.68497 421.023721 
L 669.888537 419.720277 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 728.860212 444.793766 
L 731.683234 446.505862 
L 733.330512 446.922371 
L 730.510077 445.120493 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #adef89"/>
    <path d="M 819.453358 496.298049 
L 822.314082 497.372987 
L 823.835451 498.915414 
L 820.978303 497.830497 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #01cc66"/>
    <path d="M 783.457089 477.027092 
L 786.298798 478.53816 
L 787.872644 479.961682 
L 785.034713 478.406428 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #41d973"/>
    <path d="M 796.400595 484.367145 
L 799.248244 485.746851 
L 800.802912 487.267158 
L 797.959062 485.855661 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #29d46e"/>
    <path d="M 685.580675 425.278885 
L 688.387084 426.692137 
L 690.071862 425.839479 
L 687.266206 424.31639 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1fc96"/>
    <path d="M 770.515429 469.380216 
L 773.352245 470.988482 
L 774.945146 472.260106 
L 772.111982 470.595594 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #59de78"/>
    <path d="M 705.803706 433.079264 
L 708.619021 434.679611 
L 710.2893 434.45354 
L 707.475652 432.750461 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d5f791"/>
    <path d="M 649.161797 421.580565 
L 651.944362 422.427836 
L 653.642954 420.446171 
L 650.85949 419.48715 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 695.688778 428.876782 
L 698.500042 430.38965 
L 700.178359 429.857693 
L 697.368312 428.237997 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e5fa94"/>
    <path d="M 809.350714 491.210081 
L 812.205708 492.42568 
L 813.741554 493.98759 
L 810.890274 492.75268 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #11cf69"/>
    <path d="M 757.572804 461.619167 
L 760.405401 463.290015 
L 762.016752 464.355919 
L 759.187578 462.617353 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #75e37d"/>
    <path d="M 718.740211 439.504102 
L 721.560554 441.165285 
L 723.219102 441.322644 
L 720.400965 439.565383 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c1f38d"/>
    <path d="M 744.62838 453.933781 
L 747.457059 455.633133 
L 749.085785 456.442032 
L 746.260206 454.664332 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #91e983"/>
    <path d="M 678.284237 423.632447 
L 681.087066 424.93681 
L 682.776263 423.864075 
L 679.973848 422.448278 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9fe98"/>
    <path d="M 731.683234 446.505862 
L 734.507938 448.201169 
L 736.152526 448.705555 
L 733.330512 446.922371 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a9ee88"/>
    <path d="M 656.42893 421.406573 
L 659.217418 422.368242 
L 660.914878 420.614666 
L 658.125804 419.540402 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 670.992114 422.433535 
L 673.790757 423.625311 
L 675.483538 422.327931 
L 672.68497 421.023721 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fdff99"/>
    <path d="M 663.706344 421.690426 
L 666.500202 422.767451 
L 668.195733 421.24255 
L 665.401616 420.052701 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 786.298798 478.53816 
L 789.142829 480.009155 
L 790.71288 481.473977 
L 787.872644 479.961682 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #3dd872"/>
    <path d="M 773.352245 470.988482 
L 776.191129 472.562231 
L 777.780337 473.887361 
L 774.945146 472.260106 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #55dd77"/>
    <path d="M 708.619021 434.679611 
L 711.43611 436.271994 
L 713.1046 436.147401 
L 710.2893 434.45354 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d1f690"/>
    <path d="M 799.248244 485.746851 
L 802.098534 487.081265 
L 803.649409 488.630388 
L 800.802912 487.267158 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #25d36d"/>
    <path d="M 822.314082 497.372987 
L 825.178155 498.394076 
L 826.695994 499.943488 
L 823.835451 498.915414 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #01cc66"/>
    <path d="M 688.387084 426.692137 
L 691.195491 428.103263 
L 692.879386 427.359834 
L 690.071862 425.839479 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #edfb95"/>
    <path d="M 698.500042 430.38965 
L 701.313183 431.897773 
L 702.990155 431.471704 
L 700.178359 429.857693 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e1f993"/>
    <path d="M 760.405401 463.290015 
L 763.23988 464.932061 
L 764.847744 466.063141 
L 762.016752 464.355919 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #71e37d"/>
    <path d="M 721.560554 441.165285 
L 724.382614 442.813941 
L 726.038843 443.065735 
L 723.219102 441.322644 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bdf28c"/>
    <path d="M 747.457059 455.633133 
L 750.287502 457.309374 
L 751.913046 458.194326 
L 749.085785 456.442032 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8de882"/>
    <path d="M 812.205708 492.42568 
L 815.063721 493.591281 
L 816.595882 495.16949 
L 813.741554 493.98759 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #11cf69"/>
    <path d="M 651.944362 422.427836 
L 654.729553 423.275908 
L 656.42893 421.406573 
L 653.642954 420.446171 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 734.507938 448.201169 
L 737.334352 449.878845 
L 738.976152 450.469118 
L 736.152526 448.705555 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a5ed87"/>
    <path d="M 681.087066 424.93681 
L 683.892022 426.240562 
L 685.580675 425.278885 
L 682.776263 423.864075 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f5fd97"/>
    <path d="M 659.217418 422.368242 
L 662.00842 423.331066 
L 663.706344 421.690426 
L 660.914878 420.614666 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 789.142829 480.009155 
L 791.98926 481.43947 
L 793.555502 482.942666 
L 790.71288 481.473977 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #39d771"/>
    <path d="M 711.43611 436.271994 
L 714.254986 437.85567 
L 715.921565 437.8312 
L 713.1046 436.147401 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cdf58f"/>
    <path d="M 776.191129 472.562231 
L 779.032149 474.100755 
L 780.617627 475.476597 
L 777.780337 473.887361 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #55dd77"/>
    <path d="M 673.790757 423.625311 
L 676.59166 424.817533 
L 678.284237 423.632447 
L 675.483538 422.327931 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fdff99"/>
    <path d="M 666.500202 422.767451 
L 669.296449 423.845513 
L 670.992114 422.433535 
L 668.195733 421.24255 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 691.195491 428.103263 
L 694.005897 429.5117 
L 695.688778 428.876782 
L 692.879386 427.359834 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #edfb95"/>
    <path d="M 763.23988 464.932061 
L 766.076297 466.544527 
L 767.680616 467.738177 
L 764.847744 466.063141 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #6de27c"/>
    <path d="M 802.098534 487.081265 
L 804.951552 488.369913 
L 806.498646 489.944848 
L 803.649409 488.630388 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #25d36d"/>
    <path d="M 701.313183 431.897773 
L 704.128207 433.400489 
L 705.803706 433.079264 
L 702.990155 431.471704 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ddf892"/>
    <path d="M 750.287502 457.309374 
L 753.119753 458.961687 
L 754.742036 459.920326 
L 751.913046 458.194326 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #89e781"/>
    <path d="M 724.382614 442.813941 
L 727.206413 444.449275 
L 728.860212 444.793766 
L 726.038843 443.065735 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b9f18b"/>
    <path d="M 825.178155 498.394076 
L 828.045676 499.361138 
L 829.560036 500.914533 
L 826.695994 499.943488 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #01cc66"/>
    <path d="M 737.334352 449.878845 
L 740.16251 451.53807 
L 741.801424 452.212155 
L 738.976152 450.469118 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a1ec86"/>
    <path d="M 815.063721 493.591281 
L 817.924849 494.706572 
L 819.453358 496.298049 
L 816.595882 495.16949 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #11cf69"/>
    <path d="M 683.892022 426.240562 
L 686.699107 427.543245 
L 688.387084 426.692137 
L 685.580675 425.278885 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f5fd97"/>
    <path d="M 654.729553 423.275908 
L 657.517375 424.12478 
L 659.217418 422.368242 
L 656.42893 421.406573 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 714.254986 437.85567 
L 717.075662 439.429906 
L 718.740211 439.504102 
L 715.921565 437.8312 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cdf58f"/>
    <path d="M 779.032149 474.100755 
L 781.875371 475.60338 
L 783.457089 477.027092 
L 780.617627 475.476597 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #51dc76"/>
    <path d="M 791.98926 481.43947 
L 794.83817 482.828536 
L 796.400595 484.367145 
L 793.555502 482.942666 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #39d771"/>
    <path d="M 766.076297 466.544527 
L 768.914708 468.126665 
L 770.515429 469.380216 
L 767.680616 467.738177 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #69e17b"/>
    <path d="M 694.005897 429.5117 
L 696.818305 430.916886 
L 698.500042 430.38965 
L 695.688778 428.876782 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e9fb95"/>
    <path d="M 704.128207 433.400489 
L 706.945121 434.897146 
L 708.619021 434.679611 
L 705.803706 433.079264 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ddf892"/>
    <path d="M 676.59166 424.817533 
L 679.394822 426.009856 
L 681.087066 424.93681 
L 678.284237 423.632447 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9fe98"/>
    <path d="M 662.00842 423.331066 
L 664.801936 424.294929 
L 666.500202 422.767451 
L 663.706344 421.690426 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 727.206413 444.449275 
L 730.031974 446.070503 
L 731.683234 446.505862 
L 728.860212 444.793766 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b5f08a"/>
    <path d="M 753.119753 458.961687 
L 755.953856 460.58928 
L 757.572804 461.619167 
L 754.742036 459.920326 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #85e781"/>
    <path d="M 804.951552 488.369913 
L 807.807386 489.612365 
L 809.350714 491.210081 
L 806.498646 489.944848 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #21d36d"/>
    <path d="M 740.16251 451.53807 
L 742.992444 453.178044 
L 744.62838 453.933781 
L 741.801424 452.212155 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9deb85"/>
    <path d="M 669.296449 423.845513 
L 672.095085 424.924381 
L 673.790757 423.625311 
L 670.992114 422.433535 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fdff99"/>
    <path d="M 828.045676 499.361138 
L 830.916745 500.274049 
L 832.427683 501.828417 
L 829.560036 500.914533 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #01cc66"/>
    <path d="M 717.075662 439.429906 
L 719.898155 440.993979 
L 721.560554 441.165285 
L 718.740211 439.504102 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c9f48e"/>
    <path d="M 686.699107 427.543245 
L 689.50832 428.844405 
L 691.195491 428.103263 
L 688.387084 426.692137 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1fc96"/>
    <path d="M 817.924849 494.706572 
L 820.789185 495.771288 
L 822.314082 497.372987 
L 819.453358 496.298049 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0dcf69"/>
    <path d="M 781.875371 475.60338 
L 784.720866 477.069468 
L 786.298798 478.53816 
L 783.457089 477.027092 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #4ddb75"/>
    <path d="M 768.914708 468.126665 
L 771.755172 469.677756 
L 773.352245 470.988482 
L 770.515429 469.380216 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #65e07a"/>
    <path d="M 794.83817 482.828536 
L 797.689636 484.175828 
L 799.248244 485.746851 
L 796.400595 484.367145 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #35d771"/>
    <path d="M 706.945121 434.897146 
L 709.763935 436.387096 
L 711.43611 436.271994 
L 708.619021 434.679611 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d9f791"/>
    <path d="M 730.031974 446.070503 
L 732.859322 447.676861 
L 734.507938 448.201169 
L 731.683234 446.505862 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b1ef89"/>
    <path d="M 755.953856 460.58928 
L 758.789859 462.19139 
L 760.405401 463.290015 
L 757.572804 461.619167 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #81e680"/>
    <path d="M 696.818305 430.916886 
L 699.632719 432.318264 
L 701.313183 431.897773 
L 698.500042 430.38965 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e5fa94"/>
    <path d="M 657.517375 424.12478 
L 660.307832 424.974454 
L 662.00842 423.331066 
L 659.217418 422.368242 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 742.992444 453.178044 
L 745.824191 454.797984 
L 747.457059 455.633133 
L 744.62838 453.933781 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #99eb85"/>
    <path d="M 679.394822 426.009856 
L 682.200243 427.201936 
L 683.892022 426.240562 
L 681.087066 424.93681 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9fe98"/>
    <path d="M 807.807386 489.612365 
L 810.666124 490.808235 
L 812.205708 492.42568 
L 809.350714 491.210081 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #21d36d"/>
    <path d="M 664.801936 424.294929 
L 667.597968 425.259718 
L 669.296449 423.845513 
L 666.500202 422.767451 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 672.095085 424.924381 
L 674.896111 426.003825 
L 676.59166 424.817533 
L 673.790757 423.625311 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fdff99"/>
    <path d="M 719.898155 440.993979 
L 722.72248 442.547178 
L 724.382614 442.813941 
L 721.560554 441.165285 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c5f38d"/>
    <path d="M 689.50832 428.844405 
L 692.319664 430.143589 
L 694.005897 429.5117 
L 691.195491 428.103263 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #edfb95"/>
    <path d="M 784.720866 477.069468 
L 787.568703 478.498416 
L 789.142829 480.009155 
L 786.298798 478.53816 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #4ddb75"/>
    <path d="M 771.755172 469.677756 
L 774.597747 471.197113 
L 776.191129 472.562231 
L 773.352245 470.988482 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #65e07a"/>
    <path d="M 732.859322 447.676861 
L 735.688483 449.267598 
L 737.334352 449.878845 
L 734.507938 448.201169 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #adef89"/>
    <path d="M 758.789859 462.19139 
L 761.62781 463.767274 
L 763.23988 464.932061 
L 760.405401 463.290015 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #7de57f"/>
    <path d="M 709.763935 436.387096 
L 712.584658 437.869699 
L 714.254986 437.85567 
L 711.43611 436.271994 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d5f791"/>
    <path d="M 745.824191 454.797984 
L 748.657787 456.397129 
L 750.287502 457.309374 
L 747.457059 455.633133 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #95ea84"/>
    <path d="M 797.689636 484.175828 
L 800.543741 485.480859 
L 802.098534 487.081265 
L 799.248244 485.746851 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #35d771"/>
    <path d="M 699.632719 432.318264 
L 702.449146 433.715282 
L 704.128207 433.400489 
L 701.313183 431.897773 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e5fa94"/>
    <path d="M 820.789185 495.771288 
L 823.656825 496.785213 
L 825.178155 498.394076 
L 822.314082 497.372987 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0dcf69"/>
    <path d="M 682.200243 427.201936 
L 685.007924 428.393429 
L 686.699107 427.543245 
L 683.892022 426.240562 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f5fd97"/>
    <path d="M 660.307832 424.974454 
L 663.100928 425.824932 
L 664.801936 424.294929 
L 662.00842 423.331066 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 810.666124 490.808235 
L 813.527855 491.957182 
L 815.063721 493.591281 
L 812.205708 492.42568 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #21d36d"/>
    <path d="M 722.72248 442.547178 
L 725.548657 444.088802 
L 727.206413 444.449275 
L 724.382614 442.813941 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c1f38d"/>
    <path d="M 674.896111 426.003825 
L 677.699526 427.083615 
L 679.394822 426.009856 
L 676.59166 424.817533 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fdff99"/>
    <path d="M 667.597968 425.259718 
L 670.396517 426.225318 
L 672.095085 424.924381 
L 669.296449 423.845513 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fdff99"/>
    <path d="M 774.597747 471.197113 
L 777.442497 472.684081 
L 779.032149 474.100755 
L 776.191129 472.562231 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #61df79"/>
    <path d="M 735.688483 449.267598 
L 738.519486 450.841979 
L 740.16251 451.53807 
L 737.334352 449.878845 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a9ee88"/>
    <path d="M 692.319664 430.143589 
L 695.133141 431.440346 
L 696.818305 430.916886 
L 694.005897 429.5117 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #edfb95"/>
    <path d="M 761.62781 463.767274 
L 764.467759 465.316221 
L 766.076297 466.544527 
L 763.23988 464.932061 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #79e47e"/>
    <path d="M 787.568703 478.498416 
L 790.418956 479.889659 
L 791.98926 481.43947 
L 789.142829 480.009155 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #49db75"/>
    <path d="M 748.657787 456.397129 
L 751.493272 457.974741 
L 753.119753 458.961687 
L 750.287502 457.309374 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #91e983"/>
    <path d="M 712.584658 437.869699 
L 715.407305 439.344324 
L 717.075662 439.429906 
L 714.254986 437.85567 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d1f690"/>
    <path d="M 702.449146 433.715282 
L 705.26759 435.107393 
L 706.945121 434.897146 
L 704.128207 433.400489 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e1f993"/>
    <path d="M 800.543741 485.480859 
L 803.400566 486.743183 
L 804.951552 488.369913 
L 802.098534 487.081265 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #31d670"/>
    <path d="M 823.656825 496.785213 
L 826.527863 497.748178 
L 828.045676 499.361138 
L 825.178155 498.394076 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0dcf69"/>
    <path d="M 685.007924 428.393429 
L 687.817867 429.583995 
L 689.50832 428.844405 
L 686.699107 427.543245 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f5fd97"/>
    <path d="M 725.548657 444.088802 
L 728.376707 445.618163 
L 730.031974 446.070503 
L 727.206413 444.449275 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bdf28c"/>
    <path d="M 663.100928 425.824932 
L 665.896665 426.676214 
L 667.597968 425.259718 
L 664.801936 424.294929 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fefe98"/>
    <path d="M 813.527855 491.957182 
L 816.392667 493.058911 
L 817.924849 494.706572 
L 815.063721 493.591281 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1dd26c"/>
    <path d="M 677.699526 427.083615 
L 680.505333 428.163522 
L 682.200243 427.201936 
L 679.394822 426.009856 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9fe98"/>
    <path d="M 738.519486 450.841979 
L 741.352362 452.399287 
L 742.992444 453.178044 
L 740.16251 451.53807 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a9ee88"/>
    <path d="M 777.442497 472.684081 
L 780.289482 474.138036 
L 781.875371 475.60338 
L 779.032149 474.100755 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #5ddf79"/>
    <path d="M 764.467759 465.316221 
L 767.309759 466.837544 
L 768.914708 468.126665 
L 766.076297 466.544527 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #75e37d"/>
    <path d="M 670.396517 426.225318 
L 673.197586 427.191615 
L 674.896111 426.003825 
L 672.095085 424.924381 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fdff99"/>
    <path d="M 751.493272 457.974741 
L 754.330688 459.530103 
L 755.953856 460.58928 
L 753.119753 458.961687 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #91e983"/>
    <path d="M 695.133141 431.440346 
L 697.948756 432.73423 
L 699.632719 432.318264 
L 696.818305 430.916886 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e9fb95"/>
    <path d="M 715.407305 439.344324 
L 718.231887 440.810348 
L 719.898155 440.993979 
L 717.075662 439.429906 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cdf58f"/>
    <path d="M 790.418956 479.889659 
L 793.271697 481.242667 
L 794.83817 482.828536 
L 791.98926 481.43947 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #45da74"/>
    <path d="M 705.26759 435.107393 
L 708.088062 436.494055 
L 709.763935 436.387096 
L 706.945121 434.897146 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ddf892"/>
    <path d="M 803.400566 486.743183 
L 806.260191 487.962398 
L 807.807386 489.612365 
L 804.951552 488.369913 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #31d670"/>
    <path d="M 728.376707 445.618163 
L 731.206652 447.134588 
L 732.859322 447.676861 
L 730.031974 446.070503 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b9f18b"/>
    <path d="M 687.817867 429.583995 
L 690.630073 430.773292 
L 692.319664 430.143589 
L 689.50832 428.844405 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1fc96"/>
    <path d="M 826.527863 497.748178 
L 829.402393 498.660066 
L 830.916745 500.274049 
L 828.045676 499.361138 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #0dcf69"/>
    <path d="M 741.352362 452.399287 
L 744.187142 453.938823 
L 745.824191 454.797984 
L 742.992444 453.178044 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a5ed87"/>
    <path d="M 754.330688 459.530103 
L 757.170075 461.062519 
L 758.789859 462.19139 
L 755.953856 460.58928 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8de882"/>
    <path d="M 767.309759 466.837544 
L 770.153862 468.330585 
L 771.755172 469.677756 
L 768.914708 468.126665 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #75e37d"/>
    <path d="M 780.289482 474.138036 
L 783.138769 475.558389 
L 784.720866 477.069468 
L 781.875371 475.60338 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #5ddf79"/>
    <path d="M 718.231887 440.810348 
L 721.058421 442.267158 
L 722.72248 442.547178 
L 719.898155 440.993979 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cdf58f"/>
    <path d="M 816.392667 493.058911 
L 819.260649 494.113172 
L 820.789185 495.771288 
L 817.924849 494.706572 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1dd26c"/>
    <path d="M 680.505333 428.163522 
L 683.313533 429.243317 
L 685.007924 428.393429 
L 682.200243 427.201936 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9fe98"/>
    <path d="M 665.896665 426.676214 
L 668.695048 427.528302 
L 670.396517 426.225318 
L 667.597968 425.259718 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fdff99"/>
    <path d="M 697.948756 432.73423 
L 700.766514 434.024798 
L 702.449146 433.715282 
L 699.632719 432.318264 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e9fb95"/>
    <path d="M 793.271697 481.242667 
L 796.126999 482.556951 
L 797.689636 484.175828 
L 794.83817 482.828536 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #45da74"/>
    <path d="M 673.197586 427.191615 
L 676.001176 428.158493 
L 677.699526 427.083615 
L 674.896111 426.003825 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fdff99"/>
    <path d="M 708.088062 436.494055 
L 710.910569 437.874733 
L 712.584658 437.869699 
L 709.763935 436.387096 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ddf892"/>
    <path d="M 731.206652 447.134588 
L 734.038515 448.637415 
L 735.688483 449.267598 
L 732.859322 447.676861 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b9f18b"/>
    <path d="M 806.260191 487.962398 
L 809.122701 489.138141 
L 810.666124 490.808235 
L 807.807386 489.612365 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2dd56f"/>
    <path d="M 744.187142 453.938823 
L 747.02386 455.459906 
L 748.657787 456.397129 
L 745.824191 454.797984 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a1ec86"/>
    <path d="M 690.630073 430.773292 
L 693.444545 431.960982 
L 695.133141 431.440346 
L 692.319664 430.143589 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1fc96"/>
    <path d="M 757.170075 461.062519 
L 760.011479 462.571319 
L 761.62781 463.767274 
L 758.789859 462.19139 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #89e781"/>
    <path d="M 770.153862 468.330585 
L 773.000124 469.794713 
L 774.597747 471.197113 
L 771.755172 469.677756 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #71e37d"/>
    <path d="M 783.138769 475.558389 
L 785.990421 476.944582 
L 787.568703 478.498416 
L 784.720866 477.069468 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #59de78"/>
    <path d="M 721.058421 442.267158 
L 723.886923 443.714151 
L 725.548657 444.088802 
L 722.72248 442.547178 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c9f48e"/>
    <path d="M 700.766514 434.024798 
L 703.58642 435.31161 
L 705.26759 435.107393 
L 702.449146 433.715282 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e5fa94"/>
    <path d="M 710.910569 437.874733 
L 713.735124 439.248899 
L 715.407305 439.344324 
L 712.584658 437.869699 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d9f791"/>
    <path d="M 796.126999 482.556951 
L 798.984938 483.832056 
L 800.543741 485.480859 
L 797.689636 484.175828 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #41d973"/>
    <path d="M 683.313533 429.243317 
L 686.124128 430.322771 
L 687.817867 429.583995 
L 685.007924 428.393429 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9fe98"/>
    <path d="M 819.260649 494.113172 
L 822.131891 495.11976 
L 823.656825 496.785213 
L 820.789185 495.771288 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1dd26c"/>
    <path d="M 668.695048 427.528302 
L 671.496081 428.381197 
L 673.197586 427.191615 
L 670.396517 426.225318 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fdff99"/>
    <path d="M 676.001176 428.158493 
L 678.80729 429.12584 
L 680.505333 428.163522 
L 677.699526 427.083615 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fdff99"/>
    <path d="M 734.038515 448.637415 
L 736.872322 450.125999 
L 738.519486 450.841979 
L 735.688483 449.267598 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b5f08a"/>
    <path d="M 747.02386 455.459906 
L 749.862551 456.961874 
L 751.493272 457.974741 
L 748.657787 456.397129 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9deb85"/>
    <path d="M 809.122701 489.138141 
L 811.988177 490.270093 
L 813.527855 491.957182 
L 810.666124 490.808235 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2dd56f"/>
    <path d="M 760.011479 462.571319 
L 762.854945 464.055856 
L 764.467759 465.316221 
L 761.62781 463.767274 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #85e781"/>
    <path d="M 773.000124 469.794713 
L 775.848601 471.229329 
L 777.442497 472.684081 
L 774.597747 471.197113 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #6de27c"/>
    <path d="M 693.444545 431.960982 
L 696.261288 433.14673 
L 697.948756 432.73423 
L 695.133141 431.440346 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1fc96"/>
    <path d="M 723.886923 443.714151 
L 726.71741 445.150735 
L 728.376707 445.618163 
L 725.548657 444.088802 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c5f38d"/>
    <path d="M 785.990421 476.944582 
L 788.844506 478.296092 
L 790.418956 479.889659 
L 787.568703 478.498416 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #55dd77"/>
    <path d="M 703.58642 435.31161 
L 706.408482 436.594232 
L 708.088062 436.494055 
L 705.26759 435.107393 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e5fa94"/>
    <path d="M 713.735124 439.248899 
L 716.561737 440.616031 
L 718.231887 440.810348 
L 715.407305 439.344324 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d5f791"/>
    <path d="M 798.984938 483.832056 
L 801.84559 485.067568 
L 803.400566 486.743183 
L 800.543741 485.480859 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #41d973"/>
    <path d="M 686.124128 430.322771 
L 688.93712 431.401659 
L 690.630073 430.773292 
L 687.817867 429.583995 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f5fd97"/>
    <path d="M 736.872322 450.125999 
L 739.7081 451.599707 
L 741.352362 452.399287 
L 738.519486 450.841979 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b1ef89"/>
    <path d="M 822.131891 495.11976 
L 825.006482 496.078519 
L 826.527863 497.748178 
L 823.656825 496.785213 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1dd26c"/>
    <path d="M 678.80729 429.12584 
L 681.61593 430.093539 
L 683.313533 429.243317 
L 680.505333 428.163522 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fdff99"/>
    <path d="M 749.862551 456.961874 
L 752.703252 458.444086 
L 754.330688 459.530103 
L 751.493272 457.974741 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #99eb85"/>
    <path d="M 671.496081 428.381197 
L 674.299767 429.2349 
L 676.001176 428.158493 
L 673.197586 427.191615 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fdff99"/>
    <path d="M 762.854945 464.055856 
L 765.700521 465.515507 
L 767.309759 466.837544 
L 764.467759 465.316221 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #85e781"/>
    <path d="M 775.848601 471.229329 
L 778.699351 472.63386 
L 780.289482 474.138036 
L 777.442497 472.684081 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #6de27c"/>
    <path d="M 811.988177 490.270093 
L 814.856704 491.357977 
L 816.392667 493.058911 
L 813.527855 491.957182 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2dd56f"/>
    <path d="M 726.71741 445.150735 
L 729.549903 446.576329 
L 731.206652 447.134588 
L 728.376707 445.618163 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c5f38d"/>
    <path d="M 696.261288 433.14673 
L 699.080306 434.330202 
L 700.766514 434.024798 
L 697.948756 432.73423 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #edfb95"/>
    <path d="M 788.844506 478.296092 
L 791.70109 479.612429 
L 793.271697 481.242667 
L 790.418956 479.889659 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #55dd77"/>
    <path d="M 716.561737 440.616031 
L 719.390421 441.975617 
L 721.058421 442.267158 
L 718.231887 440.810348 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d5f791"/>
    <path d="M 706.408482 436.594232 
L 709.232708 437.872234 
L 710.910569 437.874733 
L 708.088062 436.494055 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e1f993"/>
    <path d="M 739.7081 451.599707 
L 742.545876 453.057925 
L 744.187142 453.938823 
L 741.352362 452.399287 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #adef89"/>
    <path d="M 801.84559 485.067568 
L 804.70903 486.263111 
L 806.260191 487.962398 
L 803.400566 486.743183 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #3dd872"/>
    <path d="M 688.93712 431.401659 
L 691.752513 432.479753 
L 693.444545 431.960982 
L 690.630073 430.773292 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f5fd97"/>
    <path d="M 752.703252 458.444086 
L 755.546 459.90592 
L 757.170075 461.062519 
L 754.330688 459.530103 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #99eb85"/>
    <path d="M 765.700521 465.515507 
L 768.548254 466.949675 
L 770.153862 468.330585 
L 767.309759 466.837544 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #81e680"/>
    <path d="M 825.006482 496.078519 
L 827.884511 496.989336 
L 829.402393 498.660066 
L 826.527863 497.748178 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #1dd26c"/>
    <path d="M 681.61593 430.093539 
L 684.4271 431.061479 
L 686.124128 430.322771 
L 683.313533 429.243317 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9fe98"/>
    <path d="M 778.699351 472.63386 
L 781.552432 474.007765 
L 783.138769 475.558389 
L 780.289482 474.138036 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #69e17b"/>
    <path d="M 729.549903 446.576329 
L 732.384422 447.990363 
L 734.038515 448.637415 
L 731.206652 447.134588 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c1f38d"/>
    <path d="M 674.299767 429.2349 
L 677.10611 430.089411 
L 678.80729 429.12584 
L 676.001176 428.158493 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fdff99"/>
    <path d="M 699.080306 434.330202 
L 701.901604 435.511068 
L 703.58642 435.31161 
L 700.766514 434.024798 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #edfb95"/>
    <path d="M 814.856704 491.357977 
L 817.728364 492.401559 
L 819.260649 494.113172 
L 816.392667 493.058911 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #2dd56f"/>
    <path d="M 791.70109 479.612429 
L 794.560243 480.893141 
L 796.126999 482.556951 
L 793.271697 481.242667 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #51dc76"/>
    <path d="M 719.390421 441.975617 
L 722.221191 443.327151 
L 723.886923 443.714151 
L 721.058421 442.267158 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d1f690"/>
    <path d="M 709.232708 437.872234 
L 712.059107 439.145192 
L 713.735124 439.248899 
L 710.910569 437.874733 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e1f993"/>
    <path d="M 742.545876 453.057925 
L 745.385682 454.500052 
L 747.02386 455.459906 
L 744.187142 453.938823 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #adef89"/>
    <path d="M 804.70903 486.263111 
L 807.575336 487.418348 
L 809.122701 489.138141 
L 806.260191 487.962398 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #3dd872"/>
    <path d="M 755.546 459.90592 
L 758.390837 461.346775 
L 760.011479 462.571319 
L 757.170075 461.062519 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #95ea84"/>
    <path d="M 691.752513 432.479753 
L 694.57031 433.556831 
L 696.261288 433.14673 
L 693.444545 431.960982 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f5fd97"/>
    <path d="M 768.548254 466.949675 
L 771.398196 468.35779 
L 773.000124 469.794713 
L 770.153862 468.330585 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #7de57f"/>
    <path d="M 732.384422 447.990363 
L 735.220988 449.392279 
L 736.872322 450.125999 
L 734.038515 448.637415 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bdf28c"/>
    <path d="M 781.552432 474.007765 
L 784.407904 475.350534 
L 785.990421 476.944582 
L 783.138769 475.558389 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #65e07a"/>
    <path d="M 684.4271 431.061479 
L 687.240803 432.029546 
L 688.93712 431.401659 
L 686.124128 430.322771 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9fe98"/>
    <path d="M 701.901604 435.511068 
L 704.725188 436.689001 
L 706.408482 436.594232 
L 703.58642 435.31161 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e9fb95"/>
    <path d="M 794.560243 480.893141 
L 797.422034 482.137806 
L 798.984938 483.832056 
L 796.126999 482.556951 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #51dc76"/>
    <path d="M 677.10611 430.089411 
L 679.915114 430.944733 
L 681.61593 430.093539 
L 678.80729 429.12584 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fdff99"/>
    <path d="M 722.221191 443.327151 
L 725.054063 444.670138 
L 726.71741 445.150735 
L 723.886923 443.714151 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cdf58f"/>
    <path d="M 745.385682 454.500052 
L 748.227547 455.925506 
L 749.862551 456.961874 
L 747.02386 455.459906 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a9ee88"/>
    <path d="M 817.728364 492.401559 
L 820.603242 493.400648 
L 822.131891 495.11976 
L 819.260649 494.113172 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #29d46e"/>
    <path d="M 712.059107 439.145192 
L 714.887689 440.412688 
L 716.561737 440.616031 
L 713.735124 439.248899 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ddf892"/>
    <path d="M 758.390837 461.346775 
L 761.237802 462.766071 
L 762.854945 464.055856 
L 760.011479 462.571319 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #91e983"/>
    <path d="M 807.575336 487.418348 
L 810.444586 488.53298 
L 811.988177 490.270093 
L 809.122701 489.138141 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #3dd872"/>
    <path d="M 771.398196 468.35779 
L 774.250396 469.739305 
L 775.848601 471.229329 
L 773.000124 469.794713 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #7de57f"/>
    <path d="M 694.57031 433.556831 
L 697.390516 434.632669 
L 699.080306 434.330202 
L 696.261288 433.14673 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1fc96"/>
    <path d="M 735.220988 449.392279 
L 738.059627 450.781534 
L 739.7081 451.599707 
L 736.872322 450.125999 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bdf28c"/>
    <path d="M 784.407904 475.350534 
L 787.265829 476.661686 
L 788.844506 478.296092 
L 785.990421 476.944582 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #65e07a"/>
    <path d="M 725.054063 444.670138 
L 727.889053 446.004091 
L 729.549903 446.576329 
L 726.71741 445.150735 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cdf58f"/>
    <path d="M 687.240803 432.029546 
L 690.057041 432.997626 
L 691.752513 432.479753 
L 688.93712 431.401659 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9fe98"/>
    <path d="M 704.725188 436.689001 
L 707.551066 437.863679 
L 709.232708 437.872234 
L 706.408482 436.594232 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e9fb95"/>
    <path d="M 748.227547 455.925506 
L 751.071505 457.333721 
L 752.703252 458.444086 
L 749.862551 456.961874 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a5ed87"/>
    <path d="M 797.422034 482.137806 
L 800.286532 483.346042 
L 801.84559 485.067568 
L 798.984938 483.832056 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #4ddb75"/>
    <path d="M 714.887689 440.412688 
L 717.718465 441.674309 
L 719.390421 441.975617 
L 716.561737 440.616031 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ddf892"/>
    <path d="M 679.915114 430.944733 
L 682.726783 431.800867 
L 684.4271 431.061479 
L 681.61593 430.093539 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fdff99"/>
    <path d="M 761.237802 462.766071 
L 764.086939 464.163251 
L 765.700521 465.515507 
L 762.854945 464.055856 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #91e983"/>
    <path d="M 820.603242 493.400648 
L 823.481421 494.355095 
L 825.006482 496.078519 
L 822.131891 495.11976 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #29d46e"/>
    <path d="M 774.250396 469.739305 
L 777.104907 471.093702 
L 778.699351 472.63386 
L 775.848601 471.229329 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #79e47e"/>
    <path d="M 738.059627 450.781534 
L 740.900361 452.157597 
L 742.545876 453.057925 
L 739.7081 451.599707 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b9f18b"/>
    <path d="M 810.444586 488.53298 
L 813.316855 489.606751 
L 814.856704 491.357977 
L 811.988177 490.270093 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #3dd872"/>
    <path d="M 697.390516 434.632669 
L 700.213135 435.707048 
L 701.901604 435.511068 
L 699.080306 434.330202 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1fc96"/>
    <path d="M 787.265829 476.661686 
L 790.126268 477.940773 
L 791.70109 479.612429 
L 788.844506 478.296092 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #61df79"/>
    <path d="M 751.071505 457.333721 
L 753.91759 458.72415 
L 755.546 459.90592 
L 752.703252 458.444086 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a5ed87"/>
    <path d="M 727.889053 446.004091 
L 730.726179 447.328533 
L 732.384422 447.990363 
L 729.549903 446.576329 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c9f48e"/>
    <path d="M 707.551066 437.863679 
L 710.379245 439.034781 
L 712.059107 439.145192 
L 709.232708 437.872234 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e5fa94"/>
    <path d="M 800.286532 483.346042 
L 803.153808 484.517501 
L 804.70903 486.263111 
L 801.84559 485.067568 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #4ddb75"/>
    <path d="M 717.718465 441.674309 
L 720.551447 442.92965 
L 722.221191 443.327151 
L 719.390421 441.975617 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d9f791"/>
    <path d="M 690.057041 432.997626 
L 692.875819 433.965609 
L 694.57031 433.556831 
L 691.752513 432.479753 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9fe98"/>
    <path d="M 764.086939 464.163251 
L 766.93829 465.537781 
L 768.548254 466.949675 
L 765.700521 465.515507 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8de882"/>
    <path d="M 682.726783 431.800867 
L 685.54112 432.657812 
L 687.240803 432.029546 
L 684.4271 431.061479 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fdff99"/>
    <path d="M 777.104907 471.093702 
L 779.961783 472.42049 
L 781.552432 474.007765 
L 778.699351 472.63386 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #75e37d"/>
    <path d="M 823.481421 494.355095 
L 826.362985 495.264796 
L 827.884511 496.989336 
L 825.006482 496.078519 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #29d46e"/>
    <path d="M 740.900361 452.157597 
L 743.743218 453.519951 
L 745.385682 454.500052 
L 742.545876 453.057925 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b5f08a"/>
    <path d="M 790.126268 477.940773 
L 792.989283 479.187379 
L 794.560243 480.893141 
L 791.70109 479.612429 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #61df79"/>
    <path d="M 813.316855 489.606751 
L 816.192224 490.639442 
L 817.728364 492.401559 
L 814.856704 491.357977 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #39d771"/>
    <path d="M 700.213135 435.707048 
L 703.038173 436.779748 
L 704.725188 436.689001 
L 701.901604 435.511068 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1fc96"/>
    <path d="M 753.91759 458.72415 
L 756.765836 460.096263 
L 758.390837 461.346775 
L 755.546 459.90592 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a1ec86"/>
    <path d="M 730.726179 447.328533 
L 733.565459 448.642997 
L 735.220988 449.392279 
L 732.384422 447.990363 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c9f48e"/>
    <path d="M 710.379245 439.034781 
L 713.209733 440.201994 
L 714.887689 440.412688 
L 712.059107 439.145192 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e5fa94"/>
    <path d="M 720.551447 442.92965 
L 723.386648 444.178312 
L 725.054063 444.670138 
L 722.221191 443.327151 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d9f791"/>
    <path d="M 766.93829 465.537781 
L 769.7919 466.889148 
L 771.398196 468.35779 
L 768.548254 466.949675 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8de882"/>
    <path d="M 803.153808 484.517501 
L 806.023934 485.651871 
L 807.575336 487.418348 
L 804.70903 486.263111 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #4ddb75"/>
    <path d="M 692.875819 433.965609 
L 695.697141 434.933384 
L 697.390516 434.632669 
L 694.57031 433.556831 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9fe98"/>
    <path d="M 779.961783 472.42049 
L 782.821078 473.719206 
L 784.407904 475.350534 
L 781.552432 474.007765 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #75e37d"/>
    <path d="M 743.743218 453.519951 
L 746.588225 454.868092 
L 748.227547 455.925506 
L 745.385682 454.500052 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b5f08a"/>
    <path d="M 685.54112 432.657812 
L 688.358129 433.515572 
L 690.057041 432.997626 
L 687.240803 432.029546 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fdff99"/>
    <path d="M 792.989283 479.187379 
L 795.85494 480.401118 
L 797.422034 482.137806 
L 794.560243 480.893141 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #61df79"/>
    <path d="M 756.765836 460.096263 
L 759.61628 461.44955 
L 761.237802 462.766071 
L 758.390837 461.346775 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9deb85"/>
    <path d="M 703.038173 436.779748 
L 705.865636 437.850555 
L 707.551066 437.863679 
L 704.725188 436.689001 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #edfb95"/>
    <path d="M 816.192224 490.639442 
L 819.070769 491.630874 
L 820.603242 493.400648 
L 817.728364 492.401559 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #39d771"/>
    <path d="M 733.565459 448.642997 
L 736.406915 449.947027 
L 738.059627 450.781534 
L 735.220988 449.392279 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c5f38d"/>
    <path d="M 713.209733 440.201994 
L 716.04254 441.365006 
L 717.718465 441.674309 
L 714.887689 440.412688 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e5fa94"/>
    <path d="M 769.7919 466.889148 
L 772.647816 468.216864 
L 774.250396 469.739305 
L 771.398196 468.35779 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #89e781"/>
    <path d="M 723.386648 444.178312 
L 726.224083 445.419904 
L 727.889053 446.004091 
L 725.054063 444.670138 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d5f791"/>
    <path d="M 806.023934 485.651871 
L 808.896981 486.748876 
L 810.444586 488.53298 
L 807.575336 487.418348 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #4ddb75"/>
    <path d="M 782.821078 473.719206 
L 785.682848 474.989413 
L 787.265829 476.661686 
L 784.407904 475.350534 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #71e37d"/>
    <path d="M 695.697141 434.933384 
L 698.521011 435.900841 
L 700.213135 435.707048 
L 697.390516 434.632669 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f5fd97"/>
    <path d="M 746.588225 454.868092 
L 749.435409 456.201534 
L 751.071505 457.333721 
L 748.227547 455.925506 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b1ef89"/>
    <path d="M 688.358129 433.515572 
L 691.177815 434.374146 
L 692.875819 433.965609 
L 690.057041 432.997626 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fdff99"/>
    <path d="M 795.85494 480.401118 
L 798.723301 481.58164 
L 800.286532 483.346042 
L 797.422034 482.137806 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #5ddf79"/>
    <path d="M 759.61628 461.44955 
L 762.468959 462.783519 
L 764.086939 464.163251 
L 761.237802 462.766071 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9deb85"/>
    <path d="M 736.406915 449.947027 
L 739.250567 451.240178 
L 740.900361 452.157597 
L 738.059627 450.781534 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c5f38d"/>
    <path d="M 705.865636 437.850555 
L 708.695529 438.919255 
L 710.379245 439.034781 
L 707.551066 437.863679 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #edfb95"/>
    <path d="M 819.070769 491.630874 
L 821.952569 492.58091 
L 823.481421 494.355095 
L 820.603242 493.400648 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #39d771"/>
    <path d="M 772.647816 468.216864 
L 775.506084 469.520465 
L 777.104907 471.093702 
L 774.250396 469.739305 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #85e781"/>
    <path d="M 726.224083 445.419904 
L 729.063765 446.654043 
L 730.726179 447.328533 
L 727.889053 446.004091 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d5f791"/>
    <path d="M 716.04254 441.365006 
L 718.877675 442.523514 
L 720.551447 442.92965 
L 717.718465 441.674309 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e1f993"/>
    <path d="M 808.896981 486.748876 
L 811.77302 487.808278 
L 813.316855 489.606751 
L 810.444586 488.53298 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #49db75"/>
    <path d="M 749.435409 456.201534 
L 752.284801 457.519804 
L 753.91759 458.72415 
L 751.071505 457.333721 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b1ef89"/>
    <path d="M 785.682848 474.989413 
L 788.547149 476.230705 
L 790.126268 477.940773 
L 787.265829 476.661686 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #71e37d"/>
    <path d="M 698.521011 435.900841 
L 701.347433 436.86787 
L 703.038173 436.779748 
L 700.213135 435.707048 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f5fd97"/>
    <path d="M 762.468959 462.783519 
L 765.323912 464.097699 
L 766.93829 465.537781 
L 764.086939 464.163251 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #99eb85"/>
    <path d="M 739.250567 451.240178 
L 742.096437 452.522017 
L 743.743218 453.519951 
L 740.900361 452.157597 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c1f38d"/>
    <path d="M 798.723301 481.58164 
L 801.594432 482.728625 
L 803.153808 484.517501 
L 800.286532 483.346042 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #5ddf79"/>
    <path d="M 691.177815 434.374146 
L 694.00018 435.233537 
L 695.697141 434.933384 
L 692.875819 433.965609 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fdff99"/>
    <path d="M 708.695529 438.919255 
L 711.52786 439.985638 
L 713.209733 440.201994 
L 710.379245 439.034781 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #edfb95"/>
    <path d="M 775.506084 469.520465 
L 778.366753 470.799511 
L 779.961783 472.42049 
L 777.104907 471.093702 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #85e781"/>
    <path d="M 729.063765 446.654043 
L 731.905712 447.880354 
L 733.565459 448.642997 
L 730.726179 447.328533 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d1f690"/>
    <path d="M 718.877675 442.523514 
L 721.71515 443.677216 
L 723.386648 444.178312 
L 720.551447 442.92965 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e1f993"/>
    <path d="M 821.952569 492.58091 
L 824.837702 493.489452 
L 826.362985 495.264796 
L 823.481421 494.355095 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #39d771"/>
    <path d="M 752.284801 457.519804 
L 755.13643 458.822445 
L 756.765836 460.096263 
L 753.91759 458.72415 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #adef89"/>
    <path d="M 788.547149 476.230705 
L 791.414037 477.442704 
L 792.989283 479.187379 
L 790.126268 477.940773 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #71e37d"/>
    <path d="M 811.77302 487.808278 
L 814.652125 488.829875 
L 816.192224 490.639442 
L 813.316855 489.606751 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #49db75"/>
    <path d="M 701.347433 436.86787 
L 704.176413 437.834364 
L 705.865636 437.850555 
L 703.038173 436.779748 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f5fd97"/>
    <path d="M 765.323912 464.097699 
L 768.181179 465.39164 
L 769.7919 466.889148 
L 766.93829 465.537781 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #99eb85"/>
    <path d="M 742.096437 452.522017 
L 744.944548 453.792123 
L 746.588225 454.868092 
L 743.743218 453.519951 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c1f38d"/>
    <path d="M 801.594432 482.728625 
L 804.468398 483.841787 
L 806.023934 485.651871 
L 803.153808 484.517501 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #5ddf79"/>
    <path d="M 778.366753 470.799511 
L 781.229871 472.053585 
L 782.821078 473.719206 
L 779.961783 472.42049 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #81e680"/>
    <path d="M 711.52786 439.985638 
L 714.362636 441.049497 
L 716.04254 441.365006 
L 713.209733 440.201994 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #edfb95"/>
    <path d="M 694.00018 435.233537 
L 696.825229 436.093744 
L 698.521011 435.900841 
L 695.697141 434.933384 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fdff99"/>
    <path d="M 731.905712 447.880354 
L 734.749939 449.09847 
L 736.406915 449.947027 
L 733.565459 448.642997 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d1f690"/>
    <path d="M 721.71515 443.677216 
L 724.554975 444.825819 
L 726.224083 445.419904 
L 723.386648 444.178312 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ddf892"/>
    <path d="M 755.13643 458.822445 
L 757.99033 460.109016 
L 759.61628 461.44955 
L 756.765836 460.096263 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #adef89"/>
    <path d="M 791.414037 477.442704 
L 794.283571 478.625061 
L 795.85494 480.401118 
L 792.989283 479.187379 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #6de27c"/>
    <path d="M 814.652125 488.829875 
L 817.534367 489.813502 
L 819.070769 491.630874 
L 816.192224 490.639442 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #49db75"/>
    <path d="M 768.181179 465.39164 
L 771.040801 466.66491 
L 772.647816 468.216864 
L 769.7919 466.889148 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #95ea84"/>
    <path d="M 704.176413 437.834364 
L 707.007954 438.800218 
L 708.695529 438.919255 
L 705.865636 437.850555 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f5fd97"/>
    <path d="M 744.944548 453.792123 
L 747.794925 455.050087 
L 749.435409 456.201534 
L 746.588225 454.868092 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bdf28c"/>
    <path d="M 804.468398 483.841787 
L 807.345265 484.920873 
L 808.896981 486.748876 
L 806.023934 485.651871 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #59de78"/>
    <path d="M 781.229871 472.053585 
L 784.095489 473.282299 
L 785.682848 474.989413 
L 782.821078 473.719206 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #81e680"/>
    <path d="M 734.749939 449.09847 
L 737.596465 450.308033 
L 739.250567 451.240178 
L 736.406915 449.947027 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cdf58f"/>
    <path d="M 714.362636 441.049497 
L 717.199865 442.110627 
L 718.877675 442.523514 
L 716.04254 441.365006 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e9fb95"/>
    <path d="M 724.554975 444.825819 
L 727.397162 445.969033 
L 729.063765 446.654043 
L 726.224083 445.419904 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ddf892"/>
    <path d="M 696.825229 436.093744 
L 699.652966 436.95477 
L 701.347433 436.86787 
L 698.521011 435.900841 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fdff99"/>
    <path d="M 757.99033 460.109016 
L 760.846532 461.379094 
L 762.468959 462.783519 
L 759.61628 461.44955 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a9ee88"/>
    <path d="M 794.283571 478.625061 
L 797.15581 479.777456 
L 798.723301 481.58164 
L 795.85494 480.401118 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #6de27c"/>
    <path d="M 771.040801 466.66491 
L 773.902819 467.9171 
L 775.506084 469.520465 
L 772.647816 468.216864 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #95ea84"/>
    <path d="M 817.534367 489.813502 
L 820.419819 490.759031 
L 821.952569 492.58091 
L 819.070769 491.630874 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #49db75"/>
    <path d="M 747.794925 455.050087 
L 750.647594 456.295513 
L 752.284801 457.519804 
L 749.435409 456.201534 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bdf28c"/>
    <path d="M 707.007954 438.800218 
L 709.842064 439.765325 
L 711.52786 439.985638 
L 708.695529 438.919255 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f5fd97"/>
    <path d="M 784.095489 473.282299 
L 786.963656 474.485287 
L 788.547149 476.230705 
L 785.682848 474.989413 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #81e680"/>
    <path d="M 807.345265 484.920873 
L 810.225099 485.965664 
L 811.77302 487.808278 
L 808.896981 486.748876 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #59de78"/>
    <path d="M 737.596465 450.308033 
L 740.445307 451.508696 
L 742.096437 452.522017 
L 739.250567 451.240178 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cdf58f"/>
    <path d="M 717.199865 442.110627 
L 720.039555 443.168829 
L 721.71515 443.677216 
L 718.877675 442.523514 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e9fb95"/>
    <path d="M 760.846532 461.379094 
L 763.705069 462.632272 
L 765.323912 464.097699 
L 762.468959 462.783519 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a9ee88"/>
    <path d="M 727.397162 445.969033 
L 730.241725 447.106577 
L 731.905712 447.880354 
L 729.063765 446.654043 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ddf892"/>
    <path d="M 699.652966 436.95477 
L 702.483394 437.816615 
L 704.176413 437.834364 
L 701.347433 436.86787 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fdff99"/>
    <path d="M 797.15581 479.777456 
L 800.030812 480.899599 
L 801.594432 482.728625 
L 798.723301 481.58164 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #6de27c"/>
    <path d="M 773.902819 467.9171 
L 776.767276 469.147822 
L 778.366753 470.799511 
L 775.506084 469.520465 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #91e983"/>
    <path d="M 750.647594 456.295513 
L 753.502579 457.528017 
L 755.13643 458.822445 
L 752.284801 457.519804 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b9f18b"/>
    <path d="M 820.419819 490.759031 
L 823.308553 491.666373 
L 824.837702 493.489452 
L 821.952569 492.58091 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #49db75"/>
    <path d="M 709.842064 439.765325 
L 712.678746 440.729583 
L 714.362636 441.049497 
L 711.52786 439.985638 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f5fd97"/>
    <path d="M 786.963656 474.485287 
L 789.834425 475.66221 
L 791.414037 477.442704 
L 788.547149 476.230705 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #7de57f"/>
    <path d="M 740.445307 451.508696 
L 743.296486 452.700119 
L 744.944548 453.792123 
L 742.096437 452.522017 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cdf58f"/>
    <path d="M 810.225099 485.965664 
L 813.107966 486.975976 
L 814.652125 488.829875 
L 811.77302 487.808278 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #59de78"/>
    <path d="M 763.705069 462.632272 
L 766.565978 463.868161 
L 768.181179 465.39164 
L 765.323912 464.097699 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a5ed87"/>
    <path d="M 720.039555 443.168829 
L 722.881715 444.223906 
L 724.554975 444.825819 
L 721.71515 443.677216 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e9fb95"/>
    <path d="M 730.241725 447.106577 
L 733.088677 448.238175 
L 734.749939 449.09847 
L 731.905712 447.880354 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d9f791"/>
    <path d="M 702.483394 437.816615 
L 705.316517 438.679281 
L 707.007954 438.800218 
L 704.176413 437.834364 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fdff99"/>
    <path d="M 800.030812 480.899599 
L 802.908637 481.991232 
L 804.468398 483.841787 
L 801.594432 482.728625 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #69e17b"/>
    <path d="M 776.767276 469.147822 
L 779.634215 470.356711 
L 781.229871 472.053585 
L 778.366753 470.799511 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #91e983"/>
    <path d="M 753.502579 457.528017 
L 756.359909 458.747231 
L 757.99033 460.109016 
L 755.13643 458.822445 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b9f18b"/>
    <path d="M 712.678746 440.729583 
L 715.518007 441.69289 
L 717.199865 442.110627 
L 714.362636 441.049497 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1fc96"/>
    <path d="M 743.296486 452.700119 
L 746.150021 453.881973 
L 747.794925 455.050087 
L 744.944548 453.792123 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c9f48e"/>
    <path d="M 789.834425 475.66221 
L 792.707847 476.812756 
L 794.283571 478.625061 
L 791.414037 477.442704 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #7de57f"/>
    <path d="M 766.565978 463.868161 
L 769.429293 465.086389 
L 771.040801 466.66491 
L 768.181179 465.39164 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a5ed87"/>
    <path d="M 813.107966 486.975976 
L 815.993932 487.951658 
L 817.534367 489.813502 
L 814.652125 488.829875 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #59de78"/>
    <path d="M 733.088677 448.238175 
L 735.938032 449.363556 
L 737.596465 450.308033 
L 734.749939 449.09847 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d9f791"/>
    <path d="M 722.881715 444.223906 
L 725.726354 445.275664 
L 727.397162 445.969033 
L 724.554975 444.825819 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e5fa94"/>
    <path d="M 779.634215 470.356711 
L 782.50368 471.543421 
L 784.095489 473.282299 
L 781.229871 472.053585 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #91e983"/>
    <path d="M 802.908637 481.991232 
L 805.789344 483.052125 
L 807.345265 484.920873 
L 804.468398 483.841787 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #69e17b"/>
    <path d="M 705.316517 438.679281 
L 708.152339 439.542769 
L 709.842064 439.765325 
L 707.007954 438.800218 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fdff99"/>
    <path d="M 756.359909 458.747231 
L 759.21961 459.9528 
L 760.846532 461.379094 
L 757.99033 460.109016 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b5f08a"/>
    <path d="M 746.150021 453.881973 
L 749.005933 455.05394 
L 750.647594 456.295513 
L 747.794925 455.050087 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c9f48e"/>
    <path d="M 792.707847 476.812756 
L 795.583975 477.936638 
L 797.15581 479.777456 
L 794.283571 478.625061 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #7de57f"/>
    <path d="M 715.518007 441.69289 
L 718.359854 442.655146 
L 720.039555 443.168829 
L 717.199865 442.110627 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1fc96"/>
    <path d="M 769.429293 465.086389 
L 772.295051 466.286603 
L 773.902819 467.9171 
L 771.040801 466.66491 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a1ec86"/>
    <path d="M 735.938032 449.363556 
L 738.789804 450.482459 
L 740.445307 451.508696 
L 737.596465 450.308033 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d9f791"/>
    <path d="M 725.726354 445.275664 
L 728.573482 446.323915 
L 730.241725 447.106577 
L 727.397162 445.969033 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e5fa94"/>
    <path d="M 815.993932 487.951658 
L 818.883065 488.892591 
L 820.419819 490.759031 
L 817.534367 489.813502 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #59de78"/>
    <path d="M 782.50368 471.543421 
L 785.375717 472.707631 
L 786.963656 474.485287 
L 784.095489 473.282299 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8de882"/>
    <path d="M 759.21961 459.9528 
L 762.081713 461.144381 
L 763.705069 462.632272 
L 760.846532 461.379094 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b5f08a"/>
    <path d="M 805.789344 483.052125 
L 808.672994 484.082079 
L 810.225099 485.965664 
L 807.345265 484.920873 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #69e17b"/>
    <path d="M 708.152339 439.542769 
L 710.990864 440.40708 
L 712.678746 440.729583 
L 709.842064 439.765325 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #fdff99"/>
    <path d="M 749.005933 455.05394 
L 751.864244 456.215713 
L 753.502579 457.528017 
L 750.647594 456.295513 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c5f38d"/>
    <path d="M 795.583975 477.936638 
L 798.462861 479.033598 
L 800.030812 480.899599 
L 797.15581 479.777456 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #79e47e"/>
    <path d="M 772.295051 466.286603 
L 775.163288 467.468467 
L 776.767276 469.147822 
L 773.902819 467.9171 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a1ec86"/>
    <path d="M 718.359854 442.655146 
L 721.204291 443.616252 
L 722.881715 444.223906 
L 720.039555 443.168829 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1fc96"/>
    <path d="M 738.789804 450.482459 
L 741.64401 451.594628 
L 743.296486 452.700119 
L 740.445307 451.508696 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d5f791"/>
    <path d="M 728.573482 446.323915 
L 731.423109 447.368474 
L 733.088677 448.238175 
L 730.241725 447.106577 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e5fa94"/>
    <path d="M 818.883065 488.892591 
L 821.77543 489.798695 
L 823.308553 491.666373 
L 820.419819 490.759031 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #59de78"/>
    <path d="M 785.375717 472.707631 
L 788.25037 473.849043 
L 789.834425 475.66221 
L 786.963656 474.485287 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8de882"/>
    <path d="M 762.081713 461.144381 
L 764.946245 462.321649 
L 766.565978 463.868161 
L 763.705069 462.632272 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b5f08a"/>
    <path d="M 808.672994 484.082079 
L 811.559647 485.080926 
L 813.107966 486.975976 
L 810.225099 485.965664 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #69e17b"/>
    <path d="M 710.990864 440.40708 
L 713.832096 441.272215 
L 715.518007 441.69289 
L 712.678746 440.729583 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9fe98"/>
    <path d="M 751.864244 456.215713 
L 754.724975 457.366993 
L 756.359909 458.747231 
L 753.502579 457.528017 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c5f38d"/>
    <path d="M 775.163288 467.468467 
L 778.034043 468.631666 
L 779.634215 470.356711 
L 776.767276 469.147822 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a1ec86"/>
    <path d="M 798.462861 479.033598 
L 801.344561 480.103401 
L 802.908637 481.991232 
L 800.030812 480.899599 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #79e47e"/>
    <path d="M 721.204291 443.616252 
L 724.051327 444.576113 
L 725.726354 445.275664 
L 722.881715 444.223906 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1fc96"/>
    <path d="M 741.64401 451.594628 
L 744.500665 452.699816 
L 746.150021 453.881973 
L 743.296486 452.700119 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d5f791"/>
    <path d="M 731.423109 447.368474 
L 734.275246 448.409162 
L 735.938032 449.363556 
L 733.088677 448.238175 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e5fa94"/>
    <path d="M 764.946245 462.321649 
L 767.813239 463.484292 
L 769.429293 465.086389 
L 766.565978 463.868161 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b1ef89"/>
    <path d="M 788.25037 473.849043 
L 791.127687 474.967381 
L 792.707847 476.812756 
L 789.834425 475.66221 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #8de882"/>
    <path d="M 811.559647 485.080926 
L 814.449364 486.048529 
L 815.993932 487.951658 
L 813.107966 486.975976 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #69e17b"/>
    <path d="M 713.832096 441.272215 
L 716.676039 442.138176 
L 718.359854 442.655146 
L 715.518007 441.69289 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9fe98"/>
    <path d="M 754.724975 457.366993 
L 757.588152 458.507495 
L 759.21961 459.9528 
L 756.359909 458.747231 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c5f38d"/>
    <path d="M 778.034043 468.631666 
L 780.907354 469.775903 
L 782.50368 471.543421 
L 779.634215 470.356711 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9deb85"/>
    <path d="M 801.344561 480.103401 
L 804.229126 481.145844 
L 805.789344 483.052125 
L 802.908637 481.991232 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #79e47e"/>
    <path d="M 744.500665 452.699816 
L 747.359785 453.797782 
L 749.005933 455.05394 
L 746.150021 453.881973 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d5f791"/>
    <path d="M 724.051327 444.576113 
L 726.900967 445.534634 
L 728.573482 446.323915 
L 725.726354 445.275664 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1fc96"/>
    <path d="M 734.275246 448.409162 
L 737.129904 449.445803 
L 738.789804 450.482459 
L 735.938032 449.363556 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e1f993"/>
    <path d="M 767.813239 463.484292 
L 770.682723 464.632013 
L 772.295051 466.286603 
L 769.429293 465.086389 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b1ef89"/>
    <path d="M 791.127687 474.967381 
L 794.007714 476.062392 
L 795.583975 477.936638 
L 792.707847 476.812756 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #89e781"/>
    <path d="M 814.449364 486.048529 
L 817.342205 486.984783 
L 818.883065 488.892591 
L 815.993932 487.951658 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #69e17b"/>
    <path d="M 757.588152 458.507495 
L 760.453796 459.636945 
L 762.081713 461.144381 
L 759.21961 459.9528 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c1f38d"/>
    <path d="M 716.676039 442.138176 
L 719.522696 443.004963 
L 721.204291 443.616252 
L 718.359854 442.655146 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9fe98"/>
    <path d="M 780.907354 469.775903 
L 783.78326 470.9009 
L 785.375717 472.707631 
L 782.50368 471.543421 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9deb85"/>
    <path d="M 804.229126 481.145844 
L 807.116613 482.160747 
L 808.672994 484.082079 
L 805.789344 483.052125 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #79e47e"/>
    <path d="M 747.359785 453.797782 
L 750.221389 454.888295 
L 751.864244 456.215713 
L 749.005933 455.05394 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d1f690"/>
    <path d="M 726.900967 445.534634 
L 729.753219 446.491723 
L 731.423109 447.368474 
L 728.573482 446.323915 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f1fc96"/>
    <path d="M 737.129904 449.445803 
L 739.987095 450.478226 
L 741.64401 451.594628 
L 738.789804 450.482459 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e1f993"/>
    <path d="M 770.682723 464.632013 
L 773.554731 465.764532 
L 775.163288 467.468467 
L 772.295051 466.286603 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b1ef89"/>
    <path d="M 794.007714 476.062392 
L 796.890497 477.133847 
L 798.462861 479.033598 
L 795.583975 477.936638 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #89e781"/>
    <path d="M 760.453796 459.636945 
L 763.321932 460.755079 
L 764.946245 462.321649 
L 762.081713 461.144381 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c1f38d"/>
    <path d="M 817.342205 486.984783 
L 820.23823 487.889611 
L 821.77543 489.798695 
L 818.883065 488.892591 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #65e07a"/>
    <path d="M 783.78326 470.9009 
L 786.661801 472.006399 
L 788.25037 473.849043 
L 785.375717 472.707631 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #9deb85"/>
    <path d="M 719.522696 443.004963 
L 722.372071 443.872578 
L 724.051327 444.576113 
L 721.204291 443.616252 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9fe98"/>
    <path d="M 750.221389 454.888295 
L 753.085493 455.971131 
L 754.724975 457.366993 
L 751.864244 456.215713 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d1f690"/>
    <path d="M 807.116613 482.160747 
L 810.007074 483.147961 
L 811.559647 485.080926 
L 808.672994 484.082079 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #79e47e"/>
    <path d="M 729.753219 446.491723 
L 732.60809 447.447291 
L 734.275246 448.409162 
L 731.423109 447.368474 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #edfb95"/>
    <path d="M 739.987095 450.478226 
L 742.84683 451.506266 
L 744.500665 452.699816 
L 741.64401 451.594628 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e1f993"/>
    <path d="M 773.554731 465.764532 
L 776.429294 466.881583 
L 778.034043 468.631666 
L 775.163288 467.468467 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #adef89"/>
    <path d="M 796.890497 477.133847 
L 799.776085 478.181543 
L 801.344561 480.103401 
L 798.462861 479.033598 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #89e781"/>
    <path d="M 763.321932 460.755079 
L 766.192586 461.861648 
L 767.813239 463.484292 
L 764.946245 462.321649 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c1f38d"/>
    <path d="M 786.661801 472.006399 
L 789.543017 473.092162 
L 791.127687 474.967381 
L 788.25037 473.849043 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #99eb85"/>
    <path d="M 722.372071 443.872578 
L 725.224169 444.741021 
L 726.900967 445.534634 
L 724.051327 444.576113 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9fe98"/>
    <path d="M 753.085493 455.971131 
L 755.952116 457.046074 
L 757.588152 458.507495 
L 754.724975 457.366993 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d1f690"/>
    <path d="M 810.007074 483.147961 
L 812.900564 484.107363 
L 814.449364 486.048529 
L 811.559647 485.080926 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #75e37d"/>
    <path d="M 742.84683 451.506266 
L 745.709122 452.529762 
L 747.359785 453.797782 
L 744.500665 452.699816 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e1f993"/>
    <path d="M 732.60809 447.447291 
L 735.465587 448.401249 
L 737.129904 449.445803 
L 734.275246 448.409162 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #edfb95"/>
    <path d="M 776.429294 466.881583 
L 779.306446 467.982918 
L 780.907354 469.775903 
L 778.034043 468.631666 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #adef89"/>
    <path d="M 799.776085 478.181543 
L 802.664524 479.205296 
L 804.229126 481.145844 
L 801.344561 480.103401 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #89e781"/>
    <path d="M 766.192586 461.861648 
L 769.065783 462.956412 
L 770.682723 464.632013 
L 767.813239 463.484292 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bdf28c"/>
    <path d="M 789.543017 473.092162 
L 792.426949 474.157971 
L 794.007714 476.062392 
L 791.127687 474.967381 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #99eb85"/>
    <path d="M 755.952116 457.046074 
L 758.821277 458.112918 
L 760.453796 459.636945 
L 757.588152 458.507495 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d1f690"/>
    <path d="M 725.224169 444.741021 
L 728.078994 445.610295 
L 729.753219 446.491723 
L 726.900967 445.534634 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9fe98"/>
    <path d="M 812.900564 484.107363 
L 815.797138 485.038857 
L 817.342205 486.984783 
L 814.449364 486.048529 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #75e37d"/>
    <path d="M 745.709122 452.529762 
L 748.573983 453.548559 
L 750.221389 454.888295 
L 747.359785 453.797782 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e1f993"/>
    <path d="M 735.465587 448.401249 
L 738.325719 449.353513 
L 739.987095 450.478226 
L 737.129904 449.445803 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #edfb95"/>
    <path d="M 779.306446 467.982918 
L 782.186219 469.068302 
L 783.78326 470.9009 
L 780.907354 469.775903 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #adef89"/>
    <path d="M 802.664524 479.205296 
L 805.555865 480.204951 
L 807.116613 482.160747 
L 804.229126 481.145844 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #89e781"/>
    <path d="M 769.065783 462.956412 
L 771.941549 464.039145 
L 773.554731 465.764532 
L 770.682723 464.632013 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bdf28c"/>
    <path d="M 792.426949 474.157971 
L 795.313638 475.203628 
L 796.890497 477.133847 
L 794.007714 476.062392 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #99eb85"/>
    <path d="M 758.821277 458.112918 
L 761.692995 459.171464 
L 763.321932 460.755079 
L 760.453796 459.636945 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cdf58f"/>
    <path d="M 728.078994 445.610295 
L 730.936548 446.4804 
L 732.60809 447.447291 
L 729.753219 446.491723 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9fe98"/>
    <path d="M 748.573983 453.548559 
L 751.441427 454.562507 
L 753.085493 455.971131 
L 750.221389 454.888295 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ddf892"/>
    <path d="M 815.797138 485.038857 
L 818.69685 485.942377 
L 820.23823 487.889611 
L 817.342205 486.984783 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #75e37d"/>
    <path d="M 782.186219 469.068302 
L 785.068647 470.137521 
L 786.661801 472.006399 
L 783.78326 470.9009 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a9ee88"/>
    <path d="M 738.325719 449.353513 
L 741.188492 450.304 
L 742.84683 451.506266 
L 739.987095 450.478226 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #edfb95"/>
    <path d="M 805.555865 480.204951 
L 808.450153 481.180376 
L 810.007074 483.147961 
L 807.116613 482.160747 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #89e781"/>
    <path d="M 771.941549 464.039145 
L 774.819911 465.109634 
L 776.429294 466.881583 
L 773.554731 465.764532 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bdf28c"/>
    <path d="M 795.313638 475.203628 
L 798.203126 476.228957 
L 799.776085 478.181543 
L 796.890497 477.133847 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #99eb85"/>
    <path d="M 761.692995 459.171464 
L 764.567289 460.221523 
L 766.192586 461.861648 
L 763.321932 460.755079 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cdf58f"/>
    <path d="M 730.936548 446.4804 
L 733.796836 447.351338 
L 735.465587 448.401249 
L 732.60809 447.447291 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9fe98"/>
    <path d="M 751.441427 454.562507 
L 754.311467 455.571463 
L 755.952116 457.046074 
L 753.085493 455.971131 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ddf892"/>
    <path d="M 785.068647 470.137521 
L 787.953765 471.190374 
L 789.543017 473.092162 
L 786.661801 472.006399 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a9ee88"/>
    <path d="M 741.188492 450.304 
L 744.053916 451.252629 
L 745.709122 452.529762 
L 742.84683 451.506266 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #edfb95"/>
    <path d="M 808.450153 481.180376 
L 811.347438 482.13146 
L 812.900564 484.107363 
L 810.007074 483.147961 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #85e781"/>
    <path d="M 774.819911 465.109634 
L 777.700895 466.167679 
L 779.306446 467.982918 
L 776.429294 466.881583 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #bdf28c"/>
    <path d="M 798.203126 476.228957 
L 801.095453 477.233802 
L 802.664524 479.205296 
L 799.776085 478.181543 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #99eb85"/>
    <path d="M 764.567289 460.221523 
L 767.444181 461.262916 
L 769.065783 462.956412 
L 766.192586 461.861648 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cdf58f"/>
    <path d="M 754.311467 455.571463 
L 757.184117 456.575288 
L 758.821277 458.112918 
L 755.952116 457.046074 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ddf892"/>
    <path d="M 787.953765 471.190374 
L 790.841607 472.226678 
L 792.426949 474.157971 
L 789.543017 473.092162 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a9ee88"/>
    <path d="M 733.796836 447.351338 
L 736.659863 448.223109 
L 738.325719 449.353513 
L 735.465587 448.401249 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9fe98"/>
    <path d="M 744.053916 451.252629 
L 746.921998 452.199325 
L 748.573983 453.548559 
L 745.709122 452.529762 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #edfb95"/>
    <path d="M 811.347438 482.13146 
L 814.247769 483.058122 
L 815.797138 485.038857 
L 812.900564 484.107363 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #85e781"/>
    <path d="M 777.700895 466.167679 
L 780.58453 467.213091 
L 782.186219 469.068302 
L 779.306446 467.982918 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b9f18b"/>
    <path d="M 801.095453 477.233802 
L 803.990662 478.218026 
L 805.555865 480.204951 
L 802.664524 479.205296 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #99eb85"/>
    <path d="M 767.444181 461.262916 
L 770.32369 462.295472 
L 771.941549 464.039145 
L 769.065783 462.956412 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cdf58f"/>
    <path d="M 757.184117 456.575288 
L 760.059392 457.573849 
L 761.692995 459.171464 
L 758.821277 458.112918 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ddf892"/>
    <path d="M 790.841607 472.226678 
L 793.732208 473.246268 
L 795.313638 475.203628 
L 792.426949 474.157971 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a9ee88"/>
    <path d="M 736.659863 448.223109 
L 739.525631 449.095715 
L 741.188492 450.304 
L 738.325719 449.353513 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9fe98"/>
    <path d="M 746.921998 452.199325 
L 749.792747 453.144011 
L 751.441427 454.562507 
L 748.573983 453.548559 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #edfb95"/>
    <path d="M 780.58453 467.213091 
L 783.470843 468.245698 
L 785.068647 470.137521 
L 782.186219 469.068302 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b9f18b"/>
    <path d="M 814.247769 483.058122 
L 817.151193 483.960303 
L 818.69685 485.942377 
L 815.797138 485.038857 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #85e781"/>
    <path d="M 803.990662 478.218026 
L 806.888796 479.181516 
L 808.450153 481.180376 
L 805.555865 480.204951 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #95ea84"/>
    <path d="M 770.32369 462.295472 
L 773.205838 463.319031 
L 774.819911 465.109634 
L 771.941549 464.039145 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #cdf58f"/>
    <path d="M 760.059392 457.573849 
L 762.937304 458.56702 
L 764.567289 460.221523 
L 761.692995 459.171464 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ddf892"/>
    <path d="M 793.732208 473.246268 
L 796.625604 474.248996 
L 798.203126 476.228957 
L 795.313638 475.203628 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a9ee88"/>
    <path d="M 739.525631 449.095715 
L 742.394145 449.969158 
L 744.053916 451.252629 
L 741.188492 450.304 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9fe98"/>
    <path d="M 749.792747 453.144011 
L 752.666172 454.086616 
L 754.311467 455.571463 
L 751.441427 454.562507 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #edfb95"/>
    <path d="M 783.470843 468.245698 
L 786.359862 469.265338 
L 787.953765 471.190374 
L 785.068647 470.137521 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b9f18b"/>
    <path d="M 806.888796 479.181516 
L 809.789896 480.124178 
L 811.347438 482.13146 
L 808.450153 481.180376 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #95ea84"/>
    <path d="M 773.205838 463.319031 
L 776.090645 464.333441 
L 777.700895 466.167679 
L 774.819911 465.109634 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c9f48e"/>
    <path d="M 762.937304 458.56702 
L 765.817871 459.554681 
L 767.444181 461.262916 
L 764.567289 460.221523 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #ddf892"/>
    <path d="M 796.625604 474.248996 
L 799.52183 475.23473 
L 801.095453 477.233802 
L 798.203126 476.228957 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a9ee88"/>
    <path d="M 752.666172 454.086616 
L 755.542282 455.027071 
L 757.184117 456.575288 
L 754.311467 455.571463 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e9fb95"/>
    <path d="M 742.394145 449.969158 
L 745.265409 450.843437 
L 746.921998 452.199325 
L 744.053916 451.252629 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9fe98"/>
    <path d="M 786.359862 469.265338 
L 789.251616 470.271864 
L 790.841607 472.226678 
L 787.953765 471.190374 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b9f18b"/>
    <path d="M 776.090645 464.333441 
L 778.978134 465.338561 
L 780.58453 467.213091 
L 777.700895 466.167679 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c9f48e"/>
    <path d="M 809.789896 480.124178 
L 812.694004 481.04594 
L 814.247769 483.058122 
L 811.347438 482.13146 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #95ea84"/>
    <path d="M 765.817871 459.554681 
L 768.701105 460.536718 
L 770.32369 462.295472 
L 767.444181 461.262916 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d9f791"/>
    <path d="M 799.52183 475.23473 
L 802.420922 476.203356 
L 803.990662 478.218026 
L 801.095453 477.233802 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a5ed87"/>
    <path d="M 755.542282 455.027071 
L 758.421085 455.96531 
L 760.059392 457.573849 
L 757.184117 456.575288 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e9fb95"/>
    <path d="M 745.265409 450.843437 
L 748.139427 451.718556 
L 749.792747 453.144011 
L 746.921998 452.199325 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9fe98"/>
    <path d="M 789.251616 470.271864 
L 792.146134 471.265143 
L 793.732208 473.246268 
L 790.841607 472.226678 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b9f18b"/>
    <path d="M 778.978134 465.338561 
L 781.868326 466.33426 
L 783.470843 468.245698 
L 780.58453 467.213091 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c9f48e"/>
    <path d="M 812.694004 481.04594 
L 815.601163 481.946752 
L 817.151193 483.960303 
L 814.247769 483.058122 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #95ea84"/>
    <path d="M 768.701105 460.536718 
L 771.587024 461.513024 
L 773.205838 463.319031 
L 770.32369 462.295472 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d9f791"/>
    <path d="M 802.420922 476.203356 
L 805.322916 477.15478 
L 806.888796 479.181516 
L 803.990662 478.218026 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a5ed87"/>
    <path d="M 758.421085 455.96531 
L 761.302592 456.901271 
L 762.937304 458.56702 
L 760.059392 457.573849 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e9fb95"/>
    <path d="M 748.139427 451.718556 
L 751.016202 452.594513 
L 752.666172 454.086616 
L 749.792747 453.144011 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9fe98"/>
    <path d="M 792.146134 471.265143 
L 795.043446 472.245056 
L 796.625604 474.248996 
L 793.732208 473.246268 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b9f18b"/>
    <path d="M 781.868326 466.33426 
L 784.761244 467.320417 
L 786.359862 469.265338 
L 783.470843 468.245698 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c9f48e"/>
    <path d="M 771.587024 461.513024 
L 774.475642 462.483497 
L 776.090645 464.333441 
L 773.205838 463.319031 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d9f791"/>
    <path d="M 805.322916 477.15478 
L 808.227847 478.088922 
L 809.789896 480.124178 
L 806.888796 479.181516 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a5ed87"/>
    <path d="M 761.302592 456.901271 
L 764.18681 457.834892 
L 765.817871 459.554681 
L 762.937304 458.56702 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e9fb95"/>
    <path d="M 751.016202 452.594513 
L 753.89574 453.471312 
L 755.542282 455.027071 
L 752.666172 454.086616 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9fe98"/>
    <path d="M 795.043446 472.245056 
L 797.943579 473.211497 
L 799.52183 475.23473 
L 796.625604 474.248996 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b9f18b"/>
    <path d="M 784.761244 467.320417 
L 787.65691 468.296921 
L 789.251616 470.271864 
L 786.359862 469.265338 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c9f48e"/>
    <path d="M 774.475642 462.483497 
L 777.366974 463.448043 
L 778.978134 465.338561 
L 776.090645 464.333441 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d9f791"/>
    <path d="M 808.227847 478.088922 
L 811.135752 479.005723 
L 812.694004 481.04594 
L 809.789896 480.124178 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a5ed87"/>
    <path d="M 764.18681 457.834892 
L 767.073751 458.766119 
L 768.701105 460.536718 
L 765.817871 459.554681 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e9fb95"/>
    <path d="M 753.89574 453.471312 
L 756.778043 454.348953 
L 758.421085 455.96531 
L 755.542282 455.027071 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9fe98"/>
    <path d="M 797.943579 473.211497 
L 800.846565 474.164374 
L 802.420922 476.203356 
L 799.52183 475.23473 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b5f08a"/>
    <path d="M 787.65691 468.296921 
L 790.555347 469.263671 
L 792.146134 471.265143 
L 789.251616 470.271864 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c9f48e"/>
    <path d="M 777.366974 463.448043 
L 780.261038 464.406575 
L 781.868326 466.33426 
L 778.978134 465.338561 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d9f791"/>
    <path d="M 811.135752 479.005723 
L 814.046667 479.905139 
L 815.601163 481.946752 
L 812.694004 481.04594 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #a5ed87"/>
    <path d="M 767.073751 458.766119 
L 769.963422 459.694896 
L 771.587024 461.513024 
L 768.701105 460.536718 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e9fb95"/>
    <path d="M 756.778043 454.348953 
L 759.663115 455.227437 
L 761.302592 456.901271 
L 758.421085 455.96531 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9fe98"/>
    <path d="M 800.846565 474.164374 
L 803.752431 475.103612 
L 805.322916 477.15478 
L 802.420922 476.203356 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b5f08a"/>
    <path d="M 790.555347 469.263671 
L 793.456577 470.220579 
L 795.043446 472.245056 
L 792.146134 471.265143 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c9f48e"/>
    <path d="M 780.261038 464.406575 
L 783.15785 465.359012 
L 784.761244 467.320417 
L 781.868326 466.33426 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d9f791"/>
    <path d="M 769.963422 459.694896 
L 772.855836 460.621174 
L 774.475642 462.483497 
L 771.587024 461.513024 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e9fb95"/>
    <path d="M 759.663115 455.227437 
L 762.550961 456.106766 
L 764.18681 457.834892 
L 761.302592 456.901271 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9fe98"/>
    <path d="M 803.752431 475.103612 
L 806.661209 476.029146 
L 808.227847 478.088922 
L 805.322916 477.15478 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b5f08a"/>
    <path d="M 793.456577 470.220579 
L 796.360625 471.167564 
L 797.943579 473.211497 
L 795.043446 472.245056 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c9f48e"/>
    <path d="M 783.15785 465.359012 
L 786.057424 466.30528 
L 787.65691 468.296921 
L 784.761244 467.320417 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d9f791"/>
    <path d="M 772.855836 460.621174 
L 775.751 461.544907 
L 777.366974 463.448043 
L 774.475642 462.483497 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e9fb95"/>
    <path d="M 762.550961 456.106766 
L 765.441585 456.986941 
L 767.073751 458.766119 
L 764.18681 457.834892 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9fe98"/>
    <path d="M 806.661209 476.029146 
L 809.572928 476.94093 
L 811.135752 479.005723 
L 808.227847 478.088922 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b5f08a"/>
    <path d="M 796.360625 471.167564 
L 799.267512 472.104557 
L 800.846565 474.164374 
L 797.943579 473.211497 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c5f38d"/>
    <path d="M 786.057424 466.30528 
L 788.95978 467.245311 
L 790.555347 469.263671 
L 787.65691 468.296921 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d9f791"/>
    <path d="M 775.751 461.544907 
L 778.648926 462.46605 
L 780.261038 464.406575 
L 777.366974 463.448043 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e9fb95"/>
    <path d="M 765.441585 456.986941 
L 768.334991 457.867962 
L 769.963422 459.694896 
L 767.073751 458.766119 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9fe98"/>
    <path d="M 809.572928 476.94093 
L 812.487617 477.838928 
L 814.046667 479.905139 
L 811.135752 479.005723 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #b5f08a"/>
    <path d="M 799.267512 472.104557 
L 802.177263 473.031502 
L 803.752431 475.103612 
L 800.846565 474.164374 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c5f38d"/>
    <path d="M 788.95978 467.245311 
L 791.864931 468.179046 
L 793.456577 470.220579 
L 790.555347 469.263671 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d9f791"/>
    <path d="M 778.648926 462.46605 
L 781.549623 463.384564 
L 783.15785 465.359012 
L 780.261038 464.406575 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e9fb95"/>
    <path d="M 768.334991 457.867962 
L 771.231182 458.749832 
L 772.855836 460.621174 
L 769.963422 459.694896 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9fe98"/>
    <path d="M 802.177263 473.031502 
L 805.089901 473.948351 
L 806.661209 476.029146 
L 803.752431 475.103612 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c5f38d"/>
    <path d="M 791.864931 468.179046 
L 794.772897 469.106433 
L 796.360625 471.167564 
L 793.456577 470.220579 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d9f791"/>
    <path d="M 781.549623 463.384564 
L 784.453101 464.300411 
L 786.057424 466.30528 
L 783.15785 465.359012 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e9fb95"/>
    <path d="M 771.231182 458.749832 
L 774.130163 459.632551 
L 775.751 461.544907 
L 772.855836 460.621174 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9fe98"/>
    <path d="M 805.089901 473.948351 
L 808.005448 474.855068 
L 809.572928 476.94093 
L 806.661209 476.029146 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c5f38d"/>
    <path d="M 794.772897 469.106433 
L 797.683693 470.027424 
L 799.267512 472.104557 
L 796.360625 471.167564 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d5f791"/>
    <path d="M 784.453101 464.300411 
L 787.359371 465.213559 
L 788.95978 467.245311 
L 786.057424 466.30528 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e9fb95"/>
    <path d="M 774.130163 459.632551 
L 777.031938 460.516121 
L 778.648926 462.46605 
L 775.751 461.544907 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9fe98"/>
    <path d="M 808.005448 474.855068 
L 810.923929 475.751627 
L 812.487617 477.838928 
L 809.572928 476.94093 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #c5f38d"/>
    <path d="M 797.683693 470.027424 
L 800.597336 470.941983 
L 802.177263 473.031502 
L 799.267512 472.104557 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d5f791"/>
    <path d="M 787.359371 465.213559 
L 790.268444 466.123979 
L 791.864931 468.179046 
L 788.95978 467.245311 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e9fb95"/>
    <path d="M 777.031938 460.516121 
L 779.93651 461.400543 
L 781.549623 463.384564 
L 778.648926 462.46605 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9fe98"/>
    <path d="M 800.597336 470.941983 
L 803.513844 471.850078 
L 805.089901 473.948351 
L 802.177263 473.031502 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d5f791"/>
    <path d="M 790.268444 466.123979 
L 793.180329 467.031644 
L 794.772897 469.106433 
L 791.864931 468.179046 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e9fb95"/>
    <path d="M 779.93651 461.400543 
L 782.843884 462.285818 
L 784.453101 464.300411 
L 781.549623 463.384564 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9fe98"/>
    <path d="M 803.513844 471.850078 
L 806.433232 472.751684 
L 808.005448 474.855068 
L 805.089901 473.948351 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d5f791"/>
    <path d="M 793.180329 467.031644 
L 796.095037 467.936532 
L 797.683693 470.027424 
L 794.772897 469.106433 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e5fa94"/>
    <path d="M 782.843884 462.285818 
L 785.754065 463.171948 
L 787.359371 465.213559 
L 784.453101 464.300411 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9fe98"/>
    <path d="M 806.433232 472.751684 
L 809.35552 473.646786 
L 810.923929 475.751627 
L 808.005448 474.855068 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #d5f791"/>
    <path d="M 796.095037 467.936532 
L 799.012579 468.838625 
L 800.597336 470.941983 
L 797.683693 470.027424 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e5fa94"/>
    <path d="M 785.754065 463.171948 
L 788.667055 464.058933 
L 790.268444 466.123979 
L 787.359371 465.213559 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f9fe98"/>
    <path d="M 799.012579 468.838625 
L 801.932965 469.737906 
L 803.513844 471.850078 
L 800.597336 470.941983 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e5fa94"/>
    <path d="M 788.667055 464.058933 
L 791.582859 464.946774 
L 793.180329 467.031644 
L 790.268444 466.123979 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f5fd97"/>
    <path d="M 801.932965 469.737906 
L 804.856206 470.634366 
L 806.433232 472.751684 
L 803.513844 471.850078 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e5fa94"/>
    <path d="M 791.582859 464.946774 
L 794.501481 465.835474 
L 796.095037 467.936532 
L 793.180329 467.031644 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f5fd97"/>
    <path d="M 804.856206 470.634366 
L 807.782312 471.527995 
L 809.35552 473.646786 
L 806.433232 472.751684 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #e5fa94"/>
    <path d="M 794.501481 465.835474 
L 797.422926 466.725034 
L 799.012579 468.838625 
L 796.095037 467.936532 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f5fd97"/>
    <path d="M 797.422926 466.725034 
L 800.347197 467.615453 
L 801.932965 469.737906 
L 799.012579 468.838625 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f5fd97"/>
    <path d="M 800.347197 467.615453 
L 803.274298 468.506735 
L 804.856206 470.634366 
L 801.932965 469.737906 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f5fd97"/>
    <path d="M 803.274298 468.506735 
L 806.204234 469.39888 
L 807.782312 471.527995 
L 804.856206 470.634366 
z
" clip-path="url(#p2fbbe989fb)" style="fill: #f5fd97"/>
   </g>
  </g>
 </g>
 <defs>
  <clipPath id="p2fbbe989fb">
   <rect x="460.8" y="86.4" width="554.4" height="554.4"/>
  </clipPath>
 </defs>
</svg>
\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"XV, YV=np.meshgrid(xv, yv)\\nplt.figure(figsize=(20, 10))\\nax = plt.axes(projection='3d')\\nplt.figure().subplots_adjust(top=1, bottom=0, left=0, right=1, wspace=0)\\nax.plot_surface(XV, YV, z, rstride=1, cstride=1, cmap='terrain', edgecolor=None);                   \"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 13200753290457032630,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 5101273659635728255,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"The order in which the axis of the result of \\\\algo{nevaluate} should be interpreted\\nis determined by the order in which you list them in the values dictionary. \\nCompare the following:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"The order in which the axis of the result of \\\\algo{nevaluate} should be interpreted\\nis determined by the order in which you list them in the values dictionary. \\nCompare the following:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 17971765439671340505,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"z1 = np.array( nevaluate(ex, {$x$: xv, $y$: yv} ))\\nz2 = np.array( nevaluate(ex, {$y$: yv, $x$: xv} ))\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 12456077622196445642,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 11921325850843768566,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"verbatim\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}0.2512712531759243\\\\end{verbatim}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 1944803299347562704,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"verbatim\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}0.5633046988744114\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"z1[10,20];\\nz2[10,20];\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 730370848732475554,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 2572738521568116665,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\subsection*{Supported elementary functions}\\n\\nAt present the \\\\verb|nevaluate| function supports expressions with the following building blocks:\\nmultiplication/division, addition/subtraction, trigonometric functions, hyperbolic trigonometric functions,\\nlogarithms, exponential, square root.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\subsection*{Supported elementary functions}\\n\\nAt present the \\\\verb|nevaluate| function supports expressions with the following building blocks:\\nmultiplication/division, addition/subtraction, trigonometric functions, hyperbolic trigonometric functions,\\nlogarithms, exponential, square root.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 11584173555601999890,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"\"\n\t\t}\n\t],\n\t\"description\": \"Cadabra JSON notebook format\",\n\t\"version\": 1.0\n}\n"
  },
  {
    "path": "examples/ref_ordering.cnb",
    "content": "{\n\t\"cell_id\": 12537442009270116517,\n\t\"cells\": [\n\t\t{\n\t\t\t\"cell_id\": 5200063121966218726,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 10749627117119289384,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\section*{Symbol ordering and commutation properties}\\n\\nA conventional way to sort factors in a product is to use\\nlexographical ordering. However, this is almost never what one wants\\nwhen transcribing a physics problem to the computer. Therefore, Cadabra\\nallows you to specify the sort order of symbols yourself. This is done\\nby associating the \\\\prop{SortOrder} list property to a list of\\nsymbols, as in\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\section*{Symbol ordering and commutation properties}\\n\\nA conventional way to sort factors in a product is to use\\nlexographical ordering. However, this is almost never what one wants\\nwhen transcribing a physics problem to the computer. Therefore, Cadabra\\nallows you to specify the sort order of symbols yourself. This is done\\nby associating the \\\\prop{SortOrder} list property to a list of\\nsymbols, as in\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 4630586668004954392,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9786594162868805709,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 16849266693056721115,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"X X G A A B\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}X X G A A B\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"{X,G,Y,A,B}::SortOrder.\\nex:= A*B*G*X*A*X:\\nsort_product(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 1219183121018762363,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 8650713722243272991,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"More complicated objects with indices are of course also allowed, such\\nas in\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"More complicated objects with indices are of course also allowed, such\\nas in\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 1626051978006702516,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 11261042148179910614,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property SortOrder attached to~}\\\\left[W_{m n}, \\\\discretionary{}{}{}W_{m}\\\\right].\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 10510303686589897558,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 16107899499185766672,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"W_{m n} W_{q r} W_{p} W_{s} W_{t}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}W_{m n} W_{q r} W_{p} W_{s} W_{t}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"{ W_{m n}, W_{m} }::SortOrder;\\nex:= W_{m n} W_{p} W_{q r} W_{s} W_{t}:\\nsort_product(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 817057946295541244,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 3438182820960176836,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"It is not allowed to have more than one such set\\ncontain the same symbol. Thus,\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"It is not allowed to have more than one such set\\ncontain the same symbol. Thus,\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 281481927617357016,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 16144396283803958279,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property SortOrder attached to~}\\\\left[X, \\\\discretionary{}{}{}G\\\\right].\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 124040221032259103,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property SortOrder attached to~}\\\\left[X, \\\\discretionary{}{}{}A, \\\\discretionary{}{}{}B\\\\right].\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"{X,G}::SortOrder;\\n{X,A,B}::SortOrder;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 125055683918759571,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 15140788470240326016,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"is not allowed (and will, in fact, take $X$ out of the first list).\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"is not allowed (and will, in fact, take $X$ out of the first list).\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 7891865129573028133,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 1176829512545785359,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 7607187409447219690,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"X G A B\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}X G A B\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex:= A*B*G*X:\\nsort_product(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 10703969584082137669,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 12608645003842560868,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"Apart from the preferred sort order, there are more properties which\\ninfluence the way in which products can be sorted. In particular, sort\\norder is influenced by whether symbols commute or anti-commute with\\neach other.  Physicists in general use a very implicit notation as far\\nas commutativity of objects in a product is concerned. Consider for\\ninstance a situation in which we deal with two operators $\\\\hat M$ and\\n$\\\\hat N$, as well as some constants $q$ and $p$. These two expressions\\nare equivalent:\\n\\\\begin{equation}\\n2q\\\\, \\\\hat M p \\\\hat N \\\\quad\\\\text{and}\\\\quad 2pq\\\\, \\\\hat M \\\\hat N \\\\,.\\n\\\\end{equation}\\nBut this is not obvious from the notation that has been used to\\nindicate the product. In fact, the product symbol is usually left out\\ncompletely.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"Apart from the preferred sort order, there are more properties which\\ninfluence the way in which products can be sorted. In particular, sort\\norder is influenced by whether symbols commute or anti-commute with\\neach other.  Physicists in general use a very implicit notation as far\\nas commutativity of objects in a product is concerned. Consider for\\ninstance a situation in which we deal with two operators $\\\\hat M$ and\\n$\\\\hat N$, as well as some constants $q$ and $p$. These two expressions\\nare equivalent:\\n\\\\begin{equation}\\n2q\\\\, \\\\hat M p \\\\hat N \\\\quad\\\\text{and}\\\\quad 2pq\\\\, \\\\hat M \\\\hat N \\\\,.\\n\\\\end{equation}\\nBut this is not obvious from the notation that has been used to\\nindicate the product. In fact, the product symbol is usually left out\\ncompletely.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 4605361587650520474,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 3090531545332464049,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\nIn many other computer algebra systems, you have to introduce special\\ntypes of ``non-commuting'' products (e.g.~the \\\\verb|&*| operator in\\nMaple or the \\\\verb|**| operator in Mathematica). This can be rather\\ncumbersome, for a variety of reasons. The main reason, however, is\\nthat it does not match with what you do on paper. On paper, you never\\nwrite special product symbols for objects which do not commute. You\\njust string them together, and know from the properties of the symbols\\nwhether objects can be moved through each other or not.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\nIn many other computer algebra systems, you have to introduce special\\ntypes of ``non-commuting'' products (e.g.~the \\\\verb|&*| operator in\\nMaple or the \\\\verb|**| operator in Mathematica). This can be rather\\ncumbersome, for a variety of reasons. The main reason, however, is\\nthat it does not match with what you do on paper. On paper, you never\\nwrite special product symbols for objects which do not commute. You\\njust string them together, and know from the properties of the symbols\\nwhether objects can be moved through each other or not.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 10603900724913809269,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 16144138917267124877,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\nIn order to make these sort of things possible in Cadabra, it is\\nnecessary to declare ``sets'' of objects which mutually do not commute\\n(i.e.~for which the order inside a product cannot be changed without\\nconsequences) but which commute with objects of other sets. Many\\ncomputer algebra systems only use one such set: objects are either\\n``commuting'' or ``non-commuting''. This is often too restrictive. For\\ninstance, when $\\\\Psi$ is a fermion and $\\\\Gamma$ denotes a Clifford\\nalgebra element, a system with only one set of non-commuting objects\\nis unable to see that\\n\\\\begin{equation}\\n\\\\bar\\\\Psi_a (\\\\Gamma_n\\\\Gamma_m)_{ab} \\\\Psi_b \\\\quad\\\\text{and}\\\\quad\\n\\\\bar\\\\Psi_a \\\\Psi_b (\\\\Gamma_n\\\\Gamma_m)_{ab} \\n\\\\end{equation}\\nare equivalent. In Cadabra one would simply put $\\\\Psi_{a}$ and\\n$\\\\Gamma_{m}$ in two different sets, mutually commuting, but\\nnon-commuting among themselves. To be precise, the example above is\\nreproduced by\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\nIn order to make these sort of things possible in Cadabra, it is\\nnecessary to declare ``sets'' of objects which mutually do not commute\\n(i.e.~for which the order inside a product cannot be changed without\\nconsequences) but which commute with objects of other sets. Many\\ncomputer algebra systems only use one such set: objects are either\\n``commuting'' or ``non-commuting''. This is often too restrictive. For\\ninstance, when $\\\\Psi$ is a fermion and $\\\\Gamma$ denotes a Clifford\\nalgebra element, a system with only one set of non-commuting objects\\nis unable to see that\\n\\\\begin{equation}\\n\\\\bar\\\\Psi_a (\\\\Gamma_n\\\\Gamma_m)_{ab} \\\\Psi_b \\\\quad\\\\text{and}\\\\quad\\n\\\\bar\\\\Psi_a \\\\Psi_b (\\\\Gamma_n\\\\Gamma_m)_{ab} \\n\\\\end{equation}\\nare equivalent. In Cadabra one would simply put $\\\\Psi_{a}$ and\\n$\\\\Gamma_{m}$ in two different sets, mutually commuting, but\\nnon-commuting among themselves. To be precise, the example above is\\nreproduced by\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 18198511208890861354,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 4739882481462006047,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property Accent attached to~}\\\\backslash\\\\texttt{bar}\\\\{\\\\#\\\\}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9877825032413020410,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property SelfNonCommuting attached to~}\\\\Psi_{a}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 17733511168608861733,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property GammaMatrix attached to~}\\\\backslash\\\\texttt{Gamma}\\\\{\\\\#\\\\}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 2443793177241453786,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 9340474262344984867,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\bar{\\\\Psi_{a}} \\\\indexbracket(\\\\Gamma_{n} \\\\Gamma_{m})_{ab} \\\\Psi_{b}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\bar{\\\\Psi_{a}} \\\\left(\\\\Gamma_{n} \\\\Gamma_{m}\\\\right)\\\\,_{ab} \\\\Psi_{b}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9074689257260807998,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 2352024210399499253,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\bar{\\\\Psi_{a}} \\\\Psi_{b} \\\\indexbracket(\\\\Gamma_{n} \\\\Gamma_{m})_{ab}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\bar{\\\\Psi_{a}} \\\\Psi_{b} \\\\left(\\\\Gamma_{n} \\\\Gamma_{m}\\\\right)\\\\,_{ab}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"\\\\bar{#}::Accent;\\n\\\\Psi_{a}::SelfNonCommuting;\\n\\\\Gamma_{#}::GammaMatrix;\\nex:= \\\\bar{\\\\Psi_a} (\\\\Gamma_n \\\\Gamma_m)_{ab} \\\\Psi_b;\\nsort_product(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 10484759701533327357,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 2195099621354746394,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"Commutation properties always refer to components. If you associate an\\n\\\\prop{ImplicitIndex} property to an object, then it will never\\ncommute with itself or with any other such object. You can see this in\\nthe example above, as the \\\\algo{prodsort} command kept the\\norder of the two gamma matrices unchanged.\\n\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"Commutation properties always refer to components. If you associate an\\n\\\\prop{ImplicitIndex} property to an object, then it will never\\ncommute with itself or with any other such object. You can see this in\\nthe example above, as the \\\\algo{prodsort} command kept the\\norder of the two gamma matrices unchanged.\\n\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 609176986855950731,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"\"\n\t\t}\n\t],\n\t\"description\": \"Cadabra JSON notebook format\",\n\t\"version\": 1.0\n}\n"
  },
  {
    "path": "examples/ref_patterns.cnb",
    "content": "{\n\t\"cell_id\": 9785580926210345772,\n\t\"cells\": [\n\t\t{\n\t\t\t\"cell_id\": 160332340275216323,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 14935582325842510854,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\section*{Patterns, conditionals and regular expressions}\\n\\nPatterns in Cadabra are quite a bit different from those in other\\ncomputer algebra systems, because they are more tuned towards the\\npattern matching of objects common in tensorial expressions, rather\\nthan generic tree structures. Cadabra knows about three different\\npattern types: \\\\emph{name patterns} (for single names), \\\\emph{object patterns} \\n(for things which include indices and arguments) and \\n\\\\emph{dummy patterns} (things for which the name is irrelevant, like indices). \\n\\nName patterns are things which match a single name in an object, \\nwithout indices or arguments. They are constructed by writing a single question mark behind\\nthe name, as in\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\section*{Patterns, conditionals and regular expressions}\\n\\nPatterns in Cadabra are quite a bit different from those in other\\ncomputer algebra systems, because they are more tuned towards the\\npattern matching of objects common in tensorial expressions, rather\\nthan generic tree structures. Cadabra knows about three different\\npattern types: \\\\emph{name patterns} (for single names), \\\\emph{object patterns} \\n(for things which include indices and arguments) and \\n\\\\emph{dummy patterns} (things for which the name is irrelevant, like indices). \\n\\nName patterns are things which match a single name in an object, \\nwithout indices or arguments. They are constructed by writing a single question mark behind\\nthe name, as in\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 5668875961888500930,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 3481157383808353812,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 5777913681231222490,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"Q + R\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}Q\\\\discretionary{}{}{}+R\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 5714185485780672076,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 513207050875677050,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"0\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}0\\\\,\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex:= Q + R;\\nsubstitute(_, $A? + B? -> 0$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 3619463572002503546,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 17173534587798199961,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"which matches all sums with two terms, each of which is a single\\nsymbol without indices or arguments. If you want to match instead any\\nobject, with or without indices or arguments, use the double question\\nmark instead. To see the difference more explicitly, compare the two\\nsubstitute commands in the following example\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"which matches all sums with two terms, each of which is a single\\nsymbol without indices or arguments. If you want to match instead any\\nobject, with or without indices or arguments, use the double question\\nmark instead. To see the difference more explicitly, compare the two\\nsubstitute commands in the following example\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 14917233983301461690,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9809636280440810262,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 2541866235415414813,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"A_{m n} + B_{m n}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}A_{m n}\\\\discretionary{}{}{}+B_{m n}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 8945832708744423768,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 10448632814408201794,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"A_{m n} + B_{m n}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}A_{m n}\\\\discretionary{}{}{}+B_{m n}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 13533099060313289744,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 17675741056706322107,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"0\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}0\\\\,\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex:=A_{m n} + B_{m n};\\nsubstitute(_, $A? + B? -> 0$ );\\nsubstitute(_, $A?? + B?? -> 0$ );\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 1548096958967764772,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 17237064159072365431,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"Note that it does not make sense to add arguments or indices to object\\npatterns; a construction of the type \\\\verb|A??_{\\\\mu}(x)| is\\nmeaningless and will be flagged as an error.\\n\\nThere is a special handling of objects which are dummy objects. Objects of this type do not need the question\\nmark, as their explicit name is never relevant. You can therefore\\nwrite\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"Note that it does not make sense to add arguments or indices to object\\npatterns; a construction of the type \\\\verb|A??_{\\\\mu}(x)| is\\nmeaningless and will be flagged as an error.\\n\\nThere is a special handling of objects which are dummy objects. Objects of this type do not need the question\\nmark, as their explicit name is never relevant. You can therefore\\nwrite\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 17559663130956505781,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 4456575706364726991,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 149996618010105697,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"A_{m n}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}A_{m n}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 16396791494040658264,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 10446903292787089635,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"0\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}0\\\\,\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex:= A_{m n};\\nsubstitute(_, $A_{p q}->0$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 2304946575859691588,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 14478863707372105107,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"to set all occurrances of the tensor~$A$ with two subscript indices to\\nzero, regardless of the names of the indices (as you can see, this command sets\\n$A_{p q}$ to zero). When index sets are declared using the \\\\prop{Indices} property,\\nthese will be taken into account when matching.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"to set all occurrances of the tensor~$A$ with two subscript indices to\\nzero, regardless of the names of the indices (as you can see, this command sets\\n$A_{p q}$ to zero). When index sets are declared using the \\\\prop{Indices} property,\\nthese will be taken into account when matching.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 17259612194753747914,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 13604024212525675809,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"When replacing object wildcards with something else that involves\\nthese objects, use the question mark notation also on the right-hand\\nside of the rule. For instance,\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"When replacing object wildcards with something else that involves\\nthese objects, use the question mark notation also on the right-hand\\nside of the rule. For instance,\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 12165135534023690358,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 11841284874891978309,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 3130392674961536056,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"C + D + E + F\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}C\\\\discretionary{}{}{}+D\\\\discretionary{}{}{}+E\\\\discretionary{}{}{}+F\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 684917091287079818,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 5844231339622816762,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"C C + E E\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}C C\\\\discretionary{}{}{}+E E\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex:= C + D + E + F;\\nsubstitute(_, $A? + B? -> A? A?$, repeat=True);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 4646325867102889543,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 4115972840328460125,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"replaces every consecutive two terms in a sum by the square of the first\\nterm. The following example shows the difference between the\\npresence or absence of question marks on the right-hand side:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"replaces every consecutive two terms in a sum by the square of the first\\nterm. The following example shows the difference between the\\npresence or absence of question marks on the right-hand side:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 17284231611431975125,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 17263518191612201485,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 18383769434935003423,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"C + D\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}C\\\\discretionary{}{}{}+D\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 7669813663371791892,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 13975265809047128798,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"C\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}C\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex:= C + D;\\nsubstitute(_, $A? + B? -> A?$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 5518090621855640396,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 6701415081399445521,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 11560984112069523264,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"C + D\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}C\\\\discretionary{}{}{}+D\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 3698003264730786292,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 13620180229049969490,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"A A\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}A A\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex:= C + D;\\nsubstitute(_, $A? + B? -> A A$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 6344951086991989254,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 11546578025647429991,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"So be aware that the full pattern symbol needs to be used on the right-hand side (in contrast to many other computer algebra systems).\\n\\nNote that you can also use patterns to remove or add indices or\\narguments, as in\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"So be aware that the full pattern symbol needs to be used on the right-hand side (in contrast to many other computer algebra systems).\\n\\nNote that you can also use patterns to remove or add indices or\\narguments, as in\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 6969189981675113763,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 14832892756992645370,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property Indices(position=free) attached to~}\\\\left[\\\\mu, \\\\discretionary{}{}{}\\\\nu, \\\\discretionary{}{}{}\\\\rho, \\\\discretionary{}{}{}\\\\sigma\\\\right].\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 1856134002101405803,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 15876716484408287358,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"A_{\\\\mu} B_{\\\\nu} C_{\\\\nu} D_{\\\\mu}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}A_{\\\\mu} B_{\\\\nu} C_{\\\\nu} D_{\\\\mu}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 16555808855868186324,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 13853652533751481387,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\dot(A , D) \\\\dot(B , C)\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}(A\\\\cdot{}D) (B\\\\cdot{}C)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"\\\\dot(A??,B??)::LaTeXForm(\\\"(\\\", A??, \\\"\\\\cdot{}\\\", B??, \\\")\\\").\\n\\n{\\\\mu, \\\\nu, \\\\rho, \\\\sigma}::Indices(vector);\\nex:= A_{\\\\mu} B_{\\\\nu} C_{\\\\nu} D_{\\\\mu};\\nsubstitute(_, $A?_{\\\\rho} B?_{\\\\rho} -> \\\\dot{A?}{B?}$, repeat=True);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 1410572859323089449,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 3514767732742718053,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\subsection*{Conditionals}\\n\\nIn many algorithms, patterns can be supplemented by so-called\\nconditionals. These are constraints on the objects that appear in the\\npattern. In the example below, the substitution is not carried out,\\nas the rule applies only to patterns where the $n$ and $p$ indices are not \\nequal,\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\subsection*{Conditionals}\\n\\nIn many algorithms, patterns can be supplemented by so-called\\nconditionals. These are constraints on the objects that appear in the\\npattern. In the example below, the substitution is not carried out,\\nas the rule applies only to patterns where the $n$ and $p$ indices are not \\nequal,\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 13217375379356257896,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 12850485312524941672,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 8465201283805187204,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"A_{m n} B_{n q}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}A_{m n} B_{n q}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9297985124547092835,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 9504125048771628201,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"A_{m n} B_{n q}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}A_{m n} B_{n q}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex:= A_{m n} B_{n q};\\nsubstitute(_, $ A_{m n} B_{p q} | n != p -> 0$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 16749439394296118935,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 424721681098162354,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"Without the conditional, the substitution does apply,\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"Without the conditional, the substitution does apply,\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 14737000889023458641,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 6948656492478304410,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 8317744037526771493,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"A_{m n} B_{n q}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}A_{m n} B_{n q}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 7193509532863793502,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 821286224100993847,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"0\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}0\\\\,\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex:= A_{m n} B_{n q};\\nsubstitute(_, $ A_{m n} B_{p q} -> 0$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 12339261926069898099,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 18358307655016490823,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \" Note that the conditional follows\\ndirectly after the pattern, not after the full substitution rule. A\\nway to think about this is that the conditional is part of the\\npattern, not of the rule. The reason why the conditional follows the\\nfull pattern, and not directly the symbol to which it relates, is\\nclear from the example above: the conditional is a ``global''\\nconstraint on the pattern, not a local one on a single index.\\n\\nThese conditions can be used to match names of objects using regular\\nexpressions. In the following example, the pattern \\\\verb|M?| will match\\nagainst \\\\verb|C7|, \"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \" Note that the conditional follows\\ndirectly after the pattern, not after the full substitution rule. A\\nway to think about this is that the conditional is part of the\\npattern, not of the rule. The reason why the conditional follows the\\nfull pattern, and not directly the symbol to which it relates, is\\nclear from the example above: the conditional is a ``global''\\nconstraint on the pattern, not a local one on a single index.\\n\\nThese conditions can be used to match names of objects using regular\\nexpressions. In the following example, the pattern \\\\verb|M?| will match\\nagainst \\\\verb|C7|, \"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 15788446307630031338,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 15576497745988572748,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 1238837176142346782,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"A + B3 + C7\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}A\\\\discretionary{}{}{}+{B_{3}}\\\\discretionary{}{}{}+{C_{7}}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 17122184338770168058,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 14176957212472943014,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\sin(C7 B3) (B3)**(-1)\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\sin\\\\left({C_{7}} {B_{3}}\\\\right) {{B_{3}}}^{-\\\\,1}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex:= A + B3 + C7;\\nsubstitute(_, $A + M? + N? | \\\\regex{M?}{\\\"[A-Z]7\\\"} -> \\\\sin(M? N?)/N?$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 3753229044937802099,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9545837581022606915,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"Without the condition, the first match of \\\\verb|M?| would be against \\\\verb|B3|, \"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"Without the condition, the first match of \\\\verb|M?| would be against \\\\verb|B3|, \"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 7591537786226289179,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9268015412499413350,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 8005793438990069009,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"A + B3 + C7\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}A\\\\discretionary{}{}{}+{B_{3}}\\\\discretionary{}{}{}+{C_{7}}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9847437822039000310,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 580201440891836131,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\sin(B3 C7) (C7)**(-1)\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\sin\\\\left({B_{3}} {C_{7}}\\\\right) {{C_{7}}}^{-\\\\,1}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex:= A + B3 + C7;\\nsubstitute(_, $A + M? + N?  -> \\\\sin(M? N?)/N?$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 6270675271635601456,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"\"\n\t\t}\n\t],\n\t\"description\": \"Cadabra JSON notebook format\",\n\t\"flags\": {\n\t\t\"hide_input_cells\": false\n\t},\n\t\"version\": 1.0\n}\n"
  },
  {
    "path": "examples/ref_plotting.cnb",
    "content": "{\n\t\"cell_id\": 14559355512343191550,\n\t\"cells\": [\n\t\t{\n\t\t\t\"cell_id\": 10514391231412105493,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 12400102942604967547,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\section*{Plotting functions}\\n\\nCadabra can plot functions of one or two variables using the \\\\verb|cdb.graphics.plot| packages. Plotting itself is handled by matplotlib, but you do not have to know anything about that in order to use the plotting facilities.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\section*{Plotting functions}\\n\\nCadabra can plot functions of one or two variables using the \\\\verb|cdb.graphics.plot| packages. Plotting itself is handled by matplotlib, but you do not have to know anything about that in order to use the plotting facilities.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 14407017377094399323,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 2716116631827758470,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\subsection*{Functions of one variable}\\n\\nFunctions of one variable can be plotted using the \\\\verb|plot| function of the \\\\verb|cdb.graphics.plot| package. Its basic form takes a Cadabra expression which is a function of one variable, as well as a triplet containing the independent variable and its start and end value. If you right-click on the plot, you can save it to a separate file as an image.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\subsection*{Functions of one variable}\\n\\nFunctions of one variable can be plotted using the \\\\verb|plot| function of the \\\\verb|cdb.graphics.plot| package. Its basic form takes a Cadabra expression which is a function of one variable, as well as a triplet containing the independent variable and its start and end value. If you right-click on the plot, you can save it to a separate file as an image.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 2915387569513556102,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"from cdb.graphics.plot import *\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 6214835721859597116,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9500964732570577078,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"image_svg\",\n\t\t\t\t\t\"source\": \"<?xml version="1.0" encoding="utf-8" standalone="no"?>
<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
  "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="460.8pt" height="345.6pt" viewBox="0 0 460.8 345.6" xmlns="http://www.w3.org/2000/svg" version="1.1">
 <metadata>
  <rdf:RDF xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:cc="http://creativecommons.org/ns#" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
   <cc:Work>
    <dc:type rdf:resource="http://purl.org/dc/dcmitype/StillImage"/>
    <dc:date>2025-03-29T11:08:50.620993</dc:date>
    <dc:format>image/svg+xml</dc:format>
    <dc:creator>
     <cc:Agent>
      <dc:title>Matplotlib v3.6.3, https://matplotlib.org/</dc:title>
     </cc:Agent>
    </dc:creator>
   </cc:Work>
  </rdf:RDF>
 </metadata>
 <defs>
  <style type="text/css">*{stroke-linejoin: round; stroke-linecap: butt}</style>
 </defs>
 <g id="figure_1">
  <g id="patch_1">
   <path d="M 0 345.6 
L 460.8 345.6 
L 460.8 0 
L 0 0 
z
" style="fill: #ffffff"/>
  </g>
  <g id="axes_1">
   <g id="patch_2">
    <path d="M 57.6 307.584 
L 414.72 307.584 
L 414.72 41.472 
L 57.6 41.472 
z
" style="fill: #ffffff"/>
   </g>
   <g id="matplotlib.axis_1">
    <g id="xtick_1">
     <g id="line2d_1">
      <path d="M 73.832727 307.584 
L 73.832727 41.472 
" clip-path="url(#pcf4c79e8c5)" style="fill: none; stroke: #b0b0b0; stroke-width: 0.8; stroke-linecap: square"/>
     </g>
     <g id="line2d_2">
      <defs>
       <path id="mffaa7ef335" d="M 0 0 
L 0 3.5 
" style="stroke: #000000; stroke-width: 0.8"/>
      </defs>
      <g>
       <use xlink:href="#mffaa7ef335" x="73.832727" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_1">
      <!-- 0.0 -->
      <g transform="translate(65.881165 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-30" d="M 2034 4250 
Q 1547 4250 1301 3770 
Q 1056 3291 1056 2328 
Q 1056 1369 1301 889 
Q 1547 409 2034 409 
Q 2525 409 2770 889 
Q 3016 1369 3016 2328 
Q 3016 3291 2770 3770 
Q 2525 4250 2034 4250 
z
M 2034 4750 
Q 2819 4750 3233 4129 
Q 3647 3509 3647 2328 
Q 3647 1150 3233 529 
Q 2819 -91 2034 -91 
Q 1250 -91 836 529 
Q 422 1150 422 2328 
Q 422 3509 836 4129 
Q 1250 4750 2034 4750 
z
" transform="scale(0.015625)"/>
        <path id="DejaVuSans-2e" d="M 684 794 
L 1344 794 
L 1344 0 
L 684 0 
L 684 794 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-30"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-30" x="95.410156"/>
      </g>
     </g>
    </g>
    <g id="xtick_2">
     <g id="line2d_3">
      <path d="M 114.414545 307.584 
L 114.414545 41.472 
" clip-path="url(#pcf4c79e8c5)" style="fill: none; stroke: #b0b0b0; stroke-width: 0.8; stroke-linecap: square"/>
     </g>
     <g id="line2d_4">
      <g>
       <use xlink:href="#mffaa7ef335" x="114.414545" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_2">
      <!-- 2.5 -->
      <g transform="translate(106.462983 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-32" d="M 1228 531 
L 3431 531 
L 3431 0 
L 469 0 
L 469 531 
Q 828 903 1448 1529 
Q 2069 2156 2228 2338 
Q 2531 2678 2651 2914 
Q 2772 3150 2772 3378 
Q 2772 3750 2511 3984 
Q 2250 4219 1831 4219 
Q 1534 4219 1204 4116 
Q 875 4013 500 3803 
L 500 4441 
Q 881 4594 1212 4672 
Q 1544 4750 1819 4750 
Q 2544 4750 2975 4387 
Q 3406 4025 3406 3419 
Q 3406 3131 3298 2873 
Q 3191 2616 2906 2266 
Q 2828 2175 2409 1742 
Q 1991 1309 1228 531 
z
" transform="scale(0.015625)"/>
        <path id="DejaVuSans-35" d="M 691 4666 
L 3169 4666 
L 3169 4134 
L 1269 4134 
L 1269 2991 
Q 1406 3038 1543 3061 
Q 1681 3084 1819 3084 
Q 2600 3084 3056 2656 
Q 3513 2228 3513 1497 
Q 3513 744 3044 326 
Q 2575 -91 1722 -91 
Q 1428 -91 1123 -41 
Q 819 9 494 109 
L 494 744 
Q 775 591 1075 516 
Q 1375 441 1709 441 
Q 2250 441 2565 725 
Q 2881 1009 2881 1497 
Q 2881 1984 2565 2268 
Q 2250 2553 1709 2553 
Q 1456 2553 1204 2497 
Q 953 2441 691 2322 
L 691 4666 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-32"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-35" x="95.410156"/>
      </g>
     </g>
    </g>
    <g id="xtick_3">
     <g id="line2d_5">
      <path d="M 154.996364 307.584 
L 154.996364 41.472 
" clip-path="url(#pcf4c79e8c5)" style="fill: none; stroke: #b0b0b0; stroke-width: 0.8; stroke-linecap: square"/>
     </g>
     <g id="line2d_6">
      <g>
       <use xlink:href="#mffaa7ef335" x="154.996364" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_3">
      <!-- 5.0 -->
      <g transform="translate(147.044801 322.182437) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-35"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-30" x="95.410156"/>
      </g>
     </g>
    </g>
    <g id="xtick_4">
     <g id="line2d_7">
      <path d="M 195.578182 307.584 
L 195.578182 41.472 
" clip-path="url(#pcf4c79e8c5)" style="fill: none; stroke: #b0b0b0; stroke-width: 0.8; stroke-linecap: square"/>
     </g>
     <g id="line2d_8">
      <g>
       <use xlink:href="#mffaa7ef335" x="195.578182" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_4">
      <!-- 7.5 -->
      <g transform="translate(187.626619 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-37" d="M 525 4666 
L 3525 4666 
L 3525 4397 
L 1831 0 
L 1172 0 
L 2766 4134 
L 525 4134 
L 525 4666 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-37"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-35" x="95.410156"/>
      </g>
     </g>
    </g>
    <g id="xtick_5">
     <g id="line2d_9">
      <path d="M 236.16 307.584 
L 236.16 41.472 
" clip-path="url(#pcf4c79e8c5)" style="fill: none; stroke: #b0b0b0; stroke-width: 0.8; stroke-linecap: square"/>
     </g>
     <g id="line2d_10">
      <g>
       <use xlink:href="#mffaa7ef335" x="236.16" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_5">
      <!-- 10.0 -->
      <g transform="translate(225.027188 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-31" d="M 794 531 
L 1825 531 
L 1825 4091 
L 703 3866 
L 703 4441 
L 1819 4666 
L 2450 4666 
L 2450 531 
L 3481 531 
L 3481 0 
L 794 0 
L 794 531 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-31"/>
       <use xlink:href="#DejaVuSans-30" x="63.623047"/>
       <use xlink:href="#DejaVuSans-2e" x="127.246094"/>
       <use xlink:href="#DejaVuSans-30" x="159.033203"/>
      </g>
     </g>
    </g>
    <g id="xtick_6">
     <g id="line2d_11">
      <path d="M 276.741818 307.584 
L 276.741818 41.472 
" clip-path="url(#pcf4c79e8c5)" style="fill: none; stroke: #b0b0b0; stroke-width: 0.8; stroke-linecap: square"/>
     </g>
     <g id="line2d_12">
      <g>
       <use xlink:href="#mffaa7ef335" x="276.741818" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_6">
      <!-- 12.5 -->
      <g transform="translate(265.609006 322.182437) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-31"/>
       <use xlink:href="#DejaVuSans-32" x="63.623047"/>
       <use xlink:href="#DejaVuSans-2e" x="127.246094"/>
       <use xlink:href="#DejaVuSans-35" x="159.033203"/>
      </g>
     </g>
    </g>
    <g id="xtick_7">
     <g id="line2d_13">
      <path d="M 317.323636 307.584 
L 317.323636 41.472 
" clip-path="url(#pcf4c79e8c5)" style="fill: none; stroke: #b0b0b0; stroke-width: 0.8; stroke-linecap: square"/>
     </g>
     <g id="line2d_14">
      <g>
       <use xlink:href="#mffaa7ef335" x="317.323636" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_7">
      <!-- 15.0 -->
      <g transform="translate(306.190824 322.182437) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-31"/>
       <use xlink:href="#DejaVuSans-35" x="63.623047"/>
       <use xlink:href="#DejaVuSans-2e" x="127.246094"/>
       <use xlink:href="#DejaVuSans-30" x="159.033203"/>
      </g>
     </g>
    </g>
    <g id="xtick_8">
     <g id="line2d_15">
      <path d="M 357.905455 307.584 
L 357.905455 41.472 
" clip-path="url(#pcf4c79e8c5)" style="fill: none; stroke: #b0b0b0; stroke-width: 0.8; stroke-linecap: square"/>
     </g>
     <g id="line2d_16">
      <g>
       <use xlink:href="#mffaa7ef335" x="357.905455" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_8">
      <!-- 17.5 -->
      <g transform="translate(346.772642 322.182437) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-31"/>
       <use xlink:href="#DejaVuSans-37" x="63.623047"/>
       <use xlink:href="#DejaVuSans-2e" x="127.246094"/>
       <use xlink:href="#DejaVuSans-35" x="159.033203"/>
      </g>
     </g>
    </g>
    <g id="xtick_9">
     <g id="line2d_17">
      <path d="M 398.487273 307.584 
L 398.487273 41.472 
" clip-path="url(#pcf4c79e8c5)" style="fill: none; stroke: #b0b0b0; stroke-width: 0.8; stroke-linecap: square"/>
     </g>
     <g id="line2d_18">
      <g>
       <use xlink:href="#mffaa7ef335" x="398.487273" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_9">
      <!-- 20.0 -->
      <g transform="translate(387.35446 322.182437) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-32"/>
       <use xlink:href="#DejaVuSans-30" x="63.623047"/>
       <use xlink:href="#DejaVuSans-2e" x="127.246094"/>
       <use xlink:href="#DejaVuSans-30" x="159.033203"/>
      </g>
     </g>
    </g>
   </g>
   <g id="matplotlib.axis_2">
    <g id="ytick_1">
     <g id="line2d_19">
      <path d="M 57.6 272.065196 
L 414.72 272.065196 
" clip-path="url(#pcf4c79e8c5)" style="fill: none; stroke: #b0b0b0; stroke-width: 0.8; stroke-linecap: square"/>
     </g>
     <g id="line2d_20">
      <defs>
       <path id="m7d7bd46c2d" d="M 0 0 
L -3.5 0 
" style="stroke: #000000; stroke-width: 0.8"/>
      </defs>
      <g>
       <use xlink:href="#m7d7bd46c2d" x="57.6" y="272.065196" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_10">
      <!-- −300 -->
      <g transform="translate(23.132812 275.864415) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-2212" d="M 678 2272 
L 4684 2272 
L 4684 1741 
L 678 1741 
L 678 2272 
z
" transform="scale(0.015625)"/>
        <path id="DejaVuSans-33" d="M 2597 2516 
Q 3050 2419 3304 2112 
Q 3559 1806 3559 1356 
Q 3559 666 3084 287 
Q 2609 -91 1734 -91 
Q 1441 -91 1130 -33 
Q 819 25 488 141 
L 488 750 
Q 750 597 1062 519 
Q 1375 441 1716 441 
Q 2309 441 2620 675 
Q 2931 909 2931 1356 
Q 2931 1769 2642 2001 
Q 2353 2234 1838 2234 
L 1294 2234 
L 1294 2753 
L 1863 2753 
Q 2328 2753 2575 2939 
Q 2822 3125 2822 3475 
Q 2822 3834 2567 4026 
Q 2313 4219 1838 4219 
Q 1578 4219 1281 4162 
Q 984 4106 628 3988 
L 628 4550 
Q 988 4650 1302 4700 
Q 1616 4750 1894 4750 
Q 2613 4750 3031 4423 
Q 3450 4097 3450 3541 
Q 3450 3153 3228 2886 
Q 3006 2619 2597 2516 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-2212"/>
       <use xlink:href="#DejaVuSans-33" x="83.789062"/>
       <use xlink:href="#DejaVuSans-30" x="147.412109"/>
       <use xlink:href="#DejaVuSans-30" x="211.035156"/>
      </g>
     </g>
    </g>
    <g id="ytick_2">
     <g id="line2d_21">
      <path d="M 57.6 235.618067 
L 414.72 235.618067 
" clip-path="url(#pcf4c79e8c5)" style="fill: none; stroke: #b0b0b0; stroke-width: 0.8; stroke-linecap: square"/>
     </g>
     <g id="line2d_22">
      <g>
       <use xlink:href="#m7d7bd46c2d" x="57.6" y="235.618067" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_11">
      <!-- −200 -->
      <g transform="translate(23.132812 239.417286) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-2212"/>
       <use xlink:href="#DejaVuSans-32" x="83.789062"/>
       <use xlink:href="#DejaVuSans-30" x="147.412109"/>
       <use xlink:href="#DejaVuSans-30" x="211.035156"/>
      </g>
     </g>
    </g>
    <g id="ytick_3">
     <g id="line2d_23">
      <path d="M 57.6 199.170939 
L 414.72 199.170939 
" clip-path="url(#pcf4c79e8c5)" style="fill: none; stroke: #b0b0b0; stroke-width: 0.8; stroke-linecap: square"/>
     </g>
     <g id="line2d_24">
      <g>
       <use xlink:href="#m7d7bd46c2d" x="57.6" y="199.170939" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_12">
      <!-- −100 -->
      <g transform="translate(23.132812 202.970157) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-2212"/>
       <use xlink:href="#DejaVuSans-31" x="83.789062"/>
       <use xlink:href="#DejaVuSans-30" x="147.412109"/>
       <use xlink:href="#DejaVuSans-30" x="211.035156"/>
      </g>
     </g>
    </g>
    <g id="ytick_4">
     <g id="line2d_25">
      <path d="M 57.6 162.72381 
L 414.72 162.72381 
" clip-path="url(#pcf4c79e8c5)" style="fill: none; stroke: #b0b0b0; stroke-width: 0.8; stroke-linecap: square"/>
     </g>
     <g id="line2d_26">
      <g>
       <use xlink:href="#m7d7bd46c2d" x="57.6" y="162.72381" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_13">
      <!-- 0 -->
      <g transform="translate(44.2375 166.523029) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-30"/>
      </g>
     </g>
    </g>
    <g id="ytick_5">
     <g id="line2d_27">
      <path d="M 57.6 126.276681 
L 414.72 126.276681 
" clip-path="url(#pcf4c79e8c5)" style="fill: none; stroke: #b0b0b0; stroke-width: 0.8; stroke-linecap: square"/>
     </g>
     <g id="line2d_28">
      <g>
       <use xlink:href="#m7d7bd46c2d" x="57.6" y="126.276681" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_14">
      <!-- 100 -->
      <g transform="translate(31.5125 130.0759) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-31"/>
       <use xlink:href="#DejaVuSans-30" x="63.623047"/>
       <use xlink:href="#DejaVuSans-30" x="127.246094"/>
      </g>
     </g>
    </g>
    <g id="ytick_6">
     <g id="line2d_29">
      <path d="M 57.6 89.829552 
L 414.72 89.829552 
" clip-path="url(#pcf4c79e8c5)" style="fill: none; stroke: #b0b0b0; stroke-width: 0.8; stroke-linecap: square"/>
     </g>
     <g id="line2d_30">
      <g>
       <use xlink:href="#m7d7bd46c2d" x="57.6" y="89.829552" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_15">
      <!-- 200 -->
      <g transform="translate(31.5125 93.628771) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-32"/>
       <use xlink:href="#DejaVuSans-30" x="63.623047"/>
       <use xlink:href="#DejaVuSans-30" x="127.246094"/>
      </g>
     </g>
    </g>
    <g id="ytick_7">
     <g id="line2d_31">
      <path d="M 57.6 53.382424 
L 414.72 53.382424 
" clip-path="url(#pcf4c79e8c5)" style="fill: none; stroke: #b0b0b0; stroke-width: 0.8; stroke-linecap: square"/>
     </g>
     <g id="line2d_32">
      <g>
       <use xlink:href="#m7d7bd46c2d" x="57.6" y="53.382424" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_16">
      <!-- 300 -->
      <g transform="translate(31.5125 57.181642) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-33"/>
       <use xlink:href="#DejaVuSans-30" x="63.623047"/>
       <use xlink:href="#DejaVuSans-30" x="127.246094"/>
      </g>
     </g>
    </g>
   </g>
   <g id="line2d_33">
    <path d="M 73.832727 162.72381 
L 77.112066 162.653664 
L 80.391405 162.603914 
L 83.670744 162.592454 
L 86.950083 162.632374 
L 90.229421 162.730077 
L 93.50876 162.88395 
L 96.788099 163.083745 
L 100.067438 163.310725 
L 103.346777 163.538617 
L 106.626116 163.735316 
L 109.905455 163.865258 
L 113.184793 163.892327 
L 116.464132 163.783072 
L 119.743471 163.510052 
L 123.02281 163.055032 
L 126.302149 162.411808 
L 129.581488 161.588404 
L 132.860826 160.608449 
L 136.140165 159.511573 
L 139.419504 158.352688 
L 142.698843 157.20014 
L 145.978182 156.13274 
L 149.257521 155.235781 
L 152.53686 154.596216 
L 155.816198 154.297229 
L 159.095537 154.41249 
L 162.374876 155.00043 
L 165.654215 156.09889 
L 168.933554 157.720488 
L 172.212893 159.849056 
L 175.492231 162.437437 
L 178.77157 165.406882 
L 182.050909 168.648215 
L 185.330248 172.024842 
L 188.609587 175.377567 
L 191.888926 178.531106 
L 195.168264 181.302048 
L 198.447603 183.507952 
L 201.726942 184.977154 
L 205.006281 185.558821 
L 208.28562 185.132713 
L 211.564959 183.618125 
L 214.844298 180.981468 
L 218.123636 177.241994 
L 221.402975 172.47524 
L 224.682314 166.813845 
L 227.961653 160.44552 
L 231.240992 153.60809 
L 234.520331 146.581643 
L 237.799669 139.678011 
L 241.079008 133.22793 
L 244.358347 127.566364 
L 247.637686 123.016615 
L 250.917025 119.873932 
L 254.196364 118.389386 
L 257.475702 118.754822 
L 260.755041 121.0897 
L 264.03438 125.430561 
L 267.313719 131.7238 
L 270.593058 139.822287 
L 273.872397 149.48621 
L 277.151736 160.388365 
L 280.431074 172.123874 
L 283.710413 184.224128 
L 286.989752 196.17453 
L 290.269091 207.435402 
L 293.54843 217.465254 
L 296.827769 225.745444 
L 300.107107 231.805149 
L 303.386446 235.245505 
L 306.665785 235.76174 
L 309.945124 233.162189 
L 313.224463 227.383126 
L 316.503802 218.498542 
L 319.78314 206.724161 
L 323.062479 192.415217 
L 326.341818 176.057802 
L 329.621157 158.253863 
L 332.900496 139.70023 
L 336.179835 121.162352 
L 339.459174 103.443678 
L 342.738512 87.351873 
L 346.017851 73.663251 
L 349.29719 63.086949 
L 352.576529 56.23044 
L 355.855868 53.568 
L 359.135207 55.413669 
L 362.414545 61.900115 
L 365.693884 72.964601 
L 368.973223 88.342982 
L 372.252562 107.572345 
L 375.531901 130.002526 
L 378.81124 154.816377 
L 382.090579 181.058223 
L 385.369917 207.669606 
L 388.649256 233.531003 
L 391.928595 257.507938 
L 395.207934 278.499609 
L 398.487273 295.488 
" clip-path="url(#pcf4c79e8c5)" style="fill: none; stroke: #1f77b4; stroke-width: 1.5; stroke-linecap: square"/>
   </g>
   <g id="patch_3">
    <path d="M 57.6 307.584 
L 57.6 41.472 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
   <g id="patch_4">
    <path d="M 414.72 307.584 
L 414.72 41.472 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
   <g id="patch_5">
    <path d="M 57.6 307.584 
L 414.72 307.584 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
   <g id="patch_6">
    <path d="M 57.6 41.472 
L 414.72 41.472 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
  </g>
 </g>
 <defs>
  <clipPath id="pcf4c79e8c5">
   <rect x="57.6" y="41.472" width="357.12" height="266.112"/>
  </clipPath>
 </defs>
</svg>
\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"plot($\\\\sin(a x) (1-x**2)$, {$x$: (0, 20), $a$: 1}, grid=True);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 10467517237312574167,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 6264403135713685716,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"Multiple functions can be plotted in the same figure by simply feeding a list of functions as the first argument\\nto \\\\verb|plot|, as in the example below. This also shows how to customise the plot by setting the title and axes. Finally, by passing a list of equations instead of a list of functions, the plot will add a legend with the correct labels.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"Multiple functions can be plotted in the same figure by simply feeding a list of functions as the first argument\\nto \\\\verb|plot|, as in the example below. This also shows how to customise the plot by setting the title and axes. Finally, by passing a list of equations instead of a list of functions, the plot will add a legend with the correct labels.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 18446245934657724506,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 11605288957444078735,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"image_svg\",\n\t\t\t\t\t\"source\": \"<?xml version="1.0" encoding="utf-8" standalone="no"?>
<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
  "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="460.8pt" height="345.6pt" viewBox="0 0 460.8 345.6" xmlns="http://www.w3.org/2000/svg" version="1.1">
 <metadata>
  <rdf:RDF xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:cc="http://creativecommons.org/ns#" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
   <cc:Work>
    <dc:type rdf:resource="http://purl.org/dc/dcmitype/StillImage"/>
    <dc:date>2025-03-29T11:16:23.785772</dc:date>
    <dc:format>image/svg+xml</dc:format>
    <dc:creator>
     <cc:Agent>
      <dc:title>Matplotlib v3.6.3, https://matplotlib.org/</dc:title>
     </cc:Agent>
    </dc:creator>
   </cc:Work>
  </rdf:RDF>
 </metadata>
 <defs>
  <style type="text/css">*{stroke-linejoin: round; stroke-linecap: butt}</style>
 </defs>
 <g id="figure_1">
  <g id="patch_1">
   <path d="M 0 345.6 
L 460.8 345.6 
L 460.8 0 
L 0 0 
z
" style="fill: #ffffff"/>
  </g>
  <g id="axes_1">
   <g id="patch_2">
    <path d="M 57.6 307.584 
L 414.72 307.584 
L 414.72 41.472 
L 57.6 41.472 
z
" style="fill: #ffffff"/>
   </g>
   <g id="matplotlib.axis_1">
    <g id="xtick_1">
     <g id="line2d_1">
      <defs>
       <path id="m39137fd63d" d="M 0 0 
L 0 3.5 
" style="stroke: #000000; stroke-width: 0.8"/>
      </defs>
      <g>
       <use xlink:href="#m39137fd63d" x="73.832727" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_1">
      <!-- 0.0 -->
      <g transform="translate(65.881165 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-30" d="M 2034 4250 
Q 1547 4250 1301 3770 
Q 1056 3291 1056 2328 
Q 1056 1369 1301 889 
Q 1547 409 2034 409 
Q 2525 409 2770 889 
Q 3016 1369 3016 2328 
Q 3016 3291 2770 3770 
Q 2525 4250 2034 4250 
z
M 2034 4750 
Q 2819 4750 3233 4129 
Q 3647 3509 3647 2328 
Q 3647 1150 3233 529 
Q 2819 -91 2034 -91 
Q 1250 -91 836 529 
Q 422 1150 422 2328 
Q 422 3509 836 4129 
Q 1250 4750 2034 4750 
z
" transform="scale(0.015625)"/>
        <path id="DejaVuSans-2e" d="M 684 794 
L 1344 794 
L 1344 0 
L 684 0 
L 684 794 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-30"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-30" x="95.410156"/>
      </g>
     </g>
    </g>
    <g id="xtick_2">
     <g id="line2d_2">
      <g>
       <use xlink:href="#m39137fd63d" x="114.414545" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_2">
      <!-- 2.5 -->
      <g transform="translate(106.462983 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-32" d="M 1228 531 
L 3431 531 
L 3431 0 
L 469 0 
L 469 531 
Q 828 903 1448 1529 
Q 2069 2156 2228 2338 
Q 2531 2678 2651 2914 
Q 2772 3150 2772 3378 
Q 2772 3750 2511 3984 
Q 2250 4219 1831 4219 
Q 1534 4219 1204 4116 
Q 875 4013 500 3803 
L 500 4441 
Q 881 4594 1212 4672 
Q 1544 4750 1819 4750 
Q 2544 4750 2975 4387 
Q 3406 4025 3406 3419 
Q 3406 3131 3298 2873 
Q 3191 2616 2906 2266 
Q 2828 2175 2409 1742 
Q 1991 1309 1228 531 
z
" transform="scale(0.015625)"/>
        <path id="DejaVuSans-35" d="M 691 4666 
L 3169 4666 
L 3169 4134 
L 1269 4134 
L 1269 2991 
Q 1406 3038 1543 3061 
Q 1681 3084 1819 3084 
Q 2600 3084 3056 2656 
Q 3513 2228 3513 1497 
Q 3513 744 3044 326 
Q 2575 -91 1722 -91 
Q 1428 -91 1123 -41 
Q 819 9 494 109 
L 494 744 
Q 775 591 1075 516 
Q 1375 441 1709 441 
Q 2250 441 2565 725 
Q 2881 1009 2881 1497 
Q 2881 1984 2565 2268 
Q 2250 2553 1709 2553 
Q 1456 2553 1204 2497 
Q 953 2441 691 2322 
L 691 4666 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-32"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-35" x="95.410156"/>
      </g>
     </g>
    </g>
    <g id="xtick_3">
     <g id="line2d_3">
      <g>
       <use xlink:href="#m39137fd63d" x="154.996364" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_3">
      <!-- 5.0 -->
      <g transform="translate(147.044801 322.182437) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-35"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-30" x="95.410156"/>
      </g>
     </g>
    </g>
    <g id="xtick_4">
     <g id="line2d_4">
      <g>
       <use xlink:href="#m39137fd63d" x="195.578182" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_4">
      <!-- 7.5 -->
      <g transform="translate(187.626619 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-37" d="M 525 4666 
L 3525 4666 
L 3525 4397 
L 1831 0 
L 1172 0 
L 2766 4134 
L 525 4134 
L 525 4666 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-37"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-35" x="95.410156"/>
      </g>
     </g>
    </g>
    <g id="xtick_5">
     <g id="line2d_5">
      <g>
       <use xlink:href="#m39137fd63d" x="236.16" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_5">
      <!-- 10.0 -->
      <g transform="translate(225.027188 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-31" d="M 794 531 
L 1825 531 
L 1825 4091 
L 703 3866 
L 703 4441 
L 1819 4666 
L 2450 4666 
L 2450 531 
L 3481 531 
L 3481 0 
L 794 0 
L 794 531 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-31"/>
       <use xlink:href="#DejaVuSans-30" x="63.623047"/>
       <use xlink:href="#DejaVuSans-2e" x="127.246094"/>
       <use xlink:href="#DejaVuSans-30" x="159.033203"/>
      </g>
     </g>
    </g>
    <g id="xtick_6">
     <g id="line2d_6">
      <g>
       <use xlink:href="#m39137fd63d" x="276.741818" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_6">
      <!-- 12.5 -->
      <g transform="translate(265.609006 322.182437) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-31"/>
       <use xlink:href="#DejaVuSans-32" x="63.623047"/>
       <use xlink:href="#DejaVuSans-2e" x="127.246094"/>
       <use xlink:href="#DejaVuSans-35" x="159.033203"/>
      </g>
     </g>
    </g>
    <g id="xtick_7">
     <g id="line2d_7">
      <g>
       <use xlink:href="#m39137fd63d" x="317.323636" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_7">
      <!-- 15.0 -->
      <g transform="translate(306.190824 322.182437) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-31"/>
       <use xlink:href="#DejaVuSans-35" x="63.623047"/>
       <use xlink:href="#DejaVuSans-2e" x="127.246094"/>
       <use xlink:href="#DejaVuSans-30" x="159.033203"/>
      </g>
     </g>
    </g>
    <g id="xtick_8">
     <g id="line2d_8">
      <g>
       <use xlink:href="#m39137fd63d" x="357.905455" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_8">
      <!-- 17.5 -->
      <g transform="translate(346.772642 322.182437) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-31"/>
       <use xlink:href="#DejaVuSans-37" x="63.623047"/>
       <use xlink:href="#DejaVuSans-2e" x="127.246094"/>
       <use xlink:href="#DejaVuSans-35" x="159.033203"/>
      </g>
     </g>
    </g>
    <g id="xtick_9">
     <g id="line2d_9">
      <g>
       <use xlink:href="#m39137fd63d" x="398.487273" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_9">
      <!-- 20.0 -->
      <g transform="translate(387.35446 322.182437) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-32"/>
       <use xlink:href="#DejaVuSans-30" x="63.623047"/>
       <use xlink:href="#DejaVuSans-2e" x="127.246094"/>
       <use xlink:href="#DejaVuSans-30" x="159.033203"/>
      </g>
     </g>
    </g>
    <g id="text_10">
     <!-- time -->
     <g transform="translate(220.625 339.364625) scale(0.16 -0.16)">
      <defs>
       <path id="Cmr10-74" d="M 653 769 
L 653 2534 
L 122 2534 
L 122 2700 
Q 541 2700 737 3090 
Q 934 3481 934 3938 
L 1119 3938 
L 1119 2759 
L 2022 2759 
L 2022 2534 
L 1119 2534 
L 1119 781 
Q 1119 516 1208 316 
Q 1297 116 1528 116 
Q 1747 116 1844 327 
Q 1941 538 1941 781 
L 1941 1159 
L 2125 1159 
L 2125 769 
Q 2125 569 2051 373 
Q 1978 178 1834 53 
Q 1691 -72 1484 -72 
Q 1100 -72 876 158 
Q 653 388 653 769 
z
" transform="scale(0.015625)"/>
       <path id="Cmr10-69" d="M 197 0 
L 197 225 
Q 416 225 556 259 
Q 697 294 697 428 
L 697 2175 
Q 697 2422 601 2478 
Q 506 2534 225 2534 
L 225 2759 
L 1147 2828 
L 1147 428 
Q 1147 294 1269 259 
Q 1391 225 1594 225 
L 1594 0 
L 197 0 
z
M 469 3928 
Q 469 4069 575 4175 
Q 681 4281 819 4281 
Q 909 4281 993 4234 
Q 1078 4188 1125 4103 
Q 1172 4019 1172 3928 
Q 1172 3791 1065 3684 
Q 959 3578 819 3578 
Q 681 3578 575 3684 
Q 469 3791 469 3928 
z
" transform="scale(0.015625)"/>
       <path id="Cmr10-6d" d="M 191 0 
L 191 225 
Q 409 225 550 259 
Q 691 294 691 428 
L 691 2175 
Q 691 2347 639 2423 
Q 588 2500 491 2517 
Q 394 2534 191 2534 
L 191 2759 
L 1119 2828 
L 1119 2203 
Q 1247 2478 1498 2653 
Q 1750 2828 2047 2828 
Q 2784 2828 2913 2228 
Q 3041 2497 3287 2662 
Q 3534 2828 3828 2828 
Q 4119 2828 4317 2734 
Q 4516 2641 4616 2448 
Q 4716 2256 4716 1966 
L 4716 428 
Q 4716 294 4858 259 
Q 5000 225 5216 225 
L 5216 0 
L 3750 0 
L 3750 225 
Q 3969 225 4109 259 
Q 4250 294 4250 428 
L 4250 1947 
Q 4250 2269 4159 2466 
Q 4069 2663 3788 2663 
Q 3419 2663 3178 2366 
Q 2938 2069 2938 1691 
L 2938 428 
Q 2938 294 3078 259 
Q 3219 225 3438 225 
L 3438 0 
L 1972 0 
L 1972 225 
Q 2191 225 2331 259 
Q 2472 294 2472 428 
L 2472 1947 
Q 2472 2259 2381 2461 
Q 2291 2663 2009 2663 
Q 1638 2663 1398 2366 
Q 1159 2069 1159 1691 
L 1159 428 
Q 1159 294 1300 259 
Q 1441 225 1656 225 
L 1656 0 
L 191 0 
z
" transform="scale(0.015625)"/>
       <path id="Cmr10-65" d="M 1594 -72 
Q 1203 -72 876 133 
Q 550 338 364 680 
Q 178 1022 178 1403 
Q 178 1778 348 2115 
Q 519 2453 823 2661 
Q 1128 2869 1503 2869 
Q 1797 2869 2014 2770 
Q 2231 2672 2372 2497 
Q 2513 2322 2584 2084 
Q 2656 1847 2656 1563 
Q 2656 1478 2591 1478 
L 738 1478 
L 738 1409 
Q 738 878 952 497 
Q 1166 116 1650 116 
Q 1847 116 2014 203 
Q 2181 291 2304 447 
Q 2428 603 2472 781 
Q 2478 803 2495 820 
Q 2513 838 2534 838 
L 2591 838 
Q 2656 838 2656 756 
Q 2566 394 2266 161 
Q 1966 -72 1594 -72 
z
M 744 1638 
L 2203 1638 
Q 2203 1878 2136 2125 
Q 2069 2372 1912 2536 
Q 1756 2700 1503 2700 
Q 1141 2700 942 2361 
Q 744 2022 744 1638 
z
" transform="scale(0.015625)"/>
      </defs>
      <use xlink:href="#Cmr10-74"/>
      <use xlink:href="#Cmr10-69" x="38.818359"/>
      <use xlink:href="#Cmr10-6d" x="66.503906"/>
      <use xlink:href="#Cmr10-65" x="149.804688"/>
     </g>
    </g>
   </g>
   <g id="matplotlib.axis_2">
    <g id="ytick_1">
     <g id="line2d_10">
      <defs>
       <path id="m8b4567dc87" d="M 0 0 
L -3.5 0 
" style="stroke: #000000; stroke-width: 0.8"/>
      </defs>
      <g>
       <use xlink:href="#m8b4567dc87" x="57.6" y="272.065196" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_11">
      <!-- −300 -->
      <g transform="translate(23.132812 275.864415) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-2212" d="M 678 2272 
L 4684 2272 
L 4684 1741 
L 678 1741 
L 678 2272 
z
" transform="scale(0.015625)"/>
        <path id="DejaVuSans-33" d="M 2597 2516 
Q 3050 2419 3304 2112 
Q 3559 1806 3559 1356 
Q 3559 666 3084 287 
Q 2609 -91 1734 -91 
Q 1441 -91 1130 -33 
Q 819 25 488 141 
L 488 750 
Q 750 597 1062 519 
Q 1375 441 1716 441 
Q 2309 441 2620 675 
Q 2931 909 2931 1356 
Q 2931 1769 2642 2001 
Q 2353 2234 1838 2234 
L 1294 2234 
L 1294 2753 
L 1863 2753 
Q 2328 2753 2575 2939 
Q 2822 3125 2822 3475 
Q 2822 3834 2567 4026 
Q 2313 4219 1838 4219 
Q 1578 4219 1281 4162 
Q 984 4106 628 3988 
L 628 4550 
Q 988 4650 1302 4700 
Q 1616 4750 1894 4750 
Q 2613 4750 3031 4423 
Q 3450 4097 3450 3541 
Q 3450 3153 3228 2886 
Q 3006 2619 2597 2516 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-2212"/>
       <use xlink:href="#DejaVuSans-33" x="83.789062"/>
       <use xlink:href="#DejaVuSans-30" x="147.412109"/>
       <use xlink:href="#DejaVuSans-30" x="211.035156"/>
      </g>
     </g>
    </g>
    <g id="ytick_2">
     <g id="line2d_11">
      <g>
       <use xlink:href="#m8b4567dc87" x="57.6" y="235.618067" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_12">
      <!-- −200 -->
      <g transform="translate(23.132812 239.417286) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-2212"/>
       <use xlink:href="#DejaVuSans-32" x="83.789062"/>
       <use xlink:href="#DejaVuSans-30" x="147.412109"/>
       <use xlink:href="#DejaVuSans-30" x="211.035156"/>
      </g>
     </g>
    </g>
    <g id="ytick_3">
     <g id="line2d_12">
      <g>
       <use xlink:href="#m8b4567dc87" x="57.6" y="199.170939" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_13">
      <!-- −100 -->
      <g transform="translate(23.132812 202.970157) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-2212"/>
       <use xlink:href="#DejaVuSans-31" x="83.789062"/>
       <use xlink:href="#DejaVuSans-30" x="147.412109"/>
       <use xlink:href="#DejaVuSans-30" x="211.035156"/>
      </g>
     </g>
    </g>
    <g id="ytick_4">
     <g id="line2d_13">
      <g>
       <use xlink:href="#m8b4567dc87" x="57.6" y="162.72381" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_14">
      <!-- 0 -->
      <g transform="translate(44.2375 166.523029) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-30"/>
      </g>
     </g>
    </g>
    <g id="ytick_5">
     <g id="line2d_14">
      <g>
       <use xlink:href="#m8b4567dc87" x="57.6" y="126.276681" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_15">
      <!-- 100 -->
      <g transform="translate(31.5125 130.0759) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-31"/>
       <use xlink:href="#DejaVuSans-30" x="63.623047"/>
       <use xlink:href="#DejaVuSans-30" x="127.246094"/>
      </g>
     </g>
    </g>
    <g id="ytick_6">
     <g id="line2d_15">
      <g>
       <use xlink:href="#m8b4567dc87" x="57.6" y="89.829552" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_16">
      <!-- 200 -->
      <g transform="translate(31.5125 93.628771) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-32"/>
       <use xlink:href="#DejaVuSans-30" x="63.623047"/>
       <use xlink:href="#DejaVuSans-30" x="127.246094"/>
      </g>
     </g>
    </g>
    <g id="ytick_7">
     <g id="line2d_16">
      <g>
       <use xlink:href="#m8b4567dc87" x="57.6" y="53.382424" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_17">
      <!-- 300 -->
      <g transform="translate(31.5125 57.181642) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-33"/>
       <use xlink:href="#DejaVuSans-30" x="63.623047"/>
       <use xlink:href="#DejaVuSans-30" x="127.246094"/>
      </g>
     </g>
    </g>
    <g id="text_18">
     <!-- value -->
     <g transform="translate(16.030313 192.9505) rotate(-90) scale(0.16 -0.16)">
      <defs>
       <path id="Cmr10-76" d="M 1563 0 
L 628 2350 
Q 569 2469 445 2501 
Q 322 2534 122 2534 
L 122 2759 
L 1466 2759 
L 1466 2534 
Q 1106 2534 1106 2381 
Q 1106 2356 1113 2344 
L 1831 538 
L 2478 2169 
Q 2497 2219 2497 2272 
Q 2497 2394 2405 2464 
Q 2313 2534 2188 2534 
L 2188 2759 
L 3250 2759 
L 3250 2534 
Q 3053 2534 2904 2443 
Q 2756 2353 2675 2175 
L 1813 0 
Q 1788 -72 1709 -72 
L 1663 -72 
Q 1584 -72 1563 0 
z
" transform="scale(0.015625)"/>
       <path id="Cmr10-61" d="M 256 628 
Q 256 1009 556 1248 
Q 856 1488 1276 1586 
Q 1697 1684 2075 1684 
L 2075 1947 
Q 2075 2131 1994 2304 
Q 1913 2478 1759 2589 
Q 1606 2700 1422 2700 
Q 997 2700 775 2509 
Q 897 2509 976 2417 
Q 1056 2325 1056 2203 
Q 1056 2075 965 1984 
Q 875 1894 750 1894 
Q 622 1894 531 1984 
Q 441 2075 441 2203 
Q 441 2541 747 2705 
Q 1053 2869 1422 2869 
Q 1681 2869 1943 2758 
Q 2206 2647 2373 2440 
Q 2541 2234 2541 1959 
L 2541 519 
Q 2541 394 2594 289 
Q 2647 184 2759 184 
Q 2866 184 2917 290 
Q 2969 397 2969 519 
L 2969 928 
L 3156 928 
L 3156 519 
Q 3156 375 3081 245 
Q 3006 116 2879 39 
Q 2753 -38 2606 -38 
Q 2419 -38 2283 107 
Q 2147 253 2131 453 
Q 2013 213 1781 70 
Q 1550 -72 1288 -72 
Q 1044 -72 808 0 
Q 572 72 414 226 
Q 256 381 256 628 
z
M 775 628 
Q 775 403 940 250 
Q 1106 97 1331 97 
Q 1538 97 1706 200 
Q 1875 303 1975 481 
Q 2075 659 2075 856 
L 2075 1522 
Q 1784 1522 1479 1426 
Q 1175 1331 975 1128 
Q 775 925 775 628 
z
" transform="scale(0.015625)"/>
       <path id="Cmr10-6c" d="M 197 0 
L 197 225 
Q 416 225 556 259 
Q 697 294 697 428 
L 697 3788 
Q 697 3959 645 4036 
Q 594 4113 497 4130 
Q 400 4147 197 4147 
L 197 4372 
L 1147 4441 
L 1147 428 
Q 1147 294 1287 259 
Q 1428 225 1644 225 
L 1644 0 
L 197 0 
z
" transform="scale(0.015625)"/>
       <path id="Cmr10-75" d="M 691 763 
L 691 2175 
Q 691 2347 639 2423 
Q 588 2500 491 2517 
Q 394 2534 191 2534 
L 191 2759 
L 1159 2828 
L 1159 763 
Q 1159 513 1195 373 
Q 1231 234 1348 165 
Q 1466 97 1722 97 
Q 2066 97 2269 384 
Q 2472 672 2472 1038 
L 2472 2175 
Q 2472 2347 2419 2423 
Q 2366 2500 2270 2517 
Q 2175 2534 1972 2534 
L 1972 2759 
L 2938 2828 
L 2938 581 
Q 2938 413 2989 336 
Q 3041 259 3137 242 
Q 3234 225 3438 225 
L 3438 0 
L 2491 -72 
L 2491 469 
Q 2372 228 2159 78 
Q 1947 -72 1691 -72 
Q 1231 -72 961 123 
Q 691 319 691 763 
z
" transform="scale(0.015625)"/>
      </defs>
      <use xlink:href="#Cmr10-76"/>
      <use xlink:href="#Cmr10-61" x="52.685547"/>
      <use xlink:href="#Cmr10-6c" x="102.685547"/>
      <use xlink:href="#Cmr10-75" x="130.371094"/>
      <use xlink:href="#Cmr10-65" x="185.888672"/>
     </g>
    </g>
   </g>
   <g id="line2d_17">
    <path d="M 73.832727 162.72381 
L 77.112066 162.653664 
L 80.391405 162.603914 
L 83.670744 162.592454 
L 86.950083 162.632374 
L 90.229421 162.730077 
L 93.50876 162.88395 
L 96.788099 163.083745 
L 100.067438 163.310725 
L 103.346777 163.538617 
L 106.626116 163.735316 
L 109.905455 163.865258 
L 113.184793 163.892327 
L 116.464132 163.783072 
L 119.743471 163.510052 
L 123.02281 163.055032 
L 126.302149 162.411808 
L 129.581488 161.588404 
L 132.860826 160.608449 
L 136.140165 159.511573 
L 139.419504 158.352688 
L 142.698843 157.20014 
L 145.978182 156.13274 
L 149.257521 155.235781 
L 152.53686 154.596216 
L 155.816198 154.297229 
L 159.095537 154.41249 
L 162.374876 155.00043 
L 165.654215 156.09889 
L 168.933554 157.720488 
L 172.212893 159.849056 
L 175.492231 162.437437 
L 178.77157 165.406882 
L 182.050909 168.648215 
L 185.330248 172.024842 
L 188.609587 175.377567 
L 191.888926 178.531106 
L 195.168264 181.302048 
L 198.447603 183.507952 
L 201.726942 184.977154 
L 205.006281 185.558821 
L 208.28562 185.132713 
L 211.564959 183.618125 
L 214.844298 180.981468 
L 218.123636 177.241994 
L 221.402975 172.47524 
L 224.682314 166.813845 
L 227.961653 160.44552 
L 231.240992 153.60809 
L 234.520331 146.581643 
L 237.799669 139.678011 
L 241.079008 133.22793 
L 244.358347 127.566364 
L 247.637686 123.016615 
L 250.917025 119.873932 
L 254.196364 118.389386 
L 257.475702 118.754822 
L 260.755041 121.0897 
L 264.03438 125.430561 
L 267.313719 131.7238 
L 270.593058 139.822287 
L 273.872397 149.48621 
L 277.151736 160.388365 
L 280.431074 172.123874 
L 283.710413 184.224128 
L 286.989752 196.17453 
L 290.269091 207.435402 
L 293.54843 217.465254 
L 296.827769 225.745444 
L 300.107107 231.805149 
L 303.386446 235.245505 
L 306.665785 235.76174 
L 309.945124 233.162189 
L 313.224463 227.383126 
L 316.503802 218.498542 
L 319.78314 206.724161 
L 323.062479 192.415217 
L 326.341818 176.057802 
L 329.621157 158.253863 
L 332.900496 139.70023 
L 336.179835 121.162352 
L 339.459174 103.443678 
L 342.738512 87.351873 
L 346.017851 73.663251 
L 349.29719 63.086949 
L 352.576529 56.23044 
L 355.855868 53.568 
L 359.135207 55.413669 
L 362.414545 61.900115 
L 365.693884 72.964601 
L 368.973223 88.342982 
L 372.252562 107.572345 
L 375.531901 130.002526 
L 378.81124 154.816377 
L 382.090579 181.058223 
L 385.369917 207.669606 
L 388.649256 233.531003 
L 391.928595 257.507938 
L 395.207934 278.499609 
L 398.487273 295.488 
" clip-path="url(#p1aeb403f7d)" style="fill: none; stroke: #1f77b4; stroke-width: 1.5; stroke-linecap: square"/>
   </g>
   <g id="line2d_18">
    <path d="M 73.832727 126.276681 
L 77.112066 127.017898 
L 80.391405 129.211401 
L 83.670744 132.767973 
L 86.950083 137.542955 
L 90.229421 143.342131 
L 93.50876 149.92963 
L 96.788099 157.037513 
L 100.067438 164.376677 
L 103.346777 171.648614 
L 106.626116 178.557548 
L 109.905455 184.822467 
L 113.184793 190.188555 
L 116.464132 194.437555 
L 119.743471 197.396644 
L 123.02281 198.945466 
L 126.302149 199.021024 
L 129.581488 197.620247 
L 132.860826 194.800107 
L 136.140165 190.675311 
L 139.419504 185.413627 
L 142.698843 179.229069 
L 145.978182 172.373183 
L 149.257521 165.124823 
L 152.53686 157.778805 
L 155.816198 150.633918 
L 159.095537 143.980769 
L 162.374876 138.089967 
L 165.654215 133.201111 
L 168.933554 129.513047 
L 172.212893 127.175783 
L 175.492231 126.284384 
L 178.77157 126.875105 
L 182.050909 128.92392 
L 185.330248 132.347496 
L 188.609587 137.006586 
L 191.888926 142.711685 
L 195.168264 149.230749 
L 198.447603 156.298624 
L 201.726942 163.627834 
L 205.006281 170.920273 
L 208.28562 177.879334 
L 211.564959 184.221966 
L 214.844298 189.690191 
L 218.123636 194.061598 
L 221.402975 197.158386 
L 224.682314 198.854598 
L 227.961653 199.081242 
L 231.240992 197.8291 
L 234.520331 195.149102 
L 237.799669 191.150252 
L 241.079008 185.995198 
L 244.358347 179.893614 
L 247.637686 173.093673 
L 250.917025 165.871953 
L 254.196364 158.522187 
L 257.475702 151.343315 
L 260.755041 144.627329 
L 264.03438 138.647391 
L 267.313719 133.646726 
L 270.593058 129.82873 
L 273.872397 127.348693 
L 277.151736 126.307487 
L 280.431074 126.747463 
L 283.710413 128.650724 
L 286.989752 131.939859 
L 290.269091 136.481086 
L 293.54843 142.089698 
L 296.827769 148.537572 
L 300.107107 155.562451 
L 303.386446 162.878608 
L 306.665785 170.188468 
L 309.945124 177.194715 
L 313.224463 183.612378 
L 316.503802 189.18043 
L 319.78314 193.672396 
L 323.062479 196.905574 
L 326.341818 198.748458 
L 329.621157 199.126092 
L 332.900496 198.023116 
L 336.179835 195.484392 
L 339.459174 191.613179 
L 342.738512 186.566933 
L 346.017851 180.550902 
L 349.29719 173.80978 
L 352.576529 166.617753 
L 355.855868 159.267345 
L 359.135207 152.057523 
L 362.414545 145.281538 
L 365.693884 139.214991 
L 368.973223 134.104632 
L 372.252562 130.158316 
L 375.531901 127.536554 
L 378.81124 126.345983 
L 382.090579 126.635027 
L 385.369917 128.39193 
L 388.649256 131.545232 
L 391.928595 135.966678 
L 395.207934 141.476431 
L 398.487273 147.85039 
" clip-path="url(#p1aeb403f7d)" style="fill: none; stroke: #ff7f0e; stroke-width: 1.5; stroke-linecap: square"/>
   </g>
   <g id="patch_3">
    <path d="M 57.6 307.584 
L 57.6 41.472 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
   <g id="patch_4">
    <path d="M 414.72 307.584 
L 414.72 41.472 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
   <g id="patch_5">
    <path d="M 57.6 307.584 
L 414.72 307.584 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
   <g id="patch_6">
    <path d="M 57.6 41.472 
L 414.72 41.472 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
   <g id="legend_1">
    <g id="patch_7">
     <path d="M 64.6 79.668875 
L 115 79.668875 
Q 117 79.668875 117 77.668875 
L 117 48.472 
Q 117 46.472 115 46.472 
L 64.6 46.472 
Q 62.6 46.472 62.6 48.472 
L 62.6 77.668875 
Q 62.6 79.668875 64.6 79.668875 
z
" style="fill: #ffffff; opacity: 0.8; stroke: #cccccc; stroke-linejoin: miter"/>
    </g>
    <g id="line2d_19">
     <path d="M 66.6 54.570438 
L 76.6 54.570438 
L 86.6 54.570438 
" style="fill: none; stroke: #1f77b4; stroke-width: 1.5; stroke-linecap: square"/>
    </g>
    <g id="text_19">
     <!-- $f(x)$ -->
     <g transform="translate(94.6 58.070438) scale(0.1 -0.1)">
      <defs>
       <path id="Cmmi10-66" d="M 622 -1056 
Q 741 -1147 909 -1147 
Q 1138 -1147 1281 -641 
Q 1341 -397 1606 966 
L 1900 2534 
L 1350 2534 
Q 1288 2534 1288 2619 
Q 1313 2759 1369 2759 
L 1941 2759 
L 2016 3175 
Q 2053 3369 2084 3508 
Q 2116 3647 2152 3765 
Q 2188 3884 2259 4031 
Q 2369 4241 2555 4377 
Q 2741 4513 2956 4513 
Q 3097 4513 3230 4461 
Q 3363 4409 3447 4306 
Q 3531 4203 3531 4063 
Q 3531 3900 3423 3779 
Q 3316 3659 3163 3659 
Q 3059 3659 2986 3723 
Q 2913 3788 2913 3891 
Q 2913 4031 3008 4136 
Q 3103 4241 3244 4256 
Q 3125 4347 2950 4347 
Q 2853 4347 2767 4256 
Q 2681 4166 2656 4063 
Q 2616 3900 2478 3181 
L 2400 2759 
L 3059 2759 
Q 3122 2759 3122 2675 
Q 3119 2659 3109 2620 
Q 3100 2581 3083 2557 
Q 3066 2534 3041 2534 
L 2356 2534 
L 2059 972 
Q 2003 631 1929 279 
Q 1856 -72 1723 -442 
Q 1591 -813 1384 -1063 
Q 1178 -1313 897 -1313 
Q 681 -1313 511 -1189 
Q 341 -1066 341 -863 
Q 341 -700 445 -579 
Q 550 -459 709 -459 
Q 816 -459 887 -523 
Q 959 -588 959 -691 
Q 959 -828 857 -942 
Q 756 -1056 622 -1056 
z
" transform="scale(0.015625)"/>
       <path id="Cmr10-28" d="M 1984 -1588 
Q 1628 -1306 1370 -942 
Q 1113 -578 948 -165 
Q 784 247 703 697 
Q 622 1147 622 1600 
Q 622 2059 703 2509 
Q 784 2959 951 3375 
Q 1119 3791 1378 4153 
Q 1638 4516 1984 4788 
Q 1984 4800 2016 4800 
L 2075 4800 
Q 2094 4800 2109 4783 
Q 2125 4766 2125 4744 
Q 2125 4716 2113 4703 
Q 1800 4397 1592 4047 
Q 1384 3697 1257 3301 
Q 1131 2906 1075 2482 
Q 1019 2059 1019 1600 
Q 1019 -434 2106 -1491 
Q 2125 -1509 2125 -1544 
Q 2125 -1559 2108 -1579 
Q 2091 -1600 2075 -1600 
L 2016 -1600 
Q 1984 -1600 1984 -1588 
z
" transform="scale(0.015625)"/>
       <path id="Cmmi10-78" d="M 500 184 
Q 613 97 819 97 
Q 1019 97 1172 289 
Q 1325 481 1381 709 
L 1672 1844 
Q 1741 2153 1741 2266 
Q 1741 2425 1652 2544 
Q 1563 2663 1403 2663 
Q 1200 2663 1022 2536 
Q 844 2409 722 2214 
Q 600 2019 550 1819 
Q 538 1778 500 1778 
L 422 1778 
Q 372 1778 372 1838 
L 372 1856 
Q 434 2094 584 2320 
Q 734 2547 951 2687 
Q 1169 2828 1416 2828 
Q 1650 2828 1839 2703 
Q 2028 2578 2106 2363 
Q 2216 2559 2386 2693 
Q 2556 2828 2759 2828 
Q 2897 2828 3040 2779 
Q 3184 2731 3275 2631 
Q 3366 2531 3366 2381 
Q 3366 2219 3261 2101 
Q 3156 1984 2994 1984 
Q 2891 1984 2822 2050 
Q 2753 2116 2753 2216 
Q 2753 2350 2845 2451 
Q 2938 2553 3066 2572 
Q 2950 2663 2747 2663 
Q 2541 2663 2389 2472 
Q 2238 2281 2175 2047 
L 1894 916 
Q 1825 659 1825 494 
Q 1825 331 1917 214 
Q 2009 97 2163 97 
Q 2463 97 2698 361 
Q 2934 625 3009 941 
Q 3022 978 3059 978 
L 3138 978 
Q 3163 978 3178 961 
Q 3194 944 3194 922 
Q 3194 916 3188 903 
Q 3097 522 2806 225 
Q 2516 -72 2150 -72 
Q 1916 -72 1727 54 
Q 1538 181 1459 397 
Q 1359 209 1182 68 
Q 1006 -72 806 -72 
Q 669 -72 523 -23 
Q 378 25 287 125 
Q 197 225 197 378 
Q 197 528 301 651 
Q 406 775 563 775 
Q 669 775 741 711 
Q 813 647 813 544 
Q 813 409 723 309 
Q 634 209 500 184 
z
" transform="scale(0.015625)"/>
       <path id="Cmr10-29" d="M 416 -1600 
Q 359 -1600 359 -1544 
Q 359 -1516 372 -1503 
Q 1466 -434 1466 1600 
Q 1466 3634 384 4691 
Q 359 4706 359 4744 
Q 359 4766 376 4783 
Q 394 4800 416 4800 
L 475 4800 
Q 494 4800 506 4788 
Q 966 4425 1272 3906 
Q 1578 3388 1720 2800 
Q 1863 2213 1863 1600 
Q 1863 1147 1786 708 
Q 1709 269 1542 -157 
Q 1375 -584 1119 -945 
Q 863 -1306 506 -1588 
Q 494 -1600 475 -1600 
L 416 -1600 
z
" transform="scale(0.015625)"/>
      </defs>
      <use xlink:href="#Cmmi10-66"/>
      <use xlink:href="#Cmr10-28" transform="translate(48.876953 0)"/>
      <use xlink:href="#Cmmi10-78" transform="translate(87.695312 0)"/>
      <use xlink:href="#Cmr10-29" transform="translate(144.775391 0)"/>
     </g>
    </g>
    <g id="line2d_20">
     <path d="M 66.6 69.668875 
L 76.6 69.668875 
L 86.6 69.668875 
" style="fill: none; stroke: #ff7f0e; stroke-width: 1.5; stroke-linecap: square"/>
    </g>
    <g id="text_20">
     <!-- $g(x)$ -->
     <g transform="translate(94.6 73.168875) scale(0.1 -0.1)">
      <defs>
       <path id="Cmmi10-67" d="M 91 -916 
Q 91 -759 198 -642 
Q 306 -525 459 -525 
Q 563 -525 633 -589 
Q 703 -653 703 -756 
Q 703 -872 637 -964 
Q 572 -1056 469 -1094 
Q 641 -1147 1006 -1147 
Q 1300 -1147 1544 -920 
Q 1788 -694 1863 -397 
L 2047 353 
Q 1700 0 1325 0 
Q 1050 0 854 140 
Q 659 281 556 515 
Q 453 750 453 1013 
Q 453 1306 573 1628 
Q 694 1950 911 2225 
Q 1128 2500 1409 2664 
Q 1691 2828 2003 2828 
Q 2191 2828 2341 2725 
Q 2491 2622 2578 2450 
Q 2641 2700 2853 2700 
Q 2934 2700 2990 2651 
Q 3047 2603 3047 2522 
Q 3047 2503 3045 2493 
Q 3044 2484 3041 2472 
L 2309 -434 
Q 2259 -634 2125 -800 
Q 1991 -966 1809 -1077 
Q 1628 -1188 1412 -1250 
Q 1197 -1313 997 -1313 
Q 631 -1313 361 -1242 
Q 91 -1172 91 -916 
z
M 1338 166 
Q 1747 166 2144 728 
L 2497 2125 
Q 2453 2347 2322 2505 
Q 2191 2663 1991 2663 
Q 1778 2663 1589 2489 
Q 1400 2316 1275 2075 
Q 1156 1844 1045 1411 
Q 934 978 934 728 
Q 934 509 1034 337 
Q 1134 166 1338 166 
z
" transform="scale(0.015625)"/>
      </defs>
      <use xlink:href="#Cmmi10-67"/>
      <use xlink:href="#Cmr10-28" transform="translate(47.705078 0)"/>
      <use xlink:href="#Cmmi10-78" transform="translate(86.523438 0)"/>
      <use xlink:href="#Cmr10-29" transform="translate(143.603516 0)"/>
     </g>
    </g>
   </g>
  </g>
  <g id="text_21">
   <!-- Two functions -->
   <g transform="translate(174.141563 26.314313) scale(0.18 -0.18)">
    <defs>
     <path id="Cmr10-54" d="M 1081 0 
L 1081 225 
Q 1403 225 1706 261 
Q 2009 297 2009 428 
L 2009 3944 
Q 2009 4081 1932 4114 
Q 1856 4147 1684 4147 
L 1416 4147 
Q 888 4147 666 3916 
Q 550 3800 500 3545 
Q 450 3291 416 2906 
L 231 2906 
L 353 4372 
L 4263 4372 
L 4384 2906 
L 4197 2906 
Q 4159 3319 4114 3561 
Q 4069 3803 3950 3916 
Q 3725 4147 3200 4147 
L 2931 4147 
Q 2816 4147 2752 4137 
Q 2688 4128 2647 4083 
Q 2606 4038 2606 3944 
L 2606 428 
Q 2606 297 2909 261 
Q 3213 225 3531 225 
L 3531 0 
L 1081 0 
z
" transform="scale(0.015625)"/>
     <path id="Cmr10-77" d="M 1416 0 
L 588 2328 
Q 531 2469 425 2501 
Q 319 2534 116 2534 
L 116 2759 
L 1434 2759 
L 1434 2534 
Q 1056 2534 1056 2375 
Q 1059 2366 1061 2356 
Q 1063 2347 1063 2328 
L 1678 603 
L 2209 2106 
L 2125 2328 
Q 2075 2469 1965 2501 
Q 1856 2534 1656 2534 
L 1656 2759 
L 2919 2759 
L 2919 2534 
Q 2541 2534 2541 2375 
Q 2541 2350 2547 2328 
L 3188 525 
L 3769 2156 
Q 3781 2206 3781 2247 
Q 3781 2381 3667 2457 
Q 3553 2534 3413 2534 
L 3413 2759 
L 4500 2759 
L 4500 2534 
Q 4306 2534 4167 2432 
Q 4028 2331 3963 2156 
L 3200 0 
Q 3178 -72 3103 -72 
L 3053 -72 
Q 2978 -72 2956 0 
L 2309 1825 
L 1663 0 
Q 1631 -72 1563 -72 
L 1516 -72 
Q 1438 -72 1416 0 
z
" transform="scale(0.015625)"/>
     <path id="Cmr10-6f" d="M 1600 -72 
Q 1216 -72 887 123 
Q 559 319 368 647 
Q 178 975 178 1363 
Q 178 1656 283 1928 
Q 388 2200 583 2414 
Q 778 2628 1037 2748 
Q 1297 2869 1600 2869 
Q 1994 2869 2317 2661 
Q 2641 2453 2828 2104 
Q 3016 1756 3016 1363 
Q 3016 978 2825 648 
Q 2634 319 2307 123 
Q 1981 -72 1600 -72 
z
M 1600 116 
Q 2113 116 2284 487 
Q 2456 859 2456 1434 
Q 2456 1756 2422 1967 
Q 2388 2178 2272 2350 
Q 2200 2456 2089 2536 
Q 1978 2616 1854 2658 
Q 1731 2700 1600 2700 
Q 1400 2700 1220 2609 
Q 1041 2519 922 2350 
Q 803 2169 770 1951 
Q 738 1734 738 1434 
Q 738 1075 800 789 
Q 863 503 1052 309 
Q 1241 116 1600 116 
z
" transform="scale(0.015625)"/>
     <path id="Cmr10-20" transform="scale(0.015625)"/>
     <path id="Cmr10-66" d="M 206 0 
L 206 225 
Q 422 225 562 259 
Q 703 294 703 428 
L 703 2534 
L 213 2534 
L 213 2759 
L 703 2759 
L 703 3525 
Q 703 3731 789 3911 
Q 875 4091 1020 4225 
Q 1166 4359 1355 4436 
Q 1544 4513 1747 4513 
Q 1963 4513 2136 4384 
Q 2309 4256 2309 4044 
Q 2309 3922 2226 3839 
Q 2144 3756 2022 3756 
Q 1900 3756 1814 3839 
Q 1728 3922 1728 4044 
Q 1728 4244 1900 4313 
Q 1797 4347 1716 4347 
Q 1528 4347 1395 4214 
Q 1263 4081 1197 3890 
Q 1131 3700 1131 3513 
L 1131 2759 
L 1869 2759 
L 1869 2534 
L 1153 2534 
L 1153 428 
Q 1153 297 1340 261 
Q 1528 225 1772 225 
L 1772 0 
L 206 0 
z
" transform="scale(0.015625)"/>
     <path id="Cmr10-6e" d="M 191 0 
L 191 225 
Q 409 225 550 259 
Q 691 294 691 428 
L 691 2175 
Q 691 2347 639 2423 
Q 588 2500 491 2517 
Q 394 2534 191 2534 
L 191 2759 
L 1119 2828 
L 1119 2203 
Q 1247 2478 1498 2653 
Q 1750 2828 2047 2828 
Q 2491 2828 2714 2615 
Q 2938 2403 2938 1966 
L 2938 428 
Q 2938 294 3078 259 
Q 3219 225 3438 225 
L 3438 0 
L 1972 0 
L 1972 225 
Q 2191 225 2331 259 
Q 2472 294 2472 428 
L 2472 1947 
Q 2472 2259 2381 2461 
Q 2291 2663 2009 2663 
Q 1638 2663 1398 2366 
Q 1159 2069 1159 1691 
L 1159 428 
Q 1159 294 1300 259 
Q 1441 225 1656 225 
L 1656 0 
L 191 0 
z
" transform="scale(0.015625)"/>
     <path id="Cmr10-63" d="M 1594 -72 
Q 1206 -72 890 129 
Q 575 331 394 667 
Q 213 1003 213 1381 
Q 213 1759 392 2106 
Q 572 2453 889 2661 
Q 1206 2869 1594 2869 
Q 1969 2869 2276 2722 
Q 2584 2575 2584 2241 
Q 2584 2116 2495 2023 
Q 2406 1931 2278 1931 
Q 2150 1931 2061 2023 
Q 1972 2116 1972 2241 
Q 1972 2353 2044 2436 
Q 2116 2519 2222 2541 
Q 2000 2681 1600 2681 
Q 1294 2681 1106 2478 
Q 919 2275 844 1975 
Q 769 1675 769 1381 
Q 769 1072 861 783 
Q 953 494 1158 305 
Q 1363 116 1672 116 
Q 1975 116 2187 302 
Q 2400 488 2478 788 
Q 2478 825 2528 825 
L 2606 825 
Q 2625 825 2640 808 
Q 2656 791 2656 769 
L 2656 750 
Q 2559 372 2271 150 
Q 1984 -72 1594 -72 
z
" transform="scale(0.015625)"/>
     <path id="Cmr10-73" d="M 213 -19 
L 213 1025 
Q 213 1075 269 1075 
L 347 1075 
Q 384 1075 397 1025 
Q 575 97 1259 97 
Q 1563 97 1767 234 
Q 1972 372 1972 659 
Q 1972 866 1812 1011 
Q 1653 1156 1434 1209 
L 1006 1294 
Q 791 1341 614 1437 
Q 438 1534 325 1695 
Q 213 1856 213 2069 
Q 213 2350 361 2529 
Q 509 2709 746 2789 
Q 984 2869 1259 2869 
Q 1588 2869 1831 2694 
L 2016 2853 
Q 2016 2869 2047 2869 
L 2094 2869 
Q 2113 2869 2128 2851 
Q 2144 2834 2144 2816 
L 2144 1978 
Q 2144 1919 2094 1919 
L 2016 1919 
Q 1959 1919 1959 1978 
Q 1959 2313 1773 2516 
Q 1588 2719 1253 2719 
Q 966 2719 755 2612 
Q 544 2506 544 2247 
Q 544 2069 695 1955 
Q 847 1841 1050 1791 
L 1484 1709 
Q 1703 1659 1892 1540 
Q 2081 1422 2192 1240 
Q 2303 1059 2303 831 
Q 2303 600 2223 429 
Q 2144 259 2001 146 
Q 1859 34 1665 -19 
Q 1472 -72 1259 -72 
Q 859 -72 575 197 
L 341 -56 
Q 341 -72 306 -72 
L 269 -72 
Q 213 -72 213 -19 
z
" transform="scale(0.015625)"/>
    </defs>
    <use xlink:href="#Cmr10-54"/>
    <use xlink:href="#Cmr10-77" x="72.216797"/>
    <use xlink:href="#Cmr10-6f" x="144.433594"/>
    <use xlink:href="#Cmr10-20" x="194.433594"/>
    <use xlink:href="#Cmr10-66" x="227.734375"/>
    <use xlink:href="#Cmr10-75" x="258.251953"/>
    <use xlink:href="#Cmr10-6e" x="313.769531"/>
    <use xlink:href="#Cmr10-63" x="369.287109"/>
    <use xlink:href="#Cmr10-74" x="413.671875"/>
    <use xlink:href="#Cmr10-69" x="452.490234"/>
    <use xlink:href="#Cmr10-6f" x="480.175781"/>
    <use xlink:href="#Cmr10-6e" x="530.175781"/>
    <use xlink:href="#Cmr10-73" x="585.693359"/>
   </g>
  </g>
 </g>
 <defs>
  <clipPath id="p1aeb403f7d">
   <rect x="57.6" y="41.472" width="357.12" height="266.112"/>
  </clipPath>
 </defs>
</svg>
\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"plot([$f(x) = \\\\sin(x) (1-x**2)$, $g(x) = 100 \\\\cos(x)$], {$x$: (0, 20)}, title=\\\"Two functions\\\", \\n      xlabel=\\\"time\\\", ylabel=\\\"value\\\");\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 14380218034861361315,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 8732629491325863242,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"You can also add curves to an existing figure. To do this, give every curve a label. If you want to overwrite\\na curve, use the same label.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"You can also add curves to an existing figure. To do this, give every curve a label. If you want to overwrite\\na curve, use the same label.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 4890735290266881934,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9941058334865844817,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"image_svg\",\n\t\t\t\t\t\"source\": \"<?xml version="1.0" encoding="utf-8" standalone="no"?>
<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
  "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="460.8pt" height="345.6pt" viewBox="0 0 460.8 345.6" xmlns="http://www.w3.org/2000/svg" version="1.1">
 <metadata>
  <rdf:RDF xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:cc="http://creativecommons.org/ns#" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
   <cc:Work>
    <dc:type rdf:resource="http://purl.org/dc/dcmitype/StillImage"/>
    <dc:date>2025-03-29T11:10:47.256210</dc:date>
    <dc:format>image/svg+xml</dc:format>
    <dc:creator>
     <cc:Agent>
      <dc:title>Matplotlib v3.6.3, https://matplotlib.org/</dc:title>
     </cc:Agent>
    </dc:creator>
   </cc:Work>
  </rdf:RDF>
 </metadata>
 <defs>
  <style type="text/css">*{stroke-linejoin: round; stroke-linecap: butt}</style>
 </defs>
 <g id="figure_1">
  <g id="patch_1">
   <path d="M 0 345.6 
L 460.8 345.6 
L 460.8 0 
L 0 0 
z
" style="fill: #ffffff"/>
  </g>
  <g id="axes_1">
   <g id="patch_2">
    <path d="M 57.6 307.584 
L 414.72 307.584 
L 414.72 41.472 
L 57.6 41.472 
z
" style="fill: #ffffff"/>
   </g>
   <g id="matplotlib.axis_1">
    <g id="xtick_1">
     <g id="line2d_1">
      <defs>
       <path id="m57daa79cce" d="M 0 0 
L 0 3.5 
" style="stroke: #000000; stroke-width: 0.8"/>
      </defs>
      <g>
       <use xlink:href="#m57daa79cce" x="73.832727" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_1">
      <!-- 0 -->
      <g transform="translate(70.651477 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-30" d="M 2034 4250 
Q 1547 4250 1301 3770 
Q 1056 3291 1056 2328 
Q 1056 1369 1301 889 
Q 1547 409 2034 409 
Q 2525 409 2770 889 
Q 3016 1369 3016 2328 
Q 3016 3291 2770 3770 
Q 2525 4250 2034 4250 
z
M 2034 4750 
Q 2819 4750 3233 4129 
Q 3647 3509 3647 2328 
Q 3647 1150 3233 529 
Q 2819 -91 2034 -91 
Q 1250 -91 836 529 
Q 422 1150 422 2328 
Q 422 3509 836 4129 
Q 1250 4750 2034 4750 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-30"/>
      </g>
     </g>
    </g>
    <g id="xtick_2">
     <g id="line2d_2">
      <g>
       <use xlink:href="#m57daa79cce" x="138.763636" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_2">
      <!-- 2 -->
      <g transform="translate(135.582386 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-32" d="M 1228 531 
L 3431 531 
L 3431 0 
L 469 0 
L 469 531 
Q 828 903 1448 1529 
Q 2069 2156 2228 2338 
Q 2531 2678 2651 2914 
Q 2772 3150 2772 3378 
Q 2772 3750 2511 3984 
Q 2250 4219 1831 4219 
Q 1534 4219 1204 4116 
Q 875 4013 500 3803 
L 500 4441 
Q 881 4594 1212 4672 
Q 1544 4750 1819 4750 
Q 2544 4750 2975 4387 
Q 3406 4025 3406 3419 
Q 3406 3131 3298 2873 
Q 3191 2616 2906 2266 
Q 2828 2175 2409 1742 
Q 1991 1309 1228 531 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-32"/>
      </g>
     </g>
    </g>
    <g id="xtick_3">
     <g id="line2d_3">
      <g>
       <use xlink:href="#m57daa79cce" x="203.694545" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_3">
      <!-- 4 -->
      <g transform="translate(200.513295 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-34" d="M 2419 4116 
L 825 1625 
L 2419 1625 
L 2419 4116 
z
M 2253 4666 
L 3047 4666 
L 3047 1625 
L 3713 1625 
L 3713 1100 
L 3047 1100 
L 3047 0 
L 2419 0 
L 2419 1100 
L 313 1100 
L 313 1709 
L 2253 4666 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-34"/>
      </g>
     </g>
    </g>
    <g id="xtick_4">
     <g id="line2d_4">
      <g>
       <use xlink:href="#m57daa79cce" x="268.625455" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_4">
      <!-- 6 -->
      <g transform="translate(265.444205 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-36" d="M 2113 2584 
Q 1688 2584 1439 2293 
Q 1191 2003 1191 1497 
Q 1191 994 1439 701 
Q 1688 409 2113 409 
Q 2538 409 2786 701 
Q 3034 994 3034 1497 
Q 3034 2003 2786 2293 
Q 2538 2584 2113 2584 
z
M 3366 4563 
L 3366 3988 
Q 3128 4100 2886 4159 
Q 2644 4219 2406 4219 
Q 1781 4219 1451 3797 
Q 1122 3375 1075 2522 
Q 1259 2794 1537 2939 
Q 1816 3084 2150 3084 
Q 2853 3084 3261 2657 
Q 3669 2231 3669 1497 
Q 3669 778 3244 343 
Q 2819 -91 2113 -91 
Q 1303 -91 875 529 
Q 447 1150 447 2328 
Q 447 3434 972 4092 
Q 1497 4750 2381 4750 
Q 2619 4750 2861 4703 
Q 3103 4656 3366 4563 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-36"/>
      </g>
     </g>
    </g>
    <g id="xtick_5">
     <g id="line2d_5">
      <g>
       <use xlink:href="#m57daa79cce" x="333.556364" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_5">
      <!-- 8 -->
      <g transform="translate(330.375114 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-38" d="M 2034 2216 
Q 1584 2216 1326 1975 
Q 1069 1734 1069 1313 
Q 1069 891 1326 650 
Q 1584 409 2034 409 
Q 2484 409 2743 651 
Q 3003 894 3003 1313 
Q 3003 1734 2745 1975 
Q 2488 2216 2034 2216 
z
M 1403 2484 
Q 997 2584 770 2862 
Q 544 3141 544 3541 
Q 544 4100 942 4425 
Q 1341 4750 2034 4750 
Q 2731 4750 3128 4425 
Q 3525 4100 3525 3541 
Q 3525 3141 3298 2862 
Q 3072 2584 2669 2484 
Q 3125 2378 3379 2068 
Q 3634 1759 3634 1313 
Q 3634 634 3220 271 
Q 2806 -91 2034 -91 
Q 1263 -91 848 271 
Q 434 634 434 1313 
Q 434 1759 690 2068 
Q 947 2378 1403 2484 
z
M 1172 3481 
Q 1172 3119 1398 2916 
Q 1625 2713 2034 2713 
Q 2441 2713 2670 2916 
Q 2900 3119 2900 3481 
Q 2900 3844 2670 4047 
Q 2441 4250 2034 4250 
Q 1625 4250 1398 4047 
Q 1172 3844 1172 3481 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-38"/>
      </g>
     </g>
    </g>
    <g id="xtick_6">
     <g id="line2d_6">
      <g>
       <use xlink:href="#m57daa79cce" x="398.487273" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_6">
      <!-- 10 -->
      <g transform="translate(392.124773 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-31" d="M 794 531 
L 1825 531 
L 1825 4091 
L 703 3866 
L 703 4441 
L 1819 4666 
L 2450 4666 
L 2450 531 
L 3481 531 
L 3481 0 
L 794 0 
L 794 531 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-31"/>
       <use xlink:href="#DejaVuSans-30" x="63.623047"/>
      </g>
     </g>
    </g>
   </g>
   <g id="matplotlib.axis_2">
    <g id="ytick_1">
     <g id="line2d_7">
      <defs>
       <path id="m9391f06840" d="M 0 0 
L -3.5 0 
" style="stroke: #000000; stroke-width: 0.8"/>
      </defs>
      <g>
       <use xlink:href="#m9391f06840" x="57.6" y="295.562478" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_7">
      <!-- −1.00 -->
      <g transform="translate(19.954687 299.361697) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-2212" d="M 678 2272 
L 4684 2272 
L 4684 1741 
L 678 1741 
L 678 2272 
z
" transform="scale(0.015625)"/>
        <path id="DejaVuSans-2e" d="M 684 794 
L 1344 794 
L 1344 0 
L 684 0 
L 684 794 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-2212"/>
       <use xlink:href="#DejaVuSans-31" x="83.789062"/>
       <use xlink:href="#DejaVuSans-2e" x="147.412109"/>
       <use xlink:href="#DejaVuSans-30" x="179.199219"/>
       <use xlink:href="#DejaVuSans-30" x="242.822266"/>
      </g>
     </g>
    </g>
    <g id="ytick_2">
     <g id="line2d_8">
      <g>
       <use xlink:href="#m9391f06840" x="57.6" y="265.308515" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_8">
      <!-- −0.75 -->
      <g transform="translate(19.954687 269.107733) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-37" d="M 525 4666 
L 3525 4666 
L 3525 4397 
L 1831 0 
L 1172 0 
L 2766 4134 
L 525 4134 
L 525 4666 
z
" transform="scale(0.015625)"/>
        <path id="DejaVuSans-35" d="M 691 4666 
L 3169 4666 
L 3169 4134 
L 1269 4134 
L 1269 2991 
Q 1406 3038 1543 3061 
Q 1681 3084 1819 3084 
Q 2600 3084 3056 2656 
Q 3513 2228 3513 1497 
Q 3513 744 3044 326 
Q 2575 -91 1722 -91 
Q 1428 -91 1123 -41 
Q 819 9 494 109 
L 494 744 
Q 775 591 1075 516 
Q 1375 441 1709 441 
Q 2250 441 2565 725 
Q 2881 1009 2881 1497 
Q 2881 1984 2565 2268 
Q 2250 2553 1709 2553 
Q 1456 2553 1204 2497 
Q 953 2441 691 2322 
L 691 4666 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-2212"/>
       <use xlink:href="#DejaVuSans-30" x="83.789062"/>
       <use xlink:href="#DejaVuSans-2e" x="147.412109"/>
       <use xlink:href="#DejaVuSans-37" x="179.199219"/>
       <use xlink:href="#DejaVuSans-35" x="242.822266"/>
      </g>
     </g>
    </g>
    <g id="ytick_3">
     <g id="line2d_9">
      <g>
       <use xlink:href="#m9391f06840" x="57.6" y="235.054551" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_9">
      <!-- −0.50 -->
      <g transform="translate(19.954687 238.85377) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-2212"/>
       <use xlink:href="#DejaVuSans-30" x="83.789062"/>
       <use xlink:href="#DejaVuSans-2e" x="147.412109"/>
       <use xlink:href="#DejaVuSans-35" x="179.199219"/>
       <use xlink:href="#DejaVuSans-30" x="242.822266"/>
      </g>
     </g>
    </g>
    <g id="ytick_4">
     <g id="line2d_10">
      <g>
       <use xlink:href="#m9391f06840" x="57.6" y="204.800587" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_10">
      <!-- −0.25 -->
      <g transform="translate(19.954687 208.599806) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-2212"/>
       <use xlink:href="#DejaVuSans-30" x="83.789062"/>
       <use xlink:href="#DejaVuSans-2e" x="147.412109"/>
       <use xlink:href="#DejaVuSans-32" x="179.199219"/>
       <use xlink:href="#DejaVuSans-35" x="242.822266"/>
      </g>
     </g>
    </g>
    <g id="ytick_5">
     <g id="line2d_11">
      <g>
       <use xlink:href="#m9391f06840" x="57.6" y="174.546623" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_11">
      <!-- 0.00 -->
      <g transform="translate(28.334375 178.345842) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-30"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-30" x="95.410156"/>
       <use xlink:href="#DejaVuSans-30" x="159.033203"/>
      </g>
     </g>
    </g>
    <g id="ytick_6">
     <g id="line2d_12">
      <g>
       <use xlink:href="#m9391f06840" x="57.6" y="144.29266" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_12">
      <!-- 0.25 -->
      <g transform="translate(28.334375 148.091878) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-30"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-32" x="95.410156"/>
       <use xlink:href="#DejaVuSans-35" x="159.033203"/>
      </g>
     </g>
    </g>
    <g id="ytick_7">
     <g id="line2d_13">
      <g>
       <use xlink:href="#m9391f06840" x="57.6" y="114.038696" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_13">
      <!-- 0.50 -->
      <g transform="translate(28.334375 117.837915) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-30"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-35" x="95.410156"/>
       <use xlink:href="#DejaVuSans-30" x="159.033203"/>
      </g>
     </g>
    </g>
    <g id="ytick_8">
     <g id="line2d_14">
      <g>
       <use xlink:href="#m9391f06840" x="57.6" y="83.784732" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_14">
      <!-- 0.75 -->
      <g transform="translate(28.334375 87.583951) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-30"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-37" x="95.410156"/>
       <use xlink:href="#DejaVuSans-35" x="159.033203"/>
      </g>
     </g>
    </g>
    <g id="ytick_9">
     <g id="line2d_15">
      <g>
       <use xlink:href="#m9391f06840" x="57.6" y="53.530768" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_15">
      <!-- 1.00 -->
      <g transform="translate(28.334375 57.329987) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-31"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-30" x="95.410156"/>
       <use xlink:href="#DejaVuSans-30" x="159.033203"/>
      </g>
     </g>
    </g>
   </g>
   <g id="line2d_16">
    <path d="M 73.832727 174.546623 
L 77.112066 162.343576 
L 80.391405 150.26493 
L 83.670744 138.433822 
L 86.950083 126.97086 
L 90.229421 115.992903 
L 93.50876 105.611865 
L 96.788099 95.933573 
L 100.067438 87.056691 
L 103.346777 79.071714 
L 106.626116 72.060043 
L 109.905455 66.093158 
L 113.184793 61.231888 
L 116.464132 57.525789 
L 119.743471 55.012645 
L 123.02281 53.718073 
L 126.302149 53.655273 
L 129.581488 54.824883 
L 132.860826 57.214981 
L 136.140165 60.801201 
L 139.419504 65.546984 
L 142.698843 71.403949 
L 145.978182 78.312388 
L 149.257521 86.201875 
L 152.53686 94.991981 
L 155.816198 104.593096 
L 159.095537 114.907343 
L 162.374876 125.829574 
L 165.654215 137.248446 
L 168.933554 149.047548 
L 172.212893 161.106598 
L 175.492231 173.30266 
L 178.77157 185.511404 
L 182.050909 197.608368 
L 185.330248 209.470233 
L 188.609587 220.976074 
L 191.888926 232.008595 
L 195.168264 242.455328 
L 198.447603 252.209775 
L 201.726942 261.172495 
L 205.006281 269.252119 
L 208.28562 276.36628 
L 211.564959 282.442454 
L 214.844298 287.418699 
L 218.123636 291.244284 
L 221.402975 293.88021 
L 224.682314 295.299605 
L 227.961653 295.488 
L 231.240992 294.443474 
L 234.520331 292.176676 
L 237.799669 288.710713 
L 241.079008 284.080919 
L 244.358347 278.334493 
L 247.637686 271.530015 
L 250.917025 263.736852 
L 254.196364 255.034452 
L 257.475702 245.511529 
L 260.755041 235.265163 
L 264.03438 224.39981 
L 267.313719 213.026236 
L 270.593058 201.260386 
L 273.872397 189.222206 
L 277.151736 177.034418 
L 280.431074 164.821269 
L 283.710413 152.707263 
L 286.989752 140.815896 
L 290.269091 129.268392 
L 293.54843 118.182471 
L 296.827769 107.671148 
L 300.107107 97.841577 
L 303.386446 88.793966 
L 306.665785 80.620549 
L 309.945124 73.404649 
L 313.224463 67.219828 
L 316.503802 62.129135 
L 319.78314 58.184468 
L 323.062479 55.426039 
L 326.341818 53.88197 
L 329.621157 53.568 
L 332.900496 54.487331 
L 336.179835 56.630591 
L 339.459174 59.97593 
L 342.738512 64.489245 
L 346.017851 70.124525 
L 349.29719 76.824323 
L 352.576529 84.520338 
L 355.855868 93.134114 
L 359.135207 102.577839 
L 362.414545 112.755241 
L 365.693884 123.562566 
L 368.973223 134.889642 
L 372.252562 146.620996 
L 375.531901 158.637033 
L 378.81124 170.815259 
L 382.090579 183.031524 
L 385.369917 195.161291 
L 388.649256 207.080904 
L 391.928595 218.668851 
L 395.207934 229.806999 
L 398.487273 240.381803 
" clip-path="url(#pbb31748933)" style="fill: none; stroke: #1f77b4; stroke-width: 1.5; stroke-linecap: square"/>
   </g>
   <g id="patch_3">
    <path d="M 57.6 307.584 
L 57.6 41.472 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
   <g id="patch_4">
    <path d="M 414.72 307.584 
L 414.72 41.472 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
   <g id="patch_5">
    <path d="M 57.6 307.584 
L 414.72 307.584 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
   <g id="patch_6">
    <path d="M 57.6 41.472 
L 414.72 41.472 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
  </g>
 </g>
 <defs>
  <clipPath id="pbb31748933">
   <rect x="57.6" y="41.472" width="357.12" height="266.112"/>
  </clipPath>
 </defs>
</svg>
\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"fig = plot($\\\\sin(x)$, {$x$: (0, 10)}, label=\\\"curve1\\\");\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 10777735411025339092,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9939878211208562986,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"image_svg\",\n\t\t\t\t\t\"source\": \"<?xml version="1.0" encoding="utf-8" standalone="no"?>
<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
  "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="460.8pt" height="345.6pt" viewBox="0 0 460.8 345.6" xmlns="http://www.w3.org/2000/svg" version="1.1">
 <metadata>
  <rdf:RDF xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:cc="http://creativecommons.org/ns#" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
   <cc:Work>
    <dc:type rdf:resource="http://purl.org/dc/dcmitype/StillImage"/>
    <dc:date>2025-03-29T11:10:47.657849</dc:date>
    <dc:format>image/svg+xml</dc:format>
    <dc:creator>
     <cc:Agent>
      <dc:title>Matplotlib v3.6.3, https://matplotlib.org/</dc:title>
     </cc:Agent>
    </dc:creator>
   </cc:Work>
  </rdf:RDF>
 </metadata>
 <defs>
  <style type="text/css">*{stroke-linejoin: round; stroke-linecap: butt}</style>
 </defs>
 <g id="figure_1">
  <g id="patch_1">
   <path d="M 0 345.6 
L 460.8 345.6 
L 460.8 0 
L 0 0 
z
" style="fill: #ffffff"/>
  </g>
  <g id="axes_1">
   <g id="patch_2">
    <path d="M 57.6 307.584 
L 414.72 307.584 
L 414.72 41.472 
L 57.6 41.472 
z
" style="fill: #ffffff"/>
   </g>
   <g id="matplotlib.axis_1">
    <g id="xtick_1">
     <g id="line2d_1">
      <defs>
       <path id="m54aa298feb" d="M 0 0 
L 0 3.5 
" style="stroke: #000000; stroke-width: 0.8"/>
      </defs>
      <g>
       <use xlink:href="#m54aa298feb" x="73.832727" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_1">
      <!-- 0 -->
      <g transform="translate(70.651477 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-30" d="M 2034 4250 
Q 1547 4250 1301 3770 
Q 1056 3291 1056 2328 
Q 1056 1369 1301 889 
Q 1547 409 2034 409 
Q 2525 409 2770 889 
Q 3016 1369 3016 2328 
Q 3016 3291 2770 3770 
Q 2525 4250 2034 4250 
z
M 2034 4750 
Q 2819 4750 3233 4129 
Q 3647 3509 3647 2328 
Q 3647 1150 3233 529 
Q 2819 -91 2034 -91 
Q 1250 -91 836 529 
Q 422 1150 422 2328 
Q 422 3509 836 4129 
Q 1250 4750 2034 4750 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-30"/>
      </g>
     </g>
    </g>
    <g id="xtick_2">
     <g id="line2d_2">
      <g>
       <use xlink:href="#m54aa298feb" x="138.763636" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_2">
      <!-- 2 -->
      <g transform="translate(135.582386 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-32" d="M 1228 531 
L 3431 531 
L 3431 0 
L 469 0 
L 469 531 
Q 828 903 1448 1529 
Q 2069 2156 2228 2338 
Q 2531 2678 2651 2914 
Q 2772 3150 2772 3378 
Q 2772 3750 2511 3984 
Q 2250 4219 1831 4219 
Q 1534 4219 1204 4116 
Q 875 4013 500 3803 
L 500 4441 
Q 881 4594 1212 4672 
Q 1544 4750 1819 4750 
Q 2544 4750 2975 4387 
Q 3406 4025 3406 3419 
Q 3406 3131 3298 2873 
Q 3191 2616 2906 2266 
Q 2828 2175 2409 1742 
Q 1991 1309 1228 531 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-32"/>
      </g>
     </g>
    </g>
    <g id="xtick_3">
     <g id="line2d_3">
      <g>
       <use xlink:href="#m54aa298feb" x="203.694545" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_3">
      <!-- 4 -->
      <g transform="translate(200.513295 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-34" d="M 2419 4116 
L 825 1625 
L 2419 1625 
L 2419 4116 
z
M 2253 4666 
L 3047 4666 
L 3047 1625 
L 3713 1625 
L 3713 1100 
L 3047 1100 
L 3047 0 
L 2419 0 
L 2419 1100 
L 313 1100 
L 313 1709 
L 2253 4666 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-34"/>
      </g>
     </g>
    </g>
    <g id="xtick_4">
     <g id="line2d_4">
      <g>
       <use xlink:href="#m54aa298feb" x="268.625455" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_4">
      <!-- 6 -->
      <g transform="translate(265.444205 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-36" d="M 2113 2584 
Q 1688 2584 1439 2293 
Q 1191 2003 1191 1497 
Q 1191 994 1439 701 
Q 1688 409 2113 409 
Q 2538 409 2786 701 
Q 3034 994 3034 1497 
Q 3034 2003 2786 2293 
Q 2538 2584 2113 2584 
z
M 3366 4563 
L 3366 3988 
Q 3128 4100 2886 4159 
Q 2644 4219 2406 4219 
Q 1781 4219 1451 3797 
Q 1122 3375 1075 2522 
Q 1259 2794 1537 2939 
Q 1816 3084 2150 3084 
Q 2853 3084 3261 2657 
Q 3669 2231 3669 1497 
Q 3669 778 3244 343 
Q 2819 -91 2113 -91 
Q 1303 -91 875 529 
Q 447 1150 447 2328 
Q 447 3434 972 4092 
Q 1497 4750 2381 4750 
Q 2619 4750 2861 4703 
Q 3103 4656 3366 4563 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-36"/>
      </g>
     </g>
    </g>
    <g id="xtick_5">
     <g id="line2d_5">
      <g>
       <use xlink:href="#m54aa298feb" x="333.556364" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_5">
      <!-- 8 -->
      <g transform="translate(330.375114 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-38" d="M 2034 2216 
Q 1584 2216 1326 1975 
Q 1069 1734 1069 1313 
Q 1069 891 1326 650 
Q 1584 409 2034 409 
Q 2484 409 2743 651 
Q 3003 894 3003 1313 
Q 3003 1734 2745 1975 
Q 2488 2216 2034 2216 
z
M 1403 2484 
Q 997 2584 770 2862 
Q 544 3141 544 3541 
Q 544 4100 942 4425 
Q 1341 4750 2034 4750 
Q 2731 4750 3128 4425 
Q 3525 4100 3525 3541 
Q 3525 3141 3298 2862 
Q 3072 2584 2669 2484 
Q 3125 2378 3379 2068 
Q 3634 1759 3634 1313 
Q 3634 634 3220 271 
Q 2806 -91 2034 -91 
Q 1263 -91 848 271 
Q 434 634 434 1313 
Q 434 1759 690 2068 
Q 947 2378 1403 2484 
z
M 1172 3481 
Q 1172 3119 1398 2916 
Q 1625 2713 2034 2713 
Q 2441 2713 2670 2916 
Q 2900 3119 2900 3481 
Q 2900 3844 2670 4047 
Q 2441 4250 2034 4250 
Q 1625 4250 1398 4047 
Q 1172 3844 1172 3481 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-38"/>
      </g>
     </g>
    </g>
    <g id="xtick_6">
     <g id="line2d_6">
      <g>
       <use xlink:href="#m54aa298feb" x="398.487273" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_6">
      <!-- 10 -->
      <g transform="translate(392.124773 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-31" d="M 794 531 
L 1825 531 
L 1825 4091 
L 703 3866 
L 703 4441 
L 1819 4666 
L 2450 4666 
L 2450 531 
L 3481 531 
L 3481 0 
L 794 0 
L 794 531 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-31"/>
       <use xlink:href="#DejaVuSans-30" x="63.623047"/>
      </g>
     </g>
    </g>
   </g>
   <g id="matplotlib.axis_2">
    <g id="ytick_1">
     <g id="line2d_7">
      <defs>
       <path id="m8d4ab8ab75" d="M 0 0 
L -3.5 0 
" style="stroke: #000000; stroke-width: 0.8"/>
      </defs>
      <g>
       <use xlink:href="#m8d4ab8ab75" x="57.6" y="295.494391" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_7">
      <!-- −1.00 -->
      <g transform="translate(19.954687 299.29361) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-2212" d="M 678 2272 
L 4684 2272 
L 4684 1741 
L 678 1741 
L 678 2272 
z
" transform="scale(0.015625)"/>
        <path id="DejaVuSans-2e" d="M 684 794 
L 1344 794 
L 1344 0 
L 684 0 
L 684 794 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-2212"/>
       <use xlink:href="#DejaVuSans-31" x="83.789062"/>
       <use xlink:href="#DejaVuSans-2e" x="147.412109"/>
       <use xlink:href="#DejaVuSans-30" x="179.199219"/>
       <use xlink:href="#DejaVuSans-30" x="242.822266"/>
      </g>
     </g>
    </g>
    <g id="ytick_2">
     <g id="line2d_8">
      <g>
       <use xlink:href="#m8d4ab8ab75" x="57.6" y="265.253592" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_8">
      <!-- −0.75 -->
      <g transform="translate(19.954687 269.052811) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-37" d="M 525 4666 
L 3525 4666 
L 3525 4397 
L 1831 0 
L 1172 0 
L 2766 4134 
L 525 4134 
L 525 4666 
z
" transform="scale(0.015625)"/>
        <path id="DejaVuSans-35" d="M 691 4666 
L 3169 4666 
L 3169 4134 
L 1269 4134 
L 1269 2991 
Q 1406 3038 1543 3061 
Q 1681 3084 1819 3084 
Q 2600 3084 3056 2656 
Q 3513 2228 3513 1497 
Q 3513 744 3044 326 
Q 2575 -91 1722 -91 
Q 1428 -91 1123 -41 
Q 819 9 494 109 
L 494 744 
Q 775 591 1075 516 
Q 1375 441 1709 441 
Q 2250 441 2565 725 
Q 2881 1009 2881 1497 
Q 2881 1984 2565 2268 
Q 2250 2553 1709 2553 
Q 1456 2553 1204 2497 
Q 953 2441 691 2322 
L 691 4666 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-2212"/>
       <use xlink:href="#DejaVuSans-30" x="83.789062"/>
       <use xlink:href="#DejaVuSans-2e" x="147.412109"/>
       <use xlink:href="#DejaVuSans-37" x="179.199219"/>
       <use xlink:href="#DejaVuSans-35" x="242.822266"/>
      </g>
     </g>
    </g>
    <g id="ytick_3">
     <g id="line2d_9">
      <g>
       <use xlink:href="#m8d4ab8ab75" x="57.6" y="235.012793" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_9">
      <!-- −0.50 -->
      <g transform="translate(19.954687 238.812012) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-2212"/>
       <use xlink:href="#DejaVuSans-30" x="83.789062"/>
       <use xlink:href="#DejaVuSans-2e" x="147.412109"/>
       <use xlink:href="#DejaVuSans-35" x="179.199219"/>
       <use xlink:href="#DejaVuSans-30" x="242.822266"/>
      </g>
     </g>
    </g>
    <g id="ytick_4">
     <g id="line2d_10">
      <g>
       <use xlink:href="#m8d4ab8ab75" x="57.6" y="204.771994" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_10">
      <!-- −0.25 -->
      <g transform="translate(19.954687 208.571213) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-2212"/>
       <use xlink:href="#DejaVuSans-30" x="83.789062"/>
       <use xlink:href="#DejaVuSans-2e" x="147.412109"/>
       <use xlink:href="#DejaVuSans-32" x="179.199219"/>
       <use xlink:href="#DejaVuSans-35" x="242.822266"/>
      </g>
     </g>
    </g>
    <g id="ytick_5">
     <g id="line2d_11">
      <g>
       <use xlink:href="#m8d4ab8ab75" x="57.6" y="174.531195" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_11">
      <!-- 0.00 -->
      <g transform="translate(28.334375 178.330414) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-30"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-30" x="95.410156"/>
       <use xlink:href="#DejaVuSans-30" x="159.033203"/>
      </g>
     </g>
    </g>
    <g id="ytick_6">
     <g id="line2d_12">
      <g>
       <use xlink:href="#m8d4ab8ab75" x="57.6" y="144.290397" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_12">
      <!-- 0.25 -->
      <g transform="translate(28.334375 148.089615) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-30"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-32" x="95.410156"/>
       <use xlink:href="#DejaVuSans-35" x="159.033203"/>
      </g>
     </g>
    </g>
    <g id="ytick_7">
     <g id="line2d_13">
      <g>
       <use xlink:href="#m8d4ab8ab75" x="57.6" y="114.049598" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_13">
      <!-- 0.50 -->
      <g transform="translate(28.334375 117.848816) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-30"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-35" x="95.410156"/>
       <use xlink:href="#DejaVuSans-30" x="159.033203"/>
      </g>
     </g>
    </g>
    <g id="ytick_8">
     <g id="line2d_14">
      <g>
       <use xlink:href="#m8d4ab8ab75" x="57.6" y="83.808799" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_14">
      <!-- 0.75 -->
      <g transform="translate(28.334375 87.608018) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-30"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-37" x="95.410156"/>
       <use xlink:href="#DejaVuSans-35" x="159.033203"/>
      </g>
     </g>
    </g>
    <g id="ytick_9">
     <g id="line2d_15">
      <g>
       <use xlink:href="#m8d4ab8ab75" x="57.6" y="53.568" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_15">
      <!-- 1.00 -->
      <g transform="translate(28.334375 57.367219) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-31"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-30" x="95.410156"/>
       <use xlink:href="#DejaVuSans-30" x="159.033203"/>
      </g>
     </g>
    </g>
   </g>
   <g id="line2d_16">
    <path d="M 73.832727 174.531195 
L 77.112066 162.333458 
L 80.391405 150.260069 
L 83.670744 138.434108 
L 86.950083 126.976135 
L 90.229421 116.002955 
L 93.50876 105.626434 
L 96.788099 95.952353 
L 100.067438 87.079334 
L 103.346777 79.097831 
L 106.626116 72.089211 
L 109.905455 66.124923 
L 113.184793 61.265768 
L 116.464132 57.561283 
L 119.743471 55.049232 
L 123.02281 53.755224 
L 126.302149 53.69245 
L 129.581488 54.861552 
L 132.860826 57.25061 
L 136.140165 60.835269 
L 139.419504 65.578987 
L 142.698843 71.433403 
L 145.978182 78.338836 
L 149.257521 86.22489 
L 152.53686 95.011171 
L 155.816198 104.608108 
L 159.095537 114.917866 
L 162.374876 125.835345 
L 165.654215 137.249248 
L 168.933554 149.043216 
L 172.212893 161.097018 
L 175.492231 173.287774 
L 178.77157 185.491205 
L 182.050909 197.582905 
L 185.330248 209.439608 
L 188.609587 220.940442 
L 191.888926 231.968163 
L 195.168264 242.41035 
L 198.447603 252.160552 
L 201.726942 261.119372 
L 205.006281 269.195481 
L 208.28562 276.306546 
L 211.564959 282.380076 
L 214.844298 287.354155 
L 218.123636 291.178075 
L 221.402975 293.812854 
L 224.682314 295.231632 
L 227.961653 295.419945 
L 231.240992 294.375874 
L 234.520331 292.110061 
L 237.799669 288.645607 
L 241.079008 284.017828 
L 244.358347 278.273902 
L 247.637686 271.472385 
L 250.917025 263.682614 
L 254.196364 254.984 
L 257.475702 245.465221 
L 260.755041 235.223314 
L 264.03438 224.362689 
L 267.313719 212.994064 
L 270.593058 201.233334 
L 273.872397 189.200393 
L 277.151736 177.017908 
L 280.431074 164.810073 
L 283.710413 152.701339 
L 286.989752 140.815146 
L 290.269091 129.272667 
L 293.54843 118.19157 
L 296.827769 107.68482 
L 300.107107 97.859527 
L 303.386446 88.815853 
L 306.665785 80.645993 
L 309.945124 73.433233 
L 313.224463 67.251102 
L 316.503802 62.162625 
L 319.78314 58.219674 
L 323.062479 55.462446 
L 326.341818 53.919048 
L 329.621157 53.605215 
L 332.900496 54.524146 
L 336.179835 56.666474 
L 339.459174 60.010357 
L 342.738512 64.521708 
L 346.017851 70.154536 
L 349.29719 76.851419 
L 352.576529 84.544085 
L 355.855868 93.154113 
L 359.135207 102.593728 
L 362.414545 112.766701 
L 365.693884 123.569324 
L 368.973223 134.891471 
L 372.252562 146.617719 
L 375.531901 158.628528 
L 378.81124 170.801455 
L 382.090579 183.012404 
L 385.369917 195.136893 
L 388.649256 207.051319 
L 391.928595 218.634223 
L 395.207934 229.767525 
L 398.487273 240.337727 
" clip-path="url(#p510a345518)" style="fill: none; stroke: #1f77b4; stroke-width: 1.5; stroke-linecap: square"/>
   </g>
   <g id="line2d_17">
    <path d="M 73.832727 53.568 
L 77.112066 54.184572 
L 80.391405 56.028001 
L 83.670744 59.079496 
L 86.950083 63.307948 
L 90.229421 68.67025 
L 93.50876 75.111738 
L 96.788099 82.566745 
L 100.067438 90.959271 
L 103.346777 100.20376 
L 106.626116 110.20597 
L 109.905455 120.863936 
L 113.184793 132.069005 
L 116.464132 143.706949 
L 119.743471 155.659127 
L 123.02281 167.803694 
L 126.302149 180.016844 
L 129.581488 192.174071 
L 132.860826 204.151439 
L 136.140165 215.826849 
L 139.419504 227.081275 
L 142.698843 237.799986 
L 145.978182 247.873712 
L 149.257521 257.199757 
L 152.53686 265.683048 
L 155.816198 273.237104 
L 159.095537 279.784916 
L 162.374876 285.259732 
L 165.654215 289.605741 
L 168.933554 292.778638 
L 172.212893 294.746076 
L 175.492231 295.488 
L 178.77157 294.996846 
L 182.050909 293.27762 
L 185.330248 290.34785 
L 188.609587 286.237402 
L 191.888926 280.988179 
L 195.168264 274.653695 
L 198.447603 267.298526 
L 201.726942 258.997652 
L 205.006281 249.835696 
L 208.28562 239.906058 
L 211.564959 229.309965 
L 214.844298 218.155437 
L 218.123636 206.556187 
L 221.402975 194.630462 
L 224.682314 182.499839 
L 227.961653 170.28798 
L 231.240992 158.119378 
L 234.520331 146.118084 
L 237.799669 134.406443 
L 241.079008 123.10385 
L 244.358347 112.325525 
L 247.637686 102.181348 
L 250.917025 92.774732 
L 254.196364 84.201572 
L 257.475702 76.549265 
L 260.755041 69.895822 
L 264.03438 64.30907 
L 267.313719 59.845964 
L 270.593058 56.552 
L 273.872397 54.460761 
L 277.151736 53.593563 
L 280.431074 53.959248 
L 283.710413 55.554088 
L 286.989752 58.361825 
L 290.269091 62.353835 
L 293.54843 67.489422 
L 296.827769 73.716232 
L 300.107107 80.970788 
L 303.386446 89.179132 
L 306.665785 98.257587 
L 309.945124 108.113603 
L 313.224463 118.646705 
L 316.503802 129.749514 
L 319.78314 141.308843 
L 323.062479 153.206854 
L 326.341818 165.322252 
L 329.621157 177.53153 
L 332.900496 189.710222 
L 336.179835 201.734173 
L 339.459174 213.480807 
L 342.738512 224.830374 
L 346.017851 235.667173 
L 349.29719 245.880729 
L 352.576529 255.366921 
L 355.855868 264.029045 
L 359.135207 271.778794 
L 362.414545 278.537166 
L 365.693884 284.235262 
L 368.973223 288.814995 
L 372.252562 292.229677 
L 375.531901 294.444497 
L 378.81124 295.436876 
L 382.090579 295.196699 
L 385.369917 293.726413 
L 388.649256 291.041007 
L 391.928595 287.167857 
L 395.207934 282.146448 
L 398.487273 276.027969 
" clip-path="url(#p510a345518)" style="fill: none; stroke: #ff0000; stroke-width: 1.5; stroke-linecap: square"/>
   </g>
   <g id="patch_3">
    <path d="M 57.6 307.584 
L 57.6 41.472 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
   <g id="patch_4">
    <path d="M 414.72 307.584 
L 414.72 41.472 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
   <g id="patch_5">
    <path d="M 57.6 307.584 
L 414.72 307.584 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
   <g id="patch_6">
    <path d="M 57.6 41.472 
L 414.72 41.472 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
  </g>
 </g>
 <defs>
  <clipPath id="p510a345518">
   <rect x="57.6" y="41.472" width="357.12" height="266.112"/>
  </clipPath>
 </defs>
</svg>
\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"plot($\\\\cos(x)$, {$x$: (0, 10)}, fig=fig, label=\\\"curve2\\\", color=\\\"red\\\");\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 6257958220997548270,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 5400706528810547774,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"image_svg\",\n\t\t\t\t\t\"source\": \"<?xml version="1.0" encoding="utf-8" standalone="no"?>
<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
  "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="460.8pt" height="345.6pt" viewBox="0 0 460.8 345.6" xmlns="http://www.w3.org/2000/svg" version="1.1">
 <metadata>
  <rdf:RDF xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:cc="http://creativecommons.org/ns#" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
   <cc:Work>
    <dc:type rdf:resource="http://purl.org/dc/dcmitype/StillImage"/>
    <dc:date>2025-03-29T11:10:57.164526</dc:date>
    <dc:format>image/svg+xml</dc:format>
    <dc:creator>
     <cc:Agent>
      <dc:title>Matplotlib v3.6.3, https://matplotlib.org/</dc:title>
     </cc:Agent>
    </dc:creator>
   </cc:Work>
  </rdf:RDF>
 </metadata>
 <defs>
  <style type="text/css">*{stroke-linejoin: round; stroke-linecap: butt}</style>
 </defs>
 <g id="figure_1">
  <g id="patch_1">
   <path d="M 0 345.6 
L 460.8 345.6 
L 460.8 0 
L 0 0 
z
" style="fill: #ffffff"/>
  </g>
  <g id="axes_1">
   <g id="patch_2">
    <path d="M 57.6 307.584 
L 414.72 307.584 
L 414.72 41.472 
L 57.6 41.472 
z
" style="fill: #ffffff"/>
   </g>
   <g id="matplotlib.axis_1">
    <g id="xtick_1">
     <g id="line2d_1">
      <defs>
       <path id="m574345a464" d="M 0 0 
L 0 3.5 
" style="stroke: #000000; stroke-width: 0.8"/>
      </defs>
      <g>
       <use xlink:href="#m574345a464" x="73.832727" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_1">
      <!-- 0 -->
      <g transform="translate(70.651477 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-30" d="M 2034 4250 
Q 1547 4250 1301 3770 
Q 1056 3291 1056 2328 
Q 1056 1369 1301 889 
Q 1547 409 2034 409 
Q 2525 409 2770 889 
Q 3016 1369 3016 2328 
Q 3016 3291 2770 3770 
Q 2525 4250 2034 4250 
z
M 2034 4750 
Q 2819 4750 3233 4129 
Q 3647 3509 3647 2328 
Q 3647 1150 3233 529 
Q 2819 -91 2034 -91 
Q 1250 -91 836 529 
Q 422 1150 422 2328 
Q 422 3509 836 4129 
Q 1250 4750 2034 4750 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-30"/>
      </g>
     </g>
    </g>
    <g id="xtick_2">
     <g id="line2d_2">
      <g>
       <use xlink:href="#m574345a464" x="138.763636" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_2">
      <!-- 2 -->
      <g transform="translate(135.582386 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-32" d="M 1228 531 
L 3431 531 
L 3431 0 
L 469 0 
L 469 531 
Q 828 903 1448 1529 
Q 2069 2156 2228 2338 
Q 2531 2678 2651 2914 
Q 2772 3150 2772 3378 
Q 2772 3750 2511 3984 
Q 2250 4219 1831 4219 
Q 1534 4219 1204 4116 
Q 875 4013 500 3803 
L 500 4441 
Q 881 4594 1212 4672 
Q 1544 4750 1819 4750 
Q 2544 4750 2975 4387 
Q 3406 4025 3406 3419 
Q 3406 3131 3298 2873 
Q 3191 2616 2906 2266 
Q 2828 2175 2409 1742 
Q 1991 1309 1228 531 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-32"/>
      </g>
     </g>
    </g>
    <g id="xtick_3">
     <g id="line2d_3">
      <g>
       <use xlink:href="#m574345a464" x="203.694545" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_3">
      <!-- 4 -->
      <g transform="translate(200.513295 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-34" d="M 2419 4116 
L 825 1625 
L 2419 1625 
L 2419 4116 
z
M 2253 4666 
L 3047 4666 
L 3047 1625 
L 3713 1625 
L 3713 1100 
L 3047 1100 
L 3047 0 
L 2419 0 
L 2419 1100 
L 313 1100 
L 313 1709 
L 2253 4666 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-34"/>
      </g>
     </g>
    </g>
    <g id="xtick_4">
     <g id="line2d_4">
      <g>
       <use xlink:href="#m574345a464" x="268.625455" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_4">
      <!-- 6 -->
      <g transform="translate(265.444205 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-36" d="M 2113 2584 
Q 1688 2584 1439 2293 
Q 1191 2003 1191 1497 
Q 1191 994 1439 701 
Q 1688 409 2113 409 
Q 2538 409 2786 701 
Q 3034 994 3034 1497 
Q 3034 2003 2786 2293 
Q 2538 2584 2113 2584 
z
M 3366 4563 
L 3366 3988 
Q 3128 4100 2886 4159 
Q 2644 4219 2406 4219 
Q 1781 4219 1451 3797 
Q 1122 3375 1075 2522 
Q 1259 2794 1537 2939 
Q 1816 3084 2150 3084 
Q 2853 3084 3261 2657 
Q 3669 2231 3669 1497 
Q 3669 778 3244 343 
Q 2819 -91 2113 -91 
Q 1303 -91 875 529 
Q 447 1150 447 2328 
Q 447 3434 972 4092 
Q 1497 4750 2381 4750 
Q 2619 4750 2861 4703 
Q 3103 4656 3366 4563 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-36"/>
      </g>
     </g>
    </g>
    <g id="xtick_5">
     <g id="line2d_5">
      <g>
       <use xlink:href="#m574345a464" x="333.556364" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_5">
      <!-- 8 -->
      <g transform="translate(330.375114 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-38" d="M 2034 2216 
Q 1584 2216 1326 1975 
Q 1069 1734 1069 1313 
Q 1069 891 1326 650 
Q 1584 409 2034 409 
Q 2484 409 2743 651 
Q 3003 894 3003 1313 
Q 3003 1734 2745 1975 
Q 2488 2216 2034 2216 
z
M 1403 2484 
Q 997 2584 770 2862 
Q 544 3141 544 3541 
Q 544 4100 942 4425 
Q 1341 4750 2034 4750 
Q 2731 4750 3128 4425 
Q 3525 4100 3525 3541 
Q 3525 3141 3298 2862 
Q 3072 2584 2669 2484 
Q 3125 2378 3379 2068 
Q 3634 1759 3634 1313 
Q 3634 634 3220 271 
Q 2806 -91 2034 -91 
Q 1263 -91 848 271 
Q 434 634 434 1313 
Q 434 1759 690 2068 
Q 947 2378 1403 2484 
z
M 1172 3481 
Q 1172 3119 1398 2916 
Q 1625 2713 2034 2713 
Q 2441 2713 2670 2916 
Q 2900 3119 2900 3481 
Q 2900 3844 2670 4047 
Q 2441 4250 2034 4250 
Q 1625 4250 1398 4047 
Q 1172 3844 1172 3481 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-38"/>
      </g>
     </g>
    </g>
    <g id="xtick_6">
     <g id="line2d_6">
      <g>
       <use xlink:href="#m574345a464" x="398.487273" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_6">
      <!-- 10 -->
      <g transform="translate(392.124773 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-31" d="M 794 531 
L 1825 531 
L 1825 4091 
L 703 3866 
L 703 4441 
L 1819 4666 
L 2450 4666 
L 2450 531 
L 3481 531 
L 3481 0 
L 794 0 
L 794 531 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-31"/>
       <use xlink:href="#DejaVuSans-30" x="63.623047"/>
      </g>
     </g>
    </g>
   </g>
   <g id="matplotlib.axis_2">
    <g id="ytick_1">
     <g id="line2d_7">
      <defs>
       <path id="med88ccc2a0" d="M 0 0 
L -3.5 0 
" style="stroke: #000000; stroke-width: 0.8"/>
      </defs>
      <g>
       <use xlink:href="#med88ccc2a0" x="57.6" y="295.494391" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_7">
      <!-- −1.00 -->
      <g transform="translate(19.954687 299.29361) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-2212" d="M 678 2272 
L 4684 2272 
L 4684 1741 
L 678 1741 
L 678 2272 
z
" transform="scale(0.015625)"/>
        <path id="DejaVuSans-2e" d="M 684 794 
L 1344 794 
L 1344 0 
L 684 0 
L 684 794 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-2212"/>
       <use xlink:href="#DejaVuSans-31" x="83.789062"/>
       <use xlink:href="#DejaVuSans-2e" x="147.412109"/>
       <use xlink:href="#DejaVuSans-30" x="179.199219"/>
       <use xlink:href="#DejaVuSans-30" x="242.822266"/>
      </g>
     </g>
    </g>
    <g id="ytick_2">
     <g id="line2d_8">
      <g>
       <use xlink:href="#med88ccc2a0" x="57.6" y="265.253592" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_8">
      <!-- −0.75 -->
      <g transform="translate(19.954687 269.052811) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-37" d="M 525 4666 
L 3525 4666 
L 3525 4397 
L 1831 0 
L 1172 0 
L 2766 4134 
L 525 4134 
L 525 4666 
z
" transform="scale(0.015625)"/>
        <path id="DejaVuSans-35" d="M 691 4666 
L 3169 4666 
L 3169 4134 
L 1269 4134 
L 1269 2991 
Q 1406 3038 1543 3061 
Q 1681 3084 1819 3084 
Q 2600 3084 3056 2656 
Q 3513 2228 3513 1497 
Q 3513 744 3044 326 
Q 2575 -91 1722 -91 
Q 1428 -91 1123 -41 
Q 819 9 494 109 
L 494 744 
Q 775 591 1075 516 
Q 1375 441 1709 441 
Q 2250 441 2565 725 
Q 2881 1009 2881 1497 
Q 2881 1984 2565 2268 
Q 2250 2553 1709 2553 
Q 1456 2553 1204 2497 
Q 953 2441 691 2322 
L 691 4666 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-2212"/>
       <use xlink:href="#DejaVuSans-30" x="83.789062"/>
       <use xlink:href="#DejaVuSans-2e" x="147.412109"/>
       <use xlink:href="#DejaVuSans-37" x="179.199219"/>
       <use xlink:href="#DejaVuSans-35" x="242.822266"/>
      </g>
     </g>
    </g>
    <g id="ytick_3">
     <g id="line2d_9">
      <g>
       <use xlink:href="#med88ccc2a0" x="57.6" y="235.012793" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_9">
      <!-- −0.50 -->
      <g transform="translate(19.954687 238.812012) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-2212"/>
       <use xlink:href="#DejaVuSans-30" x="83.789062"/>
       <use xlink:href="#DejaVuSans-2e" x="147.412109"/>
       <use xlink:href="#DejaVuSans-35" x="179.199219"/>
       <use xlink:href="#DejaVuSans-30" x="242.822266"/>
      </g>
     </g>
    </g>
    <g id="ytick_4">
     <g id="line2d_10">
      <g>
       <use xlink:href="#med88ccc2a0" x="57.6" y="204.771994" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_10">
      <!-- −0.25 -->
      <g transform="translate(19.954687 208.571213) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-2212"/>
       <use xlink:href="#DejaVuSans-30" x="83.789062"/>
       <use xlink:href="#DejaVuSans-2e" x="147.412109"/>
       <use xlink:href="#DejaVuSans-32" x="179.199219"/>
       <use xlink:href="#DejaVuSans-35" x="242.822266"/>
      </g>
     </g>
    </g>
    <g id="ytick_5">
     <g id="line2d_11">
      <g>
       <use xlink:href="#med88ccc2a0" x="57.6" y="174.531195" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_11">
      <!-- 0.00 -->
      <g transform="translate(28.334375 178.330414) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-30"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-30" x="95.410156"/>
       <use xlink:href="#DejaVuSans-30" x="159.033203"/>
      </g>
     </g>
    </g>
    <g id="ytick_6">
     <g id="line2d_12">
      <g>
       <use xlink:href="#med88ccc2a0" x="57.6" y="144.290397" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_12">
      <!-- 0.25 -->
      <g transform="translate(28.334375 148.089615) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-30"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-32" x="95.410156"/>
       <use xlink:href="#DejaVuSans-35" x="159.033203"/>
      </g>
     </g>
    </g>
    <g id="ytick_7">
     <g id="line2d_13">
      <g>
       <use xlink:href="#med88ccc2a0" x="57.6" y="114.049598" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_13">
      <!-- 0.50 -->
      <g transform="translate(28.334375 117.848816) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-30"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-35" x="95.410156"/>
       <use xlink:href="#DejaVuSans-30" x="159.033203"/>
      </g>
     </g>
    </g>
    <g id="ytick_8">
     <g id="line2d_14">
      <g>
       <use xlink:href="#med88ccc2a0" x="57.6" y="83.808799" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_14">
      <!-- 0.75 -->
      <g transform="translate(28.334375 87.608018) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-30"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-37" x="95.410156"/>
       <use xlink:href="#DejaVuSans-35" x="159.033203"/>
      </g>
     </g>
    </g>
    <g id="ytick_9">
     <g id="line2d_15">
      <g>
       <use xlink:href="#med88ccc2a0" x="57.6" y="53.568" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_15">
      <!-- 1.00 -->
      <g transform="translate(28.334375 57.367219) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-31"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-30" x="95.410156"/>
       <use xlink:href="#DejaVuSans-30" x="159.033203"/>
      </g>
     </g>
    </g>
   </g>
   <g id="line2d_16">
    <path d="M 73.832727 53.568 
L 77.112066 54.184572 
L 80.391405 56.028001 
L 83.670744 59.079496 
L 86.950083 63.307948 
L 90.229421 68.67025 
L 93.50876 75.111738 
L 96.788099 82.566745 
L 100.067438 90.959271 
L 103.346777 100.20376 
L 106.626116 110.20597 
L 109.905455 120.863936 
L 113.184793 132.069005 
L 116.464132 143.706949 
L 119.743471 155.659127 
L 123.02281 167.803694 
L 126.302149 180.016844 
L 129.581488 192.174071 
L 132.860826 204.151439 
L 136.140165 215.826849 
L 139.419504 227.081275 
L 142.698843 237.799986 
L 145.978182 247.873712 
L 149.257521 257.199757 
L 152.53686 265.683048 
L 155.816198 273.237104 
L 159.095537 279.784916 
L 162.374876 285.259732 
L 165.654215 289.605741 
L 168.933554 292.778638 
L 172.212893 294.746076 
L 175.492231 295.488 
L 178.77157 294.996846 
L 182.050909 293.27762 
L 185.330248 290.34785 
L 188.609587 286.237402 
L 191.888926 280.988179 
L 195.168264 274.653695 
L 198.447603 267.298526 
L 201.726942 258.997652 
L 205.006281 249.835696 
L 208.28562 239.906058 
L 211.564959 229.309965 
L 214.844298 218.155437 
L 218.123636 206.556187 
L 221.402975 194.630462 
L 224.682314 182.499839 
L 227.961653 170.28798 
L 231.240992 158.119378 
L 234.520331 146.118084 
L 237.799669 134.406443 
L 241.079008 123.10385 
L 244.358347 112.325525 
L 247.637686 102.181348 
L 250.917025 92.774732 
L 254.196364 84.201572 
L 257.475702 76.549265 
L 260.755041 69.895822 
L 264.03438 64.30907 
L 267.313719 59.845964 
L 270.593058 56.552 
L 273.872397 54.460761 
L 277.151736 53.593563 
L 280.431074 53.959248 
L 283.710413 55.554088 
L 286.989752 58.361825 
L 290.269091 62.353835 
L 293.54843 67.489422 
L 296.827769 73.716232 
L 300.107107 80.970788 
L 303.386446 89.179132 
L 306.665785 98.257587 
L 309.945124 108.113603 
L 313.224463 118.646705 
L 316.503802 129.749514 
L 319.78314 141.308843 
L 323.062479 153.206854 
L 326.341818 165.322252 
L 329.621157 177.53153 
L 332.900496 189.710222 
L 336.179835 201.734173 
L 339.459174 213.480807 
L 342.738512 224.830374 
L 346.017851 235.667173 
L 349.29719 245.880729 
L 352.576529 255.366921 
L 355.855868 264.029045 
L 359.135207 271.778794 
L 362.414545 278.537166 
L 365.693884 284.235262 
L 368.973223 288.814995 
L 372.252562 292.229677 
L 375.531901 294.444497 
L 378.81124 295.436876 
L 382.090579 295.196699 
L 385.369917 293.726413 
L 388.649256 291.041007 
L 391.928595 287.167857 
L 395.207934 282.146448 
L 398.487273 276.027969 
" clip-path="url(#pd59cf47839)" style="fill: none; stroke: #ff0000; stroke-width: 1.5; stroke-linecap: square"/>
   </g>
   <g id="line2d_17">
    <path d="M 73.832727 174.531195 
L 77.112066 163.505369 
L 80.391405 154.699781 
L 83.670744 147.870727 
L 86.950083 142.782621 
L 90.229421 139.21086 
L 93.50876 136.943954 
L 96.788099 135.785031 
L 100.067438 135.552794 
L 103.346777 136.082017 
L 106.626116 137.223649 
L 109.905455 138.844611 
L 113.184793 140.827322 
L 116.464132 143.069039 
L 119.743471 145.481035 
L 123.02281 147.98767 
L 126.302149 150.525398 
L 129.581488 153.041721 
L 132.860826 155.494139 
L 136.140165 157.849106 
L 139.419504 160.081009 
L 142.698843 162.17119 
L 145.978182 164.10702 
L 149.257521 165.881024 
L 152.53686 167.490081 
L 155.816198 168.934684 
L 159.095537 170.218269 
L 162.374876 171.346613 
L 165.654215 172.3273 
L 168.933554 173.16925 
L 172.212893 173.882311 
L 175.492231 174.476907 
L 178.77157 174.96374 
L 182.050909 175.353542 
L 185.330248 175.656872 
L 188.609587 175.883953 
L 191.888926 176.044544 
L 195.168264 176.147844 
L 198.447603 176.202429 
L 201.726942 176.216202 
L 205.006281 176.196375 
L 208.28562 176.149459 
L 211.564959 176.081276 
L 214.844298 175.996973 
L 218.123636 175.901053 
L 221.402975 175.797412 
L 224.682314 175.689372 
L 227.961653 175.579733 
L 231.240992 175.470807 
L 234.520331 175.364475 
L 237.799669 175.262223 
L 241.079008 175.165191 
L 244.358347 175.074214 
L 247.637686 174.989862 
L 250.917025 174.91248 
L 254.196364 174.84222 
L 257.475702 174.779074 
L 260.755041 174.722907 
L 264.03438 174.673478 
L 267.313719 174.630466 
L 270.593058 174.593491 
L 273.872397 174.56213 
L 277.151736 174.535936 
L 280.431074 174.514445 
L 283.710413 174.497195 
L 286.989752 174.483727 
L 290.269091 174.473598 
L 293.54843 174.466384 
L 296.827769 174.461686 
L 300.107107 174.459129 
L 303.386446 174.458369 
L 306.665785 174.459091 
L 309.945124 174.461012 
L 313.224463 174.463875 
L 316.503802 174.467457 
L 319.78314 174.471559 
L 323.062479 174.476011 
L 326.341818 174.480666 
L 329.621157 174.485402 
L 332.900496 174.490116 
L 336.179835 174.494726 
L 339.459174 174.499165 
L 342.738512 174.503383 
L 346.017851 174.507342 
L 349.29719 174.511017 
L 352.576529 174.514392 
L 355.855868 174.51746 
L 359.135207 174.52022 
L 362.414545 174.522677 
L 365.693884 174.524842 
L 368.973223 174.526729 
L 372.252562 174.528352 
L 375.531901 174.529731 
L 378.81124 174.530885 
L 382.090579 174.531834 
L 385.369917 174.532597 
L 388.649256 174.533194 
L 391.928595 174.533646 
L 395.207934 174.53397 
L 398.487273 174.534183 
" clip-path="url(#pd59cf47839)" style="fill: none; stroke: #1f77b4; stroke-width: 1.5; stroke-linecap: square"/>
   </g>
   <g id="patch_3">
    <path d="M 57.6 307.584 
L 57.6 41.472 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
   <g id="patch_4">
    <path d="M 414.72 307.584 
L 414.72 41.472 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
   <g id="patch_5">
    <path d="M 57.6 307.584 
L 414.72 307.584 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
   <g id="patch_6">
    <path d="M 57.6 41.472 
L 414.72 41.472 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
  </g>
 </g>
 <defs>
  <clipPath id="pd59cf47839">
   <rect x="57.6" y="41.472" width="357.12" height="266.112"/>
  </clipPath>
 </defs>
</svg>
\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"plot($\\\\sin(x)\\\\exp(-x)$, {$x$: (0, 10)}, fig=fig, label=\\\"curve1\\\");\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 8100568731533045437,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 2658475870475301579,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"Instead of passing those labels with the \\\\verb|label| keyword, you can also just pass equations instead of functions to plot. The function names on the left-hand sides of these equations will then be used to identify individual curves in the plot, and you can later replace them.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"Instead of passing those labels with the \\\\verb|label| keyword, you can also just pass equations instead of functions to plot. The function names on the left-hand sides of these equations will then be used to identify individual curves in the plot, and you can later replace them.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 13674789098384228025,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 3665421290497272183,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"image_svg\",\n\t\t\t\t\t\"source\": \"<?xml version="1.0" encoding="utf-8" standalone="no"?>
<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
  "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="460.8pt" height="345.6pt" viewBox="0 0 460.8 345.6" xmlns="http://www.w3.org/2000/svg" version="1.1">
 <metadata>
  <rdf:RDF xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:cc="http://creativecommons.org/ns#" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
   <cc:Work>
    <dc:type rdf:resource="http://purl.org/dc/dcmitype/StillImage"/>
    <dc:date>2025-03-29T11:12:00.869629</dc:date>
    <dc:format>image/svg+xml</dc:format>
    <dc:creator>
     <cc:Agent>
      <dc:title>Matplotlib v3.6.3, https://matplotlib.org/</dc:title>
     </cc:Agent>
    </dc:creator>
   </cc:Work>
  </rdf:RDF>
 </metadata>
 <defs>
  <style type="text/css">*{stroke-linejoin: round; stroke-linecap: butt}</style>
 </defs>
 <g id="figure_1">
  <g id="patch_1">
   <path d="M 0 345.6 
L 460.8 345.6 
L 460.8 0 
L 0 0 
z
" style="fill: #ffffff"/>
  </g>
  <g id="axes_1">
   <g id="patch_2">
    <path d="M 57.6 307.584 
L 414.72 307.584 
L 414.72 41.472 
L 57.6 41.472 
z
" style="fill: #ffffff"/>
   </g>
   <g id="matplotlib.axis_1">
    <g id="xtick_1">
     <g id="line2d_1">
      <defs>
       <path id="m6a14c3abda" d="M 0 0 
L 0 3.5 
" style="stroke: #000000; stroke-width: 0.8"/>
      </defs>
      <g>
       <use xlink:href="#m6a14c3abda" x="73.832727" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_1">
      <!-- 0 -->
      <g transform="translate(70.651477 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-30" d="M 2034 4250 
Q 1547 4250 1301 3770 
Q 1056 3291 1056 2328 
Q 1056 1369 1301 889 
Q 1547 409 2034 409 
Q 2525 409 2770 889 
Q 3016 1369 3016 2328 
Q 3016 3291 2770 3770 
Q 2525 4250 2034 4250 
z
M 2034 4750 
Q 2819 4750 3233 4129 
Q 3647 3509 3647 2328 
Q 3647 1150 3233 529 
Q 2819 -91 2034 -91 
Q 1250 -91 836 529 
Q 422 1150 422 2328 
Q 422 3509 836 4129 
Q 1250 4750 2034 4750 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-30"/>
      </g>
     </g>
    </g>
    <g id="xtick_2">
     <g id="line2d_2">
      <g>
       <use xlink:href="#m6a14c3abda" x="138.763636" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_2">
      <!-- 2 -->
      <g transform="translate(135.582386 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-32" d="M 1228 531 
L 3431 531 
L 3431 0 
L 469 0 
L 469 531 
Q 828 903 1448 1529 
Q 2069 2156 2228 2338 
Q 2531 2678 2651 2914 
Q 2772 3150 2772 3378 
Q 2772 3750 2511 3984 
Q 2250 4219 1831 4219 
Q 1534 4219 1204 4116 
Q 875 4013 500 3803 
L 500 4441 
Q 881 4594 1212 4672 
Q 1544 4750 1819 4750 
Q 2544 4750 2975 4387 
Q 3406 4025 3406 3419 
Q 3406 3131 3298 2873 
Q 3191 2616 2906 2266 
Q 2828 2175 2409 1742 
Q 1991 1309 1228 531 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-32"/>
      </g>
     </g>
    </g>
    <g id="xtick_3">
     <g id="line2d_3">
      <g>
       <use xlink:href="#m6a14c3abda" x="203.694545" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_3">
      <!-- 4 -->
      <g transform="translate(200.513295 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-34" d="M 2419 4116 
L 825 1625 
L 2419 1625 
L 2419 4116 
z
M 2253 4666 
L 3047 4666 
L 3047 1625 
L 3713 1625 
L 3713 1100 
L 3047 1100 
L 3047 0 
L 2419 0 
L 2419 1100 
L 313 1100 
L 313 1709 
L 2253 4666 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-34"/>
      </g>
     </g>
    </g>
    <g id="xtick_4">
     <g id="line2d_4">
      <g>
       <use xlink:href="#m6a14c3abda" x="268.625455" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_4">
      <!-- 6 -->
      <g transform="translate(265.444205 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-36" d="M 2113 2584 
Q 1688 2584 1439 2293 
Q 1191 2003 1191 1497 
Q 1191 994 1439 701 
Q 1688 409 2113 409 
Q 2538 409 2786 701 
Q 3034 994 3034 1497 
Q 3034 2003 2786 2293 
Q 2538 2584 2113 2584 
z
M 3366 4563 
L 3366 3988 
Q 3128 4100 2886 4159 
Q 2644 4219 2406 4219 
Q 1781 4219 1451 3797 
Q 1122 3375 1075 2522 
Q 1259 2794 1537 2939 
Q 1816 3084 2150 3084 
Q 2853 3084 3261 2657 
Q 3669 2231 3669 1497 
Q 3669 778 3244 343 
Q 2819 -91 2113 -91 
Q 1303 -91 875 529 
Q 447 1150 447 2328 
Q 447 3434 972 4092 
Q 1497 4750 2381 4750 
Q 2619 4750 2861 4703 
Q 3103 4656 3366 4563 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-36"/>
      </g>
     </g>
    </g>
    <g id="xtick_5">
     <g id="line2d_5">
      <g>
       <use xlink:href="#m6a14c3abda" x="333.556364" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_5">
      <!-- 8 -->
      <g transform="translate(330.375114 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-38" d="M 2034 2216 
Q 1584 2216 1326 1975 
Q 1069 1734 1069 1313 
Q 1069 891 1326 650 
Q 1584 409 2034 409 
Q 2484 409 2743 651 
Q 3003 894 3003 1313 
Q 3003 1734 2745 1975 
Q 2488 2216 2034 2216 
z
M 1403 2484 
Q 997 2584 770 2862 
Q 544 3141 544 3541 
Q 544 4100 942 4425 
Q 1341 4750 2034 4750 
Q 2731 4750 3128 4425 
Q 3525 4100 3525 3541 
Q 3525 3141 3298 2862 
Q 3072 2584 2669 2484 
Q 3125 2378 3379 2068 
Q 3634 1759 3634 1313 
Q 3634 634 3220 271 
Q 2806 -91 2034 -91 
Q 1263 -91 848 271 
Q 434 634 434 1313 
Q 434 1759 690 2068 
Q 947 2378 1403 2484 
z
M 1172 3481 
Q 1172 3119 1398 2916 
Q 1625 2713 2034 2713 
Q 2441 2713 2670 2916 
Q 2900 3119 2900 3481 
Q 2900 3844 2670 4047 
Q 2441 4250 2034 4250 
Q 1625 4250 1398 4047 
Q 1172 3844 1172 3481 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-38"/>
      </g>
     </g>
    </g>
    <g id="xtick_6">
     <g id="line2d_6">
      <g>
       <use xlink:href="#m6a14c3abda" x="398.487273" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_6">
      <!-- 10 -->
      <g transform="translate(392.124773 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-31" d="M 794 531 
L 1825 531 
L 1825 4091 
L 703 3866 
L 703 4441 
L 1819 4666 
L 2450 4666 
L 2450 531 
L 3481 531 
L 3481 0 
L 794 0 
L 794 531 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-31"/>
       <use xlink:href="#DejaVuSans-30" x="63.623047"/>
      </g>
     </g>
    </g>
   </g>
   <g id="matplotlib.axis_2">
    <g id="ytick_1">
     <g id="line2d_7">
      <defs>
       <path id="m0e7a760f5e" d="M 0 0 
L -3.5 0 
" style="stroke: #000000; stroke-width: 0.8"/>
      </defs>
      <g>
       <use xlink:href="#m0e7a760f5e" x="57.6" y="295.562467" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_7">
      <!-- −1.00 -->
      <g transform="translate(19.954687 299.361686) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-2212" d="M 678 2272 
L 4684 2272 
L 4684 1741 
L 678 1741 
L 678 2272 
z
" transform="scale(0.015625)"/>
        <path id="DejaVuSans-2e" d="M 684 794 
L 1344 794 
L 1344 0 
L 684 0 
L 684 794 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-2212"/>
       <use xlink:href="#DejaVuSans-31" x="83.789062"/>
       <use xlink:href="#DejaVuSans-2e" x="147.412109"/>
       <use xlink:href="#DejaVuSans-30" x="179.199219"/>
       <use xlink:href="#DejaVuSans-30" x="242.822266"/>
      </g>
     </g>
    </g>
    <g id="ytick_2">
     <g id="line2d_8">
      <g>
       <use xlink:href="#m0e7a760f5e" x="57.6" y="265.313158" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_8">
      <!-- −0.75 -->
      <g transform="translate(19.954687 269.112377) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-37" d="M 525 4666 
L 3525 4666 
L 3525 4397 
L 1831 0 
L 1172 0 
L 2766 4134 
L 525 4134 
L 525 4666 
z
" transform="scale(0.015625)"/>
        <path id="DejaVuSans-35" d="M 691 4666 
L 3169 4666 
L 3169 4134 
L 1269 4134 
L 1269 2991 
Q 1406 3038 1543 3061 
Q 1681 3084 1819 3084 
Q 2600 3084 3056 2656 
Q 3513 2228 3513 1497 
Q 3513 744 3044 326 
Q 2575 -91 1722 -91 
Q 1428 -91 1123 -41 
Q 819 9 494 109 
L 494 744 
Q 775 591 1075 516 
Q 1375 441 1709 441 
Q 2250 441 2565 725 
Q 2881 1009 2881 1497 
Q 2881 1984 2565 2268 
Q 2250 2553 1709 2553 
Q 1456 2553 1204 2497 
Q 953 2441 691 2322 
L 691 4666 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-2212"/>
       <use xlink:href="#DejaVuSans-30" x="83.789062"/>
       <use xlink:href="#DejaVuSans-2e" x="147.412109"/>
       <use xlink:href="#DejaVuSans-37" x="179.199219"/>
       <use xlink:href="#DejaVuSans-35" x="242.822266"/>
      </g>
     </g>
    </g>
    <g id="ytick_3">
     <g id="line2d_9">
      <g>
       <use xlink:href="#m0e7a760f5e" x="57.6" y="235.06385" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_9">
      <!-- −0.50 -->
      <g transform="translate(19.954687 238.863069) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-2212"/>
       <use xlink:href="#DejaVuSans-30" x="83.789062"/>
       <use xlink:href="#DejaVuSans-2e" x="147.412109"/>
       <use xlink:href="#DejaVuSans-35" x="179.199219"/>
       <use xlink:href="#DejaVuSans-30" x="242.822266"/>
      </g>
     </g>
    </g>
    <g id="ytick_4">
     <g id="line2d_10">
      <g>
       <use xlink:href="#m0e7a760f5e" x="57.6" y="204.814542" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_10">
      <!-- −0.25 -->
      <g transform="translate(19.954687 208.613761) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-2212"/>
       <use xlink:href="#DejaVuSans-30" x="83.789062"/>
       <use xlink:href="#DejaVuSans-2e" x="147.412109"/>
       <use xlink:href="#DejaVuSans-32" x="179.199219"/>
       <use xlink:href="#DejaVuSans-35" x="242.822266"/>
      </g>
     </g>
    </g>
    <g id="ytick_5">
     <g id="line2d_11">
      <g>
       <use xlink:href="#m0e7a760f5e" x="57.6" y="174.565233" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_11">
      <!-- 0.00 -->
      <g transform="translate(28.334375 178.364452) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-30"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-30" x="95.410156"/>
       <use xlink:href="#DejaVuSans-30" x="159.033203"/>
      </g>
     </g>
    </g>
    <g id="ytick_6">
     <g id="line2d_12">
      <g>
       <use xlink:href="#m0e7a760f5e" x="57.6" y="144.315925" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_12">
      <!-- 0.25 -->
      <g transform="translate(28.334375 148.115144) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-30"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-32" x="95.410156"/>
       <use xlink:href="#DejaVuSans-35" x="159.033203"/>
      </g>
     </g>
    </g>
    <g id="ytick_7">
     <g id="line2d_13">
      <g>
       <use xlink:href="#m0e7a760f5e" x="57.6" y="114.066617" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_13">
      <!-- 0.50 -->
      <g transform="translate(28.334375 117.865835) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-30"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-35" x="95.410156"/>
       <use xlink:href="#DejaVuSans-30" x="159.033203"/>
      </g>
     </g>
    </g>
    <g id="ytick_8">
     <g id="line2d_14">
      <g>
       <use xlink:href="#m0e7a760f5e" x="57.6" y="83.817308" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_14">
      <!-- 0.75 -->
      <g transform="translate(28.334375 87.616527) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-30"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-37" x="95.410156"/>
       <use xlink:href="#DejaVuSans-35" x="159.033203"/>
      </g>
     </g>
    </g>
    <g id="ytick_9">
     <g id="line2d_15">
      <g>
       <use xlink:href="#m0e7a760f5e" x="57.6" y="53.568" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_15">
      <!-- 1.00 -->
      <g transform="translate(28.334375 57.367219) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-31"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-30" x="95.410156"/>
       <use xlink:href="#DejaVuSans-30" x="159.033203"/>
      </g>
     </g>
    </g>
   </g>
   <g id="line2d_16">
    <path d="M 73.832727 174.565233 
L 77.112066 162.364064 
L 80.391405 150.287277 
L 83.670744 138.457989 
L 86.950083 126.996791 
L 90.229421 116.020524 
L 93.50876 105.641082 
L 96.788099 95.964279 
L 100.067438 87.088764 
L 103.346777 79.105015 
L 106.626116 72.094423 
L 109.905455 66.128456 
L 113.184793 61.267934 
L 116.464132 57.562406 
L 119.743471 55.049648 
L 123.02281 53.755276 
L 126.302149 53.692485 
L 129.581488 54.861916 
L 132.860826 57.251646 
L 136.140165 60.837314 
L 139.419504 65.582366 
L 142.698843 71.43843 
L 145.978182 78.345807 
L 149.257521 86.234079 
L 152.53686 95.022832 
L 155.816198 104.62247 
L 159.095537 114.93513 
L 162.374876 125.855681 
L 165.654215 137.272795 
L 168.933554 149.070082 
L 172.212893 161.127276 
L 175.492231 173.321462 
L 178.77157 185.528327 
L 182.050909 197.62343 
L 185.330248 209.483469 
L 188.609587 220.987539 
L 191.888926 232.018363 
L 195.168264 242.463489 
L 198.447603 252.216435 
L 201.726942 261.177775 
L 205.006281 269.256156 
L 208.28562 276.369223 
L 211.564959 282.444462 
L 214.844298 287.419941 
L 218.123636 291.244937 
L 221.402975 293.880457 
L 224.682314 295.299634 
L 227.961653 295.488 
L 231.240992 294.443635 
L 234.520331 292.177185 
L 237.799669 288.711756 
L 241.079008 284.082675 
L 244.358347 278.337133 
L 247.637686 271.533702 
L 250.917025 263.741738 
L 254.196364 255.040677 
L 257.475702 245.519219 
L 260.755041 235.27443 
L 264.03438 224.410749 
L 267.313719 213.038925 
L 270.593058 201.274886 
L 273.872397 189.238558 
L 277.151736 177.052646 
L 280.431074 164.841375 
L 283.710413 152.729234 
L 286.989752 140.839696 
L 290.269091 129.29397 
L 293.54843 118.209755 
L 296.827769 107.700048 
L 300.107107 97.87199 
L 303.386446 88.825771 
L 306.665785 80.653612 
L 309.945124 73.438822 
L 313.224463 67.254953 
L 316.503802 62.165043 
L 319.78314 58.220983 
L 323.062479 55.462979 
L 326.341818 53.919147 
L 329.621157 53.605226 
L 332.900496 54.524416 
L 336.179835 56.667345 
L 339.459174 60.01217 
L 342.738512 64.52479 
L 346.017851 70.159204 
L 349.29719 76.85797 
L 352.576529 84.552801 
L 355.855868 93.165252 
L 359.135207 102.607524 
L 362.414545 112.783359 
L 365.693884 123.589021 
L 368.973223 134.914354 
L 372.252562 146.643903 
L 375.531901 158.658092 
L 378.81124 170.834444 
L 382.090579 183.048829 
L 385.369917 195.176729 
L 388.649256 207.094508 
L 391.928595 218.680671 
L 395.207934 229.817106 
L 398.487273 240.390283 
" clip-path="url(#p4450055c37)" style="fill: none; stroke: #1f77b4; stroke-width: 1.5; stroke-linecap: square"/>
   </g>
   <g id="line2d_17">
    <path d="M 73.832727 53.568 
L 77.112066 65.192942 
L 80.391405 75.701005 
L 83.670744 85.199494 
L 86.950083 93.785406 
L 90.229421 101.546416 
L 93.50876 108.561779 
L 96.788099 114.903134 
L 100.067438 120.635235 
L 103.346777 125.816619 
L 106.626116 130.500196 
L 109.905455 134.733793 
L 113.184793 138.560642 
L 116.464132 142.019823 
L 119.743471 145.146659 
L 123.02281 147.973081 
L 126.302149 150.527951 
L 129.581488 152.837359 
L 132.860826 154.924889 
L 136.140165 156.811856 
L 139.419504 158.517531 
L 142.698843 160.059332 
L 145.978182 161.453002 
L 149.257521 162.712774 
L 152.53686 163.851512 
L 155.816198 164.880845 
L 159.095537 165.811283 
L 162.374876 166.652329 
L 165.654215 167.41257 
L 168.933554 168.09977 
L 172.212893 168.720946 
L 175.492231 169.282442 
L 178.77157 169.789992 
L 182.050909 170.248779 
L 185.330248 170.663487 
L 188.609587 171.038352 
L 191.888926 171.377201 
L 195.168264 171.683494 
L 198.447603 171.960361 
L 201.726942 172.210627 
L 205.006281 172.436848 
L 208.28562 172.641335 
L 211.564959 172.826176 
L 214.844298 172.993258 
L 218.123636 173.144287 
L 221.402975 173.280806 
L 224.682314 173.404209 
L 227.961653 173.515755 
L 231.240992 173.616585 
L 234.520331 173.707728 
L 237.799669 173.790113 
L 241.079008 173.864584 
L 244.358347 173.9319 
L 247.637686 173.992748 
L 250.917025 174.04775 
L 254.196364 174.097468 
L 257.475702 174.142409 
L 260.755041 174.183032 
L 264.03438 174.219753 
L 267.313719 174.252945 
L 270.593058 174.282948 
L 273.872397 174.310069 
L 277.151736 174.334585 
L 280.431074 174.356744 
L 283.710413 174.376775 
L 286.989752 174.394881 
L 290.269091 174.411248 
L 293.54843 174.426043 
L 296.827769 174.439415 
L 300.107107 174.451504 
L 303.386446 174.46243 
L 306.665785 174.472307 
L 309.945124 174.481235 
L 313.224463 174.489305 
L 316.503802 174.4966 
L 319.78314 174.503194 
L 323.062479 174.509155 
L 326.341818 174.514543 
L 329.621157 174.519413 
L 332.900496 174.523815 
L 336.179835 174.527794 
L 339.459174 174.531391 
L 342.738512 174.534643 
L 346.017851 174.537582 
L 349.29719 174.540238 
L 352.576529 174.54264 
L 355.855868 174.544811 
L 359.135207 174.546773 
L 362.414545 174.548546 
L 365.693884 174.55015 
L 368.973223 174.551599 
L 372.252562 174.552909 
L 375.531901 174.554093 
L 378.81124 174.555163 
L 382.090579 174.556131 
L 385.369917 174.557005 
L 388.649256 174.557796 
L 391.928595 174.55851 
L 395.207934 174.559156 
L 398.487273 174.55974 
" clip-path="url(#p4450055c37)" style="fill: none; stroke: #ff7f0e; stroke-width: 1.5; stroke-linecap: square"/>
   </g>
   <g id="patch_3">
    <path d="M 57.6 307.584 
L 57.6 41.472 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
   <g id="patch_4">
    <path d="M 414.72 307.584 
L 414.72 41.472 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
   <g id="patch_5">
    <path d="M 57.6 307.584 
L 414.72 307.584 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
   <g id="patch_6">
    <path d="M 57.6 41.472 
L 414.72 41.472 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
   <g id="legend_1">
    <g id="patch_7">
     <path d="M 357.32 79.668875 
L 407.72 79.668875 
Q 409.72 79.668875 409.72 77.668875 
L 409.72 48.472 
Q 409.72 46.472 407.72 46.472 
L 357.32 46.472 
Q 355.32 46.472 355.32 48.472 
L 355.32 77.668875 
Q 355.32 79.668875 357.32 79.668875 
z
" style="fill: #ffffff; opacity: 0.8; stroke: #cccccc; stroke-linejoin: miter"/>
    </g>
    <g id="line2d_18">
     <path d="M 359.32 54.570438 
L 369.32 54.570438 
L 379.32 54.570438 
" style="fill: none; stroke: #1f77b4; stroke-width: 1.5; stroke-linecap: square"/>
    </g>
    <g id="text_16">
     <!-- $f(x)$ -->
     <g transform="translate(387.32 58.070438) scale(0.1 -0.1)">
      <defs>
       <path id="Cmmi10-66" d="M 622 -1056 
Q 741 -1147 909 -1147 
Q 1138 -1147 1281 -641 
Q 1341 -397 1606 966 
L 1900 2534 
L 1350 2534 
Q 1288 2534 1288 2619 
Q 1313 2759 1369 2759 
L 1941 2759 
L 2016 3175 
Q 2053 3369 2084 3508 
Q 2116 3647 2152 3765 
Q 2188 3884 2259 4031 
Q 2369 4241 2555 4377 
Q 2741 4513 2956 4513 
Q 3097 4513 3230 4461 
Q 3363 4409 3447 4306 
Q 3531 4203 3531 4063 
Q 3531 3900 3423 3779 
Q 3316 3659 3163 3659 
Q 3059 3659 2986 3723 
Q 2913 3788 2913 3891 
Q 2913 4031 3008 4136 
Q 3103 4241 3244 4256 
Q 3125 4347 2950 4347 
Q 2853 4347 2767 4256 
Q 2681 4166 2656 4063 
Q 2616 3900 2478 3181 
L 2400 2759 
L 3059 2759 
Q 3122 2759 3122 2675 
Q 3119 2659 3109 2620 
Q 3100 2581 3083 2557 
Q 3066 2534 3041 2534 
L 2356 2534 
L 2059 972 
Q 2003 631 1929 279 
Q 1856 -72 1723 -442 
Q 1591 -813 1384 -1063 
Q 1178 -1313 897 -1313 
Q 681 -1313 511 -1189 
Q 341 -1066 341 -863 
Q 341 -700 445 -579 
Q 550 -459 709 -459 
Q 816 -459 887 -523 
Q 959 -588 959 -691 
Q 959 -828 857 -942 
Q 756 -1056 622 -1056 
z
" transform="scale(0.015625)"/>
       <path id="Cmr10-28" d="M 1984 -1588 
Q 1628 -1306 1370 -942 
Q 1113 -578 948 -165 
Q 784 247 703 697 
Q 622 1147 622 1600 
Q 622 2059 703 2509 
Q 784 2959 951 3375 
Q 1119 3791 1378 4153 
Q 1638 4516 1984 4788 
Q 1984 4800 2016 4800 
L 2075 4800 
Q 2094 4800 2109 4783 
Q 2125 4766 2125 4744 
Q 2125 4716 2113 4703 
Q 1800 4397 1592 4047 
Q 1384 3697 1257 3301 
Q 1131 2906 1075 2482 
Q 1019 2059 1019 1600 
Q 1019 -434 2106 -1491 
Q 2125 -1509 2125 -1544 
Q 2125 -1559 2108 -1579 
Q 2091 -1600 2075 -1600 
L 2016 -1600 
Q 1984 -1600 1984 -1588 
z
" transform="scale(0.015625)"/>
       <path id="Cmmi10-78" d="M 500 184 
Q 613 97 819 97 
Q 1019 97 1172 289 
Q 1325 481 1381 709 
L 1672 1844 
Q 1741 2153 1741 2266 
Q 1741 2425 1652 2544 
Q 1563 2663 1403 2663 
Q 1200 2663 1022 2536 
Q 844 2409 722 2214 
Q 600 2019 550 1819 
Q 538 1778 500 1778 
L 422 1778 
Q 372 1778 372 1838 
L 372 1856 
Q 434 2094 584 2320 
Q 734 2547 951 2687 
Q 1169 2828 1416 2828 
Q 1650 2828 1839 2703 
Q 2028 2578 2106 2363 
Q 2216 2559 2386 2693 
Q 2556 2828 2759 2828 
Q 2897 2828 3040 2779 
Q 3184 2731 3275 2631 
Q 3366 2531 3366 2381 
Q 3366 2219 3261 2101 
Q 3156 1984 2994 1984 
Q 2891 1984 2822 2050 
Q 2753 2116 2753 2216 
Q 2753 2350 2845 2451 
Q 2938 2553 3066 2572 
Q 2950 2663 2747 2663 
Q 2541 2663 2389 2472 
Q 2238 2281 2175 2047 
L 1894 916 
Q 1825 659 1825 494 
Q 1825 331 1917 214 
Q 2009 97 2163 97 
Q 2463 97 2698 361 
Q 2934 625 3009 941 
Q 3022 978 3059 978 
L 3138 978 
Q 3163 978 3178 961 
Q 3194 944 3194 922 
Q 3194 916 3188 903 
Q 3097 522 2806 225 
Q 2516 -72 2150 -72 
Q 1916 -72 1727 54 
Q 1538 181 1459 397 
Q 1359 209 1182 68 
Q 1006 -72 806 -72 
Q 669 -72 523 -23 
Q 378 25 287 125 
Q 197 225 197 378 
Q 197 528 301 651 
Q 406 775 563 775 
Q 669 775 741 711 
Q 813 647 813 544 
Q 813 409 723 309 
Q 634 209 500 184 
z
" transform="scale(0.015625)"/>
       <path id="Cmr10-29" d="M 416 -1600 
Q 359 -1600 359 -1544 
Q 359 -1516 372 -1503 
Q 1466 -434 1466 1600 
Q 1466 3634 384 4691 
Q 359 4706 359 4744 
Q 359 4766 376 4783 
Q 394 4800 416 4800 
L 475 4800 
Q 494 4800 506 4788 
Q 966 4425 1272 3906 
Q 1578 3388 1720 2800 
Q 1863 2213 1863 1600 
Q 1863 1147 1786 708 
Q 1709 269 1542 -157 
Q 1375 -584 1119 -945 
Q 863 -1306 506 -1588 
Q 494 -1600 475 -1600 
L 416 -1600 
z
" transform="scale(0.015625)"/>
      </defs>
      <use xlink:href="#Cmmi10-66"/>
      <use xlink:href="#Cmr10-28" transform="translate(48.876953 0)"/>
      <use xlink:href="#Cmmi10-78" transform="translate(87.695312 0)"/>
      <use xlink:href="#Cmr10-29" transform="translate(144.775391 0)"/>
     </g>
    </g>
    <g id="line2d_19">
     <path d="M 359.32 69.668875 
L 369.32 69.668875 
L 379.32 69.668875 
" style="fill: none; stroke: #ff7f0e; stroke-width: 1.5; stroke-linecap: square"/>
    </g>
    <g id="text_17">
     <!-- $g(x)$ -->
     <g transform="translate(387.32 73.168875) scale(0.1 -0.1)">
      <defs>
       <path id="Cmmi10-67" d="M 91 -916 
Q 91 -759 198 -642 
Q 306 -525 459 -525 
Q 563 -525 633 -589 
Q 703 -653 703 -756 
Q 703 -872 637 -964 
Q 572 -1056 469 -1094 
Q 641 -1147 1006 -1147 
Q 1300 -1147 1544 -920 
Q 1788 -694 1863 -397 
L 2047 353 
Q 1700 0 1325 0 
Q 1050 0 854 140 
Q 659 281 556 515 
Q 453 750 453 1013 
Q 453 1306 573 1628 
Q 694 1950 911 2225 
Q 1128 2500 1409 2664 
Q 1691 2828 2003 2828 
Q 2191 2828 2341 2725 
Q 2491 2622 2578 2450 
Q 2641 2700 2853 2700 
Q 2934 2700 2990 2651 
Q 3047 2603 3047 2522 
Q 3047 2503 3045 2493 
Q 3044 2484 3041 2472 
L 2309 -434 
Q 2259 -634 2125 -800 
Q 1991 -966 1809 -1077 
Q 1628 -1188 1412 -1250 
Q 1197 -1313 997 -1313 
Q 631 -1313 361 -1242 
Q 91 -1172 91 -916 
z
M 1338 166 
Q 1747 166 2144 728 
L 2497 2125 
Q 2453 2347 2322 2505 
Q 2191 2663 1991 2663 
Q 1778 2663 1589 2489 
Q 1400 2316 1275 2075 
Q 1156 1844 1045 1411 
Q 934 978 934 728 
Q 934 509 1034 337 
Q 1134 166 1338 166 
z
" transform="scale(0.015625)"/>
      </defs>
      <use xlink:href="#Cmmi10-67"/>
      <use xlink:href="#Cmr10-28" transform="translate(47.705078 0)"/>
      <use xlink:href="#Cmmi10-78" transform="translate(86.523438 0)"/>
      <use xlink:href="#Cmr10-29" transform="translate(143.603516 0)"/>
     </g>
    </g>
   </g>
  </g>
 </g>
 <defs>
  <clipPath id="p4450055c37">
   <rect x="57.6" y="41.472" width="357.12" height="266.112"/>
  </clipPath>
 </defs>
</svg>
\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"fig = plot([$f(x) = \\\\sin(x)$, $g(x)=\\\\exp(-x)$], {$x$: (0,10)});\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 17402600765077350048,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 2931752801707606260,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"image_svg\",\n\t\t\t\t\t\"source\": \"<?xml version="1.0" encoding="utf-8" standalone="no"?>
<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
  "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="460.8pt" height="345.6pt" viewBox="0 0 460.8 345.6" xmlns="http://www.w3.org/2000/svg" version="1.1">
 <metadata>
  <rdf:RDF xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:cc="http://creativecommons.org/ns#" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
   <cc:Work>
    <dc:type rdf:resource="http://purl.org/dc/dcmitype/StillImage"/>
    <dc:date>2025-03-29T11:12:21.646002</dc:date>
    <dc:format>image/svg+xml</dc:format>
    <dc:creator>
     <cc:Agent>
      <dc:title>Matplotlib v3.6.3, https://matplotlib.org/</dc:title>
     </cc:Agent>
    </dc:creator>
   </cc:Work>
  </rdf:RDF>
 </metadata>
 <defs>
  <style type="text/css">*{stroke-linejoin: round; stroke-linecap: butt}</style>
 </defs>
 <g id="figure_1">
  <g id="patch_1">
   <path d="M 0 345.6 
L 460.8 345.6 
L 460.8 0 
L 0 0 
z
" style="fill: #ffffff"/>
  </g>
  <g id="axes_1">
   <g id="patch_2">
    <path d="M 57.6 307.584 
L 414.72 307.584 
L 414.72 41.472 
L 57.6 41.472 
z
" style="fill: #ffffff"/>
   </g>
   <g id="matplotlib.axis_1">
    <g id="xtick_1">
     <g id="line2d_1">
      <defs>
       <path id="maa1effdc9b" d="M 0 0 
L 0 3.5 
" style="stroke: #000000; stroke-width: 0.8"/>
      </defs>
      <g>
       <use xlink:href="#maa1effdc9b" x="73.832727" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_1">
      <!-- 0 -->
      <g transform="translate(70.651477 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-30" d="M 2034 4250 
Q 1547 4250 1301 3770 
Q 1056 3291 1056 2328 
Q 1056 1369 1301 889 
Q 1547 409 2034 409 
Q 2525 409 2770 889 
Q 3016 1369 3016 2328 
Q 3016 3291 2770 3770 
Q 2525 4250 2034 4250 
z
M 2034 4750 
Q 2819 4750 3233 4129 
Q 3647 3509 3647 2328 
Q 3647 1150 3233 529 
Q 2819 -91 2034 -91 
Q 1250 -91 836 529 
Q 422 1150 422 2328 
Q 422 3509 836 4129 
Q 1250 4750 2034 4750 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-30"/>
      </g>
     </g>
    </g>
    <g id="xtick_2">
     <g id="line2d_2">
      <g>
       <use xlink:href="#maa1effdc9b" x="138.763636" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_2">
      <!-- 2 -->
      <g transform="translate(135.582386 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-32" d="M 1228 531 
L 3431 531 
L 3431 0 
L 469 0 
L 469 531 
Q 828 903 1448 1529 
Q 2069 2156 2228 2338 
Q 2531 2678 2651 2914 
Q 2772 3150 2772 3378 
Q 2772 3750 2511 3984 
Q 2250 4219 1831 4219 
Q 1534 4219 1204 4116 
Q 875 4013 500 3803 
L 500 4441 
Q 881 4594 1212 4672 
Q 1544 4750 1819 4750 
Q 2544 4750 2975 4387 
Q 3406 4025 3406 3419 
Q 3406 3131 3298 2873 
Q 3191 2616 2906 2266 
Q 2828 2175 2409 1742 
Q 1991 1309 1228 531 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-32"/>
      </g>
     </g>
    </g>
    <g id="xtick_3">
     <g id="line2d_3">
      <g>
       <use xlink:href="#maa1effdc9b" x="203.694545" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_3">
      <!-- 4 -->
      <g transform="translate(200.513295 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-34" d="M 2419 4116 
L 825 1625 
L 2419 1625 
L 2419 4116 
z
M 2253 4666 
L 3047 4666 
L 3047 1625 
L 3713 1625 
L 3713 1100 
L 3047 1100 
L 3047 0 
L 2419 0 
L 2419 1100 
L 313 1100 
L 313 1709 
L 2253 4666 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-34"/>
      </g>
     </g>
    </g>
    <g id="xtick_4">
     <g id="line2d_4">
      <g>
       <use xlink:href="#maa1effdc9b" x="268.625455" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_4">
      <!-- 6 -->
      <g transform="translate(265.444205 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-36" d="M 2113 2584 
Q 1688 2584 1439 2293 
Q 1191 2003 1191 1497 
Q 1191 994 1439 701 
Q 1688 409 2113 409 
Q 2538 409 2786 701 
Q 3034 994 3034 1497 
Q 3034 2003 2786 2293 
Q 2538 2584 2113 2584 
z
M 3366 4563 
L 3366 3988 
Q 3128 4100 2886 4159 
Q 2644 4219 2406 4219 
Q 1781 4219 1451 3797 
Q 1122 3375 1075 2522 
Q 1259 2794 1537 2939 
Q 1816 3084 2150 3084 
Q 2853 3084 3261 2657 
Q 3669 2231 3669 1497 
Q 3669 778 3244 343 
Q 2819 -91 2113 -91 
Q 1303 -91 875 529 
Q 447 1150 447 2328 
Q 447 3434 972 4092 
Q 1497 4750 2381 4750 
Q 2619 4750 2861 4703 
Q 3103 4656 3366 4563 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-36"/>
      </g>
     </g>
    </g>
    <g id="xtick_5">
     <g id="line2d_5">
      <g>
       <use xlink:href="#maa1effdc9b" x="333.556364" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_5">
      <!-- 8 -->
      <g transform="translate(330.375114 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-38" d="M 2034 2216 
Q 1584 2216 1326 1975 
Q 1069 1734 1069 1313 
Q 1069 891 1326 650 
Q 1584 409 2034 409 
Q 2484 409 2743 651 
Q 3003 894 3003 1313 
Q 3003 1734 2745 1975 
Q 2488 2216 2034 2216 
z
M 1403 2484 
Q 997 2584 770 2862 
Q 544 3141 544 3541 
Q 544 4100 942 4425 
Q 1341 4750 2034 4750 
Q 2731 4750 3128 4425 
Q 3525 4100 3525 3541 
Q 3525 3141 3298 2862 
Q 3072 2584 2669 2484 
Q 3125 2378 3379 2068 
Q 3634 1759 3634 1313 
Q 3634 634 3220 271 
Q 2806 -91 2034 -91 
Q 1263 -91 848 271 
Q 434 634 434 1313 
Q 434 1759 690 2068 
Q 947 2378 1403 2484 
z
M 1172 3481 
Q 1172 3119 1398 2916 
Q 1625 2713 2034 2713 
Q 2441 2713 2670 2916 
Q 2900 3119 2900 3481 
Q 2900 3844 2670 4047 
Q 2441 4250 2034 4250 
Q 1625 4250 1398 4047 
Q 1172 3844 1172 3481 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-38"/>
      </g>
     </g>
    </g>
    <g id="xtick_6">
     <g id="line2d_6">
      <g>
       <use xlink:href="#maa1effdc9b" x="398.487273" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_6">
      <!-- 10 -->
      <g transform="translate(392.124773 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-31" d="M 794 531 
L 1825 531 
L 1825 4091 
L 703 3866 
L 703 4441 
L 1819 4666 
L 2450 4666 
L 2450 531 
L 3481 531 
L 3481 0 
L 794 0 
L 794 531 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-31"/>
       <use xlink:href="#DejaVuSans-30" x="63.623047"/>
      </g>
     </g>
    </g>
   </g>
   <g id="matplotlib.axis_2">
    <g id="ytick_1">
     <g id="line2d_7">
      <defs>
       <path id="m9ad2ba09c1" d="M 0 0 
L -3.5 0 
" style="stroke: #000000; stroke-width: 0.8"/>
      </defs>
      <g>
       <use xlink:href="#m9ad2ba09c1" x="57.6" y="295.494391" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_7">
      <!-- −1.00 -->
      <g transform="translate(19.954687 299.29361) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-2212" d="M 678 2272 
L 4684 2272 
L 4684 1741 
L 678 1741 
L 678 2272 
z
" transform="scale(0.015625)"/>
        <path id="DejaVuSans-2e" d="M 684 794 
L 1344 794 
L 1344 0 
L 684 0 
L 684 794 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-2212"/>
       <use xlink:href="#DejaVuSans-31" x="83.789062"/>
       <use xlink:href="#DejaVuSans-2e" x="147.412109"/>
       <use xlink:href="#DejaVuSans-30" x="179.199219"/>
       <use xlink:href="#DejaVuSans-30" x="242.822266"/>
      </g>
     </g>
    </g>
    <g id="ytick_2">
     <g id="line2d_8">
      <g>
       <use xlink:href="#m9ad2ba09c1" x="57.6" y="265.253592" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_8">
      <!-- −0.75 -->
      <g transform="translate(19.954687 269.052811) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-37" d="M 525 4666 
L 3525 4666 
L 3525 4397 
L 1831 0 
L 1172 0 
L 2766 4134 
L 525 4134 
L 525 4666 
z
" transform="scale(0.015625)"/>
        <path id="DejaVuSans-35" d="M 691 4666 
L 3169 4666 
L 3169 4134 
L 1269 4134 
L 1269 2991 
Q 1406 3038 1543 3061 
Q 1681 3084 1819 3084 
Q 2600 3084 3056 2656 
Q 3513 2228 3513 1497 
Q 3513 744 3044 326 
Q 2575 -91 1722 -91 
Q 1428 -91 1123 -41 
Q 819 9 494 109 
L 494 744 
Q 775 591 1075 516 
Q 1375 441 1709 441 
Q 2250 441 2565 725 
Q 2881 1009 2881 1497 
Q 2881 1984 2565 2268 
Q 2250 2553 1709 2553 
Q 1456 2553 1204 2497 
Q 953 2441 691 2322 
L 691 4666 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-2212"/>
       <use xlink:href="#DejaVuSans-30" x="83.789062"/>
       <use xlink:href="#DejaVuSans-2e" x="147.412109"/>
       <use xlink:href="#DejaVuSans-37" x="179.199219"/>
       <use xlink:href="#DejaVuSans-35" x="242.822266"/>
      </g>
     </g>
    </g>
    <g id="ytick_3">
     <g id="line2d_9">
      <g>
       <use xlink:href="#m9ad2ba09c1" x="57.6" y="235.012793" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_9">
      <!-- −0.50 -->
      <g transform="translate(19.954687 238.812012) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-2212"/>
       <use xlink:href="#DejaVuSans-30" x="83.789062"/>
       <use xlink:href="#DejaVuSans-2e" x="147.412109"/>
       <use xlink:href="#DejaVuSans-35" x="179.199219"/>
       <use xlink:href="#DejaVuSans-30" x="242.822266"/>
      </g>
     </g>
    </g>
    <g id="ytick_4">
     <g id="line2d_10">
      <g>
       <use xlink:href="#m9ad2ba09c1" x="57.6" y="204.771994" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_10">
      <!-- −0.25 -->
      <g transform="translate(19.954687 208.571213) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-2212"/>
       <use xlink:href="#DejaVuSans-30" x="83.789062"/>
       <use xlink:href="#DejaVuSans-2e" x="147.412109"/>
       <use xlink:href="#DejaVuSans-32" x="179.199219"/>
       <use xlink:href="#DejaVuSans-35" x="242.822266"/>
      </g>
     </g>
    </g>
    <g id="ytick_5">
     <g id="line2d_11">
      <g>
       <use xlink:href="#m9ad2ba09c1" x="57.6" y="174.531195" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_11">
      <!-- 0.00 -->
      <g transform="translate(28.334375 178.330414) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-30"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-30" x="95.410156"/>
       <use xlink:href="#DejaVuSans-30" x="159.033203"/>
      </g>
     </g>
    </g>
    <g id="ytick_6">
     <g id="line2d_12">
      <g>
       <use xlink:href="#m9ad2ba09c1" x="57.6" y="144.290397" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_12">
      <!-- 0.25 -->
      <g transform="translate(28.334375 148.089615) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-30"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-32" x="95.410156"/>
       <use xlink:href="#DejaVuSans-35" x="159.033203"/>
      </g>
     </g>
    </g>
    <g id="ytick_7">
     <g id="line2d_13">
      <g>
       <use xlink:href="#m9ad2ba09c1" x="57.6" y="114.049598" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_13">
      <!-- 0.50 -->
      <g transform="translate(28.334375 117.848816) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-30"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-35" x="95.410156"/>
       <use xlink:href="#DejaVuSans-30" x="159.033203"/>
      </g>
     </g>
    </g>
    <g id="ytick_8">
     <g id="line2d_14">
      <g>
       <use xlink:href="#m9ad2ba09c1" x="57.6" y="83.808799" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_14">
      <!-- 0.75 -->
      <g transform="translate(28.334375 87.608018) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-30"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-37" x="95.410156"/>
       <use xlink:href="#DejaVuSans-35" x="159.033203"/>
      </g>
     </g>
    </g>
    <g id="ytick_9">
     <g id="line2d_15">
      <g>
       <use xlink:href="#m9ad2ba09c1" x="57.6" y="53.568" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_15">
      <!-- 1.00 -->
      <g transform="translate(28.334375 57.367219) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-31"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-30" x="95.410156"/>
       <use xlink:href="#DejaVuSans-30" x="159.033203"/>
      </g>
     </g>
    </g>
   </g>
   <g id="line2d_16">
    <path d="M 73.832727 53.568 
L 77.112066 65.189672 
L 80.391405 75.694779 
L 83.670744 85.190596 
L 86.950083 93.774092 
L 90.229421 101.532919 
L 93.50876 108.546309 
L 96.788099 114.885879 
L 100.067438 120.616369 
L 103.346777 125.796295 
L 106.626116 130.478554 
L 109.905455 134.71096 
L 113.184793 138.536733 
L 116.464132 141.99494 
L 119.743471 145.120897 
L 123.02281 147.946523 
L 126.302149 150.500675 
L 129.581488 152.809434 
L 132.860826 154.896376 
L 136.140165 156.782813 
L 139.419504 158.488008 
L 142.698843 160.029375 
L 145.978182 161.422653 
L 149.257521 162.682071 
L 152.53686 163.820488 
L 155.816198 164.849531 
L 159.095537 165.779708 
L 162.374876 166.620517 
L 165.654215 167.380544 
L 168.933554 168.06755 
L 172.212893 168.688552 
L 175.492231 169.249891 
L 178.77157 169.757298 
L 182.050909 170.215955 
L 185.330248 170.630547 
L 188.609587 171.005306 
L 191.888926 171.34406 
L 195.168264 171.650267 
L 198.447603 171.927055 
L 201.726942 172.177251 
L 205.006281 172.403409 
L 208.28562 172.607838 
L 211.564959 172.792627 
L 214.844298 172.959662 
L 218.123636 173.110649 
L 221.402975 173.247129 
L 224.682314 173.370497 
L 227.961653 173.482013 
L 231.240992 173.582814 
L 234.520331 173.673931 
L 237.799669 173.756293 
L 241.079008 173.830743 
L 244.358347 173.89804 
L 247.637686 173.958871 
L 250.917025 174.013858 
L 254.196364 174.063561 
L 257.475702 174.10849 
L 260.755041 174.149102 
L 264.03438 174.185812 
L 267.313719 174.218995 
L 270.593058 174.24899 
L 273.872397 174.276103 
L 277.151736 174.300611 
L 280.431074 174.322765 
L 283.710413 174.34279 
L 286.989752 174.360891 
L 290.269091 174.377254 
L 293.54843 174.392044 
L 296.827769 174.405413 
L 300.107107 174.417498 
L 303.386446 174.428421 
L 306.665785 174.438295 
L 309.945124 174.447221 
L 313.224463 174.455289 
L 316.503802 174.462582 
L 319.78314 174.469174 
L 323.062479 174.475133 
L 326.341818 174.480519 
L 329.621157 174.485388 
L 332.900496 174.489789 
L 336.179835 174.493767 
L 339.459174 174.497363 
L 342.738512 174.500613 
L 346.017851 174.503552 
L 349.29719 174.506208 
L 352.576529 174.508608 
L 355.855868 174.510778 
L 359.135207 174.51274 
L 362.414545 174.514513 
L 365.693884 174.516116 
L 368.973223 174.517565 
L 372.252562 174.518874 
L 375.531901 174.520058 
L 378.81124 174.521128 
L 382.090579 174.522095 
L 385.369917 174.52297 
L 388.649256 174.52376 
L 391.928595 174.524474 
L 395.207934 174.52512 
L 398.487273 174.525704 
" clip-path="url(#p50ded04b92)" style="fill: none; stroke: #ff7f0e; stroke-width: 1.5; stroke-linecap: square"/>
   </g>
   <g id="line2d_17">
    <path d="M 73.832727 53.568 
L 77.112066 54.184572 
L 80.391405 56.028001 
L 83.670744 59.079496 
L 86.950083 63.307948 
L 90.229421 68.67025 
L 93.50876 75.111738 
L 96.788099 82.566745 
L 100.067438 90.959271 
L 103.346777 100.20376 
L 106.626116 110.20597 
L 109.905455 120.863936 
L 113.184793 132.069005 
L 116.464132 143.706949 
L 119.743471 155.659127 
L 123.02281 167.803694 
L 126.302149 180.016844 
L 129.581488 192.174071 
L 132.860826 204.151439 
L 136.140165 215.826849 
L 139.419504 227.081275 
L 142.698843 237.799986 
L 145.978182 247.873712 
L 149.257521 257.199757 
L 152.53686 265.683048 
L 155.816198 273.237104 
L 159.095537 279.784916 
L 162.374876 285.259732 
L 165.654215 289.605741 
L 168.933554 292.778638 
L 172.212893 294.746076 
L 175.492231 295.488 
L 178.77157 294.996846 
L 182.050909 293.27762 
L 185.330248 290.34785 
L 188.609587 286.237402 
L 191.888926 280.988179 
L 195.168264 274.653695 
L 198.447603 267.298526 
L 201.726942 258.997652 
L 205.006281 249.835696 
L 208.28562 239.906058 
L 211.564959 229.309965 
L 214.844298 218.155437 
L 218.123636 206.556187 
L 221.402975 194.630462 
L 224.682314 182.499839 
L 227.961653 170.28798 
L 231.240992 158.119378 
L 234.520331 146.118084 
L 237.799669 134.406443 
L 241.079008 123.10385 
L 244.358347 112.325525 
L 247.637686 102.181348 
L 250.917025 92.774732 
L 254.196364 84.201572 
L 257.475702 76.549265 
L 260.755041 69.895822 
L 264.03438 64.30907 
L 267.313719 59.845964 
L 270.593058 56.552 
L 273.872397 54.460761 
L 277.151736 53.593563 
L 280.431074 53.959248 
L 283.710413 55.554088 
L 286.989752 58.361825 
L 290.269091 62.353835 
L 293.54843 67.489422 
L 296.827769 73.716232 
L 300.107107 80.970788 
L 303.386446 89.179132 
L 306.665785 98.257587 
L 309.945124 108.113603 
L 313.224463 118.646705 
L 316.503802 129.749514 
L 319.78314 141.308843 
L 323.062479 153.206854 
L 326.341818 165.322252 
L 329.621157 177.53153 
L 332.900496 189.710222 
L 336.179835 201.734173 
L 339.459174 213.480807 
L 342.738512 224.830374 
L 346.017851 235.667173 
L 349.29719 245.880729 
L 352.576529 255.366921 
L 355.855868 264.029045 
L 359.135207 271.778794 
L 362.414545 278.537166 
L 365.693884 284.235262 
L 368.973223 288.814995 
L 372.252562 292.229677 
L 375.531901 294.444497 
L 378.81124 295.436876 
L 382.090579 295.196699 
L 385.369917 293.726413 
L 388.649256 291.041007 
L 391.928595 287.167857 
L 395.207934 282.146448 
L 398.487273 276.027969 
" clip-path="url(#p50ded04b92)" style="fill: none; stroke: #1f77b4; stroke-width: 1.5; stroke-linecap: square"/>
   </g>
   <g id="patch_3">
    <path d="M 57.6 307.584 
L 57.6 41.472 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
   <g id="patch_4">
    <path d="M 414.72 307.584 
L 414.72 41.472 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
   <g id="patch_5">
    <path d="M 57.6 307.584 
L 414.72 307.584 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
   <g id="patch_6">
    <path d="M 57.6 41.472 
L 414.72 41.472 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
   <g id="legend_1">
    <g id="patch_7">
     <path d="M 357.32 79.668875 
L 407.72 79.668875 
Q 409.72 79.668875 409.72 77.668875 
L 409.72 48.472 
Q 409.72 46.472 407.72 46.472 
L 357.32 46.472 
Q 355.32 46.472 355.32 48.472 
L 355.32 77.668875 
Q 355.32 79.668875 357.32 79.668875 
z
" style="fill: #ffffff; opacity: 0.8; stroke: #cccccc; stroke-linejoin: miter"/>
    </g>
    <g id="line2d_18">
     <path d="M 359.32 54.570438 
L 369.32 54.570438 
L 379.32 54.570438 
" style="fill: none; stroke: #ff7f0e; stroke-width: 1.5; stroke-linecap: square"/>
    </g>
    <g id="text_16">
     <!-- $g(x)$ -->
     <g transform="translate(387.32 58.070438) scale(0.1 -0.1)">
      <defs>
       <path id="Cmmi10-67" d="M 91 -916 
Q 91 -759 198 -642 
Q 306 -525 459 -525 
Q 563 -525 633 -589 
Q 703 -653 703 -756 
Q 703 -872 637 -964 
Q 572 -1056 469 -1094 
Q 641 -1147 1006 -1147 
Q 1300 -1147 1544 -920 
Q 1788 -694 1863 -397 
L 2047 353 
Q 1700 0 1325 0 
Q 1050 0 854 140 
Q 659 281 556 515 
Q 453 750 453 1013 
Q 453 1306 573 1628 
Q 694 1950 911 2225 
Q 1128 2500 1409 2664 
Q 1691 2828 2003 2828 
Q 2191 2828 2341 2725 
Q 2491 2622 2578 2450 
Q 2641 2700 2853 2700 
Q 2934 2700 2990 2651 
Q 3047 2603 3047 2522 
Q 3047 2503 3045 2493 
Q 3044 2484 3041 2472 
L 2309 -434 
Q 2259 -634 2125 -800 
Q 1991 -966 1809 -1077 
Q 1628 -1188 1412 -1250 
Q 1197 -1313 997 -1313 
Q 631 -1313 361 -1242 
Q 91 -1172 91 -916 
z
M 1338 166 
Q 1747 166 2144 728 
L 2497 2125 
Q 2453 2347 2322 2505 
Q 2191 2663 1991 2663 
Q 1778 2663 1589 2489 
Q 1400 2316 1275 2075 
Q 1156 1844 1045 1411 
Q 934 978 934 728 
Q 934 509 1034 337 
Q 1134 166 1338 166 
z
" transform="scale(0.015625)"/>
       <path id="Cmr10-28" d="M 1984 -1588 
Q 1628 -1306 1370 -942 
Q 1113 -578 948 -165 
Q 784 247 703 697 
Q 622 1147 622 1600 
Q 622 2059 703 2509 
Q 784 2959 951 3375 
Q 1119 3791 1378 4153 
Q 1638 4516 1984 4788 
Q 1984 4800 2016 4800 
L 2075 4800 
Q 2094 4800 2109 4783 
Q 2125 4766 2125 4744 
Q 2125 4716 2113 4703 
Q 1800 4397 1592 4047 
Q 1384 3697 1257 3301 
Q 1131 2906 1075 2482 
Q 1019 2059 1019 1600 
Q 1019 -434 2106 -1491 
Q 2125 -1509 2125 -1544 
Q 2125 -1559 2108 -1579 
Q 2091 -1600 2075 -1600 
L 2016 -1600 
Q 1984 -1600 1984 -1588 
z
" transform="scale(0.015625)"/>
       <path id="Cmmi10-78" d="M 500 184 
Q 613 97 819 97 
Q 1019 97 1172 289 
Q 1325 481 1381 709 
L 1672 1844 
Q 1741 2153 1741 2266 
Q 1741 2425 1652 2544 
Q 1563 2663 1403 2663 
Q 1200 2663 1022 2536 
Q 844 2409 722 2214 
Q 600 2019 550 1819 
Q 538 1778 500 1778 
L 422 1778 
Q 372 1778 372 1838 
L 372 1856 
Q 434 2094 584 2320 
Q 734 2547 951 2687 
Q 1169 2828 1416 2828 
Q 1650 2828 1839 2703 
Q 2028 2578 2106 2363 
Q 2216 2559 2386 2693 
Q 2556 2828 2759 2828 
Q 2897 2828 3040 2779 
Q 3184 2731 3275 2631 
Q 3366 2531 3366 2381 
Q 3366 2219 3261 2101 
Q 3156 1984 2994 1984 
Q 2891 1984 2822 2050 
Q 2753 2116 2753 2216 
Q 2753 2350 2845 2451 
Q 2938 2553 3066 2572 
Q 2950 2663 2747 2663 
Q 2541 2663 2389 2472 
Q 2238 2281 2175 2047 
L 1894 916 
Q 1825 659 1825 494 
Q 1825 331 1917 214 
Q 2009 97 2163 97 
Q 2463 97 2698 361 
Q 2934 625 3009 941 
Q 3022 978 3059 978 
L 3138 978 
Q 3163 978 3178 961 
Q 3194 944 3194 922 
Q 3194 916 3188 903 
Q 3097 522 2806 225 
Q 2516 -72 2150 -72 
Q 1916 -72 1727 54 
Q 1538 181 1459 397 
Q 1359 209 1182 68 
Q 1006 -72 806 -72 
Q 669 -72 523 -23 
Q 378 25 287 125 
Q 197 225 197 378 
Q 197 528 301 651 
Q 406 775 563 775 
Q 669 775 741 711 
Q 813 647 813 544 
Q 813 409 723 309 
Q 634 209 500 184 
z
" transform="scale(0.015625)"/>
       <path id="Cmr10-29" d="M 416 -1600 
Q 359 -1600 359 -1544 
Q 359 -1516 372 -1503 
Q 1466 -434 1466 1600 
Q 1466 3634 384 4691 
Q 359 4706 359 4744 
Q 359 4766 376 4783 
Q 394 4800 416 4800 
L 475 4800 
Q 494 4800 506 4788 
Q 966 4425 1272 3906 
Q 1578 3388 1720 2800 
Q 1863 2213 1863 1600 
Q 1863 1147 1786 708 
Q 1709 269 1542 -157 
Q 1375 -584 1119 -945 
Q 863 -1306 506 -1588 
Q 494 -1600 475 -1600 
L 416 -1600 
z
" transform="scale(0.015625)"/>
      </defs>
      <use xlink:href="#Cmmi10-67"/>
      <use xlink:href="#Cmr10-28" transform="translate(47.705078 0)"/>
      <use xlink:href="#Cmmi10-78" transform="translate(86.523438 0)"/>
      <use xlink:href="#Cmr10-29" transform="translate(143.603516 0)"/>
     </g>
    </g>
    <g id="line2d_19">
     <path d="M 359.32 69.668875 
L 369.32 69.668875 
L 379.32 69.668875 
" style="fill: none; stroke: #1f77b4; stroke-width: 1.5; stroke-linecap: square"/>
    </g>
    <g id="text_17">
     <!-- $f(x)$ -->
     <g transform="translate(387.32 73.168875) scale(0.1 -0.1)">
      <defs>
       <path id="Cmmi10-66" d="M 622 -1056 
Q 741 -1147 909 -1147 
Q 1138 -1147 1281 -641 
Q 1341 -397 1606 966 
L 1900 2534 
L 1350 2534 
Q 1288 2534 1288 2619 
Q 1313 2759 1369 2759 
L 1941 2759 
L 2016 3175 
Q 2053 3369 2084 3508 
Q 2116 3647 2152 3765 
Q 2188 3884 2259 4031 
Q 2369 4241 2555 4377 
Q 2741 4513 2956 4513 
Q 3097 4513 3230 4461 
Q 3363 4409 3447 4306 
Q 3531 4203 3531 4063 
Q 3531 3900 3423 3779 
Q 3316 3659 3163 3659 
Q 3059 3659 2986 3723 
Q 2913 3788 2913 3891 
Q 2913 4031 3008 4136 
Q 3103 4241 3244 4256 
Q 3125 4347 2950 4347 
Q 2853 4347 2767 4256 
Q 2681 4166 2656 4063 
Q 2616 3900 2478 3181 
L 2400 2759 
L 3059 2759 
Q 3122 2759 3122 2675 
Q 3119 2659 3109 2620 
Q 3100 2581 3083 2557 
Q 3066 2534 3041 2534 
L 2356 2534 
L 2059 972 
Q 2003 631 1929 279 
Q 1856 -72 1723 -442 
Q 1591 -813 1384 -1063 
Q 1178 -1313 897 -1313 
Q 681 -1313 511 -1189 
Q 341 -1066 341 -863 
Q 341 -700 445 -579 
Q 550 -459 709 -459 
Q 816 -459 887 -523 
Q 959 -588 959 -691 
Q 959 -828 857 -942 
Q 756 -1056 622 -1056 
z
" transform="scale(0.015625)"/>
      </defs>
      <use xlink:href="#Cmmi10-66"/>
      <use xlink:href="#Cmr10-28" transform="translate(48.876953 0)"/>
      <use xlink:href="#Cmmi10-78" transform="translate(87.695312 0)"/>
      <use xlink:href="#Cmr10-29" transform="translate(144.775391 0)"/>
     </g>
    </g>
   </g>
  </g>
 </g>
 <defs>
  <clipPath id="p50ded04b92">
   <rect x="57.6" y="41.472" width="357.12" height="266.112"/>
  </clipPath>
 </defs>
</svg>
\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"plot($f(x) = \\\\cos(x)$, {$x$: (0,10)}, fig=fig);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 16274478212373847927,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 675519595055918749,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\subsection*{Parametric plots in two dimensions}\\n\\nIf you have a parametric representation of the curve you want to plot, there is a function \\\\verb|parametric_plot|, which\\ntakes two arguments (or two lists of arguments). In the example below, we plot two parametric curves. \\nThe first argument is a list of two functions (of the parameter $t$) for the\\n$x$-coordinates, while the second argument is a list of two functions for the $y$-coordinates. In order to make this\\nmore readable, we have defined the functions as Cadabra expressions on separate lines.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\subsection*{Parametric plots in two dimensions}\\n\\nIf you have a parametric representation of the curve you want to plot, there is a function \\\\verb|parametric_plot|, which\\ntakes two arguments (or two lists of arguments). In the example below, we plot two parametric curves. \\nThe first argument is a list of two functions (of the parameter $t$) for the\\n$x$-coordinates, while the second argument is a list of two functions for the $y$-coordinates. In order to make this\\nmore readable, we have defined the functions as Cadabra expressions on separate lines.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 3758995290689034713,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9039728432500162662,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 1140056443058803633,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"(1 -  1/400 (t)**2) \\\\cos(t)\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\left(1\\\\discretionary{}{}{} - \\\\frac{1}{400}\\\\,{t}^{2\\\\,}\\\\right) \\\\cos{t}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 4506613056439518545,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 7191835543365033549,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"(1 -  1/400 (t)**2) \\\\sin(t)\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\left(1\\\\discretionary{}{}{} - \\\\frac{1}{400}\\\\,{t}^{2\\\\,}\\\\right) \\\\sin{t}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 833073951727972065,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 10254937918231982108,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"1.2\\\\cos(t)\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}1.2\\\\,\\\\cos{t}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 15711806883521750330,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 5077683621178507428,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"1.2\\\\sin(t)\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}1.2\\\\,\\\\sin{t}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 11980889046600405701,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"image_svg\",\n\t\t\t\t\t\"source\": \"<?xml version="1.0" encoding="utf-8" standalone="no"?>
<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
  "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="460.8pt" height="345.6pt" viewBox="0 0 460.8 345.6" xmlns="http://www.w3.org/2000/svg" version="1.1">
 <metadata>
  <rdf:RDF xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:cc="http://creativecommons.org/ns#" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
   <cc:Work>
    <dc:type rdf:resource="http://purl.org/dc/dcmitype/StillImage"/>
    <dc:date>2025-03-29T11:07:05.813230</dc:date>
    <dc:format>image/svg+xml</dc:format>
    <dc:creator>
     <cc:Agent>
      <dc:title>Matplotlib v3.6.3, https://matplotlib.org/</dc:title>
     </cc:Agent>
    </dc:creator>
   </cc:Work>
  </rdf:RDF>
 </metadata>
 <defs>
  <style type="text/css">*{stroke-linejoin: round; stroke-linecap: butt}</style>
 </defs>
 <g id="figure_1">
  <g id="patch_1">
   <path d="M 0 345.6 
L 460.8 345.6 
L 460.8 0 
L 0 0 
z
" style="fill: #ffffff"/>
  </g>
  <g id="axes_1">
   <g id="patch_2">
    <path d="M 103.040677 307.584 
L 369.279323 307.584 
L 369.279323 41.472 
L 103.040677 41.472 
z
" style="fill: #ffffff"/>
   </g>
   <g id="matplotlib.axis_1">
    <g id="xtick_1">
     <g id="line2d_1">
      <defs>
       <path id="m313513bb85" d="M 0 0 
L 0 3.5 
" style="stroke: #000000; stroke-width: 0.8"/>
      </defs>
      <g>
       <use xlink:href="#m313513bb85" x="135.175447" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_1">
      <!-- −1.0 -->
      <g transform="translate(123.03404 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-2212" d="M 678 2272 
L 4684 2272 
L 4684 1741 
L 678 1741 
L 678 2272 
z
" transform="scale(0.015625)"/>
        <path id="DejaVuSans-31" d="M 794 531 
L 1825 531 
L 1825 4091 
L 703 3866 
L 703 4441 
L 1819 4666 
L 2450 4666 
L 2450 531 
L 3481 531 
L 3481 0 
L 794 0 
L 794 531 
z
" transform="scale(0.015625)"/>
        <path id="DejaVuSans-2e" d="M 684 794 
L 1344 794 
L 1344 0 
L 684 0 
L 684 794 
z
" transform="scale(0.015625)"/>
        <path id="DejaVuSans-30" d="M 2034 4250 
Q 1547 4250 1301 3770 
Q 1056 3291 1056 2328 
Q 1056 1369 1301 889 
Q 1547 409 2034 409 
Q 2525 409 2770 889 
Q 3016 1369 3016 2328 
Q 3016 3291 2770 3770 
Q 2525 4250 2034 4250 
z
M 2034 4750 
Q 2819 4750 3233 4129 
Q 3647 3509 3647 2328 
Q 3647 1150 3233 529 
Q 2819 -91 2034 -91 
Q 1250 -91 836 529 
Q 422 1150 422 2328 
Q 422 3509 836 4129 
Q 1250 4750 2034 4750 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-2212"/>
       <use xlink:href="#DejaVuSans-31" x="83.789062"/>
       <use xlink:href="#DejaVuSans-2e" x="147.412109"/>
       <use xlink:href="#DejaVuSans-30" x="179.199219"/>
      </g>
     </g>
    </g>
    <g id="xtick_2">
     <g id="line2d_2">
      <g>
       <use xlink:href="#m313513bb85" x="185.630474" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_2">
      <!-- −0.5 -->
      <g transform="translate(173.489068 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-35" d="M 691 4666 
L 3169 4666 
L 3169 4134 
L 1269 4134 
L 1269 2991 
Q 1406 3038 1543 3061 
Q 1681 3084 1819 3084 
Q 2600 3084 3056 2656 
Q 3513 2228 3513 1497 
Q 3513 744 3044 326 
Q 2575 -91 1722 -91 
Q 1428 -91 1123 -41 
Q 819 9 494 109 
L 494 744 
Q 775 591 1075 516 
Q 1375 441 1709 441 
Q 2250 441 2565 725 
Q 2881 1009 2881 1497 
Q 2881 1984 2565 2268 
Q 2250 2553 1709 2553 
Q 1456 2553 1204 2497 
Q 953 2441 691 2322 
L 691 4666 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-2212"/>
       <use xlink:href="#DejaVuSans-30" x="83.789062"/>
       <use xlink:href="#DejaVuSans-2e" x="147.412109"/>
       <use xlink:href="#DejaVuSans-35" x="179.199219"/>
      </g>
     </g>
    </g>
    <g id="xtick_3">
     <g id="line2d_3">
      <g>
       <use xlink:href="#m313513bb85" x="236.085501" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_3">
      <!-- 0.0 -->
      <g transform="translate(228.133939 322.182437) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-30"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-30" x="95.410156"/>
      </g>
     </g>
    </g>
    <g id="xtick_4">
     <g id="line2d_4">
      <g>
       <use xlink:href="#m313513bb85" x="286.540529" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_4">
      <!-- 0.5 -->
      <g transform="translate(278.588966 322.182437) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-30"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-35" x="95.410156"/>
      </g>
     </g>
    </g>
    <g id="xtick_5">
     <g id="line2d_5">
      <g>
       <use xlink:href="#m313513bb85" x="336.995556" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_5">
      <!-- 1.0 -->
      <g transform="translate(329.043993 322.182437) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-31"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-30" x="95.410156"/>
      </g>
     </g>
    </g>
   </g>
   <g id="matplotlib.axis_2">
    <g id="ytick_1">
     <g id="line2d_6">
      <defs>
       <path id="md9aad7518f" d="M 0 0 
L -3.5 0 
" style="stroke: #000000; stroke-width: 0.8"/>
      </defs>
      <g>
       <use xlink:href="#md9aad7518f" x="103.040677" y="275.569028" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_6">
      <!-- −1.0 -->
      <g transform="translate(71.757864 279.368247) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-2212"/>
       <use xlink:href="#DejaVuSans-31" x="83.789062"/>
       <use xlink:href="#DejaVuSans-2e" x="147.412109"/>
       <use xlink:href="#DejaVuSans-30" x="179.199219"/>
      </g>
     </g>
    </g>
    <g id="ytick_2">
     <g id="line2d_7">
      <g>
       <use xlink:href="#md9aad7518f" x="103.040677" y="225.114001" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_7">
      <!-- −0.5 -->
      <g transform="translate(71.757864 228.913219) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-2212"/>
       <use xlink:href="#DejaVuSans-30" x="83.789062"/>
       <use xlink:href="#DejaVuSans-2e" x="147.412109"/>
       <use xlink:href="#DejaVuSans-35" x="179.199219"/>
      </g>
     </g>
    </g>
    <g id="ytick_3">
     <g id="line2d_8">
      <g>
       <use xlink:href="#md9aad7518f" x="103.040677" y="174.658973" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_8">
      <!-- 0.0 -->
      <g transform="translate(80.137552 178.458192) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-30"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-30" x="95.410156"/>
      </g>
     </g>
    </g>
    <g id="ytick_4">
     <g id="line2d_9">
      <g>
       <use xlink:href="#md9aad7518f" x="103.040677" y="124.203946" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_9">
      <!-- 0.5 -->
      <g transform="translate(80.137552 128.003165) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-30"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-35" x="95.410156"/>
      </g>
     </g>
    </g>
    <g id="ytick_5">
     <g id="line2d_10">
      <g>
       <use xlink:href="#md9aad7518f" x="103.040677" y="73.748919" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_10">
      <!-- 1.0 -->
      <g transform="translate(80.137552 77.548137) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-31"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-30" x="95.410156"/>
      </g>
     </g>
    </g>
   </g>
   <g id="line2d_11">
    <path d="M 336.995556 174.658973 
L 334.933284 154.413552 
L 328.832418 135.003727 
L 318.947154 117.229949 
L 305.689154 101.823879 
L 289.610086 89.417691 
L 271.378247 80.517625 
L 251.75027 75.482914 
L 231.53914 74.510997 
L 211.579881 77.629608 
L 192.694399 84.696094 
L 175.65698 95.403962 
L 161.161919 109.29634 
L 149.794655 125.785787 
L 142.007639 144.179549 
L 138.101952 163.709178 
L 138.215417 183.56323 
L 142.317716 202.921615 
L 150.212659 220.990134 
L 161.547481 237.033718 
L 175.82874 250.406946 
L 192.444077 260.580561 
L 210.688882 267.162869 
L 229.796689 269.915132 
L 248.971968 268.76034 
L 267.423883 263.785032 
L 284.399574 255.234147 
L 299.215523 243.49917 
L 311.285678 229.100147 
L 320.145154 212.662396 
L 325.468523 194.888962 
L 327.081968 176.530037 
L 324.968829 158.350707 
L 319.268368 141.098421 
L 310.267887 125.471597 
L 298.388593 112.090705 
L 284.165921 101.473056 
L 268.2252 94.012338 
L 251.253799 89.963735 
L 233.970986 89.435201 
L 217.096853 92.385194 
L 201.321663 98.626876 
L 187.276951 107.838518 
L 175.509616 119.579562 
L 166.460086 133.311553 
L 160.445466 148.42297 
L 157.64831 164.256787 
L 158.111445 180.139531 
L 161.738953 195.410521 
L 168.303194 209.450007 
L 177.457433 221.704978 
L 188.753429 231.711549 
L 201.663123 239.112977 
L 215.603369 243.672613 
L 229.962574 245.281271 
L 244.128004 243.958829 
L 257.512533 239.850071 
L 269.579634 233.215089 
L 279.865539 224.414776 
L 287.997608 213.892179 
L 293.708176 202.15062 
L 296.843323 189.729678 
L 297.3663 177.180144 
L 295.355553 165.039136 
L 290.997575 153.806504 
L 284.575018 143.92359 
L 276.45074 135.755258 
L 267.048612 129.575968 
L 256.832063 125.560434 
L 246.281428 123.779208 
L 235.871187 124.199253 
L 226.048185 126.689391 
L 217.211834 131.030205 
L 209.697214 136.927846 
L 203.761792 144.030954 
L 199.576325 151.949809 
L 197.220285 160.276723 
L 196.681908 168.606628 
L 197.862753 176.556856 
L 200.586437 183.785136 
L 204.610991 190.004947 
L 209.644141 194.997533 
L 215.360653 198.620036 
L 221.420821 200.809423 
L 227.489098 201.582112 
L 233.251917 201.029394 
L 238.433771 199.308997 
L 242.810747 196.63331 
L 246.220836 193.25495 
L 248.570525 189.450517 
L 249.837385 185.503414 
L 250.068554 181.686717 
L 249.375274 178.247005 
L 247.923818 175.390054 
L 245.923353 173.269162 
L 243.611429 171.976747 
L 241.237941 171.539666 
L 239.048465 171.918524 
L 237.267923 173.010992 
L 236.085501 174.658973 
" clip-path="url(#pa0de3b39b0)" style="fill: none; stroke: #1f77b4; stroke-width: 1.5; stroke-linecap: square"/>
   </g>
   <g id="line2d_12">
    <path d="M 357.177567 174.658973 
L 354.714945 150.361989 
L 347.427243 127.053249 
L 335.610877 105.680803 
L 319.74646 87.113943 
L 300.479256 72.107851 
L 278.59293 61.272877 
L 254.977675 55.049717 
L 230.594009 53.691491 
L 206.433701 57.253441 
L 183.479437 65.59069 
L 162.664848 78.364134 
L 144.836538 95.054231 
L 130.719647 114.982134 
L 120.888359 137.337307 
L 115.742548 161.210484 
L 115.491511 185.630659 
L 120.14546 209.604576 
L 129.515102 232.157132 
L 143.21934 252.371034 
L 160.700774 269.42411 
L 181.248373 282.622753 
L 204.026392 291.430125 
L 228.108369 295.488 
L 252.514804 294.63133 
L 276.253001 288.894958 
L 298.357443 278.512204 
L 317.929065 263.905371 
L 334.171818 245.668569 
L 346.425053 224.543556 
L 354.190387 201.389559 
L 357.151976 177.148335 
L 355.189363 152.80586 
L 348.382372 129.352228 
L 337.007869 107.741382 
L 321.528496 88.852313 
L 302.573853 73.453304 
L 280.914892 62.170689 
L 257.432561 55.463372 
L 233.08197 53.604163 
L 208.853543 56.668682 
L 185.732736 64.532286 
L 164.659955 76.875132 
L 146.492304 93.195194 
L 131.968727 112.828677 
L 121.679948 134.977018 
L 116.044448 158.739364 
L 115.291445 183.149218 
L 119.451564 207.213743 
L 128.355599 229.95415 
L 141.641392 250.445506 
L 158.768562 267.854355 
L 179.040485 281.472617 
L 201.632633 290.746389 
L 225.6261 295.298475 
L 250.044989 294.943723 
L 273.896095 289.696564 
L 296.209311 279.770418 
L 316.077078 265.569017 
L 332.691303 247.669982 
L 345.376228 226.80133 
L 353.615912 203.811863 
L 357.075216 179.636645 
L 355.61344 155.258967 
L 349.290038 131.670356 
L 338.362206 109.830245 
L 323.274418 90.626949 
L 304.640347 74.841533 
L 283.217907 63.116046 
L 259.878425 55.927406 
L 235.571201 53.568 
L 211.284894 56.133794 
L 188.007317 63.520427 
L 166.68525 75.427459 
L 148.185937 91.370589 
L 133.261812 110.701353 
L 122.519891 132.6335 
L 116.397086 156.274973 
L 115.142433 180.664188 
L 118.806964 204.80915 
L 127.24163 227.727797 
L 140.103362 248.487946 
L 156.869028 266.24521 
L 176.856709 280.277336 
L 199.253435 290.013589 
L 223.148252 295.05796 
L 247.569273 295.205277 
L 271.523208 290.449548 
L 294.035766 280.984206 
L 314.191281 267.19424 
L 331.169957 249.640535 
L 344.28121 229.037065 
L 352.991761 206.221845 
L 356.947319 182.122851 
L 355.986998 157.720274 
L 350.149857 134.006654 
L 339.673315 111.946509 
L 324.983489 92.437102 
L 306.677866 76.27195 
L 285.501001 64.108547 
" clip-path="url(#pa0de3b39b0)" style="fill: none; stroke: #ff7f0e; stroke-width: 1.5; stroke-linecap: square"/>
   </g>
   <g id="patch_3">
    <path d="M 103.040677 307.584 
L 103.040677 41.472 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
   <g id="patch_4">
    <path d="M 369.279323 307.584 
L 369.279323 41.472 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
   <g id="patch_5">
    <path d="M 103.040677 307.584 
L 369.279323 307.584 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
   <g id="patch_6">
    <path d="M 103.040677 41.472 
L 369.279323 41.472 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
  </g>
 </g>
 <defs>
  <clipPath id="pa0de3b39b0">
   <rect x="103.040677" y="41.472" width="266.238647" height="266.112"/>
  </clipPath>
 </defs>
</svg>
\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"f1x := (1-(t/20)**2) \\\\cos(t);\\nf1y := (1-(t/20)**2) \\\\sin(t);\\nf2x := 1.2\\\\cos(t);\\nf2y := 1.2\\\\sin(t);\\n\\nparametric_plot([f1x, f2x], [f1y, f2y], {$t$: (0, 20)}, aspect='equal');\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 4828187889946546510,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 3436909646278505520,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"Note the use of the \\\\verb|aspect| parameter to ensure that circles indeed come out as circles, not as ellipses.\\nYou can use any of the matplotlib aspect options for this parameter.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"Note the use of the \\\\verb|aspect| parameter to ensure that circles indeed come out as circles, not as ellipses.\\nYou can use any of the matplotlib aspect options for this parameter.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 10299306019942345427,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 10092687449673613253,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\subsection*{Animations}\\n\\nIt is possible to make animations of functions by plotting each successive frame separately, and re-using the output cell\\ninto which the frames are displayed. In the example below, \\\\verb|out| is the ID of the output cell (initially zero),\\nand the \\\\verb|display| function is used to display each frame, overwriting the content of the output cell (this functionality\\nis currently unavailable when using Cadabra from Jupyter).\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\subsection*{Animations}\\n\\nIt is possible to make animations of functions by plotting each successive frame separately, and re-using the output cell\\ninto which the frames are displayed. In the example below, \\\\verb|out| is the ID of the output cell (initially zero),\\nand the \\\\verb|display| function is used to display each frame, overwriting the content of the output cell (this functionality\\nis currently unavailable when using Cadabra from Jupyter).\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 2502954717605372411,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9396646536663698288,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"image_svg\",\n\t\t\t\t\t\"source\": \"<?xml version="1.0" encoding="utf-8" standalone="no"?>
<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
  "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="460.8pt" height="345.6pt" viewBox="0 0 460.8 345.6" xmlns="http://www.w3.org/2000/svg" version="1.1">
 <metadata>
  <rdf:RDF xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:cc="http://creativecommons.org/ns#" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
   <cc:Work>
    <dc:type rdf:resource="http://purl.org/dc/dcmitype/StillImage"/>
    <dc:date>2025-03-29T11:07:10.825060</dc:date>
    <dc:format>image/svg+xml</dc:format>
    <dc:creator>
     <cc:Agent>
      <dc:title>Matplotlib v3.6.3, https://matplotlib.org/</dc:title>
     </cc:Agent>
    </dc:creator>
   </cc:Work>
  </rdf:RDF>
 </metadata>
 <defs>
  <style type="text/css">*{stroke-linejoin: round; stroke-linecap: butt}</style>
 </defs>
 <g id="figure_1">
  <g id="patch_1">
   <path d="M 0 345.6 
L 460.8 345.6 
L 460.8 0 
L 0 0 
z
" style="fill: #ffffff"/>
  </g>
  <g id="axes_1">
   <g id="patch_2">
    <path d="M 57.6 307.584 
L 414.72 307.584 
L 414.72 41.472 
L 57.6 41.472 
z
" style="fill: #ffffff"/>
   </g>
   <g id="matplotlib.axis_1">
    <g id="xtick_1">
     <g id="line2d_1">
      <defs>
       <path id="m13623b995d" d="M 0 0 
L 0 3.5 
" style="stroke: #000000; stroke-width: 0.8"/>
      </defs>
      <g>
       <use xlink:href="#m13623b995d" x="73.832727" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_1">
      <!-- 0 -->
      <g transform="translate(70.651477 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-30" d="M 2034 4250 
Q 1547 4250 1301 3770 
Q 1056 3291 1056 2328 
Q 1056 1369 1301 889 
Q 1547 409 2034 409 
Q 2525 409 2770 889 
Q 3016 1369 3016 2328 
Q 3016 3291 2770 3770 
Q 2525 4250 2034 4250 
z
M 2034 4750 
Q 2819 4750 3233 4129 
Q 3647 3509 3647 2328 
Q 3647 1150 3233 529 
Q 2819 -91 2034 -91 
Q 1250 -91 836 529 
Q 422 1150 422 2328 
Q 422 3509 836 4129 
Q 1250 4750 2034 4750 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-30"/>
      </g>
     </g>
    </g>
    <g id="xtick_2">
     <g id="line2d_2">
      <g>
       <use xlink:href="#m13623b995d" x="138.763636" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_2">
      <!-- 2 -->
      <g transform="translate(135.582386 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-32" d="M 1228 531 
L 3431 531 
L 3431 0 
L 469 0 
L 469 531 
Q 828 903 1448 1529 
Q 2069 2156 2228 2338 
Q 2531 2678 2651 2914 
Q 2772 3150 2772 3378 
Q 2772 3750 2511 3984 
Q 2250 4219 1831 4219 
Q 1534 4219 1204 4116 
Q 875 4013 500 3803 
L 500 4441 
Q 881 4594 1212 4672 
Q 1544 4750 1819 4750 
Q 2544 4750 2975 4387 
Q 3406 4025 3406 3419 
Q 3406 3131 3298 2873 
Q 3191 2616 2906 2266 
Q 2828 2175 2409 1742 
Q 1991 1309 1228 531 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-32"/>
      </g>
     </g>
    </g>
    <g id="xtick_3">
     <g id="line2d_3">
      <g>
       <use xlink:href="#m13623b995d" x="203.694545" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_3">
      <!-- 4 -->
      <g transform="translate(200.513295 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-34" d="M 2419 4116 
L 825 1625 
L 2419 1625 
L 2419 4116 
z
M 2253 4666 
L 3047 4666 
L 3047 1625 
L 3713 1625 
L 3713 1100 
L 3047 1100 
L 3047 0 
L 2419 0 
L 2419 1100 
L 313 1100 
L 313 1709 
L 2253 4666 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-34"/>
      </g>
     </g>
    </g>
    <g id="xtick_4">
     <g id="line2d_4">
      <g>
       <use xlink:href="#m13623b995d" x="268.625455" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_4">
      <!-- 6 -->
      <g transform="translate(265.444205 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-36" d="M 2113 2584 
Q 1688 2584 1439 2293 
Q 1191 2003 1191 1497 
Q 1191 994 1439 701 
Q 1688 409 2113 409 
Q 2538 409 2786 701 
Q 3034 994 3034 1497 
Q 3034 2003 2786 2293 
Q 2538 2584 2113 2584 
z
M 3366 4563 
L 3366 3988 
Q 3128 4100 2886 4159 
Q 2644 4219 2406 4219 
Q 1781 4219 1451 3797 
Q 1122 3375 1075 2522 
Q 1259 2794 1537 2939 
Q 1816 3084 2150 3084 
Q 2853 3084 3261 2657 
Q 3669 2231 3669 1497 
Q 3669 778 3244 343 
Q 2819 -91 2113 -91 
Q 1303 -91 875 529 
Q 447 1150 447 2328 
Q 447 3434 972 4092 
Q 1497 4750 2381 4750 
Q 2619 4750 2861 4703 
Q 3103 4656 3366 4563 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-36"/>
      </g>
     </g>
    </g>
    <g id="xtick_5">
     <g id="line2d_5">
      <g>
       <use xlink:href="#m13623b995d" x="333.556364" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_5">
      <!-- 8 -->
      <g transform="translate(330.375114 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-38" d="M 2034 2216 
Q 1584 2216 1326 1975 
Q 1069 1734 1069 1313 
Q 1069 891 1326 650 
Q 1584 409 2034 409 
Q 2484 409 2743 651 
Q 3003 894 3003 1313 
Q 3003 1734 2745 1975 
Q 2488 2216 2034 2216 
z
M 1403 2484 
Q 997 2584 770 2862 
Q 544 3141 544 3541 
Q 544 4100 942 4425 
Q 1341 4750 2034 4750 
Q 2731 4750 3128 4425 
Q 3525 4100 3525 3541 
Q 3525 3141 3298 2862 
Q 3072 2584 2669 2484 
Q 3125 2378 3379 2068 
Q 3634 1759 3634 1313 
Q 3634 634 3220 271 
Q 2806 -91 2034 -91 
Q 1263 -91 848 271 
Q 434 634 434 1313 
Q 434 1759 690 2068 
Q 947 2378 1403 2484 
z
M 1172 3481 
Q 1172 3119 1398 2916 
Q 1625 2713 2034 2713 
Q 2441 2713 2670 2916 
Q 2900 3119 2900 3481 
Q 2900 3844 2670 4047 
Q 2441 4250 2034 4250 
Q 1625 4250 1398 4047 
Q 1172 3844 1172 3481 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-38"/>
      </g>
     </g>
    </g>
    <g id="xtick_6">
     <g id="line2d_6">
      <g>
       <use xlink:href="#m13623b995d" x="398.487273" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_6">
      <!-- 10 -->
      <g transform="translate(392.124773 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-31" d="M 794 531 
L 1825 531 
L 1825 4091 
L 703 3866 
L 703 4441 
L 1819 4666 
L 2450 4666 
L 2450 531 
L 3481 531 
L 3481 0 
L 794 0 
L 794 531 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-31"/>
       <use xlink:href="#DejaVuSans-30" x="63.623047"/>
      </g>
     </g>
    </g>
   </g>
   <g id="matplotlib.axis_2">
    <g id="ytick_1">
     <g id="line2d_7">
      <defs>
       <path id="ma764dfecc5" d="M 0 0 
L -3.5 0 
" style="stroke: #000000; stroke-width: 0.8"/>
      </defs>
      <g>
       <use xlink:href="#ma764dfecc5" x="57.6" y="280.9728" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_7">
      <!-- −40 -->
      <g transform="translate(29.495313 284.772019) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-2212" d="M 678 2272 
L 4684 2272 
L 4684 1741 
L 678 1741 
L 678 2272 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-2212"/>
       <use xlink:href="#DejaVuSans-34" x="83.789062"/>
       <use xlink:href="#DejaVuSans-30" x="147.412109"/>
      </g>
     </g>
    </g>
    <g id="ytick_2">
     <g id="line2d_8">
      <g>
       <use xlink:href="#ma764dfecc5" x="57.6" y="227.7504" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_8">
      <!-- −20 -->
      <g transform="translate(29.495313 231.549619) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-2212"/>
       <use xlink:href="#DejaVuSans-32" x="83.789062"/>
       <use xlink:href="#DejaVuSans-30" x="147.412109"/>
      </g>
     </g>
    </g>
    <g id="ytick_3">
     <g id="line2d_9">
      <g>
       <use xlink:href="#ma764dfecc5" x="57.6" y="174.528" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_9">
      <!-- 0 -->
      <g transform="translate(44.2375 178.327219) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-30"/>
      </g>
     </g>
    </g>
    <g id="ytick_4">
     <g id="line2d_10">
      <g>
       <use xlink:href="#ma764dfecc5" x="57.6" y="121.3056" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_10">
      <!-- 20 -->
      <g transform="translate(37.875 125.104819) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-32"/>
       <use xlink:href="#DejaVuSans-30" x="63.623047"/>
      </g>
     </g>
    </g>
    <g id="ytick_5">
     <g id="line2d_11">
      <g>
       <use xlink:href="#ma764dfecc5" x="57.6" y="68.0832" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_11">
      <!-- 40 -->
      <g transform="translate(37.875 71.882419) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-34"/>
       <use xlink:href="#DejaVuSans-30" x="63.623047"/>
      </g>
     </g>
    </g>
   </g>
   <g id="line2d_12">
    <path d="M 73.832727 174.528 
L 77.112066 174.395028 
L 80.391405 174.270609 
L 83.670744 174.163224 
L 86.950083 174.081216 
L 90.229421 174.032714 
L 93.50876 174.025571 
L 96.788099 174.067291 
L 100.067438 174.164969 
L 103.346777 174.325224 
L 106.626116 174.554143 
L 109.905455 174.85722 
L 113.184793 175.239301 
L 116.464132 175.704538 
L 119.743471 176.256336 
L 123.02281 176.897315 
L 126.302149 177.629269 
L 129.581488 178.453131 
L 132.860826 179.368946 
L 136.140165 180.375845 
L 139.419504 181.472026 
L 142.698843 182.654741 
L 145.978182 183.920285 
L 149.257521 185.263997 
L 152.53686 186.680258 
L 155.816198 188.162503 
L 159.095537 189.703231 
L 162.374876 191.294028 
L 165.654215 192.925591 
L 168.933554 194.587757 
L 172.212893 196.269541 
L 175.492231 197.959177 
L 178.77157 199.644165 
L 182.050909 201.311322 
L 185.330248 202.946842 
L 188.609587 204.536352 
L 191.888926 206.064983 
L 195.168264 207.517437 
L 198.447603 208.878065 
L 201.726942 210.13094 
L 205.006281 211.259943 
L 208.28562 212.248844 
L 211.564959 213.08139 
L 214.844298 213.741396 
L 218.123636 214.212831 
L 221.402975 214.479918 
L 224.682314 214.527222 
L 227.961653 214.339746 
L 231.240992 213.903027 
L 234.520331 213.20323 
L 237.799669 212.227242 
L 241.079008 210.962763 
L 244.358347 209.398401 
L 247.637686 207.523759 
L 250.917025 205.329525 
L 254.196364 202.807551 
L 257.475702 199.950939 
L 260.755041 196.754117 
L 264.03438 193.212913 
L 267.313719 189.324621 
L 270.593058 185.08807 
L 273.872397 180.503677 
L 277.151736 175.573505 
L 280.431074 170.301307 
L 283.710413 164.692568 
L 286.989752 158.754541 
L 290.269091 152.49627 
L 293.54843 145.928615 
L 296.827769 139.064262 
L 300.107107 131.917728 
L 303.386446 124.505362 
L 306.665785 116.845331 
L 309.945124 108.957601 
L 313.224463 100.863917 
L 316.503802 92.587759 
L 319.78314 84.154308 
L 323.062479 75.590386 
L 326.341818 66.924407 
L 329.621157 58.186301 
L 332.900496 49.407442 
L 336.179835 40.620566 
L 339.459174 31.859678 
L 342.738512 23.159955 
L 346.017851 14.557639 
L 349.29719 6.089928 
L 352.100091 -1 
" clip-path="url(#pb9394c8e2e)" style="fill: none; stroke: #1f77b4; stroke-width: 1.5; stroke-linecap: square"/>
   </g>
   <g id="patch_3">
    <path d="M 57.6 307.584 
L 57.6 41.472 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
   <g id="patch_4">
    <path d="M 414.72 307.584 
L 414.72 41.472 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
   <g id="patch_5">
    <path d="M 57.6 307.584 
L 414.72 307.584 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
   <g id="patch_6">
    <path d="M 57.6 41.472 
L 414.72 41.472 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
  </g>
  <g id="text_12">
   <!-- a = 0.50 -->
   <g transform="translate(196.922813 26.314313) scale(0.18 -0.18)">
    <defs>
     <path id="Cmr10-61" d="M 256 628 
Q 256 1009 556 1248 
Q 856 1488 1276 1586 
Q 1697 1684 2075 1684 
L 2075 1947 
Q 2075 2131 1994 2304 
Q 1913 2478 1759 2589 
Q 1606 2700 1422 2700 
Q 997 2700 775 2509 
Q 897 2509 976 2417 
Q 1056 2325 1056 2203 
Q 1056 2075 965 1984 
Q 875 1894 750 1894 
Q 622 1894 531 1984 
Q 441 2075 441 2203 
Q 441 2541 747 2705 
Q 1053 2869 1422 2869 
Q 1681 2869 1943 2758 
Q 2206 2647 2373 2440 
Q 2541 2234 2541 1959 
L 2541 519 
Q 2541 394 2594 289 
Q 2647 184 2759 184 
Q 2866 184 2917 290 
Q 2969 397 2969 519 
L 2969 928 
L 3156 928 
L 3156 519 
Q 3156 375 3081 245 
Q 3006 116 2879 39 
Q 2753 -38 2606 -38 
Q 2419 -38 2283 107 
Q 2147 253 2131 453 
Q 2013 213 1781 70 
Q 1550 -72 1288 -72 
Q 1044 -72 808 0 
Q 572 72 414 226 
Q 256 381 256 628 
z
M 775 628 
Q 775 403 940 250 
Q 1106 97 1331 97 
Q 1538 97 1706 200 
Q 1875 303 1975 481 
Q 2075 659 2075 856 
L 2075 1522 
Q 1784 1522 1479 1426 
Q 1175 1331 975 1128 
Q 775 925 775 628 
z
" transform="scale(0.015625)"/>
     <path id="Cmr10-20" transform="scale(0.015625)"/>
     <path id="Cmr10-3d" d="M 481 850 
Q 428 850 393 890 
Q 359 931 359 978 
Q 359 1031 393 1068 
Q 428 1106 481 1106 
L 4500 1106 
Q 4547 1106 4581 1068 
Q 4616 1031 4616 978 
Q 4616 931 4581 890 
Q 4547 850 4500 850 
L 481 850 
z
M 481 2094 
Q 428 2094 393 2131 
Q 359 2169 359 2222 
Q 359 2269 393 2309 
Q 428 2350 481 2350 
L 4500 2350 
Q 4547 2350 4581 2309 
Q 4616 2269 4616 2222 
Q 4616 2169 4581 2131 
Q 4547 2094 4500 2094 
L 481 2094 
z
" transform="scale(0.015625)"/>
     <path id="Cmr10-30" d="M 1600 -141 
Q 816 -141 533 504 
Q 250 1150 250 2041 
Q 250 2597 351 3087 
Q 453 3578 754 3920 
Q 1056 4263 1600 4263 
Q 2022 4263 2290 4056 
Q 2559 3850 2700 3523 
Q 2841 3197 2892 2823 
Q 2944 2450 2944 2041 
Q 2944 1491 2842 1011 
Q 2741 531 2444 195 
Q 2147 -141 1600 -141 
z
M 1600 25 
Q 1956 25 2131 390 
Q 2306 756 2347 1200 
Q 2388 1644 2388 2144 
Q 2388 2625 2347 3031 
Q 2306 3438 2132 3767 
Q 1959 4097 1600 4097 
Q 1238 4097 1063 3765 
Q 888 3434 847 3029 
Q 806 2625 806 2144 
Q 806 1788 823 1472 
Q 841 1156 916 820 
Q 991 484 1158 254 
Q 1325 25 1600 25 
z
" transform="scale(0.015625)"/>
     <path id="Cmr10-2e" d="M 538 353 
Q 538 497 644 600 
Q 750 703 891 703 
Q 978 703 1062 656 
Q 1147 609 1194 525 
Q 1241 441 1241 353 
Q 1241 213 1137 106 
Q 1034 0 891 0 
Q 750 0 644 106 
Q 538 213 538 353 
z
" transform="scale(0.015625)"/>
     <path id="Cmr10-35" d="M 556 728 
Q 622 541 758 387 
Q 894 234 1080 148 
Q 1266 63 1466 63 
Q 1928 63 2103 422 
Q 2278 781 2278 1294 
Q 2278 1516 2270 1667 
Q 2263 1819 2228 1959 
Q 2169 2184 2020 2353 
Q 1872 2522 1656 2522 
Q 1441 2522 1286 2456 
Q 1131 2391 1034 2303 
Q 938 2216 863 2119 
Q 788 2022 769 2016 
L 697 2016 
Q 681 2016 657 2036 
Q 634 2056 634 2075 
L 634 4213 
Q 634 4228 654 4245 
Q 675 4263 697 4263 
L 716 4263 
Q 1147 4056 1631 4056 
Q 2106 4056 2547 4263 
L 2566 4263 
Q 2588 4263 2606 4247 
Q 2625 4231 2625 4213 
L 2625 4153 
Q 2625 4122 2613 4122 
Q 2394 3831 2064 3668 
Q 1734 3506 1381 3506 
Q 1125 3506 856 3578 
L 856 2369 
Q 1069 2541 1236 2614 
Q 1403 2688 1663 2688 
Q 2016 2688 2295 2484 
Q 2575 2281 2725 1954 
Q 2875 1628 2875 1288 
Q 2875 903 2686 575 
Q 2497 247 2172 53 
Q 1847 -141 1466 -141 
Q 1150 -141 886 21 
Q 622 184 470 459 
Q 319 734 319 1044 
Q 319 1188 412 1278 
Q 506 1369 647 1369 
Q 788 1369 883 1276 
Q 978 1184 978 1044 
Q 978 906 883 811 
Q 788 716 647 716 
Q 625 716 597 720 
Q 569 725 556 728 
z
" transform="scale(0.015625)"/>
    </defs>
    <use xlink:href="#Cmr10-61"/>
    <use xlink:href="#Cmr10-20" x="50"/>
    <use xlink:href="#Cmr10-3d" x="83.300781"/>
    <use xlink:href="#Cmr10-20" x="160.986328"/>
    <use xlink:href="#Cmr10-30" x="194.287109"/>
    <use xlink:href="#Cmr10-2e" x="244.287109"/>
    <use xlink:href="#Cmr10-35" x="271.972656"/>
    <use xlink:href="#Cmr10-30" x="321.972656"/>
   </g>
  </g>
 </g>
 <defs>
  <clipPath id="pb9394c8e2e">
   <rect x="57.6" y="41.472" width="357.12" height="266.112"/>
  </clipPath>
 </defs>
</svg>
\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"out=0\\nimport time\\np = None\\nfor a in np.concatenate( [np.linspace(0.5, 5.0, 100), np.linspace(5.0, 0.5, 100)] ):\\n   p = plot($\\\\sin( @(a) x) (1 - x**2)$, {$x$: (0, 10)}, yrange=[-50, 50], title=f\\\"a = {a:.2f}\\\", fig=p)\\n   out = display(p, out)\\n   time.sleep(0.01)\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 5362080713296484344,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 15040203446082825428,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"By re-using the figure, but using plots with different labels, different curves can be animated \\nindependently. The following example has one figure, in which two plots are drawn: one called \\\"sin\\\" and another one called \\\"cos\\\".\\nWe set the $y$-axis range manually to avoid the plot fitting tight around whatever is plotted on any given frame.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"By re-using the figure, but using plots with different labels, different curves can be animated \\nindependently. The following example has one figure, in which two plots are drawn: one called \\\"sin\\\" and another one called \\\"cos\\\".\\nWe set the $y$-axis range manually to avoid the plot fitting tight around whatever is plotted on any given frame.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 17368321874240984716,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 13979276469769590412,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"image_svg\",\n\t\t\t\t\t\"source\": \"<?xml version="1.0" encoding="utf-8" standalone="no"?>
<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
  "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="460.8pt" height="345.6pt" viewBox="0 0 460.8 345.6" xmlns="http://www.w3.org/2000/svg" version="1.1">
 <metadata>
  <rdf:RDF xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:cc="http://creativecommons.org/ns#" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
   <cc:Work>
    <dc:type rdf:resource="http://purl.org/dc/dcmitype/StillImage"/>
    <dc:date>2025-03-29T11:07:16.602527</dc:date>
    <dc:format>image/svg+xml</dc:format>
    <dc:creator>
     <cc:Agent>
      <dc:title>Matplotlib v3.6.3, https://matplotlib.org/</dc:title>
     </cc:Agent>
    </dc:creator>
   </cc:Work>
  </rdf:RDF>
 </metadata>
 <defs>
  <style type="text/css">*{stroke-linejoin: round; stroke-linecap: butt}</style>
 </defs>
 <g id="figure_1">
  <g id="patch_1">
   <path d="M 0 345.6 
L 460.8 345.6 
L 460.8 0 
L 0 0 
z
" style="fill: #ffffff"/>
  </g>
  <g id="axes_1">
   <g id="patch_2">
    <path d="M 57.6 307.584 
L 414.72 307.584 
L 414.72 41.472 
L 57.6 41.472 
z
" style="fill: #ffffff"/>
   </g>
   <g id="matplotlib.axis_1">
    <g id="xtick_1">
     <g id="line2d_1">
      <defs>
       <path id="m26fb06b179" d="M 0 0 
L 0 3.5 
" style="stroke: #000000; stroke-width: 0.8"/>
      </defs>
      <g>
       <use xlink:href="#m26fb06b179" x="57.6" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_1">
      <!-- 0 -->
      <g transform="translate(54.41875 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-30" d="M 2034 4250 
Q 1547 4250 1301 3770 
Q 1056 3291 1056 2328 
Q 1056 1369 1301 889 
Q 1547 409 2034 409 
Q 2525 409 2770 889 
Q 3016 1369 3016 2328 
Q 3016 3291 2770 3770 
Q 2525 4250 2034 4250 
z
M 2034 4750 
Q 2819 4750 3233 4129 
Q 3647 3509 3647 2328 
Q 3647 1150 3233 529 
Q 2819 -91 2034 -91 
Q 1250 -91 836 529 
Q 422 1150 422 2328 
Q 422 3509 836 4129 
Q 1250 4750 2034 4750 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-30"/>
      </g>
     </g>
    </g>
    <g id="xtick_2">
     <g id="line2d_2">
      <g>
       <use xlink:href="#m26fb06b179" x="114.466242" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_2">
      <!-- 1 -->
      <g transform="translate(111.284992 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-31" d="M 794 531 
L 1825 531 
L 1825 4091 
L 703 3866 
L 703 4441 
L 1819 4666 
L 2450 4666 
L 2450 531 
L 3481 531 
L 3481 0 
L 794 0 
L 794 531 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-31"/>
      </g>
     </g>
    </g>
    <g id="xtick_3">
     <g id="line2d_3">
      <g>
       <use xlink:href="#m26fb06b179" x="171.332484" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_3">
      <!-- 2 -->
      <g transform="translate(168.151234 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-32" d="M 1228 531 
L 3431 531 
L 3431 0 
L 469 0 
L 469 531 
Q 828 903 1448 1529 
Q 2069 2156 2228 2338 
Q 2531 2678 2651 2914 
Q 2772 3150 2772 3378 
Q 2772 3750 2511 3984 
Q 2250 4219 1831 4219 
Q 1534 4219 1204 4116 
Q 875 4013 500 3803 
L 500 4441 
Q 881 4594 1212 4672 
Q 1544 4750 1819 4750 
Q 2544 4750 2975 4387 
Q 3406 4025 3406 3419 
Q 3406 3131 3298 2873 
Q 3191 2616 2906 2266 
Q 2828 2175 2409 1742 
Q 1991 1309 1228 531 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-32"/>
      </g>
     </g>
    </g>
    <g id="xtick_4">
     <g id="line2d_4">
      <g>
       <use xlink:href="#m26fb06b179" x="228.198726" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_4">
      <!-- 3 -->
      <g transform="translate(225.017476 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-33" d="M 2597 2516 
Q 3050 2419 3304 2112 
Q 3559 1806 3559 1356 
Q 3559 666 3084 287 
Q 2609 -91 1734 -91 
Q 1441 -91 1130 -33 
Q 819 25 488 141 
L 488 750 
Q 750 597 1062 519 
Q 1375 441 1716 441 
Q 2309 441 2620 675 
Q 2931 909 2931 1356 
Q 2931 1769 2642 2001 
Q 2353 2234 1838 2234 
L 1294 2234 
L 1294 2753 
L 1863 2753 
Q 2328 2753 2575 2939 
Q 2822 3125 2822 3475 
Q 2822 3834 2567 4026 
Q 2313 4219 1838 4219 
Q 1578 4219 1281 4162 
Q 984 4106 628 3988 
L 628 4550 
Q 988 4650 1302 4700 
Q 1616 4750 1894 4750 
Q 2613 4750 3031 4423 
Q 3450 4097 3450 3541 
Q 3450 3153 3228 2886 
Q 3006 2619 2597 2516 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-33"/>
      </g>
     </g>
    </g>
    <g id="xtick_5">
     <g id="line2d_5">
      <g>
       <use xlink:href="#m26fb06b179" x="285.064968" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_5">
      <!-- 4 -->
      <g transform="translate(281.883718 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-34" d="M 2419 4116 
L 825 1625 
L 2419 1625 
L 2419 4116 
z
M 2253 4666 
L 3047 4666 
L 3047 1625 
L 3713 1625 
L 3713 1100 
L 3047 1100 
L 3047 0 
L 2419 0 
L 2419 1100 
L 313 1100 
L 313 1709 
L 2253 4666 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-34"/>
      </g>
     </g>
    </g>
    <g id="xtick_6">
     <g id="line2d_6">
      <g>
       <use xlink:href="#m26fb06b179" x="341.93121" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_6">
      <!-- 5 -->
      <g transform="translate(338.74996 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-35" d="M 691 4666 
L 3169 4666 
L 3169 4134 
L 1269 4134 
L 1269 2991 
Q 1406 3038 1543 3061 
Q 1681 3084 1819 3084 
Q 2600 3084 3056 2656 
Q 3513 2228 3513 1497 
Q 3513 744 3044 326 
Q 2575 -91 1722 -91 
Q 1428 -91 1123 -41 
Q 819 9 494 109 
L 494 744 
Q 775 591 1075 516 
Q 1375 441 1709 441 
Q 2250 441 2565 725 
Q 2881 1009 2881 1497 
Q 2881 1984 2565 2268 
Q 2250 2553 1709 2553 
Q 1456 2553 1204 2497 
Q 953 2441 691 2322 
L 691 4666 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-35"/>
      </g>
     </g>
    </g>
    <g id="xtick_7">
     <g id="line2d_7">
      <g>
       <use xlink:href="#m26fb06b179" x="398.797452" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_7">
      <!-- 6 -->
      <g transform="translate(395.616202 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-36" d="M 2113 2584 
Q 1688 2584 1439 2293 
Q 1191 2003 1191 1497 
Q 1191 994 1439 701 
Q 1688 409 2113 409 
Q 2538 409 2786 701 
Q 3034 994 3034 1497 
Q 3034 2003 2786 2293 
Q 2538 2584 2113 2584 
z
M 3366 4563 
L 3366 3988 
Q 3128 4100 2886 4159 
Q 2644 4219 2406 4219 
Q 1781 4219 1451 3797 
Q 1122 3375 1075 2522 
Q 1259 2794 1537 2939 
Q 1816 3084 2150 3084 
Q 2853 3084 3261 2657 
Q 3669 2231 3669 1497 
Q 3669 778 3244 343 
Q 2819 -91 2113 -91 
Q 1303 -91 875 529 
Q 447 1150 447 2328 
Q 447 3434 972 4092 
Q 1497 4750 2381 4750 
Q 2619 4750 2861 4703 
Q 3103 4656 3366 4563 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-36"/>
      </g>
     </g>
    </g>
   </g>
   <g id="matplotlib.axis_2">
    <g id="ytick_1">
     <g id="line2d_8">
      <defs>
       <path id="mcc4bad7d18" d="M 0 0 
L -3.5 0 
" style="stroke: #000000; stroke-width: 0.8"/>
      </defs>
      <g>
       <use xlink:href="#mcc4bad7d18" x="57.6" y="285.408" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_8">
      <!-- −1.0 -->
      <g transform="translate(26.317187 289.207219) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-2212" d="M 678 2272 
L 4684 2272 
L 4684 1741 
L 678 1741 
L 678 2272 
z
" transform="scale(0.015625)"/>
        <path id="DejaVuSans-2e" d="M 684 794 
L 1344 794 
L 1344 0 
L 684 0 
L 684 794 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-2212"/>
       <use xlink:href="#DejaVuSans-31" x="83.789062"/>
       <use xlink:href="#DejaVuSans-2e" x="147.412109"/>
       <use xlink:href="#DejaVuSans-30" x="179.199219"/>
      </g>
     </g>
    </g>
    <g id="ytick_2">
     <g id="line2d_9">
      <g>
       <use xlink:href="#mcc4bad7d18" x="57.6" y="229.968" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_9">
      <!-- −0.5 -->
      <g transform="translate(26.317187 233.767219) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-2212"/>
       <use xlink:href="#DejaVuSans-30" x="83.789062"/>
       <use xlink:href="#DejaVuSans-2e" x="147.412109"/>
       <use xlink:href="#DejaVuSans-35" x="179.199219"/>
      </g>
     </g>
    </g>
    <g id="ytick_3">
     <g id="line2d_10">
      <g>
       <use xlink:href="#mcc4bad7d18" x="57.6" y="174.528" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_10">
      <!-- 0.0 -->
      <g transform="translate(34.696875 178.327219) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-30"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-30" x="95.410156"/>
      </g>
     </g>
    </g>
    <g id="ytick_4">
     <g id="line2d_11">
      <g>
       <use xlink:href="#mcc4bad7d18" x="57.6" y="119.088" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_11">
      <!-- 0.5 -->
      <g transform="translate(34.696875 122.887219) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-30"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-35" x="95.410156"/>
      </g>
     </g>
    </g>
    <g id="ytick_5">
     <g id="line2d_12">
      <g>
       <use xlink:href="#mcc4bad7d18" x="57.6" y="63.648" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_12">
      <!-- 1.0 -->
      <g transform="translate(34.696875 67.447219) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-31"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-30" x="95.410156"/>
      </g>
     </g>
    </g>
   </g>
   <g id="line2d_13">
    <path d="M -1 269.613 
L -0.989461 269.602605 
L 0.159351 268.430671 
L 1.308164 267.220415 
L 2.456977 265.97233 
L 3.60579 264.686925 
L 4.754603 263.364727 
L 5.903416 262.006273 
L 7.052229 260.612119 
L 8.201042 259.182833 
L 9.349855 257.718999 
L 10.498668 256.221214 
L 11.647481 254.690089 
L 12.796294 253.126249 
L 13.945107 251.530333 
L 15.09392 249.902992 
L 16.242733 248.24489 
L 17.391546 246.556703 
L 18.540359 244.839121 
L 19.689172 243.092844 
L 20.837985 241.318585 
L 21.986798 239.517069 
L 23.135611 237.68903 
L 24.284424 235.835214 
L 25.433237 233.956379 
L 26.58205 232.05329 
L 27.730863 230.126725 
L 28.879676 228.17747 
L 30.028489 226.20632 
L 31.177302 224.214079 
L 32.326115 222.201562 
L 33.474928 220.169588 
L 34.623741 218.118988 
L 35.772554 216.050597 
L 36.921367 213.965262 
L 38.07018 211.863831 
L 39.218992 209.747163 
L 40.367805 207.616123 
L 41.516618 205.471578 
L 42.665431 203.314406 
L 43.814244 201.145485 
L 44.963057 198.965702 
L 46.11187 196.775945 
L 47.260683 194.577109 
L 48.409496 192.370091 
L 49.558309 190.155791 
L 50.707122 187.935113 
L 51.855935 185.708964 
L 53.004748 183.478252 
L 54.153561 181.243887 
L 55.302374 179.006781 
L 56.451187 176.767848 
L 57.6 174.528 
" clip-path="url(#p0a71c56ec7)" style="fill: none; stroke: #008000; stroke-width: 1.5; stroke-linecap: square"/>
   </g>
   <g id="line2d_14">
    <path d="M 455.663694 90.935318 
L 456.812507 92.423925 
L 457.96132 93.94604 
L 459.110133 95.501041 
L 460.258946 97.088293 
L 461.407759 98.707149 
L 461.8 99.270442 
" clip-path="url(#p0a71c56ec7)" style="fill: none; stroke: #ff0000; stroke-width: 1.5; stroke-linecap: square"/>
   </g>
   <g id="patch_3">
    <path d="M 57.6 307.584 
L 57.6 41.472 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
   <g id="patch_4">
    <path d="M 414.72 307.584 
L 414.72 41.472 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
   <g id="patch_5">
    <path d="M 57.6 307.584 
L 414.72 307.584 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
   <g id="patch_6">
    <path d="M 57.6 41.472 
L 414.72 41.472 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
  </g>
  <g id="text_13">
   <!-- sin(x) and cos(x) -->
   <g transform="translate(163.380938 27.324) scale(0.18 -0.18)">
    <defs>
     <path id="Cmr10-73" d="M 213 -19 
L 213 1025 
Q 213 1075 269 1075 
L 347 1075 
Q 384 1075 397 1025 
Q 575 97 1259 97 
Q 1563 97 1767 234 
Q 1972 372 1972 659 
Q 1972 866 1812 1011 
Q 1653 1156 1434 1209 
L 1006 1294 
Q 791 1341 614 1437 
Q 438 1534 325 1695 
Q 213 1856 213 2069 
Q 213 2350 361 2529 
Q 509 2709 746 2789 
Q 984 2869 1259 2869 
Q 1588 2869 1831 2694 
L 2016 2853 
Q 2016 2869 2047 2869 
L 2094 2869 
Q 2113 2869 2128 2851 
Q 2144 2834 2144 2816 
L 2144 1978 
Q 2144 1919 2094 1919 
L 2016 1919 
Q 1959 1919 1959 1978 
Q 1959 2313 1773 2516 
Q 1588 2719 1253 2719 
Q 966 2719 755 2612 
Q 544 2506 544 2247 
Q 544 2069 695 1955 
Q 847 1841 1050 1791 
L 1484 1709 
Q 1703 1659 1892 1540 
Q 2081 1422 2192 1240 
Q 2303 1059 2303 831 
Q 2303 600 2223 429 
Q 2144 259 2001 146 
Q 1859 34 1665 -19 
Q 1472 -72 1259 -72 
Q 859 -72 575 197 
L 341 -56 
Q 341 -72 306 -72 
L 269 -72 
Q 213 -72 213 -19 
z
" transform="scale(0.015625)"/>
     <path id="Cmr10-69" d="M 197 0 
L 197 225 
Q 416 225 556 259 
Q 697 294 697 428 
L 697 2175 
Q 697 2422 601 2478 
Q 506 2534 225 2534 
L 225 2759 
L 1147 2828 
L 1147 428 
Q 1147 294 1269 259 
Q 1391 225 1594 225 
L 1594 0 
L 197 0 
z
M 469 3928 
Q 469 4069 575 4175 
Q 681 4281 819 4281 
Q 909 4281 993 4234 
Q 1078 4188 1125 4103 
Q 1172 4019 1172 3928 
Q 1172 3791 1065 3684 
Q 959 3578 819 3578 
Q 681 3578 575 3684 
Q 469 3791 469 3928 
z
" transform="scale(0.015625)"/>
     <path id="Cmr10-6e" d="M 191 0 
L 191 225 
Q 409 225 550 259 
Q 691 294 691 428 
L 691 2175 
Q 691 2347 639 2423 
Q 588 2500 491 2517 
Q 394 2534 191 2534 
L 191 2759 
L 1119 2828 
L 1119 2203 
Q 1247 2478 1498 2653 
Q 1750 2828 2047 2828 
Q 2491 2828 2714 2615 
Q 2938 2403 2938 1966 
L 2938 428 
Q 2938 294 3078 259 
Q 3219 225 3438 225 
L 3438 0 
L 1972 0 
L 1972 225 
Q 2191 225 2331 259 
Q 2472 294 2472 428 
L 2472 1947 
Q 2472 2259 2381 2461 
Q 2291 2663 2009 2663 
Q 1638 2663 1398 2366 
Q 1159 2069 1159 1691 
L 1159 428 
Q 1159 294 1300 259 
Q 1441 225 1656 225 
L 1656 0 
L 191 0 
z
" transform="scale(0.015625)"/>
     <path id="Cmr10-28" d="M 1984 -1588 
Q 1628 -1306 1370 -942 
Q 1113 -578 948 -165 
Q 784 247 703 697 
Q 622 1147 622 1600 
Q 622 2059 703 2509 
Q 784 2959 951 3375 
Q 1119 3791 1378 4153 
Q 1638 4516 1984 4788 
Q 1984 4800 2016 4800 
L 2075 4800 
Q 2094 4800 2109 4783 
Q 2125 4766 2125 4744 
Q 2125 4716 2113 4703 
Q 1800 4397 1592 4047 
Q 1384 3697 1257 3301 
Q 1131 2906 1075 2482 
Q 1019 2059 1019 1600 
Q 1019 -434 2106 -1491 
Q 2125 -1509 2125 -1544 
Q 2125 -1559 2108 -1579 
Q 2091 -1600 2075 -1600 
L 2016 -1600 
Q 1984 -1600 1984 -1588 
z
" transform="scale(0.015625)"/>
     <path id="Cmr10-78" d="M 78 0 
L 78 225 
Q 322 225 537 320 
Q 753 416 903 603 
L 1484 1344 
L 728 2328 
Q 616 2469 483 2501 
Q 350 2534 109 2534 
L 109 2759 
L 1441 2759 
L 1441 2534 
Q 1356 2534 1282 2496 
Q 1209 2459 1209 2388 
Q 1209 2363 1228 2328 
L 1741 1663 
L 2125 2156 
Q 2203 2250 2203 2344 
Q 2203 2422 2151 2478 
Q 2100 2534 2016 2534 
L 2016 2759 
L 3194 2759 
L 3194 2534 
Q 2947 2534 2730 2439 
Q 2513 2344 2363 2156 
L 1856 1509 
L 2675 428 
Q 2797 288 2928 256 
Q 3059 225 3303 225 
L 3303 0 
L 1972 0 
L 1972 225 
Q 2050 225 2122 262 
Q 2194 300 2194 372 
Q 2194 400 2175 428 
L 1600 1191 
L 1141 603 
Q 1069 522 1069 416 
Q 1069 338 1122 281 
Q 1175 225 1247 225 
L 1247 0 
L 78 0 
z
" transform="scale(0.015625)"/>
     <path id="Cmr10-29" d="M 416 -1600 
Q 359 -1600 359 -1544 
Q 359 -1516 372 -1503 
Q 1466 -434 1466 1600 
Q 1466 3634 384 4691 
Q 359 4706 359 4744 
Q 359 4766 376 4783 
Q 394 4800 416 4800 
L 475 4800 
Q 494 4800 506 4788 
Q 966 4425 1272 3906 
Q 1578 3388 1720 2800 
Q 1863 2213 1863 1600 
Q 1863 1147 1786 708 
Q 1709 269 1542 -157 
Q 1375 -584 1119 -945 
Q 863 -1306 506 -1588 
Q 494 -1600 475 -1600 
L 416 -1600 
z
" transform="scale(0.015625)"/>
     <path id="Cmr10-20" transform="scale(0.015625)"/>
     <path id="Cmr10-61" d="M 256 628 
Q 256 1009 556 1248 
Q 856 1488 1276 1586 
Q 1697 1684 2075 1684 
L 2075 1947 
Q 2075 2131 1994 2304 
Q 1913 2478 1759 2589 
Q 1606 2700 1422 2700 
Q 997 2700 775 2509 
Q 897 2509 976 2417 
Q 1056 2325 1056 2203 
Q 1056 2075 965 1984 
Q 875 1894 750 1894 
Q 622 1894 531 1984 
Q 441 2075 441 2203 
Q 441 2541 747 2705 
Q 1053 2869 1422 2869 
Q 1681 2869 1943 2758 
Q 2206 2647 2373 2440 
Q 2541 2234 2541 1959 
L 2541 519 
Q 2541 394 2594 289 
Q 2647 184 2759 184 
Q 2866 184 2917 290 
Q 2969 397 2969 519 
L 2969 928 
L 3156 928 
L 3156 519 
Q 3156 375 3081 245 
Q 3006 116 2879 39 
Q 2753 -38 2606 -38 
Q 2419 -38 2283 107 
Q 2147 253 2131 453 
Q 2013 213 1781 70 
Q 1550 -72 1288 -72 
Q 1044 -72 808 0 
Q 572 72 414 226 
Q 256 381 256 628 
z
M 775 628 
Q 775 403 940 250 
Q 1106 97 1331 97 
Q 1538 97 1706 200 
Q 1875 303 1975 481 
Q 2075 659 2075 856 
L 2075 1522 
Q 1784 1522 1479 1426 
Q 1175 1331 975 1128 
Q 775 925 775 628 
z
" transform="scale(0.015625)"/>
     <path id="Cmr10-64" d="M 1563 -72 
Q 1184 -72 871 133 
Q 559 338 386 672 
Q 213 1006 213 1381 
Q 213 1769 402 2101 
Q 591 2434 916 2631 
Q 1241 2828 1631 2828 
Q 1866 2828 2075 2729 
Q 2284 2631 2438 2456 
L 2438 3788 
Q 2438 3959 2386 4036 
Q 2334 4113 2239 4130 
Q 2144 4147 1941 4147 
L 1941 4372 
L 2888 4441 
L 2888 581 
Q 2888 413 2939 336 
Q 2991 259 3086 242 
Q 3181 225 3384 225 
L 3384 0 
L 2419 -72 
L 2419 331 
Q 2253 141 2025 34 
Q 1797 -72 1563 -72 
z
M 909 556 
Q 1019 347 1201 222 
Q 1384 97 1600 97 
Q 1866 97 2087 250 
Q 2309 403 2419 647 
L 2419 2181 
Q 2344 2322 2230 2433 
Q 2116 2544 1973 2603 
Q 1831 2663 1672 2663 
Q 1338 2663 1134 2473 
Q 931 2284 850 1990 
Q 769 1697 769 1375 
Q 769 1119 795 928 
Q 822 738 909 556 
z
" transform="scale(0.015625)"/>
     <path id="Cmr10-63" d="M 1594 -72 
Q 1206 -72 890 129 
Q 575 331 394 667 
Q 213 1003 213 1381 
Q 213 1759 392 2106 
Q 572 2453 889 2661 
Q 1206 2869 1594 2869 
Q 1969 2869 2276 2722 
Q 2584 2575 2584 2241 
Q 2584 2116 2495 2023 
Q 2406 1931 2278 1931 
Q 2150 1931 2061 2023 
Q 1972 2116 1972 2241 
Q 1972 2353 2044 2436 
Q 2116 2519 2222 2541 
Q 2000 2681 1600 2681 
Q 1294 2681 1106 2478 
Q 919 2275 844 1975 
Q 769 1675 769 1381 
Q 769 1072 861 783 
Q 953 494 1158 305 
Q 1363 116 1672 116 
Q 1975 116 2187 302 
Q 2400 488 2478 788 
Q 2478 825 2528 825 
L 2606 825 
Q 2625 825 2640 808 
Q 2656 791 2656 769 
L 2656 750 
Q 2559 372 2271 150 
Q 1984 -72 1594 -72 
z
" transform="scale(0.015625)"/>
     <path id="Cmr10-6f" d="M 1600 -72 
Q 1216 -72 887 123 
Q 559 319 368 647 
Q 178 975 178 1363 
Q 178 1656 283 1928 
Q 388 2200 583 2414 
Q 778 2628 1037 2748 
Q 1297 2869 1600 2869 
Q 1994 2869 2317 2661 
Q 2641 2453 2828 2104 
Q 3016 1756 3016 1363 
Q 3016 978 2825 648 
Q 2634 319 2307 123 
Q 1981 -72 1600 -72 
z
M 1600 116 
Q 2113 116 2284 487 
Q 2456 859 2456 1434 
Q 2456 1756 2422 1967 
Q 2388 2178 2272 2350 
Q 2200 2456 2089 2536 
Q 1978 2616 1854 2658 
Q 1731 2700 1600 2700 
Q 1400 2700 1220 2609 
Q 1041 2519 922 2350 
Q 803 2169 770 1951 
Q 738 1734 738 1434 
Q 738 1075 800 789 
Q 863 503 1052 309 
Q 1241 116 1600 116 
z
" transform="scale(0.015625)"/>
    </defs>
    <use xlink:href="#Cmr10-73"/>
    <use xlink:href="#Cmr10-69" x="39.404297"/>
    <use xlink:href="#Cmr10-6e" x="67.089844"/>
    <use xlink:href="#Cmr10-28" x="122.607422"/>
    <use xlink:href="#Cmr10-78" x="161.425781"/>
    <use xlink:href="#Cmr10-29" x="214.111328"/>
    <use xlink:href="#Cmr10-20" x="252.929688"/>
    <use xlink:href="#Cmr10-61" x="286.230469"/>
    <use xlink:href="#Cmr10-6e" x="336.230469"/>
    <use xlink:href="#Cmr10-64" x="391.748047"/>
    <use xlink:href="#Cmr10-20" x="447.265625"/>
    <use xlink:href="#Cmr10-63" x="480.566406"/>
    <use xlink:href="#Cmr10-6f" x="524.951172"/>
    <use xlink:href="#Cmr10-73" x="574.951172"/>
    <use xlink:href="#Cmr10-28" x="614.355469"/>
    <use xlink:href="#Cmr10-78" x="653.173828"/>
    <use xlink:href="#Cmr10-29" x="705.859375"/>
   </g>
  </g>
 </g>
 <defs>
  <clipPath id="p0a71c56ec7">
   <rect x="57.6" y="41.472" width="357.12" height="266.112"/>
  </clipPath>
 </defs>
</svg>
\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"out=0\\nimport time\\nf=None\\nfor n in range(3):\\n   for a in np.linspace(0, 9, 100):\\n      f = plot($\\\\sin(x)$, {$x$: (9-a-2, 9-a)}, xrange=[0, 6.28], yrange=[-1.2, 1.2], \\n               fig=f, label=\\\"sin\\\", title=f\\\"sin(x) and cos(x)\\\", color=\\\"green\\\")\\n      f = plot($\\\\cos(x)$, {$x$: (a-2, a)}, xrange=[0, 6.28], yrange=[-1.2, 1.2], \\n               fig=f, label=\\\"cos\\\", color=\\\"red\\\")\\n      out = display(f, out)\\n      time.sleep(0.001)\\n   time.sleep(1)\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 6685043858717139298,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 6404392467195724085,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"Below is an example which produces a fade-in effect by using colors with an alpha component which is animated.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"Below is an example which produces a fade-in effect by using colors with an alpha component which is animated.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 9030279638025875741,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 13149878287361244034,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"image_svg\",\n\t\t\t\t\t\"source\": \"<?xml version="1.0" encoding="utf-8" standalone="no"?>
<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
  "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="460.8pt" height="345.6pt" viewBox="0 0 460.8 345.6" xmlns="http://www.w3.org/2000/svg" version="1.1">
 <metadata>
  <rdf:RDF xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:cc="http://creativecommons.org/ns#" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
   <cc:Work>
    <dc:type rdf:resource="http://purl.org/dc/dcmitype/StillImage"/>
    <dc:date>2025-03-29T11:07:19.769177</dc:date>
    <dc:format>image/svg+xml</dc:format>
    <dc:creator>
     <cc:Agent>
      <dc:title>Matplotlib v3.6.3, https://matplotlib.org/</dc:title>
     </cc:Agent>
    </dc:creator>
   </cc:Work>
  </rdf:RDF>
 </metadata>
 <defs>
  <style type="text/css">*{stroke-linejoin: round; stroke-linecap: butt}</style>
 </defs>
 <g id="figure_1">
  <g id="patch_1">
   <path d="M 0 345.6 
L 460.8 345.6 
L 460.8 0 
L 0 0 
z
" style="fill: #ffffff"/>
  </g>
  <g id="axes_1">
   <g id="patch_2">
    <path d="M 57.6 307.584 
L 414.72 307.584 
L 414.72 41.472 
L 57.6 41.472 
z
" style="fill: #ffffff"/>
   </g>
   <g id="matplotlib.axis_1">
    <g id="xtick_1">
     <g id="line2d_1">
      <defs>
       <path id="mab2badc352" d="M 0 0 
L 0 3.5 
" style="stroke: #000000; stroke-width: 0.8"/>
      </defs>
      <g>
       <use xlink:href="#mab2badc352" x="57.6" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_1">
      <!-- 0 -->
      <g transform="translate(54.41875 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-30" d="M 2034 4250 
Q 1547 4250 1301 3770 
Q 1056 3291 1056 2328 
Q 1056 1369 1301 889 
Q 1547 409 2034 409 
Q 2525 409 2770 889 
Q 3016 1369 3016 2328 
Q 3016 3291 2770 3770 
Q 2525 4250 2034 4250 
z
M 2034 4750 
Q 2819 4750 3233 4129 
Q 3647 3509 3647 2328 
Q 3647 1150 3233 529 
Q 2819 -91 2034 -91 
Q 1250 -91 836 529 
Q 422 1150 422 2328 
Q 422 3509 836 4129 
Q 1250 4750 2034 4750 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-30"/>
      </g>
     </g>
    </g>
    <g id="xtick_2">
     <g id="line2d_2">
      <g>
       <use xlink:href="#mab2badc352" x="114.466242" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_2">
      <!-- 1 -->
      <g transform="translate(111.284992 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-31" d="M 794 531 
L 1825 531 
L 1825 4091 
L 703 3866 
L 703 4441 
L 1819 4666 
L 2450 4666 
L 2450 531 
L 3481 531 
L 3481 0 
L 794 0 
L 794 531 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-31"/>
      </g>
     </g>
    </g>
    <g id="xtick_3">
     <g id="line2d_3">
      <g>
       <use xlink:href="#mab2badc352" x="171.332484" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_3">
      <!-- 2 -->
      <g transform="translate(168.151234 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-32" d="M 1228 531 
L 3431 531 
L 3431 0 
L 469 0 
L 469 531 
Q 828 903 1448 1529 
Q 2069 2156 2228 2338 
Q 2531 2678 2651 2914 
Q 2772 3150 2772 3378 
Q 2772 3750 2511 3984 
Q 2250 4219 1831 4219 
Q 1534 4219 1204 4116 
Q 875 4013 500 3803 
L 500 4441 
Q 881 4594 1212 4672 
Q 1544 4750 1819 4750 
Q 2544 4750 2975 4387 
Q 3406 4025 3406 3419 
Q 3406 3131 3298 2873 
Q 3191 2616 2906 2266 
Q 2828 2175 2409 1742 
Q 1991 1309 1228 531 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-32"/>
      </g>
     </g>
    </g>
    <g id="xtick_4">
     <g id="line2d_4">
      <g>
       <use xlink:href="#mab2badc352" x="228.198726" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_4">
      <!-- 3 -->
      <g transform="translate(225.017476 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-33" d="M 2597 2516 
Q 3050 2419 3304 2112 
Q 3559 1806 3559 1356 
Q 3559 666 3084 287 
Q 2609 -91 1734 -91 
Q 1441 -91 1130 -33 
Q 819 25 488 141 
L 488 750 
Q 750 597 1062 519 
Q 1375 441 1716 441 
Q 2309 441 2620 675 
Q 2931 909 2931 1356 
Q 2931 1769 2642 2001 
Q 2353 2234 1838 2234 
L 1294 2234 
L 1294 2753 
L 1863 2753 
Q 2328 2753 2575 2939 
Q 2822 3125 2822 3475 
Q 2822 3834 2567 4026 
Q 2313 4219 1838 4219 
Q 1578 4219 1281 4162 
Q 984 4106 628 3988 
L 628 4550 
Q 988 4650 1302 4700 
Q 1616 4750 1894 4750 
Q 2613 4750 3031 4423 
Q 3450 4097 3450 3541 
Q 3450 3153 3228 2886 
Q 3006 2619 2597 2516 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-33"/>
      </g>
     </g>
    </g>
    <g id="xtick_5">
     <g id="line2d_5">
      <g>
       <use xlink:href="#mab2badc352" x="285.064968" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_5">
      <!-- 4 -->
      <g transform="translate(281.883718 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-34" d="M 2419 4116 
L 825 1625 
L 2419 1625 
L 2419 4116 
z
M 2253 4666 
L 3047 4666 
L 3047 1625 
L 3713 1625 
L 3713 1100 
L 3047 1100 
L 3047 0 
L 2419 0 
L 2419 1100 
L 313 1100 
L 313 1709 
L 2253 4666 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-34"/>
      </g>
     </g>
    </g>
    <g id="xtick_6">
     <g id="line2d_6">
      <g>
       <use xlink:href="#mab2badc352" x="341.93121" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_6">
      <!-- 5 -->
      <g transform="translate(338.74996 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-35" d="M 691 4666 
L 3169 4666 
L 3169 4134 
L 1269 4134 
L 1269 2991 
Q 1406 3038 1543 3061 
Q 1681 3084 1819 3084 
Q 2600 3084 3056 2656 
Q 3513 2228 3513 1497 
Q 3513 744 3044 326 
Q 2575 -91 1722 -91 
Q 1428 -91 1123 -41 
Q 819 9 494 109 
L 494 744 
Q 775 591 1075 516 
Q 1375 441 1709 441 
Q 2250 441 2565 725 
Q 2881 1009 2881 1497 
Q 2881 1984 2565 2268 
Q 2250 2553 1709 2553 
Q 1456 2553 1204 2497 
Q 953 2441 691 2322 
L 691 4666 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-35"/>
      </g>
     </g>
    </g>
    <g id="xtick_7">
     <g id="line2d_7">
      <g>
       <use xlink:href="#mab2badc352" x="398.797452" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_7">
      <!-- 6 -->
      <g transform="translate(395.616202 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-36" d="M 2113 2584 
Q 1688 2584 1439 2293 
Q 1191 2003 1191 1497 
Q 1191 994 1439 701 
Q 1688 409 2113 409 
Q 2538 409 2786 701 
Q 3034 994 3034 1497 
Q 3034 2003 2786 2293 
Q 2538 2584 2113 2584 
z
M 3366 4563 
L 3366 3988 
Q 3128 4100 2886 4159 
Q 2644 4219 2406 4219 
Q 1781 4219 1451 3797 
Q 1122 3375 1075 2522 
Q 1259 2794 1537 2939 
Q 1816 3084 2150 3084 
Q 2853 3084 3261 2657 
Q 3669 2231 3669 1497 
Q 3669 778 3244 343 
Q 2819 -91 2113 -91 
Q 1303 -91 875 529 
Q 447 1150 447 2328 
Q 447 3434 972 4092 
Q 1497 4750 2381 4750 
Q 2619 4750 2861 4703 
Q 3103 4656 3366 4563 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-36"/>
      </g>
     </g>
    </g>
   </g>
   <g id="matplotlib.axis_2">
    <g id="ytick_1">
     <g id="line2d_8">
      <defs>
       <path id="m7d8b9720ae" d="M 0 0 
L -3.5 0 
" style="stroke: #000000; stroke-width: 0.8"/>
      </defs>
      <g>
       <use xlink:href="#m7d8b9720ae" x="57.6" y="285.408" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_8">
      <!-- −1.0 -->
      <g transform="translate(26.317187 289.207219) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-2212" d="M 678 2272 
L 4684 2272 
L 4684 1741 
L 678 1741 
L 678 2272 
z
" transform="scale(0.015625)"/>
        <path id="DejaVuSans-2e" d="M 684 794 
L 1344 794 
L 1344 0 
L 684 0 
L 684 794 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-2212"/>
       <use xlink:href="#DejaVuSans-31" x="83.789062"/>
       <use xlink:href="#DejaVuSans-2e" x="147.412109"/>
       <use xlink:href="#DejaVuSans-30" x="179.199219"/>
      </g>
     </g>
    </g>
    <g id="ytick_2">
     <g id="line2d_9">
      <g>
       <use xlink:href="#m7d8b9720ae" x="57.6" y="229.968" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_9">
      <!-- −0.5 -->
      <g transform="translate(26.317187 233.767219) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-2212"/>
       <use xlink:href="#DejaVuSans-30" x="83.789062"/>
       <use xlink:href="#DejaVuSans-2e" x="147.412109"/>
       <use xlink:href="#DejaVuSans-35" x="179.199219"/>
      </g>
     </g>
    </g>
    <g id="ytick_3">
     <g id="line2d_10">
      <g>
       <use xlink:href="#m7d8b9720ae" x="57.6" y="174.528" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_10">
      <!-- 0.0 -->
      <g transform="translate(34.696875 178.327219) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-30"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-30" x="95.410156"/>
      </g>
     </g>
    </g>
    <g id="ytick_4">
     <g id="line2d_11">
      <g>
       <use xlink:href="#m7d8b9720ae" x="57.6" y="119.088" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_11">
      <!-- 0.5 -->
      <g transform="translate(34.696875 122.887219) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-30"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-35" x="95.410156"/>
      </g>
     </g>
    </g>
    <g id="ytick_5">
     <g id="line2d_12">
      <g>
       <use xlink:href="#m7d8b9720ae" x="57.6" y="63.648" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_12">
      <!-- 1.0 -->
      <g transform="translate(34.696875 67.447219) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-31"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-30" x="95.410156"/>
      </g>
     </g>
    </g>
   </g>
   <g id="line2d_13">
    <path d="M 57.6 174.528 
L 61.207273 167.499116 
L 64.814545 160.498506 
L 68.421818 153.554331 
L 72.029091 146.694524 
L 75.636364 139.946679 
L 79.243636 133.33794 
L 82.850909 126.89489 
L 86.458182 120.643448 
L 90.065455 114.60876 
L 93.672727 108.815101 
L 97.28 103.285776 
L 100.887273 98.043028 
L 104.494545 93.107946 
L 108.101818 88.500382 
L 111.709091 84.23887 
L 115.316364 80.340551 
L 118.923636 76.821108 
L 122.530909 73.694697 
L 126.138182 70.973896 
L 129.745455 68.669647 
L 133.352727 66.791221 
L 136.96 65.346173 
L 140.567273 64.340316 
L 144.174545 63.777696 
L 147.781818 63.660578 
L 151.389091 63.98943 
L 154.996364 64.762932 
L 158.603636 65.97797 
L 162.210909 67.629659 
L 165.818182 69.711353 
L 169.425455 72.214679 
L 173.032727 75.129568 
L 176.64 78.444293 
L 180.247273 82.145521 
L 183.854545 86.218364 
L 187.461818 90.646439 
L 191.069091 95.411932 
L 194.676364 100.495675 
L 198.283636 105.877219 
L 201.890909 111.534914 
L 205.498182 117.446004 
L 209.105455 123.586709 
L 212.712727 129.93233 
L 216.32 136.457339 
L 219.927273 143.13549 
L 223.534545 149.93992 
L 227.141818 156.843257 
L 230.749091 163.817732 
L 234.356364 170.83529 
L 237.963636 177.867701 
L 241.570909 184.886679 
L 245.178182 191.863988 
L 248.785455 198.771562 
L 252.392727 205.581615 
L 256 212.266752 
L 259.607273 218.800083 
L 263.214545 225.155327 
L 266.821818 231.306918 
L 270.429091 237.230113 
L 274.036364 242.901084 
L 277.643636 248.29702 
L 281.250909 253.396215 
L 284.858182 258.178157 
L 288.465455 262.623611 
L 292.072727 266.714695 
L 295.68 270.434951 
L 299.287273 273.769416 
L 302.894545 276.704675 
L 306.501818 279.228921 
L 310.109091 281.332002 
L 313.716364 283.005455 
L 317.323636 284.242552 
L 320.930909 285.038314 
L 324.538182 285.38954 
L 328.145455 285.294819 
L 331.752727 284.754531 
L 335.36 283.77085 
L 338.967273 282.347732 
L 342.574545 280.490901 
L 346.181818 278.207828 
L 349.789091 275.507696 
L 353.396364 272.401366 
L 357.003636 268.901334 
L 360.610909 265.021679 
L 364.218182 260.778007 
L 367.825455 256.187389 
L 371.432727 251.268291 
L 375.04 246.040499 
L 378.647273 240.525044 
L 382.254545 234.744111 
L 385.861818 228.720955 
L 389.469091 222.479804 
L 393.076364 216.045764 
L 396.683636 209.444715 
L 400.290909 202.703212 
L 403.898182 195.848372 
L 407.505455 188.90777 
L 411.112727 181.909324 
L 414.72 174.881186 
" clip-path="url(#p8e129a1b15)" style="fill: none; stroke: #008000; stroke-width: 1.5; stroke-linecap: square"/>
   </g>
   <g id="line2d_14">
    <path d="M 57.6 63.648 
L 61.207273 63.871011 
L 64.814545 64.539147 
L 68.421818 65.649721 
L 72.029091 67.198265 
L 75.636364 69.17855 
L 79.243636 71.58261 
L 82.850909 74.400775 
L 86.458182 77.621708 
L 90.065455 81.232453 
L 93.672727 85.218486 
L 97.28 89.563773 
L 100.887273 94.250833 
L 104.494545 99.260814 
L 108.101818 104.573562 
L 111.709091 110.167707 
L 115.316364 116.020745 
L 118.923636 122.109132 
L 122.530909 128.408378 
L 126.138182 134.893143 
L 129.745455 141.537342 
L 133.352727 148.314249 
L 136.96 155.196601 
L 140.567273 162.156716 
L 144.174545 169.166595 
L 147.781818 176.19804 
L 151.389091 183.222768 
L 154.996364 190.21252 
L 158.603636 197.13918 
L 162.210909 203.974886 
L 165.818182 210.692139 
L 169.425455 217.26392 
L 173.032727 223.663792 
L 176.64 229.866013 
L 180.247273 235.845632 
L 183.854545 241.578598 
L 187.461818 247.041847 
L 191.069091 252.213405 
L 194.676364 257.072469 
L 198.283636 261.599491 
L 201.890909 265.776263 
L 205.498182 269.585983 
L 209.105455 273.013325 
L 212.712727 276.044504 
L 216.32 278.667326 
L 219.927273 280.87124 
L 223.534545 282.647382 
L 227.141818 283.988606 
L 230.749091 284.889518 
L 234.356364 285.346493 
L 237.963636 285.357693 
L 241.570909 284.923073 
L 245.178182 284.044382 
L 248.785455 282.725154 
L 252.392727 280.970695 
L 256 278.788064 
L 259.607273 276.18604 
L 263.214545 273.175089 
L 266.821818 269.767324 
L 270.429091 265.976452 
L 274.036364 261.817723 
L 277.643636 257.307865 
L 281.250909 252.46502 
L 284.858182 247.308668 
L 288.465455 241.85955 
L 292.072727 236.139587 
L 295.68 230.171787 
L 299.287273 223.980157 
L 302.894545 217.589602 
L 306.501818 211.025828 
L 310.109091 204.31524 
L 313.716364 197.48483 
L 317.323636 190.562075 
L 320.930909 183.574822 
L 324.538182 176.551178 
L 328.145455 169.519395 
L 331.752727 162.50776 
L 335.36 155.544476 
L 338.967273 148.657556 
L 342.574545 141.874701 
L 346.181818 135.223196 
L 349.789091 128.729797 
L 353.396364 122.420624 
L 357.003636 116.321057 
L 360.610909 110.455631 
L 364.218182 104.847941 
L 367.825455 99.520543 
L 371.432727 94.494868 
L 375.04 89.791132 
L 378.647273 85.428255 
L 382.254545 81.423788 
L 385.861818 77.793838 
L 389.469091 74.553009 
L 393.076364 71.714335 
L 396.683636 69.289236 
L 400.290909 67.287467 
L 403.898182 65.717081 
L 407.505455 64.584393 
L 411.112727 63.893962 
L 414.72 63.648563 
" clip-path="url(#p8e129a1b15)" style="fill: none; stroke: #cc0000; stroke-width: 1.5; stroke-linecap: square"/>
   </g>
   <g id="patch_3">
    <path d="M 57.6 307.584 
L 57.6 41.472 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
   <g id="patch_4">
    <path d="M 414.72 307.584 
L 414.72 41.472 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
   <g id="patch_5">
    <path d="M 57.6 307.584 
L 414.72 307.584 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
   <g id="patch_6">
    <path d="M 57.6 41.472 
L 414.72 41.472 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
  </g>
  <g id="text_13">
   <!-- sin(x) and cos(x) -->
   <g transform="translate(163.380938 27.324) scale(0.18 -0.18)">
    <defs>
     <path id="Cmr10-73" d="M 213 -19 
L 213 1025 
Q 213 1075 269 1075 
L 347 1075 
Q 384 1075 397 1025 
Q 575 97 1259 97 
Q 1563 97 1767 234 
Q 1972 372 1972 659 
Q 1972 866 1812 1011 
Q 1653 1156 1434 1209 
L 1006 1294 
Q 791 1341 614 1437 
Q 438 1534 325 1695 
Q 213 1856 213 2069 
Q 213 2350 361 2529 
Q 509 2709 746 2789 
Q 984 2869 1259 2869 
Q 1588 2869 1831 2694 
L 2016 2853 
Q 2016 2869 2047 2869 
L 2094 2869 
Q 2113 2869 2128 2851 
Q 2144 2834 2144 2816 
L 2144 1978 
Q 2144 1919 2094 1919 
L 2016 1919 
Q 1959 1919 1959 1978 
Q 1959 2313 1773 2516 
Q 1588 2719 1253 2719 
Q 966 2719 755 2612 
Q 544 2506 544 2247 
Q 544 2069 695 1955 
Q 847 1841 1050 1791 
L 1484 1709 
Q 1703 1659 1892 1540 
Q 2081 1422 2192 1240 
Q 2303 1059 2303 831 
Q 2303 600 2223 429 
Q 2144 259 2001 146 
Q 1859 34 1665 -19 
Q 1472 -72 1259 -72 
Q 859 -72 575 197 
L 341 -56 
Q 341 -72 306 -72 
L 269 -72 
Q 213 -72 213 -19 
z
" transform="scale(0.015625)"/>
     <path id="Cmr10-69" d="M 197 0 
L 197 225 
Q 416 225 556 259 
Q 697 294 697 428 
L 697 2175 
Q 697 2422 601 2478 
Q 506 2534 225 2534 
L 225 2759 
L 1147 2828 
L 1147 428 
Q 1147 294 1269 259 
Q 1391 225 1594 225 
L 1594 0 
L 197 0 
z
M 469 3928 
Q 469 4069 575 4175 
Q 681 4281 819 4281 
Q 909 4281 993 4234 
Q 1078 4188 1125 4103 
Q 1172 4019 1172 3928 
Q 1172 3791 1065 3684 
Q 959 3578 819 3578 
Q 681 3578 575 3684 
Q 469 3791 469 3928 
z
" transform="scale(0.015625)"/>
     <path id="Cmr10-6e" d="M 191 0 
L 191 225 
Q 409 225 550 259 
Q 691 294 691 428 
L 691 2175 
Q 691 2347 639 2423 
Q 588 2500 491 2517 
Q 394 2534 191 2534 
L 191 2759 
L 1119 2828 
L 1119 2203 
Q 1247 2478 1498 2653 
Q 1750 2828 2047 2828 
Q 2491 2828 2714 2615 
Q 2938 2403 2938 1966 
L 2938 428 
Q 2938 294 3078 259 
Q 3219 225 3438 225 
L 3438 0 
L 1972 0 
L 1972 225 
Q 2191 225 2331 259 
Q 2472 294 2472 428 
L 2472 1947 
Q 2472 2259 2381 2461 
Q 2291 2663 2009 2663 
Q 1638 2663 1398 2366 
Q 1159 2069 1159 1691 
L 1159 428 
Q 1159 294 1300 259 
Q 1441 225 1656 225 
L 1656 0 
L 191 0 
z
" transform="scale(0.015625)"/>
     <path id="Cmr10-28" d="M 1984 -1588 
Q 1628 -1306 1370 -942 
Q 1113 -578 948 -165 
Q 784 247 703 697 
Q 622 1147 622 1600 
Q 622 2059 703 2509 
Q 784 2959 951 3375 
Q 1119 3791 1378 4153 
Q 1638 4516 1984 4788 
Q 1984 4800 2016 4800 
L 2075 4800 
Q 2094 4800 2109 4783 
Q 2125 4766 2125 4744 
Q 2125 4716 2113 4703 
Q 1800 4397 1592 4047 
Q 1384 3697 1257 3301 
Q 1131 2906 1075 2482 
Q 1019 2059 1019 1600 
Q 1019 -434 2106 -1491 
Q 2125 -1509 2125 -1544 
Q 2125 -1559 2108 -1579 
Q 2091 -1600 2075 -1600 
L 2016 -1600 
Q 1984 -1600 1984 -1588 
z
" transform="scale(0.015625)"/>
     <path id="Cmr10-78" d="M 78 0 
L 78 225 
Q 322 225 537 320 
Q 753 416 903 603 
L 1484 1344 
L 728 2328 
Q 616 2469 483 2501 
Q 350 2534 109 2534 
L 109 2759 
L 1441 2759 
L 1441 2534 
Q 1356 2534 1282 2496 
Q 1209 2459 1209 2388 
Q 1209 2363 1228 2328 
L 1741 1663 
L 2125 2156 
Q 2203 2250 2203 2344 
Q 2203 2422 2151 2478 
Q 2100 2534 2016 2534 
L 2016 2759 
L 3194 2759 
L 3194 2534 
Q 2947 2534 2730 2439 
Q 2513 2344 2363 2156 
L 1856 1509 
L 2675 428 
Q 2797 288 2928 256 
Q 3059 225 3303 225 
L 3303 0 
L 1972 0 
L 1972 225 
Q 2050 225 2122 262 
Q 2194 300 2194 372 
Q 2194 400 2175 428 
L 1600 1191 
L 1141 603 
Q 1069 522 1069 416 
Q 1069 338 1122 281 
Q 1175 225 1247 225 
L 1247 0 
L 78 0 
z
" transform="scale(0.015625)"/>
     <path id="Cmr10-29" d="M 416 -1600 
Q 359 -1600 359 -1544 
Q 359 -1516 372 -1503 
Q 1466 -434 1466 1600 
Q 1466 3634 384 4691 
Q 359 4706 359 4744 
Q 359 4766 376 4783 
Q 394 4800 416 4800 
L 475 4800 
Q 494 4800 506 4788 
Q 966 4425 1272 3906 
Q 1578 3388 1720 2800 
Q 1863 2213 1863 1600 
Q 1863 1147 1786 708 
Q 1709 269 1542 -157 
Q 1375 -584 1119 -945 
Q 863 -1306 506 -1588 
Q 494 -1600 475 -1600 
L 416 -1600 
z
" transform="scale(0.015625)"/>
     <path id="Cmr10-20" transform="scale(0.015625)"/>
     <path id="Cmr10-61" d="M 256 628 
Q 256 1009 556 1248 
Q 856 1488 1276 1586 
Q 1697 1684 2075 1684 
L 2075 1947 
Q 2075 2131 1994 2304 
Q 1913 2478 1759 2589 
Q 1606 2700 1422 2700 
Q 997 2700 775 2509 
Q 897 2509 976 2417 
Q 1056 2325 1056 2203 
Q 1056 2075 965 1984 
Q 875 1894 750 1894 
Q 622 1894 531 1984 
Q 441 2075 441 2203 
Q 441 2541 747 2705 
Q 1053 2869 1422 2869 
Q 1681 2869 1943 2758 
Q 2206 2647 2373 2440 
Q 2541 2234 2541 1959 
L 2541 519 
Q 2541 394 2594 289 
Q 2647 184 2759 184 
Q 2866 184 2917 290 
Q 2969 397 2969 519 
L 2969 928 
L 3156 928 
L 3156 519 
Q 3156 375 3081 245 
Q 3006 116 2879 39 
Q 2753 -38 2606 -38 
Q 2419 -38 2283 107 
Q 2147 253 2131 453 
Q 2013 213 1781 70 
Q 1550 -72 1288 -72 
Q 1044 -72 808 0 
Q 572 72 414 226 
Q 256 381 256 628 
z
M 775 628 
Q 775 403 940 250 
Q 1106 97 1331 97 
Q 1538 97 1706 200 
Q 1875 303 1975 481 
Q 2075 659 2075 856 
L 2075 1522 
Q 1784 1522 1479 1426 
Q 1175 1331 975 1128 
Q 775 925 775 628 
z
" transform="scale(0.015625)"/>
     <path id="Cmr10-64" d="M 1563 -72 
Q 1184 -72 871 133 
Q 559 338 386 672 
Q 213 1006 213 1381 
Q 213 1769 402 2101 
Q 591 2434 916 2631 
Q 1241 2828 1631 2828 
Q 1866 2828 2075 2729 
Q 2284 2631 2438 2456 
L 2438 3788 
Q 2438 3959 2386 4036 
Q 2334 4113 2239 4130 
Q 2144 4147 1941 4147 
L 1941 4372 
L 2888 4441 
L 2888 581 
Q 2888 413 2939 336 
Q 2991 259 3086 242 
Q 3181 225 3384 225 
L 3384 0 
L 2419 -72 
L 2419 331 
Q 2253 141 2025 34 
Q 1797 -72 1563 -72 
z
M 909 556 
Q 1019 347 1201 222 
Q 1384 97 1600 97 
Q 1866 97 2087 250 
Q 2309 403 2419 647 
L 2419 2181 
Q 2344 2322 2230 2433 
Q 2116 2544 1973 2603 
Q 1831 2663 1672 2663 
Q 1338 2663 1134 2473 
Q 931 2284 850 1990 
Q 769 1697 769 1375 
Q 769 1119 795 928 
Q 822 738 909 556 
z
" transform="scale(0.015625)"/>
     <path id="Cmr10-63" d="M 1594 -72 
Q 1206 -72 890 129 
Q 575 331 394 667 
Q 213 1003 213 1381 
Q 213 1759 392 2106 
Q 572 2453 889 2661 
Q 1206 2869 1594 2869 
Q 1969 2869 2276 2722 
Q 2584 2575 2584 2241 
Q 2584 2116 2495 2023 
Q 2406 1931 2278 1931 
Q 2150 1931 2061 2023 
Q 1972 2116 1972 2241 
Q 1972 2353 2044 2436 
Q 2116 2519 2222 2541 
Q 2000 2681 1600 2681 
Q 1294 2681 1106 2478 
Q 919 2275 844 1975 
Q 769 1675 769 1381 
Q 769 1072 861 783 
Q 953 494 1158 305 
Q 1363 116 1672 116 
Q 1975 116 2187 302 
Q 2400 488 2478 788 
Q 2478 825 2528 825 
L 2606 825 
Q 2625 825 2640 808 
Q 2656 791 2656 769 
L 2656 750 
Q 2559 372 2271 150 
Q 1984 -72 1594 -72 
z
" transform="scale(0.015625)"/>
     <path id="Cmr10-6f" d="M 1600 -72 
Q 1216 -72 887 123 
Q 559 319 368 647 
Q 178 975 178 1363 
Q 178 1656 283 1928 
Q 388 2200 583 2414 
Q 778 2628 1037 2748 
Q 1297 2869 1600 2869 
Q 1994 2869 2317 2661 
Q 2641 2453 2828 2104 
Q 3016 1756 3016 1363 
Q 3016 978 2825 648 
Q 2634 319 2307 123 
Q 1981 -72 1600 -72 
z
M 1600 116 
Q 2113 116 2284 487 
Q 2456 859 2456 1434 
Q 2456 1756 2422 1967 
Q 2388 2178 2272 2350 
Q 2200 2456 2089 2536 
Q 1978 2616 1854 2658 
Q 1731 2700 1600 2700 
Q 1400 2700 1220 2609 
Q 1041 2519 922 2350 
Q 803 2169 770 1951 
Q 738 1734 738 1434 
Q 738 1075 800 789 
Q 863 503 1052 309 
Q 1241 116 1600 116 
z
" transform="scale(0.015625)"/>
    </defs>
    <use xlink:href="#Cmr10-73"/>
    <use xlink:href="#Cmr10-69" x="39.404297"/>
    <use xlink:href="#Cmr10-6e" x="67.089844"/>
    <use xlink:href="#Cmr10-28" x="122.607422"/>
    <use xlink:href="#Cmr10-78" x="161.425781"/>
    <use xlink:href="#Cmr10-29" x="214.111328"/>
    <use xlink:href="#Cmr10-20" x="252.929688"/>
    <use xlink:href="#Cmr10-61" x="286.230469"/>
    <use xlink:href="#Cmr10-6e" x="336.230469"/>
    <use xlink:href="#Cmr10-64" x="391.748047"/>
    <use xlink:href="#Cmr10-20" x="447.265625"/>
    <use xlink:href="#Cmr10-63" x="480.566406"/>
    <use xlink:href="#Cmr10-6f" x="524.951172"/>
    <use xlink:href="#Cmr10-73" x="574.951172"/>
    <use xlink:href="#Cmr10-28" x="614.355469"/>
    <use xlink:href="#Cmr10-78" x="653.173828"/>
    <use xlink:href="#Cmr10-29" x="705.859375"/>
   </g>
  </g>
 </g>
 <defs>
  <clipPath id="p8e129a1b15">
   <rect x="57.6" y="41.472" width="357.12" height="266.112"/>
  </clipPath>
 </defs>
</svg>
\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"out=0\\nf=None\\nfor alpha in np.linspace(0, 1.0, 50):\\n   f = plot($\\\\sin(x)$, {$x$: (0, 6.28)}, xrange=[0, 6.28], yrange=[-1.2, 1.2], \\n            fig=f, label=\\\"sin\\\", title=f\\\"sin(x)\\\", color=(0, .5, 0, alpha))\\n   out = display(f, out)\\n   time.sleep(0.01)\\n\\nfor alpha in np.linspace(0, 1.0, 50):\\n   f = plot($\\\\cos(x)$, {$x$: (0, 6.28)}, xrange=[0, 6.28], yrange=[-1.2, 1.2], \\n            fig=f, label=\\\"cos\\\", title=f\\\"sin(x) and cos(x)\\\", color=(0.8, 0, 0, alpha))\\n   out = display(f, out)\\n   time.sleep(0.01)\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 16361351856156328164,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 8233462391047847579,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"You can do this with any of Cadabra's plot types, e.g. parametric plots, as in the example below.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"You can do this with any of Cadabra's plot types, e.g. parametric plots, as in the example below.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 14535915201574355545,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 2408980807471662295,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"image_svg\",\n\t\t\t\t\t\"source\": \"<?xml version="1.0" encoding="utf-8" standalone="no"?>
<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
  "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="460.8pt" height="345.6pt" viewBox="0 0 460.8 345.6" xmlns="http://www.w3.org/2000/svg" version="1.1">
 <metadata>
  <rdf:RDF xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:cc="http://creativecommons.org/ns#" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
   <cc:Work>
    <dc:type rdf:resource="http://purl.org/dc/dcmitype/StillImage"/>
    <dc:date>2025-03-29T11:07:22.747725</dc:date>
    <dc:format>image/svg+xml</dc:format>
    <dc:creator>
     <cc:Agent>
      <dc:title>Matplotlib v3.6.3, https://matplotlib.org/</dc:title>
     </cc:Agent>
    </dc:creator>
   </cc:Work>
  </rdf:RDF>
 </metadata>
 <defs>
  <style type="text/css">*{stroke-linejoin: round; stroke-linecap: butt}</style>
 </defs>
 <g id="figure_1">
  <g id="patch_1">
   <path d="M 0 345.6 
L 460.8 345.6 
L 460.8 0 
L 0 0 
z
" style="fill: #ffffff"/>
  </g>
  <g id="axes_1">
   <g id="patch_2">
    <path d="M 69.84 307.584 
L 402.48 307.584 
L 402.48 41.472 
L 69.84 41.472 
z
" style="fill: #ffffff"/>
   </g>
   <g id="matplotlib.axis_1">
    <g id="xtick_1">
     <g id="line2d_1">
      <defs>
       <path id="m9eda177aa4" d="M 0 0 
L 0 3.5 
" style="stroke: #000000; stroke-width: 0.8"/>
      </defs>
      <g>
       <use xlink:href="#m9eda177aa4" x="69.84" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_1">
      <!-- −1.5 -->
      <g transform="translate(57.698594 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-2212" d="M 678 2272 
L 4684 2272 
L 4684 1741 
L 678 1741 
L 678 2272 
z
" transform="scale(0.015625)"/>
        <path id="DejaVuSans-31" d="M 794 531 
L 1825 531 
L 1825 4091 
L 703 3866 
L 703 4441 
L 1819 4666 
L 2450 4666 
L 2450 531 
L 3481 531 
L 3481 0 
L 794 0 
L 794 531 
z
" transform="scale(0.015625)"/>
        <path id="DejaVuSans-2e" d="M 684 794 
L 1344 794 
L 1344 0 
L 684 0 
L 684 794 
z
" transform="scale(0.015625)"/>
        <path id="DejaVuSans-35" d="M 691 4666 
L 3169 4666 
L 3169 4134 
L 1269 4134 
L 1269 2991 
Q 1406 3038 1543 3061 
Q 1681 3084 1819 3084 
Q 2600 3084 3056 2656 
Q 3513 2228 3513 1497 
Q 3513 744 3044 326 
Q 2575 -91 1722 -91 
Q 1428 -91 1123 -41 
Q 819 9 494 109 
L 494 744 
Q 775 591 1075 516 
Q 1375 441 1709 441 
Q 2250 441 2565 725 
Q 2881 1009 2881 1497 
Q 2881 1984 2565 2268 
Q 2250 2553 1709 2553 
Q 1456 2553 1204 2497 
Q 953 2441 691 2322 
L 691 4666 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-2212"/>
       <use xlink:href="#DejaVuSans-31" x="83.789062"/>
       <use xlink:href="#DejaVuSans-2e" x="147.412109"/>
       <use xlink:href="#DejaVuSans-35" x="179.199219"/>
      </g>
     </g>
    </g>
    <g id="xtick_2">
     <g id="line2d_2">
      <g>
       <use xlink:href="#m9eda177aa4" x="125.28" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_2">
      <!-- −1.0 -->
      <g transform="translate(113.138594 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-30" d="M 2034 4250 
Q 1547 4250 1301 3770 
Q 1056 3291 1056 2328 
Q 1056 1369 1301 889 
Q 1547 409 2034 409 
Q 2525 409 2770 889 
Q 3016 1369 3016 2328 
Q 3016 3291 2770 3770 
Q 2525 4250 2034 4250 
z
M 2034 4750 
Q 2819 4750 3233 4129 
Q 3647 3509 3647 2328 
Q 3647 1150 3233 529 
Q 2819 -91 2034 -91 
Q 1250 -91 836 529 
Q 422 1150 422 2328 
Q 422 3509 836 4129 
Q 1250 4750 2034 4750 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-2212"/>
       <use xlink:href="#DejaVuSans-31" x="83.789062"/>
       <use xlink:href="#DejaVuSans-2e" x="147.412109"/>
       <use xlink:href="#DejaVuSans-30" x="179.199219"/>
      </g>
     </g>
    </g>
    <g id="xtick_3">
     <g id="line2d_3">
      <g>
       <use xlink:href="#m9eda177aa4" x="180.72" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_3">
      <!-- −0.5 -->
      <g transform="translate(168.578594 322.182437) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-2212"/>
       <use xlink:href="#DejaVuSans-30" x="83.789062"/>
       <use xlink:href="#DejaVuSans-2e" x="147.412109"/>
       <use xlink:href="#DejaVuSans-35" x="179.199219"/>
      </g>
     </g>
    </g>
    <g id="xtick_4">
     <g id="line2d_4">
      <g>
       <use xlink:href="#m9eda177aa4" x="236.16" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_4">
      <!-- 0.0 -->
      <g transform="translate(228.208438 322.182437) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-30"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-30" x="95.410156"/>
      </g>
     </g>
    </g>
    <g id="xtick_5">
     <g id="line2d_5">
      <g>
       <use xlink:href="#m9eda177aa4" x="291.6" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_5">
      <!-- 0.5 -->
      <g transform="translate(283.648438 322.182437) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-30"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-35" x="95.410156"/>
      </g>
     </g>
    </g>
    <g id="xtick_6">
     <g id="line2d_6">
      <g>
       <use xlink:href="#m9eda177aa4" x="347.04" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_6">
      <!-- 1.0 -->
      <g transform="translate(339.088437 322.182437) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-31"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-30" x="95.410156"/>
      </g>
     </g>
    </g>
    <g id="xtick_7">
     <g id="line2d_7">
      <g>
       <use xlink:href="#m9eda177aa4" x="402.48" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_7">
      <!-- 1.5 -->
      <g transform="translate(394.528437 322.182437) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-31"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-35" x="95.410156"/>
      </g>
     </g>
    </g>
   </g>
   <g id="matplotlib.axis_2">
    <g id="ytick_1">
     <g id="line2d_8">
      <defs>
       <path id="m4c499381ca" d="M 0 0 
L -3.5 0 
" style="stroke: #000000; stroke-width: 0.8"/>
      </defs>
      <g>
       <use xlink:href="#m4c499381ca" x="69.84" y="285.408" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_8">
      <!-- −1.0 -->
      <g transform="translate(38.557188 289.207219) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-2212"/>
       <use xlink:href="#DejaVuSans-31" x="83.789062"/>
       <use xlink:href="#DejaVuSans-2e" x="147.412109"/>
       <use xlink:href="#DejaVuSans-30" x="179.199219"/>
      </g>
     </g>
    </g>
    <g id="ytick_2">
     <g id="line2d_9">
      <g>
       <use xlink:href="#m4c499381ca" x="69.84" y="229.968" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_9">
      <!-- −0.5 -->
      <g transform="translate(38.557188 233.767219) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-2212"/>
       <use xlink:href="#DejaVuSans-30" x="83.789062"/>
       <use xlink:href="#DejaVuSans-2e" x="147.412109"/>
       <use xlink:href="#DejaVuSans-35" x="179.199219"/>
      </g>
     </g>
    </g>
    <g id="ytick_3">
     <g id="line2d_10">
      <g>
       <use xlink:href="#m4c499381ca" x="69.84" y="174.528" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_10">
      <!-- 0.0 -->
      <g transform="translate(46.936875 178.327219) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-30"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-30" x="95.410156"/>
      </g>
     </g>
    </g>
    <g id="ytick_4">
     <g id="line2d_11">
      <g>
       <use xlink:href="#m4c499381ca" x="69.84" y="119.088" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_11">
      <!-- 0.5 -->
      <g transform="translate(46.936875 122.887219) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-30"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-35" x="95.410156"/>
      </g>
     </g>
    </g>
    <g id="ytick_5">
     <g id="line2d_12">
      <g>
       <use xlink:href="#m4c499381ca" x="69.84" y="63.648" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_12">
      <!-- 1.0 -->
      <g transform="translate(46.936875 67.447219) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-31"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-30" x="95.410156"/>
      </g>
     </g>
    </g>
   </g>
   <g id="line2d_13">
    <path d="M 347.025938 176.29386 
L 347.033442 175.733911 
L 347.038119 175.173931 
L 347.039967 174.613934 
L 347.038987 174.053936 
L 347.035178 173.493949 
L 347.028542 172.933989 
L 347.019077 172.37407 
L 347.006785 171.814205 
L 346.991665 171.25441 
L 346.973718 170.694698 
L 346.952945 170.135084 
L 346.929346 169.575582 
L 346.902921 169.016207 
L 346.873671 168.456972 
L 346.841598 167.897892 
L 346.806701 167.338981 
L 346.768982 166.780253 
L 346.728441 166.221723 
L 346.68508 165.663405 
L 346.6389 165.105313 
L 346.589902 164.547461 
L 346.538087 163.989864 
L 346.483457 163.432536 
L 346.426012 162.87549 
L 346.365755 162.318742 
L 346.302687 161.762306 
L 346.236809 161.206195 
L 346.168124 160.650423 
L 346.096632 160.095006 
L 346.022336 159.539957 
L 345.945238 158.98529 
L 345.86534 158.43102 
L 345.782643 157.87716 
L 345.69715 157.323725 
L 345.608864 156.770729 
L 345.517785 156.218186 
L 345.423917 155.66611 
L 345.327262 155.114515 
L 345.227822 154.563415 
L 345.1256 154.012824 
L 345.020599 153.462757 
L 344.912821 152.913227 
L 344.802268 152.364248 
L 344.688945 151.815835 
L 344.572854 151.268001 
L 344.453997 150.72076 
L 344.332378 150.174127 
L 344.207999 149.628115 
L 344.080865 149.082737 
L 343.950977 148.538009 
L 343.818341 147.993944 
L 343.682958 147.450556 
L 343.544832 146.907858 
L 343.403968 146.365865 
L 343.260367 145.824591 
L 343.114035 145.284048 
L 342.964975 144.744251 
L 342.813191 144.205215 
L 342.658686 143.666951 
L 342.501464 143.129475 
L 342.34153 142.592799 
L 342.178888 142.056939 
L 342.013541 141.521906 
L 341.845494 140.987716 
L 341.674752 140.45438 
L 341.501318 139.921914 
L 341.325197 139.390331 
L 341.146393 138.859644 
L 340.964912 138.329867 
L 340.780757 137.801013 
L 340.593934 137.273096 
L 340.404447 136.74613 
L 340.2123 136.220127 
L 340.0175 135.695101 
L 339.820051 135.171065 
L 339.619957 134.648034 
L 339.417224 134.12602 
L 339.211858 133.605036 
L 339.003863 133.085096 
L 338.793245 132.566214 
L 338.580008 132.048401 
L 338.364159 131.531672 
L 338.145704 131.01604 
L 337.924647 130.501518 
L 337.700994 129.988119 
L 337.474751 129.475856 
L 337.245923 128.964742 
L 337.014518 128.45479 
L 336.78054 127.946014 
L 336.543995 127.438426 
L 336.304889 126.932038 
L 336.063229 126.426865 
L 335.819021 125.922919 
L 335.572271 125.420213 
L 335.322985 124.918759 
L 335.07117 124.418571 
L 334.816831 123.919661 
L 334.559977 123.422041 
L 334.300612 122.925726 
" clip-path="url(#p3b26ea03ee)" style="fill: none; stroke: #1f77b4; stroke-width: 1.5; stroke-linecap: square"/>
   </g>
   <g id="patch_3">
    <path d="M 69.84 307.584 
L 69.84 41.472 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
   <g id="patch_4">
    <path d="M 402.48 307.584 
L 402.48 41.472 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
   <g id="patch_5">
    <path d="M 69.84 307.584 
L 402.48 307.584 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
   <g id="patch_6">
    <path d="M 69.84 41.472 
L 402.48 41.472 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
  </g>
 </g>
 <defs>
  <clipPath id="p3b26ea03ee">
   <rect x="69.84" y="41.472" width="332.64" height="266.112"/>
  </clipPath>
 </defs>
</svg>
\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"out=0\\nimport time\\np = None\\nfor a in np.linspace(0, 5*6.28, 100):\\n   p = parametric_plot($\\\\cos(t)$, $\\\\sin(t)$, {$t$: (a, a+0.5)}, fig=p, \\n                       xrange=[-1.5, 1.5], yrange=[-1.2, 1.2], aspect='equal')\\n   out = display(p, out)\\n   time.sleep(0.01)\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 5006988763165666054,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"\"\n\t\t}\n\t],\n\t\"description\": \"Cadabra JSON notebook format\",\n\t\"flags\": {\n\t\t\"hide_input_cells\": false\n\t},\n\t\"version\": 1.0\n}\n"
  },
  {
    "path": "examples/ref_printing.cnb",
    "content": "{\n\t\"cell_id\": 7261669791396587189,\n\t\"cells\": [\n\t\t{\n\t\t\t\"cell_id\": 1335784694978485978,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 13774751629423835658,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\section*{Printing expressions in various formats}\\n\\\\subsection*{Basic usage}\\n\\nWith basic use of Cadabra, you will typically display your expressions by postfixing them with a semi-colon,\\nas in\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\section*{Printing expressions in various formats}\\n\\\\subsection*{Basic usage}\\n\\nWith basic use of Cadabra, you will typically display your expressions by postfixing them with a semi-colon,\\nas in\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 4599574666662704559,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 7976412321546991870,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 13420704756796341992,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"A_{m n} (B^{n} + 3C^{n})\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}A_{m n} \\\\left(B^{n}+3C^{n}\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex:=A_{m n} ( B^{n} + 3 C^{n} );\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 11217211748193580653,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 16995084653280955185,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"What happens behind the scenes is that the semi-colon gets translated to a call of \\\\verb|display| on the \\nlast-entered expression. It is therefore equivalent to \"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"What happens behind the scenes is that the semi-colon gets translated to a call of \\\\verb|display| on the \\nlast-entered expression. It is therefore equivalent to \"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 3194216578733920776,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 8711371366818187662,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 15759111152906086906,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"A_{m n} (B^{n} + 3C^{n})\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}A_{m n} \\\\left(B^{n}+3C^{n}\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"display(ex)\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 1576921483409930500,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 17726338938474972989,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"If you do not want to display the expression, post-fix with a colon, as in\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"If you do not want to display the expression, post-fix with a colon, as in\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 14523255289624488569,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"ex:=A_{m n} ( B^{n} + 3 C^{n} ):\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 11294718848976823186,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 14337180194863693573,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"If you want to display an expression again later, you can just write the name of the expression followed\\nby a semi-colon, or use the \\\\verb|display| function again,\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"If you want to display an expression again later, you can just write the name of the expression followed\\nby a semi-colon, or use the \\\\verb|display| function again,\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 6496143034130397257,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 6581067180774934363,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 851282864835364026,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"A_{m n} (B^{n} + 3C^{n})\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}A_{m n} \\\\left(B^{n}+3C^{n}\\\\right)\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 2901413102110827379,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 12388802728969897063,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"A_{m n} (B^{n} + 3C^{n})\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}A_{m n} \\\\left(B^{n}+3C^{n}\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex;\\ndisplay(ex)\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 7456309133359305085,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 16939468648029991255,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"Note that while it may be tempting to use \\\\verb|print(ex)|, the \\\\verb|display| function is better because\\nit knows about the capabilities of the interface used, and it will automatically select a text output when\\nyou use Cadabra from the terminal, or \\\\LaTeX{} output when you use it in the graphical notebook.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"Note that while it may be tempting to use \\\\verb|print(ex)|, the \\\\verb|display| function is better because\\nit knows about the capabilities of the interface used, and it will automatically select a text output when\\nyou use Cadabra from the terminal, or \\\\LaTeX{} output when you use it in the graphical notebook.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 18063100663122690440,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 14453290597389549787,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\subsection*{Other output formats}\\n\\nCadabra expressions are standard Python objects, and as such they have a \\\\verb|__str__| method which\\nconverts them into a printable expression, and a \\\\verb|__repr__| method to produce a machine readable form.\\nThese are called by the standard \\\\verb|str| and \\\\verb|repr| Python functions, as the examples below show.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\subsection*{Other output formats}\\n\\nCadabra expressions are standard Python objects, and as such they have a \\\\verb|__str__| method which\\nconverts them into a printable expression, and a \\\\verb|__repr__| method to produce a machine readable form.\\nThese are called by the standard \\\\verb|str| and \\\\verb|repr| Python functions, as the examples below show.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 8738598843828149956,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 5848166511316712933,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"output\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}A_{m n} (B^{n} + 3C^{n})\\n\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"print(str(ex))\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 5497430364262302497,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 10342375366145359860,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"output\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}\\\\prod(A_{m n})(\\\\sum(B^{n})(3C^{n}))\\n\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"print(repr(ex))\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 5790729180904443240,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 17965245563481981014,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"In addition there are some methods to obtain output useful in other software: Mathematica, \\\\LaTeX{} and Sympy:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"In addition there are some methods to obtain output useful in other software: Mathematica, \\\\LaTeX{} and Sympy:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 3952585365066537497,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 10790437579665738397,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"output\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}A[DNm, DNn]*(B[UPn]+3*C[UPn])\\n\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"print(ex.mma_form())\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 11925500088449724665,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 16001190812359436598,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"output\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}A_{m n} \\\\left(B^{n}+3C^{n}\\\\right)\\n\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"print(ex._latex_())\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 14583738995864140787,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 10144197596267121994,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"output\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}A(DNm, DNn)*(B(UPn)+3*C(UPn))\\n\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"print(ex.sympy_form())\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 13609528241788494400,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 1104115635541465770,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\subsection*{Printing custom LaTeX}\\n\\nIf you want to make sure that a string which you have created \\\"by hand\\\" will be processed by LaTeX\\nand display in typeset form, use the `\\\\verb|LaTeXString|` object. This is essentially a normal \\nstring, but \\\"tagged\\\" with the information that it contains LaTeX code.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\subsection*{Printing custom LaTeX}\\n\\nIf you want to make sure that a string which you have created \\\"by hand\\\" will be processed by LaTeX\\nand display in typeset form, use the `\\\\verb|LaTeXString|` object. This is essentially a normal \\nstring, but \\\"tagged\\\" with the information that it contains LaTeX code.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 13166633816324467370,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 8306092681814010685,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\int_{-\\\\infty}^\\\\infty \\\\exp\\\\left[ -a x^2 \\\\right] {\\\\rm d} x\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"s = LaTeXString(r\\\"\\\\int_{-\\\\infty}^\\\\infty \\\\exp\\\\left[ -a x^2 \\\\right] {\\\\rm d} x\\\");\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 1025447284169640934,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"\"\n\t\t}\n\t],\n\t\"description\": \"Cadabra JSON notebook format\",\n\t\"version\": 1.0\n}\n"
  },
  {
    "path": "examples/ref_programming.cnb",
    "content": "{\n\t\"cell_id\": 15611848448601612261,\n\t\"cells\": [\n\t\t{\n\t\t\t\"cell_id\": 11069807106896465679,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 13772716889928113498,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\section*{Programming in Cadabra}\\n\\nCadabra is fully programmable in Python. At the most basic level this means that you can make functions\\nwhich combine various Cadabra algorithms together, or write loops which repeat certain Cadabra algorithms.\\nAt a more advanced level, you can inspect the expression tree and manipulate individual subexpressions,\\nor construct expressions from elementary building blocks. \"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\section*{Programming in Cadabra}\\n\\nCadabra is fully programmable in Python. At the most basic level this means that you can make functions\\nwhich combine various Cadabra algorithms together, or write loops which repeat certain Cadabra algorithms.\\nAt a more advanced level, you can inspect the expression tree and manipulate individual subexpressions,\\nor construct expressions from elementary building blocks. \"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 16380332542575924812,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 10341321852235865106,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\subsection*{Fundamental Cadabra objects: Ex and ExNode}\\n\\nThe two fundamental Cadabra objects are the \\\\verb|Ex| and the \\\\verb|ExNode|. An object of type \\\\verb|Ex| \\nrepresents a mathematical expression, and is what is generated if you type a line containing \\\\verb|:=|, as in\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\subsection*{Fundamental Cadabra objects: Ex and ExNode}\\n\\nThe two fundamental Cadabra objects are the \\\\verb|Ex| and the \\\\verb|ExNode|. An object of type \\\\verb|Ex| \\nrepresents a mathematical expression, and is what is generated if you type a line containing \\\\verb|:=|, as in\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 14618390770609029772,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 6425573256407897,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 2272933481458126939,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"A + B\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}A+B\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 14416483452317882508,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"verbatim\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}<class 'cadabra2.Ex'>\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex:=A+B;\\ntype(ex);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 14138459692123482407,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 2847848244353766819,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"An object of type \\\\verb|ExNode| is best thought of as an iterator. It can be used to walk an expression\\ntree, and modify it in place (which is somewhat different from normal Python iterators; a point we will return\\nto shortly). The most trivial way to get an iterator is to call the \\\\verb|top| member of\\nan \\\\verb|Ex| object; think of this as returning a pointer to the topmost node of an expression,\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"An object of type \\\\verb|ExNode| is best thought of as an iterator. It can be used to walk an expression\\ntree, and modify it in place (which is somewhat different from normal Python iterators; a point we will return\\nto shortly). The most trivial way to get an iterator is to call the \\\\verb|top| member of\\nan \\\\verb|Ex| object; think of this as returning a pointer to the topmost node of an expression,\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 5475362040304825870,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 4889801859931027187,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"verbatim\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}A + B\\\\end{verbatim}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 8111178036103804680,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"verbatim\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}<class 'cadabra2.ExNode'>\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex.top();\\ntype(ex.top());\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 15665387514835589348,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 11679348138325456437,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"You will also encounter \\\\verb|ExNode|s when you do a standard Python iteration\\nover the elements of an \\\\verb|Ex|, as in\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"You will also encounter \\\\verb|ExNode|s when you do a standard Python iteration\\nover the elements of an \\\\verb|Ex|, as in\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 17819639350499126772,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 18089991928180463935,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"verbatim\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}<class 'cadabra2.ExNode'>\\\\end{verbatim}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 928705785378809404,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"verbatim\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}A + B\\\\end{verbatim}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 10171488758885056085,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"verbatim\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}<class 'cadabra2.ExNode'>\\\\end{verbatim}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 13380492898109088727,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"verbatim\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}A\\\\end{verbatim}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 5149422238246026784,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"verbatim\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}<class 'cadabra2.ExNode'>\\\\end{verbatim}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 3989053911783578317,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"verbatim\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}B\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"for n in ex:\\n\\ttype(n);\\n\\tdisplay(n)\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 4137387624913381815,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 16884227773422108099,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"As you can see, this `iterates' over the elements of the expression, but in a perhaps somewhat unexpected\\nway. We will discuss this in more detail in the next section. Important to remember from the example above\\nis that the `pointers' to the individual elements of the expression are \\\\verb|ExNode| objects. \\nThere are various other ways to obtain such pointers, using various types of `filtering', more on that\\nbelow as well.\\n\\nOnce you have an \\\\verb|ExNode| pointing to a subexpression in an expression, you can query it further\\nfor details about that subexpression. \"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"As you can see, this `iterates' over the elements of the expression, but in a perhaps somewhat unexpected\\nway. We will discuss this in more detail in the next section. Important to remember from the example above\\nis that the `pointers' to the individual elements of the expression are \\\\verb|ExNode| objects. \\nThere are various other ways to obtain such pointers, using various types of `filtering', more on that\\nbelow as well.\\n\\nOnce you have an \\\\verb|ExNode| pointing to a subexpression in an expression, you can query it further\\nfor details about that subexpression. \"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 10963956834816626859,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 6445329138816839629,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 16041054156969959119,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"A_{m n}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}A_{m n}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 6671395703449228930,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"verbatim\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}m\\\\end{verbatim}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 15687146476081198667,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"verbatim\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}n\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex:= A_{m n};\\nfor i in ex.top().free_indices():\\n\\tdisplay(i)\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 4019018513960059958,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 1841284369902058108,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"The example above shows how, starting from an iterator which points to the top of the expression, you can\\nget a new iterator which can iterate over all free indices. \"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"The example above shows how, starting from an iterator which points to the top of the expression, you can\\nget a new iterator which can iterate over all free indices. \"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 17357805698574501177,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 16163878881460526284,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\subsection*{ExNode and Python iterators}\\n\\nBefore we continue, we should make a comment on how \\\\verb|ExNode| objects relate to Python iterators.\\nFor many purposes, \\\\verb|ExNode| objects behave as you expect from Python iterators: they allow you to loop over nodes of\\nan \\\\verb|Ex| expression, you can call \\\\verb|next(...)| on them, and so on. However, there are some slight differences, which have to do with the fact that\\nCadabra wants to give you access to the nodes of the original \\\\verb|Ex|, so that you can modify this original\\n\\\\verb|Ex| in place. Consider for instance this example with a Python list of integers, with standard iterators:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\subsection*{ExNode and Python iterators}\\n\\nBefore we continue, we should make a comment on how \\\\verb|ExNode| objects relate to Python iterators.\\nFor many purposes, \\\\verb|ExNode| objects behave as you expect from Python iterators: they allow you to loop over nodes of\\nan \\\\verb|Ex| expression, you can call \\\\verb|next(...)| on them, and so on. However, there are some slight differences, which have to do with the fact that\\nCadabra wants to give you access to the nodes of the original \\\\verb|Ex|, so that you can modify this original\\n\\\\verb|Ex| in place. Consider for instance this example with a Python list of integers, with standard iterators:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 18379624562437637500,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 121314811918743201,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"{}$\\\\big[$$\\\\verb|1|$,\\\\discretionary{}{}{} $\\\\verb|2|$,\\\\discretionary{}{}{} $\\\\verb|3|$,\\\\discretionary{}{}{} $\\\\verb|4|$,\\\\discretionary{}{}{} $\\\\verb|5|$$\\\\big]$\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 17839365611770309449,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"{}$\\\\big[$$\\\\verb|1|$,\\\\discretionary{}{}{} $\\\\verb|2|$,\\\\discretionary{}{}{} $\\\\verb|3|$,\\\\discretionary{}{}{} $\\\\verb|4|$,\\\\discretionary{}{}{} $\\\\verb|5|$$\\\\big]$\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"q=[1,2,3,4,5];\\nfor element in q:\\n   element=0\\nq;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 8306700484487211471,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 4168922270321543427,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"It still produces the original list at the end of the day, because each \\\\verb|element| is a \\\\emph{copy} of the\\nelement in the list. With \\\\verb|ExNode|s you can actually modify the original \\\\verb|Ex|, as this example shows:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"It still produces the original list at the end of the day, because each \\\\verb|element| is a \\\\emph{copy} of the\\nelement in the list. With \\\\verb|ExNode|s you can actually modify the original \\\\verb|Ex|, as this example shows:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 4630927477786015140,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 4235260673562839613,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 8812632743831006438,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"A + B + C + D\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}A+B+C+D\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 8077598135092445731,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 54572110013314483,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"Q + Q + Q + Q\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}Q+Q+Q+Q\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex:=A + B + C + D;\\nfor element in ex.top().terms():\\n   element.replace($Q$)\\nex;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 4078572040632098996,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 3291457110345453070,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"In this case, \\\\verb|element| is not an \\\\verb|Ex| corresponding to each of the 5 terms, but\\nrather an \\\\verb|ExNode|, which is more like a pointer into the \\\\verb|Ex| object. The \\\\verb|replace|\\nmember function allows you to replace the building blocks of the original \\\\verb|ex| expression.\\n\\nIf you want to get a proper \\\\verb|Ex| object (so a \\\\emph{copy} of the element in the expression\\nover which you are iterating), more like what you would get if iteration over Cadabra's expressions\\nwas an ordinary Python iteration, then you can use \\\\verb|ExNode.ex()|:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"In this case, \\\\verb|element| is not an \\\\verb|Ex| corresponding to each of the 5 terms, but\\nrather an \\\\verb|ExNode|, which is more like a pointer into the \\\\verb|Ex| object. The \\\\verb|replace|\\nmember function allows you to replace the building blocks of the original \\\\verb|ex| expression.\\n\\nIf you want to get a proper \\\\verb|Ex| object (so a \\\\emph{copy} of the element in the expression\\nover which you are iterating), more like what you would get if iteration over Cadabra's expressions\\nwas an ordinary Python iteration, then you can use \\\\verb|ExNode.ex()|:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 13338472805876454539,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 8548759806933419273,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 12305928970509592519,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"A + 2B + 3C + 4D\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}A+2B+3C+4D\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 3046719146128378641,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 16359987555073575085,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"A + 2B + 3C + 4D\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}A+2B+3C+4D\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 13459390553453667032,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 10976535573212848309,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"3C\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}3C\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex:= A + 2 B + 3 C + 4 D;\\nlst=[]\\nfor element in ex.top().terms():\\n   lst.append( element.ex() )\\nex;\\nlst[2];\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 2779093920101567345,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9182058936686247795,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"Here the list \\\\verb|lst| contains copies of the individual terms of the \\\\verb|ex| expression.\\n\\nA good way to remember about this is to keep in mind that Cadabra tries its best to allow you to modify\\nexpressions \\\\emph{in-place}. The \\\\verb|ExNode| iterators provide that functionality.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"Here the list \\\\verb|lst| contains copies of the individual terms of the \\\\verb|ex| expression.\\n\\nA good way to remember about this is to keep in mind that Cadabra tries its best to allow you to modify\\nexpressions \\\\emph{in-place}. The \\\\verb|ExNode| iterators provide that functionality.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 419058726958978058,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 12917610346077137892,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\subsection*{Traversing the expression tree}\\n\\nThe \\\\verb|ExNode| iterator can be instructed to traverse expressions in various ways. The most basic\\niterator is obtained by using standard Python iteration with a \\\\verb|for| loop,\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\subsection*{Traversing the expression tree}\\n\\nThe \\\\verb|ExNode| iterator can be instructed to traverse expressions in various ways. The most basic\\niterator is obtained by using standard Python iteration with a \\\\verb|for| loop,\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 1562086486740641567,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 12410381233438750897,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 14386922931961145661,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"A + B + C_{m} D^{m}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}A+B+C_{m} D^{m}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex:= A + B + C_{m} D^{m};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 15221357359172369652,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 7445041969873337852,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"output\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}A + B + C_{m} D^{m}\\nA\\nB\\nC_{m} D^{m}\\nC_{m}\\nm\\nD^{m}\\nm\\n\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"for n in ex:\\n\\tprint(str(n))\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 10501994233898575362,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 704383322132262896,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"The iterator obtained in this way traverses the expression tree node by node, and when you ask it\\nto print what it is pointing to, it prints the entire subtree of the node it is currently visiting.\\nIf you are only interested in the name of the node, not the\\nentire expression below it, you can use the \\\\verb|.name| member of the iterator:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"The iterator obtained in this way traverses the expression tree node by node, and when you ask it\\nto print what it is pointing to, it prints the entire subtree of the node it is currently visiting.\\nIf you are only interested in the name of the node, not the\\nentire expression below it, you can use the \\\\verb|.name| member of the iterator:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 7114346388970120519,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 10182545959028033598,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"output\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}\\\\sum\\nA\\nB\\n\\\\prod\\nC\\nm\\nD\\nm\\n\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"for n in ex:\\n\\tprint(str(n.name))\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 10210203266960726041,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9630575658409744830,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"Often, this kind of `brute force' iteration over expression elements is not very useful. A more powerful\\niterator is obtained by asking for all nodes in the subtree which have a certain name. This can be the name of \\na tensor, or the name of a special node, such as a product or sum,\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"Often, this kind of `brute force' iteration over expression elements is not very useful. A more powerful\\niterator is obtained by asking for all nodes in the subtree which have a certain name. This can be the name of \\na tensor, or the name of a special node, such as a product or sum,\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 2424768294203788101,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 2014866901964486825,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"verbatim\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}C_{m}\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"for n in ex[\\\"C\\\"]:\\n\\tdisplay(n)\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 9903842259378342150,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9849116786585471912,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"verbatim\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}C_{m} D^{m}\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"for n in ex[\\\"\\\\\\\\prod\\\"]:\\n\\tdisplay(n)\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 10588142595263796342,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 10808031586959552824,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"The above two examples used an iterator obtained directly from an \\\\verb|Ex| object. \\nVarious ways of obtaining iterators over special nodes can be obtained by using member functions of\\n\\\\verb|ExNode| objects themselves. So one often uses a construction in which one first asks for an iterator\\nto the top of an expression, and then requests from that iterator a new one which can iterate over\\nvarious special nodes. The example below obtains an iterator over all top-level terms in an expression, and\\nthen loops over its values.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"The above two examples used an iterator obtained directly from an \\\\verb|Ex| object. \\nVarious ways of obtaining iterators over special nodes can be obtained by using member functions of\\n\\\\verb|ExNode| objects themselves. So one often uses a construction in which one first asks for an iterator\\nto the top of an expression, and then requests from that iterator a new one which can iterate over\\nvarious special nodes. The example below obtains an iterator over all top-level terms in an expression, and\\nthen loops over its values.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 11464792304275148656,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 4394727638444626529,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"verbatim\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}A\\\\end{verbatim}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 1554351456974996679,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"verbatim\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}B\\\\end{verbatim}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 1396820566587439115,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"verbatim\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}C_{m} D^{m}\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"for n in ex.top().terms():\\n\\tdisplay(n)\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 10977028249929669045,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 8727796298696264427,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"Two special types of iterators are those which iterate only over all arguments or only over all indices\\nof a sub-expression. These are discussed in the next section.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"Two special types of iterators are those which iterate only over all arguments or only over all indices\\nof a sub-expression. These are discussed in the next section.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 8386740853543185461,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9210025781643367835,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\subsection*{Arguments and indices}\\n\\nThere are various ways to obtain iterators which iterate over all arguments or all indices\\nof an expression. The following example, with a derivative acting on a product, prints the \\nargument of the derivative as well as all free indices.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\subsection*{Arguments and indices}\\n\\nThere are various ways to obtain iterators which iterate over all arguments or all indices\\nof an expression. The following example, with a derivative acting on a product, prints the \\nargument of the derivative as well as all free indices.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 6168677497397138422,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 17261803845107424940,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Attached property Derivative to~}\\\\nabla{\\\\#}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9873753640405935280,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 5436539438039946572,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\nabla_{m}(A^{n}_{p} V^{p})\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\nabla_{m}\\\\left(A^{n}\\\\,_{p} V^{p}\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"\\\\nabla{#}::Derivative;\\nex:= \\\\nabla_{m}{ A^{n}_{p} V^{p} };\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 114405730338281393,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 15847114993895123593,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"output\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}A^{n}_{p} V^{p}\\nm\\nn\\n\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"for nabla in ex[r'\\\\nabla']:\\n\\tfor arg in nabla.args():\\n\\t\\tprint(str(arg))\\n\\tfor i in nabla.free_indices():\\n\\t\\tprint(str(i))\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 18169081604378372890,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9204946542835539304,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\subsection*{Querying properties}\\n\\nProperties which you attach to patterns can be queried in Python, though the functionality is \\nsomewhat limited. In order to query a pattern for a particular property, use the property's name\\ntogether with the \\\\verb|get| method. An example:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\subsection*{Querying properties}\\n\\nProperties which you attach to patterns can be queried in Python, though the functionality is \\nsomewhat limited. In order to query a pattern for a particular property, use the property's name\\ntogether with the \\\\verb|get| method. An example:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 15511730119362410176,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"A_{m n}::AntiSymmetric.\\np1 = AntiSymmetric.get($A_{m n}$)\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 8304505308961258287,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 5564478070452519183,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property AntiSymmetric attached to~}A_{m n}.\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"p1;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 8636929660022469751,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 8109343310411280286,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"verbatim\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}None\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"p2 = Symmetric.get($A_{m n}$)\\np2;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 867371738363577328,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 11028315898171412377,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"Some properties, like `Weight` have an associated value. You can access these with the appropriate member function,\\nso for this particular example you would do\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"Some properties, like `Weight` have an associated value. You can access these with the appropriate member function,\\nso for this particular example you would do\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 8211547310713253802,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 815228937313619719,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property Weight attached to~}x.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9075103878800686191,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"verbatim\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}42\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"x::Weight(value=42, label=field);\\nWeight.get($x$, label=\\\"field\\\").value(\\\"field\\\");\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 15480924078324966867,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9038011217009947855,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\subsection*{Expression pattern matching}\\n\\nIf you want to check whether an expression matches a particular pattern, use the \\\\verb|match| function of\\nthe \\\\verb|Ex| object. By default this is rather strict, requiring that indices match not only their \\ntype but also their name.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\subsection*{Expression pattern matching}\\n\\nIf you want to check whether an expression matches a particular pattern, use the \\\\verb|match| function of\\nthe \\\\verb|Ex| object. By default this is rather strict, requiring that indices match not only their \\ntype but also their name.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 15428739880702009928,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 10527841463011658704,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"verbatim\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}True\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"{m, n, k, l}::Indices(vector).\\n{a, b, c, d}::Indices(spinor).\\n$A_{m n}$.matches($A_{k l}$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 5859548943414495175,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9835839441480701178,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"verbatim\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}True\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"$A_{m n}$.matches($A_{m n}$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 439816990948847934,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 10463085429454266003,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"verbatim\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}True\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"$A_{m n}$.matches($A_{k l}$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 178071254264036679,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 8520200625278449269,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"verbatim\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}False\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"$A_{m n}$.matches($A_{a b}$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 3833451727201026658,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 4681145677390692163,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"Wildcard symbols will match any symbol,\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"Wildcard symbols will match any symbol,\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 15459097290274009292,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 17514705620329867820,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"verbatim\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}True\\\\end{verbatim}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 6727724608862362495,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"verbatim\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}True\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"$A_{m? n?}$.matches($A_{k l}$);\\n$A_{m? n?}$.matches($A_{a b}$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 14689819351858877261,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 3542175063139694324,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"verbatim\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}True\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"$A??$.matches($A_{k l}$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 13699803665641708663,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 15997637797326181384,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\subsection*{Example: covariant derivatives}\\n\\nThe following example shows how you might implement the expansion of a covariant derivative\\ninto partial derivatives and connection terms.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\subsection*{Example: covariant derivatives}\\n\\nThe following example shows how you might implement the expansion of a covariant derivative\\ninto partial derivatives and connection terms.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 2872016859968266906,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"def expand_nabla(ex):\\n    for nabla in ex[r'\\\\nabla']:\\n        nabla.name=r'\\\\partial'\\n        dindex = nabla.indices().__next__() \\n        for arg in nabla.args():             \\n            ret:=0;\\n            for index in arg.free_indices():\\n                t2:= @(arg);\\n                if index.parent_rel==sub:\\n                    t1:= -\\\\Gamma^{p}_{@(dindex) @(index)};\\n                    t2[index]:= _{p};\\n                else:\\n                    t1:=  \\\\Gamma^{@(index)}_{@(dindex) p};\\n                    t2[index]:= ^{p};\\n                ret += Ex(str(nabla.multiplier)) * t1 * t2\\n            nabla += ret\\n    return ex\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 7237528541769121977,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 15359169329483093600,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"The sample expressions below show how this automatically takes care of not\\nintroducing connections for dummy indices, and how it automatically handles indices which\\nare more complicated than single symbols.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"The sample expressions below show how this automatically takes care of not\\nintroducing connections for dummy indices, and how it automatically handles indices which\\nare more complicated than single symbols.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 17469792546183949,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 4611657941845445055,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Attached property Derivative to~}\\\\nabla{\\\\#}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 16721602649639875551,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 1971978125933515575,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \" 1/2 \\\\nabla_{a}(h^{b}_{c})\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\frac{1}{2}\\\\nabla_{a}{h^{b}\\\\,_{c}}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 12329008971607097549,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 11268549708438857109,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \" 1/2 \\\\partial_{a}(h^{b}_{c}) +  1/2 \\\\Gamma^{b}_{a p} h^{p}_{c} -  1/2 \\\\Gamma^{p}_{a c} h^{b}_{p}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\frac{1}{2}\\\\partial_{a}\\\\left(h^{b}\\\\,_{c}\\\\right)+\\\\frac{1}{2}\\\\Gamma^{b}\\\\,_{a p} h^{p}\\\\,_{c} - \\\\frac{1}{2}\\\\Gamma^{p}\\\\,_{a c} h^{b}\\\\,_{p}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"\\\\nabla{#}::Derivative;\\nex:= 1/2 \\\\nabla_{a}{ h^{b}_{c} }; \\nexpand_nabla(ex);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 8847950111214242351,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 14579838225112781037,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 670483492207020752,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \" 1/4 \\\\nabla_{a}(v_{b} w^{b})\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\frac{1}{4}\\\\nabla_{a}\\\\left(v_{b} w^{b}\\\\right)\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 7192521991910884351,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 14234065611728877339,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \" 1/4 \\\\partial_{a}(v_{b} w^{b})\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\frac{1}{4}\\\\partial_{a}\\\\left(v_{b} w^{b}\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex:= 1/4 \\\\nabla_{a}{ v_{b} w^{b} };\\nexpand_nabla(ex);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 5955745636040271481,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 4792471961978253002,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 9062010348280049351,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\nabla_{\\\\hat{a}}(h_{b c} v^{c})\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\nabla_{\\\\widehat{a}}\\\\left(h_{b c} v^{c}\\\\right)\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 16288256561314012077,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 5483924240174076388,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\partial_{\\\\hat{a}}(h_{b c} v^{c})-\\\\Gamma^{p}_{\\\\hat{a} b} h_{p c} v^{c}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\partial_{\\\\widehat{a}}\\\\left(h_{b c} v^{c}\\\\right)-\\\\Gamma^{p}\\\\,_{\\\\widehat{a} b} h_{p c} v^{c}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex:= \\\\nabla_{\\\\hat{a}}{ h_{b c} v^{c} };\\nexpand_nabla(ex);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 2378579335486944368,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"\"\n\t\t}\n\t],\n\t\"description\": \"Cadabra JSON notebook format\",\n\t\"version\": 1.0\n}\n"
  },
  {
    "path": "examples/ref_properties.cnb",
    "content": "{\n\t\"cell_id\": 16024244566890424791,\n\t\"cells\": [\n\t\t{\n\t\t\t\"cell_id\": 1873743992778418631,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 7846921569529807949,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\section*{Object properties and declaration}\\n\\\\subsection*{Generic properties}\\n\\nSymbols in Cadabra have no a-priori ``meaning''. If you write\\n\\\\verb|\\\\Gamma|, the program will not know that it is supposed to be,\\nfor instance, a Clifford algebra generator.  You will have to declare\\nthe properties of symbols, i.e.~you have to tell Cadabra explicitly that\\nif you write \\\\verb|\\\\Gamma|, you actually mean a Clifford algebra\\ngenerator. This indirect way of attaching a meaning to a symbol has\\nthe advantage that you can use whatever notation you like; if you\\nprefer to write \\\\verb|\\\\gamma|, or perhaps even \\\\verb|\\\\rho| if your\\npaper uses that, then this is perfectly possible (object properties\\nare a bit like ``attributes'' in {\\\\tt Mathematica} or ``domains'' in\\n{\\\\tt Axiom} and {\\\\tt MuPAD}).\\n\\nProperties are all written using capitals to separate words, as in\\n{\\\\tt AntiSymmetric}. This makes it easier to distinguish them from\\ncommands. Properties of objects are declared by using the ``::''\\ncharacters.  This can be done ``at first use'', i.e.~by just adding\\nthe property to the object when it first appears in the input. As an\\nexample, one can write\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\section*{Object properties and declaration}\\n\\\\subsection*{Generic properties}\\n\\nSymbols in Cadabra have no a-priori ``meaning''. If you write\\n\\\\verb|\\\\Gamma|, the program will not know that it is supposed to be,\\nfor instance, a Clifford algebra generator.  You will have to declare\\nthe properties of symbols, i.e.~you have to tell Cadabra explicitly that\\nif you write \\\\verb|\\\\Gamma|, you actually mean a Clifford algebra\\ngenerator. This indirect way of attaching a meaning to a symbol has\\nthe advantage that you can use whatever notation you like; if you\\nprefer to write \\\\verb|\\\\gamma|, or perhaps even \\\\verb|\\\\rho| if your\\npaper uses that, then this is perfectly possible (object properties\\nare a bit like ``attributes'' in {\\\\tt Mathematica} or ``domains'' in\\n{\\\\tt Axiom} and {\\\\tt MuPAD}).\\n\\nProperties are all written using capitals to separate words, as in\\n{\\\\tt AntiSymmetric}. This makes it easier to distinguish them from\\ncommands. Properties of objects are declared by using the ``::''\\ncharacters.  This can be done ``at first use'', i.e.~by just adding\\nthe property to the object when it first appears in the input. As an\\nexample, one can write\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 13187362062085411141,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 8221627658201150468,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Attached property AntiSymmetric to~}F_{m n p}.\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"F_{m n p}::AntiSymmetric;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 7636864876509176699,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 12584534138819510366,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"This declares the object to be anti-symmetric in its indices. The property\\ninformation is stored separately, so that further appearances of the\\n``\\\\verb|F_{m n p}|'' object will automatically share this property. \\nA list of all properties is available from the manual pages on the web site.\\n\\nNote that properties are attached to patterns, Therefore, you can have\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"This declares the object to be anti-symmetric in its indices. The property\\ninformation is stored separately, so that further appearances of the\\n``\\\\verb|F_{m n p}|'' object will automatically share this property. \\nA list of all properties is available from the manual pages on the web site.\\n\\nNote that properties are attached to patterns, Therefore, you can have\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 11981126734626687991,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 11452579552056933733,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Attached property Symmetric to~}R_{m n}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 12593961078534850153,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Attached property TableauSymmetry to~}R_{m n p q}.\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"R_{m n}::Symmetric;\\nR_{m n p q}::RiemannTensor;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 5342420475339720929,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 10127782755222349559,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"at the same time. The program will not warn you if you use\\nincompatible properties, so if you make a declaration like above and\\nthen later on do\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"at the same time. The program will not warn you if you use\\nincompatible properties, so if you make a declaration like above and\\nthen later on do\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 16352428007357235833,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 17527508896735945989,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Attached property AntiSymmetric to~}R_{m n}.\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"R_{m n}::AntiSymmetric;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 15913947998439108974,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 1008868390112717372,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"this may lead to undefined results.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"this may lead to undefined results.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 10025164847893429769,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 12812617753453879770,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"The fact that objects are attached to patterns also means that you can\\nuse something like wildcards. In the following declaration,\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"The fact that objects are attached to patterns also means that you can\\nuse something like wildcards. In the following declaration,\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 11903162008471267303,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 16577956284977901148,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Attached property Indices(position=free) to~}\\\\left[m\\\\#,~\\\\discretionary{}{}{} n\\\\#\\\\right].\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"{m#, n#}::Indices(vector);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 4195311491037587033,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 3977418742316137404,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"the entire infinite set of objects $m1, m2, m3, \\\\ldots$ and $n1, n2,\\nn3, \\\\ldots$ are declared to be in the dummy index set\\n``vector'' (this way of declaring ranges of objects is\\nsimilar to the ``autodeclare'' declaration method of FORM). \"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"the entire infinite set of objects $m1, m2, m3, \\\\ldots$ and $n1, n2,\\nn3, \\\\ldots$ are declared to be in the dummy index set\\n``vector'' (this way of declaring ranges of objects is\\nsimilar to the ``autodeclare'' declaration method of FORM). \"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 5536004295914482032,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 12339143931885338645,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"Properties can be assigned to an entire list of symbols with one\\ncommand, namely by attaching the property to the list. For example,\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"Properties can be assigned to an entire list of symbols with one\\ncommand, namely by attaching the property to the list. For example,\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 8851937856391613984,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 10242614262625606826,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Attached property Integer to~}\\\\left[n,~\\\\discretionary{}{}{} m,~\\\\discretionary{}{}{} p,~\\\\discretionary{}{}{} q\\\\right].\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"{n, m, p, q}::Integer(1..d);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 11212186920236991312,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 1076256994014976479,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"This associates the property ``Integer'' to each and every symbol in\\nthe list.  However, there is also a concept of ``list properties'',\\nwhich are properties which are associated to the list as a\\nwhole. Examples of list properties are ``AntiCommuting'' or\\n``Indices''.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"This associates the property ``Integer'' to each and every symbol in\\nthe list.  However, there is also a concept of ``list properties'',\\nwhich are properties which are associated to the list as a\\nwhole. Examples of list properties are ``AntiCommuting'' or\\n``Indices''.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 8949535369725784252,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 8618739558652318788,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"Objects can have more than one property attached to them, and one\\nshould therefore not confuse properties with the ``type'' of the\\nobject. Consider for instance\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"Objects can have more than one property attached to them, and one\\nshould therefore not confuse properties with the ``type'' of the\\nobject. Consider for instance\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 8425453185210856818,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 7187790816160951991,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Attached property Coordinate to~}x.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 8479664987816470973,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Attached property TableauSymmetryWeylTensor to~}W_{m n p q}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 299508483589117623,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Attached property Depends to~}W_{m n p q}.\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"x::Coordinate;\\nW_{m n p q}::WeylTensor;\\nW_{m n p q}::Depends(x);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 2657066693349526767,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 16136563802631081521,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"This attaches two completely independent properties to the pattern\\n$W_{m n p q}$.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"This attaches two completely independent properties to the pattern\\n$W_{m n p q}$.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 4331078423184753435,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 4105695659204625161,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"In the examples above, several properties had arguments\\n(e.g. ``\\\\verb|vector|'' or ``\\\\verb|1..d|''). The general form of these\\narguments is a set of key-value pairs, as in\\n\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"In the examples above, several properties had arguments\\n(e.g. ``\\\\verb|vector|'' or ``\\\\verb|1..d|''). The general form of these\\narguments is a set of key-value pairs, as in\\n\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 17703789208275282885,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 16300946463127941557,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Attached property TableauSymmetry to~}T_{m n p q}.\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"T_{m n p q}::TableauSymmetry(shape={2,1}, indices={0,2,1});\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 4732372589842197888,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 14394312001827728418,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"In the simple cases discussed so far, the key and the equal sign was\\nsuppressed. This is allowed because one of the keys plays the role of\\nthe default key. Therefore, the following two are equivalent,\\n\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"In the simple cases discussed so far, the key and the equal sign was\\nsuppressed. This is allowed because one of the keys plays the role of\\nthe default key. Therefore, the following two are equivalent,\\n\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 12384953340328900440,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 7580296103947475880,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Attached property Integer to~}\\\\left[m,~\\\\discretionary{}{}{} n\\\\right].\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 1877851181871684039,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Attached property Integer to~}\\\\left[m,~\\\\discretionary{}{}{} n\\\\right].\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"{ m, n }::Integer(range=0..d);\\n{ m, n }::Integer(0..d);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 16167969896591755140,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 252799586075103098,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"See the detailed documentation of the individual properties for\\nallowed keys and the one which is taken as the default.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"See the detailed documentation of the individual properties for\\nallowed keys and the one which is taken as the default.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 1760446223062694014,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 18322724454023722463,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"Finally, there is a concept of ``inherited properties''. Consider\\ne.g.~a sum of spinors, declared as\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"Finally, there is a concept of ``inherited properties''. Consider\\ne.g.~a sum of spinors, declared as\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 4649639139262084299,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 3580666952276410048,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Attached property Spinor to~}\\\\left[\\\\psi_{1},~\\\\discretionary{}{}{} \\\\psi_{2},~\\\\discretionary{}{}{} \\\\psi_{3}\\\\right].\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 16885831544614794528,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 8148475282577177565,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\psi_{1} + \\\\psi_{2} + \\\\psi_{3}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\psi_{1}+\\\\psi_{2}+\\\\psi_{3}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"{\\\\psi_1, \\\\psi_2, \\\\psi_3}::Spinor;\\nex:= \\\\psi_1 + \\\\psi_2 + \\\\psi_3;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 17760244410863267067,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 1449664974568614276,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"Here the sum has inherited the property ``Spinor'', even though it does\\nnot have normal or intrinsic property of this type. Properties can\\nalso inherit from each other, e.g.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"Here the sum has inherited the property ``Spinor'', even though it does\\nnot have normal or intrinsic property of this type. Properties can\\nalso inherit from each other, e.g.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 9462074610843212781,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 12770109660043468401,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 13372884232421891240,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\Gamma_{p o i u y}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\Gamma_{p o i u y}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"\\\\Gamma_{#}::GammaMatrix.\\nex:=\\\\Gamma_{p o i u y};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 7700199035098393129,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 10899488318427932986,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 3919161428498386016,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"-\\\\Gamma_{i o p u y}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}-\\\\Gamma_{i o p u y}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"canonicalise(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 1850364838553237390,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 12810926342201765034,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"The \\\\prop{GammaMatrix} property inherits from\\n\\\\prop{AntiSymmetric} property, and therefore the \\\\verb|\\\\Gamma| object is automatically anti-symmetric in its\\nindices. \\nindices. \"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"The \\\\prop{GammaMatrix} property inherits from\\n\\\\prop{AntiSymmetric} property, and therefore the \\\\verb|\\\\Gamma| object is automatically anti-symmetric in its\\nindices. \\nindices. \"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 2125938839653920378,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 11907919364945406225,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\subsection*{List properties and symbol groups}\\n\\nSome properties are not naturally associated to a single symbol or\\nobject, but have to do with collections of them. A simple example of\\nsuch a property is \\\\prop{AntiCommuting}. Although it sometimes\\nmakes sense to say that ``$\\\\psi_m$ is anticommuting'' (meaning that\\n$\\\\psi_m \\\\psi_n = - \\\\psi_n \\\\psi_m$), it happens just as often that you\\nwant to say ``$\\\\psi$ and $\\\\chi$ anticommute'' (meaning that $\\\\psi\\\\chi\\n= - \\\\chi\\\\psi$). The latter property is clearly relating two different\\nobjects. \\n\\nAnother example is dummy indices. While it may make sense to say that\\n``$m$ is a dummy index'', this does not allow the program to\\nsubstitute $m$ with another index when a clash of dummy index names\\noccurs (e.g.~upon substitution of one expression into another). More\\nuseful is to say that ``$m$, $n$, and $p$ are dummy indices of the\\nsame type'', so that the program can relabel a pair of $m$'s into a\\npair of $p$'s when necessary.\\n\\nIn Cadabra such properties are called ``list properties''. You can\\nassociate a list property to a list of symbols by simply writing,\\ne.g.~for the first example above,\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\subsection*{List properties and symbol groups}\\n\\nSome properties are not naturally associated to a single symbol or\\nobject, but have to do with collections of them. A simple example of\\nsuch a property is \\\\prop{AntiCommuting}. Although it sometimes\\nmakes sense to say that ``$\\\\psi_m$ is anticommuting'' (meaning that\\n$\\\\psi_m \\\\psi_n = - \\\\psi_n \\\\psi_m$), it happens just as often that you\\nwant to say ``$\\\\psi$ and $\\\\chi$ anticommute'' (meaning that $\\\\psi\\\\chi\\n= - \\\\chi\\\\psi$). The latter property is clearly relating two different\\nobjects. \\n\\nAnother example is dummy indices. While it may make sense to say that\\n``$m$ is a dummy index'', this does not allow the program to\\nsubstitute $m$ with another index when a clash of dummy index names\\noccurs (e.g.~upon substitution of one expression into another). More\\nuseful is to say that ``$m$, $n$, and $p$ are dummy indices of the\\nsame type'', so that the program can relabel a pair of $m$'s into a\\npair of $p$'s when necessary.\\n\\nIn Cadabra such properties are called ``list properties''. You can\\nassociate a list property to a list of symbols by simply writing,\\ne.g.~for the first example above,\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 11645948506859110217,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 12491873823462977295,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Attached property AntiCommuting to~}\\\\left[\\\\psi,~\\\\discretionary{}{}{} \\\\chi\\\\right].\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"{ \\\\psi, \\\\chi }::AntiCommuting;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 17022724486968829841,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 3785515124818444956,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"Note that you can also attach normal properties to multiple symbols in one go using this\\nnotation. The program will figure out automatically whether you want\\nto associate a normal property or a list property to the symbols in\\nthe list.\\n\\nLists are ordered, although the ordering does not necessarily mean\\nanything for all list properties (it is relevant for\\ne.g.~\\\\prop{SortOrder} but irrelevant for e.g.~\\\\prop{AntiCommuting}).\\n\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"Note that you can also attach normal properties to multiple symbols in one go using this\\nnotation. The program will figure out automatically whether you want\\nto associate a normal property or a list property to the symbols in\\nthe list.\\n\\nLists are ordered, although the ordering does not necessarily mean\\nanything for all list properties (it is relevant for\\ne.g.~\\\\prop{SortOrder} but irrelevant for e.g.~\\\\prop{AntiCommuting}).\\n\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 16961965256527519584,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 10125811375617152850,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\subsection*{Querying and transferring properties}\\n\\nFor many built-in algorithms, assigning properties to the objects which appear in your expressions\\nwill be enough to make them work. However, sometimes you may want to explicitly query whether a particular symbol\\nhas a particular property. The following example shows how this works.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\subsection*{Querying and transferring properties}\\n\\nFor many built-in algorithms, assigning properties to the objects which appear in your expressions\\nwill be enough to make them work. However, sometimes you may want to explicitly query whether a particular symbol\\nhas a particular property. The following example shows how this works.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 9613954587245120616,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 12508488708618370447,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property Symmetric attached to~}A_{m n}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 6086779892467904583,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"output\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}A_{m n} is symmetric.\\n\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"A_{m n}::Symmetric;\\nif Symmetric.get($A_{m n}$):\\n   print(\\\"A_{m n} is symmetric.\\\")\\nif AntiSymmetric.get($A_{m n}$):\\n   print(\\\"A_{m n} is anti-symmetric.\\\")\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 2963590779224402878,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 17663256730765935192,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"The object returned by \\\\verb|Property.get(...)| is either \\\\verb|None| or the property which you asked about.\\nIt is possible to do something with that property, e.g. attach it to another symbol. In the example below,\\nwe start off with one tensor with a symmetry, and then attach it to another symbol.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"The object returned by \\\\verb|Property.get(...)| is either \\\\verb|None| or the property which you asked about.\\nIt is possible to do something with that property, e.g. attach it to another symbol. In the example below,\\nwe start off with one tensor with a symmetry, and then attach it to another symbol.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 9956511188880238921,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 5651396505343552990,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property TableauSymmetry attached to~}A_{m n p}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 10945815225780151485,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 5559233594360017677,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"B_{m n p}-B_{m p n}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}B_{m n p}-B_{m p n}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 13557277793536352717,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 15521744502411664671,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"2B_{m n p}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}2B_{m n p}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"A_{m n p}::TableauSymmetry(shape={1,1}, indices={1,2});\\np = TableauSymmetry.get($A_{m n p}$)\\np.attach($B_{m n p}$)\\nex:= B_{m n p} - B_{m p n};\\ncanonicalise(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 6719052246250031707,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"\"\n\t\t}\n\t],\n\t\"description\": \"Cadabra JSON notebook format\",\n\t\"version\": 1.0\n}\n"
  },
  {
    "path": "examples/ref_selecting.cnb",
    "content": "{\n\t\"cells\" : \n\t[\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\section*{Selecting parts of expressions}\\n\\nIn many other computer algebra systems, you can select parts of results using the mouse, paste\\nthem into a new input cell, and then continue the computation. Naively this sounds like a nice\\nfeature to have, and it is indeed quite useful for quick computations. However, for larger projects,\\nthis feature quickly becomes a major source of trouble.  Once you use the cut-n-paste technique, you\\nare no longer able to make any changes in cells before the one with pasted content. Or rather, you can make\\nchanges, but they will not automatically propagate to into the pasted cell. Any effect of the \\nchange at the top of the notebook will have to be evaluated until the point of the cut-n-paste, and then\\nyou have to do the cut-n-paste again by hand.\\n\\nNow this is fine if you just do a quick computation, as you will probably know precisely what you want\\nto cut-n-paste. But if you give your notebook to someone else, this may no longer be clear. Worse, \\nif you do not look at your notebook for some time, and then return after a few months (or years), you\\nwill most likely have forgotten completely what was the logic for the particular cut. \\n\\nFor this reason, Cadabra does not support cut-n-paste of output. But that does not mean that you cannot\\nselect parts of expressions for subsequent computation. For that, Cadabra has a more systematic logic,\\nwhich is built around the \\\\algo{zoom} and \\\\algo{unzoom} commands.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\section*{Selecting parts of expressions}\\n\\nIn many other computer algebra systems, you can select parts of results using the mouse, paste\\nthem into a new input cell, and then continue the computation. Naively this sounds like a nice\\nfeature to have, and it is indeed quite useful for quick computations. However, for larger projects,\\nthis feature quickly becomes a major source of trouble.  Once you use the cut-n-paste technique, you\\nare no longer able to make any changes in cells before the one with pasted content. Or rather, you can make\\nchanges, but they will not automatically propagate to into the pasted cell. Any effect of the \\nchange at the top of the notebook will have to be evaluated until the point of the cut-n-paste, and then\\nyou have to do the cut-n-paste again by hand.\\n\\nNow this is fine if you just do a quick computation, as you will probably know precisely what you want\\nto cut-n-paste. But if you give your notebook to someone else, this may no longer be clear. Worse, \\nif you do not look at your notebook for some time, and then return after a few months (or years), you\\nwill most likely have forgotten completely what was the logic for the particular cut. \\n\\nFor this reason, Cadabra does not support cut-n-paste of output. But that does not mean that you cannot\\nselect parts of expressions for subsequent computation. For that, Cadabra has a more systematic logic,\\nwhich is built around the \\\\algo{zoom} and \\\\algo{unzoom} commands.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\subsection*{Zooming into an expression}\\n\\nIf you have a large expression, and want to select a part of it for further manipulation, while\\ntemporarily ignoring the rest, use the \\\\algo{zoom} command. It takes an expression and a pattern, \\nand then suppresses all terms in the expression which do not match the pattern. An example:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\subsection*{Zooming into an expression}\\n\\nIf you have a large expression, and want to select a part of it for further manipulation, while\\ntemporarily ignoring the rest, use the \\\\algo{zoom} command. It takes an expression and a pattern, \\nand then suppresses all terms in the expression which do not match the pattern. An example:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"\\\\int{c A + (c)**2 B + c D + (c)**2 A}{x}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\int \\\\left(c A+{c}^{2} B+c D+{c}^{2} A\\\\right)\\\\,\\\\,{\\\\rm d}x\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex:= \\\\int{ c A + c**2 B + c D + c**2 A }{x};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"\\\\int{c A +  ...  + c D +  ... }{x}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\int \\\\left(c A+ \\\\ldots +c D+ \\\\ldots \\\\right)\\\\,\\\\,{\\\\rm d}x\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"zoom(_, $c Q??$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"This has selected all terms with a single factor of $c$, and suppressed the other ones (but keeping\\na reminder that those terms are still there, in the form of the dots). You can now work on the visible \\nterms as usual, e.g. doing a substitution, \"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"This has selected all terms with a single factor of $c$, and suppressed the other ones (but keeping\\na reminder that those terms are still there, in the form of the dots). You can now work on the visible \\nterms as usual, e.g. doing a substitution, \"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"\\\\int{c E +  ...  + c D +  ... }{x}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\int \\\\left(c E+ \\\\ldots +c D+ \\\\ldots \\\\right)\\\\,\\\\,{\\\\rm d}x\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"substitute(_, $A -> E$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"In order to get back to the full expression, use \\\\algo{unzoom},\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"In order to get back to the full expression, use \\\\algo{unzoom},\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"\\\\int{c E + (c)**2 B + c D + (c)**2 A}{x}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\int \\\\left(c E+{c}^{2} B+c D+{c}^{2} A\\\\right)\\\\,\\\\,{\\\\rm d}x\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"unzoom(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"As you can see, the substitution has only changed the terms which were visible at the time.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"As you can see, the substitution has only changed the terms which were visible at the time.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1\n}\n"
  },
  {
    "path": "examples/ref_spacing.cnb",
    "content": "{\n\t\"cell_id\": 6780327821501550458,\n\t\"cells\": [\n\t\t{\n\t\t\t\"cell_id\": 10095608579166230431,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 3568454378584712115,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\section*{Spacing and brackets}\\n\\nCadabra is reasonably flexible as far as spacing and brackets are\\nconcerned, but the fact that objects do not have to be declared before\\nthey can be used means that spaces have to be introduced in some cases\\nto avoid ambiguity. As a general rule, all terms in a product have to\\nbe separated by at least one whitespace character. Thus,\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\section*{Spacing and brackets}\\n\\nCadabra is reasonably flexible as far as spacing and brackets are\\nconcerned, but the fact that objects do not have to be declared before\\nthey can be used means that spaces have to be introduced in some cases\\nto avoid ambiguity. As a general rule, all terms in a product have to\\nbe separated by at least one whitespace character. Thus,\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 5243956819659161058,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 828697262279609186,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 5600925919959444274,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"A(B + C)\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}A\\\\left(B\\\\discretionary{}{}{}+C\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex:= A(B+C);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 3521492023207671027,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 6395206610982757740,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"is interpreted as a function $A$ with argument $B+C$, while\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"is interpreted as a function $A$ with argument $B+C$, while\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 3254933193926073803,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 13063679095181457061,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 14301624096609751952,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"A (B + C)\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}A \\\\left(B\\\\discretionary{}{}{}+C\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex:= A (B+C);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 9193648467922875359,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 15584829755797389306,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"(with a space inbetween the $A$ and the opening bracket) is interpreted as\\n$A$ multiplying $B+C$. In a similar spirit, two consecutive characters without\\na space are interpreted as a single symbol, so that\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"(with a space inbetween the $A$ and the opening bracket) is interpreted as\\n$A$ multiplying $B+C$. In a similar spirit, two consecutive characters without\\na space are interpreted as a single symbol, so that\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 2596882454490953534,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 4545248679347908905,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 14262944906308332001,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"AB\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}AB\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex:= AB;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 10200772961325234698,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 18174430478425350203,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"is not the product of $A$ times $B$, but rather a single, two-character\\nsymbol. Put a space inbetween if you want it to be a product, or an\\nexplicit multiplication sign,\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"is not the product of $A$ times $B$, but rather a single, two-character\\nsymbol. Put a space inbetween if you want it to be a product, or an\\nexplicit multiplication sign,\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 3657900939440613632,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 15898225287759389543,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 1107696764486452994,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"2A B\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}2A B\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex:= A*B + A B;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 9336604298712487300,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 16999472921636049313,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"If a whitespace character is absent, all brackets are interpreted as\\nenclosing \\\\emph{argument} groups.  However, spaces will automatically be\\ninserted after numbers, between a closing bracket and a name or\\nnumber, and between two names if the second name starts with a\\nbackslash. The following expressions are therefore interpreted as one\\nwould expect:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"If a whitespace character is absent, all brackets are interpreted as\\nenclosing \\\\emph{argument} groups.  However, spaces will automatically be\\ninserted after numbers, between a closing bracket and a name or\\nnumber, and between two names if the second name starts with a\\nbackslash. The following expressions are therefore interpreted as one\\nwould expect:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 213025404522232061,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 147956388667526319,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 557146378947345533,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"3A\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}3A\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 17911863916385468643,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 17293410605441509411,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"(A + B) C\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\left(A\\\\discretionary{}{}{}+B\\\\right) C\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 11032147089194360946,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 16424943557105344906,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"3A + 3B\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}3A\\\\discretionary{}{}{}+3B\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 8988874013216573119,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 18102133924784247814,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"A \\\\Gamma\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}A \\\\Gamma\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex1:= 3A;\\nex2:= (A+B)C;\\nex3:= (A+B)3;\\nex4:= A\\\\Gamma;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 2954135611539678626,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 5674456039730473675,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"Finally, note that\\nbrackets in the input \\\\emph{must} be balanced (a decision made to\\nsimplify the parser; it means that cadabra uses a different way to\\nindicate groups of symmetric or anti-symmetric indices than one often\\nencounters in the general relativity literature.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"Finally, note that\\nbrackets in the input \\\\emph{must} be balanced (a decision made to\\nsimplify the parser; it means that cadabra uses a different way to\\nindicate groups of symmetric or anti-symmetric indices than one often\\nencounters in the general relativity literature.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 13147868089044620186,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"\"\n\t\t}\n\t],\n\t\"description\": \"Cadabra JSON notebook format\",\n\t\"version\": 1.0\n}\n"
  },
  {
    "path": "examples/ref_sympy.cnb",
    "content": "{\n\t\"cell_id\": 6019221673666211598,\n\t\"cells\": [\n\t\t{\n\t\t\t\"cell_id\": 3141052395239476853,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 11719283590375328817,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\section*{Using SymPy on Cadabra expressions}\\n\\nWhile Cadabra contains a large number of function for expression manipulation, there are many things for which it does not attempt to re-invent the wheel, and calls into SymPy instead. If you want to write functions which manipulate Cadabra expressions and call SymPy functionality on them yourself, you need to know how to export expressions to SymPy form, and read them back once it has done processing. This is somewhat non-trivial, because Cadabra's notation allows for much more general expressions than SymPy. Think of \\\\LaTeX{} expressions, super- and sub-scripts but also objects which depend implicitly on other variables. These things all need converting to something which SymPy can handle, and converting back once SymPy has produced a result.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\section*{Using SymPy on Cadabra expressions}\\n\\nWhile Cadabra contains a large number of function for expression manipulation, there are many things for which it does not attempt to re-invent the wheel, and calls into SymPy instead. If you want to write functions which manipulate Cadabra expressions and call SymPy functionality on them yourself, you need to know how to export expressions to SymPy form, and read them back once it has done processing. This is somewhat non-trivial, because Cadabra's notation allows for much more general expressions than SymPy. Think of \\\\LaTeX{} expressions, super- and sub-scripts but also objects which depend implicitly on other variables. These things all need converting to something which SymPy can handle, and converting back once SymPy has produced a result.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 10363222040320991365,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 16021072591756643213,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"The main object to deal with this conversion is \\\\verb|SympyBridge|. This object takes the expression you want to share with SymPy. Let us start with a non-trivial Cadabra expression,\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"The main object to deal with this conversion is \\\\verb|SympyBridge|. This object takes the expression you want to share with SymPy. Let us start with a non-trivial Cadabra expression,\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 14640557008397293206,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 17642380777219746400,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property PartialDerivative attached to~}\\\\backslash\\\\texttt{partial}\\\\{\\\\#\\\\}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 11311532150071334257,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property Coordinate attached to~}t.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 10285511277438191052,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property Depends attached to~}x.\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"\\\\partial{#}::PartialDerivative;\\nt::Coordinate;\\nx::Depends(t);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 2257448352953451952,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 11641289790669342633,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 6829148980251860903,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"(\\\\sin(x))**2 + (\\\\cos(x))**2 + \\\\partial_{t}(x)\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}{\\\\left(\\\\sin{x}\\\\right)}^{2\\\\,}\\\\discretionary{}{}{}+{\\\\left(\\\\cos{x}\\\\right)}^{2\\\\,}\\\\discretionary{}{}{}+\\\\partial_{t}{x}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex:= \\\\sin(x)**2 + \\\\cos(x)**2 + \\\\partial_{t}{x};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 811930716112812923,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 4981305692711169774,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"The above expression contains \\\\verb|\\\\sin| and \\\\verb|\\\\cos| (which SymPy does not understand) and it also contains a variable $x$ which implicitly depends on $t$ (the dependence is not shown in the output). In order to be able to feed this into SymPy, and get it back later, we create a \\\\verb|SympyBridge| object, passing it the expression:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"The above expression contains \\\\verb|\\\\sin| and \\\\verb|\\\\cos| (which SymPy does not understand) and it also contains a variable $x$ which implicitly depends on $t$ (the dependence is not shown in the output). In order to be able to feed this into SymPy, and get it back later, we create a \\\\verb|SympyBridge| object, passing it the expression:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 14171341419325683178,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 16351361485273877233,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"verbatim\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}<cadabra2.SympyBridge object at 0xe74381340c70>\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"sb = SympyBridge(ex);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 12417034613577478302,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 12120598920304089059,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"In order to retrieve the SymPy object, use the \\\\verb|to_sympy()| function, \"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"In order to retrieve the SymPy object, use the \\\\verb|to_sympy()| function, \"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 7460301723421844097,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 12898408199579522338,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"output\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}<class 'sympy.core.add.Add'>\\n\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex_sympy = sb.to_sympy()\\nprint(type(ex_sympy))\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 14363314488499443831,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 17654699939173108028,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"As you can see, the expression is now a SymPy object. If you print it, you will note that Cadabra has converted the \\\\LaTeX{} symbols \\\\verb|\\\\sin| and \\\\verb|\\\\cos| to something SymPy understands, and it has also written out the implicit dependence on the $t$ variable,\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"As you can see, the expression is now a SymPy object. If you print it, you will note that Cadabra has converted the \\\\LaTeX{} symbols \\\\verb|\\\\sin| and \\\\verb|\\\\cos| to something SymPy understands, and it has also written out the implicit dependence on the $t$ variable,\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 12438384282863570392,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9598964413090421073,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"output\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}sin(x(t))**2 + cos(x(t))**2 + Derivative(x(t), t)\\n\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"print(ex_sympy)\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 3314936080047954075,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 164194584640500209,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"You can now manipulate this expression as you want, using standard SymPy functionality. Let's simplify this,\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"You can now manipulate this expression as you want, using standard SymPy functionality. Let's simplify this,\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 7089643061312412743,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 11685820618493173482,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\frac{d}{d t} x{\\\\left(t \\\\right)} + 1\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 546058567743717626,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"output\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}<class 'sympy.core.add.Add'>\\n\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"res = sympy.simplify( ex_sympy );\\nprint(type(res))\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 6370470393263816966,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 2806557392660395011,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"This is of course still a SymPy expression. We can pull it back into Cadabra by using the \\\\verb|SympyBridge| again,\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"This is of course still a SymPy expression. We can pull it back into Cadabra by using the \\\\verb|SympyBridge| again,\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 1133881024765925592,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 11794754683863187961,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"verbatim\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}None\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"sb.from_sympy( res );\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 17254762459033388476,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 13664737385979361090,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"This does not return a new expression (the return value is \\\\verb|None|), but instead puts the SymPy expression back into the original Cadabra expression that we started with when we constructed the bridge; here that is \\\\verb|ex|. Indeed,\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"This does not return a new expression (the return value is \\\\verb|None|), but instead puts the SymPy expression back into the original Cadabra expression that we started with when we constructed the bridge; here that is \\\\verb|ex|. Indeed,\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 17271004422718666216,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 16101485724532254709,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 8801360286293087809,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\partial_{t}(x) + 1\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\partial_{t}{x}\\\\discretionary{}{}{}+1\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 13344444686216197143,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 16158702197574445152,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"Note how this has nicely removed the explicit dependence on $t$ and turned it back into an implicit notation, writing just $x$ and not $x(t)$.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"Note how this has nicely removed the explicit dependence on $t$ and turned it back into an implicit notation, writing just $x$ and not $x(t)$.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 11664900633694074895,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"\"\n\t\t}\n\t],\n\t\"description\": \"Cadabra JSON notebook format\",\n\t\"flags\": {\n\t\t\"hide_input_cells\": false\n\t},\n\t\"version\": 1.0\n}\n"
  },
  {
    "path": "examples/reset.cnb",
    "content": "{\n\t\"cells\" : \n\t[\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Indices(position=free) to~}\\\\left(m, \\\\linebreak[0] n, \\\\linebreak[0] p\\\\right).\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"{m,n,p}::Indices;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}A_{m n}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex:=A_{m n};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"reset()\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"ex2:=B_{m n};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"error\",\n\t\t\t\t\t\"source\" : \"{\\\\color{red}{\\\\begin{verbatim}Traceback (most recent call last):\\n  File \\\"<string>\\\", line 1, in <module>\\nNameError: name 'ex' is not defined\\n\\\\end{verbatim}}}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1\n}\n"
  },
  {
    "path": "examples/sample_dyn.cnb",
    "content": "{\n\t\"cell_id\": 3856175165489560631,\n\t\"cells\": [\n\t\t{\n\t\t\t\"cell_id\": 8297576327410774289,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 12073229740054367476,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"This notebook demonstrates series expansions. Press the 'run' button above, then drag the slider.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"This notebook demonstrates series expansions. Press the 'run' button above, then drag the slider.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 10177894001909448932,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 5224948693319114343,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"Function to approximate:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"Function to approximate:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 10380147558135702280,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 10315676320490069252,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 1424978678461403845,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\sin(x)\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\sin{x}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex:=\\\\sin(x);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 2961936357451179205,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"from cdb.sympy.calculus import *\\nfrom cdb.interact.slider import *\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 11413330410640289556,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"order=2\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 7485977888536342457,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 160435110520907250,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"Series expansion:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"Series expansion:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 4279529243122204986,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 1812349966897238719,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 2069743952314228164,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"x + \\\\bigO((x)**3)\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}x\\\\discretionary{}{}{}+\\\\bigO\\\\left({x}^{3\\\\,}\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"s=series(ex, $x$, 0, order);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 15520869516496248848,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"from cdb.graphics.plot import *\\nfig=None\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 16853950691777106105,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 6593707939581339927,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"image_svg\",\n\t\t\t\t\t\"source\": \"<?xml version="1.0" encoding="utf-8" standalone="no"?>
<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
  "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="460.8pt" height="345.6pt" viewBox="0 0 460.8 345.6" xmlns="http://www.w3.org/2000/svg" version="1.1">
 <metadata>
  <rdf:RDF xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:cc="http://creativecommons.org/ns#" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
   <cc:Work>
    <dc:type rdf:resource="http://purl.org/dc/dcmitype/StillImage"/>
    <dc:date>2025-06-10T13:37:43.665927</dc:date>
    <dc:format>image/svg+xml</dc:format>
    <dc:creator>
     <cc:Agent>
      <dc:title>Matplotlib v3.6.3, https://matplotlib.org/</dc:title>
     </cc:Agent>
    </dc:creator>
   </cc:Work>
  </rdf:RDF>
 </metadata>
 <defs>
  <style type="text/css">*{stroke-linejoin: round; stroke-linecap: butt}</style>
 </defs>
 <g id="figure_1">
  <g id="patch_1">
   <path d="M 0 345.6 
L 460.8 345.6 
L 460.8 0 
L 0 0 
z
" style="fill: #ffffff"/>
  </g>
  <g id="axes_1">
   <g id="patch_2">
    <path d="M 57.6 307.584 
L 414.72 307.584 
L 414.72 41.472 
L 57.6 41.472 
z
" style="fill: #ffffff"/>
   </g>
   <g id="matplotlib.axis_1">
    <g id="xtick_1">
     <g id="line2d_1">
      <defs>
       <path id="m97546635e6" d="M 0 0 
L 0 3.5 
" style="stroke: #000000; stroke-width: 0.8"/>
      </defs>
      <g>
       <use xlink:href="#m97546635e6" x="73.832727" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_1">
      <!-- 0 -->
      <g transform="translate(70.651477 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-30" d="M 2034 4250 
Q 1547 4250 1301 3770 
Q 1056 3291 1056 2328 
Q 1056 1369 1301 889 
Q 1547 409 2034 409 
Q 2525 409 2770 889 
Q 3016 1369 3016 2328 
Q 3016 3291 2770 3770 
Q 2525 4250 2034 4250 
z
M 2034 4750 
Q 2819 4750 3233 4129 
Q 3647 3509 3647 2328 
Q 3647 1150 3233 529 
Q 2819 -91 2034 -91 
Q 1250 -91 836 529 
Q 422 1150 422 2328 
Q 422 3509 836 4129 
Q 1250 4750 2034 4750 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-30"/>
      </g>
     </g>
    </g>
    <g id="xtick_2">
     <g id="line2d_2">
      <g>
       <use xlink:href="#m97546635e6" x="138.763636" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_2">
      <!-- 2 -->
      <g transform="translate(135.582386 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-32" d="M 1228 531 
L 3431 531 
L 3431 0 
L 469 0 
L 469 531 
Q 828 903 1448 1529 
Q 2069 2156 2228 2338 
Q 2531 2678 2651 2914 
Q 2772 3150 2772 3378 
Q 2772 3750 2511 3984 
Q 2250 4219 1831 4219 
Q 1534 4219 1204 4116 
Q 875 4013 500 3803 
L 500 4441 
Q 881 4594 1212 4672 
Q 1544 4750 1819 4750 
Q 2544 4750 2975 4387 
Q 3406 4025 3406 3419 
Q 3406 3131 3298 2873 
Q 3191 2616 2906 2266 
Q 2828 2175 2409 1742 
Q 1991 1309 1228 531 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-32"/>
      </g>
     </g>
    </g>
    <g id="xtick_3">
     <g id="line2d_3">
      <g>
       <use xlink:href="#m97546635e6" x="203.694545" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_3">
      <!-- 4 -->
      <g transform="translate(200.513295 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-34" d="M 2419 4116 
L 825 1625 
L 2419 1625 
L 2419 4116 
z
M 2253 4666 
L 3047 4666 
L 3047 1625 
L 3713 1625 
L 3713 1100 
L 3047 1100 
L 3047 0 
L 2419 0 
L 2419 1100 
L 313 1100 
L 313 1709 
L 2253 4666 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-34"/>
      </g>
     </g>
    </g>
    <g id="xtick_4">
     <g id="line2d_4">
      <g>
       <use xlink:href="#m97546635e6" x="268.625455" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_4">
      <!-- 6 -->
      <g transform="translate(265.444205 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-36" d="M 2113 2584 
Q 1688 2584 1439 2293 
Q 1191 2003 1191 1497 
Q 1191 994 1439 701 
Q 1688 409 2113 409 
Q 2538 409 2786 701 
Q 3034 994 3034 1497 
Q 3034 2003 2786 2293 
Q 2538 2584 2113 2584 
z
M 3366 4563 
L 3366 3988 
Q 3128 4100 2886 4159 
Q 2644 4219 2406 4219 
Q 1781 4219 1451 3797 
Q 1122 3375 1075 2522 
Q 1259 2794 1537 2939 
Q 1816 3084 2150 3084 
Q 2853 3084 3261 2657 
Q 3669 2231 3669 1497 
Q 3669 778 3244 343 
Q 2819 -91 2113 -91 
Q 1303 -91 875 529 
Q 447 1150 447 2328 
Q 447 3434 972 4092 
Q 1497 4750 2381 4750 
Q 2619 4750 2861 4703 
Q 3103 4656 3366 4563 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-36"/>
      </g>
     </g>
    </g>
    <g id="xtick_5">
     <g id="line2d_5">
      <g>
       <use xlink:href="#m97546635e6" x="333.556364" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_5">
      <!-- 8 -->
      <g transform="translate(330.375114 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-38" d="M 2034 2216 
Q 1584 2216 1326 1975 
Q 1069 1734 1069 1313 
Q 1069 891 1326 650 
Q 1584 409 2034 409 
Q 2484 409 2743 651 
Q 3003 894 3003 1313 
Q 3003 1734 2745 1975 
Q 2488 2216 2034 2216 
z
M 1403 2484 
Q 997 2584 770 2862 
Q 544 3141 544 3541 
Q 544 4100 942 4425 
Q 1341 4750 2034 4750 
Q 2731 4750 3128 4425 
Q 3525 4100 3525 3541 
Q 3525 3141 3298 2862 
Q 3072 2584 2669 2484 
Q 3125 2378 3379 2068 
Q 3634 1759 3634 1313 
Q 3634 634 3220 271 
Q 2806 -91 2034 -91 
Q 1263 -91 848 271 
Q 434 634 434 1313 
Q 434 1759 690 2068 
Q 947 2378 1403 2484 
z
M 1172 3481 
Q 1172 3119 1398 2916 
Q 1625 2713 2034 2713 
Q 2441 2713 2670 2916 
Q 2900 3119 2900 3481 
Q 2900 3844 2670 4047 
Q 2441 4250 2034 4250 
Q 1625 4250 1398 4047 
Q 1172 3844 1172 3481 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-38"/>
      </g>
     </g>
    </g>
    <g id="xtick_6">
     <g id="line2d_6">
      <g>
       <use xlink:href="#m97546635e6" x="398.487273" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_6">
      <!-- 10 -->
      <g transform="translate(392.124773 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-31" d="M 794 531 
L 1825 531 
L 1825 4091 
L 703 3866 
L 703 4441 
L 1819 4666 
L 2450 4666 
L 2450 531 
L 3481 531 
L 3481 0 
L 794 0 
L 794 531 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-31"/>
       <use xlink:href="#DejaVuSans-30" x="63.623047"/>
      </g>
     </g>
    </g>
   </g>
   <g id="matplotlib.axis_2">
    <g id="ytick_1">
     <g id="line2d_7">
      <defs>
       <path id="mb97f88ff81" d="M 0 0 
L -3.5 0 
" style="stroke: #000000; stroke-width: 0.8"/>
      </defs>
      <g>
       <use xlink:href="#mb97f88ff81" x="57.6" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_7">
      <!-- −4 -->
      <g transform="translate(35.857813 311.383219) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-2212" d="M 678 2272 
L 4684 2272 
L 4684 1741 
L 678 1741 
L 678 2272 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-2212"/>
       <use xlink:href="#DejaVuSans-34" x="83.789062"/>
      </g>
     </g>
    </g>
    <g id="ytick_2">
     <g id="line2d_8">
      <g>
       <use xlink:href="#mb97f88ff81" x="57.6" y="274.32" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_8">
      <!-- −3 -->
      <g transform="translate(35.857813 278.119219) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-33" d="M 2597 2516 
Q 3050 2419 3304 2112 
Q 3559 1806 3559 1356 
Q 3559 666 3084 287 
Q 2609 -91 1734 -91 
Q 1441 -91 1130 -33 
Q 819 25 488 141 
L 488 750 
Q 750 597 1062 519 
Q 1375 441 1716 441 
Q 2309 441 2620 675 
Q 2931 909 2931 1356 
Q 2931 1769 2642 2001 
Q 2353 2234 1838 2234 
L 1294 2234 
L 1294 2753 
L 1863 2753 
Q 2328 2753 2575 2939 
Q 2822 3125 2822 3475 
Q 2822 3834 2567 4026 
Q 2313 4219 1838 4219 
Q 1578 4219 1281 4162 
Q 984 4106 628 3988 
L 628 4550 
Q 988 4650 1302 4700 
Q 1616 4750 1894 4750 
Q 2613 4750 3031 4423 
Q 3450 4097 3450 3541 
Q 3450 3153 3228 2886 
Q 3006 2619 2597 2516 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-2212"/>
       <use xlink:href="#DejaVuSans-33" x="83.789062"/>
      </g>
     </g>
    </g>
    <g id="ytick_3">
     <g id="line2d_9">
      <g>
       <use xlink:href="#mb97f88ff81" x="57.6" y="241.056" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_9">
      <!-- −2 -->
      <g transform="translate(35.857813 244.855219) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-2212"/>
       <use xlink:href="#DejaVuSans-32" x="83.789062"/>
      </g>
     </g>
    </g>
    <g id="ytick_4">
     <g id="line2d_10">
      <g>
       <use xlink:href="#mb97f88ff81" x="57.6" y="207.792" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_10">
      <!-- −1 -->
      <g transform="translate(35.857813 211.591219) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-2212"/>
       <use xlink:href="#DejaVuSans-31" x="83.789062"/>
      </g>
     </g>
    </g>
    <g id="ytick_5">
     <g id="line2d_11">
      <g>
       <use xlink:href="#mb97f88ff81" x="57.6" y="174.528" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_11">
      <!-- 0 -->
      <g transform="translate(44.2375 178.327219) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-30"/>
      </g>
     </g>
    </g>
    <g id="ytick_6">
     <g id="line2d_12">
      <g>
       <use xlink:href="#mb97f88ff81" x="57.6" y="141.264" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_12">
      <!-- 1 -->
      <g transform="translate(44.2375 145.063219) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-31"/>
      </g>
     </g>
    </g>
    <g id="ytick_7">
     <g id="line2d_13">
      <g>
       <use xlink:href="#mb97f88ff81" x="57.6" y="108" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_13">
      <!-- 2 -->
      <g transform="translate(44.2375 111.799219) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-32"/>
      </g>
     </g>
    </g>
    <g id="ytick_8">
     <g id="line2d_14">
      <g>
       <use xlink:href="#mb97f88ff81" x="57.6" y="74.736" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_14">
      <!-- 3 -->
      <g transform="translate(44.2375 78.535219) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-33"/>
      </g>
     </g>
    </g>
    <g id="ytick_9">
     <g id="line2d_15">
      <g>
       <use xlink:href="#mb97f88ff81" x="57.6" y="41.472" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_15">
      <!-- 4 -->
      <g transform="translate(44.2375 45.271219) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-34"/>
      </g>
     </g>
    </g>
   </g>
   <g id="line2d_16">
    <path d="M 73.832727 174.528 
L 83.582113 164.688273 
L 88.781785 159.746787 
L 93.331499 155.729247 
L 97.231253 152.57621 
L 100.806028 149.962808 
L 104.055823 147.844413 
L 107.305618 145.993165 
L 110.230434 144.57083 
L 113.15525 143.391469 
L 116.080066 142.464649 
L 118.679902 141.858941 
L 121.279738 141.462623 
L 123.879574 141.278233 
L 126.47941 141.306955 
L 129.079247 141.548603 
L 131.679083 142.001629 
L 134.278919 142.663129 
L 137.203735 143.651179 
L 140.12855 144.889662 
L 143.053366 146.368534 
L 146.303161 148.27901 
L 149.552957 150.452283 
L 153.127731 153.120371 
L 157.027486 156.325527 
L 161.252219 160.092264 
L 166.126912 164.737552 
L 172.626503 171.255149 
L 186.600622 185.366136 
L 191.800295 190.242769 
L 196.025029 193.914286 
L 199.924783 197.013737 
L 203.499558 199.571238 
L 206.749353 201.633769 
L 209.999148 203.424927 
L 212.923964 204.790064 
L 215.84878 205.909754 
L 218.773595 206.774914 
L 221.373432 207.324546 
L 223.973268 207.663973 
L 226.573104 207.791018 
L 229.17294 207.704867 
L 231.772776 207.406073 
L 234.372613 206.89655 
L 236.972449 206.179565 
L 239.897265 205.130746 
L 242.82208 203.833716 
L 245.746896 202.298996 
L 248.996691 200.330179 
L 252.246486 198.10304 
L 255.821261 195.381508 
L 259.721016 192.125724 
L 264.270729 188.010278 
L 269.470401 182.988175 
L 276.94493 175.42366 
L 287.669255 164.589786 
L 292.868927 159.654451 
L 297.41864 155.644239 
L 301.318395 152.498815 
L 304.89317 149.893375 
L 308.142965 147.782951 
L 311.39276 145.94029 
L 314.317576 144.526137 
L 317.242391 143.355321 
L 320.167207 142.437339 
L 322.767043 141.839677 
L 325.36688 141.451526 
L 327.966716 141.275376 
L 330.566552 141.312355 
L 333.166388 141.562226 
L 335.766224 142.023387 
L 338.366061 142.692884 
L 341.290876 143.689699 
L 344.215692 144.936635 
L 347.140508 146.423578 
L 350.390303 148.342497 
L 353.640098 150.523576 
L 357.214873 153.199424 
L 361.114627 156.411951 
L 365.339361 160.185265 
L 370.214054 164.836181 
L 377.038624 171.689426 
L 390.362785 185.148598 
L 395.562457 190.039838 
L 398.487273 192.624318 
L 398.487273 192.624318 
" clip-path="url(#p371e378505)" style="fill: none; stroke: #1f77b4; stroke-width: 1.5; stroke-linecap: square"/>
   </g>
   <g id="line2d_17">
    <path d="M 73.832727 174.528 
L 245.14695 -1 
L 245.14695 -1 
" clip-path="url(#p371e378505)" style="fill: none; stroke: #ff7f0e; stroke-width: 1.5; stroke-linecap: square"/>
   </g>
   <g id="patch_3">
    <path d="M 57.6 307.584 
L 57.6 41.472 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
   <g id="patch_4">
    <path d="M 414.72 307.584 
L 414.72 41.472 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
   <g id="patch_5">
    <path d="M 57.6 307.584 
L 414.72 307.584 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
   <g id="patch_6">
    <path d="M 57.6 41.472 
L 414.72 41.472 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
   <g id="legend_1">
    <g id="patch_7">
     <path d="M 341.284063 78.82825 
L 407.72 78.82825 
Q 409.72 78.82825 409.72 76.82825 
L 409.72 48.472 
Q 409.72 46.472 407.72 46.472 
L 341.284063 46.472 
Q 339.284063 46.472 339.284063 48.472 
L 339.284063 76.82825 
Q 339.284063 78.82825 341.284063 78.82825 
z
" style="fill: #ffffff; opacity: 0.8; stroke: #cccccc; stroke-linejoin: miter"/>
    </g>
    <g id="line2d_18">
     <path d="M 343.284063 54.570437 
L 353.284063 54.570437 
L 363.284063 54.570437 
" style="fill: none; stroke: #1f77b4; stroke-width: 1.5; stroke-linecap: square"/>
    </g>
    <g id="text_16">
     <!-- sin(x) -->
     <g transform="translate(371.284063 58.070437) scale(0.1 -0.1)">
      <defs>
       <path id="DejaVuSans-73" d="M 2834 3397 
L 2834 2853 
Q 2591 2978 2328 3040 
Q 2066 3103 1784 3103 
Q 1356 3103 1142 2972 
Q 928 2841 928 2578 
Q 928 2378 1081 2264 
Q 1234 2150 1697 2047 
L 1894 2003 
Q 2506 1872 2764 1633 
Q 3022 1394 3022 966 
Q 3022 478 2636 193 
Q 2250 -91 1575 -91 
Q 1294 -91 989 -36 
Q 684 19 347 128 
L 347 722 
Q 666 556 975 473 
Q 1284 391 1588 391 
Q 1994 391 2212 530 
Q 2431 669 2431 922 
Q 2431 1156 2273 1281 
Q 2116 1406 1581 1522 
L 1381 1569 
Q 847 1681 609 1914 
Q 372 2147 372 2553 
Q 372 3047 722 3315 
Q 1072 3584 1716 3584 
Q 2034 3584 2315 3537 
Q 2597 3491 2834 3397 
z
" transform="scale(0.015625)"/>
       <path id="DejaVuSans-69" d="M 603 3500 
L 1178 3500 
L 1178 0 
L 603 0 
L 603 3500 
z
M 603 4863 
L 1178 4863 
L 1178 4134 
L 603 4134 
L 603 4863 
z
" transform="scale(0.015625)"/>
       <path id="DejaVuSans-6e" d="M 3513 2113 
L 3513 0 
L 2938 0 
L 2938 2094 
Q 2938 2591 2744 2837 
Q 2550 3084 2163 3084 
Q 1697 3084 1428 2787 
Q 1159 2491 1159 1978 
L 1159 0 
L 581 0 
L 581 3500 
L 1159 3500 
L 1159 2956 
Q 1366 3272 1645 3428 
Q 1925 3584 2291 3584 
Q 2894 3584 3203 3211 
Q 3513 2838 3513 2113 
z
" transform="scale(0.015625)"/>
       <path id="DejaVuSans-28" d="M 1984 4856 
Q 1566 4138 1362 3434 
Q 1159 2731 1159 2009 
Q 1159 1288 1364 580 
Q 1569 -128 1984 -844 
L 1484 -844 
Q 1016 -109 783 600 
Q 550 1309 550 2009 
Q 550 2706 781 3412 
Q 1013 4119 1484 4856 
L 1984 4856 
z
" transform="scale(0.015625)"/>
       <path id="DejaVuSans-78" d="M 3513 3500 
L 2247 1797 
L 3578 0 
L 2900 0 
L 1881 1375 
L 863 0 
L 184 0 
L 1544 1831 
L 300 3500 
L 978 3500 
L 1906 2253 
L 2834 3500 
L 3513 3500 
z
" transform="scale(0.015625)"/>
       <path id="DejaVuSans-29" d="M 513 4856 
L 1013 4856 
Q 1481 4119 1714 3412 
Q 1947 2706 1947 2009 
Q 1947 1309 1714 600 
Q 1481 -109 1013 -844 
L 513 -844 
Q 928 -128 1133 580 
Q 1338 1288 1338 2009 
Q 1338 2731 1133 3434 
Q 928 4138 513 4856 
z
" transform="scale(0.015625)"/>
      </defs>
      <use xlink:href="#DejaVuSans-73"/>
      <use xlink:href="#DejaVuSans-69" x="52.099609"/>
      <use xlink:href="#DejaVuSans-6e" x="79.882812"/>
      <use xlink:href="#DejaVuSans-28" x="143.261719"/>
      <use xlink:href="#DejaVuSans-78" x="182.275391"/>
      <use xlink:href="#DejaVuSans-29" x="241.455078"/>
     </g>
    </g>
    <g id="line2d_19">
     <path d="M 343.284063 69.248562 
L 353.284063 69.248562 
L 363.284063 69.248562 
" style="fill: none; stroke: #ff7f0e; stroke-width: 1.5; stroke-linecap: square"/>
    </g>
    <g id="text_17">
     <!-- approx -->
     <g transform="translate(371.284063 72.748562) scale(0.1 -0.1)">
      <defs>
       <path id="DejaVuSans-61" d="M 2194 1759 
Q 1497 1759 1228 1600 
Q 959 1441 959 1056 
Q 959 750 1161 570 
Q 1363 391 1709 391 
Q 2188 391 2477 730 
Q 2766 1069 2766 1631 
L 2766 1759 
L 2194 1759 
z
M 3341 1997 
L 3341 0 
L 2766 0 
L 2766 531 
Q 2569 213 2275 61 
Q 1981 -91 1556 -91 
Q 1019 -91 701 211 
Q 384 513 384 1019 
Q 384 1609 779 1909 
Q 1175 2209 1959 2209 
L 2766 2209 
L 2766 2266 
Q 2766 2663 2505 2880 
Q 2244 3097 1772 3097 
Q 1472 3097 1187 3025 
Q 903 2953 641 2809 
L 641 3341 
Q 956 3463 1253 3523 
Q 1550 3584 1831 3584 
Q 2591 3584 2966 3190 
Q 3341 2797 3341 1997 
z
" transform="scale(0.015625)"/>
       <path id="DejaVuSans-70" d="M 1159 525 
L 1159 -1331 
L 581 -1331 
L 581 3500 
L 1159 3500 
L 1159 2969 
Q 1341 3281 1617 3432 
Q 1894 3584 2278 3584 
Q 2916 3584 3314 3078 
Q 3713 2572 3713 1747 
Q 3713 922 3314 415 
Q 2916 -91 2278 -91 
Q 1894 -91 1617 61 
Q 1341 213 1159 525 
z
M 3116 1747 
Q 3116 2381 2855 2742 
Q 2594 3103 2138 3103 
Q 1681 3103 1420 2742 
Q 1159 2381 1159 1747 
Q 1159 1113 1420 752 
Q 1681 391 2138 391 
Q 2594 391 2855 752 
Q 3116 1113 3116 1747 
z
" transform="scale(0.015625)"/>
       <path id="DejaVuSans-72" d="M 2631 2963 
Q 2534 3019 2420 3045 
Q 2306 3072 2169 3072 
Q 1681 3072 1420 2755 
Q 1159 2438 1159 1844 
L 1159 0 
L 581 0 
L 581 3500 
L 1159 3500 
L 1159 2956 
Q 1341 3275 1631 3429 
Q 1922 3584 2338 3584 
Q 2397 3584 2469 3576 
Q 2541 3569 2628 3553 
L 2631 2963 
z
" transform="scale(0.015625)"/>
       <path id="DejaVuSans-6f" d="M 1959 3097 
Q 1497 3097 1228 2736 
Q 959 2375 959 1747 
Q 959 1119 1226 758 
Q 1494 397 1959 397 
Q 2419 397 2687 759 
Q 2956 1122 2956 1747 
Q 2956 2369 2687 2733 
Q 2419 3097 1959 3097 
z
M 1959 3584 
Q 2709 3584 3137 3096 
Q 3566 2609 3566 1747 
Q 3566 888 3137 398 
Q 2709 -91 1959 -91 
Q 1206 -91 779 398 
Q 353 888 353 1747 
Q 353 2609 779 3096 
Q 1206 3584 1959 3584 
z
" transform="scale(0.015625)"/>
      </defs>
      <use xlink:href="#DejaVuSans-61"/>
      <use xlink:href="#DejaVuSans-70" x="61.279297"/>
      <use xlink:href="#DejaVuSans-70" x="124.755859"/>
      <use xlink:href="#DejaVuSans-72" x="188.232422"/>
      <use xlink:href="#DejaVuSans-6f" x="227.095703"/>
      <use xlink:href="#DejaVuSans-78" x="285.152344"/>
     </g>
    </g>
   </g>
  </g>
  <g id="text_18">
   <!-- ${\cal O}(2)$ -->
   <g transform="translate(211.68 27.324) scale(0.18 -0.18)">
    <defs>
     <path id="Cmsy10-4f" d="M 1863 -141 
Q 1159 -141 762 357 
Q 366 856 366 1581 
Q 366 2528 991 3366 
Q 1138 3559 1419 3828 
Q 1700 4097 1990 4294 
Q 2281 4491 2484 4513 
L 2516 4513 
Q 2559 4491 2559 4459 
Q 2559 4434 2534 4397 
Q 2497 4350 2214 4150 
Q 1931 3950 1900 3922 
Q 1606 3666 1394 3353 
Q 1172 3022 1053 2637 
Q 934 2253 934 1850 
Q 934 1422 1092 1051 
Q 1250 681 1567 459 
Q 1884 238 2322 238 
Q 2781 238 3173 470 
Q 3566 703 3834 1078 
Q 4103 1453 4253 1914 
Q 4403 2375 4403 2809 
Q 4403 3159 4298 3457 
Q 4194 3756 3969 3945 
Q 3744 4134 3397 4134 
Q 3256 4134 3128 4078 
Q 2919 3966 2730 3673 
Q 2541 3381 2413 3072 
Q 2347 2959 2203 2875 
Q 2059 2791 1925 2778 
L 1894 2778 
Q 1881 2784 1865 2796 
Q 1850 2809 1850 2828 
Q 1850 2841 1856 2859 
Q 2144 3581 2644 4006 
Q 2913 4238 3209 4375 
Q 3506 4513 3822 4513 
L 3859 4513 
Q 4247 4513 4494 4313 
Q 4741 4113 4856 3786 
Q 4972 3459 4972 3084 
Q 4972 2669 4861 2269 
Q 4750 1869 4545 1519 
Q 4341 1169 4044 872 
Q 3741 575 3398 350 
Q 3056 125 2668 -8 
Q 2281 -141 1894 -141 
L 1863 -141 
z
" transform="scale(0.015625)"/>
     <path id="Cmr10-28" d="M 1984 -1588 
Q 1628 -1306 1370 -942 
Q 1113 -578 948 -165 
Q 784 247 703 697 
Q 622 1147 622 1600 
Q 622 2059 703 2509 
Q 784 2959 951 3375 
Q 1119 3791 1378 4153 
Q 1638 4516 1984 4788 
Q 1984 4800 2016 4800 
L 2075 4800 
Q 2094 4800 2109 4783 
Q 2125 4766 2125 4744 
Q 2125 4716 2113 4703 
Q 1800 4397 1592 4047 
Q 1384 3697 1257 3301 
Q 1131 2906 1075 2482 
Q 1019 2059 1019 1600 
Q 1019 -434 2106 -1491 
Q 2125 -1509 2125 -1544 
Q 2125 -1559 2108 -1579 
Q 2091 -1600 2075 -1600 
L 2016 -1600 
Q 1984 -1600 1984 -1588 
z
" transform="scale(0.015625)"/>
     <path id="Cmr10-32" d="M 319 0 
L 319 172 
Q 319 188 331 206 
L 1325 1306 
Q 1550 1550 1690 1715 
Q 1831 1881 1968 2097 
Q 2106 2313 2186 2536 
Q 2266 2759 2266 3009 
Q 2266 3272 2169 3511 
Q 2072 3750 1880 3894 
Q 1688 4038 1416 4038 
Q 1138 4038 916 3870 
Q 694 3703 603 3438 
Q 628 3444 672 3444 
Q 816 3444 917 3347 
Q 1019 3250 1019 3097 
Q 1019 2950 917 2848 
Q 816 2747 672 2747 
Q 522 2747 420 2851 
Q 319 2956 319 3097 
Q 319 3338 409 3548 
Q 500 3759 670 3923 
Q 841 4088 1055 4175 
Q 1269 4263 1509 4263 
Q 1875 4263 2190 4108 
Q 2506 3953 2690 3670 
Q 2875 3388 2875 3009 
Q 2875 2731 2753 2481 
Q 2631 2231 2440 2026 
Q 2250 1822 1953 1562 
Q 1656 1303 1563 1216 
L 838 519 
L 1453 519 
Q 1906 519 2211 526 
Q 2516 534 2534 550 
Q 2609 631 2688 1141 
L 2875 1141 
L 2694 0 
L 319 0 
z
" transform="scale(0.015625)"/>
     <path id="Cmr10-29" d="M 416 -1600 
Q 359 -1600 359 -1544 
Q 359 -1516 372 -1503 
Q 1466 -434 1466 1600 
Q 1466 3634 384 4691 
Q 359 4706 359 4744 
Q 359 4766 376 4783 
Q 394 4800 416 4800 
L 475 4800 
Q 494 4800 506 4788 
Q 966 4425 1272 3906 
Q 1578 3388 1720 2800 
Q 1863 2213 1863 1600 
Q 1863 1147 1786 708 
Q 1709 269 1542 -157 
Q 1375 -584 1119 -945 
Q 863 -1306 506 -1588 
Q 494 -1600 475 -1600 
L 416 -1600 
z
" transform="scale(0.015625)"/>
    </defs>
    <use xlink:href="#Cmsy10-4f"/>
    <use xlink:href="#Cmr10-28" transform="translate(79.589844 0)"/>
    <use xlink:href="#Cmr10-32" transform="translate(118.408203 0)"/>
    <use xlink:href="#Cmr10-29" transform="translate(168.408203 0)"/>
   </g>
  </g>
 </g>
 <defs>
  <clipPath id="p371e378505">
   <rect x="57.6" y="41.472" width="357.12" height="266.112"/>
  </clipPath>
 </defs>
</svg>
\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"fig=plot([ex, s], ($x$,0,10), yrange=(-4,4), title=\\\"${\\\\\\\\cal O}(\\\"+str(int(order-1))+\\\")$\\\", label=[\\\"full\\\",\\\"approx\\\"], \\n   legend=[\\\"sin(x)\\\", \\\"approx\\\"], fig=fig);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 2766623462509477906,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 12218342040526048254,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"slider\",\n\t\t\t\t\t\"source\": \"{\\\"value\\\": 2, \\\"variable\\\": \\\"order\\\", \\\"min_value\\\": 1, \\\"max_value\\\": 40, \\\"step_size\\\": 1}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"slider(\\\"order\\\", order, min_value=1, max_value=40, step_size=1);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 158276220012627048,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"\"\n\t\t}\n\t],\n\t\"description\": \"Cadabra JSON notebook format\",\n\t\"flags\": {\n\t\t\"hide_input_cells\": true\n\t},\n\t\"version\": 1.0\n}\n"
  },
  {
    "path": "examples/scalar_manipulations.cnb",
    "content": "{\n\t\"cell_id\": 1542815176026264577,\n\t\"cells\": [\n\t\t{\n\t\t\t\"cell_id\": 2397022013342117586,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 14916212167479302859,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\section*{Using Cadabra and Sympy together}\\n\\nThis notebook illustrates the interaction of Cadabra with Sympy. In particular, it shows how Cadabra expressions\\ncan be manipulated by Sympy if they are index-free (i.e.~non-tensors). \\n\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\section*{Using Cadabra and Sympy together}\\n\\nThis notebook illustrates the interaction of Cadabra with Sympy. In particular, it shows how Cadabra expressions\\ncan be manipulated by Sympy if they are index-free (i.e.~non-tensors). \\n\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 10411792927078810246,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 14165469431464740252,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\subsection*{Scalar expression handling}\\n\\nWhile Cadabra's main strength is its handling of tensorial expressions, you can of course write down scalar\\nexpressions as well. Here is a simple example: \"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\subsection*{Scalar expression handling}\\n\\nWhile Cadabra's main strength is its handling of tensorial expressions, you can of course write down scalar\\nexpressions as well. Here is a simple example: \"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 1031975010951575642,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 12923655640842854853,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 15957131196972409545,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"((\\\\sin(x))**2 + (\\\\cos(x))**2) (x)**(-1)\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\left({\\\\left(\\\\sin{x}\\\\right)}^{2\\\\,}\\\\discretionary{}{}{}+{\\\\left(\\\\cos{x}\\\\right)}^{2\\\\,}\\\\right) {x}^{-\\\\,1}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex:=(\\\\sin(x)**2 + \\\\cos(x)**2)/x;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 14833699298536241506,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 1766423708678417973,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"Note the use of LaTeX notation for things like trigonometric functions. \\nYou can then directly call Sympy algorithms on these Cadabra expressions, for instance\\nto integrate them:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"Note the use of LaTeX notation for things like trigonometric functions. \\nYou can then directly call Sympy algorithms on these Cadabra expressions, for instance\\nto integrate them:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 3398547768646584936,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 6908699260827372934,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 4999072496678379284,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\log(x)\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\log\\\\left(x\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"map_sympy(_, \\\"integrate\\\");\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 4694496657445179560,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 2644018676051541557,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"Note how, in the spirit of Cadabra's logic that algorithms act in-place, this changes the actual expression: \\\\verb|ex| now contains\\nthe integral of the original expression:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"Note how, in the spirit of Cadabra's logic that algorithms act in-place, this changes the actual expression: \\\\verb|ex| now contains\\nthe integral of the original expression:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 10399642188525316643,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 13628102650662359458,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 1030919973831849035,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\log(x)\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\log\\\\left(x\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 18422108908642547796,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 7919340226687139919,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"You can do more complicated things as well, like integrals and sums. Here is an example which is\\nfirst entered in Cadabra form (which is inert), and then fed through Sympy, which then immediately evaluates the\\nexpression. Again note the use of \\nstandard LaTeX-like constructions to write down integrals.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"You can do more complicated things as well, like integrals and sums. Here is an example which is\\nfirst entered in Cadabra form (which is inert), and then fed through Sympy, which then immediately evaluates the\\nexpression. Again note the use of \\nstandard LaTeX-like constructions to write down integrals.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 12991923136293708135,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 4686144604360501424,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 2152737637606562916,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\int{\\\\sin(x) \\\\cos(x)}{x}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\int \\\\sin{x} \\\\cos{x}\\\\,\\\\,{\\\\rm d}x\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex2:= \\\\int{\\\\sin(x) \\\\cos(x)}{x};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 5302759014020368514,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 1818509650923832076,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 11677856907390264534,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \" 1/2 (\\\\sin(x))**2\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\frac{1}{2}\\\\,{\\\\left(\\\\sin{x}\\\\right)}^{2\\\\,}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"map_sympy(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 17515994551843006891,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9814090675240098969,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"Note how \\\\verb|map_sympy| was used without giving it any Sympy function. This simply makes Sympy evaluate the expression, which in this case\\nmeans evaluating the integral.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"Note how \\\\verb|map_sympy| was used without giving it any Sympy function. This simply makes Sympy evaluate the expression, which in this case\\nmeans evaluating the integral.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 1323182593666494251,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 6009557834554846792,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"Note that \\\\verb|map_sympy| is almost always the way in which you want to invoke Sympy. You can, alternatively, feed expressions directly into \\nSympy functions (by virtue of the fact that \\\\verb|Ex| objects have a \\\\verb|_sympy_()| method), \\nbut that has the disadvantage that you will not change the original expression (it will not act in-place):\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"Note that \\\\verb|map_sympy| is almost always the way in which you want to invoke Sympy. You can, alternatively, feed expressions directly into \\nSympy functions (by virtue of the fact that \\\\verb|Ex| objects have a \\\\verb|_sympy_()| method), \\nbut that has the disadvantage that you will not change the original expression (it will not act in-place):\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 17774675881972332128,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 3236595915667745636,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 9563883350303985708,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\sin(x) \\\\cos(x)\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\sin{x} \\\\cos{x}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex3:= \\\\sin(x)\\\\cos(x);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 9418494559682487195,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 11715319553616270803,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\sin{\\\\left(x \\\\right)} \\\\cos{\\\\left(x \\\\right)}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 14592538996949299987,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"output\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}<class 'sympy.core.mul.Mul'>\\n\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex3._sympy_();\\nprint(type(ex3._sympy_()))\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 16882035327664891703,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9793057478678632471,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\frac{\\\\sin^{2}{\\\\left(x \\\\right)}}{2}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 2689959478282900604,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"output\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}<class 'sympy.core.mul.Mul'>\\n\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"sympy.integrate(ex3);\\nprint(type(sympy.integrate(ex3)))\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 12031936897201182650,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 1219690406474710688,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"Observe how the result of these evaluations are non-Cadabra objects (they have not been converted back, the way in which \\\\verb|map_sympy| does).\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"Observe how the result of these evaluations are non-Cadabra objects (they have not been converted back, the way in which \\\\verb|map_sympy| does).\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 13885344332305935057,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 13715658223384534022,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"The fact that algorithms act in-place may sometimes be a bit unexpected. Here's an example of solving a cubic equation to make this clear:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"The fact that algorithms act in-place may sometimes be a bit unexpected. Here's an example of solving a cubic equation to make this clear:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 6944118161509755270,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 4040253492576064396,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 2826260870613456885,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"(x)**3-(x)**2-4\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}{x}^{3\\\\,}\\\\discretionary{}{}{}-\\\\,{x}^{2\\\\,}\\\\discretionary{}{}{}-4\\\\,\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex4:= x**3 -  x**2 - 4;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 2193515675547865598,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 7100293832548854216,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 9253394805466270902,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"{2,  -  1/2  -  1/2 \\\\sqrt(7) I,  -  1/2  +  1/2 \\\\sqrt(7) I}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\left[2\\\\,, \\\\discretionary{}{}{} - \\\\frac{1}{2}\\\\,\\\\discretionary{}{}{} - \\\\frac{1}{2}\\\\,\\\\sqrt{7\\\\,} I, \\\\discretionary{}{}{} - \\\\frac{1}{2}\\\\,\\\\discretionary{}{}{}+\\\\frac{1}{2}\\\\,\\\\sqrt{7\\\\,} I\\\\right]\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"map_sympy(_, \\\"solve\\\");\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 17545968025948297929,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9704727170501688178,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 12434546449003279387,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"{2,  -  1/2  -  1/2 \\\\sqrt(7) I,  -  1/2  +  1/2 \\\\sqrt(7) I}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\left[2\\\\,, \\\\discretionary{}{}{} - \\\\frac{1}{2}\\\\,\\\\discretionary{}{}{} - \\\\frac{1}{2}\\\\,\\\\sqrt{7\\\\,} I, \\\\discretionary{}{}{} - \\\\frac{1}{2}\\\\,\\\\discretionary{}{}{}+\\\\frac{1}{2}\\\\,\\\\sqrt{7\\\\,} I\\\\right]\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex4;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 6235099031437028842,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 14930237185539884179,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\subsection*{Tensor expression handling}\\n\\nThe real power of mixing Cadabra with Sympy lies in the fact that you can act with Sympy on any Cadabra subexpression which is\\na pure scalar (i.e.~which has no indices). Here is a contrived example which has a sum of tensors, with pre-factors which are\\nscalar expressions which Sympy can simplify.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\subsection*{Tensor expression handling}\\n\\nThe real power of mixing Cadabra with Sympy lies in the fact that you can act with Sympy on any Cadabra subexpression which is\\na pure scalar (i.e.~which has no indices). Here is a contrived example which has a sum of tensors, with pre-factors which are\\nscalar expressions which Sympy can simplify.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 1015689800355736399,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 1300083174549847284,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property Coordinate attached to~}\\\\left[r, \\\\discretionary{}{}{}t\\\\right].\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 4079913861977749515,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property PartialDerivative attached to~}\\\\backslash\\\\texttt{partial}\\\\{\\\\#\\\\}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 15492302890074853001,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 785307482881708175,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"((\\\\sin(r))**2 + (\\\\cos(r))**2) A_{m} \\\\partial_{r}(r)-A_{m} + \\\\int{(r)**2}{r} B_{m}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\left({\\\\left(\\\\sin{r}\\\\right)}^{2\\\\,}\\\\discretionary{}{}{}+{\\\\left(\\\\cos{r}\\\\right)}^{2\\\\,}\\\\right) A_{m} \\\\partial_{r}{r}\\\\discretionary{}{}{}-\\\\,A_{m}\\\\discretionary{}{}{}+\\\\int {r}^{2\\\\,}\\\\,\\\\,{\\\\rm d}r B_{m}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"{r,t}::Coordinate;\\n\\\\partial{#}::PartialDerivative;\\nex:= (\\\\sin(r)**2 + \\\\cos(r)**2) A_{m} \\\\partial_{r}{r} - A_{m} + \\\\int{r**2}{r} B_{m};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 16249232945008950540,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 5622463937221422894,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 4162680136818167590,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \" 1/3 (r)**3 B_{m}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\frac{1}{3}\\\\,{r}^{3\\\\,} B_{m}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"map_sympy(_, \\\"simplify\\\");\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 496590915626066002,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 15218286587952898687,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property Coordinate attached to~}\\\\left[r, \\\\discretionary{}{}{}t\\\\right].\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 6595002066047836857,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property Indices(position=free, values=\\\\{{r}\\n, {t}\\n\\\\}) attached to~}\\\\left[\\\\mu, \\\\discretionary{}{}{}\\\\nu\\\\right].\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 12697250572668705651,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 17229047564098902522,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\partial_{\\\\mu}(A^{\\\\mu \\\\nu})\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\partial_{\\\\mu}{A^{\\\\mu \\\\nu}}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 1505985386014582057,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 1307299140212615210,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"{A^{t t} -> t (\\\\sin(r))**2, A^{r r} -> \\\\int{(\\\\cos(r))**2}{r}}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\left[A^{t t} \\\\rightarrow t {\\\\left(\\\\sin{r}\\\\right)}^{2\\\\,}, \\\\discretionary{}{}{}A^{r r} \\\\rightarrow \\\\int {\\\\left(\\\\cos{r}\\\\right)}^{2\\\\,}\\\\,\\\\,{\\\\rm d}r\\\\right]\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"{r,t}::Coordinate;\\n{\\\\mu,\\\\nu}::Indices(values={r,t});\\nex:= \\\\partial_{\\\\mu}{ A^{\\\\mu \\\\nu} };\\nrl:= A^{t t} -> t \\\\sin(r)**2, A^{r r} -> \\\\int{\\\\cos{r}**2}{r};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 266316123620937444,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 4371097130403143985,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 13168617779344075381,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\components^{\\\\nu}({{r} = (\\\\cos(r))**2, {t} = (\\\\sin(r))**2})\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\square{}^{\\\\nu}\\\\left\\\\{\\\\begin{aligned}\\\\square{}^{r}& = {\\\\left(\\\\cos{r}\\\\right)}^{2\\\\,}\\\\\\\\[-.5ex]\\n\\\\square{}^{t}& = {\\\\left(\\\\sin{r}\\\\right)}^{2\\\\,}\\\\\\\\[-.5ex]\\n\\\\end{aligned}\\\\right\\\\}\\n\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"evaluate(ex, rl);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 4200993043775371094,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 3642927302528569773,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\subsection*{Sympy only with sympy notation throughout}\\n\\nOf course, if you do not like or need Cadabra's input format, then you can happily use Sympy in the way\\nyou have always used it, but taking advantage of the display logic of the Cadabra notebook:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\subsection*{Sympy only with sympy notation throughout}\\n\\nOf course, if you do not like or need Cadabra's input format, then you can happily use Sympy in the way\\nyou have always used it, but taking advantage of the display logic of the Cadabra notebook:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 11413881385092483965,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 6182082763210579204,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\int\\\\limits_{0}^{2} \\\\sin{\\\\left(x \\\\right)}\\\\, dx\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"from sympy import *\\nx,y=var('x,y')\\ni = Integral(sin(x),(x,0,2));\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 11343062090422437627,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 16948639896975914227,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}1 - \\\\cos{\\\\left(2 \\\\right)}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"i.doit();\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 16989736678816052971,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 18276766872141662081,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"Hope this has triggered your interest; as usual, any feedback to \\\\url{mailto:info@cadabra.science} is greatly appreciated.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"Hope this has triggered your interest; as usual, any feedback to \\\\url{mailto:info@cadabra.science} is greatly appreciated.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 15401019696627785290,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"\"\n\t\t}\n\t],\n\t\"description\": \"Cadabra JSON notebook format\",\n\t\"flags\": {\n\t\t\"hide_input_cells\": false\n\t},\n\t\"version\": 1.0\n}\n"
  },
  {
    "path": "examples/scalar_manipulations2.cnb",
    "content": "{\n\t\"cells\" : \n\t[\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\int_{0}^{\\\\pi}\\\\int_{0}^{\\\\pi}\\\\sin{x}\\\\,\\\\,{\\\\rm d}x\\\\,{\\\\rm d}y\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex:=\\\\int(\\\\sin(x), {x,0,\\\\pi}, {y,0,\\\\pi});\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\int_{-\\\\pi}^{\\\\pi}\\\\int_{-\\\\pi}^{\\\\pi}\\\\sin{x}\\\\,\\\\,{\\\\rm d}x\\\\,{\\\\rm d}y\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex:=\\\\int(\\\\sin(x), {x,-\\\\pi,\\\\pi}, {y,-\\\\pi,\\\\pi});\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Symbol to~}a.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\partial_{a}\\\\left(\\\\int_{0}^{\\\\pi}\\\\exp\\\\left(-a x^{2}\\\\right)\\\\,\\\\,{\\\\rm d}x\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"a::Symbol;\\nex:=\\\\partial_{a}{\\\\int( \\\\exp(-a x**2), {x,0,\\\\pi})};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}Piecewise\\\\left(\\\\left\\\\{0,~\\\\linebreak[0] Eq\\\\left(a , 0\\\\right)\\\\right\\\\} , \\\\left\\\\{\\\\pi \\\\frac{\\\\exp\\\\left(-\\\\pi^{2} a\\\\right)}{2a}-\\\\sqrt{\\\\pi} \\\\frac{erf\\\\left(\\\\pi \\\\sqrt{a}\\\\right)}{4a^{\\\\frac{3}{2}}},~\\\\linebreak[0] True\\\\right\\\\}\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"scas(ex,\\\"\\\");\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1\n}\n"
  },
  {
    "path": "examples/schwarzschild.cnb",
    "content": "{\n\t\"cell_id\": 12402901834551655302,\n\t\"cells\": [\n\t\t{\n\t\t\t\"cell_id\": 107641106113644469,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 14614611749971814590,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\section*{The Schwarzschild spacetime}\\n\\nThis notebook shows how you can do component computations in Cadabra. It illustrates this by computing\\nproperties of the Schwarzschild spacetime.\\n\\nThe first thing we always need to do is to declare the coordinates used, and the names of the indices.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\section*{The Schwarzschild spacetime}\\n\\nThis notebook shows how you can do component computations in Cadabra. It illustrates this by computing\\nproperties of the Schwarzschild spacetime.\\n\\nThe first thing we always need to do is to declare the coordinates used, and the names of the indices.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 758527607829423835,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"__cdbkernel__.display_fractions=True\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 13875889326264028817,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 6734696341669269556,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property Coordinate attached to~}\\\\left[r, \\\\discretionary{}{}{}t, \\\\discretionary{}{}{}\\\\phi, \\\\discretionary{}{}{}\\\\theta\\\\right].\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 2320613337742717521,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property Indices(position=fixed, values=\\\\{{t}\\n, {r}\\n, {\\\\phi}\\n, {\\\\theta}\\n\\\\}) attached to~}\\\\left[\\\\mu, \\\\discretionary{}{}{}\\\\nu, \\\\discretionary{}{}{}\\\\rho, \\\\discretionary{}{}{}\\\\sigma, \\\\discretionary{}{}{}\\\\lambda, \\\\discretionary{}{}{}\\\\kappa, \\\\discretionary{}{}{}\\\\chi, \\\\discretionary{}{}{}\\\\gamma\\\\right].\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 5006173505237157804,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property PartialDerivative attached to~}\\\\backslash\\\\texttt{partial}\\\\{\\\\#\\\\}.\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"{r,t,\\\\phi,\\\\theta}::Coordinate;\\n{\\\\mu,\\\\nu,\\\\rho,\\\\sigma,\\\\lambda,\\\\kappa,\\\\chi,\\\\gamma}::Indices(values={t,r,\\\\phi,\\\\theta}, position=fixed);\\n\\\\partial{#}::PartialDerivative;\\ng_{\\\\mu\\\\nu}::Metric.\\ng^{\\\\mu\\\\nu}::InverseMetric.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 8495020174273801297,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 5200281905731292096,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"Below is the Schwarzschild metric in standard coordinates. Note how the components are\\ngiven in terms of substitution rules, and how the inverse metric is computed. \\nThe \\\\algo{complete} algorithm adds the rules for the inverse metric to the rules for the metric.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"Below is the Schwarzschild metric in standard coordinates. Note how the components are\\ngiven in terms of substitution rules, and how the inverse metric is computed. \\nThe \\\\algo{complete} algorithm adds the rules for the inverse metric to the rules for the metric.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 16857916987136790274,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 2939196551435003592,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 10998810794416871102,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"{g_{t t} = -1 + 2M (r)**(-1), g_{r r} = (1-2M (r)**(-1))**(-1), g_{\\\\theta \\\\theta} = (r)**2, g_{\\\\phi \\\\phi} = (r)**2 (\\\\sin(\\\\theta))**2, g^{t t} = (2M (r)**(-1)-1)**(-1), g^{r r} = -2M (r)**(-1) + 1, g^{\\\\phi \\\\phi} = ((r)**2 (\\\\sin(\\\\theta))**2)**(-1), g^{\\\\theta \\\\theta} = (r)**(-2)}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\left[g_{t t} = -\\\\,1\\\\discretionary{}{}{}+\\\\frac{2\\\\,M}{r}, \\\\discretionary{}{}{}g_{r r} = \\\\frac{1}{1\\\\discretionary{}{}{}-\\\\frac{2\\\\,M}{r}}, \\\\discretionary{}{}{}g_{\\\\theta \\\\theta} = {r}^{2\\\\,}, \\\\discretionary{}{}{}g_{\\\\phi \\\\phi} = {r}^{2\\\\,} {\\\\left(\\\\sin{\\\\theta}\\\\right)}^{2\\\\,}, \\\\discretionary{}{}{}g^{t t} = \\\\frac{1}{\\\\frac{2\\\\,M}{r}\\\\discretionary{}{}{}-\\\\,1}, \\\\discretionary{}{}{}g^{r r} = -\\\\frac{2\\\\,M}{r}\\\\discretionary{}{}{}+1, \\\\discretionary{}{}{}g^{\\\\phi \\\\phi} = \\\\frac{1}{{r}^{2\\\\,} {\\\\left(\\\\sin{\\\\theta}\\\\right)}^{2\\\\,}}, \\\\discretionary{}{}{}g^{\\\\theta \\\\theta} = \\\\frac{1}{{r}^{2\\\\,}}\\\\right]\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ss:= { g_{t t} = -(1-2 M/r),   \\n       g_{r r} = 1/(1-2 M/r), \\n       g_{\\\\theta\\\\theta} = r**2, \\n       g_{\\\\phi\\\\phi}=r**2 \\\\sin(\\\\theta)**2\\n     }.\\n\\ncomplete(ss, $g^{\\\\mu\\\\nu}$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 1327716729350886537,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 18361467427542318125,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"We can now compute the Christoffel symbols. We give Cadabra the expression for the \\nChristoffel symbols in terms of the metric, and then evaluate the components of the\\nmetric using the \\\\algo{evaluate} algorithm.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"We can now compute the Christoffel symbols. We give Cadabra the expression for the \\nChristoffel symbols in terms of the metric, and then evaluate the components of the\\nmetric using the \\\\algo{evaluate} algorithm.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 9194094570098219913,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9383732573614944564,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 3669964185197302393,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\Gamma^{\\\\mu}_{\\\\nu \\\\rho} =  1/2 g^{\\\\mu \\\\sigma} (\\\\partial_{\\\\rho}(g_{\\\\nu \\\\sigma}) + \\\\partial_{\\\\nu}(g_{\\\\rho \\\\sigma})-\\\\partial_{\\\\sigma}(g_{\\\\nu \\\\rho}))\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\Gamma^{\\\\mu}\\\\,_{\\\\nu \\\\rho} = \\\\frac{1}{2}\\\\,g^{\\\\mu \\\\sigma} \\\\left(\\\\partial_{\\\\rho}{g_{\\\\nu \\\\sigma}}\\\\discretionary{}{}{}+\\\\partial_{\\\\nu}{g_{\\\\rho \\\\sigma}}\\\\discretionary{}{}{}-\\\\,\\\\partial_{\\\\sigma}{g_{\\\\nu \\\\rho}}\\\\right)\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 3919068990538014252,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 4354390669138566979,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\Gamma^{\\\\mu}_{\\\\nu \\\\rho} = \\\\components_{\\\\nu \\\\rho}^{\\\\mu}({{\\\\phi, r, \\\\phi} = (r)**(-1), {\\\\phi, \\\\theta, \\\\phi} = (\\\\tan(\\\\theta))**(-1), {\\\\theta, r, \\\\theta} = (r)**(-1), {r, r, r} = M (r (2M-r))**(-1), {t, r, t} = M (r (-2M + r))**(-1), {r, \\\\phi, \\\\phi} = (r)**(-1), {\\\\theta, \\\\phi, \\\\phi} = (\\\\tan(\\\\theta))**(-1), {r, \\\\theta, \\\\theta} = (r)**(-1), {r, t, t} = M (r (-2M + r))**(-1), {\\\\phi, \\\\phi, r} = (2M-r) (\\\\sin(\\\\theta))**2, {\\\\phi, \\\\phi, \\\\theta} =  -  1/2 \\\\sin(2\\\\theta), {\\\\theta, \\\\theta, r} = 2M-r, {t, t, r} = M (-2M + r) (r)**(-3)})\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\Gamma^{\\\\mu}\\\\,_{\\\\nu \\\\rho} = \\\\square{}_{\\\\nu}{}_{\\\\rho}{}^{\\\\mu}\\\\left\\\\{\\\\begin{aligned}\\\\square{}_{\\\\phi}{}_{r}{}^{\\\\phi}& = \\\\square{}_{r}{}_{\\\\phi}{}^{\\\\phi} = \\\\square{}_{r}{}_{\\\\theta}{}^{\\\\theta} = \\\\square{}_{\\\\theta}{}_{r}{}^{\\\\theta} = \\\\frac{1}{r}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{\\\\theta}{}^{\\\\phi}& = \\\\square{}_{\\\\theta}{}_{\\\\phi}{}^{\\\\phi} = \\\\frac{1}{\\\\tan{\\\\theta}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{r}{}^{r}& = \\\\frac{M}{r \\\\left(2\\\\,M\\\\discretionary{}{}{}-\\\\,r\\\\right)}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}_{r}{}^{t}& = \\\\square{}_{r}{}_{t}{}^{t} = \\\\frac{M}{r \\\\left(-2\\\\,M\\\\discretionary{}{}{}+r\\\\right)}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{\\\\phi}{}^{r}& = \\\\left(2\\\\,M\\\\discretionary{}{}{}-\\\\,r\\\\right) {\\\\left(\\\\sin{\\\\theta}\\\\right)}^{2\\\\,}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{\\\\phi}{}^{\\\\theta}& =  - \\\\frac{1}{2}\\\\,\\\\sin\\\\left(2\\\\,\\\\theta\\\\right)\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{\\\\theta}{}^{r}& = 2\\\\,M\\\\discretionary{}{}{}-\\\\,r\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}_{t}{}^{r}& = \\\\frac{M \\\\left(-2\\\\,M\\\\discretionary{}{}{}+r\\\\right)}{{r}^{3\\\\,}}\\\\\\\\[-.5ex]\\n\\\\end{aligned}\\\\right.\\n\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ch:= \\\\Gamma^{\\\\mu}_{\\\\nu\\\\rho} = 1/2 g^{\\\\mu\\\\sigma} ( \\n                                   \\\\partial_{\\\\rho}{g_{\\\\nu\\\\sigma}} \\n                                  +\\\\partial_{\\\\nu}{g_{\\\\rho\\\\sigma}}\\n                                  -\\\\partial_{\\\\sigma}{g_{\\\\nu\\\\rho}} ):\\n                          \\nevaluate(ch, ss, rhsonly=True);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 6816573319195097874,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 1639186806479824176,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"Continuing from here we can compute the Riemann tensor components. Again, we start\\nby giving this tensor in terms of the Christoffel symbols. We then subsitute the \\nChristoffel symbols just found, and work out any remaining component substitions using\\n\\\\algo{evaluate} (the computation takes a few seconds, essentially because of the round\\ntrips through Sympy).\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"Continuing from here we can compute the Riemann tensor components. Again, we start\\nby giving this tensor in terms of the Christoffel symbols. We then subsitute the \\nChristoffel symbols just found, and work out any remaining component substitions using\\n\\\\algo{evaluate} (the computation takes a few seconds, essentially because of the round\\ntrips through Sympy).\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 14100316656309379268,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 16711744503656874392,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 6180298496670094314,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"R^{\\\\rho}_{\\\\sigma \\\\mu \\\\nu} = \\\\partial_{\\\\mu}(\\\\Gamma^{\\\\rho}_{\\\\nu \\\\sigma})-\\\\partial_{\\\\nu}(\\\\Gamma^{\\\\rho}_{\\\\mu \\\\sigma}) + \\\\Gamma^{\\\\rho}_{\\\\mu \\\\lambda} \\\\Gamma^{\\\\lambda}_{\\\\nu \\\\sigma}-\\\\Gamma^{\\\\rho}_{\\\\nu \\\\lambda} \\\\Gamma^{\\\\lambda}_{\\\\mu \\\\sigma}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}R^{\\\\rho}\\\\,_{\\\\sigma \\\\mu \\\\nu} = \\\\partial_{\\\\mu}{\\\\Gamma^{\\\\rho}\\\\,_{\\\\nu \\\\sigma}}\\\\discretionary{}{}{}-\\\\,\\\\partial_{\\\\nu}{\\\\Gamma^{\\\\rho}\\\\,_{\\\\mu \\\\sigma}}\\\\discretionary{}{}{}+\\\\Gamma^{\\\\rho}\\\\,_{\\\\mu \\\\lambda} \\\\Gamma^{\\\\lambda}\\\\,_{\\\\nu \\\\sigma}\\\\discretionary{}{}{}-\\\\,\\\\Gamma^{\\\\rho}\\\\,_{\\\\nu \\\\lambda} \\\\Gamma^{\\\\lambda}\\\\,_{\\\\mu \\\\sigma}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"rm:= R^{\\\\rho}_{\\\\sigma\\\\mu\\\\nu} = \\\\partial_{\\\\mu}{\\\\Gamma^{\\\\rho}_{\\\\nu\\\\sigma}}\\n                                  -\\\\partial_{\\\\nu}{\\\\Gamma^{\\\\rho}_{\\\\mu\\\\sigma}}\\n                                  +\\\\Gamma^{\\\\rho}_{\\\\mu\\\\lambda} \\\\Gamma^{\\\\lambda}_{\\\\nu\\\\sigma}\\n                                  -\\\\Gamma^{\\\\rho}_{\\\\nu\\\\lambda} \\\\Gamma^{\\\\lambda}_{\\\\mu\\\\sigma};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 10758258395606342214,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 6104062295811774339,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 13056767289265542598,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"R^{\\\\rho}_{\\\\sigma \\\\mu \\\\nu} = \\\\components_{\\\\nu \\\\sigma}^{\\\\rho}_{\\\\mu}({{t, t, r, r} = 2M (2M-r) (r)**(-4), {\\\\theta, \\\\theta, r, r} = -M (r)**(-1), {\\\\phi, \\\\phi, \\\\theta, \\\\theta} = 2M (\\\\sin(\\\\theta))**2 (r)**(-1), {\\\\phi, \\\\phi, r, r} = -M (\\\\sin(\\\\theta))**2 (r)**(-1), {t, r, t, r} = 2M ((r)**2 (2M-r))**(-1), {\\\\phi, \\\\theta, \\\\phi, \\\\theta} = -2M (r)**(-1), {r, t, r, t} = 2M (-2M + r) (r)**(-4), {r, \\\\theta, r, \\\\theta} = M (r)**(-1), {\\\\theta, \\\\phi, \\\\theta, \\\\phi} = -2M (\\\\sin(\\\\theta))**2 (r)**(-1), {r, \\\\phi, r, \\\\phi} = M (\\\\sin(\\\\theta))**2 (r)**(-1), {r, r, t, t} = 2M ((r)**2 (-2M + r))**(-1), {r, r, \\\\theta, \\\\theta} = M ((r)**2 (2M-r))**(-1), {\\\\theta, \\\\theta, \\\\phi, \\\\phi} = 2M (r)**(-1), {r, r, \\\\phi, \\\\phi} = M ((r)**2 (2M-r))**(-1), {t, t, \\\\phi, \\\\phi} = M (-2M + r) (r)**(-4), {t, t, \\\\theta, \\\\theta} = M (-2M + r) (r)**(-4), {\\\\phi, \\\\phi, t, t} = -M (\\\\sin(\\\\theta))**2 (r)**(-1), {\\\\theta, \\\\theta, t, t} = -M (r)**(-1), {\\\\phi, r, \\\\phi, r} = M ((r)**2 (-2M + r))**(-1), {\\\\phi, t, \\\\phi, t} = M (2M-r) (r)**(-4), {\\\\theta, r, \\\\theta, r} = M ((r)**2 (-2M + r))**(-1), {\\\\theta, t, \\\\theta, t} = M (2M-r) (r)**(-4), {t, \\\\phi, t, \\\\phi} = M (\\\\sin(\\\\theta))**2 (r)**(-1), {t, \\\\theta, t, \\\\theta} = M (r)**(-1)})\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}R^{\\\\rho}\\\\,_{\\\\sigma \\\\mu \\\\nu} = \\\\square{}_{\\\\nu}{}_{\\\\sigma}{}^{\\\\rho}{}_{\\\\mu}\\\\left\\\\{\\\\begin{aligned}\\\\square{}_{t}{}_{t}{}^{r}{}_{r}& = \\\\frac{2\\\\,M \\\\left(2\\\\,M\\\\discretionary{}{}{}-\\\\,r\\\\right)}{{r}^{4\\\\,}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{\\\\theta}{}^{r}{}_{r}& = \\\\square{}_{\\\\theta}{}_{\\\\theta}{}^{t}{}_{t} = -\\\\frac{M}{r}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{\\\\phi}{}^{\\\\theta}{}_{\\\\theta}& = \\\\frac{2\\\\,M {\\\\left(\\\\sin{\\\\theta}\\\\right)}^{2\\\\,}}{r}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{\\\\phi}{}^{r}{}_{r}& = \\\\square{}_{\\\\phi}{}_{\\\\phi}{}^{t}{}_{t} = -\\\\frac{M {\\\\left(\\\\sin{\\\\theta}\\\\right)}^{2\\\\,}}{r}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}_{r}{}^{t}{}_{r}& = \\\\frac{2\\\\,M}{{r}^{2\\\\,} \\\\left(2\\\\,M\\\\discretionary{}{}{}-\\\\,r\\\\right)}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{\\\\theta}{}^{\\\\phi}{}_{\\\\theta}& = -\\\\frac{2\\\\,M}{r}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{t}{}^{r}{}_{t}& = \\\\frac{2\\\\,M \\\\left(-2\\\\,M\\\\discretionary{}{}{}+r\\\\right)}{{r}^{4\\\\,}}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{\\\\theta}{}^{r}{}_{\\\\theta}& = \\\\square{}_{t}{}_{\\\\theta}{}^{t}{}_{\\\\theta} = \\\\frac{M}{r}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{\\\\phi}{}^{\\\\theta}{}_{\\\\phi}& = -\\\\frac{2\\\\,M {\\\\left(\\\\sin{\\\\theta}\\\\right)}^{2\\\\,}}{r}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{\\\\phi}{}^{r}{}_{\\\\phi}& = \\\\square{}_{t}{}_{\\\\phi}{}^{t}{}_{\\\\phi} = \\\\frac{M {\\\\left(\\\\sin{\\\\theta}\\\\right)}^{2\\\\,}}{r}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{r}{}^{t}{}_{t}& = \\\\frac{2\\\\,M}{{r}^{2\\\\,} \\\\left(-2\\\\,M\\\\discretionary{}{}{}+r\\\\right)}\\\\\\\\[-.5ex]\\n\\\\square{}_{r}{}_{r}{}^{\\\\theta}{}_{\\\\theta}& = \\\\square{}_{r}{}_{r}{}^{\\\\phi}{}_{\\\\phi} = \\\\frac{M}{{r}^{2\\\\,} \\\\left(2\\\\,M\\\\discretionary{}{}{}-\\\\,r\\\\right)}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{\\\\theta}{}^{\\\\phi}{}_{\\\\phi}& = \\\\frac{2\\\\,M}{r}\\\\\\\\[-.5ex]\\n\\\\square{}_{t}{}_{t}{}^{\\\\phi}{}_{\\\\phi}& = \\\\square{}_{t}{}_{t}{}^{\\\\theta}{}_{\\\\theta} = \\\\frac{M \\\\left(-2\\\\,M\\\\discretionary{}{}{}+r\\\\right)}{{r}^{4\\\\,}}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{r}{}^{\\\\phi}{}_{r}& = \\\\square{}_{\\\\theta}{}_{r}{}^{\\\\theta}{}_{r} = \\\\frac{M}{{r}^{2\\\\,} \\\\left(-2\\\\,M\\\\discretionary{}{}{}+r\\\\right)}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\phi}{}_{t}{}^{\\\\phi}{}_{t}& = \\\\square{}_{\\\\theta}{}_{t}{}^{\\\\theta}{}_{t} = \\\\frac{M \\\\left(2\\\\,M\\\\discretionary{}{}{}-\\\\,r\\\\right)}{{r}^{4\\\\,}}\\\\\\\\[-.5ex]\\n\\\\end{aligned}\\\\right.\\n\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"substitute(rm, ch)\\nevaluate(rm, ss, rhsonly=True);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 2118616825111928163,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 61722704794091175,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"The Ricci tensor should of course vanish as the Schwarzschild solution is a vacuum\\nsolution. Following the same logic as above, this is easily verified:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"The Ricci tensor should of course vanish as the Schwarzschild solution is a vacuum\\nsolution. Following the same logic as above, this is easily verified:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 12782852727406056383,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 8250004034532912823,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 17146422611083234429,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"R_{\\\\sigma \\\\nu} = R^{\\\\rho}_{\\\\sigma \\\\rho \\\\nu}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}R_{\\\\sigma \\\\nu} = R^{\\\\rho}\\\\,_{\\\\sigma \\\\rho \\\\nu}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 16881565713871771463,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 15629934596915118592,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"R_{\\\\sigma \\\\nu} = 0\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}R_{\\\\sigma \\\\nu} = 0\\\\,\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"rc:= R_{\\\\sigma\\\\nu} = R^{\\\\rho}_{\\\\sigma\\\\rho\\\\nu};\\nsubstitute(rc, rm)\\nevaluate(rc, ss, rhsonly=True);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 13338363640550053354,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 1062786181174089499,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"More interesting is the Kretschmann scalar. \"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"More interesting is the Kretschmann scalar. \"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 7063690737202003477,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 12489323415407073656,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 14910662960118529248,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"K = R^{\\\\mu}_{\\\\nu \\\\rho \\\\sigma} R^{\\\\lambda}_{\\\\kappa \\\\gamma \\\\chi} g_{\\\\mu \\\\lambda} g^{\\\\nu \\\\kappa} g^{\\\\rho \\\\gamma} g^{\\\\sigma \\\\chi}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}K = R^{\\\\mu}\\\\,_{\\\\nu \\\\rho \\\\sigma} R^{\\\\lambda}\\\\,_{\\\\kappa \\\\gamma \\\\chi} g_{\\\\mu \\\\lambda} g^{\\\\nu \\\\kappa} g^{\\\\rho \\\\gamma} g^{\\\\sigma \\\\chi}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"K:= K = R^{\\\\mu}_{\\\\nu\\\\rho\\\\sigma} R^{\\\\lambda}_{\\\\kappa\\\\gamma\\\\chi} \\n           g_{\\\\mu\\\\lambda} g^{\\\\nu\\\\kappa} g^{\\\\rho\\\\gamma} g^{\\\\sigma\\\\chi};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 362606688912626112,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 7315253597065414426,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 4282987805034561470,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"K = 48(M)**2 (r)**(-6)\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}K = \\\\frac{48\\\\,{M}^{2\\\\,}}{{r}^{6\\\\,}}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"substitute(K, rm)\\nevaluate(K, ss, rhsonly=True);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 13630550448453607283,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 1442356797078228666,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"This shows that $r=0$ is a true singularity.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"This shows that $r=0$ is a true singularity.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 18022893079606648550,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 2004499864657416580,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"You could have computed the Riemann tensor in a different way, first expanding it fully in terms of the metric tensor, \\nand then substituting the components. This is a bit more wasteful on resources, but of course gives the same result:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"You could have computed the Riemann tensor in a different way, first expanding it fully in terms of the metric tensor, \\nand then substituting the components. This is a bit more wasteful on resources, but of course gives the same result:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 8826555707603312064,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 16477384227899948018,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 7390191937934717630,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"R^{\\\\rho}_{\\\\sigma \\\\mu \\\\nu} = \\\\partial_{\\\\mu}(\\\\Gamma^{\\\\rho}_{\\\\nu \\\\sigma})-\\\\partial_{\\\\nu}(\\\\Gamma^{\\\\rho}_{\\\\mu \\\\sigma}) + \\\\Gamma^{\\\\rho}_{\\\\mu \\\\lambda} \\\\Gamma^{\\\\lambda}_{\\\\nu \\\\sigma}-\\\\Gamma^{\\\\rho}_{\\\\nu \\\\lambda} \\\\Gamma^{\\\\lambda}_{\\\\mu \\\\sigma}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}R^{\\\\rho}\\\\,_{\\\\sigma \\\\mu \\\\nu} = \\\\partial_{\\\\mu}{\\\\Gamma^{\\\\rho}\\\\,_{\\\\nu \\\\sigma}}\\\\discretionary{}{}{}-\\\\,\\\\partial_{\\\\nu}{\\\\Gamma^{\\\\rho}\\\\,_{\\\\mu \\\\sigma}}\\\\discretionary{}{}{}+\\\\Gamma^{\\\\rho}\\\\,_{\\\\mu \\\\lambda} \\\\Gamma^{\\\\lambda}\\\\,_{\\\\nu \\\\sigma}\\\\discretionary{}{}{}-\\\\,\\\\Gamma^{\\\\rho}\\\\,_{\\\\nu \\\\lambda} \\\\Gamma^{\\\\lambda}\\\\,_{\\\\mu \\\\sigma}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"rm:= R^{\\\\rho}_{\\\\sigma\\\\mu\\\\nu} = \\\\partial_{\\\\mu}{\\\\Gamma^{\\\\rho}_{\\\\nu\\\\sigma}}\\n                                  -\\\\partial_{\\\\nu}{\\\\Gamma^{\\\\rho}_{\\\\mu\\\\sigma}}\\n                                  +\\\\Gamma^{\\\\rho}_{\\\\mu\\\\lambda} \\\\Gamma^{\\\\lambda}_{\\\\nu\\\\sigma}\\n                                  -\\\\Gamma^{\\\\rho}_{\\\\nu\\\\lambda} \\\\Gamma^{\\\\lambda}_{\\\\mu\\\\sigma};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 10639451114465337424,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 12291396651894976167,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 10752815987830560248,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\Gamma^{\\\\mu}_{\\\\nu \\\\rho} =  1/2 g^{\\\\mu \\\\sigma} (\\\\partial_{\\\\rho}(g_{\\\\nu \\\\sigma}) + \\\\partial_{\\\\nu}(g_{\\\\rho \\\\sigma})-\\\\partial_{\\\\sigma}(g_{\\\\nu \\\\rho}))\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\Gamma^{\\\\mu}\\\\,_{\\\\nu \\\\rho} = \\\\frac{1}{2}\\\\,g^{\\\\mu \\\\sigma} \\\\left(\\\\partial_{\\\\rho}{g_{\\\\nu \\\\sigma}}\\\\discretionary{}{}{}+\\\\partial_{\\\\nu}{g_{\\\\rho \\\\sigma}}\\\\discretionary{}{}{}-\\\\,\\\\partial_{\\\\sigma}{g_{\\\\nu \\\\rho}}\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ch:= \\\\Gamma^{\\\\mu}_{\\\\nu\\\\rho} = 1/2 g^{\\\\mu\\\\sigma} ( \\n                                   \\\\partial_{\\\\rho}{g_{\\\\nu\\\\sigma}} \\n                                  +\\\\partial_{\\\\nu}{g_{\\\\rho\\\\sigma}}\\n                                  -\\\\partial_{\\\\sigma}{g_{\\\\nu\\\\rho}} );\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 9438827020965938886,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 12867936977185550586,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 9113787109717164403,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"R^{\\\\rho}_{\\\\sigma \\\\mu \\\\nu} =  1/2 \\\\partial_{\\\\mu}(g^{\\\\rho \\\\lambda} (\\\\partial_{\\\\sigma}(g_{\\\\nu \\\\lambda}) + \\\\partial_{\\\\nu}(g_{\\\\sigma \\\\lambda})-\\\\partial_{\\\\lambda}(g_{\\\\nu \\\\sigma}))) -  1/2 \\\\partial_{\\\\nu}(g^{\\\\rho \\\\lambda} (\\\\partial_{\\\\sigma}(g_{\\\\mu \\\\lambda}) + \\\\partial_{\\\\mu}(g_{\\\\sigma \\\\lambda})-\\\\partial_{\\\\lambda}(g_{\\\\mu \\\\sigma}))) +  1/4 g^{\\\\rho \\\\kappa} (\\\\partial_{\\\\lambda}(g_{\\\\mu \\\\kappa}) + \\\\partial_{\\\\mu}(g_{\\\\lambda \\\\kappa})-\\\\partial_{\\\\kappa}(g_{\\\\mu \\\\lambda})) g^{\\\\lambda \\\\chi} (\\\\partial_{\\\\sigma}(g_{\\\\nu \\\\chi}) + \\\\partial_{\\\\nu}(g_{\\\\sigma \\\\chi})-\\\\partial_{\\\\chi}(g_{\\\\nu \\\\sigma})) -  1/4 g^{\\\\rho \\\\kappa} (\\\\partial_{\\\\lambda}(g_{\\\\nu \\\\kappa}) + \\\\partial_{\\\\nu}(g_{\\\\lambda \\\\kappa})-\\\\partial_{\\\\kappa}(g_{\\\\nu \\\\lambda})) g^{\\\\lambda \\\\chi} (\\\\partial_{\\\\sigma}(g_{\\\\mu \\\\chi}) + \\\\partial_{\\\\mu}(g_{\\\\sigma \\\\chi})-\\\\partial_{\\\\chi}(g_{\\\\mu \\\\sigma}))\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}R^{\\\\rho}\\\\,_{\\\\sigma \\\\mu \\\\nu} = \\\\frac{1}{2}\\\\,\\\\partial_{\\\\mu}\\\\left(g^{\\\\rho \\\\lambda} \\\\left(\\\\partial_{\\\\sigma}{g_{\\\\nu \\\\lambda}}\\\\discretionary{}{}{}+\\\\partial_{\\\\nu}{g_{\\\\sigma \\\\lambda}}\\\\discretionary{}{}{}-\\\\,\\\\partial_{\\\\lambda}{g_{\\\\nu \\\\sigma}}\\\\right)\\\\right)\\\\discretionary{}{}{} - \\\\frac{1}{2}\\\\,\\\\partial_{\\\\nu}\\\\left(g^{\\\\rho \\\\lambda} \\\\left(\\\\partial_{\\\\sigma}{g_{\\\\mu \\\\lambda}}\\\\discretionary{}{}{}+\\\\partial_{\\\\mu}{g_{\\\\sigma \\\\lambda}}\\\\discretionary{}{}{}-\\\\,\\\\partial_{\\\\lambda}{g_{\\\\mu \\\\sigma}}\\\\right)\\\\right)\\\\discretionary{}{}{}+\\\\frac{1}{4}\\\\,g^{\\\\rho \\\\kappa} \\\\left(\\\\partial_{\\\\lambda}{g_{\\\\mu \\\\kappa}}\\\\discretionary{}{}{}+\\\\partial_{\\\\mu}{g_{\\\\lambda \\\\kappa}}\\\\discretionary{}{}{}-\\\\,\\\\partial_{\\\\kappa}{g_{\\\\mu \\\\lambda}}\\\\right) g^{\\\\lambda \\\\chi} \\\\left(\\\\partial_{\\\\sigma}{g_{\\\\nu \\\\chi}}\\\\discretionary{}{}{}+\\\\partial_{\\\\nu}{g_{\\\\sigma \\\\chi}}\\\\discretionary{}{}{}-\\\\,\\\\partial_{\\\\chi}{g_{\\\\nu \\\\sigma}}\\\\right)\\\\discretionary{}{}{} - \\\\frac{1}{4}\\\\,g^{\\\\rho \\\\kappa} \\\\left(\\\\partial_{\\\\lambda}{g_{\\\\nu \\\\kappa}}\\\\discretionary{}{}{}+\\\\partial_{\\\\nu}{g_{\\\\lambda \\\\kappa}}\\\\discretionary{}{}{}-\\\\,\\\\partial_{\\\\kappa}{g_{\\\\nu \\\\lambda}}\\\\right) g^{\\\\lambda \\\\chi} \\\\left(\\\\partial_{\\\\sigma}{g_{\\\\mu \\\\chi}}\\\\discretionary{}{}{}+\\\\partial_{\\\\mu}{g_{\\\\sigma \\\\chi}}\\\\discretionary{}{}{}-\\\\,\\\\partial_{\\\\chi}{g_{\\\\mu \\\\sigma}}\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"substitute(rm, ch);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 12766437910772063457,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"evaluate(rm, ss, rhsonly=True)\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 779568014576992513,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 12206356522778980070,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 13619767778774910226,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"K = R^{\\\\mu}_{\\\\nu \\\\rho \\\\sigma} R^{\\\\lambda}_{\\\\kappa \\\\gamma \\\\chi} g_{\\\\mu \\\\lambda} g^{\\\\nu \\\\kappa} g^{\\\\rho \\\\gamma} g^{\\\\sigma \\\\chi}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}K = R^{\\\\mu}\\\\,_{\\\\nu \\\\rho \\\\sigma} R^{\\\\lambda}\\\\,_{\\\\kappa \\\\gamma \\\\chi} g_{\\\\mu \\\\lambda} g^{\\\\nu \\\\kappa} g^{\\\\rho \\\\gamma} g^{\\\\sigma \\\\chi}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"K:= K = R^{\\\\mu}_{\\\\nu\\\\rho\\\\sigma} R^{\\\\lambda}_{\\\\kappa\\\\gamma\\\\chi} \\n           g_{\\\\mu\\\\lambda} g^{\\\\nu\\\\kappa} g^{\\\\rho\\\\gamma} g^{\\\\sigma\\\\chi};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 5432317296520096003,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 6236948674971834662,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 1803847865196472883,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"K = 48(M)**2 (r)**(-6)\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}K = \\\\frac{48\\\\,{M}^{2\\\\,}}{{r}^{6\\\\,}}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"substitute(K, rm)\\nevaluate(K, ss);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 11447606696872464301,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"\"\n\t\t}\n\t],\n\t\"description\": \"Cadabra JSON notebook format\",\n\t\"flags\": {\n\t\t\"hide_input_cells\": false\n\t},\n\t\"version\": 1.0\n}\n"
  },
  {
    "path": "examples/schwarzschild.ipynb",
    "content": "{\n \"cells\": [\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"# The Schwarzschild spacetime\\n\",\n    \"\\n\",\n    \"This notebook shows how you can do component computations in Cadabra. It is a translation of the\\n\",\n    \"Cadabra notebook https://cadabra.science/notebooks/schwarzschild.html to Jupyter. \\n\",\n    \"\\n\",\n    \"The first thing we always need to do is to declare the coordinates used, and the names of the indices.\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 1,\n   \"metadata\": {},\n   \"outputs\": [\n    {\n     \"data\": {\n      \"text/markdown\": [\n       \"${}\\\\text{Attached property Coordinate to}\\\\left[r, t, \\\\phi, \\\\theta\\\\right].$\"\n      ]\n     },\n     \"metadata\": {},\n     \"output_type\": \"display_data\"\n    },\n    {\n     \"data\": {\n      \"text/markdown\": [\n       \"${}\\\\text{Attached property Indices(position=fixed) to}\\\\left[\\\\mu, \\\\nu, \\\\rho, \\\\sigma, \\\\lambda, \\\\kappa, \\\\chi, \\\\gamma\\\\right].$\"\n      ]\n     },\n     \"metadata\": {},\n     \"output_type\": \"display_data\"\n    },\n    {\n     \"data\": {\n      \"text/markdown\": [\n       \"${}\\\\text{Attached property PartialDerivative to}\\\\partial{\\\\#}.$\"\n      ]\n     },\n     \"metadata\": {},\n     \"output_type\": \"display_data\"\n    }\n   ],\n   \"source\": [\n    \"{r,t,\\\\phi,\\\\theta}::Coordinate;\\n\",\n    \"{\\\\mu,\\\\nu,\\\\rho,\\\\sigma,\\\\lambda,\\\\kappa,\\\\chi,\\\\gamma}::Indices(values={t,r,\\\\phi,\\\\theta}, position=fixed);\\n\",\n    \"\\\\partial{#}::PartialDerivative;\\n\",\n    \"g_{\\\\mu\\\\nu}::Metric.\\n\",\n    \"g^{\\\\mu\\\\nu}::InverseMetric.\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"Below is the Schwarzschild metric in standard coordinates. Note how the components are\\n\",\n    \"given in terms of substitution rules, and how the inverse metric is computed. \\n\",\n    \"The \\\\algo{complete} algorithm adds the rules for the inverse metric to the rules for the metric.\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 3,\n   \"metadata\": {},\n   \"outputs\": [\n    {\n     \"data\": {\n      \"text/markdown\": [\n       \"${}\\\\left[g_{t t} = -1+2M {r}^{-1}, g_{r r} = {\\\\left(1-2M {r}^{-1}\\\\right)}^{-1}, g_{\\\\theta \\\\theta} = {r}^{2}, g_{\\\\phi \\\\phi} = {r}^{2} {\\\\left(\\\\sin{\\\\theta}\\\\right)}^{2}, g^{t t} = {\\\\left(2M {r}^{-1}-1\\\\right)}^{-1}, g^{r r} = -2M {r}^{-1}+1, g^{\\\\phi \\\\phi} = {\\\\left({r}^{2} {\\\\left(\\\\sin{\\\\theta}\\\\right)}^{2}\\\\right)}^{-1}, g^{\\\\theta \\\\theta} = {r}^{-2}\\\\right]$\"\n      ]\n     },\n     \"metadata\": {},\n     \"output_type\": \"display_data\"\n    }\n   ],\n   \"source\": [\n    \"ss:= { g_{t t} = -(1-2 M/r),   \\n\",\n    \"       g_{r r} = 1/(1-2 M/r), \\n\",\n    \"       g_{\\\\theta\\\\theta} = r**2, \\n\",\n    \"       g_{\\\\phi\\\\phi}=r**2 \\\\sin(\\\\theta)**2\\n\",\n    \"     }.\\n\",\n    \"\\n\",\n    \"complete(ss, $g^{\\\\mu\\\\nu}$);\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"We can now compute the Christoffel symbols. We give Cadabra the expression for the \\n\",\n    \"Christoffel symbols in terms of the metric, and then evaluate the components of the\\n\",\n    \"metric using the `evaluate` algorithm.\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 4,\n   \"metadata\": {},\n   \"outputs\": [\n    {\n     \"data\": {\n      \"text/markdown\": [\n       \"${}\\\\Gamma^{\\\\mu}\\\\,_{\\\\nu \\\\rho} = \\\\frac{1}{2}g^{\\\\mu \\\\sigma} \\\\left(\\\\partial_{\\\\rho}{g_{\\\\nu \\\\sigma}}+\\\\partial_{\\\\nu}{g_{\\\\rho \\\\sigma}}-\\\\partial_{\\\\sigma}{g_{\\\\nu \\\\rho}}\\\\right)$\"\n      ]\n     },\n     \"metadata\": {},\n     \"output_type\": \"display_data\"\n    },\n    {\n     \"data\": {\n      \"text/markdown\": [\n       \"${}\\\\Gamma^{\\\\mu}\\\\,_{\\\\nu \\\\rho} = \\\\square{}_{\\\\nu}{}_{\\\\rho}{}^{\\\\mu}\\\\left\\\\{\\\\begin{aligned}\\\\square{}_{\\\\phi}{}_{r}{}^{\\\\phi}& = {r}^{-1}\\\\\\\\[-.5ex]\\n\",\n       \"\\\\square{}_{\\\\phi}{}_{\\\\theta}{}^{\\\\phi}& = {\\\\left(\\\\tan{\\\\theta}\\\\right)}^{-1}\\\\\\\\[-.5ex]\\n\",\n       \"\\\\square{}_{\\\\theta}{}_{r}{}^{\\\\theta}& = {r}^{-1}\\\\\\\\[-.5ex]\\n\",\n       \"\\\\square{}_{r}{}_{r}{}^{r}& = M {\\\\left(r \\\\left(2M-r\\\\right)\\\\right)}^{-1}\\\\\\\\[-.5ex]\\n\",\n       \"\\\\square{}_{t}{}_{r}{}^{t}& = M {\\\\left(r \\\\left(-2M+r\\\\right)\\\\right)}^{-1}\\\\\\\\[-.5ex]\\n\",\n       \"\\\\square{}_{r}{}_{\\\\phi}{}^{\\\\phi}& = {r}^{-1}\\\\\\\\[-.5ex]\\n\",\n       \"\\\\square{}_{\\\\theta}{}_{\\\\phi}{}^{\\\\phi}& = {\\\\left(\\\\tan{\\\\theta}\\\\right)}^{-1}\\\\\\\\[-.5ex]\\n\",\n       \"\\\\square{}_{r}{}_{\\\\theta}{}^{\\\\theta}& = {r}^{-1}\\\\\\\\[-.5ex]\\n\",\n       \"\\\\square{}_{r}{}_{t}{}^{t}& = M {\\\\left(r \\\\left(-2M+r\\\\right)\\\\right)}^{-1}\\\\\\\\[-.5ex]\\n\",\n       \"\\\\square{}_{\\\\phi}{}_{\\\\phi}{}^{r}& = \\\\left(2M-r\\\\right) {\\\\left(\\\\sin{\\\\theta}\\\\right)}^{2}\\\\\\\\[-.5ex]\\n\",\n       \"\\\\square{}_{\\\\phi}{}_{\\\\phi}{}^{\\\\theta}& =  - \\\\frac{1}{2}\\\\sin\\\\left(2\\\\theta\\\\right)\\\\\\\\[-.5ex]\\n\",\n       \"\\\\square{}_{\\\\theta}{}_{\\\\theta}{}^{r}& = 2M-r\\\\\\\\[-.5ex]\\n\",\n       \"\\\\square{}_{t}{}_{t}{}^{r}& = M \\\\left(-2M+r\\\\right) {r}^{-3}\\\\\\\\[-.5ex]\\n\",\n       \"\\\\end{aligned}\\\\right.\\n\",\n       \"$\"\n      ]\n     },\n     \"metadata\": {},\n     \"output_type\": \"display_data\"\n    }\n   ],\n   \"source\": [\n    \"ch:= \\\\Gamma^{\\\\mu}_{\\\\nu\\\\rho} = 1/2 g^{\\\\mu\\\\sigma} ( \\n\",\n    \"                                   \\\\partial_{\\\\rho}{g_{\\\\nu\\\\sigma}} \\n\",\n    \"                                  +\\\\partial_{\\\\nu}{g_{\\\\rho\\\\sigma}}\\n\",\n    \"                                  -\\\\partial_{\\\\sigma}{g_{\\\\nu\\\\rho}} ):\\n\",\n    \"                          \\n\",\n    \"evaluate(ch, ss, rhsonly=True);\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"Continuing from here we can compute the Riemann tensor components. Again, we start\\n\",\n    \"by giving this tensor in terms of the Christoffel symbols. We then subsitute the \\n\",\n    \"Christoffel symbols just found, and work out any remaining component substitions using\\n\",\n    \"`evaluate` (the computation takes a few seconds, essentially because of the round\\n\",\n    \"trips through Sympy).\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 5,\n   \"metadata\": {},\n   \"outputs\": [\n    {\n     \"data\": {\n      \"text/markdown\": [\n       \"${}R^{\\\\rho}\\\\,_{\\\\sigma \\\\mu \\\\nu} = \\\\partial_{\\\\mu}{\\\\Gamma^{\\\\rho}\\\\,_{\\\\nu \\\\sigma}}-\\\\partial_{\\\\nu}{\\\\Gamma^{\\\\rho}\\\\,_{\\\\mu \\\\sigma}}+\\\\Gamma^{\\\\rho}\\\\,_{\\\\mu \\\\lambda} \\\\Gamma^{\\\\lambda}\\\\,_{\\\\nu \\\\sigma}-\\\\Gamma^{\\\\rho}\\\\,_{\\\\nu \\\\lambda} \\\\Gamma^{\\\\lambda}\\\\,_{\\\\mu \\\\sigma}$\"\n      ]\n     },\n     \"metadata\": {},\n     \"output_type\": \"display_data\"\n    }\n   ],\n   \"source\": [\n    \"rm:= R^{\\\\rho}_{\\\\sigma\\\\mu\\\\nu} = \\\\partial_{\\\\mu}{\\\\Gamma^{\\\\rho}_{\\\\nu\\\\sigma}}\\n\",\n    \"                                  -\\\\partial_{\\\\nu}{\\\\Gamma^{\\\\rho}_{\\\\mu\\\\sigma}}\\n\",\n    \"                                  +\\\\Gamma^{\\\\rho}_{\\\\mu\\\\lambda} \\\\Gamma^{\\\\lambda}_{\\\\nu\\\\sigma}\\n\",\n    \"                                  -\\\\Gamma^{\\\\rho}_{\\\\nu\\\\lambda} \\\\Gamma^{\\\\lambda}_{\\\\mu\\\\sigma};\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 6,\n   \"metadata\": {},\n   \"outputs\": [\n    {\n     \"data\": {\n      \"text/markdown\": [\n       \"${}R^{\\\\rho}\\\\,_{\\\\sigma \\\\mu \\\\nu} = \\\\square{}_{\\\\nu}{}_{\\\\sigma}{}^{\\\\rho}{}_{\\\\mu}\\\\left\\\\{\\\\begin{aligned}\\\\square{}_{t}{}_{t}{}^{r}{}_{r}& = 2M \\\\left(2M-r\\\\right) {r}^{-4}\\\\\\\\[-.5ex]\\n\",\n       \"\\\\square{}_{\\\\theta}{}_{\\\\theta}{}^{r}{}_{r}& = -M {r}^{-1}\\\\\\\\[-.5ex]\\n\",\n       \"\\\\square{}_{\\\\phi}{}_{\\\\phi}{}^{\\\\theta}{}_{\\\\theta}& = 2M {\\\\left(\\\\sin{\\\\theta}\\\\right)}^{2} {r}^{-1}\\\\\\\\[-.5ex]\\n\",\n       \"\\\\square{}_{\\\\phi}{}_{\\\\phi}{}^{r}{}_{r}& = -M {\\\\left(\\\\sin{\\\\theta}\\\\right)}^{2} {r}^{-1}\\\\\\\\[-.5ex]\\n\",\n       \"\\\\square{}_{t}{}_{r}{}^{t}{}_{r}& = 2M {\\\\left({r}^{2} \\\\left(2M-r\\\\right)\\\\right)}^{-1}\\\\\\\\[-.5ex]\\n\",\n       \"\\\\square{}_{\\\\phi}{}_{\\\\theta}{}^{\\\\phi}{}_{\\\\theta}& = -2M {r}^{-1}\\\\\\\\[-.5ex]\\n\",\n       \"\\\\square{}_{r}{}_{t}{}^{r}{}_{t}& = 2M \\\\left(-2M+r\\\\right) {r}^{-4}\\\\\\\\[-.5ex]\\n\",\n       \"\\\\square{}_{r}{}_{\\\\theta}{}^{r}{}_{\\\\theta}& = M {r}^{-1}\\\\\\\\[-.5ex]\\n\",\n       \"\\\\square{}_{\\\\theta}{}_{\\\\phi}{}^{\\\\theta}{}_{\\\\phi}& = -2M {\\\\left(\\\\sin{\\\\theta}\\\\right)}^{2} {r}^{-1}\\\\\\\\[-.5ex]\\n\",\n       \"\\\\square{}_{r}{}_{\\\\phi}{}^{r}{}_{\\\\phi}& = M {\\\\left(\\\\sin{\\\\theta}\\\\right)}^{2} {r}^{-1}\\\\\\\\[-.5ex]\\n\",\n       \"\\\\square{}_{r}{}_{r}{}^{t}{}_{t}& = 2M {\\\\left({r}^{2} \\\\left(-2M+r\\\\right)\\\\right)}^{-1}\\\\\\\\[-.5ex]\\n\",\n       \"\\\\square{}_{r}{}_{r}{}^{\\\\theta}{}_{\\\\theta}& = M {\\\\left({r}^{2} \\\\left(2M-r\\\\right)\\\\right)}^{-1}\\\\\\\\[-.5ex]\\n\",\n       \"\\\\square{}_{\\\\theta}{}_{\\\\theta}{}^{\\\\phi}{}_{\\\\phi}& = 2M {r}^{-1}\\\\\\\\[-.5ex]\\n\",\n       \"\\\\square{}_{r}{}_{r}{}^{\\\\phi}{}_{\\\\phi}& = M {\\\\left({r}^{2} \\\\left(2M-r\\\\right)\\\\right)}^{-1}\\\\\\\\[-.5ex]\\n\",\n       \"\\\\square{}_{t}{}_{t}{}^{\\\\phi}{}_{\\\\phi}& = M \\\\left(-2M+r\\\\right) {r}^{-4}\\\\\\\\[-.5ex]\\n\",\n       \"\\\\square{}_{t}{}_{t}{}^{\\\\theta}{}_{\\\\theta}& = M \\\\left(-2M+r\\\\right) {r}^{-4}\\\\\\\\[-.5ex]\\n\",\n       \"\\\\square{}_{\\\\phi}{}_{\\\\phi}{}^{t}{}_{t}& = -M {\\\\left(\\\\sin{\\\\theta}\\\\right)}^{2} {r}^{-1}\\\\\\\\[-.5ex]\\n\",\n       \"\\\\square{}_{\\\\theta}{}_{\\\\theta}{}^{t}{}_{t}& = -M {r}^{-1}\\\\\\\\[-.5ex]\\n\",\n       \"\\\\square{}_{\\\\phi}{}_{r}{}^{\\\\phi}{}_{r}& = M {\\\\left({r}^{2} \\\\left(-2M+r\\\\right)\\\\right)}^{-1}\\\\\\\\[-.5ex]\\n\",\n       \"\\\\square{}_{\\\\phi}{}_{t}{}^{\\\\phi}{}_{t}& = M \\\\left(2M-r\\\\right) {r}^{-4}\\\\\\\\[-.5ex]\\n\",\n       \"\\\\square{}_{\\\\theta}{}_{r}{}^{\\\\theta}{}_{r}& = M {\\\\left({r}^{2} \\\\left(-2M+r\\\\right)\\\\right)}^{-1}\\\\\\\\[-.5ex]\\n\",\n       \"\\\\square{}_{\\\\theta}{}_{t}{}^{\\\\theta}{}_{t}& = M \\\\left(2M-r\\\\right) {r}^{-4}\\\\\\\\[-.5ex]\\n\",\n       \"\\\\square{}_{t}{}_{\\\\phi}{}^{t}{}_{\\\\phi}& = M {\\\\left(\\\\sin{\\\\theta}\\\\right)}^{2} {r}^{-1}\\\\\\\\[-.5ex]\\n\",\n       \"\\\\square{}_{t}{}_{\\\\theta}{}^{t}{}_{\\\\theta}& = M {r}^{-1}\\\\\\\\[-.5ex]\\n\",\n       \"\\\\end{aligned}\\\\right.\\n\",\n       \"$\"\n      ]\n     },\n     \"metadata\": {},\n     \"output_type\": \"display_data\"\n    }\n   ],\n   \"source\": [\n    \"substitute(rm, ch)\\n\",\n    \"evaluate(rm, ss, rhsonly=True);\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"The Ricci tensor should of course vanish as the Schwarzschild solution is a vacuum\\n\",\n    \"solution. Following the same logic as above, this is easily verified:\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 7,\n   \"metadata\": {},\n   \"outputs\": [\n    {\n     \"data\": {\n      \"text/markdown\": [\n       \"${}R_{\\\\sigma \\\\nu} = R^{\\\\rho}\\\\,_{\\\\sigma \\\\rho \\\\nu}$\"\n      ]\n     },\n     \"metadata\": {},\n     \"output_type\": \"display_data\"\n    },\n    {\n     \"data\": {\n      \"text/markdown\": [\n       \"${}R_{\\\\sigma \\\\nu} = 0$\"\n      ]\n     },\n     \"metadata\": {},\n     \"output_type\": \"display_data\"\n    }\n   ],\n   \"source\": [\n    \"rc:= R_{\\\\sigma\\\\nu} = R^{\\\\rho}_{\\\\sigma\\\\rho\\\\nu};\\n\",\n    \"substitute(rc, rm)\\n\",\n    \"evaluate(rc, ss, rhsonly=True);\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"More interesting is the Kretschmann scalar. \"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 8,\n   \"metadata\": {},\n   \"outputs\": [\n    {\n     \"data\": {\n      \"text/markdown\": [\n       \"${}K = R^{\\\\mu}\\\\,_{\\\\nu \\\\rho \\\\sigma} R^{\\\\lambda}\\\\,_{\\\\kappa \\\\gamma \\\\chi} g_{\\\\mu \\\\lambda} g^{\\\\nu \\\\kappa} g^{\\\\rho \\\\gamma} g^{\\\\sigma \\\\chi}$\"\n      ]\n     },\n     \"metadata\": {},\n     \"output_type\": \"display_data\"\n    }\n   ],\n   \"source\": [\n    \"K:= K = R^{\\\\mu}_{\\\\nu\\\\rho\\\\sigma} R^{\\\\lambda}_{\\\\kappa\\\\gamma\\\\chi} \\n\",\n    \"           g_{\\\\mu\\\\lambda} g^{\\\\nu\\\\kappa} g^{\\\\rho\\\\gamma} g^{\\\\sigma\\\\chi};\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 9,\n   \"metadata\": {},\n   \"outputs\": [\n    {\n     \"data\": {\n      \"text/markdown\": [\n       \"${}K = 48{M}^{2} {r}^{-6}$\"\n      ]\n     },\n     \"metadata\": {},\n     \"output_type\": \"display_data\"\n    }\n   ],\n   \"source\": [\n    \"substitute(K, rm)\\n\",\n    \"evaluate(K, ss, rhsonly=True);\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"This shows that $r=0$ is a true singularity.\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": null,\n   \"metadata\": {},\n   \"outputs\": [],\n   \"source\": []\n  }\n ],\n \"metadata\": {\n  \"kernelspec\": {\n   \"display_name\": \"Cadabra2\",\n   \"language\": \"python\",\n   \"name\": \"cadabra2\"\n  },\n  \"language_info\": {\n   \"codemirror_mode\": \"cadabra\",\n   \"file_extension\": \".ipynb\",\n   \"mimetype\": \"text/cadabra\",\n   \"name\": \"cadabra2\",\n   \"pygments_lexer\": \"cadabra\"\n  }\n },\n \"nbformat\": 4,\n \"nbformat_minor\": 4\n}\n"
  },
  {
    "path": "examples/simple_evaluate.cnb",
    "content": "{\n\t\"cell_id\": 15955037036217990901,\n\t\"cells\": [\n\t\t{\n\t\t\t\"cell_id\": 15821029921019724773,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 13581146124792910087,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property Coordinate attached to~}\\\\left[t, \\\\discretionary{}{}{}r\\\\right].\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 7213587043865807769,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property Indices(position=free, values=\\\\{{r}\\n, {t}\\n\\\\}) attached to~}\\\\left[\\\\mu, \\\\discretionary{}{}{}\\\\nu\\\\right].\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"\\\\dot{#}::Accent.\\n{t,r}::Coordinate;\\n{\\\\mu,\\\\nu}::Indices(values={r,t});\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 14507815146891810201,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 3386410755258289437,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 11458273571150299319,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\dot{X^{\\\\mu}} + A^{\\\\mu}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\dot{X^{\\\\mu}}\\\\discretionary{}{}{}+A^{\\\\mu}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex:= \\\\dot{X^\\\\mu} + A^{\\\\mu} ;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 7521066877325165882,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 4255052784837468787,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 12398809585298354188,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"{X^{t} = T, X^{r} = R, A^{r} = 3, A^{t} = 2}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\left[X^{t} = T, \\\\discretionary{}{}{}X^{r} = R, \\\\discretionary{}{}{}A^{r} = 3\\\\,, \\\\discretionary{}{}{}A^{t} = 2\\\\,\\\\right]\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"rl:= { X^{t} = T, X^{r} = R, A^{r} = 3, A^{t} = 2 };\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 4490208082992345645,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 16839994021621720773,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 7769025253073063830,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\components^{\\\\mu}({{t} = \\\\dot{T} + 2, {r} = \\\\dot{R} + 3})\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\square{}^{\\\\mu}\\\\left\\\\{\\\\begin{aligned}\\\\square{}^{t}& = \\\\dot{T}\\\\discretionary{}{}{}+2\\\\,\\\\\\\\[-.5ex]\\n\\\\square{}^{r}& = \\\\dot{R}\\\\discretionary{}{}{}+3\\\\,\\\\\\\\[-.5ex]\\n\\\\end{aligned}\\\\right.\\n\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"evaluate(ex, rl);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 14467008753384234490,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"\"\n\t\t}\n\t],\n\t\"description\": \"Cadabra JSON notebook format\",\n\t\"flags\": {\n\t\t\"hide_input_cells\": false\n\t},\n\t\"version\": 1.0\n}\n"
  },
  {
    "path": "examples/slider.cnb",
    "content": "{\n\t\"cell_id\": 13773678675781249589,\n\t\"cells\": [\n\t\t{\n\t\t\t\"cell_id\": 15820423804639485508,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9525008448762707388,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\section*{Dynamical notebooks using variable sliders}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\section*{Dynamical notebooks using variable sliders}\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 17539052725145187247,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"from cdb.graphics.plot import *\\nfrom cdb.interact.slider import *\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 10834951365496879913,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 15870737198806681073,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"In Cadabra's \\\\verb|interact| package, there is functionality which enables you to use sliders to change the numerical value of any Python variable, and re-run the cells which contain that variable. In order to see how this works, let us first make a simple plot, which depends on two parameters $q$ (the frequency) and $a$ (a phase). For now these are just set to some default values.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"In Cadabra's \\\\verb|interact| package, there is functionality which enables you to use sliders to change the numerical value of any Python variable, and re-run the cells which contain that variable. In order to see how this works, let us first make a simple plot, which depends on two parameters $q$ (the frequency) and $a$ (a phase). For now these are just set to some default values.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 8214815714251201597,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"p=None\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 1628625577823470242,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"q=3\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 12718663709217934057,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"a=0.3\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 10193414014346820971,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 17634105944153167483,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"image_svg\",\n\t\t\t\t\t\"source\": \"<?xml version="1.0" encoding="utf-8" standalone="no"?>
<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
  "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="460.8pt" height="345.6pt" viewBox="0 0 460.8 345.6" xmlns="http://www.w3.org/2000/svg" version="1.1">
 <metadata>
  <rdf:RDF xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:cc="http://creativecommons.org/ns#" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
   <cc:Work>
    <dc:type rdf:resource="http://purl.org/dc/dcmitype/StillImage"/>
    <dc:date>2025-03-29T20:33:42.107594</dc:date>
    <dc:format>image/svg+xml</dc:format>
    <dc:creator>
     <cc:Agent>
      <dc:title>Matplotlib v3.6.3, https://matplotlib.org/</dc:title>
     </cc:Agent>
    </dc:creator>
   </cc:Work>
  </rdf:RDF>
 </metadata>
 <defs>
  <style type="text/css">*{stroke-linejoin: round; stroke-linecap: butt}</style>
 </defs>
 <g id="figure_1">
  <g id="patch_1">
   <path d="M 0 345.6 
L 460.8 345.6 
L 460.8 0 
L 0 0 
z
" style="fill: #ffffff"/>
  </g>
  <g id="axes_1">
   <g id="patch_2">
    <path d="M 57.6 307.584 
L 414.72 307.584 
L 414.72 41.472 
L 57.6 41.472 
z
" style="fill: #ffffff"/>
   </g>
   <g id="matplotlib.axis_1">
    <g id="xtick_1">
     <g id="line2d_1">
      <defs>
       <path id="m645503b89c" d="M 0 0 
L 0 3.5 
" style="stroke: #000000; stroke-width: 0.8"/>
      </defs>
      <g>
       <use xlink:href="#m645503b89c" x="73.832727" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_1">
      <!-- 0 -->
      <g transform="translate(70.651477 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-30" d="M 2034 4250 
Q 1547 4250 1301 3770 
Q 1056 3291 1056 2328 
Q 1056 1369 1301 889 
Q 1547 409 2034 409 
Q 2525 409 2770 889 
Q 3016 1369 3016 2328 
Q 3016 3291 2770 3770 
Q 2525 4250 2034 4250 
z
M 2034 4750 
Q 2819 4750 3233 4129 
Q 3647 3509 3647 2328 
Q 3647 1150 3233 529 
Q 2819 -91 2034 -91 
Q 1250 -91 836 529 
Q 422 1150 422 2328 
Q 422 3509 836 4129 
Q 1250 4750 2034 4750 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-30"/>
      </g>
     </g>
    </g>
    <g id="xtick_2">
     <g id="line2d_2">
      <g>
       <use xlink:href="#m645503b89c" x="125.529311" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_2">
      <!-- 1 -->
      <g transform="translate(122.348061 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-31" d="M 794 531 
L 1825 531 
L 1825 4091 
L 703 3866 
L 703 4441 
L 1819 4666 
L 2450 4666 
L 2450 531 
L 3481 531 
L 3481 0 
L 794 0 
L 794 531 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-31"/>
      </g>
     </g>
    </g>
    <g id="xtick_3">
     <g id="line2d_3">
      <g>
       <use xlink:href="#m645503b89c" x="177.225895" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_3">
      <!-- 2 -->
      <g transform="translate(174.044645 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-32" d="M 1228 531 
L 3431 531 
L 3431 0 
L 469 0 
L 469 531 
Q 828 903 1448 1529 
Q 2069 2156 2228 2338 
Q 2531 2678 2651 2914 
Q 2772 3150 2772 3378 
Q 2772 3750 2511 3984 
Q 2250 4219 1831 4219 
Q 1534 4219 1204 4116 
Q 875 4013 500 3803 
L 500 4441 
Q 881 4594 1212 4672 
Q 1544 4750 1819 4750 
Q 2544 4750 2975 4387 
Q 3406 4025 3406 3419 
Q 3406 3131 3298 2873 
Q 3191 2616 2906 2266 
Q 2828 2175 2409 1742 
Q 1991 1309 1228 531 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-32"/>
      </g>
     </g>
    </g>
    <g id="xtick_4">
     <g id="line2d_4">
      <g>
       <use xlink:href="#m645503b89c" x="228.922478" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_4">
      <!-- 3 -->
      <g transform="translate(225.741228 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-33" d="M 2597 2516 
Q 3050 2419 3304 2112 
Q 3559 1806 3559 1356 
Q 3559 666 3084 287 
Q 2609 -91 1734 -91 
Q 1441 -91 1130 -33 
Q 819 25 488 141 
L 488 750 
Q 750 597 1062 519 
Q 1375 441 1716 441 
Q 2309 441 2620 675 
Q 2931 909 2931 1356 
Q 2931 1769 2642 2001 
Q 2353 2234 1838 2234 
L 1294 2234 
L 1294 2753 
L 1863 2753 
Q 2328 2753 2575 2939 
Q 2822 3125 2822 3475 
Q 2822 3834 2567 4026 
Q 2313 4219 1838 4219 
Q 1578 4219 1281 4162 
Q 984 4106 628 3988 
L 628 4550 
Q 988 4650 1302 4700 
Q 1616 4750 1894 4750 
Q 2613 4750 3031 4423 
Q 3450 4097 3450 3541 
Q 3450 3153 3228 2886 
Q 3006 2619 2597 2516 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-33"/>
      </g>
     </g>
    </g>
    <g id="xtick_5">
     <g id="line2d_5">
      <g>
       <use xlink:href="#m645503b89c" x="280.619062" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_5">
      <!-- 4 -->
      <g transform="translate(277.437812 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-34" d="M 2419 4116 
L 825 1625 
L 2419 1625 
L 2419 4116 
z
M 2253 4666 
L 3047 4666 
L 3047 1625 
L 3713 1625 
L 3713 1100 
L 3047 1100 
L 3047 0 
L 2419 0 
L 2419 1100 
L 313 1100 
L 313 1709 
L 2253 4666 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-34"/>
      </g>
     </g>
    </g>
    <g id="xtick_6">
     <g id="line2d_6">
      <g>
       <use xlink:href="#m645503b89c" x="332.315646" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_6">
      <!-- 5 -->
      <g transform="translate(329.134396 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-35" d="M 691 4666 
L 3169 4666 
L 3169 4134 
L 1269 4134 
L 1269 2991 
Q 1406 3038 1543 3061 
Q 1681 3084 1819 3084 
Q 2600 3084 3056 2656 
Q 3513 2228 3513 1497 
Q 3513 744 3044 326 
Q 2575 -91 1722 -91 
Q 1428 -91 1123 -41 
Q 819 9 494 109 
L 494 744 
Q 775 591 1075 516 
Q 1375 441 1709 441 
Q 2250 441 2565 725 
Q 2881 1009 2881 1497 
Q 2881 1984 2565 2268 
Q 2250 2553 1709 2553 
Q 1456 2553 1204 2497 
Q 953 2441 691 2322 
L 691 4666 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-35"/>
      </g>
     </g>
    </g>
    <g id="xtick_7">
     <g id="line2d_7">
      <g>
       <use xlink:href="#m645503b89c" x="384.012229" y="307.584" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_7">
      <!-- 6 -->
      <g transform="translate(380.830979 322.182437) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-36" d="M 2113 2584 
Q 1688 2584 1439 2293 
Q 1191 2003 1191 1497 
Q 1191 994 1439 701 
Q 1688 409 2113 409 
Q 2538 409 2786 701 
Q 3034 994 3034 1497 
Q 3034 2003 2786 2293 
Q 2538 2584 2113 2584 
z
M 3366 4563 
L 3366 3988 
Q 3128 4100 2886 4159 
Q 2644 4219 2406 4219 
Q 1781 4219 1451 3797 
Q 1122 3375 1075 2522 
Q 1259 2794 1537 2939 
Q 1816 3084 2150 3084 
Q 2853 3084 3261 2657 
Q 3669 2231 3669 1497 
Q 3669 778 3244 343 
Q 2819 -91 2113 -91 
Q 1303 -91 875 529 
Q 447 1150 447 2328 
Q 447 3434 972 4092 
Q 1497 4750 2381 4750 
Q 2619 4750 2861 4703 
Q 3103 4656 3366 4563 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-36"/>
      </g>
     </g>
    </g>
   </g>
   <g id="matplotlib.axis_2">
    <g id="ytick_1">
     <g id="line2d_8">
      <defs>
       <path id="m02c9173bc6" d="M 0 0 
L -3.5 0 
" style="stroke: #000000; stroke-width: 0.8"/>
      </defs>
      <g>
       <use xlink:href="#m02c9173bc6" x="57.6" y="295.488" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_8">
      <!-- −1.00 -->
      <g transform="translate(19.954687 299.287219) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-2212" d="M 678 2272 
L 4684 2272 
L 4684 1741 
L 678 1741 
L 678 2272 
z
" transform="scale(0.015625)"/>
        <path id="DejaVuSans-2e" d="M 684 794 
L 1344 794 
L 1344 0 
L 684 0 
L 684 794 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-2212"/>
       <use xlink:href="#DejaVuSans-31" x="83.789062"/>
       <use xlink:href="#DejaVuSans-2e" x="147.412109"/>
       <use xlink:href="#DejaVuSans-30" x="179.199219"/>
       <use xlink:href="#DejaVuSans-30" x="242.822266"/>
      </g>
     </g>
    </g>
    <g id="ytick_2">
     <g id="line2d_9">
      <g>
       <use xlink:href="#m02c9173bc6" x="57.6" y="265.248" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_9">
      <!-- −0.75 -->
      <g transform="translate(19.954687 269.047219) scale(0.1 -0.1)">
       <defs>
        <path id="DejaVuSans-37" d="M 525 4666 
L 3525 4666 
L 3525 4397 
L 1831 0 
L 1172 0 
L 2766 4134 
L 525 4134 
L 525 4666 
z
" transform="scale(0.015625)"/>
       </defs>
       <use xlink:href="#DejaVuSans-2212"/>
       <use xlink:href="#DejaVuSans-30" x="83.789062"/>
       <use xlink:href="#DejaVuSans-2e" x="147.412109"/>
       <use xlink:href="#DejaVuSans-37" x="179.199219"/>
       <use xlink:href="#DejaVuSans-35" x="242.822266"/>
      </g>
     </g>
    </g>
    <g id="ytick_3">
     <g id="line2d_10">
      <g>
       <use xlink:href="#m02c9173bc6" x="57.6" y="235.008" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_10">
      <!-- −0.50 -->
      <g transform="translate(19.954687 238.807219) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-2212"/>
       <use xlink:href="#DejaVuSans-30" x="83.789062"/>
       <use xlink:href="#DejaVuSans-2e" x="147.412109"/>
       <use xlink:href="#DejaVuSans-35" x="179.199219"/>
       <use xlink:href="#DejaVuSans-30" x="242.822266"/>
      </g>
     </g>
    </g>
    <g id="ytick_4">
     <g id="line2d_11">
      <g>
       <use xlink:href="#m02c9173bc6" x="57.6" y="204.768" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_11">
      <!-- −0.25 -->
      <g transform="translate(19.954687 208.567219) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-2212"/>
       <use xlink:href="#DejaVuSans-30" x="83.789062"/>
       <use xlink:href="#DejaVuSans-2e" x="147.412109"/>
       <use xlink:href="#DejaVuSans-32" x="179.199219"/>
       <use xlink:href="#DejaVuSans-35" x="242.822266"/>
      </g>
     </g>
    </g>
    <g id="ytick_5">
     <g id="line2d_12">
      <g>
       <use xlink:href="#m02c9173bc6" x="57.6" y="174.528" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_12">
      <!-- 0.00 -->
      <g transform="translate(28.334375 178.327219) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-30"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-30" x="95.410156"/>
       <use xlink:href="#DejaVuSans-30" x="159.033203"/>
      </g>
     </g>
    </g>
    <g id="ytick_6">
     <g id="line2d_13">
      <g>
       <use xlink:href="#m02c9173bc6" x="57.6" y="144.288" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_13">
      <!-- 0.25 -->
      <g transform="translate(28.334375 148.087219) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-30"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-32" x="95.410156"/>
       <use xlink:href="#DejaVuSans-35" x="159.033203"/>
      </g>
     </g>
    </g>
    <g id="ytick_7">
     <g id="line2d_14">
      <g>
       <use xlink:href="#m02c9173bc6" x="57.6" y="114.048" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_14">
      <!-- 0.50 -->
      <g transform="translate(28.334375 117.847219) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-30"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-35" x="95.410156"/>
       <use xlink:href="#DejaVuSans-30" x="159.033203"/>
      </g>
     </g>
    </g>
    <g id="ytick_8">
     <g id="line2d_15">
      <g>
       <use xlink:href="#m02c9173bc6" x="57.6" y="83.808" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_15">
      <!-- 0.75 -->
      <g transform="translate(28.334375 87.607219) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-30"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-37" x="95.410156"/>
       <use xlink:href="#DejaVuSans-35" x="159.033203"/>
      </g>
     </g>
    </g>
    <g id="ytick_9">
     <g id="line2d_16">
      <g>
       <use xlink:href="#m02c9173bc6" x="57.6" y="53.568" style="stroke: #000000; stroke-width: 0.8"/>
      </g>
     </g>
     <g id="text_16">
      <!-- 1.00 -->
      <g transform="translate(28.334375 57.367219) scale(0.1 -0.1)">
       <use xlink:href="#DejaVuSans-31"/>
       <use xlink:href="#DejaVuSans-2e" x="63.623047"/>
       <use xlink:href="#DejaVuSans-30" x="95.410156"/>
       <use xlink:href="#DejaVuSans-30" x="159.033203"/>
      </g>
     </g>
    </g>
   </g>
   <g id="line2d_17">
    <path d="M 73.832727 283.404149 
L 74.807666 276.414575 
L 76.107584 264.894509 
L 77.407502 251.125738 
L 79.0324 231.279153 
L 80.982277 204.628189 
L 87.806847 108.487237 
L 89.431744 89.89569 
L 90.731663 77.358376 
L 92.031581 67.239058 
L 93.006519 61.390308 
L 93.981458 57.126633 
L 94.631417 55.19522 
L 95.281376 54.007342 
L 95.606355 53.694724 
L 95.931335 53.570401 
L 96.256314 53.634566 
L 96.581294 53.887119 
L 96.906274 54.327668 
L 97.556233 55.76971 
L 98.206192 57.951709 
L 98.856151 60.860068 
L 99.831089 66.543681 
L 100.806028 73.74017 
L 102.105946 85.511706 
L 103.405864 99.498348 
L 105.030762 119.561855 
L 107.305618 151.045948 
L 113.15525 234.129286 
L 114.780147 253.613875 
L 116.080066 267.022669 
L 117.379984 278.129801 
L 118.354922 284.78106 
L 119.329861 289.887658 
L 119.97982 292.397658 
L 120.629779 294.17324 
L 121.279738 295.203339 
L 121.604717 295.436644 
L 121.929697 295.481538 
L 122.254676 295.337949 
L 122.579656 295.006102 
L 123.229615 293.779995 
L 123.879574 291.810855 
L 124.529533 289.110953 
L 125.504472 283.728937 
L 126.47941 276.817002 
L 127.454349 268.471984 
L 128.754267 255.320818 
L 130.379165 236.097881 
L 132.329042 209.94664 
L 136.228796 153.281227 
L 138.828632 117.346149 
L 140.45353 97.55302 
L 141.753448 83.837682 
L 143.053366 72.379106 
L 144.028305 65.440024 
L 145.003243 60.029279 
L 145.653202 57.309542 
L 146.303161 55.320167 
L 146.95312 54.073549 
L 147.2781 53.731383 
L 147.603079 53.577455 
L 147.928059 53.612004 
L 148.253038 53.834977 
L 148.578018 54.246025 
L 149.227977 55.629496 
L 149.877936 57.753797 
L 150.527895 60.605691 
L 151.502834 66.207686 
L 152.477772 73.327264 
L 153.77769 85.005426 
L 155.077609 98.911292 
L 156.702506 118.894573 
L 158.977363 150.310397 
L 164.826994 233.475264 
L 166.451892 253.044655 
L 167.75181 266.537396 
L 169.051728 277.74055 
L 170.026667 284.470322 
L 171.001605 289.659788 
L 171.651564 292.22688 
L 172.301523 294.060618 
L 172.951482 295.149575 
L 173.276462 295.412458 
L 173.601441 295.486966 
L 173.926421 295.372984 
L 174.2514 295.07069 
L 174.90136 293.903339 
L 175.551319 291.992187 
L 176.201278 289.349143 
L 177.176216 284.049524 
L 178.151155 277.215494 
L 179.126093 268.942797 
L 180.426011 255.877638 
L 182.050909 236.742505 
L 184.000786 210.663351 
L 187.575561 158.741117 
L 190.175397 122.27323 
L 192.125274 98.133254 
L 193.425192 84.335897 
L 194.725111 72.782904 
L 195.700049 65.766276 
L 196.674988 60.273415 
L 197.324947 57.496961 
L 197.974906 55.4497 
L 198.624865 54.14439 
L 198.949844 53.77269 
L 199.274824 53.589162 
L 199.599803 53.594094 
L 199.924783 53.787477 
L 200.249762 54.169011 
L 200.899722 55.493857 
L 201.549681 57.560377 
L 202.19964 60.355697 
L 203.174578 65.875859 
L 204.149517 72.918252 
L 205.449435 84.50259 
L 206.749353 98.327145 
L 208.374251 118.229432 
L 210.649107 149.575777 
L 216.498739 232.818975 
L 218.123636 252.472415 
L 219.423554 266.048583 
L 220.723473 277.347329 
L 221.698411 284.155356 
L 222.67335 289.427488 
L 223.323309 292.051574 
L 223.973268 293.943397 
L 224.623227 295.09117 
L 224.948206 295.38362 
L 225.273186 295.487741 
L 225.598165 295.40337 
L 225.923145 295.13064 
L 226.573104 294.02209 
L 227.223063 292.169 
L 227.873022 289.582916 
L 228.847961 284.365897 
L 229.822899 277.610034 
L 230.797838 269.409978 
L 232.097756 256.431328 
L 233.722654 237.384736 
L 235.672531 211.378671 
L 239.247305 159.48528 
L 241.847142 122.95089 
L 243.797019 98.716427 
L 245.096937 84.837581 
L 246.396855 73.190616 
L 247.371794 66.096713 
L 248.346732 60.521947 
L 248.996691 57.688882 
L 249.64665 55.583815 
L 250.296609 54.219863 
L 250.621589 53.818642 
L 250.946568 53.605523 
L 251.271548 53.580837 
L 251.596527 53.744623 
L 251.921507 54.096627 
L 252.571466 55.362797 
L 253.221425 57.371458 
L 253.871384 60.110096 
L 254.846323 65.548211 
L 255.821261 72.513149 
L 256.7962 80.907328 
L 258.096118 94.116886 
L 259.721016 113.399308 
L 261.670893 139.599156 
L 265.570647 196.27854 
L 268.170483 232.160442 
L 269.795381 251.897176 
L 271.095299 265.556249 
L 272.395217 276.950151 
L 273.370156 283.836171 
L 274.345094 289.190768 
L 274.995053 291.871746 
L 275.645012 293.821582 
L 276.294971 295.028127 
L 276.619951 295.350133 
L 276.94493 295.483862 
L 277.26991 295.429106 
L 277.594889 295.185949 
L 277.919869 294.754771 
L 278.569828 293.331331 
L 279.219787 291.167654 
L 279.869746 288.277222 
L 280.844685 282.619515 
L 281.819623 275.44743 
L 283.119541 263.70551 
L 284.419459 249.744473 
L 286.044357 229.70637 
L 288.319214 198.243835 
L 294.168845 115.134249 
L 295.793743 95.622637 
L 297.093661 82.187117 
L 298.393579 71.049432 
L 299.368518 64.373202 
L 300.343456 59.240256 
L 300.993415 56.712106 
L 301.643374 54.918041 
L 302.293333 53.869239 
L 302.618313 53.626536 
L 302.943292 53.572233 
L 303.268272 53.706417 
L 303.593251 54.028876 
L 304.24321 55.236322 
L 304.89317 57.187047 
L 305.543129 59.868896 
L 306.518067 65.224757 
L 307.493006 72.11197 
L 308.467944 80.434047 
L 309.767862 93.557943 
L 311.39276 112.753065 
L 313.342637 138.881513 
L 316.917412 190.82228 
L 319.517248 227.243986 
L 321.467125 251.31896 
L 322.767043 265.060413 
L 324.066962 276.549033 
L 325.0419 283.512781 
L 326.016839 288.949636 
L 326.666798 291.687404 
L 327.316757 293.695177 
L 327.966716 294.960447 
L 328.291695 295.311998 
L 328.616675 295.47533 
L 328.941654 295.45019 
L 329.266634 295.236617 
L 329.591613 294.834944 
L 330.241572 293.470092 
L 330.891532 291.36414 
L 331.541491 288.530207 
L 332.516429 282.954187 
L 333.491368 275.859101 
L 334.791286 264.210698 
L 336.091204 250.330607 
L 337.716102 230.372974 
L 339.990958 198.979093 
L 345.84059 115.788993 
L 347.465487 96.192818 
L 348.765405 82.673516 
L 350.065324 71.439946 
L 351.040262 64.685284 
L 352.015201 59.469534 
L 352.66516 56.884324 
L 353.315119 55.032125 
L 353.965078 53.924477 
L 354.290057 53.6522 
L 354.615037 53.568283 
L 354.940016 53.672858 
L 355.264996 53.965762 
L 355.914955 55.114436 
L 356.564914 57.007149 
L 357.214873 59.632109 
L 358.189812 64.905507 
L 359.16475 71.714732 
L 360.139689 79.964386 
L 361.439607 93.002115 
L 363.064505 112.109198 
L 365.014382 138.165241 
L 368.589156 190.078528 
L 371.188993 226.567695 
L 373.13887 250.73779 
L 374.438788 264.561094 
L 375.738706 276.14399 
L 376.713645 283.185198 
L 377.688583 288.704103 
L 378.338542 291.498554 
L 378.988501 293.564188 
L 379.63846 294.888134 
L 379.96344 295.269215 
L 380.288419 295.462144 
L 380.613399 295.466622 
L 380.938378 295.282641 
L 381.263358 294.910488 
L 381.913317 293.604278 
L 382.563276 291.55613 
L 383.213235 288.778807 
L 384.188174 283.284688 
L 385.163112 276.266873 
L 386.46303 264.712436 
L 387.762948 250.913825 
L 389.387846 231.03743 
L 391.337723 204.363163 
L 398.162293 108.258221 
L 398.487273 104.316083 
L 398.487273 104.316083 
" clip-path="url(#p55124ea593)" style="fill: none; stroke: #1f77b4; stroke-width: 1.5; stroke-linecap: square"/>
   </g>
   <g id="patch_3">
    <path d="M 57.6 307.584 
L 57.6 41.472 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
   <g id="patch_4">
    <path d="M 414.72 307.584 
L 414.72 41.472 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
   <g id="patch_5">
    <path d="M 57.6 307.584 
L 414.72 307.584 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
   <g id="patch_6">
    <path d="M 57.6 41.472 
L 414.72 41.472 
" style="fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square"/>
   </g>
  </g>
 </g>
 <defs>
  <clipPath id="p55124ea593">
   <rect x="57.6" y="41.472" width="357.12" height="266.112"/>
  </clipPath>
 </defs>
</svg>
\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 11826411828273527785,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"verbatim\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}The frequency is 6.28, shift is -1.12\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"p = plot($\\\\sin(x @(q) + @(a))$, ($x$, 0, 6.28), fig=p);\\nf\\\"The frequency is {q}, shift is {a}\\\";\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 7149254973269430401,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 4519195784007382321,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"If you want to see how this plot changes when you change the frequency, you can add a slider output cell which is connected to the $q$ variable. Note how in the \\\\verb|slider| function call below, you pass the variable name as a string. The initial value of the slider is set to the value to which $q$ was initialised above.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"If you want to see how this plot changes when you change the frequency, you can add a slider output cell which is connected to the $q$ variable. Note how in the \\\\verb|slider| function call below, you pass the variable name as a string. The initial value of the slider is set to the value to which $q$ was initialised above.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 3581638892777768553,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 1156728382899005335,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"slider\",\n\t\t\t\t\t\"source\": \"{\\\"value\\\": 3, \\\"variable\\\": \\\"q\\\", \\\"min_value\\\": 0.1, \\\"max_value\\\": 10, \\\"step_size\\\": 0.01}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"slider(\\\"q\\\", value=q, min_value=0.1, max_value=10, step_size=0.01);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 11410311769016249762,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 17353224710871695875,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"Try dragging the slider and note how the plot updates automatically. The way in which this works internally is that the server analyses each input cell, and informs the notebook frontend about any variable dependencies. When you change the slider, the notebook re-runs the cells which depend on the variable that was just changed. Note how statements which contain assignments (like that \\\\verb|q=3| line above) are skipped automatically (otherwise nothing would change).\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"Try dragging the slider and note how the plot updates automatically. The way in which this works internally is that the server analyses each input cell, and informs the notebook frontend about any variable dependencies. When you change the slider, the notebook re-runs the cells which depend on the variable that was just changed. Note how statements which contain assignments (like that \\\\verb|q=3| line above) are skipped automatically (otherwise nothing would change).\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 13098559679874341918,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9314052843529312049,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"You can add another slider, to change the value of the phase shift $a$; this works in exactly the same way:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"You can add another slider, to change the value of the phase shift $a$; this works in exactly the same way:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 14700336434814752363,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 12110886832223130205,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"slider\",\n\t\t\t\t\t\"source\": \"{\\\"value\\\": 0.3, \\\"variable\\\": \\\"a\\\", \\\"min_value\\\": -10, \\\"max_value\\\": 10, \\\"step_size\\\": 0.01}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"slider(\\\"a\\\", value=a, min_value=-10, max_value=10, step_size=0.01);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 4346203028239312843,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 8637098041923701832,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"These slider-triggered variable changes influence all cells, not only those which contain plots. As an example, let us use the $q$ variable to integrate the expression $x^q$:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"These slider-triggered variable changes influence all cells, not only those which contain plots. As an example, let us use the $q$ variable to integrate the expression $x^q$:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 14670035857985931341,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"from cdb.sympy.calculus import *\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 11636063620617060392,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 8486561892332675196,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 3617029038377795103,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"0.298507(x)**(3.35)\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}0.298507\\\\,{x}^{3.35\\\\,}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"integrate($x**@(q)$, $x$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 1043744773805189827,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 5728688999242537346,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"If you drag the slider for $q$, you will see how this expression changes.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"If you drag the slider for $q$, you will see how this expression changes.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 5711519982137323880,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"\"\n\t\t}\n\t],\n\t\"description\": \"Cadabra JSON notebook format\",\n\t\"flags\": {\n\t\t\"hide_input_cells\": false\n\t},\n\t\"version\": 1.0\n}\n"
  },
  {
    "path": "examples/sphere.cnb",
    "content": "{\n\t\"cell_id\": 16777795828450301657,\n\t\"cells\": [\n\t\t{\n\t\t\t\"cell_id\": 2055669637767503792,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 13957550933732758251,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\section*{Two-sphere curvature}\\n\\nThis notebook computes the curvature of a 2-sphere by computing connection coefficients and the\\nRiemann tensor components.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\section*{Two-sphere curvature}\\n\\nThis notebook computes the curvature of a 2-sphere by computing connection coefficients and the\\nRiemann tensor components.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 17224968359846383081,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 3395695260720640612,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property Coordinate attached to~}\\\\left[\\\\theta, \\\\discretionary{}{}{}\\\\varphi\\\\right].\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 10590307973119183666,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property Indices(position=fixed, values=\\\\{{\\\\varphi}\\n, {\\\\theta}\\n\\\\}) attached to~}\\\\left[\\\\alpha, \\\\discretionary{}{}{}\\\\beta, \\\\discretionary{}{}{}\\\\gamma, \\\\discretionary{}{}{}\\\\delta, \\\\discretionary{}{}{}\\\\rho, \\\\discretionary{}{}{}\\\\sigma, \\\\discretionary{}{}{}\\\\mu, \\\\discretionary{}{}{}\\\\nu, \\\\discretionary{}{}{}\\\\lambda\\\\right].\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 738520283293858566,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property PartialDerivative attached to~}\\\\backslash\\\\texttt{partial}\\\\{\\\\#\\\\}.\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"{\\\\theta, \\\\varphi}::Coordinate;\\n{\\\\alpha, \\\\beta, \\\\gamma, \\\\delta, \\\\rho, \\\\sigma, \\\\mu, \\\\nu, \\\\lambda}::Indices(values={\\\\varphi, \\\\theta}, position=fixed);\\n\\\\partial{#}::PartialDerivative;\\ng_{\\\\alpha\\\\beta}::Metric.\\ng^{\\\\alpha\\\\beta}::InverseMetric.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 6701522146513425631,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 14415998209061459251,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 11276829403820812076,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"{g_{\\\\theta \\\\theta} = (r)**2, g_{\\\\varphi \\\\varphi} = (r)**2 (\\\\sin(\\\\theta))**2, g^{\\\\varphi \\\\varphi} = ((r)**2 (\\\\sin(\\\\theta))**2)**(-1), g^{\\\\theta \\\\theta} = (r)**(-2)}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\left[g_{\\\\theta \\\\theta} = {r}^{2\\\\,}, \\\\discretionary{}{}{}g_{\\\\varphi \\\\varphi} = {r}^{2\\\\,} {\\\\left(\\\\sin{\\\\theta}\\\\right)}^{2\\\\,}, \\\\discretionary{}{}{}g^{\\\\varphi \\\\varphi} = {\\\\left({r}^{2\\\\,} {\\\\left(\\\\sin{\\\\theta}\\\\right)}^{2\\\\,}\\\\right)}^{-\\\\,1}, \\\\discretionary{}{}{}g^{\\\\theta \\\\theta} = {r}^{-2\\\\,}\\\\right]\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"sphe:={ g_{\\\\theta\\\\theta} = r**2,\\n         g_{\\\\varphi\\\\varphi} = r**2 \\\\sin(\\\\theta)**2 }.\\ncomplete(sphe, $g^{\\\\alpha\\\\beta}$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 12041561684483558681,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 16345076722768451795,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"The Christoffel symbols are given in terms of the metric by the following expression.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"The Christoffel symbols are given in terms of the metric by the following expression.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 5739347688053250052,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 11572072212632762650,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 17078813454439888343,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\Gamma^{\\\\alpha}_{\\\\mu \\\\nu} =  1/2 g^{\\\\alpha \\\\beta} (\\\\partial_{\\\\nu}(g_{\\\\beta \\\\mu}) + \\\\partial_{\\\\mu}(g_{\\\\beta \\\\nu})-\\\\partial_{\\\\beta}(g_{\\\\mu \\\\nu}))\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\Gamma^{\\\\alpha}\\\\,_{\\\\mu \\\\nu} = \\\\frac{1}{2}\\\\,g^{\\\\alpha \\\\beta} \\\\left(\\\\partial_{\\\\nu}{g_{\\\\beta \\\\mu}}\\\\discretionary{}{}{}+\\\\partial_{\\\\mu}{g_{\\\\beta \\\\nu}}\\\\discretionary{}{}{}-\\\\,\\\\partial_{\\\\beta}{g_{\\\\mu \\\\nu}}\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ch:= \\\\Gamma^{\\\\alpha}_{\\\\mu\\\\nu} = 1/2 g^{\\\\alpha\\\\beta} ( \\\\partial_{\\\\nu}{g_{\\\\beta\\\\mu}}\\n                                                      +\\\\partial_{\\\\mu}{g_{\\\\beta\\\\nu}}\\n                                                      -\\\\partial_{\\\\beta}{g_{\\\\mu\\\\nu}} );\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 16925562691388637166,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 8548215356720376193,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"We evaluate the components using \\\\verb|evaluate| and then massage them a bit further using sympy.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"We evaluate the components using \\\\verb|evaluate| and then massage them a bit further using sympy.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 4150928110651293535,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 11205588746198320978,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 6327868163475886027,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\Gamma^{\\\\alpha}_{\\\\mu \\\\nu} = \\\\components_{\\\\mu \\\\nu}^{\\\\alpha}({{\\\\varphi, \\\\theta, \\\\varphi} = (\\\\tan(\\\\theta))**(-1), {\\\\theta, \\\\varphi, \\\\varphi} = (\\\\tan(\\\\theta))**(-1), {\\\\varphi, \\\\varphi, \\\\theta} = -\\\\sin(\\\\theta) \\\\cos(\\\\theta)})\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\Gamma^{\\\\alpha}\\\\,_{\\\\mu \\\\nu} = \\\\square{}_{\\\\mu}{}_{\\\\nu}{}^{\\\\alpha}\\\\left\\\\{\\\\begin{aligned}\\\\square{}_{\\\\varphi}{}_{\\\\theta}{}^{\\\\varphi}& = \\\\square{}_{\\\\theta}{}_{\\\\varphi}{}^{\\\\varphi} = {\\\\left(\\\\tan{\\\\theta}\\\\right)}^{-\\\\,1}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\varphi}{}_{\\\\varphi}{}^{\\\\theta}& = -\\\\,\\\\sin{\\\\theta} \\\\cos{\\\\theta}\\\\\\\\[-.5ex]\\n\\\\end{aligned}\\\\right\\\\}\\n\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"evaluate(ch, sphe, rhsonly=True)\\nmap_sympy(ch, \\\"expand_trig\\\");\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 14521766346323177104,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 4046823456510337118,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"The Riemann tensor is given in terms of the Christoffel symbols by the expression below. \"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"The Riemann tensor is given in terms of the Christoffel symbols by the expression below. \"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 3944858388510727404,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9834398685418498922,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 1637500651299440844,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"R^{\\\\rho}_{\\\\sigma \\\\mu \\\\nu} = \\\\partial_{\\\\mu}(\\\\Gamma^{\\\\rho}_{\\\\sigma \\\\nu})-\\\\partial_{\\\\nu}(\\\\Gamma^{\\\\rho}_{\\\\sigma \\\\mu}) + \\\\Gamma^{\\\\rho}_{\\\\beta \\\\mu} \\\\Gamma^{\\\\beta}_{\\\\sigma \\\\nu}-\\\\Gamma^{\\\\rho}_{\\\\beta \\\\nu} \\\\Gamma^{\\\\beta}_{\\\\sigma \\\\mu}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}R^{\\\\rho}\\\\,_{\\\\sigma \\\\mu \\\\nu} = \\\\partial_{\\\\mu}{\\\\Gamma^{\\\\rho}\\\\,_{\\\\sigma \\\\nu}}\\\\discretionary{}{}{}-\\\\,\\\\partial_{\\\\nu}{\\\\Gamma^{\\\\rho}\\\\,_{\\\\sigma \\\\mu}}\\\\discretionary{}{}{}+\\\\Gamma^{\\\\rho}\\\\,_{\\\\beta \\\\mu} \\\\Gamma^{\\\\beta}\\\\,_{\\\\sigma \\\\nu}\\\\discretionary{}{}{}-\\\\,\\\\Gamma^{\\\\rho}\\\\,_{\\\\beta \\\\nu} \\\\Gamma^{\\\\beta}\\\\,_{\\\\sigma \\\\mu}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 3444314515231337007,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 12674395542720681939,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"R^{\\\\rho}_{\\\\sigma \\\\mu \\\\nu} = \\\\components_{\\\\sigma \\\\nu}^{\\\\rho}_{\\\\mu}({{\\\\varphi, \\\\varphi, \\\\theta, \\\\theta} = (\\\\sin(\\\\theta))**2, {\\\\theta, \\\\varphi, \\\\varphi, \\\\theta} = -1, {\\\\varphi, \\\\theta, \\\\theta, \\\\varphi} = -(\\\\sin(\\\\theta))**2, {\\\\theta, \\\\theta, \\\\varphi, \\\\varphi} = 1})\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}R^{\\\\rho}\\\\,_{\\\\sigma \\\\mu \\\\nu} = \\\\square{}_{\\\\sigma}{}_{\\\\nu}{}^{\\\\rho}{}_{\\\\mu}\\\\left\\\\{\\\\begin{aligned}\\\\square{}_{\\\\varphi}{}_{\\\\varphi}{}^{\\\\theta}{}_{\\\\theta}& = {\\\\left(\\\\sin{\\\\theta}\\\\right)}^{2\\\\,}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{\\\\varphi}{}^{\\\\varphi}{}_{\\\\theta}& = -\\\\,1\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\varphi}{}_{\\\\theta}{}^{\\\\theta}{}_{\\\\varphi}& = -\\\\,{\\\\left(\\\\sin{\\\\theta}\\\\right)}^{2\\\\,}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{\\\\theta}{}^{\\\\varphi}{}_{\\\\varphi}& = 1\\\\\\\\[-.5ex]\\n\\\\end{aligned}\\\\right\\\\}\\n\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"rm:= R^{\\\\rho}_{\\\\sigma\\\\mu\\\\nu} = +\\\\partial_{\\\\mu}{\\\\Gamma^{\\\\rho}_{\\\\sigma\\\\nu}}\\n                           -\\\\partial_{\\\\nu}{\\\\Gamma^{\\\\rho}_{\\\\sigma\\\\mu}}\\n                           +\\\\Gamma^{\\\\rho}_{\\\\beta\\\\mu} \\\\Gamma^{\\\\beta}_{\\\\sigma\\\\nu}\\n                           -\\\\Gamma^{\\\\rho}_{\\\\beta\\\\nu} \\\\Gamma^{\\\\beta}_{\\\\sigma\\\\mu};\\n\\nsubstitute(rm, ch)\\nevaluate(rm, sphe, rhsonly=True);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 3547228292253364796,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 13312641374220534483,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"From here we can continue to compute the Ricci tensor and scalar,\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"From here we can continue to compute the Ricci tensor and scalar,\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 6616744564023228987,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 6371909193127037513,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 17481774231181965956,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"R_{\\\\sigma \\\\nu} = R^{\\\\rho}_{\\\\sigma \\\\rho \\\\nu}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}R_{\\\\sigma \\\\nu} = R^{\\\\rho}\\\\,_{\\\\sigma \\\\rho \\\\nu}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 14276938888933778275,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 16756492102576180720,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"R_{\\\\sigma \\\\nu} = \\\\components_{\\\\sigma \\\\nu}({{\\\\varphi, \\\\varphi} = (\\\\sin(\\\\theta))**2, {\\\\theta, \\\\theta} = 1})\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}R_{\\\\sigma \\\\nu} = \\\\square{}_{\\\\sigma}{}_{\\\\nu}\\\\left\\\\{\\\\begin{aligned}\\\\square{}_{\\\\varphi}{}_{\\\\varphi}& = {\\\\left(\\\\sin{\\\\theta}\\\\right)}^{2\\\\,}\\\\\\\\[-.5ex]\\n\\\\square{}_{\\\\theta}{}_{\\\\theta}& = 1\\\\\\\\[-.5ex]\\n\\\\end{aligned}\\\\right\\\\}\\n\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ricci:= R_{\\\\sigma\\\\nu} = R^{\\\\rho}_{\\\\sigma\\\\rho\\\\nu};\\nsubstitute(ricci, rm)\\nevaluate(ricci, sphe, rhsonly=True);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 7170269953294657745,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 64451742489002115,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 9520879522459457044,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"R = R_{\\\\sigma \\\\nu} g^{\\\\sigma \\\\nu}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}R = R_{\\\\sigma \\\\nu} g^{\\\\sigma \\\\nu}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 5424619097004617193,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 11033875352449550387,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"R = 2(r)**(-2)\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}R = 2\\\\,{r}^{-2\\\\,}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"R:= R = R_{\\\\sigma\\\\nu} g^{\\\\sigma\\\\nu};\\nsubstitute(R, ricci)\\nevaluate(R, sphe, rhsonly=True);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 10143300888725656499,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 12877062134680465862,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"The main time computing this is spent in the rather inefficient \\\\verb|sympy| bridge. You can see timing information\\nby querying the \\\\verb|server| object for the \\\\verb|totals| list.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"The main time computing this is spent in the rather inefficient \\\\verb|sympy| bridge. You can see timing information\\nby querying the \\\\verb|server| object for the \\\\verb|totals| list.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 2141517437239533536,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 7222895749640028916,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"{}$\\\\big[$\\\\verb|cadabra::collect_terms: 21 calls, 0 steps, 0 ms|,\\\\discretionary{}{}{} \\\\verb|cadabra::complete: 1 calls, 0 steps, 268 ms|,\\\\discretionary{}{}{} \\\\verb|cadabra::evaluate: 4 calls, 0 steps, 2212 ms|,\\\\discretionary{}{}{} \\\\verb|cadabra::map_sympy: 1 calls, 0 steps, 20 ms|,\\\\discretionary{}{}{} \\\\verb|cadabra::simplify: 49 calls, 0 steps, 2209 ms|,\\\\discretionary{}{}{} \\\\verb|cadabra::substitute: 3 calls, 0 steps, 5 ms|,\\\\discretionary{}{}{} \\\\verb|scalar_backend: 49 calls, 0 steps, 2209 ms|,\\\\discretionary{}{}{} \\\\verb|sympy: 49 calls, 0 steps, 2209 ms|$\\\\big]$\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"server.totals();\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 14471520080935663166,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"\"\n\t\t}\n\t],\n\t\"description\": \"Cadabra JSON notebook format\",\n\t\"flags\": {\n\t\t\"hide_input_cells\": false\n\t},\n\t\"version\": 1.0\n}\n"
  },
  {
    "path": "examples/spinors.cnb",
    "content": "{\n\t\"cells\" : \n\t[\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property DiracBar to~}\\\\bar{\\\\#}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Spinor to~}\\\\psi.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property GammaMatrix to~}\\\\Gamma\\\\left(\\\\#\\\\right).\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"\\\\bar{\\\\Gamma^{m n p} \\\\psi}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\bar{\\\\Gamma^{m n p} \\\\psi}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"\\\\bar{#}::DiracBar;\\n\\\\psi::Spinor(dimension=10);\\n\\\\Gamma{#}::GammaMatrix;\\nex:=\\\\bar{\\\\Gamma^{m n p} \\\\psi};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"\\\\bar{\\\\psi} \\\\Gamma^{m n p}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\bar{\\\\psi} \\\\Gamma^{m n p}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"expand_diracbar(ex);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\\\\xi::Spinor(dimension =4, type=Dirac).\\n\\n\\\\bar{#}::DiracBar.\\n\\\\xi::Depends(\\\\bar).\\n\\\\gamma_{#}::GammaMatrix(metric=\\\\delta).\\n\\\\delta{#}::KroneckerDelta.\\n\\n\\\\gamma{#}::Depends(\\\\bar).\\n\\n{\\\\xi, \\\\phi}::Commuting.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"\\\\bar{\\\\gamma_{m} \\\\xi \\\\phi}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\bar{\\\\gamma_{m} \\\\xi \\\\phi}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"\\\\bar{\\\\gamma_{m} \\\\xi \\\\phi}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\bar{\\\\gamma_{m} \\\\xi \\\\phi}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"test := \\\\bar{\\\\gamma_{m}\\\\xi \\\\phi};\\nexpand_diracbar(test);  \"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"\\\\bar{\\\\gamma_{m} \\\\xi \\\\phi}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\bar{\\\\gamma_{m} \\\\xi \\\\phi}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"\\\\phi \\\\bar{\\\\gamma_{m} \\\\xi}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\phi \\\\bar{\\\\gamma_{m} \\\\xi}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"test := \\\\bar{\\\\gamma_{m}\\\\xi \\\\phi};\\nunwrap(test);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"\\\\bar{\\\\gamma_{m} \\\\xi \\\\phi}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\bar{\\\\gamma_{m} \\\\xi \\\\phi}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"\\\\phi \\\\bar{\\\\gamma_{m} \\\\xi}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\phi \\\\bar{\\\\gamma_{m} \\\\xi}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"-\\\\phi \\\\bar{\\\\xi} \\\\gamma_{m}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}-\\\\phi \\\\bar{\\\\xi} \\\\gamma_{m}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"test := \\\\bar{\\\\gamma_{m}\\\\xi \\\\phi};\\nunwrap(test);\\nexpand_diracbar(test);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1\n}\n"
  },
  {
    "path": "examples/string_states.cnb",
    "content": "{\n\t\"cell_id\": 1429147239427199861,\n\t\"cells\": [\n\t\t{\n\t\t\t\"cell_id\": 13967334573852177512,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 14315449601302494856,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\section*{Bosonic string oscillator algebra}\\n\\nThe computation below shows how you can do oscillator algebra for the (open) bosonic string.\\nWe illustrate this by the classic computation which shows that you can construct a state\\nwhich satisfies all the constraints but has negative norm when $d>26$. This is not a terribly difficult\\ncomputation with pen-and-paper, but it is tricky to do with many other computer algebra systems (and\\nif they handle it, their output will not look as nice as what you see below).\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\section*{Bosonic string oscillator algebra}\\n\\nThe computation below shows how you can do oscillator algebra for the (open) bosonic string.\\nWe illustrate this by the classic computation which shows that you can construct a state\\nwhich satisfies all the constraints but has negative norm when $d>26$. This is not a terribly difficult\\ncomputation with pen-and-paper, but it is tricky to do with many other computer algebra systems (and\\nif they handle it, their output will not look as nice as what you see below).\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 6404889668989828522,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 12219498635224641087,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property LaTeXForm attached to {\\\\texttt{\\\\backslash{}vac}}.}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 6622951027121726959,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property LaTeXForm attached to {\\\\texttt{\\\\backslash{}state}}.}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"\\\\vac::LaTeXForm(\\\"|k\\\\rangle\\\");\\n\\\\state{A??}::LaTeXForm(\\\"|\\\", A??, \\\"\\\\rangle\\\");\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 1164197569130214523,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"def post_process(ex):\\n   substitute(ex, $\\\\sqrt{2} \\\\sqrt{2} -> 2$)\\n   collect_terms(ex)\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 3379448617455362952,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 1273242589213112505,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"We first need to define the various objects, mostly non-commuting operators.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"We first need to define the various objects, mostly non-commuting operators.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 13450001497016369830,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 17854114525733755598,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property SelfNonCommuting attached to~}\\\\alpha_{n}\\\\,^{\\\\mu}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 7439065201232637219,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property NonCommuting attached to~}\\\\left[\\\\alpha_{n}\\\\,^{\\\\mu}, \\\\discretionary{}{}{}|k\\\\rangle\\\\right].\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"\\\\alpha_{n}^{\\\\mu}::SelfNonCommuting;\\n{\\\\alpha_{n}^{\\\\mu}, \\\\vac}::NonCommuting;\\n{\\\\mu,\\\\nu,\\\\rho}::Integer(0..d-1).\\n{\\\\mu,\\\\nu,\\\\rho}::Indices.\\n{m,n}::Integer.\\n{m,n}::Symbol.\\n\\\\delta{#}::KroneckerDelta.\\n\\\\delta{#}::Diagonal.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 6412040814128610434,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 17433227972433846380,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"The trial state is given by $|\\\\chi\\\\rangle = |\\\\chi_1\\\\rangle + A |\\\\chi_2\\\\rangle + B |\\\\chi_3\\\\rangle$ with the three terms\\ngiven by the following expressions:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"The trial state is given by $|\\\\chi\\\\rangle = |\\\\chi_1\\\\rangle + A |\\\\chi_2\\\\rangle + B |\\\\chi_3\\\\rangle$ with the three terms\\ngiven by the following expressions:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 14553961322849869678,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 7121571075127984182,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 5891641989506425649,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\alpha_{-1}^{\\\\mu} \\\\alpha_{-1}^{\\\\mu} \\\\vac\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\alpha_{-\\\\,1}\\\\,^{\\\\mu} \\\\alpha_{-\\\\,1}\\\\,^{\\\\mu} |k\\\\rangle\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 11102694686377995133,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 2247540854261473185,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\alpha_{0}^{\\\\mu} \\\\alpha_{-2}^{\\\\mu} \\\\vac\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\alpha_{0\\\\,}\\\\,^{\\\\mu} \\\\alpha_{-2\\\\,}\\\\,^{\\\\mu} |k\\\\rangle\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 3700299009548757784,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 11941757822541534415,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\alpha_{0}^{\\\\mu} \\\\alpha_{-1}^{\\\\mu} \\\\alpha_{0}^{\\\\nu} \\\\alpha_{-1}^{\\\\nu} \\\\vac\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\alpha_{0\\\\,}\\\\,^{\\\\mu} \\\\alpha_{-\\\\,1}\\\\,^{\\\\mu} \\\\alpha_{0\\\\,}\\\\,^{\\\\nu} \\\\alpha_{-\\\\,1}\\\\,^{\\\\nu} |k\\\\rangle\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"chi1:= \\\\alpha_{-1}^{\\\\mu} \\\\alpha_{-1}^{\\\\mu} \\\\vac;\\nchi2:= \\\\alpha_{0}^\\\\mu \\\\alpha_{-2}^\\\\mu \\\\vac;\\nchi3:= \\\\alpha_{0}^{\\\\mu} \\\\alpha_{-1}^{\\\\mu} \\\\alpha_{0}^{\\\\nu} \\\\alpha_{-1}^{\\\\nu})\\\\vac;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 11041561750698255632,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 538669882447400463,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"The main ingredient to verify that the $L_1$ and $L_2$ Virasoro constraints hold is, of course, the commutation relations\\nbetween the $\\\\alpha_{m}^\\\\mu$ operators. What we want to do is commute all annihilation operators to the right until they hit\\nthe momentum eigenstate $|k\\\\rangle$. Note that in the rule below, you need to write the indices on $\\\\delta_{m, -n}$ using two separate subscripts, otherwise\\nyou get $m-n$ as index.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"The main ingredient to verify that the $L_1$ and $L_2$ Virasoro constraints hold is, of course, the commutation relations\\nbetween the $\\\\alpha_{m}^\\\\mu$ operators. What we want to do is commute all annihilation operators to the right until they hit\\nthe momentum eigenstate $|k\\\\rangle$. Note that in the rule below, you need to write the indices on $\\\\delta_{m, -n}$ using two separate subscripts, otherwise\\nyou get $m-n$ as index.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 12410793654881196408,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 4212629900660971514,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 12803967079591093387,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"{\\\\alpha_{m}^{\\\\mu} \\\\alpha_{n}^{\\\\nu} with m > n -> \\\\alpha_{n}^{\\\\nu} \\\\alpha_{m}^{\\\\mu} + m \\\\delta_{m -n} \\\\delta^{\\\\mu \\\\nu}, \\\\alpha_{m}^{\\\\mu} \\\\vac with m > 0 -> 0, \\\\alpha_{0}^{\\\\mu} \\\\vac -> 2**( 1/2 ) k^{\\\\mu} \\\\vac, k^{\\\\mu} k^{\\\\mu} -> -1}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\left[\\\\alpha_{m}\\\\,^{\\\\mu} \\\\alpha_{n}\\\\,^{\\\\nu}\\\\quad\\\\text{with}\\\\quad{}m > n \\\\rightarrow \\\\alpha_{n}\\\\,^{\\\\nu} \\\\alpha_{m}\\\\,^{\\\\mu}\\\\discretionary{}{}{}+m \\\\delta_{m -\\\\,n} \\\\delta^{\\\\mu \\\\nu}, \\\\discretionary{}{}{}\\\\alpha_{m}\\\\,^{\\\\mu} |k\\\\rangle\\\\quad\\\\text{with}\\\\quad{}m > 0\\\\, \\\\rightarrow 0\\\\,, \\\\discretionary{}{}{}\\\\alpha_{0\\\\,}\\\\,^{\\\\mu} |k\\\\rangle \\\\rightarrow \\\\sqrt{2\\\\,} k^{\\\\mu} |k\\\\rangle, \\\\discretionary{}{}{}k^{\\\\mu} k^{\\\\mu} \\\\rightarrow -\\\\,1\\\\right]\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"rl:= { \\\\alpha_{m}^{\\\\mu} \\\\alpha_{n}^{\\\\nu} | m > n -> \\\\alpha_{n}^{\\\\nu} \\\\alpha_{m}^{\\\\mu} +  m\\\\delta_{m}_{-n} \\\\delta^{\\\\mu\\\\nu},\\n       \\\\alpha_{m}^{\\\\mu} \\\\vac | m > 0 -> 0, \\n       \\\\alpha_{0}^{\\\\mu} \\\\vac -> \\\\sqrt{2} k^{\\\\mu} \\\\vac, k^{\\\\mu} k^{\\\\mu} -> -1 };\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 9821481013280912463,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 18049050574841262273,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"Obviously we need to do this substitution a number of times, and distribute any factors over sums. We will see\\nshortly how to automate this with \\\\verb|converge|.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"Obviously we need to do this substitution a number of times, and distribute any factors over sums. We will see\\nshortly how to automate this with \\\\verb|converge|.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 6199583088169241563,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 11227807743211576698,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\subsection*{Imposing the constraints}\\n\\nThe first thing to do is to impose the Virasoro constraints on the state $|\\\\chi\\\\rangle$, which will pin down the relative coefficients of the three terms in that state. The $L_m$ Virasoro generators are given by infinite sums. The function below constructs part of that sum explicitly. Of course, you would be a bit more clever when doing things with pen and paper:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\subsection*{Imposing the constraints}\\n\\nThe first thing to do is to impose the Virasoro constraints on the state $|\\\\chi\\\\rangle$, which will pin down the relative coefficients of the three terms in that state. The $L_m$ Virasoro generators are given by infinite sums. The function below constructs part of that sum explicitly. Of course, you would be a bit more clever when doing things with pen and paper:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 3025697820827724481,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"def L(m):\\n\\t\\\"\\\"\\\" Construct the m-th Virasoro generator in terms of creation/annihilation operators \\\"\\\"\\\"\\n\\tins=''\\n\\tfor n in range(-10,10):\\n\\t\\tif n!=-10:\\n\\t\\t\\tins+='+ '\\n\\t\\tins += r'1/2 \\\\alpha_{'+str(m-n)+r'}^{\\\\mu} \\\\alpha_{'+str(n)+r'}^{\\\\mu}'\\n\\tex=Ex(ins)\\n\\treturn ex\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 13405602649577653444,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 4905468025411140223,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"Here is what $L_0$ looks like; the other operators are similar:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"Here is what $L_0$ looks like; the other operators are similar:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 14265697909429561707,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 12509002642855599097,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 10192848523477307335,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \" 1/2 \\\\alpha_{10}^{\\\\mu} \\\\alpha_{-10}^{\\\\mu} +  1/2 \\\\alpha_{9}^{\\\\mu} \\\\alpha_{-9}^{\\\\mu} +  1/2 \\\\alpha_{8}^{\\\\mu} \\\\alpha_{-8}^{\\\\mu} +  1/2 \\\\alpha_{7}^{\\\\mu} \\\\alpha_{-7}^{\\\\mu} +  1/2 \\\\alpha_{6}^{\\\\mu} \\\\alpha_{-6}^{\\\\mu} +  1/2 \\\\alpha_{5}^{\\\\mu} \\\\alpha_{-5}^{\\\\mu} +  1/2 \\\\alpha_{4}^{\\\\mu} \\\\alpha_{-4}^{\\\\mu} +  1/2 \\\\alpha_{3}^{\\\\mu} \\\\alpha_{-3}^{\\\\mu} +  1/2 \\\\alpha_{2}^{\\\\mu} \\\\alpha_{-2}^{\\\\mu} +  1/2 \\\\alpha_{1}^{\\\\mu} \\\\alpha_{-1}^{\\\\mu} +  1/2 \\\\alpha_{0}^{\\\\mu} \\\\alpha_{0}^{\\\\mu} +  1/2 \\\\alpha_{-1}^{\\\\mu} \\\\alpha_{1}^{\\\\mu} +  1/2 \\\\alpha_{-2}^{\\\\mu} \\\\alpha_{2}^{\\\\mu} +  1/2 \\\\alpha_{-3}^{\\\\mu} \\\\alpha_{3}^{\\\\mu} +  1/2 \\\\alpha_{-4}^{\\\\mu} \\\\alpha_{4}^{\\\\mu} +  1/2 \\\\alpha_{-5}^{\\\\mu} \\\\alpha_{5}^{\\\\mu} +  1/2 \\\\alpha_{-6}^{\\\\mu} \\\\alpha_{6}^{\\\\mu} +  1/2 \\\\alpha_{-7}^{\\\\mu} \\\\alpha_{7}^{\\\\mu} +  1/2 \\\\alpha_{-8}^{\\\\mu} \\\\alpha_{8}^{\\\\mu} +  1/2 \\\\alpha_{-9}^{\\\\mu} \\\\alpha_{9}^{\\\\mu}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\frac{1}{2}\\\\,\\\\alpha_{10\\\\,}\\\\,^{\\\\mu} \\\\alpha_{-10\\\\,}\\\\,^{\\\\mu}\\\\discretionary{}{}{}+\\\\frac{1}{2}\\\\,\\\\alpha_{9\\\\,}\\\\,^{\\\\mu} \\\\alpha_{-9\\\\,}\\\\,^{\\\\mu}\\\\discretionary{}{}{}+\\\\frac{1}{2}\\\\,\\\\alpha_{8\\\\,}\\\\,^{\\\\mu} \\\\alpha_{-8\\\\,}\\\\,^{\\\\mu}\\\\discretionary{}{}{}+\\\\frac{1}{2}\\\\,\\\\alpha_{7\\\\,}\\\\,^{\\\\mu} \\\\alpha_{-7\\\\,}\\\\,^{\\\\mu}\\\\discretionary{}{}{}+\\\\frac{1}{2}\\\\,\\\\alpha_{6\\\\,}\\\\,^{\\\\mu} \\\\alpha_{-6\\\\,}\\\\,^{\\\\mu}\\\\discretionary{}{}{}+\\\\frac{1}{2}\\\\,\\\\alpha_{5\\\\,}\\\\,^{\\\\mu} \\\\alpha_{-5\\\\,}\\\\,^{\\\\mu}\\\\discretionary{}{}{}+\\\\frac{1}{2}\\\\,\\\\alpha_{4\\\\,}\\\\,^{\\\\mu} \\\\alpha_{-4\\\\,}\\\\,^{\\\\mu}\\\\discretionary{}{}{}+\\\\frac{1}{2}\\\\,\\\\alpha_{3\\\\,}\\\\,^{\\\\mu} \\\\alpha_{-3\\\\,}\\\\,^{\\\\mu}\\\\discretionary{}{}{}+\\\\frac{1}{2}\\\\,\\\\alpha_{2\\\\,}\\\\,^{\\\\mu} \\\\alpha_{-2\\\\,}\\\\,^{\\\\mu}\\\\discretionary{}{}{}+\\\\frac{1}{2}\\\\,\\\\alpha_{1}\\\\,^{\\\\mu} \\\\alpha_{-\\\\,1}\\\\,^{\\\\mu}\\\\discretionary{}{}{}+\\\\frac{1}{2}\\\\,\\\\alpha_{0\\\\,}\\\\,^{\\\\mu} \\\\alpha_{0\\\\,}\\\\,^{\\\\mu}\\\\discretionary{}{}{}+\\\\frac{1}{2}\\\\,\\\\alpha_{-\\\\,1}\\\\,^{\\\\mu} \\\\alpha_{1}\\\\,^{\\\\mu}\\\\discretionary{}{}{}+\\\\frac{1}{2}\\\\,\\\\alpha_{-2\\\\,}\\\\,^{\\\\mu} \\\\alpha_{2\\\\,}\\\\,^{\\\\mu}\\\\discretionary{}{}{}+\\\\frac{1}{2}\\\\,\\\\alpha_{-3\\\\,}\\\\,^{\\\\mu} \\\\alpha_{3\\\\,}\\\\,^{\\\\mu}\\\\discretionary{}{}{}+\\\\frac{1}{2}\\\\,\\\\alpha_{-4\\\\,}\\\\,^{\\\\mu} \\\\alpha_{4\\\\,}\\\\,^{\\\\mu}\\\\discretionary{}{}{}+\\\\frac{1}{2}\\\\,\\\\alpha_{-5\\\\,}\\\\,^{\\\\mu} \\\\alpha_{5\\\\,}\\\\,^{\\\\mu}\\\\discretionary{}{}{}+\\\\frac{1}{2}\\\\,\\\\alpha_{-6\\\\,}\\\\,^{\\\\mu} \\\\alpha_{6\\\\,}\\\\,^{\\\\mu}\\\\discretionary{}{}{}+\\\\frac{1}{2}\\\\,\\\\alpha_{-7\\\\,}\\\\,^{\\\\mu} \\\\alpha_{7\\\\,}\\\\,^{\\\\mu}\\\\discretionary{}{}{}+\\\\frac{1}{2}\\\\,\\\\alpha_{-8\\\\,}\\\\,^{\\\\mu} \\\\alpha_{8\\\\,}\\\\,^{\\\\mu}\\\\discretionary{}{}{}%\\n+\\\\frac{1}{2}\\\\,\\\\alpha_{-9\\\\,}\\\\,^{\\\\mu} \\\\alpha_{9\\\\,}\\\\,^{\\\\mu}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"L0=L(0);\\nL1=L(1)\\nL2=L(2)\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 7047165091554904906,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 5118275295356374488,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"The $L_1$ operator acting on the three terms in the trial state gives the following three terms, which we will need to reduce\\nusing the commutation relations (2nd and 3rd term suppressed; you get the idea).\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"The $L_1$ operator acting on the three terms in the trial state gives the following three terms, which we will need to reduce\\nusing the commutation relations (2nd and 3rd term suppressed; you get the idea).\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 4782835140128101232,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 14990495914634320299,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 14714523208758333255,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"( 1/2 \\\\alpha_{11}^{\\\\mu} \\\\alpha_{-10}^{\\\\mu} +  1/2 \\\\alpha_{10}^{\\\\mu} \\\\alpha_{-9}^{\\\\mu} +  1/2 \\\\alpha_{9}^{\\\\mu} \\\\alpha_{-8}^{\\\\mu} +  1/2 \\\\alpha_{8}^{\\\\mu} \\\\alpha_{-7}^{\\\\mu} +  1/2 \\\\alpha_{7}^{\\\\mu} \\\\alpha_{-6}^{\\\\mu} +  1/2 \\\\alpha_{6}^{\\\\mu} \\\\alpha_{-5}^{\\\\mu} +  1/2 \\\\alpha_{5}^{\\\\mu} \\\\alpha_{-4}^{\\\\mu} +  1/2 \\\\alpha_{4}^{\\\\mu} \\\\alpha_{-3}^{\\\\mu} +  1/2 \\\\alpha_{3}^{\\\\mu} \\\\alpha_{-2}^{\\\\mu} +  1/2 \\\\alpha_{2}^{\\\\mu} \\\\alpha_{-1}^{\\\\mu} +  1/2 \\\\alpha_{1}^{\\\\mu} \\\\alpha_{0}^{\\\\mu} +  1/2 \\\\alpha_{0}^{\\\\mu} \\\\alpha_{1}^{\\\\mu} +  1/2 \\\\alpha_{-1}^{\\\\mu} \\\\alpha_{2}^{\\\\mu} +  1/2 \\\\alpha_{-2}^{\\\\mu} \\\\alpha_{3}^{\\\\mu} +  1/2 \\\\alpha_{-3}^{\\\\mu} \\\\alpha_{4}^{\\\\mu} +  1/2 \\\\alpha_{-4}^{\\\\mu} \\\\alpha_{5}^{\\\\mu} +  1/2 \\\\alpha_{-5}^{\\\\mu} \\\\alpha_{6}^{\\\\mu} +  1/2 \\\\alpha_{-6}^{\\\\mu} \\\\alpha_{7}^{\\\\mu} +  1/2 \\\\alpha_{-7}^{\\\\mu} \\\\alpha_{8}^{\\\\mu} +  1/2 \\\\alpha_{-8}^{\\\\mu} \\\\alpha_{9}^{\\\\mu}) \\\\alpha_{-1}^{\\\\nu} \\\\alpha_{-1}^{\\\\nu} \\\\vac\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\left(\\\\frac{1}{2}\\\\,\\\\alpha_{11\\\\,}\\\\,^{\\\\mu} \\\\alpha_{-10\\\\,}\\\\,^{\\\\mu}\\\\discretionary{}{}{}+\\\\frac{1}{2}\\\\,\\\\alpha_{10\\\\,}\\\\,^{\\\\mu} \\\\alpha_{-9\\\\,}\\\\,^{\\\\mu}\\\\discretionary{}{}{}+\\\\frac{1}{2}\\\\,\\\\alpha_{9\\\\,}\\\\,^{\\\\mu} \\\\alpha_{-8\\\\,}\\\\,^{\\\\mu}\\\\discretionary{}{}{}+\\\\frac{1}{2}\\\\,\\\\alpha_{8\\\\,}\\\\,^{\\\\mu} \\\\alpha_{-7\\\\,}\\\\,^{\\\\mu}\\\\discretionary{}{}{}+\\\\frac{1}{2}\\\\,\\\\alpha_{7\\\\,}\\\\,^{\\\\mu} \\\\alpha_{-6\\\\,}\\\\,^{\\\\mu}\\\\discretionary{}{}{}+\\\\frac{1}{2}\\\\,\\\\alpha_{6\\\\,}\\\\,^{\\\\mu} \\\\alpha_{-5\\\\,}\\\\,^{\\\\mu}\\\\discretionary{}{}{}+\\\\frac{1}{2}\\\\,\\\\alpha_{5\\\\,}\\\\,^{\\\\mu} \\\\alpha_{-4\\\\,}\\\\,^{\\\\mu}\\\\discretionary{}{}{}+\\\\frac{1}{2}\\\\,\\\\alpha_{4\\\\,}\\\\,^{\\\\mu} \\\\alpha_{-3\\\\,}\\\\,^{\\\\mu}\\\\discretionary{}{}{}+\\\\frac{1}{2}\\\\,\\\\alpha_{3\\\\,}\\\\,^{\\\\mu} \\\\alpha_{-2\\\\,}\\\\,^{\\\\mu}\\\\discretionary{}{}{}+\\\\frac{1}{2}\\\\,\\\\alpha_{2\\\\,}\\\\,^{\\\\mu} \\\\alpha_{-\\\\,1}\\\\,^{\\\\mu}\\\\discretionary{}{}{}+\\\\frac{1}{2}\\\\,\\\\alpha_{1}\\\\,^{\\\\mu} \\\\alpha_{0\\\\,}\\\\,^{\\\\mu}\\\\discretionary{}{}{}+\\\\frac{1}{2}\\\\,\\\\alpha_{0\\\\,}\\\\,^{\\\\mu} \\\\alpha_{1}\\\\,^{\\\\mu}\\\\discretionary{}{}{}+\\\\frac{1}{2}\\\\,\\\\alpha_{-\\\\,1}\\\\,^{\\\\mu} \\\\alpha_{2\\\\,}\\\\,^{\\\\mu}\\\\discretionary{}{}{}+\\\\frac{1}{2}\\\\,\\\\alpha_{-2\\\\,}\\\\,^{\\\\mu} \\\\alpha_{3\\\\,}\\\\,^{\\\\mu}\\\\discretionary{}{}{}+\\\\frac{1}{2}\\\\,\\\\alpha_{-3\\\\,}\\\\,^{\\\\mu} \\\\alpha_{4\\\\,}\\\\,^{\\\\mu}\\\\discretionary{}{}{}+\\\\frac{1}{2}\\\\,\\\\alpha_{-4\\\\,}\\\\,^{\\\\mu} \\\\alpha_{5\\\\,}\\\\,^{\\\\mu}\\\\discretionary{}{}{}+\\\\frac{1}{2}\\\\,\\\\alpha_{-5\\\\,}\\\\,^{\\\\mu} \\\\alpha_{6\\\\,}\\\\,^{\\\\mu}\\\\discretionary{}{}{}+\\\\frac{1}{2}\\\\,\\\\alpha_{-6\\\\,}\\\\,^{\\\\mu} \\\\alpha_{7\\\\,}\\\\,^{\\\\mu}\\\\discretionary{}{}{}+\\\\frac{1}{2}\\\\,\\\\alpha_{-7\\\\,}\\\\,^{\\\\mu} \\\\alpha_{8\\\\,}\\\\,^{\\\\mu}\\\\discretionary{}{}{}%\\n+\\\\frac{1}{2}\\\\,\\\\alpha_{-8\\\\,}\\\\,^{\\\\mu} \\\\alpha_{9\\\\,}\\\\,^{\\\\mu}\\\\right) \\\\alpha_{-\\\\,1}\\\\,^{\\\\nu} \\\\alpha_{-\\\\,1}\\\\,^{\\\\nu} |k\\\\rangle\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"L1c1:= @(L1) @(chi1);\\nL1c2:= @(L1) @(chi2).\\nL1c3:= @(L1) @(chi3).\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 16671500852189714449,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 1813454240306251257,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"We can now work out what is the action of a Virasoro operator on a state by repeatedly substituting the \\ncommutation relations of the $\\\\alpha_{m}^{\\\\mu}$ and simplifying, until the result no longer changes.\\nBelow, we stick that logic into a function \\\\verb|act| which you can apply on an expression.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"We can now work out what is the action of a Virasoro operator on a state by repeatedly substituting the \\ncommutation relations of the $\\\\alpha_{m}^{\\\\mu}$ and simplifying, until the result no longer changes.\\nBelow, we stick that logic into a function \\\\verb|act| which you can apply on an expression.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 9569013576939593407,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"def act(ex):\\n\\tconverge(ex):\\n\\t\\tdistribute(ex)\\n\\t\\tsubstitute(ex, rl)\\n\\t\\tdistribute(ex)\\n\\t\\teliminate_kronecker(ex)\\n\\t\\trename_dummies(ex)\\n\\n\\treturn ex\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 1127807017064619313,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 6349485254185012150,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"Here is what happens when you apply the commutator rules to the three terms in the state $L_1 |\\\\chi\\\\rangle$:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"Here is what happens when you apply the commutator rules to the three terms in the state $L_1 |\\\\chi\\\\rangle$:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 8356736387124619540,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9700561367777170514,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 5820230579626345328,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"2\\\\alpha_{-1}^{\\\\mu} 2**( 1/2 ) k^{\\\\mu} \\\\vac\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}2\\\\,\\\\alpha_{-\\\\,1}\\\\,^{\\\\mu} \\\\sqrt{2\\\\,} k^{\\\\mu} |k\\\\rangle\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"act(L1c1);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 15551595756512790768,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 11729531843188402201,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 17177252407339749839,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"2\\\\alpha_{-1}^{\\\\mu} 2**( 1/2 ) k^{\\\\mu} \\\\vac\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}2\\\\,\\\\alpha_{-\\\\,1}\\\\,^{\\\\mu} \\\\sqrt{2\\\\,} k^{\\\\mu} |k\\\\rangle\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"act(L1c2);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 16353780900493183719,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 1328742277609010763,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 10959090359551434310,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"-4\\\\alpha_{-1}^{\\\\mu} 2**( 1/2 ) \\\\vac k^{\\\\mu}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}-4\\\\,\\\\alpha_{-\\\\,1}\\\\,^{\\\\mu} \\\\sqrt{2\\\\,} |k\\\\rangle k^{\\\\mu}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"act(L1c3);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 7159084815180416425,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 7897092975591924024,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"The procedure works the same for $L_2|\\\\chi\\\\rangle$:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"The procedure works the same for $L_2|\\\\chi\\\\rangle$:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 17129569920299030941,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"L2c1:= @(L2) @(chi1).\\nL2c2:= @(L2) @(chi2).\\nL2c3:= @(L2) @(chi3).\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 16649294291435749747,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 6778235984817189062,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 4229702900126160237,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"d \\\\vac\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}d |k\\\\rangle\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"act(L2c1);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 15403062552222093434,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 1767126210920816023,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 9397666429387678638,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"-4\\\\vac\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}-4\\\\,|k\\\\rangle\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"act(L2c2);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 9308386491157067465,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 7336243701534558571,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 4868608633034813290,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"-2\\\\vac\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}-2\\\\,|k\\\\rangle\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"act(L2c3);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 13923559608576576884,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 446660646759431630,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"The constraints $L_1 |\\\\chi\\\\rangle=0$ and $L_2 |\\\\chi\\\\rangle=0$ thus reduce to\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"The constraints $L_1 |\\\\chi\\\\rangle=0$ and $L_2 |\\\\chi\\\\rangle=0$ thus reduce to\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 13904507812560471307,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 15711706727387074879,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 14772577574293813296,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"2\\\\alpha_{-1}^{\\\\mu} 2**( 1/2 ) \\\\vac k^{\\\\mu} + 2A \\\\alpha_{-1}^{\\\\mu} 2**( 1/2 ) \\\\vac k^{\\\\mu}-4B \\\\alpha_{-1}^{\\\\mu} 2**( 1/2 ) \\\\vac k^{\\\\mu} = 0\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}2\\\\,\\\\alpha_{-\\\\,1}\\\\,^{\\\\mu} \\\\sqrt{2\\\\,} |k\\\\rangle k^{\\\\mu}\\\\discretionary{}{}{}+2\\\\,A \\\\alpha_{-\\\\,1}\\\\,^{\\\\mu} \\\\sqrt{2\\\\,} |k\\\\rangle k^{\\\\mu}\\\\discretionary{}{}{}-4\\\\,B \\\\alpha_{-\\\\,1}\\\\,^{\\\\mu} \\\\sqrt{2\\\\,} |k\\\\rangle k^{\\\\mu} = 0\\\\,\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"tst1:=@(L1c1) + A @(L1c2) + B @(L1c3) = 0:\\nsort_product(tst1);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 14236165516015635004,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 1980851252189073104,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 16252494889117073428,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"d \\\\vac-4A \\\\vac-2B \\\\vac = 0\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}d |k\\\\rangle\\\\discretionary{}{}{}-4\\\\,A |k\\\\rangle\\\\discretionary{}{}{}-2\\\\,B |k\\\\rangle = 0\\\\,\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"tst2:=@(L2c1) + A @(L2c2) + B @(L2c3) = 0;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 12516344819539830977,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 12538660012652809938,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 17497383109365579360,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"(2 + 2A-4B) \\\\alpha_{-1}^{\\\\mu} 2**( 1/2 ) \\\\vac k^{\\\\mu} = 0\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\left(2\\\\,\\\\discretionary{}{}{}+2\\\\,A\\\\discretionary{}{}{}-4\\\\,B\\\\right) \\\\alpha_{-\\\\,1}\\\\,^{\\\\mu} \\\\sqrt{2\\\\,} |k\\\\rangle k^{\\\\mu} = 0\\\\,\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"factor_in(tst1, $d,A,B$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 105653865030971369,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 15246499768897879848,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 2807280639535753229,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"(d-4A-2B) \\\\vac = 0\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\left(d\\\\discretionary{}{}{}-4\\\\,A\\\\discretionary{}{}{}-2\\\\,B\\\\right) |k\\\\rangle = 0\\\\,\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"factor_in(tst2, $d,A,B$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 15477169422114853123,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 13242977301709297794,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"We then just need to solve this system of linear equations using SymPy's \\\\verb|linsolve|,\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"We then just need to solve this system of linear equations using SymPy's \\\\verb|linsolve|,\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 17228368543050418081,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"from cdb.sympy.solvers import *\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 5532690177225574795,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"substitute(tst1,$\\\\vac->1, \\\\alpha{#}->1, k^\\\\mu=1$)\\nsubstitute(tst2,$\\\\vac->1, \\\\alpha{#}->1$)\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 3881120526219838522,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 3749470538894674769,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 7682055029995724966,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"{{A ->  -  1/5  +  1/5 d, B ->  2/5  +  1/10 d}}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\left[\\\\left[A \\\\rightarrow  - \\\\frac{1}{5}\\\\,\\\\discretionary{}{}{}+\\\\frac{1}{5}\\\\,d, \\\\discretionary{}{}{}B \\\\rightarrow \\\\frac{2}{5}\\\\,\\\\discretionary{}{}{}+\\\\frac{1}{10}\\\\,d\\\\right]\\\\right]\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"linsolve($@(tst1),@(tst2)$,$A,B$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 18040408956066903813,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 13433475463539098231,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"These are thus (indeed) solved by $A=\\\\frac{d-1}{5}$ and $B=\\\\frac{d+4}{10}$.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"These are thus (indeed) solved by $A=\\\\frac{d-1}{5}$ and $B=\\\\frac{d+4}{10}$.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 13219877329185599024,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 13015712840735282993,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\subsection*{Computing the norm}\\n\\nHaving pinned down the coefficients $A$ and $B$, we now want to compute the norm of the state $|\\\\chi\\\\rangle$ (to be added).\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"\\\\subsection*{Computing the norm}\\n\\nHaving pinned down the coefficients $A$ and $B$, we now want to compute the norm of the state $|\\\\chi\\\\rangle$ (to be added).\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 1141840368804704987,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"\"\n\t\t}\n\t],\n\t\"description\": \"Cadabra JSON notebook format\",\n\t\"flags\": {\n\t\t\"hide_input_cells\": false\n\t},\n\t\"version\": 1.0\n}\n"
  },
  {
    "path": "examples/super_maxwell.cnb",
    "content": "\n{\n\t\"cells\" : \n\t[\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"{ a,b,c,d,e }::Indices(vector).\\n\\\\bar{#}::DiracBar.\\n\\\\partial{#}::PartialDerivative.\\n{ A_{a}, f_{a b} }::Depends(\\\\partial).\\n{ \\\\epsilon, \\\\gamma_{#} }::Depends(\\\\bar).\\n\\\\lambda::Depends(\\\\bar, \\\\partial).\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"{ \\\\lambda, \\\\gamma_{#} }::NonCommuting.\\n{ \\\\lambda, \\\\epsilon }::Spinor(dimension=4, type=Majorana).\\n{ \\\\epsilon, \\\\lambda }::SortOrder.\\n{ \\\\epsilon, \\\\lambda }::AntiCommuting.\\n\\\\lambda::SelfAntiCommuting.\\n\\\\gamma_{#}::GammaMatrix(metric=\\\\delta).\\n\\\\delta{#}::Accent.\\nf_{a b}::AntiSymmetric.\\n\\\\delta_{a b}::KroneckerDelta.\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}(\\\\delta{A_{a}} = \\\\bar{\\\\epsilon} \\\\gamma_{a} \\\\lambda, \\\\delta{\\\\lambda} =  - \\\\frac{1}{2}\\\\gamma_{a b} \\\\epsilon f_{a b})\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"susy:= { \\\\delta{A_{a}}   = \\\\bar{\\\\epsilon} \\\\gamma_{a} \\\\lambda,\\n         \\\\delta{\\\\lambda} = -(1/2) \\\\gamma_{a b} \\\\epsilon f_{a b} };\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{} - \\\\frac{1}{4}f_{a b} f_{a b} - \\\\frac{1}{2}\\\\bar{\\\\lambda} \\\\gamma_{a} \\\\partial_{a}(\\\\lambda)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"S:= -(1/4) f_{a b} f_{a b}- (1/2) \\\\bar{\\\\lambda} \\\\gamma_{a} \\\\partial_{a}{\\\\lambda};\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}(f_{a b} \\\\rightarrow \\\\partial_{a}(\\\\delta{A_{b}})-\\\\partial_{b}(\\\\delta{A_{a}}), \\\\lambda \\\\rightarrow \\\\delta{\\\\lambda})\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"rls:= f_{a b} -> \\\\partial_{a}{\\\\delta{A_{b}}}- \\\\partial_{b}{\\\\delta{A_{a}}},\\n      \\\\lambda -> \\\\delta{\\\\lambda} ;\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{} - \\\\frac{1}{4}\\\\left(\\\\partial_{a}(\\\\delta{A_{b}})-\\\\partial_{b}(\\\\delta{A_{a}})\\\\right) f_{a b} - \\\\frac{1}{4}f_{a b} \\\\left(\\\\partial_{a}(\\\\delta{A_{b}})-\\\\partial_{b}(\\\\delta{A_{a}})\\\\right) - \\\\frac{1}{2}\\\\bar{\\\\delta{\\\\lambda}} \\\\gamma_{a} \\\\partial_{a}(\\\\lambda) - \\\\frac{1}{2}\\\\bar{\\\\lambda} \\\\gamma_{a} \\\\partial_{a}(\\\\delta{\\\\lambda})\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"vary(S,rls);\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{} - \\\\frac{1}{4}\\\\partial_{a}(\\\\delta{A_{b}}) f_{a b}+\\\\frac{1}{4}\\\\partial_{b}(\\\\delta{A_{a}}) f_{a b} - \\\\frac{1}{4}f_{a b} \\\\partial_{a}(\\\\delta{A_{b}})+\\\\frac{1}{4}f_{a b} \\\\partial_{b}(\\\\delta{A_{a}}) - \\\\frac{1}{2}\\\\bar{\\\\delta{\\\\lambda}} \\\\gamma_{a} \\\\partial_{a}(\\\\lambda) - \\\\frac{1}{2}\\\\bar{\\\\lambda} \\\\gamma_{a} \\\\partial_{a}(\\\\delta{\\\\lambda})\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"distribute(_);\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{} - \\\\frac{1}{4}\\\\partial_{a}(\\\\bar{\\\\epsilon} \\\\gamma_{b} \\\\lambda) f_{a b}+\\\\frac{1}{4}\\\\partial_{b}(\\\\bar{\\\\epsilon} \\\\gamma_{a} \\\\lambda) f_{a b} - \\\\frac{1}{4}f_{a b} \\\\partial_{a}(\\\\bar{\\\\epsilon} \\\\gamma_{b} \\\\lambda)+\\\\frac{1}{4}f_{a b} \\\\partial_{b}(\\\\bar{\\\\epsilon} \\\\gamma_{a} \\\\lambda)+\\\\frac{1}{4}\\\\bar{\\\\gamma_{c b} \\\\epsilon f_{c b}} \\\\gamma_{a} \\\\partial_{a}(\\\\lambda)+\\\\frac{1}{4}\\\\bar{\\\\lambda} \\\\gamma_{a} \\\\partial_{a}(\\\\gamma_{c b} \\\\epsilon f_{c b})\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"substitute(_, susy);\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{} - \\\\frac{1}{4}\\\\left(\\\\partial_{a}(\\\\bar{\\\\epsilon}) \\\\gamma_{b} \\\\lambda+\\\\bar{\\\\epsilon} \\\\partial_{a}(\\\\gamma_{b}) \\\\lambda+\\\\bar{\\\\epsilon} \\\\gamma_{b} \\\\partial_{a}(\\\\lambda)\\\\right) f_{a b}+\\\\frac{1}{4}\\\\left(\\\\partial_{b}(\\\\bar{\\\\epsilon}) \\\\gamma_{a} \\\\lambda+\\\\bar{\\\\epsilon} \\\\partial_{b}(\\\\gamma_{a}) \\\\lambda+\\\\bar{\\\\epsilon} \\\\gamma_{a} \\\\partial_{b}(\\\\lambda)\\\\right) f_{a b} - \\\\frac{1}{4}f_{a b} \\\\left(\\\\partial_{a}(\\\\bar{\\\\epsilon}) \\\\gamma_{b} \\\\lambda+\\\\bar{\\\\epsilon} \\\\partial_{a}(\\\\gamma_{b}) \\\\lambda+\\\\bar{\\\\epsilon} \\\\gamma_{b} \\\\partial_{a}(\\\\lambda)\\\\right)+\\\\frac{1}{4}f_{a b} \\\\left(\\\\partial_{b}(\\\\bar{\\\\epsilon}) \\\\gamma_{a} \\\\lambda+\\\\bar{\\\\epsilon} \\\\partial_{b}(\\\\gamma_{a}) \\\\lambda+\\\\bar{\\\\epsilon} \\\\gamma_{a} \\\\partial_{b}(\\\\lambda)\\\\right)+\\\\frac{1}{4}\\\\bar{\\\\gamma_{c b} \\\\epsilon f_{c b}} \\\\gamma_{a} \\\\partial_{a}(\\\\lambda)+\\\\frac{1}{4}\\\\bar{\\\\lambda} \\\\gamma_{a} \\\\left(\\\\partial_{a}(\\\\gamma_{c b}) \\\\epsilon f_{c b}+\\\\gamma_{c b} \\\\partial_{a}(\\\\epsilon) f_{c b}+\\\\gamma_{c b} \\\\epsilon \\\\partial_{a}(f_{c b})\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"product_rule(_);\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{} - \\\\frac{1}{4}\\\\partial_{a}(\\\\bar{\\\\epsilon}) \\\\gamma_{b} \\\\lambda f_{a b} - \\\\frac{1}{4}\\\\bar{\\\\epsilon} \\\\partial_{a}(\\\\gamma_{b}) \\\\lambda f_{a b} - \\\\frac{1}{4}\\\\bar{\\\\epsilon} \\\\gamma_{b} \\\\partial_{a}(\\\\lambda) f_{a b}+\\\\frac{1}{4}\\\\partial_{b}(\\\\bar{\\\\epsilon}) \\\\gamma_{a} \\\\lambda f_{a b}+\\\\frac{1}{4}\\\\bar{\\\\epsilon} \\\\partial_{b}(\\\\gamma_{a}) \\\\lambda f_{a b}+\\\\frac{1}{4}\\\\bar{\\\\epsilon} \\\\gamma_{a} \\\\partial_{b}(\\\\lambda) f_{a b} - \\\\frac{1}{4}f_{a b} \\\\partial_{a}(\\\\bar{\\\\epsilon}) \\\\gamma_{b} \\\\lambda - \\\\frac{1}{4}f_{a b} \\\\bar{\\\\epsilon} \\\\partial_{a}(\\\\gamma_{b}) \\\\lambda - \\\\frac{1}{4}f_{a b} \\\\bar{\\\\epsilon} \\\\gamma_{b} \\\\partial_{a}(\\\\lambda)+\\\\frac{1}{4}f_{a b} \\\\partial_{b}(\\\\bar{\\\\epsilon}) \\\\gamma_{a} \\\\lambda+\\\\frac{1}{4}f_{a b} \\\\bar{\\\\epsilon} \\\\partial_{b}(\\\\gamma_{a}) \\\\lambda+\\\\frac{1}{4}f_{a b} \\\\bar{\\\\epsilon} \\\\gamma_{a} \\\\partial_{b}(\\\\lambda)+\\\\frac{1}{4}\\\\bar{\\\\gamma_{c b} \\\\epsilon f_{c b}} \\\\gamma_{a} \\\\partial_{a}(\\\\lambda)+\\\\frac{1}{4}\\\\bar{\\\\lambda} \\\\gamma_{a} \\\\partial_{a}(\\\\gamma_{c b}) \\\\epsilon f_{c b}+\\\\frac{1}{4}\\\\bar{\\\\lambda} \\\\gamma_{a} \\\\gamma_{c b} \\\\partial_{a}(\\\\epsilon) f_{c b}+\\\\frac{1}{4}\\\\bar{\\\\lambda} \\\\gamma_{a} \\\\gamma_{c b} \\\\epsilon \\\\partial_{a}(f_{c b})\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"distribute(_);\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{} - \\\\frac{1}{4}\\\\bar{\\\\epsilon} \\\\gamma_{b} \\\\partial_{a}(\\\\lambda) f_{a b}+\\\\frac{1}{4}\\\\bar{\\\\epsilon} \\\\gamma_{a} \\\\partial_{b}(\\\\lambda) f_{a b} - \\\\frac{1}{4}f_{a b} \\\\bar{\\\\epsilon} \\\\gamma_{b} \\\\partial_{a}(\\\\lambda)+\\\\frac{1}{4}f_{a b} \\\\bar{\\\\epsilon} \\\\gamma_{a} \\\\partial_{b}(\\\\lambda)+\\\\frac{1}{4}f_{c b} \\\\bar{\\\\gamma_{c b} \\\\epsilon} \\\\gamma_{a} \\\\partial_{a}(\\\\lambda)+\\\\frac{1}{4}\\\\bar{\\\\lambda} \\\\gamma_{a} \\\\gamma_{c b} \\\\epsilon \\\\partial_{a}(f_{c b})\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"unwrap(_);\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{} - \\\\frac{1}{4}\\\\bar{\\\\epsilon} \\\\gamma_{b} \\\\partial_{a}(\\\\lambda) f_{a b}+\\\\frac{1}{4}\\\\bar{\\\\epsilon} \\\\gamma_{a} \\\\partial_{b}(\\\\lambda) f_{a b} - \\\\frac{1}{4}f_{a b} \\\\bar{\\\\epsilon} \\\\gamma_{b} \\\\partial_{a}(\\\\lambda)+\\\\frac{1}{4}f_{a b} \\\\bar{\\\\epsilon} \\\\gamma_{a} \\\\partial_{b}(\\\\lambda) - \\\\frac{1}{4}f_{c b} \\\\bar{\\\\epsilon} \\\\gamma_{c b} \\\\gamma_{a} \\\\partial_{a}(\\\\lambda)+\\\\frac{1}{4}\\\\bar{\\\\lambda} \\\\gamma_{a} \\\\gamma_{c b} \\\\epsilon \\\\partial_{a}(f_{c b})\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"expand_diracbar(_);\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\frac{1}{2}\\\\bar{\\\\epsilon} \\\\gamma_{a} \\\\partial_{b}(\\\\lambda) f_{a b}+\\\\frac{1}{2}f_{a b} \\\\bar{\\\\epsilon} \\\\gamma_{a} \\\\partial_{b}(\\\\lambda) - \\\\frac{1}{4}f_{a b} \\\\bar{\\\\epsilon} \\\\gamma_{a b} \\\\gamma_{c} \\\\partial_{c}(\\\\lambda)+\\\\frac{1}{4}\\\\bar{\\\\lambda} \\\\gamma_{a} \\\\gamma_{b c} \\\\epsilon \\\\partial_{a}(f_{b c})\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"canonicalise(_);\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\bar{\\\\epsilon} \\\\gamma_{a} \\\\partial_{b}(\\\\lambda) f_{a b} - \\\\frac{1}{4}\\\\bar{\\\\epsilon} \\\\gamma_{a b} \\\\gamma_{c} \\\\partial_{c}(\\\\lambda) f_{a b}+\\\\frac{1}{4}\\\\bar{\\\\lambda} \\\\gamma_{a} \\\\gamma_{b c} \\\\epsilon \\\\partial_{a}(f_{b c})\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"sort_product(_);\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1.0\n}\n\n"
  },
  {
    "path": "examples/supergravity.cnb",
    "content": "{\n\t\"cells\" : \n\t[\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"def post_process(ex):\\n   eliminate_kronecker(ex)\\n   sort_product(ex)\\n   collect_terms(ex)\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"It is easier to keep track of various parts of the computation if we disable automatic\\nindex raising/lowering, so we use \\\\verb|position=independent| on the indices. \"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"It is easier to keep track of various parts of the computation if we disable automatic\\nindex raising/lowering, so we use \\\\verb|position=independent| on the indices. \"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Derivative to~}D{\\\\#}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property PartialDerivative to~}\\\\partial{\\\\#}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property DiracBar to~}\\\\bar{\\\\#}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Derivative to~}\\\\delta\\\\left(A??\\\\right).\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Indices(position=independent) to~}\\\\left[m,~\\\\discretionary{}{}{} n,~\\\\discretionary{}{}{} p,~\\\\discretionary{}{}{} q,~\\\\discretionary{}{}{} r,~\\\\discretionary{}{}{} s,~\\\\discretionary{}{}{} t,~\\\\discretionary{}{}{} u\\\\right].\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Integer to~}\\\\left[m,~\\\\discretionary{}{}{} n,~\\\\discretionary{}{}{} p,~\\\\discretionary{}{}{} q,~\\\\discretionary{}{}{} r,~\\\\discretionary{}{}{} s,~\\\\discretionary{}{}{} t,~\\\\discretionary{}{}{} u\\\\right].\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Indices(position=independent) to~}\\\\left[\\\\mu,~\\\\discretionary{}{}{} \\\\nu,~\\\\discretionary{}{}{} \\\\rho,~\\\\discretionary{}{}{} \\\\sigma,~\\\\discretionary{}{}{} \\\\kappa,~\\\\discretionary{}{}{} \\\\lambda,~\\\\discretionary{}{}{} \\\\alpha,~\\\\discretionary{}{}{} \\\\beta\\\\right].\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Integer to~}\\\\left[\\\\mu,~\\\\discretionary{}{}{} \\\\nu,~\\\\discretionary{}{}{} \\\\rho,~\\\\discretionary{}{}{} \\\\sigma,~\\\\discretionary{}{}{} \\\\kappa,~\\\\discretionary{}{}{} \\\\lambda,~\\\\discretionary{}{}{} \\\\alpha,~\\\\discretionary{}{}{} \\\\beta\\\\right].\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"D{#}::Derivative;\\n\\\\partial{#}::PartialDerivative;\\n\\\\bar{#}::DiracBar;\\n\\\\delta{A??}::Derivative;\\n{m,n,p,q,r,s,t,u}::Indices(flat, position=independent);\\n{m,n,p,q,r,s,t,u}::Integer(0..3);\\n{\\\\mu,\\\\nu,\\\\rho,\\\\sigma,\\\\kappa,\\\\lambda,\\\\alpha,\\\\beta}::Indices(curved,position=independent);\\n{\\\\mu,\\\\nu,\\\\rho,\\\\sigma,\\\\kappa,\\\\lambda,\\\\alpha,\\\\beta}::Integer(0..3);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Vielbein to~}e^{m \\\\mu}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property InverseVielbein to~}e_{m \\\\mu}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property TableauSymmetry to~}g^{\\\\mu \\\\nu}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Metric to~}g_{\\\\mu \\\\nu}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Metric to~}\\\\delta_{m n}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property TableauSymmetry to~}\\\\delta^{m n}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property KroneckerDelta to~}\\\\delta^{s}\\\\,_{r}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property TableauSymmetry to~}\\\\omega_{\\\\mu m n}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Depends to~}\\\\left[e_{m}\\\\,^{\\\\mu},~\\\\discretionary{}{}{} \\\\psi_{\\\\mu},~\\\\discretionary{}{}{} e,~\\\\discretionary{}{}{} T^{\\\\mu}\\\\,_{\\\\nu \\\\rho},~\\\\discretionary{}{}{} \\\\omega_{\\\\mu m n}\\\\right].\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"e^{m \\\\mu}::Vielbein;\\ne_{m \\\\mu}::InverseVielbein;\\ng^{\\\\mu\\\\nu}::InverseMetric;\\ng_{\\\\mu\\\\nu}::Metric;\\n\\\\delta_{m n}::Metric;\\n\\\\delta^{m n}::InverseMetric;\\n\\\\delta^{s}_{r}::KroneckerDelta;\\n\\\\omega_{\\\\mu m n}::TableauSymmetry( indices={1,2}, shape={1,1} );\\n{ e_{m}^{\\\\mu}, \\\\psi_{\\\\mu}, e, T^{\\\\mu}_{\\\\nu\\\\rho}, \\\\omega_{\\\\mu m n} }::Depends(\\\\partial{#});\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Spinor to~}\\\\left[\\\\epsilon,~\\\\discretionary{}{}{} \\\\psi_{\\\\mu},~\\\\discretionary{}{}{} \\\\psi_{\\\\mu \\\\nu}\\\\right].\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property GammaMatrix to~}\\\\Gamma_{\\\\#}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property AntiCommuting to~}\\\\left[\\\\psi_{\\\\mu \\\\nu},~\\\\discretionary{}{}{} \\\\psi_{\\\\mu},~\\\\discretionary{}{}{} \\\\epsilon\\\\right].\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property SelfAntiCommuting to~}\\\\left[\\\\psi_{\\\\mu},~\\\\discretionary{}{}{} \\\\psi_{\\\\mu \\\\nu}\\\\right].\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property SortOrder to~}\\\\left[\\\\epsilon,~\\\\discretionary{}{}{} \\\\psi_{\\\\mu},~\\\\discretionary{}{}{} \\\\psi_{\\\\mu \\\\nu}\\\\right].\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Depends to~}\\\\Gamma_{\\\\#}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property AntiSymmetric to~}\\\\psi_{\\\\mu \\\\nu}.\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"{ \\\\epsilon,\\\\psi_{\\\\mu},\\\\psi_{\\\\mu\\\\nu} }::Spinor(dimension=4, type=Majorana);\\n\\\\Gamma_{#}::GammaMatrix(metric=\\\\delta);\\n{ \\\\psi_{\\\\mu\\\\nu}, \\\\psi_{\\\\mu}, \\\\epsilon }::AntiCommuting;\\n{ \\\\psi_{\\\\mu}, \\\\psi_{\\\\mu\\\\nu} }::SelfAntiCommuting;\\n{ \\\\epsilon, \\\\psi_{\\\\mu}, \\\\psi_{\\\\mu\\\\nu} }::SortOrder;\\n\\\\Gamma_{#}::Depends(\\\\bar{#});\\n\\\\psi_{\\\\mu\\\\nu}::AntiSymmetric;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\int \\\\left( - \\\\frac{1}{2}R_{\\\\mu \\\\nu r s} \\\\delta^{m s} \\\\delta^{n r} e e_{m}\\\\,^{\\\\mu} e_{n}\\\\,^{\\\\nu} - \\\\frac{1}{2}\\\\bar{\\\\psi_{\\\\mu}} \\\\Gamma^{\\\\mu \\\\nu \\\\rho} D_{\\\\nu}{\\\\psi_{\\\\rho}} e\\\\right)\\\\,\\\\,{\\\\rm d}x\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\int \\\\left( - \\\\frac{1}{2}R_{\\\\mu \\\\nu r s} \\\\delta^{m s} \\\\delta^{n r} e e_{m}\\\\,^{\\\\mu} e_{n}\\\\,^{\\\\nu} - \\\\frac{1}{2}\\\\bar{\\\\psi_{\\\\mu}} \\\\Gamma^{m n p} D_{\\\\nu}{\\\\psi_{\\\\rho}} e e_{m}\\\\,^{\\\\mu} e_{n}\\\\,^{\\\\nu} e_{p}\\\\,^{\\\\rho}\\\\right)\\\\,\\\\,{\\\\rm d}x\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"L:= \\\\int{-1/2 e e_{n}^{\\\\nu} e_{m}^{\\\\mu} R_{\\\\mu\\\\nu r s} \\\\delta^{n r} \\\\delta^{m s}\\n                 - 1/2 e \\\\bar{\\\\psi_\\\\mu} \\\\Gamma^{\\\\mu\\\\nu\\\\rho} D_{\\\\nu}{\\\\psi_{\\\\rho}} }{x};\\nrewrite_indices(_, $\\\\Gamma^{m n p}$, $e_{n}^{\\\\mu}$ );\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\left[e_{n}\\\\,^{\\\\mu} \\\\rightarrow -\\\\bar{\\\\epsilon} \\\\Gamma^{m} \\\\psi_{\\\\nu} e_{m}\\\\,^{\\\\mu} e_{n}\\\\,^{\\\\nu},~\\\\discretionary{}{}{} e \\\\rightarrow \\\\bar{\\\\epsilon} \\\\Gamma^{n} \\\\psi_{\\\\mu} e e_{n}\\\\,^{\\\\mu},~\\\\discretionary{}{}{} \\\\psi_{\\\\mu} \\\\rightarrow D_{\\\\mu}{\\\\epsilon}\\\\right]\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"susy:= { e_{n}^{\\\\mu} -> -\\\\bar{\\\\epsilon} \\\\Gamma^m \\\\psi_\\\\nu e_{m}^{\\\\mu} e_{n}^{\\\\nu},\\n         e           -> e \\\\bar{\\\\epsilon} \\\\Gamma^n \\\\psi_\\\\mu e_{n}^{\\\\mu},\\n         \\\\psi_\\\\mu    -> D_{\\\\mu}{\\\\epsilon} };\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\int \\\\left( - \\\\frac{1}{2}R_{\\\\mu \\\\nu r s} \\\\bar{\\\\epsilon} \\\\Gamma^{p} \\\\delta^{m s} \\\\delta^{n r} \\\\psi_{\\\\rho} e e_{m}\\\\,^{\\\\mu} e_{n}\\\\,^{\\\\nu} e_{p}\\\\,^{\\\\rho}+\\\\frac{1}{2}R_{\\\\mu \\\\nu r s} \\\\bar{\\\\epsilon} \\\\Gamma^{p} \\\\delta^{m s} \\\\delta^{n r} \\\\psi_{\\\\rho} e e_{m}\\\\,^{\\\\rho} e_{n}\\\\,^{\\\\nu} e_{p}\\\\,^{\\\\mu}+\\\\frac{1}{2}R_{\\\\mu \\\\nu r s} \\\\bar{\\\\epsilon} \\\\Gamma^{p} \\\\delta^{m s} \\\\delta^{n r} \\\\psi_{\\\\rho} e e_{m}\\\\,^{\\\\mu} e_{n}\\\\,^{\\\\rho} e_{p}\\\\,^{\\\\nu} - \\\\frac{1}{2}\\\\bar{D_{\\\\mu}{\\\\epsilon}} \\\\Gamma^{m n p} D_{\\\\nu}{\\\\psi_{\\\\rho}} e e_{m}\\\\,^{\\\\mu} e_{n}\\\\,^{\\\\nu} e_{p}\\\\,^{\\\\rho} - \\\\frac{1}{2}\\\\bar{\\\\psi_{\\\\mu}} \\\\Gamma^{m n p} D_{\\\\nu}{D_{\\\\rho}{\\\\epsilon}} e e_{m}\\\\,^{\\\\mu} e_{n}\\\\,^{\\\\nu} e_{p}\\\\,^{\\\\rho} - \\\\frac{1}{2}\\\\bar{\\\\psi_{\\\\mu}} \\\\Gamma^{m n p} D_{\\\\nu}{\\\\psi_{\\\\rho}} \\\\bar{\\\\epsilon} \\\\Gamma^{q} \\\\psi_{\\\\sigma} e e_{m}\\\\,^{\\\\mu} e_{n}\\\\,^{\\\\nu} e_{p}\\\\,^{\\\\rho} e_{q}\\\\,^{\\\\sigma}+\\\\frac{1}{2}\\\\bar{\\\\psi_{\\\\mu}} \\\\Gamma^{m n p} D_{\\\\nu}{\\\\psi_{\\\\rho}} \\\\bar{\\\\epsilon} \\\\Gamma^{q} \\\\psi_{\\\\sigma} e e_{m}\\\\,^{\\\\sigma} e_{n}\\\\,^{\\\\nu} e_{p}\\\\,^{\\\\rho} e_{q}\\\\,^{\\\\mu}+\\\\frac{1}{2}\\\\bar{\\\\psi_{\\\\mu}} \\\\Gamma^{m n p} D_{\\\\nu}{\\\\psi_{\\\\rho}} \\\\bar{\\\\epsilon} \\\\Gamma^{q} \\\\psi_{\\\\sigma} e e_{m}\\\\,^{\\\\mu} e_{n}\\\\,^{\\\\sigma} e_{p}\\\\,^{\\\\rho} e_{q}\\\\,^{\\\\nu}+\\\\frac{1}{2}\\\\bar{\\\\psi_{\\\\mu}} \\\\Gamma^{m n p} D_{\\\\nu}{\\\\psi_{\\\\rho}} \\\\bar{\\\\epsilon} \\\\Gamma^{q} \\\\psi_{\\\\sigma} e e_{m}\\\\,^{\\\\mu} e_{n}\\\\,^{\\\\nu} e_{p}\\\\,^{\\\\sigma} e_{q}\\\\,^{\\\\rho}\\\\right)\\\\,\\\\,{\\\\rm d}x\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"vary(L, susy);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\int \\\\left( - \\\\frac{1}{2}R_{\\\\mu \\\\nu r s} \\\\bar{\\\\epsilon} \\\\Gamma^{p} \\\\delta^{m s} \\\\delta^{n r} \\\\psi_{\\\\rho} e e_{m}\\\\,^{\\\\mu} e_{n}\\\\,^{\\\\nu} e_{p}\\\\,^{\\\\rho}+\\\\frac{1}{2}R_{\\\\mu \\\\nu r s} \\\\bar{\\\\epsilon} \\\\Gamma^{p} \\\\delta^{m s} \\\\delta^{n r} \\\\psi_{\\\\rho} e e_{m}\\\\,^{\\\\rho} e_{n}\\\\,^{\\\\nu} e_{p}\\\\,^{\\\\mu}+\\\\frac{1}{2}R_{\\\\mu \\\\nu r s} \\\\bar{\\\\epsilon} \\\\Gamma^{p} \\\\delta^{m s} \\\\delta^{n r} \\\\psi_{\\\\rho} e e_{m}\\\\,^{\\\\mu} e_{n}\\\\,^{\\\\rho} e_{p}\\\\,^{\\\\nu} - \\\\frac{1}{2}\\\\bar{D_{\\\\mu}{\\\\epsilon}} \\\\Gamma^{m n p} D_{\\\\nu}{\\\\psi_{\\\\rho}} e e_{m}\\\\,^{\\\\mu} e_{n}\\\\,^{\\\\nu} e_{p}\\\\,^{\\\\rho} - \\\\frac{1}{8}R_{\\\\nu \\\\rho q r} \\\\bar{\\\\psi_{\\\\mu}} \\\\Gamma^{m n p} \\\\Gamma^{q r} \\\\epsilon e e_{m}\\\\,^{\\\\mu} e_{n}\\\\,^{\\\\nu} e_{p}\\\\,^{\\\\rho} - \\\\frac{1}{2}\\\\bar{\\\\psi_{\\\\mu}} \\\\Gamma^{m n p} D_{\\\\nu}{\\\\psi_{\\\\rho}} \\\\bar{\\\\epsilon} \\\\Gamma^{q} \\\\psi_{\\\\sigma} e e_{m}\\\\,^{\\\\mu} e_{n}\\\\,^{\\\\nu} e_{p}\\\\,^{\\\\rho} e_{q}\\\\,^{\\\\sigma}+\\\\frac{1}{2}\\\\bar{\\\\psi_{\\\\mu}} \\\\Gamma^{m n p} D_{\\\\nu}{\\\\psi_{\\\\rho}} \\\\bar{\\\\epsilon} \\\\Gamma^{q} \\\\psi_{\\\\sigma} e e_{m}\\\\,^{\\\\sigma} e_{n}\\\\,^{\\\\nu} e_{p}\\\\,^{\\\\rho} e_{q}\\\\,^{\\\\mu}+\\\\frac{1}{2}\\\\bar{\\\\psi_{\\\\mu}} \\\\Gamma^{m n p} D_{\\\\nu}{\\\\psi_{\\\\rho}} \\\\bar{\\\\epsilon} \\\\Gamma^{q} \\\\psi_{\\\\sigma} e e_{m}\\\\,^{\\\\mu} e_{n}\\\\,^{\\\\sigma} e_{p}\\\\,^{\\\\rho} e_{q}\\\\,^{\\\\nu}+\\\\frac{1}{2}\\\\bar{\\\\psi_{\\\\mu}} \\\\Gamma^{m n p} D_{\\\\nu}{\\\\psi_{\\\\rho}} \\\\bar{\\\\epsilon} \\\\Gamma^{q} \\\\psi_{\\\\sigma} e e_{m}\\\\,^{\\\\mu} e_{n}\\\\,^{\\\\nu} e_{p}\\\\,^{\\\\sigma} e_{q}\\\\,^{\\\\rho}\\\\right)\\\\,\\\\,{\\\\rm d}x\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"substitute(_, $D_{\\\\nu}{ D_{\\\\rho}{ \\\\epsilon } } -> 1/4 R_{\\\\nu\\\\rho m n} \\\\Gamma^{m n} \\\\epsilon$ );\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{} - \\\\frac{1}{2}\\\\int \\\\bar{D_{\\\\mu}{\\\\epsilon}} \\\\Gamma^{m n p} D_{\\\\nu}{\\\\psi_{\\\\rho}} e e_{m}\\\\,^{\\\\mu} e_{n}\\\\,^{\\\\nu} e_{p}\\\\,^{\\\\rho}\\\\,\\\\,{\\\\rm d}x\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"take_match(_, $\\\\bar{D_{\\\\mu}{\\\\epsilon}}*A??$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\bar{D_{\\\\mu}{\\\\epsilon}} = \\\\partial_{\\\\mu}\\\\left(\\\\bar{\\\\epsilon}\\\\right) - \\\\frac{1}{4}\\\\bar{\\\\epsilon} \\\\Gamma^{m n} \\\\omega_{\\\\mu m n}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{} - \\\\frac{1}{2}\\\\int \\\\left(\\\\partial_{\\\\mu}\\\\left(\\\\bar{\\\\epsilon}\\\\right) \\\\Gamma^{m n p} D_{\\\\nu}{\\\\psi_{\\\\rho}} e e_{m}\\\\,^{\\\\mu} e_{n}\\\\,^{\\\\nu} e_{p}\\\\,^{\\\\rho} - \\\\frac{1}{4}\\\\bar{\\\\epsilon} \\\\Gamma^{q r} \\\\Gamma^{m n p} D_{\\\\nu}{\\\\psi_{\\\\rho}} \\\\omega_{\\\\mu q r} e e_{m}\\\\,^{\\\\mu} e_{n}\\\\,^{\\\\nu} e_{p}\\\\,^{\\\\rho}\\\\right)\\\\,\\\\,{\\\\rm d}x\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"covD:= \\\\bar{D_{\\\\mu}{\\\\epsilon}} = \\\\partial_{\\\\mu}{\\\\bar{\\\\epsilon}} \\n                                  - 1/4 \\\\bar{\\\\epsilon}\\\\omega_{\\\\mu m n} \\\\Gamma^{m n} ):\\nsubstitute(L, covD)\\ndistribute(L);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{} - \\\\frac{1}{2}\\\\int \\\\left(-\\\\bar{\\\\epsilon} \\\\partial_{\\\\mu}\\\\left(\\\\Gamma^{m n p} D_{\\\\nu}{\\\\psi_{\\\\rho}} e e_{m}\\\\,^{\\\\mu} e_{n}\\\\,^{\\\\nu} e_{p}\\\\,^{\\\\rho}\\\\right) - \\\\frac{1}{4}\\\\bar{\\\\epsilon} \\\\Gamma^{q r} \\\\Gamma^{m n p} D_{\\\\nu}{\\\\psi_{\\\\rho}} \\\\omega_{\\\\mu q r} e e_{m}\\\\,^{\\\\mu} e_{n}\\\\,^{\\\\nu} e_{p}\\\\,^{\\\\rho}\\\\right)\\\\,\\\\,{\\\\rm d}x\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"integrate_by_parts(L, $\\\\bar{\\\\epsilon}$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{} - \\\\frac{1}{2}\\\\int \\\\left(-\\\\bar{\\\\epsilon} \\\\left(\\\\partial_{\\\\mu}{\\\\Gamma^{m n p}} D_{\\\\nu}{\\\\psi_{\\\\rho}} e e_{m}\\\\,^{\\\\mu} e_{n}\\\\,^{\\\\nu} e_{p}\\\\,^{\\\\rho}+\\\\Gamma^{m n p} \\\\partial_{\\\\mu}{D_{\\\\nu}{\\\\psi_{\\\\rho}}} e e_{m}\\\\,^{\\\\mu} e_{n}\\\\,^{\\\\nu} e_{p}\\\\,^{\\\\rho}+\\\\Gamma^{m n p} D_{\\\\nu}{\\\\psi_{\\\\rho}} \\\\partial_{\\\\mu}{e} e_{m}\\\\,^{\\\\mu} e_{n}\\\\,^{\\\\nu} e_{p}\\\\,^{\\\\rho}+\\\\Gamma^{m n p} D_{\\\\nu}{\\\\psi_{\\\\rho}} \\\\partial_{\\\\mu}{e_{m}\\\\,^{\\\\mu}} e e_{n}\\\\,^{\\\\nu} e_{p}\\\\,^{\\\\rho}+\\\\Gamma^{m n p} D_{\\\\nu}{\\\\psi_{\\\\rho}} \\\\partial_{\\\\mu}{e_{n}\\\\,^{\\\\nu}} e e_{m}\\\\,^{\\\\mu} e_{p}\\\\,^{\\\\rho}+\\\\Gamma^{m n p} D_{\\\\nu}{\\\\psi_{\\\\rho}} \\\\partial_{\\\\mu}{e_{p}\\\\,^{\\\\rho}} e e_{m}\\\\,^{\\\\mu} e_{n}\\\\,^{\\\\nu}\\\\right) - \\\\frac{1}{4}\\\\bar{\\\\epsilon} \\\\Gamma^{q r} \\\\Gamma^{m n p} D_{\\\\nu}{\\\\psi_{\\\\rho}} \\\\omega_{\\\\mu q r} e e_{m}\\\\,^{\\\\mu} e_{n}\\\\,^{\\\\nu} e_{p}\\\\,^{\\\\rho}\\\\right)\\\\,\\\\,{\\\\rm d}x\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"product_rule(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{} - \\\\frac{1}{2}\\\\int \\\\left(-\\\\bar{\\\\epsilon} \\\\partial_{\\\\mu}{\\\\Gamma^{m n p}} D_{\\\\nu}{\\\\psi_{\\\\rho}} e e_{m}\\\\,^{\\\\mu} e_{n}\\\\,^{\\\\nu} e_{p}\\\\,^{\\\\rho}-\\\\bar{\\\\epsilon} \\\\Gamma^{m n p} \\\\partial_{\\\\mu}{D_{\\\\nu}{\\\\psi_{\\\\rho}}} e e_{m}\\\\,^{\\\\mu} e_{n}\\\\,^{\\\\nu} e_{p}\\\\,^{\\\\rho}-\\\\bar{\\\\epsilon} \\\\Gamma^{m n p} D_{\\\\nu}{\\\\psi_{\\\\rho}} \\\\partial_{\\\\mu}{e} e_{m}\\\\,^{\\\\mu} e_{n}\\\\,^{\\\\nu} e_{p}\\\\,^{\\\\rho}-\\\\bar{\\\\epsilon} \\\\Gamma^{m n p} D_{\\\\nu}{\\\\psi_{\\\\rho}} \\\\partial_{\\\\mu}{e_{m}\\\\,^{\\\\mu}} e e_{n}\\\\,^{\\\\nu} e_{p}\\\\,^{\\\\rho}-\\\\bar{\\\\epsilon} \\\\Gamma^{m n p} D_{\\\\nu}{\\\\psi_{\\\\rho}} \\\\partial_{\\\\mu}{e_{n}\\\\,^{\\\\nu}} e e_{m}\\\\,^{\\\\mu} e_{p}\\\\,^{\\\\rho}-\\\\bar{\\\\epsilon} \\\\Gamma^{m n p} D_{\\\\nu}{\\\\psi_{\\\\rho}} \\\\partial_{\\\\mu}{e_{p}\\\\,^{\\\\rho}} e e_{m}\\\\,^{\\\\mu} e_{n}\\\\,^{\\\\nu} - \\\\frac{1}{4}\\\\bar{\\\\epsilon} \\\\Gamma^{q r} \\\\Gamma^{m n p} D_{\\\\nu}{\\\\psi_{\\\\rho}} \\\\omega_{\\\\mu q r} e e_{m}\\\\,^{\\\\mu} e_{n}\\\\,^{\\\\nu} e_{p}\\\\,^{\\\\rho}\\\\right)\\\\,\\\\,{\\\\rm d}x\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"distribute(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{} - \\\\frac{1}{2}\\\\int \\\\left(-\\\\bar{\\\\epsilon} \\\\Gamma^{m n p} \\\\partial_{\\\\mu}{D_{\\\\nu}{\\\\psi_{\\\\rho}}} e e_{m}\\\\,^{\\\\mu} e_{n}\\\\,^{\\\\nu} e_{p}\\\\,^{\\\\rho}-\\\\bar{\\\\epsilon} \\\\Gamma^{m n p} D_{\\\\nu}{\\\\psi_{\\\\rho}} \\\\partial_{\\\\mu}{e} e_{m}\\\\,^{\\\\mu} e_{n}\\\\,^{\\\\nu} e_{p}\\\\,^{\\\\rho}-\\\\bar{\\\\epsilon} \\\\Gamma^{m n p} D_{\\\\nu}{\\\\psi_{\\\\rho}} \\\\partial_{\\\\mu}{e_{m}\\\\,^{\\\\mu}} e e_{n}\\\\,^{\\\\nu} e_{p}\\\\,^{\\\\rho}-\\\\bar{\\\\epsilon} \\\\Gamma^{m n p} D_{\\\\nu}{\\\\psi_{\\\\rho}} \\\\partial_{\\\\mu}{e_{n}\\\\,^{\\\\nu}} e e_{m}\\\\,^{\\\\mu} e_{p}\\\\,^{\\\\rho}-\\\\bar{\\\\epsilon} \\\\Gamma^{m n p} D_{\\\\nu}{\\\\psi_{\\\\rho}} \\\\partial_{\\\\mu}{e_{p}\\\\,^{\\\\rho}} e e_{m}\\\\,^{\\\\mu} e_{n}\\\\,^{\\\\nu} - \\\\frac{1}{4}\\\\bar{\\\\epsilon} \\\\Gamma^{q r} \\\\Gamma^{m n p} D_{\\\\nu}{\\\\psi_{\\\\rho}} \\\\omega_{\\\\mu q r} e e_{m}\\\\,^{\\\\mu} e_{n}\\\\,^{\\\\nu} e_{p}\\\\,^{\\\\rho}\\\\right)\\\\,\\\\,{\\\\rm d}x\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"unwrap(_, $\\\\partial{#}$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{} - \\\\frac{1}{2}\\\\int \\\\left(-\\\\bar{\\\\epsilon} \\\\Gamma^{m n p} \\\\partial_{\\\\mu}{D_{\\\\nu}{\\\\psi_{\\\\rho}}} e e_{m}\\\\,^{\\\\mu} e_{n}\\\\,^{\\\\nu} e_{p}\\\\,^{\\\\rho}-\\\\bar{\\\\epsilon} \\\\Gamma^{m n p} D_{\\\\nu}{\\\\psi_{\\\\rho}} \\\\partial_{\\\\mu}{e} e_{m}\\\\,^{\\\\mu} e_{n}\\\\,^{\\\\nu} e_{p}\\\\,^{\\\\rho}-\\\\bar{\\\\epsilon} \\\\Gamma^{m n p} D_{\\\\nu}{\\\\psi_{\\\\rho}} \\\\partial_{\\\\mu}{e_{m}\\\\,^{\\\\mu}} e e_{n}\\\\,^{\\\\nu} e_{p}\\\\,^{\\\\rho}-\\\\bar{\\\\epsilon} \\\\Gamma^{m n p} D_{\\\\nu}{\\\\psi_{\\\\rho}} \\\\partial_{\\\\mu}{e_{n}\\\\,^{\\\\nu}} e e_{m}\\\\,^{\\\\mu} e_{p}\\\\,^{\\\\rho}-\\\\bar{\\\\epsilon} \\\\Gamma^{m n p} D_{\\\\nu}{\\\\psi_{\\\\rho}} \\\\partial_{\\\\mu}{e_{p}\\\\,^{\\\\rho}} e e_{m}\\\\,^{\\\\mu} e_{n}\\\\,^{\\\\nu} - \\\\frac{1}{4}\\\\bar{\\\\epsilon} \\\\left(\\\\Gamma^{q n p} \\\\delta^{m r}-\\\\Gamma^{q n m} \\\\delta^{p r}+\\\\Gamma^{q p m} \\\\delta^{n r}-\\\\Gamma^{r n p} \\\\delta^{m q}+\\\\Gamma^{r n m} \\\\delta^{p q}-\\\\Gamma^{r p m} \\\\delta^{n q}+\\\\Gamma^{p} \\\\delta^{m r} \\\\delta^{n q}-\\\\Gamma^{m} \\\\delta^{n q} \\\\delta^{p r}+\\\\Gamma^{n} \\\\delta^{m q} \\\\delta^{p r}-\\\\Gamma^{p} \\\\delta^{m q} \\\\delta^{n r}+\\\\Gamma^{m} \\\\delta^{n r} \\\\delta^{p q}-\\\\Gamma^{n} \\\\delta^{m r} \\\\delta^{p q}\\\\right) D_{\\\\nu}{\\\\psi_{\\\\rho}} \\\\omega_{\\\\mu q r} e e_{m}\\\\,^{\\\\mu} e_{n}\\\\,^{\\\\nu} e_{p}\\\\,^{\\\\rho}\\\\right)\\\\,\\\\,{\\\\rm d}x\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"join_gamma(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{} - \\\\frac{1}{2}\\\\int \\\\left(-\\\\bar{\\\\epsilon} \\\\Gamma^{m n p} \\\\partial_{\\\\nu}{D_{\\\\mu}{\\\\psi_{\\\\rho}}} e e_{m}\\\\,^{\\\\nu} e_{n}\\\\,^{\\\\mu} e_{p}\\\\,^{\\\\rho}-\\\\bar{\\\\epsilon} \\\\Gamma^{m n p} D_{\\\\mu}{\\\\psi_{\\\\rho}} \\\\partial_{\\\\nu}{e} e_{m}\\\\,^{\\\\mu} e_{n}\\\\,^{\\\\rho} e_{p}\\\\,^{\\\\nu}-\\\\bar{\\\\epsilon} \\\\Gamma^{m n p} D_{\\\\mu}{\\\\psi_{\\\\rho}} \\\\partial_{\\\\nu}{e_{m}\\\\,^{\\\\nu}} e e_{n}\\\\,^{\\\\mu} e_{p}\\\\,^{\\\\rho}-\\\\bar{\\\\epsilon} \\\\Gamma^{m n p} D_{\\\\mu}{\\\\psi_{\\\\rho}} \\\\partial_{\\\\nu}{e_{m}\\\\,^{\\\\mu}} e e_{n}\\\\,^{\\\\rho} e_{p}\\\\,^{\\\\nu}+\\\\bar{\\\\epsilon} \\\\Gamma^{m n p} D_{\\\\mu}{\\\\psi_{\\\\rho}} \\\\partial_{\\\\nu}{e_{m}\\\\,^{\\\\rho}} e e_{n}\\\\,^{\\\\mu} e_{p}\\\\,^{\\\\nu} - \\\\frac{1}{2}\\\\bar{\\\\epsilon} \\\\Gamma^{m n p} D_{\\\\mu}{\\\\psi_{\\\\rho}} \\\\delta^{q r} \\\\omega_{\\\\nu m q} e e_{n}\\\\,^{\\\\mu} e_{p}\\\\,^{\\\\rho} e_{r}\\\\,^{\\\\nu}+\\\\frac{1}{2}\\\\bar{\\\\epsilon} \\\\Gamma^{m n p} D_{\\\\mu}{\\\\psi_{\\\\rho}} \\\\delta^{q r} \\\\omega_{\\\\nu m q} e e_{n}\\\\,^{\\\\mu} e_{p}\\\\,^{\\\\nu} e_{r}\\\\,^{\\\\rho} - \\\\frac{1}{2}\\\\bar{\\\\epsilon} \\\\Gamma^{m n p} D_{\\\\mu}{\\\\psi_{\\\\rho}} \\\\delta^{q r} \\\\omega_{\\\\nu m q} e e_{n}\\\\,^{\\\\rho} e_{p}\\\\,^{\\\\nu} e_{r}\\\\,^{\\\\mu} - \\\\frac{1}{2}\\\\bar{\\\\epsilon} \\\\Gamma^{m} D_{\\\\mu}{\\\\psi_{\\\\rho}} \\\\delta^{n p} \\\\delta^{q r} \\\\omega_{\\\\nu n q} e e_{m}\\\\,^{\\\\rho} e_{p}\\\\,^{\\\\mu} e_{r}\\\\,^{\\\\nu}+\\\\frac{1}{2}\\\\bar{\\\\epsilon} \\\\Gamma^{m} D_{\\\\mu}{\\\\psi_{\\\\rho}} \\\\delta^{n p} \\\\delta^{q r} \\\\omega_{\\\\nu n q} e e_{m}\\\\,^{\\\\nu} e_{p}\\\\,^{\\\\mu} e_{r}\\\\,^{\\\\rho}+\\\\frac{1}{2}\\\\bar{\\\\epsilon} \\\\Gamma^{m} D_{\\\\mu}{\\\\psi_{\\\\rho}} \\\\delta^{n p} \\\\delta^{q r} \\\\omega_{\\\\nu n q} e e_{m}\\\\,^{\\\\mu} e_{p}\\\\,^{\\\\rho} e_{r}\\\\,^{\\\\nu}\\\\right)\\\\,\\\\,{\\\\rm d}x\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"distribute(_)\\ncanonicalise(_)\\nrename_dummies(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"Is the following correct, or do we miss a spin connection term here?\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"Is the following correct, or do we miss a spin connection term here?\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{} - \\\\frac{1}{2}\\\\int \\\\left( - \\\\frac{1}{4}R_{\\\\nu \\\\mu q r} \\\\bar{\\\\epsilon} \\\\Gamma^{m n p} \\\\Gamma^{q r} \\\\psi_{\\\\rho} e e_{m}\\\\,^{\\\\nu} e_{n}\\\\,^{\\\\mu} e_{p}\\\\,^{\\\\rho}-\\\\bar{\\\\epsilon} \\\\Gamma^{m n p} D_{\\\\mu}{\\\\psi_{\\\\rho}} \\\\partial_{\\\\nu}{e} e_{m}\\\\,^{\\\\mu} e_{n}\\\\,^{\\\\rho} e_{p}\\\\,^{\\\\nu}-\\\\bar{\\\\epsilon} \\\\Gamma^{m n p} D_{\\\\mu}{\\\\psi_{\\\\rho}} \\\\partial_{\\\\nu}{e_{m}\\\\,^{\\\\nu}} e e_{n}\\\\,^{\\\\mu} e_{p}\\\\,^{\\\\rho}-\\\\bar{\\\\epsilon} \\\\Gamma^{m n p} D_{\\\\mu}{\\\\psi_{\\\\rho}} \\\\partial_{\\\\nu}{e_{m}\\\\,^{\\\\mu}} e e_{n}\\\\,^{\\\\rho} e_{p}\\\\,^{\\\\nu}+\\\\bar{\\\\epsilon} \\\\Gamma^{m n p} D_{\\\\mu}{\\\\psi_{\\\\rho}} \\\\partial_{\\\\nu}{e_{m}\\\\,^{\\\\rho}} e e_{n}\\\\,^{\\\\mu} e_{p}\\\\,^{\\\\nu} - \\\\frac{1}{2}\\\\bar{\\\\epsilon} \\\\Gamma^{m n p} D_{\\\\mu}{\\\\psi_{\\\\rho}} \\\\delta^{q r} \\\\omega_{\\\\nu m q} e e_{n}\\\\,^{\\\\mu} e_{p}\\\\,^{\\\\rho} e_{r}\\\\,^{\\\\nu}+\\\\frac{1}{2}\\\\bar{\\\\epsilon} \\\\Gamma^{m n p} D_{\\\\mu}{\\\\psi_{\\\\rho}} \\\\delta^{q r} \\\\omega_{\\\\nu m q} e e_{n}\\\\,^{\\\\mu} e_{p}\\\\,^{\\\\nu} e_{r}\\\\,^{\\\\rho} - \\\\frac{1}{2}\\\\bar{\\\\epsilon} \\\\Gamma^{m n p} D_{\\\\mu}{\\\\psi_{\\\\rho}} \\\\delta^{q r} \\\\omega_{\\\\nu m q} e e_{n}\\\\,^{\\\\rho} e_{p}\\\\,^{\\\\nu} e_{r}\\\\,^{\\\\mu} - \\\\frac{1}{2}\\\\bar{\\\\epsilon} \\\\Gamma^{m} D_{\\\\mu}{\\\\psi_{\\\\rho}} \\\\delta^{n p} \\\\delta^{q r} \\\\omega_{\\\\nu n q} e e_{m}\\\\,^{\\\\rho} e_{p}\\\\,^{\\\\mu} e_{r}\\\\,^{\\\\nu}+\\\\frac{1}{2}\\\\bar{\\\\epsilon} \\\\Gamma^{m} D_{\\\\mu}{\\\\psi_{\\\\rho}} \\\\delta^{n p} \\\\delta^{q r} \\\\omega_{\\\\nu n q} e e_{m}\\\\,^{\\\\nu} e_{p}\\\\,^{\\\\mu} e_{r}\\\\,^{\\\\rho}+\\\\frac{1}{2}\\\\bar{\\\\epsilon} \\\\Gamma^{m} D_{\\\\mu}{\\\\psi_{\\\\rho}} \\\\delta^{n p} \\\\delta^{q r} \\\\omega_{\\\\nu n q} e e_{m}\\\\,^{\\\\mu} e_{p}\\\\,^{\\\\rho} e_{r}\\\\,^{\\\\nu}\\\\right)\\\\,\\\\,{\\\\rm d}x\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"substitute(_,  $\\\\partial_{\\\\mu}{D_{\\\\nu}{\\\\psi_{\\\\rho}}} -> 1/4 R_{\\\\mu\\\\nu m n}\\\\Gamma^{m n} \\\\psi_{\\\\rho}$ );\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{} - \\\\frac{1}{2}\\\\int \\\\left( - \\\\frac{1}{4}R_{\\\\nu \\\\mu q r} \\\\bar{\\\\epsilon} \\\\Gamma^{m n p} \\\\Gamma^{q r} \\\\psi_{\\\\rho} e e_{m}\\\\,^{\\\\nu} e_{n}\\\\,^{\\\\mu} e_{p}\\\\,^{\\\\rho}+\\\\bar{\\\\epsilon} \\\\Gamma^{m n p} D_{\\\\mu}{\\\\psi_{\\\\rho}} \\\\partial_{\\\\nu}{e_{q}\\\\,^{\\\\sigma}} e e^{q}\\\\,_{\\\\sigma} e_{m}\\\\,^{\\\\mu} e_{n}\\\\,^{\\\\rho} e_{p}\\\\,^{\\\\nu}-\\\\bar{\\\\epsilon} \\\\Gamma^{m n p} D_{\\\\mu}{\\\\psi_{\\\\rho}} \\\\partial_{\\\\nu}{e_{m}\\\\,^{\\\\nu}} e e_{n}\\\\,^{\\\\mu} e_{p}\\\\,^{\\\\rho}-\\\\bar{\\\\epsilon} \\\\Gamma^{m n p} D_{\\\\mu}{\\\\psi_{\\\\rho}} \\\\partial_{\\\\nu}{e_{m}\\\\,^{\\\\mu}} e e_{n}\\\\,^{\\\\rho} e_{p}\\\\,^{\\\\nu}+\\\\bar{\\\\epsilon} \\\\Gamma^{m n p} D_{\\\\mu}{\\\\psi_{\\\\rho}} \\\\partial_{\\\\nu}{e_{m}\\\\,^{\\\\rho}} e e_{n}\\\\,^{\\\\mu} e_{p}\\\\,^{\\\\nu} - \\\\frac{1}{2}\\\\bar{\\\\epsilon} \\\\Gamma^{m n p} D_{\\\\mu}{\\\\psi_{\\\\rho}} \\\\delta^{q r} \\\\omega_{\\\\nu m q} e e_{n}\\\\,^{\\\\mu} e_{p}\\\\,^{\\\\rho} e_{r}\\\\,^{\\\\nu}+\\\\frac{1}{2}\\\\bar{\\\\epsilon} \\\\Gamma^{m n p} D_{\\\\mu}{\\\\psi_{\\\\rho}} \\\\delta^{q r} \\\\omega_{\\\\nu m q} e e_{n}\\\\,^{\\\\mu} e_{p}\\\\,^{\\\\nu} e_{r}\\\\,^{\\\\rho} - \\\\frac{1}{2}\\\\bar{\\\\epsilon} \\\\Gamma^{m n p} D_{\\\\mu}{\\\\psi_{\\\\rho}} \\\\delta^{q r} \\\\omega_{\\\\nu m q} e e_{n}\\\\,^{\\\\rho} e_{p}\\\\,^{\\\\nu} e_{r}\\\\,^{\\\\mu} - \\\\frac{1}{2}\\\\bar{\\\\epsilon} \\\\Gamma^{m} D_{\\\\mu}{\\\\psi_{\\\\rho}} \\\\delta^{n p} \\\\delta^{q r} \\\\omega_{\\\\nu n q} e e_{m}\\\\,^{\\\\rho} e_{p}\\\\,^{\\\\mu} e_{r}\\\\,^{\\\\nu}+\\\\frac{1}{2}\\\\bar{\\\\epsilon} \\\\Gamma^{m} D_{\\\\mu}{\\\\psi_{\\\\rho}} \\\\delta^{n p} \\\\delta^{q r} \\\\omega_{\\\\nu n q} e e_{m}\\\\,^{\\\\nu} e_{p}\\\\,^{\\\\mu} e_{r}\\\\,^{\\\\rho}+\\\\frac{1}{2}\\\\bar{\\\\epsilon} \\\\Gamma^{m} D_{\\\\mu}{\\\\psi_{\\\\rho}} \\\\delta^{n p} \\\\delta^{q r} \\\\omega_{\\\\nu n q} e e_{m}\\\\,^{\\\\mu} e_{p}\\\\,^{\\\\rho} e_{r}\\\\,^{\\\\nu}\\\\right)\\\\,\\\\,{\\\\rm d}x\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"substitute(L, $\\\\partial_{\\\\rho}{e} -> - e e^{n}_{\\\\mu} \\\\partial_{\\\\rho}{ e_{n}^{\\\\mu} }$ );\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{} - \\\\frac{1}{2}\\\\int \\\\left( - \\\\frac{1}{4}R_{\\\\mu \\\\nu m n} \\\\bar{\\\\epsilon} \\\\Gamma^{p q r} \\\\Gamma^{m n} \\\\psi_{\\\\rho} e e_{p}\\\\,^{\\\\mu} e_{q}\\\\,^{\\\\nu} e_{r}\\\\,^{\\\\rho}+\\\\bar{\\\\epsilon} \\\\Gamma^{m n p} D_{\\\\mu}{\\\\psi_{\\\\rho}} \\\\partial_{\\\\nu}{e_{q}\\\\,^{\\\\sigma}} e e^{q}\\\\,_{\\\\sigma} e_{m}\\\\,^{\\\\mu} e_{n}\\\\,^{\\\\rho} e_{p}\\\\,^{\\\\nu}-\\\\bar{\\\\epsilon} \\\\Gamma^{m n p} D_{\\\\mu}{\\\\psi_{\\\\rho}} \\\\partial_{\\\\nu}{e_{m}\\\\,^{\\\\nu}} e e_{n}\\\\,^{\\\\mu} e_{p}\\\\,^{\\\\rho}-\\\\bar{\\\\epsilon} \\\\Gamma^{m n p} D_{\\\\mu}{\\\\psi_{\\\\rho}} \\\\partial_{\\\\nu}{e_{m}\\\\,^{\\\\mu}} e e_{n}\\\\,^{\\\\rho} e_{p}\\\\,^{\\\\nu}+\\\\bar{\\\\epsilon} \\\\Gamma^{m n p} D_{\\\\mu}{\\\\psi_{\\\\rho}} \\\\partial_{\\\\nu}{e_{m}\\\\,^{\\\\rho}} e e_{n}\\\\,^{\\\\mu} e_{p}\\\\,^{\\\\nu} - \\\\frac{1}{2}\\\\bar{\\\\epsilon} \\\\Gamma^{m n p} D_{\\\\mu}{\\\\psi_{\\\\rho}} \\\\delta^{q r} \\\\omega_{\\\\nu m q} e e_{n}\\\\,^{\\\\mu} e_{p}\\\\,^{\\\\rho} e_{r}\\\\,^{\\\\nu}+\\\\frac{1}{2}\\\\bar{\\\\epsilon} \\\\Gamma^{m n p} D_{\\\\mu}{\\\\psi_{\\\\rho}} \\\\delta^{q r} \\\\omega_{\\\\nu m q} e e_{n}\\\\,^{\\\\mu} e_{p}\\\\,^{\\\\nu} e_{r}\\\\,^{\\\\rho} - \\\\frac{1}{2}\\\\bar{\\\\epsilon} \\\\Gamma^{m n p} D_{\\\\mu}{\\\\psi_{\\\\rho}} \\\\delta^{q r} \\\\omega_{\\\\nu m q} e e_{n}\\\\,^{\\\\rho} e_{p}\\\\,^{\\\\nu} e_{r}\\\\,^{\\\\mu} - \\\\frac{1}{2}\\\\bar{\\\\epsilon} \\\\Gamma^{m} D_{\\\\mu}{\\\\psi_{\\\\rho}} \\\\delta^{n p} \\\\delta^{q r} \\\\omega_{\\\\nu n q} e e_{m}\\\\,^{\\\\rho} e_{p}\\\\,^{\\\\mu} e_{r}\\\\,^{\\\\nu}+\\\\frac{1}{2}\\\\bar{\\\\epsilon} \\\\Gamma^{m} D_{\\\\mu}{\\\\psi_{\\\\rho}} \\\\delta^{n p} \\\\delta^{q r} \\\\omega_{\\\\nu n q} e e_{m}\\\\,^{\\\\nu} e_{p}\\\\,^{\\\\mu} e_{r}\\\\,^{\\\\rho}+\\\\frac{1}{2}\\\\bar{\\\\epsilon} \\\\Gamma^{m} D_{\\\\mu}{\\\\psi_{\\\\rho}} \\\\delta^{n p} \\\\delta^{q r} \\\\omega_{\\\\nu n q} e e_{m}\\\\,^{\\\\mu} e_{p}\\\\,^{\\\\rho} e_{r}\\\\,^{\\\\nu}\\\\right)\\\\,\\\\,{\\\\rm d}x\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"canonicalise(_)\\nrename_dummies(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"Last three terms disappeared in the original computation, but that did a weird join... Is that based\\non a trick in vNh?\\nWe now need to replace the derivative of the vielbein using the fact that it is covariantly constant. So we can trade\\nthe derivative for a term with the spin connection and a term with the torsion.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"Last three terms disappeared in the original computation, but that did a weird join... Is that based\\non a trick in vNh?\\nWe now need to replace the derivative of the vielbein using the fact that it is covariantly constant. So we can trade\\nthe derivative for a term with the spin connection and a term with the torsion.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{} - \\\\frac{1}{2}\\\\int \\\\left( - \\\\frac{1}{4}R_{\\\\mu \\\\nu m n} \\\\bar{\\\\epsilon} \\\\Gamma^{p q r} \\\\Gamma^{m n} \\\\psi_{\\\\rho} e e_{p}\\\\,^{\\\\mu} e_{q}\\\\,^{\\\\nu} e_{r}\\\\,^{\\\\rho}-\\\\bar{\\\\epsilon} \\\\Gamma^{m n p} D_{\\\\mu}{\\\\psi_{\\\\rho}} \\\\delta^{s r} \\\\omega_{\\\\nu q s} e e_{r}\\\\,^{\\\\sigma} e^{q}\\\\,_{\\\\sigma} e_{m}\\\\,^{\\\\mu} e_{n}\\\\,^{\\\\rho} e_{p}\\\\,^{\\\\nu}-C^{\\\\sigma}\\\\,_{\\\\nu \\\\kappa} \\\\bar{\\\\epsilon} \\\\Gamma^{m n p} D_{\\\\mu}{\\\\psi_{\\\\rho}} e e_{q}\\\\,^{\\\\kappa} e^{q}\\\\,_{\\\\sigma} e_{m}\\\\,^{\\\\mu} e_{n}\\\\,^{\\\\rho} e_{p}\\\\,^{\\\\nu}+\\\\bar{\\\\epsilon} \\\\Gamma^{m n p} D_{\\\\mu}{\\\\psi_{\\\\rho}} \\\\delta^{r q} \\\\omega_{\\\\nu m r} e e_{n}\\\\,^{\\\\mu} e_{p}\\\\,^{\\\\rho} e_{q}\\\\,^{\\\\nu}+C^{\\\\nu}\\\\,_{\\\\nu \\\\sigma} \\\\bar{\\\\epsilon} \\\\Gamma^{m n p} D_{\\\\mu}{\\\\psi_{\\\\rho}} e e_{m}\\\\,^{\\\\sigma} e_{n}\\\\,^{\\\\mu} e_{p}\\\\,^{\\\\rho}+\\\\bar{\\\\epsilon} \\\\Gamma^{m n p} D_{\\\\mu}{\\\\psi_{\\\\rho}} \\\\delta^{r q} \\\\omega_{\\\\nu m r} e e_{n}\\\\,^{\\\\rho} e_{p}\\\\,^{\\\\nu} e_{q}\\\\,^{\\\\mu}+C^{\\\\mu}\\\\,_{\\\\nu \\\\sigma} \\\\bar{\\\\epsilon} \\\\Gamma^{m n p} D_{\\\\mu}{\\\\psi_{\\\\rho}} e e_{m}\\\\,^{\\\\sigma} e_{n}\\\\,^{\\\\rho} e_{p}\\\\,^{\\\\nu}-\\\\bar{\\\\epsilon} \\\\Gamma^{m n p} D_{\\\\mu}{\\\\psi_{\\\\rho}} \\\\delta^{r q} \\\\omega_{\\\\nu m r} e e_{n}\\\\,^{\\\\mu} e_{p}\\\\,^{\\\\nu} e_{q}\\\\,^{\\\\rho}-C^{\\\\rho}\\\\,_{\\\\nu \\\\sigma} \\\\bar{\\\\epsilon} \\\\Gamma^{m n p} D_{\\\\mu}{\\\\psi_{\\\\rho}} e e_{m}\\\\,^{\\\\sigma} e_{n}\\\\,^{\\\\mu} e_{p}\\\\,^{\\\\nu} - \\\\frac{1}{2}\\\\bar{\\\\epsilon} \\\\Gamma^{m n p} D_{\\\\mu}{\\\\psi_{\\\\rho}} \\\\delta^{q r} \\\\omega_{\\\\nu m q} e e_{n}\\\\,^{\\\\mu} e_{p}\\\\,^{\\\\rho} e_{r}\\\\,^{\\\\nu}+\\\\frac{1}{2}\\\\bar{\\\\epsilon} \\\\Gamma^{m n p} D_{\\\\mu}{\\\\psi_{\\\\rho}} \\\\delta^{q r} \\\\omega_{\\\\nu m q} e e_{n}\\\\,^{\\\\mu} e_{p}\\\\,^{\\\\nu} e_{r}\\\\,^{\\\\rho} - \\\\frac{1}{2}\\\\bar{\\\\epsilon} \\\\Gamma^{m n p} D_{\\\\mu}{\\\\psi_{\\\\rho}} \\\\delta^{q r} \\\\omega_{\\\\nu m q} e e_{n}\\\\,^{\\\\rho} e_{p}\\\\,^{\\\\nu} e_{r}\\\\,^{\\\\mu} - \\\\frac{1}{2}\\\\bar{\\\\epsilon} \\\\Gamma^{m} D_{\\\\mu}{\\\\psi_{\\\\rho}} \\\\delta^{n p} \\\\delta^{q r} \\\\omega_{\\\\nu n q} e e_{m}\\\\,^{\\\\rho} e_{p}\\\\,^{\\\\mu} e_{r}\\\\,^{\\\\nu}+\\\\frac{1}{2}\\\\bar{\\\\epsilon} \\\\Gamma^{m} D_{\\\\mu}{\\\\psi_{\\\\rho}} \\\\delta^{n p} \\\\delta^{q r} \\\\omega_{\\\\nu n q} e e_{m}\\\\,^{\\\\nu} e_{p}\\\\,^{\\\\mu} e_{r}\\\\,^{\\\\rho}+\\\\frac{1}{2}\\\\bar{\\\\epsilon} \\\\Gamma^{m} D_{\\\\mu}{\\\\psi_{\\\\rho}} \\\\delta^{n p} \\\\delta^{q r} \\\\omega_{\\\\nu n q} e e_{m}\\\\,^{\\\\mu} e_{p}\\\\,^{\\\\rho} e_{r}\\\\,^{\\\\nu}\\\\right)\\\\,\\\\,{\\\\rm d}x\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"substitute(_, $\\\\partial_{\\\\mu}{e_{m}^{\\\\nu}} -> -\\\\omega_{\\\\mu m p} \\\\delta^{p n} e_{n}^{\\\\nu} - C^{\\\\nu}_{\\\\mu\\\\rho} e_{m}^{\\\\rho}$ )\\ndistribute(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{} - \\\\frac{1}{2}\\\\int \\\\left( - \\\\frac{1}{4}R_{\\\\mu \\\\nu m n} \\\\bar{\\\\epsilon} \\\\Gamma^{p q r} \\\\Gamma^{m n} \\\\psi_{\\\\rho} e e_{p}\\\\,^{\\\\mu} e_{q}\\\\,^{\\\\nu} e_{r}\\\\,^{\\\\rho}+\\\\bar{\\\\epsilon} \\\\Gamma^{m n p} D_{\\\\mu}{\\\\psi_{\\\\rho}} \\\\delta^{q r} \\\\omega_{\\\\nu q s} e e_{m}\\\\,^{\\\\mu} e^{s}\\\\,_{\\\\sigma} e_{n}\\\\,^{\\\\rho} e_{p}\\\\,^{\\\\nu} e_{r}\\\\,^{\\\\sigma}-C^{\\\\mu}\\\\,_{\\\\nu \\\\rho} \\\\bar{\\\\epsilon} \\\\Gamma^{m n p} D_{\\\\sigma}{\\\\psi_{\\\\kappa}} e e_{m}\\\\,^{\\\\nu} e^{q}\\\\,_{\\\\mu} e_{n}\\\\,^{\\\\sigma} e_{p}\\\\,^{\\\\kappa} e_{q}\\\\,^{\\\\rho}+\\\\frac{1}{2}\\\\bar{\\\\epsilon} \\\\Gamma^{m n p} D_{\\\\mu}{\\\\psi_{\\\\rho}} \\\\delta^{q r} \\\\omega_{\\\\nu m q} e e_{n}\\\\,^{\\\\mu} e_{p}\\\\,^{\\\\rho} e_{r}\\\\,^{\\\\nu}+C^{\\\\mu}\\\\,_{\\\\mu \\\\nu} \\\\bar{\\\\epsilon} \\\\Gamma^{m n p} D_{\\\\rho}{\\\\psi_{\\\\sigma}} e e_{m}\\\\,^{\\\\nu} e_{n}\\\\,^{\\\\rho} e_{p}\\\\,^{\\\\sigma}+\\\\frac{1}{2}\\\\bar{\\\\epsilon} \\\\Gamma^{m n p} D_{\\\\mu}{\\\\psi_{\\\\rho}} \\\\delta^{q r} \\\\omega_{\\\\nu m q} e e_{n}\\\\,^{\\\\rho} e_{p}\\\\,^{\\\\nu} e_{r}\\\\,^{\\\\mu}+C^{\\\\mu}\\\\,_{\\\\nu \\\\rho} \\\\bar{\\\\epsilon} \\\\Gamma^{m n p} D_{\\\\mu}{\\\\psi_{\\\\sigma}} e e_{m}\\\\,^{\\\\nu} e_{n}\\\\,^{\\\\rho} e_{p}\\\\,^{\\\\sigma} - \\\\frac{1}{2}\\\\bar{\\\\epsilon} \\\\Gamma^{m n p} D_{\\\\mu}{\\\\psi_{\\\\rho}} \\\\delta^{q r} \\\\omega_{\\\\nu m q} e e_{n}\\\\,^{\\\\mu} e_{p}\\\\,^{\\\\nu} e_{r}\\\\,^{\\\\rho}-C^{\\\\mu}\\\\,_{\\\\nu \\\\rho} \\\\bar{\\\\epsilon} \\\\Gamma^{m n p} D_{\\\\sigma}{\\\\psi_{\\\\mu}} e e_{m}\\\\,^{\\\\nu} e_{n}\\\\,^{\\\\rho} e_{p}\\\\,^{\\\\sigma} - \\\\frac{1}{2}\\\\bar{\\\\epsilon} \\\\Gamma^{m} D_{\\\\mu}{\\\\psi_{\\\\rho}} \\\\delta^{n p} \\\\delta^{q r} \\\\omega_{\\\\nu n q} e e_{m}\\\\,^{\\\\rho} e_{p}\\\\,^{\\\\mu} e_{r}\\\\,^{\\\\nu}+\\\\frac{1}{2}\\\\bar{\\\\epsilon} \\\\Gamma^{m} D_{\\\\mu}{\\\\psi_{\\\\rho}} \\\\delta^{n p} \\\\delta^{q r} \\\\omega_{\\\\nu n q} e e_{m}\\\\,^{\\\\nu} e_{p}\\\\,^{\\\\mu} e_{r}\\\\,^{\\\\rho}+\\\\frac{1}{2}\\\\bar{\\\\epsilon} \\\\Gamma^{m} D_{\\\\mu}{\\\\psi_{\\\\rho}} \\\\delta^{n p} \\\\delta^{q r} \\\\omega_{\\\\nu n q} e e_{m}\\\\,^{\\\\mu} e_{p}\\\\,^{\\\\rho} e_{r}\\\\,^{\\\\nu}\\\\right)\\\\,\\\\,{\\\\rm d}x\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"canonicalise(_)\\nrename_dummies(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"The gamma3 omega terms should have gone now, or after eliminate of vielbeine. First indeed goes. 2,3,4 not sure?\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"The gamma3 omega terms should have gone now, or after eliminate of vielbeine. First indeed goes. 2,3,4 not sure?\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{} - \\\\frac{1}{2}\\\\int \\\\left( - \\\\frac{1}{4}R_{\\\\mu \\\\nu m n} \\\\bar{\\\\epsilon} \\\\Gamma^{p q r} \\\\Gamma^{m n} \\\\psi_{\\\\rho} e e_{p}\\\\,^{\\\\mu} e_{q}\\\\,^{\\\\nu} e_{r}\\\\,^{\\\\rho}+\\\\bar{\\\\epsilon} \\\\Gamma^{m n p} D_{\\\\mu}{\\\\psi_{\\\\rho}} \\\\delta^{q s} \\\\omega_{\\\\nu q s} e e_{m}\\\\,^{\\\\mu} e_{n}\\\\,^{\\\\rho} e_{p}\\\\,^{\\\\nu}-C^{\\\\mu}\\\\,_{\\\\nu \\\\rho} \\\\bar{\\\\epsilon} \\\\Gamma^{m n p} D_{\\\\sigma}{\\\\psi_{\\\\kappa}} e e_{m}\\\\,^{\\\\nu} e^{q}\\\\,_{\\\\mu} e_{n}\\\\,^{\\\\sigma} e_{p}\\\\,^{\\\\kappa} e_{q}\\\\,^{\\\\rho}+\\\\frac{1}{2}\\\\bar{\\\\epsilon} \\\\Gamma^{m n p} D_{\\\\mu}{\\\\psi_{\\\\rho}} \\\\delta^{q r} \\\\omega_{\\\\nu m q} e e_{n}\\\\,^{\\\\mu} e_{p}\\\\,^{\\\\rho} e_{r}\\\\,^{\\\\nu}+C^{\\\\mu}\\\\,_{\\\\mu \\\\nu} \\\\bar{\\\\epsilon} \\\\Gamma^{m n p} D_{\\\\rho}{\\\\psi_{\\\\sigma}} e e_{m}\\\\,^{\\\\nu} e_{n}\\\\,^{\\\\rho} e_{p}\\\\,^{\\\\sigma}+\\\\frac{1}{2}\\\\bar{\\\\epsilon} \\\\Gamma^{m n p} D_{\\\\mu}{\\\\psi_{\\\\rho}} \\\\delta^{q r} \\\\omega_{\\\\nu m q} e e_{n}\\\\,^{\\\\rho} e_{p}\\\\,^{\\\\nu} e_{r}\\\\,^{\\\\mu}+C^{\\\\mu}\\\\,_{\\\\nu \\\\rho} \\\\bar{\\\\epsilon} \\\\Gamma^{m n p} D_{\\\\mu}{\\\\psi_{\\\\sigma}} e e_{m}\\\\,^{\\\\nu} e_{n}\\\\,^{\\\\rho} e_{p}\\\\,^{\\\\sigma} - \\\\frac{1}{2}\\\\bar{\\\\epsilon} \\\\Gamma^{m n p} D_{\\\\mu}{\\\\psi_{\\\\rho}} \\\\delta^{q r} \\\\omega_{\\\\nu m q} e e_{n}\\\\,^{\\\\mu} e_{p}\\\\,^{\\\\nu} e_{r}\\\\,^{\\\\rho}-C^{\\\\mu}\\\\,_{\\\\nu \\\\rho} \\\\bar{\\\\epsilon} \\\\Gamma^{m n p} D_{\\\\sigma}{\\\\psi_{\\\\mu}} e e_{m}\\\\,^{\\\\nu} e_{n}\\\\,^{\\\\rho} e_{p}\\\\,^{\\\\sigma} - \\\\frac{1}{2}\\\\bar{\\\\epsilon} \\\\Gamma^{m} D_{\\\\mu}{\\\\psi_{\\\\rho}} \\\\delta^{n p} \\\\delta^{q r} \\\\omega_{\\\\nu n q} e e_{m}\\\\,^{\\\\rho} e_{p}\\\\,^{\\\\mu} e_{r}\\\\,^{\\\\nu}+\\\\frac{1}{2}\\\\bar{\\\\epsilon} \\\\Gamma^{m} D_{\\\\mu}{\\\\psi_{\\\\rho}} \\\\delta^{n p} \\\\delta^{q r} \\\\omega_{\\\\nu n q} e e_{m}\\\\,^{\\\\nu} e_{p}\\\\,^{\\\\mu} e_{r}\\\\,^{\\\\rho}+\\\\frac{1}{2}\\\\bar{\\\\epsilon} \\\\Gamma^{m} D_{\\\\mu}{\\\\psi_{\\\\rho}} \\\\delta^{n p} \\\\delta^{q r} \\\\omega_{\\\\nu n q} e e_{m}\\\\,^{\\\\mu} e_{p}\\\\,^{\\\\rho} e_{r}\\\\,^{\\\\nu}\\\\right)\\\\,\\\\,{\\\\rm d}x\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"substitute(_, $e^{s}_{\\\\sigma} e_{r}^{\\\\sigma} = \\\\delta^{s}_{r}$ );\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{} - \\\\frac{1}{2}\\\\int \\\\left( - \\\\frac{1}{4}R_{\\\\mu \\\\nu m n} \\\\bar{\\\\epsilon} \\\\Gamma^{p q r} \\\\Gamma^{m n} \\\\psi_{\\\\rho} e e_{p}\\\\,^{\\\\mu} e_{q}\\\\,^{\\\\nu} e_{r}\\\\,^{\\\\rho}-C^{\\\\kappa}\\\\,_{\\\\mu \\\\nu} \\\\bar{\\\\epsilon} \\\\Gamma^{m n p} D_{\\\\rho}{\\\\psi_{\\\\sigma}} e e_{m}\\\\,^{\\\\mu} e^{q}\\\\,_{\\\\kappa} e_{n}\\\\,^{\\\\rho} e_{p}\\\\,^{\\\\sigma} e_{q}\\\\,^{\\\\nu}+\\\\frac{1}{2}\\\\bar{\\\\epsilon} \\\\Gamma^{m n p} D_{\\\\mu}{\\\\psi_{\\\\nu}} \\\\delta^{q r} \\\\omega_{\\\\rho m q} e e_{n}\\\\,^{\\\\mu} e_{p}\\\\,^{\\\\nu} e_{r}\\\\,^{\\\\rho}+C^{\\\\mu}\\\\,_{\\\\mu \\\\nu} \\\\bar{\\\\epsilon} \\\\Gamma^{m n p} D_{\\\\rho}{\\\\psi_{\\\\sigma}} e e_{m}\\\\,^{\\\\nu} e_{n}\\\\,^{\\\\rho} e_{p}\\\\,^{\\\\sigma}+\\\\frac{1}{2}\\\\bar{\\\\epsilon} \\\\Gamma^{m n p} D_{\\\\mu}{\\\\psi_{\\\\nu}} \\\\delta^{q r} \\\\omega_{\\\\rho m q} e e_{n}\\\\,^{\\\\nu} e_{p}\\\\,^{\\\\rho} e_{r}\\\\,^{\\\\mu}+C^{\\\\mu}\\\\,_{\\\\nu \\\\rho} \\\\bar{\\\\epsilon} \\\\Gamma^{m n p} D_{\\\\mu}{\\\\psi_{\\\\sigma}} e e_{m}\\\\,^{\\\\nu} e_{n}\\\\,^{\\\\rho} e_{p}\\\\,^{\\\\sigma} - \\\\frac{1}{2}\\\\bar{\\\\epsilon} \\\\Gamma^{m n p} D_{\\\\mu}{\\\\psi_{\\\\nu}} \\\\delta^{q r} \\\\omega_{\\\\rho m q} e e_{n}\\\\,^{\\\\mu} e_{p}\\\\,^{\\\\rho} e_{r}\\\\,^{\\\\nu}-C^{\\\\mu}\\\\,_{\\\\nu \\\\rho} \\\\bar{\\\\epsilon} \\\\Gamma^{m n p} D_{\\\\sigma}{\\\\psi_{\\\\mu}} e e_{m}\\\\,^{\\\\nu} e_{n}\\\\,^{\\\\rho} e_{p}\\\\,^{\\\\sigma} - \\\\frac{1}{2}\\\\bar{\\\\epsilon} \\\\Gamma^{m} D_{\\\\mu}{\\\\psi_{\\\\nu}} \\\\delta^{n p} \\\\delta^{q r} \\\\omega_{\\\\rho n q} e e_{m}\\\\,^{\\\\nu} e_{p}\\\\,^{\\\\mu} e_{r}\\\\,^{\\\\rho}+\\\\frac{1}{2}\\\\bar{\\\\epsilon} \\\\Gamma^{m} D_{\\\\mu}{\\\\psi_{\\\\nu}} \\\\delta^{n p} \\\\delta^{q r} \\\\omega_{\\\\rho n q} e e_{m}\\\\,^{\\\\rho} e_{p}\\\\,^{\\\\mu} e_{r}\\\\,^{\\\\nu}+\\\\frac{1}{2}\\\\bar{\\\\epsilon} \\\\Gamma^{m} D_{\\\\mu}{\\\\psi_{\\\\nu}} \\\\delta^{n p} \\\\delta^{q r} \\\\omega_{\\\\rho n q} e e_{m}\\\\,^{\\\\mu} e_{p}\\\\,^{\\\\nu} e_{r}\\\\,^{\\\\rho}\\\\right)\\\\,\\\\,{\\\\rm d}x\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"canonicalise(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{} - \\\\frac{1}{2}\\\\int \\\\left( - \\\\frac{1}{4}R_{\\\\mu \\\\nu m n} \\\\bar{\\\\epsilon} \\\\Gamma^{p q r} \\\\Gamma^{m n} \\\\psi_{\\\\rho} e e_{p}\\\\,^{\\\\mu} e_{q}\\\\,^{\\\\nu} e_{r}\\\\,^{\\\\rho}-C^{\\\\mu}\\\\,_{\\\\nu \\\\rho} \\\\bar{\\\\epsilon} \\\\Gamma^{m n p} D_{\\\\sigma}{\\\\psi_{\\\\kappa}} e e_{m}\\\\,^{\\\\nu} e^{q}\\\\,_{\\\\mu} e_{n}\\\\,^{\\\\sigma} e_{p}\\\\,^{\\\\kappa} e_{q}\\\\,^{\\\\rho}+\\\\frac{1}{2}\\\\bar{\\\\epsilon} \\\\Gamma^{m n p} D_{\\\\mu}{\\\\psi_{\\\\rho}} \\\\delta^{q r} \\\\omega_{\\\\nu m q} e e_{n}\\\\,^{\\\\mu} e_{p}\\\\,^{\\\\rho} e_{r}\\\\,^{\\\\nu}+C^{\\\\mu}\\\\,_{\\\\mu \\\\nu} \\\\bar{\\\\epsilon} \\\\Gamma^{m n p} D_{\\\\rho}{\\\\psi_{\\\\sigma}} e e_{m}\\\\,^{\\\\nu} e_{n}\\\\,^{\\\\rho} e_{p}\\\\,^{\\\\sigma}+\\\\frac{1}{2}\\\\bar{\\\\epsilon} \\\\Gamma^{m n p} D_{\\\\mu}{\\\\psi_{\\\\rho}} \\\\delta^{q r} \\\\omega_{\\\\nu m q} e e_{n}\\\\,^{\\\\rho} e_{p}\\\\,^{\\\\nu} e_{r}\\\\,^{\\\\mu}+C^{\\\\mu}\\\\,_{\\\\nu \\\\rho} \\\\bar{\\\\epsilon} \\\\Gamma^{m n p} D_{\\\\mu}{\\\\psi_{\\\\sigma}} e e_{m}\\\\,^{\\\\nu} e_{n}\\\\,^{\\\\rho} e_{p}\\\\,^{\\\\sigma} - \\\\frac{1}{2}\\\\bar{\\\\epsilon} \\\\Gamma^{m n p} D_{\\\\mu}{\\\\psi_{\\\\rho}} \\\\delta^{q r} \\\\omega_{\\\\nu m q} e e_{n}\\\\,^{\\\\mu} e_{p}\\\\,^{\\\\nu} e_{r}\\\\,^{\\\\rho}-C^{\\\\mu}\\\\,_{\\\\nu \\\\rho} \\\\bar{\\\\epsilon} \\\\Gamma^{m n p} D_{\\\\sigma}{\\\\psi_{\\\\mu}} e e_{m}\\\\,^{\\\\nu} e_{n}\\\\,^{\\\\rho} e_{p}\\\\,^{\\\\sigma} - \\\\frac{1}{2}\\\\bar{\\\\epsilon} \\\\Gamma^{m} D_{\\\\mu}{\\\\psi_{\\\\rho}} \\\\delta^{n p} \\\\delta^{q r} \\\\omega_{\\\\nu n q} e e_{m}\\\\,^{\\\\rho} e_{p}\\\\,^{\\\\mu} e_{r}\\\\,^{\\\\nu}+\\\\frac{1}{2}\\\\bar{\\\\epsilon} \\\\Gamma^{m} D_{\\\\mu}{\\\\psi_{\\\\rho}} \\\\delta^{n p} \\\\delta^{q r} \\\\omega_{\\\\nu n q} e e_{m}\\\\,^{\\\\nu} e_{p}\\\\,^{\\\\mu} e_{r}\\\\,^{\\\\rho}+\\\\frac{1}{2}\\\\bar{\\\\epsilon} \\\\Gamma^{m} D_{\\\\mu}{\\\\psi_{\\\\rho}} \\\\delta^{n p} \\\\delta^{q r} \\\\omega_{\\\\nu n q} e e_{m}\\\\,^{\\\\mu} e_{p}\\\\,^{\\\\rho} e_{r}\\\\,^{\\\\nu}\\\\right)\\\\,\\\\,{\\\\rm d}x\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"rename_dummies(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\hrule\\n\\\\subsection*{Curvature}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\hrule\\n\\\\subsection*{Curvature}\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"A few quick computations to ensure that we have the right normalisations for curvatures and covariant derivatives.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"A few quick computations to ensure that we have the right normalisations for curvatures and covariant derivatives.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}D_{\\\\mu}{D_{\\\\nu}{\\\\psi_{\\\\rho}}}-D_{\\\\nu}{D_{\\\\mu}{\\\\psi_{\\\\rho}}}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"riem:= D_{\\\\mu}{D_{\\\\nu}{\\\\psi_{\\\\rho}}} - D_{\\\\nu}{D_{\\\\mu}{\\\\psi_{\\\\rho}}};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}D_{\\\\mu}\\\\left(A??\\\\right) = \\\\partial_{\\\\mu}\\\\left(A??\\\\right)+\\\\frac{1}{4}\\\\omega_{\\\\mu m n} \\\\Gamma^{m n} A??\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"covd:= D_{\\\\mu}{A??} = \\\\partial_{\\\\mu}{A??} + 1/4 \\\\omega_{\\\\mu m n} \\\\Gamma^{m n} A??;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\partial_{\\\\mu}\\\\left(\\\\partial_{\\\\nu}{\\\\psi_{\\\\rho}}+\\\\frac{1}{4}\\\\Gamma^{m n} \\\\omega_{\\\\nu m n} \\\\psi_{\\\\rho}\\\\right)+\\\\frac{1}{4}\\\\Gamma^{p q} \\\\omega_{\\\\mu p q} \\\\left(\\\\partial_{\\\\nu}{\\\\psi_{\\\\rho}}+\\\\frac{1}{4}\\\\Gamma^{m n} \\\\omega_{\\\\nu m n} \\\\psi_{\\\\rho}\\\\right)-\\\\partial_{\\\\nu}\\\\left(\\\\partial_{\\\\mu}{\\\\psi_{\\\\rho}}+\\\\frac{1}{4}\\\\Gamma^{m n} \\\\omega_{\\\\mu m n} \\\\psi_{\\\\rho}\\\\right) - \\\\frac{1}{4}\\\\Gamma^{p q} \\\\omega_{\\\\nu p q} \\\\left(\\\\partial_{\\\\mu}{\\\\psi_{\\\\rho}}+\\\\frac{1}{4}\\\\Gamma^{m n} \\\\omega_{\\\\mu m n} \\\\psi_{\\\\rho}\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"substitute(riem, covd);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\frac{1}{4}\\\\Gamma^{m n} \\\\partial_{\\\\mu}{\\\\omega_{\\\\nu m n}} \\\\psi_{\\\\rho} - \\\\frac{1}{2}\\\\Gamma^{m n} \\\\delta^{p q} \\\\omega_{\\\\mu m p} \\\\omega_{\\\\nu n q} \\\\psi_{\\\\rho} - \\\\frac{1}{4}\\\\Gamma^{m n} \\\\partial_{\\\\nu}{\\\\omega_{\\\\mu m n}} \\\\psi_{\\\\rho}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"distribute(_)\\nproduct_rule(_)\\njoin_gamma(_)\\ndistribute(_)\\nunwrap(_)\\ncanonicalise(_)\\nrename_dummies(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\frac{1}{4}\\\\Gamma^{m n} \\\\left(\\\\partial_{\\\\mu}{\\\\omega_{\\\\nu m n}}-\\\\partial_{\\\\nu}{\\\\omega_{\\\\mu m n}}+\\\\delta^{p q} \\\\omega_{\\\\mu m p} \\\\omega_{\\\\nu q n}-\\\\delta^{p q} \\\\omega_{\\\\mu q n} \\\\omega_{\\\\nu m p}\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"goal:= \\\\frac{1}{4} \\\\Gamma^{m n} ( \\\\partial_{\\\\mu}{\\\\omega_{\\\\nu m n}} - \\\\partial_{\\\\nu}{\\\\omega_{\\\\mu m n}} + \\n                                 \\\\omega_{\\\\mu m p} \\\\omega_{\\\\nu q n} \\\\delta^{p q} - \\\\omega_{\\\\nu m p} \\\\omega_{\\\\mu q n} \\\\delta^{p q});\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\frac{1}{4}\\\\Gamma^{m n} \\\\partial_{\\\\mu}{\\\\omega_{\\\\nu m n}} - \\\\frac{1}{4}\\\\Gamma^{m n} \\\\partial_{\\\\nu}{\\\\omega_{\\\\mu m n}}+\\\\frac{1}{4}\\\\Gamma^{m n} \\\\delta^{p q} \\\\omega_{\\\\mu m p} \\\\omega_{\\\\nu q n} - \\\\frac{1}{4}\\\\Gamma^{m n} \\\\delta^{p q} \\\\omega_{\\\\mu q n} \\\\omega_{\\\\nu m p}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"distribute(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\left(\\\\frac{1}{4}\\\\Gamma^{m n} \\\\partial_{\\\\mu}{\\\\omega_{\\\\nu m n}} - \\\\frac{1}{4}\\\\Gamma^{m n} \\\\partial_{\\\\nu}{\\\\omega_{\\\\mu m n}}+\\\\frac{1}{4}\\\\Gamma^{m n} \\\\delta^{p q} \\\\omega_{\\\\mu m p} \\\\omega_{\\\\nu q n} - \\\\frac{1}{4}\\\\Gamma^{m n} \\\\delta^{p q} \\\\omega_{\\\\mu q n} \\\\omega_{\\\\nu m p}\\\\right) \\\\psi_{\\\\rho} - \\\\frac{1}{4}\\\\Gamma^{m n} \\\\partial_{\\\\mu}{\\\\omega_{\\\\nu m n}} \\\\psi_{\\\\rho}+\\\\frac{1}{2}\\\\Gamma^{m n} \\\\delta^{p q} \\\\omega_{\\\\mu m p} \\\\omega_{\\\\nu n q} \\\\psi_{\\\\rho}+\\\\frac{1}{4}\\\\Gamma^{m n} \\\\partial_{\\\\nu}{\\\\omega_{\\\\mu m n}} \\\\psi_{\\\\rho}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"tst:= @(goal) \\\\psi_{\\\\rho} - @(riem);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}0\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"distribute(_)\\ncanonicalise(_)\\nrename_dummies(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1\n}\n"
  },
  {
    "path": "examples/sympy_bridge.cnb",
    "content": "{\n\t\"cell_id\": 17451107616265182499,\n\t\"cells\": [\n\t\t{\n\t\t\t\"cell_id\": 13606667274613717328,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"from cdb.sympy.calculus import diff as D\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 8968997047017838072,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 3283560223550061435,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 11846820707357212391,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"A_{a}(r) r\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}A_{a}\\\\left(r\\\\right) r\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 11895472410413471989,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 9645811331927675225,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"r \\\\partial_{r}(A_{a}(r)) + A_{a}(r)\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}r \\\\partial_{r}\\\\left(A_{a}\\\\left(r\\\\right)\\\\right)+A_{a}\\\\left(r\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex := A_{a}(r) r;\\nD( ex, $r$ );\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 15489099887050608433,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"\"\n\t\t}\n\t],\n\t\"description\": \"Cadabra JSON notebook format\",\n\t\"version\": 1.0\n}\n"
  },
  {
    "path": "examples/sympy_examples.cnb",
    "content": "{\n\t\"cell_id\" : 17675509809027771855,\n\t\"cells\" : \n\t[\n\t\t{\n\t\t\t\"cell_id\" : 11331276970875623492,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 10487953589284012654,\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"This page gives quick examples of common symbolic calculations in SymPy. Print it and keep it under your pillow!\\n\\n\\\\section*{Elementary operations}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"This page gives quick examples of common symbolic calculations in SymPy. Print it and keep it under your pillow!\\n\\n\\\\section*{Elementary operations}\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 15154326763709946409,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"from sympy import *\\n\\nx, y, z, t = symbols('x y z t')\\nk, m, n = symbols('k m n', integer=True)\\nf, g, h = map(Function, 'fgh')\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 18407827551829231535,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 8700078390901980924,\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"Construct a symbolic expression.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"Construct a symbolic expression.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 8948229468361252312,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"ex=Rational(3,2)*pi + exp(I*x) / (x**2 + y);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 12034921120364795820,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"exp(I*x).subs(x,pi).evalf();\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 9927521614042221240,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 7296363618489335925,\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"Deconstruct an expression.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"Deconstruct an expression.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 9125817323985088488,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 9223372036854775814,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"output\",\n\t\t\t\t\t\"source\" : \"\\\\begin{verbatim}<class 'sympy.core.add.Add'>\\n\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"expr = x + 2*y\\nprint(expr.__class__)\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 3883439484185178368,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 9223372036854775815,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"verbatim\",\n\t\t\t\t\t\"source\" : \"\\\\begin{verbatim}(x, 2*y)\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"expr.args;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 3059529340916885361,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 9223372036854775817,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}262537412640768743.99999999999925007259719818568888\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"exp(pi * sqrt(163)).evalf(50);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 3286360988591071588,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 15248306789586220654,\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\section*{Algebra}\\n\\nExpand products and powers.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\section*{Algebra}\\n\\nExpand products and powers.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 10957552959074670679,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 9223372036854775819,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}x^{3} + 2 x^{2} y + x^{2} + x y^{2} + 2 x y + y^{2}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"((x+y)**2 * (x+1)).expand();\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 1528128032562465733,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 2470958562984886775,\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"Simplify a formula.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"Simplify a formula.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 3879303328126739881,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 9223372036854775821,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\frac{1}{x} \\\\left(x \\\\sin{\\\\left (x \\\\right )} - 1\\\\right) + \\\\frac{1}{x}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"a = 1/x + (x*sin(x) - 1)/x;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 3766792923749550048,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 9223372036854775823,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\sin{\\\\left (x \\\\right )}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"simplify(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 7588206308252668052,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 9223372036854775825,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"{}$\\\\big[$\\\\begin{dmath*}{}-2\\\\end{dmath*},\\\\discretionary{}{}{} \\\\begin{dmath*}{}- 2 i\\\\end{dmath*},\\\\discretionary{}{}{} \\\\begin{dmath*}{}2 i\\\\end{dmath*}$\\\\big]$\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"solve(Eq(x**3 + 2*x**2 + 4*x + 8, 0), x);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 13058313213277511145,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 9223372036854775810,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}-2\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 9223372036854775812,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}2 i\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 9223372036854775827,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"{}$\\\\big[$\\\\begin{dmath*}{}-2\\\\end{dmath*},\\\\discretionary{}{}{} \\\\begin{dmath*}{}- 2 i\\\\end{dmath*},\\\\discretionary{}{}{} \\\\begin{dmath*}{}2 i\\\\end{dmath*}$\\\\big]$\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"solve(x**3 + 2*x**2 + 4*x + 8, x);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 4551526850556295932,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 9223372036854775829,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"verbatim\",\n\t\t\t\t\t\"source\" : \"\\\\begin{verbatim}{x: -3, y: 1}\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"solve([Eq(x + 5*y, 2), Eq(-3*x + 6*y, 15)], [x, y]);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 9441624389629075484,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 9223372036854775831,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"verbatim\",\n\t\t\t\t\t\"source\" : \"\\\\begin{verbatim}{x: -3, y: 1}\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"solve([x + 5*y - 2, -3*x + 6*y - 15], [x, y]);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 15793335111811853999,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 9223372036854775833,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\sum_{n=a}^{b} \\\\left(2^{n} + 6 n^{2}\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"a, b = symbols('a b')\\ns = Sum(6*n**2 + 2**n, (n, a, b));\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 10734570351295954517,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 9223372036854775835,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}- 2^{a} + 2^{b + 1} - 2 a^{3} + 3 a^{2} - a + 2 b^{3} + 3 b^{2} + b\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"s.doit();\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 2962539012478312349,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 9223372036854775837,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}{2}^{\\\\left(b\\\\right)} b!\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"product(n*(n+1), (n, 1, b));\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 4322035374377707345,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 9223372036854775839,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}f{\\\\left (\\\\frac{1}{2} \\\\right )} - 3 f{\\\\left (2 \\\\right )} = 2\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"f=Function('f')\\nex=Eq(f(1/x)-3*f(x),x)\\nex.subs(x,2);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 12166349269731912274,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 9223372036854775841,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}- 3 f{\\\\left (\\\\frac{1}{2} \\\\right )} + f{\\\\left (2 \\\\right )} = \\\\frac{1}{2}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex.subs(x,Rational(1,2));\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 330284413310941630,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 9223372036854775843,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"{}$\\\\big[$\\\\verb|{f(1/2): -7/16, f(2): -13/16}|$\\\\big]$\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"solve([f(Rational(1,2))-3*f(2)-2,-3*f(Rational(1,2))+f(2)-Rational(1,2)]);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 9234524385369034860,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 9223372036854775845,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}- \\\\frac{1}{6}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"limit((sin(x)-x)/x**3, x, 0);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 15750969388456446071,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 9223372036854775847,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}1 + \\\\frac{x^{2}}{2} + \\\\frac{5 x^{4}}{24} + \\\\mathcal{O}\\\\left(x^{6}\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"(1/cos(x)).series(x, 0, 6);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 6484240260694456001,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 9223372036854775849,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}- \\\\frac{4 x \\\\cos{\\\\left (x^{2} \\\\right )}}{x + 1} \\\\sin{\\\\left (x^{2} \\\\right )} - \\\\frac{\\\\cos^{2}{\\\\left (x^{2} \\\\right )}}{\\\\left(x + 1\\\\right)^{2}}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"diff(cos(x**2)**2 / (1+x), x);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 213825804824037968,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 9223372036854775851,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}x^{2} \\\\sin{\\\\left (x \\\\right )} + 2 x \\\\cos{\\\\left (x \\\\right )} - 2 \\\\sin{\\\\left (x \\\\right )}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"integrate(x**2 * cos(x), x);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 6936311894189510517,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 9223372036854775853,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}-2 + \\\\frac{\\\\pi^{2}}{4}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"integrate(x**2 * cos(x), (x, 0, pi/2));\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 650362031016574697,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 15333188648644086172,\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"Solve an ordinary differential equation.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"Solve an ordinary differential equation.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 10759317157061942665,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 9223372036854775855,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}9 f{\\\\left (x \\\\right )} + \\\\frac{d^{2}}{d x^{2}}  f{\\\\left (x \\\\right )} = 1\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 9223372036854775856,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}f{\\\\left (x \\\\right )} = C_{1} \\\\sin{\\\\left (3 x \\\\right )} + C_{2} \\\\cos{\\\\left (3 x \\\\right )} + \\\\frac{1}{9}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"f = Function('f')\\neq = Eq(Derivative(f(x),x,x) + 9*f(x), 1);\\ndsolve(eq, f(x));\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 17388289334876032033,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 9223372036854775858,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}9 f{\\\\left (x \\\\right )} + \\\\frac{d^{2}}{d x^{2}}  f{\\\\left (x \\\\right )} = 1\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"Eq(f(x).diff(x, x) + 9*f(x), 1);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 10194258643907557174,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 9223372036854775860,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}f{\\\\left (x \\\\right )} = C_{1} \\\\sin{\\\\left (3 x \\\\right )} + C_{2} \\\\cos{\\\\left (3 x \\\\right )} + \\\\frac{1}{9}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"dsolve(_, f(x));\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\" : 3925151094574714810,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1\n}\n"
  },
  {
    "path": "examples/tensor_monomials.cnb",
    "content": "\n{\n\t\"cells\" : \n\t[\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\section*{Tensor monomials and multi-term symmetries}\\n\\nCadabra contains powerful algorithms to bring any tensorial expression into a canonical\\nform. For multi-term symmetries, cadabra relies on Young tableau methods to generate\\na canonical form for tensor monomials.\\n\\nAs an example, consider the following identity,\\n\\\\[\\nW_{p q r s} W_{p t r u} W_{t v q w} W_{u v s w}\\n   - W_{p q r s} W_{p q t u} W_{r v t w} W_{s v u w}\\n   = W_{m n a b} W_{n p b c} W_{m s c d} W_{s p d a}\\n   - \\\\frac{1}{4} W_{m n a b} W_{p s b a} W_{m p c d} W_{n s d c}\\\\,,\\n\\\\]\\nin which $W_{m n p q}$ is a Weyl tensor (all contracted indices have been written as subscripts \\nfor easier readability). Proving this identity requires multiple uses of the Ricci cyclic\\nidentity\\n\\\\[\\nW_{m[npq]}=0\\\\,.\\n\\\\]\\nWith Cadabra's Young tableau methods the proof is simple. We first declare our \\nobjects and input the identity which we want to prove,\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\section*{Tensor monomials and multi-term symmetries}\\n\\nCadabra contains powerful algorithms to bring any tensorial expression into a canonical\\nform. For multi-term symmetries, cadabra relies on Young tableau methods to generate\\na canonical form for tensor monomials.\\n\\nAs an example, consider the following identity,\\n\\\\[\\nW_{p q r s} W_{p t r u} W_{t v q w} W_{u v s w}\\n   - W_{p q r s} W_{p q t u} W_{r v t w} W_{s v u w}\\n   = W_{m n a b} W_{n p b c} W_{m s c d} W_{s p d a}\\n   - \\\\frac{1}{4} W_{m n a b} W_{p s b a} W_{m p c d} W_{n s d c}\\\\,,\\n\\\\]\\nin which $W_{m n p q}$ is a Weyl tensor (all contracted indices have been written as subscripts \\nfor easier readability). Proving this identity requires multiple uses of the Ricci cyclic\\nidentity\\n\\\\[\\nW_{m[npq]}=0\\\\,.\\n\\\\]\\nWith Cadabra's Young tableau methods the proof is simple. We first declare our \\nobjects and input the identity which we want to prove,\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"{m,n,p,q,r,s,t,u,v,w,a,b,c,d,e,f}::Indices(vector).\\nW_{m n p q}::WeylTensor.\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}W_{p q r s} W_{p t r u} W_{t v q w} W_{u v s w}-W_{p q r s} W_{p q t u} W_{r v t w} W_{s v u w}-W_{m n a b} W_{n p b c} W_{m s c d} W_{s p d a}+\\\\frac{1}{4}W_{m n a b} W_{p s b a} W_{m p c d} W_{n s d c}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex:= W_{p q r s} W_{p t r u} W_{t v q w} W_{u v s w}\\n   - W_{p q r s} W_{p q t u} W_{r v t w} W_{s v u w}\\n   - W_{m n a b} W_{n p b c} W_{m s c d} W_{s p d a}\\n   + (1/4) W_{m n a b} W_{p s b a} W_{m p c d} W_{n s d c};\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"Using a Young projector to project all Weyl tensors onto a form which shows the Ricci symmetry in\\nmanifest form is done with\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"Using a Young projector to project all Weyl tensors onto a form which shows the Ricci symmetry in\\nmanifest form is done with\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\left(\\\\frac{2}{3}W_{p q r s} - \\\\frac{1}{3}W_{p s q r}+\\\\frac{1}{3}W_{p r q s}\\\\right) \\\\left(\\\\frac{2}{3}W_{p t r u}+\\\\frac{1}{3}W_{p u r t}+\\\\frac{1}{3}W_{p r t u}\\\\right) \\\\left(\\\\frac{2}{3}W_{q w t v}+\\\\frac{1}{3}W_{q v t w} - \\\\frac{1}{3}W_{q t v w}\\\\right) \\\\left(\\\\frac{2}{3}W_{s w u v}+\\\\frac{1}{3}W_{s v u w} - \\\\frac{1}{3}W_{s u v w}\\\\right)-\\\\left(\\\\frac{2}{3}W_{p q r s} - \\\\frac{1}{3}W_{p s q r}+\\\\frac{1}{3}W_{p r q s}\\\\right) \\\\left(\\\\frac{2}{3}W_{p q t u} - \\\\frac{1}{3}W_{p u q t}+\\\\frac{1}{3}W_{p t q u}\\\\right) \\\\left(\\\\frac{2}{3}W_{r v t w}+\\\\frac{1}{3}W_{r w t v}+\\\\frac{1}{3}W_{r t v w}\\\\right) \\\\left(\\\\frac{2}{3}W_{s v u w}+\\\\frac{1}{3}W_{s w u v}+\\\\frac{1}{3}W_{s u v w}\\\\right)-\\\\left(\\\\frac{2}{3}W_{a b m n} - \\\\frac{1}{3}W_{a n b m}+\\\\frac{1}{3}W_{a m b n}\\\\right) \\\\left(\\\\frac{2}{3}W_{b c n p} - \\\\frac{1}{3}W_{b p c n}+\\\\frac{1}{3}W_{b n c p}\\\\right) \\\\left(\\\\frac{2}{3}W_{c d m s} - \\\\frac{1}{3}W_{c s d m}+\\\\frac{1}{3}W_{c m d s}\\\\right) \\\\left(\\\\frac{2}{3}W_{a d p s} - \\\\frac{1}{3}W_{a s d p}+\\\\frac{1}{3}W_{a p d s}\\\\right)+\\\\frac{1}{4}\\\\left(\\\\frac{2}{3}W_{a b m n} - \\\\frac{1}{3}W_{a n b m}+\\\\frac{1}{3}W_{a m b n}\\\\right) \\\\left( - \\\\frac{2}{3}W_{a b p s} - \\\\frac{1}{3}W_{a p b s}+\\\\frac{1}{3}W_{a s b p}\\\\right) \\\\left(\\\\frac{2}{3}W_{c d m p} - \\\\frac{1}{3}W_{c p d m}+\\\\frac{1}{3}W_{c m d p}\\\\right) \\\\left( - \\\\frac{2}{3}W_{c d n s} - \\\\frac{1}{3}W_{c n d s}+\\\\frac{1}{3}W_{c s d n}\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"young_project_tensor(_, modulo_monoterm=True);\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"This algorithm knows that the Weyl tensor sits in the `$2\\\\times 2$ box' representation of the rotation \\ngroup $\\\\text{SO}(d)$, and effectively leads to a replacement\\n\\\\[\\n  W_{m n p q} \\\\rightarrow \\\\frac{2}{3} W_{m n p q} - \\\\frac{1}{3} W_{m q n p} + \\\\frac{1}{3} W_{m p n q}\\\\,.\\n\\\\]\\nWe then expand the products of sums and canonicalise once more using mono-term symmetries,\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"This algorithm knows that the Weyl tensor sits in the `$2\\\\times 2$ box' representation of the rotation \\ngroup $\\\\text{SO}(d)$, and effectively leads to a replacement\\n\\\\[\\n  W_{m n p q} \\\\rightarrow \\\\frac{2}{3} W_{m n p q} - \\\\frac{1}{3} W_{m q n p} + \\\\frac{1}{3} W_{m p n q}\\\\,.\\n\\\\]\\nWe then expand the products of sums and canonicalise once more using mono-term symmetries,\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}0\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"distribute(_)\\ncanonicalise(_)\\nrename_dummies(_);\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1.0\n}\n\n"
  },
  {
    "path": "examples/tensors_in_denominators.cnb",
    "content": "{\n\t\"cells\" : \n\t[\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Indices(position=free) to~}\\\\left(m, n, p, q, r, s, t, u\\\\right).\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"{m,n,p,q,r,s,t,u}::Indices;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\frac{1}{A_{m n} B_{m n}+A_{m n} C_{n m}}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex:=1/( A_{m n} B_{m n} + A_{m n} C_{n m} );\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Symmetric to~}\\\\left(A_{m n}, C_{m n}\\\\right).\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"{ A_{m n}, C_{m n} }::Symmetric;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property AntiSymmetric to~}B_{m n}.\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"B_{m n}::AntiSymmetric;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\frac{1}{A_{m n} C_{m n}}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"canonicalise(ex);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\frac{1}{\\\\left(p_{m}+q_{m}\\\\right) \\\\left(p^{m}+q^{m}\\\\right)}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex:=1/( (p_{m} + q_{m}) (p^{m} + q^{m} ) );\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\frac{1}{p_{m} p^{m}+p_{m} q^{m}+q_{m} p^{m}+q_{m} q^{m}}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"distribute(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\frac{1}{p_{m} p^{m}+p_{m} q^{m}+p^{m} q_{m}+q_{m} q^{m}}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"sort_product(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\frac{1}{p^{m} p_{m}+2p^{m} q_{m}+q^{m} q_{m}}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"canonicalise(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1\n}\n"
  },
  {
    "path": "examples/typesetting.cnb",
    "content": "{\n\t\"cell_id\": 3064264301093080805,\n\t\"cells\": [\n\t\t{\n\t\t\t\"cell_id\": 7973304362094483791,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"s=\\\"Q(\\\"\\nfor i in range(20):\\n\\ts=s+\\\"+a_{\\\"+str(i)+\\\"} \\\\\\\\frac{A+B}{C+D}\\\"\\ns=s+\\\")+R(\\\"\\nfor i in range(20):\\n\\ts=s+\\\"a_{\\\"+str(i)+\\\"} \\\\\\\\frac{A+B}{C+D},\\\"\\ns=s+\\\"M)\\\"\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 7014098435245050672,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"ex=Ex(s)\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 10945821061026520332,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"__cdbkernel__.display_fractions=True\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 14780273387048122396,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9535298439136269407,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 7911376744072660052,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"Q(a_{0} (A + B) (C + D)**(-1) + a_{1} (A + B) (C + D)**(-1) + a_{2} (A + B) (C + D)**(-1) + a_{3} (A + B) (C + D)**(-1) + a_{4} (A + B) (C + D)**(-1) + a_{5} (A + B) (C + D)**(-1) + a_{6} (A + B) (C + D)**(-1) + a_{7} (A + B) (C + D)**(-1) + a_{8} (A + B) (C + D)**(-1) + a_{9} (A + B) (C + D)**(-1) + a_{10} (A + B) (C + D)**(-1) + a_{11} (A + B) (C + D)**(-1) + a_{12} (A + B) (C + D)**(-1) + a_{13} (A + B) (C + D)**(-1) + a_{14} (A + B) (C + D)**(-1) + a_{15} (A + B) (C + D)**(-1) + a_{16} (A + B) (C + D)**(-1) + a_{17} (A + B) (C + D)**(-1) + a_{18} (A + B) (C + D)**(-1) + a_{19} (A + B) (C + D)**(-1)) + R(a_{0} (A + B) (C + D)**(-1) , a_{1} (A + B) (C + D)**(-1) , a_{2} (A + B) (C + D)**(-1) , a_{3} (A + B) (C + D)**(-1) , a_{4} (A + B) (C + D)**(-1) , a_{5} (A + B) (C + D)**(-1) , a_{6} (A + B) (C + D)**(-1) , a_{7} (A + B) (C + D)**(-1) , a_{8} (A + B) (C + D)**(-1) , a_{9} (A + B) (C + D)**(-1) , a_{10} (A + B) (C + D)**(-1) , a_{11} (A + B) (C + D)**(-1) , a_{12} (A + B) (C + D)**(-1) , a_{13} (A + B) (C + D)**(-1) , a_{14} (A + B) (C + D)**(-1) , a_{15} (A + B) (C + D)**(-1) , a_{16} (A + B) (C + D)**(-1) , a_{17} (A + B) (C + D)**(-1) , a_{18} (A + B) (C + D)**(-1) , a_{19} (A + B) (C + D)**(-1) , M)\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}Q\\\\left(\\\\frac{a_{0\\\\,} \\\\left(A\\\\discretionary{}{}{}+B\\\\right)}{\\\\left(C\\\\discretionary{}{}{}+D\\\\right)}\\\\discretionary{}{}{}+\\\\frac{a_{1} \\\\left(A\\\\discretionary{}{}{}+B\\\\right)}{\\\\left(C\\\\discretionary{}{}{}+D\\\\right)}\\\\discretionary{}{}{}+\\\\frac{a_{2\\\\,} \\\\left(A\\\\discretionary{}{}{}+B\\\\right)}{\\\\left(C\\\\discretionary{}{}{}+D\\\\right)}\\\\discretionary{}{}{}+\\\\frac{a_{3\\\\,} \\\\left(A\\\\discretionary{}{}{}+B\\\\right)}{\\\\left(C\\\\discretionary{}{}{}+D\\\\right)}\\\\discretionary{}{}{}+\\\\frac{a_{4\\\\,} \\\\left(A\\\\discretionary{}{}{}+B\\\\right)}{\\\\left(C\\\\discretionary{}{}{}+D\\\\right)}\\\\discretionary{}{}{}+\\\\frac{a_{5\\\\,} \\\\left(A\\\\discretionary{}{}{}+B\\\\right)}{\\\\left(C\\\\discretionary{}{}{}+D\\\\right)}\\\\discretionary{}{}{}+\\\\frac{a_{6\\\\,} \\\\left(A\\\\discretionary{}{}{}+B\\\\right)}{\\\\left(C\\\\discretionary{}{}{}+D\\\\right)}\\\\discretionary{}{}{}+\\\\frac{a_{7\\\\,} \\\\left(A\\\\discretionary{}{}{}+B\\\\right)}{\\\\left(C\\\\discretionary{}{}{}+D\\\\right)}\\\\discretionary{}{}{}+\\\\frac{a_{8\\\\,} \\\\left(A\\\\discretionary{}{}{}+B\\\\right)}{\\\\left(C\\\\discretionary{}{}{}+D\\\\right)}\\\\discretionary{}{}{}+\\\\frac{a_{9\\\\,} \\\\left(A\\\\discretionary{}{}{}+B\\\\right)}{\\\\left(C\\\\discretionary{}{}{}+D\\\\right)}\\\\discretionary{}{}{}+\\\\frac{a_{10\\\\,} \\\\left(A\\\\discretionary{}{}{}+B\\\\right)}{\\\\left(C\\\\discretionary{}{}{}+D\\\\right)}\\\\discretionary{}{}{}+\\\\frac{a_{11\\\\,} \\\\left(A\\\\discretionary{}{}{}+B\\\\right)}{\\\\left(C\\\\discretionary{}{}{}+D\\\\right)}\\\\discretionary{}{}{}+\\\\frac{a_{12\\\\,} \\\\left(A\\\\discretionary{}{}{}+B\\\\right)}{\\\\left(C\\\\discretionary{}{}{}+D\\\\right)}\\\\discretionary{}{}{}+\\\\frac{a_{13\\\\,} \\\\left(A\\\\discretionary{}{}{}+B\\\\right)}{\\\\left(C\\\\discretionary{}{}{}+D\\\\right)}\\\\discretionary{}{}{}+\\\\frac{a_{14\\\\,} \\\\left(A\\\\discretionary{}{}{}+B\\\\right)}{\\\\left(C\\\\discretionary{}{}{}+D\\\\right)}\\\\discretionary{}{}{}+\\\\frac{a_{15\\\\,} \\\\left(A\\\\discretionary{}{}{}+B\\\\right)}{\\\\left(C\\\\discretionary{}{}{}+D\\\\right)}\\\\discretionary{}{}{}+\\\\frac{a_{16\\\\,} \\\\left(A\\\\discretionary{}{}{}+B\\\\right)}{\\\\left(C\\\\discretionary{}{}{}+D\\\\right)}\\\\discretionary{}{}{}+\\\\frac{a_{17\\\\,} \\\\left(A\\\\discretionary{}{}{}+B\\\\right)}{\\\\left(C\\\\discretionary{}{}{}+D\\\\right)}\\\\discretionary{}{}{}+\\\\frac{a_{18\\\\,} \\\\left(A\\\\discretionary{}{}{}+B\\\\right)}{\\\\left(C\\\\discretionary{}{}{}+D\\\\right)}\\\\discretionary{}{}{}%\\n+\\\\frac{a_{19\\\\,} \\\\left(A\\\\discretionary{}{}{}+B\\\\right)}{\\\\left(C\\\\discretionary{}{}{}+D\\\\right)}\\\\right)\\\\discretionary{}{}{}+R\\\\left(\\\\frac{a_{0\\\\,} \\\\left(A\\\\discretionary{}{}{}+B\\\\right)}{\\\\left(C\\\\discretionary{}{}{}+D\\\\right)} , \\\\discretionary{}{}{}\\\\frac{a_{1} \\\\left(A\\\\discretionary{}{}{}+B\\\\right)}{\\\\left(C\\\\discretionary{}{}{}+D\\\\right)} , \\\\discretionary{}{}{}\\\\frac{a_{2\\\\,} \\\\left(A\\\\discretionary{}{}{}+B\\\\right)}{\\\\left(C\\\\discretionary{}{}{}+D\\\\right)} , \\\\discretionary{}{}{}\\\\frac{a_{3\\\\,} \\\\left(A\\\\discretionary{}{}{}+B\\\\right)}{\\\\left(C\\\\discretionary{}{}{}+D\\\\right)} , \\\\discretionary{}{}{}\\\\frac{a_{4\\\\,} \\\\left(A\\\\discretionary{}{}{}+B\\\\right)}{\\\\left(C\\\\discretionary{}{}{}+D\\\\right)} , \\\\discretionary{}{}{}\\\\frac{a_{5\\\\,} \\\\left(A\\\\discretionary{}{}{}+B\\\\right)}{\\\\left(C\\\\discretionary{}{}{}+D\\\\right)} , \\\\discretionary{}{}{}\\\\frac{a_{6\\\\,} \\\\left(A\\\\discretionary{}{}{}+B\\\\right)}{\\\\left(C\\\\discretionary{}{}{}+D\\\\right)} , \\\\discretionary{}{}{}\\\\frac{a_{7\\\\,} \\\\left(A\\\\discretionary{}{}{}+B\\\\right)}{\\\\left(C\\\\discretionary{}{}{}+D\\\\right)} , \\\\discretionary{}{}{}\\\\frac{a_{8\\\\,} \\\\left(A\\\\discretionary{}{}{}+B\\\\right)}{\\\\left(C\\\\discretionary{}{}{}+D\\\\right)} , \\\\discretionary{}{}{}\\\\frac{a_{9\\\\,} \\\\left(A\\\\discretionary{}{}{}+B\\\\right)}{\\\\left(C\\\\discretionary{}{}{}+D\\\\right)} , \\\\discretionary{}{}{}\\\\frac{a_{10\\\\,} \\\\left(A\\\\discretionary{}{}{}+B\\\\right)}{\\\\left(C\\\\discretionary{}{}{}+D\\\\right)} , \\\\discretionary{}{}{}\\\\frac{a_{11\\\\,} \\\\left(A\\\\discretionary{}{}{}+B\\\\right)}{\\\\left(C\\\\discretionary{}{}{}+D\\\\right)} , \\\\discretionary{}{}{}\\\\frac{a_{12\\\\,} \\\\left(A\\\\discretionary{}{}{}+B\\\\right)}{\\\\left(C\\\\discretionary{}{}{}+D\\\\right)} , \\\\discretionary{}{}{}\\\\frac{a_{13\\\\,} \\\\left(A\\\\discretionary{}{}{}+B\\\\right)}{\\\\left(C\\\\discretionary{}{}{}+D\\\\right)} , \\\\discretionary{}{}{}\\\\frac{a_{14\\\\,} \\\\left(A\\\\discretionary{}{}{}+B\\\\right)}{\\\\left(C\\\\discretionary{}{}{}+D\\\\right)} , \\\\discretionary{}{}{}\\\\frac{a_{15\\\\,} \\\\left(A\\\\discretionary{}{}{}+B\\\\right)}{\\\\left(C\\\\discretionary{}{}{}+D\\\\right)} , \\\\discretionary{}{}{}\\\\frac{a_{16\\\\,} \\\\left(A\\\\discretionary{}{}{}+B\\\\right)}{\\\\left(C\\\\discretionary{}{}{}+D\\\\right)} , \\\\discretionary{}{}{}\\\\frac{a_{17\\\\,} \\\\left(A\\\\discretionary{}{}{}+B\\\\right)}{\\\\left(C\\\\discretionary{}{}{}+D\\\\right)} , \\\\discretionary{}{}{}\\\\frac{a_{18\\\\,} \\\\left(A\\\\discretionary{}{}{}+B\\\\right)}{\\\\left(C\\\\discretionary{}{}{}+D\\\\right)} , \\\\discretionary{}{}{}\\\\frac{a_{19\\\\,} \\\\left(A\\\\discretionary{}{}{}+B\\\\right)}{\\\\left(C\\\\discretionary{}{}{}+D\\\\right)} , \\\\discretionary{}{}{}M\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 2345481487958191505,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"\"\n\t\t}\n\t],\n\t\"description\": \"Cadabra JSON notebook format\",\n\t\"flags\": {\n\t\t\"hide_input_cells\": false\n\t},\n\t\"version\": 1.0\n}\n"
  },
  {
    "path": "examples/utf8.cnb",
    "content": "{\n\t\"cell_id\": 4208743507568568802,\n\t\"cells\": [\n\t\t{\n\t\t\t\"cell_id\": 11663224005027881326,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 13307240755558806970,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"Cadabra now has proper UTF-8 support. 😊\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"Cadabra now has proper UTF-8 support. 😊\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 11820404449086491630,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 6826282126270786384,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"Cadabra 现在具有适当的 UTF-8 支持。😊\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"Cadabra 现在具有适当的 UTF-8 支持。😊\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 9518057759926663596,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"latex\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 6738555579131781445,\n\t\t\t\t\t\"cell_origin\": \"client\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"Цадабра сада има одговарајућу подршку за УТФ-8. 😊\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\": true,\n\t\t\t\"source\": \"Цадабра сада има одговарајућу подршку за УТФ-8. 😊\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 10704240038917635801,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"\"\n\t\t}\n\t],\n\t\"description\": \"Cadabra JSON notebook format\",\n\t\"version\": 1.0\n}\n"
  },
  {
    "path": "examples/vacuum_einstein_first_order.cnb",
    "content": "{\n\t\"cells\" : \n\t[\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{center}\\n{\\\\Large \\\\textbf{First-order perturbation of Einstein-Hilbert action}}\\\\\\\\\\nVictor Santos, 2016\\\\\\\\\\nUniversidade Federal do Cear\\\\'{a}, Brazil\\\\\\\\\\n\\\\texttt{victor\\\\_santos@fisica.ufc.br}\\n\\\\end{center}\\n\\nThis notebook illustrate some Cadabra manipulations to derive the linearized Einstein equation around a vacuum solution; that is, given a solution \\\\(\\\\eta\\\\) of\\n\\\\begin{equation}\\n\\\\textrm{Ric}(\\\\eta) = 0,\\\\label{eq:vacuum-einstein-eq}\\n\\\\end{equation}\\nwe find the linearized equation\\n\\\\begin{equation}\\n\\\\frac{\\\\textrm{d}}{\\\\textrm{d}\\\\epsilon}\\\\Big|_{\\\\epsilon=0}\\\\textrm{Ric}(g(\\\\epsilon)) = 0,\\n\\\\end{equation}\\nwhere the family \\\\(g(\\\\epsilon)\\\\) of solutions of (1) satisfy\\n\\\\begin{equation}\\ng(0) = \\\\eta,\\\\quad \\\\frac{\\\\mathrm{d}}{\\\\mathrm{d}\\\\epsilon}\\\\Big|_{\\\\epsilon=0}\\\\,g(\\\\epsilon) = h\\n\\\\end{equation}\\nwhere \\\\(h\\\\) is a symmetric 2-tensor, representing a perturbation.\\n\\n\\\\subsection*{Indices and tensors}\\nWe first declare the indices that we will use. The declarations for the metric \\\\(g\\\\) and the perturbation \\\\(h\\\\) are standard.\\n\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\begin{center}\\n{\\\\Large \\\\textbf{First-order perturbation of Einstein-Hilbert action}}\\\\\\\\\\nVictor Santos, 2016\\\\\\\\\\nUniversidade Federal do Cear\\\\'{a}, Brazil\\\\\\\\\\n\\\\texttt{victor\\\\_santos@fisica.ufc.br}\\n\\\\end{center}\\n\\nThis notebook illustrate some Cadabra manipulations to derive the linearized Einstein equation around a vacuum solution; that is, given a solution \\\\(\\\\eta\\\\) of\\n\\\\begin{equation}\\n\\\\textrm{Ric}(\\\\eta) = 0,\\\\label{eq:vacuum-einstein-eq}\\n\\\\end{equation}\\nwe find the linearized equation\\n\\\\begin{equation}\\n\\\\frac{\\\\textrm{d}}{\\\\textrm{d}\\\\epsilon}\\\\Big|_{\\\\epsilon=0}\\\\textrm{Ric}(g(\\\\epsilon)) = 0,\\n\\\\end{equation}\\nwhere the family \\\\(g(\\\\epsilon)\\\\) of solutions of (1) satisfy\\n\\\\begin{equation}\\ng(0) = \\\\eta,\\\\quad \\\\frac{\\\\mathrm{d}}{\\\\mathrm{d}\\\\epsilon}\\\\Big|_{\\\\epsilon=0}\\\\,g(\\\\epsilon) = h\\n\\\\end{equation}\\nwhere \\\\(h\\\\) is a symmetric 2-tensor, representing a perturbation.\\n\\n\\\\subsection*{Indices and tensors}\\nWe first declare the indices that we will use. The declarations for the metric \\\\(g\\\\) and the perturbation \\\\(h\\\\) are standard.\\n\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Indices(position=independent) to~}\\\\left(\\\\alpha, \\\\linebreak[0] \\\\beta, \\\\linebreak[0] \\\\gamma, \\\\linebreak[0] \\\\delta, \\\\linebreak[0] \\\\mu, \\\\linebreak[0] \\\\nu, \\\\linebreak[0] \\\\rho, \\\\linebreak[0] \\\\sigma, \\\\linebreak[0] \\\\kappa, \\\\linebreak[0] \\\\lambda, \\\\linebreak[0] \\\\chi, \\\\linebreak[0] \\\\xi\\\\#\\\\right).\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"{\\\\alpha,\\\\beta,\\\\gamma,\\\\delta,\\\\mu,\\\\nu,\\\\rho,\\\\sigma,\\\\kappa,\\\\lambda,\\\\chi,\\\\xi#}::Indices(full, position=independent);\\n\\\\nabla{#}::Derivative. \\ng_{\\\\mu\\\\nu}::Metric. \\ng^{\\\\mu\\\\nu}::InverseMetric.\\nh_{m n}::Symmetric.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\subsection*{Connection coefficients}\\n\\nWe want to expand the Ricci tensor in terms of the first-order perturbation \\\\(h\\\\). For this we write the connection coefficients \\\\(\\\\Gamma^{\\\\lambda}_{\\\\mu\\\\nu}(\\\\lambda)\\\\):\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\subsection*{Connection coefficients}\\n\\nWe want to expand the Ricci tensor in terms of the first-order perturbation \\\\(h\\\\). For this we write the connection coefficients \\\\(\\\\Gamma^{\\\\lambda}_{\\\\mu\\\\nu}(\\\\lambda)\\\\):\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\Gamma^{\\\\lambda}\\\\,_{\\\\mu \\\\nu} \\\\rightarrow \\\\frac{1}{2}g^{\\\\lambda \\\\kappa} \\\\left(\\\\nabla_{\\\\nu}{g_{\\\\kappa \\\\mu}}+\\\\nabla_{\\\\mu}{g_{\\\\kappa \\\\nu}}-\\\\nabla_{\\\\kappa}{g_{\\\\mu \\\\nu}}\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"Gtog:= \\\\Gamma^{\\\\lambda}_{\\\\mu\\\\nu} -> \\n      (1/2) * g^{\\\\lambda\\\\kappa} ( \\\\nabla_{\\\\nu}{ g_{\\\\kappa\\\\mu} } \\n                        + \\\\nabla_{\\\\mu}{ g_{\\\\kappa\\\\nu} } - \\\\nabla_{\\\\kappa}{ g_{\\\\mu\\\\nu} } );\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"and now we change the metric by the first order approximation \\\\(g\\\\mapsto g + \\\\epsilon h\\\\):\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"and now we change the metric by the first order approximation \\\\(g\\\\mapsto g + \\\\epsilon h\\\\):\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\Gamma^{\\\\lambda}\\\\,_{\\\\mu \\\\nu} \\\\rightarrow \\\\frac{1}{2}\\\\left(g^{\\\\lambda \\\\kappa}-\\\\epsilon h^{\\\\lambda \\\\kappa}\\\\right) \\\\left(\\\\nabla_{\\\\nu}\\\\left(g_{\\\\kappa \\\\mu}+\\\\epsilon h_{\\\\kappa \\\\mu}\\\\right)+\\\\nabla_{\\\\mu}\\\\left(g_{\\\\kappa \\\\nu}+\\\\epsilon h_{\\\\kappa \\\\nu}\\\\right)-\\\\nabla_{\\\\kappa}\\\\left(g_{\\\\mu \\\\nu}+\\\\epsilon h_{\\\\mu \\\\nu}\\\\right)\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"substitute(_, $g_{\\\\mu \\\\nu} -> g_{\\\\mu \\\\nu} + \\\\epsilon*h_{\\\\mu \\\\nu}$)\\nsubstitute(_, $g^{\\\\mu \\\\nu} -> g^{\\\\mu \\\\nu} - \\\\epsilon*h^{\\\\mu \\\\nu}$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"We now apply the product rule twice to write out the derivatives:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"We now apply the product rule twice to write out the derivatives:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\Gamma^{\\\\lambda}\\\\,_{\\\\mu \\\\nu} \\\\rightarrow \\\\frac{1}{2}g^{\\\\lambda \\\\kappa} \\\\nabla_{\\\\nu}{g_{\\\\kappa \\\\mu}}+\\\\frac{1}{2}g^{\\\\lambda \\\\kappa} \\\\nabla_{\\\\nu}{\\\\epsilon} h_{\\\\kappa \\\\mu}+\\\\frac{1}{2}g^{\\\\lambda \\\\kappa} \\\\epsilon \\\\nabla_{\\\\nu}{h_{\\\\kappa \\\\mu}}+\\\\frac{1}{2}g^{\\\\lambda \\\\kappa} \\\\nabla_{\\\\mu}{g_{\\\\kappa \\\\nu}}+\\\\frac{1}{2}g^{\\\\lambda \\\\kappa} \\\\nabla_{\\\\mu}{\\\\epsilon} h_{\\\\kappa \\\\nu}+\\\\frac{1}{2}g^{\\\\lambda \\\\kappa} \\\\epsilon \\\\nabla_{\\\\mu}{h_{\\\\kappa \\\\nu}} - \\\\frac{1}{2}g^{\\\\lambda \\\\kappa} \\\\nabla_{\\\\kappa}{g_{\\\\mu \\\\nu}} - \\\\frac{1}{2}g^{\\\\lambda \\\\kappa} \\\\nabla_{\\\\kappa}{\\\\epsilon} h_{\\\\mu \\\\nu} - \\\\frac{1}{2}g^{\\\\lambda \\\\kappa} \\\\epsilon \\\\nabla_{\\\\kappa}{h_{\\\\mu \\\\nu}} - \\\\frac{1}{2}\\\\epsilon h^{\\\\lambda \\\\kappa} \\\\nabla_{\\\\nu}{g_{\\\\kappa \\\\mu}} - \\\\frac{1}{2}\\\\epsilon h^{\\\\lambda \\\\kappa} \\\\nabla_{\\\\nu}{\\\\epsilon} h_{\\\\kappa \\\\mu} - \\\\frac{1}{2}\\\\epsilon h^{\\\\lambda \\\\kappa} \\\\epsilon \\\\nabla_{\\\\nu}{h_{\\\\kappa \\\\mu}} - \\\\frac{1}{2}\\\\epsilon h^{\\\\lambda \\\\kappa} \\\\nabla_{\\\\mu}{g_{\\\\kappa \\\\nu}} - \\\\frac{1}{2}\\\\epsilon h^{\\\\lambda \\\\kappa} \\\\nabla_{\\\\mu}{\\\\epsilon} h_{\\\\kappa \\\\nu} - \\\\frac{1}{2}\\\\epsilon h^{\\\\lambda \\\\kappa} \\\\epsilon \\\\nabla_{\\\\mu}{h_{\\\\kappa \\\\nu}}+\\\\frac{1}{2}\\\\epsilon h^{\\\\lambda \\\\kappa} \\\\nabla_{\\\\kappa}{g_{\\\\mu \\\\nu}}+\\\\frac{1}{2}\\\\epsilon h^{\\\\lambda \\\\kappa} \\\\nabla_{\\\\kappa}{\\\\epsilon} h_{\\\\mu \\\\nu}+\\\\frac{1}{2}\\\\epsilon h^{\\\\lambda \\\\kappa} \\\\epsilon \\\\nabla_{\\\\kappa}{h_{\\\\mu \\\\nu}}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"distribute(_)\\nproduct_rule(_)\\ndistribute(_)\\nproduct_rule(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"once \\\\(\\\\epsilon\\\\) is by assumption a constant, used only to keep track of the perturbation order, its derivatives must be zero:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"once \\\\(\\\\epsilon\\\\) is by assumption a constant, used only to keep track of the perturbation order, its derivatives must be zero:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\Gamma^{\\\\lambda}\\\\,_{\\\\mu \\\\nu} \\\\rightarrow \\\\frac{1}{2}g^{\\\\lambda \\\\kappa} \\\\nabla_{\\\\nu}{g_{\\\\kappa \\\\mu}}+\\\\frac{1}{2}g^{\\\\lambda \\\\kappa} \\\\epsilon \\\\nabla_{\\\\nu}{h_{\\\\kappa \\\\mu}}+\\\\frac{1}{2}g^{\\\\lambda \\\\kappa} \\\\nabla_{\\\\mu}{g_{\\\\kappa \\\\nu}}+\\\\frac{1}{2}g^{\\\\lambda \\\\kappa} \\\\epsilon \\\\nabla_{\\\\mu}{h_{\\\\kappa \\\\nu}} - \\\\frac{1}{2}g^{\\\\lambda \\\\kappa} \\\\nabla_{\\\\kappa}{g_{\\\\mu \\\\nu}} - \\\\frac{1}{2}g^{\\\\lambda \\\\kappa} \\\\epsilon \\\\nabla_{\\\\kappa}{h_{\\\\mu \\\\nu}} - \\\\frac{1}{2}\\\\epsilon h^{\\\\lambda \\\\kappa} \\\\nabla_{\\\\nu}{g_{\\\\kappa \\\\mu}} - \\\\frac{1}{2}\\\\epsilon h^{\\\\lambda \\\\kappa} \\\\epsilon \\\\nabla_{\\\\nu}{h_{\\\\kappa \\\\mu}} - \\\\frac{1}{2}\\\\epsilon h^{\\\\lambda \\\\kappa} \\\\nabla_{\\\\mu}{g_{\\\\kappa \\\\nu}} - \\\\frac{1}{2}\\\\epsilon h^{\\\\lambda \\\\kappa} \\\\epsilon \\\\nabla_{\\\\mu}{h_{\\\\kappa \\\\nu}}+\\\\frac{1}{2}\\\\epsilon h^{\\\\lambda \\\\kappa} \\\\nabla_{\\\\kappa}{g_{\\\\mu \\\\nu}}+\\\\frac{1}{2}\\\\epsilon h^{\\\\lambda \\\\kappa} \\\\epsilon \\\\nabla_{\\\\kappa}{h_{\\\\mu \\\\nu}}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"substitute(_, $\\\\nabla_{\\\\mu}{ \\\\epsilon } -> 0$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"We consider \\\\(\\\\nabla\\\\) to be the derivative operator compatible with the unperturbed solution \\\\(g(0)\\\\). Therefore we can set the derivatives of \\\\(g\\\\) to zero\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"We consider \\\\(\\\\nabla\\\\) to be the derivative operator compatible with the unperturbed solution \\\\(g(0)\\\\). Therefore we can set the derivatives of \\\\(g\\\\) to zero\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\Gamma^{\\\\lambda}\\\\,_{\\\\mu \\\\nu} \\\\rightarrow \\\\frac{1}{2}g^{\\\\lambda \\\\kappa} \\\\epsilon \\\\nabla_{\\\\nu}{h_{\\\\kappa \\\\mu}}+\\\\frac{1}{2}g^{\\\\lambda \\\\kappa} \\\\epsilon \\\\nabla_{\\\\mu}{h_{\\\\kappa \\\\nu}} - \\\\frac{1}{2}g^{\\\\lambda \\\\kappa} \\\\epsilon \\\\nabla_{\\\\kappa}{h_{\\\\mu \\\\nu}} - \\\\frac{1}{2}\\\\epsilon h^{\\\\lambda \\\\kappa} \\\\epsilon \\\\nabla_{\\\\nu}{h_{\\\\kappa \\\\mu}} - \\\\frac{1}{2}\\\\epsilon h^{\\\\lambda \\\\kappa} \\\\epsilon \\\\nabla_{\\\\mu}{h_{\\\\kappa \\\\nu}}+\\\\frac{1}{2}\\\\epsilon h^{\\\\lambda \\\\kappa} \\\\epsilon \\\\nabla_{\\\\kappa}{h_{\\\\mu \\\\nu}}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"substitute(_, $\\\\nabla_{\\\\mu}{ g_{\\\\nu \\\\kappa} } -> 0$)\\nsubstitute(_, $\\\\nabla_{\\\\mu}{ g^{\\\\nu \\\\kappa} } -> 0$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"we now collect the linear and second-order terms in \\\\(\\\\epsilon\\\\), and factor out the metric from the resulting expression\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"we now collect the linear and second-order terms in \\\\(\\\\epsilon\\\\), and factor out the metric from the resulting expression\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\Gamma^{\\\\lambda}\\\\,_{\\\\mu \\\\nu} \\\\rightarrow \\\\frac{1}{2}g^{\\\\lambda \\\\kappa} \\\\epsilon \\\\nabla_{\\\\nu}{h_{\\\\kappa \\\\mu}}+\\\\frac{1}{2}g^{\\\\lambda \\\\kappa} \\\\epsilon \\\\nabla_{\\\\mu}{h_{\\\\kappa \\\\nu}} - \\\\frac{1}{2}g^{\\\\lambda \\\\kappa} \\\\epsilon \\\\nabla_{\\\\kappa}{h_{\\\\mu \\\\nu}} - \\\\frac{1}{2}\\\\epsilon^{2} h^{\\\\lambda \\\\kappa} \\\\nabla_{\\\\nu}{h_{\\\\kappa \\\\mu}} - \\\\frac{1}{2}\\\\epsilon^{2} h^{\\\\lambda \\\\kappa} \\\\nabla_{\\\\mu}{h_{\\\\kappa \\\\nu}}+\\\\frac{1}{2}\\\\epsilon^{2} h^{\\\\lambda \\\\kappa} \\\\nabla_{\\\\kappa}{h_{\\\\mu \\\\nu}}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"collect_factors(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\Gamma^{\\\\lambda}\\\\,_{\\\\mu \\\\nu} \\\\rightarrow \\\\epsilon \\\\left(\\\\frac{1}{2}g^{\\\\lambda \\\\kappa} \\\\nabla_{\\\\nu}{h_{\\\\kappa \\\\mu}}+\\\\frac{1}{2}g^{\\\\lambda \\\\kappa} \\\\nabla_{\\\\mu}{h_{\\\\kappa \\\\nu}} - \\\\frac{1}{2}g^{\\\\lambda \\\\kappa} \\\\nabla_{\\\\kappa}{h_{\\\\mu \\\\nu}}\\\\right)+\\\\epsilon^{2} \\\\left( - \\\\frac{1}{2}h^{\\\\lambda \\\\kappa} \\\\nabla_{\\\\nu}{h_{\\\\kappa \\\\mu}} - \\\\frac{1}{2}h^{\\\\lambda \\\\kappa} \\\\nabla_{\\\\mu}{h_{\\\\kappa \\\\nu}}+\\\\frac{1}{2}h^{\\\\lambda \\\\kappa} \\\\nabla_{\\\\kappa}{h_{\\\\mu \\\\nu}}\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"factor_out(_,$\\\\epsilon,\\\\epsilon**2$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\Gamma^{\\\\lambda}\\\\,_{\\\\mu \\\\nu} \\\\rightarrow \\\\epsilon g^{\\\\lambda \\\\kappa} \\\\left(\\\\frac{1}{2}\\\\nabla_{\\\\nu}{h_{\\\\kappa \\\\mu}}+\\\\frac{1}{2}\\\\nabla_{\\\\mu}{h_{\\\\kappa \\\\nu}} - \\\\frac{1}{2}\\\\nabla_{\\\\kappa}{h_{\\\\mu \\\\nu}}\\\\right)+\\\\epsilon^{2} \\\\left( - \\\\frac{1}{2}h^{\\\\lambda \\\\kappa} \\\\nabla_{\\\\nu}{h_{\\\\mu \\\\kappa}} - \\\\frac{1}{2}h^{\\\\lambda \\\\kappa} \\\\nabla_{\\\\mu}{h_{\\\\nu \\\\kappa}}+\\\\frac{1}{2}h^{\\\\lambda \\\\kappa} \\\\nabla_{\\\\kappa}{h_{\\\\mu \\\\nu}}\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"factor_out(_, $g^{\\\\mu? \\\\nu?}$)\\ncanonicalise(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"and then we discard the second-order terms, as they are irrelevant for the linearization procedure\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"and then we discard the second-order terms, as they are irrelevant for the linearization procedure\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\Gamma^{\\\\lambda}\\\\,_{\\\\mu \\\\nu} \\\\rightarrow \\\\epsilon g^{\\\\lambda \\\\kappa} \\\\left(\\\\frac{1}{2}\\\\nabla_{\\\\nu}{h_{\\\\kappa \\\\mu}}+\\\\frac{1}{2}\\\\nabla_{\\\\mu}{h_{\\\\kappa \\\\nu}} - \\\\frac{1}{2}\\\\nabla_{\\\\kappa}{h_{\\\\mu \\\\nu}}\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"substitute(_, $\\\\epsilon**{2} -> 0$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\subsection*{Ricci tensor}\\n\\nThe Ricci tensor of \\\\(g(\\\\epsilon)\\\\) is given by\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\subsection*{Ricci tensor}\\n\\nThe Ricci tensor of \\\\(g(\\\\epsilon)\\\\) is given by\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}R_{\\\\mu \\\\nu} \\\\rightarrow -\\\\nabla_{\\\\mu}{\\\\Gamma^{\\\\rho}\\\\,_{\\\\rho \\\\nu}}+\\\\nabla_{\\\\rho}{\\\\Gamma^{\\\\rho}\\\\,_{\\\\mu \\\\nu}}+\\\\Gamma^{\\\\lambda}\\\\,_{\\\\nu \\\\mu} \\\\Gamma^{\\\\rho}\\\\,_{\\\\rho \\\\lambda}+\\\\Gamma^{\\\\lambda}\\\\,_{\\\\nu \\\\lambda} \\\\Gamma^{\\\\rho}\\\\,_{\\\\rho \\\\mu}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"rm:= R_{\\\\mu\\\\nu} -> -\\\\nabla_{\\\\mu}{\\\\Gamma^{\\\\rho}_{\\\\rho\\\\nu}}+\\\\nabla_{\\\\rho}{\\\\Gamma^{\\\\rho}_{\\\\mu\\\\nu}}\\n                                  +\\\\Gamma^{\\\\lambda}_{\\\\nu\\\\mu} \\\\Gamma^{\\\\rho}_{\\\\rho\\\\lambda}\\n                                  +\\\\Gamma^{\\\\lambda}_{\\\\nu\\\\lambda} \\\\Gamma^{\\\\rho}_{\\\\rho\\\\mu};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"where it was used the fact that \\\\(\\\\textrm{Ric}(g(0))=0\\\\).\\n\\nSubstituting the linearized version of the connection coefficients, we obtain\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"where it was used the fact that \\\\(\\\\textrm{Ric}(g(0))=0\\\\).\\n\\nSubstituting the linearized version of the connection coefficients, we obtain\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}R_{\\\\mu \\\\nu} \\\\rightarrow -\\\\nabla_{\\\\mu}\\\\left(\\\\epsilon g^{\\\\rho \\\\kappa} \\\\left(\\\\frac{1}{2}\\\\nabla_{\\\\nu}{h_{\\\\kappa \\\\rho}}+\\\\frac{1}{2}\\\\nabla_{\\\\rho}{h_{\\\\kappa \\\\nu}} - \\\\frac{1}{2}\\\\nabla_{\\\\kappa}{h_{\\\\rho \\\\nu}}\\\\right)\\\\right)+\\\\nabla_{\\\\rho}\\\\left(\\\\epsilon g^{\\\\rho \\\\kappa} \\\\left(\\\\frac{1}{2}\\\\nabla_{\\\\nu}{h_{\\\\kappa \\\\mu}}+\\\\frac{1}{2}\\\\nabla_{\\\\mu}{h_{\\\\kappa \\\\nu}} - \\\\frac{1}{2}\\\\nabla_{\\\\kappa}{h_{\\\\mu \\\\nu}}\\\\right)\\\\right)+\\\\epsilon g^{\\\\lambda \\\\kappa} \\\\left(\\\\frac{1}{2}\\\\nabla_{\\\\mu}{h_{\\\\kappa \\\\nu}}+\\\\frac{1}{2}\\\\nabla_{\\\\nu}{h_{\\\\kappa \\\\mu}} - \\\\frac{1}{2}\\\\nabla_{\\\\kappa}{h_{\\\\nu \\\\mu}}\\\\right) \\\\epsilon g^{\\\\rho \\\\alpha} \\\\left(\\\\frac{1}{2}\\\\nabla_{\\\\lambda}{h_{\\\\alpha \\\\rho}}+\\\\frac{1}{2}\\\\nabla_{\\\\rho}{h_{\\\\alpha \\\\lambda}} - \\\\frac{1}{2}\\\\nabla_{\\\\alpha}{h_{\\\\rho \\\\lambda}}\\\\right)+\\\\epsilon g^{\\\\lambda \\\\kappa} \\\\left(\\\\frac{1}{2}\\\\nabla_{\\\\lambda}{h_{\\\\kappa \\\\nu}}+\\\\frac{1}{2}\\\\nabla_{\\\\nu}{h_{\\\\kappa \\\\lambda}} - \\\\frac{1}{2}\\\\nabla_{\\\\kappa}{h_{\\\\nu \\\\lambda}}\\\\right) \\\\epsilon g^{\\\\rho \\\\alpha} \\\\left(\\\\frac{1}{2}\\\\nabla_{\\\\mu}{h_{\\\\alpha \\\\rho}}+\\\\frac{1}{2}\\\\nabla_{\\\\rho}{h_{\\\\alpha \\\\mu}} - \\\\frac{1}{2}\\\\nabla_{\\\\alpha}{h_{\\\\rho \\\\mu}}\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"substitute(rm,Gtog);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"Finally, we apply the same procedure of the linearization of the connection coefficients:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"Finally, we apply the same procedure of the linearization of the connection coefficients:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}R_{\\\\mu \\\\nu} \\\\rightarrow  - \\\\frac{1}{2}\\\\nabla_{\\\\mu}{\\\\epsilon} g^{\\\\rho \\\\kappa} \\\\nabla_{\\\\nu}{h_{\\\\kappa \\\\rho}} - \\\\frac{1}{2}\\\\epsilon \\\\nabla_{\\\\mu}{g^{\\\\rho \\\\kappa}} \\\\nabla_{\\\\nu}{h_{\\\\kappa \\\\rho}} - \\\\frac{1}{2}\\\\epsilon g^{\\\\rho \\\\kappa} \\\\nabla_{\\\\mu}\\\\left(\\\\nabla_{\\\\nu}{h_{\\\\kappa \\\\rho}}\\\\right) - \\\\frac{1}{2}\\\\nabla_{\\\\mu}{\\\\epsilon} g^{\\\\rho \\\\kappa} \\\\nabla_{\\\\rho}{h_{\\\\kappa \\\\nu}} - \\\\frac{1}{2}\\\\epsilon \\\\nabla_{\\\\mu}{g^{\\\\rho \\\\kappa}} \\\\nabla_{\\\\rho}{h_{\\\\kappa \\\\nu}} - \\\\frac{1}{2}\\\\epsilon g^{\\\\rho \\\\kappa} \\\\nabla_{\\\\mu}\\\\left(\\\\nabla_{\\\\rho}{h_{\\\\kappa \\\\nu}}\\\\right)+\\\\frac{1}{2}\\\\nabla_{\\\\mu}{\\\\epsilon} g^{\\\\rho \\\\kappa} \\\\nabla_{\\\\kappa}{h_{\\\\rho \\\\nu}}+\\\\frac{1}{2}\\\\epsilon \\\\nabla_{\\\\mu}{g^{\\\\rho \\\\kappa}} \\\\nabla_{\\\\kappa}{h_{\\\\rho \\\\nu}}+\\\\frac{1}{2}\\\\epsilon g^{\\\\rho \\\\kappa} \\\\nabla_{\\\\mu}\\\\left(\\\\nabla_{\\\\kappa}{h_{\\\\rho \\\\nu}}\\\\right)+\\\\frac{1}{2}\\\\nabla_{\\\\rho}{\\\\epsilon} g^{\\\\rho \\\\kappa} \\\\nabla_{\\\\nu}{h_{\\\\kappa \\\\mu}}+\\\\frac{1}{2}\\\\epsilon \\\\nabla_{\\\\rho}{g^{\\\\rho \\\\kappa}} \\\\nabla_{\\\\nu}{h_{\\\\kappa \\\\mu}}+\\\\frac{1}{2}\\\\epsilon g^{\\\\rho \\\\kappa} \\\\nabla_{\\\\rho}\\\\left(\\\\nabla_{\\\\nu}{h_{\\\\kappa \\\\mu}}\\\\right)+\\\\frac{1}{2}\\\\nabla_{\\\\rho}{\\\\epsilon} g^{\\\\rho \\\\kappa} \\\\nabla_{\\\\mu}{h_{\\\\kappa \\\\nu}}+\\\\frac{1}{2}\\\\epsilon \\\\nabla_{\\\\rho}{g^{\\\\rho \\\\kappa}} \\\\nabla_{\\\\mu}{h_{\\\\kappa \\\\nu}}+\\\\frac{1}{2}\\\\epsilon g^{\\\\rho \\\\kappa} \\\\nabla_{\\\\rho}\\\\left(\\\\nabla_{\\\\mu}{h_{\\\\kappa \\\\nu}}\\\\right) - \\\\frac{1}{2}\\\\nabla_{\\\\rho}{\\\\epsilon} g^{\\\\rho \\\\kappa} \\\\nabla_{\\\\kappa}{h_{\\\\mu \\\\nu}} - \\\\frac{1}{2}\\\\epsilon \\\\nabla_{\\\\rho}{g^{\\\\rho \\\\kappa}} \\\\nabla_{\\\\kappa}{h_{\\\\mu \\\\nu}} - \\\\frac{1}{2}\\\\epsilon g^{\\\\rho \\\\kappa} \\\\nabla_{\\\\rho}\\\\left(\\\\nabla_{\\\\kappa}{h_{\\\\mu \\\\nu}}\\\\right)+\\\\frac{1}{4}\\\\epsilon g^{\\\\lambda \\\\kappa} \\\\nabla_{\\\\mu}{h_{\\\\kappa \\\\nu}} \\\\epsilon g^{\\\\rho \\\\alpha} \\\\nabla_{\\\\lambda}{h_{\\\\alpha \\\\rho}}%\\n+\\\\frac{1}{4}\\\\epsilon g^{\\\\lambda \\\\kappa} \\\\nabla_{\\\\mu}{h_{\\\\kappa \\\\nu}} \\\\epsilon g^{\\\\rho \\\\alpha} \\\\nabla_{\\\\rho}{h_{\\\\alpha \\\\lambda}} - \\\\frac{1}{4}\\\\epsilon g^{\\\\lambda \\\\kappa} \\\\nabla_{\\\\mu}{h_{\\\\kappa \\\\nu}} \\\\epsilon g^{\\\\rho \\\\alpha} \\\\nabla_{\\\\alpha}{h_{\\\\rho \\\\lambda}}+\\\\frac{1}{4}\\\\epsilon g^{\\\\lambda \\\\kappa} \\\\nabla_{\\\\nu}{h_{\\\\kappa \\\\mu}} \\\\epsilon g^{\\\\rho \\\\alpha} \\\\nabla_{\\\\lambda}{h_{\\\\alpha \\\\rho}}+\\\\frac{1}{4}\\\\epsilon g^{\\\\lambda \\\\kappa} \\\\nabla_{\\\\nu}{h_{\\\\kappa \\\\mu}} \\\\epsilon g^{\\\\rho \\\\alpha} \\\\nabla_{\\\\rho}{h_{\\\\alpha \\\\lambda}} - \\\\frac{1}{4}\\\\epsilon g^{\\\\lambda \\\\kappa} \\\\nabla_{\\\\nu}{h_{\\\\kappa \\\\mu}} \\\\epsilon g^{\\\\rho \\\\alpha} \\\\nabla_{\\\\alpha}{h_{\\\\rho \\\\lambda}} - \\\\frac{1}{4}\\\\epsilon g^{\\\\lambda \\\\kappa} \\\\nabla_{\\\\kappa}{h_{\\\\nu \\\\mu}} \\\\epsilon g^{\\\\rho \\\\alpha} \\\\nabla_{\\\\lambda}{h_{\\\\alpha \\\\rho}} - \\\\frac{1}{4}\\\\epsilon g^{\\\\lambda \\\\kappa} \\\\nabla_{\\\\kappa}{h_{\\\\nu \\\\mu}} \\\\epsilon g^{\\\\rho \\\\alpha} \\\\nabla_{\\\\rho}{h_{\\\\alpha \\\\lambda}}+\\\\frac{1}{4}\\\\epsilon g^{\\\\lambda \\\\kappa} \\\\nabla_{\\\\kappa}{h_{\\\\nu \\\\mu}} \\\\epsilon g^{\\\\rho \\\\alpha} \\\\nabla_{\\\\alpha}{h_{\\\\rho \\\\lambda}}+\\\\frac{1}{4}\\\\epsilon g^{\\\\lambda \\\\kappa} \\\\nabla_{\\\\lambda}{h_{\\\\kappa \\\\nu}} \\\\epsilon g^{\\\\rho \\\\alpha} \\\\nabla_{\\\\mu}{h_{\\\\alpha \\\\rho}}+\\\\frac{1}{4}\\\\epsilon g^{\\\\lambda \\\\kappa} \\\\nabla_{\\\\lambda}{h_{\\\\kappa \\\\nu}} \\\\epsilon g^{\\\\rho \\\\alpha} \\\\nabla_{\\\\rho}{h_{\\\\alpha \\\\mu}} - \\\\frac{1}{4}\\\\epsilon g^{\\\\lambda \\\\kappa} \\\\nabla_{\\\\lambda}{h_{\\\\kappa \\\\nu}} \\\\epsilon g^{\\\\rho \\\\alpha} \\\\nabla_{\\\\alpha}{h_{\\\\rho \\\\mu}}+\\\\frac{1}{4}\\\\epsilon g^{\\\\lambda \\\\kappa} \\\\nabla_{\\\\nu}{h_{\\\\kappa \\\\lambda}} \\\\epsilon g^{\\\\rho \\\\alpha} \\\\nabla_{\\\\mu}{h_{\\\\alpha \\\\rho}}+\\\\frac{1}{4}\\\\epsilon g^{\\\\lambda \\\\kappa} \\\\nabla_{\\\\nu}{h_{\\\\kappa \\\\lambda}} \\\\epsilon g^{\\\\rho \\\\alpha} \\\\nabla_{\\\\rho}{h_{\\\\alpha \\\\mu}} - \\\\frac{1}{4}\\\\epsilon g^{\\\\lambda \\\\kappa} \\\\nabla_{\\\\nu}{h_{\\\\kappa \\\\lambda}} \\\\epsilon g^{\\\\rho \\\\alpha} \\\\nabla_{\\\\alpha}{h_{\\\\rho \\\\mu}} - \\\\frac{1}{4}\\\\epsilon g^{\\\\lambda \\\\kappa} \\\\nabla_{\\\\kappa}{h_{\\\\nu \\\\lambda}} \\\\epsilon g^{\\\\rho \\\\alpha} \\\\nabla_{\\\\mu}{h_{\\\\alpha \\\\rho}} - \\\\frac{1}{4}\\\\epsilon g^{\\\\lambda \\\\kappa} \\\\nabla_{\\\\kappa}{h_{\\\\nu \\\\lambda}} \\\\epsilon g^{\\\\rho \\\\alpha} \\\\nabla_{\\\\rho}{h_{\\\\alpha \\\\mu}}+\\\\frac{1}{4}\\\\epsilon g^{\\\\lambda \\\\kappa} \\\\nabla_{\\\\kappa}{h_{\\\\nu \\\\lambda}} \\\\epsilon g^{\\\\rho \\\\alpha} \\\\nabla_{\\\\alpha}{h_{\\\\rho \\\\mu}}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"distribute(_)\\nproduct_rule(_)\\ndistribute(_)\\nproduct_rule(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}R_{\\\\mu \\\\nu} \\\\rightarrow  - \\\\frac{1}{2}\\\\epsilon \\\\nabla_{\\\\mu}{g^{\\\\rho \\\\kappa}} \\\\nabla_{\\\\nu}{h_{\\\\kappa \\\\rho}} - \\\\frac{1}{2}\\\\epsilon g^{\\\\rho \\\\kappa} \\\\nabla_{\\\\mu}\\\\left(\\\\nabla_{\\\\nu}{h_{\\\\kappa \\\\rho}}\\\\right) - \\\\frac{1}{2}\\\\epsilon \\\\nabla_{\\\\mu}{g^{\\\\rho \\\\kappa}} \\\\nabla_{\\\\rho}{h_{\\\\kappa \\\\nu}} - \\\\frac{1}{2}\\\\epsilon g^{\\\\rho \\\\kappa} \\\\nabla_{\\\\mu}\\\\left(\\\\nabla_{\\\\rho}{h_{\\\\kappa \\\\nu}}\\\\right)+\\\\frac{1}{2}\\\\epsilon \\\\nabla_{\\\\mu}{g^{\\\\rho \\\\kappa}} \\\\nabla_{\\\\kappa}{h_{\\\\rho \\\\nu}}+\\\\frac{1}{2}\\\\epsilon g^{\\\\rho \\\\kappa} \\\\nabla_{\\\\mu}\\\\left(\\\\nabla_{\\\\kappa}{h_{\\\\rho \\\\nu}}\\\\right)+\\\\frac{1}{2}\\\\epsilon \\\\nabla_{\\\\rho}{g^{\\\\rho \\\\kappa}} \\\\nabla_{\\\\nu}{h_{\\\\kappa \\\\mu}}+\\\\frac{1}{2}\\\\epsilon g^{\\\\rho \\\\kappa} \\\\nabla_{\\\\rho}\\\\left(\\\\nabla_{\\\\nu}{h_{\\\\kappa \\\\mu}}\\\\right)+\\\\frac{1}{2}\\\\epsilon \\\\nabla_{\\\\rho}{g^{\\\\rho \\\\kappa}} \\\\nabla_{\\\\mu}{h_{\\\\kappa \\\\nu}}+\\\\frac{1}{2}\\\\epsilon g^{\\\\rho \\\\kappa} \\\\nabla_{\\\\rho}\\\\left(\\\\nabla_{\\\\mu}{h_{\\\\kappa \\\\nu}}\\\\right) - \\\\frac{1}{2}\\\\epsilon \\\\nabla_{\\\\rho}{g^{\\\\rho \\\\kappa}} \\\\nabla_{\\\\kappa}{h_{\\\\mu \\\\nu}} - \\\\frac{1}{2}\\\\epsilon g^{\\\\rho \\\\kappa} \\\\nabla_{\\\\rho}\\\\left(\\\\nabla_{\\\\kappa}{h_{\\\\mu \\\\nu}}\\\\right)+\\\\frac{1}{4}\\\\epsilon g^{\\\\lambda \\\\kappa} \\\\nabla_{\\\\mu}{h_{\\\\kappa \\\\nu}} \\\\epsilon g^{\\\\rho \\\\alpha} \\\\nabla_{\\\\lambda}{h_{\\\\alpha \\\\rho}}+\\\\frac{1}{4}\\\\epsilon g^{\\\\lambda \\\\kappa} \\\\nabla_{\\\\mu}{h_{\\\\kappa \\\\nu}} \\\\epsilon g^{\\\\rho \\\\alpha} \\\\nabla_{\\\\rho}{h_{\\\\alpha \\\\lambda}} - \\\\frac{1}{4}\\\\epsilon g^{\\\\lambda \\\\kappa} \\\\nabla_{\\\\mu}{h_{\\\\kappa \\\\nu}} \\\\epsilon g^{\\\\rho \\\\alpha} \\\\nabla_{\\\\alpha}{h_{\\\\rho \\\\lambda}}+\\\\frac{1}{4}\\\\epsilon g^{\\\\lambda \\\\kappa} \\\\nabla_{\\\\nu}{h_{\\\\kappa \\\\mu}} \\\\epsilon g^{\\\\rho \\\\alpha} \\\\nabla_{\\\\lambda}{h_{\\\\alpha \\\\rho}}+\\\\frac{1}{4}\\\\epsilon g^{\\\\lambda \\\\kappa} \\\\nabla_{\\\\nu}{h_{\\\\kappa \\\\mu}} \\\\epsilon g^{\\\\rho \\\\alpha} \\\\nabla_{\\\\rho}{h_{\\\\alpha \\\\lambda}} - \\\\frac{1}{4}\\\\epsilon g^{\\\\lambda \\\\kappa} \\\\nabla_{\\\\nu}{h_{\\\\kappa \\\\mu}} \\\\epsilon g^{\\\\rho \\\\alpha} \\\\nabla_{\\\\alpha}{h_{\\\\rho \\\\lambda}} - \\\\frac{1}{4}\\\\epsilon g^{\\\\lambda \\\\kappa} \\\\nabla_{\\\\kappa}{h_{\\\\nu \\\\mu}} \\\\epsilon g^{\\\\rho \\\\alpha} \\\\nabla_{\\\\lambda}{h_{\\\\alpha \\\\rho}}%\\n - \\\\frac{1}{4}\\\\epsilon g^{\\\\lambda \\\\kappa} \\\\nabla_{\\\\kappa}{h_{\\\\nu \\\\mu}} \\\\epsilon g^{\\\\rho \\\\alpha} \\\\nabla_{\\\\rho}{h_{\\\\alpha \\\\lambda}}+\\\\frac{1}{4}\\\\epsilon g^{\\\\lambda \\\\kappa} \\\\nabla_{\\\\kappa}{h_{\\\\nu \\\\mu}} \\\\epsilon g^{\\\\rho \\\\alpha} \\\\nabla_{\\\\alpha}{h_{\\\\rho \\\\lambda}}+\\\\frac{1}{4}\\\\epsilon g^{\\\\lambda \\\\kappa} \\\\nabla_{\\\\lambda}{h_{\\\\kappa \\\\nu}} \\\\epsilon g^{\\\\rho \\\\alpha} \\\\nabla_{\\\\mu}{h_{\\\\alpha \\\\rho}}+\\\\frac{1}{4}\\\\epsilon g^{\\\\lambda \\\\kappa} \\\\nabla_{\\\\lambda}{h_{\\\\kappa \\\\nu}} \\\\epsilon g^{\\\\rho \\\\alpha} \\\\nabla_{\\\\rho}{h_{\\\\alpha \\\\mu}} - \\\\frac{1}{4}\\\\epsilon g^{\\\\lambda \\\\kappa} \\\\nabla_{\\\\lambda}{h_{\\\\kappa \\\\nu}} \\\\epsilon g^{\\\\rho \\\\alpha} \\\\nabla_{\\\\alpha}{h_{\\\\rho \\\\mu}}+\\\\frac{1}{4}\\\\epsilon g^{\\\\lambda \\\\kappa} \\\\nabla_{\\\\nu}{h_{\\\\kappa \\\\lambda}} \\\\epsilon g^{\\\\rho \\\\alpha} \\\\nabla_{\\\\mu}{h_{\\\\alpha \\\\rho}}+\\\\frac{1}{4}\\\\epsilon g^{\\\\lambda \\\\kappa} \\\\nabla_{\\\\nu}{h_{\\\\kappa \\\\lambda}} \\\\epsilon g^{\\\\rho \\\\alpha} \\\\nabla_{\\\\rho}{h_{\\\\alpha \\\\mu}} - \\\\frac{1}{4}\\\\epsilon g^{\\\\lambda \\\\kappa} \\\\nabla_{\\\\nu}{h_{\\\\kappa \\\\lambda}} \\\\epsilon g^{\\\\rho \\\\alpha} \\\\nabla_{\\\\alpha}{h_{\\\\rho \\\\mu}} - \\\\frac{1}{4}\\\\epsilon g^{\\\\lambda \\\\kappa} \\\\nabla_{\\\\kappa}{h_{\\\\nu \\\\lambda}} \\\\epsilon g^{\\\\rho \\\\alpha} \\\\nabla_{\\\\mu}{h_{\\\\alpha \\\\rho}} - \\\\frac{1}{4}\\\\epsilon g^{\\\\lambda \\\\kappa} \\\\nabla_{\\\\kappa}{h_{\\\\nu \\\\lambda}} \\\\epsilon g^{\\\\rho \\\\alpha} \\\\nabla_{\\\\rho}{h_{\\\\alpha \\\\mu}}+\\\\frac{1}{4}\\\\epsilon g^{\\\\lambda \\\\kappa} \\\\nabla_{\\\\kappa}{h_{\\\\nu \\\\lambda}} \\\\epsilon g^{\\\\rho \\\\alpha} \\\\nabla_{\\\\alpha}{h_{\\\\rho \\\\mu}}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"substitute(_, $\\\\nabla_{\\\\mu}{ \\\\epsilon } -> 0$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}R_{\\\\mu \\\\nu} \\\\rightarrow  - \\\\frac{1}{2}\\\\epsilon g^{\\\\rho \\\\kappa} \\\\nabla_{\\\\mu}\\\\left(\\\\nabla_{\\\\nu}{h_{\\\\kappa \\\\rho}}\\\\right) - \\\\frac{1}{2}\\\\epsilon g^{\\\\rho \\\\kappa} \\\\nabla_{\\\\mu}\\\\left(\\\\nabla_{\\\\rho}{h_{\\\\kappa \\\\nu}}\\\\right)+\\\\frac{1}{2}\\\\epsilon g^{\\\\rho \\\\kappa} \\\\nabla_{\\\\mu}\\\\left(\\\\nabla_{\\\\kappa}{h_{\\\\rho \\\\nu}}\\\\right)+\\\\frac{1}{2}\\\\epsilon g^{\\\\rho \\\\kappa} \\\\nabla_{\\\\rho}\\\\left(\\\\nabla_{\\\\nu}{h_{\\\\kappa \\\\mu}}\\\\right)+\\\\frac{1}{2}\\\\epsilon g^{\\\\rho \\\\kappa} \\\\nabla_{\\\\rho}\\\\left(\\\\nabla_{\\\\mu}{h_{\\\\kappa \\\\nu}}\\\\right) - \\\\frac{1}{2}\\\\epsilon g^{\\\\rho \\\\kappa} \\\\nabla_{\\\\rho}\\\\left(\\\\nabla_{\\\\kappa}{h_{\\\\mu \\\\nu}}\\\\right)+\\\\frac{1}{4}\\\\epsilon g^{\\\\lambda \\\\kappa} \\\\nabla_{\\\\mu}{h_{\\\\kappa \\\\nu}} \\\\epsilon g^{\\\\rho \\\\alpha} \\\\nabla_{\\\\lambda}{h_{\\\\alpha \\\\rho}}+\\\\frac{1}{4}\\\\epsilon g^{\\\\lambda \\\\kappa} \\\\nabla_{\\\\mu}{h_{\\\\kappa \\\\nu}} \\\\epsilon g^{\\\\rho \\\\alpha} \\\\nabla_{\\\\rho}{h_{\\\\alpha \\\\lambda}} - \\\\frac{1}{4}\\\\epsilon g^{\\\\lambda \\\\kappa} \\\\nabla_{\\\\mu}{h_{\\\\kappa \\\\nu}} \\\\epsilon g^{\\\\rho \\\\alpha} \\\\nabla_{\\\\alpha}{h_{\\\\rho \\\\lambda}}+\\\\frac{1}{4}\\\\epsilon g^{\\\\lambda \\\\kappa} \\\\nabla_{\\\\nu}{h_{\\\\kappa \\\\mu}} \\\\epsilon g^{\\\\rho \\\\alpha} \\\\nabla_{\\\\lambda}{h_{\\\\alpha \\\\rho}}+\\\\frac{1}{4}\\\\epsilon g^{\\\\lambda \\\\kappa} \\\\nabla_{\\\\nu}{h_{\\\\kappa \\\\mu}} \\\\epsilon g^{\\\\rho \\\\alpha} \\\\nabla_{\\\\rho}{h_{\\\\alpha \\\\lambda}} - \\\\frac{1}{4}\\\\epsilon g^{\\\\lambda \\\\kappa} \\\\nabla_{\\\\nu}{h_{\\\\kappa \\\\mu}} \\\\epsilon g^{\\\\rho \\\\alpha} \\\\nabla_{\\\\alpha}{h_{\\\\rho \\\\lambda}} - \\\\frac{1}{4}\\\\epsilon g^{\\\\lambda \\\\kappa} \\\\nabla_{\\\\kappa}{h_{\\\\nu \\\\mu}} \\\\epsilon g^{\\\\rho \\\\alpha} \\\\nabla_{\\\\lambda}{h_{\\\\alpha \\\\rho}} - \\\\frac{1}{4}\\\\epsilon g^{\\\\lambda \\\\kappa} \\\\nabla_{\\\\kappa}{h_{\\\\nu \\\\mu}} \\\\epsilon g^{\\\\rho \\\\alpha} \\\\nabla_{\\\\rho}{h_{\\\\alpha \\\\lambda}}+\\\\frac{1}{4}\\\\epsilon g^{\\\\lambda \\\\kappa} \\\\nabla_{\\\\kappa}{h_{\\\\nu \\\\mu}} \\\\epsilon g^{\\\\rho \\\\alpha} \\\\nabla_{\\\\alpha}{h_{\\\\rho \\\\lambda}}+\\\\frac{1}{4}\\\\epsilon g^{\\\\lambda \\\\kappa} \\\\nabla_{\\\\lambda}{h_{\\\\kappa \\\\nu}} \\\\epsilon g^{\\\\rho \\\\alpha} \\\\nabla_{\\\\mu}{h_{\\\\alpha \\\\rho}}+\\\\frac{1}{4}\\\\epsilon g^{\\\\lambda \\\\kappa} \\\\nabla_{\\\\lambda}{h_{\\\\kappa \\\\nu}} \\\\epsilon g^{\\\\rho \\\\alpha} \\\\nabla_{\\\\rho}{h_{\\\\alpha \\\\mu}} - \\\\frac{1}{4}\\\\epsilon g^{\\\\lambda \\\\kappa} \\\\nabla_{\\\\lambda}{h_{\\\\kappa \\\\nu}} \\\\epsilon g^{\\\\rho \\\\alpha} \\\\nabla_{\\\\alpha}{h_{\\\\rho \\\\mu}}+\\\\frac{1}{4}\\\\epsilon g^{\\\\lambda \\\\kappa} \\\\nabla_{\\\\nu}{h_{\\\\kappa \\\\lambda}} \\\\epsilon g^{\\\\rho \\\\alpha} \\\\nabla_{\\\\mu}{h_{\\\\alpha \\\\rho}}%\\n+\\\\frac{1}{4}\\\\epsilon g^{\\\\lambda \\\\kappa} \\\\nabla_{\\\\nu}{h_{\\\\kappa \\\\lambda}} \\\\epsilon g^{\\\\rho \\\\alpha} \\\\nabla_{\\\\rho}{h_{\\\\alpha \\\\mu}} - \\\\frac{1}{4}\\\\epsilon g^{\\\\lambda \\\\kappa} \\\\nabla_{\\\\nu}{h_{\\\\kappa \\\\lambda}} \\\\epsilon g^{\\\\rho \\\\alpha} \\\\nabla_{\\\\alpha}{h_{\\\\rho \\\\mu}} - \\\\frac{1}{4}\\\\epsilon g^{\\\\lambda \\\\kappa} \\\\nabla_{\\\\kappa}{h_{\\\\nu \\\\lambda}} \\\\epsilon g^{\\\\rho \\\\alpha} \\\\nabla_{\\\\mu}{h_{\\\\alpha \\\\rho}} - \\\\frac{1}{4}\\\\epsilon g^{\\\\lambda \\\\kappa} \\\\nabla_{\\\\kappa}{h_{\\\\nu \\\\lambda}} \\\\epsilon g^{\\\\rho \\\\alpha} \\\\nabla_{\\\\rho}{h_{\\\\alpha \\\\mu}}+\\\\frac{1}{4}\\\\epsilon g^{\\\\lambda \\\\kappa} \\\\nabla_{\\\\kappa}{h_{\\\\nu \\\\lambda}} \\\\epsilon g^{\\\\rho \\\\alpha} \\\\nabla_{\\\\alpha}{h_{\\\\rho \\\\mu}}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"substitute(_, $\\\\nabla_{\\\\mu}{ g_{\\\\nu \\\\kappa} } -> 0$)\\nsubstitute(_, $\\\\nabla_{\\\\mu}{ g^{\\\\nu \\\\kappa} } -> 0$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}R_{\\\\mu \\\\nu} \\\\rightarrow \\\\epsilon \\\\left( - \\\\frac{1}{2}g^{\\\\rho \\\\kappa} \\\\nabla_{\\\\mu}\\\\left(\\\\nabla_{\\\\nu}{h_{\\\\kappa \\\\rho}}\\\\right) - \\\\frac{1}{2}g^{\\\\rho \\\\kappa} \\\\nabla_{\\\\mu}\\\\left(\\\\nabla_{\\\\rho}{h_{\\\\kappa \\\\nu}}\\\\right)+\\\\frac{1}{2}g^{\\\\rho \\\\kappa} \\\\nabla_{\\\\mu}\\\\left(\\\\nabla_{\\\\kappa}{h_{\\\\rho \\\\nu}}\\\\right)+\\\\frac{1}{2}g^{\\\\rho \\\\kappa} \\\\nabla_{\\\\rho}\\\\left(\\\\nabla_{\\\\nu}{h_{\\\\kappa \\\\mu}}\\\\right)+\\\\frac{1}{2}g^{\\\\rho \\\\kappa} \\\\nabla_{\\\\rho}\\\\left(\\\\nabla_{\\\\mu}{h_{\\\\kappa \\\\nu}}\\\\right) - \\\\frac{1}{2}g^{\\\\rho \\\\kappa} \\\\nabla_{\\\\rho}\\\\left(\\\\nabla_{\\\\kappa}{h_{\\\\mu \\\\nu}}\\\\right)\\\\right)+\\\\epsilon^{2} \\\\left(\\\\frac{1}{4}g^{\\\\lambda \\\\kappa} \\\\nabla_{\\\\mu}{h_{\\\\kappa \\\\nu}} g^{\\\\rho \\\\alpha} \\\\nabla_{\\\\lambda}{h_{\\\\alpha \\\\rho}}+\\\\frac{1}{4}g^{\\\\lambda \\\\kappa} \\\\nabla_{\\\\mu}{h_{\\\\kappa \\\\nu}} g^{\\\\rho \\\\alpha} \\\\nabla_{\\\\rho}{h_{\\\\alpha \\\\lambda}} - \\\\frac{1}{4}g^{\\\\lambda \\\\kappa} \\\\nabla_{\\\\mu}{h_{\\\\kappa \\\\nu}} g^{\\\\rho \\\\alpha} \\\\nabla_{\\\\alpha}{h_{\\\\rho \\\\lambda}}+\\\\frac{1}{4}g^{\\\\lambda \\\\kappa} \\\\nabla_{\\\\nu}{h_{\\\\kappa \\\\mu}} g^{\\\\rho \\\\alpha} \\\\nabla_{\\\\lambda}{h_{\\\\alpha \\\\rho}}+\\\\frac{1}{4}g^{\\\\lambda \\\\kappa} \\\\nabla_{\\\\nu}{h_{\\\\kappa \\\\mu}} g^{\\\\rho \\\\alpha} \\\\nabla_{\\\\rho}{h_{\\\\alpha \\\\lambda}} - \\\\frac{1}{4}g^{\\\\lambda \\\\kappa} \\\\nabla_{\\\\nu}{h_{\\\\kappa \\\\mu}} g^{\\\\rho \\\\alpha} \\\\nabla_{\\\\alpha}{h_{\\\\rho \\\\lambda}} - \\\\frac{1}{4}g^{\\\\lambda \\\\kappa} \\\\nabla_{\\\\kappa}{h_{\\\\nu \\\\mu}} g^{\\\\rho \\\\alpha} \\\\nabla_{\\\\lambda}{h_{\\\\alpha \\\\rho}} - \\\\frac{1}{4}g^{\\\\lambda \\\\kappa} \\\\nabla_{\\\\kappa}{h_{\\\\nu \\\\mu}} g^{\\\\rho \\\\alpha} \\\\nabla_{\\\\rho}{h_{\\\\alpha \\\\lambda}}+\\\\frac{1}{4}g^{\\\\lambda \\\\kappa} \\\\nabla_{\\\\kappa}{h_{\\\\nu \\\\mu}} g^{\\\\rho \\\\alpha} \\\\nabla_{\\\\alpha}{h_{\\\\rho \\\\lambda}}+\\\\frac{1}{4}g^{\\\\lambda \\\\kappa} \\\\nabla_{\\\\lambda}{h_{\\\\kappa \\\\nu}} g^{\\\\rho \\\\alpha} \\\\nabla_{\\\\mu}{h_{\\\\alpha \\\\rho}}+\\\\frac{1}{4}g^{\\\\lambda \\\\kappa} \\\\nabla_{\\\\lambda}{h_{\\\\kappa \\\\nu}} g^{\\\\rho \\\\alpha} \\\\nabla_{\\\\rho}{h_{\\\\alpha \\\\mu}} - \\\\frac{1}{4}g^{\\\\lambda \\\\kappa} \\\\nabla_{\\\\lambda}{h_{\\\\kappa \\\\nu}} g^{\\\\rho \\\\alpha} \\\\nabla_{\\\\alpha}{h_{\\\\rho \\\\mu}}+\\\\frac{1}{4}g^{\\\\lambda \\\\kappa} \\\\nabla_{\\\\nu}{h_{\\\\kappa \\\\lambda}} g^{\\\\rho \\\\alpha} \\\\nabla_{\\\\mu}{h_{\\\\alpha \\\\rho}}+\\\\frac{1}{4}g^{\\\\lambda \\\\kappa} \\\\nabla_{\\\\nu}{h_{\\\\kappa \\\\lambda}} g^{\\\\rho \\\\alpha} \\\\nabla_{\\\\rho}{h_{\\\\alpha \\\\mu}} - \\\\frac{1}{4}g^{\\\\lambda \\\\kappa} \\\\nabla_{\\\\nu}{h_{\\\\kappa \\\\lambda}} g^{\\\\rho \\\\alpha} \\\\nabla_{\\\\alpha}{h_{\\\\rho \\\\mu}} - \\\\frac{1}{4}g^{\\\\lambda \\\\kappa} \\\\nabla_{\\\\kappa}{h_{\\\\nu \\\\lambda}} g^{\\\\rho \\\\alpha} \\\\nabla_{\\\\mu}{h_{\\\\alpha \\\\rho}} - \\\\frac{1}{4}g^{\\\\lambda \\\\kappa} \\\\nabla_{\\\\kappa}{h_{\\\\nu \\\\lambda}} g^{\\\\rho \\\\alpha} \\\\nabla_{\\\\rho}{h_{\\\\alpha \\\\mu}}+\\\\frac{1}{4}g^{\\\\lambda \\\\kappa} \\\\nabla_{\\\\kappa}{h_{\\\\nu \\\\lambda}} g^{\\\\rho \\\\alpha} \\\\nabla_{\\\\alpha}{h_{\\\\rho \\\\mu}}\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"collect_factors(_)\\nfactor_out(_, $\\\\epsilon, \\\\epsilon**2$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}R_{\\\\mu \\\\nu} \\\\rightarrow \\\\epsilon \\\\left( - \\\\frac{1}{2}g^{\\\\kappa \\\\rho} \\\\nabla_{\\\\mu}\\\\left(\\\\nabla_{\\\\nu}{h_{\\\\kappa \\\\rho}}\\\\right)+\\\\frac{1}{2}g^{\\\\kappa \\\\rho} \\\\nabla_{\\\\kappa}\\\\left(\\\\nabla_{\\\\nu}{h_{\\\\mu \\\\rho}}\\\\right)+\\\\frac{1}{2}g^{\\\\kappa \\\\rho} \\\\nabla_{\\\\kappa}\\\\left(\\\\nabla_{\\\\mu}{h_{\\\\nu \\\\rho}}\\\\right) - \\\\frac{1}{2}g^{\\\\kappa \\\\rho} \\\\nabla_{\\\\kappa}\\\\left(\\\\nabla_{\\\\rho}{h_{\\\\mu \\\\nu}}\\\\right)\\\\right)+\\\\epsilon^{2} \\\\left(\\\\frac{1}{4}g^{\\\\alpha \\\\kappa} \\\\nabla_{\\\\mu}{h_{\\\\nu \\\\alpha}} g^{\\\\lambda \\\\rho} \\\\nabla_{\\\\kappa}{h_{\\\\lambda \\\\rho}}+\\\\frac{1}{4}g^{\\\\alpha \\\\kappa} \\\\nabla_{\\\\nu}{h_{\\\\mu \\\\alpha}} g^{\\\\lambda \\\\rho} \\\\nabla_{\\\\kappa}{h_{\\\\lambda \\\\rho}} - \\\\frac{1}{4}g^{\\\\alpha \\\\kappa} \\\\nabla_{\\\\alpha}{h_{\\\\mu \\\\nu}} g^{\\\\lambda \\\\rho} \\\\nabla_{\\\\kappa}{h_{\\\\lambda \\\\rho}}+\\\\frac{1}{4}g^{\\\\alpha \\\\kappa} \\\\nabla_{\\\\mu}{h_{\\\\alpha \\\\kappa}} g^{\\\\lambda \\\\rho} \\\\nabla_{\\\\nu}{h_{\\\\lambda \\\\rho}}\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"canonicalise(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"Finally we make some post processing, to obtain\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"Finally we make some post processing, to obtain\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}R_{\\\\mu \\\\nu} \\\\rightarrow  - \\\\frac{1}{2}g^{\\\\alpha \\\\beta} \\\\nabla_{\\\\mu}\\\\left(\\\\nabla_{\\\\nu}{h_{\\\\alpha \\\\beta}}\\\\right)+\\\\frac{1}{2}g^{\\\\alpha \\\\beta} \\\\nabla_{\\\\alpha}\\\\left(\\\\nabla_{\\\\nu}{h_{\\\\mu \\\\beta}}\\\\right)+\\\\frac{1}{2}g^{\\\\alpha \\\\beta} \\\\nabla_{\\\\alpha}\\\\left(\\\\nabla_{\\\\mu}{h_{\\\\nu \\\\beta}}\\\\right) - \\\\frac{1}{2}g^{\\\\alpha \\\\beta} \\\\nabla_{\\\\alpha}\\\\left(\\\\nabla_{\\\\beta}{h_{\\\\mu \\\\nu}}\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"substitute(_, $\\\\epsilon**{2} -> 0$)\\nsubstitute(_, $\\\\epsilon -> 1$)\\nrename_dummies(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"This last expression agrees with Eq. (7.5.14) showed in Wald.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"This last expression agrees with Eq. (7.5.14) showed in Wald.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1\n}\n"
  },
  {
    "path": "examples/variational_derivatives.cnb",
    "content": "{\n\t\"cells\" : \n\t[\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\section*{Variational derivatives}\\n\\nThis notebook shows how to do variational derivatives of actions in order to compute equations \\nof motion. We first start with a simple scalar field.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"\\\\section*{Variational derivatives}\\n\\nThis notebook shows how to do variational derivatives of actions in order to compute equations \\nof motion. We first start with a simple scalar field.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Coordinate to~}x.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Depends to~}\\\\phi.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Depends to~}\\\\delta\\\\left(\\\\phi\\\\right).\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property PartialDerivative to~}\\\\partial{\\\\#}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{} - \\\\frac{1}{2}\\\\int{}\\\\partial_{\\\\mu}{\\\\phi} \\\\partial^{\\\\mu}{\\\\phi}%\\n+m^{2} \\\\phi^{2}\\\\, {\\\\rm d}x\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"x::Coordinate;\\n\\\\phi::Depends(x);\\n\\\\delta{\\\\phi}::Depends(x);\\n\\\\partial{#}::PartialDerivative;\\n\\nex:= -1/2 \\\\int{\\\\partial_{\\\\mu}{\\\\phi} \\\\partial^{\\\\mu}{\\\\phi} + m**2 \\\\phi**2}{x};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{} - \\\\frac{1}{2}\\\\int{}\\\\partial_{\\\\mu}{\\\\delta\\\\left(\\\\phi\\\\right)} \\\\partial^{\\\\mu}{\\\\phi}%\\n+\\\\partial_{\\\\mu}{\\\\phi} \\\\partial^{\\\\mu}{\\\\delta\\\\left(\\\\phi\\\\right)}%\\n+2m^{2} \\\\phi \\\\delta\\\\left(\\\\phi\\\\right)\\\\, {\\\\rm d}x\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"vary(_, $\\\\phi -> \\\\delta{\\\\phi}$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{} - \\\\frac{1}{2}\\\\int{}-\\\\delta\\\\left(\\\\phi\\\\right) \\\\partial_{\\\\mu}\\\\,^{\\\\mu}{\\\\phi}%\\n-\\\\partial^{\\\\mu}\\\\,_{\\\\mu}{\\\\phi} \\\\delta\\\\left(\\\\phi\\\\right)%\\n+2m^{2} \\\\phi \\\\delta\\\\left(\\\\phi\\\\right)\\\\, {\\\\rm d}x\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"integrate_by_parts(_, $\\\\delta{\\\\phi}$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{} - \\\\frac{1}{2}\\\\int{}-\\\\delta\\\\left(\\\\phi\\\\right) \\\\partial_{\\\\mu}\\\\,^{\\\\mu}{\\\\phi}%\\n-\\\\delta\\\\left(\\\\phi\\\\right) \\\\partial^{\\\\mu}\\\\,_{\\\\mu}{\\\\phi}%\\n+2\\\\delta\\\\left(\\\\phi\\\\right) \\\\phi m^{2}\\\\, {\\\\rm d}x\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"sort_product(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{} - \\\\frac{1}{2}\\\\int{}-2\\\\delta\\\\left(\\\\phi\\\\right) \\\\partial^{\\\\mu}\\\\,_{\\\\mu}{\\\\phi}%\\n+2\\\\delta\\\\left(\\\\phi\\\\right) \\\\phi m^{2}\\\\, {\\\\rm d}x\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"canonicalise(_);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{} - \\\\frac{1}{2}\\\\int{}\\\\delta\\\\left(\\\\phi\\\\right) \\\\left(-2\\\\partial^{\\\\mu}\\\\,_{\\\\mu}{\\\\phi}%\\n+2\\\\phi m^{2}\\\\right)\\\\, {\\\\rm d}x\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"factor_out(_, $\\\\delta{\\\\phi}$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1\n}\n"
  },
  {
    "path": "examples/working_with_ex.cnb",
    "content": "{\n\t\"cells\" : \n\t[\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"There are a few built-in operators to generate new expressions from existing ones:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"There are a few built-in operators to generate new expressions from existing ones:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}A+B = C+D\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex:= A+B = C+D;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}A+B\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}A+B = C+D\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"lhs(ex);\\nex;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"It is possible to manipulate parts of an expression using standard Python methods to \\naddress the $n$-th term or factor. For example,\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"It is possible to manipulate parts of an expression using standard Python methods to \\naddress the $n$-th term or factor. For example,\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}A_{m}+B_{m}+C_{m}+D_{m}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex:=A_{m}+B_{m}+C_{m}+D_{m};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"verbatim\",\n\t\t\t\t\t\"source\" : \"\\\\begin{verbatim}4\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"len(ex);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}Q_{m}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex[2]=$Q_{m}$;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}A_{m}+B_{m}+Q_{m}+D_{m}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"If you address a term which does not exist, an exception will be thrown:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"If you address a term which does not exist, an exception will be thrown:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"error\",\n\t\t\t\t\t\"source\" : \"{\\\\color{red}{\\\\begin{verbatim}Traceback (most recent call last):\\n  File \\\"<string>\\\", line 1, in <module>\\ncadabra2.ArgumentException: index 5 out of range, must be smaller than 4\\n\\\\end{verbatim}}}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex[5]=$Q_{m}$;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"error\",\n\t\t\t\t\t\"source\" : \"{\\\\color{red}{\\\\begin{verbatim}Traceback (most recent call last):\\n  File \\\"<string>\\\", line 1, in <module>\\nBoost.Python.ArgumentError: Python argument types in\\n    Ex.__getitem__(Ex, slice)\\ndid not match C++ signature:\\n    __getitem__(Ex {lvalue}, int)\\n\\\\end{verbatim}}}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex[2:3];\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1\n}\n"
  },
  {
    "path": "examples/world-sheet_susy.cnb",
    "content": "\n{\n\t\"cells\" : \n\t[\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"{\\\\del{#}, \\\\delbar{#}}::Derivative.\\n{\\\\Psi_\\\\mu, \\\\Psibar_\\\\mu, \\\\eps, \\\\epsbar}::AntiCommuting.\\n{\\\\Psi_\\\\mu, \\\\Psibar_\\\\mu, \\\\eps, \\\\epsbar}::SelfAntiCommuting.\\n{\\\\Psi_\\\\mu, \\\\Psibar_\\\\mu, X_\\\\mu}::Depends(\\\\del,\\\\delbar).\\n{\\\\Psi_\\\\mu, \\\\Psibar_\\\\mu, \\\\eps, \\\\epsbar, X_\\\\mu, i}::SortOrder.\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\\\\del{#}::LaTeXForm(\\\"\\\\partial\\\").\\n\\\\delbar{#}::LaTeXForm(\\\"\\\\bar{\\\\partial}\\\").\\n\\\\eps::LaTeXForm(\\\"\\\\epsilon\\\").\\n\\\\epsbar::LaTeXForm(\\\"\\\\bar{\\\\epsilon}\\\").\\n\\\\Psibar{#}::LaTeXForm(\\\"\\\\bar{\\\\Psi}\\\").\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\partial(X_{\\\\mu}) \\\\bar{\\\\partial}(X_{\\\\mu})+i \\\\Psi_{\\\\mu} \\\\bar{\\\\partial}(\\\\Psi_{\\\\mu})+i \\\\bar{\\\\Psi}_{\\\\mu} \\\\partial(\\\\bar{\\\\Psi}_{\\\\mu})\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"action:= \\\\del{X_\\\\mu} \\\\delbar{X_\\\\mu}\\n           + i \\\\Psi_\\\\mu \\\\delbar{\\\\Psi_\\\\mu} + i \\\\Psibar_\\\\mu \\\\del{\\\\Psibar_\\\\mu};\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}(X_{\\\\mu} \\\\rightarrow i \\\\bar{\\\\epsilon} \\\\Psi_{\\\\mu}+i \\\\epsilon \\\\bar{\\\\Psi}_{\\\\mu}, \\\\Psi_{\\\\mu} \\\\rightarrow -\\\\bar{\\\\epsilon} \\\\partial(X_{\\\\mu}), \\\\bar{\\\\Psi}_{\\\\mu} \\\\rightarrow -\\\\epsilon \\\\bar{\\\\partial}(X_{\\\\mu}))\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"rls:= X_\\\\mu    -> i \\\\epsbar \\\\Psi_\\\\mu + i \\\\eps \\\\Psibar_\\\\mu,\\n      \\\\Psi_\\\\mu -> - \\\\epsbar \\\\del{X_\\\\mu},\\n      \\\\Psibar_\\\\mu -> - \\\\eps \\\\delbar{X_\\\\mu};\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\partial(i \\\\bar{\\\\epsilon} \\\\Psi_{\\\\mu}+i \\\\epsilon \\\\bar{\\\\Psi}_{\\\\mu}) \\\\bar{\\\\partial}(X_{\\\\mu})+\\\\partial(X_{\\\\mu}) \\\\bar{\\\\partial}(i \\\\bar{\\\\epsilon} \\\\Psi_{\\\\mu}+i \\\\epsilon \\\\bar{\\\\Psi}_{\\\\mu})+i -\\\\bar{\\\\epsilon} \\\\partial(X_{\\\\mu}) \\\\bar{\\\\partial}(\\\\Psi_{\\\\mu})+i \\\\Psi_{\\\\mu} \\\\bar{\\\\partial}(-\\\\bar{\\\\epsilon} \\\\partial(X_{\\\\mu}))+i -\\\\epsilon \\\\bar{\\\\partial}(X_{\\\\mu}) \\\\partial(\\\\bar{\\\\Psi}_{\\\\mu})+i \\\\bar{\\\\Psi}_{\\\\mu} \\\\partial(-\\\\epsilon \\\\bar{\\\\partial}(X_{\\\\mu}))\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"vary(action, rls);\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\partial(i \\\\bar{\\\\epsilon} \\\\Psi_{\\\\mu}) \\\\bar{\\\\partial}(X_{\\\\mu})+\\\\partial(i \\\\epsilon \\\\bar{\\\\Psi}_{\\\\mu}) \\\\bar{\\\\partial}(X_{\\\\mu})+\\\\partial(X_{\\\\mu}) \\\\bar{\\\\partial}(i \\\\bar{\\\\epsilon} \\\\Psi_{\\\\mu})+\\\\partial(X_{\\\\mu}) \\\\bar{\\\\partial}(i \\\\epsilon \\\\bar{\\\\Psi}_{\\\\mu})+i -\\\\bar{\\\\epsilon} \\\\partial(X_{\\\\mu}) \\\\bar{\\\\partial}(\\\\Psi_{\\\\mu})+i \\\\Psi_{\\\\mu} \\\\bar{\\\\partial}(-\\\\bar{\\\\epsilon} \\\\partial(X_{\\\\mu}))+i -\\\\epsilon \\\\bar{\\\\partial}(X_{\\\\mu}) \\\\partial(\\\\bar{\\\\Psi}_{\\\\mu})+i \\\\bar{\\\\Psi}_{\\\\mu} \\\\partial(-\\\\epsilon \\\\bar{\\\\partial}(X_{\\\\mu}))\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"distribute(_);\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\left(\\\\partial(i) \\\\bar{\\\\epsilon} \\\\Psi_{\\\\mu}+i \\\\partial(\\\\bar{\\\\epsilon}) \\\\Psi_{\\\\mu}+i \\\\bar{\\\\epsilon} \\\\partial(\\\\Psi_{\\\\mu})\\\\right) \\\\bar{\\\\partial}(X_{\\\\mu})+\\\\left(\\\\partial(i) \\\\epsilon \\\\bar{\\\\Psi}_{\\\\mu}+i \\\\partial(\\\\epsilon) \\\\bar{\\\\Psi}_{\\\\mu}+i \\\\epsilon \\\\partial(\\\\bar{\\\\Psi}_{\\\\mu})\\\\right) \\\\bar{\\\\partial}(X_{\\\\mu})+\\\\partial(X_{\\\\mu}) \\\\left(\\\\bar{\\\\partial}(i) \\\\bar{\\\\epsilon} \\\\Psi_{\\\\mu}+i \\\\bar{\\\\partial}(\\\\bar{\\\\epsilon}) \\\\Psi_{\\\\mu}+i \\\\bar{\\\\epsilon} \\\\bar{\\\\partial}(\\\\Psi_{\\\\mu})\\\\right)+\\\\partial(X_{\\\\mu}) \\\\left(\\\\bar{\\\\partial}(i) \\\\epsilon \\\\bar{\\\\Psi}_{\\\\mu}+i \\\\bar{\\\\partial}(\\\\epsilon) \\\\bar{\\\\Psi}_{\\\\mu}+i \\\\epsilon \\\\bar{\\\\partial}(\\\\bar{\\\\Psi}_{\\\\mu})\\\\right)+i -\\\\bar{\\\\epsilon} \\\\partial(X_{\\\\mu}) \\\\bar{\\\\partial}(\\\\Psi_{\\\\mu})+i \\\\Psi_{\\\\mu} \\\\left(-\\\\bar{\\\\partial}(\\\\bar{\\\\epsilon}) \\\\partial(X_{\\\\mu})-\\\\bar{\\\\epsilon} \\\\bar{\\\\partial}(\\\\partial(X_{\\\\mu}))\\\\right)+i -\\\\epsilon \\\\bar{\\\\partial}(X_{\\\\mu}) \\\\partial(\\\\bar{\\\\Psi}_{\\\\mu})+i \\\\bar{\\\\Psi}_{\\\\mu} \\\\left(-\\\\partial(\\\\epsilon) \\\\bar{\\\\partial}(X_{\\\\mu})-\\\\epsilon \\\\partial(\\\\bar{\\\\partial}(X_{\\\\mu}))\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"product_rule(_);\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\partial(i) \\\\bar{\\\\epsilon} \\\\Psi_{\\\\mu} \\\\bar{\\\\partial}(X_{\\\\mu})+i \\\\partial(\\\\bar{\\\\epsilon}) \\\\Psi_{\\\\mu} \\\\bar{\\\\partial}(X_{\\\\mu})+i \\\\bar{\\\\epsilon} \\\\partial(\\\\Psi_{\\\\mu}) \\\\bar{\\\\partial}(X_{\\\\mu})+\\\\partial(i) \\\\epsilon \\\\bar{\\\\Psi}_{\\\\mu} \\\\bar{\\\\partial}(X_{\\\\mu})+i \\\\partial(\\\\epsilon) \\\\bar{\\\\Psi}_{\\\\mu} \\\\bar{\\\\partial}(X_{\\\\mu})+i \\\\epsilon \\\\partial(\\\\bar{\\\\Psi}_{\\\\mu}) \\\\bar{\\\\partial}(X_{\\\\mu})+\\\\partial(X_{\\\\mu}) \\\\bar{\\\\partial}(i) \\\\bar{\\\\epsilon} \\\\Psi_{\\\\mu}+\\\\partial(X_{\\\\mu}) i \\\\bar{\\\\partial}(\\\\bar{\\\\epsilon}) \\\\Psi_{\\\\mu}+\\\\partial(X_{\\\\mu}) i \\\\bar{\\\\epsilon} \\\\bar{\\\\partial}(\\\\Psi_{\\\\mu})+\\\\partial(X_{\\\\mu}) \\\\bar{\\\\partial}(i) \\\\epsilon \\\\bar{\\\\Psi}_{\\\\mu}+\\\\partial(X_{\\\\mu}) i \\\\bar{\\\\partial}(\\\\epsilon) \\\\bar{\\\\Psi}_{\\\\mu}+\\\\partial(X_{\\\\mu}) i \\\\epsilon \\\\bar{\\\\partial}(\\\\bar{\\\\Psi}_{\\\\mu})+i -\\\\bar{\\\\epsilon} \\\\partial(X_{\\\\mu}) \\\\bar{\\\\partial}(\\\\Psi_{\\\\mu})-i \\\\Psi_{\\\\mu} \\\\bar{\\\\partial}(\\\\bar{\\\\epsilon}) \\\\partial(X_{\\\\mu})-i \\\\Psi_{\\\\mu} \\\\bar{\\\\epsilon} \\\\bar{\\\\partial}(\\\\partial(X_{\\\\mu}))+i -\\\\epsilon \\\\bar{\\\\partial}(X_{\\\\mu}) \\\\partial(\\\\bar{\\\\Psi}_{\\\\mu})-i \\\\bar{\\\\Psi}_{\\\\mu} \\\\partial(\\\\epsilon) \\\\bar{\\\\partial}(X_{\\\\mu})-i \\\\bar{\\\\Psi}_{\\\\mu} \\\\epsilon \\\\partial(\\\\bar{\\\\partial}(X_{\\\\mu}))\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}i \\\\bar{\\\\epsilon} \\\\partial(\\\\Psi_{\\\\mu}) \\\\bar{\\\\partial}(X_{\\\\mu})+i \\\\epsilon \\\\partial(\\\\bar{\\\\Psi}_{\\\\mu}) \\\\bar{\\\\partial}(X_{\\\\mu})+\\\\partial(X_{\\\\mu}) i \\\\bar{\\\\epsilon} \\\\bar{\\\\partial}(\\\\Psi_{\\\\mu})+\\\\partial(X_{\\\\mu}) i \\\\epsilon \\\\bar{\\\\partial}(\\\\bar{\\\\Psi}_{\\\\mu})+i -\\\\bar{\\\\epsilon} \\\\partial(X_{\\\\mu}) \\\\bar{\\\\partial}(\\\\Psi_{\\\\mu})-i \\\\epsilon \\\\bar{\\\\partial}(X_{\\\\mu}) \\\\partial(\\\\bar{\\\\Psi}_{\\\\mu})\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}-\\\\partial(\\\\Psi_{\\\\mu}) \\\\bar{\\\\partial}(X_{\\\\mu}) \\\\bar{\\\\epsilon} i-\\\\partial(X_{\\\\mu}) \\\\bar{\\\\partial}(\\\\bar{\\\\Psi}_{\\\\mu}) \\\\epsilon i\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"distribute(_);\\nunwrap(_);\\nsort_product(_);\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"should be done cleaner in v2.\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1.0\n}\n\n"
  },
  {
    "path": "frontend/CMakeLists.txt",
    "content": "# cmake_minimum_required(VERSION ${CADABRA_CMAKE_VERSION})\nproject(Cadabra)\n\n\n#---------------------------------------------------------------------------\n# Preamble.\n#---------------------------------------------------------------------------\n\nprint_header(\"Configuring native notebook frontend\")\n\nset(INSTALL_LATEX_DIR    \"share/cadabra2/latex\")\nset(INSTALL_MAN_DIR      \"share/cadabra2/manual\")\nset(INSTALL_MAN_ALGO_DIR \"share/cadabra2/manual/algorithms\")\nset(INSTALL_MAN_PROP_DIR \"share/cadabra2/manual/properties\")\n\nFILE(GLOB man_algorithms \"${PROJECT_SOURCE_DIR}/../core/algorithms/*.cnb\")\nFILE(GLOB man_properties \"${PROJECT_SOURCE_DIR}/../core/properties/*.cnb\")\n\n\n#---------------------------------------------------------------------------\n# Locate libraries.\n#---------------------------------------------------------------------------\n\n# find_package(GTKMM3)\n# if(GTKMM_FOUND)\nadd_subdirectory(gtkmm)\n# else()\n#   message(FATAL_ERROR \"ENABLE_FRONTEND is set to ON, but no supported frontend libraries were found\")\n# endif()\n\n# if(APPLE)\n#    subdirs(osx)\n#    message(\"-- Building native OSX interface\")\n# else(APPLE)\n#    message(\"-- Not building native OSX interface\")\n# endif(APPLE)\n\n\n#---------------------------------------------------------------------------\n# Installation.\n#---------------------------------------------------------------------------\n\nif (NOT INSTALL_TARGETS_ONLY)\n\tmessage(STATUS \"Installing LaTeX style files in ${INSTALL_LATEX_DIR}\")\n\n\tinstall_directory_permissions(\"${INSTALL_LATEX_DIR}\")\n\tinstall_directory_permissions(\"${INSTALL_MAN_DIR}\")\n\tinstall_directory_permissions(\"${INSTALL_MAN_ALGO_DIR}\")\n\tinstall_directory_permissions(\"${INSTALL_MAN_PROP_DIR}\")\n\n#\tinstall(FILES ${PROJECT_SOURCE_DIR}/latex/tableaux.sty  DESTINATION ${INSTALL_LATEX_DIR})\n\tinstall(FILES ${PROJECT_SOURCE_DIR}/common/preamble.tex DESTINATION ${INSTALL_LATEX_DIR})\n\tinstall(FILES ${man_algorithms} DESTINATION ${INSTALL_MAN_ALGO_DIR})\n\tinstall(FILES ${man_properties} DESTINATION ${INSTALL_MAN_PROP_DIR})\nendif()\n"
  },
  {
    "path": "frontend/common/CMakeLists.txt",
    "content": "cmake_minimum_required(VERSION 2.8)\nproject(TeXEngine)\n\n\n#---------------------------------------------------------------------------\n# Preamble.\n#---------------------------------------------------------------------------\n\nprint_subheader(\"Configuring frontend - common\")\n\nif (POLICY CMP0042)\n  cmake_policy(SET CMP0042 NEW)\nendif(POLICY CMP0042)\n\n# Set path to additional cmake files\nset(CMAKE_MODULE_PATH ${CMAKE_MODULE_PATH} \"${CMAKE_SOURCE_DIR}/../../cmake/modules\")\n\nfind_package(Threads)\nfind_package(Boost 1.71.0 REQUIRED)\nset(Boost_USE_STATIC_LIBS OFF)\nset(Boost_USE_MULTITHREADED ON)\nset(Boost_USE_STATIC_RUNTIME OFF)\n\ninclude_directories(\n  ../../core\n  ../../libs/internal/include\n  ../../libs/whereami\n  \"${Boost_INCLUDE_DIRS}\"\n  )\n\n\n# Create library; disabled to make life easier on Windows\ninclude_directories(\".\" \"../../libs/internal/include\")\n# add_library(texengine SHARED TeXEngine.cc lodepng.cc exec-stream.cc)\n# target_link_libraries(texengine ${Boost_LIBRARIES} Threads::Threads)\n\n#add_executable(test_tex test_tex.cc TeXEngine.cc lodepng.cc ../../core/InstallPrefix.cc ../../libs/whereami/whereami.c)\n#target_link_libraries(test_tex ${Boost_LIBRARIES} Threads::Threads)\n# install(TARGETS texengine ARCHIVE DESTINATION lib LIBRARY DESTINATION lib)\n\n"
  },
  {
    "path": "frontend/common/TeXEngine.cc",
    "content": "\n#include \"TeXEngine.hh\"\n#include \"Config.hh\"\n#include \"InstallPrefix.hh\"\n\n#include <iostream>\n#include <cstdio>\n#include <boost/algorithm/string.hpp>\n// #include \"lodepng.h\"\n#include <fstream>\n#include <sstream>\n#include <internal/unistd.h>\n#include <map>\n#include <regex>\n#include <glibmm/spawn.h>\n#include \"process.hpp\"\n\n//#define DEBUG\n\nnamespace tpl = TinyProcessLib;\nusing namespace cadabra;\n\n#if defined(WIN32)\nint setenv(const char *name, const char *value, int overwrite)\n\t{\n\tint errcode = 0;\n\tif(!overwrite) {\n\t\tsize_t envsize = 0;\n\t\terrcode = getenv_s(&envsize, NULL, 0, name);\n\t\tif(errcode || envsize) return errcode;\n\t\t}\n\treturn _putenv_s(name, value);\n\t}\n#endif\n\ndouble TeXEngine::millimeter_per_inch = 25.4;\n\nTeXEngine::TeXException::TeXException(const std::string& str)\n\t: std::logic_error(str)\n\t{\n\t}\n\nstd::string TeXEngine::convert_unicode_to_tex(const std::string& orig) const\n\t{\n\tstatic std::map<std::string, std::string> symmap = {\n\t\t\t{\"α\", \"\\\\alpha\"    },\n\t\t\t{\"β\", \"\\\\beta\"     },\n\t\t\t{\"γ\", \"\\\\gamma\"    },\n\t\t\t{\"δ\", \"\\\\delta\"    },\n\t\t\t{\"ε\", \"\\\\epsilon\"  },\n\t\t\t{\"ζ\", \"\\\\zeta\"     },\n\t\t\t{\"η\", \"\\\\eta\"      },\n\t\t\t{\"θ\", \"\\\\theta\"    },\n\t\t\t{\"ι\", \"\\\\iota\"     },\n\t\t\t{\"κ\", \"\\\\kappa\"    },\n\t\t\t{\"λ\", \"\\\\lambda\"   },\n\t\t\t{\"μ\", \"\\\\mu\"       },\n\t\t\t{\"ν\", \"\\\\nu\"       },\n\t\t\t{\"ξ\", \"\\\\xi\"       },\n\t\t\t{\"ο\", \"\\\\omicron\"  },\n\t\t\t{\"π\", \"\\\\pi\"       },\n\t\t\t{\"ρ\", \"\\\\rho\"      },\n\t\t\t{\"σ\", \"\\\\sigma\"    },\n\t\t\t{\"τ\", \"\\\\tau\"      },\n\t\t\t{\"υ\", \"\\\\upsilon\"  },\n\t\t\t{\"φ\", \"\\\\phi\"      },\n\t\t\t{\"χ\", \"\\\\chi\"      },\n\t\t\t{\"ψ\", \"\\\\psi\"      },\n\t\t\t{\"ω\", \"\\\\omega\"    },\n\n\t\t\t{\"Α\", \"\\\\Alpha\"    },\n\t\t\t{\"Β\", \"\\\\Beta\"     },\n\t\t\t{\"Γ\", \"\\\\Gamma\"    },\n\t\t\t{\"Δ\", \"\\\\Delta\"    },\n\t\t\t{\"Ε\", \"\\\\Epsilon\"  },\n\t\t\t{\"Ζ\", \"\\\\Zeta\"     },\n\t\t\t{\"Η\", \"\\\\Eta\"      },\n\t\t\t{\"ϴ\", \"\\\\Theta\"    },\n\t\t\t{\"Ι\", \"\\\\Iota\"     },\n\t\t\t{\"Κ\", \"\\\\Kappa\"    },\n\t\t\t{\"Λ\", \"\\\\Lambda\"   },\n\t\t\t{\"Μ\", \"\\\\Mu\"       },\n\t\t\t{\"Ν\", \"\\\\Nu\"       },\n\t\t\t{\"Ξ\", \"\\\\Xi\"       },\n\t\t\t{\"Ο\", \"\\\\Omicron\"  },\n\t\t\t{\"Π\", \"\\\\Pi\"       },\n\t\t\t{\"Ρ\", \"\\\\Rho\"      },\n\t\t\t{\"Σ\", \"\\\\Sigma\"    },\n\t\t\t{\"Τ\", \"\\\\Tau\"      },\n\t\t\t{\"Υ\", \"\\\\Upsilon\"  },\n\t\t\t{\"Φ\", \"\\\\Phi\"      },\n\t\t\t{\"Χ\", \"\\\\Chi\"      },\n\t\t\t{\"Ψ\", \"\\\\Psi\"      },\n\t\t\t{\"Ω\", \"\\\\Omega\"    }\n\t\t};\n\n\tstd::string ret=orig;\n\tauto it=symmap.begin();\n\twhile(it!=symmap.end()) {\n\t\tstd::cerr << \"*** replacing \" << (*it).first << std::endl;\n\t\tboost::replace_all(ret, (*it).first, (*it).second);\n\t\t++it;\n\t\t}\n\tstd::cerr << ret << std::endl;\n\treturn ret;\n\t}\n\nunsigned TeXEngine::TeXRequest::width() const\n\t{\n\treturn width_;\n\t}\n\nunsigned TeXEngine::TeXRequest::height() const\n\t{\n\treturn height_;\n\t}\n\nstd::string TeXEngine::TeXRequest::latex() const\n\t{\n\treturn latex_string;\n\t}\n\nconst std::vector<unsigned char>& TeXEngine::TeXRequest::image() const\n\t{\n\treturn image_;\n\t}\n\nvoid TeXEngine::erase_file(const std::string& nm) const\n\t{\n\tstd::remove(nm.c_str());\n\t}\n\nstd::string TeXEngine::handle_latex_errors(const std::string& result, int exit_code) const\n\t{\n\tstd::string::size_type pos=result.find(\"! LaTeX Error\");\n\tif(pos != std::string::npos) {\n\t\treturn \"LaTeX error, probably a missing style file. See the output below.\\n\\n\" +result;\n\t\t}\n\n\tpos=result.find(\"! TeX capacity exceeded\");\n\tif(pos != std::string::npos) {\n\t\treturn \"Output cell too large (TeX capacity exceeded), output suppressed.\";\n\t\t}\n\n\tpos=result.find(\"! Dimension too large\");\n\tif(pos != std::string::npos) {\n\t\treturn \"Output cell too large (dimension too large), output suppressed.\";\n\t\t}\n\n\tpos=result.find(\"! Double superscript.\");\n\tif(pos != std::string::npos) {\n\t\treturn \"Internal typesetting error: double superscript. Please report a bug.\\n\\n\" + result;\n\t\t}\n\tpos=result.find(\"! Double subscript.\");\n\tif(pos != std::string::npos) {\n\t\treturn \"Internal typesetting error: double subscript. Please report a bug.\\n\\n\" + result;\n\t\t}\n\n\tpos=result.find(\"! Package breqn Error: \");\n\tif(pos != std::string::npos) {\n\t\treturn \"Typesetting error (breqn.sty related). Please report a bug.\\n\\n\" + result;\n\t\t}\n\n\tpos=result.find(\"! Undefined control sequence\");\n\tif(pos != std::string::npos) {\n\t\tstd::string::size_type undefpos=result.find(\"\\n\", pos+30);\n\t\tif(undefpos==std::string::npos)\n\t\t\treturn \"Undefined control sequence (failed to parse LaTeX output).\";\n\t\tstd::string::size_type backslashpos=result.rfind(\"\\\\\", undefpos);\n\t\tif(backslashpos==std::string::npos || backslashpos < 2)\n\t\t\treturn \"Undefined control sequence (failed to parse LaTeX output).\";\n\n\t\tstd::string undefd=result.substr(backslashpos-1,undefpos-pos-30);\n\t\treturn \"Undefined control sequence:\\n\\n\" +undefd+\"\\nNote that all symbols which you use in cadabra have to be valid LaTeX expressions.\\nIf they are not, you can still use the LaTeXForm property\\nto make them print correctly; see the manual for more information.\";\n\t\t}\n\n\tif(exit_code!=0) {\n\t\treturn \"Generic typesetting error; LaTeX failed. Please report a bug.\\n\\n\" + result;\n\t\t}\n\n\treturn \"\";\n\t}\n\nTeXEngine::~TeXEngine()\n\t{\n\t}\n\nTeXEngine::TeXEngine()\n\t: horizontal_pixels_(0), font_size_(12), total_scale_(1.0), device_scale_(1.0)\n\t{\n#ifndef _WIN32\n\t//\tlatex_packages.push_back(\"breqn\");\n\tlatex_packages.push_back(\"hyperref\");\n\n\t// Load the pre-amble from file.\n\tstd::string pname = cadabra::install_prefix()+\"/share/cadabra2/latex/preamble.tex\";\n\tstd::ifstream preamble(pname);\n\tif(!preamble)\n\t\tthrow std::logic_error(\"Cannot open TeXEngine preamble at \"+pname);\n\tstd::stringstream buffer;\n\tbuffer << preamble.rdbuf();\n\tpreamble_string = buffer.str();\n#endif\n\t}\n\nvoid TeXEngine::set_geometry(int horpix)\n\t{\n\tif(horizontal_pixels_!=horpix) {\n\t\t// flag all requests as requiring an update\n\t\tstd::set<std::shared_ptr<TeXRequest> >::iterator reqit=requests.begin();\n\t\twhile(reqit!=requests.end()) {\n\t\t\t(*reqit)->needs_generating=true;\n\t\t\t++reqit;\n\t\t\t}\n\t\t}\n\thorizontal_pixels_=horpix;\n\t}\n\nint TeXEngine::get_geometry() const\n\t{\n\treturn horizontal_pixels_;\n\t}\n\nvoid TeXEngine::set_font_size(int fontsize)\n\t{\n\tif(font_size_!=fontsize) {\n\t\t// flag all requests as requiring an update\n\t\tstd::set<std::shared_ptr<TeXRequest> >::iterator reqit=requests.begin();\n\t\twhile(reqit!=requests.end()) {\n\t\t\t(*reqit)->needs_generating=true;\n\t\t\t++reqit;\n\t\t\t}\n\t\t}\n\t// std::cerr << \"FONTSIZE \" << fontsize << std::endl;\n\tfont_size_=fontsize;\n\t}\n\nint TeXEngine::get_font_size() const\n\t{\n\treturn font_size_;\n\t}\n\nvoid TeXEngine::set_scale(double total_scale, double device_scale)\n\t{\n\tif(total_scale_!=total_scale && device_scale_!=device_scale) {\n\t\t// flag all requests as requiring an update\n\t\tstd::set<std::shared_ptr<TeXRequest> >::iterator reqit=requests.begin();\n\t\twhile(reqit!=requests.end()) {\n\t\t\t(*reqit)->needs_generating=true;\n\t\t\t++reqit;\n\t\t\t}\n\t\t}\n\ttotal_scale_=total_scale;\n\tdevice_scale_=device_scale;\n\t}\n\ndouble TeXEngine::get_scale() const\n\t{\n\treturn total_scale_;\n\t}\n\ndouble TeXEngine::get_device_scale() const\n\t{\n\treturn device_scale_;\n\t}\n\nTeXEngine::TeXRequest::TeXRequest()\n\t: needs_generating(true)\n\t{\n\t}\n\nstd::shared_ptr<TeXEngine::TeXRequest> TeXEngine::checkin(const std::string& txt,\n      const std::string& startwrap, const std::string& endwrap)\n\t{\n\tauto req = std::make_shared<TeXRequest>();\n\treq->latex_string=txt;\n\treq->start_wrap=startwrap;\n\treq->end_wrap=endwrap;\n\treq->needs_generating=true;\n\trequests.insert(req);\n\treturn req;\n\t}\n\nvoid TeXEngine::checkout(std::shared_ptr<TeXRequest> req)\n\t{\n\tstd::set<std::shared_ptr<TeXRequest> >::iterator it=requests.find(req);\n\tassert(it!=requests.end());\n\trequests.erase(it);\n\t}\n\nvoid TeXEngine::checkout_all()\n\t{\n\trequests.clear();\n\t}\n\nvoid TeXEngine::invalidate_all()\n\t{\n\tauto it=requests.begin();\n\twhile(it!=requests.end()) {\n\t\t(*it)->needs_generating=true;\n\t\t++it;\n\t\t}\n\t}\n\nstd::shared_ptr<TeXEngine::TeXRequest> TeXEngine::modify(std::shared_ptr<TeXRequest> req, const std::string& txt)\n\t{\n\treq->latex_string=txt;\n\treq->needs_generating=true;\n\treturn req;\n\t}\n\nvoid TeXEngine::convert_all()\n\t{\n\tsize_t needs_generating=0;\n\tfor(const auto& req: requests) {\n\t\tif(req->needs_generating)\n\t\t\t++needs_generating;\n\t\t}\n\n\tif(needs_generating!=0 && horizontal_pixels_!=0) {\n\t\tstd::string error_string=\"\";\n\t\tdo {\n\t\t\ttry {\n\t\t\t\t// std::cerr << \"TeXEngine::convert_all: running TeX on \" << needs_generating << \" requests\" << std::endl;\n\t\t\t\tconvert_set(requests);\n\t\t\t\tneeds_generating=0;\n\t\t\t\t}\n\t\t\tcatch(TeXException& e) {\n\t\t\t\t// std::cerr << \"TeXEngine::convert_all: error happened.\" << std::endl;\n\t\t\t\terror_string += e.what();\n\t\t\t\tneeds_generating=0;\n\t\t\t\tfor(const auto& req: requests)\n\t\t\t\t\tif(req->needs_generating)\n\t\t\t\t\t\t++needs_generating;\n\t\t\t\t// Run again; the erroneous cell has had its `needs_generating` flag set\n\t\t\t\t// to false and its `has_error` set to true, so we can safely feed this\n\t\t\t\t// through again.\n\t\t\t\t}\n\t\t\t}\n\t\twhile(needs_generating>0);\n\n\t\tif(error_string!=\"\")\n\t\t\tthrow TeXException(error_string);\n\t\t}\n\t}\n\nvoid TeXEngine::convert_one(std::shared_ptr<TeXRequest> req)\n\t{\n\t//std::cerr << \"cadabra-client: running TeX on 1 request\" << std::endl;\n\tstd::set<std::shared_ptr<TeXRequest> > reqset;\n\treqset.insert(req);\n\tconvert_set(reqset);\n\t}\n\nvoid TeXEngine::convert_set(std::set<std::shared_ptr<TeXRequest> >& reqs)\n\t{\n\tthrow std::logic_error(\"TeXEngine::convert_set: disabled in favour of MicroTeX.\");\n\n#if 1==0\t\n\t\n\t// We now no longer follow\n\t//\n\t// https://www.securecoding.cert.org/confluence/display/seccode/FI039-C.+Create+temporary+files+securely\n\t//\n\t// for temporary files; it needs to work on all platforms...\n\n\tchar olddir[1024];\n\tif(getcwd(olddir, 1023)==NULL)\n\t\tolddir[0]=0;\n\tstd::string tmpdir=\"/tmp\";\n\tstd::string tmppath=std::tmpnam(0);\n#if defined(_WIN32)\n\ttmpdir=getenv(\"TEMP\");\n\t// strip tmpdir from tmppath to get just the file\n\tauto sl=tmppath.find_last_of('\\\\');\n\tif(sl!=std::string::npos)\n\t\ttmppath=tmppath.substr(sl+1);\n\ttmpdir+=\"\\\\\";\n#else\n\t// strip tmpdir from tmppath to get just the file\n\tauto sl=tmppath.find_last_of('/');\n\tif(sl!=std::string::npos) {\n\t\ttmpdir=tmppath.substr(0, sl);\n\t\ttmppath=tmppath.substr(sl+1);\n\t\t}\n\ttmpdir+=\"/\";\n#endif\n\n\tif(chdir(tmpdir.c_str())==-1)\n\t\tthrow TeXException(\"Failed to chdir to \"+tmpdir+\".\");\n\n#ifdef DEBUG\n\tstd::cerr << \"tmpdir  = \" << tmpdir << std::endl;\n\tstd::cerr << \"tmppath = \" << tmppath << std::endl;\n#endif\n\n\t//\tchar templ[]=\"/tmp/cdbXXXXXX\";\n\n\t// The size in mm or inches which we use will in the end determine how large\n\t// the font will come out.\n\t//\n\t// For given horizontal size, we stretch this up to the full window\n\t// width using horizontal_pixels/(horizontal_size/millimeter_per_inch) dots per inch.\n\t// The appropriate horizontal size in mm is determined by trial and error,\n\t// and of course scales with the number of horizontal pixels.\n\n\t// Note: the number here has no effect on the size in pixels of the generated\n\t// PDF. That is set with the -D parameter of dvipng.\n\n\tconst double horizontal_mm=horizontal_pixels_*(12.0/font_size_)/4.4/(total_scale_/device_scale_);\n\t//#ifdef DEBUG\n\t//\tstd::cerr << \"tex_it: font_size \" << font_size << std::endl\n\t//\t\t\t\t << \"        pixels    \" << horizontal_pixels_ << std::endl\n\t//\t\t\t\t << \"        mm        \" << horizontal_mm << std::endl;\n\t//#endif\n\n\t//(int)(millimeter_per_inch*horizontal_pixels/100.0); //140;\n\tconst double vertical_mm=std::min(10*horizontal_mm, 3000.0);\n\n\n\t// Write each string in the set of requests into a buffer, separating\n\t// them by a page eject.\n\n\tstd::ostringstream total;\n\tstd::ofstream outstr(tmppath);\n\t//\tint fd = mkstemp(templ);\n\t//\tif(fd == -1)\n\t//\t\t throw TeXException(\"Failed to create temporary file in /tmp.\");\n\n\ttotal << \"\\\\documentclass[11pt]{article}\\n\"\n\t      << \"\\\\usepackage[dvips,verbose,voffset=0pt,hoffset=0pt,textwidth=\"\n\t      << horizontal_mm << \"mm,textheight=\"\n\t      << vertical_mm << \"mm]{geometry}\\n\"\n#ifndef __APPLE__\n\t      //\t\t\t<< \"\\\\usepackage{inconsolata}\\n\"\n#endif\n\t      ;\n\n\tfor(size_t i=0; i<latex_packages.size(); ++i)\n\t\ttotal << \"\\\\usepackage{\" << latex_packages[i] << \"}\\n\";\n\n\ttotal << preamble_string;\n\n\n\tstd::set<std::shared_ptr<TeXRequest> >::iterator reqit=reqs.begin();\n\twhile(reqit!=reqs.end()) {\n\t\tif((*reqit)->needs_generating) {\n\t\t\tif((*reqit)->latex_string.size()>100000)\n\t\t\t\ttotal << \"Expression too long, output suppressed.\\n\";\n\t\t\telse {\n\t\t\t\tif((*reqit)->start_wrap.size()>0)\n\t\t\t\t\ttotal << (*reqit)->start_wrap;\n\n\t\t\t\tstd::string lr=(*reqit)->latex_string;\n\t\t\t\tboost::replace_all(lr, \"\\\\left(\", \"\\\\brwrap{(}{\");\n\t\t\t\tboost::replace_all(lr, \"\\\\right)\", \"}{)}\");\n\t\t\t\tboost::replace_all(lr, \"\\\\left[\", \"\\\\brwrap{[}{\");\n\t\t\t\tboost::replace_all(lr, \"\\\\right]\", \"}{]}\");\n\t\t\t\tboost::replace_all(lr, \"\\\\left\\\\{\", \"\\\\brwrap{\\\\{}{\");\n\t\t\t\tboost::replace_all(lr, \"\\\\right\\\\}\", \"}{\\\\}}\");\n\t\t\t\tboost::replace_all(lr, \"\\\\right.\", \"}{.}\");\n\t\t\t\tboost::replace_all(lr, \"\\\\begin{dmath*}\", \"$\");\n\t\t\t\tboost::replace_all(lr, \"\\\\end{dmath*}\", \"$\");\n\n\t\t\t\ttotal << lr;\n\n\t\t\t\tif((*reqit)->end_wrap.size()>0)\n\t\t\t\t\ttotal << \"\\n\" << (*reqit)->end_wrap;\n\t\t\t\telse total << \"\\n\";\n\t\t\t\t}\n\t\t\ttotal << \"\\\\eject\\n\";\n\t\t\t}\n\t\t++reqit;\n\t\t}\n\ttotal << \"\\\\end{document}\\n\";\n\n\t// Make sure there are no greek unicode characters.\n\tstd::string ltx = total.str(); // convert_unicode_to_tex(total.str());\n\n\t// Now write the 'total' buffer to the .tex file\n\n\t// std::cerr << total.str() << std::endl;\n\n\toutstr << ltx;\n\toutstr.close(); // to flush the buffer and allow us to rename\n\n#ifdef DEBUG\n\tstd::cerr  << tmppath << std::endl;\n\tstd::cerr << \"---\\n\" << ltx << \"\\n---\" << std::endl;\n#endif\n\n\tstd::string nf=tmppath+\".tex\";\n\tif(std::rename((tmpdir+tmppath).c_str(), (tmpdir+nf).c_str())!=0)\n\t\tthrow TeXException(\"Failed to rename \"+tmpdir+tmppath+\" to \"+tmpdir+nf+\" in folder \"+tmpdir+\" error \"+std::to_string(errno));\n\n#ifdef __CYGWIN__\n\t// MikTeX does not see /tmp, it needs \\cygwin\\tmp\n\tnf=\"\\\\cygwin\"+nf;\n\tnf.replace(nf.begin(), nf.end(), '/', '\\\\');\n#endif\n\n\t// Run LaTeX on the .tex file.\n\tstd::string texinputs=cadabra::install_prefix()+\"/share/cadabra2/latex/\";\n\tstd::string oldtexinputs;\n\tchar *oti = getenv(\"TEXINPUTS\");\n\tif(oti)\n\t\toldtexinputs=std::string(oti);\n\tif(oldtexinputs.size()>0)\n\t\ttexinputs=\":\"+std::string(oldtexinputs);\n\ttexinputs+=\":\";\n\tsetenv(\"TEXINPUTS\", texinputs.c_str(), 1);\n\n\t// The options below are chosen so they are compatible with MikTeX (https://docs.miktex.org/manual/pdftex.html),\n\t// standard TeXLive on Linux and OSX. We use pdflatex because several latex distributions do not seem to have\n\t// a 'latex' command anymore which supports all these options (e.g. MikTeX).\n\t// For some reason, recent pdflatex versions no longer do anything with --halt-on-error, so we\n\t// now also add the -interaction=nonstopmode (errorstopmode does not work either).\n\n\tstd::string latex_stdout, latex_stderr;\n\ttpl::Process latex_proc(\"pdflatex --halt-on-error -interaction=nonstopmode --output-format=dvi \"+nf, \"\",\n\t[&](const char *bytes, size_t n) {\n\t\tlatex_stdout+=std::string(bytes,n);\n\t\t},\n\t[&](const char *bytes, size_t n) {\n\t\tlatex_stderr+=std::string(bytes,n);\n\t\t}\n\t                       );\n\tauto latex_exit_status=latex_proc.get_exit_status();\n\n\tstd::string err=handle_latex_errors(latex_stdout+latex_stderr, latex_exit_status);\n\tsetenv(\"TEXINPUTS\", oldtexinputs.c_str(), 1);\n\n\tif(err.size()>0) {\n\t\t// std::cerr << \"ERROR: \" << latex_stderr << std::endl;\n\t\t// std::cerr << \"OUTPUT: \" << latex_stdout << std::endl;\n\t\t// std::cerr << \"FILE: \" << nf << std::endl;\n\t\tstd::regex  pat(R\"(\\[([0-9]*)\\])\");\n\t\tstd::smatch sm;\n\t\tint last_error_free_page=0;\n\t\twhile(std::regex_search( latex_stdout, sm, pat)) {\n\t\t\t// std::cerr << \"PAGE: \" << sm.str() << std::endl;\n\t\t\tlast_error_free_page = std::stoi( sm[1].str() );\n\t\t\tlatex_stdout = sm.suffix();\n\t\t\t}\n\t\t// std::cerr << \"PAGE WITH ERROR: \" << last_error_free_page+1 << std::endl;\n\t\t// Label the error request so it can be ignored next time.\n\t\treqit=reqs.begin();\n\t\tint current_page=1;\n\t\twhile(reqit!=reqs.end()) {\n\t\t\tif((*reqit)->needs_generating) {\n\t\t\t\tif(current_page == last_error_free_page+1) {\n\t\t\t\t\t// std::cerr << \"CONTAINS ERROR: \" << (*reqit)->latex_string << std::endl;\n\t\t\t\t\t(*reqit)->has_error=true;\n\t\t\t\t\t(*reqit)->needs_generating=false;\n\t\t\t\t\t}\n\t\t\t\t++current_page;\n\t\t\t\t(*reqit)->image_.clear();\n\t\t\t\t}\n\t\t\t++reqit;\n\t\t\t}\n\t\terase_file(tmppath+\".dvi\");\n\t\tif(chdir(olddir)==-1)\n\t\t\tthrow TeXException(err+\" (and cannot chdir back to original \"+olddir+\").\");\n\t\telse err+=\".\";\n\t\terr += \" See \"+tmppath+\".tex to debug this.\\n\\n\";\n\t\terr += \"TEXINPUTS = \"+texinputs+\"\\n\";\n\t\terr += \"TMPDIR = \"+tmpdir+\"\\n\";\n\t\tthrow TeXException(err);\n\t\t}\n\n\terase_file(tmppath+\".aux\");\n\terase_file(tmppath+\".log\");\n\terase_file(tmppath+\".out\");\n\n\terase_file(tmppath+\".tex\");\n\n\t// Convert the entire dvi file to png files.\n\t//\n\tstd::ostringstream resspec;\n\tresspec << horizontal_pixels_/(1.0*horizontal_mm)*millimeter_per_inch*device_scale_;\n\n\tstd::string dvipng_stdout, dvipng_stderr;\n\ttpl::Process dvipng_proc(\"dvipng -T tight -bg transparent -D \"+resspec.str()+\" \"+tmppath+\".dvi\", \"\",\n\t[&](const char *bytes, size_t n) {\n\t\tdvipng_stdout=std::string(bytes,n);\n\t\t},\n\t[&](const char *bytes, size_t n) {\n\t\tdvipng_stderr=std::string(bytes,n);\n\t\t}\n\t                        );\n\tauto dvipng_exit_status=dvipng_proc.get_exit_status();\n\n\tif(dvipng_exit_status!=0) {\n\t\t// Erase all dvi and png files and put empty pixbufs into the TeXRequests.\n\t\terase_file(tmppath+\".dvi\");\n\t\treqit=reqs.begin();\n\t\tint pagenum=1;\n\t\twhile(reqit!=reqs.end()) {\n\t\t\tif((*reqit)->needs_generating) {\n\t\t\t\tstd::ostringstream pngname;\n\t\t\t\tpngname << tmppath << pagenum << \".png\";\n\t\t\t\terase_file(pngname.str());\n\t\t\t\t(*reqit)->image_.clear();\n\t\t\t\t++pagenum;\n\t\t\t\t}\n\t\t\t++reqit;\n\t\t\t}\n\t\tif(chdir(olddir)==-1)\n\t\t\tthrow TeXException(\n\t\t\t   std::string(\"Cannot run dvipng, is it installed? (and cannot chdir back to original)\\n\\n\")+dvipng_stdout+dvipng_stderr);\n\t\tthrow TeXException(std::string(\"Cannot run dvipng, is it installed?\\n\\n\")+dvipng_stdout+dvipng_stderr);\n\t\t}\n\n\terase_file(tmppath+\".dvi\");\n\n\t// Conversion completed successfully, now convert all resulting PNG files to Pixbuf images.\n\n\t//std::cerr << \"cadabra-client: reading png\" << std::endl;\n\treqit=reqs.begin();\n\tint pagenum=1;\n\twhile(reqit!=reqs.end()) {\n\t\tif((*reqit)->needs_generating) {\n\t\t\tstd::ostringstream pngname;\n\t\t\tpngname << tmppath << pagenum << \".png\";\n\t\t\tstd::ifstream tst(pngname.str().c_str());\n\t\t\tif(tst.good()) {\n\t\t\t\t(*reqit)->image_.clear();\n\t\t\t\tunsigned error = lodepng::decode((*reqit)->image_, (*reqit)->width_,\n\t\t\t\t                                 (*reqit)->height_, pngname.str());\n\t\t\t\tif(error!=0)\n\t\t\t\t\tthrow TeXException(\"PNG conversion error\");\n\t\t\t\t(*reqit)->needs_generating=false;\n\t\t\t\terase_file(pngname.str());\n\t\t\t\t}\n\t\t\t++pagenum;\n\t\t\t}\n\t\t++reqit;\n\t\t}\n\t//std::cerr << \"cadabra-client: conversion done\" << std::endl;\n\n\tif(chdir(olddir)==-1)\n\t\tthrow TeXException(\"Failed to chdir back to \" +std::string(olddir)+\".\");\n\n#endif\n\t}\n"
  },
  {
    "path": "frontend/common/TeXEngine.hh",
    "content": "\n#pragma once\n\n#include <stdexcept>\n#include <vector>\n#include <set>\n#include <string>\n#include <memory>\n\nnamespace cadabra {\n\n\t/// \\ingroup frontend\n\t///\n\t/// TeXEngine is used to convert LaTeX strings into PNG images. This is\n\t/// a two-stage process: you first 'check in' a string into the system,\n\t/// in exchange for a pointer to a TeXRequest object. When you are\n\t/// ready to retrieve the image, call 'get_pixbuf'.\n\t///\n\t/// If you need to generate images for more than one string, simply\n\t/// check them all in and then call 'convert_all' before retrieving the\n\t/// pixbufs. This requires only one round-trip through latex/dvipng.\n\n\tclass TeXEngine {\n\t\tpublic:\n\t\t\tclass TeXException : public std::logic_error {\n\t\t\t\tpublic:\n\t\t\t\t\tTeXException(const std::string&);\n\t\t\t\t};\n\n\t\t\tclass TeXRequest {\n\t\t\t\tpublic:\n\t\t\t\t\tTeXRequest();\n\t\t\t\t\tfriend class TeXEngine;\n\n\t\t\t\t\tunsigned  width() const;\n\t\t\t\t\tunsigned  height() const;\n\t\t\t\t\tconst std::vector<unsigned char>& image() const;\n\n\t\t\t\t\t/// Get the original LaTeX string.\n\t\t\t\t\tstd::string latex() const;\n\t\t\t\t\t\n\t\t\t\tprivate:\n\t\t\t\t\tstd::string                latex_string;\n\t\t\t\t\tstd::string                start_wrap, end_wrap;\n\t\t\t\t\tbool                       needs_generating;\n\t\t\t\t\tbool                       has_error; // currently set, but never re-set, and unused.\n\t\t\t\t\tstd::vector<unsigned char> image_;\n\t\t\t\t\tunsigned                   width_, height_;\n\t\t\t\t};\n\n\t\t\tTeXEngine();\n\t\t\t~TeXEngine();\n\n\t\t\t// Set the width and font size for all images to be generated.\n\t\t\tvoid set_geometry(int horizontal_pixels);\n\n\t\t\t// Get the width.\n\t\t\tint get_geometry() const;\n\n\t\t\t// Set the scale factor for generating bitmaps. The total scale is\n\t\t\t// the product of HiDPI scale and any text-scaling factor on top of\n\t\t\t// that, so that it represents the total scale at which text renders.\n\t\t\t// The device_scale is just the HiDPI factor; we need to generate\n\t\t\t// bitmaps at the width times this size.\n\t\t\tvoid set_scale(double total_scale, double device_scale);\n\t\t\tdouble get_scale() const;\n\t\t\tdouble get_device_scale() const;\n\t\t\tvoid set_font_size(int font_size);\n\t\t\tint  get_font_size() const;\n\t\t\tstd::vector<std::string> latex_packages;\n\n\t\t\t// All checkin/checkout conversion routines. TeXEngine keeps\n\t\t\t// track of all TeXRequests in order to be able to convert\n\t\t\t// all of them in one shot (with one LaTeX run), which you can\n\t\t\t// do with 'convert_all'.\n\n\t\t\t// You can share the result in a TeXRequest in multiple\n\t\t\t// widgets, but you need to call checkout if a widget no\n\t\t\t// longer needs it. TeXEngine will then run a cleanup on all\n\t\t\t// TeXRequests that are no longer referenced except by\n\t\t\t// itself.\n\n\t\t\tstd::shared_ptr<TeXRequest> checkin(const std::string&,\n\t\t\t                                    const std::string& startwrap, const std::string& endwrap);\n\t\t\tstd::shared_ptr<TeXRequest> modify(std::shared_ptr<TeXRequest>, const std::string&);\n\n\t\t\t/// Generate images for all TeXRequests which are labelled as needing conversion.\n\t\t\tvoid                        convert_all();\n\n\t\t\t/// Mark all TeXRequests as needing re-generating. Use this e.g. when changing font\n\t\t\t/// size for the entire notebook: first invalidate_all, then convert_all.\n\t\t\tvoid                        invalidate_all();\n\n\t\t\t/// Mark a TeXRequest as no longer being needed.\n\t\t\tvoid                        checkout(std::shared_ptr<TeXRequest>);\n\t\t\tvoid                        checkout_all();\n\n\t\tprivate:\n\t\t\tstd::string convert_unicode_to_tex(const std::string&) const;\n\n\t\t\tstatic double millimeter_per_inch;\n\n\t\t\tstd::set<std::shared_ptr<TeXRequest> > requests;\n\n\t\t\tstd::string            preamble_string;\n\t\t\tint                    horizontal_pixels_;\n\t\t\tint                    font_size_;\n\t\t\tdouble                 total_scale_, device_scale_;\n\n\t\t\tvoid erase_file(const std::string&) const;\n\t\t\tvoid convert_one(std::shared_ptr<TeXRequest>);\n\t\t\tvoid convert_set(std::set<std::shared_ptr<TeXRequest> >&);\n\n\t\t\tstd::string handle_latex_errors(const std::string&, int exit_code) const;\n\t\t};\n\n\t}\n"
  },
  {
    "path": "frontend/common/lodepng.cc",
    "content": "/*\nLodePNG version 20131222\n\nCopyright (c) 2005-2013 Lode Vandevenne\n\nThis software is provided 'as-is', without any express or implied\nwarranty. In no event will the authors be held liable for any damages\narising from the use of this software.\n\nPermission is granted to anyone to use this software for any purpose,\nincluding commercial applications, and to alter it and redistribute it\nfreely, subject to the following restrictions:\n\n 1. The origin of this software must not be misrepresented; you must not\n \tclaim that you wrote the original software. If you use this software\n in a product, an acknowledgment in the product documentation would be\n appreciated but is not required.\n\n 2. Altered source versions must be plainly marked as such, and must not be\n \tmisrepresented as being the original software.\n\n 3. This notice may not be removed or altered from any source\n \tdistribution.\n*/\n\n/*\nThe manual and changelog are in the header file \"lodepng.h\"\nRename this file to lodepng.cpp to use it for C++, or to lodepng.c to use it for C.\n*/\n\n#include \"lodepng.h\"\n\n#include <stdio.h>\n#include <stdlib.h>\n\n#ifdef LODEPNG_COMPILE_CPP\n#include <fstream>\n#endif /*LODEPNG_COMPILE_CPP*/\n\n#define VERSION_STRING \"20131222\"\n\n/*\nThis source file is built up in the following large parts. The code sections\nwith the \"LODEPNG_COMPILE_\" #defines divide this up further in an intermixed way.\n-Tools for C and common code for PNG and Zlib\n-C Code for Zlib (huffman, deflate, ...)\n-C Code for PNG (file format chunks, adam7, PNG filters, color conversions, ...)\n-The C++ wrapper around all of the above\n*/\n\n/*The malloc, realloc and free functions defined here with \"lodepng_\" in front\nof the name, so that you can easily change them to others related to your\nplatform if needed. Everything else in the code calls these. Pass\n-DLODEPNG_NO_COMPILE_ALLOCATORS to the compiler, or comment out\n#define LODEPNG_COMPILE_ALLOCATORS in the header, to disable the ones here and\ndefine them in your own project's source files without needing to change\nlodepng source code. Don't forget to remove \"static\" if you copypaste them\nfrom here.*/\n\n#ifdef LODEPNG_COMPILE_ALLOCATORS\nstatic void* lodepng_malloc(size_t size)\n\t{\n\treturn malloc(size);\n\t}\n\nstatic void* lodepng_realloc(void* ptr, size_t new_size)\n\t{\n\treturn realloc(ptr, new_size);\n\t}\n\nstatic void lodepng_free(void* ptr)\n\t{\n\tfree(ptr);\n\t}\n#else /*LODEPNG_COMPILE_ALLOCATORS*/\nvoid* lodepng_malloc(size_t size);\nvoid* lodepng_realloc(void* ptr, size_t new_size);\nvoid lodepng_free(void* ptr);\n#endif /*LODEPNG_COMPILE_ALLOCATORS*/\n\n/* ////////////////////////////////////////////////////////////////////////// */\n/* ////////////////////////////////////////////////////////////////////////// */\n/* // Tools for C, and common code for PNG and Zlib.                       // */\n/* ////////////////////////////////////////////////////////////////////////// */\n/* ////////////////////////////////////////////////////////////////////////// */\n\n/*\nOften in case of an error a value is assigned to a variable and then it breaks\nout of a loop (to go to the cleanup phase of a function). This macro does that.\nIt makes the error handling code shorter and more readable.\n\nExample: if(!uivector_resizev(&frequencies_ll, 286, 0)) ERROR_BREAK(83);\n*/\n#define CERROR_BREAK(errorvar, code)\\\n\t\t\t{\\\n  \terrorvar = code;\\\n  break;\\\n\t\t\t}\n\n/*version of CERROR_BREAK that assumes the common case where the error variable is named \"error\"*/\n#define ERROR_BREAK(code) CERROR_BREAK(error, code)\n\n/*Set error var to the error code, and return it.*/\n#define CERROR_RETURN_ERROR(errorvar, code)\\\n\t\t\t{\\\n  \terrorvar = code;\\\n  \treturn code;\\\n\t\t\t}\n\n/*Try the code, if it returns error, also return the error.*/\n#define CERROR_TRY_RETURN(call)\\\n\t\t\t{\\\n  unsigned error = call;\\\n  if(error) return error;\\\n\t\t\t}\n\n/*\nAbout uivector, ucvector and string:\n-All of them wrap dynamic arrays or text strings in a similar way.\n-LodePNG was originally written in C++. The vectors replace the std::vectors that were used in the C++ version.\n-The string tools are made to avoid problems with compilers that declare things like strncat as deprecated.\n-They're not used in the interface, only internally in this file as static functions.\n-As with many other structs in this file, the init and cleanup functions serve as ctor and dtor.\n*/\n\n#ifdef LODEPNG_COMPILE_ZLIB\n/*dynamic vector of unsigned ints*/\ntypedef struct uivector {\n\tunsigned* data;\n\tsize_t size; /*size in number of unsigned longs*/\n\tsize_t allocsize; /*allocated size in bytes*/\n\t} uivector;\n\nstatic void uivector_cleanup(void* p)\n\t{\n\t((uivector*)p)->size = ((uivector*)p)->allocsize = 0;\n\tlodepng_free(((uivector*)p)->data);\n\t((uivector*)p)->data = NULL;\n\t}\n\n/*returns 1 if success, 0 if failure ==> nothing done*/\nstatic unsigned uivector_resize(uivector* p, size_t size)\n\t{\n\tif(size * sizeof(unsigned) > p->allocsize) {\n\t\tsize_t newsize = size * sizeof(unsigned) * 2;\n\t\tvoid* data = lodepng_realloc(p->data, newsize);\n\t\tif(data) {\n\t\t\tp->allocsize = newsize;\n\t\t\tp->data = (unsigned*)data;\n\t\t\tp->size = size;\n\t\t\t}\n\t\telse return 0;\n\t\t}\n\telse p->size = size;\n\treturn 1;\n\t}\n\n/*resize and give all new elements the value*/\nstatic unsigned uivector_resizev(uivector* p, size_t size, unsigned value)\n\t{\n\tsize_t oldsize = p->size, i;\n\tif(!uivector_resize(p, size)) return 0;\n\tfor(i = oldsize; i < size; i++) p->data[i] = value;\n\treturn 1;\n\t}\n\nstatic void uivector_init(uivector* p)\n\t{\n\tp->data = NULL;\n\tp->size = p->allocsize = 0;\n\t}\n\n#ifdef LODEPNG_COMPILE_ENCODER\n/*returns 1 if success, 0 if failure ==> nothing done*/\nstatic unsigned uivector_push_back(uivector* p, unsigned c)\n\t{\n\tif(!uivector_resize(p, p->size + 1)) return 0;\n\tp->data[p->size - 1] = c;\n\treturn 1;\n\t}\n\n/*copy q to p, returns 1 if success, 0 if failure ==> nothing done*/\nstatic unsigned uivector_copy(uivector* p, const uivector* q)\n\t{\n\tsize_t i;\n\tif(!uivector_resize(p, q->size)) return 0;\n\tfor(i = 0; i < q->size; i++) p->data[i] = q->data[i];\n\treturn 1;\n\t}\n#endif /*LODEPNG_COMPILE_ENCODER*/\n#endif /*LODEPNG_COMPILE_ZLIB*/\n\n/* /////////////////////////////////////////////////////////////////////////// */\n\n/*dynamic vector of unsigned chars*/\ntypedef struct ucvector {\n\tunsigned char* data;\n\tsize_t size; /*used size*/\n\tsize_t allocsize; /*allocated size*/\n\t} ucvector;\n\n/*returns 1 if success, 0 if failure ==> nothing done*/\nstatic unsigned ucvector_resize(ucvector* p, size_t size)\n\t{\n\tif(size * sizeof(unsigned char) > p->allocsize) {\n\t\tsize_t newsize = size * sizeof(unsigned char) * 2;\n\t\tvoid* data = lodepng_realloc(p->data, newsize);\n\t\tif(data) {\n\t\t\tp->allocsize = newsize;\n\t\t\tp->data = (unsigned char*)data;\n\t\t\tp->size = size;\n\t\t\t}\n\t\telse return 0;   /*error: not enough memory*/\n\t\t}\n\telse p->size = size;\n\treturn 1;\n\t}\n\n#ifdef LODEPNG_COMPILE_PNG\n\nstatic void ucvector_cleanup(void* p)\n\t{\n\t((ucvector*)p)->size = ((ucvector*)p)->allocsize = 0;\n\tlodepng_free(((ucvector*)p)->data);\n\t((ucvector*)p)->data = NULL;\n\t}\n\nstatic void ucvector_init(ucvector* p)\n\t{\n\tp->data = NULL;\n\tp->size = p->allocsize = 0;\n\t}\n\n#ifdef LODEPNG_COMPILE_DECODER\n/*resize and give all new elements the value*/\nstatic unsigned ucvector_resizev(ucvector* p, size_t size, unsigned char value)\n\t{\n\tsize_t oldsize = p->size, i;\n\tif(!ucvector_resize(p, size)) return 0;\n\tfor(i = oldsize; i < size; i++) p->data[i] = value;\n\treturn 1;\n\t}\n#endif /*LODEPNG_COMPILE_DECODER*/\n#endif /*LODEPNG_COMPILE_PNG*/\n\n#ifdef LODEPNG_COMPILE_ZLIB\n/*you can both convert from vector to buffer&size and vica versa. If you use\ninit_buffer to take over a buffer and size, it is not needed to use cleanup*/\nstatic void ucvector_init_buffer(ucvector* p, unsigned char* buffer, size_t size)\n\t{\n\tp->data = buffer;\n\tp->allocsize = p->size = size;\n\t}\n#endif /*LODEPNG_COMPILE_ZLIB*/\n\n#if (defined(LODEPNG_COMPILE_PNG) && defined(LODEPNG_COMPILE_ANCILLARY_CHUNKS)) || defined(LODEPNG_COMPILE_ENCODER)\n/*returns 1 if success, 0 if failure ==> nothing done*/\nstatic unsigned ucvector_push_back(ucvector* p, unsigned char c)\n\t{\n\tif(!ucvector_resize(p, p->size + 1)) return 0;\n\tp->data[p->size - 1] = c;\n\treturn 1;\n\t}\n#endif /*defined(LODEPNG_COMPILE_PNG) || defined(LODEPNG_COMPILE_ENCODER)*/\n\n\n/* ////////////////////////////////////////////////////////////////////////// */\n\n#ifdef LODEPNG_COMPILE_PNG\n#ifdef LODEPNG_COMPILE_ANCILLARY_CHUNKS\n/*returns 1 if success, 0 if failure ==> nothing done*/\nstatic unsigned string_resize(char** out, size_t size)\n\t{\n\tchar* data = (char*)lodepng_realloc(*out, size + 1);\n\tif(data) {\n\t\tdata[size] = 0; /*null termination char*/\n\t\t*out = data;\n\t\t}\n\treturn data != 0;\n\t}\n\n/*init a {char*, size_t} pair for use as string*/\nstatic void string_init(char** out)\n\t{\n\t*out = NULL;\n\tstring_resize(out, 0);\n\t}\n\n/*free the above pair again*/\nstatic void string_cleanup(char** out)\n\t{\n\tlodepng_free(*out);\n\t*out = NULL;\n\t}\n\nstatic void string_set(char** out, const char* in)\n\t{\n\tsize_t insize = strlen(in), i = 0;\n\tif(string_resize(out, insize)) {\n\t\tfor(i = 0; i < insize; i++) {\n\t\t\t(*out)[i] = in[i];\n\t\t\t}\n\t\t}\n\t}\n#endif /*LODEPNG_COMPILE_ANCILLARY_CHUNKS*/\n#endif /*LODEPNG_COMPILE_PNG*/\n\n/* ////////////////////////////////////////////////////////////////////////// */\n\nunsigned lodepng_read32bitInt(const unsigned char* buffer)\n\t{\n\treturn (buffer[0] << 24) | (buffer[1] << 16) | (buffer[2] << 8) | buffer[3];\n\t}\n\n#if defined(LODEPNG_COMPILE_PNG) || defined(LODEPNG_COMPILE_ENCODER)\n/*buffer must have at least 4 allocated bytes available*/\nstatic void lodepng_set32bitInt(unsigned char* buffer, unsigned value)\n\t{\n\tbuffer[0] = (unsigned char)((value >> 24) & 0xff);\n\tbuffer[1] = (unsigned char)((value >> 16) & 0xff);\n\tbuffer[2] = (unsigned char)((value >>  8) & 0xff);\n\tbuffer[3] = (unsigned char)((value      ) & 0xff);\n\t}\n#endif /*defined(LODEPNG_COMPILE_PNG) || defined(LODEPNG_COMPILE_ENCODER)*/\n\n#ifdef LODEPNG_COMPILE_ENCODER\nstatic void lodepng_add32bitInt(ucvector* buffer, unsigned value)\n\t{\n\tucvector_resize(buffer, buffer->size + 4); /*todo: give error if resize failed*/\n\tlodepng_set32bitInt(&buffer->data[buffer->size - 4], value);\n\t}\n#endif /*LODEPNG_COMPILE_ENCODER*/\n\n/* ////////////////////////////////////////////////////////////////////////// */\n/* / File IO                                                                / */\n/* ////////////////////////////////////////////////////////////////////////// */\n\n#ifdef LODEPNG_COMPILE_DISK\n\nunsigned lodepng_load_file(unsigned char** out, size_t* outsize, const char* filename)\n\t{\n\tFILE* file;\n\tlong size;\n\n\t/*provide some proper output values if error will happen*/\n\t*out = 0;\n\t*outsize = 0;\n\n\tfile = fopen(filename, \"rb\");\n\tif(!file) return 78;\n\n\t/*get filesize:*/\n\tfseek(file, 0, SEEK_END);\n\tsize = ftell(file);\n\trewind(file);\n\n\t/*read contents of the file into the vector*/\n\t*outsize = 0;\n\t*out = (unsigned char*)lodepng_malloc((size_t)size);\n\tif(size && (*out)) (*outsize) = fread(*out, 1, (size_t)size, file);\n\n\tfclose(file);\n\tif(!(*out) && size) return 83; /*the above malloc failed*/\n\treturn 0;\n\t}\n\n/*write given buffer to the file, overwriting the file, it doesn't append to it.*/\nunsigned lodepng_save_file(const unsigned char* buffer, size_t buffersize, const char* filename)\n\t{\n\tFILE* file;\n\tfile = fopen(filename, \"wb\" );\n\tif(!file) return 79;\n\tfwrite((char*)buffer, 1, buffersize, file);\n\tfclose(file);\n\treturn 0;\n\t}\n\n#endif /*LODEPNG_COMPILE_DISK*/\n\n/* ////////////////////////////////////////////////////////////////////////// */\n/* ////////////////////////////////////////////////////////////////////////// */\n/* // End of common code and tools. Begin of Zlib related code.            // */\n/* ////////////////////////////////////////////////////////////////////////// */\n/* ////////////////////////////////////////////////////////////////////////// */\n\n#ifdef LODEPNG_COMPILE_ZLIB\n#ifdef LODEPNG_COMPILE_ENCODER\n/*TODO: this ignores potential out of memory errors*/\n#define addBitToStream(/*size_t**/ bitpointer, /*ucvector**/ bitstream, /*unsigned char*/ bit)\\\n\t\t\t{\\\n  \t/*add a new byte at the end*/\\\n  if(((*bitpointer) & 7) == 0) ucvector_push_back(bitstream, (unsigned char)0);\\\n  \t/*earlier bit of huffman code is in a lesser significant bit of an earlier byte*/\\\n  (bitstream->data[bitstream->size - 1]) |= (bit << ((*bitpointer) & 0x7));\\\n  (*bitpointer)++;\\\n\t\t\t}\n\nstatic void addBitsToStream(size_t* bitpointer, ucvector* bitstream, unsigned value, size_t nbits)\n\t{\n\tsize_t i;\n\tfor(i = 0; i < nbits; i++) addBitToStream(bitpointer, bitstream, (unsigned char)((value >> i) & 1));\n\t}\n\nstatic void addBitsToStreamReversed(size_t* bitpointer, ucvector* bitstream, unsigned value, size_t nbits)\n\t{\n\tsize_t i;\n\tfor(i = 0; i < nbits; i++) addBitToStream(bitpointer, bitstream, (unsigned char)((value >> (nbits - 1 - i)) & 1));\n\t}\n#endif /*LODEPNG_COMPILE_ENCODER*/\n\n#ifdef LODEPNG_COMPILE_DECODER\n\n#define READBIT(bitpointer, bitstream) ((bitstream[bitpointer >> 3] >> (bitpointer & 0x7)) & (unsigned char)1)\n\nstatic unsigned char readBitFromStream(size_t* bitpointer, const unsigned char* bitstream)\n\t{\n\tunsigned char result = (unsigned char)(READBIT(*bitpointer, bitstream));\n\t(*bitpointer)++;\n\treturn result;\n\t}\n\nstatic unsigned readBitsFromStream(size_t* bitpointer, const unsigned char* bitstream, size_t nbits)\n\t{\n\tunsigned result = 0, i;\n\tfor(i = 0; i < nbits; i++) {\n\t\tresult += ((unsigned)READBIT(*bitpointer, bitstream)) << i;\n\t\t(*bitpointer)++;\n\t\t}\n\treturn result;\n\t}\n#endif /*LODEPNG_COMPILE_DECODER*/\n\n/* ////////////////////////////////////////////////////////////////////////// */\n/* / Deflate - Huffman                                                      / */\n/* ////////////////////////////////////////////////////////////////////////// */\n\n#define FIRST_LENGTH_CODE_INDEX 257\n#define LAST_LENGTH_CODE_INDEX 285\n/*256 literals, the end code, some length codes, and 2 unused codes*/\n#define NUM_DEFLATE_CODE_SYMBOLS 288\n/*the distance codes have their own symbols, 30 used, 2 unused*/\n#define NUM_DISTANCE_SYMBOLS 32\n/*the code length codes. 0-15: code lengths, 16: copy previous 3-6 times, 17: 3-10 zeros, 18: 11-138 zeros*/\n#define NUM_CODE_LENGTH_CODES 19\n\n/*the base lengths represented by codes 257-285*/\nstatic const unsigned LENGTHBASE[29]\n   = {3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 15, 17, 19, 23, 27, 31, 35, 43, 51, 59,\n      67, 83, 99, 115, 131, 163, 195, 227, 258\n     \t};\n\n/*the extra bits used by codes 257-285 (added to base length)*/\nstatic const unsigned LENGTHEXTRA[29]\n   = {0, 0, 0, 0, 0, 0, 0,  0,  1,  1,  1,  1,  2,  2,  2,  2,  3,  3,  3,  3,\n      4,  4,  4,   4,   5,   5,   5,   5,   0\n     \t};\n\n/*the base backwards distances (the bits of distance codes appear after length codes and use their own huffman tree)*/\nstatic const unsigned DISTANCEBASE[30]\n   = {1, 2, 3, 4, 5, 7, 9, 13, 17, 25, 33, 49, 65, 97, 129, 193, 257, 385, 513,\n      769, 1025, 1537, 2049, 3073, 4097, 6145, 8193, 12289, 16385, 24577\n     \t};\n\n/*the extra bits of backwards distances (added to base)*/\nstatic const unsigned DISTANCEEXTRA[30]\n   = {0, 0, 0, 0, 1, 1, 2,  2,  3,  3,  4,  4,  5,  5,   6,   6,   7,   7,   8,\n      8,    9,    9,   10,   10,   11,   11,   12,    12,    13,    13\n     \t};\n\n/*the order in which \"code length alphabet code lengths\" are stored, out of this\nthe huffman tree of the dynamic huffman tree lengths is generated*/\nstatic const unsigned CLCL_ORDER[NUM_CODE_LENGTH_CODES]\n   = {16, 17, 18, 0, 8, 7, 9, 6, 10, 5, 11, 4, 12, 3, 13, 2, 14, 1, 15};\n\n/* ////////////////////////////////////////////////////////////////////////// */\n\n/*\nHuffman tree struct, containing multiple representations of the tree\n*/\ntypedef struct HuffmanTree {\n\tunsigned* tree2d;\n\tunsigned* tree1d;\n\tunsigned* lengths; /*the lengths of the codes of the 1d-tree*/\n\tunsigned maxbitlen; /*maximum number of bits a single code can get*/\n\tunsigned numcodes; /*number of symbols in the alphabet = number of codes*/\n\t} HuffmanTree;\n\n/*function used for debug purposes to draw the tree in ascii art with C++*/\n/*\nstatic void HuffmanTree_draw(HuffmanTree* tree)\n\t\t\t{\nstd::cout << \"tree. length: \" << tree->numcodes << \" maxbitlen: \" << tree->maxbitlen << std::endl;\nfor(size_t i = 0; i < tree->tree1d.size; i++)\n\t\t\t{\n if(tree->lengths.data[i])\n   std::cout << i << \" \" << tree->tree1d.data[i] << \" \" << tree->lengths.data[i] << std::endl;\n\t\t\t}\nstd::cout << std::endl;\n\t\t\t}*/\n\nstatic void HuffmanTree_init(HuffmanTree* tree)\n\t{\n\ttree->tree2d = 0;\n\ttree->tree1d = 0;\n\ttree->lengths = 0;\n\t}\n\nstatic void HuffmanTree_cleanup(HuffmanTree* tree)\n\t{\n\tlodepng_free(tree->tree2d);\n\tlodepng_free(tree->tree1d);\n\tlodepng_free(tree->lengths);\n\t}\n\n/*the tree representation used by the decoder. return value is error*/\nstatic unsigned HuffmanTree_make2DTree(HuffmanTree* tree)\n\t{\n\tunsigned nodefilled = 0; /*up to which node it is filled*/\n\tunsigned treepos = 0; /*position in the tree (1 of the numcodes columns)*/\n\tunsigned n, i;\n\n\ttree->tree2d = (unsigned*)lodepng_malloc(tree->numcodes * 2 * sizeof(unsigned));\n\tif(!tree->tree2d) return 83; /*alloc fail*/\n\n\t/*\n\tconvert tree1d[] to tree2d[][]. In the 2D array, a value of 32767 means\n\tuninited, a value >= numcodes is an address to another bit, a value < numcodes\n\tis a code. The 2 rows are the 2 possible bit values (0 or 1), there are as\n\tmany columns as codes - 1.\n\tA good huffmann tree has N * 2 - 1 nodes, of which N - 1 are internal nodes.\n\tHere, the internal nodes are stored (what their 0 and 1 option point to).\n\tThere is only memory for such good tree currently, if there are more nodes\n\t(due to too long length codes), error 55 will happen\n\t*/\n\tfor(n = 0; n < tree->numcodes * 2; n++) {\n\t\ttree->tree2d[n] = 32767; /*32767 here means the tree2d isn't filled there yet*/\n\t\t}\n\n\tfor(n = 0; n < tree->numcodes; n++) { /*the codes*/\n\t\tfor(i = 0; i < tree->lengths[n]; i++) { /*the bits for this code*/\n\t\t\tunsigned char bit = (unsigned char)((tree->tree1d[n] >> (tree->lengths[n] - i - 1)) & 1);\n\t\t\tif(treepos > tree->numcodes - 2) return 55; /*oversubscribed, see comment in lodepng_error_text*/\n\t\t\tif(tree->tree2d[2 * treepos + bit] == 32767) { /*not yet filled in*/\n\t\t\t\tif(i + 1 == tree->lengths[n]) { /*last bit*/\n\t\t\t\t\ttree->tree2d[2 * treepos + bit] = n; /*put the current code in it*/\n\t\t\t\t\ttreepos = 0;\n\t\t\t\t\t}\n\t\t\t\telse {\n\t\t\t\t\t/*put address of the next step in here, first that address has to be found of course\n\t\t\t\t\t(it's just nodefilled + 1)...*/\n\t\t\t\t\tnodefilled++;\n\t\t\t\t\t/*addresses encoded with numcodes added to it*/\n\t\t\t\t\ttree->tree2d[2 * treepos + bit] = nodefilled + tree->numcodes;\n\t\t\t\t\ttreepos = nodefilled;\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\telse treepos = tree->tree2d[2 * treepos + bit] - tree->numcodes;\n\t\t\t}\n\t\t}\n\n\tfor(n = 0; n < tree->numcodes * 2; n++) {\n\t\tif(tree->tree2d[n] == 32767) tree->tree2d[n] = 0; /*remove possible remaining 32767's*/\n\t\t}\n\n\treturn 0;\n\t}\n\n/*\nSecond step for the ...makeFromLengths and ...makeFromFrequencies functions.\nnumcodes, lengths and maxbitlen must already be filled in correctly. return\nvalue is error.\n*/\nstatic unsigned HuffmanTree_makeFromLengths2(HuffmanTree* tree)\n\t{\n\tuivector blcount;\n\tuivector nextcode;\n\tunsigned bits, n, error = 0;\n\n\tuivector_init(&blcount);\n\tuivector_init(&nextcode);\n\n\ttree->tree1d = (unsigned*)lodepng_malloc(tree->numcodes * sizeof(unsigned));\n\tif(!tree->tree1d) error = 83; /*alloc fail*/\n\n\tif(!uivector_resizev(&blcount, tree->maxbitlen + 1, 0)\n\t      || !uivector_resizev(&nextcode, tree->maxbitlen + 1, 0))\n\t\terror = 83; /*alloc fail*/\n\n\tif(!error) {\n\t\t/*step 1: count number of instances of each code length*/\n\t\tfor(bits = 0; bits < tree->numcodes; bits++) blcount.data[tree->lengths[bits]]++;\n\t\t/*step 2: generate the nextcode values*/\n\t\tfor(bits = 1; bits <= tree->maxbitlen; bits++) {\n\t\t\tnextcode.data[bits] = (nextcode.data[bits - 1] + blcount.data[bits - 1]) << 1;\n\t\t\t}\n\t\t/*step 3: generate all the codes*/\n\t\tfor(n = 0; n < tree->numcodes; n++) {\n\t\t\tif(tree->lengths[n] != 0) tree->tree1d[n] = nextcode.data[tree->lengths[n]]++;\n\t\t\t}\n\t\t}\n\n\tuivector_cleanup(&blcount);\n\tuivector_cleanup(&nextcode);\n\n\tif(!error) return HuffmanTree_make2DTree(tree);\n\telse return error;\n\t}\n\n/*\ngiven the code lengths (as stored in the PNG file), generate the tree as defined\nby Deflate. maxbitlen is the maximum bits that a code in the tree can have.\nreturn value is error.\n*/\nstatic unsigned HuffmanTree_makeFromLengths(HuffmanTree* tree, const unsigned* bitlen,\n      size_t numcodes, unsigned maxbitlen)\n\t{\n\tunsigned i;\n\ttree->lengths = (unsigned*)lodepng_malloc(numcodes * sizeof(unsigned));\n\tif(!tree->lengths) return 83; /*alloc fail*/\n\tfor(i = 0; i < numcodes; i++) tree->lengths[i] = bitlen[i];\n\ttree->numcodes = (unsigned)numcodes; /*number of symbols*/\n\ttree->maxbitlen = maxbitlen;\n\treturn HuffmanTree_makeFromLengths2(tree);\n\t}\n\n#ifdef LODEPNG_COMPILE_ENCODER\n\n/*\nA coin, this is the terminology used for the package-merge algorithm and the\ncoin collector's problem. This is used to generate the huffman tree.\nA coin can be multiple coins (when they're merged)\n*/\ntypedef struct Coin {\n\tuivector symbols;\n\tfloat weight; /*the sum of all weights in this coin*/\n\t} Coin;\n\nstatic void coin_init(Coin* c)\n\t{\n\tuivector_init(&c->symbols);\n\t}\n\n/*argument c is void* so that this dtor can be given as function pointer to the vector resize function*/\nstatic void coin_cleanup(void* c)\n\t{\n\tuivector_cleanup(&((Coin*)c)->symbols);\n\t}\n\nstatic void coin_copy(Coin* c1, const Coin* c2)\n\t{\n\tc1->weight = c2->weight;\n\tuivector_copy(&c1->symbols, &c2->symbols);\n\t}\n\nstatic void add_coins(Coin* c1, const Coin* c2)\n\t{\n\tsize_t i;\n\tfor(i = 0; i < c2->symbols.size; i++) uivector_push_back(&c1->symbols, c2->symbols.data[i]);\n\tc1->weight += c2->weight;\n\t}\n\nstatic void init_coins(Coin* coins, size_t num)\n\t{\n\tsize_t i;\n\tfor(i = 0; i < num; i++) coin_init(&coins[i]);\n\t}\n\nstatic void cleanup_coins(Coin* coins, size_t num)\n\t{\n\tsize_t i;\n\tfor(i = 0; i < num; i++) coin_cleanup(&coins[i]);\n\t}\n\nstatic int coin_compare(const void* a, const void* b)\n\t{\n\tfloat wa = ((const Coin*)a)->weight;\n\tfloat wb = ((const Coin*)b)->weight;\n\treturn wa > wb ? 1 : wa < wb ? -1 : 0;\n\t}\n\nstatic unsigned append_symbol_coins(Coin* coins, const unsigned* frequencies, unsigned numcodes, size_t sum)\n\t{\n\tunsigned i;\n\tunsigned j = 0; /*index of present symbols*/\n\tfor(i = 0; i < numcodes; i++) {\n\t\tif(frequencies[i] != 0) { /*only include symbols that are present*/\n\t\t\tcoins[j].weight = frequencies[i] / (float)sum;\n\t\t\tuivector_push_back(&coins[j].symbols, i);\n\t\t\tj++;\n\t\t\t}\n\t\t}\n\treturn 0;\n\t}\n\nunsigned lodepng_huffman_code_lengths(unsigned* lengths, const unsigned* frequencies,\n                                      size_t numcodes, unsigned maxbitlen)\n\t{\n\tunsigned i, j;\n\tsize_t sum = 0, numpresent = 0;\n\tunsigned error = 0;\n\tCoin* coins; /*the coins of the currently calculated row*/\n\tCoin* prev_row; /*the previous row of coins*/\n\tunsigned numcoins;\n\tunsigned coinmem;\n\n\tif(numcodes == 0) return 80; /*error: a tree of 0 symbols is not supposed to be made*/\n\n\tfor(i = 0; i < numcodes; i++) {\n\t\tif(frequencies[i] > 0) {\n\t\t\tnumpresent++;\n\t\t\tsum += frequencies[i];\n\t\t\t}\n\t\t}\n\n\tfor(i = 0; i < numcodes; i++) lengths[i] = 0;\n\n\t/*ensure at least two present symbols. There should be at least one symbol\n\taccording to RFC 1951 section 3.2.7. To decoders incorrectly require two. To\n\tmake these work as well ensure there are at least two symbols. The\n\tPackage-Merge code below also doesn't work correctly if there's only one\n\tsymbol, it'd give it the theoritical 0 bits but in practice zlib wants 1 bit*/\n\tif(numpresent == 0) {\n\t\tlengths[0] = lengths[1] = 1; /*note that for RFC 1951 section 3.2.7, only lengths[0] = 1 is needed*/\n\t\t}\n\telse if(numpresent == 1) {\n\t\tfor(i = 0; i < numcodes; i++) {\n\t\t\tif(frequencies[i]) {\n\t\t\t\tlengths[i] = 1;\n\t\t\t\tlengths[i == 0 ? 1 : 0] = 1;\n\t\t\t\tbreak;\n\t\t\t\t}\n\t\t\t}\n\t\t}\n\telse {\n\t\t/*Package-Merge algorithm represented by coin collector's problem\n\t\tFor every symbol, maxbitlen coins will be created*/\n\n\t\tcoinmem = numpresent * 2; /*max amount of coins needed with the current algo*/\n\t\tcoins = (Coin*)lodepng_malloc(sizeof(Coin) * coinmem);\n\t\tprev_row = (Coin*)lodepng_malloc(sizeof(Coin) * coinmem);\n\t\tif(!coins || !prev_row) {\n\t\t\tlodepng_free(coins);\n\t\t\tlodepng_free(prev_row);\n\t\t\treturn 83; /*alloc fail*/\n\t\t\t}\n\t\tinit_coins(coins, coinmem);\n\t\tinit_coins(prev_row, coinmem);\n\n\t\t/*first row, lowest denominator*/\n\t\terror = append_symbol_coins(coins, frequencies, numcodes, sum);\n\t\tnumcoins = numpresent;\n\t\tqsort(coins, numcoins, sizeof(Coin), coin_compare);\n\t\tif(!error) {\n\t\t\tunsigned numprev = 0;\n\t\t\tfor(j = 1; j <= maxbitlen && !error; j++) { /*each of the remaining rows*/\n\t\t\t\tunsigned tempnum;\n\t\t\t\tCoin* tempcoins;\n\t\t\t\t/*swap prev_row and coins, and their amounts*/\n\t\t\t\ttempcoins = prev_row;\n\t\t\t\tprev_row = coins;\n\t\t\t\tcoins = tempcoins;\n\t\t\t\ttempnum = numprev;\n\t\t\t\tnumprev = numcoins;\n\t\t\t\tnumcoins = tempnum;\n\n\t\t\t\tcleanup_coins(coins, numcoins);\n\t\t\t\tinit_coins(coins, numcoins);\n\n\t\t\t\tnumcoins = 0;\n\n\t\t\t\t/*fill in the merged coins of the previous row*/\n\t\t\t\tfor(i = 0; i + 1 < numprev; i += 2) {\n\t\t\t\t\t/*merge prev_row[i] and prev_row[i + 1] into new coin*/\n\t\t\t\t\tCoin* coin = &coins[numcoins++];\n\t\t\t\t\tcoin_copy(coin, &prev_row[i]);\n\t\t\t\t\tadd_coins(coin, &prev_row[i + 1]);\n\t\t\t\t\t}\n\t\t\t\t/*fill in all the original symbols again*/\n\t\t\t\tif(j < maxbitlen) {\n\t\t\t\t\terror = append_symbol_coins(coins + numcoins, frequencies, numcodes, sum);\n\t\t\t\t\tnumcoins += numpresent;\n\t\t\t\t\t}\n\t\t\t\tqsort(coins, numcoins, sizeof(Coin), coin_compare);\n\t\t\t\t}\n\t\t\t}\n\n\t\tif(!error) {\n\t\t\t/*calculate the lenghts of each symbol, as the amount of times a coin of each symbol is used*/\n\t\t\tfor(i = 0; i < numpresent - 1; i++) {\n\t\t\t\tCoin* coin = &coins[i];\n\t\t\t\tfor(j = 0; j < coin->symbols.size; j++) lengths[coin->symbols.data[j]]++;\n\t\t\t\t}\n\t\t\t}\n\n\t\tcleanup_coins(coins, coinmem);\n\t\tlodepng_free(coins);\n\t\tcleanup_coins(prev_row, coinmem);\n\t\tlodepng_free(prev_row);\n\t\t}\n\n\treturn error;\n\t}\n\n/*Create the Huffman tree given the symbol frequencies*/\nstatic unsigned HuffmanTree_makeFromFrequencies(HuffmanTree* tree, const unsigned* frequencies,\n      size_t mincodes, size_t numcodes, unsigned maxbitlen)\n\t{\n\tunsigned error = 0;\n\twhile(!frequencies[numcodes - 1] && numcodes > mincodes) numcodes--; /*trim zeroes*/\n\ttree->maxbitlen = maxbitlen;\n\ttree->numcodes = (unsigned)numcodes; /*number of symbols*/\n\ttree->lengths = (unsigned*)lodepng_realloc(tree->lengths, numcodes * sizeof(unsigned));\n\tif(!tree->lengths) return 83; /*alloc fail*/\n\t/*initialize all lengths to 0*/\n\tmemset(tree->lengths, 0, numcodes * sizeof(unsigned));\n\n\terror = lodepng_huffman_code_lengths(tree->lengths, frequencies, numcodes, maxbitlen);\n\tif(!error) error = HuffmanTree_makeFromLengths2(tree);\n\treturn error;\n\t}\n\nstatic unsigned HuffmanTree_getCode(const HuffmanTree* tree, unsigned index)\n\t{\n\treturn tree->tree1d[index];\n\t}\n\nstatic unsigned HuffmanTree_getLength(const HuffmanTree* tree, unsigned index)\n\t{\n\treturn tree->lengths[index];\n\t}\n#endif /*LODEPNG_COMPILE_ENCODER*/\n\n/*get the literal and length code tree of a deflated block with fixed tree, as per the deflate specification*/\nstatic unsigned generateFixedLitLenTree(HuffmanTree* tree)\n\t{\n\tunsigned i, error = 0;\n\tunsigned* bitlen = (unsigned*)lodepng_malloc(NUM_DEFLATE_CODE_SYMBOLS * sizeof(unsigned));\n\tif(!bitlen) return 83; /*alloc fail*/\n\n\t/*288 possible codes: 0-255=literals, 256=endcode, 257-285=lengthcodes, 286-287=unused*/\n\tfor(i =   0; i <= 143; i++) bitlen[i] = 8;\n\tfor(i = 144; i <= 255; i++) bitlen[i] = 9;\n\tfor(i = 256; i <= 279; i++) bitlen[i] = 7;\n\tfor(i = 280; i <= 287; i++) bitlen[i] = 8;\n\n\terror = HuffmanTree_makeFromLengths(tree, bitlen, NUM_DEFLATE_CODE_SYMBOLS, 15);\n\n\tlodepng_free(bitlen);\n\treturn error;\n\t}\n\n/*get the distance code tree of a deflated block with fixed tree, as specified in the deflate specification*/\nstatic unsigned generateFixedDistanceTree(HuffmanTree* tree)\n\t{\n\tunsigned i, error = 0;\n\tunsigned* bitlen = (unsigned*)lodepng_malloc(NUM_DISTANCE_SYMBOLS * sizeof(unsigned));\n\tif(!bitlen) return 83; /*alloc fail*/\n\n\t/*there are 32 distance codes, but 30-31 are unused*/\n\tfor(i = 0; i < NUM_DISTANCE_SYMBOLS; i++) bitlen[i] = 5;\n\terror = HuffmanTree_makeFromLengths(tree, bitlen, NUM_DISTANCE_SYMBOLS, 15);\n\n\tlodepng_free(bitlen);\n\treturn error;\n\t}\n\n#ifdef LODEPNG_COMPILE_DECODER\n\n/*\nreturns the code, or (unsigned)(-1) if error happened\ninbitlength is the length of the complete buffer, in bits (so its byte length times 8)\n*/\nstatic unsigned huffmanDecodeSymbol(const unsigned char* in, size_t* bp,\n                                    const HuffmanTree* codetree, size_t inbitlength)\n\t{\n\tunsigned treepos = 0, ct;\n\tfor(;;) {\n\t\tif(*bp >= inbitlength) return (unsigned)(-1); /*error: end of input memory reached without endcode*/\n\t\t/*\n\t\tdecode the symbol from the tree. The \"readBitFromStream\" code is inlined in\n\t\tthe expression below because this is the biggest bottleneck while decoding\n\t\t*/\n\t\tct = codetree->tree2d[(treepos << 1) + READBIT(*bp, in)];\n\t\t(*bp)++;\n\t\tif(ct < codetree->numcodes) return ct; /*the symbol is decoded, return it*/\n\t\telse treepos = ct - codetree->numcodes; /*symbol not yet decoded, instead move tree position*/\n\n\t\tif(treepos >= codetree->numcodes) return (unsigned)(-1); /*error: it appeared outside the codetree*/\n\t\t}\n\t}\n#endif /*LODEPNG_COMPILE_DECODER*/\n\n#ifdef LODEPNG_COMPILE_DECODER\n\n/* ////////////////////////////////////////////////////////////////////////// */\n/* / Inflator (Decompressor)                                                / */\n/* ////////////////////////////////////////////////////////////////////////// */\n\n/*get the tree of a deflated block with fixed tree, as specified in the deflate specification*/\nstatic void getTreeInflateFixed(HuffmanTree* tree_ll, HuffmanTree* tree_d)\n\t{\n\t/*TODO: check for out of memory errors*/\n\tgenerateFixedLitLenTree(tree_ll);\n\tgenerateFixedDistanceTree(tree_d);\n\t}\n\n/*get the tree of a deflated block with dynamic tree, the tree itself is also Huffman compressed with a known tree*/\nstatic unsigned getTreeInflateDynamic(HuffmanTree* tree_ll, HuffmanTree* tree_d,\n                                      const unsigned char* in, size_t* bp, size_t inlength)\n\t{\n\t/*make sure that length values that aren't filled in will be 0, or a wrong tree will be generated*/\n\tunsigned error = 0;\n\tunsigned n, HLIT, HDIST, HCLEN, i;\n\tsize_t inbitlength = inlength * 8;\n\n\t/*see comments in deflateDynamic for explanation of the context and these variables, it is analogous*/\n\tunsigned* bitlen_ll = 0; /*lit,len code lengths*/\n\tunsigned* bitlen_d = 0; /*dist code lengths*/\n\t/*code length code lengths (\"clcl\"), the bit lengths of the huffman tree used to compress bitlen_ll and bitlen_d*/\n\tunsigned* bitlen_cl = 0;\n\tHuffmanTree tree_cl; /*the code tree for code length codes (the huffman tree for compressed huffman trees)*/\n\n\tif((*bp) >> 3 >= inlength - 2) return 49; /*error: the bit pointer is or will go past the memory*/\n\n\t/*number of literal/length codes + 257. Unlike the spec, the value 257 is added to it here already*/\n\tHLIT =  readBitsFromStream(bp, in, 5) + 257;\n\t/*number of distance codes. Unlike the spec, the value 1 is added to it here already*/\n\tHDIST = readBitsFromStream(bp, in, 5) + 1;\n\t/*number of code length codes. Unlike the spec, the value 4 is added to it here already*/\n\tHCLEN = readBitsFromStream(bp, in, 4) + 4;\n\n\tHuffmanTree_init(&tree_cl);\n\n\twhile(!error) {\n\t\t/*read the code length codes out of 3 * (amount of code length codes) bits*/\n\n\t\tbitlen_cl = (unsigned*)lodepng_malloc(NUM_CODE_LENGTH_CODES * sizeof(unsigned));\n\t\tif(!bitlen_cl) ERROR_BREAK(83 /*alloc fail*/);\n\n\t\tfor(i = 0; i < NUM_CODE_LENGTH_CODES; i++) {\n\t\t\tif(i < HCLEN) bitlen_cl[CLCL_ORDER[i]] = readBitsFromStream(bp, in, 3);\n\t\t\telse bitlen_cl[CLCL_ORDER[i]] = 0; /*if not, it must stay 0*/\n\t\t\t}\n\n\t\terror = HuffmanTree_makeFromLengths(&tree_cl, bitlen_cl, NUM_CODE_LENGTH_CODES, 7);\n\t\tif(error) break;\n\n\t\t/*now we can use this tree to read the lengths for the tree that this function will return*/\n\t\tbitlen_ll = (unsigned*)lodepng_malloc(NUM_DEFLATE_CODE_SYMBOLS * sizeof(unsigned));\n\t\tbitlen_d = (unsigned*)lodepng_malloc(NUM_DISTANCE_SYMBOLS * sizeof(unsigned));\n\t\tif(!bitlen_ll || !bitlen_d) ERROR_BREAK(83 /*alloc fail*/);\n\t\tfor(i = 0; i < NUM_DEFLATE_CODE_SYMBOLS; i++) bitlen_ll[i] = 0;\n\t\tfor(i = 0; i < NUM_DISTANCE_SYMBOLS; i++) bitlen_d[i] = 0;\n\n\t\t/*i is the current symbol we're reading in the part that contains the code lengths of lit/len and dist codes*/\n\t\ti = 0;\n\t\twhile(i < HLIT + HDIST) {\n\t\t\tunsigned code = huffmanDecodeSymbol(in, bp, &tree_cl, inbitlength);\n\t\t\tif(code <= 15) { /*a length code*/\n\t\t\t\tif(i < HLIT) bitlen_ll[i] = code;\n\t\t\t\telse bitlen_d[i - HLIT] = code;\n\t\t\t\ti++;\n\t\t\t\t}\n\t\t\telse if(code == 16) {   /*repeat previous*/\n\t\t\t\tunsigned replength = 3; /*read in the 2 bits that indicate repeat length (3-6)*/\n\t\t\t\tunsigned value; /*set value to the previous code*/\n\n\t\t\t\tif(*bp >= inbitlength) ERROR_BREAK(50); /*error, bit pointer jumps past memory*/\n\t\t\t\tif (i == 0) ERROR_BREAK(54); /*can't repeat previous if i is 0*/\n\n\t\t\t\treplength += readBitsFromStream(bp, in, 2);\n\n\t\t\t\tif(i < HLIT + 1) value = bitlen_ll[i - 1];\n\t\t\t\telse value = bitlen_d[i - HLIT - 1];\n\t\t\t\t/*repeat this value in the next lengths*/\n\t\t\t\tfor(n = 0; n < replength; n++) {\n\t\t\t\t\tif(i >= HLIT + HDIST) ERROR_BREAK(13); /*error: i is larger than the amount of codes*/\n\t\t\t\t\tif(i < HLIT) bitlen_ll[i] = value;\n\t\t\t\t\telse bitlen_d[i - HLIT] = value;\n\t\t\t\t\ti++;\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\telse if(code == 17) {   /*repeat \"0\" 3-10 times*/\n\t\t\t\tunsigned replength = 3; /*read in the bits that indicate repeat length*/\n\t\t\t\tif(*bp >= inbitlength) ERROR_BREAK(50); /*error, bit pointer jumps past memory*/\n\n\t\t\t\treplength += readBitsFromStream(bp, in, 3);\n\n\t\t\t\t/*repeat this value in the next lengths*/\n\t\t\t\tfor(n = 0; n < replength; n++) {\n\t\t\t\t\tif(i >= HLIT + HDIST) ERROR_BREAK(14); /*error: i is larger than the amount of codes*/\n\n\t\t\t\t\tif(i < HLIT) bitlen_ll[i] = 0;\n\t\t\t\t\telse bitlen_d[i - HLIT] = 0;\n\t\t\t\t\ti++;\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\telse if(code == 18) {   /*repeat \"0\" 11-138 times*/\n\t\t\t\tunsigned replength = 11; /*read in the bits that indicate repeat length*/\n\t\t\t\tif(*bp >= inbitlength) ERROR_BREAK(50); /*error, bit pointer jumps past memory*/\n\n\t\t\t\treplength += readBitsFromStream(bp, in, 7);\n\n\t\t\t\t/*repeat this value in the next lengths*/\n\t\t\t\tfor(n = 0; n < replength; n++) {\n\t\t\t\t\tif(i >= HLIT + HDIST) ERROR_BREAK(15); /*error: i is larger than the amount of codes*/\n\n\t\t\t\t\tif(i < HLIT) bitlen_ll[i] = 0;\n\t\t\t\t\telse bitlen_d[i - HLIT] = 0;\n\t\t\t\t\ti++;\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\telse {   /*if(code == (unsigned)(-1))*/\n\t\t\t\t/*huffmanDecodeSymbol returns (unsigned)(-1) in case of error*/\n\t\t\t\tif(code == (unsigned)(-1)) {\n\t\t\t\t\t/*return error code 10 or 11 depending on the situation that happened in huffmanDecodeSymbol\n\t\t\t\t\t(10=no endcode, 11=wrong jump outside of tree)*/\n\t\t\t\t\terror = (*bp) > inbitlength ? 10 : 11;\n\t\t\t\t\t}\n\t\t\t\telse error = 16;   /*unexisting code, this can never happen*/\n\t\t\t\tbreak;\n\t\t\t\t}\n\t\t\t}\n\t\tif(error) break;\n\n\t\tif(bitlen_ll[256] == 0) ERROR_BREAK(64); /*the length of the end code 256 must be larger than 0*/\n\n\t\t/*now we've finally got HLIT and HDIST, so generate the code trees, and the function is done*/\n\t\terror = HuffmanTree_makeFromLengths(tree_ll, bitlen_ll, NUM_DEFLATE_CODE_SYMBOLS, 15);\n\t\tif(error) break;\n\t\terror = HuffmanTree_makeFromLengths(tree_d, bitlen_d, NUM_DISTANCE_SYMBOLS, 15);\n\n\t\tbreak; /*end of error-while*/\n\t\t}\n\n\tlodepng_free(bitlen_cl);\n\tlodepng_free(bitlen_ll);\n\tlodepng_free(bitlen_d);\n\tHuffmanTree_cleanup(&tree_cl);\n\n\treturn error;\n\t}\n\n/*inflate a block with dynamic of fixed Huffman tree*/\nstatic unsigned inflateHuffmanBlock(ucvector* out, const unsigned char* in, size_t* bp,\n                                    size_t* pos, size_t inlength, unsigned btype)\n\t{\n\tunsigned error = 0;\n\tHuffmanTree tree_ll; /*the huffman tree for literal and length codes*/\n\tHuffmanTree tree_d; /*the huffman tree for distance codes*/\n\tsize_t inbitlength = inlength * 8;\n\n\tHuffmanTree_init(&tree_ll);\n\tHuffmanTree_init(&tree_d);\n\n\tif(btype == 1) getTreeInflateFixed(&tree_ll, &tree_d);\n\telse if(btype == 2) error = getTreeInflateDynamic(&tree_ll, &tree_d, in, bp, inlength);\n\n\twhile(!error) { /*decode all symbols until end reached, breaks at end code*/\n\t\t/*code_ll is literal, length or end code*/\n\t\tunsigned code_ll = huffmanDecodeSymbol(in, bp, &tree_ll, inbitlength);\n\t\tif(code_ll <= 255) { /*literal symbol*/\n\t\t\tif((*pos) >= out->size) {\n\t\t\t\t/*reserve more room at once*/\n\t\t\t\tif(!ucvector_resize(out, ((*pos) + 1) * 2)) ERROR_BREAK(83 /*alloc fail*/);\n\t\t\t\t}\n\t\t\tout->data[(*pos)] = (unsigned char)(code_ll);\n\t\t\t(*pos)++;\n\t\t\t}\n\t\telse if(code_ll >= FIRST_LENGTH_CODE_INDEX && code_ll <= LAST_LENGTH_CODE_INDEX) {   /*length code*/\n\t\t\tunsigned code_d, distance;\n\t\t\tunsigned numextrabits_l, numextrabits_d; /*extra bits for length and distance*/\n\t\t\tsize_t start, forward, backward, length;\n\n\t\t\t/*part 1: get length base*/\n\t\t\tlength = LENGTHBASE[code_ll - FIRST_LENGTH_CODE_INDEX];\n\n\t\t\t/*part 2: get extra bits and add the value of that to length*/\n\t\t\tnumextrabits_l = LENGTHEXTRA[code_ll - FIRST_LENGTH_CODE_INDEX];\n\t\t\tif(*bp >= inbitlength) ERROR_BREAK(51); /*error, bit pointer will jump past memory*/\n\t\t\tlength += readBitsFromStream(bp, in, numextrabits_l);\n\n\t\t\t/*part 3: get distance code*/\n\t\t\tcode_d = huffmanDecodeSymbol(in, bp, &tree_d, inbitlength);\n\t\t\tif(code_d > 29) {\n\t\t\t\tif(code_ll == (unsigned)(-1)) { /*huffmanDecodeSymbol returns (unsigned)(-1) in case of error*/\n\t\t\t\t\t/*return error code 10 or 11 depending on the situation that happened in huffmanDecodeSymbol\n\t\t\t\t\t(10=no endcode, 11=wrong jump outside of tree)*/\n\t\t\t\t\terror = (*bp) > inlength * 8 ? 10 : 11;\n\t\t\t\t\t}\n\t\t\t\telse error = 18;   /*error: invalid distance code (30-31 are never used)*/\n\t\t\t\tbreak;\n\t\t\t\t}\n\t\t\tdistance = DISTANCEBASE[code_d];\n\n\t\t\t/*part 4: get extra bits from distance*/\n\t\t\tnumextrabits_d = DISTANCEEXTRA[code_d];\n\t\t\tif(*bp >= inbitlength) ERROR_BREAK(51); /*error, bit pointer will jump past memory*/\n\n\t\t\tdistance += readBitsFromStream(bp, in, numextrabits_d);\n\n\t\t\t/*part 5: fill in all the out[n] values based on the length and dist*/\n\t\t\tstart = (*pos);\n\t\t\tif(distance > start) ERROR_BREAK(52); /*too long backward distance*/\n\t\t\tbackward = start - distance;\n\t\t\tif((*pos) + length >= out->size) {\n\t\t\t\t/*reserve more room at once*/\n\t\t\t\tif(!ucvector_resize(out, ((*pos) + length) * 2)) ERROR_BREAK(83 /*alloc fail*/);\n\t\t\t\t}\n\n\t\t\tfor(forward = 0; forward < length; forward++) {\n\t\t\t\tout->data[(*pos)] = out->data[backward];\n\t\t\t\t(*pos)++;\n\t\t\t\tbackward++;\n\t\t\t\tif(backward >= start) backward = start - distance;\n\t\t\t\t}\n\t\t\t}\n\t\telse if(code_ll == 256) {\n\t\t\tbreak; /*end code, break the loop*/\n\t\t\t}\n\t\telse {   /*if(code == (unsigned)(-1))*/\n\t\t\t/*huffmanDecodeSymbol returns (unsigned)(-1) in case of error*/\n\t\t\t/*return error code 10 or 11 depending on the situation that happened in huffmanDecodeSymbol\n\t\t\t(10=no endcode, 11=wrong jump outside of tree)*/\n\t\t\terror = (*bp) > inlength * 8 ? 10 : 11;\n\t\t\tbreak;\n\t\t\t}\n\t\t}\n\n\tHuffmanTree_cleanup(&tree_ll);\n\tHuffmanTree_cleanup(&tree_d);\n\n\treturn error;\n\t}\n\nstatic unsigned inflateNoCompression(ucvector* out, const unsigned char* in, size_t* bp, size_t* pos, size_t inlength)\n\t{\n\t/*go to first boundary of byte*/\n\tsize_t p;\n\tunsigned LEN, NLEN, n, error = 0;\n\twhile(((*bp) & 0x7) != 0) (*bp)++;\n\tp = (*bp) / 8; /*byte position*/\n\n\t/*read LEN (2 bytes) and NLEN (2 bytes)*/\n\tif(p >= inlength - 4) return 52; /*error, bit pointer will jump past memory*/\n\tLEN = in[p] + 256 * in[p + 1];\n\tp += 2;\n\tNLEN = in[p] + 256 * in[p + 1];\n\tp += 2;\n\n\t/*check if 16-bit NLEN is really the one's complement of LEN*/\n\tif(LEN + NLEN != 65535) return 21; /*error: NLEN is not one's complement of LEN*/\n\n\tif((*pos) + LEN >= out->size) {\n\t\tif(!ucvector_resize(out, (*pos) + LEN)) return 83; /*alloc fail*/\n\t\t}\n\n\t/*read the literal data: LEN bytes are now stored in the out buffer*/\n\tif(p + LEN > inlength) return 23; /*error: reading outside of in buffer*/\n\tfor(n = 0; n < LEN; n++) out->data[(*pos)++] = in[p++];\n\n\t(*bp) = p * 8;\n\n\treturn error;\n\t}\n\nstatic unsigned lodepng_inflatev(ucvector* out,\n                                 const unsigned char* in, size_t insize,\n                                 const LodePNGDecompressSettings* settings)\n\t{\n\t/*bit pointer in the \"in\" data, current byte is bp >> 3, current bit is bp & 0x7 (from lsb to msb of the byte)*/\n\tsize_t bp = 0;\n\tunsigned BFINAL = 0;\n\tsize_t pos = 0; /*byte position in the out buffer*/\n\n\tunsigned error = 0;\n\n\t(void)settings;\n\n\twhile(!BFINAL) {\n\t\tunsigned BTYPE;\n\t\tif(bp + 2 >= insize * 8) return 52; /*error, bit pointer will jump past memory*/\n\t\tBFINAL = readBitFromStream(&bp, in);\n\t\tBTYPE = 1 * readBitFromStream(&bp, in);\n\t\tBTYPE += 2 * readBitFromStream(&bp, in);\n\n\t\tif(BTYPE == 3) return 20; /*error: invalid BTYPE*/\n\t\telse if(BTYPE == 0) error = inflateNoCompression(out, in, &bp, &pos, insize); /*no compression*/\n\t\telse error = inflateHuffmanBlock(out, in, &bp, &pos, insize, BTYPE); /*compression, BTYPE 01 or 10*/\n\n\t\tif(error) return error;\n\t\t}\n\n\t/*Only now we know the true size of out, resize it to that*/\n\tif(!ucvector_resize(out, pos)) error = 83; /*alloc fail*/\n\n\treturn error;\n\t}\n\nunsigned lodepng_inflate(unsigned char** out, size_t* outsize,\n                         const unsigned char* in, size_t insize,\n                         const LodePNGDecompressSettings* settings)\n\t{\n\tunsigned error;\n\tucvector v;\n\tucvector_init_buffer(&v, *out, *outsize);\n\terror = lodepng_inflatev(&v, in, insize, settings);\n\t*out = v.data;\n\t*outsize = v.size;\n\treturn error;\n\t}\n\nstatic unsigned inflate(unsigned char** out, size_t* outsize,\n                        const unsigned char* in, size_t insize,\n                        const LodePNGDecompressSettings* settings)\n\t{\n\tif(settings->custom_inflate) {\n\t\treturn settings->custom_inflate(out, outsize, in, insize, settings);\n\t\t}\n\telse {\n\t\treturn lodepng_inflate(out, outsize, in, insize, settings);\n\t\t}\n\t}\n\n#endif /*LODEPNG_COMPILE_DECODER*/\n\n#ifdef LODEPNG_COMPILE_ENCODER\n\n/* ////////////////////////////////////////////////////////////////////////// */\n/* / Deflator (Compressor)                                                  / */\n/* ////////////////////////////////////////////////////////////////////////// */\n\nstatic const size_t MAX_SUPPORTED_DEFLATE_LENGTH = 258;\n\n/*bitlen is the size in bits of the code*/\nstatic void addHuffmanSymbol(size_t* bp, ucvector* compressed, unsigned code, unsigned bitlen)\n\t{\n\taddBitsToStreamReversed(bp, compressed, code, bitlen);\n\t}\n\n/*search the index in the array, that has the largest value smaller than or equal to the given value,\ngiven array must be sorted (if no value is smaller, it returns the size of the given array)*/\nstatic size_t searchCodeIndex(const unsigned* array, size_t array_size, size_t value)\n\t{\n\t/*linear search implementation*/\n\t/*for(size_t i = 1; i < array_size; i++) if(array[i] > value) return i - 1;\n\treturn array_size - 1;*/\n\n\t/*binary search implementation (not that much faster) (precondition: array_size > 0)*/\n\tsize_t left  = 1;\n\tsize_t right = array_size - 1;\n\twhile(left <= right) {\n\t\tsize_t mid = (left + right) / 2;\n\t\tif(array[mid] <= value) left = mid + 1; /*the value to find is more to the right*/\n\t\telse if(array[mid - 1] > value) right = mid - 1; /*the value to find is more to the left*/\n\t\telse return mid - 1;\n\t\t}\n\treturn array_size - 1;\n\t}\n\nstatic void addLengthDistance(uivector* values, size_t length, size_t distance)\n\t{\n\t/*values in encoded vector are those used by deflate:\n\t0-255: literal bytes\n\t256: end\n\t257-285: length/distance pair (length code, followed by extra length bits, distance code, extra distance bits)\n\t286-287: invalid*/\n\n\tunsigned length_code = (unsigned)searchCodeIndex(LENGTHBASE, 29, length);\n\tunsigned extra_length = (unsigned)(length - LENGTHBASE[length_code]);\n\tunsigned dist_code = (unsigned)searchCodeIndex(DISTANCEBASE, 30, distance);\n\tunsigned extra_distance = (unsigned)(distance - DISTANCEBASE[dist_code]);\n\n\tuivector_push_back(values, length_code + FIRST_LENGTH_CODE_INDEX);\n\tuivector_push_back(values, extra_length);\n\tuivector_push_back(values, dist_code);\n\tuivector_push_back(values, extra_distance);\n\t}\n\nstatic const unsigned HASH_BIT_MASK = 65535;\nstatic const unsigned HASH_NUM_VALUES = 65536;\nstatic const unsigned HASH_NUM_CHARACTERS = 3;\nstatic const unsigned HASH_SHIFT = 2;\n/*\nThe HASH_NUM_CHARACTERS value is used to make encoding faster by using longer\nsequences to generate a hash value from the stream bytes. Setting it to 3\ngives exactly the same compression as the brute force method, since deflate's\nrun length encoding starts with lengths of 3. Setting it to higher values,\nlike 6, can make the encoding faster (not always though!), but will cause the\nencoding to miss any length between 3 and this value, so that the compression\nmay be worse (but this can vary too depending on the image, sometimes it is\neven a bit better instead).\nThe HASH_NUM_VALUES is the amount of unique possible hash values that\ncombinations of bytes can give, the higher it is the more memory is needed, but\nif it's too low the advantage of hashing is gone.\n*/\n\ntypedef struct Hash {\n\tint* head; /*hash value to head circular pos*/\n\tint* val; /*circular pos to hash value*/\n\t/*circular pos to prev circular pos*/\n\tunsigned short* chain;\n\tunsigned short* zeros;\n\t} Hash;\n\nstatic unsigned hash_init(Hash* hash, unsigned windowsize)\n\t{\n\tunsigned i;\n\thash->head = (int*)lodepng_malloc(sizeof(int) * HASH_NUM_VALUES);\n\thash->val = (int*)lodepng_malloc(sizeof(int) * windowsize);\n\thash->chain = (unsigned short*)lodepng_malloc(sizeof(unsigned short) * windowsize);\n\thash->zeros = (unsigned short*)lodepng_malloc(sizeof(unsigned short) * windowsize);\n\n\tif(!hash->head || !hash->val || !hash->chain || !hash->zeros) return 83; /*alloc fail*/\n\n\t/*initialize hash table*/\n\tfor(i = 0; i < HASH_NUM_VALUES; i++) hash->head[i] = -1;\n\tfor(i = 0; i < windowsize; i++) hash->val[i] = -1;\n\tfor(i = 0; i < windowsize; i++) hash->chain[i] = i; /*same value as index indicates uninitialized*/\n\n\treturn 0;\n\t}\n\nstatic void hash_cleanup(Hash* hash)\n\t{\n\tlodepng_free(hash->head);\n\tlodepng_free(hash->val);\n\tlodepng_free(hash->chain);\n\tlodepng_free(hash->zeros);\n\t}\n\nstatic unsigned getHash(const unsigned char* data, size_t size, size_t pos)\n\t{\n\tunsigned result = 0;\n\tif (HASH_NUM_CHARACTERS == 3 && pos + 2 < size) {\n\t\tresult ^= (data[pos + 0] << (0 * HASH_SHIFT));\n\t\tresult ^= (data[pos + 1] << (1 * HASH_SHIFT));\n\t\tresult ^= (data[pos + 2] << (2 * HASH_SHIFT));\n\t\t}\n\telse {\n\t\tsize_t amount, i;\n\t\tif(pos >= size) return 0;\n\t\tamount = HASH_NUM_CHARACTERS;\n\t\tif(pos + amount >= size) amount = size - pos;\n\t\tfor(i = 0; i < amount; i++) result ^= (data[pos + i] << (i * HASH_SHIFT));\n\t\t}\n\treturn result & HASH_BIT_MASK;\n\t}\n\nstatic unsigned countZeros(const unsigned char* data, size_t size, size_t pos)\n\t{\n\tconst unsigned char* start = data + pos;\n\tconst unsigned char* end = start + MAX_SUPPORTED_DEFLATE_LENGTH;\n\tif(end > data + size) end = data + size;\n\tdata = start;\n\twhile (data != end && *data == 0) data++;\n\t/*subtracting two addresses returned as 32-bit number (max value is MAX_SUPPORTED_DEFLATE_LENGTH)*/\n\treturn (unsigned)(data - start);\n\t}\n\n/*wpos = pos & (windowsize - 1)*/\nstatic void updateHashChain(Hash* hash, size_t wpos, int hashval)\n\t{\n\thash->val[wpos] = hashval;\n\tif(hash->head[hashval] != -1) hash->chain[wpos] = hash->head[hashval];\n\thash->head[hashval] = wpos;\n\t}\n\n/*\nLZ77-encode the data. Return value is error code. The input are raw bytes, the output\nis in the form of unsigned integers with codes representing for example literal bytes, or\nlength/distance pairs.\nIt uses a hash table technique to let it encode faster. When doing LZ77 encoding, a\nsliding window (of windowsize) is used, and all past bytes in that window can be used as\nthe \"dictionary\". A brute force search through all possible distances would be slow, and\nthis hash technique is one out of several ways to speed this up.\n*/\nstatic unsigned encodeLZ77(uivector* out, Hash* hash,\n                           const unsigned char* in, size_t inpos, size_t insize, unsigned windowsize,\n                           unsigned minmatch, unsigned nicematch, unsigned lazymatching)\n\t{\n\tunsigned pos, i, error = 0;\n\t/*for large window lengths, assume the user wants no compression loss. Otherwise, max hash chain length speedup.*/\n\tunsigned maxchainlength = windowsize >= 8192 ? windowsize : windowsize / 8;\n\tunsigned maxlazymatch = windowsize >= 8192 ? MAX_SUPPORTED_DEFLATE_LENGTH : 64;\n\n\tunsigned usezeros = 1; /*not sure if setting it to false for windowsize < 8192 is better or worse*/\n\tunsigned numzeros = 0;\n\n\tunsigned offset; /*the offset represents the distance in LZ77 terminology*/\n\tunsigned length;\n\tunsigned lazy = 0;\n\tunsigned lazylength = 0, lazyoffset = 0;\n\tunsigned hashval;\n\tunsigned current_offset, current_length;\n\tconst unsigned char *lastptr, *foreptr, *backptr;\n\tunsigned hashpos, prevpos;\n\n\tif(windowsize <= 0 || windowsize > 32768) return 60; /*error: windowsize smaller/larger than allowed*/\n\tif((windowsize & (windowsize - 1)) != 0) return 90; /*error: must be power of two*/\n\n\tif(nicematch > MAX_SUPPORTED_DEFLATE_LENGTH) nicematch = MAX_SUPPORTED_DEFLATE_LENGTH;\n\n\tfor(pos = inpos; pos < insize; pos++) {\n\t\tsize_t wpos = pos & (windowsize - 1); /*position for in 'circular' hash buffers*/\n\t\tunsigned chainlength = 0;\n\n\t\thashval = getHash(in, insize, pos);\n\t\tupdateHashChain(hash, wpos, hashval);\n\n\t\tif(usezeros && hashval == 0) {\n\t\t\tif (numzeros == 0) numzeros = countZeros(in, insize, pos);\n\t\t\telse if (pos + numzeros >= insize || in[pos + numzeros - 1] != 0) numzeros--;\n\t\t\thash->zeros[wpos] = numzeros;\n\t\t\t}\n\t\telse {\n\t\t\tnumzeros = 0;\n\t\t\t}\n\n\t\t/*the length and offset found for the current position*/\n\t\tlength = 0;\n\t\toffset = 0;\n\n\t\tprevpos = hash->head[hashval];\n\t\thashpos = hash->chain[prevpos];\n\n\t\tlastptr = &in[insize < pos + MAX_SUPPORTED_DEFLATE_LENGTH ? insize : pos + MAX_SUPPORTED_DEFLATE_LENGTH];\n\n\t\t/*search for the longest string*/\n\t\tfor(;;) {\n\t\t\t/*stop when went completely around the circular buffer*/\n\t\t\tif(prevpos < wpos && hashpos > prevpos && hashpos <= wpos) break;\n\t\t\tif(prevpos > wpos && (hashpos <= wpos || hashpos > prevpos)) break;\n\t\t\tif(chainlength++ >= maxchainlength) break;\n\n\t\t\tcurrent_offset = hashpos <= wpos ? wpos - hashpos : wpos - hashpos + windowsize;\n\t\t\tif(current_offset > 0) {\n\t\t\t\t/*test the next characters*/\n\t\t\t\tforeptr = &in[pos];\n\t\t\t\tbackptr = &in[pos - current_offset];\n\n\t\t\t\t/*common case in PNGs is lots of zeros. Quickly skip over them as a speedup*/\n\t\t\t\tif(usezeros && hashval == 0 && hash->val[hashpos] == 0 /*hashval[hashpos] may be out of date*/) {\n\t\t\t\t\tunsigned skip = hash->zeros[hashpos];\n\t\t\t\t\tif(skip > numzeros) skip = numzeros;\n\t\t\t\t\tbackptr += skip;\n\t\t\t\t\tforeptr += skip;\n\t\t\t\t\t}\n\n\t\t\t\twhile(foreptr != lastptr && *backptr == *foreptr) { /*maximum supported length by deflate is max length*/\n\t\t\t\t\t++backptr;\n\t\t\t\t\t++foreptr;\n\t\t\t\t\t}\n\t\t\t\tcurrent_length = (unsigned)(foreptr - &in[pos]);\n\n\t\t\t\tif(current_length > length) {\n\t\t\t\t\tlength = current_length; /*the longest length*/\n\t\t\t\t\toffset = current_offset; /*the offset that is related to this longest length*/\n\t\t\t\t\t/*jump out once a length of max length is found (speed gain). This also jumps\n\t\t\t\t\tout if length is MAX_SUPPORTED_DEFLATE_LENGTH*/\n\t\t\t\t\tif(current_length >= nicematch) break;\n\t\t\t\t\t}\n\t\t\t\t}\n\n\t\t\tif(hashpos == hash->chain[hashpos]) break;\n\n\t\t\tprevpos = hashpos;\n\t\t\thashpos = hash->chain[hashpos];\n\t\t\t}\n\n\t\tif(lazymatching) {\n\t\t\tif(!lazy && length >= 3 && length <= maxlazymatch && length < MAX_SUPPORTED_DEFLATE_LENGTH) {\n\t\t\t\tlazy = 1;\n\t\t\t\tlazylength = length;\n\t\t\t\tlazyoffset = offset;\n\t\t\t\tcontinue; /*try the next byte*/\n\t\t\t\t}\n\t\t\tif(lazy) {\n\t\t\t\tlazy = 0;\n\t\t\t\tif(pos == 0) ERROR_BREAK(81);\n\t\t\t\tif(length > lazylength + 1) {\n\t\t\t\t\t/*push the previous character as literal*/\n\t\t\t\t\tif(!uivector_push_back(out, in[pos - 1])) ERROR_BREAK(83 /*alloc fail*/);\n\t\t\t\t\t}\n\t\t\t\telse {\n\t\t\t\t\tlength = lazylength;\n\t\t\t\t\toffset = lazyoffset;\n\t\t\t\t\thash->head[hashval] = -1; /*the same hashchain update will be done, this ensures no wrong alteration*/\n\t\t\t\t\tpos--;\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t}\n\t\tif(length >= 3 && offset > windowsize) ERROR_BREAK(86 /*too big (or overflown negative) offset*/);\n\n\t\t/*encode it as length/distance pair or literal value*/\n\t\tif(length < 3) { /*only lengths of 3 or higher are supported as length/distance pair*/\n\t\t\tif(!uivector_push_back(out, in[pos])) ERROR_BREAK(83 /*alloc fail*/);\n\t\t\t}\n\t\telse if(length < minmatch || (length == 3 && offset > 4096)) {\n\t\t\t/*compensate for the fact that longer offsets have more extra bits, a\n\t\t\tlength of only 3 may be not worth it then*/\n\t\t\tif(!uivector_push_back(out, in[pos])) ERROR_BREAK(83 /*alloc fail*/);\n\t\t\t}\n\t\telse {\n\t\t\taddLengthDistance(out, length, offset);\n\t\t\tfor(i = 1; i < length; i++) {\n\t\t\t\tpos++;\n\t\t\t\twpos = pos & (windowsize - 1);\n\t\t\t\thashval = getHash(in, insize, pos);\n\t\t\t\tupdateHashChain(hash, wpos, hashval);\n\t\t\t\tif(usezeros && hashval == 0) {\n\t\t\t\t\tif (numzeros == 0) numzeros = countZeros(in, insize, pos);\n\t\t\t\t\telse if (pos + numzeros >= insize || in[pos + numzeros - 1] != 0) numzeros--;\n\t\t\t\t\thash->zeros[wpos] = numzeros;\n\t\t\t\t\t}\n\t\t\t\telse {\n\t\t\t\t\tnumzeros = 0;\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t}\n\t\t} /*end of the loop through each character of input*/\n\n\treturn error;\n\t}\n\n/* /////////////////////////////////////////////////////////////////////////// */\n\nstatic unsigned deflateNoCompression(ucvector* out, const unsigned char* data, size_t datasize)\n\t{\n\t/*non compressed deflate block data: 1 bit BFINAL,2 bits BTYPE,(5 bits): it jumps to start of next byte,\n\t2 bytes LEN, 2 bytes NLEN, LEN bytes literal DATA*/\n\n\tsize_t i, j, numdeflateblocks = (datasize + 65534) / 65535;\n\tunsigned datapos = 0;\n\tfor(i = 0; i < numdeflateblocks; i++) {\n\t\tunsigned BFINAL, BTYPE, LEN, NLEN;\n\t\tunsigned char firstbyte;\n\n\t\tBFINAL = (i == numdeflateblocks - 1);\n\t\tBTYPE = 0;\n\n\t\tfirstbyte = (unsigned char)(BFINAL + ((BTYPE & 1) << 1) + ((BTYPE & 2) << 1));\n\t\tucvector_push_back(out, firstbyte);\n\n\t\tLEN = 65535;\n\t\tif(datasize - datapos < 65535) LEN = (unsigned)datasize - datapos;\n\t\tNLEN = 65535 - LEN;\n\n\t\tucvector_push_back(out, (unsigned char)(LEN % 256));\n\t\tucvector_push_back(out, (unsigned char)(LEN / 256));\n\t\tucvector_push_back(out, (unsigned char)(NLEN % 256));\n\t\tucvector_push_back(out, (unsigned char)(NLEN / 256));\n\n\t\t/*Decompressed data*/\n\t\tfor(j = 0; j < 65535 && datapos < datasize; j++) {\n\t\t\tucvector_push_back(out, data[datapos++]);\n\t\t\t}\n\t\t}\n\n\treturn 0;\n\t}\n\n/*\nwrite the lz77-encoded data, which has lit, len and dist codes, to compressed stream using huffman trees.\ntree_ll: the tree for lit and len codes.\ntree_d: the tree for distance codes.\n*/\nstatic void writeLZ77data(size_t* bp, ucvector* out, const uivector* lz77_encoded,\n                          const HuffmanTree* tree_ll, const HuffmanTree* tree_d)\n\t{\n\tsize_t i = 0;\n\tfor(i = 0; i < lz77_encoded->size; i++) {\n\t\tunsigned val = lz77_encoded->data[i];\n\t\taddHuffmanSymbol(bp, out, HuffmanTree_getCode(tree_ll, val), HuffmanTree_getLength(tree_ll, val));\n\t\tif(val > 256) { /*for a length code, 3 more things have to be added*/\n\t\t\tunsigned length_index = val - FIRST_LENGTH_CODE_INDEX;\n\t\t\tunsigned n_length_extra_bits = LENGTHEXTRA[length_index];\n\t\t\tunsigned length_extra_bits = lz77_encoded->data[++i];\n\n\t\t\tunsigned distance_code = lz77_encoded->data[++i];\n\n\t\t\tunsigned distance_index = distance_code;\n\t\t\tunsigned n_distance_extra_bits = DISTANCEEXTRA[distance_index];\n\t\t\tunsigned distance_extra_bits = lz77_encoded->data[++i];\n\n\t\t\taddBitsToStream(bp, out, length_extra_bits, n_length_extra_bits);\n\t\t\taddHuffmanSymbol(bp, out, HuffmanTree_getCode(tree_d, distance_code),\n\t\t\t                 HuffmanTree_getLength(tree_d, distance_code));\n\t\t\taddBitsToStream(bp, out, distance_extra_bits, n_distance_extra_bits);\n\t\t\t}\n\t\t}\n\t}\n\n/*Deflate for a block of type \"dynamic\", that is, with freely, optimally, created huffman trees*/\nstatic unsigned deflateDynamic(ucvector* out, size_t* bp, Hash* hash,\n                               const unsigned char* data, size_t datapos, size_t dataend,\n                               const LodePNGCompressSettings* settings, int final)\n\t{\n\tunsigned error = 0;\n\n\t/*\n\tA block is compressed as follows: The PNG data is lz77 encoded, resulting in\n\tliteral bytes and length/distance pairs. This is then huffman compressed with\n\ttwo huffman trees. One huffman tree is used for the lit and len values (\"ll\"),\n\tanother huffman tree is used for the dist values (\"d\"). These two trees are\n\tstored using their code lengths, and to compress even more these code lengths\n\tare also run-length encoded and huffman compressed. This gives a huffman tree\n\tof code lengths \"cl\". The code lenghts used to describe this third tree are\n\tthe code length code lengths (\"clcl\").\n\t*/\n\n\t/*The lz77 encoded data, represented with integers since there will also be length and distance codes in it*/\n\tuivector lz77_encoded;\n\tHuffmanTree tree_ll; /*tree for lit,len values*/\n\tHuffmanTree tree_d; /*tree for distance codes*/\n\tHuffmanTree tree_cl; /*tree for encoding the code lengths representing tree_ll and tree_d*/\n\tuivector frequencies_ll; /*frequency of lit,len codes*/\n\tuivector frequencies_d; /*frequency of dist codes*/\n\tuivector frequencies_cl; /*frequency of code length codes*/\n\tuivector bitlen_lld; /*lit,len,dist code lenghts (int bits), literally (without repeat codes).*/\n\tuivector bitlen_lld_e; /*bitlen_lld encoded with repeat codes (this is a rudemtary run length compression)*/\n\t/*bitlen_cl is the code length code lengths (\"clcl\"). The bit lengths of codes to represent tree_cl\n\t(these are written as is in the file, it would be crazy to compress these using yet another huffman\n\ttree that needs to be represented by yet another set of code lengths)*/\n\tuivector bitlen_cl;\n\tsize_t datasize = dataend - datapos;\n\n\t/*\n\tDue to the huffman compression of huffman tree representations (\"two levels\"), there are some anologies:\n\tbitlen_lld is to tree_cl what data is to tree_ll and tree_d.\n\tbitlen_lld_e is to bitlen_lld what lz77_encoded is to data.\n\tbitlen_cl is to bitlen_lld_e what bitlen_lld is to lz77_encoded.\n\t*/\n\n\tunsigned BFINAL = final;\n\tsize_t numcodes_ll, numcodes_d, i;\n\tunsigned HLIT, HDIST, HCLEN;\n\n\tuivector_init(&lz77_encoded);\n\tHuffmanTree_init(&tree_ll);\n\tHuffmanTree_init(&tree_d);\n\tHuffmanTree_init(&tree_cl);\n\tuivector_init(&frequencies_ll);\n\tuivector_init(&frequencies_d);\n\tuivector_init(&frequencies_cl);\n\tuivector_init(&bitlen_lld);\n\tuivector_init(&bitlen_lld_e);\n\tuivector_init(&bitlen_cl);\n\n\t/*This while loop never loops due to a break at the end, it is here to\n\tallow breaking out of it to the cleanup phase on error conditions.*/\n\twhile(!error) {\n\t\tif(settings->use_lz77) {\n\t\t\terror = encodeLZ77(&lz77_encoded, hash, data, datapos, dataend, settings->windowsize,\n\t\t\t                   settings->minmatch, settings->nicematch, settings->lazymatching);\n\t\t\tif(error) break;\n\t\t\t}\n\t\telse {\n\t\t\tif(!uivector_resize(&lz77_encoded, datasize)) ERROR_BREAK(83 /*alloc fail*/);\n\t\t\tfor(i = datapos; i < dataend; i++) lz77_encoded.data[i] = data[i]; /*no LZ77, but still will be Huffman compressed*/\n\t\t\t}\n\n\t\tif(!uivector_resizev(&frequencies_ll, 286, 0)) ERROR_BREAK(83 /*alloc fail*/);\n\t\tif(!uivector_resizev(&frequencies_d, 30, 0)) ERROR_BREAK(83 /*alloc fail*/);\n\n\t\t/*Count the frequencies of lit, len and dist codes*/\n\t\tfor(i = 0; i < lz77_encoded.size; i++) {\n\t\t\tunsigned symbol = lz77_encoded.data[i];\n\t\t\tfrequencies_ll.data[symbol]++;\n\t\t\tif(symbol > 256) {\n\t\t\t\tunsigned dist = lz77_encoded.data[i + 2];\n\t\t\t\tfrequencies_d.data[dist]++;\n\t\t\t\ti += 3;\n\t\t\t\t}\n\t\t\t}\n\t\tfrequencies_ll.data[256] = 1; /*there will be exactly 1 end code, at the end of the block*/\n\n\t\t/*Make both huffman trees, one for the lit and len codes, one for the dist codes*/\n\t\terror = HuffmanTree_makeFromFrequencies(&tree_ll, frequencies_ll.data, 257, frequencies_ll.size, 15);\n\t\tif(error) break;\n\t\t/*2, not 1, is chosen for mincodes: some buggy PNG decoders require at least 2 symbols in the dist tree*/\n\t\terror = HuffmanTree_makeFromFrequencies(&tree_d, frequencies_d.data, 2, frequencies_d.size, 15);\n\t\tif(error) break;\n\n\t\tnumcodes_ll = tree_ll.numcodes;\n\t\tif(numcodes_ll > 286) numcodes_ll = 286;\n\t\tnumcodes_d = tree_d.numcodes;\n\t\tif(numcodes_d > 30) numcodes_d = 30;\n\t\t/*store the code lengths of both generated trees in bitlen_lld*/\n\t\tfor(i = 0; i < numcodes_ll; i++) uivector_push_back(&bitlen_lld, HuffmanTree_getLength(&tree_ll, (unsigned)i));\n\t\tfor(i = 0; i < numcodes_d; i++) uivector_push_back(&bitlen_lld, HuffmanTree_getLength(&tree_d, (unsigned)i));\n\n\t\t/*run-length compress bitlen_ldd into bitlen_lld_e by using repeat codes 16 (copy length 3-6 times),\n\t\t17 (3-10 zeroes), 18 (11-138 zeroes)*/\n\t\tfor(i = 0; i < (unsigned)bitlen_lld.size; i++) {\n\t\t\tunsigned j = 0; /*amount of repititions*/\n\t\t\twhile(i + j + 1 < (unsigned)bitlen_lld.size && bitlen_lld.data[i + j + 1] == bitlen_lld.data[i]) j++;\n\n\t\t\tif(bitlen_lld.data[i] == 0 && j >= 2) { /*repeat code for zeroes*/\n\t\t\t\tj++; /*include the first zero*/\n\t\t\t\tif(j <= 10) { /*repeat code 17 supports max 10 zeroes*/\n\t\t\t\t\tuivector_push_back(&bitlen_lld_e, 17);\n\t\t\t\t\tuivector_push_back(&bitlen_lld_e, j - 3);\n\t\t\t\t\t}\n\t\t\t\telse {   /*repeat code 18 supports max 138 zeroes*/\n\t\t\t\t\tif(j > 138) j = 138;\n\t\t\t\t\tuivector_push_back(&bitlen_lld_e, 18);\n\t\t\t\t\tuivector_push_back(&bitlen_lld_e, j - 11);\n\t\t\t\t\t}\n\t\t\t\ti += (j - 1);\n\t\t\t\t}\n\t\t\telse if(j >= 3) {   /*repeat code for value other than zero*/\n\t\t\t\tsize_t k;\n\t\t\t\tunsigned num = j / 6, rest = j % 6;\n\t\t\t\tuivector_push_back(&bitlen_lld_e, bitlen_lld.data[i]);\n\t\t\t\tfor(k = 0; k < num; k++) {\n\t\t\t\t\tuivector_push_back(&bitlen_lld_e, 16);\n\t\t\t\t\tuivector_push_back(&bitlen_lld_e, 6 - 3);\n\t\t\t\t\t}\n\t\t\t\tif(rest >= 3) {\n\t\t\t\t\tuivector_push_back(&bitlen_lld_e, 16);\n\t\t\t\t\tuivector_push_back(&bitlen_lld_e, rest - 3);\n\t\t\t\t\t}\n\t\t\t\telse j -= rest;\n\t\t\t\ti += j;\n\t\t\t\t}\n\t\t\telse {   /*too short to benefit from repeat code*/\n\t\t\t\tuivector_push_back(&bitlen_lld_e, bitlen_lld.data[i]);\n\t\t\t\t}\n\t\t\t}\n\n\t\t/*generate tree_cl, the huffmantree of huffmantrees*/\n\n\t\tif(!uivector_resizev(&frequencies_cl, NUM_CODE_LENGTH_CODES, 0)) ERROR_BREAK(83 /*alloc fail*/);\n\t\tfor(i = 0; i < bitlen_lld_e.size; i++) {\n\t\t\tfrequencies_cl.data[bitlen_lld_e.data[i]]++;\n\t\t\t/*after a repeat code come the bits that specify the number of repetitions,\n\t\t\tthose don't need to be in the frequencies_cl calculation*/\n\t\t\tif(bitlen_lld_e.data[i] >= 16) i++;\n\t\t\t}\n\n\t\terror = HuffmanTree_makeFromFrequencies(&tree_cl, frequencies_cl.data,\n\t\t                                        frequencies_cl.size, frequencies_cl.size, 7);\n\t\tif(error) break;\n\n\t\tif(!uivector_resize(&bitlen_cl, tree_cl.numcodes)) ERROR_BREAK(83 /*alloc fail*/);\n\t\tfor(i = 0; i < tree_cl.numcodes; i++) {\n\t\t\t/*lenghts of code length tree is in the order as specified by deflate*/\n\t\t\tbitlen_cl.data[i] = HuffmanTree_getLength(&tree_cl, CLCL_ORDER[i]);\n\t\t\t}\n\t\twhile(bitlen_cl.data[bitlen_cl.size - 1] == 0 && bitlen_cl.size > 4) {\n\t\t\t/*remove zeros at the end, but minimum size must be 4*/\n\t\t\tif(!uivector_resize(&bitlen_cl, bitlen_cl.size - 1)) ERROR_BREAK(83 /*alloc fail*/);\n\t\t\t}\n\t\tif(error) break;\n\n\t\t/*\n\t\tWrite everything into the output\n\n\t\tAfter the BFINAL and BTYPE, the dynamic block consists out of the following:\n\t\t- 5 bits HLIT, 5 bits HDIST, 4 bits HCLEN\n\t\t- (HCLEN+4)*3 bits code lengths of code length alphabet\n\t\t- HLIT + 257 code lenghts of lit/length alphabet (encoded using the code length\n\t\talphabet, + possible repetition codes 16, 17, 18)\n\t\t- HDIST + 1 code lengths of distance alphabet (encoded using the code length\n\t\talphabet, + possible repetition codes 16, 17, 18)\n\t\t- compressed data\n\t\t- 256 (end code)\n\t\t*/\n\n\t\t/*Write block type*/\n\t\taddBitToStream(bp, out, BFINAL);\n\t\taddBitToStream(bp, out, 0); /*first bit of BTYPE \"dynamic\"*/\n\t\taddBitToStream(bp, out, 1); /*second bit of BTYPE \"dynamic\"*/\n\n\t\t/*write the HLIT, HDIST and HCLEN values*/\n\t\tHLIT = (unsigned)(numcodes_ll - 257);\n\t\tHDIST = (unsigned)(numcodes_d - 1);\n\t\tHCLEN = (unsigned)bitlen_cl.size - 4;\n\t\t/*trim zeroes for HCLEN. HLIT and HDIST were already trimmed at tree creation*/\n\t\twhile(!bitlen_cl.data[HCLEN + 4 - 1] && HCLEN > 0) HCLEN--;\n\t\taddBitsToStream(bp, out, HLIT, 5);\n\t\taddBitsToStream(bp, out, HDIST, 5);\n\t\taddBitsToStream(bp, out, HCLEN, 4);\n\n\t\t/*write the code lenghts of the code length alphabet*/\n\t\tfor(i = 0; i < HCLEN + 4; i++) addBitsToStream(bp, out, bitlen_cl.data[i], 3);\n\n\t\t/*write the lenghts of the lit/len AND the dist alphabet*/\n\t\tfor(i = 0; i < bitlen_lld_e.size; i++) {\n\t\t\taddHuffmanSymbol(bp, out, HuffmanTree_getCode(&tree_cl, bitlen_lld_e.data[i]),\n\t\t\t                 HuffmanTree_getLength(&tree_cl, bitlen_lld_e.data[i]));\n\t\t\t/*extra bits of repeat codes*/\n\t\t\tif(bitlen_lld_e.data[i] == 16) addBitsToStream(bp, out, bitlen_lld_e.data[++i], 2);\n\t\t\telse if(bitlen_lld_e.data[i] == 17) addBitsToStream(bp, out, bitlen_lld_e.data[++i], 3);\n\t\t\telse if(bitlen_lld_e.data[i] == 18) addBitsToStream(bp, out, bitlen_lld_e.data[++i], 7);\n\t\t\t}\n\n\t\t/*write the compressed data symbols*/\n\t\twriteLZ77data(bp, out, &lz77_encoded, &tree_ll, &tree_d);\n\t\t/*error: the length of the end code 256 must be larger than 0*/\n\t\tif(HuffmanTree_getLength(&tree_ll, 256) == 0) ERROR_BREAK(64);\n\n\t\t/*write the end code*/\n\t\taddHuffmanSymbol(bp, out, HuffmanTree_getCode(&tree_ll, 256), HuffmanTree_getLength(&tree_ll, 256));\n\n\t\tbreak; /*end of error-while*/\n\t\t}\n\n\t/*cleanup*/\n\tuivector_cleanup(&lz77_encoded);\n\tHuffmanTree_cleanup(&tree_ll);\n\tHuffmanTree_cleanup(&tree_d);\n\tHuffmanTree_cleanup(&tree_cl);\n\tuivector_cleanup(&frequencies_ll);\n\tuivector_cleanup(&frequencies_d);\n\tuivector_cleanup(&frequencies_cl);\n\tuivector_cleanup(&bitlen_lld_e);\n\tuivector_cleanup(&bitlen_lld);\n\tuivector_cleanup(&bitlen_cl);\n\n\treturn error;\n\t}\n\nstatic unsigned deflateFixed(ucvector* out, size_t* bp, Hash* hash,\n                             const unsigned char* data,\n                             size_t datapos, size_t dataend,\n                             const LodePNGCompressSettings* settings, int final)\n\t{\n\tHuffmanTree tree_ll; /*tree for literal values and length codes*/\n\tHuffmanTree tree_d; /*tree for distance codes*/\n\n\tunsigned BFINAL = final;\n\tunsigned error = 0;\n\tsize_t i;\n\n\tHuffmanTree_init(&tree_ll);\n\tHuffmanTree_init(&tree_d);\n\n\tgenerateFixedLitLenTree(&tree_ll);\n\tgenerateFixedDistanceTree(&tree_d);\n\n\taddBitToStream(bp, out, BFINAL);\n\taddBitToStream(bp, out, 1); /*first bit of BTYPE*/\n\taddBitToStream(bp, out, 0); /*second bit of BTYPE*/\n\n\tif(settings->use_lz77) { /*LZ77 encoded*/\n\t\tuivector lz77_encoded;\n\t\tuivector_init(&lz77_encoded);\n\t\terror = encodeLZ77(&lz77_encoded, hash, data, datapos, dataend, settings->windowsize,\n\t\t                   settings->minmatch, settings->nicematch, settings->lazymatching);\n\t\tif(!error) writeLZ77data(bp, out, &lz77_encoded, &tree_ll, &tree_d);\n\t\tuivector_cleanup(&lz77_encoded);\n\t\t}\n\telse {   /*no LZ77, but still will be Huffman compressed*/\n\t\tfor(i = datapos; i < dataend; i++) {\n\t\t\taddHuffmanSymbol(bp, out, HuffmanTree_getCode(&tree_ll, data[i]), HuffmanTree_getLength(&tree_ll, data[i]));\n\t\t\t}\n\t\t}\n\t/*add END code*/\n\tif(!error) addHuffmanSymbol(bp, out, HuffmanTree_getCode(&tree_ll, 256), HuffmanTree_getLength(&tree_ll, 256));\n\n\t/*cleanup*/\n\tHuffmanTree_cleanup(&tree_ll);\n\tHuffmanTree_cleanup(&tree_d);\n\n\treturn error;\n\t}\n\nstatic unsigned lodepng_deflatev(ucvector* out, const unsigned char* in, size_t insize,\n                                 const LodePNGCompressSettings* settings)\n\t{\n\tunsigned error = 0;\n\tsize_t i, blocksize, numdeflateblocks;\n\tsize_t bp = 0; /*the bit pointer*/\n\tHash hash;\n\n\tif(settings->btype > 2) return 61;\n\telse if(settings->btype == 0) return deflateNoCompression(out, in, insize);\n\telse if(settings->btype == 1) blocksize = insize;\n\telse { /*if(settings->btype == 2)*/\n\t\tblocksize = insize / 8 + 8;\n\t\tif(blocksize < 65535) blocksize = 65535;\n\t\t}\n\n\tnumdeflateblocks = (insize + blocksize - 1) / blocksize;\n\tif(numdeflateblocks == 0) numdeflateblocks = 1;\n\n\terror = hash_init(&hash, settings->windowsize);\n\tif(error) return error;\n\n\tfor(i = 0; i < numdeflateblocks && !error; i++) {\n\t\tint final = i == numdeflateblocks - 1;\n\t\tsize_t start = i * blocksize;\n\t\tsize_t end = start + blocksize;\n\t\tif(end > insize) end = insize;\n\n\t\tif(settings->btype == 1) error = deflateFixed(out, &bp, &hash, in, start, end, settings, final);\n\t\telse if(settings->btype == 2) error = deflateDynamic(out, &bp, &hash, in, start, end, settings, final);\n\t\t}\n\n\thash_cleanup(&hash);\n\n\treturn error;\n\t}\n\nunsigned lodepng_deflate(unsigned char** out, size_t* outsize,\n                         const unsigned char* in, size_t insize,\n                         const LodePNGCompressSettings* settings)\n\t{\n\tunsigned error;\n\tucvector v;\n\tucvector_init_buffer(&v, *out, *outsize);\n\terror = lodepng_deflatev(&v, in, insize, settings);\n\t*out = v.data;\n\t*outsize = v.size;\n\treturn error;\n\t}\n\nstatic unsigned deflate(unsigned char** out, size_t* outsize,\n                        const unsigned char* in, size_t insize,\n                        const LodePNGCompressSettings* settings)\n\t{\n\tif(settings->custom_deflate) {\n\t\treturn settings->custom_deflate(out, outsize, in, insize, settings);\n\t\t}\n\telse {\n\t\treturn lodepng_deflate(out, outsize, in, insize, settings);\n\t\t}\n\t}\n\n#endif /*LODEPNG_COMPILE_DECODER*/\n\n/* ////////////////////////////////////////////////////////////////////////// */\n/* / Adler32                                                                  */\n/* ////////////////////////////////////////////////////////////////////////// */\n\nstatic unsigned update_adler32(unsigned adler, const unsigned char* data, unsigned len)\n\t{\n\tunsigned s1 = adler & 0xffff;\n\tunsigned s2 = (adler >> 16) & 0xffff;\n\n\twhile(len > 0) {\n\t\t/*at least 5550 sums can be done before the sums overflow, saving a lot of module divisions*/\n\t\tunsigned amount = len > 5550 ? 5550 : len;\n\t\tlen -= amount;\n\t\twhile(amount > 0) {\n\t\t\ts1 += (*data++);\n\t\t\ts2 += s1;\n\t\t\tamount--;\n\t\t\t}\n\t\ts1 %= 65521;\n\t\ts2 %= 65521;\n\t\t}\n\n\treturn (s2 << 16) | s1;\n\t}\n\n/*Return the adler32 of the bytes data[0..len-1]*/\nstatic unsigned adler32(const unsigned char* data, unsigned len)\n\t{\n\treturn update_adler32(1L, data, len);\n\t}\n\n/* ////////////////////////////////////////////////////////////////////////// */\n/* / Zlib                                                                   / */\n/* ////////////////////////////////////////////////////////////////////////// */\n\n#ifdef LODEPNG_COMPILE_DECODER\n\nunsigned lodepng_zlib_decompress(unsigned char** out, size_t* outsize, const unsigned char* in,\n                                 size_t insize, const LodePNGDecompressSettings* settings)\n\t{\n\tunsigned error = 0;\n\tunsigned CM, CINFO, FDICT;\n\n\tif(insize < 2) return 53; /*error, size of zlib data too small*/\n\t/*read information from zlib header*/\n\tif((in[0] * 256 + in[1]) % 31 != 0) {\n\t\t/*error: 256 * in[0] + in[1] must be a multiple of 31, the FCHECK value is supposed to be made that way*/\n\t\treturn 24;\n\t\t}\n\n\tCM = in[0] & 15;\n\tCINFO = (in[0] >> 4) & 15;\n\t/*FCHECK = in[1] & 31;*/ /*FCHECK is already tested above*/\n\tFDICT = (in[1] >> 5) & 1;\n\t/*FLEVEL = (in[1] >> 6) & 3;*/ /*FLEVEL is not used here*/\n\n\tif(CM != 8 || CINFO > 7) {\n\t\t/*error: only compression method 8: inflate with sliding window of 32k is supported by the PNG spec*/\n\t\treturn 25;\n\t\t}\n\tif(FDICT != 0) {\n\t\t/*error: the specification of PNG says about the zlib stream:\n\t\t\"The additional flags shall not specify a preset dictionary.\"*/\n\t\treturn 26;\n\t\t}\n\n\terror = inflate(out, outsize, in + 2, insize - 2, settings);\n\tif(error) return error;\n\n\tif(!settings->ignore_adler32) {\n\t\tunsigned ADLER32 = lodepng_read32bitInt(&in[insize - 4]);\n\t\tunsigned checksum = adler32(*out, (unsigned)(*outsize));\n\t\tif(checksum != ADLER32) return 58; /*error, adler checksum not correct, data must be corrupted*/\n\t\t}\n\n\treturn 0; /*no error*/\n\t}\n\nstatic unsigned zlib_decompress(unsigned char** out, size_t* outsize, const unsigned char* in,\n                                size_t insize, const LodePNGDecompressSettings* settings)\n\t{\n\tif(settings->custom_zlib) {\n\t\treturn settings->custom_zlib(out, outsize, in, insize, settings);\n\t\t}\n\telse {\n\t\treturn lodepng_zlib_decompress(out, outsize, in, insize, settings);\n\t\t}\n\t}\n\n#endif /*LODEPNG_COMPILE_DECODER*/\n\n#ifdef LODEPNG_COMPILE_ENCODER\n\nunsigned lodepng_zlib_compress(unsigned char** out, size_t* outsize, const unsigned char* in,\n                               size_t insize, const LodePNGCompressSettings* settings)\n\t{\n\t/*initially, *out must be NULL and outsize 0, if you just give some random *out\n\tthat's pointing to a non allocated buffer, this'll crash*/\n\tucvector outv;\n\tsize_t i;\n\tunsigned error;\n\tunsigned char* deflatedata = 0;\n\tsize_t deflatesize = 0;\n\n\tunsigned ADLER32;\n\t/*zlib data: 1 byte CMF (CM+CINFO), 1 byte FLG, deflate data, 4 byte ADLER32 checksum of the Decompressed data*/\n\tunsigned CMF = 120; /*0b01111000: CM 8, CINFO 7. With CINFO 7, any window size up to 32768 can be used.*/\n\tunsigned FLEVEL = 0;\n\tunsigned FDICT = 0;\n\tunsigned CMFFLG = 256 * CMF + FDICT * 32 + FLEVEL * 64;\n\tunsigned FCHECK = 31 - CMFFLG % 31;\n\tCMFFLG += FCHECK;\n\n\t/*ucvector-controlled version of the output buffer, for dynamic array*/\n\tucvector_init_buffer(&outv, *out, *outsize);\n\n\tucvector_push_back(&outv, (unsigned char)(CMFFLG / 256));\n\tucvector_push_back(&outv, (unsigned char)(CMFFLG % 256));\n\n\terror = deflate(&deflatedata, &deflatesize, in, insize, settings);\n\n\tif(!error) {\n\t\tADLER32 = adler32(in, (unsigned)insize);\n\t\tfor(i = 0; i < deflatesize; i++) ucvector_push_back(&outv, deflatedata[i]);\n\t\tlodepng_free(deflatedata);\n\t\tlodepng_add32bitInt(&outv, ADLER32);\n\t\t}\n\n\t*out = outv.data;\n\t*outsize = outv.size;\n\n\treturn error;\n\t}\n\n/* compress using the default or custom zlib function */\nstatic unsigned zlib_compress(unsigned char** out, size_t* outsize, const unsigned char* in,\n                              size_t insize, const LodePNGCompressSettings* settings)\n\t{\n\tif(settings->custom_zlib) {\n\t\treturn settings->custom_zlib(out, outsize, in, insize, settings);\n\t\t}\n\telse {\n\t\treturn lodepng_zlib_compress(out, outsize, in, insize, settings);\n\t\t}\n\t}\n\n#endif /*LODEPNG_COMPILE_ENCODER*/\n\n#else /*no LODEPNG_COMPILE_ZLIB*/\n\n#ifdef LODEPNG_COMPILE_DECODER\nstatic unsigned zlib_decompress(unsigned char** out, size_t* outsize, const unsigned char* in,\n                                size_t insize, const LodePNGDecompressSettings* settings)\n\t{\n\tif (!settings->custom_zlib) return 87; /*no custom zlib function provided */\n\treturn settings->custom_zlib(out, outsize, in, insize, settings);\n\t}\n#endif /*LODEPNG_COMPILE_DECODER*/\n#ifdef LODEPNG_COMPILE_ENCODER\nstatic unsigned zlib_compress(unsigned char** out, size_t* outsize, const unsigned char* in,\n                              size_t insize, const LodePNGCompressSettings* settings)\n\t{\n\tif (!settings->custom_zlib) return 87; /*no custom zlib function provided */\n\treturn settings->custom_zlib(out, outsize, in, insize, settings);\n\t}\n#endif /*LODEPNG_COMPILE_ENCODER*/\n\n#endif /*LODEPNG_COMPILE_ZLIB*/\n\n/* ////////////////////////////////////////////////////////////////////////// */\n\n#ifdef LODEPNG_COMPILE_ENCODER\n\n/*this is a good tradeoff between speed and compression ratio*/\n#define DEFAULT_WINDOWSIZE 2048\n\nvoid lodepng_compress_settings_init(LodePNGCompressSettings* settings)\n\t{\n\t/*compress with dynamic huffman tree (not in the mathematical sense, just not the predefined one)*/\n\tsettings->btype = 2;\n\tsettings->use_lz77 = 1;\n\tsettings->windowsize = DEFAULT_WINDOWSIZE;\n\tsettings->minmatch = 3;\n\tsettings->nicematch = 128;\n\tsettings->lazymatching = 1;\n\n\tsettings->custom_zlib = 0;\n\tsettings->custom_deflate = 0;\n\tsettings->custom_context = 0;\n\t}\n\nconst LodePNGCompressSettings lodepng_default_compress_settings = {2, 1, DEFAULT_WINDOWSIZE, 3, 128, 1, 0, 0, 0};\n\n\n#endif /*LODEPNG_COMPILE_ENCODER*/\n\n#ifdef LODEPNG_COMPILE_DECODER\n\nvoid lodepng_decompress_settings_init(LodePNGDecompressSettings* settings)\n\t{\n\tsettings->ignore_adler32 = 0;\n\n\tsettings->custom_zlib = 0;\n\tsettings->custom_inflate = 0;\n\tsettings->custom_context = 0;\n\t}\n\nconst LodePNGDecompressSettings lodepng_default_decompress_settings = {0, 0, 0, 0};\n\n#endif /*LODEPNG_COMPILE_DECODER*/\n\n/* ////////////////////////////////////////////////////////////////////////// */\n/* ////////////////////////////////////////////////////////////////////////// */\n/* // End of Zlib related code. Begin of PNG related code.                 // */\n/* ////////////////////////////////////////////////////////////////////////// */\n/* ////////////////////////////////////////////////////////////////////////// */\n\n#ifdef LODEPNG_COMPILE_PNG\n\n/* ////////////////////////////////////////////////////////////////////////// */\n/* / CRC32                                                                  / */\n/* ////////////////////////////////////////////////////////////////////////// */\n\n/* CRC polynomial: 0xedb88320 */\nstatic unsigned lodepng_crc32_table[256] = {\n\t0u, 1996959894u, 3993919788u, 2567524794u,  124634137u, 1886057615u, 3915621685u, 2657392035u,\n\t249268274u, 2044508324u, 3772115230u, 2547177864u,  162941995u, 2125561021u, 3887607047u, 2428444049u,\n\t498536548u, 1789927666u, 4089016648u, 2227061214u,  450548861u, 1843258603u, 4107580753u, 2211677639u,\n\t325883990u, 1684777152u, 4251122042u, 2321926636u,  335633487u, 1661365465u, 4195302755u, 2366115317u,\n\t997073096u, 1281953886u, 3579855332u, 2724688242u, 1006888145u, 1258607687u, 3524101629u, 2768942443u,\n\t901097722u, 1119000684u, 3686517206u, 2898065728u,  853044451u, 1172266101u, 3705015759u, 2882616665u,\n\t651767980u, 1373503546u, 3369554304u, 3218104598u,  565507253u, 1454621731u, 3485111705u, 3099436303u,\n\t671266974u, 1594198024u, 3322730930u, 2970347812u,  795835527u, 1483230225u, 3244367275u, 3060149565u,\n\t1994146192u,   31158534u, 2563907772u, 4023717930u, 1907459465u,  112637215u, 2680153253u, 3904427059u,\n\t2013776290u,  251722036u, 2517215374u, 3775830040u, 2137656763u,  141376813u, 2439277719u, 3865271297u,\n\t1802195444u,  476864866u, 2238001368u, 4066508878u, 1812370925u,  453092731u, 2181625025u, 4111451223u,\n\t1706088902u,  314042704u, 2344532202u, 4240017532u, 1658658271u,  366619977u, 2362670323u, 4224994405u,\n\t1303535960u,  984961486u, 2747007092u, 3569037538u, 1256170817u, 1037604311u, 2765210733u, 3554079995u,\n\t1131014506u,  879679996u, 2909243462u, 3663771856u, 1141124467u,  855842277u, 2852801631u, 3708648649u,\n\t1342533948u,  654459306u, 3188396048u, 3373015174u, 1466479909u,  544179635u, 3110523913u, 3462522015u,\n\t1591671054u,  702138776u, 2966460450u, 3352799412u, 1504918807u,  783551873u, 3082640443u, 3233442989u,\n\t3988292384u, 2596254646u,   62317068u, 1957810842u, 3939845945u, 2647816111u,   81470997u, 1943803523u,\n\t3814918930u, 2489596804u,  225274430u, 2053790376u, 3826175755u, 2466906013u,  167816743u, 2097651377u,\n\t4027552580u, 2265490386u,  503444072u, 1762050814u, 4150417245u, 2154129355u,  426522225u, 1852507879u,\n\t4275313526u, 2312317920u,  282753626u, 1742555852u, 4189708143u, 2394877945u,  397917763u, 1622183637u,\n\t3604390888u, 2714866558u,  953729732u, 1340076626u, 3518719985u, 2797360999u, 1068828381u, 1219638859u,\n\t3624741850u, 2936675148u,  906185462u, 1090812512u, 3747672003u, 2825379669u,  829329135u, 1181335161u,\n\t3412177804u, 3160834842u,  628085408u, 1382605366u, 3423369109u, 3138078467u,  570562233u, 1426400815u,\n\t3317316542u, 2998733608u,  733239954u, 1555261956u, 3268935591u, 3050360625u,  752459403u, 1541320221u,\n\t2607071920u, 3965973030u, 1969922972u,   40735498u, 2617837225u, 3943577151u, 1913087877u,   83908371u,\n\t2512341634u, 3803740692u, 2075208622u,  213261112u, 2463272603u, 3855990285u, 2094854071u,  198958881u,\n\t2262029012u, 4057260610u, 1759359992u,  534414190u, 2176718541u, 4139329115u, 1873836001u,  414664567u,\n\t2282248934u, 4279200368u, 1711684554u,  285281116u, 2405801727u, 4167216745u, 1634467795u,  376229701u,\n\t2685067896u, 3608007406u, 1308918612u,  956543938u, 2808555105u, 3495958263u, 1231636301u, 1047427035u,\n\t2932959818u, 3654703836u, 1088359270u,  936918000u, 2847714899u, 3736837829u, 1202900863u,  817233897u,\n\t3183342108u, 3401237130u, 1404277552u,  615818150u, 3134207493u, 3453421203u, 1423857449u,  601450431u,\n\t3009837614u, 3294710456u, 1567103746u,  711928724u, 3020668471u, 3272380065u, 1510334235u,  755167117u\n\t};\n\n/*Return the CRC of the bytes buf[0..len-1].*/\nunsigned lodepng_crc32(const unsigned char* buf, size_t len)\n\t{\n\tunsigned c = 0xffffffffL;\n\tsize_t n;\n\n\tfor(n = 0; n < len; n++) {\n\t\tc = lodepng_crc32_table[(c ^ buf[n]) & 0xff] ^ (c >> 8);\n\t\t}\n\treturn c ^ 0xffffffffL;\n\t}\n\n/* ////////////////////////////////////////////////////////////////////////// */\n/* / Reading and writing single bits and bytes from/to stream for LodePNG   / */\n/* ////////////////////////////////////////////////////////////////////////// */\n\nstatic unsigned char readBitFromReversedStream(size_t* bitpointer, const unsigned char* bitstream)\n\t{\n\tunsigned char result = (unsigned char)((bitstream[(*bitpointer) >> 3] >> (7 - ((*bitpointer) & 0x7))) & 1);\n\t(*bitpointer)++;\n\treturn result;\n\t}\n\nstatic unsigned readBitsFromReversedStream(size_t* bitpointer, const unsigned char* bitstream, size_t nbits)\n\t{\n\tunsigned result = 0;\n\tsize_t i;\n\tfor(i = nbits - 1; i < nbits; i--) {\n\t\tresult += (unsigned)readBitFromReversedStream(bitpointer, bitstream) << i;\n\t\t}\n\treturn result;\n\t}\n\n#ifdef LODEPNG_COMPILE_DECODER\nstatic void setBitOfReversedStream0(size_t* bitpointer, unsigned char* bitstream, unsigned char bit)\n\t{\n\t/*the current bit in bitstream must be 0 for this to work*/\n\tif(bit) {\n\t\t/*earlier bit of huffman code is in a lesser significant bit of an earlier byte*/\n\t\tbitstream[(*bitpointer) >> 3] |= (bit << (7 - ((*bitpointer) & 0x7)));\n\t\t}\n\t(*bitpointer)++;\n\t}\n#endif /*LODEPNG_COMPILE_DECODER*/\n\nstatic void setBitOfReversedStream(size_t* bitpointer, unsigned char* bitstream, unsigned char bit)\n\t{\n\t/*the current bit in bitstream may be 0 or 1 for this to work*/\n\tif(bit == 0) bitstream[(*bitpointer) >> 3] &=  (unsigned char)(~(1 << (7 - ((*bitpointer) & 0x7))));\n\telse         bitstream[(*bitpointer) >> 3] |=  (1 << (7 - ((*bitpointer) & 0x7)));\n\t(*bitpointer)++;\n\t}\n\n/* ////////////////////////////////////////////////////////////////////////// */\n/* / PNG chunks                                                             / */\n/* ////////////////////////////////////////////////////////////////////////// */\n\nunsigned lodepng_chunk_length(const unsigned char* chunk)\n\t{\n\treturn lodepng_read32bitInt(&chunk[0]);\n\t}\n\nvoid lodepng_chunk_type(char type[5], const unsigned char* chunk)\n\t{\n\tunsigned i;\n\tfor(i = 0; i < 4; i++) type[i] = chunk[4 + i];\n\ttype[4] = 0; /*null termination char*/\n\t}\n\nunsigned char lodepng_chunk_type_equals(const unsigned char* chunk, const char* type)\n\t{\n\tif(strlen(type) != 4) return 0;\n\treturn (chunk[4] == type[0] && chunk[5] == type[1] && chunk[6] == type[2] && chunk[7] == type[3]);\n\t}\n\nunsigned char lodepng_chunk_ancillary(const unsigned char* chunk)\n\t{\n\treturn((chunk[4] & 32) != 0);\n\t}\n\nunsigned char lodepng_chunk_private(const unsigned char* chunk)\n\t{\n\treturn((chunk[6] & 32) != 0);\n\t}\n\nunsigned char lodepng_chunk_safetocopy(const unsigned char* chunk)\n\t{\n\treturn((chunk[7] & 32) != 0);\n\t}\n\nunsigned char* lodepng_chunk_data(unsigned char* chunk)\n\t{\n\treturn &chunk[8];\n\t}\n\nconst unsigned char* lodepng_chunk_data_const(const unsigned char* chunk)\n\t{\n\treturn &chunk[8];\n\t}\n\nunsigned lodepng_chunk_check_crc(const unsigned char* chunk)\n\t{\n\tunsigned length = lodepng_chunk_length(chunk);\n\tunsigned CRC = lodepng_read32bitInt(&chunk[length + 8]);\n\t/*the CRC is taken of the data and the 4 chunk type letters, not the length*/\n\tunsigned checksum = lodepng_crc32(&chunk[4], length + 4);\n\tif(CRC != checksum) return 1;\n\telse return 0;\n\t}\n\nvoid lodepng_chunk_generate_crc(unsigned char* chunk)\n\t{\n\tunsigned length = lodepng_chunk_length(chunk);\n\tunsigned CRC = lodepng_crc32(&chunk[4], length + 4);\n\tlodepng_set32bitInt(chunk + 8 + length, CRC);\n\t}\n\nunsigned char* lodepng_chunk_next(unsigned char* chunk)\n\t{\n\tunsigned total_chunk_length = lodepng_chunk_length(chunk) + 12;\n\treturn &chunk[total_chunk_length];\n\t}\n\nconst unsigned char* lodepng_chunk_next_const(const unsigned char* chunk)\n\t{\n\tunsigned total_chunk_length = lodepng_chunk_length(chunk) + 12;\n\treturn &chunk[total_chunk_length];\n\t}\n\nunsigned lodepng_chunk_append(unsigned char** out, size_t* outlength, const unsigned char* chunk)\n\t{\n\tunsigned i;\n\tunsigned total_chunk_length = lodepng_chunk_length(chunk) + 12;\n\tunsigned char *chunk_start, *new_buffer;\n\tsize_t new_length = (*outlength) + total_chunk_length;\n\tif(new_length < total_chunk_length || new_length < (*outlength)) return 77; /*integer overflow happened*/\n\n\tnew_buffer = (unsigned char*)lodepng_realloc(*out, new_length);\n\tif(!new_buffer) return 83; /*alloc fail*/\n\t(*out) = new_buffer;\n\t(*outlength) = new_length;\n\tchunk_start = &(*out)[new_length - total_chunk_length];\n\n\tfor(i = 0; i < total_chunk_length; i++) chunk_start[i] = chunk[i];\n\n\treturn 0;\n\t}\n\nunsigned lodepng_chunk_create(unsigned char** out, size_t* outlength, unsigned length,\n                              const char* type, const unsigned char* data)\n\t{\n\tunsigned i;\n\tunsigned char *chunk, *new_buffer;\n\tsize_t new_length = (*outlength) + length + 12;\n\tif(new_length < length + 12 || new_length < (*outlength)) return 77; /*integer overflow happened*/\n\tnew_buffer = (unsigned char*)lodepng_realloc(*out, new_length);\n\tif(!new_buffer) return 83; /*alloc fail*/\n\t(*out) = new_buffer;\n\t(*outlength) = new_length;\n\tchunk = &(*out)[(*outlength) - length - 12];\n\n\t/*1: length*/\n\tlodepng_set32bitInt(chunk, (unsigned)length);\n\n\t/*2: chunk name (4 letters)*/\n\tchunk[4] = type[0];\n\tchunk[5] = type[1];\n\tchunk[6] = type[2];\n\tchunk[7] = type[3];\n\n\t/*3: the data*/\n\tfor(i = 0; i < length; i++) chunk[8 + i] = data[i];\n\n\t/*4: CRC (of the chunkname characters and the data)*/\n\tlodepng_chunk_generate_crc(chunk);\n\n\treturn 0;\n\t}\n\n/* ////////////////////////////////////////////////////////////////////////// */\n/* / Color types and such                                                   / */\n/* ////////////////////////////////////////////////////////////////////////// */\n\n/*return type is a LodePNG error code*/\nstatic unsigned checkColorValidity(LodePNGColorType colortype, unsigned bd) /*bd = bitdepth*/\n\t{\n\tswitch(colortype) {\n\t\tcase 0:\n\t\t\tif(!(bd == 1 || bd == 2 || bd == 4 || bd == 8 || bd == 16)) return 37;\n\t\t\tbreak; /*grey*/\n\t\tcase 2:\n\t\t\tif(!(                                 bd == 8 || bd == 16)) return 37;\n\t\t\tbreak; /*RGB*/\n\t\tcase 3:\n\t\t\tif(!(bd == 1 || bd == 2 || bd == 4 || bd == 8            )) return 37;\n\t\t\tbreak; /*palette*/\n\t\tcase 4:\n\t\t\tif(!(                                 bd == 8 || bd == 16)) return 37;\n\t\t\tbreak; /*grey + alpha*/\n\t\tcase 6:\n\t\t\tif(!(                                 bd == 8 || bd == 16)) return 37;\n\t\t\tbreak; /*RGBA*/\n\t\tdefault:\n\t\t\treturn 31;\n\t\t}\n\treturn 0; /*allowed color type / bits combination*/\n\t}\n\nstatic unsigned getNumColorChannels(LodePNGColorType colortype)\n\t{\n\tswitch(colortype) {\n\t\tcase 0:\n\t\t\treturn 1; /*grey*/\n\t\tcase 2:\n\t\t\treturn 3; /*RGB*/\n\t\tcase 3:\n\t\t\treturn 1; /*palette*/\n\t\tcase 4:\n\t\t\treturn 2; /*grey + alpha*/\n\t\tcase 6:\n\t\t\treturn 4; /*RGBA*/\n\t\t}\n\treturn 0; /*unexisting color type*/\n\t}\n\nstatic unsigned lodepng_get_bpp_lct(LodePNGColorType colortype, unsigned bitdepth)\n\t{\n\t/*bits per pixel is amount of channels * bits per channel*/\n\treturn getNumColorChannels(colortype) * bitdepth;\n\t}\n\n/* ////////////////////////////////////////////////////////////////////////// */\n\nvoid lodepng_color_mode_init(LodePNGColorMode* info)\n\t{\n\tinfo->key_defined = 0;\n\tinfo->key_r = info->key_g = info->key_b = 0;\n\tinfo->colortype = LCT_RGBA;\n\tinfo->bitdepth = 8;\n\tinfo->palette = 0;\n\tinfo->palettesize = 0;\n\t}\n\nvoid lodepng_color_mode_cleanup(LodePNGColorMode* info)\n\t{\n\tlodepng_palette_clear(info);\n\t}\n\nunsigned lodepng_color_mode_copy(LodePNGColorMode* dest, const LodePNGColorMode* source)\n\t{\n\tsize_t i;\n\tlodepng_color_mode_cleanup(dest);\n\t*dest = *source;\n\tif(source->palette) {\n\t\tdest->palette = (unsigned char*)lodepng_malloc(1024);\n\t\tif(!dest->palette && source->palettesize) return 83; /*alloc fail*/\n\t\tfor(i = 0; i < source->palettesize * 4; i++) dest->palette[i] = source->palette[i];\n\t\t}\n\treturn 0;\n\t}\n\nstatic int lodepng_color_mode_equal(const LodePNGColorMode* a, const LodePNGColorMode* b)\n\t{\n\tsize_t i;\n\tif(a->colortype != b->colortype) return 0;\n\tif(a->bitdepth != b->bitdepth) return 0;\n\tif(a->key_defined != b->key_defined) return 0;\n\tif(a->key_defined) {\n\t\tif(a->key_r != b->key_r) return 0;\n\t\tif(a->key_g != b->key_g) return 0;\n\t\tif(a->key_b != b->key_b) return 0;\n\t\t}\n\tif(a->palettesize != b->palettesize) return 0;\n\tfor(i = 0; i < a->palettesize * 4; i++) {\n\t\tif(a->palette[i] != b->palette[i]) return 0;\n\t\t}\n\treturn 1;\n\t}\n\nvoid lodepng_palette_clear(LodePNGColorMode* info)\n\t{\n\tif(info->palette) lodepng_free(info->palette);\n\tinfo->palette = 0;\n\tinfo->palettesize = 0;\n\t}\n\nunsigned lodepng_palette_add(LodePNGColorMode* info,\n                             unsigned char r, unsigned char g, unsigned char b, unsigned char a)\n\t{\n\tunsigned char* data;\n\t/*the same resize technique as C++ std::vectors is used, and here it's made so that for a palette with\n\tthe max of 256 colors, it'll have the exact alloc size*/\n\tif(!info->palette) { /*allocate palette if empty*/\n\t\t/*room for 256 colors with 4 bytes each*/\n\t\tdata = (unsigned char*)lodepng_realloc(info->palette, 1024);\n\t\tif(!data) return 83; /*alloc fail*/\n\t\telse info->palette = data;\n\t\t}\n\tinfo->palette[4 * info->palettesize + 0] = r;\n\tinfo->palette[4 * info->palettesize + 1] = g;\n\tinfo->palette[4 * info->palettesize + 2] = b;\n\tinfo->palette[4 * info->palettesize + 3] = a;\n\tinfo->palettesize++;\n\treturn 0;\n\t}\n\nunsigned lodepng_get_bpp(const LodePNGColorMode* info)\n\t{\n\t/*calculate bits per pixel out of colortype and bitdepth*/\n\treturn lodepng_get_bpp_lct(info->colortype, info->bitdepth);\n\t}\n\nunsigned lodepng_get_channels(const LodePNGColorMode* info)\n\t{\n\treturn getNumColorChannels(info->colortype);\n\t}\n\nunsigned lodepng_is_greyscale_type(const LodePNGColorMode* info)\n\t{\n\treturn info->colortype == LCT_GREY || info->colortype == LCT_GREY_ALPHA;\n\t}\n\nunsigned lodepng_is_alpha_type(const LodePNGColorMode* info)\n\t{\n\treturn (info->colortype & 4) != 0; /*4 or 6*/\n\t}\n\nunsigned lodepng_is_palette_type(const LodePNGColorMode* info)\n\t{\n\treturn info->colortype == LCT_PALETTE;\n\t}\n\nunsigned lodepng_has_palette_alpha(const LodePNGColorMode* info)\n\t{\n\tsize_t i;\n\tfor(i = 0; i < info->palettesize; i++) {\n\t\tif(info->palette[i * 4 + 3] < 255) return 1;\n\t\t}\n\treturn 0;\n\t}\n\nunsigned lodepng_can_have_alpha(const LodePNGColorMode* info)\n\t{\n\treturn info->key_defined\n\t       || lodepng_is_alpha_type(info)\n\t       || lodepng_has_palette_alpha(info);\n\t}\n\nsize_t lodepng_get_raw_size(unsigned w, unsigned h, const LodePNGColorMode* color)\n\t{\n\treturn (w * h * lodepng_get_bpp(color) + 7) / 8;\n\t}\n\nsize_t lodepng_get_raw_size_lct(unsigned w, unsigned h, LodePNGColorType colortype, unsigned bitdepth)\n\t{\n\treturn (w * h * lodepng_get_bpp_lct(colortype, bitdepth) + 7) / 8;\n\t}\n\n#ifdef LODEPNG_COMPILE_ANCILLARY_CHUNKS\n\nstatic void LodePNGUnknownChunks_init(LodePNGInfo* info)\n\t{\n\tunsigned i;\n\tfor(i = 0; i < 3; i++) info->unknown_chunks_data[i] = 0;\n\tfor(i = 0; i < 3; i++) info->unknown_chunks_size[i] = 0;\n\t}\n\nstatic void LodePNGUnknownChunks_cleanup(LodePNGInfo* info)\n\t{\n\tunsigned i;\n\tfor(i = 0; i < 3; i++) lodepng_free(info->unknown_chunks_data[i]);\n\t}\n\nstatic unsigned LodePNGUnknownChunks_copy(LodePNGInfo* dest, const LodePNGInfo* src)\n\t{\n\tunsigned i;\n\n\tLodePNGUnknownChunks_cleanup(dest);\n\n\tfor(i = 0; i < 3; i++) {\n\t\tsize_t j;\n\t\tdest->unknown_chunks_size[i] = src->unknown_chunks_size[i];\n\t\tdest->unknown_chunks_data[i] = (unsigned char*)lodepng_malloc(src->unknown_chunks_size[i]);\n\t\tif(!dest->unknown_chunks_data[i] && dest->unknown_chunks_size[i]) return 83; /*alloc fail*/\n\t\tfor(j = 0; j < src->unknown_chunks_size[i]; j++) {\n\t\t\tdest->unknown_chunks_data[i][j] = src->unknown_chunks_data[i][j];\n\t\t\t}\n\t\t}\n\n\treturn 0;\n\t}\n\n/******************************************************************************/\n\nstatic void LodePNGText_init(LodePNGInfo* info)\n\t{\n\tinfo->text_num = 0;\n\tinfo->text_keys = NULL;\n\tinfo->text_strings = NULL;\n\t}\n\nstatic void LodePNGText_cleanup(LodePNGInfo* info)\n\t{\n\tsize_t i;\n\tfor(i = 0; i < info->text_num; i++) {\n\t\tstring_cleanup(&info->text_keys[i]);\n\t\tstring_cleanup(&info->text_strings[i]);\n\t\t}\n\tlodepng_free(info->text_keys);\n\tlodepng_free(info->text_strings);\n\t}\n\nstatic unsigned LodePNGText_copy(LodePNGInfo* dest, const LodePNGInfo* source)\n\t{\n\tsize_t i = 0;\n\tdest->text_keys = 0;\n\tdest->text_strings = 0;\n\tdest->text_num = 0;\n\tfor(i = 0; i < source->text_num; i++) {\n\t\tCERROR_TRY_RETURN(lodepng_add_text(dest, source->text_keys[i], source->text_strings[i]));\n\t\t}\n\treturn 0;\n\t}\n\nvoid lodepng_clear_text(LodePNGInfo* info)\n\t{\n\tLodePNGText_cleanup(info);\n\t}\n\nunsigned lodepng_add_text(LodePNGInfo* info, const char* key, const char* str)\n\t{\n\tchar** new_keys = (char**)(lodepng_realloc(info->text_keys, sizeof(char*) * (info->text_num + 1)));\n\tchar** new_strings = (char**)(lodepng_realloc(info->text_strings, sizeof(char*) * (info->text_num + 1)));\n\tif(!new_keys || !new_strings) {\n\t\tlodepng_free(new_keys);\n\t\tlodepng_free(new_strings);\n\t\treturn 83; /*alloc fail*/\n\t\t}\n\n\tinfo->text_num++;\n\tinfo->text_keys = new_keys;\n\tinfo->text_strings = new_strings;\n\n\tstring_init(&info->text_keys[info->text_num - 1]);\n\tstring_set(&info->text_keys[info->text_num - 1], key);\n\n\tstring_init(&info->text_strings[info->text_num - 1]);\n\tstring_set(&info->text_strings[info->text_num - 1], str);\n\n\treturn 0;\n\t}\n\n/******************************************************************************/\n\nstatic void LodePNGIText_init(LodePNGInfo* info)\n\t{\n\tinfo->itext_num = 0;\n\tinfo->itext_keys = NULL;\n\tinfo->itext_langtags = NULL;\n\tinfo->itext_transkeys = NULL;\n\tinfo->itext_strings = NULL;\n\t}\n\nstatic void LodePNGIText_cleanup(LodePNGInfo* info)\n\t{\n\tsize_t i;\n\tfor(i = 0; i < info->itext_num; i++) {\n\t\tstring_cleanup(&info->itext_keys[i]);\n\t\tstring_cleanup(&info->itext_langtags[i]);\n\t\tstring_cleanup(&info->itext_transkeys[i]);\n\t\tstring_cleanup(&info->itext_strings[i]);\n\t\t}\n\tlodepng_free(info->itext_keys);\n\tlodepng_free(info->itext_langtags);\n\tlodepng_free(info->itext_transkeys);\n\tlodepng_free(info->itext_strings);\n\t}\n\nstatic unsigned LodePNGIText_copy(LodePNGInfo* dest, const LodePNGInfo* source)\n\t{\n\tsize_t i = 0;\n\tdest->itext_keys = 0;\n\tdest->itext_langtags = 0;\n\tdest->itext_transkeys = 0;\n\tdest->itext_strings = 0;\n\tdest->itext_num = 0;\n\tfor(i = 0; i < source->itext_num; i++) {\n\t\tCERROR_TRY_RETURN(lodepng_add_itext(dest, source->itext_keys[i], source->itext_langtags[i],\n\t\t                                    source->itext_transkeys[i], source->itext_strings[i]));\n\t\t}\n\treturn 0;\n\t}\n\nvoid lodepng_clear_itext(LodePNGInfo* info)\n\t{\n\tLodePNGIText_cleanup(info);\n\t}\n\nunsigned lodepng_add_itext(LodePNGInfo* info, const char* key, const char* langtag,\n                           const char* transkey, const char* str)\n\t{\n\tchar** new_keys = (char**)(lodepng_realloc(info->itext_keys, sizeof(char*) * (info->itext_num + 1)));\n\tchar** new_langtags = (char**)(lodepng_realloc(info->itext_langtags, sizeof(char*) * (info->itext_num + 1)));\n\tchar** new_transkeys = (char**)(lodepng_realloc(info->itext_transkeys, sizeof(char*) * (info->itext_num + 1)));\n\tchar** new_strings = (char**)(lodepng_realloc(info->itext_strings, sizeof(char*) * (info->itext_num + 1)));\n\tif(!new_keys || !new_langtags || !new_transkeys || !new_strings) {\n\t\tlodepng_free(new_keys);\n\t\tlodepng_free(new_langtags);\n\t\tlodepng_free(new_transkeys);\n\t\tlodepng_free(new_strings);\n\t\treturn 83; /*alloc fail*/\n\t\t}\n\n\tinfo->itext_num++;\n\tinfo->itext_keys = new_keys;\n\tinfo->itext_langtags = new_langtags;\n\tinfo->itext_transkeys = new_transkeys;\n\tinfo->itext_strings = new_strings;\n\n\tstring_init(&info->itext_keys[info->itext_num - 1]);\n\tstring_set(&info->itext_keys[info->itext_num - 1], key);\n\n\tstring_init(&info->itext_langtags[info->itext_num - 1]);\n\tstring_set(&info->itext_langtags[info->itext_num - 1], langtag);\n\n\tstring_init(&info->itext_transkeys[info->itext_num - 1]);\n\tstring_set(&info->itext_transkeys[info->itext_num - 1], transkey);\n\n\tstring_init(&info->itext_strings[info->itext_num - 1]);\n\tstring_set(&info->itext_strings[info->itext_num - 1], str);\n\n\treturn 0;\n\t}\n#endif /*LODEPNG_COMPILE_ANCILLARY_CHUNKS*/\n\nvoid lodepng_info_init(LodePNGInfo* info)\n\t{\n\tlodepng_color_mode_init(&info->color);\n\tinfo->interlace_method = 0;\n\tinfo->compression_method = 0;\n\tinfo->filter_method = 0;\n#ifdef LODEPNG_COMPILE_ANCILLARY_CHUNKS\n\tinfo->background_defined = 0;\n\tinfo->background_r = info->background_g = info->background_b = 0;\n\n\tLodePNGText_init(info);\n\tLodePNGIText_init(info);\n\n\tinfo->time_defined = 0;\n\tinfo->phys_defined = 0;\n\n\tLodePNGUnknownChunks_init(info);\n#endif /*LODEPNG_COMPILE_ANCILLARY_CHUNKS*/\n\t}\n\nvoid lodepng_info_cleanup(LodePNGInfo* info)\n\t{\n\tlodepng_color_mode_cleanup(&info->color);\n#ifdef LODEPNG_COMPILE_ANCILLARY_CHUNKS\n\tLodePNGText_cleanup(info);\n\tLodePNGIText_cleanup(info);\n\n\tLodePNGUnknownChunks_cleanup(info);\n#endif /*LODEPNG_COMPILE_ANCILLARY_CHUNKS*/\n\t}\n\nunsigned lodepng_info_copy(LodePNGInfo* dest, const LodePNGInfo* source)\n\t{\n\tlodepng_info_cleanup(dest);\n\t*dest = *source;\n\tlodepng_color_mode_init(&dest->color);\n\tCERROR_TRY_RETURN(lodepng_color_mode_copy(&dest->color, &source->color));\n\n#ifdef LODEPNG_COMPILE_ANCILLARY_CHUNKS\n\tCERROR_TRY_RETURN(LodePNGText_copy(dest, source));\n\tCERROR_TRY_RETURN(LodePNGIText_copy(dest, source));\n\n\tLodePNGUnknownChunks_init(dest);\n\tCERROR_TRY_RETURN(LodePNGUnknownChunks_copy(dest, source));\n#endif /*LODEPNG_COMPILE_ANCILLARY_CHUNKS*/\n\treturn 0;\n\t}\n\nvoid lodepng_info_swap(LodePNGInfo* a, LodePNGInfo* b)\n\t{\n\tLodePNGInfo temp = *a;\n\t*a = *b;\n\t*b = temp;\n\t}\n\n/* ////////////////////////////////////////////////////////////////////////// */\n\n/*index: bitgroup index, bits: bitgroup size(1, 2 or 4), in: bitgroup value, out: octet array to add bits to*/\nstatic void addColorBits(unsigned char* out, size_t index, unsigned bits, unsigned in)\n\t{\n\tunsigned m = bits == 1 ? 7 : bits == 2 ? 3 : 1; /*8 / bits - 1*/\n\t/*p = the partial index in the byte, e.g. with 4 palettebits it is 0 for first half or 1 for second half*/\n\tunsigned p = index & m;\n\tin &= (1 << bits) - 1; /*filter out any other bits of the input value*/\n\tin = in << (bits * (m - p));\n\tif(p == 0) out[index * bits / 8] = in;\n\telse out[index * bits / 8] |= in;\n\t}\n\ntypedef struct ColorTree ColorTree;\n\n/*\nOne node of a color tree\nThis is the data structure used to count the number of unique colors and to get a palette\nindex for a color. It's like an octree, but because the alpha channel is used too, each\nnode has 16 instead of 8 children.\n*/\nstruct ColorTree {\n\tColorTree* children[16]; /*up to 16 pointers to ColorTree of next level*/\n\tint index; /*the payload. Only has a meaningful value if this is in the last level*/\n\t};\n\nstatic void color_tree_init(ColorTree* tree)\n\t{\n\tint i;\n\tfor(i = 0; i < 16; i++) tree->children[i] = 0;\n\ttree->index = -1;\n\t}\n\nstatic void color_tree_cleanup(ColorTree* tree)\n\t{\n\tint i;\n\tfor(i = 0; i < 16; i++) {\n\t\tif(tree->children[i]) {\n\t\t\tcolor_tree_cleanup(tree->children[i]);\n\t\t\tlodepng_free(tree->children[i]);\n\t\t\t}\n\t\t}\n\t}\n\n/*returns -1 if color not present, its index otherwise*/\nstatic int color_tree_get(ColorTree* tree, unsigned char r, unsigned char g, unsigned char b, unsigned char a)\n\t{\n\tint bit = 0;\n\tfor(bit = 0; bit < 8; bit++) {\n\t\tint i = 8 * ((r >> bit) & 1) + 4 * ((g >> bit) & 1) + 2 * ((b >> bit) & 1) + 1 * ((a >> bit) & 1);\n\t\tif(!tree->children[i]) return -1;\n\t\telse tree = tree->children[i];\n\t\t}\n\treturn tree ? tree->index : -1;\n\t}\n\n#ifdef LODEPNG_COMPILE_ENCODER\nstatic int color_tree_has(ColorTree* tree, unsigned char r, unsigned char g, unsigned char b, unsigned char a)\n\t{\n\treturn color_tree_get(tree, r, g, b, a) >= 0;\n\t}\n#endif /*LODEPNG_COMPILE_ENCODER*/\n\n/*color is not allowed to already exist.\nIndex should be >= 0 (it's signed to be compatible with using -1 for \"doesn't exist\")*/\nstatic void color_tree_add(ColorTree* tree,\n                           unsigned char r, unsigned char g, unsigned char b, unsigned char a, int index)\n\t{\n\tint bit;\n\tfor(bit = 0; bit < 8; bit++) {\n\t\tint i = 8 * ((r >> bit) & 1) + 4 * ((g >> bit) & 1) + 2 * ((b >> bit) & 1) + 1 * ((a >> bit) & 1);\n\t\tif(!tree->children[i]) {\n\t\t\ttree->children[i] = (ColorTree*)lodepng_malloc(sizeof(ColorTree));\n\t\t\tcolor_tree_init(tree->children[i]);\n\t\t\t}\n\t\ttree = tree->children[i];\n\t\t}\n\ttree->index = index;\n\t}\n\n/*put a pixel, given its RGBA color, into image of any color type*/\nstatic unsigned rgba8ToPixel(unsigned char* out, size_t i,\n                             const LodePNGColorMode* mode, ColorTree* tree /*for palette*/,\n                             unsigned char r, unsigned char g, unsigned char b, unsigned char a)\n\t{\n\tif(mode->colortype == LCT_GREY) {\n\t\tunsigned char grey = r; /*((unsigned short)r + g + b) / 3*/;\n\t\tif(mode->bitdepth == 8) out[i] = grey;\n\t\telse if(mode->bitdepth == 16) out[i * 2 + 0] = out[i * 2 + 1] = grey;\n\t\telse {\n\t\t\t/*take the most significant bits of grey*/\n\t\t\tgrey = (grey >> (8 - mode->bitdepth)) & ((1 << mode->bitdepth) - 1);\n\t\t\taddColorBits(out, i, mode->bitdepth, grey);\n\t\t\t}\n\t\t}\n\telse if(mode->colortype == LCT_RGB) {\n\t\tif(mode->bitdepth == 8) {\n\t\t\tout[i * 3 + 0] = r;\n\t\t\tout[i * 3 + 1] = g;\n\t\t\tout[i * 3 + 2] = b;\n\t\t\t}\n\t\telse {\n\t\t\tout[i * 6 + 0] = out[i * 6 + 1] = r;\n\t\t\tout[i * 6 + 2] = out[i * 6 + 3] = g;\n\t\t\tout[i * 6 + 4] = out[i * 6 + 5] = b;\n\t\t\t}\n\t\t}\n\telse if(mode->colortype == LCT_PALETTE) {\n\t\tint index = color_tree_get(tree, r, g, b, a);\n\t\tif(index < 0) return 82; /*color not in palette*/\n\t\tif(mode->bitdepth == 8) out[i] = index;\n\t\telse addColorBits(out, i, mode->bitdepth, index);\n\t\t}\n\telse if(mode->colortype == LCT_GREY_ALPHA) {\n\t\tunsigned char grey = r; /*((unsigned short)r + g + b) / 3*/;\n\t\tif(mode->bitdepth == 8) {\n\t\t\tout[i * 2 + 0] = grey;\n\t\t\tout[i * 2 + 1] = a;\n\t\t\t}\n\t\telse if(mode->bitdepth == 16) {\n\t\t\tout[i * 4 + 0] = out[i * 4 + 1] = grey;\n\t\t\tout[i * 4 + 2] = out[i * 4 + 3] = a;\n\t\t\t}\n\t\t}\n\telse if(mode->colortype == LCT_RGBA) {\n\t\tif(mode->bitdepth == 8) {\n\t\t\tout[i * 4 + 0] = r;\n\t\t\tout[i * 4 + 1] = g;\n\t\t\tout[i * 4 + 2] = b;\n\t\t\tout[i * 4 + 3] = a;\n\t\t\t}\n\t\telse {\n\t\t\tout[i * 8 + 0] = out[i * 8 + 1] = r;\n\t\t\tout[i * 8 + 2] = out[i * 8 + 3] = g;\n\t\t\tout[i * 8 + 4] = out[i * 8 + 5] = b;\n\t\t\tout[i * 8 + 6] = out[i * 8 + 7] = a;\n\t\t\t}\n\t\t}\n\n\treturn 0; /*no error*/\n\t}\n\n/*put a pixel, given its RGBA16 color, into image of any color 16-bitdepth type*/\nstatic unsigned rgba16ToPixel(unsigned char* out, size_t i,\n                              const LodePNGColorMode* mode,\n                              unsigned short r, unsigned short g, unsigned short b, unsigned short a)\n\t{\n\tif(mode->bitdepth != 16) return 85; /*must be 16 for this function*/\n\tif(mode->colortype == LCT_GREY) {\n\t\tunsigned short grey = r; /*((unsigned)r + g + b) / 3*/;\n\t\tout[i * 2 + 0] = (grey >> 8) & 255;\n\t\tout[i * 2 + 1] = grey & 255;\n\t\t}\n\telse if(mode->colortype == LCT_RGB) {\n\t\tout[i * 6 + 0] = (r >> 8) & 255;\n\t\tout[i * 6 + 1] = r & 255;\n\t\tout[i * 6 + 2] = (g >> 8) & 255;\n\t\tout[i * 6 + 3] = g & 255;\n\t\tout[i * 6 + 4] = (b >> 8) & 255;\n\t\tout[i * 6 + 5] = b & 255;\n\t\t}\n\telse if(mode->colortype == LCT_GREY_ALPHA) {\n\t\tunsigned short grey = r; /*((unsigned)r + g + b) / 3*/;\n\t\tout[i * 4 + 0] = (grey >> 8) & 255;\n\t\tout[i * 4 + 1] = grey & 255;\n\t\tout[i * 4 + 2] = (a >> 8) & 255;\n\t\tout[i * 4 + 3] = a & 255;\n\t\t}\n\telse if(mode->colortype == LCT_RGBA) {\n\t\tout[i * 8 + 0] = (r >> 8) & 255;\n\t\tout[i * 8 + 1] = r & 255;\n\t\tout[i * 8 + 2] = (g >> 8) & 255;\n\t\tout[i * 8 + 3] = g & 255;\n\t\tout[i * 8 + 4] = (b >> 8) & 255;\n\t\tout[i * 8 + 5] = b & 255;\n\t\tout[i * 8 + 6] = (a >> 8) & 255;\n\t\tout[i * 8 + 7] = a & 255;\n\t\t}\n\n\treturn 0; /*no error*/\n\t}\n\n/*Get RGBA8 color of pixel with index i (y * width + x) from the raw image with given color type.*/\nstatic unsigned getPixelColorRGBA8(unsigned char* r, unsigned char* g,\n                                   unsigned char* b, unsigned char* a,\n                                   const unsigned char* in, size_t i,\n                                   const LodePNGColorMode* mode,\n                                   unsigned fix_png)\n\t{\n\tif(mode->colortype == LCT_GREY) {\n\t\tif(mode->bitdepth == 8) {\n\t\t\t*r = *g = *b = in[i];\n\t\t\tif(mode->key_defined && *r == mode->key_r) *a = 0;\n\t\t\telse *a = 255;\n\t\t\t}\n\t\telse if(mode->bitdepth == 16) {\n\t\t\t*r = *g = *b = in[i * 2 + 0];\n\t\t\tif(mode->key_defined && 256U * in[i * 2 + 0] + in[i * 2 + 1] == mode->key_r) *a = 0;\n\t\t\telse *a = 255;\n\t\t\t}\n\t\telse {\n\t\t\tunsigned highest = ((1U << mode->bitdepth) - 1U); /*highest possible value for this bit depth*/\n\t\t\tsize_t j = i * mode->bitdepth;\n\t\t\tunsigned value = readBitsFromReversedStream(&j, in, mode->bitdepth);\n\t\t\t*r = *g = *b = (value * 255) / highest;\n\t\t\tif(mode->key_defined && value == mode->key_r) *a = 0;\n\t\t\telse *a = 255;\n\t\t\t}\n\t\t}\n\telse if(mode->colortype == LCT_RGB) {\n\t\tif(mode->bitdepth == 8) {\n\t\t\t*r = in[i * 3 + 0];\n\t\t\t*g = in[i * 3 + 1];\n\t\t\t*b = in[i * 3 + 2];\n\t\t\tif(mode->key_defined && *r == mode->key_r && *g == mode->key_g && *b == mode->key_b) *a = 0;\n\t\t\telse *a = 255;\n\t\t\t}\n\t\telse {\n\t\t\t*r = in[i * 6 + 0];\n\t\t\t*g = in[i * 6 + 2];\n\t\t\t*b = in[i * 6 + 4];\n\t\t\tif(mode->key_defined && 256U * in[i * 6 + 0] + in[i * 6 + 1] == mode->key_r\n\t\t\t      && 256U * in[i * 6 + 2] + in[i * 6 + 3] == mode->key_g\n\t\t\t      && 256U * in[i * 6 + 4] + in[i * 6 + 5] == mode->key_b) *a = 0;\n\t\t\telse *a = 255;\n\t\t\t}\n\t\t}\n\telse if(mode->colortype == LCT_PALETTE) {\n\t\tunsigned index;\n\t\tif(mode->bitdepth == 8) index = in[i];\n\t\telse {\n\t\t\tsize_t j = i * mode->bitdepth;\n\t\t\tindex = readBitsFromReversedStream(&j, in, mode->bitdepth);\n\t\t\t}\n\n\t\tif(index >= mode->palettesize) {\n\t\t\t/*This is an error according to the PNG spec, but fix_png can ignore it*/\n\t\t\tif(!fix_png) return (mode->bitdepth == 8 ? 46 : 47); /*index out of palette*/\n\t\t\t*r = *g = *b = 0;\n\t\t\t*a = 255;\n\t\t\t}\n\t\telse {\n\t\t\t*r = mode->palette[index * 4 + 0];\n\t\t\t*g = mode->palette[index * 4 + 1];\n\t\t\t*b = mode->palette[index * 4 + 2];\n\t\t\t*a = mode->palette[index * 4 + 3];\n\t\t\t}\n\t\t}\n\telse if(mode->colortype == LCT_GREY_ALPHA) {\n\t\tif(mode->bitdepth == 8) {\n\t\t\t*r = *g = *b = in[i * 2 + 0];\n\t\t\t*a = in[i * 2 + 1];\n\t\t\t}\n\t\telse {\n\t\t\t*r = *g = *b = in[i * 4 + 0];\n\t\t\t*a = in[i * 4 + 2];\n\t\t\t}\n\t\t}\n\telse if(mode->colortype == LCT_RGBA) {\n\t\tif(mode->bitdepth == 8) {\n\t\t\t*r = in[i * 4 + 0];\n\t\t\t*g = in[i * 4 + 1];\n\t\t\t*b = in[i * 4 + 2];\n\t\t\t*a = in[i * 4 + 3];\n\t\t\t}\n\t\telse {\n\t\t\t*r = in[i * 8 + 0];\n\t\t\t*g = in[i * 8 + 2];\n\t\t\t*b = in[i * 8 + 4];\n\t\t\t*a = in[i * 8 + 6];\n\t\t\t}\n\t\t}\n\n\treturn 0; /*no error*/\n\t}\n\n/*Similar to getPixelColorRGBA8, but with all the for loops inside of the color\nmode test cases, optimized to convert the colors much faster, when converting\nto RGBA or RGB with 8 bit per cannel. buffer must be RGBA or RGB output with\nenough memory, if has_alpha is true the output is RGBA. mode has the color mode\nof the input buffer.*/\nstatic unsigned getPixelColorsRGBA8(unsigned char* buffer, size_t numpixels,\n                                    unsigned has_alpha, const unsigned char* in,\n                                    const LodePNGColorMode* mode,\n                                    unsigned fix_png)\n\t{\n\tunsigned num_channels = has_alpha ? 4 : 3;\n\tsize_t i;\n\tif(mode->colortype == LCT_GREY) {\n\t\tif(mode->bitdepth == 8) {\n\t\t\tfor(i = 0; i < numpixels; i++, buffer += num_channels) {\n\t\t\t\tbuffer[0] = buffer[1] = buffer[2] = in[i];\n\t\t\t\tif(has_alpha) buffer[3] = mode->key_defined && in[i] == mode->key_r ? 0 : 255;\n\t\t\t\t}\n\t\t\t}\n\t\telse if(mode->bitdepth == 16) {\n\t\t\tfor(i = 0; i < numpixels; i++, buffer += num_channels) {\n\t\t\t\tbuffer[0] = buffer[1] = buffer[2] = in[i * 2];\n\t\t\t\tif(has_alpha) buffer[3] = mode->key_defined && 256U * in[i * 2 + 0] + in[i * 2 + 1] == mode->key_r ? 0 : 255;\n\t\t\t\t}\n\t\t\t}\n\t\telse {\n\t\t\tunsigned highest = ((1U << mode->bitdepth) - 1U); /*highest possible value for this bit depth*/\n\t\t\tsize_t j = 0;\n\t\t\tfor(i = 0; i < numpixels; i++, buffer += num_channels) {\n\t\t\t\tunsigned value = readBitsFromReversedStream(&j, in, mode->bitdepth);\n\t\t\t\tbuffer[0] = buffer[1] = buffer[2] = (value * 255) / highest;\n\t\t\t\tif(has_alpha) buffer[3] = mode->key_defined && value == mode->key_r ? 0 : 255;\n\t\t\t\t}\n\t\t\t}\n\t\t}\n\telse if(mode->colortype == LCT_RGB) {\n\t\tif(mode->bitdepth == 8) {\n\t\t\tfor(i = 0; i < numpixels; i++, buffer += num_channels) {\n\t\t\t\tbuffer[0] = in[i * 3 + 0];\n\t\t\t\tbuffer[1] = in[i * 3 + 1];\n\t\t\t\tbuffer[2] = in[i * 3 + 2];\n\t\t\t\tif(has_alpha) buffer[3] = mode->key_defined && buffer[0] == mode->key_r\n\t\t\t\t\t                          && buffer[1]== mode->key_g && buffer[2] == mode->key_b ? 0 : 255;\n\t\t\t\t}\n\t\t\t}\n\t\telse {\n\t\t\tfor(i = 0; i < numpixels; i++, buffer += num_channels) {\n\t\t\t\tbuffer[0] = in[i * 6 + 0];\n\t\t\t\tbuffer[1] = in[i * 6 + 2];\n\t\t\t\tbuffer[2] = in[i * 6 + 4];\n\t\t\t\tif(has_alpha) buffer[3] = mode->key_defined\n\t\t\t\t\t                          && 256U * in[i * 6 + 0] + in[i * 6 + 1] == mode->key_r\n\t\t\t\t\t                          && 256U * in[i * 6 + 2] + in[i * 6 + 3] == mode->key_g\n\t\t\t\t\t                          && 256U * in[i * 6 + 4] + in[i * 6 + 5] == mode->key_b ? 0 : 255;\n\t\t\t\t}\n\t\t\t}\n\t\t}\n\telse if(mode->colortype == LCT_PALETTE) {\n\t\tunsigned index;\n\t\tsize_t j = 0;\n\t\tfor(i = 0; i < numpixels; i++, buffer += num_channels) {\n\t\t\tif(mode->bitdepth == 8) index = in[i];\n\t\t\telse index = readBitsFromReversedStream(&j, in, mode->bitdepth);\n\n\t\t\tif(index >= mode->palettesize) {\n\t\t\t\t/*This is an error according to the PNG spec, but fix_png can ignore it*/\n\t\t\t\tif(!fix_png) return (mode->bitdepth == 8 ? 46 : 47); /*index out of palette*/\n\t\t\t\tbuffer[0] = buffer[1] = buffer[2] = 0;\n\t\t\t\tif(has_alpha) buffer[3] = 255;\n\t\t\t\t}\n\t\t\telse {\n\t\t\t\tbuffer[0] = mode->palette[index * 4 + 0];\n\t\t\t\tbuffer[1] = mode->palette[index * 4 + 1];\n\t\t\t\tbuffer[2] = mode->palette[index * 4 + 2];\n\t\t\t\tif(has_alpha) buffer[3] = mode->palette[index * 4 + 3];\n\t\t\t\t}\n\t\t\t}\n\t\t}\n\telse if(mode->colortype == LCT_GREY_ALPHA) {\n\t\tif(mode->bitdepth == 8) {\n\t\t\tfor(i = 0; i < numpixels; i++, buffer += num_channels) {\n\t\t\t\tbuffer[0] = buffer[1] = buffer[2] = in[i * 2 + 0];\n\t\t\t\tif(has_alpha) buffer[3] = in[i * 2 + 1];\n\t\t\t\t}\n\t\t\t}\n\t\telse {\n\t\t\tfor(i = 0; i < numpixels; i++, buffer += num_channels) {\n\t\t\t\tbuffer[0] = buffer[1] = buffer[2] = in[i * 4 + 0];\n\t\t\t\tif(has_alpha) buffer[3] = in[i * 4 + 2];\n\t\t\t\t}\n\t\t\t}\n\t\t}\n\telse if(mode->colortype == LCT_RGBA) {\n\t\tif(mode->bitdepth == 8) {\n\t\t\tfor(i = 0; i < numpixels; i++, buffer += num_channels) {\n\t\t\t\tbuffer[0] = in[i * 4 + 0];\n\t\t\t\tbuffer[1] = in[i * 4 + 1];\n\t\t\t\tbuffer[2] = in[i * 4 + 2];\n\t\t\t\tif(has_alpha) buffer[3] = in[i * 4 + 3];\n\t\t\t\t}\n\t\t\t}\n\t\telse {\n\t\t\tfor(i = 0; i < numpixels; i++, buffer += num_channels) {\n\t\t\t\tbuffer[0] = in[i * 8 + 0];\n\t\t\t\tbuffer[1] = in[i * 8 + 2];\n\t\t\t\tbuffer[2] = in[i * 8 + 4];\n\t\t\t\tif(has_alpha) buffer[3] = in[i * 8 + 6];\n\t\t\t\t}\n\t\t\t}\n\t\t}\n\n\treturn 0; /*no error*/\n\t}\n\n/*Get RGBA16 color of pixel with index i (y * width + x) from the raw image with\ngiven color type, but the given color type must be 16-bit itself.*/\nstatic unsigned getPixelColorRGBA16(unsigned short* r, unsigned short* g, unsigned short* b, unsigned short* a,\n                                    const unsigned char* in, size_t i, const LodePNGColorMode* mode)\n\t{\n\tif(mode->bitdepth != 16) return 85; /*error: this function only supports 16-bit input*/\n\n\tif(mode->colortype == LCT_GREY) {\n\t\t*r = *g = *b = 256 * in[i * 2 + 0] + in[i * 2 + 1];\n\t\tif(mode->key_defined && 256U * in[i * 2 + 0] + in[i * 2 + 1] == mode->key_r) *a = 0;\n\t\telse *a = 65535;\n\t\t}\n\telse if(mode->colortype == LCT_RGB) {\n\t\t*r = 256 * in[i * 6 + 0] + in[i * 6 + 1];\n\t\t*g = 256 * in[i * 6 + 2] + in[i * 6 + 3];\n\t\t*b = 256 * in[i * 6 + 4] + in[i * 6 + 5];\n\t\tif(mode->key_defined && 256U * in[i * 6 + 0] + in[i * 6 + 1] == mode->key_r\n\t\t      && 256U * in[i * 6 + 2] + in[i * 6 + 3] == mode->key_g\n\t\t      && 256U * in[i * 6 + 4] + in[i * 6 + 5] == mode->key_b) *a = 0;\n\t\telse *a = 65535;\n\t\t}\n\telse if(mode->colortype == LCT_GREY_ALPHA) {\n\t\t*r = *g = *b = 256 * in[i * 4 + 0] + in[i * 4 + 1];\n\t\t*a = 256 * in[i * 4 + 2] + in[i * 4 + 3];\n\t\t}\n\telse if(mode->colortype == LCT_RGBA) {\n\t\t*r = 256 * in[i * 8 + 0] + in[i * 8 + 1];\n\t\t*g = 256 * in[i * 8 + 2] + in[i * 8 + 3];\n\t\t*b = 256 * in[i * 8 + 4] + in[i * 8 + 5];\n\t\t*a = 256 * in[i * 8 + 6] + in[i * 8 + 7];\n\t\t}\n\telse return 85;   /*error: this function only supports 16-bit input, not palettes*/\n\n\treturn 0; /*no error*/\n\t}\n\n/*\nconverts from any color type to 24-bit or 32-bit (later maybe more supported). return value = LodePNG error code\nthe out buffer must have (w * h * bpp + 7) / 8 bytes, where bpp is the bits per pixel of the output color type\n(lodepng_get_bpp) for < 8 bpp images, there may _not_ be padding bits at the end of scanlines.\n*/\nunsigned lodepng_convert(unsigned char* out, const unsigned char* in,\n                         LodePNGColorMode* mode_out, const LodePNGColorMode* mode_in,\n                         unsigned w, unsigned h, unsigned fix_png)\n\t{\n\tunsigned error = 0;\n\tsize_t i;\n\tColorTree tree;\n\tsize_t numpixels = w * h;\n\n\tif(lodepng_color_mode_equal(mode_out, mode_in)) {\n\t\tsize_t numbytes = lodepng_get_raw_size(w, h, mode_in);\n\t\tfor(i = 0; i < numbytes; i++) out[i] = in[i];\n\t\treturn error;\n\t\t}\n\n\tif(mode_out->colortype == LCT_PALETTE) {\n\t\tsize_t palsize = 1 << mode_out->bitdepth;\n\t\tif(mode_out->palettesize < palsize) palsize = mode_out->palettesize;\n\t\tcolor_tree_init(&tree);\n\t\tfor(i = 0; i < palsize; i++) {\n\t\t\tunsigned char* p = &mode_out->palette[i * 4];\n\t\t\tcolor_tree_add(&tree, p[0], p[1], p[2], p[3], i);\n\t\t\t}\n\t\t}\n\n\tif(mode_in->bitdepth == 16 && mode_out->bitdepth == 16) {\n\t\tfor(i = 0; i < numpixels; i++) {\n\t\t\tunsigned short r = 0, g = 0, b = 0, a = 0;\n\t\t\terror = getPixelColorRGBA16(&r, &g, &b, &a, in, i, mode_in);\n\t\t\tif(error) break;\n\t\t\terror = rgba16ToPixel(out, i, mode_out, r, g, b, a);\n\t\t\tif(error) break;\n\t\t\t}\n\t\t}\n\telse if(mode_out->bitdepth == 8 && mode_out->colortype == LCT_RGBA) {\n\t\terror = getPixelColorsRGBA8(out, numpixels, 1, in, mode_in, fix_png);\n\t\t}\n\telse if(mode_out->bitdepth == 8 && mode_out->colortype == LCT_RGB) {\n\t\terror = getPixelColorsRGBA8(out, numpixels, 0, in, mode_in, fix_png);\n\t\t}\n\telse {\n\t\tunsigned char r = 0, g = 0, b = 0, a = 0;\n\t\tfor(i = 0; i < numpixels; i++) {\n\t\t\terror = getPixelColorRGBA8(&r, &g, &b, &a, in, i, mode_in, fix_png);\n\t\t\tif(error) break;\n\t\t\terror = rgba8ToPixel(out, i, mode_out, &tree, r, g, b, a);\n\t\t\tif(error) break;\n\t\t\t}\n\t\t}\n\n\tif(mode_out->colortype == LCT_PALETTE) {\n\t\tcolor_tree_cleanup(&tree);\n\t\t}\n\n\treturn error;\n\t}\n\n#ifdef LODEPNG_COMPILE_ENCODER\n\ntypedef struct ColorProfile {\n\tunsigned char sixteenbit; /*needs more than 8 bits per channel*/\n\tunsigned char sixteenbit_done;\n\n\n\tunsigned char colored; /*not greyscale*/\n\tunsigned char colored_done;\n\n\tunsigned char key; /*a color key is required, or more*/\n\tunsigned short key_r; /*these values are always in 16-bit bitdepth in the profile*/\n\tunsigned short key_g;\n\tunsigned short key_b;\n\tunsigned char alpha; /*alpha channel, or alpha palette, required*/\n\tunsigned char alpha_done;\n\n\tunsigned numcolors;\n\tColorTree tree; /*for listing the counted colors, up to 256*/\n\tunsigned char* palette; /*size 1024. Remember up to the first 256 RGBA colors*/\n\tunsigned maxnumcolors; /*if more than that amount counted*/\n\tunsigned char numcolors_done;\n\n\tunsigned greybits; /*amount of bits required for greyscale (1, 2, 4, 8). Does not take 16 bit into account.*/\n\tunsigned char greybits_done;\n\n\t} ColorProfile;\n\nstatic void color_profile_init(ColorProfile* profile, const LodePNGColorMode* mode)\n\t{\n\tprofile->sixteenbit = 0;\n\tprofile->sixteenbit_done = mode->bitdepth == 16 ? 0 : 1;\n\n\tprofile->colored = 0;\n\tprofile->colored_done = lodepng_is_greyscale_type(mode) ? 1 : 0;\n\n\tprofile->key = 0;\n\tprofile->alpha = 0;\n\tprofile->alpha_done = lodepng_can_have_alpha(mode) ? 0 : 1;\n\n\tprofile->numcolors = 0;\n\tcolor_tree_init(&profile->tree);\n\tprofile->palette = (unsigned char*)lodepng_malloc(1024);\n\tprofile->maxnumcolors = 257;\n\tif(lodepng_get_bpp(mode) <= 8) {\n\t\tint bpp = lodepng_get_bpp(mode);\n\t\tprofile->maxnumcolors = bpp == 1 ? 2 : (bpp == 2 ? 4 : (bpp == 4 ? 16 : 256));\n\t\t}\n\tprofile->numcolors_done = 0;\n\n\tprofile->greybits = 1;\n\tprofile->greybits_done = lodepng_get_bpp(mode) == 1 ? 1 : 0;\n\t}\n\nstatic void color_profile_cleanup(ColorProfile* profile)\n\t{\n\tcolor_tree_cleanup(&profile->tree);\n\tlodepng_free(profile->palette);\n\t}\n\n/*function used for debug purposes with C++*/\n/*void printColorProfile(ColorProfile* p)\n\t\t\t{\nstd::cout << \"sixteenbit: \" << (int)p->sixteenbit << std::endl;\nstd::cout << \"sixteenbit_done: \" << (int)p->sixteenbit_done << std::endl;\nstd::cout << \"colored: \" << (int)p->colored << std::endl;\nstd::cout << \"colored_done: \" << (int)p->colored_done << std::endl;\nstd::cout << \"key: \" << (int)p->key << std::endl;\nstd::cout << \"key_r: \" << (int)p->key_r << std::endl;\nstd::cout << \"key_g: \" << (int)p->key_g << std::endl;\nstd::cout << \"key_b: \" << (int)p->key_b << std::endl;\nstd::cout << \"alpha: \" << (int)p->alpha << std::endl;\nstd::cout << \"alpha_done: \" << (int)p->alpha_done << std::endl;\nstd::cout << \"numcolors: \" << (int)p->numcolors << std::endl;\nstd::cout << \"maxnumcolors: \" << (int)p->maxnumcolors << std::endl;\nstd::cout << \"numcolors_done: \" << (int)p->numcolors_done << std::endl;\nstd::cout << \"greybits: \" << (int)p->greybits << std::endl;\nstd::cout << \"greybits_done: \" << (int)p->greybits_done << std::endl;\n\t\t\t}*/\n\n/*Returns how many bits needed to represent given value (max 8 bit)*/\nunsigned getValueRequiredBits(unsigned short value)\n\t{\n\tif(value == 0 || value == 255) return 1;\n\t/*The scaling of 2-bit and 4-bit values uses multiples of 85 and 17*/\n\tif(value % 17 == 0) return value % 85 == 0 ? 2 : 4;\n\treturn 8;\n\t}\n\n/*profile must already have been inited with mode.\nIt's ok to set some parameters of profile to done already.*/\nstatic unsigned get_color_profile(ColorProfile* profile,\n                                  const unsigned char* in,\n                                  size_t numpixels /*must be full image size, for certain filesize based choices*/,\n                                  const LodePNGColorMode* mode,\n                                  unsigned fix_png)\n\t{\n\tunsigned error = 0;\n\tsize_t i;\n\n\tif(mode->bitdepth == 16) {\n\t\tfor(i = 0; i < numpixels; i++) {\n\t\t\tunsigned short r, g, b, a;\n\t\t\terror = getPixelColorRGBA16(&r, &g, &b, &a, in, i, mode);\n\t\t\tif(error) break;\n\n\t\t\t/*a color is considered good for 8-bit if the first byte and the second byte are equal,\n\t\t\t(so if it's divisible through 257), NOT necessarily if the second byte is 0*/\n\t\t\tif(!profile->sixteenbit_done\n\t\t\t      && (((r & 255) != ((r >> 8) & 255))\n\t\t\t          || ((g & 255) != ((g >> 8) & 255))\n\t\t\t          || ((b & 255) != ((b >> 8) & 255)))) {\n\t\t\t\tprofile->sixteenbit = 1;\n\t\t\t\tprofile->sixteenbit_done = 1;\n\t\t\t\tprofile->greybits_done = 1; /*greybits is not applicable anymore at 16-bit*/\n\t\t\t\tprofile->numcolors_done = 1; /*counting colors no longer useful, palette doesn't support 16-bit*/\n\t\t\t\t}\n\n\t\t\tif(!profile->colored_done && (r != g || r != b)) {\n\t\t\t\tprofile->colored = 1;\n\t\t\t\tprofile->colored_done = 1;\n\t\t\t\tprofile->greybits_done = 1; /*greybits is not applicable anymore*/\n\t\t\t\t}\n\n\t\t\tif(!profile->alpha_done && a != 65535) {\n\t\t\t\t/*only use color key if numpixels large enough to justify tRNS chunk size*/\n\t\t\t\tif(a == 0 && numpixels > 16 && !(profile->key && (r != profile->key_r || g != profile->key_g || b != profile->key_b))) {\n\t\t\t\t\tif(!profile->alpha && !profile->key) {\n\t\t\t\t\t\tprofile->key = 1;\n\t\t\t\t\t\tprofile->key_r = r;\n\t\t\t\t\t\tprofile->key_g = g;\n\t\t\t\t\t\tprofile->key_b = b;\n\t\t\t\t\t\t}\n\t\t\t\t\t}\n\t\t\t\telse {\n\t\t\t\t\tprofile->alpha = 1;\n\t\t\t\t\tprofile->alpha_done = 1;\n\t\t\t\t\tprofile->greybits_done = 1; /*greybits is not applicable anymore*/\n\t\t\t\t\t}\n\t\t\t\t}\n\n\t\t\t/* Color key cannot be used if an opaque pixel also has that RGB color. */\n\t\t\tif(!profile->alpha_done && a == 65535 && profile->key\n\t\t\t      && r == profile->key_r && g == profile->key_g && b == profile->key_b) {\n\t\t\t\tprofile->alpha = 1;\n\t\t\t\tprofile->alpha_done = 1;\n\t\t\t\tprofile->greybits_done = 1; /*greybits is not applicable anymore*/\n\t\t\t\t}\n\n\t\t\tif(!profile->greybits_done) {\n\t\t\t\t/*assuming 8-bit r, this test does not care about 16-bit*/\n\t\t\t\tunsigned bits = getValueRequiredBits(r);\n\t\t\t\tif(bits > profile->greybits) profile->greybits = bits;\n\t\t\t\tif(profile->greybits >= 8) profile->greybits_done = 1;\n\t\t\t\t}\n\n\t\t\tif(!profile->numcolors_done) {\n\t\t\t\t/*assuming 8-bit rgba, this test does not care about 16-bit*/\n\t\t\t\tif(!color_tree_has(&profile->tree, (unsigned char)r, (unsigned char)g, (unsigned char)b, (unsigned char)a)) {\n\t\t\t\t\tcolor_tree_add(&profile->tree, (unsigned char)r, (unsigned char)g, (unsigned char)b, (unsigned char)a,\n\t\t\t\t\t               profile->numcolors);\n\t\t\t\t\tif(profile->numcolors < 256) {\n\t\t\t\t\t\tunsigned char* p = profile->palette;\n\t\t\t\t\t\tunsigned i = profile->numcolors;\n\t\t\t\t\t\tp[i * 4 + 0] = (unsigned char)r;\n\t\t\t\t\t\tp[i * 4 + 1] = (unsigned char)g;\n\t\t\t\t\t\tp[i * 4 + 2] = (unsigned char)b;\n\t\t\t\t\t\tp[i * 4 + 3] = (unsigned char)a;\n\t\t\t\t\t\t}\n\t\t\t\t\tprofile->numcolors++;\n\t\t\t\t\tif(profile->numcolors >= profile->maxnumcolors) profile->numcolors_done = 1;\n\t\t\t\t\t}\n\t\t\t\t}\n\n\t\t\tif(profile->alpha_done && profile->numcolors_done\n\t\t\t      && profile->colored_done && profile->sixteenbit_done && profile->greybits_done) {\n\t\t\t\tbreak;\n\t\t\t\t}\n\t\t\t};\n\t\t}\n\telse {   /* < 16-bit */\n\t\tfor(i = 0; i < numpixels; i++) {\n\t\t\tunsigned char r = 0, g = 0, b = 0, a = 0;\n\t\t\terror = getPixelColorRGBA8(&r, &g, &b, &a, in, i, mode, fix_png);\n\t\t\tif(error) break;\n\n\t\t\tif(!profile->colored_done && (r != g || r != b)) {\n\t\t\t\tprofile->colored = 1;\n\t\t\t\tprofile->colored_done = 1;\n\t\t\t\tprofile->greybits_done = 1; /*greybits is not applicable anymore*/\n\t\t\t\t}\n\n\t\t\tif(!profile->alpha_done && a != 255) {\n\t\t\t\tif(a == 0 && !(profile->key && (r != profile->key_r || g != profile->key_g || b != profile->key_b))) {\n\t\t\t\t\tif(!profile->key) {\n\t\t\t\t\t\tprofile->key = 1;\n\t\t\t\t\t\tprofile->key_r = r;\n\t\t\t\t\t\tprofile->key_g = g;\n\t\t\t\t\t\tprofile->key_b = b;\n\t\t\t\t\t\t}\n\t\t\t\t\t}\n\t\t\t\telse {\n\t\t\t\t\tprofile->alpha = 1;\n\t\t\t\t\tprofile->alpha_done = 1;\n\t\t\t\t\tprofile->greybits_done = 1; /*greybits is not applicable anymore*/\n\t\t\t\t\t}\n\t\t\t\t}\n\n\t\t\t/* Color key cannot be used if an opaque pixel also has that RGB color. */\n\t\t\tif(!profile->alpha_done && a == 255 && profile->key\n\t\t\t      && r == profile->key_r && g == profile->key_g && b == profile->key_b) {\n\t\t\t\tprofile->alpha = 1;\n\t\t\t\tprofile->alpha_done = 1;\n\t\t\t\tprofile->greybits_done = 1; /*greybits is not applicable anymore*/\n\t\t\t\t}\n\n\t\t\tif(!profile->greybits_done) {\n\t\t\t\tunsigned bits = getValueRequiredBits(r);\n\t\t\t\tif(bits > profile->greybits) profile->greybits = bits;\n\t\t\t\tif(profile->greybits >= 8) profile->greybits_done = 1;\n\t\t\t\t}\n\n\t\t\tif(!profile->numcolors_done) {\n\t\t\t\tif(!color_tree_has(&profile->tree, r, g, b, a)) {\n\n\t\t\t\t\tcolor_tree_add(&profile->tree, r, g, b, a, profile->numcolors);\n\t\t\t\t\tif(profile->numcolors < 256) {\n\t\t\t\t\t\tunsigned char* p = profile->palette;\n\t\t\t\t\t\tunsigned i = profile->numcolors;\n\t\t\t\t\t\tp[i * 4 + 0] = r;\n\t\t\t\t\t\tp[i * 4 + 1] = g;\n\t\t\t\t\t\tp[i * 4 + 2] = b;\n\t\t\t\t\t\tp[i * 4 + 3] = a;\n\t\t\t\t\t\t}\n\t\t\t\t\tprofile->numcolors++;\n\t\t\t\t\tif(profile->numcolors >= profile->maxnumcolors) profile->numcolors_done = 1;\n\t\t\t\t\t}\n\t\t\t\t}\n\n\t\t\tif(profile->alpha_done && profile->numcolors_done && profile->colored_done && profile->greybits_done) {\n\t\t\t\tbreak;\n\t\t\t\t}\n\t\t\t};\n\t\t}\n\n\t/*make the profile's key always 16-bit for consistency*/\n\tif(mode->bitdepth < 16) {\n\t\t/*repeat each byte twice*/\n\t\tprofile->key_r *= 257;\n\t\tprofile->key_g *= 257;\n\t\tprofile->key_b *= 257;\n\t\t}\n\n\treturn error;\n\t}\n\nstatic void setColorKeyFrom16bit(LodePNGColorMode* mode_out, unsigned r, unsigned g, unsigned b, unsigned bitdepth)\n\t{\n\tunsigned mask = (1 << bitdepth) - 1;\n\tmode_out->key_defined = 1;\n\tmode_out->key_r = r & mask;\n\tmode_out->key_g = g & mask;\n\tmode_out->key_b = b & mask;\n\t}\n\n/*updates values of mode with a potentially smaller color model. mode_out should\ncontain the user chosen color model, but will be overwritten with the new chosen one.*/\nunsigned lodepng_auto_choose_color(LodePNGColorMode* mode_out,\n                                   const unsigned char* image, unsigned w, unsigned h,\n                                   const LodePNGColorMode* mode_in,\n                                   LodePNGAutoConvert auto_convert)\n\t{\n\tColorProfile profile;\n\tunsigned error = 0;\n\tint no_nibbles = auto_convert == LAC_AUTO_NO_NIBBLES || auto_convert == LAC_AUTO_NO_NIBBLES_NO_PALETTE;\n\tint no_palette = auto_convert == LAC_AUTO_NO_PALETTE || auto_convert == LAC_AUTO_NO_NIBBLES_NO_PALETTE;\n\n\tif(auto_convert == LAC_ALPHA) {\n\t\tif(mode_out->colortype != LCT_RGBA && mode_out->colortype != LCT_GREY_ALPHA) return 0;\n\t\t}\n\n\tcolor_profile_init(&profile, mode_in);\n\tif(auto_convert == LAC_ALPHA) {\n\t\tprofile.colored_done = 1;\n\t\tprofile.greybits_done = 1;\n\t\tprofile.numcolors_done = 1;\n\t\tprofile.sixteenbit_done = 1;\n\t\t}\n\terror = get_color_profile(&profile, image, w * h, mode_in, 0 /*fix_png*/);\n\tif(!error && auto_convert == LAC_ALPHA) {\n\t\tif(!profile.alpha) {\n\t\t\tmode_out->colortype = (mode_out->colortype == LCT_RGBA ? LCT_RGB : LCT_GREY);\n\t\t\tif(profile.key) setColorKeyFrom16bit(mode_out, profile.key_r, profile.key_g, profile.key_b, mode_out->bitdepth);\n\t\t\t}\n\t\t}\n\telse if(!error && auto_convert != LAC_ALPHA) {\n\t\tmode_out->key_defined = 0;\n\n\t\tif(profile.sixteenbit) {\n\t\t\tmode_out->bitdepth = 16;\n\t\t\tif(profile.alpha) {\n\t\t\t\tmode_out->colortype = profile.colored ? LCT_RGBA : LCT_GREY_ALPHA;\n\t\t\t\t}\n\t\t\telse {\n\t\t\t\tmode_out->colortype = profile.colored ? LCT_RGB : LCT_GREY;\n\t\t\t\tif(profile.key) setColorKeyFrom16bit(mode_out, profile.key_r, profile.key_g, profile.key_b, mode_out->bitdepth);\n\t\t\t\t}\n\t\t\t}\n\t\telse {   /*less than 16 bits per channel*/\n\t\t\t/*don't add palette overhead if image hasn't got a lot of pixels*/\n\t\t\tunsigned n = profile.numcolors;\n\t\t\tint palette_ok = !no_palette && n <= 256 && (n * 2 < w * h);\n\t\t\tunsigned palettebits = n <= 2 ? 1 : (n <= 4 ? 2 : (n <= 16 ? 4 : 8));\n\t\t\tint grey_ok = !profile.colored && !profile.alpha; /*grey without alpha, with potentially low bits*/\n\t\t\tif(palette_ok || grey_ok) {\n\t\t\t\tif(!palette_ok || (grey_ok && profile.greybits <= palettebits)) {\n\t\t\t\t\tunsigned grey = profile.key_r;\n\t\t\t\t\tmode_out->colortype = LCT_GREY;\n\t\t\t\t\tmode_out->bitdepth = profile.greybits;\n\t\t\t\t\tif(profile.key) setColorKeyFrom16bit(mode_out, grey, grey, grey, mode_out->bitdepth);\n\t\t\t\t\t}\n\t\t\t\telse {\n\t\t\t\t\t/*fill in the palette*/\n\t\t\t\t\tunsigned i;\n\t\t\t\t\tunsigned char* p = profile.palette;\n\t\t\t\t\t/*remove potential earlier palette*/\n\t\t\t\t\tlodepng_palette_clear(mode_out);\n\t\t\t\t\tfor(i = 0; i < profile.numcolors; i++) {\n\t\t\t\t\t\terror = lodepng_palette_add(mode_out, p[i * 4 + 0], p[i * 4 + 1], p[i * 4 + 2], p[i * 4 + 3]);\n\t\t\t\t\t\tif(error) break;\n\t\t\t\t\t\t}\n\n\t\t\t\t\tmode_out->colortype = LCT_PALETTE;\n\t\t\t\t\tmode_out->bitdepth = palettebits;\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\telse {   /*8-bit per channel*/\n\t\t\t\tmode_out->bitdepth = 8;\n\t\t\t\tif(profile.alpha) {\n\t\t\t\t\tmode_out->colortype = profile.colored ? LCT_RGBA : LCT_GREY_ALPHA;\n\t\t\t\t\t}\n\t\t\t\telse {\n\t\t\t\t\tmode_out->colortype = profile.colored ? LCT_RGB : LCT_GREY /*LCT_GREY normally won't occur, already done earlier*/;\n\t\t\t\t\tif(profile.key) setColorKeyFrom16bit(mode_out, profile.key_r, profile.key_g, profile.key_b, mode_out->bitdepth);\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t}\n\t\t}\n\n\tcolor_profile_cleanup(&profile);\n\n\tif(mode_out->colortype == LCT_PALETTE && mode_in->palettesize == mode_out->palettesize) {\n\t\t/*In this case keep the palette order of the input, so that the user can choose an optimal one*/\n\t\tsize_t i;\n\t\tfor(i = 0; i < mode_in->palettesize * 4; i++) {\n\t\t\tmode_out->palette[i] = mode_in->palette[i];\n\t\t\t}\n\t\t}\n\n\tif(no_nibbles && mode_out->bitdepth < 8) {\n\t\t/*palette can keep its small amount of colors, as long as no indices use it*/\n\t\tmode_out->bitdepth = 8;\n\t\t}\n\n\treturn error;\n\t}\n\n#endif /* #ifdef LODEPNG_COMPILE_ENCODER */\n\n/*\nPaeth predicter, used by PNG filter type 4\nThe parameters are of type short, but should come from unsigned chars, the shorts\nare only needed to make the paeth calculation correct.\n*/\nstatic unsigned char paethPredictor(short a, short b, short c)\n\t{\n\tshort pa = abs(b - c);\n\tshort pb = abs(a - c);\n\tshort pc = abs(a + b - c - c);\n\n\tif(pc < pa && pc < pb) return (unsigned char)c;\n\telse if(pb < pa) return (unsigned char)b;\n\telse return (unsigned char)a;\n\t}\n\n/*shared values used by multiple Adam7 related functions*/\n\nstatic const unsigned ADAM7_IX[7] = { 0, 4, 0, 2, 0, 1, 0 }; /*x start values*/\nstatic const unsigned ADAM7_IY[7] = { 0, 0, 4, 0, 2, 0, 1 }; /*y start values*/\nstatic const unsigned ADAM7_DX[7] = { 8, 8, 4, 4, 2, 2, 1 }; /*x delta values*/\nstatic const unsigned ADAM7_DY[7] = { 8, 8, 8, 4, 4, 2, 2 }; /*y delta values*/\n\n/*\nOutputs various dimensions and positions in the image related to the Adam7 reduced images.\npassw: output containing the width of the 7 passes\npassh: output containing the height of the 7 passes\nfilter_passstart: output containing the index of the start and end of each\nreduced image with filter bytes\npadded_passstart output containing the index of the start and end of each\nreduced image when without filter bytes but with padded scanlines\npassstart: output containing the index of the start and end of each reduced\nimage without padding between scanlines, but still padding between the images\nw, h: width and height of non-interlaced image\nbpp: bits per pixel\n\"padded\" is only relevant if bpp is less than 8 and a scanline or image does not\nend at a full byte\n*/\nstatic void Adam7_getpassvalues(unsigned passw[7], unsigned passh[7], size_t filter_passstart[8],\n                                size_t padded_passstart[8], size_t passstart[8], unsigned w, unsigned h, unsigned bpp)\n\t{\n\t/*the passstart values have 8 values: the 8th one indicates the byte after the end of the 7th (= last) pass*/\n\tunsigned i;\n\n\t/*calculate width and height in pixels of each pass*/\n\tfor(i = 0; i < 7; i++) {\n\t\tpassw[i] = (w + ADAM7_DX[i] - ADAM7_IX[i] - 1) / ADAM7_DX[i];\n\t\tpassh[i] = (h + ADAM7_DY[i] - ADAM7_IY[i] - 1) / ADAM7_DY[i];\n\t\tif(passw[i] == 0) passh[i] = 0;\n\t\tif(passh[i] == 0) passw[i] = 0;\n\t\t}\n\n\tfilter_passstart[0] = padded_passstart[0] = passstart[0] = 0;\n\tfor(i = 0; i < 7; i++) {\n\t\t/*if passw[i] is 0, it's 0 bytes, not 1 (no filtertype-byte)*/\n\t\tfilter_passstart[i + 1] = filter_passstart[i]\n\t\t                          + ((passw[i] && passh[i]) ? passh[i] * (1 + (passw[i] * bpp + 7) / 8) : 0);\n\t\t/*bits padded if needed to fill full byte at end of each scanline*/\n\t\tpadded_passstart[i + 1] = padded_passstart[i] + passh[i] * ((passw[i] * bpp + 7) / 8);\n\t\t/*only padded at end of reduced image*/\n\t\tpassstart[i + 1] = passstart[i] + (passh[i] * passw[i] * bpp + 7) / 8;\n\t\t}\n\t}\n\n#ifdef LODEPNG_COMPILE_DECODER\n\n/* ////////////////////////////////////////////////////////////////////////// */\n/* / PNG Decoder                                                            / */\n/* ////////////////////////////////////////////////////////////////////////// */\n\n/*read the information from the header and store it in the LodePNGInfo. return value is error*/\nunsigned lodepng_inspect(unsigned* w, unsigned* h, LodePNGState* state,\n                         const unsigned char* in, size_t insize)\n\t{\n\tLodePNGInfo* info = &state->info_png;\n\tif(insize == 0 || in == 0) {\n\t\tCERROR_RETURN_ERROR(state->error, 48); /*error: the given data is empty*/\n\t\t}\n\tif(insize < 29) {\n\t\tCERROR_RETURN_ERROR(state->error, 27); /*error: the data length is smaller than the length of a PNG header*/\n\t\t}\n\n\t/*when decoding a new PNG image, make sure all parameters created after previous decoding are reset*/\n\tlodepng_info_cleanup(info);\n\tlodepng_info_init(info);\n\n\tif(in[0] != 137 || in[1] != 80 || in[2] != 78 || in[3] != 71\n\t      || in[4] != 13 || in[5] != 10 || in[6] != 26 || in[7] != 10) {\n\t\tCERROR_RETURN_ERROR(state->error, 28); /*error: the first 8 bytes are not the correct PNG signature*/\n\t\t}\n\tif(in[12] != 'I' || in[13] != 'H' || in[14] != 'D' || in[15] != 'R') {\n\t\tCERROR_RETURN_ERROR(state->error, 29); /*error: it doesn't start with a IHDR chunk!*/\n\t\t}\n\n\t/*read the values given in the header*/\n\t*w = lodepng_read32bitInt(&in[16]);\n\t*h = lodepng_read32bitInt(&in[20]);\n\tinfo->color.bitdepth = in[24];\n\tinfo->color.colortype = (LodePNGColorType)in[25];\n\tinfo->compression_method = in[26];\n\tinfo->filter_method = in[27];\n\tinfo->interlace_method = in[28];\n\n\tif(!state->decoder.ignore_crc) {\n\t\tunsigned CRC = lodepng_read32bitInt(&in[29]);\n\t\tunsigned checksum = lodepng_crc32(&in[12], 17);\n\t\tif(CRC != checksum) {\n\t\t\tCERROR_RETURN_ERROR(state->error, 57); /*invalid CRC*/\n\t\t\t}\n\t\t}\n\n\t/*error: only compression method 0 is allowed in the specification*/\n\tif(info->compression_method != 0) CERROR_RETURN_ERROR(state->error, 32);\n\t/*error: only filter method 0 is allowed in the specification*/\n\tif(info->filter_method != 0) CERROR_RETURN_ERROR(state->error, 33);\n\t/*error: only interlace methods 0 and 1 exist in the specification*/\n\tif(info->interlace_method > 1) CERROR_RETURN_ERROR(state->error, 34);\n\n\tstate->error = checkColorValidity(info->color.colortype, info->color.bitdepth);\n\treturn state->error;\n\t}\n\nstatic unsigned unfilterScanline(unsigned char* recon, const unsigned char* scanline, const unsigned char* precon,\n                                 size_t bytewidth, unsigned char filterType, size_t length)\n\t{\n\t/*\n\tFor PNG filter method 0\n\tunfilter a PNG image scanline by scanline. when the pixels are smaller than 1 byte,\n\tthe filter works byte per byte (bytewidth = 1)\n\tprecon is the previous unfiltered scanline, recon the result, scanline the current one\n\tthe incoming scanlines do NOT include the filtertype byte, that one is given in the parameter filterType instead\n\trecon and scanline MAY be the same memory address! precon must be disjoint.\n\t*/\n\n\tsize_t i;\n\tswitch(filterType) {\n\t\tcase 0:\n\t\t\tfor(i = 0; i < length; i++) recon[i] = scanline[i];\n\t\t\tbreak;\n\t\tcase 1:\n\t\t\tfor(i = 0; i < bytewidth; i++) recon[i] = scanline[i];\n\t\t\tfor(i = bytewidth; i < length; i++) recon[i] = scanline[i] + recon[i - bytewidth];\n\t\t\tbreak;\n\t\tcase 2:\n\t\t\tif(precon) {\n\t\t\t\tfor(i = 0; i < length; i++) recon[i] = scanline[i] + precon[i];\n\t\t\t\t}\n\t\t\telse {\n\t\t\t\tfor(i = 0; i < length; i++) recon[i] = scanline[i];\n\t\t\t\t}\n\t\t\tbreak;\n\t\tcase 3:\n\t\t\tif(precon) {\n\t\t\t\tfor(i = 0; i < bytewidth; i++) recon[i] = scanline[i] + precon[i] / 2;\n\t\t\t\tfor(i = bytewidth; i < length; i++) recon[i] = scanline[i] + ((recon[i - bytewidth] + precon[i]) / 2);\n\t\t\t\t}\n\t\t\telse {\n\t\t\t\tfor(i = 0; i < bytewidth; i++) recon[i] = scanline[i];\n\t\t\t\tfor(i = bytewidth; i < length; i++) recon[i] = scanline[i] + recon[i - bytewidth] / 2;\n\t\t\t\t}\n\t\t\tbreak;\n\t\tcase 4:\n\t\t\tif(precon) {\n\t\t\t\tfor(i = 0; i < bytewidth; i++) {\n\t\t\t\t\trecon[i] = (scanline[i] + precon[i]); /*paethPredictor(0, precon[i], 0) is always precon[i]*/\n\t\t\t\t\t}\n\t\t\t\tfor(i = bytewidth; i < length; i++) {\n\t\t\t\t\trecon[i] = (scanline[i] + paethPredictor(recon[i - bytewidth], precon[i], precon[i - bytewidth]));\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\telse {\n\t\t\t\tfor(i = 0; i < bytewidth; i++) {\n\t\t\t\t\trecon[i] = scanline[i];\n\t\t\t\t\t}\n\t\t\t\tfor(i = bytewidth; i < length; i++) {\n\t\t\t\t\t/*paethPredictor(recon[i - bytewidth], 0, 0) is always recon[i - bytewidth]*/\n\t\t\t\t\trecon[i] = (scanline[i] + recon[i - bytewidth]);\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\tbreak;\n\t\tdefault:\n\t\t\treturn 36; /*error: unexisting filter type given*/\n\t\t}\n\treturn 0;\n\t}\n\nstatic unsigned unfilter(unsigned char* out, const unsigned char* in, unsigned w, unsigned h, unsigned bpp)\n\t{\n\t/*\n\tFor PNG filter method 0\n\tthis function unfilters a single image (e.g. without interlacing this is called once, with Adam7 seven times)\n\tout must have enough bytes allocated already, in must have the scanlines + 1 filtertype byte per scanline\n\tw and h are image dimensions or dimensions of reduced image, bpp is bits per pixel\n\tin and out are allowed to be the same memory address (but aren't the same size since in has the extra filter bytes)\n\t*/\n\n\tunsigned y;\n\tunsigned char* prevline = 0;\n\n\t/*bytewidth is used for filtering, is 1 when bpp < 8, number of bytes per pixel otherwise*/\n\tsize_t bytewidth = (bpp + 7) / 8;\n\tsize_t linebytes = (w * bpp + 7) / 8;\n\n\tfor(y = 0; y < h; y++) {\n\t\tsize_t outindex = linebytes * y;\n\t\tsize_t inindex = (1 + linebytes) * y; /*the extra filterbyte added to each row*/\n\t\tunsigned char filterType = in[inindex];\n\n\t\tCERROR_TRY_RETURN(unfilterScanline(&out[outindex], &in[inindex + 1], prevline, bytewidth, filterType, linebytes));\n\n\t\tprevline = &out[outindex];\n\t\t}\n\n\treturn 0;\n\t}\n\n/*\nin: Adam7 interlaced image, with no padding bits between scanlines, but between\nreduced images so that each reduced image starts at a byte.\nout: the same pixels, but re-ordered so that they're now a non-interlaced image with size w*h\nbpp: bits per pixel\nout has the following size in bits: w * h * bpp.\nin is possibly bigger due to padding bits between reduced images.\nout must be big enough AND must be 0 everywhere if bpp < 8 in the current implementation\n(because that's likely a little bit faster)\nNOTE: comments about padding bits are only relevant if bpp < 8\n*/\nstatic void Adam7_deinterlace(unsigned char* out, const unsigned char* in, unsigned w, unsigned h, unsigned bpp)\n\t{\n\tunsigned passw[7], passh[7];\n\tsize_t filter_passstart[8], padded_passstart[8], passstart[8];\n\tunsigned i;\n\n\tAdam7_getpassvalues(passw, passh, filter_passstart, padded_passstart, passstart, w, h, bpp);\n\n\tif(bpp >= 8) {\n\t\tfor(i = 0; i < 7; i++) {\n\t\t\tunsigned x, y, b;\n\t\t\tsize_t bytewidth = bpp / 8;\n\t\t\tfor(y = 0; y < passh[i]; y++)\n\t\t\t\tfor(x = 0; x < passw[i]; x++) {\n\t\t\t\t\tsize_t pixelinstart = passstart[i] + (y * passw[i] + x) * bytewidth;\n\t\t\t\t\tsize_t pixeloutstart = ((ADAM7_IY[i] + y * ADAM7_DY[i]) * w + ADAM7_IX[i] + x * ADAM7_DX[i]) * bytewidth;\n\t\t\t\t\tfor(b = 0; b < bytewidth; b++) {\n\t\t\t\t\t\tout[pixeloutstart + b] = in[pixelinstart + b];\n\t\t\t\t\t\t}\n\t\t\t\t\t}\n\t\t\t}\n\t\t}\n\telse {   /*bpp < 8: Adam7 with pixels < 8 bit is a bit trickier: with bit pointers*/\n\t\tfor(i = 0; i < 7; i++) {\n\t\t\tunsigned x, y, b;\n\t\t\tunsigned ilinebits = bpp * passw[i];\n\t\t\tunsigned olinebits = bpp * w;\n\t\t\tsize_t obp, ibp; /*bit pointers (for out and in buffer)*/\n\t\t\tfor(y = 0; y < passh[i]; y++)\n\t\t\t\tfor(x = 0; x < passw[i]; x++) {\n\t\t\t\t\tibp = (8 * passstart[i]) + (y * ilinebits + x * bpp);\n\t\t\t\t\tobp = (ADAM7_IY[i] + y * ADAM7_DY[i]) * olinebits + (ADAM7_IX[i] + x * ADAM7_DX[i]) * bpp;\n\t\t\t\t\tfor(b = 0; b < bpp; b++) {\n\t\t\t\t\t\tunsigned char bit = readBitFromReversedStream(&ibp, in);\n\t\t\t\t\t\t/*note that this function assumes the out buffer is completely 0, use setBitOfReversedStream otherwise*/\n\t\t\t\t\t\tsetBitOfReversedStream0(&obp, out, bit);\n\t\t\t\t\t\t}\n\t\t\t\t\t}\n\t\t\t}\n\t\t}\n\t}\n\nstatic void removePaddingBits(unsigned char* out, const unsigned char* in,\n                              size_t olinebits, size_t ilinebits, unsigned h)\n\t{\n\t/*\n\tAfter filtering there are still padding bits if scanlines have non multiple of 8 bit amounts. They need\n\tto be removed (except at last scanline of (Adam7-reduced) image) before working with pure image buffers\n\tfor the Adam7 code, the color convert code and the output to the user.\n\tin and out are allowed to be the same buffer, in may also be higher but still overlapping; in must\n\thave >= ilinebits*h bits, out must have >= olinebits*h bits, olinebits must be <= ilinebits\n\talso used to move bits after earlier such operations happened, e.g. in a sequence of reduced images from Adam7\n\tonly useful if (ilinebits - olinebits) is a value in the range 1..7\n\t*/\n\tunsigned y;\n\tsize_t diff = ilinebits - olinebits;\n\tsize_t ibp = 0, obp = 0; /*input and output bit pointers*/\n\tfor(y = 0; y < h; y++) {\n\t\tsize_t x;\n\t\tfor(x = 0; x < olinebits; x++) {\n\t\t\tunsigned char bit = readBitFromReversedStream(&ibp, in);\n\t\t\tsetBitOfReversedStream(&obp, out, bit);\n\t\t\t}\n\t\tibp += diff;\n\t\t}\n\t}\n\n/*out must be buffer big enough to contain full image, and in must contain the full decompressed data from\nthe IDAT chunks (with filter index bytes and possible padding bits)\nreturn value is error*/\nstatic unsigned postProcessScanlines(unsigned char* out, unsigned char* in,\n                                     unsigned w, unsigned h, const LodePNGInfo* info_png)\n\t{\n\t/*\n\tThis function converts the filtered-padded-interlaced data into pure 2D image buffer with the PNG's colortype.\n\tSteps:\n\t*) if no Adam7: 1) unfilter 2) remove padding bits (= posible extra bits per scanline if bpp < 8)\n\t*) if adam7: 1) 7x unfilter 2) 7x remove padding bits 3) Adam7_deinterlace\n\tNOTE: the in buffer will be overwritten with intermediate data!\n\t*/\n\tunsigned bpp = lodepng_get_bpp(&info_png->color);\n\tif(bpp == 0) return 31; /*error: invalid colortype*/\n\n\tif(info_png->interlace_method == 0) {\n\t\tif(bpp < 8 && w * bpp != ((w * bpp + 7) / 8) * 8) {\n\t\t\tCERROR_TRY_RETURN(unfilter(in, in, w, h, bpp));\n\t\t\tremovePaddingBits(out, in, w * bpp, ((w * bpp + 7) / 8) * 8, h);\n\t\t\t}\n\t\t/*we can immediatly filter into the out buffer, no other steps needed*/\n\t\telse CERROR_TRY_RETURN(unfilter(out, in, w, h, bpp));\n\t\t}\n\telse {   /*interlace_method is 1 (Adam7)*/\n\t\tunsigned passw[7], passh[7];\n\t\tsize_t filter_passstart[8], padded_passstart[8], passstart[8];\n\t\tunsigned i;\n\n\t\tAdam7_getpassvalues(passw, passh, filter_passstart, padded_passstart, passstart, w, h, bpp);\n\n\t\tfor(i = 0; i < 7; i++) {\n\t\t\tCERROR_TRY_RETURN(unfilter(&in[padded_passstart[i]], &in[filter_passstart[i]], passw[i], passh[i], bpp));\n\t\t\t/*TODO: possible efficiency improvement: if in this reduced image the bits fit nicely in 1 scanline,\n\t\t\tmove bytes instead of bits or move not at all*/\n\t\t\tif(bpp < 8) {\n\t\t\t\t/*remove padding bits in scanlines; after this there still may be padding\n\t\t\t\tbits between the different reduced images: each reduced image still starts nicely at a byte*/\n\t\t\t\tremovePaddingBits(&in[passstart[i]], &in[padded_passstart[i]], passw[i] * bpp,\n\t\t\t\t                  ((passw[i] * bpp + 7) / 8) * 8, passh[i]);\n\t\t\t\t}\n\t\t\t}\n\n\t\tAdam7_deinterlace(out, in, w, h, bpp);\n\t\t}\n\n\treturn 0;\n\t}\n\nstatic unsigned readChunk_PLTE(LodePNGColorMode* color, const unsigned char* data, size_t chunkLength)\n\t{\n\tunsigned pos = 0, i;\n\tif(color->palette) lodepng_free(color->palette);\n\tcolor->palettesize = chunkLength / 3;\n\tcolor->palette = (unsigned char*)lodepng_malloc(4 * color->palettesize);\n\tif(!color->palette && color->palettesize) {\n\t\tcolor->palettesize = 0;\n\t\treturn 83; /*alloc fail*/\n\t\t}\n\tif(color->palettesize > 256) return 38; /*error: palette too big*/\n\n\tfor(i = 0; i < color->palettesize; i++) {\n\t\tcolor->palette[4 * i + 0] = data[pos++]; /*R*/\n\t\tcolor->palette[4 * i + 1] = data[pos++]; /*G*/\n\t\tcolor->palette[4 * i + 2] = data[pos++]; /*B*/\n\t\tcolor->palette[4 * i + 3] = 255; /*alpha*/\n\t\t}\n\n\treturn 0; /* OK */\n\t}\n\nstatic unsigned readChunk_tRNS(LodePNGColorMode* color, const unsigned char* data, size_t chunkLength)\n\t{\n\tunsigned i;\n\tif(color->colortype == LCT_PALETTE) {\n\t\t/*error: more alpha values given than there are palette entries*/\n\t\tif(chunkLength > color->palettesize) return 38;\n\n\t\tfor(i = 0; i < chunkLength; i++) color->palette[4 * i + 3] = data[i];\n\t\t}\n\telse if(color->colortype == LCT_GREY) {\n\t\t/*error: this chunk must be 2 bytes for greyscale image*/\n\t\tif(chunkLength != 2) return 30;\n\n\t\tcolor->key_defined = 1;\n\t\tcolor->key_r = color->key_g = color->key_b = 256 * data[0] + data[1];\n\t\t}\n\telse if(color->colortype == LCT_RGB) {\n\t\t/*error: this chunk must be 6 bytes for RGB image*/\n\t\tif(chunkLength != 6) return 41;\n\n\t\tcolor->key_defined = 1;\n\t\tcolor->key_r = 256 * data[0] + data[1];\n\t\tcolor->key_g = 256 * data[2] + data[3];\n\t\tcolor->key_b = 256 * data[4] + data[5];\n\t\t}\n\telse return 42;   /*error: tRNS chunk not allowed for other color models*/\n\n\treturn 0; /* OK */\n\t}\n\n\n#ifdef LODEPNG_COMPILE_ANCILLARY_CHUNKS\n/*background color chunk (bKGD)*/\nstatic unsigned readChunk_bKGD(LodePNGInfo* info, const unsigned char* data, size_t chunkLength)\n\t{\n\tif(info->color.colortype == LCT_PALETTE) {\n\t\t/*error: this chunk must be 1 byte for indexed color image*/\n\t\tif(chunkLength != 1) return 43;\n\n\t\tinfo->background_defined = 1;\n\t\tinfo->background_r = info->background_g = info->background_b = data[0];\n\t\t}\n\telse if(info->color.colortype == LCT_GREY || info->color.colortype == LCT_GREY_ALPHA) {\n\t\t/*error: this chunk must be 2 bytes for greyscale image*/\n\t\tif(chunkLength != 2) return 44;\n\n\t\tinfo->background_defined = 1;\n\t\tinfo->background_r = info->background_g = info->background_b\n\t\t                     = 256 * data[0] + data[1];\n\t\t}\n\telse if(info->color.colortype == LCT_RGB || info->color.colortype == LCT_RGBA) {\n\t\t/*error: this chunk must be 6 bytes for greyscale image*/\n\t\tif(chunkLength != 6) return 45;\n\n\t\tinfo->background_defined = 1;\n\t\tinfo->background_r = 256 * data[0] + data[1];\n\t\tinfo->background_g = 256 * data[2] + data[3];\n\t\tinfo->background_b = 256 * data[4] + data[5];\n\t\t}\n\n\treturn 0; /* OK */\n\t}\n\n/*text chunk (tEXt)*/\nstatic unsigned readChunk_tEXt(LodePNGInfo* info, const unsigned char* data, size_t chunkLength)\n\t{\n\tunsigned error = 0;\n\tchar *key = 0, *str = 0;\n\tunsigned i;\n\n\twhile(!error) { /*not really a while loop, only used to break on error*/\n\t\tunsigned length, string2_begin;\n\n\t\tlength = 0;\n\t\twhile(length < chunkLength && data[length] != 0) length++;\n\t\t/*even though it's not allowed by the standard, no error is thrown if\n\t\tthere's no null termination char, if the text is empty*/\n\t\tif(length < 1 || length > 79) CERROR_BREAK(error, 89); /*keyword too short or long*/\n\n\t\tkey = (char*)lodepng_malloc(length + 1);\n\t\tif(!key) CERROR_BREAK(error, 83); /*alloc fail*/\n\n\t\tkey[length] = 0;\n\t\tfor(i = 0; i < length; i++) key[i] = data[i];\n\n\t\tstring2_begin = length + 1; /*skip keyword null terminator*/\n\n\t\tlength = chunkLength < string2_begin ? 0 : chunkLength - string2_begin;\n\t\tstr = (char*)lodepng_malloc(length + 1);\n\t\tif(!str) CERROR_BREAK(error, 83); /*alloc fail*/\n\n\t\tstr[length] = 0;\n\t\tfor(i = 0; i < length; i++) str[i] = data[string2_begin + i];\n\n\t\terror = lodepng_add_text(info, key, str);\n\n\t\tbreak;\n\t\t}\n\n\tlodepng_free(key);\n\tlodepng_free(str);\n\n\treturn error;\n\t}\n\n/*compressed text chunk (zTXt)*/\nstatic unsigned readChunk_zTXt(LodePNGInfo* info, const LodePNGDecompressSettings* zlibsettings,\n                               const unsigned char* data, size_t chunkLength)\n\t{\n\tunsigned error = 0;\n\tunsigned i;\n\n\tunsigned length, string2_begin;\n\tchar *key = 0;\n\tucvector decoded;\n\n\tucvector_init(&decoded);\n\n\twhile(!error) { /*not really a while loop, only used to break on error*/\n\t\tfor(length = 0; length < chunkLength && data[length] != 0; length++) ;\n\t\tif(length + 2 >= chunkLength) CERROR_BREAK(error, 75); /*no null termination, corrupt?*/\n\t\tif(length < 1 || length > 79) CERROR_BREAK(error, 89); /*keyword too short or long*/\n\n\t\tkey = (char*)lodepng_malloc(length + 1);\n\t\tif(!key) CERROR_BREAK(error, 83); /*alloc fail*/\n\n\t\tkey[length] = 0;\n\t\tfor(i = 0; i < length; i++) key[i] = data[i];\n\n\t\tif(data[length + 1] != 0) CERROR_BREAK(error, 72); /*the 0 byte indicating compression must be 0*/\n\n\t\tstring2_begin = length + 2;\n\t\tif(string2_begin > chunkLength) CERROR_BREAK(error, 75); /*no null termination, corrupt?*/\n\n\t\tlength = chunkLength - string2_begin;\n\t\t/*will fail if zlib error, e.g. if length is too small*/\n\t\terror = zlib_decompress(&decoded.data, &decoded.size,\n\t\t                        (unsigned char*)(&data[string2_begin]),\n\t\t                        length, zlibsettings);\n\t\tif(error) break;\n\t\tucvector_push_back(&decoded, 0);\n\n\t\terror = lodepng_add_text(info, key, (char*)decoded.data);\n\n\t\tbreak;\n\t\t}\n\n\tlodepng_free(key);\n\tucvector_cleanup(&decoded);\n\n\treturn error;\n\t}\n\n/*international text chunk (iTXt)*/\nstatic unsigned readChunk_iTXt(LodePNGInfo* info, const LodePNGDecompressSettings* zlibsettings,\n                               const unsigned char* data, size_t chunkLength)\n\t{\n\tunsigned error = 0;\n\tunsigned i;\n\n\tunsigned length, begin, compressed;\n\tchar *key = 0, *langtag = 0, *transkey = 0;\n\tucvector decoded;\n\tucvector_init(&decoded);\n\n\twhile(!error) { /*not really a while loop, only used to break on error*/\n\t\t/*Quick check if the chunk length isn't too small. Even without check\n\t\tit'd still fail with other error checks below if it's too short. This just gives a different error code.*/\n\t\tif(chunkLength < 5) CERROR_BREAK(error, 30); /*iTXt chunk too short*/\n\n\t\t/*read the key*/\n\t\tfor(length = 0; length < chunkLength && data[length] != 0; length++) ;\n\t\tif(length + 3 >= chunkLength) CERROR_BREAK(error, 75); /*no null termination char, corrupt?*/\n\t\tif(length < 1 || length > 79) CERROR_BREAK(error, 89); /*keyword too short or long*/\n\n\t\tkey = (char*)lodepng_malloc(length + 1);\n\t\tif(!key) CERROR_BREAK(error, 83); /*alloc fail*/\n\n\t\tkey[length] = 0;\n\t\tfor(i = 0; i < length; i++) key[i] = data[i];\n\n\t\t/*read the compression method*/\n\t\tcompressed = data[length + 1];\n\t\tif(data[length + 2] != 0) CERROR_BREAK(error, 72); /*the 0 byte indicating compression must be 0*/\n\n\t\t/*even though it's not allowed by the standard, no error is thrown if\n\t\tthere's no null termination char, if the text is empty for the next 3 texts*/\n\n\t\t/*read the langtag*/\n\t\tbegin = length + 3;\n\t\tlength = 0;\n\t\tfor(i = begin; i < chunkLength && data[i] != 0; i++) length++;\n\n\t\tlangtag = (char*)lodepng_malloc(length + 1);\n\t\tif(!langtag) CERROR_BREAK(error, 83); /*alloc fail*/\n\n\t\tlangtag[length] = 0;\n\t\tfor(i = 0; i < length; i++) langtag[i] = data[begin + i];\n\n\t\t/*read the transkey*/\n\t\tbegin += length + 1;\n\t\tlength = 0;\n\t\tfor(i = begin; i < chunkLength && data[i] != 0; i++) length++;\n\n\t\ttranskey = (char*)lodepng_malloc(length + 1);\n\t\tif(!transkey) CERROR_BREAK(error, 83); /*alloc fail*/\n\n\t\ttranskey[length] = 0;\n\t\tfor(i = 0; i < length; i++) transkey[i] = data[begin + i];\n\n\t\t/*read the actual text*/\n\t\tbegin += length + 1;\n\n\t\tlength = chunkLength < begin ? 0 : chunkLength - begin;\n\n\t\tif(compressed) {\n\t\t\t/*will fail if zlib error, e.g. if length is too small*/\n\t\t\terror = zlib_decompress(&decoded.data, &decoded.size,\n\t\t\t                        (unsigned char*)(&data[begin]),\n\t\t\t                        length, zlibsettings);\n\t\t\tif(error) break;\n\t\t\tif(decoded.allocsize < decoded.size) decoded.allocsize = decoded.size;\n\t\t\tucvector_push_back(&decoded, 0);\n\t\t\t}\n\t\telse {\n\t\t\tif(!ucvector_resize(&decoded, length + 1)) CERROR_BREAK(error, 83 /*alloc fail*/);\n\n\t\t\tdecoded.data[length] = 0;\n\t\t\tfor(i = 0; i < length; i++) decoded.data[i] = data[begin + i];\n\t\t\t}\n\n\t\terror = lodepng_add_itext(info, key, langtag, transkey, (char*)decoded.data);\n\n\t\tbreak;\n\t\t}\n\n\tlodepng_free(key);\n\tlodepng_free(langtag);\n\tlodepng_free(transkey);\n\tucvector_cleanup(&decoded);\n\n\treturn error;\n\t}\n\nstatic unsigned readChunk_tIME(LodePNGInfo* info, const unsigned char* data, size_t chunkLength)\n\t{\n\tif(chunkLength != 7) return 73; /*invalid tIME chunk size*/\n\n\tinfo->time_defined = 1;\n\tinfo->time.year = 256 * data[0] + data[+ 1];\n\tinfo->time.month = data[2];\n\tinfo->time.day = data[3];\n\tinfo->time.hour = data[4];\n\tinfo->time.minute = data[5];\n\tinfo->time.second = data[6];\n\n\treturn 0; /* OK */\n\t}\n\nstatic unsigned readChunk_pHYs(LodePNGInfo* info, const unsigned char* data, size_t chunkLength)\n\t{\n\tif(chunkLength != 9) return 74; /*invalid pHYs chunk size*/\n\n\tinfo->phys_defined = 1;\n\tinfo->phys_x = 16777216 * data[0] + 65536 * data[1] + 256 * data[2] + data[3];\n\tinfo->phys_y = 16777216 * data[4] + 65536 * data[5] + 256 * data[6] + data[7];\n\tinfo->phys_unit = data[8];\n\n\treturn 0; /* OK */\n\t}\n#endif /*LODEPNG_COMPILE_ANCILLARY_CHUNKS*/\n\n/*read a PNG, the result will be in the same color type as the PNG (hence \"generic\")*/\nstatic void decodeGeneric(unsigned char** out, unsigned* w, unsigned* h,\n                          LodePNGState* state,\n                          const unsigned char* in, size_t insize)\n\t{\n\tunsigned char IEND = 0;\n\tconst unsigned char* chunk;\n\tsize_t i;\n\tucvector idat; /*the data from idat chunks*/\n\tucvector scanlines;\n\n\t/*for unknown chunk order*/\n\tunsigned unknown = 0;\n#ifdef LODEPNG_COMPILE_ANCILLARY_CHUNKS\n\tunsigned critical_pos = 1; /*1 = after IHDR, 2 = after PLTE, 3 = after IDAT*/\n#endif /*LODEPNG_COMPILE_ANCILLARY_CHUNKS*/\n\n\t/*provide some proper output values if error will happen*/\n\t*out = 0;\n\n\tstate->error = lodepng_inspect(w, h, state, in, insize); /*reads header and resets other parameters in state->info_png*/\n\tif(state->error) return;\n\n\tucvector_init(&idat);\n\tchunk = &in[33]; /*first byte of the first chunk after the header*/\n\n\t/*loop through the chunks, ignoring unknown chunks and stopping at IEND chunk.\n\tIDAT data is put at the start of the in buffer*/\n\twhile(!IEND && !state->error) {\n\t\tunsigned chunkLength;\n\t\tconst unsigned char* data; /*the data in the chunk*/\n\n\t\t/*error: size of the in buffer too small to contain next chunk*/\n\t\tif((size_t)((chunk - in) + 12) > insize || chunk < in) CERROR_BREAK(state->error, 30);\n\n\t\t/*length of the data of the chunk, excluding the length bytes, chunk type and CRC bytes*/\n\t\tchunkLength = lodepng_chunk_length(chunk);\n\t\t/*error: chunk length larger than the max PNG chunk size*/\n\t\tif(chunkLength > 2147483647) CERROR_BREAK(state->error, 63);\n\n\t\tif((size_t)((chunk - in) + chunkLength + 12) > insize || (chunk + chunkLength + 12) < in) {\n\t\t\tCERROR_BREAK(state->error, 64); /*error: size of the in buffer too small to contain next chunk*/\n\t\t\t}\n\n\t\tdata = lodepng_chunk_data_const(chunk);\n\n\t\t/*IDAT chunk, containing compressed image data*/\n\t\tif(lodepng_chunk_type_equals(chunk, \"IDAT\")) {\n\t\t\tsize_t oldsize = idat.size;\n\t\t\tif(!ucvector_resize(&idat, oldsize + chunkLength)) CERROR_BREAK(state->error, 83 /*alloc fail*/);\n\t\t\tfor(i = 0; i < chunkLength; i++) idat.data[oldsize + i] = data[i];\n#ifdef LODEPNG_COMPILE_ANCILLARY_CHUNKS\n\t\t\tcritical_pos = 3;\n#endif /*LODEPNG_COMPILE_ANCILLARY_CHUNKS*/\n\t\t\t}\n\t\t/*IEND chunk*/\n\t\telse if(lodepng_chunk_type_equals(chunk, \"IEND\")) {\n\t\t\tIEND = 1;\n\t\t\t}\n\t\t/*palette chunk (PLTE)*/\n\t\telse if(lodepng_chunk_type_equals(chunk, \"PLTE\")) {\n\t\t\tstate->error = readChunk_PLTE(&state->info_png.color, data, chunkLength);\n\t\t\tif(state->error) break;\n#ifdef LODEPNG_COMPILE_ANCILLARY_CHUNKS\n\t\t\tcritical_pos = 2;\n#endif /*LODEPNG_COMPILE_ANCILLARY_CHUNKS*/\n\t\t\t}\n\t\t/*palette transparency chunk (tRNS)*/\n\t\telse if(lodepng_chunk_type_equals(chunk, \"tRNS\")) {\n\t\t\tstate->error = readChunk_tRNS(&state->info_png.color, data, chunkLength);\n\t\t\tif(state->error) break;\n\t\t\t}\n#ifdef LODEPNG_COMPILE_ANCILLARY_CHUNKS\n\t\t/*background color chunk (bKGD)*/\n\t\telse if(lodepng_chunk_type_equals(chunk, \"bKGD\")) {\n\t\t\tstate->error = readChunk_bKGD(&state->info_png, data, chunkLength);\n\t\t\tif(state->error) break;\n\t\t\t}\n\t\t/*text chunk (tEXt)*/\n\t\telse if(lodepng_chunk_type_equals(chunk, \"tEXt\")) {\n\t\t\tif(state->decoder.read_text_chunks) {\n\t\t\t\tstate->error = readChunk_tEXt(&state->info_png, data, chunkLength);\n\t\t\t\tif(state->error) break;\n\t\t\t\t}\n\t\t\t}\n\t\t/*compressed text chunk (zTXt)*/\n\t\telse if(lodepng_chunk_type_equals(chunk, \"zTXt\")) {\n\t\t\tif(state->decoder.read_text_chunks) {\n\t\t\t\tstate->error = readChunk_zTXt(&state->info_png, &state->decoder.zlibsettings, data, chunkLength);\n\t\t\t\tif(state->error) break;\n\t\t\t\t}\n\t\t\t}\n\t\t/*international text chunk (iTXt)*/\n\t\telse if(lodepng_chunk_type_equals(chunk, \"iTXt\")) {\n\t\t\tif(state->decoder.read_text_chunks) {\n\t\t\t\tstate->error = readChunk_iTXt(&state->info_png, &state->decoder.zlibsettings, data, chunkLength);\n\t\t\t\tif(state->error) break;\n\t\t\t\t}\n\t\t\t}\n\t\telse if(lodepng_chunk_type_equals(chunk, \"tIME\")) {\n\t\t\tstate->error = readChunk_tIME(&state->info_png, data, chunkLength);\n\t\t\tif(state->error) break;\n\t\t\t}\n\t\telse if(lodepng_chunk_type_equals(chunk, \"pHYs\")) {\n\t\t\tstate->error = readChunk_pHYs(&state->info_png, data, chunkLength);\n\t\t\tif(state->error) break;\n\t\t\t}\n#endif /*LODEPNG_COMPILE_ANCILLARY_CHUNKS*/\n\t\telse { /*it's not an implemented chunk type, so ignore it: skip over the data*/\n\t\t\t/*error: unknown critical chunk (5th bit of first byte of chunk type is 0)*/\n\t\t\tif(!lodepng_chunk_ancillary(chunk)) CERROR_BREAK(state->error, 69);\n\n\t\t\tunknown = 1;\n#ifdef LODEPNG_COMPILE_ANCILLARY_CHUNKS\n\t\t\tif(state->decoder.remember_unknown_chunks) {\n\t\t\t\tstate->error = lodepng_chunk_append(&state->info_png.unknown_chunks_data[critical_pos - 1],\n\t\t\t\t                                    &state->info_png.unknown_chunks_size[critical_pos - 1], chunk);\n\t\t\t\tif(state->error) break;\n\t\t\t\t}\n#endif /*LODEPNG_COMPILE_ANCILLARY_CHUNKS*/\n\t\t\t}\n\n\t\tif(!state->decoder.ignore_crc && !unknown) { /*check CRC if wanted, only on known chunk types*/\n\t\t\tif(lodepng_chunk_check_crc(chunk)) CERROR_BREAK(state->error, 57); /*invalid CRC*/\n\t\t\t}\n\n\t\tif(!IEND) chunk = lodepng_chunk_next_const(chunk);\n\t\t}\n\n\tucvector_init(&scanlines);\n\tif(!state->error) {\n\t\t/*maximum final image length is already reserved in the vector's length - this is not really necessary*/\n\t\tif(!ucvector_resize(&scanlines, lodepng_get_raw_size(*w, *h, &state->info_png.color) + *h)) {\n\t\t\tstate->error = 83; /*alloc fail*/\n\t\t\t}\n\t\t}\n\tif(!state->error) {\n\t\t/*decompress with the Zlib decompressor*/\n\t\tstate->error = zlib_decompress(&scanlines.data, &scanlines.size, idat.data,\n\t\t                               idat.size, &state->decoder.zlibsettings);\n\t\t}\n\tucvector_cleanup(&idat);\n\n\tif(!state->error) {\n\t\tucvector outv;\n\t\tucvector_init(&outv);\n\t\tif(!ucvector_resizev(&outv,\n\t\t                     lodepng_get_raw_size(*w, *h, &state->info_png.color), 0)) state->error = 83; /*alloc fail*/\n\t\tif(!state->error) state->error = postProcessScanlines(outv.data, scanlines.data, *w, *h, &state->info_png);\n\t\t*out = outv.data;\n\t\t}\n\tucvector_cleanup(&scanlines);\n\t}\n\nunsigned lodepng_decode(unsigned char** out, unsigned* w, unsigned* h,\n                        LodePNGState* state,\n                        const unsigned char* in, size_t insize)\n\t{\n\t*out = 0;\n\tdecodeGeneric(out, w, h, state, in, insize);\n\tif(state->error) return state->error;\n\tif(!state->decoder.color_convert || lodepng_color_mode_equal(&state->info_raw, &state->info_png.color)) {\n\t\t/*same color type, no copying or converting of data needed*/\n\t\t/*store the info_png color settings on the info_raw so that the info_raw still reflects what colortype\n\t\tthe raw image has to the end user*/\n\t\tif(!state->decoder.color_convert) {\n\t\t\tstate->error = lodepng_color_mode_copy(&state->info_raw, &state->info_png.color);\n\t\t\tif(state->error) return state->error;\n\t\t\t}\n\t\t}\n\telse {\n\t\t/*color conversion needed; sort of copy of the data*/\n\t\tunsigned char* data = *out;\n\t\tsize_t outsize;\n\n\t\t/*TODO: check if this works according to the statement in the documentation: \"The converter can convert\n\t\tfrom greyscale input color type, to 8-bit greyscale or greyscale with alpha\"*/\n\t\tif(!(state->info_raw.colortype == LCT_RGB || state->info_raw.colortype == LCT_RGBA)\n\t\t      && !(state->info_raw.bitdepth == 8)) {\n\t\t\treturn 56; /*unsupported color mode conversion*/\n\t\t\t}\n\n\t\toutsize = lodepng_get_raw_size(*w, *h, &state->info_raw);\n\t\t*out = (unsigned char*)lodepng_malloc(outsize);\n\t\tif(!(*out)) {\n\t\t\tstate->error = 83; /*alloc fail*/\n\t\t\t}\n\t\telse state->error = lodepng_convert(*out, data, &state->info_raw, &state->info_png.color, *w, *h, state->decoder.fix_png);\n\t\tlodepng_free(data);\n\t\t}\n\treturn state->error;\n\t}\n\nunsigned lodepng_decode_memory(unsigned char** out, unsigned* w, unsigned* h, const unsigned char* in,\n                               size_t insize, LodePNGColorType colortype, unsigned bitdepth)\n\t{\n\tunsigned error;\n\tLodePNGState state;\n\tlodepng_state_init(&state);\n\tstate.info_raw.colortype = colortype;\n\tstate.info_raw.bitdepth = bitdepth;\n\terror = lodepng_decode(out, w, h, &state, in, insize);\n\tlodepng_state_cleanup(&state);\n\treturn error;\n\t}\n\nunsigned lodepng_decode32(unsigned char** out, unsigned* w, unsigned* h, const unsigned char* in, size_t insize)\n\t{\n\treturn lodepng_decode_memory(out, w, h, in, insize, LCT_RGBA, 8);\n\t}\n\nunsigned lodepng_decode24(unsigned char** out, unsigned* w, unsigned* h, const unsigned char* in, size_t insize)\n\t{\n\treturn lodepng_decode_memory(out, w, h, in, insize, LCT_RGB, 8);\n\t}\n\n#ifdef LODEPNG_COMPILE_DISK\nunsigned lodepng_decode_file(unsigned char** out, unsigned* w, unsigned* h, const char* filename,\n                             LodePNGColorType colortype, unsigned bitdepth)\n\t{\n\tunsigned char* buffer;\n\tsize_t buffersize;\n\tunsigned error;\n\terror = lodepng_load_file(&buffer, &buffersize, filename);\n\tif(!error) error = lodepng_decode_memory(out, w, h, buffer, buffersize, colortype, bitdepth);\n\tlodepng_free(buffer);\n\treturn error;\n\t}\n\nunsigned lodepng_decode32_file(unsigned char** out, unsigned* w, unsigned* h, const char* filename)\n\t{\n\treturn lodepng_decode_file(out, w, h, filename, LCT_RGBA, 8);\n\t}\n\nunsigned lodepng_decode24_file(unsigned char** out, unsigned* w, unsigned* h, const char* filename)\n\t{\n\treturn lodepng_decode_file(out, w, h, filename, LCT_RGB, 8);\n\t}\n#endif /*LODEPNG_COMPILE_DISK*/\n\nvoid lodepng_decoder_settings_init(LodePNGDecoderSettings* settings)\n\t{\n\tsettings->color_convert = 1;\n#ifdef LODEPNG_COMPILE_ANCILLARY_CHUNKS\n\tsettings->read_text_chunks = 1;\n\tsettings->remember_unknown_chunks = 0;\n#endif /*LODEPNG_COMPILE_ANCILLARY_CHUNKS*/\n\tsettings->ignore_crc = 0;\n\tsettings->fix_png = 0;\n\tlodepng_decompress_settings_init(&settings->zlibsettings);\n\t}\n\n#endif /*LODEPNG_COMPILE_DECODER*/\n\n#if defined(LODEPNG_COMPILE_DECODER) || defined(LODEPNG_COMPILE_ENCODER)\n\nvoid lodepng_state_init(LodePNGState* state)\n\t{\n#ifdef LODEPNG_COMPILE_DECODER\n\tlodepng_decoder_settings_init(&state->decoder);\n#endif /*LODEPNG_COMPILE_DECODER*/\n#ifdef LODEPNG_COMPILE_ENCODER\n\tlodepng_encoder_settings_init(&state->encoder);\n#endif /*LODEPNG_COMPILE_ENCODER*/\n\tlodepng_color_mode_init(&state->info_raw);\n\tlodepng_info_init(&state->info_png);\n\tstate->error = 1;\n\t}\n\nvoid lodepng_state_cleanup(LodePNGState* state)\n\t{\n\tlodepng_color_mode_cleanup(&state->info_raw);\n\tlodepng_info_cleanup(&state->info_png);\n\t}\n\nvoid lodepng_state_copy(LodePNGState* dest, const LodePNGState* source)\n\t{\n\tlodepng_state_cleanup(dest);\n\t*dest = *source;\n\tlodepng_color_mode_init(&dest->info_raw);\n\tlodepng_info_init(&dest->info_png);\n\tdest->error = lodepng_color_mode_copy(&dest->info_raw, &source->info_raw);\n\tif(dest->error) return;\n\tdest->error = lodepng_info_copy(&dest->info_png, &source->info_png);\n\tif(dest->error) return;\n\t}\n\n#endif /* defined(LODEPNG_COMPILE_DECODER) || defined(LODEPNG_COMPILE_ENCODER) */\n\n#ifdef LODEPNG_COMPILE_ENCODER\n\n/* ////////////////////////////////////////////////////////////////////////// */\n/* / PNG Encoder                                                            / */\n/* ////////////////////////////////////////////////////////////////////////// */\n\n/*chunkName must be string of 4 characters*/\nstatic unsigned addChunk(ucvector* out, const char* chunkName, const unsigned char* data, size_t length)\n\t{\n\tCERROR_TRY_RETURN(lodepng_chunk_create(&out->data, &out->size, (unsigned)length, chunkName, data));\n\tout->allocsize = out->size; /*fix the allocsize again*/\n\treturn 0;\n\t}\n\nstatic void writeSignature(ucvector* out)\n\t{\n\t/*8 bytes PNG signature, aka the magic bytes*/\n\tucvector_push_back(out, 137);\n\tucvector_push_back(out, 80);\n\tucvector_push_back(out, 78);\n\tucvector_push_back(out, 71);\n\tucvector_push_back(out, 13);\n\tucvector_push_back(out, 10);\n\tucvector_push_back(out, 26);\n\tucvector_push_back(out, 10);\n\t}\n\nstatic unsigned addChunk_IHDR(ucvector* out, unsigned w, unsigned h,\n                              LodePNGColorType colortype, unsigned bitdepth, unsigned interlace_method)\n\t{\n\tunsigned error = 0;\n\tucvector header;\n\tucvector_init(&header);\n\n\tlodepng_add32bitInt(&header, w); /*width*/\n\tlodepng_add32bitInt(&header, h); /*height*/\n\tucvector_push_back(&header, (unsigned char)bitdepth); /*bit depth*/\n\tucvector_push_back(&header, (unsigned char)colortype); /*color type*/\n\tucvector_push_back(&header, 0); /*compression method*/\n\tucvector_push_back(&header, 0); /*filter method*/\n\tucvector_push_back(&header, interlace_method); /*interlace method*/\n\n\terror = addChunk(out, \"IHDR\", header.data, header.size);\n\tucvector_cleanup(&header);\n\n\treturn error;\n\t}\n\nstatic unsigned addChunk_PLTE(ucvector* out, const LodePNGColorMode* info)\n\t{\n\tunsigned error = 0;\n\tsize_t i;\n\tucvector PLTE;\n\tucvector_init(&PLTE);\n\tfor(i = 0; i < info->palettesize * 4; i++) {\n\t\t/*add all channels except alpha channel*/\n\t\tif(i % 4 != 3) ucvector_push_back(&PLTE, info->palette[i]);\n\t\t}\n\terror = addChunk(out, \"PLTE\", PLTE.data, PLTE.size);\n\tucvector_cleanup(&PLTE);\n\n\treturn error;\n\t}\n\nstatic unsigned addChunk_tRNS(ucvector* out, const LodePNGColorMode* info)\n\t{\n\tunsigned error = 0;\n\tsize_t i;\n\tucvector tRNS;\n\tucvector_init(&tRNS);\n\tif(info->colortype == LCT_PALETTE) {\n\t\tsize_t amount = info->palettesize;\n\t\t/*the tail of palette values that all have 255 as alpha, does not have to be encoded*/\n\t\tfor(i = info->palettesize; i > 0; i--) {\n\t\t\tif(info->palette[4 * (i - 1) + 3] == 255) amount--;\n\t\t\telse break;\n\t\t\t}\n\t\t/*add only alpha channel*/\n\t\tfor(i = 0; i < amount; i++) ucvector_push_back(&tRNS, info->palette[4 * i + 3]);\n\t\t}\n\telse if(info->colortype == LCT_GREY) {\n\t\tif(info->key_defined) {\n\t\t\tucvector_push_back(&tRNS, (unsigned char)(info->key_r / 256));\n\t\t\tucvector_push_back(&tRNS, (unsigned char)(info->key_r % 256));\n\t\t\t}\n\t\t}\n\telse if(info->colortype == LCT_RGB) {\n\t\tif(info->key_defined) {\n\t\t\tucvector_push_back(&tRNS, (unsigned char)(info->key_r / 256));\n\t\t\tucvector_push_back(&tRNS, (unsigned char)(info->key_r % 256));\n\t\t\tucvector_push_back(&tRNS, (unsigned char)(info->key_g / 256));\n\t\t\tucvector_push_back(&tRNS, (unsigned char)(info->key_g % 256));\n\t\t\tucvector_push_back(&tRNS, (unsigned char)(info->key_b / 256));\n\t\t\tucvector_push_back(&tRNS, (unsigned char)(info->key_b % 256));\n\t\t\t}\n\t\t}\n\n\terror = addChunk(out, \"tRNS\", tRNS.data, tRNS.size);\n\tucvector_cleanup(&tRNS);\n\n\treturn error;\n\t}\n\nstatic unsigned addChunk_IDAT(ucvector* out, const unsigned char* data, size_t datasize,\n                              LodePNGCompressSettings* zlibsettings)\n\t{\n\tucvector zlibdata;\n\tunsigned error = 0;\n\n\t/*compress with the Zlib compressor*/\n\tucvector_init(&zlibdata);\n\terror = zlib_compress(&zlibdata.data, &zlibdata.size, data, datasize, zlibsettings);\n\tif(!error) error = addChunk(out, \"IDAT\", zlibdata.data, zlibdata.size);\n\tucvector_cleanup(&zlibdata);\n\n\treturn error;\n\t}\n\nstatic unsigned addChunk_IEND(ucvector* out)\n\t{\n\tunsigned error = 0;\n\terror = addChunk(out, \"IEND\", 0, 0);\n\treturn error;\n\t}\n\n#ifdef LODEPNG_COMPILE_ANCILLARY_CHUNKS\n\nstatic unsigned addChunk_tEXt(ucvector* out, const char* keyword, const char* textstring)\n\t{\n\tunsigned error = 0;\n\tsize_t i;\n\tucvector text;\n\tucvector_init(&text);\n\tfor(i = 0; keyword[i] != 0; i++) ucvector_push_back(&text, (unsigned char)keyword[i]);\n\tif(i < 1 || i > 79) return 89; /*error: invalid keyword size*/\n\tucvector_push_back(&text, 0); /*0 termination char*/\n\tfor(i = 0; textstring[i] != 0; i++) ucvector_push_back(&text, (unsigned char)textstring[i]);\n\terror = addChunk(out, \"tEXt\", text.data, text.size);\n\tucvector_cleanup(&text);\n\n\treturn error;\n\t}\n\nstatic unsigned addChunk_zTXt(ucvector* out, const char* keyword, const char* textstring,\n                              LodePNGCompressSettings* zlibsettings)\n\t{\n\tunsigned error = 0;\n\tucvector data, compressed;\n\tsize_t i, textsize = strlen(textstring);\n\n\tucvector_init(&data);\n\tucvector_init(&compressed);\n\tfor(i = 0; keyword[i] != 0; i++) ucvector_push_back(&data, (unsigned char)keyword[i]);\n\tif(i < 1 || i > 79) return 89; /*error: invalid keyword size*/\n\tucvector_push_back(&data, 0); /*0 termination char*/\n\tucvector_push_back(&data, 0); /*compression method: 0*/\n\n\terror = zlib_compress(&compressed.data, &compressed.size,\n\t                      (unsigned char*)textstring, textsize, zlibsettings);\n\tif(!error) {\n\t\tfor(i = 0; i < compressed.size; i++) ucvector_push_back(&data, compressed.data[i]);\n\t\terror = addChunk(out, \"zTXt\", data.data, data.size);\n\t\t}\n\n\tucvector_cleanup(&compressed);\n\tucvector_cleanup(&data);\n\treturn error;\n\t}\n\nstatic unsigned addChunk_iTXt(ucvector* out, unsigned compressed, const char* keyword, const char* langtag,\n                              const char* transkey, const char* textstring, LodePNGCompressSettings* zlibsettings)\n\t{\n\tunsigned error = 0;\n\tucvector data;\n\tsize_t i, textsize = strlen(textstring);\n\n\tucvector_init(&data);\n\n\tfor(i = 0; keyword[i] != 0; i++) ucvector_push_back(&data, (unsigned char)keyword[i]);\n\tif(i < 1 || i > 79) return 89; /*error: invalid keyword size*/\n\tucvector_push_back(&data, 0); /*null termination char*/\n\tucvector_push_back(&data, compressed ? 1 : 0); /*compression flag*/\n\tucvector_push_back(&data, 0); /*compression method*/\n\tfor(i = 0; langtag[i] != 0; i++) ucvector_push_back(&data, (unsigned char)langtag[i]);\n\tucvector_push_back(&data, 0); /*null termination char*/\n\tfor(i = 0; transkey[i] != 0; i++) ucvector_push_back(&data, (unsigned char)transkey[i]);\n\tucvector_push_back(&data, 0); /*null termination char*/\n\n\tif(compressed) {\n\t\tucvector compressed_data;\n\t\tucvector_init(&compressed_data);\n\t\terror = zlib_compress(&compressed_data.data, &compressed_data.size,\n\t\t                      (unsigned char*)textstring, textsize, zlibsettings);\n\t\tif(!error) {\n\t\t\tfor(i = 0; i < compressed_data.size; i++) ucvector_push_back(&data, compressed_data.data[i]);\n\t\t\t}\n\t\tucvector_cleanup(&compressed_data);\n\t\t}\n\telse {   /*not compressed*/\n\t\tfor(i = 0; textstring[i] != 0; i++) ucvector_push_back(&data, (unsigned char)textstring[i]);\n\t\t}\n\n\tif(!error) error = addChunk(out, \"iTXt\", data.data, data.size);\n\tucvector_cleanup(&data);\n\treturn error;\n\t}\n\nstatic unsigned addChunk_bKGD(ucvector* out, const LodePNGInfo* info)\n\t{\n\tunsigned error = 0;\n\tucvector bKGD;\n\tucvector_init(&bKGD);\n\tif(info->color.colortype == LCT_GREY || info->color.colortype == LCT_GREY_ALPHA) {\n\t\tucvector_push_back(&bKGD, (unsigned char)(info->background_r / 256));\n\t\tucvector_push_back(&bKGD, (unsigned char)(info->background_r % 256));\n\t\t}\n\telse if(info->color.colortype == LCT_RGB || info->color.colortype == LCT_RGBA) {\n\t\tucvector_push_back(&bKGD, (unsigned char)(info->background_r / 256));\n\t\tucvector_push_back(&bKGD, (unsigned char)(info->background_r % 256));\n\t\tucvector_push_back(&bKGD, (unsigned char)(info->background_g / 256));\n\t\tucvector_push_back(&bKGD, (unsigned char)(info->background_g % 256));\n\t\tucvector_push_back(&bKGD, (unsigned char)(info->background_b / 256));\n\t\tucvector_push_back(&bKGD, (unsigned char)(info->background_b % 256));\n\t\t}\n\telse if(info->color.colortype == LCT_PALETTE) {\n\t\tucvector_push_back(&bKGD, (unsigned char)(info->background_r % 256)); /*palette index*/\n\t\t}\n\n\terror = addChunk(out, \"bKGD\", bKGD.data, bKGD.size);\n\tucvector_cleanup(&bKGD);\n\n\treturn error;\n\t}\n\nstatic unsigned addChunk_tIME(ucvector* out, const LodePNGTime* time)\n\t{\n\tunsigned error = 0;\n\tunsigned char* data = (unsigned char*)lodepng_malloc(7);\n\tif(!data) return 83; /*alloc fail*/\n\tdata[0] = (unsigned char)(time->year / 256);\n\tdata[1] = (unsigned char)(time->year % 256);\n\tdata[2] = time->month;\n\tdata[3] = time->day;\n\tdata[4] = time->hour;\n\tdata[5] = time->minute;\n\tdata[6] = time->second;\n\terror = addChunk(out, \"tIME\", data, 7);\n\tlodepng_free(data);\n\treturn error;\n\t}\n\nstatic unsigned addChunk_pHYs(ucvector* out, const LodePNGInfo* info)\n\t{\n\tunsigned error = 0;\n\tucvector data;\n\tucvector_init(&data);\n\n\tlodepng_add32bitInt(&data, info->phys_x);\n\tlodepng_add32bitInt(&data, info->phys_y);\n\tucvector_push_back(&data, info->phys_unit);\n\n\terror = addChunk(out, \"pHYs\", data.data, data.size);\n\tucvector_cleanup(&data);\n\n\treturn error;\n\t}\n\n#endif /*LODEPNG_COMPILE_ANCILLARY_CHUNKS*/\n\nstatic void filterScanline(unsigned char* out, const unsigned char* scanline, const unsigned char* prevline,\n                           size_t length, size_t bytewidth, unsigned char filterType)\n\t{\n\tsize_t i;\n\tswitch(filterType) {\n\t\tcase 0: /*None*/\n\t\t\tfor(i = 0; i < length; i++) out[i] = scanline[i];\n\t\t\tbreak;\n\t\tcase 1: /*Sub*/\n\t\t\tif(prevline) {\n\t\t\t\tfor(i = 0; i < bytewidth; i++) out[i] = scanline[i];\n\t\t\t\tfor(i = bytewidth; i < length; i++) out[i] = scanline[i] - scanline[i - bytewidth];\n\t\t\t\t}\n\t\t\telse {\n\t\t\t\tfor(i = 0; i < bytewidth; i++) out[i] = scanline[i];\n\t\t\t\tfor(i = bytewidth; i < length; i++) out[i] = scanline[i] - scanline[i - bytewidth];\n\t\t\t\t}\n\t\t\tbreak;\n\t\tcase 2: /*Up*/\n\t\t\tif(prevline) {\n\t\t\t\tfor(i = 0; i < length; i++) out[i] = scanline[i] - prevline[i];\n\t\t\t\t}\n\t\t\telse {\n\t\t\t\tfor(i = 0; i < length; i++) out[i] = scanline[i];\n\t\t\t\t}\n\t\t\tbreak;\n\t\tcase 3: /*Average*/\n\t\t\tif(prevline) {\n\t\t\t\tfor(i = 0; i < bytewidth; i++) out[i] = scanline[i] - prevline[i] / 2;\n\t\t\t\tfor(i = bytewidth; i < length; i++) out[i] = scanline[i] - ((scanline[i - bytewidth] + prevline[i]) / 2);\n\t\t\t\t}\n\t\t\telse {\n\t\t\t\tfor(i = 0; i < bytewidth; i++) out[i] = scanline[i];\n\t\t\t\tfor(i = bytewidth; i < length; i++) out[i] = scanline[i] - scanline[i - bytewidth] / 2;\n\t\t\t\t}\n\t\t\tbreak;\n\t\tcase 4: /*Paeth*/\n\t\t\tif(prevline) {\n\t\t\t\t/*paethPredictor(0, prevline[i], 0) is always prevline[i]*/\n\t\t\t\tfor(i = 0; i < bytewidth; i++) out[i] = (scanline[i] - prevline[i]);\n\t\t\t\tfor(i = bytewidth; i < length; i++) {\n\t\t\t\t\tout[i] = (scanline[i] - paethPredictor(scanline[i - bytewidth], prevline[i], prevline[i - bytewidth]));\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\telse {\n\t\t\t\tfor(i = 0; i < bytewidth; i++) out[i] = scanline[i];\n\t\t\t\t/*paethPredictor(scanline[i - bytewidth], 0, 0) is always scanline[i - bytewidth]*/\n\t\t\t\tfor(i = bytewidth; i < length; i++) out[i] = (scanline[i] - scanline[i - bytewidth]);\n\t\t\t\t}\n\t\t\tbreak;\n\t\tdefault:\n\t\t\treturn; /*unexisting filter type given*/\n\t\t}\n\t}\n\n/* log2 approximation. A slight bit faster than std::log. */\nstatic float flog2(float f)\n\t{\n\tfloat result = 0;\n\twhile(f > 32) {\n\t\tresult += 4;\n\t\tf /= 16;\n\t\t}\n\twhile(f > 2) {\n\t\tresult++;\n\t\tf /= 2;\n\t\t}\n\treturn result + 1.442695f * (f * f * f / 3 - 3 * f * f / 2 + 3 * f - 1.83333f);\n\t}\n\nstatic unsigned filter(unsigned char* out, const unsigned char* in, unsigned w, unsigned h,\n                       const LodePNGColorMode* info, const LodePNGEncoderSettings* settings)\n\t{\n\t/*\n\tFor PNG filter method 0\n\tout must be a buffer with as size: h + (w * h * bpp + 7) / 8, because there are\n\tthe scanlines with 1 extra byte per scanline\n\t*/\n\n\tunsigned bpp = lodepng_get_bpp(info);\n\t/*the width of a scanline in bytes, not including the filter type*/\n\tsize_t linebytes = (w * bpp + 7) / 8;\n\t/*bytewidth is used for filtering, is 1 when bpp < 8, number of bytes per pixel otherwise*/\n\tsize_t bytewidth = (bpp + 7) / 8;\n\tconst unsigned char* prevline = 0;\n\tunsigned x, y;\n\tunsigned error = 0;\n\tLodePNGFilterStrategy strategy = settings->filter_strategy;\n\n\t/*\n\tThere is a heuristic called the minimum sum of absolute differences heuristic, suggested by the PNG standard:\n\t*  If the image type is Palette, or the bit depth is smaller than 8, then do not filter the image (i.e.\n\t  use fixed filtering, with the filter None).\n\t* (The other case) If the image type is Grayscale or RGB (with or without Alpha), and the bit depth is\n\t \tnot smaller than 8, then use adaptive filtering heuristic as follows: independently for each row, apply\n\t all five filters and select the filter that produces the smallest sum of absolute values per row.\n\tThis heuristic is used if filter strategy is LFS_MINSUM and filter_palette_zero is true.\n\n\tIf filter_palette_zero is true and filter_strategy is not LFS_MINSUM, the above heuristic is followed,\n\tbut for \"the other case\", whatever strategy filter_strategy is set to instead of the minimum sum\n\theuristic is used.\n\t*/\n\tif(settings->filter_palette_zero &&\n\t      (info->colortype == LCT_PALETTE || info->bitdepth < 8)) strategy = LFS_ZERO;\n\n\tif(bpp == 0) return 31; /*error: invalid color type*/\n\n\tif(strategy == LFS_ZERO) {\n\t\tfor(y = 0; y < h; y++) {\n\t\t\tsize_t outindex = (1 + linebytes) * y; /*the extra filterbyte added to each row*/\n\t\t\tsize_t inindex = linebytes * y;\n\t\t\tout[outindex] = 0; /*filter type byte*/\n\t\t\tfilterScanline(&out[outindex + 1], &in[inindex], prevline, linebytes, bytewidth, 0);\n\t\t\tprevline = &in[inindex];\n\t\t\t}\n\t\t}\n\telse if(strategy == LFS_MINSUM) {\n\t\t/*adaptive filtering*/\n\t\tsize_t sum[5];\n\t\tucvector attempt[5]; /*five filtering attempts, one for each filter type*/\n\t\tsize_t smallest = 0;\n\t\tunsigned type, bestType = 0;\n\n\t\tfor(type = 0; type < 5; type++) {\n\t\t\tucvector_init(&attempt[type]);\n\t\t\tif(!ucvector_resize(&attempt[type], linebytes)) return 83; /*alloc fail*/\n\t\t\t}\n\n\t\tif(!error) {\n\t\t\tfor(y = 0; y < h; y++) {\n\t\t\t\t/*try the 5 filter types*/\n\t\t\t\tfor(type = 0; type < 5; type++) {\n\t\t\t\t\tfilterScanline(attempt[type].data, &in[y * linebytes], prevline, linebytes, bytewidth, type);\n\n\t\t\t\t\t/*calculate the sum of the result*/\n\t\t\t\t\tsum[type] = 0;\n\t\t\t\t\tif(type == 0) {\n\t\t\t\t\t\tfor(x = 0; x < linebytes; x++) sum[type] += (unsigned char)(attempt[type].data[x]);\n\t\t\t\t\t\t}\n\t\t\t\t\telse {\n\t\t\t\t\t\tfor(x = 0; x < linebytes; x++) {\n\t\t\t\t\t\t\t/*For differences, each byte should be treated as signed, values above 127 are negative\n\t\t\t\t\t\t\t(converted to signed char). Filtertype 0 isn't a difference though, so use unsigned there.\n\t\t\t\t\t\t\tThis means filtertype 0 is almost never chosen, but that is justified.*/\n\t\t\t\t\t\t\tsigned char s = (signed char)(attempt[type].data[x]);\n\t\t\t\t\t\t\tsum[type] += s < 0 ? -s : s;\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\t}\n\n\t\t\t\t\t/*check if this is smallest sum (or if type == 0 it's the first case so always store the values)*/\n\t\t\t\t\tif(type == 0 || sum[type] < smallest) {\n\t\t\t\t\t\tbestType = type;\n\t\t\t\t\t\tsmallest = sum[type];\n\t\t\t\t\t\t}\n\t\t\t\t\t}\n\n\t\t\t\tprevline = &in[y * linebytes];\n\n\t\t\t\t/*now fill the out values*/\n\t\t\t\tout[y * (linebytes + 1)] = bestType; /*the first byte of a scanline will be the filter type*/\n\t\t\t\tfor(x = 0; x < linebytes; x++) out[y * (linebytes + 1) + 1 + x] = attempt[bestType].data[x];\n\t\t\t\t}\n\t\t\t}\n\n\t\tfor(type = 0; type < 5; type++) ucvector_cleanup(&attempt[type]);\n\t\t}\n\telse if(strategy == LFS_ENTROPY) {\n\t\tfloat sum[5];\n\t\tucvector attempt[5]; /*five filtering attempts, one for each filter type*/\n\t\tfloat smallest = 0;\n\t\tunsigned type, bestType = 0;\n\t\tunsigned count[256];\n\n\t\tfor(type = 0; type < 5; type++) {\n\t\t\tucvector_init(&attempt[type]);\n\t\t\tif(!ucvector_resize(&attempt[type], linebytes)) return 83; /*alloc fail*/\n\t\t\t}\n\n\t\tfor(y = 0; y < h; y++) {\n\t\t\t/*try the 5 filter types*/\n\t\t\tfor(type = 0; type < 5; type++) {\n\t\t\t\tfilterScanline(attempt[type].data, &in[y * linebytes], prevline, linebytes, bytewidth, type);\n\t\t\t\tfor(x = 0; x < 256; x++) count[x] = 0;\n\t\t\t\tfor(x = 0; x < linebytes; x++) count[attempt[type].data[x]]++;\n\t\t\t\tcount[type]++; /*the filter type itself is part of the scanline*/\n\t\t\t\tsum[type] = 0;\n\t\t\t\tfor(x = 0; x < 256; x++) {\n\t\t\t\t\tfloat p = count[x] / (float)(linebytes + 1);\n\t\t\t\t\tsum[type] += count[x] == 0 ? 0 : flog2(1 / p) * p;\n\t\t\t\t\t}\n\t\t\t\t/*check if this is smallest sum (or if type == 0 it's the first case so always store the values)*/\n\t\t\t\tif(type == 0 || sum[type] < smallest) {\n\t\t\t\t\tbestType = type;\n\t\t\t\t\tsmallest = sum[type];\n\t\t\t\t\t}\n\t\t\t\t}\n\n\t\t\tprevline = &in[y * linebytes];\n\n\t\t\t/*now fill the out values*/\n\t\t\tout[y * (linebytes + 1)] = bestType; /*the first byte of a scanline will be the filter type*/\n\t\t\tfor(x = 0; x < linebytes; x++) out[y * (linebytes + 1) + 1 + x] = attempt[bestType].data[x];\n\t\t\t}\n\n\t\tfor(type = 0; type < 5; type++) ucvector_cleanup(&attempt[type]);\n\t\t}\n\telse if(strategy == LFS_PREDEFINED) {\n\t\tfor(y = 0; y < h; y++) {\n\t\t\tsize_t outindex = (1 + linebytes) * y; /*the extra filterbyte added to each row*/\n\t\t\tsize_t inindex = linebytes * y;\n\t\t\tunsigned type = settings->predefined_filters[y];\n\t\t\tout[outindex] = type; /*filter type byte*/\n\t\t\tfilterScanline(&out[outindex + 1], &in[inindex], prevline, linebytes, bytewidth, type);\n\t\t\tprevline = &in[inindex];\n\t\t\t}\n\t\t}\n\telse if(strategy == LFS_BRUTE_FORCE) {\n\t\t/*brute force filter chooser.\n\t\tdeflate the scanline after every filter attempt to see which one deflates best.\n\t\tThis is very slow and gives only slightly smaller, sometimes even larger, result*/\n\t\tsize_t size[5];\n\t\tucvector attempt[5]; /*five filtering attempts, one for each filter type*/\n\t\tsize_t smallest = 0;\n\t\tunsigned type = 0, bestType = 0;\n\t\tunsigned char* dummy;\n\t\tLodePNGCompressSettings zlibsettings = settings->zlibsettings;\n\t\t/*use fixed tree on the attempts so that the tree is not adapted to the filtertype on purpose,\n\t\tto simulate the true case where the tree is the same for the whole image. Sometimes it gives\n\t\tbetter result with dynamic tree anyway. Using the fixed tree sometimes gives worse, but in rare\n\t\tcases better compression. It does make this a bit less slow, so it's worth doing this.*/\n\t\tzlibsettings.btype = 1;\n\t\t/*a custom encoder likely doesn't read the btype setting and is optimized for complete PNG\n\t\timages only, so disable it*/\n\t\tzlibsettings.custom_zlib = 0;\n\t\tzlibsettings.custom_deflate = 0;\n\t\tfor(type = 0; type < 5; type++) {\n\t\t\tucvector_init(&attempt[type]);\n\t\t\tucvector_resize(&attempt[type], linebytes); /*todo: give error if resize failed*/\n\t\t\t}\n\t\tfor(y = 0; y < h; y++) { /*try the 5 filter types*/\n\t\t\tfor(type = 0; type < 5; type++) {\n\t\t\t\tunsigned testsize = attempt[type].size;\n\t\t\t\t/*if(testsize > 8) testsize /= 8;*/ /*it already works good enough by testing a part of the row*/\n\n\t\t\t\tfilterScanline(attempt[type].data, &in[y * linebytes], prevline, linebytes, bytewidth, type);\n\t\t\t\tsize[type] = 0;\n\t\t\t\tdummy = 0;\n\t\t\t\tzlib_compress(&dummy, &size[type], attempt[type].data, testsize, &zlibsettings);\n\t\t\t\tlodepng_free(dummy);\n\t\t\t\t/*check if this is smallest size (or if type == 0 it's the first case so always store the values)*/\n\t\t\t\tif(type == 0 || size[type] < smallest) {\n\t\t\t\t\tbestType = type;\n\t\t\t\t\tsmallest = size[type];\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\tprevline = &in[y * linebytes];\n\t\t\tout[y * (linebytes + 1)] = bestType; /*the first byte of a scanline will be the filter type*/\n\t\t\tfor(x = 0; x < linebytes; x++) out[y * (linebytes + 1) + 1 + x] = attempt[bestType].data[x];\n\t\t\t}\n\t\tfor(type = 0; type < 5; type++) ucvector_cleanup(&attempt[type]);\n\t\t}\n\telse return 88;   /* unknown filter strategy */\n\n\treturn error;\n\t}\n\nstatic void addPaddingBits(unsigned char* out, const unsigned char* in,\n                           size_t olinebits, size_t ilinebits, unsigned h)\n\t{\n\t/*The opposite of the removePaddingBits function\n\tolinebits must be >= ilinebits*/\n\tunsigned y;\n\tsize_t diff = olinebits - ilinebits;\n\tsize_t obp = 0, ibp = 0; /*bit pointers*/\n\tfor(y = 0; y < h; y++) {\n\t\tsize_t x;\n\t\tfor(x = 0; x < ilinebits; x++) {\n\t\t\tunsigned char bit = readBitFromReversedStream(&ibp, in);\n\t\t\tsetBitOfReversedStream(&obp, out, bit);\n\t\t\t}\n\t\t/*obp += diff; --> no, fill in some value in the padding bits too, to avoid\n\t\t\"Use of uninitialised value of size ###\" warning from valgrind*/\n\t\tfor(x = 0; x < diff; x++) setBitOfReversedStream(&obp, out, 0);\n\t\t}\n\t}\n\n/*\nin: non-interlaced image with size w*h\nout: the same pixels, but re-ordered according to PNG's Adam7 interlacing, with\nno padding bits between scanlines, but between reduced images so that each\nreduced image starts at a byte.\nbpp: bits per pixel\nthere are no padding bits, not between scanlines, not between reduced images\nin has the following size in bits: w * h * bpp.\nout is possibly bigger due to padding bits between reduced images\nNOTE: comments about padding bits are only relevant if bpp < 8\n*/\nstatic void Adam7_interlace(unsigned char* out, const unsigned char* in, unsigned w, unsigned h, unsigned bpp)\n\t{\n\tunsigned passw[7], passh[7];\n\tsize_t filter_passstart[8], padded_passstart[8], passstart[8];\n\tunsigned i;\n\n\tAdam7_getpassvalues(passw, passh, filter_passstart, padded_passstart, passstart, w, h, bpp);\n\n\tif(bpp >= 8) {\n\t\tfor(i = 0; i < 7; i++) {\n\t\t\tunsigned x, y, b;\n\t\t\tsize_t bytewidth = bpp / 8;\n\t\t\tfor(y = 0; y < passh[i]; y++)\n\t\t\t\tfor(x = 0; x < passw[i]; x++) {\n\t\t\t\t\tsize_t pixelinstart = ((ADAM7_IY[i] + y * ADAM7_DY[i]) * w + ADAM7_IX[i] + x * ADAM7_DX[i]) * bytewidth;\n\t\t\t\t\tsize_t pixeloutstart = passstart[i] + (y * passw[i] + x) * bytewidth;\n\t\t\t\t\tfor(b = 0; b < bytewidth; b++) {\n\t\t\t\t\t\tout[pixeloutstart + b] = in[pixelinstart + b];\n\t\t\t\t\t\t}\n\t\t\t\t\t}\n\t\t\t}\n\t\t}\n\telse {   /*bpp < 8: Adam7 with pixels < 8 bit is a bit trickier: with bit pointers*/\n\t\tfor(i = 0; i < 7; i++) {\n\t\t\tunsigned x, y, b;\n\t\t\tunsigned ilinebits = bpp * passw[i];\n\t\t\tunsigned olinebits = bpp * w;\n\t\t\tsize_t obp, ibp; /*bit pointers (for out and in buffer)*/\n\t\t\tfor(y = 0; y < passh[i]; y++)\n\t\t\t\tfor(x = 0; x < passw[i]; x++) {\n\t\t\t\t\tibp = (ADAM7_IY[i] + y * ADAM7_DY[i]) * olinebits + (ADAM7_IX[i] + x * ADAM7_DX[i]) * bpp;\n\t\t\t\t\tobp = (8 * passstart[i]) + (y * ilinebits + x * bpp);\n\t\t\t\t\tfor(b = 0; b < bpp; b++) {\n\t\t\t\t\t\tunsigned char bit = readBitFromReversedStream(&ibp, in);\n\t\t\t\t\t\tsetBitOfReversedStream(&obp, out, bit);\n\t\t\t\t\t\t}\n\t\t\t\t\t}\n\t\t\t}\n\t\t}\n\t}\n\n/*out must be buffer big enough to contain uncompressed IDAT chunk data, and in must contain the full image.\nreturn value is error**/\nstatic unsigned preProcessScanlines(unsigned char** out, size_t* outsize, const unsigned char* in,\n                                    unsigned w, unsigned h,\n                                    const LodePNGInfo* info_png, const LodePNGEncoderSettings* settings)\n\t{\n\t/*\n\tThis function converts the pure 2D image with the PNG's colortype, into filtered-padded-interlaced data. Steps:\n\t*) if no Adam7: 1) add padding bits (= posible extra bits per scanline if bpp < 8) 2) filter\n\t*) if adam7: 1) Adam7_interlace 2) 7x add padding bits 3) 7x filter\n\t*/\n\tunsigned bpp = lodepng_get_bpp(&info_png->color);\n\tunsigned error = 0;\n\n\tif(info_png->interlace_method == 0) {\n\t\t*outsize = h + (h * ((w * bpp + 7) / 8)); /*image size plus an extra byte per scanline + possible padding bits*/\n\t\t*out = (unsigned char*)lodepng_malloc(*outsize);\n\t\tif(!(*out) && (*outsize)) error = 83; /*alloc fail*/\n\n\t\tif(!error) {\n\t\t\t/*non multiple of 8 bits per scanline, padding bits needed per scanline*/\n\t\t\tif(bpp < 8 && w * bpp != ((w * bpp + 7) / 8) * 8) {\n\t\t\t\tunsigned char* padded = (unsigned char*)lodepng_malloc(h * ((w * bpp + 7) / 8));\n\t\t\t\tif(!padded) error = 83; /*alloc fail*/\n\t\t\t\tif(!error) {\n\t\t\t\t\taddPaddingBits(padded, in, ((w * bpp + 7) / 8) * 8, w * bpp, h);\n\t\t\t\t\terror = filter(*out, padded, w, h, &info_png->color, settings);\n\t\t\t\t\t}\n\t\t\t\tlodepng_free(padded);\n\t\t\t\t}\n\t\t\telse {\n\t\t\t\t/*we can immediatly filter into the out buffer, no other steps needed*/\n\t\t\t\terror = filter(*out, in, w, h, &info_png->color, settings);\n\t\t\t\t}\n\t\t\t}\n\t\t}\n\telse {   /*interlace_method is 1 (Adam7)*/\n\t\tunsigned passw[7], passh[7];\n\t\tsize_t filter_passstart[8], padded_passstart[8], passstart[8];\n\t\tunsigned char* adam7;\n\n\t\tAdam7_getpassvalues(passw, passh, filter_passstart, padded_passstart, passstart, w, h, bpp);\n\n\t\t*outsize = filter_passstart[7]; /*image size plus an extra byte per scanline + possible padding bits*/\n\t\t*out = (unsigned char*)lodepng_malloc(*outsize);\n\t\tif(!(*out)) error = 83; /*alloc fail*/\n\n\t\tadam7 = (unsigned char*)lodepng_malloc(passstart[7]);\n\t\tif(!adam7 && passstart[7]) error = 83; /*alloc fail*/\n\n\t\tif(!error) {\n\t\t\tunsigned i;\n\n\t\t\tAdam7_interlace(adam7, in, w, h, bpp);\n\t\t\tfor(i = 0; i < 7; i++) {\n\t\t\t\tif(bpp < 8) {\n\t\t\t\t\tunsigned char* padded = (unsigned char*)lodepng_malloc(padded_passstart[i + 1] - padded_passstart[i]);\n\t\t\t\t\tif(!padded) ERROR_BREAK(83); /*alloc fail*/\n\t\t\t\t\taddPaddingBits(padded, &adam7[passstart[i]],\n\t\t\t\t\t               ((passw[i] * bpp + 7) / 8) * 8, passw[i] * bpp, passh[i]);\n\t\t\t\t\terror = filter(&(*out)[filter_passstart[i]], padded,\n\t\t\t\t\t               passw[i], passh[i], &info_png->color, settings);\n\t\t\t\t\tlodepng_free(padded);\n\t\t\t\t\t}\n\t\t\t\telse {\n\t\t\t\t\terror = filter(&(*out)[filter_passstart[i]], &adam7[padded_passstart[i]],\n\t\t\t\t\t               passw[i], passh[i], &info_png->color, settings);\n\t\t\t\t\t}\n\n\t\t\t\tif(error) break;\n\t\t\t\t}\n\t\t\t}\n\n\t\tlodepng_free(adam7);\n\t\t}\n\n\treturn error;\n\t}\n\n/*\npalette must have 4 * palettesize bytes allocated, and given in format RGBARGBARGBARGBA...\nreturns 0 if the palette is opaque,\nreturns 1 if the palette has a single color with alpha 0 ==> color key\nreturns 2 if the palette is semi-translucent.\n*/\nstatic unsigned getPaletteTranslucency(const unsigned char* palette, size_t palettesize)\n\t{\n\tsize_t i, key = 0;\n\tunsigned r = 0, g = 0, b = 0; /*the value of the color with alpha 0, so long as color keying is possible*/\n\tfor(i = 0; i < palettesize; i++) {\n\t\tif(!key && palette[4 * i + 3] == 0) {\n\t\t\tr = palette[4 * i + 0];\n\t\t\tg = palette[4 * i + 1];\n\t\t\tb = palette[4 * i + 2];\n\t\t\tkey = 1;\n\t\t\ti = (size_t)(-1); /*restart from beginning, to detect earlier opaque colors with key's value*/\n\t\t\t}\n\t\telse if(palette[4 * i + 3] != 255) return 2;\n\t\t/*when key, no opaque RGB may have key's RGB*/\n\t\telse if(key && r == palette[i * 4 + 0] && g == palette[i * 4 + 1] && b == palette[i * 4 + 2]) return 2;\n\t\t}\n\treturn key;\n\t}\n\n#ifdef LODEPNG_COMPILE_ANCILLARY_CHUNKS\nstatic unsigned addUnknownChunks(ucvector* out, unsigned char* data, size_t datasize)\n\t{\n\tunsigned char* inchunk = data;\n\twhile((size_t)(inchunk - data) < datasize) {\n\t\tCERROR_TRY_RETURN(lodepng_chunk_append(&out->data, &out->size, inchunk));\n\t\tout->allocsize = out->size; /*fix the allocsize again*/\n\t\tinchunk = lodepng_chunk_next(inchunk);\n\t\t}\n\treturn 0;\n\t}\n#endif /*LODEPNG_COMPILE_ANCILLARY_CHUNKS*/\n\nunsigned lodepng_encode(unsigned char** out, size_t* outsize,\n                        const unsigned char* image, unsigned w, unsigned h,\n                        LodePNGState* state)\n\t{\n\tLodePNGInfo info;\n\tucvector outv;\n\tunsigned char* data = 0; /*uncompressed version of the IDAT chunk data*/\n\tsize_t datasize = 0;\n\n\t/*provide some proper output values if error will happen*/\n\t*out = 0;\n\t*outsize = 0;\n\tstate->error = 0;\n\n\tlodepng_info_init(&info);\n\tlodepng_info_copy(&info, &state->info_png);\n\n\tif((info.color.colortype == LCT_PALETTE || state->encoder.force_palette)\n\t      && (info.color.palettesize == 0 || info.color.palettesize > 256)) {\n\t\tstate->error = 68; /*invalid palette size, it is only allowed to be 1-256*/\n\t\treturn state->error;\n\t\t}\n\n\tif(state->encoder.auto_convert != LAC_NO) {\n\t\tstate->error = lodepng_auto_choose_color(&info.color, image, w, h, &state->info_raw,\n\t\t               state->encoder.auto_convert);\n\t\t}\n\tif(state->error) return state->error;\n\n\tif(state->encoder.zlibsettings.btype > 2) {\n\t\tCERROR_RETURN_ERROR(state->error, 61); /*error: unexisting btype*/\n\t\t}\n\tif(state->info_png.interlace_method > 1) {\n\t\tCERROR_RETURN_ERROR(state->error, 71); /*error: unexisting interlace mode*/\n\t\t}\n\n\tstate->error = checkColorValidity(info.color.colortype, info.color.bitdepth);\n\tif(state->error) return state->error; /*error: unexisting color type given*/\n\tstate->error = checkColorValidity(state->info_raw.colortype, state->info_raw.bitdepth);\n\tif(state->error) return state->error; /*error: unexisting color type given*/\n\n\tif(!lodepng_color_mode_equal(&state->info_raw, &info.color)) {\n\t\tunsigned char* converted;\n\t\tsize_t size = (w * h * lodepng_get_bpp(&info.color) + 7) / 8;\n\n\t\tconverted = (unsigned char*)lodepng_malloc(size);\n\t\tif(!converted && size) state->error = 83; /*alloc fail*/\n\t\tif(!state->error) {\n\t\t\tstate->error = lodepng_convert(converted, image, &info.color, &state->info_raw, w, h, 0 /*fix_png*/);\n\t\t\t}\n\t\tif(!state->error) preProcessScanlines(&data, &datasize, converted, w, h, &info, &state->encoder);\n\t\tlodepng_free(converted);\n\t\t}\n\telse preProcessScanlines(&data, &datasize, image, w, h, &info, &state->encoder);\n\n\tucvector_init(&outv);\n\twhile(!state->error) { /*while only executed once, to break on error*/\n#ifdef LODEPNG_COMPILE_ANCILLARY_CHUNKS\n\t\tsize_t i;\n#endif /*LODEPNG_COMPILE_ANCILLARY_CHUNKS*/\n\t\t/*write signature and chunks*/\n\t\twriteSignature(&outv);\n\t\t/*IHDR*/\n\t\taddChunk_IHDR(&outv, w, h, info.color.colortype, info.color.bitdepth, info.interlace_method);\n#ifdef LODEPNG_COMPILE_ANCILLARY_CHUNKS\n\t\t/*unknown chunks between IHDR and PLTE*/\n\t\tif(info.unknown_chunks_data[0]) {\n\t\t\tstate->error = addUnknownChunks(&outv, info.unknown_chunks_data[0], info.unknown_chunks_size[0]);\n\t\t\tif(state->error) break;\n\t\t\t}\n#endif /*LODEPNG_COMPILE_ANCILLARY_CHUNKS*/\n\t\t/*PLTE*/\n\t\tif(info.color.colortype == LCT_PALETTE) {\n\t\t\taddChunk_PLTE(&outv, &info.color);\n\t\t\t}\n\t\tif(state->encoder.force_palette && (info.color.colortype == LCT_RGB || info.color.colortype == LCT_RGBA)) {\n\t\t\taddChunk_PLTE(&outv, &info.color);\n\t\t\t}\n\t\t/*tRNS*/\n\t\tif(info.color.colortype == LCT_PALETTE && getPaletteTranslucency(info.color.palette, info.color.palettesize) != 0) {\n\t\t\taddChunk_tRNS(&outv, &info.color);\n\t\t\t}\n\t\tif((info.color.colortype == LCT_GREY || info.color.colortype == LCT_RGB) && info.color.key_defined) {\n\t\t\taddChunk_tRNS(&outv, &info.color);\n\t\t\t}\n#ifdef LODEPNG_COMPILE_ANCILLARY_CHUNKS\n\t\t/*bKGD (must come between PLTE and the IDAt chunks*/\n\t\tif(info.background_defined) addChunk_bKGD(&outv, &info);\n\t\t/*pHYs (must come before the IDAT chunks)*/\n\t\tif(info.phys_defined) addChunk_pHYs(&outv, &info);\n\n\t\t/*unknown chunks between PLTE and IDAT*/\n\t\tif(info.unknown_chunks_data[1]) {\n\t\t\tstate->error = addUnknownChunks(&outv, info.unknown_chunks_data[1], info.unknown_chunks_size[1]);\n\t\t\tif(state->error) break;\n\t\t\t}\n#endif /*LODEPNG_COMPILE_ANCILLARY_CHUNKS*/\n\t\t/*IDAT (multiple IDAT chunks must be consecutive)*/\n\t\tstate->error = addChunk_IDAT(&outv, data, datasize, &state->encoder.zlibsettings);\n\t\tif(state->error) break;\n#ifdef LODEPNG_COMPILE_ANCILLARY_CHUNKS\n\t\t/*tIME*/\n\t\tif(info.time_defined) addChunk_tIME(&outv, &info.time);\n\t\t/*tEXt and/or zTXt*/\n\t\tfor(i = 0; i < info.text_num; i++) {\n\t\t\tif(strlen(info.text_keys[i]) > 79) {\n\t\t\t\tstate->error = 66; /*text chunk too large*/\n\t\t\t\tbreak;\n\t\t\t\t}\n\t\t\tif(strlen(info.text_keys[i]) < 1) {\n\t\t\t\tstate->error = 67; /*text chunk too small*/\n\t\t\t\tbreak;\n\t\t\t\t}\n\t\t\tif(state->encoder.text_compression) {\n\t\t\t\taddChunk_zTXt(&outv, info.text_keys[i], info.text_strings[i], &state->encoder.zlibsettings);\n\t\t\t\t}\n\t\t\telse {\n\t\t\t\taddChunk_tEXt(&outv, info.text_keys[i], info.text_strings[i]);\n\t\t\t\t}\n\t\t\t}\n\t\t/*LodePNG version id in text chunk*/\n\t\tif(state->encoder.add_id) {\n\t\t\tunsigned alread_added_id_text = 0;\n\t\t\tfor(i = 0; i < info.text_num; i++) {\n\t\t\t\tif(!strcmp(info.text_keys[i], \"LodePNG\")) {\n\t\t\t\t\talread_added_id_text = 1;\n\t\t\t\t\tbreak;\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\tif(alread_added_id_text == 0) {\n\t\t\t\taddChunk_tEXt(&outv, \"LodePNG\", VERSION_STRING); /*it's shorter as tEXt than as zTXt chunk*/\n\t\t\t\t}\n\t\t\t}\n\t\t/*iTXt*/\n\t\tfor(i = 0; i < info.itext_num; i++) {\n\t\t\tif(strlen(info.itext_keys[i]) > 79) {\n\t\t\t\tstate->error = 66; /*text chunk too large*/\n\t\t\t\tbreak;\n\t\t\t\t}\n\t\t\tif(strlen(info.itext_keys[i]) < 1) {\n\t\t\t\tstate->error = 67; /*text chunk too small*/\n\t\t\t\tbreak;\n\t\t\t\t}\n\t\t\taddChunk_iTXt(&outv, state->encoder.text_compression,\n\t\t\t              info.itext_keys[i], info.itext_langtags[i], info.itext_transkeys[i], info.itext_strings[i],\n\t\t\t              &state->encoder.zlibsettings);\n\t\t\t}\n\n\t\t/*unknown chunks between IDAT and IEND*/\n\t\tif(info.unknown_chunks_data[2]) {\n\t\t\tstate->error = addUnknownChunks(&outv, info.unknown_chunks_data[2], info.unknown_chunks_size[2]);\n\t\t\tif(state->error) break;\n\t\t\t}\n#endif /*LODEPNG_COMPILE_ANCILLARY_CHUNKS*/\n\t\taddChunk_IEND(&outv);\n\n\t\tbreak; /*this isn't really a while loop; no error happened so break out now!*/\n\t\t}\n\n\tlodepng_info_cleanup(&info);\n\tlodepng_free(data);\n\t/*instead of cleaning the vector up, give it to the output*/\n\t*out = outv.data;\n\t*outsize = outv.size;\n\n\treturn state->error;\n\t}\n\nunsigned lodepng_encode_memory(unsigned char** out, size_t* outsize, const unsigned char* image,\n                               unsigned w, unsigned h, LodePNGColorType colortype, unsigned bitdepth)\n\t{\n\tunsigned error;\n\tLodePNGState state;\n\tlodepng_state_init(&state);\n\tstate.info_raw.colortype = colortype;\n\tstate.info_raw.bitdepth = bitdepth;\n\tstate.info_png.color.colortype = colortype;\n\tstate.info_png.color.bitdepth = bitdepth;\n\tlodepng_encode(out, outsize, image, w, h, &state);\n\terror = state.error;\n\tlodepng_state_cleanup(&state);\n\treturn error;\n\t}\n\nunsigned lodepng_encode32(unsigned char** out, size_t* outsize, const unsigned char* image, unsigned w, unsigned h)\n\t{\n\treturn lodepng_encode_memory(out, outsize, image, w, h, LCT_RGBA, 8);\n\t}\n\nunsigned lodepng_encode24(unsigned char** out, size_t* outsize, const unsigned char* image, unsigned w, unsigned h)\n\t{\n\treturn lodepng_encode_memory(out, outsize, image, w, h, LCT_RGB, 8);\n\t}\n\n#ifdef LODEPNG_COMPILE_DISK\nunsigned lodepng_encode_file(const char* filename, const unsigned char* image, unsigned w, unsigned h,\n                             LodePNGColorType colortype, unsigned bitdepth)\n\t{\n\tunsigned char* buffer;\n\tsize_t buffersize;\n\tunsigned error = lodepng_encode_memory(&buffer, &buffersize, image, w, h, colortype, bitdepth);\n\tif(!error) error = lodepng_save_file(buffer, buffersize, filename);\n\tlodepng_free(buffer);\n\treturn error;\n\t}\n\nunsigned lodepng_encode32_file(const char* filename, const unsigned char* image, unsigned w, unsigned h)\n\t{\n\treturn lodepng_encode_file(filename, image, w, h, LCT_RGBA, 8);\n\t}\n\nunsigned lodepng_encode24_file(const char* filename, const unsigned char* image, unsigned w, unsigned h)\n\t{\n\treturn lodepng_encode_file(filename, image, w, h, LCT_RGB, 8);\n\t}\n#endif /*LODEPNG_COMPILE_DISK*/\n\nvoid lodepng_encoder_settings_init(LodePNGEncoderSettings* settings)\n\t{\n\tlodepng_compress_settings_init(&settings->zlibsettings);\n\tsettings->filter_palette_zero = 1;\n\tsettings->filter_strategy = LFS_MINSUM;\n\tsettings->auto_convert = LAC_AUTO;\n\tsettings->force_palette = 0;\n\tsettings->predefined_filters = 0;\n#ifdef LODEPNG_COMPILE_ANCILLARY_CHUNKS\n\tsettings->add_id = 0;\n\tsettings->text_compression = 1;\n#endif /*LODEPNG_COMPILE_ANCILLARY_CHUNKS*/\n\t}\n\n#endif /*LODEPNG_COMPILE_ENCODER*/\n#endif /*LODEPNG_COMPILE_PNG*/\n\n#ifdef LODEPNG_COMPILE_ERROR_TEXT\n/*\nThis returns the description of a numerical error code in English. This is also\nthe documentation of all the error codes.\n*/\nconst char* lodepng_error_text(unsigned code)\n\t{\n\tswitch(code) {\n\t\tcase 0:\n\t\t\treturn \"no error, everything went ok\";\n\t\tcase 1:\n\t\t\treturn \"nothing done yet\"; /*the Encoder/Decoder has done nothing yet, error checking makes no sense yet*/\n\t\tcase 10:\n\t\t\treturn \"end of input memory reached without huffman end code\"; /*while huffman decoding*/\n\t\tcase 11:\n\t\t\treturn \"error in code tree made it jump outside of huffman tree\"; /*while huffman decoding*/\n\t\tcase 13:\n\t\t\treturn \"problem while processing dynamic deflate block\";\n\t\tcase 14:\n\t\t\treturn \"problem while processing dynamic deflate block\";\n\t\tcase 15:\n\t\t\treturn \"problem while processing dynamic deflate block\";\n\t\tcase 16:\n\t\t\treturn \"unexisting code while processing dynamic deflate block\";\n\t\tcase 17:\n\t\t\treturn \"end of out buffer memory reached while inflating\";\n\t\tcase 18:\n\t\t\treturn \"invalid distance code while inflating\";\n\t\tcase 19:\n\t\t\treturn \"end of out buffer memory reached while inflating\";\n\t\tcase 20:\n\t\t\treturn \"invalid deflate block BTYPE encountered while decoding\";\n\t\tcase 21:\n\t\t\treturn \"NLEN is not ones complement of LEN in a deflate block\";\n\t\t/*end of out buffer memory reached while inflating:\n\t\tThis can happen if the inflated deflate data is longer than the amount of bytes required to fill up\n\t\tall the pixels of the image, given the color depth and image dimensions. Something that doesn't\n\t\thappen in a normal, well encoded, PNG image.*/\n\t\tcase 22:\n\t\t\treturn \"end of out buffer memory reached while inflating\";\n\t\tcase 23:\n\t\t\treturn \"end of in buffer memory reached while inflating\";\n\t\tcase 24:\n\t\t\treturn \"invalid FCHECK in zlib header\";\n\t\tcase 25:\n\t\t\treturn \"invalid compression method in zlib header\";\n\t\tcase 26:\n\t\t\treturn \"FDICT encountered in zlib header while it's not used for PNG\";\n\t\tcase 27:\n\t\t\treturn \"PNG file is smaller than a PNG header\";\n\t\t/*Checks the magic file header, the first 8 bytes of the PNG file*/\n\t\tcase 28:\n\t\t\treturn \"incorrect PNG signature, it's no PNG or corrupted\";\n\t\tcase 29:\n\t\t\treturn \"first chunk is not the header chunk\";\n\t\tcase 30:\n\t\t\treturn \"chunk length too large, chunk broken off at end of file\";\n\t\tcase 31:\n\t\t\treturn \"illegal PNG color type or bpp\";\n\t\tcase 32:\n\t\t\treturn \"illegal PNG compression method\";\n\t\tcase 33:\n\t\t\treturn \"illegal PNG filter method\";\n\t\tcase 34:\n\t\t\treturn \"illegal PNG interlace method\";\n\t\tcase 35:\n\t\t\treturn \"chunk length of a chunk is too large or the chunk too small\";\n\t\tcase 36:\n\t\t\treturn \"illegal PNG filter type encountered\";\n\t\tcase 37:\n\t\t\treturn \"illegal bit depth for this color type given\";\n\t\tcase 38:\n\t\t\treturn \"the palette is too big\"; /*more than 256 colors*/\n\t\tcase 39:\n\t\t\treturn \"more palette alpha values given in tRNS chunk than there are colors in the palette\";\n\t\tcase 40:\n\t\t\treturn \"tRNS chunk has wrong size for greyscale image\";\n\t\tcase 41:\n\t\t\treturn \"tRNS chunk has wrong size for RGB image\";\n\t\tcase 42:\n\t\t\treturn \"tRNS chunk appeared while it was not allowed for this color type\";\n\t\tcase 43:\n\t\t\treturn \"bKGD chunk has wrong size for palette image\";\n\t\tcase 44:\n\t\t\treturn \"bKGD chunk has wrong size for greyscale image\";\n\t\tcase 45:\n\t\t\treturn \"bKGD chunk has wrong size for RGB image\";\n\t\t/*Is the palette too small?*/\n\t\tcase 46:\n\t\t\treturn \"a value in indexed image is larger than the palette size (bitdepth = 8)\";\n\t\t/*Is the palette too small?*/\n\t\tcase 47:\n\t\t\treturn \"a value in indexed image is larger than the palette size (bitdepth < 8)\";\n\t\t/*the input data is empty, maybe a PNG file doesn't exist or is in the wrong path*/\n\t\tcase 48:\n\t\t\treturn \"empty input or file doesn't exist\";\n\t\tcase 49:\n\t\t\treturn \"jumped past memory while generating dynamic huffman tree\";\n\t\tcase 50:\n\t\t\treturn \"jumped past memory while generating dynamic huffman tree\";\n\t\tcase 51:\n\t\t\treturn \"jumped past memory while inflating huffman block\";\n\t\tcase 52:\n\t\t\treturn \"jumped past memory while inflating\";\n\t\tcase 53:\n\t\t\treturn \"size of zlib data too small\";\n\t\tcase 54:\n\t\t\treturn \"repeat symbol in tree while there was no value symbol yet\";\n\t\t/*jumped past tree while generating huffman tree, this could be when the\n\t\ttree will have more leaves than symbols after generating it out of the\n\t\tgiven lenghts. They call this an oversubscribed dynamic bit lengths tree in zlib.*/\n\t\tcase 55:\n\t\t\treturn \"jumped past tree while generating huffman tree\";\n\t\tcase 56:\n\t\t\treturn \"given output image colortype or bitdepth not supported for color conversion\";\n\t\tcase 57:\n\t\t\treturn \"invalid CRC encountered (checking CRC can be disabled)\";\n\t\tcase 58:\n\t\t\treturn \"invalid ADLER32 encountered (checking ADLER32 can be disabled)\";\n\t\tcase 59:\n\t\t\treturn \"requested color conversion not supported\";\n\t\tcase 60:\n\t\t\treturn \"invalid window size given in the settings of the encoder (must be 0-32768)\";\n\t\tcase 61:\n\t\t\treturn \"invalid BTYPE given in the settings of the encoder (only 0, 1 and 2 are allowed)\";\n\t\t/*LodePNG leaves the choice of RGB to greyscale conversion formula to the user.*/\n\t\tcase 62:\n\t\t\treturn \"conversion from color to greyscale not supported\";\n\t\tcase 63:\n\t\t\treturn \"length of a chunk too long, max allowed for PNG is 2147483647 bytes per chunk\"; /*(2^31-1)*/\n\t\t/*this would result in the inability of a deflated block to ever contain an end code. It must be at least 1.*/\n\t\tcase 64:\n\t\t\treturn \"the length of the END symbol 256 in the Huffman tree is 0\";\n\t\tcase 66:\n\t\t\treturn \"the length of a text chunk keyword given to the encoder is longer than the maximum of 79 bytes\";\n\t\tcase 67:\n\t\t\treturn \"the length of a text chunk keyword given to the encoder is smaller than the minimum of 1 byte\";\n\t\tcase 68:\n\t\t\treturn \"tried to encode a PLTE chunk with a palette that has less than 1 or more than 256 colors\";\n\t\tcase 69:\n\t\t\treturn \"unknown chunk type with 'critical' flag encountered by the decoder\";\n\t\tcase 71:\n\t\t\treturn \"unexisting interlace mode given to encoder (must be 0 or 1)\";\n\t\tcase 72:\n\t\t\treturn \"while decoding, unexisting compression method encountering in zTXt or iTXt chunk (it must be 0)\";\n\t\tcase 73:\n\t\t\treturn \"invalid tIME chunk size\";\n\t\tcase 74:\n\t\t\treturn \"invalid pHYs chunk size\";\n\t\t/*length could be wrong, or data chopped off*/\n\t\tcase 75:\n\t\t\treturn \"no null termination char found while decoding text chunk\";\n\t\tcase 76:\n\t\t\treturn \"iTXt chunk too short to contain required bytes\";\n\t\tcase 77:\n\t\t\treturn \"integer overflow in buffer size\";\n\t\tcase 78:\n\t\t\treturn \"failed to open file for reading\"; /*file doesn't exist or couldn't be opened for reading*/\n\t\tcase 79:\n\t\t\treturn \"failed to open file for writing\";\n\t\tcase 80:\n\t\t\treturn \"tried creating a tree of 0 symbols\";\n\t\tcase 81:\n\t\t\treturn \"lazy matching at pos 0 is impossible\";\n\t\tcase 82:\n\t\t\treturn \"color conversion to palette requested while a color isn't in palette\";\n\t\tcase 83:\n\t\t\treturn \"memory allocation failed\";\n\t\tcase 84:\n\t\t\treturn \"given image too small to contain all pixels to be encoded\";\n\t\tcase 85:\n\t\t\treturn \"internal color conversion bug\";\n\t\tcase 86:\n\t\t\treturn \"impossible offset in lz77 encoding (internal bug)\";\n\t\tcase 87:\n\t\t\treturn \"must provide custom zlib function pointer if LODEPNG_COMPILE_ZLIB is not defined\";\n\t\tcase 88:\n\t\t\treturn \"invalid filter strategy given for LodePNGEncoderSettings.filter_strategy\";\n\t\tcase 89:\n\t\t\treturn \"text chunk keyword too short or long: must have size 1-79\";\n\t\t/*the windowsize in the LodePNGCompressSettings. Requiring POT(==> & instead of %) makes encoding 12% faster.*/\n\t\tcase 90:\n\t\t\treturn \"windowsize must be a power of two\";\n\t\t}\n\treturn \"unknown error code\";\n\t}\n#endif /*LODEPNG_COMPILE_ERROR_TEXT*/\n\n/* ////////////////////////////////////////////////////////////////////////// */\n/* ////////////////////////////////////////////////////////////////////////// */\n/* // C++ Wrapper                                                          // */\n/* ////////////////////////////////////////////////////////////////////////// */\n/* ////////////////////////////////////////////////////////////////////////// */\n\n#ifdef LODEPNG_COMPILE_CPP\nnamespace lodepng {\n\n#ifdef LODEPNG_COMPILE_DISK\n\tvoid load_file(std::vector<unsigned char>& buffer, const std::string& filename)\n\t\t{\n\t\tstd::ifstream file(filename.c_str(), std::ios::in|std::ios::binary|std::ios::ate);\n\n\t\t/*get filesize*/\n\t\tstd::streamsize size = 0;\n\t\tif(file.seekg(0, std::ios::end).good()) size = file.tellg();\n\t\tif(file.seekg(0, std::ios::beg).good()) size -= file.tellg();\n\n\t\t/*read contents of the file into the vector*/\n\t\tbuffer.resize(size_t(size));\n\t\tif(size > 0) file.read((char*)(&buffer[0]), size);\n\t\t}\n\n\t/*write given buffer to the file, overwriting the file, it doesn't append to it.*/\n\tvoid save_file(const std::vector<unsigned char>& buffer, const std::string& filename)\n\t\t{\n\t\tstd::ofstream file(filename.c_str(), std::ios::out|std::ios::binary);\n\t\tfile.write(buffer.empty() ? 0 : (char*)&buffer[0], std::streamsize(buffer.size()));\n\t\t}\n#endif //LODEPNG_COMPILE_DISK\n\n#ifdef LODEPNG_COMPILE_ZLIB\n#ifdef LODEPNG_COMPILE_DECODER\n\tunsigned decompress(std::vector<unsigned char>& out, const unsigned char* in, size_t insize,\n\t                    const LodePNGDecompressSettings& settings)\n\t\t{\n\t\tunsigned char* buffer = 0;\n\t\tsize_t buffersize = 0;\n\t\tunsigned error = zlib_decompress(&buffer, &buffersize, in, insize, &settings);\n\t\tif(buffer) {\n\t\t\tout.insert(out.end(), &buffer[0], &buffer[buffersize]);\n\t\t\tlodepng_free(buffer);\n\t\t\t}\n\t\treturn error;\n\t\t}\n\n\tunsigned decompress(std::vector<unsigned char>& out, const std::vector<unsigned char>& in,\n\t                    const LodePNGDecompressSettings& settings)\n\t\t{\n\t\treturn decompress(out, in.empty() ? 0 : &in[0], in.size(), settings);\n\t\t}\n#endif //LODEPNG_COMPILE_DECODER\n\n#ifdef LODEPNG_COMPILE_ENCODER\n\tunsigned compress(std::vector<unsigned char>& out, const unsigned char* in, size_t insize,\n\t                  const LodePNGCompressSettings& settings)\n\t\t{\n\t\tunsigned char* buffer = 0;\n\t\tsize_t buffersize = 0;\n\t\tunsigned error = zlib_compress(&buffer, &buffersize, in, insize, &settings);\n\t\tif(buffer) {\n\t\t\tout.insert(out.end(), &buffer[0], &buffer[buffersize]);\n\t\t\tlodepng_free(buffer);\n\t\t\t}\n\t\treturn error;\n\t\t}\n\n\tunsigned compress(std::vector<unsigned char>& out, const std::vector<unsigned char>& in,\n\t                  const LodePNGCompressSettings& settings)\n\t\t{\n\t\treturn compress(out, in.empty() ? 0 : &in[0], in.size(), settings);\n\t\t}\n#endif //LODEPNG_COMPILE_ENCODER\n#endif //LODEPNG_COMPILE_ZLIB\n\n\n#ifdef LODEPNG_COMPILE_PNG\n\n\tState::State()\n\t\t{\n\t\tlodepng_state_init(this);\n\t\t}\n\n\tState::State(const State& other)\n\t\t{\n\t\tlodepng_state_init(this);\n\t\tlodepng_state_copy(this, &other);\n\t\t}\n\n\tState::~State()\n\t\t{\n\t\tlodepng_state_cleanup(this);\n\t\t}\n\n\tState& State::operator=(const State& other)\n\t\t{\n\t\tlodepng_state_copy(this, &other);\n\t\treturn *this;\n\t\t}\n\n#ifdef LODEPNG_COMPILE_DECODER\n\n\tunsigned decode(std::vector<unsigned char>& out, unsigned& w, unsigned& h, const unsigned char* in,\n\t                size_t insize, LodePNGColorType colortype, unsigned bitdepth)\n\t\t{\n\t\tunsigned char* buffer;\n\t\tunsigned error = lodepng_decode_memory(&buffer, &w, &h, in, insize, colortype, bitdepth);\n\t\tif(buffer && !error) {\n\t\t\tState state;\n\t\t\tstate.info_raw.colortype = colortype;\n\t\t\tstate.info_raw.bitdepth = bitdepth;\n\t\t\tsize_t buffersize = lodepng_get_raw_size(w, h, &state.info_raw);\n\t\t\tout.insert(out.end(), &buffer[0], &buffer[buffersize]);\n\t\t\tlodepng_free(buffer);\n\t\t\t}\n\t\treturn error;\n\t\t}\n\n\tunsigned decode(std::vector<unsigned char>& out, unsigned& w, unsigned& h,\n\t                const std::vector<unsigned char>& in, LodePNGColorType colortype, unsigned bitdepth)\n\t\t{\n\t\treturn decode(out, w, h, in.empty() ? 0 : &in[0], (unsigned)in.size(), colortype, bitdepth);\n\t\t}\n\n\tunsigned decode(std::vector<unsigned char>& out, unsigned& w, unsigned& h,\n\t                State& state,\n\t                const unsigned char* in, size_t insize)\n\t\t{\n\t\tunsigned char* buffer = NULL;\n\t\tunsigned error = lodepng_decode(&buffer, &w, &h, &state, in, insize);\n\t\tif(buffer && !error) {\n\t\t\tsize_t buffersize = lodepng_get_raw_size(w, h, &state.info_raw);\n\t\t\tout.insert(out.end(), &buffer[0], &buffer[buffersize]);\n\t\t\t}\n\t\tlodepng_free(buffer);\n\t\treturn error;\n\t\t}\n\n\tunsigned decode(std::vector<unsigned char>& out, unsigned& w, unsigned& h,\n\t                State& state,\n\t                const std::vector<unsigned char>& in)\n\t\t{\n\t\treturn decode(out, w, h, state, in.empty() ? 0 : &in[0], in.size());\n\t\t}\n\n#ifdef LODEPNG_COMPILE_DISK\n\tunsigned decode(std::vector<unsigned char>& out, unsigned& w, unsigned& h, const std::string& filename,\n\t                LodePNGColorType colortype, unsigned bitdepth)\n\t\t{\n\t\tstd::vector<unsigned char> buffer;\n\t\tload_file(buffer, filename);\n\t\treturn decode(out, w, h, buffer, colortype, bitdepth);\n\t\t}\n#endif //LODEPNG_COMPILE_DECODER\n#endif //LODEPNG_COMPILE_DISK\n\n#ifdef LODEPNG_COMPILE_ENCODER\n\tunsigned encode(std::vector<unsigned char>& out, const unsigned char* in, unsigned w, unsigned h,\n\t                LodePNGColorType colortype, unsigned bitdepth)\n\t\t{\n\t\tunsigned char* buffer;\n\t\tsize_t buffersize;\n\t\tunsigned error = lodepng_encode_memory(&buffer, &buffersize, in, w, h, colortype, bitdepth);\n\t\tif(buffer) {\n\t\t\tout.insert(out.end(), &buffer[0], &buffer[buffersize]);\n\t\t\tlodepng_free(buffer);\n\t\t\t}\n\t\treturn error;\n\t\t}\n\n\tunsigned encode(std::vector<unsigned char>& out,\n\t                const std::vector<unsigned char>& in, unsigned w, unsigned h,\n\t                LodePNGColorType colortype, unsigned bitdepth)\n\t\t{\n\t\tif(lodepng_get_raw_size_lct(w, h, colortype, bitdepth) > in.size()) return 84;\n\t\treturn encode(out, in.empty() ? 0 : &in[0], w, h, colortype, bitdepth);\n\t\t}\n\n\tunsigned encode(std::vector<unsigned char>& out,\n\t                const unsigned char* in, unsigned w, unsigned h,\n\t                State& state)\n\t\t{\n\t\tunsigned char* buffer;\n\t\tsize_t buffersize;\n\t\tunsigned error = lodepng_encode(&buffer, &buffersize, in, w, h, &state);\n\t\tif(buffer) {\n\t\t\tout.insert(out.end(), &buffer[0], &buffer[buffersize]);\n\t\t\tlodepng_free(buffer);\n\t\t\t}\n\t\treturn error;\n\t\t}\n\n\tunsigned encode(std::vector<unsigned char>& out,\n\t                const std::vector<unsigned char>& in, unsigned w, unsigned h,\n\t                State& state)\n\t\t{\n\t\tif(lodepng_get_raw_size(w, h, &state.info_raw) > in.size()) return 84;\n\t\treturn encode(out, in.empty() ? 0 : &in[0], w, h, state);\n\t\t}\n\n#ifdef LODEPNG_COMPILE_DISK\n\tunsigned encode(const std::string& filename,\n\t                const unsigned char* in, unsigned w, unsigned h,\n\t                LodePNGColorType colortype, unsigned bitdepth)\n\t\t{\n\t\tstd::vector<unsigned char> buffer;\n\t\tunsigned error = encode(buffer, in, w, h, colortype, bitdepth);\n\t\tif(!error) save_file(buffer, filename);\n\t\treturn error;\n\t\t}\n\n\tunsigned encode(const std::string& filename,\n\t                const std::vector<unsigned char>& in, unsigned w, unsigned h,\n\t                LodePNGColorType colortype, unsigned bitdepth)\n\t\t{\n\t\tif(lodepng_get_raw_size_lct(w, h, colortype, bitdepth) > in.size()) return 84;\n\t\treturn encode(filename, in.empty() ? 0 : &in[0], w, h, colortype, bitdepth);\n\t\t}\n#endif //LODEPNG_COMPILE_DISK\n#endif //LODEPNG_COMPILE_ENCODER\n#endif //LODEPNG_COMPILE_PNG\n\t} //namespace lodepng\n#endif /*LODEPNG_COMPILE_CPP*/\n"
  },
  {
    "path": "frontend/common/lodepng.h",
    "content": "/*\nLodePNG version 20131222\n\nCopyright (c) 2005-2013 Lode Vandevenne\n\nThis software is provided 'as-is', without any express or implied\nwarranty. In no event will the authors be held liable for any damages\narising from the use of this software.\n\nPermission is granted to anyone to use this software for any purpose,\nincluding commercial applications, and to alter it and redistribute it\nfreely, subject to the following restrictions:\n\n    1. The origin of this software must not be misrepresented; you must not\n    claim that you wrote the original software. If you use this software\n    in a product, an acknowledgment in the product documentation would be\n    appreciated but is not required.\n\n    2. Altered source versions must be plainly marked as such, and must not be\n    misrepresented as being the original software.\n\n    3. This notice may not be removed or altered from any source\n    distribution.\n*/\n\n#ifndef LODEPNG_H\n#define LODEPNG_H\n\n#include <string.h> /*for size_t*/\n\n#ifdef __cplusplus\n#include <vector>\n#include <string>\n#endif /*__cplusplus*/\n\n/*\nThe following #defines are used to create code sections. They can be disabled\nto disable code sections, which can give faster compile time and smaller binary.\nThe \"NO_COMPILE\" defines are designed to be used to pass as defines to the\ncompiler command to disable them without modifying this header, e.g.\n-DLODEPNG_NO_COMPILE_ZLIB for gcc.\n*/\n/*deflate & zlib. If disabled, you must specify alternative zlib functions in\nthe custom_zlib field of the compress and decompress settings*/\n#ifndef LODEPNG_NO_COMPILE_ZLIB\n#define LODEPNG_COMPILE_ZLIB\n#endif\n/*png encoder and png decoder*/\n#ifndef LODEPNG_NO_COMPILE_PNG\n#define LODEPNG_COMPILE_PNG\n#endif\n/*deflate&zlib decoder and png decoder*/\n#ifndef LODEPNG_NO_COMPILE_DECODER\n#define LODEPNG_COMPILE_DECODER\n#endif\n/*deflate&zlib encoder and png encoder*/\n#ifndef LODEPNG_NO_COMPILE_ENCODER\n#define LODEPNG_COMPILE_ENCODER\n#endif\n/*the optional built in harddisk file loading and saving functions*/\n#ifndef LODEPNG_NO_COMPILE_DISK\n#define LODEPNG_COMPILE_DISK\n#endif\n/*support for chunks other than IHDR, IDAT, PLTE, tRNS, IEND: ancillary and unknown chunks*/\n#ifndef LODEPNG_NO_COMPILE_ANCILLARY_CHUNKS\n#define LODEPNG_COMPILE_ANCILLARY_CHUNKS\n#endif\n/*ability to convert error numerical codes to English text string*/\n#ifndef LODEPNG_NO_COMPILE_ERROR_TEXT\n#define LODEPNG_COMPILE_ERROR_TEXT\n#endif\n/*Compile the default allocators (C's free, malloc and realloc). If you disable this,\nyou can define the functions lodepng_free, lodepng_malloc and lodepng_realloc in your\nsource files with custom allocators.*/\n#ifndef LODEPNG_NO_COMPILE_ALLOCATORS\n#define LODEPNG_COMPILE_ALLOCATORS\n#endif\n/*compile the C++ version (you can disable the C++ wrapper here even when compiling for C++)*/\n#ifdef __cplusplus\n#ifndef LODEPNG_NO_COMPILE_CPP\n#define LODEPNG_COMPILE_CPP\n#endif\n#endif\n\n#ifdef LODEPNG_COMPILE_PNG\n/*The PNG color types (also used for raw).*/\ntypedef enum LodePNGColorType\n{\n  LCT_GREY = 0, /*greyscale: 1,2,4,8,16 bit*/\n  LCT_RGB = 2, /*RGB: 8,16 bit*/\n  LCT_PALETTE = 3, /*palette: 1,2,4,8 bit*/\n  LCT_GREY_ALPHA = 4, /*greyscale with alpha: 8,16 bit*/\n  LCT_RGBA = 6 /*RGB with alpha: 8,16 bit*/\n} LodePNGColorType;\n\n#ifdef LODEPNG_COMPILE_DECODER\n/*\nConverts PNG data in memory to raw pixel data.\nout: Output parameter. Pointer to buffer that will contain the raw pixel data.\n     After decoding, its size is w * h * (bytes per pixel) bytes larger than\n     initially. Bytes per pixel depends on colortype and bitdepth.\n     Must be freed after usage with free(*out).\n     Note: for 16-bit per channel colors, uses big endian format like PNG does.\nw: Output parameter. Pointer to width of pixel data.\nh: Output parameter. Pointer to height of pixel data.\nin: Memory buffer with the PNG file.\ninsize: size of the in buffer.\ncolortype: the desired color type for the raw output image. See explanation on PNG color types.\nbitdepth: the desired bit depth for the raw output image. See explanation on PNG color types.\nReturn value: LodePNG error code (0 means no error).\n*/\nunsigned lodepng_decode_memory(unsigned char** out, unsigned* w, unsigned* h,\n                               const unsigned char* in, size_t insize,\n                               LodePNGColorType colortype, unsigned bitdepth);\n\n/*Same as lodepng_decode_memory, but always decodes to 32-bit RGBA raw image*/\nunsigned lodepng_decode32(unsigned char** out, unsigned* w, unsigned* h,\n                          const unsigned char* in, size_t insize);\n\n/*Same as lodepng_decode_memory, but always decodes to 24-bit RGB raw image*/\nunsigned lodepng_decode24(unsigned char** out, unsigned* w, unsigned* h,\n                          const unsigned char* in, size_t insize);\n\n#ifdef LODEPNG_COMPILE_DISK\n/*\nLoad PNG from disk, from file with given name.\nSame as the other decode functions, but instead takes a filename as input.\n*/\nunsigned lodepng_decode_file(unsigned char** out, unsigned* w, unsigned* h,\n                             const char* filename,\n                             LodePNGColorType colortype, unsigned bitdepth);\n\n/*Same as lodepng_decode_file, but always decodes to 32-bit RGBA raw image.*/\nunsigned lodepng_decode32_file(unsigned char** out, unsigned* w, unsigned* h,\n                               const char* filename);\n\n/*Same as lodepng_decode_file, but always decodes to 24-bit RGB raw image.*/\nunsigned lodepng_decode24_file(unsigned char** out, unsigned* w, unsigned* h,\n                               const char* filename);\n#endif /*LODEPNG_COMPILE_DISK*/\n#endif /*LODEPNG_COMPILE_DECODER*/\n\n\n#ifdef LODEPNG_COMPILE_ENCODER\n/*\nConverts raw pixel data into a PNG image in memory. The colortype and bitdepth\n  of the output PNG image cannot be chosen, they are automatically determined\n  by the colortype, bitdepth and content of the input pixel data.\n  Note: for 16-bit per channel colors, needs big endian format like PNG does.\nout: Output parameter. Pointer to buffer that will contain the PNG image data.\n     Must be freed after usage with free(*out).\noutsize: Output parameter. Pointer to the size in bytes of the out buffer.\nimage: The raw pixel data to encode. The size of this buffer should be\n       w * h * (bytes per pixel), bytes per pixel depends on colortype and bitdepth.\nw: width of the raw pixel data in pixels.\nh: height of the raw pixel data in pixels.\ncolortype: the color type of the raw input image. See explanation on PNG color types.\nbitdepth: the bit depth of the raw input image. See explanation on PNG color types.\nReturn value: LodePNG error code (0 means no error).\n*/\nunsigned lodepng_encode_memory(unsigned char** out, size_t* outsize,\n                               const unsigned char* image, unsigned w, unsigned h,\n                               LodePNGColorType colortype, unsigned bitdepth);\n\n/*Same as lodepng_encode_memory, but always encodes from 32-bit RGBA raw image.*/\nunsigned lodepng_encode32(unsigned char** out, size_t* outsize,\n                          const unsigned char* image, unsigned w, unsigned h);\n\n/*Same as lodepng_encode_memory, but always encodes from 24-bit RGB raw image.*/\nunsigned lodepng_encode24(unsigned char** out, size_t* outsize,\n                          const unsigned char* image, unsigned w, unsigned h);\n\n#ifdef LODEPNG_COMPILE_DISK\n/*\nConverts raw pixel data into a PNG file on disk.\nSame as the other encode functions, but instead takes a filename as output.\nNOTE: This overwrites existing files without warning!\n*/\nunsigned lodepng_encode_file(const char* filename,\n                             const unsigned char* image, unsigned w, unsigned h,\n                             LodePNGColorType colortype, unsigned bitdepth);\n\n/*Same as lodepng_encode_file, but always encodes from 32-bit RGBA raw image.*/\nunsigned lodepng_encode32_file(const char* filename,\n                               const unsigned char* image, unsigned w, unsigned h);\n\n/*Same as lodepng_encode_file, but always encodes from 24-bit RGB raw image.*/\nunsigned lodepng_encode24_file(const char* filename,\n                               const unsigned char* image, unsigned w, unsigned h);\n#endif /*LODEPNG_COMPILE_DISK*/\n#endif /*LODEPNG_COMPILE_ENCODER*/\n\n\n#ifdef LODEPNG_COMPILE_CPP\nnamespace lodepng\n{\n#ifdef LODEPNG_COMPILE_DECODER\n/*Same as lodepng_decode_memory, but decodes to an std::vector.*/\nunsigned decode(std::vector<unsigned char>& out, unsigned& w, unsigned& h,\n                const unsigned char* in, size_t insize,\n                LodePNGColorType colortype = LCT_RGBA, unsigned bitdepth = 8);\nunsigned decode(std::vector<unsigned char>& out, unsigned& w, unsigned& h,\n                const std::vector<unsigned char>& in,\n                LodePNGColorType colortype = LCT_RGBA, unsigned bitdepth = 8);\n#ifdef LODEPNG_COMPILE_DISK\n/*\nConverts PNG file from disk to raw pixel data in memory.\nSame as the other decode functions, but instead takes a filename as input.\n*/\nunsigned decode(std::vector<unsigned char>& out, unsigned& w, unsigned& h,\n                const std::string& filename,\n                LodePNGColorType colortype = LCT_RGBA, unsigned bitdepth = 8);\n#endif //LODEPNG_COMPILE_DISK\n#endif //LODEPNG_COMPILE_DECODER\n\n#ifdef LODEPNG_COMPILE_ENCODER\n/*Same as lodepng_encode_memory, but encodes to an std::vector.*/\nunsigned encode(std::vector<unsigned char>& out,\n                const unsigned char* in, unsigned w, unsigned h,\n                LodePNGColorType colortype = LCT_RGBA, unsigned bitdepth = 8);\nunsigned encode(std::vector<unsigned char>& out,\n                const std::vector<unsigned char>& in, unsigned w, unsigned h,\n                LodePNGColorType colortype = LCT_RGBA, unsigned bitdepth = 8);\n#ifdef LODEPNG_COMPILE_DISK\n/*\nConverts 32-bit RGBA raw pixel data into a PNG file on disk.\nSame as the other encode functions, but instead takes a filename as output.\nNOTE: This overwrites existing files without warning!\n*/\nunsigned encode(const std::string& filename,\n                const unsigned char* in, unsigned w, unsigned h,\n                LodePNGColorType colortype = LCT_RGBA, unsigned bitdepth = 8);\nunsigned encode(const std::string& filename,\n                const std::vector<unsigned char>& in, unsigned w, unsigned h,\n                LodePNGColorType colortype = LCT_RGBA, unsigned bitdepth = 8);\n#endif //LODEPNG_COMPILE_DISK\n#endif //LODEPNG_COMPILE_ENCODER\n} //namespace lodepng\n#endif /*LODEPNG_COMPILE_CPP*/\n#endif /*LODEPNG_COMPILE_PNG*/\n\n#ifdef LODEPNG_COMPILE_ERROR_TEXT\n/*Returns an English description of the numerical error code.*/\nconst char* lodepng_error_text(unsigned code);\n#endif /*LODEPNG_COMPILE_ERROR_TEXT*/\n\n#ifdef LODEPNG_COMPILE_DECODER\n/*Settings for zlib decompression*/\ntypedef struct LodePNGDecompressSettings LodePNGDecompressSettings;\nstruct LodePNGDecompressSettings\n{\n  unsigned ignore_adler32; /*if 1, continue and don't give an error message if the Adler32 checksum is corrupted*/\n\n  /*use custom zlib decoder instead of built in one (default: null)*/\n  unsigned (*custom_zlib)(unsigned char**, size_t*,\n                          const unsigned char*, size_t,\n                          const LodePNGDecompressSettings*);\n  /*use custom deflate decoder instead of built in one (default: null)\n  if custom_zlib is used, custom_deflate is ignored since only the built in\n  zlib function will call custom_deflate*/\n  unsigned (*custom_inflate)(unsigned char**, size_t*,\n                             const unsigned char*, size_t,\n                             const LodePNGDecompressSettings*);\n\n  const void* custom_context; /*optional custom settings for custom functions*/\n};\n\nextern const LodePNGDecompressSettings lodepng_default_decompress_settings;\nvoid lodepng_decompress_settings_init(LodePNGDecompressSettings* settings);\n#endif /*LODEPNG_COMPILE_DECODER*/\n\n#ifdef LODEPNG_COMPILE_ENCODER\n/*\nSettings for zlib compression. Tweaking these settings tweaks the balance\nbetween speed and compression ratio.\n*/\ntypedef struct LodePNGCompressSettings LodePNGCompressSettings;\nstruct LodePNGCompressSettings /*deflate = compress*/\n{\n  /*LZ77 related settings*/\n  unsigned btype; /*the block type for LZ (0, 1, 2 or 3, see zlib standard). Should be 2 for proper compression.*/\n  unsigned use_lz77; /*whether or not to use LZ77. Should be 1 for proper compression.*/\n  unsigned windowsize; /*must be a power of two <= 32768. higher compresses more but is slower. Typical value: 2048.*/\n  unsigned minmatch; /*mininum lz77 length. 3 is normally best, 6 can be better for some PNGs. Default: 0*/\n  unsigned nicematch; /*stop searching if >= this length found. Set to 258 for best compression. Default: 128*/\n  unsigned lazymatching; /*use lazy matching: better compression but a bit slower. Default: true*/\n\n  /*use custom zlib encoder instead of built in one (default: null)*/\n  unsigned (*custom_zlib)(unsigned char**, size_t*,\n                          const unsigned char*, size_t,\n                          const LodePNGCompressSettings*);\n  /*use custom deflate encoder instead of built in one (default: null)\n  if custom_zlib is used, custom_deflate is ignored since only the built in\n  zlib function will call custom_deflate*/\n  unsigned (*custom_deflate)(unsigned char**, size_t*,\n                             const unsigned char*, size_t,\n                             const LodePNGCompressSettings*);\n\n  const void* custom_context; /*optional custom settings for custom functions*/\n};\n\nextern const LodePNGCompressSettings lodepng_default_compress_settings;\nvoid lodepng_compress_settings_init(LodePNGCompressSettings* settings);\n#endif /*LODEPNG_COMPILE_ENCODER*/\n\n#ifdef LODEPNG_COMPILE_PNG\n/*\nColor mode of an image. Contains all information required to decode the pixel\nbits to RGBA colors. This information is the same as used in the PNG file\nformat, and is used both for PNG and raw image data in LodePNG.\n*/\ntypedef struct LodePNGColorMode\n{\n  /*header (IHDR)*/\n  LodePNGColorType colortype; /*color type, see PNG standard or documentation further in this header file*/\n  unsigned bitdepth;  /*bits per sample, see PNG standard or documentation further in this header file*/\n\n  /*\n  palette (PLTE and tRNS)\n\n  Dynamically allocated with the colors of the palette, including alpha.\n  When encoding a PNG, to store your colors in the palette of the LodePNGColorMode, first use\n  lodepng_palette_clear, then for each color use lodepng_palette_add.\n  If you encode an image without alpha with palette, don't forget to put value 255 in each A byte of the palette.\n\n  When decoding, by default you can ignore this palette, since LodePNG already\n  fills the palette colors in the pixels of the raw RGBA output.\n\n  The palette is only supported for color type 3.\n  */\n  unsigned char* palette; /*palette in RGBARGBA... order. When allocated, must be either 0, or have size 1024*/\n  size_t palettesize; /*palette size in number of colors (amount of bytes is 4 * palettesize)*/\n\n  /*\n  transparent color key (tRNS)\n\n  This color uses the same bit depth as the bitdepth value in this struct, which can be 1-bit to 16-bit.\n  For greyscale PNGs, r, g and b will all 3 be set to the same.\n\n  When decoding, by default you can ignore this information, since LodePNG sets\n  pixels with this key to transparent already in the raw RGBA output.\n\n  The color key is only supported for color types 0 and 2.\n  */\n  unsigned key_defined; /*is a transparent color key given? 0 = false, 1 = true*/\n  unsigned key_r;       /*red/greyscale component of color key*/\n  unsigned key_g;       /*green component of color key*/\n  unsigned key_b;       /*blue component of color key*/\n} LodePNGColorMode;\n\n/*init, cleanup and copy functions to use with this struct*/\nvoid lodepng_color_mode_init(LodePNGColorMode* info);\nvoid lodepng_color_mode_cleanup(LodePNGColorMode* info);\n/*return value is error code (0 means no error)*/\nunsigned lodepng_color_mode_copy(LodePNGColorMode* dest, const LodePNGColorMode* source);\n\nvoid lodepng_palette_clear(LodePNGColorMode* info);\n/*add 1 color to the palette*/\nunsigned lodepng_palette_add(LodePNGColorMode* info,\n                             unsigned char r, unsigned char g, unsigned char b, unsigned char a);\n\n/*get the total amount of bits per pixel, based on colortype and bitdepth in the struct*/\nunsigned lodepng_get_bpp(const LodePNGColorMode* info);\n/*get the amount of color channels used, based on colortype in the struct.\nIf a palette is used, it counts as 1 channel.*/\nunsigned lodepng_get_channels(const LodePNGColorMode* info);\n/*is it a greyscale type? (only colortype 0 or 4)*/\nunsigned lodepng_is_greyscale_type(const LodePNGColorMode* info);\n/*has it got an alpha channel? (only colortype 2 or 6)*/\nunsigned lodepng_is_alpha_type(const LodePNGColorMode* info);\n/*has it got a palette? (only colortype 3)*/\nunsigned lodepng_is_palette_type(const LodePNGColorMode* info);\n/*only returns true if there is a palette and there is a value in the palette with alpha < 255.\nLoops through the palette to check this.*/\nunsigned lodepng_has_palette_alpha(const LodePNGColorMode* info);\n/*\nCheck if the given color info indicates the possibility of having non-opaque pixels in the PNG image.\nReturns true if the image can have translucent or invisible pixels (it still be opaque if it doesn't use such pixels).\nReturns false if the image can only have opaque pixels.\nIn detail, it returns true only if it's a color type with alpha, or has a palette with non-opaque values,\nor if \"key_defined\" is true.\n*/\nunsigned lodepng_can_have_alpha(const LodePNGColorMode* info);\n/*Returns the byte size of a raw image buffer with given width, height and color mode*/\nsize_t lodepng_get_raw_size(unsigned w, unsigned h, const LodePNGColorMode* color);\n\n#ifdef LODEPNG_COMPILE_ANCILLARY_CHUNKS\n/*The information of a Time chunk in PNG.*/\ntypedef struct LodePNGTime\n{\n  unsigned year;    /*2 bytes used (0-65535)*/\n  unsigned month;   /*1-12*/\n  unsigned day;     /*1-31*/\n  unsigned hour;    /*0-23*/\n  unsigned minute;  /*0-59*/\n  unsigned second;  /*0-60 (to allow for leap seconds)*/\n} LodePNGTime;\n#endif /*LODEPNG_COMPILE_ANCILLARY_CHUNKS*/\n\n/*Information about the PNG image, except pixels, width and height.*/\ntypedef struct LodePNGInfo\n{\n  /*header (IHDR), palette (PLTE) and transparency (tRNS) chunks*/\n  unsigned compression_method;/*compression method of the original file. Always 0.*/\n  unsigned filter_method;     /*filter method of the original file*/\n  unsigned interlace_method;  /*interlace method of the original file*/\n  LodePNGColorMode color;     /*color type and bits, palette and transparency of the PNG file*/\n\n#ifdef LODEPNG_COMPILE_ANCILLARY_CHUNKS\n  /*\n  suggested background color chunk (bKGD)\n  This color uses the same color mode as the PNG (except alpha channel), which can be 1-bit to 16-bit.\n\n  For greyscale PNGs, r, g and b will all 3 be set to the same. When encoding\n  the encoder writes the red one. For palette PNGs: When decoding, the RGB value\n  will be stored, not a palette index. But when encoding, specify the index of\n  the palette in background_r, the other two are then ignored.\n\n  The decoder does not use this background color to edit the color of pixels.\n  */\n  unsigned background_defined; /*is a suggested background color given?*/\n  unsigned background_r;       /*red component of suggested background color*/\n  unsigned background_g;       /*green component of suggested background color*/\n  unsigned background_b;       /*blue component of suggested background color*/\n\n  /*\n  non-international text chunks (tEXt and zTXt)\n\n  The char** arrays each contain num strings. The actual messages are in\n  text_strings, while text_keys are keywords that give a short description what\n  the actual text represents, e.g. Title, Author, Description, or anything else.\n\n  A keyword is minimum 1 character and maximum 79 characters long. It's\n  discouraged to use a single line length longer than 79 characters for texts.\n\n  Don't allocate these text buffers yourself. Use the init/cleanup functions\n  correctly and use lodepng_add_text and lodepng_clear_text.\n  */\n  size_t text_num; /*the amount of texts in these char** buffers (there may be more texts in itext)*/\n  char** text_keys; /*the keyword of a text chunk (e.g. \"Comment\")*/\n  char** text_strings; /*the actual text*/\n\n  /*\n  international text chunks (iTXt)\n  Similar to the non-international text chunks, but with additional strings\n  \"langtags\" and \"transkeys\".\n  */\n  size_t itext_num; /*the amount of international texts in this PNG*/\n  char** itext_keys; /*the English keyword of the text chunk (e.g. \"Comment\")*/\n  char** itext_langtags; /*language tag for this text's language, ISO/IEC 646 string, e.g. ISO 639 language tag*/\n  char** itext_transkeys; /*keyword translated to the international language - UTF-8 string*/\n  char** itext_strings; /*the actual international text - UTF-8 string*/\n\n  /*time chunk (tIME)*/\n  unsigned time_defined; /*set to 1 to make the encoder generate a tIME chunk*/\n  LodePNGTime time;\n\n  /*phys chunk (pHYs)*/\n  unsigned phys_defined; /*if 0, there is no pHYs chunk and the values below are undefined, if 1 else there is one*/\n  unsigned phys_x; /*pixels per unit in x direction*/\n  unsigned phys_y; /*pixels per unit in y direction*/\n  unsigned phys_unit; /*may be 0 (unknown unit) or 1 (metre)*/\n\n  /*\n  unknown chunks\n  There are 3 buffers, one for each position in the PNG where unknown chunks can appear\n  each buffer contains all unknown chunks for that position consecutively\n  The 3 buffers are the unknown chunks between certain critical chunks:\n  0: IHDR-PLTE, 1: PLTE-IDAT, 2: IDAT-IEND\n  Do not allocate or traverse this data yourself. Use the chunk traversing functions declared\n  later, such as lodepng_chunk_next and lodepng_chunk_append, to read/write this struct.\n  */\n  unsigned char* unknown_chunks_data[3];\n  size_t unknown_chunks_size[3]; /*size in bytes of the unknown chunks, given for protection*/\n#endif /*LODEPNG_COMPILE_ANCILLARY_CHUNKS*/\n} LodePNGInfo;\n\n/*init, cleanup and copy functions to use with this struct*/\nvoid lodepng_info_init(LodePNGInfo* info);\nvoid lodepng_info_cleanup(LodePNGInfo* info);\n/*return value is error code (0 means no error)*/\nunsigned lodepng_info_copy(LodePNGInfo* dest, const LodePNGInfo* source);\n\n#ifdef LODEPNG_COMPILE_ANCILLARY_CHUNKS\nvoid lodepng_clear_text(LodePNGInfo* info); /*use this to clear the texts again after you filled them in*/\nunsigned lodepng_add_text(LodePNGInfo* info, const char* key, const char* str); /*push back both texts at once*/\n\nvoid lodepng_clear_itext(LodePNGInfo* info); /*use this to clear the itexts again after you filled them in*/\nunsigned lodepng_add_itext(LodePNGInfo* info, const char* key, const char* langtag,\n                           const char* transkey, const char* str); /*push back the 4 texts of 1 chunk at once*/\n#endif /*LODEPNG_COMPILE_ANCILLARY_CHUNKS*/\n\n/*\nConverts raw buffer from one color type to another color type, based on\nLodePNGColorMode structs to describe the input and output color type.\nSee the reference manual at the end of this header file to see which color conversions are supported.\nreturn value = LodePNG error code (0 if all went ok, an error if the conversion isn't supported)\nThe out buffer must have size (w * h * bpp + 7) / 8, where bpp is the bits per pixel\nof the output color type (lodepng_get_bpp)\nThe fix_png value works as described in struct LodePNGDecoderSettings.\nNote: for 16-bit per channel colors, uses big endian format like PNG does.\n*/\nunsigned lodepng_convert(unsigned char* out, const unsigned char* in,\n                         LodePNGColorMode* mode_out, const LodePNGColorMode* mode_in,\n                         unsigned w, unsigned h, unsigned fix_png);\n\n#ifdef LODEPNG_COMPILE_DECODER\n/*\nSettings for the decoder. This contains settings for the PNG and the Zlib\ndecoder, but not the Info settings from the Info structs.\n*/\ntypedef struct LodePNGDecoderSettings\n{\n  LodePNGDecompressSettings zlibsettings; /*in here is the setting to ignore Adler32 checksums*/\n\n  unsigned ignore_crc; /*ignore CRC checksums*/\n  /*\n  The fix_png setting, if 1, makes the decoder tolerant towards some PNG images\n  that do not correctly follow the PNG specification. This only supports errors\n  that are fixable, were found in images that are actually used on the web, and\n  are silently tolerated by other decoders as well. Currently only one such fix\n  is implemented: if a palette index is out of bounds given the palette size,\n  interpret it as opaque black.\n  By default this value is 0, which makes it stop with an error on such images.\n  */\n  unsigned fix_png;\n  unsigned color_convert; /*whether to convert the PNG to the color type you want. Default: yes*/\n\n#ifdef LODEPNG_COMPILE_ANCILLARY_CHUNKS\n  unsigned read_text_chunks; /*if false but remember_unknown_chunks is true, they're stored in the unknown chunks*/\n  /*store all bytes from unknown chunks in the LodePNGInfo (off by default, useful for a png editor)*/\n  unsigned remember_unknown_chunks;\n#endif /*LODEPNG_COMPILE_ANCILLARY_CHUNKS*/\n} LodePNGDecoderSettings;\n\nvoid lodepng_decoder_settings_init(LodePNGDecoderSettings* settings);\n#endif /*LODEPNG_COMPILE_DECODER*/\n\n#ifdef LODEPNG_COMPILE_ENCODER\n/*automatically use color type with less bits per pixel if losslessly possible. Default: AUTO*/\ntypedef enum LodePNGFilterStrategy\n{\n  /*every filter at zero*/\n  LFS_ZERO,\n  /*Use filter that gives minumum sum, as described in the official PNG filter heuristic.*/\n  LFS_MINSUM,\n  /*Use the filter type that gives smallest Shannon entropy for this scanline. Depending\n  on the image, this is better or worse than minsum.*/\n  LFS_ENTROPY,\n  /*\n  Brute-force-search PNG filters by compressing each filter for each scanline.\n  Experimental, very slow, and only rarely gives better compression than MINSUM.\n  */\n  LFS_BRUTE_FORCE,\n  /*use predefined_filters buffer: you specify the filter type for each scanline*/\n  LFS_PREDEFINED\n} LodePNGFilterStrategy;\n\n/*automatically use color type with less bits per pixel if losslessly possible. Default: LAC_AUTO*/\ntypedef enum LodePNGAutoConvert\n{\n  LAC_NO, /*use color type user requested*/\n  LAC_ALPHA, /*use color type user requested, but if only opaque pixels and RGBA or grey+alpha, use RGB or grey*/\n  LAC_AUTO, /*use PNG color type that can losslessly represent the uncompressed image the smallest possible*/\n  /*\n  like AUTO, but do not choose 1, 2 or 4 bit per pixel types.\n  sometimes a PNG image compresses worse if less than 8 bits per pixels.\n  */\n  LAC_AUTO_NO_NIBBLES,\n  /*\n  like AUTO, but never choose palette color type. For small images, encoding\n  the palette may take more bytes than what is gained. Note that AUTO also\n  already prevents encoding the palette for extremely small images, but that may\n  not be sufficient because due to the compression it cannot predict when to\n  switch.\n  */\n  LAC_AUTO_NO_PALETTE,\n  LAC_AUTO_NO_NIBBLES_NO_PALETTE\n} LodePNGAutoConvert;\n\n\n/*\nAutomatically chooses color type that gives smallest amount of bits in the\noutput image, e.g. grey if there are only greyscale pixels, palette if there\nare less than 256 colors, ...\nThe auto_convert parameter allows limiting it to not use palette, ...\n*/\nunsigned lodepng_auto_choose_color(LodePNGColorMode* mode_out,\n                                   const unsigned char* image, unsigned w, unsigned h,\n                                   const LodePNGColorMode* mode_in,\n                                   LodePNGAutoConvert auto_convert);\n\n/*Settings for the encoder.*/\ntypedef struct LodePNGEncoderSettings\n{\n  LodePNGCompressSettings zlibsettings; /*settings for the zlib encoder, such as window size, ...*/\n\n  LodePNGAutoConvert auto_convert; /*how to automatically choose output PNG color type, if at all*/\n\n  /*If true, follows the official PNG heuristic: if the PNG uses a palette or lower than\n  8 bit depth, set all filters to zero. Otherwise use the filter_strategy. Note that to\n  completely follow the official PNG heuristic, filter_palette_zero must be true and\n  filter_strategy must be LFS_MINSUM*/\n  unsigned filter_palette_zero;\n  /*Which filter strategy to use when not using zeroes due to filter_palette_zero.\n  Set filter_palette_zero to 0 to ensure always using your chosen strategy. Default: LFS_MINSUM*/\n  LodePNGFilterStrategy filter_strategy;\n  /*used if filter_strategy is LFS_PREDEFINED. In that case, this must point to a buffer with\n  the same length as the amount of scanlines in the image, and each value must <= 5. You\n  have to cleanup this buffer, LodePNG will never free it. Don't forget that filter_palette_zero\n  must be set to 0 to ensure this is also used on palette or low bitdepth images.*/\n  const unsigned char* predefined_filters;\n\n  /*force creating a PLTE chunk if colortype is 2 or 6 (= a suggested palette).\n  If colortype is 3, PLTE is _always_ created.*/\n  unsigned force_palette;\n#ifdef LODEPNG_COMPILE_ANCILLARY_CHUNKS\n  /*add LodePNG identifier and version as a text chunk, for debugging*/\n  unsigned add_id;\n  /*encode text chunks as zTXt chunks instead of tEXt chunks, and use compression in iTXt chunks*/\n  unsigned text_compression;\n#endif /*LODEPNG_COMPILE_ANCILLARY_CHUNKS*/\n} LodePNGEncoderSettings;\n\nvoid lodepng_encoder_settings_init(LodePNGEncoderSettings* settings);\n#endif /*LODEPNG_COMPILE_ENCODER*/\n\n\n#if defined(LODEPNG_COMPILE_DECODER) || defined(LODEPNG_COMPILE_ENCODER)\n/*The settings, state and information for extended encoding and decoding.*/\ntypedef struct LodePNGState\n{\n#ifdef LODEPNG_COMPILE_DECODER\n  LodePNGDecoderSettings decoder; /*the decoding settings*/\n#endif /*LODEPNG_COMPILE_DECODER*/\n#ifdef LODEPNG_COMPILE_ENCODER\n  LodePNGEncoderSettings encoder; /*the encoding settings*/\n#endif /*LODEPNG_COMPILE_ENCODER*/\n  LodePNGColorMode info_raw; /*specifies the format in which you would like to get the raw pixel buffer*/\n  LodePNGInfo info_png; /*info of the PNG image obtained after decoding*/\n  unsigned error;\n#ifdef LODEPNG_COMPILE_CPP\n  //For the lodepng::State subclass.\n  virtual ~LodePNGState(){}\n#endif\n} LodePNGState;\n\n/*init, cleanup and copy functions to use with this struct*/\nvoid lodepng_state_init(LodePNGState* state);\nvoid lodepng_state_cleanup(LodePNGState* state);\nvoid lodepng_state_copy(LodePNGState* dest, const LodePNGState* source);\n#endif /* defined(LODEPNG_COMPILE_DECODER) || defined(LODEPNG_COMPILE_ENCODER) */\n\n#ifdef LODEPNG_COMPILE_DECODER\n/*\nSame as lodepng_decode_memory, but uses a LodePNGState to allow custom settings and\ngetting much more information about the PNG image and color mode.\n*/\nunsigned lodepng_decode(unsigned char** out, unsigned* w, unsigned* h,\n                        LodePNGState* state,\n                        const unsigned char* in, size_t insize);\n\n/*\nRead the PNG header, but not the actual data. This returns only the information\nthat is in the header chunk of the PNG, such as width, height and color type. The\ninformation is placed in the info_png field of the LodePNGState.\n*/\nunsigned lodepng_inspect(unsigned* w, unsigned* h,\n                         LodePNGState* state,\n                         const unsigned char* in, size_t insize);\n#endif /*LODEPNG_COMPILE_DECODER*/\n\n\n#ifdef LODEPNG_COMPILE_ENCODER\n/*This function allocates the out buffer with standard malloc and stores the size in *outsize.*/\nunsigned lodepng_encode(unsigned char** out, size_t* outsize,\n                        const unsigned char* image, unsigned w, unsigned h,\n                        LodePNGState* state);\n#endif /*LODEPNG_COMPILE_ENCODER*/\n\n/*\nThe lodepng_chunk functions are normally not needed, except to traverse the\nunknown chunks stored in the LodePNGInfo struct, or add new ones to it.\nIt also allows traversing the chunks of an encoded PNG file yourself.\n\nPNG standard chunk naming conventions:\nFirst byte: uppercase = critical, lowercase = ancillary\nSecond byte: uppercase = public, lowercase = private\nThird byte: must be uppercase\nFourth byte: uppercase = unsafe to copy, lowercase = safe to copy\n*/\n\n/*get the length of the data of the chunk. Total chunk length has 12 bytes more.*/\nunsigned lodepng_chunk_length(const unsigned char* chunk);\n\n/*puts the 4-byte type in null terminated string*/\nvoid lodepng_chunk_type(char type[5], const unsigned char* chunk);\n\n/*check if the type is the given type*/\nunsigned char lodepng_chunk_type_equals(const unsigned char* chunk, const char* type);\n\n/*0: it's one of the critical chunk types, 1: it's an ancillary chunk (see PNG standard)*/\nunsigned char lodepng_chunk_ancillary(const unsigned char* chunk);\n\n/*0: public, 1: private (see PNG standard)*/\nunsigned char lodepng_chunk_private(const unsigned char* chunk);\n\n/*0: the chunk is unsafe to copy, 1: the chunk is safe to copy (see PNG standard)*/\nunsigned char lodepng_chunk_safetocopy(const unsigned char* chunk);\n\n/*get pointer to the data of the chunk, where the input points to the header of the chunk*/\nunsigned char* lodepng_chunk_data(unsigned char* chunk);\nconst unsigned char* lodepng_chunk_data_const(const unsigned char* chunk);\n\n/*returns 0 if the crc is correct, 1 if it's incorrect (0 for OK as usual!)*/\nunsigned lodepng_chunk_check_crc(const unsigned char* chunk);\n\n/*generates the correct CRC from the data and puts it in the last 4 bytes of the chunk*/\nvoid lodepng_chunk_generate_crc(unsigned char* chunk);\n\n/*iterate to next chunks. don't use on IEND chunk, as there is no next chunk then*/\nunsigned char* lodepng_chunk_next(unsigned char* chunk);\nconst unsigned char* lodepng_chunk_next_const(const unsigned char* chunk);\n\n/*\nAppends chunk to the data in out. The given chunk should already have its chunk header.\nThe out variable and outlength are updated to reflect the new reallocated buffer.\nReturns error code (0 if it went ok)\n*/\nunsigned lodepng_chunk_append(unsigned char** out, size_t* outlength, const unsigned char* chunk);\n\n/*\nAppends new chunk to out. The chunk to append is given by giving its length, type\nand data separately. The type is a 4-letter string.\nThe out variable and outlength are updated to reflect the new reallocated buffer.\nReturne error code (0 if it went ok)\n*/\nunsigned lodepng_chunk_create(unsigned char** out, size_t* outlength, unsigned length,\n                              const char* type, const unsigned char* data);\n\n\n/*Calculate CRC32 of buffer*/\nunsigned lodepng_crc32(const unsigned char* buf, size_t len);\n#endif /*LODEPNG_COMPILE_PNG*/\n\n\n#ifdef LODEPNG_COMPILE_ZLIB\n/*\nThis zlib part can be used independently to zlib compress and decompress a\nbuffer. It cannot be used to create gzip files however, and it only supports the\npart of zlib that is required for PNG, it does not support dictionaries.\n*/\n\n#ifdef LODEPNG_COMPILE_DECODER\n/*Inflate a buffer. Inflate is the decompression step of deflate. Out buffer must be freed after use.*/\nunsigned lodepng_inflate(unsigned char** out, size_t* outsize,\n                         const unsigned char* in, size_t insize,\n                         const LodePNGDecompressSettings* settings);\n\n/*\nDecompresses Zlib data. Reallocates the out buffer and appends the data. The\ndata must be according to the zlib specification.\nEither, *out must be NULL and *outsize must be 0, or, *out must be a valid\nbuffer and *outsize its size in bytes. out must be freed by user after usage.\n*/\nunsigned lodepng_zlib_decompress(unsigned char** out, size_t* outsize,\n                                 const unsigned char* in, size_t insize,\n                                 const LodePNGDecompressSettings* settings);\n#endif /*LODEPNG_COMPILE_DECODER*/\n\n#ifdef LODEPNG_COMPILE_ENCODER\n/*\nCompresses data with Zlib. Reallocates the out buffer and appends the data.\nZlib adds a small header and trailer around the deflate data.\nThe data is output in the format of the zlib specification.\nEither, *out must be NULL and *outsize must be 0, or, *out must be a valid\nbuffer and *outsize its size in bytes. out must be freed by user after usage.\n*/\nunsigned lodepng_zlib_compress(unsigned char** out, size_t* outsize,\n                               const unsigned char* in, size_t insize,\n                               const LodePNGCompressSettings* settings);\n\n/*\nFind length-limited Huffman code for given frequencies. This function is in the\npublic interface only for tests, it's used internally by lodepng_deflate.\n*/\nunsigned lodepng_huffman_code_lengths(unsigned* lengths, const unsigned* frequencies,\n                                      size_t numcodes, unsigned maxbitlen);\n\n/*Compress a buffer with deflate. See RFC 1951. Out buffer must be freed after use.*/\nunsigned lodepng_deflate(unsigned char** out, size_t* outsize,\n                         const unsigned char* in, size_t insize,\n                         const LodePNGCompressSettings* settings);\n\n#endif /*LODEPNG_COMPILE_ENCODER*/\n#endif /*LODEPNG_COMPILE_ZLIB*/\n\n#ifdef LODEPNG_COMPILE_DISK\n/*\nLoad a file from disk into buffer. The function allocates the out buffer, and\nafter usage you should free it.\nout: output parameter, contains pointer to loaded buffer.\noutsize: output parameter, size of the allocated out buffer\nfilename: the path to the file to load\nreturn value: error code (0 means ok)\n*/\nunsigned lodepng_load_file(unsigned char** out, size_t* outsize, const char* filename);\n\n/*\nSave a file from buffer to disk. Warning, if it exists, this function overwrites\nthe file without warning!\nbuffer: the buffer to write\nbuffersize: size of the buffer to write\nfilename: the path to the file to save to\nreturn value: error code (0 means ok)\n*/\nunsigned lodepng_save_file(const unsigned char* buffer, size_t buffersize, const char* filename);\n#endif /*LODEPNG_COMPILE_DISK*/\n\n#ifdef LODEPNG_COMPILE_CPP\n//The LodePNG C++ wrapper uses std::vectors instead of manually allocated memory buffers.\nnamespace lodepng\n{\n#ifdef LODEPNG_COMPILE_PNG\nclass State : public LodePNGState\n{\n  public:\n    State();\n    State(const State& other);\n    virtual ~State();\n    State& operator=(const State& other);\n};\n\n#ifdef LODEPNG_COMPILE_DECODER\n//Same as other lodepng::decode, but using a State for more settings and information.\nunsigned decode(std::vector<unsigned char>& out, unsigned& w, unsigned& h,\n                State& state,\n                const unsigned char* in, size_t insize);\nunsigned decode(std::vector<unsigned char>& out, unsigned& w, unsigned& h,\n                State& state,\n                const std::vector<unsigned char>& in);\n#endif /*LODEPNG_COMPILE_DECODER*/\n\n#ifdef LODEPNG_COMPILE_ENCODER\n//Same as other lodepng::encode, but using a State for more settings and information.\nunsigned encode(std::vector<unsigned char>& out,\n                const unsigned char* in, unsigned w, unsigned h,\n                State& state);\nunsigned encode(std::vector<unsigned char>& out,\n                const std::vector<unsigned char>& in, unsigned w, unsigned h,\n                State& state);\n#endif /*LODEPNG_COMPILE_ENCODER*/\n\n#ifdef LODEPNG_COMPILE_DISK\n/*\nLoad a file from disk into an std::vector. If the vector is empty, then either\nthe file doesn't exist or is an empty file.\n*/\nvoid load_file(std::vector<unsigned char>& buffer, const std::string& filename);\n\n/*\nSave the binary data in an std::vector to a file on disk. The file is overwritten\nwithout warning.\n*/\nvoid save_file(const std::vector<unsigned char>& buffer, const std::string& filename);\n#endif //LODEPNG_COMPILE_DISK\n#endif //LODEPNG_COMPILE_PNG\n\n#ifdef LODEPNG_COMPILE_ZLIB\n#ifdef LODEPNG_COMPILE_DECODER\n//Zlib-decompress an unsigned char buffer\nunsigned decompress(std::vector<unsigned char>& out, const unsigned char* in, size_t insize,\n                    const LodePNGDecompressSettings& settings = lodepng_default_decompress_settings);\n\n//Zlib-decompress an std::vector\nunsigned decompress(std::vector<unsigned char>& out, const std::vector<unsigned char>& in,\n                    const LodePNGDecompressSettings& settings = lodepng_default_decompress_settings);\n#endif //LODEPNG_COMPILE_DECODER\n\n#ifdef LODEPNG_COMPILE_ENCODER\n//Zlib-compress an unsigned char buffer\nunsigned compress(std::vector<unsigned char>& out, const unsigned char* in, size_t insize,\n                  const LodePNGCompressSettings& settings = lodepng_default_compress_settings);\n\n//Zlib-compress an std::vector\nunsigned compress(std::vector<unsigned char>& out, const std::vector<unsigned char>& in,\n                  const LodePNGCompressSettings& settings = lodepng_default_compress_settings);\n#endif //LODEPNG_COMPILE_ENCODER\n#endif //LODEPNG_COMPILE_ZLIB\n} //namespace lodepng\n#endif /*LODEPNG_COMPILE_CPP*/\n\n/*\nTODO:\n[.] test if there are no memory leaks or security exploits - done a lot but needs to be checked often\n[.] check compatibility with vareous compilers  - done but needs to be redone for every newer version\n[X] converting color to 16-bit per channel types\n[ ] read all public PNG chunk types (but never let the color profile and gamma ones touch RGB values)\n[ ] make sure encoder generates no chunks with size > (2^31)-1\n[ ] partial decoding (stream processing)\n[X] let the \"isFullyOpaque\" function check color keys and transparent palettes too\n[X] better name for the variables \"codes\", \"codesD\", \"codelengthcodes\", \"clcl\" and \"lldl\"\n[ ] don't stop decoding on errors like 69, 57, 58 (make warnings)\n[ ] make option to choose if the raw image with non multiple of 8 bits per scanline should have padding bits or not\n[ ] let the C++ wrapper catch exceptions coming from the standard library and return LodePNG error codes\n*/\n\n#endif /*LODEPNG_H inclusion guard*/\n\n/*\nLodePNG Documentation\n---------------------\n\n0. table of contents\n--------------------\n\n  1. about\n   1.1. supported features\n   1.2. features not supported\n  2. C and C++ version\n  3. security\n  4. decoding\n  5. encoding\n  6. color conversions\n    6.1. PNG color types\n    6.2. color conversions\n    6.3. padding bits\n    6.4. A note about 16-bits per channel and endianness\n  7. error values\n  8. chunks and PNG editing\n  9. compiler support\n  10. examples\n   10.1. decoder C++ example\n   10.2. decoder C example\n  11. changes\n  12. contact information\n\n\n1. about\n--------\n\nPNG is a file format to store raster images losslessly with good compression,\nsupporting different color types and alpha channel.\n\nLodePNG is a PNG codec according to the Portable Network Graphics (PNG)\nSpecification (Second Edition) - W3C Recommendation 10 November 2003.\n\nThe specifications used are:\n\n*) Portable Network Graphics (PNG) Specification (Second Edition):\n     http://www.w3.org/TR/2003/REC-PNG-20031110\n*) RFC 1950 ZLIB Compressed Data Format version 3.3:\n     http://www.gzip.org/zlib/rfc-zlib.html\n*) RFC 1951 DEFLATE Compressed Data Format Specification ver 1.3:\n     http://www.gzip.org/zlib/rfc-deflate.html\n\nThe most recent version of LodePNG can currently be found at\nhttp://lodev.org/lodepng/\n\nLodePNG works both in C (ISO C90) and C++, with a C++ wrapper that adds\nextra functionality.\n\nLodePNG exists out of two files:\n-lodepng.h: the header file for both C and C++\n-lodepng.c(pp): give it the name lodepng.c or lodepng.cpp (or .cc) depending on your usage\n\nIf you want to start using LodePNG right away without reading this doc, get the\nexamples from the LodePNG website to see how to use it in code, or check the\nsmaller examples in chapter 13 here.\n\nLodePNG is simple but only supports the basic requirements. To achieve\nsimplicity, the following design choices were made: There are no dependencies\non any external library. There are functions to decode and encode a PNG with\na single function call, and extended versions of these functions taking a\nLodePNGState struct allowing to specify or get more information. By default\nthe colors of the raw image are always RGB or RGBA, no matter what color type\nthe PNG file uses. To read and write files, there are simple functions to\nconvert the files to/from buffers in memory.\n\nThis all makes LodePNG suitable for loading textures in games, demos and small\nprograms, ... It's less suitable for full fledged image editors, loading PNGs\nover network (it requires all the image data to be available before decoding can\nbegin), life-critical systems, ...\n\n1.1. supported features\n-----------------------\n\nThe following features are supported by the decoder:\n\n*) decoding of PNGs with any color type, bit depth and interlace mode, to a 24- or 32-bit color raw image,\n   or the same color type as the PNG\n*) encoding of PNGs, from any raw image to 24- or 32-bit color, or the same color type as the raw image\n*) Adam7 interlace and deinterlace for any color type\n*) loading the image from harddisk or decoding it from a buffer from other sources than harddisk\n*) support for alpha channels, including RGBA color model, translucent palettes and color keying\n*) zlib decompression (inflate)\n*) zlib compression (deflate)\n*) CRC32 and ADLER32 checksums\n*) handling of unknown chunks, allowing making a PNG editor that stores custom and unknown chunks.\n*) the following chunks are supported (generated/interpreted) by both encoder and decoder:\n    IHDR: header information\n    PLTE: color palette\n    IDAT: pixel data\n    IEND: the final chunk\n    tRNS: transparency for palettized images\n    tEXt: textual information\n    zTXt: compressed textual information\n    iTXt: international textual information\n    bKGD: suggested background color\n    pHYs: physical dimensions\n    tIME: modification time\n\n1.2. features not supported\n---------------------------\n\nThe following features are _not_ supported:\n\n*) some features needed to make a conformant PNG-Editor might be still missing.\n*) partial loading/stream processing. All data must be available and is processed in one call.\n*) The following public chunks are not supported but treated as unknown chunks by LodePNG\n    cHRM, gAMA, iCCP, sRGB, sBIT, hIST, sPLT\n   Some of these are not supported on purpose: LodePNG wants to provide the RGB values\n   stored in the pixels, not values modified by system dependent gamma or color models.\n\n\n2. C and C++ version\n--------------------\n\nThe C version uses buffers allocated with alloc that you need to free()\nyourself. You need to use init and cleanup functions for each struct whenever\nusing a struct from the C version to avoid exploits and memory leaks.\n\nThe C++ version has extra functions with std::vectors in the interface and the\nlodepng::State class which is a LodePNGState with constructor and destructor.\n\nThese files work without modification for both C and C++ compilers because all\nthe additional C++ code is in \"#ifdef __cplusplus\" blocks that make C-compilers\nignore it, and the C code is made to compile both with strict ISO C90 and C++.\n\nTo use the C++ version, you need to rename the source file to lodepng.cpp\n(instead of lodepng.c), and compile it with a C++ compiler.\n\nTo use the C version, you need to rename the source file to lodepng.c (instead\nof lodepng.cpp), and compile it with a C compiler.\n\n\n3. Security\n-----------\n\nEven if carefully designed, it's always possible that LodePNG contains possible\nexploits. If you discover one, please let me know, and it will be fixed.\n\nWhen using LodePNG, care has to be taken with the C version of LodePNG, as well\nas the C-style structs when working with C++. The following conventions are used\nfor all C-style structs:\n\n-if a struct has a corresponding init function, always call the init function when making a new one\n-if a struct has a corresponding cleanup function, call it before the struct disappears to avoid memory leaks\n-if a struct has a corresponding copy function, use the copy function instead of \"=\".\n The destination must also be inited already.\n\n\n4. Decoding\n-----------\n\nDecoding converts a PNG compressed image to a raw pixel buffer.\n\nMost documentation on using the decoder is at its declarations in the header\nabove. For C, simple decoding can be done with functions such as\nlodepng_decode32, and more advanced decoding can be done with the struct\nLodePNGState and lodepng_decode. For C++, all decoding can be done with the\nvarious lodepng::decode functions, and lodepng::State can be used for advanced\nfeatures.\n\nWhen using the LodePNGState, it uses the following fields for decoding:\n*) LodePNGInfo info_png: it stores extra information about the PNG (the input) in here\n*) LodePNGColorMode info_raw: here you can say what color mode of the raw image (the output) you want to get\n*) LodePNGDecoderSettings decoder: you can specify a few extra settings for the decoder to use\n\nLodePNGInfo info_png\n--------------------\n\nAfter decoding, this contains extra information of the PNG image, except the actual\npixels, width and height because these are already gotten directly from the decoder\nfunctions.\n\nIt contains for example the original color type of the PNG image, text comments,\nsuggested background color, etc... More details about the LodePNGInfo struct are\nat its declaration documentation.\n\nLodePNGColorMode info_raw\n-------------------------\n\nWhen decoding, here you can specify which color type you want\nthe resulting raw image to be. If this is different from the colortype of the\nPNG, then the decoder will automatically convert the result. This conversion\nalways works, except if you want it to convert a color PNG to greyscale or to\na palette with missing colors.\n\nBy default, 32-bit color is used for the result.\n\nLodePNGDecoderSettings decoder\n------------------------------\n\nThe settings can be used to ignore the errors created by invalid CRC and Adler32\nchunks, and to disable the decoding of tEXt chunks.\n\nThere's also a setting color_convert, true by default. If false, no conversion\nis done, the resulting data will be as it was in the PNG (after decompression)\nand you'll have to puzzle the colors of the pixels together yourself using the\ncolor type information in the LodePNGInfo.\n\n\n5. Encoding\n-----------\n\nEncoding converts a raw pixel buffer to a PNG compressed image.\n\nMost documentation on using the encoder is at its declarations in the header\nabove. For C, simple encoding can be done with functions such as\nlodepng_encode32, and more advanced decoding can be done with the struct\nLodePNGState and lodepng_encode. For C++, all encoding can be done with the\nvarious lodepng::encode functions, and lodepng::State can be used for advanced\nfeatures.\n\nLike the decoder, the encoder can also give errors. However it gives less errors\nsince the encoder input is trusted, the decoder input (a PNG image that could\nbe forged by anyone) is not trusted.\n\nWhen using the LodePNGState, it uses the following fields for encoding:\n*) LodePNGInfo info_png: here you specify how you want the PNG (the output) to be.\n*) LodePNGColorMode info_raw: here you say what color type of the raw image (the input) has\n*) LodePNGEncoderSettings encoder: you can specify a few settings for the encoder to use\n\nLodePNGInfo info_png\n--------------------\n\nWhen encoding, you use this the opposite way as when decoding: for encoding,\nyou fill in the values you want the PNG to have before encoding. By default it's\nnot needed to specify a color type for the PNG since it's automatically chosen,\nbut it's possible to choose it yourself given the right settings.\n\nThe encoder will not always exactly match the LodePNGInfo struct you give,\nit tries as close as possible. Some things are ignored by the encoder. The\nencoder uses, for example, the following settings from it when applicable:\ncolortype and bitdepth, text chunks, time chunk, the color key, the palette, the\nbackground color, the interlace method, unknown chunks, ...\n\nWhen encoding to a PNG with colortype 3, the encoder will generate a PLTE chunk.\nIf the palette contains any colors for which the alpha channel is not 255 (so\nthere are translucent colors in the palette), it'll add a tRNS chunk.\n\nLodePNGColorMode info_raw\n-------------------------\n\nYou specify the color type of the raw image that you give to the input here,\nincluding a possible transparent color key and palette you happen to be using in\nyour raw image data.\n\nBy default, 32-bit color is assumed, meaning your input has to be in RGBA\nformat with 4 bytes (unsigned chars) per pixel.\n\nLodePNGEncoderSettings encoder\n------------------------------\n\nThe following settings are supported (some are in sub-structs):\n*) auto_convert: when this option is enabled, the encoder will\nautomatically choose the smallest possible color mode (including color key) that\ncan encode the colors of all pixels without information loss.\n*) btype: the block type for LZ77. 0 = uncompressed, 1 = fixed huffman tree,\n   2 = dynamic huffman tree (best compression). Should be 2 for proper\n   compression.\n*) use_lz77: whether or not to use LZ77 for compressed block types. Should be\n   true for proper compression.\n*) windowsize: the window size used by the LZ77 encoder (1 - 32768). Has value\n   2048 by default, but can be set to 32768 for better, but slow, compression.\n*) force_palette: if colortype is 2 or 6, you can make the encoder write a PLTE\n   chunk if force_palette is true. This can used as suggested palette to convert\n   to by viewers that don't support more than 256 colors (if those still exist)\n*) add_id: add text chunk \"Encoder: LodePNG <version>\" to the image.\n*) text_compression: default 1. If 1, it'll store texts as zTXt instead of tEXt chunks.\n  zTXt chunks use zlib compression on the text. This gives a smaller result on\n  large texts but a larger result on small texts (such as a single program name).\n  It's all tEXt or all zTXt though, there's no separate setting per text yet.\n\n\n6. color conversions\n--------------------\n\nAn important thing to note about LodePNG, is that the color type of the PNG, and\nthe color type of the raw image, are completely independent. By default, when\nyou decode a PNG, you get the result as a raw image in the color type you want,\nno matter whether the PNG was encoded with a palette, greyscale or RGBA color.\nAnd if you encode an image, by default LodePNG will automatically choose the PNG\ncolor type that gives good compression based on the values of colors and amount\nof colors in the image. It can be configured to let you control it instead as\nwell, though.\n\nTo be able to do this, LodePNG does conversions from one color mode to another.\nIt can convert from almost any color type to any other color type, except the\nfollowing conversions: RGB to greyscale is not supported, and converting to a\npalette when the palette doesn't have a required color is not supported. This is\nnot supported on purpose: this is information loss which requires a color\nreduction algorithm that is beyong the scope of a PNG encoder (yes, RGB to grey\nis easy, but there are multiple ways if you want to give some channels more\nweight).\n\nBy default, when decoding, you get the raw image in 32-bit RGBA or 24-bit RGB\ncolor, no matter what color type the PNG has. And by default when encoding,\nLodePNG automatically picks the best color model for the output PNG, and expects\nthe input image to be 32-bit RGBA or 24-bit RGB. So, unless you want to control\nthe color format of the images yourself, you can skip this chapter.\n\n6.1. PNG color types\n--------------------\n\nA PNG image can have many color types, ranging from 1-bit color to 64-bit color,\nas well as palettized color modes. After the zlib decompression and unfiltering\nin the PNG image is done, the raw pixel data will have that color type and thus\na certain amount of bits per pixel. If you want the output raw image after\ndecoding to have another color type, a conversion is done by LodePNG.\n\nThe PNG specification gives the following color types:\n\n0: greyscale, bit depths 1, 2, 4, 8, 16\n2: RGB, bit depths 8 and 16\n3: palette, bit depths 1, 2, 4 and 8\n4: greyscale with alpha, bit depths 8 and 16\n6: RGBA, bit depths 8 and 16\n\nBit depth is the amount of bits per pixel per color channel. So the total amount\nof bits per pixel is: amount of channels * bitdepth.\n\n6.2. color conversions\n----------------------\n\nAs explained in the sections about the encoder and decoder, you can specify\ncolor types and bit depths in info_png and info_raw to change the default\nbehaviour.\n\nIf, when decoding, you want the raw image to be something else than the default,\nyou need to set the color type and bit depth you want in the LodePNGColorMode,\nor the parameters of the simple function of LodePNG you're using.\n\nIf, when encoding, you use another color type than the default in the input\nimage, you need to specify its color type and bit depth in the LodePNGColorMode\nof the raw image, or use the parameters of the simplefunction of LodePNG you're\nusing.\n\nIf, when encoding, you don't want LodePNG to choose the output PNG color type\nbut control it yourself, you need to set auto_convert in the encoder settings\nto LAC_NONE, and specify the color type you want in the LodePNGInfo of the\nencoder.\n\nIf you do any of the above, LodePNG may need to do a color conversion, which\nfollows the rules below, and may sometimes not be allowed.\n\nTo avoid some confusion:\n-the decoder converts from PNG to raw image\n-the encoder converts from raw image to PNG\n-the colortype and bitdepth in LodePNGColorMode info_raw, are those of the raw image\n-the colortype and bitdepth in the color field of LodePNGInfo info_png, are those of the PNG\n-when encoding, the color type in LodePNGInfo is ignored if auto_convert\n is enabled, it is automatically generated instead\n-when decoding, the color type in LodePNGInfo is set by the decoder to that of the original\n PNG image, but it can be ignored since the raw image has the color type you requested instead\n-if the color type of the LodePNGColorMode and PNG image aren't the same, a conversion\n between the color types is done if the color types are supported. If it is not\n supported, an error is returned. If the types are the same, no conversion is done.\n-even though some conversions aren't supported, LodePNG supports loading PNGs from any\n colortype and saving PNGs to any colortype, sometimes it just requires preparing\n the raw image correctly before encoding.\n-both encoder and decoder use the same color converter.\n\nNon supported color conversions:\n-color to greyscale: no error is thrown, but the result will look ugly because\nonly the red channel is taken\n-anything, to palette when that palette does not have that color in it: in this\ncase an error is thrown\n\nSupported color conversions:\n-anything to 8-bit RGB, 8-bit RGBA, 16-bit RGB, 16-bit RGBA\n-any grey or grey+alpha, to grey or grey+alpha\n-anything to a palette, as long as the palette has the requested colors in it\n-removing alpha channel\n-higher to smaller bitdepth, and vice versa\n\nIf you want no color conversion to be done:\n-In the encoder, you can make it save a PNG with any color type by giving the\nraw color mode and LodePNGInfo the same color mode, and setting auto_convert to\nLAC_NO.\n-In the decoder, you can make it store the pixel data in the same color type\nas the PNG has, by setting the color_convert setting to false. Settings in\ninfo_raw are then ignored.\n\nThe function lodepng_convert does the color conversion. It is available in the\ninterface but normally isn't needed since the encoder and decoder already call\nit.\n\n6.3. padding bits\n-----------------\n\nIn the PNG file format, if a less than 8-bit per pixel color type is used and the scanlines\nhave a bit amount that isn't a multiple of 8, then padding bits are used so that each\nscanline starts at a fresh byte. But that is NOT true for the LodePNG raw input and output.\nThe raw input image you give to the encoder, and the raw output image you get from the decoder\nwill NOT have these padding bits, e.g. in the case of a 1-bit image with a width\nof 7 pixels, the first pixel of the second scanline will the the 8th bit of the first byte,\nnot the first bit of a new byte.\n\n6.4. A note about 16-bits per channel and endianness\n----------------------------------------------------\n\nLodePNG uses unsigned char arrays for 16-bit per channel colors too, just like\nfor any other color format. The 16-bit values are stored in big endian (most\nsignificant byte first) in these arrays. This is the opposite order of the\nlittle endian used by x86 CPU's.\n\nLodePNG always uses big endian because the PNG file format does so internally.\nConversions to other formats than PNG uses internally are not supported by\nLodePNG on purpose, there are myriads of formats, including endianness of 16-bit\ncolors, the order in which you store R, G, B and A, and so on. Supporting and\nconverting to/from all that is outside the scope of LodePNG.\n\nThis may mean that, depending on your use case, you may want to convert the big\nendian output of LodePNG to little endian with a for loop. This is certainly not\nalways needed, many applications and libraries support big endian 16-bit colors\nanyway, but it means you cannot simply cast the unsigned char* buffer to an\nunsigned short* buffer on x86 CPUs.\n\n\n7. error values\n---------------\n\nAll functions in LodePNG that return an error code, return 0 if everything went\nOK, or a non-zero code if there was an error.\n\nThe meaning of the LodePNG error values can be retrieved with the function\nlodepng_error_text: given the numerical error code, it returns a description\nof the error in English as a string.\n\nCheck the implementation of lodepng_error_text to see the meaning of each code.\n\n\n8. chunks and PNG editing\n-------------------------\n\nIf you want to add extra chunks to a PNG you encode, or use LodePNG for a PNG\neditor that should follow the rules about handling of unknown chunks, or if your\nprogram is able to read other types of chunks than the ones handled by LodePNG,\nthen that's possible with the chunk functions of LodePNG.\n\nA PNG chunk has the following layout:\n\n4 bytes length\n4 bytes type name\nlength bytes data\n4 bytes CRC\n\n8.1. iterating through chunks\n-----------------------------\n\nIf you have a buffer containing the PNG image data, then the first chunk (the\nIHDR chunk) starts at byte number 8 of that buffer. The first 8 bytes are the\nsignature of the PNG and are not part of a chunk. But if you start at byte 8\nthen you have a chunk, and can check the following things of it.\n\nNOTE: none of these functions check for memory buffer boundaries. To avoid\nexploits, always make sure the buffer contains all the data of the chunks.\nWhen using lodepng_chunk_next, make sure the returned value is within the\nallocated memory.\n\nunsigned lodepng_chunk_length(const unsigned char* chunk):\n\nGet the length of the chunk's data. The total chunk length is this length + 12.\n\nvoid lodepng_chunk_type(char type[5], const unsigned char* chunk):\nunsigned char lodepng_chunk_type_equals(const unsigned char* chunk, const char* type):\n\nGet the type of the chunk or compare if it's a certain type\n\nunsigned char lodepng_chunk_critical(const unsigned char* chunk):\nunsigned char lodepng_chunk_private(const unsigned char* chunk):\nunsigned char lodepng_chunk_safetocopy(const unsigned char* chunk):\n\nCheck if the chunk is critical in the PNG standard (only IHDR, PLTE, IDAT and IEND are).\nCheck if the chunk is private (public chunks are part of the standard, private ones not).\nCheck if the chunk is safe to copy. If it's not, then, when modifying data in a critical\nchunk, unsafe to copy chunks of the old image may NOT be saved in the new one if your\nprogram doesn't handle that type of unknown chunk.\n\nunsigned char* lodepng_chunk_data(unsigned char* chunk):\nconst unsigned char* lodepng_chunk_data_const(const unsigned char* chunk):\n\nGet a pointer to the start of the data of the chunk.\n\nunsigned lodepng_chunk_check_crc(const unsigned char* chunk):\nvoid lodepng_chunk_generate_crc(unsigned char* chunk):\n\nCheck if the crc is correct or generate a correct one.\n\nunsigned char* lodepng_chunk_next(unsigned char* chunk):\nconst unsigned char* lodepng_chunk_next_const(const unsigned char* chunk):\n\nIterate to the next chunk. This works if you have a buffer with consecutive chunks. Note that these\nfunctions do no boundary checking of the allocated data whatsoever, so make sure there is enough\ndata available in the buffer to be able to go to the next chunk.\n\nunsigned lodepng_chunk_append(unsigned char** out, size_t* outlength, const unsigned char* chunk):\nunsigned lodepng_chunk_create(unsigned char** out, size_t* outlength, unsigned length,\n                              const char* type, const unsigned char* data):\n\nThese functions are used to create new chunks that are appended to the data in *out that has\nlength *outlength. The append function appends an existing chunk to the new data. The create\nfunction creates a new chunk with the given parameters and appends it. Type is the 4-letter\nname of the chunk.\n\n8.2. chunks in info_png\n-----------------------\n\nThe LodePNGInfo struct contains fields with the unknown chunk in it. It has 3\nbuffers (each with size) to contain 3 types of unknown chunks:\nthe ones that come before the PLTE chunk, the ones that come between the PLTE\nand the IDAT chunks, and the ones that come after the IDAT chunks.\nIt's necessary to make the distionction between these 3 cases because the PNG\nstandard forces to keep the ordering of unknown chunks compared to the critical\nchunks, but does not force any other ordering rules.\n\ninfo_png.unknown_chunks_data[0] is the chunks before PLTE\ninfo_png.unknown_chunks_data[1] is the chunks after PLTE, before IDAT\ninfo_png.unknown_chunks_data[2] is the chunks after IDAT\n\nThe chunks in these 3 buffers can be iterated through and read by using the same\nway described in the previous subchapter.\n\nWhen using the decoder to decode a PNG, you can make it store all unknown chunks\nif you set the option settings.remember_unknown_chunks to 1. By default, this\noption is off (0).\n\nThe encoder will always encode unknown chunks that are stored in the info_png.\nIf you need it to add a particular chunk that isn't known by LodePNG, you can\nuse lodepng_chunk_append or lodepng_chunk_create to the chunk data in\ninfo_png.unknown_chunks_data[x].\n\nChunks that are known by LodePNG should not be added in that way. E.g. to make\nLodePNG add a bKGD chunk, set background_defined to true and add the correct\nparameters there instead.\n\n\n9. compiler support\n-------------------\n\nNo libraries other than the current standard C library are needed to compile\nLodePNG. For the C++ version, only the standard C++ library is needed on top.\nAdd the files lodepng.c(pp) and lodepng.h to your project, include\nlodepng.h where needed, and your program can read/write PNG files.\n\nIf performance is important, use optimization when compiling! For both the\nencoder and decoder, this makes a large difference.\n\nMake sure that LodePNG is compiled with the same compiler of the same version\nand with the same settings as the rest of the program, or the interfaces with\nstd::vectors and std::strings in C++ can be incompatible.\n\nCHAR_BITS must be 8 or higher, because LodePNG uses unsigned chars for octets.\n\n*) gcc and g++\n\nLodePNG is developed in gcc so this compiler is natively supported. It gives no\nwarnings with compiler options \"-Wall -Wextra -pedantic -ansi\", with gcc and g++\nversion 4.7.1 on Linux, 32-bit and 64-bit.\n\n*) Mingw\n\nThe Mingw compiler (a port of gcc) for Windows is fully supported by LodePNG.\n\n*) Visual Studio 2005 and up, Visual C++ Express Edition 2005 and up\n\nVisual Studio may give warnings about 'fopen' being deprecated. A multiplatform library\ncan't support the proposed Visual Studio alternative however, so LodePNG keeps using\nfopen. If you don't want to see the deprecated warnings, put this on top of lodepng.h\nbefore the inclusions:\n#define _CRT_SECURE_NO_DEPRECATE\n\nOther than the above warnings, LodePNG should be warning-free with warning\nlevel 3 (W3). Warning level 4 (W4) will give warnings about integer conversions.\nI'm not planning to resolve these warnings. To get rid of them, let Visual\nStudio use warning level W3 for lodepng.cpp only: right click lodepng.cpp,\nProperties, C/C++, General, Warning Level: Level 3 (/W3).\n\nVisual Studio may want \"stdafx.h\" files to be included in each source file and\ngive an error \"unexpected end of file while looking for precompiled header\".\nThat is not standard C++ and will not be added to the stock LodePNG. You can\ndisable it for lodepng.cpp only by right clicking it, Properties, C/C++,\nPrecompiled Headers, and set it to Not Using Precompiled Headers there.\n\n*) Visual Studio 6.0\n\nLodePNG support for Visual Studio 6.0 is not guaranteed because VS6 doesn't\nfollow the C++ standard correctly.\n\n*) Comeau C/C++\n\nVesion 20070107 compiles without problems on the Comeau C/C++ Online Test Drive\nat http://www.comeaucomputing.com/tryitout in both C90 and C++ mode.\n\n*) Compilers on Macintosh\n\nLodePNG has been reported to work both with the gcc and LLVM for Macintosh, both\nfor C and C++.\n\n*) Other Compilers\n\nIf you encounter problems on other compilers, feel free to let me know and I may\ntry to fix it if the compiler is modern standards complient.\n\n\n10. examples\n------------\n\nThis decoder example shows the most basic usage of LodePNG. More complex\nexamples can be found on the LodePNG website.\n\n10.1. decoder C++ example\n-------------------------\n\n#include \"lodepng.h\"\n#include <iostream>\n\nint main(int argc, char *argv[])\n{\n  const char* filename = argc > 1 ? argv[1] : \"test.png\";\n\n  //load and decode\n  std::vector<unsigned char> image;\n  unsigned width, height;\n  unsigned error = lodepng::decode(image, width, height, filename);\n\n  //if there's an error, display it\n  if(error) std::cout << \"decoder error \" << error << \": \" << lodepng_error_text(error) << std::endl;\n\n  //the pixels are now in the vector \"image\", 4 bytes per pixel, ordered RGBARGBA..., use it as texture, draw it, ...\n}\n\n10.2. decoder C example\n-----------------------\n\n#include \"lodepng.h\"\n\nint main(int argc, char *argv[])\n{\n  unsigned error;\n  unsigned char* image;\n  size_t width, height;\n  const char* filename = argc > 1 ? argv[1] : \"test.png\";\n\n  error = lodepng_decode32_file(&image, &width, &height, filename);\n\n  if(error) printf(\"decoder error %u: %s\\n\", error, lodepng_error_text(error));\n\n  / * use image here * /\n\n  free(image);\n  return 0;\n}\n\n\n11. changes\n-----------\n\nThe version number of LodePNG is the date of the change given in the format\nyyyymmdd.\n\nSome changes aren't backwards compatible. Those are indicated with a (!)\nsymbol.\n\n*) 22 dec 2013: Power of two windowsize required for optimization.\n*) 15 apr 2013: Fixed bug with LAC_ALPHA and color key.\n*) 25 mar 2013: Added an optional feature to ignore some PNG errors (fix_png).\n*) 11 mar 2013 (!): Bugfix with custom free. Changed from \"my\" to \"lodepng_\"\n    prefix for the custom allocators and made it possible with a new #define to\n    use custom ones in your project without needing to change lodepng's code.\n*) 28 jan 2013: Bugfix with color key.\n*) 27 okt 2012: Tweaks in text chunk keyword length error handling.\n*) 8 okt 2012 (!): Added new filter strategy (entropy) and new auto color mode.\n    (no palette). Better deflate tree encoding. New compression tweak settings.\n    Faster color conversions while decoding. Some internal cleanups.\n*) 23 sep 2012: Reduced warnings in Visual Studio a little bit.\n*) 1 sep 2012 (!): Removed #define's for giving custom (de)compression functions\n    and made it work with function pointers instead.\n*) 23 jun 2012: Added more filter strategies. Made it easier to use custom alloc\n    and free functions and toggle #defines from compiler flags. Small fixes.\n*) 6 may 2012 (!): Made plugging in custom zlib/deflate functions more flexible.\n*) 22 apr 2012 (!): Made interface more consistent, renaming a lot. Removed\n    redundant C++ codec classes. Reduced amount of structs. Everything changed,\n    but it is cleaner now imho and functionality remains the same. Also fixed\n    several bugs and shrinked the implementation code. Made new samples.\n*) 6 nov 2011 (!): By default, the encoder now automatically chooses the best\n    PNG color model and bit depth, based on the amount and type of colors of the\n    raw image. For this, autoLeaveOutAlphaChannel replaced by auto_choose_color.\n*) 9 okt 2011: simpler hash chain implementation for the encoder.\n*) 8 sep 2011: lz77 encoder lazy matching instead of greedy matching.\n*) 23 aug 2011: tweaked the zlib compression parameters after benchmarking.\n    A bug with the PNG filtertype heuristic was fixed, so that it chooses much\n    better ones (it's quite significant). A setting to do an experimental, slow,\n    brute force search for PNG filter types is added.\n*) 17 aug 2011 (!): changed some C zlib related function names.\n*) 16 aug 2011: made the code less wide (max 120 characters per line).\n*) 17 apr 2011: code cleanup. Bugfixes. Convert low to 16-bit per sample colors.\n*) 21 feb 2011: fixed compiling for C90. Fixed compiling with sections disabled.\n*) 11 dec 2010: encoding is made faster, based on suggestion by Peter Eastman\n    to optimize long sequences of zeros.\n*) 13 nov 2010: added LodePNG_InfoColor_hasPaletteAlpha and\n    LodePNG_InfoColor_canHaveAlpha functions for convenience.\n*) 7 nov 2010: added LodePNG_error_text function to get error code description.\n*) 30 okt 2010: made decoding slightly faster\n*) 26 okt 2010: (!) changed some C function and struct names (more consistent).\n     Reorganized the documentation and the declaration order in the header.\n*) 08 aug 2010: only changed some comments and external samples.\n*) 05 jul 2010: fixed bug thanks to warnings in the new gcc version.\n*) 14 mar 2010: fixed bug where too much memory was allocated for char buffers.\n*) 02 sep 2008: fixed bug where it could create empty tree that linux apps could\n    read by ignoring the problem but windows apps couldn't.\n*) 06 jun 2008: added more error checks for out of memory cases.\n*) 26 apr 2008: added a few more checks here and there to ensure more safety.\n*) 06 mar 2008: crash with encoding of strings fixed\n*) 02 feb 2008: support for international text chunks added (iTXt)\n*) 23 jan 2008: small cleanups, and #defines to divide code in sections\n*) 20 jan 2008: support for unknown chunks allowing using LodePNG for an editor.\n*) 18 jan 2008: support for tIME and pHYs chunks added to encoder and decoder.\n*) 17 jan 2008: ability to encode and decode compressed zTXt chunks added\n    Also vareous fixes, such as in the deflate and the padding bits code.\n*) 13 jan 2008: Added ability to encode Adam7-interlaced images. Improved\n    filtering code of encoder.\n*) 07 jan 2008: (!) changed LodePNG to use ISO C90 instead of C++. A\n    C++ wrapper around this provides an interface almost identical to before.\n    Having LodePNG be pure ISO C90 makes it more portable. The C and C++ code\n    are together in these files but it works both for C and C++ compilers.\n*) 29 dec 2007: (!) changed most integer types to unsigned int + other tweaks\n*) 30 aug 2007: bug fixed which makes this Borland C++ compatible\n*) 09 aug 2007: some VS2005 warnings removed again\n*) 21 jul 2007: deflate code placed in new namespace separate from zlib code\n*) 08 jun 2007: fixed bug with 2- and 4-bit color, and small interlaced images\n*) 04 jun 2007: improved support for Visual Studio 2005: crash with accessing\n    invalid std::vector element [0] fixed, and level 3 and 4 warnings removed\n*) 02 jun 2007: made the encoder add a tag with version by default\n*) 27 may 2007: zlib and png code separated (but still in the same file),\n    simple encoder/decoder functions added for more simple usage cases\n*) 19 may 2007: minor fixes, some code cleaning, new error added (error 69),\n    moved some examples from here to lodepng_examples.cpp\n*) 12 may 2007: palette decoding bug fixed\n*) 24 apr 2007: changed the license from BSD to the zlib license\n*) 11 mar 2007: very simple addition: ability to encode bKGD chunks.\n*) 04 mar 2007: (!) tEXt chunk related fixes, and support for encoding\n    palettized PNG images. Plus little interface change with palette and texts.\n*) 03 mar 2007: Made it encode dynamic Huffman shorter with repeat codes.\n    Fixed a bug where the end code of a block had length 0 in the Huffman tree.\n*) 26 feb 2007: Huffman compression with dynamic trees (BTYPE 2) now implemented\n    and supported by the encoder, resulting in smaller PNGs at the output.\n*) 27 jan 2007: Made the Adler-32 test faster so that a timewaste is gone.\n*) 24 jan 2007: gave encoder an error interface. Added color conversion from any\n    greyscale type to 8-bit greyscale with or without alpha.\n*) 21 jan 2007: (!) Totally changed the interface. It allows more color types\n    to convert to and is more uniform. See the manual for how it works now.\n*) 07 jan 2007: Some cleanup & fixes, and a few changes over the last days:\n    encode/decode custom tEXt chunks, separate classes for zlib & deflate, and\n    at last made the decoder give errors for incorrect Adler32 or Crc.\n*) 01 jan 2007: Fixed bug with encoding PNGs with less than 8 bits per channel.\n*) 29 dec 2006: Added support for encoding images without alpha channel, and\n    cleaned out code as well as making certain parts faster.\n*) 28 dec 2006: Added \"Settings\" to the encoder.\n*) 26 dec 2006: The encoder now does LZ77 encoding and produces much smaller files now.\n    Removed some code duplication in the decoder. Fixed little bug in an example.\n*) 09 dec 2006: (!) Placed output parameters of public functions as first parameter.\n    Fixed a bug of the decoder with 16-bit per color.\n*) 15 okt 2006: Changed documentation structure\n*) 09 okt 2006: Encoder class added. It encodes a valid PNG image from the\n    given image buffer, however for now it's not compressed.\n*) 08 sep 2006: (!) Changed to interface with a Decoder class\n*) 30 jul 2006: (!) LodePNG_InfoPng , width and height are now retrieved in different\n    way. Renamed decodePNG to decodePNGGeneric.\n*) 29 jul 2006: (!) Changed the interface: image info is now returned as a\n    struct of type LodePNG::LodePNG_Info, instead of a vector, which was a bit clumsy.\n*) 28 jul 2006: Cleaned the code and added new error checks.\n    Corrected terminology \"deflate\" into \"inflate\".\n*) 23 jun 2006: Added SDL example in the documentation in the header, this\n    example allows easy debugging by displaying the PNG and its transparency.\n*) 22 jun 2006: (!) Changed way to obtain error value. Added\n    loadFile function for convenience. Made decodePNG32 faster.\n*) 21 jun 2006: (!) Changed type of info vector to unsigned.\n    Changed position of palette in info vector. Fixed an important bug that\n    happened on PNGs with an uncompressed block.\n*) 16 jun 2006: Internally changed unsigned into unsigned where\n    needed, and performed some optimizations.\n*) 07 jun 2006: (!) Renamed functions to decodePNG and placed them\n    in LodePNG namespace. Changed the order of the parameters. Rewrote the\n    documentation in the header. Renamed files to lodepng.cpp and lodepng.h\n*) 22 apr 2006: Optimized and improved some code\n*) 07 sep 2005: (!) Changed to std::vector interface\n*) 12 aug 2005: Initial release (C++, decoder only)\n\n\n12. contact information\n-----------------------\n\nFeel free to contact me with suggestions, problems, comments, ... concerning\nLodePNG. If you encounter a PNG image that doesn't work properly with this\ndecoder, feel free to send it and I'll use it to find and fix the problem.\n\nMy email address is (puzzle the account and domain together with an @ symbol):\nDomain: gmail dot com.\nAccount: lode dot vandevenne.\n\n\nCopyright (c) 2005-2013 Lode Vandevenne\n*/\n"
  },
  {
    "path": "frontend/common/preamble.tex",
    "content": "% This is the LaTeX preamble code used for all typesetting by the\n% notebook UI. It is very similar to ../client_server/notebook.tex;\n% keep them in sync.\n\n\\usepackage{setspace}\n\\usepackage[fleqn]{amsmath}\n\\usepackage{color}\n\\usepackage{ytableau}\n\\usepackage{etoolbox}\n\\usepackage{amssymb}  \n\\newcommand{\\sech}{\\operatorname{sech}} \n\\newcommand{\\csch}{\\operatorname{csch}}\n\\newcommand{\\arcsec}{\\operatorname{arcsec}}\n\\newcommand{\\arccot}{\\operatorname{arccot}}\n\\newcommand{\\arccsc}{\\operatorname{arccsc}}\n\\newcommand{\\arccosh}{\\operatorname{arccosh}}\n\\newcommand{\\arcsinh}{\\operatorname{arcsinh}}\n\\newcommand{\\arctanh}{\\operatorname{arctanh}}\n\\newcommand{\\arcsech}{\\operatorname{arcsech}}\n\\newcommand{\\arccsch}{\\operatorname{arccsch}}\n\\newcommand{\\arccoth}{\\operatorname{arccoth}}\n\\usepackage[utf8]{inputenc}\n%\\usepackage{inconsolata}\n\\usepackage[parfill]{parskip}\n%\\usepackage{tableaux}\n\\def\\specialcolon{\\mathrel{\\mathop{:}}\\hspace{-.5em}}\n\\renewcommand{\\bar}[1]{\\overline{#1}}\n\\newcommand{\\algorithm}[2]{{\\tt\\Large\\detokenize{#1}}\\\\[1ex]\n{\\emph{#2}}\\\\[1ex]\n}\n\\newcommand{\\property}[2]{{\\tt\\Large\\detokenize{#1}}\\\\[1ex]\n{\\emph{#2}}\\\\[1ex]\n}\n\\newcommand{\\package}[2]{{\\tt\\Large\\detokenize{#1}}\\\\[1ex]\n{{\\bfseries\\Large #2}}\\\\[1ex]\n}\n\\newcommand{\\algo}[1]{{\\tt \\detokenize{#1}}}\n\\newcommand{\\prop}[1]{{\\tt \\detokenize{#1}}}\n\\renewcommand{\\author}[1]{{\\bfseries \\detokenize{#1}}}\n\\newcommand{\\email}[1]{, {\\tt \\detokenize{#1}}}\n\n\\newcommand{\\bigO}{{\\cal O}}\n\n% \\newcommand{\\sequence}[2]{{#1}\\ldots{#2}}\n\n% Math expressions wrapped in \\brwrap will get typeset with\n% round brackets around them, which have the appropriate size.\n% The expression itself can still be broken over multiple lines.\n\n\\newcommand\\brwrap[3]{%\n  \\setbox0=\\hbox{$#2$}\n  \\left#1\\vbox to \\the\\ht0{\\hbox to 0pt{}}\\right.\\kern-.2em\n  \\begingroup #2\\endgroup\\kern-.15em\n  \\left.\\vbox to \\the\\ht0{\\hbox to 0pt{}}\\right#3\n}\n%\\message{\\meaning\\brwrap{\\frac{A}{B}}}\n\\everymath{\\makeatletter\\def\\old@comma{,}\\catcode`\\,=13 \\def,{%\n\\ifmmode\\old@comma\\discretionary{}{}{}\\else\\old@comma\\fi}\\makeatother}\n\n%  \\left.\\vbox to \\brwrapht {\\hbox to 0pt{!}}\\right)%\n\n% Long formulas are much easier to read if they break such that\n% the '+' or '-' sign ends up on the next line, not at the end\n% of the previous\n\n% \\makeatletter\n% \\newcommand{\\DeclareMathActive}[2]{%\n%   % #1 is the character, #2 is the definition\n%   \\expandafter\\edef\\csname keep@#1@code\\endcsname{\\mathchar\\the\\mathcode`#1 }\n%   \\begingroup\\lccode`~=`#1\\relax\n%   \\lowercase{\\endgroup\\def~}{#2}%\n%   \\AtBeginDocument{\\mathcode`#1=\"8000 }%\n% }\n% \n% \\DeclareMathActive{+}{\\mathbreak\\std{+}}\n% \n% \\newcommand{\\std}[1]{\\csname keep@#1@code\\endcsname}\n% \\patchcmd{\\newmcodes@}{\\mathcode`\\-\\relax}{\\std@minuscode\\relax}{}{\\ddt}\n% \\AtBeginDocument{\\edef\\std@minuscode{\\the\\mathcode`-}}\n% \\makeatother\n% \n% \\def\\mathbreak{\\discretionary{}{}{}}\n% \n\n% % Typesetting Young tableaux, originally in a separate style\n% % file, now included to avoid path searching problems. \n% % Some internals for the typesetting macros below; nothing\n% % user-servicable here; please read on.\n% \n% \\def\\@tabforc#1#2#3{\\expandafter\\tabf@rc\\expandafter#1{#2 \\^}{#3}}\n% \\def\\tabf@@rc#1#2#3\\tabf@@rc#4{\\def#1{#2}#4\\tabf@rc#1{#3}{#4}}\n% \\long\\def\\ReturnAfterFi#1\\fi{\\fi#1}\n%     \\def\\tabf@rc#1#2#3{%\n%       \\def\\temp@ty{#2}%\n%       \\ifx\\@empty\\temp@ty\n%       \\else\n%         \\ReturnAfterFi{%\n%           \\tabf@@rc#1#2\\tabf@@rc{#3}%\n%         }%\n%       \\fi\n%     }%\n% \n% % Sorry, some global registers for sizes and keeping track of\n% % measurements.\n%     \n% \\newdimen\\ytsize\\ytsize=2mm\n% \\newdimen\\ytfsize\\ytfsize=4mm\n% \\newcount\\repcnt\n% \\newdimen\\acchspace\n% \\newdimen\\accvspace\n% \\newdimen\\raiseh\n% \\newdimen\\maxw\n% \n% \\newcommand\\phrule[1]{\\hbox{\\vbox to0pt{\\hrule height .2pt width#1\\vss}}}\n% \n% % Typeset a Young tableau with filled boxes. Takes a single \n% % argument which is a string of symbols for each row,\n% % separated by commas. Examples:\n% %\n% %   \\ftableau{abc,de}\n% %   \\ftableau{ab{d_2},f{g_3}}\n% \n% \\newcommand\\ftableau[1]{%\n% \\def\\ctest{,}\n% \\def\\Ktest{\\^}\n% \\acchspace=0ex\n% \\accvspace=0ex\n% \\maxw=0ex\n% \\vbox{\\hbox{%\n% \\@tabforc\\thisel{#1}{%\n%  \\ifx\\thisel\\Ktest{%\n%      \\ifnum\\maxw=0\\maxw=\\acchspace\\fi%\n%      \\raisebox{\\accvspace}{\\vbox to \\ytfsize{\\hbox to\n% \t\t 0pt{\\vrule height \\ytfsize\\hss}}}\\kern\\acchspace\\kern-\\maxw}\n%  \\else\\ifx\\thisel\\ctest\n%      \\ifnum\\maxw=0\\maxw=\\acchspace\\fi%\n%      \\raisebox{\\accvspace}{\\vbox to \\ytfsize{\\hbox to 0pt{\\vrule height \\ytfsize\\hss}}}%\n%      \\kern\\acchspace\\acchspace=0ex\n% \t  \\advance\\accvspace by -\\ytfsize\n%  \\else\n%      \\setbox3=\\hbox{$\\thisel$}%\n% \t  \\raiseh=\\ytfsize%\n% \t  \\advance\\raiseh by -1ex%\n% \t  \\divide\\raiseh by 2%\n%      \\advance\\acchspace by-\\ytfsize%\n%      \\raisebox{\\accvspace}{\\vbox to \\ytfsize{\\hrule\\hbox to%\n%         \\ytfsize{\\vrule height \\ytfsize\\hskip.5ex%\n%          \\raisebox{\\raiseh}{\\tiny$\\thisel$}\\hss}\\vss\\phrule{\\ytfsize}}}%\n%  \\fi\\fi}}}}\n% \n% % Typeset a Young tableau with unlabelled boxes. Takes a single \n% % argument which is a string of numbers, one for the length of\n% % each row of the tableau. Example:\n% %\n% %   \\tableau{{10}{8}{3}}\n% %\n% % typesets a tableau with 10 boxes in the 1st row, 8 in the 2nd\n% % and 3 in the 3rd. Curly brackets can be omitted if numbers\n% % are less than 10.\n% \n% \\newcommand\\tableau[1]{%\n% \\def\\stest{ }\n% \\def\\Ktest{\\^}\n% \\acchspace=0ex\n% \\accvspace=0ex\n% \\maxw=0ex\n% \\hbox{%\n% \\@tabforc\\thisel{#1}{%\n%  \\ifx\\thisel\\Ktest{}\n%  \\else\n%      \\repcnt=\\thisel%\n%      \\loop{}%\n%      \\advance\\acchspace by-\\ytsize%\n%      \\raisebox{\\accvspace}{\\vbox to \\ytsize{\\hrule \\hbox to%\n% \t\t\t\\ytsize{\\vrule height \\ytsize\\hss}\\vss\\phrule{\\ytsize}}}%\n%      \\advance\\repcnt by -1\\ifnum\\repcnt>1{}\\repeat%\n%      \\ifnum\\maxw=0\\maxw=\\acchspace\\fi%\n%      \\raisebox{\\accvspace}{\\vbox to \\ytsize{\\hbox to 0pt{\\vrule height \\ytsize\\hss}}}%\n%      \\kern\\acchspace\\acchspace=0ex%\n% \t  \\advance\\accvspace by -\\ytsize%\n%  \\fi}\\kern-\\maxw}}\n \n\\ytableausetup{centertableaux}\n\n% Document start.\n\n\\begin{document}\n\\pagestyle{empty}\\everymath{\\displaystyle}\n\\renewcommand{\\arraystretch}{1.2}\n\\tolerance=10000\n\\relpenalty=10\n\\binoppenalty=10\n\\hyphenpenalty=10\n\\raggedright\n\n% Ensure that maths broken over multiple lines has a bit of spacing\n% between lines.\n\\lineskiplimit=0mm\n\\lineskip=1.5ex\n"
  },
  {
    "path": "frontend/common/test_tex.cc",
    "content": "\n#include \"TeXEngine.hh\"\n\nusing namespace cadabra;\n\nint main()\n\t{\n\tTeXEngine te;\n\n\tte.checkin(\"$e = mc^2$\", \"\", \"\");\n\tte.checkin(\"$\\\\int_{-\\\\infty}^{\\\\infty} e^{-ax^2} {\\\\rm d}x = \\\\sqrt{\\\\frac{\\\\pi}{a}}$\", \"\", \"\");\n\n\tte.convert_all();\n\t}\n"
  },
  {
    "path": "frontend/common/testpre.tex",
    "content": "\\documentclass{article}\n\n\\include{preamble}\n\napple pear banana apple pear banana apple pear banana apple pear banana apple pear banana apple pear banana apple pear banana apple pear banana apple pear banana apple pear banana apple pear banana apple pear banana apple pear banana \n${}A_{\\alpha} \\brwrap{\\frac{1}{2}\\brwrap{\\Gamma^{\\alpha}\\,_{\\beta \\gamma}}+\\frac{1}{2}\\Gamma^{\\alpha}\\,_{\\gamma \\beta}}+A_{\\alpha} \\brwrap{\\frac{1}{2}\\brwrap{\\Gamma^{\\alpha}\\,_{\\beta \\gamma}}+\\frac{1}{2}\\Gamma^{\\alpha}\\,_{\\gamma \\beta}}+A_{\\alpha} \\brwrap{\\frac{1}{2}\\brwrap{\\Gamma^{\\alpha}\\,_{\\beta \\gamma}}+\\frac{1}{2}\\Gamma^{\\alpha}\\,_{\\gamma \\beta}}+A_{\\alpha} \\brwrap{\\frac{1}{2}\\brwrap{\\Gamma^{\\alpha}\\,_{\\beta \\gamma}}+\\frac{1}{2}\\Gamma^{\\alpha}\\,_{\\gamma \\beta}}+A_{\\alpha} \\brwrap{\\frac{1}{2}\\brwrap{\\Gamma^{\\alpha}\\,_{\\beta \\gamma}}+\\frac{1}{2}\\Gamma^{\\alpha}\\,_{\\gamma \\beta}}+A_{\\alpha} \\brwrap{\\frac{1}{2}\\brwrap{\\Gamma^{\\alpha}\\,_{\\beta \\gamma}}+\\frac{1}{2}\\Gamma^{\\alpha}\\,_{\\gamma \\beta}}+A_{\\alpha} \\brwrap{\\frac{1}{2}\\brwrap{\\Gamma^{\\alpha}\\,_{\\beta \\gamma}}+\\frac{1}{2}\\Gamma^{\\alpha}\\,_{\\gamma \\beta}}+A_{\\alpha} \\brwrap{\\frac{1}{2}\\brwrap{\\Gamma^{\\alpha}\\,_{\\beta \\gamma}}+\\frac{1}{2}\\Gamma^{\\alpha}\\,_{\\gamma \\beta}}$\n\n\n\\end{document}\n"
  },
  {
    "path": "frontend/gtkmm/CMakeLists.txt",
    "content": "cmake_minimum_required(VERSION ${CADABRA_CMAKE_VERSION})\nproject(CadabraGtkmm)\ninclude(FetchContent)\n\nif(POLICY CMP0167)\n  cmake_policy(SET CMP0167 NEW)\nendif()\nif(POLICY CMP0177)\n  cmake_policy(SET CMP0177 NEW)\nendif()\nif(POLICY CMP0087)\n  cmake_policy(SET CMP0087 NEW)\nendif()\n\n#---------------------------------------------------------------------------\n# Preamble.\n#---------------------------------------------------------------------------\n\nmessage(STATUS \"Flags: ${CMAKE_CXX_FLAGS}\")\n\nmessage(STATUS \"Using gtkmm frontend\")\nif(USE_MICROTEX)\n  message(STATUS \"Including MicroTeX support for typesetting\")\n  set(CAIRO TRUE)\n  set(HAVE_LOG FALSE)\n  set(GRAPHICS_DEBUG FALSE)\n  set(_GLYPH_RENDER_TYPE 2)  # force rendering using otf font, not paths1\n  set(BUILD_STATIC ON)\n\n  set(MICROTEX_SUBMODULE ${CMAKE_SOURCE_DIR}/submodules/microtex/)\n  if(EXISTS ${MICROTEX_SUBMODULE}/CMakeLists.txt)\n    message(STATUS \"Found MicroTeX as submodule in ${MICROTEX_SUBMODULE}\")\n    # Someone has already checked out the microtex submodule, use that.\n    set(microtex_POPULATED TRUE)\n    set(microtex_SOURCE_DIR ${MICROTEX_SUBMODULE})\n    set(microtex_BINARY_DIR ${microtex_SOURCE_DIR}/build)\n    add_subdirectory(${microtex_SOURCE_DIR} ${microtex_BINARY_DIR} EXCLUDE_FROM_ALL)\n  else()\n    # Fetch microtex as we do not have it yet.\n    message(STATUS \"Fetching MicroTeX using FetchContent\")    \n    FetchContent_Declare(\n      microtex\n      GIT_REPOSITORY https://github.com/kpeeters/MicroTeX.git\n      # GIT_REPOSITORY file:///home/kasper/git/microtex/\n      GIT_TAG        kpeeters/cadabra\n    )\n    if(${CMAKE_VERSION} VERSION_GREATER_EQUAL \"3.14\")\n      FetchContent_MakeAvailable(microtex)\n    else()\n      FetchContent_GetProperties(microtex)\n      if(NOT microtex_POPULATED)\n\tFetchContent_Populate(microtex)\n\tadd_subdirectory(${microtex_SOURCE_DIR} ${microtex_BINARY_DIR} EXCLUDE_FROM_ALL)\n      endif()\n    endif()\n  endif()\n  \n  target_compile_options(microtex PUBLIC \"-DHAVE_AUTO_FONT_FIND=1\" \"-Wno-reorder\" \"-Wno-sign-compare\" \"-Wno-switch\" \"-Wno-unused-variable\" \"-Wno-unused-parameter\" \"-Wno-ignored-qualifiers\" \"-Wno-mismatched-tags\" \"-Wno-missing-braces\" \"-Wno-missing-field-initializers\")\nelse()\n  message(STATUS \"Only using LaTeX for typesetting (disabling MicroTeX)\")\nendif()\n\nset(INSTALL_SHARE_DIR share/cadabra2 CACHE PATH \"Installation directory for shared files.\")\nset(INSTALL_IMAGES_DIR share/cadabra2/images CACHE PATH \"Installation directory for image files.\")\nset(INSTALL_DESKTOP_DIR share/applications CACHE PATH \"Installation directory for .desktop files.\")\nset(INSTALL_ICONS_DIR share/icons CACHE PATH \"Installation directory for icons.\")\nset(INSTALL_MICROTEX_DIR \"share/cadabra2/microtex\")\n\n#---------------------------------------------------------------------------\n# Locate libraries.\n#---------------------------------------------------------------------------\n\nfind_package(Threads)\nfind_package(GMPXX REQUIRED STATIC)\nfind_package(SQLITE3)\nif(USE_GTK4)\n  message(STATUS \"Building for GTK4 (instead of GTK3)\")\n  find_package(GLIBMM4)\n  find_package(GTKMM4)\nelse()\n  message(STATUS \"Building for GTK3 (instead of GTK4)\")\n  find_package(GLIBMM3)\n  find_package(GTKMM3)\nendif()\nfind_package(Boost 1.71.0 REQUIRED)\nset(Boost_USE_STATIC_LIBS OFF)\nset(Boost_USE_MULTITHREADED ON)\nset(Boost_USE_STATIC_RUNTIME OFF)\n\n\n#---------------------------------------------------------------------------\n# Enumerate input files and directories.\n#---------------------------------------------------------------------------\n\nset(cadabra_gtk_src \n  main.cc \n  ChooseColoursDialog.cc\n  DiffViewer.cc\n  NotebookWindow.cc \n  NotebookCanvas.cc \n  SelectFileDialog.cc\n  TeXView.cc \n  CodeInput.cc \n  ImageView.cc\n  SliderView.cc\n  Cadabra.cc\n  Console.cc\n  Keywords.cc \n  ../common/TeXEngine.cc\n#  ../common/lodepng.cc\n  # ../common/exec-stream.cc\n  ${CADABRA_CORE_DIR}/CdbPython.cc \n  ${CADABRA_LIBS_DIR}/tiny-process-library/process.cpp\n  ${CADABRA_LIBS_DIR}/base64/base64.cc\n)\nif(WIN32)\n  list(APPEND cadabra_gtk_src ${CADABRA_LIBS_DIR}/tiny-process-library/process_win.cpp)\n  # Configure and add resource file to list of sources\n  configure_file(win_res.rc.in ${CMAKE_CURRENT_BINARY_DIR}/win_res.rc)\n  add_custom_command(\n    OUTPUT win_res.o\n    COMMAND windres ${CMAKE_CURRENT_BINARY_DIR}/win_res.rc ${CMAKE_CURRENT_BINARY_DIR}/win_res.o\n    COMMENT \"Convert .rc file to .o to give us an icon.\"\n  )\n  list(APPEND cadabra_gtk_src ${CMAKE_CURRENT_BINARY_DIR}/win_res.o)\nelse()\n  list(APPEND cadabra_gtk_src ${CADABRA_LIBS_DIR}/tiny-process-library/process_unix.cpp)\nendif()\n\n\n\n#---------------------------------------------------------------------------\n# Include directories and preprocessor definitions.\n#---------------------------------------------------------------------------\n\ninclude_directories(\n  \".\"\n  \"${CADABRA_CORE_DIR}\"\n  \"${CADABRA_CLIENT_SERVER_DIR}\"\n  \"${CADABRA_LIBS_DIR}/pybind11/include\"\n  \"${CADABRA_LIBS_DIR}/internal/include\"\n  \"${CADABRA_LIBS_DIR}/websocketpp\"\n  \"${CADABRA_LIBS_DIR}/tiny-process-library\"\n  \"${CADABRA_LIBS_DIR}/nlohmann\"   \n  ${GMP_INCLUDE_DIRS}\n  ${OPENSSL_INCLUDE_DIR}\n  ${Boost_INCLUDE_DIRS}\n  ${Python_INCLUDE_DIRS}\n  ${SQLITE3_INCLUDE_DIR}\n  ${Fontconfig_INCLUDE_DIRS}\n)\n\nif(ENABLE_SYSTEM_JSONCPP)\n  include_directories(\n    ${JSONCPP_INCLUDE_DIRS}\n  )\nelse()\n  include_directories(\n    \"${CADABRA_LIBS_DIR}/jsoncpp\"\n  )\nendif()\n\nadd_definitions(\n  \"-D_WEBSOCKETPP_CPP11_STL_\"\n  \"-DBOOST_LOG_DYN_LINK\"\n  \"-DGTKMM_DISABLE_DEPRECATED\"\n  \"-DGDKMM_DISABLE_DEPRECATED\"\n  \"-DGLIBMM_DISABLE_DEPRECATED\"\n  \"-DGIOMM_DISABLE_DEPRECATED\"\n  \"-DBUILD_GTK\"\n  \"-Wno-reorder\"\n)\n\n#---------------------------------------------------------------------------\n# Targets.\n#---------------------------------------------------------------------------\n\nif(WIN32)\n  add_executable(cadabra2-gtk WIN32 ${cadabra_gtk_src})\nelse()\n  add_executable(cadabra2-gtk ${cadabra_gtk_src})\nendif()\n\nif(USE_MICROTEX)\n  message(STATUS \"MicroTeX binaries will be built at ${microtex_BINARY_DIR}\")\n  include_directories(\n    ${microtex_BINARY_DIR}/lib\n    ${microtex_SOURCE_DIR}/lib\n    ${microtex_SOURCE_DIR}/platform    \n  )\n  # find_package(Fontconfig REQUIRED)\n  pkg_check_modules(Fontconfig REQUIRED IMPORTED_TARGET fontconfig)\nendif()\n\ntarget_compile_options(\n  cadabra2-gtk\n  PUBLIC\n  ${Boost_CFLAGS_OTHER} \n  ${GLIBMM_CFLAGS_OTHER} \n  ${GTKMM_CFLAGS_OTHER} \n  ${SQLITE3_CFLAGS_OTHER} \n  ${Fontconfig_CFLAGS_OTHER}\n)\n# if(WIN32)\n#   # Try disabling the terminal window.\n#   target_link_options(cadabra-gtk PRIVATE \"-mwindows\")\n#   target_compile_options(cadabra-gtk PRIVATE \"-mwindows\")\n# endif()\ntarget_link_libraries(\n  cadabra2-gtk\n  PUBLIC\n  cadabra_client \n  ${Boost_LIBRARIES} \n  PkgConfig::GLIBMM\n  PkgConfig::GTKMM\n  ${SQLITE3_LIBRARIES} \n  Threads::Threads\n)\n\nif(USE_MICROTEX)\n  if(WIN32)\n    target_link_libraries(\n      cadabra2-gtk\n      PUBLIC\n      microtex-cairo          # from MicroTeX\n      microtex                # from MicroTeX\n      ${CairoMM_LIBRARIES}\n      ${PangoMM_LIBRARIES}\n      ${Fontconfig_LIBRARIES}\n      -lws2_32 -lwsock32\n    )\n  else()\n    target_link_libraries(\n      cadabra2-gtk\n      PUBLIC\n      microtex-cairo          # from MicroTeX\n      microtex                # from MicroTeX\n      PkgConfig::CairoMM\n      PkgConfig::PangoMM\n      PkgConfig::Fontconfig\n    )\n  endif()\nendif()\n\n# Create PNG versions for our icons, for macOS where librsvg and\n# libpixbufloader_svg.dylib are currently broken.\n\nset(CDBICONS\n  cdb-cancel\n  cdb-copy-all\n  cdb-open\n  cdb-restart\n  cdb-restart-and-run-all  \n  cdb-run\n  cdb-save-as\n  cdb-save\n)\n\nset(CDBDEPS \"\")\nforeach(CDBICON ${CDBICONS})\n  add_custom_command(\n    OUTPUT  cdb-icons/${CDBICON}.png\n    DEPENDS cdb-icons/${CDBICON}.svg\n    COMMAND inkscape\n    ARGS    cdb-icons/${CDBICON}.svg --export-filename=cdb-icons/${CDBICON}.png -w 80 -h 80\n    WORKING_DIRECTORY ${CMAKE_SOURCE_DIR}/frontend/gtkmm\n    COMMENT \"Converting ${CDBICON}.svg to ${CDBICON}.png\"\n  )\n  set(CDBDEPS ${CDBDEPS} cdb-icons/${CDBICON}.png)\n\n  # Always install\n  install(FILES cdb-icons/${CDBICON}.png DESTINATION share/cadabra2/cdb-icons)\n  install(FILES cdb-icons/${CDBICON}.svg DESTINATION share/cadabra2/cdb-icons)\nendforeach()\n\nadd_custom_target(\n  \"update_icons\"\n  DEPENDS\n  ${CDBDEPS}\n)\n\n\n#---------------------------------------------------------------------------\n# Installation.\n#---------------------------------------------------------------------------\n\ninstall(TARGETS cadabra2-gtk DESTINATION ${CDB_BIN_PATH})\n\n# Create installation directories with correct permissions.\nif (NOT INSTALL_TARGETS_ONLY)\n  install_directory_permissions(${INSTALL_SHARE_DIR})\n  install_directory_permissions(${INSTALL_IMAGES_DIR})\n  install_directory_permissions(${INSTALL_DESKTOP_DIR})\n  install_directory_permissions(${INSTALL_ICONS_DIR})\n  install_directory_permissions(\"${INSTALL_ICONS_DIR}/hicolor\")\n  install_directory_permissions(\"${INSTALL_ICONS_DIR}/hicolor/64x64\")\n  install_directory_permissions(\"${INSTALL_ICONS_DIR}/hicolor/256x256\")\n  install_directory_permissions(\"${INSTALL_ICONS_DIR}/hicolor/scalable\")\n  install_directory_permissions(\"${INSTALL_ICONS_DIR}/hicolor/64x64/apps\")\n  install_directory_permissions(\"${INSTALL_ICONS_DIR}/hicolor/256x256/apps\")\n  install_directory_permissions(\"${INSTALL_ICONS_DIR}/hicolor/scalable/apps\")\n\n  install(FILES ${CADABRA_IMAGES_DIR}/256x256/cadabra2-gtk.png DESTINATION ${INSTALL_IMAGES_DIR})\n\n  #xdg-desktop-menu messes up the file permissions, so we just install things by hand...\n  #install(CODE \"execute_process(COMMAND ${XDG-DESKTOP-MENU_EXECUTABLE} install --novendor ${PROJECT_SOURCE_DIR}/../../config/cadabra2.desktop)\")\n\n  # Icons are a nightmare...\n  # \n  #   - You cannot just plainly install in /usr/share/icons/hicolor because that is not where Homebrew/OS X\n  #     stores the icons (it uses /usr/local/share/icons/hicolor).\n  #   - /usr/local/share/icons/hicolor may lack an index.theme file, which means that things below there\n  #     actually never get picked up (or at least not by cinnamon).\n  #   - So we need to copy index.theme into /usr/local if it does not exist there yet.\n  #   - In order to avoid all that, just use /usr/share/icons on Linux; package managers will install it\n  #     there anyway.\n  #   - gtk-update-icon-cache is broken and only works half of the time.\n  #\n  # BUT: package managers really do not like this approach, so we're back to doing the proper thing and\n  # hope window managers will eventually fix this.\n  \n  set(ICON_PREFIX \".\")\n\n  set(ICON_PREFIX_WITH_DESTDIR $ENV{DESTDIR}${CMAKE_INSTALL_PREFIX}/${ICON_PREFIX})\n  install(FILES    ${CADABRA_IMAGES_DIR}/64x64/cadabra2-gtk.png     DESTINATION ${ICON_PREFIX}/share/icons/hicolor/64x64/apps)\n  install(FILES    ${CADABRA_IMAGES_DIR}/128x128/cadabra2-gtk.png   DESTINATION ${ICON_PREFIX}/share/icons/hicolor/128x128/apps)\n  install(FILES    ${CADABRA_IMAGES_DIR}/256x256/cadabra2-gtk.png   DESTINATION ${ICON_PREFIX}/share/icons/hicolor/256x256/apps)\n  install(FILES    ${CADABRA_IMAGES_DIR}/cadabra2-gtk.svg           DESTINATION ${ICON_PREFIX}/share/icons/hicolor/scalable/apps)\n  install(FILES    ${CADABRA_ROOT_DIR}/config/science.cadabra.cadabra2-gtk.desktop  DESTINATION ${ICON_PREFIX}/share/applications)\n  if(NOT WIN32)\n    # FIXME: Can this go on all platforms?\n    install(CODE     \"execute_process(COMMAND gtk-update-icon-cache --ignore-theme-index ${ICON_PREFIX_WITH_DESTDIR}/share/icons/hicolor)\")\n    install(CODE     \"execute_process(COMMAND update-desktop-database ${ICON_PREFIX_WITH_DESTDIR}/share/applications)\")\n    install(CODE     \"execute_process(COMMAND chmod go+r ${ICON_PREFIX_WITH_DESTDIR}/share/icons/hicolor/icon-theme.cache)\")\n  endif()\n  # install(DIRECTORY cdb-icons  DESTINATION share/cadabra2/)\n  install(FILES     ${CMAKE_SOURCE_DIR}/config/cadabra2.ico  DESTINATION share/cadabra2/cdb-icons/)    \n\n  # Install shared libraries on Windows. \n  # https://stackoverflow.com/questions/32662215/how-do-you-install-gtk-3-0-on-windows\n  if(WIN32)\n    # All things to make GTK apps work and look decent on Windows 10.\n    # We always need the Adwaita theme for fallback icons, but VCPKG\n    # does not yet distribute it, so we include it here (also see\n    # https://github.com/Microsoft/vcpkg/pull/693). The Windows 10 theme\n    # comes from https://github.com/B00merang-Project/Windows-10.\n    # Settings as suggested by Luca Bacci on gtk-devel-list.\n    install(FILES     config/gschemas.compiled DESTINATION share/glib-2.0/schemas)\n    install(FILES     config/settings.ini      DESTINATION etc/gtk-3.0/)  \n    install(DIRECTORY theme/Windows10          DESTINATION share/themes)\n    install(DIRECTORY icons/Adwaita            DESTINATION share/icons)\n    install(DIRECTORY icons/hicolor            DESTINATION share/icons)\n    winstall(DIRECTORY /${MSYS_ENV}/lib/gdk-pixbuf-2.0  DESTINATION  lib)\n    winstall(DIRECTORY /${MSYS_ENV}/share/glib-2.0      DESTINATION  share)\n\n    set_property(INSTALL \"${CDB_BIN_PATH}/cadabra2-gtk\"\n      PROPERTY CPACK_START_MENU_SHORTCUTS \"Cadabra\"\n    )\n  endif()\nendif()\n\n# manual pages\nif(NOT MSVC)\n  install(\n    FILES\n    ../../man/man1/cadabra2-gtk.1\n    DESTINATION\n    share/man/man1\n  )\nendif()\n\nif(WIN32)\n  install(DIRECTORY ../../examples/ DESTINATION Examples)\nendif()\n\n# microtex resources\nif(USE_MICROTEX)\n  add_dependencies(cadabra2-gtk microtex-cairo)\n  install(DIRECTORY    ${PROJECT_SOURCE_DIR}/../../libs/cm DESTINATION ${INSTALL_MICROTEX_DIR})  \n  install(DIRECTORY    ${microtex_BINARY_DIR}/res/lm-math DESTINATION ${INSTALL_MICROTEX_DIR})  \n  install(FILES        ${PROJECT_SOURCE_DIR}/science.cadabra.cadabra2-gtk.appdata.xml DESTINATION share/metainfo/)\nendif()\n\n"
  },
  {
    "path": "frontend/gtkmm/Cadabra.cc",
    "content": "\n#include \"Cadabra.hh\"\n#include <signal.h>\n#include <fstream>\n#include <gtkmm/messagedialog.h>\n#include <gtkmm/entry.h>\n#if GTKMM_MINOR_VERSION < 10\n#include <gtkmm/main.h>\n#endif\n#include <gtkmm/settings.h>\n#include <giomm.h>\n#include \"Snoop.hh\"\n#include \"Config.hh\"\n\n// Signal handler for ctrl-C\n\ncadabra::NotebookWindow *signal_window;\n\nvoid signal_handler(int)\n\t{\n#if GTKMM_MINOR_VERSION >= 10\n\tsignal_window->close();\n#else\n\tGtk::Main::quit();\n#endif\n\t}\n\nGlib::RefPtr<Cadabra> Cadabra::create(int argc, char **argv)\n\t{\n\treturn Glib::RefPtr<Cadabra>( new Cadabra(argc, argv) );\n\t}\n\nCadabra::Cadabra(int argc, char **argv)\n\t: Gtk::Application(argc, argv, \"science.cadabra.cadabra2-gtk\",\n\t                   Gio::APPLICATION_HANDLES_OPEN |\n\t\t\t\t\t\t\t Gio::APPLICATION_HANDLES_COMMAND_LINE |\n\t                   Gio::APPLICATION_NON_UNIQUE),\n\t  compute(0), compute_thread(0),\n\t  server_port(0), server_ip_address(\"127.0.0.1\"),\n\t  no_registration(false)\n\t{\n\t// https://stackoverflow.com/questions/43886686/how-does-one-make-gtk3-look-native-on-windows-7\n\t//\thttps://github.com/shoes/shoes3/wiki/Changing-Gtk-theme-on-Windows\n#if defined(_WIN32)\n\t// Gtk::Settings::get_default()->property_gtk_theme_name()=\"win32\";\n#endif\n\n\t//https://github.com/GNOME/gtkmm-documentation/blob/master/examples/book/application/command_line_handling/exampleapplication.cc\n\n\tadd_main_option_entry(Gio::Application::OptionType::OPTION_TYPE_INT,\n\t                      \"server-port\",\n\t                      's',\n\t                      \"Connect to running server on given port.\",\n\t                      \"number\");\n\tadd_main_option_entry(Gio::Application::OptionType::OPTION_TYPE_STRING,\n\t                      \"geometry\",\n\t                      'g',\n\t                      \"Specify the window size (and optionally the position).\",\n\t                      \"string\");\n\tadd_main_option_entry(Gio::Application::OptionType::OPTION_TYPE_STRING,\n\t                      \"title\",\n\t                      'w',\n\t                      \"Specify the window title.\",\n\t                      \"string\");\n\tadd_main_option_entry(Gio::Application::OptionType::OPTION_TYPE_STRING,\n\t                      \"server-ip-address\",\n\t                      'a',\n\t                      \"Connect to running server on given ip address.\",\n\t                      \"string\");\n\tadd_main_option_entry(Gio::Application::OptionType::OPTION_TYPE_STRING,\n\t                      \"token\",\n\t                      't',\n\t                      \"Use the given authentication token to connect to the server.\",\n\t                      \"string\");\n\tadd_main_option_entry(Gio::Application::OptionType::OPTION_TYPE_BOOL,\n\t                      \"no-registration\",\n\t                      'n',\n\t                      \"Do not show the registration dialog.\",\n\t                      \"string\");\n\t}\n\ntemplate <typename T_ArgType>\nstatic bool get_arg_value(const Glib::RefPtr<Glib::VariantDict>& options, const Glib::ustring& arg_name, T_ArgType& arg_value)\n\t{\n\targ_value = T_ArgType();\n\tif(options->lookup_value(arg_name, arg_value)) return true;\n\telse return false;\n\t}\n\nCadabra::~Cadabra()\n\t{\n\t// The app is going away. First stop the script thread so external\n\t// programs can no longer talk to us.\n\n\tif(script)\n\t\tscript->terminate();\n\tif(script_thread)\n\t\tscript_thread->join();\n\tif(script)\n\t\tdelete script;\n\tif(script_thread)\n\t\tdelete script_thread;\n\n\t// Also stop the compute logic and join that thread waiting for it\n\t// to complete.\n\n\tif(compute)\n\t\tcompute->terminate();\n\tif(compute_thread)\n\t\tcompute_thread->join();\n\tif(compute)\n\t\tdelete compute;\n\tif(compute_thread)\n\t\tdelete compute_thread;\n\n\n\t//\tfor(auto w: windows)\n\t//\t\tdelete w;\n\t}\n\nint Cadabra::on_command_line(const Glib::RefPtr<Gio::ApplicationCommandLine>& cmd)\n\t{\n\tint argc;\n\tchar** argv = cmd->get_arguments(argc);\n\tstd::vector<Glib::RefPtr<Gio::File>> files;\n\tfor(int i = 1; i < argc; i++) {\n\t\tif(argv[i][0] != '-') {\n\t\t\tauto file = Gio::File::create_for_path(argv[i]);\n\t\t\tfiles.push_back(file);\n\t\t\t}\n\t\t}\n\t\n\t auto options = cmd->get_options_dict();\n\n\t// The template `get_arg_value` only works if the type matches exactly,\n\t// so we need to ask it to store into a `Glib::ustring` and then copy.\n\tGlib::ustring tmp;\n\tbool btmp;\n\t\n\tget_arg_value(options, \"server-port\",       server_port);\n\tget_arg_value(options, \"server-ip-address\", tmp);\n\tserver_ip_address = tmp;\n\tget_arg_value(options, \"token\",             tmp);\n\tserver_token = tmp;\n\tget_arg_value(options, \"no-registration\",   btmp);\n\tno_registration = btmp;\n\tget_arg_value(options, \"geometry\",          tmp);\n\twindow_geometry = tmp;\n\tget_arg_value(options, \"title\",             tmp);\n\tif(tmp==\"\") tmp=\"Cadabra\";\n\twindow_title = tmp;\n\n\tif(files.size()>0)\n\t\topen(files, \"\");\n\telse\n\t\tactivate();\n\n\treturn 0;\n\t}\n\nvoid Cadabra::on_startup()\n\t{\n\tGtk::Application::on_startup();\n\t}\n\nvoid Cadabra::on_activate()\n\t{\n\tGtk::Application::on_activate();\n\t\n\tcompute = new cadabra::ComputeThread(server_port, server_token, server_ip_address);\n\tcompute_thread = new std::thread(&cadabra::ComputeThread::run, compute);\n\n\tauto nw = new cadabra::NotebookWindow(this, false, window_geometry, window_title);\n\tcompute->set_master(nw, nw);\n\tnw->main_thread_id = std::this_thread::get_id();\n\n\t// Connect the two threads.\n\tnw->set_compute_thread(compute);\n\n\t// Setup ctrl-C handler so we can shut down gracefully (i.e. ask\n\t// for confirmation, shut down server).\n\tsignal_window = nw;\n\tsignal(SIGINT, signal_handler);\n\n\tadd_window(*nw);\n\tnw->show();\n\n\t// Start the script handler so external programs can talk to us.\n\tscript = new cadabra::ScriptThread(nw, nw);\n\tscript_thread = new std::thread(&cadabra::ScriptThread::run, script);\n\n\tstd::cerr << \"control channel ws://localhost:\" << script->get_local_port()\n\t\t\t\t << \"/\" << script->get_authentication_token() << std::endl;\n\n\tstd::string version=std::string(CADABRA_VERSION_SEM);\n\tsnoop::log(\"start\") << version << snoop::flush;\n\n\tif(!no_registration && !nw->prefs.is_registered && !nw->prefs.is_anonymous) {\n\t\tnw->on_help_register();\n\t\t}\n\t}\n\nvoid Cadabra::on_open(const Gio::Application::type_vec_files& files, const Glib::ustring& hint)\n\t{\n\ton_activate();\n\t// Load the first file into a string.\n\tchar* contents = nullptr;\n\tgsize length = 0;\n\tstd::string text;\n\tbool file_exists=false;\n\ttry {\n\t\tif(files[0]->load_contents(contents, length)) {\n\t\t\tif(contents && length) {\n\t\t\t\ttext=std::string(contents);\n\t\t\t\t}\n\t\t\tg_free(contents);\n\t\t\t}\n\t\tfile_exists=true;\n\t\t}\n\tcatch (const Glib::Error& ex) {\n\t\t// std::cerr << \"Open error: \" << ex.what() << std::endl;\n\t\t// File cannot be opened, assume the user wants to create a\n\t\t// new file with this name.\n\t\tfile_exists=false;\n\t\t}\n\n\t// Tell the window to open the notebook stored in the string.\n\tauto wins = get_windows();\n\tauto nw = static_cast<cadabra::NotebookWindow *>(wins[0]);\n\tadd_window(*nw);\n\tnw->set_name(files[0]->get_path());\n\tsnoop::log(\"open\") << \"command-line\" << snoop::flush;\n\tif(file_exists) {\n\t\tnw->load_from_string(text);\n\t\tGtk::Application::on_open(files, hint);\n\t\t}\n\t}\n\nbool Cadabra::open_help(const std::string& nm, const std::string& title)\n\t{\n#ifdef DEBUG\n\tstd::cerr << \"Opening help file \" << nm << std::endl;\n#endif\n\tstd::ifstream fl(nm);\n\tif(fl) {\n\t\tauto nw = new cadabra::NotebookWindow(this, true);\n\t\tnw->set_title_prefix(\"Cadabra help for \");\n\t\tnw->set_name(title);\n\t\tadd_window(*nw);\n\t\tstd::stringstream buffer;\n\t\tbuffer << fl.rdbuf();\n\t\tnw->load_from_string(buffer.str());\n\t\tnw->show();\n\t\treturn true;\n\t\t}\n\telse return false;\n\t}\n"
  },
  {
    "path": "frontend/gtkmm/Cadabra.hh",
    "content": "\n#pragma once\n\n#include <gtkmm/application.h>\n#include <gtkmm/grid.h>\n#include \"NotebookWindow.hh\"\n#include \"ComputeThread.hh\"\n#include \"ScriptThread.hh\"\n\n/// The Cadabra notebook application.\n\nclass Cadabra : public Gtk::Application {\n\tpublic:\n\t\tstatic Glib::RefPtr<Cadabra> create(int, char **);\n\n\t\tbool open_help(const std::string& filename, const std::string& title);\n\n\tprotected:\n\t\tCadabra(int, char**);\n\t\tvirtual ~Cadabra();\n\n\t\tvirtual void on_startup() override;\n\t\tvirtual void on_activate() override;\n\t\tvirtual void on_open(const Gio::Application::type_vec_files& files, const Glib::ustring& hint) override;\n\t\tvirtual int on_command_line(const Glib::RefPtr<Gio::ApplicationCommandLine>& cmd) override;\n\n\n\t\tint on_handle_local_options(const Glib::RefPtr<Glib::VariantDict> &);\n\n\tprivate:\n\t\tcadabra::ComputeThread                *compute;\n\t\tstd::thread                           *compute_thread;\n\n\t\tcadabra::ScriptThread                 *script;\n\t\tstd::thread                           *script_thread;\n\n\t\tint server_port;\n\t\tstd::string server_token;\n\t\tstd::string server_ip_address;\n\t\tstd::string window_geometry;\n\t\tstd::string window_title;\n\t\tbool        no_registration;\n\t};\n"
  },
  {
    "path": "frontend/gtkmm/ChooseColoursDialog.cc",
    "content": "#include \"ChooseColoursDialog.hh\"\n#include <gtkmm/label.h>\n#include <gtkmm/colorbutton.h>\n#include <gtkmm/messagedialog.h>\n#include <locale>\n#include <iostream>\n\nnamespace cadabra {\n\tstd::string capitalize_first(std::string in)\n\t\t{\n\t\tif (in.empty())\n\t\t\treturn in;\n\t\tin[0] = std::toupper(in[0]);\n\t\tfor (int i = 1; i < (int)in.size() - 1; ++i) {\n\t\t\tif (in[i] == ' ')\n\t\t\t\tin[i + 1] = std::toupper(in[i + 1]);\n\t\t\t}\n\t\treturn in;\n\t\t}\n\n\tChooseColoursDialog::ChooseColoursDialog(DocumentThread::Prefs& prefs, NotebookWindow& parent)\n\t\t: Gtk::Dialog(\"Choose syntax highlighting colours\", parent, true)\n\t\t, prefs(prefs)\n\t\t, main_vbox(Gtk::Orientation::ORIENTATION_VERTICAL)\n\t\t, bottom_button_box(Gtk::Orientation::ORIENTATION_HORIZONTAL)\n\t\t, button_ok(\"Ok\")\n\t\t, parent(parent)\n\t\t{\n\t\tusing namespace std::string_literals;\n\n\t\tset_transient_for(parent);\n\t\tset_modal(true);\n\t\tget_content_area()->pack_start(main_vbox);\n\t\tmain_vbox.pack_start(main_grid);\n\t\tint col = 0;\n\t\tfor (auto it = prefs.colours.begin(); it != prefs.colours.end(); ++it, ++col) {\n\t\t\t// Display the name of the language to highlight for\n\t\t\tauto sec_label = std::make_unique<Gtk::Label>(capitalize_first(it->first));\n\t\t\tauto sec_grid = std::make_unique<Gtk::Grid>();\n\t\t\tsec_grid->set_column_spacing(10);\n\t\t\tmain_grid.attach(*sec_label, col, 0, 1, 1);\n\t\t\tmain_grid.attach(*sec_grid, col, 1, 1, 1);\n\n\t\t\t//Display the highlightable things and a colour chooser\n\t\t\tint row = 0;\n\t\t\tfor (auto jt = it->second.begin(); jt != it->second.end(); ++jt, ++row) {\n\t\t\t\t// Make the label and give it the colour that type of keyword is currently highlighted as\n\t\t\t\tauto kw_label = std::make_unique<Gtk::Label>(capitalize_first(jt->first));\n\t\t\t\tauto kw_button = std::make_unique<Gtk::ColorButton>();\n\t\t\t\tkw_button->property_rgba() = Gdk::RGBA(jt->second);\n\t\t\t\tkw_button->set_title(\"Choosing colours for \"s + capitalize_first(it->first) + \": \" + capitalize_first(jt->first));\n\t\t\t\tkw_button->signal_color_set().connect(sigc::mem_fun(this, &ChooseColoursDialog::on_color_set));\n\t\t\t\tsec_grid->attach(*kw_label, 0, row, 1, 1);\n\t\t\t\tsec_grid->attach(*kw_button, 1, row, 1, 1);\n\t\t\t\tanonymous_widgets.push_back(std::move(kw_label));\n\t\t\t\tcolour_buttons[it->first][jt->first] = std::move(kw_button);\n\t\t\t\t}\n\n\t\t\t// Move sec_label and sec_grid to class scope so they don't get destroyed\n\t\t\tanonymous_widgets.push_back(std::move(sec_label));\n\t\t\tanonymous_widgets.push_back(std::move(sec_grid));\n\t\t\t}\n\t\tmain_grid.set_column_spacing(30);\n\t\tmain_grid.set_margin_start(30);\n\t\tmain_grid.set_margin_end(30);\n\t\tmain_grid.set_margin_top(10);\n\t\tmain_grid.set_margin_bottom(10);\n\n\t\tmain_vbox.pack_start(bottom_button_box);\n\t\tbottom_button_box.pack_start(button_ok);\n\n\t\tbutton_ok.signal_clicked().connect( [&]() {\n\t\t\tclose();\n\t\t\t} );\n\n\t\tmain_vbox.show_all();\n\t\t}\n\n\tvoid ChooseColoursDialog::on_color_set()\n\t\t{\n\t\tfor (auto& language : colour_buttons) {\n\t\t\tfor (auto& kw : language.second) {\n\t\t\t\tprefs.colours[language.first][kw.first] = kw.second->get_rgba().to_string();\n\t\t\t\t}\n\t\t\t}\n\t\tparent.refresh_highlighting();\n\t\t/*prefs.colours[cur_lang][cur_kw_type] = std::string(colour.to_string());\n\t\tdynamic_cast<Gtk::Label*>(label_widgets[cur_lang + cur_kw_type].get())->set_markup(\n\t\t\tstd::string(\"<span foreground=\\\"\") + colour.to_string() + \"\\\">\" + capitalize_first(cur_kw_type) + \"</span>\"\n\t\t);\n\t\tlabel_widgets[cur_lang + cur_kw_type]->show();*/\n\t\t}\n\t}\n"
  },
  {
    "path": "frontend/gtkmm/ChooseColoursDialog.hh",
    "content": "\n#pragma once\n\n#include <gtkmm/dialog.h>\n#include <gtkmm/grid.h>\n#include <gtkmm/colorbutton.h>\n#include <vector>\n#include <memory>\n#include <map>\n#include \"NotebookWindow.hh\"\n\nnamespace cadabra {\n\tclass ChooseColoursDialog : public Gtk::Dialog {\n\t\tpublic:\n\t\t\tenum responses {\n\t\t\t\tRESPONSE_PREVIEW = 101,\n\t\t\t\tRESPONSE_CHANGED\n\t\t\t\t};\n\t\t\tChooseColoursDialog(DocumentThread::Prefs& prefs, NotebookWindow& parent);\n\t\tprivate:\n\t\t\tDocumentThread::Prefs& prefs;\n\t\t\tstd::map<std::string, std::map<std::string, std::unique_ptr<Gtk::ColorButton>>> colour_buttons;\n\t\t\tstd::vector<std::unique_ptr<Gtk::Widget>> anonymous_widgets;\n\t\t\tGtk::Grid   main_grid;\n\t\t\tGtk::Box    main_vbox;\n\t\t\tGtk::Box    bottom_button_box;\n\t\t\tGtk::Button button_ok;\n\t\t\tvoid on_my_response(int response_id);\n\t\t\tvoid on_color_set();\n\t\t\tNotebookWindow& parent;\n\t\t};\n\t}\n\n\n"
  },
  {
    "path": "frontend/gtkmm/CodeInput.cc",
    "content": "#include \"CodeInput.hh\"\n#include <gdkmm/general.h>\n#include <gtkmm/messagedialog.h>\n#include <gdk/gdkkeysyms.h>\n#include <gdkmm/rgba.h>\n//#include <gdkmm/root.h>\n#include <iostream>\n#include <regex>\n#include \"Keywords.hh\"\n\nusing namespace cadabra;\n\n// General tool to strip spaces from both ends\nstd::string trim(const std::string& s)\n\t{\n\tif(s.length() == 0)\n\t\treturn s;\n\tint b = s.find_first_not_of(\" \\t\\n\");\n\tint e = s.find_last_not_of(\" \\t\\n\");\n\tif(b == -1) // No non-spaces\n\t\treturn \"\";\n\treturn std::string(s, b, e - b + 1);\n\t}\n\nCodeInput::exp_input_tv::exp_input_tv(DTree::iterator it, Glib::RefPtr<Gtk::TextBuffer> tb, double scale, double display_scale,\n\t\t\t\t\t\t\t\t\t\t\t\t  Glib::RefPtr<Gtk::Adjustment> vadjustment_)\n\t: Gtk::TextView(tb), scale_(scale), display_scale_(display_scale), datacell(it), vadjustment(vadjustment_)\n\t{\n\tset_events(Gdk::STRUCTURE_MASK);\n\t//\tget_buffer()->signal_insert().connect(sigc::mem_fun(this, &exp_input_tv::on_my_insert), false);\n\t//\tget_buffer()->signal_erase().connect(sigc::mem_fun(this, &exp_input_tv::on_my_erase), false);\n\tget_buffer()->signal_changed().connect(sigc::mem_fun(this, &exp_input_tv::on_textbuf_change), false);\n\tset_name(\"CodeInput\"); // to be able to style it with CSS\n\tauto obj = get_accessible();\n\tobj->set_name(\"CodeInput\");\n\tobj->set_role(Atk::ROLE_TEXT);\n\t}\n\nCodeInput::CodeInput(DTree::iterator it, Glib::RefPtr<Gtk::TextBuffer> tb, double s, double ds, const Prefs& prefs,\n\t\t\t\t\t\t\tGlib::RefPtr<Gtk::Adjustment> vadjustment)\n\t: Gtk::Box(Gtk::Orientation::ORIENTATION_VERTICAL)\n\t, buffer(tb)\n\t, edit(it, tb, s, ds, vadjustment)\n\t{\n\tinit(prefs, ds);\n\t}\n\nCodeInput::CodeInput(DTree::iterator it, const std::string& txt, double s, double ds, const Prefs& prefs,\n\t\t\t\t\t\t\tGlib::RefPtr<Gtk::Adjustment> vadjustment)\n\t: Gtk::Box(Gtk::Orientation::ORIENTATION_VERTICAL)\n\t, buffer(Gtk::TextBuffer::create())\n\t, edit(it, buffer, s, ds, vadjustment)\n\t{\n\tbuffer->set_text(txt);\n\tinit(prefs, ds);\n\t}\n\nvoid CodeInput::on_size_allocate(Gtk::Allocation& allocation)\n\t{\n//\tallocation.set_width(edit.window_width); // Fixed width\n\n//\tGtk::Widget* current = this;\n//\twhile (current->get_parent()) {\n//\t\tcurrent = current->get_parent();\n//\t\t}\n//\t\n//\tGtk::Window *mywindow = static_cast<Gtk::Window *>(current);\n//\tif(mywindow) {\n//\t\tstd::cerr << \"The root window of CodeInput has \" << mywindow->get_allocation().get_width() << std::endl;\n//\t\t}\t\n////\tallocation.set_width(thewidth);\n//\n\tGtk::Box::on_size_allocate(allocation);\n\t}\n\n\nGtk::SizeRequestMode CodeInput::exp_input_tv::get_request_mode_vfunc() const\n\t{\n\treturn Gtk::SizeRequestMode::SIZE_REQUEST_WIDTH_FOR_HEIGHT;\n\t}\n\nvoid CodeInput::exp_input_tv::get_preferred_width_for_height_vfunc(int height,\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t int& minimum_width, int& natural_width) const\n\t{\n\tif(datacell->cell_type==DataCell::CellType::latex) {\n\t\tminimum_width = window_width-20;\n\t\tnatural_width = window_width-20;\n\t\t// std::cerr << \"requested widths for \" << datacell->textbuf.substr(0, 20) << \": \" << window_width << std::endl;\n\t\t}\n\telse {\n\t\treturn Gtk::TextView::get_preferred_width_for_height_vfunc(height, minimum_width, natural_width);\n\t\t}\n\t}\n\nvoid CodeInput::exp_input_tv::on_size_allocate(Gtk::Allocation& allocation)\n\t{\n\t// std::cerr << \"allocation requested for \" << datacell->textbuf.substr(0, 20) << \": \" << allocation.get_width() << std::endl;\n\tif(datacell->cell_type==DataCell::CellType::latex) \n\t\tallocation.set_width(window_width-20);\n\tGtk::TextView::on_size_allocate(allocation);\n\t}\n\nvoid CodeInput::init(const Prefs& prefs, double display_scale)\n\t{\n\t//\tscroll_.set_size_request(-1,200);\n\t//\tscroll_.set_border_width(1);\n\t//\tscroll_.set_policy(Gtk::POLICY_NEVER, Gtk::POLICY_ALWAYS);\n//\tedit.set_wrap_mode(Gtk::WRAP_NONE); // WRAP_WORD_CHAR); wrapping leads to weird effects\n\tedit.set_pixels_above_lines(1);\n\tedit.set_pixels_below_lines(1);\n\tedit.set_pixels_inside_wrap(1);\n\n//\tset_size_request(400, -1);\n\t\n\t// The following two are margins around the vbox which contains the\n\t// text input and the LaTeX output(s).\n\tset_margin_top(10);\n\tset_margin_bottom(0);\n\t//\tedit.set_pixels_below_lines(Gtk::LINE_SPACING);\n\t//\tedit.set_pixels_inside_wrap(2*Gtk::LINE_SPACING);\n\n\t// Padding using CSS does not work on earlier Gtk versions, so we use set_left_margin there.\n\tedit.set_left_margin(24/display_scale);\n\t//\tif(gtk_get_minor_version()<11 || gtk_get_minor_version()>=14)\n\n\t// Determine the width of a tab.\n\tauto layout = Pango::Layout::create(edit.get_pango_context());\n\tPango::Rectangle logical_rect;\n\tlayout->set_text(\" \");\n\tint space_width, space_height;\n\tlayout->get_pixel_size(space_width, space_height);\n\n\t// Set 10 tab stops, each 3 spaces wide.\n\tedit.set_monospace(true);\n\tedit.set_accepts_tab(true);\n\tPango::TabArray tabs(10);\n\tfor(int i=0; i<10; ++i)\n\t\ttabs.set_tab(i, Pango::TAB_LEFT, 3*space_width*i);\n\tedit.set_tabs(tabs);\n\n\tedit.signal_button_press_event().connect(sigc::mem_fun(this, &CodeInput::handle_button_press), false);\n\tedit.get_buffer()->signal_insert().connect(sigc::mem_fun(this, &CodeInput::handle_insert), true /* run before default handler */);\n\tedit.get_buffer()->signal_erase().connect(sigc::mem_fun(this, &CodeInput::handle_erase), false);\n\tif (prefs.highlight) {\n\t\tusing namespace std::string_literals;\n\t\tswitch (edit.datacell->cell_type) {\n\t\t\tcase DataCell::CellType::latex:\n\t\t\t\tenable_highlighting(edit.datacell->cell_type, prefs);\n\t\t\t\tbreak;\n\t\t\tcase DataCell::CellType::python:\n\t\t\t\tenable_highlighting(edit.datacell->cell_type, prefs);\n\t\t\t\tbreak;\n\t\t\tdefault:\n\t\t\t\tbreak;\n\t\t\t}\n\t\t}\n\n\tedit.set_can_focus(true);\n\n\tauto dummy_adj = Gtk::Adjustment::create(0,0,0);\n\tedit.set_focus_hadjustment(dummy_adj);\n\n\tadd(edit);\n\t//\tset_border_width(3);\n\tshow_all();\n\t}\n\ngunichar deref(Gtk::TextBuffer::iterator it, size_t n)\n\t{\n\tit.forward_chars(n);\n\treturn it.is_end() ? '\\0' : *it;\n\t}\n\nvoid CodeInput::highlight_python()\n\t{\n\n\tauto buf = edit.get_buffer();\n\n\t// Remove all tags that are currently set\n\tbuf->remove_all_tags(buf->begin(), buf->end());\n\n\t// 0 = not set\n\t// 1 = number\n\t// 2 = comment\n\t// 3 = name\n\t// 4 = single-quoted string\n\t// 5 = double-quoted string\n\t// 6 = triple single-quoted string\n\t// 7 = triple double-quoted string\n\t// 8 = multiline math mode\n\t// 9 = singleline math mode\n\n\tauto it = buffer->begin();\n\tauto start = it;\n\tint wordtype = 0;\n\tint count = 0;\n\tbool finished = false;\n\n\twhile (!finished) {\n\t\tif (it.is_end())\n\t\t\tfinished = true;\n\n\t\tauto cur = deref(it, 0);\n\t\tauto next = deref(it, 1);\n\n\t\tif (wordtype == 1) { // End on non-number\n\t\t\tif (g_unichar_isxdigit(cur) || cur == '.' ||\n\t\t\t      cur == 'x' || cur == 'o' || cur == 'j' ||\n\t\t\t      cur == 'X' || cur == 'O' || cur == 'J');\n\t\t\telse if (cur == 'e' || cur == 'E') {\n\t\t\t\tif (next == '+' || next == '-')\n\t\t\t\t\t++it;\n\t\t\t\t}\n\t\t\telse {\n\t\t\t\tbuf->apply_tag_by_name(\"number\", start, it);\n\t\t\t\twordtype = 0;\n\t\t\t\t}\n\t\t\t}\n\t\telse if (wordtype == 2) {   // End on linebreak or end of document\n\t\t\tif (cur == '\\n' || cur == '\\0') {\n\t\t\t\tbuf->apply_tag_by_name(\"comment\", start, it);\n\t\t\t\twordtype = 0;\n\t\t\t\t}\n\t\t\t// We might have mistakenly assumed the line is a comment\n\t\t\t// due to a # sign; but this could also be in the middle of\n\t\t\t// the implicit math mode at the start of a property declaration.\n\t\t\t// Therefore, if inside comment mode we find a :: then we should\n\t\t\t// exit comment mode and let the line be reformatted accordingly,\n\t\t\t// even though this does the wrong thing if someone has typed '::'\n\t\t\t// in a comment.\n\t\t\tif (cur == ':' && next == ':') {\n\t\t\t\twordtype = 0;\n\t\t\t\t}\n\t\t\t}\n\t\telse if (wordtype == 3) {   // End if not alnum or _\n\t\t\tif (cur == '_' || g_unichar_isalnum(cur));\n\t\t\telse {\n\t\t\t\tif (*start == '@') {\n\t\t\t\t\tbuf->apply_tag_by_name(\"decorator\", start, it);\n\t\t\t\t\t}\n\t\t\t\telse {\n\t\t\t\t\tstd::string name(start, it);\n\t\t\t\t\tauto tag = get_keyword_group(name);\n\t\t\t\t\tif (tag) {\n\t\t\t\t\t\tbuf->apply_tag_by_name(tag, start, it);\n\t\t\t\t\t\t}\n\t\t\t\t\t}\n\t\t\t\twordtype = 0;\n\t\t\t\t}\n\t\t\t}\n\t\telse if (wordtype == 4) {   // End on ' but skip \\'\n\t\t\tif (cur == '\\'') {\n\t\t\t\t++it;\n\t\t\t\tbuf->apply_tag_by_name(\"string\", start, it);\n\t\t\t\twordtype = 0;\n\t\t\t\t}\n\t\t\telse if (cur == '\\\\' && next == '\\'') {\n\t\t\t\t++it;\n\t\t\t\t}\n\t\t\t}\n\t\telse if (wordtype == 5) {   // End on \" but skip \\\"\n\t\t\tif (cur == '\"') {\n\t\t\t\t++it;\n\t\t\t\tbuf->apply_tag_by_name(\"string\", start, it);\n\t\t\t\twordtype = 0;\n\t\t\t\t}\n\t\t\telse if (cur == '\\\\' && next == '\\\"') {\n\t\t\t\t++it;\n\t\t\t\t}\n\t\t\t}\n\t\telse if (wordtype == 6) {   // End on '''\n\t\t\tif (cur == '\\'') {\n\t\t\t\t++count;\n\t\t\t\tif (count == 3) {\n\t\t\t\t\tcount = 0;\n\t\t\t\t\t++it;\n\t\t\t\t\tbuf->apply_tag_by_name(\"string\", start, it);\n\t\t\t\t\twordtype = 0;\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\telse {\n\t\t\t\tif (cur == '\\\\' && next == '\\'')\n\t\t\t\t\t++it;\n\t\t\t\tcount = 0;\n\t\t\t\t}\n\n\t\t\t}\n\t\telse if (wordtype == 7) {   // End on \"\"\"\n\t\t\tif (cur == '\"') {\n\t\t\t\t++count;\n\t\t\t\tif (count == 3) {\n\t\t\t\t\tcount = 0;\n\t\t\t\t\t++it;\n\t\t\t\t\tbuf->apply_tag_by_name(\"string\", start, it);\n\t\t\t\t\twordtype = 0;\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\telse {\n\t\t\t\tif (cur == '\\\\' && next == '\"')\n\t\t\t\t\t++it;\n\t\t\t\tcount = 0;\n\t\t\t\t}\n\n\t\t\t}\n\t\telse if (wordtype == 8) {   // End on :;.\n\t\t\tif (cur == ':' || cur == ';' || cur == '.') {\n\t\t\t\tbuf->apply_tag_by_name(\"maths\", start, it);\n\t\t\t\twordtype = 0;\n\t\t\t\t}\n\t\t\t}\n\t\telse if (wordtype == 9) {   // End on $\n\t\t\tif (cur == '$') {\n\t\t\t\t// ++it;\n\t\t\t\tauto tmp=start;\n\t\t\t\t++tmp;\n\t\t\t\tbuf->apply_tag_by_name(\"comment\", start, tmp);\n\t\t\t\t++start;\n\t\t\t\tbuf->apply_tag_by_name(\"maths\", start, it);\n\t\t\t\ttmp = it;\n\t\t\t\t++tmp;\n\t\t\t\tbuf->apply_tag_by_name(\"comment\", it, tmp);\n\t\t\t\twordtype = 0;\n\t\t\t\t}\n\t\t\t}\n\t\telse if (wordtype == 10) {   // Highlight and move on\n\t\t\tbuf->apply_tag_by_name(\"brace\", start, it);\n\t\t\twordtype = 0;\n\t\t\t}\n\t\telse if (wordtype == 11) {   //Highlight and move on\n\t\t\tbuf->apply_tag_by_name(\"operator\", start, it);\n\t\t\twordtype = 0;\n\t\t\t}\n\n\t\tif (wordtype == 0) {\n\t\t\tcur = deref(it, 0);\n\t\t\tnext = deref(it, 1);\n\n\t\t\t// Set word start iterator\n\t\t\tstart = it;\n\n\t\t\t// Start a number on 0-9, or .[0-9]\n\t\t\tif (g_unichar_isdigit(cur) || (cur == '.' && g_unichar_isdigit(next))) {\n\t\t\t\twordtype = 1;\n\t\t\t\t}\n\t\t\t// Start a comment on # if the next symbol isn't }\n\t\t\telse if (cur == '#') {\n\t\t\t\twordtype = 2;\n\t\t\t\t}\n\t\t\t// Start a name on a letter or _ @\n\t\t\telse if (g_unichar_isalpha(cur) || cur == '_' || cur == '@') {\n\t\t\t\twordtype = 3;\n\t\t\t\t}\n\t\t\t// Start a single quoted string on '\n\t\t\telse if (cur == '\\'') {\n\t\t\t\t// Decide if this is triple quoted\n\t\t\t\tif (next == '\\'' && deref(it, 2) == '\\'') {\n\t\t\t\t\twordtype = 6;\n\t\t\t\t\tit.forward_chars(2);\n\t\t\t\t\t}\n\t\t\t\telse {\n\t\t\t\t\twordtype = 4;\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t// Start a double quoted string on \"\n\t\t\telse if (cur == '\"') {\n\t\t\t\t// Decide if this is triple quoted\n\t\t\t\tif (next == '\"' && deref(it, 2) == '\"') {\n\t\t\t\t\twordtype = 7;\n\t\t\t\t\tit.forward_chars(2);\n\t\t\t\t\t}\n\t\t\t\telse {\n\t\t\t\t\twordtype = 5;\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t// Start multiline math mode on :=\n\t\t\telse if (cur == ':' && next == '=') {\n\t\t\t\twordtype = 8;\n\t\t\t\tit.forward_chars(2);\n\t\t\t\tbuf->apply_tag_by_name(\"operator\", start, it);\n\t\t\t\tstart = it;\n\t\t\t\t}\n\t\t\t// Reformat current line as maths if :: found\n\t\t\telse if (cur == ':' && next == ':') {\n\t\t\t\twordtype = 11;\n\t\t\t\tauto line_begin = it;\n\t\t\t\tauto line_end = it;\n\t\t\t\tline_begin.backward_find_char([](gunichar c) {\n\t\t\t\t\treturn c == '\\n';\n\t\t\t\t\t});\n\t\t\t\tline_end.forward_to_line_end();\n\t\t\t\tbuf->remove_all_tags(line_begin, line_end);\n\t\t\t\tbuf->apply_tag_by_name(\"maths\", line_begin, it);\n\t\t\t\t}\n\t\t\t// Start inline math mode on $\n\t\t\telse if (cur == '$')\n\t\t\t\twordtype = 9;\n\t\t\t// Highlight as brace\n\t\t\telse if (cur == '{' || cur == '[' || cur == '(' ||\n\t\t\t         cur == '}' || cur == ']' || cur == ')') {\n\t\t\t\twordtype = 10;\n\t\t\t\t}\n\t\t\telse if (g_unichar_ispunct(cur)) {\n\t\t\t\twordtype = 11;\n\t\t\t\t}\n\t\t\t}\n\t\t++it;\n\t\t}\n\t}\n\nvoid CodeInput::highlight_latex()\n\t{\n\tauto buf = edit.get_buffer();\n\tbuf->remove_all_tags(buf->begin(), buf->end());\n\n\t// 0 = none\n\t// 1 = comment\n\t// 2 = command\n\t// 3 = can expect a parameter to begin\n\t// 4 = inline math mode\n\tauto it = buf->begin();\n\tauto start = it;\n\tint wordtype = 0;\n\tint curly_depth = 0;\n\tint square_depth = 0;\n\tbool finished = false;\n\n\twhile (!finished) {\n\t\tif (it.is_end())\n\t\t\tfinished = true;\n\n\t\tauto cur = deref(it, 0);\n\n\t\tif (wordtype == 1) {\n\t\t\tif (cur == '\\n' || cur == '\\0') {\n\t\t\t\tbuf->apply_tag_by_name(\"comment\", start, it);\n\t\t\t\tstart = it;\n\t\t\t\twordtype = 0;\n\t\t\t\t}\n\t\t\t}\n\t\telse if (wordtype == 2) {\n\t\t\tif (!g_unichar_isalpha(cur)) {\n\t\t\t\tbuf->apply_tag_by_name(\"command\", start, it);\n\t\t\t\tstart = it;\n\t\t\t\twordtype = 5;\n\t\t\t\t}\n\t\t\t}\n\t\telse if (wordtype == 4) {\n\t\t\tif (cur == '$') {\n\t\t\t\t++it;\n\t\t\t\tcur = deref(it, 0);\n\t\t\t\tbuf->apply_tag_by_name(\"maths\", start, it);\n\t\t\t\twordtype = 0;\n\t\t\t\t}\n\t\t\t}\n\n\t\tif (wordtype == 5) {\n\t\t\tif (cur == '{') {\n\t\t\t\t++curly_depth;\n\t\t\t\tstart = it;\n\t\t\t\t++it;\n\t\t\t\tcur = deref(it, 0);\n\t\t\t\t}\n\t\t\telse if (cur == '[') {\n\t\t\t\t++square_depth;\n\t\t\t\tstart = it;\n\t\t\t\t++it;\n\t\t\t\tcur = deref(it, 0);\n\t\t\t\t}\n\t\t\twordtype = 0;\n\t\t\t}\n\n\t\tif (wordtype == 0) {\n\t\t\tif (cur == '}' && curly_depth) {\n\t\t\t\tauto next = it;\n\t\t\t\tnext.forward_char();\n\t\t\t\tbuf->apply_tag_by_name(\"parameter\", start, next);\n\t\t\t\t--curly_depth;\n\t\t\t\twordtype = 5;\n\t\t\t\t}\n\t\t\telse if (cur == ']' && square_depth) {\n\t\t\t\tauto next = it;\n\t\t\t\tnext.forward_char();\n\t\t\t\tbuf->apply_tag_by_name(\"parameter\", start, next);\n\t\t\t\t--square_depth;\n\t\t\t\twordtype = 5;\n\t\t\t\t}\n\t\t\telse if (cur == '\\\\') {\n\t\t\t\tif (curly_depth || square_depth)\n\t\t\t\t\tbuf->apply_tag_by_name(\"parameter\", start, it);\n\t\t\t\tstart = it;\n\t\t\t\twordtype = 2;\n\t\t\t\t}\n\t\t\telse if (cur == '%') {\n\t\t\t\tif (curly_depth || square_depth)\n\t\t\t\t\tbuf->apply_tag_by_name(\"parameter\", start, it);\n\t\t\t\tstart = it;\n\t\t\t\twordtype = 1;\n\t\t\t\t}\n\t\t\telse if (cur == '$') {\n\t\t\t\twordtype = 4;\n\t\t\t\tstart = it;\n\t\t\t\t}\n\t\t\t}\n\n\t\t++it;\n\t\t}\n\t}\n\nvoid CodeInput::enable_highlighting(DataCell::CellType cell_type, const Prefs& prefs)\n\t{\n\tstd::string map_idx;\n\tvoid (CodeInput::*callback)()=0;\n\n\tswitch (cell_type) {\n\t\tcase DataCell::CellType::python:\n\t\t\tmap_idx = \"python\";\n\t\t\tcallback = &CodeInput::highlight_python;\n\t\t\tbreak;\n\t\tcase DataCell::CellType::latex:\n\t\t\tmap_idx = \"latex\";\n\t\t\tcallback = &CodeInput::highlight_latex;\n\t\t\tbreak;\n\t\tdefault:\n\t\t\tbreak;\n\t\t}\n\n\t// Create tags\n\tfor (const auto& elem : prefs.colours.at(map_idx)) {\n\t\tif (edit.get_buffer()->get_tag_table()->lookup(elem.first)) // Already set\n\t\t\tedit.get_buffer()->get_tag_table()->lookup(elem.first)->property_foreground_rgba() = Gdk::RGBA(elem.second);\n\t\telse // Need to create\n\t\t\tedit.get_buffer()->create_tag(elem.first)->property_foreground_rgba() = Gdk::RGBA(elem.second);\n\t\t}\n\n\t// Error tag\n\tif (!edit.get_buffer()->get_tag_table()->lookup(\"error\")) {\n\t\tauto error_tag = edit.get_buffer()->create_tag(\"error\");\n\t\terror_tag->property_underline() = Pango::Underline::UNDERLINE_ERROR;\n#if GTKMM_MINOR_VERSION>=20\t\t\n\t\terror_tag->property_underline_rgba() = Gdk::RGBA(\"red\");\n#endif\n\t\t}\n\n\t// Setup callback\n\tif (hl_conn.connected())\n\t\thl_conn.disconnect();\n\n\thl_conn = edit.get_buffer()->signal_changed().connect(sigc::mem_fun(*this, callback));\n\n\t// And perform an initial highlight\n\tif(callback!=0)\n\t\t(this->*callback)();\n\t}\n\n\nvoid CodeInput::disable_highlighting()\n\t{\n\t// Remove all tags that are currently set\n\tedit.get_buffer()->remove_all_tags(\n\t   edit.get_buffer()->begin(),\n\t   edit.get_buffer()->end()\n\t);\n\n\t// Disconnect the signal\n\tif (hl_conn.connected())\n\t\thl_conn.disconnect();\n\t}\n\nvoid CodeInput::relay_cursor_pos(std::function<void(int, int)> callback)\n\t{\n\tedit.get_buffer()->property_cursor_position().signal_changed().connect([this, callback]() {\n\t\tauto iter = edit.get_buffer()->get_iter_at_mark(edit.get_buffer()->get_insert());\n\t\tauto line = iter.get_line() + 1;\n\t\tauto line_offset = iter.get_line_offset() + 1;\n\t\tcallback(line, line_offset);\n\t\t});\n\t}\n\nbool CodeInput::exp_input_tv::on_key_press_event(GdkEventKey* event)\n\t{\n\t// The key symbols are in /usr/include/gtk-3.0/gdk/gdkkeysyms.h\n\tbool is_shift_return = get_editable() && event->keyval==GDK_KEY_Return && (event->state&Gdk::SHIFT_MASK);\n\t//\tbool is_shift_tab    = get_editable() && event->keyval==GDK_KEY_Tab && (event->state&Gdk::SHIFT_MASK);\n\tbool is_tab = get_editable() && event->keyval==GDK_KEY_Tab;\n\tbool is_ctrl_k = get_editable() && event->keyval==GDK_KEY_k && (event->state&Gdk::CONTROL_MASK);\n\tbool is_ctrl_a = get_editable() && event->keyval==GDK_KEY_a && (event->state&Gdk::CONTROL_MASK);\n\tbool is_ctrl_e = get_editable() && event->keyval==GDK_KEY_e && (event->state&Gdk::CONTROL_MASK);\n\tbool is_ctrl_qm = get_editable() && event->keyval==GDK_KEY_question && (event->state&Gdk::CONTROL_MASK);\n\t\n\tbool retval=false;\n//\tstd::cerr << event->keyval << \", \" << event->state << \" pressed, focus = \" << has_focus()\n//\t \t\t\t << \", editable = \" << get_editable() << \", is_shift_return = \" << is_shift_return << std::endl;\n\n\n\tGlib::RefPtr<Gtk::TextBuffer> textbuf=get_buffer();\n\n\tif(is_shift_return) {\n\t\tcontent_changed(datacell);\n\t\tcontent_execute(datacell);\n\t\treturn true;\n\t\t}\n\telse if(is_tab) {\n\t\t// If one or more lines are selected, indent the whole block.\n\t\tGtk::TextBuffer::iterator beg, end;\n\t\tif(get_buffer()->get_selection_bounds(beg, end)) {\n\t\t\tif(beg.starts_line()) {\n\t\t\t\tint start_line = beg.get_line();\n\t\t\t\tint end_line = end.get_line();\n\t\t\t\tfor (int line = start_line; line <= end_line; ++line) {\n\t\t\t\t\tauto line_start = get_buffer()->get_iter_at_line(line);\n\t\t\t\t\tget_buffer()->insert(line_start, \"\\t\"); \n\t\t\t\t\t}\n\t\t\t\t// Move start of selection back to start of line.\n\t\t\t\tget_buffer()->get_selection_bounds(beg, end);\n\t\t\t\tint line_number = beg.get_line();\n\t\t\t\tbeg = get_buffer()->get_iter_at_line(line_number);\n\t\t\t\tget_buffer()->select_range(beg, end);\n\t\t\t\t}\n\t\t\telse {\n\t\t\t\tstd::cerr << \"start of selection not at start of line\" << std::endl;\n\t\t\t\t}\n\t\t\treturn true;\n\t\t\t}\n\t\telse {\n\t\t\t// Only complete if the last character is not whitespace.\n\t\t\tGlib::RefPtr<Gtk::TextBuffer::Mark> ins = get_buffer()->get_insert();\n\t\t\tGtk::TextBuffer::iterator it=textbuf->get_iter_at_mark(ins);\n\t\t\tint ipos=textbuf->get_slice(textbuf->begin(), it).bytes();\n\t\t\t\n\t\t\tif(complete_request(datacell, ipos))\n\t\t\t\treturn true;\n\t\t\telse\n\t\t\t\tretval=Gtk::TextView::on_key_press_event(event);\n\t\t\t}\n\t\t}\n\telse if(is_ctrl_a) {\n\t\tGlib::RefPtr<Gtk::TextBuffer::Mark> ins = get_buffer()->get_insert();\n\t\tGtk::TextBuffer::iterator iter=textbuf->get_iter_at_mark(ins);\n\t\titer.set_line(iter.get_line());\n\t\ttextbuf->place_cursor(iter);\n\t\treturn true;\n\t\t}\n\telse if(is_ctrl_e) {\n\t\tGlib::RefPtr<Gtk::TextBuffer::Mark> ins = get_buffer()->get_insert();\n\t\tGtk::TextBuffer::iterator iter=textbuf->get_iter_at_mark(ins);\n\t\titer.forward_to_line_end();\n\t\ttextbuf->place_cursor(iter);\n\t\treturn true;\n\t\t}\n\telse if(is_ctrl_k) {\n\t\tGlib::RefPtr<Gtk::TextBuffer::Mark> ins = get_buffer()->get_insert();\n\t\tGtk::TextBuffer::iterator iter=textbuf->get_iter_at_mark(ins);\n\t\tauto line = iter.get_line();\n\t\tGtk::TextBuffer::iterator line_start = iter;\n\t\tGtk::TextBuffer::iterator line_end = iter;\n\n\t\tif(line_end.ends_line())\n\t\t\tline_end.forward_char();\n\t\telse\n\t\t\tline_end.forward_to_line_end();\n\n\t\tget_buffer()->erase(line_start, line_end);\t\t\n\t\treturn true;\n\t\t}\n\telse {\n\t\tretval=Gtk::TextView::on_key_press_event(event);\n\t\t}\n\t\n\t//\telse {\n\t//\t\t// If this was a real key press (i.e. not just SHIFT or ALT or similar), emit a\n\t//\t\t// signal so that the cell can be scrolled into view if necessary.\n\t//\t\t// FIXME: I do not know how to do this correctly, check docs.\n\t//\t\t// FIXME: this should be done by monitoring the buffer for changes, see\n\t//\t\t// http://stackoverflow.com/questions/9250238/detecting-text-view-change-in-gtk-and-mono\n\t//\n\t//\t\tif(event->keyval < 65000L)\n\t//\t\t\tcontent_changed(tmp, datacell);\n\t//\n\t//\t\treturn retval;\n\t//\t\t}\n\n\treturn retval;\n\t}\n\nvoid CodeInput::exp_input_tv::shift_enter_pressed()\n\t{\n//\tGlib::RefPtr<Gtk::TextBuffer> textbuf=get_buffer();\n//\tstd::string tmp(textbuf->get_text(get_buffer()->begin(), get_buffer()->end()));\n\n\tcontent_changed(datacell);\n\tcontent_execute(datacell);\n\t}\n\nvoid CodeInput::exp_input_tv::on_textbuf_change()\n\t{\n\t// When a keypress happens, this function gets called first (and for every\n\t// widget which shares the TextBuffer). This feeds through that a change\n\t// was made, but nothing else happens. The next event is the handle_insert\n\t// signal.\n\tcontent_changed(datacell);\n\t}\n\nbool CodeInput::handle_button_press(GdkEventButton* button)\n\t{\n\tif(button->button!=2 || button->type!=GDK_BUTTON_PRESS) return false;\n\n\tGlib::RefPtr<Gtk::Clipboard> refClipboard = Gtk::Clipboard::get(GDK_SELECTION_PRIMARY);\n\n\tstd::vector<Glib::ustring> sah=refClipboard->wait_for_targets();\n\tbool hascadabra=false;\n\tbool hastext=false;\n\tbool hasstring=false;\n\tGtk::SelectionData sd;\n\n\tfor(unsigned int i=0; i<sah.size(); ++i) {\n\t\tif(sah[i]==\"cadabra\") {\n\t\t\thascadabra=true;\n\t\t\tbreak;\n\t\t\t}\n\t\telse if(sah[i]==\"TEXT\")\n\t\t\thastext=true;\n\t\telse if(sah[i]==\"STRING\")\n\t\t\thasstring=true;\n\t\t}\n\n\tif(hascadabra)     sd=refClipboard->wait_for_contents(\"cadabra\");\n\telse if(hastext)   sd=refClipboard->wait_for_contents(\"TEXT\");\n\telse if(hasstring) sd=refClipboard->wait_for_contents(\"STRING\");\n\tif(hascadabra || hastext || hasstring) {\n\t\t// Figure out where the mouse cursor is, so we know where to insert.\n\t\tGtk::TextBuffer::iterator insertpos;\n\t\tint somenumber;\n\t\tedit.get_iter_at_position(insertpos, somenumber, button->x, button->y);\n\t\tif(insertpos!=edit.get_buffer()->end())\n\t\t\t++insertpos;\n\t\tinsertpos=edit.get_buffer()->insert(insertpos, sd.get_data_as_string());\n\t\tedit.get_buffer()->place_cursor(insertpos);\n\t\t}\n\n\treturn true;\n\t}\n\nbool CodeInput::exp_input_tv::on_draw(const Cairo::RefPtr<Cairo::Context>& cr)\n\t{\n\tGlib::RefPtr<Gdk::Window> win = Gtk::TextView::get_window(Gtk::TEXT_WINDOW_TEXT);\n\n\t// std::cerr << \"on draw for \" << get_buffer()->get_text() << std::endl;\n\n\tbool ret=Gtk::TextView::on_draw(cr);\n\n\tint w, h, x, y;\n\twin->get_geometry(x,y,w,h);\n\n\t// paint the background\n\tcr->set_source_rgba(1.0, 1.0, 1.0, 1.0);\n\t//\tcr->rectangle(5,3,8,h-3);\n\t//\tcr->fill();\n\n\tif(datacell->cell_type==DataCell::CellType::latex)\n\t\tcr->set_source_rgba(.2, .7, .2, 1.0);\n\telse {\n\t\tif(datacell->ignore_on_import)\n\t\t\tcr->set_source_rgba(.4, .4, .7, 0.5);\n\t\telse\n\t\t\tcr->set_source_rgba(.2, .2, .7, 1.0);\n\t\t}\n\tdouble line_width=2.0/1.6*(scale_/display_scale_);\n\tcr->set_line_width(line_width);\n\tcr->set_antialias(Cairo::ANTIALIAS_NONE);\n\tdouble hor=5/display_scale_;\n\tcr->move_to(5+hor,line_width);\n\tcr->line_to(5,line_width);\n\tcr->line_to(5,h-line_width);\n\tcr->line_to(5+hor,h-line_width);\n\tcr->stroke();\n\n\t// Mark whether cell is executing.\n\tif(datacell->running) {\n\t\t//\tcr->set_source_rgba(.8, .2, .2, 1.0);\n\t\tcr->set_source_rgba(.2, .2, .7, 0.5);\n\t\tint rem=hor-line_width;\n\t\tcr->set_line_width(2*rem);\n\t\tcr->set_antialias(Cairo::ANTIALIAS_NONE);\n\t\tcr->move_to(5+rem,  rem);\n\t\tcr->line_to(5+rem,  h-rem);\n\t\tcr->stroke();\n\t\t}\n\n\n\treturn ret;\n\t}\n\nbool CodeInput::exp_input_tv::on_focus_in_event(GdkEventFocus *event)\n\t{\n\t// std::cerr << \"FOCUS IN\" << std::endl;\n\tcell_got_focus(datacell);\n\tif(previous_value>=0) \n\t\tvadjustment->set_value(previous_value);\n\treturn Gtk::TextView::on_focus_in_event(event);\n\t}\n\nbool CodeInput::exp_input_tv::on_focus_out_event(GdkEventFocus *event)\n\t{\n\t// std::cerr << \"FOCUS OUT\" << std::endl;\n\tprevious_value = -99.0;\n\treturn Gtk::TextView::on_focus_out_event(event);\n\t}\n\nbool CodeInput::exp_input_tv::on_motion_notify_event(GdkEventMotion* event)\n\t{\n\t// static int count=0;\n   //\tstd::cerr << \"MOTION \" << ++count << std::endl;\n\tprevious_value = vadjustment->get_value();\n\treturn Gtk::TextView::on_motion_notify_event(event);\n\t}\n\n// bool CodeInput::exp_input_tv::on_move_cursor_event(Glib::RefPtr<Gtk::TextBuffer::Mark> iter, Gtk::MovementStep step, bool extend_selection)\n// \t{\n// \tstd::cerr << \"on move cursor\" << std::endl;\n// \treturn false;\n// //\treturn Gtk::TextView::on_move_cursor(iter, step, extend_selection);\n// // \tauto mark_iter = get_buffer()->get_insert();\n// // \t\n// //    // Explicitly control scrolling with the custom parameters (minimal scrolling)\n// //    // 0.0 means no scrolling, so it won't scroll automatically\n// // \tget_buffer()->scroll_to_mark(mark_iter, 0.0, false, 0.0, 0.0);\n// // \t\n// // \t// Return false to allow the cursor movement to proceed without interfering with other behaviors\n// // \treturn false;\n// \t}\n\n\nvoid CodeInput::exp_input_tv::on_show()\n\t{\n\tif(!datacell->hidden)\n\t\tGtk::TextView::on_show();\n\t}\n\nvoid CodeInput::update_buffer()\n\t{\n\tstd::string newtxt = edit.datacell->textbuf;\n\tGlib::RefPtr<Gtk::TextBuffer> textbuf=edit.get_buffer();\n\tstd::string oldtxt = textbuf->get_text(edit.get_buffer()->begin(), edit.get_buffer()->end());\n\tif(newtxt!=oldtxt) {\n\t\t// std::cerr << \"setting buffer from \"\n\t\t// \t\t\t << oldtxt\n\t\t// \t\t\t << \" to \" << newtxt << std::endl;\n\t\tbuffer->set_text(newtxt);\n\t\t}\n\n\t// Word wrapping\n\tswitch (edit.datacell->cell_type) {\n\t\tcase DataCell::CellType::latex:\n\t\t\tedit.set_hexpand(false);\n\t\t\tedit.set_wrap_mode(Gtk::WRAP_WORD_CHAR);\n\t\t\t// std::cerr << \"enabled word wrapping\" << std::endl;\n\t\t\tbreak;\n\t\tcase DataCell::CellType::python:\n\t\t\tedit.set_hexpand(true);\n\t\t\tedit.set_wrap_mode(Gtk::WRAP_NONE);\n\t\t\tbreak;\n\t\tdefault:\n\t\t\tbreak;\n\t\t}\n\n\t}\n\nvoid CodeInput::handle_insert(const Gtk::TextIter& pos, const Glib::ustring& text, int bytes)\n\t{\n\t// If we have two CodeInput widgets which share the same\n\t// TextBuffer, then manually inserting (typing) text into one will\n\t// fire handle_insert on both widgets. So we need to not propagate\n\t// this change if we are not focused.\n\n\tif(edit.has_focus()==false) {\n\t\treturn;\n\t\t}\n\t\n\tGlib::RefPtr<Gtk::TextBuffer> buf=edit.get_buffer();\n\t// warning: pos contains the cursor pos, and because we get to this handler\n\t// _after_ the default handler has run, the cursor will have moved by\n\t// the length of the insertion.\n   //\tstd::cerr << text << \", \" << text.bytes() << \"; \" << pos.get_line_index() << \", \" << std::distance(buf->begin(), pos) << \",  \" << pos.get_offset() << \", \" << bytes << std::endl;\n\t// there is no quick way to get the byte offset for the iterator, so we do:\n\tint ipos = buf->get_slice(buf->begin(), pos).bytes();\n\tedit.content_insert(text, ipos-bytes, edit.datacell);\n\t}\n\nvoid CodeInput::handle_erase(const Gtk::TextIter& start, const Gtk::TextIter& end)\n\t{\n\t// See handle_insert for the 'focus' logic.\n\tif(edit.has_focus()==false) {\n\t\treturn;\n\t\t}\n\t\n\t//std::cerr << \"handle_erase: \" << start << \", \" << end << std::endl;\n\tGlib::RefPtr<Gtk::TextBuffer> buf=edit.get_buffer();\n\tint spos = buf->get_slice(buf->begin(), start).bytes();\n\tint epos = buf->get_slice(buf->begin(), end).bytes();\t\n\tedit.content_erase(spos, epos, edit.datacell);\n\t}\n\nvoid CodeInput::slice_cell(std::string& before, std::string& after)\n\t{\n\tGlib::RefPtr<Gtk::TextBuffer> textbuf=edit.get_buffer();\n\n\tGtk::TextBuffer::iterator it=textbuf->get_iter_at_mark(textbuf->get_insert());\n\tbefore=textbuf->get_slice(textbuf->begin(), it);\n\tafter =textbuf->get_slice(it, textbuf->end());\n\t}\n\n"
  },
  {
    "path": "frontend/gtkmm/CodeInput.hh",
    "content": "\n#pragma once\n\n#include \"DataCell.hh\"\n#include \"DocumentThread.hh\"\n#include <gtkmm/box.h>\n#include <gtkmm/textview.h>\n#include <gtkmm/separator.h>\n\nnamespace cadabra {\n\n\t/// \\ingroup frontend\n\t///\n\t/// A text cell editor widget with support for editing Python and LaTeX.\n\t/// CodeInput is essentially a TextView with some additional i/o logic.\n\n\tclass CodeInput : public Gtk::Box {\n\t\tpublic:\n\t\t\tusing Prefs = cadabra::DocumentThread::Prefs;\n\t\t\t/// Initialise with existing TextBuffer and a pointer to the Datacell\n\t\t\t/// corresponding to this CodeInput widget. CodeInput is not allowed\n\t\t\t/// to modify this DataCell directly, but can read properties from\n\t\t\t/// it (e.g. in order to know when to display a 'busy' indicator).\n\t\t\t/// The scale parameter refers to hdpi scaling.\n\n\t\t\tCodeInput(DTree::iterator, Glib::RefPtr<Gtk::TextBuffer>, double scale, double display_scale, const Prefs& prefs,\n\t\t\t\t\t\t Glib::RefPtr<Gtk::Adjustment>);\n\n\t\t\t/// Initialise with a new TextBuffer (to be created by\n\t\t\t/// CodeInput), filling it with the content of the given\n\t\t\t/// string.\n\n\t\t\tCodeInput(DTree::iterator, const std::string&, double scale, double display_scale, const Prefs& prefs,\n\t\t\t\t\t\t Glib::RefPtr<Gtk::Adjustment>);\n\n\n\t\t\tvirtual void on_size_allocate(Gtk::Allocation& allocation) override;\n\t\t\t\n\t\t\t/// The actual text widget used by CodeInput.\n\n\t\t\tclass exp_input_tv : public Gtk::TextView {\n\t\t\t\tpublic:\n\t\t\t\t\texp_input_tv(DTree::iterator, Glib::RefPtr<Gtk::TextBuffer>,\n\t\t\t\t\t\t\t\t\t double scale,\n\t\t\t\t\t\t\t\t\t double display_scale,\n\t\t\t\t\t\t\t\t\t Glib::RefPtr<Gtk::Adjustment>);\n\t\t\t\t\tvirtual bool on_key_press_event(GdkEventKey*) override;\n\t\t\t\t\tvirtual bool on_draw(const Cairo::RefPtr<Cairo::Context>&) override;\n\t\t\t\t\tvirtual bool on_focus_in_event(GdkEventFocus *) override;\n\t\t\t\t\tvirtual bool on_focus_out_event(GdkEventFocus *) override;\n\t\t\t\t\tvirtual void on_show() override;\n\n\t\t\t\t\tvirtual Gtk::SizeRequestMode get_request_mode_vfunc() const override;\n\t\t\t\t\tvirtual void get_preferred_width_for_height_vfunc(int height, int& minimum_width, int& natural_width) const  override;\n\t\t\t\t\tvirtual bool on_motion_notify_event(GdkEventMotion *event) override;\n\t\t\t\t\tvirtual void on_size_allocate(Gtk::Allocation& allocation) override;\n\t\t\t\t\t\n\t\t\t\t\tvoid         shift_enter_pressed();\n\t\t\t\t\tvoid         on_textbuf_change();\n\n\t\t\t\t\tsigc::signal1<bool, DTree::iterator>                   content_execute;\n\t\t\t\t\tsigc::signal1<bool, DTree::iterator>                   content_changed;\n\t\t\t\t\tsigc::signal3<bool, std::string, int, DTree::iterator> content_insert;\n\t\t\t\t\tsigc::signal3<bool, int, int, DTree::iterator>         content_erase;\n\t\t\t\t\tsigc::signal1<bool, DTree::iterator>                   cell_got_focus;\n\t\t\t\t\tsigc::signal2<bool, DTree::iterator, int>              complete_request;\n\n\t\t\t\t\tfriend CodeInput;\n\n\t\t\t\t\tint                           window_width = 100;\n\t\t\t\tprivate:\n\t\t\t\t\tdouble                        scale_, display_scale_;\n\t\t\t\t\tDTree::iterator               datacell;\n\t\t\t\t\tGlib::RefPtr<Gtk::Adjustment> vadjustment;\n\t\t\t\t\tdouble                        previous_value = -99.0;\n\t\t\t\t};\n\n\t\t\t/// Set highlighting modes.\n\n\t\t\tvoid enable_highlighting(DataCell::CellType cell_type, const Prefs& prefs);\n\t\t\tvoid disable_highlighting();\n\n\t\t\tvoid relay_cursor_pos(std::function<void(int, int)> callback);\n\n\t\t\t/// Handle mouse buttons.\n\n\t\t\tbool handle_button_press(GdkEventButton *);\n\n\t\t\t/// Handle an insert event, which can consist of one or more\n\t\t\t/// inserted characters. This function will just massage that\n\t\t\t/// data and then feed it through to the notebook window class\n\t\t\t/// by emitting a signal on content_insert (done like this to\n\t\t\t/// separate DTree modification from the widget).\n\n\t\t\tvoid handle_insert(const Gtk::TextIter& pos, const Glib::ustring& text, int bytes);\n\n\t\t\t/// Handle an erase event. This function will just massage that\n\t\t\t/// data and then feed it through to the notebook window class\n\t\t\t/// by emitting a signal on content_erase (done like this to\n\t\t\t/// separate DTree modification from the widget).\n\n\t\t\tvoid handle_erase(const Gtk::TextIter& start, const Gtk::TextIter& end);\n\n\t\t\t/// Ensure that the visual representation matches the DTree\n\t\t\t/// cell.\n\n\t\t\tvoid update_buffer();\n\n\t\t\t/// Return two strings corresponding to the text before and\n\t\t\t/// after the current cursor position.\n\n\t\t\tvoid slice_cell(std::string& before, std::string& after);\n\n\t\t\t/// We cannot edit the content of the DataCell directly,\n\t\t\t/// because Gtk needs a Gtk::TextBuffer. However, the\n\t\t\t/// CodeInput widgets corresponding to a single DataCell all\n\t\t\t/// share their TextBuffer.\n\n\t\t\tGlib::RefPtr<Gtk::TextBuffer> buffer;\n\n\t\t\texp_input_tv                  edit;\n\n\t\tprivate:\n\t\t\tvoid init(const Prefs& prefs, double display_scale);\n\n\t\t\tvoid highlight_python();\n\t\t\tvoid highlight_latex();\n\n\t\t\tsigc::connection hl_conn; // Connection holding the syntax highlighting signal\n\t\t};\n\n\t}\n"
  },
  {
    "path": "frontend/gtkmm/Console.cc",
    "content": "#include <iostream>\n#include <gdk/gdkkeysyms.h>\n#include \"Console.hh\"\n#include \"Config.hh\"\n#include <internal/uuid.h>\n\nusing namespace cadabra;\n\nbool is_greedy(const std::string& str)\n\t{\n\tauto last = str.find_last_not_of(\" \\t\");\n\n\tif (last == std::string::npos)\n\t\treturn false;\n\treturn (str[last] == ':' || str[last] == '\\\\');\n\t}\n\nbool is_empty(const std::string& str)\n\t{\n\treturn str.find_first_not_of(\" \\t\") == std::string::npos;\n\t}\n\nConsole::TextViewProxy::TextViewProxy(Console& parent)\n\t: history_max_length(50)\n\t, parent(parent)\n\t, history_ptr(history.begin())\n\t{\n\n\t}\n\nbool Console::TextViewProxy::on_key_press_event(GdkEventKey* key_event)\n\t{\n\tauto buf = get_buffer();\n\n\tparent.scroll_to_bottom();\n\n\t// Run command if return key is pressed\n\tif (key_event->keyval == GDK_KEY_Return) {\n\t\tstd::string code = buf->get_text();\n\t\tbuf->set_text(\"\");\n\t\ttemp_in.clear();\n\t\tparent.send_input(code);\n\t\thistory.push_back(code);\n\t\tif (history.size() > history_max_length)\n\t\t\thistory.pop_front();\n\t\thistory_ptr = history.end();\n\t\treturn true;\n\t\t}\n\n\tbool ret;\n\n\tif (key_event->keyval == GDK_KEY_Up) {\n\t\t// Move up the history\n\t\tif (history_ptr == history.begin()) {\n\t\t\t// Do nothing\n\t\t\t}\n\t\telse {\n\t\t\t--history_ptr;\n\t\t\tbuf->set_text(*history_ptr);\n\t\t\t}\n\t\tret = true;\n\t\t}\n\telse if (key_event->keyval == GDK_KEY_Down) {\n\t\t// Move down the history\n\t\tif (history_ptr == history.end()) {\n\t\t\tbuf->set_text(\"\");\n\t\t\t}\n\t\telse {\n\t\t\t++history_ptr;\n\t\t\tif (history_ptr == history.end())\n\t\t\t\tbuf->set_text(temp_in);\n\t\t\telse\n\t\t\t\tbuf->set_text(*history_ptr);\n\t\t\t}\n\t\tret = true;\n\t\t}\n\telse {\n\t\t// Process the keystroke\n\t\tret = Gtk::TextView::on_key_press_event(key_event);\n\t\tif (history_ptr == history.end())\n\t\t\ttemp_in = buf->get_text();\n\t\t}\n\n\t// Update the position of the insertion point\n\tGtk::TextBuffer::iterator range_start, range_end;\n\tbuf->get_selection_bounds(range_start, range_end);\n\n\t// Update the parent's buffer to reflect the keystroke\n\tparent.set_input(\n\t   buf->get_text(),\n\t   std::distance(buf->begin(), range_start),\n\t   std::distance(buf->begin(), range_end)\n\t);\n\n\thide();\n\n\treturn ret;\n\t}\n\nConsole::Console(sigc::slot<void> run_slot)\n\t: needs_focus(false)\n\t, input(*this)\n\t{\n\tset_name(\"Console\");\n\tbuffer = tv.get_buffer();\n\n\tinput_begin = buffer->create_mark(buffer->begin());\n\tprompt_begin = buffer->create_mark(buffer->begin());\n\n\trun.connect(run_slot);\n\tdispatch_message.connect(sigc::mem_fun(this, &Console::process_message_queue));\n\n\tauto tag_table = tv.get_buffer()->get_tag_table();\n\tinput_tag = Gtk::TextTag::create();\n\tinput_tag->property_foreground() = \"black\";\n\ttag_table->add(input_tag);\n\n\toutput_tag = Gtk::TextTag::create();\n\toutput_tag->property_foreground() = \"dim gray\";\n\ttag_table->add(output_tag);\n\n\twarning_tag = Gtk::TextTag::create();\n\twarning_tag->property_foreground() = \"orange\";\n\ttag_table->add(warning_tag);\n\n\terror_tag = Gtk::TextTag::create();\n\terror_tag->property_foreground() = \"red\";\n\ttag_table->add(error_tag);\n\n\tprompt_tag = Gtk::TextTag::create();\n\tprompt_tag->property_foreground() = \"blue\";\n\ttag_table->add(prompt_tag);\n\n\twin.set_policy(Gtk::POLICY_NEVER, Gtk::POLICY_ALWAYS);\n\n\ttv.set_wrap_mode(Gtk::WRAP_WORD_CHAR);\n\ttv.set_hexpand(true);\n\ttv.set_vexpand(true);\n\ttv.set_monospace(true);\n\n\ttv.signal_key_press_event().connect(\n\t   sigc::mem_fun(&input, &TextViewProxy::on_key_press_event),\n\t   false);\n\n\ttv.signal_size_allocate().connect([this](Gtk::Allocation& ) {\n\t\tscroll_to_bottom();\n\t\t});\n\n\tadd(input);\n\tinput.hide();\n\tadd(win);\n\twin.add(tv);\n\tshow_all_children();\n\n\tset_sensitive(false);\n\t}\n\nvoid Console::initialize()\n\t{\n\tstd::string welcome_message =\n\t\t\"Cadabra v\" CADABRA_VERSION_SEM\n\t\t\" Interactive Console\\nFor more information, type help(console)\\n\";\n\tbuffer->insert_with_tag(buffer->begin(), welcome_message, output_tag);\n\tserver_cell_id = 0;\n\tprompt(false, true);\n\t}\n\nvoid Console::send_input(const std::string& code)\n{\n\tbool send = false;\n\n\tif (collect.empty()) {\n\t\tcollect += code;\n\t\tif (is_greedy(code))\n\t\t\tcollect += '\\n';\n\t\telse\n\t\t\tsend = true;\n\t}\n\telse {\n\t\tif (is_empty(code))\n\t\t\tsend = true;\n\t\telse\n\t\t\tcollect += code + '\\n';\n\t}\n\n\tif (send) {\n\t\tserver_cell_id = 0;\n\t\tauto oneback = buffer->insert(buffer->end(), \"\\n\");\n\t\toneback.backward_char();\n\t\tauto k = run_queue.emplace(collect, buffer->create_mark(oneback, false));\n\t\tcollect.clear();\n\t\tprompt(false);\n\t\tneeds_focus = true;\n\t\trun();\n\t}\n\telse {\n\t\tprompt(true, true);\n\t}\n}\n\nstd::string Console::grab_input(uint64_t& id)\n{\n\tconst auto& cell = run_queue.front();\n\tid = generate_uuid<uint64_t>();\n\tauto input = cell.first;\n\tcells.emplace(id, cell.second);\n\trun_queue.pop();\n\treturn input;\n}\n\nvoid Console::signal_message(const nlohmann::json& message)\n{\n\tmessage_queue.push(message);\n\tdispatch_message();\n}\n\nvoid Console::scroll_to_bottom()\n{\n\tGlib::RefPtr<Gtk::Adjustment> adj = win.get_vadjustment();\n\tadj->set_value(adj->get_upper());\n}\n\nvoid Console::set_input(const Glib::ustring& line, size_t range_start, size_t range_end)\n{\n\tbuffer->erase(buffer->get_iter_at_mark(input_begin), buffer->end());\n\tbuffer->insert_with_tag(buffer->get_iter_at_mark(input_begin), line, input_tag);\n\n\tif (range_start == std::string::npos)\n\t\trange_start = line.size();\n\tif (range_end == std::string::npos)\n\t\trange_end = line.size();\n\n\tauto it_start = buffer->get_iter_at_mark(input_begin);;\n\tauto it_end = it_start;\n\tit_start.forward_chars(range_start);\n\tit_end.forward_chars(range_end);\n\n\tbuffer->select_range(it_start, it_end);\n}\n\nvoid Console::prompt(bool continuation, bool newline)\n{\n\tif (newline)\n\t\tbuffer->insert(buffer->end(), \"\\n\");\n\n\tprompt_begin = buffer->create_mark(buffer->end());\n\tbuffer->insert_with_tag(buffer->end(), continuation ? \". \" : \"> \", prompt_tag);\n\tinput_begin = buffer->create_mark(buffer->end());\n}\n\nvoid Console::create_cell(uint64_t parent_id, uint64_t cell_id)\n\t{\n\tif (cells.find(parent_id) == cells.end()) {\n\t\t// Create a zombie input cell\n\t\tstd::string in = input.get_buffer()->get_text();\n\t\tset_input(\"<received input from \" + std::to_string(parent_id) + \">\\n\");\n\t\tauto backone = buffer->end();\n\t\tbackone.backward_char();\n\t\tparent_id = generate_uuid<uint64_t>();\n\t\tcells.emplace(parent_id, buffer->create_mark(backone, false));\n\t\tprompt(false, true);\n\t\tset_input(in);\n\t\t}\n\tauto it = buffer->insert(buffer->get_iter_at_mark(cells.at(parent_id)), \" \");\n\tcells.emplace(cell_id, buffer->create_mark(it));\n\t}\n\nuint64_t Console::get_server_cell()\n{\n\tif (server_cell_id == 0) {\n\t\tserver_cell_id = generate_uuid<uint64_t>();\n\t\tstd::string in = input.get_buffer()->get_text();\n\t\tset_input(\"<received input from server>\\n\");\n\t\tauto backone = buffer->end();\n\t\tbackone.backward_char();\n\t\tcells.emplace(server_cell_id, buffer->create_mark(backone, false));\n\t\tprompt(false, true);\n\t\tset_input(in);\n\t}\n\treturn server_cell_id;\n}\n\n\nvoid Console::insert_text(uint64_t cell_id, const std::string& text, const Glib::RefPtr<Gtk::TextTag>& tag)\n\t{\n\tauto& mark = cells.at(cell_id);\n\tbuffer->insert_with_tag(buffer->get_iter_at_mark(mark), \"\\n\" + text, tag);\n\t}\n\nvoid Console::insert_graphic(uint64_t cell_id, const std::string& bytes)\n\t{\n\t// Load bytes into a pixbuf\n\ttry {\n\t\tauto& mark = cells.at(cell_id);\n\t\tauto str = Gio::MemoryInputStream::create();\n\t\tstd::string dec = Glib::Base64::decode(bytes);\n\t\tstr->add_data(dec.c_str(), dec.size(), nullptr);\n\t\tauto pixbuf = Gdk::Pixbuf::create_from_stream_at_scale(str, 400, -1, true);\n\n\t\tbuffer->insert(buffer->get_iter_at_mark(mark), \"\\n\");\n\t\tbuffer->insert_pixbuf(buffer->get_iter_at_mark(mark), pixbuf);\n\t}\n\tcatch (const std::exception& err) {\n\t\tinsert_text(cell_id, err.what(), error_tag);\n\t}\n\t}\n\nvoid Console::insert_tex(uint64_t cell_id, const std::shared_ptr<TeXEngine::TeXRequest>& content)\n{\n\tauto& mark = cells.at(cell_id);\n\tauto pixbuf = Gdk::Pixbuf::create_from_data(\n\t\tcontent->image().data(), Gdk::COLORSPACE_RGB,\n\t\ttrue,\n\t\t8,\n\t\tcontent->width(), content->height(),\n\t\t4 * content->width());\n\n\tbuffer->insert(buffer->get_iter_at_mark(mark), \"\\n\");\n\tbuffer->insert_pixbuf(buffer->get_iter_at_mark(mark), pixbuf);\n}\n\nvoid Console::process_message_queue()\n{\n\tusing namespace nlohmann;\n\n\tif (tv.has_focus())\n\t\tneeds_focus = true;\n\tset_sensitive(false);\n\n\twhile (!message_queue.empty()) {\n\t\tconst json& msg = message_queue.front();\n\t\tjson header = msg.value(\"header\", json(json::value_t::object));\n\t\tjson content = msg.value(\"content\", json(json::value_t::object));\n\n\t\tstd::string msg_type = msg.value(\"msg_type\", header.value(\"msg_type\", \"\"));\n\t\tstd::string output = content.value(\"output\", \"\");\n\t\tuint64_t parent_id = header.value<uint64_t>(\"parent_id\", 0);\n\t\tuint64_t cell_id = header.value<uint64_t>(\"cell_id\", 0);\n\t\tuint64_t source_id;\n\n\t\tbool from_server = header.value(\"from_server\", false);\n\t\tif (from_server) {\n\t\t\tsource_id = get_server_cell();\n\t\t}\n\t\telse {\n\t\t\tsource_id = parent_id;\n\t\t\tneeds_focus = true;\n\t\t}\n\n\t\tcreate_cell(source_id, cell_id);\n\n\t\t// Process message\n\t\tif (msg_type == \"exit\") {\n\t\t\tinsert_text(cell_id, \"Restarting kernel...\", warning_tag);\n\t\t}\n\t\telse if (\n\t\t\tmsg_type == \"output\" ||\n\t\t\tmsg_type == \"verbatim\" ||\n\t\t\tmsg_type == \"input_form\" ||\n\t\t\tmsg_type == \"csl_out\") {\n\t\t\tinsert_text(cell_id, output, output_tag);\n\t\t}\n\t\telse if (msg_type == \"csl_warn\") {\n\t\t\tinsert_text(cell_id, \"Warning: \" + output, warning_tag);\n\t\t}\n\t\telse if (msg_type == \"csl_clear\") {\n\t\t\tbuffer->set_text(\"\");\n\t\t\ttex_engine.checkout_all();\n\t\t\t//cells.clear();\n\t\t\tprompt(false);\n\t\t}\n\t\telse if (msg_type == \"latex_view\") {\n\t\t\ttry {\n\t\t\t\tauto request = tex_engine.checkin(output, \"\", \"\");\n\t\t\t\ttex_engine.set_geometry(get_allocation().get_width());\n\t\t\t\ttex_engine.convert_all();\n\t\t\t\tinsert_tex(source_id, request);\n\t\t\t}\n\t\t\tcatch (const std::exception& err) {\n\t\t\t\tinsert_text(cell_id, err.what(), error_tag);\n\t\t\t}\n\t\t}\n\t\telse if (msg_type == \"error\") {\n\t\t\tinsert_text(cell_id, output, error_tag);\n\t\t}\n\t\telse if (msg_type == \"warning\") {\n\t\t\tinsert_text(cell_id, output, warning_tag);\n\t\t}\n\t\telse if (msg_type == \"image_png\") {\n\t\t\tinsert_graphic(cell_id, output);\n\t\t}\n\t\telse {\n\t\t\tstd::stringstream ss;\n\t\t\tss << msg.dump(2) << std::endl;\n\t\t\tinsert_text(cell_id, \"cadabra-client (console): do not know how to handle message:\\n\" + msg.dump(2), error_tag);\n\t\t}\n\n\t\tmessage_queue.pop();\n\t}\n\n\tset_sensitive(true);\n\tif (needs_focus)\n\t\ttv.grab_focus();\n\tneeds_focus = false;\n}\n\nbool Console::on_configure_event(GdkEventConfigure* cfg)\n{\n\tbool res = Gtk::Box::on_configure_event(cfg);\n\ttv.set_size_request(cfg->width, cfg->height);\n\treturn res;\n}\n"
  },
  {
    "path": "frontend/gtkmm/Console.hh",
    "content": "#pragma once\n\n#include <queue>\n#include <list>\n#include <gtkmm.h>\n#include \"nlohmann/json.hpp\"\n#include \"../common/TeXEngine.hh\"\n#include \"DataCell.hh\"\n\nnamespace cadabra {\n\tclass Console;\n\n\t// Interactive Console for Cadabra. Deived from Gtk::Box so can be packed into most\n\t// other widgets.\n\tclass Console : public Gtk::Box {\n\t\tpublic:\n\t\t\tenum class Position : int {\n\t\t\t\tHidden=0,\n\t\t\t\tDockedH=1,\n\t\t\t\tDockedV=2,\n\t\t\t\tFloating=3\n\t\t\t};\n\n\t\t\t// run_slot is the callback which should be run when the console sends input to\n\t\t\t// be run. This callback should call console.grab_input to get a line of input,\n\t\t\t// process it and then send the output block back to the console.\n\t\t\tConsole(sigc::slot<void> run_slot);\n\n\t\t\t// Display welcome message and first prompt\n\t\t\tvoid initialize();\n\n\t\t\t// Process a line of code, either creating a new prompt asking for\n\t\t\t// more input or adding a string to the run_queue and calling the run_slot callback\n\t\t\tvoid send_input(const std::string& code);\n\n\t\t\t// Grab a line of input, this should only be called fom the run_slot callback.\n\t\t\t// The id parameter will be set to a unique id which should be the parent_id of the\n\t\t\t// block when it is sent back to the console\n\t\t\tstd::string grab_input(uint64_t& id);\n\n\t\t\t// Add a message to the console's message queue and ask it to process the message queue\n\t\t\tvoid signal_message(const nlohmann::json& msg);\n\n\t\t\t// Scroll the console to the latest output\n\t\t\tvoid scroll_to_bottom();\n\n\t\tprivate:\n\t\t\t// Hidden proxy TextView which stores the user input by intercepting key press\n\t\t\t// events from the main console TextView\n\t\t\tclass TextViewProxy : public Gtk::TextView {\n\t\t\tpublic:\n\t\t\t\tTextViewProxy(Console& parent);\n\t\t\t\tbool on_key_press_event(GdkEventKey* key_event) override;\n\t\t\t\tsize_t history_max_length;\n\n\t\t\tprivate:\n\t\t\t\tConsole& parent;\n\t\t\t\tstd::string temp_in;\n\t\t\t\tstd::list<std::string> history;\n\t\t\t\tstd::list<std::string>::iterator history_ptr;\n\t\t\t};\n\n\t\t\t// Set the current prompt to particular text\n\t\t\tvoid set_input(const Glib::ustring& line, size_t range_start = std::string::npos, size_t range_end = std::string::npos);\n\n\t\t\t// Create a new prompt\n\t\t\tvoid prompt(bool continuation, bool newline = false);\n\n\t\t\t// Allocate a mark to a cell\n\t\t\tvoid create_cell(uint64_t parent_id, uint64_t cell_id);\n\n\t\t\t// Return the current server cell (pseudo-input cell for inputs received from the server) or\n\t\t\t// create one and return it if none exist\n\t\t\tuint64_t get_server_cell();\n\n\t\t\tvoid insert_text(uint64_t cell_id, const std::string& text, const Glib::RefPtr<Gtk::TextTag>& tag);\n\t\t\tvoid insert_graphic(uint64_t cell_id, const std::string& bytes);\n\t\t\tvoid insert_tex(uint64_t cell_id, const std::shared_ptr<TeXEngine::TeXRequest>& content);\n\n\t\t\t// Handle current incoming messages\n\t\t\tvoid process_message_queue();\n\n\t\t\tvirtual bool on_configure_event(GdkEventConfigure* cfg) override;\n\n\t\t\tGlib::Dispatcher dispatch_message; // callback attached to process_message_queue\n\t\t\tGlib::Dispatcher run; // initialized by run_slot, callback when cell needs running\n\n\t\t\tbool needs_focus; // True if console should grab focus on output\n\t\t\tGlib::RefPtr<Gtk::TextBuffer> buffer; // Reference to tv.get_buffer()\n\t\t\tstd::string collect; // Collected input if prompt is in continuation mode\n\t\t\tstd::queue<nlohmann::json> message_queue; // Current messages needing processing\n\t\t\tstd::queue<std::pair<std::string, Glib::RefPtr<Gtk::TextMark>>> run_queue; // Cells waiting to be run, .first is input string and .second is the input cell\n\t\t\tTeXEngine tex_engine; // Engine for compiling TeX outputs\n\t\t\tstd::map<uint64_t, Glib::RefPtr<Gtk::TextMark>> cells; // Storage of currently displayed cells\n\t\t\tuint64_t server_cell_id; // ID of current server cell, or 0 if invalidated\n\t\t\tGlib::RefPtr<Gtk::TextMark> input_begin; // Beginning of input\n\t\t\tGlib::RefPtr<Gtk::TextMark> prompt_begin; // Beginning of input prompt\n\t\t\tGlib::RefPtr<Gtk::TextTag> prompt_tag, input_tag, output_tag, warning_tag, error_tag;\n\t\t\tTextViewProxy input; // Input prompt\n\t\t\tGtk::TextView tv; // Main view\n\t\t\tGtk::ScrolledWindow win; // Main window\n\t\t};\n\n\t}\n"
  },
  {
    "path": "frontend/gtkmm/DiffViewer.cc",
    "content": "#include <internal/difflib.h>\n#include <internal/string_tools.h>\n\n#include \"DiffViewer.hh\"\n#include \"nlohmann/json.hpp\"\n\nconst Gdk::RGBA color_insert(\"rgb(200, 255, 200)\");\nconst Gdk::RGBA color_delete(\"rgb(255, 200, 200)\");\nconst Gdk::RGBA color_offwhite(\"rgb(240, 240, 240)\");\nconst Gdk::RGBA color_white(\"rgb(255, 255, 255)\");\n\nDiffTextView::DiffTextView()\n\t{\n\tauto buffer = get_buffer();\n\tbuffer->create_tag(\"insert\")->property_background_rgba() = color_insert;\n\tbuffer->create_tag(\"delete\")->property_background_rgba() = color_delete;\n\n\tset_border_width(5);\n\tset_editable(false);\n\tset_hexpand(true);\n\tset_monospace(true);\n\t}\n\nCellDiff::CellDiff(const std::string& a, const std::string& b)\n\t{\n\tset_border_width(5);\n\tset_margin_top(5);\n\tset_margin_bottom(5);\n\tset_margin_start(5);\n\tset_margin_end(5);\n\n\tgrid.set_hexpand(true);\n\tgrid.attach(sw_lhs, 1, 0, 1, 1);\n\tgrid.attach(sw_rhs, 3, 0, 1, 1);\n\tgrid.set_column_homogeneous(true);\n\tadd(grid);\n\n\tsw_lhs.set_policy(Gtk::POLICY_AUTOMATIC, Gtk::POLICY_NEVER);\n\tsw_rhs.set_policy(Gtk::POLICY_AUTOMATIC, Gtk::POLICY_NEVER);\n\tsw_lhs.add(tv_lhs);\n\tsw_rhs.add(tv_rhs);\n\n\t\t\t// FIXME: reinstate using css\n//\ttv_lhs.override_background_color(color_offwhite);\n//\ttv_rhs.override_background_color(color_white);\n\n\tcompare(a, b);\n\n\tshow_all_children();\n\t}\n\nvoid CellDiff::compare(const std::string& a_, const std::string& b_)\n\t{\n\tauto a = string_to_vec(a_);\n\tauto b = string_to_vec(b_);\n\n\tauto buf_lhs = tv_lhs.get_buffer();\n\tauto buf_rhs = tv_rhs.get_buffer();\n\n\tif (a_.empty() && !b_.empty()) {\n\t\t// Insert only\n\t\tfor (size_t i = 0; i < b.size(); ++i) {\n\t\t\t// FIXME: reinstate using css\n//\t\t\ttv_rhs.override_background_color(color_insert);\n\t\t\tbuf_rhs->insert(buf_rhs->end(), b[i]);\n\t\t\t}\n\t\t}\n\telse if (b_.empty() && !a_.empty()) {\n\t\t// Delete only\n\t\tfor (size_t i = 0; i < a.size(); ++i) {\n\t\t\t// FIXME: reinstate using css\n//\t\t\ttv_lhs.override_background_color(color_delete);\n\t\t\tbuf_lhs->insert(buf_lhs->end(), a[i]);\n\t\t\t}\n\t\t}\n\telse {\n\t\t// Compare both\n\t\tusing namespace difflib;\n\n\t\tDiffer<std::string> d;\n\n\t\tauto deltas = d.get_deltas(a, b);\n\n\t\tfor (const auto& delta : deltas) {\n\t\t\tswitch (delta.tag) {\n\t\t\t\tcase tag_t::t_delete:\n\t\t\t\t\tbuf_lhs->insert_with_tag(buf_lhs->end(), delta.a, \"delete\");\n\t\t\t\t\tbuf_rhs->insert(buf_rhs->end(), \"\\n\");\n\t\t\t\t\tbreak;\n\t\t\t\tcase tag_t::t_insert:\n\t\t\t\t\tbuf_lhs->insert(buf_lhs->end(), \"\\n\");\n\t\t\t\t\tbuf_rhs->insert_with_tag(buf_rhs->end(), delta.b, \"insert\");\n\t\t\t\t\tbreak;\n\t\t\t\tcase tag_t::t_equal:\n\t\t\t\t\tbuf_lhs->insert(buf_lhs->end(), delta.a);\n\t\t\t\t\tbuf_rhs->insert(buf_rhs->end(), delta.a);\n\t\t\t\t\tbreak;\n\t\t\t\tcase tag_t::t_replace:\n\t\t\t\t\tfor (const auto& opcode : delta.opcodes) {\n\t\t\t\t\t\tswitch (opcode.tag) {\n\t\t\t\t\t\t\tcase tag_t::t_delete:\n\t\t\t\t\t\t\t\tbuf_lhs->insert_with_tag(buf_lhs->end(), delta.a.substr(opcode.i1, opcode.i2 - opcode.i1), \"delete\");\n\t\t\t\t\t\t\t\tbreak;\n\t\t\t\t\t\t\tcase tag_t::t_insert:\n\t\t\t\t\t\t\t\tbuf_rhs->insert_with_tag(buf_rhs->end(), delta.b.substr(opcode.j1, opcode.j2 - opcode.j1), \"insert\");\n\t\t\t\t\t\t\t\tbreak;\n\t\t\t\t\t\t\tcase tag_t::t_replace:\n\t\t\t\t\t\t\t\tbuf_lhs->insert_with_tag(buf_lhs->end(), delta.a.substr(opcode.i1, opcode.i2 - opcode.i1), \"delete\");\n\t\t\t\t\t\t\t\tbuf_rhs->insert_with_tag(buf_rhs->end(), delta.b.substr(opcode.j1, opcode.j2 - opcode.j1), \"insert\");\n\t\t\t\t\t\t\t\tbreak;\n\t\t\t\t\t\t\tcase tag_t::t_equal:\n\t\t\t\t\t\t\t\tbuf_lhs->insert(buf_lhs->end(), delta.a.substr(opcode.i1, opcode.i2 - opcode.i1));\n\t\t\t\t\t\t\t\tbuf_rhs->insert(buf_rhs->end(), delta.a.substr(opcode.i1, opcode.i2 - opcode.i1));\n\t\t\t\t\t\t\t\tbreak;\n\t\t\t\t\t\t\tdefault:\n\t\t\t\t\t\t\t\tthrow std::runtime_error(\"Unexpected tag encountered in differ\");\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\t}\n\t\t\t\t\tbreak;\n\t\t\t\tdefault:\n\t\t\t\t\tthrow std::runtime_error(\"Unexpected tag encountered in differ\");\n\t\t\t\t}\n\t\t\t}\n\t\t}\n\n\t}\n\nDiffViewer::DiffViewer(std::istream& a, std::istream& b, Gtk::Window& parent)\n\t: Gtk::Dialog(\"Comparing notebooks\", parent)\n\t, box(Gtk::ORIENTATION_VERTICAL)\n\t{\n\tset_border_width(5);\n\tset_default_size(1000, 600);\n\n\tget_content_area()->add(scrolled_window);\n\n\tscrolled_window.add(box);\n\tscrolled_window.set_vexpand(true);\n\tscrolled_window.set_policy(Gtk::POLICY_NEVER, Gtk::POLICY_ALWAYS);\n\tadd_button(\"Close\", Gtk::RESPONSE_CLOSE);\n\n\tpopulate(a, b);\n\n\tshow_all();\n\t}\n\nvoid DiffViewer::run_noblock()\n\t{\n\tsignal_response().connect([this](int /* response_id */) {\n\t\thide();\n\t\t});\n\tshow();\n\tpresent();\n\t}\n\nvoid DiffViewer::populate(std::istream& a, std::istream& b)\n\t{\n\tusing namespace difflib;\n\n\tauto lhs_cells = make_cells(a);\n\tauto rhs_cells = make_cells(b);\n\n\tDiffer<std::string> d(nullptr, nullptr, 1.);\n\tfor (const auto& delta : d.get_deltas(lhs_cells.first, rhs_cells.first)) {\n\t\tif (delta.tag == tag_t::t_insert) {\n\t\t\tauto pos = std::find(rhs_cells.first.begin(), rhs_cells.first.end(), delta.b);\n\t\t\tcells.emplace_back(\"\", rhs_cells.second[std::distance(rhs_cells.first.begin(), pos)]);\n\t\t\t}\n\t\telse if (delta.tag == tag_t::t_delete) {\n\t\t\tauto pos = std::find(lhs_cells.first.begin(), lhs_cells.first.end(), delta.a);\n\t\t\tcells.emplace_back(lhs_cells.second[std::distance(lhs_cells.first.begin(), pos)], \"\");\n\t\t\t}\n\t\telse {\n\t\t\tauto pos_a = std::find(lhs_cells.first.begin(), lhs_cells.first.end(), delta.a);\n\t\t\tauto pos_b = std::find(rhs_cells.first.begin(), rhs_cells.first.end(), delta.a);\n\t\t\tcells.emplace_back(lhs_cells.second[std::distance(lhs_cells.first.begin(), pos_a)], rhs_cells.second[std::distance(rhs_cells.first.begin(), pos_b)]);\n\t\t\t}\n\t\t}\n\n\tfor (auto& cell : cells)\n\t\tbox.add(cell);\n\t}\n\nDiffViewer::Cells DiffViewer::make_cells(std::istream& stream)\n\t{\n\tCells ret;\n\n\tnlohmann::json nb;\n\tstream >> nb;\n\tnb = nb[\"cells\"];\n\tfor (auto it = nb.begin(); it != nb.end(); ++it) {\n\t\tret.first.push_back(std::to_string((*it)[\"cell_id\"].get<uint64_t>()));\n\t\tret.second.push_back((*it)[\"source\"].get<std::string>());\n\t\t}\n\n\treturn ret;\n\t}\n"
  },
  {
    "path": "frontend/gtkmm/DiffViewer.hh",
    "content": "#pragma once\n\n#include <gtkmm.h>\n#include <gtkmm/frame.h>\n#include <string>\n#include <istream>\n\nclass DiffTextView : public Gtk::TextView {\n\tpublic:\n\t\tDiffTextView();\n\t};\n\nclass CellDiff : public Gtk::Frame {\n\tpublic:\n\t\tCellDiff(const std::string& a, const std::string& b);\n\n\tprotected:\n\t\tvoid compare(const std::string& a_str, const std::string& b_str);\n\t\tGtk::Grid grid;\n\t\tDiffTextView tv_lhs, tv_rhs;\n\t\tGtk::ScrolledWindow sw_lhs, sw_rhs;\n\t};\n\nclass DiffViewer : public Gtk::Dialog {\n\tpublic:\n\t\tDiffViewer(std::istream& a, std::istream& b, Gtk::Window& parent);\n\t\tvoid run_noblock();\n\tprotected:\n\t\tusing Cells = std::pair<std::vector<std::string>, std::vector<std::string>>;\n\n\t\tvoid populate(std::istream& a, std::istream& b);\n\t\tCells make_cells(std::istream& stream);\n\n\t\tGtk::Box box;\n\t\tGtk::ScrolledWindow  scrolled_window;\n\t\tstd::vector<CellDiff> cells;\n\t};\n"
  },
  {
    "path": "frontend/gtkmm/ImageView.cc",
    "content": "\n#include \"ImageView.hh\"\n#include <giomm/memoryinputstream.h>\n#include <glibmm/base64.h>\n\n#include <gtkmm/image.h>\n#include <gdkmm/pixbuf.h>\n#include <gdkmm/window.h>\n#include <gdkmm/general.h> // set_source_pixbuf()\n#include <cairomm/surface.h>\n#include <cairomm/context.h>\n#include <gtkmm/filechooserdialog.h>\n\n#include <iostream>\n#include <fstream>\n\nusing namespace cadabra;\n\nImageView::ImageView(double display_scale_, int logical_width_)\n\t: area(logical_width_, display_scale_)\n#ifdef USE_GTK4\n\t, Gtk::Box(Gtk::Orientation::ORIENTATION_VERTICAL)\n#endif\n\t, sizing(false)\n\t, prev_x(0)\n\t, prev_y(0)\n\t, height_at_press(0)\n\t, width_at_press(0)\n\t{\n\tarea.set_halign(Gtk::ALIGN_START);\n\tadd(area);\n\t\n\tset_events(Gdk::ENTER_NOTIFY_MASK\n\t           | Gdk::LEAVE_NOTIFY_MASK\n\t           | Gdk::BUTTON_PRESS_MASK\n\t           | Gdk::BUTTON_RELEASE_MASK\n\t           | Gdk::POINTER_MOTION_MASK);\n\n\tcontext_menu.append(item_save_as);\n\titem_save_as.set_label(\"Save as SVG...\");\n\tcontext_menu.show_all();\n\titem_save_as.signal_activate().connect(sigc::mem_fun(*this, &ImageView::on_save_as));\n\t \n\tset_name(\"ImageView\"); // to be able to style it with CSS\n\tshow_all();\n\t}\n\nImageView::~ImageView()\n\t{\n\t}\n\nvoid ImageView::on_save_as() const\n\t{\n\tGtk::FileChooserDialog dialog(\"Please enter a file name for the SVG image\",\n\t                              Gtk::FILE_CHOOSER_ACTION_SAVE);\n\n//\tdialog.set_transient_for(*this);\n\tdialog.set_do_overwrite_confirmation(true);\n\tdialog.add_button(\"_Cancel\", Gtk::RESPONSE_CANCEL);\n\tdialog.add_button(\"Select\", Gtk::RESPONSE_OK);\n\n\tint result=dialog.run();\n\n\tswitch(result) {\n\t\tcase(Gtk::RESPONSE_OK): {\n\t\t\tstd::string name = dialog.get_filename();\n\t\t\tstd::ofstream temp(name);\n\t\t\ttemp << area.decoded;\n\t\t\t}\n\t\t}\n\t}\n\nbool ImageView::on_motion_notify_event(GdkEventMotion *event)\n\t{\n\t//\tstd::cerr << event->x << \", \" << event->y << std::endl;\n\tif(sizing) {\n\t\tarea.logical_width = width_at_press  + (event->x - prev_x);\n\t\tarea.rerender(area.logical_width);\n\t\t}\n\treturn true;\n\t}\n\nbool ImageView::on_button_press_event(GdkEventButton *event)\n\t{\n\tif(event->type==GDK_BUTTON_PRESS) {\n\t\tif(event->button == 1) {\n\t\t\tsizing=true;\n\t\t\tprev_x=event->x;\n\t\t\tprev_y=event->y;\n\t\t\twidth_at_press=area.pixbuf->get_width()/area.display_scale;\n\t\t\t// std::cerr << \"width_at_press = \" << width_at_press << std::endl;\n\t\t\theight_at_press=area.pixbuf->get_height()/area.display_scale;\n\t\t\t}\n\t\telse if(event->button == 3) {\n\t\t\tcontext_menu.popup_at_pointer((GdkEvent*)event);\n\t\t\t}\n\t\t}\n\treturn true;\n\t}\n\nbool ImageView::on_button_release_event(GdkEventButton *event)\n\t{\n\tif(event->type==GDK_BUTTON_RELEASE) {\n\t\tsizing=false;\n\t\t}\n\n\treturn true;\n\t}\n\nvoid ImageView::set_image_from_base64(const std::string& b64)\n\t{\n\tarea.set_image_from_base64(b64);\n\t}\n\nvoid ImageArea::set_image_from_base64(const std::string& b64)\n\t{\n\t// The data is ok:\n\t// std::ofstream tst(\"out2.png\");\n\t// tst << Glib::Base64::decode(b64);\n\t// tst.close();\n\n\tdecoded=Glib::Base64::decode(b64);\n\tis_raster=true;\n\trerender(logical_width);\n\t}\n\nvoid ImageView::set_image_from_svg(const std::string& svg)\n\t{\n\tarea.set_image_from_svg(svg);\n\t}\n\nvoid ImageArea::set_image_from_svg(const std::string& svg)\n\t{\n\tdecoded=Glib::Base64::decode(svg);\n\tis_raster=false;\n\trerender(logical_width);\n\t}\n\nvoid ImageArea::rerender(int width)\n\t{\n\tauto str = Gio::MemoryInputStream::create();\n\tstr->add_data(decoded.c_str(), decoded.size(), nullptr);\n\n\t// Widths set here are all logical pixel widths, not device pixel widths.\n\tpixbuf = Gdk::Pixbuf::create_from_stream_at_scale(str, width * display_scale, -1, true);\n\t// std::cerr << \"creating at \" << width * area.display_scale << std::endl;\n\n\tif(!pixbuf) {\n\t\tstd::cerr << \"cadabra-client: unable to create image from data\" << std::endl;\n\t\t}\n\n\tset_size_request( pixbuf->get_width()/display_scale,\n\t\t\t\t\t\t\tpixbuf->get_height()/display_scale );\n\tqueue_resize();\n\t}\n\nImageArea::ImageArea(int logical_width_, double display_scale_)\n\t: is_raster(false), logical_width(logical_width_), display_scale(display_scale_)\n\t{\n\tset_halign(Gtk::ALIGN_CENTER);\n\tset_valign(Gtk::ALIGN_CENTER);\n\t}\n\nstd::string readFile(const std::string& filename)\n\t{\n\tstd::ifstream file(filename, std::ios::binary | std::ios::ate);\n\tif (!file) return \"\";\n   \n\tstd::string str(file.tellg(), 0);\n\tfile.seekg(0);\n\tfile.read(str.data(), str.size());\n\treturn str;\n\t}\n\nImageArea::ImageArea(int logical_width_, double display_scale_,\n\t\t\t\t\t\t\tconst std::string& filename, bool raster)\n\t: ImageArea(logical_width_, display_scale_)\n\t{\n\tis_raster = raster;\n\tdecoded = readFile(filename);\n\trerender(logical_width);\n\t}\n\nbool ImageArea::on_draw(const Cairo::RefPtr<Cairo::Context>& cr)\n\t{\n\tcr->scale(1.0/display_scale, 1.0/display_scale);\n\tGdk::Cairo::set_source_pixbuf(cr, pixbuf, 0, 0);\n\tcr->paint();\n\treturn true;\n\t}\n\n"
  },
  {
    "path": "frontend/gtkmm/ImageView.hh",
    "content": "\n#pragma once\n\n#include <gtkmm/box.h>\n#include <gtkmm/image.h>\n#include <gtkmm/menu.h>\n#ifndef USE_GTK4\n#include <gtkmm/eventbox.h>\n#endif\n#include <gtkmm/drawingarea.h>\n\nnamespace cadabra {\n\n\tclass ImageView;\n\t\n\t/// Widget which behaves as Gtk::Image, but instead uses the\n\t/// full device resolution (so images come out sharp).\n\t\n\tclass ImageArea : public Gtk::DrawingArea {\n\t\tpublic:\n\t\t\tImageArea(int logical_width, double display_scale);\n\t\t\tImageArea(int logical_width, double display_scale,\n\t\t\t\t\t\t const std::string& filename, bool raster);\n\n\t\t\tvoid set_image_from_base64(const std::string& b64);\n\t\t\tvoid set_image_from_svg(const std::string& svg);\n\n\t\t\t// Re-render the image from the raw bytes at the indicated\n\t\t\t// width (in logical pixels, which may be multiple display pixels).\n\t\t\tvoid rerender(int width);\n\t\t\t\n\t\t\tfriend ImageView;\n\t\tprotected:\n\t\t\tvirtual bool on_draw(const Cairo::RefPtr<Cairo::Context>& cr) override;\n\n\t\tprivate:\n\t\t\tGlib::RefPtr<Gdk::Pixbuf> pixbuf;\n\t\t\t\n\t\t\tstd::string decoded; // raw byte content of image\n\t\t\tbool        is_raster;\n\t\t\tdouble      display_scale;\n\t\t\tint         logical_width;\n\t};\n\t\t\t\n\n\t/// \\ingroup frontend\n\t///\n\t/// An image viewing widget.\n\n#ifdef USE_GTK4\n\tclass ImageView : public Gtk::Box {\n#else\n\tclass ImageView : public Gtk::EventBox {\n#endif\n\t\tpublic:\n\t\t\tImageView(double display_scale, int logical_width);\n\t\t\tvirtual ~ImageView();\n\t\t\t\n\t\t\tvirtual bool on_motion_notify_event(GdkEventMotion *event) override;\n\t\t\tvirtual bool on_button_press_event(GdkEventButton *event) override;\n\t\t\tvirtual bool on_button_release_event(GdkEventButton *event) override;\n\t\t\tvoid on_save_as() const;\n\t\t\t\n\t\t\tvoid set_image_from_base64(const std::string& b64);\n\t\t\tvoid set_image_from_svg(const std::string& svg);\n\n\t\tprivate:\n\t\t\tImageArea area;\n\t\t\t\n\t\t\tbool      sizing;\n\t\t\tdouble    prev_x, prev_y;\n\t\t\tint       height_at_press, width_at_press;\n\n\t\t\tGtk::Menu     context_menu;\n\t\t\tGtk::MenuItem item_save_as;\n\t};\n\t\n};\n"
  },
  {
    "path": "frontend/gtkmm/Keywords.cc",
    "content": "#include <unordered_set>\n#include \"Keywords.hh\"\n\n\nconst std::unordered_set<std::string> functions = {\n\t\"__build_class__\", \"__import__\", \"_displayhook\", \"abs\", \"all\", \"any\", \"ascii\", \n\t\"asym\", \"bin\", \"breakpoint\", \"callable\", \"canonicalise\", \"cdb2python\", \n\t\"cdb2python_string\", \"chr\", \"collect_components\", \"collect_factors\", \n\t\"collect_terms\", \"combine\", \"compile\", \"compile_package__\", \"complete\", \n\t\"create_empty_scope\", \"create_scope\", \"create_scope_from_global\", \"decompose\", \n\t\"decompose_product\", \"delattr\", \"diff\", \"dir\", \"display\", \"distribute\", \n\t\"divmod\", \"drop_weight\", \"einsteinify\", \"eliminate_kronecker\", \n\t\"eliminate_metric\", \"eliminate_vielbein\", \"epsilon_to_delta\", \"eval\", \n\t\"evaluate\", \"exec\", \"expand\", \"expand_delta\", \"expand_diracbar\", \n\t\"expand_dummies\", \"expand_power\", \"explicit_indices\", \"factor\", \"factor_in\", \n\t\"factor_out\", \"fierz\", \"flatten_sum\", \"format\", \"getattr\", \"globals\", \n\t\"hasattr\", \"hash\", \"hex\", \"id\", \"indexsort\", \"init_ipython\", \"input\", \n\t\"integrate\", \"integrate_by_parts\", \"isinstance\", \"issubclass\", \"iter\", \n\t\"join_gamma\", \"keep_terms\", \"keep_weight\", \"kernel\", \"latex\", \"len\", \"lhs\", \n\t\"locals\", \"lower_free_indices\", \"lr_tensor\", \"map_sympy\", \"max\", \"meld\", \"min\", \n\t\"next\", \"oct\", \"open\", \"ord\", \"order\", \"post_process\", \"pow\", \"print\", \n\t\"product_rule\", \"properties\", \"raise_free_indices\", \"reduce_delta\", \n\t\"remember_display_hook\", \"rename_dummies\", \"replace_match\", \"repr\", \n\t\"rewrite_indices\", \"rhs\", \"round\", \"save_history\", \"setattr\", \"simplify\", \n\t\"slot_asym\", \"slot_sym\", \"sort_product\", \"sort_spinors\", \"sort_sum\", \"sorted\", \n\t\"split_gamma\", \"split_index\", \"sqrt\", \"substitute\", \"sum\", \"sym\", \"symbols\", \n\t\"tab_dimension\", \"take_match\", \"terms\", \"tree\", \"trigsimp\", \"untrace\", \n\t\"unwrap\", \"unzoom\", \"user_config_dir\", \"user_data_dir\", \"vars\", \"vary\", \n\t\"young_project\", \"young_project_product\", \"young_project_tensor\", \"zoom\", \n};\n\nconst std::unordered_set<std::string> classes = {\n\t\"Accent\", \"AntiCommuting\", \"AntiSymmetric\", \"ArithmeticError\", \n\t\"AssertionError\", \"AttributeError\", \"BaseException\", \"BlockingIOError\", \n\t\"BrokenPipeError\", \"BufferError\", \"BytesWarning\", \"ChildProcessError\", \n\t\"Commuting\", \"CommutingAsProduct\", \"CommutingAsSum\", \"CommutingBehaviour\", \n\t\"ConnectionAbortedError\", \"ConnectionError\", \"ConnectionRefusedError\", \n\t\"ConnectionResetError\", \"Console\", \"Coordinate\", \"DAntiSymmetric\", \"Depends\", \n\t\"DependsBase\", \"DeprecationWarning\", \"Derivative\", \"Determinant\", \"Diagonal\", \n\t\"DifferentialForm\", \"DifferentialFormBase\", \"DiracBar\", \"Distributable\", \n\t\"EOFError\", \"EnvironmentError\", \"EpsilonTensor\", \"Ex\", \"ExNode\", \"Exception\", \n\t\"ExteriorDerivative\", \"FileExistsError\", \"FileNotFoundError\", \"FilledTableau\", \n\t\"FloatingPointError\", \"FutureWarning\", \"GammaMatrix\", \"GeneratorExit\", \n\t\"IOError\", \"ImaginaryI\", \"ImplicitIndex\", \"ImportError\", \"ImportWarning\", \n\t\"IndentationError\", \"IndexError\", \"IndexInherit\", \"Indices\", \"Integer\", \n\t\"InterruptedError\", \"InverseMetric\", \"InverseVielbein\", \"IsADirectoryError\", \n\t\"Kernel\", \"KeyError\", \"KeyboardInterrupt\", \"KroneckerDelta\", \"LaTeXForm\", \n\t\"LookupError\", \"Matrix\", \"MemoryError\", \"MetaPathFinder\", \"Metric\", \n\t\"ModuleNotFoundError\", \"ModuleSpec\", \"NameError\", \"NonCommuting\", \n\t\"NotADirectoryError\", \"NotImplementedError\", \"NumericalFlat\", \"OSError\", \n\t\"OverflowError\", \"PackageCompiler\", \"PartialDerivative\", \"PathFinder\", \n\t\"PendingDeprecationWarning\", \"PermissionError\", \"ProcessLookupError\", \n\t\"ProgressMonitor\", \"Property\", \"RecursionError\", \"ReferenceError\", \n\t\"ResourceWarning\", \"RiemannTensor\", \"RuntimeError\", \"RuntimeWarning\", \n\t\"SatisfiesBianchi\", \"SelfAntiCommuting\", \"SelfCommuting\", \n\t\"SelfCommutingBehaviour\", \"SelfNonCommuting\", \"Server\", \"SortOrder\", \n\t\"SourceFileLoader\", \"Spinor\", \"StopAsyncIteration\", \"StopIteration\", \n\t\"Stopwatch\", \"Symbol\", \"Symmetric\", \"SympyBridge\", \"SyntaxError\", \n\t\"SyntaxWarning\", \"SystemError\", \"SystemExit\", \"TabError\", \"Tableau\", \n\t\"TableauBase\", \"TableauInherit\", \"TableauObserver\", \"TableauSymmetry\", \n\t\"TimeoutError\", \"Total\", \"Trace\", \"Traceless\", \"TypeError\", \n\t\"UnboundLocalError\", \"UnicodeDecodeError\", \"UnicodeEncodeError\", \n\t\"UnicodeError\", \"UnicodeTranslateError\", \"UnicodeWarning\", \"UserWarning\", \n\t\"ValueError\", \"Vielbein\", \"Warning\", \"Weight\", \"WeightBase\", \"WeightInherit\", \n\t\"WeylTensor\", \"WindowsError\", \"ZeroDivisionError\", \"__loader__\", \"bool\", \n\t\"bytearray\", \"bytes\", \"classmethod\", \"complex\", \"cos\", \"dict\", \"enumerate\", \n\t\"filter\", \"float\", \"frozenset\", \"int\", \"labelled_property\", \"list\", \n\t\"list_property\", \"map\", \"match_t\", \"memoryview\", \"object\", \"parent_rel_t\", \n\t\"property\", \"range\", \"result_t\", \"reversed\", \"sMatrix\", \"scalar_backend_t\", \n\t\"set\", \"sin\", \"slice\", \"staticmethod\", \"str\", \"super\", \"tan\", \"tuple\", \"type\", \n\t\"unicode\", \"warn_t\", \"zip\", \n};\n\nconst std::unordered_set<std::string> keywords = {\n\t\"False\", \"None\", \"True\", \"and\", \"as\", \"assert\", \"async\", \"await\", \"break\", \n\t\"class\", \"continue\", \"def\", \"del\", \"elif\", \"else\", \"except\", \"finally\", \"for\", \n\t\"from\", \"global\", \"if\", \"import\", \"in\", \"is\", \"lambda\", \"nonlocal\", \"not\", \n\t\"or\", \"pass\", \"raise\", \"return\", \"try\", \"while\", \"with\", \"yield\", \n};\n\nconst char* get_keyword_group(const std::string& name)\n{\n\tif (functions.find(name) != functions.end())\n\t\treturn \"function\";\n\tif (classes.find(name) != classes.end())\n\t\treturn \"class\";\n\tif (keywords.find(name) != keywords.end())\n\t\treturn \"keyword\";\n\treturn nullptr;\n}\n"
  },
  {
    "path": "frontend/gtkmm/Keywords.hh",
    "content": "#pragma once\n\n#include <string>\n\n// Returns the group name belongs to, or nullptr if not found\nconst char* get_keyword_group(const std::string& name);\n"
  },
  {
    "path": "frontend/gtkmm/NotebookCanvas.cc",
    "content": "\n#include \"NotebookCanvas.hh\"\n#include \"NotebookWindow.hh\"\n#include <gtkmm/box.h>\n#include <iostream>\n\nusing namespace cadabra;\n\nNotebookCanvas::NotebookCanvas()\n\t: Gtk::Paned(Gtk::Orientation::ORIENTATION_VERTICAL)\n\t, scroller(scroll.get_vadjustment())\n\t{\n\t// Pack the scroll widget with all document cells into the top pane.\n\tpack1(scroll, true, true);\n\tscroll.set_policy(Gtk::POLICY_ALWAYS, Gtk::POLICY_ALWAYS);\n\tscroll.set_border_width(1);\n\n\t// Do NOT do the following. This will create areas at the top\n\t// and bottom where the content of the scrolledwindow is\n\t// covered with white (except when totally at the top or\n\t// bottom of the content).\n\t// scroll.override_background_color(Gdk::RGBA(\"white\"));\n\n\t}\n\nNotebookCanvas::~NotebookCanvas()\n\t{\n\t}\n\nvoid NotebookCanvas::refresh_all()\n\t{\n\tauto it=visualcells.begin();\n\twhile(it!=visualcells.end()) {\n\t\tauto ct=it->first->cell_type;\n\t\tif(ct==DataCell::CellType::output || ct==DataCell::CellType::verbatim || ct==DataCell::CellType::latex_view) {\n\t\t\tit->second.outbox->update_image();\n\t\t\tit->second.outbox->queue_resize();\n\t\t\t}\n\t\t++it;\n\t\t}\n\t}\n\nvoid NotebookCanvas::connect_scroll_listener()\n\t{\n\t// Ensure that if the content of the ScrolledWindow is scrolled, we\n\t// immediately stop any scrolling that is still in progress (using\n\t// the smooth scroller).\n\n\t// Scrollbar drag.\n\tscroll.get_vscrollbar()->signal_change_value().connect(\n\t\t[this](Gtk::ScrollType, double) {\n\t\tscroller.stop();\n\t\tscroll_event();\n\t\treturn false;\n\t\t});\n\n\t// Catch mousewheel / trackpad scrolls.\n\tif (auto viewport = dynamic_cast<Gtk::Viewport*>(scroll.get_child())) {\n\t\tviewport->add_events(Gdk::SCROLL_MASK | Gdk::SMOOTH_SCROLL_MASK);\n\t\tviewport->signal_scroll_event().connect(\n\t\t\t[this](GdkEventScroll* event) -> bool {\n\t\t\tscroller.stop();\n\t\t\tscroll_event();\n\t\t\treturn false;\n\t\t\t});\n\t\t}\n\n\t}\n"
  },
  {
    "path": "frontend/gtkmm/NotebookCanvas.hh",
    "content": "\n#pragma once\n\n#include <map>\n#include <gtkmm/paned.h>\n#include <gtkmm/scrolledwindow.h>\n#include <gtkmm/separator.h>\n#ifndef USE_GTK4\n#include <gtkmm/eventbox.h>\n#endif\n#include <glibmm/dispatcher.h>\n\n#include \"VisualCell.hh\"\n\n/// NotebookCanvas is an actual view on the document. There can be any\n/// number of them active inside the NotebookWindow. Each DataCell in the\n/// notebook document has a corresponding VisualCell in the NotebookCanvas,\n/// which gets added by NotebookCanvas::add_cell.\n///\n/// Cells which contain child cells (e.g. CodeInput, which can contain\n/// child cells corresponding to the TeXView output) will also be\n/// hierarchically ordered in the visual tree. That is, any visual cell\n/// which can contain a child cell will have it stored inside a Gtk::Box\n/// inside the visual cell. Removing any cell will therefore also\n/// immediately remove the child cells.\n\nnamespace cadabra {\n\n\tclass NotebookWindow;\n\n\tclass SmoothScroller {\n\t\tprivate:\n\t\t\tGlib::RefPtr<Gtk::Adjustment> adjustment_;\n\t\t\tdouble target_value_;\n\t\t\tdouble start_value_;\n\t\t\tdouble duration_ms_;\n\t\t\tdouble elapsed_ms_;\n\t\t\tsigc::connection timeout_connection_;\n\t\t\n\t\t\tstatic constexpr double FRAME_RATE_MS = 16.67; // ~60 FPS\n\t\t\n\t\t\tbool on_timeout()\n\t\t\t\t{\n\t\t\t\telapsed_ms_ += FRAME_RATE_MS;\n\t\t\t\n\t\t\t\tif (elapsed_ms_ >= duration_ms_) {\n\t\t\t\t\tadjustment_->set_value(target_value_);\n\t\t\t\t\ttimeout_connection_.disconnect();\n\t\t\t\t\treturn false;\n\t\t\t\t\t}\n\t\t\t\n\t\t\t\t// Use easing function (ease-out cubic) for smooth animation\n\t\t\t\tdouble progress = elapsed_ms_ / duration_ms_;\n\t\t\t\tdouble cubic = 1 - std::pow(1 - progress, 3);\n\t\t\t\n\t\t\t\tdouble current = start_value_ + \n\t\t\t\t\t(target_value_ - start_value_) * cubic;\n\t\t\t\n\t\t\t\tadjustment_->set_value(current);\n\t\t\t\treturn true;\n\t\t\t\t}\n\t\t\n\t\tpublic:\n\t\t\tSmoothScroller(Glib::RefPtr<Gtk::Adjustment> adj) \n\t\t\t\t: adjustment_(adj)\n\t\t\t\t, elapsed_ms_(0)\n\t\t\t\t, duration_ms_(400) // 400ms default duration\n\t\t\t\t{}\n\t\t\n\t\t\tvoid scroll_to(double target)\n\t\t\t\t{\n\t\t\t\tif(target_value_==target && timeout_connection_.connected())\n\t\t\t\t\treturn;\n\t\t\t\t\n\t\t\t\ttimeout_connection_.disconnect(); // Stop any existing animation\n\t\t\t\n\t\t\t\ttarget_value_ = target;\n\t\t\t\tstart_value_ = adjustment_->get_value();\n\t\t\t\telapsed_ms_ = 0;\n\t\t\t\n\t\t\t\t// Start the animation loop\n\t\t\t\ttimeout_connection_ = Glib::signal_timeout().connect(\n\t\t\t\t\tsigc::mem_fun(*this, &SmoothScroller::on_timeout),\n\t\t\t\t\tFRAME_RATE_MS\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t  );\n\t\t\t\t}\n\n\t\t\tvoid stop() {\n\t\t\ttimeout_connection_.disconnect();\n\t\t\t}\n\t\t\t\n\t\t\tvoid set_duration(double ms) {\n\t\t\tduration_ms_ = ms;\n\t\t\t}\n\t};\n\n\tclass NotebookCanvas : public Gtk::Paned {\n\t\tpublic:\n\t\t\tNotebookCanvas();\n\t\t\t~NotebookCanvas();\n\n\t\t\tstd::map<DataCell *, VisualCell> visualcells;\n\n\t\t\tGtk::ScrolledWindow       scroll;\n\t\t\tGtk::Separator            bottomline;\n\t\t\tSmoothScroller            scroller;\n\n\t\t\t/// Whenever a user-driven scroll happens, this\n\t\t\t/// event will fire. The canvas will make sure that\n\t\t\t/// any scroll animation will stop, but NotebookWindow\n\t\t\t/// may still want to stop any cell following.\n\t\t\tsigc::signal0<bool>       scroll_event;\n\t\t\t\n\t\t\tvoid refresh_all();\n\n\t\t\t/// Connect a listener to the scroll event on the viewport; this\n\t\t\t/// needs to be called after the first (and only) widget has been\n\t\t\t/// added to the canvas.\n\t\t\tvoid connect_scroll_listener();\n\t\t};\n\n\t}\n"
  },
  {
    "path": "frontend/gtkmm/NotebookWindow.cc",
    "content": "\n#include <iostream>\n#include \"Actions.hh\"\n#include \"Functional.hh\"\n#include \"Cadabra.hh\"\n#include \"Config.hh\"\n#include \"InstallPrefix.hh\"\n#include \"NotebookWindow.hh\"\n#include \"DataCell.hh\"\n#include \"CdbPython.hh\"\n\n#include <gtkmm/box.h>\n#include <gtkmm/filechooserdialog.h>\n#include <gtkmm/messagedialog.h>\n#include <gtkmm/aboutdialog.h>\n#include <gtkmm/radioaction.h>\n#include <gtkmm/scrollbar.h>\n#include <giomm/actiongroup.h>\n#include <fstream>\n#include <glib/gstdio.h>\n\n#include <gtkmm/entry.h>\n#if GTKMM_MINOR_VERSION < 10\n#include <gtkmm/main.h>\n#endif\n#include \"Snoop.hh\"\n#include \"ChooseColoursDialog.hh\"\n#include \"SelectFileDialog.hh\"\n#include \"process.hpp\"\n#include <internal/string_tools.h>\n\n// For MicroTeX\n#include \"cairo/graphic_cairo.h\"\n#include \"microtex.h\"\n#include <pangomm/init.h>\n\n#include <nlohmann/json.hpp>\n\n// Use png icons on apple to avoid issues with broken librsvg installations.\n#if defined __APPLE__ || defined APPIMAGE_MODE\n #define ICONEXT \".png\"\n#else\n #define ICONEXT \".svg\"\n#endif\n\nusing namespace cadabra;\n\n// #define DEBUG 1\n\nNotebookWindow::NotebookWindow(Cadabra *c, bool ro, std::string geometry, std::string window_title)\n\t: Gtk::ApplicationWindow()\n\t, DocumentThread(this)\n\t, cdbapp(c)\n\t, topbox(Gtk::Orientation::ORIENTATION_VERTICAL)\n\t, toolbar(Gtk::Orientation::ORIENTATION_HORIZONTAL)\n\t, supermainbox(Gtk::Orientation::ORIENTATION_HORIZONTAL)\n\t, mainbox(Gtk::Orientation::ORIENTATION_VERTICAL)\n\t, search_hbox(Gtk::Orientation::ORIENTATION_HORIZONTAL)\n\t, statusbarbox(Gtk::Orientation::ORIENTATION_HORIZONTAL)\n\t, search_case_insensitive(\"Case insensitive\", true)\n\t, console(sigc::mem_fun(this, &NotebookWindow::interactive_execute))\n\t, current_canvas(0)\n\t, kernel_spinner_status(false)\n\t, progress_frac(0)\n\t, status_line(-1)\n\t, status_col(-1)\n\t, title_prefix(window_title)\n\t, geometry_string(geometry)\n\t, modified(false)\n\t, read_only(ro)\n\t, crash_window_hidden(true)\n\t, last_configure_width(0)\n\t, tex_running(false), tex_need_width(0)\n\t, last_find_location(doc.end(), std::string::npos)\n\t, is_configured(false)\n\t, run_all_after_restart(false)\n\t{\n\t}\n\nvoid NotebookWindow::on_realize()\n\t{\n\tGtk::ApplicationWindow::on_realize();\n\n\t// Connect the dispatcher.\n\tdispatcher.connect(sigc::mem_fun(*this, &NotebookWindow::process_todo_queue));\n\tdispatch_refresh.connect(sigc::mem_fun(*this, &NotebookWindow::refresh_after_tex_engine_run));\n\tdispatch_tex_error.connect(sigc::mem_fun(*this, &NotebookWindow::handle_thread_tex_error));\n\tdispatch_update_status.connect(sigc::mem_fun(*this, &NotebookWindow::update_status));\n\n\t// Set the window icon.\n\tset_default_icon_name(\"cadabra2-gtk\");\n\tset_icon_name(\"cadabra2-gtk\");\n\n\t// Query high-dpi settings. For all systems we can probe the\n\t// HiDPI scale, and for some window managers we also probe the\n\t// text scale factor.\n\tauto gdk_window = get_window();\n\tauto display = Gdk::Display::get_default();\n\tif(!display)\n\t\tthrow std::logic_error(\"NotebookWindow::on_realize: cannot get default display.\");\n\t\n\tauto screen = Gdk::Screen::get_default();\n\tif(!screen)\n\t\tthrow std::logic_error(\"NotebookWindow::on_realize: cannot get default screen.\");\n\t\n\tauto monitor = display->get_monitor_at_window(gdk_window);\n\tif(!monitor)\n\t\tthrow std::logic_error(\"NotebookWindow::on_realize: cannot get monitor at window.\");\n\t\n\tGdk::Rectangle monitor_geometry;\n\tmonitor->get_geometry(monitor_geometry);\n\t\n\tscale = gdk_window->get_scale_factor();\n\tdisplay_scale = scale;\n//\tstd::cerr << \"Monitor scale factor = \" << display_scale << std::endl;\n#ifndef __APPLE__\n\t// FIXME: this does not work for ssh sessions with ForwardX11.\n\tconst char *ds = std::getenv(\"DESKTOP_SESSION\");\n\tif(ds) {\n\t\tsettings = Gio::Settings::create((strcmp(ds, \"cinnamon\") == 0) ? \"org.cinnamon.desktop.interface\" : \"org.gnome.desktop.interface\");\n\t\tscale *= settings->get_double(\"text-scaling-factor\");\n\t\t}\n#endif\n\n\tengine.set_scale(scale, display_scale);\n\tengine.set_font_size(12+(prefs.font_step*2));\n\n\t// For MicroTeX\n//\tPango::init(); Gtk::Main supposedly calls this for us.\n\tstd::vector<std::string> font_paths;\n//\tfont_paths.push_back(install_prefix()+\"/share/cadabra2/microtex/newcm/\");\t\n\tfont_paths.push_back(install_prefix()+\"/share/cadabra2/microtex/lm-math/\");\t\n//\tfont_paths.push_back(install_prefix()+\"/share/cadabra2/microtex/xits/\");\n//\tfont_paths.push_back(install_prefix()+\"/share/cadabra2/microtex/cm/\");\t\n\n\t// Need to re-convert fonts setting the correct\n\n//\tfor(const std::string& path: font_paths)\n//\t\tstd::cerr << \"Will search \" << path << \" for fonts.\" << std::endl;\n\t\n\tmicrotex::MicroTeX::setDefaultMathFont(\"LatinModernMath-Regular\");\n\tauto auto_init = microtex::InitFontSenseAuto();\n//\tstd::cerr << \"microtex::InitFontSenseAuto done\" << std::endl;\n\tauto_init.search_paths=font_paths;\n\tmicrotex::Init init = auto_init;\n\tmicrotex::MicroTeX::init(init);\n\tmicrotex::MicroTeX::setDefaultMathFont(\"LatinModernMath-Regular\");\n\n   // Add all the CMR fonts (as one family). See the url below for\n\t// a list of all fonts with their standard names:\n\t//\n\t// https://usemodify.com/fonts/computer-modern/\n\t\n\tconst microtex::FontSrcFile font_rm\n\t\t= microtex::FontSrcFile(install_prefix()+\"/share/cadabra2/microtex/cm/cmunrm.clm1\",\n\t\t\t\t\t\t\t\t\t\tinstall_prefix()+\"/share/cadabra2/microtex/cm/cmunrm.otf\");\n\tconst microtex::FontSrcFile font_tt\n\t\t= microtex::FontSrcFile(install_prefix()+\"/share/cadabra2/microtex/cm/cmuntt.clm1\",\n\t\t\t\t\t\t\t\t\t\tinstall_prefix()+\"/share/cadabra2/microtex/cm/cmuntt.otf\");\n\tconst microtex::FontSrcFile font_tt_bf\n\t\t= microtex::FontSrcFile(install_prefix()+\"/share/cadabra2/microtex/cm/cmuntb.clm1\",\n\t\t\t\t\t\t\t\t\t\tinstall_prefix()+\"/share/cadabra2/microtex/cm/cmuntb.otf\");\n\tconst microtex::FontSrcFile font_bf\n\t\t= microtex::FontSrcFile(install_prefix()+\"/share/cadabra2/microtex/cm/cmunbx.clm1\",\n\t\t\t\t\t\t\t\t\t\tinstall_prefix()+\"/share/cadabra2/microtex/cm/cmunbx.otf\");\n\tconst microtex::FontSrcFile font_it\n\t\t= microtex::FontSrcFile(install_prefix()+\"/share/cadabra2/microtex/cm/cmunti.clm1\",\n\t\t\t\t\t\t\t\t\t\tinstall_prefix()+\"/share/cadabra2/microtex/cm/cmunti.otf\");\n\tconst microtex::FontSrcFile font_it_bf\n\t\t= microtex::FontSrcFile(install_prefix()+\"/share/cadabra2/microtex/cm/cmunbi.clm1\",\n\t\t\t\t\t\t\t\t\t\tinstall_prefix()+\"/share/cadabra2/microtex/cm/cmunbi.otf\");\n\n\tmicrotex::MicroTeX::addFont(font_rm,    \"Computer Modern\");\n\tmicrotex::MicroTeX::addFont(font_tt,    \"Computer Modern\");\n\tmicrotex::MicroTeX::addFont(font_tt_bf, \"Computer Modern\"); // FIXME: incorrect\n\tmicrotex::MicroTeX::addFont(font_bf,    \"Computer Modern\");\n\tmicrotex::MicroTeX::addFont(font_it,    \"Computer Modern\");\n\tmicrotex::MicroTeX::addFont(font_it_bf, \"Computer Modern\");\n\t\n\tmicrotex::MicroTeX::setDefaultMainFont(\"Computer Modern\");\n\tmicrotex::PlatformFactory::registerFactory(\"gtk\", std::make_unique<microtex::PlatformFactory_cairo>());\n\tmicrotex::PlatformFactory::activate(\"gtk\");\n\n\t// std::cerr << \"MicroTeX::hasGlyphPathRender = \" << microtex::MicroTeX::hasGlyphPathRender() << std::endl;\n\t// std::cerr << \"Math fonts:\" << std::endl;\n\t// for(const auto& n: microtex::MicroTeX::mathFontNames()) {\n\t// \tstd::cerr << \"   \" << n << std::endl;\n\t// \t}\n\t// std::cerr << \"Main fonts:\" << std::endl;\n\t// for(const auto& n: microtex::MicroTeX::mainFontFamilies()) {\n\t// \tstd::cerr << \"   \" << n << std::endl;\n\t// \t}\n\t\n#ifndef __APPLE__\n\tif(ds) {\n\t\tsettings->signal_changed().connect(\n\t\t   sigc::mem_fun(*this, &NotebookWindow::on_text_scaling_factor_changed));\n\t\t}\n#endif\n\n\n\t// Setup styling. Note that 'margin-left' and so on do not work; you need\n\t// to use 'padding'. However, 'padding-top' fails because it does not make the\n\t// widget larger enough... So we still do that with set_margin_top(...).\n\tcss_provider = Gtk::CssProvider::create();\n\t// padding-left: 20px; does not work on some versions of gtk, so we use margin in CodeInput\n\t// We use CSS selectors for old-style and new-style (post 3.20) simultaneously.\n\t// Run program with 'GTK_DEBUG=interactive' environment variable and press Ctrl-Shift-D\n\t// to inspect.\n\tload_css();\n\n\t//\tauto screen = Gdk::Screen::get_default();\n\t//\tstd::cerr << \"cadabra-client: scale = \" << screen->get_monitor_scale_factor(0) << std::endl;\n\tGtk::StyleContext::add_provider_for_screen(screen, css_provider, GTK_STYLE_PROVIDER_PRIORITY_APPLICATION);\n\n\t// Setup menu.\n\tactiongroup = Gio::SimpleActionGroup::create();\n\n\t// File menu actions.\n\tactiongroup->add_action( \"New\",                   sigc::mem_fun(*this, &NotebookWindow::on_file_new) );\n\tactiongroup->add_action( \"Open\",                  sigc::mem_fun(*this, &NotebookWindow::on_file_open) );\n\tactiongroup->add_action( \"Close\",                 sigc::mem_fun(*this, &NotebookWindow::on_file_close) );\n\tactiongroup->add_action( \"Save\",                  sigc::mem_fun(*this, &NotebookWindow::on_file_save) );\n\tactiongroup->add_action( \"SaveAs\",                sigc::mem_fun(*this, &NotebookWindow::on_file_save_as) );\n\tactiongroup->add_action( \"ExportAsJupyter\",       sigc::mem_fun(*this, &NotebookWindow::on_file_save_as_jupyter) );\n\tactiongroup->add_action( \"ExportHtml\",            sigc::mem_fun(*this, &NotebookWindow::on_file_export_html) );\n\tactiongroup->add_action( \"ExportHtmlSegment\",     sigc::mem_fun(*this, &NotebookWindow::on_file_export_html_segment) );\n\tactiongroup->add_action( \"ExportLaTeX\",           sigc::mem_fun(*this, &NotebookWindow::on_file_export_latex) );\n\tactiongroup->add_action( \"ExportPython\",          sigc::mem_fun(*this, &NotebookWindow::on_file_export_python) );\n\tactiongroup->add_action( \"Quit\",                  sigc::mem_fun(*this, &NotebookWindow::on_file_quit) );\n\n\t// Edit menu actions for undo/redo; enabling/disabling of the above\n\t// is done in update_title.\n\taction_undo = Gio::SimpleAction::create(\"EditUndo\");\n\taction_redo = Gio::SimpleAction::create(\"EditRedo\");\t\n\taction_undo->signal_activate().connect( sigc::mem_fun(*this, &NotebookWindow::on_edit_undo) );\n\taction_redo->signal_activate().connect( sigc::mem_fun(*this, &NotebookWindow::on_edit_redo) );\n\tactiongroup->add_action( action_undo );\n\tactiongroup->add_action( action_redo );\n\n\t// Edit menu actions for copy/paste.\n\taction_copy = Gio::SimpleAction::create(\"EditCopy\");\n\taction_copy->signal_activate().connect( sigc::mem_fun(*this, &NotebookWindow::on_edit_copy) );\n\taction_copy->set_enabled(false);\n\tactiongroup->add_action( action_copy );\n\tactiongroup->add_action( \"EditPaste\",             sigc::mem_fun(*this, &NotebookWindow::on_edit_paste) );\n\tactiongroup->add_action( \"EditInsertAbove\",       sigc::mem_fun(*this, &NotebookWindow::on_edit_insert_above) );\n\tactiongroup->add_action( \"EditInsertBelow\",       sigc::mem_fun(*this, &NotebookWindow::on_edit_insert_below) );\n\tactiongroup->add_action( \"EditDelete\",            sigc::mem_fun(*this, &NotebookWindow::on_edit_delete) );\n\tactiongroup->add_action( \"EditSplit\",             sigc::mem_fun(*this, &NotebookWindow::on_edit_split) );\n\tactiongroup->add_action( \"EditFind\",              sigc::mem_fun(*this, &NotebookWindow::on_edit_find) );\n\tactiongroup->add_action( \"EditFindNext\",          sigc::mem_fun(*this, &NotebookWindow::on_search_text_changed) );\n\tactiongroup->add_action( \"EditMakeCellTeX\",       sigc::mem_fun(*this, &NotebookWindow::on_edit_cell_is_latex) );\n\tactiongroup->add_action( \"EditMakeCellPython\",    sigc::mem_fun(*this, &NotebookWindow::on_edit_cell_is_python) );\t\n\tactiongroup->add_action( \"EditIgnoreCellOnImport\",sigc::mem_fun(*this, &NotebookWindow::on_ignore_cell_on_import) );\t\n\taction_auto_close_latex = Gio::SimpleAction::create_bool(\"AutoCloseLaTeX\", prefs.auto_close_latex);\n\taction_auto_close_latex->signal_activate().connect( sigc::mem_fun(*this, &NotebookWindow::on_prefs_auto_close_latex) );\n\tactiongroup->add_action(action_auto_close_latex);\n\n\taction_hide_input_cells = Gio::SimpleAction::create_bool(\"HideInputCells\", doc.hide_input_cells);\n\taction_hide_input_cells->signal_activate().connect( sigc::mem_fun(*this, &NotebookWindow::on_prefs_hide_input_cells) );\n\tactiongroup->add_action(action_hide_input_cells);\n\n\t// View menu actions.\n\tactiongroup->add_action( \"ViewSplit\",             sigc::mem_fun(*this, &NotebookWindow::on_view_split) );\n\taction_view_close = Gio::SimpleAction::create(\"ViewClose\");\n\taction_view_close->signal_activate().connect( sigc::mem_fun(*this, &NotebookWindow::on_view_close) );\t\n\tactiongroup->add_action( action_view_close );\n\t\n\taction_fontsize  = actiongroup->add_action_radio_integer( \"FontSize\",\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t sigc::mem_fun(*this, &NotebookWindow::on_prefs_font_size),\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t prefs.font_step );\t\n\taction_highlight = actiongroup->add_action_radio_integer( \"HighlightSyntax\",\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t sigc::mem_fun(*this, &NotebookWindow::on_prefs_highlight_syntax),\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t prefs.highlight );\t\n\taction_microtex = actiongroup->add_action_radio_integer( \"MicroTeX\",\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t sigc::mem_fun(*this, &NotebookWindow::on_prefs_microtex),\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t prefs.microtex );\t\n\tactiongroup->add_action( \"HighlightChoose\",       sigc::mem_fun(*this, &NotebookWindow::on_prefs_choose_colours) );\t\t\n\tactiongroup->add_action( \"ViewUseDefaultSettings\",sigc::mem_fun(*this, &NotebookWindow::on_prefs_use_defaults) );\t\t\n\n\t// Evaluate menu actions.\n\tactiongroup->add_action( \"EvaluateCell\",          sigc::mem_fun(*this, &NotebookWindow::on_run_cell) );\n\tactiongroup->add_action( \"EvaluateAll\",           sigc::mem_fun(*this, &NotebookWindow::run_all_cells) );\t\t\n\tactiongroup->add_action( \"EvaluateToCursor\",      sigc::mem_fun(*this, &NotebookWindow::on_run_runtocursor) );\t\t\n\taction_stop = actiongroup->add_action( \"EvaluateStop\",  sigc::mem_fun(*this, &NotebookWindow::on_run_stop) );\n\n\t// Kernel menu actions.\n\tactiongroup->add_action( \"KernelRestart\",         sigc::mem_fun(*this, &NotebookWindow::on_kernel_restart) );\t\t\t\n\tactiongroup->add_action( \"KernelRestartRun\",      sigc::mem_fun(*this, &NotebookWindow::on_kernel_restart_and_run_all) );\n\t\n\t// Tools menu actions.\n\tactiongroup->add_action( \"CompareFile\",           sigc::mem_fun(*this, &NotebookWindow::compare_to_file) );\n\tactiongroup->add_action( \"CompareGitLatest\",      sigc::mem_fun(*this, &NotebookWindow::compare_git_latest) );\n\tactiongroup->add_action( \"CompareGitChoose\",      sigc::mem_fun(*this, &NotebookWindow::compare_git_choose) );\n\tactiongroup->add_action( \"CompareGitSpecific\",    sigc::mem_fun(*this, &NotebookWindow::compare_git_specific) );\n\tactiongroup->add_action( \"CompareGitSelect\",      sigc::mem_fun(*this, &NotebookWindow::select_git_path) );\n\taction_console = actiongroup->add_action_radio_integer( \"Console\", sigc::mem_fun(*this, &NotebookWindow::on_prefs_set_cv), 0 );\n\tactiongroup->add_action( \"ToolsOptions\",          sigc::mem_fun(*this, &NotebookWindow::on_tools_options) );\n\tactiongroup->add_action( \"ToolsClearCache\",       sigc::mem_fun(*this, &NotebookWindow::on_tools_clear_cache) );\t\n\t\n   // Help menu actions.\n\tactiongroup->add_action( \"HelpAbout\",             sigc::mem_fun(*this, &NotebookWindow::on_help_about) );\n\tactiongroup->add_action( \"HelpContext\",           sigc::mem_fun(*this, &NotebookWindow::on_help) );\n\taction_register = actiongroup->add_action( \"HelpRegister\",  sigc::mem_fun(*this, &NotebookWindow::on_help_register) );\n\taction_register->set_enabled(!prefs.is_registered);\n\n\tinsert_action_group(\"cdb\",  actiongroup);\n\n\t// Set shortcuts for actions.\n\tcdbapp->set_accel_for_action(\"cdb.New\",                    \"<Primary>N\");\n\tcdbapp->set_accel_for_action(\"cdb.Open\",                   \"<Primary>O\");\n\tcdbapp->set_accel_for_action(\"cdb.Close\",                  \"<Primary>W\");\n\tcdbapp->set_accel_for_action(\"cdb.Save\",                   \"<Primary>S\");\n\tcdbapp->set_accel_for_action(\"cdb.Quit\",                   \"<Primary>Q\");\n\tcdbapp->set_accel_for_action(\"cdb.EditUndo\",               \"<Primary>Z\");\n\tcdbapp->set_accel_for_action(\"cdb.EditRedo\",               \"<Primary>Y\");\n\tcdbapp->set_accel_for_action(\"cdb.EditCopy\",               \"<Primary>C\");\n\tcdbapp->set_accel_for_action(\"cdb.EditPaste\",              \"<Primary>V\");\n\tcdbapp->set_accel_for_action(\"cdb.EditInsertAbove\",        \"<alt>Up\");\n\tcdbapp->set_accel_for_action(\"cdb.EditInsertBelow\",        \"<alt>Down\");\n\tcdbapp->set_accel_for_action(\"cdb.EditDelete\",             \"<ctrl>Delete\");\n\tcdbapp->set_accel_for_action(\"cdb.EditFind\",               \"<control>F\");\n\tcdbapp->set_accel_for_action(\"cdb.EditFindNext\",           \"<control>G\");\n\tcdbapp->set_accel_for_action(\"cdb.EditMakeCellTeX\",        \"<control><shift>L\");\n\tcdbapp->set_accel_for_action(\"cdb.EditMakeCellPython\",     \"<control><shift>P\");\n\tcdbapp->set_accel_for_action(\"cdb.EditIgnoreCellOnImport\", \"<control><shift>I\");\n\tcdbapp->set_accel_for_action(\"cdb.EditSplit\",              \"<control>Return\");\n\tcdbapp->set_accel_for_action(\"cdb.EvaluateCell\",           \"<shift>Return\");\n\tcdbapp->set_accel_for_action(\"cdb.KernelRestart\",          \"<control><alt>R\");\n\tcdbapp->set_accel_for_action(\"cdb.HelpContext\",            \"F1\");\n\n\t// Menu and toolbar layout.\n\tuimanager = Gtk::Builder::create();\n\tGlib::ustring ui_info=\"<interface></interface>\";\n\n\tif(!read_only) {\n\t\tui_info =\n\t   \"<interface>\"\n\t   \"  <menu id='MenuBar'>\"\n\t\t\"    <submenu>\"\n\t   \"      <attribute name='label'>File</attribute>\"\n\t\t\"      <section>\"\n\t   \"        <item>\"\n\t\t\"          <attribute name='label'>New</attribute>\"\n\t\t\"          <attribute name='action'>cdb.New</attribute>\"\n\t\t\"        </item>\"\n\t   \"        <item>\"\n\t\t\"          <attribute name='label'>Open</attribute>\"\n\t\t\"          <attribute name='action'>cdb.Open</attribute>\"\n\t\t\"        </item>\"\n\t   \"        <item>\"\n\t\t\"          <attribute name='label'>Close</attribute>\"\n\t\t\"          <attribute name='action'>cdb.Close</attribute>\"\n\t\t\"        </item>\"\n\t\t\"      </section>\"\n\t\t\"      <section>\"\n\t   \"        <item>\"\n\t\t\"          <attribute name='label'>Save</attribute>\"\n\t\t\"          <attribute name='action'>cdb.Save</attribute>\"\n\t\t\"        </item>\"\n\t   \"        <item>\"\n\t\t\"          <attribute name='label'>Save as...</attribute>\"\n\t\t\"          <attribute name='action'>cdb.SaveAs</attribute>\"\n\t\t\"        </item>\"\n\t   \"        <item>\"\n\t\t\"          <attribute name='label'>Export as Jupyter notebook</attribute>\"\n\t\t\"          <attribute name='action'>cdb.ExportAsJupyter</attribute>\"\n\t\t\"        </item>\"\n\t   \"        <item>\"\n\t\t\"          <attribute name='label'>Export as HTML</attribute>\"\n\t\t\"          <attribute name='action'>cdb.ExportHtml</attribute>\"\n\t\t\"        </item>\"\n\t   \"        <item>\"\n\t\t\"          <attribute name='label'>Export as HTML segment</attribute>\"\n\t\t\"          <attribute name='action'>cdb.ExportHtmlSegment</attribute>\"\n\t\t\"        </item>\"\n\t   \"        <item>\"\n\t\t\"          <attribute name='label'>Export as LaTex</attribute>\"\n\t\t\"          <attribute name='action'>cdb.ExportLaTeX</attribute>\"\n\t\t\"        </item>\"\n\t   \"        <item>\"\n\t\t\"          <attribute name='label'>Export as Python</attribute>\"\n\t\t\"          <attribute name='action'>cdb.ExportPython</attribute>\"\n\t\t\"        </item>\"\n\t\t\"      </section>\"\n\t\t\"      <section>\"\n\t   \"        <item>\"\n\t\t\"          <attribute name='label'>Quit</attribute>\"\n\t\t\"          <attribute name='action'>cdb.Quit</attribute>\"\n\t\t\"        </item>\"\n\t\t\"      </section>\"\n\t\t\"    </submenu>\"\n\t\t\"    <submenu>\"\n\t   \"      <attribute name='label'>Cell</attribute>\"\n\t\t\"      <section>\"\n\t   \"        <item>\"\n\t\t\"          <attribute name='label'>Insert above</attribute>\"\n\t\t\"          <attribute name='action'>cdb.EditInsertAbove</attribute>\"\n\t\t\"        </item>\"\n\t   \"        <item>\"\n\t\t\"          <attribute name='label'>Insert below</attribute>\"\n\t\t\"          <attribute name='action'>cdb.EditInsertBelow</attribute>\"\n\t\t\"        </item>\"\n\t   \"        <item>\"\n\t\t\"          <attribute name='label'>Delete cell</attribute>\"\n\t\t\"          <attribute name='action'>cdb.EditDelete</attribute>\"\n\t\t\"        </item>\"\n\t\t\"      </section>\"\n\t\t\"      <section>\"\n\t   \"        <item>\"\n\t\t\"          <attribute name='label'>Split cell</attribute>\"\n\t\t\"          <attribute name='action'>cdb.EditSplit</attribute>\"\n\t\t\"        </item>\"\n\t\t\"      </section>\"\n\t\t\"      <section>\"\n\t   \"        <item>\"\n\t\t\"          <attribute name='label'>Make cell LaTeX</attribute>\"\n\t\t\"          <attribute name='action'>cdb.EditMakeCellTeX</attribute>\"\n\t\t\"        </item>\"\n\t   \"        <item>\"\n\t\t\"          <attribute name='label'>Make cell Python</attribute>\"\n\t\t\"          <attribute name='action'>cdb.EditMakeCellPython</attribute>\"\n\t\t\"        </item>\"\n\t   \"        <item>\"\n\t\t\"          <attribute name='label'>Ignore cell on import</attribute>\"\n\t\t\"          <attribute name='action'>cdb.EditIgnoreCellOnImport</attribute>\"\n\t\t\"        </item>\"\n\t\t\"      </section>\"\n\t\t\"      <section>\"\n\t   \"        <item>\"\n\t\t\"          <attribute name='label'>Auto-close LaTeX cells</attribute>\"\n\t\t\"          <attribute name='action'>cdb.AutoCloseLaTeX</attribute>\"\n\t\t\"        </item>\"\n\t   \"        <item>\"\n\t\t\"          <attribute name='label'>Hide input cells</attribute>\"\n\t\t\"          <attribute name='action'>cdb.HideInputCells</attribute>\"\n\t\t\"        </item>\"\n\t\t\"      </section>\"\n\t\t\"    </submenu>\"\n\t\t\"    <submenu>\"\n\t   \"      <attribute name='label'>Edit</attribute>\"\n\t\t\"      <section>\"\n\t   \"        <item>\"\n\t\t\"          <attribute name='label'>Undo</attribute>\"\n\t\t\"          <attribute name='action'>cdb.EditUndo</attribute>\"\n\t\t\"        </item>\"\n\t   \"        <item>\"\n\t\t\"          <attribute name='label'>Redo</attribute>\"\n\t\t\"          <attribute name='action'>cdb.EditRedo</attribute>\"\n\t\t\"        </item>\"\n\t\t\"      </section>\"\n\t\t\"      <section>\"\n\t   \"        <item>\"\n\t\t\"          <attribute name='label'>Copy</attribute>\"\n\t\t\"          <attribute name='action'>cdb.EditCopy</attribute>\"\n\t\t\"        </item>\"\n\t   \"        <item>\"\n\t\t\"          <attribute name='label'>Paste</attribute>\"\n\t\t\"          <attribute name='action'>cdb.EditPaste</attribute>\"\n\t\t\"        </item>\"\n\t\t\"      </section>\"\n\t\t\"      <section>\"\n\t   \"        <item>\"\n\t\t\"          <attribute name='label'>Find</attribute>\"\n\t\t\"          <attribute name='action'>cdb.EditFind</attribute>\"\n\t\t\"        </item>\"\n\t   \"        <item>\"\n\t\t\"          <attribute name='label'>Find next</attribute>\"\n\t\t\"          <attribute name='action'>cdb.EditFindNext</attribute>\"\n\t\t\"        </item>\"\n\t\t\"      </section>\"\n\t\t\"    </submenu>\"\n\t\t\"    <submenu>\"\n\t   \"      <attribute name='label'>View</attribute>\"\n\t\t\"      <section>\"\n\t   \"        <item>\"\n\t\t\"          <attribute name='label'>Split view</attribute>\"\n\t\t\"          <attribute name='action'>cdb.ViewSplit</attribute>\"\n\t\t\"        </item>\"\n\t   \"        <item>\"\n\t\t\"          <attribute name='label'>Close view</attribute>\"\n\t\t\"          <attribute name='action'>cdb.ViewClose</attribute>\"\n\t\t\"        </item>\"\n\t\t\"      </section>\"\n\t\t\"      <submenu>\"\n\t\t\"        <attribute name='label'>Font size</attribute>\"\n\t\t\"        <section>\"\n\t   \"           <item>\"\n\t\t\"              <attribute name='label'>Small</attribute>\"\n\t\t\"              <attribute name='action'>cdb.FontSize</attribute>\"\n\t\t\"              <attribute name='target' type='i'>-1</attribute>\"\n\t\t\"           </item>\"\n\t   \"           <item>\"\n\t\t\"              <attribute name='label'>Medium (default)</attribute>\"\n\t\t\"              <attribute name='action'>cdb.FontSize</attribute>\"\n\t\t\"              <attribute name='target' type='i'>0</attribute>\"\n\t\t\"           </item>\"\n\t   \"           <item>\"\n\t\t\"              <attribute name='label'>Large</attribute>\"\n\t\t\"              <attribute name='action'>cdb.FontSize</attribute>\"\n\t\t\"              <attribute name='target' type='i'>2</attribute>\"\n\t\t\"           </item>\"\n\t   \"           <item>\"\n\t\t\"              <attribute name='label'>Extra large</attribute>\"\n\t\t\"              <attribute name='action'>cdb.FontSize</attribute>\"\n\t\t\"              <attribute name='target' type='i'>4</attribute>\"\n\t\t\"           </item>\"\n\t\t\"        </section>\"\n\t\t\"      </submenu>\"\n\t\t\"      <submenu>\"\n\t\t\"        <attribute name='label'>Highlighting</attribute>\"\n\t\t\"        <section>\"\n\t   \"           <item>\"\n\t\t\"              <attribute name='label'>Highlighting off</attribute>\"\n\t\t\"              <attribute name='action'>cdb.HighlightSyntax</attribute>\"\n\t\t\"              <attribute name='target' type='i'>0</attribute>\"\n\t\t\"           </item>\"\n\t   \"           <item>\"\n\t\t\"              <attribute name='label'>Highlighting on</attribute>\"\n\t\t\"              <attribute name='action'>cdb.HighlightSyntax</attribute>\"\n\t\t\"              <attribute name='target' type='i'>1</attribute>\"\n\t\t\"           </item>\"\n\t   \"           <item>\"\n\t\t\"              <attribute name='label'>Choose colours</attribute>\"\n\t\t\"              <attribute name='action'>cdb.HighlightChoose</attribute>\"\n\t\t\"           </item>\"\n\t\t\"        </section>\"\n\t\t\t\"      </submenu>\";\n\t\tconst char *appdir = getenv(\"APPDIR\");\n\t\tif(!appdir) {\n\t\t\tui_info+=\n\t\t\t\t\"      <submenu>\"\n\t\t\t\t\"        <attribute name='label'>Maths rendering</attribute>\"\n\t\t\t\t\"        <section>\"\n\t\t\t\t\"           <item>\"\n\t\t\t\t\"              <attribute name='label'>LaTeX (external)</attribute>\"\n\t\t\t\t\"              <attribute name='action'>cdb.MicroTeX</attribute>\"\n\t\t\t\t\"              <attribute name='target' type='i'>0</attribute>\"\n\t\t\t\t\"           </item>\"\n\t\t\t\t\"           <item>\"\n\t\t\t\t\"              <attribute name='label'>MicroTeX (internal)</attribute>\"\n\t\t\t\t\"              <attribute name='action'>cdb.MicroTeX</attribute>\"\n\t\t\t\t\"              <attribute name='target' type='i'>1</attribute>\"\n\t\t\t\t\"           </item>\"\n\t\t\t\t\"        </section>\"\n\t\t\t\t\"      </submenu>\";\n\t\t\t}\n\t   ui_info +=\n\t\t\"      <item>\"\n\t\t\"         <attribute name='label'>Use default settings</attribute>\"\n\t\t\"         <attribute name='action'>cdb.ViewUseDefaultSettings</attribute>\"\n\t\t\"      </item>\"\n\t\t\"    </submenu>\"\n\t\t\"    <submenu id='MenuEvaluate'>\"\n\t   \"      <attribute name='label'>Evaluate</attribute>\"\n\t\t\"      <section>\"\n\t   \"        <item>\"\n\t\t\"          <attribute name='label'>Evaluate cell</attribute>\"\n\t\t\"          <attribute name='action'>cdb.EvaluateCell</attribute>\"\n\t\t\"        </item>\"\n\t   \"        <item>\"\n\t\t\"          <attribute name='label'>Evaluate all</attribute>\"\n\t\t\"          <attribute name='action'>cdb.EvaluateAll</attribute>\"\n\t\t\"        </item>\"\n\t   \"        <item>\"\n\t\t\"          <attribute name='label'>Evaluate to cursor</attribute>\"\n\t\t\"          <attribute name='action'>cdb.EvaluateToCursor</attribute>\"\n\t\t\"        </item>\"\n\t   \"        <item>\"\n\t\t\"          <attribute name='label'>Stop evaluation</attribute>\"\n\t\t\"          <attribute name='action'>cdb.EvaluateStop</attribute>\"\n\t\t\"        </item>\"\n\t\t\"      </section>\"\n\t\t\"    </submenu>\"\n\t\t\"    <submenu>\"\n\t   \"      <attribute name='label'>Kernel</attribute>\"\n\t\t\"      <section>\"\n\t   \"        <item>\"\n\t\t\"          <attribute name='label'>Restart kernel</attribute>\"\n\t\t\"          <attribute name='action'>cdb.KernelRestart</attribute>\"\n\t\t\"        </item>\"\n\t   \"        <item>\"\n\t\t\"          <attribute name='label'>Restart kernel and run notebook</attribute>\"\n\t\t\"          <attribute name='action'>cdb.KernelRestartRun</attribute>\"\n\t\t\"        </item>\"\n\t\t\"      </section>\"\n\t\t\"    </submenu>\"\n\t\t\"    <submenu>\"\n\t   \"      <attribute name='label'>Tools</attribute>\"\n\t\t\"      <submenu>\"\n\t\t\"        <attribute name='label'>Compare</attribute>\"\n\t\t\"        <section>\"\n\t   \"           <item>\"\n\t\t\"             <attribute name='label'>With other file</attribute>\"\n\t\t\"             <attribute name='action'>cdb.CompareFile</attribute>\"\n\t\t\"           </item>\"\n\t   \"           <item>\"\n\t\t\"             <attribute name='label'>Last commit</attribute>\"\n\t\t\"             <attribute name='action'>cdb.CompareGitLatest</attribute>\"\n\t\t\"           </item>\"\n\t   \"           <item>\"\n\t\t\"             <attribute name='label'>Select commit from list</attribute>\"\n\t\t\"             <attribute name='action'>cdb.CompareGitChoose</attribute>\"\n\t\t\"           </item>\"\n\t   \"           <item>\"\n\t\t\"             <attribute name='label'>Manually enter commit hash</attribute>\"\n\t\t\"             <attribute name='action'>cdb.CompareGitSpecific</attribute>\"\n\t\t\"           </item>\"\n\t   \"           <item>\"\n\t\t\"             <attribute name='label'>Select GIT binary</attribute>\"\n\t\t\"             <attribute name='action'>cdb.CompareGitSelect</attribute>\"\n\t\t\"           </item>\"\n\t\t\"        </section>\"\n\t\t\"      </submenu>\"\n\t\t\"      <submenu>\"\n\t\t\"        <attribute name='label'>Console</attribute>\"\n\t\t\"        <section>\"\n\t   \"           <item>\"\n\t\t\"              <attribute name='label'>Hide</attribute>\"\n\t\t\"              <attribute name='action'>cdb.Console</attribute>\"\n\t\t\"              <attribute name='target' type='i'>0</attribute>\"\n\t\t\"           </item>\"\n\t   \"           <item>\"\n\t\t\"              <attribute name='label'>Dock (horizontal)</attribute>\"\n\t\t\"              <attribute name='action'>cdb.Console</attribute>\"\n\t\t\"              <attribute name='target' type='i'>1</attribute>\"\n\t\t\"           </item>\"\n\t   \"           <item>\"\n\t\t\"              <attribute name='label'>Dock (vertical)</attribute>\"\n\t\t\"              <attribute name='action'>cdb.Console</attribute>\"\n\t\t\"              <attribute name='target' type='i'>2</attribute>\"\n\t\t\"           </item>\"\n\t   \"           <item>\"\n\t\t\"              <attribute name='label'>Floating</attribute>\"\n\t\t\"              <attribute name='action'>cdb.Console</attribute>\"\n\t\t\"              <attribute name='target' type='i'>3</attribute>\"\n\t\t\"           </item>\"\n\t\t\"        </section>\"\n\t\t\"      </submenu>\"\n\t\t\"      <section>\"\n\t   \"        <item>\"\n\t\t\"          <attribute name='label'>Options</attribute>\"\n\t\t\"          <attribute name='action'>cdb.ToolsOptions</attribute>\"\n\t\t\"        </item>\"\n\t   \"        <item>\"\n\t\t\"          <attribute name='label'>Clear package cache</attribute>\"\n\t\t\"          <attribute name='action'>cdb.ToolsClearCache</attribute>\"\n\t\t\"        </item>\"\n\t\t\"      </section>\"\n\t\t\"    </submenu>\"\n\t\t\"    <submenu>\"\n\t   \"      <attribute name='label'>Help</attribute>\"\n\t\t\"      <section>\"\n\t   \"        <item>\"\n\t\t\"          <attribute name='label'>About Cadabra</attribute>\"\n\t\t\"          <attribute name='action'>cdb.HelpAbout</attribute>\"\n\t\t\"        </item>\"\n\t   \"        <item>\"\n\t\t\"          <attribute name='label'>Contextual help</attribute>\"\n\t\t\"          <attribute name='action'>cdb.HelpContext</attribute>\"\n\t\t\"        </item>\"\n\t   \"        <item>\"\n\t\t\"          <attribute name='label'>Register</attribute>\"\n\t\t\"          <attribute name='action'>cdb.HelpRegister</attribute>\"\n\t\t\"        </item>\"\n\t\t\"      </section>\"\n\t\t\"    </submenu>\"\n\t\t\"  </menu>\"\n\t   \"</interface>\";\n\t\t};\n\n\tuimanager->add_from_string(ui_info);\n\n\t// Main box structure dividing the window.\n\tadd(topbox);\n\tGlib::RefPtr<Glib::Object> menubar_obj = uimanager->get_object(\"MenuBar\");\n\tGlib::RefPtr<Gio::Menu> gmenu = Glib::RefPtr<Gio::Menu>::cast_dynamic(menubar_obj);\n\tGtk::MenuBar* pMenuBar = Gtk::make_managed<Gtk::MenuBar>(gmenu);\n\ttopbox.pack_start(*pMenuBar, Gtk::PACK_SHRINK);\n\n\tauto get_icon = [this](const std::string& nm) {\n\t\tGlib::RefPtr<Gio::File> ff = Gio::File::create_for_path(nm);\n\t\tGlib::RefPtr<Gio::FileInputStream> str = ff->read();\n\t\tGlib::RefPtr<Gdk::Pixbuf> pb = Gdk::Pixbuf::create_from_stream_at_scale(str, 50/scale, 50/scale, true);\n\t\treturn pb;\n\t\t};\n\t\n\t// Setup the toolbar and buttons in it.\n\tif(!read_only) {\n\t\ttoolbar.set_size_request(-1, 70/display_scale);\n\n\t\t// Stop button.\n\t\ttool_stop.add(*Gtk::make_managed<ImageArea>(\n\t\t\t\t\t\t\t  40/display_scale, display_scale,\n\t\t\t\t\t\t\t  install_prefix()+\"/share/cadabra2/cdb-icons/cdb-cancel\"+ICONEXT,\n\t\t\t\t\t\t\t  false));\n\t\ttool_stop.get_accessible()->set_name(\"Stop\");\n\n\t\t// Run button.\n\t\tauto img_run = Gtk::make_managed<ImageArea>(40/display_scale, display_scale,\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t  install_prefix()+\"/share/cadabra2/cdb-icons/cdb-run\"+ICONEXT,\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t  false);\n\t\timg_run->get_accessible()->set_role(Atk::ROLE_PUSH_BUTTON);\n\t\ttool_run.add(*img_run);\n\t\ttool_run.get_accessible()->set_name(\"Run\");\n\t\t//\t\ttool_run.set_label(\"run all\");\n\n\t\t// Restart button.\n\t\ttool_restart.add(*Gtk::make_managed<ImageArea>(\n\t\t\t\t\t\t\t\t  40/display_scale, display_scale,\n\t\t\t\t\t\t\t\t  install_prefix()+\"/share/cadabra2/cdb-icons/cdb-restart\"+ICONEXT,\n\t\t\t\t\t\t\t\t  false));\n\t\ttool_restart.get_accessible()->set_name(\"Restart kernel\");\n\n\t\t// Restart-and-run-all button.\n\t\ttool_restart_and_run_all.add(*Gtk::make_managed<ImageArea>(\n\t\t\t\t\t\t\t\t\t\t\t\t  40/display_scale, display_scale,\n\t\t\t\t\t\t\t\t\t\t\t\t  install_prefix()+\"/share/cadabra2/cdb-icons/cdb-restart-and-run-all\"+ICONEXT,\n\t\t\t\t\t\t\t\t\t\t\t\t  false));\n\t\ttool_restart_and_run_all.get_accessible()->set_name(\"Restart kernel and run notebook\");\n\n\t\t// Open button.\n\t\ttool_open.add(*Gtk::make_managed<ImageArea>(\n\t\t\t\t\t\t\t\t  40/display_scale, display_scale,\n\t\t\t\t\t\t\t\t  install_prefix()+\"/share/cadabra2/cdb-icons/cdb-open\"+ICONEXT,\n\t\t\t\t\t\t\t\t  false));\n\t\ttool_open.get_accessible()->set_name(\"Open\");\n\n\t\t// Save button.\n\t\ttool_save.add(*Gtk::make_managed<ImageArea>(\n\t\t\t\t\t\t\t\t  40/display_scale, display_scale,\n\t\t\t\t\t\t\t\t  install_prefix()+\"/share/cadabra2/cdb-icons/cdb-save\"+ICONEXT,\n\t\t\t\t\t\t\t\t  false));\n\t\ttool_save.get_accessible()->set_name(\"Save\");\n\n\t\t// Save as button.\n\t\ttool_save_as.add(*Gtk::make_managed<ImageArea>(\n\t\t\t\t\t\t\t\t  40/display_scale, display_scale,\n\t\t\t\t\t\t\t\t  install_prefix()+\"/share/cadabra2/cdb-icons/cdb-save-as\"+ICONEXT,\n\t\t\t\t\t\t\t\t  false));\n\t\ttool_save_as.get_accessible()->set_name(\"Save as\");\n\n\t\ttool_stop.set_size_request(70/display_scale, 70/display_scale);\n\t\ttool_run.set_size_request(70/display_scale, 70/display_scale);\n\t\ttool_restart.set_size_request(70/display_scale, 70/display_scale);\n\t\ttool_restart_and_run_all.set_size_request(70/display_scale, 70/display_scale);\n\t\ttool_open.set_size_request(70/display_scale, 70/display_scale);\n\t\ttool_save.set_size_request(70/display_scale, 70/display_scale);\n\t\ttool_save_as.set_size_request(70/display_scale, 70/display_scale);\n\n\t\ttool_run.set_tooltip_text(\"Execute all cells\");\n\t\ttool_stop.set_tooltip_text(\"Stop execution\");\n\t\ttool_restart.set_tooltip_text(\"Restart kernel\");\n\t\ttool_restart_and_run_all.set_tooltip_text(\"Restart kernel and run entire notebook\");\n\t\ttool_open.set_tooltip_text(\"Open notebook...\");\n\t\ttool_save.set_tooltip_text(\"Save notebook\");\n\t\ttool_save_as.set_tooltip_text(\"Save notebook as...\");\n\t\n\t\ttopbox.pack_start(toolbar, Gtk::PACK_SHRINK);\n\t\ttoolbar.pack_start(tool_open, Gtk::PACK_SHRINK);\n\t\ttoolbar.pack_start(tool_save, Gtk::PACK_SHRINK);\n\t\ttoolbar.pack_start(tool_save_as, Gtk::PACK_SHRINK);\n\t\ttoolbar.pack_start(tool_run, Gtk::PACK_SHRINK);\n\t\ttoolbar.pack_start(tool_stop, Gtk::PACK_SHRINK);\n\t\ttoolbar.pack_start(tool_restart, Gtk::PACK_SHRINK);\n\t\ttoolbar.pack_start(tool_restart_and_run_all, Gtk::PACK_SHRINK);\n\t\ttoolbar.pack_start(top_label);\n\t\ttoolbar.pack_end(kernel_spinner, Gtk::PACK_SHRINK);\n\t\tkernel_spinner.set_size_request(50/display_scale, 50/display_scale);\n\t\tkernel_spinner.set_margin_end(10/display_scale);\n\t\t}\n\t\n\t// Normally we would use 'set_action_name' to associate the\n\t// buttons to actions already defined, but gtkmm-3.24 has\n\t// a TODO item \"derive from and implement Actionable\". So\n\t// we re-do what we did for actions.\n\ttool_open.signal_clicked().connect(sigc::mem_fun(*this, &NotebookWindow::on_file_open));\n\ttool_save.signal_clicked().connect(sigc::mem_fun(*this, &NotebookWindow::on_file_save));\n\ttool_save_as.signal_clicked().connect(sigc::mem_fun(*this, &NotebookWindow::on_file_save_as));\n\ttool_run.signal_clicked().connect(sigc::mem_fun(*this, &NotebookWindow::run_all_cells));\n\ttool_stop.signal_clicked().connect(sigc::mem_fun(*this, &NotebookWindow::on_run_stop));\n\ttool_restart.signal_clicked().connect(sigc::mem_fun(*this, &NotebookWindow::on_kernel_restart));\n\ttool_restart_and_run_all.signal_clicked().connect(sigc::mem_fun(*this, &NotebookWindow::on_kernel_restart_and_run_all));\n\t\n//\t\n//\tGtk::Widget *toolbar=0;\n//\tuimanager->get_widget(\"/ToolBar\", toolbar);\n//\ttopbox.pack_start(*toolbar, Gtk::PACK_SHRINK);\n\ttopbox.pack_start(supermainbox, true, true);\n\ttopbox.pack_start(statusbarbox, false, false);\n\tsupermainbox.pack_start(dragbox, true, true);\n\tdragbox.add1(mainbox);\n\tmainbox.pack_start(searchbar, false, false);\n\tmainbox.set_name(\"mainbox\");\n\tsearchbar.add(search_hbox);\n//\tsearchbar.set_halign(Gtk::ALIGN_START);\n\tsearch_hbox.pack_start(searchentry, Gtk::PACK_EXPAND_WIDGET, 10);\n\tsearchentry.set_size_request(200, -1);\n\tsearch_hbox.pack_start(search_case_insensitive, Gtk::PACK_SHRINK, 10);\n\tsearch_case_insensitive.set_active(true);\n\n\t// Status bar\n\tkernel_label.set_text(\"Server: not connected\");\n\tstatusbarbox.set_size_request(-1,50/display_scale);\n\tstatusbarbox.set_homogeneous(false);\n\tstatusbarbox.pack_start(status_label, false, false, 0);\n\tstatusbarbox.pack_start(kernel_label, false, false, 0);\n\tstatusbarbox.pack_start(progressbar, true, true, 0);\n\tstatus_label.set_size_request(300,-1);\n\tkernel_label.set_size_request(300,-1);\n\t// status_label.set_halign(Gtk::Align::ALIGN_START);\n\t// kernel_label.set_halign(Gtk::Align::ALIGN_START);\n\tstatus_label.set_xalign(0);\n\tkernel_label.set_xalign(0);\n\tprogressbar.set_text(\"Idle\");\n\tprogressbar.set_show_text(true);\n\n   //\tauto context = kernel_spinner.get_style_context();\n   //\tcontext->add_class(\"spinner\");\n\tstatusbarbox.set_name(\"statusbar\");\n\n\tsearchentry.signal_search_changed().connect(sigc::mem_fun(*this, &NotebookWindow::on_search_text_changed));\n\n\t// The three main widgets\n\t//\tmainbox.pack_start(buttonbox, Gtk::PACK_SHRINK, 0);\n\n\t// We always have at least one canvas.\n\tcanvasses.push_back(manage( new NotebookCanvas() ));\n\tmainbox.pack_start(*canvasses[0], Gtk::PACK_EXPAND_WIDGET, 0);\n\n\t// FIXME: need to do this for every canvas.\n\tcanvasses[0]->scroll.signal_size_allocate().connect(\n\t   sigc::mem_fun(*this, &NotebookWindow::on_scroll_size_allocate));\n\n\tcanvasses[0]->scroll_event.connect(sigc::mem_fun(*this, &NotebookWindow::on_scroll_changed));\n\n\t// Window size and title, and ready to go.\n\tif(!read_only) {\n\t\tif(geometry_string!=\"\") {\n\t\t\tint width = 0, height = 0, x = 0, y = 0;\n\t\t\tsscanf(geometry_string.c_str(), \"%dx%d\", &width, &height);\n\t\t\t// std::cerr << \"GEOMETRY = \" << width << \" x \" << height << std::endl;\n\t\t\tset_default_size(width, height);\n\t\t\t}\n\t\telse \n\t\t\tset_default_size(monitor_geometry.get_width()/2, monitor_geometry.get_height()*0.8);\n\t\t}\n\telse {\n\t\tset_default_size(monitor_geometry.get_width()/3, monitor_geometry.get_height()*0.6);\n\t\t}\n\t// FIXME: the subtraction for the margin and scrollbar made below\n\t// is estimated but should be computed.\n\t//\tengine.set_geometry(screen->get_width()/2 - 2*30);\n\tupdate_title();\n\tshow_all();\n\tkernel_spinner.hide();\n\tif(read_only) {\n\t\tstatusbarbox.hide();\n\t\tprogressbar.hide();\n//\t\ttoolbar->hide();\n\t\t}\n\telse {\n\t\t// Buttons\n\t\tset_stop_sensitive(false);\n\t\t}\n\n\tnew_document();\n\t}\n\nNotebookWindow::~NotebookWindow()\n\t{\n\t}\n\nvoid NotebookWindow::load_css()\n\t{\n\t// std::cerr << \"(re)loading css\" << std::endl;\n\tstd::string text_colour = prefs.highlight ? \"black\" : \"blue\";\n\tGlib::ustring data = \"\";\n\n\t// https://stackoverflow.com/questions/35045469/default-gtk-css-color-scheme\n\t\n\tdata += \"scrolledwindow { background-color: @theme_base_color; }\\n\";\n\tdata += \"textview text { color: \"+text_colour+\"; background-color: @theme_base_color; -GtkWidget-cursor-aspect-ratio: 0.2; }\\n\";\n\tdata += \"textview *:focus { background-color: #eee; }\\n\";\n\tdata += \".view text selection { color: #fff; background-color: #888; }\\n\";\n\tdata += \"textview.error { background: transparent; -GtkWidget-cursor-aspect-ratio: 0.2; color: @theme_fg_color; }\\n\";\n\tdata += \"#ImageView { transition-property: padding, background-color; transition-duration: 1s; }\\n\";\n\tdata += \"#CodeInput { font-family: monospace; font-size: \"+std::to_string((100.0+(prefs.font_step*10.0)))+\"%; }\\n\";\n\tdata += \"#Console   { padding: 2px; }\\n\";\n\tdata += \"#mainbox * { transition-property: opacity; transition-duration: 0.5s; }\\n\";\n\tdata += \"#mainbox:disabled * { opacity: 0.85; }\\n\";\n\tdata += \"label { margin-left: 4px; }\\n\";\n\tdata += \"#TeXArea:selected { background-color: #eee; color: #000; }\\n\";\n\tdata += \"spinner { background: none; opacity: 1; -gtk-icon-source: -gtk-icontheme(\\\"process-working-symbolic\\\"); }\\n\";\n\tdata += \"spinner:checked { opacity: 1; animation: spin 1s linear infinite; }\\n\";\n\tdata += \"scale slider { background-color: @selected_bg_color; }\\n\";\n\tdata += \"scale { margin-bottom: 10px; }\\n\";\n\n\t// Some of the css properties defined in gtk-cadabra.css are overridden, and so are included\n\t// here to force them to be used\n#ifdef _MSC_VER\n\tdata += R\"(\n\t\t.titlebar {\n\t\t\tmargin: 0;\n\t\t\tpadding: 0;\n\t\t\tbox-shadow: inset 0 0 1px #ddd;\n\t\t\tbackground-image: none;\n\t\t\tbackground-color: #209020;\n\t\t\tcolor: white;\n\t\t}\n\n\t\t.titlebar:backdrop {\n\t\t\tbackground-color: #367d36;\n\t\t}\n\n\t\t.titlebar label:backdrop {\n\t\t\tcolor: white;\n\t\t}\n\n\t\t.titlebar .titlebutton {\n\t\t\tmargin: 0px 0px 0px -8px;\n\t\t\tpadding: 0px 8px;\n\t\t}\n\n\t\tdialog .titlebar,\n\t\tdialog .titlebar:backdrop {\n\t\t\tbackground-color: #666;\n\t\t}\n\n\t\ttooltip {\n\t\t\tbackground-color: transparent;\n\t\t}\n\n\t\ttoolbar button {\n\t\t\tpadding: 0px;\n\t\t\tmargin-right: 5px;\n\t\t}\n)\";\n#endif\n\n\t//\tdata += \"scrolledwindow { kinetic-scrolling: false; }\\n\";\n\n\tif(!css_provider->load_from_data(data)) {\n\t\tstd::cerr << \"Cannot parse internal CSS.\" << std::endl;\n\t\tthrow std::logic_error(\"Failed to parse widget CSS information.\");\n\t\t}\n\t}\n\nbool NotebookWindow::on_delete_event(GdkEventAny* event)\n\t{\n\tif (quit_safeguard(true)) {\n\t\tprefs.save();\n\t\treturn Gtk::Window::on_delete_event(event);\n\t\t}\n\telse\n\t\treturn true;\n\t}\n\nvoid NotebookWindow::on_prefs_set_cv(int npos)\n\t{\n\taction_console->set_state(Glib::Variant<int>::create(npos));\n\tConsole::Position pos=static_cast<Console::Position>(npos);\n\t// Unparent from whatever we're currently a child of\n\tconsole.hide();\n\tif (console.get_parent() == &dragbox) {\n\t\tdragbox.remove(console);\n\t\t}\n\telse if (console.get_parent() == console_win.get_content_area()) {\n\t\tconsole_win.get_content_area()->remove(console);\n\t\tconsole_win.hide();\n\t\t}\n\n\t// Reparent onto something new\n\tif (pos == Console::Position::DockedH) {\n\t\tdragbox.set_orientation(Gtk::Orientation::ORIENTATION_HORIZONTAL);\n\t\tdragbox.set_position(dragbox.get_allocation().get_width() / 2);\n\t\tdragbox.add2(console);\n\t\tconsole.show();\n\t\t}\n\telse if (pos == Console::Position::DockedV) {\n\t\tdragbox.set_orientation(Gtk::Orientation::ORIENTATION_VERTICAL);\n\t\tdragbox.set_position(dragbox.get_allocation().get_height() / 2);\n\t\tdragbox.add2(console);\n\t\tconsole.set_size_request(-1, 200);\n\t\tconsole.show();\n\t\t}\n\telse if (pos == Console::Position::Floating) {\n\t\tconsole_win.set_transient_for(*this);\n\t\tconsole_win.set_resizable(true);\n\t\tconsole_win.set_default_size(900, 300);\n\t\tconsole_win.set_title(\"Interactive Console\");\n\t\tconsole_win.get_content_area()->add(console);\n\t\t// Reflect hidden state in menu when the floating\n\t\t// console is closed.\n\t\tconsole_win.signal_response().connect( [this](int) {\n\t\t\tthis->on_prefs_set_cv(0);\n\t\t\t});\n\t\tconsole_win.show_all();\n\t\t}\n\t}\n\nvoid NotebookWindow::resize_codeinput_texview_all(int width)\n\t{\n\t// Inform CodeInput and TeXView widgets about the size; they need to\n   // have a maximum width equal to the window width (minus scrollbar),\n\t// except when they contain Python code (which does not word-wrap).\n\tauto it=doc.begin();\n\t// std::cerr << \"----\" << std::endl;\n\twhile(it!=doc.end()) {\n\t\tresize_codeinput_texview(it, width);\n\t\t++it;\n\t\t}\n\t}\n\nvoid NotebookWindow::resize_codeinput_texview(DTree::iterator it, int width)\n\t{\n\t// std::cerr << \"resizing cell to \" << width << std::endl;\n\tif(it->cell_type==DataCell::CellType::python || it->cell_type==DataCell::CellType::latex) {\n\t\tfor(unsigned int i=0; i<canvasses.size(); ++i) {\n\t\t\tauto fnd = canvasses[i]->visualcells.find(&(*it));\n\t\t\tif(fnd != canvasses[i]->visualcells.end()) {\n\t\t\t\tCodeInput *code_input = fnd->second.inbox;\n\t\t\t\t//\tcode_input->edit.set_size_request(width, -1);  seems unnecessary\n\t\t\t\tGtk::Allocation allocation = code_input->edit.get_allocation();\n\t\t\t\tallocation.set_width(width);\n\t\t\t\tcode_input->edit.size_allocate(allocation);\n\t\t\t\tcode_input->edit.queue_draw();\n\t\t\t\tcode_input->edit.window_width = width;\n\t\t\t\tcode_input->update_buffer();\n\t\t\t\t}\n\t\t\t}\n\t\t}\n\telse if(it->cell_type==DataCell::CellType::latex_view\n\t\t\t  || it->cell_type==DataCell::CellType::output\n\t\t\t  || it->cell_type==DataCell::CellType::verbatim\n\t\t\t  || it->cell_type==DataCell::CellType::error) {\n\t\tfor(unsigned int i=0; i<canvasses.size(); ++i) {\n\t\t\tauto fnd = canvasses[i]->visualcells.find(&(*it));\n\t\t\tif(fnd != canvasses[i]->visualcells.end()) {\n\t\t\t\tTeXView *tex_view = fnd->second.outbox;\n\t\t\t\ttex_view->window_width = width;\n\n\t\t\t\tGtk::Allocation allocation = tex_view->image.get_allocation();\n\t\t\t\tallocation.set_width(width - 20);\n\t\t\t\tint need_height = tex_view->image.need_height(width - 20);\n\t\t\t\t// std::cerr << \"Need height \" << need_height << std::endl;\n\t\t\t\tallocation.set_height(need_height+100);\n\t\t\t\ttex_view->image.size_allocate(allocation);\n\t\t\t\t\n\t\t\t\ttex_view->queue_draw();\n\t\t\t\tGlib::signal_timeout().connect_once([tex_view]()\n\t\t\t\t\t\t{\n\t\t\t\t\t\ttex_view->queue_resize();\n\t\t\t\t\t\t}, 50);\n\t\t\t\t}\n\t\t\t}\n\t\t}\n\t}\n\nbool NotebookWindow::on_configure_event(GdkEventConfigure *cfg)\n\t{\n\t// std::cerr << \"cadabra-client: on_configure_event \" << cfg->width << \" x \" << cfg->height << std::endl;\n\tis_configured=true;\n\n\tbool ret=Gtk::Window::on_configure_event(cfg);\n\n\tif(cfg->width != last_configure_width) {\n\t\tif(prefs.microtex) {\n\t\t\tresize_codeinput_texview_all(cfg->width);\n\t\t\tlast_configure_width = cfg->width;\n\t\t\t}\n\t\telse {\n\t\t\t// Re-run latex.\n\t\t\tstd::lock_guard<std::recursive_mutex> guard(tex_need_width_mutex);\n\t\t\tif(tex_running) {\n\t\t\t\ttex_need_width = cfg->width;\n\t\t\t\t}\n\t\t\telse {\n\t\t\t\ttex_need_width = cfg->width;\n\t\t\t\t// std::cerr << \"Attempting to run\" << std::endl;\n\t\t\ttex_run_async();\n\t\t\t// std::cerr << \"OK, running\" << std::endl;\n\t\t\t\t}\n\t\t\tlast_configure_width = cfg->width;\n\t\t\t}\n\t\t}\n\n\treturn ret;\n\t}\n\nvoid NotebookWindow::refresh_after_tex_engine_run()\n\t{\n\tfor(unsigned int i=0; i<canvasses.size(); ++i)\n\t\tcanvasses[i]->refresh_all();\n\t}\n\nvoid NotebookWindow::handle_thread_tex_error()\n\t{\n\ton_tex_error(tex_error_string, doc.end());\n\t// std::cerr << \"clicked away\" << std::endl;\n\ttex_error_string=\"\";\n\t}\n\nbool NotebookWindow::on_unhandled_error(const std::exception& err)\n{\n\tGtk::MessageDialog md(*this, err.what(), false, Gtk::MessageType::MESSAGE_ERROR, Gtk::ButtonsType::BUTTONS_OK, true);\n\tmd.run();\n\treturn true;\n}\n\nvoid NotebookWindow::set_title_prefix(const std::string& pf)\n\t{\n\ttitle_prefix=pf;\n\t}\n\nvoid NotebookWindow::update_title()\n\t{\n\tif(get_realized()==false)\n\t\treturn;\n\t\n\tif(name.size()>0) {\n\t\tif(modified)\n\t\t\tset_title(title_prefix+\": \"+name+\"*\");\n\t\telse\n\t\t\tset_title(title_prefix+\": \"+name);\n\t\t}\n\telse {\n\t\tif(modified)\n\t\t\tset_title(title_prefix+\"*\");\n\t\telse\n\t\t\tset_title(title_prefix);\n\t\t}\n\t\n\t// std::cerr << \"undo_stack.size() = \" << undo_stack.size() << std::endl;\n\t// std::cerr << \"redo_stack.size() = \" << redo_stack.size() << std::endl;\n\taction_undo->set_enabled( undo_stack.size() > 0 );\n\taction_redo->set_enabled( redo_stack.size() > 0 );\n\taction_view_close->set_enabled( canvasses.size() > 1 );\n\t}\n\nvoid NotebookWindow::set_statusbar_message(const std::string& message, int line, int col)\n\t{\n\t\t{\n\t\tstd::lock_guard<std::mutex> guard(status_mutex);\n\t\tstatus_string = message;\n\t\tstatus_line = line;\n\t\tstatus_col = col;\n\t\t}\n\tdispatch_update_status.emit();\n\t}\n\nvoid NotebookWindow::set_stop_sensitive(bool s)\n\t{\n\t// Disable menu items and toolbar items by simply disabling\n\t// the action.\n\t\n\taction_stop->set_enabled(s);\n\t}\n\nvoid NotebookWindow::process_data()\n\t{\n\t// std::cerr << \"process_data() called\" << std::endl;\n\tdispatcher.emit();\n\t}\n\n\nvoid NotebookWindow::on_connect()\n\t{\n\t// std::cerr << \"kernel connected\" << std::endl;\n\t\n\tstd::lock_guard<std::mutex> guard(status_mutex);\n\tkernel_string = \"connected\";\n\tprogress_string = \"Idle\";\n//\tdispatcher.emit();\n\tdispatch_update_status.emit();\n\tconsole.initialize();\n\t// prefs.python_path might end in a backslash which will raise an EOF syntax error, so we add a\n\t// semicolon to the end of it and then remove the (empty) last element of the resulting list\n\tif (!trim(prefs.python_path).empty())\n\t\tconsole.send_input(\"sys.path = r'''\" + escape_backslashes(prefs.python_path) + \";'''.split(';')[:-1] + sys.path\");\n\tif (!name.empty()) {\n\t\tconsole.send_input(\"sys.path.insert(0, '''\" + escape_backslashes(name.substr(0, name.find_last_of(\"\\\\/\"))) + \"''')\");\n\t\t}\n\n\tif(run_all_after_restart) {\n\t\trun_all_after_restart=false;\n\t\tstd::shared_ptr<ActionBase> action = std::make_shared<ActionRunCell>();\n\t\tqueue_action(action);\n\t\t}\n\t}\n\nvoid NotebookWindow::on_disconnect(const std::string& reason)\n\t{\n\t// std::cerr << \"***** kernel disconnected\" << std::endl;\n\tstd::lock_guard<std::mutex> guard(status_mutex);\n\tkernel_string = reason;\n\tdispatcher.emit();\n\t}\n\nvoid NotebookWindow::on_network_error()\n\t{\n\tstd::lock_guard<std::mutex> guard(status_mutex);\n\tkernel_string = \"cannot reach server, retrying...\";\n\tdispatcher.emit();\n\t}\n\nvoid NotebookWindow::on_kernel_runstatus(bool running)\n\t{\n\tstd::lock_guard<std::mutex> guard(status_mutex);\n\tkernel_spinner_status=running;\n\tif(!running) {\n\t\tif(follow_mode && follow_last_cell!=doc.end()) {\n\t\t\tfollow_cell=doc.end();\n\t\t\t// std::cerr << \"RUNSTATUS scroll\" << std::endl;\n\t\t\tscroll_cell_into_view(follow_last_cell);\n\t\t\tfollow_last_cell=doc.end();\n\t\t\t}\n\t\t}\n\t// FIXME: WHY would we need to process the queue here?\n\tdispatcher.emit();\n\t}\n\nvoid NotebookWindow::tex_run_async()\n\t{\n\tif(prefs.microtex==false) {\n\t\tif(tex_error_string!=\"\")\n\t\t\treturn;\n\t\t\n\t\t// Run TeX on a separate thread; it'll take a while and\n\t\t// we don't want to block the UI thread.\n\t\t// FIXME: join properly when exiting the program, otherwise\n\t\t// we get a 'terminate called without active exception' message.\n\t\tauto tex_code = [this]() {\n\t\t\ttry {\n\t\t\t\tfor(;;) {\n\t\t\t\t\t{  std::lock_guard<std::recursive_mutex> guard(tex_need_width_mutex);\n\t\t\t\t\t\tengine.invalidate_all();\n\t\t\t\t\t\tengine.set_geometry(tex_need_width-2*30);\n\t\t\t\t\t\t}\n\t\t\t\t\t\n\t\t\t\t\tengine.convert_all();\n\t\t\t\t\tdispatch_refresh.emit();\n\t\t\t\t\t\n\t\t\t\t\t{  std::lock_guard<std::recursive_mutex> guard(tex_need_width_mutex);\n\t\t\t\t\t\tif(tex_need_width-2*30 == engine.get_geometry()) {\n\t\t\t\t\t\t\ttex_running=false;\n\t\t\t\t\t\t\tbreak;\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\t}\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\tcatch(TeXEngine::TeXException& ex) {\n\t\t\t\t// Display the error in the main thread.\n\t\t\t\tstd::lock_guard<std::recursive_mutex> guard(tex_need_width_mutex);\n\t\t\t\ttex_error_string=ex.what();\n\t\t\t\ttex_running=false;\n\t\t\t\tdispatch_refresh.emit();\n\t\t\t\tdispatch_tex_error.emit();\n\t\t\t\t}\n\t\t\t};\n\t\t\n\t\tstd::lock_guard<std::recursive_mutex> guard(tex_need_width_mutex);\n\t\ttex_running=true;\n\t\t\n\t\t// Join any thread which may still exist.\n\t\tif(tex_thread)\n\t\t\ttex_thread->join();\n\t\t\n\t\ttex_thread = std::make_unique<std::thread>( tex_code );\n\t\t}\n\telse {\n\t\tdispatch_refresh.emit();\n\t\t}\n\t}\n\nvoid NotebookWindow::process_todo_queue()\n\t{\n\tstatic bool running=false;\n\n\t// std::cerr << \"process_todo_queue, running=\"  << running << std::endl;\n\t\n\t// Prevent from re-entering this from the process_action_queue entered below.\n\tif(running) return;\n\trunning=true;\n\n\t// Update the status/kernel messages into the corresponding widgets.\n\t\t{\n\t\tstd::lock_guard<std::mutex> guard(status_mutex);\n\t\tkernel_label.set_text(\"Server: \" + kernel_string);\n\t\tif(compute)\n\t\t\tmainbox.set_sensitive(compute->kernel_is_connected());\n\n\t\tif(kernel_spinner_status) {\n\t\t\tkernel_spinner.show();\n\t\t\tkernel_spinner.start();\n\t\t\t}\n\t\telse {\n\t\t\tkernel_spinner.stop();\n\t\t\tkernel_spinner.hide();\n\t\t\t}\n\t\t}\n\n\t// Perform any ActionBase actions.\n\tprocess_action_queue();\n\n\t// Before we pop up any dialogs, enable queue processing again, otherwise\n\t// subsequent calls to process_todo_queue will get postponed until a\n\t// dispatcher.emit() is called when the dialog is closed.\n\trunning=false;\n\n\tif(crash_window_hidden && kernel_string==\"not connected\") {\n\t\tcrash_window_hidden=false;\n\t\tGtk::MessageDialog md(\"Kernel crashed\", false, Gtk::MESSAGE_WARNING, Gtk::BUTTONS_OK, true);\n\t\tmd.set_transient_for(*this);\n\t\tmd.set_type_hint(Gdk::WINDOW_TYPE_HINT_DIALOG);\n\t\tmd.set_secondary_text(\"The kernel crashed unexpectedly, and has been restarted. You will need to re-run all cells.\");\n\t\tmd.signal_response().connect(sigc::mem_fun(*this, &NotebookWindow::on_crash_window_closed));\n\t\tmd.run();\n\n\t\tnlohmann::json req;\n\t\treq[\"msg_type\"] = \"exit\";\n\t\treq[\"header\"][\"from_server\"] = true;\n\t\ton_interactive_output(req);\n\t\t}\n\n\t}\n\nvoid NotebookWindow::on_crash_window_closed(int)\n\t{\n\tcrash_window_hidden=true;\n\t}\n\nbool NotebookWindow::on_key_press_event(GdkEventKey* event)\n\t{\n\tbool is_ctrl_up    = event->keyval==GDK_KEY_Up   && (event->state&Gdk::CONTROL_MASK);\n\tbool is_ctrl_down  = event->keyval==GDK_KEY_Down && (event->state&Gdk::CONTROL_MASK);\n\tbool is_ctrl_home  = event->keyval==GDK_KEY_Home && (event->state&Gdk::CONTROL_MASK);\n\tbool is_ctrl_end   = event->keyval==GDK_KEY_End  && (event->state&Gdk::CONTROL_MASK);\n\tbool is_pagedown   = event->keyval==GDK_KEY_Page_Down;\n\tbool is_pageup     = event->keyval==GDK_KEY_Page_Up;\n\n\tbool have_current_cell = current_cell != doc.end();\n\n\tif(is_ctrl_up && have_current_cell) {\n\t\tfollow_mode=true;\n\t\tstd::shared_ptr<ActionBase> actionpos =\n\t\t   std::make_shared<ActionPositionCursor>(current_cell->id(), ActionPositionCursor::Position::previous);\n\t\tqueue_action(actionpos);\n\t\tprocess_todo_queue();\n\t\treturn true;\n\t\t}\n\telse if(is_ctrl_down && have_current_cell) {\n\t\tfollow_mode=true;\n\t\tstd::shared_ptr<ActionBase> actionpos =\n\t\t   std::make_shared<ActionPositionCursor>(current_cell->id(), ActionPositionCursor::Position::next);\n\t\tqueue_action(actionpos);\n\t\tprocess_todo_queue();\n\t\treturn true;\n\t\t}\n\telse if(is_ctrl_home) {\n\t\tfollow_mode=false;\n//\t\tstd::shared_ptr<ActionBase> actionpos =\n//\t\t   std::make_shared<ActionPositionCursor>(current_cell->id(), ActionPositionCursor::Position::in);\n//\t\tqueue_action(actionpos);\n//\t\tprocess_todo_queue();\n\t\tGlib::RefPtr<Gtk::Adjustment> va=canvasses[current_canvas]->scroll.get_vadjustment();\n\t\tva->set_value( va->get_lower() );\n\t\treturn true;\n\t\t}\n\telse if(is_ctrl_end) {\n\t\tfollow_mode=false;\n//\t\tstd::shared_ptr<ActionBase> actionpos =\n//\t\t   std::make_shared<ActionPositionCursor>(current_cell->id(), ActionPositionCursor::Position::in);\n//\t\tqueue_action(actionpos);\n//\t\tprocess_todo_queue();\n\t\tGlib::RefPtr<Gtk::Adjustment> va=canvasses[current_canvas]->scroll.get_vadjustment();\n\t\tva->set_value( va->get_upper() );\n\t\treturn true;\n\t\t}\n\telse if(is_pageup) {\n\t\tfollow_mode=false;\n\t\tGlib::RefPtr<Gtk::Adjustment> va=canvasses[current_canvas]->scroll.get_vadjustment();\n\t\tva->set_value( va->get_value()-va->get_page_increment() );\n\t\treturn true;\n\t\t}\n\telse if(is_pagedown) {\n\t\tfollow_mode=false;\n\t\tGlib::RefPtr<Gtk::Adjustment> va=canvasses[current_canvas]->scroll.get_vadjustment();\n\t\tva->set_value( va->get_value()+va->get_page_increment() );\n\t\treturn true;\n\t\t}\n\telse {\n\t\treturn Gtk::Window::on_key_press_event(event);\n\t\t}\n\t}\n\nvoid NotebookWindow::add_cell(const DTree& tr, DTree::iterator it, bool visible)\n\t{\n\t// std::cerr << \"Add cell for \" << it->id().id << std::endl;\n\t// Add a visual cell corresponding to this document cell in\n\t// every canvas.\n\n\tif(compute!=0)\n\t\tset_stop_sensitive( compute->number_of_cells_executing()>0 );\n\n\tGlib::RefPtr<Gtk::TextBuffer>          global_buffer;\n\tstd::shared_ptr<TeXEngine::TeXRequest> global_texrequest;\n\n\tfor(unsigned int i=0; i<canvasses.size(); ++i) {\n\n\t\t// If this data cell already has a representation in the current canvas\n\t\t// we can continue to the next canvas. However, we need to set the global\n\t\t// buffer from existing cells.\n\n\t\tif(canvasses[i]->visualcells.find(&(*it))!=canvasses[i]->visualcells.end()) {\n#ifdef DEBUG\n\t\t\tstd::cerr << \"found a visualcell for cell \" << &(*it) << \" in canvas \" << i << std::endl;\n#endif\n\t\t\tif(i==0 && (it->cell_type==DataCell::CellType::python || it->cell_type==DataCell::CellType::latex)) {\n\t\t\t\tglobal_buffer = canvasses[i]->visualcells[&(*it)].inbox->buffer;\n\t\t\t\t}\n\t\t\tcontinue;\n\t\t\t}\n\n\t\t// Create a visual cell of the appropriate type.\n\n\t\tVisualCell newcell;\n\t\tGtk::Widget *w=0;\n\t\tswitch(it->cell_type) {\n\t\t\tcase DataCell::CellType::document: {\n\t\t\t\tGtk::Box *docbox = manage( new Gtk::Box(Gtk::Orientation::ORIENTATION_VERTICAL) );\n\t\t\t\tnewcell.document = docbox;\n\t\t\t\tw=newcell.document;\n\t\t\t\t// Add spacer so we can scroll a bit further than the bottom cell.\n\t\t\t\tGtk::Box* spacer = Gtk::manage(new Gtk::Box(Gtk::ORIENTATION_VERTICAL));\n\t\t\t\tspacer->set_size_request(-1, 200); // Minimum height for scrollable space\n\t\t\t\tspacer->set_vexpand(true);\n\t\t\t\tspacer->set_valign(Gtk::ALIGN_FILL);\n\t\t\t\tdocbox->pack_end(*spacer, Gtk::PACK_EXPAND_WIDGET);\n\t\t\t\tbreak;\n\t\t\t\t}\n\t\t\tcase DataCell::CellType::output:\n\t\t\tcase DataCell::CellType::error:\n\t\t\tcase DataCell::CellType::verbatim:\n\t\t\tcase DataCell::CellType::latex_view: {\n\t\t\t\t// FIXME: would be good to share the input and output of TeXView too.\n\t\t\t\t// Right now nothing is shared...\n\t\t\t\tnewcell.outbox = manage( new TeXView(engine, it, prefs.microtex) );\n\t\t\t\tif(it->cell_type==DataCell::CellType::error)\n\t\t\t\t\tnewcell.outbox->set_is_error(true);\n\t\t\t\t\n\t\t\t\tnewcell.outbox->window_width = last_configure_width;\n\t\t\t\t// std::cerr << \"Add widget \" << newcell.outbox << \" for cell \" << it->id().id << std::endl;\n\t\t\t\tnewcell.outbox->tex_error.connect(\n\t\t\t\t   sigc::bind( sigc::mem_fun(this, &NotebookWindow::on_tex_error), it ) );\n\t\t\t\tnewcell.outbox->signal_on_copy_as_latex.connect(\n\t\t\t\t\tsigc::bind( sigc::mem_fun(this, &NotebookWindow::on_copy_as_latex), it ) );\n\n\t\t\t\tnewcell.outbox->show_hide_requested.connect(\n\t\t\t\t   sigc::bind( sigc::mem_fun(this, &NotebookWindow::cell_toggle_visibility), i ) );\n\n#if GTKMM_MINOR_VERSION>=10\n\t\t\t\tto_reveal.push_back(&newcell.outbox->rbox);\n#endif\n\n\t\t\t\tw=newcell.outbox;\n\t\t\t\tnewcell.outbox->signal_button_press_event().connect(\n\t\t\t\t   sigc::bind( sigc::mem_fun(this, &NotebookWindow::handle_outbox_select), it ) );\n\t\t\t\tbreak;\n\t\t\t\t}\n\t\t\tcase DataCell::CellType::python:\n\t\t\tcase DataCell::CellType::latex: {\n\t\t\t\tCodeInput *ci;\n\t\t\t\t// Ensure that all CodeInput cells share the same text buffer.\n\t\t\t\tif(i==0) {\n\t\t\t\t\tci = new CodeInput(it, it->textbuf, scale, display_scale, prefs,\n\t\t\t\t\t\t\t\t\t\t\t canvasses[i]->scroll.get_vadjustment() );\n\t\t\t\t\tglobal_buffer=ci->buffer;\n\t\t\t\t\t}\n\t\t\t\telse ci = new CodeInput(it, global_buffer, scale, display_scale, prefs,\n\t\t\t\t\t\t\t\t\t\t\t\tcanvasses[i]->scroll.get_vadjustment());\n\n\t\t\t\tusing namespace std::placeholders;\n\t\t\t\tci->relay_cursor_pos(std::bind(&NotebookWindow::set_statusbar_message, this, \"\", _1, _2));\n\t\t\t\tif(read_only)\n\t\t\t\t\tci->edit.set_editable(false);\n\t\t\t\tci->get_style_context()->add_provider(css_provider, GTK_STYLE_PROVIDER_PRIORITY_USER);\n\n\t\t\t\tci->edit.content_changed.connect(\n\t\t\t\t   sigc::bind( sigc::mem_fun(this, &NotebookWindow::cell_content_changed), i ) );\n\t\t\t\tci->edit.content_insert.connect(\n\t\t\t\t   sigc::bind( sigc::mem_fun(this, &NotebookWindow::cell_content_insert), i ) );\n\t\t\t\tci->edit.content_erase.connect(\n\t\t\t\t   sigc::bind( sigc::mem_fun(this, &NotebookWindow::cell_content_erase), i ) );\n\n\t\t\t\tci->edit.content_execute.connect(\n\t\t\t\t   sigc::bind( sigc::mem_fun(this, &NotebookWindow::cell_content_execute), true ) );\n\t\t\t\tci->edit.complete_request.connect(\n\t\t\t\t   sigc::bind( sigc::mem_fun(this, &NotebookWindow::cell_complete_request), i ) );\n\t\t\t\tci->edit.cell_got_focus.connect(\n\t\t\t\t   sigc::bind( sigc::mem_fun(this, &NotebookWindow::cell_got_focus), i ) );\n\n\t\t\t\tnewcell.inbox = manage( ci );\n\t\t\t\tw=newcell.inbox;\n\n\t\t\t\tbreak;\n\t\t\t\t}\n\t\t\tcase DataCell::CellType::image_png: {\n\t\t\t\t// FIXME: horribly memory inefficient\n\t\t\t\tImageView *iv=new ImageView(display_scale, 800/display_scale);\n\n\t\t\t\tiv->set_image_from_base64(it->textbuf);\n\t\t\t\tnewcell.imagebox = manage( iv );\n\t\t\t\tw=newcell.imagebox;\n\t\t\t\tbreak;\n\t\t\t\t}\n\t\t\tcase DataCell::CellType::image_svg: {\n\t\t\t\t// FIXME: horribly memory inefficient\n\t\t\t\tImageView *iv=new ImageView(display_scale, 800/display_scale);\n\n\t\t\t\tiv->set_image_from_svg(it->textbuf);\n\t\t\t\tnewcell.imagebox = manage( iv );\n\t\t\t\tw=newcell.imagebox;\n\t\t\t\tbreak;\n\t\t\t\t}\n\t\t\tcase DataCell::CellType::slider: {\n\t\t\t\ttry {\n\t\t\t\t\tSliderView *iv=new SliderView(it->textbuf);\n\t\t\t\t\tiv->adjustment->signal_value_changed().connect(\n\t\t\t\t\t\t[this, iv]() {\n\t\t\t\t\t\ton_slider_changed(iv->get_variable(), iv->adjustment->get_value());\n\t\t\t\t\t\t});\n\n\t\t\t\t\tnewcell.slider = manage( iv );\n\t\t\t\t\tw=newcell.slider;\n\t\t\t\t\t}\n\t\t\t\tcatch(const nlohmann::json::parse_error& ex) {\n\t\t\t\t\tstd::cerr << \"NotebookWindow::add_cell: problem parsing SliderView JSON settings.\" << std::endl;\n\t\t\t\t\t}\n\t\t\t\tbreak;\n\t\t\t\t}\n\t\t\tcase DataCell::CellType::input_form:\n\t\t\t\t// This cell is there only for cutnpaste functionality; do not display.\n\t\t\t\tbreak;\n\n\t\t\tdefault:\n\t\t\t\tthrow std::logic_error(\"Unimplemented datacell type\");\n\t\t\t}\n\n\n\t\tif(w!=0) {\n\t\t\tcanvasses[i]->visualcells[&(*it)]=newcell;\n\t\t\tresize_codeinput_texview(it, last_configure_width);\n\n\t\t\t// Document cells are easy; just add. They have no parent in the DTree.\n\n\t\t\tif(it->cell_type==DataCell::CellType::document) {\n\t\t\t\tcanvasses[i]->scroll.add(*w);\n\n\t\t\t\tw->show_all(); // FIXME: if you drop this, the whole document remains invisible\n\n\t\t\t\tcanvasses[i]->connect_scroll_listener();\n\t\t\t\tcontinue;\n\t\t\t\t}\n\n\n\t\t\t// Figure out where to store this new VisualCell in the GUI widget\n\t\t\t// tree by exploring the DTree near the new DataCell.\n\t\t\t// First determine the parent cell and the corresponding Gtk::Box\n\t\t\t// so that we can determine where to pack_start this cell. At this\n\t\t\t// stage, all cells have parents.\n\n\t\t\tDTree::iterator parent = DTree::parent(it);\n\t\t\tassert(tr.is_valid(parent));\n\n\t\t\tVisualCell& parent_visual = canvasses[i]->visualcells[&(*parent)];\n\t\t\tGtk::Box *parentbox=0;\n\t\t\tint offset=0;\n\t\t\tif(parent->cell_type==DataCell::CellType::document)\n\t\t\t\tparentbox=parent_visual.document;\n\t\t\telse {\n\t\t\t\t// FIXME: Since we are adding children of input cells to the vbox in which\n\t\t\t\t// the exp_input_tv widget is the 0th cell, we have to offset. Would be\n\t\t\t\t// cleaner to have a separate 'children' vbox in CodeInput (or in fact\n\t\t\t\t// every widget that can potentially contain children).\n\t\t\t\toffset=1;\n\t\t\t\tparentbox=parent_visual.inbox;\n\t\t\t\t}\n\n\t\t\t//\t\tstd::cout << \"adding cell to canvas \" << i << std::endl;\n\t\t\tparentbox->pack_start(*w, false, false);\n\t\t\tunsigned int index    =tr.index(it)+offset;\n\t\t\tunsigned int index_gui=parentbox->get_children().size()-1;\n\t\t\t//\t\tstd::cout << \"is index \" << index << \" vs \" << index_gui << std::endl;\n\t\t\tif(index!=index_gui) {\n\t\t\t\t//\t\t\tstd::cout << \"need to re-order\" << std::endl;\n\t\t\t\tparentbox->reorder_child(*w, index);\n\t\t\t\t}\n\t\t\tif(visible) {\n\t\t\t\tw->show_all();\n\t\t\t\tw->show_now();\n\t\t\t\t}\n\n\t\t\tif(follow_mode) {\n\t\t\t\t// Find the next input cell.\n\t\t\t\tauto nxt = it;\n\t\t\t\twhile(!doc.is_head(doc.parent(nxt)))\n\t\t\t\t\tnxt = doc.parent(nxt);\n\t\t\t\tdo {\n\t\t\t\t\tnxt.skip_children();\n\t\t\t\t\t++nxt;\n\t\t\t\t\tif(nxt==doc.end())\n\t\t\t\t\t\tbreak;\n\t\t\t\t\t} while(nxt->cell_type!=DataCell::CellType::python);\n\t\t\t\t\n\t\t\t\tif(nxt!=doc.end()) {\n\t\t\t\t\t// std::cerr << \"going to \" << nxt->textbuf << std::endl;\n\t\t\t\t\tfollow_cell=nxt;\n\t\t\t\t\t}\n\t\t\t\telse\n\t\t\t\t\tfollow_cell=it;\n\t\t\t\t// Have to wait for the cell to be realised by GTK, we cannot\n\t\t\t\t// scroll there immediately because GTK will not know where to\n\t\t\t\t// scroll.\n            // scroll_cell_into_view(it);\n\t\t\t\t}\n\t\t\t}\n\n\t\t}\n\n\t// Connect\n\tGlib::signal_idle().connect(sigc::mem_fun(*this, &NotebookWindow::idle_handler));\n\n\t//\tif(current_cell!=doc.end())\n\t//\t\tsetup_focus_after_allocate(it);\n\t}\n\nvoid NotebookWindow::on_interactive_output(const nlohmann::json& msg)\n\t{\n\tconsole.signal_message(msg);\n\t}\n\nvoid NotebookWindow::set_progress(const std::string& msg, int cur_step, int total_steps)\n\t{\n\t\t{\n\t\tstd::lock_guard<std::mutex> guard(status_mutex);\n\t\tif (total_steps == 0) {\n\t\t\tprogress_string = msg;\n\t\t\tprogress_frac = 0.0;\n\t\t\t}\n\t\telse {\n\t\t\tprogress_frac = (double)cur_step / total_steps;\n\t\t\tprogress_string = msg + \" (\" + std::to_string(cur_step) + \"/\" + std::to_string(total_steps) + \")\";\n\t\t\t}\n\t\t}\n\tdispatch_update_status.emit();\n\t}\n\nvoid NotebookWindow::update_status()\n\t{\n\t// This should only be called from dispatch_update_status!\n\t// This will then run on the GUI thread, as it should.\n\n\t// Update status and progress, kernel status is taken card of in process_action_queue\n\tstd::lock_guard<std::mutex> guard(status_mutex);\n\tprogressbar.set_text(progress_string);\n\tprogressbar.set_fraction(progress_frac);\n\t\n\tstd::string pos = \" Line: \" + std::to_string(status_line)\n\t\t+ \"   Col: \" + std::to_string(status_col);\n\tif (status_string == \"\")\n\t\tstatus_label.set_text(pos);\n\telse\n\t\tstatus_label.set_text(pos + \"   |   \" + status_string);\n \t}\n\nvoid NotebookWindow::remove_cell(const DTree& doc, DTree::iterator it)\n\t{\n\t// Remember: this member should only remove the visual cell; the\n\t// document tree will be updated by the ActionRemove that led to this\n\t// member being called. However, we should ensure that any references\n\t// to the visual cell are removed as well; in particular, if\n\t// current_cell is pointing to this cell, we need to unset it.\n\n\t// Can only remove cells which have a parent (i.e. not the\n\t// top-level document cell).\n\n\tif(current_cell==it)\n\t\tcurrent_cell=doc.end();\n\n\t// Ensure we will not continue searching in this cell.\n\tif(last_find_location.first==it) {\n\t\tlast_find_location.first=doc.end();\n\t\tlast_find_location.second=std::string::npos;\n\t\t}\n\n\tDTree::iterator parent = DTree::parent(it);\n\tassert(doc.is_valid(parent));\n\n\tfor(unsigned int i=0; i<canvasses.size(); ++i) {\n\t\tVisualCell& parent_visual = canvasses[i]->visualcells[&(*parent)];\n\t\tGtk::Box *parentbox=0;\n\t\tif(it->cell_type==DataCell::CellType::document)\n\t\t\tparentbox=parent_visual.document;\n\t\telse\n\t\t\tparentbox=parent_visual.inbox;\n\n\n\t\tauto fnd = canvasses[i]->visualcells.find(&(*it));\n\t\t// It is possible that there is no visual cell corresponding to this\n\t\t// DTree cell (happens for instance when deleting a cell, undoing,\n\t\t// then re-evaluating: the DTree still has the output cells, while\n\t\t// they have gone from the visual tree).\n\t\tif(fnd==canvasses[i]->visualcells.end()) {\n\t\t\tstd::cerr << \"No visual cell for \" << it->id().id << std::endl;\n\t\t\tcontinue;\n\t\t\t}\n\n\t\tVisualCell& actual = fnd->second;//canvasses[i]->visualcells[&(*it)];\n\n\t\t// The pointers are all in a union, and Gtkmm does not care\n\t\t// about the precise type, so we just remove imagebox, knowing\n\t\t// that it may actually be an inbox or outbox.\n\t\t// std::cerr << \"Removing \" << actual.imagebox << std::endl;\n\t\tparentbox->remove(*actual.imagebox);\n\n\t\t// The above does not delete the Gtk widget, despite having been\n\t\t// wrapped in manage at construction. So we have to delete it\n\t\t// ourselves. Fortunately the container does not try to delete\n\t\t// it again in its destructor.\n\t\tdelete actual.imagebox;\n\n\t\t// The above removes the entire Gtk tree corresponding to the cell at\n\t\t// 'it' and the subtree below it. In order to remove all these from\n\t\t// the visualcells map, we need to walk the tree explicitly.\n\t\tdo_subtree(doc, it, [this, i](DTree::iterator rm) {\n#ifdef DEBUG\n\t\t\tstd::cerr << \"removing cell \" << &(*rm) << \" \" << rm->textbuf << \"\\n from canvas \" << i << std::endl;\n#endif\n\t\t\tauto fnd = canvasses[i]->visualcells.find(&(*rm));\n\t\t\tif(fnd!=canvasses[i]->visualcells.end()) {\n\t\t\t\tcanvasses[i]->visualcells.erase(fnd);\n\t\t\t\t}\n\t\t\telse {\n#ifdef DEBUG\n\t\t\t\tstd::cerr << \"no visualcell for that one\" << std::endl;\n#endif\n\t\t\t\t}\n\t\t\treturn rm;\n\t\t\t});\n\t\t}\n\tmodified=true;\n\tfollow_mode=true;\n\tfollow_cell=current_cell;\n\tupdate_title();\n\t}\n\nvoid NotebookWindow::remove_all_cells()\n\t{\n\t// std::cerr << \"REMOVE all cells\" << std::endl;\n\t// DTree::iterator it=doc.begin();\n\t// ++it;\n\t// while(it!=doc.end()) {\n\t// \tremove_cell(doc, it);\n\t// \t++it;\n\t// \t}\n\t\n\t// Simply removing the document cell should do the trick.\n\tfor(unsigned int i=0; i<canvasses.size(); ++i) {\n\t\tcanvasses[i]->scroll.remove();\n\t\tcanvasses[i]->visualcells.clear();\n\t\t}\n\tengine.checkout_all();\n\tupdate_title();\n\t}\n\nvoid NotebookWindow::update_cell(const DTree&, DTree::iterator it)\n\t{\n\t// We just do a redraw for now, but this may require more work later.\n\tdisable_stacks=true;\n\n\tfor(unsigned int i=0; i<canvasses.size(); ++i) {\n\t\tVisualCell& vc = canvasses[i]->visualcells[&(*it)];\n\t\tif(it->cell_type==DataCell::CellType::python || it->cell_type==DataCell::CellType::latex) {\n\t\t\tvc.inbox->update_buffer();\n\t\t\tvc.inbox->queue_draw();\n\t\t\t}\n\t\telse if(it->cell_type==DataCell::CellType::latex_view\n\t\t\t\t  || it->cell_type==DataCell::CellType::verbatim\n\t\t\t\t  || it->cell_type==DataCell::CellType::error\n\t\t\t\t  || it->cell_type==DataCell::CellType::output) {\n\t\t\tvc.outbox->image.set_latex(it->textbuf);\n\t\t\tvc.outbox->image.layout_latex();\n\t\t\tresize_codeinput_texview(it, last_configure_width);\n//\t\t\tvc.outbox->queue_draw();\n\t\t\t}\n\t\telse if(it->cell_type==DataCell::CellType::image_png) {\n\t\t\tvc.imagebox->set_image_from_base64(it->textbuf);\n\t\t\tvc.imagebox->queue_draw();\n\t\t\t}\n\t\telse if(it->cell_type==DataCell::CellType::image_svg) {\n\t\t\tvc.imagebox->set_image_from_svg(it->textbuf);\n\t\t\tvc.imagebox->queue_draw();\t\t\t\n\t\t\t}\n\t\t}\n\n\tdisable_stacks=false;\n\tupdate_title();\n\t}\n\nvoid NotebookWindow::position_cursor(const DTree& tr, DTree::iterator it, int pos)\n\t{\n\t//\tif(it==doc.end()) return;\n\t// std::cerr << \"cadabra-client: positioning cursor at cell \" << it->textbuf << std::endl;\n\tset_stop_sensitive( compute->number_of_cells_executing()>0 );\n\n\tif(canvasses[current_canvas]->visualcells.find(&(*it))==canvasses[current_canvas]->visualcells.end()) {\n\t\tstd::cerr << \"cadabra-client: Cannot find cell to position cursor.\" << std::endl;\n\t\treturn;\n\t\t}\n\n\tVisualCell& target = canvasses[current_canvas]->visualcells[&(*it)];\n\n\tGtk::Allocation alloc=target.inbox->get_allocation();\n\t// std::cerr << \"allocation for position box \" << alloc.get_width() << std::endl;\n\tif(alloc.get_width()<2) {\n\t\t// This box is not yet realised, which means that we cannot scroll to it either.\n\t\t// Re-schedule the position action for later.\n\t\t// std::cerr << \"Reschedule\" << std::endl;\n\t\tGlib::signal_timeout().connect_once(  [this, &tr, it, pos]() {\n\t\t\tposition_cursor(tr, it, pos);\n\t\t\t}, 30);\n\t\treturn;\n\t\t}\n\n\t// We now know that our target box is realized, so we can grab focus and\n\t// scroll to it.\n\ttarget.inbox->edit.grab_focus();\n\n\tif(pos>=0) {\n\t\tauto cursor=target.inbox->edit.get_buffer()->begin();\n\t\tcursor.forward_chars(pos);\n\t\ttarget.inbox->edit.get_buffer()->place_cursor(cursor);\n\t\t}\n\n\tcurrent_cell=it;\n\tif(follow_mode) {\n\t\t// std::cerr << \"POSITION follow cell\" << std::endl;\n\t\tfollow_cell=it;\n\t\tscroll_cell_into_view(it);\n\t\t}\n\t\n\tupdate_title();\n\t}\n\nvoid NotebookWindow::select_range(const DTree&, DTree::iterator it, int start, int len)\n\t{\n\tif(it->cell_type!=DataCell::CellType::python && it->cell_type!=DataCell::CellType::latex) {\n\t\tstd::cerr << \"Warning: select_range called on cell which is not python or latex.\" << std::endl;\n\t\treturn;\n\t\t}\n\n\tif(canvasses[current_canvas]->visualcells.find(&(*it))==canvasses[current_canvas]->visualcells.end()) {\n\t\tstd::cerr << \"cadabra-client: Cannot find cell to select range.\" << std::endl;\n\t\treturn;\n\t\t}\n\n\tVisualCell& target = canvasses[current_canvas]->visualcells[&(*it)];\n\n\tauto start_it=target.inbox->edit.get_buffer()->begin();\n\tstart_it.forward_chars(start);\n\tauto end_it=start_it;\n\tend_it.forward_chars(len);\n\t// std::cerr << start << \", \" << len << std::endl;\n\ttarget.inbox->edit.get_buffer()->select_range(start_it, end_it);\n\t}\n\nsize_t NotebookWindow::get_cursor_position(const DTree&, DTree::iterator it)\n\t{\n\tif(canvasses[current_canvas]->visualcells.find(&(*it))==canvasses[current_canvas]->visualcells.end()) {\n\t\tstd::cerr << \"cadabra-client: Cannot find cell to retrieve cursor position for.\" << std::endl;\n\t\treturn -1;\n\t\t}\n\n\tVisualCell& target = canvasses[current_canvas]->visualcells[&(*it)];\n\tsize_t offset = target.inbox->buffer->get_insert()->get_iter().get_offset();\n\n\treturn offset;\n\t}\n\nvoid NotebookWindow::scroll_current_cell_into_view()\n\t{\n\tif(current_cell==doc.end()) return;\n\t// FIXME: this gets triggered *a lot* on animations\n//\tstd::cerr << \"---- scroll current into view\" << std::endl;\n\tscroll_cell_into_view(current_cell);\n\t}\n\nvoid NotebookWindow::scroll_cell_into_view(DTree::iterator cell)\n\t{\n\tif(!follow_mode)\n\t\treturn;\n\n\t// This will trigger multiple times, but the scroller below\n\t// will not setup any animation for a target which is already\n\t// being pursued. So this is ok.\n\t// std::cerr << \"----- scroll into view\" << std::endl;\n\t// std::cerr << \"cell content to show: \" << cell->textbuf << std::endl;\n\n\tif(current_canvas>=(int)canvasses.size()) return;\n\n\t// std::cerr << \"canvas vadjustment = \" << canvasses[current_canvas]->scroll.get_vadjustment()->get_value() << std::endl;\n        \n\tif(canvasses[current_canvas]->visualcells.find(&(*cell))==canvasses[current_canvas]->visualcells.end()) return;\n\n\tconst VisualCell& focusbox = canvasses[current_canvas]->visualcells[&(*cell)];\n\n//\tif(focusbox.inbox==0) return;\n\n\tGtk::Allocation               al;\n\tif(cell->cell_type==DataCell::CellType::python ||\n\t\tcell->cell_type==DataCell::CellType::latex)\n\t\tal=focusbox.inbox->edit.get_allocation();\n\telse if(cell->cell_type==DataCell::CellType::latex_view ||\n\t\t\t  cell->cell_type==DataCell::CellType::output ||\n\t\t\t  cell->cell_type==DataCell::CellType::error ||\n\t\t\t  cell->cell_type==DataCell::CellType::verbatim)\n\t\tal=focusbox.outbox->get_allocation();\n\telse if(cell->cell_type==DataCell::CellType::image_png)\n\t\tal=focusbox.imagebox->get_allocation();\n\telse if(cell->cell_type==DataCell::CellType::image_svg)\n\t\tal=focusbox.imagebox->get_allocation();\n\telse if(cell->cell_type==DataCell::CellType::slider)\n\t\tal=focusbox.slider->get_allocation();\n\telse\n\t\treturn;\n\n\tGlib::RefPtr<Gtk::Adjustment> va=canvasses[current_canvas]->scroll.get_vadjustment();\n\n\tdouble upper_visible=va->get_value();\n\tdouble page_size    =va->get_page_size();\n\tdouble lower_visible=va->get_value()+page_size;\n\n\n\t// When we get called, the busybox has its allocation done and size set. However,\n\t// the edit box below still has its old position (but its correct height). So we\n\t// should make sure that busybox.y+busybox.height+editbox.height is at the bottom\n\t// of the scrollbox.\n//\tstd::cerr << \"viewport = \" << upper_visible << \" - \" << lower_visible << std::endl;\n//\tstd::cerr << \"cell to show = \" << al.get_y() << \" height \" << al.get_height() << std::endl;\n\n\tdouble should_be_visible = al.get_y()+al.get_height()+10;\n\tdouble shift = should_be_visible - lower_visible;\n//\tstd::cerr << \"position \" << should_be_visible << \" should be visible\" << std::endl;\n//\tstd::cerr << \"shift = \" << shift << std::endl;\n\tif(shift>0 || (-shift)>va->get_page_size()) {\n//\t\tva->set_value( upper_visible + shift);\n\t\t// std::cerr << \"SCROLLING \" << follow_mode << \" scroll from \" << upper_visible\n\t\t//\t\t\t << \" to \" << upper_visible + shift << std::endl;\n\t\tcanvasses[current_canvas]->scroller.scroll_to(upper_visible + shift);\n\t\t}\n\t}\n\nbool NotebookWindow::on_scroll_changed()\n\t{\n\tfollow_cell=doc.end();\n\tfollow_mode=false;\n\treturn false;\n\t}\n\nvoid NotebookWindow::on_slider_changed(std::string variable, double value)\n\t{\n\trun_cells_referencing_variable(variable, value);\n \t// std::cerr << \"Variable \" << variable << \" changed to value \" << value << std::endl;\n\t}\n\nvoid NotebookWindow::on_scroll_size_allocate(Gtk::Allocation& )\n\t{\n\t// The auto-scroll logic is as follows. Whenever a cell is ran (by\n\t// user pressing shift-enter only, not by full run), we set to\n\t// auto-scroll as soon as output for that cell appears. If multiple\n\t// cells are sent to the queue, we follow output for the last one\n\t// sent. Any scrollbar event stops auto-scrolling. Perhaps only\n\t// auto-restart when scrolling to the bottom of the notebook,\n\t// though that is not of much extra use. Could have a 'follow\n\t// current' mode when running an entire notebook, which is again\n\t// stopped by scrollbar event.\n\t\n\tif(follow_cell!=doc.end()) {\n\t\tscroll_cell_into_view(follow_cell);\n\t\t}\n\t}\n\nbool NotebookWindow::cell_toggle_visibility(DTree::iterator it, int )\n\t{\n\t// Find the parent node. If that one is a latex cell, toggle visibility of\n\t// the CodeInput widget (but not anything else in its vbox).\n\n\tif(read_only) return false;\n\tif(doc.hide_input_cells) return false;\n\t\n\tauto parent=DTree::parent(it);\n\tif(parent->cell_type==DataCell::CellType::latex) {\n\t\t// FIXME: we are not allowed to do this directly, all should go through\n\t\t// actions.\n\t\tparent->hidden = !parent->hidden;\n\t\tfor(unsigned int i=0; i<canvasses.size(); ++i) {\n\t\t\tauto vis = canvasses[i]->visualcells.find(&(*parent));\n\t\t\tif(vis==canvasses[i]->visualcells.end()) {\n\t\t\t\tthrow std::logic_error(\"Cannot find visual cell.\");\n\t\t\t\t}\n\t\t\telse {\n\t\t\t\tif(parent->hidden) {\n//\t\t\t\t\tGlib::signal_timeout().connect_once([it, this]()\n//\t\t\t\t\t\t\t{\n//\t\t\t\t\t\t\tresize_codeinput_texview(it, get_width());\n////\t\t\t\t\t\t\tw->queue_resize();\t\t\t\t\t\t\t\n//\t\t\t\t\t\t\t}, 50);\n\t\t\t\t\t(*vis).second.inbox->edit.hide();\n\t\t\t\t\tunselect_output_cell();\n//\t\t\t\t\tauto vis2 = canvasses[i]->visualcells.find(&(*it));\n//\t\t\t\t\tif(vis2==canvasses[i]->visualcells.end()) {\n//\t\t\t\t\t\tTeXView *w = (*vis2).second.outbox;\n//\t\t\t\t\t\tGlib::signal_timeout().connect_once([w]()\n//\t\t\t\t\t\t\t\t{\n//\t\t\t\t\t\t\t\tw->queue_resize();\t\t\t\t\t\t\t\n//\t\t\t\t\t\t\t\t}, 30);\n//\t\t\t\t\t\t}\n\t\t\t\t\t}\n\t\t\t\telse {\n\t\t\t\t\tCodeInput *w = (*vis).second.inbox;\n\t\t\t\t\tw->edit.show_all();\n\t\t\t\t\t// The very first time a widget is toggled to visible,\n\t\t\t\t\t// the TextView will have a height which is incorrect\n\t\t\t\t\t// (looks like it computes the maximal height if the\n\t\t\t\t\t// width would be minimal). The hack below makes that\n\t\t\t\t\t// problem go away. Similar to the hack used for\n\t\t\t\t\t// hide followed by immediate show.\n\t\t\t\t\tGlib::signal_timeout().connect_once([w]()\n\t\t\t\t\t\t\t{\n\t\t\t\t\t\t\tw->edit.queue_resize();\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t}, 30);\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t}\n\t\t}\n\n\treturn false;\n\t}\n\nbool NotebookWindow::cell_content_changed(DTree::iterator, int /* i */)\n\t{\n\tif(disable_stacks) return false;\n\n\tmodified=true;\n\tunselect_output_cell();\n\tupdate_title();\n\n\treturn false;\n\t}\n\nbool NotebookWindow::cell_content_insert(const std::string& content, int pos, DTree::iterator it, int)\n\t{\n\tif(disable_stacks) return false;\n\n\tunselect_output_cell();\n\tstd::shared_ptr<ActionBase> action = std::make_shared<ActionInsertText>(it->id(), pos, content);\n\tqueue_action(action);\n\tprocess_todo_queue();\n\n\treturn false;\n\t}\n\nbool NotebookWindow::cell_content_erase(int start, int end, DTree::iterator it, int )\n\t{\n\tif(disable_stacks) return false;\n\n\tunselect_output_cell();\n\t//std::cerr << \"cell_content_erase\" << std::endl;\n\tstd::shared_ptr<ActionBase> action = std::make_shared<ActionEraseText>(it->id(), start, end);\n\tqueue_action(action);\n\tprocess_todo_queue();\n\n\treturn false;\n\t}\n\nvoid NotebookWindow::dim_output_cells(DTree::iterator it)\n\t{\n\t// Dim the corresponding output cell, if any.\n\tauto ch=doc.begin(it);\n\twhile(ch!=doc.end(it)) {\n\t\tif(ch->cell_type==DataCell::CellType::latex_view) {\n\t\t\tfor(unsigned int i=0; i<canvasses.size(); ++i) {\n\t\t\t\tauto vc = canvasses[i]->visualcells.find(&(*ch));\n\t\t\t\tif(vc!=canvasses[i]->visualcells.end())\n\t\t\t\t\tvc->second.outbox->dim(true);\n\t\t\t\t}\n\t\t\t}\n\t\t++ch;\n\t\t}\n\n\t}\n\nbool NotebookWindow::cell_got_focus(DTree::iterator it, int canvas_number)\n\t{\n//\tstd::cerr << \"focus on cell \" << &(*it) << \" canvas \" << canvas_number << std::endl;\n\tcurrent_cell=it;\n\tcurrent_canvas=canvas_number;\n\n\tunselect_output_cell(); // cell_got_focus is an input cell, so output cells should not be selected anymore.\n\n\treturn false;\n\t}\n\nvoid NotebookWindow::interactive_execute()\n\t{\n\tuint64_t id = 0;\n\tstd::string input = console.grab_input(id);\n\tcompute->execute_interactive(id, input);\n\t}\n\nbool NotebookWindow::cell_complete_request(DTree::iterator it, int pos, int canvas_number)\n\t{\n\tif (!prefs.tab_completion)\n\t\treturn false;\n\n\tint cnum=0;\n\tif(undo_stack.size()>0) {\n\t\tauto cmp = std::dynamic_pointer_cast<ActionCompleteText>(undo_stack.top());\n\t\tif(cmp) {\n\t\t\t// std::cerr << \"Undoing last completion\" << std::endl;\n\t\t\tcmp->revert(*this, *gui);\n\t\t\tpos-=cmp->length();\n\t\t\tcnum=cmp->alternative()+1;\n\t\t\tundo_stack.pop();\n\t\t\t}\n\t\t}\n\treturn compute->complete(it, pos, cnum);\n\t}\n\nbool NotebookWindow::cell_content_execute(DTree::iterator it, bool shift_pressed)\n\t{\n\t// This callback runs on the GUI thread. The cell pointed to by\n\t// 'it' is guaranteed to be valid. This path is *not* used when\n\t// re-executing cells in response to a variable change triggered by\n\t// the notebook; that follows `on_slider_changed` which then calls\n\t// into the DocumentThread::run_cells_referencing_variable, which\n\t// in turn is responsible for the ComputeThread::execute_cell\n\t// call.\n\n\n\tset_stop_sensitive(true);\n\n\t// Since the user has initiated this cell execution, we can\n\t// turn on cell follow mode.\n\t// FIXME: this is also done in `run_cell` which we call below,\n\t// so unnecessary.\n\tfollow_cell=it;\n\tfollow_mode=true;\n\n\t// Use the `DocumentThread` method to actually run the cell.\n\trun_cell(it, shift_pressed);\n\t\n\treturn true;\n\t}\n\nvoid NotebookWindow::hide_visual_cells(DTree::iterator it)\n\t{\n\tfor(unsigned int i=0; i<canvasses.size(); ++i) {\n\t\tauto vis = canvasses[i]->visualcells.find(&(*it));\n\t\tif(vis==canvasses[i]->visualcells.end()) {\n\t\t\tthrow std::logic_error(\"Cannot find visual cell.\");\n\t\t\t}\n\t\telse {\n\t\t\t(*vis).second.inbox->edit.hide();\n\t\t\tit->hidden=true;\n\t\t\t}\n\t\t}\n\t}\n\nbool NotebookWindow::on_copy_as_latex(const DTree::iterator it)\n\t{\n\tGlib::RefPtr<Gtk::Clipboard> clipboard = Gtk::Clipboard::get(GDK_SELECTION_CLIPBOARD);\n\ton_outbox_copy(clipboard, it);\n\treturn true;\n\t}\n\nbool NotebookWindow::on_tex_error(const std::string& str, DTree::iterator it)\n\t{\n\t// Re-open the input cell if it was hidden, so we can fix the error.\n\tDTree::iterator pit = doc.parent(it);\n\tfor(unsigned int i=0; i<canvasses.size(); ++i) {\n\t\tauto vis = canvasses[i]->visualcells.find(&(*pit));\n\t\tif(vis==canvasses[i]->visualcells.end()) {\n\t\t\t}\n\t\telse {\n\t\t\tGtk::Widget& w = (*vis).second.inbox->edit;\n\t\t\t// Probably a bug: if we call show() without the delay below, we can have\n\t\t\t// the hide() and show() happen very quickly after each other, which does not\n\t\t\t// work (widget stays hidden).\n\t\t\tGlib::signal_timeout().connect_once([&w]() { w.show_all(); }, 50);\n\n\t\t\tpit->hidden=false;\n\t\t\t}\n\t\t}\n\n\tif(!prefs.microtex) {\n\t\t// Show the error in a dialog.\n\t\tGtk::MessageDialog md(\"Generic TeX error\", false, Gtk::MESSAGE_WARNING, Gtk::BUTTONS_OK, true);\n\t\tmd.set_resizable(true);\n\t\t//\tGtk::Button ok(Gtk::Stock::OK);\n\t\tmd.set_transient_for(*this);\n\t\tmd.set_type_hint(Gdk::WINDOW_TYPE_HINT_DIALOG);\n\t\tauto box = md.get_message_area();\n\t\t//\tmd.add_button(Gtk::Stock::OK, 1);\n\t\tGtk::ScrolledWindow sw;\n\t\tGtk::TextView tv;\n\t\tauto buffer = tv.get_buffer();\n\t\tbuffer->set_text(str);\n\t\t//\tauto iter = buffer->get_iter_at_offset(0);\n\t\t//\tbuffer->insert(iter, str);\n\t\ttv.set_editable(false);\n\t\tbox->add(sw);\n\t\tsw.add(tv);\n\t\tauto context = tv.get_style_context();\n\t\tcontext->add_class(\"error\");\n\n\t\tauto display = Gdk::Display::get_default();\n\t\tauto monitor = display->get_primary_monitor();\n\t\tGdk::Rectangle geometry;\n\t\tmonitor->get_geometry(geometry);\n\t\t\n\t\tsw.set_size_request(geometry.get_width()/4, geometry.get_width()/4);\n\t\tsw.show_all();\n\t\tmd.run();\n\t\t}\n\t\n\treturn true;\n\t}\n\nvoid NotebookWindow::on_file_new()\n\t{\n\tif(quit_safeguard(false)) {\n\t\tdoc.clear();\n\t\tremove_all_cells();\n\t\tnew_document();\n\t\tcompute->restart_kernel();\n\t\tposition_cursor(doc, doc.begin(doc.begin()), -1);\n\t\tname=\"\";\n\t\tupdate_title();\n\t\t}\n\t}\n\nvoid NotebookWindow::on_file_close()\n\t{\n\tif(quit_safeguard(true))\n\t\thide();\n\t}\n\nGlib::RefPtr<Gtk::FileFilter> create_filter(const Glib::ustring& name, const Glib::ustring& pattern)\n{\n\tauto filter = Gtk::FileFilter::create();\n\tfilter->set_name(name);\n\tfilter->add_pattern(pattern);\n\treturn filter;\n}\n\nvoid NotebookWindow::on_file_open()\n\t{\n\tif(quit_safeguard(false)==false)\n\t\treturn;\n\n\tGtk::FileChooserDialog dialog(\"Please choose a Cadabra notebook (.cnb file) to open\",\n\t                              Gtk::FILE_CHOOSER_ACTION_OPEN);\n\n\tdialog.set_transient_for(*this);\n\tdialog.add_filter(create_filter(\"Cadabra notebooks (*.cnb)\", \"*.cnb\"));\n\tdialog.add_filter(create_filter(\"All files\", \"*\"));\n\tdialog.add_button(\"_Cancel\", Gtk::RESPONSE_CANCEL);\n\tdialog.add_button(\"Select\", Gtk::RESPONSE_OK);\n\n\tint result=dialog.run();\n\n\tswitch(result) {\n\t\tcase(Gtk::RESPONSE_OK): {\n\t\t\tname = dialog.get_filename();\n\t\t\tsnoop::log(\"open\") << \"menu\" << snoop::flush;\n\t\t\tstd::ifstream file(name);\n\t\t\tstd::string content, line;\n\n\t\t\twhile(std::getline(file, line))\n\t\t\t\tcontent+=line;\n\n\t\t\tcompute->restart_kernel();\n\t\t\tload_from_string(content);\n\t\t\tbreak;\n\t\t\t}\n\t\t}\n\t}\n\nvoid NotebookWindow::set_name(const std::string& n)\n\t{\n\tname=n;\n\tupdate_title();\n\t}\n\nvoid NotebookWindow::load_from_string(const std::string& notebook_contents)\n\t{\n\tif(get_realized()==false) {\n\t\t// Loading new notebooks will only work if the main\n\t\t// UI elements, in particular the `mainbox`, have been\n\t\t// added to the window. This happens in `on_realize`,\n\t\t// and so we have to ensure that this has run.\n\t\trealize();\n\t\t}\n\n\tmainbox.set_sensitive(false);\n\n\tDocumentThread::load_from_string(notebook_contents);\n\n\tmainbox.show_all();\n\tmodified=false;\n\tupdate_title();\n\n\tGlib::signal_idle().connect( sigc::mem_fun(*this, &NotebookWindow::on_first_redraw) );\n\t}\n\nbool NotebookWindow::on_first_redraw()\n\t{\n\tmainbox.set_sensitive(true);\n\tif(doc.hide_input_cells)\n\t\tpropagate_global_hide_flag();\n\n\taction_hide_input_cells->set_state(Glib::Variant<bool>::create(doc.hide_input_cells));\n\n\treturn false;\n\t}\n\nvoid NotebookWindow::on_file_save()\n\t{\n\t// check if name known, otherwise call save_as\n\tif(name.size()>0) {\n\t\tsize_t dotpos = name.rfind(\".\");\n\t\tif(dotpos==std::string::npos)\n\t\t\tname += \".cnb\";\n\t\tstd::string res=save(name);\n\t\tif(res.size()>0) {\n\t\t\tGtk::MessageDialog md(\"Error saving notebook \"+name);\n\t\t\tmd.set_transient_for(*this);\n\t\t\tmd.set_secondary_text(res);\n\t\t\tmd.set_type_hint(Gdk::WINDOW_TYPE_HINT_DIALOG);\n\t\t\tmd.run();\n\t\t\t}\n\t\telse {\n\t\t\tmodified=false;\n\t\t\tupdate_title();\n\t\t\t}\n\t\t}\n\telse on_file_save_as();\n\t}\n\nvoid NotebookWindow::on_file_save_as()\n\t{\n\tGtk::FileChooserDialog dialog(\"Please choose a file name to save this notebook\",\n\t                              Gtk::FILE_CHOOSER_ACTION_SAVE);\n\n\tdialog.set_do_overwrite_confirmation(true);\n\tdialog.set_transient_for(*this);\n\tdialog.add_button(\"_Cancel\", Gtk::RESPONSE_CANCEL);\n\tdialog.add_button(\"Select\", Gtk::RESPONSE_OK);\n\n\tint result=dialog.run();\n\n\tswitch(result) {\n\tcase(Gtk::RESPONSE_OK): {\n\t\t\tstd::string old_name = name;\n\t\t\tname = dialog.get_filename();\n\t\t\tsize_t dotpos = name.rfind(\".\");\n\t\t\tif(dotpos==std::string::npos)\n\t\t\t\tname += \".cnb\";\n\t\t\tstd::string res=save(name);\n\t\t\tif(res.size()>0) {\n\t\t\t\tGtk::MessageDialog md(\"Error saving notebook \"+name);\n\t\t\t\tmd.set_transient_for(*this);\n\t\t\t\tmd.set_secondary_text(res);\n\t\t\t\tmd.set_type_hint(Gdk::WINDOW_TYPE_HINT_DIALOG);\n\t\t\t\tmd.run();\n\t\t\t\t}\n\t\t\telse {\n\t\t\t\tmodified=false;\n\t\t\t\tupdate_title();\n\t\t\t\tconsole.send_input(\"sys.path.insert(0, r'''\" + escape_backslashes(name.substr(0, name.find_last_of(\"\\\\/\"))) + \"''')\");\n\t\t\t\t}\n\t\t\tbreak;\n\t\t\t}\n\t\t}\n\t}\n\nvoid NotebookWindow::on_file_save_as_jupyter()\n\t{\n\tGtk::FileChooserDialog dialog(\"Please choose a file name to export as Jupyter notebook\",\n\t                              Gtk::FILE_CHOOSER_ACTION_SAVE);\n\n\tdialog.set_do_overwrite_confirmation(true);\n\tdialog.set_transient_for(*this);\n\tdialog.add_button(\"_Cancel\", Gtk::RESPONSE_CANCEL);\n\tdialog.add_button(\"Select\", Gtk::RESPONSE_OK);\n\n\tint result=dialog.run();\n\n\tswitch(result) {\n\t\tcase(Gtk::RESPONSE_OK): {\n\t\t\tstd::string ipynb_name = dialog.get_filename();\n\t\t\tstd::string out = JSON_serialise(doc);\n\t\t\tnlohmann::json json=nlohmann::json::parse(out);\n\t\t\tauto ipynb = cnb2ipynb(json);\n\t\t\tstd::ofstream file(ipynb_name);\n\t\t\tfile << ipynb.dump(3) << std::endl;\n\n//\t\t\tif(res.size()>0) {\n//\t\t\t\tGtk::MessageDialog md(\"Error saving Jupyter notebook \"+name);\n//\t\t\t\tmd.set_transient_for(*this);\n//\t\t\t\tmd.set_secondary_text(res);\n//\t\t\t\tmd.set_type_hint(Gdk::WINDOW_TYPE_HINT_DIALOG);\n//\t\t\t\tmd.run();\n//\t\t\t\t}\n\t\tbreak;\n\t\t}\n\t\t}\n\t}\n\nvoid NotebookWindow::on_file_export_html()\n\t{\n\tGtk::FileChooserDialog dialog(\"Please enter a file name for the HTML document\",\n\t                              Gtk::FILE_CHOOSER_ACTION_SAVE);\n\n\tdialog.set_do_overwrite_confirmation(true);\n\tdialog.set_transient_for(*this);\n\tdialog.add_button(\"_Cancel\", Gtk::RESPONSE_CANCEL);\n\tdialog.add_button(\"Select\", Gtk::RESPONSE_OK);\n\n\tint result=dialog.run();\n\n\tswitch(result) {\n\t\tcase(Gtk::RESPONSE_OK): {\n\t\t\tstd::string name = dialog.get_filename();\n\t\t\tstd::ofstream temp(name);\n\t\t\ttemp << export_as_HTML(doc);\n\t\t\t}\n\t\t}\n\t}\n\nvoid NotebookWindow::on_file_export_latex()\n\t{\n\tGtk::FileChooserDialog dialog(\"Please enter a file name for the LaTeX document\",\n\t                              Gtk::FILE_CHOOSER_ACTION_SAVE);\n\n\tdialog.set_do_overwrite_confirmation(true);\t\n\tdialog.set_transient_for(*this);\n\tdialog.add_button(\"_Cancel\", Gtk::RESPONSE_CANCEL);\n\tdialog.add_button(\"Select\", Gtk::RESPONSE_OK);\n\n\tint result=dialog.run();\n\n\tswitch(result) {\n\t\tcase(Gtk::RESPONSE_OK): {\n\t\t\tstd::string name = dialog.get_filename();\n\t\t\tsize_t dotpos = name.rfind(\".\");\n\t\t\tif(dotpos==std::string::npos) {\n\t\t\t\tname += \".tex\";\n\t\t\t\tdotpos = name.rfind(\".\");\n\t\t\t\t}\n\t\t\tstd::ofstream temp(name);\n\t\t\tstd::string base = name.substr(0, dotpos);\n\t\t\t// std::cerr << base << std::endl;\n\t\t\ttemp << export_as_LaTeX(doc, base);\n\t\t\t}\n\t\t}\n\t}\n\nvoid NotebookWindow::on_file_export_python()\n\t{\n\tGtk::FileChooserDialog dialog(\"Please enter a file name for the Python/Cadabra document\",\n\t                              Gtk::FILE_CHOOSER_ACTION_SAVE);\n\n\tdialog.set_do_overwrite_confirmation(true);\n\tdialog.set_transient_for(*this);\n\tdialog.add_button(\"_Cancel\", Gtk::RESPONSE_CANCEL);\n\tdialog.add_button(\"Select\", Gtk::RESPONSE_OK);\n\n\tint result=dialog.run();\n\n\tswitch(result) {\n\t\tcase(Gtk::RESPONSE_OK): {\n\t\t\tstd::string name = dialog.get_filename();\n\t\t\tsize_t dotpos = name.rfind(\".\");\n\t\t\tif(dotpos==std::string::npos)\n\t\t\t\tname += \".py\";\n\t\t\tstd::ofstream temp(name);\n\t\t\ttemp << export_as_python(doc);\n\t\t\t}\n\t\t}\n\t}\n\nvoid NotebookWindow::on_file_export_html_segment()\n\t{\n\t// FIXME: merge with on_file_export_html.\n\tGtk::FileChooserDialog dialog(\"Please enter a file name for the HTML segment\",\n\t                              Gtk::FILE_CHOOSER_ACTION_SAVE);\n\n\tdialog.set_do_overwrite_confirmation(true);\n\tdialog.set_transient_for(*this);\n\tdialog.add_button(\"_Cancel\", Gtk::RESPONSE_CANCEL);\n\tdialog.add_button(\"Select\", Gtk::RESPONSE_OK);\n\n\tint result=dialog.run();\n\n\tswitch(result) {\n\t\tcase(Gtk::RESPONSE_OK): {\n\t\t\tstd::string name = dialog.get_filename();\n\t\t\tsize_t dotpos = name.rfind(\".\");\n\t\t\tif(dotpos==std::string::npos)\n\t\t\t\tname += \".html\";\n\t\t\tstd::ofstream temp(name);\n\t\t\ttemp << export_as_HTML(doc, true);\n\t\t\t}\n\t\t}\n\t}\n\n// FIXME: this logic can go into DocumentThread to be system independent.\n\nstd::string NotebookWindow::save(const std::string& fn) const\n\t{\n\t// Make a backup first, just in case things go wrong.\n\tstd::ifstream old(fn.c_str());\n\tstd::ofstream temp(std::string(fn+\"~\").c_str());\n\n\tif(old) { // only backup if there is something to backup\n\t\tif(temp) {\n\t\t\tstd::string ln;\n\t\t\twhile(std::getline(old, ln)) {\n\t\t\t\ttemp << ln << \"\\n\";\n\t\t\t\tif(!temp) return \"Error writing backup file\";\n\t\t\t\t}\n\t\t\t}\n\t\telse {\n\t\t\treturn \"Failed to create backup file\";\n\t\t\t}\n\t\t}\n\n\tstd::string out = JSON_serialise(doc);\n\tstd::ofstream file(fn);\n\tfile << out << std::endl;\n\treturn \"\";\n\t}\n\nbool NotebookWindow::quit_safeguard(bool quit)\n\t{\n\tif(modified) {\n\t\tstd::string mes;\n\t\tif(quit) {\n\t\t\tif(name.size()>0) mes=\"Save changes to \"+name+\" before closing?\";\n\t\t\telse              mes=\"Save changes before closing?\";\n\t\t\t}\n\t\telse {\n\t\t\tif(name.size()>0) mes=\"Save changes to \"+name+\" before continuing?\";\n\t\t\telse              mes=\"Save changes before continuing?\";\n\t\t\t}\n\t\tGtk::MessageDialog md(mes, false, Gtk::MESSAGE_WARNING,\n\t\t                      Gtk::BUTTONS_NONE, true);\n\t\tmd.set_transient_for(*this);\n\t\tmd.set_type_hint(Gdk::WINDOW_TYPE_HINT_DIALOG);\n\t\tmd.add_button(\"Save before continuing\",1);\n\t\tmd.add_button(\"Cancel\",2);\n\t\tif(quit)\n\t\t\tmd.add_button(\"No need to save, quit now\",3);\n\t\telse\n\t\t\tmd.add_button(\"No need to save\", 3);\n\t\tint action=md.run();\n\t\tswitch(action) {\n\t\t\tcase 1:\n\t\t\t\ton_file_save();\n\t\t\t\treturn true;\n\t\t\tcase 2:\n\t\t\t\tbreak;\n\t\t\tcase 3:\n\t\t\t\treturn true;\n\t\t\t}\n\t\t}\n\telse return true;\n\n\treturn false;\n\t}\n\nvoid NotebookWindow::on_file_quit()\n\t{\n\t// FIXME: this needs to not just close the current window, but also all\n\t// other ones.\n\tif (quit_safeguard(true))\n\t\thide();\n\t}\n\nvoid NotebookWindow::on_edit_undo(const Glib::VariantBase&)\n\t{\n\tundo();\n\t}\n\nvoid NotebookWindow::on_edit_redo(const Glib::VariantBase&)\n\t{\n\tredo();\n\t}\n\nvoid NotebookWindow::on_edit_copy(const Glib::VariantBase&)\n\t{\n\tif(selected_cell!=doc.end()) {\n\t\tGlib::RefPtr<Gtk::Clipboard> clipboard = Gtk::Clipboard::get(GDK_SELECTION_CLIPBOARD);\n\t\ton_outbox_copy(clipboard, selected_cell);\n\t\t}\n\tif(current_cell!=doc.end()) {\n//\t\tstd::cerr << \"copy called for non-outbox cell\" << std::endl;\n\t\t// FIXME: handle other cell types.\n\t\t}\n\t}\n\nvoid NotebookWindow::on_edit_paste()\n\t{\n\tif(current_cell!=doc.end()) {\n\t\t// std::cerr << \"paste: \" << std::endl;\n      Glib::RefPtr<Gtk::Clipboard> clipboard = Gtk::Clipboard::get(GDK_SELECTION_CLIPBOARD);\n      clipboard->request_targets( [clipboard, this](const std::vector<Glib::ustring>& targets) {\n\t\t\t// Figure out which formats we can request.\n\t\t\tbool have_cadabra=false, have_utf8_string=false, have_text=false;\n\t\t\tfor(const auto& t: targets) {\n\t\t\t\t// std::cerr << t << std::endl;\n\t\t\t\tif(t==\"cadabra\")\n\t\t\t\t\thave_cadabra=true;\n\t\t\t\telse if(t==\"UTF8_STRING\")\n\t\t\t\t\thave_utf8_string=true;\n\t\t\t\telse if(t==\"TEXT\")\n\t\t\t\t\thave_text=true;\n\t\t\t\t}\n\t\t\t// Now insert.\n\t\t\tstd::string target;\n\t\t\tif(have_cadabra)   target=\"cadabra\";\n\t\t\telse if(have_utf8_string) target=\"UTF8_STRING\";\n\t\t\telse if(have_text)        target=\"TEXT\";\n\t\t\telse return;\n\n\t\t\t// std::cerr << \"requesting target \" << target << std::endl;\n\t\t\tclipboard->request_contents(target, [this](const Gtk::SelectionData& data) {\n\t\t\t\tstd::string content = data.get_data_as_string();\n\t\t\t\tauto vis = canvasses[current_canvas]->visualcells.find(&(*current_cell));\n\t\t\t\tif(vis!=canvasses[current_canvas]->visualcells.end()) {\n\t\t\t\t\t// std::cerr << \"inserting \" << content << std::endl;\n\t\t\t\t\tCodeInput *inbox = (*vis).second.inbox;\n\t\t\t\t\tinbox->edit.get_buffer()->insert_at_cursor(content);\n\t\t\t\t\t}\n//\t\t\t\telse {\n//\t\t\t\t\tstd::cerr << \"cannot find cell to insert into\" << std::endl;\n//\t\t\t\t\t}\n\t\t\t\t});\n\t\t\t});\n\t\t}\n\t}\n\nvoid NotebookWindow::on_edit_insert_above()\n\t{\n\tif(current_cell==doc.end()) return;\n\n\tDataCell newcell(DataCell::CellType::python, \"\");\n\tstd::shared_ptr<ActionBase> action =\n\t   std::make_shared<ActionAddCell>(newcell, current_cell->id(), ActionAddCell::Position::before);\n\tqueue_action(action);\n\tif (prefs.move_into_new_cell) {\n\t\tstd::shared_ptr<ActionBase> action2 =\n\t\t\tstd::make_shared<ActionPositionCursor>(newcell.id(), ActionPositionCursor::Position::in);\n\t\tqueue_action(action2);\n\t}\n\tprocess_data();\n\t}\n\nvoid NotebookWindow::on_edit_insert_below()\n\t{\n\tif(read_only) return;\n\t\n\tif(current_cell==doc.end()) return;\n\n\tDataCell newcell(DataCell::CellType::python, \"\");\n\tstd::shared_ptr<ActionBase> action =\n\t   std::make_shared<ActionAddCell>(newcell, current_cell->id(), ActionAddCell::Position::after);\n\tqueue_action(action);\n\tif(prefs.move_into_new_cell) {\n\t\tstd::shared_ptr<ActionBase> action2 =\n\t\t\tstd::make_shared<ActionPositionCursor>(newcell.id(), ActionPositionCursor::Position::in);\n\t\tqueue_action(action2);\n\t\t}\n\tprocess_data();\n\t}\n\nvoid NotebookWindow::on_edit_delete()\n\t{\n\tif(read_only) return;\n\t\n\tif(current_cell==doc.end()) return;\n\n\tif(current_cell->running) return; // we are still expecting results, don't delete\n\n\tDTree::sibling_iterator nxt=doc.next_sibling(current_cell);\n\tif(current_cell->textbuf==\"\" && doc.is_valid(nxt)==false) return; // Do not delete last cell if it is empty.\n\n\tstd::shared_ptr<ActionBase> action =\n\t   std::make_shared<ActionPositionCursor>(current_cell->id(), ActionPositionCursor::Position::next);\n\tqueue_action(action);\n\tstd::shared_ptr<ActionBase> action2 =\n\t   std::make_shared<ActionRemoveCell>(current_cell->id());\n\tqueue_action(action2);\n\tprocess_data();\n\t}\n\nvoid NotebookWindow::on_edit_find()\n\t{\n\tsearchbar.set_search_mode(true);\n\tsearchbar.set_show_close_button(true);\n\tsearchentry.grab_focus();\n\tsearch_result.set_text(\"\");\n\t}\n\nvoid NotebookWindow::on_search_text_changed()\n\t{\n\tconst auto text = searchentry.get_text();\n\tif(text.size()==0) return;\n\n\tauto start = std::make_pair<DTree::iterator, size_t>(doc.begin(), 0);\n\tif(last_find_location.second!=std::string::npos) {\n\t\tselect_range(doc, last_find_location.first, 0, 0);\n\t\tstart = last_find_location;\n\t\tif(last_find_string.size()==text.size())\n\t\t\t++start.second;\n\t\t}\n\telse {\n\t\t}\n\n\tauto res = find_string(start.first, start.second, text, search_case_insensitive.get_active());\n\tlast_find_location=res;\n\tlast_find_string=text;\n\tif(res.second!=std::string::npos) {\n\t\tif(res.first->cell_type!=DataCell::CellType::python &&\n\t\t\tres.first->cell_type!=DataCell::CellType::latex) {\n\t\t\tsearch_result.set_text(\"Found.\");\n\t\t\tscroll_cell_into_view(res.first);\n\t\t\t}\n\t\telse {\n\t\t\tcurrent_cell=res.first;\n\t\t\tsearch_result.set_text(\"Found.\");\n\t\t\tscroll_current_cell_into_view();\n\t\t\tselect_range(doc, res.first, res.second, text.size());\n\t\t\t}\n\t\t}\n\telse {\n\t\tlast_find_string=\"\";\n\t\tsearch_result.set_text(\"Not found, try again to start from start.\");\n\t\t}\n\t}\n\nvoid NotebookWindow::on_edit_split()\n\t{\n\tstd::shared_ptr<ActionBase> action = std::make_shared<ActionSplitCell>(current_cell->id());\n\tqueue_action(action);\n\tprocess_data();\n\t}\n\nvoid NotebookWindow::on_edit_cell_is_python()\n\t{\n\tif(current_cell==doc.end()) return;\n\n\tif(current_cell->cell_type==DataCell::CellType::latex) {\n\t\tcurrent_cell->cell_type = DataCell::CellType::python;\n\t\tupdate_cell(doc, current_cell);\n\t\t}\n\trefresh_highlighting();\n\t}\n\nvoid NotebookWindow::on_ignore_cell_on_import()\n\t{\n\tif(current_cell==doc.end()) return;\n\n\tcurrent_cell->ignore_on_import= !(current_cell->ignore_on_import);\n\tupdate_cell(doc, current_cell);\n\trefresh_highlighting();\n\t}\n\nvoid NotebookWindow::on_edit_cell_is_latex()\n\t{\n\tif(current_cell==doc.end()) return;\n\n\tif(current_cell->cell_type==DataCell::CellType::python) {\n\t\tcurrent_cell->cell_type = DataCell::CellType::latex;\n\t\tupdate_cell(doc, current_cell);\n\t\t}\n\trefresh_highlighting();\n\t}\n\nvoid NotebookWindow::on_view_split()\n\t{\n\tcanvasses.push_back(new NotebookCanvas());\n\t// Add the new canvas into the bottom pane of the last visible canvas.\n\tcanvasses[canvasses.size()-2]->pack2(*canvasses.back(), true, true);\n\tbuild_visual_representation();\n\tcanvasses.back()->show_all();\n\tcanvasses[canvasses.size()-2]->set_position(canvasses[canvasses.size()-2]->get_height()/2.0);\n\t}\n\nvoid NotebookWindow::on_view_close(const Glib::VariantBase&)\n\t{\n\t// FIXME: this always removes the last canvas, not the current one.\n\tif(canvasses.size()>1) {\n\t\tcanvasses[canvasses.size()-2]->remove(*canvasses.back());\n\t\tNotebookCanvas *oldcanvas = canvasses.back();\n\t\tcanvasses.pop_back();\n\t\tdelete oldcanvas;\n\t\t}\n\t}\n\nvoid NotebookWindow::on_run_cell()\n\t{\n\tif(read_only) return;\n\n\t// This is actually handled by the CodeInput widget, which ensures that the\n\t// DTree is up to date and then calls execute.\n\n\tVisualCell& actual = canvasses[current_canvas]->visualcells[&(*current_cell)];\n\tactual.inbox->edit.shift_enter_pressed();\n\n\t//\tcell_content_execute(current_cell, current_canvas);\n\t}\n\nvoid NotebookWindow::on_run_runtocursor()\n\t{\n\t// FIXME: It would be nicer to move this to DocumentThread, but since\n\t// we call `cell_content_execute` that's not yet possible. \n\n\tDTree::sibling_iterator sib=doc.begin(doc.begin());\n\twhile(sib!=current_cell && sib!=doc.end(doc.begin())) {\n\t\tif(sib->cell_type==DataCell::CellType::python) {\n\t\t\t// We trigger running of the cell by calling the callback\n\t\t\t// which CodeInput would call on a ctrl-enter press.\n\t\t\tscroll_cell_into_view(sib);\n\t\t\tcell_content_execute(DTree::iterator(sib), false);\n\t\t\t}\n\t\t++sib;\n\t\t}\n\t}\n\nvoid NotebookWindow::on_run_stop()\n\t{\n\tfollow_last_cell=doc.end();\n\tcompute->stop();\n\t}\n\nvoid NotebookWindow::on_kernel_restart()\n\t{\n\t// FIXME: add warnings\n\tkernel_string = \"restarting\";\n\tupdate_status();\n\tfollow_last_cell=doc.end();\n\t\n\tcompute->restart_kernel();\n\n\t\t{\n\t\tstd::lock_guard<std::mutex> guard(status_mutex);\n\t\tprogress_string = \"Idle\";\n\t\tprogress_frac = 0.0;\n\t\t}\n\n\tdispatch_update_status.emit();\n\t}\n\nvoid NotebookWindow::on_kernel_restart_and_run_all()\n\t{\n\t// Run all cells after the restart has completed.\n\trun_all_after_restart=true;\n\ton_kernel_restart();\n\t}\n\nvoid NotebookWindow::on_help() const\n\t{\n\tif(current_cell==doc.end()) return;\n\tif(current_cell->cell_type!=DataCell::CellType::python) return;\n\n\t// Figure out the keyword under the cursor.\n\tVisualCell& actual = canvasses[current_canvas]->visualcells[&(*current_cell)];\n\tstd::string before, after;\n\tactual.inbox->slice_cell(before, after);\n\n\thelp_t help_type;\n\tstd::string help_topic;\n\thelp_type_and_topic(before, after, help_type, help_topic);\n\n\tsnoop::log(\"help\") << help_topic << snoop::flush;\n\n\tbool ret=false;\n\tstd::string pref = cadabra::install_prefix()+\"/share/cadabra2/manual/\";\n\tif(help_type==help_t::algorithm)\n\t\tret=cdbapp->open_help(pref+\"algorithms/\"+help_topic+\".cnb\", help_topic);\n\tif(help_type==help_t::property)\n\t\tret=cdbapp->open_help(pref+\"properties/\"+help_topic+\".cnb\", help_topic);\n\n\tif(!ret) {\n\t\tGtk::MessageDialog md(\"No help available\", false, Gtk::MESSAGE_WARNING, Gtk::BUTTONS_OK, true);\n\t\tstd::cerr << \"NotebookWindow::on_help: did not find help in \" << pref << std::endl;\n\t\t//\t\tmd.set_transient_for(*this);\n\t\tmd.set_type_hint(Gdk::WINDOW_TYPE_HINT_DIALOG);\n\t\tmd.set_secondary_text(\"No help available for '\"+help_topic+\"'.\\nNot all algorithms and properties have manual pages yet, sorry.\");\n\t\tmd.run();\n\t\t}\n\t}\n\nvoid NotebookWindow::set_compute_thread(ComputeThread* cthread)\n\t{\n\tDocumentThread::set_compute_thread(cthread);\n\t}\n\nvoid NotebookWindow::on_help_about()\n\t{\n\tGlib::RefPtr<Gdk::Pixbuf> logo=Gdk::Pixbuf::create_from_file(cadabra::install_prefix()+\"/share/cadabra2/images/cadabra2-gtk.png\");\n\n\tGtk::AboutDialog about;\n\tabout.set_transient_for(*this);\n\tabout.set_program_name(\"Cadabra\");\n\tabout.set_comments(\"A field-theory motivated approach to computer algebra\");\n\tabout.set_version(std::string(\"Version \")+CADABRA_VERSION_SEM\n\t                  +\" (build \"+CADABRA_VERSION_BUILD+\" dated \"+CADABRA_VERSION_DATE+\")\");\n\tstd::vector<Glib::ustring> authors;\n\tauthors.push_back(\"Kasper Peeters\");\n\tabout.set_authors(authors);\n\tabout.set_copyright(std::string(\"\\xC2\\xA9 \")+COPYRIGHT_YEARS+std::string(\" Kasper Peeters\"));\n\tabout.set_license_type(Gtk::License::LICENSE_GPL_3_0);\n\tabout.set_website(\"http://cadabra.science\");\n\tabout.set_website_label(\"cadabra.science\");\n\tabout.set_logo(logo);\n\tstd::vector<Glib::ustring> special;\n\tspecial.push_back(\"José M. Martín-García (for the xPerm canonicalisation code)\");\n\tspecial.push_back(\"Dominic Price (for many additions, e.g. the conversion to pybind and the meld algorithm)\");\n\tspecial.push_back(\"Connor Behan (for various improvements related to index-free algorithms)\");\n\tspecial.push_back(\"James Allen (for writing much of the factoring code)\");\n\tspecial.push_back(\"NanoMichael (for the MicroTeX rendering library)\");\n\tspecial.push_back(\"Daniel Butter (substitute rule cache and other improvements)\");\n\tspecial.push_back(\"Software Sustainability Institute\");\n\tspecial.push_back(\"Institute of Advanced Study (for a Christopherson/Knott fellowship)\");\n\tabout.add_credit_section(\"Special thanks\", special);\n\tabout.run();\n\t}\n\nvoid NotebookWindow::on_help_register()\n\t{\n\tGtk::Dialog md(\"Welcome to Cadabra!\", *this, Gtk::MESSAGE_WARNING);\n\tmd.set_transient_for(*this);\n\tmd.set_type_hint(Gdk::WINDOW_TYPE_HINT_DIALOG);\n\tGtk::Box *box = md.get_content_area();\n\tGtk::Label txt;\n\ttxt.set_markup(\"<span font_size=\\\"large\\\" font_weight=\\\"bold\\\">Welcome to Cadabra!</span>\\n\\nWriting this software takes an incredible amount of spare time,\\nand it is extremely difficult to get funding for its development.\\n\\nPlease show your support by registering your email address,\\nso I can convince the bean-counters that this software is of interest.\\n\\nI will only use this address to count users and to email you,\\nroughly once every half a year, with a bit of news about Cadabra.\\n\\nMany thanks for your support!\\n\\nKasper Peeters, <a href=\\\"mailto:info@cadabra.science\\\">info@cadabra.science</a>\");\n\ttxt.set_line_wrap();\n\ttxt.set_margin_top(10);\n\ttxt.set_margin_start(10);\n\ttxt.set_margin_end(10);\n\ttxt.set_margin_bottom(10);\n\tbox->pack_start(txt, Gtk::PACK_EXPAND_WIDGET);\n\n\tGtk::Grid grid;\n\tgrid.set_column_homogeneous(false);\n\tgrid.set_hexpand(true);\n\tgrid.set_margin_start(10);\n\tgrid.set_margin_end(10);\n\tbox->pack_start(grid, Gtk::PACK_EXPAND_WIDGET);\n\n\tGtk::Label name_label(\"Name:\");\n\tGtk::Entry name;\n//\tname_label.set_alignment(0, 0.5);\n\tname.set_hexpand(true);\n\tgrid.attach(name_label, 0, 0, 1, 1);\n\tgrid.attach(name, 1, 0, 1, 1);\n\tGtk::Label email_label(\"Email address:\");\n//\temail_label.set_alignment(0, 0.5);\n\tGtk::Entry email;\n\temail.set_hexpand(true);\n\tgrid.attach(email_label, 0, 1, 1, 1);\n\tgrid.attach(email, 1, 1, 1, 1);\n\tGtk::Label affiliation_label(\"Affiliation:\");\n\tGtk::Entry affiliation;\n//\taffiliation_label.set_alignment(0, 0.5);\n\taffiliation.set_hexpand(true);\n\tgrid.attach(affiliation_label, 0, 2, 1, 1);\n\tgrid.attach(affiliation, 1, 2, 1, 1);\n\n\tGtk::Box hbox(Gtk::Orientation::ORIENTATION_HORIZONTAL);\n\tbox->pack_end(hbox, Gtk::PACK_SHRINK);\n\tGtk::Button reg(\"Register my support\"), nothanks(\"I prefer to stay anonymous\"), alreadyset(\"I am already registered\");\n\thbox.pack_end(reg, Gtk::PACK_SHRINK, 10);\n\thbox.pack_start(nothanks, Gtk::PACK_SHRINK, 10);\n\thbox.pack_start(alreadyset, Gtk::PACK_SHRINK, 10);\n\treg.signal_clicked().connect([&]() {\n\t\tset_user_details(name.get_text(), email.get_text(), affiliation.get_text());\n\t\tprefs.is_anonymous = false;\n\t\tprefs.is_registered = true;\n\t\tprefs.save();\n\t\tmd.hide();\n\t\t});\n\tnothanks.signal_clicked().connect([&]() {\n\t\tprefs.is_anonymous = true;\n\t\tprefs.is_registered = false;\n\t\tprefs.save();\n\t\tmd.hide();\n\t\t});\n\talreadyset.signal_clicked().connect([&]() {\n\t\tprefs.is_registered = true;\n\t\tprefs.is_anonymous = false;\n\t\tprefs.save();\n\t\tmd.hide();\n\t\t});\n\tbox->show_all();\n\tmd.run();\n\taction_register->set_enabled(!prefs.is_registered);\n\t}\n\nvoid NotebookWindow::on_text_scaling_factor_changed(const std::string& key)\n\t{\n#ifdef DEBUG\n\tstd::cerr << key << std::endl;\n#endif\n\tif(key==\"text-scaling-factor\" || key==\"scaling-factor\") {\n\t\tauto gdk_window = get_window();\n\t\tauto screen = Gdk::Screen::get_default();\n\t\tscale   = settings->get_double(\"text-scaling-factor\");\n\t\tscale  *= gdk_window->get_scale_factor();\n\t\tstd::cout << \"cadabra-client: total scaling-factor = \" << scale << std::endl;\n\t\tengine.set_scale(scale, gdk_window->get_scale_factor());\n\t\tengine.invalidate_all();\n\t\ttex_run_async();\n\n\t\t//remove_all_cells();\n\t\t//build_visual_representation();\n\t\tfor(unsigned int i=0; i<canvasses.size(); ++i)\n\t\t\tcanvasses[i]->refresh_all();\n\t\tresize_codeinput_texview_all(last_configure_width);\n\t\t}\n\t}\n\nvoid NotebookWindow::select_git_path()\n\t{\n\tSelectFileDialog dialog(\"Select git executable\", *this, true);\n\tdialog.set_transient_for(*this);\n\tdialog.set_text(prefs.git_path);\n\n\tif (dialog.run() == Gtk::RESPONSE_OK)\n\t\tprefs.git_path = dialog.get_text();\n\t}\n\nvoid NotebookWindow::compare_to_file()\n\t{\n\tstd::string filename;\n\n\tSelectFileDialog dialog(\"Select file to compare\", *this, true);\n\tdialog.set_transient_for(*this);\n\tif (dialog.run() == Gtk::RESPONSE_OK)\n\t\tfilename = dialog.get_text();\n\telse\n\t\treturn;\n\n\tstd::ifstream a(filename);\n\tif (!a.is_open()) {\n\t\tGtk::MessageDialog error_dialog(*this, \"The file '\" + filename + \"' could not be opened for reading\", false, Gtk::MESSAGE_ERROR, Gtk::BUTTONS_OK, true);\n\t\terror_dialog.set_title(\"Could not open file\");\n\t\terror_dialog.run();\n\t\treturn;\n\n\t\tstd::stringstream b;\n\t\tb << JSON_serialise(doc);\n\n\t\tdiffviewer = std::make_unique<DiffViewer>(a, b, *this);\n\t\t//diffviewer->set_transient_for(*this);\n\t\tdiffviewer->run_noblock();\n\t\t}\n\t}\n\nstd::string NotebookWindow::run_git_command(const std::string& args)\n\t{\n\tusing namespace TinyProcessLib;\n\n\tauto split_pos = name.find_last_of(\"\\\\/\");\n\tif (split_pos == std::string::npos)\n\t\tthrow std::runtime_error(\"File must be in a valid git directory\");\n\tstd::string path = name.substr(0, split_pos);\n\tstd::string output;\n\n\tProcess git(\n\t   prefs.git_path + \" \" + args,\n\t   path,\n\t[&output](const char* bytes, size_t n) {\n\t\toutput += std::string(bytes, n);\n\t\t},\n\t[&output](const char* bytes, size_t n) {\n\t\toutput += std::string(bytes, n);\n\t\t}\n\t);\n\n\tif (git.get_exit_status())\n\t\tthrow std::runtime_error(output);\n\telse\n\t\treturn output;\n\t}\n\nvoid NotebookWindow::compare_git(const std::string& commit_hash)\n\t{\n\tauto split_pos = name.find_last_of(\"\\\\/\");\n\tif (split_pos == std::string::npos || split_pos == name.size() - 1)\n\t\tthrow std::runtime_error(\"A valid file must be open\");\n\n\tauto prefix = trim(run_git_command(\"rev-parse --show-prefix\"));\n\tauto contents = run_git_command(\"show \" + commit_hash + \":\" + prefix + name.substr(split_pos + 1));\n\n\tstd::stringstream a, b;\n\ta << contents;\n\tb << JSON_serialise(doc);\n\n\tdiffviewer = std::make_unique<DiffViewer>(a, b, *this);\n\t//diffviewer->set_transient_for(*this);\n\tdiffviewer->run_noblock();\n\t}\n\nvoid NotebookWindow::compare_git_latest()\n\t{\n\ttry {\n\t\t// Get latest commit hash\n\t\tauto commit = run_git_command(\"log --pretty=format:%h -n 1\");\n\t\tcompare_git(trim(commit));\n\t\t}\n\tcatch (const std::exception& ex) {\n\t\tGtk::MessageDialog error_dialog(ex.what(), false, Gtk::MESSAGE_ERROR, Gtk::BUTTONS_OK, true);\n\t\terror_dialog.set_transient_for(*this);\n\t\terror_dialog.set_title(\"Git error\");\n\t\terror_dialog.run();\n\t\t}\n\t}\n\nclass GitChooseModelColumns : public Gtk::TreeModel::ColumnRecord {\n\tpublic:\n\t\tGitChooseModelColumns()\n\t\t\t{\n\t\t\tadd(commit_hash);\n\t\t\tadd(author);\n\t\t\tadd(timestamp);\n\t\t\tadd(description);\n\t\t\t}\n\n\t\tGtk::TreeModelColumn<std::string> commit_hash;\n\t\tGtk::TreeModelColumn<std::string> author;\n\t\tGtk::TreeModelColumn<std::string> timestamp;\n\t\tGtk::TreeModelColumn<std::string> description;\n\t};\n\n\nvoid NotebookWindow::compare_git_choose()\n\t{\n\ttry {\n\t\tstd::string commit_hash;\n\t\tstd::string max_entries = \"15\";\n\t\tauto commits = string_to_vec(run_git_command(\"log --pretty=format:%h -n \" + max_entries));\n\t\tauto authors = string_to_vec(run_git_command(\"log --pretty=format:%an -n \" + max_entries));\n\t\tauto times = string_to_vec(run_git_command(\"log --pretty=format:%ar -n \" + max_entries));\n\t\tauto descriptions = string_to_vec(run_git_command(\"log --pretty=format:%s -n \" + max_entries));\n\n\t\tGtk::TreeView tree_view;\n\t\tGitChooseModelColumns columns;\n\t\tGlib::RefPtr<Gtk::ListStore> list_store = Gtk::ListStore::create(columns);\n\n\t\tfor (size_t i = 0; i < commits.size(); ++i) {\n\t\t\tGtk::TreeModel::Row row = *(list_store->append());\n\t\t\trow[columns.commit_hash] = commits[i];\n\t\t\trow[columns.author] = authors[i];\n\t\t\trow[columns.timestamp] = times[i];\n\t\t\trow[columns.description] = descriptions[i];\n\t\t\t}\n\n\t\ttree_view.set_model(list_store);\n\t\ttree_view.append_column(\"Commit Hash\", columns.commit_hash);\n\t\ttree_view.append_column(\"Author\", columns.author);\n\t\ttree_view.append_column(\"Commit Time\", columns.timestamp);\n\t\ttree_view.append_column(\"Description\", columns.description);\n\n\t\tGtk::ScrolledWindow scrolled_window;\n\t\tscrolled_window.add(tree_view);\n\t\tscrolled_window.set_policy(Gtk::POLICY_NEVER, Gtk::POLICY_AUTOMATIC);\n\t\tscrolled_window.set_min_content_height(400);\n\n\t\tGtk::Dialog select_dialog(\"Select a commit to compare\", *this, true);\n\t\tselect_dialog.set_transient_for(*this);\n\t\tselect_dialog.get_content_area()->add(scrolled_window);\n\t\tselect_dialog.add_button(\"Compare\", Gtk::RESPONSE_OK);\n\t\tselect_dialog.add_button(\"Cancel\", Gtk::RESPONSE_CANCEL);\n\t\tselect_dialog.show_all();\n\n\t\tif (select_dialog.run() == Gtk::RESPONSE_OK)\n\t\t\tcommit_hash = tree_view.get_selection()->get_selected()->get_value(columns.commit_hash);\n\t\telse\n\t\t\treturn;\n\n\t\tcompare_git(trim(commit_hash));\n\t\t}\n\tcatch (const std::exception& ex) {\n\t\tGtk::MessageDialog error_dialog(ex.what(), false, Gtk::MESSAGE_ERROR, Gtk::BUTTONS_OK, true);\n\t\terror_dialog.set_transient_for(*this);\n\t\terror_dialog.set_title(\"Git error\");\n\t\terror_dialog.run();\n\t\t}\n\t}\n\nvoid NotebookWindow::compare_git_specific()\n\t{\n\ttry {\n\t\tstd::string commit_hash;\n\t\tGtk::Entry entry;\n\t\tGtk::Dialog entry_dialog(\"Enter hash of commit to compare against\", *this, true);\n\t\tentry_dialog.set_transient_for(*this);\n\t\tentry_dialog.get_content_area()->add(entry);\n\t\tentry_dialog.add_button(\"Compare\", Gtk::RESPONSE_OK);\n\t\tentry_dialog.add_button(\"Cancel\", Gtk::RESPONSE_CANCEL);\n\t\tentry_dialog.show_all();\n\n\t\tif (entry_dialog.run() == Gtk::RESPONSE_OK)\n\t\t\tcommit_hash = entry.get_text();\n\t\telse\n\t\t\treturn;\n\n\t\tcompare_git(trim(commit_hash));\n\t\t}\n\tcatch (const std::exception& ex) {\n\t\tGtk::MessageDialog error_dialog(ex.what(), false, Gtk::MESSAGE_ERROR, Gtk::BUTTONS_OK, true);\n\t\terror_dialog.set_transient_for(*this);\n\t\terror_dialog.set_title(\"Git error\");\n\t\terror_dialog.run();\n\t\t}\n\t}\n\nvoid NotebookWindow::on_prefs_auto_close_latex(const Glib::VariantBase& vb)\n\t{\n\tauto state_variant = action_auto_close_latex->get_state_variant(); //.get_bool();\n\tbool state = Glib::VariantBase::cast_dynamic<Glib::Variant<bool>>(state_variant).get();\n\t\n\tif(prefs.auto_close_latex == !state) return;\n\n\tprefs.auto_close_latex = !state;\n\taction_auto_close_latex->set_state(Glib::Variant<bool>::create(prefs.auto_close_latex));\n\tprefs.save();\n\t}\n\nvoid NotebookWindow::on_prefs_hide_input_cells(const Glib::VariantBase& vb)\n\t{\n\tauto state_variant = action_hide_input_cells->get_state_variant(); //.get_bool();\n\tbool state = Glib::VariantBase::cast_dynamic<Glib::Variant<bool>>(state_variant).get();\n\t\n\tif(doc.hide_input_cells == !state) return;\n\n\tmodified=true;\n\tupdate_title();\n\t\n\tdoc.hide_input_cells = !state;\n\taction_hide_input_cells->set_state(Glib::Variant<bool>::create(doc.hide_input_cells));\n\tprefs.save();\n\n\tpropagate_global_hide_flag();\n\t}\n\nvoid NotebookWindow::propagate_global_hide_flag()\n\t{\n\tauto ch=doc.begin();\n\twhile(ch!=doc.end()) {\n\t\tif(ch->cell_type==DataCell::CellType::python || ch->cell_type==DataCell::CellType::latex) {\n\t\t\tfor(unsigned int i=0; i<canvasses.size(); ++i) {\n\t\t\t\tauto vis = canvasses[i]->visualcells.find(&(*ch));\n\t\t\t\tif(vis==canvasses[i]->visualcells.end()) {\n\t\t\t\t\tthrow std::logic_error(\"Cannot find visual cell.\");\n\t\t\t\t\t}\n\t\t\t\telse {\n\t\t\t\t\tif(doc.hide_input_cells) {\n\t\t\t\t\t\t(*vis).second.inbox->edit.hide();\n\t\t\t\t\t\t}\n\t\t\t\t\telse {\n\t\t\t\t\t\tif(!ch->hidden)\n\t\t\t\t\t\t\t(*vis).second.inbox->edit.show();\n\t\t\t\t\t\t}\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t}\n\t\t++ch;\n\t\t}\n\t}\n\nvoid NotebookWindow::on_prefs_font_size(int num)\n\t{\n\tif(prefs.font_step==num) return;\n\n\tprefs.font_step=num;\n\taction_fontsize->set_state(Glib::Variant<int>::create(num));\n\tprefs.save();\n\t\n\tengine.set_font_size(12+(num*2));\n\tload_css();\n\n\tif(is_configured) {\n\t\t// std::cerr << \"cadabra-client: re-running TeX to change font size\" << std::endl;\n\t\t// No point in running TeX on all cells if we have not yet had an\n\t\t// on_configure_event signal; that will come after us and then we will\n\t\t// have to run all again.\n\t\tengine.invalidate_all();\n\t\ttex_run_async();\n\n\t\t//for(auto& canvas: canvasses) {\n\t\t//\tfor(auto& visualcell: canvas->visualcells) {\n\t\t//\t\tif(visualcell.first->cell_type==DataCell::CellType::python ||\n\t\t//\t\t      visualcell.first->cell_type==DataCell::CellType::latex) {\n\t\t//\t\t\tvisualcell.second.inbox->set_font_size(num);\n\t\t//\t\t\t}\n\t\t//\t\t}\n\t\t//\t}\n\n\t\t// remove_all_cells();\n\t\t// build_visual_representation();\n\t\tfor(unsigned int i=0; i<canvasses.size(); ++i)\n\t\t\tcanvasses[i]->refresh_all();\n\t\tresize_codeinput_texview_all(last_configure_width);\n\t\t}\n\t}\n\nvoid NotebookWindow::on_prefs_highlight_syntax(bool on)\n\t{\n\tif (prefs.highlight == on) return;\n\tprefs.highlight = on;\n\tprefs.save();\n\taction_highlight->set_state(Glib::Variant<int>::create(on));\n\t\n\tfor (auto& canvas : canvasses) {\n\t\tfor (auto& visualcell : canvas->visualcells) {\n\t\t\t// Need to be careful to only try and do this on latex or\n\t\t\t// python cells to avoid an exception being raised when\n\t\t\t// trying to edit an immutable cell type\n\t\t\tswitch (visualcell.first->cell_type) {\n\t\t\t\t// Fallthrough\n\t\t\t\tcase DataCell::CellType::python:\n\t\t\t\tcase DataCell::CellType::latex:\n\t\t\t\t\tif(on) {\n\t\t\t\t\t\tload_css();\n\t\t\t\t\t\tvisualcell.second.inbox->enable_highlighting(visualcell.first->cell_type, prefs);\n\t\t\t\t\t\t}\n\t\t\t\t\telse {\n\t\t\t\t\t\tload_css();\n\t\t\t\t\t\tvisualcell.second.inbox->disable_highlighting();\n\t\t\t\t\t\t}\n\t\t\t\t\tbreak;\n\t\t\t\tdefault:\n\t\t\t\t\tbreak;\n\t\t\t\t}\n\t\t\t}\n\t\t}\n\t}\n\nvoid NotebookWindow::on_prefs_microtex(bool on)\n\t{\n\tif (prefs.microtex == on) return;\n\tprefs.microtex = on;\n\tprefs.save();\n\taction_microtex->set_state(Glib::Variant<int>::create(on));\n\n\tGtk::MessageDialog md(\"Restart Cadabra to make the rendering setting take effect\",\n\t\t\t\t\t\t\t\t false, Gtk::MESSAGE_WARNING, Gtk::BUTTONS_OK, true);\n\tmd.set_resizable(false);\n\tmd.set_transient_for(*this);\n\tmd.set_type_hint(Gdk::WINDOW_TYPE_HINT_DIALOG);\n\tmd.run();\n\t\n// \tfor (auto& canvas : canvasses) {\n// \t\tfor (auto& visualcell : canvas->visualcells) {\n// \t\t\t// Need to be careful to only try and do this on latex or\n// \t\t\t// python cells to avoid an exception being raised when\n// \t\t\t// trying to edit an immutable cell type\n// \t\t\tswitch (visualcell.first->cell_type) {\n// \t\t\t\t// Fallthrough\n// \t\t\t\tcase DataCell::CellType::python:\n// \t\t\t\tcase DataCell::CellType::latex:\n// \t\t\t\t\tvisualcell.second.outbox->set_use_microtex(prefs.microtex);\n// \t\t\t\t\tbreak;\n// \t\t\t\tdefault:\n// \t\t\t\t\tbreak;\n// \t\t\t\t}\n// \t\t\t}\n// \t\t}\n\t}\n\nvoid NotebookWindow::on_prefs_choose_colours()\n\t{\n\tcadabra::ChooseColoursDialog dialog(prefs, *this);\n\tdialog.run();\n\tprefs.save();\n\t}\n\nvoid NotebookWindow::on_prefs_use_defaults()\n\t{\n\tGtk::MessageDialog sure(\"Use Default settings?\", false, Gtk::MESSAGE_QUESTION, Gtk::BUTTONS_YES_NO, true);\n\tsure.set_transient_for(*this);\n\tsure.set_secondary_text(\"This will effect font size and colour schemes.\");\n\tint response = sure.run();\n\tif (response == Gtk::RESPONSE_YES) {\n\t\tprefs = Prefs(true);\n\t\tfor (auto& action : default_actions)\n\t\t\taction->activate();\n\t\trefresh_highlighting();\n\t\taction_register->set_enabled(!prefs.is_registered);\n\t\tprefs.save();\n\t\t}\n\t}\n\nvoid NotebookWindow::on_tools_options()\n{\n\t// Create the dialog box\n\tGtk::Dialog options(\"Options\", false);\n\toptions.set_transient_for(*this);\n\toptions.get_content_area()->property_margin() = 5;\n\toptions.add_button(\"Apply\", Gtk::RESPONSE_APPLY);\n\toptions.add_button(\"Cancel\", Gtk::RESPONSE_CANCEL);\n\n\t// Helper functions for making option widgets\n\tauto add_label = [&options](const char* text, Gtk::Align alignment) {\n\t\tauto label = std::make_unique<Gtk::Label>();\n\t\tlabel->set_markup(text);\n\t\tlabel->set_halign(alignment);\n\t\toptions.get_content_area()->add(*label);\n\t\treturn label;\n\t};\n\tauto add_sep = [&options]() {\n\t\tauto sep = std::make_unique<Gtk::Separator>();\n\t\tsep->property_margin() = 5;\n\t\toptions.get_content_area()->add(*sep);\n\t\treturn sep;\n\t};\n\tauto add_checkbox = [&options](const char* label, bool active) {\n\t\tauto cb = std::make_unique<Gtk::CheckButton>(label);\n\t\tcb->set_active(active);\n\t\toptions.get_content_area()->add(*cb);\n\t\treturn cb;\n\t};\n\tauto add_entry = [&options](const Glib::ustring& val) {\n\t\tauto entry = std::make_unique<Gtk::Entry>();\n\t\tentry->set_text(val);\n\t\toptions.get_content_area()->add(*entry);\n\t\treturn entry;\n\t};\n\n\t// Add widgets & display\n\tauto py_opts = add_label(\"<b>Cadabra/Python Options</b>\", Gtk::ALIGN_CENTER);\n\tauto pypath_label = add_label(\"Default Python Path (semicolon separated):\", Gtk::ALIGN_START);\n\tauto pypath = add_entry(prefs.python_path);\n\tauto sep1 = add_sep();\n\tauto gui_opts = add_label(\"<b>GUI Options</b>\", Gtk::ALIGN_CENTER);\n\tauto auto_move = add_checkbox(\"Automatically move into a created cell\", prefs.move_into_new_cell);\n\tauto tab_completion = add_checkbox(\"Show possible completions with TAB\", prefs.tab_completion);\n\tauto sep2 = add_sep();\n\toptions.show_all();\n\tint res = options.run();\n\n\t// Options menu closed, run any updates\n\tif (res == Gtk::RESPONSE_APPLY) {\n\t\tif (prefs.python_path != pypath->get_text()) {\n\t\t\tprefs.python_path = pypath->get_text();\n\t\t\tGtk::MessageDialog md(*this, \"Changes to python path won't take effect until kernel is restarted; restart now?\", false, Gtk::MESSAGE_WARNING, Gtk::BUTTONS_YES_NO, true);\n\t\t\tmd.set_title(\"Python Path Changed\");\n\t\t\tmd.set_modal();\n\t\t\tmd.set_position(Gtk::WindowPosition::WIN_POS_CENTER);\n\t\t\tint res = md.run();\n\t\t\tif (res == Gtk::RESPONSE_YES) {\n\t\t\t\ton_kernel_restart();\n\t\t\t}\n\t\t}\n\t\tprefs.move_into_new_cell = auto_move->get_active();\n\t\tprefs.tab_completion = tab_completion->get_active();\n\t}\n\n}\n\nbool remove_recursive(const gchar* path)\n{\n\t// If filename is a file then we have reached the end of the recursion tree\n\tif (g_file_test(path, G_FILE_TEST_IS_REGULAR))\n\t\treturn g_remove(path) == 0;\n\tbool success = true;\n\tauto dir = g_dir_open(path, 0, NULL);\n\tfor (const gchar* child = g_dir_read_name(dir); child != NULL; child = g_dir_read_name(dir)) {\n\t\tgchar* fullpath = g_strconcat(path, G_DIR_SEPARATOR_S, child, NULL);\n\t\tsuccess = remove_recursive(fullpath);\n\t\tg_free(fullpath);\n\t\tif (!success)\n\t\t\tbreak;\n\t}\n\tg_dir_close(dir);\n\tif (!success)\n\t\treturn false;\n\n\treturn g_remove(path) == 0;\n}\n\nvoid NotebookWindow::on_tools_clear_cache()\n{\n\tGtk::MessageDialog prog(\"Removing cached library files, please wait...\", false, Gtk::MESSAGE_INFO, Gtk::BUTTONS_OK, true);\n\tprog.set_transient_for(*this);\n\tprog.set_title(\"Clearing cache\");\n\tprog.show_all();\n\n\tauto config_dir = Glib::ustring(g_get_user_config_dir()) + \"/cadabra_packages\";\n\tbool success = remove_recursive(config_dir.c_str());\n\n\tprog.set_message(success\n\t\t? \"Cache cleared!\"\n\t\t: \"Failed to remove cached library files. You can manually remove them by deleting the cadabra_packages folder in your config directory\"\n\t);\n\n\tprog.run();\n}\n\nvoid NotebookWindow::refresh_highlighting()\n\t{\n\tif (prefs.highlight) {\n\t\ton_prefs_highlight_syntax(false);\n\t\ton_prefs_highlight_syntax(true);\n\t\t}\n\t}\n\nbool NotebookWindow::idle_handler()\n\t{\n#if GTKMM_MINOR_VERSION>=10\n\tfor(auto& reveal: to_reveal) {\n\t\treveal->set_reveal_child(true);\n\t\t}\n\tto_reveal.clear();\n#endif\n\treturn false; // disconnect\n\t}\n\nvoid NotebookWindow::unselect_output_cell()\n\t{\n\tif(selected_cell==doc.end()) return;\n\n\tfor(unsigned int i=0; i<canvasses.size(); ++i) {\n\t\tif(canvasses[i]->visualcells.find(&(*selected_cell))!=canvasses[i]->visualcells.end()) {\n\t\t\tauto& outbox = canvasses[i]->visualcells[&(*selected_cell)].outbox;\n\t\t\toutbox->image.set_state_flags(Gtk::STATE_FLAG_NORMAL);\n\t\t\toutbox->queue_draw();\n\t\t\t}\n\t\t}\n\tselected_cell=doc.end();\n\taction_copy->set_enabled(false);\n\t}\n\nbool NotebookWindow::handle_outbox_select(GdkEventButton *, DTree::iterator it)\n\t{\n\t// std::cerr << \"handle_outbox_select \" << it->textbuf << std::endl;\n\tunselect_output_cell();\n\n\t// Colour the background of the selected cell, in all canvasses.\n\tfor(int i=0; i<(int)canvasses.size(); ++i) {\n\t\tif(canvasses[i]->visualcells.find(&(*it))!=canvasses[i]->visualcells.end()) {\n\t\t\tauto& outbox = canvasses[i]->visualcells[&(*it)].outbox;\n\t\t\toutbox->image.set_state_flags(Gtk::STATE_FLAG_SELECTED);\n\t\t\toutbox->queue_draw();\n\t\t\tif(i==current_canvas) {\n\t\t\t\toutbox->grab_focus();\n\t\t\t\t}\n\t\t\t}\n\t\t}\n\tselected_cell=it;\n\taction_copy->set_enabled(true);\n\n\t// We now require that the user ctrl-c's this before copying to the clipboard.\n\t// Glib::RefPtr<Gtk::Clipboard> clipboard = Gtk::Clipboard::get(GDK_SELECTION_PRIMARY);\n\t// on_outbox_copy(clipboard, selected_cell);\n\treturn true;\n\t}\n\nvoid NotebookWindow::on_outbox_copy(Glib::RefPtr<Gtk::Clipboard> refClipboard, DTree::iterator it)\n\t{\n\tstd::string cpystring=(*it).textbuf;\n\tstd::regex begin_dmath(R\"(\\\\begin\\{dmath\\*\\}\\{\\})\");\n\tstd::regex end_dmath(R\"(\\\\end\\{dmath\\*\\})\");\n\n\t// Find the child cell which contains the input_form data.\n\tauto sib=doc.begin(it);\n//\tstd::cerr << \"Finding children of \" << it->textbuf << std::endl;\n\twhile(sib!=doc.end(it)) {\n\t\tif(sib->cell_type==DataCell::CellType::input_form) {\n\t\t\tclipboard_cdb = sib->textbuf;\n\t\t\tclipboard_cdb = std::regex_replace(clipboard_cdb, begin_dmath, \"\");\n\t\t\tclipboard_cdb = std::regex_replace(clipboard_cdb, end_dmath, \"\");\n\t\t\tbreak;\n\t\t\t}\n\t\t++sib;\n\t\t}\n\n\t// Setup clipboard handling\n\tclipboard_txt = cpystring;\n\tclipboard_txt = std::regex_replace(clipboard_txt, begin_dmath, \"\");\n\tclipboard_txt = std::regex_replace(clipboard_txt, end_dmath, \"\");\n\tstd::vector<Gtk::TargetEntry> listTargets;\n\tif(clipboard_cdb.size()>0) {\n//\t\tstd::cerr << \"let them know we have cadabra format\" << std::endl;\n\t\tlistTargets.push_back( Gtk::TargetEntry(\"cadabra\") );\n\t\t}\n\tlistTargets.push_back( Gtk::TargetEntry(\"UTF8_STRING\") );\n\tlistTargets.push_back( Gtk::TargetEntry(\"TEXT\") );\n\trefClipboard->set( listTargets,\n\t                   sigc::mem_fun(this, &NotebookWindow::on_clipboard_get),\n\t                   sigc::mem_fun(this, &NotebookWindow::on_clipboard_clear) );\n\t}\n\nvoid NotebookWindow::on_clipboard_get(Gtk::SelectionData& selection_data, guint )\n\t{\n\tconst Glib::ustring target = selection_data.get_target();\n\n\tif(target == \"cadabra\") {\n//\t\tstd::cerr << \"received request for target cadabra: \" << clipboard_cdb << std::endl;\n\t\tselection_data.set(\"cadabra\", clipboard_cdb);\n\t\t}\n\telse if(target == \"UTF8_STRING\" || target==\"TEXT\") {\n\t\tselection_data.set_text(clipboard_txt);\n\t\t}\n\t}\n\nvoid NotebookWindow::on_clipboard_clear()\n\t{\n\t}\n"
  },
  {
    "path": "frontend/gtkmm/NotebookWindow.hh",
    "content": "\n#pragma once\n\n#include <gtkmm/window.h>\n#include <gtkmm/applicationwindow.h>\n#include <gtkmm/box.h>\n#include <gtkmm/progressbar.h>\n#include <gtkmm/spinner.h>\n#include <gtkmm/label.h>\n// #include <gtkmm/stock.h>\n#include <gtkmm/button.h>\n#include <gtkmm/builder.h>\n#include <gtkmm/cssprovider.h>\n// #include <gtkmm/toolbar.h>\n#include <glibmm/dispatcher.h>\n#include <giomm/settings.h>\n#include <giomm/actiongroup.h>\n\n#include <thread>\n#include <mutex>\n\n#include \"nlohmann/json.hpp\"\n\n#include \"DocumentThread.hh\"\n#include \"ComputeThread.hh\"\n#include \"Console.hh\"\n#include \"GUIBase.hh\"\n#include \"NotebookCanvas.hh\"\n#include \"../common/TeXEngine.hh\"\n#include \"DiffViewer.hh\"\n\nclass Cadabra;\n\nnamespace cadabra {\n\n\t/// \\ingroup frontend\n\t///\n\t/// Each notebook has one main window which controls it. It has a menu bar, a\n\t/// status pane and one or more panels that represent a view on the document.\n\n\tclass NotebookWindow : public Gtk::ApplicationWindow, public DocumentThread, public GUIBase {\n\t\tpublic:\n\t\t\tNotebookWindow(Cadabra *, bool read_only=false, std::string geometry=\"\", std::string title=\"\");\n\t\t\t~NotebookWindow();\n\n\t\t\t// Virtual functions from GUIBase.\n\n\t\t\tvirtual void   add_cell(const DTree&, DTree::iterator, bool) override;\n\t\t\tvirtual void   remove_cell(const DTree&, DTree::iterator) override;\n\t\t\tvirtual void   remove_all_cells() override;\n\t\t\tvirtual void   update_cell(const DTree&, DTree::iterator) override;\n\t\t\tvirtual void   position_cursor(const DTree&, DTree::iterator, int pos) override;\n\t\t\tvirtual size_t get_cursor_position(const DTree&, DTree::iterator) override;\n\t\t\tvirtual void   hide_visual_cells(DTree::iterator it) override;\n\t\t\tvirtual void   dim_output_cells(DTree::iterator it) override;\n\n\t\t\tvoid           select_range(const DTree&, DTree::iterator, int start, int len);\n\n\t\t\t// Implementations of the functions which the compute thread will\n\t\t\t// call directly. If these need to modify the GUI, they need to do\n\t\t\t// so by calling one of the dispatchers.\n\t\t\tvirtual void on_connect() override;\n\t\t\tvirtual void on_disconnect(const std::string&) override;\n\t\t\tvirtual void on_network_error() override;\n\t\t\tvirtual void on_kernel_runstatus(bool) override;\n\t\t\tvirtual void process_data() override;\n\n\t\t\t// TeX stuff\n\t\t\tTeXEngine        engine;\n\t\t\tdouble           scale; // total scale factor (hdpi and textscale)\n\t\t\tdouble           display_scale; // hdpi scale only\n\n\t\t\t// General setup.\n\t\t\tvoid on_realize() override;\n\t\t\t\n\t\t\t// Handler for vertical scrollbar changes. This gets connected to\n\t\t\t// all the `NotebookCanvas::scroll_event` signals.\n\t\t\tbool on_scroll_changed();\n\n\t\t\t// Handler for SliderView change events.\n\t\t\tvoid on_slider_changed(std::string variable, double value);\n\t\t\t\n\t\t\t// When something inside the large notebook canvas changes, we need\n\t\t\t// to make sure that the current cell stays into view (if we are\n\t\t\t// editing that cell). We can only do that once all size info is\n\t\t\t// known, which is when the scrolledwindow gets its size_allocate\n\t\t\t// signal. Here's the handler for it.\n\t\t\tvoid on_scroll_size_allocate(Gtk::Allocation&);\n\n\t\t\t// Ensure that the current cell is visible. This will assume\n\t\t\t// that all size allocations of widgets inside the scrolled window\n\t\t\t// have been made; it only does scrolling, based on the current\n\t\t\t// allocations. Calls `scroll_cell_into_view`.\n\t\t\tvoid scroll_current_cell_into_view();\n\n\t\t\t// Ensure that the indicated cell is visible.\n\t\t\tvoid scroll_cell_into_view(DTree::iterator cell);\n\n\t\t\tvoid set_name(const std::string&);\n\t\t\tvoid set_title_prefix(const std::string&);\n\n\t\t\tvoid refresh_highlighting();\n\t\t\tvoid on_help_register();\n\n\t\t\tvoid set_statusbar_message(const std::string& message = \"\", int line = -1, int col = -1);\n\n\t\t\t/// Functionality for the diff viewer.\n\t\t\tvoid select_git_path();\n\t\t\tvoid compare_to_file();\n\t\t\tvoid compare_git_latest();\n\t\t\tvoid compare_git_choose();\n\t\t\tvoid compare_git_specific();\n\t\t\tvoid compare_git(const std::string& commit_hash);\n\t\t\tstd::string run_git_command(const std::string& args);\n\n\t\t\tvirtual void load_from_string(const std::string& notebook_contents) override;\n\t\t\tvirtual void set_compute_thread(ComputeThread* compute) override;\n\n\t\t\tvirtual void on_interactive_output(const nlohmann::json& msg) override;\n\t\t\tvirtual void set_progress(const std::string& msg, int cur_step, int total_steps) override;\n\t\tprotected:\n\t\t\tvirtual bool on_key_press_event(GdkEventKey*) override;\n\t\t\tvirtual bool on_delete_event(GdkEventAny*) override;\n\t\t\tvirtual bool on_configure_event(GdkEventConfigure *cfg) override;\n\t\t\tvirtual bool on_unhandled_error(const std::exception& err) override;\n\n\t\t\tbool handle_outbox_select(GdkEventButton *, DTree::iterator it);\n\t\t\tDTree::iterator selected_cell;\n\t\t\tvoid unselect_output_cell();\n\t\t\tvoid on_outbox_copy(Glib::RefPtr<Gtk::Clipboard> refClipboard, DTree::iterator it);\n\n\t\tprivate:\n\t\t\tGlib::RefPtr<Cadabra> cdbapp;\n\n\t\t\tstd::vector<Glib::RefPtr<Gio::SimpleAction>> default_actions;\n\n\t\t\t// Main handler which fires whenever the Client object signals\n\t\t\t// that the document is changing or the network status is modified.\n\t\t\t// Runs on the GUI thread.\n\n\t\t\tGlib::Dispatcher dispatcher;\n\n\t\t\t// GUI elements.\n\n\t\t\tGlib::RefPtr<Gio::SimpleActionGroup> actiongroup;\n\t\t\tGlib::RefPtr<Gtk::Builder>           uimanager;\n\n\t\t\tGtk::Box                       topbox;\n\t\t\tGtk::Box                       toolbar;\n\t\t\tGtk::Button                    tool_open, tool_save, tool_save_as;\n\t\t\tGtk::Button                    tool_run, tool_run_to, tool_stop, tool_restart, tool_restart_and_run_all;\t\t\n\t\t\tGtk::Box                       supermainbox;\n\t\t\tGtk::Paned                     dragbox;\n\t\t\tGtk::Box                       mainbox;\n\t\t\tGtk::SearchBar                 searchbar;\n\t\t\tGtk::Box                       search_hbox;\n\t\t\tGtk::SearchEntry               searchentry;\n\t\t\tGtk::CheckButton               search_case_insensitive;\n\t\t\tGtk::Label                     search_result;\n\t\t\tGtk::Box                       statusbarbox;\n\n\t\t\tConsole console;\n\t\t\tGtk::Dialog console_win;\n\n\t\t\tstd::unique_ptr<DiffViewer> diffviewer;\n\n\t\t\t// All canvasses which are stored in the ...\n\t\t\t// These pointers are managed by gtkmm.\n\t\t\tstd::vector<NotebookCanvas *>  canvasses;\n\t\t\tint                            current_canvas;\n\n\t\t\t// Buttons\n\t\t\t//         Gtk::Button                    b_kill, b_run, b_run_to, b_run_from, b_help, b_stop, b_undo, b_redo;\n\n\t\t\t// Status bar\n\t\t\tGtk::ProgressBar               progressbar;\n\t\t\tGtk::Spinner                   kernel_spinner;\n\t\t\tbool                           kernel_spinner_status;\n\t\t\tGtk::Label                     status_label, kernel_label, top_label;\n\n\t\t\t// GUI data which is the autoritative source for things displayed in\n\t\t\t// the status bars declared above. These strings are filled on the\n\t\t\t// compute thread and then updated into the gui on the gui thread.\n\n\t\t\tstd::mutex                     status_mutex;\n\t\t\tstd::string                    status_string, kernel_string, progress_string;\n\t\t\tdouble                         progress_frac;\n\t\t\tint                            status_line, status_col;\n\n\t\t\t// Functions which get called on the compute thread can signal to\n\t\t\t// the GUI thread that elements need to be updated, by sending\n\t\t\t// signals using the following dispatchers.\n\t\t\tGlib::Dispatcher               dispatch_update_status, dispatch_refresh, dispatch_tex_error;\n\n\t\t\t// Update the status line and progress bar. This should only\n\t\t\t// be called on the GUI thread, so typically gets called\n\t\t\t// indirectly by calling `dispatch_update_status.emmit()`\n\t\t\t// from the compute thread, which calls this function.\n\t\t\tvoid                           update_status();\n\n\t\t\t// Run the TeX engine on a separate thread, then call\n\t\t\t// `dispatch_refresh` to update the display.\n\t\t\tvoid tex_run_async();\n\n\t\t\t// Name and modification data.\n\t\t\tvoid             update_title();\n\t\t\tvoid             set_stop_sensitive(bool);\n\t\t\tstd::string      name, title_prefix, geometry_string;\n\t\t\tbool             modified, read_only;\n\n\t\t\t// Menu and button callbacks.\n\t\t\tvoid on_file_new();\n\t\t\tvoid on_file_open();\n\t\t\tvoid on_file_close();\n\t\t\tvoid on_file_save();\n\t\t\tvoid on_file_save_as();\n\t\t\tvoid on_file_save_as_jupyter();\n\t\t\tvoid on_file_export_html();\n\t\t\tvoid on_file_export_html_segment();\n\t\t\tvoid on_file_export_latex();\n\t\t\tvoid on_file_export_python();\n\t\t\tvoid on_file_quit();\n\t\t\tbool quit_safeguard(bool quit);\n\t\t\tbool on_first_redraw();\n\n\t\t\tvoid on_edit_undo(const Glib::VariantBase&);\n\t\t\tvoid on_edit_redo(const Glib::VariantBase&);\n\t\t\tvoid on_edit_copy(const Glib::VariantBase&);\n\t\t\tvoid on_edit_paste();\n\t\t\tvoid on_edit_insert_above();\n\t\t\tvoid on_edit_insert_below();\n\t\t\tvoid on_edit_delete();\n\t\t\tvoid on_edit_split();\n\t\t\tvoid on_edit_cell_is_latex();\n\t\t\tvoid on_edit_cell_is_python();\n\t\t\tvoid on_ignore_cell_on_import();\n\t\t\tvoid on_edit_find();\n\n\t\t\tvoid on_view_split();\n\t\t\tvoid on_view_close(const Glib::VariantBase&);\n\n\t\t\tvoid on_run_cell();\n\t\t\tvoid on_run_runtocursor();\n\t\t\tvoid on_run_stop();\n\n\t\t\tvoid on_prefs_set_cv(int vis);\n\t\t\tvoid on_prefs_auto_close_latex(const Glib::VariantBase& vb);\n\t\t\tvoid on_prefs_hide_input_cells(const Glib::VariantBase& vb);\t\t\t\n\t\t\tvoid on_prefs_font_size(int num);\n\t\t\tvoid on_prefs_highlight_syntax(bool on);\n\t\t\tvoid on_prefs_microtex(bool on);\n\t\t\tvoid on_prefs_choose_colours();\n\t\t\tvoid on_prefs_use_defaults();\n\n\t\t\tvoid on_tools_options();\n\t\t\tvoid on_tools_clear_cache();\n\n\t\t\tvoid on_help_about();\n\t\t\tvoid on_help() const;\n\n\t\t\tvoid on_kernel_restart();\n\t\t\tvoid on_kernel_restart_and_run_all();\t\t\t\n\n\t\t\t/// Search handling.\n\t\t\tvoid on_search_text_changed();\n\n\t\t\t/// Clipboard handling\n\t\t\tvoid on_clipboard_get(Gtk::SelectionData&, guint info);\n\t\t\tvoid on_clipboard_clear();\n\t\t\tstd::string clipboard_txt, clipboard_cdb;\n\n\t\t\t// FIXME: move to DocumentThread\n\t\t\tstd::string save(const std::string& fn) const;\n\n\t\t\t/// Todo deque processing logic. This gets called by the dispatcher, but it\n\t\t\t/// is also allowed to call this from within NotebookWindow itself. The important\n\t\t\t/// thing is that it is run on the GUI thread.\n\t\t\t/// This is a wrapper around `Document::process_action_queue`, to set the\n\t\t\t/// spinner status and handle crashes.\n\t\t\tvoid process_todo_queue();\n\n\t\t\t/// Refresh the display after a TeX engine run has completed. The TeX\n\t\t\t/// engine is run on a different thread so as to not block the UI, and\n\t\t\t/// on completion triggers `dispatcher_refresh`, which calls this function\n\t\t\t/// on the main thread.\n\t\t\tvoid refresh_after_tex_engine_run();\n\n\t\t\t/// Handle a TeX error which occurred on a threaded TeX run (activated by\n\t\t\t/// `tex_run_async`) and is stored in `tex_error_string`.\n\t\t\tvoid handle_thread_tex_error();\n\n\t\t\tvoid on_crash_window_closed(int);\n\t\t\tbool crash_window_hidden;\n\n\t\t\t// The following are handlers that get called when the cell\n\t\t\t// gets focus, the content of a cell is changed, the user\n\t\t\t// requests to run it (shift-enter). The last two parameters are\n\t\t\t// always the cell in the DTree and the canvas number.\n\n\t\t\tbool cell_got_focus(DTree::iterator, int);\n\t\t\tbool cell_toggle_visibility(DTree::iterator it, int);\n\t\t\tbool cell_content_insert(const std::string&, int, DTree::iterator, int);\n\t\t\tbool cell_content_erase(int, int, DTree::iterator, int);\n\t\t\tbool cell_content_execute(DTree::iterator, bool shift_enter_pressed);\n\t\t\tbool cell_content_changed(DTree::iterator it, int i);\n\t\t\tbool cell_complete_request(DTree::iterator it, int pos, int i);\n\n\t\t\tvoid interactive_execute();\n\n\t\t\tvoid resize_codeinput_texview_all(int width);\n\t\t\tvoid resize_codeinput_texview(DTree::iterator, int width);\t\t\t\n\n\t\t\t// Handler for callbacks from TeXView cells.\n\n\t\t\tbool on_tex_error(const std::string&, DTree::iterator);\n\t\t\tbool on_copy_as_latex(const DTree::iterator it);\n\t\n\t\t\tvoid propagate_global_hide_flag();\n\t\t\t\n\t\t\t// Styling through CSS\n\t\t\tvoid                           load_css();\n\t\t\tGlib::RefPtr<Gtk::CssProvider> css_provider;\n\t\t\tGlib::RefPtr<Gio::Settings>    settings;\n\t\t\tvoid on_text_scaling_factor_changed(const std::string& key);\n\n\t\t\tint             last_configure_width;\n\n\t\t\t// Mutex to protect the variables below.\n\t\t\tstd::recursive_mutex         tex_need_width_mutex;\n\t\t\tstd::unique_ptr<std::thread> tex_thread;\n\t\t\tbool                         tex_running;\n\t\t\tint                          tex_need_width;\n\t\t\tstd::string                  tex_error_string;\n\n\t\t\tstd::pair<DTree::iterator, size_t> last_find_location;\n\t\t\tstd::string                        last_find_string;\n\n\t\t\tbool  is_configured;         // have received and handled a configure event\n\t\t\tbool  run_all_after_restart; // queue notebook running when kernel comes back\n\n\t\t\t// We keep references to a few menu actions so we can\n\t\t\t// enable/disable them at runtime.\n\t\t\tGlib::RefPtr<Gio::SimpleAction> action_copy, action_undo, action_redo,\n\t\t\t\taction_paste, action_view_close, action_fontsize, action_highlight,\n\t\t\t\taction_auto_close_latex, action_hide_input_cells,\n\t\t\t\taction_stop, action_register, action_console, action_microtex;\n\n\t\t\t// Transition animations.\n#if GTKMM_MINOR_VERSION>=10\n\t\t\tstd::vector<Gtk::Revealer *> to_reveal;\n#endif\n\t\t\tbool idle_handler();\n\t\t};\n\n\t};\n"
  },
  {
    "path": "frontend/gtkmm/Preferences.hh",
    "content": "\n#pragma once\n\n#include <gtkmm/window.h>\n#include <gtkmm/box.h>\n\nclass PreferencesWindow : public class Gtk::Window {\n\t\tpublic:\n\t\tprivate:\n\t\t\tGtk::Box mainbox;\n\t\t\tGtk::\n\t\t};\n"
  },
  {
    "path": "frontend/gtkmm/SelectFileDialog.cc",
    "content": "#include \"SelectFileDialog.hh\"\n\nSelectFileDialog::SelectFileDialog(const Glib::ustring& title, Gtk::Window& parent, bool modal)\n\t: Gtk::Dialog(title, parent, modal)\n\t, choose(\"...\")\n\t, hbox(Gtk::Orientation::ORIENTATION_HORIZONTAL)\n\t{\n\tset_resizable(false);\n\tentry.set_width_chars(60);\n\n\tchoose.signal_clicked().connect(sigc::mem_fun(*this, &SelectFileDialog::choose_dialog));\n\tchoose.set_hexpand(false);\n\n\thbox.pack_start(entry);\n\thbox.pack_end(choose);\n\n\tget_content_area()->pack_start(hbox);\n\tadd_button(\"Ok\", Gtk::RESPONSE_OK);\n\n\tshow_all();\n\t}\n\nvoid SelectFileDialog::set_text(const Glib::ustring& text)\n\t{\n\tentry.set_text(text);\n\t}\n\nGlib::ustring SelectFileDialog::get_text() const\n\t{\n\treturn entry.get_text();\n\t}\n\nGtk::Entry& SelectFileDialog::get_entry()\n\t{\n\treturn entry;\n\t}\n\nvoid SelectFileDialog::choose_dialog()\n\t{\n\tGtk::FileChooserDialog fc(\"Select a file...\");\n\tfc.set_transient_for(*this);\n\tfc.add_button(\"Cancel\", Gtk::RESPONSE_CANCEL);\n\tfc.add_button(\"Select\", Gtk::RESPONSE_OK);\n\n\tif (fc.run() == Gtk::RESPONSE_OK)\n\t\tentry.set_text(fc.get_filename());\n\t}\n"
  },
  {
    "path": "frontend/gtkmm/SelectFileDialog.hh",
    "content": "#pragma once\n\n#include <gtkmm.h>\n\nclass SelectFileDialog : public Gtk::Dialog {\n\tpublic:\n\t\tSelectFileDialog(const Glib::ustring& title, Gtk::Window& parent, bool modal = false);\n\n\t\tvoid set_text(const Glib::ustring& text);\n\t\tGlib::ustring get_text() const;\n\t\tGtk::Entry& get_entry();\n\n\tprotected:\n\t\tvoid choose_dialog();\n\n\t\tGtk::Entry entry;\n\t\tGtk::Button choose;\n\t\tGtk::Box hbox;\n\t};\n"
  },
  {
    "path": "frontend/gtkmm/SliderView.cc",
    "content": "\n#include \"SliderView.hh\"\n#include <giomm/memoryinputstream.h>\n#include <glibmm/base64.h>\n#include <iostream>\n#include <fstream>\n#include <nlohmann/json.hpp>\n\nusing namespace cadabra;\n\nint compute_scale_digits(double step_increment) {\n    if (step_increment >= 1.0) return 0;\n    \n    // Convert to string in scientific notation and find 'e-X' part\n    std::ostringstream ss;\n    ss << std::scientific << step_increment;\n    std::string str = ss.str();\n    \n    size_t e_pos = str.find('e');\n    if (e_pos == std::string::npos) return 0;\n    \n    // Parse the exponent\n    int exponent = std::stoi(str.substr(e_pos + 1));\n    return exponent < 0 ? -exponent : 0;\n}\n\nSliderView::SliderView(std::string config)\n\t{\n\t// Extract the settings from the JSON string.\n\tnlohmann::json settings = nlohmann::json::parse(config);\n\tvalue = settings.value(\"value\", 3.0);\n\tmin_value = settings.value(\"min_value\", 0.0);\n\tmax_value = settings.value(\"max_value\", 10.0);\n\tvariable  = settings.value(\"variable\", \"\");\n\tstep_size = settings.value(\"step_size\", 0.1);\n\n\tadd(vbox);\n\tadjustment = Gtk::Adjustment::create(\n\t\tvalue,       // value\n\t\tmin_value,   // lower\n\t\tmax_value,   // upper\n\t\tstep_size,   // step increment\n\t\t10.0,        // page_increment\n\t\t0.0          // page_size\n\t\t\t\t\t\t\t\t\t\t\t\t\t );\n\t\n\tscale.set_adjustment(adjustment);\n\tscale.set_digits(compute_scale_digits(step_size));\n\tscale.set_margin_start(20);\n\tscale.set_margin_end(20);\n\tvbox.pack_start(scale, Gtk::PACK_SHRINK);\n\tset_name(\"SliderView\"); // to be able to style it with CSS\n\tshow_all();\n\t}\n\nSliderView::~SliderView()\n\t{\n\t}\n\nstd::string SliderView::get_variable() const\n\t{\n\treturn variable;\n\t}\n"
  },
  {
    "path": "frontend/gtkmm/SliderView.hh",
    "content": "\n#pragma once\n\n#include <gtkmm/box.h>\n#include <gtkmm/scale.h>\n#ifndef USE_GTK4\n#include <gtkmm/eventbox.h>\n#endif\n#include <gtkmm/adjustment.h>\n\nnamespace cadabra {\n\n\t/// \\ingroup frontend\n\t///\n\t/// An slider widget. The configuration string is a JSON object\n\t/// which can contain the following key/value pairs:\n\t///\n\t///   - value:      double\n\t///   - min_value:  double\n\t///   - max_value:  double\n\t///   - variable:   string\n\n#ifdef USE_GTK4\n\tclass SliderView : public Gtk::Box {\n#else\n\tclass SliderView : public Gtk::EventBox {\n#endif\n\t\tpublic:\n\t\t\tSliderView(std::string config);\n\t\t\tvirtual ~SliderView();\n\n\t\t\tstd::string get_variable() const;\n\t\t\t\n\t\t\tGlib::RefPtr<Gtk::Adjustment> adjustment;\n\n\t\tprivate:\n\t\t\tGtk::VBox   vbox;\n\t\t\tGtk::Scale  scale;\n\n\t\t\tdouble value, min_value, max_value, step_size;\n\t\t\tstd::string variable;\n\t\t};\n\n\t};\n"
  },
  {
    "path": "frontend/gtkmm/TeXView.cc",
    "content": "\n#include \"TeXView.hh\"\n#include <iostream>\n#include <cairo/cairo.h>\n#include <cairomm/context.h>\n#include <giomm/resource.h>\n#include <gdkmm/general.h> // set_source_pixbuf()\n#include <regex>\n\n// MicroTeX\n#include \"cairo/graphic_cairo.h\"\n\nusing namespace cadabra;\n\nTeXView::TeXView(TeXEngine& eng, DTree::iterator it, bool use_microtex_, int hmargin)\n\t: content(0)\n\t, datacell(it)\n\t, vbox(Gtk::Orientation::ORIENTATION_VERTICAL, 10)\n\t, hbox(Gtk::Orientation::ORIENTATION_HORIZONTAL, hmargin)\n\t, image(use_microtex_, this)\n\t, engine(eng)\n\t, use_microtex(use_microtex_)\n\t, is_error(false)\n\t{\n\t// Still need to checkin even when using MicroTeX, otherwise\n\t// all requests will be empty.\n\tcontent = engine.checkin(datacell->textbuf, \"\", \"\");\n\t\n// \tadd(rbox);\n// \trbox.add(vbox);\n// \trbox.set_reveal_child(false);\n// \trbox.set_transition_duration(1000);\n// \trbox.set_transition_type(Gtk::REVEALER_TRANSITION_TYPE_CROSSFADE); //SLIDE_DOWN);\n\n\tvbox.set_margin_top(10);\n\tvbox.set_margin_bottom(0);\n//\tvbox.pack_start(hbox, true, 0);\n//\timage._text_size = text_size();\n//\thbox.pack_start(image, true, hmargin);\n\n\n//\tvbox.pack_start(hbox, true, 0);\n\timage._text_size = text_size();\n\tadd(image);\n\n\tadd_events( Gdk::BUTTON_PRESS_MASK | Gdk::BUTTON_RELEASE_MASK );\n\tset_can_focus(true);\n\n\tcontext_menu.append(item_copy_as_latex);\n\titem_copy_as_latex.set_label(\"Copy as LaTeX\");\n\tcontext_menu.show_all();\n\titem_copy_as_latex.signal_activate().connect(sigc::mem_fun(*this, &TeXView::on_copy_as_latex));\n\t}\n\nTeXView::~TeXView()\n\t{\n\tengine.checkout(content);\n\t}\n\nvoid TeXView::on_copy_as_latex() const\n\t{\n\tsignal_on_copy_as_latex.emit();\n\t}\n\nvoid TeXView::set_use_microtex(bool use_microtex_)\n\t{\n\tuse_microtex = use_microtex_;\n//\tremove(); // 'image' is the only child.\n\timage.use_microtex = use_microtex_;\n\tqueue_draw();\n//\tadd(image);\n\t}\n\nvoid TeXView::set_is_error(bool is_error_)\n\t{\n\tis_error=is_error_;\n\t}\n\nfloat TeXView::text_size() const\n\t{\n\t// The device pixel ratio scale is applied in the ::on_draw method,\n\t// so we do not scale the font size by that here. But we do need\n\t// to scale by the text scaling factor of the system, which is\n\t// available in engine.get_scale().\n\n\t// FIXME: we used to multiply with engine.get_scale() but that seems\n\t// wrong.\n\t\n\tfloat ret = 28.0f/12.0f*engine.get_font_size()*engine.get_scale()/engine.get_device_scale()/1.7f;\n//\tstd::cerr << \"engine.font_size = \" << engine.get_font_size() << \", .scale = \" << engine.get_scale()\n//\t\t\t\t << \", text_size = \" << ret << std::endl;\n\treturn ret;\n\t}\n\nvoid TeXView::on_show()\n\t{\n\t// std::cerr << \"**** show called\" << std::endl;\n\tconvert();\n\tGtk::EventBox::on_show();\n\t}\n\nGtk::SizeRequestMode TeXView::TeXArea::get_request_mode_vfunc() const\n\t{\n\treturn Gtk::SizeRequestMode::SIZE_REQUEST_HEIGHT_FOR_WIDTH;\n\t}\n\nvoid TeXView::TeXArea::get_preferred_height_for_width_vfunc(int width,\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tint& minimum_height, int& natural_height) const\n\t{\n\tif(use_microtex) {\n\t\tif(width==1) {\n\t\t\tminimum_height=9999;\n\t\t\tnatural_height=9999;\n\t\t\t// std::cerr << \"**** skipped bogus width\" << std::endl;\n\t\t\t}\n\t\telse {\n\t\t\t// If we are given a width which is not the window_width - 20, force the\n\t\t\t// width. This should not happen, but alas, it does.\n\t\t\t// std::cerr << width << \" > \" << owner->window_width - 20 << \"?\" << std::endl;\n\t\t\tif(owner->window_width != 0) {\n\t\t\t\tif(width > owner->window_width - 20)\n\t\t\t\t\twidth = owner->window_width - 20;\n\t\t\t\t}\n\t\t\tint remember = rendering_width;\n\t\t\trendering_width = width - 2*padding_x;\n\t\t\tlayout_latex();\n\t\t\tif(_render!=nullptr) {\n\t\t\t\tminimum_height = _render->getHeight() + 2*padding_y;\n\t\t\t\tnatural_height = _render->getHeight() + 2*padding_y;\n\t\t\t\t//\t\tstd::cerr << \"**** computed for width \" << width << \" height as \" << natural_height << std::endl;\n\t\t\t\t}\n\t\t\tif(rendering_width==9999)\n\t\t\t\trendering_width = remember;\n\t\t\t}\n      // std::cerr << \"**** asked height for width \" << width << \", replied \" << minimum_height << std::endl;\n\t\t}\n\telse {\n\t\tGtk::Widget::get_preferred_height_for_width_vfunc(width, minimum_height, natural_height);\n\t\t}\n\t}\n\nint TeXView::TeXArea::need_height(int width) const\n\t{\n\tint h1, h2;\n\tget_preferred_height_for_width_vfunc(width, h1, h2);\n\treturn h1;\n\t}\n\nvoid TeXView::TeXArea::get_preferred_width_for_height_vfunc(int height,\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tint& minimum_width, int& natural_width) const\n\t{\n\tGtk::Widget::get_preferred_width_for_height_vfunc(height, minimum_width, natural_width);\n\treturn;\n\t\n//\tif(height==0) {\n//\t\tminimum_width = 99999;\n//\t\tnatural_width = 99999;\n//\t\t}\n//\telse {\n//\t\tminimum_width = rendering_width + 2 * padding_x;\n//\t\tnatural_width = rendering_width + 2 * padding_x;\n//\t\t}\n//\tstd::cerr << \"**** asked width for height \" << height << \", replied \" << minimum_width << std::endl;\n\t}\n\nvoid TeXView::TeXArea::on_size_allocate(Gtk::Allocation& allocation)\n\t{\n\tif(owner->window_width != 0) {\n\t\t// std::cerr << \"setting texview width = \" << owner->window_width - 20 << std::endl;\n\t\tallocation.set_width(owner->window_width - 20);\n\t\t// allocation.set_height(need_height(owner->window_width - 20));\n\t\t}\n\tset_allocation(allocation);\n\t// std::cerr << \"**** offered allocation \" << allocation.get_width()\n\t// \t\t\t << \" x \" << allocation.get_height() << std::endl;\n\n\tif(use_microtex) {\n\t\tif(allocation.get_width() != rendering_width + 2*padding_x) {\n//\t\tstd::cerr << \"**** need to rerender\" << std::endl;\n\t\t\trendering_width = allocation.get_width() - 2*padding_x;\n\t\t\tlayout_latex();\n\t\t\t}\n\t\t// Some truly undocumented behaviour is happening when messing with\n\t\t// size allocation in gtk-3.0. In any case, if we need a new height,\n\t\t// we need to request a new size as below.\n\t\tint extra = (int) (padding_y * 2);\n\t\tint my_height = _render->getHeight() + extra;\n\t\tif(allocation.get_height() != my_height) {\n\t\t\t// std::cerr << \"*** need new height \" << my_height << std::endl;\n\t\t\tset_size_request(rendering_width, my_height);\n\t\t\tqueue_resize();\n\t\t\t// queue_draw();\n\t\t\t}\n\t\t}\n\t}\n\nvoid TeXView::convert()\n\t{\n//\tstd::cerr << \"*** convert called\" << std::endl;\n\ttry {\n\t\t// Ensure that all TeX cells have been rendered by TeX. This will do nothing\n\t\t// if no TeX cells need (re-)rendering. When adding many cells in one go, do so\n\t\t// in hidden state. Then, at first show, the first cell will trigger the\n\t\t// convert_all and run TeX on all cells in one shot.\n\n\t\tif(!use_microtex) {\n\t\t\tengine.convert_all();\n\t\t\t}\n\n\t\t// Set the Pixbuf to the image generated by engine.\n\t\t// The `content` variable is the TeXRequest.\n\t\timage.update_image(content, engine.get_scale());\n\t\t}\n\tcatch(TeXEngine::TeXException& ex) {\n\t\ttex_error.emit(ex.what());\n\t\t}\n\t}\n\n\nvoid TeXView::dim(bool d)\n\t{\n\tif(d) image.set_opacity(0.3);\n\telse  image.set_opacity(1.0);\n\t}\n\nbool TeXView::on_button_release_event(GdkEventButton *event)\n\t{\n\tif(event->button == 1) {\n\t\tshow_hide_requested.emit(datacell);\n\t\treturn true;\n\t\t}\n\treturn false;\n\t}\n\nbool TeXView::on_button_press_event(GdkEventButton *event)\n\t{\n\tif(event->type==GDK_BUTTON_PRESS) {\n\t\tif(event->button == 3) {\n\t\t\tcontext_menu.popup_at_pointer((GdkEvent*)event);\n\t\t\treturn true;\n\t\t\t}\n\t\t}\n\treturn false;\n\t}\n\nvoid TeXView::update_image()\n\t{\n\tfloat new_size = text_size();\n\tif(image._text_size != new_size) {\n\t\timage._text_size = new_size;\n\t\tif(use_microtex)\n\t\t\timage.layout_latex();\n\t\t}\n\timage.update_image(content, engine.get_scale());\n\t}\n\nvoid TeXView::TeXArea::update_image(std::shared_ptr<TeXEngine::TeXRequest> content, double scale)\n\t{\n\tif(use_microtex) {\n\t\tif(content) {\n\t\t\tif(content->latex()!=unfixed)\n\t\t\t\tset_latex(content->latex());\n\t\t\t}\n\t\t}\n\telse {\n\t\tif(content->image().size()==0)\n\t\t\treturn;\n\t\t\n\t\tif(content->image().data()==0)\n\t\t\treturn;\n\t\t\n\t\t\n\t\tpixbuf =\n\t\t\tGdk::Pixbuf::create_from_data(content->image().data(), Gdk::COLORSPACE_RGB,\n\t\t\t\t\t\t\t\t\t\t\t\t\ttrue,\n\t\t\t\t\t\t\t\t\t\t\t\t\t8,\n\t\t\t\t\t\t\t\t\t\t\t\t\tcontent->width(), content->height(),\n\t\t\t\t\t\t\t\t\t\t\t\t\t4*content->width());\n\t\t\n\t\tif(pixbuf)\n\t\t\tset_size_request(pixbuf->get_width(), pixbuf->get_height());\n\t\t\n\t\t//\tupdate=true;\n\t\tscale_=scale;\n\t\t// HERE\n\t\t//\timage.set(pixbuf);\n\t\t}\n\t}\n\nvoid TeXView::TeXArea::layout_latex() const\n\t{\n\tif(_render) {\n\t\tdelete _render;\n\t\t_render = nullptr;\n\t\t}\n\n//\tstd::cerr << \"running layout with text_size = \" << _text_size << std::endl;\n\ttry {\n\t\t// std::cerr << \"fixed = \" << fixed << std::endl;\n\t\t_render = microtex::MicroTeX::parse(\n\t\t\tfixed, //microtex::utf82wide(fixed),\n\t\t\trendering_width,\n\t\t\t_text_size,\n\t\t\t_text_size / 3.f,\n\t\t\t0xff424242);\n\t\t}\n\tcatch(std::exception& err) {\n\t\t// std::cerr << \"MicroTeX::parse: exception parsing input (\" << fixed << \"): \" << err.what() << std::endl;\n\t\towner->tex_error.emit(err.what());\n\n\t\t// Instead put an error message in the output cell.\n\t\tstd::cerr << err.what() << std::endl;\n\t\tstd::cerr << fixed << std::endl;\n\t\t_render = microtex::MicroTeX::parse(\n\t\t\t\"\\\\text{\\\\textcolor{red}{\\\\LaTeX error, probably mismatching brackets.}}\", //microtex::utf82wide(fixed),\n\t\t\trendering_width,\n\t\t\t_text_size,\n\t\t\t_text_size / 3.f,\n\t\t\t0xff424242);\n\t\t}\n\t}\n\nguint32 color_from_rgba(Gdk::RGBA color)\n\t{\n\treturn\n\t\t(guint8)(color.get_alpha()*255)<<24|\n\t\t(guint8)(color.get_red()*255)<<16|\n\t\t(guint8)(color.get_green()*255)<<8|\n\t\t(guint8)(color.get_blue()*255);\n\t}\n\nbool TeXView::TeXArea::on_draw(const Cairo::RefPtr<Cairo::Context>& cr)\n\t{\n\tif(use_microtex) {\n\t\tauto style_context = get_style_context();\n\t\tstyle_context->render_background(cr, 0, 0, get_width(), get_height());\n\t\tGdk::RGBA fg_colour;\n\t\t// Theme colour names can be found at\n\t\t// https://stackoverflow.com/questions/35045469/default-gtk-css-color-scheme\n\t\tif(owner->is_error) \n\t\t\tstyle_context->lookup_color(\"error_color\", fg_colour);\n\t\telse\n\t\t\tstyle_context->lookup_color(\"theme_text_color\", fg_colour);\n\t\t\n\t\tauto surface = cr->get_target();\n\t\tauto csurface = surface->cobj();\n\t\t// double device_scale_x, device_scale_y;\n\t\t// cairo_surface_get_device_scale(csurface, &device_scale_x, &device_scale_y);\n      //\tstd::cerr << \"scale = \" << device_scale_x << \", height = \"<< _render->getHeight() << std::endl;\n\t\tcr->scale(1.0, 1.0); // /device_scale_x, 1.0/device_scale_y);\n\n\t\tif (_render == nullptr) return true;\n\t\t\n\t\tmicrotex::Graphics2D_cairo g2(cr->cobj());\n\t\t_render->setForeground(color_from_rgba(fg_colour));\n\t\t_render->draw(g2, padding_x, padding_y);\n\t\t\n\t\tcr->scale(1.0, 1.0);\n\t\treturn true;\n\t\t}\n\telse {\n\t\tif(!pixbuf) return false;\n\t\t\n\t\t//\tGtk::Allocation allocation = get_allocation();\n\t\t//\tconst int width = allocation.get_width();\n\t\t//\tconst int height = allocation.get_height();\n\t\tauto surface = cr->get_target();\n\t\tauto csurface = surface->cobj();\n\t\t//\tcairo_surface_set_device_scale(csurface, 1.0, 1.0);\n\t\t//\tcairo_surface_mark_dirty(csurface);\n\t\tdouble device_scale_x, device_scale_y;\n\t\tcairo_surface_get_device_scale(csurface, &device_scale_x, &device_scale_y);\n\t\t//\tstd::cerr << device_scale_x << std::endl;\n\t\tset_size_request(pixbuf->get_width()/device_scale_x  + 2*padding_x,\n\t\t\t\t\t\t\t  pixbuf->get_height()/device_scale_y + 1 + 2*padding_y);\n\t\tcr->scale(1.0/device_scale_x, 1.0/device_scale_y);\n\t\tcr->translate(padding_x, padding_y);\n\t\tGdk::Cairo::set_source_pixbuf(cr, pixbuf, 0, 0);\n\t\tcr->paint();\n\t\tcr->scale(1.0, 1.0);\n\t\tcr->translate(0, 0);\n\t\t\n\t\treturn true;\n\t\t}\n\t}\n\nstd::string TeXView::TeXArea::verbatimise(const std::string& inp) const\n\t{\n\tstd::string line;\n\tline = std::regex_replace(inp,  std::regex(R\"(\\\\)\"), \"\\\\,\\\\backslash\\\\! \");\n\tline = std::regex_replace(line, std::regex(R\"(\\{)\"), \"\\\\{\");\n\tline = std::regex_replace(line, std::regex(R\"(\\})\"), \"\\\\}\");\t\t\t\t\t\n\tline = std::regex_replace(line, std::regex(R\"(_)\"), \"\\\\_\");\n\tline = std::regex_replace(line, std::regex(R\"(\\~)\"), \"\\\\widetilde{~}\");\n\treturn line;\n\t}\n\nvoid TeXView::TeXArea::set_latex(const std::string& latex)\n\t{\n\t//std::cout << \"**** fixing latex \" << latex << std::endl;\n\tstd::regex discretionary(R\"(\\\\discretionary\\{\\}\\{\\}\\{\\})\");\n\tstd::regex begin_dmath(R\"(\\\\begin\\{dmath\\*\\})\");\n\tstd::regex end_dmath(R\"(\\\\end\\{dmath\\*\\})\");\n\n\tunfixed = latex;\n\tif(latex.find(R\"(\\begin{dmath*})\")==0) {\n\t\t// math mode\n\t\tstd::regex spacenewline(R\"(\\\\\\\\\\[.*\\])\");\n\t\tfixed = std::regex_replace(latex, begin_dmath, \"\");\n\t\tfixed = std::regex_replace(fixed, end_dmath, \"\");\n\t\tfixed = std::regex_replace(fixed, discretionary, \"\\\\-{}\");\n\t\tfixed = std::regex_replace(fixed, spacenewline, \"\\\\\\\\\");\n\t\tfixed = std::regex_replace(fixed,\n\t\t\t\t\t\t\t\t\t\t\tstd::regex(R\"(\\+)\"),\n\t\t\t\t\t\t\t\t\t\t\t\" + \");\n\t\tfixed = std::regex_replace(fixed,\n\t\t\t\t\t\t\t\t\t\t\tstd::regex(R\"(\\\\linebreak\\[[0-9]\\])\"),\n\t\t\t\t\t\t\t\t\t\t\t\"\");\n\t\tfixed = std::regex_replace(fixed,\n\t\t\t\t\t\t\t\t\t\t\tstd::regex(R\"(\\\\square)\"),\n\t\t\t\t\t\t\t\t\t\t\t\"□\");\n\t\tfixed = std::regex_replace(fixed,\n\t\t\t\t\t\t\t\t\t\t\tstd::regex(R\"(\\\\bigO)\"),\n\t\t\t\t\t\t\t\t\t\t\t\"\\\\mathcal{O}\");\n\t\tfixed = std::regex_replace(fixed,\n\t\t\t\t\t\t\t\t\t\t\tstd::regex(R\"(\\\\dot\\{\\\\dot\\{)\"),\n\t\t\t\t\t\t\t\t\t\t\t\"\\\\ddot{{\");\n\t\tfixed = std::regex_replace(fixed, std::regex(R\"(\\{\\}_)\"), \"{\\\\,\\\\!}_\");\n\t\tfixed = std::regex_replace(fixed, std::regex(R\"(\\{\\}\\^)\"), \"{\\\\,\\\\!}^\");\n\t\tfixed = \"\\\\text{$\\\\displaystyle{}\"+fixed+\"$}\";\n\t\t}\n\telse {\n\t\t// text mode\n\n\t\t// In a verbatim block, replace all newlines with explicit '\\\\'.\n\t\tstd::string line;\n\t\tstd::istringstream ss(latex);\n\t\tbool inverbatim=false;\n\t\tstd::string beg(\"\\\\begin{verbatim}\");\n\t\tstd::string end(\"\\\\end{verbatim}\");\n\t\tfixed=\"\";\n\t\twhile(std::getline(ss, line)) {\n\t\t\tsize_t pos=line.find(beg);\n\t\t\tif(pos!=std::string::npos) {\n\t\t\t\tinverbatim=true;\n\t\t\t\tif(pos!=0)\n\t\t\t\t\tfixed += line.substr(0, pos);\n\t\t\t\tfixed += \"\\\\texttt{\";\n\t\t\t\tsize_t endpos = pos+beg.size(); \n\t\t\t\tif(line.size() > endpos)\n\t\t\t\t\tline = line.substr(endpos);\n\t\t\t\telse\n\t\t\t\t\tline = \"\";\n\t\t\t\t}\n\t\t\tpos = line.find(end);\n\t\t\tif(pos!=std::string::npos) {\n\t\t\t\tif(pos>0)\n\t\t\t\t\tline = line.substr(0, pos);\n\t\t\t\telse\n\t\t\t\t\tline = \"\";\n\t\t\t\t}\n\t\t\tif(line.size()>0) {\n\t\t\t\tif(inverbatim) {\n\t\t\t\t\tline = verbatimise(line);\n\t\t\t\t\tfixed += line+\"\\\\\\\\\";\n\t\t\t\t\t}\n\t\t\t\telse {\n\t\t\t\t\tfixed += line+\"\\n\";\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\tif(pos!=std::string::npos) {\n\t\t\t\tinverbatim=false;\n\t\t\t\tfixed += \"}\";\n\t\t\t\t}\n\t\t\t}\n\n\t\t// Now the rest.\n\t\tfixed = std::regex_replace(fixed,\n\t\t\t\t\t\t\t\t\t\t\tstd::regex(\"\\n\"),\n\t\t\t\t\t\t\t\t\t\t\t\" \");\n\t\tfixed = std::regex_replace(fixed, begin_dmath, \"\");\n\t\tfixed = std::regex_replace(fixed, end_dmath, \"\");\n\t\tfixed = std::regex_replace(fixed,\n\t\t\t\t\t\t\t\t\t\t\tstd::regex(R\"(\\\\color)\"),\n\t\t\t\t\t\t\t\t\t\t\t\"\\\\textcolor\");\n\t\tfixed = std::regex_replace(fixed, discretionary, \"\\\\-{}\");\n\t\tfixed = std::regex_replace(fixed, std::regex(R\"(\\\\textbackslash)\"), \"\\\\backslash\");\n\t\tfixed = std::regex_replace(fixed,\n\t\t\t\t\t\t\t\t\t\t\tstd::regex(R\"(\\\\section\\*\\{([^\\}]*)\\}[ ]*)\"),\n\t\t\t\t\t\t\t\t\t\t\t\"\\\\text{\\\\Large\\\\textbf{$1}}\\\\\\\\\\\\vspace{2.5ex}\");\n\t\tfixed = std::regex_replace(fixed,\n\t\t\t\t\t\t\t\t\t\t\tstd::regex(R\"(\\\\subsection\\*\\{([^\\}]*)\\}[ ]*)\"),\n\t\t\t\t\t\t\t\t\t\t\t\"\\\\text{\\\\large\\\\textbf{$1}}\\\\\\\\\\\\vspace{2.0ex}\");\n\t\tfixed = std::regex_replace(fixed,\n\t\t\t\t\t\t\t\t\t\t\tstd::regex(R\"(\\\\package\\{([^\\}]*)\\}\\{([^\\}]*)\\})\"),\n\t\t\t\t\t\t\t\t\t\t\t\"\\\\text{\\\\large\\\\texttt{$1}}\\\\\\\\\\\\vspace{2.5ex}\\\\text{\\\\textit{$2}}\\\\\\\\\");\n\t\tfixed = std::regex_replace(fixed,\n\t\t\t\t\t\t\t\t\t\t\tstd::regex(R\"(\\\\algorithm\\{([^\\}]*)\\}\\{([^\\}]*)\\}[ ]*)\"),\n\t\t\t\t\t\t\t\t\t\t\t\"\\\\text{\\\\large\\\\texttt{$1}}\\\\\\\\\\\\vspace{2.5ex}\\\\text{\\\\textit{$2}}\\\\\\\\\\\\vspace{2.5ex}\");\n\t\tfixed = std::regex_replace(fixed,\n\t\t\t\t\t\t\t\t\t\t\tstd::regex(R\"(\\\\available\\{([^\\}]*)\\}[ ]*)\"),\n\t\t\t\t\t\t\t\t\t\t\t\"{\\\\!\\\\small available since: $1}\\\\\\\\\\\\vspace{3.5ex}\");\n\t\tfixed = std::regex_replace(fixed,\n\t\t\t\t\t\t\t\t\t\t\tstd::regex(R\"(\\\\property\\{([^\\}]*)\\}\\{([^\\}]*)\\}[ ]*)\"),\n\t\t\t\t\t\t\t\t\t\t\t\"\\\\text{\\\\large\\\\texttt{$1}}\\\\\\\\\\\\vspace{2.5ex}\\\\text{\\\\textit{$2}}\\\\\\\\\\\\vspace{2.5ex}\");\n\t\tfixed = std::regex_replace(fixed,\n\t\t\t\t\t\t\t\t\t\t\tstd::regex(R\"(\\\\url\\{([^\\}]*)\\})\"),\n\t\t\t\t\t\t\t\t\t\t\t\"\\\\texttt{$1}\");\n\t\tfixed = std::regex_replace(fixed,\n\t\t\t\t\t\t\t\t\t\t\tstd::regex(R\"(\\\\href\\{([^\\}]*)\\}\\{([^\\}]*)\\})\"),\n\t\t\t\t\t\t\t\t\t\t\t\"\\\\texttt{$2}\");\n\t\tfixed = std::regex_replace(fixed,\n\t\t\t\t\t\t\t\t\t\t\tstd::regex(R\"(\\\\algo\\{([^\\}]*)\\})\"),\n\t\t\t\t\t\t\t\t\t\t\t\"\\\\texttt{$1}\");\n\t\tfixed = std::regex_replace(fixed,\n\t\t\t\t\t\t\t\t\t\t\tstd::regex(R\"(\\\\prop\\{([^\\}]*)\\})\"),\n\t\t\t\t\t\t\t\t\t\t\t\"\\\\texttt{$1}\");\n\t\tfixed = std::regex_replace(fixed,\n\t\t\t\t\t\t\t\t\t\t\tstd::regex(R\"(\\\\emph\\{([^\\}]*)\\})\"),\n\t\t\t\t\t\t\t\t\t\t\t\"\\\\textit{$1}\");\n\t\tfixed = std::regex_replace(fixed,\n\t\t\t\t\t\t\t\t\t\t\tstd::regex(R\"(\\\\begin\\{equation\\*?\\})\"),\n\t\t\t\t\t\t\t\t\t\t\t\"$\");\n\t\tfixed = std::regex_replace(fixed,\n\t\t\t\t\t\t\t\t\t\t\tstd::regex(R\"(\\\\end\\{equation\\*?\\})\"),\n\t\t\t\t\t\t\t\t\t\t\t\"$\");\n\n\t\t// Finally, the inline verbatim.\n\t\tauto verb_regex = std::regex(R\"(\\\\verb\\|([^\\|]*)\\|)\");\n\t\tstd::sregex_iterator it(fixed.begin(), fixed.end(), verb_regex);\n\t\tstd::sregex_iterator endit;\n\t\tsize_t last_pos=0;\n\t\tstd::string result;\n\t\tfor (; it != endit; ++it) {\n\t\t\tresult += fixed.substr(last_pos, it->position() - last_pos);\n\t\t\tstd::string transformed = verbatimise(it->str(1));\n\t\t\tresult += \"\\\\texttt{\" + transformed + \"}\";\n\t\t\tlast_pos = it->position() + it->length();\n\t\t\t}\n\t\tif(last_pos < fixed.length()) \n\t\t\tresult += fixed.substr(last_pos);\n\t\tfixed=result;\n\t\t\n\t\tfixed = \"\\\\text{\"+fixed+\"}\";\n\t\t}\n\n   //\tfixed = \"\\\\text{$A_{m n}$}\";\n\t// std::cout << \"**** fixed to \" << fixed << std::endl;\n\t}\n\nTeXView::TeXArea::TeXArea(bool use_microtex_, TeXView *owner_)\n\t: rendering_width(1), use_microtex(use_microtex_)\n\t, owner(owner_)\n\t, _render(nullptr), _text_size(5.f)\n\t, padding_x(15*1.7), padding_y(10)\n\t{\n\tset_hexpand(true);\n\tset_name(\"TeXArea\");\n\tauto obj = get_accessible();\n\tobj->set_name(\"TeXArea\");\n\tobj->set_role(Atk::ROLE_MATH);\n\tset_focus_on_click(true);\n\t}\n\nTeXView::TeXArea::~TeXArea()\n\t{\n\tif(_render)\n\t\tdelete _render;\n\t}\n\n"
  },
  {
    "path": "frontend/gtkmm/TeXView.hh",
    "content": "\n#pragma once\n\n#ifndef USE_GTK4\n#include <gtkmm/eventbox.h>\n#endif\n#include <gtkmm/box.h>\n#include <gtkmm/drawingarea.h>\n#include <gtkmm/menu.h>\n#if GTKMM_MINOR_VERSION>=10\n#include <gtkmm/revealer.h>\n#endif\n\n#include \"Config.hh\"\n#include \"DataCell.hh\"\n#include \"../common/TeXEngine.hh\"\n\n// MicroTeX\n#include \"microtex.h\"\n#include \"utils/utf.h\"\n\nnamespace cadabra {\n\n\t/// \\ingroup frontend\n\t/// TeXView is a widget which knows how to turn a string into\n\t/// a LaTeX-rendered image and display that.\n\t//\n\t/// See gtkmm custom widget documentation at:\n\t/// https://developer-old.gnome.org/gtkmm-tutorial/3.24/sec-custom-widgets.html.en\n\n\tclass TeXView : public Gtk::EventBox {\n\t\tpublic:\n\t\t\tTeXView(TeXEngine&, DTree::iterator, bool use_microtex_, int hmargin=25);\n\t\t\tvirtual ~TeXView();\n\n\t\t\tstd::shared_ptr<TeXEngine::TeXRequest> content;\n\n\t\t\tsigc::signal1<bool, DTree::iterator>   show_hide_requested;\n\n\t\t\tvoid set_use_microtex(bool);\n\n\t\t\tvoid set_is_error(bool);\n\t\t\t\t\t\n\t\t\tDTree::iterator           datacell;\n\t\t\tGtk::Revealer             rbox;\n\t\t\tGtk::Box                  vbox;\n\t\t\tGtk::Box                  hbox;\n\n\t\t\tint                       window_width=0;\n\n\t\t\tclass TeXArea : public Gtk::DrawingArea {\n\t\t\t\tpublic:\n\t\t\t\t\tTeXArea(bool use_microtex, TeXView *owner_);\n\t\t\t\t\t~TeXArea();\n\n\t\t\t\t\tvirtual bool on_draw(const Cairo::RefPtr<Cairo::Context>& cr) override;\n\n\t\t\t\t\t/// Update the visible image from the pixbuf. Call this in order to propagate\n\t\t\t\t\t/// changes to the pixbuf (e.g. from re-running the TeXRequest) to the\n\t\t\t\t\t/// visible widget itself.\n\n\t\t\t\t\tvoid update_image(std::shared_ptr<TeXEngine::TeXRequest>, double scale);\n\n\t\t\t\t\t/// The actual image is stored in the image referenced by pixbuf.\n\t\t\t\t\t/// FIXME: This pointer is not yet shared among instances which show the\n\t\t\t\t\t/// same content.\n\n\t\t\t\t\tGlib::RefPtr<Gdk::Pixbuf> pixbuf;\n\t\t\t\t\tdouble                    scale_;\n\t\t\t\t\tfloat                     _text_size;\n\n\t\t\t\t\t/// MicroTeX: set the LaTeX string and\n\t\t\t\t\t/// replace/substitute so that MicroTeX can render it\n\t\t\t\t\t/// (but do not actually render).\n\t\t\t\t\tvoid set_latex(const std::string& latex);\n\n\t\t\t\t\t/// MicroTeX: just run the LaTeX layout algorithms, do\n\t\t\t\t\t/// not draw.\n\t\t\t\t\tvoid layout_latex() const;\n\n\t\t\t\t\tbool                    use_microtex;\n\n\t\t\t\t\tint need_height(int width) const;\n\t\t\t\tprotected:\n\t\t\t\t\tGtk::SizeRequestMode get_request_mode_vfunc() const override;\n\t\t\t\t\tvoid get_preferred_height_for_width_vfunc(int width, int& minimum_height,\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tint& natural_height) const  override;\n\t\t\t\t\tvoid get_preferred_width_for_height_vfunc(int height, int& minimum_width,\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tint& natural_width) const  override;\n\t\t\t\t\tvoid on_size_allocate(Gtk::Allocation& allocation) override;\n\t\t\t\t\t\n\t\t\t\tprivate:\n\t\t\t\t\tTeXView        *owner;\n\t\t\t\t\tmutable int     rendering_width;\n\t\t\t\t\tint             padding_x, padding_y;\n\n\t\t\t\t\t// MicroTeX\n\t\t\t\t\tmutable microtex::Render* _render;\n\t\t\t\t\tstd::string               unfixed, fixed;\n\n\t\t\t\t\t// Return a string in which backslashes, curly braces,\n\t\t\t\t\t// underscores and tildes are properly backslashed, so they\n\t\t\t\t\t// typeset as if we are in a verbatim environment.\n\t\t\t\t\tstd::string verbatimise(const std::string&) const;\n\t\t\t\t};\n\n\t\t\tTeXArea                   image;\n\n\t\t\t/// Update the TeX image.\n\t\t\tvoid update_image();\n\n\t\t\t/// Dim the output to indicate that the result is no longer guaranteed to\n\t\t\t/// be correlated with the input cell from which it was derived.\n\n\t\t\tvoid dim(bool);\n\n\t\t\tsigc::signal1<bool, std::string> tex_error;\n\t\t\tsigc::signal0<bool>              signal_on_copy_as_latex;\n\t\t\t\n\t\tprotected:\n\t\t\tvirtual bool on_button_release_event(GdkEventButton *) override;\n\t\t\tvirtual bool on_button_press_event(GdkEventButton *event) override;\n\t\t\tvirtual void on_show() override;\n\n\t\t\tvoid convert();\n\n\t\t\tvoid on_copy_as_latex() const;\n\n\t\tprivate:\n\t\t\tTeXEngine& engine;\n\t\t\tbool use_microtex;\n\t\t\tbool is_error;\n\t\t\t\n\t\t\tGtk::Menu     context_menu;\n\t\t\tGtk::MenuItem item_copy_as_latex;\n\n\t\t\tfloat text_size() const;\n\t\t};\n\n\t}\n\n"
  },
  {
    "path": "frontend/gtkmm/VisualCell.hh",
    "content": "\n#pragma once\n\n// A VisualCell contains a pointer to a DataCell, as well as\n// pointers to the various cell widgets, one of which will be\n// representing the DataCell.\n\n#include \"TeXView.hh\"\n#include \"ImageView.hh\"\n#include \"CodeInput.hh\"\n#include \"DataCell.hh\"\n#include \"SliderView.hh\"\n\nnamespace cadabra {\n\n\t/// \\ingroup frontend\n\t///\n\t/// Structure holding a pointer to one of the possible GUI widgets that can\n\t/// appear in a document.\n\n\tclass VisualCell {\n\t\tpublic:\n\t\t\t/// Union of pointers to one of the possible GUI realisations\n\t\t\t/// of the cell types declared in DataCell::CellType. All\n\t\t\t/// of these cells below should derive from Gtk::Box.\n\n\t\t\tunion {\n\t\t\t\t\tGtk::Box     *document; // top-level cell; only one ever occurs in a document\n\t\t\t\t\tCodeInput    *inbox;\n\t\t\t\t\tTeXView      *outbox;\n\t\t\t\t\tImageView    *imagebox;\n\t\t\t\t\tSliderView   *slider;\n\t\t\t};\n\t};\n\n}\n"
  },
  {
    "path": "frontend/gtkmm/cadabra2-gtk.appdata.xml.in",
    "content": "<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n<!-- Copyright 2001-2025 Kasper Peeters <info@cadabra.science> -->\n<component type=\"desktop-application\">\n  <id>science.cadabra.cadabra2-gtk</id>\n  <metadata_license>FSFAP</metadata_license>\n  <project_license>GPL-3.0+</project_license>\n  <name>Cadabra</name>\n  <summary>Field-theory motivated symbolic computer algebra</summary>\n  <content_rating type=\"oars-1.1\">\n    <content_attribute id=\"social-info\">mild</content_attribute>\n  </content_rating>\n  \n  <description>\n    <p>\n      Cadabra is a symbolic computer algebra system, designed specifically\n      for the solution of problems encountered in quantum and classical\n      field theory. It has extensive functionality for tensor computer\n      algebra, tensor polynomial simplification including multi-term\n      symmetries, fermions and anti-commuting variables, Clifford algebras\n      and Fierz transformations, implicit coordinate dependence, multiple\n      index types and many more. The input format is a subset of TeX. Both a\n      command-line and a graphical interface are available, and there is a\n      kernel for Jupyter.\n    </p>\n  </description>\n\n  <launchable type=\"desktop-id\">science.cadabra.cadabra2-gtk.desktop</launchable>\n\n  <screenshots>\n    <screenshot type=\"default\">\n      <caption>The notebook interface</caption>\n      <image>https://cadabra.science/static/images/screenshot.png</image>\n    </screenshot>\n  </screenshots>\n\n  <url type=\"homepage\">https://cadabra.science</url>\n  <developer_name>Kasper Peeters</developer_name>\n  \n  <provides>\n    <binary>cadabra2-gtk</binary>\n  </provides>\n\n  <releases>\n    <release version=\"@CADABRA_VERSION_SEM@\" date=\"@CADABRA_VERSION_DATE@\">\n      <description>\n        <p>First release as AppImage.</p>\n      </description>\n    </release>\n  </releases>\n</component>\n"
  },
  {
    "path": "frontend/gtkmm/cdb-icons/README.md",
    "content": "Civilised systems will use the SVG icons in this folder. On macOS, the\nhomebrew installation of librsvg seriously messes up the @rpath in the\nlibpixbufloader_svg.dylib, as a result of which it becomes impossible\nto use the SVG loader on that platform without seriously messing around\nwith extra symlinks, preloading or rpath changes and subsequent binary\nresigning. \n\nSo on macOS, it's PNG again...\n\nRe-generate these PNG versions of the icons with `make update_icons`\n(requires inkscape).\n"
  },
  {
    "path": "frontend/gtkmm/config/settings.ini",
    "content": "[Settings]\ngtk-theme-name=Windows10\ngtk-font-name=Segoe UI 9\n"
  },
  {
    "path": "frontend/gtkmm/icons/Adwaita/index.theme",
    "content": "[Icon Theme]\nName=Adwaita\nComment=The Only One\nExample=folder\n\n# KDE Specific Stuff\nDisplayDepth=32\nLinkOverlay=link_overlay\nLockOverlay=lock_overlay\nZipOverlay=zip_overlay\nDesktopDefault=48\nDesktopSizes=16,22,32,48,64,72,96,128\nToolbarDefault=22\nToolbarSizes=16,22,32,48\nMainToolbarDefault=22\nMainToolbarSizes=16,22,32,48\nSmallDefault=16\nSmallSizes=16\nPanelDefault=32\nPanelSizes=16,22,32,48,64,72,96,128\n\n# Directory list\nDirectories=8x8/emblems,16x16/actions,16x16/apps,16x16/categories,16x16/devices,16x16/emblems,16x16/emotes,16x16/mimetypes,16x16/places,16x16/status,22x22/actions,22x22/apps,22x22/categories,22x22/devices,22x22/emblems,22x22/emotes,22x22/mimetypes,22x22/places,22x22/status,24x24/actions,24x24/apps,24x24/categories,24x24/devices,24x24/emblems,24x24/emotes,24x24/mimetypes,24x24/places,24x24/status,32x32/actions,32x32/apps,32x32/categories,32x32/devices,32x32/emblems,32x32/emotes,32x32/mimetypes,32x32/places,32x32/status,48x48/actions,48x48/apps,48x48/categories,48x48/devices,48x48/emblems,48x48/emotes,48x48/mimetypes,48x48/places,48x48/status,64x64/actions,64x64/apps,64x64/categories,64x64/devices,64x64/emblems,64x64/emotes,64x64/mimetypes,64x64/places,64x64/status,96x96/actions,96x96/apps,96x96/categories,96x96/devices,96x96/emblems,96x96/emotes,96x96/mimetypes,96x96/places,96x96/status,256x256/actions,256x256/apps,256x256/categories,256x256/devices,256x256/emblems,256x256/emotes,256x256/mimetypes,256x256/places,256x256/status,512x512/actions,512x512/apps,512x512/categories,512x512/devices,512x512/emblems,512x512/mimetypes,512x512/places,512x512/status,scalable/actions,scalable/apps,scalable/categories,scalable/devices,scalable/emblems,scalable/emotes,scalable/mimetypes,scalable/places,scalable/status,scalable-up-to-32/status,\n\n[8x8/emblems]\nContext=Emblems\nSize=8\nType=Fixed\n\n[16x16/actions]\nContext=Actions\nSize=16\nType=Fixed\n\n[16x16/apps]\nContext=Applications\nSize=16\nType=Fixed\n\n[16x16/categories]\nContext=Categories\nSize=16\nType=Fixed\n\n[16x16/devices]\nContext=Devices\nSize=16\nType=Fixed\n\n[16x16/emblems]\nContext=Emblems\nSize=16\nType=Fixed\n\n[16x16/emotes]\nContext=Emotes\nSize=16\nType=Fixed\n\n[16x16/mimetypes]\nContext=MimeTypes\nSize=16\nType=Fixed\n\n[16x16/places]\nContext=Places\nSize=16\nType=Fixed\n\n[16x16/status]\nContext=Status\nSize=16\nType=Fixed\n\n[22x22/actions]\nContext=Actions\nSize=22\nType=Fixed\n\n[22x22/apps]\nContext=Applications\nSize=22\nType=Fixed\n\n[22x22/categories]\nContext=Categories\nSize=22\nType=Fixed\n\n[22x22/devices]\nContext=Devices\nSize=22\nType=Fixed\n\n[22x22/emblems]\nContext=Emblems\nSize=22\nType=Fixed\n\n[22x22/emotes]\nContext=Emotes\nSize=22\nType=Fixed\n\n[22x22/mimetypes]\nContext=MimeTypes\nSize=22\nType=Fixed\n\n[22x22/places]\nContext=Places\nSize=22\nType=Fixed\n\n[22x22/status]\nContext=Status\nSize=22\nType=Fixed\n\n[24x24/actions]\nContext=Actions\nSize=24\nType=Fixed\n\n[24x24/apps]\nContext=Applications\nSize=24\nType=Fixed\n\n[24x24/categories]\nContext=Categories\nSize=24\nType=Fixed\n\n[24x24/devices]\nContext=Devices\nSize=24\nType=Fixed\n\n[24x24/emblems]\nContext=Emblems\nSize=24\nType=Fixed\n\n[24x24/emotes]\nContext=Emotes\nSize=24\nType=Fixed\n\n[24x24/mimetypes]\nContext=MimeTypes\nSize=24\nType=Fixed\n\n[24x24/places]\nContext=Places\nSize=24\nType=Fixed\n\n[24x24/status]\nContext=Status\nSize=24\nType=Fixed\n\n[32x32/actions]\nContext=Actions\nSize=32\nType=Fixed\n\n[32x32/apps]\nContext=Applications\nSize=32\nType=Fixed\n\n[32x32/categories]\nContext=Categories\nSize=32\nType=Fixed\n\n[32x32/devices]\nContext=Devices\nSize=32\nType=Fixed\n\n[32x32/emblems]\nContext=Emblems\nSize=32\nType=Fixed\n\n[32x32/emotes]\nContext=Emotes\nSize=32\nType=Fixed\n\n[32x32/mimetypes]\nContext=MimeTypes\nSize=32\nType=Fixed\n\n[32x32/places]\nContext=Places\nSize=32\nType=Fixed\n\n[32x32/status]\nContext=Status\nSize=32\nType=Fixed\n\n[48x48/actions]\nContext=Actions\nSize=48\nType=Fixed\n\n[48x48/apps]\nContext=Applications\nSize=48\nType=Fixed\n\n[48x48/categories]\nContext=Categories\nSize=48\nType=Fixed\n\n[48x48/devices]\nContext=Devices\nSize=48\nType=Fixed\n\n[48x48/emblems]\nContext=Emblems\nSize=48\nType=Fixed\n\n[48x48/emotes]\nContext=Emotes\nSize=48\nType=Fixed\n\n[48x48/mimetypes]\nContext=MimeTypes\nSize=48\nType=Fixed\n\n[48x48/places]\nContext=Places\nSize=48\nType=Fixed\n\n[48x48/status]\nContext=Status\nSize=48\nType=Fixed\n\n[64x64/actions]\nContext=Actions\nSize=64\nType=Fixed\n\n[64x64/apps]\nContext=Applications\nSize=64\nType=Fixed\n\n[64x64/categories]\nContext=Categories\nSize=64\nType=Fixed\n\n[64x64/devices]\nContext=Devices\nSize=64\nType=Fixed\n\n[64x64/emblems]\nContext=Emblems\nSize=64\nType=Fixed\n\n[64x64/emotes]\nContext=Emotes\nSize=64\nType=Fixed\n\n[64x64/mimetypes]\nContext=MimeTypes\nSize=64\nType=Fixed\n\n[64x64/places]\nContext=Places\nSize=64\nType=Fixed\n\n[64x64/status]\nContext=Status\nSize=64\nType=Fixed\n\n[96x96/actions]\nContext=Actions\nSize=96\nType=Fixed\n\n[96x96/apps]\nContext=Applications\nSize=96\nType=Fixed\n\n[96x96/categories]\nContext=Categories\nSize=96\nType=Fixed\n\n[96x96/devices]\nContext=Devices\nSize=96\nType=Fixed\n\n[96x96/emblems]\nContext=Emblems\nSize=96\nType=Fixed\n\n[96x96/emotes]\nContext=Emotes\nSize=96\nType=Fixed\n\n[96x96/mimetypes]\nContext=MimeTypes\nSize=96\nType=Fixed\n\n[96x96/places]\nContext=Places\nSize=96\nType=Fixed\n\n[96x96/status]\nContext=Status\nSize=96\nType=Fixed\n\n[256x256/actions]\nContext=Actions\nSize=256\nMinSize=56\nMaxSize=256\nType=Scalable\n\n[256x256/apps]\nContext=Applications\nSize=256\nMinSize=56\nMaxSize=256\nType=Scalable\n\n[256x256/categories]\nContext=Categories\nSize=256\nMinSize=56\nMaxSize=256\nType=Scalable\n\n[256x256/devices]\nContext=Devices\nSize=256\nMinSize=56\nMaxSize=256\nType=Scalable\n\n[256x256/emblems]\nContext=Emblems\nSize=256\nMinSize=56\nMaxSize=256\nType=Scalable\n\n[256x256/emotes]\nContext=Emotes\nSize=256\nMinSize=56\nMaxSize=256\nType=Scalable\n\n[256x256/mimetypes]\nContext=MimeTypes\nSize=256\nMinSize=56\nMaxSize=256\nType=Scalable\n\n[256x256/places]\nContext=Places\nSize=256\nMinSize=56\nMaxSize=256\nType=Scalable\n\n[256x256/status]\nContext=Status\nSize=256\nMinSize=56\nMaxSize=256\nType=Scalable\n\n[512x512/actions]\nContext=Actions\nSize=512\nMinSize=56\nMaxSize=512\nType=Scalable\n\n[512x512/apps]\nContext=Applications\nSize=512\nMinSize=56\nMaxSize=512\nType=Scalable\n\n[512x512/categories]\nContext=Categories\nSize=512\nMinSize=56\nMaxSize=512\nType=Scalable\n\n[512x512/devices]\nContext=Devices\nSize=512\nMinSize=56\nMaxSize=512\nType=Scalable\n\n[512x512/emblems]\nContext=Emblems\nSize=512\nMinSize=56\nMaxSize=512\nType=Scalable\n\n[512x512/mimetypes]\nContext=MimeTypes\nSize=512\nMinSize=56\nMaxSize=512\nType=Scalable\n\n[512x512/places]\nContext=Places\nSize=512\nMinSize=56\nMaxSize=512\nType=Scalable\n\n[512x512/status]\nContext=Status\nSize=512\nMinSize=56\nMaxSize=512\nType=Scalable\n\n[scalable/actions]\nContext=Actions\nSize=16\nMinSize=8\nMaxSize=512\nType=Scalable\n\n[scalable/apps]\nContext=Applications\nSize=16\nMinSize=8\nMaxSize=512\nType=Scalable\n\n[scalable/categories]\nContext=Categories\nSize=16\nMinSize=8\nMaxSize=512\nType=Scalable\n\n[scalable/devices]\nContext=Devices\nSize=16\nMinSize=8\nMaxSize=512\nType=Scalable\n\n[scalable/emblems]\nContext=Emblems\nSize=16\nMinSize=8\nMaxSize=512\nType=Scalable\n\n[scalable/emotes]\nContext=Emotes\nSize=16\nMinSize=8\nMaxSize=512\nType=Scalable\n\n[scalable/mimetypes]\nContext=MimeTypes\nSize=16\nMinSize=8\nMaxSize=512\nType=Scalable\n\n[scalable/places]\nContext=Places\nSize=16\nMinSize=8\nMaxSize=512\nType=Scalable\n\n[scalable/status]\nContext=Status\nSize=16\nMinSize=8\nMaxSize=512\nType=Scalable\n\n[scalable-up-to-32/status]\nContext=Status\nSize=16\nMinSize=16\nMaxSize=32\nType=Scalable\n\n"
  },
  {
    "path": "frontend/gtkmm/icons/README.txt",
    "content": "These are standard GTK icons, distributed here alongside Cadabra only\nin order to avoid additional dependencies when building the notebook\ninterface.\n"
  },
  {
    "path": "frontend/gtkmm/icons/hicolor/icon-theme.cache",
    "content": ""
  },
  {
    "path": "frontend/gtkmm/main.cc",
    "content": "\n#include \"Cadabra.hh\"\n\n#include <gtkmm/application.h>\n#include <gtkmm/cssprovider.h>\n#include <gtkmm/label.h>\n#include <glibmm/spawn.h>\n\n#ifdef _WIN32\n#include <Windows.h>\n#include <stdlib.h>\n#include <fstream>\n#include <streambuf>\n#endif\n\n#include <iostream>\n\n#define NDEBUG 1\n\n// Cadabra frontend with GTK+ interface (using gtkmm).\n// Makes use of the client classes in the client_server directory.\n\nint main(int argc, char **argv)\n\t{\n#ifdef _WIN32\n   // We are going to disable console creation. However,\n\t// that also kills any output to stdout or stderr, which may\n\t// have been useful in case of missing dlls or other errors.\n\t// Write them to a log file.\n\tstd::ofstream logFile(\"C:\\\\Windows\\\\Temp\\\\cadabra_log.txt\");\n\tstd::streambuf* oldCout = std::cout.rdbuf(logFile.rdbuf());\n\tstd::streambuf* oldCerr = std::cerr.rdbuf(logFile.rdbuf());\n\t\n\tFreeConsole();\n#endif\n\t\n\ttry {\n\t\tauto application = Cadabra::create(argc, argv);\n\t\tconst int status = application->run();\n\t\treturn status;\n\t\t}\n\tcatch (Glib::Error& er) {\n\t\tstd::cerr << er.what() << std::endl;\n\t\treturn -1;\n\t\t}\n\tcatch (std::exception& ex) {\n\t\tstd::cerr << ex.what() << std::endl;\n\t\t}\n\n#ifdef _WIN32\n\tstd::cout.rdbuf(oldCout);\n\tstd::cerr.rdbuf(oldCerr);\n#endif\n\t}\n\n// #if defined(_WIN32) && defined(NDEBUG)\n// \n// void display_error(const std::string& message)\n// {\n// \tMessageBoxA(NULL, message.c_str(), \"Error!\", MB_ICONEXCLAMATION | MB_OK);\n// }\n// \n// int WinMain(HINSTANCE hInstance, HINSTANCE hPrevInstance, LPSTR lpCmdLine, int nCmdShow)\n// \t{\n// //\tif (getenv(\"CADABRA_LOG_OUTPUT\") != NULL) {\n// \t\tauto stdout_path = Glib::get_user_data_dir() + \"/cadabra2-stdout.log\";\n// \t\tif (freopen(stdout_path.c_str(), \"w\", stdout) == NULL) {\n// \t\t\tdisplay_error(\"Could not redirect stdout to \" + stdout_path);\n// \t\t\texit(1);\n// \t\t}\n// \n// \t\tauto stderr_path = Glib::get_user_data_dir() + \"/cadabra2-stderr.log\";\n// \t\tif (freopen(stderr_path.c_str(), \"w\", stderr) == NULL) {\n// \t\t\tdisplay_error(\"Could not redirect stdout to \" + stderr_path);\n// \t\t\texit(1);\n// \t\t}\n// \n// \t\tstd::ios_base::sync_with_stdio();\n// //\t}\n// \n// \ttry {\n// \t\tauto application = Cadabra::create(__argc, __argv);\n// \t\tconst int status = application->run();\n// \t\treturn status;\n// \t\t}\n// \tcatch (Glib::Error& er) {\n// \t\tdisplay_error(er.what());\n// \t\treturn -1;\n// \t\t}\n// \tcatch (std::exception& ex) {\n// \t\tdisplay_error(ex.what());\n// \t\treturn -1;\n// \t\t}\n// \tcatch (...) {\n// \t\tdisplay_error(\"An unknown error occurred\");\n// \t\treturn -1;\n// \t\t}\n// \t}\n// #endif\n// \n"
  },
  {
    "path": "frontend/gtkmm/science.cadabra.cadabra2-gtk.appdata.xml.in",
    "content": "<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n<!-- Copyright 2001-2024 Kasper Peeters <info@cadabra.science> -->\n<component type=\"desktop-application\">\n  <id>science.cadabra.cadabra2-gtk</id>\n  <metadata_license>FSFAP</metadata_license>\n  <project_license>GPL-3.0+</project_license>\n  <name>Cadabra</name>\n  <summary>Field-theory motivated symbolic computer algebra</summary>\n  <content_rating type=\"oars-1.1\">\n    <content_attribute id=\"social-info\">mild</content_attribute>\n  </content_rating>\n  \n  <description>\n    <p>\n      Cadabra is a symbolic computer algebra system, designed specifically\n      for the solution of problems encountered in quantum and classical\n      field theory. It has extensive functionality for tensor computer\n      algebra, tensor polynomial simplification including multi-term\n      symmetries, fermions and anti-commuting variables, Clifford algebras\n      and Fierz transformations, implicit coordinate dependence, multiple\n      index types and many more. The input format is a subset of TeX. Both a\n      command-line and a graphical interface are available, and there is a\n      kernel for Jupyter.\n    </p>\n  </description>\n\n  <launchable type=\"desktop-id\">science.cadabra.cadabra2-gtk.desktop</launchable>\n\n  <screenshots>\n    <screenshot type=\"default\">\n      <caption>The notebook interface</caption>\n      <image>https://cadabra.science/static/images/screenshot.png</image>\n    </screenshot>\n  </screenshots>\n\n  <url type=\"homepage\">https://cadabra.science</url>\n  <developer_name>Kasper Peeters</developer_name>\n  \n  <provides>\n    <binary>cadabra2-gtk</binary>\n  </provides>\n\n  <releases>\n    <release version=\"@CADABRA_VERSION_SEM@\" date=\"@CADABRA_VERSION_DATE@\">\n      <description>\n        <p>First release as AppImage.</p>\n      </description>\n    </release>\n  </releases>\n</component>\n"
  },
  {
    "path": "frontend/gtkmm/theme/README.txt",
    "content": "The Windows 10 theme for GTK was made by B00merang Theming; see\n\n  https://github.com/B00merang-Project/Windows-10\n\nfor details. Many thanks for making this available under the GPLv3.\n\n\nCHANGES (Dominic Price 2020)\n- gtk-cadabra.css added\n- Buttons and assets recoloured to fit the Cadabra theme\n"
  },
  {
    "path": "frontend/gtkmm/theme/Windows10/gtk-3.20/apps/gnome-terminal.css",
    "content": "vte-terminal.terminal-screen {\n    -TerminalScreen-background-darkness: 0.95;\n    background-color: #000;\n    color: #fff;\n}\n"
  },
  {
    "path": "frontend/gtkmm/theme/Windows10/gtk-3.20/gtk-cadabra.css",
    "content": "menubar {\n    margin: 0px;\n    background-color: #f5f6f7;\n}\n\nmenubar label {\n    color: black;\n}\n\nmenuitem:hover {\n    color: black;\n    background-color: #a1cca1;\n}\n\nmenu {\n    padding: 0px;\n    background-color: white;\n}\n\n\nmenubar > menuitem {\n    border-bottom: 1px solid #ddd;\n}\n\ntoolbar {\n    background-color: #f5f6f7;\n    border-bottom: 1px solid #ddd;\n}\n\ntooltip {\n    background-color: transparent;\n}\n\ntooltip label {\n    background-color: #f5f6f7;\n    color: black;\n    border: 1px solid #aaa;\n    padding: 4px;\n    margin-top: -8px;\n}\n\n#statusbar {\n    border-top: 1px solid #ddd;\n    background-color: #f5f6f7;\n}\n\ndialog button:not(.titlebutton) {\n    background-image: none;\n    background-color: #f5f6f7;\n    padding: 0px;\n}\n\ndialog entry {\n    background-color: white;\n    padding: 5px;\n    min-height: 0px;\n}\n\ndialog button:not(.titlebutton):hover {\n    background-color: #a1cca1;\n}\n\n/*\n * The following settings are overridden somewhere else\n * and so have no effect; they are therefore added in the\n * load_css() function of NotebookWindow.cc\n */\n\n/*\n.titlebar {\n    margin: 0;\n    padding: 0;\n    box-shadow: inset 0 0 1px #ddd;\n    background-image: none;\n    background-color: #209020;\n    color: white;\n}\n\n.titlebar:backdrop {\n    background-color: #367d36;\n}\n\n.titlebar label:backdrop {\n    color: white;\n}\n\n.titlebar .titlebutton {\n    margin: 0px 0px 0px -8px;\n    padding: 0px 8px;\n}\n\ndialog .titlebar,\ndialog .titlebar:backdrop {\n    background-color: #666;\n}\n\ntooltip {\n    background-color: transparent;\n}\n\ntoolbar button {\n    padding: 0px;\n    margin-right: 5px;\n}\n*/\n"
  },
  {
    "path": "frontend/gtkmm/theme/Windows10/gtk-3.20/gtk-contained-dark.css",
    "content": "* {\n  padding: 0;\n  -GtkToolButton-icon-spacing: 4;\n  -GtkTextView-error-underline-color: @error_color;\n  -GtkScrolledWindow-scrollbar-spacing: 0;\n  -GtkToolItemGroup-expander-size: 11;\n  -GtkTreeView-expander-size: 11;\n  -GtkTreeView-horizontal-separator: 4;\n  -GtkWidget-text-handle-width: 20;\n  -GtkWidget-text-handle-height: 24;\n  -GtkDialog-button-spacing: 4;\n  -GtkDialog-action-area-border: 0;\n  outline-color: @outline_color;\n  outline-style: dashed;\n  outline-offset: -3px;\n  outline-width: 0px;\n  -gtk-outline-radius: 0;\n  -gtk-secondary-caret-color: @selected_bg_color; }\n\n/****************\n * floating bar *\n ***************/\n.floating-bar {\n    background-image: none;\n    background-color: @theme_bg_color;\n    border: 1px solid @borders;\n\n    color: @theme_fg_color;\n    text-shadow: none;\n\n    border-radius: 0;\n    border-width: 1px;\n    border-style: solid;\n    box-shadow: none;\n}\n\n.floating-bar.right {\n    border-right-width: 0;\n    border-top-right-radius: 0;\n    border-bottom-right-radius: 0;\n}\n\n.floating-bar.bottom {\n    border-bottom-width: 0;\n    border-bottom-right-radius: 0;\n    border-bottom-left-radius: 0;\n}\n\n.floating-bar.left {\n    border-left-width: 0;\n    border-top-left-radius: 0;\n    border-bottom-left-radius: 0;\n}\n\n.floating-bar:backdrop {\n    border-color: transparent;\n    color: @theme_fg_color;\n    background-image: none;\n    background-color: @theme_bg_color;\n    box-shadow: none;\n}\n\n.floating-bar .button {\n    border-color: @borders;\n    background-image: none;\n    background-color: @theme_bg_color;\n    border-style: none;\n    box-shadow: none;\n}\n\n\n/***************\n * Base States *\n ***************/\n.background {\n  color: @theme_fg_color;\n  background-color: @theme_bg_color; }\n  .background:backdrop {\n    color: @theme_unfocused_fg_color;\n    background-color: @theme_bg_color;\n    text-shadow: none;\n    -gtk-icon-shadow: none; }\n\n/*\n   These wildcard seems unavoidable, need to investigate.\n   Wildcards are bad and troublesome, use them with care,\n   or better, just don't.\n   Everytime a wildcard is used a kitten dies, painfully.\n*/\n*:disabled {\n  -gtk-icon-effect: dim; }\n\n.gtkstyle-fallback {\n  color: @theme_fg_color;\n  background-color: @theme_bg_color; }\n  .gtkstyle-fallback:hover {\n    color: @theme_fg_color;\n    background-color: @theme_bg_color; }\n  .gtkstyle-fallback:active {\n    color: @theme_fg_color;\n    background-color: #cfcfcd; }\n  .gtkstyle-fallback:disabled {\n    color: @insensitive_fg_color;\n    background-color: @insensitive_bg_color; }\n  .gtkstyle-fallback:selected {\n    color: @theme_selected_fg_color;\n    background-color: @theme_selected_bg_color; }\n\n/* dirty hex workaround */\n.view, iconview {\n  color: @theme_fg_color;\n  background-color: #111111; }\n.view text,\niconview text,\ntextview text {\n  color: @theme_fg_color;\n  background-color: @theme_bg_color; }\n  .view:backdrop, iconview:backdrop,\n  .view text:backdrop,\n  iconview text:backdrop,\n  textview text:backdrop {\n    color: @theme_unfocused_fg_color;\n    background-color: @theme_unfocused_bg_color; }\n  .view:selected:focus, iconview:selected:focus, .view:selected, iconview:selected,\n  .view text:selected:focus,\n  iconview text:selected:focus,\n  textview text:selected:focus,\n  .view text:selected,\n  iconview text:selected,\n  textview text:selected {\n    border-radius: 0; }\n\ntextview border {\n  background-color: shade(@theme_bg_color, 0.95);\n  background-image: image(rgba(0, 0, 0, 0.2));\n  background-repeat: no-repeat; }\n  textview border:backdrop {\n    background-color: shade(@theme_bg_color, 0.95); }\n  textview border.bottom {\n    background-size: 100% 1px;\n    background-position: top; }\n  textview border.top {\n    background-size: 100% 1px;\n    background-position: bottom; }\n  textview border.left {\n    background-size: 1px 100%;\n    background-position: right; }\n  textview border.right {\n    background-size: 1px 100%;\n    background-position: left; }\n\n.rubberband,\nrubberband,\nflowbox rubberband,\ntreeview.view rubberband,\n.content-view rubberband {\n  border: 1px solid @borders;\n  background-color: rgba(42, 118, 198, 0.2); }\n\nflowbox flowboxchild {\n  padding: 3px;\n  border-radius: 0; }\n  flowbox flowboxchild:selected {\n    outline-offset: -2px; }\n\nlabel.separator {\n  color: @theme_fg_color; }\n  label.separator:backdrop {\n    color: @insensitive_fg_color; }\nlabel selection {\n  background-color: @theme_selected_bg_color;\n  color: @theme_selected_fg_color; }\nlabel:disabled {\n  color: @insensitive_fg_color; }\n  label:disabled:backdrop {\n    color: shade(@theme_unfocused_fg_color, 1.1); }\nlabel:backdrop {\n  color: @insensitive_fg_color; }\n\n.dim-label, label.separator, .titlebar:not(headerbar) .subtitle,\nheaderbar .subtitle {\n  opacity: 0.55;\n  text-shadow: none; }\n\nassistant .sidebar {\n  background-color: @theme_bg_color;\n  border: none; }\n  assistant .sidebar:backdrop {\n    background-color: @theme_unfocused_bg_color;\n    border-color: transparent; }\nassistant.csd .sidebar {\n  border-top-style: none; }\nassistant .sidebar label {\n  padding: 6px 12px; }\nassistant .sidebar label.highlight {\n  background-color: shade(@theme_fg_color, 0.85); }\n\n.csd popover.background.touch-selection, .csd popover.background.magnifier, popover.background.touch-selection, popover.background.magnifier, .csd popover.background.osd, popover.background.osd, .app-notification,\n.app-notification.frame, .osd .scale-popup,\n.osd {\n  color: @osd_fg_color;\n  border: none;\n  background-color: @osd_bg_color;\n  background-clip: padding-box;\n  outline-color: @osd_outline;\n  text-shadow: 0 1px @osd_txt_shadow;\n  -gtk-icon-shadow: 0 1px @osd_txt_shadow; }\n  popover.background.touch-selection:backdrop, popover.background.magnifier:backdrop, popover.background.osd:backdrop, .app-notification:backdrop, .osd .scale-popup:backdrop,\n  .osd:backdrop {\n    text-shadow: none;\n    -gtk-icon-shadow: none; }\n    \n/* nemo icon view entry */\n.nemo-window .nemo-window-pane widget.entry {\n    border: 1px solid;\n    border-radius: 3px;\n    color: @theme_fg_color;\n    border-color: @theme_selected_bg_color;\n    background-color: @theme_base_color; }\n  \n.nemo-window .nemo-window-pane widget.entry:selected:focus, .nemo-window .nemo-window-pane widget.entry:selected {\n    background-color: @theme_selected_bg_color;\n    color: @theme_selected_fg_color;\n}\n\n/*********************\n * Spinner Animation *\n *********************/\n@keyframes spin {\n  to {\n    -gtk-icon-transform: rotate(1turn); } }\nspinner {\n  background: none;\n  opacity: 0;\n  -gtk-icon-source: -gtk-icontheme(\"process-working-symbolic\"); }\n  spinner:checked {\n    opacity: 1;\n    animation: spin 1s linear infinite; }\n    spinner:checked:disabled {\n      opacity: 0.5; }\n\n/****************\n * Text Entries *\n ****************/\nspinbutton:not(.vertical),\nentry {\n  min-height: 32px;\n  padding-left: 8px;\n  padding-right: 8px;\n  border: 1px solid;\n  border-radius: 0;\n  transition: all 200ms cubic-bezier(0.25, 0.46, 0.45, 0.94);\n  color:@theme_fg_color;\n  border-color: shade(@theme_bg_color, 0.85);\n  background-color: @theme_bg_color;\n  box-shadow: none; }\n  spinbutton:not(.vertical) image.left,\n  entry image.left {\n    padding-left: 0;\n    padding-right: 6px; }\n  spinbutton:not(.vertical) image.right,\n  entry image.right {\n    padding-left: 6px;\n    padding-right: 0; }\n\n/* what's this ??? */\n\n  spinbutton:not(.vertical) undershoot.left,\n  entry undershoot.left {\n    background-color: transparent;\n    background-image: linear-gradient(to top, rgba(255, 255, 255, 0.2) 50%, rgba(0, 0, 0, 0.2) 50%);\n    padding-left: 1px;\n    background-size: 1px 10px;\n    background-repeat: repeat-y;\n    background-origin: content-box;\n    background-position: left center;\n    border: none;\n    box-shadow: none; }\n  spinbutton:not(.vertical) undershoot.right,\n  entry undershoot.right {\n    background-color: transparent;\n    background-image: linear-gradient(to top, rgba(255, 255, 255, 0.2) 50%, rgba(0, 0, 0, 0.2) 50%);\n    padding-right: 1px;\n    background-size: 1px 10px;\n    background-repeat: repeat-y;\n    background-origin: content-box;\n    background-position: right center;\n    border: none;\n    box-shadow: none; }\n  spinbutton.flat:focus:not(.vertical), spinbutton.flat:not(.vertical),\n  entry.flat:focus,\n  entry.flat {\n    min-height: 0;\n    padding: 2px;\n    background-color: transparent;\n    border-color: transparent;\n    border-radius: 0; }\n  spinbutton:focus:not(.vertical),\n  entry:focus {\n    box-shadow: none;\n    border-color: shade(@theme_selected_bg_color, 0.6); }\n  spinbutton:disabled:not(.vertical),\n  entry:disabled {\n    color: @insensitive_fg_color;\n    border-color: shade(@borders, 1.1);\n    background-color: @insensitive_bg_color;\n    box-shadow: none; }\n  spinbutton:backdrop:not(.vertical),\n  entry:backdrop {\n    color: @theme_unfocused_fg_color;\n    border-color: shade(@borders, 0.95);\n    background-color: @theme_unfocused_bg_color;\n    box-shadow: none;\n    transition: 200ms ease-out; }\n  spinbutton:backdrop:disabled:not(.vertical),\n  entry:backdrop:disabled {\n    color: shade(@theme_unfocused_fg_color, 1.1);\n    border-color: shade(@borders, 0.95);\n    background-color: @insensitive_bg_color;\n    box-shadow: none; }\n  spinbutton.error:not(.vertical),\n  entry.error {\n    color: @error_color;\n    border-color: @error_color; }\n    spinbutton.error:focus:not(.vertical),\n    entry.error:focus {\n      box-shadow: none;\n      border-color: @error_color; }\n    spinbutton.error:selected:focus:not(.vertical), spinbutton.error:selected:not(.vertical),\n    entry.error:selected:focus,\n    entry.error:selected {\n      background-color: @error_color; }\n  spinbutton.warning:not(.vertical),\n  entry.warning {\n    color: @warning_color;\n    border-color: @warning_color; }\n    spinbutton.warning:focus:not(.vertical),\n    entry.warning:focus {\n      box-shadow: none;\n      border-color: @warning_color; }\n    spinbutton.warning:selected:focus:not(.vertical), spinbutton.warning:selected:not(.vertical),\n    entry.warning:selected:focus,\n    entry.warning:selected {\n      background-color: @warning_color; }\n  spinbutton:not(.vertical) image,\n  entry image {\n    color: @theme_fg_color; }\n    spinbutton:not(.vertical) image:hover,\n    entry image:hover {\n      color: shade(@theme_fg_color, 1.05); }\n    spinbutton:not(.vertical) image:active,\n    entry image:active {\n      color: @theme_selected_bg_color; }\n    spinbutton:not(.vertical) image:backdrop,\n    entry image:backdrop {\n      color: shade(@theme_bg_color, 0.85); }\n  spinbutton:drop(active):focus:not(.vertical), spinbutton:drop(active):not(.vertical),\n  entry:drop(active):focus,\n  entry:drop(active) {\n    border-color: @success_color;\n    box-shadow: none; }\n  .osd spinbutton:not(.vertical), .osd\n  entry {\n    color: @osd_fg_color;\n    border-color: @osd_borders;\n    background-color: @osd_bg_color;\n    background-clip: padding-box;\n    box-shadow: none;\n    text-shadow: 0 1px @osd_txt_shadow;\n    -gtk-icon-shadow: 0 1px @osd_txt_shadow; }\n    .osd spinbutton:focus:not(.vertical), .osd\n    entry:focus {\n      color: @osd_fg_color;\n      border-color: @theme_selected_bg_color;\n      background-color: @osd_bg_color;\n      background-clip: padding-box;\n      box-shadow: inset 0 0 0 1px @theme_selected_bg_color;\n      text-shadow: 0 1px @osd_txt_shadow;\n      -gtk-icon-shadow: 0 1px @osd_txt_shadow; }\n    .osd spinbutton:backdrop:not(.vertical), .osd\n    entry:backdrop {\n      color: @osd_fg_color;\n      border-color: @osd_borders;\n      background-color: @osd_bg_color;\n      background-clip: padding-box;\n      box-shadow: none;\n      text-shadow: none;\n      -gtk-icon-shadow: none; }\n    .osd spinbutton:disabled:not(.vertical), .osd\n    entry:disabled {\n      color: shade(@osd_fg_color, 0.85);\n      border-color: @osd_borders;\n      background-color: shade(@osd_bg_color, 0.95);\n      background-clip: padding-box;\n      box-shadow: none;\n      text-shadow: none;\n      -gtk-icon-shadow: none; }\nspinbutton:not(.vertical) progress,\nentry progress {\n  margin: 2px -6px;\n  background-color: transparent;\n  background-image: none;\n  border-radius: 0;\n  border-width: 0 0 2px;\n  border-color: shade(@theme_selected_bg_color, 0.6);\n  border-style: solid;\n  box-shadow: none; }\n  spinbutton:not(.vertical) progress:backdrop,\n  entry progress:backdrop {\n    background-color: transparent; }\n.linked:not(.vertical) > spinbutton:focus:not(.vertical) + spinbutton:not(.vertical), .linked:not(.vertical) > spinbutton:focus:not(.vertical) + button, .linked:not(.vertical) > spinbutton:focus:not(.vertical) + combobox > box > button.combo, .linked:not(.vertical) >\nentry:focus + spinbutton:not(.vertical), .linked:not(.vertical) >\nentry:focus + button, .linked:not(.vertical) >\nentry:focus + combobox > box > button.combo, .linked:not(.vertical) > spinbutton:focus:not(.vertical) +\nentry, .linked:not(.vertical) >\nentry:focus +\nentry {\n  border-left-color: @theme_selected_bg_color; }\n.linked:not(.vertical) > spinbutton:drop(active):not(.vertical) + spinbutton:not(.vertical), .linked:not(.vertical) > spinbutton:drop(active):not(.vertical) + button, .linked:not(.vertical) > spinbutton:drop(active):not(.vertical) + combobox > box > button.combo, .linked:not(.vertical) >\nentry:drop(active) + spinbutton:not(.vertical), .linked:not(.vertical) >\nentry:drop(active) + button, .linked:not(.vertical) >\nentry:drop(active) + combobox > box > button.combo, .linked:not(.vertical) > spinbutton:drop(active):not(.vertical) +\nentry, .linked:not(.vertical) >\nentry:drop(active) +\nentry {\n  border-left-color: @success_color; }\n.linked.vertical > spinbutton:not(:disabled):not(.vertical) + entry:not(:disabled), .linked.vertical > spinbutton:not(:disabled):not(.vertical) + spinbutton:not(:disabled):not(.vertical), .linked.vertical >\nentry:not(:disabled) + entry:not(:disabled), .linked.vertical >\nentry:not(:disabled) + spinbutton:not(:disabled):not(.vertical) {\n  border-top-color: @borders; }\n  .linked.vertical > spinbutton:not(:disabled):not(.vertical) + entry:not(:disabled):backdrop, .linked.vertical > spinbutton:not(:disabled):not(.vertical) + spinbutton:not(:disabled):backdrop:not(.vertical), .linked.vertical >\n  entry:not(:disabled) + entry:not(:disabled):backdrop, .linked.vertical >\n  entry:not(:disabled) + spinbutton:not(:disabled):backdrop:not(.vertical) {\n    border-top-color: @borders; }\n.linked.vertical > spinbutton:disabled:not(.vertical) + spinbutton:disabled:not(.vertical), .linked.vertical > spinbutton:disabled:not(.vertical) + entry:disabled, .linked.vertical >\nentry:disabled + spinbutton:disabled:not(.vertical), .linked.vertical >\nentry:disabled + entry:disabled {\n  border-top-color: @borders; }\n.linked.vertical > spinbutton:not(.vertical) + spinbutton:focus:not(:only-child):not(.vertical),\n.linked.vertical > spinbutton:not(.vertical) + entry:focus:not(:only-child), .linked.vertical >\nentry + spinbutton:focus:not(:only-child):not(.vertical),\n.linked.vertical >\nentry + entry:focus:not(:only-child) {\n  border-top-color: shade(@theme_selected_bg_color, 0.6); }\n.linked.vertical > spinbutton:not(.vertical) + spinbutton:drop(active):not(:only-child):not(.vertical),\n.linked.vertical > spinbutton:not(.vertical) + entry:drop(active):not(:only-child), .linked.vertical >\nentry + spinbutton:drop(active):not(:only-child):not(.vertical),\n.linked.vertical >\nentry + entry:drop(active):not(:only-child) {\n  border-top-color: @success_color; }\n.linked.vertical > spinbutton:focus:not(:only-child):not(.vertical) + spinbutton:not(.vertical),\n.linked.vertical > spinbutton:focus:not(:only-child):not(.vertical) + entry,\n.linked.vertical > spinbutton:focus:not(:only-child):not(.vertical) + button,\n.linked.vertical > spinbutton:focus:not(:only-child):not(.vertical) + combobox > box > button.combo, .linked.vertical >\nentry:focus:not(:only-child) + spinbutton:not(.vertical),\n.linked.vertical >\nentry:focus:not(:only-child) + entry,\n.linked.vertical >\nentry:focus:not(:only-child) + button,\n.linked.vertical >\nentry:focus:not(:only-child) + combobox > box > button.combo {\n  border-top-color: @theme_selected_bg_color; }\n.linked.vertical > spinbutton:drop(active):not(:only-child):not(.vertical) + spinbutton:not(.vertical),\n.linked.vertical > spinbutton:drop(active):not(:only-child):not(.vertical) + entry,\n.linked.vertical > spinbutton:drop(active):not(:only-child):not(.vertical) + button,\n.linked.vertical > spinbutton:drop(active):not(:only-child):not(.vertical) + combobox > box > button.combo, .linked.vertical >\nentry:drop(active):not(:only-child) + spinbutton:not(.vertical),\n.linked.vertical >\nentry:drop(active):not(:only-child) + entry,\n.linked.vertical >\nentry:drop(active):not(:only-child) + button,\n.linked.vertical >\nentry:drop(active):not(:only-child) + combobox > box > button.combo {\n  border-top-color: @success_color; }\n\ntreeview acceleditor > label {\n  background-color: @theme_selected_bg_color; }\n\ntreeview entry:focus:dir(rtl), treeview entry:focus:dir(ltr) {\n  background-color: @theme_bg_color;\n  transition-property: color, background; }\ntreeview entry.flat, treeview entry {\n  border-radius: 0;\n  background-image: none;\n  background-color: @theme_bg_color; }\n  treeview entry.flat:focus, treeview entry:focus {\n    border-color: @theme_selected_bg_color; }\n\n/***********\n * Buttons *\n ***********/\n@keyframes needs_attention {\n  from {\n    background-image: -gtk-gradient(radial, center center, 0, center center, 0.01, to(@theme_selected_bg_color), to(transparent)); }\n  to {\n    background-image: -gtk-gradient(radial, center center, 0, center center, 0.5, to(@theme_selected_bg_color), to(transparent)); } }\n\n/* Header bar & toolbar buttons */ \n\nnotebook > header > tabs > arrow, button.titlebutton {\n  min-height: 24px;\n  min-width: 16px;\n  padding: 4px 8px;\n  border: none;\n  border-radius: 0;\n  transition: all 200ms cubic-bezier(0.25, 0.46, 0.45, 0.94);\n  color: @theme_fg_color;\n  outline-color: @outline_color;\n  border-color: @borders;\n  background-image: linear-gradient(to bottom, @theme_bg_color, @theme_bg_color);\n  text-shadow: 0 1px @txt_shadow;\n  -gtk-icon-shadow: 0 1px @txt_shadow;\n  box-shadow: none; }\n  notebook > header > tabs > arrow, button.sidebar-button, button.titlebutton,\n  button.flat {\n    border-color: transparent;\n    background-color: transparent;\n    background-image: none;\n    box-shadow: inset 0 1px transparent;\n    text-shadow: none;\n    -gtk-icon-shadow: none;\n    transition: none; }\n    notebook > header > tabs > arrow:hover, button.sidebar-button:hover, button.titlebutton:hover,\n    button.flat:hover {\n      transition: all 200ms cubic-bezier(0.25, 0.46, 0.45, 0.94);\n      transition-duration: 500ms; }\n      notebook > header > tabs > arrow:hover:active, button.sidebar-button:hover:active, button.titlebutton:hover:active,\n      button.flat:hover:active {\n        transition: all 200ms cubic-bezier(0.25, 0.46, 0.45, 0.94); }\n  notebook > header > tabs > arrow:hover, button.titlebutton:hover {\n    color: @theme_fg_color;\n    outline-color: @outline_color;\n    border-color: shade(@theme_selected_bg_color, 0.7);\n    background-image: linear-gradient(to bottom, @theme_selected_bg_color, @theme_selected_bg_color);\n    text-shadow: none;\n    -gtk-icon-shadow: none;\n    box-shadow: none;\n    -gtk-icon-effect: highlight; }\n  notebook > header > tabs > arrow:active, button.titlebutton:active, notebook > header > tabs > arrow:checked, button.titlebutton:checked {\n    color: @theme_fg_color;\n    outline-color: @outline_color;\n    border-color: shade(@theme_selected_bg_color, 0.7);\n    background-image: none;\n    background-color: shade(@theme_selected_bg_color, 0.9);\n    box-shadow: none;\n    text-shadow: none;\n    -gtk-icon-shadow: none;\n    transition-duration: 50ms; }\n\n  notebook > header > tabs > arrow:backdrop, button.sidebar-button:backdrop, button.titlebutton:backdrop, notebook > header > tabs > arrow:backdrop, button.titlebutton:backdrop,\n  button:backdrop.flat {\n    border-color: shade(@borders, 0.95);\n    background-color: transparent;\n    background-image: image(@theme_bg_color);\n    text-shadow: none;\n    -gtk-icon-shadow: none;\n    box-shadow: inset 0 1px transparent;\n    transition: 200ms ease-out;\n    -gtk-icon-effect: none; }\n    notebook > header > tabs > arrow:backdrop label, button.sidebar-button:backdrop label, button.titlebutton:backdrop label, notebook > header > tabs > arrow:backdrop, button.sidebar-button:backdrop, button.titlebutton:backdrop, notebook > header > tabs > arrow:backdrop label, button.titlebutton:backdrop label, notebook > header > tabs > arrow:backdrop, button.titlebutton:backdrop,\n    button:backdrop.flat label,\n    button:backdrop.flat {\n      color: @insensitive_fg_color; }\n    notebook > header > tabs > arrow:backdrop:active, button.sidebar-button:backdrop:active, button.titlebutton:backdrop:active, notebook > header > tabs > arrow:backdrop:checked, button.sidebar-button:backdrop:checked, button.titlebutton:backdrop:checked, notebook > header > tabs > arrow:backdrop:active, button.titlebutton:backdrop:active, notebook > header > tabs > arrow:backdrop:checked, button.titlebutton:backdrop:checked,\n    button:backdrop.flat:active,\n    button:backdrop.flat:checked {\n      border-color: shade(@borders, 0.95);\n      background-color: shade(@theme_bg_color, 0.95);\n      background-image: none;\n      box-shadow: inset 0 1px transparent; }\n      notebook > header > tabs > arrow:backdrop:active label, button.sidebar-button:backdrop:active label, button.titlebutton:backdrop:active label, notebook > header > tabs > arrow:backdrop:active, button.sidebar-button:backdrop:active, button.titlebutton:backdrop:active, notebook > header > tabs > arrow:backdrop:checked label, button.sidebar-button:backdrop:checked label, button.titlebutton:backdrop:checked label, notebook > header > tabs > arrow:backdrop:checked, button.sidebar-button:backdrop:checked, button.titlebutton:backdrop:checked, notebook > header > tabs > arrow:backdrop:active label, button.titlebutton:backdrop:active label, notebook > header > tabs > arrow:backdrop:active, button.titlebutton:backdrop:active, notebook > header > tabs > arrow:backdrop:checked label, button.titlebutton:backdrop:checked label, notebook > header > tabs > arrow:backdrop:checked, button.titlebutton:backdrop:checked,\n      button:backdrop.flat:active label,\n      button:backdrop.flat:active,\n      button:backdrop.flat:checked label,\n      button:backdrop.flat:checked {\n        color: @insensitive_fg_color; }\n    notebook > header > tabs > arrow:backdrop:disabled, button.sidebar-button:backdrop:disabled, button.titlebutton:backdrop:disabled, notebook > header > tabs > arrow:backdrop:disabled, button.titlebutton:backdrop:disabled,\n    button:backdrop.flat:disabled {\n      border-color: shade(@borders, 0.95);\n      background-color: @insensitive_bg_color;\n      background-image: none;\n      text-shadow: none;\n      -gtk-icon-shadow: none;\n      box-shadow: inset 0 1px transparent; }\n      notebook > header > tabs > arrow:backdrop:disabled label, button.sidebar-button:backdrop:disabled label, button.titlebutton:backdrop:disabled label, notebook > header > tabs > arrow:backdrop:disabled, button.sidebar-button:backdrop:disabled, button.titlebutton:backdrop:disabled, notebook > header > tabs > arrow:backdrop:disabled label, button.titlebutton:backdrop:disabled label, notebook > header > tabs > arrow:backdrop:disabled, button.titlebutton:backdrop:disabled,\n      button:backdrop.flat:disabled label,\n      button:backdrop.flat:disabled {\n        color: shade(@theme_unfocused_fg_color, 1.1); }\n      notebook > header > tabs > arrow:backdrop:disabled:active, button.sidebar-button:backdrop:disabled:active, button.titlebutton:backdrop:disabled:active, notebook > header > tabs > arrow:backdrop:disabled:checked, button.sidebar-button:backdrop:disabled:checked, button.titlebutton:backdrop:disabled:checked, notebook > header > tabs > arrow:backdrop:disabled:active, button.titlebutton:backdrop:disabled:active, notebook > header > tabs > arrow:backdrop:disabled:checked, button.titlebutton:backdrop:disabled:checked,\n      button:backdrop.flat:disabled:active,\n      button:backdrop.flat:disabled:checked {\n        border-color: shade(@borders, 0.95);\n        background-color: shade(@theme_bg_color, 0.95);\n        background-image: none;\n        box-shadow: inset 0 1px transparent; }\n        notebook > header > tabs > arrow:backdrop:disabled:active label, button.sidebar-button:backdrop:disabled:active label, button.titlebutton:backdrop:disabled:active label, notebook > header > tabs > arrow:backdrop:disabled:checked label, button.sidebar-button:backdrop:disabled:checked label, button.titlebutton:backdrop:disabled:checked label, notebook > header > tabs > arrow:backdrop:disabled:active label, button.titlebutton:backdrop:disabled:active label, notebook > header > tabs > arrow:backdrop:disabled:checked label, button.titlebutton:backdrop:disabled:checked label,\n        button:backdrop.flat:disabled:active label,\n        button:backdrop.flat:disabled:checked label {\n          color: shade(@theme_unfocused_fg_color, 1.1); }\n  notebook > header > tabs > arrow:backdrop, button.sidebar-button:backdrop, button.titlebutton:backdrop, notebook > header > tabs > arrow:disabled, button.sidebar-button:disabled, button.titlebutton:disabled, notebook > header > tabs > arrow:backdrop:disabled, button.sidebar-button:backdrop:disabled, button.titlebutton:backdrop:disabled,\n  button.flat:backdrop,\n  button.flat:disabled,\n  button.flat:backdrop:disabled {\n    border-color: transparent;\n    background-color: transparent;\n    background-image: none;\n    box-shadow: inset 0 1px transparent;\n    text-shadow: none;\n    -gtk-icon-shadow: none; }\n  notebook > header > tabs > arrow:disabled, button.titlebutton:disabled {\n    border-color: @borders;\n    background-color: @insensitive_bg_color;\n    background-image: none;\n    text-shadow: none;\n    -gtk-icon-shadow: none;\n    box-shadow: inset 0 1px transparent; }\n    notebook > header > tabs > arrow:disabled label, button.titlebutton:disabled label, notebook > header > tabs > arrow:disabled, button.titlebutton:disabled {\n      color: @insensitive_fg_color; }\n    notebook > header > tabs > arrow:disabled:active, button.titlebutton:disabled:active, notebook > header > tabs > arrow:disabled:checked, button.titlebutton:disabled:checked {\n      border-color: @borders;\n      background-color: shade(@theme_bg_color, 0.95);\n      background-image: none;\n      box-shadow: inset 0 1px transparent; }\n      notebook > header > tabs > arrow:disabled:active label, button.titlebutton:disabled:active label, notebook > header > tabs > arrow:disabled:active, button.titlebutton:disabled:active, notebook > header > tabs > arrow:disabled:checked label, button.titlebutton:disabled:checked label, notebook > header > tabs > arrow:disabled:checked, button.titlebutton:disabled:checked {\n        color: @insensitive_fg_color; }\n\n/* Regular buttons */\n\nbutton {\n  min-height: 24px;\n  min-width: 16px;\n  padding: 4px 8px;\n  border: 1px solid;\n  border-radius: 0;\n  transition: all 200ms cubic-bezier(0.25, 0.46, 0.45, 0.94);\n  color: @theme_fg_color;\n  outline-color: @outline_color;\n  border-color: @borders;\n  background-image: linear-gradient(to bottom, @theme_bg_color, @theme_bg_color);\n  text-shadow: 0 0 @txt_shadow;\n  -gtk-icon-shadow: 0 0 @txt_shadow;\n  box-shadow: none; }\n\nbutton:hover {\n    color: @theme_fg_color;\n    outline-color: @outline_color;\n    border-color: shade(@theme_selected_bg_color, 0.8);\n    background-image: linear-gradient(to bottom, @theme_selected_bg_color, @theme_selected_bg_color);\n    text-shadow: none;\n    -gtk-icon-shadow: none;\n    box-shadow: none;\n    -gtk-icon-effect: highlight; }\n\nbutton:active, button:checked {\n    color: @theme_fg_color;\n    outline-color: @outline_color;\n    border-color: shade(@theme_selected_bg_color, 0.6);\n    background-image: none;\n    background-color: shade(@theme_selected_bg_color, 0.9);\n    box-shadow: none;\n    text-shadow: none;\n    -gtk-icon-shadow: none;\n    transition-duration: 50ms; }\n\nbutton:backdrop {\n    border-color: @borders;\n    background-color: transparent;\n    background-image: image(@theme_bg_color);\n    text-shadow: none;\n    -gtk-icon-shadow: none;\n    box-shadow: inset 0 0 transparent;\n    transition: 200ms ease-out;\n    -gtk-icon-effect: none; }\n\nbutton:backdrop label, button:backdrop {\n      color: @insensitive_fg_color; }\n\nbutton:backdrop:active, button:backdrop:checked {\n      border-color: @borders;\n      background-color: shade(@theme_unfocused_bg_color, 0.95);\n      background-image: none;\n      box-shadow: inset 0 0 transparent; }\n\n\nbutton:backdrop:active label, button:backdrop:active, button:backdrop:checked label,  button:backdrop:checked {\n        color: @insensitive_fg_color; }\n\nbutton:backdrop:disabled {\n      border-color: shade(@borders, 0.95);\n      background-color: @insensitive_bg_color;\n      background-image: none;\n      text-shadow: none;\n      -gtk-icon-shadow: none;\n      box-shadow: inset 0 0 transparent; }\n\n      button:backdrop:disabled label,\n      button:backdrop:disabled {\n        color: shade(@theme_unfocused_fg_color, 1.1); }\n\nbutton:backdrop:disabled:active, button:backdrop:disabled:checked {\n        border-color: shade(@borders, 0.95);\n        background-color: shade(@theme_bg_color, 0.95);\n        background-image: none;\n        box-shadow: inset 0 1px transparent; }\n\nbutton:backdrop:disabled:active label,  button:backdrop:disabled:checked label {\n          color: shade(@theme_unfocused_fg_color, 1.1); }\n\nbutton:disabled {\n    border-color: @borders;\n    background-color: @insensitive_bg_color;\n    background-image: none;\n    text-shadow: none;\n    -gtk-icon-shadow: none;\n    box-shadow: inset 0 1px transparent; }\n\nbutton:disabled label,\n    button:disabled {\n      color: @insensitive_fg_color; }\n\nbutton:disabled:active,\n    button:disabled:checked {\n      border-color: @borders;\n      background-color: shade(@theme_bg_color, 0.95);\n      background-image: none;\n      box-shadow: inset 0 1px transparent; }\n\nbutton:disabled:active label, button:disabled:active, button:disabled:checked label,  button:disabled:checked {\n        color: @insensitive_fg_color; }\n\n\n  notebook > header > tabs > arrow.image-button, button.image-button.titlebutton,\n  button.image-button {\n    min-width: 24px;\n    padding-left: 4px;\n    padding-right: 4px; }\n  notebook > header > tabs > arrow.text-button, button.text-button.titlebutton,\n  button.text-button {\n    padding-left: 16px;\n    padding-right: 16px; }\n  notebook > header > tabs > arrow.text-button.image-button, button.text-button.image-button.titlebutton,\n  button.text-button.image-button {\n    padding-left: 8px;\n    padding-right: 8px; }\n    notebook > header > tabs > arrow.text-button.image-button label, button.text-button.image-button.titlebutton label,\n    button.text-button.image-button label {\n      padding-left: 8px;\n      padding-right: 8px; }\n  combobox:drop(active) button.combo, notebook > header > tabs > arrow:drop(active), button.titlebutton:drop(active),\n  button:drop(active) {\n    color: @success_color;\n    border-color: @success_color;\n    box-shadow: inset 0 0 0 1px @success_color; }\nrow:selected\nbutton {\n  border-color: shade(@theme_selected_bg_color, 0.6); }\n  row:selected button.sidebar-button:not(:active):not(:checked):not(:hover):not(disabled), row:selected\n  button.flat:not(:active):not(:checked):not(:hover):not(disabled) {\n    color: @theme_selected_fg_color;\n    border-color: transparent; }\n    row:selected button.sidebar-button:not(:active):not(:checked):not(:hover):not(disabled):backdrop, row:selected\n    button.flat:not(:active):not(:checked):not(:hover):not(disabled):backdrop {\n      color: @theme_unfocused_bg_color; }\n\n/* OSD buttons */\n\nbutton.osd {\n  min-width: 24px;\n  min-height: 32px;\n  color: @osd_fg_color;\n  border-radius: 0;\n  outline-color: @osd_outline;\n  color: @osd_fg_color;\n  border-color: @osd_borders;\n  background-color: transparent;\n  background-image: image(@osd_bg_color);\n  background-clip: padding-box;\n  box-shadow: inset 0 1px @osd_txt_shadow;\n  text-shadow: 0 1px @osd_txt_shadow;\n  -gtk-icon-shadow: 0 1px @osd_txt_shadow;\n  outline-color: @osd_outline;\n  border: none;\n  box-shadow: none; }\n  button.osd.image-button {\n    min-width: 32px; }\n  button.osd:hover {\n    color: @osd_fg_color;\n    border-color: @osd_borders;\n    background-color: transparent;\n    background-image: image(shade(@osd_bg_color, 1.05));\n    background-clip: padding-box;\n    box-shadow: inset 0 1px @osd_txt_shadow;\n    text-shadow: 0 1px @osd_txt_shadow;\n    -gtk-icon-shadow: 0 1px @osd_txt_shadow;\n    outline-color: @osd_outline;\n    border: none;\n    box-shadow: none; }\n  button.osd:active,\n  button.osd:checked {\n    color: @osd_fg_color;\n    border-color: @osd_borders;\n    background-color: transparent;\n    background-image: image(@osd_borders);\n    background-clip: padding-box;\n    box-shadow: none;\n    text-shadow: none;\n    -gtk-icon-shadow: none;\n    outline-color: @osd_outline;\n    border: none;\n    box-shadow: none; }\n  button.osd:disabled:backdrop,\n  button.osd:disabled {\n    color: shade(@osd_fg_color, 0.85);\n    border-color: @osd_borders;\n    background-color: transparent;\n    background-image: image(shade(@osd_bg_color, 0.95));\n    background-clip: padding-box;\n    box-shadow: none;\n    text-shadow: none;\n    -gtk-icon-shadow: none;\n    border: none; }\n  button.osd:backdrop {\n    color: @theme_unfocused_fg_color;\n    border-color: @osd_borders;\n    background-color: transparent;\n    background-image: image(@osd_bg_color);\n    background-clip: padding-box;\n    box-shadow: none;\n    text-shadow: none;\n    -gtk-icon-shadow: none;\n    border: none; }\n.csd popover.background.touch-selection button, .csd popover.background.magnifier button, popover.background.touch-selection button, popover.background.magnifier button, .app-notification button,\n.app-notification.frame button, .osd\nbutton {\n  color: @osd_fg_color;\n  border-color: @osd_borders;\n  background-color: transparent;\n  background-image: image(@osd_bg_color);\n  background-clip: padding-box;\n  box-shadow: inset 0 1px @osd_txt_shadow;\n  text-shadow: 0 1px @txt_shadow;\n  -gtk-icon-shadow: 0 1px @osd_txt_shadow;\n  outline-color: @osd_outline; }\n  popover.background.touch-selection button:hover, popover.background.magnifier button:hover, .app-notification button:hover, .osd\n  button:hover {\n    color: @osd_fg_color;\n    border-color: @osd_borders;\n    background-color: transparent;\n    background-image: image(shade(@osd_bg_color, 1.05));\n    background-clip: padding-box;\n    box-shadow: inset 0 1px @osd_txt_shadow;\n    text-shadow: 0 1px @osd_txt_shadow;\n    -gtk-icon-shadow: 0 1px @osd_txt_shadow;\n    outline-color: @osd_outline; }\n  popover.background.touch-selection button:active:backdrop, popover.background.magnifier button:active:backdrop, .app-notification button:active:backdrop, popover.background.touch-selection button:active, popover.background.magnifier button:active, .app-notification button:active, popover.background.touch-selection button:checked:backdrop, popover.background.magnifier button:checked:backdrop, .app-notification button:checked:backdrop, popover.background.touch-selection button:checked, popover.background.magnifier button:checked, .app-notification button:checked, .osd\n  button:active:backdrop, .osd\n  button:active, .osd\n  button:checked:backdrop, .osd\n  button:checked {\n    color: @theme_fg_color;\n    border-color: @osd_borders;\n    background-color: transparent;\n    background-image: image(@osd_borders);\n    background-clip: padding-box;\n    box-shadow: none;\n    text-shadow: none;\n    -gtk-icon-shadow: none;\n    outline-color: @osd_outline; }\n  popover.background.touch-selection button:disabled:backdrop, popover.background.magnifier button:disabled:backdrop, .app-notification button:disabled:backdrop, popover.background.touch-selection button:disabled, popover.background.magnifier button:disabled, .app-notification button:disabled, .osd\n  button:disabled:backdrop, .osd\n  button:disabled {\n    color: shade(@osd_fg_color, 0.85);\n    border-color: @osd_borders;\n    background-color: transparent;\n    background-image: image(shade(@osd_bg_color, 0.95));\n    background-clip: padding-box;\n    box-shadow: none;\n    text-shadow: none;\n    -gtk-icon-shadow: none; }\n  popover.background.touch-selection button:backdrop, popover.background.magnifier button:backdrop, .app-notification button:backdrop, .osd\n  button:backdrop {\n    color: @theme_unfocused_fg_color;\n    border-color: @osd_borders;\n    background-color: transparent;\n    background-image: image(@osd_bg_color);\n    background-clip: padding-box;\n    box-shadow: none;\n    text-shadow: none;\n    -gtk-icon-shadow: none; }\n  popover.background.touch-selection button.flat, popover.background.magnifier button.flat, .app-notification button.flat, .osd\n  button.flat {\n    border-color: transparent;\n    background-color: transparent;\n    background-image: none;\n    box-shadow: inset 0 1px transparent;\n    text-shadow: none;\n    -gtk-icon-shadow: none;\n    box-shadow: none;\n    text-shadow: 0 1px @osd_txt_shadow;\n    -gtk-icon-shadow: 0 1px @osd_txt_shadow; }\n    popover.background.touch-selection button.flat:hover, popover.background.magnifier button.flat:hover, .app-notification button.flat:hover, .osd\n    button.flat:hover {\n      color: @osd_fg_color;\n      border-color: @osd_borders;\n      background-color: transparent;\n      background-image: image(shade(@osd_bg_color, 1.05));\n      background-clip: padding-box;\n      box-shadow: inset 0 1px @osd_txt_shadow;\n      text-shadow: 0 1px @osd_txt_shadow;\n      -gtk-icon-shadow: 0 1px @osd_txt_shadow;\n      outline-color: @osd_outline; }\n    popover.background.touch-selection button.flat:disabled, popover.background.magnifier button.flat:disabled, .app-notification button.flat:disabled, .osd\n    button.flat:disabled {\n      color: shade(@osd_fg_color, 0.85);\n      border-color: @osd_borders;\n      background-color: transparent;\n      background-image: image(shade(@osd_bg_color, 0.95));\n      background-clip: padding-box;\n      box-shadow: none;\n      text-shadow: none;\n      -gtk-icon-shadow: none;\n      background-image: none;\n      border-color: transparent;\n      box-shadow: none; }\n    popover.background.touch-selection button.flat:backdrop, popover.background.magnifier button.flat:backdrop, .app-notification button.flat:backdrop, .osd\n    button.flat:backdrop {\n      border-color: transparent;\n      background-color: transparent;\n      background-image: none;\n      box-shadow: inset 0 1px transparent;\n      text-shadow: none;\n      -gtk-icon-shadow: none; }\n    popover.background.touch-selection button.flat:active, popover.background.magnifier button.flat:active, .app-notification button.flat:active, popover.background.touch-selection button.flat:checked, popover.background.magnifier button.flat:checked, .app-notification button.flat:checked, .osd\n    button.flat:active, .osd\n    button.flat:checked {\n      color: @osd_fg_color;\n      border-color: @osd_borders;\n      background-color: transparent;\n      background-image: image(@osd_borders);\n      background-clip: padding-box;\n      box-shadow: none;\n      text-shadow: none;\n      -gtk-icon-shadow: none;\n      outline-color: @osd_outline; }\nbutton.suggested-action {\n  color: @theme_fg_color;\n  outline-color: rgba(255, 255, 255, 0.3);\n  border-color: shade(@theme_selected_bg_color, 0.6);\n  border-bottom-color: shade(@theme_selected_bg_color, 0.6);\n  background-image: linear-gradient(to bottom, @theme_selected_bg_color, @theme_selected_bg_color);\n  text-shadow: 0 -1px rgba(0, 0, 0, 0.54353);\n  -gtk-icon-shadow: 0 -1px rgba(0, 0, 0, 0.54353);\n  box-shadow: inset 0 1px rgba(255, 255, 255, 0.4); }\n  .selection-mode button.titlebutton,\n  button.suggested-action.flat {\n    border-color: transparent;\n    background-color: transparent;\n    background-image: none;\n    box-shadow: inset 0 1px transparent;\n    text-shadow: none;\n    -gtk-icon-shadow: none;\n    color: @theme_selected_bg_color; }\n  button.suggested-action:hover {\n    color: @theme_fg_color;\n    outline-color: rgba(255, 255, 255, 0.3);\n    border-color: shade(@theme_selected_bg_color, 0.6);\n    border-bottom-color: shade(@theme_selected_bg_color, 0.6);\n    background-image: linear-gradient(to bottom, @theme_selected_bg_color, @theme_selected_bg_color);\n    text-shadow: 0 -1px rgba(0, 0, 0, 0.49553);\n    -gtk-icon-shadow: 0 -1px rgba(0, 0, 0, 0.49553);\n    box-shadow: inset 0 1px rgba(255, 255, 255, 0.4); }\n  button.suggested-action:active,\n  button.suggested-action:checked {\n    color: @theme_fg_color;\n    outline-color: rgba(255, 255, 255, 0.3);\n    border-color: shade(@theme_selected_bg_color, 0.6);\n    background-image: none;\n    background-color: shade(@theme_selected_bg_color, 0.8);\n    box-shadow: inset 0 1px transparent;\n    text-shadow: none;\n    -gtk-icon-shadow: none; }\n  .selection-mode button.titlebutton:backdrop,\n  button.suggested-action:backdrop,\n  button.suggested-action.flat:backdrop {\n    border-color: @theme_selected_bg_color;\n    background-color: transparent;\n    background-image: image(@theme_selected_bg_color);\n    text-shadow: none;\n    -gtk-icon-shadow: none;\n    box-shadow: inset 0 1px transparent; }\n    .selection-mode button.titlebutton:backdrop label, .selection-mode button.titlebutton:backdrop,\n    button.suggested-action:backdrop label,\n    button.suggested-action:backdrop,\n    button.suggested-action.flat:backdrop label,\n    button.suggested-action.flat:backdrop {\n      color: @theme_unfocused_selected_bg_color; }\n    .selection-mode button.titlebutton:backdrop:active, .selection-mode button.titlebutton:backdrop:checked,\n    button.suggested-action:backdrop:active,\n    button.suggested-action:backdrop:checked,\n    button.suggested-action.flat:backdrop:active,\n    button.suggested-action.flat:backdrop:checked {\n      border-color: shade(@theme_selected_bg_color, 0.6);\n      background-color: shade(@theme_selected_bg_color, 0.6);\n      background-image: none;\n      box-shadow: inset 0 1px transparent; }\n      .selection-mode button.titlebutton:backdrop:active label, .selection-mode button.titlebutton:backdrop:active, .selection-mode button.titlebutton:backdrop:checked label, .selection-mode button.titlebutton:backdrop:checked,\n      button.suggested-action:backdrop:active label,\n      button.suggested-action:backdrop:active,\n      button.suggested-action:backdrop:checked label,\n      button.suggested-action:backdrop:checked,\n      button.suggested-action.flat:backdrop:active label,\n      button.suggested-action.flat:backdrop:active,\n      button.suggested-action.flat:backdrop:checked label,\n      button.suggested-action.flat:backdrop:checked {\n        color: @theme_unfocused_selected_bg_color; }\n    .selection-mode button.titlebutton:backdrop:disabled,\n    button.suggested-action:backdrop:disabled,\n    button.suggested-action.flat:backdrop:disabled {\n      border-color: shade(@borders, 0.95);\n      background-color: @insensitive_bg_color;\n      background-image: none;\n      text-shadow: none;\n      -gtk-icon-shadow: none;\n      box-shadow: inset 0 1px transparent; }\n      .selection-mode button.titlebutton:backdrop:disabled label, .selection-mode button.titlebutton:backdrop:disabled,\n      button.suggested-action:backdrop:disabled label,\n      button.suggested-action:backdrop:disabled,\n      button.suggested-action.flat:backdrop:disabled label,\n      button.suggested-action.flat:backdrop:disabled {\n        color: shade(@theme_unfocused_fg_color, 1.1); }\n      .selection-mode button.titlebutton:backdrop:disabled:active, .selection-mode button.titlebutton:backdrop:disabled:checked,\n      button.suggested-action:backdrop:disabled:active,\n      button.suggested-action:backdrop:disabled:checked,\n      button.suggested-action.flat:backdrop:disabled:active,\n      button.suggested-action.flat:backdrop:disabled:checked {\n        border-color: shade(@theme_selected_bg_color, 0.6);\n        background-color: shade(@theme_selected_bg_color, 0.6);\n        background-image: none;\n        box-shadow: inset 0 1px transparent; }\n        .selection-mode button.titlebutton:backdrop:disabled:active label, .selection-mode button.titlebutton:backdrop:disabled:checked label,\n        button.suggested-action:backdrop:disabled:active label,\n        button.suggested-action:backdrop:disabled:checked label,\n        button.suggested-action.flat:backdrop:disabled:active label,\n        button.suggested-action.flat:backdrop:disabled:checked label {\n          color: @insensitive_fg_color; }\n  .selection-mode button.titlebutton:backdrop, .selection-mode button.titlebutton:disabled, .selection-mode button.titlebutton:backdrop:disabled,\n  button.suggested-action.flat:backdrop,\n  button.suggested-action.flat:disabled,\n  button.suggested-action.flat:backdrop:disabled {\n    border-color: transparent;\n    background-color: transparent;\n    background-image: none;\n    box-shadow: inset 0 1px transparent;\n    text-shadow: none;\n    -gtk-icon-shadow: none;\n    color: @insensitive_fg_color; }\n  button.suggested-action:disabled {\n    border-color: @borders;\n    background-color: @insensitive_bg_color;\n    background-image: none;\n    text-shadow: none;\n    -gtk-icon-shadow: none;\n    box-shadow: inset 0 1px transparent; }\n    button.suggested-action:disabled label,\n    button.suggested-action:disabled {\n      color: @insensitive_fg_color; }\n    button.suggested-action:disabled:active,\n    button.suggested-action:disabled:checked {\n      border-color: shade(@theme_selected_bg_color, 0.6);\n      background-color: shade(@theme_selected_bg_color, 0.6);\n      background-image: none;\n      box-shadow: inset 0 1px transparent; }\n      button.suggested-action:disabled:active label,\n      button.suggested-action:disabled:active,\n      button.suggested-action:disabled:checked label,\n      button.suggested-action:disabled:checked {\n        color: @insensitive_fg_color; }\n  .osd\n\n/* default button for OSD notifications */\n\n  button.suggested-action {\n    color: @theme_fg_color;\n    border-color: @osd_borders;\n    background-color: transparent;\n    background-image: image(shade(@theme_selected_bg_color, 0.5));\n    background-clip: padding-box;\n    box-shadow: inset 0 1px @osd_txt_shadow;\n    text-shadow: 0 1px @osd_txt_shadow;\n    -gtk-icon-shadow: 0 1px @osd_txt_shadow;\n    outline-color: @osd_outline; }\n    .osd\n    button.suggested-action:hover {\n      color: @theme_fg_color;\n      border-color: @osd_borders;\n      background-color: transparent;\n      background-image: image(shade(@theme_selected_bg_color, 0.7));\n      background-clip: padding-box;\n      box-shadow: inset 0 1px @osd_txt_shadow;\n      text-shadow: 0 1px @osd_txt_shadow;\n      -gtk-icon-shadow: 0 1px @osd_txt_shadow;\n      outline-color: @osd_outline; }\n    .osd\n    button.suggested-action:active:backdrop, .osd\n    button.suggested-action:active, .osd\n    button.suggested-action:checked:backdrop, .osd\n    button.suggested-action:checked {\n      color: @theme_selected_fg_color;\n      border-color: @osd_borders;\n      background-color: transparent;\n      background-image: image(@theme_selected_bg_color);\n      background-clip: padding-box;\n      box-shadow: none;\n      text-shadow: none;\n      -gtk-icon-shadow: none;\n      outline-color: @osd_outline; }\n    .osd\n    button.suggested-action:disabled:backdrop, .osd\n    button.suggested-action:disabled {\n      color: shade(@osd_fg_color, 0.85);\n      border-color: @osd_borders;\n      background-color: transparent;\n      background-image: image(shade(@osd_bg_color, 0.95));\n      background-clip: padding-box;\n      box-shadow: none;\n      text-shadow: none;\n      -gtk-icon-shadow: none; }\n    .osd\n    button.suggested-action:backdrop {\n      color: @theme_unfocused_fg_color;\n      border-color: @osd_borders;\n      background-color: transparent;\n      background-image: image(shade(@theme_selected_bg_color, 0.5));\n      background-clip: padding-box;\n      box-shadow: none;\n      text-shadow: none;\n      -gtk-icon-shadow: none; }\n\nbutton.destructive-action {\n  color: @osd_fg_color;\n  outline-color: rgba(255, 255, 255, 0.3);\n  border-color: shade(@error_color, 0.9);\n  border-bottom-color: shade(@error_color, 0.85);\n  background-image: linear-gradient(to bottom, @error_color, @error_color);\n  text-shadow: 0 -1px rgba(0, 0, 0, 0.56078);\n  -gtk-icon-shadow: 0 -1px rgba(0, 0, 0, 0.56078);\n  box-shadow: inset 0 1px rgba(255, 255, 255, 0.4); }\n  button.destructive-action.flat {\n    border-color: transparent;\n    background-color: transparent;\n    background-image: none;\n    box-shadow: inset 0 1px transparent;\n    text-shadow: none;\n    -gtk-icon-shadow: none;\n    color: @error_color; }\n  button.destructive-action:hover {\n    color: @osd_fg_color;\n    outline-color: rgba(255, 255, 255, 0.3);\n    border-color: shade(@error_color, 0.9);\n    border-bottom-color: shade(@error_color, 0.85);\n    background-image: linear-gradient(to bottom, shade(@error_color, 1.1), shade(@error_color, 1.1));\n    text-shadow: 0 -1px rgba(0, 0, 0, 0.51278);\n    -gtk-icon-shadow: 0 -1px rgba(0, 0, 0, 0.51278);\n    box-shadow: inset 0 1px rgba(255, 255, 255, 0.4); }\n  button.destructive-action:active,\n  button.destructive-action:checked {\n    color: @osd_fg_color;\n    outline-color: rgba(255, 255, 255, 0.3);\n    border-color: shade(@error_color, 0.9);\n    background-image: none;\n    background-color: @error_color;\n    box-shadow: inset 0 1px transparent;\n    text-shadow: none;\n    -gtk-icon-shadow: none; }\n  button.destructive-action:backdrop,\n  button.destructive-action.flat:backdrop {\n    border-color: @error_color;\n    background-color: transparent;\n    background-image: image(@error_color);\n    text-shadow: none;\n    -gtk-icon-shadow: none;\n    box-shadow: inset 0 1px transparent; }\n    button.destructive-action:backdrop label,\n    button.destructive-action:backdrop,\n    button.destructive-action.flat:backdrop label,\n    button.destructive-action.flat:backdrop {\n      color: shade(@error_color, 1.3); }\n    button.destructive-action:backdrop:active,\n    button.destructive-action:backdrop:checked,\n    button.destructive-action.flat:backdrop:active,\n    button.destructive-action.flat:backdrop:checked {\n      border-color: @error_color;\n      background-color: @error_color;\n      background-image: none;\n      box-shadow: inset 0 1px transparent; }\n      button.destructive-action:backdrop:active label,\n      button.destructive-action:backdrop:active,\n      button.destructive-action:backdrop:checked label,\n      button.destructive-action:backdrop:checked,\n      button.destructive-action.flat:backdrop:active label,\n      button.destructive-action.flat:backdrop:active,\n      button.destructive-action.flat:backdrop:checked label,\n      button.destructive-action.flat:backdrop:checked {\n        color: shade(@error_color, 1.3); }\n    button.destructive-action:backdrop:disabled,\n    button.destructive-action.flat:backdrop:disabled {\n      border-color: shade(@borders, 0.95);\n      background-color: @insensitive_bg_color;\n      background-image: none;\n      text-shadow: none;\n      -gtk-icon-shadow: none;\n      box-shadow: inset 0 1px transparent; }\n      button.destructive-action:backdrop:disabled label,\n      button.destructive-action:backdrop:disabled,\n      button.destructive-action.flat:backdrop:disabled label,\n      button.destructive-action.flat:backdrop:disabled {\n        color: shade(@theme_unfocused_fg_color, 1.1); }\n      button.destructive-action:backdrop:disabled:active,\n      button.destructive-action:backdrop:disabled:checked,\n      button.destructive-action.flat:backdrop:disabled:active,\n      button.destructive-action.flat:backdrop:disabled:checked {\n        border-color: @error_color;\n        background-color: @error_color;\n        background-image: none;\n        box-shadow: inset 0 1px transparent; }\n        button.destructive-action:backdrop:disabled:active label,\n        button.destructive-action:backdrop:disabled:checked label,\n        button.destructive-action.flat:backdrop:disabled:active label,\n        button.destructive-action.flat:backdrop:disabled:checked label {\n          color: shade(@error_color, 1.2); }\n  button.destructive-action.flat:backdrop,\n  button.destructive-action.flat:disabled,\n  button.destructive-action.flat:backdrop:disabled {\n    border-color: transparent;\n    background-color: transparent;\n    background-image: none;\n    box-shadow: inset 0 1px transparent;\n    text-shadow: none;\n    -gtk-icon-shadow: none;\n    color: @error_color; }\n  button.destructive-action:disabled {\n    border-color: @borders;\n    background-color: @insensitive_bg_color;\n    background-image: none;\n    text-shadow: none;\n    -gtk-icon-shadow: none;\n    box-shadow: inset 0 1px transparent; }\n    button.destructive-action:disabled label,\n    button.destructive-action:disabled {\n      color: @insensitive_fg_color; }\n    button.destructive-action:disabled:active,\n    button.destructive-action:disabled:checked {\n      border-color: shade(@error_color, 0.9);\n      background-color: @error_color;\n      background-image: none;\n      box-shadow: inset 0 1px transparent; }\n      button.destructive-action:disabled:active label,\n      button.destructive-action:disabled:active,\n      button.destructive-action:disabled:checked label,\n      button.destructive-action:disabled:checked {\n        color: shade(@error_color, 1.2); }\n  .osd\n  button.destructive-action {\n    color: @theme_unfocused_fg_color;\n    border-color: @osd_borders;\n    background-color: transparent;\n    background-image: image(@error_color);\n    background-clip: padding-box;\n    box-shadow: inset 0 1px @osd_txt_shadow;\n    text-shadow: 0 1px @osd_txt_shadow;\n    -gtk-icon-shadow: 0 1px @osd_txt_shadow;\n    outline-color: @osd_outline; }\n    .osd\n    button.destructive-action:hover {\n      color: @osd_fg_color;\n      border-color: @osd_borders;\n      background-color: transparent;\n      background-image: image(@error_color);\n      background-clip: padding-box;\n      box-shadow: inset 0 1px @osd_txt_shadow;\n      text-shadow: 0 1px @osd_txt_shadow;\n      -gtk-icon-shadow: 0 1px @osd_txt_shadow;\n      outline-color: @osd_outline; }\n    .osd\n    button.destructive-action:active:backdrop, .osd\n    button.destructive-action:active, .osd\n    button.destructive-action:checked:backdrop, .osd\n    button.destructive-action:checked {\n      color: @osd_fg_color;\n      border-color: @osd_borders;\n      background-color: transparent;\n      background-image: image(@error_color);\n      background-clip: padding-box;\n      box-shadow: none;\n      text-shadow: none;\n      -gtk-icon-shadow: none;\n      outline-color: @osd_outline; }\n    .osd\n    button.destructive-action:disabled:backdrop, .osd\n    button.destructive-action:disabled {\n      color: shade(@insensitive_fg_color, 0.6);\n      border-color: @osd_borders;\n      background-color: transparent;\n      background-image: image(shade(@osd_bg_color, 0.95));\n      background-clip: padding-box;\n      box-shadow: none;\n      text-shadow: none;\n      -gtk-icon-shadow: none; }\n    .osd\n    button.destructive-action:backdrop {\n      color: @theme_unfocused_fg_color;\n      border-color: @osd_borders;\n      background-color: transparent;\n      background-image: image(@error_color);\n      background-clip: padding-box;\n      box-shadow: none;\n      text-shadow: none;\n      -gtk-icon-shadow: none; }\n.stack-switcher >\nbutton {\n  outline-offset: -3px; }\n  .stack-switcher >\n  button > label {\n    padding-left: 6px;\n    padding-right: 6px; }\n  .stack-switcher >\n  button > image {\n    padding-left: 6px;\n    padding-right: 6px;\n    padding-top: 3px;\n    padding-bottom: 3px; }\n  .stack-switcher >\n  button.text-button {\n    padding-left: 10px;\n    padding-right: 10px; }\n  .stack-switcher >\n  button.image-button {\n    padding-left: 2px;\n    padding-right: 2px; }\n  .stack-switcher >\n  button.needs-attention:active > label,\n  .stack-switcher >\n  button.needs-attention:active > image, .stack-switcher >\n  button.needs-attention:checked > label,\n  .stack-switcher >\n  button.needs-attention:checked > image {\n    animation: none;\n    background-image: none; }\n.inline-toolbar\nbutton, .inline-toolbar\nbutton:backdrop {\n  border-radius: 0;\n  border-width: 1px; }\n.primary-toolbar\nbutton {\n  -gtk-icon-shadow: none; }\n\n.stack-switcher >\nbutton.needs-attention > label,\n.stack-switcher >\nbutton.needs-attention > image, stacksidebar row.needs-attention > label {\n  animation: needs_attention 150ms ease-in;\n  background-image: -gtk-gradient(radial, center center, 0, center center, 0.5, to(@theme_selected_bg_color), to(transparent)), -gtk-gradient(radial, center center, 0, center center, 0.5, to(@txt_shadow), to(transparent));\n  background-size: 6px 6px, 6px 6px;\n  background-repeat: no-repeat;\n  background-position: right 3px, right 4px; }\n  .stack-switcher >\n  button.needs-attention > label:backdrop,\n  .stack-switcher >\n  button.needs-attention > image:backdrop, stacksidebar row.needs-attention > label:backdrop {\n    background-size: 6px 6px, 0 0; }\n  .stack-switcher >\n  button.needs-attention > label:dir(rtl),\n  .stack-switcher >\n  button.needs-attention > image:dir(rtl), stacksidebar row.needs-attention > label:dir(rtl) {\n    background-position: left 3px, left 4px; }\n\n/* Here we are */\n\n.inline-toolbar toolbutton > button {\n  color: @theme_fg_color;\n  outline-color: @outline_color;\n  border-color: @borders;\n  background-image: linear-gradient(to bottom, @theme_bg_color, @theme_bg_color);\n  text-shadow: 0 1px transparent;\n  -gtk-icon-shadow: 0 1px transparent;\n  box-shadow: inset 0 1px transparent; }\n  .inline-toolbar toolbutton > button:hover {\n    color: @theme_fg_color;\n    outline-color: @outline_color;\n    border-color: @borders;\n    background-image: linear-gradient(to bottom, @theme_selected_bg_color, @theme_selected_bg_color);\n    text-shadow: 0 1px @txt_shadow;\n    -gtk-icon-shadow: 0 1px @txt_shadow;\n    box-shadow: inset 0 1px @theme_bg_color; }\n  .inline-toolbar toolbutton > button:active, .inline-toolbar toolbutton > button:checked {\n    color: @theme_fg_color;\n    outline-color: @outline_color;\n    border-color: @borders;\n    background-image: none;\n    background-color: shade(@theme_bg_color, 0.9);\n    box-shadow: inset 0 1px transparent;\n    text-shadow: none;\n    -gtk-icon-shadow: none; }\n  .inline-toolbar toolbutton > button:disabled {\n    border-color: @borders;\n    background-color: @insensitive_bg_color;\n    background-image: none;\n    text-shadow: none;\n    -gtk-icon-shadow: none;\n    box-shadow: inset 0 1px transparent; }\n    .inline-toolbar toolbutton > button:disabled label, .inline-toolbar toolbutton > button:disabled {\n      color: @insensitive_fg_color; }\n    .inline-toolbar toolbutton > button:disabled:active, .inline-toolbar toolbutton > button:disabled:checked {\n      border-color: @borders;\n      background-color: shade(@theme_bg_color, 0.95);\n      background-image: none;\n      box-shadow: inset 0 1px transparent; }\n      .inline-toolbar toolbutton > button:disabled:active label, .inline-toolbar toolbutton > button:disabled:active, .inline-toolbar toolbutton > button:disabled:checked label, .inline-toolbar toolbutton > button:disabled:checked {\n        color: @insensitive_fg_color; }\n  .inline-toolbar toolbutton > button:backdrop {\n    border-color: shade(@borders, 0.95);\n    background-color: transparent;\n    background-image: image(@theme_bg_color);\n    text-shadow: none;\n    -gtk-icon-shadow: none;\n    box-shadow: inset 0 1px transparent; }\n    .inline-toolbar toolbutton > button:backdrop label, .inline-toolbar toolbutton > button:backdrop {\n      color: @insensitive_fg_color; }\n    .inline-toolbar toolbutton > button:backdrop:active, .inline-toolbar toolbutton > button:backdrop:checked {\n      border-color: shade(@borders, 0.95);\n      background-color: shade(@theme_bg_color, 0.95);\n      background-image: none;\n      box-shadow: inset 0 1px transparent; }\n      .inline-toolbar toolbutton > button:backdrop:active label, .inline-toolbar toolbutton > button:backdrop:active, .inline-toolbar toolbutton > button:backdrop:checked label, .inline-toolbar toolbutton > button:backdrop:checked {\n        color: @insensitive_fg_color; }\n    .inline-toolbar toolbutton > button:backdrop:disabled {\n      border-color: shade(@borders, 0.95);\n      background-color: @insensitive_bg_color;\n      background-image: none;\n      text-shadow: none;\n      -gtk-icon-shadow: none;\n      box-shadow: inset 0 1px transparent; }\n      .inline-toolbar toolbutton > button:backdrop:disabled label, .inline-toolbar toolbutton > button:backdrop:disabled {\n        color: shade(@theme_unfocused_fg_color, 1.1); }\n      .inline-toolbar toolbutton > button:backdrop:disabled:active, .inline-toolbar toolbutton > button:backdrop:disabled:checked {\n        border-color: shade(@borders, 0.95);\n        background-color: shade(@theme_bg_color, 0.95);\n        background-image: none;\n        box-shadow: inset 0 1px transparent; }\n        .inline-toolbar toolbutton > button:backdrop:disabled:active label, .inline-toolbar toolbutton > button:backdrop:disabled:checked label {\n          color: shade(@theme_unfocused_fg_color, 1.1); }\n\ntoolbar.inline-toolbar toolbutton > button.flat,\ntoolbar.inline-toolbar toolbutton:backdrop > button.flat, .linked:not(.vertical) > spinbutton:not(.vertical), .linked:not(.vertical) >\nentry, .inline-toolbar\nbutton, .inline-toolbar\nbutton:backdrop, .linked >\nbutton, .linked >\nbutton:hover, .linked >\nbutton:active, .linked >\nbutton:checked, .linked >\nbutton:backdrop, .linked > combobox > box > button.combo:dir(ltr), .linked > combobox > box > button.combo:dir(rtl) {\n  border-radius: 0;\n  border-right-style: none; }\n\n.linked:not(.vertical) > spinbutton:first-child:not(.vertical), .linked:not(.vertical) >\nentry:first-child, .inline-toolbar\nbutton:first-child, .linked >\nbutton:first-child, toolbar.inline-toolbar toolbutton:first-child > button.flat,\ntoolbar.inline-toolbar toolbutton:backdrop:first-child > button.flat, combobox.linked button:nth-child(2):dir(rtl), .linked:not(.vertical) > combobox:first-child > box > button.combo {\n  border-top-left-radius: 0;\n  border-bottom-left-radius: 0; }\n.linked:not(.vertical) > spinbutton:last-child:not(.vertical), .linked:not(.vertical) >\nentry:last-child, .inline-toolbar\nbutton:last-child, .linked >\nbutton:last-child, toolbar.inline-toolbar toolbutton:last-child > button.flat,\ntoolbar.inline-toolbar toolbutton:backdrop:last-child > button.flat, combobox.linked button:nth-child(2):dir(ltr), .linked:not(.vertical) > combobox:last-child > box > button.combo {\n  border-top-right-radius: 0;\n  border-bottom-right-radius: 0;\n  border-right-style: solid; }\n.linked:not(.vertical) > spinbutton:only-child:not(.vertical), .linked:not(.vertical) >\nentry:only-child, .inline-toolbar\nbutton:only-child, .linked >\nbutton:only-child, toolbar.inline-toolbar toolbutton:only-child > button.flat,\ntoolbar.inline-toolbar toolbutton:backdrop:only-child > button.flat, .linked:not(.vertical) > combobox:only-child > box > button.combo {\n  border-radius: 0;\n  border-style: solid; }\n\n.linked.vertical > spinbutton:not(.vertical), .linked.vertical >\nentry, .linked.vertical >\nbutton, .linked.vertical >\nbutton:hover, .linked.vertical >\nbutton:active, .linked.vertical >\nbutton:checked, .linked.vertical >\nbutton:backdrop, .linked.vertical > combobox > box > button.combo {\n  border-style: solid solid none solid;\n  border-radius: 0; }\n\n.linked.vertical > spinbutton:first-child:not(.vertical), .linked.vertical >\nentry:first-child, .linked.vertical >\nbutton:first-child, .linked.vertical > combobox:first-child > box > button.combo {\n  border-top-left-radius: 0;\n  border-top-right-radius: 0; }\n.linked.vertical > spinbutton:last-child:not(.vertical), .linked.vertical >\nentry:last-child, .linked.vertical >\nbutton:last-child, .linked.vertical > combobox:last-child > box > button.combo {\n  border-bottom-left-radius: 0;\n  border-bottom-right-radius: 0;\n  border-style: solid; }\n.linked.vertical > spinbutton:only-child:not(.vertical), .linked.vertical >\nentry:only-child, .linked.vertical >\nbutton:only-child, .linked.vertical > combobox:only-child > box > button.combo {\n  border-radius: 0;\n  border-style: solid; }\n\nmodelbutton.flat, popover.background checkbutton,\npopover.background radiobutton,\n.menuitem.button.flat, modelbutton.flat:backdrop, popover.background checkbutton:backdrop,\npopover.background radiobutton:backdrop, modelbutton.flat:backdrop:hover, popover.background checkbutton:backdrop:hover,\npopover.background radiobutton:backdrop:hover,\n.menuitem.button.flat:backdrop,\n.menuitem.button.flat:backdrop:hover, button:link,\nbutton:visited, button:link:hover, button:link:active, button:link:checked,\nbutton:visited:hover,\nbutton:visited:active,\nbutton:visited:checked, calendar.button, calendar.button:hover, calendar.button:backdrop, calendar.button:disabled, .scale-popup button:hover, .scale-popup button:backdrop:hover, .scale-popup button:backdrop:disabled, .scale-popup button:backdrop {\n  background-color: transparent;\n  background-image: none;\n  border-color: transparent;\n  box-shadow: inset 0 1px transparent, 0 1px transparent;\n  text-shadow: none;\n  -gtk-icon-shadow: none; }\n\n/* menu buttons */\nmodelbutton.flat, popover.background checkbutton,\npopover.background radiobutton,\n.menuitem.button.flat {\n  min-height: 26px;\n  padding-left: 5px;\n  padding-right: 5px;\n  border-radius: 0;\n  outline-offset: -2px; }\n  modelbutton.flat:hover, popover.background checkbutton:hover,\n  popover.background radiobutton:hover,\n  .menuitem.button.flat:hover {\n    background-color: shade(@theme_bg_color, 0.95); }\n  modelbutton.flat check:last-child, popover.background checkbutton check:last-child,\n  popover.background radiobutton check:last-child,\n  modelbutton.flat radio:last-child,\n  popover.background checkbutton radio:last-child,\n  popover.background radiobutton radio:last-child,\n  .menuitem.button.flat check:last-child,\n  .menuitem.button.flat radio:last-child {\n    margin-left: 8px; }\n  modelbutton.flat check:first-child, popover.background checkbutton check:first-child,\n  popover.background radiobutton check:first-child,\n  modelbutton.flat radio:first-child,\n  popover.background checkbutton radio:first-child,\n  popover.background radiobutton radio:first-child,\n  .menuitem.button.flat check:first-child,\n  .menuitem.button.flat radio:first-child {\n    margin-right: 8px; }\n\nmodelbutton.flat arrow, popover.background checkbutton arrow,\npopover.background radiobutton arrow {\n  background: none; }\n  modelbutton.flat arrow:hover, popover.background checkbutton arrow:hover,\n  popover.background radiobutton arrow:hover {\n    background: none; }\n  modelbutton.flat arrow.left, popover.background checkbutton arrow.left,\n  popover.background radiobutton arrow.left {\n    -gtk-icon-source: -gtk-icontheme(\"pan-start-symbolic\"); }\n  modelbutton.flat arrow.right, popover.background checkbutton arrow.right,\n  popover.background radiobutton arrow.right {\n    -gtk-icon-source: -gtk-icontheme(\"pan-end-symbolic\"); }\n\nbutton.color {\n  padding: 4px; }\n  button.color colorswatch:only-child {\n    box-shadow: 0 1px @txt_shadow; }\n    button.color colorswatch:only-child, button.color colorswatch:only-child overlay {\n      border-radius: 0; }\n  button.color:disabled colorswatch:only-child, button.color:backdrop colorswatch:only-child, button.color:active colorswatch:only-child, button.color:checked colorswatch:only-child {\n    box-shadow: none; }\n\n/*********\n * Links *\n *********/\nbutton:link > label,\nbutton:visited > label,\n*:link,\nbutton:link,\nbutton:visited {\n  color: @borders; }\n  button:link > label:visited,\n  button:visited > label:visited,\n  *:link:visited,\n  button:visited {\n    color: shade(@theme_selected_bg_color, 0.6); }\n    *:selected button:link > label:visited,\n    *:selected button:visited > label:visited, *:selected\n    *:link:visited, *:selected\n    button:visited:link,\n    *:selected button:visited {\n      color: #b7d3f0; }\n  button:link > label:hover,\n  button:visited > label:hover,\n  *:link:hover,\n  button:hover:link,\n  button:hover:visited {\n    color: @theme_selected_bg_color; }\n    *:selected button:link > label:hover,\n    *:selected button:visited > label:hover, *:selected\n    *:link:hover, *:selected\n    button:hover:link,\n    *:selected button:hover:visited {\n      color: #edf4fb; }\n  button:link > label:active,\n  button:visited > label:active,\n  *:link:active,\n  button:active:link,\n  button:active:visited {\n    color: @borders; }\n    *:selected button:link > label:active,\n    *:selected button:visited > label:active, *:selected\n    *:link:active, *:selected\n    button:active:link,\n    *:selected button:active:visited {\n      color: @theme_selected_bg_color; }\n  button:link > label:backdrop:backdrop:hover,\n  button:visited > label:backdrop:backdrop:hover, button:link > label:backdrop:backdrop:hover:selected,\n  button:visited > label:backdrop:backdrop:hover:selected, button:link > label:backdrop,\n  button:visited > label:backdrop,\n  *:link:backdrop:backdrop:hover,\n  button:backdrop:backdrop:hover:link,\n  button:backdrop:backdrop:hover:visited,\n  *:link:backdrop:backdrop:hover:selected,\n  button:backdrop:backdrop:hover:selected:link,\n  button:backdrop:backdrop:hover:selected:visited,\n  .selection-mode.titlebar:not(headerbar) .subtitle:backdrop:backdrop:hover:link,\n  headerbar.selection-mode .subtitle:backdrop:backdrop:hover:link,\n  *:link:backdrop,\n  button:backdrop:link,\n  button:backdrop:visited {\n    color: @theme_selected_bg_color; }\n  .info *:link, .info button:link,\n  .info button:visited,\n  .question *:link,\n  .question button:link,\n  .question button:visited,\n  .warning *:link,\n  .warning button:link,\n  .warning button:visited,\n  .error *:link,\n  .error button:link,\n  .error button:visited, button:link > label:selected,\n  button:visited > label:selected, *:selected button:link > label,\n  *:selected button:visited > label,\n  *:link:selected,\n  button:selected:link,\n  button:selected:visited,\n  .selection-mode.titlebar:not(headerbar) .subtitle:link,\n  headerbar.selection-mode .subtitle:link, *:selected\n  *:link, *:selected\n  button:link,\n  *:selected button:visited {\n    color: @theme_selected_bg_color; }\n\nbutton:link,\nbutton:visited {\n  text-shadow: none; }\n  button:link:hover, button:link:active, button:link:checked,\n  button:visited:hover,\n  button:visited:active,\n  button:visited:checked {\n    text-shadow: none; }\n  button:link > label,\n  button:visited > label {\n    text-decoration-line: underline; }\n\n/*****************\n * GtkSpinButton *\n *****************/\nspinbutton:not(.vertical) {\n  padding: 0; }\n  spinbutton:not(.vertical) entry {\n    min-width: 28px;\n    margin: 0;\n    background: none;\n    background-color: transparent;\n    border: none;\n    border-radius: 0;\n    box-shadow: none; }\n    spinbutton:not(.vertical) entry:backdrop:disabled {\n      background-color: transparent; }\n  spinbutton:not(.vertical) button {\n    min-height: 16px;\n    margin: 0;\n    padding-bottom: 0;\n    padding-top: 0;\n    color: #43484a;\n    background-image: none;\n    border-style: none none none solid;\n    border-color: rgba(182, 182, 179, 0.3);\n    border-radius: 0;\n    box-shadow: none; }\n    spinbutton:not(.vertical) button:dir(rtl) {\n      border-style: none solid none none; }\n    spinbutton:not(.vertical) button:hover {\n      color: @theme_fg_color;\n      background-color: rgba(46, 52, 54, 0.05); }\n    spinbutton:not(.vertical) button:disabled {\n      color: rgba(139, 142, 143, 0.3);\n      background-color: transparent; }\n    spinbutton:not(.vertical) button:active {\n      background-color: rgba(0, 0, 0, 0.1);\n      box-shadow: inset 0 2px 3px -1px rgba(0, 0, 0, 0.2); }\n    spinbutton:not(.vertical) button:backdrop {\n      color: #96999a;\n      background-color: transparent;\n      border-color: rgba(192, 192, 189, 0.3);\n      transition: 200ms ease-out; }\n    spinbutton:not(.vertical) button:backdrop:disabled {\n      color: rgba(195, 195, 192, 0.3);\n      background-color: transparent;\n      border-style: none none none solid; }\n      spinbutton:not(.vertical) button:backdrop:disabled:dir(rtl) {\n        border-style: none solid none none; }\n    spinbutton:not(.vertical) button:dir(ltr):last-child {\n      border-radius: 0; }\n    spinbutton:not(.vertical) button:dir(rtl):first-child {\n      border-radius: 0; }\n.osd spinbutton:not(.vertical) button {\n  border-color: transparent;\n  background-color: transparent;\n  background-image: none;\n  box-shadow: inset 0 1px transparent;\n  text-shadow: none;\n  -gtk-icon-shadow: none;\n  color: @theme_unfocused_fg_color;\n  border-style: none none none solid;\n  border-color: rgba(0, 0, 0, 0.4);\n  border-radius: 0;\n  box-shadow: none;\n  -gtk-icon-shadow: 0 1px @osd_txt_shadow; }\n  .osd spinbutton:not(.vertical) button:dir(rtl) {\n    border-style: none solid none none; }\n  .osd spinbutton:not(.vertical) button:hover {\n    border-color: transparent;\n    background-color: transparent;\n    background-image: none;\n    box-shadow: inset 0 1px transparent;\n    text-shadow: none;\n    -gtk-icon-shadow: none;\n    color: @theme_unfocused_fg_color;\n    border-color: @osd_bg_color;\n    background-color: rgba(238, 238, 236, 0.1);\n    -gtk-icon-shadow: 0 1px @osd_txt_shadow;\n    box-shadow: none; }\n  .osd spinbutton:not(.vertical) button:backdrop {\n    border-color: transparent;\n    background-color: transparent;\n    background-image: none;\n    box-shadow: inset 0 1px transparent;\n    text-shadow: none;\n    -gtk-icon-shadow: none;\n    color: @theme_unfocused_fg_color;\n    border-color: @osd_bg_color;\n    -gtk-icon-shadow: none;\n    box-shadow: none; }\n  .osd spinbutton:not(.vertical) button:disabled {\n    border-color: transparent;\n    background-color: transparent;\n    background-image: none;\n    box-shadow: inset 0 1px transparent;\n    text-shadow: none;\n    -gtk-icon-shadow: none;\n    color: shade(@osd_fg_color, 0.85);\n    border-color: @osd_bg_color;\n    -gtk-icon-shadow: none;\n    box-shadow: none; }\n  .osd spinbutton:not(.vertical) button:dir(ltr):last-child {\n    border-radius: 0; }\n  .osd spinbutton:not(.vertical) button:dir(rtl):first-child {\n    border-radius: 0; }\nspinbutton.vertical:disabled {\n  color: @insensitive_fg_color; }\nspinbutton.vertical:backdrop:disabled {\n  color: shade(@theme_unfocused_fg_color, 1.1); }\nspinbutton.vertical:drop(active) {\n  border-color: transparent;\n  box-shadow: none; }\nspinbutton.vertical entry {\n  min-height: 32px;\n  min-width: 32px;\n  padding: 0;\n  border-radius: 0; }\nspinbutton.vertical button {\n  min-height: 32px;\n  min-width: 32px;\n  padding: 0; }\nspinbutton.vertical button.up {\n  border-radius: 0;\n  border-style: solid solid none solid; }\nspinbutton.vertical button.down {\n  border-radius: 0;\n  border-style: none solid solid solid; }\n.osd spinbutton.vertical button:first-child {\n  color: @theme_unfocused_fg_color;\n  border-color: @osd_borders;\n  background-color: transparent;\n  background-image: image(@osd_bg_color);\n  background-clip: padding-box;\n  box-shadow: inset 0 1px @osd_txt_shadow;\n  text-shadow: 0 1px @osd_txt_shadow;\n  -gtk-icon-shadow: 0 1px @osd_txt_shadow;\n  outline-color: @osd_outline; }\n  .osd spinbutton.vertical button:first-child:hover {\n    color: @osd_fg_color;\n    border-color: @osd_borders;\n    background-color: transparent;\n    background-image: image(shade(@osd_bg_color, 1.05));\n    background-clip: padding-box;\n    box-shadow: inset 0 1px @osd_txt_shadow;\n    text-shadow: 0 1px @osd_txt_shadow;\n    -gtk-icon-shadow: 0 1px @osd_txt_shadow;\n    outline-color: @osd_outline; }\n  .osd spinbutton.vertical button:first-child:active {\n    color: @osd_fg_color;\n    border-color: @osd_borders;\n    background-color: transparent;\n    background-image: image(@osd_borders);\n    background-clip: padding-box;\n    box-shadow: none;\n    text-shadow: none;\n    -gtk-icon-shadow: none;\n    outline-color: @osd_outline; }\n  .osd spinbutton.vertical button:first-child:disabled {\n    color: shade(@osd_fg_color, 0.85);\n    border-color: @osd_borders;\n    background-color: transparent;\n    background-image: image(shade(@osd_bg_color, 0.95));\n    background-clip: padding-box;\n    box-shadow: none;\n    text-shadow: none;\n    -gtk-icon-shadow: none; }\n  .osd spinbutton.vertical button:first-child:backdrop {\n    color: @theme_unfocused_fg_color;\n    border-color: @osd_borders;\n    background-color: transparent;\n    background-image: image(@osd_bg_color);\n    background-clip: padding-box;\n    box-shadow: none;\n    text-shadow: none;\n    -gtk-icon-shadow: none; }\ntreeview spinbutton:not(.vertical) {\n  min-height: 0;\n  border-style: none;\n  border-radius: 0; }\n  treeview spinbutton:not(.vertical) entry {\n    min-height: 0;\n    padding: 1px 2px; }\n\n/**************\n * ComboBoxes *\n **************/\ncombobox arrow {\n  -gtk-icon-source: -gtk-icontheme(\"pan-down-symbolic\");\n  min-height: 16px;\n  min-width: 16px; }\ncombobox:drop(active) {\n  box-shadow: none; }\n\n/************\n * Toolbars *\n ************/\ntoolbar, .inline-toolbar, searchbar,\n.location-bar {\n  -GtkWidget-window-dragging: true;\n  padding: 4px;\n  background-color: @theme_bg_color; }\n\ntoolbar {\n  padding: 4px 3px 3px 4px; }\n  .osd toolbar {\n    background-color: transparent; }\n  toolbar.osd {\n    padding: 13px;\n    border: none;\n    border-radius: 0;\n    background-color: @osd_bg_color; }\n    toolbar.osd.left, toolbar.osd.right, toolbar.osd.top, toolbar.osd.bottom {\n      border-radius: 0; }\n  toolbar.horizontal separator {\n    margin: 0 7px 1px 6px; }\n  toolbar.vertical separator {\n    margin: 6px 1px 7px 0; }\n  toolbar:not(.inline-toolbar):not(.osd) switch,\n  toolbar:not(.inline-toolbar):not(.osd) scale,\n  toolbar:not(.inline-toolbar):not(.osd) entry,\n  toolbar:not(.inline-toolbar):not(.osd) spinbutton,\n  toolbar:not(.inline-toolbar):not(.osd) button {\n    margin-right: 1px;\n    margin-bottom: 1px; }\n\n.inline-toolbar {\n  padding: 3px;\n  border-width: 0 1px 1px;\n  border-radius: 0; }\n\nsearchbar,\n.location-bar {\n  border-width: 0 0 1px;\n  padding: 3px; }\n\n.inline-toolbar, searchbar,\n.location-bar {\n  border-style: solid;\n  border-color: @borders;\n  background-color: @theme_bg_color; } /*#d9d9d7*/\n  .inline-toolbar:backdrop, searchbar:backdrop,\n  .location-bar:backdrop {\n    border-color: shade(@borders, 0.95);\n    background-color: @theme_unfocused_bg_color; /*#dadad8*/\n    box-shadow: none;\n    transition: 200ms ease-out; }\n\n/***************\n * Header bars *\n ***************/\n.titlebar:not(headerbar),\nheaderbar {\n  padding: 0 6px;\n  min-height: 46px;\n  border-width: 0 0 1px;\n  border-style: solid;\n  border-color: @borders;\n  border-radius: 0;\n  background-image: linear-gradient(to top, @theme_bg_color, @theme_bg_color);\n  background-color: @theme_bg_color;\n  box-shadow: inset 0 1px rgba(20, 20, 20, 0.8); }\n  .titlebar:backdrop:not(headerbar),\n  headerbar:backdrop {\n    border-color: shade(@borders, 0.95);\n    background-color: @theme_bg_color;\n    background-image: none;\n    box-shadow: inset 0 1px rgba(20, 20, 20, 0.8);\n    transition: 200ms ease-out; }\n  .titlebar:not(headerbar) .title,\n  headerbar .title {\n    padding-left: 12px;\n    padding-right: 12px;\n    font-weight: bold; }\n  .titlebar:not(headerbar) .subtitle,\n  headerbar .subtitle {\n    font-size: smaller;\n    padding-left: 12px;\n    padding-right: 12px; }\n  .selection-mode.titlebar:not(headerbar),\n  headerbar.selection-mode {\n    color: @theme_selected_fg_color;\n    border-color: shade(@theme_selected_bg_color, 0.6);\n    text-shadow: 0 -1px @osd_bg_color;\n    background-image: image(@theme_selected_bg_color);\n    background-color: @theme_selected_bg_color;\n    box-shadow: inset 0 1px rgba(146, 188, 232, 0.9); }\n    .selection-mode.titlebar:backdrop:not(headerbar),\n    headerbar.selection-mode:backdrop {\n      background-color: @theme_selected_bg_color;\n      background-image: none;\n      box-shadow: inset 0 1px rgba(165, 200, 236, 0.88); }\n    .selection-mode.titlebar:not(headerbar) button,\n    headerbar.selection-mode button {\n      color: @theme_selected_fg_color;\n      outline-color: rgba(255, 255, 255, 0.3);\n      border-color: shade(@theme_selected_bg_color, 0.6);\n      border-bottom-color: shade(@theme_selected_bg_color, 0.6);\n      background-image: image(@theme_selected_bg_color);\n      text-shadow: 0 -1px rgba(0, 0, 0, 0.54353);\n      -gtk-icon-shadow: 0 -1px rgba(0, 0, 0, 0.54353);\n      /*box-shadow: inset 0 1px rgba(255, 255, 255, 0.4);*/ }\n      .selection-mode.titlebar:not(headerbar) button.flat,\n      headerbar.selection-mode button.flat {\n        border-color: transparent;\n        background-color: transparent;\n        background-image: none;\n        box-shadow: inset 0 1px transparent;\n        text-shadow: none;\n        -gtk-icon-shadow: none; }\n      .selection-mode.titlebar:not(headerbar) button:hover,\n      headerbar.selection-mode button:hover {\n        color: @theme_selected_fg_color;\n        outline-color: rgba(255, 255, 255, 0.3);\n        border-color: shade(@theme_selected_bg_color, 0.6);\n        border-bottom-color: shade(@theme_selected_bg_color, 0.6);\n        background-image: image(@theme_selected_bg_color);\n        text-shadow: 0 -1px rgba(0, 0, 0, 0.49553);\n        -gtk-icon-shadow: 0 -1px rgba(0, 0, 0, 0.49553);\n        box-shadow: inset 0 1px rgba(255, 255, 255, 0.4); }\n      .selection-mode.titlebar:not(headerbar) button:active, .selection-mode.titlebar:not(headerbar) button:checked,\n      headerbar.selection-mode button:active,\n      headerbar.selection-mode button:checked {\n        color: @theme_selected_fg_color;\n        outline-color: rgba(255, 255, 255, 0.3);\n        border-color: shade(@theme_selected_bg_color, 0.6);\n        background-image: none;\n        background-color: shade(@theme_selected_bg_color, 0.8);\n        box-shadow: inset 0 1px transparent;\n        text-shadow: none;\n        -gtk-icon-shadow: none; }\n      .selection-mode.titlebar:not(headerbar) button:backdrop.flat, .selection-mode.titlebar:not(headerbar) button:backdrop,\n      headerbar.selection-mode button:backdrop.flat,\n      headerbar.selection-mode button:backdrop {\n        border-color: @theme_selected_bg_color;\n        background-color: transparent;\n        background-image: image(@theme_selected_bg_color);\n        text-shadow: none;\n        -gtk-icon-shadow: none;\n        box-shadow: inset 0 1px transparent;\n        -gtk-icon-effect: none;\n        border-color: shade(@theme_selected_bg_color, 0.6); }\n        .selection-mode.titlebar:not(headerbar) button:backdrop.flat label, .selection-mode.titlebar:not(headerbar) button:backdrop.flat, .selection-mode.titlebar:not(headerbar) button:backdrop label, .selection-mode.titlebar:not(headerbar) button:backdrop,\n        headerbar.selection-mode button:backdrop.flat label,\n        headerbar.selection-mode button:backdrop.flat,\n        headerbar.selection-mode button:backdrop label,\n        headerbar.selection-mode button:backdrop {\n          color: @theme_selected_fg_color; }\n        .selection-mode.titlebar:not(headerbar) button:backdrop.flat:active, .selection-mode.titlebar:not(headerbar) button:backdrop.flat:checked, .selection-mode.titlebar:not(headerbar) button:backdrop:active, .selection-mode.titlebar:not(headerbar) button:backdrop:checked,\n        headerbar.selection-mode button:backdrop.flat:active,\n        headerbar.selection-mode button:backdrop.flat:checked,\n        headerbar.selection-mode button:backdrop:active,\n        headerbar.selection-mode button:backdrop:checked {\n          border-color: shade(@theme_selected_bg_color, 0.6);\n          background-color: shade(@theme_selected_bg_color, 0.6);\n          background-image: none;\n          box-shadow: inset 0 1px transparent;\n          border-color: shade(@theme_selected_bg_color, 0.6); }\n          .selection-mode.titlebar:not(headerbar) button:backdrop.flat:active label, .selection-mode.titlebar:not(headerbar) button:backdrop.flat:active, .selection-mode.titlebar:not(headerbar) button:backdrop.flat:checked label, .selection-mode.titlebar:not(headerbar) button:backdrop.flat:checked, .selection-mode.titlebar:not(headerbar) button:backdrop:active label, .selection-mode.titlebar:not(headerbar) button:backdrop:active, .selection-mode.titlebar:not(headerbar) button:backdrop:checked label, .selection-mode.titlebar:not(headerbar) button:backdrop:checked,\n          headerbar.selection-mode button:backdrop.flat:active label,\n          headerbar.selection-mode button:backdrop.flat:active,\n          headerbar.selection-mode button:backdrop.flat:checked label,\n          headerbar.selection-mode button:backdrop.flat:checked,\n          headerbar.selection-mode button:backdrop:active label,\n          headerbar.selection-mode button:backdrop:active,\n          headerbar.selection-mode button:backdrop:checked label,\n          headerbar.selection-mode button:backdrop:checked {\n            color: @theme_selected_fg_color; }\n        .selection-mode.titlebar:not(headerbar) button:backdrop.flat:disabled, .selection-mode.titlebar:not(headerbar) button:backdrop:disabled,\n        headerbar.selection-mode button:backdrop.flat:disabled,\n        headerbar.selection-mode button:backdrop:disabled {\n          border-color: @theme_selected_bg_color;\n          background-color: @theme_selected_bg_color;\n          background-image: none;\n          text-shadow: none;\n          -gtk-icon-shadow: none;\n          box-shadow: inset 0 1px transparent;\n          border-color: shade(@theme_selected_bg_color, 0.6); }\n          .selection-mode.titlebar:not(headerbar) button:backdrop.flat:disabled label, .selection-mode.titlebar:not(headerbar) button:backdrop.flat:disabled, .selection-mode.titlebar:not(headerbar) button:backdrop:disabled label, .selection-mode.titlebar:not(headerbar) button:backdrop:disabled,\n          headerbar.selection-mode button:backdrop.flat:disabled label,\n          headerbar.selection-mode button:backdrop.flat:disabled,\n          headerbar.selection-mode button:backdrop:disabled label,\n          headerbar.selection-mode button:backdrop:disabled {\n            color: @insensitive_fg_color; }\n          .selection-mode.titlebar:not(headerbar) button:backdrop.flat:disabled:active, .selection-mode.titlebar:not(headerbar) button:backdrop.flat:disabled:checked, .selection-mode.titlebar:not(headerbar) button:backdrop:disabled:active, .selection-mode.titlebar:not(headerbar) button:backdrop:disabled:checked,\n          headerbar.selection-mode button:backdrop.flat:disabled:active,\n          headerbar.selection-mode button:backdrop.flat:disabled:checked,\n          headerbar.selection-mode button:backdrop:disabled:active,\n          headerbar.selection-mode button:backdrop:disabled:checked {\n            border-color: shade(@theme_selected_bg_color, 0.6);\n            background-color: shade(@theme_selected_bg_color, 0.6);\n            background-image: none;\n            box-shadow: inset 0 1px transparent;\n            border-color: shade(@theme_selected_bg_color, 0.6); }\n            .selection-mode.titlebar:not(headerbar) button:backdrop.flat:disabled:active label, .selection-mode.titlebar:not(headerbar) button:backdrop.flat:disabled:checked label, .selection-mode.titlebar:not(headerbar) button:backdrop:disabled:active label, .selection-mode.titlebar:not(headerbar) button:backdrop:disabled:checked label,\n            headerbar.selection-mode button:backdrop.flat:disabled:active label,\n            headerbar.selection-mode button:backdrop.flat:disabled:checked label,\n            headerbar.selection-mode button:backdrop:disabled:active label,\n            headerbar.selection-mode button:backdrop:disabled:checked label {\n              color: @insensitive_fg_color; }\n      .selection-mode.titlebar:not(headerbar) button.flat:backdrop, .selection-mode.titlebar:not(headerbar) button.flat:disabled, .selection-mode.titlebar:not(headerbar) button.flat:backdrop:disabled,\n      headerbar.selection-mode button.flat:backdrop,\n      headerbar.selection-mode button.flat:disabled,\n      headerbar.selection-mode button.flat:backdrop:disabled {\n        border-color: transparent;\n        background-color: transparent;\n        background-image: none;\n        box-shadow: inset 0 1px transparent;\n        text-shadow: none;\n        -gtk-icon-shadow: none; }\n      .selection-mode.titlebar:not(headerbar) button:disabled,\n      headerbar.selection-mode button:disabled {\n        border-color: shade(@theme_selected_bg_color, 0.6);\n        background-color: @theme_selected_bg_color;\n        background-image: none;\n        text-shadow: none;\n        -gtk-icon-shadow: none;\n        box-shadow: inset 0 1px transparent; }\n        .selection-mode.titlebar:not(headerbar) button:disabled label, .selection-mode.titlebar:not(headerbar) button:disabled,\n        headerbar.selection-mode button:disabled label,\n        headerbar.selection-mode button:disabled {\n          color: @insensitive_fg_color; }\n        .selection-mode.titlebar:not(headerbar) button:disabled:active, .selection-mode.titlebar:not(headerbar) button:disabled:checked,\n        headerbar.selection-mode button:disabled:active,\n        headerbar.selection-mode button:disabled:checked {\n          border-color: shade(@theme_selected_bg_color, 0.6);\n          background-color: shade(@theme_selected_bg_color, 0.6);\n          background-image: none;\n          box-shadow: inset 0 1px transparent; }\n          .selection-mode.titlebar:not(headerbar) button:disabled:active label, .selection-mode.titlebar:not(headerbar) button:disabled:active, .selection-mode.titlebar:not(headerbar) button:disabled:checked label, .selection-mode.titlebar:not(headerbar) button:disabled:checked,\n          headerbar.selection-mode button:disabled:active label,\n          headerbar.selection-mode button:disabled:active,\n          headerbar.selection-mode button:disabled:checked label,\n          headerbar.selection-mode button:disabled:checked {\n            color: @insensitive_fg_color; }\n      .selection-mode.titlebar:not(headerbar) button.suggested-action,\n      headerbar.selection-mode button.suggested-action {\n        color: @theme_fg_color;\n        outline-color: @outline_color;\n        border-color: @borders;\n        border-bottom-color: @borders;\n        background-image: linear-gradient(to bottom, @theme_bg_color, @theme_bg_color);\n        text-shadow: 0 0 @txt_shadow;\n        -gtk-icon-shadow: 0 0 @txt_shadow;\n        box-shadow: inset 0 0 rgba(255, 255, 255, 0.8);\n        border-color: shade(@theme_selected_bg_color, 0.6); }\n        .selection-mode.titlebar:not(headerbar) button.suggested-action:hover,\n        headerbar.selection-mode button.suggested-action:hover {\n          color: @theme_fg_color;\n          outline-color: @outline_color;\n          border-color: @borders;\n          border-bottom-color: @borders;\n          background-image: linear-gradient(to bottom, @theme_selected_bg_color, @theme_selected_bg_color);\n          text-shadow: 0 1px @txt_shadow;\n          -gtk-icon-shadow: 0 0 @txt_shadow;\n          box-shadow: inset 0 0 @theme_bg_color;\n          border-color: shade(@theme_selected_bg_color, 0.6); }\n        .selection-mode.titlebar:not(headerbar) button.suggested-action:active,\n        headerbar.selection-mode button.suggested-action:active {\n          color: @theme_fg_color;\n          outline-color: @outline_color;\n          border-color: @borders;\n          background-image: none;\n          background-color: shade(@theme_bg_color, 0.9);\n          box-shadow: inset 0 0 transparent;\n          text-shadow: none;\n          -gtk-icon-shadow: none;\n          border-color: shade(@theme_selected_bg_color, 0.6); }\n        .selection-mode.titlebar:not(headerbar) button.suggested-action:disabled,\n        headerbar.selection-mode button.suggested-action:disabled {\n          border-color: @borders;\n          background-color: @insensitive_bg_color;\n          background-image: none;\n          text-shadow: none;\n          -gtk-icon-shadow: none;\n          box-shadow: inset 0 0 transparent;\n          border-color: shade(@theme_selected_bg_color, 0.6); }\n          .selection-mode.titlebar:not(headerbar) button.suggested-action:disabled label, .selection-mode.titlebar:not(headerbar) button.suggested-action:disabled,\n          headerbar.selection-mode button.suggested-action:disabled label,\n          headerbar.selection-mode button.suggested-action:disabled {\n            color: @insensitive_fg_color; }\n        .selection-mode.titlebar:not(headerbar) button.suggested-action:backdrop,\n        headerbar.selection-mode button.suggested-action:backdrop {\n          border-color: shade(@borders, 0.95);\n          background-color: transparent;\n          background-image: image(@theme_bg_color);\n          text-shadow: none;\n          -gtk-icon-shadow: none;\n          box-shadow: inset 0 0 transparent;\n          border-color: shade(@theme_selected_bg_color, 0.6); }\n          .selection-mode.titlebar:not(headerbar) button.suggested-action:backdrop label, .selection-mode.titlebar:not(headerbar) button.suggested-action:backdrop,\n          headerbar.selection-mode button.suggested-action:backdrop label,\n          headerbar.selection-mode button.suggested-action:backdrop {\n            color: @insensitive_fg_color; }\n        .selection-mode.titlebar:not(headerbar) button.suggested-action:backdrop:disabled,\n        headerbar.selection-mode button.suggested-action:backdrop:disabled {\n          border-color: shade(@borders, 0.95);\n          background-color: @insensitive_bg_color;\n          background-image: none;\n          text-shadow: none;\n          -gtk-icon-shadow: none;\n          box-shadow: inset 0 1px transparent;\n          border-color: shade(@theme_selected_bg_color, 0.6); }\n          .selection-mode.titlebar:not(headerbar) button.suggested-action:backdrop:disabled label, .selection-mode.titlebar:not(headerbar) button.suggested-action:backdrop:disabled,\n          headerbar.selection-mode button.suggested-action:backdrop:disabled label,\n          headerbar.selection-mode button.suggested-action:backdrop:disabled {\n            color: shade(@theme_unfocused_fg_color, 1.1); }\n    .selection-mode.titlebar:not(headerbar) .selection-menu:backdrop, .selection-mode.titlebar:not(headerbar) .selection-menu,\n    headerbar.selection-mode .selection-menu:backdrop,\n    headerbar.selection-mode .selection-menu {\n      border-color: shade(@theme_selected_bg_color, 1.0);\n      background-color: shade(@theme_selected_bg_color, 1.0);\n      background-image: none;\n      box-shadow: none;\n      padding-left: 10px;\n      padding-right: 10px; }\n      .selection-mode.titlebar:not(headerbar) .selection-menu:backdrop GtkArrow, .selection-mode.titlebar:not(headerbar) .selection-menu GtkArrow,\n      headerbar.selection-mode .selection-menu:backdrop GtkArrow,\n      headerbar.selection-mode .selection-menu GtkArrow {\n        -GtkArrow-arrow-scaling: 1; }\n      .selection-mode.titlebar:not(headerbar) .selection-menu:backdrop .arrow, .selection-mode.titlebar:not(headerbar) .selection-menu .arrow,\n      headerbar.selection-mode .selection-menu:backdrop .arrow,\n      headerbar.selection-mode .selection-menu .arrow {\n        -gtk-icon-source: -gtk-icontheme(\"pan-down-symbolic\");\n        color: rgba(255, 255, 255, 0.5);\n        -gtk-icon-shadow: none; }\n  .tiled .titlebar:backdrop:not(headerbar), .tiled .titlebar:not(headerbar), .maximized .titlebar:backdrop:not(headerbar), .maximized .titlebar:not(headerbar), .tiled\n  headerbar:backdrop, .tiled\n  headerbar, .maximized\n  headerbar:backdrop, .maximized\n  headerbar {\n    border-radius: 0; }\n  .default-decoration.titlebar:not(headerbar),\n  headerbar.default-decoration {\n    min-height: 28px;\n    padding: 4px; }\n    .default-decoration.titlebar:not(headerbar) button.titlebutton,\n    headerbar.default-decoration button.titlebutton {\n      min-height: 26px;\n      min-width: 26px;\n      margin: 0;\n      padding: 0; }\n  .solid-csd .titlebar:backdrop:dir(rtl):not(headerbar), .solid-csd .titlebar:backdrop:dir(ltr):not(headerbar), .solid-csd .titlebar:dir(rtl):not(headerbar), .solid-csd .titlebar:dir(ltr):not(headerbar), .solid-csd\n  headerbar:backdrop:dir(rtl), .solid-csd\n  headerbar:backdrop:dir(ltr), .solid-csd\n  headerbar:dir(rtl), .solid-csd\n  headerbar:dir(ltr) {\n    margin-left: -1px;\n    margin-right: -1px;\n    margin-top: -1px;\n    border-radius: 0;\n    box-shadow: none; }\n\nheaderbar entry,\nheaderbar spinbutton,\nheaderbar separator,\nheaderbar button {\n  margin-top: 6px;\n  margin-bottom: 6px; }\n\n.background:not(.tiled):not(.maximized) .titlebar:backdrop, .background:not(.tiled):not(.maximized) .titlebar {\n  border-top-left-radius: 0;\n  border-top-right-radius: 0; }\n\nwindow:not(.tiled):not(.maximized) separator:first-child + headerbar:backdrop, window:not(.tiled):not(.maximized) separator:first-child + headerbar, window:not(.tiled):not(.maximized) headerbar:first-child:backdrop, window:not(.tiled):not(.maximized) headerbar:first-child {\n  border-top-left-radius: 0; }\nwindow:not(.tiled):not(.maximized) headerbar:last-child:backdrop, window:not(.tiled):not(.maximized) headerbar:last-child {\n  border-top-right-radius: 0; }\n\nwindow.csd > .titlebar:not(headerbar) {\n  padding: 0;\n  background-color: transparent;\n  background-image: none;\n  border-style: none;\n  border-color: transparent;\n  box-shadow: none; }\n.titlebar:not(headerbar) > separator {\n  background-color: @borders; }\n\n/******************\n * Window actions *\n ******************/\n.titlebar .titlebutton.minimize {\n    color: transparent;\n    border-image: none;\n    padding: 6px 12px;\n    box-shadow: none;\n    background-position: center;\n    background-repeat: no-repeat;\n    border: none;\n    background-image: -gtk-scaled(url(\"buttons/minimize-focused-normal.png\"));\n}\n\n.titlebar .titlebutton.minimize:backdrop {\n    background-image: -gtk-scaled(url(\"buttons/minimize-unfocused-normal.png\"));\n    color: transparent;\n}\n\n.titlebar .titlebutton.minimize:hover,\n.titlebar .titlebutton.minimize:active,\n.titlebar .titlebutton.minimize:checked {\n    color: transparent;\n    border-image: none;\n    box-shadow: none;\n    background-position: center;\n    background-repeat: no-repeat;\n    background-color: transparent;\n    background-image: -gtk-scaled(url(\"buttons/minimize-focused-active.png\"));\n}\n\n.titlebar .titlebutton.maximize {\n    color: transparent;\n    border: none;\n    padding: 6px 12px;\n    border-image: none;\n    box-shadow: none;\n    background-position: center;\n    background-repeat: no-repeat;\n    background-image: -gtk-scaled(url(\"buttons/maximize-focused-normal.png\"));\n}\n\n.titlebar .titlebutton.maximize:backdrop {\n    background-image: -gtk-scaled(url(\"buttons/maximize-unfocused-normal.png\"));\n    color: transparent;\n}\n\n\n.titlebar .titlebutton.maximize:hover, \n.titlebar .titlebutton.maximize:active,\n.titlebar .titlebutton.maximize:checked {\n    color: transparent;\n    border-image: none;\n    box-shadow: none;\n    background-position: center;\n    background-repeat: no-repeat;\n    background-color: transparent;\n    background-image: -gtk-scaled(url(\"buttons/maximize-focused-active.png\"));\n}\n\n.titlebar .titlebutton.close {\n    color: transparent;\n    border: none;\n    padding: 6px 12px;\n    border-image: none;\n    box-shadow: none;\n    background-position: center;\n    background-repeat: no-repeat;\n    background-image: -gtk-scaled(url(\"buttons/close-focused-normal.png\"));\n}\n\n.titlebar .titlebutton.close:backdrop {\n    background-image: -gtk-scaled(url(\"buttons/close-unfocused-normal.png\"));\n    color: transparent;\n}\n\n\n.titlebar .titlebutton.close:hover,\n.titlebar .titlebutton.close:active,\n.titlebar .titlebutton.close:checked  {\n    color: transparent;\n    border-image: none;\n    box-shadow: none;\n    background-position: center;\n    background-repeat: no-repeat;\n    background-color: transparent;\n    background-image: -gtk-scaled(url(\"buttons/close-focused-active.png\"));\n}\n\n\n\n/************\n * Pathbars *\n ************/\n.path-bar button.text-button, .path-bar button.image-button, .path-bar button {\n  padding-left: 4px;\n  padding-right: 4px; }\n.path-bar button.text-button.image-button label {\n  padding-left: 0;\n  padding-right: 0; }\n.path-bar button.text-button.image-button label:last-child, .path-bar button label:last-child {\n  padding-right: 8px; }\n.path-bar button.text-button.image-button label:first-child, .path-bar button label:first-child {\n  padding-left: 8px; }\n.path-bar button image {\n  padding-left: 4px;\n  padding-right: 4px; }\n.path-bar button.slider-button {\n  padding-left: 0;\n  padding-right: 0; }\n\n/**************\n * Tree Views *\n **************/\ntreeview.view {\n  -GtkTreeView-grid-line-width: 1;\n  -GtkTreeView-grid-line-pattern: '';\n  -GtkTreeView-tree-line-width: 1;\n  -GtkTreeView-tree-line-pattern: '';\n  -GtkTreeView-expander-size: 16;\n  border-left-color: #979a9b;\n  border-top-color: @theme_bg_color; }\n  treeview.view:selected:focus, treeview.view:selected {\n    border-radius: 0; }\n  treeview.view:selected:backdrop, treeview.view:selected {\n    border-left-color: @theme_selected_bg_color;\n    border-top-color: @theme_selected_bg_color; }\n  treeview.view:disabled {\n    color: @insensitive_fg_color; }\n    treeview.view:disabled:selected {\n      color: #92bce8; }\n      treeview.view:disabled:selected:backdrop {\n        color: #7fb0e4; }\n    treeview.view:disabled:backdrop {\n      color: shade(@theme_unfocused_fg_color, 1.1); }\n  treeview.view.separator {\n    min-height: 2px;\n    color: @osd_fg_color; }\n    treeview.view.separator:backdrop {\n      color: rgba(232, 232, 231, 0.1); }\n  treeview.view:backdrop {\n    border-left-color: #babbbb;\n    border-top: @theme_bg_color; }\n  treeview.view:drop(active) {\n    border-style: solid none;\n    border-width: 1px;\n    border-color: shade(@theme_selected_bg_color, 0.6); }\n    treeview.view:drop(active).after {\n      border-top-style: none; }\n    treeview.view:drop(active).before {\n      border-bottom-style: none; }\n  treeview.view.expander {\n    -gtk-icon-source: -gtk-icontheme(\"pan-end-symbolic\");\n    color: #6d7172; }\n    treeview.view.expander:dir(rtl) {\n      -gtk-icon-source: -gtk-icontheme(\"pan-end-symbolic-rtl\"); }\n    treeview.view.expander:hover {\n      color: @theme_fg_color; }\n    treeview.view.expander:selected {\n      color: #c9def4; }\n      treeview.view.expander:selected:hover {\n        color: @theme_selected_fg_color; }\n      treeview.view.expander:selected:backdrop {\n        color: #c7dcf2; }\n    treeview.view.expander:checked {\n      -gtk-icon-source: -gtk-icontheme(\"pan-down-symbolic\"); }\n    treeview.view.expander:backdrop {\n      color: #adafb0; }\n  treeview.view.progressbar {\n    color: @theme_selected_fg_color;\n    border: 1px solid shade(@theme_selected_bg_color, 0.6);\n    border-radius: 0;\n    background-color: @progressbar_color;\n    background-image: linear-gradient(to bottom, @progressbar_color, @progressbar_color);\n    box-shadow: inset 0 1px rgba(255, 255, 255, 0.3), 0 1px rgba(0, 0, 0, 0.2); }\n    treeview.view.progressbar:selected:focus, treeview.view.progressbar:selected {\n      border-radius: 0;\n      color: @theme_selected_bg_color;\n      box-shadow: none;\n      background-image: linear-gradient(to bottom, #ffffff, #e6e6e6); }\n      treeview.view.progressbar:selected:focus:backdrop, treeview.view.progressbar:selected:backdrop {\n        color: @theme_selected_bg_color;\n        border-color: shade(@theme_selected_bg_color, 0.6);\n        background-color: @theme_unfocused_bg_color; }\n    treeview.view.progressbar:backdrop {\n      color: @theme_unfocused_bg_color;\n      background-image: none;\n      box-shadow: none; }\n  treeview.view.trough {\n    background-color: rgba(46, 52, 54, 0.1);\n    border-radius: 0; }\n    treeview.view.trough:selected:focus, treeview.view.trough:selected {\n      background-color: rgba(255, 255, 255, 0.3);\n      border-radius: 0;\n      border-width: 1px 0;\n      border-style: solid;\n      border-color: @theme_selected_bg_color; }\n  treeview.view header button {\n    color: #979a9b;\n    background-color: @theme_bg_color;\n    font-weight: bold;\n    text-shadow: none;\n    box-shadow: none; }\n    treeview.view header button:hover {\n      color: #636769;\n      box-shadow: none;\n      transition: none; }\n    treeview.view header button:active {\n      color: @theme_fg_color;\n      transition: none; }\n  treeview.view header button:last-child:backdrop, treeview.view header button:last-child {\n    border-right-style: none; }\n  treeview.view button.dnd:active, treeview.view button.dnd:selected, treeview.view button.dnd:hover, treeview.view button.dnd,\n  treeview.view header.button.dnd:active,\n  treeview.view header.button.dnd:selected,\n  treeview.view header.button.dnd:hover,\n  treeview.view header.button.dnd {\n    padding: 0 6px;\n    color: @theme_selected_fg_color;\n    background-image: none;\n    background-color: @theme_selected_bg_color;\n    border-style: none;\n    border-radius: 0;\n    box-shadow: inset 0 0 0 1px #ffffff;\n    text-shadow: none;\n    transition: none; }\n\ntreeview.view header button, treeview.view header button:hover, treeview.view header button:active {\n  padding: 0 6px;\n  background-image: none;\n  border-style: none solid solid none;\n  border-color: @theme_bg_color;\n  border-radius: 0;\n  text-shadow: none; }\n  treeview.view header button:disabled {\n    border-color: @theme_bg_color;\n    background-image: none; }\n  treeview.view header button:backdrop {\n    color: #babbbb;\n    border-color: @theme_bg_color;\n    border-style: none solid solid none;\n    background-image: none;\n    background-color: @theme_unfocused_bg_color; }\n    treeview.view header button:backdrop:disabled {\n      border-color: @theme_bg_color;\n      background-image: none; }\n\n/*********\n * Menus *\n *********/\nmenubar,\n.menubar {\n  -GtkWidget-window-dragging: true;\n  padding: 0px;\n  box-shadow: inset 0 -1px rgba(0, 0, 0, 0.1); }\n  menubar:backdrop,\n  .menubar:backdrop {\n    background-color: @theme_bg_color; }\n  menubar > menuitem,\n  .menubar > menuitem {\n    min-height: 16px;\n    padding: 4px 8px; }\n    menubar > menuitem:hover,\n    .menubar > menuitem:hover {\n      background-image: none;\n      background-color: @theme_selected_bg_color;\n      color: @borders; }\n    menubar > menuitem:disabled,\n    .menubar > menuitem:disabled {\n      color: @insensitive_fg_color;\n      box-shadow: none; }\n\nmenu,\n.menu {\n  margin: 4px;\n  padding: 2px 0px;\n  background-color: @theme_bg_color;\n  border: 1px solid @borders; }\n  .csd menu, .csd\n  .menu {\n    border: none; }\n  menu:backdrop,\n  .menu:backdrop {\n    background-color: @theme_unfocused_bg_color; }\n  menu menuitem,\n  .menu menuitem {\n    min-height: 16px;\n    min-width: 40px;\n    padding: 4px 6px;\n    text-shadow: none; }\n    menu menuitem:hover,\n    .menu menuitem:hover {\n      color: @theme_selected_fg_color;\n      background-color: @theme_selected_bg_color; }\n    menu menuitem:disabled,\n    .menu menuitem:disabled {\n      color: @insensitive_fg_color; }\n      menu menuitem:disabled:backdrop,\n      .menu menuitem:disabled:backdrop {\n        color: shade(@theme_unfocused_fg_color, 1.1); }\n    menu menuitem:backdrop, menu menuitem:backdrop:hover,\n    .menu menuitem:backdrop,\n    .menu menuitem:backdrop:hover {\n      color: @insensitive_fg_color;\n      background-color: transparent; }\n    menu menuitem arrow,\n    .menu menuitem arrow {\n      min-height: 16px;\n      min-width: 16px; }\n      menu menuitem arrow:dir(ltr),\n      .menu menuitem arrow:dir(ltr) {\n        -gtk-icon-source: -gtk-icontheme(\"pan-end-symbolic\");\n        margin-left: 10px; }\n      menu menuitem arrow:dir(rtl),\n      .menu menuitem arrow:dir(rtl) {\n        -gtk-icon-source: -gtk-icontheme(\"pan-end-symbolic-rtl\");\n        margin-right: 10px; }\n  menu > arrow,\n  .menu > arrow {\n    border-color: transparent;\n    background-color: transparent;\n    background-image: none;\n    box-shadow: inset 0 1px transparent;\n    text-shadow: none;\n    -gtk-icon-shadow: none;\n    min-height: 16px;\n    min-width: 16px;\n    padding: 4px;\n    background-color: @theme_bg_color;\n    border-radius: 0; }\n    menu > arrow.top,\n    .menu > arrow.top {\n      margin-top: -6px;\n      border-bottom: 1px solid #eaebeb;\n      -gtk-icon-source: -gtk-icontheme(\"pan-up-symbolic\"); }\n    menu > arrow.bottom,\n    .menu > arrow.bottom {\n      margin-bottom: -6px;\n      border-top: 1px solid #eaebeb;\n      -gtk-icon-source: -gtk-icontheme(\"pan-down-symbolic\"); }\n    menu > arrow:hover,\n    .menu > arrow:hover {\n      background-color: #eaebeb; }\n    menu > arrow:backdrop,\n    .menu > arrow:backdrop {\n      background-color: @theme_unfocused_bg_color; }\n    menu > arrow:disabled,\n    .menu > arrow:disabled {\n      color: transparent;\n      background-color: transparent;\n      border-color: transparent; }\n\nmenuitem accelerator {\n  color: alpha(currentColor,0.55); }\nmenuitem check,\nmenuitem radio {\n  min-height: 16px;\n  min-width: 16px; }\n  menuitem check:dir(ltr),\n  menuitem radio:dir(ltr) {\n    margin-right: 7px; }\n  menuitem check:dir(rtl),\n  menuitem radio:dir(rtl) {\n    margin-left: 7px; }\n\n/***************\n * Popovers   *\n ***************/\npopover.background {\n  padding: 2px;\n  border-radius: 0;\n  background-color: @theme_bg_color;\n  box-shadow: 0 1px 2px @borders; }\n  .csd popover.background, popover.background {\n    border: 1px solid @borders; }\n  popover.background:backdrop {\n    background-color: @theme_bg_color;\n    box-shadow: none; }\n  popover.background > list,\n  popover.background > .view,\n  popover.background > iconview,\n  popover.background > toolbar {\n    border-style: none;\n    background-color: transparent; }\n  .csd popover.background.touch-selection, .csd popover.background.magnifier, popover.background.touch-selection, popover.background.magnifier {\n    border: 1px solid @osd_txt_shadow; }\n  popover.background separator {\n    margin: 3px; }\n  popover.background list separator {\n    margin: 0px; }\n\n/*************\n * Notebooks *\n *************/\nnotebook > header {\n  padding: 1px;\n  border-color: @borders;\n  border-width: 1px;\n  background-color: transparent; }\n  notebook > header:backdrop {\n    border-color: shade(@borders, 0.95);\n    background-color: transparent; }\n  notebook > header tabs {\n    margin: -1px; \n    background-color: shade(@theme_bg_color, 0.95);}\n  notebook > header.top {\n    border-bottom-style: solid; }\n    notebook > header.top > tabs {\n      margin-bottom: -2px; }\n      notebook > header.top > tabs > tab:hover {\n        background-color: shade(@theme_bg_color, 0.97); }\n      notebook > header.top > tabs > tab:backdrop {\n        box-shadow: none; }\n      notebook > header.top > tabs > tab:checked {\n        background-color: @theme_selected_bg_color; }\n  notebook > header.bottom {\n    border-top-style: solid; }\n    notebook > header.bottom > tabs {\n      margin-top: -2px;\n      background-color: shade(@theme_bg_color, 0.95); }\n      notebook > header.bottom > tabs > tab:hover {\n      background-color: shade(@theme_bg_color, 0.97); }\n      notebook > header.bottom > tabs > tab:backdrop {\n        box-shadow: none; }\n      notebook > header.bottom > tabs > tab:checked {\n        background-color: @theme_selected_bg_color; }\n  notebook > header.left {\n    border-right-style: solid; }\n    notebook > header.left > tabs {\n      margin-right: -2px; \n      background-color: shade(@theme_bg_color, 0.95);}\n      notebook > header.left > tabs > tab:hover {\n      background-color: shade(@theme_bg_color, 0.97); }\n      notebook > header.left > tabs > tab:backdrop {\n        box-shadow: none; }\n      notebook > header.left > tabs > tab:checked {\n      background-color: @theme_selected_bg_color; }\n  notebook > header.right {\n    border-left-style: solid; }\n    notebook > header.right > tabs {\n      margin-left: -2px; \n      background-color: shade(@theme_bg_color, 0.95);}\n      notebook > header.right > tabs > tab:hover {\n      background-color: shade(@theme_bg_color, 0.97); }\n      notebook > header.right > tabs > tab:backdrop {\n        box-shadow: none; }\n      notebook > header.right > tabs > tab:checked {\n      background-color: @theme_selected_bg_color; }\n  notebook > header.top > tabs > arrow {\n    border-top-style: none; }\n  notebook > header.bottom > tabs > arrow {\n    border-bottom-style: none; }\n  notebook > header.top > tabs > arrow, notebook > header.bottom > tabs > arrow {\n    margin-left: -5px;\n    margin-right: -5px;\n    padding-left: 4px;\n    padding-right: 4px; }\n    notebook > header.top > tabs > arrow.down, notebook > header.bottom > tabs > arrow.down {\n      -gtk-icon-source: -gtk-icontheme(\"pan-start-symbolic\"); }\n    notebook > header.top > tabs > arrow.up, notebook > header.bottom > tabs > arrow.up {\n      -gtk-icon-source: -gtk-icontheme(\"pan-end-symbolic\"); }\n  notebook > header.left > tabs > arrow {\n    border-left-style: none; }\n  notebook > header.right > tabs > arrow {\n    border-right-style: none; }\n  notebook > header.left > tabs > arrow, notebook > header.right > tabs > arrow {\n    margin-top: -5px;\n    margin-bottom: -5px;\n    padding-top: 4px;\n    padding-bottom: 4px; }\n    notebook > header.left > tabs > arrow.down, notebook > header.right > tabs > arrow.down {\n      -gtk-icon-source: -gtk-icontheme(\"pan-up-symbolic\"); }\n    notebook > header.left > tabs > arrow.up, notebook > header.right > tabs > arrow.up {\n      -gtk-icon-source: -gtk-icontheme(\"pan-down-symbolic\"); }\n  notebook > header > tabs > arrow {\n    min-height: 16px;\n    min-width: 16px;\n    border-radius: 0; }\n    notebook > header > tabs > arrow:hover:not(:active):not(:backdrop) {\n      background-clip: padding-box;\n      background-image: none;\n      background-color: rgba(255, 255, 255, 0.3);\n      border-color: transparent;\n      box-shadow: none; }\n    notebook > header > tabs > arrow:disabled {\n      border-color: transparent;\n      background-color: transparent;\n      background-image: none;\n      box-shadow: inset 0 1px transparent;\n      text-shadow: none;\n      -gtk-icon-shadow: none; }\n  notebook > header tab {\n    min-height: 30px;\n    min-width: 30px;\n    padding: 3px 12px;\n    outline-offset: -5px;\n    color: @insensitive_fg_color;\n    font-weight: bold;\n    border-width: 1px;\n    border-color: transparent; }\n    notebook > header tab:hover {\n      color: @theme_selected_fg_color; }\n      notebook > header tab:hover.reorderable-page {\n        border-color: rgba(182, 182, 179, 0.3);\n        background-color: rgba(232, 232, 231, 0.2); }\n    notebook > header tab:backdrop {\n      color: @theme_unfocused_fg_color; }\n      notebook > header tab:backdrop.reorderable-page {\n        border-color: transparent;\n        background-color: transparent; }\n    notebook > header tab:checked {\n      color: @theme_fg_color; }\n\n/* active notebook tab in gedit */\n      notebook > header tab:checked.reorderable-page {\n        border-color: rgba(182, 182, 179, 0.5);\n        background-color: shade(@theme_selected_bg_color, 0.8); }\n        notebook > header tab:checked.reorderable-page:hover {\n          background-color: @theme_selected_bg_color; }\n    notebook > header tab:backdrop:checked {\n      color: @insensitive_fg_color; }\n      notebook > header tab:backdrop:checked.reorderable-page {\n        border-color: shade(@borders, 0.95);\n        background-color: @theme_bg_color; }\n    notebook > header tab button.flat {\n      padding: 0;\n      margin-top: 4px;\n      margin-bottom: 4px;\n      min-width: 20px;\n      min-height: 20px; }\n      notebook > header tab button.flat:hover {\n        color: currentColor; }\n      notebook > header tab button.flat, notebook > header tab button.flat:backdrop {\n        color: alpha(currentColor,0.3); }\n      notebook > header tab button.flat:last-child {\n        margin-left: 4px;\n        margin-right: -4px; }\n      notebook > header tab button.flat:first-child {\n        margin-left: -4px;\n        margin-right: 4px; }\n  notebook > header.top tabs, notebook > header.bottom tabs {\n    padding-left: 4px;\n    padding-right: 4px; }\n    notebook > header.top tabs:not(:only-child), notebook > header.bottom tabs:not(:only-child) {\n      margin-left: 3px;\n      margin-right: 3px; }\n      notebook > header.top tabs:not(:only-child):first-child, notebook > header.bottom tabs:not(:only-child):first-child {\n        margin-left: -1px; }\n      notebook > header.top tabs:not(:only-child):last-child, notebook > header.bottom tabs:not(:only-child):last-child {\n        margin-right: -1px; }\n    notebook > header.top tabs tab, notebook > header.bottom tabs tab {\n      margin-left: 4px;\n      margin-right: 4px; }\n      notebook > header.top tabs tab.reorderable-page, notebook > header.bottom tabs tab.reorderable-page {\n        border-style: none solid; }\n  notebook > header.left tabs, notebook > header.right tabs {\n    padding-top: 4px;\n    padding-bottom: 4px; }\n    notebook > header.left tabs:not(:only-child), notebook > header.right tabs:not(:only-child) {\n      margin-top: 3px;\n      margin-bottom: 3px; }\n      notebook > header.left tabs:not(:only-child):first-child, notebook > header.right tabs:not(:only-child):first-child {\n        margin-top: -1px; }\n      notebook > header.left tabs:not(:only-child):last-child, notebook > header.right tabs:not(:only-child):last-child {\n        margin-bottom: -1px; }\n    notebook > header.left tabs tab, notebook > header.right tabs tab {\n      margin-top: 4px;\n      margin-bottom: 4px; }\n      notebook > header.left tabs tab.reorderable-page, notebook > header.right tabs tab.reorderable-page {\n        border-style: solid none; }\n  notebook > header.top tab {\n    padding-bottom: 4px; }\n  notebook > header.bottom tab {\n    padding-top: 4px; }\nnotebook > stack:not(:only-child) {\n  background-color: @theme_bg_color; }\n  notebook > stack:not(:only-child):backdrop {\n    background-color: @theme_unfocused_bg_color; }\n\nscrollbar {\n    border-width: 0;\n    border-style: solid;\n    padding: 0;\n    border-radius: 0;\n    background-color: shade(@theme_bg_color, 0.9);\n    background-image: none;\n    border-image: none; }\n\nscrollbar button,\nscrollbar button:hover,\nscrollbar button:active:hover {\n    border-width: 0;\n    border-radius: 0;\n    min-height: 12px;\n    min-width: 1px;\n    padding: none;\n    box-shadow: none;\n    background-color: transparent;\n    background-image: none;\n    color: shade(@theme_fg_color, 0.4); }\n\nscrollbar.horizontal button {\n    min-height: 1px;\n    min-width: 12px; }\n\nscrollbar slider {\n    border-width: 0;\n    min-width: 45px;\n    min-height: 14px;\n    border-color: transparent;\n    border-radius: 0;\n    background-color: mix(@theme_bg_color, @theme_fg_color, 0.32); }\n\nscrollbar.vertical slider {\n    min-width: 14px;\n    min-height: 45px; }\n\nscrollbar slider:hover,\nscrollbar.vertical slider:hover {\n    border-color: transparent;\n    background-color: mix(@theme_bg_color, @theme_fg_color, 0.5); }\n\nscrollbar slider:active,\nscrollbar.vertical slider:active {\n    border-color: transparent;\n    background-color: shade(@theme_bg_color, 0.5); }\n\n  scrollbar slider.fine-tune:prelight:active {\n    border-width: 2px;\n    border-color: transparent; }\n\n  scrollbar.vertical button.down {\n    -gtk-icon-source: -gtk-icontheme(\"pan-down-symbolic\"); }\n\n  scrollbar.vertical button.up {\n    -gtk-icon-source: -gtk-icontheme(\"pan-up-symbolic\"); }\n\n  scrollbar.horizontal button.down {\n    -gtk-icon-source: -gtk-icontheme(\"pan-right-symbolic\"); }\n\n  scrollbar.horizontal button.up {\n    -gtk-icon-source: -gtk-icontheme(\"pan-left-symbolic\"); }\n\ntreeview ~ scrollbar.vertical {\n  border-top: 1px solid @borders;\n  margin-top: -1px; }\n\n/**********\n * Switch *\n **********/\nswitch {\n  font-weight: bold;\n  font-size: smaller;\n  outline-offset: -4px;\n  border: 1px solid shade(@borders, 1.3);\n  border-radius: 16px;\n  color: transparent;\n  background-color: shade(@borders, 1.3);\n  text-shadow: 0 0 transparent; }\n  switch:checked {\n    color: transparent;\n    border-color: @theme_selected_bg_color;\n    background-color: @theme_selected_bg_color;\n    text-shadow: 0 0 rgba(24, 68, 114, 0), 0 0 0 transparent; }\n  switch:disabled {\n    color: transparent;\n    border-color: @borders;\n    background-color: @borders;\n    text-shadow: none; }\n  switch:backdrop {\n    color: transparent;\n    border-color: @borders;\n    background-color: @borders;\n    text-shadow: none;\n    transition: 200ms ease-out; }\n    switch:backdrop:checked {\n      color: transparent;\n      border-color: shade(@theme_selected_bg_color, 0.6);\n      background-color: shade(@theme_selected_bg_color, 0.6); }\n    switch:backdrop:disabled {\n      color: transparent;\n      border-color: shade(@borders, 0.95);\n      background-color: shade(@borders, 0.95); }\n  switch slider {\n    margin: -1px;\n    min-width: 13px;\n    min-height: 12px;\n    border: 6px solid;\n    border-radius: 14px;\n    transition: all 200ms cubic-bezier(0.25, 0.46, 0.45, 0.94);\n    color: @theme_fg_color;\n    outline-color: @outline_color;\n    border-color: shade(@borders, 1.3);\n    text-shadow: 0 1px @txt_shadow;\n    -gtk-icon-shadow: 0 1px @txt_shadow;\n    background-image: linear-gradient(to bottom, @theme_bg_color, @theme_bg_color);\n    box-shadow: none; } /*inset 0 1px @theme_bg_color, inset 0 -2px #ededec, inset 0 -1px #cacac8, 0 1px rgba(0, 0, 0, 0.1)*/ \n  switch:hover slider {\n    color: @theme_fg_color;\n    outline-color: @outline_color;\n    border-color: shade(@borders, 1.3);\n    background-image: linear-gradient(to bottom, @theme_bg_color, @theme_bg_color);\n    box-shadow: inset 0 0 @theme_bg_color, inset 0 0 #f4f4f4, inset 0 0 #cfcfcd, 0 1px rgba(0, 0, 0, 0.1); }\n  switch:checked slider {\n    border: 6px solid @theme_selected_bg_color; }\n  switch:disabled slider {\n    border-color: @borders;\n    background-color: @insensitive_bg_color;\n    background-image: none;\n    text-shadow: none;\n    -gtk-icon-shadow: none;\n    box-shadow: inset 0 1px transparent; }\n    switch:disabled slider label, switch:disabled slider {\n      color: @insensitive_fg_color; }\n  switch:backdrop slider {\n    transition: 200ms ease-out;\n    border-color: @borders;\n    background-color: transparent;\n    background-image: image(@theme_bg_color);\n    text-shadow: none;\n    -gtk-icon-shadow: none;\n    box-shadow: inset 0 1px transparent; }\n    switch:backdrop slider label, switch:backdrop slider {\n      color: @insensitive_fg_color; }\n  switch:backdrop:checked slider {\n    border-color: shade(@theme_selected_bg_color, 0.6); }\n  switch:backdrop:disabled slider {\n    border-color: shade(@borders, 0.95);\n    background-color: @insensitive_bg_color;\n    background-image: none;\n    text-shadow: none;\n    -gtk-icon-shadow: none;\n    box-shadow: inset 0 1px transparent; }\n    switch:backdrop:disabled slider label, switch:backdrop:disabled slider {\n      color: shade(@theme_unfocused_fg_color, 1.1); }\n  row:selected switch {\n    box-shadow: none;\n    border-color: shade(@theme_selected_bg_color, 0.6); }\n    row:selected switch:backdrop {\n      border-color: shade(@theme_selected_bg_color, 0.6); }\n    row:selected switch.slider:dir(rtl) {\n      border-left-color: @borders; }\n    row:selected switch.slider:dir(ltr) {\n      border-right-color: @borders; }\n    row:selected switch.slider:checked, row:selected switch.slider {\n      border-color: shade(@theme_selected_bg_color, 0.6); }\n\n/*************************\n * Check and Radio items *\n *************************/\n@keyframes check_radio_hover {\n  from {\n    background-image: -gtk-gradient(radial, center center, 0, center center, 0.001, to(alpha(rgba(38, 50, 56, 0.75), 0.1)), to(transparent)); }\n  to {\n    background-image: -gtk-gradient(radial, center center, 0, center center, 0.5, to(alpha(rgba(38, 50, 56, 0.75), 0.1)), to(transparent)); } }\n@keyframes check_radio_active {\n  from {\n    background-image: -gtk-gradient(radial, center center, 0, center center, 0.001, to(alpha(#00BCD4, 0.1)), to(transparent)); }\n  to {\n    background-image: -gtk-gradient(radial, center center, 0, center center, 0.5, to(alpha(#00BCD4, 0.1)), to(transparent)); } }\n@keyframes check_radio_active_reverse {\n  from {\n    background-image: -gtk-gradient(radial, center center, 0, center center, 0.5, to(alpha(#00BCD4, 0.2)), to(transparent)); }\n  to {\n    background-image: -gtk-gradient(radial, center center, 0, center center, 0.001, to(alpha(#00BCD4, 0)), to(transparent)); } }\n.check, check {\n  -gtk-icon-source: -gtk-scaled(url(\"assets/checkbox-unchecked.png\"), url(\"assets/checkbox-unchecked@2.png\"));\n  -gtk-icon-shadow: none; }\n  .check:backdrop, check:backdrop {\n    opacity: 0.8;\n    transition: 0.2s; }\n\n.check:hover, check:hover {\n  -gtk-icon-source: -gtk-scaled(url(\"assets/checkbox-unchecked-over.png\"), url(\"assets/checkbox-unchecked-over@2.png\"));\n  -gtk-icon-shadow: none; }\n  .check:hover:backdrop, check:hover:backdrop {\n    opacity: 0.8;\n    transition: 0.2s; }\n\n.check:active, check:active {\n  -gtk-icon-source: -gtk-scaled(url(\"assets/checkbox-unchecked-over.png\"), url(\"assets/checkbox-unchecked-over@2.png\"));\n  -gtk-icon-shadow: none; }\n  .check:active:backdrop, check:active:backdrop {\n    opacity: 0.8;\n    transition: 0.2s; }\n\n.check:disabled, check:disabled {\n  -gtk-icon-source: -gtk-scaled(url(\"assets/checkbox-unchecked-insensitive.png\"), url(\"assets/checkbox-unchecked-insensitive@2.png\"));\n  -gtk-icon-shadow: none; }\n  .check:disabled:backdrop, check:disabled:backdrop {\n    opacity: 0.8;\n    transition: 0.2s; }\n\n.check:indeterminate, check:indeterminate {\n  -gtk-icon-source: -gtk-scaled(url(\"assets/checkbox-mixed.png\"), url(\"assets/checkbox-mixed@2.png\"));\n  -gtk-icon-shadow: none; }\n  .check:indeterminate:backdrop, check:indeterminate:backdrop {\n    opacity: 0.8;\n    transition: 0.2s; }\n\n.check:indeterminate:hover, check:indeterminate:hover {\n  -gtk-icon-source: -gtk-scaled(url(\"assets/checkbox-mixed-over.png\"), url(\"assets/checkbox-mixed-over@2.png\"));\n  -gtk-icon-shadow: none; }\n  .check:indeterminate:hover:backdrop, check:indeterminate:hover:backdrop {\n    opacity: 0.8;\n    transition: 0.2s; }\n\n.check:indeterminate:active, check:indeterminate:active {\n  -gtk-icon-source: -gtk-scaled(url(\"assets/checkbox-mixed-over.png\"), url(\"assets/checkbox-mixed-over@2.png\"));\n  -gtk-icon-shadow: none; }\n  .check:indeterminate:active:backdrop, check:indeterminate:active:backdrop {\n    opacity: 0.8;\n    transition: 0.2s; }\n\n.check:indeterminate:disabled, check:indeterminate:disabled {\n  -gtk-icon-source: -gtk-scaled(url(\"assets/checkbox-mixed-insensitive.png\"), url(\"assets/checkbox-mixed-insensitive@2.png\"));\n  -gtk-icon-shadow: none; }\n  .check:indeterminate:disabled:backdrop, check:indeterminate:disabled:backdrop {\n    opacity: 0.8;\n    transition: 0.2s; }\n\n.check:checked, check:checked {\n  -gtk-icon-source: -gtk-scaled(url(\"assets/checkbox-checked.png\"), url(\"assets/checkbox-checked@2.png\"));\n  -gtk-icon-shadow: none; }\n  .check:checked:backdrop, check:checked:backdrop {\n    opacity: 0.8;\n    transition: 0.2s; }\n\n.check:checked:hover, check:checked:hover {\n  -gtk-icon-source: -gtk-scaled(url(\"assets/checkbox-checked-over.png\"), url(\"assets/checkbox-checked-over@2.png\"));\n  -gtk-icon-shadow: none; }\n  .check:checked:hover:backdrop, check:checked:hover:backdrop {\n    opacity: 0.8;\n    transition: 0.2s; }\n\n.check:checked:active, check:checked:active {\n  -gtk-icon-source: -gtk-scaled(url(\"assets/checkbox-checked-over.png\"), url(\"assets/checkbox-checked-over@2.png\"));\n  -gtk-icon-shadow: none; }\n  .check:checked:active:backdrop, check:checked:active:backdrop {\n    opacity: 0.8;\n    transition: 0.2s; }\n\n.check:checked:disabled, check:checked:disabled {\n  -gtk-icon-source: -gtk-scaled(url(\"assets/checkbox-checked-insensitive.png\"), url(\"assets/checkbox-checked-insensitive@2.png\"));\n  -gtk-icon-shadow: none; }\n  .check:checked:disabled:backdrop, check:checked:disabled:backdrop {\n    opacity: 0.8;\n    transition: 0.2s; }\n\nmenu menuitem.check,\nmenu menuitem check {\n  -gtk-icon-source: -gtk-scaled(url(\"assets/checkbox-unchecked.png\"), url(\"assets/checkbox-unchecked@2.png\"));\n  -gtk-icon-shadow: none; }\n  menu menuitem.check:hover,\n  menu menuitem check:hover {\n    -gtk-icon-source: -gtk-scaled(url(\"assets/checkbox-unchecked.png\"), url(\"assets/checkbox-unchecked@2.png\"));\n    animation: none;\n    -gtk-icon-shadow: none;\n    transition: none; }\n  menu menuitem.check:backdrop,\n  menu menuitem check:backdrop {\n    opacity: 0.8;\n    transition: 0.2s; }\n\nmenu menuitem.check:disabled,\nmenu menuitem check:disabled {\n  -gtk-icon-source: -gtk-scaled(url(\"assets/checkbox-insensitive.png\"), url(\"assets/checkbox-insensitive@2.png\"));\n  -gtk-icon-shadow: none; }\n  menu menuitem.check:disabled:hover,\n  menu menuitem check:disabled:hover {\n    -gtk-icon-source: -gtk-scaled(url(\"assets/checkbox-insensitive.png\"), url(\"assets/checkbox-insensitive@2.png\"));\n    animation: none;\n    -gtk-icon-shadow: none;\n    transition: none; }\n  menu menuitem.check:disabled:backdrop,\n  menu menuitem check:disabled:backdrop {\n    opacity: 0.8;\n    transition: 0.2s; }\n\nmenu menuitem.check:indeterminate,\nmenu menuitem check:indeterminate {\n  -gtk-icon-source: -gtk-scaled(url(\"assets/checkbox-mixed.png\"), url(\"assets/checkbox-mixed@2.png\"));\n  -gtk-icon-shadow: none; }\n  menu menuitem.check:indeterminate:hover,\n  menu menuitem check:indeterminate:hover {\n    -gtk-icon-source: -gtk-scaled(url(\"assets/checkbox-mixed.png\"), url(\"assets/checkbox-mixed@2.png\"));\n    animation: none;\n    -gtk-icon-shadow: none;\n    transition: none; }\n  menu menuitem.check:indeterminate:backdrop,\n  menu menuitem check:indeterminate:backdrop {\n    opacity: 0.8;\n    transition: 0.2s; }\n\nmenu menuitem.check:indeterminate:disabled,\nmenu menuitem check:indeterminate:disabled {\n  -gtk-icon-source: -gtk-scaled(url(\"assets/checkbox-mixed-insensitive.png\"), url(\"assets/checkbox-mixed-insensitive@2.png\"));\n  -gtk-icon-shadow: none; }\n  menu menuitem.check:indeterminate:disabled:hover,\n  menu menuitem check:indeterminate:disabled:hover {\n    -gtk-icon-source: -gtk-scaled(url(\"assets/checkbox-mixed-insensitive.png\"), url(\"assets/checkbox-mixed-insensitive@2.png\"));\n    animation: none;\n    -gtk-icon-shadow: none;\n    transition: none; }\n  menu menuitem.check:indeterminate:disabled:backdrop,\n  menu menuitem check:indeterminate:disabled:backdrop {\n    opacity: 0.8;\n    transition: 0.2s; }\n\nmenu menuitem.check:checked,\nmenu menuitem check:checked {\n  -gtk-icon-source: -gtk-scaled(url(\"assets/checkbox-checked.png\"), url(\"assets/checkbox-checked@2.png\"));\n  -gtk-icon-shadow: none; }\n  menu menuitem.check:checked:hover,\n  menu menuitem check:checked:hover {\n    -gtk-icon-source: -gtk-scaled(url(\"assets/checkbox-checked.png\"), url(\"assets/checkbox-checked@2.png\"));\n    animation: none;\n    -gtk-icon-shadow: none;\n    transition: none; }\n  menu menuitem.check:checked:backdrop,\n  menu menuitem check:checked:backdrop {\n    opacity: 0.8;\n    transition: 0.2s; }\n\nmenu menuitem.check:checked:disabled,\nmenu menuitem check:checked:disabled {\n  -gtk-icon-source: -gtk-scaled(url(\"assets/checkbox-checked-insensitive.png\"), url(\"assets/checkbox-checked-insensitive@2.png\"));\n  -gtk-icon-shadow: none; }\n  menu menuitem.check:checked:disabled:hover,\n  menu menuitem check:checked:disabled:hover {\n    -gtk-icon-source: -gtk-scaled(url(\"assets/checkbox-checked-insensitive.png\"), url(\"assets/checkbox-checked-insensitive@2.png\"));\n    animation: none;\n    -gtk-icon-shadow: none;\n    transition: none; }\n  menu menuitem.check:checked:disabled:backdrop,\n  menu menuitem check:checked:disabled:backdrop {\n    opacity: 0.8;\n    transition: 0.2s; }\n\n.radio, radio {\n  -gtk-icon-source: -gtk-scaled(url(\"assets/radio-unselected.png\"), url(\"assets/radio-unselected@2.png\"));\n  -gtk-icon-shadow: none; }\n  .radio:backdrop, radio:backdrop {\n    opacity: 0.8;\n    transition: 0.2s; }\n\n.radio:hover, radio:hover {\n  -gtk-icon-source: -gtk-scaled(url(\"assets/radio-unselected-over.png\"), url(\"assets/radio-unselected-over@2.png\"));\n  -gtk-icon-shadow: none; }\n  .radio:hover:backdrop, radio:hover:backdrop {\n    opacity: 0.8;\n    transition: 0.2s; }\n\n.radio:active, radio:active {\n  -gtk-icon-source: -gtk-scaled(url(\"assets/radio-unselected-over.png\"), url(\"assets/radio-unselected-over@2.png\"));\n  -gtk-icon-shadow: none; }\n  .radio:active:backdrop, radio:active:backdrop {\n    opacity: 0.8;\n    transition: 0.2s; }\n\n.radio:disabled, radio:disabled {\n  -gtk-icon-source: -gtk-scaled(url(\"assets/radio-unselected-insensitive.png\"), url(\"assets/radio-unselected-insensitive@2.png\"));\n  -gtk-icon-shadow: none; }\n  .radio:disabled:backdrop, radio:disabled:backdrop {\n    opacity: 0.8;\n    transition: 0.2s; }\n\n.radio:indeterminate, radio:indeterminate {\n  -gtk-icon-source: -gtk-scaled(url(\"assets/radio-mixed.png\"), url(\"assets/radio-mixed@2.png\"));\n  -gtk-icon-shadow: none; }\n  .radio:indeterminate:backdrop, radio:indeterminate:backdrop {\n    opacity: 0.8;\n    transition: 0.2s; }\n\n.radio:indeterminate:hover, radio:indeterminate:hover {\n  -gtk-icon-source: -gtk-scaled(url(\"assets/radio-mixed-over.png\"), url(\"assets/radio-mixed-over@2.png\"));\n  -gtk-icon-shadow: none; }\n  .radio:indeterminate:hover:backdrop, radio:indeterminate:hover:backdrop {\n    opacity: 0.8;\n    transition: 0.2s; }\n\n.radio:indeterminate:active, radio:indeterminate:active {\n  -gtk-icon-source: -gtk-scaled(url(\"assets/radio-mixed-over.png\"), url(\"assets/radio-mixed-over@2.png\"));\n  -gtk-icon-shadow: none; }\n  .radio:indeterminate:active:backdrop, radio:indeterminate:active:backdrop {\n    opacity: 0.8;\n    transition: 0.2s; }\n\n.radio:indeterminate:disabled, radio:indeterminate:disabled {\n  -gtk-icon-source: -gtk-scaled(url(\"assets/radio-mixed-insensitive.png\"), url(\"assets/radio-mixed-insensitive@2.png\"));\n  -gtk-icon-shadow: none; }\n  .radio:indeterminate:disabled:backdrop, radio:indeterminate:disabled:backdrop {\n    opacity: 0.8;\n    transition: 0.2s; }\n\n.radio:checked, radio:checked {\n  -gtk-icon-source: -gtk-scaled(url(\"assets/radio-selected.png\"), url(\"assets/radio-selected@2.png\"));\n  -gtk-icon-shadow: none; }\n  .radio:checked:backdrop, radio:checked:backdrop {\n    opacity: 0.8;\n    transition: 0.2s; }\n\n.radio:checked:hover, radio:checked:hover {\n  -gtk-icon-source: -gtk-scaled(url(\"assets/radio-selected-over.png\"), url(\"assets/radio-selected-over@2.png\"));\n  -gtk-icon-shadow: none; }\n  .radio:checked:hover:backdrop, radio:checked:hover:backdrop {\n    opacity: 0.8;\n    transition: 0.2s; }\n\n.radio:checked:active, radio:checked:active {\n  -gtk-icon-source: -gtk-scaled(url(\"assets/radio-selected-over.png\"), url(\"assets/radio-selected-over@2.png\"));\n  -gtk-icon-shadow: none; }\n  .radio:checked:active:backdrop, radio:checked:active:backdrop {\n    opacity: 0.8;\n    transition: 0.2s; }\n\n.radio:checked:disabled, radio:checked:disabled {\n  -gtk-icon-source: -gtk-scaled(url(\"assets/radio-selected-insensitive.png\"), url(\"assets/radio-selected-insensitive@2.png\"));\n  -gtk-icon-shadow: none; }\n  .radio:checked:disabled:backdrop, radio:checked:disabled:backdrop {\n    opacity: 0.8;\n    transition: 0.2s; }\n\nmenu menuitem.radio,\nmenu menuitem radio {\n  -gtk-icon-source: -gtk-scaled(url(\"assets/radio-unselected.png\"), url(\"assets/radio-unselected@2.png\"));\n  -gtk-icon-shadow: none; }\n  menu menuitem.radio:hover,\n  menu menuitem radio:hover {\n    -gtk-icon-source: -gtk-scaled(url(\"assets/radio-unselected.png\"), url(\"assets/radio-unselected@2.png\"));\n    animation: none;\n    -gtk-icon-shadow: none;\n    transition: none; }\n  menu menuitem.radio:backdrop,\n  menu menuitem radio:backdrop {\n    opacity: 0.8;\n    transition: 0.2s; }\n\nmenu menuitem.radio:disabled,\nmenu menuitem radio:disabled {\n  -gtk-icon-source: -gtk-scaled(url(\"assets/radio-insensitive.png\"), url(\"assets/radio-insensitive@2.png\"));\n  -gtk-icon-shadow: none; }\n  menu menuitem.radio:disabled:hover,\n  menu menuitem radio:disabled:hover {\n    -gtk-icon-source: -gtk-scaled(url(\"assets/radio-insensitive.png\"), url(\"assets/radio-insensitive@2.png\"));\n    animation: none;\n    -gtk-icon-shadow: none;\n    transition: none; }\n  menu menuitem.radio:disabled:backdrop,\n  menu menuitem radio:disabled:backdrop {\n    opacity: 0.8;\n    transition: 0.2s; }\n\nmenu menuitem.radio:indeterminate,\nmenu menuitem radio:indeterminate {\n  -gtk-icon-source: -gtk-scaled(url(\"assets/radio-mixed.png\"), url(\"assets/radio-mixed@2.png\"));\n  -gtk-icon-shadow: none; }\n  menu menuitem.radio:indeterminate:hover,\n  menu menuitem radio:indeterminate:hover {\n    -gtk-icon-source: -gtk-scaled(url(\"assets/radio-mixed.png\"), url(\"assets/radio-mixed@2.png\"));\n    animation: none;\n    -gtk-icon-shadow: none;\n    transition: none; }\n  menu menuitem.radio:indeterminate:backdrop,\n  menu menuitem radio:indeterminate:backdrop {\n    opacity: 0.8;\n    transition: 0.2s; }\n\nmenu menuitem.radio:indeterminate:disabled,\nmenu menuitem radio:indeterminate:disabled {\n  -gtk-icon-source: -gtk-scaled(url(\"assets/radio-mixed-insensitive.png\"), url(\"assets/radio-mixed-insensitive@2.png\"));\n  -gtk-icon-shadow: none; }\n  menu menuitem.radio:indeterminate:disabled:hover,\n  menu menuitem radio:indeterminate:disabled:hover {\n    -gtk-icon-source: -gtk-scaled(url(\"assets/radio-mixed-insensitive.png\"), url(\"assets/radio-mixed-insensitive@2.png\"));\n    animation: none;\n    -gtk-icon-shadow: none;\n    transition: none; }\n  menu menuitem.radio:indeterminate:disabled:backdrop,\n  menu menuitem radio:indeterminate:disabled:backdrop {\n    opacity: 0.8;\n    transition: 0.2s; }\n\nmenu menuitem.radio:checked,\nmenu menuitem radio:checked {\n  -gtk-icon-source: -gtk-scaled(url(\"assets/radio-selected.png\"), url(\"assets/radio-selected@2.png\"));\n  -gtk-icon-shadow: none; }\n  menu menuitem.radio:checked:hover,\n  menu menuitem radio:checked:hover {\n    -gtk-icon-source: -gtk-scaled(url(\"assets/radio-selected.png\"), url(\"assets/radio-selected@2.png\"));\n    animation: none;\n    -gtk-icon-shadow: none;\n    transition: none; }\n  menu menuitem.radio:checked:backdrop,\n  menu menuitem radio:checked:backdrop {\n    opacity: 0.8;\n    transition: 0.2s; }\n\nmenu menuitem.radio:checked:disabled,\nmenu menuitem radio:checked:disabled {\n  -gtk-icon-source: -gtk-scaled(url(\"assets/radio-selected-insensitive.png\"), url(\"assets/radio-selected-insensitive@2.png\"));\n  -gtk-icon-shadow: none; }\n  menu menuitem.radio:checked:disabled:hover,\n  menu menuitem radio:checked:disabled:hover {\n    -gtk-icon-source: -gtk-scaled(url(\"assets/radio-selected-insensitive.png\"), url(\"assets/radio-selected-insensitive@2.png\"));\n    animation: none;\n    -gtk-icon-shadow: none;\n    transition: none; }\n  menu menuitem.radio:checked:disabled:backdrop,\n  menu menuitem radio:checked:disabled:backdrop {\n    opacity: 0.8;\n    transition: 0.2s; }\n\ntreeview.view check:selected:focus, treeview.view check:selected,\ntreeview.view radio:selected:focus,\ntreeview.view radio:selected {\n  color: @theme_fg_color;\n  border-color: shade(@theme_selected_bg_color, 0.6); }\ntreeview.view check:selected:disabled,\ntreeview.view radio:selected:disabled {\n  color: @insensitive_fg_color; }\n  treeview.view check:selected:disabled:backdrop,\n  treeview.view radio:selected:disabled:backdrop {\n    color: shade(@theme_unfocused_fg_color, 1.1); }\ntreeview.view check:backdrop:selected, treeview.view check:backdrop,\ntreeview.view radio:backdrop:selected,\ntreeview.view radio:backdrop {\n  color: @insensitive_fg_color; }\n\n/************\n * GtkScale *\n ************/\nscale trough, scale fill, progressbar trough {\n  border: 1px solid @borders;\n  border-radius: 0;\n  background-color: #cfcfcd; }\n  scale trough:disabled, scale fill:disabled, progressbar trough:disabled {\n    background-color: @insensitive_bg_color; }\n  scale trough:backdrop, scale fill:backdrop, progressbar trough:backdrop, progressbar:backdrop trough {\n    background-color: #dadad8;\n    border-color: shade(@borders, 0.95);\n    transition: 200ms ease-out; }\n    scale trough:backdrop:disabled, scale fill:backdrop:disabled, progressbar trough:backdrop:disabled, progressbar:backdrop trough:disabled {\n      background-color: @insensitive_bg_color; }\n  row:selected scale trough:disabled, scale row:selected trough:disabled, row:selected scale fill:disabled, scale row:selected fill:disabled, row:selected progressbar trough:disabled, progressbar row:selected trough:disabled, row:selected scale trough, scale row:selected trough, row:selected scale fill, scale row:selected fill, row:selected progressbar trough, progressbar row:selected trough {\n    border-color: shade(@theme_selected_bg_color, 0.6); }\n  .osd scale trough, scale .osd trough, .osd scale fill, scale .osd fill, .osd progressbar trough, progressbar .osd trough {\n    border-color: @osd_borders;\n    background-color: @osd_bg_color;\n    outline-color: rgba(238, 238, 236, 0.2); }\n    .osd scale trough:disabled, scale .osd trough:disabled, .osd scale fill:disabled, scale .osd fill:disabled, .osd progressbar trough:disabled, progressbar .osd trough:disabled {\n      background-color: shade(@osd_bg_color, 0.95); }\n\nprogressbar progress {\n  border: 1px solid @progressbar_color;\n  border-radius: 0;\n  background-color: @progressbar_color; }\n\n/* progressbar color */\n\nscale highlight {\n  border: 1px solid shade(@theme_selected_bg_color, 0.6);\n  border-radius: 0;\n  background-color: shade(@theme_selected_bg_color, 0.6); }\n\n  scale highlight:disabled, progressbar progress:disabled {\n    background-color: transparent;\n    border-color: transparent; }\n  scale highlight:backdrop, progressbar progress:backdrop, progressbar:backdrop progress {\n    border-color: @theme_selected_bg_color; }\n    scale highlight:backdrop:disabled, progressbar progress:backdrop:disabled, progressbar:backdrop progress:disabled {\n      background-color: transparent;\n      border-color: transparent; }\n  row:selected scale highlight:disabled, scale row:selected highlight:disabled, row:selected progressbar progress:disabled, progressbar row:selected progress:disabled, row:selected scale highlight, scale row:selected highlight, row:selected progressbar progress, progressbar row:selected progress {\n    border-color: shade(@theme_selected_bg_color, 0.6); }\n  .osd scale highlight, scale .osd highlight, .osd progressbar progress, progressbar .osd progress {\n    border-color: @osd_borders; }\n    .osd scale highlight:disabled, scale .osd highlight:disabled, .osd progressbar progress:disabled, progressbar .osd progress:disabled {\n      border-color: transparent; }\n\nscale {\n  min-height: 10px;\n  min-width: 10px;\n  padding: 12px; }\n  scale fill,\n  scale highlight {\n    margin: -1px; }\n  scale slider {\n    min-height: 18px;\n    min-width: 18px;\n    margin: -9px; }\n  scale.fine-tune.horizontal {\n    padding-top: 9px;\n    padding-bottom: 9px;\n    min-height: 16px; }\n  scale.fine-tune.vertical {\n    padding-left: 9px;\n    padding-right: 9px;\n    min-width: 16px; }\n  scale.fine-tune slider {\n    margin: -6px; }\n  scale.fine-tune fill,\n  scale.fine-tune highlight,\n  scale.fine-tune trough {\n    border-radius: 0;\n    -gtk-outline-radius: 0; }\n  scale trough {\n    outline-offset: 2px;\n    -gtk-outline-radius: 0; }\n  scale fill:backdrop, scale fill {\n    background-color: @borders; }\n  scale fill:disabled:backdrop, scale fill:disabled {\n    border-color: transparent;\n    background-color: transparent; }\n  .osd scale fill {\n    background-color: rgba(91, 91, 90, 0.775); }\n    .osd scale fill:disabled:backdrop, .osd scale fill:disabled {\n      border-color: transparent;\n      background-color: transparent; }\n\nscale slider,\nscale slider.horizontal {\n    background-image: -gtk-scaled(url(\"assets/slider-horiz.png\"));\n}\n\nscale.vertical slider {\n    background-image: -gtk-scaled(url(\"assets/slider-vert.png\"));\n}\n\nscale.vertical slider:hover, \nscale.vertical slider:active {\n    background-image: -gtk-scaled(url(\"assets/slider-vert-hover.png\")); \n}\n\nscale.vertical slider:backdrop,\nscale.vertical slider:disabled,\nscale.vertical slider:backdrop:disabled {\n    background-image: -gtk-scaled(url(\"assets/slider-vert-insensitive.png\")); \n}\n\n/* scale sliders */\n\n  scale slider {\n\tbackground-image: url(\"assets/slider-horiz.png\")); \n\tbackground-position: center;\n        background-repeat: no-repeat; }\n    scale slider:hover, scale slider:active {\n\tbackground-image: url(\"assets/slider-horiz-hover.png\")); \n\tbackground-position: center;\n        background-repeat: no-repeat; }\n    scale slider:disabled {\n\tbackground-image: url(\"assets/slider-horiz-insensitive.png\")); \n\tbackground-position: center;\n        background-repeat: no-repeat; }\n      scale slider:disabled label, scale slider:disabled {\n        color: @insensitive_fg_color; }\n    scale slider:backdrop {\n\tbackground-image: url(\"assets/slider-horiz-insensitive.png\"));\n\tbackground-position: center;\n        background-repeat: no-repeat; }\n      scale slider:backdrop:disabled {\n        border-color: shade(@borders, 0.95);\n\tbackground-image: url(\"assets/slider-horiz-insensitive.png\"));\n        text-shadow: none;\n        -gtk-icon-shadow: none;\n        box-shadow: inset 0 1px transparent; }\n        scale slider:backdrop:disabled label, scale slider:backdrop:disabled {\n          color: shade(@theme_unfocused_fg_color, 1.1); }\n    row:selected scale slider:disabled, row:selected scale slider {\n      border-color: shade(@theme_selected_bg_color, 0.6); }\n    .osd scale slider {\n      color: @theme_unfocused_fg_color;\n      border-color: @osd_borders;\n      background-color: transparent;\n      background-image: image(@osd_bg_color);\n      background-clip: padding-box;\n      box-shadow: inset 0 1px @osd_txt_shadow;\n      text-shadow: 0 1px @osd_txt_shadow;\n      -gtk-icon-shadow: 0 1px @osd_txt_shadow;\n      outline-color: @osd_outline;\n      border-color: @osd_borders;\n      border-radius: 100%;\n      background-color: #1c1f20; }\n      .osd scale slider:hover {\n        color: @osd_fg_color;\n        border-color: @osd_borders;\n        background-color: transparent;\n        background-image: image(shade(@osd_bg_color, 1.05));\n        background-clip: padding-box;\n        box-shadow: inset 0 1px @osd_txt_shadow;\n        text-shadow: 0 1px @osd_txt_shadow;\n        -gtk-icon-shadow: 0 1px @osd_txt_shadow;\n        outline-color: @osd_outline;\n        background-color: #1c1f20; }\n      .osd scale slider:active {\n        color: @osd_fg_color;\n        border-color: @osd_borders;\n        background-color: transparent;\n        background-image: image(@osd_borders);\n        background-clip: padding-box;\n        box-shadow: none;\n        text-shadow: none;\n        -gtk-icon-shadow: none;\n        outline-color: @osd_outline;\n        background-color: #1c1f20; }\n      .osd scale slider:disabled {\n        color: shade(@osd_fg_color, 0.85);\n        border-color: @osd_borders;\n        background-color: transparent;\n        background-image: image(shade(@osd_bg_color, 0.95));\n        background-clip: padding-box;\n        box-shadow: none;\n        text-shadow: none;\n        -gtk-icon-shadow: none;\n        background-color: #1c1f20; }\n      .osd scale slider:backdrop {\n        color: @theme_unfocused_fg_color;\n        border-color: @osd_borders;\n        background-color: transparent;\n        background-image: image(@osd_bg_color);\n        background-clip: padding-box;\n        box-shadow: none;\n        text-shadow: none;\n        -gtk-icon-shadow: none;\n        background-color: #1c1f20; }\n        .osd scale slider:backdrop:disabled {\n          background-color: #1c1f20; }\n  scale value {\n    color: alpha(currentColor,0.55); }\n  scale marks {\n    color: alpha(currentColor,0.55); }\n    scale marks.top {\n      margin-bottom: 6px;\n      margin-top: -12px; }\n    scale marks.bottom {\n      margin-top: 6px;\n      margin-bottom: -12px; }\n    scale marks.top {\n      margin-right: 6px;\n      margin-left: -12px; }\n    scale marks.bottom {\n      margin-left: 6px;\n      margin-right: -12px; }\n  scale.fine-tune marks.top {\n    margin-bottom: 6px;\n    margin-top: -9px; }\n  scale.fine-tune marks.bottom {\n    margin-top: 6px;\n    margin-bottom: -9px; }\n  scale.fine-tune marks.top {\n    margin-right: 6px;\n    margin-left: -9px; }\n  scale.fine-tune marks.bottom {\n    margin-left: 6px;\n    margin-right: -9px; }\n  scale.horizontal indicator {\n    min-height: 6px;\n    min-width: 1px; }\n  scale.horizontal.fine-tune indicator {\n    min-height: 3px; }\n  scale.vertical indicator {\n    min-height: 1px;\n    min-width: 6px; }\n  scale.vertical.fine-tune indicator {\n    min-width: 3px; }\n  scale.color.horizontal slider:hover, scale.color.horizontal slider:backdrop, scale.color.horizontal slider:disabled, scale.color.horizontal slider:backdrop:disabled, scale.color.horizontal slider,\n  scale.horizontal contents:last-child:not(:only-child) > trough > slider {\n    margin: -10px;\n    border-style: none;\n    border-radius: 0;\n    background-color: transparent;\n    background-image: -gtk-scaled(url(\"assets/slider-horiz-top.png\"));\n    min-height: 19px;\n    min-width: 11px;\n    margin-top: -14px;\n    background-position: top;\n    background-repeat: no-repeat;\n    box-shadow: none; }\n  scale.color.fine-tune.horizontal slider, scale.horizontal.fine-tune contents:last-child:not(:only-child) > trough > slider {\n    margin: -7px;\n    margin-top: -11px; }\n  scale.color.horizontal slider:hover, scale.color.horizontal slider:hover:backdrop:disabled,\n  scale.horizontal contents:last-child:not(:only-child) > trough > slider:hover {\n    margin: -10px;\n    border-style: none;\n    border-radius: 0;\n    background-color: transparent;\n    background-image: -gtk-scaled(url(\"assets/slider-horiz-top-hover.png\"));\n    min-height: 19px;\n    min-width: 11px;\n    margin-top: -14px;\n    background-position: top;\n    background-repeat: no-repeat;\n    box-shadow: none; }\n  scale.color.fine-tune.horizontal slider, scale.horizontal.fine-tune contents:last-child:not(:only-child) > trough > slider {\n    margin: -7px;\n    margin-top: -11px; }\n  scale.color.horizontal slider:active:backdrop:disabled, scale.color.horizontal slider:active,\n  scale.horizontal contents:last-child:not(:only-child) > trough > slider:active {\n    margin: -10px;\n    border-style: none;\n    border-radius: 0;\n    background-color: transparent;\n    background-image: -gtk-scaled(url(\"assets/slider-horiz-top-hover.png\"));\n    min-height: 19px;\n    min-width: 11px;\n    margin-top: -14px;\n    background-position: top;\n    background-repeat: no-repeat;\n    box-shadow: none; }\n  scale.color.fine-tune.horizontal slider, scale.horizontal.fine-tune contents:last-child:not(:only-child) > trough > slider {\n    margin: -7px;\n    margin-top: -11px; }\n  scale.color.horizontal slider:disabled,\n  scale.horizontal contents:last-child:not(:only-child) > trough > slider:disabled {\n    margin: -10px;\n    border-style: none;\n    border-radius: 0;\n    background-color: transparent;\n    background-image: -gtk-scaled(url(\"assets/slider-horiz-top-insensitive.png\"));\n    min-height: 19px;\n    min-width: 11px;\n    margin-top: -14px;\n    background-position: top;\n    background-repeat: no-repeat;\n    box-shadow: none; }\n  scale.color.fine-tune.horizontal slider, scale.horizontal.fine-tune contents:last-child:not(:only-child) > trough > slider {\n    margin: -7px;\n    margin-top: -11px; }\n  scale.color.horizontal slider:backdrop,\n  scale.horizontal contents:last-child:not(:only-child) > trough > slider:backdrop {\n    margin: -10px;\n    border-style: none;\n    border-radius: 0;\n    background-color: transparent;\n    background-image: -gtk-scaled(url(\"assets/slider-horiz-top-insensitive.png\"));\n    min-height: 19px;\n    min-width: 11px;\n    margin-top: -14px;\n    background-position: top;\n    background-repeat: no-repeat;\n    box-shadow: none; }\n  scale.color.fine-tune.horizontal slider, scale.horizontal.fine-tune contents:last-child:not(:only-child) > trough > slider {\n    margin: -7px;\n    margin-top: -11px; }\n  scale.color.horizontal slider:backdrop:disabled,\n  scale.horizontal contents:last-child:not(:only-child) > trough > slider:backdrop:disabled {\n    margin: -10px;\n    border-style: none;\n    border-radius: 0;\n    background-color: transparent;\n    background-image: -gtk-scaled(url(\"assets/slider-horiz-top-insensitive.png\"));\n    min-height: 19px;\n    min-width: 11px;\n    margin-top: -14px;\n    background-position: top;\n    background-repeat: no-repeat;\n    box-shadow: none; }\n  scale.color.fine-tune.horizontal slider, scale.horizontal.fine-tune contents:last-child:not(:only-child) > trough > slider {\n    margin: -7px;\n    margin-top: -11px; }\n  scale.horizontal contents:first-child:not(:only-child) > trough > slider {\n    margin: -10px;\n    border-style: none;\n    border-radius: 0;\n    background-color: transparent;\n    background-image: -gtk-scaled(url(\"assets/slider-horiz.png\"));\n    min-height: 19px;\n    min-width: 11px;\n    margin-bottom: -14px;\n    background-position: bottom;\n    background-repeat: no-repeat;\n    box-shadow: none; }\n  scale.horizontal.fine-tune contents:first-child:not(:only-child) > trough > slider {\n    margin: -7px;\n    margin-bottom: -11px; }\n  scale.horizontal contents:first-child:not(:only-child) > trough > slider:hover {\n    margin: -10px;\n    border-style: none;\n    border-radius: 0;\n    background-color: transparent;\n    background-image: -gtk-scaled(url(\"assets/slider-horiz-hover.png\"));\n    min-height: 19px;\n    min-width: 11px;\n    margin-bottom: -14px;\n    background-position: bottom;\n    background-repeat: no-repeat;\n    box-shadow: none; }\n  scale.horizontal.fine-tune contents:first-child:not(:only-child) > trough > slider {\n    margin: -7px;\n    margin-bottom: -11px; }\n  scale.horizontal contents:first-child:not(:only-child) > trough > slider:active {\n    margin: -10px;\n    border-style: none;\n    border-radius: 0;\n    background-color: transparent;\n    background-image: -gtk-scaled(url(\"assets/slider-horiz-hover.png\"));\n    min-height: 19px;\n    min-width: 11px;\n    margin-bottom: -14px;\n    background-position: bottom;\n    background-repeat: no-repeat;\n    box-shadow: none; }\n  scale.horizontal.fine-tune contents:first-child:not(:only-child) > trough > slider {\n    margin: -7px;\n    margin-bottom: -11px; }\n  scale.horizontal contents:first-child:not(:only-child) > trough > slider:disabled {\n    margin: -10px;\n    border-style: none;\n    border-radius: 0;\n    background-color: transparent;\n    background-image: -gtk-scaled(url(\"assets/slider-horiz-insensitive.png\"));\n    min-height: 19px;\n    min-width: 11px;\n    margin-bottom: -14px;\n    background-position: bottom;\n    background-repeat: no-repeat;\n    box-shadow: none; }\n  scale.horizontal.fine-tune contents:first-child:not(:only-child) > trough > slider {\n    margin: -7px;\n    margin-bottom: -11px; }\n  scale.horizontal contents:first-child:not(:only-child) > trough > slider:backdrop {\n    margin: -10px;\n    border-style: none;\n    border-radius: 0;\n    background-color: transparent;\n    background-image: -gtk-scaled(url(\"assets/slider-horiz-insensitive.png\"));\n    min-height: 19px;\n    min-width: 11px;\n    margin-bottom: -14px;\n    background-position: bottom;\n    background-repeat: no-repeat;\n    box-shadow: none; }\n  scale.horizontal.fine-tune contents:first-child:not(:only-child) > trough > slider {\n    margin: -7px;\n    margin-bottom: -11px; }\n  scale.horizontal contents:first-child:not(:only-child) > trough > slider:backdrop:disabled {\n    margin: -10px;\n    border-style: none;\n    border-radius: 0;\n    background-color: transparent;\n    background-image: -gtk-scaled(url(\"assets/slider-horiz-insensitive.png\"));\n    min-height: 19px;\n    min-width: 11px;\n    margin-bottom: -14px;\n    background-position: bottom;\n    background-repeat: no-repeat;\n    box-shadow: none; }\n  scale.horizontal.fine-tune contents:first-child:not(:only-child) > trough > slider {\n    margin: -7px;\n    margin-bottom: -11px; }\n  scale.color.vertical:dir(rtl) slider:hover, scale.color.vertical:dir(rtl) slider:backdrop, scale.color.vertical:dir(rtl) slider:disabled, scale.color.vertical:dir(rtl) slider:backdrop:disabled, scale.color.vertical:dir(rtl) slider,\n  scale.vertical contents:last-child:not(:only-child) > trough > slider {\n    margin: -10px;\n    border-style: none;\n    border-radius: 0;\n    background-color: transparent;\n    background-image: -gtk-scaled(url(\"assets/slider-vert-scale-has-marks-above.png\"), url(\"assets/slider-vert-scale-has-marks-above@2.png\"));\n    min-height: 22px;\n    min-width: 26px;\n    margin-left: -14px;\n    background-position: left bottom;\n    background-repeat: no-repeat;\n    box-shadow: none; }\n  scale.color.fine-tune.vertical:dir(rtl) slider, scale.vertical.fine-tune contents:last-child:not(:only-child) > trough > slider {\n    margin: -7px;\n    margin-left: -11px; }\n  scale.color.vertical:dir(rtl) slider:hover, scale.color.vertical:dir(rtl) slider:hover:backdrop:disabled,\n  scale.vertical contents:last-child:not(:only-child) > trough > slider:hover {\n    margin: -10px;\n    border-style: none;\n    border-radius: 0;\n    background-color: transparent;\n    background-image: -gtk-scaled(url(\"assets/slider-vert-scale-has-marks-above-hover.png\"), url(\"assets/slider-vert-scale-has-marks-above-hover@2.png\"));\n    min-height: 22px;\n    min-width: 26px;\n    margin-left: -14px;\n    background-position: left bottom;\n    background-repeat: no-repeat;\n    box-shadow: none; }\n  scale.color.fine-tune.vertical:dir(rtl) slider, scale.vertical.fine-tune contents:last-child:not(:only-child) > trough > slider {\n    margin: -7px;\n    margin-left: -11px; }\n  scale.color.vertical:dir(rtl) slider:active:backdrop:disabled, scale.color.vertical:dir(rtl) slider:active,\n  scale.vertical contents:last-child:not(:only-child) > trough > slider:active {\n    margin: -10px;\n    border-style: none;\n    border-radius: 0;\n    background-color: transparent;\n    background-image: -gtk-scaled(url(\"assets/slider-vert-scale-has-marks-above-active.png\"), url(\"assets/slider-vert-scale-has-marks-above-active@2.png\"));\n    min-height: 22px;\n    min-width: 26px;\n    margin-left: -14px;\n    background-position: left bottom;\n    background-repeat: no-repeat;\n    box-shadow: none; }\n  scale.color.fine-tune.vertical:dir(rtl) slider, scale.vertical.fine-tune contents:last-child:not(:only-child) > trough > slider {\n    margin: -7px;\n    margin-left: -11px; }\n  scale.color.vertical:dir(rtl) slider:disabled,\n  scale.vertical contents:last-child:not(:only-child) > trough > slider:disabled {\n    margin: -10px;\n    border-style: none;\n    border-radius: 0;\n    background-color: transparent;\n    background-image: -gtk-scaled(url(\"assets/slider-vert-scale-has-marks-above-insensitive.png\"), url(\"assets/slider-vert-scale-has-marks-above-insensitive@2.png\"));\n    min-height: 22px;\n    min-width: 26px;\n    margin-left: -14px;\n    background-position: left bottom;\n    background-repeat: no-repeat;\n    box-shadow: none; }\n  scale.color.fine-tune.vertical:dir(rtl) slider, scale.vertical.fine-tune contents:last-child:not(:only-child) > trough > slider {\n    margin: -7px;\n    margin-left: -11px; }\n  scale.color.vertical:dir(rtl) slider:backdrop,\n  scale.vertical contents:last-child:not(:only-child) > trough > slider:backdrop {\n    margin: -10px;\n    border-style: none;\n    border-radius: 0;\n    background-color: transparent;\n    background-image: -gtk-scaled(url(\"assets/slider-vert-scale-has-marks-above-backdrop.png\"), url(\"assets/slider-vert-scale-has-marks-above-backdrop@2.png\"));\n    min-height: 22px;\n    min-width: 26px;\n    margin-left: -14px;\n    background-position: left bottom;\n    background-repeat: no-repeat;\n    box-shadow: none; }\n  scale.color.fine-tune.vertical:dir(rtl) slider, scale.vertical.fine-tune contents:last-child:not(:only-child) > trough > slider {\n    margin: -7px;\n    margin-left: -11px; }\n  scale.color.vertical:dir(rtl) slider:backdrop:disabled,\n  scale.vertical contents:last-child:not(:only-child) > trough > slider:backdrop:disabled {\n    margin: -10px;\n    border-style: none;\n    border-radius: 0;\n    background-color: transparent;\n    background-image: -gtk-scaled(url(\"assets/slider-vert-scale-has-marks-above-backdrop-insensitive.png\"), url(\"assets/slider-vert-scale-has-marks-above-backdrop-insensitive@2.png\"));\n    min-height: 22px;\n    min-width: 26px;\n    margin-left: -14px;\n    background-position: left bottom;\n    background-repeat: no-repeat;\n    box-shadow: none; }\n  scale.color.fine-tune.vertical:dir(rtl) slider, scale.vertical.fine-tune contents:last-child:not(:only-child) > trough > slider {\n    margin: -7px;\n    margin-left: -11px; }\n  scale.color.vertical:dir(ltr) slider:hover, scale.color.vertical:dir(ltr) slider:backdrop, scale.color.vertical:dir(ltr) slider:disabled, scale.color.vertical:dir(ltr) slider:backdrop:disabled, scale.color.vertical:dir(ltr) slider,\n  scale.vertical contents:first-child:not(:only-child) > trough > slider {\n    margin: -10px;\n    border-style: none;\n    border-radius: 0;\n    background-color: transparent;\n    background-image: -gtk-scaled(url(\"assets/slider-vert-scale-has-marks-below.png\"), url(\"assets/slider-vert-scale-has-marks-below@2.png\"));\n    min-height: 22px;\n    min-width: 26px;\n    margin-right: -14px;\n    background-position: right bottom;\n    background-repeat: no-repeat;\n    box-shadow: none; }\n  scale.color.fine-tune.vertical:dir(ltr) slider, scale.vertical.fine-tune contents:first-child:not(:only-child) > trough > slider {\n    margin: -7px;\n    margin-right: -11px; }\n  scale.color.vertical:dir(ltr) slider:hover, scale.color.vertical:dir(ltr) slider:hover:backdrop:disabled,\n  scale.vertical contents:first-child:not(:only-child) > trough > slider:hover {\n    margin: -10px;\n    border-style: none;\n    border-radius: 0;\n    background-color: transparent;\n    background-image: -gtk-scaled(url(\"assets/slider-vert-scale-has-marks-below-hover.png\"), url(\"assets/slider-vert-scale-has-marks-below-hover@2.png\"));\n    min-height: 22px;\n    min-width: 26px;\n    margin-right: -14px;\n    background-position: right bottom;\n    background-repeat: no-repeat;\n    box-shadow: none; }\n  scale.color.fine-tune.vertical:dir(ltr) slider, scale.vertical.fine-tune contents:first-child:not(:only-child) > trough > slider {\n    margin: -7px;\n    margin-right: -11px; }\n  scale.color.vertical:dir(ltr) slider:active:backdrop:disabled, scale.color.vertical:dir(ltr) slider:active,\n  scale.vertical contents:first-child:not(:only-child) > trough > slider:active {\n    margin: -10px;\n    border-style: none;\n    border-radius: 0;\n    background-color: transparent;\n    background-image: -gtk-scaled(url(\"assets/slider-vert-scale-has-marks-below-active.png\"), url(\"assets/slider-vert-scale-has-marks-below-active@2.png\"));\n    min-height: 22px;\n    min-width: 26px;\n    margin-right: -14px;\n    background-position: right bottom;\n    background-repeat: no-repeat;\n    box-shadow: none; }\n  scale.color.fine-tune.vertical:dir(ltr) slider, scale.vertical.fine-tune contents:first-child:not(:only-child) > trough > slider {\n    margin: -7px;\n    margin-right: -11px; }\n  scale.color.vertical:dir(ltr) slider:disabled,\n  scale.vertical contents:first-child:not(:only-child) > trough > slider:disabled {\n    margin: -10px;\n    border-style: none;\n    border-radius: 0;\n    background-color: transparent;\n    background-image: -gtk-scaled(url(\"assets/slider-vert-scale-has-marks-below-insensitive.png\"), url(\"assets/slider-vert-scale-has-marks-below-insensitive@2.png\"));\n    min-height: 22px;\n    min-width: 26px;\n    margin-right: -14px;\n    background-position: right bottom;\n    background-repeat: no-repeat;\n    box-shadow: none; }\n  scale.color.fine-tune.vertical:dir(ltr) slider, scale.vertical.fine-tune contents:first-child:not(:only-child) > trough > slider {\n    margin: -7px;\n    margin-right: -11px; }\n  scale.color.vertical:dir(ltr) slider:backdrop,\n  scale.vertical contents:first-child:not(:only-child) > trough > slider:backdrop {\n    margin: -10px;\n    border-style: none;\n    border-radius: 0;\n    background-color: transparent;\n    background-image: -gtk-scaled(url(\"assets/slider-vert-scale-has-marks-below-backdrop.png\"), url(\"assets/slider-vert-scale-has-marks-below-backdrop@2.png\"));\n    min-height: 22px;\n    min-width: 26px;\n    margin-right: -14px;\n    background-position: right bottom;\n    background-repeat: no-repeat;\n    box-shadow: none; }\n  scale.color.fine-tune.vertical:dir(ltr) slider, scale.vertical.fine-tune contents:first-child:not(:only-child) > trough > slider {\n    margin: -7px;\n    margin-right: -11px; }\n  scale.color.vertical:dir(ltr) slider:backdrop:disabled,\n  scale.vertical contents:first-child:not(:only-child) > trough > slider:backdrop:disabled {\n    margin: -10px;\n    border-style: none;\n    border-radius: 0;\n    background-color: transparent;\n    background-image: -gtk-scaled(url(\"assets/slider-vert-scale-has-marks-below-backdrop-insensitive.png\"), url(\"assets/slider-vert-scale-has-marks-below-backdrop-insensitive@2.png\"));\n    min-height: 22px;\n    min-width: 26px;\n    margin-right: -14px;\n    background-position: right bottom;\n    background-repeat: no-repeat;\n    box-shadow: none; }\n  scale.color.fine-tune.vertical:dir(ltr) slider, scale.vertical.fine-tune contents:first-child:not(:only-child) > trough > slider {\n    margin: -7px;\n    margin-right: -11px; }\n  scale.color {\n    min-height: 0;\n    min-width: 0; }\n    scale.color trough {\n      background-image: image(@borders);\n      background-repeat: no-repeat; }\n    scale.color.horizontal {\n      padding: 0 0 15px 0; }\n      scale.color.horizontal trough {\n        padding-bottom: 4px;\n        background-position: 0 -3px;\n        border-top-left-radius: 0;\n        border-top-right-radius: 0; }\n      scale.color.horizontal slider:hover, scale.color.horizontal slider:backdrop, scale.color.horizontal slider:disabled, scale.color.horizontal slider:backdrop:disabled, scale.color.horizontal slider {\n        margin-bottom: -15px;\n        margin-top: 6px; }\n    scale.color.vertical:dir(ltr) {\n      padding: 0 0 0 15px; }\n      scale.color.vertical:dir(ltr) trough {\n        padding-left: 4px;\n        background-position: 3px 0;\n        border-bottom-right-radius: 0;\n        border-top-right-radius: 0; }\n      scale.color.vertical:dir(ltr) slider:hover, scale.color.vertical:dir(ltr) slider:backdrop, scale.color.vertical:dir(ltr) slider:disabled, scale.color.vertical:dir(ltr) slider:backdrop:disabled, scale.color.vertical:dir(ltr) slider {\n        margin-left: -15px;\n        margin-right: 6px; }\n    scale.color.vertical:dir(rtl) {\n      padding: 0 15px 0 0; }\n      scale.color.vertical:dir(rtl) trough {\n        padding-right: 4px;\n        background-position: -3px 0;\n        border-bottom-left-radius: 0;\n        border-top-left-radius: 0; }\n      scale.color.vertical:dir(rtl) slider:hover, scale.color.vertical:dir(rtl) slider:backdrop, scale.color.vertical:dir(rtl) slider:disabled, scale.color.vertical:dir(rtl) slider:backdrop:disabled, scale.color.vertical:dir(rtl) slider {\n        margin-right: -15px;\n        margin-left: 6px; }\n    scale.color.fine-tune.horizontal {\n      padding: 0 0 12px 0; }\n      scale.color.fine-tune.horizontal trough {\n        padding-bottom: 7px;\n        background-position: 0 -6px; }\n      scale.color.fine-tune.horizontal slider {\n        margin-bottom: -15px;\n        margin-top: 6px; }\n    scale.color.fine-tune.vertical:dir(ltr) {\n      padding: 0 0 0 12px; }\n      scale.color.fine-tune.vertical:dir(ltr) trough {\n        padding-left: 7px;\n        background-position: 6px 0; }\n      scale.color.fine-tune.vertical:dir(ltr) slider {\n        margin-left: -15px;\n        margin-right: 6px; }\n    scale.color.fine-tune.vertical:dir(rtl) {\n      padding: 0 12px 0 0; }\n      scale.color.fine-tune.vertical:dir(rtl) trough {\n        padding-right: 7px;\n        background-position: -6px 0; }\n      scale.color.fine-tune.vertical:dir(rtl) slider {\n        margin-right: -15px;\n        margin-left: 6px; }\n\n/*****************\n * Progress bars *\n *****************/\nprogressbar {\n  font-size: smaller;\n  color: @theme_selected_fg_color; }\n  progressbar.horizontal trough,\n  progressbar.horizontal progress {\n    min-height: 2px; }\n  progressbar.vertical trough,\n  progressbar.vertical progress {\n    min-width: 2px; }\n  progressbar.horizontal progress {\n    margin: 0 -1px; }\n  progressbar.vertical progress {\n    margin: -1px 0; }\n  progressbar:backdrop {\n    box-shadow: none;\n    transition: 200ms ease-out; }\n  progressbar progress {\n    border-radius: 0; }\n    progressbar progress.left {\n      border-top-left-radius: 0;\n      border-bottom-left-radius: 0; }\n    progressbar progress.right {\n      border-top-right-radius: 0;\n      border-bottom-right-radius: 0; }\n    progressbar progress.top {\n      border-top-right-radius: 0;\n      border-top-left-radius: 0; }\n    progressbar progress.bottom {\n      border-bottom-right-radius: 0;\n      border-bottom-left-radius: 0; }\n  progressbar.osd {\n    min-width: 3px;\n    min-height: 3px;\n    background-color: transparent; }\n    progressbar.osd trough {\n      border-style: none;\n      border-radius: 0;\n      background-color: transparent;\n      box-shadow: none; }\n    progressbar.osd progress {\n      border-style: none;\n      border-radius: 0; }\n\n/*************\n * Level Bar *\n *************/\nlevelbar block {\n  min-width: 32px;\n  min-height: 1px; }\nlevelbar.vertical block {\n  min-width: 1px;\n  min-height: 32px; }\nlevelbar:backdrop {\n  transition: 200ms ease-out; }\nlevelbar trough {\n  border: 1px solid;\n  padding: 2px;\n  border-radius: 0;\n  color: @theme_fg_color;\n  border-color: @borders;\n  background-color: @theme_bg_color;\n  box-shadow: inset 0 0 0 1px shade(@theme_selected_bg_color, 0); }\n  levelbar trough:backdrop {\n    color: @theme_unfocused_fg_color;\n    border-color: shade(@borders, 0.95);\n    background-color: @theme_unfocused_bg_color;\n    box-shadow: none; }\nlevelbar.horizontal.discrete block {\n  margin: 0 1px; }\nlevelbar.vertical.discrete block {\n  margin: 1px 0; }\nlevelbar block {\n  border: 1px solid;\n  border-radius: 0; }\n  levelbar block.low {\n    border-color: #8f4700;\n    background-color: @warning_color; }\n    levelbar block.low:backdrop {\n      border-color: @warning_color; }\n  levelbar block.high, levelbar block:not(.empty) {\n    border-color: shade(@theme_selected_bg_color, 0.6);\n    background-color: @theme_selected_bg_color; }\n    levelbar block.high:backdrop, levelbar block:not(.empty):backdrop {\n      border-color: @theme_selected_bg_color; }\n  levelbar block.full {\n    border-color: #40760c;\n    background-color: #73d216; }\n    levelbar block.full:backdrop {\n      border-color: #73d216; }\n  levelbar block.empty {\n    background-color: transparent;\n    border-color: rgba(46, 52, 54, 0.2); }\n    levelbar block.empty:backdrop {\n      border-color: rgba(139, 142, 143, 0.15); }\n\n/****************\n * Print dialog *\n*****************/\nprintdialog paper {\n  color: @theme_fg_color;\n  border: 1px solid @borders;\n  background: @theme_bg_color;\n  padding: 0; }\n  printdialog paper:backdrop {\n    color: @insensitive_fg_color;\n    border-color: shade(@borders, 0.95); }\nprintdialog .dialog-action-box {\n  margin: 12px; }\n\n/**********\n * Frames *\n **********/\nframe > border,\n.frame {\n  box-shadow: none;\n  margin: 0;\n  padding: 0;\n  border-radius: 0;\n  border: 1px solid @borders; }\n  frame > border.flat,\n  .frame.flat {\n    border-style: none; }\n  frame > border:backdrop,\n  .frame:backdrop {\n    border-color: shade(@borders, 0.95); }\n\nactionbar > revealer > box {\n  padding: 6px;\n  border-top: 1px solid @borders; }\n  actionbar > revealer > box:backdrop {\n    border-color: shade(@borders, 0.95); }\n\nscrolledwindow viewport.frame {\n  border-style: none; }\nscrolledwindow overshoot.top {\n  background-image: -gtk-gradient(radial, center top, 0, center top, 0.5, to(#9d9d99), to(rgba(157, 157, 153, 0))), -gtk-gradient(radial, center top, 0, center top, 0.6, from(rgba(46, 52, 54, 0.07)), to(rgba(46, 52, 54, 0)));\n  background-size: 100% 5%, 100% 100%;\n  background-repeat: no-repeat;\n  background-position: center top;\n  background-color: transparent;\n  border: none;\n  box-shadow: none; }\n  scrolledwindow overshoot.top:backdrop {\n    background-image: -gtk-gradient(radial, center top, 0, center top, 0.5, to(shade(@borders, 0.95)), to(rgba(192, 192, 189, 0)));\n    background-size: 100% 5%;\n    background-repeat: no-repeat;\n    background-position: center top;\n    background-color: transparent;\n    border: none;\n    box-shadow: none; }\nscrolledwindow overshoot.bottom {\n  background-image: -gtk-gradient(radial, center bottom, 0, center bottom, 0.5, to(#9d9d99), to(rgba(157, 157, 153, 0))), -gtk-gradient(radial, center bottom, 0, center bottom, 0.6, from(rgba(46, 52, 54, 0.07)), to(rgba(46, 52, 54, 0)));\n  background-size: 100% 5%, 100% 100%;\n  background-repeat: no-repeat;\n  background-position: center bottom;\n  background-color: transparent;\n  border: none;\n  box-shadow: none; }\n  scrolledwindow overshoot.bottom:backdrop {\n    background-image: -gtk-gradient(radial, center bottom, 0, center bottom, 0.5, to(shade(@borders, 0.95)), to(rgba(192, 192, 189, 0)));\n    background-size: 100% 5%;\n    background-repeat: no-repeat;\n    background-position: center bottom;\n    background-color: transparent;\n    border: none;\n    box-shadow: none; }\nscrolledwindow overshoot.left {\n  background-image: -gtk-gradient(radial, left center, 0, left center, 0.5, to(#9d9d99), to(rgba(157, 157, 153, 0))), -gtk-gradient(radial, left center, 0, left center, 0.6, from(rgba(46, 52, 54, 0.07)), to(rgba(46, 52, 54, 0)));\n  background-size: 5% 100%, 100% 100%;\n  background-repeat: no-repeat;\n  background-position: left center;\n  background-color: transparent;\n  border: none;\n  box-shadow: none; }\n  scrolledwindow overshoot.left:backdrop {\n    background-image: -gtk-gradient(radial, left center, 0, left center, 0.5, to(shade(@borders, 0.95)), to(rgba(192, 192, 189, 0)));\n    background-size: 5% 100%;\n    background-repeat: no-repeat;\n    background-position: left center;\n    background-color: transparent;\n    border: none;\n    box-shadow: none; }\nscrolledwindow overshoot.right {\n  background-image: -gtk-gradient(radial, right center, 0, right center, 0.5, to(#9d9d99), to(rgba(157, 157, 153, 0))), -gtk-gradient(radial, right center, 0, right center, 0.6, from(rgba(46, 52, 54, 0.07)), to(rgba(46, 52, 54, 0)));\n  background-size: 5% 100%, 100% 100%;\n  background-repeat: no-repeat;\n  background-position: right center;\n  background-color: transparent;\n  border: none;\n  box-shadow: none; }\n  scrolledwindow overshoot.right:backdrop {\n    background-image: -gtk-gradient(radial, right center, 0, right center, 0.5, to(shade(@borders, 0.95)), to(rgba(192, 192, 189, 0)));\n    background-size: 5% 100%;\n    background-repeat: no-repeat;\n    background-position: right center;\n    background-color: transparent;\n    border: none;\n    box-shadow: none; }\nscrolledwindow undershoot.top {\n  background-color: transparent;\n  background-image: linear-gradient(to left, rgba(255, 255, 255, 0.2) 50%, rgba(0, 0, 0, 0.2) 50%);\n  padding-top: 1px;\n  background-size: 10px 1px;\n  background-repeat: repeat-x;\n  background-origin: content-box;\n  background-position: center top;\n  border: none;\n  box-shadow: none; }\nscrolledwindow undershoot.bottom {\n  background-color: transparent;\n  background-image: linear-gradient(to left, rgba(255, 255, 255, 0.2) 50%, rgba(0, 0, 0, 0.2) 50%);\n  padding-bottom: 1px;\n  background-size: 10px 1px;\n  background-repeat: repeat-x;\n  background-origin: content-box;\n  background-position: center bottom;\n  border: none;\n  box-shadow: none; }\nscrolledwindow undershoot.left {\n  background-color: transparent;\n  background-image: linear-gradient(to top, rgba(255, 255, 255, 0.2) 50%, rgba(0, 0, 0, 0.2) 50%);\n  padding-left: 1px;\n  background-size: 1px 10px;\n  background-repeat: repeat-y;\n  background-origin: content-box;\n  background-position: left center;\n  border: none;\n  box-shadow: none; }\nscrolledwindow undershoot.right {\n  background-color: transparent;\n  background-image: linear-gradient(to top, rgba(255, 255, 255, 0.2) 50%, rgba(0, 0, 0, 0.2) 50%);\n  padding-right: 1px;\n  background-size: 1px 10px;\n  background-repeat: repeat-y;\n  background-origin: content-box;\n  background-position: right center;\n  border: none;\n  box-shadow: none; }\nscrolledwindow junction {\n  border-color: transparent;\n  border-image: linear-gradient(to bottom, @borders 1px, transparent 1px) 0 0 0 1/0 1px stretch;\n  background-color: #c3c4c4; }\n  scrolledwindow junction:dir(rtl) {\n    border-image-slice: 0 1 0 0; }\n  scrolledwindow junction:backdrop {\n    border-image-source: linear-gradient(to bottom, shade(@borders, 0.95) 1px, transparent 1px);\n    background-color: #e1e1df;\n    transition: 200ms ease-out; }\n\nseparator {\n  background: rgba(0, 0, 0, 0.1);\n  min-width: 1px;\n  min-height: 1px; }\n\n/*********\n * Lists *\n *********/\nlist {\n  color: @theme_fg_color;\n  background-color: @theme_bg_color;\n  border-color: @borders; }\n  list:backdrop {\n    background-color: @theme_unfocused_bg_color;\n    border-color: shade(@borders, 0.95); }\n  list row {\n    padding: 2px; }\n\nrow {\n  transition: all 150ms cubic-bezier(0.25, 0.46, 0.45, 0.94); }\n  row:hover {\n    transition: none; }\n  row:backdrop {\n    transition: 200ms ease-out; }\n  row.activatable.has-open-popup, row.activatable:hover {\n    background-color: rgba(46, 52, 54, 0.05); }\n  row.activatable:active {\n    box-shadow: inset 0 2px 2px -2px rgba(0, 0, 0, 0.2); }\n  row.activatable:backdrop:hover {\n    background-color: transparent; }\n  row.activatable:selected:active {\n    box-shadow: inset 0 2px 3px -1px @osd_bg_color; }\n  row.activatable:selected.has-open-popup, row.activatable:selected:hover {\n    background-color: shade(@theme_selected_bg_color, 1.05); }\n  row.activatable:selected:backdrop {\n    background-color: @theme_selected_bg_color; }\n\n/*********************\n * App Notifications *\n *********************/\n.app-notification,\n.app-notification.frame {\n  padding: 10px;\n  border-radius: 0;\n  background-color: @osd_bg_color;\n  background-image: linear-gradient(to bottom, rgba(0, 0, 0, 0.2), transparent 2px);\n  background-clip: padding-box; }\n  .app-notification:backdrop,\n  .app-notification.frame:backdrop {\n    background-image: none;\n    transition: 200ms ease-out; }\n  .app-notification border,\n  .app-notification.frame border {\n    border: none; }\n\n/*************\n * Expanders *\n *************/\nexpander arrow {\n  min-width: 16px;\n  min-height: 16px;\n  -gtk-icon-source: -gtk-icontheme(\"pan-end-symbolic\"); }\n  expander arrow:dir(rtl) {\n    -gtk-icon-source: -gtk-icontheme(\"pan-end-symbolic-rtl\"); }\n  expander arrow:hover {\n    color: #748489; }\n  expander arrow:checked {\n    -gtk-icon-source: -gtk-icontheme(\"pan-down-symbolic\"); }\n\n/************\n * Calendar *\n ***********/\ncalendar {\n  color: @theme_fg_color;\n  border: 1px solid @borders; }\n  calendar:selected {\n    border-radius: 0; }\n  calendar.header {\n    border-bottom: 1px solid rgba(0, 0, 0, 0.1);\n    border-radius: 0; }\n    calendar.header:backdrop {\n      border-color: rgba(0, 0, 0, 0.1); }\n  calendar.button {\n    color: rgba(46, 52, 54, 0.45); }\n    calendar.button:hover {\n      color: @theme_fg_color; }\n    calendar.button:backdrop {\n      color: rgba(139, 142, 143, 0.45); }\n    calendar.button:disabled {\n      color: rgba(139, 142, 143, 0.45); }\n  calendar:indeterminate, calendar:indeterminate:backdrop {\n    color: alpha(currentColor,0.55); }\n  calendar.highlight, calendar.highlight:backdrop {\n    font-size: smaller;\n    color: @theme_fg_color; }\n  calendar:backdrop {\n    color: @theme_unfocused_fg_color;\n    border-color: shade(@borders, 0.95); }\n\n/***********\n * Dialogs *\n ***********/\nmessagedialog .titlebar {\n  min-height: 20px;\n  background-image: none;\n  background-color: @theme_bg_color;\n  border-style: none;\n  border-top-left-radius: 0;\n  border-top-right-radius: 0; }\nmessagedialog.csd.background {\n  border-bottom-left-radius: 0;\n  border-bottom-right-radius: 0; }\nmessagedialog.csd .dialog-action-area button {\n  padding: 10px 14px;\n  border-radius: 0;\n  border-left-style: solid;\n  border-right-style: none;\n  border-bottom-style: none; }\n  messagedialog.csd .dialog-action-area button:first-child {\n    border-left-style: none;\n    border-bottom-left-radius: 0;\n    -gtk-outline-bottom-left-radius: 0; }\n  messagedialog.csd .dialog-action-area button:last-child {\n    border-bottom-right-radius: 0;\n    -gtk-outline-bottom-right-radius: 0; }\n\nfilechooser .dialog-action-box {\n  border-top: 1px solid @borders; }\n  filechooser .dialog-action-box:backdrop {\n    border-top-color: shade(@borders, 0.95); }\nfilechooser #pathbarbox {\n  border-bottom: 1px solid @theme_bg_color; }\n\nfilechooserbutton:drop(active) {\n  box-shadow: none;\n  border-color: transparent; }\n\n/***********\n * Sidebar *\n ***********/\n.sidebar {\n  border-style: none;\n  background-color: @theme_bg_color; }\n  stacksidebar.sidebar:dir(ltr) list, stacksidebar.sidebar.left list, stacksidebar.sidebar.left:dir(rtl) list, .sidebar:dir(ltr), .sidebar.left, .sidebar.left:dir(rtl) {\n    border-right: none;\n    border-left-style: none; }\n  stacksidebar.sidebar:dir(rtl) list\n  .sidebar:dir(rtl), stacksidebar.sidebar.right list\n  .sidebar:dir(rtl), .sidebar.right {\n    border-left: 1px solid @borders;\n    border-right-style: none; }\n  .sidebar:backdrop {\n    background-color: @theme_unfocused_bg_color;\n    border-color: shade(@borders, 0.95);\n    transition: 200ms ease-out; }\n  .sidebar list {\n    background-color: transparent; }\n  paned .sidebar.left, paned .sidebar.right, paned .sidebar.left:dir(rtl), paned .sidebar:dir(rtl), paned .sidebar:dir(ltr), paned .sidebar {\n    border-style: none; }\n\nstacksidebar row {\n  padding: 10px 4px; }\n  stacksidebar row > label {\n    padding-left: 6px;\n    padding-right: 6px; }\n  stacksidebar row.needs-attention > label {\n    background-size: 6px 6px, 0 0; }\n\n/****************\n * File chooser *\n ****************/\nplacessidebar > viewport.frame {\n  border-style: none; }\nplacessidebar row {\n  min-height: 36px;\n  padding: 0px; }\n  placessidebar row > revealer {\n    padding: 0 14px; }\n  placessidebar row:selected {\n    color: @theme_selected_fg_color; }\n  placessidebar row:disabled {\n    color: @insensitive_fg_color; }\n  placessidebar row:backdrop {\n    color: @insensitive_fg_color; }\n    placessidebar row:backdrop:selected {\n      color: @osd_bg_color; }\n    placessidebar row:backdrop:disabled {\n      color: shade(@theme_unfocused_fg_color, 1.1); }\n  placessidebar row image.sidebar-icon {\n    opacity: 0.7; }\n    placessidebar row image.sidebar-icon:dir(ltr) {\n      padding-right: 8px; }\n    placessidebar row image.sidebar-icon:dir(rtl) {\n      padding-left: 8px; }\n  placessidebar row label.sidebar-label:dir(ltr) {\n    padding-right: 2px; }\n  placessidebar row label.sidebar-label:dir(rtl) {\n    padding-left: 2px; }\n  button.sidebar-button {\n    min-height: 26px;\n    min-width: 26px;\n    margin-top: 3px;\n    margin-bottom: 3px;\n    padding: 0;\n    border-radius: 100%;\n    -gtk-outline-radius: 100%; }\n    button.sidebar-button:not(:hover):not(:active) > image, button.sidebar-button:backdrop > image {\n      opacity: 0.7; }\n  placessidebar row:selected:active {\n    box-shadow: none; }\n  placessidebar row.sidebar-placeholder-row {\n    padding: 0 8px;\n    min-height: 2px;\n    background-image: image(@success_color);\n    background-clip: content-box; }\n  placessidebar row.sidebar-new-bookmark-row {\n    color: @theme_selected_bg_color; }\n  placessidebar row:drop(active):not(:disabled) {\n    color: @success_color;\n    box-shadow: inset 0 1px @success_color, inset 0 -1px @success_color; }\n    placessidebar row:drop(active):not(:disabled):selected {\n      color: @theme_selected_fg_color;\n      background-color: @success_color; }\n\nplacesview .server-list-button > image {\n  transition: 200ms cubic-bezier(0.25, 0.46, 0.45, 0.94);\n  -gtk-icon-transform: rotate(0turn); }\nplacesview .server-list-button:checked > image {\n  transition: 200ms cubic-bezier(0.25, 0.46, 0.45, 0.94);\n  -gtk-icon-transform: rotate(-0.5turn); }\nplacesview row.activatable:hover {\n  background-color: transparent; }\nplacesview > actionbar > revealer > box > label {\n  padding-left: 8px;\n  padding-right: 8px; }\n\n/*********\n * Paned *\n *********/\npaned > separator {\n  min-width: 1px;\n  min-height: 1px;\n  -gtk-icon-source: none;\n  border-style: none;\n  background-color: transparent;\n  background-image: image(@borders);\n  background-size: 1px 1px; }\n  paned > separator:selected {\n    background-image: image(@theme_selected_bg_color); }\n  paned > separator:backdrop {\n    background-image: image(shade(@borders, 0.95)); }\n  paned > separator.wide {\n    min-width: 5px;\n    min-height: 5px;\n    background-color: @theme_bg_color;\n    background-image: image(@borders), image(@borders);\n    background-size: 1px 1px, 1px 1px; }\n    paned > separator.wide:backdrop {\n      background-color: @theme_bg_color;\n      background-image: image(shade(@borders, 0.95)), image(shade(@borders, 0.95)); }\npaned.horizontal > separator {\n  background-repeat: repeat-y; }\n  paned.horizontal > separator:dir(ltr) {\n    margin: 0 -8px 0 0;\n    padding: 0 8px 0 0;\n    background-position: left; }\n  paned.horizontal > separator:dir(rtl) {\n    margin: 0 0 0 -8px;\n    padding: 0 0 0 8px;\n    background-position: right; }\n  paned.horizontal > separator.wide {\n    margin: 0;\n    padding: 0;\n    background-repeat: repeat-y, repeat-y;\n    background-position: left, right; }\npaned.vertical > separator {\n  margin: 0 0 -8px 0;\n  padding: 0 0 8px 0;\n  background-repeat: repeat-x;\n  background-position: top; }\n  paned.vertical > separator.wide {\n    margin: 0;\n    padding: 0;\n    background-repeat: repeat-x, repeat-x;\n    background-position: bottom, top; }\n\n/**************\n * GtkInfoBar *\n **************/\ninfobar {\n  border-style: none; }\n\n.info,\n.question,\n.warning,\n.error {\n  text-shadow: 0 1px @borders; }\n  .info:backdrop, .info,\n  .question:backdrop,\n  .question,\n  .warning:backdrop,\n  .warning,\n  .error:backdrop,\n  .error {\n    background-color: @theme_selected_bg_color;\n    border-color: @borders; }\n    .info:backdrop label, .info:backdrop, .info label, .info,\n    .question:backdrop label,\n    .question:backdrop,\n    .question label,\n    .question,\n    .warning:backdrop label,\n    .warning:backdrop,\n    .warning label,\n    .warning,\n    .error:backdrop label,\n    .error:backdrop,\n    .error label,\n    .error {\n      color: @theme_selected_fg_color; }\n  .info:backdrop,\n  .question:backdrop,\n  .warning:backdrop,\n  .error:backdrop {\n    text-shadow: none; }\n  .info button,\n  .question button,\n  .warning button,\n  .error button {\n    color: @theme_selected_fg_color;\n    outline-color: rgba(255, 255, 255, 0.3);\n    border-color: shade(@theme_selected_bg_color, 0.6);\n    border-bottom-color: shade(@theme_selected_bg_color, 0.6);\n    background-image: none;\n    background-color: @theme_selected_bg_color;\n    text-shadow: 0 -1px rgba(0, 0, 0, 0.54353);\n    -gtk-icon-shadow: 0 -1px rgba(0, 0, 0, 0.54353);\n    box-shadow: inset 0 1px rgba(255, 255, 255, 0.4); }\n    .info button:hover,\n    .question button:hover,\n    .warning button:hover,\n    .error button:hover {\n      color: @theme_selected_fg_color;\n      outline-color: rgba(255, 255, 255, 0.3);\n      border-color: shade(@theme_selected_bg_color, 0.6);\n      border-bottom-color: shade(@theme_selected_bg_color, 0.6);\n      background-image: none;\n      background-color: shade(@theme_selected_bg_color, 1.1);\n      text-shadow: 0 -1px rgba(0, 0, 0, 0.49553);\n      -gtk-icon-shadow: 0 -1px rgba(0, 0, 0, 0.49553);\n      box-shadow: inset 0 1px rgba(255, 255, 255, 0.4); }\n    .info button:active, .info button:checked,\n    .question button:active,\n    .question button:checked,\n    .warning button:active,\n    .warning button:checked,\n    .error button:active,\n    .error button:checked {\n      color: @theme_selected_fg_color;\n      outline-color: rgba(255, 255, 255, 0.3);\n      border-color: shade(@theme_selected_bg_color, 0.6);\n      background-image: none;\n      background-color: shade(@theme_selected_bg_color, 0.8);\n      box-shadow: inset 0 1px transparent;\n      text-shadow: none;\n      -gtk-icon-shadow: none; }\n    .info button:disabled,\n    .question button:disabled,\n    .warning button:disabled,\n    .error button:disabled {\n      border-color: shade(@theme_selected_bg_color, 0.6);\n      background-color: @theme_selected_bg_color;\n      background-image: none;\n      text-shadow: none;\n      -gtk-icon-shadow: none;\n      box-shadow: inset 0 1px transparent; }\n      .info button:disabled label, .info button:disabled,\n      .question button:disabled label,\n      .question button:disabled,\n      .warning button:disabled label,\n      .warning button:disabled,\n      .error button:disabled label,\n      .error button:disabled {\n        color: #b2d0ef; }\n    .info button:backdrop,\n    .question button:backdrop,\n    .warning button:backdrop,\n    .error button:backdrop {\n      border-color: @theme_selected_bg_color;\n      background-color: transparent;\n      background-image: image(@theme_selected_bg_color);\n      text-shadow: none;\n      -gtk-icon-shadow: none;\n      box-shadow: inset 0 1px transparent;\n      border-color: shade(@theme_selected_bg_color, 0.6); }\n      .info button:backdrop label, .info button:backdrop,\n      .question button:backdrop label,\n      .question button:backdrop,\n      .warning button:backdrop label,\n      .warning button:backdrop,\n      .error button:backdrop label,\n      .error button:backdrop {\n        color: @theme_selected_fg_color; }\n      .info button:backdrop:disabled,\n      .question button:backdrop:disabled,\n      .warning button:backdrop:disabled,\n      .error button:backdrop:disabled {\n        border-color: @theme_selected_bg_color;\n        background-color: @theme_selected_bg_color;\n        background-image: none;\n        text-shadow: none;\n        -gtk-icon-shadow: none;\n        box-shadow: inset 0 1px transparent;\n        border-color: shade(@theme_selected_bg_color, 0.6); }\n        .info button:backdrop:disabled label, .info button:backdrop:disabled,\n        .question button:backdrop:disabled label,\n        .question button:backdrop:disabled,\n        .warning button:backdrop:disabled label,\n        .warning button:backdrop:disabled,\n        .error button:backdrop:disabled label,\n        .error button:backdrop:disabled {\n          color: @theme_unfocused_selected_fg_color; }\n  .info label:selected:focus, .info label:selected:hover, .info label:selected,\n  .question label:selected:focus,\n  .question label:selected:hover,\n  .question label:selected,\n  .warning label:selected:focus,\n  .warning label:selected:hover,\n  .warning label:selected,\n  .error label:selected:focus,\n  .error label:selected:hover,\n  .error label:selected {\n    background-color: @borders; }\n\n/************\n * Tooltips * *?*\n ************/\ntooltip {\n  padding: 4px;\n  /* not working */\n  border-radius: 0;\n  box-shadow: none;\n  text-shadow: none; }\n  tooltip.background {\n    background-color: @tooltip_bg_color;\n    background-clip: padding-box;\n    border: 1px solid @osd_txt_shadow; }\n  tooltip decoration {\n    background-color: transparent; }\n  tooltip * {\n    padding: 4px;\n    background-color: transparent;\n    color: @theme_fg_color; }\n\n/*****************\n * Color Chooser *\n *****************/\ncolorswatch:drop(active), colorswatch {\n  border-style: none; }\ncolorswatch.top {\n  border-top-left-radius: 0;\n  border-top-right-radius: 0; }\n  colorswatch.top overlay {\n    border-top-left-radius: 0;\n    border-top-right-radius: 0; }\ncolorswatch.bottom {\n  border-bottom-left-radius: 0;\n  border-bottom-right-radius: 0; }\n  colorswatch.bottom overlay {\n    border-bottom-left-radius: 0;\n    border-bottom-right-radius: 0; }\ncolorswatch.left, colorswatch:first-child:not(.top) {\n  border-top-left-radius: 0;\n  border-bottom-left-radius: 0; }\n  colorswatch.left overlay, colorswatch:first-child:not(.top) overlay {\n    border-top-left-radius: 0;\n    border-bottom-left-radius: 0; }\ncolorswatch.right, colorswatch:last-child:not(.bottom) {\n  border-top-right-radius: 0;\n  border-bottom-right-radius: 0; }\n  colorswatch.right overlay, colorswatch:last-child:not(.bottom) overlay {\n    border-top-right-radius: 0;\n    border-bottom-right-radius: 0; }\ncolorswatch.dark overlay {\n  color: @theme_selected_fg_color; }\n  colorswatch.dark overlay:hover {\n    border-color: rgba(0, 0, 0, 0.8); }\n  colorswatch.dark overlay:backdrop {\n    color: @theme_unfocused_bg_color; }\ncolorswatch.light overlay {\n  color: @theme_fg_color; }\n  colorswatch.light overlay:hover {\n    border-color: @osd_bg_color; }\n  colorswatch.light overlay:backdrop {\n    color: @theme_unfocused_fg_color; }\ncolorswatch:drop(active) {\n  box-shadow: none; }\n  colorswatch:drop(active).light overlay {\n    border-color: @success_color;\n    box-shadow: inset 0 0 0 2px #3d7805, inset 0 0 0 1px @success_color; }\n  colorswatch:drop(active).dark overlay {\n    border-color: @success_color;\n    box-shadow: inset 0 0 0 2px @borders, inset 0 0 0 1px @success_color; }\ncolorswatch overlay {\n  border: 1px solid @borders; }\n  colorswatch overlay:hover {\n    box-shadow: inset 0 1px rgba(255, 255, 255, 0.4), inset 0 -1px rgba(0, 0, 0, 0.2); }\n  colorswatch overlay:backdrop, colorswatch overlay:backdrop:hover {\n    border-color: @borders;\n    box-shadow: none; }\ncolorswatch#add-color-button {\n  border-radius: 0; }\n  colorswatch#add-color-button:only-child {\n    border-radius: 0; }\n  colorswatch#add-color-button overlay {\n    color: @theme_fg_color;\n    outline-color: @outline_color;\n    border-color: @borders;\n    border-bottom-color: @borders;\n    background-image: linear-gradient(to bottom, @theme_bg_color, @theme_bg_color);\n    text-shadow: 0 1px @txt_shadow;\n    -gtk-icon-shadow: 0 1px @txt_shadow;\n    box-shadow: inset 0 1px rgba(255, 255, 255, 0.8); }\n    colorswatch#add-color-button overlay:hover {\n      color: @theme_fg_color;\n      outline-color: @outline_color;\n      border-color: @borders;\n      border-bottom-color: @borders;\n      background-image: linear-gradient(to bottom, @theme_selected_bg_color, @theme_selected_bg_color);\n      text-shadow: 0 1px @txt_shadow;\n      -gtk-icon-shadow: 0 1px @txt_shadow;\n      box-shadow: inset 0 1px @theme_bg_color; }\n    colorswatch#add-color-button overlay:backdrop {\n      border-color: shade(@borders, 0.95);\n      background-color: transparent;\n      background-image: image(@theme_bg_color);\n      text-shadow: none;\n      -gtk-icon-shadow: none;\n      box-shadow: inset 0 1px transparent; }\n      colorswatch#add-color-button overlay:backdrop label, colorswatch#add-color-button overlay:backdrop {\n        color: @insensitive_fg_color; }\ncolorswatch:disabled {\n  opacity: 0.5; }\n  colorswatch:disabled overlay {\n    border-color: rgba(0, 0, 0, 0.6);\n    box-shadow: none; }\nrow:selected colorswatch {\n  box-shadow: 0 0 0 2px #ffffff; }\ncolorswatch#editor-color-sample {\n  border-radius: 0; }\n  colorswatch#editor-color-sample overlay {\n    border-radius: 0px; }\n\ncolorchooser .popover.osd {\n  border-radius: 0; }\n\n/********\n * Misc *\n ********/\n.content-view {\n  background-color: #d7d7d5; }\n  .content-view:hover {\n    -gtk-icon-effect: highlight; }\n  .content-view:backdrop {\n    background-color: #d7d7d5; }\n\n.osd .scale-popup button.flat {\n  border-style: none;\n  border-radius: 0; }\n.scale-popup button:hover {\n  background-color: rgba(46, 52, 54, 0.1);\n  border-radius: 0; }\n\n/**********************\n * Window Decorations *\n *********************/\ndecoration {\n  border-radius: 0;\n  border-width: 0px;\n  box-shadow: 0 3px 9px 1px @osd_bg_color, 0 0 0 1px rgba(0, 0, 0, 0.23);\n  margin: 10px; }\n  decoration:backdrop {\n    box-shadow: 0 3px 9px 1px transparent, 0 2px 6px 2px rgba(0, 0, 0, 0.2), 0 0 0 1px rgba(0, 0, 0, 0.18);\n    transition: 200ms ease-out; }\n  .maximized decoration, .fullscreen decoration, .tiled decoration {\n    border-radius: 0; }\n  .popup decoration {\n    box-shadow: none; }\n  .ssd decoration {\n    box-shadow: 0 0 0 1px rgba(0, 0, 0, 0.23); }\n  .csd.popup decoration {\n    border-radius: 0;\n    box-shadow: 0 1px 2px rgba(0, 0, 0, 0.2), 0 0 0 1px rgba(0, 0, 0, 0.13); }\n  tooltip.csd decoration {\n    border-radius: 0;\n    box-shadow: none; }\n  messagedialog.csd decoration {\n    border-radius: 0;\n    box-shadow: 0 1px 2px rgba(0, 0, 0, 0.2), 0 0 0 1px rgba(0, 0, 0, 0.13); }\n  .solid-csd decoration {\n    margin: 0;\n    padding: 4px;\n    background-color: @borders;\n    border: solid 1px @borders;\n    border-radius: 0;\n    box-shadow: inset 0 0 0 3px @theme_bg_color, inset 0 1px rgba(255, 255, 255, 0.8); }\n    .solid-csd decoration:backdrop {\n      box-shadow: inset 0 0 0 3px @theme_bg_color, inset 0 1px rgba(255, 255, 255, 0.8); }\n\n/* Server-side decoration (SSD) */\n.window-frame.ssd {\n    border-radius: 0;\n    box-shadow: 0 0 0 1px rgba(0, 0, 0, 0.18); \n}\n\n.window-frame.ssd,\n.window-frame.ssd:backdrop {\n    background-color: @theme_bg_color;\n}\n\nbutton.titlebutton {\n  text-shadow: 0 1px @txt_shadow;\n  -gtk-icon-shadow: 0 1px @txt_shadow; }\n  button.titlebutton:backdrop {\n    -gtk-icon-shadow: none; }\n\nheaderbar.selection-mode button.titlebutton,\n.titlebar.selection-mode button.titlebutton {\n  text-shadow: 0 -1px rgba(0, 0, 0, 0.54353);\n  -gtk-icon-shadow: 0 -1px rgba(0, 0, 0, 0.54353); }\n  headerbar.selection-mode button.titlebutton:backdrop,\n  .titlebar.selection-mode button.titlebutton:backdrop {\n    -gtk-icon-shadow: none; }\n\n.view:selected:focus, iconview:selected:focus, .view:selected, iconview:selected,\n.view text:selected:focus,\niconview text:selected:focus,\ntextview text:selected:focus,\n.view text:selected,\niconview text:selected,\ntextview text:selected, .view text selection:focus, iconview text selection:focus, .view text selection, iconview text selection,\ntextview text selection:focus,\ntextview text selection, flowbox flowboxchild:selected, spinbutton:not(.vertical) selection:focus, spinbutton:not(.vertical) selection,\nentry selection:focus,\nentry selection, modelbutton.flat:selected, popover.background checkbutton:selected,\npopover.background radiobutton:selected,\n.menuitem.button.flat:selected, treeview.view:selected:focus, treeview.view:selected, row:selected, calendar:selected {\n  background-color: @theme_selected_bg_color; }\n  row:selected label, label:selected, .selection-mode button.titlebutton, .view:selected:focus, iconview:selected:focus, .view:selected, iconview:selected,\n  .view text:selected:focus,\n  iconview text:selected:focus,\n  textview text:selected:focus,\n  .view text:selected,\n  iconview text:selected,\n  textview text:selected, .view text selection:focus, iconview text selection:focus, .view text selection, iconview text selection,\n  textview text selection:focus,\n  textview text selection, flowbox flowboxchild:selected, spinbutton:not(.vertical) selection:focus, spinbutton:not(.vertical) selection,\n  entry selection:focus,\n  entry selection, modelbutton.flat:selected, popover.background checkbutton:selected,\n  popover.background radiobutton:selected,\n  .menuitem.button.flat:selected, treeview.view:selected:focus, treeview.view:selected, row:selected, calendar:selected {\n    color: @theme_selected_fg_color;\n    outline-color: rgba(255, 255, 255, 0.3); }\n    row:selected label:disabled, label:disabled:selected, .selection-mode button.titlebutton:disabled, iconview:disabled:selected:focus, .view:disabled:selected, iconview:disabled:selected,\n    iconview text:disabled:selected:focus,\n    textview text:disabled:selected:focus,\n    .view text:disabled:selected,\n    iconview text:disabled:selected,\n    textview text:disabled:selected, iconview text selection:disabled:focus, .view text selection:disabled, iconview text selection:disabled,\n    textview text selection:disabled, flowbox flowboxchild:disabled:selected, label:disabled selection, spinbutton:not(.vertical) selection:disabled,\n    entry selection:disabled, modelbutton.flat:disabled:selected, popover.background checkbutton:disabled:selected,\n    popover.background radiobutton:disabled:selected,\n    .menuitem.button.flat:disabled:selected, row:disabled:selected, calendar:disabled:selected {\n      color: @theme_selected_bg_color; }\n    row:selected label:backdrop, label:backdrop:selected, .selection-mode button.titlebutton:backdrop, iconview:backdrop:selected:focus, .view:backdrop:selected, iconview:backdrop:selected,\n    iconview text:backdrop:selected:focus,\n    textview text:backdrop:selected:focus,\n    .view text:backdrop:selected,\n    iconview text:backdrop:selected,\n    textview text:backdrop:selected, iconview text selection:backdrop:focus, .view text selection:backdrop, iconview text selection:backdrop,\n    textview text selection:backdrop, flowbox flowboxchild:backdrop:selected, label:backdrop selection, spinbutton:not(.vertical) selection:backdrop,\n    entry selection:backdrop, modelbutton.flat:backdrop:selected, popover.background checkbutton:backdrop:selected,\n    popover.background radiobutton:backdrop:selected,\n    .menuitem.button.flat:backdrop:selected, row:backdrop:selected, calendar:backdrop:selected {\n      color: @theme_unfocused_bg_color; }\n      row:selected label:backdrop:disabled, label:backdrop:disabled:selected, .selection-mode button.titlebutton:backdrop:disabled, .view:backdrop:disabled:selected, iconview:backdrop:disabled:selected,\n      .view text:backdrop:disabled:selected,\n      iconview text:backdrop:disabled:selected,\n      textview text:backdrop:disabled:selected, .view text selection:backdrop:disabled, iconview text selection:backdrop:disabled,\n      textview text selection:backdrop:disabled, flowbox flowboxchild:backdrop:disabled:selected, label:disabled selection:backdrop, label:backdrop selection:disabled, spinbutton:not(.vertical) selection:backdrop:disabled,\n      entry selection:backdrop:disabled, modelbutton.flat:backdrop:disabled:selected, popover.background checkbutton:backdrop:disabled:selected,\n      popover.background radiobutton:backdrop:disabled:selected,\n      .menuitem.button.flat:backdrop:disabled:selected, row:backdrop:disabled:selected, calendar:backdrop:disabled:selected {\n        color: #7fb0e4; }\n\n.monospace {\n  font-family: monospace; }\n\n/**********************\n * Touch Copy & Paste *\n *********************/\ncursor-handle {\n  background-color: transparent;\n  background-image: none;\n  box-shadow: none;\n  border-style: none; }\n  cursor-handle.top:dir(ltr), cursor-handle.bottom:dir(rtl) {\n    -gtk-icon-source: -gtk-scaled(url(\"assets/text-select-start.png\"), url(\"assets/text-select-start@2.png\"));\n    padding-left: 10px; }\n  cursor-handle.bottom:dir(ltr), cursor-handle.top:dir(rtl) {\n    -gtk-icon-source: -gtk-scaled(url(\"assets/text-select-end.png\"), url(\"assets/text-select-end@2.png\"));\n    padding-right: 10px; }\n  cursor-handle.insertion-cursor:dir(ltr), cursor-handle.insertion-cursor:dir(rtl) {\n    -gtk-icon-source: -gtk-scaled(url(\"assets/slider-horz-scale-has-marks-above.png\"), url(\"assets/slider-horz-scale-has-marks-above@2.png\")); }\n  cursor-handle.top:hover:dir(ltr), cursor-handle.bottom:hover:dir(rtl) {\n    -gtk-icon-source: -gtk-scaled(url(\"assets/text-select-start-hover.png\"), url(\"assets/text-select-start-hover@2.png\"));\n    padding-left: 10px; }\n  cursor-handle.bottom:hover:dir(ltr), cursor-handle.top:hover:dir(rtl) {\n    -gtk-icon-source: -gtk-scaled(url(\"assets/text-select-end-hover.png\"), url(\"assets/text-select-end-hover@2.png\"));\n    padding-right: 10px; }\n  cursor-handle.insertion-cursor:hover:dir(ltr), cursor-handle.insertion-cursor:hover:dir(rtl) {\n    -gtk-icon-source: -gtk-scaled(url(\"assets/slider-horz-scale-has-marks-above-hover.png\"), url(\"assets/slider-horz-scale-has-marks-above-hover@2.png\")); }\n  cursor-handle.top:active:dir(ltr), cursor-handle.bottom:active:dir(rtl) {\n    -gtk-icon-source: -gtk-scaled(url(\"assets/text-select-start-active.png\"), url(\"assets/text-select-start-active@2.png\"));\n    padding-left: 10px; }\n  cursor-handle.bottom:active:dir(ltr), cursor-handle.top:active:dir(rtl) {\n    -gtk-icon-source: -gtk-scaled(url(\"assets/text-select-end-active.png\"), url(\"assets/text-select-end-active@2.png\"));\n    padding-right: 10px; }\n  cursor-handle.insertion-cursor:active:dir(ltr), cursor-handle.insertion-cursor:active:dir(rtl) {\n    -gtk-icon-source: -gtk-scaled(url(\"assets/slider-horz-scale-has-marks-above-active.png\"), url(\"assets/slider-horz-scale-has-marks-above-active@2.png\")); }\n\n.context-menu {\n  font: initial; }\n\nbutton.circular {\n  border-radius: 20px;\n  -gtk-outline-radius: 20px; }\n  button.circular label {\n    padding: 0; }\n\n.keycap {\n  min-width: 20px;\n  min-height: 25px;\n  margin-top: 2px;\n  padding-bottom: 3px;\n  padding-left: 6px;\n  padding-right: 6px;\n  color: @theme_fg_color;\n  background-color: @theme_bg_color;\n  border: 1px solid;\n  border-color: #cfcfcd;\n  border-radius: 0;\n  box-shadow: inset 0 -3px #ededec;\n  font-size: smaller; }\n  .keycap:backdrop {\n    background-color: @theme_unfocused_bg_color;\n    color: @insensitive_fg_color;\n    transition: 200ms ease-out; }\n\n*:drop(active):focus,\n*:drop(active) {\n  border-color: @success_color;\n  box-shadow: inset 0 0 0 1px @success_color;\n  caret-color: @success_color; }\n\nstackswitcher button.text-button {\n  min-width: 100px; }\n\nstackswitcher button.circular,\nstackswitcher button.text-button.circular {\n  min-width: 32px;\n  min-height: 32px;\n  padding: 0; }\t\n"
  },
  {
    "path": "frontend/gtkmm/theme/Windows10/gtk-3.20/gtk-contained.css",
    "content": "* {\n  padding: 0;\n  -GtkToolButton-icon-spacing: 4;\n  -GtkTextView-error-underline-color: @error_color;\n  -GtkScrolledWindow-scrollbar-spacing: 0;\n  -GtkToolItemGroup-expander-size: 11;\n  -GtkTreeView-expander-size: 11;\n  -GtkTreeView-horizontal-separator: 4;\n  -GtkScrollbar-has-backward-stepper: true;\n  -GtkScrollbar-has-forward-stepper: true;\n  -GtkWidget-text-handle-width: 20;\n  -GtkWidget-text-handle-height: 24;\n  -GtkDialog-button-spacing: 4;\n  -GtkDialog-action-area-border: 0;\n  outline-color: @outline_color;\n  outline-style: dashed;\n  outline-offset: -3px;\n  outline-width: 0px;\n  -gtk-outline-radius: 0;\n  -gtk-secondary-caret-color: @selected_bg_color; }\n\n/****************\n * floating bar *\n ***************/\n.floating-bar {\n    background-image: image(@theme_bg_color);\n    background-color: transparent;\n    border: 1px solid @borders;\n\n    color: @theme_fg_color;\n    text-shadow: none;\n\n    border-radius: 0;\n    border-width: 1px;\n    border-style: solid;\n    box-shadow: none; }\n\n.floating-bar.right {\n    border-right-width: 0;\n    border-top-right-radius: 0;\n    border-bottom-right-radius: 0; }\n\n.floating-bar.bottom {\n    border-bottom-width: 0;\n    border-bottom-right-radius: 0;\n    border-bottom-left-radius: 0; }\n\n.floating-bar.left {\n    border-left-width: 0;\n    border-top-left-radius: 0;\n    border-bottom-left-radius: 0; }\n\n.floating-bar:backdrop {\n    border-color: transparent;\n    color: @theme_fg_color;\n    background-image: image(@theme_bg_color);\n    box-shadow: none; }\n\n.floating-bar .button {\n    border-color: @borders;\n    background-image: none;\n    background-color: @theme_bg_color;\n    border-style: none;\n    box-shadow: none; }\n\n\n/***************\n * Base States *\n ***************/\n.background {\n  color: @theme_fg_color;\n  background-color: @theme_bg_color; }\n  .background:backdrop {\n    color: @theme_unfocused_fg_color;\n    background-color: @theme_bg_color;\n    text-shadow: none;\n    -gtk-icon-shadow: none; }\n\n/*\n   These wildcard seems unavoidable, need to investigate.\n   Wildcards are bad and troublesome, use them with care,\n   or better, just don't.\n   Everytime a wildcard is used a kitten dies, painfully.\n*/\n*:disabled {\n  -gtk-icon-effect: dim; }\n\n.gtkstyle-fallback {\n  color: @theme_fg_color;\n  background-color: @theme_bg_color; }\n  .gtkstyle-fallback:hover {\n    color: @theme_fg_color;\n    background-color: @theme_bg_color; }\n  .gtkstyle-fallback:active {\n    color: @theme_fg_color;\n    background-color: #cfcfcd; }\n  .gtkstyle-fallback:disabled {\n    color: @insensitive_fg_color;\n    background-color: @insensitive_bg_color; }\n  .gtkstyle-fallback:selected {\n    color: @theme_selected_fg_color;\n    background-color: @theme_selected_bg_color; }\n\n.view, iconview,\n.view text,\niconview text,\ntextview text {\n  color: @theme_fg_color;\n  background-color: @theme_bg_color; }\n  .view:backdrop, iconview:backdrop,\n  .view text:backdrop,\n  iconview text:backdrop,\n  textview text:backdrop {\n    color: @theme_unfocused_fg_color;\n    background-color: @theme_unfocused_bg_color; }\n  .view:selected:focus, iconview:selected:focus, .view:selected, iconview:selected,\n  .view text:selected:focus,\n  iconview text:selected:focus,\n  textview text:selected:focus,\n  .view text:selected,\n  iconview text:selected,\n  textview text:selected {\n    border-radius: 0; }\n\ntextview border {\n  background-color: shade(@theme_bg_color, 0.95);\n  background-image: image(rgba(0, 0, 0, 0.2));\n  background-repeat: no-repeat; }\n  textview border:backdrop {\n    background-color: shade(@theme_bg_color, 0.95); }\n  textview border.bottom {\n    background-size: 100% 1px;\n    background-position: top; }\n  textview border.top {\n    background-size: 100% 1px;\n    background-position: bottom; }\n  textview border.left {\n    background-size: 1px 100%;\n    background-position: right; }\n  textview border.right {\n    background-size: 1px 100%;\n    background-position: left; }\n\n.rubberband,\nrubberband,\nflowbox rubberband,\ntreeview.view rubberband,\n.content-view rubberband {\n  border: 1px solid @borders;\n  background-color: rgba(42, 118, 198, 0.2); }\n\nflowbox flowboxchild {\n  padding: 3px;\n  border-radius: 0; }\n  flowbox flowboxchild:selected {\n    outline-offset: -2px; }\n\nlabel.separator {\n  color: @theme_fg_color; }\n  label.separator:backdrop {\n    color: @insensitive_fg_color; }\nlabel selection {\n  background-color: @theme_selected_bg_color;\n  color: @theme_selected_fg_color; }\nlabel:disabled {\n  color: @insensitive_fg_color; }\n  label:disabled:backdrop {\n    color: shade(@theme_unfocused_fg_color, 1.1); }\nlabel:backdrop {\n  color: @insensitive_fg_color; }\n\n.dim-label, label.separator, .titlebar:not(headerbar) .subtitle,\nheaderbar .subtitle {\n  opacity: 0.55;\n  text-shadow: none; }\n\nassistant .sidebar {\n  background-color: @theme_bg_color;\n  border: none; }\n  assistant .sidebar:backdrop {\n    background-color: @theme_unfocused_bg_color;\n    border-color: transparent; }\nassistant.csd .sidebar {\n  border-top-style: none; }\nassistant .sidebar label {\n  padding: 6px 12px; }\nassistant .sidebar label.highlight {\n  background-color: shade(@theme_fg_color, 0.85); }\n\n.csd popover.background.touch-selection, .csd popover.background.magnifier, popover.background.touch-selection, popover.background.magnifier, .csd popover.background.osd, popover.background.osd, .app-notification,\n.app-notification.frame, .osd .scale-popup,\n.osd {\n  color: @osd_fg_color;\n  border: none;\n  background-color: @osd_bg_color;\n  background-clip: padding-box;\n  outline-color: @osd_outline;\n  text-shadow: 0 1px @osd_txt_shadow;\n  -gtk-icon-shadow: 0 1px @osd_txt_shadow; }\n  popover.background.touch-selection:backdrop, popover.background.magnifier:backdrop, popover.background.osd:backdrop, .app-notification:backdrop, .osd .scale-popup:backdrop,\n  .osd:backdrop {\n    text-shadow: none;\n    -gtk-icon-shadow: none; }\n\n/* nemo icon view entry */\n.nemo-window .nemo-window-pane widget.entry {\n    border: 1px solid;\n    border-radius: 3px;\n    color: @theme_fg_color;\n    border-color: @theme_selected_bg_color;\n    background-color: @theme_base_color; }\n  \n.nemo-window .nemo-window-pane widget.entry:selected:focus, .nemo-window .nemo-window-pane widget.entry:selected {\n    background-color: @theme_selected_bg_color;\n    color: @theme_selected_fg_color; }\n\n/*********************\n * Spinner Animation *\n *********************/\n@keyframes spin {\n  to {\n    -gtk-icon-transform: rotate(1turn); } }\nspinner {\n  background: none;\n  opacity: 0;\n  -gtk-icon-source: -gtk-icontheme(\"process-working-symbolic\"); }\n  spinner:checked {\n    opacity: 1;\n    animation: spin 1s linear infinite; }\n    spinner:checked:disabled {\n      opacity: 0.5; }\n\n/****************\n * Text Entries *\n ****************/\nspinbutton:not(.vertical),\nentry {\n  min-height: 32px;\n  padding-left: 8px;\n  padding-right: 8px;\n  border: 1px solid;\n  border-radius: 0;\n  transition: all 200ms cubic-bezier(0.25, 0.46, 0.45, 0.94);\n  color:@theme_fg_color;\n  border-color: shade(@theme_bg_color, 0.85);\n  background-color: @theme_bg_color;\n  box-shadow: none; }\n  spinbutton:not(.vertical) image.left,\n  entry image.left {\n    padding-left: 0;\n    padding-right: 6px; }\n  spinbutton:not(.vertical) image.right,\n  entry image.right {\n    padding-left: 6px;\n    padding-right: 0; }\n\n  spinbutton:not(.vertical) undershoot.left,\n  entry undershoot.left {\n    background-color: transparent;\n    background-image: linear-gradient(to top, rgba(255, 255, 255, 0.2) 50%, rgba(0, 0, 0, 0.2) 50%);\n    padding-left: 1px;\n    background-size: 1px 10px;\n    background-repeat: repeat-y;\n    background-origin: content-box;\n    background-position: left center;\n    border: none;\n    box-shadow: none; }\n  spinbutton:not(.vertical) undershoot.right,\n  entry undershoot.right {\n    background-color: transparent;\n    background-image: linear-gradient(to top, rgba(255, 255, 255, 0.2) 50%, rgba(0, 0, 0, 0.2) 50%);\n    padding-right: 1px;\n    background-size: 1px 10px;\n    background-repeat: repeat-y;\n    background-origin: content-box;\n    background-position: right center;\n    border: none;\n    box-shadow: none; }\n  spinbutton.flat:focus:not(.vertical), spinbutton.flat:not(.vertical),\n  entry.flat:focus,\n  entry.flat {\n    min-height: 0;\n    padding: 2px;\n    background-color: transparent;\n    border-color: transparent;\n    border-radius: 0; }\n  spinbutton:focus:not(.vertical),\n  entry:focus {\n    box-shadow: none;\n    border-color: shade(@theme_selected_bg_color, 0.6); }\n  spinbutton:disabled:not(.vertical),\n  entry:disabled {\n    color: @insensitive_fg_color;\n    border-color: shade(@borders, 1.1);\n    background-color: @insensitive_bg_color;\n    box-shadow: none; }\n  spinbutton:backdrop:not(.vertical),\n  entry:backdrop {\n    color: @theme_unfocused_fg_color;\n    border-color: shade(@borders, 0.95);\n    background-color: @theme_unfocused_bg_color;\n    box-shadow: none;\n    transition: 200ms ease-out; }\n  spinbutton:backdrop:disabled:not(.vertical),\n  entry:backdrop:disabled {\n    color: shade(@theme_unfocused_fg_color, 1.1);\n    border-color: shade(@borders, 0.95);\n    background-color: @insensitive_bg_color;\n    box-shadow: none; }\n  spinbutton.error:not(.vertical),\n  entry.error {\n    color: @error_color;\n    border-color: @error_color; }\n    spinbutton.error:focus:not(.vertical),\n    entry.error:focus {\n      box-shadow: none;\n      border-color: @error_color; }\n    spinbutton.error:selected:focus:not(.vertical), spinbutton.error:selected:not(.vertical),\n    entry.error:selected:focus,\n    entry.error:selected {\n      background-color: @error_color; }\n  spinbutton.warning:not(.vertical),\n  entry.warning {\n    color: @warning_color;\n    border-color: @warning_color; }\n    spinbutton.warning:focus:not(.vertical),\n    entry.warning:focus {\n      box-shadow: none;\n      border-color: @warning_color; }\n    spinbutton.warning:selected:focus:not(.vertical), spinbutton.warning:selected:not(.vertical),\n    entry.warning:selected:focus,\n    entry.warning:selected {\n      background-color: @warning_color; }\n  spinbutton:not(.vertical) image,\n  entry image {\n    color: @theme_fg_color; }\n    spinbutton:not(.vertical) image:hover,\n    entry image:hover {\n      color: shade(@theme_fg_color, 1.05); }\n    spinbutton:not(.vertical) image:active,\n    entry image:active {\n      color: @theme_selected_bg_color; }\n    spinbutton:not(.vertical) image:backdrop,\n    entry image:backdrop {\n      color: shade(@theme_bg_color, 0.85); }\n  spinbutton:drop(active):focus:not(.vertical), spinbutton:drop(active):not(.vertical),\n  entry:drop(active):focus,\n  entry:drop(active) {\n    border-color: @success_color;\n    box-shadow: none; }\n  .osd spinbutton:not(.vertical), .osd\n  entry {\n    color: @osd_fg_color;\n    border-color: @osd_borders;\n    background-color: @osd_bg_color;\n    background-clip: padding-box;\n    box-shadow: none;\n    text-shadow: 0 1px @osd_txt_shadow;\n    -gtk-icon-shadow: 0 1px @osd_txt_shadow; }\n    .osd spinbutton:focus:not(.vertical), .osd\n    entry:focus {\n      color: @osd_fg_color;\n      border-color: @theme_selected_bg_color;\n      background-color: @osd_bg_color;\n      background-clip: padding-box;\n      box-shadow: inset 0 0 0 1px @theme_selected_bg_color;\n      text-shadow: 0 1px @osd_txt_shadow;\n      -gtk-icon-shadow: 0 1px @osd_txt_shadow; }\n    .osd spinbutton:backdrop:not(.vertical), .osd\n    entry:backdrop {\n      color: @osd_fg_color;\n      border-color: @osd_borders;\n      background-color: @osd_bg_color;\n      background-clip: padding-box;\n      box-shadow: none;\n      text-shadow: none;\n      -gtk-icon-shadow: none; }\n    .osd spinbutton:disabled:not(.vertical), .osd\n    entry:disabled {\n      color: shade(@osd_fg_color, 0.85);\n      border-color: @osd_borders;\n      background-color: shade(@osd_bg_color, 0.95);\n      background-clip: padding-box;\n      box-shadow: none;\n      text-shadow: none;\n      -gtk-icon-shadow: none; }\nspinbutton:not(.vertical) progress,\nentry progress {\n  margin: 2px -6px;\n  background-color: transparent;\n  background-image: none;\n  border-radius: 0;\n  border-width: 0 0 2px;\n  border-color: shade(@theme_selected_bg_color, 0.6);\n  border-style: solid;\n  box-shadow: none; }\n  spinbutton:not(.vertical) progress:backdrop,\n  entry progress:backdrop {\n    background-color: transparent; }\n.linked:not(.vertical) > spinbutton:focus:not(.vertical) + spinbutton:not(.vertical), .linked:not(.vertical) > spinbutton:focus:not(.vertical) + button, .linked:not(.vertical) > spinbutton:focus:not(.vertical) + combobox > box > button.combo, .linked:not(.vertical) >\nentry:focus + spinbutton:not(.vertical), .linked:not(.vertical) >\nentry:focus + button, .linked:not(.vertical) >\nentry:focus + combobox > box > button.combo, .linked:not(.vertical) > spinbutton:focus:not(.vertical) +\nentry, .linked:not(.vertical) >\nentry:focus +\nentry {\n  border-left-color: @theme_selected_bg_color; }\n.linked:not(.vertical) > spinbutton:drop(active):not(.vertical) + spinbutton:not(.vertical), .linked:not(.vertical) > spinbutton:drop(active):not(.vertical) + button, .linked:not(.vertical) > spinbutton:drop(active):not(.vertical) + combobox > box > button.combo, .linked:not(.vertical) >\nentry:drop(active) + spinbutton:not(.vertical), .linked:not(.vertical) >\nentry:drop(active) + button, .linked:not(.vertical) >\nentry:drop(active) + combobox > box > button.combo, .linked:not(.vertical) > spinbutton:drop(active):not(.vertical) +\nentry, .linked:not(.vertical) >\nentry:drop(active) +\nentry {\n  border-left-color: @success_color; }\n.linked.vertical > spinbutton:not(:disabled):not(.vertical) + entry:not(:disabled), .linked.vertical > spinbutton:not(:disabled):not(.vertical) + spinbutton:not(:disabled):not(.vertical), .linked.vertical >\nentry:not(:disabled) + entry:not(:disabled), .linked.vertical >\nentry:not(:disabled) + spinbutton:not(:disabled):not(.vertical) {\n  border-top-color: @borders; }\n  .linked.vertical > spinbutton:not(:disabled):not(.vertical) + entry:not(:disabled):backdrop, .linked.vertical > spinbutton:not(:disabled):not(.vertical) + spinbutton:not(:disabled):backdrop:not(.vertical), .linked.vertical >\n  entry:not(:disabled) + entry:not(:disabled):backdrop, .linked.vertical >\n  entry:not(:disabled) + spinbutton:not(:disabled):backdrop:not(.vertical) {\n    border-top-color: @borders; }\n.linked.vertical > spinbutton:disabled:not(.vertical) + spinbutton:disabled:not(.vertical), .linked.vertical > spinbutton:disabled:not(.vertical) + entry:disabled, .linked.vertical >\nentry:disabled + spinbutton:disabled:not(.vertical), .linked.vertical >\nentry:disabled + entry:disabled {\n  border-top-color: @borders; }\n.linked.vertical > spinbutton:not(.vertical) + spinbutton:focus:not(:only-child):not(.vertical),\n.linked.vertical > spinbutton:not(.vertical) + entry:focus:not(:only-child), .linked.vertical >\nentry + spinbutton:focus:not(:only-child):not(.vertical),\n.linked.vertical >\nentry + entry:focus:not(:only-child) {\n  border-top-color: shade(@theme_selected_bg_color, 0.6); }\n.linked.vertical > spinbutton:not(.vertical) + spinbutton:drop(active):not(:only-child):not(.vertical),\n.linked.vertical > spinbutton:not(.vertical) + entry:drop(active):not(:only-child), .linked.vertical >\nentry + spinbutton:drop(active):not(:only-child):not(.vertical),\n.linked.vertical >\nentry + entry:drop(active):not(:only-child) {\n  border-top-color: @success_color; }\n.linked.vertical > spinbutton:focus:not(:only-child):not(.vertical) + spinbutton:not(.vertical),\n.linked.vertical > spinbutton:focus:not(:only-child):not(.vertical) + entry,\n.linked.vertical > spinbutton:focus:not(:only-child):not(.vertical) + button,\n.linked.vertical > spinbutton:focus:not(:only-child):not(.vertical) + combobox > box > button.combo, .linked.vertical >\nentry:focus:not(:only-child) + spinbutton:not(.vertical),\n.linked.vertical >\nentry:focus:not(:only-child) + entry,\n.linked.vertical >\nentry:focus:not(:only-child) + button,\n.linked.vertical >\nentry:focus:not(:only-child) + combobox > box > button.combo {\n  border-top-color: @theme_selected_bg_color; }\n.linked.vertical > spinbutton:drop(active):not(:only-child):not(.vertical) + spinbutton:not(.vertical),\n.linked.vertical > spinbutton:drop(active):not(:only-child):not(.vertical) + entry,\n.linked.vertical > spinbutton:drop(active):not(:only-child):not(.vertical) + button,\n.linked.vertical > spinbutton:drop(active):not(:only-child):not(.vertical) + combobox > box > button.combo, .linked.vertical >\nentry:drop(active):not(:only-child) + spinbutton:not(.vertical),\n.linked.vertical >\nentry:drop(active):not(:only-child) + entry,\n.linked.vertical >\nentry:drop(active):not(:only-child) + button,\n.linked.vertical >\nentry:drop(active):not(:only-child) + combobox > box > button.combo {\n  border-top-color: @success_color; }\n\ntreeview acceleditor > label {\n  background-color: @theme_selected_bg_color; }\n\ntreeview entry:focus:dir(rtl), treeview entry:focus:dir(ltr) {\n  background-color: @theme_bg_color;\n  transition-property: color, background; }\ntreeview entry.flat, treeview entry {\n  border-radius: 0;\n  background-image: none;\n  background-color: @theme_bg_color; }\n  treeview entry.flat:focus, treeview entry:focus {\n    border-color: @theme_selected_bg_color; }\n\n/***********\n * Buttons *\n ***********/\n@keyframes needs_attention {\n  from {\n    background-image: -gtk-gradient(radial, center center, 0, center center, 0.01, to(@theme_selected_bg_color), to(transparent)); }\n  to {\n    background-image: -gtk-gradient(radial, center center, 0, center center, 0.5, to(@theme_selected_bg_color), to(transparent)); } }\n\n/* Header bar & toolbar buttons */ \n\nnotebook > header > tabs > arrow, button.titlebutton {\n  min-height: 24px;\n  min-width: 16px;\n  padding: 4px 8px;\n  border: none;\n  border-radius: 0;\n  transition: all 200ms cubic-bezier(0.25, 0.46, 0.45, 0.94);\n  color: @theme_fg_color;\n  outline-color: @outline_color;\n  border-color: @borders;\n  background-image: linear-gradient(to bottom, @theme_bg_color, @theme_bg_color);\n  text-shadow: 0 1px @txt_shadow;\n  -gtk-icon-shadow: 0 1px @txt_shadow;\n  box-shadow: none; }\n  notebook > header > tabs > arrow, button.sidebar-button, button.titlebutton,\n  button.flat {\n    border-color: transparent;\n    background-color: transparent;\n    background-image: none;\n    box-shadow: inset 0 1px transparent;\n    text-shadow: none;\n    -gtk-icon-shadow: none;\n    transition: none; }\n    notebook > header > tabs > arrow:hover, button.sidebar-button:hover, button.titlebutton:hover,\n    button.flat:hover {\n      transition: all 200ms cubic-bezier(0.25, 0.46, 0.45, 0.94);\n      transition-duration: 500ms; }\n      notebook > header > tabs > arrow:hover:active, button.sidebar-button:hover:active, button.titlebutton:hover:active,\n      button.flat:hover:active {\n        transition: all 200ms cubic-bezier(0.25, 0.46, 0.45, 0.94); }\n  notebook > header > tabs > arrow:hover, button.titlebutton:hover {\n    color: @theme_fg_color;\n    outline-color: @outline_color;\n    border-color: shade(@theme_selected_bg_color, 0.7);\n    background-image: linear-gradient(to bottom, @theme_selected_bg_color, @theme_selected_bg_color);\n    text-shadow: none;\n    -gtk-icon-shadow: none;\n    box-shadow: none;\n    -gtk-icon-effect: highlight; }\n  notebook > header > tabs > arrow:active, button.titlebutton:active, notebook > header > tabs > arrow:checked, button.titlebutton:checked {\n    color: @theme_fg_color;\n    outline-color: @outline_color;\n    border-color: shade(@theme_selected_bg_color, 0.7);\n    background-image: none;\n    background-color: shade(@theme_selected_bg_color, 0.9);\n    box-shadow: none;\n    text-shadow: none;\n    -gtk-icon-shadow: none;\n    transition-duration: 50ms; }\n\n  notebook > header > tabs > arrow:backdrop, button.sidebar-button:backdrop, button.titlebutton:backdrop, notebook > header > tabs > arrow:backdrop, button.titlebutton:backdrop,\n  button:backdrop.flat {\n    border-color: shade(@borders, 0.95);\n    background-color: transparent;\n    background-image: image(@theme_bg_color);\n    text-shadow: none;\n    -gtk-icon-shadow: none;\n    box-shadow: inset 0 1px transparent;\n    transition: 200ms ease-out;\n    -gtk-icon-effect: none; }\n    notebook > header > tabs > arrow:backdrop label, button.sidebar-button:backdrop label, button.titlebutton:backdrop label, notebook > header > tabs > arrow:backdrop, button.sidebar-button:backdrop, button.titlebutton:backdrop, notebook > header > tabs > arrow:backdrop label, button.titlebutton:backdrop label, notebook > header > tabs > arrow:backdrop, button.titlebutton:backdrop,\n    button:backdrop.flat label,\n    button:backdrop.flat {\n      color: @insensitive_fg_color; }\n    notebook > header > tabs > arrow:backdrop:active, button.sidebar-button:backdrop:active, button.titlebutton:backdrop:active, notebook > header > tabs > arrow:backdrop:checked, button.sidebar-button:backdrop:checked, button.titlebutton:backdrop:checked, notebook > header > tabs > arrow:backdrop:active, button.titlebutton:backdrop:active, notebook > header > tabs > arrow:backdrop:checked, button.titlebutton:backdrop:checked,\n    button:backdrop.flat:active,\n    button:backdrop.flat:checked {\n      border-color: shade(@borders, 0.95);\n      background-color: shade(@theme_bg_color, 0.95);\n      background-image: none;\n      box-shadow: inset 0 1px transparent; }\n      notebook > header > tabs > arrow:backdrop:active label, button.sidebar-button:backdrop:active label, button.titlebutton:backdrop:active label, notebook > header > tabs > arrow:backdrop:active, button.sidebar-button:backdrop:active, button.titlebutton:backdrop:active, notebook > header > tabs > arrow:backdrop:checked label, button.sidebar-button:backdrop:checked label, button.titlebutton:backdrop:checked label, notebook > header > tabs > arrow:backdrop:checked, button.sidebar-button:backdrop:checked, button.titlebutton:backdrop:checked, notebook > header > tabs > arrow:backdrop:active label, button.titlebutton:backdrop:active label, notebook > header > tabs > arrow:backdrop:active, button.titlebutton:backdrop:active, notebook > header > tabs > arrow:backdrop:checked label, button.titlebutton:backdrop:checked label, notebook > header > tabs > arrow:backdrop:checked, button.titlebutton:backdrop:checked,\n      button:backdrop.flat:active label,\n      button:backdrop.flat:active,\n      button:backdrop.flat:checked label,\n      button:backdrop.flat:checked {\n        color: @insensitive_fg_color; }\n    notebook > header > tabs > arrow:backdrop:disabled, button.sidebar-button:backdrop:disabled, button.titlebutton:backdrop:disabled, notebook > header > tabs > arrow:backdrop:disabled, button.titlebutton:backdrop:disabled,\n    button:backdrop.flat:disabled {\n      border-color: shade(@borders, 0.95);\n      background-color: @insensitive_bg_color;\n      background-image: none;\n      text-shadow: none;\n      -gtk-icon-shadow: none;\n      box-shadow: inset 0 1px transparent; }\n      notebook > header > tabs > arrow:backdrop:disabled label, button.sidebar-button:backdrop:disabled label, button.titlebutton:backdrop:disabled label, notebook > header > tabs > arrow:backdrop:disabled, button.sidebar-button:backdrop:disabled, button.titlebutton:backdrop:disabled, notebook > header > tabs > arrow:backdrop:disabled label, button.titlebutton:backdrop:disabled label, notebook > header > tabs > arrow:backdrop:disabled, button.titlebutton:backdrop:disabled,\n      button:backdrop.flat:disabled label,\n      button:backdrop.flat:disabled {\n        color: shade(@theme_unfocused_fg_color, 1.1); }\n      notebook > header > tabs > arrow:backdrop:disabled:active, button.sidebar-button:backdrop:disabled:active, button.titlebutton:backdrop:disabled:active, notebook > header > tabs > arrow:backdrop:disabled:checked, button.sidebar-button:backdrop:disabled:checked, button.titlebutton:backdrop:disabled:checked, notebook > header > tabs > arrow:backdrop:disabled:active, button.titlebutton:backdrop:disabled:active, notebook > header > tabs > arrow:backdrop:disabled:checked, button.titlebutton:backdrop:disabled:checked,\n      button:backdrop.flat:disabled:active,\n      button:backdrop.flat:disabled:checked {\n        border-color: shade(@borders, 0.95);\n        background-color: shade(@theme_bg_color, 0.95);\n        background-image: none;\n        box-shadow: inset 0 1px transparent; }\n        notebook > header > tabs > arrow:backdrop:disabled:active label, button.sidebar-button:backdrop:disabled:active label, button.titlebutton:backdrop:disabled:active label, notebook > header > tabs > arrow:backdrop:disabled:checked label, button.sidebar-button:backdrop:disabled:checked label, button.titlebutton:backdrop:disabled:checked label, notebook > header > tabs > arrow:backdrop:disabled:active label, button.titlebutton:backdrop:disabled:active label, notebook > header > tabs > arrow:backdrop:disabled:checked label, button.titlebutton:backdrop:disabled:checked label,\n        button:backdrop.flat:disabled:active label,\n        button:backdrop.flat:disabled:checked label {\n          color: shade(@theme_unfocused_fg_color, 1.1); }\n  notebook > header > tabs > arrow:backdrop, button.sidebar-button:backdrop, button.titlebutton:backdrop, notebook > header > tabs > arrow:disabled, button.sidebar-button:disabled, button.titlebutton:disabled, notebook > header > tabs > arrow:backdrop:disabled, button.sidebar-button:backdrop:disabled, button.titlebutton:backdrop:disabled,\n  button.flat:backdrop,\n  button.flat:disabled,\n  button.flat:backdrop:disabled {\n    border-color: transparent;\n    background-color: transparent;\n    background-image: none;\n    box-shadow: inset 0 1px transparent;\n    text-shadow: none;\n    -gtk-icon-shadow: none; }\n  notebook > header > tabs > arrow:disabled, button.titlebutton:disabled {\n    border-color: @borders;\n    background-color: @insensitive_bg_color;\n    background-image: none;\n    text-shadow: none;\n    -gtk-icon-shadow: none;\n    box-shadow: inset 0 1px transparent; }\n    notebook > header > tabs > arrow:disabled label, button.titlebutton:disabled label, notebook > header > tabs > arrow:disabled, button.titlebutton:disabled {\n      color: @insensitive_fg_color; }\n    notebook > header > tabs > arrow:disabled:active, button.titlebutton:disabled:active, notebook > header > tabs > arrow:disabled:checked, button.titlebutton:disabled:checked {\n      border-color: @borders;\n      background-color: shade(@theme_bg_color, 0.95);\n      background-image: none;\n      box-shadow: inset 0 1px transparent; }\n      notebook > header > tabs > arrow:disabled:active label, button.titlebutton:disabled:active label, notebook > header > tabs > arrow:disabled:active, button.titlebutton:disabled:active, notebook > header > tabs > arrow:disabled:checked label, button.titlebutton:disabled:checked label, notebook > header > tabs > arrow:disabled:checked, button.titlebutton:disabled:checked {\n        color: @insensitive_fg_color; }\n\n/* Regular buttons */\n\nbutton {\n  min-height: 24px;\n  min-width: 16px;\n  padding: 4px 8px;\n  border: 1px solid;\n  border-radius: 0;\n  transition: all 200ms cubic-bezier(0.25, 0.46, 0.45, 0.94);\n  color: @theme_fg_color;\n  outline-color: @outline_color;\n  border-color: @borders;\n  background-image: linear-gradient(to bottom, @theme_bg_color, @theme_bg_color);\n  text-shadow: 0 0 @txt_shadow;\n  -gtk-icon-shadow: 0 0 @txt_shadow;\n  box-shadow: none; }\n\nbutton:hover {\n    color: @theme_fg_color;\n    outline-color: @outline_color;\n    border-color: shade(@theme_selected_bg_color, 0.8);\n    background-image: linear-gradient(to bottom, @theme_selected_bg_color, @theme_selected_bg_color);\n    text-shadow: none;\n    -gtk-icon-shadow: none;\n    box-shadow: none;\n    -gtk-icon-effect: highlight; }\n\nbutton:active, button:checked {\n    color: @theme_fg_color;\n    outline-color: @outline_color;\n    border-color: shade(@theme_selected_bg_color, 0.6);\n    background-image: none;\n    background-color: shade(@theme_selected_bg_color, 0.9);\n    box-shadow: none;\n    text-shadow: none;\n    -gtk-icon-shadow: none;\n    transition-duration: 50ms; }\n\nbutton:backdrop {\n    border-color: @borders;\n    background-color: transparent;\n    background-image: image(@theme_bg_color);\n    text-shadow: none;\n    -gtk-icon-shadow: none;\n    box-shadow: inset 0 0 transparent;\n    transition: 200ms ease-out;\n    -gtk-icon-effect: none; }\n\nbutton:backdrop label, button:backdrop {\n      color: @insensitive_fg_color; }\n\nbutton:backdrop:active, button:backdrop:checked {\n      border-color: @borders;\n      background-color: shade(@theme_unfocused_bg_color, 0.95);\n      background-image: none;\n      box-shadow: inset 0 0 transparent; }\n\n\nbutton:backdrop:active label, button:backdrop:active, button:backdrop:checked label,  button:backdrop:checked {\n        color: @insensitive_fg_color; }\n\nbutton:backdrop:disabled {\n      border-color: shade(@borders, 0.95);\n      background-color: @insensitive_bg_color;\n      background-image: none;\n      text-shadow: none;\n      -gtk-icon-shadow: none;\n      box-shadow: inset 0 0 transparent; }\n\n      button:backdrop:disabled label,\n      button:backdrop:disabled {\n        color: shade(@theme_unfocused_fg_color, 1.1); }\n\nbutton:backdrop:disabled:active, button:backdrop:disabled:checked {\n        border-color: shade(@borders, 0.95);\n        background-color: shade(@theme_bg_color, 0.95);\n        background-image: none;\n        box-shadow: inset 0 1px transparent; }\n\nbutton:backdrop:disabled:active label,  button:backdrop:disabled:checked label {\n          color: shade(@theme_unfocused_fg_color, 1.1); }\n\nbutton:disabled {\n    border-color: @borders;\n    background-color: @insensitive_bg_color;\n    background-image: none;\n    text-shadow: none;\n    -gtk-icon-shadow: none;\n    box-shadow: inset 0 1px transparent; }\n\nbutton:disabled label,\n    button:disabled {\n      color: @insensitive_fg_color; }\n\nbutton:disabled:active,\n    button:disabled:checked {\n      border-color: @borders;\n      background-color: shade(@theme_bg_color, 0.95);\n      background-image: none;\n      box-shadow: inset 0 1px transparent; }\n\nbutton:disabled:active label, button:disabled:active, button:disabled:checked label,  button:disabled:checked {\n        color: @insensitive_fg_color; }\n\n\n  notebook > header > tabs > arrow.image-button, button.image-button.titlebutton,\n  button.image-button {\n    min-width: 24px;\n    padding-left: 4px;\n    padding-right: 4px; }\n  notebook > header > tabs > arrow.text-button, button.text-button.titlebutton,\n  button.text-button {\n    padding-left: 16px;\n    padding-right: 16px; }\n  notebook > header > tabs > arrow.text-button.image-button, button.text-button.image-button.titlebutton,\n  button.text-button.image-button {\n    padding-left: 8px;\n    padding-right: 8px; }\n    notebook > header > tabs > arrow.text-button.image-button label, button.text-button.image-button.titlebutton label,\n    button.text-button.image-button label {\n      padding-left: 8px;\n      padding-right: 8px; }\n  combobox:drop(active) button.combo, notebook > header > tabs > arrow:drop(active), button.titlebutton:drop(active),\n  button:drop(active) {\n    color: @success_color;\n    border-color: @success_color;\n    box-shadow: inset 0 0 0 1px @success_color; }\nrow:selected\nbutton {\n  border-color: shade(@theme_selected_bg_color, 0.6); }\n  row:selected button.sidebar-button:not(:active):not(:checked):not(:hover):not(disabled), row:selected\n  button.flat:not(:active):not(:checked):not(:hover):not(disabled) {\n    color: @theme_selected_fg_color;\n    border-color: transparent; }\n    row:selected button.sidebar-button:not(:active):not(:checked):not(:hover):not(disabled):backdrop, row:selected\n    button.flat:not(:active):not(:checked):not(:hover):not(disabled):backdrop {\n      color: @theme_unfocused_bg_color; }\n\n/* OSD buttons */\n\nbutton.osd {\n  min-width: 24px;\n  min-height: 32px;\n  color: @osd_fg_color;\n  border-radius: 0;\n  outline-color: @osd_outline;\n  color: @osd_fg_color;\n  border-color: @osd_borders;\n  background-color: transparent;\n  background-image: image(@osd_bg_color);\n  background-clip: padding-box;\n  box-shadow: inset 0 1px @osd_txt_shadow;\n  text-shadow: 0 1px @osd_txt_shadow;\n  -gtk-icon-shadow: 0 1px @osd_txt_shadow;\n  outline-color: @osd_outline;\n  border: none;\n  box-shadow: none; }\n  button.osd.image-button {\n    min-width: 32px; }\n  button.osd:hover {\n    color: @osd_fg_color;\n    border-color: @osd_borders;\n    background-color: transparent;\n    background-image: image(shade(@osd_bg_color, 1.05));\n    background-clip: padding-box;\n    box-shadow: inset 0 1px @osd_txt_shadow;\n    text-shadow: 0 1px @osd_txt_shadow;\n    -gtk-icon-shadow: 0 1px @osd_txt_shadow;\n    outline-color: @osd_outline;\n    border: none;\n    box-shadow: none; }\n  button.osd:active,\n  button.osd:checked {\n    color: @osd_fg_color;\n    border-color: @osd_borders;\n    background-color: transparent;\n    background-image: image(@osd_borders);\n    background-clip: padding-box;\n    box-shadow: none;\n    text-shadow: none;\n    -gtk-icon-shadow: none;\n    outline-color: @osd_outline;\n    border: none;\n    box-shadow: none; }\n  button.osd:disabled:backdrop,\n  button.osd:disabled {\n    color: shade(@osd_fg_color, 0.85);\n    border-color: @osd_borders;\n    background-color: transparent;\n    background-image: image(shade(@osd_bg_color, 0.95));\n    background-clip: padding-box;\n    box-shadow: none;\n    text-shadow: none;\n    -gtk-icon-shadow: none;\n    border: none; }\n  button.osd:backdrop {\n    color: @theme_unfocused_fg_color;\n    border-color: @osd_borders;\n    background-color: transparent;\n    background-image: image(@osd_bg_color);\n    background-clip: padding-box;\n    box-shadow: none;\n    text-shadow: none;\n    -gtk-icon-shadow: none;\n    border: none; }\n.csd popover.background.touch-selection button, .csd popover.background.magnifier button, popover.background.touch-selection button, popover.background.magnifier button, .app-notification button,\n.app-notification.frame button, .osd\nbutton {\n  color: @osd_fg_color;\n  border-color: @osd_borders;\n  background-color: transparent;\n  background-image: image(@osd_bg_color);\n  background-clip: padding-box;\n  box-shadow: inset 0 1px @osd_txt_shadow;\n  text-shadow: 0 1px @txt_shadow;\n  -gtk-icon-shadow: 0 1px @osd_txt_shadow;\n  outline-color: @osd_outline; }\n  popover.background.touch-selection button:hover, popover.background.magnifier button:hover, .app-notification button:hover, .osd\n  button:hover {\n    color: @osd_fg_color;\n    border-color: @osd_borders;\n    background-color: transparent;\n    background-image: image(shade(@osd_bg_color, 1.05));\n    background-clip: padding-box;\n    box-shadow: inset 0 1px @osd_txt_shadow;\n    text-shadow: 0 1px @osd_txt_shadow;\n    -gtk-icon-shadow: 0 1px @osd_txt_shadow;\n    outline-color: @osd_outline; }\n  popover.background.touch-selection button:active:backdrop, popover.background.magnifier button:active:backdrop, .app-notification button:active:backdrop, popover.background.touch-selection button:active, popover.background.magnifier button:active, .app-notification button:active, popover.background.touch-selection button:checked:backdrop, popover.background.magnifier button:checked:backdrop, .app-notification button:checked:backdrop, popover.background.touch-selection button:checked, popover.background.magnifier button:checked, .app-notification button:checked, .osd\n  button:active:backdrop, .osd\n  button:active, .osd\n  button:checked:backdrop, .osd\n  button:checked {\n    color: @theme_fg_color;\n    border-color: @osd_borders;\n    background-color: transparent;\n    background-image: image(@osd_borders);\n    background-clip: padding-box;\n    box-shadow: none;\n    text-shadow: none;\n    -gtk-icon-shadow: none;\n    outline-color: @osd_outline; }\n  popover.background.touch-selection button:disabled:backdrop, popover.background.magnifier button:disabled:backdrop, .app-notification button:disabled:backdrop, popover.background.touch-selection button:disabled, popover.background.magnifier button:disabled, .app-notification button:disabled, .osd\n  button:disabled:backdrop, .osd\n  button:disabled {\n    color: shade(@osd_fg_color, 0.85);\n    border-color: @osd_borders;\n    background-color: transparent;\n    background-image: image(shade(@osd_bg_color, 0.95));\n    background-clip: padding-box;\n    box-shadow: none;\n    text-shadow: none;\n    -gtk-icon-shadow: none; }\n  popover.background.touch-selection button:backdrop, popover.background.magnifier button:backdrop, .app-notification button:backdrop, .osd\n  button:backdrop {\n    color: @theme_unfocused_fg_color;\n    border-color: @osd_borders;\n    background-color: transparent;\n    background-image: image(@osd_bg_color);\n    background-clip: padding-box;\n    box-shadow: none;\n    text-shadow: none;\n    -gtk-icon-shadow: none; }\n  popover.background.touch-selection button.flat, popover.background.magnifier button.flat, .app-notification button.flat, .osd\n  button.flat {\n    border-color: transparent;\n    background-color: transparent;\n    background-image: none;\n    box-shadow: inset 0 1px transparent;\n    text-shadow: none;\n    -gtk-icon-shadow: none;\n    box-shadow: none;\n    text-shadow: 0 1px @osd_txt_shadow;\n    -gtk-icon-shadow: 0 1px @osd_txt_shadow; }\n    popover.background.touch-selection button.flat:hover, popover.background.magnifier button.flat:hover, .app-notification button.flat:hover, .osd\n    button.flat:hover {\n      color: @osd_fg_color;\n      border-color: @osd_borders;\n      background-color: transparent;\n      background-image: image(shade(@osd_bg_color, 1.05));\n      background-clip: padding-box;\n      box-shadow: inset 0 1px @osd_txt_shadow;\n      text-shadow: 0 1px @osd_txt_shadow;\n      -gtk-icon-shadow: 0 1px @osd_txt_shadow;\n      outline-color: @osd_outline; }\n    popover.background.touch-selection button.flat:disabled, popover.background.magnifier button.flat:disabled, .app-notification button.flat:disabled, .osd\n    button.flat:disabled {\n      color: shade(@osd_fg_color, 0.85);\n      border-color: @osd_borders;\n      background-color: transparent;\n      background-image: image(shade(@osd_bg_color, 0.95));\n      background-clip: padding-box;\n      box-shadow: none;\n      text-shadow: none;\n      -gtk-icon-shadow: none;\n      background-image: none;\n      border-color: transparent;\n      box-shadow: none; }\n    popover.background.touch-selection button.flat:backdrop, popover.background.magnifier button.flat:backdrop, .app-notification button.flat:backdrop, .osd\n    button.flat:backdrop {\n      border-color: transparent;\n      background-color: transparent;\n      background-image: none;\n      box-shadow: inset 0 1px transparent;\n      text-shadow: none;\n      -gtk-icon-shadow: none; }\n    popover.background.touch-selection button.flat:active, popover.background.magnifier button.flat:active, .app-notification button.flat:active, popover.background.touch-selection button.flat:checked, popover.background.magnifier button.flat:checked, .app-notification button.flat:checked, .osd\n    button.flat:active, .osd\n    button.flat:checked {\n      color: @osd_fg_color;\n      border-color: @osd_borders;\n      background-color: transparent;\n      background-image: image(@osd_borders);\n      background-clip: padding-box;\n      box-shadow: none;\n      text-shadow: none;\n      -gtk-icon-shadow: none;\n      outline-color: @osd_outline; }\n\n/* button.default. Actually, this was present before but rarely used */\n\nbutton.suggested-action {\n  color: @theme_fg_color;\n  outline-color: rgba(255, 255, 255, 0.3);\n  border-color: shade(@theme_selected_bg_color, 0.6);\n  border-bottom-color: shade(@theme_selected_bg_color, 0.6);\n  background-image: linear-gradient(to bottom, @theme_selected_bg_color, @theme_selected_bg_color);\n\n/* unsure */\n  text-shadow: 0 -1px rgba(0, 0, 0, 0.54353);\n  -gtk-icon-shadow: 0 -1px rgba(0, 0, 0, 0.54353);\n  box-shadow: inset 0 1px rgba(255, 255, 255, 0.4); }\n  .selection-mode button.titlebutton,\n  button.suggested-action.flat {\n    border-color: transparent;\n    background-color: transparent;\n    background-image: none;\n    box-shadow: inset 0 1px transparent;\n    text-shadow: none;\n    -gtk-icon-shadow: none;\n    color: @theme_selected_bg_color; }\n  button.suggested-action:hover {\n    color: @theme_fg_color;\n    outline-color: rgba(255, 255, 255, 0.3);\n    border-color: shade(@theme_selected_bg_color, 0.6);\n    border-bottom-color: shade(@theme_selected_bg_color, 0.6);\n    background-image: linear-gradient(to bottom, @theme_selected_bg_color, @theme_selected_bg_color);\n    text-shadow: 0 -1px rgba(0, 0, 0, 0.49553);\n    -gtk-icon-shadow: 0 -1px rgba(0, 0, 0, 0.49553);\n    box-shadow: inset 0 1px rgba(255, 255, 255, 0.4); }\n  button.suggested-action:active,\n  button.suggested-action:checked {\n    color: @theme_fg_color;\n    outline-color: rgba(255, 255, 255, 0.3);\n    border-color: shade(@theme_selected_bg_color, 0.6);\n    background-image: none;\n    background-color: shade(@theme_selected_bg_color, 0.8);\n    box-shadow: inset 0 1px transparent;\n    text-shadow: none;\n    -gtk-icon-shadow: none; }\n  .selection-mode button.titlebutton:backdrop,\n  button.suggested-action:backdrop,\n  button.suggested-action.flat:backdrop {\n    border-color: @theme_selected_bg_color;\n    background-color: transparent;\n    background-image: image(@theme_selected_bg_color);\n    text-shadow: none;\n    -gtk-icon-shadow: none;\n    box-shadow: inset 0 1px transparent; }\n    .selection-mode button.titlebutton:backdrop label, .selection-mode button.titlebutton:backdrop,\n    button.suggested-action:backdrop label,\n    button.suggested-action:backdrop,\n    button.suggested-action.flat:backdrop label,\n    button.suggested-action.flat:backdrop {\n      color: @theme_selected_bg_color; }\n    .selection-mode button.titlebutton:backdrop:active, .selection-mode button.titlebutton:backdrop:checked,\n    button.suggested-action:backdrop:active,\n    button.suggested-action:backdrop:checked,\n    button.suggested-action.flat:backdrop:active,\n    button.suggested-action.flat:backdrop:checked {\n      border-color: shade(@theme_selected_bg_color, 0.6);\n      background-color: shade(@theme_selected_bg_color, 0.6);\n      background-image: none;\n      box-shadow: inset 0 1px transparent; }\n      .selection-mode button.titlebutton:backdrop:active label, .selection-mode button.titlebutton:backdrop:active, .selection-mode button.titlebutton:backdrop:checked label, .selection-mode button.titlebutton:backdrop:checked,\n      button.suggested-action:backdrop:active label,\n      button.suggested-action:backdrop:active,\n      button.suggested-action:backdrop:checked label,\n      button.suggested-action:backdrop:checked,\n      button.suggested-action.flat:backdrop:active label,\n      button.suggested-action.flat:backdrop:active,\n      button.suggested-action.flat:backdrop:checked label,\n      button.suggested-action.flat:backdrop:checked {\n        color: @theme_selected_bg_color; }\n    .selection-mode button.titlebutton:backdrop:disabled,\n    button.suggested-action:backdrop:disabled,\n    button.suggested-action.flat:backdrop:disabled {\n      border-color: shade(@borders, 0.95);\n      background-color: @insensitive_bg_color;\n      background-image: none;\n      text-shadow: none;\n      -gtk-icon-shadow: none;\n      box-shadow: inset 0 1px transparent; }\n      .selection-mode button.titlebutton:backdrop:disabled label, .selection-mode button.titlebutton:backdrop:disabled,\n      button.suggested-action:backdrop:disabled label,\n      button.suggested-action:backdrop:disabled,\n      button.suggested-action.flat:backdrop:disabled label,\n      button.suggested-action.flat:backdrop:disabled {\n        color: shade(@theme_unfocused_fg_color, 1.1); }\n      .selection-mode button.titlebutton:backdrop:disabled:active, .selection-mode button.titlebutton:backdrop:disabled:checked,\n      button.suggested-action:backdrop:disabled:active,\n      button.suggested-action:backdrop:disabled:checked,\n      button.suggested-action.flat:backdrop:disabled:active,\n      button.suggested-action.flat:backdrop:disabled:checked {\n        border-color: shade(@theme_selected_bg_color, 0.6);\n        background-color: shade(@theme_selected_bg_color, 0.6);\n        background-image: none;\n        box-shadow: inset 0 1px transparent; }\n        .selection-mode button.titlebutton:backdrop:disabled:active label, .selection-mode button.titlebutton:backdrop:disabled:checked label,\n        button.suggested-action:backdrop:disabled:active label,\n        button.suggested-action:backdrop:disabled:checked label,\n        button.suggested-action.flat:backdrop:disabled:active label,\n        button.suggested-action.flat:backdrop:disabled:checked label {\n\n/* Hex color! */\n\n          color: #85b4e6; }\n  .selection-mode button.titlebutton:backdrop, .selection-mode button.titlebutton:disabled, .selection-mode button.titlebutton:backdrop:disabled,\n  button.suggested-action.flat:backdrop,\n  button.suggested-action.flat:disabled,\n  button.suggested-action.flat:backdrop:disabled {\n    border-color: transparent;\n    background-color: transparent;\n    background-image: none;\n    box-shadow: inset 0 1px transparent;\n    text-shadow: none;\n    -gtk-icon-shadow: none;\n    color: @insensitive_fg_color; }\n  button.suggested-action:disabled {\n    border-color: @borders;\n    background-color: @insensitive_bg_color;\n    background-image: none;\n    text-shadow: none;\n    -gtk-icon-shadow: none;\n    box-shadow: inset 0 1px transparent; }\n    button.suggested-action:disabled label,\n    button.suggested-action:disabled {\n      color: @insensitive_fg_color; }\n    button.suggested-action:disabled:active,\n    button.suggested-action:disabled:checked {\n      border-color: shade(@theme_selected_bg_color, 0.6);\n      background-color: shade(@theme_selected_bg_color, 0.6);\n      background-image: none;\n      box-shadow: inset 0 1px transparent; }\n      button.suggested-action:disabled:active label,\n      button.suggested-action:disabled:active,\n      button.suggested-action:disabled:checked label,\n      button.suggested-action:disabled:checked {\n        color: @insensitive_fg_color; }\n  .osd\n\n/* default button for OSD notifications */\n\n  button.suggested-action {\n    color: @theme_fg_color;\n    border-color: @osd_borders;\n    background-color: transparent;\n    background-image: image(shade(@theme_selected_bg_color, 0.5));\n    background-clip: padding-box;\n    box-shadow: inset 0 1px @osd_txt_shadow;\n    text-shadow: 0 1px @osd_txt_shadow;\n    -gtk-icon-shadow: 0 1px @osd_txt_shadow;\n    outline-color: @osd_outline; }\n    .osd\n    button.suggested-action:hover {\n      color: @theme_fg_color;\n      border-color: @osd_borders;\n      background-color: transparent;\n      background-image: image(shade(@theme_selected_bg_color, 0.7));\n      background-clip: padding-box;\n      box-shadow: inset 0 1px @osd_txt_shadow;\n      text-shadow: 0 1px @osd_txt_shadow;\n      -gtk-icon-shadow: 0 1px @osd_txt_shadow;\n      outline-color: @osd_outline; }\n    .osd\n    button.suggested-action:active:backdrop, .osd\n    button.suggested-action:active, .osd\n    button.suggested-action:checked:backdrop, .osd\n    button.suggested-action:checked {\n      color: @theme_selected_fg_color;\n      border-color: @osd_borders;\n      background-color: transparent;\n      background-image: image(@theme_selected_bg_color);\n      background-clip: padding-box;\n      box-shadow: none;\n      text-shadow: none;\n      -gtk-icon-shadow: none;\n      outline-color: @osd_outline; }\n    .osd\n    button.suggested-action:disabled:backdrop, .osd\n    button.suggested-action:disabled {\n      color: shade(@osd_fg_color, 0.85);\n      border-color: @osd_borders;\n      background-color: transparent;\n      background-image: image(shade(@osd_bg_color, 0.95));\n      background-clip: padding-box;\n      box-shadow: none;\n      text-shadow: none;\n      -gtk-icon-shadow: none; }\n    .osd\n    button.suggested-action:backdrop {\n      color: @theme_unfocused_fg_color;\n      border-color: @osd_borders;\n      background-color: transparent;\n      background-image: image(shade(@theme_selected_bg_color, 0.5));\n      background-clip: padding-box;\n      box-shadow: none;\n      text-shadow: none;\n      -gtk-icon-shadow: none; }\n\n/* Hex color! end */\n\nbutton.destructive-action {\n  color: @osd_fg_color;\n  outline-color: rgba(255, 255, 255, 0.3);\n  border-color: shade(@error_color, 0.9);\n  border-bottom-color: shade(@error_color, 0.85);\n  background-image: linear-gradient(to bottom, @error_color, @error_color);\n  text-shadow: 0 -1px rgba(0, 0, 0, 0.56078);\n  -gtk-icon-shadow: 0 -1px rgba(0, 0, 0, 0.56078);\n  box-shadow: inset 0 1px rgba(255, 255, 255, 0.4); }\n  button.destructive-action.flat {\n    border-color: transparent;\n    background-color: transparent;\n    background-image: none;\n    box-shadow: inset 0 1px transparent;\n    text-shadow: none;\n    -gtk-icon-shadow: none;\n    color: @error_color; }\n  button.destructive-action:hover {\n    color: @osd_fg_color;\n    outline-color: rgba(255, 255, 255, 0.3);\n    border-color: shade(@error_color, 0.9);\n    border-bottom-color: shade(@error_color, 0.85);\n    background-image: linear-gradient(to bottom, shade(@error_color, 1.1), shade(@error_color, 1.1));\n    text-shadow: 0 -1px rgba(0, 0, 0, 0.51278);\n    -gtk-icon-shadow: 0 -1px rgba(0, 0, 0, 0.51278);\n    box-shadow: inset 0 1px rgba(255, 255, 255, 0.4); }\n  button.destructive-action:active,\n  button.destructive-action:checked {\n    color: @osd_fg_color;\n    outline-color: rgba(255, 255, 255, 0.3);\n    border-color: shade(@error_color, 0.9);\n    background-image: none;\n    background-color: @error_color;\n    box-shadow: inset 0 1px transparent;\n    text-shadow: none;\n    -gtk-icon-shadow: none; }\n  button.destructive-action:backdrop,\n  button.destructive-action.flat:backdrop {\n    border-color: @error_color;\n    background-color: transparent;\n    background-image: image(@error_color);\n    text-shadow: none;\n    -gtk-icon-shadow: none;\n    box-shadow: inset 0 1px transparent; }\n    button.destructive-action:backdrop label,\n    button.destructive-action:backdrop,\n    button.destructive-action.flat:backdrop label,\n    button.destructive-action.flat:backdrop {\n      color: shade(@error_color, 1.3); }\n    button.destructive-action:backdrop:active,\n    button.destructive-action:backdrop:checked,\n    button.destructive-action.flat:backdrop:active,\n    button.destructive-action.flat:backdrop:checked {\n      border-color: @error_color;\n      background-color: @error_color;\n      background-image: none;\n      box-shadow: inset 0 1px transparent; }\n      button.destructive-action:backdrop:active label,\n      button.destructive-action:backdrop:active,\n      button.destructive-action:backdrop:checked label,\n      button.destructive-action:backdrop:checked,\n      button.destructive-action.flat:backdrop:active label,\n      button.destructive-action.flat:backdrop:active,\n      button.destructive-action.flat:backdrop:checked label,\n      button.destructive-action.flat:backdrop:checked {\n        color: shade(@error_color, 1.3); }\n    button.destructive-action:backdrop:disabled,\n    button.destructive-action.flat:backdrop:disabled {\n      border-color: shade(@borders, 0.95);\n      background-color: @insensitive_bg_color;\n      background-image: none;\n      text-shadow: none;\n      -gtk-icon-shadow: none;\n      box-shadow: inset 0 1px transparent; }\n      button.destructive-action:backdrop:disabled label,\n      button.destructive-action:backdrop:disabled,\n      button.destructive-action.flat:backdrop:disabled label,\n      button.destructive-action.flat:backdrop:disabled {\n        color: shade(@theme_unfocused_fg_color, 1.1); }\n      button.destructive-action:backdrop:disabled:active,\n      button.destructive-action:backdrop:disabled:checked,\n      button.destructive-action.flat:backdrop:disabled:active,\n      button.destructive-action.flat:backdrop:disabled:checked {\n        border-color: @error_color;\n        background-color: @error_color;\n        background-image: none;\n        box-shadow: inset 0 1px transparent; }\n        button.destructive-action:backdrop:disabled:active label,\n        button.destructive-action:backdrop:disabled:checked label,\n        button.destructive-action.flat:backdrop:disabled:active label,\n        button.destructive-action.flat:backdrop:disabled:checked label {\n          color: shade(@error_color, 1.2); }\n  button.destructive-action.flat:backdrop,\n  button.destructive-action.flat:disabled,\n  button.destructive-action.flat:backdrop:disabled {\n    border-color: transparent;\n    background-color: transparent;\n    background-image: none;\n    box-shadow: inset 0 1px transparent;\n    text-shadow: none;\n    -gtk-icon-shadow: none;\n    color: @error_color; }\n  button.destructive-action:disabled {\n    border-color: @borders;\n    background-color: @insensitive_bg_color;\n    background-image: none;\n    text-shadow: none;\n    -gtk-icon-shadow: none;\n    box-shadow: inset 0 1px transparent; }\n    button.destructive-action:disabled label,\n    button.destructive-action:disabled {\n      color: @insensitive_fg_color; }\n    button.destructive-action:disabled:active,\n    button.destructive-action:disabled:checked {\n      border-color: shade(@error_color, 0.9);\n      background-color: @error_color;\n      background-image: none;\n      box-shadow: inset 0 1px transparent; }\n      button.destructive-action:disabled:active label,\n      button.destructive-action:disabled:active,\n      button.destructive-action:disabled:checked label,\n      button.destructive-action:disabled:checked {\n        color: shade(@error_color, 1.2); }\n  .osd\n  button.destructive-action {\n    color: @theme_unfocused_fg_color;\n    border-color: @osd_borders;\n    background-color: transparent;\n    background-image: image(@error_color);\n    background-clip: padding-box;\n    box-shadow: inset 0 1px @osd_txt_shadow;\n    text-shadow: 0 1px @osd_txt_shadow;\n    -gtk-icon-shadow: 0 1px @osd_txt_shadow;\n    outline-color: @osd_outline; }\n    .osd\n    button.destructive-action:hover {\n      color: @osd_fg_color;\n      border-color: @osd_borders;\n      background-color: transparent;\n      background-image: image(@error_color);\n      background-clip: padding-box;\n      box-shadow: inset 0 1px @osd_txt_shadow;\n      text-shadow: 0 1px @osd_txt_shadow;\n      -gtk-icon-shadow: 0 1px @osd_txt_shadow;\n      outline-color: @osd_outline; }\n    .osd\n    button.destructive-action:active:backdrop, .osd\n    button.destructive-action:active, .osd\n    button.destructive-action:checked:backdrop, .osd\n    button.destructive-action:checked {\n      color: @osd_fg_color;\n      border-color: @osd_borders;\n      background-color: transparent;\n      background-image: image(@error_color);\n      background-clip: padding-box;\n      box-shadow: none;\n      text-shadow: none;\n      -gtk-icon-shadow: none;\n      outline-color: @osd_outline; }\n    .osd\n    button.destructive-action:disabled:backdrop, .osd\n    button.destructive-action:disabled {\n      color: shade(@insensitive_fg_color, 0.6);\n      border-color: @osd_borders;\n      background-color: transparent;\n      background-image: image(shade(@osd_bg_color, 0.95));\n      background-clip: padding-box;\n      box-shadow: none;\n      text-shadow: none;\n      -gtk-icon-shadow: none; }\n    .osd\n    button.destructive-action:backdrop {\n      color: @theme_unfocused_fg_color;\n      border-color: @osd_borders;\n      background-color: transparent;\n      background-image: image(@error_color);\n      background-clip: padding-box;\n      box-shadow: none;\n      text-shadow: none;\n      -gtk-icon-shadow: none; }\n.stack-switcher >\nbutton {\n  outline-offset: -3px; }\n  .stack-switcher >\n  button > label {\n    padding-left: 6px;\n    padding-right: 6px; }\n  .stack-switcher >\n  button > image {\n    padding-left: 6px;\n    padding-right: 6px;\n    padding-top: 3px;\n    padding-bottom: 3px; }\n  .stack-switcher >\n  button.text-button {\n    padding-left: 10px;\n    padding-right: 10px; }\n  .stack-switcher >\n  button.image-button {\n    padding-left: 2px;\n    padding-right: 2px; }\n  .stack-switcher >\n  button.needs-attention:active > label,\n  .stack-switcher >\n  button.needs-attention:active > image, .stack-switcher >\n  button.needs-attention:checked > label,\n  .stack-switcher >\n  button.needs-attention:checked > image {\n    animation: none;\n    background-image: none; }\n.inline-toolbar\nbutton, .inline-toolbar\nbutton:backdrop {\n  border-radius: 0;\n  border-width: 1px; }\n.primary-toolbar\nbutton {\n  -gtk-icon-shadow: none; }\n\n.stack-switcher >\nbutton.needs-attention > label,\n.stack-switcher >\nbutton.needs-attention > image, stacksidebar row.needs-attention > label {\n  animation: needs_attention 150ms ease-in;\n  background-image: -gtk-gradient(radial, center center, 0, center center, 0.5, to(@theme_selected_bg_color), to(transparent)), -gtk-gradient(radial, center center, 0, center center, 0.5, to(@txt_shadow), to(transparent));\n  background-size: 6px 6px, 6px 6px;\n  background-repeat: no-repeat;\n  background-position: right 3px, right 4px; }\n  .stack-switcher >\n  button.needs-attention > label:backdrop,\n  .stack-switcher >\n  button.needs-attention > image:backdrop, stacksidebar row.needs-attention > label:backdrop {\n    background-size: 6px 6px, 0 0; }\n  .stack-switcher >\n  button.needs-attention > label:dir(rtl),\n  .stack-switcher >\n  button.needs-attention > image:dir(rtl), stacksidebar row.needs-attention > label:dir(rtl) {\n    background-position: left 3px, left 4px; }\n\n/* Here we are */\n\n.inline-toolbar toolbutton > button {\n  color: @theme_fg_color;\n  outline-color: @outline_color;\n  border-color: @borders;\n  background-image: linear-gradient(to bottom, @theme_bg_color, @theme_bg_color);\n  text-shadow: 0 1px transparent;\n  -gtk-icon-shadow: 0 1px transparent;\n  box-shadow: inset 0 1px transparent; }\n  .inline-toolbar toolbutton > button:hover {\n    color: @theme_fg_color;\n    outline-color: @outline_color;\n    border-color: @borders;\n    background-image: linear-gradient(to bottom, @theme_selected_bg_color, @theme_selected_bg_color);\n    text-shadow: 0 1px @txt_shadow;\n    -gtk-icon-shadow: 0 1px @txt_shadow;\n    box-shadow: inset 0 1px @theme_bg_color; }\n  .inline-toolbar toolbutton > button:active, .inline-toolbar toolbutton > button:checked {\n    color: @theme_fg_color;\n    outline-color: @outline_color;\n    border-color: @borders;\n    background-image: none;\n    background-color: shade(@theme_bg_color, 0.9);\n    box-shadow: inset 0 1px transparent;\n    text-shadow: none;\n    -gtk-icon-shadow: none; }\n  .inline-toolbar toolbutton > button:disabled {\n    border-color: @borders;\n    background-color: @insensitive_bg_color;\n    background-image: none;\n    text-shadow: none;\n    -gtk-icon-shadow: none;\n    box-shadow: inset 0 1px transparent; }\n    .inline-toolbar toolbutton > button:disabled label, .inline-toolbar toolbutton > button:disabled {\n      color: @insensitive_fg_color; }\n    .inline-toolbar toolbutton > button:disabled:active, .inline-toolbar toolbutton > button:disabled:checked {\n      border-color: @borders;\n      background-color: shade(@theme_bg_color, 0.95);\n      background-image: none;\n      box-shadow: inset 0 1px transparent; }\n      .inline-toolbar toolbutton > button:disabled:active label, .inline-toolbar toolbutton > button:disabled:active, .inline-toolbar toolbutton > button:disabled:checked label, .inline-toolbar toolbutton > button:disabled:checked {\n        color: @insensitive_fg_color; }\n  .inline-toolbar toolbutton > button:backdrop {\n    border-color: shade(@borders, 0.95);\n    background-color: transparent;\n    background-image: image(@theme_bg_color);\n    text-shadow: none;\n    -gtk-icon-shadow: none;\n    box-shadow: inset 0 1px transparent; }\n    .inline-toolbar toolbutton > button:backdrop label, .inline-toolbar toolbutton > button:backdrop {\n      color: @insensitive_fg_color; }\n    .inline-toolbar toolbutton > button:backdrop:active, .inline-toolbar toolbutton > button:backdrop:checked {\n      border-color: shade(@borders, 0.95);\n      background-color: shade(@theme_bg_color, 0.95);\n      background-image: none;\n      box-shadow: inset 0 1px transparent; }\n      .inline-toolbar toolbutton > button:backdrop:active label, .inline-toolbar toolbutton > button:backdrop:active, .inline-toolbar toolbutton > button:backdrop:checked label, .inline-toolbar toolbutton > button:backdrop:checked {\n        color: @insensitive_fg_color; }\n    .inline-toolbar toolbutton > button:backdrop:disabled {\n      border-color: shade(@borders, 0.95);\n      background-color: @insensitive_bg_color;\n      background-image: none;\n      text-shadow: none;\n      -gtk-icon-shadow: none;\n      box-shadow: inset 0 1px transparent; }\n      .inline-toolbar toolbutton > button:backdrop:disabled label, .inline-toolbar toolbutton > button:backdrop:disabled {\n        color: shade(@theme_unfocused_fg_color, 1.1); }\n      .inline-toolbar toolbutton > button:backdrop:disabled:active, .inline-toolbar toolbutton > button:backdrop:disabled:checked {\n        border-color: shade(@borders, 0.95);\n        background-color: shade(@theme_bg_color, 0.95);\n        background-image: none;\n        box-shadow: inset 0 1px transparent; }\n        .inline-toolbar toolbutton > button:backdrop:disabled:active label, .inline-toolbar toolbutton > button:backdrop:disabled:checked label {\n          color: shade(@theme_unfocused_fg_color, 1.1); }\n\ntoolbar.inline-toolbar toolbutton > button.flat,\ntoolbar.inline-toolbar toolbutton:backdrop > button.flat, .linked:not(.vertical) > spinbutton:not(.vertical), .linked:not(.vertical) >\nentry, .inline-toolbar\nbutton, .inline-toolbar\nbutton:backdrop, .linked >\nbutton, .linked >\nbutton:hover, .linked >\nbutton:active, .linked >\nbutton:checked, .linked >\nbutton:backdrop, .linked > combobox > box > button.combo:dir(ltr), .linked > combobox > box > button.combo:dir(rtl) {\n  border-radius: 0;\n  border-right-style: none; }\n\n.linked:not(.vertical) > spinbutton:first-child:not(.vertical), .linked:not(.vertical) >\nentry:first-child, .inline-toolbar\nbutton:first-child, .linked >\nbutton:first-child, toolbar.inline-toolbar toolbutton:first-child > button.flat,\ntoolbar.inline-toolbar toolbutton:backdrop:first-child > button.flat, combobox.linked button:nth-child(2):dir(rtl), .linked:not(.vertical) > combobox:first-child > box > button.combo {\n  border-top-left-radius: 0;\n  border-bottom-left-radius: 0; }\n.linked:not(.vertical) > spinbutton:last-child:not(.vertical), .linked:not(.vertical) >\nentry:last-child, .inline-toolbar\nbutton:last-child, .linked >\nbutton:last-child, toolbar.inline-toolbar toolbutton:last-child > button.flat,\ntoolbar.inline-toolbar toolbutton:backdrop:last-child > button.flat, combobox.linked button:nth-child(2):dir(ltr), .linked:not(.vertical) > combobox:last-child > box > button.combo {\n  border-top-right-radius: 0;\n  border-bottom-right-radius: 0;\n  border-right-style: solid; }\n.linked:not(.vertical) > spinbutton:only-child:not(.vertical), .linked:not(.vertical) >\nentry:only-child, .inline-toolbar\nbutton:only-child, .linked >\nbutton:only-child, toolbar.inline-toolbar toolbutton:only-child > button.flat,\ntoolbar.inline-toolbar toolbutton:backdrop:only-child > button.flat, .linked:not(.vertical) > combobox:only-child > box > button.combo {\n  border-radius: 0;\n  border-style: solid; }\n\n.linked.vertical > spinbutton:not(.vertical), .linked.vertical >\nentry, .linked.vertical >\nbutton, .linked.vertical >\nbutton:hover, .linked.vertical >\nbutton:active, .linked.vertical >\nbutton:checked, .linked.vertical >\nbutton:backdrop, .linked.vertical > combobox > box > button.combo {\n  border-style: solid solid none solid;\n  border-radius: 0; }\n\n.linked.vertical > spinbutton:first-child:not(.vertical), .linked.vertical >\nentry:first-child, .linked.vertical >\nbutton:first-child, .linked.vertical > combobox:first-child > box > button.combo {\n  border-top-left-radius: 0;\n  border-top-right-radius: 0; }\n.linked.vertical > spinbutton:last-child:not(.vertical), .linked.vertical >\nentry:last-child, .linked.vertical >\nbutton:last-child, .linked.vertical > combobox:last-child > box > button.combo {\n  border-bottom-left-radius: 0;\n  border-bottom-right-radius: 0;\n  border-style: solid; }\n.linked.vertical > spinbutton:only-child:not(.vertical), .linked.vertical >\nentry:only-child, .linked.vertical >\nbutton:only-child, .linked.vertical > combobox:only-child > box > button.combo {\n  border-radius: 0;\n  border-style: solid; }\n\nmodelbutton.flat, popover.background checkbutton,\npopover.background radiobutton,\n.menuitem.button.flat, modelbutton.flat:backdrop, popover.background checkbutton:backdrop,\npopover.background radiobutton:backdrop, modelbutton.flat:backdrop:hover, popover.background checkbutton:backdrop:hover,\npopover.background radiobutton:backdrop:hover,\n.menuitem.button.flat:backdrop,\n.menuitem.button.flat:backdrop:hover, button:link,\nbutton:visited, button:link:hover, button:link:active, button:link:checked,\nbutton:visited:hover,\nbutton:visited:active,\nbutton:visited:checked, calendar.button, calendar.button:hover, calendar.button:backdrop, calendar.button:disabled, .scale-popup button:hover, .scale-popup button:backdrop:hover, .scale-popup button:backdrop:disabled, .scale-popup button:backdrop {\n  background-color: transparent;\n  background-image: none;\n  border-color: transparent;\n  box-shadow: inset 0 1px transparent, 0 1px transparent;\n  text-shadow: none;\n  -gtk-icon-shadow: none; }\n\n/* menu buttons */\nmodelbutton.flat, popover.background checkbutton,\npopover.background radiobutton,\n.menuitem.button.flat {\n  min-height: 26px;\n  padding-left: 5px;\n  padding-right: 5px;\n  border-radius: 0;\n  outline-offset: -2px; }\n  modelbutton.flat:hover, popover.background checkbutton:hover,\n  popover.background radiobutton:hover,\n  .menuitem.button.flat:hover {\n    background-color: shade(@theme_bg_color, 0.95); }\n  modelbutton.flat check:last-child, popover.background checkbutton check:last-child,\n  popover.background radiobutton check:last-child,\n  modelbutton.flat radio:last-child,\n  popover.background checkbutton radio:last-child,\n  popover.background radiobutton radio:last-child,\n  .menuitem.button.flat check:last-child,\n  .menuitem.button.flat radio:last-child {\n    margin-left: 8px; }\n  modelbutton.flat check:first-child, popover.background checkbutton check:first-child,\n  popover.background radiobutton check:first-child,\n  modelbutton.flat radio:first-child,\n  popover.background checkbutton radio:first-child,\n  popover.background radiobutton radio:first-child,\n  .menuitem.button.flat check:first-child,\n  .menuitem.button.flat radio:first-child {\n    margin-right: 8px; }\n\nmodelbutton.flat arrow, popover.background checkbutton arrow,\npopover.background radiobutton arrow {\n  background: none; }\n  modelbutton.flat arrow:hover, popover.background checkbutton arrow:hover,\n  popover.background radiobutton arrow:hover {\n    background: none; }\n  modelbutton.flat arrow.left, popover.background checkbutton arrow.left,\n  popover.background radiobutton arrow.left {\n    -gtk-icon-source: -gtk-icontheme(\"pan-start-symbolic\"); }\n  modelbutton.flat arrow.right, popover.background checkbutton arrow.right,\n  popover.background radiobutton arrow.right {\n    -gtk-icon-source: -gtk-icontheme(\"pan-end-symbolic\"); }\n\nbutton.color {\n  padding: 4px; }\n  button.color colorswatch:only-child {\n    box-shadow: 0 1px @txt_shadow; }\n    button.color colorswatch:only-child, button.color colorswatch:only-child overlay {\n      border-radius: 0; }\n  button.color:disabled colorswatch:only-child, button.color:backdrop colorswatch:only-child, button.color:active colorswatch:only-child, button.color:checked colorswatch:only-child {\n    box-shadow: none; }\n\n/*********\n * Links *\n *********/\nbutton:link > label,\nbutton:visited > label,\n*:link,\nbutton:link,\nbutton:visited {\n  color: @borders; }\n  button:link > label:visited,\n  button:visited > label:visited,\n  *:link:visited,\n  button:visited {\n    color: shade(@theme_selected_bg_color, 0.6); }\n    *:selected button:link > label:visited,\n    *:selected button:visited > label:visited, *:selected\n    *:link:visited, *:selected\n    button:visited:link,\n    *:selected button:visited {\n      color: #b7d3f0; }\n  button:link > label:hover,\n  button:visited > label:hover,\n  *:link:hover,\n  button:hover:link,\n  button:hover:visited {\n    color: @theme_selected_bg_color; }\n    *:selected button:link > label:hover,\n    *:selected button:visited > label:hover, *:selected\n    *:link:hover, *:selected\n    button:hover:link,\n    *:selected button:hover:visited {\n      color: #edf4fb; }\n  button:link > label:active,\n  button:visited > label:active,\n  *:link:active,\n  button:active:link,\n  button:active:visited {\n    color: @borders; }\n    *:selected button:link > label:active,\n    *:selected button:visited > label:active, *:selected\n    *:link:active, *:selected\n    button:active:link,\n    *:selected button:active:visited {\n      color: @theme_selected_bg_color; }\n  button:link > label:backdrop:backdrop:hover,\n  button:visited > label:backdrop:backdrop:hover, button:link > label:backdrop:backdrop:hover:selected,\n  button:visited > label:backdrop:backdrop:hover:selected, button:link > label:backdrop,\n  button:visited > label:backdrop,\n  *:link:backdrop:backdrop:hover,\n  button:backdrop:backdrop:hover:link,\n  button:backdrop:backdrop:hover:visited,\n  *:link:backdrop:backdrop:hover:selected,\n  button:backdrop:backdrop:hover:selected:link,\n  button:backdrop:backdrop:hover:selected:visited,\n  .selection-mode.titlebar:not(headerbar) .subtitle:backdrop:backdrop:hover:link,\n  headerbar.selection-mode .subtitle:backdrop:backdrop:hover:link,\n  *:link:backdrop,\n  button:backdrop:link,\n  button:backdrop:visited {\n    color: @theme_selected_bg_color; }\n  .info *:link, .info button:link,\n  .info button:visited,\n  .question *:link,\n  .question button:link,\n  .question button:visited,\n  .warning *:link,\n  .warning button:link,\n  .warning button:visited,\n  .error *:link,\n  .error button:link,\n  .error button:visited, button:link > label:selected,\n  button:visited > label:selected, *:selected button:link > label,\n  *:selected button:visited > label,\n  *:link:selected,\n  button:selected:link,\n  button:selected:visited,\n  .selection-mode.titlebar:not(headerbar) .subtitle:link,\n  headerbar.selection-mode .subtitle:link, *:selected\n  *:link, *:selected\n  button:link,\n  *:selected button:visited {\n    color: @theme_selected_bg_color; }\n\nbutton:link,\nbutton:visited {\n  text-shadow: none; }\n  button:link:hover, button:link:active, button:link:checked,\n  button:visited:hover,\n  button:visited:active,\n  button:visited:checked {\n    text-shadow: none; }\n  button:link > label,\n  button:visited > label {\n    text-decoration-line: underline; }\n\n/*****************\n * GtkSpinButton *\n *****************/\nspinbutton:not(.vertical) {\n  padding: 0; }\n  spinbutton:not(.vertical) entry {\n    min-width: 28px;\n    margin: 0;\n    background: none;\n    background-color: transparent;\n    border: none;\n    border-radius: 0;\n    box-shadow: none; }\n    spinbutton:not(.vertical) entry:backdrop:disabled {\n      background-color: transparent; }\n  spinbutton:not(.vertical) button {\n    min-height: 16px;\n    margin: 0;\n    padding-bottom: 0;\n    padding-top: 0;\n    color: #43484a;\n    background-image: none;\n    border-style: none none none solid;\n    border-color: rgba(182, 182, 179, 0.3);\n    border-radius: 0;\n    box-shadow: none; }\n    spinbutton:not(.vertical) button:dir(rtl) {\n      border-style: none solid none none; }\n    spinbutton:not(.vertical) button:hover {\n      color: @theme_fg_color;\n      background-color: rgba(46, 52, 54, 0.05); }\n    spinbutton:not(.vertical) button:disabled {\n      color: rgba(139, 142, 143, 0.3);\n      background-color: transparent; }\n    spinbutton:not(.vertical) button:active {\n      background-color: rgba(0, 0, 0, 0.1);\n      box-shadow: inset 0 2px 3px -1px rgba(0, 0, 0, 0.2); }\n    spinbutton:not(.vertical) button:backdrop {\n      color: #96999a;\n      background-color: transparent;\n      border-color: rgba(192, 192, 189, 0.3);\n      transition: 200ms ease-out; }\n    spinbutton:not(.vertical) button:backdrop:disabled {\n      color: rgba(195, 195, 192, 0.3);\n      background-color: transparent;\n      border-style: none none none solid; }\n      spinbutton:not(.vertical) button:backdrop:disabled:dir(rtl) {\n        border-style: none solid none none; }\n    spinbutton:not(.vertical) button:dir(ltr):last-child {\n      border-radius: 0; }\n    spinbutton:not(.vertical) button:dir(rtl):first-child {\n      border-radius: 0; }\n.osd spinbutton:not(.vertical) button {\n  border-color: transparent;\n  background-color: transparent;\n  background-image: none;\n  box-shadow: inset 0 1px transparent;\n  text-shadow: none;\n  -gtk-icon-shadow: none;\n  color: @theme_unfocused_fg_color;\n  border-style: none none none solid;\n  border-color: rgba(0, 0, 0, 0.4);\n  border-radius: 0;\n  box-shadow: none;\n  -gtk-icon-shadow: 0 1px @osd_txt_shadow; }\n  .osd spinbutton:not(.vertical) button:dir(rtl) {\n    border-style: none solid none none; }\n  .osd spinbutton:not(.vertical) button:hover {\n    border-color: transparent;\n    background-color: transparent;\n    background-image: none;\n    box-shadow: inset 0 1px transparent;\n    text-shadow: none;\n    -gtk-icon-shadow: none;\n    color: @theme_unfocused_fg_color;\n    border-color: @osd_bg_color;\n    background-color: rgba(238, 238, 236, 0.1);\n    -gtk-icon-shadow: 0 1px @osd_txt_shadow;\n    box-shadow: none; }\n  .osd spinbutton:not(.vertical) button:backdrop {\n    border-color: transparent;\n    background-color: transparent;\n    background-image: none;\n    box-shadow: inset 0 1px transparent;\n    text-shadow: none;\n    -gtk-icon-shadow: none;\n    color: @theme_unfocused_fg_color;\n    border-color: @osd_bg_color;\n    -gtk-icon-shadow: none;\n    box-shadow: none; }\n  .osd spinbutton:not(.vertical) button:disabled {\n    border-color: transparent;\n    background-color: transparent;\n    background-image: none;\n    box-shadow: inset 0 1px transparent;\n    text-shadow: none;\n    -gtk-icon-shadow: none;\n    color: shade(@osd_fg_color, 0.85);\n    border-color: @osd_bg_color;\n    -gtk-icon-shadow: none;\n    box-shadow: none; }\n  .osd spinbutton:not(.vertical) button:dir(ltr):last-child {\n    border-radius: 0; }\n  .osd spinbutton:not(.vertical) button:dir(rtl):first-child {\n    border-radius: 0; }\nspinbutton.vertical:disabled {\n  color: @insensitive_fg_color; }\nspinbutton.vertical:backdrop:disabled {\n  color: shade(@theme_unfocused_fg_color, 1.1); }\nspinbutton.vertical:drop(active) {\n  border-color: transparent;\n  box-shadow: none; }\nspinbutton.vertical entry {\n  min-height: 32px;\n  min-width: 32px;\n  padding: 0;\n  border-radius: 0; }\nspinbutton.vertical button {\n  min-height: 32px;\n  min-width: 32px;\n  padding: 0; }\nspinbutton.vertical button.up {\n  border-radius: 0;\n  border-style: solid solid none solid; }\nspinbutton.vertical button.down {\n  border-radius: 0;\n  border-style: none solid solid solid; }\n.osd spinbutton.vertical button:first-child {\n  color: @theme_unfocused_fg_color;\n  border-color: @osd_borders;\n  background-color: transparent;\n  background-image: image(@osd_bg_color);\n  background-clip: padding-box;\n  box-shadow: inset 0 1px @osd_txt_shadow;\n  text-shadow: 0 1px @osd_txt_shadow;\n  -gtk-icon-shadow: 0 1px @osd_txt_shadow;\n  outline-color: @osd_outline; }\n  .osd spinbutton.vertical button:first-child:hover {\n    color: @osd_fg_color;\n    border-color: @osd_borders;\n    background-color: transparent;\n    background-image: image(shade(@osd_bg_color, 1.05));\n    background-clip: padding-box;\n    box-shadow: inset 0 1px @osd_txt_shadow;\n    text-shadow: 0 1px @osd_txt_shadow;\n    -gtk-icon-shadow: 0 1px @osd_txt_shadow;\n    outline-color: @osd_outline; }\n  .osd spinbutton.vertical button:first-child:active {\n    color: @osd_fg_color;\n    border-color: @osd_borders;\n    background-color: transparent;\n    background-image: image(@osd_borders);\n    background-clip: padding-box;\n    box-shadow: none;\n    text-shadow: none;\n    -gtk-icon-shadow: none;\n    outline-color: @osd_outline; }\n  .osd spinbutton.vertical button:first-child:disabled {\n    color: shade(@osd_fg_color, 0.85);\n    border-color: @osd_borders;\n    background-color: transparent;\n    background-image: image(shade(@osd_bg_color, 0.95));\n    background-clip: padding-box;\n    box-shadow: none;\n    text-shadow: none;\n    -gtk-icon-shadow: none; }\n  .osd spinbutton.vertical button:first-child:backdrop {\n    color: @theme_unfocused_fg_color;\n    border-color: @osd_borders;\n    background-color: transparent;\n    background-image: image(@osd_bg_color);\n    background-clip: padding-box;\n    box-shadow: none;\n    text-shadow: none;\n    -gtk-icon-shadow: none; }\ntreeview spinbutton:not(.vertical) {\n  min-height: 0;\n  border-style: none;\n  border-radius: 0; }\n  treeview spinbutton:not(.vertical) entry {\n    min-height: 0;\n    padding: 1px 2px; }\n\n/**************\n * ComboBoxes *\n **************/\ncombobox arrow {\n  -gtk-icon-source: -gtk-icontheme(\"pan-down-symbolic\");\n  min-height: 16px;\n  min-width: 16px; }\ncombobox:drop(active) {\n  box-shadow: none; }\n\n/************\n * Toolbars *\n ************/\ntoolbar, .inline-toolbar, searchbar,\n.location-bar {\n  -GtkWidget-window-dragging: true;\n  padding: 4px;\n  background-color: @theme_bg_color; }\n\ntoolbar {\n  padding: 4px 3px 3px 4px; }\n  .osd toolbar {\n    background-color: transparent; }\n  toolbar.osd {\n    padding: 13px;\n    border: none;\n    border-radius: 0;\n    background-color: @osd_bg_color; }\n    toolbar.osd.left, toolbar.osd.right, toolbar.osd.top, toolbar.osd.bottom {\n      border-radius: 0; }\n  toolbar.horizontal separator {\n    margin: 0 7px 1px 6px; }\n  toolbar.vertical separator {\n    margin: 6px 1px 7px 0; }\n  toolbar:not(.inline-toolbar):not(.osd) switch,\n  toolbar:not(.inline-toolbar):not(.osd) scale,\n  toolbar:not(.inline-toolbar):not(.osd) entry,\n  toolbar:not(.inline-toolbar):not(.osd) spinbutton,\n  toolbar:not(.inline-toolbar):not(.osd) button {\n    margin-right: 1px;\n    margin-bottom: 1px; }\n\n.inline-toolbar {\n  padding: 3px;\n  border-width: 0 1px 1px;\n  border-radius: 0; }\n\nsearchbar,\n.location-bar {\n  border-width: 0 0 1px;\n  padding: 3px; }\n\n.inline-toolbar, searchbar,\n.location-bar {\n  border-style: solid;\n  border-color: @borders;\n  background-color: @theme_bg_color; } /*#d9d9d7*/\n  .inline-toolbar:backdrop, searchbar:backdrop,\n  .location-bar:backdrop {\n    border-color: shade(@borders, 0.95);\n    background-color: @theme_unfocused_bg_color; /*#dadad8*/\n    box-shadow: none;\n    transition: 200ms ease-out; }\n\n/***************\n * Header bars *\n ***************/\n.titlebar:not(headerbar),\nheaderbar {\n  padding: 0 6px;\n  min-height: 46px;\n  border-width: 0 0 1px;\n  border-style: solid;\n  border-color: @borders;\n  border-radius: 0;\n  background-image: linear-gradient(to top, @theme_bg_color, @theme_bg_color);\n  background-color: @theme_bg_color;\n  box-shadow: inset 0 1px rgba(255, 255, 255, 0.8); }\n  .titlebar:backdrop:not(headerbar),\n  headerbar:backdrop {\n    border-color: shade(@borders, 0.95);\n    background-color: @theme_bg_color;\n    background-image: none;\n    box-shadow: inset 0 1px rgba(255, 255, 255, 0.8);\n    transition: 200ms ease-out; }\n  .titlebar:not(headerbar) .title,\n  headerbar .title {\n    padding-left: 12px;\n    padding-right: 12px;\n    font-weight: bold; }\n  .titlebar:not(headerbar) .subtitle,\n  headerbar .subtitle {\n    font-size: smaller;\n    padding-left: 12px;\n    padding-right: 12px; }\n  .selection-mode.titlebar:not(headerbar),\n  headerbar.selection-mode {\n    color: @theme_selected_fg_color;\n    border-color: shade(@theme_selected_bg_color, 0.6);\n    text-shadow: 0 -1px @osd_bg_color;\n    background-image: none;\n    background-color: @theme_selected_bg_color;\n    box-shadow: inset 0 1px rgba(146, 188, 232, 0.9); }\n    .selection-mode.titlebar:backdrop:not(headerbar),\n    headerbar.selection-mode:backdrop {\n      background-color: @theme_selected_bg_color;\n      background-image: none;\n      box-shadow: inset 0 1px rgba(165, 200, 236, 0.88); }\n    .selection-mode.titlebar:not(headerbar) button,\n    headerbar.selection-mode button {\n      color: @theme_selected_fg_color;\n      outline-color: rgba(255, 255, 255, 0.3);\n      border-color: shade(@theme_selected_bg_color, 0.6);\n      border-bottom-color: shade(@theme_selected_bg_color, 0.6);\n      background-image: image(@theme_selected_bg_color);\n      text-shadow: 0 -1px rgba(0, 0, 0, 0.54353);\n      -gtk-icon-shadow: 0 -1px rgba(0, 0, 0, 0.54353);\n      box-shadow: inset 0 1px rgba(255, 255, 255, 0.4); }\n      .selection-mode.titlebar:not(headerbar) button.flat,\n      headerbar.selection-mode button.flat {\n        border-color: transparent;\n        background-color: transparent;\n        background-image: none;\n        box-shadow: inset 0 1px transparent;\n        text-shadow: none;\n        -gtk-icon-shadow: none; }\n      .selection-mode.titlebar:not(headerbar) button:hover,\n      headerbar.selection-mode button:hover {\n        color: @theme_selected_fg_color;\n        outline-color: rgba(255, 255, 255, 0.3);\n        border-color: shade(@theme_selected_bg_color, 0.6);\n        border-bottom-color: shade(@theme_selected_bg_color, 0.6);\n        background-image: image(@theme_selected_bg_color);\n        text-shadow: 0 -1px rgba(0, 0, 0, 0.49553);\n        -gtk-icon-shadow: 0 -1px rgba(0, 0, 0, 0.49553);\n        box-shadow: inset 0 1px rgba(255, 255, 255, 0.4); }\n      .selection-mode.titlebar:not(headerbar) button:active, .selection-mode.titlebar:not(headerbar) button:checked,\n      headerbar.selection-mode button:active,\n      headerbar.selection-mode button:checked {\n        color: @theme_selected_fg_color;\n        outline-color: rgba(255, 255, 255, 0.3);\n        border-color: shade(@theme_selected_bg_color, 0.6);\n        background-image: none;\n        background-color: shade(@theme_selected_bg_color, 0.8);\n        box-shadow: inset 0 1px transparent;\n        text-shadow: none;\n        -gtk-icon-shadow: none; }\n      .selection-mode.titlebar:not(headerbar) button:backdrop.flat, .selection-mode.titlebar:not(headerbar) button:backdrop,\n      headerbar.selection-mode button:backdrop.flat,\n      headerbar.selection-mode button:backdrop {\n        border-color: @theme_selected_bg_color;\n        background-color: transparent;\n        background-image: image(@theme_selected_bg_color);\n        text-shadow: none;\n        -gtk-icon-shadow: none;\n        box-shadow: inset 0 1px transparent;\n        -gtk-icon-effect: none;\n        border-color: shade(@theme_selected_bg_color, 0.6); }\n        .selection-mode.titlebar:not(headerbar) button:backdrop.flat label, .selection-mode.titlebar:not(headerbar) button:backdrop.flat, .selection-mode.titlebar:not(headerbar) button:backdrop label, .selection-mode.titlebar:not(headerbar) button:backdrop,\n        headerbar.selection-mode button:backdrop.flat label,\n        headerbar.selection-mode button:backdrop.flat,\n        headerbar.selection-mode button:backdrop label,\n        headerbar.selection-mode button:backdrop {\n          color: @theme_selected_fg_color; }\n        .selection-mode.titlebar:not(headerbar) button:backdrop.flat:active, .selection-mode.titlebar:not(headerbar) button:backdrop.flat:checked, .selection-mode.titlebar:not(headerbar) button:backdrop:active, .selection-mode.titlebar:not(headerbar) button:backdrop:checked,\n        headerbar.selection-mode button:backdrop.flat:active,\n        headerbar.selection-mode button:backdrop.flat:checked,\n        headerbar.selection-mode button:backdrop:active,\n        headerbar.selection-mode button:backdrop:checked {\n          border-color: shade(@theme_selected_bg_color, 0.6);\n          background-color: shade(@theme_selected_bg_color, 0.6);\n          background-image: none;\n          box-shadow: inset 0 1px transparent;\n          border-color: shade(@theme_selected_bg_color, 0.6); }\n          .selection-mode.titlebar:not(headerbar) button:backdrop.flat:active label, .selection-mode.titlebar:not(headerbar) button:backdrop.flat:active, .selection-mode.titlebar:not(headerbar) button:backdrop.flat:checked label, .selection-mode.titlebar:not(headerbar) button:backdrop.flat:checked, .selection-mode.titlebar:not(headerbar) button:backdrop:active label, .selection-mode.titlebar:not(headerbar) button:backdrop:active, .selection-mode.titlebar:not(headerbar) button:backdrop:checked label, .selection-mode.titlebar:not(headerbar) button:backdrop:checked,\n          headerbar.selection-mode button:backdrop.flat:active label,\n          headerbar.selection-mode button:backdrop.flat:active,\n          headerbar.selection-mode button:backdrop.flat:checked label,\n          headerbar.selection-mode button:backdrop.flat:checked,\n          headerbar.selection-mode button:backdrop:active label,\n          headerbar.selection-mode button:backdrop:active,\n          headerbar.selection-mode button:backdrop:checked label,\n          headerbar.selection-mode button:backdrop:checked {\n            color: @theme_selected_fg_color; }\n        .selection-mode.titlebar:not(headerbar) button:backdrop.flat:disabled, .selection-mode.titlebar:not(headerbar) button:backdrop:disabled,\n        headerbar.selection-mode button:backdrop.flat:disabled,\n        headerbar.selection-mode button:backdrop:disabled {\n          border-color: @theme_selected_bg_color;\n          background-color: @theme_selected_bg_color;\n          background-image: none;\n          text-shadow: none;\n          -gtk-icon-shadow: none;\n          box-shadow: inset 0 1px transparent;\n          border-color: shade(@theme_selected_bg_color, 0.6); }\n          .selection-mode.titlebar:not(headerbar) button:backdrop.flat:disabled label, .selection-mode.titlebar:not(headerbar) button:backdrop.flat:disabled, .selection-mode.titlebar:not(headerbar) button:backdrop:disabled label, .selection-mode.titlebar:not(headerbar) button:backdrop:disabled,\n          headerbar.selection-mode button:backdrop.flat:disabled label,\n          headerbar.selection-mode button:backdrop.flat:disabled,\n          headerbar.selection-mode button:backdrop:disabled label,\n          headerbar.selection-mode button:backdrop:disabled {\n            color: @theme_selected_fg_color; }\n          .selection-mode.titlebar:not(headerbar) button:backdrop.flat:disabled:active, .selection-mode.titlebar:not(headerbar) button:backdrop.flat:disabled:checked, .selection-mode.titlebar:not(headerbar) button:backdrop:disabled:active, .selection-mode.titlebar:not(headerbar) button:backdrop:disabled:checked,\n          headerbar.selection-mode button:backdrop.flat:disabled:active,\n          headerbar.selection-mode button:backdrop.flat:disabled:checked,\n          headerbar.selection-mode button:backdrop:disabled:active,\n          headerbar.selection-mode button:backdrop:disabled:checked {\n            border-color: shade(@theme_selected_bg_color, 0.6);\n            background-color: shade(@theme_selected_bg_color, 0.6);\n            background-image: none;\n            box-shadow: inset 0 1px transparent;\n            border-color: shade(@theme_selected_bg_color, 0.6); }\n            .selection-mode.titlebar:not(headerbar) button:backdrop.flat:disabled:active label, .selection-mode.titlebar:not(headerbar) button:backdrop.flat:disabled:checked label, .selection-mode.titlebar:not(headerbar) button:backdrop:disabled:active label, .selection-mode.titlebar:not(headerbar) button:backdrop:disabled:checked label,\n            headerbar.selection-mode button:backdrop.flat:disabled:active label,\n            headerbar.selection-mode button:backdrop.flat:disabled:checked label,\n            headerbar.selection-mode button:backdrop:disabled:active label,\n            headerbar.selection-mode button:backdrop:disabled:checked label {\n              color: @insensitive_fg_color; }\n      .selection-mode.titlebar:not(headerbar) button.flat:backdrop, .selection-mode.titlebar:not(headerbar) button.flat:disabled, .selection-mode.titlebar:not(headerbar) button.flat:backdrop:disabled,\n      headerbar.selection-mode button.flat:backdrop,\n      headerbar.selection-mode button.flat:disabled,\n      headerbar.selection-mode button.flat:backdrop:disabled {\n        border-color: transparent;\n        background-color: transparent;\n        background-image: none;\n        box-shadow: inset 0 1px transparent;\n        text-shadow: none;\n        -gtk-icon-shadow: none; }\n      .selection-mode.titlebar:not(headerbar) button:disabled,\n      headerbar.selection-mode button:disabled {\n        border-color: shade(@theme_selected_bg_color, 0.6);\n        background-color: @theme_selected_bg_color;\n        background-image: none;\n        text-shadow: none;\n        -gtk-icon-shadow: none;\n        box-shadow: inset 0 1px transparent; }\n        .selection-mode.titlebar:not(headerbar) button:disabled label, .selection-mode.titlebar:not(headerbar) button:disabled,\n        headerbar.selection-mode button:disabled label,\n        headerbar.selection-mode button:disabled {\n          color: #b2d0ef; }\n        .selection-mode.titlebar:not(headerbar) button:disabled:active, .selection-mode.titlebar:not(headerbar) button:disabled:checked,\n        headerbar.selection-mode button:disabled:active,\n        headerbar.selection-mode button:disabled:checked {\n          border-color: shade(@theme_selected_bg_color, 0.6);\n          background-color: shade(@theme_selected_bg_color, 0.6);\n          background-image: none;\n          box-shadow: inset 0 1px transparent; }\n          .selection-mode.titlebar:not(headerbar) button:disabled:active label, .selection-mode.titlebar:not(headerbar) button:disabled:active, .selection-mode.titlebar:not(headerbar) button:disabled:checked label, .selection-mode.titlebar:not(headerbar) button:disabled:checked,\n          headerbar.selection-mode button:disabled:active label,\n          headerbar.selection-mode button:disabled:active,\n          headerbar.selection-mode button:disabled:checked label,\n          headerbar.selection-mode button:disabled:checked {\n            color: @insensitive_fg_color; }\n      .selection-mode.titlebar:not(headerbar) button.suggested-action,\n      headerbar.selection-mode button.suggested-action {\n        color: @theme_fg_color;\n        outline-color: @outline_color;\n        border-color: @borders;\n        border-bottom-color: @borders;\n        background-image: image(@theme_bg_color);\n        text-shadow: 0 0 @txt_shadow;\n        -gtk-icon-shadow: 0 0 @txt_shadow;\n        box-shadow: inset 0 0 rgba(255, 255, 255, 0.8);\n        border-color: shade(@theme_selected_bg_color, 0.6); }\n        .selection-mode.titlebar:not(headerbar) button.suggested-action:hover,\n        headerbar.selection-mode button.suggested-action:hover {\n          color: @theme_fg_color;\n          outline-color: @outline_color;\n          border-color: @borders;\n          border-bottom-color: @borders;\n          background-image: linear-gradient(to bottom, @theme_selected_bg_color, @theme_selected_bg_color);\n          text-shadow: 0 1px @txt_shadow;\n          -gtk-icon-shadow: 0 0 @txt_shadow;\n          box-shadow: inset 0 0 @theme_bg_color;\n          border-color: shade(@theme_selected_bg_color, 0.6); }\n        .selection-mode.titlebar:not(headerbar) button.suggested-action:active,\n        headerbar.selection-mode button.suggested-action:active {\n          color: @theme_fg_color;\n          outline-color: @outline_color;\n          border-color: @borders;\n          background-image: none;\n          background-color: shade(@theme_bg_color, 0.9);\n          box-shadow: inset 0 0 transparent;\n          text-shadow: none;\n          -gtk-icon-shadow: none;\n          border-color: shade(@theme_selected_bg_color, 0.6); }\n        .selection-mode.titlebar:not(headerbar) button.suggested-action:disabled,\n        headerbar.selection-mode button.suggested-action:disabled {\n          border-color: @borders;\n          background-color: @insensitive_bg_color;\n          background-image: none;\n          text-shadow: none;\n          -gtk-icon-shadow: none;\n          box-shadow: inset 0 0 transparent;\n          border-color: shade(@theme_selected_bg_color, 0.6); }\n          .selection-mode.titlebar:not(headerbar) button.suggested-action:disabled label, .selection-mode.titlebar:not(headerbar) button.suggested-action:disabled,\n          headerbar.selection-mode button.suggested-action:disabled label,\n          headerbar.selection-mode button.suggested-action:disabled {\n            color: @insensitive_fg_color; }\n        .selection-mode.titlebar:not(headerbar) button.suggested-action:backdrop,\n        headerbar.selection-mode button.suggested-action:backdrop {\n          border-color: shade(@borders, 0.95);\n          background-color: transparent;\n          background-image: image(@theme_bg_color);\n          text-shadow: none;\n          -gtk-icon-shadow: none;\n          box-shadow: inset 0 0 transparent;\n          border-color: shade(@theme_selected_bg_color, 0.6); }\n          .selection-mode.titlebar:not(headerbar) button.suggested-action:backdrop label, .selection-mode.titlebar:not(headerbar) button.suggested-action:backdrop,\n          headerbar.selection-mode button.suggested-action:backdrop label,\n          headerbar.selection-mode button.suggested-action:backdrop {\n            color: @insensitive_fg_color; }\n        .selection-mode.titlebar:not(headerbar) button.suggested-action:backdrop:disabled,\n        headerbar.selection-mode button.suggested-action:backdrop:disabled {\n          border-color: shade(@borders, 0.95);\n          background-color: @insensitive_bg_color;\n          background-image: none;\n          text-shadow: none;\n          -gtk-icon-shadow: none;\n          box-shadow: inset 0 1px transparent;\n          border-color: shade(@theme_selected_bg_color, 0.6); }\n          .selection-mode.titlebar:not(headerbar) button.suggested-action:backdrop:disabled label, .selection-mode.titlebar:not(headerbar) button.suggested-action:backdrop:disabled,\n          headerbar.selection-mode button.suggested-action:backdrop:disabled label,\n          headerbar.selection-mode button.suggested-action:backdrop:disabled {\n            color: shade(@theme_unfocused_fg_color, 1.1); }\n    .selection-mode.titlebar:not(headerbar) .selection-menu:backdrop, .selection-mode.titlebar:not(headerbar) .selection-menu,\n    headerbar.selection-mode .selection-menu:backdrop,\n    headerbar.selection-mode .selection-menu {\n      border-color: shade(@theme_selected_bg_color, 1.0);\n      background-color: shade(@theme_selected_bg_color, 1.0);\n      background-image: none;\n      box-shadow: none;\n      padding-left: 10px;\n      padding-right: 10px; }\n      .selection-mode.titlebar:not(headerbar) .selection-menu:backdrop GtkArrow, .selection-mode.titlebar:not(headerbar) .selection-menu GtkArrow,\n      headerbar.selection-mode .selection-menu:backdrop GtkArrow,\n      headerbar.selection-mode .selection-menu GtkArrow {\n        -GtkArrow-arrow-scaling: 1; }\n      .selection-mode.titlebar:not(headerbar) .selection-menu:backdrop .arrow, .selection-mode.titlebar:not(headerbar) .selection-menu .arrow,\n      headerbar.selection-mode .selection-menu:backdrop .arrow,\n      headerbar.selection-mode .selection-menu .arrow {\n        -gtk-icon-source: -gtk-icontheme(\"pan-down-symbolic\");\n        color: @theme_selected_fg_color;\n        -gtk-icon-shadow: none; }\n  .tiled .titlebar:backdrop:not(headerbar), .tiled .titlebar:not(headerbar), .maximized .titlebar:backdrop:not(headerbar), .maximized .titlebar:not(headerbar), .tiled\n  headerbar:backdrop, .tiled\n  headerbar, .maximized\n  headerbar:backdrop, .maximized\n  headerbar {\n    border-radius: 0; }\n  .default-decoration.titlebar:not(headerbar),\n  headerbar.default-decoration {\n    min-height: 28px;\n    padding: 4px; }\n    .default-decoration.titlebar:not(headerbar) button.titlebutton,\n    headerbar.default-decoration button.titlebutton {\n      min-height: 26px;\n      min-width: 26px;\n      margin: 0;\n      padding: 0; }\n  .solid-csd .titlebar:backdrop:dir(rtl):not(headerbar), .solid-csd .titlebar:backdrop:dir(ltr):not(headerbar), .solid-csd .titlebar:dir(rtl):not(headerbar), .solid-csd .titlebar:dir(ltr):not(headerbar), .solid-csd\n  headerbar:backdrop:dir(rtl), .solid-csd\n  headerbar:backdrop:dir(ltr), .solid-csd\n  headerbar:dir(rtl), .solid-csd\n  headerbar:dir(ltr) {\n    margin-left: -1px;\n    margin-right: -1px;\n    margin-top: -1px;\n    border-radius: 0;\n    box-shadow: none; }\n\nheaderbar entry,\nheaderbar spinbutton,\nheaderbar separator,\nheaderbar button {\n  margin-top: 6px;\n  margin-bottom: 6px; }\n\n.background:not(.tiled):not(.maximized) .titlebar:backdrop, .background:not(.tiled):not(.maximized) .titlebar {\n  border-top-left-radius: 0;\n  border-top-right-radius: 0; }\n\nwindow:not(.tiled):not(.maximized) separator:first-child + headerbar:backdrop, window:not(.tiled):not(.maximized) separator:first-child + headerbar, window:not(.tiled):not(.maximized) headerbar:first-child:backdrop, window:not(.tiled):not(.maximized) headerbar:first-child {\n  border-top-left-radius: 0; }\nwindow:not(.tiled):not(.maximized) headerbar:last-child:backdrop, window:not(.tiled):not(.maximized) headerbar:last-child {\n  border-top-right-radius: 0; }\n\nwindow.csd > .titlebar:not(headerbar) {\n  padding: 0;\n  background-color: transparent;\n  background-image: none;\n  border-style: none;\n  border-color: transparent;\n  box-shadow: none; }\n.titlebar:not(headerbar) > separator {\n  background-color: @borders; }\n\n/******************\n * Window actions *\n ******************/\n\n.titlebar .titlebutton.minimize {\n    color: transparent;\n    border-image: none;\n    box-shadow: none;\n    padding: 6px 12px;\n    background-position: center;\n    background-repeat: no-repeat;\n    border: none;\n    background-image: -gtk-scaled(url(\"buttons/minimize-focused-normal.png\")); }\n\n.titlebar .titlebutton.minimize:backdrop {\n    background-image: -gtk-scaled(url(\"buttons/minimize-unfocused-normal.png\"));\n    color: transparent; }\n\n.titlebar .titlebutton.minimize:hover,\n.titlebar .titlebutton.minimize:active,\n.titlebar .titlebutton.minimize:checked {\n    color: transparent;\n    border-image: none;\n    box-shadow: none;\n    background-position: center;\n    background-repeat: no-repeat;\n    background-color: transparent;\n    background-image: -gtk-scaled(url(\"buttons/minimize-focused-active.png\")); }\n\n.titlebar .titlebutton.maximize {\n    color: transparent;\n    border: none;\n    padding: 6px 12px;\n    border-image: none;\n    box-shadow: none;\n    background-position: center;\n    background-repeat: no-repeat;\n    background-image: -gtk-scaled(url(\"buttons/maximize-focused-normal.png\")); }\n\n.titlebar .titlebutton.maximize:backdrop {\n    background-image: -gtk-scaled(url(\"buttons/maximize-unfocused-normal.png\"));\n    color: transparent; }\n\n\n.titlebar .titlebutton.maximize:hover, \n.titlebar .titlebutton.maximize:active,\n.titlebar .titlebutton.maximize:checked  {\n    color: transparent;\n    border-image: none;\n    box-shadow: none;\n    background-position: center;\n    background-repeat: no-repeat;\n    background-color: transparent;\n    background-image: -gtk-scaled(url(\"buttons/maximize-focused-active.png\")); }\n\n.titlebar .titlebutton.close {\n    color: transparent;\n    border: none;\n    padding: 6px 12px;\n    border-image: none;\n    box-shadow: none;\n    background-position: center;\n    background-repeat: no-repeat;\n    background-image: -gtk-scaled(url(\"buttons/close-focused-normal.png\")); }\n\n.titlebar .titlebutton.close:backdrop {\n    background-image: -gtk-scaled(url(\"buttons/close-unfocused-normal.png\"));\n    color: transparent; }\n\n\n.titlebar .titlebutton.close:hover,\n.titlebar .titlebutton.close:active,\n.titlebar .titlebutton.close:checked  {\n    color: transparent;\n    border-image: none;\n    box-shadow: none;\n    background-position: center;\n    background-repeat: no-repeat;\n    background-color: transparent;\n    background-image: -gtk-scaled(url(\"buttons/close-focused-active.png\")); }\n\n\n\n/************\n * Pathbars *\n ************/\n.path-bar button.text-button, .path-bar button.image-button, .path-bar button {\n  padding-left: 4px;\n  padding-right: 4px; }\n.path-bar button.text-button.image-button label {\n  padding-left: 0;\n  padding-right: 0; }\n.path-bar button.text-button.image-button label:last-child, .path-bar button label:last-child {\n  padding-right: 8px; }\n.path-bar button.text-button.image-button label:first-child, .path-bar button label:first-child {\n  padding-left: 8px; }\n.path-bar button image {\n  padding-left: 4px;\n  padding-right: 4px; }\n.path-bar button.slider-button {\n  padding-left: 0;\n  padding-right: 0; }\n\n/**************\n * Tree Views *\n **************/\ntreeview.view {\n  -GtkTreeView-grid-line-width: 1;\n  -GtkTreeView-grid-line-pattern: '';\n  -GtkTreeView-tree-line-width: 1;\n  -GtkTreeView-tree-line-pattern: '';\n  -GtkTreeView-expander-size: 16;\n  border-left-color: #979a9b;\n  border-top-color: @theme_bg_color; }\n  treeview.view:selected:focus, treeview.view:selected {\n    border-radius: 0; }\n  treeview.view:selected:backdrop, treeview.view:selected {\n    border-left-color: @theme_selected_bg_color;\n    border-top-color: @theme_selected_bg_color; }\n  treeview.view:disabled {\n    color: @insensitive_fg_color; }\n    treeview.view:disabled:selected {\n      color: #92bce8; }\n      treeview.view:disabled:selected:backdrop {\n        color: #7fb0e4; }\n    treeview.view:disabled:backdrop {\n      color: shade(@theme_unfocused_fg_color, 1.1); }\n  treeview.view.separator {\n    min-height: 2px;\n    color: @osd_fg_color; }\n    treeview.view.separator:backdrop {\n      color: rgba(232, 232, 231, 0.1); }\n  treeview.view:backdrop {\n    border-left-color: #babbbb;\n    border-top: @theme_bg_color; }\n  treeview.view:drop(active) {\n    border-style: solid none;\n    border-width: 1px;\n    border-color: shade(@theme_selected_bg_color, 0.6); }\n    treeview.view:drop(active).after {\n      border-top-style: none; }\n    treeview.view:drop(active).before {\n      border-bottom-style: none; }\n  treeview.view.expander {\n    -gtk-icon-source: -gtk-icontheme(\"pan-end-symbolic\");\n    color: #6d7172; }\n    treeview.view.expander:dir(rtl) {\n      -gtk-icon-source: -gtk-icontheme(\"pan-end-symbolic-rtl\"); }\n    treeview.view.expander:hover {\n      color: @theme_fg_color; }\n    treeview.view.expander:selected {\n      color: #c9def4; }\n      treeview.view.expander:selected:hover {\n        color: @theme_selected_fg_color; }\n      treeview.view.expander:selected:backdrop {\n        color: #c7dcf2; }\n    treeview.view.expander:checked {\n      -gtk-icon-source: -gtk-icontheme(\"pan-down-symbolic\"); }\n    treeview.view.expander:backdrop {\n      color: #adafb0; }\n  treeview.view.progressbar {\n    color: @theme_selected_fg_color;\n    border: 1px solid shade(@theme_selected_bg_color, 0.6);\n    border-radius: 0;\n    background-color: @progressbar_color;\n    background-image: linear-gradient(to bottom, @progressbar_color, @progressbar_color);\n    box-shadow: inset 0 1px rgba(255, 255, 255, 0.3), 0 1px rgba(0, 0, 0, 0.2); }\n    treeview.view.progressbar:selected:focus, treeview.view.progressbar:selected {\n      border-radius: 0;\n      color: @theme_selected_bg_color;\n      box-shadow: none;\n      background-image: linear-gradient(to bottom, #ffffff, #e6e6e6); }\n      treeview.view.progressbar:selected:focus:backdrop, treeview.view.progressbar:selected:backdrop {\n        color: @theme_selected_bg_color;\n        border-color: shade(@theme_selected_bg_color, 0.6);\n        background-color: @theme_unfocused_bg_color; }\n    treeview.view.progressbar:backdrop {\n      color: @theme_unfocused_bg_color;\n      background-image: none;\n      box-shadow: none; }\n  treeview.view.trough {\n    background-color: rgba(46, 52, 54, 0.1);\n    border-radius: 0; }\n    treeview.view.trough:selected:focus, treeview.view.trough:selected {\n      background-color: rgba(255, 255, 255, 0.3);\n      border-radius: 0;\n      border-width: 1px 0;\n      border-style: solid;\n      border-color: @theme_selected_bg_color; }\n  treeview.view header button {\n    color: #979a9b;\n    background-color: @theme_bg_color;\n    font-weight: bold;\n    text-shadow: none;\n    box-shadow: none; }\n    treeview.view header button:hover {\n      color: #636769;\n      box-shadow: none;\n      transition: none; }\n    treeview.view header button:active {\n      color: @theme_fg_color;\n      transition: none; }\n  treeview.view header button:last-child:backdrop, treeview.view header button:last-child {\n    border-right-style: none; }\n  treeview.view button.dnd:active, treeview.view button.dnd:selected, treeview.view button.dnd:hover, treeview.view button.dnd,\n  treeview.view header.button.dnd:active,\n  treeview.view header.button.dnd:selected,\n  treeview.view header.button.dnd:hover,\n  treeview.view header.button.dnd {\n    padding: 0 6px;\n    color: @theme_selected_fg_color;\n    background-image: none;\n    background-color: @theme_selected_bg_color;\n    border-style: none;\n    border-radius: 0;\n    box-shadow: inset 0 0 0 1px #ffffff;\n    text-shadow: none;\n    transition: none; }\n\ntreeview.view header button, treeview.view header button:hover, treeview.view header button:active {\n  padding: 0 6px;\n  background-image: none;\n  border-style: none solid solid none;\n  border-color: @theme_bg_color;\n  border-radius: 0;\n  text-shadow: none; }\n  treeview.view header button:disabled {\n    border-color: @theme_bg_color;\n    background-image: none; }\n  treeview.view header button:backdrop {\n    color: #babbbb;\n    border-color: @theme_bg_color;\n    border-style: none solid solid none;\n    background-image: none;\n    background-color: @theme_unfocused_bg_color; }\n    treeview.view header button:backdrop:disabled {\n      border-color: @theme_bg_color;\n      background-image: none; }\n\n/*********\n * Menus *\n *********/\nmenubar,\n.menubar {\n  -GtkWidget-window-dragging: true;\n  padding: 0px;\n  box-shadow: inset 0 -1px rgba(0, 0, 0, 0.1); }\n  menubar:backdrop,\n  .menubar:backdrop {\n    background-color: @theme_bg_color; }\n  menubar > menuitem,\n  .menubar > menuitem {\n    min-height: 16px;\n    padding: 4px 8px; }\n    menubar > menuitem:hover,\n    .menubar > menuitem:hover {\n      background-image: image(@theme_selected_bg_color);\n      color: @borders; }\n    menubar > menuitem:disabled,\n    .menubar > menuitem:disabled {\n      color: @insensitive_fg_color;\n      box-shadow: none; }\n\nmenu,\n.menu {\n  margin: 4px;\n  padding: 2px 0px;\n  background-color: @theme_bg_color;\n  border: 1px solid @borders; }\n  .csd menu, .csd\n  .menu {\n    border: none; }\n  menu:backdrop,\n  .menu:backdrop {\n    background-color: @theme_unfocused_bg_color; }\n  menu menuitem,\n  .menu menuitem {\n    min-height: 16px;\n    min-width: 40px;\n    padding: 4px 6px;\n    text-shadow: none; }\n    menu menuitem:hover,\n    .menu menuitem:hover {\n      color: @theme_selected_fg_color;\n      background-color: @theme_selected_bg_color; }\n    menu menuitem:disabled,\n    .menu menuitem:disabled {\n      color: @insensitive_fg_color; }\n      menu menuitem:disabled:backdrop,\n      .menu menuitem:disabled:backdrop {\n        color: shade(@theme_unfocused_fg_color, 1.1); }\n    menu menuitem:backdrop, menu menuitem:backdrop:hover,\n    .menu menuitem:backdrop,\n    .menu menuitem:backdrop:hover {\n      color: @insensitive_fg_color;\n      background-color: transparent; }\n    menu menuitem arrow,\n    .menu menuitem arrow {\n      min-height: 16px;\n      min-width: 16px; }\n      menu menuitem arrow:dir(ltr),\n      .menu menuitem arrow:dir(ltr) {\n        -gtk-icon-source: -gtk-icontheme(\"pan-end-symbolic\");\n        margin-left: 10px; }\n      menu menuitem arrow:dir(rtl),\n      .menu menuitem arrow:dir(rtl) {\n        -gtk-icon-source: -gtk-icontheme(\"pan-end-symbolic-rtl\");\n        margin-right: 10px; }\n  menu > arrow,\n  .menu > arrow {\n    border-color: transparent;\n    background-color: transparent;\n    background-image: none;\n    box-shadow: inset 0 1px transparent;\n    text-shadow: none;\n    -gtk-icon-shadow: none;\n    min-height: 16px;\n    min-width: 16px;\n    padding: 4px;\n    background-color: @theme_bg_color;\n    border-radius: 0; }\n    menu > arrow.top,\n    .menu > arrow.top {\n      margin-top: -6px;\n      border-bottom: 1px solid #eaebeb;\n      -gtk-icon-source: -gtk-icontheme(\"pan-up-symbolic\"); }\n    menu > arrow.bottom,\n    .menu > arrow.bottom {\n      margin-bottom: -6px;\n      border-top: 1px solid #eaebeb;\n      -gtk-icon-source: -gtk-icontheme(\"pan-down-symbolic\"); }\n    menu > arrow:hover,\n    .menu > arrow:hover {\n      background-color: #eaebeb; }\n    menu > arrow:backdrop,\n    .menu > arrow:backdrop {\n      background-color: @theme_unfocused_bg_color; }\n    menu > arrow:disabled,\n    .menu > arrow:disabled {\n      color: transparent;\n      background-color: transparent;\n      border-color: transparent; }\n\nmenuitem accelerator {\n  color: alpha(currentColor,0.55); }\nmenuitem check,\nmenuitem radio {\n  min-height: 16px;\n  min-width: 16px; }\n  menuitem check:dir(ltr),\n  menuitem radio:dir(ltr) {\n    margin-right: 7px; }\n  menuitem check:dir(rtl),\n  menuitem radio:dir(rtl) {\n    margin-left: 7px; }\n\n/***************\n * Popovers   *\n ***************/\npopover.background {\n  padding: 2px;\n  border-radius: 0;\n  background-color: @theme_bg_color;\n  box-shadow: 0 1px 2px @borders; }\n  .csd popover.background, popover.background {\n    border: 1px solid @borders; }\n  popover.background:backdrop {\n    background-color: @theme_bg_color;\n    box-shadow: none; }\n  popover.background > list,\n  popover.background > .view,\n  popover.background > iconview,\n  popover.background > toolbar {\n    border-style: none;\n    background-color: transparent; }\n  .csd popover.background.touch-selection, .csd popover.background.magnifier, popover.background.touch-selection, popover.background.magnifier {\n    border: 1px solid @osd_txt_shadow; }\n  popover.background separator {\n    margin: 3px; }\n  popover.background list separator {\n    margin: 0px; }\n\n/*************\n * Notebooks *\n *************/\nnotebook > header {\n  padding: 1px;\n  border-color: @borders;\n  border-width: 1px;\n  background-color: transparent; }\n  notebook > header:backdrop {\n    border-color: shade(@borders, 0.95);\n    background-color: transparent; }\n  notebook > header tabs {\n    margin: -1px; \n    background-color: shade(@theme_bg_color, 0.95);}\n  notebook > header.top {\n    border-bottom-style: solid; }\n    notebook > header.top > tabs {\n      margin-bottom: -2px; }\n      notebook > header.top > tabs > tab:hover {\n        background-color: shade(@theme_bg_color, 0.97); }\n      notebook > header.top > tabs > tab:backdrop {\n        box-shadow: none; }\n      notebook > header.top > tabs > tab:checked {\n        background-color: @theme_bg_color; }\n  notebook > header.bottom {\n    border-top-style: solid; }\n    notebook > header.bottom > tabs {\n      margin-top: -2px;\n      background-color: shade(@theme_bg_color, 0.95); }\n      notebook > header.bottom > tabs > tab:hover {\n      background-color: shade(@theme_bg_color, 0.97); }\n      notebook > header.bottom > tabs > tab:backdrop {\n        box-shadow: none; }\n      notebook > header.bottom > tabs > tab:checked {\n        background-color: @theme_bg_color; }\n  notebook > header.left {\n    border-right-style: solid; }\n    notebook > header.left > tabs {\n      margin-right: -2px; \n      background-color: shade(@theme_bg_color, 0.95);}\n      notebook > header.left > tabs > tab:hover {\n      background-color: shade(@theme_bg_color, 0.97); }\n      notebook > header.left > tabs > tab:backdrop {\n        box-shadow: none; }\n      notebook > header.left > tabs > tab:checked {\n      background-color: @theme_bg_color; }\n  notebook > header.right {\n    border-left-style: solid; }\n    notebook > header.right > tabs {\n      margin-left: -2px; \n      background-color: shade(@theme_bg_color, 0.95);}\n      notebook > header.right > tabs > tab:hover {\n      background-color: shade(@theme_bg_color, 0.97); }\n      notebook > header.right > tabs > tab:backdrop {\n        box-shadow: none; }\n      notebook > header.right > tabs > tab:checked {\n      background-color: @theme_bg_color; }\n  notebook > header.top > tabs > arrow {\n    border-top-style: none; }\n  notebook > header.bottom > tabs > arrow {\n    border-bottom-style: none; }\n  notebook > header.top > tabs > arrow, notebook > header.bottom > tabs > arrow {\n    margin-left: -5px;\n    margin-right: -5px;\n    padding-left: 4px;\n    padding-right: 4px; }\n    notebook > header.top > tabs > arrow.down, notebook > header.bottom > tabs > arrow.down {\n      -gtk-icon-source: -gtk-icontheme(\"pan-start-symbolic\"); }\n    notebook > header.top > tabs > arrow.up, notebook > header.bottom > tabs > arrow.up {\n      -gtk-icon-source: -gtk-icontheme(\"pan-end-symbolic\"); }\n  notebook > header.left > tabs > arrow {\n    border-left-style: none; }\n  notebook > header.right > tabs > arrow {\n    border-right-style: none; }\n  notebook > header.left > tabs > arrow, notebook > header.right > tabs > arrow {\n    margin-top: -5px;\n    margin-bottom: -5px;\n    padding-top: 4px;\n    padding-bottom: 4px; }\n    notebook > header.left > tabs > arrow.down, notebook > header.right > tabs > arrow.down {\n      -gtk-icon-source: -gtk-icontheme(\"pan-up-symbolic\"); }\n    notebook > header.left > tabs > arrow.up, notebook > header.right > tabs > arrow.up {\n      -gtk-icon-source: -gtk-icontheme(\"pan-down-symbolic\"); }\n  notebook > header > tabs > arrow {\n    min-height: 16px;\n    min-width: 16px;\n    border-radius: 0; }\n    notebook > header > tabs > arrow:hover:not(:active):not(:backdrop) {\n      background-clip: padding-box;\n      background-image: none;\n      background-color: rgba(255, 255, 255, 0.3);\n      border-color: transparent;\n      box-shadow: none; }\n    notebook > header > tabs > arrow:disabled {\n      border-color: transparent;\n      background-color: transparent;\n      background-image: none;\n      box-shadow: inset 0 1px transparent;\n      text-shadow: none;\n      -gtk-icon-shadow: none; }\n  notebook > header tab {\n    min-height: 30px;\n    min-width: 30px;\n    padding: 3px 12px;\n    outline-offset: -5px;\n    color: @insensitive_fg_color;\n    font-weight: bold;\n    border-width: 1px;\n    border-color: transparent; }\n    notebook > header tab:hover {\n      color: @theme_selected_fg_color; }\n      notebook > header tab:hover.reorderable-page {\n        border-color: rgba(182, 182, 179, 0.3);\n        background-color: rgba(232, 232, 231, 0.2); }\n    notebook > header tab:backdrop {\n      color: @theme_unfocused_fg_color; }\n      notebook > header tab:backdrop.reorderable-page {\n        border-color: transparent;\n        background-color: transparent; }\n    notebook > header tab:checked {\n      color: @theme_fg_color; }\n\n/* active notebook tab in gedit */\n      notebook > header tab:checked.reorderable-page {\n        border-color: rgba(182, 182, 179, 0.5);\n        background-color: shade(@theme_bg_color, 0.7); }\n        notebook > header tab:checked.reorderable-page:hover {\n          background-color: @theme_selected_bg_color; }\n    notebook > header tab:backdrop:checked {\n      color: @insensitive_fg_color; }\n      notebook > header tab:backdrop:checked.reorderable-page {\n        border-color: shade(@borders, 0.95);\n        background-color: @theme_bg_color; }\n    notebook > header tab button.flat {\n      padding: 0;\n      margin-top: 4px;\n      margin-bottom: 4px;\n      min-width: 20px;\n      min-height: 20px; }\n      notebook > header tab button.flat:hover {\n        color: currentColor; }\n      notebook > header tab button.flat, notebook > header tab button.flat:backdrop {\n        color: alpha(currentColor,0.3); }\n      notebook > header tab button.flat:last-child {\n        margin-left: 4px;\n        margin-right: -4px; }\n      notebook > header tab button.flat:first-child {\n        margin-left: -4px;\n        margin-right: 4px; }\n  notebook > header.top tabs, notebook > header.bottom tabs {\n    padding-left: 4px;\n    padding-right: 4px; }\n    notebook > header.top tabs:not(:only-child), notebook > header.bottom tabs:not(:only-child) {\n      margin-left: 3px;\n      margin-right: 3px; }\n      notebook > header.top tabs:not(:only-child):first-child, notebook > header.bottom tabs:not(:only-child):first-child {\n        margin-left: -1px; }\n      notebook > header.top tabs:not(:only-child):last-child, notebook > header.bottom tabs:not(:only-child):last-child {\n        margin-right: -1px; }\n    notebook > header.top tabs tab, notebook > header.bottom tabs tab {\n      margin-left: 4px;\n      margin-right: 4px; }\n      notebook > header.top tabs tab.reorderable-page, notebook > header.bottom tabs tab.reorderable-page {\n        border-style: none solid; }\n  notebook > header.left tabs, notebook > header.right tabs {\n    padding-top: 4px;\n    padding-bottom: 4px; }\n    notebook > header.left tabs:not(:only-child), notebook > header.right tabs:not(:only-child) {\n      margin-top: 3px;\n      margin-bottom: 3px; }\n      notebook > header.left tabs:not(:only-child):first-child, notebook > header.right tabs:not(:only-child):first-child {\n        margin-top: -1px; }\n      notebook > header.left tabs:not(:only-child):last-child, notebook > header.right tabs:not(:only-child):last-child {\n        margin-bottom: -1px; }\n    notebook > header.left tabs tab, notebook > header.right tabs tab {\n      margin-top: 4px;\n      margin-bottom: 4px; }\n      notebook > header.left tabs tab.reorderable-page, notebook > header.right tabs tab.reorderable-page {\n        border-style: solid none; }\n  notebook > header.top tab {\n    padding-bottom: 4px; }\n  notebook > header.bottom tab {\n    padding-top: 4px; }\nnotebook > stack:not(:only-child) {\n  background-color: @theme_bg_color; }\n  notebook > stack:not(:only-child):backdrop {\n    background-color: @theme_unfocused_bg_color; }\n\n/*************\n * scrollbar *\n *************/\nscrollbar {\n    border-width: 0;\n    border-style: solid;\n    padding: 0;\n    border-radius: 0;\n    background-color: shade(@theme_bg_color, 0.9);\n    background-image: none;\n    border-image: none; }\n\nscrollbar button,\nscrollbar button:hover,\nscrollbar button:active:hover {\n    border-width: 0;\n    border-radius: 0;\n    min-height: 12px;\n    min-width: 1px;\n    padding: 0;\n    box-shadow: none;\n    background-color: transparent;\n    background-image: none;\n    color: shade(@theme_fg_color, 0.4); }\n\nscrollbar.horizontal button {\n    min-height: 1px;\n    min-width: 12px; }\n\nscrollbar slider {\n    border-width: 0;\n    min-width: 45px;\n    min-height: 14px;\n    border-color: transparent;\n    border-radius: 0;\n    background-color: mix(@theme_bg_color, @theme_fg_color, 0.32); }\n\nscrollbar.vertical slider {\n    min-width: 14px;\n    min-height: 45px; }\n\nscrollbar slider:hover,\nscrollbar.vertical slider:hover {\n    border-color: transparent;\n    background-color: mix(@theme_bg_color, @theme_fg_color, 0.5); }\n\nscrollbar slider:active,\nscrollbar.vertical slider:active {\n    border-color: transparent;\n    background-color: shade(@theme_bg_color, 0.5); }\n\n  scrollbar slider.fine-tune:hover:active {\n    border-width: 2px;\n    border-color: transparent; }\n\n  scrollbar.vertical button.down {\n    -gtk-icon-source: -gtk-icontheme(\"pan-down-symbolic\"); }\n\n  scrollbar.vertical button.up {\n    -gtk-icon-source: -gtk-icontheme(\"pan-up-symbolic\"); }\n\n  scrollbar.horizontal button.down {\n    -gtk-icon-source: -gtk-icontheme(\"pan-end-symbolic\"); }\n\n  scrollbar.horizontal button.up {\n    -gtk-icon-source: -gtk-icontheme(\"pan-start-symbolic\"); }\n\ntreeview ~ scrollbar.vertical {\n  border-top: 1px solid @borders;\n  margin-top: -1px; }\n\n/**********\n * Switch *\n **********/\nswitch {\n  font-weight: bold;\n  font-size: smaller;\n  outline-offset: -4px;\n  border: 1px solid @borders;\n  border-radius: 16px;\n  color: transparent;\n  background-color: @borders;\n  text-shadow: 0 0 transparent; }\n  switch:checked {\n    color: transparent;\n    border-color: shade(@theme_selected_bg_color, 0.6);\n    background-color: shade(@theme_selected_bg_color, 0.6);\n    text-shadow: 0 0 rgba(24, 68, 114, 0), 0 0 0 transparent; }\n  switch:disabled {\n    color: transparent;\n    border-color: @borders;\n    background-color: @borders;\n    text-shadow: none; }\n  switch:backdrop {\n    color: transparent;\n    border-color: shade(@borders, 1.3);\n    background-color: shade(@borders, 1.3);\n    text-shadow: none;\n    transition: 200ms ease-out; }\n    switch:backdrop:checked {\n      color: transparent;\n      border-color: @theme_selected_bg_color;\n      background-color: @theme_selected_bg_color; }\n    switch:backdrop:disabled {\n      color: transparent;\n      border-color: shade(@borders, 0.95);\n      background-color: shade(@borders, 0.95); }\n  switch slider {\n    margin: -1px;\n    min-width: 13px;\n    min-height: 12px;\n    border: 6px solid;\n    border-radius: 14px;\n    transition: all 200ms cubic-bezier(0.25, 0.46, 0.45, 0.94);\n    color: @theme_fg_color;\n    outline-color: @outline_color;\n    border-color: @borders;\n    text-shadow: 0 1px @txt_shadow;\n    -gtk-icon-shadow: 0 1px @txt_shadow;\n    background-image: linear-gradient(to bottom, @theme_bg_color, @theme_bg_color);\n    box-shadow: none; } /*inset 0 1px @theme_bg_color, inset 0 -2px #ededec, inset 0 -1px #cacac8, 0 1px rgba(0, 0, 0, 0.1)*/ \n  switch:hover slider {\n    color: @theme_fg_color;\n    outline-color: @outline_color;\n    border-color: @borders;\n    background-image: linear-gradient(to bottom, @theme_bg_color, @theme_bg_color);\n    box-shadow: inset 0 0 @theme_bg_color, inset 0 0 #f4f4f4, inset 0 0 #cfcfcd, 0 1px rgba(0, 0, 0, 0.1); }\n  switch:checked slider {\n    border: 6px solid shade(@theme_selected_bg_color, 0.6); }\n  switch:disabled slider {\n    border-color: @borders;\n    background-color: @insensitive_bg_color;\n    background-image: none;\n    text-shadow: none;\n    -gtk-icon-shadow: none;\n    box-shadow: inset 0 1px transparent; }\n    switch:disabled slider label, switch:disabled slider {\n      color: @insensitive_fg_color; }\n  switch:backdrop slider {\n    transition: 200ms ease-out;\n    border-color: shade(@borders, 1.3);\n    background-color: transparent;\n    background-image: image(@theme_bg_color);\n    text-shadow: none;\n    -gtk-icon-shadow: none;\n    box-shadow: inset 0 1px transparent; }\n    switch:backdrop slider label, switch:backdrop slider {\n      color: @insensitive_fg_color; }\n  switch:backdrop:checked slider {\n    border-color: @theme_selected_bg_color; }\n  switch:backdrop:disabled slider {\n    border-color: shade(@borders, 0.95);\n    background-color: @insensitive_bg_color;\n    background-image: none;\n    text-shadow: none;\n    -gtk-icon-shadow: none;\n    box-shadow: inset 0 1px transparent; }\n    switch:backdrop:disabled slider label, switch:backdrop:disabled slider {\n      color: shade(@theme_unfocused_fg_color, 1.1); }\n  row:selected switch {\n    box-shadow: none;\n    border-color: shade(@theme_selected_bg_color, 0.6); }\n    row:selected switch:backdrop {\n      border-color: shade(@theme_selected_bg_color, 0.6); }\n    row:selected switch.slider:dir(rtl) {\n      border-left-color: @borders; }\n    row:selected switch.slider:dir(ltr) {\n      border-right-color: @borders; }\n    row:selected switch.slider:checked, row:selected switch.slider {\n      border-color: shade(@theme_selected_bg_color, 0.6); }\n\n/*************************\n * Check and Radio items *\n *************************/\n@keyframes check_radio_hover {\n  from {\n    background-image: -gtk-gradient(radial, center center, 0, center center, 0.001, to(alpha(rgba(38, 50, 56, 0.75), 0.1)), to(transparent)); }\n  to {\n    background-image: -gtk-gradient(radial, center center, 0, center center, 0.5, to(alpha(rgba(38, 50, 56, 0.75), 0.1)), to(transparent)); } }\n@keyframes check_radio_active {\n  from {\n    background-image: -gtk-gradient(radial, center center, 0, center center, 0.001, to(alpha(#00BCD4, 0.1)), to(transparent)); }\n  to {\n    background-image: -gtk-gradient(radial, center center, 0, center center, 0.5, to(alpha(#00BCD4, 0.1)), to(transparent)); } }\n@keyframes check_radio_active_reverse {\n  from {\n    background-image: -gtk-gradient(radial, center center, 0, center center, 0.5, to(alpha(#00BCD4, 0.2)), to(transparent)); }\n  to {\n    background-image: -gtk-gradient(radial, center center, 0, center center, 0.001, to(alpha(#00BCD4, 0)), to(transparent)); } }\n.check, check {\n  -gtk-icon-source: -gtk-scaled(url(\"assets/checkbox-unchecked.png\"), url(\"assets/checkbox-unchecked@2.png\"));\n  -gtk-icon-shadow: none; }\n  .check:backdrop, check:backdrop {\n    opacity: 0.8;\n    transition: 0.2s; }\n\n.check:hover, check:hover {\n  -gtk-icon-source: -gtk-scaled(url(\"assets/checkbox-unchecked-over.png\"), url(\"assets/checkbox-unchecked-over@2.png\"));\n  -gtk-icon-shadow: none; }\n  .check:hover:backdrop, check:hover:backdrop {\n    opacity: 0.8;\n    transition: 0.2s; }\n\n.check:active, check:active {\n  -gtk-icon-source: -gtk-scaled(url(\"assets/checkbox-unchecked-over.png\"), url(\"assets/checkbox-unchecked-over@2.png\"));\n  -gtk-icon-shadow: none; }\n  .check:active:backdrop, check:active:backdrop {\n    opacity: 0.8;\n    transition: 0.2s; }\n\n.check:disabled, check:disabled {\n  -gtk-icon-source: -gtk-scaled(url(\"assets/checkbox-unchecked-insensitive.png\"), url(\"assets/checkbox-unchecked-insensitive@2.png\"));\n  -gtk-icon-shadow: none; }\n  .check:disabled:backdrop, check:disabled:backdrop {\n    opacity: 0.8;\n    transition: 0.2s; }\n\n.check:indeterminate, check:indeterminate {\n  -gtk-icon-source: -gtk-scaled(url(\"assets/checkbox-mixed.png\"), url(\"assets/checkbox-mixed@2.png\"));\n  -gtk-icon-shadow: none; }\n  .check:indeterminate:backdrop, check:indeterminate:backdrop {\n    opacity: 0.8;\n    transition: 0.2s; }\n\n.check:indeterminate:hover, check:indeterminate:hover {\n  -gtk-icon-source: -gtk-scaled(url(\"assets/checkbox-mixed-over.png\"), url(\"assets/checkbox-mixed-over@2.png\"));\n  -gtk-icon-shadow: none; }\n  .check:indeterminate:hover:backdrop, check:indeterminate:hover:backdrop {\n    opacity: 0.8;\n    transition: 0.2s; }\n\n.check:indeterminate:active, check:indeterminate:active {\n  -gtk-icon-source: -gtk-scaled(url(\"assets/checkbox-mixed-over.png\"), url(\"assets/checkbox-mixed-over@2.png\"));\n  -gtk-icon-shadow: none; }\n  .check:indeterminate:active:backdrop, check:indeterminate:active:backdrop {\n    opacity: 0.8;\n    transition: 0.2s; }\n\n.check:indeterminate:disabled, check:indeterminate:disabled {\n  -gtk-icon-source: -gtk-scaled(url(\"assets/checkbox-mixed-insensitive.png\"), url(\"assets/checkbox-mixed-insensitive@2.png\"));\n  -gtk-icon-shadow: none; }\n  .check:indeterminate:disabled:backdrop, check:indeterminate:disabled:backdrop {\n    opacity: 0.8;\n    transition: 0.2s; }\n\n.check:checked, check:checked {\n  -gtk-icon-source: -gtk-scaled(url(\"assets/checkbox-checked.png\"), url(\"assets/checkbox-checked@2.png\"));\n  -gtk-icon-shadow: none; }\n  .check:checked:backdrop, check:checked:backdrop {\n    opacity: 0.8;\n    transition: 0.2s; }\n\n.check:checked:hover, check:checked:hover {\n  -gtk-icon-source: -gtk-scaled(url(\"assets/checkbox-checked-over.png\"), url(\"assets/checkbox-checked-over@2.png\"));\n  -gtk-icon-shadow: none; }\n  .check:checked:hover:backdrop, check:checked:hover:backdrop {\n    opacity: 0.8;\n    transition: 0.2s; }\n\n.check:checked:active, check:checked:active {\n  -gtk-icon-source: -gtk-scaled(url(\"assets/checkbox-checked-over.png\"), url(\"assets/checkbox-checked-over@2.png\"));\n  -gtk-icon-shadow: none; }\n  .check:checked:active:backdrop, check:checked:active:backdrop {\n    opacity: 0.8;\n    transition: 0.2s; }\n\n.check:checked:disabled, check:checked:disabled {\n  -gtk-icon-source: -gtk-scaled(url(\"assets/checkbox-checked-insensitive.png\"), url(\"assets/checkbox-checked-insensitive@2.png\"));\n  -gtk-icon-shadow: none; }\n  .check:checked:disabled:backdrop, check:checked:disabled:backdrop {\n    opacity: 0.8;\n    transition: 0.2s; }\n\nmenu menuitem.check,\nmenu menuitem check {\n  -gtk-icon-source: -gtk-scaled(url(\"assets/checkbox-unchecked.png\"), url(\"assets/checkbox-unchecked@2.png\"));\n  -gtk-icon-shadow: none; }\n  menu menuitem.check:hover,\n  menu menuitem check:hover {\n    -gtk-icon-source: -gtk-scaled(url(\"assets/checkbox-unchecked.png\"), url(\"assets/checkbox-unchecked@2.png\"));\n    animation: none;\n    -gtk-icon-shadow: none;\n    transition: none; }\n  menu menuitem.check:backdrop,\n  menu menuitem check:backdrop {\n    opacity: 0.8;\n    transition: 0.2s; }\n\nmenu menuitem.check:disabled,\nmenu menuitem check:disabled {\n  -gtk-icon-source: -gtk-scaled(url(\"assets/checkbox-insensitive.png\"), url(\"assets/checkbox-insensitive@2.png\"));\n  -gtk-icon-shadow: none; }\n  menu menuitem.check:disabled:hover,\n  menu menuitem check:disabled:hover {\n    -gtk-icon-source: -gtk-scaled(url(\"assets/checkbox-insensitive.png\"), url(\"assets/checkbox-insensitive@2.png\"));\n    animation: none;\n    -gtk-icon-shadow: none;\n    transition: none; }\n  menu menuitem.check:disabled:backdrop,\n  menu menuitem check:disabled:backdrop {\n    opacity: 0.8;\n    transition: 0.2s; }\n\nmenu menuitem.check:indeterminate,\nmenu menuitem check:indeterminate {\n  -gtk-icon-source: -gtk-scaled(url(\"assets/checkbox-mixed.png\"), url(\"assets/checkbox-mixed@2.png\"));\n  -gtk-icon-shadow: none; }\n  menu menuitem.check:indeterminate:hover,\n  menu menuitem check:indeterminate:hover {\n    -gtk-icon-source: -gtk-scaled(url(\"assets/checkbox-mixed.png\"), url(\"assets/checkbox-mixed@2.png\"));\n    animation: none;\n    -gtk-icon-shadow: none;\n    transition: none; }\n  menu menuitem.check:indeterminate:backdrop,\n  menu menuitem check:indeterminate:backdrop {\n    opacity: 0.8;\n    transition: 0.2s; }\n\nmenu menuitem.check:indeterminate:disabled,\nmenu menuitem check:indeterminate:disabled {\n  -gtk-icon-source: -gtk-scaled(url(\"assets/checkbox-mixed-insensitive.png\"), url(\"assets/checkbox-mixed-insensitive@2.png\"));\n  -gtk-icon-shadow: none; }\n  menu menuitem.check:indeterminate:disabled:hover,\n  menu menuitem check:indeterminate:disabled:hover {\n    -gtk-icon-source: -gtk-scaled(url(\"assets/checkbox-mixed-insensitive.png\"), url(\"assets/checkbox-mixed-insensitive@2.png\"));\n    animation: none;\n    -gtk-icon-shadow: none;\n    transition: none; }\n  menu menuitem.check:indeterminate:disabled:backdrop,\n  menu menuitem check:indeterminate:disabled:backdrop {\n    opacity: 0.8;\n    transition: 0.2s; }\n\nmenu menuitem.check:checked,\nmenu menuitem check:checked {\n  -gtk-icon-source: -gtk-scaled(url(\"assets/checkbox-checked.png\"), url(\"assets/checkbox-checked@2.png\"));\n  -gtk-icon-shadow: none; }\n  menu menuitem.check:checked:hover,\n  menu menuitem check:checked:hover {\n    -gtk-icon-source: -gtk-scaled(url(\"assets/checkbox-checked.png\"), url(\"assets/checkbox-checked@2.png\"));\n    animation: none;\n    -gtk-icon-shadow: none;\n    transition: none; }\n  menu menuitem.check:checked:backdrop,\n  menu menuitem check:checked:backdrop {\n    opacity: 0.8;\n    transition: 0.2s; }\n\nmenu menuitem.check:checked:disabled,\nmenu menuitem check:checked:disabled {\n  -gtk-icon-source: -gtk-scaled(url(\"assets/checkbox-checked-insensitive.png\"), url(\"assets/checkbox-checked-insensitive@2.png\"));\n  -gtk-icon-shadow: none; }\n  menu menuitem.check:checked:disabled:hover,\n  menu menuitem check:checked:disabled:hover {\n    -gtk-icon-source: -gtk-scaled(url(\"assets/checkbox-checked-insensitive.png\"), url(\"assets/checkbox-checked-insensitive@2.png\"));\n    animation: none;\n    -gtk-icon-shadow: none;\n    transition: none; }\n  menu menuitem.check:checked:disabled:backdrop,\n  menu menuitem check:checked:disabled:backdrop {\n    opacity: 0.8;\n    transition: 0.2s; }\n\n.radio, radio {\n  -gtk-icon-source: -gtk-scaled(url(\"assets/radio-unselected.png\"), url(\"assets/radio-unselected@2.png\"));\n  -gtk-icon-shadow: none; }\n  .radio:backdrop, radio:backdrop {\n    opacity: 0.8;\n    transition: 0.2s; }\n\n.radio:hover, radio:hover {\n  -gtk-icon-source: -gtk-scaled(url(\"assets/radio-unselected-over.png\"), url(\"assets/radio-unselected-over@2.png\"));\n  -gtk-icon-shadow: none; }\n  .radio:hover:backdrop, radio:hover:backdrop {\n    opacity: 0.8;\n    transition: 0.2s; }\n\n.radio:active, radio:active {\n  -gtk-icon-source: -gtk-scaled(url(\"assets/radio-unselected-over.png\"), url(\"assets/radio-unselected-over@2.png\"));\n  -gtk-icon-shadow: none; }\n  .radio:active:backdrop, radio:active:backdrop {\n    opacity: 0.8;\n    transition: 0.2s; }\n\n.radio:disabled, radio:disabled {\n  -gtk-icon-source: -gtk-scaled(url(\"assets/radio-unselected-insensitive.png\"), url(\"assets/radio-unselected-insensitive@2.png\"));\n  -gtk-icon-shadow: none; }\n  .radio:disabled:backdrop, radio:disabled:backdrop {\n    opacity: 0.8;\n    transition: 0.2s; }\n\n.radio:indeterminate, radio:indeterminate {\n  -gtk-icon-source: -gtk-scaled(url(\"assets/radio-mixed.png\"), url(\"assets/radio-mixed@2.png\"));\n  -gtk-icon-shadow: none; }\n  .radio:indeterminate:backdrop, radio:indeterminate:backdrop {\n    opacity: 0.8;\n    transition: 0.2s; }\n\n.radio:indeterminate:hover, radio:indeterminate:hover {\n  -gtk-icon-source: -gtk-scaled(url(\"assets/radio-mixed-over.png\"), url(\"assets/radio-mixed-over@2.png\"));\n  -gtk-icon-shadow: none; }\n  .radio:indeterminate:hover:backdrop, radio:indeterminate:hover:backdrop {\n    opacity: 0.8;\n    transition: 0.2s; }\n\n.radio:indeterminate:active, radio:indeterminate:active {\n  -gtk-icon-source: -gtk-scaled(url(\"assets/radio-mixed-over.png\"), url(\"assets/radio-mixed-over@2.png\"));\n  -gtk-icon-shadow: none; }\n  .radio:indeterminate:active:backdrop, radio:indeterminate:active:backdrop {\n    opacity: 0.8;\n    transition: 0.2s; }\n\n.radio:indeterminate:disabled, radio:indeterminate:disabled {\n  -gtk-icon-source: -gtk-scaled(url(\"assets/radio-mixed-insensitive.png\"), url(\"assets/radio-mixed-insensitive@2.png\"));\n  -gtk-icon-shadow: none; }\n  .radio:indeterminate:disabled:backdrop, radio:indeterminate:disabled:backdrop {\n    opacity: 0.8;\n    transition: 0.2s; }\n\n.radio:checked, radio:checked {\n  -gtk-icon-source: -gtk-scaled(url(\"assets/radio-selected.png\"), url(\"assets/radio-selected@2.png\"));\n  -gtk-icon-shadow: none; }\n  .radio:checked:backdrop, radio:checked:backdrop {\n    opacity: 0.8;\n    transition: 0.2s; }\n\n.radio:checked:hover, radio:checked:hover {\n  -gtk-icon-source: -gtk-scaled(url(\"assets/radio-selected-over.png\"), url(\"assets/radio-selected-over@2.png\"));\n  -gtk-icon-shadow: none; }\n  .radio:checked:hover:backdrop, radio:checked:hover:backdrop {\n    opacity: 0.8;\n    transition: 0.2s; }\n\n.radio:checked:active, radio:checked:active {\n  -gtk-icon-source: -gtk-scaled(url(\"assets/radio-selected-over.png\"), url(\"assets/radio-selected-over@2.png\"));\n  -gtk-icon-shadow: none; }\n  .radio:checked:active:backdrop, radio:checked:active:backdrop {\n    opacity: 0.8;\n    transition: 0.2s; }\n\n.radio:checked:disabled, radio:checked:disabled {\n  -gtk-icon-source: -gtk-scaled(url(\"assets/radio-selected-insensitive.png\"), url(\"assets/radio-selected-insensitive@2.png\"));\n  -gtk-icon-shadow: none; }\n  .radio:checked:disabled:backdrop, radio:checked:disabled:backdrop {\n    opacity: 0.8;\n    transition: 0.2s; }\n\nmenu menuitem.radio,\nmenu menuitem radio {\n  -gtk-icon-source: -gtk-scaled(url(\"assets/radio-unselected.png\"), url(\"assets/radio-unselected@2.png\"));\n  -gtk-icon-shadow: none; }\n  menu menuitem.radio:hover,\n  menu menuitem radio:hover {\n    -gtk-icon-source: -gtk-scaled(url(\"assets/radio-unselected.png\"), url(\"assets/radio-unselected@2.png\"));\n    animation: none;\n    -gtk-icon-shadow: none;\n    transition: none; }\n  menu menuitem.radio:backdrop,\n  menu menuitem radio:backdrop {\n    opacity: 0.8;\n    transition: 0.2s; }\n\nmenu menuitem.radio:disabled,\nmenu menuitem radio:disabled {\n  -gtk-icon-source: -gtk-scaled(url(\"assets/radio-insensitive.png\"), url(\"assets/radio-insensitive@2.png\"));\n  -gtk-icon-shadow: none; }\n  menu menuitem.radio:disabled:hover,\n  menu menuitem radio:disabled:hover {\n    -gtk-icon-source: -gtk-scaled(url(\"assets/radio-insensitive.png\"), url(\"assets/radio-insensitive@2.png\"));\n    animation: none;\n    -gtk-icon-shadow: none;\n    transition: none; }\n  menu menuitem.radio:disabled:backdrop,\n  menu menuitem radio:disabled:backdrop {\n    opacity: 0.8;\n    transition: 0.2s; }\n\nmenu menuitem.radio:indeterminate,\nmenu menuitem radio:indeterminate {\n  -gtk-icon-source: -gtk-scaled(url(\"assets/radio-mixed.png\"), url(\"assets/radio-mixed@2.png\"));\n  -gtk-icon-shadow: none; }\n  menu menuitem.radio:indeterminate:hover,\n  menu menuitem radio:indeterminate:hover {\n    -gtk-icon-source: -gtk-scaled(url(\"assets/radio-mixed.png\"), url(\"assets/radio-mixed@2.png\"));\n    animation: none;\n    -gtk-icon-shadow: none;\n    transition: none; }\n  menu menuitem.radio:indeterminate:backdrop,\n  menu menuitem radio:indeterminate:backdrop {\n    opacity: 0.8;\n    transition: 0.2s; }\n\nmenu menuitem.radio:indeterminate:disabled,\nmenu menuitem radio:indeterminate:disabled {\n  -gtk-icon-source: -gtk-scaled(url(\"assets/radio-mixed-insensitive.png\"), url(\"assets/radio-mixed-insensitive@2.png\"));\n  -gtk-icon-shadow: none; }\n  menu menuitem.radio:indeterminate:disabled:hover,\n  menu menuitem radio:indeterminate:disabled:hover {\n    -gtk-icon-source: -gtk-scaled(url(\"assets/radio-mixed-insensitive.png\"), url(\"assets/radio-mixed-insensitive@2.png\"));\n    animation: none;\n    -gtk-icon-shadow: none;\n    transition: none; }\n  menu menuitem.radio:indeterminate:disabled:backdrop,\n  menu menuitem radio:indeterminate:disabled:backdrop {\n    opacity: 0.8;\n    transition: 0.2s; }\n\nmenu menuitem.radio:checked,\nmenu menuitem radio:checked {\n  -gtk-icon-source: -gtk-scaled(url(\"assets/radio-selected.png\"), url(\"assets/radio-selected@2.png\"));\n  -gtk-icon-shadow: none; }\n  menu menuitem.radio:checked:hover,\n  menu menuitem radio:checked:hover {\n    -gtk-icon-source: -gtk-scaled(url(\"assets/radio-selected.png\"), url(\"assets/radio-selected@2.png\"));\n    animation: none;\n    -gtk-icon-shadow: none;\n    transition: none; }\n  menu menuitem.radio:checked:backdrop,\n  menu menuitem radio:checked:backdrop {\n    opacity: 0.8;\n    transition: 0.2s; }\n\nmenu menuitem.radio:checked:disabled,\nmenu menuitem radio:checked:disabled {\n  -gtk-icon-source: -gtk-scaled(url(\"assets/radio-selected-insensitive.png\"), url(\"assets/radio-selected-insensitive@2.png\"));\n  -gtk-icon-shadow: none; }\n  menu menuitem.radio:checked:disabled:hover,\n  menu menuitem radio:checked:disabled:hover {\n    -gtk-icon-source: -gtk-scaled(url(\"assets/radio-selected-insensitive.png\"), url(\"assets/radio-selected-insensitive@2.png\"));\n    animation: none;\n    -gtk-icon-shadow: none;\n    transition: none; }\n  menu menuitem.radio:checked:disabled:backdrop,\n  menu menuitem radio:checked:disabled:backdrop {\n    opacity: 0.8;\n    transition: 0.2s; }\n\ntreeview.view check:selected:focus, treeview.view check:selected,\ntreeview.view radio:selected:focus,\ntreeview.view radio:selected {\n  color: @theme_fg_color;\n  border-color: shade(@theme_selected_bg_color, 0.6); }\ntreeview.view check:selected:disabled,\ntreeview.view radio:selected:disabled {\n  color: @insensitive_fg_color; }\n  treeview.view check:selected:disabled:backdrop,\n  treeview.view radio:selected:disabled:backdrop {\n    color: shade(@theme_unfocused_fg_color, 1.1); }\ntreeview.view check:backdrop:selected, treeview.view check:backdrop,\ntreeview.view radio:backdrop:selected,\ntreeview.view radio:backdrop {\n  color: @insensitive_fg_color; }\n\n/************\n * GtkScale *\n ************/\nscale trough, scale fill, progressbar trough {\n  border: 1px solid @borders;\n  border-radius: 0;\n  background-color: #cfcfcd; }\n  scale trough:disabled, scale fill:disabled, progressbar trough:disabled {\n    background-color: @insensitive_bg_color; }\n  scale trough:backdrop, scale fill:backdrop, progressbar trough:backdrop, progressbar:backdrop trough {\n    background-color: #dadad8;\n    border-color: shade(@borders, 0.95);\n    transition: 200ms ease-out; }\n    scale trough:backdrop:disabled, scale fill:backdrop:disabled, progressbar trough:backdrop:disabled, progressbar:backdrop trough:disabled {\n      background-color: @insensitive_bg_color; }\n  row:selected scale trough:disabled, scale row:selected trough:disabled, row:selected scale fill:disabled, scale row:selected fill:disabled, row:selected progressbar trough:disabled, progressbar row:selected trough:disabled, row:selected scale trough, scale row:selected trough, row:selected scale fill, scale row:selected fill, row:selected progressbar trough, progressbar row:selected trough {\n    border-color: shade(@theme_selected_bg_color, 0.6); }\n  .osd scale trough, scale .osd trough, .osd scale fill, scale .osd fill, .osd progressbar trough, progressbar .osd trough {\n    border-color: @osd_borders;\n    background-color: @osd_bg_color;\n    outline-color: rgba(238, 238, 236, 0.2); }\n    .osd scale trough:disabled, scale .osd trough:disabled, .osd scale fill:disabled, scale .osd fill:disabled, .osd progressbar trough:disabled, progressbar .osd trough:disabled {\n      background-color: shade(@osd_bg_color, 0.95); }\n\nprogressbar progress {\n  border: 1px solid @progressbar_color;\n  border-radius: 0;\n  background-color: @progressbar_color; }\n\n/* progressbar color */\n\nscale highlight {\n  border: 1px solid shade(@theme_selected_bg_color, 0.6);\n  border-radius: 0;\n  background-color: shade(@theme_selected_bg_color, 0.6); }\n\n  scale highlight:disabled, progressbar progress:disabled {\n    background-color: transparent;\n    border-color: transparent; }\n  scale highlight:backdrop, progressbar progress:backdrop, progressbar:backdrop progress {\n    border-color: @theme_selected_bg_color; }\n    scale highlight:backdrop:disabled, progressbar progress:backdrop:disabled, progressbar:backdrop progress:disabled {\n      background-color: transparent;\n      border-color: transparent; }\n  row:selected scale highlight:disabled, scale row:selected highlight:disabled, row:selected progressbar progress:disabled, progressbar row:selected progress:disabled, row:selected scale highlight, scale row:selected highlight, row:selected progressbar progress, progressbar row:selected progress {\n    border-color: shade(@theme_selected_bg_color, 0.6); }\n  .osd scale highlight, scale .osd highlight, .osd progressbar progress, progressbar .osd progress {\n    border-color: @osd_borders; }\n    .osd scale highlight:disabled, scale .osd highlight:disabled, .osd progressbar progress:disabled, progressbar .osd progress:disabled {\n      border-color: transparent; }\n\nscale {\n  min-height: 10px;\n  min-width: 10px;\n  padding: 12px; }\n  scale fill,\n  scale highlight {\n    margin: -1px; }\n  scale slider {\n    min-height: 18px;\n    min-width: 18px;\n    margin: -9px; }\n  scale.fine-tune.horizontal {\n    padding-top: 9px;\n    padding-bottom: 9px;\n    min-height: 16px; }\n  scale.fine-tune.vertical {\n    padding-left: 9px;\n    padding-right: 9px;\n    min-width: 16px; }\n  scale.fine-tune slider {\n    margin: -6px; }\n  scale.fine-tune fill,\n  scale.fine-tune highlight,\n  scale.fine-tune trough {\n    border-radius: 0;\n    -gtk-outline-radius: 0; }\n  scale trough {\n    outline-offset: 2px;\n    -gtk-outline-radius: 0; }\n  scale fill:backdrop, scale fill {\n    background-color: @borders; }\n  scale fill:disabled:backdrop, scale fill:disabled {\n    border-color: transparent;\n    background-color: transparent; }\n  .osd scale fill {\n    background-color: rgba(91, 91, 90, 0.775); }\n    .osd scale fill:disabled:backdrop, .osd scale fill:disabled {\n      border-color: transparent;\n      background-color: transparent; }\n\nscale slider,\nscale slider.horizontal {\n    background-image: -gtk-scaled(url(\"assets/slider-horiz.png\")); }\n\nscale.vertical slider {\n    background-image: -gtk-scaled(url(\"assets/slider-vert.png\")); }\n\nscale.vertical slider:hover, \nscale.vertical slider:active {\n    background-image: -gtk-scaled(url(\"assets/slider-vert-hover.png\")); \n}\n\nscale.vertical slider:backdrop,\nscale.vertical slider:disabled,\nscale.vertical slider:backdrop:disabled {\n    background-image: -gtk-scaled(url(\"assets/slider-vert-insensitive.png\")); \n}\n\n/* scale sliders */\n\n  scale slider {\n\tbackground-image: url(\"assets/slider-horiz.png\"); \n\tbackground-position: center;\n        background-repeat: no-repeat; }\n    scale slider:hover, scale slider:active {\n\tbackground-image: url(\"assets/slider-horiz-hover.png\"); \n\tbackground-position: center;\n        background-repeat: no-repeat; }\n    scale slider:disabled {\n\tbackground-image: url(\"assets/slider-horiz-insensitive.png\"); \n\tbackground-position: center;\n        background-repeat: no-repeat; }\n      scale slider:disabled label, scale slider:disabled {\n        color: @insensitive_fg_color; }\n    scale slider:backdrop {\n\tbackground-image: url(\"assets/slider-horiz-insensitive.png\");\n\tbackground-position: center;\n        background-repeat: no-repeat; }\n      scale slider:backdrop:disabled {\n        border-color: shade(@borders, 0.95);\n        background-color: transparent;\n\tbackground-image: url(\"assets/slider-horiz-insensitive.png\"); \n        text-shadow: none;\n        -gtk-icon-shadow: none;\n        box-shadow: inset 0 1px transparent; }\n        scale slider:backdrop:disabled label, scale slider:backdrop:disabled {\n          color: shade(@theme_unfocused_fg_color, 1.1); }\n    row:selected scale slider:disabled, row:selected scale slider {\n      border-color: shade(@theme_selected_bg_color, 0.6); }\n    .osd scale slider {\n      color: @theme_unfocused_fg_color;\n      border-color: @osd_borders;\n      background-color: transparent;\n      background-image: image(@osd_bg_color);\n      background-clip: padding-box;\n      box-shadow: inset 0 1px @osd_txt_shadow;\n      text-shadow: 0 1px @osd_txt_shadow;\n      -gtk-icon-shadow: 0 1px @osd_txt_shadow;\n      outline-color: @osd_outline;\n      border-color: @osd_borders;\n      border-radius: 100%;\n      background-color: #1c1f20; }\n      .osd scale slider:hover {\n        color: @osd_fg_color;\n        border-color: @osd_borders;\n        background-color: transparent;\n        background-image: image(shade(@osd_bg_color, 1.05));\n        background-clip: padding-box;\n        box-shadow: inset 0 1px @osd_txt_shadow;\n        text-shadow: 0 1px @osd_txt_shadow;\n        -gtk-icon-shadow: 0 1px @osd_txt_shadow;\n        outline-color: @osd_outline;\n        background-color: #1c1f20; }\n      .osd scale slider:active {\n        color: @osd_fg_color;\n        border-color: @osd_borders;\n        background-color: transparent;\n        background-image: image(@osd_borders);\n        background-clip: padding-box;\n        box-shadow: none;\n        text-shadow: none;\n        -gtk-icon-shadow: none;\n        outline-color: @osd_outline;\n        background-color: #1c1f20; }\n      .osd scale slider:disabled {\n        color: shade(@osd_fg_color, 0.85);\n        border-color: @osd_borders;\n        background-color: transparent;\n        background-image: image(shade(@osd_bg_color, 0.95));\n        background-clip: padding-box;\n        box-shadow: none;\n        text-shadow: none;\n        -gtk-icon-shadow: none;\n        background-color: #1c1f20; }\n      .osd scale slider:backdrop {\n        color: @theme_unfocused_fg_color;\n        border-color: @osd_borders;\n        background-color: transparent;\n        background-image: image(@osd_bg_color);\n        background-clip: padding-box;\n        box-shadow: none;\n        text-shadow: none;\n        -gtk-icon-shadow: none;\n        background-color: #1c1f20; }\n        .osd scale slider:backdrop:disabled {\n          background-color: #1c1f20; }\n  scale value {\n    color: alpha(currentColor,0.55); }\n  scale marks {\n    color: alpha(currentColor,0.55); }\n    scale marks.top {\n      margin-bottom: 6px;\n      margin-top: -12px; }\n    scale marks.bottom {\n      margin-top: 6px;\n      margin-bottom: -12px; }\n    scale marks.top {\n      margin-right: 6px;\n      margin-left: -12px; }\n    scale marks.bottom {\n      margin-left: 6px;\n      margin-right: -12px; }\n  scale.fine-tune marks.top {\n    margin-bottom: 6px;\n    margin-top: -9px; }\n  scale.fine-tune marks.bottom {\n    margin-top: 6px;\n    margin-bottom: -9px; }\n  scale.fine-tune marks.top {\n    margin-right: 6px;\n    margin-left: -9px; }\n  scale.fine-tune marks.bottom {\n    margin-left: 6px;\n    margin-right: -9px; }\n  scale.horizontal indicator {\n    min-height: 6px;\n    min-width: 1px; }\n  scale.horizontal.fine-tune indicator {\n    min-height: 3px; }\n  scale.vertical indicator {\n    min-height: 1px;\n    min-width: 6px; }\n  scale.vertical.fine-tune indicator {\n    min-width: 3px; }\n\n/*****************\n * Progress bars *\n *****************/\nprogressbar {\n  font-size: smaller;\n  color: @theme_selected_fg_color; }\n  progressbar.horizontal trough,\n  progressbar.horizontal progress {\n    min-height: 10px; }\n  progressbar.vertical trough,\n  progressbar.vertical progress {\n    min-width: 10px; }\n  progressbar.horizontal progress {\n    margin: 0 -1px; }\n  progressbar.vertical progress {\n    margin: -1px 0; }\n  progressbar:backdrop {\n    box-shadow: none;\n    transition: 200ms ease-out; }\n  progressbar progress {\n    border-radius: 0; }\n    progressbar progress.left {\n      border-top-left-radius: 0;\n      border-bottom-left-radius: 0; }\n    progressbar progress.right {\n      border-top-right-radius: 0;\n      border-bottom-right-radius: 0; }\n    progressbar progress.top {\n      border-top-right-radius: 0;\n      border-top-left-radius: 0; }\n    progressbar progress.bottom {\n      border-bottom-right-radius: 0;\n      border-bottom-left-radius: 0; }\n  progressbar.osd {\n    min-width: 3px;\n    min-height: 3px;\n    background-color: transparent; }\n    progressbar.osd trough {\n      border-style: none;\n      border-radius: 0;\n      background-color: shade(@theme_selected_bg_color, 0.6);\n      box-shadow: none; }\n    progressbar.osd progress {\n      border-style: none;\n      border-radius: 0; }\n\n/*************\n * Level Bar *\n *************/\nlevelbar block {\n  min-width: 32px;\n  min-height: 1px; }\nlevelbar.vertical block {\n  min-width: 1px;\n  min-height: 32px; }\nlevelbar:backdrop {\n  transition: 200ms ease-out; }\nlevelbar trough {\n  border: 1px solid;\n  padding: 2px;\n  border-radius: 0;\n  color: @theme_fg_color;\n  border-color: @borders;\n  background-color: @theme_bg_color;\n  box-shadow: inset 0 0 0 1px shade(@theme_selected_bg_color, 0); }\n  levelbar trough:backdrop {\n    color: @theme_unfocused_fg_color;\n    border-color: shade(@borders, 0.95);\n    background-color: @theme_unfocused_bg_color;\n    box-shadow: none; }\nlevelbar.horizontal.discrete block {\n  margin: 0 1px; }\nlevelbar.vertical.discrete block {\n  margin: 1px 0; }\nlevelbar block {\n  border: 1px solid;\n  border-radius: 0; }\n  levelbar block.low {\n    border-color: #8f4700;\n    background-color: @warning_color; }\n    levelbar block.low:backdrop {\n      border-color: @warning_color; }\n  levelbar block.high, levelbar block:not(.empty) {\n    border-color: shade(@theme_selected_bg_color, 0.6);\n    background-color: @theme_selected_bg_color; }\n    levelbar block.high:backdrop, levelbar block:not(.empty):backdrop {\n      border-color: @theme_selected_bg_color; }\n  levelbar block.full {\n    border-color: #40760c;\n    background-color: #73d216; }\n    levelbar block.full:backdrop {\n      border-color: #73d216; }\n  levelbar block.empty {\n    background-color: transparent;\n    border-color: rgba(46, 52, 54, 0.2); }\n    levelbar block.empty:backdrop {\n      border-color: rgba(139, 142, 143, 0.15); }\n\n/****************\n * Print dialog *\n*****************/\nprintdialog paper {\n  color: @theme_fg_color;\n  border: 1px solid @borders;\n  background: @theme_bg_color;\n  padding: 0; }\n  printdialog paper:backdrop {\n    color: @insensitive_fg_color;\n    border-color: shade(@borders, 0.95); }\nprintdialog .dialog-action-box {\n  margin: 12px; }\n\n/**********\n * Frames *\n **********/\nframe > border,\n.frame {\n  box-shadow: none;\n  margin: 0;\n  padding: 0;\n  border-radius: 0;\n  border: 1px solid @borders; }\n  frame > border.flat,\n  .frame.flat {\n    border-style: none; }\n  frame > border:backdrop,\n  .frame:backdrop {\n    border-color: shade(@borders, 0.95); }\n\nactionbar > revealer > box {\n  padding: 6px;\n  border-top: 1px solid @borders; }\n  actionbar > revealer > box:backdrop {\n    border-color: shade(@borders, 0.95); }\n\nscrolledwindow viewport.frame {\n  border-style: none; }\nscrolledwindow overshoot.top {\n  background-image: -gtk-gradient(radial, center top, 0, center top, 0.5, to(#9d9d99), to(rgba(157, 157, 153, 0))), -gtk-gradient(radial, center top, 0, center top, 0.6, from(rgba(46, 52, 54, 0.07)), to(rgba(46, 52, 54, 0)));\n  background-size: 100% 5%, 100% 100%;\n  background-repeat: no-repeat;\n  background-position: center top;\n  background-color: transparent;\n  border: none;\n  box-shadow: none; }\n  scrolledwindow overshoot.top:backdrop {\n    background-image: -gtk-gradient(radial, center top, 0, center top, 0.5, to(shade(@borders, 0.95)), to(rgba(192, 192, 189, 0)));\n    background-size: 100% 5%;\n    background-repeat: no-repeat;\n    background-position: center top;\n    background-color: transparent;\n    border: none;\n    box-shadow: none; }\nscrolledwindow overshoot.bottom {\n  background-image: -gtk-gradient(radial, center bottom, 0, center bottom, 0.5, to(#9d9d99), to(rgba(157, 157, 153, 0))), -gtk-gradient(radial, center bottom, 0, center bottom, 0.6, from(rgba(46, 52, 54, 0.07)), to(rgba(46, 52, 54, 0)));\n  background-size: 100% 5%, 100% 100%;\n  background-repeat: no-repeat;\n  background-position: center bottom;\n  background-color: transparent;\n  border: none;\n  box-shadow: none; }\n  scrolledwindow overshoot.bottom:backdrop {\n    background-image: -gtk-gradient(radial, center bottom, 0, center bottom, 0.5, to(shade(@borders, 0.95)), to(rgba(192, 192, 189, 0)));\n    background-size: 100% 5%;\n    background-repeat: no-repeat;\n    background-position: center bottom;\n    background-color: transparent;\n    border: none;\n    box-shadow: none; }\nscrolledwindow overshoot.left {\n  background-image: -gtk-gradient(radial, left center, 0, left center, 0.5, to(#9d9d99), to(rgba(157, 157, 153, 0))), -gtk-gradient(radial, left center, 0, left center, 0.6, from(rgba(46, 52, 54, 0.07)), to(rgba(46, 52, 54, 0)));\n  background-size: 5% 100%, 100% 100%;\n  background-repeat: no-repeat;\n  background-position: left center;\n  background-color: transparent;\n  border: none;\n  box-shadow: none; }\n  scrolledwindow overshoot.left:backdrop {\n    background-image: -gtk-gradient(radial, left center, 0, left center, 0.5, to(shade(@borders, 0.95)), to(rgba(192, 192, 189, 0)));\n    background-size: 5% 100%;\n    background-repeat: no-repeat;\n    background-position: left center;\n    background-color: transparent;\n    border: none;\n    box-shadow: none; }\nscrolledwindow overshoot.right {\n  background-image: -gtk-gradient(radial, right center, 0, right center, 0.5, to(#9d9d99), to(rgba(157, 157, 153, 0))), -gtk-gradient(radial, right center, 0, right center, 0.6, from(rgba(46, 52, 54, 0.07)), to(rgba(46, 52, 54, 0)));\n  background-size: 5% 100%, 100% 100%;\n  background-repeat: no-repeat;\n  background-position: right center;\n  background-color: transparent;\n  border: none;\n  box-shadow: none; }\n  scrolledwindow overshoot.right:backdrop {\n    background-image: -gtk-gradient(radial, right center, 0, right center, 0.5, to(shade(@borders, 0.95)), to(rgba(192, 192, 189, 0)));\n    background-size: 5% 100%;\n    background-repeat: no-repeat;\n    background-position: right center;\n    background-color: transparent;\n    border: none;\n    box-shadow: none; }\nscrolledwindow undershoot.top {\n  background-color: transparent;\n  background-image: linear-gradient(to left, rgba(255, 255, 255, 0.2) 50%, rgba(0, 0, 0, 0.2) 50%);\n  padding-top: 1px;\n  background-size: 10px 1px;\n  background-repeat: repeat-x;\n  background-origin: content-box;\n  background-position: center top;\n  border: none;\n  box-shadow: none; }\nscrolledwindow undershoot.bottom {\n  background-color: transparent;\n  background-image: linear-gradient(to left, rgba(255, 255, 255, 0.2) 50%, rgba(0, 0, 0, 0.2) 50%);\n  padding-bottom: 1px;\n  background-size: 10px 1px;\n  background-repeat: repeat-x;\n  background-origin: content-box;\n  background-position: center bottom;\n  border: none;\n  box-shadow: none; }\nscrolledwindow undershoot.left {\n  background-color: transparent;\n  background-image: linear-gradient(to top, rgba(255, 255, 255, 0.2) 50%, rgba(0, 0, 0, 0.2) 50%);\n  padding-left: 1px;\n  background-size: 1px 10px;\n  background-repeat: repeat-y;\n  background-origin: content-box;\n  background-position: left center;\n  border: none;\n  box-shadow: none; }\nscrolledwindow undershoot.right {\n  background-color: transparent;\n  background-image: linear-gradient(to top, rgba(255, 255, 255, 0.2) 50%, rgba(0, 0, 0, 0.2) 50%);\n  padding-right: 1px;\n  background-size: 1px 10px;\n  background-repeat: repeat-y;\n  background-origin: content-box;\n  background-position: right center;\n  border: none;\n  box-shadow: none; }\nscrolledwindow junction {\n  border-color: transparent;\n  border-image: linear-gradient(to bottom, @borders 1px, transparent 1px) 0 0 0 1/0 1px stretch;\n  background-color: #c3c4c4; }\n  scrolledwindow junction:dir(rtl) {\n    border-image-slice: 0 1 0 0; }\n  scrolledwindow junction:backdrop {\n    border-image-source: linear-gradient(to bottom, shade(@borders, 0.95) 1px, transparent 1px);\n    background-color: #e1e1df;\n    transition: 200ms ease-out; }\n\nseparator {\n  background: rgba(0, 0, 0, 0.1);\n  min-width: 1px;\n  min-height: 1px; }\n\n/*********\n * Lists *\n *********/\nlist {\n  color: @theme_fg_color;\n  background-color: @theme_bg_color;\n  border-color: @borders; }\n  list:backdrop {\n    background-color: @theme_unfocused_bg_color;\n    border-color: shade(@borders, 0.95); }\n  list row {\n    padding: 2px; }\n\nrow {\n  transition: all 150ms cubic-bezier(0.25, 0.46, 0.45, 0.94); }\n  row:hover {\n    transition: none; }\n  row:backdrop {\n    transition: 200ms ease-out; }\n  row.activatable.has-open-popup, row.activatable:hover {\n    background-color: rgba(46, 52, 54, 0.05); }\n  row.activatable:active {\n    box-shadow: inset 0 2px 2px -2px rgba(0, 0, 0, 0.2); }\n  row.activatable:backdrop:hover {\n    background-color: transparent; }\n  row.activatable:selected:active {\n    box-shadow: inset 0 2px 3px -1px @osd_bg_color; }\n  row.activatable:selected.has-open-popup, row.activatable:selected:hover {\n    background-color: shade(@theme_selected_bg_color, 1.05); }\n  row.activatable:selected:backdrop {\n    background-color: @theme_selected_bg_color; }\n\n/*********************\n * App Notifications *\n *********************/\n.app-notification,\n.app-notification.frame {\n  padding: 10px;\n  border-radius: 0;\n  background-color: @osd_bg_color;\n  background-image: linear-gradient(to bottom, rgba(0, 0, 0, 0.2), transparent 2px);\n  background-clip: padding-box; }\n  .app-notification:backdrop,\n  .app-notification.frame:backdrop {\n    background-image: none;\n    transition: 200ms ease-out; }\n  .app-notification border,\n  .app-notification.frame border {\n    border: none; }\n\n/*************\n * Expanders *\n *************/\nexpander arrow {\n  min-width: 16px;\n  min-height: 16px;\n  -gtk-icon-source: -gtk-icontheme(\"pan-end-symbolic\"); }\n  expander arrow:dir(rtl) {\n    -gtk-icon-source: -gtk-icontheme(\"pan-end-symbolic-rtl\"); }\n  expander arrow:hover {\n    color: #748489; }\n  expander arrow:checked {\n    -gtk-icon-source: -gtk-icontheme(\"pan-down-symbolic\"); }\n\n/************\n * Calendar *\n ***********/\ncalendar {\n  color: @theme_fg_color;\n  border: 1px solid @borders; }\n  calendar:selected {\n    border-radius: 0; }\n  calendar.header {\n    border-bottom: 1px solid rgba(0, 0, 0, 0.1);\n    border-radius: 0; }\n    calendar.header:backdrop {\n      border-color: rgba(0, 0, 0, 0.1); }\n  calendar.button {\n    color: rgba(46, 52, 54, 0.45); }\n    calendar.button:hover {\n      color: @theme_fg_color; }\n    calendar.button:backdrop {\n      color: rgba(139, 142, 143, 0.45); }\n    calendar.button:disabled {\n      color: rgba(139, 142, 143, 0.45); }\n  calendar:indeterminate, calendar:indeterminate:backdrop {\n    color: alpha(currentColor,0.55); }\n  calendar.highlight, calendar.highlight:backdrop {\n    font-size: smaller;\n    color: @theme_fg_color; }\n  calendar:backdrop {\n    color: @theme_unfocused_fg_color;\n    border-color: shade(@borders, 0.95); }\n\n/***********\n * Dialogs *\n ***********/\nmessagedialog .titlebar {\n  min-height: 20px;\n  background-image: none;\n  background-color: @theme_bg_color;\n  border-style: none;\n  border-top-left-radius: 0;\n  border-top-right-radius: 0; }\nmessagedialog.csd.background {\n  border-bottom-left-radius: 0;\n  border-bottom-right-radius: 0; }\nmessagedialog.csd .dialog-action-area button {\n  padding: 10px 14px;\n  border-radius: 0;\n  border-left-style: solid;\n  border-right-style: none;\n  border-bottom-style: none; }\n  messagedialog.csd .dialog-action-area button:first-child {\n    border-left-style: none;\n    border-bottom-left-radius: 0;\n    -gtk-outline-bottom-left-radius: 0; }\n  messagedialog.csd .dialog-action-area button:last-child {\n    border-bottom-right-radius: 0;\n    -gtk-outline-bottom-right-radius: 0; }\n\nfilechooser .dialog-action-box {\n  border-top: 1px solid @borders; }\n  filechooser .dialog-action-box:backdrop {\n    border-top-color: shade(@borders, 0.95); }\nfilechooser #pathbarbox {\n  border-bottom: 1px solid @theme_bg_color; }\n\nfilechooserbutton:drop(active) {\n  box-shadow: none;\n  border-color: transparent; }\n\n/***********\n * Sidebar *\n ***********/\n.sidebar {\n  border-style: none;\n  background-color: @theme_bg_color; }\n  stacksidebar.sidebar:dir(ltr) list, stacksidebar.sidebar.left list, stacksidebar.sidebar.left:dir(rtl) list, .sidebar:dir(ltr), .sidebar.left, .sidebar.left:dir(rtl) {\n    border-right: none;\n    border-left-style: none; }\n  stacksidebar.sidebar:dir(rtl) list\n  .sidebar:dir(rtl), stacksidebar.sidebar.right list\n  .sidebar:dir(rtl), .sidebar.right {\n    border-left: 1px solid @borders;\n    border-right-style: none; }\n  .sidebar:backdrop {\n    background-color: @theme_unfocused_bg_color;\n    border-color: shade(@borders, 0.95);\n    transition: 200ms ease-out; }\n  .sidebar list {\n    background-color: transparent; }\n  paned .sidebar.left, paned .sidebar.right, paned .sidebar.left:dir(rtl), paned .sidebar:dir(rtl), paned .sidebar:dir(ltr), paned .sidebar {\n    border-style: none; }\n\nstacksidebar row {\n  padding: 10px 4px; }\n  stacksidebar row > label {\n    padding-left: 6px;\n    padding-right: 6px; }\n  stacksidebar row.needs-attention > label {\n    background-size: 6px 6px, 0 0; }\n\n/****************\n * File chooser *\n ****************/\nplacessidebar > viewport.frame {\n  border-style: none; }\nplacessidebar row {\n  min-height: 36px;\n  padding: 0px; }\n  placessidebar row > revealer {\n    padding: 0 14px; }\n  placessidebar row:selected {\n    color: @theme_selected_fg_color; }\n  placessidebar row:disabled {\n    color: @insensitive_fg_color; }\n  placessidebar row:backdrop {\n    color: @insensitive_fg_color; }\n    placessidebar row:backdrop:selected {\n      color: @osd_bg_color; }\n    placessidebar row:backdrop:disabled {\n      color: shade(@theme_unfocused_fg_color, 1.1); }\n  placessidebar row image.sidebar-icon {\n    opacity: 0.7; }\n    placessidebar row image.sidebar-icon:dir(ltr) {\n      padding-right: 8px; }\n    placessidebar row image.sidebar-icon:dir(rtl) {\n      padding-left: 8px; }\n  placessidebar row label.sidebar-label:dir(ltr) {\n    padding-right: 2px; }\n  placessidebar row label.sidebar-label:dir(rtl) {\n    padding-left: 2px; }\n  button.sidebar-button {\n    min-height: 26px;\n    min-width: 26px;\n    margin-top: 3px;\n    margin-bottom: 3px;\n    padding: 0;\n    border-radius: 100%;\n    -gtk-outline-radius: 100%; }\n    button.sidebar-button:not(:hover):not(:active) > image, button.sidebar-button:backdrop > image {\n      opacity: 0.7; }\n  placessidebar row:selected:active {\n    box-shadow: none; }\n  placessidebar row.sidebar-placeholder-row {\n    padding: 0 8px;\n    min-height: 2px;\n    background-image: image(@success_color);\n    background-clip: content-box; }\n  placessidebar row.sidebar-new-bookmark-row {\n    color: @theme_selected_bg_color; }\n  placessidebar row:drop(active):not(:disabled) {\n    color: @success_color;\n    box-shadow: inset 0 1px @success_color, inset 0 -1px @success_color; }\n    placessidebar row:drop(active):not(:disabled):selected {\n      color: @theme_selected_fg_color;\n      background-color: @success_color; }\n\nplacesview .server-list-button > image {\n  transition: 200ms cubic-bezier(0.25, 0.46, 0.45, 0.94);\n  -gtk-icon-transform: rotate(0turn); }\nplacesview .server-list-button:checked > image {\n  transition: 200ms cubic-bezier(0.25, 0.46, 0.45, 0.94);\n  -gtk-icon-transform: rotate(-0.5turn); }\nplacesview row.activatable:hover {\n  background-color: transparent; }\nplacesview > actionbar > revealer > box > label {\n  padding-left: 8px;\n  padding-right: 8px; }\n\n/*********\n * Paned *\n *********/\npaned > separator {\n  min-width: 1px;\n  min-height: 1px;\n  -gtk-icon-source: none;\n  border-style: none;\n  background-color: transparent;\n  background-image: image(@borders);\n  background-size: 1px 1px; }\n  paned > separator:selected {\n    background-image: image(@theme_selected_bg_color); }\n  paned > separator:backdrop {\n    background-image: image(shade(@borders, 0.95)); }\n  paned > separator.wide {\n    min-width: 5px;\n    min-height: 5px;\n    background-color: @theme_bg_color;\n    background-image: image(@borders), image(@borders);\n    background-size: 1px 1px, 1px 1px; }\n    paned > separator.wide:backdrop {\n      background-color: @theme_bg_color;\n      background-image: image(shade(@borders, 0.95)), image(shade(@borders, 0.95)); }\npaned.horizontal > separator {\n  background-repeat: repeat-y; }\n  paned.horizontal > separator:dir(ltr) {\n    margin: 0 -8px 0 0;\n    padding: 0 8px 0 0;\n    background-position: left; }\n  paned.horizontal > separator:dir(rtl) {\n    margin: 0 0 0 -8px;\n    padding: 0 0 0 8px;\n    background-position: right; }\n  paned.horizontal > separator.wide {\n    margin: 0;\n    padding: 0;\n    background-repeat: repeat-y, repeat-y;\n    background-position: left, right; }\npaned.vertical > separator {\n  margin: 0 0 -8px 0;\n  padding: 0 0 8px 0;\n  background-repeat: repeat-x;\n  background-position: top; }\n  paned.vertical > separator.wide {\n    margin: 0;\n    padding: 0;\n    background-repeat: repeat-x, repeat-x;\n    background-position: bottom, top; }\n\n/**************\n * GtkInfoBar *\n **************/\ninfobar {\n  border-style: none; }\n\n.info,\n.question,\n.warning,\n.error {\n  text-shadow: 0 1px @borders; }\n  .info:backdrop, .info,\n  .question:backdrop,\n  .question,\n  .warning:backdrop,\n  .warning,\n  .error:backdrop,\n  .error {\n    background-color: @theme_selected_bg_color;\n    border-color: @borders; }\n    .info:backdrop label, .info:backdrop, .info label, .info,\n    .question:backdrop label,\n    .question:backdrop,\n    .question label,\n    .question,\n    .warning:backdrop label,\n    .warning:backdrop,\n    .warning label,\n    .warning,\n    .error:backdrop label,\n    .error:backdrop,\n    .error label,\n    .error {\n      color: @theme_selected_fg_color; }\n  .info:backdrop,\n  .question:backdrop,\n  .warning:backdrop,\n  .error:backdrop {\n    text-shadow: none; }\n  .info button,\n  .question button,\n  .warning button,\n  .error button {\n    color: @theme_selected_fg_color;\n    outline-color: rgba(255, 255, 255, 0.3);\n    border-color: shade(@theme_selected_bg_color, 0.6);\n    border-bottom-color: shade(@theme_selected_bg_color, 0.6);\n    background-image: image(@theme_selected_bg_color);\n    text-shadow: 0 -1px rgba(0, 0, 0, 0.54353);\n    -gtk-icon-shadow: 0 -1px rgba(0, 0, 0, 0.54353);\n    box-shadow: inset 0 1px rgba(255, 255, 255, 0.4); }\n    .info button:hover,\n    .question button:hover,\n    .warning button:hover,\n    .error button:hover {\n      color: @theme_selected_fg_color;\n      outline-color: rgba(255, 255, 255, 0.3);\n      border-color: shade(@theme_selected_bg_color, 0.6);\n      border-bottom-color: shade(@theme_selected_bg_color, 0.6);\n      background-image: image(shade(@theme_selected_bg_color, 0.9));\n      text-shadow: 0 -1px rgba(0, 0, 0, 0.49553);\n      -gtk-icon-shadow: 0 -1px rgba(0, 0, 0, 0.49553);\n      box-shadow: inset 0 1px rgba(255, 255, 255, 0.4); }\n    .info button:active, .info button:checked,\n    .question button:active,\n    .question button:checked,\n    .warning button:active,\n    .warning button:checked,\n    .error button:active,\n    .error button:checked {\n      color: @theme_selected_fg_color;\n      outline-color: rgba(255, 255, 255, 0.3);\n      border-color: shade(@theme_selected_bg_color, 0.6);\n      background-image: none;\n      background-color: shade(@theme_selected_bg_color, 0.8);\n      box-shadow: inset 0 1px transparent;\n      text-shadow: none;\n      -gtk-icon-shadow: none; }\n    .info button:disabled,\n    .question button:disabled,\n    .warning button:disabled,\n    .error button:disabled {\n      border-color: shade(@theme_selected_bg_color, 0.6);\n      background-color: @theme_selected_bg_color;\n      background-image: none;\n      text-shadow: none;\n      -gtk-icon-shadow: none;\n      box-shadow: inset 0 1px transparent; }\n      .info button:disabled label, .info button:disabled,\n      .question button:disabled label,\n      .question button:disabled,\n      .warning button:disabled label,\n      .warning button:disabled,\n      .error button:disabled label,\n      .error button:disabled {\n        color: #b2d0ef; }\n    .info button:backdrop,\n    .question button:backdrop,\n    .warning button:backdrop,\n    .error button:backdrop {\n      border-color: @theme_selected_bg_color;\n      background-color: transparent;\n      background-image: image(@theme_selected_bg_color);\n      text-shadow: none;\n      -gtk-icon-shadow: none;\n      box-shadow: inset 0 1px transparent;\n      border-color: shade(@theme_selected_bg_color, 0.6); }\n      .info button:backdrop label, .info button:backdrop,\n      .question button:backdrop label,\n      .question button:backdrop,\n      .warning button:backdrop label,\n      .warning button:backdrop,\n      .error button:backdrop label,\n      .error button:backdrop {\n        color: @theme_selected_fg_color; }\n      .info button:backdrop:disabled,\n      .question button:backdrop:disabled,\n      .warning button:backdrop:disabled,\n      .error button:backdrop:disabled {\n        border-color: @theme_selected_bg_color;\n        background-color: @theme_selected_bg_color;\n        background-image: none;\n        text-shadow: none;\n        -gtk-icon-shadow: none;\n        box-shadow: inset 0 1px transparent;\n        border-color: shade(@theme_selected_bg_color, 0.6); }\n        .info button:backdrop:disabled label, .info button:backdrop:disabled,\n        .question button:backdrop:disabled label,\n        .question button:backdrop:disabled,\n        .warning button:backdrop:disabled label,\n        .warning button:backdrop:disabled,\n        .error button:backdrop:disabled label,\n        .error button:backdrop:disabled {\n          color: @theme_unfocused_selected_fg_color; }\n  .info label:selected:focus, .info label:selected:hover, .info label:selected,\n  .question label:selected:focus,\n  .question label:selected:hover,\n  .question label:selected,\n  .warning label:selected:focus,\n  .warning label:selected:hover,\n  .warning label:selected,\n  .error label:selected:focus,\n  .error label:selected:hover,\n  .error label:selected {\n    background-color: @borders; }\n\n/************\n * Tooltips * *?*\n ************/\ntooltip {\n  padding: 4px;\n  /* not working */\n  border-radius: 0;\n  box-shadow: none;\n  text-shadow: none; }\n  tooltip.background {\n    background-color: @tooltip_bg_color;\n    background-clip: padding-box;\n    border: 1px solid @osd_txt_shadow; }\n  tooltip decoration {\n    background-color: transparent; }\n  tooltip * {\n    padding: 4px;\n    background-color: transparent;\n    color: @theme_fg_color; }\n\n/*****************\n * Color Chooser *\n *****************/\ncolorswatch:drop(active), colorswatch {\n  border-style: none; }\ncolorswatch.top {\n  border-top-left-radius: 0;\n  border-top-right-radius: 0; }\n  colorswatch.top overlay {\n    border-top-left-radius: 0;\n    border-top-right-radius: 0; }\ncolorswatch.bottom {\n  border-bottom-left-radius: 0;\n  border-bottom-right-radius: 0; }\n  colorswatch.bottom overlay {\n    border-bottom-left-radius: 0;\n    border-bottom-right-radius: 0; }\ncolorswatch.left, colorswatch:first-child:not(.top) {\n  border-top-left-radius: 0;\n  border-bottom-left-radius: 0; }\n  colorswatch.left overlay, colorswatch:first-child:not(.top) overlay {\n    border-top-left-radius: 0;\n    border-bottom-left-radius: 0; }\ncolorswatch.right, colorswatch:last-child:not(.bottom) {\n  border-top-right-radius: 0;\n  border-bottom-right-radius: 0; }\n  colorswatch.right overlay, colorswatch:last-child:not(.bottom) overlay {\n    border-top-right-radius: 0;\n    border-bottom-right-radius: 0; }\ncolorswatch.dark overlay {\n  color: @theme_selected_fg_color; }\n  colorswatch.dark overlay:hover {\n    border-color: rgba(0, 0, 0, 0.8); }\n  colorswatch.dark overlay:backdrop {\n    color: @theme_unfocused_bg_color; }\ncolorswatch.light overlay {\n  color: @theme_fg_color; }\n  colorswatch.light overlay:hover {\n    border-color: @osd_bg_color; }\n  colorswatch.light overlay:backdrop {\n    color: @theme_unfocused_fg_color; }\ncolorswatch:drop(active) {\n  box-shadow: none; }\n  colorswatch:drop(active).light overlay {\n    border-color: @success_color;\n    box-shadow: inset 0 0 0 2px #3d7805, inset 0 0 0 1px @success_color; }\n  colorswatch:drop(active).dark overlay {\n    border-color: @success_color;\n    box-shadow: inset 0 0 0 2px @borders, inset 0 0 0 1px @success_color; }\ncolorswatch overlay {\n  border: 1px solid @borders; }\n  colorswatch overlay:hover {\n    box-shadow: inset 0 1px rgba(255, 255, 255, 0.4), inset 0 -1px rgba(0, 0, 0, 0.2); }\n  colorswatch overlay:backdrop, colorswatch overlay:backdrop:hover {\n    border-color: @borders;\n    box-shadow: none; }\ncolorswatch#add-color-button {\n  border-radius: 0; }\n  colorswatch#add-color-button:only-child {\n    border-radius: 0; }\n  colorswatch#add-color-button overlay {\n    color: @theme_fg_color;\n    outline-color: @outline_color;\n    border-color: @borders;\n    border-bottom-color: @borders;\n    background-image: linear-gradient(to bottom, @theme_bg_color, @theme_bg_color);\n    text-shadow: 0 1px @txt_shadow;\n    -gtk-icon-shadow: 0 1px @txt_shadow;\n    box-shadow: inset 0 1px rgba(255, 255, 255, 0.8); }\n    colorswatch#add-color-button overlay:hover {\n      color: @theme_fg_color;\n      outline-color: @outline_color;\n      border-color: @borders;\n      border-bottom-color: @borders;\n      background-image: linear-gradient(to bottom, @theme_selected_bg_color, @theme_selected_bg_color);\n      text-shadow: 0 1px @txt_shadow;\n      -gtk-icon-shadow: 0 1px @txt_shadow;\n      box-shadow: inset 0 1px @theme_bg_color; }\n    colorswatch#add-color-button overlay:backdrop {\n      border-color: shade(@borders, 0.95);\n      background-color: transparent;\n      background-image: image(@theme_bg_color);\n      text-shadow: none;\n      -gtk-icon-shadow: none;\n      box-shadow: inset 0 1px transparent; }\n      colorswatch#add-color-button overlay:backdrop label, colorswatch#add-color-button overlay:backdrop {\n        color: @insensitive_fg_color; }\ncolorswatch:disabled {\n  opacity: 0.5; }\n  colorswatch:disabled overlay {\n    border-color: rgba(0, 0, 0, 0.6);\n    box-shadow: none; }\nrow:selected colorswatch {\n  box-shadow: 0 0 0 2px #ffffff; }\ncolorswatch#editor-color-sample {\n  border-radius: 0px; }\n  colorswatch#editor-color-sample overlay {\n    border-radius: 0px; }\n\ncolorchooser .popover.osd {\n  border-radius: 0; }\n\n/********\n * Misc *\n ********/\n.content-view {\n  background-color: #d7d7d5; }\n  .content-view:hover {\n    -gtk-icon-effect: highlight; }\n  .content-view:backdrop {\n    background-color: #d7d7d5; }\n\n.osd .scale-popup button.flat {\n  border-style: none;\n  border-radius: 0; }\n.scale-popup button:hover {\n  background-color: rgba(46, 52, 54, 0.1);\n  border-radius: 0; }\n\n/**********************\n * Window Decorations *\n *********************/\ndecoration {\n  border-radius: 0;\n  border-width: 0px;\n  box-shadow: 0 3px 9px 1px @osd_bg_color, 0 0 0 1px rgba(0, 0, 0, 0.23);\n  margin: 10px; }\n  decoration:backdrop {\n    box-shadow: 0 3px 9px 1px transparent, 0 2px 6px 2px rgba(0, 0, 0, 0.2), 0 0 0 1px rgba(0, 0, 0, 0.18);\n    transition: 200ms ease-out; }\n  .maximized decoration, .fullscreen decoration, .tiled decoration {\n    border-radius: 0; }\n  .popup decoration {\n    box-shadow: none; }\n  .ssd decoration {\n    box-shadow: 0 0 0 1px rgba(0, 0, 0, 0.23); }\n  .csd.popup decoration {\n    border-radius: 0;\n    box-shadow: 0 1px 2px rgba(0, 0, 0, 0.2), 0 0 0 1px rgba(0, 0, 0, 0.13); }\n  tooltip.csd decoration {\n    border-radius: 0;\n    box-shadow: none; }\n  messagedialog.csd decoration {\n    border-radius: 0;\n    box-shadow: 0 1px 2px rgba(0, 0, 0, 0.2), 0 0 0 1px rgba(0, 0, 0, 0.13); }\n  .solid-csd decoration {\n    margin: 0;\n    padding: 4px;\n    background-color: @borders;\n    border: solid 1px @borders;\n    border-radius: 0;\n    box-shadow: inset 0 0 0 3px @theme_bg_color, inset 0 1px rgba(255, 255, 255, 0.8); }\n    .solid-csd decoration:backdrop {\n      box-shadow: inset 0 0 0 3px @theme_bg_color, inset 0 1px rgba(255, 255, 255, 0.8); }\n\n/* Server-side decoration (SSD) */\n.window-frame.ssd {\n    border-radius: 0;\n    box-shadow: 0 0 0 1px rgba(0, 0, 0, 0.18); \n}\n\n.window-frame.ssd,\n.window-frame.ssd:backdrop {\n    background-color: @theme_bg_color; }\n\nbutton.titlebutton {\n  text-shadow: 0 1px @txt_shadow;\n  -gtk-icon-shadow: 0 1px @txt_shadow; }\n  button.titlebutton:backdrop {\n    -gtk-icon-shadow: none; }\n\nheaderbar.selection-mode button.titlebutton,\n.titlebar.selection-mode button.titlebutton {\n  text-shadow: 0 -1px rgba(0, 0, 0, 0.54353);\n  -gtk-icon-shadow: 0 -1px rgba(0, 0, 0, 0.54353); }\n  headerbar.selection-mode button.titlebutton:backdrop,\n  .titlebar.selection-mode button.titlebutton:backdrop {\n    -gtk-icon-shadow: none; }\n\n.view:selected:focus, iconview:selected:focus, .view:selected, iconview:selected,\n.view text:selected:focus,\niconview text:selected:focus,\ntextview text:selected:focus,\n.view text:selected,\niconview text:selected,\ntextview text:selected, .view text selection:focus, iconview text selection:focus, .view text selection, iconview text selection,\ntextview text selection:focus,\ntextview text selection, flowbox flowboxchild:selected, spinbutton:not(.vertical) selection:focus, spinbutton:not(.vertical) selection,\nentry selection:focus,\nentry selection, modelbutton.flat:selected, popover.background checkbutton:selected,\npopover.background radiobutton:selected,\n.menuitem.button.flat:selected, treeview.view:selected:focus, treeview.view:selected, row:selected, calendar:selected {\n  background-color: @theme_selected_bg_color; }\n  row:selected label, label:selected, .selection-mode button.titlebutton, .view:selected:focus, iconview:selected:focus, .view:selected, iconview:selected,\n  .view text:selected:focus,\n  iconview text:selected:focus,\n  textview text:selected:focus,\n  .view text:selected,\n  iconview text:selected,\n  textview text:selected, .view text selection:focus, iconview text selection:focus, .view text selection, iconview text selection,\n  textview text selection:focus,\n  textview text selection, flowbox flowboxchild:selected, spinbutton:not(.vertical) selection:focus, spinbutton:not(.vertical) selection,\n  entry selection:focus,\n  entry selection, modelbutton.flat:selected, popover.background checkbutton:selected,\n  popover.background radiobutton:selected,\n  .menuitem.button.flat:selected, treeview.view:selected:focus, treeview.view:selected, row:selected, calendar:selected {\n    color: @theme_selected_fg_color;\n    outline-color: rgba(255, 255, 255, 0.3); }\n    row:selected label:disabled, label:disabled:selected, .selection-mode button.titlebutton:disabled, iconview:disabled:selected:focus, .view:disabled:selected, iconview:disabled:selected,\n    iconview text:disabled:selected:focus,\n    textview text:disabled:selected:focus,\n    .view text:disabled:selected,\n    iconview text:disabled:selected,\n    textview text:disabled:selected, iconview text selection:disabled:focus, .view text selection:disabled, iconview text selection:disabled,\n    textview text selection:disabled, flowbox flowboxchild:disabled:selected, label:disabled selection, spinbutton:not(.vertical) selection:disabled,\n    entry selection:disabled, modelbutton.flat:disabled:selected, popover.background checkbutton:disabled:selected,\n    popover.background radiobutton:disabled:selected,\n    .menuitem.button.flat:disabled:selected, row:disabled:selected, calendar:disabled:selected {\n      color: @theme_selected_bg_color; }\n    row:selected label:backdrop, label:backdrop:selected, .selection-mode button.titlebutton:backdrop, iconview:backdrop:selected:focus, .view:backdrop:selected, iconview:backdrop:selected,\n    iconview text:backdrop:selected:focus,\n    textview text:backdrop:selected:focus,\n    .view text:backdrop:selected,\n    iconview text:backdrop:selected,\n    textview text:backdrop:selected, iconview text selection:backdrop:focus, .view text selection:backdrop, iconview text selection:backdrop,\n    textview text selection:backdrop, flowbox flowboxchild:backdrop:selected, label:backdrop selection, spinbutton:not(.vertical) selection:backdrop,\n    entry selection:backdrop, modelbutton.flat:backdrop:selected, popover.background checkbutton:backdrop:selected,\n    popover.background radiobutton:backdrop:selected,\n    .menuitem.button.flat:backdrop:selected, row:backdrop:selected, calendar:backdrop:selected {\n      color: @theme_unfocused_bg_color; }\n      row:selected label:backdrop:disabled, label:backdrop:disabled:selected, .selection-mode button.titlebutton:backdrop:disabled, .view:backdrop:disabled:selected, iconview:backdrop:disabled:selected,\n      .view text:backdrop:disabled:selected,\n      iconview text:backdrop:disabled:selected,\n      textview text:backdrop:disabled:selected, .view text selection:backdrop:disabled, iconview text selection:backdrop:disabled,\n      textview text selection:backdrop:disabled, flowbox flowboxchild:backdrop:disabled:selected, label:disabled selection:backdrop, label:backdrop selection:disabled, spinbutton:not(.vertical) selection:backdrop:disabled,\n      entry selection:backdrop:disabled, modelbutton.flat:backdrop:disabled:selected, popover.background checkbutton:backdrop:disabled:selected,\n      popover.background radiobutton:backdrop:disabled:selected,\n      .menuitem.button.flat:backdrop:disabled:selected, row:backdrop:disabled:selected, calendar:backdrop:disabled:selected {\n        color: #7fb0e4; }\n\n.monospace {\n  font-family: monospace; }\n\n/**********************\n * Touch Copy & Paste *\n *********************/\ncursor-handle {\n  background-color: transparent;\n  background-image: none;\n  box-shadow: none;\n  border-style: none; }\n  cursor-handle.top:dir(ltr), cursor-handle.bottom:dir(rtl) {\n    -gtk-icon-source: -gtk-scaled(url(\"assets/text-select-start.png\"), url(\"assets/text-select-start@2.png\"));\n    padding-left: 10px; }\n  cursor-handle.bottom:dir(ltr), cursor-handle.top:dir(rtl) {\n    -gtk-icon-source: -gtk-scaled(url(\"assets/text-select-end.png\"), url(\"assets/text-select-end@2.png\"));\n    padding-right: 10px; }\n  cursor-handle.insertion-cursor:dir(ltr), cursor-handle.insertion-cursor:dir(rtl) {\n    -gtk-icon-source: -gtk-scaled(url(\"assets/slider-horiz-top.png\"), url(\"assets/slider-horiz-top@2.png\")); }\n  cursor-handle.top:hover:dir(ltr), cursor-handle.bottom:hover:dir(rtl) {\n    -gtk-icon-source: -gtk-scaled(url(\"assets/text-select-start-hover.png\"), url(\"assets/text-select-start-hover@2.png\"));\n    padding-left: 10px; }\n  cursor-handle.bottom:hover:dir(ltr), cursor-handle.top:hover:dir(rtl) {\n    -gtk-icon-source: -gtk-scaled(url(\"assets/text-select-end-hover.png\"), url(\"assets/text-select-end-hover@2.png\"));\n    padding-right: 10px; }\n  cursor-handle.insertion-cursor:hover:dir(ltr), cursor-handle.insertion-cursor:hover:dir(rtl) {\n    -gtk-icon-source: -gtk-scaled(url(\"assets/slider-horiz-top-hover.png\"), url(\"assets/slider-horiz-top-hover@2.png\")); }\n  cursor-handle.top:active:dir(ltr), cursor-handle.bottom:active:dir(rtl) {\n    -gtk-icon-source: -gtk-scaled(url(\"assets/text-select-start-active.png\"), url(\"assets/text-select-start-active@2.png\"));\n    padding-left: 10px; }\n  cursor-handle.bottom:active:dir(ltr), cursor-handle.top:active:dir(rtl) {\n    -gtk-icon-source: -gtk-scaled(url(\"assets/text-select-end-active.png\"), url(\"assets/text-select-end-active@2.png\"));\n    padding-right: 10px; }\n  cursor-handle.insertion-cursor:active:dir(ltr), cursor-handle.insertion-cursor:active:dir(rtl) {\n    -gtk-icon-source: -gtk-scaled(url(\"assets/slider-horiz-top-active.png\"), url(\"assets/slider-horiz-top-active@2.png\")); }\n\n.context-menu {\n  font: initial; }\n\nbutton.circular {\n  border-radius: 20px;\n  -gtk-outline-radius: 20px; }\n  button.circular label {\n    padding: 0; }\n\n.keycap {\n  min-width: 20px;\n  min-height: 25px;\n  margin-top: 2px;\n  padding-bottom: 3px;\n  padding-left: 6px;\n  padding-right: 6px;\n  color: @theme_fg_color;\n  background-color: @theme_bg_color;\n  border: 1px solid;\n  border-color: #cfcfcd;\n  border-radius: 0;\n  box-shadow: inset 0 -3px #ededec;\n  font-size: smaller; }\n  .keycap:backdrop {\n    background-color: @theme_unfocused_bg_color;\n    color: @insensitive_fg_color;\n    transition: 200ms ease-out; }\n\n*:drop(active):focus,\n*:drop(active) {\n  border-color: @success_color;\n  box-shadow: inset 0 0 0 1px @success_color;\n  caret-color: @success_color; }\n\nstackswitcher button.text-button {\n  min-width: 100px; }\n\nstackswitcher button.circular,\nstackswitcher button.text-button.circular {\n  min-width: 32px;\n  min-height: 32px;\n  padding: 0; }\t\n"
  },
  {
    "path": "frontend/gtkmm/theme/Windows10/gtk-3.20/gtk-dark.css",
    "content": "/* search for rgba value important! 46, 52, 54 */\n\n/* default color scheme */\n@define-color bg_color #000000;\n@define-color fg_color #ffffff;\n@define-color base_color #000000;\n@define-color text_color #ffffff;\n@define-color selected_bg_color #0084f0;\n@define-color selected_fg_color #ffffff;\n@define-color tooltip_bg_color #000000;\n@define-color tooltip_fg_color #ffffff;\n@define-color progressbar_color #0084f0;\n\n@define-color outline_color rgba(164,164,164,0.3);\n@define-color txt_shadow rgba(20, 20, 20, 0.76923);\n\n/* OSD colors */\n@define-color osd_bg_color alpha(#111111, 0.95);\n@define-color osd_fg_color #ffffff;\n@define-color osd_borders #8c8c8c;\n@define-color osd_outline #5e5e5e;\n@define-color osd_txt_shadow rgba(255,255,255,0.1);\n\n/* widget text/foreground color */\n@define-color theme_fg_color #ffffff;\n/*\ntext color for entries, views and content in general */\n@define-color theme_text_color #ffffff;\n/*\nwidget base background color */\n@define-color theme_bg_color #000000;\n/*\ntext widgets and the like base background color */\n@define-color theme_base_color #000000;\n/*\nbase background color of selections */\n@define-color theme_selected_bg_color #0084f0;\n/*\ntext/foreground color of selections */\n@define-color theme_selected_fg_color #ffffff;\n/*\nbase background color of insensitive widgets */\n@define-color insensitive_bg_color #000000;\n/*\ntext foreground color of insensitive widgets */\n@define-color insensitive_fg_color #e8e8e8;\n/*\ninsensitive text widgets and the like base background color */\n@define-color insensitive_base_color #000000;\n/*\nwidget text/foreground color on backdrop windows */\n@define-color theme_unfocused_fg_color #f1f1f1;\n/*\ntext color for entries, views and content in general on backdrop windows */\n@define-color theme_unfocused_text_color #f1f1f1;\n/*\nwidget base background color on backdrop windows */\n@define-color theme_unfocused_bg_color #000000;\n/*\ntext widgets and the like base background color on backdrop windows */\n@define-color theme_unfocused_base_color #000000;\n/*\nbase background color of selections on backdrop windows */\n@define-color theme_unfocused_selected_bg_color #8e8e8e;\n/*\ntext/foreground color of selections on backdrop windows */\n@define-color theme_unfocused_selected_fg_color #2c2c2c;\n/*\nwidgets main borders color */\n@define-color borders #343434;\n/*\nwidgets main borders color on backdrop windows */\n@define-color unfocused_borders #4a4a4a;\n/*\nthese are pretty self explicative */\n@define-color warning_color #f57900;\n@define-color error_color #cc0000;\n@define-color success_color #73d216;\n/*\nthese colors are exported for the window manager and shouldn't be used in applications,\nread if you used those and something break with a version upgrade you're on your own... */\n@define-color wm_title shade(#2e3436, 1.8);\n@define-color wm_unfocused_title #8b8e8f;\n@define-color wm_highlight rgba(255, 255, 255, 0.8);\n@define-color wm_borders_edge rgba(255, 255, 255, 0.8);\n@define-color wm_bg_a shade(#e8e8e7, 1.2);\n@define-color wm_bg_b #e8e8e7;\n@define-color wm_shadow alpha(black, 0.35);\n@define-color wm_border alpha(black, 0.18);\n@define-color wm_button_hover_color_a shade(#e8e8e7, 1.3);\n@define-color wm_button_hover_color_b #e8e8e7;\n@define-color wm_button_active_color_a shade(#e8e8e7, 0.85);\n@define-color wm_button_active_color_b shade(#e8e8e7, 0.89);\n@define-color wm_button_active_color_c shade(#e8e8e7, 0.9);\n@define-color content_view_bg #000000;\n\n@import url(\"gtk-contained-dark.css\");\n"
  },
  {
    "path": "frontend/gtkmm/theme/Windows10/gtk-3.20/gtk.css",
    "content": "/* search for rgba value important! 46, 52, 54 */\n\n/* default color scheme */\n@define-color bg_color #ffffff;\n@define-color fg_color #4c4c4c;\n@define-color base_color #ffffff;\n@define-color text_color #4c4c4c;\n@define-color selected_bg_color #cce8ff;\n@define-color selected_fg_color #262626;\n@define-color tooltip_bg_color #ffffff;\n@define-color tooltip_fg_color #4c4c4c;\n@define-color progressbar_color #06B025;\n\n@define-color outline_color rgba(46,52,54,0.3);\n@define-color txt_shadow rgba(255, 255, 255, 0.76923);\n\n/* OSD colors */\n@define-color osd_bg_color alpha(#111111, 0.9);\n@define-color osd_fg_color #ffffff;\n@define-color osd_borders #8c8c8c;\n@define-color osd_outline #eeeeec;\n@define-color osd_txt_shadow rgba(255,255,255,0.1);\n\n/* widget text/foreground color */\n@define-color theme_fg_color #2e3436;\n/*\ntext color for entries, views and content in general */\n@define-color theme_text_color black;\n/*\nwidget base background color */\n@define-color theme_bg_color #ffffff;\n/*\ntext widgets and the like base background color */\n@define-color theme_base_color #ffffff;\n/*\nbase background color of selections */\n@define-color theme_selected_bg_color #a1cca1;\n/*\ntext/foreground color of selections */\n@define-color theme_selected_fg_color #262626;\n/*\nbase background color of insensitive widgets */\n@define-color insensitive_bg_color #fcfcfc;\n/*\ntext foreground color of insensitive widgets */\n@define-color insensitive_fg_color #8c8c8c;\n/*\ninsensitive text widgets and the like base background color */\n@define-color insensitive_base_color #ffffff;\n/*\nwidget text/foreground color on backdrop windows */\n@define-color theme_unfocused_fg_color #8c8c8c;\n/*\ntext color for entries, views and content in general on backdrop windows */\n@define-color theme_unfocused_text_color black;\n/*\nwidget base background color on backdrop windows */\n@define-color theme_unfocused_bg_color #fcfcfc;\n/*\ntext widgets and the like base background color on backdrop windows */\n@define-color theme_unfocused_base_color #fcfcfc;\n/*\nbase background color of selections on backdrop windows */\n@define-color theme_unfocused_selected_bg_color #d1d1d1;\n/*\ntext/foreground color of selections on backdrop windows */\n@define-color theme_unfocused_selected_fg_color #000000;\n/*\nwidgets main borders color */\n@define-color borders #aaaaaa;\n/*\nwidgets main borders color on backdrop windows */\n@define-color unfocused_borders #8c8c8c;\n/*\nthese are pretty self explicative */\n@define-color warning_color #f57900;\n@define-color error_color #cc0000;\n@define-color success_color #73d216;\n/*\nthese colors are exported for the window manager and shouldn't be used in applications,\nread if you used those and something break with a version upgrade you're on your own... */\n@define-color wm_title shade(#2e3436, 1.8);\n@define-color wm_unfocused_title #8b8e8f;\n@define-color wm_highlight rgba(255, 255, 255, 0.8);\n@define-color wm_borders_edge rgba(255, 255, 255, 0.8);\n@define-color wm_bg_a shade(#e8e8e7, 1.2);\n@define-color wm_bg_b #e8e8e7;\n@define-color wm_shadow alpha(black, 0.35);\n@define-color wm_border alpha(black, 0.18);\n@define-color wm_button_hover_color_a shade(#e8e8e7, 1.3);\n@define-color wm_button_hover_color_b #e8e8e7;\n@define-color wm_button_active_color_a shade(#e8e8e7, 0.85);\n@define-color wm_button_active_color_b shade(#e8e8e7, 0.89);\n@define-color wm_button_active_color_c shade(#e8e8e7, 0.9);\n@define-color content_view_bg #ffffff;\n\n@import url(\"gtk-contained.css\");\n@import url(\"apps/gnome-terminal.css\");\n@import url(\"gtk-cadabra.css\");\n"
  },
  {
    "path": "frontend/gtkmm/theme/Windows10/gtk-3.20/settings.ini",
    "content": "[Settings]\ngtk-auto-mnemonics = 1\ngtk-visible-focus = automatic\n"
  },
  {
    "path": "frontend/gtkmm/win_res.rc.in",
    "content": "102\tICON\t\"@CADABRA_ROOT_DIR@/config/cadabra2.ico\"\n"
  },
  {
    "path": "frontend/latex/install.cmake",
    "content": "execute_process(COMMAND texhash)\n"
  },
  {
    "path": "frontend/latex/tableaux.sty",
    "content": "%\n% tableaux.sty version 1.2\n% Copyright (C) 2007-2017  by Kasper Peeters\n%\n% A LaTeX style file for drawing Young diagrams and Young tableaux.\n%\n% This file is part of the Cadabra computer algebra system,\n%\n%   http://cadabra.science/\n%\n% but may be distributed /or modified under the conditions of the\n% LaTeX Project Public License, either version 1.3 of this license or\n% (at your option) any later version. The latest version of this\n% license is in\n%\n%   http://www.latex-project.org/lppl.txt\n%\n% and version 1.3 or later is part of all distributions of LaTeX\n% version 2005/12/01 or later.\n%\n% This work has the LPPL maintenance status `maintained'.\n% The current maintainer of this work is Kasper Peeters.\n%\n\n% Some internals for the typesetting macros below; nothing\n% user-servicable here; please read on.\n\n\\def\\@tabforc#1#2#3{\\expandafter\\tabf@rc\\expandafter#1{#2 \\^}{#3}}\n\\def\\tabf@@rc#1#2#3\\tabf@@rc#4{\\def#1{#2}#4\\tabf@rc#1{#3}{#4}}\n\\long\\def\\ReturnAfterFi#1\\fi{\\fi#1}\n    \\def\\tabf@rc#1#2#3{%\n      \\def\\temp@ty{#2}%\n      \\ifx\\@empty\\temp@ty\n      \\else\n        \\ReturnAfterFi{%\n          \\tabf@@rc#1#2\\tabf@@rc{#3}%\n        }%\n      \\fi\n    }%\n\n% Sorry, some global registers for sizes and keeping track of\n% measurements.\n    \n\\newdimen\\ytsize\\ytsize=2mm\n\\newdimen\\ytfsize\\ytfsize=4mm\n\\newcount\\repcnt\n\\newdimen\\acchspace\n\\newdimen\\accvspace\n\\newdimen\\raiseh\n\\newdimen\\maxw\n\n\\newcommand\\phrule[1]{\\hbox{\\vbox to0pt{\\hrule height .2pt width#1\\vss}}}\n\n% Typeset a Young tableau with filled boxes. Takes a single \n% argument which is a string of symbols for each row,\n% separated by commas. Examples:\n%\n%   \\ftableau{abc,de}\n%   \\ftableau{ab{d_2},f{g_3}}\n\n\\newcommand\\ftableau[1]{%\n\\def\\ctest{,}\n\\def\\Ktest{\\^}\n\\acchspace=0ex\n\\accvspace=0ex\n\\maxw=0ex\n\\vbox{\\hbox{%\n\\@tabforc\\thisel{#1}{%\n \\ifx\\thisel\\Ktest{%\n     \\ifnum\\maxw=0\\maxw=\\acchspace\\fi%\n     \\raisebox{\\accvspace}{\\vbox to \\ytfsize{\\hbox to\n\t\t 0pt{\\vrule height \\ytfsize\\hss}}}\\kern\\acchspace\\kern-\\maxw}\n \\else\\ifx\\thisel\\ctest\n     \\ifnum\\maxw=0\\maxw=\\acchspace\\fi%\n     \\raisebox{\\accvspace}{\\vbox to \\ytfsize{\\hbox to 0pt{\\vrule height \\ytfsize\\hss}}}%\n     \\kern\\acchspace\\acchspace=0ex\n\t  \\advance\\accvspace by -\\ytfsize\n \\else\n     \\setbox3=\\hbox{$\\thisel$}%\n\t  \\raiseh=\\ytfsize%\n\t  \\advance\\raiseh by -1ex%\n\t  \\divide\\raiseh by 2%\n     \\advance\\acchspace by-\\ytfsize%\n     \\raisebox{\\accvspace}{\\vbox to \\ytfsize{\\hrule\\hbox to%\n        \\ytfsize{\\vrule height \\ytfsize\\hskip.5ex%\n         \\raisebox{\\raiseh}{\\tiny$\\thisel$}\\hss}\\vss\\phrule{\\ytfsize}}}%\n \\fi\\fi}}}}\n\n% Typeset a Young tableau with unlabelled boxes. Takes a single \n% argument which is a string of numbers, one for the length of\n% each row of the tableau. Example:\n%\n%   \\tableau{{10}{8}{3}}\n%\n% typesets a tableau with 10 boxes in the 1st row, 8 in the 2nd\n% and 3 in the 3rd. Curly brackets can be omitted if numbers\n% are less than 10.\n\n\\newcommand\\tableau[1]{%\n\\def\\stest{ }\n\\def\\Ktest{\\^}\n\\acchspace=0ex\n\\accvspace=0ex\n\\maxw=0ex\n\\hbox{%\n\\@tabforc\\thisel{#1}{%\n \\ifx\\thisel\\Ktest{}\n \\else\n     \\repcnt=\\thisel%\n     \\loop{}%\n     \\advance\\acchspace by-\\ytsize%\n     \\raisebox{\\accvspace}{\\vbox to \\ytsize{\\hrule \\hbox to%\n\t\t\t\\ytsize{\\vrule height \\ytsize\\hss}\\vss\\phrule{\\ytsize}}}%\n     \\advance\\repcnt by -1\\ifnum\\repcnt>1{}\\repeat%\n     \\ifnum\\maxw=0\\maxw=\\acchspace\\fi%\n     \\raisebox{\\accvspace}{\\vbox to \\ytsize{\\hbox to 0pt{\\vrule height \\ytsize\\hss}}}%\n     \\kern\\acchspace\\acchspace=0ex%\n\t  \\advance\\accvspace by -\\ytsize%\n \\fi}\\kern-\\maxw}}\n\n\n"
  },
  {
    "path": "frontend/latex/young.html",
    "content": "<!DOCTYPE html>\n<html>\n  <head>\n\t <style>\n\t\tdiv.box {\n\t\tdisplay: inline-block;\n\t\tborder: 1px solid black;\n\t\twidth: 10px;\n\t\tmin-width: 10px;\n\t\theight: 10px;\n\t\tmin-height: 10px;\n\t\tmargin: 0px;\n\t\tpadding: 0px;\n\t\t}\n\t\tdiv.young_tableau {\n\t\tdisplay: inline-block;\n\t\t}\n\t\tdiv.young_row {\n\t\tpadding: 0px;\n\t\tmargin: 0px;\n\t\theight: 10px;\n\t\t}\n\t </style>\n\t <script src='https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML'></script>\t \n  </head>\n  <body>\n\t \\( \\displaystyle \\int_a^b \\sin(x) \\) \n\t <div class=\"young_tableau\">\n\t\t<div class=\"young_row\">\n\t\t  <div class=\"box\"></div><div class=\"box\"></div><div class=\"box\"></div>\n\t\t</div>\n\t\t<div class=\"young_row\">\n\t\t  <div class=\"box\"></div><div class=\"box\"></div>\n\t\t</div>\n\t </div>\n\t \\( = \\cos(x)^2 \\)\n\n\t <br/>\n\n\t \\(\\def\\place#1#2#3{\\smash{\\rlap{\\hskip{#1em}\\raise{-#2em}{#3}}}}\\)\n\t \\(\\place{0}{0}{\\boxed{\\scriptsize 0}}\n\t \\place{1}{0}{\\boxed{\\scriptsize 1}}\n\t \\place{2}{0}{\\boxed{\\scriptsize 1}}\n\t \\place{0}{1}{\\boxed{\\scriptsize 2}}\n\t \\place{0}{2}{\\boxed{\\scriptsize 3}}\\hspace{3em}+\\place{0}{0}{\\boxed{\\scriptsize 0}}\n\t \\place{1}{0}{\\boxed{\\scriptsize 1}}\n\t \\place{2}{0}{\\boxed{\\scriptsize 1}}\n\t \\place{0}{1}{\\boxed{\\scriptsize 2}}\n\t \\place{0}{2}{\\boxed{\\scriptsize 3}}\\hspace{3em}+\\place{0}{0}{\\boxed{\\scriptsize 0}}\n\t \\place{1}{0}{\\boxed{\\scriptsize 1}}\n\t \\place{2}{0}{\\boxed{\\scriptsize 1}}\n\t \\place{0}{1}{\\boxed{\\scriptsize 2}}\n\t \\place{0}{2}{\\boxed{\\scriptsize 3}}\\hspace{3em}+\\place{0}{0}{\\boxed{\\scriptsize 0}}\n\t \\place{1}{0}{\\boxed{\\scriptsize 1}}\n\t \\place{2}{0}{\\boxed{\\scriptsize 1}}\n\t \\place{0}{1}{\\boxed{\\scriptsize 2}}\n\t \\place{0}{2}{\\boxed{\\scriptsize 3}}\\hspace{3em}+\\place{0}{0}{\\boxed{\\scriptsize 0}}\n\t \\place{1}{0}{\\boxed{\\scriptsize 1}}\n\t \\place{2}{0}{\\boxed{\\scriptsize 1}}\n\t \\place{0}{1}{\\boxed{\\scriptsize 2}}\n\t \\place{0}{2}{\\boxed{\\scriptsize 3}}\\hspace{3em}+\\place{0}{0}{\\boxed{\\scriptsize 0}}\n\t \\place{1}{0}{\\boxed{\\scriptsize 1}}\n\t \\place{2}{0}{\\boxed{\\scriptsize 1}}\n\t \\place{0}{1}{\\boxed{\\scriptsize 2}}\n\t \\place{0}{2}{\\boxed{\\scriptsize 3}}\\hspace{3em}+\\place{0}{0}{\\boxed{\\scriptsize 0}}\n\t \\place{1}{0}{\\boxed{\\scriptsize 1}}\n\t \\place{2}{0}{\\boxed{\\scriptsize 1}}\n\t \\place{0}{1}{\\boxed{\\scriptsize 2}}\n\t \\place{0}{2}{\\boxed{\\scriptsize 3}}\\hspace{3em}+\\place{0}{0}{\\boxed{\\scriptsize 0}}\n\t \\place{1}{0}{\\boxed{\\scriptsize 1}}\n\t \\place{2}{0}{\\boxed{\\scriptsize 1}}\n\t \\place{0}{1}{\\boxed{\\scriptsize 2}}\n\t \\place{0}{2}{\\boxed{\\scriptsize 3}}\\hspace{3em}+\\place{0}{0}{\\boxed{\\scriptsize 0}}\n\t \\place{1}{0}{\\boxed{\\scriptsize 1}}\n\t \\place{2}{0}{\\boxed{\\scriptsize 1}}\n\t \\place{0}{1}{\\boxed{\\scriptsize 2}}\n\t \\place{0}{2}{\\boxed{\\scriptsize 3}}\\hspace{3em}+\\place{0}{0}{\\boxed{\\scriptsize 0}}\n\t \\place{1}{0}{\\boxed{\\scriptsize 1}}\n\t \\place{2}{0}{\\boxed{\\scriptsize 1}}\n\t \\place{0}{1}{\\boxed{\\scriptsize 2}}\n\t \\place{0}{2}{\\boxed{\\scriptsize 3}}\\hspace{3em}+\\place{0}{0}{\\boxed{\\scriptsize 0}}\n\t \\place{1}{0}{\\boxed{\\scriptsize 1}}\n\t \\place{2}{0}{\\boxed{\\scriptsize 1}}\n\t \\place{0}{1}{\\boxed{\\scriptsize 2}}\n\t \\place{0}{2}{\\boxed{\\scriptsize 3}}\\hspace{3em}+\\place{0}{0}{\\boxed{\\scriptsize 0}}\n\t \\place{1}{0}{\\boxed{\\scriptsize 1}}\n\t \\place{2}{0}{\\boxed{\\scriptsize 1}}\n\t \\place{0}{1}{\\boxed{\\scriptsize 2}}\n\t \\place{0}{2}{\\boxed{\\scriptsize 3}}\\hspace{3em}+\\place{0}{0}{\\boxed{\\scriptsize 0}}\n\t \\place{1}{0}{\\boxed{\\scriptsize 1}}\n\t \\place{2}{0}{\\boxed{\\scriptsize 1}}\n\t \\place{0}{1}{\\boxed{\\scriptsize 2}}\n\t \\place{0}{2}{\\boxed{\\scriptsize 3}}\\hspace{3em}+\\place{0}{0}{\\boxed{\\scriptsize 0}}\n\t \\place{1}{0}{\\boxed{\\scriptsize 1}}\n\t \\place{2}{0}{\\boxed{\\scriptsize 1}}\n\t \\place{0}{1}{\\boxed{\\scriptsize 2}}\n\t \\place{0}{2}{\\boxed{\\scriptsize 3}}\\hspace{3em}+\\place{0}{0}{\\boxed{\\scriptsize 0}}\n\t \\place{1}{0}{\\boxed{\\scriptsize 1}}\n\t \\place{2}{0}{\\boxed{\\scriptsize 1}}\n\t \\place{0}{1}{\\boxed{\\scriptsize 2}}\n\t \\place{0}{2}{\\boxed{\\scriptsize 3}}\\hspace{3em}+\\place{0}{0}{\\boxed{\\scriptsize 0}}\n\t \\place{1}{0}{\\boxed{\\scriptsize 1}}\n\t \\place{2}{0}{\\boxed{\\scriptsize 1}}\n\t \\place{0}{1}{\\boxed{\\scriptsize 2}}\n\t \\place{0}{2}{\\boxed{\\scriptsize 3}}\\hspace{3em}+\\place{0}{0}{\\boxed{1}} \n\t \\)\n\t \n  </body>\n</html>\n"
  },
  {
    "path": "frontend/osx/CMakeLists.txt",
    "content": "cmake_minimum_required(VERSION 2.8)\n\nproject(Cadabra)\n\nadd_executable(cadabra-osx fake.cc)\nadd_custom_command(TARGET cadabra-osx\n\t\t   POST_BUILD\n                   COMMAND xcodebuild \n\t\t   COMMAND rm ${CMAKE_CURRENT_BINARY_DIR}/cadabra-osx\n\t\t   WORKING_DIRECTORY ${CMAKE_CURRENT_SOURCE_DIR}/Cadabra\n\t\t   )\n"
  },
  {
    "path": "frontend/osx/Cadabra/Cadabra/AppDelegate.h",
    "content": "//\n//  AppDelegate.h\n//  Cadabra\n//\n//  Created by Kasper Peeters on 01/11/2014.\n//  Copyright (c) 2014 phi-sci. All rights reserved.\n//\n\n#import <Cocoa/Cocoa.h>\n#include \"NotebookController.h\"\n\n@interface AppDelegate : NSObject <NSApplicationDelegate>\n\n\n@end\n\n"
  },
  {
    "path": "frontend/osx/Cadabra/Cadabra/AppDelegate.mm",
    "content": "//\n//  AppDelegate.m\n//  Cadabra\n//\n//  Created by Kasper Peeters on 01/11/2014.\n//  Copyright (c) 2014 phi-sci. All rights reserved.\n//\n\n#import \"AppDelegate.h\"\n\n@interface  AppDelegate()\n\n@property (weak) IBOutlet NSWindow *window;\n@property (nonatomic,strong) IBOutlet NotebookController *notebookController;\n\n@end\n\n\n@implementation AppDelegate {\n    \n}\n\n- (void)applicationDidFinishLaunching:(NSNotification *)aNotification {\n    self.notebookController = [[NotebookController alloc] initWithNibName:@\"Notebook\" bundle:nil];\n    \n    [self.window.contentView addSubview:self.notebookController.view];\n    [self.notebookController.view setAutoresizingMask:NSViewWidthSizable | NSViewHeightSizable];\n    self.notebookController.view.frame = ((NSView*)self.window.contentView).bounds;\n}\n\n- (void)applicationWillTerminate:(NSNotification *)aNotification {\n    // Insert code here to tear down your application\n}\n- (IBAction)menuAboutCadabra:(id)sender {\n    NSLog(@\"About\");\n}\n\n@end\n"
  },
  {
    "path": "frontend/osx/Cadabra/Cadabra/Base.lproj/Cadabra.xib",
    "content": "<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n<document type=\"com.apple.InterfaceBuilder3.Cocoa.XIB\" version=\"3.0\" toolsVersion=\"6254\" systemVersion=\"13F34\" targetRuntime=\"MacOSX.Cocoa\" propertyAccessControl=\"none\" useAutolayout=\"YES\">\n    <dependencies>\n        <deployment identifier=\"macosx\"/>\n        <plugIn identifier=\"com.apple.InterfaceBuilder.CocoaPlugin\" version=\"6254\"/>\n    </dependencies>\n    <objects>\n        <customObject id=\"-2\" userLabel=\"File's Owner\" customClass=\"NotebookController\">\n            <connections>\n                <outlet property=\"delegate\" destination=\"Voe-Tx-rLC\" id=\"GzC-gU-4Uq\"/>\n            </connections>\n        </customObject>\n        <customObject id=\"-1\" userLabel=\"First Responder\" customClass=\"FirstResponder\"/>\n        <customObject id=\"-3\" userLabel=\"Application\" customClass=\"NSObject\"/>\n        <customObject id=\"Voe-Tx-rLC\" customClass=\"AppDelegate\">\n            <connections>\n                <outlet property=\"window\" destination=\"QvC-M9-y7g\" id=\"3Vy-tc-b2y\"/>\n            </connections>\n        </customObject>\n        <customObject id=\"YLy-65-1bz\" customClass=\"NSFontManager\"/>\n        <menu title=\"Main Menu\" systemMenu=\"main\" id=\"AYu-sK-qS6\">\n            <items>\n                <menuItem title=\"Cadabra\" id=\"1Xt-HY-uBw\">\n                    <modifierMask key=\"keyEquivalentModifierMask\"/>\n                    <menu key=\"submenu\" title=\"Cadabra\" systemMenu=\"apple\" id=\"uQy-DD-JDr\">\n                        <items>\n                            <menuItem title=\"About Cadabra\" id=\"5kV-Vb-QxS\">\n                                <modifierMask key=\"keyEquivalentModifierMask\"/>\n                                <connections>\n                                    <action selector=\"menuAboutCadabra:\" target=\"Voe-Tx-rLC\" id=\"wlH-eR-oaz\"/>\n                                </connections>\n                            </menuItem>\n                            <menuItem isSeparatorItem=\"YES\" id=\"VOq-y0-SEH\"/>\n                            <menuItem title=\"Preferences…\" keyEquivalent=\",\" id=\"BOF-NM-1cW\"/>\n                            <menuItem isSeparatorItem=\"YES\" id=\"wFC-TO-SCJ\"/>\n                            <menuItem title=\"Hide Cadabra\" keyEquivalent=\"h\" id=\"Olw-nP-bQN\">\n                                <connections>\n                                    <action selector=\"hide:\" target=\"-1\" id=\"PnN-Uc-m68\"/>\n                                </connections>\n                            </menuItem>\n                            <menuItem title=\"Hide Others\" keyEquivalent=\"h\" id=\"Vdr-fp-XzO\">\n                                <modifierMask key=\"keyEquivalentModifierMask\" option=\"YES\" command=\"YES\"/>\n                                <connections>\n                                    <action selector=\"hideOtherApplications:\" target=\"-1\" id=\"VT4-aY-XCT\"/>\n                                </connections>\n                            </menuItem>\n                            <menuItem title=\"Show All\" id=\"Kd2-mp-pUS\">\n                                <modifierMask key=\"keyEquivalentModifierMask\"/>\n                                <connections>\n                                    <action selector=\"unhideAllApplications:\" target=\"-1\" id=\"Dhg-Le-xox\"/>\n                                </connections>\n                            </menuItem>\n                            <menuItem isSeparatorItem=\"YES\" id=\"kCx-OE-vgT\"/>\n                            <menuItem title=\"Quit Cadabra\" keyEquivalent=\"q\" id=\"4sb-4s-VLi\"/>\n                        </items>\n                        <connections>\n                            <outlet property=\"delegate\" destination=\"-2\" id=\"biQ-Qz-lhA\"/>\n                        </connections>\n                    </menu>\n                </menuItem>\n                <menuItem title=\"File\" id=\"dMs-cI-mzQ\">\n                    <modifierMask key=\"keyEquivalentModifierMask\"/>\n                    <menu key=\"submenu\" title=\"File\" id=\"bib-Uj-vzu\">\n                        <items>\n                            <menuItem title=\"New\" keyEquivalent=\"n\" id=\"Was-JA-tGl\"/>\n                            <menuItem title=\"Open…\" keyEquivalent=\"o\" id=\"IAo-SY-fd9\">\n                                <connections>\n                                    <action selector=\"openDocument:\" target=\"-1\" id=\"bVn-NM-KNZ\"/>\n                                </connections>\n                            </menuItem>\n                            <menuItem title=\"Open Recent\" id=\"tXI-mr-wws\">\n                                <modifierMask key=\"keyEquivalentModifierMask\"/>\n                                <menu key=\"submenu\" title=\"Open Recent\" systemMenu=\"recentDocuments\" id=\"oas-Oc-fiZ\">\n                                    <items>\n                                        <menuItem title=\"Clear Menu\" id=\"vNY-rz-j42\">\n                                            <modifierMask key=\"keyEquivalentModifierMask\"/>\n                                            <connections>\n                                                <action selector=\"clearRecentDocuments:\" target=\"-1\" id=\"Daa-9d-B3U\"/>\n                                            </connections>\n                                        </menuItem>\n                                    </items>\n                                </menu>\n                            </menuItem>\n                            <menuItem isSeparatorItem=\"YES\" id=\"m54-Is-iLE\"/>\n                            <menuItem title=\"Close\" keyEquivalent=\"w\" id=\"DVo-aG-piG\">\n                                <connections>\n                                    <action selector=\"performClose:\" target=\"-1\" id=\"HmO-Ls-i7Q\"/>\n                                </connections>\n                            </menuItem>\n                            <menuItem title=\"Save…\" keyEquivalent=\"s\" id=\"pxx-59-PXV\">\n                                <connections>\n                                    <action selector=\"saveDocument:\" target=\"-1\" id=\"teZ-XB-qJY\"/>\n                                </connections>\n                            </menuItem>\n                            <menuItem title=\"Save As…\" keyEquivalent=\"S\" id=\"Bw7-FT-i3A\">\n                                <connections>\n                                    <action selector=\"saveDocumentAs:\" target=\"-1\" id=\"mDf-zr-I0C\"/>\n                                </connections>\n                            </menuItem>\n                            <menuItem title=\"Revert to Saved\" id=\"KaW-ft-85H\">\n                                <modifierMask key=\"keyEquivalentModifierMask\"/>\n                                <connections>\n                                    <action selector=\"revertDocumentToSaved:\" target=\"-1\" id=\"iJ3-Pv-kwq\"/>\n                                </connections>\n                            </menuItem>\n                            <menuItem isSeparatorItem=\"YES\" id=\"aJh-i4-bef\"/>\n                            <menuItem title=\"Page Setup…\" keyEquivalent=\"P\" id=\"qIS-W8-SiK\">\n                                <modifierMask key=\"keyEquivalentModifierMask\" shift=\"YES\" command=\"YES\"/>\n                                <connections>\n                                    <action selector=\"runPageLayout:\" target=\"-1\" id=\"Din-rz-gC5\"/>\n                                </connections>\n                            </menuItem>\n                            <menuItem title=\"Print…\" keyEquivalent=\"p\" id=\"aTl-1u-JFS\">\n                                <connections>\n                                    <action selector=\"print:\" target=\"-1\" id=\"qaZ-4w-aoO\"/>\n                                </connections>\n                            </menuItem>\n                        </items>\n                    </menu>\n                </menuItem>\n                <menuItem title=\"Edit\" id=\"5QF-Oa-p0T\">\n                    <modifierMask key=\"keyEquivalentModifierMask\"/>\n                    <menu key=\"submenu\" title=\"Edit\" id=\"W48-6f-4Dl\">\n                        <items>\n                            <menuItem title=\"Undo\" keyEquivalent=\"z\" id=\"dRJ-4n-Yzg\">\n                                <connections>\n                                    <action selector=\"undo:\" target=\"-1\" id=\"M6e-cu-g7V\"/>\n                                </connections>\n                            </menuItem>\n                            <menuItem title=\"Redo\" keyEquivalent=\"Z\" id=\"6dh-zS-Vam\">\n                                <connections>\n                                    <action selector=\"redo:\" target=\"-1\" id=\"oIA-Rs-6OD\"/>\n                                </connections>\n                            </menuItem>\n                            <menuItem isSeparatorItem=\"YES\" id=\"WRV-NI-Exz\"/>\n                            <menuItem title=\"Cut\" keyEquivalent=\"x\" id=\"uRl-iY-unG\">\n                                <connections>\n                                    <action selector=\"cut:\" target=\"-1\" id=\"YJe-68-I9s\"/>\n                                </connections>\n                            </menuItem>\n                            <menuItem title=\"Copy\" keyEquivalent=\"c\" id=\"x3v-GG-iWU\">\n                                <connections>\n                                    <action selector=\"copy:\" target=\"-1\" id=\"G1f-GL-Joy\"/>\n                                </connections>\n                            </menuItem>\n                            <menuItem title=\"Paste\" keyEquivalent=\"v\" id=\"gVA-U4-sdL\">\n                                <connections>\n                                    <action selector=\"paste:\" target=\"-1\" id=\"UvS-8e-Qdg\"/>\n                                </connections>\n                            </menuItem>\n                            <menuItem title=\"Paste and Match Style\" keyEquivalent=\"V\" id=\"WeT-3V-zwk\">\n                                <modifierMask key=\"keyEquivalentModifierMask\" option=\"YES\" command=\"YES\"/>\n                                <connections>\n                                    <action selector=\"pasteAsPlainText:\" target=\"-1\" id=\"cEh-KX-wJQ\"/>\n                                </connections>\n                            </menuItem>\n                            <menuItem title=\"Delete\" id=\"pa3-QI-u2k\">\n                                <modifierMask key=\"keyEquivalentModifierMask\"/>\n                                <connections>\n                                    <action selector=\"delete:\" target=\"-1\" id=\"0Mk-Ml-PaM\"/>\n                                </connections>\n                            </menuItem>\n                            <menuItem title=\"Select All\" keyEquivalent=\"a\" id=\"Ruw-6m-B2m\">\n                                <connections>\n                                    <action selector=\"selectAll:\" target=\"-1\" id=\"VNm-Mi-diN\"/>\n                                </connections>\n                            </menuItem>\n                            <menuItem isSeparatorItem=\"YES\" id=\"uyl-h8-XO2\"/>\n                            <menuItem title=\"Find\" id=\"4EN-yA-p0u\">\n                                <modifierMask key=\"keyEquivalentModifierMask\"/>\n                                <menu key=\"submenu\" title=\"Find\" id=\"1b7-l0-nxx\">\n                                    <items>\n                                        <menuItem title=\"Find…\" tag=\"1\" keyEquivalent=\"f\" id=\"Xz5-n4-O0W\">\n                                            <connections>\n                                                <action selector=\"performFindPanelAction:\" target=\"-1\" id=\"cD7-Qs-BN4\"/>\n                                            </connections>\n                                        </menuItem>\n                                        <menuItem title=\"Find and Replace…\" tag=\"12\" keyEquivalent=\"f\" id=\"YEy-JH-Tfz\">\n                                            <modifierMask key=\"keyEquivalentModifierMask\" option=\"YES\" command=\"YES\"/>\n                                            <connections>\n                                                <action selector=\"performFindPanelAction:\" target=\"-1\" id=\"WD3-Gg-5AJ\"/>\n                                            </connections>\n                                        </menuItem>\n                                        <menuItem title=\"Find Next\" tag=\"2\" keyEquivalent=\"g\" id=\"q09-fT-Sye\">\n                                            <connections>\n                                                <action selector=\"performFindPanelAction:\" target=\"-1\" id=\"NDo-RZ-v9R\"/>\n                                            </connections>\n                                        </menuItem>\n                                        <menuItem title=\"Find Previous\" tag=\"3\" keyEquivalent=\"G\" id=\"OwM-mh-QMV\">\n                                            <connections>\n                                                <action selector=\"performFindPanelAction:\" target=\"-1\" id=\"HOh-sY-3ay\"/>\n                                            </connections>\n                                        </menuItem>\n                                        <menuItem title=\"Use Selection for Find\" tag=\"7\" keyEquivalent=\"e\" id=\"buJ-ug-pKt\">\n                                            <connections>\n                                                <action selector=\"performFindPanelAction:\" target=\"-1\" id=\"U76-nv-p5D\"/>\n                                            </connections>\n                                        </menuItem>\n                                        <menuItem title=\"Jump to Selection\" keyEquivalent=\"j\" id=\"S0p-oC-mLd\">\n                                            <connections>\n                                                <action selector=\"centerSelectionInVisibleArea:\" target=\"-1\" id=\"IOG-6D-g5B\"/>\n                                            </connections>\n                                        </menuItem>\n                                    </items>\n                                </menu>\n                            </menuItem>\n                            <menuItem title=\"Spelling and Grammar\" id=\"Dv1-io-Yv7\">\n                                <modifierMask key=\"keyEquivalentModifierMask\"/>\n                                <menu key=\"submenu\" title=\"Spelling\" id=\"3IN-sU-3Bg\">\n                                    <items>\n                                        <menuItem title=\"Show Spelling and Grammar\" keyEquivalent=\":\" id=\"HFo-cy-zxI\">\n                                            <connections>\n                                                <action selector=\"showGuessPanel:\" target=\"-1\" id=\"vFj-Ks-hy3\"/>\n                                            </connections>\n                                        </menuItem>\n                                        <menuItem title=\"Check Document Now\" keyEquivalent=\";\" id=\"hz2-CU-CR7\">\n                                            <connections>\n                                                <action selector=\"checkSpelling:\" target=\"-1\" id=\"fz7-VC-reM\"/>\n                                            </connections>\n                                        </menuItem>\n                                        <menuItem isSeparatorItem=\"YES\" id=\"bNw-od-mp5\"/>\n                                        <menuItem title=\"Check Spelling While Typing\" id=\"rbD-Rh-wIN\">\n                                            <modifierMask key=\"keyEquivalentModifierMask\"/>\n                                            <connections>\n                                                <action selector=\"toggleContinuousSpellChecking:\" target=\"-1\" id=\"7w6-Qz-0kB\"/>\n                                            </connections>\n                                        </menuItem>\n                                        <menuItem title=\"Check Grammar With Spelling\" id=\"mK6-2p-4JG\">\n                                            <modifierMask key=\"keyEquivalentModifierMask\"/>\n                                            <connections>\n                                                <action selector=\"toggleGrammarChecking:\" target=\"-1\" id=\"muD-Qn-j4w\"/>\n                                            </connections>\n                                        </menuItem>\n                                        <menuItem title=\"Correct Spelling Automatically\" id=\"78Y-hA-62v\">\n                                            <modifierMask key=\"keyEquivalentModifierMask\"/>\n                                            <connections>\n                                                <action selector=\"toggleAutomaticSpellingCorrection:\" target=\"-1\" id=\"2lM-Qi-WAP\"/>\n                                            </connections>\n                                        </menuItem>\n                                    </items>\n                                </menu>\n                            </menuItem>\n                            <menuItem title=\"Substitutions\" id=\"9ic-FL-obx\">\n                                <modifierMask key=\"keyEquivalentModifierMask\"/>\n                                <menu key=\"submenu\" title=\"Substitutions\" id=\"FeM-D8-WVr\">\n                                    <items>\n                                        <menuItem title=\"Show Substitutions\" id=\"z6F-FW-3nz\">\n                                            <modifierMask key=\"keyEquivalentModifierMask\"/>\n                                            <connections>\n                                                <action selector=\"orderFrontSubstitutionsPanel:\" target=\"-1\" id=\"oku-mr-iSq\"/>\n                                            </connections>\n                                        </menuItem>\n                                        <menuItem isSeparatorItem=\"YES\" id=\"gPx-C9-uUO\"/>\n                                        <menuItem title=\"Smart Copy/Paste\" id=\"9yt-4B-nSM\">\n                                            <modifierMask key=\"keyEquivalentModifierMask\"/>\n                                            <connections>\n                                                <action selector=\"toggleSmartInsertDelete:\" target=\"-1\" id=\"3IJ-Se-DZD\"/>\n                                            </connections>\n                                        </menuItem>\n                                        <menuItem title=\"Smart Quotes\" id=\"hQb-2v-fYv\">\n                                            <modifierMask key=\"keyEquivalentModifierMask\"/>\n                                            <connections>\n                                                <action selector=\"toggleAutomaticQuoteSubstitution:\" target=\"-1\" id=\"ptq-xd-QOA\"/>\n                                            </connections>\n                                        </menuItem>\n                                        <menuItem title=\"Smart Dashes\" id=\"rgM-f4-ycn\">\n                                            <modifierMask key=\"keyEquivalentModifierMask\"/>\n                                            <connections>\n                                                <action selector=\"toggleAutomaticDashSubstitution:\" target=\"-1\" id=\"oCt-pO-9gS\"/>\n                                            </connections>\n                                        </menuItem>\n                                        <menuItem title=\"Smart Links\" id=\"cwL-P1-jid\">\n                                            <modifierMask key=\"keyEquivalentModifierMask\"/>\n                                            <connections>\n                                                <action selector=\"toggleAutomaticLinkDetection:\" target=\"-1\" id=\"Gip-E3-Fov\"/>\n                                            </connections>\n                                        </menuItem>\n                                        <menuItem title=\"Data Detectors\" id=\"tRr-pd-1PS\">\n                                            <modifierMask key=\"keyEquivalentModifierMask\"/>\n                                            <connections>\n                                                <action selector=\"toggleAutomaticDataDetection:\" target=\"-1\" id=\"R1I-Nq-Kbl\"/>\n                                            </connections>\n                                        </menuItem>\n                                        <menuItem title=\"Text Replacement\" id=\"HFQ-gK-NFA\">\n                                            <modifierMask key=\"keyEquivalentModifierMask\"/>\n                                            <connections>\n                                                <action selector=\"toggleAutomaticTextReplacement:\" target=\"-1\" id=\"DvP-Fe-Py6\"/>\n                                            </connections>\n                                        </menuItem>\n                                    </items>\n                                </menu>\n                            </menuItem>\n                            <menuItem title=\"Transformations\" id=\"2oI-Rn-ZJC\">\n                                <modifierMask key=\"keyEquivalentModifierMask\"/>\n                                <menu key=\"submenu\" title=\"Transformations\" id=\"c8a-y6-VQd\">\n                                    <items>\n                                        <menuItem title=\"Make Upper Case\" id=\"vmV-6d-7jI\">\n                                            <modifierMask key=\"keyEquivalentModifierMask\"/>\n                                            <connections>\n                                                <action selector=\"uppercaseWord:\" target=\"-1\" id=\"sPh-Tk-edu\"/>\n                                            </connections>\n                                        </menuItem>\n                                        <menuItem title=\"Make Lower Case\" id=\"d9M-CD-aMd\">\n                                            <modifierMask key=\"keyEquivalentModifierMask\"/>\n                                            <connections>\n                                                <action selector=\"lowercaseWord:\" target=\"-1\" id=\"iUZ-b5-hil\"/>\n                                            </connections>\n                                        </menuItem>\n                                        <menuItem title=\"Capitalize\" id=\"UEZ-Bs-lqG\">\n                                            <modifierMask key=\"keyEquivalentModifierMask\"/>\n                                            <connections>\n                                                <action selector=\"capitalizeWord:\" target=\"-1\" id=\"26H-TL-nsh\"/>\n                                            </connections>\n                                        </menuItem>\n                                    </items>\n                                </menu>\n                            </menuItem>\n                            <menuItem title=\"Speech\" id=\"xrE-MZ-jX0\">\n                                <modifierMask key=\"keyEquivalentModifierMask\"/>\n                                <menu key=\"submenu\" title=\"Speech\" id=\"3rS-ZA-NoH\">\n                                    <items>\n                                        <menuItem title=\"Start Speaking\" id=\"Ynk-f8-cLZ\">\n                                            <modifierMask key=\"keyEquivalentModifierMask\"/>\n                                            <connections>\n                                                <action selector=\"startSpeaking:\" target=\"-1\" id=\"654-Ng-kyl\"/>\n                                            </connections>\n                                        </menuItem>\n                                        <menuItem title=\"Stop Speaking\" id=\"Oyz-dy-DGm\">\n                                            <modifierMask key=\"keyEquivalentModifierMask\"/>\n                                            <connections>\n                                                <action selector=\"stopSpeaking:\" target=\"-1\" id=\"dX8-6p-jy9\"/>\n                                            </connections>\n                                        </menuItem>\n                                    </items>\n                                </menu>\n                            </menuItem>\n                        </items>\n                    </menu>\n                </menuItem>\n                <menuItem title=\"Format\" id=\"jxT-CU-nIS\">\n                    <modifierMask key=\"keyEquivalentModifierMask\"/>\n                    <menu key=\"submenu\" title=\"Format\" id=\"GEO-Iw-cKr\">\n                        <items>\n                            <menuItem title=\"Font\" id=\"Gi5-1S-RQB\">\n                                <modifierMask key=\"keyEquivalentModifierMask\"/>\n                                <menu key=\"submenu\" title=\"Font\" systemMenu=\"font\" id=\"aXa-aM-Jaq\">\n                                    <items>\n                                        <menuItem title=\"Show Fonts\" keyEquivalent=\"t\" id=\"Q5e-8K-NDq\">\n                                            <connections>\n                                                <action selector=\"orderFrontFontPanel:\" target=\"YLy-65-1bz\" id=\"WHr-nq-2xA\"/>\n                                            </connections>\n                                        </menuItem>\n                                        <menuItem title=\"Bold\" tag=\"2\" keyEquivalent=\"b\" id=\"GB9-OM-e27\">\n                                            <connections>\n                                                <action selector=\"addFontTrait:\" target=\"YLy-65-1bz\" id=\"hqk-hr-sYV\"/>\n                                            </connections>\n                                        </menuItem>\n                                        <menuItem title=\"Italic\" tag=\"1\" keyEquivalent=\"i\" id=\"Vjx-xi-njq\">\n                                            <connections>\n                                                <action selector=\"addFontTrait:\" target=\"YLy-65-1bz\" id=\"IHV-OB-c03\"/>\n                                            </connections>\n                                        </menuItem>\n                                        <menuItem title=\"Underline\" keyEquivalent=\"u\" id=\"WRG-CD-K1S\">\n                                            <connections>\n                                                <action selector=\"underline:\" target=\"-1\" id=\"FYS-2b-JAY\"/>\n                                            </connections>\n                                        </menuItem>\n                                        <menuItem isSeparatorItem=\"YES\" id=\"5gT-KC-WSO\"/>\n                                        <menuItem title=\"Bigger\" tag=\"3\" keyEquivalent=\"+\" id=\"Ptp-SP-VEL\">\n                                            <connections>\n                                                <action selector=\"modifyFont:\" target=\"YLy-65-1bz\" id=\"Uc7-di-UnL\"/>\n                                            </connections>\n                                        </menuItem>\n                                        <menuItem title=\"Smaller\" tag=\"4\" keyEquivalent=\"-\" id=\"i1d-Er-qST\">\n                                            <connections>\n                                                <action selector=\"modifyFont:\" target=\"YLy-65-1bz\" id=\"HcX-Lf-eNd\"/>\n                                            </connections>\n                                        </menuItem>\n                                        <menuItem isSeparatorItem=\"YES\" id=\"kx3-Dk-x3B\"/>\n                                        <menuItem title=\"Kern\" id=\"jBQ-r6-VK2\">\n                                            <modifierMask key=\"keyEquivalentModifierMask\"/>\n                                            <menu key=\"submenu\" title=\"Kern\" id=\"tlD-Oa-oAM\">\n                                                <items>\n                                                    <menuItem title=\"Use Default\" id=\"GUa-eO-cwY\">\n                                                        <modifierMask key=\"keyEquivalentModifierMask\"/>\n                                                        <connections>\n                                                            <action selector=\"useStandardKerning:\" target=\"-1\" id=\"6dk-9l-Ckg\"/>\n                                                        </connections>\n                                                    </menuItem>\n                                                    <menuItem title=\"Use None\" id=\"cDB-IK-hbR\">\n                                                        <modifierMask key=\"keyEquivalentModifierMask\"/>\n                                                        <connections>\n                                                            <action selector=\"turnOffKerning:\" target=\"-1\" id=\"U8a-gz-Maa\"/>\n                                                        </connections>\n                                                    </menuItem>\n                                                    <menuItem title=\"Tighten\" id=\"46P-cB-AYj\">\n                                                        <modifierMask key=\"keyEquivalentModifierMask\"/>\n                                                        <connections>\n                                                            <action selector=\"tightenKerning:\" target=\"-1\" id=\"hr7-Nz-8ro\"/>\n                                                        </connections>\n                                                    </menuItem>\n                                                    <menuItem title=\"Loosen\" id=\"ogc-rX-tC1\">\n                                                        <modifierMask key=\"keyEquivalentModifierMask\"/>\n                                                        <connections>\n                                                            <action selector=\"loosenKerning:\" target=\"-1\" id=\"8i4-f9-FKE\"/>\n                                                        </connections>\n                                                    </menuItem>\n                                                </items>\n                                            </menu>\n                                        </menuItem>\n                                        <menuItem title=\"Ligatures\" id=\"o6e-r0-MWq\">\n                                            <modifierMask key=\"keyEquivalentModifierMask\"/>\n                                            <menu key=\"submenu\" title=\"Ligatures\" id=\"w0m-vy-SC9\">\n                                                <items>\n                                                    <menuItem title=\"Use Default\" id=\"agt-UL-0e3\">\n                                                        <modifierMask key=\"keyEquivalentModifierMask\"/>\n                                                        <connections>\n                                                            <action selector=\"useStandardLigatures:\" target=\"-1\" id=\"7uR-wd-Dx6\"/>\n                                                        </connections>\n                                                    </menuItem>\n                                                    <menuItem title=\"Use None\" id=\"J7y-lM-qPV\">\n                                                        <modifierMask key=\"keyEquivalentModifierMask\"/>\n                                                        <connections>\n                                                            <action selector=\"turnOffLigatures:\" target=\"-1\" id=\"iX2-gA-Ilz\"/>\n                                                        </connections>\n                                                    </menuItem>\n                                                    <menuItem title=\"Use All\" id=\"xQD-1f-W4t\">\n                                                        <modifierMask key=\"keyEquivalentModifierMask\"/>\n                                                        <connections>\n                                                            <action selector=\"useAllLigatures:\" target=\"-1\" id=\"KcB-kA-TuK\"/>\n                                                        </connections>\n                                                    </menuItem>\n                                                </items>\n                                            </menu>\n                                        </menuItem>\n                                        <menuItem title=\"Baseline\" id=\"OaQ-X3-Vso\">\n                                            <modifierMask key=\"keyEquivalentModifierMask\"/>\n                                            <menu key=\"submenu\" title=\"Baseline\" id=\"ijk-EB-dga\">\n                                                <items>\n                                                    <menuItem title=\"Use Default\" id=\"3Om-Ey-2VK\">\n                                                        <modifierMask key=\"keyEquivalentModifierMask\"/>\n                                                        <connections>\n                                                            <action selector=\"unscript:\" target=\"-1\" id=\"0vZ-95-Ywn\"/>\n                                                        </connections>\n                                                    </menuItem>\n                                                    <menuItem title=\"Superscript\" id=\"Rqc-34-cIF\">\n                                                        <modifierMask key=\"keyEquivalentModifierMask\"/>\n                                                        <connections>\n                                                            <action selector=\"superscript:\" target=\"-1\" id=\"3qV-fo-wpU\"/>\n                                                        </connections>\n                                                    </menuItem>\n                                                    <menuItem title=\"Subscript\" id=\"I0S-gh-46l\">\n                                                        <modifierMask key=\"keyEquivalentModifierMask\"/>\n                                                        <connections>\n                                                            <action selector=\"subscript:\" target=\"-1\" id=\"Q6W-4W-IGz\"/>\n                                                        </connections>\n                                                    </menuItem>\n                                                    <menuItem title=\"Raise\" id=\"2h7-ER-AoG\">\n                                                        <modifierMask key=\"keyEquivalentModifierMask\"/>\n                                                        <connections>\n                                                            <action selector=\"raiseBaseline:\" target=\"-1\" id=\"4sk-31-7Q9\"/>\n                                                        </connections>\n                                                    </menuItem>\n                                                    <menuItem title=\"Lower\" id=\"1tx-W0-xDw\">\n                                                        <modifierMask key=\"keyEquivalentModifierMask\"/>\n                                                        <connections>\n                                                            <action selector=\"lowerBaseline:\" target=\"-1\" id=\"OF1-bc-KW4\"/>\n                                                        </connections>\n                                                    </menuItem>\n                                                </items>\n                                            </menu>\n                                        </menuItem>\n                                        <menuItem isSeparatorItem=\"YES\" id=\"Ndw-q3-faq\"/>\n                                        <menuItem title=\"Show Colors\" keyEquivalent=\"C\" id=\"bgn-CT-cEk\">\n                                            <connections>\n                                                <action selector=\"orderFrontColorPanel:\" target=\"-1\" id=\"mSX-Xz-DV3\"/>\n                                            </connections>\n                                        </menuItem>\n                                        <menuItem isSeparatorItem=\"YES\" id=\"iMs-zA-UFJ\"/>\n                                        <menuItem title=\"Copy Style\" keyEquivalent=\"c\" id=\"5Vv-lz-BsD\">\n                                            <modifierMask key=\"keyEquivalentModifierMask\" option=\"YES\" command=\"YES\"/>\n                                            <connections>\n                                                <action selector=\"copyFont:\" target=\"-1\" id=\"GJO-xA-L4q\"/>\n                                            </connections>\n                                        </menuItem>\n                                        <menuItem title=\"Paste Style\" keyEquivalent=\"v\" id=\"vKC-jM-MkH\">\n                                            <modifierMask key=\"keyEquivalentModifierMask\" option=\"YES\" command=\"YES\"/>\n                                            <connections>\n                                                <action selector=\"pasteFont:\" target=\"-1\" id=\"JfD-CL-leO\"/>\n                                            </connections>\n                                        </menuItem>\n                                    </items>\n                                </menu>\n                            </menuItem>\n                            <menuItem title=\"Text\" id=\"Fal-I4-PZk\">\n                                <modifierMask key=\"keyEquivalentModifierMask\"/>\n                                <menu key=\"submenu\" title=\"Text\" id=\"d9c-me-L2H\">\n                                    <items>\n                                        <menuItem title=\"Align Left\" keyEquivalent=\"{\" id=\"ZM1-6Q-yy1\">\n                                            <connections>\n                                                <action selector=\"alignLeft:\" target=\"-1\" id=\"zUv-R1-uAa\"/>\n                                            </connections>\n                                        </menuItem>\n                                        <menuItem title=\"Center\" keyEquivalent=\"|\" id=\"VIY-Ag-zcb\">\n                                            <connections>\n                                                <action selector=\"alignCenter:\" target=\"-1\" id=\"spX-mk-kcS\"/>\n                                            </connections>\n                                        </menuItem>\n                                        <menuItem title=\"Justify\" id=\"J5U-5w-g23\">\n                                            <modifierMask key=\"keyEquivalentModifierMask\"/>\n                                            <connections>\n                                                <action selector=\"alignJustified:\" target=\"-1\" id=\"ljL-7U-jND\"/>\n                                            </connections>\n                                        </menuItem>\n                                        <menuItem title=\"Align Right\" keyEquivalent=\"}\" id=\"wb2-vD-lq4\">\n                                            <connections>\n                                                <action selector=\"alignRight:\" target=\"-1\" id=\"r48-bG-YeY\"/>\n                                            </connections>\n                                        </menuItem>\n                                        <menuItem isSeparatorItem=\"YES\" id=\"4s2-GY-VfK\"/>\n                                        <menuItem title=\"Writing Direction\" id=\"H1b-Si-o9J\">\n                                            <modifierMask key=\"keyEquivalentModifierMask\"/>\n                                            <menu key=\"submenu\" title=\"Writing Direction\" id=\"8mr-sm-Yjd\">\n                                                <items>\n                                                    <menuItem title=\"Paragraph\" enabled=\"NO\" id=\"ZvO-Gk-QUH\">\n                                                        <modifierMask key=\"keyEquivalentModifierMask\"/>\n                                                    </menuItem>\n                                                    <menuItem id=\"YGs-j5-SAR\">\n                                                        <string key=\"title\">\tDefault</string>\n                                                        <modifierMask key=\"keyEquivalentModifierMask\"/>\n                                                        <connections>\n                                                            <action selector=\"makeBaseWritingDirectionNatural:\" target=\"-1\" id=\"qtV-5e-UBP\"/>\n                                                        </connections>\n                                                    </menuItem>\n                                                    <menuItem id=\"Lbh-J2-qVU\">\n                                                        <string key=\"title\">\tLeft to Right</string>\n                                                        <modifierMask key=\"keyEquivalentModifierMask\"/>\n                                                        <connections>\n                                                            <action selector=\"makeBaseWritingDirectionLeftToRight:\" target=\"-1\" id=\"S0X-9S-QSf\"/>\n                                                        </connections>\n                                                    </menuItem>\n                                                    <menuItem id=\"jFq-tB-4Kx\">\n                                                        <string key=\"title\">\tRight to Left</string>\n                                                        <modifierMask key=\"keyEquivalentModifierMask\"/>\n                                                        <connections>\n                                                            <action selector=\"makeBaseWritingDirectionRightToLeft:\" target=\"-1\" id=\"5fk-qB-AqJ\"/>\n                                                        </connections>\n                                                    </menuItem>\n                                                    <menuItem isSeparatorItem=\"YES\" id=\"swp-gr-a21\"/>\n                                                    <menuItem title=\"Selection\" enabled=\"NO\" id=\"cqv-fj-IhA\">\n                                                        <modifierMask key=\"keyEquivalentModifierMask\"/>\n                                                    </menuItem>\n                                                    <menuItem id=\"Nop-cj-93Q\">\n                                                        <string key=\"title\">\tDefault</string>\n                                                        <modifierMask key=\"keyEquivalentModifierMask\"/>\n                                                        <connections>\n                                                            <action selector=\"makeTextWritingDirectionNatural:\" target=\"-1\" id=\"lPI-Se-ZHp\"/>\n                                                        </connections>\n                                                    </menuItem>\n                                                    <menuItem id=\"BgM-ve-c93\">\n                                                        <string key=\"title\">\tLeft to Right</string>\n                                                        <modifierMask key=\"keyEquivalentModifierMask\"/>\n                                                        <connections>\n                                                            <action selector=\"makeTextWritingDirectionLeftToRight:\" target=\"-1\" id=\"caW-Bv-w94\"/>\n                                                        </connections>\n                                                    </menuItem>\n                                                    <menuItem id=\"RB4-Sm-HuC\">\n                                                        <string key=\"title\">\tRight to Left</string>\n                                                        <modifierMask key=\"keyEquivalentModifierMask\"/>\n                                                        <connections>\n                                                            <action selector=\"makeTextWritingDirectionRightToLeft:\" target=\"-1\" id=\"EXD-6r-ZUu\"/>\n                                                        </connections>\n                                                    </menuItem>\n                                                </items>\n                                            </menu>\n                                        </menuItem>\n                                        <menuItem isSeparatorItem=\"YES\" id=\"fKy-g9-1gm\"/>\n                                        <menuItem title=\"Show Ruler\" id=\"vLm-3I-IUL\">\n                                            <modifierMask key=\"keyEquivalentModifierMask\"/>\n                                            <connections>\n                                                <action selector=\"toggleRuler:\" target=\"-1\" id=\"FOx-HJ-KwY\"/>\n                                            </connections>\n                                        </menuItem>\n                                        <menuItem title=\"Copy Ruler\" keyEquivalent=\"c\" id=\"MkV-Pr-PK5\">\n                                            <modifierMask key=\"keyEquivalentModifierMask\" control=\"YES\" command=\"YES\"/>\n                                            <connections>\n                                                <action selector=\"copyRuler:\" target=\"-1\" id=\"71i-fW-3W2\"/>\n                                            </connections>\n                                        </menuItem>\n                                        <menuItem title=\"Paste Ruler\" keyEquivalent=\"v\" id=\"LVM-kO-fVI\">\n                                            <modifierMask key=\"keyEquivalentModifierMask\" control=\"YES\" command=\"YES\"/>\n                                            <connections>\n                                                <action selector=\"pasteRuler:\" target=\"-1\" id=\"cSh-wd-qM2\"/>\n                                            </connections>\n                                        </menuItem>\n                                    </items>\n                                </menu>\n                            </menuItem>\n                        </items>\n                    </menu>\n                </menuItem>\n                <menuItem title=\"Window\" id=\"aUF-d1-5bR\">\n                    <modifierMask key=\"keyEquivalentModifierMask\"/>\n                    <menu key=\"submenu\" title=\"Window\" systemMenu=\"window\" id=\"Td7-aD-5lo\">\n                        <items>\n                            <menuItem title=\"Minimize\" keyEquivalent=\"m\" id=\"OY7-WF-poV\">\n                                <connections>\n                                    <action selector=\"performMiniaturize:\" target=\"-1\" id=\"VwT-WD-YPe\"/>\n                                </connections>\n                            </menuItem>\n                            <menuItem title=\"Zoom\" id=\"R4o-n2-Eq4\">\n                                <modifierMask key=\"keyEquivalentModifierMask\"/>\n                                <connections>\n                                    <action selector=\"performZoom:\" target=\"-1\" id=\"DIl-cC-cCs\"/>\n                                </connections>\n                            </menuItem>\n                            <menuItem isSeparatorItem=\"YES\" id=\"eu3-7i-yIM\"/>\n                            <menuItem title=\"Bring All to Front\" id=\"LE2-aR-0XJ\">\n                                <modifierMask key=\"keyEquivalentModifierMask\"/>\n                                <connections>\n                                    <action selector=\"arrangeInFront:\" target=\"-1\" id=\"DRN-fu-gQh\"/>\n                                </connections>\n                            </menuItem>\n                        </items>\n                    </menu>\n                </menuItem>\n                <menuItem title=\"View\" id=\"H8h-7b-M4v\">\n                    <modifierMask key=\"keyEquivalentModifierMask\"/>\n                    <menu key=\"submenu\" title=\"View\" id=\"HyV-fh-RgO\">\n                        <items>\n                            <menuItem title=\"Show Toolbar\" keyEquivalent=\"t\" id=\"snW-S8-Cw5\">\n                                <modifierMask key=\"keyEquivalentModifierMask\" option=\"YES\" command=\"YES\"/>\n                                <connections>\n                                    <action selector=\"toggleToolbarShown:\" target=\"-1\" id=\"BXY-wc-z0C\"/>\n                                </connections>\n                            </menuItem>\n                            <menuItem title=\"Customize Toolbar…\" id=\"1UK-8n-QPP\">\n                                <modifierMask key=\"keyEquivalentModifierMask\"/>\n                                <connections>\n                                    <action selector=\"runToolbarCustomizationPalette:\" target=\"-1\" id=\"pQI-g3-MTW\"/>\n                                </connections>\n                            </menuItem>\n                        </items>\n                    </menu>\n                </menuItem>\n                <menuItem title=\"Help\" id=\"wpr-3q-Mcd\">\n                    <modifierMask key=\"keyEquivalentModifierMask\"/>\n                    <menu key=\"submenu\" title=\"Help\" systemMenu=\"help\" id=\"F2S-fz-NVQ\">\n                        <items>\n                            <menuItem title=\"Cadabra Help\" keyEquivalent=\"?\" id=\"FKE-Sm-Kum\">\n                                <connections>\n                                    <action selector=\"showHelp:\" target=\"-1\" id=\"y7X-2Q-9no\"/>\n                                </connections>\n                            </menuItem>\n                        </items>\n                    </menu>\n                </menuItem>\n            </items>\n        </menu>\n        <window title=\"Cadabra\" allowsToolTipsWhenApplicationIsInactive=\"NO\" autorecalculatesKeyViewLoop=\"NO\" releasedWhenClosed=\"NO\" animationBehavior=\"default\" id=\"QvC-M9-y7g\">\n            <windowStyleMask key=\"styleMask\" titled=\"YES\" closable=\"YES\" miniaturizable=\"YES\" resizable=\"YES\"/>\n            <windowPositionMask key=\"initialPositionMask\" leftStrut=\"YES\" rightStrut=\"YES\" topStrut=\"YES\" bottomStrut=\"YES\"/>\n            <rect key=\"contentRect\" x=\"335\" y=\"390\" width=\"579\" height=\"533\"/>\n            <rect key=\"screenRect\" x=\"0.0\" y=\"0.0\" width=\"1920\" height=\"1058\"/>\n            <view key=\"contentView\" id=\"EiT-Mj-1SZ\">\n                <rect key=\"frame\" x=\"0.0\" y=\"0.0\" width=\"579\" height=\"533\"/>\n                <autoresizingMask key=\"autoresizingMask\"/>\n            </view>\n            <toolbar key=\"toolbar\" implicitIdentifier=\"5C634DAB-EA27-4EA1-96F6-615755935E0E\" autosavesConfiguration=\"NO\" displayMode=\"iconAndLabel\" sizeMode=\"regular\" id=\"ESj-Yv-BOs\">\n                <allowedToolbarItems>\n                    <toolbarItem implicitItemIdentifier=\"NSToolbarShowColorsItem\" id=\"QBo-0p-8ex\"/>\n                    <toolbarItem implicitItemIdentifier=\"NSToolbarShowFontsItem\" id=\"yRE-d4-M4A\"/>\n                    <toolbarItem implicitItemIdentifier=\"NSToolbarPrintItem\" id=\"yiC-pz-gIG\"/>\n                    <toolbarItem implicitItemIdentifier=\"NSToolbarSpaceItem\" id=\"KMS-Qq-9aC\"/>\n                    <toolbarItem implicitItemIdentifier=\"NSToolbarFlexibleSpaceItem\" id=\"76J-xq-euD\"/>\n                    <toolbarItem implicitItemIdentifier=\"85CCF954-422F-435D-A750-C317559A1FAF\" label=\"Restart kernel\" paletteLabel=\"Restart kernel\" tag=\"-1\" image=\"NSRefreshTemplate\" id=\"KYe-HT-5ad\"/>\n                    <toolbarItem implicitItemIdentifier=\"9409E054-C05D-46CA-8326-22EB15F9AC08\" label=\"Help\" paletteLabel=\"Help\" id=\"tON-nW-XWx\">\n                        <nil key=\"toolTip\"/>\n                        <size key=\"minSize\" width=\"25\" height=\"25\"/>\n                        <size key=\"maxSize\" width=\"25\" height=\"25\"/>\n                        <button key=\"view\" horizontalHuggingPriority=\"750\" verticalHuggingPriority=\"750\" id=\"Acl-Fr-kV4\">\n                            <rect key=\"frame\" x=\"11\" y=\"10\" width=\"25\" height=\"25\"/>\n                            <autoresizingMask key=\"autoresizingMask\" flexibleMaxX=\"YES\" flexibleMinY=\"YES\"/>\n                            <buttonCell key=\"cell\" type=\"help\" bezelStyle=\"helpButton\" alignment=\"center\" borderStyle=\"border\" imageScaling=\"proportionallyDown\" inset=\"2\" id=\"fta-k4-xgY\">\n                                <behavior key=\"behavior\" pushIn=\"YES\" lightByBackground=\"YES\" lightByGray=\"YES\"/>\n                                <font key=\"font\" metaFont=\"system\"/>\n                            </buttonCell>\n                        </button>\n                    </toolbarItem>\n                </allowedToolbarItems>\n                <defaultToolbarItems>\n                    <toolbarItem reference=\"76J-xq-euD\"/>\n                    <toolbarItem reference=\"yiC-pz-gIG\"/>\n                    <toolbarItem reference=\"KYe-HT-5ad\"/>\n                    <toolbarItem reference=\"tON-nW-XWx\"/>\n                </defaultToolbarItems>\n            </toolbar>\n            <point key=\"canvasLocation\" x=\"331.5\" y=\"496.5\"/>\n        </window>\n        <userDefaultsController representsSharedInstance=\"YES\" id=\"oxW-YI-VC5\"/>\n    </objects>\n    <resources>\n        <image name=\"NSRefreshTemplate\" width=\"10\" height=\"12\"/>\n    </resources>\n</document>\n"
  },
  {
    "path": "frontend/osx/Cadabra/Cadabra/Images.xcassets/AppIcon.appiconset/Contents.json",
    "content": "{\n  \"images\" : [\n    {\n      \"size\" : \"16x16\",\n      \"idiom\" : \"mac\",\n      \"filename\" : \"cadabra-3.png\",\n      \"scale\" : \"1x\"\n    },\n    {\n      \"size\" : \"16x16\",\n      \"idiom\" : \"mac\",\n      \"filename\" : \"cadabra-2.png\",\n      \"scale\" : \"2x\"\n    },\n    {\n      \"size\" : \"32x32\",\n      \"idiom\" : \"mac\",\n      \"filename\" : \"cadabra-1.png\",\n      \"scale\" : \"1x\"\n    },\n    {\n      \"size\" : \"32x32\",\n      \"idiom\" : \"mac\",\n      \"filename\" : \"cadabra.png\",\n      \"scale\" : \"2x\"\n    },\n    {\n      \"size\" : \"128x128\",\n      \"idiom\" : \"mac\",\n      \"filename\" : \"cadabra-4.png\",\n      \"scale\" : \"1x\"\n    },\n    {\n      \"size\" : \"128x128\",\n      \"idiom\" : \"mac\",\n      \"filename\" : \"cadabra-5.png\",\n      \"scale\" : \"2x\"\n    },\n    {\n      \"size\" : \"256x256\",\n      \"idiom\" : \"mac\",\n      \"filename\" : \"cadabra-6.png\",\n      \"scale\" : \"1x\"\n    },\n    {\n      \"idiom\" : \"mac\",\n      \"size\" : \"256x256\",\n      \"scale\" : \"2x\"\n    },\n    {\n      \"idiom\" : \"mac\",\n      \"size\" : \"512x512\",\n      \"scale\" : \"1x\"\n    },\n    {\n      \"idiom\" : \"mac\",\n      \"size\" : \"512x512\",\n      \"scale\" : \"2x\"\n    }\n  ],\n  \"info\" : {\n    \"version\" : 1,\n    \"author\" : \"xcode\"\n  }\n}"
  },
  {
    "path": "frontend/osx/Cadabra/Cadabra/Info.plist",
    "content": "<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n<!DOCTYPE plist PUBLIC \"-//Apple//DTD PLIST 1.0//EN\" \"http://www.apple.com/DTDs/PropertyList-1.0.dtd\">\n<plist version=\"1.0\">\n<dict>\n\t<key>CFBundleDevelopmentRegion</key>\n\t<string>en</string>\n\t<key>CFBundleExecutable</key>\n\t<string>$(EXECUTABLE_NAME)</string>\n\t<key>CFBundleIconFile</key>\n\t<string></string>\n\t<key>CFBundleIdentifier</key>\n\t<string>$(PRODUCT_BUNDLE_IDENTIFIER)</string>\n\t<key>CFBundleInfoDictionaryVersion</key>\n\t<string>6.0</string>\n\t<key>CFBundleName</key>\n\t<string>$(PRODUCT_NAME)</string>\n\t<key>CFBundlePackageType</key>\n\t<string>APPL</string>\n\t<key>CFBundleShortVersionString</key>\n\t<string>1.0</string>\n\t<key>CFBundleSignature</key>\n\t<string>????</string>\n\t<key>CFBundleVersion</key>\n\t<string>1</string>\n\t<key>LSMinimumSystemVersion</key>\n\t<string>$(MACOSX_DEPLOYMENT_TARGET)</string>\n\t<key>NSHumanReadableCopyright</key>\n\t<string>Copyright © 2014 phi-sci. All rights reserved.</string>\n\t<key>NSMainNibFile</key>\n\t<string>Cadabra</string>\n\t<key>NSPrincipalClass</key>\n\t<string>NSApplication</string>\n</dict>\n</plist>\n"
  },
  {
    "path": "frontend/osx/Cadabra/Cadabra/Notebook.xib",
    "content": "<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n<document type=\"com.apple.InterfaceBuilder3.Cocoa.XIB\" version=\"3.0\" toolsVersion=\"6254\" systemVersion=\"13F34\" targetRuntime=\"MacOSX.Cocoa\" propertyAccessControl=\"none\" useAutolayout=\"YES\" customObjectInstantitationMethod=\"direct\">\n    <dependencies>\n        <deployment identifier=\"macosx\"/>\n        <plugIn identifier=\"com.apple.InterfaceBuilder.CocoaPlugin\" version=\"6254\"/>\n    </dependencies>\n    <objects>\n        <customObject id=\"-2\" userLabel=\"File's Owner\" customClass=\"NotebookController\">\n            <connections>\n                <outlet property=\"scrollbox\" destination=\"2yl-Je-0GT\" id=\"C7M-4e-HqK\"/>\n                <outlet property=\"status_label\" destination=\"rqn-VV-TKi\" id=\"tWb-JJ-ow8\"/>\n                <outlet property=\"view\" destination=\"c22-O7-iKe\" id=\"OpU-VK-mr3\"/>\n            </connections>\n        </customObject>\n        <customObject id=\"-1\" userLabel=\"First Responder\" customClass=\"FirstResponder\"/>\n        <customObject id=\"-3\" userLabel=\"Application\" customClass=\"NSObject\"/>\n        <customView id=\"c22-O7-iKe\">\n            <rect key=\"frame\" x=\"0.0\" y=\"0.0\" width=\"608\" height=\"474\"/>\n            <autoresizingMask key=\"autoresizingMask\" flexibleMaxX=\"YES\" flexibleMinY=\"YES\"/>\n            <subviews>\n                <textField horizontalHuggingPriority=\"251\" verticalHuggingPriority=\"750\" misplaced=\"YES\" translatesAutoresizingMaskIntoConstraints=\"NO\" id=\"rqn-VV-TKi\">\n                    <rect key=\"frame\" x=\"5\" y=\"1\" width=\"304\" height=\"17\"/>\n                    <textFieldCell key=\"cell\" scrollable=\"YES\" lineBreakMode=\"clipping\" sendsActionOnEndEditing=\"YES\" title=\"Label\" id=\"7t1-lJ-0By\">\n                        <font key=\"font\" metaFont=\"system\"/>\n                        <color key=\"textColor\" name=\"controlTextColor\" catalog=\"System\" colorSpace=\"catalog\"/>\n                        <color key=\"backgroundColor\" name=\"controlColor\" catalog=\"System\" colorSpace=\"catalog\"/>\n                    </textFieldCell>\n                </textField>\n                <box autoresizesSubviews=\"NO\" verticalHuggingPriority=\"750\" title=\"Box\" boxType=\"separator\" titlePosition=\"noTitle\" translatesAutoresizingMaskIntoConstraints=\"NO\" id=\"8Wf-GJ-sS1\">\n                    <rect key=\"frame\" x=\"0.0\" y=\"15\" width=\"608\" height=\"5\"/>\n                    <color key=\"borderColor\" white=\"0.0\" alpha=\"0.41999999999999998\" colorSpace=\"calibratedWhite\"/>\n                    <color key=\"fillColor\" white=\"0.0\" alpha=\"0.0\" colorSpace=\"calibratedWhite\"/>\n                    <font key=\"titleFont\" metaFont=\"system\"/>\n                </box>\n                <progressIndicator verticalHuggingPriority=\"1000\" ambiguous=\"YES\" misplaced=\"YES\" maxValue=\"100\" indeterminate=\"YES\" style=\"bar\" translatesAutoresizingMaskIntoConstraints=\"NO\" id=\"qKv-52-RZV\">\n                    <rect key=\"frame\" x=\"464\" y=\"-1\" width=\"144\" height=\"20\"/>\n                </progressIndicator>\n                <scrollView horizontalLineScroll=\"10\" horizontalPageScroll=\"10\" verticalLineScroll=\"10\" verticalPageScroll=\"10\" usesPredominantAxisScrolling=\"NO\" translatesAutoresizingMaskIntoConstraints=\"NO\" id=\"2yl-Je-0GT\">\n                    <rect key=\"frame\" x=\"0.0\" y=\"18\" width=\"608\" height=\"456\"/>\n                    <clipView key=\"contentView\" id=\"wGw-d2-scB\">\n                        <rect key=\"frame\" x=\"1\" y=\"1\" width=\"181\" height=\"94\"/>\n                        <autoresizingMask key=\"autoresizingMask\" widthSizable=\"YES\" heightSizable=\"YES\"/>\n                        <subviews>\n                            <view fixedFrame=\"YES\" translatesAutoresizingMaskIntoConstraints=\"NO\" id=\"10M-bc-rrx\">\n                                <rect key=\"frame\" x=\"0.0\" y=\"0.0\" width=\"181\" height=\"94\"/>\n                            </view>\n                        </subviews>\n                    </clipView>\n                    <scroller key=\"horizontalScroller\" verticalHuggingPriority=\"750\" horizontal=\"YES\" id=\"kMP-op-Mc0\">\n                        <rect key=\"frame\" x=\"1\" y=\"79\" width=\"181\" height=\"16\"/>\n                        <autoresizingMask key=\"autoresizingMask\"/>\n                    </scroller>\n                    <scroller key=\"verticalScroller\" verticalHuggingPriority=\"750\" doubleValue=\"1\" horizontal=\"NO\" id=\"2T2-rH-Yts\">\n                        <rect key=\"frame\" x=\"166\" y=\"1\" width=\"16\" height=\"94\"/>\n                        <autoresizingMask key=\"autoresizingMask\"/>\n                    </scroller>\n                </scrollView>\n            </subviews>\n            <constraints>\n                <constraint firstAttribute=\"trailing\" secondItem=\"2yl-Je-0GT\" secondAttribute=\"trailing\" id=\"0Cp-HW-4en\"/>\n                <constraint firstAttribute=\"bottom\" secondItem=\"qKv-52-RZV\" secondAttribute=\"bottom\" id=\"2K2-t5-FJq\"/>\n                <constraint firstAttribute=\"bottom\" secondItem=\"rqn-VV-TKi\" secondAttribute=\"bottom\" constant=\"1\" id=\"7zl-Zp-BwJ\"/>\n                <constraint firstAttribute=\"trailing\" secondItem=\"8Wf-GJ-sS1\" secondAttribute=\"trailing\" id=\"8LC-i1-cDy\"/>\n                <constraint firstItem=\"rqn-VV-TKi\" firstAttribute=\"leading\" secondItem=\"c22-O7-iKe\" secondAttribute=\"leading\" constant=\"7\" id=\"CnR-vY-ZMj\"/>\n                <constraint firstItem=\"8Wf-GJ-sS1\" firstAttribute=\"leading\" secondItem=\"c22-O7-iKe\" secondAttribute=\"leading\" id=\"DL2-TG-1oI\"/>\n                <constraint firstItem=\"rqn-VV-TKi\" firstAttribute=\"top\" secondItem=\"2yl-Je-0GT\" secondAttribute=\"bottom\" id=\"Hvt-lC-9Wl\"/>\n                <constraint firstAttribute=\"trailing\" secondItem=\"qKv-52-RZV\" secondAttribute=\"trailing\" id=\"Hy6-mP-HUz\"/>\n                <constraint firstItem=\"2yl-Je-0GT\" firstAttribute=\"top\" secondItem=\"c22-O7-iKe\" secondAttribute=\"top\" id=\"eDC-0O-idk\"/>\n                <constraint firstAttribute=\"trailing\" secondItem=\"qKv-52-RZV\" secondAttribute=\"trailing\" id=\"kvp-Us-SP7\"/>\n                <constraint firstItem=\"qKv-52-RZV\" firstAttribute=\"top\" secondItem=\"8Wf-GJ-sS1\" secondAttribute=\"bottom\" constant=\"-1\" id=\"nGY-cy-AfG\"/>\n                <constraint firstItem=\"2yl-Je-0GT\" firstAttribute=\"leading\" secondItem=\"c22-O7-iKe\" secondAttribute=\"leading\" id=\"nQO-aF-VjH\"/>\n            </constraints>\n            <point key=\"canvasLocation\" x=\"204\" y=\"256\"/>\n        </customView>\n        <button verticalHuggingPriority=\"750\" id=\"PKi-ii-Hwl\">\n            <rect key=\"frame\" x=\"0.0\" y=\"0.0\" width=\"82\" height=\"32\"/>\n            <autoresizingMask key=\"autoresizingMask\" flexibleMaxX=\"YES\" flexibleMinY=\"YES\"/>\n            <buttonCell key=\"cell\" type=\"push\" title=\"Button\" bezelStyle=\"rounded\" alignment=\"center\" borderStyle=\"border\" imageScaling=\"proportionallyDown\" inset=\"2\" id=\"jch-6q-adH\">\n                <behavior key=\"behavior\" pushIn=\"YES\" lightByBackground=\"YES\" lightByGray=\"YES\"/>\n                <font key=\"font\" metaFont=\"system\"/>\n            </buttonCell>\n            <point key=\"canvasLocation\" x=\"646\" y=\"361.5\"/>\n        </button>\n        <customView id=\"ROT-Jv-Ghy\">\n            <rect key=\"frame\" x=\"0.0\" y=\"0.0\" width=\"163\" height=\"96\"/>\n            <autoresizingMask key=\"autoresizingMask\" flexibleMaxX=\"YES\" flexibleMinY=\"YES\"/>\n            <point key=\"canvasLocation\" x=\"608.5\" y=\"396\"/>\n        </customView>\n    </objects>\n</document>\n"
  },
  {
    "path": "frontend/osx/Cadabra/Cadabra/NotebookCanvas.hh",
    "content": "//\n//  NotebookCanvas.hh\n//  Cadabra\n//\n//  Created by Kasper Peeters on 04/03/2015.\n//  Copyright (c) 2015 phi-sci. All rights reserved.\n//\n\n#ifndef Cadabra_NotebookCanvas_hh\n#define Cadabra_NotebookCanvas_hh\n\nnamespace cadabra {\n\n\tclass NotebookCanvas {\n\t\tpublic:\n\t\t\tstd::map<DataCell *, NSTextView *> visualcells;\n\t\t};\n\n\t}\n\n\n#endif\n"
  },
  {
    "path": "frontend/osx/Cadabra/Cadabra/NotebookCanvas.mm",
    "content": "//\n//  NotebookCanvas.m\n//  Cadabra\n//\n//  Created by Kasper Peeters on 04/03/2015.\n//  Copyright (c) 2015 phi-sci. All rights reserved.\n//\n\n#import <Foundation/Foundation.h>\n"
  },
  {
    "path": "frontend/osx/Cadabra/Cadabra/NotebookWindow.hh",
    "content": "//\n//  NotebookWindow.h\n//  Cadabra\n//\n//  Created by Kasper Peeters on 05/01/2015.\n//  Copyright (c) 2015 phi-sci. All rights reserved.\n//\n\n#ifndef __Cadabra__NotebookWindow__\n#define __Cadabra__NotebookWindow__\n\n#include <stdio.h>\n#include \"DocumentThread.hh\"\n#include \"GUIBase.hh\"\n#include \"NotebookController.h\"\n#include \"NotebookCanvas.hh\"\n\nnamespace cadabra_osx {\n\n\t/// \\ingroup osx\n\t///\n\t/// Objective-C++ class implementing DocumentThread and providing an OS-X\n\t/// notebook interface.\n\n\tclass NotebookWindow : public DocumentThread, public GUIBase {\n\t\tpublic:\n\t\t\tNotebookWindow(NotebookController *);\n\n\t\t\tvirtual void add_cell(const DTree&, DTree::iterator, bool visible) override;\n\t\t\tvirtual void remove_cell(const DTree&, DTree::iterator) override;\n\t\t\tvirtual void update_cell(const DTree&, DTree::iterator) override;\n\t\t\tvirtual void position_cursor(const DTree&, DTree::iterator) override;\n\t\t\tvirtual void remove_all_cells() override;\n\n\t\t\tvirtual void on_connect() override;\n\t\t\tvirtual void on_disconnect() override;\n\t\t\tvirtual void on_network_error() override;\n\n\t\t\tvirtual void process_data() override;\n\n\t\tprivate:\n\t\t\tNotebookController *controller;\n\n\t\t\tstd::vector<NotebookCanvas *> canvasses;\n\t\t\tint                           current_canvas;\n\t\t};\n\n\t};\n\n#endif /* defined(__Cadabra__NotebookWindow__) */\n"
  },
  {
    "path": "frontend/osx/Cadabra/Cadabra/NotebookWindow.mm",
    "content": "//\n//  NotebookWindow.cc\n//  Cadabra\n//\n//  Created by Kasper Peeters on 05/01/2015.\n//  Copyright (c) 2015 phi-sci. All rights reserved.\n//\n\n#include \"NotebookWindow.hh\"\n#import <Cocoa/Cocoa.h>\n\nusing namespace cadabra_osx;\n\nNotebookWindow::NotebookWindow(NotebookController *nc)\n: DocumentThread(this), controller(nc)\n{\n    canvasses.push_back(new NotebookCanvas());\n    current_canvas=0;\n    \n    new_document();\n}\n\nvoid NotebookWindow::add_cell(const DTree &tr, DTree::iterator it, bool visible)\n{\n    NSLog(@\"adding cell\");\n    NSSize contentSize = [controller.scrollbox contentSize];\n\n    NSView *container = [[NSView alloc] initWithFrame:CGRectMake(0,0,contentSize.width,contentSize.height)];\n    //[container setAutoresizingMask:NSViewWidthSizable|NSViewHeightSizable];\n    \n    NSTextView *label = [[NSTextView alloc] initWithFrame:CGRectMake(0,0,contentSize.width,100)];\n    [[label.textStorage mutableString] setString:@\"hello world\"];\n    [label setAutoresizingMask:NSViewWidthSizable|NSViewHeightSizable];\n    [[label textContainer] setContainerSize:NSMakeSize(contentSize.width, FLT_MAX)];\n    [[label textContainer] setWidthTracksTextView:YES];\n    \n    NSTextView *label2 = [[NSTextView alloc] initWithFrame:CGRectMake(0,0,contentSize.width,100)];\n    [[label2.textStorage mutableString] setString:@\"this is fun\"];\n    [label2 setAutoresizingMask:NSViewWidthSizable|NSViewHeightSizable];\n    [[label2 textContainer] setContainerSize:NSMakeSize(contentSize.width, FLT_MAX)];\n    [[label2 textContainer] setWidthTracksTextView:YES];\n\n    //[label  setTranslatesAutoresizingMaskIntoConstraints:NO];\n    //[label2 setTranslatesAutoresizingMaskIntoConstraints:NO];\n    \n    NSLayoutConstraint *c3=[NSLayoutConstraint constraintWithItem:label attribute:NSLayoutAttributeBottom\n                                                          relatedBy:NSLayoutRelationEqual toItem:label2\n                                                        attribute:NSLayoutAttributeTop multiplier:1.0 constant:0];\n    \n  //  [container addConstraint:c3];\n    \n    canvasses[current_canvas]->visualcells[&(*it)]=label;\n\n    [container addSubview:label];\n    [container addSubview:label2];\n    [controller.scrollbox setHasVerticalScroller:YES];\n    //[controller.scrollbox setAutoresizingMask:NSViewWidthSizable|NSViewHeightSizable];\n    [controller.scrollbox setDocumentView:container];\n    [controller.scrollbox setNeedsDisplay:YES];\n}\n\nvoid NotebookWindow::remove_cell(const DTree&, DTree::iterator)\n{\n    \n}\n\nvoid NotebookWindow::update_cell(const DTree&, DTree::iterator)\n{\n    \n}\n\nvoid NotebookWindow::position_cursor(const DTree&, DTree::iterator)\n{\n    \n}\n\nvoid NotebookWindow::remove_all_cells()\n{\n    \n}\n\nvoid NotebookWindow::on_connect()\n{\n    [controller.status_label setStringValue:@\"Connected\"];\n}\n\nvoid NotebookWindow::on_disconnect()\n{\n    \n}\n\nvoid NotebookWindow::on_network_error()\n{\n    [controller.status_label setStringValue:@\"Network error\"];\n}\n\nvoid NotebookWindow::process_data()\n{\n    \n}\n"
  },
  {
    "path": "frontend/osx/Cadabra/Cadabra/Test.xib",
    "content": "<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n<document type=\"com.apple.InterfaceBuilder3.Cocoa.XIB\" version=\"3.0\" toolsVersion=\"6254\" systemVersion=\"13F34\" targetRuntime=\"MacOSX.Cocoa\" propertyAccessControl=\"none\" useAutolayout=\"YES\" customObjectInstantitationMethod=\"direct\">\n    <dependencies>\n        <deployment identifier=\"macosx\"/>\n        <plugIn identifier=\"com.apple.InterfaceBuilder.CocoaPlugin\" version=\"6254\"/>\n    </dependencies>\n    <objects>\n        <customObject id=\"-2\" userLabel=\"File's Owner\"/>\n        <customObject id=\"-1\" userLabel=\"First Responder\" customClass=\"FirstResponder\"/>\n        <customObject id=\"-3\" userLabel=\"Application\" customClass=\"NSObject\"/>\n        <window title=\"Window\" allowsToolTipsWhenApplicationIsInactive=\"NO\" autorecalculatesKeyViewLoop=\"NO\" oneShot=\"NO\" releasedWhenClosed=\"NO\" animationBehavior=\"default\" id=\"QvC-M9-y7g\">\n            <windowStyleMask key=\"styleMask\" titled=\"YES\" closable=\"YES\" miniaturizable=\"YES\" resizable=\"YES\"/>\n            <windowPositionMask key=\"initialPositionMask\" leftStrut=\"YES\" rightStrut=\"YES\" topStrut=\"YES\" bottomStrut=\"YES\"/>\n            <rect key=\"contentRect\" x=\"196\" y=\"240\" width=\"480\" height=\"270\"/>\n            <rect key=\"screenRect\" x=\"0.0\" y=\"0.0\" width=\"1680\" height=\"1028\"/>\n            <view key=\"contentView\" id=\"EiT-Mj-1SZ\">\n                <rect key=\"frame\" x=\"0.0\" y=\"0.0\" width=\"480\" height=\"270\"/>\n                <autoresizingMask key=\"autoresizingMask\"/>\n                <subviews>\n                    <customView fixedFrame=\"YES\" translatesAutoresizingMaskIntoConstraints=\"NO\" id=\"yZX-Zv-TWe\">\n                        <rect key=\"frame\" x=\"251\" y=\"50\" width=\"163\" height=\"96\"/>\n                    </customView>\n                </subviews>\n            </view>\n        </window>\n    </objects>\n</document>\n"
  },
  {
    "path": "frontend/osx/Cadabra/Cadabra/main.m",
    "content": "//\n//  main.m\n//  Cadabra\n//\n//  Created by Kasper Peeters on 01/11/2014.\n//  Copyright (c) 2014 phi-sci. All rights reserved.\n//\n\n#import <Cocoa/Cocoa.h>\n\nint main(int argc, const char * argv[]) {\n    return NSApplicationMain(argc, argv);\n}\n"
  },
  {
    "path": "frontend/osx/Cadabra/Cadabra.xcodeproj/project.pbxproj",
    "content": "// !$*UTF8*$!\n{\n\tarchiveVersion = 1;\n\tclasses = {\n\t};\n\tobjectVersion = 46;\n\tobjects = {\n\n/* Begin PBXBuildFile section */\n\t\tA7ACFC5D1A5B3F2A003F01E2 /* NotebookWindow.mm in Sources */ = {isa = PBXBuildFile; fileRef = A7ACFC5B1A5B3F2A003F01E2 /* NotebookWindow.mm */; };\n\t\tA7B0F7171A05663700FCC711 /* main.m in Sources */ = {isa = PBXBuildFile; fileRef = A7B0F7161A05663700FCC711 /* main.m */; };\n\t\tA7B0F71A1A05663700FCC711 /* AppDelegate.mm in Sources */ = {isa = PBXBuildFile; fileRef = A7B0F7191A05663700FCC711 /* AppDelegate.mm */; };\n\t\tA7B0F71C1A05663700FCC711 /* Images.xcassets in Resources */ = {isa = PBXBuildFile; fileRef = A7B0F71B1A05663700FCC711 /* Images.xcassets */; };\n\t\tA7B0F71F1A05663700FCC711 /* Cadabra.xib in Resources */ = {isa = PBXBuildFile; fileRef = A7B0F71D1A05663700FCC711 /* Cadabra.xib */; };\n\t\tA7B0F72B1A05663700FCC711 /* CadabraTests.m in Sources */ = {isa = PBXBuildFile; fileRef = A7B0F72A1A05663700FCC711 /* CadabraTests.m */; };\n\t\tA7B2F2011AA71C3700D0DDA6 /* NotebookCanvas.mm in Sources */ = {isa = PBXBuildFile; fileRef = A7B2F2001AA71C3700D0DDA6 /* NotebookCanvas.mm */; };\n\t\tA7B2F2041AA73EFA00D0DDA6 /* Test.xib in Resources */ = {isa = PBXBuildFile; fileRef = A7B2F2031AA73EFA00D0DDA6 /* Test.xib */; };\n\t\tA7B39FD71A6AC137007FBB93 /* libboost_system.a in Frameworks */ = {isa = PBXBuildFile; fileRef = A7B39FD61A6AC137007FBB93 /* libboost_system.a */; };\n\t\tA7B39FE01A6AC194007FBB93 /* Actions.cc in Sources */ = {isa = PBXBuildFile; fileRef = A7B39FD81A6AC194007FBB93 /* Actions.cc */; };\n\t\tA7B39FE11A6AC194007FBB93 /* Actions.hh in Sources */ = {isa = PBXBuildFile; fileRef = A7B39FD91A6AC194007FBB93 /* Actions.hh */; };\n\t\tA7B39FE21A6AC194007FBB93 /* ComputeThread.cc in Sources */ = {isa = PBXBuildFile; fileRef = A7B39FDA1A6AC194007FBB93 /* ComputeThread.cc */; };\n\t\tA7B39FE31A6AC194007FBB93 /* ComputeThread.hh in Sources */ = {isa = PBXBuildFile; fileRef = A7B39FDB1A6AC194007FBB93 /* ComputeThread.hh */; };\n\t\tA7B39FE41A6AC194007FBB93 /* DocumentThread.cc in Sources */ = {isa = PBXBuildFile; fileRef = A7B39FDC1A6AC194007FBB93 /* DocumentThread.cc */; };\n\t\tA7B39FE51A6AC194007FBB93 /* DocumentThread.hh in Sources */ = {isa = PBXBuildFile; fileRef = A7B39FDD1A6AC194007FBB93 /* DocumentThread.hh */; };\n\t\tA7B39FE61A6AC194007FBB93 /* Server.cc in Sources */ = {isa = PBXBuildFile; fileRef = A7B39FDE1A6AC194007FBB93 /* Server.cc */; };\n\t\tA7B39FE71A6AC194007FBB93 /* Server.hh in Sources */ = {isa = PBXBuildFile; fileRef = A7B39FDF1A6AC194007FBB93 /* Server.hh */; };\n\t\tA7B460951A7D40CD0081D96D /* NotebookController.mm in Sources */ = {isa = PBXBuildFile; fileRef = A7B460931A7D40CD0081D96D /* NotebookController.mm */; };\n\t\tA7B460991A7D49060081D96D /* Notebook.xib in Resources */ = {isa = PBXBuildFile; fileRef = A7B460981A7D49060081D96D /* Notebook.xib */; };\n\t\tA7BAFC951A7AAD82008DEAED /* libjsoncpp.a in Frameworks */ = {isa = PBXBuildFile; fileRef = A7BAFC941A7AAD82008DEAED /* libjsoncpp.a */; };\n\t\tA7BAFC991A7AADD0008DEAED /* DataCell.cc in Sources */ = {isa = PBXBuildFile; fileRef = A7BAFC961A7AADD0008DEAED /* DataCell.cc */; };\n\t\tA7BAFC9C1A7AB29C008DEAED /* Python in Frameworks */ = {isa = PBXBuildFile; fileRef = A7BAFC9B1A7AB29C008DEAED /* Python */; };\n\t\tA7BAFC9E1A7AB2C2008DEAED /* libboost_python.dylib in Frameworks */ = {isa = PBXBuildFile; fileRef = A7BAFC9D1A7AB2C2008DEAED /* libboost_python.dylib */; };\n/* End PBXBuildFile section */\n\n/* Begin PBXContainerItemProxy section */\n\t\tA7B0F7251A05663700FCC711 /* PBXContainerItemProxy */ = {\n\t\t\tisa = PBXContainerItemProxy;\n\t\t\tcontainerPortal = A7B0F7091A05663700FCC711 /* Project object */;\n\t\t\tproxyType = 1;\n\t\t\tremoteGlobalIDString = A7B0F7101A05663700FCC711;\n\t\t\tremoteInfo = Cadabra;\n\t\t};\n/* End PBXContainerItemProxy section */\n\n/* Begin PBXFileReference section */\n\t\tA7ACFC5B1A5B3F2A003F01E2 /* NotebookWindow.mm */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.cpp.objcpp; path = NotebookWindow.mm; sourceTree = \"<group>\"; };\n\t\tA7ACFC5C1A5B3F2A003F01E2 /* NotebookWindow.hh */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.cpp.h; path = NotebookWindow.hh; sourceTree = \"<group>\"; };\n\t\tA7B0F7111A05663700FCC711 /* Cadabra.app */ = {isa = PBXFileReference; explicitFileType = wrapper.application; includeInIndex = 0; path = Cadabra.app; sourceTree = BUILT_PRODUCTS_DIR; };\n\t\tA7B0F7151A05663700FCC711 /* Info.plist */ = {isa = PBXFileReference; lastKnownFileType = text.plist.xml; path = Info.plist; sourceTree = \"<group>\"; };\n\t\tA7B0F7161A05663700FCC711 /* main.m */ = {isa = PBXFileReference; lastKnownFileType = sourcecode.c.objc; path = main.m; sourceTree = \"<group>\"; };\n\t\tA7B0F7181A05663700FCC711 /* AppDelegate.h */ = {isa = PBXFileReference; lastKnownFileType = sourcecode.c.h; path = AppDelegate.h; sourceTree = \"<group>\"; };\n\t\tA7B0F7191A05663700FCC711 /* AppDelegate.mm */ = {isa = PBXFileReference; lastKnownFileType = sourcecode.cpp.objcpp; path = AppDelegate.mm; sourceTree = \"<group>\"; };\n\t\tA7B0F71B1A05663700FCC711 /* Images.xcassets */ = {isa = PBXFileReference; lastKnownFileType = folder.assetcatalog; path = Images.xcassets; sourceTree = \"<group>\"; };\n\t\tA7B0F71E1A05663700FCC711 /* Base */ = {isa = PBXFileReference; lastKnownFileType = file.xib; name = Base; path = Base.lproj/Cadabra.xib; sourceTree = \"<group>\"; };\n\t\tA7B0F7241A05663700FCC711 /* CadabraTests.xctest */ = {isa = PBXFileReference; explicitFileType = wrapper.cfbundle; includeInIndex = 0; path = CadabraTests.xctest; sourceTree = BUILT_PRODUCTS_DIR; };\n\t\tA7B0F7291A05663700FCC711 /* Info.plist */ = {isa = PBXFileReference; lastKnownFileType = text.plist.xml; path = Info.plist; sourceTree = \"<group>\"; };\n\t\tA7B0F72A1A05663700FCC711 /* CadabraTests.m */ = {isa = PBXFileReference; lastKnownFileType = sourcecode.c.objc; path = CadabraTests.m; sourceTree = \"<group>\"; };\n\t\tA7B2F2001AA71C3700D0DDA6 /* NotebookCanvas.mm */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.cpp.objcpp; path = NotebookCanvas.mm; sourceTree = \"<group>\"; };\n\t\tA7B2F2021AA71C4E00D0DDA6 /* NotebookCanvas.hh */ = {isa = PBXFileReference; lastKnownFileType = sourcecode.cpp.h; path = NotebookCanvas.hh; sourceTree = \"<group>\"; };\n\t\tA7B2F2031AA73EFA00D0DDA6 /* Test.xib */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = file.xib; path = Test.xib; sourceTree = \"<group>\"; };\n\t\tA7B39FD61A6AC137007FBB93 /* libboost_system.a */ = {isa = PBXFileReference; lastKnownFileType = archive.ar; name = libboost_system.a; path = ../../../../../../../usr/local/Cellar/boost/1.56.0/lib/libboost_system.a; sourceTree = \"<group>\"; };\n\t\tA7B39FD81A6AC194007FBB93 /* Actions.cc */ = {isa = PBXFileReference; lastKnownFileType = sourcecode.cpp.cpp; name = Actions.cc; path = ../../../../client_server/Actions.cc; sourceTree = \"<group>\"; };\n\t\tA7B39FD91A6AC194007FBB93 /* Actions.hh */ = {isa = PBXFileReference; lastKnownFileType = sourcecode.cpp.h; name = Actions.hh; path = ../../../../client_server/Actions.hh; sourceTree = \"<group>\"; };\n\t\tA7B39FDA1A6AC194007FBB93 /* ComputeThread.cc */ = {isa = PBXFileReference; lastKnownFileType = sourcecode.cpp.cpp; name = ComputeThread.cc; path = ../../../../client_server/ComputeThread.cc; sourceTree = \"<group>\"; };\n\t\tA7B39FDB1A6AC194007FBB93 /* ComputeThread.hh */ = {isa = PBXFileReference; lastKnownFileType = sourcecode.cpp.h; name = ComputeThread.hh; path = ../../../../client_server/ComputeThread.hh; sourceTree = \"<group>\"; };\n\t\tA7B39FDC1A6AC194007FBB93 /* DocumentThread.cc */ = {isa = PBXFileReference; lastKnownFileType = sourcecode.cpp.cpp; name = DocumentThread.cc; path = ../../../../client_server/DocumentThread.cc; sourceTree = \"<group>\"; };\n\t\tA7B39FDD1A6AC194007FBB93 /* DocumentThread.hh */ = {isa = PBXFileReference; lastKnownFileType = sourcecode.cpp.h; name = DocumentThread.hh; path = ../../../../client_server/DocumentThread.hh; sourceTree = \"<group>\"; };\n\t\tA7B39FDE1A6AC194007FBB93 /* Server.cc */ = {isa = PBXFileReference; lastKnownFileType = sourcecode.cpp.cpp; name = Server.cc; path = ../../../../client_server/Server.cc; sourceTree = \"<group>\"; };\n\t\tA7B39FDF1A6AC194007FBB93 /* Server.hh */ = {isa = PBXFileReference; lastKnownFileType = sourcecode.cpp.h; name = Server.hh; path = ../../../../client_server/Server.hh; sourceTree = \"<group>\"; };\n\t\tA7B39FE91A6AC26B007FBB93 /* Python.framework */ = {isa = PBXFileReference; lastKnownFileType = wrapper.framework; name = Python.framework; path = ../../../../../../../usr/local/Cellar/python/2.7.8_2/Frameworks/Python.framework; sourceTree = \"<group>\"; };\n\t\tA7B460921A7D40CD0081D96D /* NotebookController.h */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.c.h; name = NotebookController.h; path = ../NotebookController.h; sourceTree = \"<group>\"; };\n\t\tA7B460931A7D40CD0081D96D /* NotebookController.mm */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.cpp.objcpp; name = NotebookController.mm; path = ../NotebookController.mm; sourceTree = \"<group>\"; };\n\t\tA7B460981A7D49060081D96D /* Notebook.xib */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = file.xib; path = Notebook.xib; sourceTree = \"<group>\"; };\n\t\tA7BAFC921A7AAD6B008DEAED /* jsoncpp */ = {isa = PBXFileReference; lastKnownFileType = folder; name = jsoncpp; path = ../../../../../../../usr/local/Cellar/jsoncpp; sourceTree = \"<group>\"; };\n\t\tA7BAFC941A7AAD82008DEAED /* libjsoncpp.a */ = {isa = PBXFileReference; lastKnownFileType = archive.ar; name = libjsoncpp.a; path = \"../../../../../../../usr/local/Cellar/jsoncpp/0.6.0-rc2/lib/libjsoncpp.a\"; sourceTree = \"<group>\"; };\n\t\tA7BAFC961A7AADD0008DEAED /* DataCell.cc */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.cpp.cpp; name = DataCell.cc; path = ../../../../client_server/DataCell.cc; sourceTree = \"<group>\"; };\n\t\tA7BAFC971A7AADD0008DEAED /* DataCell.hh */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.cpp.h; name = DataCell.hh; path = ../../../../client_server/DataCell.hh; sourceTree = \"<group>\"; };\n\t\tA7BAFC981A7AADD0008DEAED /* GUIBase.hh */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.cpp.h; name = GUIBase.hh; path = ../../../../client_server/GUIBase.hh; sourceTree = \"<group>\"; };\n\t\tA7BAFC9B1A7AB29C008DEAED /* Python */ = {isa = PBXFileReference; lastKnownFileType = \"compiled.mach-o.dylib\"; name = Python; path = ../../../../../../../usr/local/Cellar/python/2.7.8_2/Frameworks/Python.framework/Versions/2.7/Python; sourceTree = \"<group>\"; };\n\t\tA7BAFC9D1A7AB2C2008DEAED /* libboost_python.dylib */ = {isa = PBXFileReference; lastKnownFileType = \"compiled.mach-o.dylib\"; name = libboost_python.dylib; path = \"../../../../../../../usr/local/Cellar/boost-python/1.56.0/lib/libboost_python.dylib\"; sourceTree = \"<group>\"; };\n/* End PBXFileReference section */\n\n/* Begin PBXFrameworksBuildPhase section */\n\t\tA7B0F70E1A05663700FCC711 /* Frameworks */ = {\n\t\t\tisa = PBXFrameworksBuildPhase;\n\t\t\tbuildActionMask = 2147483647;\n\t\t\tfiles = (\n\t\t\t\tA7BAFC9E1A7AB2C2008DEAED /* libboost_python.dylib in Frameworks */,\n\t\t\t\tA7BAFC9C1A7AB29C008DEAED /* Python in Frameworks */,\n\t\t\t\tA7BAFC951A7AAD82008DEAED /* libjsoncpp.a in Frameworks */,\n\t\t\t\tA7B39FD71A6AC137007FBB93 /* libboost_system.a in Frameworks */,\n\t\t\t);\n\t\t\trunOnlyForDeploymentPostprocessing = 0;\n\t\t};\n\t\tA7B0F7211A05663700FCC711 /* Frameworks */ = {\n\t\t\tisa = PBXFrameworksBuildPhase;\n\t\t\tbuildActionMask = 2147483647;\n\t\t\tfiles = (\n\t\t\t);\n\t\t\trunOnlyForDeploymentPostprocessing = 0;\n\t\t};\n/* End PBXFrameworksBuildPhase section */\n\n/* Begin PBXGroup section */\n\t\tA7B0F7081A05663700FCC711 = {\n\t\t\tisa = PBXGroup;\n\t\t\tchildren = (\n\t\t\t\tA7BAFC9D1A7AB2C2008DEAED /* libboost_python.dylib */,\n\t\t\t\tA7BAFC9B1A7AB29C008DEAED /* Python */,\n\t\t\t\tA7BAFC941A7AAD82008DEAED /* libjsoncpp.a */,\n\t\t\t\tA7BAFC921A7AAD6B008DEAED /* jsoncpp */,\n\t\t\t\tA7B39FE91A6AC26B007FBB93 /* Python.framework */,\n\t\t\t\tA7B39FD61A6AC137007FBB93 /* libboost_system.a */,\n\t\t\t\tA7B0F7131A05663700FCC711 /* Cadabra */,\n\t\t\t\tA7B0F7271A05663700FCC711 /* CadabraTests */,\n\t\t\t\tA7B0F7121A05663700FCC711 /* Products */,\n\t\t\t);\n\t\t\tsourceTree = \"<group>\";\n\t\t};\n\t\tA7B0F7121A05663700FCC711 /* Products */ = {\n\t\t\tisa = PBXGroup;\n\t\t\tchildren = (\n\t\t\t\tA7B0F7111A05663700FCC711 /* Cadabra.app */,\n\t\t\t\tA7B0F7241A05663700FCC711 /* CadabraTests.xctest */,\n\t\t\t);\n\t\t\tname = Products;\n\t\t\tsourceTree = \"<group>\";\n\t\t};\n\t\tA7B0F7131A05663700FCC711 /* Cadabra */ = {\n\t\t\tisa = PBXGroup;\n\t\t\tchildren = (\n\t\t\t\tA7B39FE81A6AC1AD007FBB93 /* client_server */,\n\t\t\t\tA7B0F7181A05663700FCC711 /* AppDelegate.h */,\n\t\t\t\tA7B0F7191A05663700FCC711 /* AppDelegate.mm */,\n\t\t\t\tA7ACFC5B1A5B3F2A003F01E2 /* NotebookWindow.mm */,\n\t\t\t\tA7ACFC5C1A5B3F2A003F01E2 /* NotebookWindow.hh */,\n\t\t\t\tA7B2F2001AA71C3700D0DDA6 /* NotebookCanvas.mm */,\n\t\t\t\tA7B2F2021AA71C4E00D0DDA6 /* NotebookCanvas.hh */,\n\t\t\t\tA7B460921A7D40CD0081D96D /* NotebookController.h */,\n\t\t\t\tA7B460931A7D40CD0081D96D /* NotebookController.mm */,\n\t\t\t\tA7B0F71D1A05663700FCC711 /* Cadabra.xib */,\n\t\t\t\tA7B460981A7D49060081D96D /* Notebook.xib */,\n\t\t\t\tA7B2F2031AA73EFA00D0DDA6 /* Test.xib */,\n\t\t\t\tA7B0F71B1A05663700FCC711 /* Images.xcassets */,\n\t\t\t\tA7B0F7141A05663700FCC711 /* Supporting Files */,\n\t\t\t);\n\t\t\tpath = Cadabra;\n\t\t\tsourceTree = \"<group>\";\n\t\t};\n\t\tA7B0F7141A05663700FCC711 /* Supporting Files */ = {\n\t\t\tisa = PBXGroup;\n\t\t\tchildren = (\n\t\t\t\tA7B0F7151A05663700FCC711 /* Info.plist */,\n\t\t\t\tA7B0F7161A05663700FCC711 /* main.m */,\n\t\t\t);\n\t\t\tname = \"Supporting Files\";\n\t\t\tsourceTree = \"<group>\";\n\t\t};\n\t\tA7B0F7271A05663700FCC711 /* CadabraTests */ = {\n\t\t\tisa = PBXGroup;\n\t\t\tchildren = (\n\t\t\t\tA7B0F72A1A05663700FCC711 /* CadabraTests.m */,\n\t\t\t\tA7B0F7281A05663700FCC711 /* Supporting Files */,\n\t\t\t);\n\t\t\tpath = CadabraTests;\n\t\t\tsourceTree = \"<group>\";\n\t\t};\n\t\tA7B0F7281A05663700FCC711 /* Supporting Files */ = {\n\t\t\tisa = PBXGroup;\n\t\t\tchildren = (\n\t\t\t\tA7B0F7291A05663700FCC711 /* Info.plist */,\n\t\t\t);\n\t\t\tname = \"Supporting Files\";\n\t\t\tsourceTree = \"<group>\";\n\t\t};\n\t\tA7B39FE81A6AC1AD007FBB93 /* client_server */ = {\n\t\t\tisa = PBXGroup;\n\t\t\tchildren = (\n\t\t\t\tA7BAFC961A7AADD0008DEAED /* DataCell.cc */,\n\t\t\t\tA7BAFC971A7AADD0008DEAED /* DataCell.hh */,\n\t\t\t\tA7BAFC981A7AADD0008DEAED /* GUIBase.hh */,\n\t\t\t\tA7B39FD81A6AC194007FBB93 /* Actions.cc */,\n\t\t\t\tA7B39FD91A6AC194007FBB93 /* Actions.hh */,\n\t\t\t\tA7B39FDA1A6AC194007FBB93 /* ComputeThread.cc */,\n\t\t\t\tA7B39FDB1A6AC194007FBB93 /* ComputeThread.hh */,\n\t\t\t\tA7B39FDC1A6AC194007FBB93 /* DocumentThread.cc */,\n\t\t\t\tA7B39FDD1A6AC194007FBB93 /* DocumentThread.hh */,\n\t\t\t\tA7B39FDE1A6AC194007FBB93 /* Server.cc */,\n\t\t\t\tA7B39FDF1A6AC194007FBB93 /* Server.hh */,\n\t\t\t);\n\t\t\tname = client_server;\n\t\t\tsourceTree = \"<group>\";\n\t\t};\n/* End PBXGroup section */\n\n/* Begin PBXNativeTarget section */\n\t\tA7B0F7101A05663700FCC711 /* Cadabra */ = {\n\t\t\tisa = PBXNativeTarget;\n\t\t\tbuildConfigurationList = A7B0F72E1A05663700FCC711 /* Build configuration list for PBXNativeTarget \"Cadabra\" */;\n\t\t\tbuildPhases = (\n\t\t\t\tA7B0F70D1A05663700FCC711 /* Sources */,\n\t\t\t\tA7B0F70E1A05663700FCC711 /* Frameworks */,\n\t\t\t\tA7B0F70F1A05663700FCC711 /* Resources */,\n\t\t\t);\n\t\t\tbuildRules = (\n\t\t\t);\n\t\t\tdependencies = (\n\t\t\t);\n\t\t\tname = Cadabra;\n\t\t\tproductName = Cadabra;\n\t\t\tproductReference = A7B0F7111A05663700FCC711 /* Cadabra.app */;\n\t\t\tproductType = \"com.apple.product-type.application\";\n\t\t};\n\t\tA7B0F7231A05663700FCC711 /* CadabraTests */ = {\n\t\t\tisa = PBXNativeTarget;\n\t\t\tbuildConfigurationList = A7B0F7311A05663700FCC711 /* Build configuration list for PBXNativeTarget \"CadabraTests\" */;\n\t\t\tbuildPhases = (\n\t\t\t\tA7B0F7201A05663700FCC711 /* Sources */,\n\t\t\t\tA7B0F7211A05663700FCC711 /* Frameworks */,\n\t\t\t\tA7B0F7221A05663700FCC711 /* Resources */,\n\t\t\t);\n\t\t\tbuildRules = (\n\t\t\t);\n\t\t\tdependencies = (\n\t\t\t\tA7B0F7261A05663700FCC711 /* PBXTargetDependency */,\n\t\t\t);\n\t\t\tname = CadabraTests;\n\t\t\tproductName = CadabraTests;\n\t\t\tproductReference = A7B0F7241A05663700FCC711 /* CadabraTests.xctest */;\n\t\t\tproductType = \"com.apple.product-type.bundle.unit-test\";\n\t\t};\n/* End PBXNativeTarget section */\n\n/* Begin PBXProject section */\n\t\tA7B0F7091A05663700FCC711 /* Project object */ = {\n\t\t\tisa = PBXProject;\n\t\t\tattributes = {\n\t\t\t\tLastUpgradeCheck = 0710;\n\t\t\t\tORGANIZATIONNAME = \"phi-sci\";\n\t\t\t\tTargetAttributes = {\n\t\t\t\t\tA7B0F7101A05663700FCC711 = {\n\t\t\t\t\t\tCreatedOnToolsVersion = 6.0.1;\n\t\t\t\t\t};\n\t\t\t\t\tA7B0F7231A05663700FCC711 = {\n\t\t\t\t\t\tCreatedOnToolsVersion = 6.0.1;\n\t\t\t\t\t\tTestTargetID = A7B0F7101A05663700FCC711;\n\t\t\t\t\t};\n\t\t\t\t};\n\t\t\t};\n\t\t\tbuildConfigurationList = A7B0F70C1A05663700FCC711 /* Build configuration list for PBXProject \"Cadabra\" */;\n\t\t\tcompatibilityVersion = \"Xcode 3.2\";\n\t\t\tdevelopmentRegion = English;\n\t\t\thasScannedForEncodings = 0;\n\t\t\tknownRegions = (\n\t\t\t\ten,\n\t\t\t\tBase,\n\t\t\t);\n\t\t\tmainGroup = A7B0F7081A05663700FCC711;\n\t\t\tproductRefGroup = A7B0F7121A05663700FCC711 /* Products */;\n\t\t\tprojectDirPath = \"\";\n\t\t\tprojectRoot = \"\";\n\t\t\ttargets = (\n\t\t\t\tA7B0F7101A05663700FCC711 /* Cadabra */,\n\t\t\t\tA7B0F7231A05663700FCC711 /* CadabraTests */,\n\t\t\t);\n\t\t};\n/* End PBXProject section */\n\n/* Begin PBXResourcesBuildPhase section */\n\t\tA7B0F70F1A05663700FCC711 /* Resources */ = {\n\t\t\tisa = PBXResourcesBuildPhase;\n\t\t\tbuildActionMask = 2147483647;\n\t\t\tfiles = (\n\t\t\t\tA7B0F71C1A05663700FCC711 /* Images.xcassets in Resources */,\n\t\t\t\tA7B2F2041AA73EFA00D0DDA6 /* Test.xib in Resources */,\n\t\t\t\tA7B460991A7D49060081D96D /* Notebook.xib in Resources */,\n\t\t\t\tA7B0F71F1A05663700FCC711 /* Cadabra.xib in Resources */,\n\t\t\t);\n\t\t\trunOnlyForDeploymentPostprocessing = 0;\n\t\t};\n\t\tA7B0F7221A05663700FCC711 /* Resources */ = {\n\t\t\tisa = PBXResourcesBuildPhase;\n\t\t\tbuildActionMask = 2147483647;\n\t\t\tfiles = (\n\t\t\t);\n\t\t\trunOnlyForDeploymentPostprocessing = 0;\n\t\t};\n/* End PBXResourcesBuildPhase section */\n\n/* Begin PBXSourcesBuildPhase section */\n\t\tA7B0F70D1A05663700FCC711 /* Sources */ = {\n\t\t\tisa = PBXSourcesBuildPhase;\n\t\t\tbuildActionMask = 2147483647;\n\t\t\tfiles = (\n\t\t\t\tA7B39FE01A6AC194007FBB93 /* Actions.cc in Sources */,\n\t\t\t\tA7B460951A7D40CD0081D96D /* NotebookController.mm in Sources */,\n\t\t\t\tA7B39FE11A6AC194007FBB93 /* Actions.hh in Sources */,\n\t\t\t\tA7B39FE21A6AC194007FBB93 /* ComputeThread.cc in Sources */,\n\t\t\t\tA7B2F2011AA71C3700D0DDA6 /* NotebookCanvas.mm in Sources */,\n\t\t\t\tA7B39FE31A6AC194007FBB93 /* ComputeThread.hh in Sources */,\n\t\t\t\tA7B39FE41A6AC194007FBB93 /* DocumentThread.cc in Sources */,\n\t\t\t\tA7B39FE51A6AC194007FBB93 /* DocumentThread.hh in Sources */,\n\t\t\t\tA7B39FE61A6AC194007FBB93 /* Server.cc in Sources */,\n\t\t\t\tA7B39FE71A6AC194007FBB93 /* Server.hh in Sources */,\n\t\t\t\tA7ACFC5D1A5B3F2A003F01E2 /* NotebookWindow.mm in Sources */,\n\t\t\t\tA7BAFC991A7AADD0008DEAED /* DataCell.cc in Sources */,\n\t\t\t\tA7B0F71A1A05663700FCC711 /* AppDelegate.mm in Sources */,\n\t\t\t\tA7B0F7171A05663700FCC711 /* main.m in Sources */,\n\t\t\t);\n\t\t\trunOnlyForDeploymentPostprocessing = 0;\n\t\t};\n\t\tA7B0F7201A05663700FCC711 /* Sources */ = {\n\t\t\tisa = PBXSourcesBuildPhase;\n\t\t\tbuildActionMask = 2147483647;\n\t\t\tfiles = (\n\t\t\t\tA7B0F72B1A05663700FCC711 /* CadabraTests.m in Sources */,\n\t\t\t);\n\t\t\trunOnlyForDeploymentPostprocessing = 0;\n\t\t};\n/* End PBXSourcesBuildPhase section */\n\n/* Begin PBXTargetDependency section */\n\t\tA7B0F7261A05663700FCC711 /* PBXTargetDependency */ = {\n\t\t\tisa = PBXTargetDependency;\n\t\t\ttarget = A7B0F7101A05663700FCC711 /* Cadabra */;\n\t\t\ttargetProxy = A7B0F7251A05663700FCC711 /* PBXContainerItemProxy */;\n\t\t};\n/* End PBXTargetDependency section */\n\n/* Begin PBXVariantGroup section */\n\t\tA7B0F71D1A05663700FCC711 /* Cadabra.xib */ = {\n\t\t\tisa = PBXVariantGroup;\n\t\t\tchildren = (\n\t\t\t\tA7B0F71E1A05663700FCC711 /* Base */,\n\t\t\t);\n\t\t\tname = Cadabra.xib;\n\t\t\tsourceTree = \"<group>\";\n\t\t};\n/* End PBXVariantGroup section */\n\n/* Begin XCBuildConfiguration section */\n\t\tA7B0F72C1A05663700FCC711 /* Debug */ = {\n\t\t\tisa = XCBuildConfiguration;\n\t\t\tbuildSettings = {\n\t\t\t\tALWAYS_SEARCH_USER_PATHS = NO;\n\t\t\t\tCLANG_CXX_LANGUAGE_STANDARD = \"gnu++0x\";\n\t\t\t\tCLANG_CXX_LIBRARY = \"libc++\";\n\t\t\t\tCLANG_ENABLE_MODULES = YES;\n\t\t\t\tCLANG_ENABLE_OBJC_ARC = YES;\n\t\t\t\tCLANG_WARN_BOOL_CONVERSION = YES;\n\t\t\t\tCLANG_WARN_CONSTANT_CONVERSION = YES;\n\t\t\t\tCLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;\n\t\t\t\tCLANG_WARN_EMPTY_BODY = YES;\n\t\t\t\tCLANG_WARN_ENUM_CONVERSION = YES;\n\t\t\t\tCLANG_WARN_INT_CONVERSION = YES;\n\t\t\t\tCLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;\n\t\t\t\tCLANG_WARN_UNREACHABLE_CODE = YES;\n\t\t\t\tCLANG_WARN__DUPLICATE_METHOD_MATCH = YES;\n\t\t\t\tCODE_SIGN_IDENTITY = \"-\";\n\t\t\t\tCOPY_PHASE_STRIP = NO;\n\t\t\t\tENABLE_STRICT_OBJC_MSGSEND = YES;\n\t\t\t\tENABLE_TESTABILITY = YES;\n\t\t\t\tGCC_C_LANGUAGE_STANDARD = gnu99;\n\t\t\t\tGCC_DYNAMIC_NO_PIC = NO;\n\t\t\t\tGCC_OPTIMIZATION_LEVEL = 0;\n\t\t\t\tGCC_PREPROCESSOR_DEFINITIONS = (\n\t\t\t\t\t\"DEBUG=1\",\n\t\t\t\t\t\"$(inherited)\",\n\t\t\t\t);\n\t\t\t\tGCC_SYMBOLS_PRIVATE_EXTERN = NO;\n\t\t\t\tGCC_WARN_64_TO_32_BIT_CONVERSION = YES;\n\t\t\t\tGCC_WARN_ABOUT_RETURN_TYPE = YES_ERROR;\n\t\t\t\tGCC_WARN_UNDECLARED_SELECTOR = YES;\n\t\t\t\tGCC_WARN_UNINITIALIZED_AUTOS = YES_AGGRESSIVE;\n\t\t\t\tGCC_WARN_UNUSED_FUNCTION = YES;\n\t\t\t\tGCC_WARN_UNUSED_VARIABLE = YES;\n\t\t\t\tMACOSX_DEPLOYMENT_TARGET = 10.9;\n\t\t\t\tMTL_ENABLE_DEBUG_INFO = YES;\n\t\t\t\tONLY_ACTIVE_ARCH = YES;\n\t\t\t\tSDKROOT = macosx;\n\t\t\t};\n\t\t\tname = Debug;\n\t\t};\n\t\tA7B0F72D1A05663700FCC711 /* Release */ = {\n\t\t\tisa = XCBuildConfiguration;\n\t\t\tbuildSettings = {\n\t\t\t\tALWAYS_SEARCH_USER_PATHS = NO;\n\t\t\t\tCLANG_CXX_LANGUAGE_STANDARD = \"gnu++0x\";\n\t\t\t\tCLANG_CXX_LIBRARY = \"libc++\";\n\t\t\t\tCLANG_ENABLE_MODULES = YES;\n\t\t\t\tCLANG_ENABLE_OBJC_ARC = YES;\n\t\t\t\tCLANG_WARN_BOOL_CONVERSION = YES;\n\t\t\t\tCLANG_WARN_CONSTANT_CONVERSION = YES;\n\t\t\t\tCLANG_WARN_DIRECT_OBJC_ISA_USAGE = YES_ERROR;\n\t\t\t\tCLANG_WARN_EMPTY_BODY = YES;\n\t\t\t\tCLANG_WARN_ENUM_CONVERSION = YES;\n\t\t\t\tCLANG_WARN_INT_CONVERSION = YES;\n\t\t\t\tCLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;\n\t\t\t\tCLANG_WARN_UNREACHABLE_CODE = YES;\n\t\t\t\tCLANG_WARN__DUPLICATE_METHOD_MATCH = YES;\n\t\t\t\tCODE_SIGN_IDENTITY = \"-\";\n\t\t\t\tCOPY_PHASE_STRIP = YES;\n\t\t\t\tDEBUG_INFORMATION_FORMAT = \"dwarf-with-dsym\";\n\t\t\t\tENABLE_NS_ASSERTIONS = NO;\n\t\t\t\tENABLE_STRICT_OBJC_MSGSEND = YES;\n\t\t\t\tGCC_C_LANGUAGE_STANDARD = gnu99;\n\t\t\t\tGCC_WARN_64_TO_32_BIT_CONVERSION = YES;\n\t\t\t\tGCC_WARN_ABOUT_RETURN_TYPE = YES_ERROR;\n\t\t\t\tGCC_WARN_UNDECLARED_SELECTOR = YES;\n\t\t\t\tGCC_WARN_UNINITIALIZED_AUTOS = YES_AGGRESSIVE;\n\t\t\t\tGCC_WARN_UNUSED_FUNCTION = YES;\n\t\t\t\tGCC_WARN_UNUSED_VARIABLE = YES;\n\t\t\t\tMACOSX_DEPLOYMENT_TARGET = 10.9;\n\t\t\t\tMTL_ENABLE_DEBUG_INFO = NO;\n\t\t\t\tSDKROOT = macosx;\n\t\t\t};\n\t\t\tname = Release;\n\t\t};\n\t\tA7B0F72F1A05663700FCC711 /* Debug */ = {\n\t\t\tisa = XCBuildConfiguration;\n\t\t\tbuildSettings = {\n\t\t\t\tALWAYS_SEARCH_USER_PATHS = YES;\n\t\t\t\tASSETCATALOG_COMPILER_APPICON_NAME = AppIcon;\n\t\t\t\tCOMBINE_HIDPI_IMAGES = YES;\n\t\t\t\tFRAMEWORK_SEARCH_PATHS = (\n\t\t\t\t\t\"$(inherited)\",\n\t\t\t\t\t/usr/local/Cellar/python/2.7.8_2/Frameworks,\n\t\t\t\t);\n\t\t\t\tINFOPLIST_FILE = Cadabra/Info.plist;\n\t\t\t\tLD_RUNPATH_SEARCH_PATHS = \"$(inherited) @executable_path/../Frameworks\";\n\t\t\t\tLIBRARY_SEARCH_PATHS = (\n\t\t\t\t\t\"$(inherited)\",\n\t\t\t\t\t/usr/local/Cellar/boost/1.56.0/lib,\n\t\t\t\t\t\"/usr/local/Cellar/jsoncpp/0.6.0-rc2/lib\",\n\t\t\t\t\t/usr/local/Cellar/python/2.7.8_2/Frameworks/Python.framework/Versions/2.7,\n\t\t\t\t\t\"/usr/local/Cellar/boost-python/1.56.0/lib\",\n\t\t\t\t);\n\t\t\t\t\"OTHER_CPLUSPLUSFLAGS[arch=*]\" = (\n\t\t\t\t\t\"$(OTHER_CFLAGS)\",\n\t\t\t\t\t\"-D_WEBSOCKETPP_CPP11_STL_\",\n\t\t\t\t);\n\t\t\t\tPRODUCT_BUNDLE_IDENTIFIER = \"com.phi-sci.$(PRODUCT_NAME:rfc1034identifier)\";\n\t\t\t\tPRODUCT_NAME = \"$(TARGET_NAME)\";\n\t\t\t\tUSER_HEADER_SEARCH_PATHS = \"\";\n\t\t\t\t\"USER_HEADER_SEARCH_PATHS[arch=*]\" = \"../../../client_server /usr/local/Cellar/boost/1.56.0/include/ /usr/local/Cellar/jsoncpp/0.6.0-rc2/include/ /System/Library/Frameworks/Python.framework/Versions/2.7/include/python2.7\";\n\t\t\t};\n\t\t\tname = Debug;\n\t\t};\n\t\tA7B0F7301A05663700FCC711 /* Release */ = {\n\t\t\tisa = XCBuildConfiguration;\n\t\t\tbuildSettings = {\n\t\t\t\tALWAYS_SEARCH_USER_PATHS = YES;\n\t\t\t\tASSETCATALOG_COMPILER_APPICON_NAME = AppIcon;\n\t\t\t\tCOMBINE_HIDPI_IMAGES = YES;\n\t\t\t\tFRAMEWORK_SEARCH_PATHS = (\n\t\t\t\t\t\"$(inherited)\",\n\t\t\t\t\t/usr/local/Cellar/python/2.7.8_2/Frameworks,\n\t\t\t\t);\n\t\t\t\tINFOPLIST_FILE = Cadabra/Info.plist;\n\t\t\t\tLD_RUNPATH_SEARCH_PATHS = \"$(inherited) @executable_path/../Frameworks\";\n\t\t\t\tLIBRARY_SEARCH_PATHS = (\n\t\t\t\t\t\"$(inherited)\",\n\t\t\t\t\t/usr/local/Cellar/boost/1.56.0/lib,\n\t\t\t\t\t\"/usr/local/Cellar/jsoncpp/0.6.0-rc2/lib\",\n\t\t\t\t\t/usr/local/Cellar/python/2.7.8_2/Frameworks/Python.framework/Versions/2.7,\n\t\t\t\t\t\"/usr/local/Cellar/boost-python/1.56.0/lib\",\n\t\t\t\t);\n\t\t\t\t\"OTHER_CPLUSPLUSFLAGS[arch=*]\" = (\n\t\t\t\t\t\"$(OTHER_CFLAGS)\",\n\t\t\t\t\t\"-D_WEBSOCKETPP_CPP11_STL_\",\n\t\t\t\t);\n\t\t\t\tPRODUCT_BUNDLE_IDENTIFIER = \"com.phi-sci.$(PRODUCT_NAME:rfc1034identifier)\";\n\t\t\t\tPRODUCT_NAME = \"$(TARGET_NAME)\";\n\t\t\t\tUSER_HEADER_SEARCH_PATHS = \"\";\n\t\t\t\t\"USER_HEADER_SEARCH_PATHS[arch=*]\" = \"../../../client_server /usr/local/Cellar/boost/1.56.0/include/ /usr/local/Cellar/jsoncpp/0.6.0-rc2/include/ /System/Library/Frameworks/Python.framework/Versions/2.7/include/python2.7\";\n\t\t\t};\n\t\t\tname = Release;\n\t\t};\n\t\tA7B0F7321A05663700FCC711 /* Debug */ = {\n\t\t\tisa = XCBuildConfiguration;\n\t\t\tbuildSettings = {\n\t\t\t\tBUNDLE_LOADER = \"$(TEST_HOST)\";\n\t\t\t\tCOMBINE_HIDPI_IMAGES = YES;\n\t\t\t\tFRAMEWORK_SEARCH_PATHS = (\n\t\t\t\t\t\"$(DEVELOPER_FRAMEWORKS_DIR)\",\n\t\t\t\t\t\"$(inherited)\",\n\t\t\t\t);\n\t\t\t\tGCC_PREPROCESSOR_DEFINITIONS = (\n\t\t\t\t\t\"DEBUG=1\",\n\t\t\t\t\t\"$(inherited)\",\n\t\t\t\t);\n\t\t\t\tINFOPLIST_FILE = CadabraTests/Info.plist;\n\t\t\t\tLD_RUNPATH_SEARCH_PATHS = \"$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks\";\n\t\t\t\tPRODUCT_BUNDLE_IDENTIFIER = \"com.phi-sci.$(PRODUCT_NAME:rfc1034identifier)\";\n\t\t\t\tPRODUCT_NAME = \"$(TARGET_NAME)\";\n\t\t\t\tTEST_HOST = \"$(BUILT_PRODUCTS_DIR)/Cadabra.app/Contents/MacOS/Cadabra\";\n\t\t\t};\n\t\t\tname = Debug;\n\t\t};\n\t\tA7B0F7331A05663700FCC711 /* Release */ = {\n\t\t\tisa = XCBuildConfiguration;\n\t\t\tbuildSettings = {\n\t\t\t\tBUNDLE_LOADER = \"$(TEST_HOST)\";\n\t\t\t\tCOMBINE_HIDPI_IMAGES = YES;\n\t\t\t\tFRAMEWORK_SEARCH_PATHS = (\n\t\t\t\t\t\"$(DEVELOPER_FRAMEWORKS_DIR)\",\n\t\t\t\t\t\"$(inherited)\",\n\t\t\t\t);\n\t\t\t\tINFOPLIST_FILE = CadabraTests/Info.plist;\n\t\t\t\tLD_RUNPATH_SEARCH_PATHS = \"$(inherited) @executable_path/../Frameworks @loader_path/../Frameworks\";\n\t\t\t\tPRODUCT_BUNDLE_IDENTIFIER = \"com.phi-sci.$(PRODUCT_NAME:rfc1034identifier)\";\n\t\t\t\tPRODUCT_NAME = \"$(TARGET_NAME)\";\n\t\t\t\tTEST_HOST = \"$(BUILT_PRODUCTS_DIR)/Cadabra.app/Contents/MacOS/Cadabra\";\n\t\t\t};\n\t\t\tname = Release;\n\t\t};\n/* End XCBuildConfiguration section */\n\n/* Begin XCConfigurationList section */\n\t\tA7B0F70C1A05663700FCC711 /* Build configuration list for PBXProject \"Cadabra\" */ = {\n\t\t\tisa = XCConfigurationList;\n\t\t\tbuildConfigurations = (\n\t\t\t\tA7B0F72C1A05663700FCC711 /* Debug */,\n\t\t\t\tA7B0F72D1A05663700FCC711 /* Release */,\n\t\t\t);\n\t\t\tdefaultConfigurationIsVisible = 0;\n\t\t\tdefaultConfigurationName = Release;\n\t\t};\n\t\tA7B0F72E1A05663700FCC711 /* Build configuration list for PBXNativeTarget \"Cadabra\" */ = {\n\t\t\tisa = XCConfigurationList;\n\t\t\tbuildConfigurations = (\n\t\t\t\tA7B0F72F1A05663700FCC711 /* Debug */,\n\t\t\t\tA7B0F7301A05663700FCC711 /* Release */,\n\t\t\t);\n\t\t\tdefaultConfigurationIsVisible = 0;\n\t\t\tdefaultConfigurationName = Release;\n\t\t};\n\t\tA7B0F7311A05663700FCC711 /* Build configuration list for PBXNativeTarget \"CadabraTests\" */ = {\n\t\t\tisa = XCConfigurationList;\n\t\t\tbuildConfigurations = (\n\t\t\t\tA7B0F7321A05663700FCC711 /* Debug */,\n\t\t\t\tA7B0F7331A05663700FCC711 /* Release */,\n\t\t\t);\n\t\t\tdefaultConfigurationIsVisible = 0;\n\t\t\tdefaultConfigurationName = Release;\n\t\t};\n/* End XCConfigurationList section */\n\t};\n\trootObject = A7B0F7091A05663700FCC711 /* Project object */;\n}\n"
  },
  {
    "path": "frontend/osx/Cadabra/Cadabra.xcodeproj/project.xcworkspace/contents.xcworkspacedata",
    "content": "<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n<Workspace\n   version = \"1.0\">\n   <FileRef\n      location = \"self:Cadabra.xcodeproj\">\n   </FileRef>\n</Workspace>\n"
  },
  {
    "path": "frontend/osx/Cadabra/Cadabra.xcodeproj/project.xcworkspace/xcshareddata/Cadabra.xccheckout",
    "content": "<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n<!DOCTYPE plist PUBLIC \"-//Apple//DTD PLIST 1.0//EN\" \"http://www.apple.com/DTDs/PropertyList-1.0.dtd\">\n<plist version=\"1.0\">\n<dict>\n\t<key>IDESourceControlProjectFavoriteDictionaryKey</key>\n\t<false/>\n\t<key>IDESourceControlProjectIdentifier</key>\n\t<string>62127305-9BF3-4416-96E4-2FB6F92F74A5</string>\n\t<key>IDESourceControlProjectName</key>\n\t<string>Cadabra</string>\n\t<key>IDESourceControlProjectOriginsDictionary</key>\n\t<dict>\n\t\t<key>132ED0CF11D1415DFD474AA74F8D590CB479F277</key>\n\t\t<string>git:cadabra2</string>\n\t\t<key>995AABD49A028E610D29FFC44D560D9DAC1EAC0B</key>\n\t\t<string>https://github.com/zaphoyd/websocketpp.git</string>\n\t</dict>\n\t<key>IDESourceControlProjectPath</key>\n\t<string>frontend/osx/Cadabra/Cadabra.xcodeproj</string>\n\t<key>IDESourceControlProjectRelativeInstallPathDictionary</key>\n\t<dict>\n\t\t<key>132ED0CF11D1415DFD474AA74F8D590CB479F277</key>\n\t\t<string>../../../../..</string>\n\t\t<key>995AABD49A028E610D29FFC44D560D9DAC1EAC0B</key>\n\t\t<string>../../../../../client_server/websocketpp</string>\n\t</dict>\n\t<key>IDESourceControlProjectURL</key>\n\t<string>git:cadabra2</string>\n\t<key>IDESourceControlProjectVersion</key>\n\t<integer>111</integer>\n\t<key>IDESourceControlProjectWCCIdentifier</key>\n\t<string>132ED0CF11D1415DFD474AA74F8D590CB479F277</string>\n\t<key>IDESourceControlProjectWCConfigurations</key>\n\t<array>\n\t\t<dict>\n\t\t\t<key>IDESourceControlRepositoryExtensionIdentifierKey</key>\n\t\t\t<string>public.vcs.git</string>\n\t\t\t<key>IDESourceControlWCCIdentifierKey</key>\n\t\t\t<string>132ED0CF11D1415DFD474AA74F8D590CB479F277</string>\n\t\t\t<key>IDESourceControlWCCName</key>\n\t\t\t<string>cadabra2</string>\n\t\t</dict>\n\t\t<dict>\n\t\t\t<key>IDESourceControlRepositoryExtensionIdentifierKey</key>\n\t\t\t<string>public.vcs.git</string>\n\t\t\t<key>IDESourceControlWCCIdentifierKey</key>\n\t\t\t<string>995AABD49A028E610D29FFC44D560D9DAC1EAC0B</string>\n\t\t\t<key>IDESourceControlWCCName</key>\n\t\t\t<string>websocketpp</string>\n\t\t</dict>\n\t</array>\n</dict>\n</plist>\n"
  },
  {
    "path": "frontend/osx/Cadabra/Cadabra.xcodeproj/xcuserdata/kasper.xcuserdatad/.gitignore",
    "content": "xcdebugger\n"
  },
  {
    "path": "frontend/osx/Cadabra/Cadabra.xcodeproj/xcuserdata/kasper.xcuserdatad/xcschemes/Cadabra.xcscheme",
    "content": "<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n<Scheme\n   LastUpgradeVersion = \"0710\"\n   version = \"1.3\">\n   <BuildAction\n      parallelizeBuildables = \"YES\"\n      buildImplicitDependencies = \"YES\">\n      <BuildActionEntries>\n         <BuildActionEntry\n            buildForTesting = \"YES\"\n            buildForRunning = \"YES\"\n            buildForProfiling = \"YES\"\n            buildForArchiving = \"YES\"\n            buildForAnalyzing = \"YES\">\n            <BuildableReference\n               BuildableIdentifier = \"primary\"\n               BlueprintIdentifier = \"A7B0F7101A05663700FCC711\"\n               BuildableName = \"Cadabra.app\"\n               BlueprintName = \"Cadabra\"\n               ReferencedContainer = \"container:Cadabra.xcodeproj\">\n            </BuildableReference>\n         </BuildActionEntry>\n         <BuildActionEntry\n            buildForTesting = \"YES\"\n            buildForRunning = \"YES\"\n            buildForProfiling = \"NO\"\n            buildForArchiving = \"NO\"\n            buildForAnalyzing = \"YES\">\n            <BuildableReference\n               BuildableIdentifier = \"primary\"\n               BlueprintIdentifier = \"A7B0F7231A05663700FCC711\"\n               BuildableName = \"CadabraTests.xctest\"\n               BlueprintName = \"CadabraTests\"\n               ReferencedContainer = \"container:Cadabra.xcodeproj\">\n            </BuildableReference>\n         </BuildActionEntry>\n      </BuildActionEntries>\n   </BuildAction>\n   <TestAction\n      buildConfiguration = \"Debug\"\n      selectedDebuggerIdentifier = \"Xcode.DebuggerFoundation.Debugger.LLDB\"\n      selectedLauncherIdentifier = \"Xcode.DebuggerFoundation.Launcher.LLDB\"\n      shouldUseLaunchSchemeArgsEnv = \"YES\">\n      <Testables>\n         <TestableReference\n            skipped = \"NO\">\n            <BuildableReference\n               BuildableIdentifier = \"primary\"\n               BlueprintIdentifier = \"A7B0F7231A05663700FCC711\"\n               BuildableName = \"CadabraTests.xctest\"\n               BlueprintName = \"CadabraTests\"\n               ReferencedContainer = \"container:Cadabra.xcodeproj\">\n            </BuildableReference>\n         </TestableReference>\n      </Testables>\n      <MacroExpansion>\n         <BuildableReference\n            BuildableIdentifier = \"primary\"\n            BlueprintIdentifier = \"A7B0F7101A05663700FCC711\"\n            BuildableName = \"Cadabra.app\"\n            BlueprintName = \"Cadabra\"\n            ReferencedContainer = \"container:Cadabra.xcodeproj\">\n         </BuildableReference>\n      </MacroExpansion>\n      <AdditionalOptions>\n      </AdditionalOptions>\n   </TestAction>\n   <LaunchAction\n      buildConfiguration = \"Debug\"\n      selectedDebuggerIdentifier = \"Xcode.DebuggerFoundation.Debugger.LLDB\"\n      selectedLauncherIdentifier = \"Xcode.DebuggerFoundation.Launcher.LLDB\"\n      launchStyle = \"0\"\n      useCustomWorkingDirectory = \"NO\"\n      ignoresPersistentStateOnLaunch = \"NO\"\n      debugDocumentVersioning = \"YES\"\n      debugServiceExtension = \"internal\"\n      allowLocationSimulation = \"YES\">\n      <BuildableProductRunnable\n         runnableDebuggingMode = \"0\">\n         <BuildableReference\n            BuildableIdentifier = \"primary\"\n            BlueprintIdentifier = \"A7B0F7101A05663700FCC711\"\n            BuildableName = \"Cadabra.app\"\n            BlueprintName = \"Cadabra\"\n            ReferencedContainer = \"container:Cadabra.xcodeproj\">\n         </BuildableReference>\n      </BuildableProductRunnable>\n      <AdditionalOptions>\n      </AdditionalOptions>\n   </LaunchAction>\n   <ProfileAction\n      buildConfiguration = \"Release\"\n      shouldUseLaunchSchemeArgsEnv = \"YES\"\n      savedToolIdentifier = \"\"\n      useCustomWorkingDirectory = \"NO\"\n      debugDocumentVersioning = \"YES\">\n      <BuildableProductRunnable\n         runnableDebuggingMode = \"0\">\n         <BuildableReference\n            BuildableIdentifier = \"primary\"\n            BlueprintIdentifier = \"A7B0F7101A05663700FCC711\"\n            BuildableName = \"Cadabra.app\"\n            BlueprintName = \"Cadabra\"\n            ReferencedContainer = \"container:Cadabra.xcodeproj\">\n         </BuildableReference>\n      </BuildableProductRunnable>\n   </ProfileAction>\n   <AnalyzeAction\n      buildConfiguration = \"Debug\">\n   </AnalyzeAction>\n   <ArchiveAction\n      buildConfiguration = \"Release\"\n      revealArchiveInOrganizer = \"YES\">\n   </ArchiveAction>\n</Scheme>\n"
  },
  {
    "path": "frontend/osx/Cadabra/Cadabra.xcodeproj/xcuserdata/kasper.xcuserdatad/xcschemes/xcschememanagement.plist",
    "content": "<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n<!DOCTYPE plist PUBLIC \"-//Apple//DTD PLIST 1.0//EN\" \"http://www.apple.com/DTDs/PropertyList-1.0.dtd\">\n<plist version=\"1.0\">\n<dict>\n\t<key>SchemeUserState</key>\n\t<dict>\n\t\t<key>Cadabra.xcscheme</key>\n\t\t<dict>\n\t\t\t<key>orderHint</key>\n\t\t\t<integer>0</integer>\n\t\t</dict>\n\t</dict>\n\t<key>SuppressBuildableAutocreation</key>\n\t<dict>\n\t\t<key>A7B0F7101A05663700FCC711</key>\n\t\t<dict>\n\t\t\t<key>primary</key>\n\t\t\t<true/>\n\t\t</dict>\n\t\t<key>A7B0F7231A05663700FCC711</key>\n\t\t<dict>\n\t\t\t<key>primary</key>\n\t\t\t<true/>\n\t\t</dict>\n\t</dict>\n</dict>\n</plist>\n"
  },
  {
    "path": "frontend/osx/Cadabra/CadabraTests/CadabraTests.m",
    "content": "//\n//  CadabraTests.m\n//  CadabraTests\n//\n//  Created by Kasper Peeters on 01/11/2014.\n//  Copyright (c) 2014 phi-sci. All rights reserved.\n//\n\n#import <Cocoa/Cocoa.h>\n#import <XCTest/XCTest.h>\n\n@interface CadabraTests : XCTestCase\n\n@end\n\n@implementation CadabraTests\n\n- (void)setUp {\n    [super setUp];\n    // Put setup code here. This method is called before the invocation of each test method in the class.\n}\n\n- (void)tearDown {\n    // Put teardown code here. This method is called after the invocation of each test method in the class.\n    [super tearDown];\n}\n\n- (void)testExample {\n    // This is an example of a functional test case.\n    XCTAssert(YES, @\"Pass\");\n}\n\n- (void)testPerformanceExample {\n    // This is an example of a performance test case.\n    [self measureBlock:^{\n        // Put the code you want to measure the time of here.\n    }];\n}\n\n@end\n"
  },
  {
    "path": "frontend/osx/Cadabra/CadabraTests/Info.plist",
    "content": "<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n<!DOCTYPE plist PUBLIC \"-//Apple//DTD PLIST 1.0//EN\" \"http://www.apple.com/DTDs/PropertyList-1.0.dtd\">\n<plist version=\"1.0\">\n<dict>\n\t<key>CFBundleDevelopmentRegion</key>\n\t<string>en</string>\n\t<key>CFBundleExecutable</key>\n\t<string>$(EXECUTABLE_NAME)</string>\n\t<key>CFBundleIdentifier</key>\n\t<string>$(PRODUCT_BUNDLE_IDENTIFIER)</string>\n\t<key>CFBundleInfoDictionaryVersion</key>\n\t<string>6.0</string>\n\t<key>CFBundleName</key>\n\t<string>$(PRODUCT_NAME)</string>\n\t<key>CFBundlePackageType</key>\n\t<string>BNDL</string>\n\t<key>CFBundleShortVersionString</key>\n\t<string>1.0</string>\n\t<key>CFBundleSignature</key>\n\t<string>????</string>\n\t<key>CFBundleVersion</key>\n\t<string>1</string>\n</dict>\n</plist>\n"
  },
  {
    "path": "frontend/osx/Cadabra/NotebookController.h",
    "content": "//\n//  NotebookController.h\n//  Cadabra\n//\n//  Created by Kasper Peeters on 31/01/2015.\n//  Copyright (c) 2015 phi-sci. All rights reserved.\n//\n\n\n#import <Cocoa/Cocoa.h>\n\n@interface NotebookController : NSViewController {\n}\n\n@property (weak) IBOutlet NSTextField  *status_label;\n@property (weak) IBOutlet NSScrollView *scrollbox;\n\n@end\n"
  },
  {
    "path": "frontend/osx/Cadabra/NotebookController.mm",
    "content": "//\n//  NotebookController.m\n//  Cadabra\n//\n//  Created by Kasper Peeters on 31/01/2015.\n//  Copyright (c) 2015 phi-sci. All rights reserved.\n//\n\n#import \"NotebookController.h\"\n#include <thread>\n#include \"ComputeThread.hh\"\n#include \"NotebookWindow.hh\"\n\n@interface NotebookController ()\n\n@end\n\n@implementation NotebookController {\n    \n    cadabra::NotebookWindow *nw;\n    cadabra::ComputeThread  *compute;\n    std::thread             *compute_thread;\n}\n\n- (void)loadView {\n    BOOL ownImp = ![NSViewController instancesRespondToSelector:@selector(readySetGo)];\n    \n    [super loadView];\n    \n    if(ownImp) {\n        [self readySetGo];\n    }\n}\n\n-(void)readySetGo\n{\n   \n    [_status_label setStringValue:@\"Ready\"];\n    \n    nw = new cadabra::NotebookWindow(self);\n    \n    compute        = new cadabra::ComputeThread(nw, *nw);\n    compute_thread = new std::thread(&cadabra::ComputeThread::run, compute);\n    \n    nw->set_compute_thread(compute);\n}\n\n\n@end\n"
  },
  {
    "path": "frontend/osx/fake.cc",
    "content": "int main(int, char **)\n\t{\n\t}\n"
  },
  {
    "path": "frontend/qt5/README.txt",
    "content": "This folder does NOT YET contain a functional Cadabra frontend.\n\nhttp://doc.qt.io/qt-5/qtwidgets-layouts-dynamiclayouts-example.html\n"
  },
  {
    "path": "frontend/web/CMakeLists.txt",
    "content": "\n# Cadabra for the web.\n\ncmake_minimum_required(VERSION 3.5)\n\nproject(CadabraWeb)\n\nif(${CMAKE_VERSION} VERSION_LESS \"3.8.0\")\n\tmessage(STATUS \"Using C++14 as you are using CMake < 3.8, consider upgrading as future versions of Cadabra may use C++17 features)\n\tset(CMAKE_CXX_STANDARD 14)\nelse()\n\tset(CMAKE_CXX_STANDARD 17)\nendif()\n\nif(NOT \"${CMAKE_SYSTEM_NAME}\" STREQUAL \"Emscripten\")\n  message(FATAL_ERROR\n\t \"Emscripten toolchain not active, \"\n    \"system name is ${CMAKE_SYSTEM_NAME}, \"\n\t \"did you 'source ${EMSDK}/emsdk_env.sh' \"\n\t \"and use the correct CMAKE_TOOLCHAIN_FILE:\"\n    \"-DCMAKE_TOOLCHAIN_FILE=${EMSCRIPTEN}/cmake/Modules/Platform/Emscripten.cmake\"\n\t )\nelse()\n  message(STATUS \"Emscripten active, good.\")\nendif()\n\n\n#----------------------------------------------------------------------------------------------\n# Building the native (C++) part of the app.\n#----------------------------------------------------------------------------------------------\n\nset(SOURCES\n  ../../core/DataCell.cc\n  ../../client_server/DocumentThread.cc\n  src/NotebookWindow.cc\n  )\n\ninclude_directories(\n  ../../libs/jsoncpp\n  ../../libs/internal/include\n  ../../core\n  ../../client_server\n  )\n\nadd_executable(cadabra ${SOURCES})\n"
  },
  {
    "path": "frontend/web/Makefile",
    "content": "\n.PHONY: docker\n\n# Prepare a tarball with \ndocker-prepare:\n\t(cd ../..; git archive --format=tar.gz --prefix=cadabra2/ web > frontend/web/docker/master.tar.gz)\n\ndocker-build:\n\tdocker build -t kpeeters/cadabra2:master --force-rm docker\n\ndocker-run:\n\tdocker run -t -i --expose=80 -P kpeeters/cadabra2:master /bin/bash\n\n"
  },
  {
    "path": "frontend/web/README.md",
    "content": "\nCadabraWeb\n==========\n\n\nCadabraWeb consists of two parts: a server part written in Python, and\na client part which is mostly C++ compiled for the web using\nEmscripten, with some thin Javascript glue to bind it together.\n\nWhy not JupyterLab?\n-------------------\n\nI do not agree with the philosophy behind JupyterLab. It duplicates\nloads of things for which I already have perfect solutions: text\neditor, terminal window, file manager, window manager. For people who\ndo not want to install anything except a browser on their own machine,\nit is no doubt a useful tool. But for people who are not afraid to\nuse a reasonably standard Linux or macOS machine, JupyterLab simply\nimplements a lot of functionality which is already available, often in\na much better form.\n\nSo CadabraWeb takes the approach that the notebook tool should only do\nthat: let you interact with notebooks. Everything else, like editing\ntext, running commands in a terminal, managing files or windows,\nbelongs elsewhere.\n\n\n\nBuilding the server\n-------------------\n\n# Create the docker instance\n\nDo `make docker-prepare` to create the source tarball, `make docker`\nto create the docker image.\n\n\n# Create the server\n\nThe server is a simple python program which requires no separate\nbuilding, just run `src/server.py`.\n\n\nBuilding the client\n-------------------\n\nFor the client you need an installation of emscripten. Activate it by\ndoing::\n\n    source emsdk_env.sh\n    \nin the top-level emscripten directory. After that, build the client\nwith::\n\n    mkdir build\n    cd build\n    cmake .. \\\n       -DCMAKE_TOOLCHAIN_FILE=${EMSCRIPTEN}/cmake/Modules/Platform/Emscripten.cmake\n    make\n    \n\n    \n    \n"
  },
  {
    "path": "frontend/web/css/cadabra.css",
    "content": "textarea {\n    border-style: none;\n    border-left: 2px solid blue;\n    padding-left: 10px;\n    width: 100%;\n    resize: none;\n    overflow: hidden;\n    font-family: monospace;\n    color: blue;\n    font-size: 14px;\n    padding-top: 4px;\n    padding-bottom: 4px;\n}\n.MathJax { \n    text-align: left !important;\n    margin-left: 15px !important;\n}\n"
  },
  {
    "path": "frontend/web/docker/.gitignore",
    "content": "master.tar.gz\n"
  },
  {
    "path": "frontend/web/docker/Dockerfile",
    "content": "# our base image\nFROM library/debian\n#continuumio/miniconda3\nLABEL maintainer=\"info@cadabra.science\"\n\nADD master.tar.gz /tmp\nRUN adduser --disabled-password cadabra && apt update && apt install -y cmake g++ pkg-config \\\n                      python3-dev python3-sympy \\\n                      libgmp3-dev \\\n                      libglibmm-2.4-dev \\\n                      libboost-system-dev \\\n                      libboost-program-options-dev \\\n                      libboost-date-time-dev \\\n                      libboost-filesystem-dev \\\n                      libgmp-dev libsqlite3-dev uuid-dev && rm -rf /var/lib/apt/lists/* && \\\n    cd /tmp/cadabra2 && mkdir build && cd build && cmake -DENABLE_FRONTEND=OFF .. && make -j4 && make install && \\\n    rm -Rf /tmp/cadabra2\n# RUN apt remove -y     cmake g++ pkg-config \\\n#                       libgmp3-dev \\\n#                       libglibmm-2.4-dev \\\n#                       libboost-system-dev \\\n#                       libboost-program-options-dev \\\n#                       libboost-date-time-dev \\\n#                       libboost-filesystem-dev \\\n#                       libgmp-dev libsqlite3-dev uuid-dev \n\n#COPY cadabra-server /usr/bin/cadabra-server\n\n# Start the Cadabra server on port 32768, do not exit process\nCMD [\"su\", \"-\", \"cadabra\", \"-c\", \"/usr/local/bin/cadabra-server 32768 0\"]\n\nEXPOSE 32768\n "
  },
  {
    "path": "frontend/web/html/index.html",
    "content": "<html>\n  <head>\n    <script src=\"https://polyfill.io/v3/polyfill.min.js?features=es6\"></script>\n    <script id=\"MathJax-script\"\n            async\n            src=\"https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js\"></script>\n    <script\n      src=\"https://code.jquery.com/jquery-3.5.1.min.js\"\n      integrity=\"sha256-9/aliU8dGd2tb6OSsuzixeV4y/faTqgFtohetphbbj0=\"\n      crossorigin=\"anonymous\"></script>\n    <script src=\"js/cadabra.js\"></script>\n    <link rel=\"stylesheet\" type=\"text/css\" href=\"css/cadabra.css\" />\n  </head>\n  <body>\n    {{ title }}\n    <input id=\"start\" type=\"button\" value=\"connect\"></input>\n\n    <div id=\"notebook\">\n    </div>\n  </body>\n</html>\n"
  },
  {
    "path": "frontend/web/js/cadabra.js",
    "content": "\nvar ws=null;\nvar token=\"\";\n\nvar evaluate_cell = function(txt) {\n    req = {};\n    header = {};\n    content = {};\n    header[\"uuid\"]=\"none\";\n    header[\"cell_id\"]=1;\n    header[\"cell_origin\"]=\"client\";\n    header[\"msg_type\"]=\"execute_request\";\n    content[\"code\"]=txt;\n    req[\"auth_token\"]=token;\n    req[\"header\"]=header;\n    req[\"content\"]=content;\n    console.log(req);\n    ws.send(JSON.stringify(req));\n};\n\nvar init_notebook = function() {\n    $(\"#notebook\").on('keypress', function(event) {\n        if(event.originalEvent.shiftKey && event.originalEvent.charCode==13) {\n            event.preventDefault();\n            let val = $(event.target).val();\n            if(val!=\"\") {\n                console.log(\"Sending \"+val);\n                evaluate_cell(val);\n            }\n        }\n    });\n    add_cell();\n};\n\nvar add_cell = function() {\n    cell_id = Math.floor((Math.random() * 100000) + 1);\n    $(\"<div id='\"+cell_id+\"' class='cell'></div>\")\n        .appendTo(\"#notebook\")\n        .append(\"<textarea></textarea>\");\n    $(\"#\"+cell_id+\" textarea\").on(\"keydown keyup\", function(){\n        this.style.height = \"1px\";\n        this.style.height = (this.scrollHeight+2) + \"px\"; \n    }).focus();\n};\n\nvar connect_to_kernel = function() {\n    if(ws!=null) return;\n    \n    let url=\"ws:\"+window.location.origin.substr(window.location.protocol.length)+\"/ws\";\n    console.log(url);\n    ws = new WebSocket(url);\n    ws.onopen = function() {\n        console.log(\"Connection to Cadabra server open.\");\n        init_notebook();\n    };\n    ws.onmessage = function(wsm) {\n        console.log(\"Received message from server.\");\n        let msg=JSON.parse(wsm.data);\n        console.log(msg);\n        if(msg[\"header\"][\"msg_type\"]==\"hello\") {\n            token=msg[\"header\"][\"token\"];\n            console.log(token);\n        }\n        if(msg[\"msg_type\"]==\"latex_view\") {\n            ltx=msg[\"content\"][\"output\"];\n            cell_id=msg[\"header\"][\"cell_id\"];\n            ltx=ltx.replace(\"\\\\begin{dmath*}\", \"\").replace(\"\\\\end{dmath*}\", \"\");\n            $(\"#notebook\").append(\"<div id='\"+cell_id+\"' class='latex'>$$\"+ltx+\"$$</div>\");\n            selec=\"#\"+cell_id;\n            console.log(selec);\n            MathJax.typesetPromise($(selec));\n        }\n        if(msg[\"msg_type\"]==\"output\" && msg[\"header\"][\"last_in_sequence\"])\n            add_cell();\n    };\n    ws.onclose = function() {\n        console.log(\"Connection to Cadabra server closed.\");\n    };\n    ws.onerror = function() {\n        console.log(\"Error in connection to Cadabra server.\");\n    };\n};\n\n$(document).ready( function() {\n    $(\"#start\").click( function() {\n        connect_to_kernel();\n    });\n});\n"
  },
  {
    "path": "frontend/web/src/NotebookWindow.cc",
    "content": "\n\n#include \"NotebookWindow.hh\"\n"
  },
  {
    "path": "frontend/web/src/NotebookWindow.hh",
    "content": "\n#include \"DocumentThread.hh\"\n#include \"GUIBase.hh\"\n\nnamespace cadabra {\n\n\t/// \\ingroup frontend\n\t///\n\t///\n\n\tclass NotebookWindow : public DocumentThread, public GUIBase {\n\t\t\t\n\t};\n\n\t};\n"
  },
  {
    "path": "frontend/web/src/server.py",
    "content": "import docker\nimport tornado.websocket\nimport tornado.ioloop\nimport tornado.web\nimport json\n\n\nclass CadabraHub(tornado.web.RequestHandler):\n    def get(self):\n        self.render(\"index.html\", title=\"Cadabra2\")\n\n\nclass CadabraProxy(tornado.websocket.WebSocketHandler):\n    def open(self, *args, **kwargs):\n        print(\"WebSocket opened\")\n        res = self.start_cadabra_server()\n        print(res)\n        self.cdb_data=res\n        msg={\"header\": {\"msg_type\": \"hello\", \"token\": res[\"token\"]}}\n        self.write_message(json.dumps(msg))\n        url = \"ws://localhost:\"+str(res[\"port\"])\n        print(url)\n        self.cdb_data[\"conn_fut\"] = tornado.websocket.websocket_connect(url, on_message_callback=self.on_cdb_message)\n        self.cdb_data[\"conn_fut\"].add_done_callback(self.on_cdb_connected)\n\n    # Handler for messages which come in from the browser app and need to be\n    # forwarded to the kernel.\n    \n    def on_message(self, message):\n        print(\"message from \"+str(self.cdb_data))\n        print(message)\n#        self.write_message(u\"You said: \" + message)\n        if \"conn\" in self.cdb_data:\n            self.cdb_data[\"conn\"].write_message(message)\n        else:\n            print(\"Received before kernel connected\")\n\n    def on_close(self):\n        print(\"WebSocket for \"+str(self.cdb_data)+\" closed\")\n        self.cdb_data[\"container\"].stop()\n\n    def on_cdb_connected(self, fut):\n        print(\"Websocket to kernel connected\")\n        conn = fut.result()\n        self.cdb_data[\"conn\"]=conn\n#         req = {}\n#         header = {}\n#         content = {}\n#         header[\"uuid\"]=\"none\"\n#         header[\"cell_id\"]=1\n#         header[\"cell_origin\"]=\"client\"\n#         header[\"msg_type\"]=\"execute_request\"\n#         content[\"code\"]=\"ex:= A_{m n};\"\n#         req[\"auth_token\"]=self.cdb_data[\"token\"]\n#         req[\"header\"]=header\n#         req[\"content\"]=content\n#         conn.write_message(json.dumps(req))\n        \n    def on_cdb_message(self, msg):\n        #print(\"Received message from cdb kernel\")\n        #print(str(msg))\n        if msg!=None:\n            # Forward to the browser.\n            # First change any header/cell_id to a string to prevent\n            # Javascript from rounding it...\n            jmsg=json.loads(msg)\n            jmsg[\"header\"][\"cell_id\"]=str(jmsg[\"header\"][\"cell_id\"])\n            self.write_message(json.dumps(jmsg))\n        \n    def start_cadabra_server(self):\n        \"\"\" Start a Cadabra server in a docker container.\n            Returns a port and authentication token.\n        \"\"\"\n        client=docker.from_env()\n        container = client.containers.run(\"kpeeters/cadabra2:master\",\n                                          ports={'32768/tcp': None},\n                                          detach=True,\n                                          auto_remove=True)\n        container.reload()\n        nws = container.attrs[\"NetworkSettings\"]\n        pfw = nws[\"Ports\"][\"32768/tcp\"]\n        port = pfw[0][\"HostPort\"]\n        print(\"Cadabra port at\", port)\n        out = container.logs(stream=True)\n        i=0\n        tok=\"\"\n        for line in out:\n            tok=line\n            if i==1:\n                break\n            i+=1\n        tok=tok.decode(\"utf-8\") \n        tok=tok.rstrip(\"\\n\")\n        print(\"Authentication token\", tok)\n        return { \"port\": port, \"token\": tok, \"container\": container };\n\n\n#print(client.containers.list())    \n#print(client.images.list())\n#start()\n\n\nif __name__ == \"__main__\":\n    app =  tornado.web.Application([\n        (r\"/\",   CadabraHub),\n        (r\"/ws\", CadabraProxy),\n        (r\"/js/(.*)\",\n         tornado.web.StaticFileHandler,\n         {'path': '../js/'}),\n        (r\"/css/(.*)\",\n         tornado.web.StaticFileHandler,\n         {'path': '../css/'})\n    ])\n    app.settings[\"template_path\"]=\"../html\"\n    app.listen(8888)\n    tornado.ioloop.IOLoop.current().start()\n"
  },
  {
    "path": "jupyterkernel/.gitignore",
    "content": "kernelspec/kernel.json\ncadabra2_jupyter/__init__.py\n"
  },
  {
    "path": "jupyterkernel/CMakeLists.txt",
    "content": "cmake_minimum_required(VERSION ${CADABRA_CMAKE_VERSION})\nproject(Cadabra)\n\n\nconfigure_file(\n\t\"${CMAKE_CURRENT_SOURCE_DIR}/kernelspec/kernel.json.in\"\n\t\"${CMAKE_CURRENT_SOURCE_DIR}/kernelspec/kernel.json\"\n)\nconfigure_file(\n\t\"${CMAKE_CURRENT_SOURCE_DIR}/cadabra2_jupyter/__init__.py.in\"\n\t\"${CMAKE_CURRENT_SOURCE_DIR}/cadabra2_jupyter/__init__.py\"\n)\n\ninstall(FILES\n   kernelspec/kernel.json\n   kernelspec/logo-32x32.png\n   kernelspec/logo-64x64.png\n   DESTINATION\n   share/jupyter/kernels/cadabra2\n   )\n\ninstall(FILES\n   cadabra2_jupyter/__init__.py\n   cadabra2_jupyter/__main__.py\n   cadabra2_jupyter/context.py\n   cadabra2_jupyter/completer.py\n   cadabra2_jupyter/kernel.py\n   cadabra2_jupyter/server.py\n   DESTINATION\n   \"${PYTHON_SITE_PATH}/cadabra2_jupyter\"\n   )\n\ninstall(FILES\n  lexer/cadabra.js\n  DESTINATION\n  \"${PYTHON_SITE_PATH}/notebook/static/components/codemirror/mode/cadabra\"\n  )\n"
  },
  {
    "path": "jupyterkernel/cadabra2_jupyter/__init__.py.in",
    "content": "__version__ = \"@CADABRA_VERSION_SEM@\"\n\n"
  },
  {
    "path": "jupyterkernel/cadabra2_jupyter/__main__.py",
    "content": "from ipykernel.kernelapp import IPKernelApp\nfrom cadabra2_jupyter.kernel import CadabraJupyterKernel\n\nif __name__ == \"__main__\":\n    IPKernelApp.launch_instance(kernel_class=CadabraJupyterKernel)\n"
  },
  {
    "path": "jupyterkernel/cadabra2_jupyter/completer.py",
    "content": "\"\"\" keywords scraped from cadabra.science/man.html \"\"\"\n\nproperties = [\n    \"Accent\",\n    \"AntiCommuting\",\n    \"AntiSymmetric\",\n    \"Commuting\",\n    \"CommutingAsProduct\",\n    \"CommutingAsSum\",\n    \"Coordinate\",\n    \"DAntiSymmetric\",\n    \"Depends\",\n    \"Derivative\",\n    \"Determinant\",\n    \"Diagonal\",\n    \"DiracBar\",\n    \"EpsilonTensor\",\n    \"FilledTableau\",\n    \"GammaMatrix\",\n    \"ImplicitIndex\",\n    \"IndexInherit\",\n    \"Indices\",\n    \"Integer\",\n    \"InverseMetric\",\n    \"KroneckerDelta\",\n    \"LaTeXForm\",\n    \"Metric\",\n    \"NonCommuting\",\n    \"PartialDerivative\",\n    \"RiemannTensor\",\n    \"SatisfiesBianchi\",\n    \"SelfAntiCommuting\",\n    \"SelfCommuting\",\n    \"SelfNonCommuting\",\n    \"SortOrder\",\n    \"Spinor\",\n    \"Symbol\",\n    \"Symmetric\",\n    \"Tableau\",\n    \"TableauSymmetry\",\n    \"WeightInherit\",\n]\n\n\nimport re\nimport string\n\n\nclass CodeCompleter:\n    def __init__(self, kernel):\n        self._kernel = kernel\n        self.code = \"\"\n\n    @property\n    def triggers(self):\n        return string.ascii_letters + \":;.\"\n\n    def get_last_word(self):\n        return re.compile(r\"[\\W\\s]\").split(self.code)[-1]\n\n    def cursor_on_property(self, last):\n        search_query = re.compile(\".*::{}$\".format(last), re.MULTILINE)\n        return re.search(search_query, self.code)\n\n    def match(self, last, options):\n        opts = list(filter(lambda i: re.match(\"^{}.*\".format(last), i), options))\n        # return options and length of the last matched word\n        return opts, len(last)\n\n    def match_member(self, last, klass):\n        \"\"\" matches last word in the namespace of the currently selected class \"\"\"\n        instance = self._kernel._sandbox_context._sandbox[klass]\n        #  filter out hidden namespace, unless typing hidden namespace\n        return self.match(last, (i for i in dir(instance) if \"__\" not in i))\n\n    def get_class(self):\n        \"\"\" get class currently behind cursor  \"\"\"\n        return re.findall(r\"(\\w+)\\.\\w*$\", self.code)\n\n    def __call__(self, code, cursor_pos, namespace):\n        # only choose up until current cursor position\n        self.code = code[:cursor_pos]\n\n        last = self.get_last_word()\n        matched_klass = self.get_class()\n\n        if self.cursor_on_property(last):\n            # cursor on cadabra property\n            if last:\n                return self.match(last, properties)\n            else:\n                return properties, 0\n\n        elif matched_klass and matched_klass[-1] in namespace:\n            # cursor on member function\n            return self.match_member(last, matched_klass[-1])\n        else:\n            return self.match(last, namespace)\n"
  },
  {
    "path": "jupyterkernel/cadabra2_jupyter/context.py",
    "content": "from io import StringIO\nimport sys, os\nimport cadabra2\n\n# super important\n__cdbkernel__ = cadabra2.__cdbkernel__\n\n#  setup stdout, stderr hook\nclass _StdCatch:\n    def __init__(self, kernel):\n        self._kernel = kernel\n\n    def __enter__(self):\n        sys.stdout = self.stdout = StringIO()\n        sys.stderr = self.stderr = StringIO()\n\n    def __exit__(self, exc_type, exc_val, exc_traceback):\n        sys.stdout = sys.__stdout__\n        sys.stderr = sys.__stderr__\n\n        for line in self.stdout.getvalue().splitlines():\n            # insert missing newline\n            self._kernel._send_code(line + \"\\n\")\n\n        # ignore exc_type reporting, since it always gives 'JSON serializable'\n        # error, echoing the same message as provided by the __stderr__ catch\n        for line in self.stderr.getvalue().splitlines():\n            # insert missing newline\n            self._kernel._send_error(line + \"\\n\")\n\n\nclass SandboxContext:\n    def __init__(self, kernel):\n        self._sandbox = {\n            \"server\": kernel._cdb_server,\n            \"__cdbkernel__\": cadabra2.__cdbkernel__,\n        }\n        # Since we have been able to `import cadabra2`, we know where\n        # that module is located. The `cadabra2_defaults.py` is at the\n        # same location.\n        with open(os.path.join(os.path.dirname(cadabra2.__file__), \"cadabra2_defaults.py\")) as f:\n            code = compile(f.read(), \"cadabra2_defaults.py\", \"exec\")\n        exec(code, self._sandbox)\n\n        self._kernel = kernel\n        self._context = _StdCatch(kernel)\n\n    def __call__(self, code):\n        # redefine, as is catastrophic if accidentally overwritten\n        self._sandbox[\"server\"] = self._kernel._cdb_server\n        with self._context:\n            exec(code, self._sandbox)\n\n    @property\n    def namespace(self):\n        return self._sandbox.keys()\n"
  },
  {
    "path": "jupyterkernel/cadabra2_jupyter/kernel.py",
    "content": "import ipykernel.kernelbase\nimport sys\nimport traceback\n\nimport cadabra2\nfrom cadabra2_jupyter.context import SandboxContext\nfrom cadabra2_jupyter.server import Server\nfrom cadabra2_jupyter.completer import CodeCompleter\nfrom cadabra2_jupyter import __version__\n\n# This is a simple 'Python wrapper kernel' along the lines of\n# https://jupyter-protocol.readthedocs.io/en/latest/wrapperkernels.html\n\nclass CadabraJupyterKernel(ipykernel.kernelbase.Kernel):\n    implementation = \"cadabra_kernel\"\n    implementation_version = __version__\n    language_info = {\n        \"name\": \"cadabra2\",\n        \"codemirror_mode\": \"cadabra\",\n        \"pygments_lexer\": \"cadabra\",\n        \"mimetype\": \"text/cadabra2\",\n        \"file_extension\": \".ipynb\",\n    }\n\n    @property\n    def banner(self):\n        return \"Cadabra (C) 2001-2025 Kasper Peeters\\nJupyter kernel by Fergus Baker and Kasper Peeters\\nMore info at https://cadabra.science/\\nAvailable under the terms of the GNU General Public License v3\"\n\n    def __init__(self, **kwargs):\n        ipykernel.kernelbase.Kernel.__init__(self, **kwargs)\n        self._parse_cadabra = cadabra2.cdb2python_string\n\n        # attach the server class for callbacks\n        self._cdb_server = Server(self)\n\n        # init the sandbox\n        self._sandbox_context = SandboxContext(self)\n\n        # init code completion\n        self._completer = CodeCompleter(self)\n\n    def do_execute(\n        self, code, silent, store_history=True, user_expressions=None, allow_stdin=False\n    ):\n        \"\"\" callback for iPython kernel: code execution \"\"\"\n        self.silent = silent\n        # check for blank input\n        if not code.strip():\n            return self._status_ok\n\n        interrupted = False\n\n        try:\n            #  main execution calls\n            errstr = \"\"\n            pycode = self._parse_cadabra(code, True, errstr)\n            self._execute_python(pycode)\n\n        except KeyboardInterrupt:\n            interrupted = True\n\n        except Exception as e:\n            # get traceback; not massively informative but can be useful\n            err_str = traceback.format_exc()\n            self._send_error(err_str)\n\n        if interrupted:\n            return {\"status\": \"abort\", \"execution_count\": self.execution_count}\n        else:\n            return self._status_ok\n\n    def do_complete(self, code, cursor_pos):\n        \"\"\" callback for iPython kernel: code completion \"\"\"\n\n        # if no code, or last character is whitespace\n        if not code or code[-1] not in self._completer.triggers:\n            return self._default_complete(cursor_pos)\n\n        # sandbox namespace\n        namespace = self._sandbox_context.namespace\n\n        options, rewind = self._completer(code, cursor_pos, namespace)\n        return {\n            \"matches\": sorted(options),\n            \"cursor_start\": cursor_pos - rewind,\n            \"cursor_end\": cursor_pos,\n            \"status\": \"ok\",\n            \"metadata\": dict(),\n        }\n\n    @property\n    def _status_ok(self):\n        return {\n            \"status\": \"ok\",\n            \"execution_count\": self.execution_count,\n            \"payload\": [],\n            \"user_expressions\": {},\n        }\n\n    def _default_complete(self, cursor_pos):\n        return {\n            \"matches\": [],\n            \"cursor_start\": 0,\n            \"cursor_end\": cursor_pos,\n            \"metadata\": dict(),\n            \"status\": \"ok\",\n        }\n\n    def _execute_python(self, pycode):\n        \"\"\" executes python code in the cadabra context \"\"\"\n        self._sandbox_context(pycode)\n\n    def _send_result(self, res_str):\n        self.send_response(\n            self.iopub_socket,\n            \"display_data\",\n            {\"data\": {\"text/markdown\": \"{}\".format(res_str)}, \"metadata\": {}},\n        )\n\n    def _send_image(self, img, img_type):\n        self.send_response(\n            self.iopub_socket,\n            \"display_data\",\n            {\"data\": {\"image/\"+img_type: \"{}\".format(img.decode(\"utf-8\"))}, \"metadata\": {}},\n        )\n\n    def _send_code(self, res_str):\n        self.send_response(\n            self.iopub_socket,\n            \"stream\",\n            {\"name\": \"stdout\", \"text\": res_str},\n        )\n\n    def _send_error(self, err_str):\n        self.send_response(\n            self.iopub_socket, \"stream\", {\"name\": \"stderr\", \"text\": err_str}\n        )\n"
  },
  {
    "path": "jupyterkernel/cadabra2_jupyter/server.py",
    "content": "import base64\n\ndef _latex_post_parser(text):\n    return (\n        text.replace(\"\\\\begin{dmath*}\", \"$\")\n        .replace(\"\\\\end{dmath*}\", \"$\")\n        .replace(\"\\\\discretionary{}{}{}\", \"\")\n        .replace(\"~\", \"\")\n    )\n\n\nclass Server:\n    def __init__(self, kernel_instance):\n        self._kernel = kernel_instance\n\n    def send(self, data, typestr, parent_id, cell_id, last_in_sequence):\n        if typestr == \"latex_view\":\n            data = _latex_post_parser(data)\n            self._kernel._send_result(data)\n        elif typestr == \"image_svg\":\n            self._kernel._send_image(base64.b64decode(data), \"svg+xml\")\n        elif typestr == \"image_png\":\n            self._kernel._send_image(data, \"png\")\n        elif typestr == \"verbatim\":\n            self._kernel._send_code(data)\n        elif typestr == \"input_form\":\n            #  pass\n            ...\n        else:\n            raise Exception(\"Unknown typestr '{}'\".format(typestr))\n        return 0\n\n    def architecture(self):\n        return \"jupyter-kernel\"\n\n    def test(self):\n        self._kernel._send_result(\"Test: We've gone on holiday by mistake!\")\n\n    def handles(self, otype):\n        if otype == \"latex_view\" or otype == \"image_png\" or otype==\"image_svg\" or otype == \"verbatim\":\n            return True\n        return False\n\n    def totals(self):\n        # what does this do?\n        return -1\n"
  },
  {
    "path": "jupyterkernel/kernelspec/kernel.json.in",
    "content": "{\n  \"argv\": [\n     \"@Python_EXECUTABLE@\", \"-Xfrozen_modules=off\", \"-m\", \"cadabra2_jupyter\", \"-f\", \"{connection_file}\"\n  ],\n  \"display_name\":\"Cadabra2\",\n  \"language\":\"python\"\n}\n"
  },
  {
    "path": "jupyterkernel/lexer/cadabra.js",
    "content": "// CodeMirror, copyright (c) by Marijn Haverbeke and others\n// Distributed under an MIT license: https://codemirror.net/LICENSE\n\n// Adapted by Fergus Baker for Cadabra 2 (c) Kasper Peeters\n\n(function(mod) {\n  if (typeof exports == \"object\" && typeof module == \"object\") // CommonJS\n    mod(require(\"../../lib/codemirror\"));\n  else if (typeof define == \"function\" && define.amd) // AMD\n    define([\"../../lib/codemirror\"], mod);\n  else // Plain browser env\n    mod(CodeMirror);\n})(function(CodeMirror) {\n  \"use strict\";\n\n  // lexing starts here!\n  CodeMirror.defineMode('cadabra', function(cfg, cfg_parser) {\n    // use the python code mirror mode\n    var pythonmode = CodeMirror.getMode(cfg, {name:'python'});\n\n    function isWhitespace(char) {\n      return !(char) || char == ' ' || char == '\\n' || char == '\\t'\n    }\n\n    function eatWord(stream) {\n      var count = 0;\n      while(stream.eat(/[\\w\\d]+/g)){\n        // eat word\n        count++;\n      }\n      return count;\n    }\n\n    function cadabraToken(stream, state) {\n      // big long basic if/else parser\n\n      // get current token string\n      var current = stream.current();\n\n      // ignore if string; use lookbehind to see if escaped\n      if (current.match(/^(?<!\\\\)\".*(?<!\\\\)\"/g)) {\n        return 'python';\n      }\n\n      if (current.match(/#/)) {\n        // lines containing '::' or ':=' must be escaped\n        // controlled by the state.allow_comments\n        if (state.allow_comments && (! current.match(/(::|:=)/g) || stream.indentation() == stream.column() )) {\n          // python comment\n          return 'python';\n        } else {\n          // escape python comments\n          stream.backUp(current.length-1);\n          return \"operator\";\n        }\n      }\n      else if (current.match(/\\?/g)) {\n        return 'operator';\n      }\n      else if (current.match(/:/g)) {\n        // don't indent; have to update scopes\n\n        if (stream.peek() == ':') {\n          // handle property assign operator\n          state.lastToken=\"::\"\n          state.scopes.pop();\n\n          // modify state for cadabra comments\n          state.allow_comments = false;\n\n          // consume second :\n          stream.next();\n          // eat property\n          eatWord(stream);\n          return 'builtin';\n        } else if (stream.peek() == '=') {\n          // handle walrus assign operator\n          state.lastToken=\":=\"\n          state.scopes.pop();\n\n          // modify state for cadabra comments\n          state.allow_comments = false;\n\n          // consume = \n          stream.next();\n          return 'operator';\n\n        } else return 'python';\n      }\n      else if (current.match(/[.;]$/gm)) {\n        if ( isWhitespace(stream.peek()) ) {\n          return 'operator';\n        }\n      }\n      else if (current.match(/_/g)) {\n        // handle lowering indices operator\n        // ensure stream not in variable\n        if (current.length > 1) {\n          stream.backUp(1);\n          return null;\n        }\n        if (stream.peek() == '{') {\n          return 'operator'\n        }\n      }\n      else if (current.match(/\\$/g)) {\n        // cadabra lambdas\n        return 'def';\n      }\n      else if (current.match(/\\\\/)) {\n        var count = eatWord(stream);\n        current = stream.current();\n        if (current.match(/(lambda|int)/g)) {\n          return null;\n        } else {\n          stream.backUp(count);\n          return 'python';\n        }\n\n      }\n      else {\n        // leave alone\n        return 'python';\n      }\n    }\n\n    // global multiline match triggers; this could probably be done more\n    // efficiently with doing explicit checks for positioning, but this code\n    // doesn't need to run particularly fast, so for convenience\n    // grouping together\n    const triggers = /[\\?:#_;.$\\\\]/gm\n\n    return {\n      startState: () => {\n        // init python mode, cadabra mode adds allow_comments to state\n        var init_state = pythonmode.startState();\n        init_state.allow_comments = true;\n        return init_state;\n      },\n      token: (stream, state) => {\n        // clear stored cadabra state\n        if (stream.sol()) {\n          state.allow_comments = true;\n        }\n\n        var ret = pythonmode.token(stream, state);\n\n        // cadabra parse if triggered\n        if (stream.current().match(triggers)) {\n          var cdb_ret = cadabraToken(stream, state);\n          ret = cdb_ret !== 'python' ? cdb_ret : ret;\n        }\n        return ret;\n      },\n      indent: (state, textAfter) => {\n        // so that properties don't indent oddly\n\n        if (state.lastToken == '::') return 0;\n\n        // let python handle indents\n        return pythonmode.indent(state, textAfter);\n      }\n    }\n  });\n    CodeMirror.defineMIME(\"text/cadabra2\", \"cadabra\");\n});\n"
  },
  {
    "path": "jupyterkernel/lexer/cadabra.py",
    "content": "\"\"\" very basic implementation of a pygments lexer for Cadabra2 \"\"\"\n\nfrom pygments.lexers import PythonLexer\nimport pygments.token as token\n\n__all__ = [\"CadabraLexer\"]\n\nCADABRA_ROOT = [\n    (r\"::[\\w\\d]*\", token.Keyword), # property attaches\n    (r\"\\S#}.*\", token.Text), # some comment exceptions\n    (r\"[;.(:=)]\\s*$\", token.Operator) # ; . operators\n] + Python3Lexer.tokens['root']\n\nclass CadabraLexer(PythonLexer):\n    name=\"Cadabra\",\n    aliases=[\"cadabra\",\"cadabra2\"]\n    filenames=\"*.cdb\"\n\n    tokens = {\n        **Python3Lexer.tokens,\n        **{'root':CADABRA_ROOT}\n    }\n"
  },
  {
    "path": "jupyterkernel/readme.txt",
    "content": "Py-Jupyter Cadabra2 Kernel\n\nFeatures:\n  - latex filtered output\n  - syntax highlighting and indentation with CodeMirror\n  - code completion on tab press\n  - sandboxed and sequential execution\n\nTodo:\n  - images/figures\n  - code inspection with ? (at the moment can only use `help`)\n  - input html widgets\n  - neaten lexers; momentarily written as learning so not very clean\n  - magic commands for kernel control \n"
  },
  {
    "path": "libs/appdirs/cdb_appdirs.py",
    "content": "#!/usr/bin/env python\n# -*- coding: utf-8 -*-\n# Copyright (c) 2005-2010 ActiveState Software Inc.\n# Copyright (c) 2013 Eddy Petrișor\n\n\"\"\"Utilities for determining application-specific dirs.\n\nSee <https://github.com/ActiveState/appdirs> for details and usage.\n\"\"\"\n# Dev Notes:\n# - MSDN on where to store app data files:\n#   http://support.microsoft.com/default.aspx?scid=kb;en-us;310294#XSLTH3194121123120121120120\n# - Mac OS X: http://developer.apple.com/documentation/MacOSX/Conceptual/BPFileSystem/index.html\n# - XDG spec for Un*x: https://standards.freedesktop.org/basedir-spec/basedir-spec-latest.html\n\n__version__ = \"1.4.4\"\n__version_info__ = tuple(int(segment) for segment in __version__.split(\".\"))\n\n\nimport sys\nimport os\n\nPY3 = sys.version_info[0] == 3\n\nif PY3:\n    unicode = str\n\nif sys.platform.startswith('java'):\n    import platform\n    os_name = platform.java_ver()[3][0]\n    if os_name.startswith('Windows'): # \"Windows XP\", \"Windows 7\", etc.\n        system = 'win32'\n    elif os_name.startswith('Mac'): # \"Mac OS X\", etc.\n        system = 'darwin'\n    else: # \"Linux\", \"SunOS\", \"FreeBSD\", etc.\n        # Setting this to \"linux2\" is not ideal, but only Windows or Mac\n        # are actually checked for and the rest of the module expects\n        # *sys.platform* style strings.\n        system = 'linux2'\nelse:\n    system = sys.platform\n\n\n\ndef user_data_dir(appname=None, appauthor=None, version=None, roaming=False):\n    r\"\"\"Return full path to the user-specific data dir for this application.\n\n        \"appname\" is the name of application.\n            If None, just the system directory is returned.\n        \"appauthor\" (only used on Windows) is the name of the\n            appauthor or distributing body for this application. Typically\n            it is the owning company name. This falls back to appname. You may\n            pass False to disable it.\n        \"version\" is an optional version path element to append to the\n            path. You might want to use this if you want multiple versions\n            of your app to be able to run independently. If used, this\n            would typically be \"<major>.<minor>\".\n            Only applied when appname is present.\n        \"roaming\" (boolean, default False) can be set True to use the Windows\n            roaming appdata directory. That means that for users on a Windows\n            network setup for roaming profiles, this user data will be\n            sync'd on login. See\n            <http://technet.microsoft.com/en-us/library/cc766489(WS.10).aspx>\n            for a discussion of issues.\n\n    Typical user data directories are:\n        Mac OS X:               ~/Library/Application Support/<AppName>\n        Unix:                   ~/.local/share/<AppName>    # or in $XDG_DATA_HOME, if defined\n        Win XP (not roaming):   C:\\Documents and Settings\\<username>\\Application Data\\<AppAuthor>\\<AppName>\n        Win XP (roaming):       C:\\Documents and Settings\\<username>\\Local Settings\\Application Data\\<AppAuthor>\\<AppName>\n        Win 7  (not roaming):   C:\\Users\\<username>\\AppData\\Local\\<AppAuthor>\\<AppName>\n        Win 7  (roaming):       C:\\Users\\<username>\\AppData\\Roaming\\<AppAuthor>\\<AppName>\n\n    For Unix, we follow the XDG spec and support $XDG_DATA_HOME.\n    That means, by default \"~/.local/share/<AppName>\".\n    \"\"\"\n    if system == \"win32\":\n        if appauthor is None:\n            appauthor = appname\n        const = roaming and \"CSIDL_APPDATA\" or \"CSIDL_LOCAL_APPDATA\"\n        path = os.path.normpath(_get_win_folder(const))\n        if appname:\n            if appauthor is not False:\n                path = os.path.join(path, appauthor, appname)\n            else:\n                path = os.path.join(path, appname)\n    elif system == 'darwin':\n        path = os.path.expanduser('~/Library/Application Support/')\n        if appname:\n            path = os.path.join(path, appname)\n    else:\n        path = os.getenv('XDG_DATA_HOME', os.path.expanduser(\"~/.local/share\"))\n        if appname:\n            path = os.path.join(path, appname)\n    if appname and version:\n        path = os.path.join(path, version)\n    return path\n\n\ndef site_data_dir(appname=None, appauthor=None, version=None, multipath=False):\n    r\"\"\"Return full path to the user-shared data dir for this application.\n\n        \"appname\" is the name of application.\n            If None, just the system directory is returned.\n        \"appauthor\" (only used on Windows) is the name of the\n            appauthor or distributing body for this application. Typically\n            it is the owning company name. This falls back to appname. You may\n            pass False to disable it.\n        \"version\" is an optional version path element to append to the\n            path. You might want to use this if you want multiple versions\n            of your app to be able to run independently. If used, this\n            would typically be \"<major>.<minor>\".\n            Only applied when appname is present.\n        \"multipath\" is an optional parameter only applicable to *nix\n            which indicates that the entire list of data dirs should be\n            returned. By default, the first item from XDG_DATA_DIRS is\n            returned, or '/usr/local/share/<AppName>',\n            if XDG_DATA_DIRS is not set\n\n    Typical site data directories are:\n        Mac OS X:   /Library/Application Support/<AppName>\n        Unix:       /usr/local/share/<AppName> or /usr/share/<AppName>\n        Win XP:     C:\\Documents and Settings\\All Users\\Application Data\\<AppAuthor>\\<AppName>\n        Vista:      (Fail! \"C:\\ProgramData\" is a hidden *system* directory on Vista.)\n        Win 7:      C:\\ProgramData\\<AppAuthor>\\<AppName>   # Hidden, but writeable on Win 7.\n\n    For Unix, this is using the $XDG_DATA_DIRS[0] default.\n\n    WARNING: Do not use this on Windows. See the Vista-Fail note above for why.\n    \"\"\"\n    if system == \"win32\":\n        if appauthor is None:\n            appauthor = appname\n        path = os.path.normpath(_get_win_folder(\"CSIDL_COMMON_APPDATA\"))\n        if appname:\n            if appauthor is not False:\n                path = os.path.join(path, appauthor, appname)\n            else:\n                path = os.path.join(path, appname)\n    elif system == 'darwin':\n        path = os.path.expanduser('/Library/Application Support')\n        if appname:\n            path = os.path.join(path, appname)\n    else:\n        # XDG default for $XDG_DATA_DIRS\n        # only first, if multipath is False\n        path = os.getenv('XDG_DATA_DIRS',\n                         os.pathsep.join(['/usr/local/share', '/usr/share']))\n        pathlist = [os.path.expanduser(x.rstrip(os.sep)) for x in path.split(os.pathsep)]\n        if appname:\n            if version:\n                appname = os.path.join(appname, version)\n            pathlist = [os.sep.join([x, appname]) for x in pathlist]\n\n        if multipath:\n            path = os.pathsep.join(pathlist)\n        else:\n            path = pathlist[0]\n        return path\n\n    if appname and version:\n        path = os.path.join(path, version)\n    return path\n\n\ndef user_config_dir(appname=None, appauthor=None, version=None, roaming=False):\n    r\"\"\"Return full path to the user-specific config dir for this application.\n\n        \"appname\" is the name of application.\n            If None, just the system directory is returned.\n        \"appauthor\" (only used on Windows) is the name of the\n            appauthor or distributing body for this application. Typically\n            it is the owning company name. This falls back to appname. You may\n            pass False to disable it.\n        \"version\" is an optional version path element to append to the\n            path. You might want to use this if you want multiple versions\n            of your app to be able to run independently. If used, this\n            would typically be \"<major>.<minor>\".\n            Only applied when appname is present.\n        \"roaming\" (boolean, default False) can be set True to use the Windows\n            roaming appdata directory. That means that for users on a Windows\n            network setup for roaming profiles, this user data will be\n            sync'd on login. See\n            <http://technet.microsoft.com/en-us/library/cc766489(WS.10).aspx>\n            for a discussion of issues.\n\n    Typical user config directories are:\n        Mac OS X:               ~/Library/Preferences/<AppName>\n        Unix:                   ~/.config/<AppName>     # or in $XDG_CONFIG_HOME, if defined\n        Win *:                  same as user_data_dir\n\n    For Unix, we follow the XDG spec and support $XDG_CONFIG_HOME.\n    That means, by default \"~/.config/<AppName>\".\n    \"\"\"\n    if system == \"win32\":\n        path = user_data_dir(appname, appauthor, None, roaming)\n    elif system == 'darwin':\n        path = os.path.expanduser('~/Library/Preferences/')\n        if appname:\n            path = os.path.join(path, appname)\n    else:\n        path = os.getenv('XDG_CONFIG_HOME', os.path.expanduser(\"~/.config\"))\n        if appname:\n            path = os.path.join(path, appname)\n    if appname and version:\n        path = os.path.join(path, version)\n    return path\n\n\ndef site_config_dir(appname=None, appauthor=None, version=None, multipath=False):\n    r\"\"\"Return full path to the user-shared data dir for this application.\n\n        \"appname\" is the name of application.\n            If None, just the system directory is returned.\n        \"appauthor\" (only used on Windows) is the name of the\n            appauthor or distributing body for this application. Typically\n            it is the owning company name. This falls back to appname. You may\n            pass False to disable it.\n        \"version\" is an optional version path element to append to the\n            path. You might want to use this if you want multiple versions\n            of your app to be able to run independently. If used, this\n            would typically be \"<major>.<minor>\".\n            Only applied when appname is present.\n        \"multipath\" is an optional parameter only applicable to *nix\n            which indicates that the entire list of config dirs should be\n            returned. By default, the first item from XDG_CONFIG_DIRS is\n            returned, or '/etc/xdg/<AppName>', if XDG_CONFIG_DIRS is not set\n\n    Typical site config directories are:\n        Mac OS X:   same as site_data_dir\n        Unix:       /etc/xdg/<AppName> or $XDG_CONFIG_DIRS[i]/<AppName> for each value in\n                    $XDG_CONFIG_DIRS\n        Win *:      same as site_data_dir\n        Vista:      (Fail! \"C:\\ProgramData\" is a hidden *system* directory on Vista.)\n\n    For Unix, this is using the $XDG_CONFIG_DIRS[0] default, if multipath=False\n\n    WARNING: Do not use this on Windows. See the Vista-Fail note above for why.\n    \"\"\"\n    if system == 'win32':\n        path = site_data_dir(appname, appauthor)\n        if appname and version:\n            path = os.path.join(path, version)\n    elif system == 'darwin':\n        path = os.path.expanduser('/Library/Preferences')\n        if appname:\n            path = os.path.join(path, appname)\n    else:\n        # XDG default for $XDG_CONFIG_DIRS\n        # only first, if multipath is False\n        path = os.getenv('XDG_CONFIG_DIRS', '/etc/xdg')\n        pathlist = [os.path.expanduser(x.rstrip(os.sep)) for x in path.split(os.pathsep)]\n        if appname:\n            if version:\n                appname = os.path.join(appname, version)\n            pathlist = [os.sep.join([x, appname]) for x in pathlist]\n\n        if multipath:\n            path = os.pathsep.join(pathlist)\n        else:\n            path = pathlist[0]\n    return path\n\n\ndef user_cache_dir(appname=None, appauthor=None, version=None, opinion=True):\n    r\"\"\"Return full path to the user-specific cache dir for this application.\n\n        \"appname\" is the name of application.\n            If None, just the system directory is returned.\n        \"appauthor\" (only used on Windows) is the name of the\n            appauthor or distributing body for this application. Typically\n            it is the owning company name. This falls back to appname. You may\n            pass False to disable it.\n        \"version\" is an optional version path element to append to the\n            path. You might want to use this if you want multiple versions\n            of your app to be able to run independently. If used, this\n            would typically be \"<major>.<minor>\".\n            Only applied when appname is present.\n        \"opinion\" (boolean) can be False to disable the appending of\n            \"Cache\" to the base app data dir for Windows. See\n            discussion below.\n\n    Typical user cache directories are:\n        Mac OS X:   ~/Library/Caches/<AppName>\n        Unix:       ~/.cache/<AppName> (XDG default)\n        Win XP:     C:\\Documents and Settings\\<username>\\Local Settings\\Application Data\\<AppAuthor>\\<AppName>\\Cache\n        Vista:      C:\\Users\\<username>\\AppData\\Local\\<AppAuthor>\\<AppName>\\Cache\n\n    On Windows the only suggestion in the MSDN docs is that local settings go in\n    the `CSIDL_LOCAL_APPDATA` directory. This is identical to the non-roaming\n    app data dir (the default returned by `user_data_dir` above). Apps typically\n    put cache data somewhere *under* the given dir here. Some examples:\n        ...\\Mozilla\\Firefox\\Profiles\\<ProfileName>\\Cache\n        ...\\Acme\\SuperApp\\Cache\\1.0\n    OPINION: This function appends \"Cache\" to the `CSIDL_LOCAL_APPDATA` value.\n    This can be disabled with the `opinion=False` option.\n    \"\"\"\n    if system == \"win32\":\n        if appauthor is None:\n            appauthor = appname\n        path = os.path.normpath(_get_win_folder(\"CSIDL_LOCAL_APPDATA\"))\n        if appname:\n            if appauthor is not False:\n                path = os.path.join(path, appauthor, appname)\n            else:\n                path = os.path.join(path, appname)\n            if opinion:\n                path = os.path.join(path, \"Cache\")\n    elif system == 'darwin':\n        path = os.path.expanduser('~/Library/Caches')\n        if appname:\n            path = os.path.join(path, appname)\n    else:\n        path = os.getenv('XDG_CACHE_HOME', os.path.expanduser('~/.cache'))\n        if appname:\n            path = os.path.join(path, appname)\n    if appname and version:\n        path = os.path.join(path, version)\n    return path\n\n\ndef user_state_dir(appname=None, appauthor=None, version=None, roaming=False):\n    r\"\"\"Return full path to the user-specific state dir for this application.\n\n        \"appname\" is the name of application.\n            If None, just the system directory is returned.\n        \"appauthor\" (only used on Windows) is the name of the\n            appauthor or distributing body for this application. Typically\n            it is the owning company name. This falls back to appname. You may\n            pass False to disable it.\n        \"version\" is an optional version path element to append to the\n            path. You might want to use this if you want multiple versions\n            of your app to be able to run independently. If used, this\n            would typically be \"<major>.<minor>\".\n            Only applied when appname is present.\n        \"roaming\" (boolean, default False) can be set True to use the Windows\n            roaming appdata directory. That means that for users on a Windows\n            network setup for roaming profiles, this user data will be\n            sync'd on login. See\n            <http://technet.microsoft.com/en-us/library/cc766489(WS.10).aspx>\n            for a discussion of issues.\n\n    Typical user state directories are:\n        Mac OS X:  same as user_data_dir\n        Unix:      ~/.local/state/<AppName>   # or in $XDG_STATE_HOME, if defined\n        Win *:     same as user_data_dir\n\n    For Unix, we follow this Debian proposal <https://wiki.debian.org/XDGBaseDirectorySpecification#state>\n    to extend the XDG spec and support $XDG_STATE_HOME.\n\n    That means, by default \"~/.local/state/<AppName>\".\n    \"\"\"\n    if system in [\"win32\", \"darwin\"]:\n        path = user_data_dir(appname, appauthor, None, roaming)\n    else:\n        path = os.getenv('XDG_STATE_HOME', os.path.expanduser(\"~/.local/state\"))\n        if appname:\n            path = os.path.join(path, appname)\n    if appname and version:\n        path = os.path.join(path, version)\n    return path\n\n\ndef user_log_dir(appname=None, appauthor=None, version=None, opinion=True):\n    r\"\"\"Return full path to the user-specific log dir for this application.\n\n        \"appname\" is the name of application.\n            If None, just the system directory is returned.\n        \"appauthor\" (only used on Windows) is the name of the\n            appauthor or distributing body for this application. Typically\n            it is the owning company name. This falls back to appname. You may\n            pass False to disable it.\n        \"version\" is an optional version path element to append to the\n            path. You might want to use this if you want multiple versions\n            of your app to be able to run independently. If used, this\n            would typically be \"<major>.<minor>\".\n            Only applied when appname is present.\n        \"opinion\" (boolean) can be False to disable the appending of\n            \"Logs\" to the base app data dir for Windows, and \"log\" to the\n            base cache dir for Unix. See discussion below.\n\n    Typical user log directories are:\n        Mac OS X:   ~/Library/Logs/<AppName>\n        Unix:       ~/.cache/<AppName>/log  # or under $XDG_CACHE_HOME if defined\n        Win XP:     C:\\Documents and Settings\\<username>\\Local Settings\\Application Data\\<AppAuthor>\\<AppName>\\Logs\n        Vista:      C:\\Users\\<username>\\AppData\\Local\\<AppAuthor>\\<AppName>\\Logs\n\n    On Windows the only suggestion in the MSDN docs is that local settings\n    go in the `CSIDL_LOCAL_APPDATA` directory. (Note: I'm interested in\n    examples of what some windows apps use for a logs dir.)\n\n    OPINION: This function appends \"Logs\" to the `CSIDL_LOCAL_APPDATA`\n    value for Windows and appends \"log\" to the user cache dir for Unix.\n    This can be disabled with the `opinion=False` option.\n    \"\"\"\n    if system == \"darwin\":\n        path = os.path.join(\n            os.path.expanduser('~/Library/Logs'),\n            appname)\n    elif system == \"win32\":\n        path = user_data_dir(appname, appauthor, version)\n        version = False\n        if opinion:\n            path = os.path.join(path, \"Logs\")\n    else:\n        path = user_cache_dir(appname, appauthor, version)\n        version = False\n        if opinion:\n            path = os.path.join(path, \"log\")\n    if appname and version:\n        path = os.path.join(path, version)\n    return path\n\n\nclass AppDirs(object):\n    \"\"\"Convenience wrapper for getting application dirs.\"\"\"\n    def __init__(self, appname=None, appauthor=None, version=None,\n            roaming=False, multipath=False):\n        self.appname = appname\n        self.appauthor = appauthor\n        self.version = version\n        self.roaming = roaming\n        self.multipath = multipath\n\n    @property\n    def user_data_dir(self):\n        return user_data_dir(self.appname, self.appauthor,\n                             version=self.version, roaming=self.roaming)\n\n    @property\n    def site_data_dir(self):\n        return site_data_dir(self.appname, self.appauthor,\n                             version=self.version, multipath=self.multipath)\n\n    @property\n    def user_config_dir(self):\n        return user_config_dir(self.appname, self.appauthor,\n                               version=self.version, roaming=self.roaming)\n\n    @property\n    def site_config_dir(self):\n        return site_config_dir(self.appname, self.appauthor,\n                             version=self.version, multipath=self.multipath)\n\n    @property\n    def user_cache_dir(self):\n        return user_cache_dir(self.appname, self.appauthor,\n                              version=self.version)\n\n    @property\n    def user_state_dir(self):\n        return user_state_dir(self.appname, self.appauthor,\n                              version=self.version)\n\n    @property\n    def user_log_dir(self):\n        return user_log_dir(self.appname, self.appauthor,\n                            version=self.version)\n\n\n#---- internal support stuff\n\ndef _get_win_folder_from_registry(csidl_name):\n    \"\"\"This is a fallback technique at best. I'm not sure if using the\n    registry for this guarantees us the correct answer for all CSIDL_*\n    names.\n    \"\"\"\n    if PY3:\n      import winreg as _winreg\n    else:\n      import _winreg\n\n    shell_folder_name = {\n        \"CSIDL_APPDATA\": \"AppData\",\n        \"CSIDL_COMMON_APPDATA\": \"Common AppData\",\n        \"CSIDL_LOCAL_APPDATA\": \"Local AppData\",\n    }[csidl_name]\n\n    key = _winreg.OpenKey(\n        _winreg.HKEY_CURRENT_USER,\n        r\"Software\\Microsoft\\Windows\\CurrentVersion\\Explorer\\Shell Folders\"\n    )\n    dir, type = _winreg.QueryValueEx(key, shell_folder_name)\n    return dir\n\n\ndef _get_win_folder_with_pywin32(csidl_name):\n    from win32com.shell import shellcon, shell\n    dir = shell.SHGetFolderPath(0, getattr(shellcon, csidl_name), 0, 0)\n    # Try to make this a unicode path because SHGetFolderPath does\n    # not return unicode strings when there is unicode data in the\n    # path.\n    try:\n        dir = unicode(dir)\n\n        # Downgrade to short path name if have highbit chars. See\n        # <http://bugs.activestate.com/show_bug.cgi?id=85099>.\n        has_high_char = False\n        for c in dir:\n            if ord(c) > 255:\n                has_high_char = True\n                break\n        if has_high_char:\n            try:\n                import win32api\n                dir = win32api.GetShortPathName(dir)\n            except ImportError:\n                pass\n    except UnicodeError:\n        pass\n    return dir\n\n\ndef _get_win_folder_with_ctypes(csidl_name):\n    import ctypes\n\n    csidl_const = {\n        \"CSIDL_APPDATA\": 26,\n        \"CSIDL_COMMON_APPDATA\": 35,\n        \"CSIDL_LOCAL_APPDATA\": 28,\n    }[csidl_name]\n\n    buf = ctypes.create_unicode_buffer(1024)\n    ctypes.windll.shell32.SHGetFolderPathW(None, csidl_const, None, 0, buf)\n\n    # Downgrade to short path name if have highbit chars. See\n    # <http://bugs.activestate.com/show_bug.cgi?id=85099>.\n    has_high_char = False\n    for c in buf:\n        if ord(c) > 255:\n            has_high_char = True\n            break\n    if has_high_char:\n        buf2 = ctypes.create_unicode_buffer(1024)\n        if ctypes.windll.kernel32.GetShortPathNameW(buf.value, buf2, 1024):\n            buf = buf2\n\n    return buf.value\n\ndef _get_win_folder_with_jna(csidl_name):\n    import array\n    from com.sun import jna\n    from com.sun.jna.platform import win32\n\n    buf_size = win32.WinDef.MAX_PATH * 2\n    buf = array.zeros('c', buf_size)\n    shell = win32.Shell32.INSTANCE\n    shell.SHGetFolderPath(None, getattr(win32.ShlObj, csidl_name), None, win32.ShlObj.SHGFP_TYPE_CURRENT, buf)\n    dir = jna.Native.toString(buf.tostring()).rstrip(\"\\0\")\n\n    # Downgrade to short path name if have highbit chars. See\n    # <http://bugs.activestate.com/show_bug.cgi?id=85099>.\n    has_high_char = False\n    for c in dir:\n        if ord(c) > 255:\n            has_high_char = True\n            break\n    if has_high_char:\n        buf = array.zeros('c', buf_size)\n        kernel = win32.Kernel32.INSTANCE\n        if kernel.GetShortPathName(dir, buf, buf_size):\n            dir = jna.Native.toString(buf.tostring()).rstrip(\"\\0\")\n\n    return dir\n\nif system == \"win32\":\n    try:\n        import win32com.shell\n        _get_win_folder = _get_win_folder_with_pywin32\n    except ImportError:\n        try:\n            from ctypes import windll\n            _get_win_folder = _get_win_folder_with_ctypes\n        except ImportError:\n            try:\n                import com.sun.jna\n                _get_win_folder = _get_win_folder_with_jna\n            except ImportError:\n                _get_win_folder = _get_win_folder_from_registry\n\n\n#---- self test code\n\nif __name__ == \"__main__\":\n    appname = \"MyApp\"\n    appauthor = \"MyCompany\"\n\n    props = (\"user_data_dir\",\n             \"user_config_dir\",\n             \"user_cache_dir\",\n             \"user_state_dir\",\n             \"user_log_dir\",\n             \"site_data_dir\",\n             \"site_config_dir\")\n\n    print(\"-- app dirs %s --\" % __version__)\n\n    print(\"-- app dirs (with optional 'version')\")\n    dirs = AppDirs(appname, appauthor, version=\"1.0\")\n    for prop in props:\n        print(\"%s: %s\" % (prop, getattr(dirs, prop)))\n\n    print(\"\\n-- app dirs (without optional 'version')\")\n    dirs = AppDirs(appname, appauthor)\n    for prop in props:\n        print(\"%s: %s\" % (prop, getattr(dirs, prop)))\n\n    print(\"\\n-- app dirs (without optional 'appauthor')\")\n    dirs = AppDirs(appname)\n    for prop in props:\n        print(\"%s: %s\" % (prop, getattr(dirs, prop)))\n\n    print(\"\\n-- app dirs (with disabled 'appauthor')\")\n    dirs = AppDirs(appname, appauthor=False)\n    for prop in props:\n        print(\"%s: %s\" % (prop, getattr(dirs, prop)))\n"
  },
  {
    "path": "libs/base64/base64.cc",
    "content": "/* \n   base64.cpp and base64.h\n\n   Copyright (C) 2004-2008 René Nyffenegger\n\n   This source code is provided 'as-is', without any express or implied\n   warranty. In no event will the author be held liable for any damages\n   arising from the use of this software.\n\n   Permission is granted to anyone to use this software for any purpose,\n   including commercial applications, and to alter it and redistribute it\n   freely, subject to the following restrictions:\n\n   1. The origin of this source code must not be misrepresented; you must not\n      claim that you wrote the original source code. If you use this source code\n      in a product, an acknowledgment in the product documentation would be\n      appreciated but is not required.\n\n   2. Altered source versions must be plainly marked as such, and must not be\n      misrepresented as being the original source code.\n\n   3. This notice may not be removed or altered from any source distribution.\n\n   René Nyffenegger rene.nyffenegger@adp-gmbh.ch\n\n*/\n\n#include \"base64.hh\"\n\nstatic const std::string base64_chars = \n             \"ABCDEFGHIJKLMNOPQRSTUVWXYZ\"\n             \"abcdefghijklmnopqrstuvwxyz\"\n             \"0123456789+/\";\n\n\nstatic inline bool is_base64(unsigned char c) {\n  return (isalnum(c) || (c == '+') || (c == '/'));\n}\n\nstd::string base64_encode(unsigned char const* bytes_to_encode, unsigned int in_len) {\n  std::string ret;\n  int i = 0;\n  int j = 0;\n  unsigned char char_array_3[3];\n  unsigned char char_array_4[4];\n\n  while (in_len--) {\n    char_array_3[i++] = *(bytes_to_encode++);\n    if (i == 3) {\n      char_array_4[0] = (char_array_3[0] & 0xfc) >> 2;\n      char_array_4[1] = ((char_array_3[0] & 0x03) << 4) + ((char_array_3[1] & 0xf0) >> 4);\n      char_array_4[2] = ((char_array_3[1] & 0x0f) << 2) + ((char_array_3[2] & 0xc0) >> 6);\n      char_array_4[3] = char_array_3[2] & 0x3f;\n\n      for(i = 0; (i <4) ; i++)\n        ret += base64_chars[char_array_4[i]];\n      i = 0;\n    }\n  }\n\n  if (i)\n  {\n    for(j = i; j < 3; j++)\n      char_array_3[j] = '\\0';\n\n    char_array_4[0] = (char_array_3[0] & 0xfc) >> 2;\n    char_array_4[1] = ((char_array_3[0] & 0x03) << 4) + ((char_array_3[1] & 0xf0) >> 4);\n    char_array_4[2] = ((char_array_3[1] & 0x0f) << 2) + ((char_array_3[2] & 0xc0) >> 6);\n    char_array_4[3] = char_array_3[2] & 0x3f;\n\n    for (j = 0; (j < i + 1); j++)\n      ret += base64_chars[char_array_4[j]];\n\n    while((i++ < 3))\n      ret += '=';\n\n  }\n\n  return ret;\n\n}\nstd::string base64_decode(std::string const& encoded_string) {\n  int in_len = encoded_string.size();\n  int i = 0;\n  int j = 0;\n  int in_ = 0;\n  unsigned char char_array_4[4], char_array_3[3];\n  std::string ret;\n\n  while (in_len-- && ( encoded_string[in_] != '=') && is_base64(encoded_string[in_])) {\n    char_array_4[i++] = encoded_string[in_]; in_++;\n    if (i ==4) {\n      for (i = 0; i <4; i++)\n        char_array_4[i] = base64_chars.find(char_array_4[i]);\n\n      char_array_3[0] = (char_array_4[0] << 2) + ((char_array_4[1] & 0x30) >> 4);\n      char_array_3[1] = ((char_array_4[1] & 0xf) << 4) + ((char_array_4[2] & 0x3c) >> 2);\n      char_array_3[2] = ((char_array_4[2] & 0x3) << 6) + char_array_4[3];\n\n      for (i = 0; (i < 3); i++)\n        ret += char_array_3[i];\n      i = 0;\n    }\n  }\n\n  if (i) {\n    for (j = i; j <4; j++)\n      char_array_4[j] = 0;\n\n    for (j = 0; j <4; j++)\n      char_array_4[j] = base64_chars.find(char_array_4[j]);\n\n    char_array_3[0] = (char_array_4[0] << 2) + ((char_array_4[1] & 0x30) >> 4);\n    char_array_3[1] = ((char_array_4[1] & 0xf) << 4) + ((char_array_4[2] & 0x3c) >> 2);\n    char_array_3[2] = ((char_array_4[2] & 0x3) << 6) + char_array_4[3];\n\n    for (j = 0; (j < i - 1); j++) ret += char_array_3[j];\n  }\n\n  return ret;\n}\n"
  },
  {
    "path": "libs/base64/base64.hh",
    "content": "#pragma once\n\n#include <string>\n\nstd::string base64_encode(unsigned char const* bytes_to_encode, unsigned int in_len);\nstd::string base64_decode(std::string const& encoded_string);\n"
  },
  {
    "path": "libs/dbg/dbg.h",
    "content": "/*****************************************************************************\n\n                                dbg(...) macro\n\nLicense (MIT):\n\n  Copyright (c) 2019 David Peter <mail@david-peter.de>\n\n  Permission is hereby granted, free of charge, to any person obtaining a copy\n  of this software and associated documentation files (the \"Software\"), to\n  deal in the Software without restriction, including without limitation the\n  rights to use, copy, modify, merge, publish, distribute, sublicense, and/or\n  sell copies of the Software, and to permit persons to whom the Software is\n  furnished to do so, subject to the following conditions:\n\n  The above copyright notice and this permission notice shall be included in\n  all copies or substantial portions of the Software.\n\n  THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n  IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n  FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL\n  THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n  LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,\n  OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE\n  SOFTWARE.\n\n*****************************************************************************/\n\n#ifndef DBG_MACRO_DBG_H\n#define DBG_MACRO_DBG_H\n\n#ifndef DBG_MACRO_NO_WARNING\n#pragma message(\"WARNING: the 'dbg.h' header is included in your code base\")\n#endif  // DBG_MACRO_NO_WARNING\n\n#include <algorithm>\n#include <iomanip>\n#include <ios>\n#include <iostream>\n#include <memory>\n#include <sstream>\n#include <string>\n#include <tuple>\n#include <type_traits>\n#include <vector>\n\n#if defined(__unix__) || (defined(__APPLE__) && defined(__MACH__))\n#include <unistd.h>\n#endif\n\n#if __cplusplus >= 201703L\n#include <optional>\n#include <variant>\n#endif\n\nnamespace dbg_macro {\n\n#if defined(__unix__) || (defined(__APPLE__) && defined(__MACH__))\ninline bool isColorizedOutputEnabled() {\n  return isatty(fileno(stderr));\n}\n#else\ninline bool isColorizedOutputEnabled() {\n  return true;\n}\n#endif\n\nnamespace pretty_function {\n\n// Compiler-agnostic version of __PRETTY_FUNCTION__ and constants to\n// extract the template argument in `type_name_impl`\n\n#if defined(__clang__)\n#define DBG_MACRO_PRETTY_FUNCTION __PRETTY_FUNCTION__\nstatic constexpr size_t PREFIX_LENGTH =\n    sizeof(\"const char *dbg_macro::type_name_impl() [T = \") - 1;\nstatic constexpr size_t SUFFIX_LENGTH = sizeof(\"]\") - 1;\n#elif defined(__GNUC__) && !defined(__clang__)\n#define DBG_MACRO_PRETTY_FUNCTION __PRETTY_FUNCTION__\nstatic constexpr size_t PREFIX_LENGTH =\n    sizeof(\"const char* dbg_macro::type_name_impl() [with T = \") - 1;\nstatic constexpr size_t SUFFIX_LENGTH = sizeof(\"]\") - 1;\n#elif defined(_MSC_VER)\n#define DBG_MACRO_PRETTY_FUNCTION __FUNCSIG__\nstatic constexpr size_t PREFIX_LENGTH =\n    sizeof(\"const char *__cdecl dbg_macro::type_name_impl<\") - 1;\nstatic constexpr size_t SUFFIX_LENGTH = sizeof(\">(void)\") - 1;\n#else\n#error \"This compiler is currently not supported by dbg_macro.\"\n#endif\n\n}  // namespace pretty_function\n\n// Implementation of 'type_name<T>()'\n\ntemplate <typename T>\nconst char* type_name_impl() {\n  return DBG_MACRO_PRETTY_FUNCTION;\n}\n\ntemplate <typename T>\nstruct type_tag {};\n\ntemplate <int&... ExplicitArgumentBarrier, typename T>\nstd::string get_type_name(type_tag<T>) {\n  namespace pf = pretty_function;\n\n  std::string type = type_name_impl<T>();\n  return type.substr(pf::PREFIX_LENGTH,\n                     type.size() - pf::PREFIX_LENGTH - pf::SUFFIX_LENGTH);\n}\n\ntemplate <typename T>\nstd::string type_name() {\n  if (std::is_volatile<T>::value) {\n    if (std::is_pointer<T>::value) {\n      return type_name<typename std::remove_volatile<T>::type>() + \" volatile\";\n    } else {\n      return \"volatile \" + type_name<typename std::remove_volatile<T>::type>();\n    }\n  }\n  if (std::is_const<T>::value) {\n    if (std::is_pointer<T>::value) {\n      return type_name<typename std::remove_const<T>::type>() + \" const\";\n    } else {\n      return \"const \" + type_name<typename std::remove_const<T>::type>();\n    }\n  }\n  if (std::is_pointer<T>::value) {\n    return type_name<typename std::remove_pointer<T>::type>() + \"*\";\n  }\n  if (std::is_lvalue_reference<T>::value) {\n    return type_name<typename std::remove_reference<T>::type>() + \"&\";\n  }\n  if (std::is_rvalue_reference<T>::value) {\n    return type_name<typename std::remove_reference<T>::type>() + \"&&\";\n  }\n  return get_type_name(type_tag<T>{});\n}\n\ninline std::string get_type_name(type_tag<short>) {\n  return \"short\";\n}\n\ninline std::string get_type_name(type_tag<unsigned short>) {\n  return \"unsigned short\";\n}\n\ninline std::string get_type_name(type_tag<long>) {\n  return \"long\";\n}\n\ninline std::string get_type_name(type_tag<unsigned long>) {\n  return \"unsigned long\";\n}\n\ninline std::string get_type_name(type_tag<std::string>) {\n  return \"std::string\";\n}\n\ntemplate <typename T>\nstd::string get_type_name(type_tag<std::vector<T, std::allocator<T>>>) {\n  return \"std::vector<\" + type_name<T>() + \">\";\n}\n\n// Implementation of 'is_detected' to specialize for container-like types\n\nnamespace detail_detector {\n\nstruct nonesuch {\n  nonesuch() = delete;\n  ~nonesuch() = delete;\n  nonesuch(nonesuch const&) = delete;\n  void operator=(nonesuch const&) = delete;\n};\n\ntemplate <typename...>\nusing void_t = void;\n\ntemplate <class Default,\n          class AlwaysVoid,\n          template <class...>\n          class Op,\n          class... Args>\nstruct detector {\n  using value_t = std::false_type;\n  using type = Default;\n};\n\ntemplate <class Default, template <class...> class Op, class... Args>\nstruct detector<Default, void_t<Op<Args...>>, Op, Args...> {\n  using value_t = std::true_type;\n  using type = Op<Args...>;\n};\n\n}  // namespace detail_detector\n\ntemplate <template <class...> class Op, class... Args>\nusing is_detected = typename detail_detector::\n    detector<detail_detector::nonesuch, void, Op, Args...>::value_t;\n\nnamespace detail {\n\nnamespace {\nusing std::begin;\nusing std::end;\n#if __cplusplus < 201703L\ntemplate <typename T>\nconstexpr auto size(const T& c) -> decltype(c.size()) {\n  return c.size();\n}\ntemplate <typename T, std::size_t N>\nconstexpr std::size_t size(const T (&)[N]) {\n  return N;\n}\n#else\nusing std::size;\n#endif\n}  // namespace\n\ntemplate <typename T>\nusing detect_begin_t = decltype(detail::begin(std::declval<T>()));\n\ntemplate <typename T>\nusing detect_end_t = decltype(detail::end(std::declval<T>()));\n\ntemplate <typename T>\nusing detect_size_t = decltype(detail::size(std::declval<T>()));\n\ntemplate <typename T>\nstruct has_begin_end_size {\n  static constexpr bool value = is_detected<detect_begin_t, T>::value &&\n                                is_detected<detect_end_t, T>::value &&\n                                is_detected<detect_size_t, T>::value;\n};\n\ntemplate <typename T>\nusing ostream_operator_t =\n    decltype(std::declval<std::ostream&>() << std::declval<T>());\n\ntemplate <typename T>\nstruct has_ostream_operator {\n  static constexpr bool value = is_detected<ostream_operator_t, T>::value;\n};\n\n}  // namespace detail\n\n// Specializations of \"pretty_print\"\n\ntemplate <typename T>\ninline void pretty_print(std::ostream& stream, const T& value, std::true_type) {\n  stream << value;\n}\n\ntemplate <typename T>\ninline void pretty_print(std::ostream&, const T&, std::false_type) {\n  static_assert(detail::has_ostream_operator<const T&>::value,\n                \"Type does not support the << ostream operator\");\n}\n\ntemplate <typename T>\ninline typename std::enable_if<!detail::has_begin_end_size<const T&>::value &&\n                                   !std::is_enum<T>::value,\n                               bool>::type\npretty_print(std::ostream& stream, const T& value) {\n  pretty_print(\n      stream, value,\n      std::integral_constant<bool,\n                             detail::has_ostream_operator<const T&>::value>{});\n  return true;\n}\n\ninline bool pretty_print(std::ostream& stream, const bool& value) {\n  stream << std::boolalpha << value;\n  return true;\n}\n\ninline bool pretty_print(std::ostream& stream, const char& value) {\n  const bool printable = value >= 0x20 && value <= 0x7E;\n\n  if (printable) {\n    stream << \"'\" << value << \"'\";\n  } else {\n    stream << \"'\\\\x\" << std::setw(2) << std::setfill('0') << std::hex\n           << std::uppercase << (0xFF & value) << \"'\";\n  }\n  return true;\n}\n\ntemplate <typename P>\ninline bool pretty_print(std::ostream& stream, P* const& value) {\n  if (value == nullptr) {\n    stream << \"nullptr\";\n  } else {\n    stream << value;\n  }\n  return true;\n}\n\ntemplate <typename T, typename Deleter>\ninline bool pretty_print(std::ostream& stream,\n                         std::unique_ptr<T, Deleter>& value) {\n  pretty_print(stream, value.get());\n  return true;\n}\n\ntemplate <typename T>\ninline bool pretty_print(std::ostream& stream, std::shared_ptr<T>& value) {\n  pretty_print(stream, value.get());\n  stream << \" (use_count = \" << value.use_count() << \")\";\n\n  return true;\n}\n\ntemplate <size_t N>\ninline bool pretty_print(std::ostream& stream, const char (&value)[N]) {\n  stream << value;\n  return false;\n}\n\ntemplate <>\ninline bool pretty_print(std::ostream& stream, const char* const& value) {\n  stream << '\"' << value << '\"';\n  return true;\n}\n\ntemplate <size_t Idx>\nstruct pretty_print_tuple {\n  template <typename... Ts>\n  static void print(std::ostream& stream, const std::tuple<Ts...>& tuple) {\n    pretty_print_tuple<Idx - 1>::print(stream, tuple);\n    stream << \", \";\n    pretty_print(stream, std::get<Idx>(tuple));\n  }\n};\n\ntemplate <>\nstruct pretty_print_tuple<0> {\n  template <typename... Ts>\n  static void print(std::ostream& stream, const std::tuple<Ts...>& tuple) {\n    pretty_print(stream, std::get<0>(tuple));\n  }\n};\n\ntemplate <typename... Ts>\ninline bool pretty_print(std::ostream& stream, const std::tuple<Ts...>& value) {\n  stream << \"{\";\n  pretty_print_tuple<sizeof...(Ts) - 1>::print(stream, value);\n  stream << \"}\";\n\n  return true;\n}\n\ntemplate <>\ninline bool pretty_print(std::ostream& stream, const std::tuple<>&) {\n  stream << \"{}\";\n\n  return true;\n}\n\ntemplate <typename Container>\ninline\n    typename std::enable_if<detail::has_begin_end_size<const Container&>::value,\n                            bool>::type\n    pretty_print(std::ostream& stream, const Container& value) {\n  stream << \"{\";\n  const size_t size = detail::size(value);\n  const size_t n = std::min(size_t{10}, size);\n  size_t i = 0;\n  using std::begin;\n  using std::end;\n  for (auto it = begin(value); it != end(value) && i < n; ++it, ++i) {\n    pretty_print(stream, *it);\n    if (i != n - 1) {\n      stream << \", \";\n    }\n  }\n\n  if (size > n) {\n    stream << \", ...\";\n    stream << \" size:\" << size;\n  }\n\n  stream << \"}\";\n  return true;\n}\n\ntemplate <typename Enum>\ninline typename std::enable_if<std::is_enum<Enum>::value, bool>::type\npretty_print(std::ostream& stream, Enum const& value) {\n  using UnderlyingType = typename std::underlying_type<Enum>::type;\n  stream << static_cast<UnderlyingType>(value);\n\n  return true;\n}\n\ninline bool pretty_print(std::ostream& stream, const std::string& value) {\n  stream << '\"' << value << '\"';\n  return true;\n}\n\n#if __cplusplus >= 201703L\n\ntemplate <typename T>\ninline bool pretty_print(std::ostream& stream, const std::optional<T>& value) {\n  if (value) {\n    stream << '{';\n    pretty_print(stream, *value);\n    stream << '}';\n  } else {\n    stream << \"nullopt\";\n  }\n\n  return true;\n}\n\ntemplate <typename... Ts>\ninline bool pretty_print(std::ostream& stream,\n                         const std::variant<Ts...>& value) {\n  stream << \"{\";\n  std::visit([&stream](auto&& arg) { pretty_print(stream, arg); }, value);\n  stream << \"}\";\n\n  return true;\n}\n\n#endif  // __cplusplus >= 201703L\n\nclass DebugOutput {\n public:\n  DebugOutput(const char* filepath,\n              int line,\n              const char* function_name,\n              const char* expression)\n      : m_use_colorized_output(isColorizedOutputEnabled()),\n        m_filepath(filepath),\n        m_line(line),\n        m_function_name(function_name),\n        m_expression(expression) {\n    const std::size_t path_length = m_filepath.length();\n    if (path_length > MAX_PATH_LENGTH) {\n      m_filepath = \"..\" + m_filepath.substr(path_length - MAX_PATH_LENGTH,\n                                            MAX_PATH_LENGTH);\n    }\n  }\n\n  template <typename T>\n  T&& print(const std::string& type, T&& value) const {\n    const T& ref = value;\n    std::stringstream stream_value;\n    const bool print_expr_and_type = pretty_print(stream_value, ref);\n\n    std::stringstream output;\n    output << ansi(ANSI_DEBUG) << \"[\" << m_filepath << \":\" << m_line << \" (\"\n           << m_function_name << \")] \" << ansi(ANSI_RESET);\n    if (print_expr_and_type) {\n      output << ansi(ANSI_EXPRESSION) << m_expression << ansi(ANSI_RESET)\n             << \" = \";\n    }\n    output << ansi(ANSI_VALUE) << stream_value.str() << ansi(ANSI_RESET);\n    if (print_expr_and_type) {\n      output << \" (\" << ansi(ANSI_TYPE) << type << ansi(ANSI_RESET) << \")\";\n    }\n    output << std::endl;\n    std::cerr << output.str();\n\n    return std::forward<T>(value);\n  }\n\n private:\n  const char* ansi(const char* code) const {\n    if (m_use_colorized_output) {\n      return code;\n    } else {\n      return ANSI_EMPTY;\n    }\n  }\n\n  const bool m_use_colorized_output;\n\n  std::string m_filepath;\n  const int m_line;\n  const std::string m_function_name;\n  const std::string m_expression;\n\n  static constexpr std::size_t MAX_PATH_LENGTH = 20;\n\n  static constexpr const char* const ANSI_EMPTY = \"\";\n  static constexpr const char* const ANSI_DEBUG = \"\\x1b[02m\";\n  static constexpr const char* const ANSI_EXPRESSION = \"\\x1b[36m\";\n  static constexpr const char* const ANSI_VALUE = \"\\x1b[01m\";\n  static constexpr const char* const ANSI_TYPE = \"\\x1b[32m\";\n  static constexpr const char* const ANSI_RESET = \"\\x1b[0m\";\n};\n\n// Identity function to suppress \"-Wunused-value\" warnings in DBG_MACRO_DISABLE\n// mode\ntemplate <typename T>\nT&& identity(T&& t) {\n  return std::forward<T>(t);\n}\n\n}  // namespace dbg_macro\n\n#ifndef DBG_MACRO_DISABLE\n// We use a variadic macro to support commas inside expressions (e.g.\n// initializer lists):\n#define dbg(...)                                                     \\\n  dbg_macro::DebugOutput(__FILE__, __LINE__, __func__, #__VA_ARGS__) \\\n      .print(dbg_macro::type_name<decltype(__VA_ARGS__)>(), (__VA_ARGS__))\n#else\n#define dbg(...) dbg_macro::identity(__VA_ARGS__)\n#endif  // DBG_MACRO_DISABLE\n\n#endif  // DBG_MACRO_DBG_H\n"
  },
  {
    "path": "libs/internal/include/internal/difflib.h",
    "content": "//---------------------------------------------------------------------------------\n// C++ port of the Python difflib -- helpers for computing deltas between objects.\n//\n// Function get_close_matches(word, possibilities, n = 3, cutoff = 0.6) :\n//\t Use SequenceMatcher to return list of the best \"good enough\" matches.\n// Function context_diff(a, b) :\n//\t For two lists of strings, return a delta in context diff format.\n// Function ndiff(a, b) :\n//\t Return a delta : the difference between `a` and `b` (lists of strings).\n// Function restore(delta, which) :\n//\t Return one of the two sequences that generated an ndiff delta.\n// Function unified_diff(a, b) :\n//\t For two lists of strings, return a delta in unified diff format.\n// Class SequenceMatcher :\n//   A flexible class for comparing pairs of sequences of any type.\n// Class Differ :\n//   For producing human - readable deltas from sequences of lines of text.\n// Class HtmlDiff :\n//   For producing HTML side by side comparison with change highlights.\n//---------------------------------------------------------------------------------\n\n#ifndef DIFFLIB_HPP\n#define DIFFLIB_HPP\n\n#include <tuple> // std::pair\n#include <vector> // std::vector\n#include <map> // std::map\n#include <set> // std::set\n#include <algorithm> // std::sort, std::max, std::min\n#include <iostream> // std::ostream\n#include <locale> // std::isspace\n\nnamespace difflib\n{\n\tnamespace detail\n\t{\n\t\tinline double calculate_ratio(size_t matches, size_t length)\n\t\t{\n\t\t\tif (length == 0)\n\t\t\t\treturn 1;\n\t\t\treturn\t(2. * matches) / length;\n\t\t}\n\n\t\ttemplate <typename string_type>\n\t\tinline size_t count_leading(const string_type& line, const typename string_type::value_type& ch)\n\t\t{\n\t\t\tsize_t i = 0;\n\t\t\tsize_t n = line.size();\n\t\t\twhile (i < n && line[i] == ch)\n\t\t\t\t++i;\n\t\t\treturn i;\n\t\t}\n\n\t\ttemplate <typename string_type>\n\t\tinline void rtrim(string_type& s)\n\t\t{\n\t\t\ts.erase(\n\t\t\t\tstd::find_if(\n\t\t\t\t\ts.rbegin(),\n\t\t\t\t\ts.rend(),\n\t\t\t\t\t[](const typename string_type::value_type& ch) { return !std::isspace(ch, std::locale{}); })\n\t\t\t\t.base(),\n\t\t\t\ts.end());\n\t\t}\n\t}\n\n\tenum class tag_t\n\t{\n\t\tt_replace,\n\t\tt_delete,\n\t\tt_insert,\n\t\tt_equal,\n\t\tt_unknown\n\t};\n\n\tinline std::ostream& operator << (std::ostream& stream, tag_t tag)\n\t{\n\t\tswitch (tag) {\n\t\tcase tag_t::t_replace: return stream << \"replace\";\n\t\tcase tag_t::t_delete: return stream << \"delete\";\n\t\tcase tag_t::t_insert: return stream << \"insert\";\n\t\tcase tag_t::t_equal: return stream << \"equal\";\n\t\tdefault: return stream << \"unknown\";\n\t\t}\n\t}\n\n\tstruct Block\n\t{\n\t\tBlock(size_t i, size_t j, size_t length) : i(i), j(j), length(length) {}\n\t\tsize_t i, j, length;\n\t};\n\n\tinline std::ostream& operator << (std::ostream& stream, const Block& rhs)\n\t{\n\t\treturn stream << \"Block(\" << rhs.i << \", \" << rhs.j << \", \" << rhs.length << \")\";\n\t}\n\n\tstruct OpCode\n\t{\n\t\tOpCode(tag_t tag, size_t i1, size_t i2, size_t j1, size_t j2) : tag(tag), i1(i1), i2(i2), j1(j1), j2(j2) {}\n\t\ttag_t tag;\n\t\tsize_t i1, i2, j1, j2;\n\t};\n\n\tinline std::ostream& operator << (std::ostream& stream, const OpCode& rhs)\n\t{\n\t\treturn stream << \"OpCode(tag_t::t_\" << rhs.tag << \", \" << rhs.i1 << \", \" << rhs.i2 << \", \" << rhs.j1 << \", \" << rhs.j2 << \")\";\n\t}\n\n\ttemplate <typename StringT>\n\tstruct Delta\n\t{\n\t\tDelta(tag_t tag, const StringT& a, const StringT& b, const std::vector<OpCode>& opcodes = {}) : tag(tag), a(a), b(b), opcodes(opcodes) {}\n\t\ttag_t tag;\n\t\tStringT a, b;\n\t\tstd::vector<OpCode> opcodes;\n\t};\n\n\t// SequenceMatcher is a flexible class for comparing pairs of sequences of\n\t// any type, so long as the sequence elements are hashable.The basic\n\t// algorithm predates, and is a little fancier than, an algorithm\n\t// published in the late 1980's by Ratcliff and Obershelp under the\n\t// hyperbolic name \"gestalt pattern matching\".The basic idea is to find\n\t// the longest contiguous matching subsequence that contains no \"junk\"\n\t// elements(R - O doesn't address junk).  The same idea is then applied\n\t// recursively to the pieces of the sequences to the left and to the right\n\t// of the matching subsequence.This does not yield minimal edit\n\t// sequences, but does tend to yield matches that \"look right\" to people.\n\t//\n\t// SequenceMatcher tries to compute a \"human-friendly diff\" between two\n\t// sequences.Unlike e.g.UNIX(tm) diff, the fundamental notion is the\n\t// longest *contiguous* & junk - free matching subsequence.That's what\n\t// catches peoples' eyes.  The Windows(tm) windiff has another interesting\n\t// notion, pairing up elements that appear uniquely in each sequence.\n\t// That, and the method here, appear to yield more intuitive difference\n\t// reports than does diff.This method appears to be the least vulnerable\n\t// to synching up on blocks of \"junk lines\", though(like blank lines in\n\t// ordinary text files, or maybe \"<P>\" lines in HTML files).That may be\n\t// because this is the only method of the 3 that has a *concept* of\n\t// \"junk\" <wink>.\n\ttemplate <typename StringT>\n\tclass SequenceMatcher\n\t{\n\tpublic:\n\t\tusing string_type = StringT;\n\t\tusing char_type = typename StringT::value_type;\n\t\tusing JunkPred = bool(*)(const char_type&);\n\n\t\t// Construct a SequenceMatcher\n\t\t//\n\t\t// Optional arg isjunk is nullptr (the default), or a one - argument\n\t\t// function that takes a sequence element and returns true iff the\n\t\t// element is junk. NO_JUNK is equivalent to passing \"return false\", i.e.\n\t\t// no elements are considered to be junk.\n\t\t//\n\t\t// Optional arg a is the first of two sequences to be compared. By\n\t\t// default, an empty string. The elements of a must overload operator <.\n\t\t//\n\t\t// Optional arg b is the second of two sequences to be compared.By\n\t\t// default, an empty string. The elements of b must overload operator <.\n\t\t//\n\t\t// Optional arg autojunk should be set to false to disable the\n\t\t// \"automatic junk heuristic\" that treats popular elements as junk\n\t\t// (see module documentation for more information).\n\t\tSequenceMatcher(\n\t\t\tJunkPred is_junk = nullptr,\n\t\t\tconst string_type& a = \"\",\n\t\t\tconst string_type& b = \"\",\n\t\t\tbool auto_junk = true\n\t\t)\n\t\t\t: is_junk(is_junk)\n\t\t\t, a_(nullptr)\n\t\t\t, b_(nullptr)\n\t\t\t, auto_junk(auto_junk)\n\t\t{\n\t\t\tset_seqs(a, b);\n\t\t}\n\n\t\t// Construct a SequenceMatcher with no junk\n\t\tSequenceMatcher(const string_type& a, const string_type& b)\n\t\t\t: SequenceMatcher(nullptr, a, b, false)\n\t\t{\n\n\t\t}\n\n\t\t// Set the two sequences to be compared\n\t\tvoid set_seqs(const string_type& a, const string_type& b)\n\t\t{\n\t\t\tset_seq1(a);\n\t\t\tset_seq2(b);\n\t\t}\n\n\t\t// Set the first sequence to be compared\n\t\t//\n\t\t// The second sequence to be compared is not changed.\n\t\t//\n\t\t// SequenceMatcher computes and caches detailed information about the\n\t\t// second sequence, so if you want to compare one sequence S against\n\t\t// many sequences, use.set_seq2(S) once and call.set_seq1(x)\n\t\t// repeatedly for each of the other sequences.\n\t\tvoid set_seq1(const string_type& a)\n\t\t{\n\t\t\tif (a_ == &a)\n\t\t\t\treturn;\n\n\t\t\ta_ = &a;\n\t\t\tmatching_blocks.clear();\n\t\t\topcodes.clear();\n\t\t}\n\n\t\t// Set the second sequence to be compared\n\t\t//\n\t\t// The first sequence to be compared is not changed.\n\t\t//\n\t\t// SequenceMatcher computes and caches detailed information about the\n\t\t// second sequence, so if you want to compare one sequence S against\n\t\t// many sequences, use.set_seq2(S) once and call.set_seq1(x)\n\t\t// repeatedly for each of the other sequences.\n\t\tvoid set_seq2(const string_type& b)\n\t\t{\n\t\t\tif (b_ == &b)\n\t\t\t\treturn;\n\n\t\t\tb_ = &b;\n\t\t\tmatching_blocks.clear();\n\t\t\topcodes.clear();\n\t\t\tfull_b_count.clear();;\n\t\t\tchain_b();\n\t\t}\n\n\t\t// Find the longest matching block in a[i1:i2] and b[j1:j2]\n\t\t//\n\t\t// Of all maximal matching blocks, return one that starts earliest in a, and \n\t\t// of all those maximal matching blocks that start earliest in a, return the one\n\t\t// that starts earliest in b\n\t\t//\n\t\t// If is_junk is defined, first the longest matching block is\n\t\t// determined as above, but with the additional restriction that no\n\t\t// junk element appears in the block.Then that block is extended as\n\t\t// far as possible by matching(only) junk elements on both sides.So\n\t\t// the resulting block never matches on junk except as identical junk\n\t\t// happens to be adjacent to an \"interesting\" match.\n\t\t//\n\t\t// If no blocks match, return (i1, j1, 0)\n\t\tBlock find_longest_match(size_t i1, size_t i2, size_t j1, size_t j2)\n\t\t{\n\t\t\tconst string_type& a = *a_;\n\t\t\tconst string_type& b = *b_;\n\n\t\t\tsize_t best_i = i1;\n\t\t\tsize_t best_j = j1;\n\t\t\tsize_t best_size = 0;\n\n\t\t\tstd::map<size_t, size_t> j2len;\n\n\t\t\tfor (size_t i = i1; i < i2; ++i) {\n\t\t\t\tstd::map<size_t, size_t> newj2len;\n\t\t\t\tfor (size_t j : b2j[a[i]]) {\n\t\t\t\t\tif (j < j1)\n\t\t\t\t\t\tcontinue;\n\t\t\t\t\tif (j >= j2)\n\t\t\t\t\t\tbreak;\n\t\t\t\t\tsize_t k = newj2len[j] = j2len[j - 1] + 1;\n\t\t\t\t\tif (k > best_size) {\n\t\t\t\t\t\tbest_i = i - k + 1;\n\t\t\t\t\t\tbest_j = j - k + 1;\n\t\t\t\t\t\tbest_size = k;\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t\tj2len = newj2len;\n\t\t\t}\n\n\t\t\twhile (\n\t\t\t\tbest_i > i1 &&\n\t\t\t\tbest_j > j1 &&\n\t\t\t\t!is_b_junk(b[best_j - 1]) &&\n\t\t\t\ta[best_i - 1] == b[best_j - 1]\n\t\t\t\t) {\n\t\t\t\t--best_i;\n\t\t\t\t--best_j;\n\t\t\t\t++best_size;\n\t\t\t}\n\n\t\t\twhile (\n\t\t\t\tbest_i + best_size < i2 &&\n\t\t\t\tbest_j + best_size < j2 &&\n\t\t\t\t!is_b_junk(b[best_j + best_size]) &&\n\t\t\t\ta[best_i + best_size] == b[best_j + best_size]\n\t\t\t\t) {\n\t\t\t\t++best_size;\n\t\t\t}\n\n\t\t\twhile (\n\t\t\t\tbest_i > i1 &&\n\t\t\t\tbest_j > j1 &&\n\t\t\t\tis_b_junk(b[best_j - 1]) &&\n\t\t\t\ta[best_i - 1] == b[best_j - 1]\n\t\t\t\t) {\n\t\t\t\t--best_i;\n\t\t\t\t--best_j;\n\t\t\t\t++best_size;\n\t\t\t}\n\n\t\t\twhile (\n\t\t\t\tbest_i + best_size < i2 &&\n\t\t\t\tbest_j + best_size < j2 &&\n\t\t\t\tis_b_junk(b[best_j + best_size]) &&\n\t\t\t\ta[best_i + best_size] == b[best_j + best_size]\n\t\t\t\t) {\n\t\t\t\t++best_size;\n\t\t\t}\n\n\t\t\treturn Block{ best_i, best_j, best_size };\n\t\t}\n\n\t\t// Return list of Blocks describing matching subsequences\n\t\tconst std::vector<Block>& get_matching_blocks()\n\t\t{\n\t\t\tif (!matching_blocks.empty())\n\t\t\t\treturn matching_blocks;\n\n\t\t\tsize_t len_a = a_->size();\n\t\t\tsize_t len_b = b_->size();\n\n\t\t\tstd::vector<OpCode> queue{ 1,{ tag_t::t_unknown, 0, len_a, 0, len_b } };\n\n\t\t\twhile (!queue.empty()) {\n\t\t\t\tOpCode op = queue.back();\n\t\t\t\tqueue.pop_back();\n\t\t\t\tBlock b = find_longest_match(op.i1, op.i2, op.j1, op.j2);\n\t\t\t\tif (b.length != 0) {\n\t\t\t\t\tmatching_blocks.push_back(b);\n\t\t\t\t\tif (op.i1 < b.i && op.j1 < b.j)\n\t\t\t\t\t\tqueue.emplace_back(tag_t::t_unknown, op.i1, b.i, op.j1, b.j);\n\t\t\t\t\tif (b.i + b.length < op.i2 && b.j + b.length < op.j2)\n\t\t\t\t\t\tqueue.emplace_back(tag_t::t_unknown, b.i + b.length, op.i2, b.j + b.length, op.j2);\n\t\t\t\t}\n\t\t\t}\n\t\t\tstd::sort(matching_blocks.begin(), matching_blocks.end(), [](const Block& lhs, const Block& rhs) { return lhs.i == rhs.i ? lhs.j < rhs.j : lhs.i < rhs.i; });\n\n\t\t\tBlock b1{ 0, 0, 0 };\n\t\t\tstd::vector<Block> non_adjacent;\n\t\t\tfor (const Block& b2 : matching_blocks) {\n\t\t\t\tif (b1.i + b1.length == b2.i && b1.j + b1.length == b2.j)\n\t\t\t\t\tb1.length += b2.length;\n\t\t\t\telse {\n\t\t\t\t\tif (b1.length != 0)\n\t\t\t\t\t\tnon_adjacent.push_back(b1);\n\t\t\t\t\tb1 = b2;\n\t\t\t\t}\n\n\t\t\t}\n\t\t\tif (b1.length != 0)\n\t\t\t\tnon_adjacent.push_back(b1);\n\t\t\tnon_adjacent.emplace_back(len_a, len_b, 0);\n\t\t\tmatching_blocks = non_adjacent;\n\t\t\treturn matching_blocks;\n\t\t}\n\n\t\t// Return list of opcodes describing how to turn a into b\n\t\tconst std::vector<OpCode>& get_opcodes()\n\t\t{\n\t\t\tif (!opcodes.empty())\n\t\t\t\treturn opcodes;\n\n\t\t\tsize_t i = 0;\n\t\t\tsize_t j = 0;\n\n\t\t\tfor (const Block& b : get_matching_blocks()) {\n\t\t\t\ttag_t tag = tag_t::t_unknown;\n\t\t\t\tif (i < b.i && j < b.j)\n\t\t\t\t\ttag = tag_t::t_replace;\n\t\t\t\telse if (i < b.i)\n\t\t\t\t\ttag = tag_t::t_delete;\n\t\t\t\telse if (j < b.j)\n\t\t\t\t\ttag = tag_t::t_insert;\n\n\t\t\t\tif (tag != tag_t::t_unknown)\n\t\t\t\t\topcodes.emplace_back(tag, i, b.i, j, b.j);\n\n\t\t\t\ti = b.i + b.length;\n\t\t\t\tj = b.j + b.length;\n\n\t\t\t\tif (b.length != 0)\n\t\t\t\t\topcodes.emplace_back(tag_t::t_equal, b.i, i, b.j, j);\n\t\t\t}\n\n\t\t\treturn opcodes;\n\t\t}\n\n\t\tstd::vector<std::vector<OpCode>> get_grouped_opcodes(size_t n = 3)\n\t\t{\n\t\t\tstd::vector<OpCode> codes = opcodes;\n\t\t\tif (codes.empty())\n\t\t\t\tcodes.emplace_back(tag_t::t_equal, 0, 1, 0, 1);\n\t\t\tif (codes.front().tag == tag_t::t_equal) {\n\t\t\t\tOpCode cur = codes.front();\n\t\t\t\tcodes.front() = OpCode{ cur.tag, std::max(cur.i1, cur.i2 - n), cur.i2, std::max(cur.j1, cur.j2 - n), cur.j2 };\n\t\t\t}\n\t\t\tif (codes.back().tag == tag_t::t_equal) {\n\t\t\t\tOpCode cur = codes.back();\n\t\t\t\tcodes.back() = OpCode{ cur.tag, cur.i1, std::min(cur.i2, cur.i1 + n), cur.j1, std::min(cur.j2, cur.j1 + n) };\n\t\t\t}\n\n\t\t\tsize_t nn = 2 * n;\n\n\t\t\tstd::vector<std::vector<OpCode>> all_groups;\n\t\t\tstd::vector<OpCode> group;\n\t\t\tfor (OpCode cur : codes) {\n\t\t\t\tif (cur.tag == tag_t::t_equal && cur.i2 - cur.i1 > nn) {\n\t\t\t\t\tgroup.emplace_back(cur.tag, cur.i1, std::min(cur.i2, cur.i1 + n), cur.j1, std::min(cur.j2, cur.j1 + n));\n\t\t\t\t\tall_groups.push_back(group);\n\t\t\t\t\tgroup.clear();\n\t\t\t\t\tcur.i1 = std::max(cur.i1, cur.i2 - n);\n\t\t\t\t\tcur.j1 = std::max(cur.j1, cur.j2 - n);\n\t\t\t\t}\n\t\t\t\tgroup.push_back(cur);\n\t\t\t}\n\t\t\tif (!group.empty() && !(group.size() == 1 && group.front().tag == tag_t::t_equal))\n\t\t\t\tall_groups.push_back(group);\n\n\t\t\treturn all_groups;\n\t\t}\n\n\t\t// Return a measure of the sequences' similarity (double in [0, 1])\n\t\tdouble ratio()\n\t\t{\n\t\t\tsize_t matches = 0;\n\t\t\tfor (const Block& b : get_matching_blocks())\n\t\t\t\tmatches += b.length;\n\n\t\t\treturn detail::calculate_ratio(matches, a_->size() + b_->size());\n\t\t}\n\n\t\t// Return an upper bound on .ratio() relatively quickly\n\t\tdouble quick_ratio()\n\t\t{\n\t\t\tif (full_b_count.empty()) {\n\t\t\t\tfor (char_type c : *b_)\n\t\t\t\t\t++full_b_count[c];\n\t\t\t}\n\n\t\t\tstd::map<char_type, int> avail;\n\t\t\tsize_t matches = 0;\n\n\t\t\tfor (char_type c : *a_) {\n\t\t\t\tint numb;\n\t\t\t\tif (avail.find(c) != avail.end())\n\t\t\t\t\tnumb = avail[c];\n\t\t\t\telse\n\t\t\t\t\tnumb = static_cast<int>(full_b_count[c]);\n\t\t\t\tavail[c] = numb - 1;\n\t\t\t\tif (numb > 0)\n\t\t\t\t\tmatches++;\n\t\t\t}\n\n\t\t\treturn detail::calculate_ratio(matches, a_->size() + b_->size());\n\t\t}\n\n\t\t// Return an upper bound on ratio() very quickly\n\t\tdouble real_quick_ratio()\n\t\t{\n\t\t\treturn detail::calculate_ratio(std::min(a_->size(), b_->size()), a_->size() + b_->size());\n\t\t}\n\tprivate:\n\t\tvoid chain_b()\n\t\t{\n\t\t\tconst string_type& b = *b_; // For convenience\n\n\t\t\t\t\t\t\t\t\t\t// Build b2j ignoring junk\n\t\t\tb2j.clear();\n\t\t\tfor (size_t i = 0; i < b.size(); ++i)\n\t\t\t\tb2j[b[i]].push_back(i);\n\n\t\t\t// Purge junk elements\n\t\t\tb_junk.clear();\n\t\t\tif (is_junk) {\n\t\t\t\tfor (const auto& pair : b2j) {\n\t\t\t\t\tif (is_junk(pair.first))\n\t\t\t\t\t\tb_junk.insert(pair.first);\n\t\t\t\t}\n\t\t\t\tfor (const auto& elt : b_junk)\n\t\t\t\t\tb2j.erase(elt);\n\t\t\t}\n\n\t\t\t// Purge popular elements that are not junk\n\t\t\tb_popular.clear();\n\t\t\tif (auto_junk && b.size() > 200) {\n\t\t\t\tsize_t n_test = (b.size() / 100) + 1;\n\t\t\t\tfor (const auto& pair : b2j) {\n\t\t\t\t\tif (pair.second.size() > n_test)\n\t\t\t\t\t\tb_popular.insert(pair.first);\n\t\t\t\t}\n\t\t\t\tfor (const auto& elt : b_popular)\n\t\t\t\t\tb2j.erase(elt);\n\t\t\t}\n\n\t\t}\n\n\t\tbool is_b_junk(char_type s)\n\t\t{\n\t\t\treturn b_junk.find(s) != b_junk.end();\n\t\t}\n\n\t\tJunkPred is_junk; // User supplied function that takes a sequence element and returns true if the element is junk\n\t\tconst string_type* a_; // First sequence\n\t\tconst string_type* b_; // Second sequence\n\t\tstd::map<char_type, std::vector<size_t>> b2j; // List of non-junk indices into b where each element of b appears\n\t\tstd::map<char_type, size_t> full_b_count; // Number of times each element in b appears\n\t\tstd::vector<OpCode> opcodes; // List of opcodes\n\t\tstd::vector<Block> matching_blocks; // List of matching blocks\n\t\tstd::set<char_type> b_junk; // Items in b for which is_junk returns true\n\t\tstd::set<char_type> b_popular; // Nonjunk element in b treated as junk by the heuristic (if enabled)\n\t\tbool auto_junk; // If true, heuristic junk collection is enabled\n\t};\n\n\ttemplate <typename string_type, typename It>\n\tstd::vector<string_type> get_close_matches(const string_type& word, It begin, It end, size_t n = 3, double cutoff = 0.6)\n\t{\n\t\tif (n == 0)\n\t\t\tthrow std::invalid_argument(\"n must be > 0\");\n\t\tif (cutoff < 0. || cutoff > 1.)\n\t\t\tthrow std::invalid_argument(\"cutoff must be in the range 0.0 < cutoff < 1.0\");\n\n\t\tstd::vector<std::pair<double, string_type>> result;\n\n\t\tSequenceMatcher<string_type> s;\n\t\ts.set_seq2(word);\n\t\twhile (begin != end) {\n\t\t\ts.set_seq1(*begin);\n\t\t\tif (s.real_quick_ratio() >= cutoff && s.quick_ratio() >= cutoff && s.ratio() >= cutoff)\n\t\t\t\tresult.emplace_back(s.ratio(), *begin);\n\t\t\t++begin;\n\t\t}\n\n\t\tstd::vector<string_type> ret;\n\t\tif (result.size() > n) {\n\t\t\tstd::nth_element(result.begin(), result.end() - n, result.end(), [](const auto& lhs, const auto& rhs) {return lhs.first < rhs.first; });\n\t\t\tresult = decltype(result)(result.end() - n, result.end());\n\t\t}\n\n\t\tstd::sort(result.begin(), result.end(), [](const auto& lhs, const auto& rhs) {return lhs.first > rhs.first; });\n\t\tfor (auto it = result.begin(), end = result.end(); it != end; ++it)\n\t\t\tret.push_back(it->second);\n\t\treturn ret;\n\t}\n\n\n\ttemplate <typename StringT>\n\tclass Differ\n\t{\n\tpublic:\n\t\tusing string_type = StringT;\n\t\tusing delta_type = Delta<StringT>;\n\t\tusing char_type = typename StringT::value_type;\n\t\tusing LineJunkPred = bool(*)(const string_type&);\n\t\tusing CharJunkPred = bool(*)(const char_type&);\n\n\t\tDiffer(LineJunkPred line_junk = nullptr, CharJunkPred char_junk = nullptr, double cutoff = 0.75)\n\t\t\t: line_junk(line_junk)\n\t\t\t, char_junk(char_junk)\n\t\t\t, a_ptr(nullptr)\n\t\t\t, b_ptr(nullptr)\n\t\t\t, cutoff(cutoff)\n\t\t{\n\n\t\t}\n\n\t\ttemplate <typename SequenceT>\n\t\tstd::vector<delta_type> get_deltas(const SequenceT& a, const SequenceT& b)\n\t\t{\n\t\t\tcompare(a, b);\n\t\t\treturn deltas;\n\t\t}\n\n\t\ttemplate <typename SequenceT>\n\t\tconst std::vector<string_type>& compare(const SequenceT& a, const SequenceT& b)\n\t\t{\n\t\t\tif (set_seqs(a, b) && !diffs.empty())\n\t\t\t\treturn diffs;\n\n\t\t\tSequenceMatcher<SequenceT> cruncher(line_junk, a, b);\n\t\t\tfor (const auto& opcode : cruncher.get_opcodes()) {\n\t\t\t\tswitch (opcode.tag) {\n\t\t\t\tcase tag_t::t_replace:\n\t\t\t\t\tfancy_replace(a, opcode.i1, opcode.i2, b, opcode.j1, opcode.j2);\n\t\t\t\t\tbreak;\n\t\t\t\tcase tag_t::t_delete:\n\t\t\t\t\tdump(tag_t::t_delete, a, opcode.i1, opcode.i2);\n\t\t\t\t\tbreak;\n\t\t\t\tcase tag_t::t_insert:\n\t\t\t\t\tdump(tag_t::t_insert, b, opcode.j1, opcode.j2);\n\t\t\t\t\tbreak;\n\t\t\t\tcase tag_t::t_equal:\n\t\t\t\t\tdump(tag_t::t_equal, a, opcode.i1, opcode.i2);\n\t\t\t\t\tbreak;\n\t\t\t\tdefault:\n\t\t\t\t\tthrow std::invalid_argument(\"unknown tag\");\n\t\t\t\t}\n\t\t\t}\n\t\t\treturn diffs;\n\t\t}\n\n\tprivate:\n\t\ttemplate <typename SequenceT>\n\t\tvoid dump(tag_t tag, const SequenceT& x, size_t i1, size_t i2)\n\t\t{\n\t\t\tfor (size_t i = i1; i < i2; ++i) {\n\t\t\t\tswitch (tag) {\n\t\t\t\tcase tag_t::t_delete:\n\t\t\t\t\tdiffs.push_back(\"- \" + x[i]);\n\t\t\t\t\tdeltas.emplace_back(tag_t::t_delete, x[i], \"\");\n\t\t\t\t\tbreak;\n\t\t\t\tcase tag_t::t_insert:\n\t\t\t\t\tdiffs.push_back(\"+ \" + x[i]);\n\t\t\t\t\tdeltas.emplace_back(tag_t::t_insert, \"\", x[i]);\n\t\t\t\t\tbreak;\n\t\t\t\tcase tag_t::t_equal:\n\t\t\t\t\tdiffs.push_back(\"  \" + x[i]);\n\t\t\t\t\tdeltas.emplace_back(tag_t::t_equal, x[i], \"\");\n\t\t\t\t\tbreak;\n\t\t\t\tdefault:\n\t\t\t\t\tthrow std::invalid_argument(\"unknown tag\");\n\t\t\t\t}\n\t\t\t}\n\t\t}\n\n\t\ttemplate <typename SequenceT>\n\t\tvoid plain_replace(const SequenceT& a, size_t i1, size_t i2, const SequenceT& b, size_t j1, size_t j2)\n\t\t{\n\t\t\tif (j2 - j1 < i2 - i1) {\n\t\t\t\tdump(tag_t::t_insert, b, j1, j2);\n\t\t\t\tdump(tag_t::t_delete, a, i1, i2);\n\t\t\t}\n\t\t\telse {\n\t\t\t\tdump(tag_t::t_delete, a, i1, i2);\n\t\t\t\tdump(tag_t::t_insert, b, j1, j2);\n\t\t\t}\n\t\t}\n\n\t\ttemplate <typename SequenceT>\n\t\tvoid fancy_replace(const SequenceT& a, size_t i1, size_t i2, const SequenceT& b, size_t j1, size_t j2)\n\t\t{\n\t\t\tSequenceMatcher<string_type> cruncher(char_junk);\n\t\t\tdouble best_ratio = 0.74;\n\t\t\tsize_t eq_i = 0;\n\t\t\tsize_t eq_j = 0;\n\t\t\tbool eq_found = false;\n\t\t\tsize_t best_i = 0;\n\t\t\tsize_t best_j = 0;\n\n\t\t\tfor (size_t j = j1; j < j2; ++j) {\n\t\t\t\tconst string_type& b_j = b[j];\n\t\t\t\tcruncher.set_seq2(b_j);\n\t\t\t\tfor (size_t i = i1; i < i2; ++i) {\n\t\t\t\t\tconst string_type& a_i = a[i];\n\t\t\t\t\tif (a_i == b_j) {\n\t\t\t\t\t\tif (!eq_found) {\n\t\t\t\t\t\t\teq_found = true;\n\t\t\t\t\t\t\teq_i = i;\n\t\t\t\t\t\t\teq_j = j;\n\t\t\t\t\t\t}\n\t\t\t\t\t\tcontinue;\n\t\t\t\t\t}\n\t\t\t\t\tcruncher.set_seq1(a_i);\n\t\t\t\t\tif (\n\t\t\t\t\t\tcruncher.real_quick_ratio() > best_ratio &&\n\t\t\t\t\t\tcruncher.quick_ratio() > best_ratio &&\n\t\t\t\t\t\tcruncher.ratio() > best_ratio\n\t\t\t\t\t\t) {\n\t\t\t\t\t\tbest_ratio = cruncher.ratio();\n\t\t\t\t\t\tbest_i = i;\n\t\t\t\t\t\tbest_j = j;\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t}\n\n\t\t\tif (best_ratio < cutoff) {\n\t\t\t\tif (!eq_found)\n\t\t\t\t\treturn plain_replace(a, i1, i2, b, j1, j2);\n\t\t\t\tbest_i = eq_i;\n\t\t\t\tbest_j = eq_j;\n\t\t\t\tbest_ratio = 1.0;\n\t\t\t}\n\t\t\telse {\n\t\t\t\teq_found = false;\n\t\t\t}\n\n\t\t\tfancy_helper(a, i1, best_i, b, j1, best_j);\n\n\t\t\tconst string_type& a_elt = a[best_i];\n\t\t\tconst string_type& b_elt = b[best_j];\n\t\t\tif (!eq_found) {\n\t\t\t\tstring_type a_tags, b_tags;\n\t\t\t\tcruncher.set_seqs(a_elt, b_elt);\n\t\t\t\tdeltas.emplace_back(tag_t::t_replace, a_elt, b_elt, cruncher.get_opcodes());\n\t\t\t\tfor (const auto& opcode : cruncher.get_opcodes()) {\n\t\t\t\t\tsize_t len_a = opcode.i2 - opcode.i1;\n\t\t\t\t\tsize_t len_b = opcode.j2 - opcode.j1;\n\t\t\t\t\tswitch (opcode.tag) {\n\t\t\t\t\tcase tag_t::t_replace:\n\t\t\t\t\t\ta_tags += string_type(len_a, '^');\n\t\t\t\t\t\tb_tags += string_type(len_b, '^');\n\t\t\t\t\t\tbreak;\n\t\t\t\t\tcase tag_t::t_delete:\n\t\t\t\t\t\ta_tags += string_type(len_a, '-');\n\t\t\t\t\t\tbreak;\n\t\t\t\t\tcase tag_t::t_insert:\n\t\t\t\t\t\tb_tags += string_type(len_b, '+');\n\t\t\t\t\t\tbreak;\n\t\t\t\t\tcase tag_t::t_equal:\n\t\t\t\t\t\ta_tags += string_type(len_a, ' ');\n\t\t\t\t\t\tb_tags += string_type(len_b, ' ');\n\t\t\t\t\t\tbreak;\n\t\t\t\t\tdefault:\n\t\t\t\t\t\tthrow std::invalid_argument(\"unknown tag\");\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t\tqformat(a_elt, b_elt, a_tags, b_tags);\n\t\t\t}\n\t\t\telse {\n\t\t\t\tdiffs.push_back(\"  \" + a_elt);\n\t\t\t\tdeltas.emplace_back(tag_t::t_equal, a_elt, \"\");\n\t\t\t}\n\n\t\t\tfancy_helper(a, best_i + 1, i2, b, best_j + 1, j2);\n\t\t}\n\n\t\ttemplate <typename SequenceT>\n\t\tvoid fancy_helper(const SequenceT& a, size_t i1, size_t i2, const SequenceT& b, size_t j1, size_t j2)\n\t\t{\n\t\t\tif (i1 < i2) {\n\t\t\t\tif (j1 < j2)\n\t\t\t\t\tfancy_replace(a, i1, i2, b, j1, j2);\n\t\t\t\telse\n\t\t\t\t\tdump(tag_t::t_delete, a, i1, i2);\n\t\t\t}\n\t\t\telse if (j1 < j2) {\n\t\t\t\tdump(tag_t::t_insert, b, j1, j2);\n\t\t\t}\n\t\t}\n\n\t\tvoid qformat(const string_type& a_line, const string_type& b_line, string_type a_tags, string_type b_tags)\n\t\t{\n\t\t\tusing detail::count_leading;\n\t\t\tusing detail::rtrim;\n\n\t\t\tsize_t common = std::min(count_leading(a_line, '\\t'), count_leading(b_line, '\\t'));\n\t\t\tcommon = std::min(common, count_leading(a_tags.substr(0, common), ' '));\n\t\t\tcommon = std::min(common, count_leading(b_tags.substr(0, common), ' '));\n\n\t\t\ta_tags = a_tags.substr(common);\n\t\t\tb_tags = b_tags.substr(common);\n\t\t\trtrim(a_tags);\n\t\t\trtrim(b_tags);\n\n\t\t\tdiffs.push_back(\"- \" + a_line);\n\t\t\tif (!a_tags.empty())\n\t\t\t\tdiffs.push_back(\"? \" + string_type(common, '\\t') + a_tags + \"\\n\");\n\n\t\t\tdiffs.push_back(\"+ \" + b_line);\n\t\t\tif (!b_tags.empty())\n\t\t\t\tdiffs.push_back(\"? \" + string_type(common, '\\t') + b_tags + \"\\n\");\n\t\t}\n\n\t\ttemplate <typename SequenceT>\n\t\tbool set_seqs(const SequenceT& a, const SequenceT& b)\n\t\t{\n\t\t\tif (reinterpret_cast<const void*>(std::addressof(a)) == a_ptr && reinterpret_cast<const void*>(std::addressof(b)) == b_ptr) {\n\t\t\t\treturn true;\n\t\t\t}\n\n\t\t\ta_ptr = reinterpret_cast<const void*>(std::addressof(a));\n\t\t\tb_ptr = reinterpret_cast<const void*>(std::addressof(b));\n\t\t\tdeltas.clear();\n\t\t\tdiffs.clear();\n\n\t\t\treturn false;\n\t\t}\n\n\t\tLineJunkPred line_junk;\n\t\tCharJunkPred char_junk;\n\t\tstd::vector<string_type> diffs;\n\t\tstd::vector<delta_type> deltas;\n\t\tconst void* a_ptr;\n\t\tconst void* b_ptr;\n\t\tconst double cutoff;\n\t};\n}\n\n#endif\n"
  },
  {
    "path": "libs/internal/include/internal/string_tools.h",
    "content": "#include <algorithm> \n#include <cctype>\n#include <locale>\n#include <string>\n#include <vector>\n\ninline std::string ltrim(std::string s)\n{\n\ts.erase(s.begin(), std::find_if(s.begin(), s.end(), [](int ch) {\n\t\treturn !std::isspace(ch);\n\t\t}));\n\treturn s;\n}\n\ninline std::string rtrim(std::string s)\n{\n\ts.erase(std::find_if(s.rbegin(), s.rend(), [](int ch) {\n\t\treturn !std::isspace(ch);\n\t\t}).base(), s.end());\n\treturn s;\n}\n\ninline std::string trim(std::string s)\n{\n\treturn ltrim(rtrim(s));\n}\ninline std::vector<std::string> string_to_vec(const std::string& s)\n{\n\tstd::vector<std::string> v;\n\tauto pos = s.begin();\n\twhile (pos != s.end()) {\n\t\tauto it = std::find(pos, s.end(), '\\n');\n\t\tif (it != s.end())\n\t\t\t++it;\n\t\tv.push_back(std::string(pos, it));\n\t\tpos = it;\n\t}\n\treturn v;\n}\n\ninline std::string nth_line(const std::string& s, size_t n)\n{\n\tsize_t pos = 0;\n\twhile (n > 0) {\n\t\tpos = s.find('\\n', pos) + 1;\n\t\tif (pos == 0)\n\t\t\treturn \"\";\n\t\t--n;\n\t}\n\treturn s.substr(pos, s.find('\\n', pos) - pos);\n}\n\ninline std::string escape_backslashes(std::string s)\n{\n\tsize_t start = 0;\n\twhile ((start = s.find('\\\\', start)) != std::string::npos) {\n\t\ts.replace(start, 1, \"\\\\\\\\\");\n\t\tstart += 2;\n\t}\n\treturn s;\n}\n\ninline void replace_all(std::string& str, const std::string& from, const std::string& to) {\n\tsize_t start_pos = 0;\n\twhile ((start_pos = str.find(from, start_pos)) != std::string::npos) {\n\t\tstr.replace(start_pos, from.length(), to);\n\t\tstart_pos += to.length(); // Handles case where 'to' is a substring of 'from'\n\t}\n}\n"
  },
  {
    "path": "libs/internal/include/internal/uniconv.h",
    "content": "#include <locale>\n#include <codecvt>\n#include <string>\n\n#ifdef _MSC_VER\n\nstruct utf_converter\n{\npublic:\n\tstd::string to_utf8(const std::u32string& utf32_string)\n\t{\n\t\tstd::basic_string<__int32> inp(utf32_string.begin(), utf32_string.end());\n\t\treturn conv.to_bytes(inp);\n\t}\n\tstd::u32string to_utf32(const std::string& utf8_string)\n\t{\n\t\tauto int32str = conv.from_bytes(utf8_string);\n\t\treturn std::u32string(int32str.begin(), int32str.end());\n\t}\n\nprivate:\n\tstd::wstring_convert<std::codecvt_utf8<__int32>, __int32> conv;\n};\n\n#else\n\nstruct utf_converter\n{\npublic:\n\tstd::string to_utf8(const std::u32string& utf32_string)\n\t{\n\t\treturn conv.to_bytes(utf32_string);\n\t}\n\tstd::u32string to_utf32(const std::string& utf8_string)\n\t{\n\t\treturn conv.from_bytes(utf8_string);\n\t}\n\nprivate:\n\tstd::wstring_convert<std::codecvt_utf8<char32_t>, char32_t> conv;\n};\n\n#endif\n"
  },
  {
    "path": "libs/internal/include/internal/unistd.h",
    "content": "\n// Compatibility include to substitute for unistd.h on Windows.\n\n#ifdef _MSC_VER\n  #include <io.h>\n  #include <process.h>\n  #include <direct.h>\n  #define pid_t int\n  #define sleep(x) Sleep(1000 * x)\n#else\n  #include <unistd.h>\n#endif\n"
  },
  {
    "path": "libs/internal/include/internal/uuid.h",
    "content": "#pragma once\n#include <stdlib.h>\n#include <chrono>\n#include <random>\n#include <vector>\n\nnamespace cadabra\n{\n\tnamespace detail\n\t{\n\t\tinline unsigned int get_seed()\n\t\t{\n\t\t\tauto tp = std::chrono::system_clock::now();\n\t\t\treturn static_cast<unsigned long>(tp.time_since_epoch().count());\n\t\t}\n\t}\n\n\ttemplate <typename IntegerT>\n\tIntegerT generate_uuid()\n\t{\n\t\tstatic std::random_device rd;\n\t\tstatic std::mt19937 rng(rd());\n\t\tstatic std::uniform_int_distribution<IntegerT> uni(1);\n\n\t\treturn uni(rng);\n\t}\n}\n"
  },
  {
    "path": "libs/linenoise/LICENSE",
    "content": "Copyright (c) 2015 yhirose\nAll rights reserved.\n\nRedistribution and use in source and binary forms, with or without\nmodification, are permitted provided that the following conditions are met:\n\n1. Redistributions of source code must retain the above copyright notice, this\n   list of conditions and the following disclaimer.\n2. Redistributions in binary form must reproduce the above copyright notice,\n   this list of conditions and the following disclaimer in the documentation\n   and/or other materials provided with the distribution.\n\nTHIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS \"AS IS\" AND\nANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED\nWARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE\nDISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR\nANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES\n(INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;\nLOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND\nON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT\n(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS\nSOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.\n"
  },
  {
    "path": "libs/linenoise/linenoise.hpp",
    "content": "/*\n *  linenoise.hpp -- Multi-platfrom C++ header-only linenoise library.\n *\n *  All credits and commendations have to go to the authors of the\n *  following excellent libraries.\n *\n *  - linenoise.h and linenose.c (https://github.com/antirez/linenoise)\n *  - ANSI.c (https://github.com/adoxa/ansicon)\n *  - Win32_ANSI.h and Win32_ANSI.c (https://github.com/MSOpenTech/redis)\n *\n * ------------------------------------------------------------------------\n *\n *  Copyright (c) 2015 yhirose\n *  All rights reserved.\n *  \n *  Redistribution and use in source and binary forms, with or without\n *  modification, are permitted provided that the following conditions are met:\n *  \n *  1. Redistributions of source code must retain the above copyright notice, this\n *     list of conditions and the following disclaimer.\n *  2. Redistributions in binary form must reproduce the above copyright notice,\n *     this list of conditions and the following disclaimer in the documentation\n *     and/or other materials provided with the distribution.\n *  \n *  THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS \"AS IS\" AND\n *  ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED\n *  WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE\n *  DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR\n *  ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES\n *  (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;\n *  LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND\n *  ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT\n *  (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS\n *  SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.\n */\n\n/* linenoise.h -- guerrilla line editing library against the idea that a\n * line editing lib needs to be 20,000 lines of C code.\n *\n * See linenoise.c for more information.\n *\n * ------------------------------------------------------------------------\n *\n * Copyright (c) 2010, Salvatore Sanfilippo <antirez at gmail dot com>\n * Copyright (c) 2010, Pieter Noordhuis <pcnoordhuis at gmail dot com>\n *\n * All rights reserved.\n *\n * Redistribution and use in source and binary forms, with or without\n * modification, are permitted provided that the following conditions are\n * met:\n *\n *  *  Redistributions of source code must retain the above copyright\n *     notice, this list of conditions and the following disclaimer.\n *\n *  *  Redistributions in binary form must reproduce the above copyright\n *     notice, this list of conditions and the following disclaimer in the\n *     documentation and/or other materials provided with the distribution.\n *\n * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS\n * \"AS IS\" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT\n * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR\n * A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT\n * HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,\n * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT\n * LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,\n * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY\n * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT\n * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE\n * OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.\n */\n\n/*\n * ANSI.c - ANSI escape sequence console driver.\n *\n * Copyright (C) 2005-2014 Jason Hood\n * This software is provided 'as-is', without any express or implied\n * warranty.  In no event will the author be held liable for any damages\n * arising from the use of this software.\n * \n * Permission is granted to anyone to use this software for any purpose,\n * including commercial applications, and to alter it and redistribute it\n * freely, subject to the following restrictions:\n * \n * 1. The origin of this software must not be misrepresented; you must not\n *    claim that you wrote the original software. If you use this software\n *    in a product, an acknowledgment in the product documentation would be\n *    appreciated but is not required.\n * 2. Altered source versions must be plainly marked as such, and must not be\n *    misrepresented as being the original software.\n * 3. This notice may not be removed or altered from any source distribution.\n * \n * Jason Hood\n * jadoxa@yahoo.com.au\n */\n\n/*\n * Win32_ANSI.h and Win32_ANSI.c\n *\n * Derived from ANSI.c by Jason Hood, from his ansicon project (https://github.com/adoxa/ansicon), with modifications.\n *\n * Copyright (c), Microsoft Open Technologies, Inc.\n * All rights reserved.\n * Redistribution and use in source and binary forms, with or without\n * modification, are permitted provided that the following conditions are met:\n *  - Redistributions of source code must retain the above copyright notice,\n *    this list of conditions and the following disclaimer.\n *  - Redistributions in binary form must reproduce the above copyright notice,\n *    this list of conditions and the following disclaimer in the documentation\n *    and/or other materials provided with the distribution.\n * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS \"AS IS\"\n * AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE\n * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE\n * DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE\n * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL\n * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR\n * SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER\n * CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,\n * OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE\n * OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.\n */\n\n#ifndef LINENOISE_HPP\n#define LINENOISE_HPP\n\n#ifndef _WIN32\n#include <termios.h>\n#include <unistd.h>\n#include <sys/ioctl.h>\n#else\n#ifndef NOMINMAX\n#define NOMINMAX\n#endif\n#include <Windows.h>\n#include <io.h>\n#ifndef STDIN_FILENO\n#define STDIN_FILENO (_fileno(stdin))\n#endif\n#ifndef STDOUT_FILENO\n#define STDOUT_FILENO 1\n#endif\n#define isatty _isatty\n#define write win32_write\n#define read _read\n#pragma warning(push)\n#pragma warning(disable : 4996)\n#endif\n#include <stdlib.h>\n#include <stdio.h>\n#include <errno.h>\n#include <string.h>\n#include <ctype.h>\n#include <sys/types.h>\n#include <string>\n#include <fstream>\n#include <functional>\n#include <vector>\n#include <iostream>\n\nnamespace linenoise {\n\ntypedef std::function<void (const char*, std::vector<std::string>&)> CompletionCallback;\n\n#ifdef _WIN32\n\nnamespace ansi {\n\n#define lenof(array) (sizeof(array)/sizeof(*(array)))\n\ntypedef struct\n{\n    BYTE foreground;    // ANSI base color (0 to 7; add 30)\n    BYTE background;    // ANSI base color (0 to 7; add 40)\n    BYTE bold;  // console FOREGROUND_INTENSITY bit\n    BYTE underline; // console BACKGROUND_INTENSITY bit\n    BYTE rvideo;    // swap foreground/bold & background/underline\n    BYTE concealed; // set foreground/bold to background/underline\n    BYTE reverse; // swap console foreground & background attributes\n} GRM, *PGRM;   // Graphic Rendition Mode\n\n\ninline bool is_digit(char c) { return '0' <= c && c <= '9'; }\n\n// ========== Global variables and constants\n\nHANDLE    hConOut;      // handle to CONOUT$\n\nconst char ESC = '\\x1B'; // ESCape character\nconst char BEL = '\\x07';\nconst char SO = '\\x0E';  // Shift Out\nconst char SI = '\\x0F';  // Shift In\n\nconst int MAX_ARG = 16;     // max number of args in an escape sequence\nint   state;                // automata state\nWCHAR prefix;               // escape sequence prefix ( '[', ']' or '(' );\nWCHAR prefix2;              // secondary prefix ( '?' or '>' );\nWCHAR suffix;               // escape sequence suffix\nint   es_argc;              // escape sequence args count\nint   es_argv[MAX_ARG];     // escape sequence args\nWCHAR Pt_arg[MAX_PATH * 2]; // text parameter for Operating System Command\nint   Pt_len;\nBOOL  shifted;\n\n\n// DEC Special Graphics Character Set from\n// http://vt100.net/docs/vt220-rm/table2-4.html\n// Some of these may not look right, depending on the font and code page (in\n// particular, the Control Pictures probably won't work at all).\nconst WCHAR G1[] =\n{\n    ' ',          // _ - blank\n    L'\\x2666',    // ` - Black Diamond Suit\n    L'\\x2592',    // a - Medium Shade\n    L'\\x2409',    // b - HT\n    L'\\x240c',    // c - FF\n    L'\\x240d',    // d - CR\n    L'\\x240a',    // e - LF\n    L'\\x00b0',    // f - Degree Sign\n    L'\\x00b1',    // g - Plus-Minus Sign\n    L'\\x2424',    // h - NL\n    L'\\x240b',    // i - VT\n    L'\\x2518',    // j - Box Drawings Light Up And Left\n    L'\\x2510',    // k - Box Drawings Light Down And Left\n    L'\\x250c',    // l - Box Drawings Light Down And Right\n    L'\\x2514',    // m - Box Drawings Light Up And Right\n    L'\\x253c',    // n - Box Drawings Light Vertical And Horizontal\n    L'\\x00af',    // o - SCAN 1 - Macron\n    L'\\x25ac',    // p - SCAN 3 - Black Rectangle\n    L'\\x2500',    // q - SCAN 5 - Box Drawings Light Horizontal\n    L'_',         // r - SCAN 7 - Low Line\n    L'_',         // s - SCAN 9 - Low Line\n    L'\\x251c',    // t - Box Drawings Light Vertical And Right\n    L'\\x2524',    // u - Box Drawings Light Vertical And Left\n    L'\\x2534',    // v - Box Drawings Light Up And Horizontal\n    L'\\x252c',    // w - Box Drawings Light Down And Horizontal\n    L'\\x2502',    // x - Box Drawings Light Vertical\n    L'\\x2264',    // y - Less-Than Or Equal To\n    L'\\x2265',    // z - Greater-Than Or Equal To\n    L'\\x03c0',    // { - Greek Small Letter Pi\n    L'\\x2260',    // | - Not Equal To\n    L'\\x00a3',    // } - Pound Sign\n    L'\\x00b7',    // ~ - Middle Dot\n};\n\n#define FIRST_G1 '_'\n#define LAST_G1  '~'\n\n\n// color constants\n\n#define FOREGROUND_BLACK 0\n#define FOREGROUND_WHITE FOREGROUND_RED|FOREGROUND_GREEN|FOREGROUND_BLUE\n\n#define BACKGROUND_BLACK 0\n#define BACKGROUND_WHITE BACKGROUND_RED|BACKGROUND_GREEN|BACKGROUND_BLUE\n\nconst BYTE foregroundcolor[8] =\n    {\n    FOREGROUND_BLACK,                   // black foreground\n    FOREGROUND_RED,                     // red foreground\n    FOREGROUND_GREEN,                   // green foreground\n    FOREGROUND_RED | FOREGROUND_GREEN,  // yellow foreground\n    FOREGROUND_BLUE,                    // blue foreground\n    FOREGROUND_BLUE | FOREGROUND_RED,   // magenta foreground\n    FOREGROUND_BLUE | FOREGROUND_GREEN, // cyan foreground\n    FOREGROUND_WHITE                    // white foreground\n    };\n\nconst BYTE backgroundcolor[8] =\n    {\n    BACKGROUND_BLACK,           // black background\n    BACKGROUND_RED,         // red background\n    BACKGROUND_GREEN,           // green background\n    BACKGROUND_RED | BACKGROUND_GREEN,  // yellow background\n    BACKGROUND_BLUE,            // blue background\n    BACKGROUND_BLUE | BACKGROUND_RED,   // magenta background\n    BACKGROUND_BLUE | BACKGROUND_GREEN, // cyan background\n    BACKGROUND_WHITE,           // white background\n    };\n\nconst BYTE attr2ansi[8] =       // map console attribute to ANSI number\n{\n    0,                  // black\n    4,                  // blue\n    2,                  // green\n    6,                  // cyan\n    1,                  // red\n    5,                  // magenta\n    3,                  // yellow\n    7                   // white\n};\n\nGRM grm;\n\n// saved cursor position\nCOORD SavePos;\n\n// ========== Print Buffer functions\n\n#define BUFFER_SIZE 2048\n\nint   nCharInBuffer;\nWCHAR ChBuffer[BUFFER_SIZE];\n\n//-----------------------------------------------------------------------------\n//   FlushBuffer()\n// Writes the buffer to the console and empties it.\n//-----------------------------------------------------------------------------\n\ninline void FlushBuffer(void)\n{\n    DWORD nWritten;\n    if (nCharInBuffer <= 0) return;\n    WriteConsoleW(hConOut, ChBuffer, nCharInBuffer, &nWritten, NULL);\n    nCharInBuffer = 0;\n}\n\n//-----------------------------------------------------------------------------\n//   PushBuffer( WCHAR c )\n// Adds a character in the buffer.\n//-----------------------------------------------------------------------------\n\ninline void PushBuffer(WCHAR c)\n{\n    if (shifted && c >= FIRST_G1 && c <= LAST_G1)\n        c = G1[c - FIRST_G1];\n    ChBuffer[nCharInBuffer] = c;\n    if (++nCharInBuffer == BUFFER_SIZE)\n        FlushBuffer();\n}\n\n//-----------------------------------------------------------------------------\n//   SendSequence( LPCWSTR seq )\n// Send the string to the input buffer.\n//-----------------------------------------------------------------------------\n\ninline void SendSequence(LPCWSTR seq)\n{\n    DWORD out;\n    INPUT_RECORD in;\n    HANDLE hStdIn = GetStdHandle(STD_INPUT_HANDLE);\n\n    in.EventType = KEY_EVENT;\n    in.Event.KeyEvent.bKeyDown = TRUE;\n    in.Event.KeyEvent.wRepeatCount = 1;\n    in.Event.KeyEvent.wVirtualKeyCode = 0;\n    in.Event.KeyEvent.wVirtualScanCode = 0;\n    in.Event.KeyEvent.dwControlKeyState = 0;\n    for (; *seq; ++seq)\n        {\n        in.Event.KeyEvent.uChar.UnicodeChar = *seq;\n        WriteConsoleInput(hStdIn, &in, 1, &out);\n        }\n}\n\n// ========== Print functions\n\n//-----------------------------------------------------------------------------\n//   InterpretEscSeq()\n// Interprets the last escape sequence scanned by ParseAndPrintANSIString\n//   prefix             escape sequence prefix\n//   es_argc            escape sequence args count\n//   es_argv[]          escape sequence args array\n//   suffix             escape sequence suffix\n//\n// for instance, with \\e[33;45;1m we have\n// prefix = '[',\n// es_argc = 3, es_argv[0] = 33, es_argv[1] = 45, es_argv[2] = 1\n// suffix = 'm'\n//-----------------------------------------------------------------------------\n\ninline void InterpretEscSeq(void)\n{\n    int  i;\n    WORD attribut;\n    CONSOLE_SCREEN_BUFFER_INFO Info;\n    CONSOLE_CURSOR_INFO CursInfo;\n    DWORD len, NumberOfCharsWritten;\n    COORD Pos;\n    SMALL_RECT Rect;\n    CHAR_INFO  CharInfo;\n\n    if (prefix == '[')\n        {\n        if (prefix2 == '?' && (suffix == 'h' || suffix == 'l'))\n            {\n            if (es_argc == 1 && es_argv[0] == 25)\n                {\n                GetConsoleCursorInfo(hConOut, &CursInfo);\n                CursInfo.bVisible = (suffix == 'h');\n                SetConsoleCursorInfo(hConOut, &CursInfo);\n                return;\n                }\n            }\n        // Ignore any other \\e[? or \\e[> sequences.\n        if (prefix2 != 0)\n            return;\n\n        GetConsoleScreenBufferInfo(hConOut, &Info);\n        switch (suffix)\n            {\n                case 'm':\n                    if (es_argc == 0) es_argv[es_argc++] = 0;\n                    for (i = 0; i < es_argc; i++)\n                        {\n                        if (30 <= es_argv[i] && es_argv[i] <= 37)\n                            grm.foreground = es_argv[i] - 30;\n                        else if (40 <= es_argv[i] && es_argv[i] <= 47)\n                            grm.background = es_argv[i] - 40;\n                        else switch (es_argv[i])\n                            {\n                                case 0:\n                                case 39:\n                                case 49:\n                                        {\n                                        WCHAR def[4];\n                                        int   a;\n                                        *def = '7'; def[1] = '\\0';\n                                        GetEnvironmentVariableW(L\"ANSICON_DEF\", def, lenof(def));\n                                        a = wcstol(def, NULL, 16);\n                                        grm.reverse = FALSE;\n                                        if (a < 0)\n                                            {\n                                            grm.reverse = TRUE;\n                                            a = -a;\n                                            }\n                                        if (es_argv[i] != 49)\n                                            grm.foreground = attr2ansi[a & 7];\n                                        if (es_argv[i] != 39)\n                                            grm.background = attr2ansi[(a >> 4) & 7];\n                                        if (es_argv[i] == 0)\n                                            {\n                                            if (es_argc == 1)\n                                                {\n                                                grm.bold = a & FOREGROUND_INTENSITY;\n                                                grm.underline = a & BACKGROUND_INTENSITY;\n                                                }\n                                            else\n                                                {\n                                                grm.bold = 0;\n                                                grm.underline = 0;\n                                                }\n                                            grm.rvideo = 0;\n                                            grm.concealed = 0;\n                                            }\n                                        }\n                                        break;\n\n                                case  1: grm.bold = FOREGROUND_INTENSITY; break;\n                                case  5: // blink\n                                case  4: grm.underline = BACKGROUND_INTENSITY; break;\n                                case  7: grm.rvideo = 1; break;\n                                case  8: grm.concealed = 1; break;\n                                case 21: // oops, this actually turns on double underline\n                                case 22: grm.bold = 0; break;\n                                case 25:\n                                case 24: grm.underline = 0; break;\n                                case 27: grm.rvideo = 0; break;\n                                case 28: grm.concealed = 0; break;\n                            }\n                        }\n                    if (grm.concealed)\n                        {\n                        if (grm.rvideo)\n                            {\n                            attribut = foregroundcolor[grm.foreground]\n                                | backgroundcolor[grm.foreground];\n                            if (grm.bold)\n                                attribut |= FOREGROUND_INTENSITY | BACKGROUND_INTENSITY;\n                            }\n                        else\n                            {\n                            attribut = foregroundcolor[grm.background]\n                                | backgroundcolor[grm.background];\n                            if (grm.underline)\n                                attribut |= FOREGROUND_INTENSITY | BACKGROUND_INTENSITY;\n                            }\n                        }\n                    else if (grm.rvideo)\n                        {\n                        attribut = foregroundcolor[grm.background]\n                            | backgroundcolor[grm.foreground];\n                        if (grm.bold)\n                            attribut |= BACKGROUND_INTENSITY;\n                        if (grm.underline)\n                            attribut |= FOREGROUND_INTENSITY;\n                        }\n                    else\n                        attribut = foregroundcolor[grm.foreground] | grm.bold\n                        | backgroundcolor[grm.background] | grm.underline;\n                    if (grm.reverse)\n                        attribut = ((attribut >> 4) & 15) | ((attribut & 15) << 4);\n                    SetConsoleTextAttribute(hConOut, attribut);\n                    return;\n\n                case 'J':\n                    if (es_argc == 0) es_argv[es_argc++] = 0; // ESC[J == ESC[0J\n                    if (es_argc != 1) return;\n                    switch (es_argv[0])\n                        {\n                            case 0:     // ESC[0J erase from cursor to end of display\n                                len = (Info.dwSize.Y - Info.dwCursorPosition.Y - 1) * Info.dwSize.X\n                                    + Info.dwSize.X - Info.dwCursorPosition.X - 1;\n                                FillConsoleOutputCharacter(hConOut, ' ', len,\n                                    Info.dwCursorPosition,\n                                    &NumberOfCharsWritten);\n                                FillConsoleOutputAttribute(hConOut, Info.wAttributes, len,\n                                    Info.dwCursorPosition,\n                                    &NumberOfCharsWritten);\n                                return;\n\n                            case 1:     // ESC[1J erase from start to cursor.\n                                Pos.X = 0;\n                                Pos.Y = 0;\n                                len = Info.dwCursorPosition.Y * Info.dwSize.X\n                                    + Info.dwCursorPosition.X + 1;\n                                FillConsoleOutputCharacter(hConOut, ' ', len, Pos,\n                                    &NumberOfCharsWritten);\n                                FillConsoleOutputAttribute(hConOut, Info.wAttributes, len, Pos,\n                                    &NumberOfCharsWritten);\n                                return;\n\n                            case 2:     // ESC[2J Clear screen and home cursor\n                                Pos.X = 0;\n                                Pos.Y = 0;\n                                len = Info.dwSize.X * Info.dwSize.Y;\n                                FillConsoleOutputCharacter(hConOut, ' ', len, Pos,\n                                    &NumberOfCharsWritten);\n                                FillConsoleOutputAttribute(hConOut, Info.wAttributes, len, Pos,\n                                    &NumberOfCharsWritten);\n                                SetConsoleCursorPosition(hConOut, Pos);\n                                return;\n\n                            default:\n                                return;\n                        }\n\n                case 'K':\n                    if (es_argc == 0) es_argv[es_argc++] = 0; // ESC[K == ESC[0K\n                    if (es_argc != 1) return;\n                    switch (es_argv[0])\n                        {\n                            case 0:     // ESC[0K Clear to end of line\n                                len = Info.dwSize.X - Info.dwCursorPosition.X + 1;\n                                FillConsoleOutputCharacter(hConOut, ' ', len,\n                                    Info.dwCursorPosition,\n                                    &NumberOfCharsWritten);\n                                FillConsoleOutputAttribute(hConOut, Info.wAttributes, len,\n                                    Info.dwCursorPosition,\n                                    &NumberOfCharsWritten);\n                                return;\n\n                            case 1:     // ESC[1K Clear from start of line to cursor\n                                Pos.X = 0;\n                                Pos.Y = Info.dwCursorPosition.Y;\n                                FillConsoleOutputCharacter(hConOut, ' ',\n                                    Info.dwCursorPosition.X + 1, Pos,\n                                    &NumberOfCharsWritten);\n                                FillConsoleOutputAttribute(hConOut, Info.wAttributes,\n                                    Info.dwCursorPosition.X + 1, Pos,\n                                    &NumberOfCharsWritten);\n                                return;\n\n                            case 2:     // ESC[2K Clear whole line.\n                                Pos.X = 0;\n                                Pos.Y = Info.dwCursorPosition.Y;\n                                FillConsoleOutputCharacter(hConOut, ' ', Info.dwSize.X, Pos,\n                                    &NumberOfCharsWritten);\n                                FillConsoleOutputAttribute(hConOut, Info.wAttributes,\n                                    Info.dwSize.X, Pos,\n                                    &NumberOfCharsWritten);\n                                return;\n\n                            default:\n                                return;\n                        }\n\n                case 'X':                 // ESC[#X Erase # characters.\n                    if (es_argc == 0) es_argv[es_argc++] = 1; // ESC[X == ESC[1X\n                    if (es_argc != 1) return;\n                    FillConsoleOutputCharacter(hConOut, ' ', es_argv[0],\n                        Info.dwCursorPosition,\n                        &NumberOfCharsWritten);\n                    FillConsoleOutputAttribute(hConOut, Info.wAttributes, es_argv[0],\n                        Info.dwCursorPosition,\n                        &NumberOfCharsWritten);\n                    return;\n\n                case 'L':                 // ESC[#L Insert # blank lines.\n                    if (es_argc == 0) es_argv[es_argc++] = 1; // ESC[L == ESC[1L\n                    if (es_argc != 1) return;\n                    Rect.Left = 0;\n                    Rect.Top = Info.dwCursorPosition.Y;\n                    Rect.Right = Info.dwSize.X - 1;\n                    Rect.Bottom = Info.dwSize.Y - 1;\n                    Pos.X = 0;\n                    Pos.Y = Info.dwCursorPosition.Y + es_argv[0];\n                    CharInfo.Char.UnicodeChar = ' ';\n                    CharInfo.Attributes = Info.wAttributes;\n                    ScrollConsoleScreenBuffer(hConOut, &Rect, NULL, Pos, &CharInfo);\n                    return;\n\n                case 'M':                 // ESC[#M Delete # lines.\n                    if (es_argc == 0) es_argv[es_argc++] = 1; // ESC[M == ESC[1M\n                    if (es_argc != 1) return;\n                    if (es_argv[0] > Info.dwSize.Y - Info.dwCursorPosition.Y)\n                        es_argv[0] = Info.dwSize.Y - Info.dwCursorPosition.Y;\n                    Rect.Left = 0;\n                    Rect.Top = Info.dwCursorPosition.Y + es_argv[0];\n                    Rect.Right = Info.dwSize.X - 1;\n                    Rect.Bottom = Info.dwSize.Y - 1;\n                    Pos.X = 0;\n                    Pos.Y = Info.dwCursorPosition.Y;\n                    CharInfo.Char.UnicodeChar = ' ';\n                    CharInfo.Attributes = Info.wAttributes;\n                    ScrollConsoleScreenBuffer(hConOut, &Rect, NULL, Pos, &CharInfo);\n                    return;\n\n                case 'P':                 // ESC[#P Delete # characters.\n                    if (es_argc == 0) es_argv[es_argc++] = 1; // ESC[P == ESC[1P\n                    if (es_argc != 1) return;\n                    if (Info.dwCursorPosition.X + es_argv[0] > Info.dwSize.X - 1)\n                        es_argv[0] = Info.dwSize.X - Info.dwCursorPosition.X;\n                    Rect.Left = Info.dwCursorPosition.X + es_argv[0];\n                    Rect.Top = Info.dwCursorPosition.Y;\n                    Rect.Right = Info.dwSize.X - 1;\n                    Rect.Bottom = Info.dwCursorPosition.Y;\n                    CharInfo.Char.UnicodeChar = ' ';\n                    CharInfo.Attributes = Info.wAttributes;\n                    ScrollConsoleScreenBuffer(hConOut, &Rect, NULL, Info.dwCursorPosition,\n                        &CharInfo);\n                    return;\n\n                case '@':                 // ESC[#@ Insert # blank characters.\n                    if (es_argc == 0) es_argv[es_argc++] = 1; // ESC[@ == ESC[1@\n                    if (es_argc != 1) return;\n                    if (Info.dwCursorPosition.X + es_argv[0] > Info.dwSize.X - 1)\n                        es_argv[0] = Info.dwSize.X - Info.dwCursorPosition.X;\n                    Rect.Left = Info.dwCursorPosition.X;\n                    Rect.Top = Info.dwCursorPosition.Y;\n                    Rect.Right = Info.dwSize.X - 1 - es_argv[0];\n                    Rect.Bottom = Info.dwCursorPosition.Y;\n                    Pos.X = Info.dwCursorPosition.X + es_argv[0];\n                    Pos.Y = Info.dwCursorPosition.Y;\n                    CharInfo.Char.UnicodeChar = ' ';\n                    CharInfo.Attributes = Info.wAttributes;\n                    ScrollConsoleScreenBuffer(hConOut, &Rect, NULL, Pos, &CharInfo);\n                    return;\n\n                case 'k':                 // ESC[#k\n                case 'A':                 // ESC[#A Moves cursor up # lines\n                    if (es_argc == 0) es_argv[es_argc++] = 1; // ESC[A == ESC[1A\n                    if (es_argc != 1) return;\n                    Pos.Y = Info.dwCursorPosition.Y - es_argv[0];\n                    if (Pos.Y < 0) Pos.Y = 0;\n                    Pos.X = Info.dwCursorPosition.X;\n                    SetConsoleCursorPosition(hConOut, Pos);\n                    return;\n\n                case 'e':                 // ESC[#e\n                case 'B':                 // ESC[#B Moves cursor down # lines\n                    if (es_argc == 0) es_argv[es_argc++] = 1; // ESC[B == ESC[1B\n                    if (es_argc != 1) return;\n                    Pos.Y = Info.dwCursorPosition.Y + es_argv[0];\n                    if (Pos.Y >= Info.dwSize.Y) Pos.Y = Info.dwSize.Y - 1;\n                    Pos.X = Info.dwCursorPosition.X;\n                    SetConsoleCursorPosition(hConOut, Pos);\n                    return;\n\n                case 'a':                 // ESC[#a\n                case 'C':                 // ESC[#C Moves cursor forward # spaces\n                    if (es_argc == 0) es_argv[es_argc++] = 1; // ESC[C == ESC[1C\n                    if (es_argc != 1) return;\n                    Pos.X = Info.dwCursorPosition.X + es_argv[0];\n                    if (Pos.X >= Info.dwSize.X) Pos.X = Info.dwSize.X - 1;\n                    Pos.Y = Info.dwCursorPosition.Y;\n                    SetConsoleCursorPosition(hConOut, Pos);\n                    return;\n\n                case 'j':                 // ESC[#j\n                case 'D':                 // ESC[#D Moves cursor back # spaces\n                    if (es_argc == 0) es_argv[es_argc++] = 1; // ESC[D == ESC[1D\n                    if (es_argc != 1) return;\n                    Pos.X = Info.dwCursorPosition.X - es_argv[0];\n                    if (Pos.X < 0) Pos.X = 0;\n                    Pos.Y = Info.dwCursorPosition.Y;\n                    SetConsoleCursorPosition(hConOut, Pos);\n                    return;\n\n                case 'E':                 // ESC[#E Moves cursor down # lines, column 1.\n                    if (es_argc == 0) es_argv[es_argc++] = 1; // ESC[E == ESC[1E\n                    if (es_argc != 1) return;\n                    Pos.Y = Info.dwCursorPosition.Y + es_argv[0];\n                    if (Pos.Y >= Info.dwSize.Y) Pos.Y = Info.dwSize.Y - 1;\n                    Pos.X = 0;\n                    SetConsoleCursorPosition(hConOut, Pos);\n                    return;\n\n                case 'F':                 // ESC[#F Moves cursor up # lines, column 1.\n                    if (es_argc == 0) es_argv[es_argc++] = 1; // ESC[F == ESC[1F\n                    if (es_argc != 1) return;\n                    Pos.Y = Info.dwCursorPosition.Y - es_argv[0];\n                    if (Pos.Y < 0) Pos.Y = 0;\n                    Pos.X = 0;\n                    SetConsoleCursorPosition(hConOut, Pos);\n                    return;\n\n                case '`':                 // ESC[#`\n                case 'G':                 // ESC[#G Moves cursor column # in current row.\n                    if (es_argc == 0) es_argv[es_argc++] = 1; // ESC[G == ESC[1G\n                    if (es_argc != 1) return;\n                    Pos.X = es_argv[0] - 1;\n                    if (Pos.X >= Info.dwSize.X) Pos.X = Info.dwSize.X - 1;\n                    if (Pos.X < 0) Pos.X = 0;\n                    Pos.Y = Info.dwCursorPosition.Y;\n                    SetConsoleCursorPosition(hConOut, Pos);\n                    return;\n\n                case 'd':                 // ESC[#d Moves cursor row #, current column.\n                    if (es_argc == 0) es_argv[es_argc++] = 1; // ESC[d == ESC[1d\n                    if (es_argc != 1) return;\n                    Pos.Y = es_argv[0] - 1;\n                    if (Pos.Y < 0) Pos.Y = 0;\n                    if (Pos.Y >= Info.dwSize.Y) Pos.Y = Info.dwSize.Y - 1;\n                    SetConsoleCursorPosition(hConOut, Pos);\n                    return;\n\n                case 'f':                 // ESC[#;#f\n                case 'H':                 // ESC[#;#H Moves cursor to line #, column #\n                    if (es_argc == 0)\n                        es_argv[es_argc++] = 1; // ESC[H == ESC[1;1H\n                    if (es_argc == 1)\n                        es_argv[es_argc++] = 1; // ESC[#H == ESC[#;1H\n                    if (es_argc > 2) return;\n                    Pos.X = es_argv[1] - 1;\n                    if (Pos.X < 0) Pos.X = 0;\n                    if (Pos.X >= Info.dwSize.X) Pos.X = Info.dwSize.X - 1;\n                    Pos.Y = es_argv[0] - 1;\n                    if (Pos.Y < 0) Pos.Y = 0;\n                    if (Pos.Y >= Info.dwSize.Y) Pos.Y = Info.dwSize.Y - 1;\n                    SetConsoleCursorPosition(hConOut, Pos);\n                    return;\n\n                case 's':                 // ESC[s Saves cursor position for recall later\n                    if (es_argc != 0) return;\n                    SavePos = Info.dwCursorPosition;\n                    return;\n\n                case 'u':                 // ESC[u Return to saved cursor position\n                    if (es_argc != 0) return;\n                    SetConsoleCursorPosition(hConOut, SavePos);\n                    return;\n\n                case 'n':                 // ESC[#n Device status report\n                    if (es_argc != 1) return; // ESC[n == ESC[0n -> ignored\n                    switch (es_argv[0])\n                        {\n                            case 5:     // ESC[5n Report status\n                                SendSequence(L\"\\33[0n\"); // \"OK\"\n                                return;\n\n                            case 6:     // ESC[6n Report cursor position\n                                    {\n                                    WCHAR buf[32];\n                                    swprintf(buf, 32, L\"\\33[%d;%dR\", Info.dwCursorPosition.Y + 1,\n                                        Info.dwCursorPosition.X + 1);\n                                    SendSequence(buf);\n                                    }\n                                    return;\n\n                            default:\n                                return;\n                        }\n\n                case 't':                 // ESC[#t Window manipulation\n                    if (es_argc != 1) return;\n                    if (es_argv[0] == 21)   // ESC[21t Report xterm window's title\n                        {\n                        WCHAR buf[MAX_PATH * 2];\n                        len = GetConsoleTitleW(buf + 3, lenof(buf) - 3 - 2);\n                        // Too bad if it's too big or fails.\n                        buf[0] = ESC;\n                        buf[1] = ']';\n                        buf[2] = 'l';\n                        buf[3 + len] = ESC;\n                        buf[3 + len + 1] = '\\\\';\n                        buf[3 + len + 2] = '\\0';\n                        SendSequence(buf);\n                        }\n                    return;\n\n                default:\n                    return;\n            }\n        }\n    else // (prefix == ']')\n        {\n        // Ignore any \\e]? or \\e]> sequences.\n        if (prefix2 != 0)\n            return;\n\n        if (es_argc == 1 && es_argv[0] == 0) // ESC]0;titleST\n            {\n            SetConsoleTitleW(Pt_arg);\n            }\n        }\n}\n\n//-----------------------------------------------------------------------------\n//   ParseAndPrintANSIString(hDev, lpBuffer, nNumberOfBytesToWrite)\n// Parses the string lpBuffer, interprets the escapes sequences and prints the\n// characters in the device hDev (console).\n// The lexer is a three states automata.\n// If the number of arguments es_argc > MAX_ARG, only the MAX_ARG-1 firsts and\n// the last arguments are processed (no es_argv[] overflow).\n//-----------------------------------------------------------------------------\n\ninline BOOL ParseAndPrintANSIString(HANDLE hDev, LPCVOID lpBuffer, DWORD nNumberOfBytesToWrite, LPDWORD lpNumberOfBytesWritten)\n{\n    DWORD   i;\n    LPCSTR s;\n\n    if (hDev != hConOut)    // reinit if device has changed\n        {\n        hConOut = hDev;\n        state = 1;\n        shifted = FALSE;\n        }\n    for (i = nNumberOfBytesToWrite, s = (LPCSTR)lpBuffer; i > 0; i--, s++)\n        {\n        if (state == 1)\n            {\n            if (*s == ESC) state = 2;\n            else if (*s == SO) shifted = TRUE;\n            else if (*s == SI) shifted = FALSE;\n            else PushBuffer(*s);\n            }\n        else if (state == 2)\n            {\n            if (*s == ESC); // \\e\\e...\\e == \\e\n            else if ((*s == '[') || (*s == ']'))\n                {\n                FlushBuffer();\n                prefix = *s;\n                prefix2 = 0;\n                state = 3;\n                Pt_len = 0;\n                *Pt_arg = '\\0';\n                }\n            else if (*s == ')' || *s == '(') state = 6;\n            else state = 1;\n            }\n        else if (state == 3)\n            {\n            if (is_digit(*s))\n                {\n                es_argc = 0;\n                es_argv[0] = *s - '0';\n                state = 4;\n                }\n            else if (*s == ';')\n                {\n                es_argc = 1;\n                es_argv[0] = 0;\n                es_argv[1] = 0;\n                state = 4;\n                }\n            else if (*s == '?' || *s == '>')\n                {\n                prefix2 = *s;\n                }\n            else\n                {\n                es_argc = 0;\n                suffix = *s;\n                InterpretEscSeq();\n                state = 1;\n                }\n            }\n        else if (state == 4)\n            {\n            if (is_digit(*s))\n                {\n                es_argv[es_argc] = 10 * es_argv[es_argc] + (*s - '0');\n                }\n            else if (*s == ';')\n                {\n                if (es_argc < MAX_ARG - 1) es_argc++;\n                es_argv[es_argc] = 0;\n                if (prefix == ']')\n                    state = 5;\n                }\n            else\n                {\n                es_argc++;\n                suffix = *s;\n                InterpretEscSeq();\n                state = 1;\n                }\n            }\n        else if (state == 5)\n            {\n            if (*s == BEL)\n                {\n                Pt_arg[Pt_len] = '\\0';\n                InterpretEscSeq();\n                state = 1;\n                }\n            else if (*s == '\\\\' && Pt_len > 0 && Pt_arg[Pt_len - 1] == ESC)\n                {\n                Pt_arg[--Pt_len] = '\\0';\n                InterpretEscSeq();\n                state = 1;\n                }\n            else if (Pt_len < lenof(Pt_arg) - 1)\n                Pt_arg[Pt_len++] = *s;\n            }\n        else if (state == 6)\n            {\n            // Ignore it (ESC ) 0 is implicit; nothing else is supported).\n            state = 1;\n            }\n        }\n    FlushBuffer();\n    if (lpNumberOfBytesWritten != NULL)\n        *lpNumberOfBytesWritten = nNumberOfBytesToWrite - i;\n    return (i == 0);\n}\n\n} // namespace ansi\n\nHANDLE hOut;\nHANDLE hIn;\nDWORD consolemodeIn = 0;\n\ninline int win32read(int *c) {\n    DWORD foo;\n    INPUT_RECORD b;\n    KEY_EVENT_RECORD e;\n    BOOL altgr;\n\n    while (1) {\n        if (!ReadConsoleInput(hIn, &b, 1, &foo)) return 0;\n        if (!foo) return 0;\n\n        if (b.EventType == KEY_EVENT && b.Event.KeyEvent.bKeyDown) {\n\n            e = b.Event.KeyEvent;\n            *c = b.Event.KeyEvent.uChar.AsciiChar;\n\n            altgr = e.dwControlKeyState & (LEFT_CTRL_PRESSED | RIGHT_ALT_PRESSED);\n\n            if (e.dwControlKeyState & (LEFT_CTRL_PRESSED | RIGHT_CTRL_PRESSED) && !altgr) {\n\n                /* Ctrl+Key */\n                switch (*c) {\n                    case 'D':\n                        *c = 4;\n                        return 1;\n                    case 'C':\n                        *c = 3;\n                        return 1;\n                    case 'H':\n                        *c = 8;\n                        return 1;\n                    case 'T':\n                        *c = 20;\n                        return 1;\n                    case 'B': /* ctrl-b, left_arrow */\n                        *c = 2;\n                        return 1;\n                    case 'F': /* ctrl-f right_arrow*/\n                        *c = 6;\n                        return 1;\n                    case 'P': /* ctrl-p up_arrow*/\n                        *c = 16;\n                        return 1;\n                    case 'N': /* ctrl-n down_arrow*/\n                        *c = 14;\n                        return 1;\n                    case 'U': /* Ctrl+u, delete the whole line. */\n                        *c = 21;\n                        return 1;\n                    case 'K': /* Ctrl+k, delete from current to end of line. */\n                        *c = 11;\n                        return 1;\n                    case 'A': /* Ctrl+a, go to the start of the line */\n                        *c = 1;\n                        return 1;\n                    case 'E': /* ctrl+e, go to the end of the line */\n                        *c = 5;\n                        return 1;\n\t\t\t\t\t\t case '\\\\':\n\t\t\t\t\t\t\t *c = 28;\n\t\t\t\t\t\t\t return 1;\n                }\n\n                /* Other Ctrl+KEYs ignored */\n            } else {\n\n                switch (e.wVirtualKeyCode) {\n\n                    case VK_ESCAPE: /* ignore - send ctrl-c, will return -1 */\n                        *c = 3;\n                        return 1;\n                    case VK_RETURN:  /* enter */\n                        *c = 13;\n                        return 1;\n                    case VK_LEFT:   /* left */\n                        *c = 2;\n                        return 1;\n                    case VK_RIGHT: /* right */\n                        *c = 6;\n                        return 1;\n                    case VK_UP:   /* up */\n                        *c = 16;\n                        return 1;\n                    case VK_DOWN:  /* down */\n                        *c = 14;\n                        return 1;\n                    case VK_HOME:\n                        *c = 1;\n                        return 1;\n                    case VK_END:\n                        *c = 5;\n                        return 1;\n                    case VK_BACK:\n                        *c = 8;\n                        return 1;\n                    case VK_DELETE:\n                        *c = 4; /* same as Ctrl+D above */\n                        return 1;\n                    default:\n                        if (*c) return 1;\n                }\n            }\n        }\n    }\n\n    return -1; /* Makes compiler happy */\n}\n\ninline int win32_write(int fd, const void *buffer, unsigned int count) {\n    if (fd == _fileno(stdout)) {\n        DWORD bytesWritten = 0;\n        if (FALSE != ansi::ParseAndPrintANSIString(GetStdHandle(STD_OUTPUT_HANDLE), buffer, (DWORD)count, &bytesWritten)) {\n            return (int)bytesWritten;\n        } else {\n            errno = GetLastError();\n            return 0;\n        }\n    } else if (fd == _fileno(stderr)) {\n        DWORD bytesWritten = 0;\n        if (FALSE != ansi::ParseAndPrintANSIString(GetStdHandle(STD_ERROR_HANDLE), buffer, (DWORD)count, &bytesWritten)) {\n            return (int)bytesWritten;\n        } else {\n            errno = GetLastError();\n            return 0;\n        }\n    } else {\n        return _write(fd, buffer, count);\n    }\n}\n#endif // _WIN32\n\n#define LINENOISE_DEFAULT_HISTORY_MAX_LEN 100\n#define LINENOISE_MAX_LINE 4096\n#ifndef _WIN32\nstatic const char *unsupported_term[] = {\"dumb\",\"cons25\",\"emacs\",NULL};\n#endif\nstatic CompletionCallback completionCallback;\n\n#ifndef _WIN32\nstatic struct termios orig_termios; /* In order to restore at exit.*/\n#endif\nstatic bool rawmode = false; /* For atexit() function to check if restore is needed*/\nstatic bool mlmode = false;  /* Multi line mode. Default is single line. */\nstatic bool atexit_registered = false; /* Register atexit just 1 time. */\nstatic size_t history_max_len = LINENOISE_DEFAULT_HISTORY_MAX_LEN;\nstatic std::vector<std::string> history;\n\n/* The linenoiseState structure represents the state during line editing.\n * We pass this state to functions implementing specific editing\n * functionalities. */\nstruct linenoiseState {\n    int ifd;            /* Terminal stdin file descriptor. */\n    int ofd;            /* Terminal stdout file descriptor. */\n    char *buf;          /* Edited line buffer. */\n    int buflen;         /* Edited line buffer size. */\n    std::string prompt; /* Prompt to display. */\n    int pos;            /* Current cursor position. */\n    int oldcolpos;      /* Previous refresh cursor column position. */\n    int len;            /* Current edited line length. */\n    int cols;           /* Number of columns in terminal. */\n    int maxrows;        /* Maximum num of rows used so far (multiline mode) */\n    int history_index;  /* The history index we are currently editing. */\n};\n\nenum KEY_ACTION {\n    KEY_NULL = 0,       /* NULL */\n    CTRL_A = 1,         /* Ctrl+a */\n    CTRL_B = 2,         /* Ctrl-b */\n    CTRL_C = 3,         /* Ctrl-c */\n    CTRL_D = 4,         /* Ctrl-d */\n    CTRL_E = 5,         /* Ctrl-e */\n    CTRL_F = 6,         /* Ctrl-f */\n    CTRL_H = 8,         /* Ctrl-h */\n    TAB = 9,            /* Tab */\n    CTRL_K = 11,        /* Ctrl+k */\n    CTRL_L = 12,        /* Ctrl+l */\n    ENTER = 13,         /* Enter */\n    CTRL_N = 14,        /* Ctrl-n */\n    CTRL_P = 16,        /* Ctrl-p */\n    CTRL_T = 20,        /* Ctrl-t */\n    CTRL_U = 21,        /* Ctrl+u */\n    CTRL_W = 23,        /* Ctrl+w */\n\t CTRL_BACKSLASH = 28,/* Ctrl-backslash */\n    ESC = 27,           /* Escape */\n    BACKSPACE =  127    /* Backspace */\n};\n\nvoid linenoiseAtExit(void);\nbool AddHistory(const char *line);\nvoid refreshLine(struct linenoiseState *l);\n\n/* ============================ UTF8 utilities ============================== */\n\nstatic unsigned long unicodeWideCharTable[][2] = {\n    { 0x1100, 0x115F }, { 0x2329, 0x232A }, { 0x2E80, 0x2E99, }, { 0x2E9B, 0x2EF3, },\n    { 0x2F00, 0x2FD5, }, { 0x2FF0, 0x2FFB, }, { 0x3000, 0x303E, }, { 0x3041, 0x3096, },\n    { 0x3099, 0x30FF, }, { 0x3105, 0x312D, }, { 0x3131, 0x318E, }, { 0x3190, 0x31BA, },\n    { 0x31C0, 0x31E3, }, { 0x31F0, 0x321E, }, { 0x3220, 0x3247, }, { 0x3250, 0x4DBF, },\n    { 0x4E00, 0xA48C, }, { 0xA490, 0xA4C6, }, { 0xA960, 0xA97C, }, { 0xAC00, 0xD7A3, },\n    { 0xF900, 0xFAFF, }, { 0xFE10, 0xFE19, }, { 0xFE30, 0xFE52, }, { 0xFE54, 0xFE66, },\n    { 0xFE68, 0xFE6B, }, { 0xFF01, 0xFFE6, },\n    { 0x1B000, 0x1B001, }, { 0x1F200, 0x1F202, }, { 0x1F210, 0x1F23A, },\n    { 0x1F240, 0x1F248, }, { 0x1F250, 0x1F251, }, { 0x20000, 0x3FFFD, },\n};\n\nstatic int unicodeWideCharTableSize = sizeof(unicodeWideCharTable) / sizeof(unicodeWideCharTable[0]);\n\nstatic int unicodeIsWideChar(unsigned long cp)\n{\n    int i;\n    for (i = 0; i < unicodeWideCharTableSize; i++) {\n        if (unicodeWideCharTable[i][0] <= cp && cp <= unicodeWideCharTable[i][1]) {\n            return 1;\n        }\n    }\n    return 0;\n}\n\nstatic unsigned long unicodeCombiningCharTable[] = {\n    0x0300,0x0301,0x0302,0x0303,0x0304,0x0305,0x0306,0x0307,\n    0x0308,0x0309,0x030A,0x030B,0x030C,0x030D,0x030E,0x030F,\n    0x0310,0x0311,0x0312,0x0313,0x0314,0x0315,0x0316,0x0317,\n    0x0318,0x0319,0x031A,0x031B,0x031C,0x031D,0x031E,0x031F,\n    0x0320,0x0321,0x0322,0x0323,0x0324,0x0325,0x0326,0x0327,\n    0x0328,0x0329,0x032A,0x032B,0x032C,0x032D,0x032E,0x032F,\n    0x0330,0x0331,0x0332,0x0333,0x0334,0x0335,0x0336,0x0337,\n    0x0338,0x0339,0x033A,0x033B,0x033C,0x033D,0x033E,0x033F,\n    0x0340,0x0341,0x0342,0x0343,0x0344,0x0345,0x0346,0x0347,\n    0x0348,0x0349,0x034A,0x034B,0x034C,0x034D,0x034E,0x034F,\n    0x0350,0x0351,0x0352,0x0353,0x0354,0x0355,0x0356,0x0357,\n    0x0358,0x0359,0x035A,0x035B,0x035C,0x035D,0x035E,0x035F,\n    0x0360,0x0361,0x0362,0x0363,0x0364,0x0365,0x0366,0x0367,\n    0x0368,0x0369,0x036A,0x036B,0x036C,0x036D,0x036E,0x036F,\n    0x0483,0x0484,0x0485,0x0486,0x0487,0x0591,0x0592,0x0593,\n    0x0594,0x0595,0x0596,0x0597,0x0598,0x0599,0x059A,0x059B,\n    0x059C,0x059D,0x059E,0x059F,0x05A0,0x05A1,0x05A2,0x05A3,\n    0x05A4,0x05A5,0x05A6,0x05A7,0x05A8,0x05A9,0x05AA,0x05AB,\n    0x05AC,0x05AD,0x05AE,0x05AF,0x05B0,0x05B1,0x05B2,0x05B3,\n    0x05B4,0x05B5,0x05B6,0x05B7,0x05B8,0x05B9,0x05BA,0x05BB,\n    0x05BC,0x05BD,0x05BF,0x05C1,0x05C2,0x05C4,0x05C5,0x05C7,\n    0x0610,0x0611,0x0612,0x0613,0x0614,0x0615,0x0616,0x0617,\n    0x0618,0x0619,0x061A,0x064B,0x064C,0x064D,0x064E,0x064F,\n    0x0650,0x0651,0x0652,0x0653,0x0654,0x0655,0x0656,0x0657,\n    0x0658,0x0659,0x065A,0x065B,0x065C,0x065D,0x065E,0x065F,\n    0x0670,0x06D6,0x06D7,0x06D8,0x06D9,0x06DA,0x06DB,0x06DC,\n    0x06DF,0x06E0,0x06E1,0x06E2,0x06E3,0x06E4,0x06E7,0x06E8,\n    0x06EA,0x06EB,0x06EC,0x06ED,0x0711,0x0730,0x0731,0x0732,\n    0x0733,0x0734,0x0735,0x0736,0x0737,0x0738,0x0739,0x073A,\n    0x073B,0x073C,0x073D,0x073E,0x073F,0x0740,0x0741,0x0742,\n    0x0743,0x0744,0x0745,0x0746,0x0747,0x0748,0x0749,0x074A,\n    0x07A6,0x07A7,0x07A8,0x07A9,0x07AA,0x07AB,0x07AC,0x07AD,\n    0x07AE,0x07AF,0x07B0,0x07EB,0x07EC,0x07ED,0x07EE,0x07EF,\n    0x07F0,0x07F1,0x07F2,0x07F3,0x0816,0x0817,0x0818,0x0819,\n    0x081B,0x081C,0x081D,0x081E,0x081F,0x0820,0x0821,0x0822,\n    0x0823,0x0825,0x0826,0x0827,0x0829,0x082A,0x082B,0x082C,\n    0x082D,0x0859,0x085A,0x085B,0x08E3,0x08E4,0x08E5,0x08E6,\n    0x08E7,0x08E8,0x08E9,0x08EA,0x08EB,0x08EC,0x08ED,0x08EE,\n    0x08EF,0x08F0,0x08F1,0x08F2,0x08F3,0x08F4,0x08F5,0x08F6,\n    0x08F7,0x08F8,0x08F9,0x08FA,0x08FB,0x08FC,0x08FD,0x08FE,\n    0x08FF,0x0900,0x0901,0x0902,0x093A,0x093C,0x0941,0x0942,\n    0x0943,0x0944,0x0945,0x0946,0x0947,0x0948,0x094D,0x0951,\n    0x0952,0x0953,0x0954,0x0955,0x0956,0x0957,0x0962,0x0963,\n    0x0981,0x09BC,0x09C1,0x09C2,0x09C3,0x09C4,0x09CD,0x09E2,\n    0x09E3,0x0A01,0x0A02,0x0A3C,0x0A41,0x0A42,0x0A47,0x0A48,\n    0x0A4B,0x0A4C,0x0A4D,0x0A51,0x0A70,0x0A71,0x0A75,0x0A81,\n    0x0A82,0x0ABC,0x0AC1,0x0AC2,0x0AC3,0x0AC4,0x0AC5,0x0AC7,\n    0x0AC8,0x0ACD,0x0AE2,0x0AE3,0x0B01,0x0B3C,0x0B3F,0x0B41,\n    0x0B42,0x0B43,0x0B44,0x0B4D,0x0B56,0x0B62,0x0B63,0x0B82,\n    0x0BC0,0x0BCD,0x0C00,0x0C3E,0x0C3F,0x0C40,0x0C46,0x0C47,\n    0x0C48,0x0C4A,0x0C4B,0x0C4C,0x0C4D,0x0C55,0x0C56,0x0C62,\n    0x0C63,0x0C81,0x0CBC,0x0CBF,0x0CC6,0x0CCC,0x0CCD,0x0CE2,\n    0x0CE3,0x0D01,0x0D41,0x0D42,0x0D43,0x0D44,0x0D4D,0x0D62,\n    0x0D63,0x0DCA,0x0DD2,0x0DD3,0x0DD4,0x0DD6,0x0E31,0x0E34,\n    0x0E35,0x0E36,0x0E37,0x0E38,0x0E39,0x0E3A,0x0E47,0x0E48,\n    0x0E49,0x0E4A,0x0E4B,0x0E4C,0x0E4D,0x0E4E,0x0EB1,0x0EB4,\n    0x0EB5,0x0EB6,0x0EB7,0x0EB8,0x0EB9,0x0EBB,0x0EBC,0x0EC8,\n    0x0EC9,0x0ECA,0x0ECB,0x0ECC,0x0ECD,0x0F18,0x0F19,0x0F35,\n    0x0F37,0x0F39,0x0F71,0x0F72,0x0F73,0x0F74,0x0F75,0x0F76,\n    0x0F77,0x0F78,0x0F79,0x0F7A,0x0F7B,0x0F7C,0x0F7D,0x0F7E,\n    0x0F80,0x0F81,0x0F82,0x0F83,0x0F84,0x0F86,0x0F87,0x0F8D,\n    0x0F8E,0x0F8F,0x0F90,0x0F91,0x0F92,0x0F93,0x0F94,0x0F95,\n    0x0F96,0x0F97,0x0F99,0x0F9A,0x0F9B,0x0F9C,0x0F9D,0x0F9E,\n    0x0F9F,0x0FA0,0x0FA1,0x0FA2,0x0FA3,0x0FA4,0x0FA5,0x0FA6,\n    0x0FA7,0x0FA8,0x0FA9,0x0FAA,0x0FAB,0x0FAC,0x0FAD,0x0FAE,\n    0x0FAF,0x0FB0,0x0FB1,0x0FB2,0x0FB3,0x0FB4,0x0FB5,0x0FB6,\n    0x0FB7,0x0FB8,0x0FB9,0x0FBA,0x0FBB,0x0FBC,0x0FC6,0x102D,\n    0x102E,0x102F,0x1030,0x1032,0x1033,0x1034,0x1035,0x1036,\n    0x1037,0x1039,0x103A,0x103D,0x103E,0x1058,0x1059,0x105E,\n    0x105F,0x1060,0x1071,0x1072,0x1073,0x1074,0x1082,0x1085,\n    0x1086,0x108D,0x109D,0x135D,0x135E,0x135F,0x1712,0x1713,\n    0x1714,0x1732,0x1733,0x1734,0x1752,0x1753,0x1772,0x1773,\n    0x17B4,0x17B5,0x17B7,0x17B8,0x17B9,0x17BA,0x17BB,0x17BC,\n    0x17BD,0x17C6,0x17C9,0x17CA,0x17CB,0x17CC,0x17CD,0x17CE,\n    0x17CF,0x17D0,0x17D1,0x17D2,0x17D3,0x17DD,0x180B,0x180C,\n    0x180D,0x18A9,0x1920,0x1921,0x1922,0x1927,0x1928,0x1932,\n    0x1939,0x193A,0x193B,0x1A17,0x1A18,0x1A1B,0x1A56,0x1A58,\n    0x1A59,0x1A5A,0x1A5B,0x1A5C,0x1A5D,0x1A5E,0x1A60,0x1A62,\n    0x1A65,0x1A66,0x1A67,0x1A68,0x1A69,0x1A6A,0x1A6B,0x1A6C,\n    0x1A73,0x1A74,0x1A75,0x1A76,0x1A77,0x1A78,0x1A79,0x1A7A,\n    0x1A7B,0x1A7C,0x1A7F,0x1AB0,0x1AB1,0x1AB2,0x1AB3,0x1AB4,\n    0x1AB5,0x1AB6,0x1AB7,0x1AB8,0x1AB9,0x1ABA,0x1ABB,0x1ABC,\n    0x1ABD,0x1B00,0x1B01,0x1B02,0x1B03,0x1B34,0x1B36,0x1B37,\n    0x1B38,0x1B39,0x1B3A,0x1B3C,0x1B42,0x1B6B,0x1B6C,0x1B6D,\n    0x1B6E,0x1B6F,0x1B70,0x1B71,0x1B72,0x1B73,0x1B80,0x1B81,\n    0x1BA2,0x1BA3,0x1BA4,0x1BA5,0x1BA8,0x1BA9,0x1BAB,0x1BAC,\n    0x1BAD,0x1BE6,0x1BE8,0x1BE9,0x1BED,0x1BEF,0x1BF0,0x1BF1,\n    0x1C2C,0x1C2D,0x1C2E,0x1C2F,0x1C30,0x1C31,0x1C32,0x1C33,\n    0x1C36,0x1C37,0x1CD0,0x1CD1,0x1CD2,0x1CD4,0x1CD5,0x1CD6,\n    0x1CD7,0x1CD8,0x1CD9,0x1CDA,0x1CDB,0x1CDC,0x1CDD,0x1CDE,\n    0x1CDF,0x1CE0,0x1CE2,0x1CE3,0x1CE4,0x1CE5,0x1CE6,0x1CE7,\n    0x1CE8,0x1CED,0x1CF4,0x1CF8,0x1CF9,0x1DC0,0x1DC1,0x1DC2,\n    0x1DC3,0x1DC4,0x1DC5,0x1DC6,0x1DC7,0x1DC8,0x1DC9,0x1DCA,\n    0x1DCB,0x1DCC,0x1DCD,0x1DCE,0x1DCF,0x1DD0,0x1DD1,0x1DD2,\n    0x1DD3,0x1DD4,0x1DD5,0x1DD6,0x1DD7,0x1DD8,0x1DD9,0x1DDA,\n    0x1DDB,0x1DDC,0x1DDD,0x1DDE,0x1DDF,0x1DE0,0x1DE1,0x1DE2,\n    0x1DE3,0x1DE4,0x1DE5,0x1DE6,0x1DE7,0x1DE8,0x1DE9,0x1DEA,\n    0x1DEB,0x1DEC,0x1DED,0x1DEE,0x1DEF,0x1DF0,0x1DF1,0x1DF2,\n    0x1DF3,0x1DF4,0x1DF5,0x1DFC,0x1DFD,0x1DFE,0x1DFF,0x20D0,\n    0x20D1,0x20D2,0x20D3,0x20D4,0x20D5,0x20D6,0x20D7,0x20D8,\n    0x20D9,0x20DA,0x20DB,0x20DC,0x20E1,0x20E5,0x20E6,0x20E7,\n    0x20E8,0x20E9,0x20EA,0x20EB,0x20EC,0x20ED,0x20EE,0x20EF,\n    0x20F0,0x2CEF,0x2CF0,0x2CF1,0x2D7F,0x2DE0,0x2DE1,0x2DE2,\n    0x2DE3,0x2DE4,0x2DE5,0x2DE6,0x2DE7,0x2DE8,0x2DE9,0x2DEA,\n    0x2DEB,0x2DEC,0x2DED,0x2DEE,0x2DEF,0x2DF0,0x2DF1,0x2DF2,\n    0x2DF3,0x2DF4,0x2DF5,0x2DF6,0x2DF7,0x2DF8,0x2DF9,0x2DFA,\n    0x2DFB,0x2DFC,0x2DFD,0x2DFE,0x2DFF,0x302A,0x302B,0x302C,\n    0x302D,0x3099,0x309A,0xA66F,0xA674,0xA675,0xA676,0xA677,\n    0xA678,0xA679,0xA67A,0xA67B,0xA67C,0xA67D,0xA69E,0xA69F,\n    0xA6F0,0xA6F1,0xA802,0xA806,0xA80B,0xA825,0xA826,0xA8C4,\n    0xA8E0,0xA8E1,0xA8E2,0xA8E3,0xA8E4,0xA8E5,0xA8E6,0xA8E7,\n    0xA8E8,0xA8E9,0xA8EA,0xA8EB,0xA8EC,0xA8ED,0xA8EE,0xA8EF,\n    0xA8F0,0xA8F1,0xA926,0xA927,0xA928,0xA929,0xA92A,0xA92B,\n    0xA92C,0xA92D,0xA947,0xA948,0xA949,0xA94A,0xA94B,0xA94C,\n    0xA94D,0xA94E,0xA94F,0xA950,0xA951,0xA980,0xA981,0xA982,\n    0xA9B3,0xA9B6,0xA9B7,0xA9B8,0xA9B9,0xA9BC,0xA9E5,0xAA29,\n    0xAA2A,0xAA2B,0xAA2C,0xAA2D,0xAA2E,0xAA31,0xAA32,0xAA35,\n    0xAA36,0xAA43,0xAA4C,0xAA7C,0xAAB0,0xAAB2,0xAAB3,0xAAB4,\n    0xAAB7,0xAAB8,0xAABE,0xAABF,0xAAC1,0xAAEC,0xAAED,0xAAF6,\n    0xABE5,0xABE8,0xABED,0xFB1E,0xFE00,0xFE01,0xFE02,0xFE03,\n    0xFE04,0xFE05,0xFE06,0xFE07,0xFE08,0xFE09,0xFE0A,0xFE0B,\n    0xFE0C,0xFE0D,0xFE0E,0xFE0F,0xFE20,0xFE21,0xFE22,0xFE23,\n    0xFE24,0xFE25,0xFE26,0xFE27,0xFE28,0xFE29,0xFE2A,0xFE2B,\n    0xFE2C,0xFE2D,0xFE2E,0xFE2F,\n    0x101FD,0x102E0,0x10376,0x10377,0x10378,0x10379,0x1037A,0x10A01,\n    0x10A02,0x10A03,0x10A05,0x10A06,0x10A0C,0x10A0D,0x10A0E,0x10A0F,\n    0x10A38,0x10A39,0x10A3A,0x10A3F,0x10AE5,0x10AE6,0x11001,0x11038,\n    0x11039,0x1103A,0x1103B,0x1103C,0x1103D,0x1103E,0x1103F,0x11040,\n    0x11041,0x11042,0x11043,0x11044,0x11045,0x11046,0x1107F,0x11080,\n    0x11081,0x110B3,0x110B4,0x110B5,0x110B6,0x110B9,0x110BA,0x11100,\n    0x11101,0x11102,0x11127,0x11128,0x11129,0x1112A,0x1112B,0x1112D,\n    0x1112E,0x1112F,0x11130,0x11131,0x11132,0x11133,0x11134,0x11173,\n    0x11180,0x11181,0x111B6,0x111B7,0x111B8,0x111B9,0x111BA,0x111BB,\n    0x111BC,0x111BD,0x111BE,0x111CA,0x111CB,0x111CC,0x1122F,0x11230,\n    0x11231,0x11234,0x11236,0x11237,0x112DF,0x112E3,0x112E4,0x112E5,\n    0x112E6,0x112E7,0x112E8,0x112E9,0x112EA,0x11300,0x11301,0x1133C,\n    0x11340,0x11366,0x11367,0x11368,0x11369,0x1136A,0x1136B,0x1136C,\n    0x11370,0x11371,0x11372,0x11373,0x11374,0x114B3,0x114B4,0x114B5,\n    0x114B6,0x114B7,0x114B8,0x114BA,0x114BF,0x114C0,0x114C2,0x114C3,\n    0x115B2,0x115B3,0x115B4,0x115B5,0x115BC,0x115BD,0x115BF,0x115C0,\n    0x115DC,0x115DD,0x11633,0x11634,0x11635,0x11636,0x11637,0x11638,\n    0x11639,0x1163A,0x1163D,0x1163F,0x11640,0x116AB,0x116AD,0x116B0,\n    0x116B1,0x116B2,0x116B3,0x116B4,0x116B5,0x116B7,0x1171D,0x1171E,\n    0x1171F,0x11722,0x11723,0x11724,0x11725,0x11727,0x11728,0x11729,\n    0x1172A,0x1172B,0x16AF0,0x16AF1,0x16AF2,0x16AF3,0x16AF4,0x16B30,\n    0x16B31,0x16B32,0x16B33,0x16B34,0x16B35,0x16B36,0x16F8F,0x16F90,\n    0x16F91,0x16F92,0x1BC9D,0x1BC9E,0x1D167,0x1D168,0x1D169,0x1D17B,\n    0x1D17C,0x1D17D,0x1D17E,0x1D17F,0x1D180,0x1D181,0x1D182,0x1D185,\n    0x1D186,0x1D187,0x1D188,0x1D189,0x1D18A,0x1D18B,0x1D1AA,0x1D1AB,\n    0x1D1AC,0x1D1AD,0x1D242,0x1D243,0x1D244,0x1DA00,0x1DA01,0x1DA02,\n    0x1DA03,0x1DA04,0x1DA05,0x1DA06,0x1DA07,0x1DA08,0x1DA09,0x1DA0A,\n    0x1DA0B,0x1DA0C,0x1DA0D,0x1DA0E,0x1DA0F,0x1DA10,0x1DA11,0x1DA12,\n    0x1DA13,0x1DA14,0x1DA15,0x1DA16,0x1DA17,0x1DA18,0x1DA19,0x1DA1A,\n    0x1DA1B,0x1DA1C,0x1DA1D,0x1DA1E,0x1DA1F,0x1DA20,0x1DA21,0x1DA22,\n    0x1DA23,0x1DA24,0x1DA25,0x1DA26,0x1DA27,0x1DA28,0x1DA29,0x1DA2A,\n    0x1DA2B,0x1DA2C,0x1DA2D,0x1DA2E,0x1DA2F,0x1DA30,0x1DA31,0x1DA32,\n    0x1DA33,0x1DA34,0x1DA35,0x1DA36,0x1DA3B,0x1DA3C,0x1DA3D,0x1DA3E,\n    0x1DA3F,0x1DA40,0x1DA41,0x1DA42,0x1DA43,0x1DA44,0x1DA45,0x1DA46,\n    0x1DA47,0x1DA48,0x1DA49,0x1DA4A,0x1DA4B,0x1DA4C,0x1DA4D,0x1DA4E,\n    0x1DA4F,0x1DA50,0x1DA51,0x1DA52,0x1DA53,0x1DA54,0x1DA55,0x1DA56,\n    0x1DA57,0x1DA58,0x1DA59,0x1DA5A,0x1DA5B,0x1DA5C,0x1DA5D,0x1DA5E,\n    0x1DA5F,0x1DA60,0x1DA61,0x1DA62,0x1DA63,0x1DA64,0x1DA65,0x1DA66,\n    0x1DA67,0x1DA68,0x1DA69,0x1DA6A,0x1DA6B,0x1DA6C,0x1DA75,0x1DA84,\n    0x1DA9B,0x1DA9C,0x1DA9D,0x1DA9E,0x1DA9F,0x1DAA1,0x1DAA2,0x1DAA3,\n    0x1DAA4,0x1DAA5,0x1DAA6,0x1DAA7,0x1DAA8,0x1DAA9,0x1DAAA,0x1DAAB,\n    0x1DAAC,0x1DAAD,0x1DAAE,0x1DAAF,0x1E8D0,0x1E8D1,0x1E8D2,0x1E8D3,\n    0x1E8D4,0x1E8D5,0x1E8D6,0xE0100,0xE0101,0xE0102,0xE0103,0xE0104,\n    0xE0105,0xE0106,0xE0107,0xE0108,0xE0109,0xE010A,0xE010B,0xE010C,\n    0xE010D,0xE010E,0xE010F,0xE0110,0xE0111,0xE0112,0xE0113,0xE0114,\n    0xE0115,0xE0116,0xE0117,0xE0118,0xE0119,0xE011A,0xE011B,0xE011C,\n    0xE011D,0xE011E,0xE011F,0xE0120,0xE0121,0xE0122,0xE0123,0xE0124,\n    0xE0125,0xE0126,0xE0127,0xE0128,0xE0129,0xE012A,0xE012B,0xE012C,\n    0xE012D,0xE012E,0xE012F,0xE0130,0xE0131,0xE0132,0xE0133,0xE0134,\n    0xE0135,0xE0136,0xE0137,0xE0138,0xE0139,0xE013A,0xE013B,0xE013C,\n    0xE013D,0xE013E,0xE013F,0xE0140,0xE0141,0xE0142,0xE0143,0xE0144,\n    0xE0145,0xE0146,0xE0147,0xE0148,0xE0149,0xE014A,0xE014B,0xE014C,\n    0xE014D,0xE014E,0xE014F,0xE0150,0xE0151,0xE0152,0xE0153,0xE0154,\n    0xE0155,0xE0156,0xE0157,0xE0158,0xE0159,0xE015A,0xE015B,0xE015C,\n    0xE015D,0xE015E,0xE015F,0xE0160,0xE0161,0xE0162,0xE0163,0xE0164,\n    0xE0165,0xE0166,0xE0167,0xE0168,0xE0169,0xE016A,0xE016B,0xE016C,\n    0xE016D,0xE016E,0xE016F,0xE0170,0xE0171,0xE0172,0xE0173,0xE0174,\n    0xE0175,0xE0176,0xE0177,0xE0178,0xE0179,0xE017A,0xE017B,0xE017C,\n    0xE017D,0xE017E,0xE017F,0xE0180,0xE0181,0xE0182,0xE0183,0xE0184,\n    0xE0185,0xE0186,0xE0187,0xE0188,0xE0189,0xE018A,0xE018B,0xE018C,\n    0xE018D,0xE018E,0xE018F,0xE0190,0xE0191,0xE0192,0xE0193,0xE0194,\n    0xE0195,0xE0196,0xE0197,0xE0198,0xE0199,0xE019A,0xE019B,0xE019C,\n    0xE019D,0xE019E,0xE019F,0xE01A0,0xE01A1,0xE01A2,0xE01A3,0xE01A4,\n    0xE01A5,0xE01A6,0xE01A7,0xE01A8,0xE01A9,0xE01AA,0xE01AB,0xE01AC,\n    0xE01AD,0xE01AE,0xE01AF,0xE01B0,0xE01B1,0xE01B2,0xE01B3,0xE01B4,\n    0xE01B5,0xE01B6,0xE01B7,0xE01B8,0xE01B9,0xE01BA,0xE01BB,0xE01BC,\n    0xE01BD,0xE01BE,0xE01BF,0xE01C0,0xE01C1,0xE01C2,0xE01C3,0xE01C4,\n    0xE01C5,0xE01C6,0xE01C7,0xE01C8,0xE01C9,0xE01CA,0xE01CB,0xE01CC,\n    0xE01CD,0xE01CE,0xE01CF,0xE01D0,0xE01D1,0xE01D2,0xE01D3,0xE01D4,\n    0xE01D5,0xE01D6,0xE01D7,0xE01D8,0xE01D9,0xE01DA,0xE01DB,0xE01DC,\n    0xE01DD,0xE01DE,0xE01DF,0xE01E0,0xE01E1,0xE01E2,0xE01E3,0xE01E4,\n    0xE01E5,0xE01E6,0xE01E7,0xE01E8,0xE01E9,0xE01EA,0xE01EB,0xE01EC,\n    0xE01ED,0xE01EE,0xE01EF,\n};\n\nstatic int unicodeCombiningCharTableSize = sizeof(unicodeCombiningCharTable) / sizeof(unicodeCombiningCharTable[0]);\n\ninline int unicodeIsCombiningChar(unsigned long cp)\n{\n    int i;\n    for (i = 0; i < unicodeCombiningCharTableSize; i++) {\n        if (unicodeCombiningCharTable[i] == cp) {\n            return 1;\n        }\n    }\n    return 0;\n}\n\n/* Get length of previous UTF8 character\n */\ninline int unicodePrevUTF8CharLen(char* buf, int pos)\n{\n    int end = pos--;\n    while (pos >= 0 && ((unsigned char)buf[pos] & 0xC0) == 0x80) {\n        pos--;\n    }\n    return end - pos;\n}\n\n/* Get length of previous UTF8 character\n */\ninline int unicodeUTF8CharLen(char* buf, int buf_len, int pos)\n{\n    if (pos == buf_len) { return 0; }\n    unsigned char ch = buf[pos];\n    if (ch < 0x80) { return 1; }\n    else if (ch < 0xE0) { return 2; }\n    else if (ch < 0xF0) { return 3; }\n    else { return 4; }\n}\n\n/* Convert UTF8 to Unicode code point\n */\ninline int unicodeUTF8CharToCodePoint(\n   const char* buf,\n   int         len,\n   int*        cp)\n{\n    if (len) {\n        unsigned char byte = buf[0];\n        if ((byte & 0x80) == 0) {\n            *cp = byte;\n            return 1;\n        } else if ((byte & 0xE0) == 0xC0) {\n            if (len >= 2) {\n                *cp = (((unsigned long)(buf[0] & 0x1F)) << 6) |\n                       ((unsigned long)(buf[1] & 0x3F));\n                return 2;\n            }\n        } else if ((byte & 0xF0) == 0xE0) {\n            if (len >= 3) {\n                *cp = (((unsigned long)(buf[0] & 0x0F)) << 12) |\n                      (((unsigned long)(buf[1] & 0x3F)) << 6) |\n                       ((unsigned long)(buf[2] & 0x3F));\n                return 3;\n            }\n        } else if ((byte & 0xF8) == 0xF0) {\n            if (len >= 4) {\n                *cp = (((unsigned long)(buf[0] & 0x07)) << 18) |\n                      (((unsigned long)(buf[1] & 0x3F)) << 12) |\n                      (((unsigned long)(buf[2] & 0x3F)) << 6) |\n                       ((unsigned long)(buf[3] & 0x3F));\n                return 4;\n            }\n        }\n    }\n    return 0;\n}\n\n/* Get length of grapheme\n */\ninline int unicodeGraphemeLen(char* buf, int buf_len, int pos)\n{\n    if (pos == buf_len) {\n        return 0;\n    }\n    int beg = pos;\n    pos += unicodeUTF8CharLen(buf, buf_len, pos);\n    while (pos < buf_len) {\n        int len = unicodeUTF8CharLen(buf, buf_len, pos);\n        int cp = 0;\n        unicodeUTF8CharToCodePoint(buf + pos, len, &cp);\n        if (!unicodeIsCombiningChar(cp)) {\n            return pos - beg;\n        }\n        pos += len;\n    }\n    return pos - beg;\n}\n\n/* Get length of previous grapheme\n */\ninline int unicodePrevGraphemeLen(char* buf, int pos)\n{\n    if (pos == 0) {\n        return 0;\n    }\n    int end = pos;\n    while (pos > 0) {\n        int len = unicodePrevUTF8CharLen(buf, pos);\n        pos -= len;\n        int cp = 0;\n        unicodeUTF8CharToCodePoint(buf + pos, len, &cp);\n        if (!unicodeIsCombiningChar(cp)) {\n            return end - pos;\n        }\n    }\n    return 0;\n}\n\ninline int isAnsiEscape(const char* buf, int buf_len, int* len)\n{\n    if (buf_len > 2 && !memcmp(\"\\033[\", buf, 2)) {\n        int off = 2;\n        while (off < buf_len) {\n            switch (buf[off++]) {\n            case 'A': case 'B': case 'C': case 'D':\n            case 'E': case 'F': case 'G': case 'H':\n            case 'J': case 'K': case 'S': case 'T':\n            case 'f': case 'm':\n                *len = off;\n                return 1;\n            }\n        }\n    }\n    return 0;\n}\n\n/* Get column position for the single line mode.\n */\ninline int unicodeColumnPos(const char* buf, int buf_len)\n{\n    int ret = 0;\n\n    int off = 0;\n    while (off < buf_len) {\n        int len;\n        if (isAnsiEscape(buf + off, buf_len - off, &len)) {\n            off += len;\n            continue;\n        }\n\n        int cp = 0;\n        len = unicodeUTF8CharToCodePoint(buf + off, buf_len - off, &cp);\n\n        if (!unicodeIsCombiningChar(cp)) {\n            ret += unicodeIsWideChar(cp) ? 2 : 1;\n        }\n\n        off += len;\n    }\n\n    return ret;\n}\n\n/* Get column position for the multi line mode.\n */\ninline int unicodeColumnPosForMultiLine(char* buf, int buf_len, int pos, int cols, int ini_pos)\n{\n    int ret = 0;\n    int colwid = ini_pos;\n\n    int off = 0;\n    while (off < buf_len) {\n        int cp = 0;\n        int len = unicodeUTF8CharToCodePoint(buf + off, buf_len - off, &cp);\n\n        int wid = 0;\n        if (!unicodeIsCombiningChar(cp)) {\n            wid = unicodeIsWideChar(cp) ? 2 : 1;\n        }\n\n        int dif = (int)(colwid + wid) - (int)cols;\n        if (dif > 0) {\n            ret += dif;\n            colwid = wid;\n        } else if (dif == 0) {\n            colwid = 0;\n        } else {\n            colwid += wid;\n        }\n\n        if (off >= pos) {\n            break;\n        }\n\n        off += len;\n        ret += wid;\n    }\n\n    return ret;\n}\n\n/* Read UTF8 character from file.\n */\ninline int unicodeReadUTF8Char(int fd, char* buf, int* cp)\n{\n    int nread = read(fd,&buf[0],1);\n\n    if (nread <= 0) { return nread; }\n\n    unsigned char byte = buf[0];\n\n    if ((byte & 0x80) == 0) {\n        ;\n    } else if ((byte & 0xE0) == 0xC0) {\n        nread = read(fd,&buf[1],1);\n        if (nread <= 0) { return nread; }\n    } else if ((byte & 0xF0) == 0xE0) {\n        nread = read(fd,&buf[1],2);\n        if (nread <= 0) { return nread; }\n    } else if ((byte & 0xF8) == 0xF0) {\n        nread = read(fd,&buf[1],3);\n        if (nread <= 0) { return nread; }\n    } else {\n        return -1;\n    }\n\n    return unicodeUTF8CharToCodePoint(buf, 4, cp);\n}\n\n/* ======================= Low level terminal handling ====================== */\n\n/* Set if to use or not the multi line mode. */\ninline void SetMultiLine(bool ml) {\n    mlmode = ml;\n}\n\n/* Return true if the terminal name is in the list of terminals we know are\n * not able to understand basic escape sequences. */\ninline bool isUnsupportedTerm(void) {\n#ifndef _WIN32\n    char *term = getenv(\"TERM\");\n    int j;\n\n    if (term == NULL) return false;\n    for (j = 0; unsupported_term[j]; j++)\n        if (!strcasecmp(term,unsupported_term[j])) return true;\n#endif\n    return false;\n}\n\n/* Raw mode: 1960 magic shit. */\ninline bool enableRawMode(int fd) {\n#ifndef _WIN32\n    struct termios raw;\n\n    if (!isatty(STDIN_FILENO)) goto fatal;\n    if (!atexit_registered) {\n        atexit(linenoiseAtExit);\n        atexit_registered = true;\n    }\n    if (tcgetattr(fd,&orig_termios) == -1) goto fatal;\n\n    raw = orig_termios;  /* modify the original mode */\n    /* input modes: no break, no CR to NL, no parity check, no strip char,\n     * no start/stop output control. */\n    raw.c_iflag &= ~(BRKINT | ICRNL | INPCK | ISTRIP | IXON);\n    /* output modes - disable post processing */\n    // NOTE: Multithreaded issue #20 (https://github.com/yhirose/cpp-linenoise/issues/20)\n    // raw.c_oflag &= ~(OPOST);\n    /* control modes - set 8 bit chars */\n    raw.c_cflag |= (CS8);\n    /* local modes - echoing off, canonical off, no extended functions,\n     * no signal chars (^Z,^C) */\n    raw.c_lflag &= ~(ECHO | ICANON | IEXTEN | ISIG);\n    /* control chars - set return condition: min number of bytes and timer.\n     * We want read to return every single byte, without timeout. */\n    raw.c_cc[VMIN] = 1; raw.c_cc[VTIME] = 0; /* 1 byte, no timer */\n\n    /* put terminal in raw mode after flushing */\n    if (tcsetattr(fd,TCSADRAIN,&raw) < 0) goto fatal;\n    rawmode = true;\n#else\n    if (!atexit_registered) {\n        /* Cleanup them at exit */\n        atexit(linenoiseAtExit);\n        atexit_registered = true;\n\n        /* Init windows console handles only once */\n        hOut = GetStdHandle(STD_OUTPUT_HANDLE);\n        if (hOut==INVALID_HANDLE_VALUE) goto fatal;\n    }\n\n    DWORD consolemodeOut;\n    if (!GetConsoleMode(hOut, &consolemodeOut)) {\n        CloseHandle(hOut);\n        errno = ENOTTY;\n        return false;\n    };\n\n    hIn = GetStdHandle(STD_INPUT_HANDLE);\n    if (hIn == INVALID_HANDLE_VALUE) {\n        CloseHandle(hOut);\n        errno = ENOTTY;\n        return false;\n    }\n\n    GetConsoleMode(hIn, &consolemodeIn);\n    /* Enable raw mode */\n    SetConsoleMode(hIn, consolemodeIn & ~ENABLE_PROCESSED_INPUT);\n\n    rawmode = true;\n#endif\n    return true;\n\nfatal:\n    errno = ENOTTY;\n    return false;\n}\n\ninline void disableRawMode(int fd) {\n#ifdef _WIN32\n    if (consolemodeIn) {\n      SetConsoleMode(hIn, consolemodeIn);\n      consolemodeIn = 0;\n    }\n    rawmode = false;\n#else\n    /* Don't even check the return value as it's too late. */\n    if (rawmode && tcsetattr(fd,TCSADRAIN,&orig_termios) != -1)\n        rawmode = false;\n#endif\n}\n\n/* Use the ESC [6n escape sequence to query the horizontal cursor position\n * and return it. On error -1 is returned, on success the position of the\n * cursor. */\ninline int getCursorPosition(int ifd, int ofd) {\n    char buf[32];\n    int cols, rows;\n    unsigned int i = 0;\n\n    /* Report cursor location */\n    if (write(ofd, \"\\x1b[6n\", 4) != 4) return -1;\n\n    /* Read the response: ESC [ rows ; cols R */\n    while (i < sizeof(buf)-1) {\n        if (read(ifd,buf+i,1) != 1) break;\n        if (buf[i] == 'R') break;\n        i++;\n    }\n    buf[i] = '\\0';\n\n    /* Parse it. */\n    if (buf[0] != ESC || buf[1] != '[') return -1;\n    if (sscanf(buf+2,\"%d;%d\",&rows,&cols) != 2) return -1;\n    return cols;\n}\n\n/* Try to get the number of columns in the current terminal, or assume 80\n * if it fails. */\ninline int getColumns(int ifd, int ofd) {\n#ifdef _WIN32\n    CONSOLE_SCREEN_BUFFER_INFO b;\n\n    if (!GetConsoleScreenBufferInfo(hOut, &b)) return 80;\n    return b.srWindow.Right - b.srWindow.Left;\n#else\n    struct winsize ws;\n\n    if (ioctl(1, TIOCGWINSZ, &ws) == -1 || ws.ws_col == 0) {\n        /* ioctl() failed. Try to query the terminal itself. */\n        int start, cols;\n\n        /* Get the initial position so we can restore it later. */\n        start = getCursorPosition(ifd,ofd);\n        if (start == -1) goto failed;\n\n        /* Go to right margin and get position. */\n        if (write(ofd,\"\\x1b[999C\",6) != 6) goto failed;\n        cols = getCursorPosition(ifd,ofd);\n        if (cols == -1) goto failed;\n\n        /* Restore position. */\n        if (cols > start) {\n            char seq[32];\n            snprintf(seq,32,\"\\x1b[%dD\",cols-start);\n            if (write(ofd,seq,strlen(seq)) == -1) {\n                /* Can't recover... */\n            }\n        }\n        return cols;\n    } else {\n        return ws.ws_col;\n    }\n\nfailed:\n    return 80;\n#endif\n}\n\n/* Clear the screen. Used to handle ctrl+l */\ninline void linenoiseClearScreen(void) {\n    if (write(STDOUT_FILENO,\"\\x1b[H\\x1b[2J\",7) <= 0) {\n        /* nothing to do, just to avoid warning. */\n    }\n}\n\n/* Beep, used for completion when there is nothing to complete or when all\n * the choices were already shown. */\ninline void linenoiseBeep(void) {\n    fprintf(stderr, \"\\x7\");\n    fflush(stderr);\n}\n\n/* ============================== Completion ================================ */\n\n/* This is an helper function for linenoiseEdit() and is called when the\n * user types the <tab> key in order to complete the string currently in the\n * input.\n *\n * The state of the editing is encapsulated into the pointed linenoiseState\n * structure as described in the structure definition. */\ninline int completeLine(struct linenoiseState *ls, char *cbuf, int *c) {\n    std::vector<std::string> lc;\n    int nread = 0, nwritten;\n    *c = 0;\n\n    completionCallback(ls->buf,lc);\n    if (lc.empty()) {\n        linenoiseBeep();\n    } else {\n        int stop = 0, i = 0;\n\n        while(!stop) {\n            /* Show completion or original buffer */\n            if (i < static_cast<int>(lc.size())) {\n                struct linenoiseState saved = *ls;\n\n                ls->len = ls->pos = static_cast<int>(lc[i].size());\n                ls->buf = &lc[i][0];\n                refreshLine(ls);\n                ls->len = saved.len;\n                ls->pos = saved.pos;\n                ls->buf = saved.buf;\n            } else {\n                refreshLine(ls);\n            }\n\n            //nread = read(ls->ifd,&c,1);\n#ifdef _WIN32\n            nread = win32read(c);\n            if (nread == 1) {\n                cbuf[0] = *c;\n            }\n#else\n            nread = unicodeReadUTF8Char(ls->ifd,cbuf,c);\n#endif\n            if (nread <= 0) {\n                *c = -1;\n                return nread;\n            }\n\n            switch(*c) {\n                case 9: /* tab */\n                    i = (i+1) % (lc.size()+1);\n                    if (i == static_cast<int>(lc.size())) linenoiseBeep();\n                    break;\n                case 27: /* escape */\n                    /* Re-show original buffer */\n                    if (i < static_cast<int>(lc.size())) refreshLine(ls);\n                    stop = 1;\n                    break;\n                default:\n                    /* Update buffer and return */\n                    if (i < static_cast<int>(lc.size())) {\n                        nwritten = snprintf(ls->buf,ls->buflen,\"%s\",&lc[i][0]);\n                        ls->len = ls->pos = nwritten;\n                    }\n                    stop = 1;\n                    break;\n            }\n        }\n    }\n\n    return nread;\n}\n\n/* Register a callback function to be called for tab-completion. */\ninline void SetCompletionCallback(CompletionCallback fn) {\n    completionCallback = fn;\n}\n\n/* =========================== Line editing ================================= */\n\n/* Single line low level line refresh.\n *\n * Rewrite the currently edited line accordingly to the buffer content,\n * cursor position, and number of columns of the terminal. */\ninline void refreshSingleLine(struct linenoiseState *l) {\n    char seq[64];\n    int pcolwid = unicodeColumnPos(l->prompt.c_str(), static_cast<int>(l->prompt.length()));\n    int fd = l->ofd;\n    char *buf = l->buf;\n    int len = l->len;\n    int pos = l->pos;\n    std::string ab;\n\n    while((pcolwid+unicodeColumnPos(buf, pos)) >= l->cols) {\n        int glen = unicodeGraphemeLen(buf, len, 0);\n        buf += glen;\n        len -= glen;\n        pos -= glen;\n    }\n    while (pcolwid+unicodeColumnPos(buf, len) > l->cols) {\n        len -= unicodePrevGraphemeLen(buf, len);\n    }\n\n    /* Cursor to left edge */\n    snprintf(seq,64,\"\\r\");\n    ab += seq;\n    /* Write the prompt and the current buffer content */\n    ab += l->prompt;\n    ab.append(buf, len);\n    /* Erase to right */\n    snprintf(seq,64,\"\\x1b[0K\");\n    ab += seq;\n    /* Move cursor to original position. */\n    snprintf(seq,64,\"\\r\\x1b[%dC\", (int)(unicodeColumnPos(buf, pos)+pcolwid));\n    ab += seq;\n    if (write(fd,ab.c_str(), static_cast<int>(ab.length())) == -1) {} /* Can't recover from write error. */\n}\n\n/* Multi line low level line refresh.\n *\n * Rewrite the currently edited line accordingly to the buffer content,\n * cursor position, and number of columns of the terminal. */\ninline void refreshMultiLine(struct linenoiseState *l) {\n    char seq[64];\n    int pcolwid = unicodeColumnPos(l->prompt.c_str(), static_cast<int>(l->prompt.length()));\n    int colpos = unicodeColumnPosForMultiLine(l->buf, l->len, l->len, l->cols, pcolwid);\n    int colpos2; /* cursor column position. */\n    int rows = (pcolwid+colpos+l->cols-1)/l->cols; /* rows used by current buf. */\n    int rpos = (pcolwid+l->oldcolpos+l->cols)/l->cols; /* cursor relative row. */\n    int rpos2; /* rpos after refresh. */\n    int col; /* colum position, zero-based. */\n    int old_rows = (int)l->maxrows;\n    int fd = l->ofd, j;\n    std::string ab;\n\n    /* Update maxrows if needed. */\n    if (rows > (int)l->maxrows) l->maxrows = rows;\n\n    /* First step: clear all the lines used before. To do so start by\n     * going to the last row. */\n    if (old_rows-rpos > 0) {\n        snprintf(seq,64,\"\\x1b[%dB\", old_rows-rpos);\n        ab += seq;\n    }\n\n    /* Now for every row clear it, go up. */\n    for (j = 0; j < old_rows-1; j++) {\n        snprintf(seq,64,\"\\r\\x1b[0K\\x1b[1A\");\n        ab += seq;\n    }\n\n    /* Clean the top line. */\n    snprintf(seq,64,\"\\r\\x1b[0K\");\n    ab += seq;\n\n    /* Write the prompt and the current buffer content */\n    ab += l->prompt;\n    ab.append(l->buf, l->len);\n\n    /* Get text width to cursor position */\n    colpos2 = unicodeColumnPosForMultiLine(l->buf, l->len, l->pos, l->cols, pcolwid);\n\n    /* If we are at the very end of the screen with our prompt, we need to\n     * emit a newline and move the prompt to the first column. */\n    if (l->pos &&\n        l->pos == l->len &&\n        (colpos2+pcolwid) % l->cols == 0)\n    {\n        ab += \"\\n\";\n        snprintf(seq,64,\"\\r\");\n        ab += seq;\n        rows++;\n        if (rows > (int)l->maxrows) l->maxrows = rows;\n    }\n\n    /* Move cursor to right position. */\n    rpos2 = (pcolwid+colpos2+l->cols)/l->cols; /* current cursor relative row. */\n\n    /* Go up till we reach the expected positon. */\n    if (rows-rpos2 > 0) {\n        snprintf(seq,64,\"\\x1b[%dA\", rows-rpos2);\n        ab += seq;\n    }\n\n    /* Set column. */\n    col = (pcolwid + colpos2) % l->cols;\n    if (col)\n        snprintf(seq,64,\"\\r\\x1b[%dC\", col);\n    else\n        snprintf(seq,64,\"\\r\");\n    ab += seq;\n\n    l->oldcolpos = colpos2;\n\n    if (write(fd,ab.c_str(), static_cast<int>(ab.length())) == -1) {} /* Can't recover from write error. */\n}\n\n/* Calls the two low level functions refreshSingleLine() or\n * refreshMultiLine() according to the selected mode. */\ninline void refreshLine(struct linenoiseState *l) {\n    if (mlmode)\n        refreshMultiLine(l);\n    else\n        refreshSingleLine(l);\n}\n\n/* Insert the character 'c' at cursor current position.\n *\n * On error writing to the terminal -1 is returned, otherwise 0. */\ninline int linenoiseEditInsert(struct linenoiseState *l, const char* cbuf, int clen) {\n    if (l->len < l->buflen) {\n        if (l->len == l->pos) {\n            memcpy(&l->buf[l->pos],cbuf,clen);\n            l->pos+=clen;\n            l->len+=clen;;\n            l->buf[l->len] = '\\0';\n            if ((!mlmode && unicodeColumnPos(l->prompt.c_str(), static_cast<int>(l->prompt.length()))+unicodeColumnPos(l->buf,l->len) < l->cols) /* || mlmode */) {\n                /* Avoid a full update of the line in the\n                 * trivial case. */\n                if (write(l->ofd,cbuf,clen) == -1) return -1;\n            } else {\n                refreshLine(l);\n            }\n        } else {\n            memmove(l->buf+l->pos+clen,l->buf+l->pos,l->len-l->pos);\n            memcpy(&l->buf[l->pos],cbuf,clen);\n            l->pos+=clen;\n            l->len+=clen;\n            l->buf[l->len] = '\\0';\n            refreshLine(l);\n        }\n    }\n    return 0;\n}\n\n/* Move cursor on the left. */\ninline void linenoiseEditMoveLeft(struct linenoiseState *l) {\n    if (l->pos > 0) {\n        l->pos -= unicodePrevGraphemeLen(l->buf, l->pos);\n        refreshLine(l);\n    }\n}\n\n/* Move cursor on the right. */\ninline void linenoiseEditMoveRight(struct linenoiseState *l) {\n    if (l->pos != l->len) {\n        l->pos += unicodeGraphemeLen(l->buf, l->len, l->pos);\n        refreshLine(l);\n    }\n}\n\n/* Move cursor to the start of the line. */\ninline void linenoiseEditMoveHome(struct linenoiseState *l) {\n    if (l->pos != 0) {\n        l->pos = 0;\n        refreshLine(l);\n    }\n}\n\n/* Move cursor to the end of the line. */\ninline void linenoiseEditMoveEnd(struct linenoiseState *l) {\n    if (l->pos != l->len) {\n        l->pos = l->len;\n        refreshLine(l);\n    }\n}\n\n/* Substitute the currently edited line with the next or previous history\n * entry as specified by 'dir'. */\n#define LINENOISE_HISTORY_NEXT 0\n#define LINENOISE_HISTORY_PREV 1\ninline void linenoiseEditHistoryNext(struct linenoiseState *l, int dir) {\n    if (history.size() > 1) {\n        /* Update the current history entry before to\n         * overwrite it with the next one. */\n        history[history.size() - 1 - l->history_index] = l->buf;\n        /* Show the new entry */\n        l->history_index += (dir == LINENOISE_HISTORY_PREV) ? 1 : -1;\n        if (l->history_index < 0) {\n            l->history_index = 0;\n            return;\n        } else if (l->history_index >= (int)history.size()) {\n            l->history_index = static_cast<int>(history.size())-1;\n            return;\n        }\n        memset(l->buf, 0, l->buflen);\n        strcpy(l->buf,history[history.size() - 1 - l->history_index].c_str());\n        l->len = l->pos = static_cast<int>(strlen(l->buf));\n        refreshLine(l);\n    }\n}\n\n/* Delete the character at the right of the cursor without altering the cursor\n * position. Basically this is what happens with the \"Delete\" keyboard key. */\ninline void linenoiseEditDelete(struct linenoiseState *l) {\n    if (l->len > 0 && l->pos < l->len) {\n        int glen = unicodeGraphemeLen(l->buf,l->len,l->pos);\n        memmove(l->buf+l->pos,l->buf+l->pos+glen,l->len-l->pos-glen);\n        l->len-=glen;\n        l->buf[l->len] = '\\0';\n        refreshLine(l);\n    }\n}\n\n/* Backspace implementation. */\ninline void linenoiseEditBackspace(struct linenoiseState *l) {\n    if (l->pos > 0 && l->len > 0) {\n        int glen = unicodePrevGraphemeLen(l->buf,l->pos);\n        memmove(l->buf+l->pos-glen,l->buf+l->pos,l->len-l->pos);\n        l->pos-=glen;\n        l->len-=glen;\n        l->buf[l->len] = '\\0';\n        refreshLine(l);\n    }\n}\n\n/* Delete the previosu word, maintaining the cursor at the start of the\n * current word. */\ninline void linenoiseEditDeletePrevWord(struct linenoiseState *l) {\n    int old_pos = l->pos;\n    int diff;\n\n    while (l->pos > 0 && l->buf[l->pos-1] == ' ')\n        l->pos--;\n    while (l->pos > 0 && l->buf[l->pos-1] != ' ')\n        l->pos--;\n    diff = old_pos - l->pos;\n    memmove(l->buf+l->pos,l->buf+old_pos,l->len-old_pos+1);\n    l->len -= diff;\n    refreshLine(l);\n}\n\nvoid debug_key(int code) {\n    fprintf(stderr, \"Key pressed: %d (0x%x)\\n\", code, code);\n    fflush(stderr);\n}\n\n/* This function is the core of the line editing capability of linenoise.\n * It expects 'fd' to be already in \"raw mode\" so that every key pressed\n * will be returned ASAP to read().\n *\n * The resulting string is put into 'buf' when the user type enter, or\n * when ctrl+d is typed.\n *\n * The function returns the length of the current buffer. */\ninline int linenoiseEdit(int stdin_fd, int stdout_fd, char *buf, int buflen, const char *prompt)\n{\n    struct linenoiseState l;\n\n    /* Populate the linenoise state that we pass to functions implementing\n     * specific editing functionalities. */\n    l.ifd = stdin_fd;\n    l.ofd = stdout_fd;\n    l.buf = buf;\n    l.buflen = buflen;\n    l.prompt = prompt;\n    l.oldcolpos = l.pos = 0;\n    l.len = 0;\n    l.cols = getColumns(stdin_fd, stdout_fd);\n    l.maxrows = 0;\n    l.history_index = 0;\n\n    /* Buffer starts empty. */\n    l.buf[0] = '\\0';\n    l.buflen--; /* Make sure there is always space for the nulterm */\n\n    /* The latest history entry is always our current buffer, that\n     * initially is just an empty string. */\n    AddHistory(\"\");\n\n    if (write(l.ofd,prompt, static_cast<int>(l.prompt.length())) == -1) return -1;\n    while(1) {\n        int c;\n        char cbuf[4];\n        int nread;\n        char seq[3];\n\n#ifdef _WIN32\n        nread = win32read(&c);\n        if (nread == 1) {\n            cbuf[0] = c;\n        }\n#else\n        nread = unicodeReadUTF8Char(l.ifd,cbuf,&c);\n#endif\n        if (nread <= 0) return (int)l.len;\n\n        /* Only autocomplete when the callback is set. It returns < 0 when\n         * there was an error reading from fd. Otherwise it will return the\n         * character that should be handled next. */\n        if (c == 9 && completionCallback != NULL) {\n            nread = completeLine(&l,cbuf,&c);\n            /* Return on errors */\n            if (c < 0) return l.len;\n            /* Read next character when 0 */\n            if (c == 0) continue;\n        }\n\n\t\t  // debug_key(c);\n        switch(c) {\n        case ENTER:    /* enter */\n            if (!history.empty()) history.pop_back();\n            if (mlmode) linenoiseEditMoveEnd(&l);\n            return (int)l.len;\n        case CTRL_C:     /* ctrl-c */\n            errno = EAGAIN;\n            return -1;\n        case BACKSPACE:   /* backspace */\n        case 8:     /* ctrl-h */\n            linenoiseEditBackspace(&l);\n            break;\n        case CTRL_D:     /* ctrl-d, remove char at right of cursor, or if the\n                            line is empty, act as end-of-file. */\n            if (l.len > 0) {\n                linenoiseEditDelete(&l);\n            } else {\n                history.pop_back();\n                return -1;\n            }\n            break;\n        case CTRL_T:    /* ctrl-t, swaps current character with previous. */\n            if (l.pos > 0 && l.pos < l.len) {\n                char aux = buf[l.pos-1];\n                buf[l.pos-1] = buf[l.pos];\n                buf[l.pos] = aux;\n                if (l.pos != l.len-1) l.pos++;\n                refreshLine(&l);\n            }\n            break;\n        case CTRL_B:     /* ctrl-b */\n            linenoiseEditMoveLeft(&l);\n            break;\n        case CTRL_F:     /* ctrl-f */\n            linenoiseEditMoveRight(&l);\n            break;\n        case CTRL_P:    /* ctrl-p */\n            linenoiseEditHistoryNext(&l, LINENOISE_HISTORY_PREV);\n            break;\n        case CTRL_N:    /* ctrl-n */\n            linenoiseEditHistoryNext(&l, LINENOISE_HISTORY_NEXT);\n            break;\n        case ESC:    /* escape sequence */\n            /* Read the next two bytes representing the escape sequence.\n             * Use two calls to handle slow terminals returning the two\n             * chars at different times. */\n            if (read(l.ifd,seq,1) == -1) break;\n            if (read(l.ifd,seq+1,1) == -1) break;\n\n            /* ESC [ sequences. */\n            if (seq[0] == '[') {\n                if (seq[1] >= '0' && seq[1] <= '9') {\n                    /* Extended escape, read additional byte. */\n                    if (read(l.ifd,seq+2,1) == -1) break;\n                    if (seq[2] == '~') {\n                        switch(seq[1]) {\n                        case '3': /* Delete key. */\n                            linenoiseEditDelete(&l);\n                            break;\n                        }\n                    }\n                } else {\n                    switch(seq[1]) {\n                    case 'A': /* Up */\n                        linenoiseEditHistoryNext(&l, LINENOISE_HISTORY_PREV);\n                        break;\n                    case 'B': /* Down */\n                        linenoiseEditHistoryNext(&l, LINENOISE_HISTORY_NEXT);\n                        break;\n                    case 'C': /* Right */\n                        linenoiseEditMoveRight(&l);\n                        break;\n                    case 'D': /* Left */\n                        linenoiseEditMoveLeft(&l);\n                        break;\n                    case 'H': /* Home */\n                        linenoiseEditMoveHome(&l);\n                        break;\n                    case 'F': /* End*/\n                        linenoiseEditMoveEnd(&l);\n                        break;\n                    }\n                }\n            }\n\n            /* ESC O sequences. */\n            else if (seq[0] == 'O') {\n                switch(seq[1]) {\n                case 'H': /* Home */\n                    linenoiseEditMoveHome(&l);\n                    break;\n                case 'F': /* End*/\n                    linenoiseEditMoveEnd(&l);\n                    break;\n                }\n            }\n            break;\n        default:\n            if (linenoiseEditInsert(&l,cbuf,nread)) return -1;\n            break;\n        case CTRL_U: /* Ctrl+u, delete the whole line. */\n            buf[0] = '\\0';\n            l.pos = l.len = 0;\n            refreshLine(&l);\n            break;\n        case CTRL_K: /* Ctrl+k, delete from current to end of line. */\n            buf[l.pos] = '\\0';\n            l.len = l.pos;\n            refreshLine(&l);\n            break;\n        case CTRL_A: /* Ctrl+a, go to the start of the line */\n            linenoiseEditMoveHome(&l);\n            break;\n        case CTRL_E: /* ctrl+e, go to the end of the line */\n            linenoiseEditMoveEnd(&l);\n            break;\n        case CTRL_L: /* ctrl+l, clear screen */\n            linenoiseClearScreen();\n            refreshLine(&l);\n            break;\n        case CTRL_W: /* ctrl+w, delete previous word */\n            linenoiseEditDeletePrevWord(&l);\n            break;\n\t\t  case CTRL_BACKSLASH:\n\t\t\t\t  throw std::logic_error(\"SIGQUIT: program terminated.\");\n        }\n    }\n    return l.len;\n}\n\n/* This function calls the line editing function linenoiseEdit() using\n * the STDIN file descriptor set in raw mode. */\ninline bool linenoiseRaw(const char *prompt, std::string& line) {\n    bool quit = false;\n\n    if (!isatty(STDIN_FILENO)) {\n        /* Not a tty: read from file / pipe. */\n        std::getline(std::cin, line);\n    } else {\n        /* Interactive editing. */\n        if (enableRawMode(STDIN_FILENO) == false) {\n            return quit;\n        }\n\n        char buf[LINENOISE_MAX_LINE];\n        auto count = linenoiseEdit(STDIN_FILENO, STDOUT_FILENO, buf, LINENOISE_MAX_LINE, prompt);\n        if (count == -1) {\n            quit = true;\n        } else {\n            line.assign(buf, count);\n        }\n\n        disableRawMode(STDIN_FILENO);\n        printf(\"\\n\");\n    }\n    return quit;\n}\n\n/* The high level function that is the main API of the linenoise library.\n * This function checks if the terminal has basic capabilities, just checking\n * for a blacklist of stupid terminals, and later either calls the line\n * editing function or uses dummy fgets() so that you will be able to type\n * something even in the most desperate of the conditions. */\ninline bool Readline(const char *prompt, std::string& line) {\n    if (isUnsupportedTerm()) {\n        printf(\"%s\",prompt);\n        fflush(stdout);\n        std::getline(std::cin, line);\n        return false;\n    } else {\n        return linenoiseRaw(prompt, line);\n    }\n}\n\ninline std::string Readline(const char *prompt, bool& quit) {\n    std::string line;\n    quit = Readline(prompt, line);\n    return line;\n}\n\ninline std::string Readline(const char *prompt) {\n    bool quit; // dummy\n    return Readline(prompt, quit);\n}\n\n/* ================================ History ================================= */\n\n/* At exit we'll try to fix the terminal to the initial conditions. */\ninline void linenoiseAtExit(void) {\n    disableRawMode(STDIN_FILENO);\n}\n\n/* This is the API call to add a new entry in the linenoise history.\n * It uses a fixed array of char pointers that are shifted (memmoved)\n * when the history max length is reached in order to remove the older\n * entry and make room for the new one, so it is not exactly suitable for huge\n * histories, but will work well for a few hundred of entries.\n *\n * Using a circular buffer is smarter, but a bit more complex to handle. */\ninline bool AddHistory(const char* line) {\n    if (history_max_len == 0) return false;\n\n    /* Don't add duplicated lines. */\n    if (!history.empty() && history.back() == line) return false;\n\n    /* If we reached the max length, remove the older line. */\n    if (history.size() == history_max_len) {\n        history.erase(history.begin());\n    }\n    history.push_back(line);\n\n    return true;\n}\n\n/* Set the maximum length for the history. This function can be called even\n * if there is already some history, the function will make sure to retain\n * just the latest 'len' elements if the new history length value is smaller\n * than the amount of items already inside the history. */\ninline bool SetHistoryMaxLen(size_t len) {\n    if (len < 1) return false;\n    history_max_len = len;\n    if (len < history.size()) {\n        history.resize(len);\n    }\n    return true;\n}\n\n/* Save the history in the specified file. On success *true* is returned\n * otherwise *false* is returned. */\ninline bool SaveHistory(const char* path) {\n    std::ofstream f(path); // TODO: need 'std::ios::binary'?\n    if (!f) return false;\n    for (const auto& h: history) {\n        f << h << std::endl;\n    }\n    return true;\n}\n\n/* Load the history from the specified file. If the file does not exist\n * zero is returned and no operation is performed.\n *\n * If the file exists and the operation succeeded *true* is returned, otherwise\n * on error *false* is returned. */\ninline bool LoadHistory(const char* path) {\n    std::ifstream f(path);\n    if (!f) return false;\n    std::string line;\n    while (std::getline(f, line)) {\n        AddHistory(line.c_str());\n    }\n    return true;\n}\n\ninline const std::vector<std::string>& GetHistory() {\n    return history;\n}\n\n} // namespace linenoise\n\n#ifdef _WIN32\n#undef isatty\n#undef write\n#undef read\n#pragma warning(pop)\n#endif\n\n#endif /* __LINENOISE_HPP */\n"
  },
  {
    "path": "libs/nlohmann/nlohmann/json.hpp",
    "content": "//     __ _____ _____ _____\n//  __|  |   __|     |   | |  JSON for Modern C++\n// |  |  |__   |  |  | | | |  version 3.11.3\n// |_____|_____|_____|_|___|  https://github.com/nlohmann/json\n//\n// SPDX-FileCopyrightText: 2013-2023 Niels Lohmann <https://nlohmann.me>\n// SPDX-License-Identifier: MIT\n\n/****************************************************************************\\\n * Note on documentation: The source files contain links to the online      *\n * documentation of the public API at https://json.nlohmann.me. This URL    *\n * contains the most recent documentation and should also be applicable to  *\n * previous versions; documentation for deprecated functions is not         *\n * removed, but marked deprecated. See \"Generate documentation\" section in  *\n * file docs/README.md.                                                     *\n\\****************************************************************************/\n\n#ifndef INCLUDE_NLOHMANN_JSON_HPP_\n#define INCLUDE_NLOHMANN_JSON_HPP_\n\n#include <algorithm> // all_of, find, for_each\n#include <cstddef> // nullptr_t, ptrdiff_t, size_t\n#include <functional> // hash, less\n#include <initializer_list> // initializer_list\n#ifndef JSON_NO_IO\n    #include <iosfwd> // istream, ostream\n#endif  // JSON_NO_IO\n#include <iterator> // random_access_iterator_tag\n#include <memory> // unique_ptr\n#include <string> // string, stoi, to_string\n#include <utility> // declval, forward, move, pair, swap\n#include <vector> // vector\n\n// #include <nlohmann/adl_serializer.hpp>\n//     __ _____ _____ _____\n//  __|  |   __|     |   | |  JSON for Modern C++\n// |  |  |__   |  |  | | | |  version 3.11.3\n// |_____|_____|_____|_|___|  https://github.com/nlohmann/json\n//\n// SPDX-FileCopyrightText: 2013-2023 Niels Lohmann <https://nlohmann.me>\n// SPDX-License-Identifier: MIT\n\n\n\n#include <utility>\n\n// #include <nlohmann/detail/abi_macros.hpp>\n//     __ _____ _____ _____\n//  __|  |   __|     |   | |  JSON for Modern C++\n// |  |  |__   |  |  | | | |  version 3.11.3\n// |_____|_____|_____|_|___|  https://github.com/nlohmann/json\n//\n// SPDX-FileCopyrightText: 2013-2023 Niels Lohmann <https://nlohmann.me>\n// SPDX-License-Identifier: MIT\n\n\n\n// This file contains all macro definitions affecting or depending on the ABI\n\n#ifndef JSON_SKIP_LIBRARY_VERSION_CHECK\n    #if defined(NLOHMANN_JSON_VERSION_MAJOR) && defined(NLOHMANN_JSON_VERSION_MINOR) && defined(NLOHMANN_JSON_VERSION_PATCH)\n        #if NLOHMANN_JSON_VERSION_MAJOR != 3 || NLOHMANN_JSON_VERSION_MINOR != 11 || NLOHMANN_JSON_VERSION_PATCH != 3\n            #warning \"Already included a different version of the library!\"\n        #endif\n    #endif\n#endif\n\n#define NLOHMANN_JSON_VERSION_MAJOR 3   // NOLINT(modernize-macro-to-enum)\n#define NLOHMANN_JSON_VERSION_MINOR 11  // NOLINT(modernize-macro-to-enum)\n#define NLOHMANN_JSON_VERSION_PATCH 3   // NOLINT(modernize-macro-to-enum)\n\n#ifndef JSON_DIAGNOSTICS\n    #define JSON_DIAGNOSTICS 0\n#endif\n\n#ifndef JSON_USE_LEGACY_DISCARDED_VALUE_COMPARISON\n    #define JSON_USE_LEGACY_DISCARDED_VALUE_COMPARISON 0\n#endif\n\n#if JSON_DIAGNOSTICS\n    #define NLOHMANN_JSON_ABI_TAG_DIAGNOSTICS _diag\n#else\n    #define NLOHMANN_JSON_ABI_TAG_DIAGNOSTICS\n#endif\n\n#if JSON_USE_LEGACY_DISCARDED_VALUE_COMPARISON\n    #define NLOHMANN_JSON_ABI_TAG_LEGACY_DISCARDED_VALUE_COMPARISON _ldvcmp\n#else\n    #define NLOHMANN_JSON_ABI_TAG_LEGACY_DISCARDED_VALUE_COMPARISON\n#endif\n\n#ifndef NLOHMANN_JSON_NAMESPACE_NO_VERSION\n    #define NLOHMANN_JSON_NAMESPACE_NO_VERSION 0\n#endif\n\n// Construct the namespace ABI tags component\n#define NLOHMANN_JSON_ABI_TAGS_CONCAT_EX(a, b) json_abi ## a ## b\n#define NLOHMANN_JSON_ABI_TAGS_CONCAT(a, b) \\\n    NLOHMANN_JSON_ABI_TAGS_CONCAT_EX(a, b)\n\n#define NLOHMANN_JSON_ABI_TAGS                                       \\\n    NLOHMANN_JSON_ABI_TAGS_CONCAT(                                   \\\n            NLOHMANN_JSON_ABI_TAG_DIAGNOSTICS,                       \\\n            NLOHMANN_JSON_ABI_TAG_LEGACY_DISCARDED_VALUE_COMPARISON)\n\n// Construct the namespace version component\n#define NLOHMANN_JSON_NAMESPACE_VERSION_CONCAT_EX(major, minor, patch) \\\n    _v ## major ## _ ## minor ## _ ## patch\n#define NLOHMANN_JSON_NAMESPACE_VERSION_CONCAT(major, minor, patch) \\\n    NLOHMANN_JSON_NAMESPACE_VERSION_CONCAT_EX(major, minor, patch)\n\n#if NLOHMANN_JSON_NAMESPACE_NO_VERSION\n#define NLOHMANN_JSON_NAMESPACE_VERSION\n#else\n#define NLOHMANN_JSON_NAMESPACE_VERSION                                 \\\n    NLOHMANN_JSON_NAMESPACE_VERSION_CONCAT(NLOHMANN_JSON_VERSION_MAJOR, \\\n                                           NLOHMANN_JSON_VERSION_MINOR, \\\n                                           NLOHMANN_JSON_VERSION_PATCH)\n#endif\n\n// Combine namespace components\n#define NLOHMANN_JSON_NAMESPACE_CONCAT_EX(a, b) a ## b\n#define NLOHMANN_JSON_NAMESPACE_CONCAT(a, b) \\\n    NLOHMANN_JSON_NAMESPACE_CONCAT_EX(a, b)\n\n#ifndef NLOHMANN_JSON_NAMESPACE\n#define NLOHMANN_JSON_NAMESPACE               \\\n    nlohmann::NLOHMANN_JSON_NAMESPACE_CONCAT( \\\n            NLOHMANN_JSON_ABI_TAGS,           \\\n            NLOHMANN_JSON_NAMESPACE_VERSION)\n#endif\n\n#ifndef NLOHMANN_JSON_NAMESPACE_BEGIN\n#define NLOHMANN_JSON_NAMESPACE_BEGIN                \\\n    namespace nlohmann                               \\\n    {                                                \\\n    inline namespace NLOHMANN_JSON_NAMESPACE_CONCAT( \\\n                NLOHMANN_JSON_ABI_TAGS,              \\\n                NLOHMANN_JSON_NAMESPACE_VERSION)     \\\n    {\n#endif\n\n#ifndef NLOHMANN_JSON_NAMESPACE_END\n#define NLOHMANN_JSON_NAMESPACE_END                                     \\\n    }  /* namespace (inline namespace) NOLINT(readability/namespace) */ \\\n    }  // namespace nlohmann\n#endif\n\n// #include <nlohmann/detail/conversions/from_json.hpp>\n//     __ _____ _____ _____\n//  __|  |   __|     |   | |  JSON for Modern C++\n// |  |  |__   |  |  | | | |  version 3.11.3\n// |_____|_____|_____|_|___|  https://github.com/nlohmann/json\n//\n// SPDX-FileCopyrightText: 2013-2023 Niels Lohmann <https://nlohmann.me>\n// SPDX-License-Identifier: MIT\n\n\n\n#include <algorithm> // transform\n#include <array> // array\n#include <forward_list> // forward_list\n#include <iterator> // inserter, front_inserter, end\n#include <map> // map\n#include <string> // string\n#include <tuple> // tuple, make_tuple\n#include <type_traits> // is_arithmetic, is_same, is_enum, underlying_type, is_convertible\n#include <unordered_map> // unordered_map\n#include <utility> // pair, declval\n#include <valarray> // valarray\n\n// #include <nlohmann/detail/exceptions.hpp>\n//     __ _____ _____ _____\n//  __|  |   __|     |   | |  JSON for Modern C++\n// |  |  |__   |  |  | | | |  version 3.11.3\n// |_____|_____|_____|_|___|  https://github.com/nlohmann/json\n//\n// SPDX-FileCopyrightText: 2013-2023 Niels Lohmann <https://nlohmann.me>\n// SPDX-License-Identifier: MIT\n\n\n\n#include <cstddef> // nullptr_t\n#include <exception> // exception\n#if JSON_DIAGNOSTICS\n    #include <numeric> // accumulate\n#endif\n#include <stdexcept> // runtime_error\n#include <string> // to_string\n#include <vector> // vector\n\n// #include <nlohmann/detail/value_t.hpp>\n//     __ _____ _____ _____\n//  __|  |   __|     |   | |  JSON for Modern C++\n// |  |  |__   |  |  | | | |  version 3.11.3\n// |_____|_____|_____|_|___|  https://github.com/nlohmann/json\n//\n// SPDX-FileCopyrightText: 2013-2023 Niels Lohmann <https://nlohmann.me>\n// SPDX-License-Identifier: MIT\n\n\n\n#include <array> // array\n#include <cstddef> // size_t\n#include <cstdint> // uint8_t\n#include <string> // string\n\n// #include <nlohmann/detail/macro_scope.hpp>\n//     __ _____ _____ _____\n//  __|  |   __|     |   | |  JSON for Modern C++\n// |  |  |__   |  |  | | | |  version 3.11.3\n// |_____|_____|_____|_|___|  https://github.com/nlohmann/json\n//\n// SPDX-FileCopyrightText: 2013-2023 Niels Lohmann <https://nlohmann.me>\n// SPDX-License-Identifier: MIT\n\n\n\n#include <utility> // declval, pair\n// #include <nlohmann/detail/meta/detected.hpp>\n//     __ _____ _____ _____\n//  __|  |   __|     |   | |  JSON for Modern C++\n// |  |  |__   |  |  | | | |  version 3.11.3\n// |_____|_____|_____|_|___|  https://github.com/nlohmann/json\n//\n// SPDX-FileCopyrightText: 2013-2023 Niels Lohmann <https://nlohmann.me>\n// SPDX-License-Identifier: MIT\n\n\n\n#include <type_traits>\n\n// #include <nlohmann/detail/meta/void_t.hpp>\n//     __ _____ _____ _____\n//  __|  |   __|     |   | |  JSON for Modern C++\n// |  |  |__   |  |  | | | |  version 3.11.3\n// |_____|_____|_____|_|___|  https://github.com/nlohmann/json\n//\n// SPDX-FileCopyrightText: 2013-2023 Niels Lohmann <https://nlohmann.me>\n// SPDX-License-Identifier: MIT\n\n\n\n// #include <nlohmann/detail/abi_macros.hpp>\n\n\nNLOHMANN_JSON_NAMESPACE_BEGIN\nnamespace detail\n{\n\ntemplate<typename ...Ts> struct make_void\n{\n    using type = void;\n};\ntemplate<typename ...Ts> using void_t = typename make_void<Ts...>::type;\n\n}  // namespace detail\nNLOHMANN_JSON_NAMESPACE_END\n\n\nNLOHMANN_JSON_NAMESPACE_BEGIN\nnamespace detail\n{\n\n// https://en.cppreference.com/w/cpp/experimental/is_detected\nstruct nonesuch\n{\n    nonesuch() = delete;\n    ~nonesuch() = delete;\n    nonesuch(nonesuch const&) = delete;\n    nonesuch(nonesuch const&&) = delete;\n    void operator=(nonesuch const&) = delete;\n    void operator=(nonesuch&&) = delete;\n};\n\ntemplate<class Default,\n         class AlwaysVoid,\n         template<class...> class Op,\n         class... Args>\nstruct detector\n{\n    using value_t = std::false_type;\n    using type = Default;\n};\n\ntemplate<class Default, template<class...> class Op, class... Args>\nstruct detector<Default, void_t<Op<Args...>>, Op, Args...>\n{\n    using value_t = std::true_type;\n    using type = Op<Args...>;\n};\n\ntemplate<template<class...> class Op, class... Args>\nusing is_detected = typename detector<nonesuch, void, Op, Args...>::value_t;\n\ntemplate<template<class...> class Op, class... Args>\nstruct is_detected_lazy : is_detected<Op, Args...> { };\n\ntemplate<template<class...> class Op, class... Args>\nusing detected_t = typename detector<nonesuch, void, Op, Args...>::type;\n\ntemplate<class Default, template<class...> class Op, class... Args>\nusing detected_or = detector<Default, void, Op, Args...>;\n\ntemplate<class Default, template<class...> class Op, class... Args>\nusing detected_or_t = typename detected_or<Default, Op, Args...>::type;\n\ntemplate<class Expected, template<class...> class Op, class... Args>\nusing is_detected_exact = std::is_same<Expected, detected_t<Op, Args...>>;\n\ntemplate<class To, template<class...> class Op, class... Args>\nusing is_detected_convertible =\n    std::is_convertible<detected_t<Op, Args...>, To>;\n\n}  // namespace detail\nNLOHMANN_JSON_NAMESPACE_END\n\n// #include <nlohmann/thirdparty/hedley/hedley.hpp>\n\n\n//     __ _____ _____ _____\n//  __|  |   __|     |   | |  JSON for Modern C++\n// |  |  |__   |  |  | | | |  version 3.11.3\n// |_____|_____|_____|_|___|  https://github.com/nlohmann/json\n//\n// SPDX-FileCopyrightText: 2013-2023 Niels Lohmann <https://nlohmann.me>\n// SPDX-FileCopyrightText: 2016-2021 Evan Nemerson <evan@nemerson.com>\n// SPDX-License-Identifier: MIT\n\n/* Hedley - https://nemequ.github.io/hedley\n * Created by Evan Nemerson <evan@nemerson.com>\n */\n\n#if !defined(JSON_HEDLEY_VERSION) || (JSON_HEDLEY_VERSION < 15)\n#if defined(JSON_HEDLEY_VERSION)\n    #undef JSON_HEDLEY_VERSION\n#endif\n#define JSON_HEDLEY_VERSION 15\n\n#if defined(JSON_HEDLEY_STRINGIFY_EX)\n    #undef JSON_HEDLEY_STRINGIFY_EX\n#endif\n#define JSON_HEDLEY_STRINGIFY_EX(x) #x\n\n#if defined(JSON_HEDLEY_STRINGIFY)\n    #undef JSON_HEDLEY_STRINGIFY\n#endif\n#define JSON_HEDLEY_STRINGIFY(x) JSON_HEDLEY_STRINGIFY_EX(x)\n\n#if defined(JSON_HEDLEY_CONCAT_EX)\n    #undef JSON_HEDLEY_CONCAT_EX\n#endif\n#define JSON_HEDLEY_CONCAT_EX(a,b) a##b\n\n#if defined(JSON_HEDLEY_CONCAT)\n    #undef JSON_HEDLEY_CONCAT\n#endif\n#define JSON_HEDLEY_CONCAT(a,b) JSON_HEDLEY_CONCAT_EX(a,b)\n\n#if defined(JSON_HEDLEY_CONCAT3_EX)\n    #undef JSON_HEDLEY_CONCAT3_EX\n#endif\n#define JSON_HEDLEY_CONCAT3_EX(a,b,c) a##b##c\n\n#if defined(JSON_HEDLEY_CONCAT3)\n    #undef JSON_HEDLEY_CONCAT3\n#endif\n#define JSON_HEDLEY_CONCAT3(a,b,c) JSON_HEDLEY_CONCAT3_EX(a,b,c)\n\n#if defined(JSON_HEDLEY_VERSION_ENCODE)\n    #undef JSON_HEDLEY_VERSION_ENCODE\n#endif\n#define JSON_HEDLEY_VERSION_ENCODE(major,minor,revision) (((major) * 1000000) + ((minor) * 1000) + (revision))\n\n#if defined(JSON_HEDLEY_VERSION_DECODE_MAJOR)\n    #undef JSON_HEDLEY_VERSION_DECODE_MAJOR\n#endif\n#define JSON_HEDLEY_VERSION_DECODE_MAJOR(version) ((version) / 1000000)\n\n#if defined(JSON_HEDLEY_VERSION_DECODE_MINOR)\n    #undef JSON_HEDLEY_VERSION_DECODE_MINOR\n#endif\n#define JSON_HEDLEY_VERSION_DECODE_MINOR(version) (((version) % 1000000) / 1000)\n\n#if defined(JSON_HEDLEY_VERSION_DECODE_REVISION)\n    #undef JSON_HEDLEY_VERSION_DECODE_REVISION\n#endif\n#define JSON_HEDLEY_VERSION_DECODE_REVISION(version) ((version) % 1000)\n\n#if defined(JSON_HEDLEY_GNUC_VERSION)\n    #undef JSON_HEDLEY_GNUC_VERSION\n#endif\n#if defined(__GNUC__) && defined(__GNUC_PATCHLEVEL__)\n    #define JSON_HEDLEY_GNUC_VERSION JSON_HEDLEY_VERSION_ENCODE(__GNUC__, __GNUC_MINOR__, __GNUC_PATCHLEVEL__)\n#elif defined(__GNUC__)\n    #define JSON_HEDLEY_GNUC_VERSION JSON_HEDLEY_VERSION_ENCODE(__GNUC__, __GNUC_MINOR__, 0)\n#endif\n\n#if defined(JSON_HEDLEY_GNUC_VERSION_CHECK)\n    #undef JSON_HEDLEY_GNUC_VERSION_CHECK\n#endif\n#if defined(JSON_HEDLEY_GNUC_VERSION)\n    #define JSON_HEDLEY_GNUC_VERSION_CHECK(major,minor,patch) (JSON_HEDLEY_GNUC_VERSION >= JSON_HEDLEY_VERSION_ENCODE(major, minor, patch))\n#else\n    #define JSON_HEDLEY_GNUC_VERSION_CHECK(major,minor,patch) (0)\n#endif\n\n#if defined(JSON_HEDLEY_MSVC_VERSION)\n    #undef JSON_HEDLEY_MSVC_VERSION\n#endif\n#if defined(_MSC_FULL_VER) && (_MSC_FULL_VER >= 140000000) && !defined(__ICL)\n    #define JSON_HEDLEY_MSVC_VERSION JSON_HEDLEY_VERSION_ENCODE(_MSC_FULL_VER / 10000000, (_MSC_FULL_VER % 10000000) / 100000, (_MSC_FULL_VER % 100000) / 100)\n#elif defined(_MSC_FULL_VER) && !defined(__ICL)\n    #define JSON_HEDLEY_MSVC_VERSION JSON_HEDLEY_VERSION_ENCODE(_MSC_FULL_VER / 1000000, (_MSC_FULL_VER % 1000000) / 10000, (_MSC_FULL_VER % 10000) / 10)\n#elif defined(_MSC_VER) && !defined(__ICL)\n    #define JSON_HEDLEY_MSVC_VERSION JSON_HEDLEY_VERSION_ENCODE(_MSC_VER / 100, _MSC_VER % 100, 0)\n#endif\n\n#if defined(JSON_HEDLEY_MSVC_VERSION_CHECK)\n    #undef JSON_HEDLEY_MSVC_VERSION_CHECK\n#endif\n#if !defined(JSON_HEDLEY_MSVC_VERSION)\n    #define JSON_HEDLEY_MSVC_VERSION_CHECK(major,minor,patch) (0)\n#elif defined(_MSC_VER) && (_MSC_VER >= 1400)\n    #define JSON_HEDLEY_MSVC_VERSION_CHECK(major,minor,patch) (_MSC_FULL_VER >= ((major * 10000000) + (minor * 100000) + (patch)))\n#elif defined(_MSC_VER) && (_MSC_VER >= 1200)\n    #define JSON_HEDLEY_MSVC_VERSION_CHECK(major,minor,patch) (_MSC_FULL_VER >= ((major * 1000000) + (minor * 10000) + (patch)))\n#else\n    #define JSON_HEDLEY_MSVC_VERSION_CHECK(major,minor,patch) (_MSC_VER >= ((major * 100) + (minor)))\n#endif\n\n#if defined(JSON_HEDLEY_INTEL_VERSION)\n    #undef JSON_HEDLEY_INTEL_VERSION\n#endif\n#if defined(__INTEL_COMPILER) && defined(__INTEL_COMPILER_UPDATE) && !defined(__ICL)\n    #define JSON_HEDLEY_INTEL_VERSION JSON_HEDLEY_VERSION_ENCODE(__INTEL_COMPILER / 100, __INTEL_COMPILER % 100, __INTEL_COMPILER_UPDATE)\n#elif defined(__INTEL_COMPILER) && !defined(__ICL)\n    #define JSON_HEDLEY_INTEL_VERSION JSON_HEDLEY_VERSION_ENCODE(__INTEL_COMPILER / 100, __INTEL_COMPILER % 100, 0)\n#endif\n\n#if defined(JSON_HEDLEY_INTEL_VERSION_CHECK)\n    #undef JSON_HEDLEY_INTEL_VERSION_CHECK\n#endif\n#if defined(JSON_HEDLEY_INTEL_VERSION)\n    #define JSON_HEDLEY_INTEL_VERSION_CHECK(major,minor,patch) (JSON_HEDLEY_INTEL_VERSION >= JSON_HEDLEY_VERSION_ENCODE(major, minor, patch))\n#else\n    #define JSON_HEDLEY_INTEL_VERSION_CHECK(major,minor,patch) (0)\n#endif\n\n#if defined(JSON_HEDLEY_INTEL_CL_VERSION)\n    #undef JSON_HEDLEY_INTEL_CL_VERSION\n#endif\n#if defined(__INTEL_COMPILER) && defined(__INTEL_COMPILER_UPDATE) && defined(__ICL)\n    #define JSON_HEDLEY_INTEL_CL_VERSION JSON_HEDLEY_VERSION_ENCODE(__INTEL_COMPILER, __INTEL_COMPILER_UPDATE, 0)\n#endif\n\n#if defined(JSON_HEDLEY_INTEL_CL_VERSION_CHECK)\n    #undef JSON_HEDLEY_INTEL_CL_VERSION_CHECK\n#endif\n#if defined(JSON_HEDLEY_INTEL_CL_VERSION)\n    #define JSON_HEDLEY_INTEL_CL_VERSION_CHECK(major,minor,patch) (JSON_HEDLEY_INTEL_CL_VERSION >= JSON_HEDLEY_VERSION_ENCODE(major, minor, patch))\n#else\n    #define JSON_HEDLEY_INTEL_CL_VERSION_CHECK(major,minor,patch) (0)\n#endif\n\n#if defined(JSON_HEDLEY_PGI_VERSION)\n    #undef JSON_HEDLEY_PGI_VERSION\n#endif\n#if defined(__PGI) && defined(__PGIC__) && defined(__PGIC_MINOR__) && defined(__PGIC_PATCHLEVEL__)\n    #define JSON_HEDLEY_PGI_VERSION JSON_HEDLEY_VERSION_ENCODE(__PGIC__, __PGIC_MINOR__, __PGIC_PATCHLEVEL__)\n#endif\n\n#if defined(JSON_HEDLEY_PGI_VERSION_CHECK)\n    #undef JSON_HEDLEY_PGI_VERSION_CHECK\n#endif\n#if defined(JSON_HEDLEY_PGI_VERSION)\n    #define JSON_HEDLEY_PGI_VERSION_CHECK(major,minor,patch) (JSON_HEDLEY_PGI_VERSION >= JSON_HEDLEY_VERSION_ENCODE(major, minor, patch))\n#else\n    #define JSON_HEDLEY_PGI_VERSION_CHECK(major,minor,patch) (0)\n#endif\n\n#if defined(JSON_HEDLEY_SUNPRO_VERSION)\n    #undef JSON_HEDLEY_SUNPRO_VERSION\n#endif\n#if defined(__SUNPRO_C) && (__SUNPRO_C > 0x1000)\n    #define JSON_HEDLEY_SUNPRO_VERSION JSON_HEDLEY_VERSION_ENCODE((((__SUNPRO_C >> 16) & 0xf) * 10) + ((__SUNPRO_C >> 12) & 0xf), (((__SUNPRO_C >> 8) & 0xf) * 10) + ((__SUNPRO_C >> 4) & 0xf), (__SUNPRO_C & 0xf) * 10)\n#elif defined(__SUNPRO_C)\n    #define JSON_HEDLEY_SUNPRO_VERSION JSON_HEDLEY_VERSION_ENCODE((__SUNPRO_C >> 8) & 0xf, (__SUNPRO_C >> 4) & 0xf, (__SUNPRO_C) & 0xf)\n#elif defined(__SUNPRO_CC) && (__SUNPRO_CC > 0x1000)\n    #define JSON_HEDLEY_SUNPRO_VERSION JSON_HEDLEY_VERSION_ENCODE((((__SUNPRO_CC >> 16) & 0xf) * 10) + ((__SUNPRO_CC >> 12) & 0xf), (((__SUNPRO_CC >> 8) & 0xf) * 10) + ((__SUNPRO_CC >> 4) & 0xf), (__SUNPRO_CC & 0xf) * 10)\n#elif defined(__SUNPRO_CC)\n    #define JSON_HEDLEY_SUNPRO_VERSION JSON_HEDLEY_VERSION_ENCODE((__SUNPRO_CC >> 8) & 0xf, (__SUNPRO_CC >> 4) & 0xf, (__SUNPRO_CC) & 0xf)\n#endif\n\n#if defined(JSON_HEDLEY_SUNPRO_VERSION_CHECK)\n    #undef JSON_HEDLEY_SUNPRO_VERSION_CHECK\n#endif\n#if defined(JSON_HEDLEY_SUNPRO_VERSION)\n    #define JSON_HEDLEY_SUNPRO_VERSION_CHECK(major,minor,patch) (JSON_HEDLEY_SUNPRO_VERSION >= JSON_HEDLEY_VERSION_ENCODE(major, minor, patch))\n#else\n    #define JSON_HEDLEY_SUNPRO_VERSION_CHECK(major,minor,patch) (0)\n#endif\n\n#if defined(JSON_HEDLEY_EMSCRIPTEN_VERSION)\n    #undef JSON_HEDLEY_EMSCRIPTEN_VERSION\n#endif\n#if defined(__EMSCRIPTEN__)\n    #define JSON_HEDLEY_EMSCRIPTEN_VERSION JSON_HEDLEY_VERSION_ENCODE(__EMSCRIPTEN_major__, __EMSCRIPTEN_minor__, __EMSCRIPTEN_tiny__)\n#endif\n\n#if defined(JSON_HEDLEY_EMSCRIPTEN_VERSION_CHECK)\n    #undef JSON_HEDLEY_EMSCRIPTEN_VERSION_CHECK\n#endif\n#if defined(JSON_HEDLEY_EMSCRIPTEN_VERSION)\n    #define JSON_HEDLEY_EMSCRIPTEN_VERSION_CHECK(major,minor,patch) (JSON_HEDLEY_EMSCRIPTEN_VERSION >= JSON_HEDLEY_VERSION_ENCODE(major, minor, patch))\n#else\n    #define JSON_HEDLEY_EMSCRIPTEN_VERSION_CHECK(major,minor,patch) (0)\n#endif\n\n#if defined(JSON_HEDLEY_ARM_VERSION)\n    #undef JSON_HEDLEY_ARM_VERSION\n#endif\n#if defined(__CC_ARM) && defined(__ARMCOMPILER_VERSION)\n    #define JSON_HEDLEY_ARM_VERSION JSON_HEDLEY_VERSION_ENCODE(__ARMCOMPILER_VERSION / 1000000, (__ARMCOMPILER_VERSION % 1000000) / 10000, (__ARMCOMPILER_VERSION % 10000) / 100)\n#elif defined(__CC_ARM) && defined(__ARMCC_VERSION)\n    #define JSON_HEDLEY_ARM_VERSION JSON_HEDLEY_VERSION_ENCODE(__ARMCC_VERSION / 1000000, (__ARMCC_VERSION % 1000000) / 10000, (__ARMCC_VERSION % 10000) / 100)\n#endif\n\n#if defined(JSON_HEDLEY_ARM_VERSION_CHECK)\n    #undef JSON_HEDLEY_ARM_VERSION_CHECK\n#endif\n#if defined(JSON_HEDLEY_ARM_VERSION)\n    #define JSON_HEDLEY_ARM_VERSION_CHECK(major,minor,patch) (JSON_HEDLEY_ARM_VERSION >= JSON_HEDLEY_VERSION_ENCODE(major, minor, patch))\n#else\n    #define JSON_HEDLEY_ARM_VERSION_CHECK(major,minor,patch) (0)\n#endif\n\n#if defined(JSON_HEDLEY_IBM_VERSION)\n    #undef JSON_HEDLEY_IBM_VERSION\n#endif\n#if defined(__ibmxl__)\n    #define JSON_HEDLEY_IBM_VERSION JSON_HEDLEY_VERSION_ENCODE(__ibmxl_version__, __ibmxl_release__, __ibmxl_modification__)\n#elif defined(__xlC__) && defined(__xlC_ver__)\n    #define JSON_HEDLEY_IBM_VERSION JSON_HEDLEY_VERSION_ENCODE(__xlC__ >> 8, __xlC__ & 0xff, (__xlC_ver__ >> 8) & 0xff)\n#elif defined(__xlC__)\n    #define JSON_HEDLEY_IBM_VERSION JSON_HEDLEY_VERSION_ENCODE(__xlC__ >> 8, __xlC__ & 0xff, 0)\n#endif\n\n#if defined(JSON_HEDLEY_IBM_VERSION_CHECK)\n    #undef JSON_HEDLEY_IBM_VERSION_CHECK\n#endif\n#if defined(JSON_HEDLEY_IBM_VERSION)\n    #define JSON_HEDLEY_IBM_VERSION_CHECK(major,minor,patch) (JSON_HEDLEY_IBM_VERSION >= JSON_HEDLEY_VERSION_ENCODE(major, minor, patch))\n#else\n    #define JSON_HEDLEY_IBM_VERSION_CHECK(major,minor,patch) (0)\n#endif\n\n#if defined(JSON_HEDLEY_TI_VERSION)\n    #undef JSON_HEDLEY_TI_VERSION\n#endif\n#if \\\n    defined(__TI_COMPILER_VERSION__) && \\\n    ( \\\n      defined(__TMS470__) || defined(__TI_ARM__) || \\\n      defined(__MSP430__) || \\\n      defined(__TMS320C2000__) \\\n    )\n#if (__TI_COMPILER_VERSION__ >= 16000000)\n    #define JSON_HEDLEY_TI_VERSION JSON_HEDLEY_VERSION_ENCODE(__TI_COMPILER_VERSION__ / 1000000, (__TI_COMPILER_VERSION__ % 1000000) / 1000, (__TI_COMPILER_VERSION__ % 1000))\n#endif\n#endif\n\n#if defined(JSON_HEDLEY_TI_VERSION_CHECK)\n    #undef JSON_HEDLEY_TI_VERSION_CHECK\n#endif\n#if defined(JSON_HEDLEY_TI_VERSION)\n    #define JSON_HEDLEY_TI_VERSION_CHECK(major,minor,patch) (JSON_HEDLEY_TI_VERSION >= JSON_HEDLEY_VERSION_ENCODE(major, minor, patch))\n#else\n    #define JSON_HEDLEY_TI_VERSION_CHECK(major,minor,patch) (0)\n#endif\n\n#if defined(JSON_HEDLEY_TI_CL2000_VERSION)\n    #undef JSON_HEDLEY_TI_CL2000_VERSION\n#endif\n#if defined(__TI_COMPILER_VERSION__) && defined(__TMS320C2000__)\n    #define JSON_HEDLEY_TI_CL2000_VERSION JSON_HEDLEY_VERSION_ENCODE(__TI_COMPILER_VERSION__ / 1000000, (__TI_COMPILER_VERSION__ % 1000000) / 1000, (__TI_COMPILER_VERSION__ % 1000))\n#endif\n\n#if defined(JSON_HEDLEY_TI_CL2000_VERSION_CHECK)\n    #undef JSON_HEDLEY_TI_CL2000_VERSION_CHECK\n#endif\n#if defined(JSON_HEDLEY_TI_CL2000_VERSION)\n    #define JSON_HEDLEY_TI_CL2000_VERSION_CHECK(major,minor,patch) (JSON_HEDLEY_TI_CL2000_VERSION >= JSON_HEDLEY_VERSION_ENCODE(major, minor, patch))\n#else\n    #define JSON_HEDLEY_TI_CL2000_VERSION_CHECK(major,minor,patch) (0)\n#endif\n\n#if defined(JSON_HEDLEY_TI_CL430_VERSION)\n    #undef JSON_HEDLEY_TI_CL430_VERSION\n#endif\n#if defined(__TI_COMPILER_VERSION__) && defined(__MSP430__)\n    #define JSON_HEDLEY_TI_CL430_VERSION JSON_HEDLEY_VERSION_ENCODE(__TI_COMPILER_VERSION__ / 1000000, (__TI_COMPILER_VERSION__ % 1000000) / 1000, (__TI_COMPILER_VERSION__ % 1000))\n#endif\n\n#if defined(JSON_HEDLEY_TI_CL430_VERSION_CHECK)\n    #undef JSON_HEDLEY_TI_CL430_VERSION_CHECK\n#endif\n#if defined(JSON_HEDLEY_TI_CL430_VERSION)\n    #define JSON_HEDLEY_TI_CL430_VERSION_CHECK(major,minor,patch) (JSON_HEDLEY_TI_CL430_VERSION >= JSON_HEDLEY_VERSION_ENCODE(major, minor, patch))\n#else\n    #define JSON_HEDLEY_TI_CL430_VERSION_CHECK(major,minor,patch) (0)\n#endif\n\n#if defined(JSON_HEDLEY_TI_ARMCL_VERSION)\n    #undef JSON_HEDLEY_TI_ARMCL_VERSION\n#endif\n#if defined(__TI_COMPILER_VERSION__) && (defined(__TMS470__) || defined(__TI_ARM__))\n    #define JSON_HEDLEY_TI_ARMCL_VERSION JSON_HEDLEY_VERSION_ENCODE(__TI_COMPILER_VERSION__ / 1000000, (__TI_COMPILER_VERSION__ % 1000000) / 1000, (__TI_COMPILER_VERSION__ % 1000))\n#endif\n\n#if defined(JSON_HEDLEY_TI_ARMCL_VERSION_CHECK)\n    #undef JSON_HEDLEY_TI_ARMCL_VERSION_CHECK\n#endif\n#if defined(JSON_HEDLEY_TI_ARMCL_VERSION)\n    #define JSON_HEDLEY_TI_ARMCL_VERSION_CHECK(major,minor,patch) (JSON_HEDLEY_TI_ARMCL_VERSION >= JSON_HEDLEY_VERSION_ENCODE(major, minor, patch))\n#else\n    #define JSON_HEDLEY_TI_ARMCL_VERSION_CHECK(major,minor,patch) (0)\n#endif\n\n#if defined(JSON_HEDLEY_TI_CL6X_VERSION)\n    #undef JSON_HEDLEY_TI_CL6X_VERSION\n#endif\n#if defined(__TI_COMPILER_VERSION__) && defined(__TMS320C6X__)\n    #define JSON_HEDLEY_TI_CL6X_VERSION JSON_HEDLEY_VERSION_ENCODE(__TI_COMPILER_VERSION__ / 1000000, (__TI_COMPILER_VERSION__ % 1000000) / 1000, (__TI_COMPILER_VERSION__ % 1000))\n#endif\n\n#if defined(JSON_HEDLEY_TI_CL6X_VERSION_CHECK)\n    #undef JSON_HEDLEY_TI_CL6X_VERSION_CHECK\n#endif\n#if defined(JSON_HEDLEY_TI_CL6X_VERSION)\n    #define JSON_HEDLEY_TI_CL6X_VERSION_CHECK(major,minor,patch) (JSON_HEDLEY_TI_CL6X_VERSION >= JSON_HEDLEY_VERSION_ENCODE(major, minor, patch))\n#else\n    #define JSON_HEDLEY_TI_CL6X_VERSION_CHECK(major,minor,patch) (0)\n#endif\n\n#if defined(JSON_HEDLEY_TI_CL7X_VERSION)\n    #undef JSON_HEDLEY_TI_CL7X_VERSION\n#endif\n#if defined(__TI_COMPILER_VERSION__) && defined(__C7000__)\n    #define JSON_HEDLEY_TI_CL7X_VERSION JSON_HEDLEY_VERSION_ENCODE(__TI_COMPILER_VERSION__ / 1000000, (__TI_COMPILER_VERSION__ % 1000000) / 1000, (__TI_COMPILER_VERSION__ % 1000))\n#endif\n\n#if defined(JSON_HEDLEY_TI_CL7X_VERSION_CHECK)\n    #undef JSON_HEDLEY_TI_CL7X_VERSION_CHECK\n#endif\n#if defined(JSON_HEDLEY_TI_CL7X_VERSION)\n    #define JSON_HEDLEY_TI_CL7X_VERSION_CHECK(major,minor,patch) (JSON_HEDLEY_TI_CL7X_VERSION >= JSON_HEDLEY_VERSION_ENCODE(major, minor, patch))\n#else\n    #define JSON_HEDLEY_TI_CL7X_VERSION_CHECK(major,minor,patch) (0)\n#endif\n\n#if defined(JSON_HEDLEY_TI_CLPRU_VERSION)\n    #undef JSON_HEDLEY_TI_CLPRU_VERSION\n#endif\n#if defined(__TI_COMPILER_VERSION__) && defined(__PRU__)\n    #define JSON_HEDLEY_TI_CLPRU_VERSION JSON_HEDLEY_VERSION_ENCODE(__TI_COMPILER_VERSION__ / 1000000, (__TI_COMPILER_VERSION__ % 1000000) / 1000, (__TI_COMPILER_VERSION__ % 1000))\n#endif\n\n#if defined(JSON_HEDLEY_TI_CLPRU_VERSION_CHECK)\n    #undef JSON_HEDLEY_TI_CLPRU_VERSION_CHECK\n#endif\n#if defined(JSON_HEDLEY_TI_CLPRU_VERSION)\n    #define JSON_HEDLEY_TI_CLPRU_VERSION_CHECK(major,minor,patch) (JSON_HEDLEY_TI_CLPRU_VERSION >= JSON_HEDLEY_VERSION_ENCODE(major, minor, patch))\n#else\n    #define JSON_HEDLEY_TI_CLPRU_VERSION_CHECK(major,minor,patch) (0)\n#endif\n\n#if defined(JSON_HEDLEY_CRAY_VERSION)\n    #undef JSON_HEDLEY_CRAY_VERSION\n#endif\n#if defined(_CRAYC)\n    #if defined(_RELEASE_PATCHLEVEL)\n        #define JSON_HEDLEY_CRAY_VERSION JSON_HEDLEY_VERSION_ENCODE(_RELEASE_MAJOR, _RELEASE_MINOR, _RELEASE_PATCHLEVEL)\n    #else\n        #define JSON_HEDLEY_CRAY_VERSION JSON_HEDLEY_VERSION_ENCODE(_RELEASE_MAJOR, _RELEASE_MINOR, 0)\n    #endif\n#endif\n\n#if defined(JSON_HEDLEY_CRAY_VERSION_CHECK)\n    #undef JSON_HEDLEY_CRAY_VERSION_CHECK\n#endif\n#if defined(JSON_HEDLEY_CRAY_VERSION)\n    #define JSON_HEDLEY_CRAY_VERSION_CHECK(major,minor,patch) (JSON_HEDLEY_CRAY_VERSION >= JSON_HEDLEY_VERSION_ENCODE(major, minor, patch))\n#else\n    #define JSON_HEDLEY_CRAY_VERSION_CHECK(major,minor,patch) (0)\n#endif\n\n#if defined(JSON_HEDLEY_IAR_VERSION)\n    #undef JSON_HEDLEY_IAR_VERSION\n#endif\n#if defined(__IAR_SYSTEMS_ICC__)\n    #if __VER__ > 1000\n        #define JSON_HEDLEY_IAR_VERSION JSON_HEDLEY_VERSION_ENCODE((__VER__ / 1000000), ((__VER__ / 1000) % 1000), (__VER__ % 1000))\n    #else\n        #define JSON_HEDLEY_IAR_VERSION JSON_HEDLEY_VERSION_ENCODE(__VER__ / 100, __VER__ % 100, 0)\n    #endif\n#endif\n\n#if defined(JSON_HEDLEY_IAR_VERSION_CHECK)\n    #undef JSON_HEDLEY_IAR_VERSION_CHECK\n#endif\n#if defined(JSON_HEDLEY_IAR_VERSION)\n    #define JSON_HEDLEY_IAR_VERSION_CHECK(major,minor,patch) (JSON_HEDLEY_IAR_VERSION >= JSON_HEDLEY_VERSION_ENCODE(major, minor, patch))\n#else\n    #define JSON_HEDLEY_IAR_VERSION_CHECK(major,minor,patch) (0)\n#endif\n\n#if defined(JSON_HEDLEY_TINYC_VERSION)\n    #undef JSON_HEDLEY_TINYC_VERSION\n#endif\n#if defined(__TINYC__)\n    #define JSON_HEDLEY_TINYC_VERSION JSON_HEDLEY_VERSION_ENCODE(__TINYC__ / 1000, (__TINYC__ / 100) % 10, __TINYC__ % 100)\n#endif\n\n#if defined(JSON_HEDLEY_TINYC_VERSION_CHECK)\n    #undef JSON_HEDLEY_TINYC_VERSION_CHECK\n#endif\n#if defined(JSON_HEDLEY_TINYC_VERSION)\n    #define JSON_HEDLEY_TINYC_VERSION_CHECK(major,minor,patch) (JSON_HEDLEY_TINYC_VERSION >= JSON_HEDLEY_VERSION_ENCODE(major, minor, patch))\n#else\n    #define JSON_HEDLEY_TINYC_VERSION_CHECK(major,minor,patch) (0)\n#endif\n\n#if defined(JSON_HEDLEY_DMC_VERSION)\n    #undef JSON_HEDLEY_DMC_VERSION\n#endif\n#if defined(__DMC__)\n    #define JSON_HEDLEY_DMC_VERSION JSON_HEDLEY_VERSION_ENCODE(__DMC__ >> 8, (__DMC__ >> 4) & 0xf, __DMC__ & 0xf)\n#endif\n\n#if defined(JSON_HEDLEY_DMC_VERSION_CHECK)\n    #undef JSON_HEDLEY_DMC_VERSION_CHECK\n#endif\n#if defined(JSON_HEDLEY_DMC_VERSION)\n    #define JSON_HEDLEY_DMC_VERSION_CHECK(major,minor,patch) (JSON_HEDLEY_DMC_VERSION >= JSON_HEDLEY_VERSION_ENCODE(major, minor, patch))\n#else\n    #define JSON_HEDLEY_DMC_VERSION_CHECK(major,minor,patch) (0)\n#endif\n\n#if defined(JSON_HEDLEY_COMPCERT_VERSION)\n    #undef JSON_HEDLEY_COMPCERT_VERSION\n#endif\n#if defined(__COMPCERT_VERSION__)\n    #define JSON_HEDLEY_COMPCERT_VERSION JSON_HEDLEY_VERSION_ENCODE(__COMPCERT_VERSION__ / 10000, (__COMPCERT_VERSION__ / 100) % 100, __COMPCERT_VERSION__ % 100)\n#endif\n\n#if defined(JSON_HEDLEY_COMPCERT_VERSION_CHECK)\n    #undef JSON_HEDLEY_COMPCERT_VERSION_CHECK\n#endif\n#if defined(JSON_HEDLEY_COMPCERT_VERSION)\n    #define JSON_HEDLEY_COMPCERT_VERSION_CHECK(major,minor,patch) (JSON_HEDLEY_COMPCERT_VERSION >= JSON_HEDLEY_VERSION_ENCODE(major, minor, patch))\n#else\n    #define JSON_HEDLEY_COMPCERT_VERSION_CHECK(major,minor,patch) (0)\n#endif\n\n#if defined(JSON_HEDLEY_PELLES_VERSION)\n    #undef JSON_HEDLEY_PELLES_VERSION\n#endif\n#if defined(__POCC__)\n    #define JSON_HEDLEY_PELLES_VERSION JSON_HEDLEY_VERSION_ENCODE(__POCC__ / 100, __POCC__ % 100, 0)\n#endif\n\n#if defined(JSON_HEDLEY_PELLES_VERSION_CHECK)\n    #undef JSON_HEDLEY_PELLES_VERSION_CHECK\n#endif\n#if defined(JSON_HEDLEY_PELLES_VERSION)\n    #define JSON_HEDLEY_PELLES_VERSION_CHECK(major,minor,patch) (JSON_HEDLEY_PELLES_VERSION >= JSON_HEDLEY_VERSION_ENCODE(major, minor, patch))\n#else\n    #define JSON_HEDLEY_PELLES_VERSION_CHECK(major,minor,patch) (0)\n#endif\n\n#if defined(JSON_HEDLEY_MCST_LCC_VERSION)\n    #undef JSON_HEDLEY_MCST_LCC_VERSION\n#endif\n#if defined(__LCC__) && defined(__LCC_MINOR__)\n    #define JSON_HEDLEY_MCST_LCC_VERSION JSON_HEDLEY_VERSION_ENCODE(__LCC__ / 100, __LCC__ % 100, __LCC_MINOR__)\n#endif\n\n#if defined(JSON_HEDLEY_MCST_LCC_VERSION_CHECK)\n    #undef JSON_HEDLEY_MCST_LCC_VERSION_CHECK\n#endif\n#if defined(JSON_HEDLEY_MCST_LCC_VERSION)\n    #define JSON_HEDLEY_MCST_LCC_VERSION_CHECK(major,minor,patch) (JSON_HEDLEY_MCST_LCC_VERSION >= JSON_HEDLEY_VERSION_ENCODE(major, minor, patch))\n#else\n    #define JSON_HEDLEY_MCST_LCC_VERSION_CHECK(major,minor,patch) (0)\n#endif\n\n#if defined(JSON_HEDLEY_GCC_VERSION)\n    #undef JSON_HEDLEY_GCC_VERSION\n#endif\n#if \\\n    defined(JSON_HEDLEY_GNUC_VERSION) && \\\n    !defined(__clang__) && \\\n    !defined(JSON_HEDLEY_INTEL_VERSION) && \\\n    !defined(JSON_HEDLEY_PGI_VERSION) && \\\n    !defined(JSON_HEDLEY_ARM_VERSION) && \\\n    !defined(JSON_HEDLEY_CRAY_VERSION) && \\\n    !defined(JSON_HEDLEY_TI_VERSION) && \\\n    !defined(JSON_HEDLEY_TI_ARMCL_VERSION) && \\\n    !defined(JSON_HEDLEY_TI_CL430_VERSION) && \\\n    !defined(JSON_HEDLEY_TI_CL2000_VERSION) && \\\n    !defined(JSON_HEDLEY_TI_CL6X_VERSION) && \\\n    !defined(JSON_HEDLEY_TI_CL7X_VERSION) && \\\n    !defined(JSON_HEDLEY_TI_CLPRU_VERSION) && \\\n    !defined(__COMPCERT__) && \\\n    !defined(JSON_HEDLEY_MCST_LCC_VERSION)\n    #define JSON_HEDLEY_GCC_VERSION JSON_HEDLEY_GNUC_VERSION\n#endif\n\n#if defined(JSON_HEDLEY_GCC_VERSION_CHECK)\n    #undef JSON_HEDLEY_GCC_VERSION_CHECK\n#endif\n#if defined(JSON_HEDLEY_GCC_VERSION)\n    #define JSON_HEDLEY_GCC_VERSION_CHECK(major,minor,patch) (JSON_HEDLEY_GCC_VERSION >= JSON_HEDLEY_VERSION_ENCODE(major, minor, patch))\n#else\n    #define JSON_HEDLEY_GCC_VERSION_CHECK(major,minor,patch) (0)\n#endif\n\n#if defined(JSON_HEDLEY_HAS_ATTRIBUTE)\n    #undef JSON_HEDLEY_HAS_ATTRIBUTE\n#endif\n#if \\\n  defined(__has_attribute) && \\\n  ( \\\n    (!defined(JSON_HEDLEY_IAR_VERSION) || JSON_HEDLEY_IAR_VERSION_CHECK(8,5,9)) \\\n  )\n#  define JSON_HEDLEY_HAS_ATTRIBUTE(attribute) __has_attribute(attribute)\n#else\n#  define JSON_HEDLEY_HAS_ATTRIBUTE(attribute) (0)\n#endif\n\n#if defined(JSON_HEDLEY_GNUC_HAS_ATTRIBUTE)\n    #undef JSON_HEDLEY_GNUC_HAS_ATTRIBUTE\n#endif\n#if defined(__has_attribute)\n    #define JSON_HEDLEY_GNUC_HAS_ATTRIBUTE(attribute,major,minor,patch) JSON_HEDLEY_HAS_ATTRIBUTE(attribute)\n#else\n    #define JSON_HEDLEY_GNUC_HAS_ATTRIBUTE(attribute,major,minor,patch) JSON_HEDLEY_GNUC_VERSION_CHECK(major,minor,patch)\n#endif\n\n#if defined(JSON_HEDLEY_GCC_HAS_ATTRIBUTE)\n    #undef JSON_HEDLEY_GCC_HAS_ATTRIBUTE\n#endif\n#if defined(__has_attribute)\n    #define JSON_HEDLEY_GCC_HAS_ATTRIBUTE(attribute,major,minor,patch) JSON_HEDLEY_HAS_ATTRIBUTE(attribute)\n#else\n    #define JSON_HEDLEY_GCC_HAS_ATTRIBUTE(attribute,major,minor,patch) JSON_HEDLEY_GCC_VERSION_CHECK(major,minor,patch)\n#endif\n\n#if defined(JSON_HEDLEY_HAS_CPP_ATTRIBUTE)\n    #undef JSON_HEDLEY_HAS_CPP_ATTRIBUTE\n#endif\n#if \\\n    defined(__has_cpp_attribute) && \\\n    defined(__cplusplus) && \\\n    (!defined(JSON_HEDLEY_SUNPRO_VERSION) || JSON_HEDLEY_SUNPRO_VERSION_CHECK(5,15,0))\n    #define JSON_HEDLEY_HAS_CPP_ATTRIBUTE(attribute) __has_cpp_attribute(attribute)\n#else\n    #define JSON_HEDLEY_HAS_CPP_ATTRIBUTE(attribute) (0)\n#endif\n\n#if defined(JSON_HEDLEY_HAS_CPP_ATTRIBUTE_NS)\n    #undef JSON_HEDLEY_HAS_CPP_ATTRIBUTE_NS\n#endif\n#if !defined(__cplusplus) || !defined(__has_cpp_attribute)\n    #define JSON_HEDLEY_HAS_CPP_ATTRIBUTE_NS(ns,attribute) (0)\n#elif \\\n    !defined(JSON_HEDLEY_PGI_VERSION) && \\\n    !defined(JSON_HEDLEY_IAR_VERSION) && \\\n    (!defined(JSON_HEDLEY_SUNPRO_VERSION) || JSON_HEDLEY_SUNPRO_VERSION_CHECK(5,15,0)) && \\\n    (!defined(JSON_HEDLEY_MSVC_VERSION) || JSON_HEDLEY_MSVC_VERSION_CHECK(19,20,0))\n    #define JSON_HEDLEY_HAS_CPP_ATTRIBUTE_NS(ns,attribute) JSON_HEDLEY_HAS_CPP_ATTRIBUTE(ns::attribute)\n#else\n    #define JSON_HEDLEY_HAS_CPP_ATTRIBUTE_NS(ns,attribute) (0)\n#endif\n\n#if defined(JSON_HEDLEY_GNUC_HAS_CPP_ATTRIBUTE)\n    #undef JSON_HEDLEY_GNUC_HAS_CPP_ATTRIBUTE\n#endif\n#if defined(__has_cpp_attribute) && defined(__cplusplus)\n    #define JSON_HEDLEY_GNUC_HAS_CPP_ATTRIBUTE(attribute,major,minor,patch) __has_cpp_attribute(attribute)\n#else\n    #define JSON_HEDLEY_GNUC_HAS_CPP_ATTRIBUTE(attribute,major,minor,patch) JSON_HEDLEY_GNUC_VERSION_CHECK(major,minor,patch)\n#endif\n\n#if defined(JSON_HEDLEY_GCC_HAS_CPP_ATTRIBUTE)\n    #undef JSON_HEDLEY_GCC_HAS_CPP_ATTRIBUTE\n#endif\n#if defined(__has_cpp_attribute) && defined(__cplusplus)\n    #define JSON_HEDLEY_GCC_HAS_CPP_ATTRIBUTE(attribute,major,minor,patch) __has_cpp_attribute(attribute)\n#else\n    #define JSON_HEDLEY_GCC_HAS_CPP_ATTRIBUTE(attribute,major,minor,patch) JSON_HEDLEY_GCC_VERSION_CHECK(major,minor,patch)\n#endif\n\n#if defined(JSON_HEDLEY_HAS_BUILTIN)\n    #undef JSON_HEDLEY_HAS_BUILTIN\n#endif\n#if defined(__has_builtin)\n    #define JSON_HEDLEY_HAS_BUILTIN(builtin) __has_builtin(builtin)\n#else\n    #define JSON_HEDLEY_HAS_BUILTIN(builtin) (0)\n#endif\n\n#if defined(JSON_HEDLEY_GNUC_HAS_BUILTIN)\n    #undef JSON_HEDLEY_GNUC_HAS_BUILTIN\n#endif\n#if defined(__has_builtin)\n    #define JSON_HEDLEY_GNUC_HAS_BUILTIN(builtin,major,minor,patch) __has_builtin(builtin)\n#else\n    #define JSON_HEDLEY_GNUC_HAS_BUILTIN(builtin,major,minor,patch) JSON_HEDLEY_GNUC_VERSION_CHECK(major,minor,patch)\n#endif\n\n#if defined(JSON_HEDLEY_GCC_HAS_BUILTIN)\n    #undef JSON_HEDLEY_GCC_HAS_BUILTIN\n#endif\n#if defined(__has_builtin)\n    #define JSON_HEDLEY_GCC_HAS_BUILTIN(builtin,major,minor,patch) __has_builtin(builtin)\n#else\n    #define JSON_HEDLEY_GCC_HAS_BUILTIN(builtin,major,minor,patch) JSON_HEDLEY_GCC_VERSION_CHECK(major,minor,patch)\n#endif\n\n#if defined(JSON_HEDLEY_HAS_FEATURE)\n    #undef JSON_HEDLEY_HAS_FEATURE\n#endif\n#if defined(__has_feature)\n    #define JSON_HEDLEY_HAS_FEATURE(feature) __has_feature(feature)\n#else\n    #define JSON_HEDLEY_HAS_FEATURE(feature) (0)\n#endif\n\n#if defined(JSON_HEDLEY_GNUC_HAS_FEATURE)\n    #undef JSON_HEDLEY_GNUC_HAS_FEATURE\n#endif\n#if defined(__has_feature)\n    #define JSON_HEDLEY_GNUC_HAS_FEATURE(feature,major,minor,patch) __has_feature(feature)\n#else\n    #define JSON_HEDLEY_GNUC_HAS_FEATURE(feature,major,minor,patch) JSON_HEDLEY_GNUC_VERSION_CHECK(major,minor,patch)\n#endif\n\n#if defined(JSON_HEDLEY_GCC_HAS_FEATURE)\n    #undef JSON_HEDLEY_GCC_HAS_FEATURE\n#endif\n#if defined(__has_feature)\n    #define JSON_HEDLEY_GCC_HAS_FEATURE(feature,major,minor,patch) __has_feature(feature)\n#else\n    #define JSON_HEDLEY_GCC_HAS_FEATURE(feature,major,minor,patch) JSON_HEDLEY_GCC_VERSION_CHECK(major,minor,patch)\n#endif\n\n#if defined(JSON_HEDLEY_HAS_EXTENSION)\n    #undef JSON_HEDLEY_HAS_EXTENSION\n#endif\n#if defined(__has_extension)\n    #define JSON_HEDLEY_HAS_EXTENSION(extension) __has_extension(extension)\n#else\n    #define JSON_HEDLEY_HAS_EXTENSION(extension) (0)\n#endif\n\n#if defined(JSON_HEDLEY_GNUC_HAS_EXTENSION)\n    #undef JSON_HEDLEY_GNUC_HAS_EXTENSION\n#endif\n#if defined(__has_extension)\n    #define JSON_HEDLEY_GNUC_HAS_EXTENSION(extension,major,minor,patch) __has_extension(extension)\n#else\n    #define JSON_HEDLEY_GNUC_HAS_EXTENSION(extension,major,minor,patch) JSON_HEDLEY_GNUC_VERSION_CHECK(major,minor,patch)\n#endif\n\n#if defined(JSON_HEDLEY_GCC_HAS_EXTENSION)\n    #undef JSON_HEDLEY_GCC_HAS_EXTENSION\n#endif\n#if defined(__has_extension)\n    #define JSON_HEDLEY_GCC_HAS_EXTENSION(extension,major,minor,patch) __has_extension(extension)\n#else\n    #define JSON_HEDLEY_GCC_HAS_EXTENSION(extension,major,minor,patch) JSON_HEDLEY_GCC_VERSION_CHECK(major,minor,patch)\n#endif\n\n#if defined(JSON_HEDLEY_HAS_DECLSPEC_ATTRIBUTE)\n    #undef JSON_HEDLEY_HAS_DECLSPEC_ATTRIBUTE\n#endif\n#if defined(__has_declspec_attribute)\n    #define JSON_HEDLEY_HAS_DECLSPEC_ATTRIBUTE(attribute) __has_declspec_attribute(attribute)\n#else\n    #define JSON_HEDLEY_HAS_DECLSPEC_ATTRIBUTE(attribute) (0)\n#endif\n\n#if defined(JSON_HEDLEY_GNUC_HAS_DECLSPEC_ATTRIBUTE)\n    #undef JSON_HEDLEY_GNUC_HAS_DECLSPEC_ATTRIBUTE\n#endif\n#if defined(__has_declspec_attribute)\n    #define JSON_HEDLEY_GNUC_HAS_DECLSPEC_ATTRIBUTE(attribute,major,minor,patch) __has_declspec_attribute(attribute)\n#else\n    #define JSON_HEDLEY_GNUC_HAS_DECLSPEC_ATTRIBUTE(attribute,major,minor,patch) JSON_HEDLEY_GNUC_VERSION_CHECK(major,minor,patch)\n#endif\n\n#if defined(JSON_HEDLEY_GCC_HAS_DECLSPEC_ATTRIBUTE)\n    #undef JSON_HEDLEY_GCC_HAS_DECLSPEC_ATTRIBUTE\n#endif\n#if defined(__has_declspec_attribute)\n    #define JSON_HEDLEY_GCC_HAS_DECLSPEC_ATTRIBUTE(attribute,major,minor,patch) __has_declspec_attribute(attribute)\n#else\n    #define JSON_HEDLEY_GCC_HAS_DECLSPEC_ATTRIBUTE(attribute,major,minor,patch) JSON_HEDLEY_GCC_VERSION_CHECK(major,minor,patch)\n#endif\n\n#if defined(JSON_HEDLEY_HAS_WARNING)\n    #undef JSON_HEDLEY_HAS_WARNING\n#endif\n#if defined(__has_warning)\n    #define JSON_HEDLEY_HAS_WARNING(warning) __has_warning(warning)\n#else\n    #define JSON_HEDLEY_HAS_WARNING(warning) (0)\n#endif\n\n#if defined(JSON_HEDLEY_GNUC_HAS_WARNING)\n    #undef JSON_HEDLEY_GNUC_HAS_WARNING\n#endif\n#if defined(__has_warning)\n    #define JSON_HEDLEY_GNUC_HAS_WARNING(warning,major,minor,patch) __has_warning(warning)\n#else\n    #define JSON_HEDLEY_GNUC_HAS_WARNING(warning,major,minor,patch) JSON_HEDLEY_GNUC_VERSION_CHECK(major,minor,patch)\n#endif\n\n#if defined(JSON_HEDLEY_GCC_HAS_WARNING)\n    #undef JSON_HEDLEY_GCC_HAS_WARNING\n#endif\n#if defined(__has_warning)\n    #define JSON_HEDLEY_GCC_HAS_WARNING(warning,major,minor,patch) __has_warning(warning)\n#else\n    #define JSON_HEDLEY_GCC_HAS_WARNING(warning,major,minor,patch) JSON_HEDLEY_GCC_VERSION_CHECK(major,minor,patch)\n#endif\n\n#if \\\n    (defined(__STDC_VERSION__) && (__STDC_VERSION__ >= 199901L)) || \\\n    defined(__clang__) || \\\n    JSON_HEDLEY_GCC_VERSION_CHECK(3,0,0) || \\\n    JSON_HEDLEY_INTEL_VERSION_CHECK(13,0,0) || \\\n    JSON_HEDLEY_IAR_VERSION_CHECK(8,0,0) || \\\n    JSON_HEDLEY_PGI_VERSION_CHECK(18,4,0) || \\\n    JSON_HEDLEY_ARM_VERSION_CHECK(4,1,0) || \\\n    JSON_HEDLEY_TI_VERSION_CHECK(15,12,0) || \\\n    JSON_HEDLEY_TI_ARMCL_VERSION_CHECK(4,7,0) || \\\n    JSON_HEDLEY_TI_CL430_VERSION_CHECK(2,0,1) || \\\n    JSON_HEDLEY_TI_CL2000_VERSION_CHECK(6,1,0) || \\\n    JSON_HEDLEY_TI_CL6X_VERSION_CHECK(7,0,0) || \\\n    JSON_HEDLEY_TI_CL7X_VERSION_CHECK(1,2,0) || \\\n    JSON_HEDLEY_TI_CLPRU_VERSION_CHECK(2,1,0) || \\\n    JSON_HEDLEY_CRAY_VERSION_CHECK(5,0,0) || \\\n    JSON_HEDLEY_TINYC_VERSION_CHECK(0,9,17) || \\\n    JSON_HEDLEY_SUNPRO_VERSION_CHECK(8,0,0) || \\\n    (JSON_HEDLEY_IBM_VERSION_CHECK(10,1,0) && defined(__C99_PRAGMA_OPERATOR))\n    #define JSON_HEDLEY_PRAGMA(value) _Pragma(#value)\n#elif JSON_HEDLEY_MSVC_VERSION_CHECK(15,0,0)\n    #define JSON_HEDLEY_PRAGMA(value) __pragma(value)\n#else\n    #define JSON_HEDLEY_PRAGMA(value)\n#endif\n\n#if defined(JSON_HEDLEY_DIAGNOSTIC_PUSH)\n    #undef JSON_HEDLEY_DIAGNOSTIC_PUSH\n#endif\n#if defined(JSON_HEDLEY_DIAGNOSTIC_POP)\n    #undef JSON_HEDLEY_DIAGNOSTIC_POP\n#endif\n#if defined(__clang__)\n    #define JSON_HEDLEY_DIAGNOSTIC_PUSH _Pragma(\"clang diagnostic push\")\n    #define JSON_HEDLEY_DIAGNOSTIC_POP _Pragma(\"clang diagnostic pop\")\n#elif JSON_HEDLEY_INTEL_VERSION_CHECK(13,0,0)\n    #define JSON_HEDLEY_DIAGNOSTIC_PUSH _Pragma(\"warning(push)\")\n    #define JSON_HEDLEY_DIAGNOSTIC_POP _Pragma(\"warning(pop)\")\n#elif JSON_HEDLEY_GCC_VERSION_CHECK(4,6,0)\n    #define JSON_HEDLEY_DIAGNOSTIC_PUSH _Pragma(\"GCC diagnostic push\")\n    #define JSON_HEDLEY_DIAGNOSTIC_POP _Pragma(\"GCC diagnostic pop\")\n#elif \\\n    JSON_HEDLEY_MSVC_VERSION_CHECK(15,0,0) || \\\n    JSON_HEDLEY_INTEL_CL_VERSION_CHECK(2021,1,0)\n    #define JSON_HEDLEY_DIAGNOSTIC_PUSH __pragma(warning(push))\n    #define JSON_HEDLEY_DIAGNOSTIC_POP __pragma(warning(pop))\n#elif JSON_HEDLEY_ARM_VERSION_CHECK(5,6,0)\n    #define JSON_HEDLEY_DIAGNOSTIC_PUSH _Pragma(\"push\")\n    #define JSON_HEDLEY_DIAGNOSTIC_POP _Pragma(\"pop\")\n#elif \\\n    JSON_HEDLEY_TI_VERSION_CHECK(15,12,0) || \\\n    JSON_HEDLEY_TI_ARMCL_VERSION_CHECK(5,2,0) || \\\n    JSON_HEDLEY_TI_CL430_VERSION_CHECK(4,4,0) || \\\n    JSON_HEDLEY_TI_CL6X_VERSION_CHECK(8,1,0) || \\\n    JSON_HEDLEY_TI_CL7X_VERSION_CHECK(1,2,0) || \\\n    JSON_HEDLEY_TI_CLPRU_VERSION_CHECK(2,1,0)\n    #define JSON_HEDLEY_DIAGNOSTIC_PUSH _Pragma(\"diag_push\")\n    #define JSON_HEDLEY_DIAGNOSTIC_POP _Pragma(\"diag_pop\")\n#elif JSON_HEDLEY_PELLES_VERSION_CHECK(2,90,0)\n    #define JSON_HEDLEY_DIAGNOSTIC_PUSH _Pragma(\"warning(push)\")\n    #define JSON_HEDLEY_DIAGNOSTIC_POP _Pragma(\"warning(pop)\")\n#else\n    #define JSON_HEDLEY_DIAGNOSTIC_PUSH\n    #define JSON_HEDLEY_DIAGNOSTIC_POP\n#endif\n\n/* JSON_HEDLEY_DIAGNOSTIC_DISABLE_CPP98_COMPAT_WRAP_ is for\n   HEDLEY INTERNAL USE ONLY.  API subject to change without notice. */\n#if defined(JSON_HEDLEY_DIAGNOSTIC_DISABLE_CPP98_COMPAT_WRAP_)\n    #undef JSON_HEDLEY_DIAGNOSTIC_DISABLE_CPP98_COMPAT_WRAP_\n#endif\n#if defined(__cplusplus)\n#  if JSON_HEDLEY_HAS_WARNING(\"-Wc++98-compat\")\n#    if JSON_HEDLEY_HAS_WARNING(\"-Wc++17-extensions\")\n#      if JSON_HEDLEY_HAS_WARNING(\"-Wc++1z-extensions\")\n#        define JSON_HEDLEY_DIAGNOSTIC_DISABLE_CPP98_COMPAT_WRAP_(xpr) \\\n    JSON_HEDLEY_DIAGNOSTIC_PUSH \\\n    _Pragma(\"clang diagnostic ignored \\\"-Wc++98-compat\\\"\") \\\n    _Pragma(\"clang diagnostic ignored \\\"-Wc++17-extensions\\\"\") \\\n    _Pragma(\"clang diagnostic ignored \\\"-Wc++1z-extensions\\\"\") \\\n    xpr \\\n    JSON_HEDLEY_DIAGNOSTIC_POP\n#      else\n#        define JSON_HEDLEY_DIAGNOSTIC_DISABLE_CPP98_COMPAT_WRAP_(xpr) \\\n    JSON_HEDLEY_DIAGNOSTIC_PUSH \\\n    _Pragma(\"clang diagnostic ignored \\\"-Wc++98-compat\\\"\") \\\n    _Pragma(\"clang diagnostic ignored \\\"-Wc++17-extensions\\\"\") \\\n    xpr \\\n    JSON_HEDLEY_DIAGNOSTIC_POP\n#      endif\n#    else\n#      define JSON_HEDLEY_DIAGNOSTIC_DISABLE_CPP98_COMPAT_WRAP_(xpr) \\\n    JSON_HEDLEY_DIAGNOSTIC_PUSH \\\n    _Pragma(\"clang diagnostic ignored \\\"-Wc++98-compat\\\"\") \\\n    xpr \\\n    JSON_HEDLEY_DIAGNOSTIC_POP\n#    endif\n#  endif\n#endif\n#if !defined(JSON_HEDLEY_DIAGNOSTIC_DISABLE_CPP98_COMPAT_WRAP_)\n    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_CPP98_COMPAT_WRAP_(x) x\n#endif\n\n#if defined(JSON_HEDLEY_CONST_CAST)\n    #undef JSON_HEDLEY_CONST_CAST\n#endif\n#if defined(__cplusplus)\n#  define JSON_HEDLEY_CONST_CAST(T, expr) (const_cast<T>(expr))\n#elif \\\n  JSON_HEDLEY_HAS_WARNING(\"-Wcast-qual\") || \\\n  JSON_HEDLEY_GCC_VERSION_CHECK(4,6,0) || \\\n  JSON_HEDLEY_INTEL_VERSION_CHECK(13,0,0)\n#  define JSON_HEDLEY_CONST_CAST(T, expr) (__extension__ ({ \\\n        JSON_HEDLEY_DIAGNOSTIC_PUSH \\\n        JSON_HEDLEY_DIAGNOSTIC_DISABLE_CAST_QUAL \\\n        ((T) (expr)); \\\n        JSON_HEDLEY_DIAGNOSTIC_POP \\\n    }))\n#else\n#  define JSON_HEDLEY_CONST_CAST(T, expr) ((T) (expr))\n#endif\n\n#if defined(JSON_HEDLEY_REINTERPRET_CAST)\n    #undef JSON_HEDLEY_REINTERPRET_CAST\n#endif\n#if defined(__cplusplus)\n    #define JSON_HEDLEY_REINTERPRET_CAST(T, expr) (reinterpret_cast<T>(expr))\n#else\n    #define JSON_HEDLEY_REINTERPRET_CAST(T, expr) ((T) (expr))\n#endif\n\n#if defined(JSON_HEDLEY_STATIC_CAST)\n    #undef JSON_HEDLEY_STATIC_CAST\n#endif\n#if defined(__cplusplus)\n    #define JSON_HEDLEY_STATIC_CAST(T, expr) (static_cast<T>(expr))\n#else\n    #define JSON_HEDLEY_STATIC_CAST(T, expr) ((T) (expr))\n#endif\n\n#if defined(JSON_HEDLEY_CPP_CAST)\n    #undef JSON_HEDLEY_CPP_CAST\n#endif\n#if defined(__cplusplus)\n#  if JSON_HEDLEY_HAS_WARNING(\"-Wold-style-cast\")\n#    define JSON_HEDLEY_CPP_CAST(T, expr) \\\n    JSON_HEDLEY_DIAGNOSTIC_PUSH \\\n    _Pragma(\"clang diagnostic ignored \\\"-Wold-style-cast\\\"\") \\\n    ((T) (expr)) \\\n    JSON_HEDLEY_DIAGNOSTIC_POP\n#  elif JSON_HEDLEY_IAR_VERSION_CHECK(8,3,0)\n#    define JSON_HEDLEY_CPP_CAST(T, expr) \\\n    JSON_HEDLEY_DIAGNOSTIC_PUSH \\\n    _Pragma(\"diag_suppress=Pe137\") \\\n    JSON_HEDLEY_DIAGNOSTIC_POP\n#  else\n#    define JSON_HEDLEY_CPP_CAST(T, expr) ((T) (expr))\n#  endif\n#else\n#  define JSON_HEDLEY_CPP_CAST(T, expr) (expr)\n#endif\n\n#if defined(JSON_HEDLEY_DIAGNOSTIC_DISABLE_DEPRECATED)\n    #undef JSON_HEDLEY_DIAGNOSTIC_DISABLE_DEPRECATED\n#endif\n#if JSON_HEDLEY_HAS_WARNING(\"-Wdeprecated-declarations\")\n    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_DEPRECATED _Pragma(\"clang diagnostic ignored \\\"-Wdeprecated-declarations\\\"\")\n#elif JSON_HEDLEY_INTEL_VERSION_CHECK(13,0,0)\n    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_DEPRECATED _Pragma(\"warning(disable:1478 1786)\")\n#elif JSON_HEDLEY_INTEL_CL_VERSION_CHECK(2021,1,0)\n    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_DEPRECATED __pragma(warning(disable:1478 1786))\n#elif JSON_HEDLEY_PGI_VERSION_CHECK(20,7,0)\n    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_DEPRECATED _Pragma(\"diag_suppress 1215,1216,1444,1445\")\n#elif JSON_HEDLEY_PGI_VERSION_CHECK(17,10,0)\n    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_DEPRECATED _Pragma(\"diag_suppress 1215,1444\")\n#elif JSON_HEDLEY_GCC_VERSION_CHECK(4,3,0)\n    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_DEPRECATED _Pragma(\"GCC diagnostic ignored \\\"-Wdeprecated-declarations\\\"\")\n#elif JSON_HEDLEY_MSVC_VERSION_CHECK(15,0,0)\n    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_DEPRECATED __pragma(warning(disable:4996))\n#elif JSON_HEDLEY_MCST_LCC_VERSION_CHECK(1,25,10)\n    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_DEPRECATED _Pragma(\"diag_suppress 1215,1444\")\n#elif \\\n    JSON_HEDLEY_TI_VERSION_CHECK(15,12,0) || \\\n    (JSON_HEDLEY_TI_ARMCL_VERSION_CHECK(4,8,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \\\n    JSON_HEDLEY_TI_ARMCL_VERSION_CHECK(5,2,0) || \\\n    (JSON_HEDLEY_TI_CL2000_VERSION_CHECK(6,0,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \\\n    JSON_HEDLEY_TI_CL2000_VERSION_CHECK(6,4,0) || \\\n    (JSON_HEDLEY_TI_CL430_VERSION_CHECK(4,0,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \\\n    JSON_HEDLEY_TI_CL430_VERSION_CHECK(4,3,0) || \\\n    (JSON_HEDLEY_TI_CL6X_VERSION_CHECK(7,2,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \\\n    JSON_HEDLEY_TI_CL6X_VERSION_CHECK(7,5,0) || \\\n    JSON_HEDLEY_TI_CL7X_VERSION_CHECK(1,2,0) || \\\n    JSON_HEDLEY_TI_CLPRU_VERSION_CHECK(2,1,0)\n    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_DEPRECATED _Pragma(\"diag_suppress 1291,1718\")\n#elif JSON_HEDLEY_SUNPRO_VERSION_CHECK(5,13,0) && !defined(__cplusplus)\n    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_DEPRECATED _Pragma(\"error_messages(off,E_DEPRECATED_ATT,E_DEPRECATED_ATT_MESS)\")\n#elif JSON_HEDLEY_SUNPRO_VERSION_CHECK(5,13,0) && defined(__cplusplus)\n    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_DEPRECATED _Pragma(\"error_messages(off,symdeprecated,symdeprecated2)\")\n#elif JSON_HEDLEY_IAR_VERSION_CHECK(8,0,0)\n    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_DEPRECATED _Pragma(\"diag_suppress=Pe1444,Pe1215\")\n#elif JSON_HEDLEY_PELLES_VERSION_CHECK(2,90,0)\n    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_DEPRECATED _Pragma(\"warn(disable:2241)\")\n#else\n    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_DEPRECATED\n#endif\n\n#if defined(JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNKNOWN_PRAGMAS)\n    #undef JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNKNOWN_PRAGMAS\n#endif\n#if JSON_HEDLEY_HAS_WARNING(\"-Wunknown-pragmas\")\n    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNKNOWN_PRAGMAS _Pragma(\"clang diagnostic ignored \\\"-Wunknown-pragmas\\\"\")\n#elif JSON_HEDLEY_INTEL_VERSION_CHECK(13,0,0)\n    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNKNOWN_PRAGMAS _Pragma(\"warning(disable:161)\")\n#elif JSON_HEDLEY_INTEL_CL_VERSION_CHECK(2021,1,0)\n    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNKNOWN_PRAGMAS __pragma(warning(disable:161))\n#elif JSON_HEDLEY_PGI_VERSION_CHECK(17,10,0)\n    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNKNOWN_PRAGMAS _Pragma(\"diag_suppress 1675\")\n#elif JSON_HEDLEY_GCC_VERSION_CHECK(4,3,0)\n    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNKNOWN_PRAGMAS _Pragma(\"GCC diagnostic ignored \\\"-Wunknown-pragmas\\\"\")\n#elif JSON_HEDLEY_MSVC_VERSION_CHECK(15,0,0)\n    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNKNOWN_PRAGMAS __pragma(warning(disable:4068))\n#elif \\\n    JSON_HEDLEY_TI_VERSION_CHECK(16,9,0) || \\\n    JSON_HEDLEY_TI_CL6X_VERSION_CHECK(8,0,0) || \\\n    JSON_HEDLEY_TI_CL7X_VERSION_CHECK(1,2,0) || \\\n    JSON_HEDLEY_TI_CLPRU_VERSION_CHECK(2,3,0)\n    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNKNOWN_PRAGMAS _Pragma(\"diag_suppress 163\")\n#elif JSON_HEDLEY_TI_CL6X_VERSION_CHECK(8,0,0)\n    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNKNOWN_PRAGMAS _Pragma(\"diag_suppress 163\")\n#elif JSON_HEDLEY_IAR_VERSION_CHECK(8,0,0)\n    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNKNOWN_PRAGMAS _Pragma(\"diag_suppress=Pe161\")\n#elif JSON_HEDLEY_MCST_LCC_VERSION_CHECK(1,25,10)\n    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNKNOWN_PRAGMAS _Pragma(\"diag_suppress 161\")\n#else\n    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNKNOWN_PRAGMAS\n#endif\n\n#if defined(JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNKNOWN_CPP_ATTRIBUTES)\n    #undef JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNKNOWN_CPP_ATTRIBUTES\n#endif\n#if JSON_HEDLEY_HAS_WARNING(\"-Wunknown-attributes\")\n    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNKNOWN_CPP_ATTRIBUTES _Pragma(\"clang diagnostic ignored \\\"-Wunknown-attributes\\\"\")\n#elif JSON_HEDLEY_GCC_VERSION_CHECK(4,6,0)\n    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNKNOWN_CPP_ATTRIBUTES _Pragma(\"GCC diagnostic ignored \\\"-Wdeprecated-declarations\\\"\")\n#elif JSON_HEDLEY_INTEL_VERSION_CHECK(17,0,0)\n    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNKNOWN_CPP_ATTRIBUTES _Pragma(\"warning(disable:1292)\")\n#elif JSON_HEDLEY_INTEL_CL_VERSION_CHECK(2021,1,0)\n    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNKNOWN_CPP_ATTRIBUTES __pragma(warning(disable:1292))\n#elif JSON_HEDLEY_MSVC_VERSION_CHECK(19,0,0)\n    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNKNOWN_CPP_ATTRIBUTES __pragma(warning(disable:5030))\n#elif JSON_HEDLEY_PGI_VERSION_CHECK(20,7,0)\n    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNKNOWN_CPP_ATTRIBUTES _Pragma(\"diag_suppress 1097,1098\")\n#elif JSON_HEDLEY_PGI_VERSION_CHECK(17,10,0)\n    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNKNOWN_CPP_ATTRIBUTES _Pragma(\"diag_suppress 1097\")\n#elif JSON_HEDLEY_SUNPRO_VERSION_CHECK(5,14,0) && defined(__cplusplus)\n    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNKNOWN_CPP_ATTRIBUTES _Pragma(\"error_messages(off,attrskipunsup)\")\n#elif \\\n    JSON_HEDLEY_TI_VERSION_CHECK(18,1,0) || \\\n    JSON_HEDLEY_TI_CL6X_VERSION_CHECK(8,3,0) || \\\n    JSON_HEDLEY_TI_CL7X_VERSION_CHECK(1,2,0)\n    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNKNOWN_CPP_ATTRIBUTES _Pragma(\"diag_suppress 1173\")\n#elif JSON_HEDLEY_IAR_VERSION_CHECK(8,0,0)\n    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNKNOWN_CPP_ATTRIBUTES _Pragma(\"diag_suppress=Pe1097\")\n#elif JSON_HEDLEY_MCST_LCC_VERSION_CHECK(1,25,10)\n    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNKNOWN_CPP_ATTRIBUTES _Pragma(\"diag_suppress 1097\")\n#else\n    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNKNOWN_CPP_ATTRIBUTES\n#endif\n\n#if defined(JSON_HEDLEY_DIAGNOSTIC_DISABLE_CAST_QUAL)\n    #undef JSON_HEDLEY_DIAGNOSTIC_DISABLE_CAST_QUAL\n#endif\n#if JSON_HEDLEY_HAS_WARNING(\"-Wcast-qual\")\n    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_CAST_QUAL _Pragma(\"clang diagnostic ignored \\\"-Wcast-qual\\\"\")\n#elif JSON_HEDLEY_INTEL_VERSION_CHECK(13,0,0)\n    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_CAST_QUAL _Pragma(\"warning(disable:2203 2331)\")\n#elif JSON_HEDLEY_GCC_VERSION_CHECK(3,0,0)\n    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_CAST_QUAL _Pragma(\"GCC diagnostic ignored \\\"-Wcast-qual\\\"\")\n#else\n    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_CAST_QUAL\n#endif\n\n#if defined(JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNUSED_FUNCTION)\n    #undef JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNUSED_FUNCTION\n#endif\n#if JSON_HEDLEY_HAS_WARNING(\"-Wunused-function\")\n    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNUSED_FUNCTION _Pragma(\"clang diagnostic ignored \\\"-Wunused-function\\\"\")\n#elif JSON_HEDLEY_GCC_VERSION_CHECK(3,4,0)\n    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNUSED_FUNCTION _Pragma(\"GCC diagnostic ignored \\\"-Wunused-function\\\"\")\n#elif JSON_HEDLEY_MSVC_VERSION_CHECK(1,0,0)\n    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNUSED_FUNCTION __pragma(warning(disable:4505))\n#elif JSON_HEDLEY_MCST_LCC_VERSION_CHECK(1,25,10)\n    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNUSED_FUNCTION _Pragma(\"diag_suppress 3142\")\n#else\n    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNUSED_FUNCTION\n#endif\n\n#if defined(JSON_HEDLEY_DEPRECATED)\n    #undef JSON_HEDLEY_DEPRECATED\n#endif\n#if defined(JSON_HEDLEY_DEPRECATED_FOR)\n    #undef JSON_HEDLEY_DEPRECATED_FOR\n#endif\n#if \\\n    JSON_HEDLEY_MSVC_VERSION_CHECK(14,0,0) || \\\n    JSON_HEDLEY_INTEL_CL_VERSION_CHECK(2021,1,0)\n    #define JSON_HEDLEY_DEPRECATED(since) __declspec(deprecated(\"Since \" # since))\n    #define JSON_HEDLEY_DEPRECATED_FOR(since, replacement) __declspec(deprecated(\"Since \" #since \"; use \" #replacement))\n#elif \\\n    (JSON_HEDLEY_HAS_EXTENSION(attribute_deprecated_with_message) && !defined(JSON_HEDLEY_IAR_VERSION)) || \\\n    JSON_HEDLEY_GCC_VERSION_CHECK(4,5,0) || \\\n    JSON_HEDLEY_INTEL_VERSION_CHECK(13,0,0) || \\\n    JSON_HEDLEY_ARM_VERSION_CHECK(5,6,0) || \\\n    JSON_HEDLEY_SUNPRO_VERSION_CHECK(5,13,0) || \\\n    JSON_HEDLEY_PGI_VERSION_CHECK(17,10,0) || \\\n    JSON_HEDLEY_TI_VERSION_CHECK(18,1,0) || \\\n    JSON_HEDLEY_TI_ARMCL_VERSION_CHECK(18,1,0) || \\\n    JSON_HEDLEY_TI_CL6X_VERSION_CHECK(8,3,0) || \\\n    JSON_HEDLEY_TI_CL7X_VERSION_CHECK(1,2,0) || \\\n    JSON_HEDLEY_TI_CLPRU_VERSION_CHECK(2,3,0) || \\\n    JSON_HEDLEY_MCST_LCC_VERSION_CHECK(1,25,10)\n    #define JSON_HEDLEY_DEPRECATED(since) __attribute__((__deprecated__(\"Since \" #since)))\n    #define JSON_HEDLEY_DEPRECATED_FOR(since, replacement) __attribute__((__deprecated__(\"Since \" #since \"; use \" #replacement)))\n#elif defined(__cplusplus) && (__cplusplus >= 201402L)\n    #define JSON_HEDLEY_DEPRECATED(since) JSON_HEDLEY_DIAGNOSTIC_DISABLE_CPP98_COMPAT_WRAP_([[deprecated(\"Since \" #since)]])\n    #define JSON_HEDLEY_DEPRECATED_FOR(since, replacement) JSON_HEDLEY_DIAGNOSTIC_DISABLE_CPP98_COMPAT_WRAP_([[deprecated(\"Since \" #since \"; use \" #replacement)]])\n#elif \\\n    JSON_HEDLEY_HAS_ATTRIBUTE(deprecated) || \\\n    JSON_HEDLEY_GCC_VERSION_CHECK(3,1,0) || \\\n    JSON_HEDLEY_ARM_VERSION_CHECK(4,1,0) || \\\n    JSON_HEDLEY_TI_VERSION_CHECK(15,12,0) || \\\n    (JSON_HEDLEY_TI_ARMCL_VERSION_CHECK(4,8,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \\\n    JSON_HEDLEY_TI_ARMCL_VERSION_CHECK(5,2,0) || \\\n    (JSON_HEDLEY_TI_CL2000_VERSION_CHECK(6,0,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \\\n    JSON_HEDLEY_TI_CL2000_VERSION_CHECK(6,4,0) || \\\n    (JSON_HEDLEY_TI_CL430_VERSION_CHECK(4,0,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \\\n    JSON_HEDLEY_TI_CL430_VERSION_CHECK(4,3,0) || \\\n    (JSON_HEDLEY_TI_CL6X_VERSION_CHECK(7,2,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \\\n    JSON_HEDLEY_TI_CL6X_VERSION_CHECK(7,5,0) || \\\n    JSON_HEDLEY_TI_CL7X_VERSION_CHECK(1,2,0) || \\\n    JSON_HEDLEY_TI_CLPRU_VERSION_CHECK(2,1,0) || \\\n    JSON_HEDLEY_MCST_LCC_VERSION_CHECK(1,25,10) || \\\n    JSON_HEDLEY_IAR_VERSION_CHECK(8,10,0)\n    #define JSON_HEDLEY_DEPRECATED(since) __attribute__((__deprecated__))\n    #define JSON_HEDLEY_DEPRECATED_FOR(since, replacement) __attribute__((__deprecated__))\n#elif \\\n    JSON_HEDLEY_MSVC_VERSION_CHECK(13,10,0) || \\\n    JSON_HEDLEY_PELLES_VERSION_CHECK(6,50,0) || \\\n    JSON_HEDLEY_INTEL_CL_VERSION_CHECK(2021,1,0)\n    #define JSON_HEDLEY_DEPRECATED(since) __declspec(deprecated)\n    #define JSON_HEDLEY_DEPRECATED_FOR(since, replacement) __declspec(deprecated)\n#elif JSON_HEDLEY_IAR_VERSION_CHECK(8,0,0)\n    #define JSON_HEDLEY_DEPRECATED(since) _Pragma(\"deprecated\")\n    #define JSON_HEDLEY_DEPRECATED_FOR(since, replacement) _Pragma(\"deprecated\")\n#else\n    #define JSON_HEDLEY_DEPRECATED(since)\n    #define JSON_HEDLEY_DEPRECATED_FOR(since, replacement)\n#endif\n\n#if defined(JSON_HEDLEY_UNAVAILABLE)\n    #undef JSON_HEDLEY_UNAVAILABLE\n#endif\n#if \\\n    JSON_HEDLEY_HAS_ATTRIBUTE(warning) || \\\n    JSON_HEDLEY_GCC_VERSION_CHECK(4,3,0) || \\\n    JSON_HEDLEY_INTEL_VERSION_CHECK(13,0,0) || \\\n    JSON_HEDLEY_MCST_LCC_VERSION_CHECK(1,25,10)\n    #define JSON_HEDLEY_UNAVAILABLE(available_since) __attribute__((__warning__(\"Not available until \" #available_since)))\n#else\n    #define JSON_HEDLEY_UNAVAILABLE(available_since)\n#endif\n\n#if defined(JSON_HEDLEY_WARN_UNUSED_RESULT)\n    #undef JSON_HEDLEY_WARN_UNUSED_RESULT\n#endif\n#if defined(JSON_HEDLEY_WARN_UNUSED_RESULT_MSG)\n    #undef JSON_HEDLEY_WARN_UNUSED_RESULT_MSG\n#endif\n#if \\\n    JSON_HEDLEY_HAS_ATTRIBUTE(warn_unused_result) || \\\n    JSON_HEDLEY_GCC_VERSION_CHECK(3,4,0) || \\\n    JSON_HEDLEY_INTEL_VERSION_CHECK(13,0,0) || \\\n    JSON_HEDLEY_TI_VERSION_CHECK(15,12,0) || \\\n    (JSON_HEDLEY_TI_ARMCL_VERSION_CHECK(4,8,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \\\n    JSON_HEDLEY_TI_ARMCL_VERSION_CHECK(5,2,0) || \\\n    (JSON_HEDLEY_TI_CL2000_VERSION_CHECK(6,0,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \\\n    JSON_HEDLEY_TI_CL2000_VERSION_CHECK(6,4,0) || \\\n    (JSON_HEDLEY_TI_CL430_VERSION_CHECK(4,0,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \\\n    JSON_HEDLEY_TI_CL430_VERSION_CHECK(4,3,0) || \\\n    (JSON_HEDLEY_TI_CL6X_VERSION_CHECK(7,2,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \\\n    JSON_HEDLEY_TI_CL6X_VERSION_CHECK(7,5,0) || \\\n    JSON_HEDLEY_TI_CL7X_VERSION_CHECK(1,2,0) || \\\n    JSON_HEDLEY_TI_CLPRU_VERSION_CHECK(2,1,0) || \\\n    (JSON_HEDLEY_SUNPRO_VERSION_CHECK(5,15,0) && defined(__cplusplus)) || \\\n    JSON_HEDLEY_PGI_VERSION_CHECK(17,10,0) || \\\n    JSON_HEDLEY_MCST_LCC_VERSION_CHECK(1,25,10)\n    #define JSON_HEDLEY_WARN_UNUSED_RESULT __attribute__((__warn_unused_result__))\n    #define JSON_HEDLEY_WARN_UNUSED_RESULT_MSG(msg) __attribute__((__warn_unused_result__))\n#elif (JSON_HEDLEY_HAS_CPP_ATTRIBUTE(nodiscard) >= 201907L)\n    #define JSON_HEDLEY_WARN_UNUSED_RESULT JSON_HEDLEY_DIAGNOSTIC_DISABLE_CPP98_COMPAT_WRAP_([[nodiscard]])\n    #define JSON_HEDLEY_WARN_UNUSED_RESULT_MSG(msg) JSON_HEDLEY_DIAGNOSTIC_DISABLE_CPP98_COMPAT_WRAP_([[nodiscard(msg)]])\n#elif JSON_HEDLEY_HAS_CPP_ATTRIBUTE(nodiscard)\n    #define JSON_HEDLEY_WARN_UNUSED_RESULT JSON_HEDLEY_DIAGNOSTIC_DISABLE_CPP98_COMPAT_WRAP_([[nodiscard]])\n    #define JSON_HEDLEY_WARN_UNUSED_RESULT_MSG(msg) JSON_HEDLEY_DIAGNOSTIC_DISABLE_CPP98_COMPAT_WRAP_([[nodiscard]])\n#elif defined(_Check_return_) /* SAL */\n    #define JSON_HEDLEY_WARN_UNUSED_RESULT _Check_return_\n    #define JSON_HEDLEY_WARN_UNUSED_RESULT_MSG(msg) _Check_return_\n#else\n    #define JSON_HEDLEY_WARN_UNUSED_RESULT\n    #define JSON_HEDLEY_WARN_UNUSED_RESULT_MSG(msg)\n#endif\n\n#if defined(JSON_HEDLEY_SENTINEL)\n    #undef JSON_HEDLEY_SENTINEL\n#endif\n#if \\\n    JSON_HEDLEY_HAS_ATTRIBUTE(sentinel) || \\\n    JSON_HEDLEY_GCC_VERSION_CHECK(4,0,0) || \\\n    JSON_HEDLEY_INTEL_VERSION_CHECK(13,0,0) || \\\n    JSON_HEDLEY_ARM_VERSION_CHECK(5,4,0) || \\\n    JSON_HEDLEY_MCST_LCC_VERSION_CHECK(1,25,10)\n    #define JSON_HEDLEY_SENTINEL(position) __attribute__((__sentinel__(position)))\n#else\n    #define JSON_HEDLEY_SENTINEL(position)\n#endif\n\n#if defined(JSON_HEDLEY_NO_RETURN)\n    #undef JSON_HEDLEY_NO_RETURN\n#endif\n#if JSON_HEDLEY_IAR_VERSION_CHECK(8,0,0)\n    #define JSON_HEDLEY_NO_RETURN __noreturn\n#elif \\\n    JSON_HEDLEY_INTEL_VERSION_CHECK(13,0,0) || \\\n    JSON_HEDLEY_MCST_LCC_VERSION_CHECK(1,25,10)\n    #define JSON_HEDLEY_NO_RETURN __attribute__((__noreturn__))\n#elif defined(__STDC_VERSION__) && __STDC_VERSION__ >= 201112L\n    #define JSON_HEDLEY_NO_RETURN _Noreturn\n#elif defined(__cplusplus) && (__cplusplus >= 201103L)\n    #define JSON_HEDLEY_NO_RETURN JSON_HEDLEY_DIAGNOSTIC_DISABLE_CPP98_COMPAT_WRAP_([[noreturn]])\n#elif \\\n    JSON_HEDLEY_HAS_ATTRIBUTE(noreturn) || \\\n    JSON_HEDLEY_GCC_VERSION_CHECK(3,2,0) || \\\n    JSON_HEDLEY_SUNPRO_VERSION_CHECK(5,11,0) || \\\n    JSON_HEDLEY_ARM_VERSION_CHECK(4,1,0) || \\\n    JSON_HEDLEY_IBM_VERSION_CHECK(10,1,0) || \\\n    JSON_HEDLEY_TI_VERSION_CHECK(15,12,0) || \\\n    (JSON_HEDLEY_TI_ARMCL_VERSION_CHECK(4,8,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \\\n    JSON_HEDLEY_TI_ARMCL_VERSION_CHECK(5,2,0) || \\\n    (JSON_HEDLEY_TI_CL2000_VERSION_CHECK(6,0,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \\\n    JSON_HEDLEY_TI_CL2000_VERSION_CHECK(6,4,0) || \\\n    (JSON_HEDLEY_TI_CL430_VERSION_CHECK(4,0,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \\\n    JSON_HEDLEY_TI_CL430_VERSION_CHECK(4,3,0) || \\\n    (JSON_HEDLEY_TI_CL6X_VERSION_CHECK(7,2,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \\\n    JSON_HEDLEY_TI_CL6X_VERSION_CHECK(7,5,0) || \\\n    JSON_HEDLEY_TI_CL7X_VERSION_CHECK(1,2,0) || \\\n    JSON_HEDLEY_TI_CLPRU_VERSION_CHECK(2,1,0) || \\\n    JSON_HEDLEY_IAR_VERSION_CHECK(8,10,0)\n    #define JSON_HEDLEY_NO_RETURN __attribute__((__noreturn__))\n#elif JSON_HEDLEY_SUNPRO_VERSION_CHECK(5,10,0)\n    #define JSON_HEDLEY_NO_RETURN _Pragma(\"does_not_return\")\n#elif \\\n    JSON_HEDLEY_MSVC_VERSION_CHECK(13,10,0) || \\\n    JSON_HEDLEY_INTEL_CL_VERSION_CHECK(2021,1,0)\n    #define JSON_HEDLEY_NO_RETURN __declspec(noreturn)\n#elif JSON_HEDLEY_TI_CL6X_VERSION_CHECK(6,0,0) && defined(__cplusplus)\n    #define JSON_HEDLEY_NO_RETURN _Pragma(\"FUNC_NEVER_RETURNS;\")\n#elif JSON_HEDLEY_COMPCERT_VERSION_CHECK(3,2,0)\n    #define JSON_HEDLEY_NO_RETURN __attribute((noreturn))\n#elif JSON_HEDLEY_PELLES_VERSION_CHECK(9,0,0)\n    #define JSON_HEDLEY_NO_RETURN __declspec(noreturn)\n#else\n    #define JSON_HEDLEY_NO_RETURN\n#endif\n\n#if defined(JSON_HEDLEY_NO_ESCAPE)\n    #undef JSON_HEDLEY_NO_ESCAPE\n#endif\n#if JSON_HEDLEY_HAS_ATTRIBUTE(noescape)\n    #define JSON_HEDLEY_NO_ESCAPE __attribute__((__noescape__))\n#else\n    #define JSON_HEDLEY_NO_ESCAPE\n#endif\n\n#if defined(JSON_HEDLEY_UNREACHABLE)\n    #undef JSON_HEDLEY_UNREACHABLE\n#endif\n#if defined(JSON_HEDLEY_UNREACHABLE_RETURN)\n    #undef JSON_HEDLEY_UNREACHABLE_RETURN\n#endif\n#if defined(JSON_HEDLEY_ASSUME)\n    #undef JSON_HEDLEY_ASSUME\n#endif\n#if \\\n    JSON_HEDLEY_MSVC_VERSION_CHECK(13,10,0) || \\\n    JSON_HEDLEY_INTEL_VERSION_CHECK(13,0,0) || \\\n    JSON_HEDLEY_INTEL_CL_VERSION_CHECK(2021,1,0)\n    #define JSON_HEDLEY_ASSUME(expr) __assume(expr)\n#elif JSON_HEDLEY_HAS_BUILTIN(__builtin_assume)\n    #define JSON_HEDLEY_ASSUME(expr) __builtin_assume(expr)\n#elif \\\n    JSON_HEDLEY_TI_CL2000_VERSION_CHECK(6,2,0) || \\\n    JSON_HEDLEY_TI_CL6X_VERSION_CHECK(4,0,0)\n    #if defined(__cplusplus)\n        #define JSON_HEDLEY_ASSUME(expr) std::_nassert(expr)\n    #else\n        #define JSON_HEDLEY_ASSUME(expr) _nassert(expr)\n    #endif\n#endif\n#if \\\n    (JSON_HEDLEY_HAS_BUILTIN(__builtin_unreachable) && (!defined(JSON_HEDLEY_ARM_VERSION))) || \\\n    JSON_HEDLEY_GCC_VERSION_CHECK(4,5,0) || \\\n    JSON_HEDLEY_PGI_VERSION_CHECK(18,10,0) || \\\n    JSON_HEDLEY_INTEL_VERSION_CHECK(13,0,0) || \\\n    JSON_HEDLEY_IBM_VERSION_CHECK(13,1,5) || \\\n    JSON_HEDLEY_CRAY_VERSION_CHECK(10,0,0) || \\\n    JSON_HEDLEY_MCST_LCC_VERSION_CHECK(1,25,10)\n    #define JSON_HEDLEY_UNREACHABLE() __builtin_unreachable()\n#elif defined(JSON_HEDLEY_ASSUME)\n    #define JSON_HEDLEY_UNREACHABLE() JSON_HEDLEY_ASSUME(0)\n#endif\n#if !defined(JSON_HEDLEY_ASSUME)\n    #if defined(JSON_HEDLEY_UNREACHABLE)\n        #define JSON_HEDLEY_ASSUME(expr) JSON_HEDLEY_STATIC_CAST(void, ((expr) ? 1 : (JSON_HEDLEY_UNREACHABLE(), 1)))\n    #else\n        #define JSON_HEDLEY_ASSUME(expr) JSON_HEDLEY_STATIC_CAST(void, expr)\n    #endif\n#endif\n#if defined(JSON_HEDLEY_UNREACHABLE)\n    #if  \\\n        JSON_HEDLEY_TI_CL2000_VERSION_CHECK(6,2,0) || \\\n        JSON_HEDLEY_TI_CL6X_VERSION_CHECK(4,0,0)\n        #define JSON_HEDLEY_UNREACHABLE_RETURN(value) return (JSON_HEDLEY_STATIC_CAST(void, JSON_HEDLEY_ASSUME(0)), (value))\n    #else\n        #define JSON_HEDLEY_UNREACHABLE_RETURN(value) JSON_HEDLEY_UNREACHABLE()\n    #endif\n#else\n    #define JSON_HEDLEY_UNREACHABLE_RETURN(value) return (value)\n#endif\n#if !defined(JSON_HEDLEY_UNREACHABLE)\n    #define JSON_HEDLEY_UNREACHABLE() JSON_HEDLEY_ASSUME(0)\n#endif\n\nJSON_HEDLEY_DIAGNOSTIC_PUSH\n#if JSON_HEDLEY_HAS_WARNING(\"-Wpedantic\")\n    #pragma clang diagnostic ignored \"-Wpedantic\"\n#endif\n#if JSON_HEDLEY_HAS_WARNING(\"-Wc++98-compat-pedantic\") && defined(__cplusplus)\n    #pragma clang diagnostic ignored \"-Wc++98-compat-pedantic\"\n#endif\n#if JSON_HEDLEY_GCC_HAS_WARNING(\"-Wvariadic-macros\",4,0,0)\n    #if defined(__clang__)\n        #pragma clang diagnostic ignored \"-Wvariadic-macros\"\n    #elif defined(JSON_HEDLEY_GCC_VERSION)\n        #pragma GCC diagnostic ignored \"-Wvariadic-macros\"\n    #endif\n#endif\n#if defined(JSON_HEDLEY_NON_NULL)\n    #undef JSON_HEDLEY_NON_NULL\n#endif\n#if \\\n    JSON_HEDLEY_HAS_ATTRIBUTE(nonnull) || \\\n    JSON_HEDLEY_GCC_VERSION_CHECK(3,3,0) || \\\n    JSON_HEDLEY_INTEL_VERSION_CHECK(13,0,0) || \\\n    JSON_HEDLEY_ARM_VERSION_CHECK(4,1,0)\n    #define JSON_HEDLEY_NON_NULL(...) __attribute__((__nonnull__(__VA_ARGS__)))\n#else\n    #define JSON_HEDLEY_NON_NULL(...)\n#endif\nJSON_HEDLEY_DIAGNOSTIC_POP\n\n#if defined(JSON_HEDLEY_PRINTF_FORMAT)\n    #undef JSON_HEDLEY_PRINTF_FORMAT\n#endif\n#if defined(__MINGW32__) && JSON_HEDLEY_GCC_HAS_ATTRIBUTE(format,4,4,0) && !defined(__USE_MINGW_ANSI_STDIO)\n    #define JSON_HEDLEY_PRINTF_FORMAT(string_idx,first_to_check) __attribute__((__format__(ms_printf, string_idx, first_to_check)))\n#elif defined(__MINGW32__) && JSON_HEDLEY_GCC_HAS_ATTRIBUTE(format,4,4,0) && defined(__USE_MINGW_ANSI_STDIO)\n    #define JSON_HEDLEY_PRINTF_FORMAT(string_idx,first_to_check) __attribute__((__format__(gnu_printf, string_idx, first_to_check)))\n#elif \\\n    JSON_HEDLEY_HAS_ATTRIBUTE(format) || \\\n    JSON_HEDLEY_GCC_VERSION_CHECK(3,1,0) || \\\n    JSON_HEDLEY_INTEL_VERSION_CHECK(13,0,0) || \\\n    JSON_HEDLEY_ARM_VERSION_CHECK(5,6,0) || \\\n    JSON_HEDLEY_IBM_VERSION_CHECK(10,1,0) || \\\n    JSON_HEDLEY_TI_VERSION_CHECK(15,12,0) || \\\n    (JSON_HEDLEY_TI_ARMCL_VERSION_CHECK(4,8,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \\\n    JSON_HEDLEY_TI_ARMCL_VERSION_CHECK(5,2,0) || \\\n    (JSON_HEDLEY_TI_CL2000_VERSION_CHECK(6,0,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \\\n    JSON_HEDLEY_TI_CL2000_VERSION_CHECK(6,4,0) || \\\n    (JSON_HEDLEY_TI_CL430_VERSION_CHECK(4,0,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \\\n    JSON_HEDLEY_TI_CL430_VERSION_CHECK(4,3,0) || \\\n    (JSON_HEDLEY_TI_CL6X_VERSION_CHECK(7,2,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \\\n    JSON_HEDLEY_TI_CL6X_VERSION_CHECK(7,5,0) || \\\n    JSON_HEDLEY_TI_CL7X_VERSION_CHECK(1,2,0) || \\\n    JSON_HEDLEY_TI_CLPRU_VERSION_CHECK(2,1,0) || \\\n    JSON_HEDLEY_MCST_LCC_VERSION_CHECK(1,25,10)\n    #define JSON_HEDLEY_PRINTF_FORMAT(string_idx,first_to_check) __attribute__((__format__(__printf__, string_idx, first_to_check)))\n#elif JSON_HEDLEY_PELLES_VERSION_CHECK(6,0,0)\n    #define JSON_HEDLEY_PRINTF_FORMAT(string_idx,first_to_check) __declspec(vaformat(printf,string_idx,first_to_check))\n#else\n    #define JSON_HEDLEY_PRINTF_FORMAT(string_idx,first_to_check)\n#endif\n\n#if defined(JSON_HEDLEY_CONSTEXPR)\n    #undef JSON_HEDLEY_CONSTEXPR\n#endif\n#if defined(__cplusplus)\n    #if __cplusplus >= 201103L\n        #define JSON_HEDLEY_CONSTEXPR JSON_HEDLEY_DIAGNOSTIC_DISABLE_CPP98_COMPAT_WRAP_(constexpr)\n    #endif\n#endif\n#if !defined(JSON_HEDLEY_CONSTEXPR)\n    #define JSON_HEDLEY_CONSTEXPR\n#endif\n\n#if defined(JSON_HEDLEY_PREDICT)\n    #undef JSON_HEDLEY_PREDICT\n#endif\n#if defined(JSON_HEDLEY_LIKELY)\n    #undef JSON_HEDLEY_LIKELY\n#endif\n#if defined(JSON_HEDLEY_UNLIKELY)\n    #undef JSON_HEDLEY_UNLIKELY\n#endif\n#if defined(JSON_HEDLEY_UNPREDICTABLE)\n    #undef JSON_HEDLEY_UNPREDICTABLE\n#endif\n#if JSON_HEDLEY_HAS_BUILTIN(__builtin_unpredictable)\n    #define JSON_HEDLEY_UNPREDICTABLE(expr) __builtin_unpredictable((expr))\n#endif\n#if \\\n  (JSON_HEDLEY_HAS_BUILTIN(__builtin_expect_with_probability) && !defined(JSON_HEDLEY_PGI_VERSION)) || \\\n  JSON_HEDLEY_GCC_VERSION_CHECK(9,0,0) || \\\n  JSON_HEDLEY_MCST_LCC_VERSION_CHECK(1,25,10)\n#  define JSON_HEDLEY_PREDICT(expr, value, probability) __builtin_expect_with_probability(  (expr), (value), (probability))\n#  define JSON_HEDLEY_PREDICT_TRUE(expr, probability)   __builtin_expect_with_probability(!!(expr),    1   , (probability))\n#  define JSON_HEDLEY_PREDICT_FALSE(expr, probability)  __builtin_expect_with_probability(!!(expr),    0   , (probability))\n#  define JSON_HEDLEY_LIKELY(expr)                      __builtin_expect                 (!!(expr),    1                  )\n#  define JSON_HEDLEY_UNLIKELY(expr)                    __builtin_expect                 (!!(expr),    0                  )\n#elif \\\n  (JSON_HEDLEY_HAS_BUILTIN(__builtin_expect) && !defined(JSON_HEDLEY_INTEL_CL_VERSION)) || \\\n  JSON_HEDLEY_GCC_VERSION_CHECK(3,0,0) || \\\n  JSON_HEDLEY_INTEL_VERSION_CHECK(13,0,0) || \\\n  (JSON_HEDLEY_SUNPRO_VERSION_CHECK(5,15,0) && defined(__cplusplus)) || \\\n  JSON_HEDLEY_ARM_VERSION_CHECK(4,1,0) || \\\n  JSON_HEDLEY_IBM_VERSION_CHECK(10,1,0) || \\\n  JSON_HEDLEY_TI_VERSION_CHECK(15,12,0) || \\\n  JSON_HEDLEY_TI_ARMCL_VERSION_CHECK(4,7,0) || \\\n  JSON_HEDLEY_TI_CL430_VERSION_CHECK(3,1,0) || \\\n  JSON_HEDLEY_TI_CL2000_VERSION_CHECK(6,1,0) || \\\n  JSON_HEDLEY_TI_CL6X_VERSION_CHECK(6,1,0) || \\\n  JSON_HEDLEY_TI_CL7X_VERSION_CHECK(1,2,0) || \\\n  JSON_HEDLEY_TI_CLPRU_VERSION_CHECK(2,1,0) || \\\n  JSON_HEDLEY_TINYC_VERSION_CHECK(0,9,27) || \\\n  JSON_HEDLEY_CRAY_VERSION_CHECK(8,1,0) || \\\n  JSON_HEDLEY_MCST_LCC_VERSION_CHECK(1,25,10)\n#  define JSON_HEDLEY_PREDICT(expr, expected, probability) \\\n    (((probability) >= 0.9) ? __builtin_expect((expr), (expected)) : (JSON_HEDLEY_STATIC_CAST(void, expected), (expr)))\n#  define JSON_HEDLEY_PREDICT_TRUE(expr, probability) \\\n    (__extension__ ({ \\\n        double hedley_probability_ = (probability); \\\n        ((hedley_probability_ >= 0.9) ? __builtin_expect(!!(expr), 1) : ((hedley_probability_ <= 0.1) ? __builtin_expect(!!(expr), 0) : !!(expr))); \\\n    }))\n#  define JSON_HEDLEY_PREDICT_FALSE(expr, probability) \\\n    (__extension__ ({ \\\n        double hedley_probability_ = (probability); \\\n        ((hedley_probability_ >= 0.9) ? __builtin_expect(!!(expr), 0) : ((hedley_probability_ <= 0.1) ? __builtin_expect(!!(expr), 1) : !!(expr))); \\\n    }))\n#  define JSON_HEDLEY_LIKELY(expr)   __builtin_expect(!!(expr), 1)\n#  define JSON_HEDLEY_UNLIKELY(expr) __builtin_expect(!!(expr), 0)\n#else\n#  define JSON_HEDLEY_PREDICT(expr, expected, probability) (JSON_HEDLEY_STATIC_CAST(void, expected), (expr))\n#  define JSON_HEDLEY_PREDICT_TRUE(expr, probability) (!!(expr))\n#  define JSON_HEDLEY_PREDICT_FALSE(expr, probability) (!!(expr))\n#  define JSON_HEDLEY_LIKELY(expr) (!!(expr))\n#  define JSON_HEDLEY_UNLIKELY(expr) (!!(expr))\n#endif\n#if !defined(JSON_HEDLEY_UNPREDICTABLE)\n    #define JSON_HEDLEY_UNPREDICTABLE(expr) JSON_HEDLEY_PREDICT(expr, 1, 0.5)\n#endif\n\n#if defined(JSON_HEDLEY_MALLOC)\n    #undef JSON_HEDLEY_MALLOC\n#endif\n#if \\\n    JSON_HEDLEY_HAS_ATTRIBUTE(malloc) || \\\n    JSON_HEDLEY_GCC_VERSION_CHECK(3,1,0) || \\\n    JSON_HEDLEY_INTEL_VERSION_CHECK(13,0,0) || \\\n    JSON_HEDLEY_SUNPRO_VERSION_CHECK(5,11,0) || \\\n    JSON_HEDLEY_ARM_VERSION_CHECK(4,1,0) || \\\n    JSON_HEDLEY_IBM_VERSION_CHECK(12,1,0) || \\\n    JSON_HEDLEY_TI_VERSION_CHECK(15,12,0) || \\\n    (JSON_HEDLEY_TI_ARMCL_VERSION_CHECK(4,8,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \\\n    JSON_HEDLEY_TI_ARMCL_VERSION_CHECK(5,2,0) || \\\n    (JSON_HEDLEY_TI_CL2000_VERSION_CHECK(6,0,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \\\n    JSON_HEDLEY_TI_CL2000_VERSION_CHECK(6,4,0) || \\\n    (JSON_HEDLEY_TI_CL430_VERSION_CHECK(4,0,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \\\n    JSON_HEDLEY_TI_CL430_VERSION_CHECK(4,3,0) || \\\n    (JSON_HEDLEY_TI_CL6X_VERSION_CHECK(7,2,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \\\n    JSON_HEDLEY_TI_CL6X_VERSION_CHECK(7,5,0) || \\\n    JSON_HEDLEY_TI_CL7X_VERSION_CHECK(1,2,0) || \\\n    JSON_HEDLEY_TI_CLPRU_VERSION_CHECK(2,1,0) || \\\n    JSON_HEDLEY_MCST_LCC_VERSION_CHECK(1,25,10)\n    #define JSON_HEDLEY_MALLOC __attribute__((__malloc__))\n#elif JSON_HEDLEY_SUNPRO_VERSION_CHECK(5,10,0)\n    #define JSON_HEDLEY_MALLOC _Pragma(\"returns_new_memory\")\n#elif \\\n    JSON_HEDLEY_MSVC_VERSION_CHECK(14,0,0) || \\\n    JSON_HEDLEY_INTEL_CL_VERSION_CHECK(2021,1,0)\n    #define JSON_HEDLEY_MALLOC __declspec(restrict)\n#else\n    #define JSON_HEDLEY_MALLOC\n#endif\n\n#if defined(JSON_HEDLEY_PURE)\n    #undef JSON_HEDLEY_PURE\n#endif\n#if \\\n  JSON_HEDLEY_HAS_ATTRIBUTE(pure) || \\\n  JSON_HEDLEY_GCC_VERSION_CHECK(2,96,0) || \\\n  JSON_HEDLEY_INTEL_VERSION_CHECK(13,0,0) || \\\n  JSON_HEDLEY_SUNPRO_VERSION_CHECK(5,11,0) || \\\n  JSON_HEDLEY_ARM_VERSION_CHECK(4,1,0) || \\\n  JSON_HEDLEY_IBM_VERSION_CHECK(10,1,0) || \\\n  JSON_HEDLEY_TI_VERSION_CHECK(15,12,0) || \\\n  (JSON_HEDLEY_TI_ARMCL_VERSION_CHECK(4,8,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \\\n  JSON_HEDLEY_TI_ARMCL_VERSION_CHECK(5,2,0) || \\\n  (JSON_HEDLEY_TI_CL2000_VERSION_CHECK(6,0,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \\\n  JSON_HEDLEY_TI_CL2000_VERSION_CHECK(6,4,0) || \\\n  (JSON_HEDLEY_TI_CL430_VERSION_CHECK(4,0,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \\\n  JSON_HEDLEY_TI_CL430_VERSION_CHECK(4,3,0) || \\\n  (JSON_HEDLEY_TI_CL6X_VERSION_CHECK(7,2,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \\\n  JSON_HEDLEY_TI_CL6X_VERSION_CHECK(7,5,0) || \\\n  JSON_HEDLEY_TI_CL7X_VERSION_CHECK(1,2,0) || \\\n  JSON_HEDLEY_TI_CLPRU_VERSION_CHECK(2,1,0) || \\\n  JSON_HEDLEY_PGI_VERSION_CHECK(17,10,0) || \\\n  JSON_HEDLEY_MCST_LCC_VERSION_CHECK(1,25,10)\n#  define JSON_HEDLEY_PURE __attribute__((__pure__))\n#elif JSON_HEDLEY_SUNPRO_VERSION_CHECK(5,10,0)\n#  define JSON_HEDLEY_PURE _Pragma(\"does_not_write_global_data\")\n#elif defined(__cplusplus) && \\\n    ( \\\n      JSON_HEDLEY_TI_CL430_VERSION_CHECK(2,0,1) || \\\n      JSON_HEDLEY_TI_CL6X_VERSION_CHECK(4,0,0) || \\\n      JSON_HEDLEY_TI_CL7X_VERSION_CHECK(1,2,0) \\\n    )\n#  define JSON_HEDLEY_PURE _Pragma(\"FUNC_IS_PURE;\")\n#else\n#  define JSON_HEDLEY_PURE\n#endif\n\n#if defined(JSON_HEDLEY_CONST)\n    #undef JSON_HEDLEY_CONST\n#endif\n#if \\\n    JSON_HEDLEY_HAS_ATTRIBUTE(const) || \\\n    JSON_HEDLEY_GCC_VERSION_CHECK(2,5,0) || \\\n    JSON_HEDLEY_INTEL_VERSION_CHECK(13,0,0) || \\\n    JSON_HEDLEY_SUNPRO_VERSION_CHECK(5,11,0) || \\\n    JSON_HEDLEY_ARM_VERSION_CHECK(4,1,0) || \\\n    JSON_HEDLEY_IBM_VERSION_CHECK(10,1,0) || \\\n    JSON_HEDLEY_TI_VERSION_CHECK(15,12,0) || \\\n    (JSON_HEDLEY_TI_ARMCL_VERSION_CHECK(4,8,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \\\n    JSON_HEDLEY_TI_ARMCL_VERSION_CHECK(5,2,0) || \\\n    (JSON_HEDLEY_TI_CL2000_VERSION_CHECK(6,0,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \\\n    JSON_HEDLEY_TI_CL2000_VERSION_CHECK(6,4,0) || \\\n    (JSON_HEDLEY_TI_CL430_VERSION_CHECK(4,0,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \\\n    JSON_HEDLEY_TI_CL430_VERSION_CHECK(4,3,0) || \\\n    (JSON_HEDLEY_TI_CL6X_VERSION_CHECK(7,2,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \\\n    JSON_HEDLEY_TI_CL6X_VERSION_CHECK(7,5,0) || \\\n    JSON_HEDLEY_TI_CL7X_VERSION_CHECK(1,2,0) || \\\n    JSON_HEDLEY_TI_CLPRU_VERSION_CHECK(2,1,0) || \\\n    JSON_HEDLEY_PGI_VERSION_CHECK(17,10,0) || \\\n    JSON_HEDLEY_MCST_LCC_VERSION_CHECK(1,25,10)\n    #define JSON_HEDLEY_CONST __attribute__((__const__))\n#elif \\\n    JSON_HEDLEY_SUNPRO_VERSION_CHECK(5,10,0)\n    #define JSON_HEDLEY_CONST _Pragma(\"no_side_effect\")\n#else\n    #define JSON_HEDLEY_CONST JSON_HEDLEY_PURE\n#endif\n\n#if defined(JSON_HEDLEY_RESTRICT)\n    #undef JSON_HEDLEY_RESTRICT\n#endif\n#if defined(__STDC_VERSION__) && (__STDC_VERSION__ >= 199901L) && !defined(__cplusplus)\n    #define JSON_HEDLEY_RESTRICT restrict\n#elif \\\n    JSON_HEDLEY_GCC_VERSION_CHECK(3,1,0) || \\\n    JSON_HEDLEY_MSVC_VERSION_CHECK(14,0,0) || \\\n    JSON_HEDLEY_INTEL_VERSION_CHECK(13,0,0) || \\\n    JSON_HEDLEY_INTEL_CL_VERSION_CHECK(2021,1,0) || \\\n    JSON_HEDLEY_ARM_VERSION_CHECK(4,1,0) || \\\n    JSON_HEDLEY_IBM_VERSION_CHECK(10,1,0) || \\\n    JSON_HEDLEY_PGI_VERSION_CHECK(17,10,0) || \\\n    JSON_HEDLEY_TI_CL430_VERSION_CHECK(4,3,0) || \\\n    JSON_HEDLEY_TI_CL2000_VERSION_CHECK(6,2,4) || \\\n    JSON_HEDLEY_TI_CL6X_VERSION_CHECK(8,1,0) || \\\n    JSON_HEDLEY_TI_CL7X_VERSION_CHECK(1,2,0) || \\\n    (JSON_HEDLEY_SUNPRO_VERSION_CHECK(5,14,0) && defined(__cplusplus)) || \\\n    JSON_HEDLEY_IAR_VERSION_CHECK(8,0,0) || \\\n    defined(__clang__) || \\\n    JSON_HEDLEY_MCST_LCC_VERSION_CHECK(1,25,10)\n    #define JSON_HEDLEY_RESTRICT __restrict\n#elif JSON_HEDLEY_SUNPRO_VERSION_CHECK(5,3,0) && !defined(__cplusplus)\n    #define JSON_HEDLEY_RESTRICT _Restrict\n#else\n    #define JSON_HEDLEY_RESTRICT\n#endif\n\n#if defined(JSON_HEDLEY_INLINE)\n    #undef JSON_HEDLEY_INLINE\n#endif\n#if \\\n    (defined(__STDC_VERSION__) && (__STDC_VERSION__ >= 199901L)) || \\\n    (defined(__cplusplus) && (__cplusplus >= 199711L))\n    #define JSON_HEDLEY_INLINE inline\n#elif \\\n    defined(JSON_HEDLEY_GCC_VERSION) || \\\n    JSON_HEDLEY_ARM_VERSION_CHECK(6,2,0)\n    #define JSON_HEDLEY_INLINE __inline__\n#elif \\\n    JSON_HEDLEY_MSVC_VERSION_CHECK(12,0,0) || \\\n    JSON_HEDLEY_INTEL_CL_VERSION_CHECK(2021,1,0) || \\\n    JSON_HEDLEY_ARM_VERSION_CHECK(4,1,0) || \\\n    JSON_HEDLEY_TI_ARMCL_VERSION_CHECK(5,1,0) || \\\n    JSON_HEDLEY_TI_CL430_VERSION_CHECK(3,1,0) || \\\n    JSON_HEDLEY_TI_CL2000_VERSION_CHECK(6,2,0) || \\\n    JSON_HEDLEY_TI_CL6X_VERSION_CHECK(8,0,0) || \\\n    JSON_HEDLEY_TI_CL7X_VERSION_CHECK(1,2,0) || \\\n    JSON_HEDLEY_TI_CLPRU_VERSION_CHECK(2,1,0) || \\\n    JSON_HEDLEY_MCST_LCC_VERSION_CHECK(1,25,10)\n    #define JSON_HEDLEY_INLINE __inline\n#else\n    #define JSON_HEDLEY_INLINE\n#endif\n\n#if defined(JSON_HEDLEY_ALWAYS_INLINE)\n    #undef JSON_HEDLEY_ALWAYS_INLINE\n#endif\n#if \\\n  JSON_HEDLEY_HAS_ATTRIBUTE(always_inline) || \\\n  JSON_HEDLEY_GCC_VERSION_CHECK(4,0,0) || \\\n  JSON_HEDLEY_INTEL_VERSION_CHECK(13,0,0) || \\\n  JSON_HEDLEY_SUNPRO_VERSION_CHECK(5,11,0) || \\\n  JSON_HEDLEY_ARM_VERSION_CHECK(4,1,0) || \\\n  JSON_HEDLEY_IBM_VERSION_CHECK(10,1,0) || \\\n  JSON_HEDLEY_TI_VERSION_CHECK(15,12,0) || \\\n  (JSON_HEDLEY_TI_ARMCL_VERSION_CHECK(4,8,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \\\n  JSON_HEDLEY_TI_ARMCL_VERSION_CHECK(5,2,0) || \\\n  (JSON_HEDLEY_TI_CL2000_VERSION_CHECK(6,0,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \\\n  JSON_HEDLEY_TI_CL2000_VERSION_CHECK(6,4,0) || \\\n  (JSON_HEDLEY_TI_CL430_VERSION_CHECK(4,0,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \\\n  JSON_HEDLEY_TI_CL430_VERSION_CHECK(4,3,0) || \\\n  (JSON_HEDLEY_TI_CL6X_VERSION_CHECK(7,2,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \\\n  JSON_HEDLEY_TI_CL6X_VERSION_CHECK(7,5,0) || \\\n  JSON_HEDLEY_TI_CL7X_VERSION_CHECK(1,2,0) || \\\n  JSON_HEDLEY_TI_CLPRU_VERSION_CHECK(2,1,0) || \\\n  JSON_HEDLEY_MCST_LCC_VERSION_CHECK(1,25,10) || \\\n  JSON_HEDLEY_IAR_VERSION_CHECK(8,10,0)\n#  define JSON_HEDLEY_ALWAYS_INLINE __attribute__((__always_inline__)) JSON_HEDLEY_INLINE\n#elif \\\n  JSON_HEDLEY_MSVC_VERSION_CHECK(12,0,0) || \\\n  JSON_HEDLEY_INTEL_CL_VERSION_CHECK(2021,1,0)\n#  define JSON_HEDLEY_ALWAYS_INLINE __forceinline\n#elif defined(__cplusplus) && \\\n    ( \\\n      JSON_HEDLEY_TI_ARMCL_VERSION_CHECK(5,2,0) || \\\n      JSON_HEDLEY_TI_CL430_VERSION_CHECK(4,3,0) || \\\n      JSON_HEDLEY_TI_CL2000_VERSION_CHECK(6,4,0) || \\\n      JSON_HEDLEY_TI_CL6X_VERSION_CHECK(6,1,0) || \\\n      JSON_HEDLEY_TI_CL7X_VERSION_CHECK(1,2,0) || \\\n      JSON_HEDLEY_TI_CLPRU_VERSION_CHECK(2,1,0) \\\n    )\n#  define JSON_HEDLEY_ALWAYS_INLINE _Pragma(\"FUNC_ALWAYS_INLINE;\")\n#elif JSON_HEDLEY_IAR_VERSION_CHECK(8,0,0)\n#  define JSON_HEDLEY_ALWAYS_INLINE _Pragma(\"inline=forced\")\n#else\n#  define JSON_HEDLEY_ALWAYS_INLINE JSON_HEDLEY_INLINE\n#endif\n\n#if defined(JSON_HEDLEY_NEVER_INLINE)\n    #undef JSON_HEDLEY_NEVER_INLINE\n#endif\n#if \\\n    JSON_HEDLEY_HAS_ATTRIBUTE(noinline) || \\\n    JSON_HEDLEY_GCC_VERSION_CHECK(4,0,0) || \\\n    JSON_HEDLEY_INTEL_VERSION_CHECK(13,0,0) || \\\n    JSON_HEDLEY_SUNPRO_VERSION_CHECK(5,11,0) || \\\n    JSON_HEDLEY_ARM_VERSION_CHECK(4,1,0) || \\\n    JSON_HEDLEY_IBM_VERSION_CHECK(10,1,0) || \\\n    JSON_HEDLEY_TI_VERSION_CHECK(15,12,0) || \\\n    (JSON_HEDLEY_TI_ARMCL_VERSION_CHECK(4,8,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \\\n    JSON_HEDLEY_TI_ARMCL_VERSION_CHECK(5,2,0) || \\\n    (JSON_HEDLEY_TI_CL2000_VERSION_CHECK(6,0,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \\\n    JSON_HEDLEY_TI_CL2000_VERSION_CHECK(6,4,0) || \\\n    (JSON_HEDLEY_TI_CL430_VERSION_CHECK(4,0,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \\\n    JSON_HEDLEY_TI_CL430_VERSION_CHECK(4,3,0) || \\\n    (JSON_HEDLEY_TI_CL6X_VERSION_CHECK(7,2,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \\\n    JSON_HEDLEY_TI_CL6X_VERSION_CHECK(7,5,0) || \\\n    JSON_HEDLEY_TI_CL7X_VERSION_CHECK(1,2,0) || \\\n    JSON_HEDLEY_TI_CLPRU_VERSION_CHECK(2,1,0) || \\\n    JSON_HEDLEY_MCST_LCC_VERSION_CHECK(1,25,10) || \\\n    JSON_HEDLEY_IAR_VERSION_CHECK(8,10,0)\n    #define JSON_HEDLEY_NEVER_INLINE __attribute__((__noinline__))\n#elif \\\n    JSON_HEDLEY_MSVC_VERSION_CHECK(13,10,0) || \\\n    JSON_HEDLEY_INTEL_CL_VERSION_CHECK(2021,1,0)\n    #define JSON_HEDLEY_NEVER_INLINE __declspec(noinline)\n#elif JSON_HEDLEY_PGI_VERSION_CHECK(10,2,0)\n    #define JSON_HEDLEY_NEVER_INLINE _Pragma(\"noinline\")\n#elif JSON_HEDLEY_TI_CL6X_VERSION_CHECK(6,0,0) && defined(__cplusplus)\n    #define JSON_HEDLEY_NEVER_INLINE _Pragma(\"FUNC_CANNOT_INLINE;\")\n#elif JSON_HEDLEY_IAR_VERSION_CHECK(8,0,0)\n    #define JSON_HEDLEY_NEVER_INLINE _Pragma(\"inline=never\")\n#elif JSON_HEDLEY_COMPCERT_VERSION_CHECK(3,2,0)\n    #define JSON_HEDLEY_NEVER_INLINE __attribute((noinline))\n#elif JSON_HEDLEY_PELLES_VERSION_CHECK(9,0,0)\n    #define JSON_HEDLEY_NEVER_INLINE __declspec(noinline)\n#else\n    #define JSON_HEDLEY_NEVER_INLINE\n#endif\n\n#if defined(JSON_HEDLEY_PRIVATE)\n    #undef JSON_HEDLEY_PRIVATE\n#endif\n#if defined(JSON_HEDLEY_PUBLIC)\n    #undef JSON_HEDLEY_PUBLIC\n#endif\n#if defined(JSON_HEDLEY_IMPORT)\n    #undef JSON_HEDLEY_IMPORT\n#endif\n#if defined(_WIN32) || defined(__CYGWIN__)\n#  define JSON_HEDLEY_PRIVATE\n#  define JSON_HEDLEY_PUBLIC   __declspec(dllexport)\n#  define JSON_HEDLEY_IMPORT   __declspec(dllimport)\n#else\n#  if \\\n    JSON_HEDLEY_HAS_ATTRIBUTE(visibility) || \\\n    JSON_HEDLEY_GCC_VERSION_CHECK(3,3,0) || \\\n    JSON_HEDLEY_SUNPRO_VERSION_CHECK(5,11,0) || \\\n    JSON_HEDLEY_INTEL_VERSION_CHECK(13,0,0) || \\\n    JSON_HEDLEY_ARM_VERSION_CHECK(4,1,0) || \\\n    JSON_HEDLEY_IBM_VERSION_CHECK(13,1,0) || \\\n    ( \\\n      defined(__TI_EABI__) && \\\n      ( \\\n        (JSON_HEDLEY_TI_CL6X_VERSION_CHECK(7,2,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \\\n        JSON_HEDLEY_TI_CL6X_VERSION_CHECK(7,5,0) \\\n      ) \\\n    ) || \\\n    JSON_HEDLEY_MCST_LCC_VERSION_CHECK(1,25,10)\n#    define JSON_HEDLEY_PRIVATE __attribute__((__visibility__(\"hidden\")))\n#    define JSON_HEDLEY_PUBLIC  __attribute__((__visibility__(\"default\")))\n#  else\n#    define JSON_HEDLEY_PRIVATE\n#    define JSON_HEDLEY_PUBLIC\n#  endif\n#  define JSON_HEDLEY_IMPORT    extern\n#endif\n\n#if defined(JSON_HEDLEY_NO_THROW)\n    #undef JSON_HEDLEY_NO_THROW\n#endif\n#if \\\n    JSON_HEDLEY_HAS_ATTRIBUTE(nothrow) || \\\n    JSON_HEDLEY_GCC_VERSION_CHECK(3,3,0) || \\\n    JSON_HEDLEY_INTEL_VERSION_CHECK(13,0,0) || \\\n    JSON_HEDLEY_MCST_LCC_VERSION_CHECK(1,25,10)\n    #define JSON_HEDLEY_NO_THROW __attribute__((__nothrow__))\n#elif \\\n    JSON_HEDLEY_MSVC_VERSION_CHECK(13,1,0) || \\\n    JSON_HEDLEY_INTEL_CL_VERSION_CHECK(2021,1,0) || \\\n    JSON_HEDLEY_ARM_VERSION_CHECK(4,1,0)\n    #define JSON_HEDLEY_NO_THROW __declspec(nothrow)\n#else\n    #define JSON_HEDLEY_NO_THROW\n#endif\n\n#if defined(JSON_HEDLEY_FALL_THROUGH)\n    #undef JSON_HEDLEY_FALL_THROUGH\n#endif\n#if \\\n    JSON_HEDLEY_HAS_ATTRIBUTE(fallthrough) || \\\n    JSON_HEDLEY_GCC_VERSION_CHECK(7,0,0) || \\\n    JSON_HEDLEY_MCST_LCC_VERSION_CHECK(1,25,10)\n    #define JSON_HEDLEY_FALL_THROUGH __attribute__((__fallthrough__))\n#elif JSON_HEDLEY_HAS_CPP_ATTRIBUTE_NS(clang,fallthrough)\n    #define JSON_HEDLEY_FALL_THROUGH JSON_HEDLEY_DIAGNOSTIC_DISABLE_CPP98_COMPAT_WRAP_([[clang::fallthrough]])\n#elif JSON_HEDLEY_HAS_CPP_ATTRIBUTE(fallthrough)\n    #define JSON_HEDLEY_FALL_THROUGH JSON_HEDLEY_DIAGNOSTIC_DISABLE_CPP98_COMPAT_WRAP_([[fallthrough]])\n#elif defined(__fallthrough) /* SAL */\n    #define JSON_HEDLEY_FALL_THROUGH __fallthrough\n#else\n    #define JSON_HEDLEY_FALL_THROUGH\n#endif\n\n#if defined(JSON_HEDLEY_RETURNS_NON_NULL)\n    #undef JSON_HEDLEY_RETURNS_NON_NULL\n#endif\n#if \\\n    JSON_HEDLEY_HAS_ATTRIBUTE(returns_nonnull) || \\\n    JSON_HEDLEY_GCC_VERSION_CHECK(4,9,0) || \\\n    JSON_HEDLEY_MCST_LCC_VERSION_CHECK(1,25,10)\n    #define JSON_HEDLEY_RETURNS_NON_NULL __attribute__((__returns_nonnull__))\n#elif defined(_Ret_notnull_) /* SAL */\n    #define JSON_HEDLEY_RETURNS_NON_NULL _Ret_notnull_\n#else\n    #define JSON_HEDLEY_RETURNS_NON_NULL\n#endif\n\n#if defined(JSON_HEDLEY_ARRAY_PARAM)\n    #undef JSON_HEDLEY_ARRAY_PARAM\n#endif\n#if \\\n    defined(__STDC_VERSION__) && (__STDC_VERSION__ >= 199901L) && \\\n    !defined(__STDC_NO_VLA__) && \\\n    !defined(__cplusplus) && \\\n    !defined(JSON_HEDLEY_PGI_VERSION) && \\\n    !defined(JSON_HEDLEY_TINYC_VERSION)\n    #define JSON_HEDLEY_ARRAY_PARAM(name) (name)\n#else\n    #define JSON_HEDLEY_ARRAY_PARAM(name)\n#endif\n\n#if defined(JSON_HEDLEY_IS_CONSTANT)\n    #undef JSON_HEDLEY_IS_CONSTANT\n#endif\n#if defined(JSON_HEDLEY_REQUIRE_CONSTEXPR)\n    #undef JSON_HEDLEY_REQUIRE_CONSTEXPR\n#endif\n/* JSON_HEDLEY_IS_CONSTEXPR_ is for\n   HEDLEY INTERNAL USE ONLY.  API subject to change without notice. */\n#if defined(JSON_HEDLEY_IS_CONSTEXPR_)\n    #undef JSON_HEDLEY_IS_CONSTEXPR_\n#endif\n#if \\\n    JSON_HEDLEY_HAS_BUILTIN(__builtin_constant_p) || \\\n    JSON_HEDLEY_GCC_VERSION_CHECK(3,4,0) || \\\n    JSON_HEDLEY_INTEL_VERSION_CHECK(13,0,0) || \\\n    JSON_HEDLEY_TINYC_VERSION_CHECK(0,9,19) || \\\n    JSON_HEDLEY_ARM_VERSION_CHECK(4,1,0) || \\\n    JSON_HEDLEY_IBM_VERSION_CHECK(13,1,0) || \\\n    JSON_HEDLEY_TI_CL6X_VERSION_CHECK(6,1,0) || \\\n    (JSON_HEDLEY_SUNPRO_VERSION_CHECK(5,10,0) && !defined(__cplusplus)) || \\\n    JSON_HEDLEY_CRAY_VERSION_CHECK(8,1,0) || \\\n    JSON_HEDLEY_MCST_LCC_VERSION_CHECK(1,25,10)\n    #define JSON_HEDLEY_IS_CONSTANT(expr) __builtin_constant_p(expr)\n#endif\n#if !defined(__cplusplus)\n#  if \\\n       JSON_HEDLEY_HAS_BUILTIN(__builtin_types_compatible_p) || \\\n       JSON_HEDLEY_GCC_VERSION_CHECK(3,4,0) || \\\n       JSON_HEDLEY_INTEL_VERSION_CHECK(13,0,0) || \\\n       JSON_HEDLEY_IBM_VERSION_CHECK(13,1,0) || \\\n       JSON_HEDLEY_CRAY_VERSION_CHECK(8,1,0) || \\\n       JSON_HEDLEY_ARM_VERSION_CHECK(5,4,0) || \\\n       JSON_HEDLEY_TINYC_VERSION_CHECK(0,9,24)\n#if defined(__INTPTR_TYPE__)\n    #define JSON_HEDLEY_IS_CONSTEXPR_(expr) __builtin_types_compatible_p(__typeof__((1 ? (void*) ((__INTPTR_TYPE__) ((expr) * 0)) : (int*) 0)), int*)\n#else\n    #include <stdint.h>\n    #define JSON_HEDLEY_IS_CONSTEXPR_(expr) __builtin_types_compatible_p(__typeof__((1 ? (void*) ((intptr_t) ((expr) * 0)) : (int*) 0)), int*)\n#endif\n#  elif \\\n       ( \\\n          defined(__STDC_VERSION__) && (__STDC_VERSION__ >= 201112L) && \\\n          !defined(JSON_HEDLEY_SUNPRO_VERSION) && \\\n          !defined(JSON_HEDLEY_PGI_VERSION) && \\\n          !defined(JSON_HEDLEY_IAR_VERSION)) || \\\n       (JSON_HEDLEY_HAS_EXTENSION(c_generic_selections) && !defined(JSON_HEDLEY_IAR_VERSION)) || \\\n       JSON_HEDLEY_GCC_VERSION_CHECK(4,9,0) || \\\n       JSON_HEDLEY_INTEL_VERSION_CHECK(17,0,0) || \\\n       JSON_HEDLEY_IBM_VERSION_CHECK(12,1,0) || \\\n       JSON_HEDLEY_ARM_VERSION_CHECK(5,3,0)\n#if defined(__INTPTR_TYPE__)\n    #define JSON_HEDLEY_IS_CONSTEXPR_(expr) _Generic((1 ? (void*) ((__INTPTR_TYPE__) ((expr) * 0)) : (int*) 0), int*: 1, void*: 0)\n#else\n    #include <stdint.h>\n    #define JSON_HEDLEY_IS_CONSTEXPR_(expr) _Generic((1 ? (void*) ((intptr_t) * 0) : (int*) 0), int*: 1, void*: 0)\n#endif\n#  elif \\\n       defined(JSON_HEDLEY_GCC_VERSION) || \\\n       defined(JSON_HEDLEY_INTEL_VERSION) || \\\n       defined(JSON_HEDLEY_TINYC_VERSION) || \\\n       defined(JSON_HEDLEY_TI_ARMCL_VERSION) || \\\n       JSON_HEDLEY_TI_CL430_VERSION_CHECK(18,12,0) || \\\n       defined(JSON_HEDLEY_TI_CL2000_VERSION) || \\\n       defined(JSON_HEDLEY_TI_CL6X_VERSION) || \\\n       defined(JSON_HEDLEY_TI_CL7X_VERSION) || \\\n       defined(JSON_HEDLEY_TI_CLPRU_VERSION) || \\\n       defined(__clang__)\n#    define JSON_HEDLEY_IS_CONSTEXPR_(expr) ( \\\n        sizeof(void) != \\\n        sizeof(*( \\\n                  1 ? \\\n                  ((void*) ((expr) * 0L) ) : \\\n((struct { char v[sizeof(void) * 2]; } *) 1) \\\n                ) \\\n              ) \\\n                                            )\n#  endif\n#endif\n#if defined(JSON_HEDLEY_IS_CONSTEXPR_)\n    #if !defined(JSON_HEDLEY_IS_CONSTANT)\n        #define JSON_HEDLEY_IS_CONSTANT(expr) JSON_HEDLEY_IS_CONSTEXPR_(expr)\n    #endif\n    #define JSON_HEDLEY_REQUIRE_CONSTEXPR(expr) (JSON_HEDLEY_IS_CONSTEXPR_(expr) ? (expr) : (-1))\n#else\n    #if !defined(JSON_HEDLEY_IS_CONSTANT)\n        #define JSON_HEDLEY_IS_CONSTANT(expr) (0)\n    #endif\n    #define JSON_HEDLEY_REQUIRE_CONSTEXPR(expr) (expr)\n#endif\n\n#if defined(JSON_HEDLEY_BEGIN_C_DECLS)\n    #undef JSON_HEDLEY_BEGIN_C_DECLS\n#endif\n#if defined(JSON_HEDLEY_END_C_DECLS)\n    #undef JSON_HEDLEY_END_C_DECLS\n#endif\n#if defined(JSON_HEDLEY_C_DECL)\n    #undef JSON_HEDLEY_C_DECL\n#endif\n#if defined(__cplusplus)\n    #define JSON_HEDLEY_BEGIN_C_DECLS extern \"C\" {\n    #define JSON_HEDLEY_END_C_DECLS }\n    #define JSON_HEDLEY_C_DECL extern \"C\"\n#else\n    #define JSON_HEDLEY_BEGIN_C_DECLS\n    #define JSON_HEDLEY_END_C_DECLS\n    #define JSON_HEDLEY_C_DECL\n#endif\n\n#if defined(JSON_HEDLEY_STATIC_ASSERT)\n    #undef JSON_HEDLEY_STATIC_ASSERT\n#endif\n#if \\\n  !defined(__cplusplus) && ( \\\n      (defined(__STDC_VERSION__) && (__STDC_VERSION__ >= 201112L)) || \\\n      (JSON_HEDLEY_HAS_FEATURE(c_static_assert) && !defined(JSON_HEDLEY_INTEL_CL_VERSION)) || \\\n      JSON_HEDLEY_GCC_VERSION_CHECK(6,0,0) || \\\n      JSON_HEDLEY_INTEL_VERSION_CHECK(13,0,0) || \\\n      defined(_Static_assert) \\\n    )\n#  define JSON_HEDLEY_STATIC_ASSERT(expr, message) _Static_assert(expr, message)\n#elif \\\n  (defined(__cplusplus) && (__cplusplus >= 201103L)) || \\\n  JSON_HEDLEY_MSVC_VERSION_CHECK(16,0,0) || \\\n  JSON_HEDLEY_INTEL_CL_VERSION_CHECK(2021,1,0)\n#  define JSON_HEDLEY_STATIC_ASSERT(expr, message) JSON_HEDLEY_DIAGNOSTIC_DISABLE_CPP98_COMPAT_WRAP_(static_assert(expr, message))\n#else\n#  define JSON_HEDLEY_STATIC_ASSERT(expr, message)\n#endif\n\n#if defined(JSON_HEDLEY_NULL)\n    #undef JSON_HEDLEY_NULL\n#endif\n#if defined(__cplusplus)\n    #if __cplusplus >= 201103L\n        #define JSON_HEDLEY_NULL JSON_HEDLEY_DIAGNOSTIC_DISABLE_CPP98_COMPAT_WRAP_(nullptr)\n    #elif defined(NULL)\n        #define JSON_HEDLEY_NULL NULL\n    #else\n        #define JSON_HEDLEY_NULL JSON_HEDLEY_STATIC_CAST(void*, 0)\n    #endif\n#elif defined(NULL)\n    #define JSON_HEDLEY_NULL NULL\n#else\n    #define JSON_HEDLEY_NULL ((void*) 0)\n#endif\n\n#if defined(JSON_HEDLEY_MESSAGE)\n    #undef JSON_HEDLEY_MESSAGE\n#endif\n#if JSON_HEDLEY_HAS_WARNING(\"-Wunknown-pragmas\")\n#  define JSON_HEDLEY_MESSAGE(msg) \\\n    JSON_HEDLEY_DIAGNOSTIC_PUSH \\\n    JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNKNOWN_PRAGMAS \\\n    JSON_HEDLEY_PRAGMA(message msg) \\\n    JSON_HEDLEY_DIAGNOSTIC_POP\n#elif \\\n  JSON_HEDLEY_GCC_VERSION_CHECK(4,4,0) || \\\n  JSON_HEDLEY_INTEL_VERSION_CHECK(13,0,0)\n#  define JSON_HEDLEY_MESSAGE(msg) JSON_HEDLEY_PRAGMA(message msg)\n#elif JSON_HEDLEY_CRAY_VERSION_CHECK(5,0,0)\n#  define JSON_HEDLEY_MESSAGE(msg) JSON_HEDLEY_PRAGMA(_CRI message msg)\n#elif JSON_HEDLEY_IAR_VERSION_CHECK(8,0,0)\n#  define JSON_HEDLEY_MESSAGE(msg) JSON_HEDLEY_PRAGMA(message(msg))\n#elif JSON_HEDLEY_PELLES_VERSION_CHECK(2,0,0)\n#  define JSON_HEDLEY_MESSAGE(msg) JSON_HEDLEY_PRAGMA(message(msg))\n#else\n#  define JSON_HEDLEY_MESSAGE(msg)\n#endif\n\n#if defined(JSON_HEDLEY_WARNING)\n    #undef JSON_HEDLEY_WARNING\n#endif\n#if JSON_HEDLEY_HAS_WARNING(\"-Wunknown-pragmas\")\n#  define JSON_HEDLEY_WARNING(msg) \\\n    JSON_HEDLEY_DIAGNOSTIC_PUSH \\\n    JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNKNOWN_PRAGMAS \\\n    JSON_HEDLEY_PRAGMA(clang warning msg) \\\n    JSON_HEDLEY_DIAGNOSTIC_POP\n#elif \\\n  JSON_HEDLEY_GCC_VERSION_CHECK(4,8,0) || \\\n  JSON_HEDLEY_PGI_VERSION_CHECK(18,4,0) || \\\n  JSON_HEDLEY_INTEL_VERSION_CHECK(13,0,0)\n#  define JSON_HEDLEY_WARNING(msg) JSON_HEDLEY_PRAGMA(GCC warning msg)\n#elif \\\n  JSON_HEDLEY_MSVC_VERSION_CHECK(15,0,0) || \\\n  JSON_HEDLEY_INTEL_CL_VERSION_CHECK(2021,1,0)\n#  define JSON_HEDLEY_WARNING(msg) JSON_HEDLEY_PRAGMA(message(msg))\n#else\n#  define JSON_HEDLEY_WARNING(msg) JSON_HEDLEY_MESSAGE(msg)\n#endif\n\n#if defined(JSON_HEDLEY_REQUIRE)\n    #undef JSON_HEDLEY_REQUIRE\n#endif\n#if defined(JSON_HEDLEY_REQUIRE_MSG)\n    #undef JSON_HEDLEY_REQUIRE_MSG\n#endif\n#if JSON_HEDLEY_HAS_ATTRIBUTE(diagnose_if)\n#  if JSON_HEDLEY_HAS_WARNING(\"-Wgcc-compat\")\n#    define JSON_HEDLEY_REQUIRE(expr) \\\n    JSON_HEDLEY_DIAGNOSTIC_PUSH \\\n    _Pragma(\"clang diagnostic ignored \\\"-Wgcc-compat\\\"\") \\\n    __attribute__((diagnose_if(!(expr), #expr, \"error\"))) \\\n    JSON_HEDLEY_DIAGNOSTIC_POP\n#    define JSON_HEDLEY_REQUIRE_MSG(expr,msg) \\\n    JSON_HEDLEY_DIAGNOSTIC_PUSH \\\n    _Pragma(\"clang diagnostic ignored \\\"-Wgcc-compat\\\"\") \\\n    __attribute__((diagnose_if(!(expr), msg, \"error\"))) \\\n    JSON_HEDLEY_DIAGNOSTIC_POP\n#  else\n#    define JSON_HEDLEY_REQUIRE(expr) __attribute__((diagnose_if(!(expr), #expr, \"error\")))\n#    define JSON_HEDLEY_REQUIRE_MSG(expr,msg) __attribute__((diagnose_if(!(expr), msg, \"error\")))\n#  endif\n#else\n#  define JSON_HEDLEY_REQUIRE(expr)\n#  define JSON_HEDLEY_REQUIRE_MSG(expr,msg)\n#endif\n\n#if defined(JSON_HEDLEY_FLAGS)\n    #undef JSON_HEDLEY_FLAGS\n#endif\n#if JSON_HEDLEY_HAS_ATTRIBUTE(flag_enum) && (!defined(__cplusplus) || JSON_HEDLEY_HAS_WARNING(\"-Wbitfield-enum-conversion\"))\n    #define JSON_HEDLEY_FLAGS __attribute__((__flag_enum__))\n#else\n    #define JSON_HEDLEY_FLAGS\n#endif\n\n#if defined(JSON_HEDLEY_FLAGS_CAST)\n    #undef JSON_HEDLEY_FLAGS_CAST\n#endif\n#if JSON_HEDLEY_INTEL_VERSION_CHECK(19,0,0)\n#  define JSON_HEDLEY_FLAGS_CAST(T, expr) (__extension__ ({ \\\n        JSON_HEDLEY_DIAGNOSTIC_PUSH \\\n        _Pragma(\"warning(disable:188)\") \\\n        ((T) (expr)); \\\n        JSON_HEDLEY_DIAGNOSTIC_POP \\\n    }))\n#else\n#  define JSON_HEDLEY_FLAGS_CAST(T, expr) JSON_HEDLEY_STATIC_CAST(T, expr)\n#endif\n\n#if defined(JSON_HEDLEY_EMPTY_BASES)\n    #undef JSON_HEDLEY_EMPTY_BASES\n#endif\n#if \\\n    (JSON_HEDLEY_MSVC_VERSION_CHECK(19,0,23918) && !JSON_HEDLEY_MSVC_VERSION_CHECK(20,0,0)) || \\\n    JSON_HEDLEY_INTEL_CL_VERSION_CHECK(2021,1,0)\n    #define JSON_HEDLEY_EMPTY_BASES __declspec(empty_bases)\n#else\n    #define JSON_HEDLEY_EMPTY_BASES\n#endif\n\n/* Remaining macros are deprecated. */\n\n#if defined(JSON_HEDLEY_GCC_NOT_CLANG_VERSION_CHECK)\n    #undef JSON_HEDLEY_GCC_NOT_CLANG_VERSION_CHECK\n#endif\n#if defined(__clang__)\n    #define JSON_HEDLEY_GCC_NOT_CLANG_VERSION_CHECK(major,minor,patch) (0)\n#else\n    #define JSON_HEDLEY_GCC_NOT_CLANG_VERSION_CHECK(major,minor,patch) JSON_HEDLEY_GCC_VERSION_CHECK(major,minor,patch)\n#endif\n\n#if defined(JSON_HEDLEY_CLANG_HAS_ATTRIBUTE)\n    #undef JSON_HEDLEY_CLANG_HAS_ATTRIBUTE\n#endif\n#define JSON_HEDLEY_CLANG_HAS_ATTRIBUTE(attribute) JSON_HEDLEY_HAS_ATTRIBUTE(attribute)\n\n#if defined(JSON_HEDLEY_CLANG_HAS_CPP_ATTRIBUTE)\n    #undef JSON_HEDLEY_CLANG_HAS_CPP_ATTRIBUTE\n#endif\n#define JSON_HEDLEY_CLANG_HAS_CPP_ATTRIBUTE(attribute) JSON_HEDLEY_HAS_CPP_ATTRIBUTE(attribute)\n\n#if defined(JSON_HEDLEY_CLANG_HAS_BUILTIN)\n    #undef JSON_HEDLEY_CLANG_HAS_BUILTIN\n#endif\n#define JSON_HEDLEY_CLANG_HAS_BUILTIN(builtin) JSON_HEDLEY_HAS_BUILTIN(builtin)\n\n#if defined(JSON_HEDLEY_CLANG_HAS_FEATURE)\n    #undef JSON_HEDLEY_CLANG_HAS_FEATURE\n#endif\n#define JSON_HEDLEY_CLANG_HAS_FEATURE(feature) JSON_HEDLEY_HAS_FEATURE(feature)\n\n#if defined(JSON_HEDLEY_CLANG_HAS_EXTENSION)\n    #undef JSON_HEDLEY_CLANG_HAS_EXTENSION\n#endif\n#define JSON_HEDLEY_CLANG_HAS_EXTENSION(extension) JSON_HEDLEY_HAS_EXTENSION(extension)\n\n#if defined(JSON_HEDLEY_CLANG_HAS_DECLSPEC_DECLSPEC_ATTRIBUTE)\n    #undef JSON_HEDLEY_CLANG_HAS_DECLSPEC_DECLSPEC_ATTRIBUTE\n#endif\n#define JSON_HEDLEY_CLANG_HAS_DECLSPEC_ATTRIBUTE(attribute) JSON_HEDLEY_HAS_DECLSPEC_ATTRIBUTE(attribute)\n\n#if defined(JSON_HEDLEY_CLANG_HAS_WARNING)\n    #undef JSON_HEDLEY_CLANG_HAS_WARNING\n#endif\n#define JSON_HEDLEY_CLANG_HAS_WARNING(warning) JSON_HEDLEY_HAS_WARNING(warning)\n\n#endif /* !defined(JSON_HEDLEY_VERSION) || (JSON_HEDLEY_VERSION < X) */\n\n\n// This file contains all internal macro definitions (except those affecting ABI)\n// You MUST include macro_unscope.hpp at the end of json.hpp to undef all of them\n\n// #include <nlohmann/detail/abi_macros.hpp>\n\n\n// exclude unsupported compilers\n#if !defined(JSON_SKIP_UNSUPPORTED_COMPILER_CHECK)\n    #if defined(__clang__)\n        #if (__clang_major__ * 10000 + __clang_minor__ * 100 + __clang_patchlevel__) < 30400\n            #error \"unsupported Clang version - see https://github.com/nlohmann/json#supported-compilers\"\n        #endif\n    #elif defined(__GNUC__) && !(defined(__ICC) || defined(__INTEL_COMPILER))\n        #if (__GNUC__ * 10000 + __GNUC_MINOR__ * 100 + __GNUC_PATCHLEVEL__) < 40800\n            #error \"unsupported GCC version - see https://github.com/nlohmann/json#supported-compilers\"\n        #endif\n    #endif\n#endif\n\n// C++ language standard detection\n// if the user manually specified the used c++ version this is skipped\n#if !defined(JSON_HAS_CPP_20) && !defined(JSON_HAS_CPP_17) && !defined(JSON_HAS_CPP_14) && !defined(JSON_HAS_CPP_11)\n    #if (defined(__cplusplus) && __cplusplus >= 202002L) || (defined(_MSVC_LANG) && _MSVC_LANG >= 202002L)\n        #define JSON_HAS_CPP_20\n        #define JSON_HAS_CPP_17\n        #define JSON_HAS_CPP_14\n    #elif (defined(__cplusplus) && __cplusplus >= 201703L) || (defined(_HAS_CXX17) && _HAS_CXX17 == 1) // fix for issue #464\n        #define JSON_HAS_CPP_17\n        #define JSON_HAS_CPP_14\n    #elif (defined(__cplusplus) && __cplusplus >= 201402L) || (defined(_HAS_CXX14) && _HAS_CXX14 == 1)\n        #define JSON_HAS_CPP_14\n    #endif\n    // the cpp 11 flag is always specified because it is the minimal required version\n    #define JSON_HAS_CPP_11\n#endif\n\n#ifdef __has_include\n    #if __has_include(<version>)\n        #include <version>\n    #endif\n#endif\n\n#if !defined(JSON_HAS_FILESYSTEM) && !defined(JSON_HAS_EXPERIMENTAL_FILESYSTEM)\n    #ifdef JSON_HAS_CPP_17\n        #if defined(__cpp_lib_filesystem)\n            #define JSON_HAS_FILESYSTEM 1\n        #elif defined(__cpp_lib_experimental_filesystem)\n            #define JSON_HAS_EXPERIMENTAL_FILESYSTEM 1\n        #elif !defined(__has_include)\n            #define JSON_HAS_EXPERIMENTAL_FILESYSTEM 1\n        #elif __has_include(<filesystem>)\n            #define JSON_HAS_FILESYSTEM 1\n        #elif __has_include(<experimental/filesystem>)\n            #define JSON_HAS_EXPERIMENTAL_FILESYSTEM 1\n        #endif\n\n        // std::filesystem does not work on MinGW GCC 8: https://sourceforge.net/p/mingw-w64/bugs/737/\n        #if defined(__MINGW32__) && defined(__GNUC__) && __GNUC__ == 8\n            #undef JSON_HAS_FILESYSTEM\n            #undef JSON_HAS_EXPERIMENTAL_FILESYSTEM\n        #endif\n\n        // no filesystem support before GCC 8: https://en.cppreference.com/w/cpp/compiler_support\n        #if defined(__GNUC__) && !defined(__clang__) && __GNUC__ < 8\n            #undef JSON_HAS_FILESYSTEM\n            #undef JSON_HAS_EXPERIMENTAL_FILESYSTEM\n        #endif\n\n        // no filesystem support before Clang 7: https://en.cppreference.com/w/cpp/compiler_support\n        #if defined(__clang_major__) && __clang_major__ < 7\n            #undef JSON_HAS_FILESYSTEM\n            #undef JSON_HAS_EXPERIMENTAL_FILESYSTEM\n        #endif\n\n        // no filesystem support before MSVC 19.14: https://en.cppreference.com/w/cpp/compiler_support\n        #if defined(_MSC_VER) && _MSC_VER < 1914\n            #undef JSON_HAS_FILESYSTEM\n            #undef JSON_HAS_EXPERIMENTAL_FILESYSTEM\n        #endif\n\n        // no filesystem support before iOS 13\n        #if defined(__IPHONE_OS_VERSION_MIN_REQUIRED) && __IPHONE_OS_VERSION_MIN_REQUIRED < 130000\n            #undef JSON_HAS_FILESYSTEM\n            #undef JSON_HAS_EXPERIMENTAL_FILESYSTEM\n        #endif\n\n        // no filesystem support before macOS Catalina\n        #if defined(__MAC_OS_X_VERSION_MIN_REQUIRED) && __MAC_OS_X_VERSION_MIN_REQUIRED < 101500\n            #undef JSON_HAS_FILESYSTEM\n            #undef JSON_HAS_EXPERIMENTAL_FILESYSTEM\n        #endif\n    #endif\n#endif\n\n#ifndef JSON_HAS_EXPERIMENTAL_FILESYSTEM\n    #define JSON_HAS_EXPERIMENTAL_FILESYSTEM 0\n#endif\n\n#ifndef JSON_HAS_FILESYSTEM\n    #define JSON_HAS_FILESYSTEM 0\n#endif\n\n#ifndef JSON_HAS_THREE_WAY_COMPARISON\n    #if defined(__cpp_impl_three_way_comparison) && __cpp_impl_three_way_comparison >= 201907L \\\n        && defined(__cpp_lib_three_way_comparison) && __cpp_lib_three_way_comparison >= 201907L\n        #define JSON_HAS_THREE_WAY_COMPARISON 1\n    #else\n        #define JSON_HAS_THREE_WAY_COMPARISON 0\n    #endif\n#endif\n\n#ifndef JSON_HAS_RANGES\n    // ranges header shipping in GCC 11.1.0 (released 2021-04-27) has syntax error\n    #if defined(__GLIBCXX__) && __GLIBCXX__ == 20210427\n        #define JSON_HAS_RANGES 0\n    #elif defined(__cpp_lib_ranges)\n        #define JSON_HAS_RANGES 1\n    #else\n        #define JSON_HAS_RANGES 0\n    #endif\n#endif\n\n#ifndef JSON_HAS_STATIC_RTTI\n    #if !defined(_HAS_STATIC_RTTI) || _HAS_STATIC_RTTI != 0\n        #define JSON_HAS_STATIC_RTTI 1\n    #else\n        #define JSON_HAS_STATIC_RTTI 0\n    #endif\n#endif\n\n#ifdef JSON_HAS_CPP_17\n    #define JSON_INLINE_VARIABLE inline\n#else\n    #define JSON_INLINE_VARIABLE\n#endif\n\n#if JSON_HEDLEY_HAS_ATTRIBUTE(no_unique_address)\n    #define JSON_NO_UNIQUE_ADDRESS [[no_unique_address]]\n#else\n    #define JSON_NO_UNIQUE_ADDRESS\n#endif\n\n// disable documentation warnings on clang\n#if defined(__clang__)\n    #pragma clang diagnostic push\n    #pragma clang diagnostic ignored \"-Wdocumentation\"\n    #pragma clang diagnostic ignored \"-Wdocumentation-unknown-command\"\n#endif\n\n// allow disabling exceptions\n#if (defined(__cpp_exceptions) || defined(__EXCEPTIONS) || defined(_CPPUNWIND)) && !defined(JSON_NOEXCEPTION)\n    #define JSON_THROW(exception) throw exception\n    #define JSON_TRY try\n    #define JSON_CATCH(exception) catch(exception)\n    #define JSON_INTERNAL_CATCH(exception) catch(exception)\n#else\n    #include <cstdlib>\n    #define JSON_THROW(exception) std::abort()\n    #define JSON_TRY if(true)\n    #define JSON_CATCH(exception) if(false)\n    #define JSON_INTERNAL_CATCH(exception) if(false)\n#endif\n\n// override exception macros\n#if defined(JSON_THROW_USER)\n    #undef JSON_THROW\n    #define JSON_THROW JSON_THROW_USER\n#endif\n#if defined(JSON_TRY_USER)\n    #undef JSON_TRY\n    #define JSON_TRY JSON_TRY_USER\n#endif\n#if defined(JSON_CATCH_USER)\n    #undef JSON_CATCH\n    #define JSON_CATCH JSON_CATCH_USER\n    #undef JSON_INTERNAL_CATCH\n    #define JSON_INTERNAL_CATCH JSON_CATCH_USER\n#endif\n#if defined(JSON_INTERNAL_CATCH_USER)\n    #undef JSON_INTERNAL_CATCH\n    #define JSON_INTERNAL_CATCH JSON_INTERNAL_CATCH_USER\n#endif\n\n// allow overriding assert\n#if !defined(JSON_ASSERT)\n    #include <cassert> // assert\n    #define JSON_ASSERT(x) assert(x)\n#endif\n\n// allow to access some private functions (needed by the test suite)\n#if defined(JSON_TESTS_PRIVATE)\n    #define JSON_PRIVATE_UNLESS_TESTED public\n#else\n    #define JSON_PRIVATE_UNLESS_TESTED private\n#endif\n\n/*!\n@brief macro to briefly define a mapping between an enum and JSON\n@def NLOHMANN_JSON_SERIALIZE_ENUM\n@since version 3.4.0\n*/\n#define NLOHMANN_JSON_SERIALIZE_ENUM(ENUM_TYPE, ...)                                            \\\n    template<typename BasicJsonType>                                                            \\\n    inline void to_json(BasicJsonType& j, const ENUM_TYPE& e)                                   \\\n    {                                                                                           \\\n        static_assert(std::is_enum<ENUM_TYPE>::value, #ENUM_TYPE \" must be an enum!\");          \\\n        static const std::pair<ENUM_TYPE, BasicJsonType> m[] = __VA_ARGS__;                     \\\n        auto it = std::find_if(std::begin(m), std::end(m),                                      \\\n                               [e](const std::pair<ENUM_TYPE, BasicJsonType>& ej_pair) -> bool  \\\n        {                                                                                       \\\n            return ej_pair.first == e;                                                          \\\n        });                                                                                     \\\n        j = ((it != std::end(m)) ? it : std::begin(m))->second;                                 \\\n    }                                                                                           \\\n    template<typename BasicJsonType>                                                            \\\n    inline void from_json(const BasicJsonType& j, ENUM_TYPE& e)                                 \\\n    {                                                                                           \\\n        static_assert(std::is_enum<ENUM_TYPE>::value, #ENUM_TYPE \" must be an enum!\");          \\\n        static const std::pair<ENUM_TYPE, BasicJsonType> m[] = __VA_ARGS__;                     \\\n        auto it = std::find_if(std::begin(m), std::end(m),                                      \\\n                               [&j](const std::pair<ENUM_TYPE, BasicJsonType>& ej_pair) -> bool \\\n        {                                                                                       \\\n            return ej_pair.second == j;                                                         \\\n        });                                                                                     \\\n        e = ((it != std::end(m)) ? it : std::begin(m))->first;                                  \\\n    }\n\n// Ugly macros to avoid uglier copy-paste when specializing basic_json. They\n// may be removed in the future once the class is split.\n\n#define NLOHMANN_BASIC_JSON_TPL_DECLARATION                                \\\n    template<template<typename, typename, typename...> class ObjectType,   \\\n             template<typename, typename...> class ArrayType,              \\\n             class StringType, class BooleanType, class NumberIntegerType, \\\n             class NumberUnsignedType, class NumberFloatType,              \\\n             template<typename> class AllocatorType,                       \\\n             template<typename, typename = void> class JSONSerializer,     \\\n             class BinaryType,                                             \\\n             class CustomBaseClass>\n\n#define NLOHMANN_BASIC_JSON_TPL                                            \\\n    basic_json<ObjectType, ArrayType, StringType, BooleanType,             \\\n    NumberIntegerType, NumberUnsignedType, NumberFloatType,                \\\n    AllocatorType, JSONSerializer, BinaryType, CustomBaseClass>\n\n// Macros to simplify conversion from/to types\n\n#define NLOHMANN_JSON_EXPAND( x ) x\n#define NLOHMANN_JSON_GET_MACRO(_1, _2, _3, _4, _5, _6, _7, _8, _9, _10, _11, _12, _13, _14, _15, _16, _17, _18, _19, _20, _21, _22, _23, _24, _25, _26, _27, _28, _29, _30, _31, _32, _33, _34, _35, _36, _37, _38, _39, _40, _41, _42, _43, _44, _45, _46, _47, _48, _49, _50, _51, _52, _53, _54, _55, _56, _57, _58, _59, _60, _61, _62, _63, _64, NAME,...) NAME\n#define NLOHMANN_JSON_PASTE(...) NLOHMANN_JSON_EXPAND(NLOHMANN_JSON_GET_MACRO(__VA_ARGS__, \\\n        NLOHMANN_JSON_PASTE64, \\\n        NLOHMANN_JSON_PASTE63, \\\n        NLOHMANN_JSON_PASTE62, \\\n        NLOHMANN_JSON_PASTE61, \\\n        NLOHMANN_JSON_PASTE60, \\\n        NLOHMANN_JSON_PASTE59, \\\n        NLOHMANN_JSON_PASTE58, \\\n        NLOHMANN_JSON_PASTE57, \\\n        NLOHMANN_JSON_PASTE56, \\\n        NLOHMANN_JSON_PASTE55, \\\n        NLOHMANN_JSON_PASTE54, \\\n        NLOHMANN_JSON_PASTE53, \\\n        NLOHMANN_JSON_PASTE52, \\\n        NLOHMANN_JSON_PASTE51, \\\n        NLOHMANN_JSON_PASTE50, \\\n        NLOHMANN_JSON_PASTE49, \\\n        NLOHMANN_JSON_PASTE48, \\\n        NLOHMANN_JSON_PASTE47, \\\n        NLOHMANN_JSON_PASTE46, \\\n        NLOHMANN_JSON_PASTE45, \\\n        NLOHMANN_JSON_PASTE44, \\\n        NLOHMANN_JSON_PASTE43, \\\n        NLOHMANN_JSON_PASTE42, \\\n        NLOHMANN_JSON_PASTE41, \\\n        NLOHMANN_JSON_PASTE40, \\\n        NLOHMANN_JSON_PASTE39, \\\n        NLOHMANN_JSON_PASTE38, \\\n        NLOHMANN_JSON_PASTE37, \\\n        NLOHMANN_JSON_PASTE36, \\\n        NLOHMANN_JSON_PASTE35, \\\n        NLOHMANN_JSON_PASTE34, \\\n        NLOHMANN_JSON_PASTE33, \\\n        NLOHMANN_JSON_PASTE32, \\\n        NLOHMANN_JSON_PASTE31, \\\n        NLOHMANN_JSON_PASTE30, \\\n        NLOHMANN_JSON_PASTE29, \\\n        NLOHMANN_JSON_PASTE28, \\\n        NLOHMANN_JSON_PASTE27, \\\n        NLOHMANN_JSON_PASTE26, \\\n        NLOHMANN_JSON_PASTE25, \\\n        NLOHMANN_JSON_PASTE24, \\\n        NLOHMANN_JSON_PASTE23, \\\n        NLOHMANN_JSON_PASTE22, \\\n        NLOHMANN_JSON_PASTE21, \\\n        NLOHMANN_JSON_PASTE20, \\\n        NLOHMANN_JSON_PASTE19, \\\n        NLOHMANN_JSON_PASTE18, \\\n        NLOHMANN_JSON_PASTE17, \\\n        NLOHMANN_JSON_PASTE16, \\\n        NLOHMANN_JSON_PASTE15, \\\n        NLOHMANN_JSON_PASTE14, \\\n        NLOHMANN_JSON_PASTE13, \\\n        NLOHMANN_JSON_PASTE12, \\\n        NLOHMANN_JSON_PASTE11, \\\n        NLOHMANN_JSON_PASTE10, \\\n        NLOHMANN_JSON_PASTE9, \\\n        NLOHMANN_JSON_PASTE8, \\\n        NLOHMANN_JSON_PASTE7, \\\n        NLOHMANN_JSON_PASTE6, \\\n        NLOHMANN_JSON_PASTE5, \\\n        NLOHMANN_JSON_PASTE4, \\\n        NLOHMANN_JSON_PASTE3, \\\n        NLOHMANN_JSON_PASTE2, \\\n        NLOHMANN_JSON_PASTE1)(__VA_ARGS__))\n#define NLOHMANN_JSON_PASTE2(func, v1) func(v1)\n#define NLOHMANN_JSON_PASTE3(func, v1, v2) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE2(func, v2)\n#define NLOHMANN_JSON_PASTE4(func, v1, v2, v3) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE3(func, v2, v3)\n#define NLOHMANN_JSON_PASTE5(func, v1, v2, v3, v4) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE4(func, v2, v3, v4)\n#define NLOHMANN_JSON_PASTE6(func, v1, v2, v3, v4, v5) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE5(func, v2, v3, v4, v5)\n#define NLOHMANN_JSON_PASTE7(func, v1, v2, v3, v4, v5, v6) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE6(func, v2, v3, v4, v5, v6)\n#define NLOHMANN_JSON_PASTE8(func, v1, v2, v3, v4, v5, v6, v7) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE7(func, v2, v3, v4, v5, v6, v7)\n#define NLOHMANN_JSON_PASTE9(func, v1, v2, v3, v4, v5, v6, v7, v8) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE8(func, v2, v3, v4, v5, v6, v7, v8)\n#define NLOHMANN_JSON_PASTE10(func, v1, v2, v3, v4, v5, v6, v7, v8, v9) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE9(func, v2, v3, v4, v5, v6, v7, v8, v9)\n#define NLOHMANN_JSON_PASTE11(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE10(func, v2, v3, v4, v5, v6, v7, v8, v9, v10)\n#define NLOHMANN_JSON_PASTE12(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE11(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11)\n#define NLOHMANN_JSON_PASTE13(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE12(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12)\n#define NLOHMANN_JSON_PASTE14(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE13(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13)\n#define NLOHMANN_JSON_PASTE15(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE14(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14)\n#define NLOHMANN_JSON_PASTE16(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE15(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15)\n#define NLOHMANN_JSON_PASTE17(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE16(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16)\n#define NLOHMANN_JSON_PASTE18(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE17(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17)\n#define NLOHMANN_JSON_PASTE19(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE18(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18)\n#define NLOHMANN_JSON_PASTE20(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE19(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19)\n#define NLOHMANN_JSON_PASTE21(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE20(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20)\n#define NLOHMANN_JSON_PASTE22(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE21(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21)\n#define NLOHMANN_JSON_PASTE23(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE22(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22)\n#define NLOHMANN_JSON_PASTE24(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE23(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23)\n#define NLOHMANN_JSON_PASTE25(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE24(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24)\n#define NLOHMANN_JSON_PASTE26(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE25(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25)\n#define NLOHMANN_JSON_PASTE27(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE26(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26)\n#define NLOHMANN_JSON_PASTE28(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE27(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27)\n#define NLOHMANN_JSON_PASTE29(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE28(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28)\n#define NLOHMANN_JSON_PASTE30(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE29(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29)\n#define NLOHMANN_JSON_PASTE31(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE30(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30)\n#define NLOHMANN_JSON_PASTE32(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE31(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31)\n#define NLOHMANN_JSON_PASTE33(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE32(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32)\n#define NLOHMANN_JSON_PASTE34(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE33(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33)\n#define NLOHMANN_JSON_PASTE35(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE34(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34)\n#define NLOHMANN_JSON_PASTE36(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE35(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35)\n#define NLOHMANN_JSON_PASTE37(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE36(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36)\n#define NLOHMANN_JSON_PASTE38(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE37(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37)\n#define NLOHMANN_JSON_PASTE39(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE38(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38)\n#define NLOHMANN_JSON_PASTE40(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE39(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39)\n#define NLOHMANN_JSON_PASTE41(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE40(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40)\n#define NLOHMANN_JSON_PASTE42(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE41(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41)\n#define NLOHMANN_JSON_PASTE43(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE42(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42)\n#define NLOHMANN_JSON_PASTE44(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE43(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43)\n#define NLOHMANN_JSON_PASTE45(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE44(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44)\n#define NLOHMANN_JSON_PASTE46(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE45(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45)\n#define NLOHMANN_JSON_PASTE47(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE46(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46)\n#define NLOHMANN_JSON_PASTE48(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE47(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47)\n#define NLOHMANN_JSON_PASTE49(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47, v48) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE48(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47, v48)\n#define NLOHMANN_JSON_PASTE50(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47, v48, v49) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE49(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47, v48, v49)\n#define NLOHMANN_JSON_PASTE51(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47, v48, v49, v50) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE50(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47, v48, v49, v50)\n#define NLOHMANN_JSON_PASTE52(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47, v48, v49, v50, v51) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE51(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47, v48, v49, v50, v51)\n#define NLOHMANN_JSON_PASTE53(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47, v48, v49, v50, v51, v52) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE52(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47, v48, v49, v50, v51, v52)\n#define NLOHMANN_JSON_PASTE54(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47, v48, v49, v50, v51, v52, v53) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE53(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47, v48, v49, v50, v51, v52, v53)\n#define NLOHMANN_JSON_PASTE55(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47, v48, v49, v50, v51, v52, v53, v54) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE54(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47, v48, v49, v50, v51, v52, v53, v54)\n#define NLOHMANN_JSON_PASTE56(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47, v48, v49, v50, v51, v52, v53, v54, v55) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE55(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47, v48, v49, v50, v51, v52, v53, v54, v55)\n#define NLOHMANN_JSON_PASTE57(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47, v48, v49, v50, v51, v52, v53, v54, v55, v56) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE56(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47, v48, v49, v50, v51, v52, v53, v54, v55, v56)\n#define NLOHMANN_JSON_PASTE58(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47, v48, v49, v50, v51, v52, v53, v54, v55, v56, v57) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE57(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47, v48, v49, v50, v51, v52, v53, v54, v55, v56, v57)\n#define NLOHMANN_JSON_PASTE59(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47, v48, v49, v50, v51, v52, v53, v54, v55, v56, v57, v58) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE58(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47, v48, v49, v50, v51, v52, v53, v54, v55, v56, v57, v58)\n#define NLOHMANN_JSON_PASTE60(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47, v48, v49, v50, v51, v52, v53, v54, v55, v56, v57, v58, v59) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE59(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47, v48, v49, v50, v51, v52, v53, v54, v55, v56, v57, v58, v59)\n#define NLOHMANN_JSON_PASTE61(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47, v48, v49, v50, v51, v52, v53, v54, v55, v56, v57, v58, v59, v60) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE60(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47, v48, v49, v50, v51, v52, v53, v54, v55, v56, v57, v58, v59, v60)\n#define NLOHMANN_JSON_PASTE62(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47, v48, v49, v50, v51, v52, v53, v54, v55, v56, v57, v58, v59, v60, v61) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE61(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47, v48, v49, v50, v51, v52, v53, v54, v55, v56, v57, v58, v59, v60, v61)\n#define NLOHMANN_JSON_PASTE63(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47, v48, v49, v50, v51, v52, v53, v54, v55, v56, v57, v58, v59, v60, v61, v62) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE62(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47, v48, v49, v50, v51, v52, v53, v54, v55, v56, v57, v58, v59, v60, v61, v62)\n#define NLOHMANN_JSON_PASTE64(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47, v48, v49, v50, v51, v52, v53, v54, v55, v56, v57, v58, v59, v60, v61, v62, v63) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE63(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47, v48, v49, v50, v51, v52, v53, v54, v55, v56, v57, v58, v59, v60, v61, v62, v63)\n\n#define NLOHMANN_JSON_TO(v1) nlohmann_json_j[#v1] = nlohmann_json_t.v1;\n#define NLOHMANN_JSON_FROM(v1) nlohmann_json_j.at(#v1).get_to(nlohmann_json_t.v1);\n#define NLOHMANN_JSON_FROM_WITH_DEFAULT(v1) nlohmann_json_t.v1 = nlohmann_json_j.value(#v1, nlohmann_json_default_obj.v1);\n\n/*!\n@brief macro\n@def NLOHMANN_DEFINE_TYPE_INTRUSIVE\n@since version 3.9.0\n*/\n#define NLOHMANN_DEFINE_TYPE_INTRUSIVE(Type, ...)  \\\n    friend void to_json(nlohmann::json& nlohmann_json_j, const Type& nlohmann_json_t) { NLOHMANN_JSON_EXPAND(NLOHMANN_JSON_PASTE(NLOHMANN_JSON_TO, __VA_ARGS__)) } \\\n    friend void from_json(const nlohmann::json& nlohmann_json_j, Type& nlohmann_json_t) { NLOHMANN_JSON_EXPAND(NLOHMANN_JSON_PASTE(NLOHMANN_JSON_FROM, __VA_ARGS__)) }\n\n#define NLOHMANN_DEFINE_TYPE_INTRUSIVE_WITH_DEFAULT(Type, ...)  \\\n    friend void to_json(nlohmann::json& nlohmann_json_j, const Type& nlohmann_json_t) { NLOHMANN_JSON_EXPAND(NLOHMANN_JSON_PASTE(NLOHMANN_JSON_TO, __VA_ARGS__)) } \\\n    friend void from_json(const nlohmann::json& nlohmann_json_j, Type& nlohmann_json_t) { const Type nlohmann_json_default_obj{}; NLOHMANN_JSON_EXPAND(NLOHMANN_JSON_PASTE(NLOHMANN_JSON_FROM_WITH_DEFAULT, __VA_ARGS__)) }\n\n#define NLOHMANN_DEFINE_TYPE_INTRUSIVE_ONLY_SERIALIZE(Type, ...)  \\\n    friend void to_json(nlohmann::json& nlohmann_json_j, const Type& nlohmann_json_t) { NLOHMANN_JSON_EXPAND(NLOHMANN_JSON_PASTE(NLOHMANN_JSON_TO, __VA_ARGS__)) }\n\n/*!\n@brief macro\n@def NLOHMANN_DEFINE_TYPE_NON_INTRUSIVE\n@since version 3.9.0\n*/\n#define NLOHMANN_DEFINE_TYPE_NON_INTRUSIVE(Type, ...)  \\\n    inline void to_json(nlohmann::json& nlohmann_json_j, const Type& nlohmann_json_t) { NLOHMANN_JSON_EXPAND(NLOHMANN_JSON_PASTE(NLOHMANN_JSON_TO, __VA_ARGS__)) } \\\n    inline void from_json(const nlohmann::json& nlohmann_json_j, Type& nlohmann_json_t) { NLOHMANN_JSON_EXPAND(NLOHMANN_JSON_PASTE(NLOHMANN_JSON_FROM, __VA_ARGS__)) }\n\n#define NLOHMANN_DEFINE_TYPE_NON_INTRUSIVE_ONLY_SERIALIZE(Type, ...)  \\\n    inline void to_json(nlohmann::json& nlohmann_json_j, const Type& nlohmann_json_t) { NLOHMANN_JSON_EXPAND(NLOHMANN_JSON_PASTE(NLOHMANN_JSON_TO, __VA_ARGS__)) }\n\n#define NLOHMANN_DEFINE_TYPE_NON_INTRUSIVE_WITH_DEFAULT(Type, ...)  \\\n    inline void to_json(nlohmann::json& nlohmann_json_j, const Type& nlohmann_json_t) { NLOHMANN_JSON_EXPAND(NLOHMANN_JSON_PASTE(NLOHMANN_JSON_TO, __VA_ARGS__)) } \\\n    inline void from_json(const nlohmann::json& nlohmann_json_j, Type& nlohmann_json_t) { const Type nlohmann_json_default_obj{}; NLOHMANN_JSON_EXPAND(NLOHMANN_JSON_PASTE(NLOHMANN_JSON_FROM_WITH_DEFAULT, __VA_ARGS__)) }\n\n// inspired from https://stackoverflow.com/a/26745591\n// allows to call any std function as if (e.g. with begin):\n// using std::begin; begin(x);\n//\n// it allows using the detected idiom to retrieve the return type\n// of such an expression\n#define NLOHMANN_CAN_CALL_STD_FUNC_IMPL(std_name)                                 \\\n    namespace detail {                                                            \\\n    using std::std_name;                                                          \\\n    \\\n    template<typename... T>                                                       \\\n    using result_of_##std_name = decltype(std_name(std::declval<T>()...));        \\\n    }                                                                             \\\n    \\\n    namespace detail2 {                                                           \\\n    struct std_name##_tag                                                         \\\n    {                                                                             \\\n    };                                                                            \\\n    \\\n    template<typename... T>                                                       \\\n    std_name##_tag std_name(T&&...);                                              \\\n    \\\n    template<typename... T>                                                       \\\n    using result_of_##std_name = decltype(std_name(std::declval<T>()...));        \\\n    \\\n    template<typename... T>                                                       \\\n    struct would_call_std_##std_name                                              \\\n    {                                                                             \\\n        static constexpr auto const value = ::nlohmann::detail::                  \\\n                                            is_detected_exact<std_name##_tag, result_of_##std_name, T...>::value; \\\n    };                                                                            \\\n    } /* namespace detail2 */ \\\n    \\\n    template<typename... T>                                                       \\\n    struct would_call_std_##std_name : detail2::would_call_std_##std_name<T...>   \\\n    {                                                                             \\\n    }\n\n#ifndef JSON_USE_IMPLICIT_CONVERSIONS\n    #define JSON_USE_IMPLICIT_CONVERSIONS 1\n#endif\n\n#if JSON_USE_IMPLICIT_CONVERSIONS\n    #define JSON_EXPLICIT\n#else\n    #define JSON_EXPLICIT explicit\n#endif\n\n#ifndef JSON_DISABLE_ENUM_SERIALIZATION\n    #define JSON_DISABLE_ENUM_SERIALIZATION 0\n#endif\n\n#ifndef JSON_USE_GLOBAL_UDLS\n    #define JSON_USE_GLOBAL_UDLS 1\n#endif\n\n#if JSON_HAS_THREE_WAY_COMPARISON\n    #include <compare> // partial_ordering\n#endif\n\nNLOHMANN_JSON_NAMESPACE_BEGIN\nnamespace detail\n{\n\n///////////////////////////\n// JSON type enumeration //\n///////////////////////////\n\n/*!\n@brief the JSON type enumeration\n\nThis enumeration collects the different JSON types. It is internally used to\ndistinguish the stored values, and the functions @ref basic_json::is_null(),\n@ref basic_json::is_object(), @ref basic_json::is_array(),\n@ref basic_json::is_string(), @ref basic_json::is_boolean(),\n@ref basic_json::is_number() (with @ref basic_json::is_number_integer(),\n@ref basic_json::is_number_unsigned(), and @ref basic_json::is_number_float()),\n@ref basic_json::is_discarded(), @ref basic_json::is_primitive(), and\n@ref basic_json::is_structured() rely on it.\n\n@note There are three enumeration entries (number_integer, number_unsigned, and\nnumber_float), because the library distinguishes these three types for numbers:\n@ref basic_json::number_unsigned_t is used for unsigned integers,\n@ref basic_json::number_integer_t is used for signed integers, and\n@ref basic_json::number_float_t is used for floating-point numbers or to\napproximate integers which do not fit in the limits of their respective type.\n\n@sa see @ref basic_json::basic_json(const value_t value_type) -- create a JSON\nvalue with the default value for a given type\n\n@since version 1.0.0\n*/\nenum class value_t : std::uint8_t\n{\n    null,             ///< null value\n    object,           ///< object (unordered set of name/value pairs)\n    array,            ///< array (ordered collection of values)\n    string,           ///< string value\n    boolean,          ///< boolean value\n    number_integer,   ///< number value (signed integer)\n    number_unsigned,  ///< number value (unsigned integer)\n    number_float,     ///< number value (floating-point)\n    binary,           ///< binary array (ordered collection of bytes)\n    discarded         ///< discarded by the parser callback function\n};\n\n/*!\n@brief comparison operator for JSON types\n\nReturns an ordering that is similar to Python:\n- order: null < boolean < number < object < array < string < binary\n- furthermore, each type is not smaller than itself\n- discarded values are not comparable\n- binary is represented as a b\"\" string in python and directly comparable to a\n  string; however, making a binary array directly comparable with a string would\n  be surprising behavior in a JSON file.\n\n@since version 1.0.0\n*/\n#if JSON_HAS_THREE_WAY_COMPARISON\n    inline std::partial_ordering operator<=>(const value_t lhs, const value_t rhs) noexcept // *NOPAD*\n#else\n    inline bool operator<(const value_t lhs, const value_t rhs) noexcept\n#endif\n{\n    static constexpr std::array<std::uint8_t, 9> order = {{\n            0 /* null */, 3 /* object */, 4 /* array */, 5 /* string */,\n            1 /* boolean */, 2 /* integer */, 2 /* unsigned */, 2 /* float */,\n            6 /* binary */\n        }\n    };\n\n    const auto l_index = static_cast<std::size_t>(lhs);\n    const auto r_index = static_cast<std::size_t>(rhs);\n#if JSON_HAS_THREE_WAY_COMPARISON\n    if (l_index < order.size() && r_index < order.size())\n    {\n        return order[l_index] <=> order[r_index]; // *NOPAD*\n    }\n    return std::partial_ordering::unordered;\n#else\n    return l_index < order.size() && r_index < order.size() && order[l_index] < order[r_index];\n#endif\n}\n\n// GCC selects the built-in operator< over an operator rewritten from\n// a user-defined spaceship operator\n// Clang, MSVC, and ICC select the rewritten candidate\n// (see GCC bug https://gcc.gnu.org/bugzilla/show_bug.cgi?id=105200)\n#if JSON_HAS_THREE_WAY_COMPARISON && defined(__GNUC__)\ninline bool operator<(const value_t lhs, const value_t rhs) noexcept\n{\n    return std::is_lt(lhs <=> rhs); // *NOPAD*\n}\n#endif\n\n}  // namespace detail\nNLOHMANN_JSON_NAMESPACE_END\n\n// #include <nlohmann/detail/string_escape.hpp>\n//     __ _____ _____ _____\n//  __|  |   __|     |   | |  JSON for Modern C++\n// |  |  |__   |  |  | | | |  version 3.11.3\n// |_____|_____|_____|_|___|  https://github.com/nlohmann/json\n//\n// SPDX-FileCopyrightText: 2013-2023 Niels Lohmann <https://nlohmann.me>\n// SPDX-License-Identifier: MIT\n\n\n\n// #include <nlohmann/detail/abi_macros.hpp>\n\n\nNLOHMANN_JSON_NAMESPACE_BEGIN\nnamespace detail\n{\n\n/*!\n@brief replace all occurrences of a substring by another string\n\n@param[in,out] s  the string to manipulate; changed so that all\n               occurrences of @a f are replaced with @a t\n@param[in]     f  the substring to replace with @a t\n@param[in]     t  the string to replace @a f\n\n@pre The search string @a f must not be empty. **This precondition is\nenforced with an assertion.**\n\n@since version 2.0.0\n*/\ntemplate<typename StringType>\ninline void replace_substring(StringType& s, const StringType& f,\n                              const StringType& t)\n{\n    JSON_ASSERT(!f.empty());\n    for (auto pos = s.find(f);                // find first occurrence of f\n            pos != StringType::npos;          // make sure f was found\n            s.replace(pos, f.size(), t),      // replace with t, and\n            pos = s.find(f, pos + t.size()))  // find next occurrence of f\n    {}\n}\n\n/*!\n * @brief string escaping as described in RFC 6901 (Sect. 4)\n * @param[in] s string to escape\n * @return    escaped string\n *\n * Note the order of escaping \"~\" to \"~0\" and \"/\" to \"~1\" is important.\n */\ntemplate<typename StringType>\ninline StringType escape(StringType s)\n{\n    replace_substring(s, StringType{\"~\"}, StringType{\"~0\"});\n    replace_substring(s, StringType{\"/\"}, StringType{\"~1\"});\n    return s;\n}\n\n/*!\n * @brief string unescaping as described in RFC 6901 (Sect. 4)\n * @param[in] s string to unescape\n * @return    unescaped string\n *\n * Note the order of escaping \"~1\" to \"/\" and \"~0\" to \"~\" is important.\n */\ntemplate<typename StringType>\nstatic void unescape(StringType& s)\n{\n    replace_substring(s, StringType{\"~1\"}, StringType{\"/\"});\n    replace_substring(s, StringType{\"~0\"}, StringType{\"~\"});\n}\n\n}  // namespace detail\nNLOHMANN_JSON_NAMESPACE_END\n\n// #include <nlohmann/detail/input/position_t.hpp>\n//     __ _____ _____ _____\n//  __|  |   __|     |   | |  JSON for Modern C++\n// |  |  |__   |  |  | | | |  version 3.11.3\n// |_____|_____|_____|_|___|  https://github.com/nlohmann/json\n//\n// SPDX-FileCopyrightText: 2013-2023 Niels Lohmann <https://nlohmann.me>\n// SPDX-License-Identifier: MIT\n\n\n\n#include <cstddef> // size_t\n\n// #include <nlohmann/detail/abi_macros.hpp>\n\n\nNLOHMANN_JSON_NAMESPACE_BEGIN\nnamespace detail\n{\n\n/// struct to capture the start position of the current token\nstruct position_t\n{\n    /// the total number of characters read\n    std::size_t chars_read_total = 0;\n    /// the number of characters read in the current line\n    std::size_t chars_read_current_line = 0;\n    /// the number of lines read\n    std::size_t lines_read = 0;\n\n    /// conversion to size_t to preserve SAX interface\n    constexpr operator size_t() const\n    {\n        return chars_read_total;\n    }\n};\n\n}  // namespace detail\nNLOHMANN_JSON_NAMESPACE_END\n\n// #include <nlohmann/detail/macro_scope.hpp>\n\n// #include <nlohmann/detail/meta/cpp_future.hpp>\n//     __ _____ _____ _____\n//  __|  |   __|     |   | |  JSON for Modern C++\n// |  |  |__   |  |  | | | |  version 3.11.3\n// |_____|_____|_____|_|___|  https://github.com/nlohmann/json\n//\n// SPDX-FileCopyrightText: 2013-2023 Niels Lohmann <https://nlohmann.me>\n// SPDX-FileCopyrightText: 2018 The Abseil Authors\n// SPDX-License-Identifier: MIT\n\n\n\n#include <array> // array\n#include <cstddef> // size_t\n#include <type_traits> // conditional, enable_if, false_type, integral_constant, is_constructible, is_integral, is_same, remove_cv, remove_reference, true_type\n#include <utility> // index_sequence, make_index_sequence, index_sequence_for\n\n// #include <nlohmann/detail/macro_scope.hpp>\n\n\nNLOHMANN_JSON_NAMESPACE_BEGIN\nnamespace detail\n{\n\ntemplate<typename T>\nusing uncvref_t = typename std::remove_cv<typename std::remove_reference<T>::type>::type;\n\n#ifdef JSON_HAS_CPP_14\n\n// the following utilities are natively available in C++14\nusing std::enable_if_t;\nusing std::index_sequence;\nusing std::make_index_sequence;\nusing std::index_sequence_for;\n\n#else\n\n// alias templates to reduce boilerplate\ntemplate<bool B, typename T = void>\nusing enable_if_t = typename std::enable_if<B, T>::type;\n\n// The following code is taken from https://github.com/abseil/abseil-cpp/blob/10cb35e459f5ecca5b2ff107635da0bfa41011b4/absl/utility/utility.h\n// which is part of Google Abseil (https://github.com/abseil/abseil-cpp), licensed under the Apache License 2.0.\n\n//// START OF CODE FROM GOOGLE ABSEIL\n\n// integer_sequence\n//\n// Class template representing a compile-time integer sequence. An instantiation\n// of `integer_sequence<T, Ints...>` has a sequence of integers encoded in its\n// type through its template arguments (which is a common need when\n// working with C++11 variadic templates). `absl::integer_sequence` is designed\n// to be a drop-in replacement for C++14's `std::integer_sequence`.\n//\n// Example:\n//\n//   template< class T, T... Ints >\n//   void user_function(integer_sequence<T, Ints...>);\n//\n//   int main()\n//   {\n//     // user_function's `T` will be deduced to `int` and `Ints...`\n//     // will be deduced to `0, 1, 2, 3, 4`.\n//     user_function(make_integer_sequence<int, 5>());\n//   }\ntemplate <typename T, T... Ints>\nstruct integer_sequence\n{\n    using value_type = T;\n    static constexpr std::size_t size() noexcept\n    {\n        return sizeof...(Ints);\n    }\n};\n\n// index_sequence\n//\n// A helper template for an `integer_sequence` of `size_t`,\n// `absl::index_sequence` is designed to be a drop-in replacement for C++14's\n// `std::index_sequence`.\ntemplate <size_t... Ints>\nusing index_sequence = integer_sequence<size_t, Ints...>;\n\nnamespace utility_internal\n{\n\ntemplate <typename Seq, size_t SeqSize, size_t Rem>\nstruct Extend;\n\n// Note that SeqSize == sizeof...(Ints). It's passed explicitly for efficiency.\ntemplate <typename T, T... Ints, size_t SeqSize>\nstruct Extend<integer_sequence<T, Ints...>, SeqSize, 0>\n{\n    using type = integer_sequence < T, Ints..., (Ints + SeqSize)... >;\n};\n\ntemplate <typename T, T... Ints, size_t SeqSize>\nstruct Extend<integer_sequence<T, Ints...>, SeqSize, 1>\n{\n    using type = integer_sequence < T, Ints..., (Ints + SeqSize)..., 2 * SeqSize >;\n};\n\n// Recursion helper for 'make_integer_sequence<T, N>'.\n// 'Gen<T, N>::type' is an alias for 'integer_sequence<T, 0, 1, ... N-1>'.\ntemplate <typename T, size_t N>\nstruct Gen\n{\n    using type =\n        typename Extend < typename Gen < T, N / 2 >::type, N / 2, N % 2 >::type;\n};\n\ntemplate <typename T>\nstruct Gen<T, 0>\n{\n    using type = integer_sequence<T>;\n};\n\n}  // namespace utility_internal\n\n// Compile-time sequences of integers\n\n// make_integer_sequence\n//\n// This template alias is equivalent to\n// `integer_sequence<int, 0, 1, ..., N-1>`, and is designed to be a drop-in\n// replacement for C++14's `std::make_integer_sequence`.\ntemplate <typename T, T N>\nusing make_integer_sequence = typename utility_internal::Gen<T, N>::type;\n\n// make_index_sequence\n//\n// This template alias is equivalent to `index_sequence<0, 1, ..., N-1>`,\n// and is designed to be a drop-in replacement for C++14's\n// `std::make_index_sequence`.\ntemplate <size_t N>\nusing make_index_sequence = make_integer_sequence<size_t, N>;\n\n// index_sequence_for\n//\n// Converts a typename pack into an index sequence of the same length, and\n// is designed to be a drop-in replacement for C++14's\n// `std::index_sequence_for()`\ntemplate <typename... Ts>\nusing index_sequence_for = make_index_sequence<sizeof...(Ts)>;\n\n//// END OF CODE FROM GOOGLE ABSEIL\n\n#endif\n\n// dispatch utility (taken from ranges-v3)\ntemplate<unsigned N> struct priority_tag : priority_tag < N - 1 > {};\ntemplate<> struct priority_tag<0> {};\n\n// taken from ranges-v3\ntemplate<typename T>\nstruct static_const\n{\n    static JSON_INLINE_VARIABLE constexpr T value{};\n};\n\n#ifndef JSON_HAS_CPP_17\n    template<typename T>\n    constexpr T static_const<T>::value;\n#endif\n\ntemplate<typename T, typename... Args>\ninline constexpr std::array<T, sizeof...(Args)> make_array(Args&& ... args)\n{\n    return std::array<T, sizeof...(Args)> {{static_cast<T>(std::forward<Args>(args))...}};\n}\n\n}  // namespace detail\nNLOHMANN_JSON_NAMESPACE_END\n\n// #include <nlohmann/detail/meta/type_traits.hpp>\n//     __ _____ _____ _____\n//  __|  |   __|     |   | |  JSON for Modern C++\n// |  |  |__   |  |  | | | |  version 3.11.3\n// |_____|_____|_____|_|___|  https://github.com/nlohmann/json\n//\n// SPDX-FileCopyrightText: 2013-2023 Niels Lohmann <https://nlohmann.me>\n// SPDX-License-Identifier: MIT\n\n\n\n#include <limits> // numeric_limits\n#include <type_traits> // false_type, is_constructible, is_integral, is_same, true_type\n#include <utility> // declval\n#include <tuple> // tuple\n#include <string> // char_traits\n\n// #include <nlohmann/detail/iterators/iterator_traits.hpp>\n//     __ _____ _____ _____\n//  __|  |   __|     |   | |  JSON for Modern C++\n// |  |  |__   |  |  | | | |  version 3.11.3\n// |_____|_____|_____|_|___|  https://github.com/nlohmann/json\n//\n// SPDX-FileCopyrightText: 2013-2023 Niels Lohmann <https://nlohmann.me>\n// SPDX-License-Identifier: MIT\n\n\n\n#include <iterator> // random_access_iterator_tag\n\n// #include <nlohmann/detail/abi_macros.hpp>\n\n// #include <nlohmann/detail/meta/void_t.hpp>\n\n// #include <nlohmann/detail/meta/cpp_future.hpp>\n\n\nNLOHMANN_JSON_NAMESPACE_BEGIN\nnamespace detail\n{\n\ntemplate<typename It, typename = void>\nstruct iterator_types {};\n\ntemplate<typename It>\nstruct iterator_types <\n    It,\n    void_t<typename It::difference_type, typename It::value_type, typename It::pointer,\n    typename It::reference, typename It::iterator_category >>\n{\n    using difference_type = typename It::difference_type;\n    using value_type = typename It::value_type;\n    using pointer = typename It::pointer;\n    using reference = typename It::reference;\n    using iterator_category = typename It::iterator_category;\n};\n\n// This is required as some compilers implement std::iterator_traits in a way that\n// doesn't work with SFINAE. See https://github.com/nlohmann/json/issues/1341.\ntemplate<typename T, typename = void>\nstruct iterator_traits\n{\n};\n\ntemplate<typename T>\nstruct iterator_traits < T, enable_if_t < !std::is_pointer<T>::value >>\n            : iterator_types<T>\n{\n};\n\ntemplate<typename T>\nstruct iterator_traits<T*, enable_if_t<std::is_object<T>::value>>\n{\n    using iterator_category = std::random_access_iterator_tag;\n    using value_type = T;\n    using difference_type = ptrdiff_t;\n    using pointer = T*;\n    using reference = T&;\n};\n\n}  // namespace detail\nNLOHMANN_JSON_NAMESPACE_END\n\n// #include <nlohmann/detail/macro_scope.hpp>\n\n// #include <nlohmann/detail/meta/call_std/begin.hpp>\n//     __ _____ _____ _____\n//  __|  |   __|     |   | |  JSON for Modern C++\n// |  |  |__   |  |  | | | |  version 3.11.3\n// |_____|_____|_____|_|___|  https://github.com/nlohmann/json\n//\n// SPDX-FileCopyrightText: 2013-2023 Niels Lohmann <https://nlohmann.me>\n// SPDX-License-Identifier: MIT\n\n\n\n// #include <nlohmann/detail/macro_scope.hpp>\n\n\nNLOHMANN_JSON_NAMESPACE_BEGIN\n\nNLOHMANN_CAN_CALL_STD_FUNC_IMPL(begin);\n\nNLOHMANN_JSON_NAMESPACE_END\n\n// #include <nlohmann/detail/meta/call_std/end.hpp>\n//     __ _____ _____ _____\n//  __|  |   __|     |   | |  JSON for Modern C++\n// |  |  |__   |  |  | | | |  version 3.11.3\n// |_____|_____|_____|_|___|  https://github.com/nlohmann/json\n//\n// SPDX-FileCopyrightText: 2013-2023 Niels Lohmann <https://nlohmann.me>\n// SPDX-License-Identifier: MIT\n\n\n\n// #include <nlohmann/detail/macro_scope.hpp>\n\n\nNLOHMANN_JSON_NAMESPACE_BEGIN\n\nNLOHMANN_CAN_CALL_STD_FUNC_IMPL(end);\n\nNLOHMANN_JSON_NAMESPACE_END\n\n// #include <nlohmann/detail/meta/cpp_future.hpp>\n\n// #include <nlohmann/detail/meta/detected.hpp>\n\n// #include <nlohmann/json_fwd.hpp>\n//     __ _____ _____ _____\n//  __|  |   __|     |   | |  JSON for Modern C++\n// |  |  |__   |  |  | | | |  version 3.11.3\n// |_____|_____|_____|_|___|  https://github.com/nlohmann/json\n//\n// SPDX-FileCopyrightText: 2013-2023 Niels Lohmann <https://nlohmann.me>\n// SPDX-License-Identifier: MIT\n\n#ifndef INCLUDE_NLOHMANN_JSON_FWD_HPP_\n    #define INCLUDE_NLOHMANN_JSON_FWD_HPP_\n\n    #include <cstdint> // int64_t, uint64_t\n    #include <map> // map\n    #include <memory> // allocator\n    #include <string> // string\n    #include <vector> // vector\n\n    // #include <nlohmann/detail/abi_macros.hpp>\n\n\n    /*!\n    @brief namespace for Niels Lohmann\n    @see https://github.com/nlohmann\n    @since version 1.0.0\n    */\n    NLOHMANN_JSON_NAMESPACE_BEGIN\n\n    /*!\n    @brief default JSONSerializer template argument\n\n    This serializer ignores the template arguments and uses ADL\n    ([argument-dependent lookup](https://en.cppreference.com/w/cpp/language/adl))\n    for serialization.\n    */\n    template<typename T = void, typename SFINAE = void>\n    struct adl_serializer;\n\n    /// a class to store JSON values\n    /// @sa https://json.nlohmann.me/api/basic_json/\n    template<template<typename U, typename V, typename... Args> class ObjectType =\n    std::map,\n    template<typename U, typename... Args> class ArrayType = std::vector,\n    class StringType = std::string, class BooleanType = bool,\n    class NumberIntegerType = std::int64_t,\n    class NumberUnsignedType = std::uint64_t,\n    class NumberFloatType = double,\n    template<typename U> class AllocatorType = std::allocator,\n    template<typename T, typename SFINAE = void> class JSONSerializer =\n    adl_serializer,\n    class BinaryType = std::vector<std::uint8_t>, // cppcheck-suppress syntaxError\n    class CustomBaseClass = void>\n    class basic_json;\n\n    /// @brief JSON Pointer defines a string syntax for identifying a specific value within a JSON document\n    /// @sa https://json.nlohmann.me/api/json_pointer/\n    template<typename RefStringType>\n    class json_pointer;\n\n    /*!\n    @brief default specialization\n    @sa https://json.nlohmann.me/api/json/\n    */\n    using json = basic_json<>;\n\n    /// @brief a minimal map-like container that preserves insertion order\n    /// @sa https://json.nlohmann.me/api/ordered_map/\n    template<class Key, class T, class IgnoredLess, class Allocator>\n    struct ordered_map;\n\n    /// @brief specialization that maintains the insertion order of object keys\n    /// @sa https://json.nlohmann.me/api/ordered_json/\n    using ordered_json = basic_json<nlohmann::ordered_map>;\n\n    NLOHMANN_JSON_NAMESPACE_END\n\n#endif  // INCLUDE_NLOHMANN_JSON_FWD_HPP_\n\n\nNLOHMANN_JSON_NAMESPACE_BEGIN\n/*!\n@brief detail namespace with internal helper functions\n\nThis namespace collects functions that should not be exposed,\nimplementations of some @ref basic_json methods, and meta-programming helpers.\n\n@since version 2.1.0\n*/\nnamespace detail\n{\n\n/////////////\n// helpers //\n/////////////\n\n// Note to maintainers:\n//\n// Every trait in this file expects a non CV-qualified type.\n// The only exceptions are in the 'aliases for detected' section\n// (i.e. those of the form: decltype(T::member_function(std::declval<T>())))\n//\n// In this case, T has to be properly CV-qualified to constraint the function arguments\n// (e.g. to_json(BasicJsonType&, const T&))\n\ntemplate<typename> struct is_basic_json : std::false_type {};\n\nNLOHMANN_BASIC_JSON_TPL_DECLARATION\nstruct is_basic_json<NLOHMANN_BASIC_JSON_TPL> : std::true_type {};\n\n// used by exceptions create() member functions\n// true_type for pointer to possibly cv-qualified basic_json or std::nullptr_t\n// false_type otherwise\ntemplate<typename BasicJsonContext>\nstruct is_basic_json_context :\n    std::integral_constant < bool,\n    is_basic_json<typename std::remove_cv<typename std::remove_pointer<BasicJsonContext>::type>::type>::value\n    || std::is_same<BasicJsonContext, std::nullptr_t>::value >\n{};\n\n//////////////////////\n// json_ref helpers //\n//////////////////////\n\ntemplate<typename>\nclass json_ref;\n\ntemplate<typename>\nstruct is_json_ref : std::false_type {};\n\ntemplate<typename T>\nstruct is_json_ref<json_ref<T>> : std::true_type {};\n\n//////////////////////////\n// aliases for detected //\n//////////////////////////\n\ntemplate<typename T>\nusing mapped_type_t = typename T::mapped_type;\n\ntemplate<typename T>\nusing key_type_t = typename T::key_type;\n\ntemplate<typename T>\nusing value_type_t = typename T::value_type;\n\ntemplate<typename T>\nusing difference_type_t = typename T::difference_type;\n\ntemplate<typename T>\nusing pointer_t = typename T::pointer;\n\ntemplate<typename T>\nusing reference_t = typename T::reference;\n\ntemplate<typename T>\nusing iterator_category_t = typename T::iterator_category;\n\ntemplate<typename T, typename... Args>\nusing to_json_function = decltype(T::to_json(std::declval<Args>()...));\n\ntemplate<typename T, typename... Args>\nusing from_json_function = decltype(T::from_json(std::declval<Args>()...));\n\ntemplate<typename T, typename U>\nusing get_template_function = decltype(std::declval<T>().template get<U>());\n\n// trait checking if JSONSerializer<T>::from_json(json const&, udt&) exists\ntemplate<typename BasicJsonType, typename T, typename = void>\nstruct has_from_json : std::false_type {};\n\n// trait checking if j.get<T> is valid\n// use this trait instead of std::is_constructible or std::is_convertible,\n// both rely on, or make use of implicit conversions, and thus fail when T\n// has several constructors/operator= (see https://github.com/nlohmann/json/issues/958)\ntemplate <typename BasicJsonType, typename T>\nstruct is_getable\n{\n    static constexpr bool value = is_detected<get_template_function, const BasicJsonType&, T>::value;\n};\n\ntemplate<typename BasicJsonType, typename T>\nstruct has_from_json < BasicJsonType, T, enable_if_t < !is_basic_json<T>::value >>\n{\n    using serializer = typename BasicJsonType::template json_serializer<T, void>;\n\n    static constexpr bool value =\n        is_detected_exact<void, from_json_function, serializer,\n        const BasicJsonType&, T&>::value;\n};\n\n// This trait checks if JSONSerializer<T>::from_json(json const&) exists\n// this overload is used for non-default-constructible user-defined-types\ntemplate<typename BasicJsonType, typename T, typename = void>\nstruct has_non_default_from_json : std::false_type {};\n\ntemplate<typename BasicJsonType, typename T>\nstruct has_non_default_from_json < BasicJsonType, T, enable_if_t < !is_basic_json<T>::value >>\n{\n    using serializer = typename BasicJsonType::template json_serializer<T, void>;\n\n    static constexpr bool value =\n        is_detected_exact<T, from_json_function, serializer,\n        const BasicJsonType&>::value;\n};\n\n// This trait checks if BasicJsonType::json_serializer<T>::to_json exists\n// Do not evaluate the trait when T is a basic_json type, to avoid template instantiation infinite recursion.\ntemplate<typename BasicJsonType, typename T, typename = void>\nstruct has_to_json : std::false_type {};\n\ntemplate<typename BasicJsonType, typename T>\nstruct has_to_json < BasicJsonType, T, enable_if_t < !is_basic_json<T>::value >>\n{\n    using serializer = typename BasicJsonType::template json_serializer<T, void>;\n\n    static constexpr bool value =\n        is_detected_exact<void, to_json_function, serializer, BasicJsonType&,\n        T>::value;\n};\n\ntemplate<typename T>\nusing detect_key_compare = typename T::key_compare;\n\ntemplate<typename T>\nstruct has_key_compare : std::integral_constant<bool, is_detected<detect_key_compare, T>::value> {};\n\n// obtains the actual object key comparator\ntemplate<typename BasicJsonType>\nstruct actual_object_comparator\n{\n    using object_t = typename BasicJsonType::object_t;\n    using object_comparator_t = typename BasicJsonType::default_object_comparator_t;\n    using type = typename std::conditional < has_key_compare<object_t>::value,\n          typename object_t::key_compare, object_comparator_t>::type;\n};\n\ntemplate<typename BasicJsonType>\nusing actual_object_comparator_t = typename actual_object_comparator<BasicJsonType>::type;\n\n/////////////////\n// char_traits //\n/////////////////\n\n// Primary template of char_traits calls std char_traits\ntemplate<typename T>\nstruct char_traits : std::char_traits<T>\n{};\n\n// Explicitly define char traits for unsigned char since it is not standard\ntemplate<>\nstruct char_traits<unsigned char> : std::char_traits<char>\n{\n    using char_type = unsigned char;\n    using int_type = uint64_t;\n\n    // Redefine to_int_type function\n    static int_type to_int_type(char_type c) noexcept\n    {\n        return static_cast<int_type>(c);\n    }\n\n    static char_type to_char_type(int_type i) noexcept\n    {\n        return static_cast<char_type>(i);\n    }\n\n    static constexpr int_type eof() noexcept\n    {\n        return static_cast<int_type>(EOF);\n    }\n};\n\n// Explicitly define char traits for signed char since it is not standard\ntemplate<>\nstruct char_traits<signed char> : std::char_traits<char>\n{\n    using char_type = signed char;\n    using int_type = uint64_t;\n\n    // Redefine to_int_type function\n    static int_type to_int_type(char_type c) noexcept\n    {\n        return static_cast<int_type>(c);\n    }\n\n    static char_type to_char_type(int_type i) noexcept\n    {\n        return static_cast<char_type>(i);\n    }\n\n    static constexpr int_type eof() noexcept\n    {\n        return static_cast<int_type>(EOF);\n    }\n};\n\n///////////////////\n// is_ functions //\n///////////////////\n\n// https://en.cppreference.com/w/cpp/types/conjunction\ntemplate<class...> struct conjunction : std::true_type { };\ntemplate<class B> struct conjunction<B> : B { };\ntemplate<class B, class... Bn>\nstruct conjunction<B, Bn...>\n: std::conditional<static_cast<bool>(B::value), conjunction<Bn...>, B>::type {};\n\n// https://en.cppreference.com/w/cpp/types/negation\ntemplate<class B> struct negation : std::integral_constant < bool, !B::value > { };\n\n// Reimplementation of is_constructible and is_default_constructible, due to them being broken for\n// std::pair and std::tuple until LWG 2367 fix (see https://cplusplus.github.io/LWG/lwg-defects.html#2367).\n// This causes compile errors in e.g. clang 3.5 or gcc 4.9.\ntemplate <typename T>\nstruct is_default_constructible : std::is_default_constructible<T> {};\n\ntemplate <typename T1, typename T2>\nstruct is_default_constructible<std::pair<T1, T2>>\n            : conjunction<is_default_constructible<T1>, is_default_constructible<T2>> {};\n\ntemplate <typename T1, typename T2>\nstruct is_default_constructible<const std::pair<T1, T2>>\n            : conjunction<is_default_constructible<T1>, is_default_constructible<T2>> {};\n\ntemplate <typename... Ts>\nstruct is_default_constructible<std::tuple<Ts...>>\n            : conjunction<is_default_constructible<Ts>...> {};\n\ntemplate <typename... Ts>\nstruct is_default_constructible<const std::tuple<Ts...>>\n            : conjunction<is_default_constructible<Ts>...> {};\n\ntemplate <typename T, typename... Args>\nstruct is_constructible : std::is_constructible<T, Args...> {};\n\ntemplate <typename T1, typename T2>\nstruct is_constructible<std::pair<T1, T2>> : is_default_constructible<std::pair<T1, T2>> {};\n\ntemplate <typename T1, typename T2>\nstruct is_constructible<const std::pair<T1, T2>> : is_default_constructible<const std::pair<T1, T2>> {};\n\ntemplate <typename... Ts>\nstruct is_constructible<std::tuple<Ts...>> : is_default_constructible<std::tuple<Ts...>> {};\n\ntemplate <typename... Ts>\nstruct is_constructible<const std::tuple<Ts...>> : is_default_constructible<const std::tuple<Ts...>> {};\n\ntemplate<typename T, typename = void>\nstruct is_iterator_traits : std::false_type {};\n\ntemplate<typename T>\nstruct is_iterator_traits<iterator_traits<T>>\n{\n  private:\n    using traits = iterator_traits<T>;\n\n  public:\n    static constexpr auto value =\n        is_detected<value_type_t, traits>::value &&\n        is_detected<difference_type_t, traits>::value &&\n        is_detected<pointer_t, traits>::value &&\n        is_detected<iterator_category_t, traits>::value &&\n        is_detected<reference_t, traits>::value;\n};\n\ntemplate<typename T>\nstruct is_range\n{\n  private:\n    using t_ref = typename std::add_lvalue_reference<T>::type;\n\n    using iterator = detected_t<result_of_begin, t_ref>;\n    using sentinel = detected_t<result_of_end, t_ref>;\n\n    // to be 100% correct, it should use https://en.cppreference.com/w/cpp/iterator/input_or_output_iterator\n    // and https://en.cppreference.com/w/cpp/iterator/sentinel_for\n    // but reimplementing these would be too much work, as a lot of other concepts are used underneath\n    static constexpr auto is_iterator_begin =\n        is_iterator_traits<iterator_traits<iterator>>::value;\n\n  public:\n    static constexpr bool value = !std::is_same<iterator, nonesuch>::value && !std::is_same<sentinel, nonesuch>::value && is_iterator_begin;\n};\n\ntemplate<typename R>\nusing iterator_t = enable_if_t<is_range<R>::value, result_of_begin<decltype(std::declval<R&>())>>;\n\ntemplate<typename T>\nusing range_value_t = value_type_t<iterator_traits<iterator_t<T>>>;\n\n// The following implementation of is_complete_type is taken from\n// https://blogs.msdn.microsoft.com/vcblog/2015/12/02/partial-support-for-expression-sfinae-in-vs-2015-update-1/\n// and is written by Xiang Fan who agreed to using it in this library.\n\ntemplate<typename T, typename = void>\nstruct is_complete_type : std::false_type {};\n\ntemplate<typename T>\nstruct is_complete_type<T, decltype(void(sizeof(T)))> : std::true_type {};\n\ntemplate<typename BasicJsonType, typename CompatibleObjectType,\n         typename = void>\nstruct is_compatible_object_type_impl : std::false_type {};\n\ntemplate<typename BasicJsonType, typename CompatibleObjectType>\nstruct is_compatible_object_type_impl <\n    BasicJsonType, CompatibleObjectType,\n    enable_if_t < is_detected<mapped_type_t, CompatibleObjectType>::value&&\n    is_detected<key_type_t, CompatibleObjectType>::value >>\n{\n    using object_t = typename BasicJsonType::object_t;\n\n    // macOS's is_constructible does not play well with nonesuch...\n    static constexpr bool value =\n        is_constructible<typename object_t::key_type,\n        typename CompatibleObjectType::key_type>::value &&\n        is_constructible<typename object_t::mapped_type,\n        typename CompatibleObjectType::mapped_type>::value;\n};\n\ntemplate<typename BasicJsonType, typename CompatibleObjectType>\nstruct is_compatible_object_type\n    : is_compatible_object_type_impl<BasicJsonType, CompatibleObjectType> {};\n\ntemplate<typename BasicJsonType, typename ConstructibleObjectType,\n         typename = void>\nstruct is_constructible_object_type_impl : std::false_type {};\n\ntemplate<typename BasicJsonType, typename ConstructibleObjectType>\nstruct is_constructible_object_type_impl <\n    BasicJsonType, ConstructibleObjectType,\n    enable_if_t < is_detected<mapped_type_t, ConstructibleObjectType>::value&&\n    is_detected<key_type_t, ConstructibleObjectType>::value >>\n{\n    using object_t = typename BasicJsonType::object_t;\n\n    static constexpr bool value =\n        (is_default_constructible<ConstructibleObjectType>::value &&\n         (std::is_move_assignable<ConstructibleObjectType>::value ||\n          std::is_copy_assignable<ConstructibleObjectType>::value) &&\n         (is_constructible<typename ConstructibleObjectType::key_type,\n          typename object_t::key_type>::value &&\n          std::is_same <\n          typename object_t::mapped_type,\n          typename ConstructibleObjectType::mapped_type >::value)) ||\n        (has_from_json<BasicJsonType,\n         typename ConstructibleObjectType::mapped_type>::value ||\n         has_non_default_from_json <\n         BasicJsonType,\n         typename ConstructibleObjectType::mapped_type >::value);\n};\n\ntemplate<typename BasicJsonType, typename ConstructibleObjectType>\nstruct is_constructible_object_type\n    : is_constructible_object_type_impl<BasicJsonType,\n      ConstructibleObjectType> {};\n\ntemplate<typename BasicJsonType, typename CompatibleStringType>\nstruct is_compatible_string_type\n{\n    static constexpr auto value =\n        is_constructible<typename BasicJsonType::string_t, CompatibleStringType>::value;\n};\n\ntemplate<typename BasicJsonType, typename ConstructibleStringType>\nstruct is_constructible_string_type\n{\n    // launder type through decltype() to fix compilation failure on ICPC\n#ifdef __INTEL_COMPILER\n    using laundered_type = decltype(std::declval<ConstructibleStringType>());\n#else\n    using laundered_type = ConstructibleStringType;\n#endif\n\n    static constexpr auto value =\n        conjunction <\n        is_constructible<laundered_type, typename BasicJsonType::string_t>,\n        is_detected_exact<typename BasicJsonType::string_t::value_type,\n        value_type_t, laundered_type >>::value;\n};\n\ntemplate<typename BasicJsonType, typename CompatibleArrayType, typename = void>\nstruct is_compatible_array_type_impl : std::false_type {};\n\ntemplate<typename BasicJsonType, typename CompatibleArrayType>\nstruct is_compatible_array_type_impl <\n    BasicJsonType, CompatibleArrayType,\n    enable_if_t <\n    is_detected<iterator_t, CompatibleArrayType>::value&&\n    is_iterator_traits<iterator_traits<detected_t<iterator_t, CompatibleArrayType>>>::value&&\n// special case for types like std::filesystem::path whose iterator's value_type are themselves\n// c.f. https://github.com/nlohmann/json/pull/3073\n    !std::is_same<CompatibleArrayType, detected_t<range_value_t, CompatibleArrayType>>::value >>\n{\n    static constexpr bool value =\n        is_constructible<BasicJsonType,\n        range_value_t<CompatibleArrayType>>::value;\n};\n\ntemplate<typename BasicJsonType, typename CompatibleArrayType>\nstruct is_compatible_array_type\n    : is_compatible_array_type_impl<BasicJsonType, CompatibleArrayType> {};\n\ntemplate<typename BasicJsonType, typename ConstructibleArrayType, typename = void>\nstruct is_constructible_array_type_impl : std::false_type {};\n\ntemplate<typename BasicJsonType, typename ConstructibleArrayType>\nstruct is_constructible_array_type_impl <\n    BasicJsonType, ConstructibleArrayType,\n    enable_if_t<std::is_same<ConstructibleArrayType,\n    typename BasicJsonType::value_type>::value >>\n            : std::true_type {};\n\ntemplate<typename BasicJsonType, typename ConstructibleArrayType>\nstruct is_constructible_array_type_impl <\n    BasicJsonType, ConstructibleArrayType,\n    enable_if_t < !std::is_same<ConstructibleArrayType,\n    typename BasicJsonType::value_type>::value&&\n    !is_compatible_string_type<BasicJsonType, ConstructibleArrayType>::value&&\n    is_default_constructible<ConstructibleArrayType>::value&&\n(std::is_move_assignable<ConstructibleArrayType>::value ||\n std::is_copy_assignable<ConstructibleArrayType>::value)&&\nis_detected<iterator_t, ConstructibleArrayType>::value&&\nis_iterator_traits<iterator_traits<detected_t<iterator_t, ConstructibleArrayType>>>::value&&\nis_detected<range_value_t, ConstructibleArrayType>::value&&\n// special case for types like std::filesystem::path whose iterator's value_type are themselves\n// c.f. https://github.com/nlohmann/json/pull/3073\n!std::is_same<ConstructibleArrayType, detected_t<range_value_t, ConstructibleArrayType>>::value&&\n        is_complete_type <\n        detected_t<range_value_t, ConstructibleArrayType >>::value >>\n{\n    using value_type = range_value_t<ConstructibleArrayType>;\n\n    static constexpr bool value =\n        std::is_same<value_type,\n        typename BasicJsonType::array_t::value_type>::value ||\n        has_from_json<BasicJsonType,\n        value_type>::value ||\n        has_non_default_from_json <\n        BasicJsonType,\n        value_type >::value;\n};\n\ntemplate<typename BasicJsonType, typename ConstructibleArrayType>\nstruct is_constructible_array_type\n    : is_constructible_array_type_impl<BasicJsonType, ConstructibleArrayType> {};\n\ntemplate<typename RealIntegerType, typename CompatibleNumberIntegerType,\n         typename = void>\nstruct is_compatible_integer_type_impl : std::false_type {};\n\ntemplate<typename RealIntegerType, typename CompatibleNumberIntegerType>\nstruct is_compatible_integer_type_impl <\n    RealIntegerType, CompatibleNumberIntegerType,\n    enable_if_t < std::is_integral<RealIntegerType>::value&&\n    std::is_integral<CompatibleNumberIntegerType>::value&&\n    !std::is_same<bool, CompatibleNumberIntegerType>::value >>\n{\n    // is there an assert somewhere on overflows?\n    using RealLimits = std::numeric_limits<RealIntegerType>;\n    using CompatibleLimits = std::numeric_limits<CompatibleNumberIntegerType>;\n\n    static constexpr auto value =\n        is_constructible<RealIntegerType,\n        CompatibleNumberIntegerType>::value &&\n        CompatibleLimits::is_integer &&\n        RealLimits::is_signed == CompatibleLimits::is_signed;\n};\n\ntemplate<typename RealIntegerType, typename CompatibleNumberIntegerType>\nstruct is_compatible_integer_type\n    : is_compatible_integer_type_impl<RealIntegerType,\n      CompatibleNumberIntegerType> {};\n\ntemplate<typename BasicJsonType, typename CompatibleType, typename = void>\nstruct is_compatible_type_impl: std::false_type {};\n\ntemplate<typename BasicJsonType, typename CompatibleType>\nstruct is_compatible_type_impl <\n    BasicJsonType, CompatibleType,\n    enable_if_t<is_complete_type<CompatibleType>::value >>\n{\n    static constexpr bool value =\n        has_to_json<BasicJsonType, CompatibleType>::value;\n};\n\ntemplate<typename BasicJsonType, typename CompatibleType>\nstruct is_compatible_type\n    : is_compatible_type_impl<BasicJsonType, CompatibleType> {};\n\ntemplate<typename T1, typename T2>\nstruct is_constructible_tuple : std::false_type {};\n\ntemplate<typename T1, typename... Args>\nstruct is_constructible_tuple<T1, std::tuple<Args...>> : conjunction<is_constructible<T1, Args>...> {};\n\ntemplate<typename BasicJsonType, typename T>\nstruct is_json_iterator_of : std::false_type {};\n\ntemplate<typename BasicJsonType>\nstruct is_json_iterator_of<BasicJsonType, typename BasicJsonType::iterator> : std::true_type {};\n\ntemplate<typename BasicJsonType>\nstruct is_json_iterator_of<BasicJsonType, typename BasicJsonType::const_iterator> : std::true_type\n{};\n\n// checks if a given type T is a template specialization of Primary\ntemplate<template <typename...> class Primary, typename T>\nstruct is_specialization_of : std::false_type {};\n\ntemplate<template <typename...> class Primary, typename... Args>\nstruct is_specialization_of<Primary, Primary<Args...>> : std::true_type {};\n\ntemplate<typename T>\nusing is_json_pointer = is_specialization_of<::nlohmann::json_pointer, uncvref_t<T>>;\n\n// checks if A and B are comparable using Compare functor\ntemplate<typename Compare, typename A, typename B, typename = void>\nstruct is_comparable : std::false_type {};\n\ntemplate<typename Compare, typename A, typename B>\nstruct is_comparable<Compare, A, B, void_t<\ndecltype(std::declval<Compare>()(std::declval<A>(), std::declval<B>())),\ndecltype(std::declval<Compare>()(std::declval<B>(), std::declval<A>()))\n>> : std::true_type {};\n\ntemplate<typename T>\nusing detect_is_transparent = typename T::is_transparent;\n\n// type trait to check if KeyType can be used as object key (without a BasicJsonType)\n// see is_usable_as_basic_json_key_type below\ntemplate<typename Comparator, typename ObjectKeyType, typename KeyTypeCVRef, bool RequireTransparentComparator = true,\n         bool ExcludeObjectKeyType = RequireTransparentComparator, typename KeyType = uncvref_t<KeyTypeCVRef>>\nusing is_usable_as_key_type = typename std::conditional <\n                              is_comparable<Comparator, ObjectKeyType, KeyTypeCVRef>::value\n                              && !(ExcludeObjectKeyType && std::is_same<KeyType,\n                                   ObjectKeyType>::value)\n                              && (!RequireTransparentComparator\n                                  || is_detected <detect_is_transparent, Comparator>::value)\n                              && !is_json_pointer<KeyType>::value,\n                              std::true_type,\n                              std::false_type >::type;\n\n// type trait to check if KeyType can be used as object key\n// true if:\n//   - KeyType is comparable with BasicJsonType::object_t::key_type\n//   - if ExcludeObjectKeyType is true, KeyType is not BasicJsonType::object_t::key_type\n//   - the comparator is transparent or RequireTransparentComparator is false\n//   - KeyType is not a JSON iterator or json_pointer\ntemplate<typename BasicJsonType, typename KeyTypeCVRef, bool RequireTransparentComparator = true,\n         bool ExcludeObjectKeyType = RequireTransparentComparator, typename KeyType = uncvref_t<KeyTypeCVRef>>\nusing is_usable_as_basic_json_key_type = typename std::conditional <\n        is_usable_as_key_type<typename BasicJsonType::object_comparator_t,\n        typename BasicJsonType::object_t::key_type, KeyTypeCVRef,\n        RequireTransparentComparator, ExcludeObjectKeyType>::value\n        && !is_json_iterator_of<BasicJsonType, KeyType>::value,\n        std::true_type,\n        std::false_type >::type;\n\ntemplate<typename ObjectType, typename KeyType>\nusing detect_erase_with_key_type = decltype(std::declval<ObjectType&>().erase(std::declval<KeyType>()));\n\n// type trait to check if object_t has an erase() member functions accepting KeyType\ntemplate<typename BasicJsonType, typename KeyType>\nusing has_erase_with_key_type = typename std::conditional <\n                                is_detected <\n                                detect_erase_with_key_type,\n                                typename BasicJsonType::object_t, KeyType >::value,\n                                std::true_type,\n                                std::false_type >::type;\n\n// a naive helper to check if a type is an ordered_map (exploits the fact that\n// ordered_map inherits capacity() from std::vector)\ntemplate <typename T>\nstruct is_ordered_map\n{\n    using one = char;\n\n    struct two\n    {\n        char x[2]; // NOLINT(cppcoreguidelines-avoid-c-arrays,hicpp-avoid-c-arrays,modernize-avoid-c-arrays)\n    };\n\n    template <typename C> static one test( decltype(&C::capacity) ) ;\n    template <typename C> static two test(...);\n\n    enum { value = sizeof(test<T>(nullptr)) == sizeof(char) }; // NOLINT(cppcoreguidelines-pro-type-vararg,hicpp-vararg)\n};\n\n// to avoid useless casts (see https://github.com/nlohmann/json/issues/2893#issuecomment-889152324)\ntemplate < typename T, typename U, enable_if_t < !std::is_same<T, U>::value, int > = 0 >\nT conditional_static_cast(U value)\n{\n    return static_cast<T>(value);\n}\n\ntemplate<typename T, typename U, enable_if_t<std::is_same<T, U>::value, int> = 0>\nT conditional_static_cast(U value)\n{\n    return value;\n}\n\ntemplate<typename... Types>\nusing all_integral = conjunction<std::is_integral<Types>...>;\n\ntemplate<typename... Types>\nusing all_signed = conjunction<std::is_signed<Types>...>;\n\ntemplate<typename... Types>\nusing all_unsigned = conjunction<std::is_unsigned<Types>...>;\n\n// there's a disjunction trait in another PR; replace when merged\ntemplate<typename... Types>\nusing same_sign = std::integral_constant < bool,\n      all_signed<Types...>::value || all_unsigned<Types...>::value >;\n\ntemplate<typename OfType, typename T>\nusing never_out_of_range = std::integral_constant < bool,\n      (std::is_signed<OfType>::value && (sizeof(T) < sizeof(OfType)))\n      || (same_sign<OfType, T>::value && sizeof(OfType) == sizeof(T)) >;\n\ntemplate<typename OfType, typename T,\n         bool OfTypeSigned = std::is_signed<OfType>::value,\n         bool TSigned = std::is_signed<T>::value>\nstruct value_in_range_of_impl2;\n\ntemplate<typename OfType, typename T>\nstruct value_in_range_of_impl2<OfType, T, false, false>\n{\n    static constexpr bool test(T val)\n    {\n        using CommonType = typename std::common_type<OfType, T>::type;\n        return static_cast<CommonType>(val) <= static_cast<CommonType>((std::numeric_limits<OfType>::max)());\n    }\n};\n\ntemplate<typename OfType, typename T>\nstruct value_in_range_of_impl2<OfType, T, true, false>\n{\n    static constexpr bool test(T val)\n    {\n        using CommonType = typename std::common_type<OfType, T>::type;\n        return static_cast<CommonType>(val) <= static_cast<CommonType>((std::numeric_limits<OfType>::max)());\n    }\n};\n\ntemplate<typename OfType, typename T>\nstruct value_in_range_of_impl2<OfType, T, false, true>\n{\n    static constexpr bool test(T val)\n    {\n        using CommonType = typename std::common_type<OfType, T>::type;\n        return val >= 0 && static_cast<CommonType>(val) <= static_cast<CommonType>((std::numeric_limits<OfType>::max)());\n    }\n};\n\ntemplate<typename OfType, typename T>\nstruct value_in_range_of_impl2<OfType, T, true, true>\n{\n    static constexpr bool test(T val)\n    {\n        using CommonType = typename std::common_type<OfType, T>::type;\n        return static_cast<CommonType>(val) >= static_cast<CommonType>((std::numeric_limits<OfType>::min)())\n               && static_cast<CommonType>(val) <= static_cast<CommonType>((std::numeric_limits<OfType>::max)());\n    }\n};\n\ntemplate<typename OfType, typename T,\n         bool NeverOutOfRange = never_out_of_range<OfType, T>::value,\n         typename = detail::enable_if_t<all_integral<OfType, T>::value>>\nstruct value_in_range_of_impl1;\n\ntemplate<typename OfType, typename T>\nstruct value_in_range_of_impl1<OfType, T, false>\n{\n    static constexpr bool test(T val)\n    {\n        return value_in_range_of_impl2<OfType, T>::test(val);\n    }\n};\n\ntemplate<typename OfType, typename T>\nstruct value_in_range_of_impl1<OfType, T, true>\n{\n    static constexpr bool test(T /*val*/)\n    {\n        return true;\n    }\n};\n\ntemplate<typename OfType, typename T>\ninline constexpr bool value_in_range_of(T val)\n{\n    return value_in_range_of_impl1<OfType, T>::test(val);\n}\n\ntemplate<bool Value>\nusing bool_constant = std::integral_constant<bool, Value>;\n\n///////////////////////////////////////////////////////////////////////////////\n// is_c_string\n///////////////////////////////////////////////////////////////////////////////\n\nnamespace impl\n{\n\ntemplate<typename T>\ninline constexpr bool is_c_string()\n{\n    using TUnExt = typename std::remove_extent<T>::type;\n    using TUnCVExt = typename std::remove_cv<TUnExt>::type;\n    using TUnPtr = typename std::remove_pointer<T>::type;\n    using TUnCVPtr = typename std::remove_cv<TUnPtr>::type;\n    return\n        (std::is_array<T>::value && std::is_same<TUnCVExt, char>::value)\n        || (std::is_pointer<T>::value && std::is_same<TUnCVPtr, char>::value);\n}\n\n}  // namespace impl\n\n// checks whether T is a [cv] char */[cv] char[] C string\ntemplate<typename T>\nstruct is_c_string : bool_constant<impl::is_c_string<T>()> {};\n\ntemplate<typename T>\nusing is_c_string_uncvref = is_c_string<uncvref_t<T>>;\n\n///////////////////////////////////////////////////////////////////////////////\n// is_transparent\n///////////////////////////////////////////////////////////////////////////////\n\nnamespace impl\n{\n\ntemplate<typename T>\ninline constexpr bool is_transparent()\n{\n    return is_detected<detect_is_transparent, T>::value;\n}\n\n}  // namespace impl\n\n// checks whether T has a member named is_transparent\ntemplate<typename T>\nstruct is_transparent : bool_constant<impl::is_transparent<T>()> {};\n\n///////////////////////////////////////////////////////////////////////////////\n\n}  // namespace detail\nNLOHMANN_JSON_NAMESPACE_END\n\n// #include <nlohmann/detail/string_concat.hpp>\n//     __ _____ _____ _____\n//  __|  |   __|     |   | |  JSON for Modern C++\n// |  |  |__   |  |  | | | |  version 3.11.3\n// |_____|_____|_____|_|___|  https://github.com/nlohmann/json\n//\n// SPDX-FileCopyrightText: 2013-2023 Niels Lohmann <https://nlohmann.me>\n// SPDX-License-Identifier: MIT\n\n\n\n#include <cstring> // strlen\n#include <string> // string\n#include <utility> // forward\n\n// #include <nlohmann/detail/meta/cpp_future.hpp>\n\n// #include <nlohmann/detail/meta/detected.hpp>\n\n\nNLOHMANN_JSON_NAMESPACE_BEGIN\nnamespace detail\n{\n\ninline std::size_t concat_length()\n{\n    return 0;\n}\n\ntemplate<typename... Args>\ninline std::size_t concat_length(const char* cstr, const Args& ... rest);\n\ntemplate<typename StringType, typename... Args>\ninline std::size_t concat_length(const StringType& str, const Args& ... rest);\n\ntemplate<typename... Args>\ninline std::size_t concat_length(const char /*c*/, const Args& ... rest)\n{\n    return 1 + concat_length(rest...);\n}\n\ntemplate<typename... Args>\ninline std::size_t concat_length(const char* cstr, const Args& ... rest)\n{\n    // cppcheck-suppress ignoredReturnValue\n    return ::strlen(cstr) + concat_length(rest...);\n}\n\ntemplate<typename StringType, typename... Args>\ninline std::size_t concat_length(const StringType& str, const Args& ... rest)\n{\n    return str.size() + concat_length(rest...);\n}\n\ntemplate<typename OutStringType>\ninline void concat_into(OutStringType& /*out*/)\n{}\n\ntemplate<typename StringType, typename Arg>\nusing string_can_append = decltype(std::declval<StringType&>().append(std::declval < Arg && > ()));\n\ntemplate<typename StringType, typename Arg>\nusing detect_string_can_append = is_detected<string_can_append, StringType, Arg>;\n\ntemplate<typename StringType, typename Arg>\nusing string_can_append_op = decltype(std::declval<StringType&>() += std::declval < Arg && > ());\n\ntemplate<typename StringType, typename Arg>\nusing detect_string_can_append_op = is_detected<string_can_append_op, StringType, Arg>;\n\ntemplate<typename StringType, typename Arg>\nusing string_can_append_iter = decltype(std::declval<StringType&>().append(std::declval<const Arg&>().begin(), std::declval<const Arg&>().end()));\n\ntemplate<typename StringType, typename Arg>\nusing detect_string_can_append_iter = is_detected<string_can_append_iter, StringType, Arg>;\n\ntemplate<typename StringType, typename Arg>\nusing string_can_append_data = decltype(std::declval<StringType&>().append(std::declval<const Arg&>().data(), std::declval<const Arg&>().size()));\n\ntemplate<typename StringType, typename Arg>\nusing detect_string_can_append_data = is_detected<string_can_append_data, StringType, Arg>;\n\ntemplate < typename OutStringType, typename Arg, typename... Args,\n           enable_if_t < !detect_string_can_append<OutStringType, Arg>::value\n                         && detect_string_can_append_op<OutStringType, Arg>::value, int > = 0 >\ninline void concat_into(OutStringType& out, Arg && arg, Args && ... rest);\n\ntemplate < typename OutStringType, typename Arg, typename... Args,\n           enable_if_t < !detect_string_can_append<OutStringType, Arg>::value\n                         && !detect_string_can_append_op<OutStringType, Arg>::value\n                         && detect_string_can_append_iter<OutStringType, Arg>::value, int > = 0 >\ninline void concat_into(OutStringType& out, const Arg& arg, Args && ... rest);\n\ntemplate < typename OutStringType, typename Arg, typename... Args,\n           enable_if_t < !detect_string_can_append<OutStringType, Arg>::value\n                         && !detect_string_can_append_op<OutStringType, Arg>::value\n                         && !detect_string_can_append_iter<OutStringType, Arg>::value\n                         && detect_string_can_append_data<OutStringType, Arg>::value, int > = 0 >\ninline void concat_into(OutStringType& out, const Arg& arg, Args && ... rest);\n\ntemplate<typename OutStringType, typename Arg, typename... Args,\n         enable_if_t<detect_string_can_append<OutStringType, Arg>::value, int> = 0>\ninline void concat_into(OutStringType& out, Arg && arg, Args && ... rest)\n{\n    out.append(std::forward<Arg>(arg));\n    concat_into(out, std::forward<Args>(rest)...);\n}\n\ntemplate < typename OutStringType, typename Arg, typename... Args,\n           enable_if_t < !detect_string_can_append<OutStringType, Arg>::value\n                         && detect_string_can_append_op<OutStringType, Arg>::value, int > >\ninline void concat_into(OutStringType& out, Arg&& arg, Args&& ... rest)\n{\n    out += std::forward<Arg>(arg);\n    concat_into(out, std::forward<Args>(rest)...);\n}\n\ntemplate < typename OutStringType, typename Arg, typename... Args,\n           enable_if_t < !detect_string_can_append<OutStringType, Arg>::value\n                         && !detect_string_can_append_op<OutStringType, Arg>::value\n                         && detect_string_can_append_iter<OutStringType, Arg>::value, int > >\ninline void concat_into(OutStringType& out, const Arg& arg, Args&& ... rest)\n{\n    out.append(arg.begin(), arg.end());\n    concat_into(out, std::forward<Args>(rest)...);\n}\n\ntemplate < typename OutStringType, typename Arg, typename... Args,\n           enable_if_t < !detect_string_can_append<OutStringType, Arg>::value\n                         && !detect_string_can_append_op<OutStringType, Arg>::value\n                         && !detect_string_can_append_iter<OutStringType, Arg>::value\n                         && detect_string_can_append_data<OutStringType, Arg>::value, int > >\ninline void concat_into(OutStringType& out, const Arg& arg, Args&& ... rest)\n{\n    out.append(arg.data(), arg.size());\n    concat_into(out, std::forward<Args>(rest)...);\n}\n\ntemplate<typename OutStringType = std::string, typename... Args>\ninline OutStringType concat(Args && ... args)\n{\n    OutStringType str;\n    str.reserve(concat_length(args...));\n    concat_into(str, std::forward<Args>(args)...);\n    return str;\n}\n\n}  // namespace detail\nNLOHMANN_JSON_NAMESPACE_END\n\n\nNLOHMANN_JSON_NAMESPACE_BEGIN\nnamespace detail\n{\n\n////////////////\n// exceptions //\n////////////////\n\n/// @brief general exception of the @ref basic_json class\n/// @sa https://json.nlohmann.me/api/basic_json/exception/\nclass exception : public std::exception\n{\n  public:\n    /// returns the explanatory string\n    const char* what() const noexcept override\n    {\n        return m.what();\n    }\n\n    /// the id of the exception\n    const int id; // NOLINT(cppcoreguidelines-non-private-member-variables-in-classes)\n\n  protected:\n    JSON_HEDLEY_NON_NULL(3)\n    exception(int id_, const char* what_arg) : id(id_), m(what_arg) {} // NOLINT(bugprone-throw-keyword-missing)\n\n    static std::string name(const std::string& ename, int id_)\n    {\n        return concat(\"[json.exception.\", ename, '.', std::to_string(id_), \"] \");\n    }\n\n    static std::string diagnostics(std::nullptr_t /*leaf_element*/)\n    {\n        return \"\";\n    }\n\n    template<typename BasicJsonType>\n    static std::string diagnostics(const BasicJsonType* leaf_element)\n    {\n#if JSON_DIAGNOSTICS\n        std::vector<std::string> tokens;\n        for (const auto* current = leaf_element; current != nullptr && current->m_parent != nullptr; current = current->m_parent)\n        {\n            switch (current->m_parent->type())\n            {\n                case value_t::array:\n                {\n                    for (std::size_t i = 0; i < current->m_parent->m_data.m_value.array->size(); ++i)\n                    {\n                        if (&current->m_parent->m_data.m_value.array->operator[](i) == current)\n                        {\n                            tokens.emplace_back(std::to_string(i));\n                            break;\n                        }\n                    }\n                    break;\n                }\n\n                case value_t::object:\n                {\n                    for (const auto& element : *current->m_parent->m_data.m_value.object)\n                    {\n                        if (&element.second == current)\n                        {\n                            tokens.emplace_back(element.first.c_str());\n                            break;\n                        }\n                    }\n                    break;\n                }\n\n                case value_t::null: // LCOV_EXCL_LINE\n                case value_t::string: // LCOV_EXCL_LINE\n                case value_t::boolean: // LCOV_EXCL_LINE\n                case value_t::number_integer: // LCOV_EXCL_LINE\n                case value_t::number_unsigned: // LCOV_EXCL_LINE\n                case value_t::number_float: // LCOV_EXCL_LINE\n                case value_t::binary: // LCOV_EXCL_LINE\n                case value_t::discarded: // LCOV_EXCL_LINE\n                default:   // LCOV_EXCL_LINE\n                    break; // LCOV_EXCL_LINE\n            }\n        }\n\n        if (tokens.empty())\n        {\n            return \"\";\n        }\n\n        auto str = std::accumulate(tokens.rbegin(), tokens.rend(), std::string{},\n                                   [](const std::string & a, const std::string & b)\n        {\n            return concat(a, '/', detail::escape(b));\n        });\n        return concat('(', str, \") \");\n#else\n        static_cast<void>(leaf_element);\n        return \"\";\n#endif\n    }\n\n  private:\n    /// an exception object as storage for error messages\n    std::runtime_error m;\n};\n\n/// @brief exception indicating a parse error\n/// @sa https://json.nlohmann.me/api/basic_json/parse_error/\nclass parse_error : public exception\n{\n  public:\n    /*!\n    @brief create a parse error exception\n    @param[in] id_       the id of the exception\n    @param[in] pos       the position where the error occurred (or with\n                         chars_read_total=0 if the position cannot be\n                         determined)\n    @param[in] what_arg  the explanatory string\n    @return parse_error object\n    */\n    template<typename BasicJsonContext, enable_if_t<is_basic_json_context<BasicJsonContext>::value, int> = 0>\n    static parse_error create(int id_, const position_t& pos, const std::string& what_arg, BasicJsonContext context)\n    {\n        const std::string w = concat(exception::name(\"parse_error\", id_), \"parse error\",\n                                     position_string(pos), \": \", exception::diagnostics(context), what_arg);\n        return {id_, pos.chars_read_total, w.c_str()};\n    }\n\n    template<typename BasicJsonContext, enable_if_t<is_basic_json_context<BasicJsonContext>::value, int> = 0>\n    static parse_error create(int id_, std::size_t byte_, const std::string& what_arg, BasicJsonContext context)\n    {\n        const std::string w = concat(exception::name(\"parse_error\", id_), \"parse error\",\n                                     (byte_ != 0 ? (concat(\" at byte \", std::to_string(byte_))) : \"\"),\n                                     \": \", exception::diagnostics(context), what_arg);\n        return {id_, byte_, w.c_str()};\n    }\n\n    /*!\n    @brief byte index of the parse error\n\n    The byte index of the last read character in the input file.\n\n    @note For an input with n bytes, 1 is the index of the first character and\n          n+1 is the index of the terminating null byte or the end of file.\n          This also holds true when reading a byte vector (CBOR or MessagePack).\n    */\n    const std::size_t byte;\n\n  private:\n    parse_error(int id_, std::size_t byte_, const char* what_arg)\n        : exception(id_, what_arg), byte(byte_) {}\n\n    static std::string position_string(const position_t& pos)\n    {\n        return concat(\" at line \", std::to_string(pos.lines_read + 1),\n                      \", column \", std::to_string(pos.chars_read_current_line));\n    }\n};\n\n/// @brief exception indicating errors with iterators\n/// @sa https://json.nlohmann.me/api/basic_json/invalid_iterator/\nclass invalid_iterator : public exception\n{\n  public:\n    template<typename BasicJsonContext, enable_if_t<is_basic_json_context<BasicJsonContext>::value, int> = 0>\n    static invalid_iterator create(int id_, const std::string& what_arg, BasicJsonContext context)\n    {\n        const std::string w = concat(exception::name(\"invalid_iterator\", id_), exception::diagnostics(context), what_arg);\n        return {id_, w.c_str()};\n    }\n\n  private:\n    JSON_HEDLEY_NON_NULL(3)\n    invalid_iterator(int id_, const char* what_arg)\n        : exception(id_, what_arg) {}\n};\n\n/// @brief exception indicating executing a member function with a wrong type\n/// @sa https://json.nlohmann.me/api/basic_json/type_error/\nclass type_error : public exception\n{\n  public:\n    template<typename BasicJsonContext, enable_if_t<is_basic_json_context<BasicJsonContext>::value, int> = 0>\n    static type_error create(int id_, const std::string& what_arg, BasicJsonContext context)\n    {\n        const std::string w = concat(exception::name(\"type_error\", id_), exception::diagnostics(context), what_arg);\n        return {id_, w.c_str()};\n    }\n\n  private:\n    JSON_HEDLEY_NON_NULL(3)\n    type_error(int id_, const char* what_arg) : exception(id_, what_arg) {}\n};\n\n/// @brief exception indicating access out of the defined range\n/// @sa https://json.nlohmann.me/api/basic_json/out_of_range/\nclass out_of_range : public exception\n{\n  public:\n    template<typename BasicJsonContext, enable_if_t<is_basic_json_context<BasicJsonContext>::value, int> = 0>\n    static out_of_range create(int id_, const std::string& what_arg, BasicJsonContext context)\n    {\n        const std::string w = concat(exception::name(\"out_of_range\", id_), exception::diagnostics(context), what_arg);\n        return {id_, w.c_str()};\n    }\n\n  private:\n    JSON_HEDLEY_NON_NULL(3)\n    out_of_range(int id_, const char* what_arg) : exception(id_, what_arg) {}\n};\n\n/// @brief exception indicating other library errors\n/// @sa https://json.nlohmann.me/api/basic_json/other_error/\nclass other_error : public exception\n{\n  public:\n    template<typename BasicJsonContext, enable_if_t<is_basic_json_context<BasicJsonContext>::value, int> = 0>\n    static other_error create(int id_, const std::string& what_arg, BasicJsonContext context)\n    {\n        const std::string w = concat(exception::name(\"other_error\", id_), exception::diagnostics(context), what_arg);\n        return {id_, w.c_str()};\n    }\n\n  private:\n    JSON_HEDLEY_NON_NULL(3)\n    other_error(int id_, const char* what_arg) : exception(id_, what_arg) {}\n};\n\n}  // namespace detail\nNLOHMANN_JSON_NAMESPACE_END\n\n// #include <nlohmann/detail/macro_scope.hpp>\n\n// #include <nlohmann/detail/meta/cpp_future.hpp>\n\n// #include <nlohmann/detail/meta/identity_tag.hpp>\n//     __ _____ _____ _____\n//  __|  |   __|     |   | |  JSON for Modern C++\n// |  |  |__   |  |  | | | |  version 3.11.3\n// |_____|_____|_____|_|___|  https://github.com/nlohmann/json\n//\n// SPDX-FileCopyrightText: 2013-2023 Niels Lohmann <https://nlohmann.me>\n// SPDX-License-Identifier: MIT\n\n\n\n// #include <nlohmann/detail/abi_macros.hpp>\n\n\nNLOHMANN_JSON_NAMESPACE_BEGIN\nnamespace detail\n{\n\n// dispatching helper struct\ntemplate <class T> struct identity_tag {};\n\n}  // namespace detail\nNLOHMANN_JSON_NAMESPACE_END\n\n// #include <nlohmann/detail/meta/std_fs.hpp>\n//     __ _____ _____ _____\n//  __|  |   __|     |   | |  JSON for Modern C++\n// |  |  |__   |  |  | | | |  version 3.11.3\n// |_____|_____|_____|_|___|  https://github.com/nlohmann/json\n//\n// SPDX-FileCopyrightText: 2013-2023 Niels Lohmann <https://nlohmann.me>\n// SPDX-License-Identifier: MIT\n\n\n\n// #include <nlohmann/detail/macro_scope.hpp>\n\n\n#if JSON_HAS_EXPERIMENTAL_FILESYSTEM\n#include <experimental/filesystem>\nNLOHMANN_JSON_NAMESPACE_BEGIN\nnamespace detail\n{\nnamespace std_fs = std::experimental::filesystem;\n}  // namespace detail\nNLOHMANN_JSON_NAMESPACE_END\n#elif JSON_HAS_FILESYSTEM\n#include <filesystem>\nNLOHMANN_JSON_NAMESPACE_BEGIN\nnamespace detail\n{\nnamespace std_fs = std::filesystem;\n}  // namespace detail\nNLOHMANN_JSON_NAMESPACE_END\n#endif\n\n// #include <nlohmann/detail/meta/type_traits.hpp>\n\n// #include <nlohmann/detail/string_concat.hpp>\n\n// #include <nlohmann/detail/value_t.hpp>\n\n\nNLOHMANN_JSON_NAMESPACE_BEGIN\nnamespace detail\n{\n\ntemplate<typename BasicJsonType>\ninline void from_json(const BasicJsonType& j, typename std::nullptr_t& n)\n{\n    if (JSON_HEDLEY_UNLIKELY(!j.is_null()))\n    {\n        JSON_THROW(type_error::create(302, concat(\"type must be null, but is \", j.type_name()), &j));\n    }\n    n = nullptr;\n}\n\n// overloads for basic_json template parameters\ntemplate < typename BasicJsonType, typename ArithmeticType,\n           enable_if_t < std::is_arithmetic<ArithmeticType>::value&&\n                         !std::is_same<ArithmeticType, typename BasicJsonType::boolean_t>::value,\n                         int > = 0 >\nvoid get_arithmetic_value(const BasicJsonType& j, ArithmeticType& val)\n{\n    switch (static_cast<value_t>(j))\n    {\n        case value_t::number_unsigned:\n        {\n            val = static_cast<ArithmeticType>(*j.template get_ptr<const typename BasicJsonType::number_unsigned_t*>());\n            break;\n        }\n        case value_t::number_integer:\n        {\n            val = static_cast<ArithmeticType>(*j.template get_ptr<const typename BasicJsonType::number_integer_t*>());\n            break;\n        }\n        case value_t::number_float:\n        {\n            val = static_cast<ArithmeticType>(*j.template get_ptr<const typename BasicJsonType::number_float_t*>());\n            break;\n        }\n\n        case value_t::null:\n        case value_t::object:\n        case value_t::array:\n        case value_t::string:\n        case value_t::boolean:\n        case value_t::binary:\n        case value_t::discarded:\n        default:\n            JSON_THROW(type_error::create(302, concat(\"type must be number, but is \", j.type_name()), &j));\n    }\n}\n\ntemplate<typename BasicJsonType>\ninline void from_json(const BasicJsonType& j, typename BasicJsonType::boolean_t& b)\n{\n    if (JSON_HEDLEY_UNLIKELY(!j.is_boolean()))\n    {\n        JSON_THROW(type_error::create(302, concat(\"type must be boolean, but is \", j.type_name()), &j));\n    }\n    b = *j.template get_ptr<const typename BasicJsonType::boolean_t*>();\n}\n\ntemplate<typename BasicJsonType>\ninline void from_json(const BasicJsonType& j, typename BasicJsonType::string_t& s)\n{\n    if (JSON_HEDLEY_UNLIKELY(!j.is_string()))\n    {\n        JSON_THROW(type_error::create(302, concat(\"type must be string, but is \", j.type_name()), &j));\n    }\n    s = *j.template get_ptr<const typename BasicJsonType::string_t*>();\n}\n\ntemplate <\n    typename BasicJsonType, typename StringType,\n    enable_if_t <\n        std::is_assignable<StringType&, const typename BasicJsonType::string_t>::value\n        && is_detected_exact<typename BasicJsonType::string_t::value_type, value_type_t, StringType>::value\n        && !std::is_same<typename BasicJsonType::string_t, StringType>::value\n        && !is_json_ref<StringType>::value, int > = 0 >\ninline void from_json(const BasicJsonType& j, StringType& s)\n{\n    if (JSON_HEDLEY_UNLIKELY(!j.is_string()))\n    {\n        JSON_THROW(type_error::create(302, concat(\"type must be string, but is \", j.type_name()), &j));\n    }\n\n    s = *j.template get_ptr<const typename BasicJsonType::string_t*>();\n}\n\ntemplate<typename BasicJsonType>\ninline void from_json(const BasicJsonType& j, typename BasicJsonType::number_float_t& val)\n{\n    get_arithmetic_value(j, val);\n}\n\ntemplate<typename BasicJsonType>\ninline void from_json(const BasicJsonType& j, typename BasicJsonType::number_unsigned_t& val)\n{\n    get_arithmetic_value(j, val);\n}\n\ntemplate<typename BasicJsonType>\ninline void from_json(const BasicJsonType& j, typename BasicJsonType::number_integer_t& val)\n{\n    get_arithmetic_value(j, val);\n}\n\n#if !JSON_DISABLE_ENUM_SERIALIZATION\ntemplate<typename BasicJsonType, typename EnumType,\n         enable_if_t<std::is_enum<EnumType>::value, int> = 0>\ninline void from_json(const BasicJsonType& j, EnumType& e)\n{\n    typename std::underlying_type<EnumType>::type val;\n    get_arithmetic_value(j, val);\n    e = static_cast<EnumType>(val);\n}\n#endif  // JSON_DISABLE_ENUM_SERIALIZATION\n\n// forward_list doesn't have an insert method\ntemplate<typename BasicJsonType, typename T, typename Allocator,\n         enable_if_t<is_getable<BasicJsonType, T>::value, int> = 0>\ninline void from_json(const BasicJsonType& j, std::forward_list<T, Allocator>& l)\n{\n    if (JSON_HEDLEY_UNLIKELY(!j.is_array()))\n    {\n        JSON_THROW(type_error::create(302, concat(\"type must be array, but is \", j.type_name()), &j));\n    }\n    l.clear();\n    std::transform(j.rbegin(), j.rend(),\n                   std::front_inserter(l), [](const BasicJsonType & i)\n    {\n        return i.template get<T>();\n    });\n}\n\n// valarray doesn't have an insert method\ntemplate<typename BasicJsonType, typename T,\n         enable_if_t<is_getable<BasicJsonType, T>::value, int> = 0>\ninline void from_json(const BasicJsonType& j, std::valarray<T>& l)\n{\n    if (JSON_HEDLEY_UNLIKELY(!j.is_array()))\n    {\n        JSON_THROW(type_error::create(302, concat(\"type must be array, but is \", j.type_name()), &j));\n    }\n    l.resize(j.size());\n    std::transform(j.begin(), j.end(), std::begin(l),\n                   [](const BasicJsonType & elem)\n    {\n        return elem.template get<T>();\n    });\n}\n\ntemplate<typename BasicJsonType, typename T, std::size_t N>\nauto from_json(const BasicJsonType& j, T (&arr)[N])  // NOLINT(cppcoreguidelines-avoid-c-arrays,hicpp-avoid-c-arrays,modernize-avoid-c-arrays)\n-> decltype(j.template get<T>(), void())\n{\n    for (std::size_t i = 0; i < N; ++i)\n    {\n        arr[i] = j.at(i).template get<T>();\n    }\n}\n\ntemplate<typename BasicJsonType>\ninline void from_json_array_impl(const BasicJsonType& j, typename BasicJsonType::array_t& arr, priority_tag<3> /*unused*/)\n{\n    arr = *j.template get_ptr<const typename BasicJsonType::array_t*>();\n}\n\ntemplate<typename BasicJsonType, typename T, std::size_t N>\nauto from_json_array_impl(const BasicJsonType& j, std::array<T, N>& arr,\n                          priority_tag<2> /*unused*/)\n-> decltype(j.template get<T>(), void())\n{\n    for (std::size_t i = 0; i < N; ++i)\n    {\n        arr[i] = j.at(i).template get<T>();\n    }\n}\n\ntemplate<typename BasicJsonType, typename ConstructibleArrayType,\n         enable_if_t<\n             std::is_assignable<ConstructibleArrayType&, ConstructibleArrayType>::value,\n             int> = 0>\nauto from_json_array_impl(const BasicJsonType& j, ConstructibleArrayType& arr, priority_tag<1> /*unused*/)\n-> decltype(\n    arr.reserve(std::declval<typename ConstructibleArrayType::size_type>()),\n    j.template get<typename ConstructibleArrayType::value_type>(),\n    void())\n{\n    using std::end;\n\n    ConstructibleArrayType ret;\n    ret.reserve(j.size());\n    std::transform(j.begin(), j.end(),\n                   std::inserter(ret, end(ret)), [](const BasicJsonType & i)\n    {\n        // get<BasicJsonType>() returns *this, this won't call a from_json\n        // method when value_type is BasicJsonType\n        return i.template get<typename ConstructibleArrayType::value_type>();\n    });\n    arr = std::move(ret);\n}\n\ntemplate<typename BasicJsonType, typename ConstructibleArrayType,\n         enable_if_t<\n             std::is_assignable<ConstructibleArrayType&, ConstructibleArrayType>::value,\n             int> = 0>\ninline void from_json_array_impl(const BasicJsonType& j, ConstructibleArrayType& arr,\n                                 priority_tag<0> /*unused*/)\n{\n    using std::end;\n\n    ConstructibleArrayType ret;\n    std::transform(\n        j.begin(), j.end(), std::inserter(ret, end(ret)),\n        [](const BasicJsonType & i)\n    {\n        // get<BasicJsonType>() returns *this, this won't call a from_json\n        // method when value_type is BasicJsonType\n        return i.template get<typename ConstructibleArrayType::value_type>();\n    });\n    arr = std::move(ret);\n}\n\ntemplate < typename BasicJsonType, typename ConstructibleArrayType,\n           enable_if_t <\n               is_constructible_array_type<BasicJsonType, ConstructibleArrayType>::value&&\n               !is_constructible_object_type<BasicJsonType, ConstructibleArrayType>::value&&\n               !is_constructible_string_type<BasicJsonType, ConstructibleArrayType>::value&&\n               !std::is_same<ConstructibleArrayType, typename BasicJsonType::binary_t>::value&&\n               !is_basic_json<ConstructibleArrayType>::value,\n               int > = 0 >\nauto from_json(const BasicJsonType& j, ConstructibleArrayType& arr)\n-> decltype(from_json_array_impl(j, arr, priority_tag<3> {}),\nj.template get<typename ConstructibleArrayType::value_type>(),\nvoid())\n{\n    if (JSON_HEDLEY_UNLIKELY(!j.is_array()))\n    {\n        JSON_THROW(type_error::create(302, concat(\"type must be array, but is \", j.type_name()), &j));\n    }\n\n    from_json_array_impl(j, arr, priority_tag<3> {});\n}\n\ntemplate < typename BasicJsonType, typename T, std::size_t... Idx >\nstd::array<T, sizeof...(Idx)> from_json_inplace_array_impl(BasicJsonType&& j,\n        identity_tag<std::array<T, sizeof...(Idx)>> /*unused*/, index_sequence<Idx...> /*unused*/)\n{\n    return { { std::forward<BasicJsonType>(j).at(Idx).template get<T>()... } };\n}\n\ntemplate < typename BasicJsonType, typename T, std::size_t N >\nauto from_json(BasicJsonType&& j, identity_tag<std::array<T, N>> tag)\n-> decltype(from_json_inplace_array_impl(std::forward<BasicJsonType>(j), tag, make_index_sequence<N> {}))\n{\n    if (JSON_HEDLEY_UNLIKELY(!j.is_array()))\n    {\n        JSON_THROW(type_error::create(302, concat(\"type must be array, but is \", j.type_name()), &j));\n    }\n\n    return from_json_inplace_array_impl(std::forward<BasicJsonType>(j), tag, make_index_sequence<N> {});\n}\n\ntemplate<typename BasicJsonType>\ninline void from_json(const BasicJsonType& j, typename BasicJsonType::binary_t& bin)\n{\n    if (JSON_HEDLEY_UNLIKELY(!j.is_binary()))\n    {\n        JSON_THROW(type_error::create(302, concat(\"type must be binary, but is \", j.type_name()), &j));\n    }\n\n    bin = *j.template get_ptr<const typename BasicJsonType::binary_t*>();\n}\n\ntemplate<typename BasicJsonType, typename ConstructibleObjectType,\n         enable_if_t<is_constructible_object_type<BasicJsonType, ConstructibleObjectType>::value, int> = 0>\ninline void from_json(const BasicJsonType& j, ConstructibleObjectType& obj)\n{\n    if (JSON_HEDLEY_UNLIKELY(!j.is_object()))\n    {\n        JSON_THROW(type_error::create(302, concat(\"type must be object, but is \", j.type_name()), &j));\n    }\n\n    ConstructibleObjectType ret;\n    const auto* inner_object = j.template get_ptr<const typename BasicJsonType::object_t*>();\n    using value_type = typename ConstructibleObjectType::value_type;\n    std::transform(\n        inner_object->begin(), inner_object->end(),\n        std::inserter(ret, ret.begin()),\n        [](typename BasicJsonType::object_t::value_type const & p)\n    {\n        return value_type(p.first, p.second.template get<typename ConstructibleObjectType::mapped_type>());\n    });\n    obj = std::move(ret);\n}\n\n// overload for arithmetic types, not chosen for basic_json template arguments\n// (BooleanType, etc..); note: Is it really necessary to provide explicit\n// overloads for boolean_t etc. in case of a custom BooleanType which is not\n// an arithmetic type?\ntemplate < typename BasicJsonType, typename ArithmeticType,\n           enable_if_t <\n               std::is_arithmetic<ArithmeticType>::value&&\n               !std::is_same<ArithmeticType, typename BasicJsonType::number_unsigned_t>::value&&\n               !std::is_same<ArithmeticType, typename BasicJsonType::number_integer_t>::value&&\n               !std::is_same<ArithmeticType, typename BasicJsonType::number_float_t>::value&&\n               !std::is_same<ArithmeticType, typename BasicJsonType::boolean_t>::value,\n               int > = 0 >\ninline void from_json(const BasicJsonType& j, ArithmeticType& val)\n{\n    switch (static_cast<value_t>(j))\n    {\n        case value_t::number_unsigned:\n        {\n            val = static_cast<ArithmeticType>(*j.template get_ptr<const typename BasicJsonType::number_unsigned_t*>());\n            break;\n        }\n        case value_t::number_integer:\n        {\n            val = static_cast<ArithmeticType>(*j.template get_ptr<const typename BasicJsonType::number_integer_t*>());\n            break;\n        }\n        case value_t::number_float:\n        {\n            val = static_cast<ArithmeticType>(*j.template get_ptr<const typename BasicJsonType::number_float_t*>());\n            break;\n        }\n        case value_t::boolean:\n        {\n            val = static_cast<ArithmeticType>(*j.template get_ptr<const typename BasicJsonType::boolean_t*>());\n            break;\n        }\n\n        case value_t::null:\n        case value_t::object:\n        case value_t::array:\n        case value_t::string:\n        case value_t::binary:\n        case value_t::discarded:\n        default:\n            JSON_THROW(type_error::create(302, concat(\"type must be number, but is \", j.type_name()), &j));\n    }\n}\n\ntemplate<typename BasicJsonType, typename... Args, std::size_t... Idx>\nstd::tuple<Args...> from_json_tuple_impl_base(BasicJsonType&& j, index_sequence<Idx...> /*unused*/)\n{\n    return std::make_tuple(std::forward<BasicJsonType>(j).at(Idx).template get<Args>()...);\n}\n\ntemplate < typename BasicJsonType, class A1, class A2 >\nstd::pair<A1, A2> from_json_tuple_impl(BasicJsonType&& j, identity_tag<std::pair<A1, A2>> /*unused*/, priority_tag<0> /*unused*/)\n{\n    return {std::forward<BasicJsonType>(j).at(0).template get<A1>(),\n            std::forward<BasicJsonType>(j).at(1).template get<A2>()};\n}\n\ntemplate<typename BasicJsonType, typename A1, typename A2>\ninline void from_json_tuple_impl(BasicJsonType&& j, std::pair<A1, A2>& p, priority_tag<1> /*unused*/)\n{\n    p = from_json_tuple_impl(std::forward<BasicJsonType>(j), identity_tag<std::pair<A1, A2>> {}, priority_tag<0> {});\n}\n\ntemplate<typename BasicJsonType, typename... Args>\nstd::tuple<Args...> from_json_tuple_impl(BasicJsonType&& j, identity_tag<std::tuple<Args...>> /*unused*/, priority_tag<2> /*unused*/)\n{\n    return from_json_tuple_impl_base<BasicJsonType, Args...>(std::forward<BasicJsonType>(j), index_sequence_for<Args...> {});\n}\n\ntemplate<typename BasicJsonType, typename... Args>\ninline void from_json_tuple_impl(BasicJsonType&& j, std::tuple<Args...>& t, priority_tag<3> /*unused*/)\n{\n    t = from_json_tuple_impl_base<BasicJsonType, Args...>(std::forward<BasicJsonType>(j), index_sequence_for<Args...> {});\n}\n\ntemplate<typename BasicJsonType, typename TupleRelated>\nauto from_json(BasicJsonType&& j, TupleRelated&& t)\n-> decltype(from_json_tuple_impl(std::forward<BasicJsonType>(j), std::forward<TupleRelated>(t), priority_tag<3> {}))\n{\n    if (JSON_HEDLEY_UNLIKELY(!j.is_array()))\n    {\n        JSON_THROW(type_error::create(302, concat(\"type must be array, but is \", j.type_name()), &j));\n    }\n\n    return from_json_tuple_impl(std::forward<BasicJsonType>(j), std::forward<TupleRelated>(t), priority_tag<3> {});\n}\n\ntemplate < typename BasicJsonType, typename Key, typename Value, typename Compare, typename Allocator,\n           typename = enable_if_t < !std::is_constructible <\n                                        typename BasicJsonType::string_t, Key >::value >>\ninline void from_json(const BasicJsonType& j, std::map<Key, Value, Compare, Allocator>& m)\n{\n    if (JSON_HEDLEY_UNLIKELY(!j.is_array()))\n    {\n        JSON_THROW(type_error::create(302, concat(\"type must be array, but is \", j.type_name()), &j));\n    }\n    m.clear();\n    for (const auto& p : j)\n    {\n        if (JSON_HEDLEY_UNLIKELY(!p.is_array()))\n        {\n            JSON_THROW(type_error::create(302, concat(\"type must be array, but is \", p.type_name()), &j));\n        }\n        m.emplace(p.at(0).template get<Key>(), p.at(1).template get<Value>());\n    }\n}\n\ntemplate < typename BasicJsonType, typename Key, typename Value, typename Hash, typename KeyEqual, typename Allocator,\n           typename = enable_if_t < !std::is_constructible <\n                                        typename BasicJsonType::string_t, Key >::value >>\ninline void from_json(const BasicJsonType& j, std::unordered_map<Key, Value, Hash, KeyEqual, Allocator>& m)\n{\n    if (JSON_HEDLEY_UNLIKELY(!j.is_array()))\n    {\n        JSON_THROW(type_error::create(302, concat(\"type must be array, but is \", j.type_name()), &j));\n    }\n    m.clear();\n    for (const auto& p : j)\n    {\n        if (JSON_HEDLEY_UNLIKELY(!p.is_array()))\n        {\n            JSON_THROW(type_error::create(302, concat(\"type must be array, but is \", p.type_name()), &j));\n        }\n        m.emplace(p.at(0).template get<Key>(), p.at(1).template get<Value>());\n    }\n}\n\n#if JSON_HAS_FILESYSTEM || JSON_HAS_EXPERIMENTAL_FILESYSTEM\ntemplate<typename BasicJsonType>\ninline void from_json(const BasicJsonType& j, std_fs::path& p)\n{\n    if (JSON_HEDLEY_UNLIKELY(!j.is_string()))\n    {\n        JSON_THROW(type_error::create(302, concat(\"type must be string, but is \", j.type_name()), &j));\n    }\n    p = *j.template get_ptr<const typename BasicJsonType::string_t*>();\n}\n#endif\n\nstruct from_json_fn\n{\n    template<typename BasicJsonType, typename T>\n    auto operator()(const BasicJsonType& j, T&& val) const\n    noexcept(noexcept(from_json(j, std::forward<T>(val))))\n    -> decltype(from_json(j, std::forward<T>(val)))\n    {\n        return from_json(j, std::forward<T>(val));\n    }\n};\n\n}  // namespace detail\n\n#ifndef JSON_HAS_CPP_17\n/// namespace to hold default `from_json` function\n/// to see why this is required:\n/// http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2015/n4381.html\nnamespace // NOLINT(cert-dcl59-cpp,fuchsia-header-anon-namespaces,google-build-namespaces)\n{\n#endif\nJSON_INLINE_VARIABLE constexpr const auto& from_json = // NOLINT(misc-definitions-in-headers)\n    detail::static_const<detail::from_json_fn>::value;\n#ifndef JSON_HAS_CPP_17\n}  // namespace\n#endif\n\nNLOHMANN_JSON_NAMESPACE_END\n\n// #include <nlohmann/detail/conversions/to_json.hpp>\n//     __ _____ _____ _____\n//  __|  |   __|     |   | |  JSON for Modern C++\n// |  |  |__   |  |  | | | |  version 3.11.3\n// |_____|_____|_____|_|___|  https://github.com/nlohmann/json\n//\n// SPDX-FileCopyrightText: 2013-2023 Niels Lohmann <https://nlohmann.me>\n// SPDX-License-Identifier: MIT\n\n\n\n#include <algorithm> // copy\n#include <iterator> // begin, end\n#include <string> // string\n#include <tuple> // tuple, get\n#include <type_traits> // is_same, is_constructible, is_floating_point, is_enum, underlying_type\n#include <utility> // move, forward, declval, pair\n#include <valarray> // valarray\n#include <vector> // vector\n\n// #include <nlohmann/detail/iterators/iteration_proxy.hpp>\n//     __ _____ _____ _____\n//  __|  |   __|     |   | |  JSON for Modern C++\n// |  |  |__   |  |  | | | |  version 3.11.3\n// |_____|_____|_____|_|___|  https://github.com/nlohmann/json\n//\n// SPDX-FileCopyrightText: 2013-2023 Niels Lohmann <https://nlohmann.me>\n// SPDX-License-Identifier: MIT\n\n\n\n#include <cstddef> // size_t\n#include <iterator> // input_iterator_tag\n#include <string> // string, to_string\n#include <tuple> // tuple_size, get, tuple_element\n#include <utility> // move\n\n#if JSON_HAS_RANGES\n    #include <ranges> // enable_borrowed_range\n#endif\n\n// #include <nlohmann/detail/abi_macros.hpp>\n\n// #include <nlohmann/detail/meta/type_traits.hpp>\n\n// #include <nlohmann/detail/value_t.hpp>\n\n\nNLOHMANN_JSON_NAMESPACE_BEGIN\nnamespace detail\n{\n\ntemplate<typename string_type>\nvoid int_to_string( string_type& target, std::size_t value )\n{\n    // For ADL\n    using std::to_string;\n    target = to_string(value);\n}\ntemplate<typename IteratorType> class iteration_proxy_value\n{\n  public:\n    using difference_type = std::ptrdiff_t;\n    using value_type = iteration_proxy_value;\n    using pointer = value_type *;\n    using reference = value_type &;\n    using iterator_category = std::input_iterator_tag;\n    using string_type = typename std::remove_cv< typename std::remove_reference<decltype( std::declval<IteratorType>().key() ) >::type >::type;\n\n  private:\n    /// the iterator\n    IteratorType anchor{};\n    /// an index for arrays (used to create key names)\n    std::size_t array_index = 0;\n    /// last stringified array index\n    mutable std::size_t array_index_last = 0;\n    /// a string representation of the array index\n    mutable string_type array_index_str = \"0\";\n    /// an empty string (to return a reference for primitive values)\n    string_type empty_str{};\n\n  public:\n    explicit iteration_proxy_value() = default;\n    explicit iteration_proxy_value(IteratorType it, std::size_t array_index_ = 0)\n    noexcept(std::is_nothrow_move_constructible<IteratorType>::value\n             && std::is_nothrow_default_constructible<string_type>::value)\n        : anchor(std::move(it))\n        , array_index(array_index_)\n    {}\n\n    iteration_proxy_value(iteration_proxy_value const&) = default;\n    iteration_proxy_value& operator=(iteration_proxy_value const&) = default;\n    // older GCCs are a bit fussy and require explicit noexcept specifiers on defaulted functions\n    iteration_proxy_value(iteration_proxy_value&&)\n    noexcept(std::is_nothrow_move_constructible<IteratorType>::value\n             && std::is_nothrow_move_constructible<string_type>::value) = default; // NOLINT(hicpp-noexcept-move,performance-noexcept-move-constructor,cppcoreguidelines-noexcept-move-operations)\n    iteration_proxy_value& operator=(iteration_proxy_value&&)\n    noexcept(std::is_nothrow_move_assignable<IteratorType>::value\n             && std::is_nothrow_move_assignable<string_type>::value) = default; // NOLINT(hicpp-noexcept-move,performance-noexcept-move-constructor,cppcoreguidelines-noexcept-move-operations)\n    ~iteration_proxy_value() = default;\n\n    /// dereference operator (needed for range-based for)\n    const iteration_proxy_value& operator*() const\n    {\n        return *this;\n    }\n\n    /// increment operator (needed for range-based for)\n    iteration_proxy_value& operator++()\n    {\n        ++anchor;\n        ++array_index;\n\n        return *this;\n    }\n\n    iteration_proxy_value operator++(int)& // NOLINT(cert-dcl21-cpp)\n    {\n        auto tmp = iteration_proxy_value(anchor, array_index);\n        ++anchor;\n        ++array_index;\n        return tmp;\n    }\n\n    /// equality operator (needed for InputIterator)\n    bool operator==(const iteration_proxy_value& o) const\n    {\n        return anchor == o.anchor;\n    }\n\n    /// inequality operator (needed for range-based for)\n    bool operator!=(const iteration_proxy_value& o) const\n    {\n        return anchor != o.anchor;\n    }\n\n    /// return key of the iterator\n    const string_type& key() const\n    {\n        JSON_ASSERT(anchor.m_object != nullptr);\n\n        switch (anchor.m_object->type())\n        {\n            // use integer array index as key\n            case value_t::array:\n            {\n                if (array_index != array_index_last)\n                {\n                    int_to_string( array_index_str, array_index );\n                    array_index_last = array_index;\n                }\n                return array_index_str;\n            }\n\n            // use key from the object\n            case value_t::object:\n                return anchor.key();\n\n            // use an empty key for all primitive types\n            case value_t::null:\n            case value_t::string:\n            case value_t::boolean:\n            case value_t::number_integer:\n            case value_t::number_unsigned:\n            case value_t::number_float:\n            case value_t::binary:\n            case value_t::discarded:\n            default:\n                return empty_str;\n        }\n    }\n\n    /// return value of the iterator\n    typename IteratorType::reference value() const\n    {\n        return anchor.value();\n    }\n};\n\n/// proxy class for the items() function\ntemplate<typename IteratorType> class iteration_proxy\n{\n  private:\n    /// the container to iterate\n    typename IteratorType::pointer container = nullptr;\n\n  public:\n    explicit iteration_proxy() = default;\n\n    /// construct iteration proxy from a container\n    explicit iteration_proxy(typename IteratorType::reference cont) noexcept\n        : container(&cont) {}\n\n    iteration_proxy(iteration_proxy const&) = default;\n    iteration_proxy& operator=(iteration_proxy const&) = default;\n    iteration_proxy(iteration_proxy&&) noexcept = default;\n    iteration_proxy& operator=(iteration_proxy&&) noexcept = default;\n    ~iteration_proxy() = default;\n\n    /// return iterator begin (needed for range-based for)\n    iteration_proxy_value<IteratorType> begin() const noexcept\n    {\n        return iteration_proxy_value<IteratorType>(container->begin());\n    }\n\n    /// return iterator end (needed for range-based for)\n    iteration_proxy_value<IteratorType> end() const noexcept\n    {\n        return iteration_proxy_value<IteratorType>(container->end());\n    }\n};\n\n// Structured Bindings Support\n// For further reference see https://blog.tartanllama.xyz/structured-bindings/\n// And see https://github.com/nlohmann/json/pull/1391\ntemplate<std::size_t N, typename IteratorType, enable_if_t<N == 0, int> = 0>\nauto get(const nlohmann::detail::iteration_proxy_value<IteratorType>& i) -> decltype(i.key())\n{\n    return i.key();\n}\n// Structured Bindings Support\n// For further reference see https://blog.tartanllama.xyz/structured-bindings/\n// And see https://github.com/nlohmann/json/pull/1391\ntemplate<std::size_t N, typename IteratorType, enable_if_t<N == 1, int> = 0>\nauto get(const nlohmann::detail::iteration_proxy_value<IteratorType>& i) -> decltype(i.value())\n{\n    return i.value();\n}\n\n}  // namespace detail\nNLOHMANN_JSON_NAMESPACE_END\n\n// The Addition to the STD Namespace is required to add\n// Structured Bindings Support to the iteration_proxy_value class\n// For further reference see https://blog.tartanllama.xyz/structured-bindings/\n// And see https://github.com/nlohmann/json/pull/1391\nnamespace std\n{\n\n#if defined(__clang__)\n    // Fix: https://github.com/nlohmann/json/issues/1401\n    #pragma clang diagnostic push\n    #pragma clang diagnostic ignored \"-Wmismatched-tags\"\n#endif\ntemplate<typename IteratorType>\nclass tuple_size<::nlohmann::detail::iteration_proxy_value<IteratorType>> // NOLINT(cert-dcl58-cpp)\n            : public std::integral_constant<std::size_t, 2> {};\n\ntemplate<std::size_t N, typename IteratorType>\nclass tuple_element<N, ::nlohmann::detail::iteration_proxy_value<IteratorType >> // NOLINT(cert-dcl58-cpp)\n{\n  public:\n    using type = decltype(\n                     get<N>(std::declval <\n                            ::nlohmann::detail::iteration_proxy_value<IteratorType >> ()));\n};\n#if defined(__clang__)\n    #pragma clang diagnostic pop\n#endif\n\n}  // namespace std\n\n#if JSON_HAS_RANGES\n    template <typename IteratorType>\n    inline constexpr bool ::std::ranges::enable_borrowed_range<::nlohmann::detail::iteration_proxy<IteratorType>> = true;\n#endif\n\n// #include <nlohmann/detail/macro_scope.hpp>\n\n// #include <nlohmann/detail/meta/cpp_future.hpp>\n\n// #include <nlohmann/detail/meta/std_fs.hpp>\n\n// #include <nlohmann/detail/meta/type_traits.hpp>\n\n// #include <nlohmann/detail/value_t.hpp>\n\n\nNLOHMANN_JSON_NAMESPACE_BEGIN\nnamespace detail\n{\n\n//////////////////\n// constructors //\n//////////////////\n\n/*\n * Note all external_constructor<>::construct functions need to call\n * j.m_data.m_value.destroy(j.m_data.m_type) to avoid a memory leak in case j contains an\n * allocated value (e.g., a string). See bug issue\n * https://github.com/nlohmann/json/issues/2865 for more information.\n */\n\ntemplate<value_t> struct external_constructor;\n\ntemplate<>\nstruct external_constructor<value_t::boolean>\n{\n    template<typename BasicJsonType>\n    static void construct(BasicJsonType& j, typename BasicJsonType::boolean_t b) noexcept\n    {\n        j.m_data.m_value.destroy(j.m_data.m_type);\n        j.m_data.m_type = value_t::boolean;\n        j.m_data.m_value = b;\n        j.assert_invariant();\n    }\n};\n\ntemplate<>\nstruct external_constructor<value_t::string>\n{\n    template<typename BasicJsonType>\n    static void construct(BasicJsonType& j, const typename BasicJsonType::string_t& s)\n    {\n        j.m_data.m_value.destroy(j.m_data.m_type);\n        j.m_data.m_type = value_t::string;\n        j.m_data.m_value = s;\n        j.assert_invariant();\n    }\n\n    template<typename BasicJsonType>\n    static void construct(BasicJsonType& j, typename BasicJsonType::string_t&& s)\n    {\n        j.m_data.m_value.destroy(j.m_data.m_type);\n        j.m_data.m_type = value_t::string;\n        j.m_data.m_value = std::move(s);\n        j.assert_invariant();\n    }\n\n    template < typename BasicJsonType, typename CompatibleStringType,\n               enable_if_t < !std::is_same<CompatibleStringType, typename BasicJsonType::string_t>::value,\n                             int > = 0 >\n    static void construct(BasicJsonType& j, const CompatibleStringType& str)\n    {\n        j.m_data.m_value.destroy(j.m_data.m_type);\n        j.m_data.m_type = value_t::string;\n        j.m_data.m_value.string = j.template create<typename BasicJsonType::string_t>(str);\n        j.assert_invariant();\n    }\n};\n\ntemplate<>\nstruct external_constructor<value_t::binary>\n{\n    template<typename BasicJsonType>\n    static void construct(BasicJsonType& j, const typename BasicJsonType::binary_t& b)\n    {\n        j.m_data.m_value.destroy(j.m_data.m_type);\n        j.m_data.m_type = value_t::binary;\n        j.m_data.m_value = typename BasicJsonType::binary_t(b);\n        j.assert_invariant();\n    }\n\n    template<typename BasicJsonType>\n    static void construct(BasicJsonType& j, typename BasicJsonType::binary_t&& b)\n    {\n        j.m_data.m_value.destroy(j.m_data.m_type);\n        j.m_data.m_type = value_t::binary;\n        j.m_data.m_value = typename BasicJsonType::binary_t(std::move(b));\n        j.assert_invariant();\n    }\n};\n\ntemplate<>\nstruct external_constructor<value_t::number_float>\n{\n    template<typename BasicJsonType>\n    static void construct(BasicJsonType& j, typename BasicJsonType::number_float_t val) noexcept\n    {\n        j.m_data.m_value.destroy(j.m_data.m_type);\n        j.m_data.m_type = value_t::number_float;\n        j.m_data.m_value = val;\n        j.assert_invariant();\n    }\n};\n\ntemplate<>\nstruct external_constructor<value_t::number_unsigned>\n{\n    template<typename BasicJsonType>\n    static void construct(BasicJsonType& j, typename BasicJsonType::number_unsigned_t val) noexcept\n    {\n        j.m_data.m_value.destroy(j.m_data.m_type);\n        j.m_data.m_type = value_t::number_unsigned;\n        j.m_data.m_value = val;\n        j.assert_invariant();\n    }\n};\n\ntemplate<>\nstruct external_constructor<value_t::number_integer>\n{\n    template<typename BasicJsonType>\n    static void construct(BasicJsonType& j, typename BasicJsonType::number_integer_t val) noexcept\n    {\n        j.m_data.m_value.destroy(j.m_data.m_type);\n        j.m_data.m_type = value_t::number_integer;\n        j.m_data.m_value = val;\n        j.assert_invariant();\n    }\n};\n\ntemplate<>\nstruct external_constructor<value_t::array>\n{\n    template<typename BasicJsonType>\n    static void construct(BasicJsonType& j, const typename BasicJsonType::array_t& arr)\n    {\n        j.m_data.m_value.destroy(j.m_data.m_type);\n        j.m_data.m_type = value_t::array;\n        j.m_data.m_value = arr;\n        j.set_parents();\n        j.assert_invariant();\n    }\n\n    template<typename BasicJsonType>\n    static void construct(BasicJsonType& j, typename BasicJsonType::array_t&& arr)\n    {\n        j.m_data.m_value.destroy(j.m_data.m_type);\n        j.m_data.m_type = value_t::array;\n        j.m_data.m_value = std::move(arr);\n        j.set_parents();\n        j.assert_invariant();\n    }\n\n    template < typename BasicJsonType, typename CompatibleArrayType,\n               enable_if_t < !std::is_same<CompatibleArrayType, typename BasicJsonType::array_t>::value,\n                             int > = 0 >\n    static void construct(BasicJsonType& j, const CompatibleArrayType& arr)\n    {\n        using std::begin;\n        using std::end;\n\n        j.m_data.m_value.destroy(j.m_data.m_type);\n        j.m_data.m_type = value_t::array;\n        j.m_data.m_value.array = j.template create<typename BasicJsonType::array_t>(begin(arr), end(arr));\n        j.set_parents();\n        j.assert_invariant();\n    }\n\n    template<typename BasicJsonType>\n    static void construct(BasicJsonType& j, const std::vector<bool>& arr)\n    {\n        j.m_data.m_value.destroy(j.m_data.m_type);\n        j.m_data.m_type = value_t::array;\n        j.m_data.m_value = value_t::array;\n        j.m_data.m_value.array->reserve(arr.size());\n        for (const bool x : arr)\n        {\n            j.m_data.m_value.array->push_back(x);\n            j.set_parent(j.m_data.m_value.array->back());\n        }\n        j.assert_invariant();\n    }\n\n    template<typename BasicJsonType, typename T,\n             enable_if_t<std::is_convertible<T, BasicJsonType>::value, int> = 0>\n    static void construct(BasicJsonType& j, const std::valarray<T>& arr)\n    {\n        j.m_data.m_value.destroy(j.m_data.m_type);\n        j.m_data.m_type = value_t::array;\n        j.m_data.m_value = value_t::array;\n        j.m_data.m_value.array->resize(arr.size());\n        if (arr.size() > 0)\n        {\n            std::copy(std::begin(arr), std::end(arr), j.m_data.m_value.array->begin());\n        }\n        j.set_parents();\n        j.assert_invariant();\n    }\n};\n\ntemplate<>\nstruct external_constructor<value_t::object>\n{\n    template<typename BasicJsonType>\n    static void construct(BasicJsonType& j, const typename BasicJsonType::object_t& obj)\n    {\n        j.m_data.m_value.destroy(j.m_data.m_type);\n        j.m_data.m_type = value_t::object;\n        j.m_data.m_value = obj;\n        j.set_parents();\n        j.assert_invariant();\n    }\n\n    template<typename BasicJsonType>\n    static void construct(BasicJsonType& j, typename BasicJsonType::object_t&& obj)\n    {\n        j.m_data.m_value.destroy(j.m_data.m_type);\n        j.m_data.m_type = value_t::object;\n        j.m_data.m_value = std::move(obj);\n        j.set_parents();\n        j.assert_invariant();\n    }\n\n    template < typename BasicJsonType, typename CompatibleObjectType,\n               enable_if_t < !std::is_same<CompatibleObjectType, typename BasicJsonType::object_t>::value, int > = 0 >\n    static void construct(BasicJsonType& j, const CompatibleObjectType& obj)\n    {\n        using std::begin;\n        using std::end;\n\n        j.m_data.m_value.destroy(j.m_data.m_type);\n        j.m_data.m_type = value_t::object;\n        j.m_data.m_value.object = j.template create<typename BasicJsonType::object_t>(begin(obj), end(obj));\n        j.set_parents();\n        j.assert_invariant();\n    }\n};\n\n/////////////\n// to_json //\n/////////////\n\ntemplate<typename BasicJsonType, typename T,\n         enable_if_t<std::is_same<T, typename BasicJsonType::boolean_t>::value, int> = 0>\ninline void to_json(BasicJsonType& j, T b) noexcept\n{\n    external_constructor<value_t::boolean>::construct(j, b);\n}\n\ntemplate < typename BasicJsonType, typename BoolRef,\n           enable_if_t <\n               ((std::is_same<std::vector<bool>::reference, BoolRef>::value\n                 && !std::is_same <std::vector<bool>::reference, typename BasicJsonType::boolean_t&>::value)\n                || (std::is_same<std::vector<bool>::const_reference, BoolRef>::value\n                    && !std::is_same <detail::uncvref_t<std::vector<bool>::const_reference>,\n                                      typename BasicJsonType::boolean_t >::value))\n               && std::is_convertible<const BoolRef&, typename BasicJsonType::boolean_t>::value, int > = 0 >\ninline void to_json(BasicJsonType& j, const BoolRef& b) noexcept\n{\n    external_constructor<value_t::boolean>::construct(j, static_cast<typename BasicJsonType::boolean_t>(b));\n}\n\ntemplate<typename BasicJsonType, typename CompatibleString,\n         enable_if_t<std::is_constructible<typename BasicJsonType::string_t, CompatibleString>::value, int> = 0>\ninline void to_json(BasicJsonType& j, const CompatibleString& s)\n{\n    external_constructor<value_t::string>::construct(j, s);\n}\n\ntemplate<typename BasicJsonType>\ninline void to_json(BasicJsonType& j, typename BasicJsonType::string_t&& s)\n{\n    external_constructor<value_t::string>::construct(j, std::move(s));\n}\n\ntemplate<typename BasicJsonType, typename FloatType,\n         enable_if_t<std::is_floating_point<FloatType>::value, int> = 0>\ninline void to_json(BasicJsonType& j, FloatType val) noexcept\n{\n    external_constructor<value_t::number_float>::construct(j, static_cast<typename BasicJsonType::number_float_t>(val));\n}\n\ntemplate<typename BasicJsonType, typename CompatibleNumberUnsignedType,\n         enable_if_t<is_compatible_integer_type<typename BasicJsonType::number_unsigned_t, CompatibleNumberUnsignedType>::value, int> = 0>\ninline void to_json(BasicJsonType& j, CompatibleNumberUnsignedType val) noexcept\n{\n    external_constructor<value_t::number_unsigned>::construct(j, static_cast<typename BasicJsonType::number_unsigned_t>(val));\n}\n\ntemplate<typename BasicJsonType, typename CompatibleNumberIntegerType,\n         enable_if_t<is_compatible_integer_type<typename BasicJsonType::number_integer_t, CompatibleNumberIntegerType>::value, int> = 0>\ninline void to_json(BasicJsonType& j, CompatibleNumberIntegerType val) noexcept\n{\n    external_constructor<value_t::number_integer>::construct(j, static_cast<typename BasicJsonType::number_integer_t>(val));\n}\n\n#if !JSON_DISABLE_ENUM_SERIALIZATION\ntemplate<typename BasicJsonType, typename EnumType,\n         enable_if_t<std::is_enum<EnumType>::value, int> = 0>\ninline void to_json(BasicJsonType& j, EnumType e) noexcept\n{\n    using underlying_type = typename std::underlying_type<EnumType>::type;\n    external_constructor<value_t::number_integer>::construct(j, static_cast<underlying_type>(e));\n}\n#endif  // JSON_DISABLE_ENUM_SERIALIZATION\n\ntemplate<typename BasicJsonType>\ninline void to_json(BasicJsonType& j, const std::vector<bool>& e)\n{\n    external_constructor<value_t::array>::construct(j, e);\n}\n\ntemplate < typename BasicJsonType, typename CompatibleArrayType,\n           enable_if_t < is_compatible_array_type<BasicJsonType,\n                         CompatibleArrayType>::value&&\n                         !is_compatible_object_type<BasicJsonType, CompatibleArrayType>::value&&\n                         !is_compatible_string_type<BasicJsonType, CompatibleArrayType>::value&&\n                         !std::is_same<typename BasicJsonType::binary_t, CompatibleArrayType>::value&&\n                         !is_basic_json<CompatibleArrayType>::value,\n                         int > = 0 >\ninline void to_json(BasicJsonType& j, const CompatibleArrayType& arr)\n{\n    external_constructor<value_t::array>::construct(j, arr);\n}\n\ntemplate<typename BasicJsonType>\ninline void to_json(BasicJsonType& j, const typename BasicJsonType::binary_t& bin)\n{\n    external_constructor<value_t::binary>::construct(j, bin);\n}\n\ntemplate<typename BasicJsonType, typename T,\n         enable_if_t<std::is_convertible<T, BasicJsonType>::value, int> = 0>\ninline void to_json(BasicJsonType& j, const std::valarray<T>& arr)\n{\n    external_constructor<value_t::array>::construct(j, std::move(arr));\n}\n\ntemplate<typename BasicJsonType>\ninline void to_json(BasicJsonType& j, typename BasicJsonType::array_t&& arr)\n{\n    external_constructor<value_t::array>::construct(j, std::move(arr));\n}\n\ntemplate < typename BasicJsonType, typename CompatibleObjectType,\n           enable_if_t < is_compatible_object_type<BasicJsonType, CompatibleObjectType>::value&& !is_basic_json<CompatibleObjectType>::value, int > = 0 >\ninline void to_json(BasicJsonType& j, const CompatibleObjectType& obj)\n{\n    external_constructor<value_t::object>::construct(j, obj);\n}\n\ntemplate<typename BasicJsonType>\ninline void to_json(BasicJsonType& j, typename BasicJsonType::object_t&& obj)\n{\n    external_constructor<value_t::object>::construct(j, std::move(obj));\n}\n\ntemplate <\n    typename BasicJsonType, typename T, std::size_t N,\n    enable_if_t < !std::is_constructible<typename BasicJsonType::string_t,\n                  const T(&)[N]>::value, // NOLINT(cppcoreguidelines-avoid-c-arrays,hicpp-avoid-c-arrays,modernize-avoid-c-arrays)\n                  int > = 0 >\ninline void to_json(BasicJsonType& j, const T(&arr)[N]) // NOLINT(cppcoreguidelines-avoid-c-arrays,hicpp-avoid-c-arrays,modernize-avoid-c-arrays)\n{\n    external_constructor<value_t::array>::construct(j, arr);\n}\n\ntemplate < typename BasicJsonType, typename T1, typename T2, enable_if_t < std::is_constructible<BasicJsonType, T1>::value&& std::is_constructible<BasicJsonType, T2>::value, int > = 0 >\ninline void to_json(BasicJsonType& j, const std::pair<T1, T2>& p)\n{\n    j = { p.first, p.second };\n}\n\n// for https://github.com/nlohmann/json/pull/1134\ntemplate<typename BasicJsonType, typename T,\n         enable_if_t<std::is_same<T, iteration_proxy_value<typename BasicJsonType::iterator>>::value, int> = 0>\ninline void to_json(BasicJsonType& j, const T& b)\n{\n    j = { {b.key(), b.value()} };\n}\n\ntemplate<typename BasicJsonType, typename Tuple, std::size_t... Idx>\ninline void to_json_tuple_impl(BasicJsonType& j, const Tuple& t, index_sequence<Idx...> /*unused*/)\n{\n    j = { std::get<Idx>(t)... };\n}\n\ntemplate<typename BasicJsonType, typename T, enable_if_t<is_constructible_tuple<BasicJsonType, T>::value, int > = 0>\ninline void to_json(BasicJsonType& j, const T& t)\n{\n    to_json_tuple_impl(j, t, make_index_sequence<std::tuple_size<T>::value> {});\n}\n\n#if JSON_HAS_FILESYSTEM || JSON_HAS_EXPERIMENTAL_FILESYSTEM\ntemplate<typename BasicJsonType>\ninline void to_json(BasicJsonType& j, const std_fs::path& p)\n{\n    j = p.string();\n}\n#endif\n\nstruct to_json_fn\n{\n    template<typename BasicJsonType, typename T>\n    auto operator()(BasicJsonType& j, T&& val) const noexcept(noexcept(to_json(j, std::forward<T>(val))))\n    -> decltype(to_json(j, std::forward<T>(val)), void())\n    {\n        return to_json(j, std::forward<T>(val));\n    }\n};\n}  // namespace detail\n\n#ifndef JSON_HAS_CPP_17\n/// namespace to hold default `to_json` function\n/// to see why this is required:\n/// http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2015/n4381.html\nnamespace // NOLINT(cert-dcl59-cpp,fuchsia-header-anon-namespaces,google-build-namespaces)\n{\n#endif\nJSON_INLINE_VARIABLE constexpr const auto& to_json = // NOLINT(misc-definitions-in-headers)\n    detail::static_const<detail::to_json_fn>::value;\n#ifndef JSON_HAS_CPP_17\n}  // namespace\n#endif\n\nNLOHMANN_JSON_NAMESPACE_END\n\n// #include <nlohmann/detail/meta/identity_tag.hpp>\n\n\nNLOHMANN_JSON_NAMESPACE_BEGIN\n\n/// @sa https://json.nlohmann.me/api/adl_serializer/\ntemplate<typename ValueType, typename>\nstruct adl_serializer\n{\n    /// @brief convert a JSON value to any value type\n    /// @sa https://json.nlohmann.me/api/adl_serializer/from_json/\n    template<typename BasicJsonType, typename TargetType = ValueType>\n    static auto from_json(BasicJsonType && j, TargetType& val) noexcept(\n        noexcept(::nlohmann::from_json(std::forward<BasicJsonType>(j), val)))\n    -> decltype(::nlohmann::from_json(std::forward<BasicJsonType>(j), val), void())\n    {\n        ::nlohmann::from_json(std::forward<BasicJsonType>(j), val);\n    }\n\n    /// @brief convert a JSON value to any value type\n    /// @sa https://json.nlohmann.me/api/adl_serializer/from_json/\n    template<typename BasicJsonType, typename TargetType = ValueType>\n    static auto from_json(BasicJsonType && j) noexcept(\n    noexcept(::nlohmann::from_json(std::forward<BasicJsonType>(j), detail::identity_tag<TargetType> {})))\n    -> decltype(::nlohmann::from_json(std::forward<BasicJsonType>(j), detail::identity_tag<TargetType> {}))\n    {\n        return ::nlohmann::from_json(std::forward<BasicJsonType>(j), detail::identity_tag<TargetType> {});\n    }\n\n    /// @brief convert any value type to a JSON value\n    /// @sa https://json.nlohmann.me/api/adl_serializer/to_json/\n    template<typename BasicJsonType, typename TargetType = ValueType>\n    static auto to_json(BasicJsonType& j, TargetType && val) noexcept(\n        noexcept(::nlohmann::to_json(j, std::forward<TargetType>(val))))\n    -> decltype(::nlohmann::to_json(j, std::forward<TargetType>(val)), void())\n    {\n        ::nlohmann::to_json(j, std::forward<TargetType>(val));\n    }\n};\n\nNLOHMANN_JSON_NAMESPACE_END\n\n// #include <nlohmann/byte_container_with_subtype.hpp>\n//     __ _____ _____ _____\n//  __|  |   __|     |   | |  JSON for Modern C++\n// |  |  |__   |  |  | | | |  version 3.11.3\n// |_____|_____|_____|_|___|  https://github.com/nlohmann/json\n//\n// SPDX-FileCopyrightText: 2013-2023 Niels Lohmann <https://nlohmann.me>\n// SPDX-License-Identifier: MIT\n\n\n\n#include <cstdint> // uint8_t, uint64_t\n#include <tuple> // tie\n#include <utility> // move\n\n// #include <nlohmann/detail/abi_macros.hpp>\n\n\nNLOHMANN_JSON_NAMESPACE_BEGIN\n\n/// @brief an internal type for a backed binary type\n/// @sa https://json.nlohmann.me/api/byte_container_with_subtype/\ntemplate<typename BinaryType>\nclass byte_container_with_subtype : public BinaryType\n{\n  public:\n    using container_type = BinaryType;\n    using subtype_type = std::uint64_t;\n\n    /// @sa https://json.nlohmann.me/api/byte_container_with_subtype/byte_container_with_subtype/\n    byte_container_with_subtype() noexcept(noexcept(container_type()))\n        : container_type()\n    {}\n\n    /// @sa https://json.nlohmann.me/api/byte_container_with_subtype/byte_container_with_subtype/\n    byte_container_with_subtype(const container_type& b) noexcept(noexcept(container_type(b)))\n        : container_type(b)\n    {}\n\n    /// @sa https://json.nlohmann.me/api/byte_container_with_subtype/byte_container_with_subtype/\n    byte_container_with_subtype(container_type&& b) noexcept(noexcept(container_type(std::move(b))))\n        : container_type(std::move(b))\n    {}\n\n    /// @sa https://json.nlohmann.me/api/byte_container_with_subtype/byte_container_with_subtype/\n    byte_container_with_subtype(const container_type& b, subtype_type subtype_) noexcept(noexcept(container_type(b)))\n        : container_type(b)\n        , m_subtype(subtype_)\n        , m_has_subtype(true)\n    {}\n\n    /// @sa https://json.nlohmann.me/api/byte_container_with_subtype/byte_container_with_subtype/\n    byte_container_with_subtype(container_type&& b, subtype_type subtype_) noexcept(noexcept(container_type(std::move(b))))\n        : container_type(std::move(b))\n        , m_subtype(subtype_)\n        , m_has_subtype(true)\n    {}\n\n    bool operator==(const byte_container_with_subtype& rhs) const\n    {\n        return std::tie(static_cast<const BinaryType&>(*this), m_subtype, m_has_subtype) ==\n               std::tie(static_cast<const BinaryType&>(rhs), rhs.m_subtype, rhs.m_has_subtype);\n    }\n\n    bool operator!=(const byte_container_with_subtype& rhs) const\n    {\n        return !(rhs == *this);\n    }\n\n    /// @brief sets the binary subtype\n    /// @sa https://json.nlohmann.me/api/byte_container_with_subtype/set_subtype/\n    void set_subtype(subtype_type subtype_) noexcept\n    {\n        m_subtype = subtype_;\n        m_has_subtype = true;\n    }\n\n    /// @brief return the binary subtype\n    /// @sa https://json.nlohmann.me/api/byte_container_with_subtype/subtype/\n    constexpr subtype_type subtype() const noexcept\n    {\n        return m_has_subtype ? m_subtype : static_cast<subtype_type>(-1);\n    }\n\n    /// @brief return whether the value has a subtype\n    /// @sa https://json.nlohmann.me/api/byte_container_with_subtype/has_subtype/\n    constexpr bool has_subtype() const noexcept\n    {\n        return m_has_subtype;\n    }\n\n    /// @brief clears the binary subtype\n    /// @sa https://json.nlohmann.me/api/byte_container_with_subtype/clear_subtype/\n    void clear_subtype() noexcept\n    {\n        m_subtype = 0;\n        m_has_subtype = false;\n    }\n\n  private:\n    subtype_type m_subtype = 0;\n    bool m_has_subtype = false;\n};\n\nNLOHMANN_JSON_NAMESPACE_END\n\n// #include <nlohmann/detail/conversions/from_json.hpp>\n\n// #include <nlohmann/detail/conversions/to_json.hpp>\n\n// #include <nlohmann/detail/exceptions.hpp>\n\n// #include <nlohmann/detail/hash.hpp>\n//     __ _____ _____ _____\n//  __|  |   __|     |   | |  JSON for Modern C++\n// |  |  |__   |  |  | | | |  version 3.11.3\n// |_____|_____|_____|_|___|  https://github.com/nlohmann/json\n//\n// SPDX-FileCopyrightText: 2013-2023 Niels Lohmann <https://nlohmann.me>\n// SPDX-License-Identifier: MIT\n\n\n\n#include <cstdint> // uint8_t\n#include <cstddef> // size_t\n#include <functional> // hash\n\n// #include <nlohmann/detail/abi_macros.hpp>\n\n// #include <nlohmann/detail/value_t.hpp>\n\n\nNLOHMANN_JSON_NAMESPACE_BEGIN\nnamespace detail\n{\n\n// boost::hash_combine\ninline std::size_t combine(std::size_t seed, std::size_t h) noexcept\n{\n    seed ^= h + 0x9e3779b9 + (seed << 6U) + (seed >> 2U);\n    return seed;\n}\n\n/*!\n@brief hash a JSON value\n\nThe hash function tries to rely on std::hash where possible. Furthermore, the\ntype of the JSON value is taken into account to have different hash values for\nnull, 0, 0U, and false, etc.\n\n@tparam BasicJsonType basic_json specialization\n@param j JSON value to hash\n@return hash value of j\n*/\ntemplate<typename BasicJsonType>\nstd::size_t hash(const BasicJsonType& j)\n{\n    using string_t = typename BasicJsonType::string_t;\n    using number_integer_t = typename BasicJsonType::number_integer_t;\n    using number_unsigned_t = typename BasicJsonType::number_unsigned_t;\n    using number_float_t = typename BasicJsonType::number_float_t;\n\n    const auto type = static_cast<std::size_t>(j.type());\n    switch (j.type())\n    {\n        case BasicJsonType::value_t::null:\n        case BasicJsonType::value_t::discarded:\n        {\n            return combine(type, 0);\n        }\n\n        case BasicJsonType::value_t::object:\n        {\n            auto seed = combine(type, j.size());\n            for (const auto& element : j.items())\n            {\n                const auto h = std::hash<string_t> {}(element.key());\n                seed = combine(seed, h);\n                seed = combine(seed, hash(element.value()));\n            }\n            return seed;\n        }\n\n        case BasicJsonType::value_t::array:\n        {\n            auto seed = combine(type, j.size());\n            for (const auto& element : j)\n            {\n                seed = combine(seed, hash(element));\n            }\n            return seed;\n        }\n\n        case BasicJsonType::value_t::string:\n        {\n            const auto h = std::hash<string_t> {}(j.template get_ref<const string_t&>());\n            return combine(type, h);\n        }\n\n        case BasicJsonType::value_t::boolean:\n        {\n            const auto h = std::hash<bool> {}(j.template get<bool>());\n            return combine(type, h);\n        }\n\n        case BasicJsonType::value_t::number_integer:\n        {\n            const auto h = std::hash<number_integer_t> {}(j.template get<number_integer_t>());\n            return combine(type, h);\n        }\n\n        case BasicJsonType::value_t::number_unsigned:\n        {\n            const auto h = std::hash<number_unsigned_t> {}(j.template get<number_unsigned_t>());\n            return combine(type, h);\n        }\n\n        case BasicJsonType::value_t::number_float:\n        {\n            const auto h = std::hash<number_float_t> {}(j.template get<number_float_t>());\n            return combine(type, h);\n        }\n\n        case BasicJsonType::value_t::binary:\n        {\n            auto seed = combine(type, j.get_binary().size());\n            const auto h = std::hash<bool> {}(j.get_binary().has_subtype());\n            seed = combine(seed, h);\n            seed = combine(seed, static_cast<std::size_t>(j.get_binary().subtype()));\n            for (const auto byte : j.get_binary())\n            {\n                seed = combine(seed, std::hash<std::uint8_t> {}(byte));\n            }\n            return seed;\n        }\n\n        default:                   // LCOV_EXCL_LINE\n            JSON_ASSERT(false); // NOLINT(cert-dcl03-c,hicpp-static-assert,misc-static-assert) LCOV_EXCL_LINE\n            return 0;              // LCOV_EXCL_LINE\n    }\n}\n\n}  // namespace detail\nNLOHMANN_JSON_NAMESPACE_END\n\n// #include <nlohmann/detail/input/binary_reader.hpp>\n//     __ _____ _____ _____\n//  __|  |   __|     |   | |  JSON for Modern C++\n// |  |  |__   |  |  | | | |  version 3.11.3\n// |_____|_____|_____|_|___|  https://github.com/nlohmann/json\n//\n// SPDX-FileCopyrightText: 2013-2023 Niels Lohmann <https://nlohmann.me>\n// SPDX-License-Identifier: MIT\n\n\n\n#include <algorithm> // generate_n\n#include <array> // array\n#include <cmath> // ldexp\n#include <cstddef> // size_t\n#include <cstdint> // uint8_t, uint16_t, uint32_t, uint64_t\n#include <cstdio> // snprintf\n#include <cstring> // memcpy\n#include <iterator> // back_inserter\n#include <limits> // numeric_limits\n#include <string> // char_traits, string\n#include <utility> // make_pair, move\n#include <vector> // vector\n\n// #include <nlohmann/detail/exceptions.hpp>\n\n// #include <nlohmann/detail/input/input_adapters.hpp>\n//     __ _____ _____ _____\n//  __|  |   __|     |   | |  JSON for Modern C++\n// |  |  |__   |  |  | | | |  version 3.11.3\n// |_____|_____|_____|_|___|  https://github.com/nlohmann/json\n//\n// SPDX-FileCopyrightText: 2013-2023 Niels Lohmann <https://nlohmann.me>\n// SPDX-License-Identifier: MIT\n\n\n\n#include <array> // array\n#include <cstddef> // size_t\n#include <cstring> // strlen\n#include <iterator> // begin, end, iterator_traits, random_access_iterator_tag, distance, next\n#include <memory> // shared_ptr, make_shared, addressof\n#include <numeric> // accumulate\n#include <string> // string, char_traits\n#include <type_traits> // enable_if, is_base_of, is_pointer, is_integral, remove_pointer\n#include <utility> // pair, declval\n\n#ifndef JSON_NO_IO\n    #include <cstdio>   // FILE *\n    #include <istream>  // istream\n#endif                  // JSON_NO_IO\n\n// #include <nlohmann/detail/iterators/iterator_traits.hpp>\n\n// #include <nlohmann/detail/macro_scope.hpp>\n\n// #include <nlohmann/detail/meta/type_traits.hpp>\n\n\nNLOHMANN_JSON_NAMESPACE_BEGIN\nnamespace detail\n{\n\n/// the supported input formats\nenum class input_format_t { json, cbor, msgpack, ubjson, bson, bjdata };\n\n////////////////////\n// input adapters //\n////////////////////\n\n#ifndef JSON_NO_IO\n/*!\nInput adapter for stdio file access. This adapter read only 1 byte and do not use any\n buffer. This adapter is a very low level adapter.\n*/\nclass file_input_adapter\n{\n  public:\n    using char_type = char;\n\n    JSON_HEDLEY_NON_NULL(2)\n    explicit file_input_adapter(std::FILE* f) noexcept\n        : m_file(f)\n    {\n        JSON_ASSERT(m_file != nullptr);\n    }\n\n    // make class move-only\n    file_input_adapter(const file_input_adapter&) = delete;\n    file_input_adapter(file_input_adapter&&) noexcept = default;\n    file_input_adapter& operator=(const file_input_adapter&) = delete;\n    file_input_adapter& operator=(file_input_adapter&&) = delete;\n    ~file_input_adapter() = default;\n\n    std::char_traits<char>::int_type get_character() noexcept\n    {\n        return std::fgetc(m_file);\n    }\n\n  private:\n    /// the file pointer to read from\n    std::FILE* m_file;\n};\n\n/*!\nInput adapter for a (caching) istream. Ignores a UFT Byte Order Mark at\nbeginning of input. Does not support changing the underlying std::streambuf\nin mid-input. Maintains underlying std::istream and std::streambuf to support\nsubsequent use of standard std::istream operations to process any input\ncharacters following those used in parsing the JSON input.  Clears the\nstd::istream flags; any input errors (e.g., EOF) will be detected by the first\nsubsequent call for input from the std::istream.\n*/\nclass input_stream_adapter\n{\n  public:\n    using char_type = char;\n\n    ~input_stream_adapter()\n    {\n        // clear stream flags; we use underlying streambuf I/O, do not\n        // maintain ifstream flags, except eof\n        if (is != nullptr)\n        {\n            is->clear(is->rdstate() & std::ios::eofbit);\n        }\n    }\n\n    explicit input_stream_adapter(std::istream& i)\n        : is(&i), sb(i.rdbuf())\n    {}\n\n    // delete because of pointer members\n    input_stream_adapter(const input_stream_adapter&) = delete;\n    input_stream_adapter& operator=(input_stream_adapter&) = delete;\n    input_stream_adapter& operator=(input_stream_adapter&&) = delete;\n\n    input_stream_adapter(input_stream_adapter&& rhs) noexcept\n        : is(rhs.is), sb(rhs.sb)\n    {\n        rhs.is = nullptr;\n        rhs.sb = nullptr;\n    }\n\n    // std::istream/std::streambuf use std::char_traits<char>::to_int_type, to\n    // ensure that std::char_traits<char>::eof() and the character 0xFF do not\n    // end up as the same value, e.g. 0xFFFFFFFF.\n    std::char_traits<char>::int_type get_character()\n    {\n        auto res = sb->sbumpc();\n        // set eof manually, as we don't use the istream interface.\n        if (JSON_HEDLEY_UNLIKELY(res == std::char_traits<char>::eof()))\n        {\n            is->clear(is->rdstate() | std::ios::eofbit);\n        }\n        return res;\n    }\n\n  private:\n    /// the associated input stream\n    std::istream* is = nullptr;\n    std::streambuf* sb = nullptr;\n};\n#endif  // JSON_NO_IO\n\n// General-purpose iterator-based adapter. It might not be as fast as\n// theoretically possible for some containers, but it is extremely versatile.\ntemplate<typename IteratorType>\nclass iterator_input_adapter\n{\n  public:\n    using char_type = typename std::iterator_traits<IteratorType>::value_type;\n\n    iterator_input_adapter(IteratorType first, IteratorType last)\n        : current(std::move(first)), end(std::move(last))\n    {}\n\n    typename char_traits<char_type>::int_type get_character()\n    {\n        if (JSON_HEDLEY_LIKELY(current != end))\n        {\n            auto result = char_traits<char_type>::to_int_type(*current);\n            std::advance(current, 1);\n            return result;\n        }\n\n        return char_traits<char_type>::eof();\n    }\n\n  private:\n    IteratorType current;\n    IteratorType end;\n\n    template<typename BaseInputAdapter, size_t T>\n    friend struct wide_string_input_helper;\n\n    bool empty() const\n    {\n        return current == end;\n    }\n};\n\ntemplate<typename BaseInputAdapter, size_t T>\nstruct wide_string_input_helper;\n\ntemplate<typename BaseInputAdapter>\nstruct wide_string_input_helper<BaseInputAdapter, 4>\n{\n    // UTF-32\n    static void fill_buffer(BaseInputAdapter& input,\n                            std::array<std::char_traits<char>::int_type, 4>& utf8_bytes,\n                            size_t& utf8_bytes_index,\n                            size_t& utf8_bytes_filled)\n    {\n        utf8_bytes_index = 0;\n\n        if (JSON_HEDLEY_UNLIKELY(input.empty()))\n        {\n            utf8_bytes[0] = std::char_traits<char>::eof();\n            utf8_bytes_filled = 1;\n        }\n        else\n        {\n            // get the current character\n            const auto wc = input.get_character();\n\n            // UTF-32 to UTF-8 encoding\n            if (wc < 0x80)\n            {\n                utf8_bytes[0] = static_cast<std::char_traits<char>::int_type>(wc);\n                utf8_bytes_filled = 1;\n            }\n            else if (wc <= 0x7FF)\n            {\n                utf8_bytes[0] = static_cast<std::char_traits<char>::int_type>(0xC0u | ((static_cast<unsigned int>(wc) >> 6u) & 0x1Fu));\n                utf8_bytes[1] = static_cast<std::char_traits<char>::int_type>(0x80u | (static_cast<unsigned int>(wc) & 0x3Fu));\n                utf8_bytes_filled = 2;\n            }\n            else if (wc <= 0xFFFF)\n            {\n                utf8_bytes[0] = static_cast<std::char_traits<char>::int_type>(0xE0u | ((static_cast<unsigned int>(wc) >> 12u) & 0x0Fu));\n                utf8_bytes[1] = static_cast<std::char_traits<char>::int_type>(0x80u | ((static_cast<unsigned int>(wc) >> 6u) & 0x3Fu));\n                utf8_bytes[2] = static_cast<std::char_traits<char>::int_type>(0x80u | (static_cast<unsigned int>(wc) & 0x3Fu));\n                utf8_bytes_filled = 3;\n            }\n            else if (wc <= 0x10FFFF)\n            {\n                utf8_bytes[0] = static_cast<std::char_traits<char>::int_type>(0xF0u | ((static_cast<unsigned int>(wc) >> 18u) & 0x07u));\n                utf8_bytes[1] = static_cast<std::char_traits<char>::int_type>(0x80u | ((static_cast<unsigned int>(wc) >> 12u) & 0x3Fu));\n                utf8_bytes[2] = static_cast<std::char_traits<char>::int_type>(0x80u | ((static_cast<unsigned int>(wc) >> 6u) & 0x3Fu));\n                utf8_bytes[3] = static_cast<std::char_traits<char>::int_type>(0x80u | (static_cast<unsigned int>(wc) & 0x3Fu));\n                utf8_bytes_filled = 4;\n            }\n            else\n            {\n                // unknown character\n                utf8_bytes[0] = static_cast<std::char_traits<char>::int_type>(wc);\n                utf8_bytes_filled = 1;\n            }\n        }\n    }\n};\n\ntemplate<typename BaseInputAdapter>\nstruct wide_string_input_helper<BaseInputAdapter, 2>\n{\n    // UTF-16\n    static void fill_buffer(BaseInputAdapter& input,\n                            std::array<std::char_traits<char>::int_type, 4>& utf8_bytes,\n                            size_t& utf8_bytes_index,\n                            size_t& utf8_bytes_filled)\n    {\n        utf8_bytes_index = 0;\n\n        if (JSON_HEDLEY_UNLIKELY(input.empty()))\n        {\n            utf8_bytes[0] = std::char_traits<char>::eof();\n            utf8_bytes_filled = 1;\n        }\n        else\n        {\n            // get the current character\n            const auto wc = input.get_character();\n\n            // UTF-16 to UTF-8 encoding\n            if (wc < 0x80)\n            {\n                utf8_bytes[0] = static_cast<std::char_traits<char>::int_type>(wc);\n                utf8_bytes_filled = 1;\n            }\n            else if (wc <= 0x7FF)\n            {\n                utf8_bytes[0] = static_cast<std::char_traits<char>::int_type>(0xC0u | ((static_cast<unsigned int>(wc) >> 6u)));\n                utf8_bytes[1] = static_cast<std::char_traits<char>::int_type>(0x80u | (static_cast<unsigned int>(wc) & 0x3Fu));\n                utf8_bytes_filled = 2;\n            }\n            else if (0xD800 > wc || wc >= 0xE000)\n            {\n                utf8_bytes[0] = static_cast<std::char_traits<char>::int_type>(0xE0u | ((static_cast<unsigned int>(wc) >> 12u)));\n                utf8_bytes[1] = static_cast<std::char_traits<char>::int_type>(0x80u | ((static_cast<unsigned int>(wc) >> 6u) & 0x3Fu));\n                utf8_bytes[2] = static_cast<std::char_traits<char>::int_type>(0x80u | (static_cast<unsigned int>(wc) & 0x3Fu));\n                utf8_bytes_filled = 3;\n            }\n            else\n            {\n                if (JSON_HEDLEY_UNLIKELY(!input.empty()))\n                {\n                    const auto wc2 = static_cast<unsigned int>(input.get_character());\n                    const auto charcode = 0x10000u + (((static_cast<unsigned int>(wc) & 0x3FFu) << 10u) | (wc2 & 0x3FFu));\n                    utf8_bytes[0] = static_cast<std::char_traits<char>::int_type>(0xF0u | (charcode >> 18u));\n                    utf8_bytes[1] = static_cast<std::char_traits<char>::int_type>(0x80u | ((charcode >> 12u) & 0x3Fu));\n                    utf8_bytes[2] = static_cast<std::char_traits<char>::int_type>(0x80u | ((charcode >> 6u) & 0x3Fu));\n                    utf8_bytes[3] = static_cast<std::char_traits<char>::int_type>(0x80u | (charcode & 0x3Fu));\n                    utf8_bytes_filled = 4;\n                }\n                else\n                {\n                    utf8_bytes[0] = static_cast<std::char_traits<char>::int_type>(wc);\n                    utf8_bytes_filled = 1;\n                }\n            }\n        }\n    }\n};\n\n// Wraps another input adapter to convert wide character types into individual bytes.\ntemplate<typename BaseInputAdapter, typename WideCharType>\nclass wide_string_input_adapter\n{\n  public:\n    using char_type = char;\n\n    wide_string_input_adapter(BaseInputAdapter base)\n        : base_adapter(base) {}\n\n    typename std::char_traits<char>::int_type get_character() noexcept\n    {\n        // check if buffer needs to be filled\n        if (utf8_bytes_index == utf8_bytes_filled)\n        {\n            fill_buffer<sizeof(WideCharType)>();\n\n            JSON_ASSERT(utf8_bytes_filled > 0);\n            JSON_ASSERT(utf8_bytes_index == 0);\n        }\n\n        // use buffer\n        JSON_ASSERT(utf8_bytes_filled > 0);\n        JSON_ASSERT(utf8_bytes_index < utf8_bytes_filled);\n        return utf8_bytes[utf8_bytes_index++];\n    }\n\n  private:\n    BaseInputAdapter base_adapter;\n\n    template<size_t T>\n    void fill_buffer()\n    {\n        wide_string_input_helper<BaseInputAdapter, T>::fill_buffer(base_adapter, utf8_bytes, utf8_bytes_index, utf8_bytes_filled);\n    }\n\n    /// a buffer for UTF-8 bytes\n    std::array<std::char_traits<char>::int_type, 4> utf8_bytes = {{0, 0, 0, 0}};\n\n    /// index to the utf8_codes array for the next valid byte\n    std::size_t utf8_bytes_index = 0;\n    /// number of valid bytes in the utf8_codes array\n    std::size_t utf8_bytes_filled = 0;\n};\n\ntemplate<typename IteratorType, typename Enable = void>\nstruct iterator_input_adapter_factory\n{\n    using iterator_type = IteratorType;\n    using char_type = typename std::iterator_traits<iterator_type>::value_type;\n    using adapter_type = iterator_input_adapter<iterator_type>;\n\n    static adapter_type create(IteratorType first, IteratorType last)\n    {\n        return adapter_type(std::move(first), std::move(last));\n    }\n};\n\ntemplate<typename T>\nstruct is_iterator_of_multibyte\n{\n    using value_type = typename std::iterator_traits<T>::value_type;\n    enum\n    {\n        value = sizeof(value_type) > 1\n    };\n};\n\ntemplate<typename IteratorType>\nstruct iterator_input_adapter_factory<IteratorType, enable_if_t<is_iterator_of_multibyte<IteratorType>::value>>\n{\n    using iterator_type = IteratorType;\n    using char_type = typename std::iterator_traits<iterator_type>::value_type;\n    using base_adapter_type = iterator_input_adapter<iterator_type>;\n    using adapter_type = wide_string_input_adapter<base_adapter_type, char_type>;\n\n    static adapter_type create(IteratorType first, IteratorType last)\n    {\n        return adapter_type(base_adapter_type(std::move(first), std::move(last)));\n    }\n};\n\n// General purpose iterator-based input\ntemplate<typename IteratorType>\ntypename iterator_input_adapter_factory<IteratorType>::adapter_type input_adapter(IteratorType first, IteratorType last)\n{\n    using factory_type = iterator_input_adapter_factory<IteratorType>;\n    return factory_type::create(first, last);\n}\n\n// Convenience shorthand from container to iterator\n// Enables ADL on begin(container) and end(container)\n// Encloses the using declarations in namespace for not to leak them to outside scope\n\nnamespace container_input_adapter_factory_impl\n{\n\nusing std::begin;\nusing std::end;\n\ntemplate<typename ContainerType, typename Enable = void>\nstruct container_input_adapter_factory {};\n\ntemplate<typename ContainerType>\nstruct container_input_adapter_factory< ContainerType,\n       void_t<decltype(begin(std::declval<ContainerType>()), end(std::declval<ContainerType>()))>>\n       {\n           using adapter_type = decltype(input_adapter(begin(std::declval<ContainerType>()), end(std::declval<ContainerType>())));\n\n           static adapter_type create(const ContainerType& container)\n{\n    return input_adapter(begin(container), end(container));\n}\n       };\n\n}  // namespace container_input_adapter_factory_impl\n\ntemplate<typename ContainerType>\ntypename container_input_adapter_factory_impl::container_input_adapter_factory<ContainerType>::adapter_type input_adapter(const ContainerType& container)\n{\n    return container_input_adapter_factory_impl::container_input_adapter_factory<ContainerType>::create(container);\n}\n\n#ifndef JSON_NO_IO\n// Special cases with fast paths\ninline file_input_adapter input_adapter(std::FILE* file)\n{\n    return file_input_adapter(file);\n}\n\ninline input_stream_adapter input_adapter(std::istream& stream)\n{\n    return input_stream_adapter(stream);\n}\n\ninline input_stream_adapter input_adapter(std::istream&& stream)\n{\n    return input_stream_adapter(stream);\n}\n#endif  // JSON_NO_IO\n\nusing contiguous_bytes_input_adapter = decltype(input_adapter(std::declval<const char*>(), std::declval<const char*>()));\n\n// Null-delimited strings, and the like.\ntemplate < typename CharT,\n           typename std::enable_if <\n               std::is_pointer<CharT>::value&&\n               !std::is_array<CharT>::value&&\n               std::is_integral<typename std::remove_pointer<CharT>::type>::value&&\n               sizeof(typename std::remove_pointer<CharT>::type) == 1,\n               int >::type = 0 >\ncontiguous_bytes_input_adapter input_adapter(CharT b)\n{\n    auto length = std::strlen(reinterpret_cast<const char*>(b));\n    const auto* ptr = reinterpret_cast<const char*>(b);\n    return input_adapter(ptr, ptr + length);\n}\n\ntemplate<typename T, std::size_t N>\nauto input_adapter(T (&array)[N]) -> decltype(input_adapter(array, array + N)) // NOLINT(cppcoreguidelines-avoid-c-arrays,hicpp-avoid-c-arrays,modernize-avoid-c-arrays)\n{\n    return input_adapter(array, array + N);\n}\n\n// This class only handles inputs of input_buffer_adapter type.\n// It's required so that expressions like {ptr, len} can be implicitly cast\n// to the correct adapter.\nclass span_input_adapter\n{\n  public:\n    template < typename CharT,\n               typename std::enable_if <\n                   std::is_pointer<CharT>::value&&\n                   std::is_integral<typename std::remove_pointer<CharT>::type>::value&&\n                   sizeof(typename std::remove_pointer<CharT>::type) == 1,\n                   int >::type = 0 >\n    span_input_adapter(CharT b, std::size_t l)\n        : ia(reinterpret_cast<const char*>(b), reinterpret_cast<const char*>(b) + l) {}\n\n    template<class IteratorType,\n             typename std::enable_if<\n                 std::is_same<typename iterator_traits<IteratorType>::iterator_category, std::random_access_iterator_tag>::value,\n                 int>::type = 0>\n    span_input_adapter(IteratorType first, IteratorType last)\n        : ia(input_adapter(first, last)) {}\n\n    contiguous_bytes_input_adapter&& get()\n    {\n        return std::move(ia); // NOLINT(hicpp-move-const-arg,performance-move-const-arg)\n    }\n\n  private:\n    contiguous_bytes_input_adapter ia;\n};\n\n}  // namespace detail\nNLOHMANN_JSON_NAMESPACE_END\n\n// #include <nlohmann/detail/input/json_sax.hpp>\n//     __ _____ _____ _____\n//  __|  |   __|     |   | |  JSON for Modern C++\n// |  |  |__   |  |  | | | |  version 3.11.3\n// |_____|_____|_____|_|___|  https://github.com/nlohmann/json\n//\n// SPDX-FileCopyrightText: 2013-2023 Niels Lohmann <https://nlohmann.me>\n// SPDX-License-Identifier: MIT\n\n\n\n#include <cstddef>\n#include <string> // string\n#include <utility> // move\n#include <vector> // vector\n\n// #include <nlohmann/detail/exceptions.hpp>\n\n// #include <nlohmann/detail/macro_scope.hpp>\n\n// #include <nlohmann/detail/string_concat.hpp>\n\n\nNLOHMANN_JSON_NAMESPACE_BEGIN\n\n/*!\n@brief SAX interface\n\nThis class describes the SAX interface used by @ref nlohmann::json::sax_parse.\nEach function is called in different situations while the input is parsed. The\nboolean return value informs the parser whether to continue processing the\ninput.\n*/\ntemplate<typename BasicJsonType>\nstruct json_sax\n{\n    using number_integer_t = typename BasicJsonType::number_integer_t;\n    using number_unsigned_t = typename BasicJsonType::number_unsigned_t;\n    using number_float_t = typename BasicJsonType::number_float_t;\n    using string_t = typename BasicJsonType::string_t;\n    using binary_t = typename BasicJsonType::binary_t;\n\n    /*!\n    @brief a null value was read\n    @return whether parsing should proceed\n    */\n    virtual bool null() = 0;\n\n    /*!\n    @brief a boolean value was read\n    @param[in] val  boolean value\n    @return whether parsing should proceed\n    */\n    virtual bool boolean(bool val) = 0;\n\n    /*!\n    @brief an integer number was read\n    @param[in] val  integer value\n    @return whether parsing should proceed\n    */\n    virtual bool number_integer(number_integer_t val) = 0;\n\n    /*!\n    @brief an unsigned integer number was read\n    @param[in] val  unsigned integer value\n    @return whether parsing should proceed\n    */\n    virtual bool number_unsigned(number_unsigned_t val) = 0;\n\n    /*!\n    @brief a floating-point number was read\n    @param[in] val  floating-point value\n    @param[in] s    raw token value\n    @return whether parsing should proceed\n    */\n    virtual bool number_float(number_float_t val, const string_t& s) = 0;\n\n    /*!\n    @brief a string value was read\n    @param[in] val  string value\n    @return whether parsing should proceed\n    @note It is safe to move the passed string value.\n    */\n    virtual bool string(string_t& val) = 0;\n\n    /*!\n    @brief a binary value was read\n    @param[in] val  binary value\n    @return whether parsing should proceed\n    @note It is safe to move the passed binary value.\n    */\n    virtual bool binary(binary_t& val) = 0;\n\n    /*!\n    @brief the beginning of an object was read\n    @param[in] elements  number of object elements or -1 if unknown\n    @return whether parsing should proceed\n    @note binary formats may report the number of elements\n    */\n    virtual bool start_object(std::size_t elements) = 0;\n\n    /*!\n    @brief an object key was read\n    @param[in] val  object key\n    @return whether parsing should proceed\n    @note It is safe to move the passed string.\n    */\n    virtual bool key(string_t& val) = 0;\n\n    /*!\n    @brief the end of an object was read\n    @return whether parsing should proceed\n    */\n    virtual bool end_object() = 0;\n\n    /*!\n    @brief the beginning of an array was read\n    @param[in] elements  number of array elements or -1 if unknown\n    @return whether parsing should proceed\n    @note binary formats may report the number of elements\n    */\n    virtual bool start_array(std::size_t elements) = 0;\n\n    /*!\n    @brief the end of an array was read\n    @return whether parsing should proceed\n    */\n    virtual bool end_array() = 0;\n\n    /*!\n    @brief a parse error occurred\n    @param[in] position    the position in the input where the error occurs\n    @param[in] last_token  the last read token\n    @param[in] ex          an exception object describing the error\n    @return whether parsing should proceed (must return false)\n    */\n    virtual bool parse_error(std::size_t position,\n                             const std::string& last_token,\n                             const detail::exception& ex) = 0;\n\n    json_sax() = default;\n    json_sax(const json_sax&) = default;\n    json_sax(json_sax&&) noexcept = default;\n    json_sax& operator=(const json_sax&) = default;\n    json_sax& operator=(json_sax&&) noexcept = default;\n    virtual ~json_sax() = default;\n};\n\nnamespace detail\n{\n/*!\n@brief SAX implementation to create a JSON value from SAX events\n\nThis class implements the @ref json_sax interface and processes the SAX events\nto create a JSON value which makes it basically a DOM parser. The structure or\nhierarchy of the JSON value is managed by the stack `ref_stack` which contains\na pointer to the respective array or object for each recursion depth.\n\nAfter successful parsing, the value that is passed by reference to the\nconstructor contains the parsed value.\n\n@tparam BasicJsonType  the JSON type\n*/\ntemplate<typename BasicJsonType>\nclass json_sax_dom_parser\n{\n  public:\n    using number_integer_t = typename BasicJsonType::number_integer_t;\n    using number_unsigned_t = typename BasicJsonType::number_unsigned_t;\n    using number_float_t = typename BasicJsonType::number_float_t;\n    using string_t = typename BasicJsonType::string_t;\n    using binary_t = typename BasicJsonType::binary_t;\n\n    /*!\n    @param[in,out] r  reference to a JSON value that is manipulated while\n                       parsing\n    @param[in] allow_exceptions_  whether parse errors yield exceptions\n    */\n    explicit json_sax_dom_parser(BasicJsonType& r, const bool allow_exceptions_ = true)\n        : root(r), allow_exceptions(allow_exceptions_)\n    {}\n\n    // make class move-only\n    json_sax_dom_parser(const json_sax_dom_parser&) = delete;\n    json_sax_dom_parser(json_sax_dom_parser&&) = default; // NOLINT(hicpp-noexcept-move,performance-noexcept-move-constructor)\n    json_sax_dom_parser& operator=(const json_sax_dom_parser&) = delete;\n    json_sax_dom_parser& operator=(json_sax_dom_parser&&) = default; // NOLINT(hicpp-noexcept-move,performance-noexcept-move-constructor)\n    ~json_sax_dom_parser() = default;\n\n    bool null()\n    {\n        handle_value(nullptr);\n        return true;\n    }\n\n    bool boolean(bool val)\n    {\n        handle_value(val);\n        return true;\n    }\n\n    bool number_integer(number_integer_t val)\n    {\n        handle_value(val);\n        return true;\n    }\n\n    bool number_unsigned(number_unsigned_t val)\n    {\n        handle_value(val);\n        return true;\n    }\n\n    bool number_float(number_float_t val, const string_t& /*unused*/)\n    {\n        handle_value(val);\n        return true;\n    }\n\n    bool string(string_t& val)\n    {\n        handle_value(val);\n        return true;\n    }\n\n    bool binary(binary_t& val)\n    {\n        handle_value(std::move(val));\n        return true;\n    }\n\n    bool start_object(std::size_t len)\n    {\n        ref_stack.push_back(handle_value(BasicJsonType::value_t::object));\n\n        if (JSON_HEDLEY_UNLIKELY(len != static_cast<std::size_t>(-1) && len > ref_stack.back()->max_size()))\n        {\n            JSON_THROW(out_of_range::create(408, concat(\"excessive object size: \", std::to_string(len)), ref_stack.back()));\n        }\n\n        return true;\n    }\n\n    bool key(string_t& val)\n    {\n        JSON_ASSERT(!ref_stack.empty());\n        JSON_ASSERT(ref_stack.back()->is_object());\n\n        // add null at given key and store the reference for later\n        object_element = &(ref_stack.back()->m_data.m_value.object->operator[](val));\n        return true;\n    }\n\n    bool end_object()\n    {\n        JSON_ASSERT(!ref_stack.empty());\n        JSON_ASSERT(ref_stack.back()->is_object());\n\n        ref_stack.back()->set_parents();\n        ref_stack.pop_back();\n        return true;\n    }\n\n    bool start_array(std::size_t len)\n    {\n        ref_stack.push_back(handle_value(BasicJsonType::value_t::array));\n\n        if (JSON_HEDLEY_UNLIKELY(len != static_cast<std::size_t>(-1) && len > ref_stack.back()->max_size()))\n        {\n            JSON_THROW(out_of_range::create(408, concat(\"excessive array size: \", std::to_string(len)), ref_stack.back()));\n        }\n\n        return true;\n    }\n\n    bool end_array()\n    {\n        JSON_ASSERT(!ref_stack.empty());\n        JSON_ASSERT(ref_stack.back()->is_array());\n\n        ref_stack.back()->set_parents();\n        ref_stack.pop_back();\n        return true;\n    }\n\n    template<class Exception>\n    bool parse_error(std::size_t /*unused*/, const std::string& /*unused*/,\n                     const Exception& ex)\n    {\n        errored = true;\n        static_cast<void>(ex);\n        if (allow_exceptions)\n        {\n            JSON_THROW(ex);\n        }\n        return false;\n    }\n\n    constexpr bool is_errored() const\n    {\n        return errored;\n    }\n\n  private:\n    /*!\n    @invariant If the ref stack is empty, then the passed value will be the new\n               root.\n    @invariant If the ref stack contains a value, then it is an array or an\n               object to which we can add elements\n    */\n    template<typename Value>\n    JSON_HEDLEY_RETURNS_NON_NULL\n    BasicJsonType* handle_value(Value&& v)\n    {\n        if (ref_stack.empty())\n        {\n            root = BasicJsonType(std::forward<Value>(v));\n            return &root;\n        }\n\n        JSON_ASSERT(ref_stack.back()->is_array() || ref_stack.back()->is_object());\n\n        if (ref_stack.back()->is_array())\n        {\n            ref_stack.back()->m_data.m_value.array->emplace_back(std::forward<Value>(v));\n            return &(ref_stack.back()->m_data.m_value.array->back());\n        }\n\n        JSON_ASSERT(ref_stack.back()->is_object());\n        JSON_ASSERT(object_element);\n        *object_element = BasicJsonType(std::forward<Value>(v));\n        return object_element;\n    }\n\n    /// the parsed JSON value\n    BasicJsonType& root;\n    /// stack to model hierarchy of values\n    std::vector<BasicJsonType*> ref_stack {};\n    /// helper to hold the reference for the next object element\n    BasicJsonType* object_element = nullptr;\n    /// whether a syntax error occurred\n    bool errored = false;\n    /// whether to throw exceptions in case of errors\n    const bool allow_exceptions = true;\n};\n\ntemplate<typename BasicJsonType>\nclass json_sax_dom_callback_parser\n{\n  public:\n    using number_integer_t = typename BasicJsonType::number_integer_t;\n    using number_unsigned_t = typename BasicJsonType::number_unsigned_t;\n    using number_float_t = typename BasicJsonType::number_float_t;\n    using string_t = typename BasicJsonType::string_t;\n    using binary_t = typename BasicJsonType::binary_t;\n    using parser_callback_t = typename BasicJsonType::parser_callback_t;\n    using parse_event_t = typename BasicJsonType::parse_event_t;\n\n    json_sax_dom_callback_parser(BasicJsonType& r,\n                                 const parser_callback_t cb,\n                                 const bool allow_exceptions_ = true)\n        : root(r), callback(cb), allow_exceptions(allow_exceptions_)\n    {\n        keep_stack.push_back(true);\n    }\n\n    // make class move-only\n    json_sax_dom_callback_parser(const json_sax_dom_callback_parser&) = delete;\n    json_sax_dom_callback_parser(json_sax_dom_callback_parser&&) = default; // NOLINT(hicpp-noexcept-move,performance-noexcept-move-constructor)\n    json_sax_dom_callback_parser& operator=(const json_sax_dom_callback_parser&) = delete;\n    json_sax_dom_callback_parser& operator=(json_sax_dom_callback_parser&&) = default; // NOLINT(hicpp-noexcept-move,performance-noexcept-move-constructor)\n    ~json_sax_dom_callback_parser() = default;\n\n    bool null()\n    {\n        handle_value(nullptr);\n        return true;\n    }\n\n    bool boolean(bool val)\n    {\n        handle_value(val);\n        return true;\n    }\n\n    bool number_integer(number_integer_t val)\n    {\n        handle_value(val);\n        return true;\n    }\n\n    bool number_unsigned(number_unsigned_t val)\n    {\n        handle_value(val);\n        return true;\n    }\n\n    bool number_float(number_float_t val, const string_t& /*unused*/)\n    {\n        handle_value(val);\n        return true;\n    }\n\n    bool string(string_t& val)\n    {\n        handle_value(val);\n        return true;\n    }\n\n    bool binary(binary_t& val)\n    {\n        handle_value(std::move(val));\n        return true;\n    }\n\n    bool start_object(std::size_t len)\n    {\n        // check callback for object start\n        const bool keep = callback(static_cast<int>(ref_stack.size()), parse_event_t::object_start, discarded);\n        keep_stack.push_back(keep);\n\n        auto val = handle_value(BasicJsonType::value_t::object, true);\n        ref_stack.push_back(val.second);\n\n        // check object limit\n        if (ref_stack.back() && JSON_HEDLEY_UNLIKELY(len != static_cast<std::size_t>(-1) && len > ref_stack.back()->max_size()))\n        {\n            JSON_THROW(out_of_range::create(408, concat(\"excessive object size: \", std::to_string(len)), ref_stack.back()));\n        }\n\n        return true;\n    }\n\n    bool key(string_t& val)\n    {\n        BasicJsonType k = BasicJsonType(val);\n\n        // check callback for key\n        const bool keep = callback(static_cast<int>(ref_stack.size()), parse_event_t::key, k);\n        key_keep_stack.push_back(keep);\n\n        // add discarded value at given key and store the reference for later\n        if (keep && ref_stack.back())\n        {\n            object_element = &(ref_stack.back()->m_data.m_value.object->operator[](val) = discarded);\n        }\n\n        return true;\n    }\n\n    bool end_object()\n    {\n        if (ref_stack.back())\n        {\n            if (!callback(static_cast<int>(ref_stack.size()) - 1, parse_event_t::object_end, *ref_stack.back()))\n            {\n                // discard object\n                *ref_stack.back() = discarded;\n            }\n            else\n            {\n                ref_stack.back()->set_parents();\n            }\n        }\n\n        JSON_ASSERT(!ref_stack.empty());\n        JSON_ASSERT(!keep_stack.empty());\n        ref_stack.pop_back();\n        keep_stack.pop_back();\n\n        if (!ref_stack.empty() && ref_stack.back() && ref_stack.back()->is_structured())\n        {\n            // remove discarded value\n            for (auto it = ref_stack.back()->begin(); it != ref_stack.back()->end(); ++it)\n            {\n                if (it->is_discarded())\n                {\n                    ref_stack.back()->erase(it);\n                    break;\n                }\n            }\n        }\n\n        return true;\n    }\n\n    bool start_array(std::size_t len)\n    {\n        const bool keep = callback(static_cast<int>(ref_stack.size()), parse_event_t::array_start, discarded);\n        keep_stack.push_back(keep);\n\n        auto val = handle_value(BasicJsonType::value_t::array, true);\n        ref_stack.push_back(val.second);\n\n        // check array limit\n        if (ref_stack.back() && JSON_HEDLEY_UNLIKELY(len != static_cast<std::size_t>(-1) && len > ref_stack.back()->max_size()))\n        {\n            JSON_THROW(out_of_range::create(408, concat(\"excessive array size: \", std::to_string(len)), ref_stack.back()));\n        }\n\n        return true;\n    }\n\n    bool end_array()\n    {\n        bool keep = true;\n\n        if (ref_stack.back())\n        {\n            keep = callback(static_cast<int>(ref_stack.size()) - 1, parse_event_t::array_end, *ref_stack.back());\n            if (keep)\n            {\n                ref_stack.back()->set_parents();\n            }\n            else\n            {\n                // discard array\n                *ref_stack.back() = discarded;\n            }\n        }\n\n        JSON_ASSERT(!ref_stack.empty());\n        JSON_ASSERT(!keep_stack.empty());\n        ref_stack.pop_back();\n        keep_stack.pop_back();\n\n        // remove discarded value\n        if (!keep && !ref_stack.empty() && ref_stack.back()->is_array())\n        {\n            ref_stack.back()->m_data.m_value.array->pop_back();\n        }\n\n        return true;\n    }\n\n    template<class Exception>\n    bool parse_error(std::size_t /*unused*/, const std::string& /*unused*/,\n                     const Exception& ex)\n    {\n        errored = true;\n        static_cast<void>(ex);\n        if (allow_exceptions)\n        {\n            JSON_THROW(ex);\n        }\n        return false;\n    }\n\n    constexpr bool is_errored() const\n    {\n        return errored;\n    }\n\n  private:\n    /*!\n    @param[in] v  value to add to the JSON value we build during parsing\n    @param[in] skip_callback  whether we should skip calling the callback\n               function; this is required after start_array() and\n               start_object() SAX events, because otherwise we would call the\n               callback function with an empty array or object, respectively.\n\n    @invariant If the ref stack is empty, then the passed value will be the new\n               root.\n    @invariant If the ref stack contains a value, then it is an array or an\n               object to which we can add elements\n\n    @return pair of boolean (whether value should be kept) and pointer (to the\n            passed value in the ref_stack hierarchy; nullptr if not kept)\n    */\n    template<typename Value>\n    std::pair<bool, BasicJsonType*> handle_value(Value&& v, const bool skip_callback = false)\n    {\n        JSON_ASSERT(!keep_stack.empty());\n\n        // do not handle this value if we know it would be added to a discarded\n        // container\n        if (!keep_stack.back())\n        {\n            return {false, nullptr};\n        }\n\n        // create value\n        auto value = BasicJsonType(std::forward<Value>(v));\n\n        // check callback\n        const bool keep = skip_callback || callback(static_cast<int>(ref_stack.size()), parse_event_t::value, value);\n\n        // do not handle this value if we just learnt it shall be discarded\n        if (!keep)\n        {\n            return {false, nullptr};\n        }\n\n        if (ref_stack.empty())\n        {\n            root = std::move(value);\n            return {true, & root};\n        }\n\n        // skip this value if we already decided to skip the parent\n        // (https://github.com/nlohmann/json/issues/971#issuecomment-413678360)\n        if (!ref_stack.back())\n        {\n            return {false, nullptr};\n        }\n\n        // we now only expect arrays and objects\n        JSON_ASSERT(ref_stack.back()->is_array() || ref_stack.back()->is_object());\n\n        // array\n        if (ref_stack.back()->is_array())\n        {\n            ref_stack.back()->m_data.m_value.array->emplace_back(std::move(value));\n            return {true, & (ref_stack.back()->m_data.m_value.array->back())};\n        }\n\n        // object\n        JSON_ASSERT(ref_stack.back()->is_object());\n        // check if we should store an element for the current key\n        JSON_ASSERT(!key_keep_stack.empty());\n        const bool store_element = key_keep_stack.back();\n        key_keep_stack.pop_back();\n\n        if (!store_element)\n        {\n            return {false, nullptr};\n        }\n\n        JSON_ASSERT(object_element);\n        *object_element = std::move(value);\n        return {true, object_element};\n    }\n\n    /// the parsed JSON value\n    BasicJsonType& root;\n    /// stack to model hierarchy of values\n    std::vector<BasicJsonType*> ref_stack {};\n    /// stack to manage which values to keep\n    std::vector<bool> keep_stack {};\n    /// stack to manage which object keys to keep\n    std::vector<bool> key_keep_stack {};\n    /// helper to hold the reference for the next object element\n    BasicJsonType* object_element = nullptr;\n    /// whether a syntax error occurred\n    bool errored = false;\n    /// callback function\n    const parser_callback_t callback = nullptr;\n    /// whether to throw exceptions in case of errors\n    const bool allow_exceptions = true;\n    /// a discarded value for the callback\n    BasicJsonType discarded = BasicJsonType::value_t::discarded;\n};\n\ntemplate<typename BasicJsonType>\nclass json_sax_acceptor\n{\n  public:\n    using number_integer_t = typename BasicJsonType::number_integer_t;\n    using number_unsigned_t = typename BasicJsonType::number_unsigned_t;\n    using number_float_t = typename BasicJsonType::number_float_t;\n    using string_t = typename BasicJsonType::string_t;\n    using binary_t = typename BasicJsonType::binary_t;\n\n    bool null()\n    {\n        return true;\n    }\n\n    bool boolean(bool /*unused*/)\n    {\n        return true;\n    }\n\n    bool number_integer(number_integer_t /*unused*/)\n    {\n        return true;\n    }\n\n    bool number_unsigned(number_unsigned_t /*unused*/)\n    {\n        return true;\n    }\n\n    bool number_float(number_float_t /*unused*/, const string_t& /*unused*/)\n    {\n        return true;\n    }\n\n    bool string(string_t& /*unused*/)\n    {\n        return true;\n    }\n\n    bool binary(binary_t& /*unused*/)\n    {\n        return true;\n    }\n\n    bool start_object(std::size_t /*unused*/ = static_cast<std::size_t>(-1))\n    {\n        return true;\n    }\n\n    bool key(string_t& /*unused*/)\n    {\n        return true;\n    }\n\n    bool end_object()\n    {\n        return true;\n    }\n\n    bool start_array(std::size_t /*unused*/ = static_cast<std::size_t>(-1))\n    {\n        return true;\n    }\n\n    bool end_array()\n    {\n        return true;\n    }\n\n    bool parse_error(std::size_t /*unused*/, const std::string& /*unused*/, const detail::exception& /*unused*/)\n    {\n        return false;\n    }\n};\n\n}  // namespace detail\nNLOHMANN_JSON_NAMESPACE_END\n\n// #include <nlohmann/detail/input/lexer.hpp>\n//     __ _____ _____ _____\n//  __|  |   __|     |   | |  JSON for Modern C++\n// |  |  |__   |  |  | | | |  version 3.11.3\n// |_____|_____|_____|_|___|  https://github.com/nlohmann/json\n//\n// SPDX-FileCopyrightText: 2013-2023 Niels Lohmann <https://nlohmann.me>\n// SPDX-License-Identifier: MIT\n\n\n\n#include <array> // array\n#include <clocale> // localeconv\n#include <cstddef> // size_t\n#include <cstdio> // snprintf\n#include <cstdlib> // strtof, strtod, strtold, strtoll, strtoull\n#include <initializer_list> // initializer_list\n#include <string> // char_traits, string\n#include <utility> // move\n#include <vector> // vector\n\n// #include <nlohmann/detail/input/input_adapters.hpp>\n\n// #include <nlohmann/detail/input/position_t.hpp>\n\n// #include <nlohmann/detail/macro_scope.hpp>\n\n// #include <nlohmann/detail/meta/type_traits.hpp>\n\n\nNLOHMANN_JSON_NAMESPACE_BEGIN\nnamespace detail\n{\n\n///////////\n// lexer //\n///////////\n\ntemplate<typename BasicJsonType>\nclass lexer_base\n{\n  public:\n    /// token types for the parser\n    enum class token_type\n    {\n        uninitialized,    ///< indicating the scanner is uninitialized\n        literal_true,     ///< the `true` literal\n        literal_false,    ///< the `false` literal\n        literal_null,     ///< the `null` literal\n        value_string,     ///< a string -- use get_string() for actual value\n        value_unsigned,   ///< an unsigned integer -- use get_number_unsigned() for actual value\n        value_integer,    ///< a signed integer -- use get_number_integer() for actual value\n        value_float,      ///< an floating point number -- use get_number_float() for actual value\n        begin_array,      ///< the character for array begin `[`\n        begin_object,     ///< the character for object begin `{`\n        end_array,        ///< the character for array end `]`\n        end_object,       ///< the character for object end `}`\n        name_separator,   ///< the name separator `:`\n        value_separator,  ///< the value separator `,`\n        parse_error,      ///< indicating a parse error\n        end_of_input,     ///< indicating the end of the input buffer\n        literal_or_value  ///< a literal or the begin of a value (only for diagnostics)\n    };\n\n    /// return name of values of type token_type (only used for errors)\n    JSON_HEDLEY_RETURNS_NON_NULL\n    JSON_HEDLEY_CONST\n    static const char* token_type_name(const token_type t) noexcept\n    {\n        switch (t)\n        {\n            case token_type::uninitialized:\n                return \"<uninitialized>\";\n            case token_type::literal_true:\n                return \"true literal\";\n            case token_type::literal_false:\n                return \"false literal\";\n            case token_type::literal_null:\n                return \"null literal\";\n            case token_type::value_string:\n                return \"string literal\";\n            case token_type::value_unsigned:\n            case token_type::value_integer:\n            case token_type::value_float:\n                return \"number literal\";\n            case token_type::begin_array:\n                return \"'['\";\n            case token_type::begin_object:\n                return \"'{'\";\n            case token_type::end_array:\n                return \"']'\";\n            case token_type::end_object:\n                return \"'}'\";\n            case token_type::name_separator:\n                return \"':'\";\n            case token_type::value_separator:\n                return \"','\";\n            case token_type::parse_error:\n                return \"<parse error>\";\n            case token_type::end_of_input:\n                return \"end of input\";\n            case token_type::literal_or_value:\n                return \"'[', '{', or a literal\";\n            // LCOV_EXCL_START\n            default: // catch non-enum values\n                return \"unknown token\";\n                // LCOV_EXCL_STOP\n        }\n    }\n};\n/*!\n@brief lexical analysis\n\nThis class organizes the lexical analysis during JSON deserialization.\n*/\ntemplate<typename BasicJsonType, typename InputAdapterType>\nclass lexer : public lexer_base<BasicJsonType>\n{\n    using number_integer_t = typename BasicJsonType::number_integer_t;\n    using number_unsigned_t = typename BasicJsonType::number_unsigned_t;\n    using number_float_t = typename BasicJsonType::number_float_t;\n    using string_t = typename BasicJsonType::string_t;\n    using char_type = typename InputAdapterType::char_type;\n    using char_int_type = typename char_traits<char_type>::int_type;\n\n  public:\n    using token_type = typename lexer_base<BasicJsonType>::token_type;\n\n    explicit lexer(InputAdapterType&& adapter, bool ignore_comments_ = false) noexcept\n        : ia(std::move(adapter))\n        , ignore_comments(ignore_comments_)\n        , decimal_point_char(static_cast<char_int_type>(get_decimal_point()))\n    {}\n\n    // delete because of pointer members\n    lexer(const lexer&) = delete;\n    lexer(lexer&&) = default; // NOLINT(hicpp-noexcept-move,performance-noexcept-move-constructor)\n    lexer& operator=(lexer&) = delete;\n    lexer& operator=(lexer&&) = default; // NOLINT(hicpp-noexcept-move,performance-noexcept-move-constructor)\n    ~lexer() = default;\n\n  private:\n    /////////////////////\n    // locales\n    /////////////////////\n\n    /// return the locale-dependent decimal point\n    JSON_HEDLEY_PURE\n    static char get_decimal_point() noexcept\n    {\n        const auto* loc = localeconv();\n        JSON_ASSERT(loc != nullptr);\n        return (loc->decimal_point == nullptr) ? '.' : *(loc->decimal_point);\n    }\n\n    /////////////////////\n    // scan functions\n    /////////////////////\n\n    /*!\n    @brief get codepoint from 4 hex characters following `\\u`\n\n    For input \"\\u c1 c2 c3 c4\" the codepoint is:\n      (c1 * 0x1000) + (c2 * 0x0100) + (c3 * 0x0010) + c4\n    = (c1 << 12) + (c2 << 8) + (c3 << 4) + (c4 << 0)\n\n    Furthermore, the possible characters '0'..'9', 'A'..'F', and 'a'..'f'\n    must be converted to the integers 0x0..0x9, 0xA..0xF, 0xA..0xF, resp. The\n    conversion is done by subtracting the offset (0x30, 0x37, and 0x57)\n    between the ASCII value of the character and the desired integer value.\n\n    @return codepoint (0x0000..0xFFFF) or -1 in case of an error (e.g. EOF or\n            non-hex character)\n    */\n    int get_codepoint()\n    {\n        // this function only makes sense after reading `\\u`\n        JSON_ASSERT(current == 'u');\n        int codepoint = 0;\n\n        const auto factors = { 12u, 8u, 4u, 0u };\n        for (const auto factor : factors)\n        {\n            get();\n\n            if (current >= '0' && current <= '9')\n            {\n                codepoint += static_cast<int>((static_cast<unsigned int>(current) - 0x30u) << factor);\n            }\n            else if (current >= 'A' && current <= 'F')\n            {\n                codepoint += static_cast<int>((static_cast<unsigned int>(current) - 0x37u) << factor);\n            }\n            else if (current >= 'a' && current <= 'f')\n            {\n                codepoint += static_cast<int>((static_cast<unsigned int>(current) - 0x57u) << factor);\n            }\n            else\n            {\n                return -1;\n            }\n        }\n\n        JSON_ASSERT(0x0000 <= codepoint && codepoint <= 0xFFFF);\n        return codepoint;\n    }\n\n    /*!\n    @brief check if the next byte(s) are inside a given range\n\n    Adds the current byte and, for each passed range, reads a new byte and\n    checks if it is inside the range. If a violation was detected, set up an\n    error message and return false. Otherwise, return true.\n\n    @param[in] ranges  list of integers; interpreted as list of pairs of\n                       inclusive lower and upper bound, respectively\n\n    @pre The passed list @a ranges must have 2, 4, or 6 elements; that is,\n         1, 2, or 3 pairs. This precondition is enforced by an assertion.\n\n    @return true if and only if no range violation was detected\n    */\n    bool next_byte_in_range(std::initializer_list<char_int_type> ranges)\n    {\n        JSON_ASSERT(ranges.size() == 2 || ranges.size() == 4 || ranges.size() == 6);\n        add(current);\n\n        for (auto range = ranges.begin(); range != ranges.end(); ++range)\n        {\n            get();\n            if (JSON_HEDLEY_LIKELY(*range <= current && current <= *(++range))) // NOLINT(bugprone-inc-dec-in-conditions)\n            {\n                add(current);\n            }\n            else\n            {\n                error_message = \"invalid string: ill-formed UTF-8 byte\";\n                return false;\n            }\n        }\n\n        return true;\n    }\n\n    /*!\n    @brief scan a string literal\n\n    This function scans a string according to Sect. 7 of RFC 8259. While\n    scanning, bytes are escaped and copied into buffer token_buffer. Then the\n    function returns successfully, token_buffer is *not* null-terminated (as it\n    may contain \\0 bytes), and token_buffer.size() is the number of bytes in the\n    string.\n\n    @return token_type::value_string if string could be successfully scanned,\n            token_type::parse_error otherwise\n\n    @note In case of errors, variable error_message contains a textual\n          description.\n    */\n    token_type scan_string()\n    {\n        // reset token_buffer (ignore opening quote)\n        reset();\n\n        // we entered the function by reading an open quote\n        JSON_ASSERT(current == '\\\"');\n\n        while (true)\n        {\n            // get next character\n            switch (get())\n            {\n                // end of file while parsing string\n                case char_traits<char_type>::eof():\n                {\n                    error_message = \"invalid string: missing closing quote\";\n                    return token_type::parse_error;\n                }\n\n                // closing quote\n                case '\\\"':\n                {\n                    return token_type::value_string;\n                }\n\n                // escapes\n                case '\\\\':\n                {\n                    switch (get())\n                    {\n                        // quotation mark\n                        case '\\\"':\n                            add('\\\"');\n                            break;\n                        // reverse solidus\n                        case '\\\\':\n                            add('\\\\');\n                            break;\n                        // solidus\n                        case '/':\n                            add('/');\n                            break;\n                        // backspace\n                        case 'b':\n                            add('\\b');\n                            break;\n                        // form feed\n                        case 'f':\n                            add('\\f');\n                            break;\n                        // line feed\n                        case 'n':\n                            add('\\n');\n                            break;\n                        // carriage return\n                        case 'r':\n                            add('\\r');\n                            break;\n                        // tab\n                        case 't':\n                            add('\\t');\n                            break;\n\n                        // unicode escapes\n                        case 'u':\n                        {\n                            const int codepoint1 = get_codepoint();\n                            int codepoint = codepoint1; // start with codepoint1\n\n                            if (JSON_HEDLEY_UNLIKELY(codepoint1 == -1))\n                            {\n                                error_message = \"invalid string: '\\\\u' must be followed by 4 hex digits\";\n                                return token_type::parse_error;\n                            }\n\n                            // check if code point is a high surrogate\n                            if (0xD800 <= codepoint1 && codepoint1 <= 0xDBFF)\n                            {\n                                // expect next \\uxxxx entry\n                                if (JSON_HEDLEY_LIKELY(get() == '\\\\' && get() == 'u'))\n                                {\n                                    const int codepoint2 = get_codepoint();\n\n                                    if (JSON_HEDLEY_UNLIKELY(codepoint2 == -1))\n                                    {\n                                        error_message = \"invalid string: '\\\\u' must be followed by 4 hex digits\";\n                                        return token_type::parse_error;\n                                    }\n\n                                    // check if codepoint2 is a low surrogate\n                                    if (JSON_HEDLEY_LIKELY(0xDC00 <= codepoint2 && codepoint2 <= 0xDFFF))\n                                    {\n                                        // overwrite codepoint\n                                        codepoint = static_cast<int>(\n                                                        // high surrogate occupies the most significant 22 bits\n                                                        (static_cast<unsigned int>(codepoint1) << 10u)\n                                                        // low surrogate occupies the least significant 15 bits\n                                                        + static_cast<unsigned int>(codepoint2)\n                                                        // there is still the 0xD800, 0xDC00 and 0x10000 noise\n                                                        // in the result, so we have to subtract with:\n                                                        // (0xD800 << 10) + DC00 - 0x10000 = 0x35FDC00\n                                                        - 0x35FDC00u);\n                                    }\n                                    else\n                                    {\n                                        error_message = \"invalid string: surrogate U+D800..U+DBFF must be followed by U+DC00..U+DFFF\";\n                                        return token_type::parse_error;\n                                    }\n                                }\n                                else\n                                {\n                                    error_message = \"invalid string: surrogate U+D800..U+DBFF must be followed by U+DC00..U+DFFF\";\n                                    return token_type::parse_error;\n                                }\n                            }\n                            else\n                            {\n                                if (JSON_HEDLEY_UNLIKELY(0xDC00 <= codepoint1 && codepoint1 <= 0xDFFF))\n                                {\n                                    error_message = \"invalid string: surrogate U+DC00..U+DFFF must follow U+D800..U+DBFF\";\n                                    return token_type::parse_error;\n                                }\n                            }\n\n                            // result of the above calculation yields a proper codepoint\n                            JSON_ASSERT(0x00 <= codepoint && codepoint <= 0x10FFFF);\n\n                            // translate codepoint into bytes\n                            if (codepoint < 0x80)\n                            {\n                                // 1-byte characters: 0xxxxxxx (ASCII)\n                                add(static_cast<char_int_type>(codepoint));\n                            }\n                            else if (codepoint <= 0x7FF)\n                            {\n                                // 2-byte characters: 110xxxxx 10xxxxxx\n                                add(static_cast<char_int_type>(0xC0u | (static_cast<unsigned int>(codepoint) >> 6u)));\n                                add(static_cast<char_int_type>(0x80u | (static_cast<unsigned int>(codepoint) & 0x3Fu)));\n                            }\n                            else if (codepoint <= 0xFFFF)\n                            {\n                                // 3-byte characters: 1110xxxx 10xxxxxx 10xxxxxx\n                                add(static_cast<char_int_type>(0xE0u | (static_cast<unsigned int>(codepoint) >> 12u)));\n                                add(static_cast<char_int_type>(0x80u | ((static_cast<unsigned int>(codepoint) >> 6u) & 0x3Fu)));\n                                add(static_cast<char_int_type>(0x80u | (static_cast<unsigned int>(codepoint) & 0x3Fu)));\n                            }\n                            else\n                            {\n                                // 4-byte characters: 11110xxx 10xxxxxx 10xxxxxx 10xxxxxx\n                                add(static_cast<char_int_type>(0xF0u | (static_cast<unsigned int>(codepoint) >> 18u)));\n                                add(static_cast<char_int_type>(0x80u | ((static_cast<unsigned int>(codepoint) >> 12u) & 0x3Fu)));\n                                add(static_cast<char_int_type>(0x80u | ((static_cast<unsigned int>(codepoint) >> 6u) & 0x3Fu)));\n                                add(static_cast<char_int_type>(0x80u | (static_cast<unsigned int>(codepoint) & 0x3Fu)));\n                            }\n\n                            break;\n                        }\n\n                        // other characters after escape\n                        default:\n                            error_message = \"invalid string: forbidden character after backslash\";\n                            return token_type::parse_error;\n                    }\n\n                    break;\n                }\n\n                // invalid control characters\n                case 0x00:\n                {\n                    error_message = \"invalid string: control character U+0000 (NUL) must be escaped to \\\\u0000\";\n                    return token_type::parse_error;\n                }\n\n                case 0x01:\n                {\n                    error_message = \"invalid string: control character U+0001 (SOH) must be escaped to \\\\u0001\";\n                    return token_type::parse_error;\n                }\n\n                case 0x02:\n                {\n                    error_message = \"invalid string: control character U+0002 (STX) must be escaped to \\\\u0002\";\n                    return token_type::parse_error;\n                }\n\n                case 0x03:\n                {\n                    error_message = \"invalid string: control character U+0003 (ETX) must be escaped to \\\\u0003\";\n                    return token_type::parse_error;\n                }\n\n                case 0x04:\n                {\n                    error_message = \"invalid string: control character U+0004 (EOT) must be escaped to \\\\u0004\";\n                    return token_type::parse_error;\n                }\n\n                case 0x05:\n                {\n                    error_message = \"invalid string: control character U+0005 (ENQ) must be escaped to \\\\u0005\";\n                    return token_type::parse_error;\n                }\n\n                case 0x06:\n                {\n                    error_message = \"invalid string: control character U+0006 (ACK) must be escaped to \\\\u0006\";\n                    return token_type::parse_error;\n                }\n\n                case 0x07:\n                {\n                    error_message = \"invalid string: control character U+0007 (BEL) must be escaped to \\\\u0007\";\n                    return token_type::parse_error;\n                }\n\n                case 0x08:\n                {\n                    error_message = \"invalid string: control character U+0008 (BS) must be escaped to \\\\u0008 or \\\\b\";\n                    return token_type::parse_error;\n                }\n\n                case 0x09:\n                {\n                    error_message = \"invalid string: control character U+0009 (HT) must be escaped to \\\\u0009 or \\\\t\";\n                    return token_type::parse_error;\n                }\n\n                case 0x0A:\n                {\n                    error_message = \"invalid string: control character U+000A (LF) must be escaped to \\\\u000A or \\\\n\";\n                    return token_type::parse_error;\n                }\n\n                case 0x0B:\n                {\n                    error_message = \"invalid string: control character U+000B (VT) must be escaped to \\\\u000B\";\n                    return token_type::parse_error;\n                }\n\n                case 0x0C:\n                {\n                    error_message = \"invalid string: control character U+000C (FF) must be escaped to \\\\u000C or \\\\f\";\n                    return token_type::parse_error;\n                }\n\n                case 0x0D:\n                {\n                    error_message = \"invalid string: control character U+000D (CR) must be escaped to \\\\u000D or \\\\r\";\n                    return token_type::parse_error;\n                }\n\n                case 0x0E:\n                {\n                    error_message = \"invalid string: control character U+000E (SO) must be escaped to \\\\u000E\";\n                    return token_type::parse_error;\n                }\n\n                case 0x0F:\n                {\n                    error_message = \"invalid string: control character U+000F (SI) must be escaped to \\\\u000F\";\n                    return token_type::parse_error;\n                }\n\n                case 0x10:\n                {\n                    error_message = \"invalid string: control character U+0010 (DLE) must be escaped to \\\\u0010\";\n                    return token_type::parse_error;\n                }\n\n                case 0x11:\n                {\n                    error_message = \"invalid string: control character U+0011 (DC1) must be escaped to \\\\u0011\";\n                    return token_type::parse_error;\n                }\n\n                case 0x12:\n                {\n                    error_message = \"invalid string: control character U+0012 (DC2) must be escaped to \\\\u0012\";\n                    return token_type::parse_error;\n                }\n\n                case 0x13:\n                {\n                    error_message = \"invalid string: control character U+0013 (DC3) must be escaped to \\\\u0013\";\n                    return token_type::parse_error;\n                }\n\n                case 0x14:\n                {\n                    error_message = \"invalid string: control character U+0014 (DC4) must be escaped to \\\\u0014\";\n                    return token_type::parse_error;\n                }\n\n                case 0x15:\n                {\n                    error_message = \"invalid string: control character U+0015 (NAK) must be escaped to \\\\u0015\";\n                    return token_type::parse_error;\n                }\n\n                case 0x16:\n                {\n                    error_message = \"invalid string: control character U+0016 (SYN) must be escaped to \\\\u0016\";\n                    return token_type::parse_error;\n                }\n\n                case 0x17:\n                {\n                    error_message = \"invalid string: control character U+0017 (ETB) must be escaped to \\\\u0017\";\n                    return token_type::parse_error;\n                }\n\n                case 0x18:\n                {\n                    error_message = \"invalid string: control character U+0018 (CAN) must be escaped to \\\\u0018\";\n                    return token_type::parse_error;\n                }\n\n                case 0x19:\n                {\n                    error_message = \"invalid string: control character U+0019 (EM) must be escaped to \\\\u0019\";\n                    return token_type::parse_error;\n                }\n\n                case 0x1A:\n                {\n                    error_message = \"invalid string: control character U+001A (SUB) must be escaped to \\\\u001A\";\n                    return token_type::parse_error;\n                }\n\n                case 0x1B:\n                {\n                    error_message = \"invalid string: control character U+001B (ESC) must be escaped to \\\\u001B\";\n                    return token_type::parse_error;\n                }\n\n                case 0x1C:\n                {\n                    error_message = \"invalid string: control character U+001C (FS) must be escaped to \\\\u001C\";\n                    return token_type::parse_error;\n                }\n\n                case 0x1D:\n                {\n                    error_message = \"invalid string: control character U+001D (GS) must be escaped to \\\\u001D\";\n                    return token_type::parse_error;\n                }\n\n                case 0x1E:\n                {\n                    error_message = \"invalid string: control character U+001E (RS) must be escaped to \\\\u001E\";\n                    return token_type::parse_error;\n                }\n\n                case 0x1F:\n                {\n                    error_message = \"invalid string: control character U+001F (US) must be escaped to \\\\u001F\";\n                    return token_type::parse_error;\n                }\n\n                // U+0020..U+007F (except U+0022 (quote) and U+005C (backspace))\n                case 0x20:\n                case 0x21:\n                case 0x23:\n                case 0x24:\n                case 0x25:\n                case 0x26:\n                case 0x27:\n                case 0x28:\n                case 0x29:\n                case 0x2A:\n                case 0x2B:\n                case 0x2C:\n                case 0x2D:\n                case 0x2E:\n                case 0x2F:\n                case 0x30:\n                case 0x31:\n                case 0x32:\n                case 0x33:\n                case 0x34:\n                case 0x35:\n                case 0x36:\n                case 0x37:\n                case 0x38:\n                case 0x39:\n                case 0x3A:\n                case 0x3B:\n                case 0x3C:\n                case 0x3D:\n                case 0x3E:\n                case 0x3F:\n                case 0x40:\n                case 0x41:\n                case 0x42:\n                case 0x43:\n                case 0x44:\n                case 0x45:\n                case 0x46:\n                case 0x47:\n                case 0x48:\n                case 0x49:\n                case 0x4A:\n                case 0x4B:\n                case 0x4C:\n                case 0x4D:\n                case 0x4E:\n                case 0x4F:\n                case 0x50:\n                case 0x51:\n                case 0x52:\n                case 0x53:\n                case 0x54:\n                case 0x55:\n                case 0x56:\n                case 0x57:\n                case 0x58:\n                case 0x59:\n                case 0x5A:\n                case 0x5B:\n                case 0x5D:\n                case 0x5E:\n                case 0x5F:\n                case 0x60:\n                case 0x61:\n                case 0x62:\n                case 0x63:\n                case 0x64:\n                case 0x65:\n                case 0x66:\n                case 0x67:\n                case 0x68:\n                case 0x69:\n                case 0x6A:\n                case 0x6B:\n                case 0x6C:\n                case 0x6D:\n                case 0x6E:\n                case 0x6F:\n                case 0x70:\n                case 0x71:\n                case 0x72:\n                case 0x73:\n                case 0x74:\n                case 0x75:\n                case 0x76:\n                case 0x77:\n                case 0x78:\n                case 0x79:\n                case 0x7A:\n                case 0x7B:\n                case 0x7C:\n                case 0x7D:\n                case 0x7E:\n                case 0x7F:\n                {\n                    add(current);\n                    break;\n                }\n\n                // U+0080..U+07FF: bytes C2..DF 80..BF\n                case 0xC2:\n                case 0xC3:\n                case 0xC4:\n                case 0xC5:\n                case 0xC6:\n                case 0xC7:\n                case 0xC8:\n                case 0xC9:\n                case 0xCA:\n                case 0xCB:\n                case 0xCC:\n                case 0xCD:\n                case 0xCE:\n                case 0xCF:\n                case 0xD0:\n                case 0xD1:\n                case 0xD2:\n                case 0xD3:\n                case 0xD4:\n                case 0xD5:\n                case 0xD6:\n                case 0xD7:\n                case 0xD8:\n                case 0xD9:\n                case 0xDA:\n                case 0xDB:\n                case 0xDC:\n                case 0xDD:\n                case 0xDE:\n                case 0xDF:\n                {\n                    if (JSON_HEDLEY_UNLIKELY(!next_byte_in_range({0x80, 0xBF})))\n                    {\n                        return token_type::parse_error;\n                    }\n                    break;\n                }\n\n                // U+0800..U+0FFF: bytes E0 A0..BF 80..BF\n                case 0xE0:\n                {\n                    if (JSON_HEDLEY_UNLIKELY(!(next_byte_in_range({0xA0, 0xBF, 0x80, 0xBF}))))\n                    {\n                        return token_type::parse_error;\n                    }\n                    break;\n                }\n\n                // U+1000..U+CFFF: bytes E1..EC 80..BF 80..BF\n                // U+E000..U+FFFF: bytes EE..EF 80..BF 80..BF\n                case 0xE1:\n                case 0xE2:\n                case 0xE3:\n                case 0xE4:\n                case 0xE5:\n                case 0xE6:\n                case 0xE7:\n                case 0xE8:\n                case 0xE9:\n                case 0xEA:\n                case 0xEB:\n                case 0xEC:\n                case 0xEE:\n                case 0xEF:\n                {\n                    if (JSON_HEDLEY_UNLIKELY(!(next_byte_in_range({0x80, 0xBF, 0x80, 0xBF}))))\n                    {\n                        return token_type::parse_error;\n                    }\n                    break;\n                }\n\n                // U+D000..U+D7FF: bytes ED 80..9F 80..BF\n                case 0xED:\n                {\n                    if (JSON_HEDLEY_UNLIKELY(!(next_byte_in_range({0x80, 0x9F, 0x80, 0xBF}))))\n                    {\n                        return token_type::parse_error;\n                    }\n                    break;\n                }\n\n                // U+10000..U+3FFFF F0 90..BF 80..BF 80..BF\n                case 0xF0:\n                {\n                    if (JSON_HEDLEY_UNLIKELY(!(next_byte_in_range({0x90, 0xBF, 0x80, 0xBF, 0x80, 0xBF}))))\n                    {\n                        return token_type::parse_error;\n                    }\n                    break;\n                }\n\n                // U+40000..U+FFFFF F1..F3 80..BF 80..BF 80..BF\n                case 0xF1:\n                case 0xF2:\n                case 0xF3:\n                {\n                    if (JSON_HEDLEY_UNLIKELY(!(next_byte_in_range({0x80, 0xBF, 0x80, 0xBF, 0x80, 0xBF}))))\n                    {\n                        return token_type::parse_error;\n                    }\n                    break;\n                }\n\n                // U+100000..U+10FFFF F4 80..8F 80..BF 80..BF\n                case 0xF4:\n                {\n                    if (JSON_HEDLEY_UNLIKELY(!(next_byte_in_range({0x80, 0x8F, 0x80, 0xBF, 0x80, 0xBF}))))\n                    {\n                        return token_type::parse_error;\n                    }\n                    break;\n                }\n\n                // remaining bytes (80..C1 and F5..FF) are ill-formed\n                default:\n                {\n                    error_message = \"invalid string: ill-formed UTF-8 byte\";\n                    return token_type::parse_error;\n                }\n            }\n        }\n    }\n\n    /*!\n     * @brief scan a comment\n     * @return whether comment could be scanned successfully\n     */\n    bool scan_comment()\n    {\n        switch (get())\n        {\n            // single-line comments skip input until a newline or EOF is read\n            case '/':\n            {\n                while (true)\n                {\n                    switch (get())\n                    {\n                        case '\\n':\n                        case '\\r':\n                        case char_traits<char_type>::eof():\n                        case '\\0':\n                            return true;\n\n                        default:\n                            break;\n                    }\n                }\n            }\n\n            // multi-line comments skip input until */ is read\n            case '*':\n            {\n                while (true)\n                {\n                    switch (get())\n                    {\n                        case char_traits<char_type>::eof():\n                        case '\\0':\n                        {\n                            error_message = \"invalid comment; missing closing '*/'\";\n                            return false;\n                        }\n\n                        case '*':\n                        {\n                            switch (get())\n                            {\n                                case '/':\n                                    return true;\n\n                                default:\n                                {\n                                    unget();\n                                    continue;\n                                }\n                            }\n                        }\n\n                        default:\n                            continue;\n                    }\n                }\n            }\n\n            // unexpected character after reading '/'\n            default:\n            {\n                error_message = \"invalid comment; expecting '/' or '*' after '/'\";\n                return false;\n            }\n        }\n    }\n\n    JSON_HEDLEY_NON_NULL(2)\n    static void strtof(float& f, const char* str, char** endptr) noexcept\n    {\n        f = std::strtof(str, endptr);\n    }\n\n    JSON_HEDLEY_NON_NULL(2)\n    static void strtof(double& f, const char* str, char** endptr) noexcept\n    {\n        f = std::strtod(str, endptr);\n    }\n\n    JSON_HEDLEY_NON_NULL(2)\n    static void strtof(long double& f, const char* str, char** endptr) noexcept\n    {\n        f = std::strtold(str, endptr);\n    }\n\n    /*!\n    @brief scan a number literal\n\n    This function scans a string according to Sect. 6 of RFC 8259.\n\n    The function is realized with a deterministic finite state machine derived\n    from the grammar described in RFC 8259. Starting in state \"init\", the\n    input is read and used to determined the next state. Only state \"done\"\n    accepts the number. State \"error\" is a trap state to model errors. In the\n    table below, \"anything\" means any character but the ones listed before.\n\n    state    | 0        | 1-9      | e E      | +       | -       | .        | anything\n    ---------|----------|----------|----------|---------|---------|----------|-----------\n    init     | zero     | any1     | [error]  | [error] | minus   | [error]  | [error]\n    minus    | zero     | any1     | [error]  | [error] | [error] | [error]  | [error]\n    zero     | done     | done     | exponent | done    | done    | decimal1 | done\n    any1     | any1     | any1     | exponent | done    | done    | decimal1 | done\n    decimal1 | decimal2 | decimal2 | [error]  | [error] | [error] | [error]  | [error]\n    decimal2 | decimal2 | decimal2 | exponent | done    | done    | done     | done\n    exponent | any2     | any2     | [error]  | sign    | sign    | [error]  | [error]\n    sign     | any2     | any2     | [error]  | [error] | [error] | [error]  | [error]\n    any2     | any2     | any2     | done     | done    | done    | done     | done\n\n    The state machine is realized with one label per state (prefixed with\n    \"scan_number_\") and `goto` statements between them. The state machine\n    contains cycles, but any cycle can be left when EOF is read. Therefore,\n    the function is guaranteed to terminate.\n\n    During scanning, the read bytes are stored in token_buffer. This string is\n    then converted to a signed integer, an unsigned integer, or a\n    floating-point number.\n\n    @return token_type::value_unsigned, token_type::value_integer, or\n            token_type::value_float if number could be successfully scanned,\n            token_type::parse_error otherwise\n\n    @note The scanner is independent of the current locale. Internally, the\n          locale's decimal point is used instead of `.` to work with the\n          locale-dependent converters.\n    */\n    token_type scan_number()  // lgtm [cpp/use-of-goto]\n    {\n        // reset token_buffer to store the number's bytes\n        reset();\n\n        // the type of the parsed number; initially set to unsigned; will be\n        // changed if minus sign, decimal point or exponent is read\n        token_type number_type = token_type::value_unsigned;\n\n        // state (init): we just found out we need to scan a number\n        switch (current)\n        {\n            case '-':\n            {\n                add(current);\n                goto scan_number_minus;\n            }\n\n            case '0':\n            {\n                add(current);\n                goto scan_number_zero;\n            }\n\n            case '1':\n            case '2':\n            case '3':\n            case '4':\n            case '5':\n            case '6':\n            case '7':\n            case '8':\n            case '9':\n            {\n                add(current);\n                goto scan_number_any1;\n            }\n\n            // all other characters are rejected outside scan_number()\n            default:            // LCOV_EXCL_LINE\n                JSON_ASSERT(false); // NOLINT(cert-dcl03-c,hicpp-static-assert,misc-static-assert) LCOV_EXCL_LINE\n        }\n\nscan_number_minus:\n        // state: we just parsed a leading minus sign\n        number_type = token_type::value_integer;\n        switch (get())\n        {\n            case '0':\n            {\n                add(current);\n                goto scan_number_zero;\n            }\n\n            case '1':\n            case '2':\n            case '3':\n            case '4':\n            case '5':\n            case '6':\n            case '7':\n            case '8':\n            case '9':\n            {\n                add(current);\n                goto scan_number_any1;\n            }\n\n            default:\n            {\n                error_message = \"invalid number; expected digit after '-'\";\n                return token_type::parse_error;\n            }\n        }\n\nscan_number_zero:\n        // state: we just parse a zero (maybe with a leading minus sign)\n        switch (get())\n        {\n            case '.':\n            {\n                add(decimal_point_char);\n                goto scan_number_decimal1;\n            }\n\n            case 'e':\n            case 'E':\n            {\n                add(current);\n                goto scan_number_exponent;\n            }\n\n            default:\n                goto scan_number_done;\n        }\n\nscan_number_any1:\n        // state: we just parsed a number 0-9 (maybe with a leading minus sign)\n        switch (get())\n        {\n            case '0':\n            case '1':\n            case '2':\n            case '3':\n            case '4':\n            case '5':\n            case '6':\n            case '7':\n            case '8':\n            case '9':\n            {\n                add(current);\n                goto scan_number_any1;\n            }\n\n            case '.':\n            {\n                add(decimal_point_char);\n                goto scan_number_decimal1;\n            }\n\n            case 'e':\n            case 'E':\n            {\n                add(current);\n                goto scan_number_exponent;\n            }\n\n            default:\n                goto scan_number_done;\n        }\n\nscan_number_decimal1:\n        // state: we just parsed a decimal point\n        number_type = token_type::value_float;\n        switch (get())\n        {\n            case '0':\n            case '1':\n            case '2':\n            case '3':\n            case '4':\n            case '5':\n            case '6':\n            case '7':\n            case '8':\n            case '9':\n            {\n                add(current);\n                goto scan_number_decimal2;\n            }\n\n            default:\n            {\n                error_message = \"invalid number; expected digit after '.'\";\n                return token_type::parse_error;\n            }\n        }\n\nscan_number_decimal2:\n        // we just parsed at least one number after a decimal point\n        switch (get())\n        {\n            case '0':\n            case '1':\n            case '2':\n            case '3':\n            case '4':\n            case '5':\n            case '6':\n            case '7':\n            case '8':\n            case '9':\n            {\n                add(current);\n                goto scan_number_decimal2;\n            }\n\n            case 'e':\n            case 'E':\n            {\n                add(current);\n                goto scan_number_exponent;\n            }\n\n            default:\n                goto scan_number_done;\n        }\n\nscan_number_exponent:\n        // we just parsed an exponent\n        number_type = token_type::value_float;\n        switch (get())\n        {\n            case '+':\n            case '-':\n            {\n                add(current);\n                goto scan_number_sign;\n            }\n\n            case '0':\n            case '1':\n            case '2':\n            case '3':\n            case '4':\n            case '5':\n            case '6':\n            case '7':\n            case '8':\n            case '9':\n            {\n                add(current);\n                goto scan_number_any2;\n            }\n\n            default:\n            {\n                error_message =\n                    \"invalid number; expected '+', '-', or digit after exponent\";\n                return token_type::parse_error;\n            }\n        }\n\nscan_number_sign:\n        // we just parsed an exponent sign\n        switch (get())\n        {\n            case '0':\n            case '1':\n            case '2':\n            case '3':\n            case '4':\n            case '5':\n            case '6':\n            case '7':\n            case '8':\n            case '9':\n            {\n                add(current);\n                goto scan_number_any2;\n            }\n\n            default:\n            {\n                error_message = \"invalid number; expected digit after exponent sign\";\n                return token_type::parse_error;\n            }\n        }\n\nscan_number_any2:\n        // we just parsed a number after the exponent or exponent sign\n        switch (get())\n        {\n            case '0':\n            case '1':\n            case '2':\n            case '3':\n            case '4':\n            case '5':\n            case '6':\n            case '7':\n            case '8':\n            case '9':\n            {\n                add(current);\n                goto scan_number_any2;\n            }\n\n            default:\n                goto scan_number_done;\n        }\n\nscan_number_done:\n        // unget the character after the number (we only read it to know that\n        // we are done scanning a number)\n        unget();\n\n        char* endptr = nullptr; // NOLINT(cppcoreguidelines-pro-type-vararg,hicpp-vararg)\n        errno = 0;\n\n        // try to parse integers first and fall back to floats\n        if (number_type == token_type::value_unsigned)\n        {\n            const auto x = std::strtoull(token_buffer.data(), &endptr, 10);\n\n            // we checked the number format before\n            JSON_ASSERT(endptr == token_buffer.data() + token_buffer.size());\n\n            if (errno == 0)\n            {\n                value_unsigned = static_cast<number_unsigned_t>(x);\n                if (value_unsigned == x)\n                {\n                    return token_type::value_unsigned;\n                }\n            }\n        }\n        else if (number_type == token_type::value_integer)\n        {\n            const auto x = std::strtoll(token_buffer.data(), &endptr, 10);\n\n            // we checked the number format before\n            JSON_ASSERT(endptr == token_buffer.data() + token_buffer.size());\n\n            if (errno == 0)\n            {\n                value_integer = static_cast<number_integer_t>(x);\n                if (value_integer == x)\n                {\n                    return token_type::value_integer;\n                }\n            }\n        }\n\n        // this code is reached if we parse a floating-point number or if an\n        // integer conversion above failed\n        strtof(value_float, token_buffer.data(), &endptr);\n\n        // we checked the number format before\n        JSON_ASSERT(endptr == token_buffer.data() + token_buffer.size());\n\n        return token_type::value_float;\n    }\n\n    /*!\n    @param[in] literal_text  the literal text to expect\n    @param[in] length        the length of the passed literal text\n    @param[in] return_type   the token type to return on success\n    */\n    JSON_HEDLEY_NON_NULL(2)\n    token_type scan_literal(const char_type* literal_text, const std::size_t length,\n                            token_type return_type)\n    {\n        JSON_ASSERT(char_traits<char_type>::to_char_type(current) == literal_text[0]);\n        for (std::size_t i = 1; i < length; ++i)\n        {\n            if (JSON_HEDLEY_UNLIKELY(char_traits<char_type>::to_char_type(get()) != literal_text[i]))\n            {\n                error_message = \"invalid literal\";\n                return token_type::parse_error;\n            }\n        }\n        return return_type;\n    }\n\n    /////////////////////\n    // input management\n    /////////////////////\n\n    /// reset token_buffer; current character is beginning of token\n    void reset() noexcept\n    {\n        token_buffer.clear();\n        token_string.clear();\n        token_string.push_back(char_traits<char_type>::to_char_type(current));\n    }\n\n    /*\n    @brief get next character from the input\n\n    This function provides the interface to the used input adapter. It does\n    not throw in case the input reached EOF, but returns a\n    `char_traits<char>::eof()` in that case.  Stores the scanned characters\n    for use in error messages.\n\n    @return character read from the input\n    */\n    char_int_type get()\n    {\n        ++position.chars_read_total;\n        ++position.chars_read_current_line;\n\n        if (next_unget)\n        {\n            // just reset the next_unget variable and work with current\n            next_unget = false;\n        }\n        else\n        {\n            current = ia.get_character();\n        }\n\n        if (JSON_HEDLEY_LIKELY(current != char_traits<char_type>::eof()))\n        {\n            token_string.push_back(char_traits<char_type>::to_char_type(current));\n        }\n\n        if (current == '\\n')\n        {\n            ++position.lines_read;\n            position.chars_read_current_line = 0;\n        }\n\n        return current;\n    }\n\n    /*!\n    @brief unget current character (read it again on next get)\n\n    We implement unget by setting variable next_unget to true. The input is not\n    changed - we just simulate ungetting by modifying chars_read_total,\n    chars_read_current_line, and token_string. The next call to get() will\n    behave as if the unget character is read again.\n    */\n    void unget()\n    {\n        next_unget = true;\n\n        --position.chars_read_total;\n\n        // in case we \"unget\" a newline, we have to also decrement the lines_read\n        if (position.chars_read_current_line == 0)\n        {\n            if (position.lines_read > 0)\n            {\n                --position.lines_read;\n            }\n        }\n        else\n        {\n            --position.chars_read_current_line;\n        }\n\n        if (JSON_HEDLEY_LIKELY(current != char_traits<char_type>::eof()))\n        {\n            JSON_ASSERT(!token_string.empty());\n            token_string.pop_back();\n        }\n    }\n\n    /// add a character to token_buffer\n    void add(char_int_type c)\n    {\n        token_buffer.push_back(static_cast<typename string_t::value_type>(c));\n    }\n\n  public:\n    /////////////////////\n    // value getters\n    /////////////////////\n\n    /// return integer value\n    constexpr number_integer_t get_number_integer() const noexcept\n    {\n        return value_integer;\n    }\n\n    /// return unsigned integer value\n    constexpr number_unsigned_t get_number_unsigned() const noexcept\n    {\n        return value_unsigned;\n    }\n\n    /// return floating-point value\n    constexpr number_float_t get_number_float() const noexcept\n    {\n        return value_float;\n    }\n\n    /// return current string value (implicitly resets the token; useful only once)\n    string_t& get_string()\n    {\n        return token_buffer;\n    }\n\n    /////////////////////\n    // diagnostics\n    /////////////////////\n\n    /// return position of last read token\n    constexpr position_t get_position() const noexcept\n    {\n        return position;\n    }\n\n    /// return the last read token (for errors only).  Will never contain EOF\n    /// (an arbitrary value that is not a valid char value, often -1), because\n    /// 255 may legitimately occur.  May contain NUL, which should be escaped.\n    std::string get_token_string() const\n    {\n        // escape control characters\n        std::string result;\n        for (const auto c : token_string)\n        {\n            if (static_cast<unsigned char>(c) <= '\\x1F')\n            {\n                // escape control characters\n                std::array<char, 9> cs{{}};\n                static_cast<void>((std::snprintf)(cs.data(), cs.size(), \"<U+%.4X>\", static_cast<unsigned char>(c))); // NOLINT(cppcoreguidelines-pro-type-vararg,hicpp-vararg)\n                result += cs.data();\n            }\n            else\n            {\n                // add character as is\n                result.push_back(static_cast<std::string::value_type>(c));\n            }\n        }\n\n        return result;\n    }\n\n    /// return syntax error message\n    JSON_HEDLEY_RETURNS_NON_NULL\n    constexpr const char* get_error_message() const noexcept\n    {\n        return error_message;\n    }\n\n    /////////////////////\n    // actual scanner\n    /////////////////////\n\n    /*!\n    @brief skip the UTF-8 byte order mark\n    @return true iff there is no BOM or the correct BOM has been skipped\n    */\n    bool skip_bom()\n    {\n        if (get() == 0xEF)\n        {\n            // check if we completely parse the BOM\n            return get() == 0xBB && get() == 0xBF;\n        }\n\n        // the first character is not the beginning of the BOM; unget it to\n        // process is later\n        unget();\n        return true;\n    }\n\n    void skip_whitespace()\n    {\n        do\n        {\n            get();\n        }\n        while (current == ' ' || current == '\\t' || current == '\\n' || current == '\\r');\n    }\n\n    token_type scan()\n    {\n        // initially, skip the BOM\n        if (position.chars_read_total == 0 && !skip_bom())\n        {\n            error_message = \"invalid BOM; must be 0xEF 0xBB 0xBF if given\";\n            return token_type::parse_error;\n        }\n\n        // read next character and ignore whitespace\n        skip_whitespace();\n\n        // ignore comments\n        while (ignore_comments && current == '/')\n        {\n            if (!scan_comment())\n            {\n                return token_type::parse_error;\n            }\n\n            // skip following whitespace\n            skip_whitespace();\n        }\n\n        switch (current)\n        {\n            // structural characters\n            case '[':\n                return token_type::begin_array;\n            case ']':\n                return token_type::end_array;\n            case '{':\n                return token_type::begin_object;\n            case '}':\n                return token_type::end_object;\n            case ':':\n                return token_type::name_separator;\n            case ',':\n                return token_type::value_separator;\n\n            // literals\n            case 't':\n            {\n                std::array<char_type, 4> true_literal = {{static_cast<char_type>('t'), static_cast<char_type>('r'), static_cast<char_type>('u'), static_cast<char_type>('e')}};\n                return scan_literal(true_literal.data(), true_literal.size(), token_type::literal_true);\n            }\n            case 'f':\n            {\n                std::array<char_type, 5> false_literal = {{static_cast<char_type>('f'), static_cast<char_type>('a'), static_cast<char_type>('l'), static_cast<char_type>('s'), static_cast<char_type>('e')}};\n                return scan_literal(false_literal.data(), false_literal.size(), token_type::literal_false);\n            }\n            case 'n':\n            {\n                std::array<char_type, 4> null_literal = {{static_cast<char_type>('n'), static_cast<char_type>('u'), static_cast<char_type>('l'), static_cast<char_type>('l')}};\n                return scan_literal(null_literal.data(), null_literal.size(), token_type::literal_null);\n            }\n\n            // string\n            case '\\\"':\n                return scan_string();\n\n            // number\n            case '-':\n            case '0':\n            case '1':\n            case '2':\n            case '3':\n            case '4':\n            case '5':\n            case '6':\n            case '7':\n            case '8':\n            case '9':\n                return scan_number();\n\n            // end of input (the null byte is needed when parsing from\n            // string literals)\n            case '\\0':\n            case char_traits<char_type>::eof():\n                return token_type::end_of_input;\n\n            // error\n            default:\n                error_message = \"invalid literal\";\n                return token_type::parse_error;\n        }\n    }\n\n  private:\n    /// input adapter\n    InputAdapterType ia;\n\n    /// whether comments should be ignored (true) or signaled as errors (false)\n    const bool ignore_comments = false;\n\n    /// the current character\n    char_int_type current = char_traits<char_type>::eof();\n\n    /// whether the next get() call should just return current\n    bool next_unget = false;\n\n    /// the start position of the current token\n    position_t position {};\n\n    /// raw input token string (for error messages)\n    std::vector<char_type> token_string {};\n\n    /// buffer for variable-length tokens (numbers, strings)\n    string_t token_buffer {};\n\n    /// a description of occurred lexer errors\n    const char* error_message = \"\";\n\n    // number values\n    number_integer_t value_integer = 0;\n    number_unsigned_t value_unsigned = 0;\n    number_float_t value_float = 0;\n\n    /// the decimal point\n    const char_int_type decimal_point_char = '.';\n};\n\n}  // namespace detail\nNLOHMANN_JSON_NAMESPACE_END\n\n// #include <nlohmann/detail/macro_scope.hpp>\n\n// #include <nlohmann/detail/meta/is_sax.hpp>\n//     __ _____ _____ _____\n//  __|  |   __|     |   | |  JSON for Modern C++\n// |  |  |__   |  |  | | | |  version 3.11.3\n// |_____|_____|_____|_|___|  https://github.com/nlohmann/json\n//\n// SPDX-FileCopyrightText: 2013-2023 Niels Lohmann <https://nlohmann.me>\n// SPDX-License-Identifier: MIT\n\n\n\n#include <cstdint> // size_t\n#include <utility> // declval\n#include <string> // string\n\n// #include <nlohmann/detail/abi_macros.hpp>\n\n// #include <nlohmann/detail/meta/detected.hpp>\n\n// #include <nlohmann/detail/meta/type_traits.hpp>\n\n\nNLOHMANN_JSON_NAMESPACE_BEGIN\nnamespace detail\n{\n\ntemplate<typename T>\nusing null_function_t = decltype(std::declval<T&>().null());\n\ntemplate<typename T>\nusing boolean_function_t =\n    decltype(std::declval<T&>().boolean(std::declval<bool>()));\n\ntemplate<typename T, typename Integer>\nusing number_integer_function_t =\n    decltype(std::declval<T&>().number_integer(std::declval<Integer>()));\n\ntemplate<typename T, typename Unsigned>\nusing number_unsigned_function_t =\n    decltype(std::declval<T&>().number_unsigned(std::declval<Unsigned>()));\n\ntemplate<typename T, typename Float, typename String>\nusing number_float_function_t = decltype(std::declval<T&>().number_float(\n                                    std::declval<Float>(), std::declval<const String&>()));\n\ntemplate<typename T, typename String>\nusing string_function_t =\n    decltype(std::declval<T&>().string(std::declval<String&>()));\n\ntemplate<typename T, typename Binary>\nusing binary_function_t =\n    decltype(std::declval<T&>().binary(std::declval<Binary&>()));\n\ntemplate<typename T>\nusing start_object_function_t =\n    decltype(std::declval<T&>().start_object(std::declval<std::size_t>()));\n\ntemplate<typename T, typename String>\nusing key_function_t =\n    decltype(std::declval<T&>().key(std::declval<String&>()));\n\ntemplate<typename T>\nusing end_object_function_t = decltype(std::declval<T&>().end_object());\n\ntemplate<typename T>\nusing start_array_function_t =\n    decltype(std::declval<T&>().start_array(std::declval<std::size_t>()));\n\ntemplate<typename T>\nusing end_array_function_t = decltype(std::declval<T&>().end_array());\n\ntemplate<typename T, typename Exception>\nusing parse_error_function_t = decltype(std::declval<T&>().parse_error(\n        std::declval<std::size_t>(), std::declval<const std::string&>(),\n        std::declval<const Exception&>()));\n\ntemplate<typename SAX, typename BasicJsonType>\nstruct is_sax\n{\n  private:\n    static_assert(is_basic_json<BasicJsonType>::value,\n                  \"BasicJsonType must be of type basic_json<...>\");\n\n    using number_integer_t = typename BasicJsonType::number_integer_t;\n    using number_unsigned_t = typename BasicJsonType::number_unsigned_t;\n    using number_float_t = typename BasicJsonType::number_float_t;\n    using string_t = typename BasicJsonType::string_t;\n    using binary_t = typename BasicJsonType::binary_t;\n    using exception_t = typename BasicJsonType::exception;\n\n  public:\n    static constexpr bool value =\n        is_detected_exact<bool, null_function_t, SAX>::value &&\n        is_detected_exact<bool, boolean_function_t, SAX>::value &&\n        is_detected_exact<bool, number_integer_function_t, SAX, number_integer_t>::value &&\n        is_detected_exact<bool, number_unsigned_function_t, SAX, number_unsigned_t>::value &&\n        is_detected_exact<bool, number_float_function_t, SAX, number_float_t, string_t>::value &&\n        is_detected_exact<bool, string_function_t, SAX, string_t>::value &&\n        is_detected_exact<bool, binary_function_t, SAX, binary_t>::value &&\n        is_detected_exact<bool, start_object_function_t, SAX>::value &&\n        is_detected_exact<bool, key_function_t, SAX, string_t>::value &&\n        is_detected_exact<bool, end_object_function_t, SAX>::value &&\n        is_detected_exact<bool, start_array_function_t, SAX>::value &&\n        is_detected_exact<bool, end_array_function_t, SAX>::value &&\n        is_detected_exact<bool, parse_error_function_t, SAX, exception_t>::value;\n};\n\ntemplate<typename SAX, typename BasicJsonType>\nstruct is_sax_static_asserts\n{\n  private:\n    static_assert(is_basic_json<BasicJsonType>::value,\n                  \"BasicJsonType must be of type basic_json<...>\");\n\n    using number_integer_t = typename BasicJsonType::number_integer_t;\n    using number_unsigned_t = typename BasicJsonType::number_unsigned_t;\n    using number_float_t = typename BasicJsonType::number_float_t;\n    using string_t = typename BasicJsonType::string_t;\n    using binary_t = typename BasicJsonType::binary_t;\n    using exception_t = typename BasicJsonType::exception;\n\n  public:\n    static_assert(is_detected_exact<bool, null_function_t, SAX>::value,\n                  \"Missing/invalid function: bool null()\");\n    static_assert(is_detected_exact<bool, boolean_function_t, SAX>::value,\n                  \"Missing/invalid function: bool boolean(bool)\");\n    static_assert(is_detected_exact<bool, boolean_function_t, SAX>::value,\n                  \"Missing/invalid function: bool boolean(bool)\");\n    static_assert(\n        is_detected_exact<bool, number_integer_function_t, SAX,\n        number_integer_t>::value,\n        \"Missing/invalid function: bool number_integer(number_integer_t)\");\n    static_assert(\n        is_detected_exact<bool, number_unsigned_function_t, SAX,\n        number_unsigned_t>::value,\n        \"Missing/invalid function: bool number_unsigned(number_unsigned_t)\");\n    static_assert(is_detected_exact<bool, number_float_function_t, SAX,\n                  number_float_t, string_t>::value,\n                  \"Missing/invalid function: bool number_float(number_float_t, const string_t&)\");\n    static_assert(\n        is_detected_exact<bool, string_function_t, SAX, string_t>::value,\n        \"Missing/invalid function: bool string(string_t&)\");\n    static_assert(\n        is_detected_exact<bool, binary_function_t, SAX, binary_t>::value,\n        \"Missing/invalid function: bool binary(binary_t&)\");\n    static_assert(is_detected_exact<bool, start_object_function_t, SAX>::value,\n                  \"Missing/invalid function: bool start_object(std::size_t)\");\n    static_assert(is_detected_exact<bool, key_function_t, SAX, string_t>::value,\n                  \"Missing/invalid function: bool key(string_t&)\");\n    static_assert(is_detected_exact<bool, end_object_function_t, SAX>::value,\n                  \"Missing/invalid function: bool end_object()\");\n    static_assert(is_detected_exact<bool, start_array_function_t, SAX>::value,\n                  \"Missing/invalid function: bool start_array(std::size_t)\");\n    static_assert(is_detected_exact<bool, end_array_function_t, SAX>::value,\n                  \"Missing/invalid function: bool end_array()\");\n    static_assert(\n        is_detected_exact<bool, parse_error_function_t, SAX, exception_t>::value,\n        \"Missing/invalid function: bool parse_error(std::size_t, const \"\n        \"std::string&, const exception&)\");\n};\n\n}  // namespace detail\nNLOHMANN_JSON_NAMESPACE_END\n\n// #include <nlohmann/detail/meta/type_traits.hpp>\n\n// #include <nlohmann/detail/string_concat.hpp>\n\n// #include <nlohmann/detail/value_t.hpp>\n\n\nNLOHMANN_JSON_NAMESPACE_BEGIN\nnamespace detail\n{\n\n/// how to treat CBOR tags\nenum class cbor_tag_handler_t\n{\n    error,   ///< throw a parse_error exception in case of a tag\n    ignore,  ///< ignore tags\n    store    ///< store tags as binary type\n};\n\n/*!\n@brief determine system byte order\n\n@return true if and only if system's byte order is little endian\n\n@note from https://stackoverflow.com/a/1001328/266378\n*/\nstatic inline bool little_endianness(int num = 1) noexcept\n{\n    return *reinterpret_cast<char*>(&num) == 1;\n}\n\n///////////////////\n// binary reader //\n///////////////////\n\n/*!\n@brief deserialization of CBOR, MessagePack, and UBJSON values\n*/\ntemplate<typename BasicJsonType, typename InputAdapterType, typename SAX = json_sax_dom_parser<BasicJsonType>>\nclass binary_reader\n{\n    using number_integer_t = typename BasicJsonType::number_integer_t;\n    using number_unsigned_t = typename BasicJsonType::number_unsigned_t;\n    using number_float_t = typename BasicJsonType::number_float_t;\n    using string_t = typename BasicJsonType::string_t;\n    using binary_t = typename BasicJsonType::binary_t;\n    using json_sax_t = SAX;\n    using char_type = typename InputAdapterType::char_type;\n    using char_int_type = typename char_traits<char_type>::int_type;\n\n  public:\n    /*!\n    @brief create a binary reader\n\n    @param[in] adapter  input adapter to read from\n    */\n    explicit binary_reader(InputAdapterType&& adapter, const input_format_t format = input_format_t::json) noexcept : ia(std::move(adapter)), input_format(format)\n    {\n        (void)detail::is_sax_static_asserts<SAX, BasicJsonType> {};\n    }\n\n    // make class move-only\n    binary_reader(const binary_reader&) = delete;\n    binary_reader(binary_reader&&) = default; // NOLINT(hicpp-noexcept-move,performance-noexcept-move-constructor)\n    binary_reader& operator=(const binary_reader&) = delete;\n    binary_reader& operator=(binary_reader&&) = default; // NOLINT(hicpp-noexcept-move,performance-noexcept-move-constructor)\n    ~binary_reader() = default;\n\n    /*!\n    @param[in] format  the binary format to parse\n    @param[in] sax_    a SAX event processor\n    @param[in] strict  whether to expect the input to be consumed completed\n    @param[in] tag_handler  how to treat CBOR tags\n\n    @return whether parsing was successful\n    */\n    JSON_HEDLEY_NON_NULL(3)\n    bool sax_parse(const input_format_t format,\n                   json_sax_t* sax_,\n                   const bool strict = true,\n                   const cbor_tag_handler_t tag_handler = cbor_tag_handler_t::error)\n    {\n        sax = sax_;\n        bool result = false;\n\n        switch (format)\n        {\n            case input_format_t::bson:\n                result = parse_bson_internal();\n                break;\n\n            case input_format_t::cbor:\n                result = parse_cbor_internal(true, tag_handler);\n                break;\n\n            case input_format_t::msgpack:\n                result = parse_msgpack_internal();\n                break;\n\n            case input_format_t::ubjson:\n            case input_format_t::bjdata:\n                result = parse_ubjson_internal();\n                break;\n\n            case input_format_t::json: // LCOV_EXCL_LINE\n            default:            // LCOV_EXCL_LINE\n                JSON_ASSERT(false); // NOLINT(cert-dcl03-c,hicpp-static-assert,misc-static-assert) LCOV_EXCL_LINE\n        }\n\n        // strict mode: next byte must be EOF\n        if (result && strict)\n        {\n            if (input_format == input_format_t::ubjson || input_format == input_format_t::bjdata)\n            {\n                get_ignore_noop();\n            }\n            else\n            {\n                get();\n            }\n\n            if (JSON_HEDLEY_UNLIKELY(current != char_traits<char_type>::eof()))\n            {\n                return sax->parse_error(chars_read, get_token_string(), parse_error::create(110, chars_read,\n                                        exception_message(input_format, concat(\"expected end of input; last byte: 0x\", get_token_string()), \"value\"), nullptr));\n            }\n        }\n\n        return result;\n    }\n\n  private:\n    //////////\n    // BSON //\n    //////////\n\n    /*!\n    @brief Reads in a BSON-object and passes it to the SAX-parser.\n    @return whether a valid BSON-value was passed to the SAX parser\n    */\n    bool parse_bson_internal()\n    {\n        std::int32_t document_size{};\n        get_number<std::int32_t, true>(input_format_t::bson, document_size);\n\n        if (JSON_HEDLEY_UNLIKELY(!sax->start_object(static_cast<std::size_t>(-1))))\n        {\n            return false;\n        }\n\n        if (JSON_HEDLEY_UNLIKELY(!parse_bson_element_list(/*is_array*/false)))\n        {\n            return false;\n        }\n\n        return sax->end_object();\n    }\n\n    /*!\n    @brief Parses a C-style string from the BSON input.\n    @param[in,out] result  A reference to the string variable where the read\n                            string is to be stored.\n    @return `true` if the \\x00-byte indicating the end of the string was\n             encountered before the EOF; false` indicates an unexpected EOF.\n    */\n    bool get_bson_cstr(string_t& result)\n    {\n        auto out = std::back_inserter(result);\n        while (true)\n        {\n            get();\n            if (JSON_HEDLEY_UNLIKELY(!unexpect_eof(input_format_t::bson, \"cstring\")))\n            {\n                return false;\n            }\n            if (current == 0x00)\n            {\n                return true;\n            }\n            *out++ = static_cast<typename string_t::value_type>(current);\n        }\n    }\n\n    /*!\n    @brief Parses a zero-terminated string of length @a len from the BSON\n           input.\n    @param[in] len  The length (including the zero-byte at the end) of the\n                    string to be read.\n    @param[in,out] result  A reference to the string variable where the read\n                            string is to be stored.\n    @tparam NumberType The type of the length @a len\n    @pre len >= 1\n    @return `true` if the string was successfully parsed\n    */\n    template<typename NumberType>\n    bool get_bson_string(const NumberType len, string_t& result)\n    {\n        if (JSON_HEDLEY_UNLIKELY(len < 1))\n        {\n            auto last_token = get_token_string();\n            return sax->parse_error(chars_read, last_token, parse_error::create(112, chars_read,\n                                    exception_message(input_format_t::bson, concat(\"string length must be at least 1, is \", std::to_string(len)), \"string\"), nullptr));\n        }\n\n        return get_string(input_format_t::bson, len - static_cast<NumberType>(1), result) && get() != char_traits<char_type>::eof();\n    }\n\n    /*!\n    @brief Parses a byte array input of length @a len from the BSON input.\n    @param[in] len  The length of the byte array to be read.\n    @param[in,out] result  A reference to the binary variable where the read\n                            array is to be stored.\n    @tparam NumberType The type of the length @a len\n    @pre len >= 0\n    @return `true` if the byte array was successfully parsed\n    */\n    template<typename NumberType>\n    bool get_bson_binary(const NumberType len, binary_t& result)\n    {\n        if (JSON_HEDLEY_UNLIKELY(len < 0))\n        {\n            auto last_token = get_token_string();\n            return sax->parse_error(chars_read, last_token, parse_error::create(112, chars_read,\n                                    exception_message(input_format_t::bson, concat(\"byte array length cannot be negative, is \", std::to_string(len)), \"binary\"), nullptr));\n        }\n\n        // All BSON binary values have a subtype\n        std::uint8_t subtype{};\n        get_number<std::uint8_t>(input_format_t::bson, subtype);\n        result.set_subtype(subtype);\n\n        return get_binary(input_format_t::bson, len, result);\n    }\n\n    /*!\n    @brief Read a BSON document element of the given @a element_type.\n    @param[in] element_type The BSON element type, c.f. http://bsonspec.org/spec.html\n    @param[in] element_type_parse_position The position in the input stream,\n               where the `element_type` was read.\n    @warning Not all BSON element types are supported yet. An unsupported\n             @a element_type will give rise to a parse_error.114:\n             Unsupported BSON record type 0x...\n    @return whether a valid BSON-object/array was passed to the SAX parser\n    */\n    bool parse_bson_element_internal(const char_int_type element_type,\n                                     const std::size_t element_type_parse_position)\n    {\n        switch (element_type)\n        {\n            case 0x01: // double\n            {\n                double number{};\n                return get_number<double, true>(input_format_t::bson, number) && sax->number_float(static_cast<number_float_t>(number), \"\");\n            }\n\n            case 0x02: // string\n            {\n                std::int32_t len{};\n                string_t value;\n                return get_number<std::int32_t, true>(input_format_t::bson, len) && get_bson_string(len, value) && sax->string(value);\n            }\n\n            case 0x03: // object\n            {\n                return parse_bson_internal();\n            }\n\n            case 0x04: // array\n            {\n                return parse_bson_array();\n            }\n\n            case 0x05: // binary\n            {\n                std::int32_t len{};\n                binary_t value;\n                return get_number<std::int32_t, true>(input_format_t::bson, len) && get_bson_binary(len, value) && sax->binary(value);\n            }\n\n            case 0x08: // boolean\n            {\n                return sax->boolean(get() != 0);\n            }\n\n            case 0x0A: // null\n            {\n                return sax->null();\n            }\n\n            case 0x10: // int32\n            {\n                std::int32_t value{};\n                return get_number<std::int32_t, true>(input_format_t::bson, value) && sax->number_integer(value);\n            }\n\n            case 0x12: // int64\n            {\n                std::int64_t value{};\n                return get_number<std::int64_t, true>(input_format_t::bson, value) && sax->number_integer(value);\n            }\n\n            default: // anything else not supported (yet)\n            {\n                std::array<char, 3> cr{{}};\n                static_cast<void>((std::snprintf)(cr.data(), cr.size(), \"%.2hhX\", static_cast<unsigned char>(element_type))); // NOLINT(cppcoreguidelines-pro-type-vararg,hicpp-vararg)\n                const std::string cr_str{cr.data()};\n                return sax->parse_error(element_type_parse_position, cr_str,\n                                        parse_error::create(114, element_type_parse_position, concat(\"Unsupported BSON record type 0x\", cr_str), nullptr));\n            }\n        }\n    }\n\n    /*!\n    @brief Read a BSON element list (as specified in the BSON-spec)\n\n    The same binary layout is used for objects and arrays, hence it must be\n    indicated with the argument @a is_array which one is expected\n    (true --> array, false --> object).\n\n    @param[in] is_array Determines if the element list being read is to be\n                        treated as an object (@a is_array == false), or as an\n                        array (@a is_array == true).\n    @return whether a valid BSON-object/array was passed to the SAX parser\n    */\n    bool parse_bson_element_list(const bool is_array)\n    {\n        string_t key;\n\n        while (auto element_type = get())\n        {\n            if (JSON_HEDLEY_UNLIKELY(!unexpect_eof(input_format_t::bson, \"element list\")))\n            {\n                return false;\n            }\n\n            const std::size_t element_type_parse_position = chars_read;\n            if (JSON_HEDLEY_UNLIKELY(!get_bson_cstr(key)))\n            {\n                return false;\n            }\n\n            if (!is_array && !sax->key(key))\n            {\n                return false;\n            }\n\n            if (JSON_HEDLEY_UNLIKELY(!parse_bson_element_internal(element_type, element_type_parse_position)))\n            {\n                return false;\n            }\n\n            // get_bson_cstr only appends\n            key.clear();\n        }\n\n        return true;\n    }\n\n    /*!\n    @brief Reads an array from the BSON input and passes it to the SAX-parser.\n    @return whether a valid BSON-array was passed to the SAX parser\n    */\n    bool parse_bson_array()\n    {\n        std::int32_t document_size{};\n        get_number<std::int32_t, true>(input_format_t::bson, document_size);\n\n        if (JSON_HEDLEY_UNLIKELY(!sax->start_array(static_cast<std::size_t>(-1))))\n        {\n            return false;\n        }\n\n        if (JSON_HEDLEY_UNLIKELY(!parse_bson_element_list(/*is_array*/true)))\n        {\n            return false;\n        }\n\n        return sax->end_array();\n    }\n\n    //////////\n    // CBOR //\n    //////////\n\n    /*!\n    @param[in] get_char  whether a new character should be retrieved from the\n                         input (true) or whether the last read character should\n                         be considered instead (false)\n    @param[in] tag_handler how CBOR tags should be treated\n\n    @return whether a valid CBOR value was passed to the SAX parser\n    */\n    bool parse_cbor_internal(const bool get_char,\n                             const cbor_tag_handler_t tag_handler)\n    {\n        switch (get_char ? get() : current)\n        {\n            // EOF\n            case char_traits<char_type>::eof():\n                return unexpect_eof(input_format_t::cbor, \"value\");\n\n            // Integer 0x00..0x17 (0..23)\n            case 0x00:\n            case 0x01:\n            case 0x02:\n            case 0x03:\n            case 0x04:\n            case 0x05:\n            case 0x06:\n            case 0x07:\n            case 0x08:\n            case 0x09:\n            case 0x0A:\n            case 0x0B:\n            case 0x0C:\n            case 0x0D:\n            case 0x0E:\n            case 0x0F:\n            case 0x10:\n            case 0x11:\n            case 0x12:\n            case 0x13:\n            case 0x14:\n            case 0x15:\n            case 0x16:\n            case 0x17:\n                return sax->number_unsigned(static_cast<number_unsigned_t>(current));\n\n            case 0x18: // Unsigned integer (one-byte uint8_t follows)\n            {\n                std::uint8_t number{};\n                return get_number(input_format_t::cbor, number) && sax->number_unsigned(number);\n            }\n\n            case 0x19: // Unsigned integer (two-byte uint16_t follows)\n            {\n                std::uint16_t number{};\n                return get_number(input_format_t::cbor, number) && sax->number_unsigned(number);\n            }\n\n            case 0x1A: // Unsigned integer (four-byte uint32_t follows)\n            {\n                std::uint32_t number{};\n                return get_number(input_format_t::cbor, number) && sax->number_unsigned(number);\n            }\n\n            case 0x1B: // Unsigned integer (eight-byte uint64_t follows)\n            {\n                std::uint64_t number{};\n                return get_number(input_format_t::cbor, number) && sax->number_unsigned(number);\n            }\n\n            // Negative integer -1-0x00..-1-0x17 (-1..-24)\n            case 0x20:\n            case 0x21:\n            case 0x22:\n            case 0x23:\n            case 0x24:\n            case 0x25:\n            case 0x26:\n            case 0x27:\n            case 0x28:\n            case 0x29:\n            case 0x2A:\n            case 0x2B:\n            case 0x2C:\n            case 0x2D:\n            case 0x2E:\n            case 0x2F:\n            case 0x30:\n            case 0x31:\n            case 0x32:\n            case 0x33:\n            case 0x34:\n            case 0x35:\n            case 0x36:\n            case 0x37:\n                return sax->number_integer(static_cast<std::int8_t>(0x20 - 1 - current));\n\n            case 0x38: // Negative integer (one-byte uint8_t follows)\n            {\n                std::uint8_t number{};\n                return get_number(input_format_t::cbor, number) && sax->number_integer(static_cast<number_integer_t>(-1) - number);\n            }\n\n            case 0x39: // Negative integer -1-n (two-byte uint16_t follows)\n            {\n                std::uint16_t number{};\n                return get_number(input_format_t::cbor, number) && sax->number_integer(static_cast<number_integer_t>(-1) - number);\n            }\n\n            case 0x3A: // Negative integer -1-n (four-byte uint32_t follows)\n            {\n                std::uint32_t number{};\n                return get_number(input_format_t::cbor, number) && sax->number_integer(static_cast<number_integer_t>(-1) - number);\n            }\n\n            case 0x3B: // Negative integer -1-n (eight-byte uint64_t follows)\n            {\n                std::uint64_t number{};\n                return get_number(input_format_t::cbor, number) && sax->number_integer(static_cast<number_integer_t>(-1)\n                        - static_cast<number_integer_t>(number));\n            }\n\n            // Binary data (0x00..0x17 bytes follow)\n            case 0x40:\n            case 0x41:\n            case 0x42:\n            case 0x43:\n            case 0x44:\n            case 0x45:\n            case 0x46:\n            case 0x47:\n            case 0x48:\n            case 0x49:\n            case 0x4A:\n            case 0x4B:\n            case 0x4C:\n            case 0x4D:\n            case 0x4E:\n            case 0x4F:\n            case 0x50:\n            case 0x51:\n            case 0x52:\n            case 0x53:\n            case 0x54:\n            case 0x55:\n            case 0x56:\n            case 0x57:\n            case 0x58: // Binary data (one-byte uint8_t for n follows)\n            case 0x59: // Binary data (two-byte uint16_t for n follow)\n            case 0x5A: // Binary data (four-byte uint32_t for n follow)\n            case 0x5B: // Binary data (eight-byte uint64_t for n follow)\n            case 0x5F: // Binary data (indefinite length)\n            {\n                binary_t b;\n                return get_cbor_binary(b) && sax->binary(b);\n            }\n\n            // UTF-8 string (0x00..0x17 bytes follow)\n            case 0x60:\n            case 0x61:\n            case 0x62:\n            case 0x63:\n            case 0x64:\n            case 0x65:\n            case 0x66:\n            case 0x67:\n            case 0x68:\n            case 0x69:\n            case 0x6A:\n            case 0x6B:\n            case 0x6C:\n            case 0x6D:\n            case 0x6E:\n            case 0x6F:\n            case 0x70:\n            case 0x71:\n            case 0x72:\n            case 0x73:\n            case 0x74:\n            case 0x75:\n            case 0x76:\n            case 0x77:\n            case 0x78: // UTF-8 string (one-byte uint8_t for n follows)\n            case 0x79: // UTF-8 string (two-byte uint16_t for n follow)\n            case 0x7A: // UTF-8 string (four-byte uint32_t for n follow)\n            case 0x7B: // UTF-8 string (eight-byte uint64_t for n follow)\n            case 0x7F: // UTF-8 string (indefinite length)\n            {\n                string_t s;\n                return get_cbor_string(s) && sax->string(s);\n            }\n\n            // array (0x00..0x17 data items follow)\n            case 0x80:\n            case 0x81:\n            case 0x82:\n            case 0x83:\n            case 0x84:\n            case 0x85:\n            case 0x86:\n            case 0x87:\n            case 0x88:\n            case 0x89:\n            case 0x8A:\n            case 0x8B:\n            case 0x8C:\n            case 0x8D:\n            case 0x8E:\n            case 0x8F:\n            case 0x90:\n            case 0x91:\n            case 0x92:\n            case 0x93:\n            case 0x94:\n            case 0x95:\n            case 0x96:\n            case 0x97:\n                return get_cbor_array(\n                           conditional_static_cast<std::size_t>(static_cast<unsigned int>(current) & 0x1Fu), tag_handler);\n\n            case 0x98: // array (one-byte uint8_t for n follows)\n            {\n                std::uint8_t len{};\n                return get_number(input_format_t::cbor, len) && get_cbor_array(static_cast<std::size_t>(len), tag_handler);\n            }\n\n            case 0x99: // array (two-byte uint16_t for n follow)\n            {\n                std::uint16_t len{};\n                return get_number(input_format_t::cbor, len) && get_cbor_array(static_cast<std::size_t>(len), tag_handler);\n            }\n\n            case 0x9A: // array (four-byte uint32_t for n follow)\n            {\n                std::uint32_t len{};\n                return get_number(input_format_t::cbor, len) && get_cbor_array(conditional_static_cast<std::size_t>(len), tag_handler);\n            }\n\n            case 0x9B: // array (eight-byte uint64_t for n follow)\n            {\n                std::uint64_t len{};\n                return get_number(input_format_t::cbor, len) && get_cbor_array(conditional_static_cast<std::size_t>(len), tag_handler);\n            }\n\n            case 0x9F: // array (indefinite length)\n                return get_cbor_array(static_cast<std::size_t>(-1), tag_handler);\n\n            // map (0x00..0x17 pairs of data items follow)\n            case 0xA0:\n            case 0xA1:\n            case 0xA2:\n            case 0xA3:\n            case 0xA4:\n            case 0xA5:\n            case 0xA6:\n            case 0xA7:\n            case 0xA8:\n            case 0xA9:\n            case 0xAA:\n            case 0xAB:\n            case 0xAC:\n            case 0xAD:\n            case 0xAE:\n            case 0xAF:\n            case 0xB0:\n            case 0xB1:\n            case 0xB2:\n            case 0xB3:\n            case 0xB4:\n            case 0xB5:\n            case 0xB6:\n            case 0xB7:\n                return get_cbor_object(conditional_static_cast<std::size_t>(static_cast<unsigned int>(current) & 0x1Fu), tag_handler);\n\n            case 0xB8: // map (one-byte uint8_t for n follows)\n            {\n                std::uint8_t len{};\n                return get_number(input_format_t::cbor, len) && get_cbor_object(static_cast<std::size_t>(len), tag_handler);\n            }\n\n            case 0xB9: // map (two-byte uint16_t for n follow)\n            {\n                std::uint16_t len{};\n                return get_number(input_format_t::cbor, len) && get_cbor_object(static_cast<std::size_t>(len), tag_handler);\n            }\n\n            case 0xBA: // map (four-byte uint32_t for n follow)\n            {\n                std::uint32_t len{};\n                return get_number(input_format_t::cbor, len) && get_cbor_object(conditional_static_cast<std::size_t>(len), tag_handler);\n            }\n\n            case 0xBB: // map (eight-byte uint64_t for n follow)\n            {\n                std::uint64_t len{};\n                return get_number(input_format_t::cbor, len) && get_cbor_object(conditional_static_cast<std::size_t>(len), tag_handler);\n            }\n\n            case 0xBF: // map (indefinite length)\n                return get_cbor_object(static_cast<std::size_t>(-1), tag_handler);\n\n            case 0xC6: // tagged item\n            case 0xC7:\n            case 0xC8:\n            case 0xC9:\n            case 0xCA:\n            case 0xCB:\n            case 0xCC:\n            case 0xCD:\n            case 0xCE:\n            case 0xCF:\n            case 0xD0:\n            case 0xD1:\n            case 0xD2:\n            case 0xD3:\n            case 0xD4:\n            case 0xD8: // tagged item (1 bytes follow)\n            case 0xD9: // tagged item (2 bytes follow)\n            case 0xDA: // tagged item (4 bytes follow)\n            case 0xDB: // tagged item (8 bytes follow)\n            {\n                switch (tag_handler)\n                {\n                    case cbor_tag_handler_t::error:\n                    {\n                        auto last_token = get_token_string();\n                        return sax->parse_error(chars_read, last_token, parse_error::create(112, chars_read,\n                                                exception_message(input_format_t::cbor, concat(\"invalid byte: 0x\", last_token), \"value\"), nullptr));\n                    }\n\n                    case cbor_tag_handler_t::ignore:\n                    {\n                        // ignore binary subtype\n                        switch (current)\n                        {\n                            case 0xD8:\n                            {\n                                std::uint8_t subtype_to_ignore{};\n                                get_number(input_format_t::cbor, subtype_to_ignore);\n                                break;\n                            }\n                            case 0xD9:\n                            {\n                                std::uint16_t subtype_to_ignore{};\n                                get_number(input_format_t::cbor, subtype_to_ignore);\n                                break;\n                            }\n                            case 0xDA:\n                            {\n                                std::uint32_t subtype_to_ignore{};\n                                get_number(input_format_t::cbor, subtype_to_ignore);\n                                break;\n                            }\n                            case 0xDB:\n                            {\n                                std::uint64_t subtype_to_ignore{};\n                                get_number(input_format_t::cbor, subtype_to_ignore);\n                                break;\n                            }\n                            default:\n                                break;\n                        }\n                        return parse_cbor_internal(true, tag_handler);\n                    }\n\n                    case cbor_tag_handler_t::store:\n                    {\n                        binary_t b;\n                        // use binary subtype and store in binary container\n                        switch (current)\n                        {\n                            case 0xD8:\n                            {\n                                std::uint8_t subtype{};\n                                get_number(input_format_t::cbor, subtype);\n                                b.set_subtype(detail::conditional_static_cast<typename binary_t::subtype_type>(subtype));\n                                break;\n                            }\n                            case 0xD9:\n                            {\n                                std::uint16_t subtype{};\n                                get_number(input_format_t::cbor, subtype);\n                                b.set_subtype(detail::conditional_static_cast<typename binary_t::subtype_type>(subtype));\n                                break;\n                            }\n                            case 0xDA:\n                            {\n                                std::uint32_t subtype{};\n                                get_number(input_format_t::cbor, subtype);\n                                b.set_subtype(detail::conditional_static_cast<typename binary_t::subtype_type>(subtype));\n                                break;\n                            }\n                            case 0xDB:\n                            {\n                                std::uint64_t subtype{};\n                                get_number(input_format_t::cbor, subtype);\n                                b.set_subtype(detail::conditional_static_cast<typename binary_t::subtype_type>(subtype));\n                                break;\n                            }\n                            default:\n                                return parse_cbor_internal(true, tag_handler);\n                        }\n                        get();\n                        return get_cbor_binary(b) && sax->binary(b);\n                    }\n\n                    default:                 // LCOV_EXCL_LINE\n                        JSON_ASSERT(false); // NOLINT(cert-dcl03-c,hicpp-static-assert,misc-static-assert) LCOV_EXCL_LINE\n                        return false;        // LCOV_EXCL_LINE\n                }\n            }\n\n            case 0xF4: // false\n                return sax->boolean(false);\n\n            case 0xF5: // true\n                return sax->boolean(true);\n\n            case 0xF6: // null\n                return sax->null();\n\n            case 0xF9: // Half-Precision Float (two-byte IEEE 754)\n            {\n                const auto byte1_raw = get();\n                if (JSON_HEDLEY_UNLIKELY(!unexpect_eof(input_format_t::cbor, \"number\")))\n                {\n                    return false;\n                }\n                const auto byte2_raw = get();\n                if (JSON_HEDLEY_UNLIKELY(!unexpect_eof(input_format_t::cbor, \"number\")))\n                {\n                    return false;\n                }\n\n                const auto byte1 = static_cast<unsigned char>(byte1_raw);\n                const auto byte2 = static_cast<unsigned char>(byte2_raw);\n\n                // code from RFC 7049, Appendix D, Figure 3:\n                // As half-precision floating-point numbers were only added\n                // to IEEE 754 in 2008, today's programming platforms often\n                // still only have limited support for them. It is very\n                // easy to include at least decoding support for them even\n                // without such support. An example of a small decoder for\n                // half-precision floating-point numbers in the C language\n                // is shown in Fig. 3.\n                const auto half = static_cast<unsigned int>((byte1 << 8u) + byte2);\n                const double val = [&half]\n                {\n                    const int exp = (half >> 10u) & 0x1Fu;\n                    const unsigned int mant = half & 0x3FFu;\n                    JSON_ASSERT(0 <= exp&& exp <= 32);\n                    JSON_ASSERT(mant <= 1024);\n                    switch (exp)\n                    {\n                        case 0:\n                            return std::ldexp(mant, -24);\n                        case 31:\n                            return (mant == 0)\n                            ? std::numeric_limits<double>::infinity()\n                            : std::numeric_limits<double>::quiet_NaN();\n                        default:\n                            return std::ldexp(mant + 1024, exp - 25);\n                    }\n                }();\n                return sax->number_float((half & 0x8000u) != 0\n                                         ? static_cast<number_float_t>(-val)\n                                         : static_cast<number_float_t>(val), \"\");\n            }\n\n            case 0xFA: // Single-Precision Float (four-byte IEEE 754)\n            {\n                float number{};\n                return get_number(input_format_t::cbor, number) && sax->number_float(static_cast<number_float_t>(number), \"\");\n            }\n\n            case 0xFB: // Double-Precision Float (eight-byte IEEE 754)\n            {\n                double number{};\n                return get_number(input_format_t::cbor, number) && sax->number_float(static_cast<number_float_t>(number), \"\");\n            }\n\n            default: // anything else (0xFF is handled inside the other types)\n            {\n                auto last_token = get_token_string();\n                return sax->parse_error(chars_read, last_token, parse_error::create(112, chars_read,\n                                        exception_message(input_format_t::cbor, concat(\"invalid byte: 0x\", last_token), \"value\"), nullptr));\n            }\n        }\n    }\n\n    /*!\n    @brief reads a CBOR string\n\n    This function first reads starting bytes to determine the expected\n    string length and then copies this number of bytes into a string.\n    Additionally, CBOR's strings with indefinite lengths are supported.\n\n    @param[out] result  created string\n\n    @return whether string creation completed\n    */\n    bool get_cbor_string(string_t& result)\n    {\n        if (JSON_HEDLEY_UNLIKELY(!unexpect_eof(input_format_t::cbor, \"string\")))\n        {\n            return false;\n        }\n\n        switch (current)\n        {\n            // UTF-8 string (0x00..0x17 bytes follow)\n            case 0x60:\n            case 0x61:\n            case 0x62:\n            case 0x63:\n            case 0x64:\n            case 0x65:\n            case 0x66:\n            case 0x67:\n            case 0x68:\n            case 0x69:\n            case 0x6A:\n            case 0x6B:\n            case 0x6C:\n            case 0x6D:\n            case 0x6E:\n            case 0x6F:\n            case 0x70:\n            case 0x71:\n            case 0x72:\n            case 0x73:\n            case 0x74:\n            case 0x75:\n            case 0x76:\n            case 0x77:\n            {\n                return get_string(input_format_t::cbor, static_cast<unsigned int>(current) & 0x1Fu, result);\n            }\n\n            case 0x78: // UTF-8 string (one-byte uint8_t for n follows)\n            {\n                std::uint8_t len{};\n                return get_number(input_format_t::cbor, len) && get_string(input_format_t::cbor, len, result);\n            }\n\n            case 0x79: // UTF-8 string (two-byte uint16_t for n follow)\n            {\n                std::uint16_t len{};\n                return get_number(input_format_t::cbor, len) && get_string(input_format_t::cbor, len, result);\n            }\n\n            case 0x7A: // UTF-8 string (four-byte uint32_t for n follow)\n            {\n                std::uint32_t len{};\n                return get_number(input_format_t::cbor, len) && get_string(input_format_t::cbor, len, result);\n            }\n\n            case 0x7B: // UTF-8 string (eight-byte uint64_t for n follow)\n            {\n                std::uint64_t len{};\n                return get_number(input_format_t::cbor, len) && get_string(input_format_t::cbor, len, result);\n            }\n\n            case 0x7F: // UTF-8 string (indefinite length)\n            {\n                while (get() != 0xFF)\n                {\n                    string_t chunk;\n                    if (!get_cbor_string(chunk))\n                    {\n                        return false;\n                    }\n                    result.append(chunk);\n                }\n                return true;\n            }\n\n            default:\n            {\n                auto last_token = get_token_string();\n                return sax->parse_error(chars_read, last_token, parse_error::create(113, chars_read,\n                                        exception_message(input_format_t::cbor, concat(\"expected length specification (0x60-0x7B) or indefinite string type (0x7F); last byte: 0x\", last_token), \"string\"), nullptr));\n            }\n        }\n    }\n\n    /*!\n    @brief reads a CBOR byte array\n\n    This function first reads starting bytes to determine the expected\n    byte array length and then copies this number of bytes into the byte array.\n    Additionally, CBOR's byte arrays with indefinite lengths are supported.\n\n    @param[out] result  created byte array\n\n    @return whether byte array creation completed\n    */\n    bool get_cbor_binary(binary_t& result)\n    {\n        if (JSON_HEDLEY_UNLIKELY(!unexpect_eof(input_format_t::cbor, \"binary\")))\n        {\n            return false;\n        }\n\n        switch (current)\n        {\n            // Binary data (0x00..0x17 bytes follow)\n            case 0x40:\n            case 0x41:\n            case 0x42:\n            case 0x43:\n            case 0x44:\n            case 0x45:\n            case 0x46:\n            case 0x47:\n            case 0x48:\n            case 0x49:\n            case 0x4A:\n            case 0x4B:\n            case 0x4C:\n            case 0x4D:\n            case 0x4E:\n            case 0x4F:\n            case 0x50:\n            case 0x51:\n            case 0x52:\n            case 0x53:\n            case 0x54:\n            case 0x55:\n            case 0x56:\n            case 0x57:\n            {\n                return get_binary(input_format_t::cbor, static_cast<unsigned int>(current) & 0x1Fu, result);\n            }\n\n            case 0x58: // Binary data (one-byte uint8_t for n follows)\n            {\n                std::uint8_t len{};\n                return get_number(input_format_t::cbor, len) &&\n                       get_binary(input_format_t::cbor, len, result);\n            }\n\n            case 0x59: // Binary data (two-byte uint16_t for n follow)\n            {\n                std::uint16_t len{};\n                return get_number(input_format_t::cbor, len) &&\n                       get_binary(input_format_t::cbor, len, result);\n            }\n\n            case 0x5A: // Binary data (four-byte uint32_t for n follow)\n            {\n                std::uint32_t len{};\n                return get_number(input_format_t::cbor, len) &&\n                       get_binary(input_format_t::cbor, len, result);\n            }\n\n            case 0x5B: // Binary data (eight-byte uint64_t for n follow)\n            {\n                std::uint64_t len{};\n                return get_number(input_format_t::cbor, len) &&\n                       get_binary(input_format_t::cbor, len, result);\n            }\n\n            case 0x5F: // Binary data (indefinite length)\n            {\n                while (get() != 0xFF)\n                {\n                    binary_t chunk;\n                    if (!get_cbor_binary(chunk))\n                    {\n                        return false;\n                    }\n                    result.insert(result.end(), chunk.begin(), chunk.end());\n                }\n                return true;\n            }\n\n            default:\n            {\n                auto last_token = get_token_string();\n                return sax->parse_error(chars_read, last_token, parse_error::create(113, chars_read,\n                                        exception_message(input_format_t::cbor, concat(\"expected length specification (0x40-0x5B) or indefinite binary array type (0x5F); last byte: 0x\", last_token), \"binary\"), nullptr));\n            }\n        }\n    }\n\n    /*!\n    @param[in] len  the length of the array or static_cast<std::size_t>(-1) for an\n                    array of indefinite size\n    @param[in] tag_handler how CBOR tags should be treated\n    @return whether array creation completed\n    */\n    bool get_cbor_array(const std::size_t len,\n                        const cbor_tag_handler_t tag_handler)\n    {\n        if (JSON_HEDLEY_UNLIKELY(!sax->start_array(len)))\n        {\n            return false;\n        }\n\n        if (len != static_cast<std::size_t>(-1))\n        {\n            for (std::size_t i = 0; i < len; ++i)\n            {\n                if (JSON_HEDLEY_UNLIKELY(!parse_cbor_internal(true, tag_handler)))\n                {\n                    return false;\n                }\n            }\n        }\n        else\n        {\n            while (get() != 0xFF)\n            {\n                if (JSON_HEDLEY_UNLIKELY(!parse_cbor_internal(false, tag_handler)))\n                {\n                    return false;\n                }\n            }\n        }\n\n        return sax->end_array();\n    }\n\n    /*!\n    @param[in] len  the length of the object or static_cast<std::size_t>(-1) for an\n                    object of indefinite size\n    @param[in] tag_handler how CBOR tags should be treated\n    @return whether object creation completed\n    */\n    bool get_cbor_object(const std::size_t len,\n                         const cbor_tag_handler_t tag_handler)\n    {\n        if (JSON_HEDLEY_UNLIKELY(!sax->start_object(len)))\n        {\n            return false;\n        }\n\n        if (len != 0)\n        {\n            string_t key;\n            if (len != static_cast<std::size_t>(-1))\n            {\n                for (std::size_t i = 0; i < len; ++i)\n                {\n                    get();\n                    if (JSON_HEDLEY_UNLIKELY(!get_cbor_string(key) || !sax->key(key)))\n                    {\n                        return false;\n                    }\n\n                    if (JSON_HEDLEY_UNLIKELY(!parse_cbor_internal(true, tag_handler)))\n                    {\n                        return false;\n                    }\n                    key.clear();\n                }\n            }\n            else\n            {\n                while (get() != 0xFF)\n                {\n                    if (JSON_HEDLEY_UNLIKELY(!get_cbor_string(key) || !sax->key(key)))\n                    {\n                        return false;\n                    }\n\n                    if (JSON_HEDLEY_UNLIKELY(!parse_cbor_internal(true, tag_handler)))\n                    {\n                        return false;\n                    }\n                    key.clear();\n                }\n            }\n        }\n\n        return sax->end_object();\n    }\n\n    /////////////\n    // MsgPack //\n    /////////////\n\n    /*!\n    @return whether a valid MessagePack value was passed to the SAX parser\n    */\n    bool parse_msgpack_internal()\n    {\n        switch (get())\n        {\n            // EOF\n            case char_traits<char_type>::eof():\n                return unexpect_eof(input_format_t::msgpack, \"value\");\n\n            // positive fixint\n            case 0x00:\n            case 0x01:\n            case 0x02:\n            case 0x03:\n            case 0x04:\n            case 0x05:\n            case 0x06:\n            case 0x07:\n            case 0x08:\n            case 0x09:\n            case 0x0A:\n            case 0x0B:\n            case 0x0C:\n            case 0x0D:\n            case 0x0E:\n            case 0x0F:\n            case 0x10:\n            case 0x11:\n            case 0x12:\n            case 0x13:\n            case 0x14:\n            case 0x15:\n            case 0x16:\n            case 0x17:\n            case 0x18:\n            case 0x19:\n            case 0x1A:\n            case 0x1B:\n            case 0x1C:\n            case 0x1D:\n            case 0x1E:\n            case 0x1F:\n            case 0x20:\n            case 0x21:\n            case 0x22:\n            case 0x23:\n            case 0x24:\n            case 0x25:\n            case 0x26:\n            case 0x27:\n            case 0x28:\n            case 0x29:\n            case 0x2A:\n            case 0x2B:\n            case 0x2C:\n            case 0x2D:\n            case 0x2E:\n            case 0x2F:\n            case 0x30:\n            case 0x31:\n            case 0x32:\n            case 0x33:\n            case 0x34:\n            case 0x35:\n            case 0x36:\n            case 0x37:\n            case 0x38:\n            case 0x39:\n            case 0x3A:\n            case 0x3B:\n            case 0x3C:\n            case 0x3D:\n            case 0x3E:\n            case 0x3F:\n            case 0x40:\n            case 0x41:\n            case 0x42:\n            case 0x43:\n            case 0x44:\n            case 0x45:\n            case 0x46:\n            case 0x47:\n            case 0x48:\n            case 0x49:\n            case 0x4A:\n            case 0x4B:\n            case 0x4C:\n            case 0x4D:\n            case 0x4E:\n            case 0x4F:\n            case 0x50:\n            case 0x51:\n            case 0x52:\n            case 0x53:\n            case 0x54:\n            case 0x55:\n            case 0x56:\n            case 0x57:\n            case 0x58:\n            case 0x59:\n            case 0x5A:\n            case 0x5B:\n            case 0x5C:\n            case 0x5D:\n            case 0x5E:\n            case 0x5F:\n            case 0x60:\n            case 0x61:\n            case 0x62:\n            case 0x63:\n            case 0x64:\n            case 0x65:\n            case 0x66:\n            case 0x67:\n            case 0x68:\n            case 0x69:\n            case 0x6A:\n            case 0x6B:\n            case 0x6C:\n            case 0x6D:\n            case 0x6E:\n            case 0x6F:\n            case 0x70:\n            case 0x71:\n            case 0x72:\n            case 0x73:\n            case 0x74:\n            case 0x75:\n            case 0x76:\n            case 0x77:\n            case 0x78:\n            case 0x79:\n            case 0x7A:\n            case 0x7B:\n            case 0x7C:\n            case 0x7D:\n            case 0x7E:\n            case 0x7F:\n                return sax->number_unsigned(static_cast<number_unsigned_t>(current));\n\n            // fixmap\n            case 0x80:\n            case 0x81:\n            case 0x82:\n            case 0x83:\n            case 0x84:\n            case 0x85:\n            case 0x86:\n            case 0x87:\n            case 0x88:\n            case 0x89:\n            case 0x8A:\n            case 0x8B:\n            case 0x8C:\n            case 0x8D:\n            case 0x8E:\n            case 0x8F:\n                return get_msgpack_object(conditional_static_cast<std::size_t>(static_cast<unsigned int>(current) & 0x0Fu));\n\n            // fixarray\n            case 0x90:\n            case 0x91:\n            case 0x92:\n            case 0x93:\n            case 0x94:\n            case 0x95:\n            case 0x96:\n            case 0x97:\n            case 0x98:\n            case 0x99:\n            case 0x9A:\n            case 0x9B:\n            case 0x9C:\n            case 0x9D:\n            case 0x9E:\n            case 0x9F:\n                return get_msgpack_array(conditional_static_cast<std::size_t>(static_cast<unsigned int>(current) & 0x0Fu));\n\n            // fixstr\n            case 0xA0:\n            case 0xA1:\n            case 0xA2:\n            case 0xA3:\n            case 0xA4:\n            case 0xA5:\n            case 0xA6:\n            case 0xA7:\n            case 0xA8:\n            case 0xA9:\n            case 0xAA:\n            case 0xAB:\n            case 0xAC:\n            case 0xAD:\n            case 0xAE:\n            case 0xAF:\n            case 0xB0:\n            case 0xB1:\n            case 0xB2:\n            case 0xB3:\n            case 0xB4:\n            case 0xB5:\n            case 0xB6:\n            case 0xB7:\n            case 0xB8:\n            case 0xB9:\n            case 0xBA:\n            case 0xBB:\n            case 0xBC:\n            case 0xBD:\n            case 0xBE:\n            case 0xBF:\n            case 0xD9: // str 8\n            case 0xDA: // str 16\n            case 0xDB: // str 32\n            {\n                string_t s;\n                return get_msgpack_string(s) && sax->string(s);\n            }\n\n            case 0xC0: // nil\n                return sax->null();\n\n            case 0xC2: // false\n                return sax->boolean(false);\n\n            case 0xC3: // true\n                return sax->boolean(true);\n\n            case 0xC4: // bin 8\n            case 0xC5: // bin 16\n            case 0xC6: // bin 32\n            case 0xC7: // ext 8\n            case 0xC8: // ext 16\n            case 0xC9: // ext 32\n            case 0xD4: // fixext 1\n            case 0xD5: // fixext 2\n            case 0xD6: // fixext 4\n            case 0xD7: // fixext 8\n            case 0xD8: // fixext 16\n            {\n                binary_t b;\n                return get_msgpack_binary(b) && sax->binary(b);\n            }\n\n            case 0xCA: // float 32\n            {\n                float number{};\n                return get_number(input_format_t::msgpack, number) && sax->number_float(static_cast<number_float_t>(number), \"\");\n            }\n\n            case 0xCB: // float 64\n            {\n                double number{};\n                return get_number(input_format_t::msgpack, number) && sax->number_float(static_cast<number_float_t>(number), \"\");\n            }\n\n            case 0xCC: // uint 8\n            {\n                std::uint8_t number{};\n                return get_number(input_format_t::msgpack, number) && sax->number_unsigned(number);\n            }\n\n            case 0xCD: // uint 16\n            {\n                std::uint16_t number{};\n                return get_number(input_format_t::msgpack, number) && sax->number_unsigned(number);\n            }\n\n            case 0xCE: // uint 32\n            {\n                std::uint32_t number{};\n                return get_number(input_format_t::msgpack, number) && sax->number_unsigned(number);\n            }\n\n            case 0xCF: // uint 64\n            {\n                std::uint64_t number{};\n                return get_number(input_format_t::msgpack, number) && sax->number_unsigned(number);\n            }\n\n            case 0xD0: // int 8\n            {\n                std::int8_t number{};\n                return get_number(input_format_t::msgpack, number) && sax->number_integer(number);\n            }\n\n            case 0xD1: // int 16\n            {\n                std::int16_t number{};\n                return get_number(input_format_t::msgpack, number) && sax->number_integer(number);\n            }\n\n            case 0xD2: // int 32\n            {\n                std::int32_t number{};\n                return get_number(input_format_t::msgpack, number) && sax->number_integer(number);\n            }\n\n            case 0xD3: // int 64\n            {\n                std::int64_t number{};\n                return get_number(input_format_t::msgpack, number) && sax->number_integer(number);\n            }\n\n            case 0xDC: // array 16\n            {\n                std::uint16_t len{};\n                return get_number(input_format_t::msgpack, len) && get_msgpack_array(static_cast<std::size_t>(len));\n            }\n\n            case 0xDD: // array 32\n            {\n                std::uint32_t len{};\n                return get_number(input_format_t::msgpack, len) && get_msgpack_array(conditional_static_cast<std::size_t>(len));\n            }\n\n            case 0xDE: // map 16\n            {\n                std::uint16_t len{};\n                return get_number(input_format_t::msgpack, len) && get_msgpack_object(static_cast<std::size_t>(len));\n            }\n\n            case 0xDF: // map 32\n            {\n                std::uint32_t len{};\n                return get_number(input_format_t::msgpack, len) && get_msgpack_object(conditional_static_cast<std::size_t>(len));\n            }\n\n            // negative fixint\n            case 0xE0:\n            case 0xE1:\n            case 0xE2:\n            case 0xE3:\n            case 0xE4:\n            case 0xE5:\n            case 0xE6:\n            case 0xE7:\n            case 0xE8:\n            case 0xE9:\n            case 0xEA:\n            case 0xEB:\n            case 0xEC:\n            case 0xED:\n            case 0xEE:\n            case 0xEF:\n            case 0xF0:\n            case 0xF1:\n            case 0xF2:\n            case 0xF3:\n            case 0xF4:\n            case 0xF5:\n            case 0xF6:\n            case 0xF7:\n            case 0xF8:\n            case 0xF9:\n            case 0xFA:\n            case 0xFB:\n            case 0xFC:\n            case 0xFD:\n            case 0xFE:\n            case 0xFF:\n                return sax->number_integer(static_cast<std::int8_t>(current));\n\n            default: // anything else\n            {\n                auto last_token = get_token_string();\n                return sax->parse_error(chars_read, last_token, parse_error::create(112, chars_read,\n                                        exception_message(input_format_t::msgpack, concat(\"invalid byte: 0x\", last_token), \"value\"), nullptr));\n            }\n        }\n    }\n\n    /*!\n    @brief reads a MessagePack string\n\n    This function first reads starting bytes to determine the expected\n    string length and then copies this number of bytes into a string.\n\n    @param[out] result  created string\n\n    @return whether string creation completed\n    */\n    bool get_msgpack_string(string_t& result)\n    {\n        if (JSON_HEDLEY_UNLIKELY(!unexpect_eof(input_format_t::msgpack, \"string\")))\n        {\n            return false;\n        }\n\n        switch (current)\n        {\n            // fixstr\n            case 0xA0:\n            case 0xA1:\n            case 0xA2:\n            case 0xA3:\n            case 0xA4:\n            case 0xA5:\n            case 0xA6:\n            case 0xA7:\n            case 0xA8:\n            case 0xA9:\n            case 0xAA:\n            case 0xAB:\n            case 0xAC:\n            case 0xAD:\n            case 0xAE:\n            case 0xAF:\n            case 0xB0:\n            case 0xB1:\n            case 0xB2:\n            case 0xB3:\n            case 0xB4:\n            case 0xB5:\n            case 0xB6:\n            case 0xB7:\n            case 0xB8:\n            case 0xB9:\n            case 0xBA:\n            case 0xBB:\n            case 0xBC:\n            case 0xBD:\n            case 0xBE:\n            case 0xBF:\n            {\n                return get_string(input_format_t::msgpack, static_cast<unsigned int>(current) & 0x1Fu, result);\n            }\n\n            case 0xD9: // str 8\n            {\n                std::uint8_t len{};\n                return get_number(input_format_t::msgpack, len) && get_string(input_format_t::msgpack, len, result);\n            }\n\n            case 0xDA: // str 16\n            {\n                std::uint16_t len{};\n                return get_number(input_format_t::msgpack, len) && get_string(input_format_t::msgpack, len, result);\n            }\n\n            case 0xDB: // str 32\n            {\n                std::uint32_t len{};\n                return get_number(input_format_t::msgpack, len) && get_string(input_format_t::msgpack, len, result);\n            }\n\n            default:\n            {\n                auto last_token = get_token_string();\n                return sax->parse_error(chars_read, last_token, parse_error::create(113, chars_read,\n                                        exception_message(input_format_t::msgpack, concat(\"expected length specification (0xA0-0xBF, 0xD9-0xDB); last byte: 0x\", last_token), \"string\"), nullptr));\n            }\n        }\n    }\n\n    /*!\n    @brief reads a MessagePack byte array\n\n    This function first reads starting bytes to determine the expected\n    byte array length and then copies this number of bytes into a byte array.\n\n    @param[out] result  created byte array\n\n    @return whether byte array creation completed\n    */\n    bool get_msgpack_binary(binary_t& result)\n    {\n        // helper function to set the subtype\n        auto assign_and_return_true = [&result](std::int8_t subtype)\n        {\n            result.set_subtype(static_cast<std::uint8_t>(subtype));\n            return true;\n        };\n\n        switch (current)\n        {\n            case 0xC4: // bin 8\n            {\n                std::uint8_t len{};\n                return get_number(input_format_t::msgpack, len) &&\n                       get_binary(input_format_t::msgpack, len, result);\n            }\n\n            case 0xC5: // bin 16\n            {\n                std::uint16_t len{};\n                return get_number(input_format_t::msgpack, len) &&\n                       get_binary(input_format_t::msgpack, len, result);\n            }\n\n            case 0xC6: // bin 32\n            {\n                std::uint32_t len{};\n                return get_number(input_format_t::msgpack, len) &&\n                       get_binary(input_format_t::msgpack, len, result);\n            }\n\n            case 0xC7: // ext 8\n            {\n                std::uint8_t len{};\n                std::int8_t subtype{};\n                return get_number(input_format_t::msgpack, len) &&\n                       get_number(input_format_t::msgpack, subtype) &&\n                       get_binary(input_format_t::msgpack, len, result) &&\n                       assign_and_return_true(subtype);\n            }\n\n            case 0xC8: // ext 16\n            {\n                std::uint16_t len{};\n                std::int8_t subtype{};\n                return get_number(input_format_t::msgpack, len) &&\n                       get_number(input_format_t::msgpack, subtype) &&\n                       get_binary(input_format_t::msgpack, len, result) &&\n                       assign_and_return_true(subtype);\n            }\n\n            case 0xC9: // ext 32\n            {\n                std::uint32_t len{};\n                std::int8_t subtype{};\n                return get_number(input_format_t::msgpack, len) &&\n                       get_number(input_format_t::msgpack, subtype) &&\n                       get_binary(input_format_t::msgpack, len, result) &&\n                       assign_and_return_true(subtype);\n            }\n\n            case 0xD4: // fixext 1\n            {\n                std::int8_t subtype{};\n                return get_number(input_format_t::msgpack, subtype) &&\n                       get_binary(input_format_t::msgpack, 1, result) &&\n                       assign_and_return_true(subtype);\n            }\n\n            case 0xD5: // fixext 2\n            {\n                std::int8_t subtype{};\n                return get_number(input_format_t::msgpack, subtype) &&\n                       get_binary(input_format_t::msgpack, 2, result) &&\n                       assign_and_return_true(subtype);\n            }\n\n            case 0xD6: // fixext 4\n            {\n                std::int8_t subtype{};\n                return get_number(input_format_t::msgpack, subtype) &&\n                       get_binary(input_format_t::msgpack, 4, result) &&\n                       assign_and_return_true(subtype);\n            }\n\n            case 0xD7: // fixext 8\n            {\n                std::int8_t subtype{};\n                return get_number(input_format_t::msgpack, subtype) &&\n                       get_binary(input_format_t::msgpack, 8, result) &&\n                       assign_and_return_true(subtype);\n            }\n\n            case 0xD8: // fixext 16\n            {\n                std::int8_t subtype{};\n                return get_number(input_format_t::msgpack, subtype) &&\n                       get_binary(input_format_t::msgpack, 16, result) &&\n                       assign_and_return_true(subtype);\n            }\n\n            default:           // LCOV_EXCL_LINE\n                return false;  // LCOV_EXCL_LINE\n        }\n    }\n\n    /*!\n    @param[in] len  the length of the array\n    @return whether array creation completed\n    */\n    bool get_msgpack_array(const std::size_t len)\n    {\n        if (JSON_HEDLEY_UNLIKELY(!sax->start_array(len)))\n        {\n            return false;\n        }\n\n        for (std::size_t i = 0; i < len; ++i)\n        {\n            if (JSON_HEDLEY_UNLIKELY(!parse_msgpack_internal()))\n            {\n                return false;\n            }\n        }\n\n        return sax->end_array();\n    }\n\n    /*!\n    @param[in] len  the length of the object\n    @return whether object creation completed\n    */\n    bool get_msgpack_object(const std::size_t len)\n    {\n        if (JSON_HEDLEY_UNLIKELY(!sax->start_object(len)))\n        {\n            return false;\n        }\n\n        string_t key;\n        for (std::size_t i = 0; i < len; ++i)\n        {\n            get();\n            if (JSON_HEDLEY_UNLIKELY(!get_msgpack_string(key) || !sax->key(key)))\n            {\n                return false;\n            }\n\n            if (JSON_HEDLEY_UNLIKELY(!parse_msgpack_internal()))\n            {\n                return false;\n            }\n            key.clear();\n        }\n\n        return sax->end_object();\n    }\n\n    ////////////\n    // UBJSON //\n    ////////////\n\n    /*!\n    @param[in] get_char  whether a new character should be retrieved from the\n                         input (true, default) or whether the last read\n                         character should be considered instead\n\n    @return whether a valid UBJSON value was passed to the SAX parser\n    */\n    bool parse_ubjson_internal(const bool get_char = true)\n    {\n        return get_ubjson_value(get_char ? get_ignore_noop() : current);\n    }\n\n    /*!\n    @brief reads a UBJSON string\n\n    This function is either called after reading the 'S' byte explicitly\n    indicating a string, or in case of an object key where the 'S' byte can be\n    left out.\n\n    @param[out] result   created string\n    @param[in] get_char  whether a new character should be retrieved from the\n                         input (true, default) or whether the last read\n                         character should be considered instead\n\n    @return whether string creation completed\n    */\n    bool get_ubjson_string(string_t& result, const bool get_char = true)\n    {\n        if (get_char)\n        {\n            get();  // TODO(niels): may we ignore N here?\n        }\n\n        if (JSON_HEDLEY_UNLIKELY(!unexpect_eof(input_format, \"value\")))\n        {\n            return false;\n        }\n\n        switch (current)\n        {\n            case 'U':\n            {\n                std::uint8_t len{};\n                return get_number(input_format, len) && get_string(input_format, len, result);\n            }\n\n            case 'i':\n            {\n                std::int8_t len{};\n                return get_number(input_format, len) && get_string(input_format, len, result);\n            }\n\n            case 'I':\n            {\n                std::int16_t len{};\n                return get_number(input_format, len) && get_string(input_format, len, result);\n            }\n\n            case 'l':\n            {\n                std::int32_t len{};\n                return get_number(input_format, len) && get_string(input_format, len, result);\n            }\n\n            case 'L':\n            {\n                std::int64_t len{};\n                return get_number(input_format, len) && get_string(input_format, len, result);\n            }\n\n            case 'u':\n            {\n                if (input_format != input_format_t::bjdata)\n                {\n                    break;\n                }\n                std::uint16_t len{};\n                return get_number(input_format, len) && get_string(input_format, len, result);\n            }\n\n            case 'm':\n            {\n                if (input_format != input_format_t::bjdata)\n                {\n                    break;\n                }\n                std::uint32_t len{};\n                return get_number(input_format, len) && get_string(input_format, len, result);\n            }\n\n            case 'M':\n            {\n                if (input_format != input_format_t::bjdata)\n                {\n                    break;\n                }\n                std::uint64_t len{};\n                return get_number(input_format, len) && get_string(input_format, len, result);\n            }\n\n            default:\n                break;\n        }\n        auto last_token = get_token_string();\n        std::string message;\n\n        if (input_format != input_format_t::bjdata)\n        {\n            message = \"expected length type specification (U, i, I, l, L); last byte: 0x\" + last_token;\n        }\n        else\n        {\n            message = \"expected length type specification (U, i, u, I, m, l, M, L); last byte: 0x\" + last_token;\n        }\n        return sax->parse_error(chars_read, last_token, parse_error::create(113, chars_read, exception_message(input_format, message, \"string\"), nullptr));\n    }\n\n    /*!\n    @param[out] dim  an integer vector storing the ND array dimensions\n    @return whether reading ND array size vector is successful\n    */\n    bool get_ubjson_ndarray_size(std::vector<size_t>& dim)\n    {\n        std::pair<std::size_t, char_int_type> size_and_type;\n        size_t dimlen = 0;\n        bool no_ndarray = true;\n\n        if (JSON_HEDLEY_UNLIKELY(!get_ubjson_size_type(size_and_type, no_ndarray)))\n        {\n            return false;\n        }\n\n        if (size_and_type.first != npos)\n        {\n            if (size_and_type.second != 0)\n            {\n                if (size_and_type.second != 'N')\n                {\n                    for (std::size_t i = 0; i < size_and_type.first; ++i)\n                    {\n                        if (JSON_HEDLEY_UNLIKELY(!get_ubjson_size_value(dimlen, no_ndarray, size_and_type.second)))\n                        {\n                            return false;\n                        }\n                        dim.push_back(dimlen);\n                    }\n                }\n            }\n            else\n            {\n                for (std::size_t i = 0; i < size_and_type.first; ++i)\n                {\n                    if (JSON_HEDLEY_UNLIKELY(!get_ubjson_size_value(dimlen, no_ndarray)))\n                    {\n                        return false;\n                    }\n                    dim.push_back(dimlen);\n                }\n            }\n        }\n        else\n        {\n            while (current != ']')\n            {\n                if (JSON_HEDLEY_UNLIKELY(!get_ubjson_size_value(dimlen, no_ndarray, current)))\n                {\n                    return false;\n                }\n                dim.push_back(dimlen);\n                get_ignore_noop();\n            }\n        }\n        return true;\n    }\n\n    /*!\n    @param[out] result  determined size\n    @param[in,out] is_ndarray  for input, `true` means already inside an ndarray vector\n                               or ndarray dimension is not allowed; `false` means ndarray\n                               is allowed; for output, `true` means an ndarray is found;\n                               is_ndarray can only return `true` when its initial value\n                               is `false`\n    @param[in] prefix  type marker if already read, otherwise set to 0\n\n    @return whether size determination completed\n    */\n    bool get_ubjson_size_value(std::size_t& result, bool& is_ndarray, char_int_type prefix = 0)\n    {\n        if (prefix == 0)\n        {\n            prefix = get_ignore_noop();\n        }\n\n        switch (prefix)\n        {\n            case 'U':\n            {\n                std::uint8_t number{};\n                if (JSON_HEDLEY_UNLIKELY(!get_number(input_format, number)))\n                {\n                    return false;\n                }\n                result = static_cast<std::size_t>(number);\n                return true;\n            }\n\n            case 'i':\n            {\n                std::int8_t number{};\n                if (JSON_HEDLEY_UNLIKELY(!get_number(input_format, number)))\n                {\n                    return false;\n                }\n                if (number < 0)\n                {\n                    return sax->parse_error(chars_read, get_token_string(), parse_error::create(113, chars_read,\n                                            exception_message(input_format, \"count in an optimized container must be positive\", \"size\"), nullptr));\n                }\n                result = static_cast<std::size_t>(number); // NOLINT(bugprone-signed-char-misuse,cert-str34-c): number is not a char\n                return true;\n            }\n\n            case 'I':\n            {\n                std::int16_t number{};\n                if (JSON_HEDLEY_UNLIKELY(!get_number(input_format, number)))\n                {\n                    return false;\n                }\n                if (number < 0)\n                {\n                    return sax->parse_error(chars_read, get_token_string(), parse_error::create(113, chars_read,\n                                            exception_message(input_format, \"count in an optimized container must be positive\", \"size\"), nullptr));\n                }\n                result = static_cast<std::size_t>(number);\n                return true;\n            }\n\n            case 'l':\n            {\n                std::int32_t number{};\n                if (JSON_HEDLEY_UNLIKELY(!get_number(input_format, number)))\n                {\n                    return false;\n                }\n                if (number < 0)\n                {\n                    return sax->parse_error(chars_read, get_token_string(), parse_error::create(113, chars_read,\n                                            exception_message(input_format, \"count in an optimized container must be positive\", \"size\"), nullptr));\n                }\n                result = static_cast<std::size_t>(number);\n                return true;\n            }\n\n            case 'L':\n            {\n                std::int64_t number{};\n                if (JSON_HEDLEY_UNLIKELY(!get_number(input_format, number)))\n                {\n                    return false;\n                }\n                if (number < 0)\n                {\n                    return sax->parse_error(chars_read, get_token_string(), parse_error::create(113, chars_read,\n                                            exception_message(input_format, \"count in an optimized container must be positive\", \"size\"), nullptr));\n                }\n                if (!value_in_range_of<std::size_t>(number))\n                {\n                    return sax->parse_error(chars_read, get_token_string(), out_of_range::create(408,\n                                            exception_message(input_format, \"integer value overflow\", \"size\"), nullptr));\n                }\n                result = static_cast<std::size_t>(number);\n                return true;\n            }\n\n            case 'u':\n            {\n                if (input_format != input_format_t::bjdata)\n                {\n                    break;\n                }\n                std::uint16_t number{};\n                if (JSON_HEDLEY_UNLIKELY(!get_number(input_format, number)))\n                {\n                    return false;\n                }\n                result = static_cast<std::size_t>(number);\n                return true;\n            }\n\n            case 'm':\n            {\n                if (input_format != input_format_t::bjdata)\n                {\n                    break;\n                }\n                std::uint32_t number{};\n                if (JSON_HEDLEY_UNLIKELY(!get_number(input_format, number)))\n                {\n                    return false;\n                }\n                result = conditional_static_cast<std::size_t>(number);\n                return true;\n            }\n\n            case 'M':\n            {\n                if (input_format != input_format_t::bjdata)\n                {\n                    break;\n                }\n                std::uint64_t number{};\n                if (JSON_HEDLEY_UNLIKELY(!get_number(input_format, number)))\n                {\n                    return false;\n                }\n                if (!value_in_range_of<std::size_t>(number))\n                {\n                    return sax->parse_error(chars_read, get_token_string(), out_of_range::create(408,\n                                            exception_message(input_format, \"integer value overflow\", \"size\"), nullptr));\n                }\n                result = detail::conditional_static_cast<std::size_t>(number);\n                return true;\n            }\n\n            case '[':\n            {\n                if (input_format != input_format_t::bjdata)\n                {\n                    break;\n                }\n                if (is_ndarray) // ndarray dimensional vector can only contain integers, and can not embed another array\n                {\n                    return sax->parse_error(chars_read, get_token_string(), parse_error::create(113, chars_read, exception_message(input_format, \"ndarray dimensional vector is not allowed\", \"size\"), nullptr));\n                }\n                std::vector<size_t> dim;\n                if (JSON_HEDLEY_UNLIKELY(!get_ubjson_ndarray_size(dim)))\n                {\n                    return false;\n                }\n                if (dim.size() == 1 || (dim.size() == 2 && dim.at(0) == 1)) // return normal array size if 1D row vector\n                {\n                    result = dim.at(dim.size() - 1);\n                    return true;\n                }\n                if (!dim.empty())  // if ndarray, convert to an object in JData annotated array format\n                {\n                    for (auto i : dim) // test if any dimension in an ndarray is 0, if so, return a 1D empty container\n                    {\n                        if ( i == 0 )\n                        {\n                            result = 0;\n                            return true;\n                        }\n                    }\n\n                    string_t key = \"_ArraySize_\";\n                    if (JSON_HEDLEY_UNLIKELY(!sax->start_object(3) || !sax->key(key) || !sax->start_array(dim.size())))\n                    {\n                        return false;\n                    }\n                    result = 1;\n                    for (auto i : dim)\n                    {\n                        result *= i;\n                        if (result == 0 || result == npos) // because dim elements shall not have zeros, result = 0 means overflow happened; it also can't be npos as it is used to initialize size in get_ubjson_size_type()\n                        {\n                            return sax->parse_error(chars_read, get_token_string(), out_of_range::create(408, exception_message(input_format, \"excessive ndarray size caused overflow\", \"size\"), nullptr));\n                        }\n                        if (JSON_HEDLEY_UNLIKELY(!sax->number_unsigned(static_cast<number_unsigned_t>(i))))\n                        {\n                            return false;\n                        }\n                    }\n                    is_ndarray = true;\n                    return sax->end_array();\n                }\n                result = 0;\n                return true;\n            }\n\n            default:\n                break;\n        }\n        auto last_token = get_token_string();\n        std::string message;\n\n        if (input_format != input_format_t::bjdata)\n        {\n            message = \"expected length type specification (U, i, I, l, L) after '#'; last byte: 0x\" + last_token;\n        }\n        else\n        {\n            message = \"expected length type specification (U, i, u, I, m, l, M, L) after '#'; last byte: 0x\" + last_token;\n        }\n        return sax->parse_error(chars_read, last_token, parse_error::create(113, chars_read, exception_message(input_format, message, \"size\"), nullptr));\n    }\n\n    /*!\n    @brief determine the type and size for a container\n\n    In the optimized UBJSON format, a type and a size can be provided to allow\n    for a more compact representation.\n\n    @param[out] result  pair of the size and the type\n    @param[in] inside_ndarray  whether the parser is parsing an ND array dimensional vector\n\n    @return whether pair creation completed\n    */\n    bool get_ubjson_size_type(std::pair<std::size_t, char_int_type>& result, bool inside_ndarray = false)\n    {\n        result.first = npos; // size\n        result.second = 0; // type\n        bool is_ndarray = false;\n\n        get_ignore_noop();\n\n        if (current == '$')\n        {\n            result.second = get();  // must not ignore 'N', because 'N' maybe the type\n            if (input_format == input_format_t::bjdata\n                    && JSON_HEDLEY_UNLIKELY(std::binary_search(bjd_optimized_type_markers.begin(), bjd_optimized_type_markers.end(), result.second)))\n            {\n                auto last_token = get_token_string();\n                return sax->parse_error(chars_read, last_token, parse_error::create(112, chars_read,\n                                        exception_message(input_format, concat(\"marker 0x\", last_token, \" is not a permitted optimized array type\"), \"type\"), nullptr));\n            }\n\n            if (JSON_HEDLEY_UNLIKELY(!unexpect_eof(input_format, \"type\")))\n            {\n                return false;\n            }\n\n            get_ignore_noop();\n            if (JSON_HEDLEY_UNLIKELY(current != '#'))\n            {\n                if (JSON_HEDLEY_UNLIKELY(!unexpect_eof(input_format, \"value\")))\n                {\n                    return false;\n                }\n                auto last_token = get_token_string();\n                return sax->parse_error(chars_read, last_token, parse_error::create(112, chars_read,\n                                        exception_message(input_format, concat(\"expected '#' after type information; last byte: 0x\", last_token), \"size\"), nullptr));\n            }\n\n            const bool is_error = get_ubjson_size_value(result.first, is_ndarray);\n            if (input_format == input_format_t::bjdata && is_ndarray)\n            {\n                if (inside_ndarray)\n                {\n                    return sax->parse_error(chars_read, get_token_string(), parse_error::create(112, chars_read,\n                                            exception_message(input_format, \"ndarray can not be recursive\", \"size\"), nullptr));\n                }\n                result.second |= (1 << 8); // use bit 8 to indicate ndarray, all UBJSON and BJData markers should be ASCII letters\n            }\n            return is_error;\n        }\n\n        if (current == '#')\n        {\n            const bool is_error = get_ubjson_size_value(result.first, is_ndarray);\n            if (input_format == input_format_t::bjdata && is_ndarray)\n            {\n                return sax->parse_error(chars_read, get_token_string(), parse_error::create(112, chars_read,\n                                        exception_message(input_format, \"ndarray requires both type and size\", \"size\"), nullptr));\n            }\n            return is_error;\n        }\n\n        return true;\n    }\n\n    /*!\n    @param prefix  the previously read or set type prefix\n    @return whether value creation completed\n    */\n    bool get_ubjson_value(const char_int_type prefix)\n    {\n        switch (prefix)\n        {\n            case char_traits<char_type>::eof():  // EOF\n                return unexpect_eof(input_format, \"value\");\n\n            case 'T':  // true\n                return sax->boolean(true);\n            case 'F':  // false\n                return sax->boolean(false);\n\n            case 'Z':  // null\n                return sax->null();\n\n            case 'U':\n            {\n                std::uint8_t number{};\n                return get_number(input_format, number) && sax->number_unsigned(number);\n            }\n\n            case 'i':\n            {\n                std::int8_t number{};\n                return get_number(input_format, number) && sax->number_integer(number);\n            }\n\n            case 'I':\n            {\n                std::int16_t number{};\n                return get_number(input_format, number) && sax->number_integer(number);\n            }\n\n            case 'l':\n            {\n                std::int32_t number{};\n                return get_number(input_format, number) && sax->number_integer(number);\n            }\n\n            case 'L':\n            {\n                std::int64_t number{};\n                return get_number(input_format, number) && sax->number_integer(number);\n            }\n\n            case 'u':\n            {\n                if (input_format != input_format_t::bjdata)\n                {\n                    break;\n                }\n                std::uint16_t number{};\n                return get_number(input_format, number) && sax->number_unsigned(number);\n            }\n\n            case 'm':\n            {\n                if (input_format != input_format_t::bjdata)\n                {\n                    break;\n                }\n                std::uint32_t number{};\n                return get_number(input_format, number) && sax->number_unsigned(number);\n            }\n\n            case 'M':\n            {\n                if (input_format != input_format_t::bjdata)\n                {\n                    break;\n                }\n                std::uint64_t number{};\n                return get_number(input_format, number) && sax->number_unsigned(number);\n            }\n\n            case 'h':\n            {\n                if (input_format != input_format_t::bjdata)\n                {\n                    break;\n                }\n                const auto byte1_raw = get();\n                if (JSON_HEDLEY_UNLIKELY(!unexpect_eof(input_format, \"number\")))\n                {\n                    return false;\n                }\n                const auto byte2_raw = get();\n                if (JSON_HEDLEY_UNLIKELY(!unexpect_eof(input_format, \"number\")))\n                {\n                    return false;\n                }\n\n                const auto byte1 = static_cast<unsigned char>(byte1_raw);\n                const auto byte2 = static_cast<unsigned char>(byte2_raw);\n\n                // code from RFC 7049, Appendix D, Figure 3:\n                // As half-precision floating-point numbers were only added\n                // to IEEE 754 in 2008, today's programming platforms often\n                // still only have limited support for them. It is very\n                // easy to include at least decoding support for them even\n                // without such support. An example of a small decoder for\n                // half-precision floating-point numbers in the C language\n                // is shown in Fig. 3.\n                const auto half = static_cast<unsigned int>((byte2 << 8u) + byte1);\n                const double val = [&half]\n                {\n                    const int exp = (half >> 10u) & 0x1Fu;\n                    const unsigned int mant = half & 0x3FFu;\n                    JSON_ASSERT(0 <= exp&& exp <= 32);\n                    JSON_ASSERT(mant <= 1024);\n                    switch (exp)\n                    {\n                        case 0:\n                            return std::ldexp(mant, -24);\n                        case 31:\n                            return (mant == 0)\n                            ? std::numeric_limits<double>::infinity()\n                            : std::numeric_limits<double>::quiet_NaN();\n                        default:\n                            return std::ldexp(mant + 1024, exp - 25);\n                    }\n                }();\n                return sax->number_float((half & 0x8000u) != 0\n                                         ? static_cast<number_float_t>(-val)\n                                         : static_cast<number_float_t>(val), \"\");\n            }\n\n            case 'd':\n            {\n                float number{};\n                return get_number(input_format, number) && sax->number_float(static_cast<number_float_t>(number), \"\");\n            }\n\n            case 'D':\n            {\n                double number{};\n                return get_number(input_format, number) && sax->number_float(static_cast<number_float_t>(number), \"\");\n            }\n\n            case 'H':\n            {\n                return get_ubjson_high_precision_number();\n            }\n\n            case 'C':  // char\n            {\n                get();\n                if (JSON_HEDLEY_UNLIKELY(!unexpect_eof(input_format, \"char\")))\n                {\n                    return false;\n                }\n                if (JSON_HEDLEY_UNLIKELY(current > 127))\n                {\n                    auto last_token = get_token_string();\n                    return sax->parse_error(chars_read, last_token, parse_error::create(113, chars_read,\n                                            exception_message(input_format, concat(\"byte after 'C' must be in range 0x00..0x7F; last byte: 0x\", last_token), \"char\"), nullptr));\n                }\n                string_t s(1, static_cast<typename string_t::value_type>(current));\n                return sax->string(s);\n            }\n\n            case 'S':  // string\n            {\n                string_t s;\n                return get_ubjson_string(s) && sax->string(s);\n            }\n\n            case '[':  // array\n                return get_ubjson_array();\n\n            case '{':  // object\n                return get_ubjson_object();\n\n            default: // anything else\n                break;\n        }\n        auto last_token = get_token_string();\n        return sax->parse_error(chars_read, last_token, parse_error::create(112, chars_read, exception_message(input_format, \"invalid byte: 0x\" + last_token, \"value\"), nullptr));\n    }\n\n    /*!\n    @return whether array creation completed\n    */\n    bool get_ubjson_array()\n    {\n        std::pair<std::size_t, char_int_type> size_and_type;\n        if (JSON_HEDLEY_UNLIKELY(!get_ubjson_size_type(size_and_type)))\n        {\n            return false;\n        }\n\n        // if bit-8 of size_and_type.second is set to 1, encode bjdata ndarray as an object in JData annotated array format (https://github.com/NeuroJSON/jdata):\n        // {\"_ArrayType_\" : \"typeid\", \"_ArraySize_\" : [n1, n2, ...], \"_ArrayData_\" : [v1, v2, ...]}\n\n        if (input_format == input_format_t::bjdata && size_and_type.first != npos && (size_and_type.second & (1 << 8)) != 0)\n        {\n            size_and_type.second &= ~(static_cast<char_int_type>(1) << 8);  // use bit 8 to indicate ndarray, here we remove the bit to restore the type marker\n            auto it = std::lower_bound(bjd_types_map.begin(), bjd_types_map.end(), size_and_type.second, [](const bjd_type & p, char_int_type t)\n            {\n                return p.first < t;\n            });\n            string_t key = \"_ArrayType_\";\n            if (JSON_HEDLEY_UNLIKELY(it == bjd_types_map.end() || it->first != size_and_type.second))\n            {\n                auto last_token = get_token_string();\n                return sax->parse_error(chars_read, last_token, parse_error::create(112, chars_read,\n                                        exception_message(input_format, \"invalid byte: 0x\" + last_token, \"type\"), nullptr));\n            }\n\n            string_t type = it->second; // sax->string() takes a reference\n            if (JSON_HEDLEY_UNLIKELY(!sax->key(key) || !sax->string(type)))\n            {\n                return false;\n            }\n\n            if (size_and_type.second == 'C')\n            {\n                size_and_type.second = 'U';\n            }\n\n            key = \"_ArrayData_\";\n            if (JSON_HEDLEY_UNLIKELY(!sax->key(key) || !sax->start_array(size_and_type.first) ))\n            {\n                return false;\n            }\n\n            for (std::size_t i = 0; i < size_and_type.first; ++i)\n            {\n                if (JSON_HEDLEY_UNLIKELY(!get_ubjson_value(size_and_type.second)))\n                {\n                    return false;\n                }\n            }\n\n            return (sax->end_array() && sax->end_object());\n        }\n\n        if (size_and_type.first != npos)\n        {\n            if (JSON_HEDLEY_UNLIKELY(!sax->start_array(size_and_type.first)))\n            {\n                return false;\n            }\n\n            if (size_and_type.second != 0)\n            {\n                if (size_and_type.second != 'N')\n                {\n                    for (std::size_t i = 0; i < size_and_type.first; ++i)\n                    {\n                        if (JSON_HEDLEY_UNLIKELY(!get_ubjson_value(size_and_type.second)))\n                        {\n                            return false;\n                        }\n                    }\n                }\n            }\n            else\n            {\n                for (std::size_t i = 0; i < size_and_type.first; ++i)\n                {\n                    if (JSON_HEDLEY_UNLIKELY(!parse_ubjson_internal()))\n                    {\n                        return false;\n                    }\n                }\n            }\n        }\n        else\n        {\n            if (JSON_HEDLEY_UNLIKELY(!sax->start_array(static_cast<std::size_t>(-1))))\n            {\n                return false;\n            }\n\n            while (current != ']')\n            {\n                if (JSON_HEDLEY_UNLIKELY(!parse_ubjson_internal(false)))\n                {\n                    return false;\n                }\n                get_ignore_noop();\n            }\n        }\n\n        return sax->end_array();\n    }\n\n    /*!\n    @return whether object creation completed\n    */\n    bool get_ubjson_object()\n    {\n        std::pair<std::size_t, char_int_type> size_and_type;\n        if (JSON_HEDLEY_UNLIKELY(!get_ubjson_size_type(size_and_type)))\n        {\n            return false;\n        }\n\n        // do not accept ND-array size in objects in BJData\n        if (input_format == input_format_t::bjdata && size_and_type.first != npos && (size_and_type.second & (1 << 8)) != 0)\n        {\n            auto last_token = get_token_string();\n            return sax->parse_error(chars_read, last_token, parse_error::create(112, chars_read,\n                                    exception_message(input_format, \"BJData object does not support ND-array size in optimized format\", \"object\"), nullptr));\n        }\n\n        string_t key;\n        if (size_and_type.first != npos)\n        {\n            if (JSON_HEDLEY_UNLIKELY(!sax->start_object(size_and_type.first)))\n            {\n                return false;\n            }\n\n            if (size_and_type.second != 0)\n            {\n                for (std::size_t i = 0; i < size_and_type.first; ++i)\n                {\n                    if (JSON_HEDLEY_UNLIKELY(!get_ubjson_string(key) || !sax->key(key)))\n                    {\n                        return false;\n                    }\n                    if (JSON_HEDLEY_UNLIKELY(!get_ubjson_value(size_and_type.second)))\n                    {\n                        return false;\n                    }\n                    key.clear();\n                }\n            }\n            else\n            {\n                for (std::size_t i = 0; i < size_and_type.first; ++i)\n                {\n                    if (JSON_HEDLEY_UNLIKELY(!get_ubjson_string(key) || !sax->key(key)))\n                    {\n                        return false;\n                    }\n                    if (JSON_HEDLEY_UNLIKELY(!parse_ubjson_internal()))\n                    {\n                        return false;\n                    }\n                    key.clear();\n                }\n            }\n        }\n        else\n        {\n            if (JSON_HEDLEY_UNLIKELY(!sax->start_object(static_cast<std::size_t>(-1))))\n            {\n                return false;\n            }\n\n            while (current != '}')\n            {\n                if (JSON_HEDLEY_UNLIKELY(!get_ubjson_string(key, false) || !sax->key(key)))\n                {\n                    return false;\n                }\n                if (JSON_HEDLEY_UNLIKELY(!parse_ubjson_internal()))\n                {\n                    return false;\n                }\n                get_ignore_noop();\n                key.clear();\n            }\n        }\n\n        return sax->end_object();\n    }\n\n    // Note, no reader for UBJSON binary types is implemented because they do\n    // not exist\n\n    bool get_ubjson_high_precision_number()\n    {\n        // get size of following number string\n        std::size_t size{};\n        bool no_ndarray = true;\n        auto res = get_ubjson_size_value(size, no_ndarray);\n        if (JSON_HEDLEY_UNLIKELY(!res))\n        {\n            return res;\n        }\n\n        // get number string\n        std::vector<char> number_vector;\n        for (std::size_t i = 0; i < size; ++i)\n        {\n            get();\n            if (JSON_HEDLEY_UNLIKELY(!unexpect_eof(input_format, \"number\")))\n            {\n                return false;\n            }\n            number_vector.push_back(static_cast<char>(current));\n        }\n\n        // parse number string\n        using ia_type = decltype(detail::input_adapter(number_vector));\n        auto number_lexer = detail::lexer<BasicJsonType, ia_type>(detail::input_adapter(number_vector), false);\n        const auto result_number = number_lexer.scan();\n        const auto number_string = number_lexer.get_token_string();\n        const auto result_remainder = number_lexer.scan();\n\n        using token_type = typename detail::lexer_base<BasicJsonType>::token_type;\n\n        if (JSON_HEDLEY_UNLIKELY(result_remainder != token_type::end_of_input))\n        {\n            return sax->parse_error(chars_read, number_string, parse_error::create(115, chars_read,\n                                    exception_message(input_format, concat(\"invalid number text: \", number_lexer.get_token_string()), \"high-precision number\"), nullptr));\n        }\n\n        switch (result_number)\n        {\n            case token_type::value_integer:\n                return sax->number_integer(number_lexer.get_number_integer());\n            case token_type::value_unsigned:\n                return sax->number_unsigned(number_lexer.get_number_unsigned());\n            case token_type::value_float:\n                return sax->number_float(number_lexer.get_number_float(), std::move(number_string));\n            case token_type::uninitialized:\n            case token_type::literal_true:\n            case token_type::literal_false:\n            case token_type::literal_null:\n            case token_type::value_string:\n            case token_type::begin_array:\n            case token_type::begin_object:\n            case token_type::end_array:\n            case token_type::end_object:\n            case token_type::name_separator:\n            case token_type::value_separator:\n            case token_type::parse_error:\n            case token_type::end_of_input:\n            case token_type::literal_or_value:\n            default:\n                return sax->parse_error(chars_read, number_string, parse_error::create(115, chars_read,\n                                        exception_message(input_format, concat(\"invalid number text: \", number_lexer.get_token_string()), \"high-precision number\"), nullptr));\n        }\n    }\n\n    ///////////////////////\n    // Utility functions //\n    ///////////////////////\n\n    /*!\n    @brief get next character from the input\n\n    This function provides the interface to the used input adapter. It does\n    not throw in case the input reached EOF, but returns a -'ve valued\n    `char_traits<char_type>::eof()` in that case.\n\n    @return character read from the input\n    */\n    char_int_type get()\n    {\n        ++chars_read;\n        return current = ia.get_character();\n    }\n\n    /*!\n    @return character read from the input after ignoring all 'N' entries\n    */\n    char_int_type get_ignore_noop()\n    {\n        do\n        {\n            get();\n        }\n        while (current == 'N');\n\n        return current;\n    }\n\n    /*\n    @brief read a number from the input\n\n    @tparam NumberType the type of the number\n    @param[in] format   the current format (for diagnostics)\n    @param[out] result  number of type @a NumberType\n\n    @return whether conversion completed\n\n    @note This function needs to respect the system's endianness, because\n          bytes in CBOR, MessagePack, and UBJSON are stored in network order\n          (big endian) and therefore need reordering on little endian systems.\n          On the other hand, BSON and BJData use little endian and should reorder\n          on big endian systems.\n    */\n    template<typename NumberType, bool InputIsLittleEndian = false>\n    bool get_number(const input_format_t format, NumberType& result)\n    {\n        // step 1: read input into array with system's byte order\n        std::array<std::uint8_t, sizeof(NumberType)> vec{};\n        for (std::size_t i = 0; i < sizeof(NumberType); ++i)\n        {\n            get();\n            if (JSON_HEDLEY_UNLIKELY(!unexpect_eof(format, \"number\")))\n            {\n                return false;\n            }\n\n            // reverse byte order prior to conversion if necessary\n            if (is_little_endian != (InputIsLittleEndian || format == input_format_t::bjdata))\n            {\n                vec[sizeof(NumberType) - i - 1] = static_cast<std::uint8_t>(current);\n            }\n            else\n            {\n                vec[i] = static_cast<std::uint8_t>(current); // LCOV_EXCL_LINE\n            }\n        }\n\n        // step 2: convert array into number of type T and return\n        std::memcpy(&result, vec.data(), sizeof(NumberType));\n        return true;\n    }\n\n    /*!\n    @brief create a string by reading characters from the input\n\n    @tparam NumberType the type of the number\n    @param[in] format the current format (for diagnostics)\n    @param[in] len number of characters to read\n    @param[out] result string created by reading @a len bytes\n\n    @return whether string creation completed\n\n    @note We can not reserve @a len bytes for the result, because @a len\n          may be too large. Usually, @ref unexpect_eof() detects the end of\n          the input before we run out of string memory.\n    */\n    template<typename NumberType>\n    bool get_string(const input_format_t format,\n                    const NumberType len,\n                    string_t& result)\n    {\n        bool success = true;\n        for (NumberType i = 0; i < len; i++)\n        {\n            get();\n            if (JSON_HEDLEY_UNLIKELY(!unexpect_eof(format, \"string\")))\n            {\n                success = false;\n                break;\n            }\n            result.push_back(static_cast<typename string_t::value_type>(current));\n        }\n        return success;\n    }\n\n    /*!\n    @brief create a byte array by reading bytes from the input\n\n    @tparam NumberType the type of the number\n    @param[in] format the current format (for diagnostics)\n    @param[in] len number of bytes to read\n    @param[out] result byte array created by reading @a len bytes\n\n    @return whether byte array creation completed\n\n    @note We can not reserve @a len bytes for the result, because @a len\n          may be too large. Usually, @ref unexpect_eof() detects the end of\n          the input before we run out of memory.\n    */\n    template<typename NumberType>\n    bool get_binary(const input_format_t format,\n                    const NumberType len,\n                    binary_t& result)\n    {\n        bool success = true;\n        for (NumberType i = 0; i < len; i++)\n        {\n            get();\n            if (JSON_HEDLEY_UNLIKELY(!unexpect_eof(format, \"binary\")))\n            {\n                success = false;\n                break;\n            }\n            result.push_back(static_cast<std::uint8_t>(current));\n        }\n        return success;\n    }\n\n    /*!\n    @param[in] format   the current format (for diagnostics)\n    @param[in] context  further context information (for diagnostics)\n    @return whether the last read character is not EOF\n    */\n    JSON_HEDLEY_NON_NULL(3)\n    bool unexpect_eof(const input_format_t format, const char* context) const\n    {\n        if (JSON_HEDLEY_UNLIKELY(current == char_traits<char_type>::eof()))\n        {\n            return sax->parse_error(chars_read, \"<end of file>\",\n                                    parse_error::create(110, chars_read, exception_message(format, \"unexpected end of input\", context), nullptr));\n        }\n        return true;\n    }\n\n    /*!\n    @return a string representation of the last read byte\n    */\n    std::string get_token_string() const\n    {\n        std::array<char, 3> cr{{}};\n        static_cast<void>((std::snprintf)(cr.data(), cr.size(), \"%.2hhX\", static_cast<unsigned char>(current))); // NOLINT(cppcoreguidelines-pro-type-vararg,hicpp-vararg)\n        return std::string{cr.data()};\n    }\n\n    /*!\n    @param[in] format   the current format\n    @param[in] detail   a detailed error message\n    @param[in] context  further context information\n    @return a message string to use in the parse_error exceptions\n    */\n    std::string exception_message(const input_format_t format,\n                                  const std::string& detail,\n                                  const std::string& context) const\n    {\n        std::string error_msg = \"syntax error while parsing \";\n\n        switch (format)\n        {\n            case input_format_t::cbor:\n                error_msg += \"CBOR\";\n                break;\n\n            case input_format_t::msgpack:\n                error_msg += \"MessagePack\";\n                break;\n\n            case input_format_t::ubjson:\n                error_msg += \"UBJSON\";\n                break;\n\n            case input_format_t::bson:\n                error_msg += \"BSON\";\n                break;\n\n            case input_format_t::bjdata:\n                error_msg += \"BJData\";\n                break;\n\n            case input_format_t::json: // LCOV_EXCL_LINE\n            default:            // LCOV_EXCL_LINE\n                JSON_ASSERT(false); // NOLINT(cert-dcl03-c,hicpp-static-assert,misc-static-assert) LCOV_EXCL_LINE\n        }\n\n        return concat(error_msg, ' ', context, \": \", detail);\n    }\n\n  private:\n    static JSON_INLINE_VARIABLE constexpr std::size_t npos = static_cast<std::size_t>(-1);\n\n    /// input adapter\n    InputAdapterType ia;\n\n    /// the current character\n    char_int_type current = char_traits<char_type>::eof();\n\n    /// the number of characters read\n    std::size_t chars_read = 0;\n\n    /// whether we can assume little endianness\n    const bool is_little_endian = little_endianness();\n\n    /// input format\n    const input_format_t input_format = input_format_t::json;\n\n    /// the SAX parser\n    json_sax_t* sax = nullptr;\n\n    // excluded markers in bjdata optimized type\n#define JSON_BINARY_READER_MAKE_BJD_OPTIMIZED_TYPE_MARKERS_ \\\n    make_array<char_int_type>('F', 'H', 'N', 'S', 'T', 'Z', '[', '{')\n\n#define JSON_BINARY_READER_MAKE_BJD_TYPES_MAP_ \\\n    make_array<bjd_type>(                      \\\n    bjd_type{'C', \"char\"},                     \\\n    bjd_type{'D', \"double\"},                   \\\n    bjd_type{'I', \"int16\"},                    \\\n    bjd_type{'L', \"int64\"},                    \\\n    bjd_type{'M', \"uint64\"},                   \\\n    bjd_type{'U', \"uint8\"},                    \\\n    bjd_type{'d', \"single\"},                   \\\n    bjd_type{'i', \"int8\"},                     \\\n    bjd_type{'l', \"int32\"},                    \\\n    bjd_type{'m', \"uint32\"},                   \\\n    bjd_type{'u', \"uint16\"})\n\n  JSON_PRIVATE_UNLESS_TESTED:\n    // lookup tables\n    // NOLINTNEXTLINE(cppcoreguidelines-non-private-member-variables-in-classes)\n    const decltype(JSON_BINARY_READER_MAKE_BJD_OPTIMIZED_TYPE_MARKERS_) bjd_optimized_type_markers =\n        JSON_BINARY_READER_MAKE_BJD_OPTIMIZED_TYPE_MARKERS_;\n\n    using bjd_type = std::pair<char_int_type, string_t>;\n    // NOLINTNEXTLINE(cppcoreguidelines-non-private-member-variables-in-classes)\n    const decltype(JSON_BINARY_READER_MAKE_BJD_TYPES_MAP_) bjd_types_map =\n        JSON_BINARY_READER_MAKE_BJD_TYPES_MAP_;\n\n#undef JSON_BINARY_READER_MAKE_BJD_OPTIMIZED_TYPE_MARKERS_\n#undef JSON_BINARY_READER_MAKE_BJD_TYPES_MAP_\n};\n\n#ifndef JSON_HAS_CPP_17\n    template<typename BasicJsonType, typename InputAdapterType, typename SAX>\n    constexpr std::size_t binary_reader<BasicJsonType, InputAdapterType, SAX>::npos;\n#endif\n\n}  // namespace detail\nNLOHMANN_JSON_NAMESPACE_END\n\n// #include <nlohmann/detail/input/input_adapters.hpp>\n\n// #include <nlohmann/detail/input/lexer.hpp>\n\n// #include <nlohmann/detail/input/parser.hpp>\n//     __ _____ _____ _____\n//  __|  |   __|     |   | |  JSON for Modern C++\n// |  |  |__   |  |  | | | |  version 3.11.3\n// |_____|_____|_____|_|___|  https://github.com/nlohmann/json\n//\n// SPDX-FileCopyrightText: 2013-2023 Niels Lohmann <https://nlohmann.me>\n// SPDX-License-Identifier: MIT\n\n\n\n#include <cmath> // isfinite\n#include <cstdint> // uint8_t\n#include <functional> // function\n#include <string> // string\n#include <utility> // move\n#include <vector> // vector\n\n// #include <nlohmann/detail/exceptions.hpp>\n\n// #include <nlohmann/detail/input/input_adapters.hpp>\n\n// #include <nlohmann/detail/input/json_sax.hpp>\n\n// #include <nlohmann/detail/input/lexer.hpp>\n\n// #include <nlohmann/detail/macro_scope.hpp>\n\n// #include <nlohmann/detail/meta/is_sax.hpp>\n\n// #include <nlohmann/detail/string_concat.hpp>\n\n// #include <nlohmann/detail/value_t.hpp>\n\n\nNLOHMANN_JSON_NAMESPACE_BEGIN\nnamespace detail\n{\n////////////\n// parser //\n////////////\n\nenum class parse_event_t : std::uint8_t\n{\n    /// the parser read `{` and started to process a JSON object\n    object_start,\n    /// the parser read `}` and finished processing a JSON object\n    object_end,\n    /// the parser read `[` and started to process a JSON array\n    array_start,\n    /// the parser read `]` and finished processing a JSON array\n    array_end,\n    /// the parser read a key of a value in an object\n    key,\n    /// the parser finished reading a JSON value\n    value\n};\n\ntemplate<typename BasicJsonType>\nusing parser_callback_t =\n    std::function<bool(int /*depth*/, parse_event_t /*event*/, BasicJsonType& /*parsed*/)>;\n\n/*!\n@brief syntax analysis\n\nThis class implements a recursive descent parser.\n*/\ntemplate<typename BasicJsonType, typename InputAdapterType>\nclass parser\n{\n    using number_integer_t = typename BasicJsonType::number_integer_t;\n    using number_unsigned_t = typename BasicJsonType::number_unsigned_t;\n    using number_float_t = typename BasicJsonType::number_float_t;\n    using string_t = typename BasicJsonType::string_t;\n    using lexer_t = lexer<BasicJsonType, InputAdapterType>;\n    using token_type = typename lexer_t::token_type;\n\n  public:\n    /// a parser reading from an input adapter\n    explicit parser(InputAdapterType&& adapter,\n                    const parser_callback_t<BasicJsonType> cb = nullptr,\n                    const bool allow_exceptions_ = true,\n                    const bool skip_comments = false)\n        : callback(cb)\n        , m_lexer(std::move(adapter), skip_comments)\n        , allow_exceptions(allow_exceptions_)\n    {\n        // read first token\n        get_token();\n    }\n\n    /*!\n    @brief public parser interface\n\n    @param[in] strict      whether to expect the last token to be EOF\n    @param[in,out] result  parsed JSON value\n\n    @throw parse_error.101 in case of an unexpected token\n    @throw parse_error.102 if to_unicode fails or surrogate error\n    @throw parse_error.103 if to_unicode fails\n    */\n    void parse(const bool strict, BasicJsonType& result)\n    {\n        if (callback)\n        {\n            json_sax_dom_callback_parser<BasicJsonType> sdp(result, callback, allow_exceptions);\n            sax_parse_internal(&sdp);\n\n            // in strict mode, input must be completely read\n            if (strict && (get_token() != token_type::end_of_input))\n            {\n                sdp.parse_error(m_lexer.get_position(),\n                                m_lexer.get_token_string(),\n                                parse_error::create(101, m_lexer.get_position(),\n                                                    exception_message(token_type::end_of_input, \"value\"), nullptr));\n            }\n\n            // in case of an error, return discarded value\n            if (sdp.is_errored())\n            {\n                result = value_t::discarded;\n                return;\n            }\n\n            // set top-level value to null if it was discarded by the callback\n            // function\n            if (result.is_discarded())\n            {\n                result = nullptr;\n            }\n        }\n        else\n        {\n            json_sax_dom_parser<BasicJsonType> sdp(result, allow_exceptions);\n            sax_parse_internal(&sdp);\n\n            // in strict mode, input must be completely read\n            if (strict && (get_token() != token_type::end_of_input))\n            {\n                sdp.parse_error(m_lexer.get_position(),\n                                m_lexer.get_token_string(),\n                                parse_error::create(101, m_lexer.get_position(), exception_message(token_type::end_of_input, \"value\"), nullptr));\n            }\n\n            // in case of an error, return discarded value\n            if (sdp.is_errored())\n            {\n                result = value_t::discarded;\n                return;\n            }\n        }\n\n        result.assert_invariant();\n    }\n\n    /*!\n    @brief public accept interface\n\n    @param[in] strict  whether to expect the last token to be EOF\n    @return whether the input is a proper JSON text\n    */\n    bool accept(const bool strict = true)\n    {\n        json_sax_acceptor<BasicJsonType> sax_acceptor;\n        return sax_parse(&sax_acceptor, strict);\n    }\n\n    template<typename SAX>\n    JSON_HEDLEY_NON_NULL(2)\n    bool sax_parse(SAX* sax, const bool strict = true)\n    {\n        (void)detail::is_sax_static_asserts<SAX, BasicJsonType> {};\n        const bool result = sax_parse_internal(sax);\n\n        // strict mode: next byte must be EOF\n        if (result && strict && (get_token() != token_type::end_of_input))\n        {\n            return sax->parse_error(m_lexer.get_position(),\n                                    m_lexer.get_token_string(),\n                                    parse_error::create(101, m_lexer.get_position(), exception_message(token_type::end_of_input, \"value\"), nullptr));\n        }\n\n        return result;\n    }\n\n  private:\n    template<typename SAX>\n    JSON_HEDLEY_NON_NULL(2)\n    bool sax_parse_internal(SAX* sax)\n    {\n        // stack to remember the hierarchy of structured values we are parsing\n        // true = array; false = object\n        std::vector<bool> states;\n        // value to avoid a goto (see comment where set to true)\n        bool skip_to_state_evaluation = false;\n\n        while (true)\n        {\n            if (!skip_to_state_evaluation)\n            {\n                // invariant: get_token() was called before each iteration\n                switch (last_token)\n                {\n                    case token_type::begin_object:\n                    {\n                        if (JSON_HEDLEY_UNLIKELY(!sax->start_object(static_cast<std::size_t>(-1))))\n                        {\n                            return false;\n                        }\n\n                        // closing } -> we are done\n                        if (get_token() == token_type::end_object)\n                        {\n                            if (JSON_HEDLEY_UNLIKELY(!sax->end_object()))\n                            {\n                                return false;\n                            }\n                            break;\n                        }\n\n                        // parse key\n                        if (JSON_HEDLEY_UNLIKELY(last_token != token_type::value_string))\n                        {\n                            return sax->parse_error(m_lexer.get_position(),\n                                                    m_lexer.get_token_string(),\n                                                    parse_error::create(101, m_lexer.get_position(), exception_message(token_type::value_string, \"object key\"), nullptr));\n                        }\n                        if (JSON_HEDLEY_UNLIKELY(!sax->key(m_lexer.get_string())))\n                        {\n                            return false;\n                        }\n\n                        // parse separator (:)\n                        if (JSON_HEDLEY_UNLIKELY(get_token() != token_type::name_separator))\n                        {\n                            return sax->parse_error(m_lexer.get_position(),\n                                                    m_lexer.get_token_string(),\n                                                    parse_error::create(101, m_lexer.get_position(), exception_message(token_type::name_separator, \"object separator\"), nullptr));\n                        }\n\n                        // remember we are now inside an object\n                        states.push_back(false);\n\n                        // parse values\n                        get_token();\n                        continue;\n                    }\n\n                    case token_type::begin_array:\n                    {\n                        if (JSON_HEDLEY_UNLIKELY(!sax->start_array(static_cast<std::size_t>(-1))))\n                        {\n                            return false;\n                        }\n\n                        // closing ] -> we are done\n                        if (get_token() == token_type::end_array)\n                        {\n                            if (JSON_HEDLEY_UNLIKELY(!sax->end_array()))\n                            {\n                                return false;\n                            }\n                            break;\n                        }\n\n                        // remember we are now inside an array\n                        states.push_back(true);\n\n                        // parse values (no need to call get_token)\n                        continue;\n                    }\n\n                    case token_type::value_float:\n                    {\n                        const auto res = m_lexer.get_number_float();\n\n                        if (JSON_HEDLEY_UNLIKELY(!std::isfinite(res)))\n                        {\n                            return sax->parse_error(m_lexer.get_position(),\n                                                    m_lexer.get_token_string(),\n                                                    out_of_range::create(406, concat(\"number overflow parsing '\", m_lexer.get_token_string(), '\\''), nullptr));\n                        }\n\n                        if (JSON_HEDLEY_UNLIKELY(!sax->number_float(res, m_lexer.get_string())))\n                        {\n                            return false;\n                        }\n\n                        break;\n                    }\n\n                    case token_type::literal_false:\n                    {\n                        if (JSON_HEDLEY_UNLIKELY(!sax->boolean(false)))\n                        {\n                            return false;\n                        }\n                        break;\n                    }\n\n                    case token_type::literal_null:\n                    {\n                        if (JSON_HEDLEY_UNLIKELY(!sax->null()))\n                        {\n                            return false;\n                        }\n                        break;\n                    }\n\n                    case token_type::literal_true:\n                    {\n                        if (JSON_HEDLEY_UNLIKELY(!sax->boolean(true)))\n                        {\n                            return false;\n                        }\n                        break;\n                    }\n\n                    case token_type::value_integer:\n                    {\n                        if (JSON_HEDLEY_UNLIKELY(!sax->number_integer(m_lexer.get_number_integer())))\n                        {\n                            return false;\n                        }\n                        break;\n                    }\n\n                    case token_type::value_string:\n                    {\n                        if (JSON_HEDLEY_UNLIKELY(!sax->string(m_lexer.get_string())))\n                        {\n                            return false;\n                        }\n                        break;\n                    }\n\n                    case token_type::value_unsigned:\n                    {\n                        if (JSON_HEDLEY_UNLIKELY(!sax->number_unsigned(m_lexer.get_number_unsigned())))\n                        {\n                            return false;\n                        }\n                        break;\n                    }\n\n                    case token_type::parse_error:\n                    {\n                        // using \"uninitialized\" to avoid \"expected\" message\n                        return sax->parse_error(m_lexer.get_position(),\n                                                m_lexer.get_token_string(),\n                                                parse_error::create(101, m_lexer.get_position(), exception_message(token_type::uninitialized, \"value\"), nullptr));\n                    }\n                    case token_type::end_of_input:\n                    {\n                        if (JSON_HEDLEY_UNLIKELY(m_lexer.get_position().chars_read_total == 1))\n                        {\n                            return sax->parse_error(m_lexer.get_position(),\n                                                    m_lexer.get_token_string(),\n                                                    parse_error::create(101, m_lexer.get_position(),\n                                                            \"attempting to parse an empty input; check that your input string or stream contains the expected JSON\", nullptr));\n                        }\n\n                        return sax->parse_error(m_lexer.get_position(),\n                                                m_lexer.get_token_string(),\n                                                parse_error::create(101, m_lexer.get_position(), exception_message(token_type::literal_or_value, \"value\"), nullptr));\n                    }\n                    case token_type::uninitialized:\n                    case token_type::end_array:\n                    case token_type::end_object:\n                    case token_type::name_separator:\n                    case token_type::value_separator:\n                    case token_type::literal_or_value:\n                    default: // the last token was unexpected\n                    {\n                        return sax->parse_error(m_lexer.get_position(),\n                                                m_lexer.get_token_string(),\n                                                parse_error::create(101, m_lexer.get_position(), exception_message(token_type::literal_or_value, \"value\"), nullptr));\n                    }\n                }\n            }\n            else\n            {\n                skip_to_state_evaluation = false;\n            }\n\n            // we reached this line after we successfully parsed a value\n            if (states.empty())\n            {\n                // empty stack: we reached the end of the hierarchy: done\n                return true;\n            }\n\n            if (states.back())  // array\n            {\n                // comma -> next value\n                if (get_token() == token_type::value_separator)\n                {\n                    // parse a new value\n                    get_token();\n                    continue;\n                }\n\n                // closing ]\n                if (JSON_HEDLEY_LIKELY(last_token == token_type::end_array))\n                {\n                    if (JSON_HEDLEY_UNLIKELY(!sax->end_array()))\n                    {\n                        return false;\n                    }\n\n                    // We are done with this array. Before we can parse a\n                    // new value, we need to evaluate the new state first.\n                    // By setting skip_to_state_evaluation to false, we\n                    // are effectively jumping to the beginning of this if.\n                    JSON_ASSERT(!states.empty());\n                    states.pop_back();\n                    skip_to_state_evaluation = true;\n                    continue;\n                }\n\n                return sax->parse_error(m_lexer.get_position(),\n                                        m_lexer.get_token_string(),\n                                        parse_error::create(101, m_lexer.get_position(), exception_message(token_type::end_array, \"array\"), nullptr));\n            }\n\n            // states.back() is false -> object\n\n            // comma -> next value\n            if (get_token() == token_type::value_separator)\n            {\n                // parse key\n                if (JSON_HEDLEY_UNLIKELY(get_token() != token_type::value_string))\n                {\n                    return sax->parse_error(m_lexer.get_position(),\n                                            m_lexer.get_token_string(),\n                                            parse_error::create(101, m_lexer.get_position(), exception_message(token_type::value_string, \"object key\"), nullptr));\n                }\n\n                if (JSON_HEDLEY_UNLIKELY(!sax->key(m_lexer.get_string())))\n                {\n                    return false;\n                }\n\n                // parse separator (:)\n                if (JSON_HEDLEY_UNLIKELY(get_token() != token_type::name_separator))\n                {\n                    return sax->parse_error(m_lexer.get_position(),\n                                            m_lexer.get_token_string(),\n                                            parse_error::create(101, m_lexer.get_position(), exception_message(token_type::name_separator, \"object separator\"), nullptr));\n                }\n\n                // parse values\n                get_token();\n                continue;\n            }\n\n            // closing }\n            if (JSON_HEDLEY_LIKELY(last_token == token_type::end_object))\n            {\n                if (JSON_HEDLEY_UNLIKELY(!sax->end_object()))\n                {\n                    return false;\n                }\n\n                // We are done with this object. Before we can parse a\n                // new value, we need to evaluate the new state first.\n                // By setting skip_to_state_evaluation to false, we\n                // are effectively jumping to the beginning of this if.\n                JSON_ASSERT(!states.empty());\n                states.pop_back();\n                skip_to_state_evaluation = true;\n                continue;\n            }\n\n            return sax->parse_error(m_lexer.get_position(),\n                                    m_lexer.get_token_string(),\n                                    parse_error::create(101, m_lexer.get_position(), exception_message(token_type::end_object, \"object\"), nullptr));\n        }\n    }\n\n    /// get next token from lexer\n    token_type get_token()\n    {\n        return last_token = m_lexer.scan();\n    }\n\n    std::string exception_message(const token_type expected, const std::string& context)\n    {\n        std::string error_msg = \"syntax error \";\n\n        if (!context.empty())\n        {\n            error_msg += concat(\"while parsing \", context, ' ');\n        }\n\n        error_msg += \"- \";\n\n        if (last_token == token_type::parse_error)\n        {\n            error_msg += concat(m_lexer.get_error_message(), \"; last read: '\",\n                                m_lexer.get_token_string(), '\\'');\n        }\n        else\n        {\n            error_msg += concat(\"unexpected \", lexer_t::token_type_name(last_token));\n        }\n\n        if (expected != token_type::uninitialized)\n        {\n            error_msg += concat(\"; expected \", lexer_t::token_type_name(expected));\n        }\n\n        return error_msg;\n    }\n\n  private:\n    /// callback function\n    const parser_callback_t<BasicJsonType> callback = nullptr;\n    /// the type of the last read token\n    token_type last_token = token_type::uninitialized;\n    /// the lexer\n    lexer_t m_lexer;\n    /// whether to throw exceptions in case of errors\n    const bool allow_exceptions = true;\n};\n\n}  // namespace detail\nNLOHMANN_JSON_NAMESPACE_END\n\n// #include <nlohmann/detail/iterators/internal_iterator.hpp>\n//     __ _____ _____ _____\n//  __|  |   __|     |   | |  JSON for Modern C++\n// |  |  |__   |  |  | | | |  version 3.11.3\n// |_____|_____|_____|_|___|  https://github.com/nlohmann/json\n//\n// SPDX-FileCopyrightText: 2013-2023 Niels Lohmann <https://nlohmann.me>\n// SPDX-License-Identifier: MIT\n\n\n\n// #include <nlohmann/detail/abi_macros.hpp>\n\n// #include <nlohmann/detail/iterators/primitive_iterator.hpp>\n//     __ _____ _____ _____\n//  __|  |   __|     |   | |  JSON for Modern C++\n// |  |  |__   |  |  | | | |  version 3.11.3\n// |_____|_____|_____|_|___|  https://github.com/nlohmann/json\n//\n// SPDX-FileCopyrightText: 2013-2023 Niels Lohmann <https://nlohmann.me>\n// SPDX-License-Identifier: MIT\n\n\n\n#include <cstddef> // ptrdiff_t\n#include <limits>  // numeric_limits\n\n// #include <nlohmann/detail/macro_scope.hpp>\n\n\nNLOHMANN_JSON_NAMESPACE_BEGIN\nnamespace detail\n{\n\n/*\n@brief an iterator for primitive JSON types\n\nThis class models an iterator for primitive JSON types (boolean, number,\nstring). It's only purpose is to allow the iterator/const_iterator classes\nto \"iterate\" over primitive values. Internally, the iterator is modeled by\na `difference_type` variable. Value begin_value (`0`) models the begin,\nend_value (`1`) models past the end.\n*/\nclass primitive_iterator_t\n{\n  private:\n    using difference_type = std::ptrdiff_t;\n    static constexpr difference_type begin_value = 0;\n    static constexpr difference_type end_value = begin_value + 1;\n\n  JSON_PRIVATE_UNLESS_TESTED:\n    /// iterator as signed integer type\n    difference_type m_it = (std::numeric_limits<std::ptrdiff_t>::min)();\n\n  public:\n    constexpr difference_type get_value() const noexcept\n    {\n        return m_it;\n    }\n\n    /// set iterator to a defined beginning\n    void set_begin() noexcept\n    {\n        m_it = begin_value;\n    }\n\n    /// set iterator to a defined past the end\n    void set_end() noexcept\n    {\n        m_it = end_value;\n    }\n\n    /// return whether the iterator can be dereferenced\n    constexpr bool is_begin() const noexcept\n    {\n        return m_it == begin_value;\n    }\n\n    /// return whether the iterator is at end\n    constexpr bool is_end() const noexcept\n    {\n        return m_it == end_value;\n    }\n\n    friend constexpr bool operator==(primitive_iterator_t lhs, primitive_iterator_t rhs) noexcept\n    {\n        return lhs.m_it == rhs.m_it;\n    }\n\n    friend constexpr bool operator<(primitive_iterator_t lhs, primitive_iterator_t rhs) noexcept\n    {\n        return lhs.m_it < rhs.m_it;\n    }\n\n    primitive_iterator_t operator+(difference_type n) noexcept\n    {\n        auto result = *this;\n        result += n;\n        return result;\n    }\n\n    friend constexpr difference_type operator-(primitive_iterator_t lhs, primitive_iterator_t rhs) noexcept\n    {\n        return lhs.m_it - rhs.m_it;\n    }\n\n    primitive_iterator_t& operator++() noexcept\n    {\n        ++m_it;\n        return *this;\n    }\n\n    primitive_iterator_t operator++(int)& noexcept // NOLINT(cert-dcl21-cpp)\n    {\n        auto result = *this;\n        ++m_it;\n        return result;\n    }\n\n    primitive_iterator_t& operator--() noexcept\n    {\n        --m_it;\n        return *this;\n    }\n\n    primitive_iterator_t operator--(int)& noexcept // NOLINT(cert-dcl21-cpp)\n    {\n        auto result = *this;\n        --m_it;\n        return result;\n    }\n\n    primitive_iterator_t& operator+=(difference_type n) noexcept\n    {\n        m_it += n;\n        return *this;\n    }\n\n    primitive_iterator_t& operator-=(difference_type n) noexcept\n    {\n        m_it -= n;\n        return *this;\n    }\n};\n\n}  // namespace detail\nNLOHMANN_JSON_NAMESPACE_END\n\n\nNLOHMANN_JSON_NAMESPACE_BEGIN\nnamespace detail\n{\n\n/*!\n@brief an iterator value\n\n@note This structure could easily be a union, but MSVC currently does not allow\nunions members with complex constructors, see https://github.com/nlohmann/json/pull/105.\n*/\ntemplate<typename BasicJsonType> struct internal_iterator\n{\n    /// iterator for JSON objects\n    typename BasicJsonType::object_t::iterator object_iterator {};\n    /// iterator for JSON arrays\n    typename BasicJsonType::array_t::iterator array_iterator {};\n    /// generic iterator for all other types\n    primitive_iterator_t primitive_iterator {};\n};\n\n}  // namespace detail\nNLOHMANN_JSON_NAMESPACE_END\n\n// #include <nlohmann/detail/iterators/iter_impl.hpp>\n//     __ _____ _____ _____\n//  __|  |   __|     |   | |  JSON for Modern C++\n// |  |  |__   |  |  | | | |  version 3.11.3\n// |_____|_____|_____|_|___|  https://github.com/nlohmann/json\n//\n// SPDX-FileCopyrightText: 2013-2023 Niels Lohmann <https://nlohmann.me>\n// SPDX-License-Identifier: MIT\n\n\n\n#include <iterator> // iterator, random_access_iterator_tag, bidirectional_iterator_tag, advance, next\n#include <type_traits> // conditional, is_const, remove_const\n\n// #include <nlohmann/detail/exceptions.hpp>\n\n// #include <nlohmann/detail/iterators/internal_iterator.hpp>\n\n// #include <nlohmann/detail/iterators/primitive_iterator.hpp>\n\n// #include <nlohmann/detail/macro_scope.hpp>\n\n// #include <nlohmann/detail/meta/cpp_future.hpp>\n\n// #include <nlohmann/detail/meta/type_traits.hpp>\n\n// #include <nlohmann/detail/value_t.hpp>\n\n\nNLOHMANN_JSON_NAMESPACE_BEGIN\nnamespace detail\n{\n\n// forward declare, to be able to friend it later on\ntemplate<typename IteratorType> class iteration_proxy;\ntemplate<typename IteratorType> class iteration_proxy_value;\n\n/*!\n@brief a template for a bidirectional iterator for the @ref basic_json class\nThis class implements a both iterators (iterator and const_iterator) for the\n@ref basic_json class.\n@note An iterator is called *initialized* when a pointer to a JSON value has\n      been set (e.g., by a constructor or a copy assignment). If the iterator is\n      default-constructed, it is *uninitialized* and most methods are undefined.\n      **The library uses assertions to detect calls on uninitialized iterators.**\n@requirement The class satisfies the following concept requirements:\n-\n[BidirectionalIterator](https://en.cppreference.com/w/cpp/named_req/BidirectionalIterator):\n  The iterator that can be moved can be moved in both directions (i.e.\n  incremented and decremented).\n@since version 1.0.0, simplified in version 2.0.9, change to bidirectional\n       iterators in version 3.0.0 (see https://github.com/nlohmann/json/issues/593)\n*/\ntemplate<typename BasicJsonType>\nclass iter_impl // NOLINT(cppcoreguidelines-special-member-functions,hicpp-special-member-functions)\n{\n    /// the iterator with BasicJsonType of different const-ness\n    using other_iter_impl = iter_impl<typename std::conditional<std::is_const<BasicJsonType>::value, typename std::remove_const<BasicJsonType>::type, const BasicJsonType>::type>;\n    /// allow basic_json to access private members\n    friend other_iter_impl;\n    friend BasicJsonType;\n    friend iteration_proxy<iter_impl>;\n    friend iteration_proxy_value<iter_impl>;\n\n    using object_t = typename BasicJsonType::object_t;\n    using array_t = typename BasicJsonType::array_t;\n    // make sure BasicJsonType is basic_json or const basic_json\n    static_assert(is_basic_json<typename std::remove_const<BasicJsonType>::type>::value,\n                  \"iter_impl only accepts (const) basic_json\");\n    // superficial check for the LegacyBidirectionalIterator named requirement\n    static_assert(std::is_base_of<std::bidirectional_iterator_tag, std::bidirectional_iterator_tag>::value\n                  &&  std::is_base_of<std::bidirectional_iterator_tag, typename std::iterator_traits<typename array_t::iterator>::iterator_category>::value,\n                  \"basic_json iterator assumes array and object type iterators satisfy the LegacyBidirectionalIterator named requirement.\");\n\n  public:\n    /// The std::iterator class template (used as a base class to provide typedefs) is deprecated in C++17.\n    /// The C++ Standard has never required user-defined iterators to derive from std::iterator.\n    /// A user-defined iterator should provide publicly accessible typedefs named\n    /// iterator_category, value_type, difference_type, pointer, and reference.\n    /// Note that value_type is required to be non-const, even for constant iterators.\n    using iterator_category = std::bidirectional_iterator_tag;\n\n    /// the type of the values when the iterator is dereferenced\n    using value_type = typename BasicJsonType::value_type;\n    /// a type to represent differences between iterators\n    using difference_type = typename BasicJsonType::difference_type;\n    /// defines a pointer to the type iterated over (value_type)\n    using pointer = typename std::conditional<std::is_const<BasicJsonType>::value,\n          typename BasicJsonType::const_pointer,\n          typename BasicJsonType::pointer>::type;\n    /// defines a reference to the type iterated over (value_type)\n    using reference =\n        typename std::conditional<std::is_const<BasicJsonType>::value,\n        typename BasicJsonType::const_reference,\n        typename BasicJsonType::reference>::type;\n\n    iter_impl() = default;\n    ~iter_impl() = default;\n    iter_impl(iter_impl&&) noexcept = default;\n    iter_impl& operator=(iter_impl&&) noexcept = default;\n\n    /*!\n    @brief constructor for a given JSON instance\n    @param[in] object  pointer to a JSON object for this iterator\n    @pre object != nullptr\n    @post The iterator is initialized; i.e. `m_object != nullptr`.\n    */\n    explicit iter_impl(pointer object) noexcept : m_object(object)\n    {\n        JSON_ASSERT(m_object != nullptr);\n\n        switch (m_object->m_data.m_type)\n        {\n            case value_t::object:\n            {\n                m_it.object_iterator = typename object_t::iterator();\n                break;\n            }\n\n            case value_t::array:\n            {\n                m_it.array_iterator = typename array_t::iterator();\n                break;\n            }\n\n            case value_t::null:\n            case value_t::string:\n            case value_t::boolean:\n            case value_t::number_integer:\n            case value_t::number_unsigned:\n            case value_t::number_float:\n            case value_t::binary:\n            case value_t::discarded:\n            default:\n            {\n                m_it.primitive_iterator = primitive_iterator_t();\n                break;\n            }\n        }\n    }\n\n    /*!\n    @note The conventional copy constructor and copy assignment are implicitly\n          defined. Combined with the following converting constructor and\n          assignment, they support: (1) copy from iterator to iterator, (2)\n          copy from const iterator to const iterator, and (3) conversion from\n          iterator to const iterator. However conversion from const iterator\n          to iterator is not defined.\n    */\n\n    /*!\n    @brief const copy constructor\n    @param[in] other const iterator to copy from\n    @note This copy constructor had to be defined explicitly to circumvent a bug\n          occurring on msvc v19.0 compiler (VS 2015) debug build. For more\n          information refer to: https://github.com/nlohmann/json/issues/1608\n    */\n    iter_impl(const iter_impl<const BasicJsonType>& other) noexcept\n        : m_object(other.m_object), m_it(other.m_it)\n    {}\n\n    /*!\n    @brief converting assignment\n    @param[in] other const iterator to copy from\n    @return const/non-const iterator\n    @note It is not checked whether @a other is initialized.\n    */\n    iter_impl& operator=(const iter_impl<const BasicJsonType>& other) noexcept\n    {\n        if (&other != this)\n        {\n            m_object = other.m_object;\n            m_it = other.m_it;\n        }\n        return *this;\n    }\n\n    /*!\n    @brief converting constructor\n    @param[in] other  non-const iterator to copy from\n    @note It is not checked whether @a other is initialized.\n    */\n    iter_impl(const iter_impl<typename std::remove_const<BasicJsonType>::type>& other) noexcept\n        : m_object(other.m_object), m_it(other.m_it)\n    {}\n\n    /*!\n    @brief converting assignment\n    @param[in] other  non-const iterator to copy from\n    @return const/non-const iterator\n    @note It is not checked whether @a other is initialized.\n    */\n    iter_impl& operator=(const iter_impl<typename std::remove_const<BasicJsonType>::type>& other) noexcept // NOLINT(cert-oop54-cpp)\n    {\n        m_object = other.m_object;\n        m_it = other.m_it;\n        return *this;\n    }\n\n  JSON_PRIVATE_UNLESS_TESTED:\n    /*!\n    @brief set the iterator to the first value\n    @pre The iterator is initialized; i.e. `m_object != nullptr`.\n    */\n    void set_begin() noexcept\n    {\n        JSON_ASSERT(m_object != nullptr);\n\n        switch (m_object->m_data.m_type)\n        {\n            case value_t::object:\n            {\n                m_it.object_iterator = m_object->m_data.m_value.object->begin();\n                break;\n            }\n\n            case value_t::array:\n            {\n                m_it.array_iterator = m_object->m_data.m_value.array->begin();\n                break;\n            }\n\n            case value_t::null:\n            {\n                // set to end so begin()==end() is true: null is empty\n                m_it.primitive_iterator.set_end();\n                break;\n            }\n\n            case value_t::string:\n            case value_t::boolean:\n            case value_t::number_integer:\n            case value_t::number_unsigned:\n            case value_t::number_float:\n            case value_t::binary:\n            case value_t::discarded:\n            default:\n            {\n                m_it.primitive_iterator.set_begin();\n                break;\n            }\n        }\n    }\n\n    /*!\n    @brief set the iterator past the last value\n    @pre The iterator is initialized; i.e. `m_object != nullptr`.\n    */\n    void set_end() noexcept\n    {\n        JSON_ASSERT(m_object != nullptr);\n\n        switch (m_object->m_data.m_type)\n        {\n            case value_t::object:\n            {\n                m_it.object_iterator = m_object->m_data.m_value.object->end();\n                break;\n            }\n\n            case value_t::array:\n            {\n                m_it.array_iterator = m_object->m_data.m_value.array->end();\n                break;\n            }\n\n            case value_t::null:\n            case value_t::string:\n            case value_t::boolean:\n            case value_t::number_integer:\n            case value_t::number_unsigned:\n            case value_t::number_float:\n            case value_t::binary:\n            case value_t::discarded:\n            default:\n            {\n                m_it.primitive_iterator.set_end();\n                break;\n            }\n        }\n    }\n\n  public:\n    /*!\n    @brief return a reference to the value pointed to by the iterator\n    @pre The iterator is initialized; i.e. `m_object != nullptr`.\n    */\n    reference operator*() const\n    {\n        JSON_ASSERT(m_object != nullptr);\n\n        switch (m_object->m_data.m_type)\n        {\n            case value_t::object:\n            {\n                JSON_ASSERT(m_it.object_iterator != m_object->m_data.m_value.object->end());\n                return m_it.object_iterator->second;\n            }\n\n            case value_t::array:\n            {\n                JSON_ASSERT(m_it.array_iterator != m_object->m_data.m_value.array->end());\n                return *m_it.array_iterator;\n            }\n\n            case value_t::null:\n                JSON_THROW(invalid_iterator::create(214, \"cannot get value\", m_object));\n\n            case value_t::string:\n            case value_t::boolean:\n            case value_t::number_integer:\n            case value_t::number_unsigned:\n            case value_t::number_float:\n            case value_t::binary:\n            case value_t::discarded:\n            default:\n            {\n                if (JSON_HEDLEY_LIKELY(m_it.primitive_iterator.is_begin()))\n                {\n                    return *m_object;\n                }\n\n                JSON_THROW(invalid_iterator::create(214, \"cannot get value\", m_object));\n            }\n        }\n    }\n\n    /*!\n    @brief dereference the iterator\n    @pre The iterator is initialized; i.e. `m_object != nullptr`.\n    */\n    pointer operator->() const\n    {\n        JSON_ASSERT(m_object != nullptr);\n\n        switch (m_object->m_data.m_type)\n        {\n            case value_t::object:\n            {\n                JSON_ASSERT(m_it.object_iterator != m_object->m_data.m_value.object->end());\n                return &(m_it.object_iterator->second);\n            }\n\n            case value_t::array:\n            {\n                JSON_ASSERT(m_it.array_iterator != m_object->m_data.m_value.array->end());\n                return &*m_it.array_iterator;\n            }\n\n            case value_t::null:\n            case value_t::string:\n            case value_t::boolean:\n            case value_t::number_integer:\n            case value_t::number_unsigned:\n            case value_t::number_float:\n            case value_t::binary:\n            case value_t::discarded:\n            default:\n            {\n                if (JSON_HEDLEY_LIKELY(m_it.primitive_iterator.is_begin()))\n                {\n                    return m_object;\n                }\n\n                JSON_THROW(invalid_iterator::create(214, \"cannot get value\", m_object));\n            }\n        }\n    }\n\n    /*!\n    @brief post-increment (it++)\n    @pre The iterator is initialized; i.e. `m_object != nullptr`.\n    */\n    iter_impl operator++(int)& // NOLINT(cert-dcl21-cpp)\n    {\n        auto result = *this;\n        ++(*this);\n        return result;\n    }\n\n    /*!\n    @brief pre-increment (++it)\n    @pre The iterator is initialized; i.e. `m_object != nullptr`.\n    */\n    iter_impl& operator++()\n    {\n        JSON_ASSERT(m_object != nullptr);\n\n        switch (m_object->m_data.m_type)\n        {\n            case value_t::object:\n            {\n                std::advance(m_it.object_iterator, 1);\n                break;\n            }\n\n            case value_t::array:\n            {\n                std::advance(m_it.array_iterator, 1);\n                break;\n            }\n\n            case value_t::null:\n            case value_t::string:\n            case value_t::boolean:\n            case value_t::number_integer:\n            case value_t::number_unsigned:\n            case value_t::number_float:\n            case value_t::binary:\n            case value_t::discarded:\n            default:\n            {\n                ++m_it.primitive_iterator;\n                break;\n            }\n        }\n\n        return *this;\n    }\n\n    /*!\n    @brief post-decrement (it--)\n    @pre The iterator is initialized; i.e. `m_object != nullptr`.\n    */\n    iter_impl operator--(int)& // NOLINT(cert-dcl21-cpp)\n    {\n        auto result = *this;\n        --(*this);\n        return result;\n    }\n\n    /*!\n    @brief pre-decrement (--it)\n    @pre The iterator is initialized; i.e. `m_object != nullptr`.\n    */\n    iter_impl& operator--()\n    {\n        JSON_ASSERT(m_object != nullptr);\n\n        switch (m_object->m_data.m_type)\n        {\n            case value_t::object:\n            {\n                std::advance(m_it.object_iterator, -1);\n                break;\n            }\n\n            case value_t::array:\n            {\n                std::advance(m_it.array_iterator, -1);\n                break;\n            }\n\n            case value_t::null:\n            case value_t::string:\n            case value_t::boolean:\n            case value_t::number_integer:\n            case value_t::number_unsigned:\n            case value_t::number_float:\n            case value_t::binary:\n            case value_t::discarded:\n            default:\n            {\n                --m_it.primitive_iterator;\n                break;\n            }\n        }\n\n        return *this;\n    }\n\n    /*!\n    @brief comparison: equal\n    @pre The iterator is initialized; i.e. `m_object != nullptr`.\n    */\n    template < typename IterImpl, detail::enable_if_t < (std::is_same<IterImpl, iter_impl>::value || std::is_same<IterImpl, other_iter_impl>::value), std::nullptr_t > = nullptr >\n    bool operator==(const IterImpl& other) const\n    {\n        // if objects are not the same, the comparison is undefined\n        if (JSON_HEDLEY_UNLIKELY(m_object != other.m_object))\n        {\n            JSON_THROW(invalid_iterator::create(212, \"cannot compare iterators of different containers\", m_object));\n        }\n\n        JSON_ASSERT(m_object != nullptr);\n\n        switch (m_object->m_data.m_type)\n        {\n            case value_t::object:\n                return (m_it.object_iterator == other.m_it.object_iterator);\n\n            case value_t::array:\n                return (m_it.array_iterator == other.m_it.array_iterator);\n\n            case value_t::null:\n            case value_t::string:\n            case value_t::boolean:\n            case value_t::number_integer:\n            case value_t::number_unsigned:\n            case value_t::number_float:\n            case value_t::binary:\n            case value_t::discarded:\n            default:\n                return (m_it.primitive_iterator == other.m_it.primitive_iterator);\n        }\n    }\n\n    /*!\n    @brief comparison: not equal\n    @pre The iterator is initialized; i.e. `m_object != nullptr`.\n    */\n    template < typename IterImpl, detail::enable_if_t < (std::is_same<IterImpl, iter_impl>::value || std::is_same<IterImpl, other_iter_impl>::value), std::nullptr_t > = nullptr >\n    bool operator!=(const IterImpl& other) const\n    {\n        return !operator==(other);\n    }\n\n    /*!\n    @brief comparison: smaller\n    @pre The iterator is initialized; i.e. `m_object != nullptr`.\n    */\n    bool operator<(const iter_impl& other) const\n    {\n        // if objects are not the same, the comparison is undefined\n        if (JSON_HEDLEY_UNLIKELY(m_object != other.m_object))\n        {\n            JSON_THROW(invalid_iterator::create(212, \"cannot compare iterators of different containers\", m_object));\n        }\n\n        JSON_ASSERT(m_object != nullptr);\n\n        switch (m_object->m_data.m_type)\n        {\n            case value_t::object:\n                JSON_THROW(invalid_iterator::create(213, \"cannot compare order of object iterators\", m_object));\n\n            case value_t::array:\n                return (m_it.array_iterator < other.m_it.array_iterator);\n\n            case value_t::null:\n            case value_t::string:\n            case value_t::boolean:\n            case value_t::number_integer:\n            case value_t::number_unsigned:\n            case value_t::number_float:\n            case value_t::binary:\n            case value_t::discarded:\n            default:\n                return (m_it.primitive_iterator < other.m_it.primitive_iterator);\n        }\n    }\n\n    /*!\n    @brief comparison: less than or equal\n    @pre The iterator is initialized; i.e. `m_object != nullptr`.\n    */\n    bool operator<=(const iter_impl& other) const\n    {\n        return !other.operator < (*this);\n    }\n\n    /*!\n    @brief comparison: greater than\n    @pre The iterator is initialized; i.e. `m_object != nullptr`.\n    */\n    bool operator>(const iter_impl& other) const\n    {\n        return !operator<=(other);\n    }\n\n    /*!\n    @brief comparison: greater than or equal\n    @pre The iterator is initialized; i.e. `m_object != nullptr`.\n    */\n    bool operator>=(const iter_impl& other) const\n    {\n        return !operator<(other);\n    }\n\n    /*!\n    @brief add to iterator\n    @pre The iterator is initialized; i.e. `m_object != nullptr`.\n    */\n    iter_impl& operator+=(difference_type i)\n    {\n        JSON_ASSERT(m_object != nullptr);\n\n        switch (m_object->m_data.m_type)\n        {\n            case value_t::object:\n                JSON_THROW(invalid_iterator::create(209, \"cannot use offsets with object iterators\", m_object));\n\n            case value_t::array:\n            {\n                std::advance(m_it.array_iterator, i);\n                break;\n            }\n\n            case value_t::null:\n            case value_t::string:\n            case value_t::boolean:\n            case value_t::number_integer:\n            case value_t::number_unsigned:\n            case value_t::number_float:\n            case value_t::binary:\n            case value_t::discarded:\n            default:\n            {\n                m_it.primitive_iterator += i;\n                break;\n            }\n        }\n\n        return *this;\n    }\n\n    /*!\n    @brief subtract from iterator\n    @pre The iterator is initialized; i.e. `m_object != nullptr`.\n    */\n    iter_impl& operator-=(difference_type i)\n    {\n        return operator+=(-i);\n    }\n\n    /*!\n    @brief add to iterator\n    @pre The iterator is initialized; i.e. `m_object != nullptr`.\n    */\n    iter_impl operator+(difference_type i) const\n    {\n        auto result = *this;\n        result += i;\n        return result;\n    }\n\n    /*!\n    @brief addition of distance and iterator\n    @pre The iterator is initialized; i.e. `m_object != nullptr`.\n    */\n    friend iter_impl operator+(difference_type i, const iter_impl& it)\n    {\n        auto result = it;\n        result += i;\n        return result;\n    }\n\n    /*!\n    @brief subtract from iterator\n    @pre The iterator is initialized; i.e. `m_object != nullptr`.\n    */\n    iter_impl operator-(difference_type i) const\n    {\n        auto result = *this;\n        result -= i;\n        return result;\n    }\n\n    /*!\n    @brief return difference\n    @pre The iterator is initialized; i.e. `m_object != nullptr`.\n    */\n    difference_type operator-(const iter_impl& other) const\n    {\n        JSON_ASSERT(m_object != nullptr);\n\n        switch (m_object->m_data.m_type)\n        {\n            case value_t::object:\n                JSON_THROW(invalid_iterator::create(209, \"cannot use offsets with object iterators\", m_object));\n\n            case value_t::array:\n                return m_it.array_iterator - other.m_it.array_iterator;\n\n            case value_t::null:\n            case value_t::string:\n            case value_t::boolean:\n            case value_t::number_integer:\n            case value_t::number_unsigned:\n            case value_t::number_float:\n            case value_t::binary:\n            case value_t::discarded:\n            default:\n                return m_it.primitive_iterator - other.m_it.primitive_iterator;\n        }\n    }\n\n    /*!\n    @brief access to successor\n    @pre The iterator is initialized; i.e. `m_object != nullptr`.\n    */\n    reference operator[](difference_type n) const\n    {\n        JSON_ASSERT(m_object != nullptr);\n\n        switch (m_object->m_data.m_type)\n        {\n            case value_t::object:\n                JSON_THROW(invalid_iterator::create(208, \"cannot use operator[] for object iterators\", m_object));\n\n            case value_t::array:\n                return *std::next(m_it.array_iterator, n);\n\n            case value_t::null:\n                JSON_THROW(invalid_iterator::create(214, \"cannot get value\", m_object));\n\n            case value_t::string:\n            case value_t::boolean:\n            case value_t::number_integer:\n            case value_t::number_unsigned:\n            case value_t::number_float:\n            case value_t::binary:\n            case value_t::discarded:\n            default:\n            {\n                if (JSON_HEDLEY_LIKELY(m_it.primitive_iterator.get_value() == -n))\n                {\n                    return *m_object;\n                }\n\n                JSON_THROW(invalid_iterator::create(214, \"cannot get value\", m_object));\n            }\n        }\n    }\n\n    /*!\n    @brief return the key of an object iterator\n    @pre The iterator is initialized; i.e. `m_object != nullptr`.\n    */\n    const typename object_t::key_type& key() const\n    {\n        JSON_ASSERT(m_object != nullptr);\n\n        if (JSON_HEDLEY_LIKELY(m_object->is_object()))\n        {\n            return m_it.object_iterator->first;\n        }\n\n        JSON_THROW(invalid_iterator::create(207, \"cannot use key() for non-object iterators\", m_object));\n    }\n\n    /*!\n    @brief return the value of an iterator\n    @pre The iterator is initialized; i.e. `m_object != nullptr`.\n    */\n    reference value() const\n    {\n        return operator*();\n    }\n\n  JSON_PRIVATE_UNLESS_TESTED:\n    /// associated JSON instance\n    pointer m_object = nullptr;\n    /// the actual iterator of the associated instance\n    internal_iterator<typename std::remove_const<BasicJsonType>::type> m_it {};\n};\n\n}  // namespace detail\nNLOHMANN_JSON_NAMESPACE_END\n\n// #include <nlohmann/detail/iterators/iteration_proxy.hpp>\n\n// #include <nlohmann/detail/iterators/json_reverse_iterator.hpp>\n//     __ _____ _____ _____\n//  __|  |   __|     |   | |  JSON for Modern C++\n// |  |  |__   |  |  | | | |  version 3.11.3\n// |_____|_____|_____|_|___|  https://github.com/nlohmann/json\n//\n// SPDX-FileCopyrightText: 2013-2023 Niels Lohmann <https://nlohmann.me>\n// SPDX-License-Identifier: MIT\n\n\n\n#include <cstddef> // ptrdiff_t\n#include <iterator> // reverse_iterator\n#include <utility> // declval\n\n// #include <nlohmann/detail/abi_macros.hpp>\n\n\nNLOHMANN_JSON_NAMESPACE_BEGIN\nnamespace detail\n{\n\n//////////////////////\n// reverse_iterator //\n//////////////////////\n\n/*!\n@brief a template for a reverse iterator class\n\n@tparam Base the base iterator type to reverse. Valid types are @ref\niterator (to create @ref reverse_iterator) and @ref const_iterator (to\ncreate @ref const_reverse_iterator).\n\n@requirement The class satisfies the following concept requirements:\n-\n[BidirectionalIterator](https://en.cppreference.com/w/cpp/named_req/BidirectionalIterator):\n  The iterator that can be moved can be moved in both directions (i.e.\n  incremented and decremented).\n- [OutputIterator](https://en.cppreference.com/w/cpp/named_req/OutputIterator):\n  It is possible to write to the pointed-to element (only if @a Base is\n  @ref iterator).\n\n@since version 1.0.0\n*/\ntemplate<typename Base>\nclass json_reverse_iterator : public std::reverse_iterator<Base>\n{\n  public:\n    using difference_type = std::ptrdiff_t;\n    /// shortcut to the reverse iterator adapter\n    using base_iterator = std::reverse_iterator<Base>;\n    /// the reference type for the pointed-to element\n    using reference = typename Base::reference;\n\n    /// create reverse iterator from iterator\n    explicit json_reverse_iterator(const typename base_iterator::iterator_type& it) noexcept\n        : base_iterator(it) {}\n\n    /// create reverse iterator from base class\n    explicit json_reverse_iterator(const base_iterator& it) noexcept : base_iterator(it) {}\n\n    /// post-increment (it++)\n    json_reverse_iterator operator++(int)& // NOLINT(cert-dcl21-cpp)\n    {\n        return static_cast<json_reverse_iterator>(base_iterator::operator++(1));\n    }\n\n    /// pre-increment (++it)\n    json_reverse_iterator& operator++()\n    {\n        return static_cast<json_reverse_iterator&>(base_iterator::operator++());\n    }\n\n    /// post-decrement (it--)\n    json_reverse_iterator operator--(int)& // NOLINT(cert-dcl21-cpp)\n    {\n        return static_cast<json_reverse_iterator>(base_iterator::operator--(1));\n    }\n\n    /// pre-decrement (--it)\n    json_reverse_iterator& operator--()\n    {\n        return static_cast<json_reverse_iterator&>(base_iterator::operator--());\n    }\n\n    /// add to iterator\n    json_reverse_iterator& operator+=(difference_type i)\n    {\n        return static_cast<json_reverse_iterator&>(base_iterator::operator+=(i));\n    }\n\n    /// add to iterator\n    json_reverse_iterator operator+(difference_type i) const\n    {\n        return static_cast<json_reverse_iterator>(base_iterator::operator+(i));\n    }\n\n    /// subtract from iterator\n    json_reverse_iterator operator-(difference_type i) const\n    {\n        return static_cast<json_reverse_iterator>(base_iterator::operator-(i));\n    }\n\n    /// return difference\n    difference_type operator-(const json_reverse_iterator& other) const\n    {\n        return base_iterator(*this) - base_iterator(other);\n    }\n\n    /// access to successor\n    reference operator[](difference_type n) const\n    {\n        return *(this->operator+(n));\n    }\n\n    /// return the key of an object iterator\n    auto key() const -> decltype(std::declval<Base>().key())\n    {\n        auto it = --this->base();\n        return it.key();\n    }\n\n    /// return the value of an iterator\n    reference value() const\n    {\n        auto it = --this->base();\n        return it.operator * ();\n    }\n};\n\n}  // namespace detail\nNLOHMANN_JSON_NAMESPACE_END\n\n// #include <nlohmann/detail/iterators/primitive_iterator.hpp>\n\n// #include <nlohmann/detail/json_custom_base_class.hpp>\n//     __ _____ _____ _____\n//  __|  |   __|     |   | |  JSON for Modern C++\n// |  |  |__   |  |  | | | |  version 3.11.3\n// |_____|_____|_____|_|___|  https://github.com/nlohmann/json\n//\n// SPDX-FileCopyrightText: 2013-2023 Niels Lohmann <https://nlohmann.me>\n// SPDX-License-Identifier: MIT\n\n\n\n#include <type_traits> // conditional, is_same\n\n// #include <nlohmann/detail/abi_macros.hpp>\n\n\nNLOHMANN_JSON_NAMESPACE_BEGIN\nnamespace detail\n{\n\n/*!\n@brief Default base class of the @ref basic_json class.\n\nSo that the correct implementations of the copy / move ctors / assign operators\nof @ref basic_json do not require complex case distinctions\n(no base class / custom base class used as customization point),\n@ref basic_json always has a base class.\nBy default, this class is used because it is empty and thus has no effect\non the behavior of @ref basic_json.\n*/\nstruct json_default_base {};\n\ntemplate<class T>\nusing json_base_class = typename std::conditional <\n                        std::is_same<T, void>::value,\n                        json_default_base,\n                        T\n                        >::type;\n\n}  // namespace detail\nNLOHMANN_JSON_NAMESPACE_END\n\n// #include <nlohmann/detail/json_pointer.hpp>\n//     __ _____ _____ _____\n//  __|  |   __|     |   | |  JSON for Modern C++\n// |  |  |__   |  |  | | | |  version 3.11.3\n// |_____|_____|_____|_|___|  https://github.com/nlohmann/json\n//\n// SPDX-FileCopyrightText: 2013-2023 Niels Lohmann <https://nlohmann.me>\n// SPDX-License-Identifier: MIT\n\n\n\n#include <algorithm> // all_of\n#include <cctype> // isdigit\n#include <cerrno> // errno, ERANGE\n#include <cstdlib> // strtoull\n#ifndef JSON_NO_IO\n    #include <iosfwd> // ostream\n#endif  // JSON_NO_IO\n#include <limits> // max\n#include <numeric> // accumulate\n#include <string> // string\n#include <utility> // move\n#include <vector> // vector\n\n// #include <nlohmann/detail/exceptions.hpp>\n\n// #include <nlohmann/detail/macro_scope.hpp>\n\n// #include <nlohmann/detail/string_concat.hpp>\n\n// #include <nlohmann/detail/string_escape.hpp>\n\n// #include <nlohmann/detail/value_t.hpp>\n\n\nNLOHMANN_JSON_NAMESPACE_BEGIN\n\n/// @brief JSON Pointer defines a string syntax for identifying a specific value within a JSON document\n/// @sa https://json.nlohmann.me/api/json_pointer/\ntemplate<typename RefStringType>\nclass json_pointer\n{\n    // allow basic_json to access private members\n    NLOHMANN_BASIC_JSON_TPL_DECLARATION\n    friend class basic_json;\n\n    template<typename>\n    friend class json_pointer;\n\n    template<typename T>\n    struct string_t_helper\n    {\n        using type = T;\n    };\n\n    NLOHMANN_BASIC_JSON_TPL_DECLARATION\n    struct string_t_helper<NLOHMANN_BASIC_JSON_TPL>\n    {\n        using type = StringType;\n    };\n\n  public:\n    // for backwards compatibility accept BasicJsonType\n    using string_t = typename string_t_helper<RefStringType>::type;\n\n    /// @brief create JSON pointer\n    /// @sa https://json.nlohmann.me/api/json_pointer/json_pointer/\n    explicit json_pointer(const string_t& s = \"\")\n        : reference_tokens(split(s))\n    {}\n\n    /// @brief return a string representation of the JSON pointer\n    /// @sa https://json.nlohmann.me/api/json_pointer/to_string/\n    string_t to_string() const\n    {\n        return std::accumulate(reference_tokens.begin(), reference_tokens.end(),\n                               string_t{},\n                               [](const string_t& a, const string_t& b)\n        {\n            return detail::concat(a, '/', detail::escape(b));\n        });\n    }\n\n    /// @brief return a string representation of the JSON pointer\n    /// @sa https://json.nlohmann.me/api/json_pointer/operator_string/\n    JSON_HEDLEY_DEPRECATED_FOR(3.11.0, to_string())\n    operator string_t() const\n    {\n        return to_string();\n    }\n\n#ifndef JSON_NO_IO\n    /// @brief write string representation of the JSON pointer to stream\n    /// @sa https://json.nlohmann.me/api/basic_json/operator_ltlt/\n    friend std::ostream& operator<<(std::ostream& o, const json_pointer& ptr)\n    {\n        o << ptr.to_string();\n        return o;\n    }\n#endif\n\n    /// @brief append another JSON pointer at the end of this JSON pointer\n    /// @sa https://json.nlohmann.me/api/json_pointer/operator_slasheq/\n    json_pointer& operator/=(const json_pointer& ptr)\n    {\n        reference_tokens.insert(reference_tokens.end(),\n                                ptr.reference_tokens.begin(),\n                                ptr.reference_tokens.end());\n        return *this;\n    }\n\n    /// @brief append an unescaped reference token at the end of this JSON pointer\n    /// @sa https://json.nlohmann.me/api/json_pointer/operator_slasheq/\n    json_pointer& operator/=(string_t token)\n    {\n        push_back(std::move(token));\n        return *this;\n    }\n\n    /// @brief append an array index at the end of this JSON pointer\n    /// @sa https://json.nlohmann.me/api/json_pointer/operator_slasheq/\n    json_pointer& operator/=(std::size_t array_idx)\n    {\n        return *this /= std::to_string(array_idx);\n    }\n\n    /// @brief create a new JSON pointer by appending the right JSON pointer at the end of the left JSON pointer\n    /// @sa https://json.nlohmann.me/api/json_pointer/operator_slash/\n    friend json_pointer operator/(const json_pointer& lhs,\n                                  const json_pointer& rhs)\n    {\n        return json_pointer(lhs) /= rhs;\n    }\n\n    /// @brief create a new JSON pointer by appending the unescaped token at the end of the JSON pointer\n    /// @sa https://json.nlohmann.me/api/json_pointer/operator_slash/\n    friend json_pointer operator/(const json_pointer& lhs, string_t token) // NOLINT(performance-unnecessary-value-param)\n    {\n        return json_pointer(lhs) /= std::move(token);\n    }\n\n    /// @brief create a new JSON pointer by appending the array-index-token at the end of the JSON pointer\n    /// @sa https://json.nlohmann.me/api/json_pointer/operator_slash/\n    friend json_pointer operator/(const json_pointer& lhs, std::size_t array_idx)\n    {\n        return json_pointer(lhs) /= array_idx;\n    }\n\n    /// @brief returns the parent of this JSON pointer\n    /// @sa https://json.nlohmann.me/api/json_pointer/parent_pointer/\n    json_pointer parent_pointer() const\n    {\n        if (empty())\n        {\n            return *this;\n        }\n\n        json_pointer res = *this;\n        res.pop_back();\n        return res;\n    }\n\n    /// @brief remove last reference token\n    /// @sa https://json.nlohmann.me/api/json_pointer/pop_back/\n    void pop_back()\n    {\n        if (JSON_HEDLEY_UNLIKELY(empty()))\n        {\n            JSON_THROW(detail::out_of_range::create(405, \"JSON pointer has no parent\", nullptr));\n        }\n\n        reference_tokens.pop_back();\n    }\n\n    /// @brief return last reference token\n    /// @sa https://json.nlohmann.me/api/json_pointer/back/\n    const string_t& back() const\n    {\n        if (JSON_HEDLEY_UNLIKELY(empty()))\n        {\n            JSON_THROW(detail::out_of_range::create(405, \"JSON pointer has no parent\", nullptr));\n        }\n\n        return reference_tokens.back();\n    }\n\n    /// @brief append an unescaped token at the end of the reference pointer\n    /// @sa https://json.nlohmann.me/api/json_pointer/push_back/\n    void push_back(const string_t& token)\n    {\n        reference_tokens.push_back(token);\n    }\n\n    /// @brief append an unescaped token at the end of the reference pointer\n    /// @sa https://json.nlohmann.me/api/json_pointer/push_back/\n    void push_back(string_t&& token)\n    {\n        reference_tokens.push_back(std::move(token));\n    }\n\n    /// @brief return whether pointer points to the root document\n    /// @sa https://json.nlohmann.me/api/json_pointer/empty/\n    bool empty() const noexcept\n    {\n        return reference_tokens.empty();\n    }\n\n  private:\n    /*!\n    @param[in] s  reference token to be converted into an array index\n\n    @return integer representation of @a s\n\n    @throw parse_error.106  if an array index begins with '0'\n    @throw parse_error.109  if an array index begins not with a digit\n    @throw out_of_range.404 if string @a s could not be converted to an integer\n    @throw out_of_range.410 if an array index exceeds size_type\n    */\n    template<typename BasicJsonType>\n    static typename BasicJsonType::size_type array_index(const string_t& s)\n    {\n        using size_type = typename BasicJsonType::size_type;\n\n        // error condition (cf. RFC 6901, Sect. 4)\n        if (JSON_HEDLEY_UNLIKELY(s.size() > 1 && s[0] == '0'))\n        {\n            JSON_THROW(detail::parse_error::create(106, 0, detail::concat(\"array index '\", s, \"' must not begin with '0'\"), nullptr));\n        }\n\n        // error condition (cf. RFC 6901, Sect. 4)\n        if (JSON_HEDLEY_UNLIKELY(s.size() > 1 && !(s[0] >= '1' && s[0] <= '9')))\n        {\n            JSON_THROW(detail::parse_error::create(109, 0, detail::concat(\"array index '\", s, \"' is not a number\"), nullptr));\n        }\n\n        const char* p = s.c_str();\n        char* p_end = nullptr;\n        errno = 0; // strtoull doesn't reset errno\n        const unsigned long long res = std::strtoull(p, &p_end, 10); // NOLINT(runtime/int)\n        if (p == p_end // invalid input or empty string\n                || errno == ERANGE // out of range\n                || JSON_HEDLEY_UNLIKELY(static_cast<std::size_t>(p_end - p) != s.size())) // incomplete read\n        {\n            JSON_THROW(detail::out_of_range::create(404, detail::concat(\"unresolved reference token '\", s, \"'\"), nullptr));\n        }\n\n        // only triggered on special platforms (like 32bit), see also\n        // https://github.com/nlohmann/json/pull/2203\n        if (res >= static_cast<unsigned long long>((std::numeric_limits<size_type>::max)()))  // NOLINT(runtime/int)\n        {\n            JSON_THROW(detail::out_of_range::create(410, detail::concat(\"array index \", s, \" exceeds size_type\"), nullptr));   // LCOV_EXCL_LINE\n        }\n\n        return static_cast<size_type>(res);\n    }\n\n  JSON_PRIVATE_UNLESS_TESTED:\n    json_pointer top() const\n    {\n        if (JSON_HEDLEY_UNLIKELY(empty()))\n        {\n            JSON_THROW(detail::out_of_range::create(405, \"JSON pointer has no parent\", nullptr));\n        }\n\n        json_pointer result = *this;\n        result.reference_tokens = {reference_tokens[0]};\n        return result;\n    }\n\n  private:\n    /*!\n    @brief create and return a reference to the pointed to value\n\n    @complexity Linear in the number of reference tokens.\n\n    @throw parse_error.109 if array index is not a number\n    @throw type_error.313 if value cannot be unflattened\n    */\n    template<typename BasicJsonType>\n    BasicJsonType& get_and_create(BasicJsonType& j) const\n    {\n        auto* result = &j;\n\n        // in case no reference tokens exist, return a reference to the JSON value\n        // j which will be overwritten by a primitive value\n        for (const auto& reference_token : reference_tokens)\n        {\n            switch (result->type())\n            {\n                case detail::value_t::null:\n                {\n                    if (reference_token == \"0\")\n                    {\n                        // start a new array if reference token is 0\n                        result = &result->operator[](0);\n                    }\n                    else\n                    {\n                        // start a new object otherwise\n                        result = &result->operator[](reference_token);\n                    }\n                    break;\n                }\n\n                case detail::value_t::object:\n                {\n                    // create an entry in the object\n                    result = &result->operator[](reference_token);\n                    break;\n                }\n\n                case detail::value_t::array:\n                {\n                    // create an entry in the array\n                    result = &result->operator[](array_index<BasicJsonType>(reference_token));\n                    break;\n                }\n\n                /*\n                The following code is only reached if there exists a reference\n                token _and_ the current value is primitive. In this case, we have\n                an error situation, because primitive values may only occur as\n                single value; that is, with an empty list of reference tokens.\n                */\n                case detail::value_t::string:\n                case detail::value_t::boolean:\n                case detail::value_t::number_integer:\n                case detail::value_t::number_unsigned:\n                case detail::value_t::number_float:\n                case detail::value_t::binary:\n                case detail::value_t::discarded:\n                default:\n                    JSON_THROW(detail::type_error::create(313, \"invalid value to unflatten\", &j));\n            }\n        }\n\n        return *result;\n    }\n\n    /*!\n    @brief return a reference to the pointed to value\n\n    @note This version does not throw if a value is not present, but tries to\n          create nested values instead. For instance, calling this function\n          with pointer `\"/this/that\"` on a null value is equivalent to calling\n          `operator[](\"this\").operator[](\"that\")` on that value, effectively\n          changing the null value to an object.\n\n    @param[in] ptr  a JSON value\n\n    @return reference to the JSON value pointed to by the JSON pointer\n\n    @complexity Linear in the length of the JSON pointer.\n\n    @throw parse_error.106   if an array index begins with '0'\n    @throw parse_error.109   if an array index was not a number\n    @throw out_of_range.404  if the JSON pointer can not be resolved\n    */\n    template<typename BasicJsonType>\n    BasicJsonType& get_unchecked(BasicJsonType* ptr) const\n    {\n        for (const auto& reference_token : reference_tokens)\n        {\n            // convert null values to arrays or objects before continuing\n            if (ptr->is_null())\n            {\n                // check if reference token is a number\n                const bool nums =\n                    std::all_of(reference_token.begin(), reference_token.end(),\n                                [](const unsigned char x)\n                {\n                    return std::isdigit(x);\n                });\n\n                // change value to array for numbers or \"-\" or to object otherwise\n                *ptr = (nums || reference_token == \"-\")\n                       ? detail::value_t::array\n                       : detail::value_t::object;\n            }\n\n            switch (ptr->type())\n            {\n                case detail::value_t::object:\n                {\n                    // use unchecked object access\n                    ptr = &ptr->operator[](reference_token);\n                    break;\n                }\n\n                case detail::value_t::array:\n                {\n                    if (reference_token == \"-\")\n                    {\n                        // explicitly treat \"-\" as index beyond the end\n                        ptr = &ptr->operator[](ptr->m_data.m_value.array->size());\n                    }\n                    else\n                    {\n                        // convert array index to number; unchecked access\n                        ptr = &ptr->operator[](array_index<BasicJsonType>(reference_token));\n                    }\n                    break;\n                }\n\n                case detail::value_t::null:\n                case detail::value_t::string:\n                case detail::value_t::boolean:\n                case detail::value_t::number_integer:\n                case detail::value_t::number_unsigned:\n                case detail::value_t::number_float:\n                case detail::value_t::binary:\n                case detail::value_t::discarded:\n                default:\n                    JSON_THROW(detail::out_of_range::create(404, detail::concat(\"unresolved reference token '\", reference_token, \"'\"), ptr));\n            }\n        }\n\n        return *ptr;\n    }\n\n    /*!\n    @throw parse_error.106   if an array index begins with '0'\n    @throw parse_error.109   if an array index was not a number\n    @throw out_of_range.402  if the array index '-' is used\n    @throw out_of_range.404  if the JSON pointer can not be resolved\n    */\n    template<typename BasicJsonType>\n    BasicJsonType& get_checked(BasicJsonType* ptr) const\n    {\n        for (const auto& reference_token : reference_tokens)\n        {\n            switch (ptr->type())\n            {\n                case detail::value_t::object:\n                {\n                    // note: at performs range check\n                    ptr = &ptr->at(reference_token);\n                    break;\n                }\n\n                case detail::value_t::array:\n                {\n                    if (JSON_HEDLEY_UNLIKELY(reference_token == \"-\"))\n                    {\n                        // \"-\" always fails the range check\n                        JSON_THROW(detail::out_of_range::create(402, detail::concat(\n                                \"array index '-' (\", std::to_string(ptr->m_data.m_value.array->size()),\n                                \") is out of range\"), ptr));\n                    }\n\n                    // note: at performs range check\n                    ptr = &ptr->at(array_index<BasicJsonType>(reference_token));\n                    break;\n                }\n\n                case detail::value_t::null:\n                case detail::value_t::string:\n                case detail::value_t::boolean:\n                case detail::value_t::number_integer:\n                case detail::value_t::number_unsigned:\n                case detail::value_t::number_float:\n                case detail::value_t::binary:\n                case detail::value_t::discarded:\n                default:\n                    JSON_THROW(detail::out_of_range::create(404, detail::concat(\"unresolved reference token '\", reference_token, \"'\"), ptr));\n            }\n        }\n\n        return *ptr;\n    }\n\n    /*!\n    @brief return a const reference to the pointed to value\n\n    @param[in] ptr  a JSON value\n\n    @return const reference to the JSON value pointed to by the JSON\n    pointer\n\n    @throw parse_error.106   if an array index begins with '0'\n    @throw parse_error.109   if an array index was not a number\n    @throw out_of_range.402  if the array index '-' is used\n    @throw out_of_range.404  if the JSON pointer can not be resolved\n    */\n    template<typename BasicJsonType>\n    const BasicJsonType& get_unchecked(const BasicJsonType* ptr) const\n    {\n        for (const auto& reference_token : reference_tokens)\n        {\n            switch (ptr->type())\n            {\n                case detail::value_t::object:\n                {\n                    // use unchecked object access\n                    ptr = &ptr->operator[](reference_token);\n                    break;\n                }\n\n                case detail::value_t::array:\n                {\n                    if (JSON_HEDLEY_UNLIKELY(reference_token == \"-\"))\n                    {\n                        // \"-\" cannot be used for const access\n                        JSON_THROW(detail::out_of_range::create(402, detail::concat(\"array index '-' (\", std::to_string(ptr->m_data.m_value.array->size()), \") is out of range\"), ptr));\n                    }\n\n                    // use unchecked array access\n                    ptr = &ptr->operator[](array_index<BasicJsonType>(reference_token));\n                    break;\n                }\n\n                case detail::value_t::null:\n                case detail::value_t::string:\n                case detail::value_t::boolean:\n                case detail::value_t::number_integer:\n                case detail::value_t::number_unsigned:\n                case detail::value_t::number_float:\n                case detail::value_t::binary:\n                case detail::value_t::discarded:\n                default:\n                    JSON_THROW(detail::out_of_range::create(404, detail::concat(\"unresolved reference token '\", reference_token, \"'\"), ptr));\n            }\n        }\n\n        return *ptr;\n    }\n\n    /*!\n    @throw parse_error.106   if an array index begins with '0'\n    @throw parse_error.109   if an array index was not a number\n    @throw out_of_range.402  if the array index '-' is used\n    @throw out_of_range.404  if the JSON pointer can not be resolved\n    */\n    template<typename BasicJsonType>\n    const BasicJsonType& get_checked(const BasicJsonType* ptr) const\n    {\n        for (const auto& reference_token : reference_tokens)\n        {\n            switch (ptr->type())\n            {\n                case detail::value_t::object:\n                {\n                    // note: at performs range check\n                    ptr = &ptr->at(reference_token);\n                    break;\n                }\n\n                case detail::value_t::array:\n                {\n                    if (JSON_HEDLEY_UNLIKELY(reference_token == \"-\"))\n                    {\n                        // \"-\" always fails the range check\n                        JSON_THROW(detail::out_of_range::create(402, detail::concat(\n                                \"array index '-' (\", std::to_string(ptr->m_data.m_value.array->size()),\n                                \") is out of range\"), ptr));\n                    }\n\n                    // note: at performs range check\n                    ptr = &ptr->at(array_index<BasicJsonType>(reference_token));\n                    break;\n                }\n\n                case detail::value_t::null:\n                case detail::value_t::string:\n                case detail::value_t::boolean:\n                case detail::value_t::number_integer:\n                case detail::value_t::number_unsigned:\n                case detail::value_t::number_float:\n                case detail::value_t::binary:\n                case detail::value_t::discarded:\n                default:\n                    JSON_THROW(detail::out_of_range::create(404, detail::concat(\"unresolved reference token '\", reference_token, \"'\"), ptr));\n            }\n        }\n\n        return *ptr;\n    }\n\n    /*!\n    @throw parse_error.106   if an array index begins with '0'\n    @throw parse_error.109   if an array index was not a number\n    */\n    template<typename BasicJsonType>\n    bool contains(const BasicJsonType* ptr) const\n    {\n        for (const auto& reference_token : reference_tokens)\n        {\n            switch (ptr->type())\n            {\n                case detail::value_t::object:\n                {\n                    if (!ptr->contains(reference_token))\n                    {\n                        // we did not find the key in the object\n                        return false;\n                    }\n\n                    ptr = &ptr->operator[](reference_token);\n                    break;\n                }\n\n                case detail::value_t::array:\n                {\n                    if (JSON_HEDLEY_UNLIKELY(reference_token == \"-\"))\n                    {\n                        // \"-\" always fails the range check\n                        return false;\n                    }\n                    if (JSON_HEDLEY_UNLIKELY(reference_token.size() == 1 && !(\"0\" <= reference_token && reference_token <= \"9\")))\n                    {\n                        // invalid char\n                        return false;\n                    }\n                    if (JSON_HEDLEY_UNLIKELY(reference_token.size() > 1))\n                    {\n                        if (JSON_HEDLEY_UNLIKELY(!('1' <= reference_token[0] && reference_token[0] <= '9')))\n                        {\n                            // first char should be between '1' and '9'\n                            return false;\n                        }\n                        for (std::size_t i = 1; i < reference_token.size(); i++)\n                        {\n                            if (JSON_HEDLEY_UNLIKELY(!('0' <= reference_token[i] && reference_token[i] <= '9')))\n                            {\n                                // other char should be between '0' and '9'\n                                return false;\n                            }\n                        }\n                    }\n\n                    const auto idx = array_index<BasicJsonType>(reference_token);\n                    if (idx >= ptr->size())\n                    {\n                        // index out of range\n                        return false;\n                    }\n\n                    ptr = &ptr->operator[](idx);\n                    break;\n                }\n\n                case detail::value_t::null:\n                case detail::value_t::string:\n                case detail::value_t::boolean:\n                case detail::value_t::number_integer:\n                case detail::value_t::number_unsigned:\n                case detail::value_t::number_float:\n                case detail::value_t::binary:\n                case detail::value_t::discarded:\n                default:\n                {\n                    // we do not expect primitive values if there is still a\n                    // reference token to process\n                    return false;\n                }\n            }\n        }\n\n        // no reference token left means we found a primitive value\n        return true;\n    }\n\n    /*!\n    @brief split the string input to reference tokens\n\n    @note This function is only called by the json_pointer constructor.\n          All exceptions below are documented there.\n\n    @throw parse_error.107  if the pointer is not empty or begins with '/'\n    @throw parse_error.108  if character '~' is not followed by '0' or '1'\n    */\n    static std::vector<string_t> split(const string_t& reference_string)\n    {\n        std::vector<string_t> result;\n\n        // special case: empty reference string -> no reference tokens\n        if (reference_string.empty())\n        {\n            return result;\n        }\n\n        // check if nonempty reference string begins with slash\n        if (JSON_HEDLEY_UNLIKELY(reference_string[0] != '/'))\n        {\n            JSON_THROW(detail::parse_error::create(107, 1, detail::concat(\"JSON pointer must be empty or begin with '/' - was: '\", reference_string, \"'\"), nullptr));\n        }\n\n        // extract the reference tokens:\n        // - slash: position of the last read slash (or end of string)\n        // - start: position after the previous slash\n        for (\n            // search for the first slash after the first character\n            std::size_t slash = reference_string.find_first_of('/', 1),\n            // set the beginning of the first reference token\n            start = 1;\n            // we can stop if start == 0 (if slash == string_t::npos)\n            start != 0;\n            // set the beginning of the next reference token\n            // (will eventually be 0 if slash == string_t::npos)\n            start = (slash == string_t::npos) ? 0 : slash + 1,\n            // find next slash\n            slash = reference_string.find_first_of('/', start))\n        {\n            // use the text between the beginning of the reference token\n            // (start) and the last slash (slash).\n            auto reference_token = reference_string.substr(start, slash - start);\n\n            // check reference tokens are properly escaped\n            for (std::size_t pos = reference_token.find_first_of('~');\n                    pos != string_t::npos;\n                    pos = reference_token.find_first_of('~', pos + 1))\n            {\n                JSON_ASSERT(reference_token[pos] == '~');\n\n                // ~ must be followed by 0 or 1\n                if (JSON_HEDLEY_UNLIKELY(pos == reference_token.size() - 1 ||\n                                         (reference_token[pos + 1] != '0' &&\n                                          reference_token[pos + 1] != '1')))\n                {\n                    JSON_THROW(detail::parse_error::create(108, 0, \"escape character '~' must be followed with '0' or '1'\", nullptr));\n                }\n            }\n\n            // finally, store the reference token\n            detail::unescape(reference_token);\n            result.push_back(reference_token);\n        }\n\n        return result;\n    }\n\n  private:\n    /*!\n    @param[in] reference_string  the reference string to the current value\n    @param[in] value             the value to consider\n    @param[in,out] result        the result object to insert values to\n\n    @note Empty objects or arrays are flattened to `null`.\n    */\n    template<typename BasicJsonType>\n    static void flatten(const string_t& reference_string,\n                        const BasicJsonType& value,\n                        BasicJsonType& result)\n    {\n        switch (value.type())\n        {\n            case detail::value_t::array:\n            {\n                if (value.m_data.m_value.array->empty())\n                {\n                    // flatten empty array as null\n                    result[reference_string] = nullptr;\n                }\n                else\n                {\n                    // iterate array and use index as reference string\n                    for (std::size_t i = 0; i < value.m_data.m_value.array->size(); ++i)\n                    {\n                        flatten(detail::concat(reference_string, '/', std::to_string(i)),\n                                value.m_data.m_value.array->operator[](i), result);\n                    }\n                }\n                break;\n            }\n\n            case detail::value_t::object:\n            {\n                if (value.m_data.m_value.object->empty())\n                {\n                    // flatten empty object as null\n                    result[reference_string] = nullptr;\n                }\n                else\n                {\n                    // iterate object and use keys as reference string\n                    for (const auto& element : *value.m_data.m_value.object)\n                    {\n                        flatten(detail::concat(reference_string, '/', detail::escape(element.first)), element.second, result);\n                    }\n                }\n                break;\n            }\n\n            case detail::value_t::null:\n            case detail::value_t::string:\n            case detail::value_t::boolean:\n            case detail::value_t::number_integer:\n            case detail::value_t::number_unsigned:\n            case detail::value_t::number_float:\n            case detail::value_t::binary:\n            case detail::value_t::discarded:\n            default:\n            {\n                // add primitive value with its reference string\n                result[reference_string] = value;\n                break;\n            }\n        }\n    }\n\n    /*!\n    @param[in] value  flattened JSON\n\n    @return unflattened JSON\n\n    @throw parse_error.109 if array index is not a number\n    @throw type_error.314  if value is not an object\n    @throw type_error.315  if object values are not primitive\n    @throw type_error.313  if value cannot be unflattened\n    */\n    template<typename BasicJsonType>\n    static BasicJsonType\n    unflatten(const BasicJsonType& value)\n    {\n        if (JSON_HEDLEY_UNLIKELY(!value.is_object()))\n        {\n            JSON_THROW(detail::type_error::create(314, \"only objects can be unflattened\", &value));\n        }\n\n        BasicJsonType result;\n\n        // iterate the JSON object values\n        for (const auto& element : *value.m_data.m_value.object)\n        {\n            if (JSON_HEDLEY_UNLIKELY(!element.second.is_primitive()))\n            {\n                JSON_THROW(detail::type_error::create(315, \"values in object must be primitive\", &element.second));\n            }\n\n            // assign value to reference pointed to by JSON pointer; Note that if\n            // the JSON pointer is \"\" (i.e., points to the whole value), function\n            // get_and_create returns a reference to result itself. An assignment\n            // will then create a primitive value.\n            json_pointer(element.first).get_and_create(result) = element.second;\n        }\n\n        return result;\n    }\n\n    // can't use conversion operator because of ambiguity\n    json_pointer<string_t> convert() const&\n    {\n        json_pointer<string_t> result;\n        result.reference_tokens = reference_tokens;\n        return result;\n    }\n\n    json_pointer<string_t> convert()&&\n    {\n        json_pointer<string_t> result;\n        result.reference_tokens = std::move(reference_tokens);\n        return result;\n    }\n\n  public:\n#if JSON_HAS_THREE_WAY_COMPARISON\n    /// @brief compares two JSON pointers for equality\n    /// @sa https://json.nlohmann.me/api/json_pointer/operator_eq/\n    template<typename RefStringTypeRhs>\n    bool operator==(const json_pointer<RefStringTypeRhs>& rhs) const noexcept\n    {\n        return reference_tokens == rhs.reference_tokens;\n    }\n\n    /// @brief compares JSON pointer and string for equality\n    /// @sa https://json.nlohmann.me/api/json_pointer/operator_eq/\n    JSON_HEDLEY_DEPRECATED_FOR(3.11.2, operator==(json_pointer))\n    bool operator==(const string_t& rhs) const\n    {\n        return *this == json_pointer(rhs);\n    }\n\n    /// @brief 3-way compares two JSON pointers\n    template<typename RefStringTypeRhs>\n    std::strong_ordering operator<=>(const json_pointer<RefStringTypeRhs>& rhs) const noexcept // *NOPAD*\n    {\n        return  reference_tokens <=> rhs.reference_tokens; // *NOPAD*\n    }\n#else\n    /// @brief compares two JSON pointers for equality\n    /// @sa https://json.nlohmann.me/api/json_pointer/operator_eq/\n    template<typename RefStringTypeLhs, typename RefStringTypeRhs>\n    // NOLINTNEXTLINE(readability-redundant-declaration)\n    friend bool operator==(const json_pointer<RefStringTypeLhs>& lhs,\n                           const json_pointer<RefStringTypeRhs>& rhs) noexcept;\n\n    /// @brief compares JSON pointer and string for equality\n    /// @sa https://json.nlohmann.me/api/json_pointer/operator_eq/\n    template<typename RefStringTypeLhs, typename StringType>\n    // NOLINTNEXTLINE(readability-redundant-declaration)\n    friend bool operator==(const json_pointer<RefStringTypeLhs>& lhs,\n                           const StringType& rhs);\n\n    /// @brief compares string and JSON pointer for equality\n    /// @sa https://json.nlohmann.me/api/json_pointer/operator_eq/\n    template<typename RefStringTypeRhs, typename StringType>\n    // NOLINTNEXTLINE(readability-redundant-declaration)\n    friend bool operator==(const StringType& lhs,\n                           const json_pointer<RefStringTypeRhs>& rhs);\n\n    /// @brief compares two JSON pointers for inequality\n    /// @sa https://json.nlohmann.me/api/json_pointer/operator_ne/\n    template<typename RefStringTypeLhs, typename RefStringTypeRhs>\n    // NOLINTNEXTLINE(readability-redundant-declaration)\n    friend bool operator!=(const json_pointer<RefStringTypeLhs>& lhs,\n                           const json_pointer<RefStringTypeRhs>& rhs) noexcept;\n\n    /// @brief compares JSON pointer and string for inequality\n    /// @sa https://json.nlohmann.me/api/json_pointer/operator_ne/\n    template<typename RefStringTypeLhs, typename StringType>\n    // NOLINTNEXTLINE(readability-redundant-declaration)\n    friend bool operator!=(const json_pointer<RefStringTypeLhs>& lhs,\n                           const StringType& rhs);\n\n    /// @brief compares string and JSON pointer for inequality\n    /// @sa https://json.nlohmann.me/api/json_pointer/operator_ne/\n    template<typename RefStringTypeRhs, typename StringType>\n    // NOLINTNEXTLINE(readability-redundant-declaration)\n    friend bool operator!=(const StringType& lhs,\n                           const json_pointer<RefStringTypeRhs>& rhs);\n\n    /// @brief compares two JSON pointer for less-than\n    template<typename RefStringTypeLhs, typename RefStringTypeRhs>\n    // NOLINTNEXTLINE(readability-redundant-declaration)\n    friend bool operator<(const json_pointer<RefStringTypeLhs>& lhs,\n                          const json_pointer<RefStringTypeRhs>& rhs) noexcept;\n#endif\n\n  private:\n    /// the reference tokens\n    std::vector<string_t> reference_tokens;\n};\n\n#if !JSON_HAS_THREE_WAY_COMPARISON\n// functions cannot be defined inside class due to ODR violations\ntemplate<typename RefStringTypeLhs, typename RefStringTypeRhs>\ninline bool operator==(const json_pointer<RefStringTypeLhs>& lhs,\n                       const json_pointer<RefStringTypeRhs>& rhs) noexcept\n{\n    return lhs.reference_tokens == rhs.reference_tokens;\n}\n\ntemplate<typename RefStringTypeLhs,\n         typename StringType = typename json_pointer<RefStringTypeLhs>::string_t>\nJSON_HEDLEY_DEPRECATED_FOR(3.11.2, operator==(json_pointer, json_pointer))\ninline bool operator==(const json_pointer<RefStringTypeLhs>& lhs,\n                       const StringType& rhs)\n{\n    return lhs == json_pointer<RefStringTypeLhs>(rhs);\n}\n\ntemplate<typename RefStringTypeRhs,\n         typename StringType = typename json_pointer<RefStringTypeRhs>::string_t>\nJSON_HEDLEY_DEPRECATED_FOR(3.11.2, operator==(json_pointer, json_pointer))\ninline bool operator==(const StringType& lhs,\n                       const json_pointer<RefStringTypeRhs>& rhs)\n{\n    return json_pointer<RefStringTypeRhs>(lhs) == rhs;\n}\n\ntemplate<typename RefStringTypeLhs, typename RefStringTypeRhs>\ninline bool operator!=(const json_pointer<RefStringTypeLhs>& lhs,\n                       const json_pointer<RefStringTypeRhs>& rhs) noexcept\n{\n    return !(lhs == rhs);\n}\n\ntemplate<typename RefStringTypeLhs,\n         typename StringType = typename json_pointer<RefStringTypeLhs>::string_t>\nJSON_HEDLEY_DEPRECATED_FOR(3.11.2, operator!=(json_pointer, json_pointer))\ninline bool operator!=(const json_pointer<RefStringTypeLhs>& lhs,\n                       const StringType& rhs)\n{\n    return !(lhs == rhs);\n}\n\ntemplate<typename RefStringTypeRhs,\n         typename StringType = typename json_pointer<RefStringTypeRhs>::string_t>\nJSON_HEDLEY_DEPRECATED_FOR(3.11.2, operator!=(json_pointer, json_pointer))\ninline bool operator!=(const StringType& lhs,\n                       const json_pointer<RefStringTypeRhs>& rhs)\n{\n    return !(lhs == rhs);\n}\n\ntemplate<typename RefStringTypeLhs, typename RefStringTypeRhs>\ninline bool operator<(const json_pointer<RefStringTypeLhs>& lhs,\n                      const json_pointer<RefStringTypeRhs>& rhs) noexcept\n{\n    return lhs.reference_tokens < rhs.reference_tokens;\n}\n#endif\n\nNLOHMANN_JSON_NAMESPACE_END\n\n// #include <nlohmann/detail/json_ref.hpp>\n//     __ _____ _____ _____\n//  __|  |   __|     |   | |  JSON for Modern C++\n// |  |  |__   |  |  | | | |  version 3.11.3\n// |_____|_____|_____|_|___|  https://github.com/nlohmann/json\n//\n// SPDX-FileCopyrightText: 2013-2023 Niels Lohmann <https://nlohmann.me>\n// SPDX-License-Identifier: MIT\n\n\n\n#include <initializer_list>\n#include <utility>\n\n// #include <nlohmann/detail/abi_macros.hpp>\n\n// #include <nlohmann/detail/meta/type_traits.hpp>\n\n\nNLOHMANN_JSON_NAMESPACE_BEGIN\nnamespace detail\n{\n\ntemplate<typename BasicJsonType>\nclass json_ref\n{\n  public:\n    using value_type = BasicJsonType;\n\n    json_ref(value_type&& value)\n        : owned_value(std::move(value))\n    {}\n\n    json_ref(const value_type& value)\n        : value_ref(&value)\n    {}\n\n    json_ref(std::initializer_list<json_ref> init)\n        : owned_value(init)\n    {}\n\n    template <\n        class... Args,\n        enable_if_t<std::is_constructible<value_type, Args...>::value, int> = 0 >\n    json_ref(Args && ... args)\n        : owned_value(std::forward<Args>(args)...)\n    {}\n\n    // class should be movable only\n    json_ref(json_ref&&) noexcept = default;\n    json_ref(const json_ref&) = delete;\n    json_ref& operator=(const json_ref&) = delete;\n    json_ref& operator=(json_ref&&) = delete;\n    ~json_ref() = default;\n\n    value_type moved_or_copied() const\n    {\n        if (value_ref == nullptr)\n        {\n            return std::move(owned_value);\n        }\n        return *value_ref;\n    }\n\n    value_type const& operator*() const\n    {\n        return value_ref ? *value_ref : owned_value;\n    }\n\n    value_type const* operator->() const\n    {\n        return &** this;\n    }\n\n  private:\n    mutable value_type owned_value = nullptr;\n    value_type const* value_ref = nullptr;\n};\n\n}  // namespace detail\nNLOHMANN_JSON_NAMESPACE_END\n\n// #include <nlohmann/detail/macro_scope.hpp>\n\n// #include <nlohmann/detail/string_concat.hpp>\n\n// #include <nlohmann/detail/string_escape.hpp>\n\n// #include <nlohmann/detail/meta/cpp_future.hpp>\n\n// #include <nlohmann/detail/meta/type_traits.hpp>\n\n// #include <nlohmann/detail/output/binary_writer.hpp>\n//     __ _____ _____ _____\n//  __|  |   __|     |   | |  JSON for Modern C++\n// |  |  |__   |  |  | | | |  version 3.11.3\n// |_____|_____|_____|_|___|  https://github.com/nlohmann/json\n//\n// SPDX-FileCopyrightText: 2013-2023 Niels Lohmann <https://nlohmann.me>\n// SPDX-License-Identifier: MIT\n\n\n\n#include <algorithm> // reverse\n#include <array> // array\n#include <map> // map\n#include <cmath> // isnan, isinf\n#include <cstdint> // uint8_t, uint16_t, uint32_t, uint64_t\n#include <cstring> // memcpy\n#include <limits> // numeric_limits\n#include <string> // string\n#include <utility> // move\n#include <vector> // vector\n\n// #include <nlohmann/detail/input/binary_reader.hpp>\n\n// #include <nlohmann/detail/macro_scope.hpp>\n\n// #include <nlohmann/detail/output/output_adapters.hpp>\n//     __ _____ _____ _____\n//  __|  |   __|     |   | |  JSON for Modern C++\n// |  |  |__   |  |  | | | |  version 3.11.3\n// |_____|_____|_____|_|___|  https://github.com/nlohmann/json\n//\n// SPDX-FileCopyrightText: 2013-2023 Niels Lohmann <https://nlohmann.me>\n// SPDX-License-Identifier: MIT\n\n\n\n#include <algorithm> // copy\n#include <cstddef> // size_t\n#include <iterator> // back_inserter\n#include <memory> // shared_ptr, make_shared\n#include <string> // basic_string\n#include <vector> // vector\n\n#ifndef JSON_NO_IO\n    #include <ios>      // streamsize\n    #include <ostream>  // basic_ostream\n#endif  // JSON_NO_IO\n\n// #include <nlohmann/detail/macro_scope.hpp>\n\n\nNLOHMANN_JSON_NAMESPACE_BEGIN\nnamespace detail\n{\n\n/// abstract output adapter interface\ntemplate<typename CharType> struct output_adapter_protocol\n{\n    virtual void write_character(CharType c) = 0;\n    virtual void write_characters(const CharType* s, std::size_t length) = 0;\n    virtual ~output_adapter_protocol() = default;\n\n    output_adapter_protocol() = default;\n    output_adapter_protocol(const output_adapter_protocol&) = default;\n    output_adapter_protocol(output_adapter_protocol&&) noexcept = default;\n    output_adapter_protocol& operator=(const output_adapter_protocol&) = default;\n    output_adapter_protocol& operator=(output_adapter_protocol&&) noexcept = default;\n};\n\n/// a type to simplify interfaces\ntemplate<typename CharType>\nusing output_adapter_t = std::shared_ptr<output_adapter_protocol<CharType>>;\n\n/// output adapter for byte vectors\ntemplate<typename CharType, typename AllocatorType = std::allocator<CharType>>\nclass output_vector_adapter : public output_adapter_protocol<CharType>\n{\n  public:\n    explicit output_vector_adapter(std::vector<CharType, AllocatorType>& vec) noexcept\n        : v(vec)\n    {}\n\n    void write_character(CharType c) override\n    {\n        v.push_back(c);\n    }\n\n    JSON_HEDLEY_NON_NULL(2)\n    void write_characters(const CharType* s, std::size_t length) override\n    {\n        v.insert(v.end(), s, s + length);\n    }\n\n  private:\n    std::vector<CharType, AllocatorType>& v;\n};\n\n#ifndef JSON_NO_IO\n/// output adapter for output streams\ntemplate<typename CharType>\nclass output_stream_adapter : public output_adapter_protocol<CharType>\n{\n  public:\n    explicit output_stream_adapter(std::basic_ostream<CharType>& s) noexcept\n        : stream(s)\n    {}\n\n    void write_character(CharType c) override\n    {\n        stream.put(c);\n    }\n\n    JSON_HEDLEY_NON_NULL(2)\n    void write_characters(const CharType* s, std::size_t length) override\n    {\n        stream.write(s, static_cast<std::streamsize>(length));\n    }\n\n  private:\n    std::basic_ostream<CharType>& stream;\n};\n#endif  // JSON_NO_IO\n\n/// output adapter for basic_string\ntemplate<typename CharType, typename StringType = std::basic_string<CharType>>\nclass output_string_adapter : public output_adapter_protocol<CharType>\n{\n  public:\n    explicit output_string_adapter(StringType& s) noexcept\n        : str(s)\n    {}\n\n    void write_character(CharType c) override\n    {\n        str.push_back(c);\n    }\n\n    JSON_HEDLEY_NON_NULL(2)\n    void write_characters(const CharType* s, std::size_t length) override\n    {\n        str.append(s, length);\n    }\n\n  private:\n    StringType& str;\n};\n\ntemplate<typename CharType, typename StringType = std::basic_string<CharType>>\nclass output_adapter\n{\n  public:\n    template<typename AllocatorType = std::allocator<CharType>>\n    output_adapter(std::vector<CharType, AllocatorType>& vec)\n        : oa(std::make_shared<output_vector_adapter<CharType, AllocatorType>>(vec)) {}\n\n#ifndef JSON_NO_IO\n    output_adapter(std::basic_ostream<CharType>& s)\n        : oa(std::make_shared<output_stream_adapter<CharType>>(s)) {}\n#endif  // JSON_NO_IO\n\n    output_adapter(StringType& s)\n        : oa(std::make_shared<output_string_adapter<CharType, StringType>>(s)) {}\n\n    operator output_adapter_t<CharType>()\n    {\n        return oa;\n    }\n\n  private:\n    output_adapter_t<CharType> oa = nullptr;\n};\n\n}  // namespace detail\nNLOHMANN_JSON_NAMESPACE_END\n\n// #include <nlohmann/detail/string_concat.hpp>\n\n\nNLOHMANN_JSON_NAMESPACE_BEGIN\nnamespace detail\n{\n\n///////////////////\n// binary writer //\n///////////////////\n\n/*!\n@brief serialization to CBOR and MessagePack values\n*/\ntemplate<typename BasicJsonType, typename CharType>\nclass binary_writer\n{\n    using string_t = typename BasicJsonType::string_t;\n    using binary_t = typename BasicJsonType::binary_t;\n    using number_float_t = typename BasicJsonType::number_float_t;\n\n  public:\n    /*!\n    @brief create a binary writer\n\n    @param[in] adapter  output adapter to write to\n    */\n    explicit binary_writer(output_adapter_t<CharType> adapter) : oa(std::move(adapter))\n    {\n        JSON_ASSERT(oa);\n    }\n\n    /*!\n    @param[in] j  JSON value to serialize\n    @pre       j.type() == value_t::object\n    */\n    void write_bson(const BasicJsonType& j)\n    {\n        switch (j.type())\n        {\n            case value_t::object:\n            {\n                write_bson_object(*j.m_data.m_value.object);\n                break;\n            }\n\n            case value_t::null:\n            case value_t::array:\n            case value_t::string:\n            case value_t::boolean:\n            case value_t::number_integer:\n            case value_t::number_unsigned:\n            case value_t::number_float:\n            case value_t::binary:\n            case value_t::discarded:\n            default:\n            {\n                JSON_THROW(type_error::create(317, concat(\"to serialize to BSON, top-level type must be object, but is \", j.type_name()), &j));\n            }\n        }\n    }\n\n    /*!\n    @param[in] j  JSON value to serialize\n    */\n    void write_cbor(const BasicJsonType& j)\n    {\n        switch (j.type())\n        {\n            case value_t::null:\n            {\n                oa->write_character(to_char_type(0xF6));\n                break;\n            }\n\n            case value_t::boolean:\n            {\n                oa->write_character(j.m_data.m_value.boolean\n                                    ? to_char_type(0xF5)\n                                    : to_char_type(0xF4));\n                break;\n            }\n\n            case value_t::number_integer:\n            {\n                if (j.m_data.m_value.number_integer >= 0)\n                {\n                    // CBOR does not differentiate between positive signed\n                    // integers and unsigned integers. Therefore, we used the\n                    // code from the value_t::number_unsigned case here.\n                    if (j.m_data.m_value.number_integer <= 0x17)\n                    {\n                        write_number(static_cast<std::uint8_t>(j.m_data.m_value.number_integer));\n                    }\n                    else if (j.m_data.m_value.number_integer <= (std::numeric_limits<std::uint8_t>::max)())\n                    {\n                        oa->write_character(to_char_type(0x18));\n                        write_number(static_cast<std::uint8_t>(j.m_data.m_value.number_integer));\n                    }\n                    else if (j.m_data.m_value.number_integer <= (std::numeric_limits<std::uint16_t>::max)())\n                    {\n                        oa->write_character(to_char_type(0x19));\n                        write_number(static_cast<std::uint16_t>(j.m_data.m_value.number_integer));\n                    }\n                    else if (j.m_data.m_value.number_integer <= (std::numeric_limits<std::uint32_t>::max)())\n                    {\n                        oa->write_character(to_char_type(0x1A));\n                        write_number(static_cast<std::uint32_t>(j.m_data.m_value.number_integer));\n                    }\n                    else\n                    {\n                        oa->write_character(to_char_type(0x1B));\n                        write_number(static_cast<std::uint64_t>(j.m_data.m_value.number_integer));\n                    }\n                }\n                else\n                {\n                    // The conversions below encode the sign in the first\n                    // byte, and the value is converted to a positive number.\n                    const auto positive_number = -1 - j.m_data.m_value.number_integer;\n                    if (j.m_data.m_value.number_integer >= -24)\n                    {\n                        write_number(static_cast<std::uint8_t>(0x20 + positive_number));\n                    }\n                    else if (positive_number <= (std::numeric_limits<std::uint8_t>::max)())\n                    {\n                        oa->write_character(to_char_type(0x38));\n                        write_number(static_cast<std::uint8_t>(positive_number));\n                    }\n                    else if (positive_number <= (std::numeric_limits<std::uint16_t>::max)())\n                    {\n                        oa->write_character(to_char_type(0x39));\n                        write_number(static_cast<std::uint16_t>(positive_number));\n                    }\n                    else if (positive_number <= (std::numeric_limits<std::uint32_t>::max)())\n                    {\n                        oa->write_character(to_char_type(0x3A));\n                        write_number(static_cast<std::uint32_t>(positive_number));\n                    }\n                    else\n                    {\n                        oa->write_character(to_char_type(0x3B));\n                        write_number(static_cast<std::uint64_t>(positive_number));\n                    }\n                }\n                break;\n            }\n\n            case value_t::number_unsigned:\n            {\n                if (j.m_data.m_value.number_unsigned <= 0x17)\n                {\n                    write_number(static_cast<std::uint8_t>(j.m_data.m_value.number_unsigned));\n                }\n                else if (j.m_data.m_value.number_unsigned <= (std::numeric_limits<std::uint8_t>::max)())\n                {\n                    oa->write_character(to_char_type(0x18));\n                    write_number(static_cast<std::uint8_t>(j.m_data.m_value.number_unsigned));\n                }\n                else if (j.m_data.m_value.number_unsigned <= (std::numeric_limits<std::uint16_t>::max)())\n                {\n                    oa->write_character(to_char_type(0x19));\n                    write_number(static_cast<std::uint16_t>(j.m_data.m_value.number_unsigned));\n                }\n                else if (j.m_data.m_value.number_unsigned <= (std::numeric_limits<std::uint32_t>::max)())\n                {\n                    oa->write_character(to_char_type(0x1A));\n                    write_number(static_cast<std::uint32_t>(j.m_data.m_value.number_unsigned));\n                }\n                else\n                {\n                    oa->write_character(to_char_type(0x1B));\n                    write_number(static_cast<std::uint64_t>(j.m_data.m_value.number_unsigned));\n                }\n                break;\n            }\n\n            case value_t::number_float:\n            {\n                if (std::isnan(j.m_data.m_value.number_float))\n                {\n                    // NaN is 0xf97e00 in CBOR\n                    oa->write_character(to_char_type(0xF9));\n                    oa->write_character(to_char_type(0x7E));\n                    oa->write_character(to_char_type(0x00));\n                }\n                else if (std::isinf(j.m_data.m_value.number_float))\n                {\n                    // Infinity is 0xf97c00, -Infinity is 0xf9fc00\n                    oa->write_character(to_char_type(0xf9));\n                    oa->write_character(j.m_data.m_value.number_float > 0 ? to_char_type(0x7C) : to_char_type(0xFC));\n                    oa->write_character(to_char_type(0x00));\n                }\n                else\n                {\n                    write_compact_float(j.m_data.m_value.number_float, detail::input_format_t::cbor);\n                }\n                break;\n            }\n\n            case value_t::string:\n            {\n                // step 1: write control byte and the string length\n                const auto N = j.m_data.m_value.string->size();\n                if (N <= 0x17)\n                {\n                    write_number(static_cast<std::uint8_t>(0x60 + N));\n                }\n                else if (N <= (std::numeric_limits<std::uint8_t>::max)())\n                {\n                    oa->write_character(to_char_type(0x78));\n                    write_number(static_cast<std::uint8_t>(N));\n                }\n                else if (N <= (std::numeric_limits<std::uint16_t>::max)())\n                {\n                    oa->write_character(to_char_type(0x79));\n                    write_number(static_cast<std::uint16_t>(N));\n                }\n                else if (N <= (std::numeric_limits<std::uint32_t>::max)())\n                {\n                    oa->write_character(to_char_type(0x7A));\n                    write_number(static_cast<std::uint32_t>(N));\n                }\n                // LCOV_EXCL_START\n                else if (N <= (std::numeric_limits<std::uint64_t>::max)())\n                {\n                    oa->write_character(to_char_type(0x7B));\n                    write_number(static_cast<std::uint64_t>(N));\n                }\n                // LCOV_EXCL_STOP\n\n                // step 2: write the string\n                oa->write_characters(\n                    reinterpret_cast<const CharType*>(j.m_data.m_value.string->c_str()),\n                    j.m_data.m_value.string->size());\n                break;\n            }\n\n            case value_t::array:\n            {\n                // step 1: write control byte and the array size\n                const auto N = j.m_data.m_value.array->size();\n                if (N <= 0x17)\n                {\n                    write_number(static_cast<std::uint8_t>(0x80 + N));\n                }\n                else if (N <= (std::numeric_limits<std::uint8_t>::max)())\n                {\n                    oa->write_character(to_char_type(0x98));\n                    write_number(static_cast<std::uint8_t>(N));\n                }\n                else if (N <= (std::numeric_limits<std::uint16_t>::max)())\n                {\n                    oa->write_character(to_char_type(0x99));\n                    write_number(static_cast<std::uint16_t>(N));\n                }\n                else if (N <= (std::numeric_limits<std::uint32_t>::max)())\n                {\n                    oa->write_character(to_char_type(0x9A));\n                    write_number(static_cast<std::uint32_t>(N));\n                }\n                // LCOV_EXCL_START\n                else if (N <= (std::numeric_limits<std::uint64_t>::max)())\n                {\n                    oa->write_character(to_char_type(0x9B));\n                    write_number(static_cast<std::uint64_t>(N));\n                }\n                // LCOV_EXCL_STOP\n\n                // step 2: write each element\n                for (const auto& el : *j.m_data.m_value.array)\n                {\n                    write_cbor(el);\n                }\n                break;\n            }\n\n            case value_t::binary:\n            {\n                if (j.m_data.m_value.binary->has_subtype())\n                {\n                    if (j.m_data.m_value.binary->subtype() <= (std::numeric_limits<std::uint8_t>::max)())\n                    {\n                        write_number(static_cast<std::uint8_t>(0xd8));\n                        write_number(static_cast<std::uint8_t>(j.m_data.m_value.binary->subtype()));\n                    }\n                    else if (j.m_data.m_value.binary->subtype() <= (std::numeric_limits<std::uint16_t>::max)())\n                    {\n                        write_number(static_cast<std::uint8_t>(0xd9));\n                        write_number(static_cast<std::uint16_t>(j.m_data.m_value.binary->subtype()));\n                    }\n                    else if (j.m_data.m_value.binary->subtype() <= (std::numeric_limits<std::uint32_t>::max)())\n                    {\n                        write_number(static_cast<std::uint8_t>(0xda));\n                        write_number(static_cast<std::uint32_t>(j.m_data.m_value.binary->subtype()));\n                    }\n                    else if (j.m_data.m_value.binary->subtype() <= (std::numeric_limits<std::uint64_t>::max)())\n                    {\n                        write_number(static_cast<std::uint8_t>(0xdb));\n                        write_number(static_cast<std::uint64_t>(j.m_data.m_value.binary->subtype()));\n                    }\n                }\n\n                // step 1: write control byte and the binary array size\n                const auto N = j.m_data.m_value.binary->size();\n                if (N <= 0x17)\n                {\n                    write_number(static_cast<std::uint8_t>(0x40 + N));\n                }\n                else if (N <= (std::numeric_limits<std::uint8_t>::max)())\n                {\n                    oa->write_character(to_char_type(0x58));\n                    write_number(static_cast<std::uint8_t>(N));\n                }\n                else if (N <= (std::numeric_limits<std::uint16_t>::max)())\n                {\n                    oa->write_character(to_char_type(0x59));\n                    write_number(static_cast<std::uint16_t>(N));\n                }\n                else if (N <= (std::numeric_limits<std::uint32_t>::max)())\n                {\n                    oa->write_character(to_char_type(0x5A));\n                    write_number(static_cast<std::uint32_t>(N));\n                }\n                // LCOV_EXCL_START\n                else if (N <= (std::numeric_limits<std::uint64_t>::max)())\n                {\n                    oa->write_character(to_char_type(0x5B));\n                    write_number(static_cast<std::uint64_t>(N));\n                }\n                // LCOV_EXCL_STOP\n\n                // step 2: write each element\n                oa->write_characters(\n                    reinterpret_cast<const CharType*>(j.m_data.m_value.binary->data()),\n                    N);\n\n                break;\n            }\n\n            case value_t::object:\n            {\n                // step 1: write control byte and the object size\n                const auto N = j.m_data.m_value.object->size();\n                if (N <= 0x17)\n                {\n                    write_number(static_cast<std::uint8_t>(0xA0 + N));\n                }\n                else if (N <= (std::numeric_limits<std::uint8_t>::max)())\n                {\n                    oa->write_character(to_char_type(0xB8));\n                    write_number(static_cast<std::uint8_t>(N));\n                }\n                else if (N <= (std::numeric_limits<std::uint16_t>::max)())\n                {\n                    oa->write_character(to_char_type(0xB9));\n                    write_number(static_cast<std::uint16_t>(N));\n                }\n                else if (N <= (std::numeric_limits<std::uint32_t>::max)())\n                {\n                    oa->write_character(to_char_type(0xBA));\n                    write_number(static_cast<std::uint32_t>(N));\n                }\n                // LCOV_EXCL_START\n                else if (N <= (std::numeric_limits<std::uint64_t>::max)())\n                {\n                    oa->write_character(to_char_type(0xBB));\n                    write_number(static_cast<std::uint64_t>(N));\n                }\n                // LCOV_EXCL_STOP\n\n                // step 2: write each element\n                for (const auto& el : *j.m_data.m_value.object)\n                {\n                    write_cbor(el.first);\n                    write_cbor(el.second);\n                }\n                break;\n            }\n\n            case value_t::discarded:\n            default:\n                break;\n        }\n    }\n\n    /*!\n    @param[in] j  JSON value to serialize\n    */\n    void write_msgpack(const BasicJsonType& j)\n    {\n        switch (j.type())\n        {\n            case value_t::null: // nil\n            {\n                oa->write_character(to_char_type(0xC0));\n                break;\n            }\n\n            case value_t::boolean: // true and false\n            {\n                oa->write_character(j.m_data.m_value.boolean\n                                    ? to_char_type(0xC3)\n                                    : to_char_type(0xC2));\n                break;\n            }\n\n            case value_t::number_integer:\n            {\n                if (j.m_data.m_value.number_integer >= 0)\n                {\n                    // MessagePack does not differentiate between positive\n                    // signed integers and unsigned integers. Therefore, we used\n                    // the code from the value_t::number_unsigned case here.\n                    if (j.m_data.m_value.number_unsigned < 128)\n                    {\n                        // positive fixnum\n                        write_number(static_cast<std::uint8_t>(j.m_data.m_value.number_integer));\n                    }\n                    else if (j.m_data.m_value.number_unsigned <= (std::numeric_limits<std::uint8_t>::max)())\n                    {\n                        // uint 8\n                        oa->write_character(to_char_type(0xCC));\n                        write_number(static_cast<std::uint8_t>(j.m_data.m_value.number_integer));\n                    }\n                    else if (j.m_data.m_value.number_unsigned <= (std::numeric_limits<std::uint16_t>::max)())\n                    {\n                        // uint 16\n                        oa->write_character(to_char_type(0xCD));\n                        write_number(static_cast<std::uint16_t>(j.m_data.m_value.number_integer));\n                    }\n                    else if (j.m_data.m_value.number_unsigned <= (std::numeric_limits<std::uint32_t>::max)())\n                    {\n                        // uint 32\n                        oa->write_character(to_char_type(0xCE));\n                        write_number(static_cast<std::uint32_t>(j.m_data.m_value.number_integer));\n                    }\n                    else if (j.m_data.m_value.number_unsigned <= (std::numeric_limits<std::uint64_t>::max)())\n                    {\n                        // uint 64\n                        oa->write_character(to_char_type(0xCF));\n                        write_number(static_cast<std::uint64_t>(j.m_data.m_value.number_integer));\n                    }\n                }\n                else\n                {\n                    if (j.m_data.m_value.number_integer >= -32)\n                    {\n                        // negative fixnum\n                        write_number(static_cast<std::int8_t>(j.m_data.m_value.number_integer));\n                    }\n                    else if (j.m_data.m_value.number_integer >= (std::numeric_limits<std::int8_t>::min)() &&\n                             j.m_data.m_value.number_integer <= (std::numeric_limits<std::int8_t>::max)())\n                    {\n                        // int 8\n                        oa->write_character(to_char_type(0xD0));\n                        write_number(static_cast<std::int8_t>(j.m_data.m_value.number_integer));\n                    }\n                    else if (j.m_data.m_value.number_integer >= (std::numeric_limits<std::int16_t>::min)() &&\n                             j.m_data.m_value.number_integer <= (std::numeric_limits<std::int16_t>::max)())\n                    {\n                        // int 16\n                        oa->write_character(to_char_type(0xD1));\n                        write_number(static_cast<std::int16_t>(j.m_data.m_value.number_integer));\n                    }\n                    else if (j.m_data.m_value.number_integer >= (std::numeric_limits<std::int32_t>::min)() &&\n                             j.m_data.m_value.number_integer <= (std::numeric_limits<std::int32_t>::max)())\n                    {\n                        // int 32\n                        oa->write_character(to_char_type(0xD2));\n                        write_number(static_cast<std::int32_t>(j.m_data.m_value.number_integer));\n                    }\n                    else if (j.m_data.m_value.number_integer >= (std::numeric_limits<std::int64_t>::min)() &&\n                             j.m_data.m_value.number_integer <= (std::numeric_limits<std::int64_t>::max)())\n                    {\n                        // int 64\n                        oa->write_character(to_char_type(0xD3));\n                        write_number(static_cast<std::int64_t>(j.m_data.m_value.number_integer));\n                    }\n                }\n                break;\n            }\n\n            case value_t::number_unsigned:\n            {\n                if (j.m_data.m_value.number_unsigned < 128)\n                {\n                    // positive fixnum\n                    write_number(static_cast<std::uint8_t>(j.m_data.m_value.number_integer));\n                }\n                else if (j.m_data.m_value.number_unsigned <= (std::numeric_limits<std::uint8_t>::max)())\n                {\n                    // uint 8\n                    oa->write_character(to_char_type(0xCC));\n                    write_number(static_cast<std::uint8_t>(j.m_data.m_value.number_integer));\n                }\n                else if (j.m_data.m_value.number_unsigned <= (std::numeric_limits<std::uint16_t>::max)())\n                {\n                    // uint 16\n                    oa->write_character(to_char_type(0xCD));\n                    write_number(static_cast<std::uint16_t>(j.m_data.m_value.number_integer));\n                }\n                else if (j.m_data.m_value.number_unsigned <= (std::numeric_limits<std::uint32_t>::max)())\n                {\n                    // uint 32\n                    oa->write_character(to_char_type(0xCE));\n                    write_number(static_cast<std::uint32_t>(j.m_data.m_value.number_integer));\n                }\n                else if (j.m_data.m_value.number_unsigned <= (std::numeric_limits<std::uint64_t>::max)())\n                {\n                    // uint 64\n                    oa->write_character(to_char_type(0xCF));\n                    write_number(static_cast<std::uint64_t>(j.m_data.m_value.number_integer));\n                }\n                break;\n            }\n\n            case value_t::number_float:\n            {\n                write_compact_float(j.m_data.m_value.number_float, detail::input_format_t::msgpack);\n                break;\n            }\n\n            case value_t::string:\n            {\n                // step 1: write control byte and the string length\n                const auto N = j.m_data.m_value.string->size();\n                if (N <= 31)\n                {\n                    // fixstr\n                    write_number(static_cast<std::uint8_t>(0xA0 | N));\n                }\n                else if (N <= (std::numeric_limits<std::uint8_t>::max)())\n                {\n                    // str 8\n                    oa->write_character(to_char_type(0xD9));\n                    write_number(static_cast<std::uint8_t>(N));\n                }\n                else if (N <= (std::numeric_limits<std::uint16_t>::max)())\n                {\n                    // str 16\n                    oa->write_character(to_char_type(0xDA));\n                    write_number(static_cast<std::uint16_t>(N));\n                }\n                else if (N <= (std::numeric_limits<std::uint32_t>::max)())\n                {\n                    // str 32\n                    oa->write_character(to_char_type(0xDB));\n                    write_number(static_cast<std::uint32_t>(N));\n                }\n\n                // step 2: write the string\n                oa->write_characters(\n                    reinterpret_cast<const CharType*>(j.m_data.m_value.string->c_str()),\n                    j.m_data.m_value.string->size());\n                break;\n            }\n\n            case value_t::array:\n            {\n                // step 1: write control byte and the array size\n                const auto N = j.m_data.m_value.array->size();\n                if (N <= 15)\n                {\n                    // fixarray\n                    write_number(static_cast<std::uint8_t>(0x90 | N));\n                }\n                else if (N <= (std::numeric_limits<std::uint16_t>::max)())\n                {\n                    // array 16\n                    oa->write_character(to_char_type(0xDC));\n                    write_number(static_cast<std::uint16_t>(N));\n                }\n                else if (N <= (std::numeric_limits<std::uint32_t>::max)())\n                {\n                    // array 32\n                    oa->write_character(to_char_type(0xDD));\n                    write_number(static_cast<std::uint32_t>(N));\n                }\n\n                // step 2: write each element\n                for (const auto& el : *j.m_data.m_value.array)\n                {\n                    write_msgpack(el);\n                }\n                break;\n            }\n\n            case value_t::binary:\n            {\n                // step 0: determine if the binary type has a set subtype to\n                // determine whether or not to use the ext or fixext types\n                const bool use_ext = j.m_data.m_value.binary->has_subtype();\n\n                // step 1: write control byte and the byte string length\n                const auto N = j.m_data.m_value.binary->size();\n                if (N <= (std::numeric_limits<std::uint8_t>::max)())\n                {\n                    std::uint8_t output_type{};\n                    bool fixed = true;\n                    if (use_ext)\n                    {\n                        switch (N)\n                        {\n                            case 1:\n                                output_type = 0xD4; // fixext 1\n                                break;\n                            case 2:\n                                output_type = 0xD5; // fixext 2\n                                break;\n                            case 4:\n                                output_type = 0xD6; // fixext 4\n                                break;\n                            case 8:\n                                output_type = 0xD7; // fixext 8\n                                break;\n                            case 16:\n                                output_type = 0xD8; // fixext 16\n                                break;\n                            default:\n                                output_type = 0xC7; // ext 8\n                                fixed = false;\n                                break;\n                        }\n\n                    }\n                    else\n                    {\n                        output_type = 0xC4; // bin 8\n                        fixed = false;\n                    }\n\n                    oa->write_character(to_char_type(output_type));\n                    if (!fixed)\n                    {\n                        write_number(static_cast<std::uint8_t>(N));\n                    }\n                }\n                else if (N <= (std::numeric_limits<std::uint16_t>::max)())\n                {\n                    const std::uint8_t output_type = use_ext\n                                                     ? 0xC8 // ext 16\n                                                     : 0xC5; // bin 16\n\n                    oa->write_character(to_char_type(output_type));\n                    write_number(static_cast<std::uint16_t>(N));\n                }\n                else if (N <= (std::numeric_limits<std::uint32_t>::max)())\n                {\n                    const std::uint8_t output_type = use_ext\n                                                     ? 0xC9 // ext 32\n                                                     : 0xC6; // bin 32\n\n                    oa->write_character(to_char_type(output_type));\n                    write_number(static_cast<std::uint32_t>(N));\n                }\n\n                // step 1.5: if this is an ext type, write the subtype\n                if (use_ext)\n                {\n                    write_number(static_cast<std::int8_t>(j.m_data.m_value.binary->subtype()));\n                }\n\n                // step 2: write the byte string\n                oa->write_characters(\n                    reinterpret_cast<const CharType*>(j.m_data.m_value.binary->data()),\n                    N);\n\n                break;\n            }\n\n            case value_t::object:\n            {\n                // step 1: write control byte and the object size\n                const auto N = j.m_data.m_value.object->size();\n                if (N <= 15)\n                {\n                    // fixmap\n                    write_number(static_cast<std::uint8_t>(0x80 | (N & 0xF)));\n                }\n                else if (N <= (std::numeric_limits<std::uint16_t>::max)())\n                {\n                    // map 16\n                    oa->write_character(to_char_type(0xDE));\n                    write_number(static_cast<std::uint16_t>(N));\n                }\n                else if (N <= (std::numeric_limits<std::uint32_t>::max)())\n                {\n                    // map 32\n                    oa->write_character(to_char_type(0xDF));\n                    write_number(static_cast<std::uint32_t>(N));\n                }\n\n                // step 2: write each element\n                for (const auto& el : *j.m_data.m_value.object)\n                {\n                    write_msgpack(el.first);\n                    write_msgpack(el.second);\n                }\n                break;\n            }\n\n            case value_t::discarded:\n            default:\n                break;\n        }\n    }\n\n    /*!\n    @param[in] j  JSON value to serialize\n    @param[in] use_count   whether to use '#' prefixes (optimized format)\n    @param[in] use_type    whether to use '$' prefixes (optimized format)\n    @param[in] add_prefix  whether prefixes need to be used for this value\n    @param[in] use_bjdata  whether write in BJData format, default is false\n    */\n    void write_ubjson(const BasicJsonType& j, const bool use_count,\n                      const bool use_type, const bool add_prefix = true,\n                      const bool use_bjdata = false)\n    {\n        switch (j.type())\n        {\n            case value_t::null:\n            {\n                if (add_prefix)\n                {\n                    oa->write_character(to_char_type('Z'));\n                }\n                break;\n            }\n\n            case value_t::boolean:\n            {\n                if (add_prefix)\n                {\n                    oa->write_character(j.m_data.m_value.boolean\n                                        ? to_char_type('T')\n                                        : to_char_type('F'));\n                }\n                break;\n            }\n\n            case value_t::number_integer:\n            {\n                write_number_with_ubjson_prefix(j.m_data.m_value.number_integer, add_prefix, use_bjdata);\n                break;\n            }\n\n            case value_t::number_unsigned:\n            {\n                write_number_with_ubjson_prefix(j.m_data.m_value.number_unsigned, add_prefix, use_bjdata);\n                break;\n            }\n\n            case value_t::number_float:\n            {\n                write_number_with_ubjson_prefix(j.m_data.m_value.number_float, add_prefix, use_bjdata);\n                break;\n            }\n\n            case value_t::string:\n            {\n                if (add_prefix)\n                {\n                    oa->write_character(to_char_type('S'));\n                }\n                write_number_with_ubjson_prefix(j.m_data.m_value.string->size(), true, use_bjdata);\n                oa->write_characters(\n                    reinterpret_cast<const CharType*>(j.m_data.m_value.string->c_str()),\n                    j.m_data.m_value.string->size());\n                break;\n            }\n\n            case value_t::array:\n            {\n                if (add_prefix)\n                {\n                    oa->write_character(to_char_type('['));\n                }\n\n                bool prefix_required = true;\n                if (use_type && !j.m_data.m_value.array->empty())\n                {\n                    JSON_ASSERT(use_count);\n                    const CharType first_prefix = ubjson_prefix(j.front(), use_bjdata);\n                    const bool same_prefix = std::all_of(j.begin() + 1, j.end(),\n                                                         [this, first_prefix, use_bjdata](const BasicJsonType & v)\n                    {\n                        return ubjson_prefix(v, use_bjdata) == first_prefix;\n                    });\n\n                    std::vector<CharType> bjdx = {'[', '{', 'S', 'H', 'T', 'F', 'N', 'Z'}; // excluded markers in bjdata optimized type\n\n                    if (same_prefix && !(use_bjdata && std::find(bjdx.begin(), bjdx.end(), first_prefix) != bjdx.end()))\n                    {\n                        prefix_required = false;\n                        oa->write_character(to_char_type('$'));\n                        oa->write_character(first_prefix);\n                    }\n                }\n\n                if (use_count)\n                {\n                    oa->write_character(to_char_type('#'));\n                    write_number_with_ubjson_prefix(j.m_data.m_value.array->size(), true, use_bjdata);\n                }\n\n                for (const auto& el : *j.m_data.m_value.array)\n                {\n                    write_ubjson(el, use_count, use_type, prefix_required, use_bjdata);\n                }\n\n                if (!use_count)\n                {\n                    oa->write_character(to_char_type(']'));\n                }\n\n                break;\n            }\n\n            case value_t::binary:\n            {\n                if (add_prefix)\n                {\n                    oa->write_character(to_char_type('['));\n                }\n\n                if (use_type && !j.m_data.m_value.binary->empty())\n                {\n                    JSON_ASSERT(use_count);\n                    oa->write_character(to_char_type('$'));\n                    oa->write_character('U');\n                }\n\n                if (use_count)\n                {\n                    oa->write_character(to_char_type('#'));\n                    write_number_with_ubjson_prefix(j.m_data.m_value.binary->size(), true, use_bjdata);\n                }\n\n                if (use_type)\n                {\n                    oa->write_characters(\n                        reinterpret_cast<const CharType*>(j.m_data.m_value.binary->data()),\n                        j.m_data.m_value.binary->size());\n                }\n                else\n                {\n                    for (size_t i = 0; i < j.m_data.m_value.binary->size(); ++i)\n                    {\n                        oa->write_character(to_char_type('U'));\n                        oa->write_character(j.m_data.m_value.binary->data()[i]);\n                    }\n                }\n\n                if (!use_count)\n                {\n                    oa->write_character(to_char_type(']'));\n                }\n\n                break;\n            }\n\n            case value_t::object:\n            {\n                if (use_bjdata && j.m_data.m_value.object->size() == 3 && j.m_data.m_value.object->find(\"_ArrayType_\") != j.m_data.m_value.object->end() && j.m_data.m_value.object->find(\"_ArraySize_\") != j.m_data.m_value.object->end() && j.m_data.m_value.object->find(\"_ArrayData_\") != j.m_data.m_value.object->end())\n                {\n                    if (!write_bjdata_ndarray(*j.m_data.m_value.object, use_count, use_type))  // decode bjdata ndarray in the JData format (https://github.com/NeuroJSON/jdata)\n                    {\n                        break;\n                    }\n                }\n\n                if (add_prefix)\n                {\n                    oa->write_character(to_char_type('{'));\n                }\n\n                bool prefix_required = true;\n                if (use_type && !j.m_data.m_value.object->empty())\n                {\n                    JSON_ASSERT(use_count);\n                    const CharType first_prefix = ubjson_prefix(j.front(), use_bjdata);\n                    const bool same_prefix = std::all_of(j.begin(), j.end(),\n                                                         [this, first_prefix, use_bjdata](const BasicJsonType & v)\n                    {\n                        return ubjson_prefix(v, use_bjdata) == first_prefix;\n                    });\n\n                    std::vector<CharType> bjdx = {'[', '{', 'S', 'H', 'T', 'F', 'N', 'Z'}; // excluded markers in bjdata optimized type\n\n                    if (same_prefix && !(use_bjdata && std::find(bjdx.begin(), bjdx.end(), first_prefix) != bjdx.end()))\n                    {\n                        prefix_required = false;\n                        oa->write_character(to_char_type('$'));\n                        oa->write_character(first_prefix);\n                    }\n                }\n\n                if (use_count)\n                {\n                    oa->write_character(to_char_type('#'));\n                    write_number_with_ubjson_prefix(j.m_data.m_value.object->size(), true, use_bjdata);\n                }\n\n                for (const auto& el : *j.m_data.m_value.object)\n                {\n                    write_number_with_ubjson_prefix(el.first.size(), true, use_bjdata);\n                    oa->write_characters(\n                        reinterpret_cast<const CharType*>(el.first.c_str()),\n                        el.first.size());\n                    write_ubjson(el.second, use_count, use_type, prefix_required, use_bjdata);\n                }\n\n                if (!use_count)\n                {\n                    oa->write_character(to_char_type('}'));\n                }\n\n                break;\n            }\n\n            case value_t::discarded:\n            default:\n                break;\n        }\n    }\n\n  private:\n    //////////\n    // BSON //\n    //////////\n\n    /*!\n    @return The size of a BSON document entry header, including the id marker\n            and the entry name size (and its null-terminator).\n    */\n    static std::size_t calc_bson_entry_header_size(const string_t& name, const BasicJsonType& j)\n    {\n        const auto it = name.find(static_cast<typename string_t::value_type>(0));\n        if (JSON_HEDLEY_UNLIKELY(it != BasicJsonType::string_t::npos))\n        {\n            JSON_THROW(out_of_range::create(409, concat(\"BSON key cannot contain code point U+0000 (at byte \", std::to_string(it), \")\"), &j));\n            static_cast<void>(j);\n        }\n\n        return /*id*/ 1ul + name.size() + /*zero-terminator*/1u;\n    }\n\n    /*!\n    @brief Writes the given @a element_type and @a name to the output adapter\n    */\n    void write_bson_entry_header(const string_t& name,\n                                 const std::uint8_t element_type)\n    {\n        oa->write_character(to_char_type(element_type)); // boolean\n        oa->write_characters(\n            reinterpret_cast<const CharType*>(name.c_str()),\n            name.size() + 1u);\n    }\n\n    /*!\n    @brief Writes a BSON element with key @a name and boolean value @a value\n    */\n    void write_bson_boolean(const string_t& name,\n                            const bool value)\n    {\n        write_bson_entry_header(name, 0x08);\n        oa->write_character(value ? to_char_type(0x01) : to_char_type(0x00));\n    }\n\n    /*!\n    @brief Writes a BSON element with key @a name and double value @a value\n    */\n    void write_bson_double(const string_t& name,\n                           const double value)\n    {\n        write_bson_entry_header(name, 0x01);\n        write_number<double>(value, true);\n    }\n\n    /*!\n    @return The size of the BSON-encoded string in @a value\n    */\n    static std::size_t calc_bson_string_size(const string_t& value)\n    {\n        return sizeof(std::int32_t) + value.size() + 1ul;\n    }\n\n    /*!\n    @brief Writes a BSON element with key @a name and string value @a value\n    */\n    void write_bson_string(const string_t& name,\n                           const string_t& value)\n    {\n        write_bson_entry_header(name, 0x02);\n\n        write_number<std::int32_t>(static_cast<std::int32_t>(value.size() + 1ul), true);\n        oa->write_characters(\n            reinterpret_cast<const CharType*>(value.c_str()),\n            value.size() + 1);\n    }\n\n    /*!\n    @brief Writes a BSON element with key @a name and null value\n    */\n    void write_bson_null(const string_t& name)\n    {\n        write_bson_entry_header(name, 0x0A);\n    }\n\n    /*!\n    @return The size of the BSON-encoded integer @a value\n    */\n    static std::size_t calc_bson_integer_size(const std::int64_t value)\n    {\n        return (std::numeric_limits<std::int32_t>::min)() <= value && value <= (std::numeric_limits<std::int32_t>::max)()\n               ? sizeof(std::int32_t)\n               : sizeof(std::int64_t);\n    }\n\n    /*!\n    @brief Writes a BSON element with key @a name and integer @a value\n    */\n    void write_bson_integer(const string_t& name,\n                            const std::int64_t value)\n    {\n        if ((std::numeric_limits<std::int32_t>::min)() <= value && value <= (std::numeric_limits<std::int32_t>::max)())\n        {\n            write_bson_entry_header(name, 0x10); // int32\n            write_number<std::int32_t>(static_cast<std::int32_t>(value), true);\n        }\n        else\n        {\n            write_bson_entry_header(name, 0x12); // int64\n            write_number<std::int64_t>(static_cast<std::int64_t>(value), true);\n        }\n    }\n\n    /*!\n    @return The size of the BSON-encoded unsigned integer in @a j\n    */\n    static constexpr std::size_t calc_bson_unsigned_size(const std::uint64_t value) noexcept\n    {\n        return (value <= static_cast<std::uint64_t>((std::numeric_limits<std::int32_t>::max)()))\n               ? sizeof(std::int32_t)\n               : sizeof(std::int64_t);\n    }\n\n    /*!\n    @brief Writes a BSON element with key @a name and unsigned @a value\n    */\n    void write_bson_unsigned(const string_t& name,\n                             const BasicJsonType& j)\n    {\n        if (j.m_data.m_value.number_unsigned <= static_cast<std::uint64_t>((std::numeric_limits<std::int32_t>::max)()))\n        {\n            write_bson_entry_header(name, 0x10 /* int32 */);\n            write_number<std::int32_t>(static_cast<std::int32_t>(j.m_data.m_value.number_unsigned), true);\n        }\n        else if (j.m_data.m_value.number_unsigned <= static_cast<std::uint64_t>((std::numeric_limits<std::int64_t>::max)()))\n        {\n            write_bson_entry_header(name, 0x12 /* int64 */);\n            write_number<std::int64_t>(static_cast<std::int64_t>(j.m_data.m_value.number_unsigned), true);\n        }\n        else\n        {\n            JSON_THROW(out_of_range::create(407, concat(\"integer number \", std::to_string(j.m_data.m_value.number_unsigned), \" cannot be represented by BSON as it does not fit int64\"), &j));\n        }\n    }\n\n    /*!\n    @brief Writes a BSON element with key @a name and object @a value\n    */\n    void write_bson_object_entry(const string_t& name,\n                                 const typename BasicJsonType::object_t& value)\n    {\n        write_bson_entry_header(name, 0x03); // object\n        write_bson_object(value);\n    }\n\n    /*!\n    @return The size of the BSON-encoded array @a value\n    */\n    static std::size_t calc_bson_array_size(const typename BasicJsonType::array_t& value)\n    {\n        std::size_t array_index = 0ul;\n\n        const std::size_t embedded_document_size = std::accumulate(std::begin(value), std::end(value), static_cast<std::size_t>(0), [&array_index](std::size_t result, const typename BasicJsonType::array_t::value_type & el)\n        {\n            return result + calc_bson_element_size(std::to_string(array_index++), el);\n        });\n\n        return sizeof(std::int32_t) + embedded_document_size + 1ul;\n    }\n\n    /*!\n    @return The size of the BSON-encoded binary array @a value\n    */\n    static std::size_t calc_bson_binary_size(const typename BasicJsonType::binary_t& value)\n    {\n        return sizeof(std::int32_t) + value.size() + 1ul;\n    }\n\n    /*!\n    @brief Writes a BSON element with key @a name and array @a value\n    */\n    void write_bson_array(const string_t& name,\n                          const typename BasicJsonType::array_t& value)\n    {\n        write_bson_entry_header(name, 0x04); // array\n        write_number<std::int32_t>(static_cast<std::int32_t>(calc_bson_array_size(value)), true);\n\n        std::size_t array_index = 0ul;\n\n        for (const auto& el : value)\n        {\n            write_bson_element(std::to_string(array_index++), el);\n        }\n\n        oa->write_character(to_char_type(0x00));\n    }\n\n    /*!\n    @brief Writes a BSON element with key @a name and binary value @a value\n    */\n    void write_bson_binary(const string_t& name,\n                           const binary_t& value)\n    {\n        write_bson_entry_header(name, 0x05);\n\n        write_number<std::int32_t>(static_cast<std::int32_t>(value.size()), true);\n        write_number(value.has_subtype() ? static_cast<std::uint8_t>(value.subtype()) : static_cast<std::uint8_t>(0x00));\n\n        oa->write_characters(reinterpret_cast<const CharType*>(value.data()), value.size());\n    }\n\n    /*!\n    @brief Calculates the size necessary to serialize the JSON value @a j with its @a name\n    @return The calculated size for the BSON document entry for @a j with the given @a name.\n    */\n    static std::size_t calc_bson_element_size(const string_t& name,\n            const BasicJsonType& j)\n    {\n        const auto header_size = calc_bson_entry_header_size(name, j);\n        switch (j.type())\n        {\n            case value_t::object:\n                return header_size + calc_bson_object_size(*j.m_data.m_value.object);\n\n            case value_t::array:\n                return header_size + calc_bson_array_size(*j.m_data.m_value.array);\n\n            case value_t::binary:\n                return header_size + calc_bson_binary_size(*j.m_data.m_value.binary);\n\n            case value_t::boolean:\n                return header_size + 1ul;\n\n            case value_t::number_float:\n                return header_size + 8ul;\n\n            case value_t::number_integer:\n                return header_size + calc_bson_integer_size(j.m_data.m_value.number_integer);\n\n            case value_t::number_unsigned:\n                return header_size + calc_bson_unsigned_size(j.m_data.m_value.number_unsigned);\n\n            case value_t::string:\n                return header_size + calc_bson_string_size(*j.m_data.m_value.string);\n\n            case value_t::null:\n                return header_size + 0ul;\n\n            // LCOV_EXCL_START\n            case value_t::discarded:\n            default:\n                JSON_ASSERT(false); // NOLINT(cert-dcl03-c,hicpp-static-assert,misc-static-assert)\n                return 0ul;\n                // LCOV_EXCL_STOP\n        }\n    }\n\n    /*!\n    @brief Serializes the JSON value @a j to BSON and associates it with the\n           key @a name.\n    @param name The name to associate with the JSON entity @a j within the\n                current BSON document\n    */\n    void write_bson_element(const string_t& name,\n                            const BasicJsonType& j)\n    {\n        switch (j.type())\n        {\n            case value_t::object:\n                return write_bson_object_entry(name, *j.m_data.m_value.object);\n\n            case value_t::array:\n                return write_bson_array(name, *j.m_data.m_value.array);\n\n            case value_t::binary:\n                return write_bson_binary(name, *j.m_data.m_value.binary);\n\n            case value_t::boolean:\n                return write_bson_boolean(name, j.m_data.m_value.boolean);\n\n            case value_t::number_float:\n                return write_bson_double(name, j.m_data.m_value.number_float);\n\n            case value_t::number_integer:\n                return write_bson_integer(name, j.m_data.m_value.number_integer);\n\n            case value_t::number_unsigned:\n                return write_bson_unsigned(name, j);\n\n            case value_t::string:\n                return write_bson_string(name, *j.m_data.m_value.string);\n\n            case value_t::null:\n                return write_bson_null(name);\n\n            // LCOV_EXCL_START\n            case value_t::discarded:\n            default:\n                JSON_ASSERT(false); // NOLINT(cert-dcl03-c,hicpp-static-assert,misc-static-assert)\n                return;\n                // LCOV_EXCL_STOP\n        }\n    }\n\n    /*!\n    @brief Calculates the size of the BSON serialization of the given\n           JSON-object @a j.\n    @param[in] value  JSON value to serialize\n    @pre       value.type() == value_t::object\n    */\n    static std::size_t calc_bson_object_size(const typename BasicJsonType::object_t& value)\n    {\n        const std::size_t document_size = std::accumulate(value.begin(), value.end(), static_cast<std::size_t>(0),\n                                          [](size_t result, const typename BasicJsonType::object_t::value_type & el)\n        {\n            return result += calc_bson_element_size(el.first, el.second);\n        });\n\n        return sizeof(std::int32_t) + document_size + 1ul;\n    }\n\n    /*!\n    @param[in] value  JSON value to serialize\n    @pre       value.type() == value_t::object\n    */\n    void write_bson_object(const typename BasicJsonType::object_t& value)\n    {\n        write_number<std::int32_t>(static_cast<std::int32_t>(calc_bson_object_size(value)), true);\n\n        for (const auto& el : value)\n        {\n            write_bson_element(el.first, el.second);\n        }\n\n        oa->write_character(to_char_type(0x00));\n    }\n\n    //////////\n    // CBOR //\n    //////////\n\n    static constexpr CharType get_cbor_float_prefix(float /*unused*/)\n    {\n        return to_char_type(0xFA);  // Single-Precision Float\n    }\n\n    static constexpr CharType get_cbor_float_prefix(double /*unused*/)\n    {\n        return to_char_type(0xFB);  // Double-Precision Float\n    }\n\n    /////////////\n    // MsgPack //\n    /////////////\n\n    static constexpr CharType get_msgpack_float_prefix(float /*unused*/)\n    {\n        return to_char_type(0xCA);  // float 32\n    }\n\n    static constexpr CharType get_msgpack_float_prefix(double /*unused*/)\n    {\n        return to_char_type(0xCB);  // float 64\n    }\n\n    ////////////\n    // UBJSON //\n    ////////////\n\n    // UBJSON: write number (floating point)\n    template<typename NumberType, typename std::enable_if<\n                 std::is_floating_point<NumberType>::value, int>::type = 0>\n    void write_number_with_ubjson_prefix(const NumberType n,\n                                         const bool add_prefix,\n                                         const bool use_bjdata)\n    {\n        if (add_prefix)\n        {\n            oa->write_character(get_ubjson_float_prefix(n));\n        }\n        write_number(n, use_bjdata);\n    }\n\n    // UBJSON: write number (unsigned integer)\n    template<typename NumberType, typename std::enable_if<\n                 std::is_unsigned<NumberType>::value, int>::type = 0>\n    void write_number_with_ubjson_prefix(const NumberType n,\n                                         const bool add_prefix,\n                                         const bool use_bjdata)\n    {\n        if (n <= static_cast<std::uint64_t>((std::numeric_limits<std::int8_t>::max)()))\n        {\n            if (add_prefix)\n            {\n                oa->write_character(to_char_type('i'));  // int8\n            }\n            write_number(static_cast<std::uint8_t>(n), use_bjdata);\n        }\n        else if (n <= (std::numeric_limits<std::uint8_t>::max)())\n        {\n            if (add_prefix)\n            {\n                oa->write_character(to_char_type('U'));  // uint8\n            }\n            write_number(static_cast<std::uint8_t>(n), use_bjdata);\n        }\n        else if (n <= static_cast<std::uint64_t>((std::numeric_limits<std::int16_t>::max)()))\n        {\n            if (add_prefix)\n            {\n                oa->write_character(to_char_type('I'));  // int16\n            }\n            write_number(static_cast<std::int16_t>(n), use_bjdata);\n        }\n        else if (use_bjdata && n <= static_cast<uint64_t>((std::numeric_limits<uint16_t>::max)()))\n        {\n            if (add_prefix)\n            {\n                oa->write_character(to_char_type('u'));  // uint16 - bjdata only\n            }\n            write_number(static_cast<std::uint16_t>(n), use_bjdata);\n        }\n        else if (n <= static_cast<std::uint64_t>((std::numeric_limits<std::int32_t>::max)()))\n        {\n            if (add_prefix)\n            {\n                oa->write_character(to_char_type('l'));  // int32\n            }\n            write_number(static_cast<std::int32_t>(n), use_bjdata);\n        }\n        else if (use_bjdata && n <= static_cast<uint64_t>((std::numeric_limits<uint32_t>::max)()))\n        {\n            if (add_prefix)\n            {\n                oa->write_character(to_char_type('m'));  // uint32 - bjdata only\n            }\n            write_number(static_cast<std::uint32_t>(n), use_bjdata);\n        }\n        else if (n <= static_cast<std::uint64_t>((std::numeric_limits<std::int64_t>::max)()))\n        {\n            if (add_prefix)\n            {\n                oa->write_character(to_char_type('L'));  // int64\n            }\n            write_number(static_cast<std::int64_t>(n), use_bjdata);\n        }\n        else if (use_bjdata && n <= (std::numeric_limits<uint64_t>::max)())\n        {\n            if (add_prefix)\n            {\n                oa->write_character(to_char_type('M'));  // uint64 - bjdata only\n            }\n            write_number(static_cast<std::uint64_t>(n), use_bjdata);\n        }\n        else\n        {\n            if (add_prefix)\n            {\n                oa->write_character(to_char_type('H'));  // high-precision number\n            }\n\n            const auto number = BasicJsonType(n).dump();\n            write_number_with_ubjson_prefix(number.size(), true, use_bjdata);\n            for (std::size_t i = 0; i < number.size(); ++i)\n            {\n                oa->write_character(to_char_type(static_cast<std::uint8_t>(number[i])));\n            }\n        }\n    }\n\n    // UBJSON: write number (signed integer)\n    template < typename NumberType, typename std::enable_if <\n                   std::is_signed<NumberType>::value&&\n                   !std::is_floating_point<NumberType>::value, int >::type = 0 >\n    void write_number_with_ubjson_prefix(const NumberType n,\n                                         const bool add_prefix,\n                                         const bool use_bjdata)\n    {\n        if ((std::numeric_limits<std::int8_t>::min)() <= n && n <= (std::numeric_limits<std::int8_t>::max)())\n        {\n            if (add_prefix)\n            {\n                oa->write_character(to_char_type('i'));  // int8\n            }\n            write_number(static_cast<std::int8_t>(n), use_bjdata);\n        }\n        else if (static_cast<std::int64_t>((std::numeric_limits<std::uint8_t>::min)()) <= n && n <= static_cast<std::int64_t>((std::numeric_limits<std::uint8_t>::max)()))\n        {\n            if (add_prefix)\n            {\n                oa->write_character(to_char_type('U'));  // uint8\n            }\n            write_number(static_cast<std::uint8_t>(n), use_bjdata);\n        }\n        else if ((std::numeric_limits<std::int16_t>::min)() <= n && n <= (std::numeric_limits<std::int16_t>::max)())\n        {\n            if (add_prefix)\n            {\n                oa->write_character(to_char_type('I'));  // int16\n            }\n            write_number(static_cast<std::int16_t>(n), use_bjdata);\n        }\n        else if (use_bjdata && (static_cast<std::int64_t>((std::numeric_limits<std::uint16_t>::min)()) <= n && n <= static_cast<std::int64_t>((std::numeric_limits<std::uint16_t>::max)())))\n        {\n            if (add_prefix)\n            {\n                oa->write_character(to_char_type('u'));  // uint16 - bjdata only\n            }\n            write_number(static_cast<uint16_t>(n), use_bjdata);\n        }\n        else if ((std::numeric_limits<std::int32_t>::min)() <= n && n <= (std::numeric_limits<std::int32_t>::max)())\n        {\n            if (add_prefix)\n            {\n                oa->write_character(to_char_type('l'));  // int32\n            }\n            write_number(static_cast<std::int32_t>(n), use_bjdata);\n        }\n        else if (use_bjdata && (static_cast<std::int64_t>((std::numeric_limits<std::uint32_t>::min)()) <= n && n <= static_cast<std::int64_t>((std::numeric_limits<std::uint32_t>::max)())))\n        {\n            if (add_prefix)\n            {\n                oa->write_character(to_char_type('m'));  // uint32 - bjdata only\n            }\n            write_number(static_cast<uint32_t>(n), use_bjdata);\n        }\n        else if ((std::numeric_limits<std::int64_t>::min)() <= n && n <= (std::numeric_limits<std::int64_t>::max)())\n        {\n            if (add_prefix)\n            {\n                oa->write_character(to_char_type('L'));  // int64\n            }\n            write_number(static_cast<std::int64_t>(n), use_bjdata);\n        }\n        // LCOV_EXCL_START\n        else\n        {\n            if (add_prefix)\n            {\n                oa->write_character(to_char_type('H'));  // high-precision number\n            }\n\n            const auto number = BasicJsonType(n).dump();\n            write_number_with_ubjson_prefix(number.size(), true, use_bjdata);\n            for (std::size_t i = 0; i < number.size(); ++i)\n            {\n                oa->write_character(to_char_type(static_cast<std::uint8_t>(number[i])));\n            }\n        }\n        // LCOV_EXCL_STOP\n    }\n\n    /*!\n    @brief determine the type prefix of container values\n    */\n    CharType ubjson_prefix(const BasicJsonType& j, const bool use_bjdata) const noexcept\n    {\n        switch (j.type())\n        {\n            case value_t::null:\n                return 'Z';\n\n            case value_t::boolean:\n                return j.m_data.m_value.boolean ? 'T' : 'F';\n\n            case value_t::number_integer:\n            {\n                if ((std::numeric_limits<std::int8_t>::min)() <= j.m_data.m_value.number_integer && j.m_data.m_value.number_integer <= (std::numeric_limits<std::int8_t>::max)())\n                {\n                    return 'i';\n                }\n                if ((std::numeric_limits<std::uint8_t>::min)() <= j.m_data.m_value.number_integer && j.m_data.m_value.number_integer <= (std::numeric_limits<std::uint8_t>::max)())\n                {\n                    return 'U';\n                }\n                if ((std::numeric_limits<std::int16_t>::min)() <= j.m_data.m_value.number_integer && j.m_data.m_value.number_integer <= (std::numeric_limits<std::int16_t>::max)())\n                {\n                    return 'I';\n                }\n                if (use_bjdata && ((std::numeric_limits<std::uint16_t>::min)() <= j.m_data.m_value.number_integer && j.m_data.m_value.number_integer <= (std::numeric_limits<std::uint16_t>::max)()))\n                {\n                    return 'u';\n                }\n                if ((std::numeric_limits<std::int32_t>::min)() <= j.m_data.m_value.number_integer && j.m_data.m_value.number_integer <= (std::numeric_limits<std::int32_t>::max)())\n                {\n                    return 'l';\n                }\n                if (use_bjdata && ((std::numeric_limits<std::uint32_t>::min)() <= j.m_data.m_value.number_integer && j.m_data.m_value.number_integer <= (std::numeric_limits<std::uint32_t>::max)()))\n                {\n                    return 'm';\n                }\n                if ((std::numeric_limits<std::int64_t>::min)() <= j.m_data.m_value.number_integer && j.m_data.m_value.number_integer <= (std::numeric_limits<std::int64_t>::max)())\n                {\n                    return 'L';\n                }\n                // anything else is treated as high-precision number\n                return 'H'; // LCOV_EXCL_LINE\n            }\n\n            case value_t::number_unsigned:\n            {\n                if (j.m_data.m_value.number_unsigned <= static_cast<std::uint64_t>((std::numeric_limits<std::int8_t>::max)()))\n                {\n                    return 'i';\n                }\n                if (j.m_data.m_value.number_unsigned <= static_cast<std::uint64_t>((std::numeric_limits<std::uint8_t>::max)()))\n                {\n                    return 'U';\n                }\n                if (j.m_data.m_value.number_unsigned <= static_cast<std::uint64_t>((std::numeric_limits<std::int16_t>::max)()))\n                {\n                    return 'I';\n                }\n                if (use_bjdata && j.m_data.m_value.number_unsigned <= static_cast<std::uint64_t>((std::numeric_limits<std::uint16_t>::max)()))\n                {\n                    return 'u';\n                }\n                if (j.m_data.m_value.number_unsigned <= static_cast<std::uint64_t>((std::numeric_limits<std::int32_t>::max)()))\n                {\n                    return 'l';\n                }\n                if (use_bjdata && j.m_data.m_value.number_unsigned <= static_cast<std::uint64_t>((std::numeric_limits<std::uint32_t>::max)()))\n                {\n                    return 'm';\n                }\n                if (j.m_data.m_value.number_unsigned <= static_cast<std::uint64_t>((std::numeric_limits<std::int64_t>::max)()))\n                {\n                    return 'L';\n                }\n                if (use_bjdata && j.m_data.m_value.number_unsigned <= (std::numeric_limits<std::uint64_t>::max)())\n                {\n                    return 'M';\n                }\n                // anything else is treated as high-precision number\n                return 'H'; // LCOV_EXCL_LINE\n            }\n\n            case value_t::number_float:\n                return get_ubjson_float_prefix(j.m_data.m_value.number_float);\n\n            case value_t::string:\n                return 'S';\n\n            case value_t::array: // fallthrough\n            case value_t::binary:\n                return '[';\n\n            case value_t::object:\n                return '{';\n\n            case value_t::discarded:\n            default:  // discarded values\n                return 'N';\n        }\n    }\n\n    static constexpr CharType get_ubjson_float_prefix(float /*unused*/)\n    {\n        return 'd';  // float 32\n    }\n\n    static constexpr CharType get_ubjson_float_prefix(double /*unused*/)\n    {\n        return 'D';  // float 64\n    }\n\n    /*!\n    @return false if the object is successfully converted to a bjdata ndarray, true if the type or size is invalid\n    */\n    bool write_bjdata_ndarray(const typename BasicJsonType::object_t& value, const bool use_count, const bool use_type)\n    {\n        std::map<string_t, CharType> bjdtype = {{\"uint8\", 'U'},  {\"int8\", 'i'},  {\"uint16\", 'u'}, {\"int16\", 'I'},\n            {\"uint32\", 'm'}, {\"int32\", 'l'}, {\"uint64\", 'M'}, {\"int64\", 'L'}, {\"single\", 'd'}, {\"double\", 'D'}, {\"char\", 'C'}\n        };\n\n        string_t key = \"_ArrayType_\";\n        auto it = bjdtype.find(static_cast<string_t>(value.at(key)));\n        if (it == bjdtype.end())\n        {\n            return true;\n        }\n        CharType dtype = it->second;\n\n        key = \"_ArraySize_\";\n        std::size_t len = (value.at(key).empty() ? 0 : 1);\n        for (const auto& el : value.at(key))\n        {\n            len *= static_cast<std::size_t>(el.m_data.m_value.number_unsigned);\n        }\n\n        key = \"_ArrayData_\";\n        if (value.at(key).size() != len)\n        {\n            return true;\n        }\n\n        oa->write_character('[');\n        oa->write_character('$');\n        oa->write_character(dtype);\n        oa->write_character('#');\n\n        key = \"_ArraySize_\";\n        write_ubjson(value.at(key), use_count, use_type, true,  true);\n\n        key = \"_ArrayData_\";\n        if (dtype == 'U' || dtype == 'C')\n        {\n            for (const auto& el : value.at(key))\n            {\n                write_number(static_cast<std::uint8_t>(el.m_data.m_value.number_unsigned), true);\n            }\n        }\n        else if (dtype == 'i')\n        {\n            for (const auto& el : value.at(key))\n            {\n                write_number(static_cast<std::int8_t>(el.m_data.m_value.number_integer), true);\n            }\n        }\n        else if (dtype == 'u')\n        {\n            for (const auto& el : value.at(key))\n            {\n                write_number(static_cast<std::uint16_t>(el.m_data.m_value.number_unsigned), true);\n            }\n        }\n        else if (dtype == 'I')\n        {\n            for (const auto& el : value.at(key))\n            {\n                write_number(static_cast<std::int16_t>(el.m_data.m_value.number_integer), true);\n            }\n        }\n        else if (dtype == 'm')\n        {\n            for (const auto& el : value.at(key))\n            {\n                write_number(static_cast<std::uint32_t>(el.m_data.m_value.number_unsigned), true);\n            }\n        }\n        else if (dtype == 'l')\n        {\n            for (const auto& el : value.at(key))\n            {\n                write_number(static_cast<std::int32_t>(el.m_data.m_value.number_integer), true);\n            }\n        }\n        else if (dtype == 'M')\n        {\n            for (const auto& el : value.at(key))\n            {\n                write_number(static_cast<std::uint64_t>(el.m_data.m_value.number_unsigned), true);\n            }\n        }\n        else if (dtype == 'L')\n        {\n            for (const auto& el : value.at(key))\n            {\n                write_number(static_cast<std::int64_t>(el.m_data.m_value.number_integer), true);\n            }\n        }\n        else if (dtype == 'd')\n        {\n            for (const auto& el : value.at(key))\n            {\n                write_number(static_cast<float>(el.m_data.m_value.number_float), true);\n            }\n        }\n        else if (dtype == 'D')\n        {\n            for (const auto& el : value.at(key))\n            {\n                write_number(static_cast<double>(el.m_data.m_value.number_float), true);\n            }\n        }\n        return false;\n    }\n\n    ///////////////////////\n    // Utility functions //\n    ///////////////////////\n\n    /*\n    @brief write a number to output input\n    @param[in] n number of type @a NumberType\n    @param[in] OutputIsLittleEndian Set to true if output data is\n                                 required to be little endian\n    @tparam NumberType the type of the number\n\n    @note This function needs to respect the system's endianness, because bytes\n          in CBOR, MessagePack, and UBJSON are stored in network order (big\n          endian) and therefore need reordering on little endian systems.\n          On the other hand, BSON and BJData use little endian and should reorder\n          on big endian systems.\n    */\n    template<typename NumberType>\n    void write_number(const NumberType n, const bool OutputIsLittleEndian = false)\n    {\n        // step 1: write number to array of length NumberType\n        std::array<CharType, sizeof(NumberType)> vec{};\n        std::memcpy(vec.data(), &n, sizeof(NumberType));\n\n        // step 2: write array to output (with possible reordering)\n        if (is_little_endian != OutputIsLittleEndian)\n        {\n            // reverse byte order prior to conversion if necessary\n            std::reverse(vec.begin(), vec.end());\n        }\n\n        oa->write_characters(vec.data(), sizeof(NumberType));\n    }\n\n    void write_compact_float(const number_float_t n, detail::input_format_t format)\n    {\n#ifdef __GNUC__\n#pragma GCC diagnostic push\n#pragma GCC diagnostic ignored \"-Wfloat-equal\"\n#endif\n        if (static_cast<double>(n) >= static_cast<double>(std::numeric_limits<float>::lowest()) &&\n                static_cast<double>(n) <= static_cast<double>((std::numeric_limits<float>::max)()) &&\n                static_cast<double>(static_cast<float>(n)) == static_cast<double>(n))\n        {\n            oa->write_character(format == detail::input_format_t::cbor\n                                ? get_cbor_float_prefix(static_cast<float>(n))\n                                : get_msgpack_float_prefix(static_cast<float>(n)));\n            write_number(static_cast<float>(n));\n        }\n        else\n        {\n            oa->write_character(format == detail::input_format_t::cbor\n                                ? get_cbor_float_prefix(n)\n                                : get_msgpack_float_prefix(n));\n            write_number(n);\n        }\n#ifdef __GNUC__\n#pragma GCC diagnostic pop\n#endif\n    }\n\n  public:\n    // The following to_char_type functions are implement the conversion\n    // between uint8_t and CharType. In case CharType is not unsigned,\n    // such a conversion is required to allow values greater than 128.\n    // See <https://github.com/nlohmann/json/issues/1286> for a discussion.\n    template < typename C = CharType,\n               enable_if_t < std::is_signed<C>::value && std::is_signed<char>::value > * = nullptr >\n    static constexpr CharType to_char_type(std::uint8_t x) noexcept\n    {\n        return *reinterpret_cast<char*>(&x);\n    }\n\n    template < typename C = CharType,\n               enable_if_t < std::is_signed<C>::value && std::is_unsigned<char>::value > * = nullptr >\n    static CharType to_char_type(std::uint8_t x) noexcept\n    {\n        static_assert(sizeof(std::uint8_t) == sizeof(CharType), \"size of CharType must be equal to std::uint8_t\");\n        static_assert(std::is_trivial<CharType>::value, \"CharType must be trivial\");\n        CharType result;\n        std::memcpy(&result, &x, sizeof(x));\n        return result;\n    }\n\n    template<typename C = CharType,\n             enable_if_t<std::is_unsigned<C>::value>* = nullptr>\n    static constexpr CharType to_char_type(std::uint8_t x) noexcept\n    {\n        return x;\n    }\n\n    template < typename InputCharType, typename C = CharType,\n               enable_if_t <\n                   std::is_signed<C>::value &&\n                   std::is_signed<char>::value &&\n                   std::is_same<char, typename std::remove_cv<InputCharType>::type>::value\n                   > * = nullptr >\n    static constexpr CharType to_char_type(InputCharType x) noexcept\n    {\n        return x;\n    }\n\n  private:\n    /// whether we can assume little endianness\n    const bool is_little_endian = little_endianness();\n\n    /// the output\n    output_adapter_t<CharType> oa = nullptr;\n};\n\n}  // namespace detail\nNLOHMANN_JSON_NAMESPACE_END\n\n// #include <nlohmann/detail/output/output_adapters.hpp>\n\n// #include <nlohmann/detail/output/serializer.hpp>\n//     __ _____ _____ _____\n//  __|  |   __|     |   | |  JSON for Modern C++\n// |  |  |__   |  |  | | | |  version 3.11.3\n// |_____|_____|_____|_|___|  https://github.com/nlohmann/json\n//\n// SPDX-FileCopyrightText: 2008-2009 Björn Hoehrmann <bjoern@hoehrmann.de>\n// SPDX-FileCopyrightText: 2013-2023 Niels Lohmann <https://nlohmann.me>\n// SPDX-License-Identifier: MIT\n\n\n\n#include <algorithm> // reverse, remove, fill, find, none_of\n#include <array> // array\n#include <clocale> // localeconv, lconv\n#include <cmath> // labs, isfinite, isnan, signbit\n#include <cstddef> // size_t, ptrdiff_t\n#include <cstdint> // uint8_t\n#include <cstdio> // snprintf\n#include <limits> // numeric_limits\n#include <string> // string, char_traits\n#include <iomanip> // setfill, setw\n#include <type_traits> // is_same\n#include <utility> // move\n\n// #include <nlohmann/detail/conversions/to_chars.hpp>\n//     __ _____ _____ _____\n//  __|  |   __|     |   | |  JSON for Modern C++\n// |  |  |__   |  |  | | | |  version 3.11.3\n// |_____|_____|_____|_|___|  https://github.com/nlohmann/json\n//\n// SPDX-FileCopyrightText: 2009 Florian Loitsch <https://florian.loitsch.com/>\n// SPDX-FileCopyrightText: 2013-2023 Niels Lohmann <https://nlohmann.me>\n// SPDX-License-Identifier: MIT\n\n\n\n#include <array> // array\n#include <cmath>   // signbit, isfinite\n#include <cstdint> // intN_t, uintN_t\n#include <cstring> // memcpy, memmove\n#include <limits> // numeric_limits\n#include <type_traits> // conditional\n\n// #include <nlohmann/detail/macro_scope.hpp>\n\n\nNLOHMANN_JSON_NAMESPACE_BEGIN\nnamespace detail\n{\n\n/*!\n@brief implements the Grisu2 algorithm for binary to decimal floating-point\nconversion.\n\nThis implementation is a slightly modified version of the reference\nimplementation which may be obtained from\nhttp://florian.loitsch.com/publications (bench.tar.gz).\n\nThe code is distributed under the MIT license, Copyright (c) 2009 Florian Loitsch.\n\nFor a detailed description of the algorithm see:\n\n[1] Loitsch, \"Printing Floating-Point Numbers Quickly and Accurately with\n    Integers\", Proceedings of the ACM SIGPLAN 2010 Conference on Programming\n    Language Design and Implementation, PLDI 2010\n[2] Burger, Dybvig, \"Printing Floating-Point Numbers Quickly and Accurately\",\n    Proceedings of the ACM SIGPLAN 1996 Conference on Programming Language\n    Design and Implementation, PLDI 1996\n*/\nnamespace dtoa_impl\n{\n\ntemplate<typename Target, typename Source>\nTarget reinterpret_bits(const Source source)\n{\n    static_assert(sizeof(Target) == sizeof(Source), \"size mismatch\");\n\n    Target target;\n    std::memcpy(&target, &source, sizeof(Source));\n    return target;\n}\n\nstruct diyfp // f * 2^e\n{\n    static constexpr int kPrecision = 64; // = q\n\n    std::uint64_t f = 0;\n    int e = 0;\n\n    constexpr diyfp(std::uint64_t f_, int e_) noexcept : f(f_), e(e_) {}\n\n    /*!\n    @brief returns x - y\n    @pre x.e == y.e and x.f >= y.f\n    */\n    static diyfp sub(const diyfp& x, const diyfp& y) noexcept\n    {\n        JSON_ASSERT(x.e == y.e);\n        JSON_ASSERT(x.f >= y.f);\n\n        return {x.f - y.f, x.e};\n    }\n\n    /*!\n    @brief returns x * y\n    @note The result is rounded. (Only the upper q bits are returned.)\n    */\n    static diyfp mul(const diyfp& x, const diyfp& y) noexcept\n    {\n        static_assert(kPrecision == 64, \"internal error\");\n\n        // Computes:\n        //  f = round((x.f * y.f) / 2^q)\n        //  e = x.e + y.e + q\n\n        // Emulate the 64-bit * 64-bit multiplication:\n        //\n        // p = u * v\n        //   = (u_lo + 2^32 u_hi) (v_lo + 2^32 v_hi)\n        //   = (u_lo v_lo         ) + 2^32 ((u_lo v_hi         ) + (u_hi v_lo         )) + 2^64 (u_hi v_hi         )\n        //   = (p0                ) + 2^32 ((p1                ) + (p2                )) + 2^64 (p3                )\n        //   = (p0_lo + 2^32 p0_hi) + 2^32 ((p1_lo + 2^32 p1_hi) + (p2_lo + 2^32 p2_hi)) + 2^64 (p3                )\n        //   = (p0_lo             ) + 2^32 (p0_hi + p1_lo + p2_lo                      ) + 2^64 (p1_hi + p2_hi + p3)\n        //   = (p0_lo             ) + 2^32 (Q                                          ) + 2^64 (H                 )\n        //   = (p0_lo             ) + 2^32 (Q_lo + 2^32 Q_hi                           ) + 2^64 (H                 )\n        //\n        // (Since Q might be larger than 2^32 - 1)\n        //\n        //   = (p0_lo + 2^32 Q_lo) + 2^64 (Q_hi + H)\n        //\n        // (Q_hi + H does not overflow a 64-bit int)\n        //\n        //   = p_lo + 2^64 p_hi\n\n        const std::uint64_t u_lo = x.f & 0xFFFFFFFFu;\n        const std::uint64_t u_hi = x.f >> 32u;\n        const std::uint64_t v_lo = y.f & 0xFFFFFFFFu;\n        const std::uint64_t v_hi = y.f >> 32u;\n\n        const std::uint64_t p0 = u_lo * v_lo;\n        const std::uint64_t p1 = u_lo * v_hi;\n        const std::uint64_t p2 = u_hi * v_lo;\n        const std::uint64_t p3 = u_hi * v_hi;\n\n        const std::uint64_t p0_hi = p0 >> 32u;\n        const std::uint64_t p1_lo = p1 & 0xFFFFFFFFu;\n        const std::uint64_t p1_hi = p1 >> 32u;\n        const std::uint64_t p2_lo = p2 & 0xFFFFFFFFu;\n        const std::uint64_t p2_hi = p2 >> 32u;\n\n        std::uint64_t Q = p0_hi + p1_lo + p2_lo;\n\n        // The full product might now be computed as\n        //\n        // p_hi = p3 + p2_hi + p1_hi + (Q >> 32)\n        // p_lo = p0_lo + (Q << 32)\n        //\n        // But in this particular case here, the full p_lo is not required.\n        // Effectively we only need to add the highest bit in p_lo to p_hi (and\n        // Q_hi + 1 does not overflow).\n\n        Q += std::uint64_t{1} << (64u - 32u - 1u); // round, ties up\n\n        const std::uint64_t h = p3 + p2_hi + p1_hi + (Q >> 32u);\n\n        return {h, x.e + y.e + 64};\n    }\n\n    /*!\n    @brief normalize x such that the significand is >= 2^(q-1)\n    @pre x.f != 0\n    */\n    static diyfp normalize(diyfp x) noexcept\n    {\n        JSON_ASSERT(x.f != 0);\n\n        while ((x.f >> 63u) == 0)\n        {\n            x.f <<= 1u;\n            x.e--;\n        }\n\n        return x;\n    }\n\n    /*!\n    @brief normalize x such that the result has the exponent E\n    @pre e >= x.e and the upper e - x.e bits of x.f must be zero.\n    */\n    static diyfp normalize_to(const diyfp& x, const int target_exponent) noexcept\n    {\n        const int delta = x.e - target_exponent;\n\n        JSON_ASSERT(delta >= 0);\n        JSON_ASSERT(((x.f << delta) >> delta) == x.f);\n\n        return {x.f << delta, target_exponent};\n    }\n};\n\nstruct boundaries\n{\n    diyfp w;\n    diyfp minus;\n    diyfp plus;\n};\n\n/*!\nCompute the (normalized) diyfp representing the input number 'value' and its\nboundaries.\n\n@pre value must be finite and positive\n*/\ntemplate<typename FloatType>\nboundaries compute_boundaries(FloatType value)\n{\n    JSON_ASSERT(std::isfinite(value));\n    JSON_ASSERT(value > 0);\n\n    // Convert the IEEE representation into a diyfp.\n    //\n    // If v is denormal:\n    //      value = 0.F * 2^(1 - bias) = (          F) * 2^(1 - bias - (p-1))\n    // If v is normalized:\n    //      value = 1.F * 2^(E - bias) = (2^(p-1) + F) * 2^(E - bias - (p-1))\n\n    static_assert(std::numeric_limits<FloatType>::is_iec559,\n                  \"internal error: dtoa_short requires an IEEE-754 floating-point implementation\");\n\n    constexpr int      kPrecision = std::numeric_limits<FloatType>::digits; // = p (includes the hidden bit)\n    constexpr int      kBias      = std::numeric_limits<FloatType>::max_exponent - 1 + (kPrecision - 1);\n    constexpr int      kMinExp    = 1 - kBias;\n    constexpr std::uint64_t kHiddenBit = std::uint64_t{1} << (kPrecision - 1); // = 2^(p-1)\n\n    using bits_type = typename std::conditional<kPrecision == 24, std::uint32_t, std::uint64_t >::type;\n\n    const auto bits = static_cast<std::uint64_t>(reinterpret_bits<bits_type>(value));\n    const std::uint64_t E = bits >> (kPrecision - 1);\n    const std::uint64_t F = bits & (kHiddenBit - 1);\n\n    const bool is_denormal = E == 0;\n    const diyfp v = is_denormal\n                    ? diyfp(F, kMinExp)\n                    : diyfp(F + kHiddenBit, static_cast<int>(E) - kBias);\n\n    // Compute the boundaries m- and m+ of the floating-point value\n    // v = f * 2^e.\n    //\n    // Determine v- and v+, the floating-point predecessor and successor if v,\n    // respectively.\n    //\n    //      v- = v - 2^e        if f != 2^(p-1) or e == e_min                (A)\n    //         = v - 2^(e-1)    if f == 2^(p-1) and e > e_min                (B)\n    //\n    //      v+ = v + 2^e\n    //\n    // Let m- = (v- + v) / 2 and m+ = (v + v+) / 2. All real numbers _strictly_\n    // between m- and m+ round to v, regardless of how the input rounding\n    // algorithm breaks ties.\n    //\n    //      ---+-------------+-------------+-------------+-------------+---  (A)\n    //         v-            m-            v             m+            v+\n    //\n    //      -----------------+------+------+-------------+-------------+---  (B)\n    //                       v-     m-     v             m+            v+\n\n    const bool lower_boundary_is_closer = F == 0 && E > 1;\n    const diyfp m_plus = diyfp(2 * v.f + 1, v.e - 1);\n    const diyfp m_minus = lower_boundary_is_closer\n                          ? diyfp(4 * v.f - 1, v.e - 2)  // (B)\n                          : diyfp(2 * v.f - 1, v.e - 1); // (A)\n\n    // Determine the normalized w+ = m+.\n    const diyfp w_plus = diyfp::normalize(m_plus);\n\n    // Determine w- = m- such that e_(w-) = e_(w+).\n    const diyfp w_minus = diyfp::normalize_to(m_minus, w_plus.e);\n\n    return {diyfp::normalize(v), w_minus, w_plus};\n}\n\n// Given normalized diyfp w, Grisu needs to find a (normalized) cached\n// power-of-ten c, such that the exponent of the product c * w = f * 2^e lies\n// within a certain range [alpha, gamma] (Definition 3.2 from [1])\n//\n//      alpha <= e = e_c + e_w + q <= gamma\n//\n// or\n//\n//      f_c * f_w * 2^alpha <= f_c 2^(e_c) * f_w 2^(e_w) * 2^q\n//                          <= f_c * f_w * 2^gamma\n//\n// Since c and w are normalized, i.e. 2^(q-1) <= f < 2^q, this implies\n//\n//      2^(q-1) * 2^(q-1) * 2^alpha <= c * w * 2^q < 2^q * 2^q * 2^gamma\n//\n// or\n//\n//      2^(q - 2 + alpha) <= c * w < 2^(q + gamma)\n//\n// The choice of (alpha,gamma) determines the size of the table and the form of\n// the digit generation procedure. Using (alpha,gamma)=(-60,-32) works out well\n// in practice:\n//\n// The idea is to cut the number c * w = f * 2^e into two parts, which can be\n// processed independently: An integral part p1, and a fractional part p2:\n//\n//      f * 2^e = ( (f div 2^-e) * 2^-e + (f mod 2^-e) ) * 2^e\n//              = (f div 2^-e) + (f mod 2^-e) * 2^e\n//              = p1 + p2 * 2^e\n//\n// The conversion of p1 into decimal form requires a series of divisions and\n// modulos by (a power of) 10. These operations are faster for 32-bit than for\n// 64-bit integers, so p1 should ideally fit into a 32-bit integer. This can be\n// achieved by choosing\n//\n//      -e >= 32   or   e <= -32 := gamma\n//\n// In order to convert the fractional part\n//\n//      p2 * 2^e = p2 / 2^-e = d[-1] / 10^1 + d[-2] / 10^2 + ...\n//\n// into decimal form, the fraction is repeatedly multiplied by 10 and the digits\n// d[-i] are extracted in order:\n//\n//      (10 * p2) div 2^-e = d[-1]\n//      (10 * p2) mod 2^-e = d[-2] / 10^1 + ...\n//\n// The multiplication by 10 must not overflow. It is sufficient to choose\n//\n//      10 * p2 < 16 * p2 = 2^4 * p2 <= 2^64.\n//\n// Since p2 = f mod 2^-e < 2^-e,\n//\n//      -e <= 60   or   e >= -60 := alpha\n\nconstexpr int kAlpha = -60;\nconstexpr int kGamma = -32;\n\nstruct cached_power // c = f * 2^e ~= 10^k\n{\n    std::uint64_t f;\n    int e;\n    int k;\n};\n\n/*!\nFor a normalized diyfp w = f * 2^e, this function returns a (normalized) cached\npower-of-ten c = f_c * 2^e_c, such that the exponent of the product w * c\nsatisfies (Definition 3.2 from [1])\n\n     alpha <= e_c + e + q <= gamma.\n*/\ninline cached_power get_cached_power_for_binary_exponent(int e)\n{\n    // Now\n    //\n    //      alpha <= e_c + e + q <= gamma                                    (1)\n    //      ==> f_c * 2^alpha <= c * 2^e * 2^q\n    //\n    // and since the c's are normalized, 2^(q-1) <= f_c,\n    //\n    //      ==> 2^(q - 1 + alpha) <= c * 2^(e + q)\n    //      ==> 2^(alpha - e - 1) <= c\n    //\n    // If c were an exact power of ten, i.e. c = 10^k, one may determine k as\n    //\n    //      k = ceil( log_10( 2^(alpha - e - 1) ) )\n    //        = ceil( (alpha - e - 1) * log_10(2) )\n    //\n    // From the paper:\n    // \"In theory the result of the procedure could be wrong since c is rounded,\n    //  and the computation itself is approximated [...]. In practice, however,\n    //  this simple function is sufficient.\"\n    //\n    // For IEEE double precision floating-point numbers converted into\n    // normalized diyfp's w = f * 2^e, with q = 64,\n    //\n    //      e >= -1022      (min IEEE exponent)\n    //           -52        (p - 1)\n    //           -52        (p - 1, possibly normalize denormal IEEE numbers)\n    //           -11        (normalize the diyfp)\n    //         = -1137\n    //\n    // and\n    //\n    //      e <= +1023      (max IEEE exponent)\n    //           -52        (p - 1)\n    //           -11        (normalize the diyfp)\n    //         = 960\n    //\n    // This binary exponent range [-1137,960] results in a decimal exponent\n    // range [-307,324]. One does not need to store a cached power for each\n    // k in this range. For each such k it suffices to find a cached power\n    // such that the exponent of the product lies in [alpha,gamma].\n    // This implies that the difference of the decimal exponents of adjacent\n    // table entries must be less than or equal to\n    //\n    //      floor( (gamma - alpha) * log_10(2) ) = 8.\n    //\n    // (A smaller distance gamma-alpha would require a larger table.)\n\n    // NB:\n    // Actually this function returns c, such that -60 <= e_c + e + 64 <= -34.\n\n    constexpr int kCachedPowersMinDecExp = -300;\n    constexpr int kCachedPowersDecStep = 8;\n\n    static constexpr std::array<cached_power, 79> kCachedPowers =\n    {\n        {\n            { 0xAB70FE17C79AC6CA, -1060, -300 },\n            { 0xFF77B1FCBEBCDC4F, -1034, -292 },\n            { 0xBE5691EF416BD60C, -1007, -284 },\n            { 0x8DD01FAD907FFC3C,  -980, -276 },\n            { 0xD3515C2831559A83,  -954, -268 },\n            { 0x9D71AC8FADA6C9B5,  -927, -260 },\n            { 0xEA9C227723EE8BCB,  -901, -252 },\n            { 0xAECC49914078536D,  -874, -244 },\n            { 0x823C12795DB6CE57,  -847, -236 },\n            { 0xC21094364DFB5637,  -821, -228 },\n            { 0x9096EA6F3848984F,  -794, -220 },\n            { 0xD77485CB25823AC7,  -768, -212 },\n            { 0xA086CFCD97BF97F4,  -741, -204 },\n            { 0xEF340A98172AACE5,  -715, -196 },\n            { 0xB23867FB2A35B28E,  -688, -188 },\n            { 0x84C8D4DFD2C63F3B,  -661, -180 },\n            { 0xC5DD44271AD3CDBA,  -635, -172 },\n            { 0x936B9FCEBB25C996,  -608, -164 },\n            { 0xDBAC6C247D62A584,  -582, -156 },\n            { 0xA3AB66580D5FDAF6,  -555, -148 },\n            { 0xF3E2F893DEC3F126,  -529, -140 },\n            { 0xB5B5ADA8AAFF80B8,  -502, -132 },\n            { 0x87625F056C7C4A8B,  -475, -124 },\n            { 0xC9BCFF6034C13053,  -449, -116 },\n            { 0x964E858C91BA2655,  -422, -108 },\n            { 0xDFF9772470297EBD,  -396, -100 },\n            { 0xA6DFBD9FB8E5B88F,  -369,  -92 },\n            { 0xF8A95FCF88747D94,  -343,  -84 },\n            { 0xB94470938FA89BCF,  -316,  -76 },\n            { 0x8A08F0F8BF0F156B,  -289,  -68 },\n            { 0xCDB02555653131B6,  -263,  -60 },\n            { 0x993FE2C6D07B7FAC,  -236,  -52 },\n            { 0xE45C10C42A2B3B06,  -210,  -44 },\n            { 0xAA242499697392D3,  -183,  -36 },\n            { 0xFD87B5F28300CA0E,  -157,  -28 },\n            { 0xBCE5086492111AEB,  -130,  -20 },\n            { 0x8CBCCC096F5088CC,  -103,  -12 },\n            { 0xD1B71758E219652C,   -77,   -4 },\n            { 0x9C40000000000000,   -50,    4 },\n            { 0xE8D4A51000000000,   -24,   12 },\n            { 0xAD78EBC5AC620000,     3,   20 },\n            { 0x813F3978F8940984,    30,   28 },\n            { 0xC097CE7BC90715B3,    56,   36 },\n            { 0x8F7E32CE7BEA5C70,    83,   44 },\n            { 0xD5D238A4ABE98068,   109,   52 },\n            { 0x9F4F2726179A2245,   136,   60 },\n            { 0xED63A231D4C4FB27,   162,   68 },\n            { 0xB0DE65388CC8ADA8,   189,   76 },\n            { 0x83C7088E1AAB65DB,   216,   84 },\n            { 0xC45D1DF942711D9A,   242,   92 },\n            { 0x924D692CA61BE758,   269,  100 },\n            { 0xDA01EE641A708DEA,   295,  108 },\n            { 0xA26DA3999AEF774A,   322,  116 },\n            { 0xF209787BB47D6B85,   348,  124 },\n            { 0xB454E4A179DD1877,   375,  132 },\n            { 0x865B86925B9BC5C2,   402,  140 },\n            { 0xC83553C5C8965D3D,   428,  148 },\n            { 0x952AB45CFA97A0B3,   455,  156 },\n            { 0xDE469FBD99A05FE3,   481,  164 },\n            { 0xA59BC234DB398C25,   508,  172 },\n            { 0xF6C69A72A3989F5C,   534,  180 },\n            { 0xB7DCBF5354E9BECE,   561,  188 },\n            { 0x88FCF317F22241E2,   588,  196 },\n            { 0xCC20CE9BD35C78A5,   614,  204 },\n            { 0x98165AF37B2153DF,   641,  212 },\n            { 0xE2A0B5DC971F303A,   667,  220 },\n            { 0xA8D9D1535CE3B396,   694,  228 },\n            { 0xFB9B7CD9A4A7443C,   720,  236 },\n            { 0xBB764C4CA7A44410,   747,  244 },\n            { 0x8BAB8EEFB6409C1A,   774,  252 },\n            { 0xD01FEF10A657842C,   800,  260 },\n            { 0x9B10A4E5E9913129,   827,  268 },\n            { 0xE7109BFBA19C0C9D,   853,  276 },\n            { 0xAC2820D9623BF429,   880,  284 },\n            { 0x80444B5E7AA7CF85,   907,  292 },\n            { 0xBF21E44003ACDD2D,   933,  300 },\n            { 0x8E679C2F5E44FF8F,   960,  308 },\n            { 0xD433179D9C8CB841,   986,  316 },\n            { 0x9E19DB92B4E31BA9,  1013,  324 },\n        }\n    };\n\n    // This computation gives exactly the same results for k as\n    //      k = ceil((kAlpha - e - 1) * 0.30102999566398114)\n    // for |e| <= 1500, but doesn't require floating-point operations.\n    // NB: log_10(2) ~= 78913 / 2^18\n    JSON_ASSERT(e >= -1500);\n    JSON_ASSERT(e <=  1500);\n    const int f = kAlpha - e - 1;\n    const int k = (f * 78913) / (1 << 18) + static_cast<int>(f > 0);\n\n    const int index = (-kCachedPowersMinDecExp + k + (kCachedPowersDecStep - 1)) / kCachedPowersDecStep;\n    JSON_ASSERT(index >= 0);\n    JSON_ASSERT(static_cast<std::size_t>(index) < kCachedPowers.size());\n\n    const cached_power cached = kCachedPowers[static_cast<std::size_t>(index)];\n    JSON_ASSERT(kAlpha <= cached.e + e + 64);\n    JSON_ASSERT(kGamma >= cached.e + e + 64);\n\n    return cached;\n}\n\n/*!\nFor n != 0, returns k, such that pow10 := 10^(k-1) <= n < 10^k.\nFor n == 0, returns 1 and sets pow10 := 1.\n*/\ninline int find_largest_pow10(const std::uint32_t n, std::uint32_t& pow10)\n{\n    // LCOV_EXCL_START\n    if (n >= 1000000000)\n    {\n        pow10 = 1000000000;\n        return 10;\n    }\n    // LCOV_EXCL_STOP\n    if (n >= 100000000)\n    {\n        pow10 = 100000000;\n        return  9;\n    }\n    if (n >= 10000000)\n    {\n        pow10 = 10000000;\n        return  8;\n    }\n    if (n >= 1000000)\n    {\n        pow10 = 1000000;\n        return  7;\n    }\n    if (n >= 100000)\n    {\n        pow10 = 100000;\n        return  6;\n    }\n    if (n >= 10000)\n    {\n        pow10 = 10000;\n        return  5;\n    }\n    if (n >= 1000)\n    {\n        pow10 = 1000;\n        return  4;\n    }\n    if (n >= 100)\n    {\n        pow10 = 100;\n        return  3;\n    }\n    if (n >= 10)\n    {\n        pow10 = 10;\n        return  2;\n    }\n\n    pow10 = 1;\n    return 1;\n}\n\ninline void grisu2_round(char* buf, int len, std::uint64_t dist, std::uint64_t delta,\n                         std::uint64_t rest, std::uint64_t ten_k)\n{\n    JSON_ASSERT(len >= 1);\n    JSON_ASSERT(dist <= delta);\n    JSON_ASSERT(rest <= delta);\n    JSON_ASSERT(ten_k > 0);\n\n    //               <--------------------------- delta ---->\n    //                                  <---- dist --------->\n    // --------------[------------------+-------------------]--------------\n    //               M-                 w                   M+\n    //\n    //                                  ten_k\n    //                                <------>\n    //                                       <---- rest ---->\n    // --------------[------------------+----+--------------]--------------\n    //                                  w    V\n    //                                       = buf * 10^k\n    //\n    // ten_k represents a unit-in-the-last-place in the decimal representation\n    // stored in buf.\n    // Decrement buf by ten_k while this takes buf closer to w.\n\n    // The tests are written in this order to avoid overflow in unsigned\n    // integer arithmetic.\n\n    while (rest < dist\n            && delta - rest >= ten_k\n            && (rest + ten_k < dist || dist - rest > rest + ten_k - dist))\n    {\n        JSON_ASSERT(buf[len - 1] != '0');\n        buf[len - 1]--;\n        rest += ten_k;\n    }\n}\n\n/*!\nGenerates V = buffer * 10^decimal_exponent, such that M- <= V <= M+.\nM- and M+ must be normalized and share the same exponent -60 <= e <= -32.\n*/\ninline void grisu2_digit_gen(char* buffer, int& length, int& decimal_exponent,\n                             diyfp M_minus, diyfp w, diyfp M_plus)\n{\n    static_assert(kAlpha >= -60, \"internal error\");\n    static_assert(kGamma <= -32, \"internal error\");\n\n    // Generates the digits (and the exponent) of a decimal floating-point\n    // number V = buffer * 10^decimal_exponent in the range [M-, M+]. The diyfp's\n    // w, M- and M+ share the same exponent e, which satisfies alpha <= e <= gamma.\n    //\n    //               <--------------------------- delta ---->\n    //                                  <---- dist --------->\n    // --------------[------------------+-------------------]--------------\n    //               M-                 w                   M+\n    //\n    // Grisu2 generates the digits of M+ from left to right and stops as soon as\n    // V is in [M-,M+].\n\n    JSON_ASSERT(M_plus.e >= kAlpha);\n    JSON_ASSERT(M_plus.e <= kGamma);\n\n    std::uint64_t delta = diyfp::sub(M_plus, M_minus).f; // (significand of (M+ - M-), implicit exponent is e)\n    std::uint64_t dist  = diyfp::sub(M_plus, w      ).f; // (significand of (M+ - w ), implicit exponent is e)\n\n    // Split M+ = f * 2^e into two parts p1 and p2 (note: e < 0):\n    //\n    //      M+ = f * 2^e\n    //         = ((f div 2^-e) * 2^-e + (f mod 2^-e)) * 2^e\n    //         = ((p1        ) * 2^-e + (p2        )) * 2^e\n    //         = p1 + p2 * 2^e\n\n    const diyfp one(std::uint64_t{1} << -M_plus.e, M_plus.e);\n\n    auto p1 = static_cast<std::uint32_t>(M_plus.f >> -one.e); // p1 = f div 2^-e (Since -e >= 32, p1 fits into a 32-bit int.)\n    std::uint64_t p2 = M_plus.f & (one.f - 1);                    // p2 = f mod 2^-e\n\n    // 1)\n    //\n    // Generate the digits of the integral part p1 = d[n-1]...d[1]d[0]\n\n    JSON_ASSERT(p1 > 0);\n\n    std::uint32_t pow10{};\n    const int k = find_largest_pow10(p1, pow10);\n\n    //      10^(k-1) <= p1 < 10^k, pow10 = 10^(k-1)\n    //\n    //      p1 = (p1 div 10^(k-1)) * 10^(k-1) + (p1 mod 10^(k-1))\n    //         = (d[k-1]         ) * 10^(k-1) + (p1 mod 10^(k-1))\n    //\n    //      M+ = p1                                             + p2 * 2^e\n    //         = d[k-1] * 10^(k-1) + (p1 mod 10^(k-1))          + p2 * 2^e\n    //         = d[k-1] * 10^(k-1) + ((p1 mod 10^(k-1)) * 2^-e + p2) * 2^e\n    //         = d[k-1] * 10^(k-1) + (                         rest) * 2^e\n    //\n    // Now generate the digits d[n] of p1 from left to right (n = k-1,...,0)\n    //\n    //      p1 = d[k-1]...d[n] * 10^n + d[n-1]...d[0]\n    //\n    // but stop as soon as\n    //\n    //      rest * 2^e = (d[n-1]...d[0] * 2^-e + p2) * 2^e <= delta * 2^e\n\n    int n = k;\n    while (n > 0)\n    {\n        // Invariants:\n        //      M+ = buffer * 10^n + (p1 + p2 * 2^e)    (buffer = 0 for n = k)\n        //      pow10 = 10^(n-1) <= p1 < 10^n\n        //\n        const std::uint32_t d = p1 / pow10;  // d = p1 div 10^(n-1)\n        const std::uint32_t r = p1 % pow10;  // r = p1 mod 10^(n-1)\n        //\n        //      M+ = buffer * 10^n + (d * 10^(n-1) + r) + p2 * 2^e\n        //         = (buffer * 10 + d) * 10^(n-1) + (r + p2 * 2^e)\n        //\n        JSON_ASSERT(d <= 9);\n        buffer[length++] = static_cast<char>('0' + d); // buffer := buffer * 10 + d\n        //\n        //      M+ = buffer * 10^(n-1) + (r + p2 * 2^e)\n        //\n        p1 = r;\n        n--;\n        //\n        //      M+ = buffer * 10^n + (p1 + p2 * 2^e)\n        //      pow10 = 10^n\n        //\n\n        // Now check if enough digits have been generated.\n        // Compute\n        //\n        //      p1 + p2 * 2^e = (p1 * 2^-e + p2) * 2^e = rest * 2^e\n        //\n        // Note:\n        // Since rest and delta share the same exponent e, it suffices to\n        // compare the significands.\n        const std::uint64_t rest = (std::uint64_t{p1} << -one.e) + p2;\n        if (rest <= delta)\n        {\n            // V = buffer * 10^n, with M- <= V <= M+.\n\n            decimal_exponent += n;\n\n            // We may now just stop. But instead look if the buffer could be\n            // decremented to bring V closer to w.\n            //\n            // pow10 = 10^n is now 1 ulp in the decimal representation V.\n            // The rounding procedure works with diyfp's with an implicit\n            // exponent of e.\n            //\n            //      10^n = (10^n * 2^-e) * 2^e = ulp * 2^e\n            //\n            const std::uint64_t ten_n = std::uint64_t{pow10} << -one.e;\n            grisu2_round(buffer, length, dist, delta, rest, ten_n);\n\n            return;\n        }\n\n        pow10 /= 10;\n        //\n        //      pow10 = 10^(n-1) <= p1 < 10^n\n        // Invariants restored.\n    }\n\n    // 2)\n    //\n    // The digits of the integral part have been generated:\n    //\n    //      M+ = d[k-1]...d[1]d[0] + p2 * 2^e\n    //         = buffer            + p2 * 2^e\n    //\n    // Now generate the digits of the fractional part p2 * 2^e.\n    //\n    // Note:\n    // No decimal point is generated: the exponent is adjusted instead.\n    //\n    // p2 actually represents the fraction\n    //\n    //      p2 * 2^e\n    //          = p2 / 2^-e\n    //          = d[-1] / 10^1 + d[-2] / 10^2 + ...\n    //\n    // Now generate the digits d[-m] of p1 from left to right (m = 1,2,...)\n    //\n    //      p2 * 2^e = d[-1]d[-2]...d[-m] * 10^-m\n    //                      + 10^-m * (d[-m-1] / 10^1 + d[-m-2] / 10^2 + ...)\n    //\n    // using\n    //\n    //      10^m * p2 = ((10^m * p2) div 2^-e) * 2^-e + ((10^m * p2) mod 2^-e)\n    //                = (                   d) * 2^-e + (                   r)\n    //\n    // or\n    //      10^m * p2 * 2^e = d + r * 2^e\n    //\n    // i.e.\n    //\n    //      M+ = buffer + p2 * 2^e\n    //         = buffer + 10^-m * (d + r * 2^e)\n    //         = (buffer * 10^m + d) * 10^-m + 10^-m * r * 2^e\n    //\n    // and stop as soon as 10^-m * r * 2^e <= delta * 2^e\n\n    JSON_ASSERT(p2 > delta);\n\n    int m = 0;\n    for (;;)\n    {\n        // Invariant:\n        //      M+ = buffer * 10^-m + 10^-m * (d[-m-1] / 10 + d[-m-2] / 10^2 + ...) * 2^e\n        //         = buffer * 10^-m + 10^-m * (p2                                 ) * 2^e\n        //         = buffer * 10^-m + 10^-m * (1/10 * (10 * p2)                   ) * 2^e\n        //         = buffer * 10^-m + 10^-m * (1/10 * ((10*p2 div 2^-e) * 2^-e + (10*p2 mod 2^-e)) * 2^e\n        //\n        JSON_ASSERT(p2 <= (std::numeric_limits<std::uint64_t>::max)() / 10);\n        p2 *= 10;\n        const std::uint64_t d = p2 >> -one.e;     // d = (10 * p2) div 2^-e\n        const std::uint64_t r = p2 & (one.f - 1); // r = (10 * p2) mod 2^-e\n        //\n        //      M+ = buffer * 10^-m + 10^-m * (1/10 * (d * 2^-e + r) * 2^e\n        //         = buffer * 10^-m + 10^-m * (1/10 * (d + r * 2^e))\n        //         = (buffer * 10 + d) * 10^(-m-1) + 10^(-m-1) * r * 2^e\n        //\n        JSON_ASSERT(d <= 9);\n        buffer[length++] = static_cast<char>('0' + d); // buffer := buffer * 10 + d\n        //\n        //      M+ = buffer * 10^(-m-1) + 10^(-m-1) * r * 2^e\n        //\n        p2 = r;\n        m++;\n        //\n        //      M+ = buffer * 10^-m + 10^-m * p2 * 2^e\n        // Invariant restored.\n\n        // Check if enough digits have been generated.\n        //\n        //      10^-m * p2 * 2^e <= delta * 2^e\n        //              p2 * 2^e <= 10^m * delta * 2^e\n        //                    p2 <= 10^m * delta\n        delta *= 10;\n        dist  *= 10;\n        if (p2 <= delta)\n        {\n            break;\n        }\n    }\n\n    // V = buffer * 10^-m, with M- <= V <= M+.\n\n    decimal_exponent -= m;\n\n    // 1 ulp in the decimal representation is now 10^-m.\n    // Since delta and dist are now scaled by 10^m, we need to do the\n    // same with ulp in order to keep the units in sync.\n    //\n    //      10^m * 10^-m = 1 = 2^-e * 2^e = ten_m * 2^e\n    //\n    const std::uint64_t ten_m = one.f;\n    grisu2_round(buffer, length, dist, delta, p2, ten_m);\n\n    // By construction this algorithm generates the shortest possible decimal\n    // number (Loitsch, Theorem 6.2) which rounds back to w.\n    // For an input number of precision p, at least\n    //\n    //      N = 1 + ceil(p * log_10(2))\n    //\n    // decimal digits are sufficient to identify all binary floating-point\n    // numbers (Matula, \"In-and-Out conversions\").\n    // This implies that the algorithm does not produce more than N decimal\n    // digits.\n    //\n    //      N = 17 for p = 53 (IEEE double precision)\n    //      N = 9  for p = 24 (IEEE single precision)\n}\n\n/*!\nv = buf * 10^decimal_exponent\nlen is the length of the buffer (number of decimal digits)\nThe buffer must be large enough, i.e. >= max_digits10.\n*/\nJSON_HEDLEY_NON_NULL(1)\ninline void grisu2(char* buf, int& len, int& decimal_exponent,\n                   diyfp m_minus, diyfp v, diyfp m_plus)\n{\n    JSON_ASSERT(m_plus.e == m_minus.e);\n    JSON_ASSERT(m_plus.e == v.e);\n\n    //  --------(-----------------------+-----------------------)--------    (A)\n    //          m-                      v                       m+\n    //\n    //  --------------------(-----------+-----------------------)--------    (B)\n    //                      m-          v                       m+\n    //\n    // First scale v (and m- and m+) such that the exponent is in the range\n    // [alpha, gamma].\n\n    const cached_power cached = get_cached_power_for_binary_exponent(m_plus.e);\n\n    const diyfp c_minus_k(cached.f, cached.e); // = c ~= 10^-k\n\n    // The exponent of the products is = v.e + c_minus_k.e + q and is in the range [alpha,gamma]\n    const diyfp w       = diyfp::mul(v,       c_minus_k);\n    const diyfp w_minus = diyfp::mul(m_minus, c_minus_k);\n    const diyfp w_plus  = diyfp::mul(m_plus,  c_minus_k);\n\n    //  ----(---+---)---------------(---+---)---------------(---+---)----\n    //          w-                      w                       w+\n    //          = c*m-                  = c*v                   = c*m+\n    //\n    // diyfp::mul rounds its result and c_minus_k is approximated too. w, w- and\n    // w+ are now off by a small amount.\n    // In fact:\n    //\n    //      w - v * 10^k < 1 ulp\n    //\n    // To account for this inaccuracy, add resp. subtract 1 ulp.\n    //\n    //  --------+---[---------------(---+---)---------------]---+--------\n    //          w-  M-                  w                   M+  w+\n    //\n    // Now any number in [M-, M+] (bounds included) will round to w when input,\n    // regardless of how the input rounding algorithm breaks ties.\n    //\n    // And digit_gen generates the shortest possible such number in [M-, M+].\n    // Note that this does not mean that Grisu2 always generates the shortest\n    // possible number in the interval (m-, m+).\n    const diyfp M_minus(w_minus.f + 1, w_minus.e);\n    const diyfp M_plus (w_plus.f  - 1, w_plus.e );\n\n    decimal_exponent = -cached.k; // = -(-k) = k\n\n    grisu2_digit_gen(buf, len, decimal_exponent, M_minus, w, M_plus);\n}\n\n/*!\nv = buf * 10^decimal_exponent\nlen is the length of the buffer (number of decimal digits)\nThe buffer must be large enough, i.e. >= max_digits10.\n*/\ntemplate<typename FloatType>\nJSON_HEDLEY_NON_NULL(1)\nvoid grisu2(char* buf, int& len, int& decimal_exponent, FloatType value)\n{\n    static_assert(diyfp::kPrecision >= std::numeric_limits<FloatType>::digits + 3,\n                  \"internal error: not enough precision\");\n\n    JSON_ASSERT(std::isfinite(value));\n    JSON_ASSERT(value > 0);\n\n    // If the neighbors (and boundaries) of 'value' are always computed for double-precision\n    // numbers, all float's can be recovered using strtod (and strtof). However, the resulting\n    // decimal representations are not exactly \"short\".\n    //\n    // The documentation for 'std::to_chars' (https://en.cppreference.com/w/cpp/utility/to_chars)\n    // says \"value is converted to a string as if by std::sprintf in the default (\"C\") locale\"\n    // and since sprintf promotes floats to doubles, I think this is exactly what 'std::to_chars'\n    // does.\n    // On the other hand, the documentation for 'std::to_chars' requires that \"parsing the\n    // representation using the corresponding std::from_chars function recovers value exactly\". That\n    // indicates that single precision floating-point numbers should be recovered using\n    // 'std::strtof'.\n    //\n    // NB: If the neighbors are computed for single-precision numbers, there is a single float\n    //     (7.0385307e-26f) which can't be recovered using strtod. The resulting double precision\n    //     value is off by 1 ulp.\n#if 0 // NOLINT(readability-avoid-unconditional-preprocessor-if)\n    const boundaries w = compute_boundaries(static_cast<double>(value));\n#else\n    const boundaries w = compute_boundaries(value);\n#endif\n\n    grisu2(buf, len, decimal_exponent, w.minus, w.w, w.plus);\n}\n\n/*!\n@brief appends a decimal representation of e to buf\n@return a pointer to the element following the exponent.\n@pre -1000 < e < 1000\n*/\nJSON_HEDLEY_NON_NULL(1)\nJSON_HEDLEY_RETURNS_NON_NULL\ninline char* append_exponent(char* buf, int e)\n{\n    JSON_ASSERT(e > -1000);\n    JSON_ASSERT(e <  1000);\n\n    if (e < 0)\n    {\n        e = -e;\n        *buf++ = '-';\n    }\n    else\n    {\n        *buf++ = '+';\n    }\n\n    auto k = static_cast<std::uint32_t>(e);\n    if (k < 10)\n    {\n        // Always print at least two digits in the exponent.\n        // This is for compatibility with printf(\"%g\").\n        *buf++ = '0';\n        *buf++ = static_cast<char>('0' + k);\n    }\n    else if (k < 100)\n    {\n        *buf++ = static_cast<char>('0' + k / 10);\n        k %= 10;\n        *buf++ = static_cast<char>('0' + k);\n    }\n    else\n    {\n        *buf++ = static_cast<char>('0' + k / 100);\n        k %= 100;\n        *buf++ = static_cast<char>('0' + k / 10);\n        k %= 10;\n        *buf++ = static_cast<char>('0' + k);\n    }\n\n    return buf;\n}\n\n/*!\n@brief prettify v = buf * 10^decimal_exponent\n\nIf v is in the range [10^min_exp, 10^max_exp) it will be printed in fixed-point\nnotation. Otherwise it will be printed in exponential notation.\n\n@pre min_exp < 0\n@pre max_exp > 0\n*/\nJSON_HEDLEY_NON_NULL(1)\nJSON_HEDLEY_RETURNS_NON_NULL\ninline char* format_buffer(char* buf, int len, int decimal_exponent,\n                           int min_exp, int max_exp)\n{\n    JSON_ASSERT(min_exp < 0);\n    JSON_ASSERT(max_exp > 0);\n\n    const int k = len;\n    const int n = len + decimal_exponent;\n\n    // v = buf * 10^(n-k)\n    // k is the length of the buffer (number of decimal digits)\n    // n is the position of the decimal point relative to the start of the buffer.\n\n    if (k <= n && n <= max_exp)\n    {\n        // digits[000]\n        // len <= max_exp + 2\n\n        std::memset(buf + k, '0', static_cast<size_t>(n) - static_cast<size_t>(k));\n        // Make it look like a floating-point number (#362, #378)\n        buf[n + 0] = '.';\n        buf[n + 1] = '0';\n        return buf + (static_cast<size_t>(n) + 2);\n    }\n\n    if (0 < n && n <= max_exp)\n    {\n        // dig.its\n        // len <= max_digits10 + 1\n\n        JSON_ASSERT(k > n);\n\n        std::memmove(buf + (static_cast<size_t>(n) + 1), buf + n, static_cast<size_t>(k) - static_cast<size_t>(n));\n        buf[n] = '.';\n        return buf + (static_cast<size_t>(k) + 1U);\n    }\n\n    if (min_exp < n && n <= 0)\n    {\n        // 0.[000]digits\n        // len <= 2 + (-min_exp - 1) + max_digits10\n\n        std::memmove(buf + (2 + static_cast<size_t>(-n)), buf, static_cast<size_t>(k));\n        buf[0] = '0';\n        buf[1] = '.';\n        std::memset(buf + 2, '0', static_cast<size_t>(-n));\n        return buf + (2U + static_cast<size_t>(-n) + static_cast<size_t>(k));\n    }\n\n    if (k == 1)\n    {\n        // dE+123\n        // len <= 1 + 5\n\n        buf += 1;\n    }\n    else\n    {\n        // d.igitsE+123\n        // len <= max_digits10 + 1 + 5\n\n        std::memmove(buf + 2, buf + 1, static_cast<size_t>(k) - 1);\n        buf[1] = '.';\n        buf += 1 + static_cast<size_t>(k);\n    }\n\n    *buf++ = 'e';\n    return append_exponent(buf, n - 1);\n}\n\n}  // namespace dtoa_impl\n\n/*!\n@brief generates a decimal representation of the floating-point number value in [first, last).\n\nThe format of the resulting decimal representation is similar to printf's %g\nformat. Returns an iterator pointing past-the-end of the decimal representation.\n\n@note The input number must be finite, i.e. NaN's and Inf's are not supported.\n@note The buffer must be large enough.\n@note The result is NOT null-terminated.\n*/\ntemplate<typename FloatType>\nJSON_HEDLEY_NON_NULL(1, 2)\nJSON_HEDLEY_RETURNS_NON_NULL\nchar* to_chars(char* first, const char* last, FloatType value)\n{\n    static_cast<void>(last); // maybe unused - fix warning\n    JSON_ASSERT(std::isfinite(value));\n\n    // Use signbit(value) instead of (value < 0) since signbit works for -0.\n    if (std::signbit(value))\n    {\n        value = -value;\n        *first++ = '-';\n    }\n\n#ifdef __GNUC__\n#pragma GCC diagnostic push\n#pragma GCC diagnostic ignored \"-Wfloat-equal\"\n#endif\n    if (value == 0) // +-0\n    {\n        *first++ = '0';\n        // Make it look like a floating-point number (#362, #378)\n        *first++ = '.';\n        *first++ = '0';\n        return first;\n    }\n#ifdef __GNUC__\n#pragma GCC diagnostic pop\n#endif\n\n    JSON_ASSERT(last - first >= std::numeric_limits<FloatType>::max_digits10);\n\n    // Compute v = buffer * 10^decimal_exponent.\n    // The decimal digits are stored in the buffer, which needs to be interpreted\n    // as an unsigned decimal integer.\n    // len is the length of the buffer, i.e. the number of decimal digits.\n    int len = 0;\n    int decimal_exponent = 0;\n    dtoa_impl::grisu2(first, len, decimal_exponent, value);\n\n    JSON_ASSERT(len <= std::numeric_limits<FloatType>::max_digits10);\n\n    // Format the buffer like printf(\"%.*g\", prec, value)\n    constexpr int kMinExp = -4;\n    // Use digits10 here to increase compatibility with version 2.\n    constexpr int kMaxExp = std::numeric_limits<FloatType>::digits10;\n\n    JSON_ASSERT(last - first >= kMaxExp + 2);\n    JSON_ASSERT(last - first >= 2 + (-kMinExp - 1) + std::numeric_limits<FloatType>::max_digits10);\n    JSON_ASSERT(last - first >= std::numeric_limits<FloatType>::max_digits10 + 6);\n\n    return dtoa_impl::format_buffer(first, len, decimal_exponent, kMinExp, kMaxExp);\n}\n\n}  // namespace detail\nNLOHMANN_JSON_NAMESPACE_END\n\n// #include <nlohmann/detail/exceptions.hpp>\n\n// #include <nlohmann/detail/macro_scope.hpp>\n\n// #include <nlohmann/detail/meta/cpp_future.hpp>\n\n// #include <nlohmann/detail/output/binary_writer.hpp>\n\n// #include <nlohmann/detail/output/output_adapters.hpp>\n\n// #include <nlohmann/detail/string_concat.hpp>\n\n// #include <nlohmann/detail/value_t.hpp>\n\n\nNLOHMANN_JSON_NAMESPACE_BEGIN\nnamespace detail\n{\n\n///////////////////\n// serialization //\n///////////////////\n\n/// how to treat decoding errors\nenum class error_handler_t\n{\n    strict,  ///< throw a type_error exception in case of invalid UTF-8\n    replace, ///< replace invalid UTF-8 sequences with U+FFFD\n    ignore   ///< ignore invalid UTF-8 sequences\n};\n\ntemplate<typename BasicJsonType>\nclass serializer\n{\n    using string_t = typename BasicJsonType::string_t;\n    using number_float_t = typename BasicJsonType::number_float_t;\n    using number_integer_t = typename BasicJsonType::number_integer_t;\n    using number_unsigned_t = typename BasicJsonType::number_unsigned_t;\n    using binary_char_t = typename BasicJsonType::binary_t::value_type;\n    static constexpr std::uint8_t UTF8_ACCEPT = 0;\n    static constexpr std::uint8_t UTF8_REJECT = 1;\n\n  public:\n    /*!\n    @param[in] s  output stream to serialize to\n    @param[in] ichar  indentation character to use\n    @param[in] error_handler_  how to react on decoding errors\n    */\n    serializer(output_adapter_t<char> s, const char ichar,\n               error_handler_t error_handler_ = error_handler_t::strict)\n        : o(std::move(s))\n        , loc(std::localeconv())\n        , thousands_sep(loc->thousands_sep == nullptr ? '\\0' : std::char_traits<char>::to_char_type(* (loc->thousands_sep)))\n        , decimal_point(loc->decimal_point == nullptr ? '\\0' : std::char_traits<char>::to_char_type(* (loc->decimal_point)))\n        , indent_char(ichar)\n        , indent_string(512, indent_char)\n        , error_handler(error_handler_)\n    {}\n\n    // delete because of pointer members\n    serializer(const serializer&) = delete;\n    serializer& operator=(const serializer&) = delete;\n    serializer(serializer&&) = delete;\n    serializer& operator=(serializer&&) = delete;\n    ~serializer() = default;\n\n    /*!\n    @brief internal implementation of the serialization function\n\n    This function is called by the public member function dump and organizes\n    the serialization internally. The indentation level is propagated as\n    additional parameter. In case of arrays and objects, the function is\n    called recursively.\n\n    - strings and object keys are escaped using `escape_string()`\n    - integer numbers are converted implicitly via `operator<<`\n    - floating-point numbers are converted to a string using `\"%g\"` format\n    - binary values are serialized as objects containing the subtype and the\n      byte array\n\n    @param[in] val               value to serialize\n    @param[in] pretty_print      whether the output shall be pretty-printed\n    @param[in] ensure_ascii If @a ensure_ascii is true, all non-ASCII characters\n    in the output are escaped with `\\uXXXX` sequences, and the result consists\n    of ASCII characters only.\n    @param[in] indent_step       the indent level\n    @param[in] current_indent    the current indent level (only used internally)\n    */\n    void dump(const BasicJsonType& val,\n              const bool pretty_print,\n              const bool ensure_ascii,\n              const unsigned int indent_step,\n              const unsigned int current_indent = 0)\n    {\n        switch (val.m_data.m_type)\n        {\n            case value_t::object:\n            {\n                if (val.m_data.m_value.object->empty())\n                {\n                    o->write_characters(\"{}\", 2);\n                    return;\n                }\n\n                if (pretty_print)\n                {\n                    o->write_characters(\"{\\n\", 2);\n\n                    // variable to hold indentation for recursive calls\n                    const auto new_indent = current_indent + indent_step;\n                    if (JSON_HEDLEY_UNLIKELY(indent_string.size() < new_indent))\n                    {\n                        indent_string.resize(indent_string.size() * 2, ' ');\n                    }\n\n                    // first n-1 elements\n                    auto i = val.m_data.m_value.object->cbegin();\n                    for (std::size_t cnt = 0; cnt < val.m_data.m_value.object->size() - 1; ++cnt, ++i)\n                    {\n                        o->write_characters(indent_string.c_str(), new_indent);\n                        o->write_character('\\\"');\n                        dump_escaped(i->first, ensure_ascii);\n                        o->write_characters(\"\\\": \", 3);\n                        dump(i->second, true, ensure_ascii, indent_step, new_indent);\n                        o->write_characters(\",\\n\", 2);\n                    }\n\n                    // last element\n                    JSON_ASSERT(i != val.m_data.m_value.object->cend());\n                    JSON_ASSERT(std::next(i) == val.m_data.m_value.object->cend());\n                    o->write_characters(indent_string.c_str(), new_indent);\n                    o->write_character('\\\"');\n                    dump_escaped(i->first, ensure_ascii);\n                    o->write_characters(\"\\\": \", 3);\n                    dump(i->second, true, ensure_ascii, indent_step, new_indent);\n\n                    o->write_character('\\n');\n                    o->write_characters(indent_string.c_str(), current_indent);\n                    o->write_character('}');\n                }\n                else\n                {\n                    o->write_character('{');\n\n                    // first n-1 elements\n                    auto i = val.m_data.m_value.object->cbegin();\n                    for (std::size_t cnt = 0; cnt < val.m_data.m_value.object->size() - 1; ++cnt, ++i)\n                    {\n                        o->write_character('\\\"');\n                        dump_escaped(i->first, ensure_ascii);\n                        o->write_characters(\"\\\":\", 2);\n                        dump(i->second, false, ensure_ascii, indent_step, current_indent);\n                        o->write_character(',');\n                    }\n\n                    // last element\n                    JSON_ASSERT(i != val.m_data.m_value.object->cend());\n                    JSON_ASSERT(std::next(i) == val.m_data.m_value.object->cend());\n                    o->write_character('\\\"');\n                    dump_escaped(i->first, ensure_ascii);\n                    o->write_characters(\"\\\":\", 2);\n                    dump(i->second, false, ensure_ascii, indent_step, current_indent);\n\n                    o->write_character('}');\n                }\n\n                return;\n            }\n\n            case value_t::array:\n            {\n                if (val.m_data.m_value.array->empty())\n                {\n                    o->write_characters(\"[]\", 2);\n                    return;\n                }\n\n                if (pretty_print)\n                {\n                    o->write_characters(\"[\\n\", 2);\n\n                    // variable to hold indentation for recursive calls\n                    const auto new_indent = current_indent + indent_step;\n                    if (JSON_HEDLEY_UNLIKELY(indent_string.size() < new_indent))\n                    {\n                        indent_string.resize(indent_string.size() * 2, ' ');\n                    }\n\n                    // first n-1 elements\n                    for (auto i = val.m_data.m_value.array->cbegin();\n                            i != val.m_data.m_value.array->cend() - 1; ++i)\n                    {\n                        o->write_characters(indent_string.c_str(), new_indent);\n                        dump(*i, true, ensure_ascii, indent_step, new_indent);\n                        o->write_characters(\",\\n\", 2);\n                    }\n\n                    // last element\n                    JSON_ASSERT(!val.m_data.m_value.array->empty());\n                    o->write_characters(indent_string.c_str(), new_indent);\n                    dump(val.m_data.m_value.array->back(), true, ensure_ascii, indent_step, new_indent);\n\n                    o->write_character('\\n');\n                    o->write_characters(indent_string.c_str(), current_indent);\n                    o->write_character(']');\n                }\n                else\n                {\n                    o->write_character('[');\n\n                    // first n-1 elements\n                    for (auto i = val.m_data.m_value.array->cbegin();\n                            i != val.m_data.m_value.array->cend() - 1; ++i)\n                    {\n                        dump(*i, false, ensure_ascii, indent_step, current_indent);\n                        o->write_character(',');\n                    }\n\n                    // last element\n                    JSON_ASSERT(!val.m_data.m_value.array->empty());\n                    dump(val.m_data.m_value.array->back(), false, ensure_ascii, indent_step, current_indent);\n\n                    o->write_character(']');\n                }\n\n                return;\n            }\n\n            case value_t::string:\n            {\n                o->write_character('\\\"');\n                dump_escaped(*val.m_data.m_value.string, ensure_ascii);\n                o->write_character('\\\"');\n                return;\n            }\n\n            case value_t::binary:\n            {\n                if (pretty_print)\n                {\n                    o->write_characters(\"{\\n\", 2);\n\n                    // variable to hold indentation for recursive calls\n                    const auto new_indent = current_indent + indent_step;\n                    if (JSON_HEDLEY_UNLIKELY(indent_string.size() < new_indent))\n                    {\n                        indent_string.resize(indent_string.size() * 2, ' ');\n                    }\n\n                    o->write_characters(indent_string.c_str(), new_indent);\n\n                    o->write_characters(\"\\\"bytes\\\": [\", 10);\n\n                    if (!val.m_data.m_value.binary->empty())\n                    {\n                        for (auto i = val.m_data.m_value.binary->cbegin();\n                                i != val.m_data.m_value.binary->cend() - 1; ++i)\n                        {\n                            dump_integer(*i);\n                            o->write_characters(\", \", 2);\n                        }\n                        dump_integer(val.m_data.m_value.binary->back());\n                    }\n\n                    o->write_characters(\"],\\n\", 3);\n                    o->write_characters(indent_string.c_str(), new_indent);\n\n                    o->write_characters(\"\\\"subtype\\\": \", 11);\n                    if (val.m_data.m_value.binary->has_subtype())\n                    {\n                        dump_integer(val.m_data.m_value.binary->subtype());\n                    }\n                    else\n                    {\n                        o->write_characters(\"null\", 4);\n                    }\n                    o->write_character('\\n');\n                    o->write_characters(indent_string.c_str(), current_indent);\n                    o->write_character('}');\n                }\n                else\n                {\n                    o->write_characters(\"{\\\"bytes\\\":[\", 10);\n\n                    if (!val.m_data.m_value.binary->empty())\n                    {\n                        for (auto i = val.m_data.m_value.binary->cbegin();\n                                i != val.m_data.m_value.binary->cend() - 1; ++i)\n                        {\n                            dump_integer(*i);\n                            o->write_character(',');\n                        }\n                        dump_integer(val.m_data.m_value.binary->back());\n                    }\n\n                    o->write_characters(\"],\\\"subtype\\\":\", 12);\n                    if (val.m_data.m_value.binary->has_subtype())\n                    {\n                        dump_integer(val.m_data.m_value.binary->subtype());\n                        o->write_character('}');\n                    }\n                    else\n                    {\n                        o->write_characters(\"null}\", 5);\n                    }\n                }\n                return;\n            }\n\n            case value_t::boolean:\n            {\n                if (val.m_data.m_value.boolean)\n                {\n                    o->write_characters(\"true\", 4);\n                }\n                else\n                {\n                    o->write_characters(\"false\", 5);\n                }\n                return;\n            }\n\n            case value_t::number_integer:\n            {\n                dump_integer(val.m_data.m_value.number_integer);\n                return;\n            }\n\n            case value_t::number_unsigned:\n            {\n                dump_integer(val.m_data.m_value.number_unsigned);\n                return;\n            }\n\n            case value_t::number_float:\n            {\n                dump_float(val.m_data.m_value.number_float);\n                return;\n            }\n\n            case value_t::discarded:\n            {\n                o->write_characters(\"<discarded>\", 11);\n                return;\n            }\n\n            case value_t::null:\n            {\n                o->write_characters(\"null\", 4);\n                return;\n            }\n\n            default:            // LCOV_EXCL_LINE\n                JSON_ASSERT(false); // NOLINT(cert-dcl03-c,hicpp-static-assert,misc-static-assert) LCOV_EXCL_LINE\n        }\n    }\n\n  JSON_PRIVATE_UNLESS_TESTED:\n    /*!\n    @brief dump escaped string\n\n    Escape a string by replacing certain special characters by a sequence of an\n    escape character (backslash) and another character and other control\n    characters by a sequence of \"\\u\" followed by a four-digit hex\n    representation. The escaped string is written to output stream @a o.\n\n    @param[in] s  the string to escape\n    @param[in] ensure_ascii  whether to escape non-ASCII characters with\n                             \\uXXXX sequences\n\n    @complexity Linear in the length of string @a s.\n    */\n    void dump_escaped(const string_t& s, const bool ensure_ascii)\n    {\n        std::uint32_t codepoint{};\n        std::uint8_t state = UTF8_ACCEPT;\n        std::size_t bytes = 0;  // number of bytes written to string_buffer\n\n        // number of bytes written at the point of the last valid byte\n        std::size_t bytes_after_last_accept = 0;\n        std::size_t undumped_chars = 0;\n\n        for (std::size_t i = 0; i < s.size(); ++i)\n        {\n            const auto byte = static_cast<std::uint8_t>(s[i]);\n\n            switch (decode(state, codepoint, byte))\n            {\n                case UTF8_ACCEPT:  // decode found a new code point\n                {\n                    switch (codepoint)\n                    {\n                        case 0x08: // backspace\n                        {\n                            string_buffer[bytes++] = '\\\\';\n                            string_buffer[bytes++] = 'b';\n                            break;\n                        }\n\n                        case 0x09: // horizontal tab\n                        {\n                            string_buffer[bytes++] = '\\\\';\n                            string_buffer[bytes++] = 't';\n                            break;\n                        }\n\n                        case 0x0A: // newline\n                        {\n                            string_buffer[bytes++] = '\\\\';\n                            string_buffer[bytes++] = 'n';\n                            break;\n                        }\n\n                        case 0x0C: // formfeed\n                        {\n                            string_buffer[bytes++] = '\\\\';\n                            string_buffer[bytes++] = 'f';\n                            break;\n                        }\n\n                        case 0x0D: // carriage return\n                        {\n                            string_buffer[bytes++] = '\\\\';\n                            string_buffer[bytes++] = 'r';\n                            break;\n                        }\n\n                        case 0x22: // quotation mark\n                        {\n                            string_buffer[bytes++] = '\\\\';\n                            string_buffer[bytes++] = '\\\"';\n                            break;\n                        }\n\n                        case 0x5C: // reverse solidus\n                        {\n                            string_buffer[bytes++] = '\\\\';\n                            string_buffer[bytes++] = '\\\\';\n                            break;\n                        }\n\n                        default:\n                        {\n                            // escape control characters (0x00..0x1F) or, if\n                            // ensure_ascii parameter is used, non-ASCII characters\n                            if ((codepoint <= 0x1F) || (ensure_ascii && (codepoint >= 0x7F)))\n                            {\n                                if (codepoint <= 0xFFFF)\n                                {\n                                    // NOLINTNEXTLINE(cppcoreguidelines-pro-type-vararg,hicpp-vararg)\n                                    static_cast<void>((std::snprintf)(string_buffer.data() + bytes, 7, \"\\\\u%04x\",\n                                                                      static_cast<std::uint16_t>(codepoint)));\n                                    bytes += 6;\n                                }\n                                else\n                                {\n                                    // NOLINTNEXTLINE(cppcoreguidelines-pro-type-vararg,hicpp-vararg)\n                                    static_cast<void>((std::snprintf)(string_buffer.data() + bytes, 13, \"\\\\u%04x\\\\u%04x\",\n                                                                      static_cast<std::uint16_t>(0xD7C0u + (codepoint >> 10u)),\n                                                                      static_cast<std::uint16_t>(0xDC00u + (codepoint & 0x3FFu))));\n                                    bytes += 12;\n                                }\n                            }\n                            else\n                            {\n                                // copy byte to buffer (all previous bytes\n                                // been copied have in default case above)\n                                string_buffer[bytes++] = s[i];\n                            }\n                            break;\n                        }\n                    }\n\n                    // write buffer and reset index; there must be 13 bytes\n                    // left, as this is the maximal number of bytes to be\n                    // written (\"\\uxxxx\\uxxxx\\0\") for one code point\n                    if (string_buffer.size() - bytes < 13)\n                    {\n                        o->write_characters(string_buffer.data(), bytes);\n                        bytes = 0;\n                    }\n\n                    // remember the byte position of this accept\n                    bytes_after_last_accept = bytes;\n                    undumped_chars = 0;\n                    break;\n                }\n\n                case UTF8_REJECT:  // decode found invalid UTF-8 byte\n                {\n                    switch (error_handler)\n                    {\n                        case error_handler_t::strict:\n                        {\n                            JSON_THROW(type_error::create(316, concat(\"invalid UTF-8 byte at index \", std::to_string(i), \": 0x\", hex_bytes(byte | 0)), nullptr));\n                        }\n\n                        case error_handler_t::ignore:\n                        case error_handler_t::replace:\n                        {\n                            // in case we saw this character the first time, we\n                            // would like to read it again, because the byte\n                            // may be OK for itself, but just not OK for the\n                            // previous sequence\n                            if (undumped_chars > 0)\n                            {\n                                --i;\n                            }\n\n                            // reset length buffer to the last accepted index;\n                            // thus removing/ignoring the invalid characters\n                            bytes = bytes_after_last_accept;\n\n                            if (error_handler == error_handler_t::replace)\n                            {\n                                // add a replacement character\n                                if (ensure_ascii)\n                                {\n                                    string_buffer[bytes++] = '\\\\';\n                                    string_buffer[bytes++] = 'u';\n                                    string_buffer[bytes++] = 'f';\n                                    string_buffer[bytes++] = 'f';\n                                    string_buffer[bytes++] = 'f';\n                                    string_buffer[bytes++] = 'd';\n                                }\n                                else\n                                {\n                                    string_buffer[bytes++] = detail::binary_writer<BasicJsonType, char>::to_char_type('\\xEF');\n                                    string_buffer[bytes++] = detail::binary_writer<BasicJsonType, char>::to_char_type('\\xBF');\n                                    string_buffer[bytes++] = detail::binary_writer<BasicJsonType, char>::to_char_type('\\xBD');\n                                }\n\n                                // write buffer and reset index; there must be 13 bytes\n                                // left, as this is the maximal number of bytes to be\n                                // written (\"\\uxxxx\\uxxxx\\0\") for one code point\n                                if (string_buffer.size() - bytes < 13)\n                                {\n                                    o->write_characters(string_buffer.data(), bytes);\n                                    bytes = 0;\n                                }\n\n                                bytes_after_last_accept = bytes;\n                            }\n\n                            undumped_chars = 0;\n\n                            // continue processing the string\n                            state = UTF8_ACCEPT;\n                            break;\n                        }\n\n                        default:            // LCOV_EXCL_LINE\n                            JSON_ASSERT(false); // NOLINT(cert-dcl03-c,hicpp-static-assert,misc-static-assert) LCOV_EXCL_LINE\n                    }\n                    break;\n                }\n\n                default:  // decode found yet incomplete multi-byte code point\n                {\n                    if (!ensure_ascii)\n                    {\n                        // code point will not be escaped - copy byte to buffer\n                        string_buffer[bytes++] = s[i];\n                    }\n                    ++undumped_chars;\n                    break;\n                }\n            }\n        }\n\n        // we finished processing the string\n        if (JSON_HEDLEY_LIKELY(state == UTF8_ACCEPT))\n        {\n            // write buffer\n            if (bytes > 0)\n            {\n                o->write_characters(string_buffer.data(), bytes);\n            }\n        }\n        else\n        {\n            // we finish reading, but do not accept: string was incomplete\n            switch (error_handler)\n            {\n                case error_handler_t::strict:\n                {\n                    JSON_THROW(type_error::create(316, concat(\"incomplete UTF-8 string; last byte: 0x\", hex_bytes(static_cast<std::uint8_t>(s.back() | 0))), nullptr));\n                }\n\n                case error_handler_t::ignore:\n                {\n                    // write all accepted bytes\n                    o->write_characters(string_buffer.data(), bytes_after_last_accept);\n                    break;\n                }\n\n                case error_handler_t::replace:\n                {\n                    // write all accepted bytes\n                    o->write_characters(string_buffer.data(), bytes_after_last_accept);\n                    // add a replacement character\n                    if (ensure_ascii)\n                    {\n                        o->write_characters(\"\\\\ufffd\", 6);\n                    }\n                    else\n                    {\n                        o->write_characters(\"\\xEF\\xBF\\xBD\", 3);\n                    }\n                    break;\n                }\n\n                default:            // LCOV_EXCL_LINE\n                    JSON_ASSERT(false); // NOLINT(cert-dcl03-c,hicpp-static-assert,misc-static-assert) LCOV_EXCL_LINE\n            }\n        }\n    }\n\n  private:\n    /*!\n    @brief count digits\n\n    Count the number of decimal (base 10) digits for an input unsigned integer.\n\n    @param[in] x  unsigned integer number to count its digits\n    @return    number of decimal digits\n    */\n    inline unsigned int count_digits(number_unsigned_t x) noexcept\n    {\n        unsigned int n_digits = 1;\n        for (;;)\n        {\n            if (x < 10)\n            {\n                return n_digits;\n            }\n            if (x < 100)\n            {\n                return n_digits + 1;\n            }\n            if (x < 1000)\n            {\n                return n_digits + 2;\n            }\n            if (x < 10000)\n            {\n                return n_digits + 3;\n            }\n            x = x / 10000u;\n            n_digits += 4;\n        }\n    }\n\n    /*!\n     * @brief convert a byte to a uppercase hex representation\n     * @param[in] byte byte to represent\n     * @return representation (\"00\"..\"FF\")\n     */\n    static std::string hex_bytes(std::uint8_t byte)\n    {\n        std::string result = \"FF\";\n        constexpr const char* nibble_to_hex = \"0123456789ABCDEF\";\n        result[0] = nibble_to_hex[byte / 16];\n        result[1] = nibble_to_hex[byte % 16];\n        return result;\n    }\n\n    // templates to avoid warnings about useless casts\n    template <typename NumberType, enable_if_t<std::is_signed<NumberType>::value, int> = 0>\n    bool is_negative_number(NumberType x)\n    {\n        return x < 0;\n    }\n\n    template < typename NumberType, enable_if_t <std::is_unsigned<NumberType>::value, int > = 0 >\n    bool is_negative_number(NumberType /*unused*/)\n    {\n        return false;\n    }\n\n    /*!\n    @brief dump an integer\n\n    Dump a given integer to output stream @a o. Works internally with\n    @a number_buffer.\n\n    @param[in] x  integer number (signed or unsigned) to dump\n    @tparam NumberType either @a number_integer_t or @a number_unsigned_t\n    */\n    template < typename NumberType, detail::enable_if_t <\n                   std::is_integral<NumberType>::value ||\n                   std::is_same<NumberType, number_unsigned_t>::value ||\n                   std::is_same<NumberType, number_integer_t>::value ||\n                   std::is_same<NumberType, binary_char_t>::value,\n                   int > = 0 >\n    void dump_integer(NumberType x)\n    {\n        static constexpr std::array<std::array<char, 2>, 100> digits_to_99\n        {\n            {\n                {{'0', '0'}}, {{'0', '1'}}, {{'0', '2'}}, {{'0', '3'}}, {{'0', '4'}}, {{'0', '5'}}, {{'0', '6'}}, {{'0', '7'}}, {{'0', '8'}}, {{'0', '9'}},\n                {{'1', '0'}}, {{'1', '1'}}, {{'1', '2'}}, {{'1', '3'}}, {{'1', '4'}}, {{'1', '5'}}, {{'1', '6'}}, {{'1', '7'}}, {{'1', '8'}}, {{'1', '9'}},\n                {{'2', '0'}}, {{'2', '1'}}, {{'2', '2'}}, {{'2', '3'}}, {{'2', '4'}}, {{'2', '5'}}, {{'2', '6'}}, {{'2', '7'}}, {{'2', '8'}}, {{'2', '9'}},\n                {{'3', '0'}}, {{'3', '1'}}, {{'3', '2'}}, {{'3', '3'}}, {{'3', '4'}}, {{'3', '5'}}, {{'3', '6'}}, {{'3', '7'}}, {{'3', '8'}}, {{'3', '9'}},\n                {{'4', '0'}}, {{'4', '1'}}, {{'4', '2'}}, {{'4', '3'}}, {{'4', '4'}}, {{'4', '5'}}, {{'4', '6'}}, {{'4', '7'}}, {{'4', '8'}}, {{'4', '9'}},\n                {{'5', '0'}}, {{'5', '1'}}, {{'5', '2'}}, {{'5', '3'}}, {{'5', '4'}}, {{'5', '5'}}, {{'5', '6'}}, {{'5', '7'}}, {{'5', '8'}}, {{'5', '9'}},\n                {{'6', '0'}}, {{'6', '1'}}, {{'6', '2'}}, {{'6', '3'}}, {{'6', '4'}}, {{'6', '5'}}, {{'6', '6'}}, {{'6', '7'}}, {{'6', '8'}}, {{'6', '9'}},\n                {{'7', '0'}}, {{'7', '1'}}, {{'7', '2'}}, {{'7', '3'}}, {{'7', '4'}}, {{'7', '5'}}, {{'7', '6'}}, {{'7', '7'}}, {{'7', '8'}}, {{'7', '9'}},\n                {{'8', '0'}}, {{'8', '1'}}, {{'8', '2'}}, {{'8', '3'}}, {{'8', '4'}}, {{'8', '5'}}, {{'8', '6'}}, {{'8', '7'}}, {{'8', '8'}}, {{'8', '9'}},\n                {{'9', '0'}}, {{'9', '1'}}, {{'9', '2'}}, {{'9', '3'}}, {{'9', '4'}}, {{'9', '5'}}, {{'9', '6'}}, {{'9', '7'}}, {{'9', '8'}}, {{'9', '9'}},\n            }\n        };\n\n        // special case for \"0\"\n        if (x == 0)\n        {\n            o->write_character('0');\n            return;\n        }\n\n        // use a pointer to fill the buffer\n        auto buffer_ptr = number_buffer.begin(); // NOLINT(llvm-qualified-auto,readability-qualified-auto,cppcoreguidelines-pro-type-vararg,hicpp-vararg)\n\n        number_unsigned_t abs_value;\n\n        unsigned int n_chars{};\n\n        if (is_negative_number(x))\n        {\n            *buffer_ptr = '-';\n            abs_value = remove_sign(static_cast<number_integer_t>(x));\n\n            // account one more byte for the minus sign\n            n_chars = 1 + count_digits(abs_value);\n        }\n        else\n        {\n            abs_value = static_cast<number_unsigned_t>(x);\n            n_chars = count_digits(abs_value);\n        }\n\n        // spare 1 byte for '\\0'\n        JSON_ASSERT(n_chars < number_buffer.size() - 1);\n\n        // jump to the end to generate the string from backward,\n        // so we later avoid reversing the result\n        buffer_ptr += n_chars;\n\n        // Fast int2ascii implementation inspired by \"Fastware\" talk by Andrei Alexandrescu\n        // See: https://www.youtube.com/watch?v=o4-CwDo2zpg\n        while (abs_value >= 100)\n        {\n            const auto digits_index = static_cast<unsigned>((abs_value % 100));\n            abs_value /= 100;\n            *(--buffer_ptr) = digits_to_99[digits_index][1];\n            *(--buffer_ptr) = digits_to_99[digits_index][0];\n        }\n\n        if (abs_value >= 10)\n        {\n            const auto digits_index = static_cast<unsigned>(abs_value);\n            *(--buffer_ptr) = digits_to_99[digits_index][1];\n            *(--buffer_ptr) = digits_to_99[digits_index][0];\n        }\n        else\n        {\n            *(--buffer_ptr) = static_cast<char>('0' + abs_value);\n        }\n\n        o->write_characters(number_buffer.data(), n_chars);\n    }\n\n    /*!\n    @brief dump a floating-point number\n\n    Dump a given floating-point number to output stream @a o. Works internally\n    with @a number_buffer.\n\n    @param[in] x  floating-point number to dump\n    */\n    void dump_float(number_float_t x)\n    {\n        // NaN / inf\n        if (!std::isfinite(x))\n        {\n            o->write_characters(\"null\", 4);\n            return;\n        }\n\n        // If number_float_t is an IEEE-754 single or double precision number,\n        // use the Grisu2 algorithm to produce short numbers which are\n        // guaranteed to round-trip, using strtof and strtod, resp.\n        //\n        // NB: The test below works if <long double> == <double>.\n        static constexpr bool is_ieee_single_or_double\n            = (std::numeric_limits<number_float_t>::is_iec559 && std::numeric_limits<number_float_t>::digits == 24 && std::numeric_limits<number_float_t>::max_exponent == 128) ||\n              (std::numeric_limits<number_float_t>::is_iec559 && std::numeric_limits<number_float_t>::digits == 53 && std::numeric_limits<number_float_t>::max_exponent == 1024);\n\n        dump_float(x, std::integral_constant<bool, is_ieee_single_or_double>());\n    }\n\n    void dump_float(number_float_t x, std::true_type /*is_ieee_single_or_double*/)\n    {\n        auto* begin = number_buffer.data();\n        auto* end = ::nlohmann::detail::to_chars(begin, begin + number_buffer.size(), x);\n\n        o->write_characters(begin, static_cast<size_t>(end - begin));\n    }\n\n    void dump_float(number_float_t x, std::false_type /*is_ieee_single_or_double*/)\n    {\n        // get number of digits for a float -> text -> float round-trip\n        static constexpr auto d = std::numeric_limits<number_float_t>::max_digits10;\n\n        // the actual conversion\n        // NOLINTNEXTLINE(cppcoreguidelines-pro-type-vararg,hicpp-vararg)\n        std::ptrdiff_t len = (std::snprintf)(number_buffer.data(), number_buffer.size(), \"%.*g\", d, x);\n\n        // negative value indicates an error\n        JSON_ASSERT(len > 0);\n        // check if buffer was large enough\n        JSON_ASSERT(static_cast<std::size_t>(len) < number_buffer.size());\n\n        // erase thousands separator\n        if (thousands_sep != '\\0')\n        {\n            // NOLINTNEXTLINE(readability-qualified-auto,llvm-qualified-auto): std::remove returns an iterator, see https://github.com/nlohmann/json/issues/3081\n            const auto end = std::remove(number_buffer.begin(), number_buffer.begin() + len, thousands_sep);\n            std::fill(end, number_buffer.end(), '\\0');\n            JSON_ASSERT((end - number_buffer.begin()) <= len);\n            len = (end - number_buffer.begin());\n        }\n\n        // convert decimal point to '.'\n        if (decimal_point != '\\0' && decimal_point != '.')\n        {\n            // NOLINTNEXTLINE(readability-qualified-auto,llvm-qualified-auto): std::find returns an iterator, see https://github.com/nlohmann/json/issues/3081\n            const auto dec_pos = std::find(number_buffer.begin(), number_buffer.end(), decimal_point);\n            if (dec_pos != number_buffer.end())\n            {\n                *dec_pos = '.';\n            }\n        }\n\n        o->write_characters(number_buffer.data(), static_cast<std::size_t>(len));\n\n        // determine if we need to append \".0\"\n        const bool value_is_int_like =\n            std::none_of(number_buffer.begin(), number_buffer.begin() + len + 1,\n                         [](char c)\n        {\n            return c == '.' || c == 'e';\n        });\n\n        if (value_is_int_like)\n        {\n            o->write_characters(\".0\", 2);\n        }\n    }\n\n    /*!\n    @brief check whether a string is UTF-8 encoded\n\n    The function checks each byte of a string whether it is UTF-8 encoded. The\n    result of the check is stored in the @a state parameter. The function must\n    be called initially with state 0 (accept). State 1 means the string must\n    be rejected, because the current byte is not allowed. If the string is\n    completely processed, but the state is non-zero, the string ended\n    prematurely; that is, the last byte indicated more bytes should have\n    followed.\n\n    @param[in,out] state  the state of the decoding\n    @param[in,out] codep  codepoint (valid only if resulting state is UTF8_ACCEPT)\n    @param[in] byte       next byte to decode\n    @return               new state\n\n    @note The function has been edited: a std::array is used.\n\n    @copyright Copyright (c) 2008-2009 Bjoern Hoehrmann <bjoern@hoehrmann.de>\n    @sa http://bjoern.hoehrmann.de/utf-8/decoder/dfa/\n    */\n    static std::uint8_t decode(std::uint8_t& state, std::uint32_t& codep, const std::uint8_t byte) noexcept\n    {\n        static const std::array<std::uint8_t, 400> utf8d =\n        {\n            {\n                0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, // 00..1F\n                0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, // 20..3F\n                0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, // 40..5F\n                0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, // 60..7F\n                1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, // 80..9F\n                7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, // A0..BF\n                8, 8, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, // C0..DF\n                0xA, 0x3, 0x3, 0x3, 0x3, 0x3, 0x3, 0x3, 0x3, 0x3, 0x3, 0x3, 0x3, 0x4, 0x3, 0x3, // E0..EF\n                0xB, 0x6, 0x6, 0x6, 0x5, 0x8, 0x8, 0x8, 0x8, 0x8, 0x8, 0x8, 0x8, 0x8, 0x8, 0x8, // F0..FF\n                0x0, 0x1, 0x2, 0x3, 0x5, 0x8, 0x7, 0x1, 0x1, 0x1, 0x4, 0x6, 0x1, 0x1, 0x1, 0x1, // s0..s0\n                1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, // s1..s2\n                1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, // s3..s4\n                1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 3, 1, 1, 1, 1, 1, 1, // s5..s6\n                1, 3, 1, 1, 1, 1, 1, 3, 1, 3, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 // s7..s8\n            }\n        };\n\n        JSON_ASSERT(byte < utf8d.size());\n        const std::uint8_t type = utf8d[byte];\n\n        codep = (state != UTF8_ACCEPT)\n                ? (byte & 0x3fu) | (codep << 6u)\n                : (0xFFu >> type) & (byte);\n\n        const std::size_t index = 256u + static_cast<size_t>(state) * 16u + static_cast<size_t>(type);\n        JSON_ASSERT(index < utf8d.size());\n        state = utf8d[index];\n        return state;\n    }\n\n    /*\n     * Overload to make the compiler happy while it is instantiating\n     * dump_integer for number_unsigned_t.\n     * Must never be called.\n     */\n    number_unsigned_t remove_sign(number_unsigned_t x)\n    {\n        JSON_ASSERT(false); // NOLINT(cert-dcl03-c,hicpp-static-assert,misc-static-assert) LCOV_EXCL_LINE\n        return x; // LCOV_EXCL_LINE\n    }\n\n    /*\n     * Helper function for dump_integer\n     *\n     * This function takes a negative signed integer and returns its absolute\n     * value as unsigned integer. The plus/minus shuffling is necessary as we can\n     * not directly remove the sign of an arbitrary signed integer as the\n     * absolute values of INT_MIN and INT_MAX are usually not the same. See\n     * #1708 for details.\n     */\n    inline number_unsigned_t remove_sign(number_integer_t x) noexcept\n    {\n        JSON_ASSERT(x < 0 && x < (std::numeric_limits<number_integer_t>::max)()); // NOLINT(misc-redundant-expression)\n        return static_cast<number_unsigned_t>(-(x + 1)) + 1;\n    }\n\n  private:\n    /// the output of the serializer\n    output_adapter_t<char> o = nullptr;\n\n    /// a (hopefully) large enough character buffer\n    std::array<char, 64> number_buffer{{}};\n\n    /// the locale\n    const std::lconv* loc = nullptr;\n    /// the locale's thousand separator character\n    const char thousands_sep = '\\0';\n    /// the locale's decimal point character\n    const char decimal_point = '\\0';\n\n    /// string buffer\n    std::array<char, 512> string_buffer{{}};\n\n    /// the indentation character\n    const char indent_char;\n    /// the indentation string\n    string_t indent_string;\n\n    /// error_handler how to react on decoding errors\n    const error_handler_t error_handler;\n};\n\n}  // namespace detail\nNLOHMANN_JSON_NAMESPACE_END\n\n// #include <nlohmann/detail/value_t.hpp>\n\n// #include <nlohmann/json_fwd.hpp>\n\n// #include <nlohmann/ordered_map.hpp>\n//     __ _____ _____ _____\n//  __|  |   __|     |   | |  JSON for Modern C++\n// |  |  |__   |  |  | | | |  version 3.11.3\n// |_____|_____|_____|_|___|  https://github.com/nlohmann/json\n//\n// SPDX-FileCopyrightText: 2013-2023 Niels Lohmann <https://nlohmann.me>\n// SPDX-License-Identifier: MIT\n\n\n\n#include <functional> // equal_to, less\n#include <initializer_list> // initializer_list\n#include <iterator> // input_iterator_tag, iterator_traits\n#include <memory> // allocator\n#include <stdexcept> // for out_of_range\n#include <type_traits> // enable_if, is_convertible\n#include <utility> // pair\n#include <vector> // vector\n\n// #include <nlohmann/detail/macro_scope.hpp>\n\n// #include <nlohmann/detail/meta/type_traits.hpp>\n\n\nNLOHMANN_JSON_NAMESPACE_BEGIN\n\n/// ordered_map: a minimal map-like container that preserves insertion order\n/// for use within nlohmann::basic_json<ordered_map>\ntemplate <class Key, class T, class IgnoredLess = std::less<Key>,\n          class Allocator = std::allocator<std::pair<const Key, T>>>\n                  struct ordered_map : std::vector<std::pair<const Key, T>, Allocator>\n{\n    using key_type = Key;\n    using mapped_type = T;\n    using Container = std::vector<std::pair<const Key, T>, Allocator>;\n    using iterator = typename Container::iterator;\n    using const_iterator = typename Container::const_iterator;\n    using size_type = typename Container::size_type;\n    using value_type = typename Container::value_type;\n#ifdef JSON_HAS_CPP_14\n    using key_compare = std::equal_to<>;\n#else\n    using key_compare = std::equal_to<Key>;\n#endif\n\n    // Explicit constructors instead of `using Container::Container`\n    // otherwise older compilers choke on it (GCC <= 5.5, xcode <= 9.4)\n    ordered_map() noexcept(noexcept(Container())) : Container{} {}\n    explicit ordered_map(const Allocator& alloc) noexcept(noexcept(Container(alloc))) : Container{alloc} {}\n    template <class It>\n    ordered_map(It first, It last, const Allocator& alloc = Allocator())\n        : Container{first, last, alloc} {}\n    ordered_map(std::initializer_list<value_type> init, const Allocator& alloc = Allocator() )\n        : Container{init, alloc} {}\n\n    std::pair<iterator, bool> emplace(const key_type& key, T&& t)\n    {\n        for (auto it = this->begin(); it != this->end(); ++it)\n        {\n            if (m_compare(it->first, key))\n            {\n                return {it, false};\n            }\n        }\n        Container::emplace_back(key, std::forward<T>(t));\n        return {std::prev(this->end()), true};\n    }\n\n    template<class KeyType, detail::enable_if_t<\n                 detail::is_usable_as_key_type<key_compare, key_type, KeyType>::value, int> = 0>\n    std::pair<iterator, bool> emplace(KeyType && key, T && t)\n    {\n        for (auto it = this->begin(); it != this->end(); ++it)\n        {\n            if (m_compare(it->first, key))\n            {\n                return {it, false};\n            }\n        }\n        Container::emplace_back(std::forward<KeyType>(key), std::forward<T>(t));\n        return {std::prev(this->end()), true};\n    }\n\n    T& operator[](const key_type& key)\n    {\n        return emplace(key, T{}).first->second;\n    }\n\n    template<class KeyType, detail::enable_if_t<\n                 detail::is_usable_as_key_type<key_compare, key_type, KeyType>::value, int> = 0>\n    T & operator[](KeyType && key)\n    {\n        return emplace(std::forward<KeyType>(key), T{}).first->second;\n    }\n\n    const T& operator[](const key_type& key) const\n    {\n        return at(key);\n    }\n\n    template<class KeyType, detail::enable_if_t<\n                 detail::is_usable_as_key_type<key_compare, key_type, KeyType>::value, int> = 0>\n    const T & operator[](KeyType && key) const\n    {\n        return at(std::forward<KeyType>(key));\n    }\n\n    T& at(const key_type& key)\n    {\n        for (auto it = this->begin(); it != this->end(); ++it)\n        {\n            if (m_compare(it->first, key))\n            {\n                return it->second;\n            }\n        }\n\n        JSON_THROW(std::out_of_range(\"key not found\"));\n    }\n\n    template<class KeyType, detail::enable_if_t<\n                 detail::is_usable_as_key_type<key_compare, key_type, KeyType>::value, int> = 0>\n    T & at(KeyType && key) // NOLINT(cppcoreguidelines-missing-std-forward)\n    {\n        for (auto it = this->begin(); it != this->end(); ++it)\n        {\n            if (m_compare(it->first, key))\n            {\n                return it->second;\n            }\n        }\n\n        JSON_THROW(std::out_of_range(\"key not found\"));\n    }\n\n    const T& at(const key_type& key) const\n    {\n        for (auto it = this->begin(); it != this->end(); ++it)\n        {\n            if (m_compare(it->first, key))\n            {\n                return it->second;\n            }\n        }\n\n        JSON_THROW(std::out_of_range(\"key not found\"));\n    }\n\n    template<class KeyType, detail::enable_if_t<\n                 detail::is_usable_as_key_type<key_compare, key_type, KeyType>::value, int> = 0>\n    const T & at(KeyType && key) const // NOLINT(cppcoreguidelines-missing-std-forward)\n    {\n        for (auto it = this->begin(); it != this->end(); ++it)\n        {\n            if (m_compare(it->first, key))\n            {\n                return it->second;\n            }\n        }\n\n        JSON_THROW(std::out_of_range(\"key not found\"));\n    }\n\n    size_type erase(const key_type& key)\n    {\n        for (auto it = this->begin(); it != this->end(); ++it)\n        {\n            if (m_compare(it->first, key))\n            {\n                // Since we cannot move const Keys, re-construct them in place\n                for (auto next = it; ++next != this->end(); ++it)\n                {\n                    it->~value_type(); // Destroy but keep allocation\n                    new (&*it) value_type{std::move(*next)};\n                }\n                Container::pop_back();\n                return 1;\n            }\n        }\n        return 0;\n    }\n\n    template<class KeyType, detail::enable_if_t<\n                 detail::is_usable_as_key_type<key_compare, key_type, KeyType>::value, int> = 0>\n    size_type erase(KeyType && key) // NOLINT(cppcoreguidelines-missing-std-forward)\n    {\n        for (auto it = this->begin(); it != this->end(); ++it)\n        {\n            if (m_compare(it->first, key))\n            {\n                // Since we cannot move const Keys, re-construct them in place\n                for (auto next = it; ++next != this->end(); ++it)\n                {\n                    it->~value_type(); // Destroy but keep allocation\n                    new (&*it) value_type{std::move(*next)};\n                }\n                Container::pop_back();\n                return 1;\n            }\n        }\n        return 0;\n    }\n\n    iterator erase(iterator pos)\n    {\n        return erase(pos, std::next(pos));\n    }\n\n    iterator erase(iterator first, iterator last)\n    {\n        if (first == last)\n        {\n            return first;\n        }\n\n        const auto elements_affected = std::distance(first, last);\n        const auto offset = std::distance(Container::begin(), first);\n\n        // This is the start situation. We need to delete elements_affected\n        // elements (3 in this example: e, f, g), and need to return an\n        // iterator past the last deleted element (h in this example).\n        // Note that offset is the distance from the start of the vector\n        // to first. We will need this later.\n\n        // [ a, b, c, d, e, f, g, h, i, j ]\n        //               ^        ^\n        //             first    last\n\n        // Since we cannot move const Keys, we re-construct them in place.\n        // We start at first and re-construct (viz. copy) the elements from\n        // the back of the vector. Example for first iteration:\n\n        //               ,--------.\n        //               v        |   destroy e and re-construct with h\n        // [ a, b, c, d, e, f, g, h, i, j ]\n        //               ^        ^\n        //               it       it + elements_affected\n\n        for (auto it = first; std::next(it, elements_affected) != Container::end(); ++it)\n        {\n            it->~value_type(); // destroy but keep allocation\n            new (&*it) value_type{std::move(*std::next(it, elements_affected))}; // \"move\" next element to it\n        }\n\n        // [ a, b, c, d, h, i, j, h, i, j ]\n        //               ^        ^\n        //             first    last\n\n        // remove the unneeded elements at the end of the vector\n        Container::resize(this->size() - static_cast<size_type>(elements_affected));\n\n        // [ a, b, c, d, h, i, j ]\n        //               ^        ^\n        //             first    last\n\n        // first is now pointing past the last deleted element, but we cannot\n        // use this iterator, because it may have been invalidated by the\n        // resize call. Instead, we can return begin() + offset.\n        return Container::begin() + offset;\n    }\n\n    size_type count(const key_type& key) const\n    {\n        for (auto it = this->begin(); it != this->end(); ++it)\n        {\n            if (m_compare(it->first, key))\n            {\n                return 1;\n            }\n        }\n        return 0;\n    }\n\n    template<class KeyType, detail::enable_if_t<\n                 detail::is_usable_as_key_type<key_compare, key_type, KeyType>::value, int> = 0>\n    size_type count(KeyType && key) const // NOLINT(cppcoreguidelines-missing-std-forward)\n    {\n        for (auto it = this->begin(); it != this->end(); ++it)\n        {\n            if (m_compare(it->first, key))\n            {\n                return 1;\n            }\n        }\n        return 0;\n    }\n\n    iterator find(const key_type& key)\n    {\n        for (auto it = this->begin(); it != this->end(); ++it)\n        {\n            if (m_compare(it->first, key))\n            {\n                return it;\n            }\n        }\n        return Container::end();\n    }\n\n    template<class KeyType, detail::enable_if_t<\n                 detail::is_usable_as_key_type<key_compare, key_type, KeyType>::value, int> = 0>\n    iterator find(KeyType && key) // NOLINT(cppcoreguidelines-missing-std-forward)\n    {\n        for (auto it = this->begin(); it != this->end(); ++it)\n        {\n            if (m_compare(it->first, key))\n            {\n                return it;\n            }\n        }\n        return Container::end();\n    }\n\n    const_iterator find(const key_type& key) const\n    {\n        for (auto it = this->begin(); it != this->end(); ++it)\n        {\n            if (m_compare(it->first, key))\n            {\n                return it;\n            }\n        }\n        return Container::end();\n    }\n\n    std::pair<iterator, bool> insert( value_type&& value )\n    {\n        return emplace(value.first, std::move(value.second));\n    }\n\n    std::pair<iterator, bool> insert( const value_type& value )\n    {\n        for (auto it = this->begin(); it != this->end(); ++it)\n        {\n            if (m_compare(it->first, value.first))\n            {\n                return {it, false};\n            }\n        }\n        Container::push_back(value);\n        return {--this->end(), true};\n    }\n\n    template<typename InputIt>\n    using require_input_iter = typename std::enable_if<std::is_convertible<typename std::iterator_traits<InputIt>::iterator_category,\n            std::input_iterator_tag>::value>::type;\n\n    template<typename InputIt, typename = require_input_iter<InputIt>>\n    void insert(InputIt first, InputIt last)\n    {\n        for (auto it = first; it != last; ++it)\n        {\n            insert(*it);\n        }\n    }\n\nprivate:\n    JSON_NO_UNIQUE_ADDRESS key_compare m_compare = key_compare();\n};\n\nNLOHMANN_JSON_NAMESPACE_END\n\n\n#if defined(JSON_HAS_CPP_17)\n    #if JSON_HAS_STATIC_RTTI\n        #include <any>\n    #endif\n    #include <string_view>\n#endif\n\n/*!\n@brief namespace for Niels Lohmann\n@see https://github.com/nlohmann\n@since version 1.0.0\n*/\nNLOHMANN_JSON_NAMESPACE_BEGIN\n\n/*!\n@brief a class to store JSON values\n\n@internal\n@invariant The member variables @a m_value and @a m_type have the following\nrelationship:\n- If `m_type == value_t::object`, then `m_value.object != nullptr`.\n- If `m_type == value_t::array`, then `m_value.array != nullptr`.\n- If `m_type == value_t::string`, then `m_value.string != nullptr`.\nThe invariants are checked by member function assert_invariant().\n\n@note ObjectType trick from https://stackoverflow.com/a/9860911\n@endinternal\n\n@since version 1.0.0\n\n@nosubgrouping\n*/\nNLOHMANN_BASIC_JSON_TPL_DECLARATION\nclass basic_json // NOLINT(cppcoreguidelines-special-member-functions,hicpp-special-member-functions)\n    : public ::nlohmann::detail::json_base_class<CustomBaseClass>\n{\n  private:\n    template<detail::value_t> friend struct detail::external_constructor;\n\n    template<typename>\n    friend class ::nlohmann::json_pointer;\n    // can be restored when json_pointer backwards compatibility is removed\n    // friend ::nlohmann::json_pointer<StringType>;\n\n    template<typename BasicJsonType, typename InputType>\n    friend class ::nlohmann::detail::parser;\n    friend ::nlohmann::detail::serializer<basic_json>;\n    template<typename BasicJsonType>\n    friend class ::nlohmann::detail::iter_impl;\n    template<typename BasicJsonType, typename CharType>\n    friend class ::nlohmann::detail::binary_writer;\n    template<typename BasicJsonType, typename InputType, typename SAX>\n    friend class ::nlohmann::detail::binary_reader;\n    template<typename BasicJsonType>\n    friend class ::nlohmann::detail::json_sax_dom_parser;\n    template<typename BasicJsonType>\n    friend class ::nlohmann::detail::json_sax_dom_callback_parser;\n    friend class ::nlohmann::detail::exception;\n\n    /// workaround type for MSVC\n    using basic_json_t = NLOHMANN_BASIC_JSON_TPL;\n    using json_base_class_t = ::nlohmann::detail::json_base_class<CustomBaseClass>;\n\n  JSON_PRIVATE_UNLESS_TESTED:\n    // convenience aliases for types residing in namespace detail;\n    using lexer = ::nlohmann::detail::lexer_base<basic_json>;\n\n    template<typename InputAdapterType>\n    static ::nlohmann::detail::parser<basic_json, InputAdapterType> parser(\n        InputAdapterType adapter,\n        detail::parser_callback_t<basic_json>cb = nullptr,\n        const bool allow_exceptions = true,\n        const bool ignore_comments = false\n                                 )\n    {\n        return ::nlohmann::detail::parser<basic_json, InputAdapterType>(std::move(adapter),\n                std::move(cb), allow_exceptions, ignore_comments);\n    }\n\n  private:\n    using primitive_iterator_t = ::nlohmann::detail::primitive_iterator_t;\n    template<typename BasicJsonType>\n    using internal_iterator = ::nlohmann::detail::internal_iterator<BasicJsonType>;\n    template<typename BasicJsonType>\n    using iter_impl = ::nlohmann::detail::iter_impl<BasicJsonType>;\n    template<typename Iterator>\n    using iteration_proxy = ::nlohmann::detail::iteration_proxy<Iterator>;\n    template<typename Base> using json_reverse_iterator = ::nlohmann::detail::json_reverse_iterator<Base>;\n\n    template<typename CharType>\n    using output_adapter_t = ::nlohmann::detail::output_adapter_t<CharType>;\n\n    template<typename InputType>\n    using binary_reader = ::nlohmann::detail::binary_reader<basic_json, InputType>;\n    template<typename CharType> using binary_writer = ::nlohmann::detail::binary_writer<basic_json, CharType>;\n\n  JSON_PRIVATE_UNLESS_TESTED:\n    using serializer = ::nlohmann::detail::serializer<basic_json>;\n\n  public:\n    using value_t = detail::value_t;\n    /// JSON Pointer, see @ref nlohmann::json_pointer\n    using json_pointer = ::nlohmann::json_pointer<StringType>;\n    template<typename T, typename SFINAE>\n    using json_serializer = JSONSerializer<T, SFINAE>;\n    /// how to treat decoding errors\n    using error_handler_t = detail::error_handler_t;\n    /// how to treat CBOR tags\n    using cbor_tag_handler_t = detail::cbor_tag_handler_t;\n    /// helper type for initializer lists of basic_json values\n    using initializer_list_t = std::initializer_list<detail::json_ref<basic_json>>;\n\n    using input_format_t = detail::input_format_t;\n    /// SAX interface type, see @ref nlohmann::json_sax\n    using json_sax_t = json_sax<basic_json>;\n\n    ////////////////\n    // exceptions //\n    ////////////////\n\n    /// @name exceptions\n    /// Classes to implement user-defined exceptions.\n    /// @{\n\n    using exception = detail::exception;\n    using parse_error = detail::parse_error;\n    using invalid_iterator = detail::invalid_iterator;\n    using type_error = detail::type_error;\n    using out_of_range = detail::out_of_range;\n    using other_error = detail::other_error;\n\n    /// @}\n\n    /////////////////////\n    // container types //\n    /////////////////////\n\n    /// @name container types\n    /// The canonic container types to use @ref basic_json like any other STL\n    /// container.\n    /// @{\n\n    /// the type of elements in a basic_json container\n    using value_type = basic_json;\n\n    /// the type of an element reference\n    using reference = value_type&;\n    /// the type of an element const reference\n    using const_reference = const value_type&;\n\n    /// a type to represent differences between iterators\n    using difference_type = std::ptrdiff_t;\n    /// a type to represent container sizes\n    using size_type = std::size_t;\n\n    /// the allocator type\n    using allocator_type = AllocatorType<basic_json>;\n\n    /// the type of an element pointer\n    using pointer = typename std::allocator_traits<allocator_type>::pointer;\n    /// the type of an element const pointer\n    using const_pointer = typename std::allocator_traits<allocator_type>::const_pointer;\n\n    /// an iterator for a basic_json container\n    using iterator = iter_impl<basic_json>;\n    /// a const iterator for a basic_json container\n    using const_iterator = iter_impl<const basic_json>;\n    /// a reverse iterator for a basic_json container\n    using reverse_iterator = json_reverse_iterator<typename basic_json::iterator>;\n    /// a const reverse iterator for a basic_json container\n    using const_reverse_iterator = json_reverse_iterator<typename basic_json::const_iterator>;\n\n    /// @}\n\n    /// @brief returns the allocator associated with the container\n    /// @sa https://json.nlohmann.me/api/basic_json/get_allocator/\n    static allocator_type get_allocator()\n    {\n        return allocator_type();\n    }\n\n    /// @brief returns version information on the library\n    /// @sa https://json.nlohmann.me/api/basic_json/meta/\n    JSON_HEDLEY_WARN_UNUSED_RESULT\n    static basic_json meta()\n    {\n        basic_json result;\n\n        result[\"copyright\"] = \"(C) 2013-2023 Niels Lohmann\";\n        result[\"name\"] = \"JSON for Modern C++\";\n        result[\"url\"] = \"https://github.com/nlohmann/json\";\n        result[\"version\"][\"string\"] =\n            detail::concat(std::to_string(NLOHMANN_JSON_VERSION_MAJOR), '.',\n                           std::to_string(NLOHMANN_JSON_VERSION_MINOR), '.',\n                           std::to_string(NLOHMANN_JSON_VERSION_PATCH));\n        result[\"version\"][\"major\"] = NLOHMANN_JSON_VERSION_MAJOR;\n        result[\"version\"][\"minor\"] = NLOHMANN_JSON_VERSION_MINOR;\n        result[\"version\"][\"patch\"] = NLOHMANN_JSON_VERSION_PATCH;\n\n#ifdef _WIN32\n        result[\"platform\"] = \"win32\";\n#elif defined __linux__\n        result[\"platform\"] = \"linux\";\n#elif defined __APPLE__\n        result[\"platform\"] = \"apple\";\n#elif defined __unix__\n        result[\"platform\"] = \"unix\";\n#else\n        result[\"platform\"] = \"unknown\";\n#endif\n\n#if defined(__ICC) || defined(__INTEL_COMPILER)\n        result[\"compiler\"] = {{\"family\", \"icc\"}, {\"version\", __INTEL_COMPILER}};\n#elif defined(__clang__)\n        result[\"compiler\"] = {{\"family\", \"clang\"}, {\"version\", __clang_version__}};\n#elif defined(__GNUC__) || defined(__GNUG__)\n        result[\"compiler\"] = {{\"family\", \"gcc\"}, {\"version\", detail::concat(\n                    std::to_string(__GNUC__), '.',\n                    std::to_string(__GNUC_MINOR__), '.',\n                    std::to_string(__GNUC_PATCHLEVEL__))\n            }\n        };\n#elif defined(__HP_cc) || defined(__HP_aCC)\n        result[\"compiler\"] = \"hp\"\n#elif defined(__IBMCPP__)\n        result[\"compiler\"] = {{\"family\", \"ilecpp\"}, {\"version\", __IBMCPP__}};\n#elif defined(_MSC_VER)\n        result[\"compiler\"] = {{\"family\", \"msvc\"}, {\"version\", _MSC_VER}};\n#elif defined(__PGI)\n        result[\"compiler\"] = {{\"family\", \"pgcpp\"}, {\"version\", __PGI}};\n#elif defined(__SUNPRO_CC)\n        result[\"compiler\"] = {{\"family\", \"sunpro\"}, {\"version\", __SUNPRO_CC}};\n#else\n        result[\"compiler\"] = {{\"family\", \"unknown\"}, {\"version\", \"unknown\"}};\n#endif\n\n#if defined(_MSVC_LANG)\n        result[\"compiler\"][\"c++\"] = std::to_string(_MSVC_LANG);\n#elif defined(__cplusplus)\n        result[\"compiler\"][\"c++\"] = std::to_string(__cplusplus);\n#else\n        result[\"compiler\"][\"c++\"] = \"unknown\";\n#endif\n        return result;\n    }\n\n    ///////////////////////////\n    // JSON value data types //\n    ///////////////////////////\n\n    /// @name JSON value data types\n    /// The data types to store a JSON value. These types are derived from\n    /// the template arguments passed to class @ref basic_json.\n    /// @{\n\n    /// @brief default object key comparator type\n    /// The actual object key comparator type (@ref object_comparator_t) may be\n    /// different.\n    /// @sa https://json.nlohmann.me/api/basic_json/default_object_comparator_t/\n#if defined(JSON_HAS_CPP_14)\n    // use of transparent comparator avoids unnecessary repeated construction of temporaries\n    // in functions involving lookup by key with types other than object_t::key_type (aka. StringType)\n    using default_object_comparator_t = std::less<>;\n#else\n    using default_object_comparator_t = std::less<StringType>;\n#endif\n\n    /// @brief a type for an object\n    /// @sa https://json.nlohmann.me/api/basic_json/object_t/\n    using object_t = ObjectType<StringType,\n          basic_json,\n          default_object_comparator_t,\n          AllocatorType<std::pair<const StringType,\n          basic_json>>>;\n\n    /// @brief a type for an array\n    /// @sa https://json.nlohmann.me/api/basic_json/array_t/\n    using array_t = ArrayType<basic_json, AllocatorType<basic_json>>;\n\n    /// @brief a type for a string\n    /// @sa https://json.nlohmann.me/api/basic_json/string_t/\n    using string_t = StringType;\n\n    /// @brief a type for a boolean\n    /// @sa https://json.nlohmann.me/api/basic_json/boolean_t/\n    using boolean_t = BooleanType;\n\n    /// @brief a type for a number (integer)\n    /// @sa https://json.nlohmann.me/api/basic_json/number_integer_t/\n    using number_integer_t = NumberIntegerType;\n\n    /// @brief a type for a number (unsigned)\n    /// @sa https://json.nlohmann.me/api/basic_json/number_unsigned_t/\n    using number_unsigned_t = NumberUnsignedType;\n\n    /// @brief a type for a number (floating-point)\n    /// @sa https://json.nlohmann.me/api/basic_json/number_float_t/\n    using number_float_t = NumberFloatType;\n\n    /// @brief a type for a packed binary type\n    /// @sa https://json.nlohmann.me/api/basic_json/binary_t/\n    using binary_t = nlohmann::byte_container_with_subtype<BinaryType>;\n\n    /// @brief object key comparator type\n    /// @sa https://json.nlohmann.me/api/basic_json/object_comparator_t/\n    using object_comparator_t = detail::actual_object_comparator_t<basic_json>;\n\n    /// @}\n\n  private:\n\n    /// helper for exception-safe object creation\n    template<typename T, typename... Args>\n    JSON_HEDLEY_RETURNS_NON_NULL\n    static T* create(Args&& ... args)\n    {\n        AllocatorType<T> alloc;\n        using AllocatorTraits = std::allocator_traits<AllocatorType<T>>;\n\n        auto deleter = [&](T * obj)\n        {\n            AllocatorTraits::deallocate(alloc, obj, 1);\n        };\n        std::unique_ptr<T, decltype(deleter)> obj(AllocatorTraits::allocate(alloc, 1), deleter);\n        AllocatorTraits::construct(alloc, obj.get(), std::forward<Args>(args)...);\n        JSON_ASSERT(obj != nullptr);\n        return obj.release();\n    }\n\n    ////////////////////////\n    // JSON value storage //\n    ////////////////////////\n\n  JSON_PRIVATE_UNLESS_TESTED:\n    /*!\n    @brief a JSON value\n\n    The actual storage for a JSON value of the @ref basic_json class. This\n    union combines the different storage types for the JSON value types\n    defined in @ref value_t.\n\n    JSON type | value_t type    | used type\n    --------- | --------------- | ------------------------\n    object    | object          | pointer to @ref object_t\n    array     | array           | pointer to @ref array_t\n    string    | string          | pointer to @ref string_t\n    boolean   | boolean         | @ref boolean_t\n    number    | number_integer  | @ref number_integer_t\n    number    | number_unsigned | @ref number_unsigned_t\n    number    | number_float    | @ref number_float_t\n    binary    | binary          | pointer to @ref binary_t\n    null      | null            | *no value is stored*\n\n    @note Variable-length types (objects, arrays, and strings) are stored as\n    pointers. The size of the union should not exceed 64 bits if the default\n    value types are used.\n\n    @since version 1.0.0\n    */\n    union json_value\n    {\n        /// object (stored with pointer to save storage)\n        object_t* object;\n        /// array (stored with pointer to save storage)\n        array_t* array;\n        /// string (stored with pointer to save storage)\n        string_t* string;\n        /// binary (stored with pointer to save storage)\n        binary_t* binary;\n        /// boolean\n        boolean_t boolean;\n        /// number (integer)\n        number_integer_t number_integer;\n        /// number (unsigned integer)\n        number_unsigned_t number_unsigned;\n        /// number (floating-point)\n        number_float_t number_float;\n\n        /// default constructor (for null values)\n        json_value() = default;\n        /// constructor for booleans\n        json_value(boolean_t v) noexcept : boolean(v) {}\n        /// constructor for numbers (integer)\n        json_value(number_integer_t v) noexcept : number_integer(v) {}\n        /// constructor for numbers (unsigned)\n        json_value(number_unsigned_t v) noexcept : number_unsigned(v) {}\n        /// constructor for numbers (floating-point)\n        json_value(number_float_t v) noexcept : number_float(v) {}\n        /// constructor for empty values of a given type\n        json_value(value_t t)\n        {\n            switch (t)\n            {\n                case value_t::object:\n                {\n                    object = create<object_t>();\n                    break;\n                }\n\n                case value_t::array:\n                {\n                    array = create<array_t>();\n                    break;\n                }\n\n                case value_t::string:\n                {\n                    string = create<string_t>(\"\");\n                    break;\n                }\n\n                case value_t::binary:\n                {\n                    binary = create<binary_t>();\n                    break;\n                }\n\n                case value_t::boolean:\n                {\n                    boolean = static_cast<boolean_t>(false);\n                    break;\n                }\n\n                case value_t::number_integer:\n                {\n                    number_integer = static_cast<number_integer_t>(0);\n                    break;\n                }\n\n                case value_t::number_unsigned:\n                {\n                    number_unsigned = static_cast<number_unsigned_t>(0);\n                    break;\n                }\n\n                case value_t::number_float:\n                {\n                    number_float = static_cast<number_float_t>(0.0);\n                    break;\n                }\n\n                case value_t::null:\n                {\n                    object = nullptr;  // silence warning, see #821\n                    break;\n                }\n\n                case value_t::discarded:\n                default:\n                {\n                    object = nullptr;  // silence warning, see #821\n                    if (JSON_HEDLEY_UNLIKELY(t == value_t::null))\n                    {\n                        JSON_THROW(other_error::create(500, \"961c151d2e87f2686a955a9be24d316f1362bf21 3.11.3\", nullptr)); // LCOV_EXCL_LINE\n                    }\n                    break;\n                }\n            }\n        }\n\n        /// constructor for strings\n        json_value(const string_t& value) : string(create<string_t>(value)) {}\n\n        /// constructor for rvalue strings\n        json_value(string_t&& value) : string(create<string_t>(std::move(value))) {}\n\n        /// constructor for objects\n        json_value(const object_t& value) : object(create<object_t>(value)) {}\n\n        /// constructor for rvalue objects\n        json_value(object_t&& value) : object(create<object_t>(std::move(value))) {}\n\n        /// constructor for arrays\n        json_value(const array_t& value) : array(create<array_t>(value)) {}\n\n        /// constructor for rvalue arrays\n        json_value(array_t&& value) : array(create<array_t>(std::move(value))) {}\n\n        /// constructor for binary arrays\n        json_value(const typename binary_t::container_type& value) : binary(create<binary_t>(value)) {}\n\n        /// constructor for rvalue binary arrays\n        json_value(typename binary_t::container_type&& value) : binary(create<binary_t>(std::move(value))) {}\n\n        /// constructor for binary arrays (internal type)\n        json_value(const binary_t& value) : binary(create<binary_t>(value)) {}\n\n        /// constructor for rvalue binary arrays (internal type)\n        json_value(binary_t&& value) : binary(create<binary_t>(std::move(value))) {}\n\n        void destroy(value_t t)\n        {\n            if (\n                (t == value_t::object && object == nullptr) ||\n                (t == value_t::array && array == nullptr) ||\n                (t == value_t::string && string == nullptr) ||\n                (t == value_t::binary && binary == nullptr)\n            )\n            {\n                //not initialized (e.g. due to exception in the ctor)\n                return;\n            }\n            if (t == value_t::array || t == value_t::object)\n            {\n                // flatten the current json_value to a heap-allocated stack\n                std::vector<basic_json> stack;\n\n                // move the top-level items to stack\n                if (t == value_t::array)\n                {\n                    stack.reserve(array->size());\n                    std::move(array->begin(), array->end(), std::back_inserter(stack));\n                }\n                else\n                {\n                    stack.reserve(object->size());\n                    for (auto&& it : *object)\n                    {\n                        stack.push_back(std::move(it.second));\n                    }\n                }\n\n                while (!stack.empty())\n                {\n                    // move the last item to local variable to be processed\n                    basic_json current_item(std::move(stack.back()));\n                    stack.pop_back();\n\n                    // if current_item is array/object, move\n                    // its children to the stack to be processed later\n                    if (current_item.is_array())\n                    {\n                        std::move(current_item.m_data.m_value.array->begin(), current_item.m_data.m_value.array->end(), std::back_inserter(stack));\n\n                        current_item.m_data.m_value.array->clear();\n                    }\n                    else if (current_item.is_object())\n                    {\n                        for (auto&& it : *current_item.m_data.m_value.object)\n                        {\n                            stack.push_back(std::move(it.second));\n                        }\n\n                        current_item.m_data.m_value.object->clear();\n                    }\n\n                    // it's now safe that current_item get destructed\n                    // since it doesn't have any children\n                }\n            }\n\n            switch (t)\n            {\n                case value_t::object:\n                {\n                    AllocatorType<object_t> alloc;\n                    std::allocator_traits<decltype(alloc)>::destroy(alloc, object);\n                    std::allocator_traits<decltype(alloc)>::deallocate(alloc, object, 1);\n                    break;\n                }\n\n                case value_t::array:\n                {\n                    AllocatorType<array_t> alloc;\n                    std::allocator_traits<decltype(alloc)>::destroy(alloc, array);\n                    std::allocator_traits<decltype(alloc)>::deallocate(alloc, array, 1);\n                    break;\n                }\n\n                case value_t::string:\n                {\n                    AllocatorType<string_t> alloc;\n                    std::allocator_traits<decltype(alloc)>::destroy(alloc, string);\n                    std::allocator_traits<decltype(alloc)>::deallocate(alloc, string, 1);\n                    break;\n                }\n\n                case value_t::binary:\n                {\n                    AllocatorType<binary_t> alloc;\n                    std::allocator_traits<decltype(alloc)>::destroy(alloc, binary);\n                    std::allocator_traits<decltype(alloc)>::deallocate(alloc, binary, 1);\n                    break;\n                }\n\n                case value_t::null:\n                case value_t::boolean:\n                case value_t::number_integer:\n                case value_t::number_unsigned:\n                case value_t::number_float:\n                case value_t::discarded:\n                default:\n                {\n                    break;\n                }\n            }\n        }\n    };\n\n  private:\n    /*!\n    @brief checks the class invariants\n\n    This function asserts the class invariants. It needs to be called at the\n    end of every constructor to make sure that created objects respect the\n    invariant. Furthermore, it has to be called each time the type of a JSON\n    value is changed, because the invariant expresses a relationship between\n    @a m_type and @a m_value.\n\n    Furthermore, the parent relation is checked for arrays and objects: If\n    @a check_parents true and the value is an array or object, then the\n    container's elements must have the current value as parent.\n\n    @param[in] check_parents  whether the parent relation should be checked.\n               The value is true by default and should only be set to false\n               during destruction of objects when the invariant does not\n               need to hold.\n    */\n    void assert_invariant(bool check_parents = true) const noexcept\n    {\n        JSON_ASSERT(m_data.m_type != value_t::object || m_data.m_value.object != nullptr);\n        JSON_ASSERT(m_data.m_type != value_t::array || m_data.m_value.array != nullptr);\n        JSON_ASSERT(m_data.m_type != value_t::string || m_data.m_value.string != nullptr);\n        JSON_ASSERT(m_data.m_type != value_t::binary || m_data.m_value.binary != nullptr);\n\n#if JSON_DIAGNOSTICS\n        JSON_TRY\n        {\n            // cppcheck-suppress assertWithSideEffect\n            JSON_ASSERT(!check_parents || !is_structured() || std::all_of(begin(), end(), [this](const basic_json & j)\n            {\n                return j.m_parent == this;\n            }));\n        }\n        JSON_CATCH(...) {} // LCOV_EXCL_LINE\n#endif\n        static_cast<void>(check_parents);\n    }\n\n    void set_parents()\n    {\n#if JSON_DIAGNOSTICS\n        switch (m_data.m_type)\n        {\n            case value_t::array:\n            {\n                for (auto& element : *m_data.m_value.array)\n                {\n                    element.m_parent = this;\n                }\n                break;\n            }\n\n            case value_t::object:\n            {\n                for (auto& element : *m_data.m_value.object)\n                {\n                    element.second.m_parent = this;\n                }\n                break;\n            }\n\n            case value_t::null:\n            case value_t::string:\n            case value_t::boolean:\n            case value_t::number_integer:\n            case value_t::number_unsigned:\n            case value_t::number_float:\n            case value_t::binary:\n            case value_t::discarded:\n            default:\n                break;\n        }\n#endif\n    }\n\n    iterator set_parents(iterator it, typename iterator::difference_type count_set_parents)\n    {\n#if JSON_DIAGNOSTICS\n        for (typename iterator::difference_type i = 0; i < count_set_parents; ++i)\n        {\n            (it + i)->m_parent = this;\n        }\n#else\n        static_cast<void>(count_set_parents);\n#endif\n        return it;\n    }\n\n    reference set_parent(reference j, std::size_t old_capacity = static_cast<std::size_t>(-1))\n    {\n#if JSON_DIAGNOSTICS\n        if (old_capacity != static_cast<std::size_t>(-1))\n        {\n            // see https://github.com/nlohmann/json/issues/2838\n            JSON_ASSERT(type() == value_t::array);\n            if (JSON_HEDLEY_UNLIKELY(m_data.m_value.array->capacity() != old_capacity))\n            {\n                // capacity has changed: update all parents\n                set_parents();\n                return j;\n            }\n        }\n\n        // ordered_json uses a vector internally, so pointers could have\n        // been invalidated; see https://github.com/nlohmann/json/issues/2962\n#ifdef JSON_HEDLEY_MSVC_VERSION\n#pragma warning(push )\n#pragma warning(disable : 4127) // ignore warning to replace if with if constexpr\n#endif\n        if (detail::is_ordered_map<object_t>::value)\n        {\n            set_parents();\n            return j;\n        }\n#ifdef JSON_HEDLEY_MSVC_VERSION\n#pragma warning( pop )\n#endif\n\n        j.m_parent = this;\n#else\n        static_cast<void>(j);\n        static_cast<void>(old_capacity);\n#endif\n        return j;\n    }\n\n  public:\n    //////////////////////////\n    // JSON parser callback //\n    //////////////////////////\n\n    /// @brief parser event types\n    /// @sa https://json.nlohmann.me/api/basic_json/parse_event_t/\n    using parse_event_t = detail::parse_event_t;\n\n    /// @brief per-element parser callback type\n    /// @sa https://json.nlohmann.me/api/basic_json/parser_callback_t/\n    using parser_callback_t = detail::parser_callback_t<basic_json>;\n\n    //////////////////\n    // constructors //\n    //////////////////\n\n    /// @name constructors and destructors\n    /// Constructors of class @ref basic_json, copy/move constructor, copy\n    /// assignment, static functions creating objects, and the destructor.\n    /// @{\n\n    /// @brief create an empty value with a given type\n    /// @sa https://json.nlohmann.me/api/basic_json/basic_json/\n    basic_json(const value_t v)\n        : m_data(v)\n    {\n        assert_invariant();\n    }\n\n    /// @brief create a null object\n    /// @sa https://json.nlohmann.me/api/basic_json/basic_json/\n    basic_json(std::nullptr_t = nullptr) noexcept // NOLINT(bugprone-exception-escape)\n        : basic_json(value_t::null)\n    {\n        assert_invariant();\n    }\n\n    /// @brief create a JSON value from compatible types\n    /// @sa https://json.nlohmann.me/api/basic_json/basic_json/\n    template < typename CompatibleType,\n               typename U = detail::uncvref_t<CompatibleType>,\n               detail::enable_if_t <\n                   !detail::is_basic_json<U>::value && detail::is_compatible_type<basic_json_t, U>::value, int > = 0 >\n    basic_json(CompatibleType && val) noexcept(noexcept( // NOLINT(bugprone-forwarding-reference-overload,bugprone-exception-escape)\n                JSONSerializer<U>::to_json(std::declval<basic_json_t&>(),\n                                           std::forward<CompatibleType>(val))))\n    {\n        JSONSerializer<U>::to_json(*this, std::forward<CompatibleType>(val));\n        set_parents();\n        assert_invariant();\n    }\n\n    /// @brief create a JSON value from an existing one\n    /// @sa https://json.nlohmann.me/api/basic_json/basic_json/\n    template < typename BasicJsonType,\n               detail::enable_if_t <\n                   detail::is_basic_json<BasicJsonType>::value&& !std::is_same<basic_json, BasicJsonType>::value, int > = 0 >\n    basic_json(const BasicJsonType& val)\n    {\n        using other_boolean_t = typename BasicJsonType::boolean_t;\n        using other_number_float_t = typename BasicJsonType::number_float_t;\n        using other_number_integer_t = typename BasicJsonType::number_integer_t;\n        using other_number_unsigned_t = typename BasicJsonType::number_unsigned_t;\n        using other_string_t = typename BasicJsonType::string_t;\n        using other_object_t = typename BasicJsonType::object_t;\n        using other_array_t = typename BasicJsonType::array_t;\n        using other_binary_t = typename BasicJsonType::binary_t;\n\n        switch (val.type())\n        {\n            case value_t::boolean:\n                JSONSerializer<other_boolean_t>::to_json(*this, val.template get<other_boolean_t>());\n                break;\n            case value_t::number_float:\n                JSONSerializer<other_number_float_t>::to_json(*this, val.template get<other_number_float_t>());\n                break;\n            case value_t::number_integer:\n                JSONSerializer<other_number_integer_t>::to_json(*this, val.template get<other_number_integer_t>());\n                break;\n            case value_t::number_unsigned:\n                JSONSerializer<other_number_unsigned_t>::to_json(*this, val.template get<other_number_unsigned_t>());\n                break;\n            case value_t::string:\n                JSONSerializer<other_string_t>::to_json(*this, val.template get_ref<const other_string_t&>());\n                break;\n            case value_t::object:\n                JSONSerializer<other_object_t>::to_json(*this, val.template get_ref<const other_object_t&>());\n                break;\n            case value_t::array:\n                JSONSerializer<other_array_t>::to_json(*this, val.template get_ref<const other_array_t&>());\n                break;\n            case value_t::binary:\n                JSONSerializer<other_binary_t>::to_json(*this, val.template get_ref<const other_binary_t&>());\n                break;\n            case value_t::null:\n                *this = nullptr;\n                break;\n            case value_t::discarded:\n                m_data.m_type = value_t::discarded;\n                break;\n            default:            // LCOV_EXCL_LINE\n                JSON_ASSERT(false); // NOLINT(cert-dcl03-c,hicpp-static-assert,misc-static-assert) LCOV_EXCL_LINE\n        }\n        JSON_ASSERT(m_data.m_type == val.type());\n        set_parents();\n        assert_invariant();\n    }\n\n    /// @brief create a container (array or object) from an initializer list\n    /// @sa https://json.nlohmann.me/api/basic_json/basic_json/\n    basic_json(initializer_list_t init,\n               bool type_deduction = true,\n               value_t manual_type = value_t::array)\n    {\n        // check if each element is an array with two elements whose first\n        // element is a string\n        bool is_an_object = std::all_of(init.begin(), init.end(),\n                                        [](const detail::json_ref<basic_json>& element_ref)\n        {\n            // The cast is to ensure op[size_type] is called, bearing in mind size_type may not be int;\n            // (many string types can be constructed from 0 via its null-pointer guise, so we get a\n            // broken call to op[key_type], the wrong semantics and a 4804 warning on Windows)\n            return element_ref->is_array() && element_ref->size() == 2 && (*element_ref)[static_cast<size_type>(0)].is_string();\n        });\n\n        // adjust type if type deduction is not wanted\n        if (!type_deduction)\n        {\n            // if array is wanted, do not create an object though possible\n            if (manual_type == value_t::array)\n            {\n                is_an_object = false;\n            }\n\n            // if object is wanted but impossible, throw an exception\n            if (JSON_HEDLEY_UNLIKELY(manual_type == value_t::object && !is_an_object))\n            {\n                JSON_THROW(type_error::create(301, \"cannot create object from initializer list\", nullptr));\n            }\n        }\n\n        if (is_an_object)\n        {\n            // the initializer list is a list of pairs -> create object\n            m_data.m_type = value_t::object;\n            m_data.m_value = value_t::object;\n\n            for (auto& element_ref : init)\n            {\n                auto element = element_ref.moved_or_copied();\n                m_data.m_value.object->emplace(\n                    std::move(*((*element.m_data.m_value.array)[0].m_data.m_value.string)),\n                    std::move((*element.m_data.m_value.array)[1]));\n            }\n        }\n        else\n        {\n            // the initializer list describes an array -> create array\n            m_data.m_type = value_t::array;\n            m_data.m_value.array = create<array_t>(init.begin(), init.end());\n        }\n\n        set_parents();\n        assert_invariant();\n    }\n\n    /// @brief explicitly create a binary array (without subtype)\n    /// @sa https://json.nlohmann.me/api/basic_json/binary/\n    JSON_HEDLEY_WARN_UNUSED_RESULT\n    static basic_json binary(const typename binary_t::container_type& init)\n    {\n        auto res = basic_json();\n        res.m_data.m_type = value_t::binary;\n        res.m_data.m_value = init;\n        return res;\n    }\n\n    /// @brief explicitly create a binary array (with subtype)\n    /// @sa https://json.nlohmann.me/api/basic_json/binary/\n    JSON_HEDLEY_WARN_UNUSED_RESULT\n    static basic_json binary(const typename binary_t::container_type& init, typename binary_t::subtype_type subtype)\n    {\n        auto res = basic_json();\n        res.m_data.m_type = value_t::binary;\n        res.m_data.m_value = binary_t(init, subtype);\n        return res;\n    }\n\n    /// @brief explicitly create a binary array\n    /// @sa https://json.nlohmann.me/api/basic_json/binary/\n    JSON_HEDLEY_WARN_UNUSED_RESULT\n    static basic_json binary(typename binary_t::container_type&& init)\n    {\n        auto res = basic_json();\n        res.m_data.m_type = value_t::binary;\n        res.m_data.m_value = std::move(init);\n        return res;\n    }\n\n    /// @brief explicitly create a binary array (with subtype)\n    /// @sa https://json.nlohmann.me/api/basic_json/binary/\n    JSON_HEDLEY_WARN_UNUSED_RESULT\n    static basic_json binary(typename binary_t::container_type&& init, typename binary_t::subtype_type subtype)\n    {\n        auto res = basic_json();\n        res.m_data.m_type = value_t::binary;\n        res.m_data.m_value = binary_t(std::move(init), subtype);\n        return res;\n    }\n\n    /// @brief explicitly create an array from an initializer list\n    /// @sa https://json.nlohmann.me/api/basic_json/array/\n    JSON_HEDLEY_WARN_UNUSED_RESULT\n    static basic_json array(initializer_list_t init = {})\n    {\n        return basic_json(init, false, value_t::array);\n    }\n\n    /// @brief explicitly create an object from an initializer list\n    /// @sa https://json.nlohmann.me/api/basic_json/object/\n    JSON_HEDLEY_WARN_UNUSED_RESULT\n    static basic_json object(initializer_list_t init = {})\n    {\n        return basic_json(init, false, value_t::object);\n    }\n\n    /// @brief construct an array with count copies of given value\n    /// @sa https://json.nlohmann.me/api/basic_json/basic_json/\n    basic_json(size_type cnt, const basic_json& val):\n        m_data{cnt, val}\n    {\n        set_parents();\n        assert_invariant();\n    }\n\n    /// @brief construct a JSON container given an iterator range\n    /// @sa https://json.nlohmann.me/api/basic_json/basic_json/\n    template < class InputIT, typename std::enable_if <\n                   std::is_same<InputIT, typename basic_json_t::iterator>::value ||\n                   std::is_same<InputIT, typename basic_json_t::const_iterator>::value, int >::type = 0 >\n    basic_json(InputIT first, InputIT last)\n    {\n        JSON_ASSERT(first.m_object != nullptr);\n        JSON_ASSERT(last.m_object != nullptr);\n\n        // make sure iterator fits the current value\n        if (JSON_HEDLEY_UNLIKELY(first.m_object != last.m_object))\n        {\n            JSON_THROW(invalid_iterator::create(201, \"iterators are not compatible\", nullptr));\n        }\n\n        // copy type from first iterator\n        m_data.m_type = first.m_object->m_data.m_type;\n\n        // check if iterator range is complete for primitive values\n        switch (m_data.m_type)\n        {\n            case value_t::boolean:\n            case value_t::number_float:\n            case value_t::number_integer:\n            case value_t::number_unsigned:\n            case value_t::string:\n            {\n                if (JSON_HEDLEY_UNLIKELY(!first.m_it.primitive_iterator.is_begin()\n                                         || !last.m_it.primitive_iterator.is_end()))\n                {\n                    JSON_THROW(invalid_iterator::create(204, \"iterators out of range\", first.m_object));\n                }\n                break;\n            }\n\n            case value_t::null:\n            case value_t::object:\n            case value_t::array:\n            case value_t::binary:\n            case value_t::discarded:\n            default:\n                break;\n        }\n\n        switch (m_data.m_type)\n        {\n            case value_t::number_integer:\n            {\n                m_data.m_value.number_integer = first.m_object->m_data.m_value.number_integer;\n                break;\n            }\n\n            case value_t::number_unsigned:\n            {\n                m_data.m_value.number_unsigned = first.m_object->m_data.m_value.number_unsigned;\n                break;\n            }\n\n            case value_t::number_float:\n            {\n                m_data.m_value.number_float = first.m_object->m_data.m_value.number_float;\n                break;\n            }\n\n            case value_t::boolean:\n            {\n                m_data.m_value.boolean = first.m_object->m_data.m_value.boolean;\n                break;\n            }\n\n            case value_t::string:\n            {\n                m_data.m_value = *first.m_object->m_data.m_value.string;\n                break;\n            }\n\n            case value_t::object:\n            {\n                m_data.m_value.object = create<object_t>(first.m_it.object_iterator,\n                                        last.m_it.object_iterator);\n                break;\n            }\n\n            case value_t::array:\n            {\n                m_data.m_value.array = create<array_t>(first.m_it.array_iterator,\n                                                       last.m_it.array_iterator);\n                break;\n            }\n\n            case value_t::binary:\n            {\n                m_data.m_value = *first.m_object->m_data.m_value.binary;\n                break;\n            }\n\n            case value_t::null:\n            case value_t::discarded:\n            default:\n                JSON_THROW(invalid_iterator::create(206, detail::concat(\"cannot construct with iterators from \", first.m_object->type_name()), first.m_object));\n        }\n\n        set_parents();\n        assert_invariant();\n    }\n\n    ///////////////////////////////////////\n    // other constructors and destructor //\n    ///////////////////////////////////////\n\n    template<typename JsonRef,\n             detail::enable_if_t<detail::conjunction<detail::is_json_ref<JsonRef>,\n                                 std::is_same<typename JsonRef::value_type, basic_json>>::value, int> = 0 >\n    basic_json(const JsonRef& ref) : basic_json(ref.moved_or_copied()) {}\n\n    /// @brief copy constructor\n    /// @sa https://json.nlohmann.me/api/basic_json/basic_json/\n    basic_json(const basic_json& other)\n        : json_base_class_t(other)\n    {\n        m_data.m_type = other.m_data.m_type;\n        // check of passed value is valid\n        other.assert_invariant();\n\n        switch (m_data.m_type)\n        {\n            case value_t::object:\n            {\n                m_data.m_value = *other.m_data.m_value.object;\n                break;\n            }\n\n            case value_t::array:\n            {\n                m_data.m_value = *other.m_data.m_value.array;\n                break;\n            }\n\n            case value_t::string:\n            {\n                m_data.m_value = *other.m_data.m_value.string;\n                break;\n            }\n\n            case value_t::boolean:\n            {\n                m_data.m_value = other.m_data.m_value.boolean;\n                break;\n            }\n\n            case value_t::number_integer:\n            {\n                m_data.m_value = other.m_data.m_value.number_integer;\n                break;\n            }\n\n            case value_t::number_unsigned:\n            {\n                m_data.m_value = other.m_data.m_value.number_unsigned;\n                break;\n            }\n\n            case value_t::number_float:\n            {\n                m_data.m_value = other.m_data.m_value.number_float;\n                break;\n            }\n\n            case value_t::binary:\n            {\n                m_data.m_value = *other.m_data.m_value.binary;\n                break;\n            }\n\n            case value_t::null:\n            case value_t::discarded:\n            default:\n                break;\n        }\n\n        set_parents();\n        assert_invariant();\n    }\n\n    /// @brief move constructor\n    /// @sa https://json.nlohmann.me/api/basic_json/basic_json/\n    basic_json(basic_json&& other) noexcept\n        : json_base_class_t(std::forward<json_base_class_t>(other)),\n          m_data(std::move(other.m_data))\n    {\n        // check that passed value is valid\n        other.assert_invariant(false);\n\n        // invalidate payload\n        other.m_data.m_type = value_t::null;\n        other.m_data.m_value = {};\n\n        set_parents();\n        assert_invariant();\n    }\n\n    /// @brief copy assignment\n    /// @sa https://json.nlohmann.me/api/basic_json/operator=/\n    basic_json& operator=(basic_json other) noexcept (\n        std::is_nothrow_move_constructible<value_t>::value&&\n        std::is_nothrow_move_assignable<value_t>::value&&\n        std::is_nothrow_move_constructible<json_value>::value&&\n        std::is_nothrow_move_assignable<json_value>::value&&\n        std::is_nothrow_move_assignable<json_base_class_t>::value\n    )\n    {\n        // check that passed value is valid\n        other.assert_invariant();\n\n        using std::swap;\n        swap(m_data.m_type, other.m_data.m_type);\n        swap(m_data.m_value, other.m_data.m_value);\n        json_base_class_t::operator=(std::move(other));\n\n        set_parents();\n        assert_invariant();\n        return *this;\n    }\n\n    /// @brief destructor\n    /// @sa https://json.nlohmann.me/api/basic_json/~basic_json/\n    ~basic_json() noexcept\n    {\n        assert_invariant(false);\n    }\n\n    /// @}\n\n  public:\n    ///////////////////////\n    // object inspection //\n    ///////////////////////\n\n    /// @name object inspection\n    /// Functions to inspect the type of a JSON value.\n    /// @{\n\n    /// @brief serialization\n    /// @sa https://json.nlohmann.me/api/basic_json/dump/\n    string_t dump(const int indent = -1,\n                  const char indent_char = ' ',\n                  const bool ensure_ascii = false,\n                  const error_handler_t error_handler = error_handler_t::strict) const\n    {\n        string_t result;\n        serializer s(detail::output_adapter<char, string_t>(result), indent_char, error_handler);\n\n        if (indent >= 0)\n        {\n            s.dump(*this, true, ensure_ascii, static_cast<unsigned int>(indent));\n        }\n        else\n        {\n            s.dump(*this, false, ensure_ascii, 0);\n        }\n\n        return result;\n    }\n\n    /// @brief return the type of the JSON value (explicit)\n    /// @sa https://json.nlohmann.me/api/basic_json/type/\n    constexpr value_t type() const noexcept\n    {\n        return m_data.m_type;\n    }\n\n    /// @brief return whether type is primitive\n    /// @sa https://json.nlohmann.me/api/basic_json/is_primitive/\n    constexpr bool is_primitive() const noexcept\n    {\n        return is_null() || is_string() || is_boolean() || is_number() || is_binary();\n    }\n\n    /// @brief return whether type is structured\n    /// @sa https://json.nlohmann.me/api/basic_json/is_structured/\n    constexpr bool is_structured() const noexcept\n    {\n        return is_array() || is_object();\n    }\n\n    /// @brief return whether value is null\n    /// @sa https://json.nlohmann.me/api/basic_json/is_null/\n    constexpr bool is_null() const noexcept\n    {\n        return m_data.m_type == value_t::null;\n    }\n\n    /// @brief return whether value is a boolean\n    /// @sa https://json.nlohmann.me/api/basic_json/is_boolean/\n    constexpr bool is_boolean() const noexcept\n    {\n        return m_data.m_type == value_t::boolean;\n    }\n\n    /// @brief return whether value is a number\n    /// @sa https://json.nlohmann.me/api/basic_json/is_number/\n    constexpr bool is_number() const noexcept\n    {\n        return is_number_integer() || is_number_float();\n    }\n\n    /// @brief return whether value is an integer number\n    /// @sa https://json.nlohmann.me/api/basic_json/is_number_integer/\n    constexpr bool is_number_integer() const noexcept\n    {\n        return m_data.m_type == value_t::number_integer || m_data.m_type == value_t::number_unsigned;\n    }\n\n    /// @brief return whether value is an unsigned integer number\n    /// @sa https://json.nlohmann.me/api/basic_json/is_number_unsigned/\n    constexpr bool is_number_unsigned() const noexcept\n    {\n        return m_data.m_type == value_t::number_unsigned;\n    }\n\n    /// @brief return whether value is a floating-point number\n    /// @sa https://json.nlohmann.me/api/basic_json/is_number_float/\n    constexpr bool is_number_float() const noexcept\n    {\n        return m_data.m_type == value_t::number_float;\n    }\n\n    /// @brief return whether value is an object\n    /// @sa https://json.nlohmann.me/api/basic_json/is_object/\n    constexpr bool is_object() const noexcept\n    {\n        return m_data.m_type == value_t::object;\n    }\n\n    /// @brief return whether value is an array\n    /// @sa https://json.nlohmann.me/api/basic_json/is_array/\n    constexpr bool is_array() const noexcept\n    {\n        return m_data.m_type == value_t::array;\n    }\n\n    /// @brief return whether value is a string\n    /// @sa https://json.nlohmann.me/api/basic_json/is_string/\n    constexpr bool is_string() const noexcept\n    {\n        return m_data.m_type == value_t::string;\n    }\n\n    /// @brief return whether value is a binary array\n    /// @sa https://json.nlohmann.me/api/basic_json/is_binary/\n    constexpr bool is_binary() const noexcept\n    {\n        return m_data.m_type == value_t::binary;\n    }\n\n    /// @brief return whether value is discarded\n    /// @sa https://json.nlohmann.me/api/basic_json/is_discarded/\n    constexpr bool is_discarded() const noexcept\n    {\n        return m_data.m_type == value_t::discarded;\n    }\n\n    /// @brief return the type of the JSON value (implicit)\n    /// @sa https://json.nlohmann.me/api/basic_json/operator_value_t/\n    constexpr operator value_t() const noexcept\n    {\n        return m_data.m_type;\n    }\n\n    /// @}\n\n  private:\n    //////////////////\n    // value access //\n    //////////////////\n\n    /// get a boolean (explicit)\n    boolean_t get_impl(boolean_t* /*unused*/) const\n    {\n        if (JSON_HEDLEY_LIKELY(is_boolean()))\n        {\n            return m_data.m_value.boolean;\n        }\n\n        JSON_THROW(type_error::create(302, detail::concat(\"type must be boolean, but is \", type_name()), this));\n    }\n\n    /// get a pointer to the value (object)\n    object_t* get_impl_ptr(object_t* /*unused*/) noexcept\n    {\n        return is_object() ? m_data.m_value.object : nullptr;\n    }\n\n    /// get a pointer to the value (object)\n    constexpr const object_t* get_impl_ptr(const object_t* /*unused*/) const noexcept\n    {\n        return is_object() ? m_data.m_value.object : nullptr;\n    }\n\n    /// get a pointer to the value (array)\n    array_t* get_impl_ptr(array_t* /*unused*/) noexcept\n    {\n        return is_array() ? m_data.m_value.array : nullptr;\n    }\n\n    /// get a pointer to the value (array)\n    constexpr const array_t* get_impl_ptr(const array_t* /*unused*/) const noexcept\n    {\n        return is_array() ? m_data.m_value.array : nullptr;\n    }\n\n    /// get a pointer to the value (string)\n    string_t* get_impl_ptr(string_t* /*unused*/) noexcept\n    {\n        return is_string() ? m_data.m_value.string : nullptr;\n    }\n\n    /// get a pointer to the value (string)\n    constexpr const string_t* get_impl_ptr(const string_t* /*unused*/) const noexcept\n    {\n        return is_string() ? m_data.m_value.string : nullptr;\n    }\n\n    /// get a pointer to the value (boolean)\n    boolean_t* get_impl_ptr(boolean_t* /*unused*/) noexcept\n    {\n        return is_boolean() ? &m_data.m_value.boolean : nullptr;\n    }\n\n    /// get a pointer to the value (boolean)\n    constexpr const boolean_t* get_impl_ptr(const boolean_t* /*unused*/) const noexcept\n    {\n        return is_boolean() ? &m_data.m_value.boolean : nullptr;\n    }\n\n    /// get a pointer to the value (integer number)\n    number_integer_t* get_impl_ptr(number_integer_t* /*unused*/) noexcept\n    {\n        return is_number_integer() ? &m_data.m_value.number_integer : nullptr;\n    }\n\n    /// get a pointer to the value (integer number)\n    constexpr const number_integer_t* get_impl_ptr(const number_integer_t* /*unused*/) const noexcept\n    {\n        return is_number_integer() ? &m_data.m_value.number_integer : nullptr;\n    }\n\n    /// get a pointer to the value (unsigned number)\n    number_unsigned_t* get_impl_ptr(number_unsigned_t* /*unused*/) noexcept\n    {\n        return is_number_unsigned() ? &m_data.m_value.number_unsigned : nullptr;\n    }\n\n    /// get a pointer to the value (unsigned number)\n    constexpr const number_unsigned_t* get_impl_ptr(const number_unsigned_t* /*unused*/) const noexcept\n    {\n        return is_number_unsigned() ? &m_data.m_value.number_unsigned : nullptr;\n    }\n\n    /// get a pointer to the value (floating-point number)\n    number_float_t* get_impl_ptr(number_float_t* /*unused*/) noexcept\n    {\n        return is_number_float() ? &m_data.m_value.number_float : nullptr;\n    }\n\n    /// get a pointer to the value (floating-point number)\n    constexpr const number_float_t* get_impl_ptr(const number_float_t* /*unused*/) const noexcept\n    {\n        return is_number_float() ? &m_data.m_value.number_float : nullptr;\n    }\n\n    /// get a pointer to the value (binary)\n    binary_t* get_impl_ptr(binary_t* /*unused*/) noexcept\n    {\n        return is_binary() ? m_data.m_value.binary : nullptr;\n    }\n\n    /// get a pointer to the value (binary)\n    constexpr const binary_t* get_impl_ptr(const binary_t* /*unused*/) const noexcept\n    {\n        return is_binary() ? m_data.m_value.binary : nullptr;\n    }\n\n    /*!\n    @brief helper function to implement get_ref()\n\n    This function helps to implement get_ref() without code duplication for\n    const and non-const overloads\n\n    @tparam ThisType will be deduced as `basic_json` or `const basic_json`\n\n    @throw type_error.303 if ReferenceType does not match underlying value\n    type of the current JSON\n    */\n    template<typename ReferenceType, typename ThisType>\n    static ReferenceType get_ref_impl(ThisType& obj)\n    {\n        // delegate the call to get_ptr<>()\n        auto* ptr = obj.template get_ptr<typename std::add_pointer<ReferenceType>::type>();\n\n        if (JSON_HEDLEY_LIKELY(ptr != nullptr))\n        {\n            return *ptr;\n        }\n\n        JSON_THROW(type_error::create(303, detail::concat(\"incompatible ReferenceType for get_ref, actual type is \", obj.type_name()), &obj));\n    }\n\n  public:\n    /// @name value access\n    /// Direct access to the stored value of a JSON value.\n    /// @{\n\n    /// @brief get a pointer value (implicit)\n    /// @sa https://json.nlohmann.me/api/basic_json/get_ptr/\n    template<typename PointerType, typename std::enable_if<\n                 std::is_pointer<PointerType>::value, int>::type = 0>\n    auto get_ptr() noexcept -> decltype(std::declval<basic_json_t&>().get_impl_ptr(std::declval<PointerType>()))\n    {\n        // delegate the call to get_impl_ptr<>()\n        return get_impl_ptr(static_cast<PointerType>(nullptr));\n    }\n\n    /// @brief get a pointer value (implicit)\n    /// @sa https://json.nlohmann.me/api/basic_json/get_ptr/\n    template < typename PointerType, typename std::enable_if <\n                   std::is_pointer<PointerType>::value&&\n                   std::is_const<typename std::remove_pointer<PointerType>::type>::value, int >::type = 0 >\n    constexpr auto get_ptr() const noexcept -> decltype(std::declval<const basic_json_t&>().get_impl_ptr(std::declval<PointerType>()))\n    {\n        // delegate the call to get_impl_ptr<>() const\n        return get_impl_ptr(static_cast<PointerType>(nullptr));\n    }\n\n  private:\n    /*!\n    @brief get a value (explicit)\n\n    Explicit type conversion between the JSON value and a compatible value\n    which is [CopyConstructible](https://en.cppreference.com/w/cpp/named_req/CopyConstructible)\n    and [DefaultConstructible](https://en.cppreference.com/w/cpp/named_req/DefaultConstructible).\n    The value is converted by calling the @ref json_serializer<ValueType>\n    `from_json()` method.\n\n    The function is equivalent to executing\n    @code {.cpp}\n    ValueType ret;\n    JSONSerializer<ValueType>::from_json(*this, ret);\n    return ret;\n    @endcode\n\n    This overloads is chosen if:\n    - @a ValueType is not @ref basic_json,\n    - @ref json_serializer<ValueType> has a `from_json()` method of the form\n      `void from_json(const basic_json&, ValueType&)`, and\n    - @ref json_serializer<ValueType> does not have a `from_json()` method of\n      the form `ValueType from_json(const basic_json&)`\n\n    @tparam ValueType the returned value type\n\n    @return copy of the JSON value, converted to @a ValueType\n\n    @throw what @ref json_serializer<ValueType> `from_json()` method throws\n\n    @liveexample{The example below shows several conversions from JSON values\n    to other types. There a few things to note: (1) Floating-point numbers can\n    be converted to integers\\, (2) A JSON array can be converted to a standard\n    `std::vector<short>`\\, (3) A JSON object can be converted to C++\n    associative containers such as `std::unordered_map<std::string\\,\n    json>`.,get__ValueType_const}\n\n    @since version 2.1.0\n    */\n    template < typename ValueType,\n               detail::enable_if_t <\n                   detail::is_default_constructible<ValueType>::value&&\n                   detail::has_from_json<basic_json_t, ValueType>::value,\n                   int > = 0 >\n    ValueType get_impl(detail::priority_tag<0> /*unused*/) const noexcept(noexcept(\n                JSONSerializer<ValueType>::from_json(std::declval<const basic_json_t&>(), std::declval<ValueType&>())))\n    {\n        auto ret = ValueType();\n        JSONSerializer<ValueType>::from_json(*this, ret);\n        return ret;\n    }\n\n    /*!\n    @brief get a value (explicit); special case\n\n    Explicit type conversion between the JSON value and a compatible value\n    which is **not** [CopyConstructible](https://en.cppreference.com/w/cpp/named_req/CopyConstructible)\n    and **not** [DefaultConstructible](https://en.cppreference.com/w/cpp/named_req/DefaultConstructible).\n    The value is converted by calling the @ref json_serializer<ValueType>\n    `from_json()` method.\n\n    The function is equivalent to executing\n    @code {.cpp}\n    return JSONSerializer<ValueType>::from_json(*this);\n    @endcode\n\n    This overloads is chosen if:\n    - @a ValueType is not @ref basic_json and\n    - @ref json_serializer<ValueType> has a `from_json()` method of the form\n      `ValueType from_json(const basic_json&)`\n\n    @note If @ref json_serializer<ValueType> has both overloads of\n    `from_json()`, this one is chosen.\n\n    @tparam ValueType the returned value type\n\n    @return copy of the JSON value, converted to @a ValueType\n\n    @throw what @ref json_serializer<ValueType> `from_json()` method throws\n\n    @since version 2.1.0\n    */\n    template < typename ValueType,\n               detail::enable_if_t <\n                   detail::has_non_default_from_json<basic_json_t, ValueType>::value,\n                   int > = 0 >\n    ValueType get_impl(detail::priority_tag<1> /*unused*/) const noexcept(noexcept(\n                JSONSerializer<ValueType>::from_json(std::declval<const basic_json_t&>())))\n    {\n        return JSONSerializer<ValueType>::from_json(*this);\n    }\n\n    /*!\n    @brief get special-case overload\n\n    This overloads converts the current @ref basic_json in a different\n    @ref basic_json type\n\n    @tparam BasicJsonType == @ref basic_json\n\n    @return a copy of *this, converted into @a BasicJsonType\n\n    @complexity Depending on the implementation of the called `from_json()`\n                method.\n\n    @since version 3.2.0\n    */\n    template < typename BasicJsonType,\n               detail::enable_if_t <\n                   detail::is_basic_json<BasicJsonType>::value,\n                   int > = 0 >\n    BasicJsonType get_impl(detail::priority_tag<2> /*unused*/) const\n    {\n        return *this;\n    }\n\n    /*!\n    @brief get special-case overload\n\n    This overloads avoids a lot of template boilerplate, it can be seen as the\n    identity method\n\n    @tparam BasicJsonType == @ref basic_json\n\n    @return a copy of *this\n\n    @complexity Constant.\n\n    @since version 2.1.0\n    */\n    template<typename BasicJsonType,\n             detail::enable_if_t<\n                 std::is_same<BasicJsonType, basic_json_t>::value,\n                 int> = 0>\n    basic_json get_impl(detail::priority_tag<3> /*unused*/) const\n    {\n        return *this;\n    }\n\n    /*!\n    @brief get a pointer value (explicit)\n    @copydoc get()\n    */\n    template<typename PointerType,\n             detail::enable_if_t<\n                 std::is_pointer<PointerType>::value,\n                 int> = 0>\n    constexpr auto get_impl(detail::priority_tag<4> /*unused*/) const noexcept\n    -> decltype(std::declval<const basic_json_t&>().template get_ptr<PointerType>())\n    {\n        // delegate the call to get_ptr\n        return get_ptr<PointerType>();\n    }\n\n  public:\n    /*!\n    @brief get a (pointer) value (explicit)\n\n    Performs explicit type conversion between the JSON value and a compatible value if required.\n\n    - If the requested type is a pointer to the internally stored JSON value that pointer is returned.\n    No copies are made.\n\n    - If the requested type is the current @ref basic_json, or a different @ref basic_json convertible\n    from the current @ref basic_json.\n\n    - Otherwise the value is converted by calling the @ref json_serializer<ValueType> `from_json()`\n    method.\n\n    @tparam ValueTypeCV the provided value type\n    @tparam ValueType the returned value type\n\n    @return copy of the JSON value, converted to @tparam ValueType if necessary\n\n    @throw what @ref json_serializer<ValueType> `from_json()` method throws if conversion is required\n\n    @since version 2.1.0\n    */\n    template < typename ValueTypeCV, typename ValueType = detail::uncvref_t<ValueTypeCV>>\n#if defined(JSON_HAS_CPP_14)\n    constexpr\n#endif\n    auto get() const noexcept(\n    noexcept(std::declval<const basic_json_t&>().template get_impl<ValueType>(detail::priority_tag<4> {})))\n    -> decltype(std::declval<const basic_json_t&>().template get_impl<ValueType>(detail::priority_tag<4> {}))\n    {\n        // we cannot static_assert on ValueTypeCV being non-const, because\n        // there is support for get<const basic_json_t>(), which is why we\n        // still need the uncvref\n        static_assert(!std::is_reference<ValueTypeCV>::value,\n                      \"get() cannot be used with reference types, you might want to use get_ref()\");\n        return get_impl<ValueType>(detail::priority_tag<4> {});\n    }\n\n    /*!\n    @brief get a pointer value (explicit)\n\n    Explicit pointer access to the internally stored JSON value. No copies are\n    made.\n\n    @warning The pointer becomes invalid if the underlying JSON object\n    changes.\n\n    @tparam PointerType pointer type; must be a pointer to @ref array_t, @ref\n    object_t, @ref string_t, @ref boolean_t, @ref number_integer_t,\n    @ref number_unsigned_t, or @ref number_float_t.\n\n    @return pointer to the internally stored JSON value if the requested\n    pointer type @a PointerType fits to the JSON value; `nullptr` otherwise\n\n    @complexity Constant.\n\n    @liveexample{The example below shows how pointers to internal values of a\n    JSON value can be requested. Note that no type conversions are made and a\n    `nullptr` is returned if the value and the requested pointer type does not\n    match.,get__PointerType}\n\n    @sa see @ref get_ptr() for explicit pointer-member access\n\n    @since version 1.0.0\n    */\n    template<typename PointerType, typename std::enable_if<\n                 std::is_pointer<PointerType>::value, int>::type = 0>\n    auto get() noexcept -> decltype(std::declval<basic_json_t&>().template get_ptr<PointerType>())\n    {\n        // delegate the call to get_ptr\n        return get_ptr<PointerType>();\n    }\n\n    /// @brief get a value (explicit)\n    /// @sa https://json.nlohmann.me/api/basic_json/get_to/\n    template < typename ValueType,\n               detail::enable_if_t <\n                   !detail::is_basic_json<ValueType>::value&&\n                   detail::has_from_json<basic_json_t, ValueType>::value,\n                   int > = 0 >\n    ValueType & get_to(ValueType& v) const noexcept(noexcept(\n                JSONSerializer<ValueType>::from_json(std::declval<const basic_json_t&>(), v)))\n    {\n        JSONSerializer<ValueType>::from_json(*this, v);\n        return v;\n    }\n\n    // specialization to allow calling get_to with a basic_json value\n    // see https://github.com/nlohmann/json/issues/2175\n    template<typename ValueType,\n             detail::enable_if_t <\n                 detail::is_basic_json<ValueType>::value,\n                 int> = 0>\n    ValueType & get_to(ValueType& v) const\n    {\n        v = *this;\n        return v;\n    }\n\n    template <\n        typename T, std::size_t N,\n        typename Array = T (&)[N], // NOLINT(cppcoreguidelines-avoid-c-arrays,hicpp-avoid-c-arrays,modernize-avoid-c-arrays)\n        detail::enable_if_t <\n            detail::has_from_json<basic_json_t, Array>::value, int > = 0 >\n    Array get_to(T (&v)[N]) const // NOLINT(cppcoreguidelines-avoid-c-arrays,hicpp-avoid-c-arrays,modernize-avoid-c-arrays)\n    noexcept(noexcept(JSONSerializer<Array>::from_json(\n                          std::declval<const basic_json_t&>(), v)))\n    {\n        JSONSerializer<Array>::from_json(*this, v);\n        return v;\n    }\n\n    /// @brief get a reference value (implicit)\n    /// @sa https://json.nlohmann.me/api/basic_json/get_ref/\n    template<typename ReferenceType, typename std::enable_if<\n                 std::is_reference<ReferenceType>::value, int>::type = 0>\n    ReferenceType get_ref()\n    {\n        // delegate call to get_ref_impl\n        return get_ref_impl<ReferenceType>(*this);\n    }\n\n    /// @brief get a reference value (implicit)\n    /// @sa https://json.nlohmann.me/api/basic_json/get_ref/\n    template < typename ReferenceType, typename std::enable_if <\n                   std::is_reference<ReferenceType>::value&&\n                   std::is_const<typename std::remove_reference<ReferenceType>::type>::value, int >::type = 0 >\n    ReferenceType get_ref() const\n    {\n        // delegate call to get_ref_impl\n        return get_ref_impl<ReferenceType>(*this);\n    }\n\n    /*!\n    @brief get a value (implicit)\n\n    Implicit type conversion between the JSON value and a compatible value.\n    The call is realized by calling @ref get() const.\n\n    @tparam ValueType non-pointer type compatible to the JSON value, for\n    instance `int` for JSON integer numbers, `bool` for JSON booleans, or\n    `std::vector` types for JSON arrays. The character type of @ref string_t\n    as well as an initializer list of this type is excluded to avoid\n    ambiguities as these types implicitly convert to `std::string`.\n\n    @return copy of the JSON value, converted to type @a ValueType\n\n    @throw type_error.302 in case passed type @a ValueType is incompatible\n    to the JSON value type (e.g., the JSON value is of type boolean, but a\n    string is requested); see example below\n\n    @complexity Linear in the size of the JSON value.\n\n    @liveexample{The example below shows several conversions from JSON values\n    to other types. There a few things to note: (1) Floating-point numbers can\n    be converted to integers\\, (2) A JSON array can be converted to a standard\n    `std::vector<short>`\\, (3) A JSON object can be converted to C++\n    associative containers such as `std::unordered_map<std::string\\,\n    json>`.,operator__ValueType}\n\n    @since version 1.0.0\n    */\n    template < typename ValueType, typename std::enable_if <\n                   detail::conjunction <\n                       detail::negation<std::is_pointer<ValueType>>,\n                       detail::negation<std::is_same<ValueType, std::nullptr_t>>,\n                       detail::negation<std::is_same<ValueType, detail::json_ref<basic_json>>>,\n                                        detail::negation<std::is_same<ValueType, typename string_t::value_type>>,\n                                        detail::negation<detail::is_basic_json<ValueType>>,\n                                        detail::negation<std::is_same<ValueType, std::initializer_list<typename string_t::value_type>>>,\n#if defined(JSON_HAS_CPP_17) && (defined(__GNUC__) || (defined(_MSC_VER) && _MSC_VER >= 1910 && _MSC_VER <= 1914))\n                                                detail::negation<std::is_same<ValueType, std::string_view>>,\n#endif\n#if defined(JSON_HAS_CPP_17) && JSON_HAS_STATIC_RTTI\n                                                detail::negation<std::is_same<ValueType, std::any>>,\n#endif\n                                                detail::is_detected_lazy<detail::get_template_function, const basic_json_t&, ValueType>\n                                                >::value, int >::type = 0 >\n                                        JSON_EXPLICIT operator ValueType() const\n    {\n        // delegate the call to get<>() const\n        return get<ValueType>();\n    }\n\n    /// @brief get a binary value\n    /// @sa https://json.nlohmann.me/api/basic_json/get_binary/\n    binary_t& get_binary()\n    {\n        if (!is_binary())\n        {\n            JSON_THROW(type_error::create(302, detail::concat(\"type must be binary, but is \", type_name()), this));\n        }\n\n        return *get_ptr<binary_t*>();\n    }\n\n    /// @brief get a binary value\n    /// @sa https://json.nlohmann.me/api/basic_json/get_binary/\n    const binary_t& get_binary() const\n    {\n        if (!is_binary())\n        {\n            JSON_THROW(type_error::create(302, detail::concat(\"type must be binary, but is \", type_name()), this));\n        }\n\n        return *get_ptr<const binary_t*>();\n    }\n\n    /// @}\n\n    ////////////////////\n    // element access //\n    ////////////////////\n\n    /// @name element access\n    /// Access to the JSON value.\n    /// @{\n\n    /// @brief access specified array element with bounds checking\n    /// @sa https://json.nlohmann.me/api/basic_json/at/\n    reference at(size_type idx)\n    {\n        // at only works for arrays\n        if (JSON_HEDLEY_LIKELY(is_array()))\n        {\n            JSON_TRY\n            {\n                return set_parent(m_data.m_value.array->at(idx));\n            }\n            JSON_CATCH (std::out_of_range&)\n            {\n                // create better exception explanation\n                JSON_THROW(out_of_range::create(401, detail::concat(\"array index \", std::to_string(idx), \" is out of range\"), this));\n            }\n        }\n        else\n        {\n            JSON_THROW(type_error::create(304, detail::concat(\"cannot use at() with \", type_name()), this));\n        }\n    }\n\n    /// @brief access specified array element with bounds checking\n    /// @sa https://json.nlohmann.me/api/basic_json/at/\n    const_reference at(size_type idx) const\n    {\n        // at only works for arrays\n        if (JSON_HEDLEY_LIKELY(is_array()))\n        {\n            JSON_TRY\n            {\n                return m_data.m_value.array->at(idx);\n            }\n            JSON_CATCH (std::out_of_range&)\n            {\n                // create better exception explanation\n                JSON_THROW(out_of_range::create(401, detail::concat(\"array index \", std::to_string(idx), \" is out of range\"), this));\n            }\n        }\n        else\n        {\n            JSON_THROW(type_error::create(304, detail::concat(\"cannot use at() with \", type_name()), this));\n        }\n    }\n\n    /// @brief access specified object element with bounds checking\n    /// @sa https://json.nlohmann.me/api/basic_json/at/\n    reference at(const typename object_t::key_type& key)\n    {\n        // at only works for objects\n        if (JSON_HEDLEY_UNLIKELY(!is_object()))\n        {\n            JSON_THROW(type_error::create(304, detail::concat(\"cannot use at() with \", type_name()), this));\n        }\n\n        auto it = m_data.m_value.object->find(key);\n        if (it == m_data.m_value.object->end())\n        {\n            JSON_THROW(out_of_range::create(403, detail::concat(\"key '\", key, \"' not found\"), this));\n        }\n        return set_parent(it->second);\n    }\n\n    /// @brief access specified object element with bounds checking\n    /// @sa https://json.nlohmann.me/api/basic_json/at/\n    template<class KeyType, detail::enable_if_t<\n                 detail::is_usable_as_basic_json_key_type<basic_json_t, KeyType>::value, int> = 0>\n    reference at(KeyType && key)\n    {\n        // at only works for objects\n        if (JSON_HEDLEY_UNLIKELY(!is_object()))\n        {\n            JSON_THROW(type_error::create(304, detail::concat(\"cannot use at() with \", type_name()), this));\n        }\n\n        auto it = m_data.m_value.object->find(std::forward<KeyType>(key));\n        if (it == m_data.m_value.object->end())\n        {\n            JSON_THROW(out_of_range::create(403, detail::concat(\"key '\", string_t(std::forward<KeyType>(key)), \"' not found\"), this));\n        }\n        return set_parent(it->second);\n    }\n\n    /// @brief access specified object element with bounds checking\n    /// @sa https://json.nlohmann.me/api/basic_json/at/\n    const_reference at(const typename object_t::key_type& key) const\n    {\n        // at only works for objects\n        if (JSON_HEDLEY_UNLIKELY(!is_object()))\n        {\n            JSON_THROW(type_error::create(304, detail::concat(\"cannot use at() with \", type_name()), this));\n        }\n\n        auto it = m_data.m_value.object->find(key);\n        if (it == m_data.m_value.object->end())\n        {\n            JSON_THROW(out_of_range::create(403, detail::concat(\"key '\", key, \"' not found\"), this));\n        }\n        return it->second;\n    }\n\n    /// @brief access specified object element with bounds checking\n    /// @sa https://json.nlohmann.me/api/basic_json/at/\n    template<class KeyType, detail::enable_if_t<\n                 detail::is_usable_as_basic_json_key_type<basic_json_t, KeyType>::value, int> = 0>\n    const_reference at(KeyType && key) const\n    {\n        // at only works for objects\n        if (JSON_HEDLEY_UNLIKELY(!is_object()))\n        {\n            JSON_THROW(type_error::create(304, detail::concat(\"cannot use at() with \", type_name()), this));\n        }\n\n        auto it = m_data.m_value.object->find(std::forward<KeyType>(key));\n        if (it == m_data.m_value.object->end())\n        {\n            JSON_THROW(out_of_range::create(403, detail::concat(\"key '\", string_t(std::forward<KeyType>(key)), \"' not found\"), this));\n        }\n        return it->second;\n    }\n\n    /// @brief access specified array element\n    /// @sa https://json.nlohmann.me/api/basic_json/operator%5B%5D/\n    reference operator[](size_type idx)\n    {\n        // implicitly convert null value to an empty array\n        if (is_null())\n        {\n            m_data.m_type = value_t::array;\n            m_data.m_value.array = create<array_t>();\n            assert_invariant();\n        }\n\n        // operator[] only works for arrays\n        if (JSON_HEDLEY_LIKELY(is_array()))\n        {\n            // fill up array with null values if given idx is outside range\n            if (idx >= m_data.m_value.array->size())\n            {\n#if JSON_DIAGNOSTICS\n                // remember array size & capacity before resizing\n                const auto old_size = m_data.m_value.array->size();\n                const auto old_capacity = m_data.m_value.array->capacity();\n#endif\n                m_data.m_value.array->resize(idx + 1);\n\n#if JSON_DIAGNOSTICS\n                if (JSON_HEDLEY_UNLIKELY(m_data.m_value.array->capacity() != old_capacity))\n                {\n                    // capacity has changed: update all parents\n                    set_parents();\n                }\n                else\n                {\n                    // set parent for values added above\n                    set_parents(begin() + static_cast<typename iterator::difference_type>(old_size), static_cast<typename iterator::difference_type>(idx + 1 - old_size));\n                }\n#endif\n                assert_invariant();\n            }\n\n            return m_data.m_value.array->operator[](idx);\n        }\n\n        JSON_THROW(type_error::create(305, detail::concat(\"cannot use operator[] with a numeric argument with \", type_name()), this));\n    }\n\n    /// @brief access specified array element\n    /// @sa https://json.nlohmann.me/api/basic_json/operator%5B%5D/\n    const_reference operator[](size_type idx) const\n    {\n        // const operator[] only works for arrays\n        if (JSON_HEDLEY_LIKELY(is_array()))\n        {\n            return m_data.m_value.array->operator[](idx);\n        }\n\n        JSON_THROW(type_error::create(305, detail::concat(\"cannot use operator[] with a numeric argument with \", type_name()), this));\n    }\n\n    /// @brief access specified object element\n    /// @sa https://json.nlohmann.me/api/basic_json/operator%5B%5D/\n    reference operator[](typename object_t::key_type key)\n    {\n        // implicitly convert null value to an empty object\n        if (is_null())\n        {\n            m_data.m_type = value_t::object;\n            m_data.m_value.object = create<object_t>();\n            assert_invariant();\n        }\n\n        // operator[] only works for objects\n        if (JSON_HEDLEY_LIKELY(is_object()))\n        {\n            auto result = m_data.m_value.object->emplace(std::move(key), nullptr);\n            return set_parent(result.first->second);\n        }\n\n        JSON_THROW(type_error::create(305, detail::concat(\"cannot use operator[] with a string argument with \", type_name()), this));\n    }\n\n    /// @brief access specified object element\n    /// @sa https://json.nlohmann.me/api/basic_json/operator%5B%5D/\n    const_reference operator[](const typename object_t::key_type& key) const\n    {\n        // const operator[] only works for objects\n        if (JSON_HEDLEY_LIKELY(is_object()))\n        {\n            auto it = m_data.m_value.object->find(key);\n            JSON_ASSERT(it != m_data.m_value.object->end());\n            return it->second;\n        }\n\n        JSON_THROW(type_error::create(305, detail::concat(\"cannot use operator[] with a string argument with \", type_name()), this));\n    }\n\n    // these two functions resolve a (const) char * ambiguity affecting Clang and MSVC\n    // (they seemingly cannot be constrained to resolve the ambiguity)\n    template<typename T>\n    reference operator[](T* key)\n    {\n        return operator[](typename object_t::key_type(key));\n    }\n\n    template<typename T>\n    const_reference operator[](T* key) const\n    {\n        return operator[](typename object_t::key_type(key));\n    }\n\n    /// @brief access specified object element\n    /// @sa https://json.nlohmann.me/api/basic_json/operator%5B%5D/\n    template<class KeyType, detail::enable_if_t<\n                 detail::is_usable_as_basic_json_key_type<basic_json_t, KeyType>::value, int > = 0 >\n    reference operator[](KeyType && key)\n    {\n        // implicitly convert null value to an empty object\n        if (is_null())\n        {\n            m_data.m_type = value_t::object;\n            m_data.m_value.object = create<object_t>();\n            assert_invariant();\n        }\n\n        // operator[] only works for objects\n        if (JSON_HEDLEY_LIKELY(is_object()))\n        {\n            auto result = m_data.m_value.object->emplace(std::forward<KeyType>(key), nullptr);\n            return set_parent(result.first->second);\n        }\n\n        JSON_THROW(type_error::create(305, detail::concat(\"cannot use operator[] with a string argument with \", type_name()), this));\n    }\n\n    /// @brief access specified object element\n    /// @sa https://json.nlohmann.me/api/basic_json/operator%5B%5D/\n    template<class KeyType, detail::enable_if_t<\n                 detail::is_usable_as_basic_json_key_type<basic_json_t, KeyType>::value, int > = 0 >\n    const_reference operator[](KeyType && key) const\n    {\n        // const operator[] only works for objects\n        if (JSON_HEDLEY_LIKELY(is_object()))\n        {\n            auto it = m_data.m_value.object->find(std::forward<KeyType>(key));\n            JSON_ASSERT(it != m_data.m_value.object->end());\n            return it->second;\n        }\n\n        JSON_THROW(type_error::create(305, detail::concat(\"cannot use operator[] with a string argument with \", type_name()), this));\n    }\n\n  private:\n    template<typename KeyType>\n    using is_comparable_with_object_key = detail::is_comparable <\n        object_comparator_t, const typename object_t::key_type&, KeyType >;\n\n    template<typename ValueType>\n    using value_return_type = std::conditional <\n        detail::is_c_string_uncvref<ValueType>::value,\n        string_t, typename std::decay<ValueType>::type >;\n\n  public:\n    /// @brief access specified object element with default value\n    /// @sa https://json.nlohmann.me/api/basic_json/value/\n    template < class ValueType, detail::enable_if_t <\n                   !detail::is_transparent<object_comparator_t>::value\n                   && detail::is_getable<basic_json_t, ValueType>::value\n                   && !std::is_same<value_t, detail::uncvref_t<ValueType>>::value, int > = 0 >\n    ValueType value(const typename object_t::key_type& key, const ValueType& default_value) const\n    {\n        // value only works for objects\n        if (JSON_HEDLEY_LIKELY(is_object()))\n        {\n            // if key is found, return value and given default value otherwise\n            const auto it = find(key);\n            if (it != end())\n            {\n                return it->template get<ValueType>();\n            }\n\n            return default_value;\n        }\n\n        JSON_THROW(type_error::create(306, detail::concat(\"cannot use value() with \", type_name()), this));\n    }\n\n    /// @brief access specified object element with default value\n    /// @sa https://json.nlohmann.me/api/basic_json/value/\n    template < class ValueType, class ReturnType = typename value_return_type<ValueType>::type,\n               detail::enable_if_t <\n                   !detail::is_transparent<object_comparator_t>::value\n                   && detail::is_getable<basic_json_t, ReturnType>::value\n                   && !std::is_same<value_t, detail::uncvref_t<ValueType>>::value, int > = 0 >\n    ReturnType value(const typename object_t::key_type& key, ValueType && default_value) const\n    {\n        // value only works for objects\n        if (JSON_HEDLEY_LIKELY(is_object()))\n        {\n            // if key is found, return value and given default value otherwise\n            const auto it = find(key);\n            if (it != end())\n            {\n                return it->template get<ReturnType>();\n            }\n\n            return std::forward<ValueType>(default_value);\n        }\n\n        JSON_THROW(type_error::create(306, detail::concat(\"cannot use value() with \", type_name()), this));\n    }\n\n    /// @brief access specified object element with default value\n    /// @sa https://json.nlohmann.me/api/basic_json/value/\n    template < class ValueType, class KeyType, detail::enable_if_t <\n                   detail::is_transparent<object_comparator_t>::value\n                   && !detail::is_json_pointer<KeyType>::value\n                   && is_comparable_with_object_key<KeyType>::value\n                   && detail::is_getable<basic_json_t, ValueType>::value\n                   && !std::is_same<value_t, detail::uncvref_t<ValueType>>::value, int > = 0 >\n    ValueType value(KeyType && key, const ValueType& default_value) const\n    {\n        // value only works for objects\n        if (JSON_HEDLEY_LIKELY(is_object()))\n        {\n            // if key is found, return value and given default value otherwise\n            const auto it = find(std::forward<KeyType>(key));\n            if (it != end())\n            {\n                return it->template get<ValueType>();\n            }\n\n            return default_value;\n        }\n\n        JSON_THROW(type_error::create(306, detail::concat(\"cannot use value() with \", type_name()), this));\n    }\n\n    /// @brief access specified object element via JSON Pointer with default value\n    /// @sa https://json.nlohmann.me/api/basic_json/value/\n    template < class ValueType, class KeyType, class ReturnType = typename value_return_type<ValueType>::type,\n               detail::enable_if_t <\n                   detail::is_transparent<object_comparator_t>::value\n                   && !detail::is_json_pointer<KeyType>::value\n                   && is_comparable_with_object_key<KeyType>::value\n                   && detail::is_getable<basic_json_t, ReturnType>::value\n                   && !std::is_same<value_t, detail::uncvref_t<ValueType>>::value, int > = 0 >\n    ReturnType value(KeyType && key, ValueType && default_value) const\n    {\n        // value only works for objects\n        if (JSON_HEDLEY_LIKELY(is_object()))\n        {\n            // if key is found, return value and given default value otherwise\n            const auto it = find(std::forward<KeyType>(key));\n            if (it != end())\n            {\n                return it->template get<ReturnType>();\n            }\n\n            return std::forward<ValueType>(default_value);\n        }\n\n        JSON_THROW(type_error::create(306, detail::concat(\"cannot use value() with \", type_name()), this));\n    }\n\n    /// @brief access specified object element via JSON Pointer with default value\n    /// @sa https://json.nlohmann.me/api/basic_json/value/\n    template < class ValueType, detail::enable_if_t <\n                   detail::is_getable<basic_json_t, ValueType>::value\n                   && !std::is_same<value_t, detail::uncvref_t<ValueType>>::value, int > = 0 >\n    ValueType value(const json_pointer& ptr, const ValueType& default_value) const\n    {\n        // value only works for objects\n        if (JSON_HEDLEY_LIKELY(is_object()))\n        {\n            // if pointer resolves a value, return it or use default value\n            JSON_TRY\n            {\n                return ptr.get_checked(this).template get<ValueType>();\n            }\n            JSON_INTERNAL_CATCH (out_of_range&)\n            {\n                return default_value;\n            }\n        }\n\n        JSON_THROW(type_error::create(306, detail::concat(\"cannot use value() with \", type_name()), this));\n    }\n\n    /// @brief access specified object element via JSON Pointer with default value\n    /// @sa https://json.nlohmann.me/api/basic_json/value/\n    template < class ValueType, class ReturnType = typename value_return_type<ValueType>::type,\n               detail::enable_if_t <\n                   detail::is_getable<basic_json_t, ReturnType>::value\n                   && !std::is_same<value_t, detail::uncvref_t<ValueType>>::value, int > = 0 >\n    ReturnType value(const json_pointer& ptr, ValueType && default_value) const\n    {\n        // value only works for objects\n        if (JSON_HEDLEY_LIKELY(is_object()))\n        {\n            // if pointer resolves a value, return it or use default value\n            JSON_TRY\n            {\n                return ptr.get_checked(this).template get<ReturnType>();\n            }\n            JSON_INTERNAL_CATCH (out_of_range&)\n            {\n                return std::forward<ValueType>(default_value);\n            }\n        }\n\n        JSON_THROW(type_error::create(306, detail::concat(\"cannot use value() with \", type_name()), this));\n    }\n\n    template < class ValueType, class BasicJsonType, detail::enable_if_t <\n                   detail::is_basic_json<BasicJsonType>::value\n                   && detail::is_getable<basic_json_t, ValueType>::value\n                   && !std::is_same<value_t, detail::uncvref_t<ValueType>>::value, int > = 0 >\n    JSON_HEDLEY_DEPRECATED_FOR(3.11.0, basic_json::json_pointer or nlohmann::json_pointer<basic_json::string_t>) // NOLINT(readability/alt_tokens)\n    ValueType value(const ::nlohmann::json_pointer<BasicJsonType>& ptr, const ValueType& default_value) const\n    {\n        return value(ptr.convert(), default_value);\n    }\n\n    template < class ValueType, class BasicJsonType, class ReturnType = typename value_return_type<ValueType>::type,\n               detail::enable_if_t <\n                   detail::is_basic_json<BasicJsonType>::value\n                   && detail::is_getable<basic_json_t, ReturnType>::value\n                   && !std::is_same<value_t, detail::uncvref_t<ValueType>>::value, int > = 0 >\n    JSON_HEDLEY_DEPRECATED_FOR(3.11.0, basic_json::json_pointer or nlohmann::json_pointer<basic_json::string_t>) // NOLINT(readability/alt_tokens)\n    ReturnType value(const ::nlohmann::json_pointer<BasicJsonType>& ptr, ValueType && default_value) const\n    {\n        return value(ptr.convert(), std::forward<ValueType>(default_value));\n    }\n\n    /// @brief access the first element\n    /// @sa https://json.nlohmann.me/api/basic_json/front/\n    reference front()\n    {\n        return *begin();\n    }\n\n    /// @brief access the first element\n    /// @sa https://json.nlohmann.me/api/basic_json/front/\n    const_reference front() const\n    {\n        return *cbegin();\n    }\n\n    /// @brief access the last element\n    /// @sa https://json.nlohmann.me/api/basic_json/back/\n    reference back()\n    {\n        auto tmp = end();\n        --tmp;\n        return *tmp;\n    }\n\n    /// @brief access the last element\n    /// @sa https://json.nlohmann.me/api/basic_json/back/\n    const_reference back() const\n    {\n        auto tmp = cend();\n        --tmp;\n        return *tmp;\n    }\n\n    /// @brief remove element given an iterator\n    /// @sa https://json.nlohmann.me/api/basic_json/erase/\n    template < class IteratorType, detail::enable_if_t <\n                   std::is_same<IteratorType, typename basic_json_t::iterator>::value ||\n                   std::is_same<IteratorType, typename basic_json_t::const_iterator>::value, int > = 0 >\n    IteratorType erase(IteratorType pos)\n    {\n        // make sure iterator fits the current value\n        if (JSON_HEDLEY_UNLIKELY(this != pos.m_object))\n        {\n            JSON_THROW(invalid_iterator::create(202, \"iterator does not fit current value\", this));\n        }\n\n        IteratorType result = end();\n\n        switch (m_data.m_type)\n        {\n            case value_t::boolean:\n            case value_t::number_float:\n            case value_t::number_integer:\n            case value_t::number_unsigned:\n            case value_t::string:\n            case value_t::binary:\n            {\n                if (JSON_HEDLEY_UNLIKELY(!pos.m_it.primitive_iterator.is_begin()))\n                {\n                    JSON_THROW(invalid_iterator::create(205, \"iterator out of range\", this));\n                }\n\n                if (is_string())\n                {\n                    AllocatorType<string_t> alloc;\n                    std::allocator_traits<decltype(alloc)>::destroy(alloc, m_data.m_value.string);\n                    std::allocator_traits<decltype(alloc)>::deallocate(alloc, m_data.m_value.string, 1);\n                    m_data.m_value.string = nullptr;\n                }\n                else if (is_binary())\n                {\n                    AllocatorType<binary_t> alloc;\n                    std::allocator_traits<decltype(alloc)>::destroy(alloc, m_data.m_value.binary);\n                    std::allocator_traits<decltype(alloc)>::deallocate(alloc, m_data.m_value.binary, 1);\n                    m_data.m_value.binary = nullptr;\n                }\n\n                m_data.m_type = value_t::null;\n                assert_invariant();\n                break;\n            }\n\n            case value_t::object:\n            {\n                result.m_it.object_iterator = m_data.m_value.object->erase(pos.m_it.object_iterator);\n                break;\n            }\n\n            case value_t::array:\n            {\n                result.m_it.array_iterator = m_data.m_value.array->erase(pos.m_it.array_iterator);\n                break;\n            }\n\n            case value_t::null:\n            case value_t::discarded:\n            default:\n                JSON_THROW(type_error::create(307, detail::concat(\"cannot use erase() with \", type_name()), this));\n        }\n\n        return result;\n    }\n\n    /// @brief remove elements given an iterator range\n    /// @sa https://json.nlohmann.me/api/basic_json/erase/\n    template < class IteratorType, detail::enable_if_t <\n                   std::is_same<IteratorType, typename basic_json_t::iterator>::value ||\n                   std::is_same<IteratorType, typename basic_json_t::const_iterator>::value, int > = 0 >\n    IteratorType erase(IteratorType first, IteratorType last)\n    {\n        // make sure iterator fits the current value\n        if (JSON_HEDLEY_UNLIKELY(this != first.m_object || this != last.m_object))\n        {\n            JSON_THROW(invalid_iterator::create(203, \"iterators do not fit current value\", this));\n        }\n\n        IteratorType result = end();\n\n        switch (m_data.m_type)\n        {\n            case value_t::boolean:\n            case value_t::number_float:\n            case value_t::number_integer:\n            case value_t::number_unsigned:\n            case value_t::string:\n            case value_t::binary:\n            {\n                if (JSON_HEDLEY_LIKELY(!first.m_it.primitive_iterator.is_begin()\n                                       || !last.m_it.primitive_iterator.is_end()))\n                {\n                    JSON_THROW(invalid_iterator::create(204, \"iterators out of range\", this));\n                }\n\n                if (is_string())\n                {\n                    AllocatorType<string_t> alloc;\n                    std::allocator_traits<decltype(alloc)>::destroy(alloc, m_data.m_value.string);\n                    std::allocator_traits<decltype(alloc)>::deallocate(alloc, m_data.m_value.string, 1);\n                    m_data.m_value.string = nullptr;\n                }\n                else if (is_binary())\n                {\n                    AllocatorType<binary_t> alloc;\n                    std::allocator_traits<decltype(alloc)>::destroy(alloc, m_data.m_value.binary);\n                    std::allocator_traits<decltype(alloc)>::deallocate(alloc, m_data.m_value.binary, 1);\n                    m_data.m_value.binary = nullptr;\n                }\n\n                m_data.m_type = value_t::null;\n                assert_invariant();\n                break;\n            }\n\n            case value_t::object:\n            {\n                result.m_it.object_iterator = m_data.m_value.object->erase(first.m_it.object_iterator,\n                                              last.m_it.object_iterator);\n                break;\n            }\n\n            case value_t::array:\n            {\n                result.m_it.array_iterator = m_data.m_value.array->erase(first.m_it.array_iterator,\n                                             last.m_it.array_iterator);\n                break;\n            }\n\n            case value_t::null:\n            case value_t::discarded:\n            default:\n                JSON_THROW(type_error::create(307, detail::concat(\"cannot use erase() with \", type_name()), this));\n        }\n\n        return result;\n    }\n\n  private:\n    template < typename KeyType, detail::enable_if_t <\n                   detail::has_erase_with_key_type<basic_json_t, KeyType>::value, int > = 0 >\n    size_type erase_internal(KeyType && key)\n    {\n        // this erase only works for objects\n        if (JSON_HEDLEY_UNLIKELY(!is_object()))\n        {\n            JSON_THROW(type_error::create(307, detail::concat(\"cannot use erase() with \", type_name()), this));\n        }\n\n        return m_data.m_value.object->erase(std::forward<KeyType>(key));\n    }\n\n    template < typename KeyType, detail::enable_if_t <\n                   !detail::has_erase_with_key_type<basic_json_t, KeyType>::value, int > = 0 >\n    size_type erase_internal(KeyType && key)\n    {\n        // this erase only works for objects\n        if (JSON_HEDLEY_UNLIKELY(!is_object()))\n        {\n            JSON_THROW(type_error::create(307, detail::concat(\"cannot use erase() with \", type_name()), this));\n        }\n\n        const auto it = m_data.m_value.object->find(std::forward<KeyType>(key));\n        if (it != m_data.m_value.object->end())\n        {\n            m_data.m_value.object->erase(it);\n            return 1;\n        }\n        return 0;\n    }\n\n  public:\n\n    /// @brief remove element from a JSON object given a key\n    /// @sa https://json.nlohmann.me/api/basic_json/erase/\n    size_type erase(const typename object_t::key_type& key)\n    {\n        // the indirection via erase_internal() is added to avoid making this\n        // function a template and thus de-rank it during overload resolution\n        return erase_internal(key);\n    }\n\n    /// @brief remove element from a JSON object given a key\n    /// @sa https://json.nlohmann.me/api/basic_json/erase/\n    template<class KeyType, detail::enable_if_t<\n                 detail::is_usable_as_basic_json_key_type<basic_json_t, KeyType>::value, int> = 0>\n    size_type erase(KeyType && key)\n    {\n        return erase_internal(std::forward<KeyType>(key));\n    }\n\n    /// @brief remove element from a JSON array given an index\n    /// @sa https://json.nlohmann.me/api/basic_json/erase/\n    void erase(const size_type idx)\n    {\n        // this erase only works for arrays\n        if (JSON_HEDLEY_LIKELY(is_array()))\n        {\n            if (JSON_HEDLEY_UNLIKELY(idx >= size()))\n            {\n                JSON_THROW(out_of_range::create(401, detail::concat(\"array index \", std::to_string(idx), \" is out of range\"), this));\n            }\n\n            m_data.m_value.array->erase(m_data.m_value.array->begin() + static_cast<difference_type>(idx));\n        }\n        else\n        {\n            JSON_THROW(type_error::create(307, detail::concat(\"cannot use erase() with \", type_name()), this));\n        }\n    }\n\n    /// @}\n\n    ////////////\n    // lookup //\n    ////////////\n\n    /// @name lookup\n    /// @{\n\n    /// @brief find an element in a JSON object\n    /// @sa https://json.nlohmann.me/api/basic_json/find/\n    iterator find(const typename object_t::key_type& key)\n    {\n        auto result = end();\n\n        if (is_object())\n        {\n            result.m_it.object_iterator = m_data.m_value.object->find(key);\n        }\n\n        return result;\n    }\n\n    /// @brief find an element in a JSON object\n    /// @sa https://json.nlohmann.me/api/basic_json/find/\n    const_iterator find(const typename object_t::key_type& key) const\n    {\n        auto result = cend();\n\n        if (is_object())\n        {\n            result.m_it.object_iterator = m_data.m_value.object->find(key);\n        }\n\n        return result;\n    }\n\n    /// @brief find an element in a JSON object\n    /// @sa https://json.nlohmann.me/api/basic_json/find/\n    template<class KeyType, detail::enable_if_t<\n                 detail::is_usable_as_basic_json_key_type<basic_json_t, KeyType>::value, int> = 0>\n    iterator find(KeyType && key)\n    {\n        auto result = end();\n\n        if (is_object())\n        {\n            result.m_it.object_iterator = m_data.m_value.object->find(std::forward<KeyType>(key));\n        }\n\n        return result;\n    }\n\n    /// @brief find an element in a JSON object\n    /// @sa https://json.nlohmann.me/api/basic_json/find/\n    template<class KeyType, detail::enable_if_t<\n                 detail::is_usable_as_basic_json_key_type<basic_json_t, KeyType>::value, int> = 0>\n    const_iterator find(KeyType && key) const\n    {\n        auto result = cend();\n\n        if (is_object())\n        {\n            result.m_it.object_iterator = m_data.m_value.object->find(std::forward<KeyType>(key));\n        }\n\n        return result;\n    }\n\n    /// @brief returns the number of occurrences of a key in a JSON object\n    /// @sa https://json.nlohmann.me/api/basic_json/count/\n    size_type count(const typename object_t::key_type& key) const\n    {\n        // return 0 for all nonobject types\n        return is_object() ? m_data.m_value.object->count(key) : 0;\n    }\n\n    /// @brief returns the number of occurrences of a key in a JSON object\n    /// @sa https://json.nlohmann.me/api/basic_json/count/\n    template<class KeyType, detail::enable_if_t<\n                 detail::is_usable_as_basic_json_key_type<basic_json_t, KeyType>::value, int> = 0>\n    size_type count(KeyType && key) const\n    {\n        // return 0 for all nonobject types\n        return is_object() ? m_data.m_value.object->count(std::forward<KeyType>(key)) : 0;\n    }\n\n    /// @brief check the existence of an element in a JSON object\n    /// @sa https://json.nlohmann.me/api/basic_json/contains/\n    bool contains(const typename object_t::key_type& key) const\n    {\n        return is_object() && m_data.m_value.object->find(key) != m_data.m_value.object->end();\n    }\n\n    /// @brief check the existence of an element in a JSON object\n    /// @sa https://json.nlohmann.me/api/basic_json/contains/\n    template<class KeyType, detail::enable_if_t<\n                 detail::is_usable_as_basic_json_key_type<basic_json_t, KeyType>::value, int> = 0>\n    bool contains(KeyType && key) const\n    {\n        return is_object() && m_data.m_value.object->find(std::forward<KeyType>(key)) != m_data.m_value.object->end();\n    }\n\n    /// @brief check the existence of an element in a JSON object given a JSON pointer\n    /// @sa https://json.nlohmann.me/api/basic_json/contains/\n    bool contains(const json_pointer& ptr) const\n    {\n        return ptr.contains(this);\n    }\n\n    template<typename BasicJsonType, detail::enable_if_t<detail::is_basic_json<BasicJsonType>::value, int> = 0>\n    JSON_HEDLEY_DEPRECATED_FOR(3.11.0, basic_json::json_pointer or nlohmann::json_pointer<basic_json::string_t>) // NOLINT(readability/alt_tokens)\n    bool contains(const typename ::nlohmann::json_pointer<BasicJsonType>& ptr) const\n    {\n        return ptr.contains(this);\n    }\n\n    /// @}\n\n    ///////////////\n    // iterators //\n    ///////////////\n\n    /// @name iterators\n    /// @{\n\n    /// @brief returns an iterator to the first element\n    /// @sa https://json.nlohmann.me/api/basic_json/begin/\n    iterator begin() noexcept\n    {\n        iterator result(this);\n        result.set_begin();\n        return result;\n    }\n\n    /// @brief returns an iterator to the first element\n    /// @sa https://json.nlohmann.me/api/basic_json/begin/\n    const_iterator begin() const noexcept\n    {\n        return cbegin();\n    }\n\n    /// @brief returns a const iterator to the first element\n    /// @sa https://json.nlohmann.me/api/basic_json/cbegin/\n    const_iterator cbegin() const noexcept\n    {\n        const_iterator result(this);\n        result.set_begin();\n        return result;\n    }\n\n    /// @brief returns an iterator to one past the last element\n    /// @sa https://json.nlohmann.me/api/basic_json/end/\n    iterator end() noexcept\n    {\n        iterator result(this);\n        result.set_end();\n        return result;\n    }\n\n    /// @brief returns an iterator to one past the last element\n    /// @sa https://json.nlohmann.me/api/basic_json/end/\n    const_iterator end() const noexcept\n    {\n        return cend();\n    }\n\n    /// @brief returns an iterator to one past the last element\n    /// @sa https://json.nlohmann.me/api/basic_json/cend/\n    const_iterator cend() const noexcept\n    {\n        const_iterator result(this);\n        result.set_end();\n        return result;\n    }\n\n    /// @brief returns an iterator to the reverse-beginning\n    /// @sa https://json.nlohmann.me/api/basic_json/rbegin/\n    reverse_iterator rbegin() noexcept\n    {\n        return reverse_iterator(end());\n    }\n\n    /// @brief returns an iterator to the reverse-beginning\n    /// @sa https://json.nlohmann.me/api/basic_json/rbegin/\n    const_reverse_iterator rbegin() const noexcept\n    {\n        return crbegin();\n    }\n\n    /// @brief returns an iterator to the reverse-end\n    /// @sa https://json.nlohmann.me/api/basic_json/rend/\n    reverse_iterator rend() noexcept\n    {\n        return reverse_iterator(begin());\n    }\n\n    /// @brief returns an iterator to the reverse-end\n    /// @sa https://json.nlohmann.me/api/basic_json/rend/\n    const_reverse_iterator rend() const noexcept\n    {\n        return crend();\n    }\n\n    /// @brief returns a const reverse iterator to the last element\n    /// @sa https://json.nlohmann.me/api/basic_json/crbegin/\n    const_reverse_iterator crbegin() const noexcept\n    {\n        return const_reverse_iterator(cend());\n    }\n\n    /// @brief returns a const reverse iterator to one before the first\n    /// @sa https://json.nlohmann.me/api/basic_json/crend/\n    const_reverse_iterator crend() const noexcept\n    {\n        return const_reverse_iterator(cbegin());\n    }\n\n  public:\n    /// @brief wrapper to access iterator member functions in range-based for\n    /// @sa https://json.nlohmann.me/api/basic_json/items/\n    /// @deprecated This function is deprecated since 3.1.0 and will be removed in\n    ///             version 4.0.0 of the library. Please use @ref items() instead;\n    ///             that is, replace `json::iterator_wrapper(j)` with `j.items()`.\n    JSON_HEDLEY_DEPRECATED_FOR(3.1.0, items())\n    static iteration_proxy<iterator> iterator_wrapper(reference ref) noexcept\n    {\n        return ref.items();\n    }\n\n    /// @brief wrapper to access iterator member functions in range-based for\n    /// @sa https://json.nlohmann.me/api/basic_json/items/\n    /// @deprecated This function is deprecated since 3.1.0 and will be removed in\n    ///         version 4.0.0 of the library. Please use @ref items() instead;\n    ///         that is, replace `json::iterator_wrapper(j)` with `j.items()`.\n    JSON_HEDLEY_DEPRECATED_FOR(3.1.0, items())\n    static iteration_proxy<const_iterator> iterator_wrapper(const_reference ref) noexcept\n    {\n        return ref.items();\n    }\n\n    /// @brief helper to access iterator member functions in range-based for\n    /// @sa https://json.nlohmann.me/api/basic_json/items/\n    iteration_proxy<iterator> items() noexcept\n    {\n        return iteration_proxy<iterator>(*this);\n    }\n\n    /// @brief helper to access iterator member functions in range-based for\n    /// @sa https://json.nlohmann.me/api/basic_json/items/\n    iteration_proxy<const_iterator> items() const noexcept\n    {\n        return iteration_proxy<const_iterator>(*this);\n    }\n\n    /// @}\n\n    //////////////\n    // capacity //\n    //////////////\n\n    /// @name capacity\n    /// @{\n\n    /// @brief checks whether the container is empty.\n    /// @sa https://json.nlohmann.me/api/basic_json/empty/\n    bool empty() const noexcept\n    {\n        switch (m_data.m_type)\n        {\n            case value_t::null:\n            {\n                // null values are empty\n                return true;\n            }\n\n            case value_t::array:\n            {\n                // delegate call to array_t::empty()\n                return m_data.m_value.array->empty();\n            }\n\n            case value_t::object:\n            {\n                // delegate call to object_t::empty()\n                return m_data.m_value.object->empty();\n            }\n\n            case value_t::string:\n            case value_t::boolean:\n            case value_t::number_integer:\n            case value_t::number_unsigned:\n            case value_t::number_float:\n            case value_t::binary:\n            case value_t::discarded:\n            default:\n            {\n                // all other types are nonempty\n                return false;\n            }\n        }\n    }\n\n    /// @brief returns the number of elements\n    /// @sa https://json.nlohmann.me/api/basic_json/size/\n    size_type size() const noexcept\n    {\n        switch (m_data.m_type)\n        {\n            case value_t::null:\n            {\n                // null values are empty\n                return 0;\n            }\n\n            case value_t::array:\n            {\n                // delegate call to array_t::size()\n                return m_data.m_value.array->size();\n            }\n\n            case value_t::object:\n            {\n                // delegate call to object_t::size()\n                return m_data.m_value.object->size();\n            }\n\n            case value_t::string:\n            case value_t::boolean:\n            case value_t::number_integer:\n            case value_t::number_unsigned:\n            case value_t::number_float:\n            case value_t::binary:\n            case value_t::discarded:\n            default:\n            {\n                // all other types have size 1\n                return 1;\n            }\n        }\n    }\n\n    /// @brief returns the maximum possible number of elements\n    /// @sa https://json.nlohmann.me/api/basic_json/max_size/\n    size_type max_size() const noexcept\n    {\n        switch (m_data.m_type)\n        {\n            case value_t::array:\n            {\n                // delegate call to array_t::max_size()\n                return m_data.m_value.array->max_size();\n            }\n\n            case value_t::object:\n            {\n                // delegate call to object_t::max_size()\n                return m_data.m_value.object->max_size();\n            }\n\n            case value_t::null:\n            case value_t::string:\n            case value_t::boolean:\n            case value_t::number_integer:\n            case value_t::number_unsigned:\n            case value_t::number_float:\n            case value_t::binary:\n            case value_t::discarded:\n            default:\n            {\n                // all other types have max_size() == size()\n                return size();\n            }\n        }\n    }\n\n    /// @}\n\n    ///////////////\n    // modifiers //\n    ///////////////\n\n    /// @name modifiers\n    /// @{\n\n    /// @brief clears the contents\n    /// @sa https://json.nlohmann.me/api/basic_json/clear/\n    void clear() noexcept\n    {\n        switch (m_data.m_type)\n        {\n            case value_t::number_integer:\n            {\n                m_data.m_value.number_integer = 0;\n                break;\n            }\n\n            case value_t::number_unsigned:\n            {\n                m_data.m_value.number_unsigned = 0;\n                break;\n            }\n\n            case value_t::number_float:\n            {\n                m_data.m_value.number_float = 0.0;\n                break;\n            }\n\n            case value_t::boolean:\n            {\n                m_data.m_value.boolean = false;\n                break;\n            }\n\n            case value_t::string:\n            {\n                m_data.m_value.string->clear();\n                break;\n            }\n\n            case value_t::binary:\n            {\n                m_data.m_value.binary->clear();\n                break;\n            }\n\n            case value_t::array:\n            {\n                m_data.m_value.array->clear();\n                break;\n            }\n\n            case value_t::object:\n            {\n                m_data.m_value.object->clear();\n                break;\n            }\n\n            case value_t::null:\n            case value_t::discarded:\n            default:\n                break;\n        }\n    }\n\n    /// @brief add an object to an array\n    /// @sa https://json.nlohmann.me/api/basic_json/push_back/\n    void push_back(basic_json&& val)\n    {\n        // push_back only works for null objects or arrays\n        if (JSON_HEDLEY_UNLIKELY(!(is_null() || is_array())))\n        {\n            JSON_THROW(type_error::create(308, detail::concat(\"cannot use push_back() with \", type_name()), this));\n        }\n\n        // transform null object into an array\n        if (is_null())\n        {\n            m_data.m_type = value_t::array;\n            m_data.m_value = value_t::array;\n            assert_invariant();\n        }\n\n        // add element to array (move semantics)\n        const auto old_capacity = m_data.m_value.array->capacity();\n        m_data.m_value.array->push_back(std::move(val));\n        set_parent(m_data.m_value.array->back(), old_capacity);\n        // if val is moved from, basic_json move constructor marks it null, so we do not call the destructor\n    }\n\n    /// @brief add an object to an array\n    /// @sa https://json.nlohmann.me/api/basic_json/operator+=/\n    reference operator+=(basic_json&& val)\n    {\n        push_back(std::move(val));\n        return *this;\n    }\n\n    /// @brief add an object to an array\n    /// @sa https://json.nlohmann.me/api/basic_json/push_back/\n    void push_back(const basic_json& val)\n    {\n        // push_back only works for null objects or arrays\n        if (JSON_HEDLEY_UNLIKELY(!(is_null() || is_array())))\n        {\n            JSON_THROW(type_error::create(308, detail::concat(\"cannot use push_back() with \", type_name()), this));\n        }\n\n        // transform null object into an array\n        if (is_null())\n        {\n            m_data.m_type = value_t::array;\n            m_data.m_value = value_t::array;\n            assert_invariant();\n        }\n\n        // add element to array\n        const auto old_capacity = m_data.m_value.array->capacity();\n        m_data.m_value.array->push_back(val);\n        set_parent(m_data.m_value.array->back(), old_capacity);\n    }\n\n    /// @brief add an object to an array\n    /// @sa https://json.nlohmann.me/api/basic_json/operator+=/\n    reference operator+=(const basic_json& val)\n    {\n        push_back(val);\n        return *this;\n    }\n\n    /// @brief add an object to an object\n    /// @sa https://json.nlohmann.me/api/basic_json/push_back/\n    void push_back(const typename object_t::value_type& val)\n    {\n        // push_back only works for null objects or objects\n        if (JSON_HEDLEY_UNLIKELY(!(is_null() || is_object())))\n        {\n            JSON_THROW(type_error::create(308, detail::concat(\"cannot use push_back() with \", type_name()), this));\n        }\n\n        // transform null object into an object\n        if (is_null())\n        {\n            m_data.m_type = value_t::object;\n            m_data.m_value = value_t::object;\n            assert_invariant();\n        }\n\n        // add element to object\n        auto res = m_data.m_value.object->insert(val);\n        set_parent(res.first->second);\n    }\n\n    /// @brief add an object to an object\n    /// @sa https://json.nlohmann.me/api/basic_json/operator+=/\n    reference operator+=(const typename object_t::value_type& val)\n    {\n        push_back(val);\n        return *this;\n    }\n\n    /// @brief add an object to an object\n    /// @sa https://json.nlohmann.me/api/basic_json/push_back/\n    void push_back(initializer_list_t init)\n    {\n        if (is_object() && init.size() == 2 && (*init.begin())->is_string())\n        {\n            basic_json&& key = init.begin()->moved_or_copied();\n            push_back(typename object_t::value_type(\n                          std::move(key.get_ref<string_t&>()), (init.begin() + 1)->moved_or_copied()));\n        }\n        else\n        {\n            push_back(basic_json(init));\n        }\n    }\n\n    /// @brief add an object to an object\n    /// @sa https://json.nlohmann.me/api/basic_json/operator+=/\n    reference operator+=(initializer_list_t init)\n    {\n        push_back(init);\n        return *this;\n    }\n\n    /// @brief add an object to an array\n    /// @sa https://json.nlohmann.me/api/basic_json/emplace_back/\n    template<class... Args>\n    reference emplace_back(Args&& ... args)\n    {\n        // emplace_back only works for null objects or arrays\n        if (JSON_HEDLEY_UNLIKELY(!(is_null() || is_array())))\n        {\n            JSON_THROW(type_error::create(311, detail::concat(\"cannot use emplace_back() with \", type_name()), this));\n        }\n\n        // transform null object into an array\n        if (is_null())\n        {\n            m_data.m_type = value_t::array;\n            m_data.m_value = value_t::array;\n            assert_invariant();\n        }\n\n        // add element to array (perfect forwarding)\n        const auto old_capacity = m_data.m_value.array->capacity();\n        m_data.m_value.array->emplace_back(std::forward<Args>(args)...);\n        return set_parent(m_data.m_value.array->back(), old_capacity);\n    }\n\n    /// @brief add an object to an object if key does not exist\n    /// @sa https://json.nlohmann.me/api/basic_json/emplace/\n    template<class... Args>\n    std::pair<iterator, bool> emplace(Args&& ... args)\n    {\n        // emplace only works for null objects or arrays\n        if (JSON_HEDLEY_UNLIKELY(!(is_null() || is_object())))\n        {\n            JSON_THROW(type_error::create(311, detail::concat(\"cannot use emplace() with \", type_name()), this));\n        }\n\n        // transform null object into an object\n        if (is_null())\n        {\n            m_data.m_type = value_t::object;\n            m_data.m_value = value_t::object;\n            assert_invariant();\n        }\n\n        // add element to array (perfect forwarding)\n        auto res = m_data.m_value.object->emplace(std::forward<Args>(args)...);\n        set_parent(res.first->second);\n\n        // create result iterator and set iterator to the result of emplace\n        auto it = begin();\n        it.m_it.object_iterator = res.first;\n\n        // return pair of iterator and boolean\n        return {it, res.second};\n    }\n\n    /// Helper for insertion of an iterator\n    /// @note: This uses std::distance to support GCC 4.8,\n    ///        see https://github.com/nlohmann/json/pull/1257\n    template<typename... Args>\n    iterator insert_iterator(const_iterator pos, Args&& ... args)\n    {\n        iterator result(this);\n        JSON_ASSERT(m_data.m_value.array != nullptr);\n\n        auto insert_pos = std::distance(m_data.m_value.array->begin(), pos.m_it.array_iterator);\n        m_data.m_value.array->insert(pos.m_it.array_iterator, std::forward<Args>(args)...);\n        result.m_it.array_iterator = m_data.m_value.array->begin() + insert_pos;\n\n        // This could have been written as:\n        // result.m_it.array_iterator = m_data.m_value.array->insert(pos.m_it.array_iterator, cnt, val);\n        // but the return value of insert is missing in GCC 4.8, so it is written this way instead.\n\n        set_parents();\n        return result;\n    }\n\n    /// @brief inserts element into array\n    /// @sa https://json.nlohmann.me/api/basic_json/insert/\n    iterator insert(const_iterator pos, const basic_json& val)\n    {\n        // insert only works for arrays\n        if (JSON_HEDLEY_LIKELY(is_array()))\n        {\n            // check if iterator pos fits to this JSON value\n            if (JSON_HEDLEY_UNLIKELY(pos.m_object != this))\n            {\n                JSON_THROW(invalid_iterator::create(202, \"iterator does not fit current value\", this));\n            }\n\n            // insert to array and return iterator\n            return insert_iterator(pos, val);\n        }\n\n        JSON_THROW(type_error::create(309, detail::concat(\"cannot use insert() with \", type_name()), this));\n    }\n\n    /// @brief inserts element into array\n    /// @sa https://json.nlohmann.me/api/basic_json/insert/\n    iterator insert(const_iterator pos, basic_json&& val)\n    {\n        return insert(pos, val);\n    }\n\n    /// @brief inserts copies of element into array\n    /// @sa https://json.nlohmann.me/api/basic_json/insert/\n    iterator insert(const_iterator pos, size_type cnt, const basic_json& val)\n    {\n        // insert only works for arrays\n        if (JSON_HEDLEY_LIKELY(is_array()))\n        {\n            // check if iterator pos fits to this JSON value\n            if (JSON_HEDLEY_UNLIKELY(pos.m_object != this))\n            {\n                JSON_THROW(invalid_iterator::create(202, \"iterator does not fit current value\", this));\n            }\n\n            // insert to array and return iterator\n            return insert_iterator(pos, cnt, val);\n        }\n\n        JSON_THROW(type_error::create(309, detail::concat(\"cannot use insert() with \", type_name()), this));\n    }\n\n    /// @brief inserts range of elements into array\n    /// @sa https://json.nlohmann.me/api/basic_json/insert/\n    iterator insert(const_iterator pos, const_iterator first, const_iterator last)\n    {\n        // insert only works for arrays\n        if (JSON_HEDLEY_UNLIKELY(!is_array()))\n        {\n            JSON_THROW(type_error::create(309, detail::concat(\"cannot use insert() with \", type_name()), this));\n        }\n\n        // check if iterator pos fits to this JSON value\n        if (JSON_HEDLEY_UNLIKELY(pos.m_object != this))\n        {\n            JSON_THROW(invalid_iterator::create(202, \"iterator does not fit current value\", this));\n        }\n\n        // check if range iterators belong to the same JSON object\n        if (JSON_HEDLEY_UNLIKELY(first.m_object != last.m_object))\n        {\n            JSON_THROW(invalid_iterator::create(210, \"iterators do not fit\", this));\n        }\n\n        if (JSON_HEDLEY_UNLIKELY(first.m_object == this))\n        {\n            JSON_THROW(invalid_iterator::create(211, \"passed iterators may not belong to container\", this));\n        }\n\n        // insert to array and return iterator\n        return insert_iterator(pos, first.m_it.array_iterator, last.m_it.array_iterator);\n    }\n\n    /// @brief inserts elements from initializer list into array\n    /// @sa https://json.nlohmann.me/api/basic_json/insert/\n    iterator insert(const_iterator pos, initializer_list_t ilist)\n    {\n        // insert only works for arrays\n        if (JSON_HEDLEY_UNLIKELY(!is_array()))\n        {\n            JSON_THROW(type_error::create(309, detail::concat(\"cannot use insert() with \", type_name()), this));\n        }\n\n        // check if iterator pos fits to this JSON value\n        if (JSON_HEDLEY_UNLIKELY(pos.m_object != this))\n        {\n            JSON_THROW(invalid_iterator::create(202, \"iterator does not fit current value\", this));\n        }\n\n        // insert to array and return iterator\n        return insert_iterator(pos, ilist.begin(), ilist.end());\n    }\n\n    /// @brief inserts range of elements into object\n    /// @sa https://json.nlohmann.me/api/basic_json/insert/\n    void insert(const_iterator first, const_iterator last)\n    {\n        // insert only works for objects\n        if (JSON_HEDLEY_UNLIKELY(!is_object()))\n        {\n            JSON_THROW(type_error::create(309, detail::concat(\"cannot use insert() with \", type_name()), this));\n        }\n\n        // check if range iterators belong to the same JSON object\n        if (JSON_HEDLEY_UNLIKELY(first.m_object != last.m_object))\n        {\n            JSON_THROW(invalid_iterator::create(210, \"iterators do not fit\", this));\n        }\n\n        // passed iterators must belong to objects\n        if (JSON_HEDLEY_UNLIKELY(!first.m_object->is_object()))\n        {\n            JSON_THROW(invalid_iterator::create(202, \"iterators first and last must point to objects\", this));\n        }\n\n        m_data.m_value.object->insert(first.m_it.object_iterator, last.m_it.object_iterator);\n    }\n\n    /// @brief updates a JSON object from another object, overwriting existing keys\n    /// @sa https://json.nlohmann.me/api/basic_json/update/\n    void update(const_reference j, bool merge_objects = false)\n    {\n        update(j.begin(), j.end(), merge_objects);\n    }\n\n    /// @brief updates a JSON object from another object, overwriting existing keys\n    /// @sa https://json.nlohmann.me/api/basic_json/update/\n    void update(const_iterator first, const_iterator last, bool merge_objects = false)\n    {\n        // implicitly convert null value to an empty object\n        if (is_null())\n        {\n            m_data.m_type = value_t::object;\n            m_data.m_value.object = create<object_t>();\n            assert_invariant();\n        }\n\n        if (JSON_HEDLEY_UNLIKELY(!is_object()))\n        {\n            JSON_THROW(type_error::create(312, detail::concat(\"cannot use update() with \", type_name()), this));\n        }\n\n        // check if range iterators belong to the same JSON object\n        if (JSON_HEDLEY_UNLIKELY(first.m_object != last.m_object))\n        {\n            JSON_THROW(invalid_iterator::create(210, \"iterators do not fit\", this));\n        }\n\n        // passed iterators must belong to objects\n        if (JSON_HEDLEY_UNLIKELY(!first.m_object->is_object()))\n        {\n            JSON_THROW(type_error::create(312, detail::concat(\"cannot use update() with \", first.m_object->type_name()), first.m_object));\n        }\n\n        for (auto it = first; it != last; ++it)\n        {\n            if (merge_objects && it.value().is_object())\n            {\n                auto it2 = m_data.m_value.object->find(it.key());\n                if (it2 != m_data.m_value.object->end())\n                {\n                    it2->second.update(it.value(), true);\n                    continue;\n                }\n            }\n            m_data.m_value.object->operator[](it.key()) = it.value();\n#if JSON_DIAGNOSTICS\n            m_data.m_value.object->operator[](it.key()).m_parent = this;\n#endif\n        }\n    }\n\n    /// @brief exchanges the values\n    /// @sa https://json.nlohmann.me/api/basic_json/swap/\n    void swap(reference other) noexcept (\n        std::is_nothrow_move_constructible<value_t>::value&&\n        std::is_nothrow_move_assignable<value_t>::value&&\n        std::is_nothrow_move_constructible<json_value>::value&& // NOLINT(cppcoreguidelines-noexcept-swap,performance-noexcept-swap)\n        std::is_nothrow_move_assignable<json_value>::value\n    )\n    {\n        std::swap(m_data.m_type, other.m_data.m_type);\n        std::swap(m_data.m_value, other.m_data.m_value);\n\n        set_parents();\n        other.set_parents();\n        assert_invariant();\n    }\n\n    /// @brief exchanges the values\n    /// @sa https://json.nlohmann.me/api/basic_json/swap/\n    friend void swap(reference left, reference right) noexcept (\n        std::is_nothrow_move_constructible<value_t>::value&&\n        std::is_nothrow_move_assignable<value_t>::value&&\n        std::is_nothrow_move_constructible<json_value>::value&& // NOLINT(cppcoreguidelines-noexcept-swap,performance-noexcept-swap)\n        std::is_nothrow_move_assignable<json_value>::value\n    )\n    {\n        left.swap(right);\n    }\n\n    /// @brief exchanges the values\n    /// @sa https://json.nlohmann.me/api/basic_json/swap/\n    void swap(array_t& other) // NOLINT(bugprone-exception-escape,cppcoreguidelines-noexcept-swap,performance-noexcept-swap)\n    {\n        // swap only works for arrays\n        if (JSON_HEDLEY_LIKELY(is_array()))\n        {\n            using std::swap;\n            swap(*(m_data.m_value.array), other);\n        }\n        else\n        {\n            JSON_THROW(type_error::create(310, detail::concat(\"cannot use swap(array_t&) with \", type_name()), this));\n        }\n    }\n\n    /// @brief exchanges the values\n    /// @sa https://json.nlohmann.me/api/basic_json/swap/\n    void swap(object_t& other) // NOLINT(bugprone-exception-escape,cppcoreguidelines-noexcept-swap,performance-noexcept-swap)\n    {\n        // swap only works for objects\n        if (JSON_HEDLEY_LIKELY(is_object()))\n        {\n            using std::swap;\n            swap(*(m_data.m_value.object), other);\n        }\n        else\n        {\n            JSON_THROW(type_error::create(310, detail::concat(\"cannot use swap(object_t&) with \", type_name()), this));\n        }\n    }\n\n    /// @brief exchanges the values\n    /// @sa https://json.nlohmann.me/api/basic_json/swap/\n    void swap(string_t& other) // NOLINT(bugprone-exception-escape,cppcoreguidelines-noexcept-swap,performance-noexcept-swap)\n    {\n        // swap only works for strings\n        if (JSON_HEDLEY_LIKELY(is_string()))\n        {\n            using std::swap;\n            swap(*(m_data.m_value.string), other);\n        }\n        else\n        {\n            JSON_THROW(type_error::create(310, detail::concat(\"cannot use swap(string_t&) with \", type_name()), this));\n        }\n    }\n\n    /// @brief exchanges the values\n    /// @sa https://json.nlohmann.me/api/basic_json/swap/\n    void swap(binary_t& other) // NOLINT(bugprone-exception-escape,cppcoreguidelines-noexcept-swap,performance-noexcept-swap)\n    {\n        // swap only works for strings\n        if (JSON_HEDLEY_LIKELY(is_binary()))\n        {\n            using std::swap;\n            swap(*(m_data.m_value.binary), other);\n        }\n        else\n        {\n            JSON_THROW(type_error::create(310, detail::concat(\"cannot use swap(binary_t&) with \", type_name()), this));\n        }\n    }\n\n    /// @brief exchanges the values\n    /// @sa https://json.nlohmann.me/api/basic_json/swap/\n    void swap(typename binary_t::container_type& other) // NOLINT(bugprone-exception-escape)\n    {\n        // swap only works for strings\n        if (JSON_HEDLEY_LIKELY(is_binary()))\n        {\n            using std::swap;\n            swap(*(m_data.m_value.binary), other);\n        }\n        else\n        {\n            JSON_THROW(type_error::create(310, detail::concat(\"cannot use swap(binary_t::container_type&) with \", type_name()), this));\n        }\n    }\n\n    /// @}\n\n    //////////////////////////////////////////\n    // lexicographical comparison operators //\n    //////////////////////////////////////////\n\n    /// @name lexicographical comparison operators\n    /// @{\n\n    // note parentheses around operands are necessary; see\n    // https://github.com/nlohmann/json/issues/1530\n#define JSON_IMPLEMENT_OPERATOR(op, null_result, unordered_result, default_result)                       \\\n    const auto lhs_type = lhs.type();                                                                    \\\n    const auto rhs_type = rhs.type();                                                                    \\\n    \\\n    if (lhs_type == rhs_type) /* NOLINT(readability/braces) */                                           \\\n    {                                                                                                    \\\n        switch (lhs_type)                                                                                \\\n        {                                                                                                \\\n            case value_t::array:                                                                         \\\n                return (*lhs.m_data.m_value.array) op (*rhs.m_data.m_value.array);                                     \\\n                \\\n            case value_t::object:                                                                        \\\n                return (*lhs.m_data.m_value.object) op (*rhs.m_data.m_value.object);                                   \\\n                \\\n            case value_t::null:                                                                          \\\n                return (null_result);                                                                    \\\n                \\\n            case value_t::string:                                                                        \\\n                return (*lhs.m_data.m_value.string) op (*rhs.m_data.m_value.string);                                   \\\n                \\\n            case value_t::boolean:                                                                       \\\n                return (lhs.m_data.m_value.boolean) op (rhs.m_data.m_value.boolean);                                   \\\n                \\\n            case value_t::number_integer:                                                                \\\n                return (lhs.m_data.m_value.number_integer) op (rhs.m_data.m_value.number_integer);                     \\\n                \\\n            case value_t::number_unsigned:                                                               \\\n                return (lhs.m_data.m_value.number_unsigned) op (rhs.m_data.m_value.number_unsigned);                   \\\n                \\\n            case value_t::number_float:                                                                  \\\n                return (lhs.m_data.m_value.number_float) op (rhs.m_data.m_value.number_float);                         \\\n                \\\n            case value_t::binary:                                                                        \\\n                return (*lhs.m_data.m_value.binary) op (*rhs.m_data.m_value.binary);                                   \\\n                \\\n            case value_t::discarded:                                                                     \\\n            default:                                                                                     \\\n                return (unordered_result);                                                               \\\n        }                                                                                                \\\n    }                                                                                                    \\\n    else if (lhs_type == value_t::number_integer && rhs_type == value_t::number_float)                   \\\n    {                                                                                                    \\\n        return static_cast<number_float_t>(lhs.m_data.m_value.number_integer) op rhs.m_data.m_value.number_float;      \\\n    }                                                                                                    \\\n    else if (lhs_type == value_t::number_float && rhs_type == value_t::number_integer)                   \\\n    {                                                                                                    \\\n        return lhs.m_data.m_value.number_float op static_cast<number_float_t>(rhs.m_data.m_value.number_integer);      \\\n    }                                                                                                    \\\n    else if (lhs_type == value_t::number_unsigned && rhs_type == value_t::number_float)                  \\\n    {                                                                                                    \\\n        return static_cast<number_float_t>(lhs.m_data.m_value.number_unsigned) op rhs.m_data.m_value.number_float;     \\\n    }                                                                                                    \\\n    else if (lhs_type == value_t::number_float && rhs_type == value_t::number_unsigned)                  \\\n    {                                                                                                    \\\n        return lhs.m_data.m_value.number_float op static_cast<number_float_t>(rhs.m_data.m_value.number_unsigned);     \\\n    }                                                                                                    \\\n    else if (lhs_type == value_t::number_unsigned && rhs_type == value_t::number_integer)                \\\n    {                                                                                                    \\\n        return static_cast<number_integer_t>(lhs.m_data.m_value.number_unsigned) op rhs.m_data.m_value.number_integer; \\\n    }                                                                                                    \\\n    else if (lhs_type == value_t::number_integer && rhs_type == value_t::number_unsigned)                \\\n    {                                                                                                    \\\n        return lhs.m_data.m_value.number_integer op static_cast<number_integer_t>(rhs.m_data.m_value.number_unsigned); \\\n    }                                                                                                    \\\n    else if(compares_unordered(lhs, rhs))\\\n    {\\\n        return (unordered_result);\\\n    }\\\n    \\\n    return (default_result);\n\n  JSON_PRIVATE_UNLESS_TESTED:\n    // returns true if:\n    // - any operand is NaN and the other operand is of number type\n    // - any operand is discarded\n    // in legacy mode, discarded values are considered ordered if\n    // an operation is computed as an odd number of inverses of others\n    static bool compares_unordered(const_reference lhs, const_reference rhs, bool inverse = false) noexcept\n    {\n        if ((lhs.is_number_float() && std::isnan(lhs.m_data.m_value.number_float) && rhs.is_number())\n                || (rhs.is_number_float() && std::isnan(rhs.m_data.m_value.number_float) && lhs.is_number()))\n        {\n            return true;\n        }\n#if JSON_USE_LEGACY_DISCARDED_VALUE_COMPARISON\n        return (lhs.is_discarded() || rhs.is_discarded()) && !inverse;\n#else\n        static_cast<void>(inverse);\n        return lhs.is_discarded() || rhs.is_discarded();\n#endif\n    }\n\n  private:\n    bool compares_unordered(const_reference rhs, bool inverse = false) const noexcept\n    {\n        return compares_unordered(*this, rhs, inverse);\n    }\n\n  public:\n#if JSON_HAS_THREE_WAY_COMPARISON\n    /// @brief comparison: equal\n    /// @sa https://json.nlohmann.me/api/basic_json/operator_eq/\n    bool operator==(const_reference rhs) const noexcept\n    {\n#ifdef __GNUC__\n#pragma GCC diagnostic push\n#pragma GCC diagnostic ignored \"-Wfloat-equal\"\n#endif\n        const_reference lhs = *this;\n        JSON_IMPLEMENT_OPERATOR( ==, true, false, false)\n#ifdef __GNUC__\n#pragma GCC diagnostic pop\n#endif\n    }\n\n    /// @brief comparison: equal\n    /// @sa https://json.nlohmann.me/api/basic_json/operator_eq/\n    template<typename ScalarType>\n    requires std::is_scalar_v<ScalarType>\n    bool operator==(ScalarType rhs) const noexcept\n    {\n        return *this == basic_json(rhs);\n    }\n\n    /// @brief comparison: not equal\n    /// @sa https://json.nlohmann.me/api/basic_json/operator_ne/\n    bool operator!=(const_reference rhs) const noexcept\n    {\n        if (compares_unordered(rhs, true))\n        {\n            return false;\n        }\n        return !operator==(rhs);\n    }\n\n    /// @brief comparison: 3-way\n    /// @sa https://json.nlohmann.me/api/basic_json/operator_spaceship/\n    std::partial_ordering operator<=>(const_reference rhs) const noexcept // *NOPAD*\n    {\n        const_reference lhs = *this;\n        // default_result is used if we cannot compare values. In that case,\n        // we compare types.\n        JSON_IMPLEMENT_OPERATOR(<=>, // *NOPAD*\n                                std::partial_ordering::equivalent,\n                                std::partial_ordering::unordered,\n                                lhs_type <=> rhs_type) // *NOPAD*\n    }\n\n    /// @brief comparison: 3-way\n    /// @sa https://json.nlohmann.me/api/basic_json/operator_spaceship/\n    template<typename ScalarType>\n    requires std::is_scalar_v<ScalarType>\n    std::partial_ordering operator<=>(ScalarType rhs) const noexcept // *NOPAD*\n    {\n        return *this <=> basic_json(rhs); // *NOPAD*\n    }\n\n#if JSON_USE_LEGACY_DISCARDED_VALUE_COMPARISON\n    // all operators that are computed as an odd number of inverses of others\n    // need to be overloaded to emulate the legacy comparison behavior\n\n    /// @brief comparison: less than or equal\n    /// @sa https://json.nlohmann.me/api/basic_json/operator_le/\n    JSON_HEDLEY_DEPRECATED_FOR(3.11.0, undef JSON_USE_LEGACY_DISCARDED_VALUE_COMPARISON)\n    bool operator<=(const_reference rhs) const noexcept\n    {\n        if (compares_unordered(rhs, true))\n        {\n            return false;\n        }\n        return !(rhs < *this);\n    }\n\n    /// @brief comparison: less than or equal\n    /// @sa https://json.nlohmann.me/api/basic_json/operator_le/\n    template<typename ScalarType>\n    requires std::is_scalar_v<ScalarType>\n    bool operator<=(ScalarType rhs) const noexcept\n    {\n        return *this <= basic_json(rhs);\n    }\n\n    /// @brief comparison: greater than or equal\n    /// @sa https://json.nlohmann.me/api/basic_json/operator_ge/\n    JSON_HEDLEY_DEPRECATED_FOR(3.11.0, undef JSON_USE_LEGACY_DISCARDED_VALUE_COMPARISON)\n    bool operator>=(const_reference rhs) const noexcept\n    {\n        if (compares_unordered(rhs, true))\n        {\n            return false;\n        }\n        return !(*this < rhs);\n    }\n\n    /// @brief comparison: greater than or equal\n    /// @sa https://json.nlohmann.me/api/basic_json/operator_ge/\n    template<typename ScalarType>\n    requires std::is_scalar_v<ScalarType>\n    bool operator>=(ScalarType rhs) const noexcept\n    {\n        return *this >= basic_json(rhs);\n    }\n#endif\n#else\n    /// @brief comparison: equal\n    /// @sa https://json.nlohmann.me/api/basic_json/operator_eq/\n    friend bool operator==(const_reference lhs, const_reference rhs) noexcept\n    {\n#ifdef __GNUC__\n#pragma GCC diagnostic push\n#pragma GCC diagnostic ignored \"-Wfloat-equal\"\n#endif\n        JSON_IMPLEMENT_OPERATOR( ==, true, false, false)\n#ifdef __GNUC__\n#pragma GCC diagnostic pop\n#endif\n    }\n\n    /// @brief comparison: equal\n    /// @sa https://json.nlohmann.me/api/basic_json/operator_eq/\n    template<typename ScalarType, typename std::enable_if<\n                 std::is_scalar<ScalarType>::value, int>::type = 0>\n    friend bool operator==(const_reference lhs, ScalarType rhs) noexcept\n    {\n        return lhs == basic_json(rhs);\n    }\n\n    /// @brief comparison: equal\n    /// @sa https://json.nlohmann.me/api/basic_json/operator_eq/\n    template<typename ScalarType, typename std::enable_if<\n                 std::is_scalar<ScalarType>::value, int>::type = 0>\n    friend bool operator==(ScalarType lhs, const_reference rhs) noexcept\n    {\n        return basic_json(lhs) == rhs;\n    }\n\n    /// @brief comparison: not equal\n    /// @sa https://json.nlohmann.me/api/basic_json/operator_ne/\n    friend bool operator!=(const_reference lhs, const_reference rhs) noexcept\n    {\n        if (compares_unordered(lhs, rhs, true))\n        {\n            return false;\n        }\n        return !(lhs == rhs);\n    }\n\n    /// @brief comparison: not equal\n    /// @sa https://json.nlohmann.me/api/basic_json/operator_ne/\n    template<typename ScalarType, typename std::enable_if<\n                 std::is_scalar<ScalarType>::value, int>::type = 0>\n    friend bool operator!=(const_reference lhs, ScalarType rhs) noexcept\n    {\n        return lhs != basic_json(rhs);\n    }\n\n    /// @brief comparison: not equal\n    /// @sa https://json.nlohmann.me/api/basic_json/operator_ne/\n    template<typename ScalarType, typename std::enable_if<\n                 std::is_scalar<ScalarType>::value, int>::type = 0>\n    friend bool operator!=(ScalarType lhs, const_reference rhs) noexcept\n    {\n        return basic_json(lhs) != rhs;\n    }\n\n    /// @brief comparison: less than\n    /// @sa https://json.nlohmann.me/api/basic_json/operator_lt/\n    friend bool operator<(const_reference lhs, const_reference rhs) noexcept\n    {\n        // default_result is used if we cannot compare values. In that case,\n        // we compare types. Note we have to call the operator explicitly,\n        // because MSVC has problems otherwise.\n        JSON_IMPLEMENT_OPERATOR( <, false, false, operator<(lhs_type, rhs_type))\n    }\n\n    /// @brief comparison: less than\n    /// @sa https://json.nlohmann.me/api/basic_json/operator_lt/\n    template<typename ScalarType, typename std::enable_if<\n                 std::is_scalar<ScalarType>::value, int>::type = 0>\n    friend bool operator<(const_reference lhs, ScalarType rhs) noexcept\n    {\n        return lhs < basic_json(rhs);\n    }\n\n    /// @brief comparison: less than\n    /// @sa https://json.nlohmann.me/api/basic_json/operator_lt/\n    template<typename ScalarType, typename std::enable_if<\n                 std::is_scalar<ScalarType>::value, int>::type = 0>\n    friend bool operator<(ScalarType lhs, const_reference rhs) noexcept\n    {\n        return basic_json(lhs) < rhs;\n    }\n\n    /// @brief comparison: less than or equal\n    /// @sa https://json.nlohmann.me/api/basic_json/operator_le/\n    friend bool operator<=(const_reference lhs, const_reference rhs) noexcept\n    {\n        if (compares_unordered(lhs, rhs, true))\n        {\n            return false;\n        }\n        return !(rhs < lhs);\n    }\n\n    /// @brief comparison: less than or equal\n    /// @sa https://json.nlohmann.me/api/basic_json/operator_le/\n    template<typename ScalarType, typename std::enable_if<\n                 std::is_scalar<ScalarType>::value, int>::type = 0>\n    friend bool operator<=(const_reference lhs, ScalarType rhs) noexcept\n    {\n        return lhs <= basic_json(rhs);\n    }\n\n    /// @brief comparison: less than or equal\n    /// @sa https://json.nlohmann.me/api/basic_json/operator_le/\n    template<typename ScalarType, typename std::enable_if<\n                 std::is_scalar<ScalarType>::value, int>::type = 0>\n    friend bool operator<=(ScalarType lhs, const_reference rhs) noexcept\n    {\n        return basic_json(lhs) <= rhs;\n    }\n\n    /// @brief comparison: greater than\n    /// @sa https://json.nlohmann.me/api/basic_json/operator_gt/\n    friend bool operator>(const_reference lhs, const_reference rhs) noexcept\n    {\n        // double inverse\n        if (compares_unordered(lhs, rhs))\n        {\n            return false;\n        }\n        return !(lhs <= rhs);\n    }\n\n    /// @brief comparison: greater than\n    /// @sa https://json.nlohmann.me/api/basic_json/operator_gt/\n    template<typename ScalarType, typename std::enable_if<\n                 std::is_scalar<ScalarType>::value, int>::type = 0>\n    friend bool operator>(const_reference lhs, ScalarType rhs) noexcept\n    {\n        return lhs > basic_json(rhs);\n    }\n\n    /// @brief comparison: greater than\n    /// @sa https://json.nlohmann.me/api/basic_json/operator_gt/\n    template<typename ScalarType, typename std::enable_if<\n                 std::is_scalar<ScalarType>::value, int>::type = 0>\n    friend bool operator>(ScalarType lhs, const_reference rhs) noexcept\n    {\n        return basic_json(lhs) > rhs;\n    }\n\n    /// @brief comparison: greater than or equal\n    /// @sa https://json.nlohmann.me/api/basic_json/operator_ge/\n    friend bool operator>=(const_reference lhs, const_reference rhs) noexcept\n    {\n        if (compares_unordered(lhs, rhs, true))\n        {\n            return false;\n        }\n        return !(lhs < rhs);\n    }\n\n    /// @brief comparison: greater than or equal\n    /// @sa https://json.nlohmann.me/api/basic_json/operator_ge/\n    template<typename ScalarType, typename std::enable_if<\n                 std::is_scalar<ScalarType>::value, int>::type = 0>\n    friend bool operator>=(const_reference lhs, ScalarType rhs) noexcept\n    {\n        return lhs >= basic_json(rhs);\n    }\n\n    /// @brief comparison: greater than or equal\n    /// @sa https://json.nlohmann.me/api/basic_json/operator_ge/\n    template<typename ScalarType, typename std::enable_if<\n                 std::is_scalar<ScalarType>::value, int>::type = 0>\n    friend bool operator>=(ScalarType lhs, const_reference rhs) noexcept\n    {\n        return basic_json(lhs) >= rhs;\n    }\n#endif\n\n#undef JSON_IMPLEMENT_OPERATOR\n\n    /// @}\n\n    ///////////////////\n    // serialization //\n    ///////////////////\n\n    /// @name serialization\n    /// @{\n#ifndef JSON_NO_IO\n    /// @brief serialize to stream\n    /// @sa https://json.nlohmann.me/api/basic_json/operator_ltlt/\n    friend std::ostream& operator<<(std::ostream& o, const basic_json& j)\n    {\n        // read width member and use it as indentation parameter if nonzero\n        const bool pretty_print = o.width() > 0;\n        const auto indentation = pretty_print ? o.width() : 0;\n\n        // reset width to 0 for subsequent calls to this stream\n        o.width(0);\n\n        // do the actual serialization\n        serializer s(detail::output_adapter<char>(o), o.fill());\n        s.dump(j, pretty_print, false, static_cast<unsigned int>(indentation));\n        return o;\n    }\n\n    /// @brief serialize to stream\n    /// @sa https://json.nlohmann.me/api/basic_json/operator_ltlt/\n    /// @deprecated This function is deprecated since 3.0.0 and will be removed in\n    ///             version 4.0.0 of the library. Please use\n    ///             operator<<(std::ostream&, const basic_json&) instead; that is,\n    ///             replace calls like `j >> o;` with `o << j;`.\n    JSON_HEDLEY_DEPRECATED_FOR(3.0.0, operator<<(std::ostream&, const basic_json&))\n    friend std::ostream& operator>>(const basic_json& j, std::ostream& o)\n    {\n        return o << j;\n    }\n#endif  // JSON_NO_IO\n    /// @}\n\n    /////////////////////\n    // deserialization //\n    /////////////////////\n\n    /// @name deserialization\n    /// @{\n\n    /// @brief deserialize from a compatible input\n    /// @sa https://json.nlohmann.me/api/basic_json/parse/\n    template<typename InputType>\n    JSON_HEDLEY_WARN_UNUSED_RESULT\n    static basic_json parse(InputType&& i,\n                            const parser_callback_t cb = nullptr,\n                            const bool allow_exceptions = true,\n                            const bool ignore_comments = false)\n    {\n        basic_json result;\n        parser(detail::input_adapter(std::forward<InputType>(i)), cb, allow_exceptions, ignore_comments).parse(true, result);\n        return result;\n    }\n\n    /// @brief deserialize from a pair of character iterators\n    /// @sa https://json.nlohmann.me/api/basic_json/parse/\n    template<typename IteratorType>\n    JSON_HEDLEY_WARN_UNUSED_RESULT\n    static basic_json parse(IteratorType first,\n                            IteratorType last,\n                            const parser_callback_t cb = nullptr,\n                            const bool allow_exceptions = true,\n                            const bool ignore_comments = false)\n    {\n        basic_json result;\n        parser(detail::input_adapter(std::move(first), std::move(last)), cb, allow_exceptions, ignore_comments).parse(true, result);\n        return result;\n    }\n\n    JSON_HEDLEY_WARN_UNUSED_RESULT\n    JSON_HEDLEY_DEPRECATED_FOR(3.8.0, parse(ptr, ptr + len))\n    static basic_json parse(detail::span_input_adapter&& i,\n                            const parser_callback_t cb = nullptr,\n                            const bool allow_exceptions = true,\n                            const bool ignore_comments = false)\n    {\n        basic_json result;\n        parser(i.get(), cb, allow_exceptions, ignore_comments).parse(true, result);\n        return result;\n    }\n\n    /// @brief check if the input is valid JSON\n    /// @sa https://json.nlohmann.me/api/basic_json/accept/\n    template<typename InputType>\n    static bool accept(InputType&& i,\n                       const bool ignore_comments = false)\n    {\n        return parser(detail::input_adapter(std::forward<InputType>(i)), nullptr, false, ignore_comments).accept(true);\n    }\n\n    /// @brief check if the input is valid JSON\n    /// @sa https://json.nlohmann.me/api/basic_json/accept/\n    template<typename IteratorType>\n    static bool accept(IteratorType first, IteratorType last,\n                       const bool ignore_comments = false)\n    {\n        return parser(detail::input_adapter(std::move(first), std::move(last)), nullptr, false, ignore_comments).accept(true);\n    }\n\n    JSON_HEDLEY_WARN_UNUSED_RESULT\n    JSON_HEDLEY_DEPRECATED_FOR(3.8.0, accept(ptr, ptr + len))\n    static bool accept(detail::span_input_adapter&& i,\n                       const bool ignore_comments = false)\n    {\n        return parser(i.get(), nullptr, false, ignore_comments).accept(true);\n    }\n\n    /// @brief generate SAX events\n    /// @sa https://json.nlohmann.me/api/basic_json/sax_parse/\n    template <typename InputType, typename SAX>\n    JSON_HEDLEY_NON_NULL(2)\n    static bool sax_parse(InputType&& i, SAX* sax,\n                          input_format_t format = input_format_t::json,\n                          const bool strict = true,\n                          const bool ignore_comments = false)\n    {\n        auto ia = detail::input_adapter(std::forward<InputType>(i));\n        return format == input_format_t::json\n               ? parser(std::move(ia), nullptr, true, ignore_comments).sax_parse(sax, strict)\n               : detail::binary_reader<basic_json, decltype(ia), SAX>(std::move(ia), format).sax_parse(format, sax, strict);\n    }\n\n    /// @brief generate SAX events\n    /// @sa https://json.nlohmann.me/api/basic_json/sax_parse/\n    template<class IteratorType, class SAX>\n    JSON_HEDLEY_NON_NULL(3)\n    static bool sax_parse(IteratorType first, IteratorType last, SAX* sax,\n                          input_format_t format = input_format_t::json,\n                          const bool strict = true,\n                          const bool ignore_comments = false)\n    {\n        auto ia = detail::input_adapter(std::move(first), std::move(last));\n        return format == input_format_t::json\n               ? parser(std::move(ia), nullptr, true, ignore_comments).sax_parse(sax, strict)\n               : detail::binary_reader<basic_json, decltype(ia), SAX>(std::move(ia), format).sax_parse(format, sax, strict);\n    }\n\n    /// @brief generate SAX events\n    /// @sa https://json.nlohmann.me/api/basic_json/sax_parse/\n    /// @deprecated This function is deprecated since 3.8.0 and will be removed in\n    ///             version 4.0.0 of the library. Please use\n    ///             sax_parse(ptr, ptr + len) instead.\n    template <typename SAX>\n    JSON_HEDLEY_DEPRECATED_FOR(3.8.0, sax_parse(ptr, ptr + len, ...))\n    JSON_HEDLEY_NON_NULL(2)\n    static bool sax_parse(detail::span_input_adapter&& i, SAX* sax,\n                          input_format_t format = input_format_t::json,\n                          const bool strict = true,\n                          const bool ignore_comments = false)\n    {\n        auto ia = i.get();\n        return format == input_format_t::json\n               // NOLINTNEXTLINE(hicpp-move-const-arg,performance-move-const-arg)\n               ? parser(std::move(ia), nullptr, true, ignore_comments).sax_parse(sax, strict)\n               // NOLINTNEXTLINE(hicpp-move-const-arg,performance-move-const-arg)\n               : detail::binary_reader<basic_json, decltype(ia), SAX>(std::move(ia), format).sax_parse(format, sax, strict);\n    }\n#ifndef JSON_NO_IO\n    /// @brief deserialize from stream\n    /// @sa https://json.nlohmann.me/api/basic_json/operator_gtgt/\n    /// @deprecated This stream operator is deprecated since 3.0.0 and will be removed in\n    ///             version 4.0.0 of the library. Please use\n    ///             operator>>(std::istream&, basic_json&) instead; that is,\n    ///             replace calls like `j << i;` with `i >> j;`.\n    JSON_HEDLEY_DEPRECATED_FOR(3.0.0, operator>>(std::istream&, basic_json&))\n    friend std::istream& operator<<(basic_json& j, std::istream& i)\n    {\n        return operator>>(i, j);\n    }\n\n    /// @brief deserialize from stream\n    /// @sa https://json.nlohmann.me/api/basic_json/operator_gtgt/\n    friend std::istream& operator>>(std::istream& i, basic_json& j)\n    {\n        parser(detail::input_adapter(i)).parse(false, j);\n        return i;\n    }\n#endif  // JSON_NO_IO\n    /// @}\n\n    ///////////////////////////\n    // convenience functions //\n    ///////////////////////////\n\n    /// @brief return the type as string\n    /// @sa https://json.nlohmann.me/api/basic_json/type_name/\n    JSON_HEDLEY_RETURNS_NON_NULL\n    const char* type_name() const noexcept\n    {\n        switch (m_data.m_type)\n        {\n            case value_t::null:\n                return \"null\";\n            case value_t::object:\n                return \"object\";\n            case value_t::array:\n                return \"array\";\n            case value_t::string:\n                return \"string\";\n            case value_t::boolean:\n                return \"boolean\";\n            case value_t::binary:\n                return \"binary\";\n            case value_t::discarded:\n                return \"discarded\";\n            case value_t::number_integer:\n            case value_t::number_unsigned:\n            case value_t::number_float:\n            default:\n                return \"number\";\n        }\n    }\n\n  JSON_PRIVATE_UNLESS_TESTED:\n    //////////////////////\n    // member variables //\n    //////////////////////\n\n    struct data\n    {\n        /// the type of the current element\n        value_t m_type = value_t::null;\n\n        /// the value of the current element\n        json_value m_value = {};\n\n        data(const value_t v)\n            : m_type(v), m_value(v)\n        {\n        }\n\n        data(size_type cnt, const basic_json& val)\n            : m_type(value_t::array)\n        {\n            m_value.array = create<array_t>(cnt, val);\n        }\n\n        data() noexcept = default;\n        data(data&&) noexcept = default;\n        data(const data&) noexcept = delete;\n        data& operator=(data&&) noexcept = delete;\n        data& operator=(const data&) noexcept = delete;\n\n        ~data() noexcept\n        {\n            m_value.destroy(m_type);\n        }\n    };\n\n    data m_data = {};\n\n#if JSON_DIAGNOSTICS\n    /// a pointer to a parent value (for debugging purposes)\n    basic_json* m_parent = nullptr;\n#endif\n\n    //////////////////////////////////////////\n    // binary serialization/deserialization //\n    //////////////////////////////////////////\n\n    /// @name binary serialization/deserialization support\n    /// @{\n\n  public:\n    /// @brief create a CBOR serialization of a given JSON value\n    /// @sa https://json.nlohmann.me/api/basic_json/to_cbor/\n    static std::vector<std::uint8_t> to_cbor(const basic_json& j)\n    {\n        std::vector<std::uint8_t> result;\n        to_cbor(j, result);\n        return result;\n    }\n\n    /// @brief create a CBOR serialization of a given JSON value\n    /// @sa https://json.nlohmann.me/api/basic_json/to_cbor/\n    static void to_cbor(const basic_json& j, detail::output_adapter<std::uint8_t> o)\n    {\n        binary_writer<std::uint8_t>(o).write_cbor(j);\n    }\n\n    /// @brief create a CBOR serialization of a given JSON value\n    /// @sa https://json.nlohmann.me/api/basic_json/to_cbor/\n    static void to_cbor(const basic_json& j, detail::output_adapter<char> o)\n    {\n        binary_writer<char>(o).write_cbor(j);\n    }\n\n    /// @brief create a MessagePack serialization of a given JSON value\n    /// @sa https://json.nlohmann.me/api/basic_json/to_msgpack/\n    static std::vector<std::uint8_t> to_msgpack(const basic_json& j)\n    {\n        std::vector<std::uint8_t> result;\n        to_msgpack(j, result);\n        return result;\n    }\n\n    /// @brief create a MessagePack serialization of a given JSON value\n    /// @sa https://json.nlohmann.me/api/basic_json/to_msgpack/\n    static void to_msgpack(const basic_json& j, detail::output_adapter<std::uint8_t> o)\n    {\n        binary_writer<std::uint8_t>(o).write_msgpack(j);\n    }\n\n    /// @brief create a MessagePack serialization of a given JSON value\n    /// @sa https://json.nlohmann.me/api/basic_json/to_msgpack/\n    static void to_msgpack(const basic_json& j, detail::output_adapter<char> o)\n    {\n        binary_writer<char>(o).write_msgpack(j);\n    }\n\n    /// @brief create a UBJSON serialization of a given JSON value\n    /// @sa https://json.nlohmann.me/api/basic_json/to_ubjson/\n    static std::vector<std::uint8_t> to_ubjson(const basic_json& j,\n            const bool use_size = false,\n            const bool use_type = false)\n    {\n        std::vector<std::uint8_t> result;\n        to_ubjson(j, result, use_size, use_type);\n        return result;\n    }\n\n    /// @brief create a UBJSON serialization of a given JSON value\n    /// @sa https://json.nlohmann.me/api/basic_json/to_ubjson/\n    static void to_ubjson(const basic_json& j, detail::output_adapter<std::uint8_t> o,\n                          const bool use_size = false, const bool use_type = false)\n    {\n        binary_writer<std::uint8_t>(o).write_ubjson(j, use_size, use_type);\n    }\n\n    /// @brief create a UBJSON serialization of a given JSON value\n    /// @sa https://json.nlohmann.me/api/basic_json/to_ubjson/\n    static void to_ubjson(const basic_json& j, detail::output_adapter<char> o,\n                          const bool use_size = false, const bool use_type = false)\n    {\n        binary_writer<char>(o).write_ubjson(j, use_size, use_type);\n    }\n\n    /// @brief create a BJData serialization of a given JSON value\n    /// @sa https://json.nlohmann.me/api/basic_json/to_bjdata/\n    static std::vector<std::uint8_t> to_bjdata(const basic_json& j,\n            const bool use_size = false,\n            const bool use_type = false)\n    {\n        std::vector<std::uint8_t> result;\n        to_bjdata(j, result, use_size, use_type);\n        return result;\n    }\n\n    /// @brief create a BJData serialization of a given JSON value\n    /// @sa https://json.nlohmann.me/api/basic_json/to_bjdata/\n    static void to_bjdata(const basic_json& j, detail::output_adapter<std::uint8_t> o,\n                          const bool use_size = false, const bool use_type = false)\n    {\n        binary_writer<std::uint8_t>(o).write_ubjson(j, use_size, use_type, true, true);\n    }\n\n    /// @brief create a BJData serialization of a given JSON value\n    /// @sa https://json.nlohmann.me/api/basic_json/to_bjdata/\n    static void to_bjdata(const basic_json& j, detail::output_adapter<char> o,\n                          const bool use_size = false, const bool use_type = false)\n    {\n        binary_writer<char>(o).write_ubjson(j, use_size, use_type, true, true);\n    }\n\n    /// @brief create a BSON serialization of a given JSON value\n    /// @sa https://json.nlohmann.me/api/basic_json/to_bson/\n    static std::vector<std::uint8_t> to_bson(const basic_json& j)\n    {\n        std::vector<std::uint8_t> result;\n        to_bson(j, result);\n        return result;\n    }\n\n    /// @brief create a BSON serialization of a given JSON value\n    /// @sa https://json.nlohmann.me/api/basic_json/to_bson/\n    static void to_bson(const basic_json& j, detail::output_adapter<std::uint8_t> o)\n    {\n        binary_writer<std::uint8_t>(o).write_bson(j);\n    }\n\n    /// @brief create a BSON serialization of a given JSON value\n    /// @sa https://json.nlohmann.me/api/basic_json/to_bson/\n    static void to_bson(const basic_json& j, detail::output_adapter<char> o)\n    {\n        binary_writer<char>(o).write_bson(j);\n    }\n\n    /// @brief create a JSON value from an input in CBOR format\n    /// @sa https://json.nlohmann.me/api/basic_json/from_cbor/\n    template<typename InputType>\n    JSON_HEDLEY_WARN_UNUSED_RESULT\n    static basic_json from_cbor(InputType&& i,\n                                const bool strict = true,\n                                const bool allow_exceptions = true,\n                                const cbor_tag_handler_t tag_handler = cbor_tag_handler_t::error)\n    {\n        basic_json result;\n        detail::json_sax_dom_parser<basic_json> sdp(result, allow_exceptions);\n        auto ia = detail::input_adapter(std::forward<InputType>(i));\n        const bool res = binary_reader<decltype(ia)>(std::move(ia), input_format_t::cbor).sax_parse(input_format_t::cbor, &sdp, strict, tag_handler);\n        return res ? result : basic_json(value_t::discarded);\n    }\n\n    /// @brief create a JSON value from an input in CBOR format\n    /// @sa https://json.nlohmann.me/api/basic_json/from_cbor/\n    template<typename IteratorType>\n    JSON_HEDLEY_WARN_UNUSED_RESULT\n    static basic_json from_cbor(IteratorType first, IteratorType last,\n                                const bool strict = true,\n                                const bool allow_exceptions = true,\n                                const cbor_tag_handler_t tag_handler = cbor_tag_handler_t::error)\n    {\n        basic_json result;\n        detail::json_sax_dom_parser<basic_json> sdp(result, allow_exceptions);\n        auto ia = detail::input_adapter(std::move(first), std::move(last));\n        const bool res = binary_reader<decltype(ia)>(std::move(ia), input_format_t::cbor).sax_parse(input_format_t::cbor, &sdp, strict, tag_handler);\n        return res ? result : basic_json(value_t::discarded);\n    }\n\n    template<typename T>\n    JSON_HEDLEY_WARN_UNUSED_RESULT\n    JSON_HEDLEY_DEPRECATED_FOR(3.8.0, from_cbor(ptr, ptr + len))\n    static basic_json from_cbor(const T* ptr, std::size_t len,\n                                const bool strict = true,\n                                const bool allow_exceptions = true,\n                                const cbor_tag_handler_t tag_handler = cbor_tag_handler_t::error)\n    {\n        return from_cbor(ptr, ptr + len, strict, allow_exceptions, tag_handler);\n    }\n\n    JSON_HEDLEY_WARN_UNUSED_RESULT\n    JSON_HEDLEY_DEPRECATED_FOR(3.8.0, from_cbor(ptr, ptr + len))\n    static basic_json from_cbor(detail::span_input_adapter&& i,\n                                const bool strict = true,\n                                const bool allow_exceptions = true,\n                                const cbor_tag_handler_t tag_handler = cbor_tag_handler_t::error)\n    {\n        basic_json result;\n        detail::json_sax_dom_parser<basic_json> sdp(result, allow_exceptions);\n        auto ia = i.get();\n        // NOLINTNEXTLINE(hicpp-move-const-arg,performance-move-const-arg)\n        const bool res = binary_reader<decltype(ia)>(std::move(ia), input_format_t::cbor).sax_parse(input_format_t::cbor, &sdp, strict, tag_handler);\n        return res ? result : basic_json(value_t::discarded);\n    }\n\n    /// @brief create a JSON value from an input in MessagePack format\n    /// @sa https://json.nlohmann.me/api/basic_json/from_msgpack/\n    template<typename InputType>\n    JSON_HEDLEY_WARN_UNUSED_RESULT\n    static basic_json from_msgpack(InputType&& i,\n                                   const bool strict = true,\n                                   const bool allow_exceptions = true)\n    {\n        basic_json result;\n        detail::json_sax_dom_parser<basic_json> sdp(result, allow_exceptions);\n        auto ia = detail::input_adapter(std::forward<InputType>(i));\n        const bool res = binary_reader<decltype(ia)>(std::move(ia), input_format_t::msgpack).sax_parse(input_format_t::msgpack, &sdp, strict);\n        return res ? result : basic_json(value_t::discarded);\n    }\n\n    /// @brief create a JSON value from an input in MessagePack format\n    /// @sa https://json.nlohmann.me/api/basic_json/from_msgpack/\n    template<typename IteratorType>\n    JSON_HEDLEY_WARN_UNUSED_RESULT\n    static basic_json from_msgpack(IteratorType first, IteratorType last,\n                                   const bool strict = true,\n                                   const bool allow_exceptions = true)\n    {\n        basic_json result;\n        detail::json_sax_dom_parser<basic_json> sdp(result, allow_exceptions);\n        auto ia = detail::input_adapter(std::move(first), std::move(last));\n        const bool res = binary_reader<decltype(ia)>(std::move(ia), input_format_t::msgpack).sax_parse(input_format_t::msgpack, &sdp, strict);\n        return res ? result : basic_json(value_t::discarded);\n    }\n\n    template<typename T>\n    JSON_HEDLEY_WARN_UNUSED_RESULT\n    JSON_HEDLEY_DEPRECATED_FOR(3.8.0, from_msgpack(ptr, ptr + len))\n    static basic_json from_msgpack(const T* ptr, std::size_t len,\n                                   const bool strict = true,\n                                   const bool allow_exceptions = true)\n    {\n        return from_msgpack(ptr, ptr + len, strict, allow_exceptions);\n    }\n\n    JSON_HEDLEY_WARN_UNUSED_RESULT\n    JSON_HEDLEY_DEPRECATED_FOR(3.8.0, from_msgpack(ptr, ptr + len))\n    static basic_json from_msgpack(detail::span_input_adapter&& i,\n                                   const bool strict = true,\n                                   const bool allow_exceptions = true)\n    {\n        basic_json result;\n        detail::json_sax_dom_parser<basic_json> sdp(result, allow_exceptions);\n        auto ia = i.get();\n        // NOLINTNEXTLINE(hicpp-move-const-arg,performance-move-const-arg)\n        const bool res = binary_reader<decltype(ia)>(std::move(ia), input_format_t::msgpack).sax_parse(input_format_t::msgpack, &sdp, strict);\n        return res ? result : basic_json(value_t::discarded);\n    }\n\n    /// @brief create a JSON value from an input in UBJSON format\n    /// @sa https://json.nlohmann.me/api/basic_json/from_ubjson/\n    template<typename InputType>\n    JSON_HEDLEY_WARN_UNUSED_RESULT\n    static basic_json from_ubjson(InputType&& i,\n                                  const bool strict = true,\n                                  const bool allow_exceptions = true)\n    {\n        basic_json result;\n        detail::json_sax_dom_parser<basic_json> sdp(result, allow_exceptions);\n        auto ia = detail::input_adapter(std::forward<InputType>(i));\n        const bool res = binary_reader<decltype(ia)>(std::move(ia), input_format_t::ubjson).sax_parse(input_format_t::ubjson, &sdp, strict);\n        return res ? result : basic_json(value_t::discarded);\n    }\n\n    /// @brief create a JSON value from an input in UBJSON format\n    /// @sa https://json.nlohmann.me/api/basic_json/from_ubjson/\n    template<typename IteratorType>\n    JSON_HEDLEY_WARN_UNUSED_RESULT\n    static basic_json from_ubjson(IteratorType first, IteratorType last,\n                                  const bool strict = true,\n                                  const bool allow_exceptions = true)\n    {\n        basic_json result;\n        detail::json_sax_dom_parser<basic_json> sdp(result, allow_exceptions);\n        auto ia = detail::input_adapter(std::move(first), std::move(last));\n        const bool res = binary_reader<decltype(ia)>(std::move(ia), input_format_t::ubjson).sax_parse(input_format_t::ubjson, &sdp, strict);\n        return res ? result : basic_json(value_t::discarded);\n    }\n\n    template<typename T>\n    JSON_HEDLEY_WARN_UNUSED_RESULT\n    JSON_HEDLEY_DEPRECATED_FOR(3.8.0, from_ubjson(ptr, ptr + len))\n    static basic_json from_ubjson(const T* ptr, std::size_t len,\n                                  const bool strict = true,\n                                  const bool allow_exceptions = true)\n    {\n        return from_ubjson(ptr, ptr + len, strict, allow_exceptions);\n    }\n\n    JSON_HEDLEY_WARN_UNUSED_RESULT\n    JSON_HEDLEY_DEPRECATED_FOR(3.8.0, from_ubjson(ptr, ptr + len))\n    static basic_json from_ubjson(detail::span_input_adapter&& i,\n                                  const bool strict = true,\n                                  const bool allow_exceptions = true)\n    {\n        basic_json result;\n        detail::json_sax_dom_parser<basic_json> sdp(result, allow_exceptions);\n        auto ia = i.get();\n        // NOLINTNEXTLINE(hicpp-move-const-arg,performance-move-const-arg)\n        const bool res = binary_reader<decltype(ia)>(std::move(ia), input_format_t::ubjson).sax_parse(input_format_t::ubjson, &sdp, strict);\n        return res ? result : basic_json(value_t::discarded);\n    }\n\n    /// @brief create a JSON value from an input in BJData format\n    /// @sa https://json.nlohmann.me/api/basic_json/from_bjdata/\n    template<typename InputType>\n    JSON_HEDLEY_WARN_UNUSED_RESULT\n    static basic_json from_bjdata(InputType&& i,\n                                  const bool strict = true,\n                                  const bool allow_exceptions = true)\n    {\n        basic_json result;\n        detail::json_sax_dom_parser<basic_json> sdp(result, allow_exceptions);\n        auto ia = detail::input_adapter(std::forward<InputType>(i));\n        const bool res = binary_reader<decltype(ia)>(std::move(ia), input_format_t::bjdata).sax_parse(input_format_t::bjdata, &sdp, strict);\n        return res ? result : basic_json(value_t::discarded);\n    }\n\n    /// @brief create a JSON value from an input in BJData format\n    /// @sa https://json.nlohmann.me/api/basic_json/from_bjdata/\n    template<typename IteratorType>\n    JSON_HEDLEY_WARN_UNUSED_RESULT\n    static basic_json from_bjdata(IteratorType first, IteratorType last,\n                                  const bool strict = true,\n                                  const bool allow_exceptions = true)\n    {\n        basic_json result;\n        detail::json_sax_dom_parser<basic_json> sdp(result, allow_exceptions);\n        auto ia = detail::input_adapter(std::move(first), std::move(last));\n        const bool res = binary_reader<decltype(ia)>(std::move(ia), input_format_t::bjdata).sax_parse(input_format_t::bjdata, &sdp, strict);\n        return res ? result : basic_json(value_t::discarded);\n    }\n\n    /// @brief create a JSON value from an input in BSON format\n    /// @sa https://json.nlohmann.me/api/basic_json/from_bson/\n    template<typename InputType>\n    JSON_HEDLEY_WARN_UNUSED_RESULT\n    static basic_json from_bson(InputType&& i,\n                                const bool strict = true,\n                                const bool allow_exceptions = true)\n    {\n        basic_json result;\n        detail::json_sax_dom_parser<basic_json> sdp(result, allow_exceptions);\n        auto ia = detail::input_adapter(std::forward<InputType>(i));\n        const bool res = binary_reader<decltype(ia)>(std::move(ia), input_format_t::bson).sax_parse(input_format_t::bson, &sdp, strict);\n        return res ? result : basic_json(value_t::discarded);\n    }\n\n    /// @brief create a JSON value from an input in BSON format\n    /// @sa https://json.nlohmann.me/api/basic_json/from_bson/\n    template<typename IteratorType>\n    JSON_HEDLEY_WARN_UNUSED_RESULT\n    static basic_json from_bson(IteratorType first, IteratorType last,\n                                const bool strict = true,\n                                const bool allow_exceptions = true)\n    {\n        basic_json result;\n        detail::json_sax_dom_parser<basic_json> sdp(result, allow_exceptions);\n        auto ia = detail::input_adapter(std::move(first), std::move(last));\n        const bool res = binary_reader<decltype(ia)>(std::move(ia), input_format_t::bson).sax_parse(input_format_t::bson, &sdp, strict);\n        return res ? result : basic_json(value_t::discarded);\n    }\n\n    template<typename T>\n    JSON_HEDLEY_WARN_UNUSED_RESULT\n    JSON_HEDLEY_DEPRECATED_FOR(3.8.0, from_bson(ptr, ptr + len))\n    static basic_json from_bson(const T* ptr, std::size_t len,\n                                const bool strict = true,\n                                const bool allow_exceptions = true)\n    {\n        return from_bson(ptr, ptr + len, strict, allow_exceptions);\n    }\n\n    JSON_HEDLEY_WARN_UNUSED_RESULT\n    JSON_HEDLEY_DEPRECATED_FOR(3.8.0, from_bson(ptr, ptr + len))\n    static basic_json from_bson(detail::span_input_adapter&& i,\n                                const bool strict = true,\n                                const bool allow_exceptions = true)\n    {\n        basic_json result;\n        detail::json_sax_dom_parser<basic_json> sdp(result, allow_exceptions);\n        auto ia = i.get();\n        // NOLINTNEXTLINE(hicpp-move-const-arg,performance-move-const-arg)\n        const bool res = binary_reader<decltype(ia)>(std::move(ia), input_format_t::bson).sax_parse(input_format_t::bson, &sdp, strict);\n        return res ? result : basic_json(value_t::discarded);\n    }\n    /// @}\n\n    //////////////////////////\n    // JSON Pointer support //\n    //////////////////////////\n\n    /// @name JSON Pointer functions\n    /// @{\n\n    /// @brief access specified element via JSON Pointer\n    /// @sa https://json.nlohmann.me/api/basic_json/operator%5B%5D/\n    reference operator[](const json_pointer& ptr)\n    {\n        return ptr.get_unchecked(this);\n    }\n\n    template<typename BasicJsonType, detail::enable_if_t<detail::is_basic_json<BasicJsonType>::value, int> = 0>\n    JSON_HEDLEY_DEPRECATED_FOR(3.11.0, basic_json::json_pointer or nlohmann::json_pointer<basic_json::string_t>) // NOLINT(readability/alt_tokens)\n    reference operator[](const ::nlohmann::json_pointer<BasicJsonType>& ptr)\n    {\n        return ptr.get_unchecked(this);\n    }\n\n    /// @brief access specified element via JSON Pointer\n    /// @sa https://json.nlohmann.me/api/basic_json/operator%5B%5D/\n    const_reference operator[](const json_pointer& ptr) const\n    {\n        return ptr.get_unchecked(this);\n    }\n\n    template<typename BasicJsonType, detail::enable_if_t<detail::is_basic_json<BasicJsonType>::value, int> = 0>\n    JSON_HEDLEY_DEPRECATED_FOR(3.11.0, basic_json::json_pointer or nlohmann::json_pointer<basic_json::string_t>) // NOLINT(readability/alt_tokens)\n    const_reference operator[](const ::nlohmann::json_pointer<BasicJsonType>& ptr) const\n    {\n        return ptr.get_unchecked(this);\n    }\n\n    /// @brief access specified element via JSON Pointer\n    /// @sa https://json.nlohmann.me/api/basic_json/at/\n    reference at(const json_pointer& ptr)\n    {\n        return ptr.get_checked(this);\n    }\n\n    template<typename BasicJsonType, detail::enable_if_t<detail::is_basic_json<BasicJsonType>::value, int> = 0>\n    JSON_HEDLEY_DEPRECATED_FOR(3.11.0, basic_json::json_pointer or nlohmann::json_pointer<basic_json::string_t>) // NOLINT(readability/alt_tokens)\n    reference at(const ::nlohmann::json_pointer<BasicJsonType>& ptr)\n    {\n        return ptr.get_checked(this);\n    }\n\n    /// @brief access specified element via JSON Pointer\n    /// @sa https://json.nlohmann.me/api/basic_json/at/\n    const_reference at(const json_pointer& ptr) const\n    {\n        return ptr.get_checked(this);\n    }\n\n    template<typename BasicJsonType, detail::enable_if_t<detail::is_basic_json<BasicJsonType>::value, int> = 0>\n    JSON_HEDLEY_DEPRECATED_FOR(3.11.0, basic_json::json_pointer or nlohmann::json_pointer<basic_json::string_t>) // NOLINT(readability/alt_tokens)\n    const_reference at(const ::nlohmann::json_pointer<BasicJsonType>& ptr) const\n    {\n        return ptr.get_checked(this);\n    }\n\n    /// @brief return flattened JSON value\n    /// @sa https://json.nlohmann.me/api/basic_json/flatten/\n    basic_json flatten() const\n    {\n        basic_json result(value_t::object);\n        json_pointer::flatten(\"\", *this, result);\n        return result;\n    }\n\n    /// @brief unflatten a previously flattened JSON value\n    /// @sa https://json.nlohmann.me/api/basic_json/unflatten/\n    basic_json unflatten() const\n    {\n        return json_pointer::unflatten(*this);\n    }\n\n    /// @}\n\n    //////////////////////////\n    // JSON Patch functions //\n    //////////////////////////\n\n    /// @name JSON Patch functions\n    /// @{\n\n    /// @brief applies a JSON patch in-place without copying the object\n    /// @sa https://json.nlohmann.me/api/basic_json/patch/\n    void patch_inplace(const basic_json& json_patch)\n    {\n        basic_json& result = *this;\n        // the valid JSON Patch operations\n        enum class patch_operations {add, remove, replace, move, copy, test, invalid};\n\n        const auto get_op = [](const std::string & op)\n        {\n            if (op == \"add\")\n            {\n                return patch_operations::add;\n            }\n            if (op == \"remove\")\n            {\n                return patch_operations::remove;\n            }\n            if (op == \"replace\")\n            {\n                return patch_operations::replace;\n            }\n            if (op == \"move\")\n            {\n                return patch_operations::move;\n            }\n            if (op == \"copy\")\n            {\n                return patch_operations::copy;\n            }\n            if (op == \"test\")\n            {\n                return patch_operations::test;\n            }\n\n            return patch_operations::invalid;\n        };\n\n        // wrapper for \"add\" operation; add value at ptr\n        const auto operation_add = [&result](json_pointer & ptr, basic_json val)\n        {\n            // adding to the root of the target document means replacing it\n            if (ptr.empty())\n            {\n                result = val;\n                return;\n            }\n\n            // make sure the top element of the pointer exists\n            json_pointer const top_pointer = ptr.top();\n            if (top_pointer != ptr)\n            {\n                result.at(top_pointer);\n            }\n\n            // get reference to parent of JSON pointer ptr\n            const auto last_path = ptr.back();\n            ptr.pop_back();\n            // parent must exist when performing patch add per RFC6902 specs\n            basic_json& parent = result.at(ptr);\n\n            switch (parent.m_data.m_type)\n            {\n                case value_t::null:\n                case value_t::object:\n                {\n                    // use operator[] to add value\n                    parent[last_path] = val;\n                    break;\n                }\n\n                case value_t::array:\n                {\n                    if (last_path == \"-\")\n                    {\n                        // special case: append to back\n                        parent.push_back(val);\n                    }\n                    else\n                    {\n                        const auto idx = json_pointer::template array_index<basic_json_t>(last_path);\n                        if (JSON_HEDLEY_UNLIKELY(idx > parent.size()))\n                        {\n                            // avoid undefined behavior\n                            JSON_THROW(out_of_range::create(401, detail::concat(\"array index \", std::to_string(idx), \" is out of range\"), &parent));\n                        }\n\n                        // default case: insert add offset\n                        parent.insert(parent.begin() + static_cast<difference_type>(idx), val);\n                    }\n                    break;\n                }\n\n                // if there exists a parent it cannot be primitive\n                case value_t::string: // LCOV_EXCL_LINE\n                case value_t::boolean: // LCOV_EXCL_LINE\n                case value_t::number_integer: // LCOV_EXCL_LINE\n                case value_t::number_unsigned: // LCOV_EXCL_LINE\n                case value_t::number_float: // LCOV_EXCL_LINE\n                case value_t::binary: // LCOV_EXCL_LINE\n                case value_t::discarded: // LCOV_EXCL_LINE\n                default:            // LCOV_EXCL_LINE\n                    JSON_ASSERT(false); // NOLINT(cert-dcl03-c,hicpp-static-assert,misc-static-assert) LCOV_EXCL_LINE\n            }\n        };\n\n        // wrapper for \"remove\" operation; remove value at ptr\n        const auto operation_remove = [this, & result](json_pointer & ptr)\n        {\n            // get reference to parent of JSON pointer ptr\n            const auto last_path = ptr.back();\n            ptr.pop_back();\n            basic_json& parent = result.at(ptr);\n\n            // remove child\n            if (parent.is_object())\n            {\n                // perform range check\n                auto it = parent.find(last_path);\n                if (JSON_HEDLEY_LIKELY(it != parent.end()))\n                {\n                    parent.erase(it);\n                }\n                else\n                {\n                    JSON_THROW(out_of_range::create(403, detail::concat(\"key '\", last_path, \"' not found\"), this));\n                }\n            }\n            else if (parent.is_array())\n            {\n                // note erase performs range check\n                parent.erase(json_pointer::template array_index<basic_json_t>(last_path));\n            }\n        };\n\n        // type check: top level value must be an array\n        if (JSON_HEDLEY_UNLIKELY(!json_patch.is_array()))\n        {\n            JSON_THROW(parse_error::create(104, 0, \"JSON patch must be an array of objects\", &json_patch));\n        }\n\n        // iterate and apply the operations\n        for (const auto& val : json_patch)\n        {\n            // wrapper to get a value for an operation\n            const auto get_value = [&val](const std::string & op,\n                                          const std::string & member,\n                                          bool string_type) -> basic_json &\n            {\n                // find value\n                auto it = val.m_data.m_value.object->find(member);\n\n                // context-sensitive error message\n                const auto error_msg = (op == \"op\") ? \"operation\" : detail::concat(\"operation '\", op, '\\'');\n\n                // check if desired value is present\n                if (JSON_HEDLEY_UNLIKELY(it == val.m_data.m_value.object->end()))\n                {\n                    // NOLINTNEXTLINE(performance-inefficient-string-concatenation)\n                    JSON_THROW(parse_error::create(105, 0, detail::concat(error_msg, \" must have member '\", member, \"'\"), &val));\n                }\n\n                // check if result is of type string\n                if (JSON_HEDLEY_UNLIKELY(string_type && !it->second.is_string()))\n                {\n                    // NOLINTNEXTLINE(performance-inefficient-string-concatenation)\n                    JSON_THROW(parse_error::create(105, 0, detail::concat(error_msg, \" must have string member '\", member, \"'\"), &val));\n                }\n\n                // no error: return value\n                return it->second;\n            };\n\n            // type check: every element of the array must be an object\n            if (JSON_HEDLEY_UNLIKELY(!val.is_object()))\n            {\n                JSON_THROW(parse_error::create(104, 0, \"JSON patch must be an array of objects\", &val));\n            }\n\n            // collect mandatory members\n            const auto op = get_value(\"op\", \"op\", true).template get<std::string>();\n            const auto path = get_value(op, \"path\", true).template get<std::string>();\n            json_pointer ptr(path);\n\n            switch (get_op(op))\n            {\n                case patch_operations::add:\n                {\n                    operation_add(ptr, get_value(\"add\", \"value\", false));\n                    break;\n                }\n\n                case patch_operations::remove:\n                {\n                    operation_remove(ptr);\n                    break;\n                }\n\n                case patch_operations::replace:\n                {\n                    // the \"path\" location must exist - use at()\n                    result.at(ptr) = get_value(\"replace\", \"value\", false);\n                    break;\n                }\n\n                case patch_operations::move:\n                {\n                    const auto from_path = get_value(\"move\", \"from\", true).template get<std::string>();\n                    json_pointer from_ptr(from_path);\n\n                    // the \"from\" location must exist - use at()\n                    basic_json const v = result.at(from_ptr);\n\n                    // The move operation is functionally identical to a\n                    // \"remove\" operation on the \"from\" location, followed\n                    // immediately by an \"add\" operation at the target\n                    // location with the value that was just removed.\n                    operation_remove(from_ptr);\n                    operation_add(ptr, v);\n                    break;\n                }\n\n                case patch_operations::copy:\n                {\n                    const auto from_path = get_value(\"copy\", \"from\", true).template get<std::string>();\n                    const json_pointer from_ptr(from_path);\n\n                    // the \"from\" location must exist - use at()\n                    basic_json const v = result.at(from_ptr);\n\n                    // The copy is functionally identical to an \"add\"\n                    // operation at the target location using the value\n                    // specified in the \"from\" member.\n                    operation_add(ptr, v);\n                    break;\n                }\n\n                case patch_operations::test:\n                {\n                    bool success = false;\n                    JSON_TRY\n                    {\n                        // check if \"value\" matches the one at \"path\"\n                        // the \"path\" location must exist - use at()\n                        success = (result.at(ptr) == get_value(\"test\", \"value\", false));\n                    }\n                    JSON_INTERNAL_CATCH (out_of_range&)\n                    {\n                        // ignore out of range errors: success remains false\n                    }\n\n                    // throw an exception if test fails\n                    if (JSON_HEDLEY_UNLIKELY(!success))\n                    {\n                        JSON_THROW(other_error::create(501, detail::concat(\"unsuccessful: \", val.dump()), &val));\n                    }\n\n                    break;\n                }\n\n                case patch_operations::invalid:\n                default:\n                {\n                    // op must be \"add\", \"remove\", \"replace\", \"move\", \"copy\", or\n                    // \"test\"\n                    JSON_THROW(parse_error::create(105, 0, detail::concat(\"operation value '\", op, \"' is invalid\"), &val));\n                }\n            }\n        }\n    }\n\n    /// @brief applies a JSON patch to a copy of the current object\n    /// @sa https://json.nlohmann.me/api/basic_json/patch/\n    basic_json patch(const basic_json& json_patch) const\n    {\n        basic_json result = *this;\n        result.patch_inplace(json_patch);\n        return result;\n    }\n\n    /// @brief creates a diff as a JSON patch\n    /// @sa https://json.nlohmann.me/api/basic_json/diff/\n    JSON_HEDLEY_WARN_UNUSED_RESULT\n    static basic_json diff(const basic_json& source, const basic_json& target,\n                           const std::string& path = \"\")\n    {\n        // the patch\n        basic_json result(value_t::array);\n\n        // if the values are the same, return empty patch\n        if (source == target)\n        {\n            return result;\n        }\n\n        if (source.type() != target.type())\n        {\n            // different types: replace value\n            result.push_back(\n            {\n                {\"op\", \"replace\"}, {\"path\", path}, {\"value\", target}\n            });\n            return result;\n        }\n\n        switch (source.type())\n        {\n            case value_t::array:\n            {\n                // first pass: traverse common elements\n                std::size_t i = 0;\n                while (i < source.size() && i < target.size())\n                {\n                    // recursive call to compare array values at index i\n                    auto temp_diff = diff(source[i], target[i], detail::concat(path, '/', std::to_string(i)));\n                    result.insert(result.end(), temp_diff.begin(), temp_diff.end());\n                    ++i;\n                }\n\n                // We now reached the end of at least one array\n                // in a second pass, traverse the remaining elements\n\n                // remove my remaining elements\n                const auto end_index = static_cast<difference_type>(result.size());\n                while (i < source.size())\n                {\n                    // add operations in reverse order to avoid invalid\n                    // indices\n                    result.insert(result.begin() + end_index, object(\n                    {\n                        {\"op\", \"remove\"},\n                        {\"path\", detail::concat(path, '/', std::to_string(i))}\n                    }));\n                    ++i;\n                }\n\n                // add other remaining elements\n                while (i < target.size())\n                {\n                    result.push_back(\n                    {\n                        {\"op\", \"add\"},\n                        {\"path\", detail::concat(path, \"/-\")},\n                        {\"value\", target[i]}\n                    });\n                    ++i;\n                }\n\n                break;\n            }\n\n            case value_t::object:\n            {\n                // first pass: traverse this object's elements\n                for (auto it = source.cbegin(); it != source.cend(); ++it)\n                {\n                    // escape the key name to be used in a JSON patch\n                    const auto path_key = detail::concat(path, '/', detail::escape(it.key()));\n\n                    if (target.find(it.key()) != target.end())\n                    {\n                        // recursive call to compare object values at key it\n                        auto temp_diff = diff(it.value(), target[it.key()], path_key);\n                        result.insert(result.end(), temp_diff.begin(), temp_diff.end());\n                    }\n                    else\n                    {\n                        // found a key that is not in o -> remove it\n                        result.push_back(object(\n                        {\n                            {\"op\", \"remove\"}, {\"path\", path_key}\n                        }));\n                    }\n                }\n\n                // second pass: traverse other object's elements\n                for (auto it = target.cbegin(); it != target.cend(); ++it)\n                {\n                    if (source.find(it.key()) == source.end())\n                    {\n                        // found a key that is not in this -> add it\n                        const auto path_key = detail::concat(path, '/', detail::escape(it.key()));\n                        result.push_back(\n                        {\n                            {\"op\", \"add\"}, {\"path\", path_key},\n                            {\"value\", it.value()}\n                        });\n                    }\n                }\n\n                break;\n            }\n\n            case value_t::null:\n            case value_t::string:\n            case value_t::boolean:\n            case value_t::number_integer:\n            case value_t::number_unsigned:\n            case value_t::number_float:\n            case value_t::binary:\n            case value_t::discarded:\n            default:\n            {\n                // both primitive type: replace value\n                result.push_back(\n                {\n                    {\"op\", \"replace\"}, {\"path\", path}, {\"value\", target}\n                });\n                break;\n            }\n        }\n\n        return result;\n    }\n    /// @}\n\n    ////////////////////////////////\n    // JSON Merge Patch functions //\n    ////////////////////////////////\n\n    /// @name JSON Merge Patch functions\n    /// @{\n\n    /// @brief applies a JSON Merge Patch\n    /// @sa https://json.nlohmann.me/api/basic_json/merge_patch/\n    void merge_patch(const basic_json& apply_patch)\n    {\n        if (apply_patch.is_object())\n        {\n            if (!is_object())\n            {\n                *this = object();\n            }\n            for (auto it = apply_patch.begin(); it != apply_patch.end(); ++it)\n            {\n                if (it.value().is_null())\n                {\n                    erase(it.key());\n                }\n                else\n                {\n                    operator[](it.key()).merge_patch(it.value());\n                }\n            }\n        }\n        else\n        {\n            *this = apply_patch;\n        }\n    }\n\n    /// @}\n};\n\n/// @brief user-defined to_string function for JSON values\n/// @sa https://json.nlohmann.me/api/basic_json/to_string/\nNLOHMANN_BASIC_JSON_TPL_DECLARATION\nstd::string to_string(const NLOHMANN_BASIC_JSON_TPL& j)\n{\n    return j.dump();\n}\n\ninline namespace literals\n{\ninline namespace json_literals\n{\n\n/// @brief user-defined string literal for JSON values\n/// @sa https://json.nlohmann.me/api/basic_json/operator_literal_json/\nJSON_HEDLEY_NON_NULL(1)\n#if !defined(JSON_HEDLEY_GCC_VERSION) || JSON_HEDLEY_GCC_VERSION_CHECK(4,9,0)\n    inline nlohmann::json operator \"\"_json(const char* s, std::size_t n)\n#else\n    inline nlohmann::json operator \"\" _json(const char* s, std::size_t n)\n#endif\n{\n    return nlohmann::json::parse(s, s + n);\n}\n\n/// @brief user-defined string literal for JSON pointer\n/// @sa https://json.nlohmann.me/api/basic_json/operator_literal_json_pointer/\nJSON_HEDLEY_NON_NULL(1)\n#if !defined(JSON_HEDLEY_GCC_VERSION) || JSON_HEDLEY_GCC_VERSION_CHECK(4,9,0)\n    inline nlohmann::json::json_pointer operator \"\"_json_pointer(const char* s, std::size_t n)\n#else\n    inline nlohmann::json::json_pointer operator \"\" _json_pointer(const char* s, std::size_t n)\n#endif\n{\n    return nlohmann::json::json_pointer(std::string(s, n));\n}\n\n}  // namespace json_literals\n}  // namespace literals\nNLOHMANN_JSON_NAMESPACE_END\n\n///////////////////////\n// nonmember support //\n///////////////////////\n\nnamespace std // NOLINT(cert-dcl58-cpp)\n{\n\n/// @brief hash value for JSON objects\n/// @sa https://json.nlohmann.me/api/basic_json/std_hash/\nNLOHMANN_BASIC_JSON_TPL_DECLARATION\nstruct hash<nlohmann::NLOHMANN_BASIC_JSON_TPL> // NOLINT(cert-dcl58-cpp)\n{\n    std::size_t operator()(const nlohmann::NLOHMANN_BASIC_JSON_TPL& j) const\n    {\n        return nlohmann::detail::hash(j);\n    }\n};\n\n// specialization for std::less<value_t>\ntemplate<>\nstruct less< ::nlohmann::detail::value_t> // do not remove the space after '<', see https://github.com/nlohmann/json/pull/679\n{\n    /*!\n    @brief compare two value_t enum values\n    @since version 3.0.0\n    */\n    bool operator()(::nlohmann::detail::value_t lhs,\n                    ::nlohmann::detail::value_t rhs) const noexcept\n    {\n#if JSON_HAS_THREE_WAY_COMPARISON\n        return std::is_lt(lhs <=> rhs); // *NOPAD*\n#else\n        return ::nlohmann::detail::operator<(lhs, rhs);\n#endif\n    }\n};\n\n// C++20 prohibit function specialization in the std namespace.\n#ifndef JSON_HAS_CPP_20\n\n/// @brief exchanges the values of two JSON objects\n/// @sa https://json.nlohmann.me/api/basic_json/std_swap/\nNLOHMANN_BASIC_JSON_TPL_DECLARATION\ninline void swap(nlohmann::NLOHMANN_BASIC_JSON_TPL& j1, nlohmann::NLOHMANN_BASIC_JSON_TPL& j2) noexcept(  // NOLINT(readability-inconsistent-declaration-parameter-name, cert-dcl58-cpp)\n    is_nothrow_move_constructible<nlohmann::NLOHMANN_BASIC_JSON_TPL>::value&&                          // NOLINT(misc-redundant-expression,cppcoreguidelines-noexcept-swap,performance-noexcept-swap)\n    is_nothrow_move_assignable<nlohmann::NLOHMANN_BASIC_JSON_TPL>::value)\n{\n    j1.swap(j2);\n}\n\n#endif\n\n}  // namespace std\n\n#if JSON_USE_GLOBAL_UDLS\n    #if !defined(JSON_HEDLEY_GCC_VERSION) || JSON_HEDLEY_GCC_VERSION_CHECK(4,9,0)\n        using nlohmann::literals::json_literals::operator \"\"_json; // NOLINT(misc-unused-using-decls,google-global-names-in-headers)\n        using nlohmann::literals::json_literals::operator \"\"_json_pointer; //NOLINT(misc-unused-using-decls,google-global-names-in-headers)\n    #else\n        using nlohmann::literals::json_literals::operator \"\" _json; // NOLINT(misc-unused-using-decls,google-global-names-in-headers)\n        using nlohmann::literals::json_literals::operator \"\" _json_pointer; //NOLINT(misc-unused-using-decls,google-global-names-in-headers)\n    #endif\n#endif\n\n// #include <nlohmann/detail/macro_unscope.hpp>\n//     __ _____ _____ _____\n//  __|  |   __|     |   | |  JSON for Modern C++\n// |  |  |__   |  |  | | | |  version 3.11.3\n// |_____|_____|_____|_|___|  https://github.com/nlohmann/json\n//\n// SPDX-FileCopyrightText: 2013-2023 Niels Lohmann <https://nlohmann.me>\n// SPDX-License-Identifier: MIT\n\n\n\n// restore clang diagnostic settings\n#if defined(__clang__)\n    #pragma clang diagnostic pop\n#endif\n\n// clean up\n#undef JSON_ASSERT\n#undef JSON_INTERNAL_CATCH\n#undef JSON_THROW\n#undef JSON_PRIVATE_UNLESS_TESTED\n#undef NLOHMANN_BASIC_JSON_TPL_DECLARATION\n#undef NLOHMANN_BASIC_JSON_TPL\n#undef JSON_EXPLICIT\n#undef NLOHMANN_CAN_CALL_STD_FUNC_IMPL\n#undef JSON_INLINE_VARIABLE\n#undef JSON_NO_UNIQUE_ADDRESS\n#undef JSON_DISABLE_ENUM_SERIALIZATION\n#undef JSON_USE_GLOBAL_UDLS\n\n#ifndef JSON_TEST_KEEP_MACROS\n    #undef JSON_CATCH\n    #undef JSON_TRY\n    #undef JSON_HAS_CPP_11\n    #undef JSON_HAS_CPP_14\n    #undef JSON_HAS_CPP_17\n    #undef JSON_HAS_CPP_20\n    #undef JSON_HAS_FILESYSTEM\n    #undef JSON_HAS_EXPERIMENTAL_FILESYSTEM\n    #undef JSON_HAS_THREE_WAY_COMPARISON\n    #undef JSON_HAS_RANGES\n    #undef JSON_HAS_STATIC_RTTI\n    #undef JSON_USE_LEGACY_DISCARDED_VALUE_COMPARISON\n#endif\n\n// #include <nlohmann/thirdparty/hedley/hedley_undef.hpp>\n//     __ _____ _____ _____\n//  __|  |   __|     |   | |  JSON for Modern C++\n// |  |  |__   |  |  | | | |  version 3.11.3\n// |_____|_____|_____|_|___|  https://github.com/nlohmann/json\n//\n// SPDX-FileCopyrightText: 2013-2023 Niels Lohmann <https://nlohmann.me>\n// SPDX-License-Identifier: MIT\n\n\n\n#undef JSON_HEDLEY_ALWAYS_INLINE\n#undef JSON_HEDLEY_ARM_VERSION\n#undef JSON_HEDLEY_ARM_VERSION_CHECK\n#undef JSON_HEDLEY_ARRAY_PARAM\n#undef JSON_HEDLEY_ASSUME\n#undef JSON_HEDLEY_BEGIN_C_DECLS\n#undef JSON_HEDLEY_CLANG_HAS_ATTRIBUTE\n#undef JSON_HEDLEY_CLANG_HAS_BUILTIN\n#undef JSON_HEDLEY_CLANG_HAS_CPP_ATTRIBUTE\n#undef JSON_HEDLEY_CLANG_HAS_DECLSPEC_DECLSPEC_ATTRIBUTE\n#undef JSON_HEDLEY_CLANG_HAS_EXTENSION\n#undef JSON_HEDLEY_CLANG_HAS_FEATURE\n#undef JSON_HEDLEY_CLANG_HAS_WARNING\n#undef JSON_HEDLEY_COMPCERT_VERSION\n#undef JSON_HEDLEY_COMPCERT_VERSION_CHECK\n#undef JSON_HEDLEY_CONCAT\n#undef JSON_HEDLEY_CONCAT3\n#undef JSON_HEDLEY_CONCAT3_EX\n#undef JSON_HEDLEY_CONCAT_EX\n#undef JSON_HEDLEY_CONST\n#undef JSON_HEDLEY_CONSTEXPR\n#undef JSON_HEDLEY_CONST_CAST\n#undef JSON_HEDLEY_CPP_CAST\n#undef JSON_HEDLEY_CRAY_VERSION\n#undef JSON_HEDLEY_CRAY_VERSION_CHECK\n#undef JSON_HEDLEY_C_DECL\n#undef JSON_HEDLEY_DEPRECATED\n#undef JSON_HEDLEY_DEPRECATED_FOR\n#undef JSON_HEDLEY_DIAGNOSTIC_DISABLE_CAST_QUAL\n#undef JSON_HEDLEY_DIAGNOSTIC_DISABLE_CPP98_COMPAT_WRAP_\n#undef JSON_HEDLEY_DIAGNOSTIC_DISABLE_DEPRECATED\n#undef JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNKNOWN_CPP_ATTRIBUTES\n#undef JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNKNOWN_PRAGMAS\n#undef JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNUSED_FUNCTION\n#undef JSON_HEDLEY_DIAGNOSTIC_POP\n#undef JSON_HEDLEY_DIAGNOSTIC_PUSH\n#undef JSON_HEDLEY_DMC_VERSION\n#undef JSON_HEDLEY_DMC_VERSION_CHECK\n#undef JSON_HEDLEY_EMPTY_BASES\n#undef JSON_HEDLEY_EMSCRIPTEN_VERSION\n#undef JSON_HEDLEY_EMSCRIPTEN_VERSION_CHECK\n#undef JSON_HEDLEY_END_C_DECLS\n#undef JSON_HEDLEY_FLAGS\n#undef JSON_HEDLEY_FLAGS_CAST\n#undef JSON_HEDLEY_GCC_HAS_ATTRIBUTE\n#undef JSON_HEDLEY_GCC_HAS_BUILTIN\n#undef JSON_HEDLEY_GCC_HAS_CPP_ATTRIBUTE\n#undef JSON_HEDLEY_GCC_HAS_DECLSPEC_ATTRIBUTE\n#undef JSON_HEDLEY_GCC_HAS_EXTENSION\n#undef JSON_HEDLEY_GCC_HAS_FEATURE\n#undef JSON_HEDLEY_GCC_HAS_WARNING\n#undef JSON_HEDLEY_GCC_NOT_CLANG_VERSION_CHECK\n#undef JSON_HEDLEY_GCC_VERSION\n#undef JSON_HEDLEY_GCC_VERSION_CHECK\n#undef JSON_HEDLEY_GNUC_HAS_ATTRIBUTE\n#undef JSON_HEDLEY_GNUC_HAS_BUILTIN\n#undef JSON_HEDLEY_GNUC_HAS_CPP_ATTRIBUTE\n#undef JSON_HEDLEY_GNUC_HAS_DECLSPEC_ATTRIBUTE\n#undef JSON_HEDLEY_GNUC_HAS_EXTENSION\n#undef JSON_HEDLEY_GNUC_HAS_FEATURE\n#undef JSON_HEDLEY_GNUC_HAS_WARNING\n#undef JSON_HEDLEY_GNUC_VERSION\n#undef JSON_HEDLEY_GNUC_VERSION_CHECK\n#undef JSON_HEDLEY_HAS_ATTRIBUTE\n#undef JSON_HEDLEY_HAS_BUILTIN\n#undef JSON_HEDLEY_HAS_CPP_ATTRIBUTE\n#undef JSON_HEDLEY_HAS_CPP_ATTRIBUTE_NS\n#undef JSON_HEDLEY_HAS_DECLSPEC_ATTRIBUTE\n#undef JSON_HEDLEY_HAS_EXTENSION\n#undef JSON_HEDLEY_HAS_FEATURE\n#undef JSON_HEDLEY_HAS_WARNING\n#undef JSON_HEDLEY_IAR_VERSION\n#undef JSON_HEDLEY_IAR_VERSION_CHECK\n#undef JSON_HEDLEY_IBM_VERSION\n#undef JSON_HEDLEY_IBM_VERSION_CHECK\n#undef JSON_HEDLEY_IMPORT\n#undef JSON_HEDLEY_INLINE\n#undef JSON_HEDLEY_INTEL_CL_VERSION\n#undef JSON_HEDLEY_INTEL_CL_VERSION_CHECK\n#undef JSON_HEDLEY_INTEL_VERSION\n#undef JSON_HEDLEY_INTEL_VERSION_CHECK\n#undef JSON_HEDLEY_IS_CONSTANT\n#undef JSON_HEDLEY_IS_CONSTEXPR_\n#undef JSON_HEDLEY_LIKELY\n#undef JSON_HEDLEY_MALLOC\n#undef JSON_HEDLEY_MCST_LCC_VERSION\n#undef JSON_HEDLEY_MCST_LCC_VERSION_CHECK\n#undef JSON_HEDLEY_MESSAGE\n#undef JSON_HEDLEY_MSVC_VERSION\n#undef JSON_HEDLEY_MSVC_VERSION_CHECK\n#undef JSON_HEDLEY_NEVER_INLINE\n#undef JSON_HEDLEY_NON_NULL\n#undef JSON_HEDLEY_NO_ESCAPE\n#undef JSON_HEDLEY_NO_RETURN\n#undef JSON_HEDLEY_NO_THROW\n#undef JSON_HEDLEY_NULL\n#undef JSON_HEDLEY_PELLES_VERSION\n#undef JSON_HEDLEY_PELLES_VERSION_CHECK\n#undef JSON_HEDLEY_PGI_VERSION\n#undef JSON_HEDLEY_PGI_VERSION_CHECK\n#undef JSON_HEDLEY_PREDICT\n#undef JSON_HEDLEY_PRINTF_FORMAT\n#undef JSON_HEDLEY_PRIVATE\n#undef JSON_HEDLEY_PUBLIC\n#undef JSON_HEDLEY_PURE\n#undef JSON_HEDLEY_REINTERPRET_CAST\n#undef JSON_HEDLEY_REQUIRE\n#undef JSON_HEDLEY_REQUIRE_CONSTEXPR\n#undef JSON_HEDLEY_REQUIRE_MSG\n#undef JSON_HEDLEY_RESTRICT\n#undef JSON_HEDLEY_RETURNS_NON_NULL\n#undef JSON_HEDLEY_SENTINEL\n#undef JSON_HEDLEY_STATIC_ASSERT\n#undef JSON_HEDLEY_STATIC_CAST\n#undef JSON_HEDLEY_STRINGIFY\n#undef JSON_HEDLEY_STRINGIFY_EX\n#undef JSON_HEDLEY_SUNPRO_VERSION\n#undef JSON_HEDLEY_SUNPRO_VERSION_CHECK\n#undef JSON_HEDLEY_TINYC_VERSION\n#undef JSON_HEDLEY_TINYC_VERSION_CHECK\n#undef JSON_HEDLEY_TI_ARMCL_VERSION\n#undef JSON_HEDLEY_TI_ARMCL_VERSION_CHECK\n#undef JSON_HEDLEY_TI_CL2000_VERSION\n#undef JSON_HEDLEY_TI_CL2000_VERSION_CHECK\n#undef JSON_HEDLEY_TI_CL430_VERSION\n#undef JSON_HEDLEY_TI_CL430_VERSION_CHECK\n#undef JSON_HEDLEY_TI_CL6X_VERSION\n#undef JSON_HEDLEY_TI_CL6X_VERSION_CHECK\n#undef JSON_HEDLEY_TI_CL7X_VERSION\n#undef JSON_HEDLEY_TI_CL7X_VERSION_CHECK\n#undef JSON_HEDLEY_TI_CLPRU_VERSION\n#undef JSON_HEDLEY_TI_CLPRU_VERSION_CHECK\n#undef JSON_HEDLEY_TI_VERSION\n#undef JSON_HEDLEY_TI_VERSION_CHECK\n#undef JSON_HEDLEY_UNAVAILABLE\n#undef JSON_HEDLEY_UNLIKELY\n#undef JSON_HEDLEY_UNPREDICTABLE\n#undef JSON_HEDLEY_UNREACHABLE\n#undef JSON_HEDLEY_UNREACHABLE_RETURN\n#undef JSON_HEDLEY_VERSION\n#undef JSON_HEDLEY_VERSION_DECODE_MAJOR\n#undef JSON_HEDLEY_VERSION_DECODE_MINOR\n#undef JSON_HEDLEY_VERSION_DECODE_REVISION\n#undef JSON_HEDLEY_VERSION_ENCODE\n#undef JSON_HEDLEY_WARNING\n#undef JSON_HEDLEY_WARN_UNUSED_RESULT\n#undef JSON_HEDLEY_WARN_UNUSED_RESULT_MSG\n#undef JSON_HEDLEY_FALL_THROUGH\n\n\n\n#endif  // INCLUDE_NLOHMANN_JSON_HPP_\n"
  },
  {
    "path": "libs/pybind11/CMakeLists.txt",
    "content": "# CMakeLists.txt -- Build system for the pybind11 modules\n#\n# Copyright (c) 2015 Wenzel Jakob <wenzel@inf.ethz.ch>\n#\n# All rights reserved. Use of this source code is governed by a\n# BSD-style license that can be found in the LICENSE file.\n\ncmake_minimum_required(VERSION 3.5)\n\n# The `cmake_minimum_required(VERSION 3.5...3.26)` syntax does not work with\n# some versions of VS that have a patched CMake 3.11. This forces us to emulate\n# the behavior using the following workaround:\nif(${CMAKE_VERSION} VERSION_LESS 3.26)\n  cmake_policy(VERSION ${CMAKE_MAJOR_VERSION}.${CMAKE_MINOR_VERSION})\nelse()\n  cmake_policy(VERSION 3.26)\nendif()\n\n# Avoid infinite recursion if tests include this as a subdirectory\nif(DEFINED PYBIND11_MASTER_PROJECT)\n  return()\nendif()\n\n# Extract project version from source\nfile(STRINGS \"${CMAKE_CURRENT_SOURCE_DIR}/include/pybind11/detail/common.h\"\n     pybind11_version_defines REGEX \"#define PYBIND11_VERSION_(MAJOR|MINOR|PATCH) \")\n\nforeach(ver ${pybind11_version_defines})\n  if(ver MATCHES [[#define PYBIND11_VERSION_(MAJOR|MINOR|PATCH) +([^ ]+)$]])\n    set(PYBIND11_VERSION_${CMAKE_MATCH_1} \"${CMAKE_MATCH_2}\")\n  endif()\nendforeach()\n\nif(PYBIND11_VERSION_PATCH MATCHES [[\\.([a-zA-Z0-9]+)$]])\n  set(pybind11_VERSION_TYPE \"${CMAKE_MATCH_1}\")\nendif()\nstring(REGEX MATCH \"^[0-9]+\" PYBIND11_VERSION_PATCH \"${PYBIND11_VERSION_PATCH}\")\n\nproject(\n  pybind11\n  LANGUAGES CXX\n  VERSION \"${PYBIND11_VERSION_MAJOR}.${PYBIND11_VERSION_MINOR}.${PYBIND11_VERSION_PATCH}\")\n\n# Standard includes\ninclude(GNUInstallDirs)\ninclude(CMakePackageConfigHelpers)\ninclude(CMakeDependentOption)\n\nif(NOT pybind11_FIND_QUIETLY)\n  message(STATUS \"pybind11 v${pybind11_VERSION} ${pybind11_VERSION_TYPE}\")\nendif()\n\n# Check if pybind11 is being used directly or via add_subdirectory\nif(CMAKE_SOURCE_DIR STREQUAL PROJECT_SOURCE_DIR)\n  ### Warn if not an out-of-source builds\n  if(CMAKE_CURRENT_SOURCE_DIR STREQUAL CMAKE_CURRENT_BINARY_DIR)\n    set(lines\n        \"You are building in-place. If that is not what you intended to \"\n        \"do, you can clean the source directory with:\\n\"\n        \"rm -r CMakeCache.txt CMakeFiles/ cmake_uninstall.cmake pybind11Config.cmake \"\n        \"pybind11ConfigVersion.cmake tests/CMakeFiles/\\n\")\n    message(AUTHOR_WARNING ${lines})\n  endif()\n\n  set(PYBIND11_MASTER_PROJECT ON)\n\n  if(OSX AND CMAKE_VERSION VERSION_LESS 3.7)\n    # Bug in macOS CMake < 3.7 is unable to download catch\n    message(WARNING \"CMAKE 3.7+ needed on macOS to download catch, and newer HIGHLY recommended\")\n  elseif(WINDOWS AND CMAKE_VERSION VERSION_LESS 3.8)\n    # Only tested with 3.8+ in CI.\n    message(WARNING \"CMAKE 3.8+ tested on Windows, previous versions untested\")\n  endif()\n\n  message(STATUS \"CMake ${CMAKE_VERSION}\")\n\n  if(CMAKE_CXX_STANDARD)\n    set(CMAKE_CXX_EXTENSIONS OFF)\n    set(CMAKE_CXX_STANDARD_REQUIRED ON)\n  endif()\n\n  set(pybind11_system \"\")\n\n  set_property(GLOBAL PROPERTY USE_FOLDERS ON)\nelse()\n  set(PYBIND11_MASTER_PROJECT OFF)\n  set(pybind11_system SYSTEM)\nendif()\n\n# Options\noption(PYBIND11_INSTALL \"Install pybind11 header files?\" ${PYBIND11_MASTER_PROJECT})\noption(PYBIND11_TEST \"Build pybind11 test suite?\" ${PYBIND11_MASTER_PROJECT})\noption(PYBIND11_NOPYTHON \"Disable search for Python\" OFF)\noption(PYBIND11_SIMPLE_GIL_MANAGEMENT\n       \"Use simpler GIL management logic that does not support disassociation\" OFF)\nset(PYBIND11_INTERNALS_VERSION\n    \"\"\n    CACHE STRING \"Override the ABI version, may be used to enable the unstable ABI.\")\n\nif(PYBIND11_SIMPLE_GIL_MANAGEMENT)\n  add_compile_definitions(PYBIND11_SIMPLE_GIL_MANAGEMENT)\nendif()\n\ncmake_dependent_option(\n  USE_PYTHON_INCLUDE_DIR\n  \"Install pybind11 headers in Python include directory instead of default installation prefix\"\n  OFF \"PYBIND11_INSTALL\" OFF)\n\ncmake_dependent_option(PYBIND11_FINDPYTHON \"Force new FindPython\" OFF\n                       \"NOT CMAKE_VERSION VERSION_LESS 3.12\" OFF)\n\n# NB: when adding a header don't forget to also add it to setup.py\nset(PYBIND11_HEADERS\n    include/pybind11/detail/class.h\n    include/pybind11/detail/common.h\n    include/pybind11/detail/descr.h\n    include/pybind11/detail/init.h\n    include/pybind11/detail/internals.h\n    include/pybind11/detail/type_caster_base.h\n    include/pybind11/detail/typeid.h\n    include/pybind11/attr.h\n    include/pybind11/buffer_info.h\n    include/pybind11/cast.h\n    include/pybind11/chrono.h\n    include/pybind11/common.h\n    include/pybind11/complex.h\n    include/pybind11/options.h\n    include/pybind11/eigen.h\n    include/pybind11/eigen/common.h\n    include/pybind11/eigen/matrix.h\n    include/pybind11/eigen/tensor.h\n    include/pybind11/embed.h\n    include/pybind11/eval.h\n    include/pybind11/gil.h\n    include/pybind11/iostream.h\n    include/pybind11/functional.h\n    include/pybind11/numpy.h\n    include/pybind11/operators.h\n    include/pybind11/pybind11.h\n    include/pybind11/pytypes.h\n    include/pybind11/stl.h\n    include/pybind11/stl_bind.h\n    include/pybind11/stl/filesystem.h\n    include/pybind11/type_caster_pyobject_ptr.h\n    include/pybind11/typing.h)\n\n# Compare with grep and warn if mismatched\nif(PYBIND11_MASTER_PROJECT AND NOT CMAKE_VERSION VERSION_LESS 3.12)\n  file(\n    GLOB_RECURSE _pybind11_header_check\n    LIST_DIRECTORIES false\n    RELATIVE \"${CMAKE_CURRENT_SOURCE_DIR}\"\n    CONFIGURE_DEPENDS \"include/pybind11/*.h\")\n  set(_pybind11_here_only ${PYBIND11_HEADERS})\n  set(_pybind11_disk_only ${_pybind11_header_check})\n  list(REMOVE_ITEM _pybind11_here_only ${_pybind11_header_check})\n  list(REMOVE_ITEM _pybind11_disk_only ${PYBIND11_HEADERS})\n  if(_pybind11_here_only)\n    message(AUTHOR_WARNING \"PYBIND11_HEADERS has extra files:\" ${_pybind11_here_only})\n  endif()\n  if(_pybind11_disk_only)\n    message(AUTHOR_WARNING \"PYBIND11_HEADERS is missing files:\" ${_pybind11_disk_only})\n  endif()\nendif()\n\n# CMake 3.12 added list(TRANSFORM <list> PREPEND\n# But we can't use it yet\nstring(REPLACE \"include/\" \"${CMAKE_CURRENT_SOURCE_DIR}/include/\" PYBIND11_HEADERS\n               \"${PYBIND11_HEADERS}\")\n\n# Cache variable so this can be used in parent projects\nset(pybind11_INCLUDE_DIR\n    \"${CMAKE_CURRENT_LIST_DIR}/include\"\n    CACHE INTERNAL \"Directory where pybind11 headers are located\")\n\n# Backward compatible variable for add_subdirectory mode\nif(NOT PYBIND11_MASTER_PROJECT)\n  set(PYBIND11_INCLUDE_DIR\n      \"${pybind11_INCLUDE_DIR}\"\n      CACHE INTERNAL \"\")\nendif()\n\n# Note: when creating targets, you cannot use if statements at configure time -\n# you need generator expressions, because those will be placed in the target file.\n# You can also place ifs *in* the Config.in, but not here.\n\n# This section builds targets, but does *not* touch Python\n# Non-IMPORT targets cannot be defined twice\nif(NOT TARGET pybind11_headers)\n  # Build the headers-only target (no Python included):\n  # (long name used here to keep this from clashing in subdirectory mode)\n  add_library(pybind11_headers INTERFACE)\n  add_library(pybind11::pybind11_headers ALIAS pybind11_headers) # to match exported target\n  add_library(pybind11::headers ALIAS pybind11_headers) # easier to use/remember\n\n  target_include_directories(\n    pybind11_headers ${pybind11_system} INTERFACE $<BUILD_INTERFACE:${pybind11_INCLUDE_DIR}>\n                                                  $<INSTALL_INTERFACE:${CMAKE_INSTALL_INCLUDEDIR}>)\n\n  target_compile_features(pybind11_headers INTERFACE cxx_inheriting_constructors cxx_user_literals\n                                                     cxx_right_angle_brackets)\n  if(NOT \"${PYBIND11_INTERNALS_VERSION}\" STREQUAL \"\")\n    target_compile_definitions(\n      pybind11_headers INTERFACE \"PYBIND11_INTERNALS_VERSION=${PYBIND11_INTERNALS_VERSION}\")\n  endif()\nelse()\n  # It is invalid to install a target twice, too.\n  set(PYBIND11_INSTALL OFF)\nendif()\n\n# KP: eventually this policy inheritance will all work, for now set set the policy by hand.\nif(POLICY CMP0148)\n  cmake_policy(SET CMP0148 NEW)\nendif()\n\ninclude(\"${CMAKE_CURRENT_SOURCE_DIR}/tools/pybind11Common.cmake\")\n# https://github.com/jtojnar/cmake-snips/#concatenating-paths-when-building-pkg-config-files\n# TODO: cmake 3.20 adds the cmake_path() function, which obsoletes this snippet\ninclude(\"${CMAKE_CURRENT_SOURCE_DIR}/tools/JoinPaths.cmake\")\n\n# Relative directory setting\nif(USE_PYTHON_INCLUDE_DIR AND DEFINED Python_INCLUDE_DIRS)\n  file(RELATIVE_PATH CMAKE_INSTALL_INCLUDEDIR ${CMAKE_INSTALL_PREFIX} ${Python_INCLUDE_DIRS})\nelseif(USE_PYTHON_INCLUDE_DIR AND DEFINED PYTHON_INCLUDE_DIR)\n  file(RELATIVE_PATH CMAKE_INSTALL_INCLUDEDIR ${CMAKE_INSTALL_PREFIX} ${PYTHON_INCLUDE_DIRS})\nendif()\n\nif(PYBIND11_INSTALL)\n  install(DIRECTORY ${pybind11_INCLUDE_DIR}/pybind11 DESTINATION ${CMAKE_INSTALL_INCLUDEDIR})\n  set(PYBIND11_CMAKECONFIG_INSTALL_DIR\n      \"${CMAKE_INSTALL_DATAROOTDIR}/cmake/${PROJECT_NAME}\"\n      CACHE STRING \"install path for pybind11Config.cmake\")\n\n  if(IS_ABSOLUTE \"${CMAKE_INSTALL_INCLUDEDIR}\")\n    set(pybind11_INCLUDEDIR \"${CMAKE_INSTALL_FULL_INCLUDEDIR}\")\n  else()\n    set(pybind11_INCLUDEDIR \"\\$\\{PACKAGE_PREFIX_DIR\\}/${CMAKE_INSTALL_INCLUDEDIR}\")\n  endif()\n\n  configure_package_config_file(\n    tools/${PROJECT_NAME}Config.cmake.in \"${CMAKE_CURRENT_BINARY_DIR}/${PROJECT_NAME}Config.cmake\"\n    INSTALL_DESTINATION ${PYBIND11_CMAKECONFIG_INSTALL_DIR})\n\n  if(CMAKE_VERSION VERSION_LESS 3.14)\n    # Remove CMAKE_SIZEOF_VOID_P from ConfigVersion.cmake since the library does\n    # not depend on architecture specific settings or libraries.\n    set(_PYBIND11_CMAKE_SIZEOF_VOID_P ${CMAKE_SIZEOF_VOID_P})\n    unset(CMAKE_SIZEOF_VOID_P)\n\n    write_basic_package_version_file(\n      ${CMAKE_CURRENT_BINARY_DIR}/${PROJECT_NAME}ConfigVersion.cmake\n      VERSION ${PROJECT_VERSION}\n      COMPATIBILITY AnyNewerVersion)\n\n    set(CMAKE_SIZEOF_VOID_P ${_PYBIND11_CMAKE_SIZEOF_VOID_P})\n  else()\n    # CMake 3.14+ natively supports header-only libraries\n    write_basic_package_version_file(\n      ${CMAKE_CURRENT_BINARY_DIR}/${PROJECT_NAME}ConfigVersion.cmake\n      VERSION ${PROJECT_VERSION}\n      COMPATIBILITY AnyNewerVersion ARCH_INDEPENDENT)\n  endif()\n\n  install(\n    FILES ${CMAKE_CURRENT_BINARY_DIR}/${PROJECT_NAME}Config.cmake\n          ${CMAKE_CURRENT_BINARY_DIR}/${PROJECT_NAME}ConfigVersion.cmake\n          tools/FindPythonLibsNew.cmake\n          tools/pybind11Common.cmake\n          tools/pybind11Tools.cmake\n          tools/pybind11NewTools.cmake\n    DESTINATION ${PYBIND11_CMAKECONFIG_INSTALL_DIR})\n\n  if(NOT PYBIND11_EXPORT_NAME)\n    set(PYBIND11_EXPORT_NAME \"${PROJECT_NAME}Targets\")\n  endif()\n\n  install(TARGETS pybind11_headers EXPORT \"${PYBIND11_EXPORT_NAME}\")\n\n  install(\n    EXPORT \"${PYBIND11_EXPORT_NAME}\"\n    NAMESPACE \"pybind11::\"\n    DESTINATION ${PYBIND11_CMAKECONFIG_INSTALL_DIR})\n\n  # pkg-config support\n  if(NOT prefix_for_pc_file)\n    set(prefix_for_pc_file \"${CMAKE_INSTALL_PREFIX}\")\n  endif()\n  join_paths(includedir_for_pc_file \"\\${prefix}\" \"${CMAKE_INSTALL_INCLUDEDIR}\")\n  configure_file(\"${CMAKE_CURRENT_SOURCE_DIR}/tools/pybind11.pc.in\"\n                 \"${CMAKE_CURRENT_BINARY_DIR}/pybind11.pc\" @ONLY)\n  install(FILES \"${CMAKE_CURRENT_BINARY_DIR}/pybind11.pc\"\n          DESTINATION \"${CMAKE_INSTALL_DATAROOTDIR}/pkgconfig/\")\n\n  # Uninstall target\n  if(PYBIND11_MASTER_PROJECT)\n    configure_file(\"${CMAKE_CURRENT_SOURCE_DIR}/tools/cmake_uninstall.cmake.in\"\n                   \"${CMAKE_CURRENT_BINARY_DIR}/cmake_uninstall.cmake\" IMMEDIATE @ONLY)\n\n    add_custom_target(uninstall COMMAND ${CMAKE_COMMAND} -P\n                                        ${CMAKE_CURRENT_BINARY_DIR}/cmake_uninstall.cmake)\n  endif()\nendif()\n\n# BUILD_TESTING takes priority, but only if this is the master project\nif(PYBIND11_MASTER_PROJECT AND DEFINED BUILD_TESTING)\n  if(BUILD_TESTING)\n    if(_pybind11_nopython)\n      message(FATAL_ERROR \"Cannot activate tests in NOPYTHON mode\")\n    else()\n      add_subdirectory(tests)\n    endif()\n  endif()\nelse()\n  if(PYBIND11_TEST)\n    if(_pybind11_nopython)\n      message(FATAL_ERROR \"Cannot activate tests in NOPYTHON mode\")\n    else()\n      add_subdirectory(tests)\n    endif()\n  endif()\nendif()\n\n# Better symmetry with find_package(pybind11 CONFIG) mode.\nif(NOT PYBIND11_MASTER_PROJECT)\n  set(pybind11_FOUND\n      TRUE\n      CACHE INTERNAL \"True if pybind11 and all required components found on the system\")\nendif()\n"
  },
  {
    "path": "libs/pybind11/LICENSE",
    "content": "Copyright (c) 2016 Wenzel Jakob <wenzel.jakob@epfl.ch>, All rights reserved.\n\nRedistribution and use in source and binary forms, with or without\nmodification, are permitted provided that the following conditions are met:\n\n1. Redistributions of source code must retain the above copyright notice, this\n   list of conditions and the following disclaimer.\n\n2. Redistributions in binary form must reproduce the above copyright notice,\n   this list of conditions and the following disclaimer in the documentation\n   and/or other materials provided with the distribution.\n\n3. Neither the name of the copyright holder nor the names of its contributors\n   may be used to endorse or promote products derived from this software\n   without specific prior written permission.\n\nTHIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS \"AS IS\" AND\nANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED\nWARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE\nDISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE\nFOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL\nDAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR\nSERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER\nCAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,\nOR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE\nOF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.\n\nPlease also refer to the file .github/CONTRIBUTING.md, which clarifies licensing of\nexternal contributions to this project including patches, pull requests, etc.\n"
  },
  {
    "path": "libs/pybind11/include/pybind11/attr.h",
    "content": "/*\n    pybind11/attr.h: Infrastructure for processing custom\n    type and function attributes\n\n    Copyright (c) 2016 Wenzel Jakob <wenzel.jakob@epfl.ch>\n\n    All rights reserved. Use of this source code is governed by a\n    BSD-style license that can be found in the LICENSE file.\n*/\n\n#pragma once\n\n#include \"detail/common.h\"\n#include \"cast.h\"\n\n#include <functional>\n\nPYBIND11_NAMESPACE_BEGIN(PYBIND11_NAMESPACE)\n\n/// \\addtogroup annotations\n/// @{\n\n/// Annotation for methods\nstruct is_method {\n    handle class_;\n    explicit is_method(const handle &c) : class_(c) {}\n};\n\n/// Annotation for setters\nstruct is_setter {};\n\n/// Annotation for operators\nstruct is_operator {};\n\n/// Annotation for classes that cannot be subclassed\nstruct is_final {};\n\n/// Annotation for parent scope\nstruct scope {\n    handle value;\n    explicit scope(const handle &s) : value(s) {}\n};\n\n/// Annotation for documentation\nstruct doc {\n    const char *value;\n    explicit doc(const char *value) : value(value) {}\n};\n\n/// Annotation for function names\nstruct name {\n    const char *value;\n    explicit name(const char *value) : value(value) {}\n};\n\n/// Annotation indicating that a function is an overload associated with a given \"sibling\"\nstruct sibling {\n    handle value;\n    explicit sibling(const handle &value) : value(value.ptr()) {}\n};\n\n/// Annotation indicating that a class derives from another given type\ntemplate <typename T>\nstruct base {\n\n    PYBIND11_DEPRECATED(\n        \"base<T>() was deprecated in favor of specifying 'T' as a template argument to class_\")\n    base() = default;\n};\n\n/// Keep patient alive while nurse lives\ntemplate <size_t Nurse, size_t Patient>\nstruct keep_alive {};\n\n/// Annotation indicating that a class is involved in a multiple inheritance relationship\nstruct multiple_inheritance {};\n\n/// Annotation which enables dynamic attributes, i.e. adds `__dict__` to a class\nstruct dynamic_attr {};\n\n/// Annotation which enables the buffer protocol for a type\nstruct buffer_protocol {};\n\n/// Annotation which requests that a special metaclass is created for a type\nstruct metaclass {\n    handle value;\n\n    PYBIND11_DEPRECATED(\"py::metaclass() is no longer required. It's turned on by default now.\")\n    metaclass() = default;\n\n    /// Override pybind11's default metaclass\n    explicit metaclass(handle value) : value(value) {}\n};\n\n/// Specifies a custom callback with signature `void (PyHeapTypeObject*)` that\n/// may be used to customize the Python type.\n///\n/// The callback is invoked immediately before `PyType_Ready`.\n///\n/// Note: This is an advanced interface, and uses of it may require changes to\n/// work with later versions of pybind11.  You may wish to consult the\n/// implementation of `make_new_python_type` in `detail/classes.h` to understand\n/// the context in which the callback will be run.\nstruct custom_type_setup {\n    using callback = std::function<void(PyHeapTypeObject *heap_type)>;\n\n    explicit custom_type_setup(callback value) : value(std::move(value)) {}\n\n    callback value;\n};\n\n/// Annotation that marks a class as local to the module:\nstruct module_local {\n    const bool value;\n    constexpr explicit module_local(bool v = true) : value(v) {}\n};\n\n/// Annotation to mark enums as an arithmetic type\nstruct arithmetic {};\n\n/// Mark a function for addition at the beginning of the existing overload chain instead of the end\nstruct prepend {};\n\n/** \\rst\n    A call policy which places one or more guard variables (``Ts...``) around the function call.\n\n    For example, this definition:\n\n    .. code-block:: cpp\n\n        m.def(\"foo\", foo, py::call_guard<T>());\n\n    is equivalent to the following pseudocode:\n\n    .. code-block:: cpp\n\n        m.def(\"foo\", [](args...) {\n            T scope_guard;\n            return foo(args...); // forwarded arguments\n        });\n \\endrst */\ntemplate <typename... Ts>\nstruct call_guard;\n\ntemplate <>\nstruct call_guard<> {\n    using type = detail::void_type;\n};\n\ntemplate <typename T>\nstruct call_guard<T> {\n    static_assert(std::is_default_constructible<T>::value,\n                  \"The guard type must be default constructible\");\n\n    using type = T;\n};\n\ntemplate <typename T, typename... Ts>\nstruct call_guard<T, Ts...> {\n    struct type {\n        T guard{}; // Compose multiple guard types with left-to-right default-constructor order\n        typename call_guard<Ts...>::type next{};\n    };\n};\n\n/// @} annotations\n\nPYBIND11_NAMESPACE_BEGIN(detail)\n/* Forward declarations */\nenum op_id : int;\nenum op_type : int;\nstruct undefined_t;\ntemplate <op_id id, op_type ot, typename L = undefined_t, typename R = undefined_t>\nstruct op_;\nvoid keep_alive_impl(size_t Nurse, size_t Patient, function_call &call, handle ret);\n\n/// Internal data structure which holds metadata about a keyword argument\nstruct argument_record {\n    const char *name;  ///< Argument name\n    const char *descr; ///< Human-readable version of the argument value\n    handle value;      ///< Associated Python object\n    bool convert : 1;  ///< True if the argument is allowed to convert when loading\n    bool none : 1;     ///< True if None is allowed when loading\n\n    argument_record(const char *name, const char *descr, handle value, bool convert, bool none)\n        : name(name), descr(descr), value(value), convert(convert), none(none) {}\n};\n\n/// Internal data structure which holds metadata about a bound function (signature, overloads,\n/// etc.)\nstruct function_record {\n    function_record()\n        : is_constructor(false), is_new_style_constructor(false), is_stateless(false),\n          is_operator(false), is_method(false), is_setter(false), has_args(false),\n          has_kwargs(false), prepend(false) {}\n\n    /// Function name\n    char *name = nullptr; /* why no C++ strings? They generate heavier code.. */\n\n    // User-specified documentation string\n    char *doc = nullptr;\n\n    /// Human-readable version of the function signature\n    char *signature = nullptr;\n\n    /// List of registered keyword arguments\n    std::vector<argument_record> args;\n\n    /// Pointer to lambda function which converts arguments and performs the actual call\n    handle (*impl)(function_call &) = nullptr;\n\n    /// Storage for the wrapped function pointer and captured data, if any\n    void *data[3] = {};\n\n    /// Pointer to custom destructor for 'data' (if needed)\n    void (*free_data)(function_record *ptr) = nullptr;\n\n    /// Return value policy associated with this function\n    return_value_policy policy = return_value_policy::automatic;\n\n    /// True if name == '__init__'\n    bool is_constructor : 1;\n\n    /// True if this is a new-style `__init__` defined in `detail/init.h`\n    bool is_new_style_constructor : 1;\n\n    /// True if this is a stateless function pointer\n    bool is_stateless : 1;\n\n    /// True if this is an operator (__add__), etc.\n    bool is_operator : 1;\n\n    /// True if this is a method\n    bool is_method : 1;\n\n    /// True if this is a setter\n    bool is_setter : 1;\n\n    /// True if the function has a '*args' argument\n    bool has_args : 1;\n\n    /// True if the function has a '**kwargs' argument\n    bool has_kwargs : 1;\n\n    /// True if this function is to be inserted at the beginning of the overload resolution chain\n    bool prepend : 1;\n\n    /// Number of arguments (including py::args and/or py::kwargs, if present)\n    std::uint16_t nargs;\n\n    /// Number of leading positional arguments, which are terminated by a py::args or py::kwargs\n    /// argument or by a py::kw_only annotation.\n    std::uint16_t nargs_pos = 0;\n\n    /// Number of leading arguments (counted in `nargs`) that are positional-only\n    std::uint16_t nargs_pos_only = 0;\n\n    /// Python method object\n    PyMethodDef *def = nullptr;\n\n    /// Python handle to the parent scope (a class or a module)\n    handle scope;\n\n    /// Python handle to the sibling function representing an overload chain\n    handle sibling;\n\n    /// Pointer to next overload\n    function_record *next = nullptr;\n};\n\n/// Special data structure which (temporarily) holds metadata about a bound class\nstruct type_record {\n    PYBIND11_NOINLINE type_record()\n        : multiple_inheritance(false), dynamic_attr(false), buffer_protocol(false),\n          default_holder(true), module_local(false), is_final(false) {}\n\n    /// Handle to the parent scope\n    handle scope;\n\n    /// Name of the class\n    const char *name = nullptr;\n\n    // Pointer to RTTI type_info data structure\n    const std::type_info *type = nullptr;\n\n    /// How large is the underlying C++ type?\n    size_t type_size = 0;\n\n    /// What is the alignment of the underlying C++ type?\n    size_t type_align = 0;\n\n    /// How large is the type's holder?\n    size_t holder_size = 0;\n\n    /// The global operator new can be overridden with a class-specific variant\n    void *(*operator_new)(size_t) = nullptr;\n\n    /// Function pointer to class_<..>::init_instance\n    void (*init_instance)(instance *, const void *) = nullptr;\n\n    /// Function pointer to class_<..>::dealloc\n    void (*dealloc)(detail::value_and_holder &) = nullptr;\n\n    /// List of base classes of the newly created type\n    list bases;\n\n    /// Optional docstring\n    const char *doc = nullptr;\n\n    /// Custom metaclass (optional)\n    handle metaclass;\n\n    /// Custom type setup.\n    custom_type_setup::callback custom_type_setup_callback;\n\n    /// Multiple inheritance marker\n    bool multiple_inheritance : 1;\n\n    /// Does the class manage a __dict__?\n    bool dynamic_attr : 1;\n\n    /// Does the class implement the buffer protocol?\n    bool buffer_protocol : 1;\n\n    /// Is the default (unique_ptr) holder type used?\n    bool default_holder : 1;\n\n    /// Is the class definition local to the module shared object?\n    bool module_local : 1;\n\n    /// Is the class inheritable from python classes?\n    bool is_final : 1;\n\n    PYBIND11_NOINLINE void add_base(const std::type_info &base, void *(*caster)(void *) ) {\n        auto *base_info = detail::get_type_info(base, false);\n        if (!base_info) {\n            std::string tname(base.name());\n            detail::clean_type_id(tname);\n            pybind11_fail(\"generic_type: type \\\"\" + std::string(name)\n                          + \"\\\" referenced unknown base type \\\"\" + tname + \"\\\"\");\n        }\n\n        if (default_holder != base_info->default_holder) {\n            std::string tname(base.name());\n            detail::clean_type_id(tname);\n            pybind11_fail(\"generic_type: type \\\"\" + std::string(name) + \"\\\" \"\n                          + (default_holder ? \"does not have\" : \"has\")\n                          + \" a non-default holder type while its base \\\"\" + tname + \"\\\" \"\n                          + (base_info->default_holder ? \"does not\" : \"does\"));\n        }\n\n        bases.append((PyObject *) base_info->type);\n\n#if PY_VERSION_HEX < 0x030B0000\n        dynamic_attr |= base_info->type->tp_dictoffset != 0;\n#else\n        dynamic_attr |= (base_info->type->tp_flags & Py_TPFLAGS_MANAGED_DICT) != 0;\n#endif\n\n        if (caster) {\n            base_info->implicit_casts.emplace_back(type, caster);\n        }\n    }\n};\n\ninline function_call::function_call(const function_record &f, handle p) : func(f), parent(p) {\n    args.reserve(f.nargs);\n    args_convert.reserve(f.nargs);\n}\n\n/// Tag for a new-style `__init__` defined in `detail/init.h`\nstruct is_new_style_constructor {};\n\n/**\n * Partial template specializations to process custom attributes provided to\n * cpp_function_ and class_. These are either used to initialize the respective\n * fields in the type_record and function_record data structures or executed at\n * runtime to deal with custom call policies (e.g. keep_alive).\n */\ntemplate <typename T, typename SFINAE = void>\nstruct process_attribute;\n\ntemplate <typename T>\nstruct process_attribute_default {\n    /// Default implementation: do nothing\n    static void init(const T &, function_record *) {}\n    static void init(const T &, type_record *) {}\n    static void precall(function_call &) {}\n    static void postcall(function_call &, handle) {}\n};\n\n/// Process an attribute specifying the function's name\ntemplate <>\nstruct process_attribute<name> : process_attribute_default<name> {\n    static void init(const name &n, function_record *r) { r->name = const_cast<char *>(n.value); }\n};\n\n/// Process an attribute specifying the function's docstring\ntemplate <>\nstruct process_attribute<doc> : process_attribute_default<doc> {\n    static void init(const doc &n, function_record *r) { r->doc = const_cast<char *>(n.value); }\n};\n\n/// Process an attribute specifying the function's docstring (provided as a C-style string)\ntemplate <>\nstruct process_attribute<const char *> : process_attribute_default<const char *> {\n    static void init(const char *d, function_record *r) { r->doc = const_cast<char *>(d); }\n    static void init(const char *d, type_record *r) { r->doc = d; }\n};\ntemplate <>\nstruct process_attribute<char *> : process_attribute<const char *> {};\n\n/// Process an attribute indicating the function's return value policy\ntemplate <>\nstruct process_attribute<return_value_policy> : process_attribute_default<return_value_policy> {\n    static void init(const return_value_policy &p, function_record *r) { r->policy = p; }\n};\n\n/// Process an attribute which indicates that this is an overloaded function associated with a\n/// given sibling\ntemplate <>\nstruct process_attribute<sibling> : process_attribute_default<sibling> {\n    static void init(const sibling &s, function_record *r) { r->sibling = s.value; }\n};\n\n/// Process an attribute which indicates that this function is a method\ntemplate <>\nstruct process_attribute<is_method> : process_attribute_default<is_method> {\n    static void init(const is_method &s, function_record *r) {\n        r->is_method = true;\n        r->scope = s.class_;\n    }\n};\n\n/// Process an attribute which indicates that this function is a setter\ntemplate <>\nstruct process_attribute<is_setter> : process_attribute_default<is_setter> {\n    static void init(const is_setter &, function_record *r) { r->is_setter = true; }\n};\n\n/// Process an attribute which indicates the parent scope of a method\ntemplate <>\nstruct process_attribute<scope> : process_attribute_default<scope> {\n    static void init(const scope &s, function_record *r) { r->scope = s.value; }\n};\n\n/// Process an attribute which indicates that this function is an operator\ntemplate <>\nstruct process_attribute<is_operator> : process_attribute_default<is_operator> {\n    static void init(const is_operator &, function_record *r) { r->is_operator = true; }\n};\n\ntemplate <>\nstruct process_attribute<is_new_style_constructor>\n    : process_attribute_default<is_new_style_constructor> {\n    static void init(const is_new_style_constructor &, function_record *r) {\n        r->is_new_style_constructor = true;\n    }\n};\n\ninline void check_kw_only_arg(const arg &a, function_record *r) {\n    if (r->args.size() > r->nargs_pos && (!a.name || a.name[0] == '\\0')) {\n        pybind11_fail(\"arg(): cannot specify an unnamed argument after a kw_only() annotation or \"\n                      \"args() argument\");\n    }\n}\n\ninline void append_self_arg_if_needed(function_record *r) {\n    if (r->is_method && r->args.empty()) {\n        r->args.emplace_back(\"self\", nullptr, handle(), /*convert=*/true, /*none=*/false);\n    }\n}\n\n/// Process a keyword argument attribute (*without* a default value)\ntemplate <>\nstruct process_attribute<arg> : process_attribute_default<arg> {\n    static void init(const arg &a, function_record *r) {\n        append_self_arg_if_needed(r);\n        r->args.emplace_back(a.name, nullptr, handle(), !a.flag_noconvert, a.flag_none);\n\n        check_kw_only_arg(a, r);\n    }\n};\n\n/// Process a keyword argument attribute (*with* a default value)\ntemplate <>\nstruct process_attribute<arg_v> : process_attribute_default<arg_v> {\n    static void init(const arg_v &a, function_record *r) {\n        if (r->is_method && r->args.empty()) {\n            r->args.emplace_back(\n                \"self\", /*descr=*/nullptr, /*parent=*/handle(), /*convert=*/true, /*none=*/false);\n        }\n\n        if (!a.value) {\n#if defined(PYBIND11_DETAILED_ERROR_MESSAGES)\n            std::string descr(\"'\");\n            if (a.name) {\n                descr += std::string(a.name) + \": \";\n            }\n            descr += a.type + \"'\";\n            if (r->is_method) {\n                if (r->name) {\n                    descr += \" in method '\" + (std::string) str(r->scope) + \".\"\n                             + (std::string) r->name + \"'\";\n                } else {\n                    descr += \" in method of '\" + (std::string) str(r->scope) + \"'\";\n                }\n            } else if (r->name) {\n                descr += \" in function '\" + (std::string) r->name + \"'\";\n            }\n            pybind11_fail(\"arg(): could not convert default argument \" + descr\n                          + \" into a Python object (type not registered yet?)\");\n#else\n            pybind11_fail(\"arg(): could not convert default argument \"\n                          \"into a Python object (type not registered yet?). \"\n                          \"#define PYBIND11_DETAILED_ERROR_MESSAGES or compile in debug mode for \"\n                          \"more information.\");\n#endif\n        }\n        r->args.emplace_back(a.name, a.descr, a.value.inc_ref(), !a.flag_noconvert, a.flag_none);\n\n        check_kw_only_arg(a, r);\n    }\n};\n\n/// Process a keyword-only-arguments-follow pseudo argument\ntemplate <>\nstruct process_attribute<kw_only> : process_attribute_default<kw_only> {\n    static void init(const kw_only &, function_record *r) {\n        append_self_arg_if_needed(r);\n        if (r->has_args && r->nargs_pos != static_cast<std::uint16_t>(r->args.size())) {\n            pybind11_fail(\"Mismatched args() and kw_only(): they must occur at the same relative \"\n                          \"argument location (or omit kw_only() entirely)\");\n        }\n        r->nargs_pos = static_cast<std::uint16_t>(r->args.size());\n    }\n};\n\n/// Process a positional-only-argument maker\ntemplate <>\nstruct process_attribute<pos_only> : process_attribute_default<pos_only> {\n    static void init(const pos_only &, function_record *r) {\n        append_self_arg_if_needed(r);\n        r->nargs_pos_only = static_cast<std::uint16_t>(r->args.size());\n        if (r->nargs_pos_only > r->nargs_pos) {\n            pybind11_fail(\"pos_only(): cannot follow a py::args() argument\");\n        }\n        // It also can't follow a kw_only, but a static_assert in pybind11.h checks that\n    }\n};\n\n/// Process a parent class attribute.  Single inheritance only (class_ itself already guarantees\n/// that)\ntemplate <typename T>\nstruct process_attribute<T, enable_if_t<is_pyobject<T>::value>>\n    : process_attribute_default<handle> {\n    static void init(const handle &h, type_record *r) { r->bases.append(h); }\n};\n\n/// Process a parent class attribute (deprecated, does not support multiple inheritance)\ntemplate <typename T>\nstruct process_attribute<base<T>> : process_attribute_default<base<T>> {\n    static void init(const base<T> &, type_record *r) { r->add_base(typeid(T), nullptr); }\n};\n\n/// Process a multiple inheritance attribute\ntemplate <>\nstruct process_attribute<multiple_inheritance> : process_attribute_default<multiple_inheritance> {\n    static void init(const multiple_inheritance &, type_record *r) {\n        r->multiple_inheritance = true;\n    }\n};\n\ntemplate <>\nstruct process_attribute<dynamic_attr> : process_attribute_default<dynamic_attr> {\n    static void init(const dynamic_attr &, type_record *r) { r->dynamic_attr = true; }\n};\n\ntemplate <>\nstruct process_attribute<custom_type_setup> {\n    static void init(const custom_type_setup &value, type_record *r) {\n        r->custom_type_setup_callback = value.value;\n    }\n};\n\ntemplate <>\nstruct process_attribute<is_final> : process_attribute_default<is_final> {\n    static void init(const is_final &, type_record *r) { r->is_final = true; }\n};\n\ntemplate <>\nstruct process_attribute<buffer_protocol> : process_attribute_default<buffer_protocol> {\n    static void init(const buffer_protocol &, type_record *r) { r->buffer_protocol = true; }\n};\n\ntemplate <>\nstruct process_attribute<metaclass> : process_attribute_default<metaclass> {\n    static void init(const metaclass &m, type_record *r) { r->metaclass = m.value; }\n};\n\ntemplate <>\nstruct process_attribute<module_local> : process_attribute_default<module_local> {\n    static void init(const module_local &l, type_record *r) { r->module_local = l.value; }\n};\n\n/// Process a 'prepend' attribute, putting this at the beginning of the overload chain\ntemplate <>\nstruct process_attribute<prepend> : process_attribute_default<prepend> {\n    static void init(const prepend &, function_record *r) { r->prepend = true; }\n};\n\n/// Process an 'arithmetic' attribute for enums (does nothing here)\ntemplate <>\nstruct process_attribute<arithmetic> : process_attribute_default<arithmetic> {};\n\ntemplate <typename... Ts>\nstruct process_attribute<call_guard<Ts...>> : process_attribute_default<call_guard<Ts...>> {};\n\n/**\n * Process a keep_alive call policy -- invokes keep_alive_impl during the\n * pre-call handler if both Nurse, Patient != 0 and use the post-call handler\n * otherwise\n */\ntemplate <size_t Nurse, size_t Patient>\nstruct process_attribute<keep_alive<Nurse, Patient>>\n    : public process_attribute_default<keep_alive<Nurse, Patient>> {\n    template <size_t N = Nurse, size_t P = Patient, enable_if_t<N != 0 && P != 0, int> = 0>\n    static void precall(function_call &call) {\n        keep_alive_impl(Nurse, Patient, call, handle());\n    }\n    template <size_t N = Nurse, size_t P = Patient, enable_if_t<N != 0 && P != 0, int> = 0>\n    static void postcall(function_call &, handle) {}\n    template <size_t N = Nurse, size_t P = Patient, enable_if_t<N == 0 || P == 0, int> = 0>\n    static void precall(function_call &) {}\n    template <size_t N = Nurse, size_t P = Patient, enable_if_t<N == 0 || P == 0, int> = 0>\n    static void postcall(function_call &call, handle ret) {\n        keep_alive_impl(Nurse, Patient, call, ret);\n    }\n};\n\n/// Recursively iterate over variadic template arguments\ntemplate <typename... Args>\nstruct process_attributes {\n    static void init(const Args &...args, function_record *r) {\n        PYBIND11_WORKAROUND_INCORRECT_MSVC_C4100(r);\n        PYBIND11_WORKAROUND_INCORRECT_GCC_UNUSED_BUT_SET_PARAMETER(r);\n        using expander = int[];\n        (void) expander{\n            0, ((void) process_attribute<typename std::decay<Args>::type>::init(args, r), 0)...};\n    }\n    static void init(const Args &...args, type_record *r) {\n        PYBIND11_WORKAROUND_INCORRECT_MSVC_C4100(r);\n        PYBIND11_WORKAROUND_INCORRECT_GCC_UNUSED_BUT_SET_PARAMETER(r);\n        using expander = int[];\n        (void) expander{0,\n                        (process_attribute<typename std::decay<Args>::type>::init(args, r), 0)...};\n    }\n    static void precall(function_call &call) {\n        PYBIND11_WORKAROUND_INCORRECT_MSVC_C4100(call);\n        using expander = int[];\n        (void) expander{0,\n                        (process_attribute<typename std::decay<Args>::type>::precall(call), 0)...};\n    }\n    static void postcall(function_call &call, handle fn_ret) {\n        PYBIND11_WORKAROUND_INCORRECT_MSVC_C4100(call, fn_ret);\n        PYBIND11_WORKAROUND_INCORRECT_GCC_UNUSED_BUT_SET_PARAMETER(fn_ret);\n        using expander = int[];\n        (void) expander{\n            0, (process_attribute<typename std::decay<Args>::type>::postcall(call, fn_ret), 0)...};\n    }\n};\n\ntemplate <typename T>\nusing is_call_guard = is_instantiation<call_guard, T>;\n\n/// Extract the ``type`` from the first `call_guard` in `Extras...` (or `void_type` if none found)\ntemplate <typename... Extra>\nusing extract_guard_t = typename exactly_one_t<is_call_guard, call_guard<>, Extra...>::type;\n\n/// Check the number of named arguments at compile time\ntemplate <typename... Extra,\n          size_t named = constexpr_sum(std::is_base_of<arg, Extra>::value...),\n          size_t self = constexpr_sum(std::is_same<is_method, Extra>::value...)>\nconstexpr bool expected_num_args(size_t nargs, bool has_args, bool has_kwargs) {\n    PYBIND11_WORKAROUND_INCORRECT_MSVC_C4100(nargs, has_args, has_kwargs);\n    return named == 0 || (self + named + size_t(has_args) + size_t(has_kwargs)) == nargs;\n}\n\nPYBIND11_NAMESPACE_END(detail)\nPYBIND11_NAMESPACE_END(PYBIND11_NAMESPACE)\n"
  },
  {
    "path": "libs/pybind11/include/pybind11/buffer_info.h",
    "content": "/*\n    pybind11/buffer_info.h: Python buffer object interface\n\n    Copyright (c) 2016 Wenzel Jakob <wenzel.jakob@epfl.ch>\n\n    All rights reserved. Use of this source code is governed by a\n    BSD-style license that can be found in the LICENSE file.\n*/\n\n#pragma once\n\n#include \"detail/common.h\"\n\nPYBIND11_NAMESPACE_BEGIN(PYBIND11_NAMESPACE)\n\nPYBIND11_NAMESPACE_BEGIN(detail)\n\n// Default, C-style strides\ninline std::vector<ssize_t> c_strides(const std::vector<ssize_t> &shape, ssize_t itemsize) {\n    auto ndim = shape.size();\n    std::vector<ssize_t> strides(ndim, itemsize);\n    if (ndim > 0) {\n        for (size_t i = ndim - 1; i > 0; --i) {\n            strides[i - 1] = strides[i] * shape[i];\n        }\n    }\n    return strides;\n}\n\n// F-style strides; default when constructing an array_t with `ExtraFlags & f_style`\ninline std::vector<ssize_t> f_strides(const std::vector<ssize_t> &shape, ssize_t itemsize) {\n    auto ndim = shape.size();\n    std::vector<ssize_t> strides(ndim, itemsize);\n    for (size_t i = 1; i < ndim; ++i) {\n        strides[i] = strides[i - 1] * shape[i - 1];\n    }\n    return strides;\n}\n\ntemplate <typename T, typename SFINAE = void>\nstruct compare_buffer_info;\n\nPYBIND11_NAMESPACE_END(detail)\n\n/// Information record describing a Python buffer object\nstruct buffer_info {\n    void *ptr = nullptr;          // Pointer to the underlying storage\n    ssize_t itemsize = 0;         // Size of individual items in bytes\n    ssize_t size = 0;             // Total number of entries\n    std::string format;           // For homogeneous buffers, this should be set to\n                                  // format_descriptor<T>::format()\n    ssize_t ndim = 0;             // Number of dimensions\n    std::vector<ssize_t> shape;   // Shape of the tensor (1 entry per dimension)\n    std::vector<ssize_t> strides; // Number of bytes between adjacent entries\n                                  // (for each per dimension)\n    bool readonly = false;        // flag to indicate if the underlying storage may be written to\n\n    buffer_info() = default;\n\n    buffer_info(void *ptr,\n                ssize_t itemsize,\n                const std::string &format,\n                ssize_t ndim,\n                detail::any_container<ssize_t> shape_in,\n                detail::any_container<ssize_t> strides_in,\n                bool readonly = false)\n        : ptr(ptr), itemsize(itemsize), size(1), format(format), ndim(ndim),\n          shape(std::move(shape_in)), strides(std::move(strides_in)), readonly(readonly) {\n        if (ndim != (ssize_t) shape.size() || ndim != (ssize_t) strides.size()) {\n            pybind11_fail(\"buffer_info: ndim doesn't match shape and/or strides length\");\n        }\n        for (size_t i = 0; i < (size_t) ndim; ++i) {\n            size *= shape[i];\n        }\n    }\n\n    template <typename T>\n    buffer_info(T *ptr,\n                detail::any_container<ssize_t> shape_in,\n                detail::any_container<ssize_t> strides_in,\n                bool readonly = false)\n        : buffer_info(private_ctr_tag(),\n                      ptr,\n                      sizeof(T),\n                      format_descriptor<T>::format(),\n                      static_cast<ssize_t>(shape_in->size()),\n                      std::move(shape_in),\n                      std::move(strides_in),\n                      readonly) {}\n\n    buffer_info(void *ptr,\n                ssize_t itemsize,\n                const std::string &format,\n                ssize_t size,\n                bool readonly = false)\n        : buffer_info(ptr, itemsize, format, 1, {size}, {itemsize}, readonly) {}\n\n    template <typename T>\n    buffer_info(T *ptr, ssize_t size, bool readonly = false)\n        : buffer_info(ptr, sizeof(T), format_descriptor<T>::format(), size, readonly) {}\n\n    template <typename T>\n    buffer_info(const T *ptr, ssize_t size, bool readonly = true)\n        : buffer_info(\n              const_cast<T *>(ptr), sizeof(T), format_descriptor<T>::format(), size, readonly) {}\n\n    explicit buffer_info(Py_buffer *view, bool ownview = true)\n        : buffer_info(\n              view->buf,\n              view->itemsize,\n              view->format,\n              view->ndim,\n              {view->shape, view->shape + view->ndim},\n              /* Though buffer::request() requests PyBUF_STRIDES, ctypes objects\n               * ignore this flag and return a view with NULL strides.\n               * When strides are NULL, build them manually.  */\n              view->strides\n                  ? std::vector<ssize_t>(view->strides, view->strides + view->ndim)\n                  : detail::c_strides({view->shape, view->shape + view->ndim}, view->itemsize),\n              (view->readonly != 0)) {\n        // NOLINTNEXTLINE(cppcoreguidelines-prefer-member-initializer)\n        this->m_view = view;\n        // NOLINTNEXTLINE(cppcoreguidelines-prefer-member-initializer)\n        this->ownview = ownview;\n    }\n\n    buffer_info(const buffer_info &) = delete;\n    buffer_info &operator=(const buffer_info &) = delete;\n\n    buffer_info(buffer_info &&other) noexcept { (*this) = std::move(other); }\n\n    buffer_info &operator=(buffer_info &&rhs) noexcept {\n        ptr = rhs.ptr;\n        itemsize = rhs.itemsize;\n        size = rhs.size;\n        format = std::move(rhs.format);\n        ndim = rhs.ndim;\n        shape = std::move(rhs.shape);\n        strides = std::move(rhs.strides);\n        std::swap(m_view, rhs.m_view);\n        std::swap(ownview, rhs.ownview);\n        readonly = rhs.readonly;\n        return *this;\n    }\n\n    ~buffer_info() {\n        if (m_view && ownview) {\n            PyBuffer_Release(m_view);\n            delete m_view;\n        }\n    }\n\n    Py_buffer *view() const { return m_view; }\n    Py_buffer *&view() { return m_view; }\n\n    /* True if the buffer item type is equivalent to `T`. */\n    // To define \"equivalent\" by example:\n    // `buffer_info::item_type_is_equivalent_to<int>(b)` and\n    // `buffer_info::item_type_is_equivalent_to<long>(b)` may both be true\n    // on some platforms, but `int` and `unsigned` will never be equivalent.\n    // For the ground truth, please inspect `detail::compare_buffer_info<>`.\n    template <typename T>\n    bool item_type_is_equivalent_to() const {\n        return detail::compare_buffer_info<T>::compare(*this);\n    }\n\nprivate:\n    struct private_ctr_tag {};\n\n    buffer_info(private_ctr_tag,\n                void *ptr,\n                ssize_t itemsize,\n                const std::string &format,\n                ssize_t ndim,\n                detail::any_container<ssize_t> &&shape_in,\n                detail::any_container<ssize_t> &&strides_in,\n                bool readonly)\n        : buffer_info(\n              ptr, itemsize, format, ndim, std::move(shape_in), std::move(strides_in), readonly) {}\n\n    Py_buffer *m_view = nullptr;\n    bool ownview = false;\n};\n\nPYBIND11_NAMESPACE_BEGIN(detail)\n\ntemplate <typename T, typename SFINAE>\nstruct compare_buffer_info {\n    static bool compare(const buffer_info &b) {\n        // NOLINTNEXTLINE(bugprone-sizeof-expression) Needed for `PyObject *`\n        return b.format == format_descriptor<T>::format() && b.itemsize == (ssize_t) sizeof(T);\n    }\n};\n\ntemplate <typename T>\nstruct compare_buffer_info<T, detail::enable_if_t<std::is_integral<T>::value>> {\n    static bool compare(const buffer_info &b) {\n        return (size_t) b.itemsize == sizeof(T)\n               && (b.format == format_descriptor<T>::value\n                   || ((sizeof(T) == sizeof(long))\n                       && b.format == (std::is_unsigned<T>::value ? \"L\" : \"l\"))\n                   || ((sizeof(T) == sizeof(size_t))\n                       && b.format == (std::is_unsigned<T>::value ? \"N\" : \"n\")));\n    }\n};\n\nPYBIND11_NAMESPACE_END(detail)\nPYBIND11_NAMESPACE_END(PYBIND11_NAMESPACE)\n"
  },
  {
    "path": "libs/pybind11/include/pybind11/cast.h",
    "content": "/*\n    pybind11/cast.h: Partial template specializations to cast between\n    C++ and Python types\n\n    Copyright (c) 2016 Wenzel Jakob <wenzel.jakob@epfl.ch>\n\n    All rights reserved. Use of this source code is governed by a\n    BSD-style license that can be found in the LICENSE file.\n*/\n\n#pragma once\n\n#include \"detail/common.h\"\n#include \"detail/descr.h\"\n#include \"detail/type_caster_base.h\"\n#include \"detail/typeid.h\"\n#include \"pytypes.h\"\n\n#include <array>\n#include <cstring>\n#include <functional>\n#include <iosfwd>\n#include <iterator>\n#include <memory>\n#include <string>\n#include <tuple>\n#include <type_traits>\n#include <utility>\n#include <vector>\n\nPYBIND11_NAMESPACE_BEGIN(PYBIND11_NAMESPACE)\n\nPYBIND11_WARNING_DISABLE_MSVC(4127)\n\nPYBIND11_NAMESPACE_BEGIN(detail)\n\ntemplate <typename type, typename SFINAE = void>\nclass type_caster : public type_caster_base<type> {};\ntemplate <typename type>\nusing make_caster = type_caster<intrinsic_t<type>>;\n\n// Shortcut for calling a caster's `cast_op_type` cast operator for casting a type_caster to a T\ntemplate <typename T>\ntypename make_caster<T>::template cast_op_type<T> cast_op(make_caster<T> &caster) {\n    using result_t = typename make_caster<T>::template cast_op_type<T>; // See PR #4893\n    return caster.operator result_t();\n}\ntemplate <typename T>\ntypename make_caster<T>::template cast_op_type<typename std::add_rvalue_reference<T>::type>\ncast_op(make_caster<T> &&caster) {\n    using result_t = typename make_caster<T>::template cast_op_type<\n        typename std::add_rvalue_reference<T>::type>; // See PR #4893\n    return std::move(caster).operator result_t();\n}\n\ntemplate <typename type>\nclass type_caster<std::reference_wrapper<type>> {\nprivate:\n    using caster_t = make_caster<type>;\n    caster_t subcaster;\n    using reference_t = type &;\n    using subcaster_cast_op_type = typename caster_t::template cast_op_type<reference_t>;\n\n    static_assert(\n        std::is_same<typename std::remove_const<type>::type &, subcaster_cast_op_type>::value\n            || std::is_same<reference_t, subcaster_cast_op_type>::value,\n        \"std::reference_wrapper<T> caster requires T to have a caster with an \"\n        \"`operator T &()` or `operator const T &()`\");\n\npublic:\n    bool load(handle src, bool convert) { return subcaster.load(src, convert); }\n    static constexpr auto name = caster_t::name;\n    static handle\n    cast(const std::reference_wrapper<type> &src, return_value_policy policy, handle parent) {\n        // It is definitely wrong to take ownership of this pointer, so mask that rvp\n        if (policy == return_value_policy::take_ownership\n            || policy == return_value_policy::automatic) {\n            policy = return_value_policy::automatic_reference;\n        }\n        return caster_t::cast(&src.get(), policy, parent);\n    }\n    template <typename T>\n    using cast_op_type = std::reference_wrapper<type>;\n    explicit operator std::reference_wrapper<type>() { return cast_op<type &>(subcaster); }\n};\n\n#define PYBIND11_TYPE_CASTER(type, py_name)                                                       \\\nprotected:                                                                                        \\\n    type value;                                                                                   \\\n                                                                                                  \\\npublic:                                                                                           \\\n    static constexpr auto name = py_name;                                                         \\\n    template <typename T_,                                                                        \\\n              ::pybind11::detail::enable_if_t<                                                    \\\n                  std::is_same<type, ::pybind11::detail::remove_cv_t<T_>>::value,                 \\\n                  int>                                                                            \\\n              = 0>                                                                                \\\n    static ::pybind11::handle cast(                                                               \\\n        T_ *src, ::pybind11::return_value_policy policy, ::pybind11::handle parent) {             \\\n        if (!src)                                                                                 \\\n            return ::pybind11::none().release();                                                  \\\n        if (policy == ::pybind11::return_value_policy::take_ownership) {                          \\\n            auto h = cast(std::move(*src), policy, parent);                                       \\\n            delete src;                                                                           \\\n            return h;                                                                             \\\n        }                                                                                         \\\n        return cast(*src, policy, parent);                                                        \\\n    }                                                                                             \\\n    operator type *() { return &value; }               /* NOLINT(bugprone-macro-parentheses) */   \\\n    operator type &() { return value; }                /* NOLINT(bugprone-macro-parentheses) */   \\\n    operator type &&() && { return std::move(value); } /* NOLINT(bugprone-macro-parentheses) */   \\\n    template <typename T_>                                                                        \\\n    using cast_op_type = ::pybind11::detail::movable_cast_op_type<T_>\n\ntemplate <typename CharT>\nusing is_std_char_type = any_of<std::is_same<CharT, char>, /* std::string */\n#if defined(PYBIND11_HAS_U8STRING)\n                                std::is_same<CharT, char8_t>, /* std::u8string */\n#endif\n                                std::is_same<CharT, char16_t>, /* std::u16string */\n                                std::is_same<CharT, char32_t>, /* std::u32string */\n                                std::is_same<CharT, wchar_t>   /* std::wstring */\n                                >;\n\ntemplate <typename T>\nstruct type_caster<T, enable_if_t<std::is_arithmetic<T>::value && !is_std_char_type<T>::value>> {\n    using _py_type_0 = conditional_t<sizeof(T) <= sizeof(long), long, long long>;\n    using _py_type_1 = conditional_t<std::is_signed<T>::value,\n                                     _py_type_0,\n                                     typename std::make_unsigned<_py_type_0>::type>;\n    using py_type = conditional_t<std::is_floating_point<T>::value, double, _py_type_1>;\n\npublic:\n    bool load(handle src, bool convert) {\n        py_type py_value;\n\n        if (!src) {\n            return false;\n        }\n\n#if !defined(PYPY_VERSION)\n        auto index_check = [](PyObject *o) { return PyIndex_Check(o); };\n#else\n        // In PyPy 7.3.3, `PyIndex_Check` is implemented by calling `__index__`,\n        // while CPython only considers the existence of `nb_index`/`__index__`.\n        auto index_check = [](PyObject *o) { return hasattr(o, \"__index__\"); };\n#endif\n\n        if (std::is_floating_point<T>::value) {\n            if (convert || PyFloat_Check(src.ptr())) {\n                py_value = (py_type) PyFloat_AsDouble(src.ptr());\n            } else {\n                return false;\n            }\n        } else if (PyFloat_Check(src.ptr())\n                   || (!convert && !PYBIND11_LONG_CHECK(src.ptr()) && !index_check(src.ptr()))) {\n            return false;\n        } else {\n            handle src_or_index = src;\n            // PyPy: 7.3.7's 3.8 does not implement PyLong_*'s __index__ calls.\n#if PY_VERSION_HEX < 0x03080000 || defined(PYPY_VERSION)\n            object index;\n            if (!PYBIND11_LONG_CHECK(src.ptr())) { // So: index_check(src.ptr())\n                index = reinterpret_steal<object>(PyNumber_Index(src.ptr()));\n                if (!index) {\n                    PyErr_Clear();\n                    if (!convert)\n                        return false;\n                } else {\n                    src_or_index = index;\n                }\n            }\n#endif\n            if (std::is_unsigned<py_type>::value) {\n                py_value = as_unsigned<py_type>(src_or_index.ptr());\n            } else { // signed integer:\n                py_value = sizeof(T) <= sizeof(long)\n                               ? (py_type) PyLong_AsLong(src_or_index.ptr())\n                               : (py_type) PYBIND11_LONG_AS_LONGLONG(src_or_index.ptr());\n            }\n        }\n\n        // Python API reported an error\n        bool py_err = py_value == (py_type) -1 && PyErr_Occurred();\n\n        // Check to see if the conversion is valid (integers should match exactly)\n        // Signed/unsigned checks happen elsewhere\n        if (py_err\n            || (std::is_integral<T>::value && sizeof(py_type) != sizeof(T)\n                && py_value != (py_type) (T) py_value)) {\n            PyErr_Clear();\n            if (py_err && convert && (PyNumber_Check(src.ptr()) != 0)) {\n                auto tmp = reinterpret_steal<object>(std::is_floating_point<T>::value\n                                                         ? PyNumber_Float(src.ptr())\n                                                         : PyNumber_Long(src.ptr()));\n                PyErr_Clear();\n                return load(tmp, false);\n            }\n            return false;\n        }\n\n        value = (T) py_value;\n        return true;\n    }\n\n    template <typename U = T>\n    static typename std::enable_if<std::is_floating_point<U>::value, handle>::type\n    cast(U src, return_value_policy /* policy */, handle /* parent */) {\n        return PyFloat_FromDouble((double) src);\n    }\n\n    template <typename U = T>\n    static typename std::enable_if<!std::is_floating_point<U>::value && std::is_signed<U>::value\n                                       && (sizeof(U) <= sizeof(long)),\n                                   handle>::type\n    cast(U src, return_value_policy /* policy */, handle /* parent */) {\n        return PYBIND11_LONG_FROM_SIGNED((long) src);\n    }\n\n    template <typename U = T>\n    static typename std::enable_if<!std::is_floating_point<U>::value && std::is_unsigned<U>::value\n                                       && (sizeof(U) <= sizeof(unsigned long)),\n                                   handle>::type\n    cast(U src, return_value_policy /* policy */, handle /* parent */) {\n        return PYBIND11_LONG_FROM_UNSIGNED((unsigned long) src);\n    }\n\n    template <typename U = T>\n    static typename std::enable_if<!std::is_floating_point<U>::value && std::is_signed<U>::value\n                                       && (sizeof(U) > sizeof(long)),\n                                   handle>::type\n    cast(U src, return_value_policy /* policy */, handle /* parent */) {\n        return PyLong_FromLongLong((long long) src);\n    }\n\n    template <typename U = T>\n    static typename std::enable_if<!std::is_floating_point<U>::value && std::is_unsigned<U>::value\n                                       && (sizeof(U) > sizeof(unsigned long)),\n                                   handle>::type\n    cast(U src, return_value_policy /* policy */, handle /* parent */) {\n        return PyLong_FromUnsignedLongLong((unsigned long long) src);\n    }\n\n    PYBIND11_TYPE_CASTER(T, const_name<std::is_integral<T>::value>(\"int\", \"float\"));\n};\n\ntemplate <typename T>\nstruct void_caster {\npublic:\n    bool load(handle src, bool) {\n        if (src && src.is_none()) {\n            return true;\n        }\n        return false;\n    }\n    static handle cast(T, return_value_policy /* policy */, handle /* parent */) {\n        return none().release();\n    }\n    PYBIND11_TYPE_CASTER(T, const_name(\"None\"));\n};\n\ntemplate <>\nclass type_caster<void_type> : public void_caster<void_type> {};\n\ntemplate <>\nclass type_caster<void> : public type_caster<void_type> {\npublic:\n    using type_caster<void_type>::cast;\n\n    bool load(handle h, bool) {\n        if (!h) {\n            return false;\n        }\n        if (h.is_none()) {\n            value = nullptr;\n            return true;\n        }\n\n        /* Check if this is a capsule */\n        if (isinstance<capsule>(h)) {\n            value = reinterpret_borrow<capsule>(h);\n            return true;\n        }\n\n        /* Check if this is a C++ type */\n        const auto &bases = all_type_info((PyTypeObject *) type::handle_of(h).ptr());\n        if (bases.size() == 1) { // Only allowing loading from a single-value type\n            value = values_and_holders(reinterpret_cast<instance *>(h.ptr())).begin()->value_ptr();\n            return true;\n        }\n\n        /* Fail */\n        return false;\n    }\n\n    static handle cast(const void *ptr, return_value_policy /* policy */, handle /* parent */) {\n        if (ptr) {\n            return capsule(ptr).release();\n        }\n        return none().release();\n    }\n\n    template <typename T>\n    using cast_op_type = void *&;\n    explicit operator void *&() { return value; }\n    static constexpr auto name = const_name(\"capsule\");\n\nprivate:\n    void *value = nullptr;\n};\n\ntemplate <>\nclass type_caster<std::nullptr_t> : public void_caster<std::nullptr_t> {};\n\ntemplate <>\nclass type_caster<bool> {\npublic:\n    bool load(handle src, bool convert) {\n        if (!src) {\n            return false;\n        }\n        if (src.ptr() == Py_True) {\n            value = true;\n            return true;\n        }\n        if (src.ptr() == Py_False) {\n            value = false;\n            return true;\n        }\n        if (convert || is_numpy_bool(src)) {\n            // (allow non-implicit conversion for numpy booleans), use strncmp\n            // since NumPy 1.x had an additional trailing underscore.\n\n            Py_ssize_t res = -1;\n            if (src.is_none()) {\n                res = 0; // None is implicitly converted to False\n            }\n#if defined(PYPY_VERSION)\n            // On PyPy, check that \"__bool__\" attr exists\n            else if (hasattr(src, PYBIND11_BOOL_ATTR)) {\n                res = PyObject_IsTrue(src.ptr());\n            }\n#else\n            // Alternate approach for CPython: this does the same as the above, but optimized\n            // using the CPython API so as to avoid an unneeded attribute lookup.\n            else if (auto *tp_as_number = src.ptr()->ob_type->tp_as_number) {\n                if (PYBIND11_NB_BOOL(tp_as_number)) {\n                    res = (*PYBIND11_NB_BOOL(tp_as_number))(src.ptr());\n                }\n            }\n#endif\n            if (res == 0 || res == 1) {\n                value = (res != 0);\n                return true;\n            }\n            PyErr_Clear();\n        }\n        return false;\n    }\n    static handle cast(bool src, return_value_policy /* policy */, handle /* parent */) {\n        return handle(src ? Py_True : Py_False).inc_ref();\n    }\n    PYBIND11_TYPE_CASTER(bool, const_name(\"bool\"));\n\nprivate:\n    // Test if an object is a NumPy boolean (without fetching the type).\n    static inline bool is_numpy_bool(handle object) {\n        const char *type_name = Py_TYPE(object.ptr())->tp_name;\n        // Name changed to `numpy.bool` in NumPy 2, `numpy.bool_` is needed for 1.x support\n        return std::strcmp(\"numpy.bool\", type_name) == 0\n               || std::strcmp(\"numpy.bool_\", type_name) == 0;\n    }\n};\n\n// Helper class for UTF-{8,16,32} C++ stl strings:\ntemplate <typename StringType, bool IsView = false>\nstruct string_caster {\n    using CharT = typename StringType::value_type;\n\n    // Simplify life by being able to assume standard char sizes (the standard only guarantees\n    // minimums, but Python requires exact sizes)\n    static_assert(!std::is_same<CharT, char>::value || sizeof(CharT) == 1,\n                  \"Unsupported char size != 1\");\n#if defined(PYBIND11_HAS_U8STRING)\n    static_assert(!std::is_same<CharT, char8_t>::value || sizeof(CharT) == 1,\n                  \"Unsupported char8_t size != 1\");\n#endif\n    static_assert(!std::is_same<CharT, char16_t>::value || sizeof(CharT) == 2,\n                  \"Unsupported char16_t size != 2\");\n    static_assert(!std::is_same<CharT, char32_t>::value || sizeof(CharT) == 4,\n                  \"Unsupported char32_t size != 4\");\n    // wchar_t can be either 16 bits (Windows) or 32 (everywhere else)\n    static_assert(!std::is_same<CharT, wchar_t>::value || sizeof(CharT) == 2 || sizeof(CharT) == 4,\n                  \"Unsupported wchar_t size != 2/4\");\n    static constexpr size_t UTF_N = 8 * sizeof(CharT);\n\n    bool load(handle src, bool) {\n        handle load_src = src;\n        if (!src) {\n            return false;\n        }\n        if (!PyUnicode_Check(load_src.ptr())) {\n            return load_raw(load_src);\n        }\n\n        // For UTF-8 we avoid the need for a temporary `bytes` object by using\n        // `PyUnicode_AsUTF8AndSize`.\n        if (UTF_N == 8) {\n            Py_ssize_t size = -1;\n            const auto *buffer\n                = reinterpret_cast<const CharT *>(PyUnicode_AsUTF8AndSize(load_src.ptr(), &size));\n            if (!buffer) {\n                PyErr_Clear();\n                return false;\n            }\n            value = StringType(buffer, static_cast<size_t>(size));\n            return true;\n        }\n\n        auto utfNbytes\n            = reinterpret_steal<object>(PyUnicode_AsEncodedString(load_src.ptr(),\n                                                                  UTF_N == 8    ? \"utf-8\"\n                                                                  : UTF_N == 16 ? \"utf-16\"\n                                                                                : \"utf-32\",\n                                                                  nullptr));\n        if (!utfNbytes) {\n            PyErr_Clear();\n            return false;\n        }\n\n        const auto *buffer\n            = reinterpret_cast<const CharT *>(PYBIND11_BYTES_AS_STRING(utfNbytes.ptr()));\n        size_t length = (size_t) PYBIND11_BYTES_SIZE(utfNbytes.ptr()) / sizeof(CharT);\n        // Skip BOM for UTF-16/32\n        if (UTF_N > 8) {\n            buffer++;\n            length--;\n        }\n        value = StringType(buffer, length);\n\n        // If we're loading a string_view we need to keep the encoded Python object alive:\n        if (IsView) {\n            loader_life_support::add_patient(utfNbytes);\n        }\n\n        return true;\n    }\n\n    static handle\n    cast(const StringType &src, return_value_policy /* policy */, handle /* parent */) {\n        const char *buffer = reinterpret_cast<const char *>(src.data());\n        auto nbytes = ssize_t(src.size() * sizeof(CharT));\n        handle s = decode_utfN(buffer, nbytes);\n        if (!s) {\n            throw error_already_set();\n        }\n        return s;\n    }\n\n    PYBIND11_TYPE_CASTER(StringType, const_name(PYBIND11_STRING_NAME));\n\nprivate:\n    static handle decode_utfN(const char *buffer, ssize_t nbytes) {\n#if !defined(PYPY_VERSION)\n        return UTF_N == 8    ? PyUnicode_DecodeUTF8(buffer, nbytes, nullptr)\n               : UTF_N == 16 ? PyUnicode_DecodeUTF16(buffer, nbytes, nullptr, nullptr)\n                             : PyUnicode_DecodeUTF32(buffer, nbytes, nullptr, nullptr);\n#else\n        // PyPy segfaults when on PyUnicode_DecodeUTF16 (and possibly on PyUnicode_DecodeUTF32 as\n        // well), so bypass the whole thing by just passing the encoding as a string value, which\n        // works properly:\n        return PyUnicode_Decode(buffer,\n                                nbytes,\n                                UTF_N == 8    ? \"utf-8\"\n                                : UTF_N == 16 ? \"utf-16\"\n                                              : \"utf-32\",\n                                nullptr);\n#endif\n    }\n\n    // When loading into a std::string or char*, accept a bytes/bytearray object as-is (i.e.\n    // without any encoding/decoding attempt).  For other C++ char sizes this is a no-op.\n    // which supports loading a unicode from a str, doesn't take this path.\n    template <typename C = CharT>\n    bool load_raw(enable_if_t<std::is_same<C, char>::value, handle> src) {\n        if (PYBIND11_BYTES_CHECK(src.ptr())) {\n            // We were passed raw bytes; accept it into a std::string or char*\n            // without any encoding attempt.\n            const char *bytes = PYBIND11_BYTES_AS_STRING(src.ptr());\n            if (!bytes) {\n                pybind11_fail(\"Unexpected PYBIND11_BYTES_AS_STRING() failure.\");\n            }\n            value = StringType(bytes, (size_t) PYBIND11_BYTES_SIZE(src.ptr()));\n            return true;\n        }\n        if (PyByteArray_Check(src.ptr())) {\n            // We were passed a bytearray; accept it into a std::string or char*\n            // without any encoding attempt.\n            const char *bytearray = PyByteArray_AsString(src.ptr());\n            if (!bytearray) {\n                pybind11_fail(\"Unexpected PyByteArray_AsString() failure.\");\n            }\n            value = StringType(bytearray, (size_t) PyByteArray_Size(src.ptr()));\n            return true;\n        }\n\n        return false;\n    }\n\n    template <typename C = CharT>\n    bool load_raw(enable_if_t<!std::is_same<C, char>::value, handle>) {\n        return false;\n    }\n};\n\ntemplate <typename CharT, class Traits, class Allocator>\nstruct type_caster<std::basic_string<CharT, Traits, Allocator>,\n                   enable_if_t<is_std_char_type<CharT>::value>>\n    : string_caster<std::basic_string<CharT, Traits, Allocator>> {};\n\n#ifdef PYBIND11_HAS_STRING_VIEW\ntemplate <typename CharT, class Traits>\nstruct type_caster<std::basic_string_view<CharT, Traits>,\n                   enable_if_t<is_std_char_type<CharT>::value>>\n    : string_caster<std::basic_string_view<CharT, Traits>, true> {};\n#endif\n\n// Type caster for C-style strings.  We basically use a std::string type caster, but also add the\n// ability to use None as a nullptr char* (which the string caster doesn't allow).\ntemplate <typename CharT>\nstruct type_caster<CharT, enable_if_t<is_std_char_type<CharT>::value>> {\n    using StringType = std::basic_string<CharT>;\n    using StringCaster = make_caster<StringType>;\n    StringCaster str_caster;\n    bool none = false;\n    CharT one_char = 0;\n\npublic:\n    bool load(handle src, bool convert) {\n        if (!src) {\n            return false;\n        }\n        if (src.is_none()) {\n            // Defer accepting None to other overloads (if we aren't in convert mode):\n            if (!convert) {\n                return false;\n            }\n            none = true;\n            return true;\n        }\n        return str_caster.load(src, convert);\n    }\n\n    static handle cast(const CharT *src, return_value_policy policy, handle parent) {\n        if (src == nullptr) {\n            return pybind11::none().release();\n        }\n        return StringCaster::cast(StringType(src), policy, parent);\n    }\n\n    static handle cast(CharT src, return_value_policy policy, handle parent) {\n        if (std::is_same<char, CharT>::value) {\n            handle s = PyUnicode_DecodeLatin1((const char *) &src, 1, nullptr);\n            if (!s) {\n                throw error_already_set();\n            }\n            return s;\n        }\n        return StringCaster::cast(StringType(1, src), policy, parent);\n    }\n\n    explicit operator CharT *() {\n        return none ? nullptr : const_cast<CharT *>(static_cast<StringType &>(str_caster).c_str());\n    }\n    explicit operator CharT &() {\n        if (none) {\n            throw value_error(\"Cannot convert None to a character\");\n        }\n\n        auto &value = static_cast<StringType &>(str_caster);\n        size_t str_len = value.size();\n        if (str_len == 0) {\n            throw value_error(\"Cannot convert empty string to a character\");\n        }\n\n        // If we're in UTF-8 mode, we have two possible failures: one for a unicode character that\n        // is too high, and one for multiple unicode characters (caught later), so we need to\n        // figure out how long the first encoded character is in bytes to distinguish between these\n        // two errors.  We also allow want to allow unicode characters U+0080 through U+00FF, as\n        // those can fit into a single char value.\n        if (StringCaster::UTF_N == 8 && str_len > 1 && str_len <= 4) {\n            auto v0 = static_cast<unsigned char>(value[0]);\n            // low bits only: 0-127\n            // 0b110xxxxx - start of 2-byte sequence\n            // 0b1110xxxx - start of 3-byte sequence\n            // 0b11110xxx - start of 4-byte sequence\n            size_t char0_bytes = (v0 & 0x80) == 0      ? 1\n                                 : (v0 & 0xE0) == 0xC0 ? 2\n                                 : (v0 & 0xF0) == 0xE0 ? 3\n                                                       : 4;\n\n            if (char0_bytes == str_len) {\n                // If we have a 128-255 value, we can decode it into a single char:\n                if (char0_bytes == 2 && (v0 & 0xFC) == 0xC0) { // 0x110000xx 0x10xxxxxx\n                    one_char = static_cast<CharT>(((v0 & 3) << 6)\n                                                  + (static_cast<unsigned char>(value[1]) & 0x3F));\n                    return one_char;\n                }\n                // Otherwise we have a single character, but it's > U+00FF\n                throw value_error(\"Character code point not in range(0x100)\");\n            }\n        }\n\n        // UTF-16 is much easier: we can only have a surrogate pair for values above U+FFFF, thus a\n        // surrogate pair with total length 2 instantly indicates a range error (but not a \"your\n        // string was too long\" error).\n        else if (StringCaster::UTF_N == 16 && str_len == 2) {\n            one_char = static_cast<CharT>(value[0]);\n            if (one_char >= 0xD800 && one_char < 0xE000) {\n                throw value_error(\"Character code point not in range(0x10000)\");\n            }\n        }\n\n        if (str_len != 1) {\n            throw value_error(\"Expected a character, but multi-character string found\");\n        }\n\n        one_char = value[0];\n        return one_char;\n    }\n\n    static constexpr auto name = const_name(PYBIND11_STRING_NAME);\n    template <typename _T>\n    using cast_op_type = pybind11::detail::cast_op_type<_T>;\n};\n\n// Base implementation for std::tuple and std::pair\ntemplate <template <typename...> class Tuple, typename... Ts>\nclass tuple_caster {\n    using type = Tuple<Ts...>;\n    static constexpr auto size = sizeof...(Ts);\n    using indices = make_index_sequence<size>;\n\npublic:\n    bool load(handle src, bool convert) {\n        if (!isinstance<sequence>(src)) {\n            return false;\n        }\n        const auto seq = reinterpret_borrow<sequence>(src);\n        if (seq.size() != size) {\n            return false;\n        }\n        return load_impl(seq, convert, indices{});\n    }\n\n    template <typename T>\n    static handle cast(T &&src, return_value_policy policy, handle parent) {\n        return cast_impl(std::forward<T>(src), policy, parent, indices{});\n    }\n\n    // copied from the PYBIND11_TYPE_CASTER macro\n    template <typename T>\n    static handle cast(T *src, return_value_policy policy, handle parent) {\n        if (!src) {\n            return none().release();\n        }\n        if (policy == return_value_policy::take_ownership) {\n            auto h = cast(std::move(*src), policy, parent);\n            delete src;\n            return h;\n        }\n        return cast(*src, policy, parent);\n    }\n\n    static constexpr auto name = const_name(\"tuple[\")\n                                 + ::pybind11::detail::concat(make_caster<Ts>::name...)\n                                 + const_name(\"]\");\n\n    template <typename T>\n    using cast_op_type = type;\n\n    explicit operator type() & { return implicit_cast(indices{}); }\n    explicit operator type() && { return std::move(*this).implicit_cast(indices{}); }\n\nprotected:\n    template <size_t... Is>\n    type implicit_cast(index_sequence<Is...>) & {\n        return type(cast_op<Ts>(std::get<Is>(subcasters))...);\n    }\n    template <size_t... Is>\n    type implicit_cast(index_sequence<Is...>) && {\n        return type(cast_op<Ts>(std::move(std::get<Is>(subcasters)))...);\n    }\n\n    static constexpr bool load_impl(const sequence &, bool, index_sequence<>) { return true; }\n\n    template <size_t... Is>\n    bool load_impl(const sequence &seq, bool convert, index_sequence<Is...>) {\n#ifdef __cpp_fold_expressions\n        if ((... || !std::get<Is>(subcasters).load(seq[Is], convert))) {\n            return false;\n        }\n#else\n        for (bool r : {std::get<Is>(subcasters).load(seq[Is], convert)...}) {\n            if (!r) {\n                return false;\n            }\n        }\n#endif\n        return true;\n    }\n\n    /* Implementation: Convert a C++ tuple into a Python tuple */\n    template <typename T, size_t... Is>\n    static handle\n    cast_impl(T &&src, return_value_policy policy, handle parent, index_sequence<Is...>) {\n        PYBIND11_WORKAROUND_INCORRECT_MSVC_C4100(src, policy, parent);\n        PYBIND11_WORKAROUND_INCORRECT_GCC_UNUSED_BUT_SET_PARAMETER(policy, parent);\n        std::array<object, size> entries{{reinterpret_steal<object>(\n            make_caster<Ts>::cast(std::get<Is>(std::forward<T>(src)), policy, parent))...}};\n        for (const auto &entry : entries) {\n            if (!entry) {\n                return handle();\n            }\n        }\n        tuple result(size);\n        int counter = 0;\n        for (auto &entry : entries) {\n            PyTuple_SET_ITEM(result.ptr(), counter++, entry.release().ptr());\n        }\n        return result.release();\n    }\n\n    Tuple<make_caster<Ts>...> subcasters;\n};\n\ntemplate <typename T1, typename T2>\nclass type_caster<std::pair<T1, T2>> : public tuple_caster<std::pair, T1, T2> {};\n\ntemplate <typename... Ts>\nclass type_caster<std::tuple<Ts...>> : public tuple_caster<std::tuple, Ts...> {};\n\ntemplate <>\nclass type_caster<std::tuple<>> : public tuple_caster<std::tuple> {\npublic:\n    // PEP 484 specifies this syntax for an empty tuple\n    static constexpr auto name = const_name(\"tuple[()]\");\n};\n\n/// Helper class which abstracts away certain actions. Users can provide specializations for\n/// custom holders, but it's only necessary if the type has a non-standard interface.\ntemplate <typename T>\nstruct holder_helper {\n    static auto get(const T &p) -> decltype(p.get()) { return p.get(); }\n};\n\n/// Type caster for holder types like std::shared_ptr, etc.\n/// The SFINAE hook is provided to help work around the current lack of support\n/// for smart-pointer interoperability. Please consider it an implementation\n/// detail that may change in the future, as formal support for smart-pointer\n/// interoperability is added into pybind11.\ntemplate <typename type, typename holder_type, typename SFINAE = void>\nstruct copyable_holder_caster : public type_caster_base<type> {\npublic:\n    using base = type_caster_base<type>;\n    static_assert(std::is_base_of<base, type_caster<type>>::value,\n                  \"Holder classes are only supported for custom types\");\n    using base::base;\n    using base::cast;\n    using base::typeinfo;\n    using base::value;\n\n    bool load(handle src, bool convert) {\n        return base::template load_impl<copyable_holder_caster<type, holder_type>>(src, convert);\n    }\n\n    explicit operator type *() { return this->value; }\n    // static_cast works around compiler error with MSVC 17 and CUDA 10.2\n    // see issue #2180\n    explicit operator type &() { return *(static_cast<type *>(this->value)); }\n    explicit operator holder_type *() { return std::addressof(holder); }\n    explicit operator holder_type &() { return holder; }\n\n    static handle cast(const holder_type &src, return_value_policy, handle) {\n        const auto *ptr = holder_helper<holder_type>::get(src);\n        return type_caster_base<type>::cast_holder(ptr, &src);\n    }\n\nprotected:\n    friend class type_caster_generic;\n    void check_holder_compat() {\n        if (typeinfo->default_holder) {\n            throw cast_error(\"Unable to load a custom holder type from a default-holder instance\");\n        }\n    }\n\n    void load_value(value_and_holder &&v_h) {\n        if (v_h.holder_constructed()) {\n            value = v_h.value_ptr();\n            holder = v_h.template holder<holder_type>();\n            return;\n        }\n        throw cast_error(\"Unable to cast from non-held to held instance (T& to Holder<T>) \"\n#if !defined(PYBIND11_DETAILED_ERROR_MESSAGES)\n                         \"(#define PYBIND11_DETAILED_ERROR_MESSAGES or compile in debug mode for \"\n                         \"type information)\");\n#else\n                         \"of type '\"\n                         + type_id<holder_type>() + \"''\");\n#endif\n    }\n\n    template <typename T = holder_type,\n              detail::enable_if_t<!std::is_constructible<T, const T &, type *>::value, int> = 0>\n    bool try_implicit_casts(handle, bool) {\n        return false;\n    }\n\n    template <typename T = holder_type,\n              detail::enable_if_t<std::is_constructible<T, const T &, type *>::value, int> = 0>\n    bool try_implicit_casts(handle src, bool convert) {\n        for (auto &cast : typeinfo->implicit_casts) {\n            copyable_holder_caster sub_caster(*cast.first);\n            if (sub_caster.load(src, convert)) {\n                value = cast.second(sub_caster.value);\n                holder = holder_type(sub_caster.holder, (type *) value);\n                return true;\n            }\n        }\n        return false;\n    }\n\n    static bool try_direct_conversions(handle) { return false; }\n\n    holder_type holder;\n};\n\n/// Specialize for the common std::shared_ptr, so users don't need to\ntemplate <typename T>\nclass type_caster<std::shared_ptr<T>> : public copyable_holder_caster<T, std::shared_ptr<T>> {};\n\n/// Type caster for holder types like std::unique_ptr.\n/// Please consider the SFINAE hook an implementation detail, as explained\n/// in the comment for the copyable_holder_caster.\ntemplate <typename type, typename holder_type, typename SFINAE = void>\nstruct move_only_holder_caster {\n    static_assert(std::is_base_of<type_caster_base<type>, type_caster<type>>::value,\n                  \"Holder classes are only supported for custom types\");\n\n    static handle cast(holder_type &&src, return_value_policy, handle) {\n        auto *ptr = holder_helper<holder_type>::get(src);\n        return type_caster_base<type>::cast_holder(ptr, std::addressof(src));\n    }\n    static constexpr auto name = type_caster_base<type>::name;\n};\n\ntemplate <typename type, typename deleter>\nclass type_caster<std::unique_ptr<type, deleter>>\n    : public move_only_holder_caster<type, std::unique_ptr<type, deleter>> {};\n\ntemplate <typename type, typename holder_type>\nusing type_caster_holder = conditional_t<is_copy_constructible<holder_type>::value,\n                                         copyable_holder_caster<type, holder_type>,\n                                         move_only_holder_caster<type, holder_type>>;\n\ntemplate <typename T, bool Value = false>\nstruct always_construct_holder {\n    static constexpr bool value = Value;\n};\n\n/// Create a specialization for custom holder types (silently ignores std::shared_ptr)\n#define PYBIND11_DECLARE_HOLDER_TYPE(type, holder_type, ...)                                      \\\n    PYBIND11_NAMESPACE_BEGIN(PYBIND11_NAMESPACE)                                                  \\\n    namespace detail {                                                                            \\\n    template <typename type>                                                                      \\\n    struct always_construct_holder<holder_type> : always_construct_holder<void, ##__VA_ARGS__> {  \\\n    };                                                                                            \\\n    template <typename type>                                                                      \\\n    class type_caster<holder_type, enable_if_t<!is_shared_ptr<holder_type>::value>>               \\\n        : public type_caster_holder<type, holder_type> {};                                        \\\n    }                                                                                             \\\n    PYBIND11_NAMESPACE_END(PYBIND11_NAMESPACE)\n\n// PYBIND11_DECLARE_HOLDER_TYPE holder types:\ntemplate <typename base, typename holder>\nstruct is_holder_type\n    : std::is_base_of<detail::type_caster_holder<base, holder>, detail::type_caster<holder>> {};\n// Specialization for always-supported unique_ptr holders:\ntemplate <typename base, typename deleter>\nstruct is_holder_type<base, std::unique_ptr<base, deleter>> : std::true_type {};\n\n#ifdef PYBIND11_DISABLE_HANDLE_TYPE_NAME_DEFAULT_IMPLEMENTATION // See PR #4888\n\n// This leads to compilation errors if a specialization is missing.\ntemplate <typename T>\nstruct handle_type_name;\n\n#else\n\ntemplate <typename T>\nstruct handle_type_name {\n    static constexpr auto name = const_name<T>();\n};\n\n#endif\n\ntemplate <>\nstruct handle_type_name<object> {\n    static constexpr auto name = const_name(\"object\");\n};\ntemplate <>\nstruct handle_type_name<list> {\n    static constexpr auto name = const_name(\"list\");\n};\ntemplate <>\nstruct handle_type_name<dict> {\n    static constexpr auto name = const_name(\"dict\");\n};\ntemplate <>\nstruct handle_type_name<anyset> {\n    static constexpr auto name = const_name(\"Union[set, frozenset]\");\n};\ntemplate <>\nstruct handle_type_name<set> {\n    static constexpr auto name = const_name(\"set\");\n};\ntemplate <>\nstruct handle_type_name<frozenset> {\n    static constexpr auto name = const_name(\"frozenset\");\n};\ntemplate <>\nstruct handle_type_name<str> {\n    static constexpr auto name = const_name(\"str\");\n};\ntemplate <>\nstruct handle_type_name<tuple> {\n    static constexpr auto name = const_name(\"tuple\");\n};\ntemplate <>\nstruct handle_type_name<bool_> {\n    static constexpr auto name = const_name(\"bool\");\n};\ntemplate <>\nstruct handle_type_name<bytes> {\n    static constexpr auto name = const_name(PYBIND11_BYTES_NAME);\n};\ntemplate <>\nstruct handle_type_name<buffer> {\n    static constexpr auto name = const_name(\"Buffer\");\n};\ntemplate <>\nstruct handle_type_name<int_> {\n    static constexpr auto name = const_name(\"int\");\n};\ntemplate <>\nstruct handle_type_name<iterable> {\n    static constexpr auto name = const_name(\"Iterable\");\n};\ntemplate <>\nstruct handle_type_name<iterator> {\n    static constexpr auto name = const_name(\"Iterator\");\n};\ntemplate <>\nstruct handle_type_name<float_> {\n    static constexpr auto name = const_name(\"float\");\n};\ntemplate <>\nstruct handle_type_name<function> {\n    static constexpr auto name = const_name(\"Callable\");\n};\ntemplate <>\nstruct handle_type_name<handle> {\n    static constexpr auto name = handle_type_name<object>::name;\n};\ntemplate <>\nstruct handle_type_name<none> {\n    static constexpr auto name = const_name(\"None\");\n};\ntemplate <>\nstruct handle_type_name<sequence> {\n    static constexpr auto name = const_name(\"Sequence\");\n};\ntemplate <>\nstruct handle_type_name<bytearray> {\n    static constexpr auto name = const_name(\"bytearray\");\n};\ntemplate <>\nstruct handle_type_name<memoryview> {\n    static constexpr auto name = const_name(\"memoryview\");\n};\ntemplate <>\nstruct handle_type_name<slice> {\n    static constexpr auto name = const_name(\"slice\");\n};\ntemplate <>\nstruct handle_type_name<type> {\n    static constexpr auto name = const_name(\"type\");\n};\ntemplate <>\nstruct handle_type_name<capsule> {\n    static constexpr auto name = const_name(\"capsule\");\n};\ntemplate <>\nstruct handle_type_name<ellipsis> {\n    static constexpr auto name = const_name(\"ellipsis\");\n};\ntemplate <>\nstruct handle_type_name<weakref> {\n    static constexpr auto name = const_name(\"weakref\");\n};\ntemplate <>\nstruct handle_type_name<args> {\n    static constexpr auto name = const_name(\"*args\");\n};\ntemplate <>\nstruct handle_type_name<kwargs> {\n    static constexpr auto name = const_name(\"**kwargs\");\n};\ntemplate <>\nstruct handle_type_name<obj_attr_accessor> {\n    static constexpr auto name = const_name<obj_attr_accessor>();\n};\ntemplate <>\nstruct handle_type_name<str_attr_accessor> {\n    static constexpr auto name = const_name<str_attr_accessor>();\n};\ntemplate <>\nstruct handle_type_name<item_accessor> {\n    static constexpr auto name = const_name<item_accessor>();\n};\ntemplate <>\nstruct handle_type_name<sequence_accessor> {\n    static constexpr auto name = const_name<sequence_accessor>();\n};\ntemplate <>\nstruct handle_type_name<list_accessor> {\n    static constexpr auto name = const_name<list_accessor>();\n};\ntemplate <>\nstruct handle_type_name<tuple_accessor> {\n    static constexpr auto name = const_name<tuple_accessor>();\n};\n\ntemplate <typename type>\nstruct pyobject_caster {\n    template <typename T = type, enable_if_t<std::is_same<T, handle>::value, int> = 0>\n    pyobject_caster() : value() {}\n\n    // `type` may not be default constructible (e.g. frozenset, anyset).  Initializing `value`\n    // to a nil handle is safe since it will only be accessed if `load` succeeds.\n    template <typename T = type, enable_if_t<std::is_base_of<object, T>::value, int> = 0>\n    pyobject_caster() : value(reinterpret_steal<type>(handle())) {}\n\n    template <typename T = type, enable_if_t<std::is_same<T, handle>::value, int> = 0>\n    bool load(handle src, bool /* convert */) {\n        value = src;\n        return static_cast<bool>(value);\n    }\n\n    template <typename T = type, enable_if_t<std::is_base_of<object, T>::value, int> = 0>\n    bool load(handle src, bool /* convert */) {\n        if (!isinstance<type>(src)) {\n            return false;\n        }\n        value = reinterpret_borrow<type>(src);\n        return true;\n    }\n\n    static handle cast(const handle &src, return_value_policy /* policy */, handle /* parent */) {\n        return src.inc_ref();\n    }\n    PYBIND11_TYPE_CASTER(type, handle_type_name<type>::name);\n};\n\ntemplate <typename T>\nclass type_caster<T, enable_if_t<is_pyobject<T>::value>> : public pyobject_caster<T> {};\n\n// Our conditions for enabling moving are quite restrictive:\n// At compile time:\n// - T needs to be a non-const, non-pointer, non-reference type\n// - type_caster<T>::operator T&() must exist\n// - the type must be move constructible (obviously)\n// At run-time:\n// - if the type is non-copy-constructible, the object must be the sole owner of the type (i.e. it\n//   must have ref_count() == 1)h\n// If any of the above are not satisfied, we fall back to copying.\ntemplate <typename T>\nusing move_is_plain_type\n    = satisfies_none_of<T, std::is_void, std::is_pointer, std::is_reference, std::is_const>;\ntemplate <typename T, typename SFINAE = void>\nstruct move_always : std::false_type {};\ntemplate <typename T>\nstruct move_always<\n    T,\n    enable_if_t<\n        all_of<move_is_plain_type<T>,\n               negation<is_copy_constructible<T>>,\n               is_move_constructible<T>,\n               std::is_same<decltype(std::declval<make_caster<T>>().operator T &()), T &>>::value>>\n    : std::true_type {};\ntemplate <typename T, typename SFINAE = void>\nstruct move_if_unreferenced : std::false_type {};\ntemplate <typename T>\nstruct move_if_unreferenced<\n    T,\n    enable_if_t<\n        all_of<move_is_plain_type<T>,\n               negation<move_always<T>>,\n               is_move_constructible<T>,\n               std::is_same<decltype(std::declval<make_caster<T>>().operator T &()), T &>>::value>>\n    : std::true_type {};\ntemplate <typename T>\nusing move_never = none_of<move_always<T>, move_if_unreferenced<T>>;\n\n// Detect whether returning a `type` from a cast on type's type_caster is going to result in a\n// reference or pointer to a local variable of the type_caster.  Basically, only\n// non-reference/pointer `type`s and reference/pointers from a type_caster_generic are safe;\n// everything else returns a reference/pointer to a local variable.\ntemplate <typename type>\nusing cast_is_temporary_value_reference\n    = bool_constant<(std::is_reference<type>::value || std::is_pointer<type>::value)\n                    && !std::is_base_of<type_caster_generic, make_caster<type>>::value\n                    && !std::is_same<intrinsic_t<type>, void>::value>;\n\n// When a value returned from a C++ function is being cast back to Python, we almost always want to\n// force `policy = move`, regardless of the return value policy the function/method was declared\n// with.\ntemplate <typename Return, typename SFINAE = void>\nstruct return_value_policy_override {\n    static return_value_policy policy(return_value_policy p) { return p; }\n};\n\ntemplate <typename Return>\nstruct return_value_policy_override<\n    Return,\n    detail::enable_if_t<std::is_base_of<type_caster_generic, make_caster<Return>>::value, void>> {\n    static return_value_policy policy(return_value_policy p) {\n        return !std::is_lvalue_reference<Return>::value && !std::is_pointer<Return>::value\n                   ? return_value_policy::move\n                   : p;\n    }\n};\n\n// Basic python -> C++ casting; throws if casting fails\ntemplate <typename T, typename SFINAE>\ntype_caster<T, SFINAE> &load_type(type_caster<T, SFINAE> &conv, const handle &handle) {\n    static_assert(!detail::is_pyobject<T>::value,\n                  \"Internal error: type_caster should only be used for C++ types\");\n    if (!conv.load(handle, true)) {\n#if !defined(PYBIND11_DETAILED_ERROR_MESSAGES)\n        throw cast_error(\n            \"Unable to cast Python instance of type \"\n            + str(type::handle_of(handle)).cast<std::string>()\n            + \" to C++ type '?' (#define \"\n              \"PYBIND11_DETAILED_ERROR_MESSAGES or compile in debug mode for details)\");\n#else\n        throw cast_error(\"Unable to cast Python instance of type \"\n                         + str(type::handle_of(handle)).cast<std::string>() + \" to C++ type '\"\n                         + type_id<T>() + \"'\");\n#endif\n    }\n    return conv;\n}\n// Wrapper around the above that also constructs and returns a type_caster\ntemplate <typename T>\nmake_caster<T> load_type(const handle &handle) {\n    make_caster<T> conv;\n    load_type(conv, handle);\n    return conv;\n}\n\nPYBIND11_NAMESPACE_END(detail)\n\n// pytype -> C++ type\ntemplate <typename T,\n          detail::enable_if_t<!detail::is_pyobject<T>::value\n                                  && !detail::is_same_ignoring_cvref<T, PyObject *>::value,\n                              int>\n          = 0>\nT cast(const handle &handle) {\n    using namespace detail;\n    static_assert(!cast_is_temporary_value_reference<T>::value,\n                  \"Unable to cast type to reference: value is local to type caster\");\n    return cast_op<T>(load_type<T>(handle));\n}\n\n// pytype -> pytype (calls converting constructor)\ntemplate <typename T, detail::enable_if_t<detail::is_pyobject<T>::value, int> = 0>\nT cast(const handle &handle) {\n    return T(reinterpret_borrow<object>(handle));\n}\n\n// Note that `cast<PyObject *>(obj)` increments the reference count of `obj`.\n// This is necessary for the case that `obj` is a temporary, and could\n// not possibly be different, given\n// 1. the established convention that the passed `handle` is borrowed, and\n// 2. we don't want to force all generic code using `cast<T>()` to special-case\n//    handling of `T` = `PyObject *` (to increment the reference count there).\n// It is the responsibility of the caller to ensure that the reference count\n// is decremented.\ntemplate <typename T,\n          typename Handle,\n          detail::enable_if_t<detail::is_same_ignoring_cvref<T, PyObject *>::value\n                                  && detail::is_same_ignoring_cvref<Handle, handle>::value,\n                              int>\n          = 0>\nT cast(Handle &&handle) {\n    return handle.inc_ref().ptr();\n}\n// To optimize way an inc_ref/dec_ref cycle:\ntemplate <typename T,\n          typename Object,\n          detail::enable_if_t<detail::is_same_ignoring_cvref<T, PyObject *>::value\n                                  && detail::is_same_ignoring_cvref<Object, object>::value,\n                              int>\n          = 0>\nT cast(Object &&obj) {\n    return obj.release().ptr();\n}\n\n// C++ type -> py::object\ntemplate <typename T, detail::enable_if_t<!detail::is_pyobject<T>::value, int> = 0>\nobject cast(T &&value,\n            return_value_policy policy = return_value_policy::automatic_reference,\n            handle parent = handle()) {\n    using no_ref_T = typename std::remove_reference<T>::type;\n    if (policy == return_value_policy::automatic) {\n        policy = std::is_pointer<no_ref_T>::value     ? return_value_policy::take_ownership\n                 : std::is_lvalue_reference<T>::value ? return_value_policy::copy\n                                                      : return_value_policy::move;\n    } else if (policy == return_value_policy::automatic_reference) {\n        policy = std::is_pointer<no_ref_T>::value     ? return_value_policy::reference\n                 : std::is_lvalue_reference<T>::value ? return_value_policy::copy\n                                                      : return_value_policy::move;\n    }\n    return reinterpret_steal<object>(\n        detail::make_caster<T>::cast(std::forward<T>(value), policy, parent));\n}\n\ntemplate <typename T>\nT handle::cast() const {\n    return pybind11::cast<T>(*this);\n}\ntemplate <>\ninline void handle::cast() const {\n    return;\n}\n\ntemplate <typename T>\ndetail::enable_if_t<!detail::move_never<T>::value, T> move(object &&obj) {\n    if (obj.ref_count() > 1) {\n#if !defined(PYBIND11_DETAILED_ERROR_MESSAGES)\n        throw cast_error(\n            \"Unable to cast Python \" + str(type::handle_of(obj)).cast<std::string>()\n            + \" instance to C++ rvalue: instance has multiple references\"\n              \" (#define PYBIND11_DETAILED_ERROR_MESSAGES or compile in debug mode for details)\");\n#else\n        throw cast_error(\"Unable to move from Python \"\n                         + str(type::handle_of(obj)).cast<std::string>() + \" instance to C++ \"\n                         + type_id<T>() + \" instance: instance has multiple references\");\n#endif\n    }\n\n    // Move into a temporary and return that, because the reference may be a local value of `conv`\n    T ret = std::move(detail::load_type<T>(obj).operator T &());\n    return ret;\n}\n\n// Calling cast() on an rvalue calls pybind11::cast with the object rvalue, which does:\n// - If we have to move (because T has no copy constructor), do it.  This will fail if the moved\n//   object has multiple references, but trying to copy will fail to compile.\n// - If both movable and copyable, check ref count: if 1, move; otherwise copy\n// - Otherwise (not movable), copy.\ntemplate <typename T>\ndetail::enable_if_t<!detail::is_pyobject<T>::value && detail::move_always<T>::value, T>\ncast(object &&object) {\n    return move<T>(std::move(object));\n}\ntemplate <typename T>\ndetail::enable_if_t<!detail::is_pyobject<T>::value && detail::move_if_unreferenced<T>::value, T>\ncast(object &&object) {\n    if (object.ref_count() > 1) {\n        return cast<T>(object);\n    }\n    return move<T>(std::move(object));\n}\ntemplate <typename T>\ndetail::enable_if_t<!detail::is_pyobject<T>::value && detail::move_never<T>::value, T>\ncast(object &&object) {\n    return cast<T>(object);\n}\n\n// pytype rvalue -> pytype (calls converting constructor)\ntemplate <typename T>\ndetail::enable_if_t<detail::is_pyobject<T>::value, T> cast(object &&object) {\n    return T(std::move(object));\n}\n\ntemplate <typename T>\nT object::cast() const & {\n    return pybind11::cast<T>(*this);\n}\ntemplate <typename T>\nT object::cast() && {\n    return pybind11::cast<T>(std::move(*this));\n}\ntemplate <>\ninline void object::cast() const & {\n    return;\n}\ntemplate <>\ninline void object::cast() && {\n    return;\n}\n\nPYBIND11_NAMESPACE_BEGIN(detail)\n\n// Declared in pytypes.h:\ntemplate <typename T, enable_if_t<!is_pyobject<T>::value, int>>\nobject object_or_cast(T &&o) {\n    return pybind11::cast(std::forward<T>(o));\n}\n\n// Placeholder type for the unneeded (and dead code) static variable in the\n// PYBIND11_OVERRIDE_OVERRIDE macro\nstruct override_unused {};\ntemplate <typename ret_type>\nusing override_caster_t = conditional_t<cast_is_temporary_value_reference<ret_type>::value,\n                                        make_caster<ret_type>,\n                                        override_unused>;\n\n// Trampoline use: for reference/pointer types to value-converted values, we do a value cast, then\n// store the result in the given variable.  For other types, this is a no-op.\ntemplate <typename T>\nenable_if_t<cast_is_temporary_value_reference<T>::value, T> cast_ref(object &&o,\n                                                                     make_caster<T> &caster) {\n    return cast_op<T>(load_type(caster, o));\n}\ntemplate <typename T>\nenable_if_t<!cast_is_temporary_value_reference<T>::value, T> cast_ref(object &&,\n                                                                      override_unused &) {\n    pybind11_fail(\"Internal error: cast_ref fallback invoked\");\n}\n\n// Trampoline use: Having a pybind11::cast with an invalid reference type is going to\n// static_assert, even though if it's in dead code, so we provide a \"trampoline\" to pybind11::cast\n// that only does anything in cases where pybind11::cast is valid.\ntemplate <typename T>\nenable_if_t<cast_is_temporary_value_reference<T>::value\n                && !detail::is_same_ignoring_cvref<T, PyObject *>::value,\n            T>\ncast_safe(object &&) {\n    pybind11_fail(\"Internal error: cast_safe fallback invoked\");\n}\ntemplate <typename T>\nenable_if_t<std::is_void<T>::value, void> cast_safe(object &&) {}\ntemplate <typename T>\nenable_if_t<detail::is_same_ignoring_cvref<T, PyObject *>::value, PyObject *>\ncast_safe(object &&o) {\n    return o.release().ptr();\n}\ntemplate <typename T>\nenable_if_t<detail::none_of<cast_is_temporary_value_reference<T>,\n                            detail::is_same_ignoring_cvref<T, PyObject *>,\n                            std::is_void<T>>::value,\n            T>\ncast_safe(object &&o) {\n    return pybind11::cast<T>(std::move(o));\n}\n\nPYBIND11_NAMESPACE_END(detail)\n\n// The overloads could coexist, i.e. the #if is not strictly speaking needed,\n// but it is an easy minor optimization.\n#if !defined(PYBIND11_DETAILED_ERROR_MESSAGES)\ninline cast_error cast_error_unable_to_convert_call_arg(const std::string &name) {\n    return cast_error(\"Unable to convert call argument '\" + name\n                      + \"' to Python object (#define \"\n                        \"PYBIND11_DETAILED_ERROR_MESSAGES or compile in debug mode for details)\");\n}\n#else\ninline cast_error cast_error_unable_to_convert_call_arg(const std::string &name,\n                                                        const std::string &type) {\n    return cast_error(\"Unable to convert call argument '\" + name + \"' of type '\" + type\n                      + \"' to Python object\");\n}\n#endif\n\ntemplate <return_value_policy policy = return_value_policy::automatic_reference>\ntuple make_tuple() {\n    return tuple(0);\n}\n\ntemplate <return_value_policy policy = return_value_policy::automatic_reference, typename... Args>\ntuple make_tuple(Args &&...args_) {\n    constexpr size_t size = sizeof...(Args);\n    std::array<object, size> args{{reinterpret_steal<object>(\n        detail::make_caster<Args>::cast(std::forward<Args>(args_), policy, nullptr))...}};\n    for (size_t i = 0; i < args.size(); i++) {\n        if (!args[i]) {\n#if !defined(PYBIND11_DETAILED_ERROR_MESSAGES)\n            throw cast_error_unable_to_convert_call_arg(std::to_string(i));\n#else\n            std::array<std::string, size> argtypes{{type_id<Args>()...}};\n            throw cast_error_unable_to_convert_call_arg(std::to_string(i), argtypes[i]);\n#endif\n        }\n    }\n    tuple result(size);\n    int counter = 0;\n    for (auto &arg_value : args) {\n        PyTuple_SET_ITEM(result.ptr(), counter++, arg_value.release().ptr());\n    }\n    return result;\n}\n\n/// \\ingroup annotations\n/// Annotation for arguments\nstruct arg {\n    /// Constructs an argument with the name of the argument; if null or omitted, this is a\n    /// positional argument.\n    constexpr explicit arg(const char *name = nullptr)\n        : name(name), flag_noconvert(false), flag_none(true) {}\n    /// Assign a value to this argument\n    template <typename T>\n    arg_v operator=(T &&value) const;\n    /// Indicate that the type should not be converted in the type caster\n    arg &noconvert(bool flag = true) {\n        flag_noconvert = flag;\n        return *this;\n    }\n    /// Indicates that the argument should/shouldn't allow None (e.g. for nullable pointer args)\n    arg &none(bool flag = true) {\n        flag_none = flag;\n        return *this;\n    }\n\n    const char *name;        ///< If non-null, this is a named kwargs argument\n    bool flag_noconvert : 1; ///< If set, do not allow conversion (requires a supporting type\n                             ///< caster!)\n    bool flag_none : 1;      ///< If set (the default), allow None to be passed to this argument\n};\n\n/// \\ingroup annotations\n/// Annotation for arguments with values\nstruct arg_v : arg {\nprivate:\n    template <typename T>\n    arg_v(arg &&base, T &&x, const char *descr = nullptr)\n        : arg(base), value(reinterpret_steal<object>(detail::make_caster<T>::cast(\n                         std::forward<T>(x), return_value_policy::automatic, {}))),\n          descr(descr)\n#if defined(PYBIND11_DETAILED_ERROR_MESSAGES)\n          ,\n          type(type_id<T>())\n#endif\n    {\n        // Workaround! See:\n        // https://github.com/pybind/pybind11/issues/2336\n        // https://github.com/pybind/pybind11/pull/2685#issuecomment-731286700\n        if (PyErr_Occurred()) {\n            PyErr_Clear();\n        }\n    }\n\npublic:\n    /// Direct construction with name, default, and description\n    template <typename T>\n    arg_v(const char *name, T &&x, const char *descr = nullptr)\n        : arg_v(arg(name), std::forward<T>(x), descr) {}\n\n    /// Called internally when invoking `py::arg(\"a\") = value`\n    template <typename T>\n    arg_v(const arg &base, T &&x, const char *descr = nullptr)\n        : arg_v(arg(base), std::forward<T>(x), descr) {}\n\n    /// Same as `arg::noconvert()`, but returns *this as arg_v&, not arg&\n    arg_v &noconvert(bool flag = true) {\n        arg::noconvert(flag);\n        return *this;\n    }\n\n    /// Same as `arg::nonone()`, but returns *this as arg_v&, not arg&\n    arg_v &none(bool flag = true) {\n        arg::none(flag);\n        return *this;\n    }\n\n    /// The default value\n    object value;\n    /// The (optional) description of the default value\n    const char *descr;\n#if defined(PYBIND11_DETAILED_ERROR_MESSAGES)\n    /// The C++ type name of the default value (only available when compiled in debug mode)\n    std::string type;\n#endif\n};\n\n/// \\ingroup annotations\n/// Annotation indicating that all following arguments are keyword-only; the is the equivalent of\n/// an unnamed '*' argument\nstruct kw_only {};\n\n/// \\ingroup annotations\n/// Annotation indicating that all previous arguments are positional-only; the is the equivalent of\n/// an unnamed '/' argument (in Python 3.8)\nstruct pos_only {};\n\ntemplate <typename T>\narg_v arg::operator=(T &&value) const {\n    return {*this, std::forward<T>(value)};\n}\n\n/// Alias for backward compatibility -- to be removed in version 2.0\ntemplate <typename /*unused*/>\nusing arg_t = arg_v;\n\ninline namespace literals {\n/** \\rst\n    String literal version of `arg`\n \\endrst */\nconstexpr arg\n#if !defined(__clang__) && defined(__GNUC__) && __GNUC__ < 5\noperator\"\" _a // gcc 4.8.5 insists on having a space (hard error).\n#else\noperator\"\"_a // clang 17 generates a deprecation warning if there is a space.\n#endif\n    (const char *name, size_t) {\n    return arg(name);\n}\n} // namespace literals\n\nPYBIND11_NAMESPACE_BEGIN(detail)\n\ntemplate <typename T>\nusing is_kw_only = std::is_same<intrinsic_t<T>, kw_only>;\ntemplate <typename T>\nusing is_pos_only = std::is_same<intrinsic_t<T>, pos_only>;\n\n// forward declaration (definition in attr.h)\nstruct function_record;\n\n/// Internal data associated with a single function call\nstruct function_call {\n    function_call(const function_record &f, handle p); // Implementation in attr.h\n\n    /// The function data:\n    const function_record &func;\n\n    /// Arguments passed to the function:\n    std::vector<handle> args;\n\n    /// The `convert` value the arguments should be loaded with\n    std::vector<bool> args_convert;\n\n    /// Extra references for the optional `py::args` and/or `py::kwargs` arguments (which, if\n    /// present, are also in `args` but without a reference).\n    object args_ref, kwargs_ref;\n\n    /// The parent, if any\n    handle parent;\n\n    /// If this is a call to an initializer, this argument contains `self`\n    handle init_self;\n};\n\n/// Helper class which loads arguments for C++ functions called from Python\ntemplate <typename... Args>\nclass argument_loader {\n    using indices = make_index_sequence<sizeof...(Args)>;\n\n    template <typename Arg>\n    using argument_is_args = std::is_same<intrinsic_t<Arg>, args>;\n    template <typename Arg>\n    using argument_is_kwargs = std::is_same<intrinsic_t<Arg>, kwargs>;\n    // Get kwargs argument position, or -1 if not present:\n    static constexpr auto kwargs_pos = constexpr_last<argument_is_kwargs, Args...>();\n\n    static_assert(kwargs_pos == -1 || kwargs_pos == (int) sizeof...(Args) - 1,\n                  \"py::kwargs is only permitted as the last argument of a function\");\n\npublic:\n    static constexpr bool has_kwargs = kwargs_pos != -1;\n\n    // py::args argument position; -1 if not present.\n    static constexpr int args_pos = constexpr_last<argument_is_args, Args...>();\n\n    static_assert(args_pos == -1 || args_pos == constexpr_first<argument_is_args, Args...>(),\n                  \"py::args cannot be specified more than once\");\n\n    static constexpr auto arg_names\n        = ::pybind11::detail::concat(type_descr(make_caster<Args>::name)...);\n\n    bool load_args(function_call &call) { return load_impl_sequence(call, indices{}); }\n\n    template <typename Return, typename Guard, typename Func>\n    // NOLINTNEXTLINE(readability-const-return-type)\n    enable_if_t<!std::is_void<Return>::value, Return> call(Func &&f) && {\n        return std::move(*this).template call_impl<remove_cv_t<Return>>(\n            std::forward<Func>(f), indices{}, Guard{});\n    }\n\n    template <typename Return, typename Guard, typename Func>\n    enable_if_t<std::is_void<Return>::value, void_type> call(Func &&f) && {\n        std::move(*this).template call_impl<remove_cv_t<Return>>(\n            std::forward<Func>(f), indices{}, Guard{});\n        return void_type();\n    }\n\nprivate:\n    static bool load_impl_sequence(function_call &, index_sequence<>) { return true; }\n\n    template <size_t... Is>\n    bool load_impl_sequence(function_call &call, index_sequence<Is...>) {\n#ifdef __cpp_fold_expressions\n        if ((... || !std::get<Is>(argcasters).load(call.args[Is], call.args_convert[Is]))) {\n            return false;\n        }\n#else\n        for (bool r : {std::get<Is>(argcasters).load(call.args[Is], call.args_convert[Is])...}) {\n            if (!r) {\n                return false;\n            }\n        }\n#endif\n        return true;\n    }\n\n    template <typename Return, typename Func, size_t... Is, typename Guard>\n    Return call_impl(Func &&f, index_sequence<Is...>, Guard &&) && {\n        return std::forward<Func>(f)(cast_op<Args>(std::move(std::get<Is>(argcasters)))...);\n    }\n\n    std::tuple<make_caster<Args>...> argcasters;\n};\n\n/// Helper class which collects only positional arguments for a Python function call.\n/// A fancier version below can collect any argument, but this one is optimal for simple calls.\ntemplate <return_value_policy policy>\nclass simple_collector {\npublic:\n    template <typename... Ts>\n    explicit simple_collector(Ts &&...values)\n        : m_args(pybind11::make_tuple<policy>(std::forward<Ts>(values)...)) {}\n\n    const tuple &args() const & { return m_args; }\n    dict kwargs() const { return {}; }\n\n    tuple args() && { return std::move(m_args); }\n\n    /// Call a Python function and pass the collected arguments\n    object call(PyObject *ptr) const {\n        PyObject *result = PyObject_CallObject(ptr, m_args.ptr());\n        if (!result) {\n            throw error_already_set();\n        }\n        return reinterpret_steal<object>(result);\n    }\n\nprivate:\n    tuple m_args;\n};\n\n/// Helper class which collects positional, keyword, * and ** arguments for a Python function call\ntemplate <return_value_policy policy>\nclass unpacking_collector {\npublic:\n    template <typename... Ts>\n    explicit unpacking_collector(Ts &&...values) {\n        // Tuples aren't (easily) resizable so a list is needed for collection,\n        // but the actual function call strictly requires a tuple.\n        auto args_list = list();\n        using expander = int[];\n        (void) expander{0, (process(args_list, std::forward<Ts>(values)), 0)...};\n\n        m_args = std::move(args_list);\n    }\n\n    const tuple &args() const & { return m_args; }\n    const dict &kwargs() const & { return m_kwargs; }\n\n    tuple args() && { return std::move(m_args); }\n    dict kwargs() && { return std::move(m_kwargs); }\n\n    /// Call a Python function and pass the collected arguments\n    object call(PyObject *ptr) const {\n        PyObject *result = PyObject_Call(ptr, m_args.ptr(), m_kwargs.ptr());\n        if (!result) {\n            throw error_already_set();\n        }\n        return reinterpret_steal<object>(result);\n    }\n\nprivate:\n    template <typename T>\n    void process(list &args_list, T &&x) {\n        auto o = reinterpret_steal<object>(\n            detail::make_caster<T>::cast(std::forward<T>(x), policy, {}));\n        if (!o) {\n#if !defined(PYBIND11_DETAILED_ERROR_MESSAGES)\n            throw cast_error_unable_to_convert_call_arg(std::to_string(args_list.size()));\n#else\n            throw cast_error_unable_to_convert_call_arg(std::to_string(args_list.size()),\n                                                        type_id<T>());\n#endif\n        }\n        args_list.append(std::move(o));\n    }\n\n    void process(list &args_list, detail::args_proxy ap) {\n        for (auto a : ap) {\n            args_list.append(a);\n        }\n    }\n\n    void process(list & /*args_list*/, arg_v a) {\n        if (!a.name) {\n#if !defined(PYBIND11_DETAILED_ERROR_MESSAGES)\n            nameless_argument_error();\n#else\n            nameless_argument_error(a.type);\n#endif\n        }\n        if (m_kwargs.contains(a.name)) {\n#if !defined(PYBIND11_DETAILED_ERROR_MESSAGES)\n            multiple_values_error();\n#else\n            multiple_values_error(a.name);\n#endif\n        }\n        if (!a.value) {\n#if !defined(PYBIND11_DETAILED_ERROR_MESSAGES)\n            throw cast_error_unable_to_convert_call_arg(a.name);\n#else\n            throw cast_error_unable_to_convert_call_arg(a.name, a.type);\n#endif\n        }\n        m_kwargs[a.name] = std::move(a.value);\n    }\n\n    void process(list & /*args_list*/, detail::kwargs_proxy kp) {\n        if (!kp) {\n            return;\n        }\n        for (auto k : reinterpret_borrow<dict>(kp)) {\n            if (m_kwargs.contains(k.first)) {\n#if !defined(PYBIND11_DETAILED_ERROR_MESSAGES)\n                multiple_values_error();\n#else\n                multiple_values_error(str(k.first));\n#endif\n            }\n            m_kwargs[k.first] = k.second;\n        }\n    }\n\n    [[noreturn]] static void nameless_argument_error() {\n        throw type_error(\n            \"Got kwargs without a name; only named arguments \"\n            \"may be passed via py::arg() to a python function call. \"\n            \"(#define PYBIND11_DETAILED_ERROR_MESSAGES or compile in debug mode for details)\");\n    }\n    [[noreturn]] static void nameless_argument_error(const std::string &type) {\n        throw type_error(\"Got kwargs without a name of type '\" + type\n                         + \"'; only named \"\n                           \"arguments may be passed via py::arg() to a python function call. \");\n    }\n    [[noreturn]] static void multiple_values_error() {\n        throw type_error(\n            \"Got multiple values for keyword argument \"\n            \"(#define PYBIND11_DETAILED_ERROR_MESSAGES or compile in debug mode for details)\");\n    }\n\n    [[noreturn]] static void multiple_values_error(const std::string &name) {\n        throw type_error(\"Got multiple values for keyword argument '\" + name + \"'\");\n    }\n\nprivate:\n    tuple m_args;\n    dict m_kwargs;\n};\n\n// [workaround(intel)] Separate function required here\n// We need to put this into a separate function because the Intel compiler\n// fails to compile enable_if_t<!all_of<is_positional<Args>...>::value>\n// (tested with ICC 2021.1 Beta 20200827).\ntemplate <typename... Args>\nconstexpr bool args_are_all_positional() {\n    return all_of<is_positional<Args>...>::value;\n}\n\n/// Collect only positional arguments for a Python function call\ntemplate <return_value_policy policy,\n          typename... Args,\n          typename = enable_if_t<args_are_all_positional<Args...>()>>\nsimple_collector<policy> collect_arguments(Args &&...args) {\n    return simple_collector<policy>(std::forward<Args>(args)...);\n}\n\n/// Collect all arguments, including keywords and unpacking (only instantiated when needed)\ntemplate <return_value_policy policy,\n          typename... Args,\n          typename = enable_if_t<!args_are_all_positional<Args...>()>>\nunpacking_collector<policy> collect_arguments(Args &&...args) {\n    // Following argument order rules for generalized unpacking according to PEP 448\n    static_assert(constexpr_last<is_positional, Args...>()\n                          < constexpr_first<is_keyword_or_ds, Args...>()\n                      && constexpr_last<is_s_unpacking, Args...>()\n                             < constexpr_first<is_ds_unpacking, Args...>(),\n                  \"Invalid function call: positional args must precede keywords and ** unpacking; \"\n                  \"* unpacking must precede ** unpacking\");\n    return unpacking_collector<policy>(std::forward<Args>(args)...);\n}\n\ntemplate <typename Derived>\ntemplate <return_value_policy policy, typename... Args>\nobject object_api<Derived>::operator()(Args &&...args) const {\n#ifndef NDEBUG\n    if (!PyGILState_Check()) {\n        pybind11_fail(\"pybind11::object_api<>::operator() PyGILState_Check() failure.\");\n    }\n#endif\n    return detail::collect_arguments<policy>(std::forward<Args>(args)...).call(derived().ptr());\n}\n\ntemplate <typename Derived>\ntemplate <return_value_policy policy, typename... Args>\nobject object_api<Derived>::call(Args &&...args) const {\n    return operator()<policy>(std::forward<Args>(args)...);\n}\n\nPYBIND11_NAMESPACE_END(detail)\n\ntemplate <typename T>\nhandle type::handle_of() {\n    static_assert(std::is_base_of<detail::type_caster_generic, detail::make_caster<T>>::value,\n                  \"py::type::of<T> only supports the case where T is a registered C++ types.\");\n\n    return detail::get_type_handle(typeid(T), true);\n}\n\n#define PYBIND11_MAKE_OPAQUE(...)                                                                 \\\n    PYBIND11_NAMESPACE_BEGIN(PYBIND11_NAMESPACE)                                                  \\\n    namespace detail {                                                                            \\\n    template <>                                                                                   \\\n    class type_caster<__VA_ARGS__> : public type_caster_base<__VA_ARGS__> {};                     \\\n    }                                                                                             \\\n    PYBIND11_NAMESPACE_END(PYBIND11_NAMESPACE)\n\n/// Lets you pass a type containing a `,` through a macro parameter without needing a separate\n/// typedef, e.g.:\n/// `PYBIND11_OVERRIDE(PYBIND11_TYPE(ReturnType<A, B>), PYBIND11_TYPE(Parent<C, D>), f, arg)`\n#define PYBIND11_TYPE(...) __VA_ARGS__\n\nPYBIND11_NAMESPACE_END(PYBIND11_NAMESPACE)\n"
  },
  {
    "path": "libs/pybind11/include/pybind11/chrono.h",
    "content": "/*\n    pybind11/chrono.h: Transparent conversion between std::chrono and python's datetime\n\n    Copyright (c) 2016 Trent Houliston <trent@houliston.me> and\n                       Wenzel Jakob <wenzel.jakob@epfl.ch>\n\n    All rights reserved. Use of this source code is governed by a\n    BSD-style license that can be found in the LICENSE file.\n*/\n\n#pragma once\n\n#include \"pybind11.h\"\n\n#include <chrono>\n#include <cmath>\n#include <ctime>\n#include <datetime.h>\n#include <mutex>\n\nPYBIND11_NAMESPACE_BEGIN(PYBIND11_NAMESPACE)\nPYBIND11_NAMESPACE_BEGIN(detail)\n\ntemplate <typename type>\nclass duration_caster {\npublic:\n    using rep = typename type::rep;\n    using period = typename type::period;\n\n    // signed 25 bits required by the standard.\n    using days = std::chrono::duration<int_least32_t, std::ratio<86400>>;\n\n    bool load(handle src, bool) {\n        using namespace std::chrono;\n\n        // Lazy initialise the PyDateTime import\n        if (!PyDateTimeAPI) {\n            PyDateTime_IMPORT;\n        }\n\n        if (!src) {\n            return false;\n        }\n        // If invoked with datetime.delta object\n        if (PyDelta_Check(src.ptr())) {\n            value = type(duration_cast<duration<rep, period>>(\n                days(PyDateTime_DELTA_GET_DAYS(src.ptr()))\n                + seconds(PyDateTime_DELTA_GET_SECONDS(src.ptr()))\n                + microseconds(PyDateTime_DELTA_GET_MICROSECONDS(src.ptr()))));\n            return true;\n        }\n        // If invoked with a float we assume it is seconds and convert\n        if (PyFloat_Check(src.ptr())) {\n            value = type(duration_cast<duration<rep, period>>(\n                duration<double>(PyFloat_AsDouble(src.ptr()))));\n            return true;\n        }\n        return false;\n    }\n\n    // If this is a duration just return it back\n    static const std::chrono::duration<rep, period> &\n    get_duration(const std::chrono::duration<rep, period> &src) {\n        return src;\n    }\n\n    // If this is a time_point get the time_since_epoch\n    template <typename Clock>\n    static std::chrono::duration<rep, period>\n    get_duration(const std::chrono::time_point<Clock, std::chrono::duration<rep, period>> &src) {\n        return src.time_since_epoch();\n    }\n\n    static handle cast(const type &src, return_value_policy /* policy */, handle /* parent */) {\n        using namespace std::chrono;\n\n        // Use overloaded function to get our duration from our source\n        // Works out if it is a duration or time_point and get the duration\n        auto d = get_duration(src);\n\n        // Lazy initialise the PyDateTime import\n        if (!PyDateTimeAPI) {\n            PyDateTime_IMPORT;\n        }\n\n        // Declare these special duration types so the conversions happen with the correct\n        // primitive types (int)\n        using dd_t = duration<int, std::ratio<86400>>;\n        using ss_t = duration<int, std::ratio<1>>;\n        using us_t = duration<int, std::micro>;\n\n        auto dd = duration_cast<dd_t>(d);\n        auto subd = d - dd;\n        auto ss = duration_cast<ss_t>(subd);\n        auto us = duration_cast<us_t>(subd - ss);\n        return PyDelta_FromDSU(dd.count(), ss.count(), us.count());\n    }\n\n    PYBIND11_TYPE_CASTER(type, const_name(\"datetime.timedelta\"));\n};\n\ninline std::tm *localtime_thread_safe(const std::time_t *time, std::tm *buf) {\n#if (defined(__STDC_LIB_EXT1__) && defined(__STDC_WANT_LIB_EXT1__)) || defined(_MSC_VER)\n    if (localtime_s(buf, time))\n        return nullptr;\n    return buf;\n#else\n    static std::mutex mtx;\n    std::lock_guard<std::mutex> lock(mtx);\n    std::tm *tm_ptr = std::localtime(time);\n    if (tm_ptr != nullptr) {\n        *buf = *tm_ptr;\n    }\n    return tm_ptr;\n#endif\n}\n\n// This is for casting times on the system clock into datetime.datetime instances\ntemplate <typename Duration>\nclass type_caster<std::chrono::time_point<std::chrono::system_clock, Duration>> {\npublic:\n    using type = std::chrono::time_point<std::chrono::system_clock, Duration>;\n    bool load(handle src, bool) {\n        using namespace std::chrono;\n\n        // Lazy initialise the PyDateTime import\n        if (!PyDateTimeAPI) {\n            PyDateTime_IMPORT;\n        }\n\n        if (!src) {\n            return false;\n        }\n\n        std::tm cal;\n        microseconds msecs;\n\n        if (PyDateTime_Check(src.ptr())) {\n            cal.tm_sec = PyDateTime_DATE_GET_SECOND(src.ptr());\n            cal.tm_min = PyDateTime_DATE_GET_MINUTE(src.ptr());\n            cal.tm_hour = PyDateTime_DATE_GET_HOUR(src.ptr());\n            cal.tm_mday = PyDateTime_GET_DAY(src.ptr());\n            cal.tm_mon = PyDateTime_GET_MONTH(src.ptr()) - 1;\n            cal.tm_year = PyDateTime_GET_YEAR(src.ptr()) - 1900;\n            cal.tm_isdst = -1;\n            msecs = microseconds(PyDateTime_DATE_GET_MICROSECOND(src.ptr()));\n        } else if (PyDate_Check(src.ptr())) {\n            cal.tm_sec = 0;\n            cal.tm_min = 0;\n            cal.tm_hour = 0;\n            cal.tm_mday = PyDateTime_GET_DAY(src.ptr());\n            cal.tm_mon = PyDateTime_GET_MONTH(src.ptr()) - 1;\n            cal.tm_year = PyDateTime_GET_YEAR(src.ptr()) - 1900;\n            cal.tm_isdst = -1;\n            msecs = microseconds(0);\n        } else if (PyTime_Check(src.ptr())) {\n            cal.tm_sec = PyDateTime_TIME_GET_SECOND(src.ptr());\n            cal.tm_min = PyDateTime_TIME_GET_MINUTE(src.ptr());\n            cal.tm_hour = PyDateTime_TIME_GET_HOUR(src.ptr());\n            cal.tm_mday = 1;  // This date (day, month, year) = (1, 0, 70)\n            cal.tm_mon = 0;   // represents 1-Jan-1970, which is the first\n            cal.tm_year = 70; // earliest available date for Python's datetime\n            cal.tm_isdst = -1;\n            msecs = microseconds(PyDateTime_TIME_GET_MICROSECOND(src.ptr()));\n        } else {\n            return false;\n        }\n\n        value = time_point_cast<Duration>(system_clock::from_time_t(std::mktime(&cal)) + msecs);\n        return true;\n    }\n\n    static handle cast(const std::chrono::time_point<std::chrono::system_clock, Duration> &src,\n                       return_value_policy /* policy */,\n                       handle /* parent */) {\n        using namespace std::chrono;\n\n        // Lazy initialise the PyDateTime import\n        if (!PyDateTimeAPI) {\n            PyDateTime_IMPORT;\n        }\n\n        // Get out microseconds, and make sure they are positive, to avoid bug in eastern\n        // hemisphere time zones (cfr. https://github.com/pybind/pybind11/issues/2417)\n        using us_t = duration<int, std::micro>;\n        auto us = duration_cast<us_t>(src.time_since_epoch() % seconds(1));\n        if (us.count() < 0) {\n            us += seconds(1);\n        }\n\n        // Subtract microseconds BEFORE `system_clock::to_time_t`, because:\n        // > If std::time_t has lower precision, it is implementation-defined whether the value is\n        // rounded or truncated. (https://en.cppreference.com/w/cpp/chrono/system_clock/to_time_t)\n        std::time_t tt\n            = system_clock::to_time_t(time_point_cast<system_clock::duration>(src - us));\n\n        std::tm localtime;\n        std::tm *localtime_ptr = localtime_thread_safe(&tt, &localtime);\n        if (!localtime_ptr) {\n            throw cast_error(\"Unable to represent system_clock in local time\");\n        }\n        return PyDateTime_FromDateAndTime(localtime.tm_year + 1900,\n                                          localtime.tm_mon + 1,\n                                          localtime.tm_mday,\n                                          localtime.tm_hour,\n                                          localtime.tm_min,\n                                          localtime.tm_sec,\n                                          us.count());\n    }\n    PYBIND11_TYPE_CASTER(type, const_name(\"datetime.datetime\"));\n};\n\n// Other clocks that are not the system clock are not measured as datetime.datetime objects\n// since they are not measured on calendar time. So instead we just make them timedeltas\n// Or if they have passed us a time as a float we convert that\ntemplate <typename Clock, typename Duration>\nclass type_caster<std::chrono::time_point<Clock, Duration>>\n    : public duration_caster<std::chrono::time_point<Clock, Duration>> {};\n\ntemplate <typename Rep, typename Period>\nclass type_caster<std::chrono::duration<Rep, Period>>\n    : public duration_caster<std::chrono::duration<Rep, Period>> {};\n\nPYBIND11_NAMESPACE_END(detail)\nPYBIND11_NAMESPACE_END(PYBIND11_NAMESPACE)\n"
  },
  {
    "path": "libs/pybind11/include/pybind11/common.h",
    "content": "#include \"detail/common.h\"\n#warning \"Including 'common.h' is deprecated. It will be removed in v3.0. Use 'pybind11.h'.\"\n"
  },
  {
    "path": "libs/pybind11/include/pybind11/complex.h",
    "content": "/*\n    pybind11/complex.h: Complex number support\n\n    Copyright (c) 2016 Wenzel Jakob <wenzel.jakob@epfl.ch>\n\n    All rights reserved. Use of this source code is governed by a\n    BSD-style license that can be found in the LICENSE file.\n*/\n\n#pragma once\n\n#include \"pybind11.h\"\n\n#include <complex>\n\n/// glibc defines I as a macro which breaks things, e.g., boost template names\n#ifdef I\n#    undef I\n#endif\n\nPYBIND11_NAMESPACE_BEGIN(PYBIND11_NAMESPACE)\n\ntemplate <typename T>\nstruct format_descriptor<std::complex<T>, detail::enable_if_t<std::is_floating_point<T>::value>> {\n    static constexpr const char c = format_descriptor<T>::c;\n    static constexpr const char value[3] = {'Z', c, '\\0'};\n    static std::string format() { return std::string(value); }\n};\n\n#ifndef PYBIND11_CPP17\n\ntemplate <typename T>\nconstexpr const char\n    format_descriptor<std::complex<T>,\n                      detail::enable_if_t<std::is_floating_point<T>::value>>::value[3];\n\n#endif\n\nPYBIND11_NAMESPACE_BEGIN(detail)\n\ntemplate <typename T>\nstruct is_fmt_numeric<std::complex<T>, detail::enable_if_t<std::is_floating_point<T>::value>> {\n    static constexpr bool value = true;\n    static constexpr int index = is_fmt_numeric<T>::index + 3;\n};\n\ntemplate <typename T>\nclass type_caster<std::complex<T>> {\npublic:\n    bool load(handle src, bool convert) {\n        if (!src) {\n            return false;\n        }\n        if (!convert && !PyComplex_Check(src.ptr())) {\n            return false;\n        }\n        Py_complex result = PyComplex_AsCComplex(src.ptr());\n        if (result.real == -1.0 && PyErr_Occurred()) {\n            PyErr_Clear();\n            return false;\n        }\n        value = std::complex<T>((T) result.real, (T) result.imag);\n        return true;\n    }\n\n    static handle\n    cast(const std::complex<T> &src, return_value_policy /* policy */, handle /* parent */) {\n        return PyComplex_FromDoubles((double) src.real(), (double) src.imag());\n    }\n\n    PYBIND11_TYPE_CASTER(std::complex<T>, const_name(\"complex\"));\n};\nPYBIND11_NAMESPACE_END(detail)\nPYBIND11_NAMESPACE_END(PYBIND11_NAMESPACE)\n"
  },
  {
    "path": "libs/pybind11/include/pybind11/detail/class.h",
    "content": "/*\n    pybind11/detail/class.h: Python C API implementation details for py::class_\n\n    Copyright (c) 2017 Wenzel Jakob <wenzel.jakob@epfl.ch>\n\n    All rights reserved. Use of this source code is governed by a\n    BSD-style license that can be found in the LICENSE file.\n*/\n\n#pragma once\n\n#include <pybind11/attr.h>\n#include <pybind11/options.h>\n\n#include \"exception_translation.h\"\n\nPYBIND11_NAMESPACE_BEGIN(PYBIND11_NAMESPACE)\nPYBIND11_NAMESPACE_BEGIN(detail)\n\n#if !defined(PYPY_VERSION)\n#    define PYBIND11_BUILTIN_QUALNAME\n#    define PYBIND11_SET_OLDPY_QUALNAME(obj, nameobj)\n#else\n// In PyPy, we still set __qualname__ so that we can produce reliable function type\n// signatures; in CPython this macro expands to nothing:\n#    define PYBIND11_SET_OLDPY_QUALNAME(obj, nameobj)                                             \\\n        setattr((PyObject *) obj, \"__qualname__\", nameobj)\n#endif\n\ninline std::string get_fully_qualified_tp_name(PyTypeObject *type) {\n#if !defined(PYPY_VERSION)\n    return type->tp_name;\n#else\n    auto module_name = handle((PyObject *) type).attr(\"__module__\").cast<std::string>();\n    if (module_name == PYBIND11_BUILTINS_MODULE)\n        return type->tp_name;\n    else\n        return std::move(module_name) + \".\" + type->tp_name;\n#endif\n}\n\ninline PyTypeObject *type_incref(PyTypeObject *type) {\n    Py_INCREF(type);\n    return type;\n}\n\n#if !defined(PYPY_VERSION)\n\n/// `pybind11_static_property.__get__()`: Always pass the class instead of the instance.\nextern \"C\" inline PyObject *pybind11_static_get(PyObject *self, PyObject * /*ob*/, PyObject *cls) {\n    return PyProperty_Type.tp_descr_get(self, cls, cls);\n}\n\n/// `pybind11_static_property.__set__()`: Just like the above `__get__()`.\nextern \"C\" inline int pybind11_static_set(PyObject *self, PyObject *obj, PyObject *value) {\n    PyObject *cls = PyType_Check(obj) ? obj : (PyObject *) Py_TYPE(obj);\n    return PyProperty_Type.tp_descr_set(self, cls, value);\n}\n\n// Forward declaration to use in `make_static_property_type()`\ninline void enable_dynamic_attributes(PyHeapTypeObject *heap_type);\n\n/** A `static_property` is the same as a `property` but the `__get__()` and `__set__()`\n    methods are modified to always use the object type instead of a concrete instance.\n    Return value: New reference. */\ninline PyTypeObject *make_static_property_type() {\n    constexpr auto *name = \"pybind11_static_property\";\n    auto name_obj = reinterpret_steal<object>(PYBIND11_FROM_STRING(name));\n\n    /* Danger zone: from now (and until PyType_Ready), make sure to\n       issue no Python C API calls which could potentially invoke the\n       garbage collector (the GC will call type_traverse(), which will in\n       turn find the newly constructed type in an invalid state) */\n    auto *heap_type = (PyHeapTypeObject *) PyType_Type.tp_alloc(&PyType_Type, 0);\n    if (!heap_type) {\n        pybind11_fail(\"make_static_property_type(): error allocating type!\");\n    }\n\n    heap_type->ht_name = name_obj.inc_ref().ptr();\n#    ifdef PYBIND11_BUILTIN_QUALNAME\n    heap_type->ht_qualname = name_obj.inc_ref().ptr();\n#    endif\n\n    auto *type = &heap_type->ht_type;\n    type->tp_name = name;\n    type->tp_base = type_incref(&PyProperty_Type);\n    type->tp_flags = Py_TPFLAGS_DEFAULT | Py_TPFLAGS_BASETYPE | Py_TPFLAGS_HEAPTYPE;\n    type->tp_descr_get = pybind11_static_get;\n    type->tp_descr_set = pybind11_static_set;\n\n#    if PY_VERSION_HEX >= 0x030C0000\n    // Since Python-3.12 property-derived types are required to\n    // have dynamic attributes (to set `__doc__`)\n    enable_dynamic_attributes(heap_type);\n#    endif\n\n    if (PyType_Ready(type) < 0) {\n        pybind11_fail(\"make_static_property_type(): failure in PyType_Ready()!\");\n    }\n\n    setattr((PyObject *) type, \"__module__\", str(\"pybind11_builtins\"));\n    PYBIND11_SET_OLDPY_QUALNAME(type, name_obj);\n\n    return type;\n}\n\n#else // PYPY\n\n/** PyPy has some issues with the above C API, so we evaluate Python code instead.\n    This function will only be called once so performance isn't really a concern.\n    Return value: New reference. */\ninline PyTypeObject *make_static_property_type() {\n    auto d = dict();\n    PyObject *result = PyRun_String(R\"(\\\nclass pybind11_static_property(property):\n    def __get__(self, obj, cls):\n        return property.__get__(self, cls, cls)\n\n    def __set__(self, obj, value):\n        cls = obj if isinstance(obj, type) else type(obj)\n        property.__set__(self, cls, value)\n)\",\n                                    Py_file_input,\n                                    d.ptr(),\n                                    d.ptr());\n    if (result == nullptr)\n        throw error_already_set();\n    Py_DECREF(result);\n    return (PyTypeObject *) d[\"pybind11_static_property\"].cast<object>().release().ptr();\n}\n\n#endif // PYPY\n\n/** Types with static properties need to handle `Type.static_prop = x` in a specific way.\n    By default, Python replaces the `static_property` itself, but for wrapped C++ types\n    we need to call `static_property.__set__()` in order to propagate the new value to\n    the underlying C++ data structure. */\nextern \"C\" inline int pybind11_meta_setattro(PyObject *obj, PyObject *name, PyObject *value) {\n    // Use `_PyType_Lookup()` instead of `PyObject_GetAttr()` in order to get the raw\n    // descriptor (`property`) instead of calling `tp_descr_get` (`property.__get__()`).\n    PyObject *descr = _PyType_Lookup((PyTypeObject *) obj, name);\n\n    // The following assignment combinations are possible:\n    //   1. `Type.static_prop = value`             --> descr_set: `Type.static_prop.__set__(value)`\n    //   2. `Type.static_prop = other_static_prop` --> setattro:  replace existing `static_prop`\n    //   3. `Type.regular_attribute = value`       --> setattro:  regular attribute assignment\n    auto *const static_prop = (PyObject *) get_internals().static_property_type;\n    const auto call_descr_set = (descr != nullptr) && (value != nullptr)\n                                && (PyObject_IsInstance(descr, static_prop) != 0)\n                                && (PyObject_IsInstance(value, static_prop) == 0);\n    if (call_descr_set) {\n        // Call `static_property.__set__()` instead of replacing the `static_property`.\n#if !defined(PYPY_VERSION)\n        return Py_TYPE(descr)->tp_descr_set(descr, obj, value);\n#else\n        if (PyObject *result = PyObject_CallMethod(descr, \"__set__\", \"OO\", obj, value)) {\n            Py_DECREF(result);\n            return 0;\n        } else {\n            return -1;\n        }\n#endif\n    } else {\n        // Replace existing attribute.\n        return PyType_Type.tp_setattro(obj, name, value);\n    }\n}\n\n/**\n * Python 3's PyInstanceMethod_Type hides itself via its tp_descr_get, which prevents aliasing\n * methods via cls.attr(\"m2\") = cls.attr(\"m1\"): instead the tp_descr_get returns a plain function,\n * when called on a class, or a PyMethod, when called on an instance.  Override that behaviour here\n * to do a special case bypass for PyInstanceMethod_Types.\n */\nextern \"C\" inline PyObject *pybind11_meta_getattro(PyObject *obj, PyObject *name) {\n    PyObject *descr = _PyType_Lookup((PyTypeObject *) obj, name);\n    if (descr && PyInstanceMethod_Check(descr)) {\n        Py_INCREF(descr);\n        return descr;\n    }\n    return PyType_Type.tp_getattro(obj, name);\n}\n\n/// metaclass `__call__` function that is used to create all pybind11 objects.\nextern \"C\" inline PyObject *pybind11_meta_call(PyObject *type, PyObject *args, PyObject *kwargs) {\n\n    // use the default metaclass call to create/initialize the object\n    PyObject *self = PyType_Type.tp_call(type, args, kwargs);\n    if (self == nullptr) {\n        return nullptr;\n    }\n\n    // Ensure that the base __init__ function(s) were called\n    values_and_holders vhs(self);\n    for (const auto &vh : vhs) {\n        if (!vh.holder_constructed() && !vhs.is_redundant_value_and_holder(vh)) {\n            PyErr_Format(PyExc_TypeError,\n                         \"%.200s.__init__() must be called when overriding __init__\",\n                         get_fully_qualified_tp_name(vh.type->type).c_str());\n            Py_DECREF(self);\n            return nullptr;\n        }\n    }\n\n    return self;\n}\n\n/// Cleanup the type-info for a pybind11-registered type.\nextern \"C\" inline void pybind11_meta_dealloc(PyObject *obj) {\n    with_internals([obj](internals &internals) {\n        auto *type = (PyTypeObject *) obj;\n\n        // A pybind11-registered type will:\n        // 1) be found in internals.registered_types_py\n        // 2) have exactly one associated `detail::type_info`\n        auto found_type = internals.registered_types_py.find(type);\n        if (found_type != internals.registered_types_py.end() && found_type->second.size() == 1\n            && found_type->second[0]->type == type) {\n\n            auto *tinfo = found_type->second[0];\n            auto tindex = std::type_index(*tinfo->cpptype);\n            internals.direct_conversions.erase(tindex);\n\n            if (tinfo->module_local) {\n                get_local_internals().registered_types_cpp.erase(tindex);\n            } else {\n                internals.registered_types_cpp.erase(tindex);\n            }\n            internals.registered_types_py.erase(tinfo->type);\n\n            // Actually just `std::erase_if`, but that's only available in C++20\n            auto &cache = internals.inactive_override_cache;\n            for (auto it = cache.begin(), last = cache.end(); it != last;) {\n                if (it->first == (PyObject *) tinfo->type) {\n                    it = cache.erase(it);\n                } else {\n                    ++it;\n                }\n            }\n\n            delete tinfo;\n        }\n    });\n\n    PyType_Type.tp_dealloc(obj);\n}\n\n/** This metaclass is assigned by default to all pybind11 types and is required in order\n    for static properties to function correctly. Users may override this using `py::metaclass`.\n    Return value: New reference. */\ninline PyTypeObject *make_default_metaclass() {\n    constexpr auto *name = \"pybind11_type\";\n    auto name_obj = reinterpret_steal<object>(PYBIND11_FROM_STRING(name));\n\n    /* Danger zone: from now (and until PyType_Ready), make sure to\n       issue no Python C API calls which could potentially invoke the\n       garbage collector (the GC will call type_traverse(), which will in\n       turn find the newly constructed type in an invalid state) */\n    auto *heap_type = (PyHeapTypeObject *) PyType_Type.tp_alloc(&PyType_Type, 0);\n    if (!heap_type) {\n        pybind11_fail(\"make_default_metaclass(): error allocating metaclass!\");\n    }\n\n    heap_type->ht_name = name_obj.inc_ref().ptr();\n#ifdef PYBIND11_BUILTIN_QUALNAME\n    heap_type->ht_qualname = name_obj.inc_ref().ptr();\n#endif\n\n    auto *type = &heap_type->ht_type;\n    type->tp_name = name;\n    type->tp_base = type_incref(&PyType_Type);\n    type->tp_flags = Py_TPFLAGS_DEFAULT | Py_TPFLAGS_BASETYPE | Py_TPFLAGS_HEAPTYPE;\n\n    type->tp_call = pybind11_meta_call;\n\n    type->tp_setattro = pybind11_meta_setattro;\n    type->tp_getattro = pybind11_meta_getattro;\n\n    type->tp_dealloc = pybind11_meta_dealloc;\n\n    if (PyType_Ready(type) < 0) {\n        pybind11_fail(\"make_default_metaclass(): failure in PyType_Ready()!\");\n    }\n\n    setattr((PyObject *) type, \"__module__\", str(\"pybind11_builtins\"));\n    PYBIND11_SET_OLDPY_QUALNAME(type, name_obj);\n\n    return type;\n}\n\n/// For multiple inheritance types we need to recursively register/deregister base pointers for any\n/// base classes with pointers that are difference from the instance value pointer so that we can\n/// correctly recognize an offset base class pointer. This calls a function with any offset base\n/// ptrs.\ninline void traverse_offset_bases(void *valueptr,\n                                  const detail::type_info *tinfo,\n                                  instance *self,\n                                  bool (*f)(void * /*parentptr*/, instance * /*self*/)) {\n    for (handle h : reinterpret_borrow<tuple>(tinfo->type->tp_bases)) {\n        if (auto *parent_tinfo = get_type_info((PyTypeObject *) h.ptr())) {\n            for (auto &c : parent_tinfo->implicit_casts) {\n                if (c.first == tinfo->cpptype) {\n                    auto *parentptr = c.second(valueptr);\n                    if (parentptr != valueptr) {\n                        f(parentptr, self);\n                    }\n                    traverse_offset_bases(parentptr, parent_tinfo, self, f);\n                    break;\n                }\n            }\n        }\n    }\n}\n\ninline bool register_instance_impl(void *ptr, instance *self) {\n    with_instance_map(ptr, [&](instance_map &instances) { instances.emplace(ptr, self); });\n    return true; // unused, but gives the same signature as the deregister func\n}\ninline bool deregister_instance_impl(void *ptr, instance *self) {\n    return with_instance_map(ptr, [&](instance_map &instances) {\n        auto range = instances.equal_range(ptr);\n        for (auto it = range.first; it != range.second; ++it) {\n            if (self == it->second) {\n                instances.erase(it);\n                return true;\n            }\n        }\n        return false;\n    });\n}\n\ninline void register_instance(instance *self, void *valptr, const type_info *tinfo) {\n    register_instance_impl(valptr, self);\n    if (!tinfo->simple_ancestors) {\n        traverse_offset_bases(valptr, tinfo, self, register_instance_impl);\n    }\n}\n\ninline bool deregister_instance(instance *self, void *valptr, const type_info *tinfo) {\n    bool ret = deregister_instance_impl(valptr, self);\n    if (!tinfo->simple_ancestors) {\n        traverse_offset_bases(valptr, tinfo, self, deregister_instance_impl);\n    }\n    return ret;\n}\n\n/// Instance creation function for all pybind11 types. It allocates the internal instance layout\n/// for holding C++ objects and holders.  Allocation is done lazily (the first time the instance is\n/// cast to a reference or pointer), and initialization is done by an `__init__` function.\ninline PyObject *make_new_instance(PyTypeObject *type) {\n#if defined(PYPY_VERSION)\n    // PyPy gets tp_basicsize wrong (issue 2482) under multiple inheritance when the first\n    // inherited object is a plain Python type (i.e. not derived from an extension type).  Fix it.\n    ssize_t instance_size = static_cast<ssize_t>(sizeof(instance));\n    if (type->tp_basicsize < instance_size) {\n        type->tp_basicsize = instance_size;\n    }\n#endif\n    PyObject *self = type->tp_alloc(type, 0);\n    auto *inst = reinterpret_cast<instance *>(self);\n    // Allocate the value/holder internals:\n    inst->allocate_layout();\n\n    return self;\n}\n\n/// Instance creation function for all pybind11 types. It only allocates space for the\n/// C++ object, but doesn't call the constructor -- an `__init__` function must do that.\nextern \"C\" inline PyObject *pybind11_object_new(PyTypeObject *type, PyObject *, PyObject *) {\n    return make_new_instance(type);\n}\n\n/// An `__init__` function constructs the C++ object. Users should provide at least one\n/// of these using `py::init` or directly with `.def(__init__, ...)`. Otherwise, the\n/// following default function will be used which simply throws an exception.\nextern \"C\" inline int pybind11_object_init(PyObject *self, PyObject *, PyObject *) {\n    PyTypeObject *type = Py_TYPE(self);\n    std::string msg = get_fully_qualified_tp_name(type) + \": No constructor defined!\";\n    set_error(PyExc_TypeError, msg.c_str());\n    return -1;\n}\n\ninline void add_patient(PyObject *nurse, PyObject *patient) {\n    auto *instance = reinterpret_cast<detail::instance *>(nurse);\n    instance->has_patients = true;\n    Py_INCREF(patient);\n\n    with_internals([&](internals &internals) { internals.patients[nurse].push_back(patient); });\n}\n\ninline void clear_patients(PyObject *self) {\n    auto *instance = reinterpret_cast<detail::instance *>(self);\n    std::vector<PyObject *> patients;\n\n    with_internals([&](internals &internals) {\n        auto pos = internals.patients.find(self);\n\n        if (pos == internals.patients.end()) {\n            pybind11_fail(\n                \"FATAL: Internal consistency check failed: Invalid clear_patients() call.\");\n        }\n\n        // Clearing the patients can cause more Python code to run, which\n        // can invalidate the iterator. Extract the vector of patients\n        // from the unordered_map first.\n        patients = std::move(pos->second);\n        internals.patients.erase(pos);\n    });\n\n    instance->has_patients = false;\n    for (PyObject *&patient : patients) {\n        Py_CLEAR(patient);\n    }\n}\n\n/// Clears all internal data from the instance and removes it from registered instances in\n/// preparation for deallocation.\ninline void clear_instance(PyObject *self) {\n    auto *instance = reinterpret_cast<detail::instance *>(self);\n\n    // Deallocate any values/holders, if present:\n    for (auto &v_h : values_and_holders(instance)) {\n        if (v_h) {\n\n            // We have to deregister before we call dealloc because, for virtual MI types, we still\n            // need to be able to get the parent pointers.\n            if (v_h.instance_registered()\n                && !deregister_instance(instance, v_h.value_ptr(), v_h.type)) {\n                pybind11_fail(\n                    \"pybind11_object_dealloc(): Tried to deallocate unregistered instance!\");\n            }\n\n            if (instance->owned || v_h.holder_constructed()) {\n                v_h.type->dealloc(v_h);\n            }\n        }\n    }\n    // Deallocate the value/holder layout internals:\n    instance->deallocate_layout();\n\n    if (instance->weakrefs) {\n        PyObject_ClearWeakRefs(self);\n    }\n\n    PyObject **dict_ptr = _PyObject_GetDictPtr(self);\n    if (dict_ptr) {\n        Py_CLEAR(*dict_ptr);\n    }\n\n    if (instance->has_patients) {\n        clear_patients(self);\n    }\n}\n\n/// Instance destructor function for all pybind11 types. It calls `type_info.dealloc`\n/// to destroy the C++ object itself, while the rest is Python bookkeeping.\nextern \"C\" inline void pybind11_object_dealloc(PyObject *self) {\n    auto *type = Py_TYPE(self);\n\n    // If this is a GC tracked object, untrack it first\n    // Note that the track call is implicitly done by the\n    // default tp_alloc, which we never override.\n    if (PyType_HasFeature(type, Py_TPFLAGS_HAVE_GC) != 0) {\n        PyObject_GC_UnTrack(self);\n    }\n\n    clear_instance(self);\n\n    type->tp_free(self);\n\n#if PY_VERSION_HEX < 0x03080000\n    // `type->tp_dealloc != pybind11_object_dealloc` means that we're being called\n    // as part of a derived type's dealloc, in which case we're not allowed to decref\n    // the type here. For cross-module compatibility, we shouldn't compare directly\n    // with `pybind11_object_dealloc`, but with the common one stashed in internals.\n    auto pybind11_object_type = (PyTypeObject *) get_internals().instance_base;\n    if (type->tp_dealloc == pybind11_object_type->tp_dealloc)\n        Py_DECREF(type);\n#else\n    // This was not needed before Python 3.8 (Python issue 35810)\n    // https://github.com/pybind/pybind11/issues/1946\n    Py_DECREF(type);\n#endif\n}\n\nstd::string error_string();\n\n/** Create the type which can be used as a common base for all classes.  This is\n    needed in order to satisfy Python's requirements for multiple inheritance.\n    Return value: New reference. */\ninline PyObject *make_object_base_type(PyTypeObject *metaclass) {\n    constexpr auto *name = \"pybind11_object\";\n    auto name_obj = reinterpret_steal<object>(PYBIND11_FROM_STRING(name));\n\n    /* Danger zone: from now (and until PyType_Ready), make sure to\n       issue no Python C API calls which could potentially invoke the\n       garbage collector (the GC will call type_traverse(), which will in\n       turn find the newly constructed type in an invalid state) */\n    auto *heap_type = (PyHeapTypeObject *) metaclass->tp_alloc(metaclass, 0);\n    if (!heap_type) {\n        pybind11_fail(\"make_object_base_type(): error allocating type!\");\n    }\n\n    heap_type->ht_name = name_obj.inc_ref().ptr();\n#ifdef PYBIND11_BUILTIN_QUALNAME\n    heap_type->ht_qualname = name_obj.inc_ref().ptr();\n#endif\n\n    auto *type = &heap_type->ht_type;\n    type->tp_name = name;\n    type->tp_base = type_incref(&PyBaseObject_Type);\n    type->tp_basicsize = static_cast<ssize_t>(sizeof(instance));\n    type->tp_flags = Py_TPFLAGS_DEFAULT | Py_TPFLAGS_BASETYPE | Py_TPFLAGS_HEAPTYPE;\n\n    type->tp_new = pybind11_object_new;\n    type->tp_init = pybind11_object_init;\n    type->tp_dealloc = pybind11_object_dealloc;\n\n    /* Support weak references (needed for the keep_alive feature) */\n    type->tp_weaklistoffset = offsetof(instance, weakrefs);\n\n    if (PyType_Ready(type) < 0) {\n        pybind11_fail(\"PyType_Ready failed in make_object_base_type(): \" + error_string());\n    }\n\n    setattr((PyObject *) type, \"__module__\", str(\"pybind11_builtins\"));\n    PYBIND11_SET_OLDPY_QUALNAME(type, name_obj);\n\n    assert(!PyType_HasFeature(type, Py_TPFLAGS_HAVE_GC));\n    return (PyObject *) heap_type;\n}\n\n/// dynamic_attr: Allow the garbage collector to traverse the internal instance `__dict__`.\nextern \"C\" inline int pybind11_traverse(PyObject *self, visitproc visit, void *arg) {\n#if PY_VERSION_HEX >= 0x030D0000\n    PyObject_VisitManagedDict(self, visit, arg);\n#else\n    PyObject *&dict = *_PyObject_GetDictPtr(self);\n    Py_VISIT(dict);\n#endif\n// https://docs.python.org/3/c-api/typeobj.html#c.PyTypeObject.tp_traverse\n#if PY_VERSION_HEX >= 0x03090000\n    Py_VISIT(Py_TYPE(self));\n#endif\n    return 0;\n}\n\n/// dynamic_attr: Allow the GC to clear the dictionary.\nextern \"C\" inline int pybind11_clear(PyObject *self) {\n#if PY_VERSION_HEX >= 0x030D0000\n    PyObject_ClearManagedDict(self);\n#else\n    PyObject *&dict = *_PyObject_GetDictPtr(self);\n    Py_CLEAR(dict);\n#endif\n    return 0;\n}\n\n/// Give instances of this type a `__dict__` and opt into garbage collection.\ninline void enable_dynamic_attributes(PyHeapTypeObject *heap_type) {\n    auto *type = &heap_type->ht_type;\n    type->tp_flags |= Py_TPFLAGS_HAVE_GC;\n#if PY_VERSION_HEX < 0x030B0000\n    type->tp_dictoffset = type->tp_basicsize;           // place dict at the end\n    type->tp_basicsize += (ssize_t) sizeof(PyObject *); // and allocate enough space for it\n#else\n    type->tp_flags |= Py_TPFLAGS_MANAGED_DICT;\n#endif\n    type->tp_traverse = pybind11_traverse;\n    type->tp_clear = pybind11_clear;\n\n    static PyGetSetDef getset[]\n        = {{\"__dict__\", PyObject_GenericGetDict, PyObject_GenericSetDict, nullptr, nullptr},\n           {nullptr, nullptr, nullptr, nullptr, nullptr}};\n    type->tp_getset = getset;\n}\n\n/// buffer_protocol: Fill in the view as specified by flags.\nextern \"C\" inline int pybind11_getbuffer(PyObject *obj, Py_buffer *view, int flags) {\n    // Look for a `get_buffer` implementation in this type's info or any bases (following MRO).\n    type_info *tinfo = nullptr;\n    for (auto type : reinterpret_borrow<tuple>(Py_TYPE(obj)->tp_mro)) {\n        tinfo = get_type_info((PyTypeObject *) type.ptr());\n        if (tinfo && tinfo->get_buffer) {\n            break;\n        }\n    }\n    if (view == nullptr || !tinfo || !tinfo->get_buffer) {\n        if (view) {\n            view->obj = nullptr;\n        }\n        set_error(PyExc_BufferError, \"pybind11_getbuffer(): Internal error\");\n        return -1;\n    }\n    std::memset(view, 0, sizeof(Py_buffer));\n    buffer_info *info = nullptr;\n    try {\n        info = tinfo->get_buffer(obj, tinfo->get_buffer_data);\n    } catch (...) {\n        try_translate_exceptions();\n        raise_from(PyExc_BufferError, \"Error getting buffer\");\n        return -1;\n    }\n    if (info == nullptr) {\n        pybind11_fail(\"FATAL UNEXPECTED SITUATION: tinfo->get_buffer() returned nullptr.\");\n    }\n\n    if ((flags & PyBUF_WRITABLE) == PyBUF_WRITABLE && info->readonly) {\n        delete info;\n        // view->obj = nullptr;  // Was just memset to 0, so not necessary\n        set_error(PyExc_BufferError, \"Writable buffer requested for readonly storage\");\n        return -1;\n    }\n    view->obj = obj;\n    view->ndim = 1;\n    view->internal = info;\n    view->buf = info->ptr;\n    view->itemsize = info->itemsize;\n    view->len = view->itemsize;\n    for (auto s : info->shape) {\n        view->len *= s;\n    }\n    view->readonly = static_cast<int>(info->readonly);\n    if ((flags & PyBUF_FORMAT) == PyBUF_FORMAT) {\n        view->format = const_cast<char *>(info->format.c_str());\n    }\n    if ((flags & PyBUF_STRIDES) == PyBUF_STRIDES) {\n        view->ndim = (int) info->ndim;\n        view->strides = info->strides.data();\n        view->shape = info->shape.data();\n    }\n    Py_INCREF(view->obj);\n    return 0;\n}\n\n/// buffer_protocol: Release the resources of the buffer.\nextern \"C\" inline void pybind11_releasebuffer(PyObject *, Py_buffer *view) {\n    delete (buffer_info *) view->internal;\n}\n\n/// Give this type a buffer interface.\ninline void enable_buffer_protocol(PyHeapTypeObject *heap_type) {\n    heap_type->ht_type.tp_as_buffer = &heap_type->as_buffer;\n\n    heap_type->as_buffer.bf_getbuffer = pybind11_getbuffer;\n    heap_type->as_buffer.bf_releasebuffer = pybind11_releasebuffer;\n}\n\n/** Create a brand new Python type according to the `type_record` specification.\n    Return value: New reference. */\ninline PyObject *make_new_python_type(const type_record &rec) {\n    auto name = reinterpret_steal<object>(PYBIND11_FROM_STRING(rec.name));\n\n    auto qualname = name;\n    if (rec.scope && !PyModule_Check(rec.scope.ptr()) && hasattr(rec.scope, \"__qualname__\")) {\n        qualname = reinterpret_steal<object>(\n            PyUnicode_FromFormat(\"%U.%U\", rec.scope.attr(\"__qualname__\").ptr(), name.ptr()));\n    }\n\n    object module_;\n    if (rec.scope) {\n        if (hasattr(rec.scope, \"__module__\")) {\n            module_ = rec.scope.attr(\"__module__\");\n        } else if (hasattr(rec.scope, \"__name__\")) {\n            module_ = rec.scope.attr(\"__name__\");\n        }\n    }\n\n    const auto *full_name = c_str(\n#if !defined(PYPY_VERSION)\n        module_ ? str(module_).cast<std::string>() + \".\" + rec.name :\n#endif\n                rec.name);\n\n    char *tp_doc = nullptr;\n    if (rec.doc && options::show_user_defined_docstrings()) {\n        /* Allocate memory for docstring (Python will free this later on) */\n        size_t size = std::strlen(rec.doc) + 1;\n#if PY_VERSION_HEX >= 0x030D0000\n        tp_doc = (char *) PyMem_MALLOC(size);\n#else\n        tp_doc = (char *) PyObject_MALLOC(size);\n#endif\n        std::memcpy((void *) tp_doc, rec.doc, size);\n    }\n\n    auto &internals = get_internals();\n    auto bases = tuple(rec.bases);\n    auto *base = (bases.empty()) ? internals.instance_base : bases[0].ptr();\n\n    /* Danger zone: from now (and until PyType_Ready), make sure to\n       issue no Python C API calls which could potentially invoke the\n       garbage collector (the GC will call type_traverse(), which will in\n       turn find the newly constructed type in an invalid state) */\n    auto *metaclass\n        = rec.metaclass.ptr() ? (PyTypeObject *) rec.metaclass.ptr() : internals.default_metaclass;\n\n    auto *heap_type = (PyHeapTypeObject *) metaclass->tp_alloc(metaclass, 0);\n    if (!heap_type) {\n        pybind11_fail(std::string(rec.name) + \": Unable to create type object!\");\n    }\n\n    heap_type->ht_name = name.release().ptr();\n#ifdef PYBIND11_BUILTIN_QUALNAME\n    heap_type->ht_qualname = qualname.inc_ref().ptr();\n#endif\n\n    auto *type = &heap_type->ht_type;\n    type->tp_name = full_name;\n    type->tp_doc = tp_doc;\n    type->tp_base = type_incref((PyTypeObject *) base);\n    type->tp_basicsize = static_cast<ssize_t>(sizeof(instance));\n    if (!bases.empty()) {\n        type->tp_bases = bases.release().ptr();\n    }\n\n    /* Don't inherit base __init__ */\n    type->tp_init = pybind11_object_init;\n\n    /* Supported protocols */\n    type->tp_as_number = &heap_type->as_number;\n    type->tp_as_sequence = &heap_type->as_sequence;\n    type->tp_as_mapping = &heap_type->as_mapping;\n    type->tp_as_async = &heap_type->as_async;\n\n    /* Flags */\n    type->tp_flags |= Py_TPFLAGS_DEFAULT | Py_TPFLAGS_HEAPTYPE;\n    if (!rec.is_final) {\n        type->tp_flags |= Py_TPFLAGS_BASETYPE;\n    }\n\n    if (rec.dynamic_attr) {\n        enable_dynamic_attributes(heap_type);\n    }\n\n    if (rec.buffer_protocol) {\n        enable_buffer_protocol(heap_type);\n    }\n\n    if (rec.custom_type_setup_callback) {\n        rec.custom_type_setup_callback(heap_type);\n    }\n\n    if (PyType_Ready(type) < 0) {\n        pybind11_fail(std::string(rec.name) + \": PyType_Ready failed: \" + error_string());\n    }\n\n    assert(!rec.dynamic_attr || PyType_HasFeature(type, Py_TPFLAGS_HAVE_GC));\n\n    /* Register type with the parent scope */\n    if (rec.scope) {\n        setattr(rec.scope, rec.name, (PyObject *) type);\n    } else {\n        Py_INCREF(type); // Keep it alive forever (reference leak)\n    }\n\n    if (module_) { // Needed by pydoc\n        setattr((PyObject *) type, \"__module__\", module_);\n    }\n\n    PYBIND11_SET_OLDPY_QUALNAME(type, qualname);\n\n    return (PyObject *) type;\n}\n\nPYBIND11_NAMESPACE_END(detail)\nPYBIND11_NAMESPACE_END(PYBIND11_NAMESPACE)\n"
  },
  {
    "path": "libs/pybind11/include/pybind11/detail/common.h",
    "content": "/*\n    pybind11/detail/common.h -- Basic macros\n\n    Copyright (c) 2016 Wenzel Jakob <wenzel.jakob@epfl.ch>\n\n    All rights reserved. Use of this source code is governed by a\n    BSD-style license that can be found in the LICENSE file.\n*/\n\n#pragma once\n\n#define PYBIND11_VERSION_MAJOR 2\n#define PYBIND11_VERSION_MINOR 13\n#define PYBIND11_VERSION_PATCH 6\n\n// Similar to Python's convention: https://docs.python.org/3/c-api/apiabiversion.html\n// Additional convention: 0xD = dev\n#define PYBIND11_VERSION_HEX 0x020D0600\n\n// Define some generic pybind11 helper macros for warning management.\n//\n// Note that compiler-specific push/pop pairs are baked into the\n// PYBIND11_NAMESPACE_BEGIN/PYBIND11_NAMESPACE_END pair of macros. Therefore manual\n// PYBIND11_WARNING_PUSH/PYBIND11_WARNING_POP are usually only needed in `#include` sections.\n//\n// If you find you need to suppress a warning, please try to make the suppression as local as\n// possible using these macros. Please also be sure to push/pop with the pybind11 macros. Please\n// only use compiler specifics if you need to check specific versions, e.g. Apple Clang vs. vanilla\n// Clang.\n#if defined(_MSC_VER)\n#    define PYBIND11_COMPILER_MSVC\n#    define PYBIND11_PRAGMA(...) __pragma(__VA_ARGS__)\n#    define PYBIND11_WARNING_PUSH PYBIND11_PRAGMA(warning(push))\n#    define PYBIND11_WARNING_POP PYBIND11_PRAGMA(warning(pop))\n#elif defined(__INTEL_COMPILER)\n#    define PYBIND11_COMPILER_INTEL\n#    define PYBIND11_PRAGMA(...) _Pragma(#__VA_ARGS__)\n#    define PYBIND11_WARNING_PUSH PYBIND11_PRAGMA(warning push)\n#    define PYBIND11_WARNING_POP PYBIND11_PRAGMA(warning pop)\n#elif defined(__clang__)\n#    define PYBIND11_COMPILER_CLANG\n#    define PYBIND11_PRAGMA(...) _Pragma(#__VA_ARGS__)\n#    define PYBIND11_WARNING_PUSH PYBIND11_PRAGMA(clang diagnostic push)\n#    define PYBIND11_WARNING_POP PYBIND11_PRAGMA(clang diagnostic push)\n#elif defined(__GNUC__)\n#    define PYBIND11_COMPILER_GCC\n#    define PYBIND11_PRAGMA(...) _Pragma(#__VA_ARGS__)\n#    define PYBIND11_WARNING_PUSH PYBIND11_PRAGMA(GCC diagnostic push)\n#    define PYBIND11_WARNING_POP PYBIND11_PRAGMA(GCC diagnostic pop)\n#endif\n\n#ifdef PYBIND11_COMPILER_MSVC\n#    define PYBIND11_WARNING_DISABLE_MSVC(name) PYBIND11_PRAGMA(warning(disable : name))\n#else\n#    define PYBIND11_WARNING_DISABLE_MSVC(name)\n#endif\n\n#ifdef PYBIND11_COMPILER_CLANG\n#    define PYBIND11_WARNING_DISABLE_CLANG(name) PYBIND11_PRAGMA(clang diagnostic ignored name)\n#else\n#    define PYBIND11_WARNING_DISABLE_CLANG(name)\n#endif\n\n#ifdef PYBIND11_COMPILER_GCC\n#    define PYBIND11_WARNING_DISABLE_GCC(name) PYBIND11_PRAGMA(GCC diagnostic ignored name)\n#else\n#    define PYBIND11_WARNING_DISABLE_GCC(name)\n#endif\n\n#ifdef PYBIND11_COMPILER_INTEL\n#    define PYBIND11_WARNING_DISABLE_INTEL(name) PYBIND11_PRAGMA(warning disable name)\n#else\n#    define PYBIND11_WARNING_DISABLE_INTEL(name)\n#endif\n\n#define PYBIND11_NAMESPACE_BEGIN(name)                                                            \\\n    namespace name {                                                                              \\\n    PYBIND11_WARNING_PUSH\n\n#define PYBIND11_NAMESPACE_END(name)                                                              \\\n    PYBIND11_WARNING_POP                                                                          \\\n    }\n\n// Robust support for some features and loading modules compiled against different pybind versions\n// requires forcing hidden visibility on pybind code, so we enforce this by setting the attribute\n// on the main `pybind11` namespace.\n#if !defined(PYBIND11_NAMESPACE)\n#    ifdef __GNUG__\n#        define PYBIND11_NAMESPACE pybind11 __attribute__((visibility(\"hidden\")))\n#    else\n#        define PYBIND11_NAMESPACE pybind11\n#    endif\n#endif\n\n#if !(defined(_MSC_VER) && __cplusplus == 199711L)\n#    if __cplusplus >= 201402L\n#        define PYBIND11_CPP14\n#        if __cplusplus >= 201703L\n#            define PYBIND11_CPP17\n#            if __cplusplus >= 202002L\n#                define PYBIND11_CPP20\n// Please update tests/pybind11_tests.cpp `cpp_std()` when adding a macro here.\n#            endif\n#        endif\n#    endif\n#elif defined(_MSC_VER) && __cplusplus == 199711L\n// MSVC sets _MSVC_LANG rather than __cplusplus (supposedly until the standard is fully\n// implemented). Unless you use the /Zc:__cplusplus flag on Visual Studio 2017 15.7 Preview 3\n// or newer.\n#    if _MSVC_LANG >= 201402L\n#        define PYBIND11_CPP14\n#        if _MSVC_LANG > 201402L\n#            define PYBIND11_CPP17\n#            if _MSVC_LANG >= 202002L\n#                define PYBIND11_CPP20\n#            endif\n#        endif\n#    endif\n#endif\n\n#if defined(PYBIND11_CPP20)\n#    define PYBIND11_CONSTINIT constinit\n#    define PYBIND11_DTOR_CONSTEXPR constexpr\n#else\n#    define PYBIND11_CONSTINIT\n#    define PYBIND11_DTOR_CONSTEXPR\n#endif\n\n// Compiler version assertions\n#if defined(__INTEL_COMPILER)\n#    if __INTEL_COMPILER < 1800\n#        error pybind11 requires Intel C++ compiler v18 or newer\n#    elif __INTEL_COMPILER < 1900 && defined(PYBIND11_CPP14)\n#        error pybind11 supports only C++11 with Intel C++ compiler v18. Use v19 or newer for C++14.\n#    endif\n/* The following pragma cannot be pop'ed:\n   https://community.intel.com/t5/Intel-C-Compiler/Inline-and-no-inline-warning/td-p/1216764 */\n#    pragma warning disable 2196 // warning #2196: routine is both \"inline\" and \"noinline\"\n#elif defined(__clang__) && !defined(__apple_build_version__)\n#    if __clang_major__ < 3 || (__clang_major__ == 3 && __clang_minor__ < 3)\n#        error pybind11 requires clang 3.3 or newer\n#    endif\n#elif defined(__clang__)\n// Apple changes clang version macros to its Xcode version; the first Xcode release based on\n// (upstream) clang 3.3 was Xcode 5:\n#    if __clang_major__ < 5\n#        error pybind11 requires Xcode/clang 5.0 or newer\n#    endif\n#elif defined(__GNUG__)\n#    if __GNUC__ < 4 || (__GNUC__ == 4 && __GNUC_MINOR__ < 8)\n#        error pybind11 requires gcc 4.8 or newer\n#    endif\n#elif defined(_MSC_VER)\n#    if _MSC_VER < 1910\n#        error pybind11 2.10+ requires MSVC 2017 or newer\n#    endif\n#endif\n\n#if !defined(PYBIND11_EXPORT)\n#    if defined(WIN32) || defined(_WIN32)\n#        define PYBIND11_EXPORT __declspec(dllexport)\n#    else\n#        define PYBIND11_EXPORT __attribute__((visibility(\"default\")))\n#    endif\n#endif\n\n#if !defined(PYBIND11_EXPORT_EXCEPTION)\n#    if defined(__apple_build_version__)\n#        define PYBIND11_EXPORT_EXCEPTION PYBIND11_EXPORT\n#    else\n#        define PYBIND11_EXPORT_EXCEPTION\n#    endif\n#endif\n\n// For CUDA, GCC7, GCC8:\n// PYBIND11_NOINLINE_FORCED is incompatible with `-Wattributes -Werror`.\n// When defining PYBIND11_NOINLINE_FORCED, it is best to also use `-Wno-attributes`.\n// However, the measured shared-library size saving when using noinline are only\n// 1.7% for CUDA, -0.2% for GCC7, and 0.0% for GCC8 (using -DCMAKE_BUILD_TYPE=MinSizeRel,\n// the default under pybind11/tests).\n#if !defined(PYBIND11_NOINLINE_FORCED)                                                            \\\n    && (defined(__CUDACC__) || (defined(__GNUC__) && (__GNUC__ == 7 || __GNUC__ == 8)))\n#    define PYBIND11_NOINLINE_DISABLED\n#endif\n\n// The PYBIND11_NOINLINE macro is for function DEFINITIONS.\n// In contrast, FORWARD DECLARATIONS should never use this macro:\n// https://stackoverflow.com/questions/9317473/forward-declaration-of-inline-functions\n#if defined(PYBIND11_NOINLINE_DISABLED) // Option for maximum portability and experimentation.\n#    define PYBIND11_NOINLINE inline\n#elif defined(_MSC_VER)\n#    define PYBIND11_NOINLINE __declspec(noinline) inline\n#else\n#    define PYBIND11_NOINLINE __attribute__((noinline)) inline\n#endif\n\n#if defined(__MINGW32__)\n// For unknown reasons all PYBIND11_DEPRECATED member trigger a warning when declared\n// whether it is used or not\n#    define PYBIND11_DEPRECATED(reason)\n#elif defined(PYBIND11_CPP14)\n#    define PYBIND11_DEPRECATED(reason) [[deprecated(reason)]]\n#else\n#    define PYBIND11_DEPRECATED(reason) __attribute__((deprecated(reason)))\n#endif\n\n#if defined(PYBIND11_CPP17)\n#    define PYBIND11_MAYBE_UNUSED [[maybe_unused]]\n#elif defined(_MSC_VER) && !defined(__clang__)\n#    define PYBIND11_MAYBE_UNUSED\n#else\n#    define PYBIND11_MAYBE_UNUSED __attribute__((__unused__))\n#endif\n\n/* Don't let Python.h #define (v)snprintf as macro because they are implemented\n   properly in Visual Studio since 2015. */\n#if defined(_MSC_VER)\n#    define HAVE_SNPRINTF 1\n#endif\n\n/// Include Python header, disable linking to pythonX_d.lib on Windows in debug mode\n#if defined(_MSC_VER)\nPYBIND11_WARNING_PUSH\nPYBIND11_WARNING_DISABLE_MSVC(4505)\n// C4505: 'PySlice_GetIndicesEx': unreferenced local function has been removed (PyPy only)\n#    if defined(_DEBUG) && !defined(Py_DEBUG)\n// Workaround for a VS 2022 issue.\n// NOTE: This workaround knowingly violates the Python.h include order requirement:\n// https://docs.python.org/3/c-api/intro.html#include-files\n// See https://github.com/pybind/pybind11/pull/3497 for full context.\n#        include <yvals.h>\n#        if _MSVC_STL_VERSION >= 143\n#            include <crtdefs.h>\n#        endif\n#        define PYBIND11_DEBUG_MARKER\n#        undef _DEBUG\n#    endif\n#endif\n\n// https://en.cppreference.com/w/c/chrono/localtime\n#if defined(__STDC_LIB_EXT1__) && !defined(__STDC_WANT_LIB_EXT1__)\n#    define __STDC_WANT_LIB_EXT1__\n#endif\n\n#ifdef __has_include\n// std::optional (but including it in c++14 mode isn't allowed)\n#    if defined(PYBIND11_CPP17) && __has_include(<optional>)\n#        define PYBIND11_HAS_OPTIONAL 1\n#    endif\n// std::experimental::optional (but not allowed in c++11 mode)\n#    if defined(PYBIND11_CPP14) && (__has_include(<experimental/optional>) && \\\n                                 !__has_include(<optional>))\n#        define PYBIND11_HAS_EXP_OPTIONAL 1\n#    endif\n// std::variant\n#    if defined(PYBIND11_CPP17) && __has_include(<variant>)\n#        define PYBIND11_HAS_VARIANT 1\n#    endif\n#elif defined(_MSC_VER) && defined(PYBIND11_CPP17)\n#    define PYBIND11_HAS_OPTIONAL 1\n#    define PYBIND11_HAS_VARIANT 1\n#endif\n\n#if defined(PYBIND11_CPP17)\n#    if defined(__has_include)\n#        if __has_include(<string_view>)\n#            define PYBIND11_HAS_STRING_VIEW\n#        endif\n#    elif defined(_MSC_VER)\n#        define PYBIND11_HAS_STRING_VIEW\n#    endif\n#endif\n\n#include <Python.h>\n#if PY_VERSION_HEX < 0x03070000\n#    error \"PYTHON < 3.7 IS UNSUPPORTED. pybind11 v2.12 was the last to support Python 3.6.\"\n#endif\n#include <frameobject.h>\n#include <pythread.h>\n\n/* Python #defines overrides on all sorts of core functions, which\n   tends to weak havok in C++ codebases that expect these to work\n   like regular functions (potentially with several overloads) */\n#if defined(isalnum)\n#    undef isalnum\n#    undef isalpha\n#    undef islower\n#    undef isspace\n#    undef isupper\n#    undef tolower\n#    undef toupper\n#endif\n\n#if defined(copysign)\n#    undef copysign\n#endif\n\n#if defined(PYBIND11_NUMPY_1_ONLY)\n#    define PYBIND11_INTERNAL_NUMPY_1_ONLY_DETECTED\n#endif\n\n#if defined(PYPY_VERSION) && !defined(PYBIND11_SIMPLE_GIL_MANAGEMENT)\n#    define PYBIND11_SIMPLE_GIL_MANAGEMENT\n#endif\n\n#if defined(_MSC_VER)\n#    if defined(PYBIND11_DEBUG_MARKER)\n#        define _DEBUG\n#        undef PYBIND11_DEBUG_MARKER\n#    endif\nPYBIND11_WARNING_POP\n#endif\n\n#include <cstddef>\n#include <cstring>\n#include <exception>\n#include <forward_list>\n#include <memory>\n#include <stdexcept>\n#include <string>\n#include <type_traits>\n#include <typeindex>\n#include <unordered_map>\n#include <unordered_set>\n#include <vector>\n#if defined(__has_include)\n#    if __has_include(<version>)\n#        include <version>\n#    endif\n#endif\n\n// Must be after including <version> or one of the other headers specified by the standard\n#if defined(__cpp_lib_char8_t) && __cpp_lib_char8_t >= 201811L\n#    define PYBIND11_HAS_U8STRING\n#endif\n\n// See description of PR #4246:\n#if !defined(PYBIND11_NO_ASSERT_GIL_HELD_INCREF_DECREF) && !defined(NDEBUG)                       \\\n    && !defined(PYPY_VERSION) && !defined(PYBIND11_ASSERT_GIL_HELD_INCREF_DECREF)\n#    define PYBIND11_ASSERT_GIL_HELD_INCREF_DECREF\n#endif\n\n// #define PYBIND11_STR_LEGACY_PERMISSIVE\n// If DEFINED, pybind11::str can hold PyUnicodeObject or PyBytesObject\n//             (probably surprising and never documented, but this was the\n//             legacy behavior until and including v2.6.x). As a side-effect,\n//             pybind11::isinstance<str>() is true for both pybind11::str and\n//             pybind11::bytes.\n// If UNDEFINED, pybind11::str can only hold PyUnicodeObject, and\n//               pybind11::isinstance<str>() is true only for pybind11::str.\n//               However, for Python 2 only (!), the pybind11::str caster\n//               implicitly decoded bytes to PyUnicodeObject. This was to ease\n//               the transition from the legacy behavior to the non-permissive\n//               behavior.\n\n/// Compatibility macros for Python 2 / Python 3 versions TODO: remove\n#define PYBIND11_INSTANCE_METHOD_NEW(ptr, class_) PyInstanceMethod_New(ptr)\n#define PYBIND11_INSTANCE_METHOD_CHECK PyInstanceMethod_Check\n#define PYBIND11_INSTANCE_METHOD_GET_FUNCTION PyInstanceMethod_GET_FUNCTION\n#define PYBIND11_BYTES_CHECK PyBytes_Check\n#define PYBIND11_BYTES_FROM_STRING PyBytes_FromString\n#define PYBIND11_BYTES_FROM_STRING_AND_SIZE PyBytes_FromStringAndSize\n#define PYBIND11_BYTES_AS_STRING_AND_SIZE PyBytes_AsStringAndSize\n#define PYBIND11_BYTES_AS_STRING PyBytes_AsString\n#define PYBIND11_BYTES_SIZE PyBytes_Size\n#define PYBIND11_LONG_CHECK(o) PyLong_Check(o)\n#define PYBIND11_LONG_AS_LONGLONG(o) PyLong_AsLongLong(o)\n#define PYBIND11_LONG_FROM_SIGNED(o) PyLong_FromSsize_t((ssize_t) (o))\n#define PYBIND11_LONG_FROM_UNSIGNED(o) PyLong_FromSize_t((size_t) (o))\n#define PYBIND11_BYTES_NAME \"bytes\"\n#define PYBIND11_STRING_NAME \"str\"\n#define PYBIND11_SLICE_OBJECT PyObject\n#define PYBIND11_FROM_STRING PyUnicode_FromString\n#define PYBIND11_STR_TYPE ::pybind11::str\n#define PYBIND11_BOOL_ATTR \"__bool__\"\n#define PYBIND11_NB_BOOL(ptr) ((ptr)->nb_bool)\n#define PYBIND11_BUILTINS_MODULE \"builtins\"\n// Providing a separate declaration to make Clang's -Wmissing-prototypes happy.\n// See comment for PYBIND11_MODULE below for why this is marked \"maybe unused\".\n#define PYBIND11_PLUGIN_IMPL(name)                                                                \\\n    extern \"C\" PYBIND11_MAYBE_UNUSED PYBIND11_EXPORT PyObject *PyInit_##name();                   \\\n    extern \"C\" PYBIND11_EXPORT PyObject *PyInit_##name()\n\n#define PYBIND11_TRY_NEXT_OVERLOAD ((PyObject *) 1) // special failure return code\n#define PYBIND11_STRINGIFY(x) #x\n#define PYBIND11_TOSTRING(x) PYBIND11_STRINGIFY(x)\n#define PYBIND11_CONCAT(first, second) first##second\n#define PYBIND11_ENSURE_INTERNALS_READY pybind11::detail::get_internals();\n\n#define PYBIND11_CHECK_PYTHON_VERSION                                                             \\\n    {                                                                                             \\\n        const char *compiled_ver                                                                  \\\n            = PYBIND11_TOSTRING(PY_MAJOR_VERSION) \".\" PYBIND11_TOSTRING(PY_MINOR_VERSION);        \\\n        const char *runtime_ver = Py_GetVersion();                                                \\\n        size_t len = std::strlen(compiled_ver);                                                   \\\n        if (std::strncmp(runtime_ver, compiled_ver, len) != 0                                     \\\n            || (runtime_ver[len] >= '0' && runtime_ver[len] <= '9')) {                            \\\n            PyErr_Format(PyExc_ImportError,                                                       \\\n                         \"Python version mismatch: module was compiled for Python %s, \"           \\\n                         \"but the interpreter version is incompatible: %s.\",                      \\\n                         compiled_ver,                                                            \\\n                         runtime_ver);                                                            \\\n            return nullptr;                                                                       \\\n        }                                                                                         \\\n    }\n\n#define PYBIND11_CATCH_INIT_EXCEPTIONS                                                            \\\n    catch (pybind11::error_already_set & e) {                                                     \\\n        pybind11::raise_from(e, PyExc_ImportError, \"initialization failed\");                      \\\n        return nullptr;                                                                           \\\n    }                                                                                             \\\n    catch (const std::exception &e) {                                                             \\\n        ::pybind11::set_error(PyExc_ImportError, e.what());                                       \\\n        return nullptr;                                                                           \\\n    }\n\n/** \\rst\n    ***Deprecated in favor of PYBIND11_MODULE***\n\n    This macro creates the entry point that will be invoked when the Python interpreter\n    imports a plugin library. Please create a `module_` in the function body and return\n    the pointer to its underlying Python object at the end.\n\n    .. code-block:: cpp\n\n        PYBIND11_PLUGIN(example) {\n            pybind11::module_ m(\"example\", \"pybind11 example plugin\");\n            /// Set up bindings here\n            return m.ptr();\n        }\n\\endrst */\n#define PYBIND11_PLUGIN(name)                                                                     \\\n    PYBIND11_DEPRECATED(\"PYBIND11_PLUGIN is deprecated, use PYBIND11_MODULE\")                     \\\n    static PyObject *pybind11_init();                                                             \\\n    PYBIND11_PLUGIN_IMPL(name) {                                                                  \\\n        PYBIND11_CHECK_PYTHON_VERSION                                                             \\\n        PYBIND11_ENSURE_INTERNALS_READY                                                           \\\n        try {                                                                                     \\\n            return pybind11_init();                                                               \\\n        }                                                                                         \\\n        PYBIND11_CATCH_INIT_EXCEPTIONS                                                            \\\n    }                                                                                             \\\n    PyObject *pybind11_init()\n\n/** \\rst\n    This macro creates the entry point that will be invoked when the Python interpreter\n    imports an extension module. The module name is given as the first argument and it\n    should not be in quotes. The second macro argument defines a variable of type\n    `py::module_` which can be used to initialize the module.\n\n    The entry point is marked as \"maybe unused\" to aid dead-code detection analysis:\n    since the entry point is typically only looked up at runtime and not referenced\n    during translation, it would otherwise appear as unused (\"dead\") code.\n\n    .. code-block:: cpp\n\n        PYBIND11_MODULE(example, m) {\n            m.doc() = \"pybind11 example module\";\n\n            // Add bindings here\n            m.def(\"foo\", []() {\n                return \"Hello, World!\";\n            });\n        }\n\n    The third macro argument is optional (available since 2.13.0), and can be used to\n    mark the extension module as safe to run without the GIL under a free-threaded CPython\n    interpreter. Passing this argument has no effect on other interpreters.\n\n    .. code-block:: cpp\n\n        PYBIND11_MODULE(example, m, py::mod_gil_not_used()) {\n            m.doc() = \"pybind11 example module safe to run without the GIL\";\n\n            // Add bindings here\n            m.def(\"foo\", []() {\n                return \"Hello, Free-threaded World!\";\n            });\n        }\n\n\\endrst */\nPYBIND11_WARNING_PUSH\nPYBIND11_WARNING_DISABLE_CLANG(\"-Wgnu-zero-variadic-macro-arguments\")\n#define PYBIND11_MODULE(name, variable, ...)                                                      \\\n    static ::pybind11::module_::module_def PYBIND11_CONCAT(pybind11_module_def_, name)            \\\n        PYBIND11_MAYBE_UNUSED;                                                                    \\\n    PYBIND11_MAYBE_UNUSED                                                                         \\\n    static void PYBIND11_CONCAT(pybind11_init_, name)(::pybind11::module_ &);                     \\\n    PYBIND11_PLUGIN_IMPL(name) {                                                                  \\\n        PYBIND11_CHECK_PYTHON_VERSION                                                             \\\n        PYBIND11_ENSURE_INTERNALS_READY                                                           \\\n        auto m = ::pybind11::module_::create_extension_module(                                    \\\n            PYBIND11_TOSTRING(name),                                                              \\\n            nullptr,                                                                              \\\n            &PYBIND11_CONCAT(pybind11_module_def_, name),                                         \\\n            ##__VA_ARGS__);                                                                       \\\n        try {                                                                                     \\\n            PYBIND11_CONCAT(pybind11_init_, name)(m);                                             \\\n            return m.ptr();                                                                       \\\n        }                                                                                         \\\n        PYBIND11_CATCH_INIT_EXCEPTIONS                                                            \\\n    }                                                                                             \\\n    void PYBIND11_CONCAT(pybind11_init_, name)(::pybind11::module_ & (variable))\nPYBIND11_WARNING_POP\n\nPYBIND11_NAMESPACE_BEGIN(PYBIND11_NAMESPACE)\n\nusing ssize_t = Py_ssize_t;\nusing size_t = std::size_t;\n\ntemplate <typename IntType>\ninline ssize_t ssize_t_cast(const IntType &val) {\n    static_assert(sizeof(IntType) <= sizeof(ssize_t), \"Implicit narrowing is not permitted.\");\n    return static_cast<ssize_t>(val);\n}\n\n/// Approach used to cast a previously unknown C++ instance into a Python object\nenum class return_value_policy : uint8_t {\n    /** This is the default return value policy, which falls back to the policy\n        return_value_policy::take_ownership when the return value is a pointer.\n        Otherwise, it uses return_value::move or return_value::copy for rvalue\n        and lvalue references, respectively. See below for a description of what\n        all of these different policies do. */\n    automatic = 0,\n\n    /** As above, but use policy return_value_policy::reference when the return\n        value is a pointer. This is the default conversion policy for function\n        arguments when calling Python functions manually from C++ code (i.e. via\n        handle::operator()). You probably won't need to use this. */\n    automatic_reference,\n\n    /** Reference an existing object (i.e. do not create a new copy) and take\n        ownership. Python will call the destructor and delete operator when the\n        object's reference count reaches zero. Undefined behavior ensues when\n        the C++ side does the same.. */\n    take_ownership,\n\n    /** Create a new copy of the returned object, which will be owned by\n        Python. This policy is comparably safe because the lifetimes of the two\n        instances are decoupled. */\n    copy,\n\n    /** Use std::move to move the return value contents into a new instance\n        that will be owned by Python. This policy is comparably safe because the\n        lifetimes of the two instances (move source and destination) are\n        decoupled. */\n    move,\n\n    /** Reference an existing object, but do not take ownership. The C++ side\n        is responsible for managing the object's lifetime and deallocating it\n        when it is no longer used. Warning: undefined behavior will ensue when\n        the C++ side deletes an object that is still referenced and used by\n        Python. */\n    reference,\n\n    /** This policy only applies to methods and properties. It references the\n        object without taking ownership similar to the above\n        return_value_policy::reference policy. In contrast to that policy, the\n        function or property's implicit this argument (called the parent) is\n        considered to be the owner of the return value (the child).\n        pybind11 then couples the lifetime of the parent to the child via a\n        reference relationship that ensures that the parent cannot be garbage\n        collected while Python is still using the child. More advanced\n        variations of this scheme are also possible using combinations of\n        return_value_policy::reference and the keep_alive call policy */\n    reference_internal\n};\n\nPYBIND11_NAMESPACE_BEGIN(detail)\n\ninline static constexpr int log2(size_t n, int k = 0) {\n    return (n <= 1) ? k : log2(n >> 1, k + 1);\n}\n\n// Returns the size as a multiple of sizeof(void *), rounded up.\ninline static constexpr size_t size_in_ptrs(size_t s) {\n    return 1 + ((s - 1) >> log2(sizeof(void *)));\n}\n\n/**\n * The space to allocate for simple layout instance holders (see below) in multiple of the size of\n * a pointer (e.g.  2 means 16 bytes on 64-bit architectures).  The default is the minimum required\n * to holder either a std::unique_ptr or std::shared_ptr (which is almost always\n * sizeof(std::shared_ptr<T>)).\n */\nconstexpr size_t instance_simple_holder_in_ptrs() {\n    static_assert(sizeof(std::shared_ptr<int>) >= sizeof(std::unique_ptr<int>),\n                  \"pybind assumes std::shared_ptrs are at least as big as std::unique_ptrs\");\n    return size_in_ptrs(sizeof(std::shared_ptr<int>));\n}\n\n// Forward declarations\nstruct type_info;\nstruct value_and_holder;\n\nstruct nonsimple_values_and_holders {\n    void **values_and_holders;\n    uint8_t *status;\n};\n\n/// The 'instance' type which needs to be standard layout (need to be able to use 'offsetof')\nstruct instance {\n    PyObject_HEAD\n    /// Storage for pointers and holder; see simple_layout, below, for a description\n    union {\n        void *simple_value_holder[1 + instance_simple_holder_in_ptrs()];\n        nonsimple_values_and_holders nonsimple;\n    };\n    /// Weak references\n    PyObject *weakrefs;\n    /// If true, the pointer is owned which means we're free to manage it with a holder.\n    bool owned : 1;\n    /**\n     * An instance has two possible value/holder layouts.\n     *\n     * Simple layout (when this flag is true), means the `simple_value_holder` is set with a\n     * pointer and the holder object governing that pointer, i.e. [val1*][holder].  This layout is\n     * applied whenever there is no python-side multiple inheritance of bound C++ types *and* the\n     * type's holder will fit in the default space (which is large enough to hold either a\n     * std::unique_ptr or std::shared_ptr).\n     *\n     * Non-simple layout applies when using custom holders that require more space than\n     * `shared_ptr` (which is typically the size of two pointers), or when multiple inheritance is\n     * used on the python side.  Non-simple layout allocates the required amount of memory to have\n     * multiple bound C++ classes as parents.  Under this layout, `nonsimple.values_and_holders` is\n     * set to a pointer to allocated space of the required space to hold a sequence of value\n     * pointers and holders followed `status`, a set of bit flags (1 byte each), i.e.\n     * [val1*][holder1][val2*][holder2]...[bb...]  where each [block] is rounded up to a multiple\n     * of `sizeof(void *)`.  `nonsimple.status` is, for convenience, a pointer to the beginning of\n     * the [bb...] block (but not independently allocated).\n     *\n     * Status bits indicate whether the associated holder is constructed (&\n     * status_holder_constructed) and whether the value pointer is registered (&\n     * status_instance_registered) in `registered_instances`.\n     */\n    bool simple_layout : 1;\n    /// For simple layout, tracks whether the holder has been constructed\n    bool simple_holder_constructed : 1;\n    /// For simple layout, tracks whether the instance is registered in `registered_instances`\n    bool simple_instance_registered : 1;\n    /// If true, get_internals().patients has an entry for this object\n    bool has_patients : 1;\n\n    /// Initializes all of the above type/values/holders data (but not the instance values\n    /// themselves)\n    void allocate_layout();\n\n    /// Destroys/deallocates all of the above\n    void deallocate_layout();\n\n    /// Returns the value_and_holder wrapper for the given type (or the first, if `find_type`\n    /// omitted).  Returns a default-constructed (with `.inst = nullptr`) object on failure if\n    /// `throw_if_missing` is false.\n    value_and_holder get_value_and_holder(const type_info *find_type = nullptr,\n                                          bool throw_if_missing = true);\n\n    /// Bit values for the non-simple status flags\n    static constexpr uint8_t status_holder_constructed = 1;\n    static constexpr uint8_t status_instance_registered = 2;\n};\n\nstatic_assert(std::is_standard_layout<instance>::value,\n              \"Internal error: `pybind11::detail::instance` is not standard layout!\");\n\n/// from __cpp_future__ import (convenient aliases from C++14/17)\n#if defined(PYBIND11_CPP14)\nusing std::conditional_t;\nusing std::enable_if_t;\nusing std::remove_cv_t;\nusing std::remove_reference_t;\n#else\ntemplate <bool B, typename T = void>\nusing enable_if_t = typename std::enable_if<B, T>::type;\ntemplate <bool B, typename T, typename F>\nusing conditional_t = typename std::conditional<B, T, F>::type;\ntemplate <typename T>\nusing remove_cv_t = typename std::remove_cv<T>::type;\ntemplate <typename T>\nusing remove_reference_t = typename std::remove_reference<T>::type;\n#endif\n\n#if defined(PYBIND11_CPP20)\nusing std::remove_cvref;\nusing std::remove_cvref_t;\n#else\ntemplate <class T>\nstruct remove_cvref {\n    using type = remove_cv_t<remove_reference_t<T>>;\n};\ntemplate <class T>\nusing remove_cvref_t = typename remove_cvref<T>::type;\n#endif\n\n/// Example usage: is_same_ignoring_cvref<T, PyObject *>::value\ntemplate <typename T, typename U>\nusing is_same_ignoring_cvref = std::is_same<detail::remove_cvref_t<T>, U>;\n\n/// Index sequences\n#if defined(PYBIND11_CPP14)\nusing std::index_sequence;\nusing std::make_index_sequence;\n#else\ntemplate <size_t...>\nstruct index_sequence {};\ntemplate <size_t N, size_t... S>\nstruct make_index_sequence_impl : make_index_sequence_impl<N - 1, N - 1, S...> {};\ntemplate <size_t... S>\nstruct make_index_sequence_impl<0, S...> {\n    using type = index_sequence<S...>;\n};\ntemplate <size_t N>\nusing make_index_sequence = typename make_index_sequence_impl<N>::type;\n#endif\n\n/// Make an index sequence of the indices of true arguments\ntemplate <typename ISeq, size_t, bool...>\nstruct select_indices_impl {\n    using type = ISeq;\n};\ntemplate <size_t... IPrev, size_t I, bool B, bool... Bs>\nstruct select_indices_impl<index_sequence<IPrev...>, I, B, Bs...>\n    : select_indices_impl<conditional_t<B, index_sequence<IPrev..., I>, index_sequence<IPrev...>>,\n                          I + 1,\n                          Bs...> {};\ntemplate <bool... Bs>\nusing select_indices = typename select_indices_impl<index_sequence<>, 0, Bs...>::type;\n\n/// Backports of std::bool_constant and std::negation to accommodate older compilers\ntemplate <bool B>\nusing bool_constant = std::integral_constant<bool, B>;\ntemplate <typename T>\nstruct negation : bool_constant<!T::value> {};\n\n// PGI/Intel cannot detect operator delete with the \"compatible\" void_t impl, so\n// using the new one (C++14 defect, so generally works on newer compilers, even\n// if not in C++17 mode)\n#if defined(__PGIC__) || defined(__INTEL_COMPILER)\ntemplate <typename...>\nusing void_t = void;\n#else\ntemplate <typename...>\nstruct void_t_impl {\n    using type = void;\n};\ntemplate <typename... Ts>\nusing void_t = typename void_t_impl<Ts...>::type;\n#endif\n\n/// Compile-time all/any/none of that check the boolean value of all template types\n#if defined(__cpp_fold_expressions) && !(defined(_MSC_VER) && (_MSC_VER < 1916))\ntemplate <class... Ts>\nusing all_of = bool_constant<(Ts::value && ...)>;\ntemplate <class... Ts>\nusing any_of = bool_constant<(Ts::value || ...)>;\n#elif !defined(_MSC_VER)\ntemplate <bool...>\nstruct bools {};\ntemplate <class... Ts>\nusing all_of = std::is_same<bools<Ts::value..., true>, bools<true, Ts::value...>>;\ntemplate <class... Ts>\nusing any_of = negation<all_of<negation<Ts>...>>;\n#else\n// MSVC has trouble with the above, but supports std::conjunction, which we can use instead (albeit\n// at a slight loss of compilation efficiency).\ntemplate <class... Ts>\nusing all_of = std::conjunction<Ts...>;\ntemplate <class... Ts>\nusing any_of = std::disjunction<Ts...>;\n#endif\ntemplate <class... Ts>\nusing none_of = negation<any_of<Ts...>>;\n\ntemplate <class T, template <class> class... Predicates>\nusing satisfies_all_of = all_of<Predicates<T>...>;\ntemplate <class T, template <class> class... Predicates>\nusing satisfies_any_of = any_of<Predicates<T>...>;\ntemplate <class T, template <class> class... Predicates>\nusing satisfies_none_of = none_of<Predicates<T>...>;\n\n/// Strip the class from a method type\ntemplate <typename T>\nstruct remove_class {};\ntemplate <typename C, typename R, typename... A>\nstruct remove_class<R (C::*)(A...)> {\n    using type = R(A...);\n};\ntemplate <typename C, typename R, typename... A>\nstruct remove_class<R (C::*)(A...) const> {\n    using type = R(A...);\n};\n#ifdef __cpp_noexcept_function_type\ntemplate <typename C, typename R, typename... A>\nstruct remove_class<R (C::*)(A...) noexcept> {\n    using type = R(A...);\n};\ntemplate <typename C, typename R, typename... A>\nstruct remove_class<R (C::*)(A...) const noexcept> {\n    using type = R(A...);\n};\n#endif\n/// Helper template to strip away type modifiers\ntemplate <typename T>\nstruct intrinsic_type {\n    using type = T;\n};\ntemplate <typename T>\nstruct intrinsic_type<const T> {\n    using type = typename intrinsic_type<T>::type;\n};\ntemplate <typename T>\nstruct intrinsic_type<T *> {\n    using type = typename intrinsic_type<T>::type;\n};\ntemplate <typename T>\nstruct intrinsic_type<T &> {\n    using type = typename intrinsic_type<T>::type;\n};\ntemplate <typename T>\nstruct intrinsic_type<T &&> {\n    using type = typename intrinsic_type<T>::type;\n};\ntemplate <typename T, size_t N>\nstruct intrinsic_type<const T[N]> {\n    using type = typename intrinsic_type<T>::type;\n};\ntemplate <typename T, size_t N>\nstruct intrinsic_type<T[N]> {\n    using type = typename intrinsic_type<T>::type;\n};\ntemplate <typename T>\nusing intrinsic_t = typename intrinsic_type<T>::type;\n\n/// Helper type to replace 'void' in some expressions\nstruct void_type {};\n\n/// Helper template which holds a list of types\ntemplate <typename...>\nstruct type_list {};\n\n/// Compile-time integer sum\n#ifdef __cpp_fold_expressions\ntemplate <typename... Ts>\nconstexpr size_t constexpr_sum(Ts... ns) {\n    return (0 + ... + size_t{ns});\n}\n#else\nconstexpr size_t constexpr_sum() { return 0; }\ntemplate <typename T, typename... Ts>\nconstexpr size_t constexpr_sum(T n, Ts... ns) {\n    return size_t{n} + constexpr_sum(ns...);\n}\n#endif\n\nPYBIND11_NAMESPACE_BEGIN(constexpr_impl)\n/// Implementation details for constexpr functions\nconstexpr int first(int i) { return i; }\ntemplate <typename T, typename... Ts>\nconstexpr int first(int i, T v, Ts... vs) {\n    return v ? i : first(i + 1, vs...);\n}\n\nconstexpr int last(int /*i*/, int result) { return result; }\ntemplate <typename T, typename... Ts>\nconstexpr int last(int i, int result, T v, Ts... vs) {\n    return last(i + 1, v ? i : result, vs...);\n}\nPYBIND11_NAMESPACE_END(constexpr_impl)\n\n/// Return the index of the first type in Ts which satisfies Predicate<T>.\n/// Returns sizeof...(Ts) if none match.\ntemplate <template <typename> class Predicate, typename... Ts>\nconstexpr int constexpr_first() {\n    return constexpr_impl::first(0, Predicate<Ts>::value...);\n}\n\n/// Return the index of the last type in Ts which satisfies Predicate<T>, or -1 if none match.\ntemplate <template <typename> class Predicate, typename... Ts>\nconstexpr int constexpr_last() {\n    return constexpr_impl::last(0, -1, Predicate<Ts>::value...);\n}\n\n/// Return the Nth element from the parameter pack\ntemplate <size_t N, typename T, typename... Ts>\nstruct pack_element {\n    using type = typename pack_element<N - 1, Ts...>::type;\n};\ntemplate <typename T, typename... Ts>\nstruct pack_element<0, T, Ts...> {\n    using type = T;\n};\n\n/// Return the one and only type which matches the predicate, or Default if none match.\n/// If more than one type matches the predicate, fail at compile-time.\ntemplate <template <typename> class Predicate, typename Default, typename... Ts>\nstruct exactly_one {\n    static constexpr auto found = constexpr_sum(Predicate<Ts>::value...);\n    static_assert(found <= 1, \"Found more than one type matching the predicate\");\n\n    static constexpr auto index = found ? constexpr_first<Predicate, Ts...>() : 0;\n    using type = conditional_t<found, typename pack_element<index, Ts...>::type, Default>;\n};\ntemplate <template <typename> class P, typename Default>\nstruct exactly_one<P, Default> {\n    using type = Default;\n};\n\ntemplate <template <typename> class Predicate, typename Default, typename... Ts>\nusing exactly_one_t = typename exactly_one<Predicate, Default, Ts...>::type;\n\n/// Defer the evaluation of type T until types Us are instantiated\ntemplate <typename T, typename... /*Us*/>\nstruct deferred_type {\n    using type = T;\n};\ntemplate <typename T, typename... Us>\nusing deferred_t = typename deferred_type<T, Us...>::type;\n\n/// Like is_base_of, but requires a strict base (i.e. `is_strict_base_of<T, T>::value == false`,\n/// unlike `std::is_base_of`)\ntemplate <typename Base, typename Derived>\nusing is_strict_base_of\n    = bool_constant<std::is_base_of<Base, Derived>::value && !std::is_same<Base, Derived>::value>;\n\n/// Like is_base_of, but also requires that the base type is accessible (i.e. that a Derived\n/// pointer can be converted to a Base pointer) For unions, `is_base_of<T, T>::value` is False, so\n/// we need to check `is_same` as well.\ntemplate <typename Base, typename Derived>\nusing is_accessible_base_of\n    = bool_constant<(std::is_same<Base, Derived>::value || std::is_base_of<Base, Derived>::value)\n                    && std::is_convertible<Derived *, Base *>::value>;\n\ntemplate <template <typename...> class Base>\nstruct is_template_base_of_impl {\n    template <typename... Us>\n    static std::true_type check(Base<Us...> *);\n    static std::false_type check(...);\n};\n\n/// Check if a template is the base of a type. For example:\n/// `is_template_base_of<Base, T>` is true if `struct T : Base<U> {}` where U can be anything\ntemplate <template <typename...> class Base, typename T>\n// Sadly, all MSVC versions incl. 2022 need the workaround, even in C++20 mode.\n// See also: https://github.com/pybind/pybind11/pull/3741\n#if !defined(_MSC_VER)\nusing is_template_base_of\n    = decltype(is_template_base_of_impl<Base>::check((intrinsic_t<T> *) nullptr));\n#else\nstruct is_template_base_of\n    : decltype(is_template_base_of_impl<Base>::check((intrinsic_t<T> *) nullptr)){};\n#endif\n\n/// Check if T is an instantiation of the template `Class`. For example:\n/// `is_instantiation<shared_ptr, T>` is true if `T == shared_ptr<U>` where U can be anything.\ntemplate <template <typename...> class Class, typename T>\nstruct is_instantiation : std::false_type {};\ntemplate <template <typename...> class Class, typename... Us>\nstruct is_instantiation<Class, Class<Us...>> : std::true_type {};\n\n/// Check if T is std::shared_ptr<U> where U can be anything\ntemplate <typename T>\nusing is_shared_ptr = is_instantiation<std::shared_ptr, T>;\n\n/// Check if T looks like an input iterator\ntemplate <typename T, typename = void>\nstruct is_input_iterator : std::false_type {};\ntemplate <typename T>\nstruct is_input_iterator<T,\n                         void_t<decltype(*std::declval<T &>()), decltype(++std::declval<T &>())>>\n    : std::true_type {};\n\ntemplate <typename T>\nusing is_function_pointer\n    = bool_constant<std::is_pointer<T>::value\n                    && std::is_function<typename std::remove_pointer<T>::type>::value>;\n\ntemplate <typename F>\nstruct strip_function_object {\n    // If you are encountering an\n    // 'error: name followed by \"::\" must be a class or namespace name'\n    // with the Intel compiler and a noexcept function here,\n    // try to use noexcept(true) instead of plain noexcept.\n    using type = typename remove_class<decltype(&F::operator())>::type;\n};\n\n// Extracts the function signature from a function, function pointer or lambda.\ntemplate <typename Function, typename F = remove_reference_t<Function>>\nusing function_signature_t = conditional_t<\n    std::is_function<F>::value,\n    F,\n    typename conditional_t<std::is_pointer<F>::value || std::is_member_pointer<F>::value,\n                           std::remove_pointer<F>,\n                           strip_function_object<F>>::type>;\n\n/// Returns true if the type looks like a lambda: that is, isn't a function, pointer or member\n/// pointer.  Note that this can catch all sorts of other things, too; this is intended to be used\n/// in a place where passing a lambda makes sense.\ntemplate <typename T>\nusing is_lambda = satisfies_none_of<remove_reference_t<T>,\n                                    std::is_function,\n                                    std::is_pointer,\n                                    std::is_member_pointer>;\n\n// [workaround(intel)] Internal error on fold expression\n/// Apply a function over each element of a parameter pack\n#if defined(__cpp_fold_expressions) && !defined(__INTEL_COMPILER)\n// Intel compiler produces an internal error on this fold expression (tested with ICC 19.0.2)\n#    define PYBIND11_EXPAND_SIDE_EFFECTS(PATTERN) (((PATTERN), void()), ...)\n#else\nusing expand_side_effects = bool[];\n#    define PYBIND11_EXPAND_SIDE_EFFECTS(PATTERN)                                                 \\\n        (void) pybind11::detail::expand_side_effects { ((PATTERN), void(), false)..., false }\n#endif\n\nPYBIND11_NAMESPACE_END(detail)\n\n/// C++ bindings of builtin Python exceptions\nclass PYBIND11_EXPORT_EXCEPTION builtin_exception : public std::runtime_error {\npublic:\n    using std::runtime_error::runtime_error;\n    /// Set the error using the Python C API\n    virtual void set_error() const = 0;\n};\n\n#define PYBIND11_RUNTIME_EXCEPTION(name, type)                                                    \\\n    class PYBIND11_EXPORT_EXCEPTION name : public builtin_exception {                             \\\n    public:                                                                                       \\\n        using builtin_exception::builtin_exception;                                               \\\n        name() : name(\"\") {}                                                                      \\\n        void set_error() const override { PyErr_SetString(type, what()); }                        \\\n    };\n\nPYBIND11_RUNTIME_EXCEPTION(stop_iteration, PyExc_StopIteration)\nPYBIND11_RUNTIME_EXCEPTION(index_error, PyExc_IndexError)\nPYBIND11_RUNTIME_EXCEPTION(key_error, PyExc_KeyError)\nPYBIND11_RUNTIME_EXCEPTION(value_error, PyExc_ValueError)\nPYBIND11_RUNTIME_EXCEPTION(type_error, PyExc_TypeError)\nPYBIND11_RUNTIME_EXCEPTION(buffer_error, PyExc_BufferError)\nPYBIND11_RUNTIME_EXCEPTION(import_error, PyExc_ImportError)\nPYBIND11_RUNTIME_EXCEPTION(attribute_error, PyExc_AttributeError)\nPYBIND11_RUNTIME_EXCEPTION(cast_error, PyExc_RuntimeError) /// Thrown when pybind11::cast or\n                                                           /// handle::call fail due to a type\n                                                           /// casting error\nPYBIND11_RUNTIME_EXCEPTION(reference_cast_error, PyExc_RuntimeError) /// Used internally\n\n[[noreturn]] PYBIND11_NOINLINE void pybind11_fail(const char *reason) {\n    assert(!PyErr_Occurred());\n    throw std::runtime_error(reason);\n}\n[[noreturn]] PYBIND11_NOINLINE void pybind11_fail(const std::string &reason) {\n    assert(!PyErr_Occurred());\n    throw std::runtime_error(reason);\n}\n\ntemplate <typename T, typename SFINAE = void>\nstruct format_descriptor {};\n\ntemplate <typename T>\nstruct format_descriptor<\n    T,\n    detail::enable_if_t<detail::is_same_ignoring_cvref<T, PyObject *>::value>> {\n    static constexpr const char c = 'O';\n    static constexpr const char value[2] = {c, '\\0'};\n    static std::string format() { return std::string(1, c); }\n};\n\nPYBIND11_NAMESPACE_BEGIN(detail)\n// Returns the index of the given type in the type char array below, and in the list in numpy.h\n// The order here is: bool; 8 ints ((signed,unsigned)x(8,16,32,64)bits); float,double,long double;\n// complex float,double,long double.  Note that the long double types only participate when long\n// double is actually longer than double (it isn't under MSVC).\n// NB: not only the string below but also complex.h and numpy.h rely on this order.\ntemplate <typename T, typename SFINAE = void>\nstruct is_fmt_numeric {\n    static constexpr bool value = false;\n};\ntemplate <typename T>\nstruct is_fmt_numeric<T, enable_if_t<std::is_arithmetic<T>::value>> {\n    static constexpr bool value = true;\n    static constexpr int index\n        = std::is_same<T, bool>::value\n              ? 0\n              : 1\n                    + (std::is_integral<T>::value\n                           ? detail::log2(sizeof(T)) * 2 + std::is_unsigned<T>::value\n                           : 8\n                                 + (std::is_same<T, double>::value        ? 1\n                                    : std::is_same<T, long double>::value ? 2\n                                                                          : 0));\n};\nPYBIND11_NAMESPACE_END(detail)\n\ntemplate <typename T>\nstruct format_descriptor<T, detail::enable_if_t<std::is_arithmetic<T>::value>> {\n    static constexpr const char c = \"?bBhHiIqQfdg\"[detail::is_fmt_numeric<T>::index];\n    static constexpr const char value[2] = {c, '\\0'};\n    static std::string format() { return std::string(1, c); }\n};\n\n#if !defined(PYBIND11_CPP17)\n\ntemplate <typename T>\nconstexpr const char\n    format_descriptor<T, detail::enable_if_t<std::is_arithmetic<T>::value>>::value[2];\n\n#endif\n\n/// RAII wrapper that temporarily clears any Python error state\nstruct error_scope {\n    PyObject *type, *value, *trace;\n    error_scope() { PyErr_Fetch(&type, &value, &trace); }\n    error_scope(const error_scope &) = delete;\n    error_scope &operator=(const error_scope &) = delete;\n    ~error_scope() { PyErr_Restore(type, value, trace); }\n};\n\n/// Dummy destructor wrapper that can be used to expose classes with a private destructor\nstruct nodelete {\n    template <typename T>\n    void operator()(T *) {}\n};\n\nPYBIND11_NAMESPACE_BEGIN(detail)\ntemplate <typename... Args>\nstruct overload_cast_impl {\n    template <typename Return>\n    constexpr auto operator()(Return (*pf)(Args...)) const noexcept -> decltype(pf) {\n        return pf;\n    }\n\n    template <typename Return, typename Class>\n    constexpr auto operator()(Return (Class::*pmf)(Args...),\n                              std::false_type = {}) const noexcept -> decltype(pmf) {\n        return pmf;\n    }\n\n    template <typename Return, typename Class>\n    constexpr auto operator()(Return (Class::*pmf)(Args...) const,\n                              std::true_type) const noexcept -> decltype(pmf) {\n        return pmf;\n    }\n};\nPYBIND11_NAMESPACE_END(detail)\n\n// overload_cast requires variable templates: C++14\n#if defined(PYBIND11_CPP14)\n#    define PYBIND11_OVERLOAD_CAST 1\n/// Syntax sugar for resolving overloaded function pointers:\n///  - regular: static_cast<Return (Class::*)(Arg0, Arg1, Arg2)>(&Class::func)\n///  - sweet:   overload_cast<Arg0, Arg1, Arg2>(&Class::func)\ntemplate <typename... Args>\nstatic constexpr detail::overload_cast_impl<Args...> overload_cast{};\n#endif\n\n/// Const member function selector for overload_cast\n///  - regular: static_cast<Return (Class::*)(Arg) const>(&Class::func)\n///  - sweet:   overload_cast<Arg>(&Class::func, const_)\nstatic constexpr auto const_ = std::true_type{};\n\n#if !defined(PYBIND11_CPP14) // no overload_cast: providing something that static_assert-fails:\ntemplate <typename... Args>\nstruct overload_cast {\n    static_assert(detail::deferred_t<std::false_type, Args...>::value,\n                  \"pybind11::overload_cast<...> requires compiling in C++14 mode\");\n};\n#endif // overload_cast\n\nPYBIND11_NAMESPACE_BEGIN(detail)\n\n// Adaptor for converting arbitrary container arguments into a vector; implicitly convertible from\n// any standard container (or C-style array) supporting std::begin/std::end, any singleton\n// arithmetic type (if T is arithmetic), or explicitly constructible from an iterator pair.\ntemplate <typename T>\nclass any_container {\n    std::vector<T> v;\n\npublic:\n    any_container() = default;\n\n    // Can construct from a pair of iterators\n    template <typename It, typename = enable_if_t<is_input_iterator<It>::value>>\n    any_container(It first, It last) : v(first, last) {}\n\n    // Implicit conversion constructor from any arbitrary container type\n    // with values convertible to T\n    template <typename Container,\n              typename = enable_if_t<\n                  std::is_convertible<decltype(*std::begin(std::declval<const Container &>())),\n                                      T>::value>>\n    // NOLINTNEXTLINE(google-explicit-constructor)\n    any_container(const Container &c) : any_container(std::begin(c), std::end(c)) {}\n\n    // initializer_list's aren't deducible, so don't get matched by the above template;\n    // we need this to explicitly allow implicit conversion from one:\n    template <typename TIn, typename = enable_if_t<std::is_convertible<TIn, T>::value>>\n    any_container(const std::initializer_list<TIn> &c) : any_container(c.begin(), c.end()) {}\n\n    // Avoid copying if given an rvalue vector of the correct type.\n    // NOLINTNEXTLINE(google-explicit-constructor)\n    any_container(std::vector<T> &&v) : v(std::move(v)) {}\n\n    // Moves the vector out of an rvalue any_container\n    // NOLINTNEXTLINE(google-explicit-constructor)\n    operator std::vector<T> &&() && { return std::move(v); }\n\n    // Dereferencing obtains a reference to the underlying vector\n    std::vector<T> &operator*() { return v; }\n    const std::vector<T> &operator*() const { return v; }\n\n    // -> lets you call methods on the underlying vector\n    std::vector<T> *operator->() { return &v; }\n    const std::vector<T> *operator->() const { return &v; }\n};\n\n// Forward-declaration; see detail/class.h\nstd::string get_fully_qualified_tp_name(PyTypeObject *);\n\ntemplate <typename T>\ninline static std::shared_ptr<T>\ntry_get_shared_from_this(std::enable_shared_from_this<T> *holder_value_ptr) {\n// Pre C++17, this code path exploits undefined behavior, but is known to work on many platforms.\n// Use at your own risk!\n// See also https://en.cppreference.com/w/cpp/memory/enable_shared_from_this, and in particular\n// the `std::shared_ptr<Good> gp1 = not_so_good.getptr();` and `try`-`catch` parts of the example.\n#if defined(__cpp_lib_enable_shared_from_this) && (!defined(_MSC_VER) || _MSC_VER >= 1912)\n    return holder_value_ptr->weak_from_this().lock();\n#else\n    try {\n        return holder_value_ptr->shared_from_this();\n    } catch (const std::bad_weak_ptr &) {\n        return nullptr;\n    }\n#endif\n}\n\n// For silencing \"unused\" compiler warnings in special situations.\ntemplate <typename... Args>\n#if defined(_MSC_VER) && _MSC_VER < 1920 // MSVC 2017\nconstexpr\n#endif\n    inline void\n    silence_unused_warnings(Args &&...) {\n}\n\n// MSVC warning C4100: Unreferenced formal parameter\n#if defined(_MSC_VER) && _MSC_VER <= 1916\n#    define PYBIND11_WORKAROUND_INCORRECT_MSVC_C4100(...)                                         \\\n        detail::silence_unused_warnings(__VA_ARGS__)\n#else\n#    define PYBIND11_WORKAROUND_INCORRECT_MSVC_C4100(...)\n#endif\n\n// GCC -Wunused-but-set-parameter  All GCC versions (as of July 2021).\n#if defined(__GNUG__) && !defined(__clang__) && !defined(__INTEL_COMPILER)\n#    define PYBIND11_WORKAROUND_INCORRECT_GCC_UNUSED_BUT_SET_PARAMETER(...)                       \\\n        detail::silence_unused_warnings(__VA_ARGS__)\n#else\n#    define PYBIND11_WORKAROUND_INCORRECT_GCC_UNUSED_BUT_SET_PARAMETER(...)\n#endif\n\n#if defined(__clang__)                                                                            \\\n    && (defined(__apple_build_version__) /* AppleClang 13.0.0.13000029 was the only data point    \\\n                                            available. */                                         \\\n        || (__clang_major__ >= 7                                                                  \\\n            && __clang_major__ <= 12) /* Clang 3, 5, 13, 14, 15 do not generate the warning. */   \\\n    )\n#    define PYBIND11_DETECTED_CLANG_WITH_MISLEADING_CALL_STD_MOVE_EXPLICITLY_WARNING\n// Example:\n// tests/test_kwargs_and_defaults.cpp:46:68: error: local variable 'args' will be copied despite\n// being returned by name [-Werror,-Wreturn-std-move]\n//     m.def(\"args_function\", [](py::args args) -> py::tuple { return args; });\n//                                                                    ^~~~\n// test_kwargs_and_defaults.cpp:46:68: note: call 'std::move' explicitly to avoid copying\n//     m.def(\"args_function\", [](py::args args) -> py::tuple { return args; });\n//                                                                    ^~~~\n//                                                                    std::move(args)\n#endif\n\n// Pybind offers detailed error messages by default for all builts that are debug (through the\n// negation of NDEBUG). This can also be manually enabled by users, for any builds, through\n// defining PYBIND11_DETAILED_ERROR_MESSAGES. This information is primarily useful for those\n// who are writing (as opposed to merely using) libraries that use pybind11.\n#if !defined(PYBIND11_DETAILED_ERROR_MESSAGES) && !defined(NDEBUG)\n#    define PYBIND11_DETAILED_ERROR_MESSAGES\n#endif\n\nPYBIND11_NAMESPACE_END(detail)\nPYBIND11_NAMESPACE_END(PYBIND11_NAMESPACE)\n"
  },
  {
    "path": "libs/pybind11/include/pybind11/detail/cpp_conduit.h",
    "content": "// Copyright (c) 2024 The pybind Community.\n\n#pragma once\n\n#include <pybind11/pytypes.h>\n\n#include \"common.h\"\n#include \"internals.h\"\n\n#include <typeinfo>\n\nPYBIND11_NAMESPACE_BEGIN(PYBIND11_NAMESPACE)\nPYBIND11_NAMESPACE_BEGIN(detail)\n\n// Forward declaration needed here: Refactoring opportunity.\nextern \"C\" inline PyObject *pybind11_object_new(PyTypeObject *type, PyObject *, PyObject *);\n\ninline bool type_is_managed_by_our_internals(PyTypeObject *type_obj) {\n#if defined(PYPY_VERSION)\n    auto &internals = get_internals();\n    return bool(internals.registered_types_py.find(type_obj)\n                != internals.registered_types_py.end());\n#else\n    return bool(type_obj->tp_new == pybind11_object_new);\n#endif\n}\n\ninline bool is_instance_method_of_type(PyTypeObject *type_obj, PyObject *attr_name) {\n    PyObject *descr = _PyType_Lookup(type_obj, attr_name);\n    return bool((descr != nullptr) && PyInstanceMethod_Check(descr));\n}\n\ninline object try_get_cpp_conduit_method(PyObject *obj) {\n    if (PyType_Check(obj)) {\n        return object();\n    }\n    PyTypeObject *type_obj = Py_TYPE(obj);\n    str attr_name(\"_pybind11_conduit_v1_\");\n    bool assumed_to_be_callable = false;\n    if (type_is_managed_by_our_internals(type_obj)) {\n        if (!is_instance_method_of_type(type_obj, attr_name.ptr())) {\n            return object();\n        }\n        assumed_to_be_callable = true;\n    }\n    PyObject *method = PyObject_GetAttr(obj, attr_name.ptr());\n    if (method == nullptr) {\n        PyErr_Clear();\n        return object();\n    }\n    if (!assumed_to_be_callable && PyCallable_Check(method) == 0) {\n        Py_DECREF(method);\n        return object();\n    }\n    return reinterpret_steal<object>(method);\n}\n\ninline void *try_raw_pointer_ephemeral_from_cpp_conduit(handle src,\n                                                        const std::type_info *cpp_type_info) {\n    object method = try_get_cpp_conduit_method(src.ptr());\n    if (method) {\n        capsule cpp_type_info_capsule(const_cast<void *>(static_cast<const void *>(cpp_type_info)),\n                                      typeid(std::type_info).name());\n        object cpp_conduit = method(bytes(PYBIND11_PLATFORM_ABI_ID),\n                                    cpp_type_info_capsule,\n                                    bytes(\"raw_pointer_ephemeral\"));\n        if (isinstance<capsule>(cpp_conduit)) {\n            return reinterpret_borrow<capsule>(cpp_conduit).get_pointer();\n        }\n    }\n    return nullptr;\n}\n\n#define PYBIND11_HAS_CPP_CONDUIT 1\n\nPYBIND11_NAMESPACE_END(detail)\nPYBIND11_NAMESPACE_END(PYBIND11_NAMESPACE)\n"
  },
  {
    "path": "libs/pybind11/include/pybind11/detail/descr.h",
    "content": "/*\n    pybind11/detail/descr.h: Helper type for concatenating type signatures at compile time\n\n    Copyright (c) 2016 Wenzel Jakob <wenzel.jakob@epfl.ch>\n\n    All rights reserved. Use of this source code is governed by a\n    BSD-style license that can be found in the LICENSE file.\n*/\n\n#pragma once\n\n#include \"common.h\"\n\nPYBIND11_NAMESPACE_BEGIN(PYBIND11_NAMESPACE)\nPYBIND11_NAMESPACE_BEGIN(detail)\n\n#if !defined(_MSC_VER)\n#    define PYBIND11_DESCR_CONSTEXPR static constexpr\n#else\n#    define PYBIND11_DESCR_CONSTEXPR const\n#endif\n\n/* Concatenate type signatures at compile time */\ntemplate <size_t N, typename... Ts>\nstruct descr {\n    char text[N + 1]{'\\0'};\n\n    constexpr descr() = default;\n    // NOLINTNEXTLINE(google-explicit-constructor)\n    constexpr descr(char const (&s)[N + 1]) : descr(s, make_index_sequence<N>()) {}\n\n    template <size_t... Is>\n    constexpr descr(char const (&s)[N + 1], index_sequence<Is...>) : text{s[Is]..., '\\0'} {}\n\n    template <typename... Chars>\n    // NOLINTNEXTLINE(google-explicit-constructor)\n    constexpr descr(char c, Chars... cs) : text{c, static_cast<char>(cs)..., '\\0'} {}\n\n    static constexpr std::array<const std::type_info *, sizeof...(Ts) + 1> types() {\n        return {{&typeid(Ts)..., nullptr}};\n    }\n};\n\ntemplate <size_t N1, size_t N2, typename... Ts1, typename... Ts2, size_t... Is1, size_t... Is2>\nconstexpr descr<N1 + N2, Ts1..., Ts2...> plus_impl(const descr<N1, Ts1...> &a,\n                                                   const descr<N2, Ts2...> &b,\n                                                   index_sequence<Is1...>,\n                                                   index_sequence<Is2...>) {\n    PYBIND11_WORKAROUND_INCORRECT_MSVC_C4100(b);\n    return {a.text[Is1]..., b.text[Is2]...};\n}\n\ntemplate <size_t N1, size_t N2, typename... Ts1, typename... Ts2>\nconstexpr descr<N1 + N2, Ts1..., Ts2...> operator+(const descr<N1, Ts1...> &a,\n                                                   const descr<N2, Ts2...> &b) {\n    return plus_impl(a, b, make_index_sequence<N1>(), make_index_sequence<N2>());\n}\n\ntemplate <size_t N>\nconstexpr descr<N - 1> const_name(char const (&text)[N]) {\n    return descr<N - 1>(text);\n}\nconstexpr descr<0> const_name(char const (&)[1]) { return {}; }\n\ntemplate <size_t Rem, size_t... Digits>\nstruct int_to_str : int_to_str<Rem / 10, Rem % 10, Digits...> {};\ntemplate <size_t... Digits>\nstruct int_to_str<0, Digits...> {\n    // WARNING: This only works with C++17 or higher.\n    static constexpr auto digits = descr<sizeof...(Digits)>(('0' + Digits)...);\n};\n\n// Ternary description (like std::conditional)\ntemplate <bool B, size_t N1, size_t N2>\nconstexpr enable_if_t<B, descr<N1 - 1>> const_name(char const (&text1)[N1], char const (&)[N2]) {\n    return const_name(text1);\n}\ntemplate <bool B, size_t N1, size_t N2>\nconstexpr enable_if_t<!B, descr<N2 - 1>> const_name(char const (&)[N1], char const (&text2)[N2]) {\n    return const_name(text2);\n}\n\ntemplate <bool B, typename T1, typename T2>\nconstexpr enable_if_t<B, T1> const_name(const T1 &d, const T2 &) {\n    return d;\n}\ntemplate <bool B, typename T1, typename T2>\nconstexpr enable_if_t<!B, T2> const_name(const T1 &, const T2 &d) {\n    return d;\n}\n\ntemplate <size_t Size>\nauto constexpr const_name() -> remove_cv_t<decltype(int_to_str<Size / 10, Size % 10>::digits)> {\n    return int_to_str<Size / 10, Size % 10>::digits;\n}\n\ntemplate <typename Type>\nconstexpr descr<1, Type> const_name() {\n    return {'%'};\n}\n\n// If \"_\" is defined as a macro, py::detail::_ cannot be provided.\n// It is therefore best to use py::detail::const_name universally.\n// This block is for backward compatibility only.\n// (The const_name code is repeated to avoid introducing a \"_\" #define ourselves.)\n#ifndef _\n#    define PYBIND11_DETAIL_UNDERSCORE_BACKWARD_COMPATIBILITY\ntemplate <size_t N>\nconstexpr descr<N - 1> _(char const (&text)[N]) {\n    return const_name<N>(text);\n}\ntemplate <bool B, size_t N1, size_t N2>\nconstexpr enable_if_t<B, descr<N1 - 1>> _(char const (&text1)[N1], char const (&text2)[N2]) {\n    return const_name<B, N1, N2>(text1, text2);\n}\ntemplate <bool B, size_t N1, size_t N2>\nconstexpr enable_if_t<!B, descr<N2 - 1>> _(char const (&text1)[N1], char const (&text2)[N2]) {\n    return const_name<B, N1, N2>(text1, text2);\n}\ntemplate <bool B, typename T1, typename T2>\nconstexpr enable_if_t<B, T1> _(const T1 &d1, const T2 &d2) {\n    return const_name<B, T1, T2>(d1, d2);\n}\ntemplate <bool B, typename T1, typename T2>\nconstexpr enable_if_t<!B, T2> _(const T1 &d1, const T2 &d2) {\n    return const_name<B, T1, T2>(d1, d2);\n}\n\ntemplate <size_t Size>\nauto constexpr _() -> remove_cv_t<decltype(int_to_str<Size / 10, Size % 10>::digits)> {\n    return const_name<Size>();\n}\ntemplate <typename Type>\nconstexpr descr<1, Type> _() {\n    return const_name<Type>();\n}\n#endif // #ifndef _\n\nconstexpr descr<0> concat() { return {}; }\n\ntemplate <size_t N, typename... Ts>\nconstexpr descr<N, Ts...> concat(const descr<N, Ts...> &descr) {\n    return descr;\n}\n\n#ifdef __cpp_fold_expressions\ntemplate <size_t N1, size_t N2, typename... Ts1, typename... Ts2>\nconstexpr descr<N1 + N2 + 2, Ts1..., Ts2...> operator,(const descr<N1, Ts1...> &a,\n                                                       const descr<N2, Ts2...> &b) {\n    return a + const_name(\", \") + b;\n}\n\ntemplate <size_t N, typename... Ts, typename... Args>\nconstexpr auto concat(const descr<N, Ts...> &d, const Args &...args) {\n    return (d, ..., args);\n}\n#else\ntemplate <size_t N, typename... Ts, typename... Args>\nconstexpr auto concat(const descr<N, Ts...> &d,\n                      const Args &...args) -> decltype(std::declval<descr<N + 2, Ts...>>()\n                                                       + concat(args...)) {\n    return d + const_name(\", \") + concat(args...);\n}\n#endif\n\ntemplate <size_t N, typename... Ts>\nconstexpr descr<N + 2, Ts...> type_descr(const descr<N, Ts...> &descr) {\n    return const_name(\"{\") + descr + const_name(\"}\");\n}\n\nPYBIND11_NAMESPACE_END(detail)\nPYBIND11_NAMESPACE_END(PYBIND11_NAMESPACE)\n"
  },
  {
    "path": "libs/pybind11/include/pybind11/detail/exception_translation.h",
    "content": "/*\n    pybind11/detail/exception_translation.h: means to translate C++ exceptions to Python exceptions\n\n    Copyright (c) 2024 The Pybind Development Team.\n\n    All rights reserved. Use of this source code is governed by a\n    BSD-style license that can be found in the LICENSE file.\n*/\n\n#pragma once\n\n#include \"common.h\"\n#include \"internals.h\"\n\nPYBIND11_NAMESPACE_BEGIN(PYBIND11_NAMESPACE)\nPYBIND11_NAMESPACE_BEGIN(detail)\n\n// Apply all the extensions translators from a list\n// Return true if one of the translators completed without raising an exception\n// itself. Return of false indicates that if there are other translators\n// available, they should be tried.\ninline bool apply_exception_translators(std::forward_list<ExceptionTranslator> &translators) {\n    auto last_exception = std::current_exception();\n\n    for (auto &translator : translators) {\n        try {\n            translator(last_exception);\n            return true;\n        } catch (...) {\n            last_exception = std::current_exception();\n        }\n    }\n    return false;\n}\n\ninline void try_translate_exceptions() {\n    /* When an exception is caught, give each registered exception\n        translator a chance to translate it to a Python exception. First\n        all module-local translators will be tried in reverse order of\n        registration. If none of the module-locale translators handle\n        the exception (or there are no module-locale translators) then\n        the global translators will be tried, also in reverse order of\n        registration.\n\n        A translator may choose to do one of the following:\n\n        - catch the exception and call py::set_error()\n            to set a standard (or custom) Python exception, or\n        - do nothing and let the exception fall through to the next translator, or\n        - delegate translation to the next translator by throwing a new type of exception.\n        */\n\n    bool handled = with_internals([&](internals &internals) {\n        auto &local_exception_translators = get_local_internals().registered_exception_translators;\n        if (detail::apply_exception_translators(local_exception_translators)) {\n            return true;\n        }\n        auto &exception_translators = internals.registered_exception_translators;\n        if (detail::apply_exception_translators(exception_translators)) {\n            return true;\n        }\n        return false;\n    });\n\n    if (!handled) {\n        set_error(PyExc_SystemError, \"Exception escaped from default exception translator!\");\n    }\n}\n\nPYBIND11_NAMESPACE_END(detail)\nPYBIND11_NAMESPACE_END(PYBIND11_NAMESPACE)\n"
  },
  {
    "path": "libs/pybind11/include/pybind11/detail/init.h",
    "content": "/*\n    pybind11/detail/init.h: init factory function implementation and support code.\n\n    Copyright (c) 2017 Jason Rhinelander <jason@imaginary.ca>\n\n    All rights reserved. Use of this source code is governed by a\n    BSD-style license that can be found in the LICENSE file.\n*/\n\n#pragma once\n\n#include \"class.h\"\n\nPYBIND11_NAMESPACE_BEGIN(PYBIND11_NAMESPACE)\n\nPYBIND11_WARNING_DISABLE_MSVC(4127)\n\nPYBIND11_NAMESPACE_BEGIN(detail)\n\ntemplate <>\nclass type_caster<value_and_holder> {\npublic:\n    bool load(handle h, bool) {\n        value = reinterpret_cast<value_and_holder *>(h.ptr());\n        return true;\n    }\n\n    template <typename>\n    using cast_op_type = value_and_holder &;\n    explicit operator value_and_holder &() { return *value; }\n    static constexpr auto name = const_name<value_and_holder>();\n\nprivate:\n    value_and_holder *value = nullptr;\n};\n\nPYBIND11_NAMESPACE_BEGIN(initimpl)\n\ninline void no_nullptr(void *ptr) {\n    if (!ptr) {\n        throw type_error(\"pybind11::init(): factory function returned nullptr\");\n    }\n}\n\n// Implementing functions for all forms of py::init<...> and py::init(...)\ntemplate <typename Class>\nusing Cpp = typename Class::type;\ntemplate <typename Class>\nusing Alias = typename Class::type_alias;\ntemplate <typename Class>\nusing Holder = typename Class::holder_type;\n\ntemplate <typename Class>\nusing is_alias_constructible = std::is_constructible<Alias<Class>, Cpp<Class> &&>;\n\n// Takes a Cpp pointer and returns true if it actually is a polymorphic Alias instance.\ntemplate <typename Class, enable_if_t<Class::has_alias, int> = 0>\nbool is_alias(Cpp<Class> *ptr) {\n    return dynamic_cast<Alias<Class> *>(ptr) != nullptr;\n}\n// Failing fallback version of the above for a no-alias class (always returns false)\ntemplate <typename /*Class*/>\nconstexpr bool is_alias(void *) {\n    return false;\n}\n\n// Constructs and returns a new object; if the given arguments don't map to a constructor, we fall\n// back to brace aggregate initialization so that for aggregate initialization can be used with\n// py::init, e.g.  `py::init<int, int>` to initialize a `struct T { int a; int b; }`.  For\n// non-aggregate types, we need to use an ordinary T(...) constructor (invoking as `T{...}` usually\n// works, but will not do the expected thing when `T` has an `initializer_list<T>` constructor).\ntemplate <typename Class,\n          typename... Args,\n          detail::enable_if_t<std::is_constructible<Class, Args...>::value, int> = 0>\ninline Class *construct_or_initialize(Args &&...args) {\n    return new Class(std::forward<Args>(args)...);\n}\ntemplate <typename Class,\n          typename... Args,\n          detail::enable_if_t<!std::is_constructible<Class, Args...>::value, int> = 0>\ninline Class *construct_or_initialize(Args &&...args) {\n    return new Class{std::forward<Args>(args)...};\n}\n\n// Attempts to constructs an alias using a `Alias(Cpp &&)` constructor.  This allows types with\n// an alias to provide only a single Cpp factory function as long as the Alias can be\n// constructed from an rvalue reference of the base Cpp type.  This means that Alias classes\n// can, when appropriate, simply define a `Alias(Cpp &&)` constructor rather than needing to\n// inherit all the base class constructors.\ntemplate <typename Class>\nvoid construct_alias_from_cpp(std::true_type /*is_alias_constructible*/,\n                              value_and_holder &v_h,\n                              Cpp<Class> &&base) {\n    v_h.value_ptr() = new Alias<Class>(std::move(base));\n}\ntemplate <typename Class>\n[[noreturn]] void construct_alias_from_cpp(std::false_type /*!is_alias_constructible*/,\n                                           value_and_holder &,\n                                           Cpp<Class> &&) {\n    throw type_error(\"pybind11::init(): unable to convert returned instance to required \"\n                     \"alias class: no `Alias<Class>(Class &&)` constructor available\");\n}\n\n// Error-generating fallback for factories that don't match one of the below construction\n// mechanisms.\ntemplate <typename Class>\nvoid construct(...) {\n    static_assert(!std::is_same<Class, Class>::value /* always false */,\n                  \"pybind11::init(): init function must return a compatible pointer, \"\n                  \"holder, or value\");\n}\n\n// Pointer return v1: the factory function returns a class pointer for a registered class.\n// If we don't need an alias (because this class doesn't have one, or because the final type is\n// inherited on the Python side) we can simply take over ownership.  Otherwise we need to try to\n// construct an Alias from the returned base instance.\ntemplate <typename Class>\nvoid construct(value_and_holder &v_h, Cpp<Class> *ptr, bool need_alias) {\n    PYBIND11_WORKAROUND_INCORRECT_MSVC_C4100(need_alias);\n    no_nullptr(ptr);\n    if (Class::has_alias && need_alias && !is_alias<Class>(ptr)) {\n        // We're going to try to construct an alias by moving the cpp type.  Whether or not\n        // that succeeds, we still need to destroy the original cpp pointer (either the\n        // moved away leftover, if the alias construction works, or the value itself if we\n        // throw an error), but we can't just call `delete ptr`: it might have a special\n        // deleter, or might be shared_from_this.  So we construct a holder around it as if\n        // it was a normal instance, then steal the holder away into a local variable; thus\n        // the holder and destruction happens when we leave the C++ scope, and the holder\n        // class gets to handle the destruction however it likes.\n        v_h.value_ptr() = ptr;\n        v_h.set_instance_registered(true); // Trick to prevent init_instance from registering it\n        // DANGER ZONE BEGIN: exceptions will leave v_h in an invalid state.\n        v_h.type->init_instance(v_h.inst, nullptr);                        // Set up the holder\n        Holder<Class> temp_holder(std::move(v_h.holder<Holder<Class>>())); // Steal the holder\n        v_h.type->dealloc(v_h); // Destroys the moved-out holder remains, resets value ptr to null\n        v_h.set_instance_registered(false);\n        // DANGER ZONE END.\n\n        construct_alias_from_cpp<Class>(is_alias_constructible<Class>{}, v_h, std::move(*ptr));\n    } else {\n        // Otherwise the type isn't inherited, so we don't need an Alias\n        v_h.value_ptr() = ptr;\n    }\n}\n\n// Pointer return v2: a factory that always returns an alias instance ptr.  We simply take over\n// ownership of the pointer.\ntemplate <typename Class, enable_if_t<Class::has_alias, int> = 0>\nvoid construct(value_and_holder &v_h, Alias<Class> *alias_ptr, bool) {\n    no_nullptr(alias_ptr);\n    v_h.value_ptr() = static_cast<Cpp<Class> *>(alias_ptr);\n}\n\n// Holder return: copy its pointer, and move or copy the returned holder into the new instance's\n// holder.  This also handles types like std::shared_ptr<T> and std::unique_ptr<T> where T is a\n// derived type (through those holder's implicit conversion from derived class holder\n// constructors).\ntemplate <typename Class>\nvoid construct(value_and_holder &v_h, Holder<Class> holder, bool need_alias) {\n    PYBIND11_WORKAROUND_INCORRECT_MSVC_C4100(need_alias);\n    auto *ptr = holder_helper<Holder<Class>>::get(holder);\n    no_nullptr(ptr);\n    // If we need an alias, check that the held pointer is actually an alias instance\n    if (Class::has_alias && need_alias && !is_alias<Class>(ptr)) {\n        throw type_error(\"pybind11::init(): construction failed: returned holder-wrapped instance \"\n                         \"is not an alias instance\");\n    }\n\n    v_h.value_ptr() = ptr;\n    v_h.type->init_instance(v_h.inst, &holder);\n}\n\n// return-by-value version 1: returning a cpp class by value.  If the class has an alias and an\n// alias is required the alias must have an `Alias(Cpp &&)` constructor so that we can construct\n// the alias from the base when needed (i.e. because of Python-side inheritance).  When we don't\n// need it, we simply move-construct the cpp value into a new instance.\ntemplate <typename Class>\nvoid construct(value_and_holder &v_h, Cpp<Class> &&result, bool need_alias) {\n    PYBIND11_WORKAROUND_INCORRECT_MSVC_C4100(need_alias);\n    static_assert(is_move_constructible<Cpp<Class>>::value,\n                  \"pybind11::init() return-by-value factory function requires a movable class\");\n    if (Class::has_alias && need_alias) {\n        construct_alias_from_cpp<Class>(is_alias_constructible<Class>{}, v_h, std::move(result));\n    } else {\n        v_h.value_ptr() = new Cpp<Class>(std::move(result));\n    }\n}\n\n// return-by-value version 2: returning a value of the alias type itself.  We move-construct an\n// Alias instance (even if no the python-side inheritance is involved).  The is intended for\n// cases where Alias initialization is always desired.\ntemplate <typename Class>\nvoid construct(value_and_holder &v_h, Alias<Class> &&result, bool) {\n    static_assert(\n        is_move_constructible<Alias<Class>>::value,\n        \"pybind11::init() return-by-alias-value factory function requires a movable alias class\");\n    v_h.value_ptr() = new Alias<Class>(std::move(result));\n}\n\n// Implementing class for py::init<...>()\ntemplate <typename... Args>\nstruct constructor {\n    template <typename Class, typename... Extra, enable_if_t<!Class::has_alias, int> = 0>\n    static void execute(Class &cl, const Extra &...extra) {\n        cl.def(\n            \"__init__\",\n            [](value_and_holder &v_h, Args... args) {\n                v_h.value_ptr() = construct_or_initialize<Cpp<Class>>(std::forward<Args>(args)...);\n            },\n            is_new_style_constructor(),\n            extra...);\n    }\n\n    template <\n        typename Class,\n        typename... Extra,\n        enable_if_t<Class::has_alias && std::is_constructible<Cpp<Class>, Args...>::value, int>\n        = 0>\n    static void execute(Class &cl, const Extra &...extra) {\n        cl.def(\n            \"__init__\",\n            [](value_and_holder &v_h, Args... args) {\n                if (Py_TYPE(v_h.inst) == v_h.type->type) {\n                    v_h.value_ptr()\n                        = construct_or_initialize<Cpp<Class>>(std::forward<Args>(args)...);\n                } else {\n                    v_h.value_ptr()\n                        = construct_or_initialize<Alias<Class>>(std::forward<Args>(args)...);\n                }\n            },\n            is_new_style_constructor(),\n            extra...);\n    }\n\n    template <\n        typename Class,\n        typename... Extra,\n        enable_if_t<Class::has_alias && !std::is_constructible<Cpp<Class>, Args...>::value, int>\n        = 0>\n    static void execute(Class &cl, const Extra &...extra) {\n        cl.def(\n            \"__init__\",\n            [](value_and_holder &v_h, Args... args) {\n                v_h.value_ptr()\n                    = construct_or_initialize<Alias<Class>>(std::forward<Args>(args)...);\n            },\n            is_new_style_constructor(),\n            extra...);\n    }\n};\n\n// Implementing class for py::init_alias<...>()\ntemplate <typename... Args>\nstruct alias_constructor {\n    template <\n        typename Class,\n        typename... Extra,\n        enable_if_t<Class::has_alias && std::is_constructible<Alias<Class>, Args...>::value, int>\n        = 0>\n    static void execute(Class &cl, const Extra &...extra) {\n        cl.def(\n            \"__init__\",\n            [](value_and_holder &v_h, Args... args) {\n                v_h.value_ptr()\n                    = construct_or_initialize<Alias<Class>>(std::forward<Args>(args)...);\n            },\n            is_new_style_constructor(),\n            extra...);\n    }\n};\n\n// Implementation class for py::init(Func) and py::init(Func, AliasFunc)\ntemplate <typename CFunc,\n          typename AFunc = void_type (*)(),\n          typename = function_signature_t<CFunc>,\n          typename = function_signature_t<AFunc>>\nstruct factory;\n\n// Specialization for py::init(Func)\ntemplate <typename Func, typename Return, typename... Args>\nstruct factory<Func, void_type (*)(), Return(Args...)> {\n    remove_reference_t<Func> class_factory;\n\n    // NOLINTNEXTLINE(google-explicit-constructor)\n    factory(Func &&f) : class_factory(std::forward<Func>(f)) {}\n\n    // The given class either has no alias or has no separate alias factory;\n    // this always constructs the class itself.  If the class is registered with an alias\n    // type and an alias instance is needed (i.e. because the final type is a Python class\n    // inheriting from the C++ type) the returned value needs to either already be an alias\n    // instance, or the alias needs to be constructible from a `Class &&` argument.\n    template <typename Class, typename... Extra>\n    void execute(Class &cl, const Extra &...extra) && {\n#if defined(PYBIND11_CPP14)\n        cl.def(\n            \"__init__\",\n            [func = std::move(class_factory)]\n#else\n        auto &func = class_factory;\n        cl.def(\n            \"__init__\",\n            [func]\n#endif\n            (value_and_holder &v_h, Args... args) {\n                construct<Class>(\n                    v_h, func(std::forward<Args>(args)...), Py_TYPE(v_h.inst) != v_h.type->type);\n            },\n            is_new_style_constructor(),\n            extra...);\n    }\n};\n\n// Specialization for py::init(Func, AliasFunc)\ntemplate <typename CFunc,\n          typename AFunc,\n          typename CReturn,\n          typename... CArgs,\n          typename AReturn,\n          typename... AArgs>\nstruct factory<CFunc, AFunc, CReturn(CArgs...), AReturn(AArgs...)> {\n    static_assert(sizeof...(CArgs) == sizeof...(AArgs),\n                  \"pybind11::init(class_factory, alias_factory): class and alias factories \"\n                  \"must have identical argument signatures\");\n    static_assert(all_of<std::is_same<CArgs, AArgs>...>::value,\n                  \"pybind11::init(class_factory, alias_factory): class and alias factories \"\n                  \"must have identical argument signatures\");\n\n    remove_reference_t<CFunc> class_factory;\n    remove_reference_t<AFunc> alias_factory;\n\n    factory(CFunc &&c, AFunc &&a)\n        : class_factory(std::forward<CFunc>(c)), alias_factory(std::forward<AFunc>(a)) {}\n\n    // The class factory is called when the `self` type passed to `__init__` is the direct\n    // class (i.e. not inherited), the alias factory when `self` is a Python-side subtype.\n    template <typename Class, typename... Extra>\n    void execute(Class &cl, const Extra &...extra) && {\n        static_assert(Class::has_alias,\n                      \"The two-argument version of `py::init()` can \"\n                      \"only be used if the class has an alias\");\n#if defined(PYBIND11_CPP14)\n        cl.def(\n            \"__init__\",\n            [class_func = std::move(class_factory), alias_func = std::move(alias_factory)]\n#else\n        auto &class_func = class_factory;\n        auto &alias_func = alias_factory;\n        cl.def(\n            \"__init__\",\n            [class_func, alias_func]\n#endif\n            (value_and_holder &v_h, CArgs... args) {\n                if (Py_TYPE(v_h.inst) == v_h.type->type) {\n                    // If the instance type equals the registered type we don't have inheritance,\n                    // so don't need the alias and can construct using the class function:\n                    construct<Class>(v_h, class_func(std::forward<CArgs>(args)...), false);\n                } else {\n                    construct<Class>(v_h, alias_func(std::forward<CArgs>(args)...), true);\n                }\n            },\n            is_new_style_constructor(),\n            extra...);\n    }\n};\n\n/// Set just the C++ state. Same as `__init__`.\ntemplate <typename Class, typename T>\nvoid setstate(value_and_holder &v_h, T &&result, bool need_alias) {\n    construct<Class>(v_h, std::forward<T>(result), need_alias);\n}\n\n/// Set both the C++ and Python states\ntemplate <typename Class,\n          typename T,\n          typename O,\n          enable_if_t<std::is_convertible<O, handle>::value, int> = 0>\nvoid setstate(value_and_holder &v_h, std::pair<T, O> &&result, bool need_alias) {\n    construct<Class>(v_h, std::move(result.first), need_alias);\n    auto d = handle(result.second);\n    if (PyDict_Check(d.ptr()) && PyDict_Size(d.ptr()) == 0) {\n        // Skipping setattr below, to not force use of py::dynamic_attr() for Class unnecessarily.\n        // See PR #2972 for details.\n        return;\n    }\n    setattr((PyObject *) v_h.inst, \"__dict__\", d);\n}\n\n/// Implementation for py::pickle(GetState, SetState)\ntemplate <typename Get,\n          typename Set,\n          typename = function_signature_t<Get>,\n          typename = function_signature_t<Set>>\nstruct pickle_factory;\n\ntemplate <typename Get,\n          typename Set,\n          typename RetState,\n          typename Self,\n          typename NewInstance,\n          typename ArgState>\nstruct pickle_factory<Get, Set, RetState(Self), NewInstance(ArgState)> {\n    static_assert(std::is_same<intrinsic_t<RetState>, intrinsic_t<ArgState>>::value,\n                  \"The type returned by `__getstate__` must be the same \"\n                  \"as the argument accepted by `__setstate__`\");\n\n    remove_reference_t<Get> get;\n    remove_reference_t<Set> set;\n\n    pickle_factory(Get get, Set set) : get(std::forward<Get>(get)), set(std::forward<Set>(set)) {}\n\n    template <typename Class, typename... Extra>\n    void execute(Class &cl, const Extra &...extra) && {\n        cl.def(\"__getstate__\", std::move(get));\n\n#if defined(PYBIND11_CPP14)\n        cl.def(\n            \"__setstate__\",\n            [func = std::move(set)]\n#else\n        auto &func = set;\n        cl.def(\n            \"__setstate__\",\n            [func]\n#endif\n            (value_and_holder &v_h, ArgState state) {\n                setstate<Class>(\n                    v_h, func(std::forward<ArgState>(state)), Py_TYPE(v_h.inst) != v_h.type->type);\n            },\n            is_new_style_constructor(),\n            extra...);\n    }\n};\n\nPYBIND11_NAMESPACE_END(initimpl)\nPYBIND11_NAMESPACE_END(detail)\nPYBIND11_NAMESPACE_END(PYBIND11_NAMESPACE)\n"
  },
  {
    "path": "libs/pybind11/include/pybind11/detail/internals.h",
    "content": "/*\n    pybind11/detail/internals.h: Internal data structure and related functions\n\n    Copyright (c) 2017 Wenzel Jakob <wenzel.jakob@epfl.ch>\n\n    All rights reserved. Use of this source code is governed by a\n    BSD-style license that can be found in the LICENSE file.\n*/\n\n#pragma once\n\n#include \"common.h\"\n\n#if defined(PYBIND11_SIMPLE_GIL_MANAGEMENT)\n#    include <pybind11/gil.h>\n#endif\n\n#include <pybind11/pytypes.h>\n\n#include <exception>\n#include <mutex>\n#include <thread>\n\n/// Tracks the `internals` and `type_info` ABI version independent of the main library version.\n///\n/// Some portions of the code use an ABI that is conditional depending on this\n/// version number.  That allows ABI-breaking changes to be \"pre-implemented\".\n/// Once the default version number is incremented, the conditional logic that\n/// no longer applies can be removed.  Additionally, users that need not\n/// maintain ABI compatibility can increase the version number in order to take\n/// advantage of any functionality/efficiency improvements that depend on the\n/// newer ABI.\n///\n/// WARNING: If you choose to manually increase the ABI version, note that\n/// pybind11 may not be tested as thoroughly with a non-default ABI version, and\n/// further ABI-incompatible changes may be made before the ABI is officially\n/// changed to the new version.\n#ifndef PYBIND11_INTERNALS_VERSION\n#    if PY_VERSION_HEX >= 0x030C0000 || defined(_MSC_VER)\n// Version bump for Python 3.12+, before first 3.12 beta release.\n// Version bump for MSVC piggy-backed on PR #4779. See comments there.\n#        define PYBIND11_INTERNALS_VERSION 5\n#    else\n#        define PYBIND11_INTERNALS_VERSION 4\n#    endif\n#endif\n\n// This requirement is mainly to reduce the support burden (see PR #4570).\nstatic_assert(PY_VERSION_HEX < 0x030C0000 || PYBIND11_INTERNALS_VERSION >= 5,\n              \"pybind11 ABI version 5 is the minimum for Python 3.12+\");\n\nPYBIND11_NAMESPACE_BEGIN(PYBIND11_NAMESPACE)\n\nusing ExceptionTranslator = void (*)(std::exception_ptr);\n\nPYBIND11_NAMESPACE_BEGIN(detail)\n\nconstexpr const char *internals_function_record_capsule_name = \"pybind11_function_record_capsule\";\n\n// Forward declarations\ninline PyTypeObject *make_static_property_type();\ninline PyTypeObject *make_default_metaclass();\ninline PyObject *make_object_base_type(PyTypeObject *metaclass);\n\n// The old Python Thread Local Storage (TLS) API is deprecated in Python 3.7 in favor of the new\n// Thread Specific Storage (TSS) API.\n// Avoid unnecessary allocation of `Py_tss_t`, since we cannot use\n// `Py_LIMITED_API` anyway.\n#if PYBIND11_INTERNALS_VERSION > 4\n#    define PYBIND11_TLS_KEY_REF Py_tss_t &\n#    if defined(__clang__)\n#        define PYBIND11_TLS_KEY_INIT(var)                                                        \\\n            _Pragma(\"clang diagnostic push\")                                         /**/         \\\n                _Pragma(\"clang diagnostic ignored \\\"-Wmissing-field-initializers\\\"\") /**/         \\\n                Py_tss_t var                                                                      \\\n                = Py_tss_NEEDS_INIT;                                                              \\\n            _Pragma(\"clang diagnostic pop\")\n#    elif defined(__GNUC__) && !defined(__INTEL_COMPILER)\n#        define PYBIND11_TLS_KEY_INIT(var)                                                        \\\n            _Pragma(\"GCC diagnostic push\")                                         /**/           \\\n                _Pragma(\"GCC diagnostic ignored \\\"-Wmissing-field-initializers\\\"\") /**/           \\\n                Py_tss_t var                                                                      \\\n                = Py_tss_NEEDS_INIT;                                                              \\\n            _Pragma(\"GCC diagnostic pop\")\n#    else\n#        define PYBIND11_TLS_KEY_INIT(var) Py_tss_t var = Py_tss_NEEDS_INIT;\n#    endif\n#    define PYBIND11_TLS_KEY_CREATE(var) (PyThread_tss_create(&(var)) == 0)\n#    define PYBIND11_TLS_GET_VALUE(key) PyThread_tss_get(&(key))\n#    define PYBIND11_TLS_REPLACE_VALUE(key, value) PyThread_tss_set(&(key), (value))\n#    define PYBIND11_TLS_DELETE_VALUE(key) PyThread_tss_set(&(key), nullptr)\n#    define PYBIND11_TLS_FREE(key) PyThread_tss_delete(&(key))\n#else\n#    define PYBIND11_TLS_KEY_REF Py_tss_t *\n#    define PYBIND11_TLS_KEY_INIT(var) Py_tss_t *var = nullptr;\n#    define PYBIND11_TLS_KEY_CREATE(var)                                                          \\\n        (((var) = PyThread_tss_alloc()) != nullptr && (PyThread_tss_create((var)) == 0))\n#    define PYBIND11_TLS_GET_VALUE(key) PyThread_tss_get((key))\n#    define PYBIND11_TLS_REPLACE_VALUE(key, value) PyThread_tss_set((key), (value))\n#    define PYBIND11_TLS_DELETE_VALUE(key) PyThread_tss_set((key), nullptr)\n#    define PYBIND11_TLS_FREE(key) PyThread_tss_free(key)\n#endif\n\n// Python loads modules by default with dlopen with the RTLD_LOCAL flag; under libc++ and possibly\n// other STLs, this means `typeid(A)` from one module won't equal `typeid(A)` from another module\n// even when `A` is the same, non-hidden-visibility type (e.g. from a common include).  Under\n// libstdc++, this doesn't happen: equality and the type_index hash are based on the type name,\n// which works.  If not under a known-good stl, provide our own name-based hash and equality\n// functions that use the type name.\n#if (PYBIND11_INTERNALS_VERSION <= 4 && defined(__GLIBCXX__))                                     \\\n    || (PYBIND11_INTERNALS_VERSION >= 5 && !defined(_LIBCPP_VERSION))\ninline bool same_type(const std::type_info &lhs, const std::type_info &rhs) { return lhs == rhs; }\nusing type_hash = std::hash<std::type_index>;\nusing type_equal_to = std::equal_to<std::type_index>;\n#else\ninline bool same_type(const std::type_info &lhs, const std::type_info &rhs) {\n    return lhs.name() == rhs.name() || std::strcmp(lhs.name(), rhs.name()) == 0;\n}\n\nstruct type_hash {\n    size_t operator()(const std::type_index &t) const {\n        size_t hash = 5381;\n        const char *ptr = t.name();\n        while (auto c = static_cast<unsigned char>(*ptr++)) {\n            hash = (hash * 33) ^ c;\n        }\n        return hash;\n    }\n};\n\nstruct type_equal_to {\n    bool operator()(const std::type_index &lhs, const std::type_index &rhs) const {\n        return lhs.name() == rhs.name() || std::strcmp(lhs.name(), rhs.name()) == 0;\n    }\n};\n#endif\n\ntemplate <typename value_type>\nusing type_map = std::unordered_map<std::type_index, value_type, type_hash, type_equal_to>;\n\nstruct override_hash {\n    inline size_t operator()(const std::pair<const PyObject *, const char *> &v) const {\n        size_t value = std::hash<const void *>()(v.first);\n        value ^= std::hash<const void *>()(v.second) + 0x9e3779b9 + (value << 6) + (value >> 2);\n        return value;\n    }\n};\n\nusing instance_map = std::unordered_multimap<const void *, instance *>;\n\n#ifdef Py_GIL_DISABLED\n// Wrapper around PyMutex to provide BasicLockable semantics\nclass pymutex {\n    PyMutex mutex;\n\npublic:\n    pymutex() : mutex({}) {}\n    void lock() { PyMutex_Lock(&mutex); }\n    void unlock() { PyMutex_Unlock(&mutex); }\n};\n\n// Instance map shards are used to reduce mutex contention in free-threaded Python.\nstruct instance_map_shard {\n    instance_map registered_instances;\n    pymutex mutex;\n    // alignas(64) would be better, but causes compile errors in macOS before 10.14 (see #5200)\n    char padding[64 - (sizeof(instance_map) + sizeof(pymutex)) % 64];\n};\n\nstatic_assert(sizeof(instance_map_shard) % 64 == 0,\n              \"instance_map_shard size is not a multiple of 64 bytes\");\n#endif\n\n/// Internal data structure used to track registered instances and types.\n/// Whenever binary incompatible changes are made to this structure,\n/// `PYBIND11_INTERNALS_VERSION` must be incremented.\nstruct internals {\n#ifdef Py_GIL_DISABLED\n    pymutex mutex;\n#endif\n    // std::type_index -> pybind11's type information\n    type_map<type_info *> registered_types_cpp;\n    // PyTypeObject* -> base type_info(s)\n    std::unordered_map<PyTypeObject *, std::vector<type_info *>> registered_types_py;\n#ifdef Py_GIL_DISABLED\n    std::unique_ptr<instance_map_shard[]> instance_shards; // void * -> instance*\n    size_t instance_shards_mask;\n#else\n    instance_map registered_instances; // void * -> instance*\n#endif\n    std::unordered_set<std::pair<const PyObject *, const char *>, override_hash>\n        inactive_override_cache;\n    type_map<std::vector<bool (*)(PyObject *, void *&)>> direct_conversions;\n    std::unordered_map<const PyObject *, std::vector<PyObject *>> patients;\n    std::forward_list<ExceptionTranslator> registered_exception_translators;\n    std::unordered_map<std::string, void *> shared_data; // Custom data to be shared across\n                                                         // extensions\n#if PYBIND11_INTERNALS_VERSION == 4\n    std::vector<PyObject *> unused_loader_patient_stack_remove_at_v5;\n#endif\n    std::forward_list<std::string> static_strings; // Stores the std::strings backing\n                                                   // detail::c_str()\n    PyTypeObject *static_property_type;\n    PyTypeObject *default_metaclass;\n    PyObject *instance_base;\n    // Unused if PYBIND11_SIMPLE_GIL_MANAGEMENT is defined:\n    PYBIND11_TLS_KEY_INIT(tstate)\n#if PYBIND11_INTERNALS_VERSION > 4\n    PYBIND11_TLS_KEY_INIT(loader_life_support_tls_key)\n#endif // PYBIND11_INTERNALS_VERSION > 4\n    // Unused if PYBIND11_SIMPLE_GIL_MANAGEMENT is defined:\n    PyInterpreterState *istate = nullptr;\n\n#if PYBIND11_INTERNALS_VERSION > 4\n    // Note that we have to use a std::string to allocate memory to ensure a unique address\n    // We want unique addresses since we use pointer equality to compare function records\n    std::string function_record_capsule_name = internals_function_record_capsule_name;\n#endif\n\n    internals() = default;\n    internals(const internals &other) = delete;\n    internals &operator=(const internals &other) = delete;\n    ~internals() {\n#if PYBIND11_INTERNALS_VERSION > 4\n        PYBIND11_TLS_FREE(loader_life_support_tls_key);\n#endif // PYBIND11_INTERNALS_VERSION > 4\n\n        // This destructor is called *after* Py_Finalize() in finalize_interpreter().\n        // That *SHOULD BE* fine. The following details what happens when PyThread_tss_free is\n        // called. PYBIND11_TLS_FREE is PyThread_tss_free on python 3.7+. On older python, it does\n        // nothing. PyThread_tss_free calls PyThread_tss_delete and PyMem_RawFree.\n        // PyThread_tss_delete just calls TlsFree (on Windows) or pthread_key_delete (on *NIX).\n        // Neither of those have anything to do with CPython internals. PyMem_RawFree *requires*\n        // that the `tstate` be allocated with the CPython allocator.\n        PYBIND11_TLS_FREE(tstate);\n    }\n};\n\n/// Additional type information which does not fit into the PyTypeObject.\n/// Changes to this struct also require bumping `PYBIND11_INTERNALS_VERSION`.\nstruct type_info {\n    PyTypeObject *type;\n    const std::type_info *cpptype;\n    size_t type_size, type_align, holder_size_in_ptrs;\n    void *(*operator_new)(size_t);\n    void (*init_instance)(instance *, const void *);\n    void (*dealloc)(value_and_holder &v_h);\n    std::vector<PyObject *(*) (PyObject *, PyTypeObject *)> implicit_conversions;\n    std::vector<std::pair<const std::type_info *, void *(*) (void *)>> implicit_casts;\n    std::vector<bool (*)(PyObject *, void *&)> *direct_conversions;\n    buffer_info *(*get_buffer)(PyObject *, void *) = nullptr;\n    void *get_buffer_data = nullptr;\n    void *(*module_local_load)(PyObject *, const type_info *) = nullptr;\n    /* A simple type never occurs as a (direct or indirect) parent\n     * of a class that makes use of multiple inheritance.\n     * A type can be simple even if it has non-simple ancestors as long as it has no descendants.\n     */\n    bool simple_type : 1;\n    /* True if there is no multiple inheritance in this type's inheritance tree */\n    bool simple_ancestors : 1;\n    /* for base vs derived holder_type checks */\n    bool default_holder : 1;\n    /* true if this is a type registered with py::module_local */\n    bool module_local : 1;\n};\n\n/// On MSVC, debug and release builds are not ABI-compatible!\n#if defined(_MSC_VER) && defined(_DEBUG)\n#    define PYBIND11_BUILD_TYPE \"_debug\"\n#else\n#    define PYBIND11_BUILD_TYPE \"\"\n#endif\n\n/// Let's assume that different compilers are ABI-incompatible.\n/// A user can manually set this string if they know their\n/// compiler is compatible.\n#ifndef PYBIND11_COMPILER_TYPE\n#    if defined(_MSC_VER)\n#        define PYBIND11_COMPILER_TYPE \"_msvc\"\n#    elif defined(__INTEL_COMPILER)\n#        define PYBIND11_COMPILER_TYPE \"_icc\"\n#    elif defined(__clang__)\n#        define PYBIND11_COMPILER_TYPE \"_clang\"\n#    elif defined(__PGI)\n#        define PYBIND11_COMPILER_TYPE \"_pgi\"\n#    elif defined(__MINGW32__)\n#        define PYBIND11_COMPILER_TYPE \"_mingw\"\n#    elif defined(__CYGWIN__)\n#        define PYBIND11_COMPILER_TYPE \"_gcc_cygwin\"\n#    elif defined(__GNUC__)\n#        define PYBIND11_COMPILER_TYPE \"_gcc\"\n#    else\n#        define PYBIND11_COMPILER_TYPE \"_unknown\"\n#    endif\n#endif\n\n/// Also standard libs\n#ifndef PYBIND11_STDLIB\n#    if defined(_LIBCPP_VERSION)\n#        define PYBIND11_STDLIB \"_libcpp\"\n#    elif defined(__GLIBCXX__) || defined(__GLIBCPP__)\n#        define PYBIND11_STDLIB \"_libstdcpp\"\n#    else\n#        define PYBIND11_STDLIB \"\"\n#    endif\n#endif\n\n/// On Linux/OSX, changes in __GXX_ABI_VERSION__ indicate ABI incompatibility.\n/// On MSVC, changes in _MSC_VER may indicate ABI incompatibility (#2898).\n#ifndef PYBIND11_BUILD_ABI\n#    if defined(__GXX_ABI_VERSION)\n#        define PYBIND11_BUILD_ABI \"_cxxabi\" PYBIND11_TOSTRING(__GXX_ABI_VERSION)\n#    elif defined(_MSC_VER)\n#        define PYBIND11_BUILD_ABI \"_mscver\" PYBIND11_TOSTRING(_MSC_VER)\n#    else\n#        define PYBIND11_BUILD_ABI \"\"\n#    endif\n#endif\n\n#ifndef PYBIND11_INTERNALS_KIND\n#    define PYBIND11_INTERNALS_KIND \"\"\n#endif\n\n#define PYBIND11_PLATFORM_ABI_ID                                                                  \\\n    PYBIND11_INTERNALS_KIND PYBIND11_COMPILER_TYPE PYBIND11_STDLIB PYBIND11_BUILD_ABI             \\\n        PYBIND11_BUILD_TYPE\n\n#define PYBIND11_INTERNALS_ID                                                                     \\\n    \"__pybind11_internals_v\" PYBIND11_TOSTRING(PYBIND11_INTERNALS_VERSION)                        \\\n        PYBIND11_PLATFORM_ABI_ID \"__\"\n\n#define PYBIND11_MODULE_LOCAL_ID                                                                  \\\n    \"__pybind11_module_local_v\" PYBIND11_TOSTRING(PYBIND11_INTERNALS_VERSION)                     \\\n        PYBIND11_PLATFORM_ABI_ID \"__\"\n\n/// Each module locally stores a pointer to the `internals` data. The data\n/// itself is shared among modules with the same `PYBIND11_INTERNALS_ID`.\ninline internals **&get_internals_pp() {\n    static internals **internals_pp = nullptr;\n    return internals_pp;\n}\n\n// forward decl\ninline void translate_exception(std::exception_ptr);\n\ntemplate <class T,\n          enable_if_t<std::is_same<std::nested_exception, remove_cvref_t<T>>::value, int> = 0>\nbool handle_nested_exception(const T &exc, const std::exception_ptr &p) {\n    std::exception_ptr nested = exc.nested_ptr();\n    if (nested != nullptr && nested != p) {\n        translate_exception(nested);\n        return true;\n    }\n    return false;\n}\n\ntemplate <class T,\n          enable_if_t<!std::is_same<std::nested_exception, remove_cvref_t<T>>::value, int> = 0>\nbool handle_nested_exception(const T &exc, const std::exception_ptr &p) {\n    if (const auto *nep = dynamic_cast<const std::nested_exception *>(std::addressof(exc))) {\n        return handle_nested_exception(*nep, p);\n    }\n    return false;\n}\n\ninline bool raise_err(PyObject *exc_type, const char *msg) {\n    if (PyErr_Occurred()) {\n        raise_from(exc_type, msg);\n        return true;\n    }\n    set_error(exc_type, msg);\n    return false;\n}\n\ninline void translate_exception(std::exception_ptr p) {\n    if (!p) {\n        return;\n    }\n    try {\n        std::rethrow_exception(p);\n    } catch (error_already_set &e) {\n        handle_nested_exception(e, p);\n        e.restore();\n        return;\n    } catch (const builtin_exception &e) {\n        // Could not use template since it's an abstract class.\n        if (const auto *nep = dynamic_cast<const std::nested_exception *>(std::addressof(e))) {\n            handle_nested_exception(*nep, p);\n        }\n        e.set_error();\n        return;\n    } catch (const std::bad_alloc &e) {\n        handle_nested_exception(e, p);\n        raise_err(PyExc_MemoryError, e.what());\n        return;\n    } catch (const std::domain_error &e) {\n        handle_nested_exception(e, p);\n        raise_err(PyExc_ValueError, e.what());\n        return;\n    } catch (const std::invalid_argument &e) {\n        handle_nested_exception(e, p);\n        raise_err(PyExc_ValueError, e.what());\n        return;\n    } catch (const std::length_error &e) {\n        handle_nested_exception(e, p);\n        raise_err(PyExc_ValueError, e.what());\n        return;\n    } catch (const std::out_of_range &e) {\n        handle_nested_exception(e, p);\n        raise_err(PyExc_IndexError, e.what());\n        return;\n    } catch (const std::range_error &e) {\n        handle_nested_exception(e, p);\n        raise_err(PyExc_ValueError, e.what());\n        return;\n    } catch (const std::overflow_error &e) {\n        handle_nested_exception(e, p);\n        raise_err(PyExc_OverflowError, e.what());\n        return;\n    } catch (const std::exception &e) {\n        handle_nested_exception(e, p);\n        raise_err(PyExc_RuntimeError, e.what());\n        return;\n    } catch (const std::nested_exception &e) {\n        handle_nested_exception(e, p);\n        raise_err(PyExc_RuntimeError, \"Caught an unknown nested exception!\");\n        return;\n    } catch (...) {\n        raise_err(PyExc_RuntimeError, \"Caught an unknown exception!\");\n        return;\n    }\n}\n\n#if !defined(__GLIBCXX__)\ninline void translate_local_exception(std::exception_ptr p) {\n    try {\n        if (p) {\n            std::rethrow_exception(p);\n        }\n    } catch (error_already_set &e) {\n        e.restore();\n        return;\n    } catch (const builtin_exception &e) {\n        e.set_error();\n        return;\n    }\n}\n#endif\n\ninline object get_python_state_dict() {\n    object state_dict;\n#if PYBIND11_INTERNALS_VERSION <= 4 || PY_VERSION_HEX < 0x03080000 || defined(PYPY_VERSION)\n    state_dict = reinterpret_borrow<object>(PyEval_GetBuiltins());\n#else\n#    if PY_VERSION_HEX < 0x03090000\n    PyInterpreterState *istate = _PyInterpreterState_Get();\n#    else\n    PyInterpreterState *istate = PyInterpreterState_Get();\n#    endif\n    if (istate) {\n        state_dict = reinterpret_borrow<object>(PyInterpreterState_GetDict(istate));\n    }\n#endif\n    if (!state_dict) {\n        raise_from(PyExc_SystemError, \"pybind11::detail::get_python_state_dict() FAILED\");\n        throw error_already_set();\n    }\n    return state_dict;\n}\n\ninline object get_internals_obj_from_state_dict(handle state_dict) {\n    return reinterpret_steal<object>(\n        dict_getitemstringref(state_dict.ptr(), PYBIND11_INTERNALS_ID));\n}\n\ninline internals **get_internals_pp_from_capsule(handle obj) {\n    void *raw_ptr = PyCapsule_GetPointer(obj.ptr(), /*name=*/nullptr);\n    if (raw_ptr == nullptr) {\n        raise_from(PyExc_SystemError, \"pybind11::detail::get_internals_pp_from_capsule() FAILED\");\n        throw error_already_set();\n    }\n    return static_cast<internals **>(raw_ptr);\n}\n\ninline uint64_t round_up_to_next_pow2(uint64_t x) {\n    // Round-up to the next power of two.\n    // See https://graphics.stanford.edu/~seander/bithacks.html#RoundUpPowerOf2\n    x--;\n    x |= (x >> 1);\n    x |= (x >> 2);\n    x |= (x >> 4);\n    x |= (x >> 8);\n    x |= (x >> 16);\n    x |= (x >> 32);\n    x++;\n    return x;\n}\n\n/// Return a reference to the current `internals` data\nPYBIND11_NOINLINE internals &get_internals() {\n    auto **&internals_pp = get_internals_pp();\n    if (internals_pp && *internals_pp) {\n        return **internals_pp;\n    }\n\n#if defined(PYBIND11_SIMPLE_GIL_MANAGEMENT)\n    gil_scoped_acquire gil;\n#else\n    // Ensure that the GIL is held since we will need to make Python calls.\n    // Cannot use py::gil_scoped_acquire here since that constructor calls get_internals.\n    struct gil_scoped_acquire_local {\n        gil_scoped_acquire_local() : state(PyGILState_Ensure()) {}\n        gil_scoped_acquire_local(const gil_scoped_acquire_local &) = delete;\n        gil_scoped_acquire_local &operator=(const gil_scoped_acquire_local &) = delete;\n        ~gil_scoped_acquire_local() { PyGILState_Release(state); }\n        const PyGILState_STATE state;\n    } gil;\n#endif\n    error_scope err_scope;\n\n    dict state_dict = get_python_state_dict();\n    if (object internals_obj = get_internals_obj_from_state_dict(state_dict)) {\n        internals_pp = get_internals_pp_from_capsule(internals_obj);\n    }\n    if (internals_pp && *internals_pp) {\n        // We loaded the internals through `state_dict`, which means that our `error_already_set`\n        // and `builtin_exception` may be different local classes than the ones set up in the\n        // initial exception translator, below, so add another for our local exception classes.\n        //\n        // libstdc++ doesn't require this (types there are identified only by name)\n        // libc++ with CPython doesn't require this (types are explicitly exported)\n        // libc++ with PyPy still need it, awaiting further investigation\n#if !defined(__GLIBCXX__)\n        (*internals_pp)->registered_exception_translators.push_front(&translate_local_exception);\n#endif\n    } else {\n        if (!internals_pp) {\n            internals_pp = new internals *();\n        }\n        auto *&internals_ptr = *internals_pp;\n        internals_ptr = new internals();\n\n        PyThreadState *tstate = PyThreadState_Get();\n        // NOLINTNEXTLINE(bugprone-assignment-in-if-condition)\n        if (!PYBIND11_TLS_KEY_CREATE(internals_ptr->tstate)) {\n            pybind11_fail(\"get_internals: could not successfully initialize the tstate TSS key!\");\n        }\n        PYBIND11_TLS_REPLACE_VALUE(internals_ptr->tstate, tstate);\n\n#if PYBIND11_INTERNALS_VERSION > 4\n        // NOLINTNEXTLINE(bugprone-assignment-in-if-condition)\n        if (!PYBIND11_TLS_KEY_CREATE(internals_ptr->loader_life_support_tls_key)) {\n            pybind11_fail(\"get_internals: could not successfully initialize the \"\n                          \"loader_life_support TSS key!\");\n        }\n#endif\n        internals_ptr->istate = tstate->interp;\n        state_dict[PYBIND11_INTERNALS_ID] = capsule(reinterpret_cast<void *>(internals_pp));\n        internals_ptr->registered_exception_translators.push_front(&translate_exception);\n        internals_ptr->static_property_type = make_static_property_type();\n        internals_ptr->default_metaclass = make_default_metaclass();\n        internals_ptr->instance_base = make_object_base_type(internals_ptr->default_metaclass);\n#ifdef Py_GIL_DISABLED\n        // Scale proportional to the number of cores. 2x is a heuristic to reduce contention.\n        auto num_shards\n            = static_cast<size_t>(round_up_to_next_pow2(2 * std::thread::hardware_concurrency()));\n        if (num_shards == 0) {\n            num_shards = 1;\n        }\n        internals_ptr->instance_shards.reset(new instance_map_shard[num_shards]);\n        internals_ptr->instance_shards_mask = num_shards - 1;\n#endif // Py_GIL_DISABLED\n    }\n    return **internals_pp;\n}\n\n// the internals struct (above) is shared between all the modules. local_internals are only\n// for a single module. Any changes made to internals may require an update to\n// PYBIND11_INTERNALS_VERSION, breaking backwards compatibility. local_internals is, by design,\n// restricted to a single module. Whether a module has local internals or not should not\n// impact any other modules, because the only things accessing the local internals is the\n// module that contains them.\nstruct local_internals {\n    type_map<type_info *> registered_types_cpp;\n    std::forward_list<ExceptionTranslator> registered_exception_translators;\n#if PYBIND11_INTERNALS_VERSION == 4\n\n    // For ABI compatibility, we can't store the loader_life_support TLS key in\n    // the `internals` struct directly.  Instead, we store it in `shared_data` and\n    // cache a copy in `local_internals`.  If we allocated a separate TLS key for\n    // each instance of `local_internals`, we could end up allocating hundreds of\n    // TLS keys if hundreds of different pybind11 modules are loaded (which is a\n    // plausible number).\n    PYBIND11_TLS_KEY_INIT(loader_life_support_tls_key)\n\n    // Holds the shared TLS key for the loader_life_support stack.\n    struct shared_loader_life_support_data {\n        PYBIND11_TLS_KEY_INIT(loader_life_support_tls_key)\n        shared_loader_life_support_data() {\n            // NOLINTNEXTLINE(bugprone-assignment-in-if-condition)\n            if (!PYBIND11_TLS_KEY_CREATE(loader_life_support_tls_key)) {\n                pybind11_fail(\"local_internals: could not successfully initialize the \"\n                              \"loader_life_support TLS key!\");\n            }\n        }\n        // We can't help but leak the TLS key, because Python never unloads extension modules.\n    };\n\n    local_internals() {\n        auto &internals = get_internals();\n        // Get or create the `loader_life_support_stack_key`.\n        auto &ptr = internals.shared_data[\"_life_support\"];\n        if (!ptr) {\n            ptr = new shared_loader_life_support_data;\n        }\n        loader_life_support_tls_key\n            = static_cast<shared_loader_life_support_data *>(ptr)->loader_life_support_tls_key;\n    }\n#endif //  PYBIND11_INTERNALS_VERSION == 4\n};\n\n/// Works like `get_internals`, but for things which are locally registered.\ninline local_internals &get_local_internals() {\n    // Current static can be created in the interpreter finalization routine. If the later will be\n    // destroyed in another static variable destructor, creation of this static there will cause\n    // static deinitialization fiasco. In order to avoid it we avoid destruction of the\n    // local_internals static. One can read more about the problem and current solution here:\n    // https://google.github.io/styleguide/cppguide.html#Static_and_Global_Variables\n    static auto *locals = new local_internals();\n    return *locals;\n}\n\n#ifdef Py_GIL_DISABLED\n#    define PYBIND11_LOCK_INTERNALS(internals) std::unique_lock<pymutex> lock((internals).mutex)\n#else\n#    define PYBIND11_LOCK_INTERNALS(internals)\n#endif\n\ntemplate <typename F>\ninline auto with_internals(const F &cb) -> decltype(cb(get_internals())) {\n    auto &internals = get_internals();\n    PYBIND11_LOCK_INTERNALS(internals);\n    return cb(internals);\n}\n\ninline std::uint64_t mix64(std::uint64_t z) {\n    // David Stafford's variant 13 of the MurmurHash3 finalizer popularized\n    // by the SplitMix PRNG.\n    // https://zimbry.blogspot.com/2011/09/better-bit-mixing-improving-on.html\n    z = (z ^ (z >> 30)) * 0xbf58476d1ce4e5b9;\n    z = (z ^ (z >> 27)) * 0x94d049bb133111eb;\n    return z ^ (z >> 31);\n}\n\ntemplate <typename F>\ninline auto with_instance_map(const void *ptr,\n                              const F &cb) -> decltype(cb(std::declval<instance_map &>())) {\n    auto &internals = get_internals();\n\n#ifdef Py_GIL_DISABLED\n    // Hash address to compute shard, but ignore low bits. We'd like allocations\n    // from the same thread/core to map to the same shard and allocations from\n    // other threads/cores to map to other shards. Using the high bits is a good\n    // heuristic because memory allocators often have a per-thread\n    // arena/superblock/segment from which smaller allocations are served.\n    auto addr = reinterpret_cast<std::uintptr_t>(ptr);\n    auto hash = mix64(static_cast<std::uint64_t>(addr >> 20));\n    auto idx = static_cast<size_t>(hash & internals.instance_shards_mask);\n\n    auto &shard = internals.instance_shards[idx];\n    std::unique_lock<pymutex> lock(shard.mutex);\n    return cb(shard.registered_instances);\n#else\n    (void) ptr;\n    return cb(internals.registered_instances);\n#endif\n}\n\n// Returns the number of registered instances for testing purposes.  The result may not be\n// consistent if other threads are registering or unregistering instances concurrently.\ninline size_t num_registered_instances() {\n    auto &internals = get_internals();\n#ifdef Py_GIL_DISABLED\n    size_t count = 0;\n    for (size_t i = 0; i <= internals.instance_shards_mask; ++i) {\n        auto &shard = internals.instance_shards[i];\n        std::unique_lock<pymutex> lock(shard.mutex);\n        count += shard.registered_instances.size();\n    }\n    return count;\n#else\n    return internals.registered_instances.size();\n#endif\n}\n\n/// Constructs a std::string with the given arguments, stores it in `internals`, and returns its\n/// `c_str()`.  Such strings objects have a long storage duration -- the internal strings are only\n/// cleared when the program exits or after interpreter shutdown (when embedding), and so are\n/// suitable for c-style strings needed by Python internals (such as PyTypeObject's tp_name).\ntemplate <typename... Args>\nconst char *c_str(Args &&...args) {\n    // GCC 4.8 doesn't like parameter unpack within lambda capture, so use\n    // PYBIND11_LOCK_INTERNALS.\n    auto &internals = get_internals();\n    PYBIND11_LOCK_INTERNALS(internals);\n    auto &strings = internals.static_strings;\n    strings.emplace_front(std::forward<Args>(args)...);\n    return strings.front().c_str();\n}\n\ninline const char *get_function_record_capsule_name() {\n#if PYBIND11_INTERNALS_VERSION > 4\n    return get_internals().function_record_capsule_name.c_str();\n#else\n    return nullptr;\n#endif\n}\n\n// Determine whether or not the following capsule contains a pybind11 function record.\n// Note that we use `internals` to make sure that only ABI compatible records are touched.\n//\n// This check is currently used in two places:\n// - An important optimization in functional.h to avoid overhead in C++ -> Python -> C++\n// - The sibling feature of cpp_function to allow overloads\ninline bool is_function_record_capsule(const capsule &cap) {\n    // Pointer equality as we rely on internals() to ensure unique pointers\n    return cap.name() == get_function_record_capsule_name();\n}\n\nPYBIND11_NAMESPACE_END(detail)\n\n/// Returns a named pointer that is shared among all extension modules (using the same\n/// pybind11 version) running in the current interpreter. Names starting with underscores\n/// are reserved for internal usage. Returns `nullptr` if no matching entry was found.\nPYBIND11_NOINLINE void *get_shared_data(const std::string &name) {\n    return detail::with_internals([&](detail::internals &internals) {\n        auto it = internals.shared_data.find(name);\n        return it != internals.shared_data.end() ? it->second : nullptr;\n    });\n}\n\n/// Set the shared data that can be later recovered by `get_shared_data()`.\nPYBIND11_NOINLINE void *set_shared_data(const std::string &name, void *data) {\n    return detail::with_internals([&](detail::internals &internals) {\n        internals.shared_data[name] = data;\n        return data;\n    });\n}\n\n/// Returns a typed reference to a shared data entry (by using `get_shared_data()`) if\n/// such entry exists. Otherwise, a new object of default-constructible type `T` is\n/// added to the shared data under the given name and a reference to it is returned.\ntemplate <typename T>\nT &get_or_create_shared_data(const std::string &name) {\n    return *detail::with_internals([&](detail::internals &internals) {\n        auto it = internals.shared_data.find(name);\n        T *ptr = (T *) (it != internals.shared_data.end() ? it->second : nullptr);\n        if (!ptr) {\n            ptr = new T();\n            internals.shared_data[name] = ptr;\n        }\n        return ptr;\n    });\n}\n\nPYBIND11_NAMESPACE_END(PYBIND11_NAMESPACE)\n"
  },
  {
    "path": "libs/pybind11/include/pybind11/detail/type_caster_base.h",
    "content": "/*\n    pybind11/detail/type_caster_base.h (originally first part of pybind11/cast.h)\n\n    Copyright (c) 2016 Wenzel Jakob <wenzel.jakob@epfl.ch>\n\n    All rights reserved. Use of this source code is governed by a\n    BSD-style license that can be found in the LICENSE file.\n*/\n\n#pragma once\n\n#include <pybind11/pytypes.h>\n\n#include \"common.h\"\n#include \"cpp_conduit.h\"\n#include \"descr.h\"\n#include \"internals.h\"\n#include \"typeid.h\"\n#include \"value_and_holder.h\"\n\n#include <cstdint>\n#include <cstring>\n#include <iterator>\n#include <new>\n#include <stdexcept>\n#include <string>\n#include <type_traits>\n#include <typeindex>\n#include <typeinfo>\n#include <unordered_map>\n#include <utility>\n#include <vector>\n\nPYBIND11_NAMESPACE_BEGIN(PYBIND11_NAMESPACE)\nPYBIND11_NAMESPACE_BEGIN(detail)\n\n/// A life support system for temporary objects created by `type_caster::load()`.\n/// Adding a patient will keep it alive up until the enclosing function returns.\nclass loader_life_support {\nprivate:\n    loader_life_support *parent = nullptr;\n    std::unordered_set<PyObject *> keep_alive;\n\n    // Store stack pointer in thread-local storage.\n    static PYBIND11_TLS_KEY_REF get_stack_tls_key() {\n#if PYBIND11_INTERNALS_VERSION == 4\n        return get_local_internals().loader_life_support_tls_key;\n#else\n        return get_internals().loader_life_support_tls_key;\n#endif\n    }\n    static loader_life_support *get_stack_top() {\n        return static_cast<loader_life_support *>(PYBIND11_TLS_GET_VALUE(get_stack_tls_key()));\n    }\n    static void set_stack_top(loader_life_support *value) {\n        PYBIND11_TLS_REPLACE_VALUE(get_stack_tls_key(), value);\n    }\n\npublic:\n    /// A new patient frame is created when a function is entered\n    loader_life_support() : parent{get_stack_top()} { set_stack_top(this); }\n\n    /// ... and destroyed after it returns\n    ~loader_life_support() {\n        if (get_stack_top() != this) {\n            pybind11_fail(\"loader_life_support: internal error\");\n        }\n        set_stack_top(parent);\n        for (auto *item : keep_alive) {\n            Py_DECREF(item);\n        }\n    }\n\n    /// This can only be used inside a pybind11-bound function, either by `argument_loader`\n    /// at argument preparation time or by `py::cast()` at execution time.\n    PYBIND11_NOINLINE static void add_patient(handle h) {\n        loader_life_support *frame = get_stack_top();\n        if (!frame) {\n            // NOTE: It would be nice to include the stack frames here, as this indicates\n            // use of pybind11::cast<> outside the normal call framework, finding such\n            // a location is challenging. Developers could consider printing out\n            // stack frame addresses here using something like __builtin_frame_address(0)\n            throw cast_error(\"When called outside a bound function, py::cast() cannot \"\n                             \"do Python -> C++ conversions which require the creation \"\n                             \"of temporary values\");\n        }\n\n        if (frame->keep_alive.insert(h.ptr()).second) {\n            Py_INCREF(h.ptr());\n        }\n    }\n};\n\n// Gets the cache entry for the given type, creating it if necessary.  The return value is the pair\n// returned by emplace, i.e. an iterator for the entry and a bool set to `true` if the entry was\n// just created.\ninline std::pair<decltype(internals::registered_types_py)::iterator, bool>\nall_type_info_get_cache(PyTypeObject *type);\n\n// Band-aid workaround to fix a subtle but serious bug in a minimalistic fashion. See PR #4762.\ninline void all_type_info_add_base_most_derived_first(std::vector<type_info *> &bases,\n                                                      type_info *addl_base) {\n    for (auto it = bases.begin(); it != bases.end(); it++) {\n        type_info *existing_base = *it;\n        if (PyType_IsSubtype(addl_base->type, existing_base->type) != 0) {\n            bases.insert(it, addl_base);\n            return;\n        }\n    }\n    bases.push_back(addl_base);\n}\n\n// Populates a just-created cache entry.\nPYBIND11_NOINLINE void all_type_info_populate(PyTypeObject *t, std::vector<type_info *> &bases) {\n    assert(bases.empty());\n    std::vector<PyTypeObject *> check;\n    for (handle parent : reinterpret_borrow<tuple>(t->tp_bases)) {\n        check.push_back((PyTypeObject *) parent.ptr());\n    }\n\n    auto const &type_dict = get_internals().registered_types_py;\n    for (size_t i = 0; i < check.size(); i++) {\n        auto *type = check[i];\n        // Ignore Python2 old-style class super type:\n        if (!PyType_Check((PyObject *) type)) {\n            continue;\n        }\n\n        // Check `type` in the current set of registered python types:\n        auto it = type_dict.find(type);\n        if (it != type_dict.end()) {\n            // We found a cache entry for it, so it's either pybind-registered or has pre-computed\n            // pybind bases, but we have to make sure we haven't already seen the type(s) before:\n            // we want to follow Python/virtual C++ rules that there should only be one instance of\n            // a common base.\n            for (auto *tinfo : it->second) {\n                // NB: Could use a second set here, rather than doing a linear search, but since\n                // having a large number of immediate pybind11-registered types seems fairly\n                // unlikely, that probably isn't worthwhile.\n                bool found = false;\n                for (auto *known : bases) {\n                    if (known == tinfo) {\n                        found = true;\n                        break;\n                    }\n                }\n                if (!found) {\n                    all_type_info_add_base_most_derived_first(bases, tinfo);\n                }\n            }\n        } else if (type->tp_bases) {\n            // It's some python type, so keep follow its bases classes to look for one or more\n            // registered types\n            if (i + 1 == check.size()) {\n                // When we're at the end, we can pop off the current element to avoid growing\n                // `check` when adding just one base (which is typical--i.e. when there is no\n                // multiple inheritance)\n                check.pop_back();\n                i--;\n            }\n            for (handle parent : reinterpret_borrow<tuple>(type->tp_bases)) {\n                check.push_back((PyTypeObject *) parent.ptr());\n            }\n        }\n    }\n}\n\n/**\n * Extracts vector of type_info pointers of pybind-registered roots of the given Python type.  Will\n * be just 1 pybind type for the Python type of a pybind-registered class, or for any Python-side\n * derived class that uses single inheritance.  Will contain as many types as required for a Python\n * class that uses multiple inheritance to inherit (directly or indirectly) from multiple\n * pybind-registered classes.  Will be empty if neither the type nor any base classes are\n * pybind-registered.\n *\n * The value is cached for the lifetime of the Python type.\n */\ninline const std::vector<detail::type_info *> &all_type_info(PyTypeObject *type) {\n    auto ins = all_type_info_get_cache(type);\n    if (ins.second) {\n        // New cache entry: populate it\n        all_type_info_populate(type, ins.first->second);\n    }\n\n    return ins.first->second;\n}\n\n/**\n * Gets a single pybind11 type info for a python type.  Returns nullptr if neither the type nor any\n * ancestors are pybind11-registered.  Throws an exception if there are multiple bases--use\n * `all_type_info` instead if you want to support multiple bases.\n */\nPYBIND11_NOINLINE detail::type_info *get_type_info(PyTypeObject *type) {\n    const auto &bases = all_type_info(type);\n    if (bases.empty()) {\n        return nullptr;\n    }\n    if (bases.size() > 1) {\n        pybind11_fail(\n            \"pybind11::detail::get_type_info: type has multiple pybind11-registered bases\");\n    }\n    return bases.front();\n}\n\ninline detail::type_info *get_local_type_info(const std::type_index &tp) {\n    auto &locals = get_local_internals().registered_types_cpp;\n    auto it = locals.find(tp);\n    if (it != locals.end()) {\n        return it->second;\n    }\n    return nullptr;\n}\n\ninline detail::type_info *get_global_type_info(const std::type_index &tp) {\n    return with_internals([&](internals &internals) {\n        detail::type_info *type_info = nullptr;\n        auto &types = internals.registered_types_cpp;\n        auto it = types.find(tp);\n        if (it != types.end()) {\n            type_info = it->second;\n        }\n        return type_info;\n    });\n}\n\n/// Return the type info for a given C++ type; on lookup failure can either throw or return\n/// nullptr.\nPYBIND11_NOINLINE detail::type_info *get_type_info(const std::type_index &tp,\n                                                   bool throw_if_missing = false) {\n    if (auto *ltype = get_local_type_info(tp)) {\n        return ltype;\n    }\n    if (auto *gtype = get_global_type_info(tp)) {\n        return gtype;\n    }\n\n    if (throw_if_missing) {\n        std::string tname = tp.name();\n        detail::clean_type_id(tname);\n        pybind11_fail(\"pybind11::detail::get_type_info: unable to find type info for \\\"\"\n                      + std::move(tname) + '\"');\n    }\n    return nullptr;\n}\n\nPYBIND11_NOINLINE handle get_type_handle(const std::type_info &tp, bool throw_if_missing) {\n    detail::type_info *type_info = get_type_info(tp, throw_if_missing);\n    return handle(type_info ? ((PyObject *) type_info->type) : nullptr);\n}\n\n// Searches the inheritance graph for a registered Python instance, using all_type_info().\nPYBIND11_NOINLINE handle find_registered_python_instance(void *src,\n                                                         const detail::type_info *tinfo) {\n    return with_instance_map(src, [&](instance_map &instances) {\n        auto it_instances = instances.equal_range(src);\n        for (auto it_i = it_instances.first; it_i != it_instances.second; ++it_i) {\n            for (auto *instance_type : detail::all_type_info(Py_TYPE(it_i->second))) {\n                if (instance_type && same_type(*instance_type->cpptype, *tinfo->cpptype)) {\n                    return handle((PyObject *) it_i->second).inc_ref();\n                }\n            }\n        }\n        return handle();\n    });\n}\n\n// Container for accessing and iterating over an instance's values/holders\nstruct values_and_holders {\nprivate:\n    instance *inst;\n    using type_vec = std::vector<detail::type_info *>;\n    const type_vec &tinfo;\n\npublic:\n    explicit values_and_holders(instance *inst)\n        : inst{inst}, tinfo(all_type_info(Py_TYPE(inst))) {}\n\n    explicit values_and_holders(PyObject *obj)\n        : inst{nullptr}, tinfo(all_type_info(Py_TYPE(obj))) {\n        if (!tinfo.empty()) {\n            inst = reinterpret_cast<instance *>(obj);\n        }\n    }\n\n    struct iterator {\n    private:\n        instance *inst = nullptr;\n        const type_vec *types = nullptr;\n        value_and_holder curr;\n        friend struct values_and_holders;\n        iterator(instance *inst, const type_vec *tinfo) : inst{inst}, types{tinfo} {\n            if (inst != nullptr) {\n                assert(!types->empty());\n                curr = value_and_holder(\n                    inst /* instance */,\n                    (*types)[0] /* type info */,\n                    0, /* vpos: (non-simple types only): the first vptr comes first */\n                    0 /* index */);\n            }\n        }\n        // Past-the-end iterator:\n        explicit iterator(size_t end) : curr(end) {}\n\n    public:\n        bool operator==(const iterator &other) const { return curr.index == other.curr.index; }\n        bool operator!=(const iterator &other) const { return curr.index != other.curr.index; }\n        iterator &operator++() {\n            if (!inst->simple_layout) {\n                curr.vh += 1 + (*types)[curr.index]->holder_size_in_ptrs;\n            }\n            ++curr.index;\n            curr.type = curr.index < types->size() ? (*types)[curr.index] : nullptr;\n            return *this;\n        }\n        value_and_holder &operator*() { return curr; }\n        value_and_holder *operator->() { return &curr; }\n    };\n\n    iterator begin() { return iterator(inst, &tinfo); }\n    iterator end() { return iterator(tinfo.size()); }\n\n    iterator find(const type_info *find_type) {\n        auto it = begin(), endit = end();\n        while (it != endit && it->type != find_type) {\n            ++it;\n        }\n        return it;\n    }\n\n    size_t size() { return tinfo.size(); }\n\n    // Band-aid workaround to fix a subtle but serious bug in a minimalistic fashion. See PR #4762.\n    bool is_redundant_value_and_holder(const value_and_holder &vh) {\n        for (size_t i = 0; i < vh.index; i++) {\n            if (PyType_IsSubtype(tinfo[i]->type, tinfo[vh.index]->type) != 0) {\n                return true;\n            }\n        }\n        return false;\n    }\n};\n\n/**\n * Extracts C++ value and holder pointer references from an instance (which may contain multiple\n * values/holders for python-side multiple inheritance) that match the given type.  Throws an error\n * if the given type (or ValueType, if omitted) is not a pybind11 base of the given instance.  If\n * `find_type` is omitted (or explicitly specified as nullptr) the first value/holder are returned,\n * regardless of type (and the resulting .type will be nullptr).\n *\n * The returned object should be short-lived: in particular, it must not outlive the called-upon\n * instance.\n */\nPYBIND11_NOINLINE value_and_holder\ninstance::get_value_and_holder(const type_info *find_type /*= nullptr default in common.h*/,\n                               bool throw_if_missing /*= true in common.h*/) {\n    // Optimize common case:\n    if (!find_type || Py_TYPE(this) == find_type->type) {\n        return value_and_holder(this, find_type, 0, 0);\n    }\n\n    detail::values_and_holders vhs(this);\n    auto it = vhs.find(find_type);\n    if (it != vhs.end()) {\n        return *it;\n    }\n\n    if (!throw_if_missing) {\n        return value_and_holder();\n    }\n\n#if defined(PYBIND11_DETAILED_ERROR_MESSAGES)\n    pybind11_fail(\"pybind11::detail::instance::get_value_and_holder: `\"\n                  + get_fully_qualified_tp_name(find_type->type)\n                  + \"' is not a pybind11 base of the given `\"\n                  + get_fully_qualified_tp_name(Py_TYPE(this)) + \"' instance\");\n#else\n    pybind11_fail(\n        \"pybind11::detail::instance::get_value_and_holder: \"\n        \"type is not a pybind11 base of the given instance \"\n        \"(#define PYBIND11_DETAILED_ERROR_MESSAGES or compile in debug mode for type details)\");\n#endif\n}\n\nPYBIND11_NOINLINE void instance::allocate_layout() {\n    const auto &tinfo = all_type_info(Py_TYPE(this));\n\n    const size_t n_types = tinfo.size();\n\n    if (n_types == 0) {\n        pybind11_fail(\n            \"instance allocation failed: new instance has no pybind11-registered base types\");\n    }\n\n    simple_layout\n        = n_types == 1 && tinfo.front()->holder_size_in_ptrs <= instance_simple_holder_in_ptrs();\n\n    // Simple path: no python-side multiple inheritance, and a small-enough holder\n    if (simple_layout) {\n        simple_value_holder[0] = nullptr;\n        simple_holder_constructed = false;\n        simple_instance_registered = false;\n    } else { // multiple base types or a too-large holder\n        // Allocate space to hold: [v1*][h1][v2*][h2]...[bb...] where [vN*] is a value pointer,\n        // [hN] is the (uninitialized) holder instance for value N, and [bb...] is a set of bool\n        // values that tracks whether each associated holder has been initialized.  Each [block] is\n        // padded, if necessary, to an integer multiple of sizeof(void *).\n        size_t space = 0;\n        for (auto *t : tinfo) {\n            space += 1;                      // value pointer\n            space += t->holder_size_in_ptrs; // holder instance\n        }\n        size_t flags_at = space;\n        space += size_in_ptrs(n_types); // status bytes (holder_constructed and\n                                        // instance_registered)\n\n        // Allocate space for flags, values, and holders, and initialize it to 0 (flags and values,\n        // in particular, need to be 0).  Use Python's memory allocation\n        // functions: Python is using pymalloc, which is designed to be\n        // efficient for small allocations like the one we're doing here;\n        // for larger allocations they are just wrappers around malloc.\n        // TODO: is this still true for pure Python 3.6?\n        nonsimple.values_and_holders = (void **) PyMem_Calloc(space, sizeof(void *));\n        if (!nonsimple.values_and_holders) {\n            throw std::bad_alloc();\n        }\n        nonsimple.status\n            = reinterpret_cast<std::uint8_t *>(&nonsimple.values_and_holders[flags_at]);\n    }\n    owned = true;\n}\n\n// NOLINTNEXTLINE(readability-make-member-function-const)\nPYBIND11_NOINLINE void instance::deallocate_layout() {\n    if (!simple_layout) {\n        PyMem_Free(reinterpret_cast<void *>(nonsimple.values_and_holders));\n    }\n}\n\nPYBIND11_NOINLINE bool isinstance_generic(handle obj, const std::type_info &tp) {\n    handle type = detail::get_type_handle(tp, false);\n    if (!type) {\n        return false;\n    }\n    return isinstance(obj, type);\n}\n\nPYBIND11_NOINLINE handle get_object_handle(const void *ptr, const detail::type_info *type) {\n    return with_instance_map(ptr, [&](instance_map &instances) {\n        auto range = instances.equal_range(ptr);\n        for (auto it = range.first; it != range.second; ++it) {\n            for (const auto &vh : values_and_holders(it->second)) {\n                if (vh.type == type) {\n                    return handle((PyObject *) it->second);\n                }\n            }\n        }\n        return handle();\n    });\n}\n\ninline PyThreadState *get_thread_state_unchecked() {\n#if defined(PYPY_VERSION)\n    return PyThreadState_GET();\n#elif PY_VERSION_HEX < 0x030D0000\n    return _PyThreadState_UncheckedGet();\n#else\n    return PyThreadState_GetUnchecked();\n#endif\n}\n\n// Forward declarations\nvoid keep_alive_impl(handle nurse, handle patient);\ninline PyObject *make_new_instance(PyTypeObject *type);\n\nclass type_caster_generic {\npublic:\n    PYBIND11_NOINLINE explicit type_caster_generic(const std::type_info &type_info)\n        : typeinfo(get_type_info(type_info)), cpptype(&type_info) {}\n\n    explicit type_caster_generic(const type_info *typeinfo)\n        : typeinfo(typeinfo), cpptype(typeinfo ? typeinfo->cpptype : nullptr) {}\n\n    bool load(handle src, bool convert) { return load_impl<type_caster_generic>(src, convert); }\n\n    PYBIND11_NOINLINE static handle cast(const void *_src,\n                                         return_value_policy policy,\n                                         handle parent,\n                                         const detail::type_info *tinfo,\n                                         void *(*copy_constructor)(const void *),\n                                         void *(*move_constructor)(const void *),\n                                         const void *existing_holder = nullptr) {\n        if (!tinfo) { // no type info: error will be set already\n            return handle();\n        }\n\n        void *src = const_cast<void *>(_src);\n        if (src == nullptr) {\n            return none().release();\n        }\n\n        if (handle registered_inst = find_registered_python_instance(src, tinfo)) {\n            return registered_inst;\n        }\n\n        auto inst = reinterpret_steal<object>(make_new_instance(tinfo->type));\n        auto *wrapper = reinterpret_cast<instance *>(inst.ptr());\n        wrapper->owned = false;\n        void *&valueptr = values_and_holders(wrapper).begin()->value_ptr();\n\n        switch (policy) {\n            case return_value_policy::automatic:\n            case return_value_policy::take_ownership:\n                valueptr = src;\n                wrapper->owned = true;\n                break;\n\n            case return_value_policy::automatic_reference:\n            case return_value_policy::reference:\n                valueptr = src;\n                wrapper->owned = false;\n                break;\n\n            case return_value_policy::copy:\n                if (copy_constructor) {\n                    valueptr = copy_constructor(src);\n                } else {\n#if defined(PYBIND11_DETAILED_ERROR_MESSAGES)\n                    std::string type_name(tinfo->cpptype->name());\n                    detail::clean_type_id(type_name);\n                    throw cast_error(\"return_value_policy = copy, but type \" + type_name\n                                     + \" is non-copyable!\");\n#else\n                    throw cast_error(\"return_value_policy = copy, but type is \"\n                                     \"non-copyable! (#define PYBIND11_DETAILED_ERROR_MESSAGES or \"\n                                     \"compile in debug mode for details)\");\n#endif\n                }\n                wrapper->owned = true;\n                break;\n\n            case return_value_policy::move:\n                if (move_constructor) {\n                    valueptr = move_constructor(src);\n                } else if (copy_constructor) {\n                    valueptr = copy_constructor(src);\n                } else {\n#if defined(PYBIND11_DETAILED_ERROR_MESSAGES)\n                    std::string type_name(tinfo->cpptype->name());\n                    detail::clean_type_id(type_name);\n                    throw cast_error(\"return_value_policy = move, but type \" + type_name\n                                     + \" is neither movable nor copyable!\");\n#else\n                    throw cast_error(\"return_value_policy = move, but type is neither \"\n                                     \"movable nor copyable! \"\n                                     \"(#define PYBIND11_DETAILED_ERROR_MESSAGES or compile in \"\n                                     \"debug mode for details)\");\n#endif\n                }\n                wrapper->owned = true;\n                break;\n\n            case return_value_policy::reference_internal:\n                valueptr = src;\n                wrapper->owned = false;\n                keep_alive_impl(inst, parent);\n                break;\n\n            default:\n                throw cast_error(\"unhandled return_value_policy: should not happen!\");\n        }\n\n        tinfo->init_instance(wrapper, existing_holder);\n\n        return inst.release();\n    }\n\n    // Base methods for generic caster; there are overridden in copyable_holder_caster\n    void load_value(value_and_holder &&v_h) {\n        auto *&vptr = v_h.value_ptr();\n        // Lazy allocation for unallocated values:\n        if (vptr == nullptr) {\n            const auto *type = v_h.type ? v_h.type : typeinfo;\n            if (type->operator_new) {\n                vptr = type->operator_new(type->type_size);\n            } else {\n#if defined(__cpp_aligned_new) && (!defined(_MSC_VER) || _MSC_VER >= 1912)\n                if (type->type_align > __STDCPP_DEFAULT_NEW_ALIGNMENT__) {\n                    vptr = ::operator new(type->type_size, std::align_val_t(type->type_align));\n                } else {\n                    vptr = ::operator new(type->type_size);\n                }\n#else\n                vptr = ::operator new(type->type_size);\n#endif\n            }\n        }\n        value = vptr;\n    }\n    bool try_implicit_casts(handle src, bool convert) {\n        for (const auto &cast : typeinfo->implicit_casts) {\n            type_caster_generic sub_caster(*cast.first);\n            if (sub_caster.load(src, convert)) {\n                value = cast.second(sub_caster.value);\n                return true;\n            }\n        }\n        return false;\n    }\n    bool try_direct_conversions(handle src) {\n        for (auto &converter : *typeinfo->direct_conversions) {\n            if (converter(src.ptr(), value)) {\n                return true;\n            }\n        }\n        return false;\n    }\n    bool try_cpp_conduit(handle src) {\n        value = try_raw_pointer_ephemeral_from_cpp_conduit(src, cpptype);\n        if (value != nullptr) {\n            return true;\n        }\n        return false;\n    }\n    void check_holder_compat() {}\n\n    PYBIND11_NOINLINE static void *local_load(PyObject *src, const type_info *ti) {\n        auto caster = type_caster_generic(ti);\n        if (caster.load(src, false)) {\n            return caster.value;\n        }\n        return nullptr;\n    }\n\n    /// Try to load with foreign typeinfo, if available. Used when there is no\n    /// native typeinfo, or when the native one wasn't able to produce a value.\n    PYBIND11_NOINLINE bool try_load_foreign_module_local(handle src) {\n        constexpr auto *local_key = PYBIND11_MODULE_LOCAL_ID;\n        const auto pytype = type::handle_of(src);\n        if (!hasattr(pytype, local_key)) {\n            return false;\n        }\n\n        type_info *foreign_typeinfo = reinterpret_borrow<capsule>(getattr(pytype, local_key));\n        // Only consider this foreign loader if actually foreign and is a loader of the correct cpp\n        // type\n        if (foreign_typeinfo->module_local_load == &local_load\n            || (cpptype && !same_type(*cpptype, *foreign_typeinfo->cpptype))) {\n            return false;\n        }\n\n        if (auto *result = foreign_typeinfo->module_local_load(src.ptr(), foreign_typeinfo)) {\n            value = result;\n            return true;\n        }\n        return false;\n    }\n\n    // Implementation of `load`; this takes the type of `this` so that it can dispatch the relevant\n    // bits of code between here and copyable_holder_caster where the two classes need different\n    // logic (without having to resort to virtual inheritance).\n    template <typename ThisT>\n    PYBIND11_NOINLINE bool load_impl(handle src, bool convert) {\n        if (!src) {\n            return false;\n        }\n        if (!typeinfo) {\n            return try_load_foreign_module_local(src);\n        }\n\n        auto &this_ = static_cast<ThisT &>(*this);\n        this_.check_holder_compat();\n\n        PyTypeObject *srctype = Py_TYPE(src.ptr());\n\n        // Case 1: If src is an exact type match for the target type then we can reinterpret_cast\n        // the instance's value pointer to the target type:\n        if (srctype == typeinfo->type) {\n            this_.load_value(reinterpret_cast<instance *>(src.ptr())->get_value_and_holder());\n            return true;\n        }\n        // Case 2: We have a derived class\n        if (PyType_IsSubtype(srctype, typeinfo->type)) {\n            const auto &bases = all_type_info(srctype);\n            bool no_cpp_mi = typeinfo->simple_type;\n\n            // Case 2a: the python type is a Python-inherited derived class that inherits from just\n            // one simple (no MI) pybind11 class, or is an exact match, so the C++ instance is of\n            // the right type and we can use reinterpret_cast.\n            // (This is essentially the same as case 2b, but because not using multiple inheritance\n            // is extremely common, we handle it specially to avoid the loop iterator and type\n            // pointer lookup overhead)\n            if (bases.size() == 1 && (no_cpp_mi || bases.front()->type == typeinfo->type)) {\n                this_.load_value(reinterpret_cast<instance *>(src.ptr())->get_value_and_holder());\n                return true;\n            }\n            // Case 2b: the python type inherits from multiple C++ bases.  Check the bases to see\n            // if we can find an exact match (or, for a simple C++ type, an inherited match); if\n            // so, we can safely reinterpret_cast to the relevant pointer.\n            if (bases.size() > 1) {\n                for (auto *base : bases) {\n                    if (no_cpp_mi ? PyType_IsSubtype(base->type, typeinfo->type)\n                                  : base->type == typeinfo->type) {\n                        this_.load_value(\n                            reinterpret_cast<instance *>(src.ptr())->get_value_and_holder(base));\n                        return true;\n                    }\n                }\n            }\n\n            // Case 2c: C++ multiple inheritance is involved and we couldn't find an exact type\n            // match in the registered bases, above, so try implicit casting (needed for proper C++\n            // casting when MI is involved).\n            if (this_.try_implicit_casts(src, convert)) {\n                return true;\n            }\n        }\n\n        // Perform an implicit conversion\n        if (convert) {\n            for (const auto &converter : typeinfo->implicit_conversions) {\n                auto temp = reinterpret_steal<object>(converter(src.ptr(), typeinfo->type));\n                if (load_impl<ThisT>(temp, false)) {\n                    loader_life_support::add_patient(temp);\n                    return true;\n                }\n            }\n            if (this_.try_direct_conversions(src)) {\n                return true;\n            }\n        }\n\n        // Failed to match local typeinfo. Try again with global.\n        if (typeinfo->module_local) {\n            if (auto *gtype = get_global_type_info(*typeinfo->cpptype)) {\n                typeinfo = gtype;\n                return load(src, false);\n            }\n        }\n\n        // Global typeinfo has precedence over foreign module_local\n        if (try_load_foreign_module_local(src)) {\n            return true;\n        }\n\n        // Custom converters didn't take None, now we convert None to nullptr.\n        if (src.is_none()) {\n            // Defer accepting None to other overloads (if we aren't in convert mode):\n            if (!convert) {\n                return false;\n            }\n            value = nullptr;\n            return true;\n        }\n\n        if (convert && cpptype && this_.try_cpp_conduit(src)) {\n            return true;\n        }\n\n        return false;\n    }\n\n    // Called to do type lookup and wrap the pointer and type in a pair when a dynamic_cast\n    // isn't needed or can't be used.  If the type is unknown, sets the error and returns a pair\n    // with .second = nullptr.  (p.first = nullptr is not an error: it becomes None).\n    PYBIND11_NOINLINE static std::pair<const void *, const type_info *>\n    src_and_type(const void *src,\n                 const std::type_info &cast_type,\n                 const std::type_info *rtti_type = nullptr) {\n        if (auto *tpi = get_type_info(cast_type)) {\n            return {src, const_cast<const type_info *>(tpi)};\n        }\n\n        // Not found, set error:\n        std::string tname = rtti_type ? rtti_type->name() : cast_type.name();\n        detail::clean_type_id(tname);\n        std::string msg = \"Unregistered type : \" + tname;\n        set_error(PyExc_TypeError, msg.c_str());\n        return {nullptr, nullptr};\n    }\n\n    const type_info *typeinfo = nullptr;\n    const std::type_info *cpptype = nullptr;\n    void *value = nullptr;\n};\n\ninline object cpp_conduit_method(handle self,\n                                 const bytes &pybind11_platform_abi_id,\n                                 const capsule &cpp_type_info_capsule,\n                                 const bytes &pointer_kind) {\n#ifdef PYBIND11_HAS_STRING_VIEW\n    using cpp_str = std::string_view;\n#else\n    using cpp_str = std::string;\n#endif\n    if (cpp_str(pybind11_platform_abi_id) != PYBIND11_PLATFORM_ABI_ID) {\n        return none();\n    }\n    if (std::strcmp(cpp_type_info_capsule.name(), typeid(std::type_info).name()) != 0) {\n        return none();\n    }\n    if (cpp_str(pointer_kind) != \"raw_pointer_ephemeral\") {\n        throw std::runtime_error(\"Invalid pointer_kind: \\\"\" + std::string(pointer_kind) + \"\\\"\");\n    }\n    const auto *cpp_type_info = cpp_type_info_capsule.get_pointer<const std::type_info>();\n    type_caster_generic caster(*cpp_type_info);\n    if (!caster.load(self, false)) {\n        return none();\n    }\n    return capsule(caster.value, cpp_type_info->name());\n}\n\n/**\n * Determine suitable casting operator for pointer-or-lvalue-casting type casters.  The type caster\n * needs to provide `operator T*()` and `operator T&()` operators.\n *\n * If the type supports moving the value away via an `operator T&&() &&` method, it should use\n * `movable_cast_op_type` instead.\n */\ntemplate <typename T>\nusing cast_op_type = conditional_t<std::is_pointer<remove_reference_t<T>>::value,\n                                   typename std::add_pointer<intrinsic_t<T>>::type,\n                                   typename std::add_lvalue_reference<intrinsic_t<T>>::type>;\n\n/**\n * Determine suitable casting operator for a type caster with a movable value.  Such a type caster\n * needs to provide `operator T*()`, `operator T&()`, and `operator T&&() &&`.  The latter will be\n * called in appropriate contexts where the value can be moved rather than copied.\n *\n * These operator are automatically provided when using the PYBIND11_TYPE_CASTER macro.\n */\ntemplate <typename T>\nusing movable_cast_op_type\n    = conditional_t<std::is_pointer<typename std::remove_reference<T>::type>::value,\n                    typename std::add_pointer<intrinsic_t<T>>::type,\n                    conditional_t<std::is_rvalue_reference<T>::value,\n                                  typename std::add_rvalue_reference<intrinsic_t<T>>::type,\n                                  typename std::add_lvalue_reference<intrinsic_t<T>>::type>>;\n\n// Does the container have a mapped type and is it recursive?\n// Implemented by specializations below.\ntemplate <typename Container, typename SFINAE = void>\nstruct container_mapped_type_traits {\n    static constexpr bool has_mapped_type = false;\n    static constexpr bool has_recursive_mapped_type = false;\n};\n\ntemplate <typename Container>\nstruct container_mapped_type_traits<\n    Container,\n    typename std::enable_if<\n        std::is_same<typename Container::mapped_type, Container>::value>::type> {\n    static constexpr bool has_mapped_type = true;\n    static constexpr bool has_recursive_mapped_type = true;\n};\n\ntemplate <typename Container>\nstruct container_mapped_type_traits<\n    Container,\n    typename std::enable_if<\n        negation<std::is_same<typename Container::mapped_type, Container>>::value>::type> {\n    static constexpr bool has_mapped_type = true;\n    static constexpr bool has_recursive_mapped_type = false;\n};\n\n// Does the container have a value type and is it recursive?\n// Implemented by specializations below.\ntemplate <typename Container, typename SFINAE = void>\nstruct container_value_type_traits : std::false_type {\n    static constexpr bool has_value_type = false;\n    static constexpr bool has_recursive_value_type = false;\n};\n\ntemplate <typename Container>\nstruct container_value_type_traits<\n    Container,\n    typename std::enable_if<\n        std::is_same<typename Container::value_type, Container>::value>::type> {\n    static constexpr bool has_value_type = true;\n    static constexpr bool has_recursive_value_type = true;\n};\n\ntemplate <typename Container>\nstruct container_value_type_traits<\n    Container,\n    typename std::enable_if<\n        negation<std::is_same<typename Container::value_type, Container>>::value>::type> {\n    static constexpr bool has_value_type = true;\n    static constexpr bool has_recursive_value_type = false;\n};\n\n/*\n * Tag to be used for representing the bottom of recursively defined types.\n * Define this tag so we don't have to use void.\n */\nstruct recursive_bottom {};\n\n/*\n * Implementation detail of `recursive_container_traits` below.\n * `T` is the `value_type` of the container, which might need to be modified to\n * avoid recursive types and const types.\n */\ntemplate <typename T, bool is_this_a_map>\nstruct impl_type_to_check_recursively {\n    /*\n     * If the container is recursive, then no further recursion should be done.\n     */\n    using if_recursive = recursive_bottom;\n    /*\n     * Otherwise yield `T` unchanged.\n     */\n    using if_not_recursive = T;\n};\n\n/*\n * For pairs - only as value type of a map -, the first type should remove the `const`.\n * Also, if the map is recursive, then the recursive checking should consider\n * the first type only.\n */\ntemplate <typename A, typename B>\nstruct impl_type_to_check_recursively<std::pair<A, B>, /* is_this_a_map = */ true> {\n    using if_recursive = typename std::remove_const<A>::type;\n    using if_not_recursive = std::pair<typename std::remove_const<A>::type, B>;\n};\n\n/*\n * Implementation of `recursive_container_traits` below.\n */\ntemplate <typename Container, typename SFINAE = void>\nstruct impl_recursive_container_traits {\n    using type_to_check_recursively = recursive_bottom;\n};\n\ntemplate <typename Container>\nstruct impl_recursive_container_traits<\n    Container,\n    typename std::enable_if<container_value_type_traits<Container>::has_value_type>::type> {\n    static constexpr bool is_recursive\n        = container_mapped_type_traits<Container>::has_recursive_mapped_type\n          || container_value_type_traits<Container>::has_recursive_value_type;\n    /*\n     * This member dictates which type Pybind11 should check recursively in traits\n     * such as `is_move_constructible`, `is_copy_constructible`, `is_move_assignable`, ...\n     * Direct access to `value_type` should be avoided:\n     * 1. `value_type` might recursively contain the type again\n     * 2. `value_type` of STL map types is `std::pair<A const, B>`, the `const`\n     *    should be removed.\n     *\n     */\n    using type_to_check_recursively = typename std::conditional<\n        is_recursive,\n        typename impl_type_to_check_recursively<\n            typename Container::value_type,\n            container_mapped_type_traits<Container>::has_mapped_type>::if_recursive,\n        typename impl_type_to_check_recursively<\n            typename Container::value_type,\n            container_mapped_type_traits<Container>::has_mapped_type>::if_not_recursive>::type;\n};\n\n/*\n * This trait defines the `type_to_check_recursively` which is needed to properly\n * handle recursively defined traits such as `is_move_constructible` without going\n * into an infinite recursion.\n * Should be used instead of directly accessing the `value_type`.\n * It cancels the recursion by returning the `recursive_bottom` tag.\n *\n * The default definition of `type_to_check_recursively` is as follows:\n *\n * 1. By default, it is `recursive_bottom`, so that the recursion is canceled.\n * 2. If the type is non-recursive and defines a `value_type`, then the `value_type` is used.\n *    If the `value_type` is a pair and a `mapped_type` is defined,\n *    then the `const` is removed from the first type.\n * 3. If the type is recursive and `value_type` is not a pair, then `recursive_bottom` is returned.\n * 4. If the type is recursive and `value_type` is a pair and a `mapped_type` is defined,\n *    then `const` is removed from the first type and the first type is returned.\n *\n * This behavior can be extended by the user as seen in test_stl_binders.cpp.\n *\n * This struct is exactly the same as impl_recursive_container_traits.\n * The duplication achieves that user-defined specializations don't compete\n * with internal specializations, but take precedence.\n */\ntemplate <typename Container, typename SFINAE = void>\nstruct recursive_container_traits : impl_recursive_container_traits<Container> {};\n\ntemplate <typename T>\nstruct is_move_constructible\n    : all_of<std::is_move_constructible<T>,\n             is_move_constructible<\n                 typename recursive_container_traits<T>::type_to_check_recursively>> {};\n\ntemplate <>\nstruct is_move_constructible<recursive_bottom> : std::true_type {};\n\n// Likewise for std::pair\n// (after C++17 it is mandatory that the move constructor not exist when the two types aren't\n// themselves move constructible, but this can not be relied upon when T1 or T2 are themselves\n// containers).\ntemplate <typename T1, typename T2>\nstruct is_move_constructible<std::pair<T1, T2>>\n    : all_of<is_move_constructible<T1>, is_move_constructible<T2>> {};\n\n// std::is_copy_constructible isn't quite enough: it lets std::vector<T> (and similar) through when\n// T is non-copyable, but code containing such a copy constructor fails to actually compile.\ntemplate <typename T>\nstruct is_copy_constructible\n    : all_of<std::is_copy_constructible<T>,\n             is_copy_constructible<\n                 typename recursive_container_traits<T>::type_to_check_recursively>> {};\n\ntemplate <>\nstruct is_copy_constructible<recursive_bottom> : std::true_type {};\n\n// Likewise for std::pair\n// (after C++17 it is mandatory that the copy constructor not exist when the two types aren't\n// themselves copy constructible, but this can not be relied upon when T1 or T2 are themselves\n// containers).\ntemplate <typename T1, typename T2>\nstruct is_copy_constructible<std::pair<T1, T2>>\n    : all_of<is_copy_constructible<T1>, is_copy_constructible<T2>> {};\n\n// The same problems arise with std::is_copy_assignable, so we use the same workaround.\ntemplate <typename T>\nstruct is_copy_assignable\n    : all_of<\n          std::is_copy_assignable<T>,\n          is_copy_assignable<typename recursive_container_traits<T>::type_to_check_recursively>> {\n};\n\ntemplate <>\nstruct is_copy_assignable<recursive_bottom> : std::true_type {};\n\ntemplate <typename T1, typename T2>\nstruct is_copy_assignable<std::pair<T1, T2>>\n    : all_of<is_copy_assignable<T1>, is_copy_assignable<T2>> {};\n\nPYBIND11_NAMESPACE_END(detail)\n\n// polymorphic_type_hook<itype>::get(src, tinfo) determines whether the object pointed\n// to by `src` actually is an instance of some class derived from `itype`.\n// If so, it sets `tinfo` to point to the std::type_info representing that derived\n// type, and returns a pointer to the start of the most-derived object of that type\n// (in which `src` is a subobject; this will be the same address as `src` in most\n// single inheritance cases). If not, or if `src` is nullptr, it simply returns `src`\n// and leaves `tinfo` at its default value of nullptr.\n//\n// The default polymorphic_type_hook just returns src. A specialization for polymorphic\n// types determines the runtime type of the passed object and adjusts the this-pointer\n// appropriately via dynamic_cast<void*>. This is what enables a C++ Animal* to appear\n// to Python as a Dog (if Dog inherits from Animal, Animal is polymorphic, Dog is\n// registered with pybind11, and this Animal is in fact a Dog).\n//\n// You may specialize polymorphic_type_hook yourself for types that want to appear\n// polymorphic to Python but do not use C++ RTTI. (This is a not uncommon pattern\n// in performance-sensitive applications, used most notably in LLVM.)\n//\n// polymorphic_type_hook_base allows users to specialize polymorphic_type_hook with\n// std::enable_if. User provided specializations will always have higher priority than\n// the default implementation and specialization provided in polymorphic_type_hook_base.\ntemplate <typename itype, typename SFINAE = void>\nstruct polymorphic_type_hook_base {\n    static const void *get(const itype *src, const std::type_info *&) { return src; }\n};\ntemplate <typename itype>\nstruct polymorphic_type_hook_base<itype, detail::enable_if_t<std::is_polymorphic<itype>::value>> {\n    static const void *get(const itype *src, const std::type_info *&type) {\n        type = src ? &typeid(*src) : nullptr;\n        return dynamic_cast<const void *>(src);\n    }\n};\ntemplate <typename itype, typename SFINAE = void>\nstruct polymorphic_type_hook : public polymorphic_type_hook_base<itype> {};\n\nPYBIND11_NAMESPACE_BEGIN(detail)\n\n/// Generic type caster for objects stored on the heap\ntemplate <typename type>\nclass type_caster_base : public type_caster_generic {\n    using itype = intrinsic_t<type>;\n\npublic:\n    static constexpr auto name = const_name<type>();\n\n    type_caster_base() : type_caster_base(typeid(type)) {}\n    explicit type_caster_base(const std::type_info &info) : type_caster_generic(info) {}\n\n    static handle cast(const itype &src, return_value_policy policy, handle parent) {\n        if (policy == return_value_policy::automatic\n            || policy == return_value_policy::automatic_reference) {\n            policy = return_value_policy::copy;\n        }\n        return cast(std::addressof(src), policy, parent);\n    }\n\n    static handle cast(itype &&src, return_value_policy, handle parent) {\n        return cast(std::addressof(src), return_value_policy::move, parent);\n    }\n\n    // Returns a (pointer, type_info) pair taking care of necessary type lookup for a\n    // polymorphic type (using RTTI by default, but can be overridden by specializing\n    // polymorphic_type_hook). If the instance isn't derived, returns the base version.\n    static std::pair<const void *, const type_info *> src_and_type(const itype *src) {\n        const auto &cast_type = typeid(itype);\n        const std::type_info *instance_type = nullptr;\n        const void *vsrc = polymorphic_type_hook<itype>::get(src, instance_type);\n        if (instance_type && !same_type(cast_type, *instance_type)) {\n            // This is a base pointer to a derived type. If the derived type is registered\n            // with pybind11, we want to make the full derived object available.\n            // In the typical case where itype is polymorphic, we get the correct\n            // derived pointer (which may be != base pointer) by a dynamic_cast to\n            // most derived type. If itype is not polymorphic, we won't get here\n            // except via a user-provided specialization of polymorphic_type_hook,\n            // and the user has promised that no this-pointer adjustment is\n            // required in that case, so it's OK to use static_cast.\n            if (const auto *tpi = get_type_info(*instance_type)) {\n                return {vsrc, tpi};\n            }\n        }\n        // Otherwise we have either a nullptr, an `itype` pointer, or an unknown derived pointer,\n        // so don't do a cast\n        return type_caster_generic::src_and_type(src, cast_type, instance_type);\n    }\n\n    static handle cast(const itype *src, return_value_policy policy, handle parent) {\n        auto st = src_and_type(src);\n        return type_caster_generic::cast(st.first,\n                                         policy,\n                                         parent,\n                                         st.second,\n                                         make_copy_constructor(src),\n                                         make_move_constructor(src));\n    }\n\n    static handle cast_holder(const itype *src, const void *holder) {\n        auto st = src_and_type(src);\n        return type_caster_generic::cast(st.first,\n                                         return_value_policy::take_ownership,\n                                         {},\n                                         st.second,\n                                         nullptr,\n                                         nullptr,\n                                         holder);\n    }\n\n    template <typename T>\n    using cast_op_type = detail::cast_op_type<T>;\n\n    // NOLINTNEXTLINE(google-explicit-constructor)\n    operator itype *() { return (type *) value; }\n    // NOLINTNEXTLINE(google-explicit-constructor)\n    operator itype &() {\n        if (!value) {\n            throw reference_cast_error();\n        }\n        return *((itype *) value);\n    }\n\nprotected:\n    using Constructor = void *(*) (const void *);\n\n    /* Only enabled when the types are {copy,move}-constructible *and* when the type\n       does not have a private operator new implementation. A comma operator is used in the\n       decltype argument to apply SFINAE to the public copy/move constructors.*/\n    template <typename T, typename = enable_if_t<is_copy_constructible<T>::value>>\n    static auto make_copy_constructor(const T *) -> decltype(new T(std::declval<const T>()),\n                                                             Constructor{}) {\n        return [](const void *arg) -> void * { return new T(*reinterpret_cast<const T *>(arg)); };\n    }\n\n    template <typename T, typename = enable_if_t<is_move_constructible<T>::value>>\n    static auto make_move_constructor(const T *) -> decltype(new T(std::declval<T &&>()),\n                                                             Constructor{}) {\n        return [](const void *arg) -> void * {\n            return new T(std::move(*const_cast<T *>(reinterpret_cast<const T *>(arg))));\n        };\n    }\n\n    static Constructor make_copy_constructor(...) { return nullptr; }\n    static Constructor make_move_constructor(...) { return nullptr; }\n};\n\ninline std::string quote_cpp_type_name(const std::string &cpp_type_name) {\n    return cpp_type_name; // No-op for now. See PR #4888\n}\n\nPYBIND11_NOINLINE std::string type_info_description(const std::type_info &ti) {\n    if (auto *type_data = get_type_info(ti)) {\n        handle th((PyObject *) type_data->type);\n        return th.attr(\"__module__\").cast<std::string>() + '.'\n               + th.attr(\"__qualname__\").cast<std::string>();\n    }\n    return quote_cpp_type_name(clean_type_id(ti.name()));\n}\n\nPYBIND11_NAMESPACE_END(detail)\nPYBIND11_NAMESPACE_END(PYBIND11_NAMESPACE)\n"
  },
  {
    "path": "libs/pybind11/include/pybind11/detail/typeid.h",
    "content": "/*\n    pybind11/detail/typeid.h: Compiler-independent access to type identifiers\n\n    Copyright (c) 2016 Wenzel Jakob <wenzel.jakob@epfl.ch>\n\n    All rights reserved. Use of this source code is governed by a\n    BSD-style license that can be found in the LICENSE file.\n*/\n\n#pragma once\n\n#include <cstdio>\n#include <cstdlib>\n\n#if defined(__GNUG__)\n#    include <cxxabi.h>\n#endif\n\n#include \"common.h\"\n\nPYBIND11_NAMESPACE_BEGIN(PYBIND11_NAMESPACE)\nPYBIND11_NAMESPACE_BEGIN(detail)\n\n/// Erase all occurrences of a substring\ninline void erase_all(std::string &string, const std::string &search) {\n    for (size_t pos = 0;;) {\n        pos = string.find(search, pos);\n        if (pos == std::string::npos) {\n            break;\n        }\n        string.erase(pos, search.length());\n    }\n}\n\nPYBIND11_NOINLINE void clean_type_id(std::string &name) {\n#if defined(__GNUG__)\n    int status = 0;\n    std::unique_ptr<char, void (*)(void *)> res{\n        abi::__cxa_demangle(name.c_str(), nullptr, nullptr, &status), std::free};\n    if (status == 0) {\n        name = res.get();\n    }\n#else\n    detail::erase_all(name, \"class \");\n    detail::erase_all(name, \"struct \");\n    detail::erase_all(name, \"enum \");\n#endif\n    detail::erase_all(name, \"pybind11::\");\n}\n\ninline std::string clean_type_id(const char *typeid_name) {\n    std::string name(typeid_name);\n    detail::clean_type_id(name);\n    return name;\n}\n\nPYBIND11_NAMESPACE_END(detail)\n\n/// Return a string representation of a C++ type\ntemplate <typename T>\nstatic std::string type_id() {\n    return detail::clean_type_id(typeid(T).name());\n}\n\nPYBIND11_NAMESPACE_END(PYBIND11_NAMESPACE)\n"
  },
  {
    "path": "libs/pybind11/include/pybind11/detail/value_and_holder.h",
    "content": "// Copyright (c) 2016-2024 The Pybind Development Team.\n// All rights reserved. Use of this source code is governed by a\n// BSD-style license that can be found in the LICENSE file.\n\n#pragma once\n\n#include \"common.h\"\n\n#include <cstddef>\n#include <typeinfo>\n\nPYBIND11_NAMESPACE_BEGIN(PYBIND11_NAMESPACE)\nPYBIND11_NAMESPACE_BEGIN(detail)\n\nstruct value_and_holder {\n    instance *inst = nullptr;\n    size_t index = 0u;\n    const detail::type_info *type = nullptr;\n    void **vh = nullptr;\n\n    // Main constructor for a found value/holder:\n    value_and_holder(instance *i, const detail::type_info *type, size_t vpos, size_t index)\n        : inst{i}, index{index}, type{type},\n          vh{inst->simple_layout ? inst->simple_value_holder\n                                 : &inst->nonsimple.values_and_holders[vpos]} {}\n\n    // Default constructor (used to signal a value-and-holder not found by get_value_and_holder())\n    value_and_holder() = default;\n\n    // Used for past-the-end iterator\n    explicit value_and_holder(size_t index) : index{index} {}\n\n    template <typename V = void>\n    V *&value_ptr() const {\n        return reinterpret_cast<V *&>(vh[0]);\n    }\n    // True if this `value_and_holder` has a non-null value pointer\n    explicit operator bool() const { return value_ptr() != nullptr; }\n\n    template <typename H>\n    H &holder() const {\n        return reinterpret_cast<H &>(vh[1]);\n    }\n    bool holder_constructed() const {\n        return inst->simple_layout\n                   ? inst->simple_holder_constructed\n                   : (inst->nonsimple.status[index] & instance::status_holder_constructed) != 0u;\n    }\n    // NOLINTNEXTLINE(readability-make-member-function-const)\n    void set_holder_constructed(bool v = true) {\n        if (inst->simple_layout) {\n            inst->simple_holder_constructed = v;\n        } else if (v) {\n            inst->nonsimple.status[index] |= instance::status_holder_constructed;\n        } else {\n            inst->nonsimple.status[index] &= (std::uint8_t) ~instance::status_holder_constructed;\n        }\n    }\n    bool instance_registered() const {\n        return inst->simple_layout\n                   ? inst->simple_instance_registered\n                   : ((inst->nonsimple.status[index] & instance::status_instance_registered) != 0);\n    }\n    // NOLINTNEXTLINE(readability-make-member-function-const)\n    void set_instance_registered(bool v = true) {\n        if (inst->simple_layout) {\n            inst->simple_instance_registered = v;\n        } else if (v) {\n            inst->nonsimple.status[index] |= instance::status_instance_registered;\n        } else {\n            inst->nonsimple.status[index] &= (std::uint8_t) ~instance::status_instance_registered;\n        }\n    }\n};\n\nPYBIND11_NAMESPACE_END(detail)\nPYBIND11_NAMESPACE_END(PYBIND11_NAMESPACE)\n"
  },
  {
    "path": "libs/pybind11/include/pybind11/eigen/common.h",
    "content": "// Copyright (c) 2023 The pybind Community.\n\n#pragma once\n\n// Common message for `static_assert()`s, which are useful to easily\n// preempt much less obvious errors.\n#define PYBIND11_EIGEN_MESSAGE_POINTER_TYPES_ARE_NOT_SUPPORTED                                    \\\n    \"Pointer types (in particular `PyObject *`) are not supported as scalar types for Eigen \"     \\\n    \"types.\"\n"
  },
  {
    "path": "libs/pybind11/include/pybind11/eigen/matrix.h",
    "content": "/*\n    pybind11/eigen/matrix.h: Transparent conversion for dense and sparse Eigen matrices\n\n    Copyright (c) 2016 Wenzel Jakob <wenzel.jakob@epfl.ch>\n\n    All rights reserved. Use of this source code is governed by a\n    BSD-style license that can be found in the LICENSE file.\n*/\n\n#pragma once\n\n#include <pybind11/numpy.h>\n\n#include \"common.h\"\n\n/* HINT: To suppress warnings originating from the Eigen headers, use -isystem.\n   See also:\n       https://stackoverflow.com/questions/2579576/i-dir-vs-isystem-dir\n       https://stackoverflow.com/questions/1741816/isystem-for-ms-visual-studio-c-compiler\n*/\nPYBIND11_WARNING_PUSH\nPYBIND11_WARNING_DISABLE_MSVC(5054) // https://github.com/pybind/pybind11/pull/3741\n//       C5054: operator '&': deprecated between enumerations of different types\n#if defined(__MINGW32__)\nPYBIND11_WARNING_DISABLE_GCC(\"-Wmaybe-uninitialized\")\n#endif\n\n#include <Eigen/Core>\n#include <Eigen/SparseCore>\n\nPYBIND11_WARNING_POP\n\n// Eigen prior to 3.2.7 doesn't have proper move constructors--but worse, some classes get implicit\n// move constructors that break things.  We could detect this an explicitly copy, but an extra copy\n// of matrices seems highly undesirable.\nstatic_assert(EIGEN_VERSION_AT_LEAST(3, 2, 7),\n              \"Eigen matrix support in pybind11 requires Eigen >= 3.2.7\");\n\nPYBIND11_NAMESPACE_BEGIN(PYBIND11_NAMESPACE)\n\nPYBIND11_WARNING_DISABLE_MSVC(4127)\n\n// Provide a convenience alias for easier pass-by-ref usage with fully dynamic strides:\nusing EigenDStride = Eigen::Stride<Eigen::Dynamic, Eigen::Dynamic>;\ntemplate <typename MatrixType>\nusing EigenDRef = Eigen::Ref<MatrixType, 0, EigenDStride>;\ntemplate <typename MatrixType>\nusing EigenDMap = Eigen::Map<MatrixType, 0, EigenDStride>;\n\nPYBIND11_NAMESPACE_BEGIN(detail)\n\n#if EIGEN_VERSION_AT_LEAST(3, 3, 0)\nusing EigenIndex = Eigen::Index;\ntemplate <typename Scalar, int Flags, typename StorageIndex>\nusing EigenMapSparseMatrix = Eigen::Map<Eigen::SparseMatrix<Scalar, Flags, StorageIndex>>;\n#else\nusing EigenIndex = EIGEN_DEFAULT_DENSE_INDEX_TYPE;\ntemplate <typename Scalar, int Flags, typename StorageIndex>\nusing EigenMapSparseMatrix = Eigen::MappedSparseMatrix<Scalar, Flags, StorageIndex>;\n#endif\n\n// Matches Eigen::Map, Eigen::Ref, blocks, etc:\ntemplate <typename T>\nusing is_eigen_dense_map = all_of<is_template_base_of<Eigen::DenseBase, T>,\n                                  std::is_base_of<Eigen::MapBase<T, Eigen::ReadOnlyAccessors>, T>>;\ntemplate <typename T>\nusing is_eigen_mutable_map = std::is_base_of<Eigen::MapBase<T, Eigen::WriteAccessors>, T>;\ntemplate <typename T>\nusing is_eigen_dense_plain\n    = all_of<negation<is_eigen_dense_map<T>>, is_template_base_of<Eigen::PlainObjectBase, T>>;\ntemplate <typename T>\nusing is_eigen_sparse = is_template_base_of<Eigen::SparseMatrixBase, T>;\n// Test for objects inheriting from EigenBase<Derived> that aren't captured by the above.  This\n// basically covers anything that can be assigned to a dense matrix but that don't have a typical\n// matrix data layout that can be copied from their .data().  For example, DiagonalMatrix and\n// SelfAdjointView fall into this category.\ntemplate <typename T>\nusing is_eigen_other\n    = all_of<is_template_base_of<Eigen::EigenBase, T>,\n             negation<any_of<is_eigen_dense_map<T>, is_eigen_dense_plain<T>, is_eigen_sparse<T>>>>;\n\n// Captures numpy/eigen conformability status (returned by EigenProps::conformable()):\ntemplate <bool EigenRowMajor>\nstruct EigenConformable {\n    bool conformable = false;\n    EigenIndex rows = 0, cols = 0;\n    EigenDStride stride{0, 0};    // Only valid if negativestrides is false!\n    bool negativestrides = false; // If true, do not use stride!\n\n    // NOLINTNEXTLINE(google-explicit-constructor)\n    EigenConformable(bool fits = false) : conformable{fits} {}\n    // Matrix type:\n    EigenConformable(EigenIndex r, EigenIndex c, EigenIndex rstride, EigenIndex cstride)\n        : conformable{true}, rows{r}, cols{c},\n          // TODO: when Eigen bug #747 is fixed, remove the tests for non-negativity.\n          // http://eigen.tuxfamily.org/bz/show_bug.cgi?id=747\n          stride{EigenRowMajor ? (rstride > 0 ? rstride : 0)\n                               : (cstride > 0 ? cstride : 0) /* outer stride */,\n                 EigenRowMajor ? (cstride > 0 ? cstride : 0)\n                               : (rstride > 0 ? rstride : 0) /* inner stride */},\n          negativestrides{rstride < 0 || cstride < 0} {}\n    // Vector type:\n    EigenConformable(EigenIndex r, EigenIndex c, EigenIndex stride)\n        : EigenConformable(r, c, r == 1 ? c * stride : stride, c == 1 ? r : r * stride) {}\n\n    template <typename props>\n    bool stride_compatible() const {\n        // To have compatible strides, we need (on both dimensions) one of fully dynamic strides,\n        // matching strides, or a dimension size of 1 (in which case the stride value is\n        // irrelevant). Alternatively, if any dimension size is 0, the strides are not relevant\n        // (and numpy ≥ 1.23 sets the strides to 0 in that case, so we need to check explicitly).\n        if (negativestrides) {\n            return false;\n        }\n        if (rows == 0 || cols == 0) {\n            return true;\n        }\n        return (props::inner_stride == Eigen::Dynamic || props::inner_stride == stride.inner()\n                || (EigenRowMajor ? cols : rows) == 1)\n               && (props::outer_stride == Eigen::Dynamic || props::outer_stride == stride.outer()\n                   || (EigenRowMajor ? rows : cols) == 1);\n    }\n    // NOLINTNEXTLINE(google-explicit-constructor)\n    operator bool() const { return conformable; }\n};\n\ntemplate <typename Type>\nstruct eigen_extract_stride {\n    using type = Type;\n};\ntemplate <typename PlainObjectType, int MapOptions, typename StrideType>\nstruct eigen_extract_stride<Eigen::Map<PlainObjectType, MapOptions, StrideType>> {\n    using type = StrideType;\n};\ntemplate <typename PlainObjectType, int Options, typename StrideType>\nstruct eigen_extract_stride<Eigen::Ref<PlainObjectType, Options, StrideType>> {\n    using type = StrideType;\n};\n\n// Helper struct for extracting information from an Eigen type\ntemplate <typename Type_>\nstruct EigenProps {\n    using Type = Type_;\n    using Scalar = typename Type::Scalar;\n    using StrideType = typename eigen_extract_stride<Type>::type;\n    static constexpr EigenIndex rows = Type::RowsAtCompileTime, cols = Type::ColsAtCompileTime,\n                                size = Type::SizeAtCompileTime;\n    static constexpr bool row_major = Type::IsRowMajor,\n                          vector\n                          = Type::IsVectorAtCompileTime, // At least one dimension has fixed size 1\n        fixed_rows = rows != Eigen::Dynamic, fixed_cols = cols != Eigen::Dynamic,\n                          fixed = size != Eigen::Dynamic, // Fully-fixed size\n        dynamic = !fixed_rows && !fixed_cols;             // Fully-dynamic size\n\n    template <EigenIndex i, EigenIndex ifzero>\n    using if_zero = std::integral_constant<EigenIndex, i == 0 ? ifzero : i>;\n    static constexpr EigenIndex inner_stride\n        = if_zero<StrideType::InnerStrideAtCompileTime, 1>::value,\n        outer_stride = if_zero < StrideType::OuterStrideAtCompileTime,\n        vector      ? size\n        : row_major ? cols\n                    : rows > ::value;\n    static constexpr bool dynamic_stride\n        = inner_stride == Eigen::Dynamic && outer_stride == Eigen::Dynamic;\n    static constexpr bool requires_row_major\n        = !dynamic_stride && !vector && (row_major ? inner_stride : outer_stride) == 1;\n    static constexpr bool requires_col_major\n        = !dynamic_stride && !vector && (row_major ? outer_stride : inner_stride) == 1;\n\n    // Takes an input array and determines whether we can make it fit into the Eigen type.  If\n    // the array is a vector, we attempt to fit it into either an Eigen 1xN or Nx1 vector\n    // (preferring the latter if it will fit in either, i.e. for a fully dynamic matrix type).\n    static EigenConformable<row_major> conformable(const array &a) {\n        const auto dims = a.ndim();\n        if (dims < 1 || dims > 2) {\n            return false;\n        }\n\n        if (dims == 2) { // Matrix type: require exact match (or dynamic)\n\n            EigenIndex np_rows = a.shape(0), np_cols = a.shape(1),\n                       np_rstride = a.strides(0) / static_cast<ssize_t>(sizeof(Scalar)),\n                       np_cstride = a.strides(1) / static_cast<ssize_t>(sizeof(Scalar));\n            if ((fixed_rows && np_rows != rows) || (fixed_cols && np_cols != cols)) {\n                return false;\n            }\n\n            return {np_rows, np_cols, np_rstride, np_cstride};\n        }\n\n        // Otherwise we're storing an n-vector.  Only one of the strides will be used, but\n        // whichever is used, we want the (single) numpy stride value.\n        const EigenIndex n = a.shape(0),\n                         stride = a.strides(0) / static_cast<ssize_t>(sizeof(Scalar));\n\n        if (vector) { // Eigen type is a compile-time vector\n            if (fixed && size != n) {\n                return false; // Vector size mismatch\n            }\n            return {rows == 1 ? 1 : n, cols == 1 ? 1 : n, stride};\n        }\n        if (fixed) {\n            // The type has a fixed size, but is not a vector: abort\n            return false;\n        }\n        if (fixed_cols) {\n            // Since this isn't a vector, cols must be != 1.  We allow this only if it exactly\n            // equals the number of elements (rows is Dynamic, and so 1 row is allowed).\n            if (cols != n) {\n                return false;\n            }\n            return {1, n, stride};\n        } // Otherwise it's either fully dynamic, or column dynamic; both become a column vector\n        if (fixed_rows && rows != n) {\n            return false;\n        }\n        return {n, 1, stride};\n    }\n\n    static constexpr bool show_writeable\n        = is_eigen_dense_map<Type>::value && is_eigen_mutable_map<Type>::value;\n    static constexpr bool show_order = is_eigen_dense_map<Type>::value;\n    static constexpr bool show_c_contiguous = show_order && requires_row_major;\n    static constexpr bool show_f_contiguous\n        = !show_c_contiguous && show_order && requires_col_major;\n\n    static constexpr auto descriptor\n        = const_name(\"numpy.ndarray[\") + npy_format_descriptor<Scalar>::name + const_name(\"[\")\n          + const_name<fixed_rows>(const_name<(size_t) rows>(), const_name(\"m\")) + const_name(\", \")\n          + const_name<fixed_cols>(const_name<(size_t) cols>(), const_name(\"n\")) + const_name(\"]\")\n          +\n          // For a reference type (e.g. Ref<MatrixXd>) we have other constraints that might need to\n          // be satisfied: writeable=True (for a mutable reference), and, depending on the map's\n          // stride options, possibly f_contiguous or c_contiguous.  We include them in the\n          // descriptor output to provide some hint as to why a TypeError is occurring (otherwise\n          // it can be confusing to see that a function accepts a 'numpy.ndarray[float64[3,2]]' and\n          // an error message that you *gave* a numpy.ndarray of the right type and dimensions.\n          const_name<show_writeable>(\", flags.writeable\", \"\")\n          + const_name<show_c_contiguous>(\", flags.c_contiguous\", \"\")\n          + const_name<show_f_contiguous>(\", flags.f_contiguous\", \"\") + const_name(\"]\");\n};\n\n// Casts an Eigen type to numpy array.  If given a base, the numpy array references the src data,\n// otherwise it'll make a copy.  writeable lets you turn off the writeable flag for the array.\ntemplate <typename props>\nhandle\neigen_array_cast(typename props::Type const &src, handle base = handle(), bool writeable = true) {\n    constexpr ssize_t elem_size = sizeof(typename props::Scalar);\n    array a;\n    if (props::vector) {\n        a = array({src.size()}, {elem_size * src.innerStride()}, src.data(), base);\n    } else {\n        a = array({src.rows(), src.cols()},\n                  {elem_size * src.rowStride(), elem_size * src.colStride()},\n                  src.data(),\n                  base);\n    }\n\n    if (!writeable) {\n        array_proxy(a.ptr())->flags &= ~detail::npy_api::NPY_ARRAY_WRITEABLE_;\n    }\n\n    return a.release();\n}\n\n// Takes an lvalue ref to some Eigen type and a (python) base object, creating a numpy array that\n// reference the Eigen object's data with `base` as the python-registered base class (if omitted,\n// the base will be set to None, and lifetime management is up to the caller).  The numpy array is\n// non-writeable if the given type is const.\ntemplate <typename props, typename Type>\nhandle eigen_ref_array(Type &src, handle parent = none()) {\n    // none here is to get past array's should-we-copy detection, which currently always\n    // copies when there is no base.  Setting the base to None should be harmless.\n    return eigen_array_cast<props>(src, parent, !std::is_const<Type>::value);\n}\n\n// Takes a pointer to some dense, plain Eigen type, builds a capsule around it, then returns a\n// numpy array that references the encapsulated data with a python-side reference to the capsule to\n// tie its destruction to that of any dependent python objects.  Const-ness is determined by\n// whether or not the Type of the pointer given is const.\ntemplate <typename props, typename Type, typename = enable_if_t<is_eigen_dense_plain<Type>::value>>\nhandle eigen_encapsulate(Type *src) {\n    capsule base(src, [](void *o) { delete static_cast<Type *>(o); });\n    return eigen_ref_array<props>(*src, base);\n}\n\n// Type caster for regular, dense matrix types (e.g. MatrixXd), but not maps/refs/etc. of dense\n// types.\ntemplate <typename Type>\nstruct type_caster<Type, enable_if_t<is_eigen_dense_plain<Type>::value>> {\n    using Scalar = typename Type::Scalar;\n    static_assert(!std::is_pointer<Scalar>::value,\n                  PYBIND11_EIGEN_MESSAGE_POINTER_TYPES_ARE_NOT_SUPPORTED);\n    using props = EigenProps<Type>;\n\n    bool load(handle src, bool convert) {\n        // If we're in no-convert mode, only load if given an array of the correct type\n        if (!convert && !isinstance<array_t<Scalar>>(src)) {\n            return false;\n        }\n\n        // Coerce into an array, but don't do type conversion yet; the copy below handles it.\n        auto buf = array::ensure(src);\n\n        if (!buf) {\n            return false;\n        }\n\n        auto dims = buf.ndim();\n        if (dims < 1 || dims > 2) {\n            return false;\n        }\n\n        auto fits = props::conformable(buf);\n        if (!fits) {\n            return false;\n        }\n\n        // Allocate the new type, then build a numpy reference into it\n        value = Type(fits.rows, fits.cols);\n        auto ref = reinterpret_steal<array>(eigen_ref_array<props>(value));\n        if (dims == 1) {\n            ref = ref.squeeze();\n        } else if (ref.ndim() == 1) {\n            buf = buf.squeeze();\n        }\n\n        int result = detail::npy_api::get().PyArray_CopyInto_(ref.ptr(), buf.ptr());\n\n        if (result < 0) { // Copy failed!\n            PyErr_Clear();\n            return false;\n        }\n\n        return true;\n    }\n\nprivate:\n    // Cast implementation\n    template <typename CType>\n    static handle cast_impl(CType *src, return_value_policy policy, handle parent) {\n        switch (policy) {\n            case return_value_policy::take_ownership:\n            case return_value_policy::automatic:\n                return eigen_encapsulate<props>(src);\n            case return_value_policy::move:\n                return eigen_encapsulate<props>(new CType(std::move(*src)));\n            case return_value_policy::copy:\n                return eigen_array_cast<props>(*src);\n            case return_value_policy::reference:\n            case return_value_policy::automatic_reference:\n                return eigen_ref_array<props>(*src);\n            case return_value_policy::reference_internal:\n                return eigen_ref_array<props>(*src, parent);\n            default:\n                throw cast_error(\"unhandled return_value_policy: should not happen!\");\n        };\n    }\n\npublic:\n    // Normal returned non-reference, non-const value:\n    static handle cast(Type &&src, return_value_policy /* policy */, handle parent) {\n        return cast_impl(&src, return_value_policy::move, parent);\n    }\n    // If you return a non-reference const, we mark the numpy array readonly:\n    static handle cast(const Type &&src, return_value_policy /* policy */, handle parent) {\n        return cast_impl(&src, return_value_policy::move, parent);\n    }\n    // lvalue reference return; default (automatic) becomes copy\n    static handle cast(Type &src, return_value_policy policy, handle parent) {\n        if (policy == return_value_policy::automatic\n            || policy == return_value_policy::automatic_reference) {\n            policy = return_value_policy::copy;\n        }\n        return cast_impl(&src, policy, parent);\n    }\n    // const lvalue reference return; default (automatic) becomes copy\n    static handle cast(const Type &src, return_value_policy policy, handle parent) {\n        if (policy == return_value_policy::automatic\n            || policy == return_value_policy::automatic_reference) {\n            policy = return_value_policy::copy;\n        }\n        return cast(&src, policy, parent);\n    }\n    // non-const pointer return\n    static handle cast(Type *src, return_value_policy policy, handle parent) {\n        return cast_impl(src, policy, parent);\n    }\n    // const pointer return\n    static handle cast(const Type *src, return_value_policy policy, handle parent) {\n        return cast_impl(src, policy, parent);\n    }\n\n    static constexpr auto name = props::descriptor;\n\n    // NOLINTNEXTLINE(google-explicit-constructor)\n    operator Type *() { return &value; }\n    // NOLINTNEXTLINE(google-explicit-constructor)\n    operator Type &() { return value; }\n    // NOLINTNEXTLINE(google-explicit-constructor)\n    operator Type &&() && { return std::move(value); }\n    template <typename T>\n    using cast_op_type = movable_cast_op_type<T>;\n\nprivate:\n    Type value;\n};\n\n// Base class for casting reference/map/block/etc. objects back to python.\ntemplate <typename MapType>\nstruct eigen_map_caster {\n    static_assert(!std::is_pointer<typename MapType::Scalar>::value,\n                  PYBIND11_EIGEN_MESSAGE_POINTER_TYPES_ARE_NOT_SUPPORTED);\n\nprivate:\n    using props = EigenProps<MapType>;\n\npublic:\n    // Directly referencing a ref/map's data is a bit dangerous (whatever the map/ref points to has\n    // to stay around), but we'll allow it under the assumption that you know what you're doing\n    // (and have an appropriate keep_alive in place).  We return a numpy array pointing directly at\n    // the ref's data (The numpy array ends up read-only if the ref was to a const matrix type.)\n    // Note that this means you need to ensure you don't destroy the object in some other way (e.g.\n    // with an appropriate keep_alive, or with a reference to a statically allocated matrix).\n    static handle cast(const MapType &src, return_value_policy policy, handle parent) {\n        switch (policy) {\n            case return_value_policy::copy:\n                return eigen_array_cast<props>(src);\n            case return_value_policy::reference_internal:\n                return eigen_array_cast<props>(src, parent, is_eigen_mutable_map<MapType>::value);\n            case return_value_policy::reference:\n            case return_value_policy::automatic:\n            case return_value_policy::automatic_reference:\n                return eigen_array_cast<props>(src, none(), is_eigen_mutable_map<MapType>::value);\n            default:\n                // move, take_ownership don't make any sense for a ref/map:\n                pybind11_fail(\"Invalid return_value_policy for Eigen Map/Ref/Block type\");\n        }\n    }\n\n    static constexpr auto name = props::descriptor;\n\n    // Explicitly delete these: support python -> C++ conversion on these (i.e. these can be return\n    // types but not bound arguments).  We still provide them (with an explicitly delete) so that\n    // you end up here if you try anyway.\n    bool load(handle, bool) = delete;\n    operator MapType() = delete;\n    template <typename>\n    using cast_op_type = MapType;\n};\n\n// We can return any map-like object (but can only load Refs, specialized next):\ntemplate <typename Type>\nstruct type_caster<Type, enable_if_t<is_eigen_dense_map<Type>::value>> : eigen_map_caster<Type> {};\n\n// Loader for Ref<...> arguments.  See the documentation for info on how to make this work without\n// copying (it requires some extra effort in many cases).\ntemplate <typename PlainObjectType, typename StrideType>\nstruct type_caster<\n    Eigen::Ref<PlainObjectType, 0, StrideType>,\n    enable_if_t<is_eigen_dense_map<Eigen::Ref<PlainObjectType, 0, StrideType>>::value>>\n    : public eigen_map_caster<Eigen::Ref<PlainObjectType, 0, StrideType>> {\nprivate:\n    using Type = Eigen::Ref<PlainObjectType, 0, StrideType>;\n    using props = EigenProps<Type>;\n    using Scalar = typename props::Scalar;\n    static_assert(!std::is_pointer<Scalar>::value,\n                  PYBIND11_EIGEN_MESSAGE_POINTER_TYPES_ARE_NOT_SUPPORTED);\n    using MapType = Eigen::Map<PlainObjectType, 0, StrideType>;\n    using Array\n        = array_t<Scalar,\n                  array::forcecast\n                      | ((props::row_major ? props::inner_stride : props::outer_stride) == 1\n                             ? array::c_style\n                         : (props::row_major ? props::outer_stride : props::inner_stride) == 1\n                             ? array::f_style\n                             : 0)>;\n    static constexpr bool need_writeable = is_eigen_mutable_map<Type>::value;\n    // Delay construction (these have no default constructor)\n    std::unique_ptr<MapType> map;\n    std::unique_ptr<Type> ref;\n    // Our array.  When possible, this is just a numpy array pointing to the source data, but\n    // sometimes we can't avoid copying (e.g. input is not a numpy array at all, has an\n    // incompatible layout, or is an array of a type that needs to be converted).  Using a numpy\n    // temporary (rather than an Eigen temporary) saves an extra copy when we need both type\n    // conversion and storage order conversion.  (Note that we refuse to use this temporary copy\n    // when loading an argument for a Ref<M> with M non-const, i.e. a read-write reference).\n    Array copy_or_ref;\n\npublic:\n    bool load(handle src, bool convert) {\n        // First check whether what we have is already an array of the right type.  If not, we\n        // can't avoid a copy (because the copy is also going to do type conversion).\n        bool need_copy = !isinstance<Array>(src);\n\n        EigenConformable<props::row_major> fits;\n        if (!need_copy) {\n            // We don't need a converting copy, but we also need to check whether the strides are\n            // compatible with the Ref's stride requirements\n            auto aref = reinterpret_borrow<Array>(src);\n\n            if (aref && (!need_writeable || aref.writeable())) {\n                fits = props::conformable(aref);\n                if (!fits) {\n                    return false; // Incompatible dimensions\n                }\n                if (!fits.template stride_compatible<props>()) {\n                    need_copy = true;\n                } else {\n                    copy_or_ref = std::move(aref);\n                }\n            } else {\n                need_copy = true;\n            }\n        }\n\n        if (need_copy) {\n            // We need to copy: If we need a mutable reference, or we're not supposed to convert\n            // (either because we're in the no-convert overload pass, or because we're explicitly\n            // instructed not to copy (via `py::arg().noconvert()`) we have to fail loading.\n            if (!convert || need_writeable) {\n                return false;\n            }\n\n            Array copy = Array::ensure(src);\n            if (!copy) {\n                return false;\n            }\n            fits = props::conformable(copy);\n            if (!fits || !fits.template stride_compatible<props>()) {\n                return false;\n            }\n            copy_or_ref = std::move(copy);\n            loader_life_support::add_patient(copy_or_ref);\n        }\n\n        ref.reset();\n        map.reset(new MapType(data(copy_or_ref),\n                              fits.rows,\n                              fits.cols,\n                              make_stride(fits.stride.outer(), fits.stride.inner())));\n        ref.reset(new Type(*map));\n\n        return true;\n    }\n\n    // NOLINTNEXTLINE(google-explicit-constructor)\n    operator Type *() { return ref.get(); }\n    // NOLINTNEXTLINE(google-explicit-constructor)\n    operator Type &() { return *ref; }\n    template <typename _T>\n    using cast_op_type = pybind11::detail::cast_op_type<_T>;\n\nprivate:\n    template <typename T = Type, enable_if_t<is_eigen_mutable_map<T>::value, int> = 0>\n    Scalar *data(Array &a) {\n        return a.mutable_data();\n    }\n\n    template <typename T = Type, enable_if_t<!is_eigen_mutable_map<T>::value, int> = 0>\n    const Scalar *data(Array &a) {\n        return a.data();\n    }\n\n    // Attempt to figure out a constructor of `Stride` that will work.\n    // If both strides are fixed, use a default constructor:\n    template <typename S>\n    using stride_ctor_default = bool_constant<S::InnerStrideAtCompileTime != Eigen::Dynamic\n                                              && S::OuterStrideAtCompileTime != Eigen::Dynamic\n                                              && std::is_default_constructible<S>::value>;\n    // Otherwise, if there is a two-index constructor, assume it is (outer,inner) like\n    // Eigen::Stride, and use it:\n    template <typename S>\n    using stride_ctor_dual\n        = bool_constant<!stride_ctor_default<S>::value\n                        && std::is_constructible<S, EigenIndex, EigenIndex>::value>;\n    // Otherwise, if there is a one-index constructor, and just one of the strides is dynamic, use\n    // it (passing whichever stride is dynamic).\n    template <typename S>\n    using stride_ctor_outer\n        = bool_constant<!any_of<stride_ctor_default<S>, stride_ctor_dual<S>>::value\n                        && S::OuterStrideAtCompileTime == Eigen::Dynamic\n                        && S::InnerStrideAtCompileTime != Eigen::Dynamic\n                        && std::is_constructible<S, EigenIndex>::value>;\n    template <typename S>\n    using stride_ctor_inner\n        = bool_constant<!any_of<stride_ctor_default<S>, stride_ctor_dual<S>>::value\n                        && S::InnerStrideAtCompileTime == Eigen::Dynamic\n                        && S::OuterStrideAtCompileTime != Eigen::Dynamic\n                        && std::is_constructible<S, EigenIndex>::value>;\n\n    template <typename S = StrideType, enable_if_t<stride_ctor_default<S>::value, int> = 0>\n    static S make_stride(EigenIndex, EigenIndex) {\n        return S();\n    }\n    template <typename S = StrideType, enable_if_t<stride_ctor_dual<S>::value, int> = 0>\n    static S make_stride(EigenIndex outer, EigenIndex inner) {\n        return S(outer, inner);\n    }\n    template <typename S = StrideType, enable_if_t<stride_ctor_outer<S>::value, int> = 0>\n    static S make_stride(EigenIndex outer, EigenIndex) {\n        return S(outer);\n    }\n    template <typename S = StrideType, enable_if_t<stride_ctor_inner<S>::value, int> = 0>\n    static S make_stride(EigenIndex, EigenIndex inner) {\n        return S(inner);\n    }\n};\n\n// type_caster for special matrix types (e.g. DiagonalMatrix), which are EigenBase, but not\n// EigenDense (i.e. they don't have a data(), at least not with the usual matrix layout).\n// load() is not supported, but we can cast them into the python domain by first copying to a\n// regular Eigen::Matrix, then casting that.\ntemplate <typename Type>\nstruct type_caster<Type, enable_if_t<is_eigen_other<Type>::value>> {\n    static_assert(!std::is_pointer<typename Type::Scalar>::value,\n                  PYBIND11_EIGEN_MESSAGE_POINTER_TYPES_ARE_NOT_SUPPORTED);\n\nprotected:\n    using Matrix\n        = Eigen::Matrix<typename Type::Scalar, Type::RowsAtCompileTime, Type::ColsAtCompileTime>;\n    using props = EigenProps<Matrix>;\n\npublic:\n    static handle cast(const Type &src, return_value_policy /* policy */, handle /* parent */) {\n        handle h = eigen_encapsulate<props>(new Matrix(src));\n        return h;\n    }\n    static handle cast(const Type *src, return_value_policy policy, handle parent) {\n        return cast(*src, policy, parent);\n    }\n\n    static constexpr auto name = props::descriptor;\n\n    // Explicitly delete these: support python -> C++ conversion on these (i.e. these can be return\n    // types but not bound arguments).  We still provide them (with an explicitly delete) so that\n    // you end up here if you try anyway.\n    bool load(handle, bool) = delete;\n    operator Type() = delete;\n    template <typename>\n    using cast_op_type = Type;\n};\n\ntemplate <typename Type>\nstruct type_caster<Type, enable_if_t<is_eigen_sparse<Type>::value>> {\n    using Scalar = typename Type::Scalar;\n    static_assert(!std::is_pointer<Scalar>::value,\n                  PYBIND11_EIGEN_MESSAGE_POINTER_TYPES_ARE_NOT_SUPPORTED);\n    using StorageIndex = remove_reference_t<decltype(*std::declval<Type>().outerIndexPtr())>;\n    using Index = typename Type::Index;\n    static constexpr bool rowMajor = Type::IsRowMajor;\n\n    bool load(handle src, bool) {\n        if (!src) {\n            return false;\n        }\n\n        auto obj = reinterpret_borrow<object>(src);\n        object sparse_module = module_::import(\"scipy.sparse\");\n        object matrix_type = sparse_module.attr(rowMajor ? \"csr_matrix\" : \"csc_matrix\");\n\n        if (!type::handle_of(obj).is(matrix_type)) {\n            try {\n                obj = matrix_type(obj);\n            } catch (const error_already_set &) {\n                return false;\n            }\n        }\n\n        auto values = array_t<Scalar>((object) obj.attr(\"data\"));\n        auto innerIndices = array_t<StorageIndex>((object) obj.attr(\"indices\"));\n        auto outerIndices = array_t<StorageIndex>((object) obj.attr(\"indptr\"));\n        auto shape = pybind11::tuple((pybind11::object) obj.attr(\"shape\"));\n        auto nnz = obj.attr(\"nnz\").cast<Index>();\n\n        if (!values || !innerIndices || !outerIndices) {\n            return false;\n        }\n\n        value = EigenMapSparseMatrix<Scalar,\n                                     Type::Flags &(Eigen::RowMajor | Eigen::ColMajor),\n                                     StorageIndex>(shape[0].cast<Index>(),\n                                                   shape[1].cast<Index>(),\n                                                   std::move(nnz),\n                                                   outerIndices.mutable_data(),\n                                                   innerIndices.mutable_data(),\n                                                   values.mutable_data());\n\n        return true;\n    }\n\n    static handle cast(const Type &src, return_value_policy /* policy */, handle /* parent */) {\n        const_cast<Type &>(src).makeCompressed();\n\n        object matrix_type\n            = module_::import(\"scipy.sparse\").attr(rowMajor ? \"csr_matrix\" : \"csc_matrix\");\n\n        array data(src.nonZeros(), src.valuePtr());\n        array outerIndices((rowMajor ? src.rows() : src.cols()) + 1, src.outerIndexPtr());\n        array innerIndices(src.nonZeros(), src.innerIndexPtr());\n\n        return matrix_type(pybind11::make_tuple(\n                               std::move(data), std::move(innerIndices), std::move(outerIndices)),\n                           pybind11::make_tuple(src.rows(), src.cols()))\n            .release();\n    }\n\n    PYBIND11_TYPE_CASTER(Type,\n                         const_name<(Type::IsRowMajor) != 0>(\"scipy.sparse.csr_matrix[\",\n                                                             \"scipy.sparse.csc_matrix[\")\n                             + npy_format_descriptor<Scalar>::name + const_name(\"]\"));\n};\n\nPYBIND11_NAMESPACE_END(detail)\nPYBIND11_NAMESPACE_END(PYBIND11_NAMESPACE)\n"
  },
  {
    "path": "libs/pybind11/include/pybind11/eigen/tensor.h",
    "content": "/*\n    pybind11/eigen/tensor.h: Transparent conversion for Eigen tensors\n\n    All rights reserved. Use of this source code is governed by a\n    BSD-style license that can be found in the LICENSE file.\n*/\n\n#pragma once\n\n#include <pybind11/numpy.h>\n\n#include \"common.h\"\n\n#if defined(__GNUC__) && !defined(__clang__) && !defined(__INTEL_COMPILER)\nstatic_assert(__GNUC__ > 5, \"Eigen Tensor support in pybind11 requires GCC > 5.0\");\n#endif\n\n// Disable warnings for Eigen\nPYBIND11_WARNING_PUSH\nPYBIND11_WARNING_DISABLE_MSVC(4554)\nPYBIND11_WARNING_DISABLE_MSVC(4127)\n#if defined(__MINGW32__)\nPYBIND11_WARNING_DISABLE_GCC(\"-Wmaybe-uninitialized\")\n#endif\n\n#include <unsupported/Eigen/CXX11/Tensor>\n\nPYBIND11_WARNING_POP\n\nstatic_assert(EIGEN_VERSION_AT_LEAST(3, 3, 0),\n              \"Eigen Tensor support in pybind11 requires Eigen >= 3.3.0\");\n\nPYBIND11_NAMESPACE_BEGIN(PYBIND11_NAMESPACE)\n\nPYBIND11_WARNING_DISABLE_MSVC(4127)\n\nPYBIND11_NAMESPACE_BEGIN(detail)\n\ninline bool is_tensor_aligned(const void *data) {\n    return (reinterpret_cast<std::size_t>(data) % EIGEN_DEFAULT_ALIGN_BYTES) == 0;\n}\n\ntemplate <typename T>\nconstexpr int compute_array_flag_from_tensor() {\n    static_assert((static_cast<int>(T::Layout) == static_cast<int>(Eigen::RowMajor))\n                      || (static_cast<int>(T::Layout) == static_cast<int>(Eigen::ColMajor)),\n                  \"Layout must be row or column major\");\n    return (static_cast<int>(T::Layout) == static_cast<int>(Eigen::RowMajor)) ? array::c_style\n                                                                              : array::f_style;\n}\n\ntemplate <typename T>\nstruct eigen_tensor_helper {};\n\ntemplate <typename Scalar_, int NumIndices_, int Options_, typename IndexType>\nstruct eigen_tensor_helper<Eigen::Tensor<Scalar_, NumIndices_, Options_, IndexType>> {\n    using Type = Eigen::Tensor<Scalar_, NumIndices_, Options_, IndexType>;\n    using ValidType = void;\n\n    static Eigen::DSizes<typename Type::Index, Type::NumIndices> get_shape(const Type &f) {\n        return f.dimensions();\n    }\n\n    static constexpr bool\n    is_correct_shape(const Eigen::DSizes<typename Type::Index, Type::NumIndices> & /*shape*/) {\n        return true;\n    }\n\n    template <typename T>\n    struct helper {};\n\n    template <size_t... Is>\n    struct helper<index_sequence<Is...>> {\n        static constexpr auto value = ::pybind11::detail::concat(const_name(((void) Is, \"?\"))...);\n    };\n\n    static constexpr auto dimensions_descriptor\n        = helper<decltype(make_index_sequence<Type::NumIndices>())>::value;\n\n    template <typename... Args>\n    static Type *alloc(Args &&...args) {\n        return new Type(std::forward<Args>(args)...);\n    }\n\n    static void free(Type *tensor) { delete tensor; }\n};\n\ntemplate <typename Scalar_, typename std::ptrdiff_t... Indices, int Options_, typename IndexType>\nstruct eigen_tensor_helper<\n    Eigen::TensorFixedSize<Scalar_, Eigen::Sizes<Indices...>, Options_, IndexType>> {\n    using Type = Eigen::TensorFixedSize<Scalar_, Eigen::Sizes<Indices...>, Options_, IndexType>;\n    using ValidType = void;\n\n    static constexpr Eigen::DSizes<typename Type::Index, Type::NumIndices>\n    get_shape(const Type & /*f*/) {\n        return get_shape();\n    }\n\n    static constexpr Eigen::DSizes<typename Type::Index, Type::NumIndices> get_shape() {\n        return Eigen::DSizes<typename Type::Index, Type::NumIndices>(Indices...);\n    }\n\n    static bool\n    is_correct_shape(const Eigen::DSizes<typename Type::Index, Type::NumIndices> &shape) {\n        return get_shape() == shape;\n    }\n\n    static constexpr auto dimensions_descriptor\n        = ::pybind11::detail::concat(const_name<Indices>()...);\n\n    template <typename... Args>\n    static Type *alloc(Args &&...args) {\n        Eigen::aligned_allocator<Type> allocator;\n        return ::new (allocator.allocate(1)) Type(std::forward<Args>(args)...);\n    }\n\n    static void free(Type *tensor) {\n        Eigen::aligned_allocator<Type> allocator;\n        tensor->~Type();\n        allocator.deallocate(tensor, 1);\n    }\n};\n\ntemplate <typename Type, bool ShowDetails, bool NeedsWriteable = false>\nstruct get_tensor_descriptor {\n    static constexpr auto details\n        = const_name<NeedsWriteable>(\", flags.writeable\", \"\")\n          + const_name<static_cast<int>(Type::Layout) == static_cast<int>(Eigen::RowMajor)>(\n              \", flags.c_contiguous\", \", flags.f_contiguous\");\n    static constexpr auto value\n        = const_name(\"numpy.ndarray[\") + npy_format_descriptor<typename Type::Scalar>::name\n          + const_name(\"[\") + eigen_tensor_helper<remove_cv_t<Type>>::dimensions_descriptor\n          + const_name(\"]\") + const_name<ShowDetails>(details, const_name(\"\")) + const_name(\"]\");\n};\n\n// When EIGEN_AVOID_STL_ARRAY is defined, Eigen::DSizes<T, 0> does not have the begin() member\n// function. Falling back to a simple loop works around this issue.\n//\n// We need to disable the type-limits warning for the inner loop when size = 0.\n\nPYBIND11_WARNING_PUSH\nPYBIND11_WARNING_DISABLE_GCC(\"-Wtype-limits\")\n\ntemplate <typename T, int size>\nstd::vector<T> convert_dsizes_to_vector(const Eigen::DSizes<T, size> &arr) {\n    std::vector<T> result(size);\n\n    for (size_t i = 0; i < size; i++) {\n        result[i] = arr[i];\n    }\n\n    return result;\n}\n\ntemplate <typename T, int size>\nEigen::DSizes<T, size> get_shape_for_array(const array &arr) {\n    Eigen::DSizes<T, size> result;\n    const T *shape = arr.shape();\n    for (size_t i = 0; i < size; i++) {\n        result[i] = shape[i];\n    }\n\n    return result;\n}\n\nPYBIND11_WARNING_POP\n\ntemplate <typename Type>\nstruct type_caster<Type, typename eigen_tensor_helper<Type>::ValidType> {\n    static_assert(!std::is_pointer<typename Type::Scalar>::value,\n                  PYBIND11_EIGEN_MESSAGE_POINTER_TYPES_ARE_NOT_SUPPORTED);\n    using Helper = eigen_tensor_helper<Type>;\n    static constexpr auto temp_name = get_tensor_descriptor<Type, false>::value;\n    PYBIND11_TYPE_CASTER(Type, temp_name);\n\n    bool load(handle src, bool convert) {\n        if (!convert) {\n            if (!isinstance<array>(src)) {\n                return false;\n            }\n            array temp = array::ensure(src);\n            if (!temp) {\n                return false;\n            }\n\n            if (!temp.dtype().is(dtype::of<typename Type::Scalar>())) {\n                return false;\n            }\n        }\n\n        array_t<typename Type::Scalar, compute_array_flag_from_tensor<Type>()> arr(\n            reinterpret_borrow<object>(src));\n\n        if (arr.ndim() != Type::NumIndices) {\n            return false;\n        }\n        auto shape = get_shape_for_array<typename Type::Index, Type::NumIndices>(arr);\n\n        if (!Helper::is_correct_shape(shape)) {\n            return false;\n        }\n\n#if EIGEN_VERSION_AT_LEAST(3, 4, 0)\n        auto data_pointer = arr.data();\n#else\n        // Handle Eigen bug\n        auto data_pointer = const_cast<typename Type::Scalar *>(arr.data());\n#endif\n\n        if (is_tensor_aligned(arr.data())) {\n            value = Eigen::TensorMap<const Type, Eigen::Aligned>(data_pointer, shape);\n        } else {\n            value = Eigen::TensorMap<const Type>(data_pointer, shape);\n        }\n\n        return true;\n    }\n\n    static handle cast(Type &&src, return_value_policy policy, handle parent) {\n        if (policy == return_value_policy::reference\n            || policy == return_value_policy::reference_internal) {\n            pybind11_fail(\"Cannot use a reference return value policy for an rvalue\");\n        }\n        return cast_impl(&src, return_value_policy::move, parent);\n    }\n\n    static handle cast(const Type &&src, return_value_policy policy, handle parent) {\n        if (policy == return_value_policy::reference\n            || policy == return_value_policy::reference_internal) {\n            pybind11_fail(\"Cannot use a reference return value policy for an rvalue\");\n        }\n        return cast_impl(&src, return_value_policy::move, parent);\n    }\n\n    static handle cast(Type &src, return_value_policy policy, handle parent) {\n        if (policy == return_value_policy::automatic\n            || policy == return_value_policy::automatic_reference) {\n            policy = return_value_policy::copy;\n        }\n        return cast_impl(&src, policy, parent);\n    }\n\n    static handle cast(const Type &src, return_value_policy policy, handle parent) {\n        if (policy == return_value_policy::automatic\n            || policy == return_value_policy::automatic_reference) {\n            policy = return_value_policy::copy;\n        }\n        return cast(&src, policy, parent);\n    }\n\n    static handle cast(Type *src, return_value_policy policy, handle parent) {\n        if (policy == return_value_policy::automatic) {\n            policy = return_value_policy::take_ownership;\n        } else if (policy == return_value_policy::automatic_reference) {\n            policy = return_value_policy::reference;\n        }\n        return cast_impl(src, policy, parent);\n    }\n\n    static handle cast(const Type *src, return_value_policy policy, handle parent) {\n        if (policy == return_value_policy::automatic) {\n            policy = return_value_policy::take_ownership;\n        } else if (policy == return_value_policy::automatic_reference) {\n            policy = return_value_policy::reference;\n        }\n        return cast_impl(src, policy, parent);\n    }\n\n    template <typename C>\n    static handle cast_impl(C *src, return_value_policy policy, handle parent) {\n        object parent_object;\n        bool writeable = false;\n        switch (policy) {\n            case return_value_policy::move:\n                if (std::is_const<C>::value) {\n                    pybind11_fail(\"Cannot move from a constant reference\");\n                }\n\n                src = Helper::alloc(std::move(*src));\n\n                parent_object\n                    = capsule(src, [](void *ptr) { Helper::free(reinterpret_cast<Type *>(ptr)); });\n                writeable = true;\n                break;\n\n            case return_value_policy::take_ownership:\n                if (std::is_const<C>::value) {\n                    // This cast is ugly, and might be UB in some cases, but we don't have an\n                    // alternative here as we must free that memory\n                    Helper::free(const_cast<Type *>(src));\n                    pybind11_fail(\"Cannot take ownership of a const reference\");\n                }\n\n                parent_object\n                    = capsule(src, [](void *ptr) { Helper::free(reinterpret_cast<Type *>(ptr)); });\n                writeable = true;\n                break;\n\n            case return_value_policy::copy:\n                writeable = true;\n                break;\n\n            case return_value_policy::reference:\n                parent_object = none();\n                writeable = !std::is_const<C>::value;\n                break;\n\n            case return_value_policy::reference_internal:\n                // Default should do the right thing\n                if (!parent) {\n                    pybind11_fail(\"Cannot use reference internal when there is no parent\");\n                }\n                parent_object = reinterpret_borrow<object>(parent);\n                writeable = !std::is_const<C>::value;\n                break;\n\n            default:\n                pybind11_fail(\"pybind11 bug in eigen.h, please file a bug report\");\n        }\n\n        auto result = array_t<typename Type::Scalar, compute_array_flag_from_tensor<Type>()>(\n            convert_dsizes_to_vector(Helper::get_shape(*src)), src->data(), parent_object);\n\n        if (!writeable) {\n            array_proxy(result.ptr())->flags &= ~detail::npy_api::NPY_ARRAY_WRITEABLE_;\n        }\n\n        return result.release();\n    }\n};\n\ntemplate <typename StoragePointerType,\n          bool needs_writeable,\n          enable_if_t<!needs_writeable, bool> = true>\nStoragePointerType get_array_data_for_type(array &arr) {\n#if EIGEN_VERSION_AT_LEAST(3, 4, 0)\n    return reinterpret_cast<StoragePointerType>(arr.data());\n#else\n    // Handle Eigen bug\n    return reinterpret_cast<StoragePointerType>(const_cast<void *>(arr.data()));\n#endif\n}\n\ntemplate <typename StoragePointerType,\n          bool needs_writeable,\n          enable_if_t<needs_writeable, bool> = true>\nStoragePointerType get_array_data_for_type(array &arr) {\n    return reinterpret_cast<StoragePointerType>(arr.mutable_data());\n}\n\ntemplate <typename T, typename = void>\nstruct get_storage_pointer_type;\n\ntemplate <typename MapType>\nstruct get_storage_pointer_type<MapType, void_t<typename MapType::StoragePointerType>> {\n    using SPT = typename MapType::StoragePointerType;\n};\n\ntemplate <typename MapType>\nstruct get_storage_pointer_type<MapType, void_t<typename MapType::PointerArgType>> {\n    using SPT = typename MapType::PointerArgType;\n};\n\ntemplate <typename Type, int Options>\nstruct type_caster<Eigen::TensorMap<Type, Options>,\n                   typename eigen_tensor_helper<remove_cv_t<Type>>::ValidType> {\n    static_assert(!std::is_pointer<typename Type::Scalar>::value,\n                  PYBIND11_EIGEN_MESSAGE_POINTER_TYPES_ARE_NOT_SUPPORTED);\n    using MapType = Eigen::TensorMap<Type, Options>;\n    using Helper = eigen_tensor_helper<remove_cv_t<Type>>;\n\n    bool load(handle src, bool /*convert*/) {\n        // Note that we have a lot more checks here as we want to make sure to avoid copies\n        if (!isinstance<array>(src)) {\n            return false;\n        }\n        auto arr = reinterpret_borrow<array>(src);\n        if ((arr.flags() & compute_array_flag_from_tensor<Type>()) == 0) {\n            return false;\n        }\n\n        if (!arr.dtype().is(dtype::of<typename Type::Scalar>())) {\n            return false;\n        }\n\n        if (arr.ndim() != Type::NumIndices) {\n            return false;\n        }\n\n        constexpr bool is_aligned = (Options & Eigen::Aligned) != 0;\n\n        if (is_aligned && !is_tensor_aligned(arr.data())) {\n            return false;\n        }\n\n        auto shape = get_shape_for_array<typename Type::Index, Type::NumIndices>(arr);\n\n        if (!Helper::is_correct_shape(shape)) {\n            return false;\n        }\n\n        if (needs_writeable && !arr.writeable()) {\n            return false;\n        }\n\n        auto result = get_array_data_for_type<typename get_storage_pointer_type<MapType>::SPT,\n                                              needs_writeable>(arr);\n\n        value.reset(new MapType(std::move(result), std::move(shape)));\n\n        return true;\n    }\n\n    static handle cast(MapType &&src, return_value_policy policy, handle parent) {\n        return cast_impl(&src, policy, parent);\n    }\n\n    static handle cast(const MapType &&src, return_value_policy policy, handle parent) {\n        return cast_impl(&src, policy, parent);\n    }\n\n    static handle cast(MapType &src, return_value_policy policy, handle parent) {\n        if (policy == return_value_policy::automatic\n            || policy == return_value_policy::automatic_reference) {\n            policy = return_value_policy::copy;\n        }\n        return cast_impl(&src, policy, parent);\n    }\n\n    static handle cast(const MapType &src, return_value_policy policy, handle parent) {\n        if (policy == return_value_policy::automatic\n            || policy == return_value_policy::automatic_reference) {\n            policy = return_value_policy::copy;\n        }\n        return cast(&src, policy, parent);\n    }\n\n    static handle cast(MapType *src, return_value_policy policy, handle parent) {\n        if (policy == return_value_policy::automatic) {\n            policy = return_value_policy::take_ownership;\n        } else if (policy == return_value_policy::automatic_reference) {\n            policy = return_value_policy::reference;\n        }\n        return cast_impl(src, policy, parent);\n    }\n\n    static handle cast(const MapType *src, return_value_policy policy, handle parent) {\n        if (policy == return_value_policy::automatic) {\n            policy = return_value_policy::take_ownership;\n        } else if (policy == return_value_policy::automatic_reference) {\n            policy = return_value_policy::reference;\n        }\n        return cast_impl(src, policy, parent);\n    }\n\n    template <typename C>\n    static handle cast_impl(C *src, return_value_policy policy, handle parent) {\n        object parent_object;\n        constexpr bool writeable = !std::is_const<C>::value;\n        switch (policy) {\n            case return_value_policy::reference:\n                parent_object = none();\n                break;\n\n            case return_value_policy::reference_internal:\n                // Default should do the right thing\n                if (!parent) {\n                    pybind11_fail(\"Cannot use reference internal when there is no parent\");\n                }\n                parent_object = reinterpret_borrow<object>(parent);\n                break;\n\n            default:\n                // move, take_ownership don't make any sense for a ref/map:\n                pybind11_fail(\"Invalid return_value_policy for Eigen Map type, must be either \"\n                              \"reference or reference_internal\");\n        }\n\n        auto result = array_t<typename Type::Scalar, compute_array_flag_from_tensor<Type>()>(\n            convert_dsizes_to_vector(Helper::get_shape(*src)),\n            src->data(),\n            std::move(parent_object));\n\n        if (!writeable) {\n            array_proxy(result.ptr())->flags &= ~detail::npy_api::NPY_ARRAY_WRITEABLE_;\n        }\n\n        return result.release();\n    }\n\n#if EIGEN_VERSION_AT_LEAST(3, 4, 0)\n\n    static constexpr bool needs_writeable = !std::is_const<typename std::remove_pointer<\n        typename get_storage_pointer_type<MapType>::SPT>::type>::value;\n#else\n    // Handle Eigen bug\n    static constexpr bool needs_writeable = !std::is_const<Type>::value;\n#endif\n\nprotected:\n    // TODO: Move to std::optional once std::optional has more support\n    std::unique_ptr<MapType> value;\n\npublic:\n    static constexpr auto name = get_tensor_descriptor<Type, true, needs_writeable>::value;\n    explicit operator MapType *() { return value.get(); }\n    explicit operator MapType &() { return *value; }\n    explicit operator MapType &&() && { return std::move(*value); }\n\n    template <typename T_>\n    using cast_op_type = ::pybind11::detail::movable_cast_op_type<T_>;\n};\n\nPYBIND11_NAMESPACE_END(detail)\nPYBIND11_NAMESPACE_END(PYBIND11_NAMESPACE)\n"
  },
  {
    "path": "libs/pybind11/include/pybind11/eigen.h",
    "content": "/*\n    pybind11/eigen.h: Transparent conversion for dense and sparse Eigen matrices\n\n    Copyright (c) 2016 Wenzel Jakob <wenzel.jakob@epfl.ch>\n\n    All rights reserved. Use of this source code is governed by a\n    BSD-style license that can be found in the LICENSE file.\n*/\n\n#pragma once\n\n#include \"eigen/matrix.h\"\n"
  },
  {
    "path": "libs/pybind11/include/pybind11/embed.h",
    "content": "/*\n    pybind11/embed.h: Support for embedding the interpreter\n\n    Copyright (c) 2017 Wenzel Jakob <wenzel.jakob@epfl.ch>\n\n    All rights reserved. Use of this source code is governed by a\n    BSD-style license that can be found in the LICENSE file.\n*/\n\n#pragma once\n\n#include \"pybind11.h\"\n#include \"eval.h\"\n\n#include <memory>\n#include <vector>\n\n#if defined(PYPY_VERSION)\n#    error Embedding the interpreter is not supported with PyPy\n#endif\n\n#define PYBIND11_EMBEDDED_MODULE_IMPL(name)                                                       \\\n    extern \"C\" PyObject *pybind11_init_impl_##name();                                             \\\n    extern \"C\" PyObject *pybind11_init_impl_##name() { return pybind11_init_wrapper_##name(); }\n\n/** \\rst\n    Add a new module to the table of builtins for the interpreter. Must be\n    defined in global scope. The first macro parameter is the name of the\n    module (without quotes). The second parameter is the variable which will\n    be used as the interface to add functions and classes to the module.\n\n    .. code-block:: cpp\n\n        PYBIND11_EMBEDDED_MODULE(example, m) {\n            // ... initialize functions and classes here\n            m.def(\"foo\", []() {\n                return \"Hello, World!\";\n            });\n        }\n \\endrst */\n#define PYBIND11_EMBEDDED_MODULE(name, variable)                                                  \\\n    static ::pybind11::module_::module_def PYBIND11_CONCAT(pybind11_module_def_, name);           \\\n    static void PYBIND11_CONCAT(pybind11_init_, name)(::pybind11::module_ &);                     \\\n    static PyObject PYBIND11_CONCAT(*pybind11_init_wrapper_, name)() {                            \\\n        auto m = ::pybind11::module_::create_extension_module(                                    \\\n            PYBIND11_TOSTRING(name), nullptr, &PYBIND11_CONCAT(pybind11_module_def_, name));      \\\n        try {                                                                                     \\\n            PYBIND11_CONCAT(pybind11_init_, name)(m);                                             \\\n            return m.ptr();                                                                       \\\n        }                                                                                         \\\n        PYBIND11_CATCH_INIT_EXCEPTIONS                                                            \\\n    }                                                                                             \\\n    PYBIND11_EMBEDDED_MODULE_IMPL(name)                                                           \\\n    ::pybind11::detail::embedded_module PYBIND11_CONCAT(pybind11_module_, name)(                  \\\n        PYBIND11_TOSTRING(name), PYBIND11_CONCAT(pybind11_init_impl_, name));                     \\\n    void PYBIND11_CONCAT(pybind11_init_, name)(::pybind11::module_                                \\\n                                               & variable) // NOLINT(bugprone-macro-parentheses)\n\nPYBIND11_NAMESPACE_BEGIN(PYBIND11_NAMESPACE)\nPYBIND11_NAMESPACE_BEGIN(detail)\n\n/// Python 2.7/3.x compatible version of `PyImport_AppendInittab` and error checks.\nstruct embedded_module {\n    using init_t = PyObject *(*) ();\n    embedded_module(const char *name, init_t init) {\n        if (Py_IsInitialized() != 0) {\n            pybind11_fail(\"Can't add new modules after the interpreter has been initialized\");\n        }\n\n        auto result = PyImport_AppendInittab(name, init);\n        if (result == -1) {\n            pybind11_fail(\"Insufficient memory to add a new module\");\n        }\n    }\n};\n\nstruct wide_char_arg_deleter {\n    void operator()(wchar_t *ptr) const {\n        // API docs: https://docs.python.org/3/c-api/sys.html#c.Py_DecodeLocale\n        PyMem_RawFree(ptr);\n    }\n};\n\ninline wchar_t *widen_chars(const char *safe_arg) {\n    wchar_t *widened_arg = Py_DecodeLocale(safe_arg, nullptr);\n    return widened_arg;\n}\n\ninline void precheck_interpreter() {\n    if (Py_IsInitialized() != 0) {\n        pybind11_fail(\"The interpreter is already running\");\n    }\n}\n\n#if !defined(PYBIND11_PYCONFIG_SUPPORT_PY_VERSION_HEX)\n#    define PYBIND11_PYCONFIG_SUPPORT_PY_VERSION_HEX (0x03080000)\n#endif\n\n#if PY_VERSION_HEX < PYBIND11_PYCONFIG_SUPPORT_PY_VERSION_HEX\ninline void initialize_interpreter_pre_pyconfig(bool init_signal_handlers,\n                                                int argc,\n                                                const char *const *argv,\n                                                bool add_program_dir_to_path) {\n    detail::precheck_interpreter();\n    Py_InitializeEx(init_signal_handlers ? 1 : 0);\n\n    // Before it was special-cased in python 3.8, passing an empty or null argv\n    // caused a segfault, so we have to reimplement the special case ourselves.\n    bool special_case = (argv == nullptr || argc <= 0);\n\n    const char *const empty_argv[]{\"\\0\"};\n    const char *const *safe_argv = special_case ? empty_argv : argv;\n    if (special_case) {\n        argc = 1;\n    }\n\n    auto argv_size = static_cast<size_t>(argc);\n    // SetArgv* on python 3 takes wchar_t, so we have to convert.\n    std::unique_ptr<wchar_t *[]> widened_argv(new wchar_t *[argv_size]);\n    std::vector<std::unique_ptr<wchar_t[], detail::wide_char_arg_deleter>> widened_argv_entries;\n    widened_argv_entries.reserve(argv_size);\n    for (size_t ii = 0; ii < argv_size; ++ii) {\n        widened_argv_entries.emplace_back(detail::widen_chars(safe_argv[ii]));\n        if (!widened_argv_entries.back()) {\n            // A null here indicates a character-encoding failure or the python\n            // interpreter out of memory. Give up.\n            return;\n        }\n        widened_argv[ii] = widened_argv_entries.back().get();\n    }\n\n    auto *pysys_argv = widened_argv.get();\n\n    PySys_SetArgvEx(argc, pysys_argv, static_cast<int>(add_program_dir_to_path));\n}\n#endif\n\nPYBIND11_NAMESPACE_END(detail)\n\n#if PY_VERSION_HEX >= PYBIND11_PYCONFIG_SUPPORT_PY_VERSION_HEX\ninline void initialize_interpreter(PyConfig *config,\n                                   int argc = 0,\n                                   const char *const *argv = nullptr,\n                                   bool add_program_dir_to_path = true) {\n    detail::precheck_interpreter();\n    PyStatus status = PyConfig_SetBytesArgv(config, argc, const_cast<char *const *>(argv));\n    if (PyStatus_Exception(status) != 0) {\n        // A failure here indicates a character-encoding failure or the python\n        // interpreter out of memory. Give up.\n        PyConfig_Clear(config);\n        throw std::runtime_error(PyStatus_IsError(status) != 0 ? status.err_msg\n                                                               : \"Failed to prepare CPython\");\n    }\n    status = Py_InitializeFromConfig(config);\n    if (PyStatus_Exception(status) != 0) {\n        PyConfig_Clear(config);\n        throw std::runtime_error(PyStatus_IsError(status) != 0 ? status.err_msg\n                                                               : \"Failed to init CPython\");\n    }\n    if (add_program_dir_to_path) {\n        PyRun_SimpleString(\"import sys, os.path; \"\n                           \"sys.path.insert(0, \"\n                           \"os.path.abspath(os.path.dirname(sys.argv[0])) \"\n                           \"if sys.argv and os.path.exists(sys.argv[0]) else '')\");\n    }\n    PyConfig_Clear(config);\n}\n#endif\n\n/** \\rst\n    Initialize the Python interpreter. No other pybind11 or CPython API functions can be\n    called before this is done; with the exception of `PYBIND11_EMBEDDED_MODULE`. The\n    optional `init_signal_handlers` parameter can be used to skip the registration of\n    signal handlers (see the `Python documentation`_ for details). Calling this function\n    again after the interpreter has already been initialized is a fatal error.\n\n    If initializing the Python interpreter fails, then the program is terminated.  (This\n    is controlled by the CPython runtime and is an exception to pybind11's normal behavior\n    of throwing exceptions on errors.)\n\n    The remaining optional parameters, `argc`, `argv`, and `add_program_dir_to_path` are\n    used to populate ``sys.argv`` and ``sys.path``.\n    See the |PySys_SetArgvEx documentation|_ for details.\n\n    .. _Python documentation: https://docs.python.org/3/c-api/init.html#c.Py_InitializeEx\n    .. |PySys_SetArgvEx documentation| replace:: ``PySys_SetArgvEx`` documentation\n    .. _PySys_SetArgvEx documentation: https://docs.python.org/3/c-api/init.html#c.PySys_SetArgvEx\n \\endrst */\ninline void initialize_interpreter(bool init_signal_handlers = true,\n                                   int argc = 0,\n                                   const char *const *argv = nullptr,\n                                   bool add_program_dir_to_path = true) {\n#if PY_VERSION_HEX < PYBIND11_PYCONFIG_SUPPORT_PY_VERSION_HEX\n    detail::initialize_interpreter_pre_pyconfig(\n        init_signal_handlers, argc, argv, add_program_dir_to_path);\n#else\n    PyConfig config;\n    PyConfig_InitPythonConfig(&config);\n    // See PR #4473 for background\n    config.parse_argv = 0;\n\n    config.install_signal_handlers = init_signal_handlers ? 1 : 0;\n    initialize_interpreter(&config, argc, argv, add_program_dir_to_path);\n#endif\n}\n\n/** \\rst\n    Shut down the Python interpreter. No pybind11 or CPython API functions can be called\n    after this. In addition, pybind11 objects must not outlive the interpreter:\n\n    .. code-block:: cpp\n\n        { // BAD\n            py::initialize_interpreter();\n            auto hello = py::str(\"Hello, World!\");\n            py::finalize_interpreter();\n        } // <-- BOOM, hello's destructor is called after interpreter shutdown\n\n        { // GOOD\n            py::initialize_interpreter();\n            { // scoped\n                auto hello = py::str(\"Hello, World!\");\n            } // <-- OK, hello is cleaned up properly\n            py::finalize_interpreter();\n        }\n\n        { // BETTER\n            py::scoped_interpreter guard{};\n            auto hello = py::str(\"Hello, World!\");\n        }\n\n    .. warning::\n\n        The interpreter can be restarted by calling `initialize_interpreter` again.\n        Modules created using pybind11 can be safely re-initialized. However, Python\n        itself cannot completely unload binary extension modules and there are several\n        caveats with regard to interpreter restarting. All the details can be found\n        in the CPython documentation. In short, not all interpreter memory may be\n        freed, either due to reference cycles or user-created global data.\n\n \\endrst */\ninline void finalize_interpreter() {\n    // Get the internals pointer (without creating it if it doesn't exist).  It's possible for the\n    // internals to be created during Py_Finalize() (e.g. if a py::capsule calls `get_internals()`\n    // during destruction), so we get the pointer-pointer here and check it after Py_Finalize().\n    detail::internals **internals_ptr_ptr = detail::get_internals_pp();\n    // It could also be stashed in state_dict, so look there too:\n    if (object internals_obj\n        = get_internals_obj_from_state_dict(detail::get_python_state_dict())) {\n        internals_ptr_ptr = detail::get_internals_pp_from_capsule(internals_obj);\n    }\n    // Local internals contains data managed by the current interpreter, so we must clear them to\n    // avoid undefined behaviors when initializing another interpreter\n    detail::get_local_internals().registered_types_cpp.clear();\n    detail::get_local_internals().registered_exception_translators.clear();\n\n    Py_Finalize();\n\n    if (internals_ptr_ptr) {\n        delete *internals_ptr_ptr;\n        *internals_ptr_ptr = nullptr;\n    }\n}\n\n/** \\rst\n    Scope guard version of `initialize_interpreter` and `finalize_interpreter`.\n    This a move-only guard and only a single instance can exist.\n\n    See `initialize_interpreter` for a discussion of its constructor arguments.\n\n    .. code-block:: cpp\n\n        #include <pybind11/embed.h>\n\n        int main() {\n            py::scoped_interpreter guard{};\n            py::print(Hello, World!);\n        } // <-- interpreter shutdown\n \\endrst */\nclass scoped_interpreter {\npublic:\n    explicit scoped_interpreter(bool init_signal_handlers = true,\n                                int argc = 0,\n                                const char *const *argv = nullptr,\n                                bool add_program_dir_to_path = true) {\n        initialize_interpreter(init_signal_handlers, argc, argv, add_program_dir_to_path);\n    }\n\n#if PY_VERSION_HEX >= PYBIND11_PYCONFIG_SUPPORT_PY_VERSION_HEX\n    explicit scoped_interpreter(PyConfig *config,\n                                int argc = 0,\n                                const char *const *argv = nullptr,\n                                bool add_program_dir_to_path = true) {\n        initialize_interpreter(config, argc, argv, add_program_dir_to_path);\n    }\n#endif\n\n    scoped_interpreter(const scoped_interpreter &) = delete;\n    scoped_interpreter(scoped_interpreter &&other) noexcept { other.is_valid = false; }\n    scoped_interpreter &operator=(const scoped_interpreter &) = delete;\n    scoped_interpreter &operator=(scoped_interpreter &&) = delete;\n\n    ~scoped_interpreter() {\n        if (is_valid) {\n            finalize_interpreter();\n        }\n    }\n\nprivate:\n    bool is_valid = true;\n};\n\nPYBIND11_NAMESPACE_END(PYBIND11_NAMESPACE)\n"
  },
  {
    "path": "libs/pybind11/include/pybind11/eval.h",
    "content": "/*\n    pybind11/eval.h: Support for evaluating Python expressions and statements\n    from strings and files\n\n    Copyright (c) 2016 Klemens Morgenstern <klemens.morgenstern@ed-chemnitz.de> and\n                       Wenzel Jakob <wenzel.jakob@epfl.ch>\n\n    All rights reserved. Use of this source code is governed by a\n    BSD-style license that can be found in the LICENSE file.\n*/\n\n#pragma once\n\n#include \"pybind11.h\"\n\n#include <utility>\n\nPYBIND11_NAMESPACE_BEGIN(PYBIND11_NAMESPACE)\nPYBIND11_NAMESPACE_BEGIN(detail)\n\ninline void ensure_builtins_in_globals(object &global) {\n#if defined(PYPY_VERSION) || PY_VERSION_HEX < 0x03080000\n    // Running exec and eval adds `builtins` module under `__builtins__` key to\n    // globals if not yet present.  Python 3.8 made PyRun_String behave\n    // similarly. Let's also do that for older versions, for consistency. This\n    // was missing from PyPy3.8 7.3.7.\n    if (!global.contains(\"__builtins__\"))\n        global[\"__builtins__\"] = module_::import(PYBIND11_BUILTINS_MODULE);\n#else\n    (void) global;\n#endif\n}\n\nPYBIND11_NAMESPACE_END(detail)\n\nenum eval_mode {\n    /// Evaluate a string containing an isolated expression\n    eval_expr,\n\n    /// Evaluate a string containing a single statement. Returns \\c none\n    eval_single_statement,\n\n    /// Evaluate a string containing a sequence of statement. Returns \\c none\n    eval_statements\n};\n\ntemplate <eval_mode mode = eval_expr>\nobject eval(const str &expr, object global = globals(), object local = object()) {\n    if (!local) {\n        local = global;\n    }\n\n    detail::ensure_builtins_in_globals(global);\n\n    /* PyRun_String does not accept a PyObject / encoding specifier,\n       this seems to be the only alternative */\n    std::string buffer = \"# -*- coding: utf-8 -*-\\n\" + (std::string) expr;\n\n    int start = 0;\n    switch (mode) {\n        case eval_expr:\n            start = Py_eval_input;\n            break;\n        case eval_single_statement:\n            start = Py_single_input;\n            break;\n        case eval_statements:\n            start = Py_file_input;\n            break;\n        default:\n            pybind11_fail(\"invalid evaluation mode\");\n    }\n\n    PyObject *result = PyRun_String(buffer.c_str(), start, global.ptr(), local.ptr());\n    if (!result) {\n        throw error_already_set();\n    }\n    return reinterpret_steal<object>(result);\n}\n\ntemplate <eval_mode mode = eval_expr, size_t N>\nobject eval(const char (&s)[N], object global = globals(), object local = object()) {\n    /* Support raw string literals by removing common leading whitespace */\n    auto expr = (s[0] == '\\n') ? str(module_::import(\"textwrap\").attr(\"dedent\")(s)) : str(s);\n    return eval<mode>(expr, std::move(global), std::move(local));\n}\n\ninline void exec(const str &expr, object global = globals(), object local = object()) {\n    eval<eval_statements>(expr, std::move(global), std::move(local));\n}\n\ntemplate <size_t N>\nvoid exec(const char (&s)[N], object global = globals(), object local = object()) {\n    eval<eval_statements>(s, std::move(global), std::move(local));\n}\n\n#if defined(PYPY_VERSION)\ntemplate <eval_mode mode = eval_statements>\nobject eval_file(str, object, object) {\n    pybind11_fail(\"eval_file not supported in PyPy3. Use eval\");\n}\ntemplate <eval_mode mode = eval_statements>\nobject eval_file(str, object) {\n    pybind11_fail(\"eval_file not supported in PyPy3. Use eval\");\n}\ntemplate <eval_mode mode = eval_statements>\nobject eval_file(str) {\n    pybind11_fail(\"eval_file not supported in PyPy3. Use eval\");\n}\n#else\ntemplate <eval_mode mode = eval_statements>\nobject eval_file(str fname, object global = globals(), object local = object()) {\n    if (!local) {\n        local = global;\n    }\n\n    detail::ensure_builtins_in_globals(global);\n\n    int start = 0;\n    switch (mode) {\n        case eval_expr:\n            start = Py_eval_input;\n            break;\n        case eval_single_statement:\n            start = Py_single_input;\n            break;\n        case eval_statements:\n            start = Py_file_input;\n            break;\n        default:\n            pybind11_fail(\"invalid evaluation mode\");\n    }\n\n    int closeFile = 1;\n    std::string fname_str = (std::string) fname;\n    FILE *f = _Py_fopen_obj(fname.ptr(), \"r\");\n    if (!f) {\n        PyErr_Clear();\n        pybind11_fail(\"File \\\"\" + fname_str + \"\\\" could not be opened!\");\n    }\n\n    if (!global.contains(\"__file__\")) {\n        global[\"__file__\"] = std::move(fname);\n    }\n\n    PyObject *result\n        = PyRun_FileEx(f, fname_str.c_str(), start, global.ptr(), local.ptr(), closeFile);\n\n    if (!result) {\n        throw error_already_set();\n    }\n    return reinterpret_steal<object>(result);\n}\n#endif\n\nPYBIND11_NAMESPACE_END(PYBIND11_NAMESPACE)\n"
  },
  {
    "path": "libs/pybind11/include/pybind11/functional.h",
    "content": "/*\n    pybind11/functional.h: std::function<> support\n\n    Copyright (c) 2016 Wenzel Jakob <wenzel.jakob@epfl.ch>\n\n    All rights reserved. Use of this source code is governed by a\n    BSD-style license that can be found in the LICENSE file.\n*/\n\n#pragma once\n\n#define PYBIND11_HAS_TYPE_CASTER_STD_FUNCTION_SPECIALIZATIONS\n\n#include \"pybind11.h\"\n\n#include <functional>\n\nPYBIND11_NAMESPACE_BEGIN(PYBIND11_NAMESPACE)\nPYBIND11_NAMESPACE_BEGIN(detail)\nPYBIND11_NAMESPACE_BEGIN(type_caster_std_function_specializations)\n\n// ensure GIL is held during functor destruction\nstruct func_handle {\n    function f;\n#if !(defined(_MSC_VER) && _MSC_VER == 1916 && defined(PYBIND11_CPP17))\n    // This triggers a syntax error under very special conditions (very weird indeed).\n    explicit\n#endif\n        func_handle(function &&f_) noexcept\n        : f(std::move(f_)) {\n    }\n    func_handle(const func_handle &f_) { operator=(f_); }\n    func_handle &operator=(const func_handle &f_) {\n        gil_scoped_acquire acq;\n        f = f_.f;\n        return *this;\n    }\n    ~func_handle() {\n        gil_scoped_acquire acq;\n        function kill_f(std::move(f));\n    }\n};\n\n// to emulate 'move initialization capture' in C++11\nstruct func_wrapper_base {\n    func_handle hfunc;\n    explicit func_wrapper_base(func_handle &&hf) noexcept : hfunc(hf) {}\n};\n\ntemplate <typename Return, typename... Args>\nstruct func_wrapper : func_wrapper_base {\n    using func_wrapper_base::func_wrapper_base;\n    Return operator()(Args... args) const {\n        gil_scoped_acquire acq;\n        // casts the returned object as a rvalue to the return type\n        return hfunc.f(std::forward<Args>(args)...).template cast<Return>();\n    }\n};\n\nPYBIND11_NAMESPACE_END(type_caster_std_function_specializations)\n\ntemplate <typename Return, typename... Args>\nstruct type_caster<std::function<Return(Args...)>> {\n    using type = std::function<Return(Args...)>;\n    using retval_type = conditional_t<std::is_same<Return, void>::value, void_type, Return>;\n    using function_type = Return (*)(Args...);\n\npublic:\n    bool load(handle src, bool convert) {\n        if (src.is_none()) {\n            // Defer accepting None to other overloads (if we aren't in convert mode):\n            if (!convert) {\n                return false;\n            }\n            return true;\n        }\n\n        if (!isinstance<function>(src)) {\n            return false;\n        }\n\n        auto func = reinterpret_borrow<function>(src);\n\n        /*\n           When passing a C++ function as an argument to another C++\n           function via Python, every function call would normally involve\n           a full C++ -> Python -> C++ roundtrip, which can be prohibitive.\n           Here, we try to at least detect the case where the function is\n           stateless (i.e. function pointer or lambda function without\n           captured variables), in which case the roundtrip can be avoided.\n         */\n        if (auto cfunc = func.cpp_function()) {\n            auto *cfunc_self = PyCFunction_GET_SELF(cfunc.ptr());\n            if (cfunc_self == nullptr) {\n                PyErr_Clear();\n            } else if (isinstance<capsule>(cfunc_self)) {\n                auto c = reinterpret_borrow<capsule>(cfunc_self);\n\n                function_record *rec = nullptr;\n                // Check that we can safely reinterpret the capsule into a function_record\n                if (detail::is_function_record_capsule(c)) {\n                    rec = c.get_pointer<function_record>();\n                }\n\n                while (rec != nullptr) {\n                    if (rec->is_stateless\n                        && same_type(typeid(function_type),\n                                     *reinterpret_cast<const std::type_info *>(rec->data[1]))) {\n                        struct capture {\n                            function_type f;\n                        };\n                        value = ((capture *) &rec->data)->f;\n                        return true;\n                    }\n                    rec = rec->next;\n                }\n            }\n            // PYPY segfaults here when passing builtin function like sum.\n            // Raising an fail exception here works to prevent the segfault, but only on gcc.\n            // See PR #1413 for full details\n        }\n\n        value = type_caster_std_function_specializations::func_wrapper<Return, Args...>(\n            type_caster_std_function_specializations::func_handle(std::move(func)));\n        return true;\n    }\n\n    template <typename Func>\n    static handle cast(Func &&f_, return_value_policy policy, handle /* parent */) {\n        if (!f_) {\n            return none().release();\n        }\n\n        auto result = f_.template target<function_type>();\n        if (result) {\n            return cpp_function(*result, policy).release();\n        }\n        return cpp_function(std::forward<Func>(f_), policy).release();\n    }\n\n    PYBIND11_TYPE_CASTER(type,\n                         const_name(\"Callable[[\")\n                             + ::pybind11::detail::concat(make_caster<Args>::name...)\n                             + const_name(\"], \") + make_caster<retval_type>::name\n                             + const_name(\"]\"));\n};\n\nPYBIND11_NAMESPACE_END(detail)\nPYBIND11_NAMESPACE_END(PYBIND11_NAMESPACE)\n"
  },
  {
    "path": "libs/pybind11/include/pybind11/gil.h",
    "content": "/*\n    pybind11/gil.h: RAII helpers for managing the GIL\n\n    Copyright (c) 2016 Wenzel Jakob <wenzel.jakob@epfl.ch>\n\n    All rights reserved. Use of this source code is governed by a\n    BSD-style license that can be found in the LICENSE file.\n*/\n\n#pragma once\n\n#include \"detail/common.h\"\n\n#include <cassert>\n\n#if !defined(PYBIND11_SIMPLE_GIL_MANAGEMENT)\n#    include \"detail/internals.h\"\n#endif\n\nPYBIND11_NAMESPACE_BEGIN(PYBIND11_NAMESPACE)\n\nPYBIND11_NAMESPACE_BEGIN(detail)\n\n// forward declarations\nPyThreadState *get_thread_state_unchecked();\n\nPYBIND11_NAMESPACE_END(detail)\n\n#if !defined(PYBIND11_SIMPLE_GIL_MANAGEMENT)\n\n/* The functions below essentially reproduce the PyGILState_* API using a RAII\n * pattern, but there are a few important differences:\n *\n * 1. When acquiring the GIL from an non-main thread during the finalization\n *    phase, the GILState API blindly terminates the calling thread, which\n *    is often not what is wanted. This API does not do this.\n *\n * 2. The gil_scoped_release function can optionally cut the relationship\n *    of a PyThreadState and its associated thread, which allows moving it to\n *    another thread (this is a fairly rare/advanced use case).\n *\n * 3. The reference count of an acquired thread state can be controlled. This\n *    can be handy to prevent cases where callbacks issued from an external\n *    thread would otherwise constantly construct and destroy thread state data\n *    structures.\n *\n * See the Python bindings of NanoGUI (http://github.com/wjakob/nanogui) for an\n * example which uses features 2 and 3 to migrate the Python thread of\n * execution to another thread (to run the event loop on the original thread,\n * in this case).\n */\n\nclass gil_scoped_acquire {\npublic:\n    PYBIND11_NOINLINE gil_scoped_acquire() {\n        auto &internals = detail::get_internals();\n        tstate = (PyThreadState *) PYBIND11_TLS_GET_VALUE(internals.tstate);\n\n        if (!tstate) {\n            /* Check if the GIL was acquired using the PyGILState_* API instead (e.g. if\n               calling from a Python thread). Since we use a different key, this ensures\n               we don't create a new thread state and deadlock in PyEval_AcquireThread\n               below. Note we don't save this state with internals.tstate, since we don't\n               create it we would fail to clear it (its reference count should be > 0). */\n            tstate = PyGILState_GetThisThreadState();\n        }\n\n        if (!tstate) {\n            tstate = PyThreadState_New(internals.istate);\n#    if defined(PYBIND11_DETAILED_ERROR_MESSAGES)\n            if (!tstate) {\n                pybind11_fail(\"scoped_acquire: could not create thread state!\");\n            }\n#    endif\n            tstate->gilstate_counter = 0;\n            PYBIND11_TLS_REPLACE_VALUE(internals.tstate, tstate);\n        } else {\n            release = detail::get_thread_state_unchecked() != tstate;\n        }\n\n        if (release) {\n            PyEval_AcquireThread(tstate);\n        }\n\n        inc_ref();\n    }\n\n    gil_scoped_acquire(const gil_scoped_acquire &) = delete;\n    gil_scoped_acquire &operator=(const gil_scoped_acquire &) = delete;\n\n    void inc_ref() { ++tstate->gilstate_counter; }\n\n    PYBIND11_NOINLINE void dec_ref() {\n        --tstate->gilstate_counter;\n#    if defined(PYBIND11_DETAILED_ERROR_MESSAGES)\n        if (detail::get_thread_state_unchecked() != tstate) {\n            pybind11_fail(\"scoped_acquire::dec_ref(): thread state must be current!\");\n        }\n        if (tstate->gilstate_counter < 0) {\n            pybind11_fail(\"scoped_acquire::dec_ref(): reference count underflow!\");\n        }\n#    endif\n        if (tstate->gilstate_counter == 0) {\n#    if defined(PYBIND11_DETAILED_ERROR_MESSAGES)\n            if (!release) {\n                pybind11_fail(\"scoped_acquire::dec_ref(): internal error!\");\n            }\n#    endif\n            PyThreadState_Clear(tstate);\n            if (active) {\n                PyThreadState_DeleteCurrent();\n            }\n            PYBIND11_TLS_DELETE_VALUE(detail::get_internals().tstate);\n            release = false;\n        }\n    }\n\n    /// This method will disable the PyThreadState_DeleteCurrent call and the\n    /// GIL won't be acquired. This method should be used if the interpreter\n    /// could be shutting down when this is called, as thread deletion is not\n    /// allowed during shutdown. Check _Py_IsFinalizing() on Python 3.7+, and\n    /// protect subsequent code.\n    PYBIND11_NOINLINE void disarm() { active = false; }\n\n    PYBIND11_NOINLINE ~gil_scoped_acquire() {\n        dec_ref();\n        if (release) {\n            PyEval_SaveThread();\n        }\n    }\n\nprivate:\n    PyThreadState *tstate = nullptr;\n    bool release = true;\n    bool active = true;\n};\n\nclass gil_scoped_release {\npublic:\n    // PRECONDITION: The GIL must be held when this constructor is called.\n    explicit gil_scoped_release(bool disassoc = false) : disassoc(disassoc) {\n        assert(PyGILState_Check());\n        // `get_internals()` must be called here unconditionally in order to initialize\n        // `internals.tstate` for subsequent `gil_scoped_acquire` calls. Otherwise, an\n        // initialization race could occur as multiple threads try `gil_scoped_acquire`.\n        auto &internals = detail::get_internals();\n        // NOLINTNEXTLINE(cppcoreguidelines-prefer-member-initializer)\n        tstate = PyEval_SaveThread();\n        if (disassoc) {\n            // Python >= 3.7 can remove this, it's an int before 3.7\n            // NOLINTNEXTLINE(readability-qualified-auto)\n            auto key = internals.tstate;\n            PYBIND11_TLS_DELETE_VALUE(key);\n        }\n    }\n\n    gil_scoped_release(const gil_scoped_release &) = delete;\n    gil_scoped_release &operator=(const gil_scoped_release &) = delete;\n\n    /// This method will disable the PyThreadState_DeleteCurrent call and the\n    /// GIL won't be acquired. This method should be used if the interpreter\n    /// could be shutting down when this is called, as thread deletion is not\n    /// allowed during shutdown. Check _Py_IsFinalizing() on Python 3.7+, and\n    /// protect subsequent code.\n    PYBIND11_NOINLINE void disarm() { active = false; }\n\n    ~gil_scoped_release() {\n        if (!tstate) {\n            return;\n        }\n        // `PyEval_RestoreThread()` should not be called if runtime is finalizing\n        if (active) {\n            PyEval_RestoreThread(tstate);\n        }\n        if (disassoc) {\n            // Python >= 3.7 can remove this, it's an int before 3.7\n            // NOLINTNEXTLINE(readability-qualified-auto)\n            auto key = detail::get_internals().tstate;\n            PYBIND11_TLS_REPLACE_VALUE(key, tstate);\n        }\n    }\n\nprivate:\n    PyThreadState *tstate;\n    bool disassoc;\n    bool active = true;\n};\n\n#else // PYBIND11_SIMPLE_GIL_MANAGEMENT\n\nclass gil_scoped_acquire {\n    PyGILState_STATE state;\n\npublic:\n    gil_scoped_acquire() : state{PyGILState_Ensure()} {}\n    gil_scoped_acquire(const gil_scoped_acquire &) = delete;\n    gil_scoped_acquire &operator=(const gil_scoped_acquire &) = delete;\n    ~gil_scoped_acquire() { PyGILState_Release(state); }\n    void disarm() {}\n};\n\nclass gil_scoped_release {\n    PyThreadState *state;\n\npublic:\n    // PRECONDITION: The GIL must be held when this constructor is called.\n    gil_scoped_release() {\n        assert(PyGILState_Check());\n        state = PyEval_SaveThread();\n    }\n    gil_scoped_release(const gil_scoped_release &) = delete;\n    gil_scoped_release &operator=(const gil_scoped_release &) = delete;\n    ~gil_scoped_release() { PyEval_RestoreThread(state); }\n    void disarm() {}\n};\n\n#endif // PYBIND11_SIMPLE_GIL_MANAGEMENT\n\nPYBIND11_NAMESPACE_END(PYBIND11_NAMESPACE)\n"
  },
  {
    "path": "libs/pybind11/include/pybind11/gil_safe_call_once.h",
    "content": "// Copyright (c) 2023 The pybind Community.\n\n#pragma once\n\n#include \"detail/common.h\"\n#include \"gil.h\"\n\n#include <cassert>\n#include <mutex>\n\n#ifdef Py_GIL_DISABLED\n#    include <atomic>\n#endif\n\nPYBIND11_NAMESPACE_BEGIN(PYBIND11_NAMESPACE)\n\n// Use the `gil_safe_call_once_and_store` class below instead of the naive\n//\n//   static auto imported_obj = py::module_::import(\"module_name\"); // BAD, DO NOT USE!\n//\n// which has two serious issues:\n//\n//     1. Py_DECREF() calls potentially after the Python interpreter was finalized already, and\n//     2. deadlocks in multi-threaded processes (because of missing lock ordering).\n//\n// The following alternative avoids both problems:\n//\n//   PYBIND11_CONSTINIT static py::gil_safe_call_once_and_store<py::object> storage;\n//   auto &imported_obj = storage // Do NOT make this `static`!\n//       .call_once_and_store_result([]() {\n//           return py::module_::import(\"module_name\");\n//       })\n//       .get_stored();\n//\n// The parameter of `call_once_and_store_result()` must be callable. It can make\n// CPython API calls, and in particular, it can temporarily release the GIL.\n//\n// `T` can be any C++ type, it does not have to involve CPython API types.\n//\n// The behavior with regard to signals, e.g. `SIGINT` (`KeyboardInterrupt`),\n// is not ideal. If the main thread is the one to actually run the `Callable`,\n// then a `KeyboardInterrupt` will interrupt it if it is running normal Python\n// code. The situation is different if a non-main thread runs the\n// `Callable`, and then the main thread starts waiting for it to complete:\n// a `KeyboardInterrupt` will not interrupt the non-main thread, but it will\n// get processed only when it is the main thread's turn again and it is running\n// normal Python code. However, this will be unnoticeable for quick call-once\n// functions, which is usually the case.\ntemplate <typename T>\nclass gil_safe_call_once_and_store {\npublic:\n    // PRECONDITION: The GIL must be held when `call_once_and_store_result()` is called.\n    template <typename Callable>\n    gil_safe_call_once_and_store &call_once_and_store_result(Callable &&fn) {\n        if (!is_initialized_) { // This read is guarded by the GIL.\n            // Multiple threads may enter here, because the GIL is released in the next line and\n            // CPython API calls in the `fn()` call below may release and reacquire the GIL.\n            gil_scoped_release gil_rel; // Needed to establish lock ordering.\n            std::call_once(once_flag_, [&] {\n                // Only one thread will ever enter here.\n                gil_scoped_acquire gil_acq;\n                ::new (storage_) T(fn()); // fn may release, but will reacquire, the GIL.\n                is_initialized_ = true;   // This write is guarded by the GIL.\n            });\n            // All threads will observe `is_initialized_` as true here.\n        }\n        // Intentionally not returning `T &` to ensure the calling code is self-documenting.\n        return *this;\n    }\n\n    // This must only be called after `call_once_and_store_result()` was called.\n    T &get_stored() {\n        assert(is_initialized_);\n        PYBIND11_WARNING_PUSH\n#if !defined(__clang__) && defined(__GNUC__) && __GNUC__ < 5\n        // Needed for gcc 4.8.5\n        PYBIND11_WARNING_DISABLE_GCC(\"-Wstrict-aliasing\")\n#endif\n        return *reinterpret_cast<T *>(storage_);\n        PYBIND11_WARNING_POP\n    }\n\n    constexpr gil_safe_call_once_and_store() = default;\n    PYBIND11_DTOR_CONSTEXPR ~gil_safe_call_once_and_store() = default;\n\nprivate:\n    alignas(T) char storage_[sizeof(T)] = {};\n    std::once_flag once_flag_ = {};\n#ifdef Py_GIL_DISABLED\n    std::atomic_bool\n#else\n    bool\n#endif\n        is_initialized_{false};\n    // The `is_initialized_`-`storage_` pair is very similar to `std::optional`,\n    // but the latter does not have the triviality properties of former,\n    // therefore `std::optional` is not a viable alternative here.\n};\n\nPYBIND11_NAMESPACE_END(PYBIND11_NAMESPACE)\n"
  },
  {
    "path": "libs/pybind11/include/pybind11/iostream.h",
    "content": "/*\n    pybind11/iostream.h -- Tools to assist with redirecting cout and cerr to Python\n\n    Copyright (c) 2017 Henry F. Schreiner\n\n    All rights reserved. Use of this source code is governed by a\n    BSD-style license that can be found in the LICENSE file.\n\n    WARNING: The implementation in this file is NOT thread safe. Multiple\n    threads writing to a redirected ostream concurrently cause data races\n    and potentially buffer overflows. Therefore it is currently a requirement\n    that all (possibly) concurrent redirected ostream writes are protected by\n    a mutex.\n    #HelpAppreciated: Work on iostream.h thread safety.\n    For more background see the discussions under\n    https://github.com/pybind/pybind11/pull/2982 and\n    https://github.com/pybind/pybind11/pull/2995.\n*/\n\n#pragma once\n\n#include \"pybind11.h\"\n\n#include <algorithm>\n#include <cstring>\n#include <iostream>\n#include <iterator>\n#include <memory>\n#include <ostream>\n#include <streambuf>\n#include <string>\n#include <utility>\n\nPYBIND11_NAMESPACE_BEGIN(PYBIND11_NAMESPACE)\nPYBIND11_NAMESPACE_BEGIN(detail)\n\n// Buffer that writes to Python instead of C++\nclass pythonbuf : public std::streambuf {\nprivate:\n    using traits_type = std::streambuf::traits_type;\n\n    const size_t buf_size;\n    std::unique_ptr<char[]> d_buffer;\n    object pywrite;\n    object pyflush;\n\n    int overflow(int c) override {\n        if (!traits_type::eq_int_type(c, traits_type::eof())) {\n            *pptr() = traits_type::to_char_type(c);\n            pbump(1);\n        }\n        return sync() == 0 ? traits_type::not_eof(c) : traits_type::eof();\n    }\n\n    // Computes how many bytes at the end of the buffer are part of an\n    // incomplete sequence of UTF-8 bytes.\n    // Precondition: pbase() < pptr()\n    size_t utf8_remainder() const {\n        const auto rbase = std::reverse_iterator<char *>(pbase());\n        const auto rpptr = std::reverse_iterator<char *>(pptr());\n        auto is_ascii = [](char c) { return (static_cast<unsigned char>(c) & 0x80) == 0x00; };\n        auto is_leading = [](char c) { return (static_cast<unsigned char>(c) & 0xC0) == 0xC0; };\n        auto is_leading_2b = [](char c) { return static_cast<unsigned char>(c) <= 0xDF; };\n        auto is_leading_3b = [](char c) { return static_cast<unsigned char>(c) <= 0xEF; };\n        // If the last character is ASCII, there are no incomplete code points\n        if (is_ascii(*rpptr)) {\n            return 0;\n        }\n        // Otherwise, work back from the end of the buffer and find the first\n        // UTF-8 leading byte\n        const auto rpend = rbase - rpptr >= 3 ? rpptr + 3 : rbase;\n        const auto leading = std::find_if(rpptr, rpend, is_leading);\n        if (leading == rbase) {\n            return 0;\n        }\n        const auto dist = static_cast<size_t>(leading - rpptr);\n        size_t remainder = 0;\n\n        if (dist == 0) {\n            remainder = 1; // 1-byte code point is impossible\n        } else if (dist == 1) {\n            remainder = is_leading_2b(*leading) ? 0 : dist + 1;\n        } else if (dist == 2) {\n            remainder = is_leading_3b(*leading) ? 0 : dist + 1;\n        }\n        // else if (dist >= 3), at least 4 bytes before encountering an UTF-8\n        // leading byte, either no remainder or invalid UTF-8.\n        // Invalid UTF-8 will cause an exception later when converting\n        // to a Python string, so that's not handled here.\n        return remainder;\n    }\n\n    // This function must be non-virtual to be called in a destructor.\n    int _sync() {\n        if (pbase() != pptr()) { // If buffer is not empty\n            gil_scoped_acquire tmp;\n            // This subtraction cannot be negative, so dropping the sign.\n            auto size = static_cast<size_t>(pptr() - pbase());\n            size_t remainder = utf8_remainder();\n\n            if (size > remainder) {\n                str line(pbase(), size - remainder);\n                pywrite(std::move(line));\n                pyflush();\n            }\n\n            // Copy the remainder at the end of the buffer to the beginning:\n            if (remainder > 0) {\n                std::memmove(pbase(), pptr() - remainder, remainder);\n            }\n            setp(pbase(), epptr());\n            pbump(static_cast<int>(remainder));\n        }\n        return 0;\n    }\n\n    int sync() override { return _sync(); }\n\npublic:\n    explicit pythonbuf(const object &pyostream, size_t buffer_size = 1024)\n        : buf_size(buffer_size), d_buffer(new char[buf_size]), pywrite(pyostream.attr(\"write\")),\n          pyflush(pyostream.attr(\"flush\")) {\n        setp(d_buffer.get(), d_buffer.get() + buf_size - 1);\n    }\n\n    pythonbuf(pythonbuf &&) = default;\n\n    /// Sync before destroy\n    ~pythonbuf() override { _sync(); }\n};\n\nPYBIND11_NAMESPACE_END(detail)\n\n/** \\rst\n    This a move-only guard that redirects output.\n\n    .. code-block:: cpp\n\n        #include <pybind11/iostream.h>\n\n        ...\n\n        {\n            py::scoped_ostream_redirect output;\n            std::cout << \"Hello, World!\"; // Python stdout\n        } // <-- return std::cout to normal\n\n    You can explicitly pass the c++ stream and the python object,\n    for example to guard stderr instead.\n\n    .. code-block:: cpp\n\n        {\n            py::scoped_ostream_redirect output{\n                std::cerr, py::module::import(\"sys\").attr(\"stderr\")};\n            std::cout << \"Hello, World!\";\n        }\n \\endrst */\nclass scoped_ostream_redirect {\nprotected:\n    std::streambuf *old;\n    std::ostream &costream;\n    detail::pythonbuf buffer;\n\npublic:\n    explicit scoped_ostream_redirect(std::ostream &costream = std::cout,\n                                     const object &pyostream\n                                     = module_::import(\"sys\").attr(\"stdout\"))\n        : costream(costream), buffer(pyostream) {\n        old = costream.rdbuf(&buffer);\n    }\n\n    ~scoped_ostream_redirect() { costream.rdbuf(old); }\n\n    scoped_ostream_redirect(const scoped_ostream_redirect &) = delete;\n    scoped_ostream_redirect(scoped_ostream_redirect &&other) = default;\n    scoped_ostream_redirect &operator=(const scoped_ostream_redirect &) = delete;\n    scoped_ostream_redirect &operator=(scoped_ostream_redirect &&) = delete;\n};\n\n/** \\rst\n    Like `scoped_ostream_redirect`, but redirects cerr by default. This class\n    is provided primary to make ``py::call_guard`` easier to make.\n\n    .. code-block:: cpp\n\n     m.def(\"noisy_func\", &noisy_func,\n           py::call_guard<scoped_ostream_redirect,\n                          scoped_estream_redirect>());\n\n\\endrst */\nclass scoped_estream_redirect : public scoped_ostream_redirect {\npublic:\n    explicit scoped_estream_redirect(std::ostream &costream = std::cerr,\n                                     const object &pyostream\n                                     = module_::import(\"sys\").attr(\"stderr\"))\n        : scoped_ostream_redirect(costream, pyostream) {}\n};\n\nPYBIND11_NAMESPACE_BEGIN(detail)\n\n// Class to redirect output as a context manager. C++ backend.\nclass OstreamRedirect {\n    bool do_stdout_;\n    bool do_stderr_;\n    std::unique_ptr<scoped_ostream_redirect> redirect_stdout;\n    std::unique_ptr<scoped_estream_redirect> redirect_stderr;\n\npublic:\n    explicit OstreamRedirect(bool do_stdout = true, bool do_stderr = true)\n        : do_stdout_(do_stdout), do_stderr_(do_stderr) {}\n\n    void enter() {\n        if (do_stdout_) {\n            redirect_stdout.reset(new scoped_ostream_redirect());\n        }\n        if (do_stderr_) {\n            redirect_stderr.reset(new scoped_estream_redirect());\n        }\n    }\n\n    void exit() {\n        redirect_stdout.reset();\n        redirect_stderr.reset();\n    }\n};\n\nPYBIND11_NAMESPACE_END(detail)\n\n/** \\rst\n    This is a helper function to add a C++ redirect context manager to Python\n    instead of using a C++ guard. To use it, add the following to your binding code:\n\n    .. code-block:: cpp\n\n        #include <pybind11/iostream.h>\n\n        ...\n\n        py::add_ostream_redirect(m, \"ostream_redirect\");\n\n    You now have a Python context manager that redirects your output:\n\n    .. code-block:: python\n\n        with m.ostream_redirect():\n            m.print_to_cout_function()\n\n    This manager can optionally be told which streams to operate on:\n\n    .. code-block:: python\n\n        with m.ostream_redirect(stdout=true, stderr=true):\n            m.noisy_function_with_error_printing()\n\n \\endrst */\ninline class_<detail::OstreamRedirect>\nadd_ostream_redirect(module_ m, const std::string &name = \"ostream_redirect\") {\n    return class_<detail::OstreamRedirect>(std::move(m), name.c_str(), module_local())\n        .def(init<bool, bool>(), arg(\"stdout\") = true, arg(\"stderr\") = true)\n        .def(\"__enter__\", &detail::OstreamRedirect::enter)\n        .def(\"__exit__\", [](detail::OstreamRedirect &self_, const args &) { self_.exit(); });\n}\n\nPYBIND11_NAMESPACE_END(PYBIND11_NAMESPACE)\n"
  },
  {
    "path": "libs/pybind11/include/pybind11/numpy.h",
    "content": "/*\n    pybind11/numpy.h: Basic NumPy support, vectorize() wrapper\n\n    Copyright (c) 2016 Wenzel Jakob <wenzel.jakob@epfl.ch>\n\n    All rights reserved. Use of this source code is governed by a\n    BSD-style license that can be found in the LICENSE file.\n*/\n\n#pragma once\n\n#include \"pybind11.h\"\n#include \"detail/common.h\"\n#include \"complex.h\"\n#include \"gil_safe_call_once.h\"\n#include \"pytypes.h\"\n\n#include <algorithm>\n#include <array>\n#include <cstdint>\n#include <cstdlib>\n#include <cstring>\n#include <functional>\n#include <numeric>\n#include <sstream>\n#include <string>\n#include <type_traits>\n#include <typeindex>\n#include <utility>\n#include <vector>\n\n#if defined(PYBIND11_NUMPY_1_ONLY) && !defined(PYBIND11_INTERNAL_NUMPY_1_ONLY_DETECTED)\n#    error PYBIND11_NUMPY_1_ONLY must be defined before any pybind11 header is included.\n#endif\n\n/* This will be true on all flat address space platforms and allows us to reduce the\n   whole npy_intp / ssize_t / Py_intptr_t business down to just ssize_t for all size\n   and dimension types (e.g. shape, strides, indexing), instead of inflicting this\n   upon the library user.\n   Note that NumPy 2 now uses ssize_t for `npy_intp` to simplify this. */\nstatic_assert(sizeof(::pybind11::ssize_t) == sizeof(Py_intptr_t), \"ssize_t != Py_intptr_t\");\nstatic_assert(std::is_signed<Py_intptr_t>::value, \"Py_intptr_t must be signed\");\n// We now can reinterpret_cast between py::ssize_t and Py_intptr_t (MSVC + PyPy cares)\n\nPYBIND11_NAMESPACE_BEGIN(PYBIND11_NAMESPACE)\n\nPYBIND11_WARNING_DISABLE_MSVC(4127)\n\nclass dtype; // Forward declaration\nclass array; // Forward declaration\n\nPYBIND11_NAMESPACE_BEGIN(detail)\n\ntemplate <>\nstruct handle_type_name<dtype> {\n    static constexpr auto name = const_name(\"numpy.dtype\");\n};\n\ntemplate <>\nstruct handle_type_name<array> {\n    static constexpr auto name = const_name(\"numpy.ndarray\");\n};\n\ntemplate <typename type, typename SFINAE = void>\nstruct npy_format_descriptor;\n\n/* NumPy 1 proxy (always includes legacy fields) */\nstruct PyArrayDescr1_Proxy {\n    PyObject_HEAD\n    PyObject *typeobj;\n    char kind;\n    char type;\n    char byteorder;\n    char flags;\n    int type_num;\n    int elsize;\n    int alignment;\n    char *subarray;\n    PyObject *fields;\n    PyObject *names;\n};\n\n#ifndef PYBIND11_NUMPY_1_ONLY\nstruct PyArrayDescr_Proxy {\n    PyObject_HEAD\n    PyObject *typeobj;\n    char kind;\n    char type;\n    char byteorder;\n    char _former_flags;\n    int type_num;\n    /* Additional fields are NumPy version specific. */\n};\n#else\n/* NumPy 1.x only, we can expose all fields */\nusing PyArrayDescr_Proxy = PyArrayDescr1_Proxy;\n#endif\n\n/* NumPy 2 proxy, including legacy fields */\nstruct PyArrayDescr2_Proxy {\n    PyObject_HEAD\n    PyObject *typeobj;\n    char kind;\n    char type;\n    char byteorder;\n    char _former_flags;\n    int type_num;\n    std::uint64_t flags;\n    ssize_t elsize;\n    ssize_t alignment;\n    PyObject *metadata;\n    Py_hash_t hash;\n    void *reserved_null[2];\n    /* The following fields only exist if 0 <= type_num < 2056 */\n    char *subarray;\n    PyObject *fields;\n    PyObject *names;\n};\n\nstruct PyArray_Proxy {\n    PyObject_HEAD\n    char *data;\n    int nd;\n    ssize_t *dimensions;\n    ssize_t *strides;\n    PyObject *base;\n    PyObject *descr;\n    int flags;\n};\n\nstruct PyVoidScalarObject_Proxy {\n    PyObject_VAR_HEAD char *obval;\n    PyArrayDescr_Proxy *descr;\n    int flags;\n    PyObject *base;\n};\n\nstruct numpy_type_info {\n    PyObject *dtype_ptr;\n    std::string format_str;\n};\n\nstruct numpy_internals {\n    std::unordered_map<std::type_index, numpy_type_info> registered_dtypes;\n\n    numpy_type_info *get_type_info(const std::type_info &tinfo, bool throw_if_missing = true) {\n        auto it = registered_dtypes.find(std::type_index(tinfo));\n        if (it != registered_dtypes.end()) {\n            return &(it->second);\n        }\n        if (throw_if_missing) {\n            pybind11_fail(std::string(\"NumPy type info missing for \") + tinfo.name());\n        }\n        return nullptr;\n    }\n\n    template <typename T>\n    numpy_type_info *get_type_info(bool throw_if_missing = true) {\n        return get_type_info(typeid(typename std::remove_cv<T>::type), throw_if_missing);\n    }\n};\n\nPYBIND11_NOINLINE void load_numpy_internals(numpy_internals *&ptr) {\n    ptr = &get_or_create_shared_data<numpy_internals>(\"_numpy_internals\");\n}\n\ninline numpy_internals &get_numpy_internals() {\n    static numpy_internals *ptr = nullptr;\n    if (!ptr) {\n        load_numpy_internals(ptr);\n    }\n    return *ptr;\n}\n\nPYBIND11_NOINLINE module_ import_numpy_core_submodule(const char *submodule_name) {\n    module_ numpy = module_::import(\"numpy\");\n    str version_string = numpy.attr(\"__version__\");\n\n    module_ numpy_lib = module_::import(\"numpy.lib\");\n    object numpy_version = numpy_lib.attr(\"NumpyVersion\")(version_string);\n    int major_version = numpy_version.attr(\"major\").cast<int>();\n\n#ifdef PYBIND11_NUMPY_1_ONLY\n    if (major_version >= 2) {\n        throw std::runtime_error(\n            \"This extension was built with PYBIND11_NUMPY_1_ONLY defined, \"\n            \"but NumPy 2 is used in this process. For NumPy2 compatibility, \"\n            \"this extension needs to be rebuilt without the PYBIND11_NUMPY_1_ONLY define.\");\n    }\n#endif\n    /* `numpy.core` was renamed to `numpy._core` in NumPy 2.0 as it officially\n        became a private module. */\n    std::string numpy_core_path = major_version >= 2 ? \"numpy._core\" : \"numpy.core\";\n    return module_::import((numpy_core_path + \".\" + submodule_name).c_str());\n}\n\ntemplate <typename T>\nstruct same_size {\n    template <typename U>\n    using as = bool_constant<sizeof(T) == sizeof(U)>;\n};\n\ntemplate <typename Concrete>\nconstexpr int platform_lookup() {\n    return -1;\n}\n\n// Lookup a type according to its size, and return a value corresponding to the NumPy typenum.\ntemplate <typename Concrete, typename T, typename... Ts, typename... Ints>\nconstexpr int platform_lookup(int I, Ints... Is) {\n    return sizeof(Concrete) == sizeof(T) ? I : platform_lookup<Concrete, Ts...>(Is...);\n}\n\nstruct npy_api {\n    enum constants {\n        NPY_ARRAY_C_CONTIGUOUS_ = 0x0001,\n        NPY_ARRAY_F_CONTIGUOUS_ = 0x0002,\n        NPY_ARRAY_OWNDATA_ = 0x0004,\n        NPY_ARRAY_FORCECAST_ = 0x0010,\n        NPY_ARRAY_ENSUREARRAY_ = 0x0040,\n        NPY_ARRAY_ALIGNED_ = 0x0100,\n        NPY_ARRAY_WRITEABLE_ = 0x0400,\n        NPY_BOOL_ = 0,\n        NPY_BYTE_,\n        NPY_UBYTE_,\n        NPY_SHORT_,\n        NPY_USHORT_,\n        NPY_INT_,\n        NPY_UINT_,\n        NPY_LONG_,\n        NPY_ULONG_,\n        NPY_LONGLONG_,\n        NPY_ULONGLONG_,\n        NPY_FLOAT_,\n        NPY_DOUBLE_,\n        NPY_LONGDOUBLE_,\n        NPY_CFLOAT_,\n        NPY_CDOUBLE_,\n        NPY_CLONGDOUBLE_,\n        NPY_OBJECT_ = 17,\n        NPY_STRING_,\n        NPY_UNICODE_,\n        NPY_VOID_,\n        // Platform-dependent normalization\n        NPY_INT8_ = NPY_BYTE_,\n        NPY_UINT8_ = NPY_UBYTE_,\n        NPY_INT16_ = NPY_SHORT_,\n        NPY_UINT16_ = NPY_USHORT_,\n        // `npy_common.h` defines the integer aliases. In order, it checks:\n        // NPY_BITSOF_LONG, NPY_BITSOF_LONGLONG, NPY_BITSOF_INT, NPY_BITSOF_SHORT, NPY_BITSOF_CHAR\n        // and assigns the alias to the first matching size, so we should check in this order.\n        NPY_INT32_\n        = platform_lookup<std::int32_t, long, int, short>(NPY_LONG_, NPY_INT_, NPY_SHORT_),\n        NPY_UINT32_ = platform_lookup<std::uint32_t, unsigned long, unsigned int, unsigned short>(\n            NPY_ULONG_, NPY_UINT_, NPY_USHORT_),\n        NPY_INT64_\n        = platform_lookup<std::int64_t, long, long long, int>(NPY_LONG_, NPY_LONGLONG_, NPY_INT_),\n        NPY_UINT64_\n        = platform_lookup<std::uint64_t, unsigned long, unsigned long long, unsigned int>(\n            NPY_ULONG_, NPY_ULONGLONG_, NPY_UINT_),\n    };\n\n    unsigned int PyArray_RUNTIME_VERSION_;\n\n    struct PyArray_Dims {\n        Py_intptr_t *ptr;\n        int len;\n    };\n\n    static npy_api &get() {\n        PYBIND11_CONSTINIT static gil_safe_call_once_and_store<npy_api> storage;\n        return storage.call_once_and_store_result(lookup).get_stored();\n    }\n\n    bool PyArray_Check_(PyObject *obj) const {\n        return PyObject_TypeCheck(obj, PyArray_Type_) != 0;\n    }\n    bool PyArrayDescr_Check_(PyObject *obj) const {\n        return PyObject_TypeCheck(obj, PyArrayDescr_Type_) != 0;\n    }\n\n    unsigned int (*PyArray_GetNDArrayCFeatureVersion_)();\n    PyObject *(*PyArray_DescrFromType_)(int);\n    PyObject *(*PyArray_NewFromDescr_)(PyTypeObject *,\n                                       PyObject *,\n                                       int,\n                                       Py_intptr_t const *,\n                                       Py_intptr_t const *,\n                                       void *,\n                                       int,\n                                       PyObject *);\n    // Unused. Not removed because that affects ABI of the class.\n    PyObject *(*PyArray_DescrNewFromType_)(int);\n    int (*PyArray_CopyInto_)(PyObject *, PyObject *);\n    PyObject *(*PyArray_NewCopy_)(PyObject *, int);\n    PyTypeObject *PyArray_Type_;\n    PyTypeObject *PyVoidArrType_Type_;\n    PyTypeObject *PyArrayDescr_Type_;\n    PyObject *(*PyArray_DescrFromScalar_)(PyObject *);\n    PyObject *(*PyArray_FromAny_)(PyObject *, PyObject *, int, int, int, PyObject *);\n    int (*PyArray_DescrConverter_)(PyObject *, PyObject **);\n    bool (*PyArray_EquivTypes_)(PyObject *, PyObject *);\n#ifdef PYBIND11_NUMPY_1_ONLY\n    int (*PyArray_GetArrayParamsFromObject_)(PyObject *,\n                                             PyObject *,\n                                             unsigned char,\n                                             PyObject **,\n                                             int *,\n                                             Py_intptr_t *,\n                                             PyObject **,\n                                             PyObject *);\n#endif\n    PyObject *(*PyArray_Squeeze_)(PyObject *);\n    // Unused. Not removed because that affects ABI of the class.\n    int (*PyArray_SetBaseObject_)(PyObject *, PyObject *);\n    PyObject *(*PyArray_Resize_)(PyObject *, PyArray_Dims *, int, int);\n    PyObject *(*PyArray_Newshape_)(PyObject *, PyArray_Dims *, int);\n    PyObject *(*PyArray_View_)(PyObject *, PyObject *, PyObject *);\n\nprivate:\n    enum functions {\n        API_PyArray_GetNDArrayCFeatureVersion = 211,\n        API_PyArray_Type = 2,\n        API_PyArrayDescr_Type = 3,\n        API_PyVoidArrType_Type = 39,\n        API_PyArray_DescrFromType = 45,\n        API_PyArray_DescrFromScalar = 57,\n        API_PyArray_FromAny = 69,\n        API_PyArray_Resize = 80,\n        // CopyInto was slot 82 and 50 was effectively an alias. NumPy 2 removed 82.\n        API_PyArray_CopyInto = 50,\n        API_PyArray_NewCopy = 85,\n        API_PyArray_NewFromDescr = 94,\n        API_PyArray_DescrNewFromType = 96,\n        API_PyArray_Newshape = 135,\n        API_PyArray_Squeeze = 136,\n        API_PyArray_View = 137,\n        API_PyArray_DescrConverter = 174,\n        API_PyArray_EquivTypes = 182,\n#ifdef PYBIND11_NUMPY_1_ONLY\n        API_PyArray_GetArrayParamsFromObject = 278,\n#endif\n        API_PyArray_SetBaseObject = 282\n    };\n\n    static npy_api lookup() {\n        module_ m = detail::import_numpy_core_submodule(\"multiarray\");\n        auto c = m.attr(\"_ARRAY_API\");\n        void **api_ptr = (void **) PyCapsule_GetPointer(c.ptr(), nullptr);\n        if (api_ptr == nullptr) {\n            raise_from(PyExc_SystemError, \"FAILURE obtaining numpy _ARRAY_API pointer.\");\n            throw error_already_set();\n        }\n        npy_api api;\n#define DECL_NPY_API(Func) api.Func##_ = (decltype(api.Func##_)) api_ptr[API_##Func];\n        DECL_NPY_API(PyArray_GetNDArrayCFeatureVersion);\n        api.PyArray_RUNTIME_VERSION_ = api.PyArray_GetNDArrayCFeatureVersion_();\n        if (api.PyArray_RUNTIME_VERSION_ < 0x7) {\n            pybind11_fail(\"pybind11 numpy support requires numpy >= 1.7.0\");\n        }\n        DECL_NPY_API(PyArray_Type);\n        DECL_NPY_API(PyVoidArrType_Type);\n        DECL_NPY_API(PyArrayDescr_Type);\n        DECL_NPY_API(PyArray_DescrFromType);\n        DECL_NPY_API(PyArray_DescrFromScalar);\n        DECL_NPY_API(PyArray_FromAny);\n        DECL_NPY_API(PyArray_Resize);\n        DECL_NPY_API(PyArray_CopyInto);\n        DECL_NPY_API(PyArray_NewCopy);\n        DECL_NPY_API(PyArray_NewFromDescr);\n        DECL_NPY_API(PyArray_DescrNewFromType);\n        DECL_NPY_API(PyArray_Newshape);\n        DECL_NPY_API(PyArray_Squeeze);\n        DECL_NPY_API(PyArray_View);\n        DECL_NPY_API(PyArray_DescrConverter);\n        DECL_NPY_API(PyArray_EquivTypes);\n#ifdef PYBIND11_NUMPY_1_ONLY\n        DECL_NPY_API(PyArray_GetArrayParamsFromObject);\n#endif\n        DECL_NPY_API(PyArray_SetBaseObject);\n\n#undef DECL_NPY_API\n        return api;\n    }\n};\n\ninline PyArray_Proxy *array_proxy(void *ptr) { return reinterpret_cast<PyArray_Proxy *>(ptr); }\n\ninline const PyArray_Proxy *array_proxy(const void *ptr) {\n    return reinterpret_cast<const PyArray_Proxy *>(ptr);\n}\n\ninline PyArrayDescr_Proxy *array_descriptor_proxy(PyObject *ptr) {\n    return reinterpret_cast<PyArrayDescr_Proxy *>(ptr);\n}\n\ninline const PyArrayDescr_Proxy *array_descriptor_proxy(const PyObject *ptr) {\n    return reinterpret_cast<const PyArrayDescr_Proxy *>(ptr);\n}\n\ninline const PyArrayDescr1_Proxy *array_descriptor1_proxy(const PyObject *ptr) {\n    return reinterpret_cast<const PyArrayDescr1_Proxy *>(ptr);\n}\n\ninline const PyArrayDescr2_Proxy *array_descriptor2_proxy(const PyObject *ptr) {\n    return reinterpret_cast<const PyArrayDescr2_Proxy *>(ptr);\n}\n\ninline bool check_flags(const void *ptr, int flag) {\n    return (flag == (array_proxy(ptr)->flags & flag));\n}\n\ntemplate <typename T>\nstruct is_std_array : std::false_type {};\ntemplate <typename T, size_t N>\nstruct is_std_array<std::array<T, N>> : std::true_type {};\ntemplate <typename T>\nstruct is_complex : std::false_type {};\ntemplate <typename T>\nstruct is_complex<std::complex<T>> : std::true_type {};\n\ntemplate <typename T>\nstruct array_info_scalar {\n    using type = T;\n    static constexpr bool is_array = false;\n    static constexpr bool is_empty = false;\n    static constexpr auto extents = const_name(\"\");\n    static void append_extents(list & /* shape */) {}\n};\n// Computes underlying type and a comma-separated list of extents for array\n// types (any mix of std::array and built-in arrays). An array of char is\n// treated as scalar because it gets special handling.\ntemplate <typename T>\nstruct array_info : array_info_scalar<T> {};\ntemplate <typename T, size_t N>\nstruct array_info<std::array<T, N>> {\n    using type = typename array_info<T>::type;\n    static constexpr bool is_array = true;\n    static constexpr bool is_empty = (N == 0) || array_info<T>::is_empty;\n    static constexpr size_t extent = N;\n\n    // appends the extents to shape\n    static void append_extents(list &shape) {\n        shape.append(N);\n        array_info<T>::append_extents(shape);\n    }\n\n    static constexpr auto extents = const_name<array_info<T>::is_array>(\n        ::pybind11::detail::concat(const_name<N>(), array_info<T>::extents), const_name<N>());\n};\n// For numpy we have special handling for arrays of characters, so we don't include\n// the size in the array extents.\ntemplate <size_t N>\nstruct array_info<char[N]> : array_info_scalar<char[N]> {};\ntemplate <size_t N>\nstruct array_info<std::array<char, N>> : array_info_scalar<std::array<char, N>> {};\ntemplate <typename T, size_t N>\nstruct array_info<T[N]> : array_info<std::array<T, N>> {};\ntemplate <typename T>\nusing remove_all_extents_t = typename array_info<T>::type;\n\ntemplate <typename T>\nusing is_pod_struct\n    = all_of<std::is_standard_layout<T>, // since we're accessing directly in memory\n                                         // we need a standard layout type\n#if defined(__GLIBCXX__)                                                                          \\\n    && (__GLIBCXX__ < 20150422 || __GLIBCXX__ == 20150426 || __GLIBCXX__ == 20150623              \\\n        || __GLIBCXX__ == 20150626 || __GLIBCXX__ == 20160803)\n             // libstdc++ < 5 (including versions 4.8.5, 4.9.3 and 4.9.4 which were released after\n             // 5) don't implement is_trivially_copyable, so approximate it\n             std::is_trivially_destructible<T>,\n             satisfies_any_of<T, std::has_trivial_copy_constructor, std::has_trivial_copy_assign>,\n#else\n             std::is_trivially_copyable<T>,\n#endif\n             satisfies_none_of<T,\n                               std::is_reference,\n                               std::is_array,\n                               is_std_array,\n                               std::is_arithmetic,\n                               is_complex,\n                               std::is_enum>>;\n\n// Replacement for std::is_pod (deprecated in C++20)\ntemplate <typename T>\nusing is_pod = all_of<std::is_standard_layout<T>, std::is_trivial<T>>;\n\ntemplate <ssize_t Dim = 0, typename Strides>\nssize_t byte_offset_unsafe(const Strides &) {\n    return 0;\n}\ntemplate <ssize_t Dim = 0, typename Strides, typename... Ix>\nssize_t byte_offset_unsafe(const Strides &strides, ssize_t i, Ix... index) {\n    return i * strides[Dim] + byte_offset_unsafe<Dim + 1>(strides, index...);\n}\n\n/**\n * Proxy class providing unsafe, unchecked const access to array data.  This is constructed through\n * the `unchecked<T, N>()` method of `array` or the `unchecked<N>()` method of `array_t<T>`. `Dims`\n * will be -1 for dimensions determined at runtime.\n */\ntemplate <typename T, ssize_t Dims>\nclass unchecked_reference {\nprotected:\n    static constexpr bool Dynamic = Dims < 0;\n    const unsigned char *data_;\n    // Storing the shape & strides in local variables (i.e. these arrays) allows the compiler to\n    // make large performance gains on big, nested loops, but requires compile-time dimensions\n    conditional_t<Dynamic, const ssize_t *, std::array<ssize_t, (size_t) Dims>> shape_, strides_;\n    const ssize_t dims_;\n\n    friend class pybind11::array;\n    // Constructor for compile-time dimensions:\n    template <bool Dyn = Dynamic>\n    unchecked_reference(const void *data,\n                        const ssize_t *shape,\n                        const ssize_t *strides,\n                        enable_if_t<!Dyn, ssize_t>)\n        : data_{reinterpret_cast<const unsigned char *>(data)}, dims_{Dims} {\n        for (size_t i = 0; i < (size_t) dims_; i++) {\n            shape_[i] = shape[i];\n            strides_[i] = strides[i];\n        }\n    }\n    // Constructor for runtime dimensions:\n    template <bool Dyn = Dynamic>\n    unchecked_reference(const void *data,\n                        const ssize_t *shape,\n                        const ssize_t *strides,\n                        enable_if_t<Dyn, ssize_t> dims)\n        : data_{reinterpret_cast<const unsigned char *>(data)}, shape_{shape}, strides_{strides},\n          dims_{dims} {}\n\npublic:\n    /**\n     * Unchecked const reference access to data at the given indices.  For a compile-time known\n     * number of dimensions, this requires the correct number of arguments; for run-time\n     * dimensionality, this is not checked (and so is up to the caller to use safely).\n     */\n    template <typename... Ix>\n    const T &operator()(Ix... index) const {\n        static_assert(ssize_t{sizeof...(Ix)} == Dims || Dynamic,\n                      \"Invalid number of indices for unchecked array reference\");\n        return *reinterpret_cast<const T *>(data_\n                                            + byte_offset_unsafe(strides_, ssize_t(index)...));\n    }\n    /**\n     * Unchecked const reference access to data; this operator only participates if the reference\n     * is to a 1-dimensional array.  When present, this is exactly equivalent to `obj(index)`.\n     */\n    template <ssize_t D = Dims, typename = enable_if_t<D == 1 || Dynamic>>\n    const T &operator[](ssize_t index) const {\n        return operator()(index);\n    }\n\n    /// Pointer access to the data at the given indices.\n    template <typename... Ix>\n    const T *data(Ix... ix) const {\n        return &operator()(ssize_t(ix)...);\n    }\n\n    /// Returns the item size, i.e. sizeof(T)\n    constexpr static ssize_t itemsize() { return sizeof(T); }\n\n    /// Returns the shape (i.e. size) of dimension `dim`\n    ssize_t shape(ssize_t dim) const { return shape_[(size_t) dim]; }\n\n    /// Returns the number of dimensions of the array\n    ssize_t ndim() const { return dims_; }\n\n    /// Returns the total number of elements in the referenced array, i.e. the product of the\n    /// shapes\n    template <bool Dyn = Dynamic>\n    enable_if_t<!Dyn, ssize_t> size() const {\n        return std::accumulate(\n            shape_.begin(), shape_.end(), (ssize_t) 1, std::multiplies<ssize_t>());\n    }\n    template <bool Dyn = Dynamic>\n    enable_if_t<Dyn, ssize_t> size() const {\n        return std::accumulate(shape_, shape_ + ndim(), (ssize_t) 1, std::multiplies<ssize_t>());\n    }\n\n    /// Returns the total number of bytes used by the referenced data.  Note that the actual span\n    /// in memory may be larger if the referenced array has non-contiguous strides (e.g. for a\n    /// slice).\n    ssize_t nbytes() const { return size() * itemsize(); }\n};\n\ntemplate <typename T, ssize_t Dims>\nclass unchecked_mutable_reference : public unchecked_reference<T, Dims> {\n    friend class pybind11::array;\n    using ConstBase = unchecked_reference<T, Dims>;\n    using ConstBase::ConstBase;\n    using ConstBase::Dynamic;\n\npublic:\n    // Bring in const-qualified versions from base class\n    using ConstBase::operator();\n    using ConstBase::operator[];\n\n    /// Mutable, unchecked access to data at the given indices.\n    template <typename... Ix>\n    T &operator()(Ix... index) {\n        static_assert(ssize_t{sizeof...(Ix)} == Dims || Dynamic,\n                      \"Invalid number of indices for unchecked array reference\");\n        return const_cast<T &>(ConstBase::operator()(index...));\n    }\n    /**\n     * Mutable, unchecked access data at the given index; this operator only participates if the\n     * reference is to a 1-dimensional array (or has runtime dimensions).  When present, this is\n     * exactly equivalent to `obj(index)`.\n     */\n    template <ssize_t D = Dims, typename = enable_if_t<D == 1 || Dynamic>>\n    T &operator[](ssize_t index) {\n        return operator()(index);\n    }\n\n    /// Mutable pointer access to the data at the given indices.\n    template <typename... Ix>\n    T *mutable_data(Ix... ix) {\n        return &operator()(ssize_t(ix)...);\n    }\n};\n\ntemplate <typename T, ssize_t Dim>\nstruct type_caster<unchecked_reference<T, Dim>> {\n    static_assert(Dim == 0 && Dim > 0 /* always fail */,\n                  \"unchecked array proxy object is not castable\");\n};\ntemplate <typename T, ssize_t Dim>\nstruct type_caster<unchecked_mutable_reference<T, Dim>>\n    : type_caster<unchecked_reference<T, Dim>> {};\n\nPYBIND11_NAMESPACE_END(detail)\n\nclass dtype : public object {\npublic:\n    PYBIND11_OBJECT_DEFAULT(dtype, object, detail::npy_api::get().PyArrayDescr_Check_)\n\n    explicit dtype(const buffer_info &info) {\n        dtype descr(_dtype_from_pep3118()(pybind11::str(info.format)));\n        // If info.itemsize == 0, use the value calculated from the format string\n        m_ptr = descr.strip_padding(info.itemsize != 0 ? info.itemsize : descr.itemsize())\n                    .release()\n                    .ptr();\n    }\n\n    explicit dtype(const pybind11::str &format) : dtype(from_args(format)) {}\n\n    explicit dtype(const std::string &format) : dtype(pybind11::str(format)) {}\n\n    explicit dtype(const char *format) : dtype(pybind11::str(format)) {}\n\n    dtype(list names, list formats, list offsets, ssize_t itemsize) {\n        dict args;\n        args[\"names\"] = std::move(names);\n        args[\"formats\"] = std::move(formats);\n        args[\"offsets\"] = std::move(offsets);\n        args[\"itemsize\"] = pybind11::int_(itemsize);\n        m_ptr = from_args(args).release().ptr();\n    }\n\n    /// Return dtype for the given typenum (one of the NPY_TYPES).\n    /// https://numpy.org/devdocs/reference/c-api/array.html#c.PyArray_DescrFromType\n    explicit dtype(int typenum)\n        : object(detail::npy_api::get().PyArray_DescrFromType_(typenum), stolen_t{}) {\n        if (m_ptr == nullptr) {\n            throw error_already_set();\n        }\n    }\n\n    /// This is essentially the same as calling numpy.dtype(args) in Python.\n    static dtype from_args(const object &args) {\n        PyObject *ptr = nullptr;\n        if ((detail::npy_api::get().PyArray_DescrConverter_(args.ptr(), &ptr) == 0) || !ptr) {\n            throw error_already_set();\n        }\n        return reinterpret_steal<dtype>(ptr);\n    }\n\n    /// Return dtype associated with a C++ type.\n    template <typename T>\n    static dtype of() {\n        return detail::npy_format_descriptor<typename std::remove_cv<T>::type>::dtype();\n    }\n\n    /// Size of the data type in bytes.\n#ifdef PYBIND11_NUMPY_1_ONLY\n    ssize_t itemsize() const { return detail::array_descriptor_proxy(m_ptr)->elsize; }\n#else\n    ssize_t itemsize() const {\n        if (detail::npy_api::get().PyArray_RUNTIME_VERSION_ < 0x12) {\n            return detail::array_descriptor1_proxy(m_ptr)->elsize;\n        }\n        return detail::array_descriptor2_proxy(m_ptr)->elsize;\n    }\n#endif\n\n    /// Returns true for structured data types.\n#ifdef PYBIND11_NUMPY_1_ONLY\n    bool has_fields() const { return detail::array_descriptor_proxy(m_ptr)->names != nullptr; }\n#else\n    bool has_fields() const {\n        if (detail::npy_api::get().PyArray_RUNTIME_VERSION_ < 0x12) {\n            return detail::array_descriptor1_proxy(m_ptr)->names != nullptr;\n        }\n        const auto *proxy = detail::array_descriptor2_proxy(m_ptr);\n        if (proxy->type_num < 0 || proxy->type_num >= 2056) {\n            return false;\n        }\n        return proxy->names != nullptr;\n    }\n#endif\n\n    /// Single-character code for dtype's kind.\n    /// For example, floating point types are 'f' and integral types are 'i'.\n    char kind() const { return detail::array_descriptor_proxy(m_ptr)->kind; }\n\n    /// Single-character for dtype's type.\n    /// For example, ``float`` is 'f', ``double`` 'd', ``int`` 'i', and ``long`` 'l'.\n    char char_() const {\n        // Note: The signature, `dtype::char_` follows the naming of NumPy's\n        // public Python API (i.e., ``dtype.char``), rather than its internal\n        // C API (``PyArray_Descr::type``).\n        return detail::array_descriptor_proxy(m_ptr)->type;\n    }\n\n    /// type number of dtype.\n    int num() const {\n        // Note: The signature, `dtype::num` follows the naming of NumPy's public\n        // Python API (i.e., ``dtype.num``), rather than its internal\n        // C API (``PyArray_Descr::type_num``).\n        return detail::array_descriptor_proxy(m_ptr)->type_num;\n    }\n\n    /// Single character for byteorder\n    char byteorder() const { return detail::array_descriptor_proxy(m_ptr)->byteorder; }\n\n/// Alignment of the data type\n#ifdef PYBIND11_NUMPY_1_ONLY\n    int alignment() const { return detail::array_descriptor_proxy(m_ptr)->alignment; }\n#else\n    ssize_t alignment() const {\n        if (detail::npy_api::get().PyArray_RUNTIME_VERSION_ < 0x12) {\n            return detail::array_descriptor1_proxy(m_ptr)->alignment;\n        }\n        return detail::array_descriptor2_proxy(m_ptr)->alignment;\n    }\n#endif\n\n/// Flags for the array descriptor\n#ifdef PYBIND11_NUMPY_1_ONLY\n    char flags() const { return detail::array_descriptor_proxy(m_ptr)->flags; }\n#else\n    std::uint64_t flags() const {\n        if (detail::npy_api::get().PyArray_RUNTIME_VERSION_ < 0x12) {\n            return (unsigned char) detail::array_descriptor1_proxy(m_ptr)->flags;\n        }\n        return detail::array_descriptor2_proxy(m_ptr)->flags;\n    }\n#endif\n\nprivate:\n    static object &_dtype_from_pep3118() {\n        PYBIND11_CONSTINIT static gil_safe_call_once_and_store<object> storage;\n        return storage\n            .call_once_and_store_result([]() {\n                return detail::import_numpy_core_submodule(\"_internal\")\n                    .attr(\"_dtype_from_pep3118\");\n            })\n            .get_stored();\n    }\n\n    dtype strip_padding(ssize_t itemsize) {\n        // Recursively strip all void fields with empty names that are generated for\n        // padding fields (as of NumPy v1.11).\n        if (!has_fields()) {\n            return *this;\n        }\n\n        struct field_descr {\n            pybind11::str name;\n            object format;\n            pybind11::int_ offset;\n            field_descr(pybind11::str &&name, object &&format, pybind11::int_ &&offset)\n                : name{std::move(name)}, format{std::move(format)}, offset{std::move(offset)} {};\n        };\n        auto field_dict = attr(\"fields\").cast<dict>();\n        std::vector<field_descr> field_descriptors;\n        field_descriptors.reserve(field_dict.size());\n\n        for (auto field : field_dict.attr(\"items\")()) {\n            auto spec = field.cast<tuple>();\n            auto name = spec[0].cast<pybind11::str>();\n            auto spec_fo = spec[1].cast<tuple>();\n            auto format = spec_fo[0].cast<dtype>();\n            auto offset = spec_fo[1].cast<pybind11::int_>();\n            if ((len(name) == 0u) && format.kind() == 'V') {\n                continue;\n            }\n            field_descriptors.emplace_back(\n                std::move(name), format.strip_padding(format.itemsize()), std::move(offset));\n        }\n\n        std::sort(field_descriptors.begin(),\n                  field_descriptors.end(),\n                  [](const field_descr &a, const field_descr &b) {\n                      return a.offset.cast<int>() < b.offset.cast<int>();\n                  });\n\n        list names, formats, offsets;\n        for (auto &descr : field_descriptors) {\n            names.append(std::move(descr.name));\n            formats.append(std::move(descr.format));\n            offsets.append(std::move(descr.offset));\n        }\n        return dtype(std::move(names), std::move(formats), std::move(offsets), itemsize);\n    }\n};\n\nclass array : public buffer {\npublic:\n    PYBIND11_OBJECT_CVT(array, buffer, detail::npy_api::get().PyArray_Check_, raw_array)\n\n    enum {\n        c_style = detail::npy_api::NPY_ARRAY_C_CONTIGUOUS_,\n        f_style = detail::npy_api::NPY_ARRAY_F_CONTIGUOUS_,\n        forcecast = detail::npy_api::NPY_ARRAY_FORCECAST_\n    };\n\n    array() : array(0, static_cast<const double *>(nullptr)) {}\n\n    using ShapeContainer = detail::any_container<ssize_t>;\n    using StridesContainer = detail::any_container<ssize_t>;\n\n    // Constructs an array taking shape/strides from arbitrary container types\n    array(const pybind11::dtype &dt,\n          ShapeContainer shape,\n          StridesContainer strides,\n          const void *ptr = nullptr,\n          handle base = handle()) {\n\n        if (strides->empty()) {\n            *strides = detail::c_strides(*shape, dt.itemsize());\n        }\n\n        auto ndim = shape->size();\n        if (ndim != strides->size()) {\n            pybind11_fail(\"NumPy: shape ndim doesn't match strides ndim\");\n        }\n        auto descr = dt;\n\n        int flags = 0;\n        if (base && ptr) {\n            if (isinstance<array>(base)) {\n                /* Copy flags from base (except ownership bit) */\n                flags = reinterpret_borrow<array>(base).flags()\n                        & ~detail::npy_api::NPY_ARRAY_OWNDATA_;\n            } else {\n                /* Writable by default, easy to downgrade later on if needed */\n                flags = detail::npy_api::NPY_ARRAY_WRITEABLE_;\n            }\n        }\n\n        auto &api = detail::npy_api::get();\n        auto tmp = reinterpret_steal<object>(api.PyArray_NewFromDescr_(\n            api.PyArray_Type_,\n            descr.release().ptr(),\n            (int) ndim,\n            // Use reinterpret_cast for PyPy on Windows (remove if fixed, checked on 7.3.1)\n            reinterpret_cast<Py_intptr_t *>(shape->data()),\n            reinterpret_cast<Py_intptr_t *>(strides->data()),\n            const_cast<void *>(ptr),\n            flags,\n            nullptr));\n        if (!tmp) {\n            throw error_already_set();\n        }\n        if (ptr) {\n            if (base) {\n                api.PyArray_SetBaseObject_(tmp.ptr(), base.inc_ref().ptr());\n            } else {\n                tmp = reinterpret_steal<object>(\n                    api.PyArray_NewCopy_(tmp.ptr(), -1 /* any order */));\n            }\n        }\n        m_ptr = tmp.release().ptr();\n    }\n\n    array(const pybind11::dtype &dt,\n          ShapeContainer shape,\n          const void *ptr = nullptr,\n          handle base = handle())\n        : array(dt, std::move(shape), {}, ptr, base) {}\n\n    template <typename T,\n              typename\n              = detail::enable_if_t<std::is_integral<T>::value && !std::is_same<bool, T>::value>>\n    array(const pybind11::dtype &dt, T count, const void *ptr = nullptr, handle base = handle())\n        : array(dt, {{count}}, ptr, base) {}\n\n    template <typename T>\n    array(ShapeContainer shape, StridesContainer strides, const T *ptr, handle base = handle())\n        : array(pybind11::dtype::of<T>(),\n                std::move(shape),\n                std::move(strides),\n                reinterpret_cast<const void *>(ptr),\n                base) {}\n\n    template <typename T>\n    array(ShapeContainer shape, const T *ptr, handle base = handle())\n        : array(std::move(shape), {}, ptr, base) {}\n\n    template <typename T>\n    explicit array(ssize_t count, const T *ptr, handle base = handle())\n        : array({count}, {}, ptr, base) {}\n\n    explicit array(const buffer_info &info, handle base = handle())\n        : array(pybind11::dtype(info), info.shape, info.strides, info.ptr, base) {}\n\n    /// Array descriptor (dtype)\n    pybind11::dtype dtype() const {\n        return reinterpret_borrow<pybind11::dtype>(detail::array_proxy(m_ptr)->descr);\n    }\n\n    /// Total number of elements\n    ssize_t size() const {\n        return std::accumulate(shape(), shape() + ndim(), (ssize_t) 1, std::multiplies<ssize_t>());\n    }\n\n    /// Byte size of a single element\n    ssize_t itemsize() const { return dtype().itemsize(); }\n\n    /// Total number of bytes\n    ssize_t nbytes() const { return size() * itemsize(); }\n\n    /// Number of dimensions\n    ssize_t ndim() const { return detail::array_proxy(m_ptr)->nd; }\n\n    /// Base object\n    object base() const { return reinterpret_borrow<object>(detail::array_proxy(m_ptr)->base); }\n\n    /// Dimensions of the array\n    const ssize_t *shape() const { return detail::array_proxy(m_ptr)->dimensions; }\n\n    /// Dimension along a given axis\n    ssize_t shape(ssize_t dim) const {\n        if (dim >= ndim()) {\n            fail_dim_check(dim, \"invalid axis\");\n        }\n        return shape()[dim];\n    }\n\n    /// Strides of the array\n    const ssize_t *strides() const { return detail::array_proxy(m_ptr)->strides; }\n\n    /// Stride along a given axis\n    ssize_t strides(ssize_t dim) const {\n        if (dim >= ndim()) {\n            fail_dim_check(dim, \"invalid axis\");\n        }\n        return strides()[dim];\n    }\n\n    /// Return the NumPy array flags\n    int flags() const { return detail::array_proxy(m_ptr)->flags; }\n\n    /// If set, the array is writeable (otherwise the buffer is read-only)\n    bool writeable() const {\n        return detail::check_flags(m_ptr, detail::npy_api::NPY_ARRAY_WRITEABLE_);\n    }\n\n    /// If set, the array owns the data (will be freed when the array is deleted)\n    bool owndata() const {\n        return detail::check_flags(m_ptr, detail::npy_api::NPY_ARRAY_OWNDATA_);\n    }\n\n    /// Pointer to the contained data. If index is not provided, points to the\n    /// beginning of the buffer. May throw if the index would lead to out of bounds access.\n    template <typename... Ix>\n    const void *data(Ix... index) const {\n        return static_cast<const void *>(detail::array_proxy(m_ptr)->data + offset_at(index...));\n    }\n\n    /// Mutable pointer to the contained data. If index is not provided, points to the\n    /// beginning of the buffer. May throw if the index would lead to out of bounds access.\n    /// May throw if the array is not writeable.\n    template <typename... Ix>\n    void *mutable_data(Ix... index) {\n        check_writeable();\n        return static_cast<void *>(detail::array_proxy(m_ptr)->data + offset_at(index...));\n    }\n\n    /// Byte offset from beginning of the array to a given index (full or partial).\n    /// May throw if the index would lead to out of bounds access.\n    template <typename... Ix>\n    ssize_t offset_at(Ix... index) const {\n        if ((ssize_t) sizeof...(index) > ndim()) {\n            fail_dim_check(sizeof...(index), \"too many indices for an array\");\n        }\n        return byte_offset(ssize_t(index)...);\n    }\n\n    ssize_t offset_at() const { return 0; }\n\n    /// Item count from beginning of the array to a given index (full or partial).\n    /// May throw if the index would lead to out of bounds access.\n    template <typename... Ix>\n    ssize_t index_at(Ix... index) const {\n        return offset_at(index...) / itemsize();\n    }\n\n    /**\n     * Returns a proxy object that provides access to the array's data without bounds or\n     * dimensionality checking.  Will throw if the array is missing the `writeable` flag.  Use with\n     * care: the array must not be destroyed or reshaped for the duration of the returned object,\n     * and the caller must take care not to access invalid dimensions or dimension indices.\n     */\n    template <typename T, ssize_t Dims = -1>\n    detail::unchecked_mutable_reference<T, Dims> mutable_unchecked() & {\n        if (Dims >= 0 && ndim() != Dims) {\n            throw std::domain_error(\"array has incorrect number of dimensions: \"\n                                    + std::to_string(ndim()) + \"; expected \"\n                                    + std::to_string(Dims));\n        }\n        return detail::unchecked_mutable_reference<T, Dims>(\n            mutable_data(), shape(), strides(), ndim());\n    }\n\n    /**\n     * Returns a proxy object that provides const access to the array's data without bounds or\n     * dimensionality checking.  Unlike `mutable_unchecked()`, this does not require that the\n     * underlying array have the `writable` flag.  Use with care: the array must not be destroyed\n     * or reshaped for the duration of the returned object, and the caller must take care not to\n     * access invalid dimensions or dimension indices.\n     */\n    template <typename T, ssize_t Dims = -1>\n    detail::unchecked_reference<T, Dims> unchecked() const & {\n        if (Dims >= 0 && ndim() != Dims) {\n            throw std::domain_error(\"array has incorrect number of dimensions: \"\n                                    + std::to_string(ndim()) + \"; expected \"\n                                    + std::to_string(Dims));\n        }\n        return detail::unchecked_reference<T, Dims>(data(), shape(), strides(), ndim());\n    }\n\n    /// Return a new view with all of the dimensions of length 1 removed\n    array squeeze() {\n        auto &api = detail::npy_api::get();\n        return reinterpret_steal<array>(api.PyArray_Squeeze_(m_ptr));\n    }\n\n    /// Resize array to given shape\n    /// If refcheck is true and more that one reference exist to this array\n    /// then resize will succeed only if it makes a reshape, i.e. original size doesn't change\n    void resize(ShapeContainer new_shape, bool refcheck = true) {\n        detail::npy_api::PyArray_Dims d\n            = {// Use reinterpret_cast for PyPy on Windows (remove if fixed, checked on 7.3.1)\n               reinterpret_cast<Py_intptr_t *>(new_shape->data()),\n               int(new_shape->size())};\n        // try to resize, set ordering param to -1 cause it's not used anyway\n        auto new_array = reinterpret_steal<object>(\n            detail::npy_api::get().PyArray_Resize_(m_ptr, &d, int(refcheck), -1));\n        if (!new_array) {\n            throw error_already_set();\n        }\n        if (isinstance<array>(new_array)) {\n            *this = std::move(new_array);\n        }\n    }\n\n    /// Optional `order` parameter omitted, to be added as needed.\n    array reshape(ShapeContainer new_shape) {\n        detail::npy_api::PyArray_Dims d\n            = {reinterpret_cast<Py_intptr_t *>(new_shape->data()), int(new_shape->size())};\n        auto new_array\n            = reinterpret_steal<array>(detail::npy_api::get().PyArray_Newshape_(m_ptr, &d, 0));\n        if (!new_array) {\n            throw error_already_set();\n        }\n        return new_array;\n    }\n\n    /// Create a view of an array in a different data type.\n    /// This function may fundamentally reinterpret the data in the array.\n    /// It is the responsibility of the caller to ensure that this is safe.\n    /// Only supports the `dtype` argument, the `type` argument is omitted,\n    /// to be added as needed.\n    array view(const std::string &dtype) {\n        auto &api = detail::npy_api::get();\n        auto new_view = reinterpret_steal<array>(api.PyArray_View_(\n            m_ptr, dtype::from_args(pybind11::str(dtype)).release().ptr(), nullptr));\n        if (!new_view) {\n            throw error_already_set();\n        }\n        return new_view;\n    }\n\n    /// Ensure that the argument is a NumPy array\n    /// In case of an error, nullptr is returned and the Python error is cleared.\n    static array ensure(handle h, int ExtraFlags = 0) {\n        auto result = reinterpret_steal<array>(raw_array(h.ptr(), ExtraFlags));\n        if (!result) {\n            PyErr_Clear();\n        }\n        return result;\n    }\n\nprotected:\n    template <typename, typename>\n    friend struct detail::npy_format_descriptor;\n\n    void fail_dim_check(ssize_t dim, const std::string &msg) const {\n        throw index_error(msg + \": \" + std::to_string(dim) + \" (ndim = \" + std::to_string(ndim())\n                          + ')');\n    }\n\n    template <typename... Ix>\n    ssize_t byte_offset(Ix... index) const {\n        check_dimensions(index...);\n        return detail::byte_offset_unsafe(strides(), ssize_t(index)...);\n    }\n\n    void check_writeable() const {\n        if (!writeable()) {\n            throw std::domain_error(\"array is not writeable\");\n        }\n    }\n\n    template <typename... Ix>\n    void check_dimensions(Ix... index) const {\n        check_dimensions_impl(ssize_t(0), shape(), ssize_t(index)...);\n    }\n\n    void check_dimensions_impl(ssize_t, const ssize_t *) const {}\n\n    template <typename... Ix>\n    void check_dimensions_impl(ssize_t axis, const ssize_t *shape, ssize_t i, Ix... index) const {\n        if (i >= *shape) {\n            throw index_error(std::string(\"index \") + std::to_string(i)\n                              + \" is out of bounds for axis \" + std::to_string(axis)\n                              + \" with size \" + std::to_string(*shape));\n        }\n        check_dimensions_impl(axis + 1, shape + 1, index...);\n    }\n\n    /// Create array from any object -- always returns a new reference\n    static PyObject *raw_array(PyObject *ptr, int ExtraFlags = 0) {\n        if (ptr == nullptr) {\n            set_error(PyExc_ValueError, \"cannot create a pybind11::array from a nullptr\");\n            return nullptr;\n        }\n        return detail::npy_api::get().PyArray_FromAny_(\n            ptr, nullptr, 0, 0, detail::npy_api::NPY_ARRAY_ENSUREARRAY_ | ExtraFlags, nullptr);\n    }\n};\n\ntemplate <typename T, int ExtraFlags = array::forcecast>\nclass array_t : public array {\nprivate:\n    struct private_ctor {};\n    // Delegating constructor needed when both moving and accessing in the same constructor\n    array_t(private_ctor,\n            ShapeContainer &&shape,\n            StridesContainer &&strides,\n            const T *ptr,\n            handle base)\n        : array(std::move(shape), std::move(strides), ptr, base) {}\n\npublic:\n    static_assert(!detail::array_info<T>::is_array, \"Array types cannot be used with array_t\");\n\n    using value_type = T;\n\n    array_t() : array(0, static_cast<const T *>(nullptr)) {}\n    array_t(handle h, borrowed_t) : array(h, borrowed_t{}) {}\n    array_t(handle h, stolen_t) : array(h, stolen_t{}) {}\n\n    PYBIND11_DEPRECATED(\"Use array_t<T>::ensure() instead\")\n    array_t(handle h, bool is_borrowed) : array(raw_array_t(h.ptr()), stolen_t{}) {\n        if (!m_ptr) {\n            PyErr_Clear();\n        }\n        if (!is_borrowed) {\n            Py_XDECREF(h.ptr());\n        }\n    }\n\n    // NOLINTNEXTLINE(google-explicit-constructor)\n    array_t(const object &o) : array(raw_array_t(o.ptr()), stolen_t{}) {\n        if (!m_ptr) {\n            throw error_already_set();\n        }\n    }\n\n    explicit array_t(const buffer_info &info, handle base = handle()) : array(info, base) {}\n\n    array_t(ShapeContainer shape,\n            StridesContainer strides,\n            const T *ptr = nullptr,\n            handle base = handle())\n        : array(std::move(shape), std::move(strides), ptr, base) {}\n\n    explicit array_t(ShapeContainer shape, const T *ptr = nullptr, handle base = handle())\n        : array_t(private_ctor{},\n                  std::move(shape),\n                  (ExtraFlags & f_style) != 0 ? detail::f_strides(*shape, itemsize())\n                                              : detail::c_strides(*shape, itemsize()),\n                  ptr,\n                  base) {}\n\n    explicit array_t(ssize_t count, const T *ptr = nullptr, handle base = handle())\n        : array({count}, {}, ptr, base) {}\n\n    constexpr ssize_t itemsize() const { return sizeof(T); }\n\n    template <typename... Ix>\n    ssize_t index_at(Ix... index) const {\n        return offset_at(index...) / itemsize();\n    }\n\n    template <typename... Ix>\n    const T *data(Ix... index) const {\n        return static_cast<const T *>(array::data(index...));\n    }\n\n    template <typename... Ix>\n    T *mutable_data(Ix... index) {\n        return static_cast<T *>(array::mutable_data(index...));\n    }\n\n    // Reference to element at a given index\n    template <typename... Ix>\n    const T &at(Ix... index) const {\n        if ((ssize_t) sizeof...(index) != ndim()) {\n            fail_dim_check(sizeof...(index), \"index dimension mismatch\");\n        }\n        return *(static_cast<const T *>(array::data())\n                 + byte_offset(ssize_t(index)...) / itemsize());\n    }\n\n    // Mutable reference to element at a given index\n    template <typename... Ix>\n    T &mutable_at(Ix... index) {\n        if ((ssize_t) sizeof...(index) != ndim()) {\n            fail_dim_check(sizeof...(index), \"index dimension mismatch\");\n        }\n        return *(static_cast<T *>(array::mutable_data())\n                 + byte_offset(ssize_t(index)...) / itemsize());\n    }\n\n    /**\n     * Returns a proxy object that provides access to the array's data without bounds or\n     * dimensionality checking.  Will throw if the array is missing the `writeable` flag.  Use with\n     * care: the array must not be destroyed or reshaped for the duration of the returned object,\n     * and the caller must take care not to access invalid dimensions or dimension indices.\n     */\n    template <ssize_t Dims = -1>\n    detail::unchecked_mutable_reference<T, Dims> mutable_unchecked() & {\n        return array::mutable_unchecked<T, Dims>();\n    }\n\n    /**\n     * Returns a proxy object that provides const access to the array's data without bounds or\n     * dimensionality checking.  Unlike `mutable_unchecked()`, this does not require that the\n     * underlying array have the `writable` flag.  Use with care: the array must not be destroyed\n     * or reshaped for the duration of the returned object, and the caller must take care not to\n     * access invalid dimensions or dimension indices.\n     */\n    template <ssize_t Dims = -1>\n    detail::unchecked_reference<T, Dims> unchecked() const & {\n        return array::unchecked<T, Dims>();\n    }\n\n    /// Ensure that the argument is a NumPy array of the correct dtype (and if not, try to convert\n    /// it).  In case of an error, nullptr is returned and the Python error is cleared.\n    static array_t ensure(handle h) {\n        auto result = reinterpret_steal<array_t>(raw_array_t(h.ptr()));\n        if (!result) {\n            PyErr_Clear();\n        }\n        return result;\n    }\n\n    static bool check_(handle h) {\n        const auto &api = detail::npy_api::get();\n        return api.PyArray_Check_(h.ptr())\n               && api.PyArray_EquivTypes_(detail::array_proxy(h.ptr())->descr,\n                                          dtype::of<T>().ptr())\n               && detail::check_flags(h.ptr(), ExtraFlags & (array::c_style | array::f_style));\n    }\n\nprotected:\n    /// Create array from any object -- always returns a new reference\n    static PyObject *raw_array_t(PyObject *ptr) {\n        if (ptr == nullptr) {\n            set_error(PyExc_ValueError, \"cannot create a pybind11::array_t from a nullptr\");\n            return nullptr;\n        }\n        return detail::npy_api::get().PyArray_FromAny_(ptr,\n                                                       dtype::of<T>().release().ptr(),\n                                                       0,\n                                                       0,\n                                                       detail::npy_api::NPY_ARRAY_ENSUREARRAY_\n                                                           | ExtraFlags,\n                                                       nullptr);\n    }\n};\n\ntemplate <typename T>\nstruct format_descriptor<T, detail::enable_if_t<detail::is_pod_struct<T>::value>> {\n    static std::string format() {\n        return detail::npy_format_descriptor<typename std::remove_cv<T>::type>::format();\n    }\n};\n\ntemplate <size_t N>\nstruct format_descriptor<char[N]> {\n    static std::string format() { return std::to_string(N) + 's'; }\n};\ntemplate <size_t N>\nstruct format_descriptor<std::array<char, N>> {\n    static std::string format() { return std::to_string(N) + 's'; }\n};\n\ntemplate <typename T>\nstruct format_descriptor<T, detail::enable_if_t<std::is_enum<T>::value>> {\n    static std::string format() {\n        return format_descriptor<\n            typename std::remove_cv<typename std::underlying_type<T>::type>::type>::format();\n    }\n};\n\ntemplate <typename T>\nstruct format_descriptor<T, detail::enable_if_t<detail::array_info<T>::is_array>> {\n    static std::string format() {\n        using namespace detail;\n        static constexpr auto extents = const_name(\"(\") + array_info<T>::extents + const_name(\")\");\n        return extents.text + format_descriptor<remove_all_extents_t<T>>::format();\n    }\n};\n\nPYBIND11_NAMESPACE_BEGIN(detail)\ntemplate <typename T, int ExtraFlags>\nstruct pyobject_caster<array_t<T, ExtraFlags>> {\n    using type = array_t<T, ExtraFlags>;\n\n    bool load(handle src, bool convert) {\n        if (!convert && !type::check_(src)) {\n            return false;\n        }\n        value = type::ensure(src);\n        return static_cast<bool>(value);\n    }\n\n    static handle cast(const handle &src, return_value_policy /* policy */, handle /* parent */) {\n        return src.inc_ref();\n    }\n    PYBIND11_TYPE_CASTER(type, handle_type_name<type>::name);\n};\n\ntemplate <typename T>\nstruct compare_buffer_info<T, detail::enable_if_t<detail::is_pod_struct<T>::value>> {\n    static bool compare(const buffer_info &b) {\n        return npy_api::get().PyArray_EquivTypes_(dtype::of<T>().ptr(), dtype(b).ptr());\n    }\n};\n\ntemplate <typename T, typename = void>\nstruct npy_format_descriptor_name;\n\ntemplate <typename T>\nstruct npy_format_descriptor_name<T, enable_if_t<std::is_integral<T>::value>> {\n    static constexpr auto name = const_name<std::is_same<T, bool>::value>(\n        const_name(\"bool\"),\n        const_name<std::is_signed<T>::value>(\"numpy.int\", \"numpy.uint\")\n            + const_name<sizeof(T) * 8>());\n};\n\ntemplate <typename T>\nstruct npy_format_descriptor_name<T, enable_if_t<std::is_floating_point<T>::value>> {\n    static constexpr auto name = const_name < std::is_same<T, float>::value\n                                 || std::is_same<T, const float>::value\n                                 || std::is_same<T, double>::value\n                                 || std::is_same<T, const double>::value\n                                        > (const_name(\"numpy.float\") + const_name<sizeof(T) * 8>(),\n                                           const_name(\"numpy.longdouble\"));\n};\n\ntemplate <typename T>\nstruct npy_format_descriptor_name<T, enable_if_t<is_complex<T>::value>> {\n    static constexpr auto name = const_name < std::is_same<typename T::value_type, float>::value\n                                 || std::is_same<typename T::value_type, const float>::value\n                                 || std::is_same<typename T::value_type, double>::value\n                                 || std::is_same<typename T::value_type, const double>::value\n                                        > (const_name(\"numpy.complex\")\n                                               + const_name<sizeof(typename T::value_type) * 16>(),\n                                           const_name(\"numpy.longcomplex\"));\n};\n\ntemplate <typename T>\nstruct npy_format_descriptor<\n    T,\n    enable_if_t<satisfies_any_of<T, std::is_arithmetic, is_complex>::value>>\n    : npy_format_descriptor_name<T> {\nprivate:\n    // NB: the order here must match the one in common.h\n    constexpr static const int values[15] = {npy_api::NPY_BOOL_,\n                                             npy_api::NPY_BYTE_,\n                                             npy_api::NPY_UBYTE_,\n                                             npy_api::NPY_INT16_,\n                                             npy_api::NPY_UINT16_,\n                                             npy_api::NPY_INT32_,\n                                             npy_api::NPY_UINT32_,\n                                             npy_api::NPY_INT64_,\n                                             npy_api::NPY_UINT64_,\n                                             npy_api::NPY_FLOAT_,\n                                             npy_api::NPY_DOUBLE_,\n                                             npy_api::NPY_LONGDOUBLE_,\n                                             npy_api::NPY_CFLOAT_,\n                                             npy_api::NPY_CDOUBLE_,\n                                             npy_api::NPY_CLONGDOUBLE_};\n\npublic:\n    static constexpr int value = values[detail::is_fmt_numeric<T>::index];\n\n    static pybind11::dtype dtype() { return pybind11::dtype(/*typenum*/ value); }\n};\n\ntemplate <typename T>\nstruct npy_format_descriptor<T, enable_if_t<is_same_ignoring_cvref<T, PyObject *>::value>> {\n    static constexpr auto name = const_name(\"object\");\n\n    static constexpr int value = npy_api::NPY_OBJECT_;\n\n    static pybind11::dtype dtype() { return pybind11::dtype(/*typenum*/ value); }\n};\n\n#define PYBIND11_DECL_CHAR_FMT                                                                    \\\n    static constexpr auto name = const_name(\"S\") + const_name<N>();                               \\\n    static pybind11::dtype dtype() {                                                              \\\n        return pybind11::dtype(std::string(\"S\") + std::to_string(N));                             \\\n    }\ntemplate <size_t N>\nstruct npy_format_descriptor<char[N]> {\n    PYBIND11_DECL_CHAR_FMT\n};\ntemplate <size_t N>\nstruct npy_format_descriptor<std::array<char, N>> {\n    PYBIND11_DECL_CHAR_FMT\n};\n#undef PYBIND11_DECL_CHAR_FMT\n\ntemplate <typename T>\nstruct npy_format_descriptor<T, enable_if_t<array_info<T>::is_array>> {\nprivate:\n    using base_descr = npy_format_descriptor<typename array_info<T>::type>;\n\npublic:\n    static_assert(!array_info<T>::is_empty, \"Zero-sized arrays are not supported\");\n\n    static constexpr auto name\n        = const_name(\"(\") + array_info<T>::extents + const_name(\")\") + base_descr::name;\n    static pybind11::dtype dtype() {\n        list shape;\n        array_info<T>::append_extents(shape);\n        return pybind11::dtype::from_args(\n            pybind11::make_tuple(base_descr::dtype(), std::move(shape)));\n    }\n};\n\ntemplate <typename T>\nstruct npy_format_descriptor<T, enable_if_t<std::is_enum<T>::value>> {\nprivate:\n    using base_descr = npy_format_descriptor<typename std::underlying_type<T>::type>;\n\npublic:\n    static constexpr auto name = base_descr::name;\n    static pybind11::dtype dtype() { return base_descr::dtype(); }\n};\n\nstruct field_descriptor {\n    const char *name;\n    ssize_t offset;\n    ssize_t size;\n    std::string format;\n    dtype descr;\n};\n\nPYBIND11_NOINLINE void register_structured_dtype(any_container<field_descriptor> fields,\n                                                 const std::type_info &tinfo,\n                                                 ssize_t itemsize,\n                                                 bool (*direct_converter)(PyObject *, void *&)) {\n\n    auto &numpy_internals = get_numpy_internals();\n    if (numpy_internals.get_type_info(tinfo, false)) {\n        pybind11_fail(\"NumPy: dtype is already registered\");\n    }\n\n    // Use ordered fields because order matters as of NumPy 1.14:\n    // https://docs.scipy.org/doc/numpy/release.html#multiple-field-indexing-assignment-of-structured-arrays\n    std::vector<field_descriptor> ordered_fields(std::move(fields));\n    std::sort(\n        ordered_fields.begin(),\n        ordered_fields.end(),\n        [](const field_descriptor &a, const field_descriptor &b) { return a.offset < b.offset; });\n\n    list names, formats, offsets;\n    for (auto &field : ordered_fields) {\n        if (!field.descr) {\n            pybind11_fail(std::string(\"NumPy: unsupported field dtype: `\") + field.name + \"` @ \"\n                          + tinfo.name());\n        }\n        names.append(pybind11::str(field.name));\n        formats.append(field.descr);\n        offsets.append(pybind11::int_(field.offset));\n    }\n    auto *dtype_ptr\n        = pybind11::dtype(std::move(names), std::move(formats), std::move(offsets), itemsize)\n              .release()\n              .ptr();\n\n    // There is an existing bug in NumPy (as of v1.11): trailing bytes are\n    // not encoded explicitly into the format string. This will supposedly\n    // get fixed in v1.12; for further details, see these:\n    // - https://github.com/numpy/numpy/issues/7797\n    // - https://github.com/numpy/numpy/pull/7798\n    // Because of this, we won't use numpy's logic to generate buffer format\n    // strings and will just do it ourselves.\n    ssize_t offset = 0;\n    std::ostringstream oss;\n    // mark the structure as unaligned with '^', because numpy and C++ don't\n    // always agree about alignment (particularly for complex), and we're\n    // explicitly listing all our padding. This depends on none of the fields\n    // overriding the endianness. Putting the ^ in front of individual fields\n    // isn't guaranteed to work due to https://github.com/numpy/numpy/issues/9049\n    oss << \"^T{\";\n    for (auto &field : ordered_fields) {\n        if (field.offset > offset) {\n            oss << (field.offset - offset) << 'x';\n        }\n        oss << field.format << ':' << field.name << ':';\n        offset = field.offset + field.size;\n    }\n    if (itemsize > offset) {\n        oss << (itemsize - offset) << 'x';\n    }\n    oss << '}';\n    auto format_str = oss.str();\n\n    // Smoke test: verify that NumPy properly parses our buffer format string\n    auto &api = npy_api::get();\n    auto arr = array(buffer_info(nullptr, itemsize, format_str, 1));\n    if (!api.PyArray_EquivTypes_(dtype_ptr, arr.dtype().ptr())) {\n        pybind11_fail(\"NumPy: invalid buffer descriptor!\");\n    }\n\n    auto tindex = std::type_index(tinfo);\n    numpy_internals.registered_dtypes[tindex] = {dtype_ptr, std::move(format_str)};\n    with_internals([tindex, &direct_converter](internals &internals) {\n        internals.direct_conversions[tindex].push_back(direct_converter);\n    });\n}\n\ntemplate <typename T, typename SFINAE>\nstruct npy_format_descriptor {\n    static_assert(is_pod_struct<T>::value,\n                  \"Attempt to use a non-POD or unimplemented POD type as a numpy dtype\");\n\n    static constexpr auto name = make_caster<T>::name;\n\n    static pybind11::dtype dtype() { return reinterpret_borrow<pybind11::dtype>(dtype_ptr()); }\n\n    static std::string format() {\n        static auto format_str = get_numpy_internals().get_type_info<T>(true)->format_str;\n        return format_str;\n    }\n\n    static void register_dtype(any_container<field_descriptor> fields) {\n        register_structured_dtype(std::move(fields),\n                                  typeid(typename std::remove_cv<T>::type),\n                                  sizeof(T),\n                                  &direct_converter);\n    }\n\nprivate:\n    static PyObject *dtype_ptr() {\n        static PyObject *ptr = get_numpy_internals().get_type_info<T>(true)->dtype_ptr;\n        return ptr;\n    }\n\n    static bool direct_converter(PyObject *obj, void *&value) {\n        auto &api = npy_api::get();\n        if (!PyObject_TypeCheck(obj, api.PyVoidArrType_Type_)) {\n            return false;\n        }\n        if (auto descr = reinterpret_steal<object>(api.PyArray_DescrFromScalar_(obj))) {\n            if (api.PyArray_EquivTypes_(dtype_ptr(), descr.ptr())) {\n                value = ((PyVoidScalarObject_Proxy *) obj)->obval;\n                return true;\n            }\n        }\n        return false;\n    }\n};\n\n#ifdef __CLION_IDE__ // replace heavy macro with dummy code for the IDE (doesn't affect code)\n#    define PYBIND11_NUMPY_DTYPE(Type, ...) ((void) 0)\n#    define PYBIND11_NUMPY_DTYPE_EX(Type, ...) ((void) 0)\n#else\n\n#    define PYBIND11_FIELD_DESCRIPTOR_EX(T, Field, Name)                                          \\\n        ::pybind11::detail::field_descriptor {                                                    \\\n            Name, offsetof(T, Field), sizeof(decltype(std::declval<T>().Field)),                  \\\n                ::pybind11::format_descriptor<decltype(std::declval<T>().Field)>::format(),       \\\n                ::pybind11::detail::npy_format_descriptor<                                        \\\n                    decltype(std::declval<T>().Field)>::dtype()                                   \\\n        }\n\n// Extract name, offset and format descriptor for a struct field\n#    define PYBIND11_FIELD_DESCRIPTOR(T, Field) PYBIND11_FIELD_DESCRIPTOR_EX(T, Field, #Field)\n\n// The main idea of this macro is borrowed from https://github.com/swansontec/map-macro\n// (C) William Swanson, Paul Fultz\n#    define PYBIND11_EVAL0(...) __VA_ARGS__\n#    define PYBIND11_EVAL1(...) PYBIND11_EVAL0(PYBIND11_EVAL0(PYBIND11_EVAL0(__VA_ARGS__)))\n#    define PYBIND11_EVAL2(...) PYBIND11_EVAL1(PYBIND11_EVAL1(PYBIND11_EVAL1(__VA_ARGS__)))\n#    define PYBIND11_EVAL3(...) PYBIND11_EVAL2(PYBIND11_EVAL2(PYBIND11_EVAL2(__VA_ARGS__)))\n#    define PYBIND11_EVAL4(...) PYBIND11_EVAL3(PYBIND11_EVAL3(PYBIND11_EVAL3(__VA_ARGS__)))\n#    define PYBIND11_EVAL(...) PYBIND11_EVAL4(PYBIND11_EVAL4(PYBIND11_EVAL4(__VA_ARGS__)))\n#    define PYBIND11_MAP_END(...)\n#    define PYBIND11_MAP_OUT\n#    define PYBIND11_MAP_COMMA ,\n#    define PYBIND11_MAP_GET_END() 0, PYBIND11_MAP_END\n#    define PYBIND11_MAP_NEXT0(test, next, ...) next PYBIND11_MAP_OUT\n#    define PYBIND11_MAP_NEXT1(test, next) PYBIND11_MAP_NEXT0(test, next, 0)\n#    define PYBIND11_MAP_NEXT(test, next) PYBIND11_MAP_NEXT1(PYBIND11_MAP_GET_END test, next)\n#    if defined(_MSC_VER)                                                                         \\\n        && !defined(__clang__) // MSVC is not as eager to expand macros, hence this workaround\n#        define PYBIND11_MAP_LIST_NEXT1(test, next)                                               \\\n            PYBIND11_EVAL0(PYBIND11_MAP_NEXT0(test, PYBIND11_MAP_COMMA next, 0))\n#    else\n#        define PYBIND11_MAP_LIST_NEXT1(test, next)                                               \\\n            PYBIND11_MAP_NEXT0(test, PYBIND11_MAP_COMMA next, 0)\n#    endif\n#    define PYBIND11_MAP_LIST_NEXT(test, next)                                                    \\\n        PYBIND11_MAP_LIST_NEXT1(PYBIND11_MAP_GET_END test, next)\n#    define PYBIND11_MAP_LIST0(f, t, x, peek, ...)                                                \\\n        f(t, x) PYBIND11_MAP_LIST_NEXT(peek, PYBIND11_MAP_LIST1)(f, t, peek, __VA_ARGS__)\n#    define PYBIND11_MAP_LIST1(f, t, x, peek, ...)                                                \\\n        f(t, x) PYBIND11_MAP_LIST_NEXT(peek, PYBIND11_MAP_LIST0)(f, t, peek, __VA_ARGS__)\n// PYBIND11_MAP_LIST(f, t, a1, a2, ...) expands to f(t, a1), f(t, a2), ...\n#    define PYBIND11_MAP_LIST(f, t, ...)                                                          \\\n        PYBIND11_EVAL(PYBIND11_MAP_LIST1(f, t, __VA_ARGS__, (), 0))\n\n#    define PYBIND11_NUMPY_DTYPE(Type, ...)                                                       \\\n        ::pybind11::detail::npy_format_descriptor<Type>::register_dtype(                          \\\n            ::std::vector<::pybind11::detail::field_descriptor>{                                  \\\n                PYBIND11_MAP_LIST(PYBIND11_FIELD_DESCRIPTOR, Type, __VA_ARGS__)})\n\n#    if defined(_MSC_VER) && !defined(__clang__)\n#        define PYBIND11_MAP2_LIST_NEXT1(test, next)                                              \\\n            PYBIND11_EVAL0(PYBIND11_MAP_NEXT0(test, PYBIND11_MAP_COMMA next, 0))\n#    else\n#        define PYBIND11_MAP2_LIST_NEXT1(test, next)                                              \\\n            PYBIND11_MAP_NEXT0(test, PYBIND11_MAP_COMMA next, 0)\n#    endif\n#    define PYBIND11_MAP2_LIST_NEXT(test, next)                                                   \\\n        PYBIND11_MAP2_LIST_NEXT1(PYBIND11_MAP_GET_END test, next)\n#    define PYBIND11_MAP2_LIST0(f, t, x1, x2, peek, ...)                                          \\\n        f(t, x1, x2) PYBIND11_MAP2_LIST_NEXT(peek, PYBIND11_MAP2_LIST1)(f, t, peek, __VA_ARGS__)\n#    define PYBIND11_MAP2_LIST1(f, t, x1, x2, peek, ...)                                          \\\n        f(t, x1, x2) PYBIND11_MAP2_LIST_NEXT(peek, PYBIND11_MAP2_LIST0)(f, t, peek, __VA_ARGS__)\n// PYBIND11_MAP2_LIST(f, t, a1, a2, ...) expands to f(t, a1, a2), f(t, a3, a4), ...\n#    define PYBIND11_MAP2_LIST(f, t, ...)                                                         \\\n        PYBIND11_EVAL(PYBIND11_MAP2_LIST1(f, t, __VA_ARGS__, (), 0))\n\n#    define PYBIND11_NUMPY_DTYPE_EX(Type, ...)                                                    \\\n        ::pybind11::detail::npy_format_descriptor<Type>::register_dtype(                          \\\n            ::std::vector<::pybind11::detail::field_descriptor>{                                  \\\n                PYBIND11_MAP2_LIST(PYBIND11_FIELD_DESCRIPTOR_EX, Type, __VA_ARGS__)})\n\n#endif // __CLION_IDE__\n\nclass common_iterator {\npublic:\n    using container_type = std::vector<ssize_t>;\n    using value_type = container_type::value_type;\n    using size_type = container_type::size_type;\n\n    common_iterator() : m_strides() {}\n\n    common_iterator(void *ptr, const container_type &strides, const container_type &shape)\n        : p_ptr(reinterpret_cast<char *>(ptr)), m_strides(strides.size()) {\n        m_strides.back() = static_cast<value_type>(strides.back());\n        for (size_type i = m_strides.size() - 1; i != 0; --i) {\n            size_type j = i - 1;\n            auto s = static_cast<value_type>(shape[i]);\n            m_strides[j] = strides[j] + m_strides[i] - strides[i] * s;\n        }\n    }\n\n    void increment(size_type dim) { p_ptr += m_strides[dim]; }\n\n    void *data() const { return p_ptr; }\n\nprivate:\n    char *p_ptr{nullptr};\n    container_type m_strides;\n};\n\ntemplate <size_t N>\nclass multi_array_iterator {\npublic:\n    using container_type = std::vector<ssize_t>;\n\n    multi_array_iterator(const std::array<buffer_info, N> &buffers, const container_type &shape)\n        : m_shape(shape.size()), m_index(shape.size(), 0), m_common_iterator() {\n\n        // Manual copy to avoid conversion warning if using std::copy\n        for (size_t i = 0; i < shape.size(); ++i) {\n            m_shape[i] = shape[i];\n        }\n\n        container_type strides(shape.size());\n        for (size_t i = 0; i < N; ++i) {\n            init_common_iterator(buffers[i], shape, m_common_iterator[i], strides);\n        }\n    }\n\n    multi_array_iterator &operator++() {\n        for (size_t j = m_index.size(); j != 0; --j) {\n            size_t i = j - 1;\n            if (++m_index[i] != m_shape[i]) {\n                increment_common_iterator(i);\n                break;\n            }\n            m_index[i] = 0;\n        }\n        return *this;\n    }\n\n    template <size_t K, class T = void>\n    T *data() const {\n        return reinterpret_cast<T *>(m_common_iterator[K].data());\n    }\n\nprivate:\n    using common_iter = common_iterator;\n\n    void init_common_iterator(const buffer_info &buffer,\n                              const container_type &shape,\n                              common_iter &iterator,\n                              container_type &strides) {\n        auto buffer_shape_iter = buffer.shape.rbegin();\n        auto buffer_strides_iter = buffer.strides.rbegin();\n        auto shape_iter = shape.rbegin();\n        auto strides_iter = strides.rbegin();\n\n        while (buffer_shape_iter != buffer.shape.rend()) {\n            if (*shape_iter == *buffer_shape_iter) {\n                *strides_iter = *buffer_strides_iter;\n            } else {\n                *strides_iter = 0;\n            }\n\n            ++buffer_shape_iter;\n            ++buffer_strides_iter;\n            ++shape_iter;\n            ++strides_iter;\n        }\n\n        std::fill(strides_iter, strides.rend(), 0);\n        iterator = common_iter(buffer.ptr, strides, shape);\n    }\n\n    void increment_common_iterator(size_t dim) {\n        for (auto &iter : m_common_iterator) {\n            iter.increment(dim);\n        }\n    }\n\n    container_type m_shape;\n    container_type m_index;\n    std::array<common_iter, N> m_common_iterator;\n};\n\nenum class broadcast_trivial { non_trivial, c_trivial, f_trivial };\n\n// Populates the shape and number of dimensions for the set of buffers.  Returns a\n// broadcast_trivial enum value indicating whether the broadcast is \"trivial\"--that is, has each\n// buffer being either a singleton or a full-size, C-contiguous (`c_trivial`) or Fortran-contiguous\n// (`f_trivial`) storage buffer; returns `non_trivial` otherwise.\ntemplate <size_t N>\nbroadcast_trivial\nbroadcast(const std::array<buffer_info, N> &buffers, ssize_t &ndim, std::vector<ssize_t> &shape) {\n    ndim = std::accumulate(\n        buffers.begin(), buffers.end(), ssize_t(0), [](ssize_t res, const buffer_info &buf) {\n            return std::max(res, buf.ndim);\n        });\n\n    shape.clear();\n    shape.resize((size_t) ndim, 1);\n\n    // Figure out the output size, and make sure all input arrays conform (i.e. are either size 1\n    // or the full size).\n    for (size_t i = 0; i < N; ++i) {\n        auto res_iter = shape.rbegin();\n        auto end = buffers[i].shape.rend();\n        for (auto shape_iter = buffers[i].shape.rbegin(); shape_iter != end;\n             ++shape_iter, ++res_iter) {\n            const auto &dim_size_in = *shape_iter;\n            auto &dim_size_out = *res_iter;\n\n            // Each input dimension can either be 1 or `n`, but `n` values must match across\n            // buffers\n            if (dim_size_out == 1) {\n                dim_size_out = dim_size_in;\n            } else if (dim_size_in != 1 && dim_size_in != dim_size_out) {\n                pybind11_fail(\"pybind11::vectorize: incompatible size/dimension of inputs!\");\n            }\n        }\n    }\n\n    bool trivial_broadcast_c = true;\n    bool trivial_broadcast_f = true;\n    for (size_t i = 0; i < N && (trivial_broadcast_c || trivial_broadcast_f); ++i) {\n        if (buffers[i].size == 1) {\n            continue;\n        }\n\n        // Require the same number of dimensions:\n        if (buffers[i].ndim != ndim) {\n            return broadcast_trivial::non_trivial;\n        }\n\n        // Require all dimensions be full-size:\n        if (!std::equal(buffers[i].shape.cbegin(), buffers[i].shape.cend(), shape.cbegin())) {\n            return broadcast_trivial::non_trivial;\n        }\n\n        // Check for C contiguity (but only if previous inputs were also C contiguous)\n        if (trivial_broadcast_c) {\n            ssize_t expect_stride = buffers[i].itemsize;\n            auto end = buffers[i].shape.crend();\n            for (auto shape_iter = buffers[i].shape.crbegin(),\n                      stride_iter = buffers[i].strides.crbegin();\n                 trivial_broadcast_c && shape_iter != end;\n                 ++shape_iter, ++stride_iter) {\n                if (expect_stride == *stride_iter) {\n                    expect_stride *= *shape_iter;\n                } else {\n                    trivial_broadcast_c = false;\n                }\n            }\n        }\n\n        // Check for Fortran contiguity (if previous inputs were also F contiguous)\n        if (trivial_broadcast_f) {\n            ssize_t expect_stride = buffers[i].itemsize;\n            auto end = buffers[i].shape.cend();\n            for (auto shape_iter = buffers[i].shape.cbegin(),\n                      stride_iter = buffers[i].strides.cbegin();\n                 trivial_broadcast_f && shape_iter != end;\n                 ++shape_iter, ++stride_iter) {\n                if (expect_stride == *stride_iter) {\n                    expect_stride *= *shape_iter;\n                } else {\n                    trivial_broadcast_f = false;\n                }\n            }\n        }\n    }\n\n    return trivial_broadcast_c   ? broadcast_trivial::c_trivial\n           : trivial_broadcast_f ? broadcast_trivial::f_trivial\n                                 : broadcast_trivial::non_trivial;\n}\n\ntemplate <typename T>\nstruct vectorize_arg {\n    static_assert(!std::is_rvalue_reference<T>::value,\n                  \"Functions with rvalue reference arguments cannot be vectorized\");\n    // The wrapped function gets called with this type:\n    using call_type = remove_reference_t<T>;\n    // Is this a vectorized argument?\n    static constexpr bool vectorize\n        = satisfies_any_of<call_type, std::is_arithmetic, is_complex, is_pod>::value\n          && satisfies_none_of<call_type,\n                               std::is_pointer,\n                               std::is_array,\n                               is_std_array,\n                               std::is_enum>::value\n          && (!std::is_reference<T>::value\n              || (std::is_lvalue_reference<T>::value && std::is_const<call_type>::value));\n    // Accept this type: an array for vectorized types, otherwise the type as-is:\n    using type = conditional_t<vectorize, array_t<remove_cv_t<call_type>, array::forcecast>, T>;\n};\n\n// py::vectorize when a return type is present\ntemplate <typename Func, typename Return, typename... Args>\nstruct vectorize_returned_array {\n    using Type = array_t<Return>;\n\n    static Type create(broadcast_trivial trivial, const std::vector<ssize_t> &shape) {\n        if (trivial == broadcast_trivial::f_trivial) {\n            return array_t<Return, array::f_style>(shape);\n        }\n        return array_t<Return>(shape);\n    }\n\n    static Return *mutable_data(Type &array) { return array.mutable_data(); }\n\n    static Return call(Func &f, Args &...args) { return f(args...); }\n\n    static void call(Return *out, size_t i, Func &f, Args &...args) { out[i] = f(args...); }\n};\n\n// py::vectorize when a return type is not present\ntemplate <typename Func, typename... Args>\nstruct vectorize_returned_array<Func, void, Args...> {\n    using Type = none;\n\n    static Type create(broadcast_trivial, const std::vector<ssize_t> &) { return none(); }\n\n    static void *mutable_data(Type &) { return nullptr; }\n\n    static detail::void_type call(Func &f, Args &...args) {\n        f(args...);\n        return {};\n    }\n\n    static void call(void *, size_t, Func &f, Args &...args) { f(args...); }\n};\n\ntemplate <typename Func, typename Return, typename... Args>\nstruct vectorize_helper {\n\n// NVCC for some reason breaks if NVectorized is private\n#ifdef __CUDACC__\npublic:\n#else\nprivate:\n#endif\n\n    static constexpr size_t N = sizeof...(Args);\n    static constexpr size_t NVectorized = constexpr_sum(vectorize_arg<Args>::vectorize...);\n    static_assert(\n        NVectorized >= 1,\n        \"pybind11::vectorize(...) requires a function with at least one vectorizable argument\");\n\npublic:\n    template <typename T,\n              // SFINAE to prevent shadowing the copy constructor.\n              typename = detail::enable_if_t<\n                  !std::is_same<vectorize_helper, typename std::decay<T>::type>::value>>\n    explicit vectorize_helper(T &&f) : f(std::forward<T>(f)) {}\n\n    object operator()(typename vectorize_arg<Args>::type... args) {\n        return run(args...,\n                   make_index_sequence<N>(),\n                   select_indices<vectorize_arg<Args>::vectorize...>(),\n                   make_index_sequence<NVectorized>());\n    }\n\nprivate:\n    remove_reference_t<Func> f;\n\n    // Internal compiler error in MSVC 19.16.27025.1 (Visual Studio 2017 15.9.4), when compiling\n    // with \"/permissive-\" flag when arg_call_types is manually inlined.\n    using arg_call_types = std::tuple<typename vectorize_arg<Args>::call_type...>;\n    template <size_t Index>\n    using param_n_t = typename std::tuple_element<Index, arg_call_types>::type;\n\n    using returned_array = vectorize_returned_array<Func, Return, Args...>;\n\n    // Runs a vectorized function given arguments tuple and three index sequences:\n    //     - Index is the full set of 0 ... (N-1) argument indices;\n    //     - VIndex is the subset of argument indices with vectorized parameters, letting us access\n    //       vectorized arguments (anything not in this sequence is passed through)\n    //     - BIndex is a incremental sequence (beginning at 0) of the same size as VIndex, so that\n    //       we can store vectorized buffer_infos in an array (argument VIndex has its buffer at\n    //       index BIndex in the array).\n    template <size_t... Index, size_t... VIndex, size_t... BIndex>\n    object run(typename vectorize_arg<Args>::type &...args,\n               index_sequence<Index...> i_seq,\n               index_sequence<VIndex...> vi_seq,\n               index_sequence<BIndex...> bi_seq) {\n\n        // Pointers to values the function was called with; the vectorized ones set here will start\n        // out as array_t<T> pointers, but they will be changed them to T pointers before we make\n        // call the wrapped function.  Non-vectorized pointers are left as-is.\n        std::array<void *, N> params{{reinterpret_cast<void *>(&args)...}};\n\n        // The array of `buffer_info`s of vectorized arguments:\n        std::array<buffer_info, NVectorized> buffers{\n            {reinterpret_cast<array *>(params[VIndex])->request()...}};\n\n        /* Determine dimensions parameters of output array */\n        ssize_t nd = 0;\n        std::vector<ssize_t> shape(0);\n        auto trivial = broadcast(buffers, nd, shape);\n        auto ndim = (size_t) nd;\n\n        size_t size\n            = std::accumulate(shape.begin(), shape.end(), (size_t) 1, std::multiplies<size_t>());\n\n        // If all arguments are 0-dimension arrays (i.e. single values) return a plain value (i.e.\n        // not wrapped in an array).\n        if (size == 1 && ndim == 0) {\n            PYBIND11_EXPAND_SIDE_EFFECTS(params[VIndex] = buffers[BIndex].ptr);\n            return cast(\n                returned_array::call(f, *reinterpret_cast<param_n_t<Index> *>(params[Index])...));\n        }\n\n        auto result = returned_array::create(trivial, shape);\n\n        PYBIND11_WARNING_PUSH\n#ifdef PYBIND11_DETECTED_CLANG_WITH_MISLEADING_CALL_STD_MOVE_EXPLICITLY_WARNING\n        PYBIND11_WARNING_DISABLE_CLANG(\"-Wreturn-std-move\")\n#endif\n\n        if (size == 0) {\n            return result;\n        }\n\n        /* Call the function */\n        auto *mutable_data = returned_array::mutable_data(result);\n        if (trivial == broadcast_trivial::non_trivial) {\n            apply_broadcast(buffers, params, mutable_data, size, shape, i_seq, vi_seq, bi_seq);\n        } else {\n            apply_trivial(buffers, params, mutable_data, size, i_seq, vi_seq, bi_seq);\n        }\n\n        return result;\n        PYBIND11_WARNING_POP\n    }\n\n    template <size_t... Index, size_t... VIndex, size_t... BIndex>\n    void apply_trivial(std::array<buffer_info, NVectorized> &buffers,\n                       std::array<void *, N> &params,\n                       Return *out,\n                       size_t size,\n                       index_sequence<Index...>,\n                       index_sequence<VIndex...>,\n                       index_sequence<BIndex...>) {\n\n        // Initialize an array of mutable byte references and sizes with references set to the\n        // appropriate pointer in `params`; as we iterate, we'll increment each pointer by its size\n        // (except for singletons, which get an increment of 0).\n        std::array<std::pair<unsigned char *&, const size_t>, NVectorized> vecparams{\n            {std::pair<unsigned char *&, const size_t>(\n                reinterpret_cast<unsigned char *&>(params[VIndex] = buffers[BIndex].ptr),\n                buffers[BIndex].size == 1 ? 0 : sizeof(param_n_t<VIndex>))...}};\n\n        for (size_t i = 0; i < size; ++i) {\n            returned_array::call(\n                out, i, f, *reinterpret_cast<param_n_t<Index> *>(params[Index])...);\n            for (auto &x : vecparams) {\n                x.first += x.second;\n            }\n        }\n    }\n\n    template <size_t... Index, size_t... VIndex, size_t... BIndex>\n    void apply_broadcast(std::array<buffer_info, NVectorized> &buffers,\n                         std::array<void *, N> &params,\n                         Return *out,\n                         size_t size,\n                         const std::vector<ssize_t> &output_shape,\n                         index_sequence<Index...>,\n                         index_sequence<VIndex...>,\n                         index_sequence<BIndex...>) {\n\n        multi_array_iterator<NVectorized> input_iter(buffers, output_shape);\n\n        for (size_t i = 0; i < size; ++i, ++input_iter) {\n            PYBIND11_EXPAND_SIDE_EFFECTS((params[VIndex] = input_iter.template data<BIndex>()));\n            returned_array::call(\n                out, i, f, *reinterpret_cast<param_n_t<Index> *>(std::get<Index>(params))...);\n        }\n    }\n};\n\ntemplate <typename Func, typename Return, typename... Args>\nvectorize_helper<Func, Return, Args...> vectorize_extractor(const Func &f, Return (*)(Args...)) {\n    return detail::vectorize_helper<Func, Return, Args...>(f);\n}\n\ntemplate <typename T, int Flags>\nstruct handle_type_name<array_t<T, Flags>> {\n    static constexpr auto name\n        = const_name(\"numpy.ndarray[\") + npy_format_descriptor<T>::name + const_name(\"]\");\n};\n\nPYBIND11_NAMESPACE_END(detail)\n\n// Vanilla pointer vectorizer:\ntemplate <typename Return, typename... Args>\ndetail::vectorize_helper<Return (*)(Args...), Return, Args...> vectorize(Return (*f)(Args...)) {\n    return detail::vectorize_helper<Return (*)(Args...), Return, Args...>(f);\n}\n\n// lambda vectorizer:\ntemplate <typename Func, detail::enable_if_t<detail::is_lambda<Func>::value, int> = 0>\nauto vectorize(Func &&f)\n    -> decltype(detail::vectorize_extractor(std::forward<Func>(f),\n                                            (detail::function_signature_t<Func> *) nullptr)) {\n    return detail::vectorize_extractor(std::forward<Func>(f),\n                                       (detail::function_signature_t<Func> *) nullptr);\n}\n\n// Vectorize a class method (non-const):\ntemplate <typename Return,\n          typename Class,\n          typename... Args,\n          typename Helper = detail::vectorize_helper<\n              decltype(std::mem_fn(std::declval<Return (Class::*)(Args...)>())),\n              Return,\n              Class *,\n              Args...>>\nHelper vectorize(Return (Class::*f)(Args...)) {\n    return Helper(std::mem_fn(f));\n}\n\n// Vectorize a class method (const):\ntemplate <typename Return,\n          typename Class,\n          typename... Args,\n          typename Helper = detail::vectorize_helper<\n              decltype(std::mem_fn(std::declval<Return (Class::*)(Args...) const>())),\n              Return,\n              const Class *,\n              Args...>>\nHelper vectorize(Return (Class::*f)(Args...) const) {\n    return Helper(std::mem_fn(f));\n}\n\nPYBIND11_NAMESPACE_END(PYBIND11_NAMESPACE)\n"
  },
  {
    "path": "libs/pybind11/include/pybind11/operators.h",
    "content": "/*\n    pybind11/operator.h: Metatemplates for operator overloading\n\n    Copyright (c) 2016 Wenzel Jakob <wenzel.jakob@epfl.ch>\n\n    All rights reserved. Use of this source code is governed by a\n    BSD-style license that can be found in the LICENSE file.\n*/\n\n#pragma once\n\n#include \"pybind11.h\"\n\nPYBIND11_NAMESPACE_BEGIN(PYBIND11_NAMESPACE)\nPYBIND11_NAMESPACE_BEGIN(detail)\n\n/// Enumeration with all supported operator types\nenum op_id : int {\n    op_add,\n    op_sub,\n    op_mul,\n    op_div,\n    op_mod,\n    op_divmod,\n    op_pow,\n    op_lshift,\n    op_rshift,\n    op_and,\n    op_xor,\n    op_or,\n    op_neg,\n    op_pos,\n    op_abs,\n    op_invert,\n    op_int,\n    op_long,\n    op_float,\n    op_str,\n    op_cmp,\n    op_gt,\n    op_ge,\n    op_lt,\n    op_le,\n    op_eq,\n    op_ne,\n    op_iadd,\n    op_isub,\n    op_imul,\n    op_idiv,\n    op_imod,\n    op_ilshift,\n    op_irshift,\n    op_iand,\n    op_ixor,\n    op_ior,\n    op_complex,\n    op_bool,\n    op_nonzero,\n    op_repr,\n    op_truediv,\n    op_itruediv,\n    op_hash\n};\n\nenum op_type : int {\n    op_l, /* base type on left */\n    op_r, /* base type on right */\n    op_u  /* unary operator */\n};\n\nstruct self_t {};\nstatic const self_t self = self_t();\n\n/// Type for an unused type slot\nstruct undefined_t {};\n\n/// Don't warn about an unused variable\ninline self_t __self() { return self; }\n\n/// base template of operator implementations\ntemplate <op_id, op_type, typename B, typename L, typename R>\nstruct op_impl {};\n\n/// Operator implementation generator\ntemplate <op_id id, op_type ot, typename L, typename R>\nstruct op_ {\n    static constexpr bool op_enable_if_hook = true;\n    template <typename Class, typename... Extra>\n    void execute(Class &cl, const Extra &...extra) const {\n        using Base = typename Class::type;\n        using L_type = conditional_t<std::is_same<L, self_t>::value, Base, L>;\n        using R_type = conditional_t<std::is_same<R, self_t>::value, Base, R>;\n        using op = op_impl<id, ot, Base, L_type, R_type>;\n        cl.def(op::name(), &op::execute, is_operator(), extra...);\n    }\n    template <typename Class, typename... Extra>\n    void execute_cast(Class &cl, const Extra &...extra) const {\n        using Base = typename Class::type;\n        using L_type = conditional_t<std::is_same<L, self_t>::value, Base, L>;\n        using R_type = conditional_t<std::is_same<R, self_t>::value, Base, R>;\n        using op = op_impl<id, ot, Base, L_type, R_type>;\n        cl.def(op::name(), &op::execute_cast, is_operator(), extra...);\n    }\n};\n\n#define PYBIND11_BINARY_OPERATOR(id, rid, op, expr)                                               \\\n    template <typename B, typename L, typename R>                                                 \\\n    struct op_impl<op_##id, op_l, B, L, R> {                                                      \\\n        static char const *name() { return \"__\" #id \"__\"; }                                       \\\n        static auto execute(const L &l, const R &r) -> decltype(expr) { return (expr); }          \\\n        static B execute_cast(const L &l, const R &r) { return B(expr); }                         \\\n    };                                                                                            \\\n    template <typename B, typename L, typename R>                                                 \\\n    struct op_impl<op_##id, op_r, B, L, R> {                                                      \\\n        static char const *name() { return \"__\" #rid \"__\"; }                                      \\\n        static auto execute(const R &r, const L &l) -> decltype(expr) { return (expr); }          \\\n        static B execute_cast(const R &r, const L &l) { return B(expr); }                         \\\n    };                                                                                            \\\n    inline op_<op_##id, op_l, self_t, self_t> op(const self_t &, const self_t &) {                \\\n        return op_<op_##id, op_l, self_t, self_t>();                                              \\\n    }                                                                                             \\\n    template <typename T>                                                                         \\\n    op_<op_##id, op_l, self_t, T> op(const self_t &, const T &) {                                 \\\n        return op_<op_##id, op_l, self_t, T>();                                                   \\\n    }                                                                                             \\\n    template <typename T>                                                                         \\\n    op_<op_##id, op_r, T, self_t> op(const T &, const self_t &) {                                 \\\n        return op_<op_##id, op_r, T, self_t>();                                                   \\\n    }\n\n#define PYBIND11_INPLACE_OPERATOR(id, op, expr)                                                   \\\n    template <typename B, typename L, typename R>                                                 \\\n    struct op_impl<op_##id, op_l, B, L, R> {                                                      \\\n        static char const *name() { return \"__\" #id \"__\"; }                                       \\\n        static auto execute(L &l, const R &r) -> decltype(expr) { return expr; }                  \\\n        static B execute_cast(L &l, const R &r) { return B(expr); }                               \\\n    };                                                                                            \\\n    template <typename T>                                                                         \\\n    op_<op_##id, op_l, self_t, T> op(const self_t &, const T &) {                                 \\\n        return op_<op_##id, op_l, self_t, T>();                                                   \\\n    }\n\n#define PYBIND11_UNARY_OPERATOR(id, op, expr)                                                     \\\n    template <typename B, typename L>                                                             \\\n    struct op_impl<op_##id, op_u, B, L, undefined_t> {                                            \\\n        static char const *name() { return \"__\" #id \"__\"; }                                       \\\n        static auto execute(const L &l) -> decltype(expr) { return expr; }                        \\\n        static B execute_cast(const L &l) { return B(expr); }                                     \\\n    };                                                                                            \\\n    inline op_<op_##id, op_u, self_t, undefined_t> op(const self_t &) {                           \\\n        return op_<op_##id, op_u, self_t, undefined_t>();                                         \\\n    }\n\nPYBIND11_BINARY_OPERATOR(sub, rsub, operator-, l - r)\nPYBIND11_BINARY_OPERATOR(add, radd, operator+, l + r)\nPYBIND11_BINARY_OPERATOR(mul, rmul, operator*, l *r)\nPYBIND11_BINARY_OPERATOR(truediv, rtruediv, operator/, l / r)\nPYBIND11_BINARY_OPERATOR(mod, rmod, operator%, l % r)\nPYBIND11_BINARY_OPERATOR(lshift, rlshift, operator<<, l << r)\nPYBIND11_BINARY_OPERATOR(rshift, rrshift, operator>>, l >> r)\nPYBIND11_BINARY_OPERATOR(and, rand, operator&, l &r)\nPYBIND11_BINARY_OPERATOR(xor, rxor, operator^, l ^ r)\nPYBIND11_BINARY_OPERATOR(eq, eq, operator==, l == r)\nPYBIND11_BINARY_OPERATOR(ne, ne, operator!=, l != r)\nPYBIND11_BINARY_OPERATOR(or, ror, operator|, l | r)\nPYBIND11_BINARY_OPERATOR(gt, lt, operator>, l > r)\nPYBIND11_BINARY_OPERATOR(ge, le, operator>=, l >= r)\nPYBIND11_BINARY_OPERATOR(lt, gt, operator<, l < r)\nPYBIND11_BINARY_OPERATOR(le, ge, operator<=, l <= r)\n// PYBIND11_BINARY_OPERATOR(pow,       rpow,         pow,          std::pow(l,  r))\nPYBIND11_INPLACE_OPERATOR(iadd, operator+=, l += r)\nPYBIND11_INPLACE_OPERATOR(isub, operator-=, l -= r)\nPYBIND11_INPLACE_OPERATOR(imul, operator*=, l *= r)\nPYBIND11_INPLACE_OPERATOR(itruediv, operator/=, l /= r)\nPYBIND11_INPLACE_OPERATOR(imod, operator%=, l %= r)\nPYBIND11_INPLACE_OPERATOR(ilshift, operator<<=, l <<= r)\nPYBIND11_INPLACE_OPERATOR(irshift, operator>>=, l >>= r)\nPYBIND11_INPLACE_OPERATOR(iand, operator&=, l &= r)\nPYBIND11_INPLACE_OPERATOR(ixor, operator^=, l ^= r)\nPYBIND11_INPLACE_OPERATOR(ior, operator|=, l |= r)\nPYBIND11_UNARY_OPERATOR(neg, operator-, -l)\nPYBIND11_UNARY_OPERATOR(pos, operator+, +l)\n// WARNING: This usage of `abs` should only be done for existing STL overloads.\n// Adding overloads directly in to the `std::` namespace is advised against:\n// https://en.cppreference.com/w/cpp/language/extending_std\nPYBIND11_UNARY_OPERATOR(abs, abs, std::abs(l))\nPYBIND11_UNARY_OPERATOR(hash, hash, std::hash<L>()(l))\nPYBIND11_UNARY_OPERATOR(invert, operator~, (~l))\nPYBIND11_UNARY_OPERATOR(bool, operator!, !!l)\nPYBIND11_UNARY_OPERATOR(int, int_, (int) l)\nPYBIND11_UNARY_OPERATOR(float, float_, (double) l)\n\n#undef PYBIND11_BINARY_OPERATOR\n#undef PYBIND11_INPLACE_OPERATOR\n#undef PYBIND11_UNARY_OPERATOR\nPYBIND11_NAMESPACE_END(detail)\n\nusing detail::self;\n// Add named operators so that they are accessible via `py::`.\nusing detail::hash;\n\nPYBIND11_NAMESPACE_END(PYBIND11_NAMESPACE)\n"
  },
  {
    "path": "libs/pybind11/include/pybind11/options.h",
    "content": "/*\n    pybind11/options.h: global settings that are configurable at runtime.\n\n    Copyright (c) 2016 Wenzel Jakob <wenzel.jakob@epfl.ch>\n\n    All rights reserved. Use of this source code is governed by a\n    BSD-style license that can be found in the LICENSE file.\n*/\n\n#pragma once\n\n#include \"detail/common.h\"\n\nPYBIND11_NAMESPACE_BEGIN(PYBIND11_NAMESPACE)\n\nclass options {\npublic:\n    // Default RAII constructor, which leaves settings as they currently are.\n    options() : previous_state(global_state()) {}\n\n    // Class is non-copyable.\n    options(const options &) = delete;\n    options &operator=(const options &) = delete;\n\n    // Destructor, which restores settings that were in effect before.\n    ~options() { global_state() = previous_state; }\n\n    // Setter methods (affect the global state):\n\n    options &disable_user_defined_docstrings() & {\n        global_state().show_user_defined_docstrings = false;\n        return *this;\n    }\n\n    options &enable_user_defined_docstrings() & {\n        global_state().show_user_defined_docstrings = true;\n        return *this;\n    }\n\n    options &disable_function_signatures() & {\n        global_state().show_function_signatures = false;\n        return *this;\n    }\n\n    options &enable_function_signatures() & {\n        global_state().show_function_signatures = true;\n        return *this;\n    }\n\n    options &disable_enum_members_docstring() & {\n        global_state().show_enum_members_docstring = false;\n        return *this;\n    }\n\n    options &enable_enum_members_docstring() & {\n        global_state().show_enum_members_docstring = true;\n        return *this;\n    }\n\n    // Getter methods (return the global state):\n\n    static bool show_user_defined_docstrings() {\n        return global_state().show_user_defined_docstrings;\n    }\n\n    static bool show_function_signatures() { return global_state().show_function_signatures; }\n\n    static bool show_enum_members_docstring() {\n        return global_state().show_enum_members_docstring;\n    }\n\n    // This type is not meant to be allocated on the heap.\n    void *operator new(size_t) = delete;\n\nprivate:\n    struct state {\n        bool show_user_defined_docstrings = true; //< Include user-supplied texts in docstrings.\n        bool show_function_signatures = true;     //< Include auto-generated function signatures\n                                                  //  in docstrings.\n        bool show_enum_members_docstring = true;  //< Include auto-generated member list in enum\n                                                  //  docstrings.\n    };\n\n    static state &global_state() {\n        static state instance;\n        return instance;\n    }\n\n    state previous_state;\n};\n\nPYBIND11_NAMESPACE_END(PYBIND11_NAMESPACE)\n"
  },
  {
    "path": "libs/pybind11/include/pybind11/pybind11.h",
    "content": "/*\n    pybind11/pybind11.h: Main header file of the C++11 python\n    binding generator library\n\n    Copyright (c) 2016 Wenzel Jakob <wenzel.jakob@epfl.ch>\n\n    All rights reserved. Use of this source code is governed by a\n    BSD-style license that can be found in the LICENSE file.\n*/\n\n#pragma once\n#include \"detail/class.h\"\n#include \"detail/exception_translation.h\"\n#include \"detail/init.h\"\n#include \"attr.h\"\n#include \"gil.h\"\n#include \"gil_safe_call_once.h\"\n#include \"options.h\"\n#include \"typing.h\"\n\n#include <cstdlib>\n#include <cstring>\n#include <memory>\n#include <new>\n#include <string>\n#include <utility>\n#include <vector>\n\n#if defined(__cpp_lib_launder) && !(defined(_MSC_VER) && (_MSC_VER < 1914))\n#    define PYBIND11_STD_LAUNDER std::launder\n#    define PYBIND11_HAS_STD_LAUNDER 1\n#else\n#    define PYBIND11_STD_LAUNDER\n#    define PYBIND11_HAS_STD_LAUNDER 0\n#endif\n#if defined(__GNUG__) && !defined(__clang__)\n#    include <cxxabi.h>\n#endif\n\nPYBIND11_NAMESPACE_BEGIN(PYBIND11_NAMESPACE)\n\n/* https://stackoverflow.com/questions/46798456/handling-gccs-noexcept-type-warning\n   This warning is about ABI compatibility, not code health.\n   It is only actually needed in a couple places, but apparently GCC 7 \"generates this warning if\n   and only if the first template instantiation ... involves noexcept\" [stackoverflow], therefore\n   it could get triggered from seemingly random places, depending on user code.\n   No other GCC version generates this warning.\n */\n#if defined(__GNUC__) && __GNUC__ == 7\nPYBIND11_WARNING_DISABLE_GCC(\"-Wnoexcept-type\")\n#endif\n\nPYBIND11_WARNING_DISABLE_MSVC(4127)\n\nPYBIND11_NAMESPACE_BEGIN(detail)\n\ninline std::string replace_newlines_and_squash(const char *text) {\n    const char *whitespaces = \" \\t\\n\\r\\f\\v\";\n    std::string result(text);\n    bool previous_is_whitespace = false;\n\n    if (result.size() >= 2) {\n        // Do not modify string representations\n        char first_char = result[0];\n        char last_char = result[result.size() - 1];\n        if (first_char == last_char && first_char == '\\'') {\n            return result;\n        }\n    }\n    result.clear();\n\n    // Replace characters in whitespaces array with spaces and squash consecutive spaces\n    while (*text != '\\0') {\n        if (std::strchr(whitespaces, *text)) {\n            if (!previous_is_whitespace) {\n                result += ' ';\n                previous_is_whitespace = true;\n            }\n        } else {\n            result += *text;\n            previous_is_whitespace = false;\n        }\n        ++text;\n    }\n\n    // Strip leading and trailing whitespaces\n    const size_t str_begin = result.find_first_not_of(whitespaces);\n    if (str_begin == std::string::npos) {\n        return \"\";\n    }\n\n    const size_t str_end = result.find_last_not_of(whitespaces);\n    const size_t str_range = str_end - str_begin + 1;\n\n    return result.substr(str_begin, str_range);\n}\n\n#if defined(_MSC_VER)\n#    define PYBIND11_COMPAT_STRDUP _strdup\n#else\n#    define PYBIND11_COMPAT_STRDUP strdup\n#endif\n\nPYBIND11_NAMESPACE_END(detail)\n\n/// Wraps an arbitrary C++ function/method/lambda function/.. into a callable Python object\nclass cpp_function : public function {\npublic:\n    cpp_function() = default;\n    // NOLINTNEXTLINE(google-explicit-constructor)\n    cpp_function(std::nullptr_t) {}\n    cpp_function(std::nullptr_t, const is_setter &) {}\n\n    /// Construct a cpp_function from a vanilla function pointer\n    template <typename Return, typename... Args, typename... Extra>\n    // NOLINTNEXTLINE(google-explicit-constructor)\n    cpp_function(Return (*f)(Args...), const Extra &...extra) {\n        initialize(f, f, extra...);\n    }\n\n    /// Construct a cpp_function from a lambda function (possibly with internal state)\n    template <typename Func,\n              typename... Extra,\n              typename = detail::enable_if_t<detail::is_lambda<Func>::value>>\n    // NOLINTNEXTLINE(google-explicit-constructor)\n    cpp_function(Func &&f, const Extra &...extra) {\n        initialize(\n            std::forward<Func>(f), (detail::function_signature_t<Func> *) nullptr, extra...);\n    }\n\n    /// Construct a cpp_function from a class method (non-const, no ref-qualifier)\n    template <typename Return, typename Class, typename... Arg, typename... Extra>\n    // NOLINTNEXTLINE(google-explicit-constructor)\n    cpp_function(Return (Class::*f)(Arg...), const Extra &...extra) {\n        initialize(\n            [f](Class *c, Arg... args) -> Return { return (c->*f)(std::forward<Arg>(args)...); },\n            (Return(*)(Class *, Arg...)) nullptr,\n            extra...);\n    }\n\n    /// Construct a cpp_function from a class method (non-const, lvalue ref-qualifier)\n    /// A copy of the overload for non-const functions without explicit ref-qualifier\n    /// but with an added `&`.\n    template <typename Return, typename Class, typename... Arg, typename... Extra>\n    // NOLINTNEXTLINE(google-explicit-constructor)\n    cpp_function(Return (Class::*f)(Arg...) &, const Extra &...extra) {\n        initialize(\n            [f](Class *c, Arg... args) -> Return { return (c->*f)(std::forward<Arg>(args)...); },\n            (Return(*)(Class *, Arg...)) nullptr,\n            extra...);\n    }\n\n    /// Construct a cpp_function from a class method (const, no ref-qualifier)\n    template <typename Return, typename Class, typename... Arg, typename... Extra>\n    // NOLINTNEXTLINE(google-explicit-constructor)\n    cpp_function(Return (Class::*f)(Arg...) const, const Extra &...extra) {\n        initialize([f](const Class *c,\n                       Arg... args) -> Return { return (c->*f)(std::forward<Arg>(args)...); },\n                   (Return(*)(const Class *, Arg...)) nullptr,\n                   extra...);\n    }\n\n    /// Construct a cpp_function from a class method (const, lvalue ref-qualifier)\n    /// A copy of the overload for const functions without explicit ref-qualifier\n    /// but with an added `&`.\n    template <typename Return, typename Class, typename... Arg, typename... Extra>\n    // NOLINTNEXTLINE(google-explicit-constructor)\n    cpp_function(Return (Class::*f)(Arg...) const &, const Extra &...extra) {\n        initialize([f](const Class *c,\n                       Arg... args) -> Return { return (c->*f)(std::forward<Arg>(args)...); },\n                   (Return(*)(const Class *, Arg...)) nullptr,\n                   extra...);\n    }\n\n    /// Return the function name\n    object name() const { return attr(\"__name__\"); }\n\nprotected:\n    struct InitializingFunctionRecordDeleter {\n        // `destruct(function_record, false)`: `initialize_generic` copies strings and\n        // takes care of cleaning up in case of exceptions. So pass `false` to `free_strings`.\n        void operator()(detail::function_record *rec) { destruct(rec, false); }\n    };\n    using unique_function_record\n        = std::unique_ptr<detail::function_record, InitializingFunctionRecordDeleter>;\n\n    /// Space optimization: don't inline this frequently instantiated fragment\n    PYBIND11_NOINLINE unique_function_record make_function_record() {\n        return unique_function_record(new detail::function_record());\n    }\n\n    /// Special internal constructor for functors, lambda functions, etc.\n    template <typename Func, typename Return, typename... Args, typename... Extra>\n    void initialize(Func &&f, Return (*)(Args...), const Extra &...extra) {\n        using namespace detail;\n        struct capture {\n            remove_reference_t<Func> f;\n        };\n\n        /* Store the function including any extra state it might have (e.g. a lambda capture\n         * object) */\n        // The unique_ptr makes sure nothing is leaked in case of an exception.\n        auto unique_rec = make_function_record();\n        auto *rec = unique_rec.get();\n\n        /* Store the capture object directly in the function record if there is enough space */\n        if (sizeof(capture) <= sizeof(rec->data)) {\n            /* Without these pragmas, GCC warns that there might not be\n               enough space to use the placement new operator. However, the\n               'if' statement above ensures that this is the case. */\n            PYBIND11_WARNING_PUSH\n\n#if defined(__GNUG__) && __GNUC__ >= 6\n            PYBIND11_WARNING_DISABLE_GCC(\"-Wplacement-new\")\n#endif\n\n            new ((capture *) &rec->data) capture{std::forward<Func>(f)};\n\n#if !PYBIND11_HAS_STD_LAUNDER\n            PYBIND11_WARNING_DISABLE_GCC(\"-Wstrict-aliasing\")\n#endif\n\n            // UB without std::launder, but without breaking ABI and/or\n            // a significant refactoring it's \"impossible\" to solve.\n            if (!std::is_trivially_destructible<capture>::value) {\n                rec->free_data = [](function_record *r) {\n                    auto data = PYBIND11_STD_LAUNDER((capture *) &r->data);\n                    (void) data;\n                    data->~capture();\n                };\n            }\n            PYBIND11_WARNING_POP\n        } else {\n            rec->data[0] = new capture{std::forward<Func>(f)};\n            rec->free_data = [](function_record *r) { delete ((capture *) r->data[0]); };\n        }\n\n        /* Type casters for the function arguments and return value */\n        using cast_in = argument_loader<Args...>;\n        using cast_out\n            = make_caster<conditional_t<std::is_void<Return>::value, void_type, Return>>;\n\n        static_assert(\n            expected_num_args<Extra...>(\n                sizeof...(Args), cast_in::args_pos >= 0, cast_in::has_kwargs),\n            \"The number of argument annotations does not match the number of function arguments\");\n\n        /* Dispatch code which converts function arguments and performs the actual function call */\n        rec->impl = [](function_call &call) -> handle {\n            cast_in args_converter;\n\n            /* Try to cast the function arguments into the C++ domain */\n            if (!args_converter.load_args(call)) {\n                return PYBIND11_TRY_NEXT_OVERLOAD;\n            }\n\n            /* Invoke call policy pre-call hook */\n            process_attributes<Extra...>::precall(call);\n\n            /* Get a pointer to the capture object */\n            const auto *data = (sizeof(capture) <= sizeof(call.func.data) ? &call.func.data\n                                                                          : call.func.data[0]);\n            auto *cap = const_cast<capture *>(reinterpret_cast<const capture *>(data));\n\n            /* Override policy for rvalues -- usually to enforce rvp::move on an rvalue */\n            return_value_policy policy\n                = return_value_policy_override<Return>::policy(call.func.policy);\n\n            /* Function scope guard -- defaults to the compile-to-nothing `void_type` */\n            using Guard = extract_guard_t<Extra...>;\n\n            /* Perform the function call */\n            handle result;\n            if (call.func.is_setter) {\n                (void) std::move(args_converter).template call<Return, Guard>(cap->f);\n                result = none().release();\n            } else {\n                result = cast_out::cast(\n                    std::move(args_converter).template call<Return, Guard>(cap->f),\n                    policy,\n                    call.parent);\n            }\n\n            /* Invoke call policy post-call hook */\n            process_attributes<Extra...>::postcall(call, result);\n\n            return result;\n        };\n\n        rec->nargs_pos = cast_in::args_pos >= 0\n                             ? static_cast<std::uint16_t>(cast_in::args_pos)\n                             : sizeof...(Args) - cast_in::has_kwargs; // Will get reduced more if\n                                                                      // we have a kw_only\n        rec->has_args = cast_in::args_pos >= 0;\n        rec->has_kwargs = cast_in::has_kwargs;\n\n        /* Process any user-provided function attributes */\n        process_attributes<Extra...>::init(extra..., rec);\n\n        {\n            constexpr bool has_kw_only_args = any_of<std::is_same<kw_only, Extra>...>::value,\n                           has_pos_only_args = any_of<std::is_same<pos_only, Extra>...>::value,\n                           has_arg_annotations = any_of<is_keyword<Extra>...>::value;\n            static_assert(has_arg_annotations || !has_kw_only_args,\n                          \"py::kw_only requires the use of argument annotations\");\n            static_assert(has_arg_annotations || !has_pos_only_args,\n                          \"py::pos_only requires the use of argument annotations (for docstrings \"\n                          \"and aligning the annotations to the argument)\");\n\n            static_assert(constexpr_sum(is_kw_only<Extra>::value...) <= 1,\n                          \"py::kw_only may be specified only once\");\n            static_assert(constexpr_sum(is_pos_only<Extra>::value...) <= 1,\n                          \"py::pos_only may be specified only once\");\n            constexpr auto kw_only_pos = constexpr_first<is_kw_only, Extra...>();\n            constexpr auto pos_only_pos = constexpr_first<is_pos_only, Extra...>();\n            static_assert(!(has_kw_only_args && has_pos_only_args) || pos_only_pos < kw_only_pos,\n                          \"py::pos_only must come before py::kw_only\");\n        }\n\n        /* Generate a readable signature describing the function's arguments and return\n           value types */\n        static constexpr auto signature\n            = const_name(\"(\") + cast_in::arg_names + const_name(\") -> \") + cast_out::name;\n        PYBIND11_DESCR_CONSTEXPR auto types = decltype(signature)::types();\n\n        /* Register the function with Python from generic (non-templated) code */\n        // Pass on the ownership over the `unique_rec` to `initialize_generic`. `rec` stays valid.\n        initialize_generic(std::move(unique_rec), signature.text, types.data(), sizeof...(Args));\n\n        /* Stash some additional information used by an important optimization in 'functional.h' */\n        using FunctionType = Return (*)(Args...);\n        constexpr bool is_function_ptr\n            = std::is_convertible<Func, FunctionType>::value && sizeof(capture) == sizeof(void *);\n        if (is_function_ptr) {\n            rec->is_stateless = true;\n            rec->data[1]\n                = const_cast<void *>(reinterpret_cast<const void *>(&typeid(FunctionType)));\n        }\n    }\n\n    // Utility class that keeps track of all duplicated strings, and cleans them up in its\n    // destructor, unless they are released. Basically a RAII-solution to deal with exceptions\n    // along the way.\n    class strdup_guard {\n    public:\n        strdup_guard() = default;\n        strdup_guard(const strdup_guard &) = delete;\n        strdup_guard &operator=(const strdup_guard &) = delete;\n\n        ~strdup_guard() {\n            for (auto *s : strings) {\n                std::free(s);\n            }\n        }\n        char *operator()(const char *s) {\n            auto *t = PYBIND11_COMPAT_STRDUP(s);\n            strings.push_back(t);\n            return t;\n        }\n        void release() { strings.clear(); }\n\n    private:\n        std::vector<char *> strings;\n    };\n\n    /// Register a function call with Python (generic non-templated code goes here)\n    void initialize_generic(unique_function_record &&unique_rec,\n                            const char *text,\n                            const std::type_info *const *types,\n                            size_t args) {\n        // Do NOT receive `unique_rec` by value. If this function fails to move out the unique_ptr,\n        // we do not want this to destruct the pointer. `initialize` (the caller) still relies on\n        // the pointee being alive after this call. Only move out if a `capsule` is going to keep\n        // it alive.\n        auto *rec = unique_rec.get();\n\n        // Keep track of strdup'ed strings, and clean them up as long as the function's capsule\n        // has not taken ownership yet (when `unique_rec.release()` is called).\n        // Note: This cannot easily be fixed by a `unique_ptr` with custom deleter, because the\n        // strings are only referenced before strdup'ing. So only *after* the following block could\n        // `destruct` safely be called, but even then, `repr` could still throw in the middle of\n        // copying all strings.\n        strdup_guard guarded_strdup;\n\n        /* Create copies of all referenced C-style strings */\n        rec->name = guarded_strdup(rec->name ? rec->name : \"\");\n        if (rec->doc) {\n            rec->doc = guarded_strdup(rec->doc);\n        }\n        for (auto &a : rec->args) {\n            if (a.name) {\n                a.name = guarded_strdup(a.name);\n            }\n            if (a.descr) {\n                a.descr = guarded_strdup(a.descr);\n            } else if (a.value) {\n                a.descr = guarded_strdup(repr(a.value).cast<std::string>().c_str());\n            }\n        }\n\n        rec->is_constructor = (std::strcmp(rec->name, \"__init__\") == 0)\n                              || (std::strcmp(rec->name, \"__setstate__\") == 0);\n\n#if defined(PYBIND11_DETAILED_ERROR_MESSAGES) && !defined(PYBIND11_DISABLE_NEW_STYLE_INIT_WARNING)\n        if (rec->is_constructor && !rec->is_new_style_constructor) {\n            const auto class_name\n                = detail::get_fully_qualified_tp_name((PyTypeObject *) rec->scope.ptr());\n            const auto func_name = std::string(rec->name);\n            PyErr_WarnEx(PyExc_FutureWarning,\n                         (\"pybind11-bound class '\" + class_name\n                          + \"' is using an old-style \"\n                            \"placement-new '\"\n                          + func_name\n                          + \"' which has been deprecated. See \"\n                            \"the upgrade guide in pybind11's docs. This message is only visible \"\n                            \"when compiled in debug mode.\")\n                             .c_str(),\n                         0);\n        }\n#endif\n\n        /* Generate a proper function signature */\n        std::string signature;\n        size_t type_index = 0, arg_index = 0;\n        bool is_starred = false;\n        for (const auto *pc = text; *pc != '\\0'; ++pc) {\n            const auto c = *pc;\n\n            if (c == '{') {\n                // Write arg name for everything except *args and **kwargs.\n                is_starred = *(pc + 1) == '*';\n                if (is_starred) {\n                    continue;\n                }\n                // Separator for keyword-only arguments, placed before the kw\n                // arguments start (unless we are already putting an *args)\n                if (!rec->has_args && arg_index == rec->nargs_pos) {\n                    signature += \"*, \";\n                }\n                if (arg_index < rec->args.size() && rec->args[arg_index].name) {\n                    signature += rec->args[arg_index].name;\n                } else if (arg_index == 0 && rec->is_method) {\n                    signature += \"self\";\n                } else {\n                    signature += \"arg\" + std::to_string(arg_index - (rec->is_method ? 1 : 0));\n                }\n                signature += \": \";\n            } else if (c == '}') {\n                // Write default value if available.\n                if (!is_starred && arg_index < rec->args.size() && rec->args[arg_index].descr) {\n                    signature += \" = \";\n                    signature += detail::replace_newlines_and_squash(rec->args[arg_index].descr);\n                }\n                // Separator for positional-only arguments (placed after the\n                // argument, rather than before like *\n                if (rec->nargs_pos_only > 0 && (arg_index + 1) == rec->nargs_pos_only) {\n                    signature += \", /\";\n                }\n                if (!is_starred) {\n                    arg_index++;\n                }\n            } else if (c == '%') {\n                const std::type_info *t = types[type_index++];\n                if (!t) {\n                    pybind11_fail(\"Internal error while parsing type signature (1)\");\n                }\n                if (auto *tinfo = detail::get_type_info(*t)) {\n                    handle th((PyObject *) tinfo->type);\n                    signature += th.attr(\"__module__\").cast<std::string>() + \".\"\n                                 + th.attr(\"__qualname__\").cast<std::string>();\n                } else if (rec->is_new_style_constructor && arg_index == 0) {\n                    // A new-style `__init__` takes `self` as `value_and_holder`.\n                    // Rewrite it to the proper class type.\n                    signature += rec->scope.attr(\"__module__\").cast<std::string>() + \".\"\n                                 + rec->scope.attr(\"__qualname__\").cast<std::string>();\n                } else {\n                    signature += detail::quote_cpp_type_name(detail::clean_type_id(t->name()));\n                }\n            } else {\n                signature += c;\n            }\n        }\n\n        if (arg_index != args - rec->has_args - rec->has_kwargs || types[type_index] != nullptr) {\n            pybind11_fail(\"Internal error while parsing type signature (2)\");\n        }\n\n        rec->signature = guarded_strdup(signature.c_str());\n        rec->args.shrink_to_fit();\n        rec->nargs = (std::uint16_t) args;\n\n        if (rec->sibling && PYBIND11_INSTANCE_METHOD_CHECK(rec->sibling.ptr())) {\n            rec->sibling = PYBIND11_INSTANCE_METHOD_GET_FUNCTION(rec->sibling.ptr());\n        }\n\n        detail::function_record *chain = nullptr, *chain_start = rec;\n        if (rec->sibling) {\n            if (PyCFunction_Check(rec->sibling.ptr())) {\n                auto *self = PyCFunction_GET_SELF(rec->sibling.ptr());\n                if (!isinstance<capsule>(self)) {\n                    chain = nullptr;\n                } else {\n                    auto rec_capsule = reinterpret_borrow<capsule>(self);\n                    if (detail::is_function_record_capsule(rec_capsule)) {\n                        chain = rec_capsule.get_pointer<detail::function_record>();\n                        /* Never append a method to an overload chain of a parent class;\n                           instead, hide the parent's overloads in this case */\n                        if (!chain->scope.is(rec->scope)) {\n                            chain = nullptr;\n                        }\n                    } else {\n                        chain = nullptr;\n                    }\n                }\n            }\n            // Don't trigger for things like the default __init__, which are wrapper_descriptors\n            // that we are intentionally replacing\n            else if (!rec->sibling.is_none() && rec->name[0] != '_') {\n                pybind11_fail(\"Cannot overload existing non-function object \\\"\"\n                              + std::string(rec->name) + \"\\\" with a function of the same name\");\n            }\n        }\n\n        if (!chain) {\n            /* No existing overload was found, create a new function object */\n            rec->def = new PyMethodDef();\n            std::memset(rec->def, 0, sizeof(PyMethodDef));\n            rec->def->ml_name = rec->name;\n            rec->def->ml_meth\n                = reinterpret_cast<PyCFunction>(reinterpret_cast<void (*)()>(dispatcher));\n            rec->def->ml_flags = METH_VARARGS | METH_KEYWORDS;\n\n            capsule rec_capsule(unique_rec.release(),\n                                detail::get_function_record_capsule_name(),\n                                [](void *ptr) { destruct((detail::function_record *) ptr); });\n            guarded_strdup.release();\n\n            object scope_module;\n            if (rec->scope) {\n                if (hasattr(rec->scope, \"__module__\")) {\n                    scope_module = rec->scope.attr(\"__module__\");\n                } else if (hasattr(rec->scope, \"__name__\")) {\n                    scope_module = rec->scope.attr(\"__name__\");\n                }\n            }\n\n            m_ptr = PyCFunction_NewEx(rec->def, rec_capsule.ptr(), scope_module.ptr());\n            if (!m_ptr) {\n                pybind11_fail(\"cpp_function::cpp_function(): Could not allocate function object\");\n            }\n        } else {\n            /* Append at the beginning or end of the overload chain */\n            m_ptr = rec->sibling.ptr();\n            inc_ref();\n            if (chain->is_method != rec->is_method) {\n                pybind11_fail(\n                    \"overloading a method with both static and instance methods is not supported; \"\n#if !defined(PYBIND11_DETAILED_ERROR_MESSAGES)\n                    \"#define PYBIND11_DETAILED_ERROR_MESSAGES or compile in debug mode for more \"\n                    \"details\"\n#else\n                    \"error while attempting to bind \"\n                    + std::string(rec->is_method ? \"instance\" : \"static\") + \" method \"\n                    + std::string(pybind11::str(rec->scope.attr(\"__name__\"))) + \".\"\n                    + std::string(rec->name) + signature\n#endif\n                );\n            }\n\n            if (rec->prepend) {\n                // Beginning of chain; we need to replace the capsule's current head-of-the-chain\n                // pointer with this one, then make this one point to the previous head of the\n                // chain.\n                chain_start = rec;\n                rec->next = chain;\n                auto rec_capsule\n                    = reinterpret_borrow<capsule>(((PyCFunctionObject *) m_ptr)->m_self);\n                rec_capsule.set_pointer(unique_rec.release());\n                guarded_strdup.release();\n            } else {\n                // Or end of chain (normal behavior)\n                chain_start = chain;\n                while (chain->next) {\n                    chain = chain->next;\n                }\n                chain->next = unique_rec.release();\n                guarded_strdup.release();\n            }\n        }\n\n        std::string signatures;\n        int index = 0;\n        /* Create a nice pydoc rec including all signatures and\n           docstrings of the functions in the overload chain */\n        if (chain && options::show_function_signatures()\n            && std::strcmp(rec->name, \"_pybind11_conduit_v1_\") != 0) {\n            // First a generic signature\n            signatures += rec->name;\n            signatures += \"(*args, **kwargs)\\n\";\n            signatures += \"Overloaded function.\\n\\n\";\n        }\n        // Then specific overload signatures\n        bool first_user_def = true;\n        for (auto *it = chain_start; it != nullptr; it = it->next) {\n            if (options::show_function_signatures()\n                && std::strcmp(rec->name, \"_pybind11_conduit_v1_\") != 0) {\n                if (index > 0) {\n                    signatures += '\\n';\n                }\n                if (chain) {\n                    signatures += std::to_string(++index) + \". \";\n                }\n                signatures += rec->name;\n                signatures += it->signature;\n                signatures += '\\n';\n            }\n            if (it->doc && it->doc[0] != '\\0' && options::show_user_defined_docstrings()) {\n                // If we're appending another docstring, and aren't printing function signatures,\n                // we need to append a newline first:\n                if (!options::show_function_signatures()) {\n                    if (first_user_def) {\n                        first_user_def = false;\n                    } else {\n                        signatures += '\\n';\n                    }\n                }\n                if (options::show_function_signatures()) {\n                    signatures += '\\n';\n                }\n                signatures += it->doc;\n                if (options::show_function_signatures()) {\n                    signatures += '\\n';\n                }\n            }\n        }\n\n        /* Install docstring */\n        auto *func = (PyCFunctionObject *) m_ptr;\n        std::free(const_cast<char *>(func->m_ml->ml_doc));\n        // Install docstring if it's non-empty (when at least one option is enabled)\n        func->m_ml->ml_doc\n            = signatures.empty() ? nullptr : PYBIND11_COMPAT_STRDUP(signatures.c_str());\n\n        if (rec->is_method) {\n            m_ptr = PYBIND11_INSTANCE_METHOD_NEW(m_ptr, rec->scope.ptr());\n            if (!m_ptr) {\n                pybind11_fail(\n                    \"cpp_function::cpp_function(): Could not allocate instance method object\");\n            }\n            Py_DECREF(func);\n        }\n    }\n\n    /// When a cpp_function is GCed, release any memory allocated by pybind11\n    static void destruct(detail::function_record *rec, bool free_strings = true) {\n// If on Python 3.9, check the interpreter \"MICRO\" (patch) version.\n// If this is running on 3.9.0, we have to work around a bug.\n#if !defined(PYPY_VERSION) && PY_MAJOR_VERSION == 3 && PY_MINOR_VERSION == 9\n        static bool is_zero = Py_GetVersion()[4] == '0';\n#endif\n\n        while (rec) {\n            detail::function_record *next = rec->next;\n            if (rec->free_data) {\n                rec->free_data(rec);\n            }\n            // During initialization, these strings might not have been copied yet,\n            // so they cannot be freed. Once the function has been created, they can.\n            // Check `make_function_record` for more details.\n            if (free_strings) {\n                std::free((char *) rec->name);\n                std::free((char *) rec->doc);\n                std::free((char *) rec->signature);\n                for (auto &arg : rec->args) {\n                    std::free(const_cast<char *>(arg.name));\n                    std::free(const_cast<char *>(arg.descr));\n                }\n            }\n            for (auto &arg : rec->args) {\n                arg.value.dec_ref();\n            }\n            if (rec->def) {\n                std::free(const_cast<char *>(rec->def->ml_doc));\n// Python 3.9.0 decref's these in the wrong order; rec->def\n// If loaded on 3.9.0, let these leak (use Python 3.9.1 at runtime to fix)\n// See https://github.com/python/cpython/pull/22670\n#if !defined(PYPY_VERSION) && PY_MAJOR_VERSION == 3 && PY_MINOR_VERSION == 9\n                if (!is_zero) {\n                    delete rec->def;\n                }\n#else\n                delete rec->def;\n#endif\n            }\n            delete rec;\n            rec = next;\n        }\n    }\n\n    /// Main dispatch logic for calls to functions bound using pybind11\n    static PyObject *dispatcher(PyObject *self, PyObject *args_in, PyObject *kwargs_in) {\n        using namespace detail;\n        assert(isinstance<capsule>(self));\n\n        /* Iterator over the list of potentially admissible overloads */\n        const function_record *overloads = reinterpret_cast<function_record *>(\n                                  PyCapsule_GetPointer(self, get_function_record_capsule_name())),\n                              *current_overload = overloads;\n        assert(overloads != nullptr);\n\n        /* Need to know how many arguments + keyword arguments there are to pick the right\n           overload */\n        const auto n_args_in = (size_t) PyTuple_GET_SIZE(args_in);\n\n        handle parent = n_args_in > 0 ? PyTuple_GET_ITEM(args_in, 0) : nullptr,\n               result = PYBIND11_TRY_NEXT_OVERLOAD;\n\n        auto self_value_and_holder = value_and_holder();\n        if (overloads->is_constructor) {\n            if (!parent\n                || !PyObject_TypeCheck(parent.ptr(), (PyTypeObject *) overloads->scope.ptr())) {\n                set_error(PyExc_TypeError,\n                          \"__init__(self, ...) called with invalid or missing `self` argument\");\n                return nullptr;\n            }\n\n            auto *const tinfo = get_type_info((PyTypeObject *) overloads->scope.ptr());\n            auto *const pi = reinterpret_cast<instance *>(parent.ptr());\n            self_value_and_holder = pi->get_value_and_holder(tinfo, true);\n\n            // If this value is already registered it must mean __init__ is invoked multiple times;\n            // we really can't support that in C++, so just ignore the second __init__.\n            if (self_value_and_holder.instance_registered()) {\n                return none().release().ptr();\n            }\n        }\n\n        try {\n            // We do this in two passes: in the first pass, we load arguments with `convert=false`;\n            // in the second, we allow conversion (except for arguments with an explicit\n            // py::arg().noconvert()).  This lets us prefer calls without conversion, with\n            // conversion as a fallback.\n            std::vector<function_call> second_pass;\n\n            // However, if there are no overloads, we can just skip the no-convert pass entirely\n            const bool overloaded\n                = current_overload != nullptr && current_overload->next != nullptr;\n\n            for (; current_overload != nullptr; current_overload = current_overload->next) {\n\n                /* For each overload:\n                   1. Copy all positional arguments we were given, also checking to make sure that\n                      named positional arguments weren't *also* specified via kwarg.\n                   2. If we weren't given enough, try to make up the omitted ones by checking\n                      whether they were provided by a kwarg matching the `py::arg(\"name\")` name. If\n                      so, use it (and remove it from kwargs); if not, see if the function binding\n                      provided a default that we can use.\n                   3. Ensure that either all keyword arguments were \"consumed\", or that the\n                   function takes a kwargs argument to accept unconsumed kwargs.\n                   4. Any positional arguments still left get put into a tuple (for args), and any\n                      leftover kwargs get put into a dict.\n                   5. Pack everything into a vector; if we have py::args or py::kwargs, they are an\n                      extra tuple or dict at the end of the positional arguments.\n                   6. Call the function call dispatcher (function_record::impl)\n\n                   If one of these fail, move on to the next overload and keep trying until we get\n                   a result other than PYBIND11_TRY_NEXT_OVERLOAD.\n                 */\n\n                const function_record &func = *current_overload;\n                size_t num_args = func.nargs; // Number of positional arguments that we need\n                if (func.has_args) {\n                    --num_args; // (but don't count py::args\n                }\n                if (func.has_kwargs) {\n                    --num_args; //  or py::kwargs)\n                }\n                size_t pos_args = func.nargs_pos;\n\n                if (!func.has_args && n_args_in > pos_args) {\n                    continue; // Too many positional arguments for this overload\n                }\n\n                if (n_args_in < pos_args && func.args.size() < pos_args) {\n                    continue; // Not enough positional arguments given, and not enough defaults to\n                              // fill in the blanks\n                }\n\n                function_call call(func, parent);\n\n                // Protect std::min with parentheses\n                size_t args_to_copy = (std::min)(pos_args, n_args_in);\n                size_t args_copied = 0;\n\n                // 0. Inject new-style `self` argument\n                if (func.is_new_style_constructor) {\n                    // The `value` may have been preallocated by an old-style `__init__`\n                    // if it was a preceding candidate for overload resolution.\n                    if (self_value_and_holder) {\n                        self_value_and_holder.type->dealloc(self_value_and_holder);\n                    }\n\n                    call.init_self = PyTuple_GET_ITEM(args_in, 0);\n                    call.args.emplace_back(reinterpret_cast<PyObject *>(&self_value_and_holder));\n                    call.args_convert.push_back(false);\n                    ++args_copied;\n                }\n\n                // 1. Copy any position arguments given.\n                bool bad_arg = false;\n                for (; args_copied < args_to_copy; ++args_copied) {\n                    const argument_record *arg_rec\n                        = args_copied < func.args.size() ? &func.args[args_copied] : nullptr;\n                    if (kwargs_in && arg_rec && arg_rec->name\n                        && dict_getitemstring(kwargs_in, arg_rec->name)) {\n                        bad_arg = true;\n                        break;\n                    }\n\n                    handle arg(PyTuple_GET_ITEM(args_in, args_copied));\n                    if (arg_rec && !arg_rec->none && arg.is_none()) {\n                        bad_arg = true;\n                        break;\n                    }\n                    call.args.push_back(arg);\n                    call.args_convert.push_back(arg_rec ? arg_rec->convert : true);\n                }\n                if (bad_arg) {\n                    continue; // Maybe it was meant for another overload (issue #688)\n                }\n\n                // Keep track of how many position args we copied out in case we need to come back\n                // to copy the rest into a py::args argument.\n                size_t positional_args_copied = args_copied;\n\n                // We'll need to copy this if we steal some kwargs for defaults\n                dict kwargs = reinterpret_borrow<dict>(kwargs_in);\n\n                // 1.5. Fill in any missing pos_only args from defaults if they exist\n                if (args_copied < func.nargs_pos_only) {\n                    for (; args_copied < func.nargs_pos_only; ++args_copied) {\n                        const auto &arg_rec = func.args[args_copied];\n                        handle value;\n\n                        if (arg_rec.value) {\n                            value = arg_rec.value;\n                        }\n                        if (value) {\n                            call.args.push_back(value);\n                            call.args_convert.push_back(arg_rec.convert);\n                        } else {\n                            break;\n                        }\n                    }\n\n                    if (args_copied < func.nargs_pos_only) {\n                        continue; // Not enough defaults to fill the positional arguments\n                    }\n                }\n\n                // 2. Check kwargs and, failing that, defaults that may help complete the list\n                if (args_copied < num_args) {\n                    bool copied_kwargs = false;\n\n                    for (; args_copied < num_args; ++args_copied) {\n                        const auto &arg_rec = func.args[args_copied];\n\n                        handle value;\n                        if (kwargs_in && arg_rec.name) {\n                            value = dict_getitemstring(kwargs.ptr(), arg_rec.name);\n                        }\n\n                        if (value) {\n                            // Consume a kwargs value\n                            if (!copied_kwargs) {\n                                kwargs = reinterpret_steal<dict>(PyDict_Copy(kwargs.ptr()));\n                                copied_kwargs = true;\n                            }\n                            if (PyDict_DelItemString(kwargs.ptr(), arg_rec.name) == -1) {\n                                throw error_already_set();\n                            }\n                        } else if (arg_rec.value) {\n                            value = arg_rec.value;\n                        }\n\n                        if (!arg_rec.none && value.is_none()) {\n                            break;\n                        }\n\n                        if (value) {\n                            // If we're at the py::args index then first insert a stub for it to be\n                            // replaced later\n                            if (func.has_args && call.args.size() == func.nargs_pos) {\n                                call.args.push_back(none());\n                            }\n\n                            call.args.push_back(value);\n                            call.args_convert.push_back(arg_rec.convert);\n                        } else {\n                            break;\n                        }\n                    }\n\n                    if (args_copied < num_args) {\n                        continue; // Not enough arguments, defaults, or kwargs to fill the\n                                  // positional arguments\n                    }\n                }\n\n                // 3. Check everything was consumed (unless we have a kwargs arg)\n                if (kwargs && !kwargs.empty() && !func.has_kwargs) {\n                    continue; // Unconsumed kwargs, but no py::kwargs argument to accept them\n                }\n\n                // 4a. If we have a py::args argument, create a new tuple with leftovers\n                if (func.has_args) {\n                    tuple extra_args;\n                    if (args_to_copy == 0) {\n                        // We didn't copy out any position arguments from the args_in tuple, so we\n                        // can reuse it directly without copying:\n                        extra_args = reinterpret_borrow<tuple>(args_in);\n                    } else if (positional_args_copied >= n_args_in) {\n                        extra_args = tuple(0);\n                    } else {\n                        size_t args_size = n_args_in - positional_args_copied;\n                        extra_args = tuple(args_size);\n                        for (size_t i = 0; i < args_size; ++i) {\n                            extra_args[i] = PyTuple_GET_ITEM(args_in, positional_args_copied + i);\n                        }\n                    }\n                    if (call.args.size() <= func.nargs_pos) {\n                        call.args.push_back(extra_args);\n                    } else {\n                        call.args[func.nargs_pos] = extra_args;\n                    }\n                    call.args_convert.push_back(false);\n                    call.args_ref = std::move(extra_args);\n                }\n\n                // 4b. If we have a py::kwargs, pass on any remaining kwargs\n                if (func.has_kwargs) {\n                    if (!kwargs.ptr()) {\n                        kwargs = dict(); // If we didn't get one, send an empty one\n                    }\n                    call.args.push_back(kwargs);\n                    call.args_convert.push_back(false);\n                    call.kwargs_ref = std::move(kwargs);\n                }\n\n// 5. Put everything in a vector.  Not technically step 5, we've been building it\n// in `call.args` all along.\n#if defined(PYBIND11_DETAILED_ERROR_MESSAGES)\n                if (call.args.size() != func.nargs || call.args_convert.size() != func.nargs) {\n                    pybind11_fail(\"Internal error: function call dispatcher inserted wrong number \"\n                                  \"of arguments!\");\n                }\n#endif\n\n                std::vector<bool> second_pass_convert;\n                if (overloaded) {\n                    // We're in the first no-convert pass, so swap out the conversion flags for a\n                    // set of all-false flags.  If the call fails, we'll swap the flags back in for\n                    // the conversion-allowed call below.\n                    second_pass_convert.resize(func.nargs, false);\n                    call.args_convert.swap(second_pass_convert);\n                }\n\n                // 6. Call the function.\n                try {\n                    loader_life_support guard{};\n                    result = func.impl(call);\n                } catch (reference_cast_error &) {\n                    result = PYBIND11_TRY_NEXT_OVERLOAD;\n                }\n\n                if (result.ptr() != PYBIND11_TRY_NEXT_OVERLOAD) {\n                    break;\n                }\n\n                if (overloaded) {\n                    // The (overloaded) call failed; if the call has at least one argument that\n                    // permits conversion (i.e. it hasn't been explicitly specified `.noconvert()`)\n                    // then add this call to the list of second pass overloads to try.\n                    for (size_t i = func.is_method ? 1 : 0; i < pos_args; i++) {\n                        if (second_pass_convert[i]) {\n                            // Found one: swap the converting flags back in and store the call for\n                            // the second pass.\n                            call.args_convert.swap(second_pass_convert);\n                            second_pass.push_back(std::move(call));\n                            break;\n                        }\n                    }\n                }\n            }\n\n            if (overloaded && !second_pass.empty() && result.ptr() == PYBIND11_TRY_NEXT_OVERLOAD) {\n                // The no-conversion pass finished without success, try again with conversion\n                // allowed\n                for (auto &call : second_pass) {\n                    try {\n                        loader_life_support guard{};\n                        result = call.func.impl(call);\n                    } catch (reference_cast_error &) {\n                        result = PYBIND11_TRY_NEXT_OVERLOAD;\n                    }\n\n                    if (result.ptr() != PYBIND11_TRY_NEXT_OVERLOAD) {\n                        // The error reporting logic below expects 'current_overload' to be valid,\n                        // as it would be if we'd encountered this failure in the first-pass loop.\n                        if (!result) {\n                            current_overload = &call.func;\n                        }\n                        break;\n                    }\n                }\n            }\n        } catch (error_already_set &e) {\n            e.restore();\n            return nullptr;\n#ifdef __GLIBCXX__\n        } catch (abi::__forced_unwind &) {\n            throw;\n#endif\n        } catch (...) {\n            try_translate_exceptions();\n            return nullptr;\n        }\n\n        auto append_note_if_missing_header_is_suspected = [](std::string &msg) {\n            if (msg.find(\"std::\") != std::string::npos) {\n                msg += \"\\n\\n\"\n                       \"Did you forget to `#include <pybind11/stl.h>`? Or <pybind11/complex.h>,\\n\"\n                       \"<pybind11/functional.h>, <pybind11/chrono.h>, etc. Some automatic\\n\"\n                       \"conversions are optional and require extra headers to be included\\n\"\n                       \"when compiling your pybind11 module.\";\n            }\n        };\n\n        if (result.ptr() == PYBIND11_TRY_NEXT_OVERLOAD) {\n            if (overloads->is_operator) {\n                return handle(Py_NotImplemented).inc_ref().ptr();\n            }\n\n            std::string msg = std::string(overloads->name) + \"(): incompatible \"\n                              + std::string(overloads->is_constructor ? \"constructor\" : \"function\")\n                              + \" arguments. The following argument types are supported:\\n\";\n\n            int ctr = 0;\n            for (const function_record *it2 = overloads; it2 != nullptr; it2 = it2->next) {\n                msg += \"    \" + std::to_string(++ctr) + \". \";\n\n                bool wrote_sig = false;\n                if (overloads->is_constructor) {\n                    // For a constructor, rewrite `(self: Object, arg0, ...) -> NoneType` as\n                    // `Object(arg0, ...)`\n                    std::string sig = it2->signature;\n                    size_t start = sig.find('(') + 7; // skip \"(self: \"\n                    if (start < sig.size()) {\n                        // End at the , for the next argument\n                        size_t end = sig.find(\", \"), next = end + 2;\n                        size_t ret = sig.rfind(\" -> \");\n                        // Or the ), if there is no comma:\n                        if (end >= sig.size()) {\n                            next = end = sig.find(')');\n                        }\n                        if (start < end && next < sig.size()) {\n                            msg.append(sig, start, end - start);\n                            msg += '(';\n                            msg.append(sig, next, ret - next);\n                            wrote_sig = true;\n                        }\n                    }\n                }\n                if (!wrote_sig) {\n                    msg += it2->signature;\n                }\n\n                msg += '\\n';\n            }\n            msg += \"\\nInvoked with: \";\n            auto args_ = reinterpret_borrow<tuple>(args_in);\n            bool some_args = false;\n            for (size_t ti = overloads->is_constructor ? 1 : 0; ti < args_.size(); ++ti) {\n                if (!some_args) {\n                    some_args = true;\n                } else {\n                    msg += \", \";\n                }\n                try {\n                    msg += pybind11::repr(args_[ti]);\n                } catch (const error_already_set &) {\n                    msg += \"<repr raised Error>\";\n                }\n            }\n            if (kwargs_in) {\n                auto kwargs = reinterpret_borrow<dict>(kwargs_in);\n                if (!kwargs.empty()) {\n                    if (some_args) {\n                        msg += \"; \";\n                    }\n                    msg += \"kwargs: \";\n                    bool first = true;\n                    for (const auto &kwarg : kwargs) {\n                        if (first) {\n                            first = false;\n                        } else {\n                            msg += \", \";\n                        }\n                        msg += pybind11::str(\"{}=\").format(kwarg.first);\n                        try {\n                            msg += pybind11::repr(kwarg.second);\n                        } catch (const error_already_set &) {\n                            msg += \"<repr raised Error>\";\n                        }\n                    }\n                }\n            }\n\n            append_note_if_missing_header_is_suspected(msg);\n            // Attach additional error info to the exception if supported\n            if (PyErr_Occurred()) {\n                // #HelpAppreciated: unit test coverage for this branch.\n                raise_from(PyExc_TypeError, msg.c_str());\n                return nullptr;\n            }\n            set_error(PyExc_TypeError, msg.c_str());\n            return nullptr;\n        }\n        if (!result) {\n            std::string msg = \"Unable to convert function return value to a \"\n                              \"Python type! The signature was\\n\\t\";\n            assert(current_overload != nullptr);\n            msg += current_overload->signature;\n            append_note_if_missing_header_is_suspected(msg);\n            // Attach additional error info to the exception if supported\n            if (PyErr_Occurred()) {\n                raise_from(PyExc_TypeError, msg.c_str());\n                return nullptr;\n            }\n            set_error(PyExc_TypeError, msg.c_str());\n            return nullptr;\n        }\n        if (overloads->is_constructor && !self_value_and_holder.holder_constructed()) {\n            auto *pi = reinterpret_cast<instance *>(parent.ptr());\n            self_value_and_holder.type->init_instance(pi, nullptr);\n        }\n        return result.ptr();\n    }\n};\n\nPYBIND11_NAMESPACE_BEGIN(detail)\n\ntemplate <>\nstruct handle_type_name<cpp_function> {\n    static constexpr auto name = const_name(\"Callable\");\n};\n\nPYBIND11_NAMESPACE_END(detail)\n\n// Use to activate Py_MOD_GIL_NOT_USED.\nclass mod_gil_not_used {\npublic:\n    explicit mod_gil_not_used(bool flag = true) : flag_(flag) {}\n    bool flag() const { return flag_; }\n\nprivate:\n    bool flag_;\n};\n\n/// Wrapper for Python extension modules\nclass module_ : public object {\npublic:\n    PYBIND11_OBJECT_DEFAULT(module_, object, PyModule_Check)\n\n    /// Create a new top-level Python module with the given name and docstring\n    PYBIND11_DEPRECATED(\"Use PYBIND11_MODULE or module_::create_extension_module instead\")\n    explicit module_(const char *name, const char *doc = nullptr) {\n        *this = create_extension_module(name, doc, new PyModuleDef());\n    }\n\n    /** \\rst\n        Create Python binding for a new function within the module scope. ``Func``\n        can be a plain C++ function, a function pointer, or a lambda function. For\n        details on the ``Extra&& ... extra`` argument, see section :ref:`extras`.\n    \\endrst */\n    template <typename Func, typename... Extra>\n    module_ &def(const char *name_, Func &&f, const Extra &...extra) {\n        cpp_function func(std::forward<Func>(f),\n                          name(name_),\n                          scope(*this),\n                          sibling(getattr(*this, name_, none())),\n                          extra...);\n        // NB: allow overwriting here because cpp_function sets up a chain with the intention of\n        // overwriting (and has already checked internally that it isn't overwriting\n        // non-functions).\n        add_object(name_, func, true /* overwrite */);\n        return *this;\n    }\n\n    /** \\rst\n        Create and return a new Python submodule with the given name and docstring.\n        This also works recursively, i.e.\n\n        .. code-block:: cpp\n\n            py::module_ m(\"example\", \"pybind11 example plugin\");\n            py::module_ m2 = m.def_submodule(\"sub\", \"A submodule of 'example'\");\n            py::module_ m3 = m2.def_submodule(\"subsub\", \"A submodule of 'example.sub'\");\n    \\endrst */\n    module_ def_submodule(const char *name, const char *doc = nullptr) {\n        const char *this_name = PyModule_GetName(m_ptr);\n        if (this_name == nullptr) {\n            throw error_already_set();\n        }\n        std::string full_name = std::string(this_name) + '.' + name;\n        handle submodule = PyImport_AddModule(full_name.c_str());\n        if (!submodule) {\n            throw error_already_set();\n        }\n        auto result = reinterpret_borrow<module_>(submodule);\n        if (doc && options::show_user_defined_docstrings()) {\n            result.attr(\"__doc__\") = pybind11::str(doc);\n        }\n        attr(name) = result;\n        return result;\n    }\n\n    /// Import and return a module or throws `error_already_set`.\n    static module_ import(const char *name) {\n        PyObject *obj = PyImport_ImportModule(name);\n        if (!obj) {\n            throw error_already_set();\n        }\n        return reinterpret_steal<module_>(obj);\n    }\n\n    /// Reload the module or throws `error_already_set`.\n    void reload() {\n        PyObject *obj = PyImport_ReloadModule(ptr());\n        if (!obj) {\n            throw error_already_set();\n        }\n        *this = reinterpret_steal<module_>(obj);\n    }\n\n    /** \\rst\n        Adds an object to the module using the given name.  Throws if an object with the given name\n        already exists.\n\n        ``overwrite`` should almost always be false: attempting to overwrite objects that pybind11\n        has established will, in most cases, break things.\n    \\endrst */\n    PYBIND11_NOINLINE void add_object(const char *name, handle obj, bool overwrite = false) {\n        if (!overwrite && hasattr(*this, name)) {\n            pybind11_fail(\n                \"Error during initialization: multiple incompatible definitions with name \\\"\"\n                + std::string(name) + \"\\\"\");\n        }\n\n        PyModule_AddObject(ptr(), name, obj.inc_ref().ptr() /* steals a reference */);\n    }\n\n    using module_def = PyModuleDef; // TODO: Can this be removed (it was needed only for Python 2)?\n\n    /** \\rst\n        Create a new top-level module that can be used as the main module of a C extension.\n\n        ``def`` should point to a statically allocated module_def.\n    \\endrst */\n    static module_ create_extension_module(const char *name,\n                                           const char *doc,\n                                           module_def *def,\n                                           mod_gil_not_used gil_not_used\n                                           = mod_gil_not_used(false)) {\n        // module_def is PyModuleDef\n        // Placement new (not an allocation).\n        def = new (def)\n            PyModuleDef{/* m_base */ PyModuleDef_HEAD_INIT,\n                        /* m_name */ name,\n                        /* m_doc */ options::show_user_defined_docstrings() ? doc : nullptr,\n                        /* m_size */ -1,\n                        /* m_methods */ nullptr,\n                        /* m_slots */ nullptr,\n                        /* m_traverse */ nullptr,\n                        /* m_clear */ nullptr,\n                        /* m_free */ nullptr};\n        auto *m = PyModule_Create(def);\n        if (m == nullptr) {\n            if (PyErr_Occurred()) {\n                throw error_already_set();\n            }\n            pybind11_fail(\"Internal error in module_::create_extension_module()\");\n        }\n        if (gil_not_used.flag()) {\n#ifdef Py_GIL_DISABLED\n            PyUnstable_Module_SetGIL(m, Py_MOD_GIL_NOT_USED);\n#endif\n        }\n        // TODO: Should be reinterpret_steal for Python 3, but Python also steals it again when\n        //       returned from PyInit_...\n        //       For Python 2, reinterpret_borrow was correct.\n        return reinterpret_borrow<module_>(m);\n    }\n};\n\nPYBIND11_NAMESPACE_BEGIN(detail)\n\ntemplate <>\nstruct handle_type_name<module_> {\n    static constexpr auto name = const_name(\"module\");\n};\n\nPYBIND11_NAMESPACE_END(detail)\n\n// When inside a namespace (or anywhere as long as it's not the first item on a line),\n// C++20 allows \"module\" to be used. This is provided for backward compatibility, and for\n// simplicity, if someone wants to use py::module for example, that is perfectly safe.\nusing module = module_;\n\n/// \\ingroup python_builtins\n/// Return a dictionary representing the global variables in the current execution frame,\n/// or ``__main__.__dict__`` if there is no frame (usually when the interpreter is embedded).\ninline dict globals() {\n#if PY_VERSION_HEX >= 0x030d0000\n    PyObject *p = PyEval_GetFrameGlobals();\n    return p ? reinterpret_steal<dict>(p)\n             : reinterpret_borrow<dict>(module_::import(\"__main__\").attr(\"__dict__\").ptr());\n#else\n    PyObject *p = PyEval_GetGlobals();\n    return reinterpret_borrow<dict>(p ? p : module_::import(\"__main__\").attr(\"__dict__\").ptr());\n#endif\n}\n\ntemplate <typename... Args, typename = detail::enable_if_t<args_are_all_keyword_or_ds<Args...>()>>\nPYBIND11_DEPRECATED(\"make_simple_namespace should be replaced with \"\n                    \"py::module_::import(\\\"types\\\").attr(\\\"SimpleNamespace\\\") \")\nobject make_simple_namespace(Args &&...args_) {\n    return module_::import(\"types\").attr(\"SimpleNamespace\")(std::forward<Args>(args_)...);\n}\n\nPYBIND11_NAMESPACE_BEGIN(detail)\n/// Generic support for creating new Python heap types\nclass generic_type : public object {\npublic:\n    PYBIND11_OBJECT_DEFAULT(generic_type, object, PyType_Check)\nprotected:\n    void initialize(const type_record &rec) {\n        if (rec.scope && hasattr(rec.scope, \"__dict__\")\n            && rec.scope.attr(\"__dict__\").contains(rec.name)) {\n            pybind11_fail(\"generic_type: cannot initialize type \\\"\" + std::string(rec.name)\n                          + \"\\\": an object with that name is already defined\");\n        }\n\n        if ((rec.module_local ? get_local_type_info(*rec.type) : get_global_type_info(*rec.type))\n            != nullptr) {\n            pybind11_fail(\"generic_type: type \\\"\" + std::string(rec.name)\n                          + \"\\\" is already registered!\");\n        }\n\n        m_ptr = make_new_python_type(rec);\n\n        /* Register supplemental type information in C++ dict */\n        auto *tinfo = new detail::type_info();\n        tinfo->type = (PyTypeObject *) m_ptr;\n        tinfo->cpptype = rec.type;\n        tinfo->type_size = rec.type_size;\n        tinfo->type_align = rec.type_align;\n        tinfo->operator_new = rec.operator_new;\n        tinfo->holder_size_in_ptrs = size_in_ptrs(rec.holder_size);\n        tinfo->init_instance = rec.init_instance;\n        tinfo->dealloc = rec.dealloc;\n        tinfo->simple_type = true;\n        tinfo->simple_ancestors = true;\n        tinfo->default_holder = rec.default_holder;\n        tinfo->module_local = rec.module_local;\n\n        with_internals([&](internals &internals) {\n            auto tindex = std::type_index(*rec.type);\n            tinfo->direct_conversions = &internals.direct_conversions[tindex];\n            if (rec.module_local) {\n                get_local_internals().registered_types_cpp[tindex] = tinfo;\n            } else {\n                internals.registered_types_cpp[tindex] = tinfo;\n            }\n            internals.registered_types_py[(PyTypeObject *) m_ptr] = {tinfo};\n        });\n\n        if (rec.bases.size() > 1 || rec.multiple_inheritance) {\n            mark_parents_nonsimple(tinfo->type);\n            tinfo->simple_ancestors = false;\n        } else if (rec.bases.size() == 1) {\n            auto *parent_tinfo = get_type_info((PyTypeObject *) rec.bases[0].ptr());\n            assert(parent_tinfo != nullptr);\n            bool parent_simple_ancestors = parent_tinfo->simple_ancestors;\n            tinfo->simple_ancestors = parent_simple_ancestors;\n            // The parent can no longer be a simple type if it has MI and has a child\n            parent_tinfo->simple_type = parent_tinfo->simple_type && parent_simple_ancestors;\n        }\n\n        if (rec.module_local) {\n            // Stash the local typeinfo and loader so that external modules can access it.\n            tinfo->module_local_load = &type_caster_generic::local_load;\n            setattr(m_ptr, PYBIND11_MODULE_LOCAL_ID, capsule(tinfo));\n        }\n    }\n\n    /// Helper function which tags all parents of a type using mult. inheritance\n    void mark_parents_nonsimple(PyTypeObject *value) {\n        auto t = reinterpret_borrow<tuple>(value->tp_bases);\n        for (handle h : t) {\n            auto *tinfo2 = get_type_info((PyTypeObject *) h.ptr());\n            if (tinfo2) {\n                tinfo2->simple_type = false;\n            }\n            mark_parents_nonsimple((PyTypeObject *) h.ptr());\n        }\n    }\n\n    void install_buffer_funcs(buffer_info *(*get_buffer)(PyObject *, void *),\n                              void *get_buffer_data) {\n        auto *type = (PyHeapTypeObject *) m_ptr;\n        auto *tinfo = detail::get_type_info(&type->ht_type);\n\n        if (!type->ht_type.tp_as_buffer) {\n            pybind11_fail(\"To be able to register buffer protocol support for the type '\"\n                          + get_fully_qualified_tp_name(tinfo->type)\n                          + \"' the associated class<>(..) invocation must \"\n                            \"include the pybind11::buffer_protocol() annotation!\");\n        }\n\n        tinfo->get_buffer = get_buffer;\n        tinfo->get_buffer_data = get_buffer_data;\n    }\n\n    // rec_func must be set for either fget or fset.\n    void def_property_static_impl(const char *name,\n                                  handle fget,\n                                  handle fset,\n                                  detail::function_record *rec_func) {\n        const auto is_static = (rec_func != nullptr) && !(rec_func->is_method && rec_func->scope);\n        const auto has_doc = (rec_func != nullptr) && (rec_func->doc != nullptr)\n                             && pybind11::options::show_user_defined_docstrings();\n        auto property = handle(\n            (PyObject *) (is_static ? get_internals().static_property_type : &PyProperty_Type));\n        attr(name) = property(fget.ptr() ? fget : none(),\n                              fset.ptr() ? fset : none(),\n                              /*deleter*/ none(),\n                              pybind11::str(has_doc ? rec_func->doc : \"\"));\n    }\n};\n\n/// Set the pointer to operator new if it exists. The cast is needed because it can be overloaded.\ntemplate <typename T,\n          typename = void_t<decltype(static_cast<void *(*) (size_t)>(T::operator new))>>\nvoid set_operator_new(type_record *r) {\n    r->operator_new = &T::operator new;\n}\n\ntemplate <typename>\nvoid set_operator_new(...) {}\n\ntemplate <typename T, typename SFINAE = void>\nstruct has_operator_delete : std::false_type {};\ntemplate <typename T>\nstruct has_operator_delete<T, void_t<decltype(static_cast<void (*)(void *)>(T::operator delete))>>\n    : std::true_type {};\ntemplate <typename T, typename SFINAE = void>\nstruct has_operator_delete_size : std::false_type {};\ntemplate <typename T>\nstruct has_operator_delete_size<\n    T,\n    void_t<decltype(static_cast<void (*)(void *, size_t)>(T::operator delete))>> : std::true_type {\n};\n/// Call class-specific delete if it exists or global otherwise. Can also be an overload set.\ntemplate <typename T, enable_if_t<has_operator_delete<T>::value, int> = 0>\nvoid call_operator_delete(T *p, size_t, size_t) {\n    T::operator delete(p);\n}\ntemplate <typename T,\n          enable_if_t<!has_operator_delete<T>::value && has_operator_delete_size<T>::value, int>\n          = 0>\nvoid call_operator_delete(T *p, size_t s, size_t) {\n    T::operator delete(p, s);\n}\n\ninline void call_operator_delete(void *p, size_t s, size_t a) {\n    (void) s;\n    (void) a;\n#if defined(__cpp_aligned_new) && (!defined(_MSC_VER) || _MSC_VER >= 1912)\n    if (a > __STDCPP_DEFAULT_NEW_ALIGNMENT__) {\n#    ifdef __cpp_sized_deallocation\n        ::operator delete(p, s, std::align_val_t(a));\n#    else\n        ::operator delete(p, std::align_val_t(a));\n#    endif\n        return;\n    }\n#endif\n#ifdef __cpp_sized_deallocation\n    ::operator delete(p, s);\n#else\n    ::operator delete(p);\n#endif\n}\n\ninline void add_class_method(object &cls, const char *name_, const cpp_function &cf) {\n    cls.attr(cf.name()) = cf;\n    if (std::strcmp(name_, \"__eq__\") == 0 && !cls.attr(\"__dict__\").contains(\"__hash__\")) {\n        cls.attr(\"__hash__\") = none();\n    }\n}\n\nPYBIND11_NAMESPACE_END(detail)\n\n/// Given a pointer to a member function, cast it to its `Derived` version.\n/// Forward everything else unchanged.\ntemplate <typename /*Derived*/, typename F>\nauto method_adaptor(F &&f) -> decltype(std::forward<F>(f)) {\n    return std::forward<F>(f);\n}\n\ntemplate <typename Derived, typename Return, typename Class, typename... Args>\nauto method_adaptor(Return (Class::*pmf)(Args...)) -> Return (Derived::*)(Args...) {\n    static_assert(\n        detail::is_accessible_base_of<Class, Derived>::value,\n        \"Cannot bind an inaccessible base class method; use a lambda definition instead\");\n    return pmf;\n}\n\ntemplate <typename Derived, typename Return, typename Class, typename... Args>\nauto method_adaptor(Return (Class::*pmf)(Args...) const) -> Return (Derived::*)(Args...) const {\n    static_assert(\n        detail::is_accessible_base_of<Class, Derived>::value,\n        \"Cannot bind an inaccessible base class method; use a lambda definition instead\");\n    return pmf;\n}\n\ntemplate <typename type_, typename... options>\nclass class_ : public detail::generic_type {\n    template <typename T>\n    using is_holder = detail::is_holder_type<type_, T>;\n    template <typename T>\n    using is_subtype = detail::is_strict_base_of<type_, T>;\n    template <typename T>\n    using is_base = detail::is_strict_base_of<T, type_>;\n    // struct instead of using here to help MSVC:\n    template <typename T>\n    struct is_valid_class_option : detail::any_of<is_holder<T>, is_subtype<T>, is_base<T>> {};\n\npublic:\n    using type = type_;\n    using type_alias = detail::exactly_one_t<is_subtype, void, options...>;\n    constexpr static bool has_alias = !std::is_void<type_alias>::value;\n    using holder_type = detail::exactly_one_t<is_holder, std::unique_ptr<type>, options...>;\n\n    static_assert(detail::all_of<is_valid_class_option<options>...>::value,\n                  \"Unknown/invalid class_ template parameters provided\");\n\n    static_assert(!has_alias || std::is_polymorphic<type>::value,\n                  \"Cannot use an alias class with a non-polymorphic type\");\n\n    PYBIND11_OBJECT(class_, generic_type, PyType_Check)\n\n    template <typename... Extra>\n    class_(handle scope, const char *name, const Extra &...extra) {\n        using namespace detail;\n\n        // MI can only be specified via class_ template options, not constructor parameters\n        static_assert(\n            none_of<is_pyobject<Extra>...>::value || // no base class arguments, or:\n                (constexpr_sum(is_pyobject<Extra>::value...) == 1 && // Exactly one base\n                 constexpr_sum(is_base<options>::value...) == 0 &&   // no template option bases\n                 // no multiple_inheritance attr\n                 none_of<std::is_same<multiple_inheritance, Extra>...>::value),\n            \"Error: multiple inheritance bases must be specified via class_ template options\");\n\n        type_record record;\n        record.scope = scope;\n        record.name = name;\n        record.type = &typeid(type);\n        record.type_size = sizeof(conditional_t<has_alias, type_alias, type>);\n        record.type_align = alignof(conditional_t<has_alias, type_alias, type> &);\n        record.holder_size = sizeof(holder_type);\n        record.init_instance = init_instance;\n        record.dealloc = dealloc;\n        record.default_holder = detail::is_instantiation<std::unique_ptr, holder_type>::value;\n\n        set_operator_new<type>(&record);\n\n        /* Register base classes specified via template arguments to class_, if any */\n        PYBIND11_EXPAND_SIDE_EFFECTS(add_base<options>(record));\n\n        /* Process optional arguments, if any */\n        process_attributes<Extra...>::init(extra..., &record);\n\n        generic_type::initialize(record);\n\n        if (has_alias) {\n            with_internals([&](internals &internals) {\n                auto &instances = record.module_local ? get_local_internals().registered_types_cpp\n                                                      : internals.registered_types_cpp;\n                instances[std::type_index(typeid(type_alias))]\n                    = instances[std::type_index(typeid(type))];\n            });\n        }\n        def(\"_pybind11_conduit_v1_\", cpp_conduit_method);\n    }\n\n    template <typename Base, detail::enable_if_t<is_base<Base>::value, int> = 0>\n    static void add_base(detail::type_record &rec) {\n        rec.add_base(typeid(Base), [](void *src) -> void * {\n            return static_cast<Base *>(reinterpret_cast<type *>(src));\n        });\n    }\n\n    template <typename Base, detail::enable_if_t<!is_base<Base>::value, int> = 0>\n    static void add_base(detail::type_record &) {}\n\n    template <typename Func, typename... Extra>\n    class_ &def(const char *name_, Func &&f, const Extra &...extra) {\n        cpp_function cf(method_adaptor<type>(std::forward<Func>(f)),\n                        name(name_),\n                        is_method(*this),\n                        sibling(getattr(*this, name_, none())),\n                        extra...);\n        add_class_method(*this, name_, cf);\n        return *this;\n    }\n\n    template <typename Func, typename... Extra>\n    class_ &def_static(const char *name_, Func &&f, const Extra &...extra) {\n        static_assert(!std::is_member_function_pointer<Func>::value,\n                      \"def_static(...) called with a non-static member function pointer\");\n        cpp_function cf(std::forward<Func>(f),\n                        name(name_),\n                        scope(*this),\n                        sibling(getattr(*this, name_, none())),\n                        extra...);\n        auto cf_name = cf.name();\n        attr(std::move(cf_name)) = staticmethod(std::move(cf));\n        return *this;\n    }\n\n    template <typename T, typename... Extra, detail::enable_if_t<T::op_enable_if_hook, int> = 0>\n    class_ &def(const T &op, const Extra &...extra) {\n        op.execute(*this, extra...);\n        return *this;\n    }\n\n    template <typename T, typename... Extra, detail::enable_if_t<T::op_enable_if_hook, int> = 0>\n    class_ &def_cast(const T &op, const Extra &...extra) {\n        op.execute_cast(*this, extra...);\n        return *this;\n    }\n\n    template <typename... Args, typename... Extra>\n    class_ &def(const detail::initimpl::constructor<Args...> &init, const Extra &...extra) {\n        PYBIND11_WORKAROUND_INCORRECT_MSVC_C4100(init);\n        init.execute(*this, extra...);\n        return *this;\n    }\n\n    template <typename... Args, typename... Extra>\n    class_ &def(const detail::initimpl::alias_constructor<Args...> &init, const Extra &...extra) {\n        PYBIND11_WORKAROUND_INCORRECT_MSVC_C4100(init);\n        init.execute(*this, extra...);\n        return *this;\n    }\n\n    template <typename... Args, typename... Extra>\n    class_ &def(detail::initimpl::factory<Args...> &&init, const Extra &...extra) {\n        std::move(init).execute(*this, extra...);\n        return *this;\n    }\n\n    template <typename... Args, typename... Extra>\n    class_ &def(detail::initimpl::pickle_factory<Args...> &&pf, const Extra &...extra) {\n        std::move(pf).execute(*this, extra...);\n        return *this;\n    }\n\n    template <typename Func>\n    class_ &def_buffer(Func &&func) {\n        struct capture {\n            Func func;\n        };\n        auto *ptr = new capture{std::forward<Func>(func)};\n        install_buffer_funcs(\n            [](PyObject *obj, void *ptr) -> buffer_info * {\n                detail::make_caster<type> caster;\n                if (!caster.load(obj, false)) {\n                    return nullptr;\n                }\n                return new buffer_info(((capture *) ptr)->func(std::move(caster)));\n            },\n            ptr);\n        weakref(m_ptr, cpp_function([ptr](handle wr) {\n                    delete ptr;\n                    wr.dec_ref();\n                }))\n            .release();\n        return *this;\n    }\n\n    template <typename Return, typename Class, typename... Args>\n    class_ &def_buffer(Return (Class::*func)(Args...)) {\n        return def_buffer([func](type &obj) { return (obj.*func)(); });\n    }\n\n    template <typename Return, typename Class, typename... Args>\n    class_ &def_buffer(Return (Class::*func)(Args...) const) {\n        return def_buffer([func](const type &obj) { return (obj.*func)(); });\n    }\n\n    template <typename C, typename D, typename... Extra>\n    class_ &def_readwrite(const char *name, D C::*pm, const Extra &...extra) {\n        static_assert(std::is_same<C, type>::value || std::is_base_of<C, type>::value,\n                      \"def_readwrite() requires a class member (or base class member)\");\n        cpp_function fget([pm](const type &c) -> const D & { return c.*pm; }, is_method(*this)),\n            fset([pm](type &c, const D &value) { c.*pm = value; }, is_method(*this));\n        def_property(name, fget, fset, return_value_policy::reference_internal, extra...);\n        return *this;\n    }\n\n    template <typename C, typename D, typename... Extra>\n    class_ &def_readonly(const char *name, const D C::*pm, const Extra &...extra) {\n        static_assert(std::is_same<C, type>::value || std::is_base_of<C, type>::value,\n                      \"def_readonly() requires a class member (or base class member)\");\n        cpp_function fget([pm](const type &c) -> const D & { return c.*pm; }, is_method(*this));\n        def_property_readonly(name, fget, return_value_policy::reference_internal, extra...);\n        return *this;\n    }\n\n    template <typename D, typename... Extra>\n    class_ &def_readwrite_static(const char *name, D *pm, const Extra &...extra) {\n        cpp_function fget([pm](const object &) -> const D & { return *pm; }, scope(*this)),\n            fset([pm](const object &, const D &value) { *pm = value; }, scope(*this));\n        def_property_static(name, fget, fset, return_value_policy::reference, extra...);\n        return *this;\n    }\n\n    template <typename D, typename... Extra>\n    class_ &def_readonly_static(const char *name, const D *pm, const Extra &...extra) {\n        cpp_function fget([pm](const object &) -> const D & { return *pm; }, scope(*this));\n        def_property_readonly_static(name, fget, return_value_policy::reference, extra...);\n        return *this;\n    }\n\n    /// Uses return_value_policy::reference_internal by default\n    template <typename Getter, typename... Extra>\n    class_ &def_property_readonly(const char *name, const Getter &fget, const Extra &...extra) {\n        return def_property_readonly(name,\n                                     cpp_function(method_adaptor<type>(fget)),\n                                     return_value_policy::reference_internal,\n                                     extra...);\n    }\n\n    /// Uses cpp_function's return_value_policy by default\n    template <typename... Extra>\n    class_ &\n    def_property_readonly(const char *name, const cpp_function &fget, const Extra &...extra) {\n        return def_property(name, fget, nullptr, extra...);\n    }\n\n    /// Uses return_value_policy::reference by default\n    template <typename Getter, typename... Extra>\n    class_ &\n    def_property_readonly_static(const char *name, const Getter &fget, const Extra &...extra) {\n        return def_property_readonly_static(\n            name, cpp_function(fget), return_value_policy::reference, extra...);\n    }\n\n    /// Uses cpp_function's return_value_policy by default\n    template <typename... Extra>\n    class_ &def_property_readonly_static(const char *name,\n                                         const cpp_function &fget,\n                                         const Extra &...extra) {\n        return def_property_static(name, fget, nullptr, extra...);\n    }\n\n    /// Uses return_value_policy::reference_internal by default\n    template <typename Getter, typename Setter, typename... Extra>\n    class_ &\n    def_property(const char *name, const Getter &fget, const Setter &fset, const Extra &...extra) {\n        return def_property(\n            name, fget, cpp_function(method_adaptor<type>(fset), is_setter()), extra...);\n    }\n    template <typename Getter, typename... Extra>\n    class_ &def_property(const char *name,\n                         const Getter &fget,\n                         const cpp_function &fset,\n                         const Extra &...extra) {\n        return def_property(name,\n                            cpp_function(method_adaptor<type>(fget)),\n                            fset,\n                            return_value_policy::reference_internal,\n                            extra...);\n    }\n\n    /// Uses cpp_function's return_value_policy by default\n    template <typename... Extra>\n    class_ &def_property(const char *name,\n                         const cpp_function &fget,\n                         const cpp_function &fset,\n                         const Extra &...extra) {\n        return def_property_static(name, fget, fset, is_method(*this), extra...);\n    }\n\n    /// Uses return_value_policy::reference by default\n    template <typename Getter, typename... Extra>\n    class_ &def_property_static(const char *name,\n                                const Getter &fget,\n                                const cpp_function &fset,\n                                const Extra &...extra) {\n        return def_property_static(\n            name, cpp_function(fget), fset, return_value_policy::reference, extra...);\n    }\n\n    /// Uses cpp_function's return_value_policy by default\n    template <typename... Extra>\n    class_ &def_property_static(const char *name,\n                                const cpp_function &fget,\n                                const cpp_function &fset,\n                                const Extra &...extra) {\n        static_assert(0 == detail::constexpr_sum(std::is_base_of<arg, Extra>::value...),\n                      \"Argument annotations are not allowed for properties\");\n        auto rec_fget = get_function_record(fget), rec_fset = get_function_record(fset);\n        auto *rec_active = rec_fget;\n        if (rec_fget) {\n            char *doc_prev = rec_fget->doc; /* 'extra' field may include a property-specific\n                                               documentation string */\n            detail::process_attributes<Extra...>::init(extra..., rec_fget);\n            if (rec_fget->doc && rec_fget->doc != doc_prev) {\n                std::free(doc_prev);\n                rec_fget->doc = PYBIND11_COMPAT_STRDUP(rec_fget->doc);\n            }\n        }\n        if (rec_fset) {\n            char *doc_prev = rec_fset->doc;\n            detail::process_attributes<Extra...>::init(extra..., rec_fset);\n            if (rec_fset->doc && rec_fset->doc != doc_prev) {\n                std::free(doc_prev);\n                rec_fset->doc = PYBIND11_COMPAT_STRDUP(rec_fset->doc);\n            }\n            if (!rec_active) {\n                rec_active = rec_fset;\n            }\n        }\n        def_property_static_impl(name, fget, fset, rec_active);\n        return *this;\n    }\n\nprivate:\n    /// Initialize holder object, variant 1: object derives from enable_shared_from_this\n    template <typename T>\n    static void init_holder(detail::instance *inst,\n                            detail::value_and_holder &v_h,\n                            const holder_type * /* unused */,\n                            const std::enable_shared_from_this<T> * /* dummy */) {\n\n        auto sh = std::dynamic_pointer_cast<typename holder_type::element_type>(\n            detail::try_get_shared_from_this(v_h.value_ptr<type>()));\n        if (sh) {\n            new (std::addressof(v_h.holder<holder_type>())) holder_type(std::move(sh));\n            v_h.set_holder_constructed();\n        }\n\n        if (!v_h.holder_constructed() && inst->owned) {\n            new (std::addressof(v_h.holder<holder_type>())) holder_type(v_h.value_ptr<type>());\n            v_h.set_holder_constructed();\n        }\n    }\n\n    static void init_holder_from_existing(const detail::value_and_holder &v_h,\n                                          const holder_type *holder_ptr,\n                                          std::true_type /*is_copy_constructible*/) {\n        new (std::addressof(v_h.holder<holder_type>()))\n            holder_type(*reinterpret_cast<const holder_type *>(holder_ptr));\n    }\n\n    static void init_holder_from_existing(const detail::value_and_holder &v_h,\n                                          const holder_type *holder_ptr,\n                                          std::false_type /*is_copy_constructible*/) {\n        new (std::addressof(v_h.holder<holder_type>()))\n            holder_type(std::move(*const_cast<holder_type *>(holder_ptr)));\n    }\n\n    /// Initialize holder object, variant 2: try to construct from existing holder object, if\n    /// possible\n    static void init_holder(detail::instance *inst,\n                            detail::value_and_holder &v_h,\n                            const holder_type *holder_ptr,\n                            const void * /* dummy -- not enable_shared_from_this<T>) */) {\n        if (holder_ptr) {\n            init_holder_from_existing(v_h, holder_ptr, std::is_copy_constructible<holder_type>());\n            v_h.set_holder_constructed();\n        } else if (detail::always_construct_holder<holder_type>::value || inst->owned) {\n            new (std::addressof(v_h.holder<holder_type>())) holder_type(v_h.value_ptr<type>());\n            v_h.set_holder_constructed();\n        }\n    }\n\n    /// Performs instance initialization including constructing a holder and registering the known\n    /// instance.  Should be called as soon as the `type` value_ptr is set for an instance.  Takes\n    /// an optional pointer to an existing holder to use; if not specified and the instance is\n    /// `.owned`, a new holder will be constructed to manage the value pointer.\n    static void init_instance(detail::instance *inst, const void *holder_ptr) {\n        auto v_h = inst->get_value_and_holder(detail::get_type_info(typeid(type)));\n        if (!v_h.instance_registered()) {\n            register_instance(inst, v_h.value_ptr(), v_h.type);\n            v_h.set_instance_registered();\n        }\n        init_holder(inst, v_h, (const holder_type *) holder_ptr, v_h.value_ptr<type>());\n    }\n\n    /// Deallocates an instance; via holder, if constructed; otherwise via operator delete.\n    static void dealloc(detail::value_and_holder &v_h) {\n        // We could be deallocating because we are cleaning up after a Python exception.\n        // If so, the Python error indicator will be set. We need to clear that before\n        // running the destructor, in case the destructor code calls more Python.\n        // If we don't, the Python API will exit with an exception, and pybind11 will\n        // throw error_already_set from the C++ destructor which is forbidden and triggers\n        // std::terminate().\n        error_scope scope;\n        if (v_h.holder_constructed()) {\n            v_h.holder<holder_type>().~holder_type();\n            v_h.set_holder_constructed(false);\n        } else {\n            detail::call_operator_delete(\n                v_h.value_ptr<type>(), v_h.type->type_size, v_h.type->type_align);\n        }\n        v_h.value_ptr() = nullptr;\n    }\n\n    static detail::function_record *get_function_record(handle h) {\n        h = detail::get_function(h);\n        if (!h) {\n            return nullptr;\n        }\n\n        handle func_self = PyCFunction_GET_SELF(h.ptr());\n        if (!func_self) {\n            throw error_already_set();\n        }\n        if (!isinstance<capsule>(func_self)) {\n            return nullptr;\n        }\n        auto cap = reinterpret_borrow<capsule>(func_self);\n        if (!detail::is_function_record_capsule(cap)) {\n            return nullptr;\n        }\n        return cap.get_pointer<detail::function_record>();\n    }\n};\n\n/// Binds an existing constructor taking arguments Args...\ntemplate <typename... Args>\ndetail::initimpl::constructor<Args...> init() {\n    return {};\n}\n/// Like `init<Args...>()`, but the instance is always constructed through the alias class (even\n/// when not inheriting on the Python side).\ntemplate <typename... Args>\ndetail::initimpl::alias_constructor<Args...> init_alias() {\n    return {};\n}\n\n/// Binds a factory function as a constructor\ntemplate <typename Func, typename Ret = detail::initimpl::factory<Func>>\nRet init(Func &&f) {\n    return {std::forward<Func>(f)};\n}\n\n/// Dual-argument factory function: the first function is called when no alias is needed, the\n/// second when an alias is needed (i.e. due to python-side inheritance).  Arguments must be\n/// identical.\ntemplate <typename CFunc, typename AFunc, typename Ret = detail::initimpl::factory<CFunc, AFunc>>\nRet init(CFunc &&c, AFunc &&a) {\n    return {std::forward<CFunc>(c), std::forward<AFunc>(a)};\n}\n\n/// Binds pickling functions `__getstate__` and `__setstate__` and ensures that the type\n/// returned by `__getstate__` is the same as the argument accepted by `__setstate__`.\ntemplate <typename GetState, typename SetState>\ndetail::initimpl::pickle_factory<GetState, SetState> pickle(GetState &&g, SetState &&s) {\n    return {std::forward<GetState>(g), std::forward<SetState>(s)};\n}\n\nPYBIND11_NAMESPACE_BEGIN(detail)\n\ninline str enum_name(handle arg) {\n    dict entries = arg.get_type().attr(\"__entries\");\n    for (auto kv : entries) {\n        if (handle(kv.second[int_(0)]).equal(arg)) {\n            return pybind11::str(kv.first);\n        }\n    }\n    return \"???\";\n}\n\nstruct enum_base {\n    enum_base(const handle &base, const handle &parent) : m_base(base), m_parent(parent) {}\n\n    PYBIND11_NOINLINE void init(bool is_arithmetic, bool is_convertible) {\n        m_base.attr(\"__entries\") = dict();\n        auto property = handle((PyObject *) &PyProperty_Type);\n        auto static_property = handle((PyObject *) get_internals().static_property_type);\n\n        m_base.attr(\"__repr__\") = cpp_function(\n            [](const object &arg) -> str {\n                handle type = type::handle_of(arg);\n                object type_name = type.attr(\"__name__\");\n                return pybind11::str(\"<{}.{}: {}>\")\n                    .format(std::move(type_name), enum_name(arg), int_(arg));\n            },\n            name(\"__repr__\"),\n            is_method(m_base));\n\n        m_base.attr(\"name\") = property(cpp_function(&enum_name, name(\"name\"), is_method(m_base)));\n\n        m_base.attr(\"__str__\") = cpp_function(\n            [](handle arg) -> str {\n                object type_name = type::handle_of(arg).attr(\"__name__\");\n                return pybind11::str(\"{}.{}\").format(std::move(type_name), enum_name(arg));\n            },\n            name(\"__str__\"),\n            is_method(m_base));\n\n        if (options::show_enum_members_docstring()) {\n            m_base.attr(\"__doc__\") = static_property(\n                cpp_function(\n                    [](handle arg) -> std::string {\n                        std::string docstring;\n                        dict entries = arg.attr(\"__entries\");\n                        if (((PyTypeObject *) arg.ptr())->tp_doc) {\n                            docstring += std::string(\n                                reinterpret_cast<PyTypeObject *>(arg.ptr())->tp_doc);\n                            docstring += \"\\n\\n\";\n                        }\n                        docstring += \"Members:\";\n                        for (auto kv : entries) {\n                            auto key = std::string(pybind11::str(kv.first));\n                            auto comment = kv.second[int_(1)];\n                            docstring += \"\\n\\n  \";\n                            docstring += key;\n                            if (!comment.is_none()) {\n                                docstring += \" : \";\n                                docstring += pybind11::str(comment).cast<std::string>();\n                            }\n                        }\n                        return docstring;\n                    },\n                    name(\"__doc__\")),\n                none(),\n                none(),\n                \"\");\n        }\n\n        m_base.attr(\"__members__\") = static_property(cpp_function(\n                                                         [](handle arg) -> dict {\n                                                             dict entries = arg.attr(\"__entries\"),\n                                                                  m;\n                                                             for (auto kv : entries) {\n                                                                 m[kv.first] = kv.second[int_(0)];\n                                                             }\n                                                             return m;\n                                                         },\n                                                         name(\"__members__\")),\n                                                     none(),\n                                                     none(),\n                                                     \"\");\n\n#define PYBIND11_ENUM_OP_STRICT(op, expr, strict_behavior)                                        \\\n    m_base.attr(op) = cpp_function(                                                               \\\n        [](const object &a, const object &b) {                                                    \\\n            if (!type::handle_of(a).is(type::handle_of(b)))                                       \\\n                strict_behavior; /* NOLINT(bugprone-macro-parentheses) */                         \\\n            return expr;                                                                          \\\n        },                                                                                        \\\n        name(op),                                                                                 \\\n        is_method(m_base),                                                                        \\\n        arg(\"other\"))\n\n#define PYBIND11_ENUM_OP_CONV(op, expr)                                                           \\\n    m_base.attr(op) = cpp_function(                                                               \\\n        [](const object &a_, const object &b_) {                                                  \\\n            int_ a(a_), b(b_);                                                                    \\\n            return expr;                                                                          \\\n        },                                                                                        \\\n        name(op),                                                                                 \\\n        is_method(m_base),                                                                        \\\n        arg(\"other\"))\n\n#define PYBIND11_ENUM_OP_CONV_LHS(op, expr)                                                       \\\n    m_base.attr(op) = cpp_function(                                                               \\\n        [](const object &a_, const object &b) {                                                   \\\n            int_ a(a_);                                                                           \\\n            return expr;                                                                          \\\n        },                                                                                        \\\n        name(op),                                                                                 \\\n        is_method(m_base),                                                                        \\\n        arg(\"other\"))\n\n        if (is_convertible) {\n            PYBIND11_ENUM_OP_CONV_LHS(\"__eq__\", !b.is_none() && a.equal(b));\n            PYBIND11_ENUM_OP_CONV_LHS(\"__ne__\", b.is_none() || !a.equal(b));\n\n            if (is_arithmetic) {\n                PYBIND11_ENUM_OP_CONV(\"__lt__\", a < b);\n                PYBIND11_ENUM_OP_CONV(\"__gt__\", a > b);\n                PYBIND11_ENUM_OP_CONV(\"__le__\", a <= b);\n                PYBIND11_ENUM_OP_CONV(\"__ge__\", a >= b);\n                PYBIND11_ENUM_OP_CONV(\"__and__\", a & b);\n                PYBIND11_ENUM_OP_CONV(\"__rand__\", a & b);\n                PYBIND11_ENUM_OP_CONV(\"__or__\", a | b);\n                PYBIND11_ENUM_OP_CONV(\"__ror__\", a | b);\n                PYBIND11_ENUM_OP_CONV(\"__xor__\", a ^ b);\n                PYBIND11_ENUM_OP_CONV(\"__rxor__\", a ^ b);\n                m_base.attr(\"__invert__\")\n                    = cpp_function([](const object &arg) { return ~(int_(arg)); },\n                                   name(\"__invert__\"),\n                                   is_method(m_base));\n            }\n        } else {\n            PYBIND11_ENUM_OP_STRICT(\"__eq__\", int_(a).equal(int_(b)), return false);\n            PYBIND11_ENUM_OP_STRICT(\"__ne__\", !int_(a).equal(int_(b)), return true);\n\n            if (is_arithmetic) {\n#define PYBIND11_THROW throw type_error(\"Expected an enumeration of matching type!\");\n                PYBIND11_ENUM_OP_STRICT(\"__lt__\", int_(a) < int_(b), PYBIND11_THROW);\n                PYBIND11_ENUM_OP_STRICT(\"__gt__\", int_(a) > int_(b), PYBIND11_THROW);\n                PYBIND11_ENUM_OP_STRICT(\"__le__\", int_(a) <= int_(b), PYBIND11_THROW);\n                PYBIND11_ENUM_OP_STRICT(\"__ge__\", int_(a) >= int_(b), PYBIND11_THROW);\n#undef PYBIND11_THROW\n            }\n        }\n\n#undef PYBIND11_ENUM_OP_CONV_LHS\n#undef PYBIND11_ENUM_OP_CONV\n#undef PYBIND11_ENUM_OP_STRICT\n\n        m_base.attr(\"__getstate__\") = cpp_function(\n            [](const object &arg) { return int_(arg); }, name(\"__getstate__\"), is_method(m_base));\n\n        m_base.attr(\"__hash__\") = cpp_function(\n            [](const object &arg) { return int_(arg); }, name(\"__hash__\"), is_method(m_base));\n    }\n\n    PYBIND11_NOINLINE void value(char const *name_, object value, const char *doc = nullptr) {\n        dict entries = m_base.attr(\"__entries\");\n        str name(name_);\n        if (entries.contains(name)) {\n            std::string type_name = (std::string) str(m_base.attr(\"__name__\"));\n            throw value_error(std::move(type_name) + \": element \\\"\" + std::string(name_)\n                              + \"\\\" already exists!\");\n        }\n\n        entries[name] = pybind11::make_tuple(value, doc);\n        m_base.attr(std::move(name)) = std::move(value);\n    }\n\n    PYBIND11_NOINLINE void export_values() {\n        dict entries = m_base.attr(\"__entries\");\n        for (auto kv : entries) {\n            m_parent.attr(kv.first) = kv.second[int_(0)];\n        }\n    }\n\n    handle m_base;\n    handle m_parent;\n};\n\ntemplate <bool is_signed, size_t length>\nstruct equivalent_integer {};\ntemplate <>\nstruct equivalent_integer<true, 1> {\n    using type = int8_t;\n};\ntemplate <>\nstruct equivalent_integer<false, 1> {\n    using type = uint8_t;\n};\ntemplate <>\nstruct equivalent_integer<true, 2> {\n    using type = int16_t;\n};\ntemplate <>\nstruct equivalent_integer<false, 2> {\n    using type = uint16_t;\n};\ntemplate <>\nstruct equivalent_integer<true, 4> {\n    using type = int32_t;\n};\ntemplate <>\nstruct equivalent_integer<false, 4> {\n    using type = uint32_t;\n};\ntemplate <>\nstruct equivalent_integer<true, 8> {\n    using type = int64_t;\n};\ntemplate <>\nstruct equivalent_integer<false, 8> {\n    using type = uint64_t;\n};\n\ntemplate <typename IntLike>\nusing equivalent_integer_t =\n    typename equivalent_integer<std::is_signed<IntLike>::value, sizeof(IntLike)>::type;\n\nPYBIND11_NAMESPACE_END(detail)\n\n/// Binds C++ enumerations and enumeration classes to Python\ntemplate <typename Type>\nclass enum_ : public class_<Type> {\npublic:\n    using Base = class_<Type>;\n    using Base::attr;\n    using Base::def;\n    using Base::def_property_readonly;\n    using Base::def_property_readonly_static;\n    using Underlying = typename std::underlying_type<Type>::type;\n    // Scalar is the integer representation of underlying type\n    using Scalar = detail::conditional_t<detail::any_of<detail::is_std_char_type<Underlying>,\n                                                        std::is_same<Underlying, bool>>::value,\n                                         detail::equivalent_integer_t<Underlying>,\n                                         Underlying>;\n\n    template <typename... Extra>\n    enum_(const handle &scope, const char *name, const Extra &...extra)\n        : class_<Type>(scope, name, extra...), m_base(*this, scope) {\n        constexpr bool is_arithmetic = detail::any_of<std::is_same<arithmetic, Extra>...>::value;\n        constexpr bool is_convertible = std::is_convertible<Type, Underlying>::value;\n        m_base.init(is_arithmetic, is_convertible);\n\n        def(init([](Scalar i) { return static_cast<Type>(i); }), arg(\"value\"));\n        def_property_readonly(\"value\", [](Type value) { return (Scalar) value; });\n        def(\"__int__\", [](Type value) { return (Scalar) value; });\n        def(\"__index__\", [](Type value) { return (Scalar) value; });\n        attr(\"__setstate__\") = cpp_function(\n            [](detail::value_and_holder &v_h, Scalar arg) {\n                detail::initimpl::setstate<Base>(\n                    v_h, static_cast<Type>(arg), Py_TYPE(v_h.inst) != v_h.type->type);\n            },\n            detail::is_new_style_constructor(),\n            pybind11::name(\"__setstate__\"),\n            is_method(*this),\n            arg(\"state\"));\n    }\n\n    /// Export enumeration entries into the parent scope\n    enum_ &export_values() {\n        m_base.export_values();\n        return *this;\n    }\n\n    /// Add an enumeration entry\n    enum_ &value(char const *name, Type value, const char *doc = nullptr) {\n        m_base.value(name, pybind11::cast(value, return_value_policy::copy), doc);\n        return *this;\n    }\n\nprivate:\n    detail::enum_base m_base;\n};\n\nPYBIND11_NAMESPACE_BEGIN(detail)\n\nPYBIND11_NOINLINE void keep_alive_impl(handle nurse, handle patient) {\n    if (!nurse || !patient) {\n        pybind11_fail(\"Could not activate keep_alive!\");\n    }\n\n    if (patient.is_none() || nurse.is_none()) {\n        return; /* Nothing to keep alive or nothing to be kept alive by */\n    }\n\n    auto tinfo = all_type_info(Py_TYPE(nurse.ptr()));\n    if (!tinfo.empty()) {\n        /* It's a pybind-registered type, so we can store the patient in the\n         * internal list. */\n        add_patient(nurse.ptr(), patient.ptr());\n    } else {\n        /* Fall back to clever approach based on weak references taken from\n         * Boost.Python. This is not used for pybind-registered types because\n         * the objects can be destroyed out-of-order in a GC pass. */\n        cpp_function disable_lifesupport([patient](handle weakref) {\n            patient.dec_ref();\n            weakref.dec_ref();\n        });\n\n        weakref wr(nurse, disable_lifesupport);\n\n        patient.inc_ref(); /* reference patient and leak the weak reference */\n        (void) wr.release();\n    }\n}\n\nPYBIND11_NOINLINE void\nkeep_alive_impl(size_t Nurse, size_t Patient, function_call &call, handle ret) {\n    auto get_arg = [&](size_t n) {\n        if (n == 0) {\n            return ret;\n        }\n        if (n == 1 && call.init_self) {\n            return call.init_self;\n        }\n        if (n <= call.args.size()) {\n            return call.args[n - 1];\n        }\n        return handle();\n    };\n\n    keep_alive_impl(get_arg(Nurse), get_arg(Patient));\n}\n\ninline std::pair<decltype(internals::registered_types_py)::iterator, bool>\nall_type_info_get_cache(PyTypeObject *type) {\n    auto res = with_internals([type](internals &internals) {\n        return internals\n            .registered_types_py\n#ifdef __cpp_lib_unordered_map_try_emplace\n            .try_emplace(type);\n#else\n            .emplace(type, std::vector<detail::type_info *>());\n#endif\n    });\n    if (res.second) {\n        // New cache entry created; set up a weak reference to automatically remove it if the type\n        // gets destroyed:\n        weakref((PyObject *) type, cpp_function([type](handle wr) {\n                    with_internals([type](internals &internals) {\n                        internals.registered_types_py.erase(type);\n\n                        // TODO consolidate the erasure code in pybind11_meta_dealloc() in class.h\n                        auto &cache = internals.inactive_override_cache;\n                        for (auto it = cache.begin(), last = cache.end(); it != last;) {\n                            if (it->first == reinterpret_cast<PyObject *>(type)) {\n                                it = cache.erase(it);\n                            } else {\n                                ++it;\n                            }\n                        }\n                    });\n\n                    wr.dec_ref();\n                }))\n            .release();\n    }\n\n    return res;\n}\n\n/* There are a large number of apparently unused template arguments because\n * each combination requires a separate py::class_ registration.\n */\ntemplate <typename Access,\n          return_value_policy Policy,\n          typename Iterator,\n          typename Sentinel,\n          typename ValueType,\n          typename... Extra>\nstruct iterator_state {\n    Iterator it;\n    Sentinel end;\n    bool first_or_done;\n};\n\n// Note: these helpers take the iterator by non-const reference because some\n// iterators in the wild can't be dereferenced when const. The & after Iterator\n// is required for MSVC < 16.9. SFINAE cannot be reused for result_type due to\n// bugs in ICC, NVCC, and PGI compilers. See PR #3293.\ntemplate <typename Iterator, typename SFINAE = decltype(*std::declval<Iterator &>())>\nstruct iterator_access {\n    using result_type = decltype(*std::declval<Iterator &>());\n    // NOLINTNEXTLINE(readability-const-return-type) // PR #3263\n    result_type operator()(Iterator &it) const { return *it; }\n};\n\ntemplate <typename Iterator, typename SFINAE = decltype((*std::declval<Iterator &>()).first)>\nclass iterator_key_access {\nprivate:\n    using pair_type = decltype(*std::declval<Iterator &>());\n\npublic:\n    /* If either the pair itself or the element of the pair is a reference, we\n     * want to return a reference, otherwise a value. When the decltype\n     * expression is parenthesized it is based on the value category of the\n     * expression; otherwise it is the declared type of the pair member.\n     * The use of declval<pair_type> in the second branch rather than directly\n     * using *std::declval<Iterator &>() is a workaround for nvcc\n     * (it's not used in the first branch because going via decltype and back\n     * through declval does not perfectly preserve references).\n     */\n    using result_type\n        = conditional_t<std::is_reference<decltype(*std::declval<Iterator &>())>::value,\n                        decltype(((*std::declval<Iterator &>()).first)),\n                        decltype(std::declval<pair_type>().first)>;\n    result_type operator()(Iterator &it) const { return (*it).first; }\n};\n\ntemplate <typename Iterator, typename SFINAE = decltype((*std::declval<Iterator &>()).second)>\nclass iterator_value_access {\nprivate:\n    using pair_type = decltype(*std::declval<Iterator &>());\n\npublic:\n    using result_type\n        = conditional_t<std::is_reference<decltype(*std::declval<Iterator &>())>::value,\n                        decltype(((*std::declval<Iterator &>()).second)),\n                        decltype(std::declval<pair_type>().second)>;\n    result_type operator()(Iterator &it) const { return (*it).second; }\n};\n\ntemplate <typename Access,\n          return_value_policy Policy,\n          typename Iterator,\n          typename Sentinel,\n          typename ValueType,\n          typename... Extra>\niterator make_iterator_impl(Iterator first, Sentinel last, Extra &&...extra) {\n    using state = detail::iterator_state<Access, Policy, Iterator, Sentinel, ValueType, Extra...>;\n    // TODO: state captures only the types of Extra, not the values\n\n    if (!detail::get_type_info(typeid(state), false)) {\n        class_<state>(handle(), \"iterator\", pybind11::module_local())\n            .def(\"__iter__\", [](state &s) -> state & { return s; })\n            .def(\n                \"__next__\",\n                [](state &s) -> ValueType {\n                    if (!s.first_or_done) {\n                        ++s.it;\n                    } else {\n                        s.first_or_done = false;\n                    }\n                    if (s.it == s.end) {\n                        s.first_or_done = true;\n                        throw stop_iteration();\n                    }\n                    return Access()(s.it);\n                    // NOLINTNEXTLINE(readability-const-return-type) // PR #3263\n                },\n                std::forward<Extra>(extra)...,\n                Policy);\n    }\n\n    return cast(state{std::forward<Iterator>(first), std::forward<Sentinel>(last), true});\n}\n\nPYBIND11_NAMESPACE_END(detail)\n\n/// Makes a python iterator from a first and past-the-end C++ InputIterator.\ntemplate <return_value_policy Policy = return_value_policy::reference_internal,\n          typename Iterator,\n          typename Sentinel,\n          typename ValueType = typename detail::iterator_access<Iterator>::result_type,\n          typename... Extra>\ntyping::Iterator<ValueType> make_iterator(Iterator first, Sentinel last, Extra &&...extra) {\n    return detail::make_iterator_impl<detail::iterator_access<Iterator>,\n                                      Policy,\n                                      Iterator,\n                                      Sentinel,\n                                      ValueType,\n                                      Extra...>(std::forward<Iterator>(first),\n                                                std::forward<Sentinel>(last),\n                                                std::forward<Extra>(extra)...);\n}\n\n/// Makes a python iterator over the keys (`.first`) of a iterator over pairs from a\n/// first and past-the-end InputIterator.\ntemplate <return_value_policy Policy = return_value_policy::reference_internal,\n          typename Iterator,\n          typename Sentinel,\n          typename KeyType = typename detail::iterator_key_access<Iterator>::result_type,\n          typename... Extra>\ntyping::Iterator<KeyType> make_key_iterator(Iterator first, Sentinel last, Extra &&...extra) {\n    return detail::make_iterator_impl<detail::iterator_key_access<Iterator>,\n                                      Policy,\n                                      Iterator,\n                                      Sentinel,\n                                      KeyType,\n                                      Extra...>(std::forward<Iterator>(first),\n                                                std::forward<Sentinel>(last),\n                                                std::forward<Extra>(extra)...);\n}\n\n/// Makes a python iterator over the values (`.second`) of a iterator over pairs from a\n/// first and past-the-end InputIterator.\ntemplate <return_value_policy Policy = return_value_policy::reference_internal,\n          typename Iterator,\n          typename Sentinel,\n          typename ValueType = typename detail::iterator_value_access<Iterator>::result_type,\n          typename... Extra>\ntyping::Iterator<ValueType> make_value_iterator(Iterator first, Sentinel last, Extra &&...extra) {\n    return detail::make_iterator_impl<detail::iterator_value_access<Iterator>,\n                                      Policy,\n                                      Iterator,\n                                      Sentinel,\n                                      ValueType,\n                                      Extra...>(std::forward<Iterator>(first),\n                                                std::forward<Sentinel>(last),\n                                                std::forward<Extra>(extra)...);\n}\n\n/// Makes an iterator over values of an stl container or other container supporting\n/// `std::begin()`/`std::end()`\ntemplate <return_value_policy Policy = return_value_policy::reference_internal,\n          typename Type,\n          typename ValueType = typename detail::iterator_access<\n              decltype(std::begin(std::declval<Type &>()))>::result_type,\n          typename... Extra>\ntyping::Iterator<ValueType> make_iterator(Type &value, Extra &&...extra) {\n    return make_iterator<Policy>(\n        std::begin(value), std::end(value), std::forward<Extra>(extra)...);\n}\n\n/// Makes an iterator over the keys (`.first`) of a stl map-like container supporting\n/// `std::begin()`/`std::end()`\ntemplate <return_value_policy Policy = return_value_policy::reference_internal,\n          typename Type,\n          typename KeyType = typename detail::iterator_key_access<\n              decltype(std::begin(std::declval<Type &>()))>::result_type,\n          typename... Extra>\ntyping::Iterator<KeyType> make_key_iterator(Type &value, Extra &&...extra) {\n    return make_key_iterator<Policy>(\n        std::begin(value), std::end(value), std::forward<Extra>(extra)...);\n}\n\n/// Makes an iterator over the values (`.second`) of a stl map-like container supporting\n/// `std::begin()`/`std::end()`\ntemplate <return_value_policy Policy = return_value_policy::reference_internal,\n          typename Type,\n          typename ValueType = typename detail::iterator_value_access<\n              decltype(std::begin(std::declval<Type &>()))>::result_type,\n          typename... Extra>\ntyping::Iterator<ValueType> make_value_iterator(Type &value, Extra &&...extra) {\n    return make_value_iterator<Policy>(\n        std::begin(value), std::end(value), std::forward<Extra>(extra)...);\n}\n\ntemplate <typename InputType, typename OutputType>\nvoid implicitly_convertible() {\n    struct set_flag {\n        bool &flag;\n        explicit set_flag(bool &flag_) : flag(flag_) { flag_ = true; }\n        ~set_flag() { flag = false; }\n    };\n    auto implicit_caster = [](PyObject *obj, PyTypeObject *type) -> PyObject * {\n#ifdef Py_GIL_DISABLED\n        thread_local bool currently_used = false;\n#else\n        static bool currently_used = false;\n#endif\n        if (currently_used) { // implicit conversions are non-reentrant\n            return nullptr;\n        }\n        set_flag flag_helper(currently_used);\n        if (!detail::make_caster<InputType>().load(obj, false)) {\n            return nullptr;\n        }\n        tuple args(1);\n        args[0] = obj;\n        PyObject *result = PyObject_Call((PyObject *) type, args.ptr(), nullptr);\n        if (result == nullptr) {\n            PyErr_Clear();\n        }\n        return result;\n    };\n\n    if (auto *tinfo = detail::get_type_info(typeid(OutputType))) {\n        tinfo->implicit_conversions.emplace_back(std::move(implicit_caster));\n    } else {\n        pybind11_fail(\"implicitly_convertible: Unable to find type \" + type_id<OutputType>());\n    }\n}\n\ninline void register_exception_translator(ExceptionTranslator &&translator) {\n    detail::with_internals([&](detail::internals &internals) {\n        internals.registered_exception_translators.push_front(\n            std::forward<ExceptionTranslator>(translator));\n    });\n}\n\n/**\n * Add a new module-local exception translator. Locally registered functions\n * will be tried before any globally registered exception translators, which\n * will only be invoked if the module-local handlers do not deal with\n * the exception.\n */\ninline void register_local_exception_translator(ExceptionTranslator &&translator) {\n    detail::with_internals([&](detail::internals &internals) {\n        (void) internals;\n        detail::get_local_internals().registered_exception_translators.push_front(\n            std::forward<ExceptionTranslator>(translator));\n    });\n}\n\n/**\n * Wrapper to generate a new Python exception type.\n *\n * This should only be used with py::set_error() for now.\n * It is not (yet) possible to use as a py::base.\n * Template type argument is reserved for future use.\n */\ntemplate <typename type>\nclass exception : public object {\npublic:\n    exception() = default;\n    exception(handle scope, const char *name, handle base = PyExc_Exception) {\n        std::string full_name\n            = scope.attr(\"__name__\").cast<std::string>() + std::string(\".\") + name;\n        m_ptr = PyErr_NewException(const_cast<char *>(full_name.c_str()), base.ptr(), nullptr);\n        if (hasattr(scope, \"__dict__\") && scope.attr(\"__dict__\").contains(name)) {\n            pybind11_fail(\"Error during initialization: multiple incompatible \"\n                          \"definitions with name \\\"\"\n                          + std::string(name) + \"\\\"\");\n        }\n        scope.attr(name) = *this;\n    }\n\n    // Sets the current python exception to this exception object with the given message\n    PYBIND11_DEPRECATED(\"Please use py::set_error() instead \"\n                        \"(https://github.com/pybind/pybind11/pull/4772)\")\n    void operator()(const char *message) const { set_error(*this, message); }\n};\n\nPYBIND11_NAMESPACE_BEGIN(detail)\n\ntemplate <>\nstruct handle_type_name<exception<void>> {\n    static constexpr auto name = const_name(\"Exception\");\n};\n\n// Helper function for register_exception and register_local_exception\ntemplate <typename CppException>\nexception<CppException> &\nregister_exception_impl(handle scope, const char *name, handle base, bool isLocal) {\n    PYBIND11_CONSTINIT static gil_safe_call_once_and_store<exception<CppException>> exc_storage;\n    exc_storage.call_once_and_store_result(\n        [&]() { return exception<CppException>(scope, name, base); });\n\n    auto register_func\n        = isLocal ? &register_local_exception_translator : &register_exception_translator;\n\n    register_func([](std::exception_ptr p) {\n        if (!p) {\n            return;\n        }\n        try {\n            std::rethrow_exception(p);\n        } catch (const CppException &e) {\n            set_error(exc_storage.get_stored(), e.what());\n        }\n    });\n    return exc_storage.get_stored();\n}\n\nPYBIND11_NAMESPACE_END(detail)\n\n/**\n * Registers a Python exception in `m` of the given `name` and installs a translator to\n * translate the C++ exception to the created Python exception using the what() method.\n * This is intended for simple exception translations; for more complex translation, register the\n * exception object and translator directly.\n */\ntemplate <typename CppException>\nexception<CppException> &\nregister_exception(handle scope, const char *name, handle base = PyExc_Exception) {\n    return detail::register_exception_impl<CppException>(scope, name, base, false /* isLocal */);\n}\n\n/**\n * Registers a Python exception in `m` of the given `name` and installs a translator to\n * translate the C++ exception to the created Python exception using the what() method.\n * This translator will only be used for exceptions that are thrown in this module and will be\n * tried before global exception translators, including those registered with register_exception.\n * This is intended for simple exception translations; for more complex translation, register the\n * exception object and translator directly.\n */\ntemplate <typename CppException>\nexception<CppException> &\nregister_local_exception(handle scope, const char *name, handle base = PyExc_Exception) {\n    return detail::register_exception_impl<CppException>(scope, name, base, true /* isLocal */);\n}\n\nPYBIND11_NAMESPACE_BEGIN(detail)\nPYBIND11_NOINLINE void print(const tuple &args, const dict &kwargs) {\n    auto strings = tuple(args.size());\n    for (size_t i = 0; i < args.size(); ++i) {\n        strings[i] = str(args[i]);\n    }\n    auto sep = kwargs.contains(\"sep\") ? kwargs[\"sep\"] : str(\" \");\n    auto line = sep.attr(\"join\")(std::move(strings));\n\n    object file;\n    if (kwargs.contains(\"file\")) {\n        file = kwargs[\"file\"].cast<object>();\n    } else {\n        try {\n            file = module_::import(\"sys\").attr(\"stdout\");\n        } catch (const error_already_set &) {\n            /* If print() is called from code that is executed as\n               part of garbage collection during interpreter shutdown,\n               importing 'sys' can fail. Give up rather than crashing the\n               interpreter in this case. */\n            return;\n        }\n    }\n\n    auto write = file.attr(\"write\");\n    write(std::move(line));\n    write(kwargs.contains(\"end\") ? kwargs[\"end\"] : str(\"\\n\"));\n\n    if (kwargs.contains(\"flush\") && kwargs[\"flush\"].cast<bool>()) {\n        file.attr(\"flush\")();\n    }\n}\nPYBIND11_NAMESPACE_END(detail)\n\ntemplate <return_value_policy policy = return_value_policy::automatic_reference, typename... Args>\nvoid print(Args &&...args) {\n    auto c = detail::collect_arguments<policy>(std::forward<Args>(args)...);\n    detail::print(c.args(), c.kwargs());\n}\n\ninline void\nerror_already_set::m_fetched_error_deleter(detail::error_fetch_and_normalize *raw_ptr) {\n    gil_scoped_acquire gil;\n    error_scope scope;\n    delete raw_ptr;\n}\n\ninline const char *error_already_set::what() const noexcept {\n    gil_scoped_acquire gil;\n    error_scope scope;\n    return m_fetched_error->error_string().c_str();\n}\n\nPYBIND11_NAMESPACE_BEGIN(detail)\n\ninline function\nget_type_override(const void *this_ptr, const type_info *this_type, const char *name) {\n    handle self = get_object_handle(this_ptr, this_type);\n    if (!self) {\n        return function();\n    }\n    handle type = type::handle_of(self);\n    auto key = std::make_pair(type.ptr(), name);\n\n    /* Cache functions that aren't overridden in Python to avoid\n       many costly Python dictionary lookups below */\n    bool not_overridden = with_internals([&key](internals &internals) {\n        auto &cache = internals.inactive_override_cache;\n        return cache.find(key) != cache.end();\n    });\n    if (not_overridden) {\n        return function();\n    }\n\n    function override = getattr(self, name, function());\n    if (override.is_cpp_function()) {\n        with_internals([&](internals &internals) {\n            internals.inactive_override_cache.insert(std::move(key));\n        });\n        return function();\n    }\n\n    /* Don't call dispatch code if invoked from overridden function.\n       Unfortunately this doesn't work on PyPy. */\n#if !defined(PYPY_VERSION)\n#    if PY_VERSION_HEX >= 0x03090000\n    PyFrameObject *frame = PyThreadState_GetFrame(PyThreadState_Get());\n    if (frame != nullptr) {\n        PyCodeObject *f_code = PyFrame_GetCode(frame);\n        // f_code is guaranteed to not be NULL\n        if ((std::string) str(f_code->co_name) == name && f_code->co_argcount > 0) {\n#        if PY_VERSION_HEX >= 0x030d0000\n            PyObject *locals = PyEval_GetFrameLocals();\n#        else\n            PyObject *locals = PyEval_GetLocals();\n            Py_XINCREF(locals);\n#        endif\n            if (locals != nullptr) {\n#        if PY_VERSION_HEX >= 0x030b0000\n                PyObject *co_varnames = PyCode_GetVarnames(f_code);\n#        else\n                PyObject *co_varnames = PyObject_GetAttrString((PyObject *) f_code, \"co_varnames\");\n#        endif\n                PyObject *self_arg = PyTuple_GET_ITEM(co_varnames, 0);\n                Py_DECREF(co_varnames);\n                PyObject *self_caller = dict_getitem(locals, self_arg);\n                Py_DECREF(locals);\n                if (self_caller == self.ptr()) {\n                    Py_DECREF(f_code);\n                    Py_DECREF(frame);\n                    return function();\n                }\n            }\n        }\n        Py_DECREF(f_code);\n        Py_DECREF(frame);\n    }\n#    else\n    PyFrameObject *frame = PyThreadState_Get()->frame;\n    if (frame != nullptr && (std::string) str(frame->f_code->co_name) == name\n        && frame->f_code->co_argcount > 0) {\n        PyFrame_FastToLocals(frame);\n        PyObject *self_caller\n            = dict_getitem(frame->f_locals, PyTuple_GET_ITEM(frame->f_code->co_varnames, 0));\n        if (self_caller == self.ptr()) {\n            return function();\n        }\n    }\n#    endif\n\n#else\n    /* PyPy currently doesn't provide a detailed cpyext emulation of\n       frame objects, so we have to emulate this using Python. This\n       is going to be slow..*/\n    dict d;\n    d[\"self\"] = self;\n    d[\"name\"] = pybind11::str(name);\n    PyObject *result\n        = PyRun_String(\"import inspect\\n\"\n                       \"frame = inspect.currentframe()\\n\"\n                       \"if frame is not None:\\n\"\n                       \"    frame = frame.f_back\\n\"\n                       \"    if frame is not None and str(frame.f_code.co_name) == name and \"\n                       \"frame.f_code.co_argcount > 0:\\n\"\n                       \"        self_caller = frame.f_locals[frame.f_code.co_varnames[0]]\\n\"\n                       \"        if self_caller == self:\\n\"\n                       \"            self = None\\n\",\n                       Py_file_input,\n                       d.ptr(),\n                       d.ptr());\n    if (result == nullptr)\n        throw error_already_set();\n    Py_DECREF(result);\n    if (d[\"self\"].is_none())\n        return function();\n#endif\n\n    return override;\n}\nPYBIND11_NAMESPACE_END(detail)\n\n/** \\rst\n  Try to retrieve a python method by the provided name from the instance pointed to by the\n  this_ptr.\n\n  :this_ptr: The pointer to the object the overridden method should be retrieved for. This should\n             be the first non-trampoline class encountered in the inheritance chain.\n  :name: The name of the overridden Python method to retrieve.\n  :return: The Python method by this name from the object or an empty function wrapper.\n \\endrst */\ntemplate <class T>\nfunction get_override(const T *this_ptr, const char *name) {\n    auto *tinfo = detail::get_type_info(typeid(T));\n    return tinfo ? detail::get_type_override(this_ptr, tinfo, name) : function();\n}\n\n#define PYBIND11_OVERRIDE_IMPL(ret_type, cname, name, ...)                                        \\\n    do {                                                                                          \\\n        pybind11::gil_scoped_acquire gil;                                                         \\\n        pybind11::function override                                                               \\\n            = pybind11::get_override(static_cast<const cname *>(this), name);                     \\\n        if (override) {                                                                           \\\n            auto o = override(__VA_ARGS__);                                                       \\\n            PYBIND11_WARNING_PUSH                                                                 \\\n            PYBIND11_WARNING_DISABLE_MSVC(4127)                                                   \\\n            if (pybind11::detail::cast_is_temporary_value_reference<ret_type>::value              \\\n                && !pybind11::detail::is_same_ignoring_cvref<ret_type, PyObject *>::value) {      \\\n                static pybind11::detail::override_caster_t<ret_type> caster;                      \\\n                return pybind11::detail::cast_ref<ret_type>(std::move(o), caster);                \\\n            }                                                                                     \\\n            PYBIND11_WARNING_POP                                                                  \\\n            return pybind11::detail::cast_safe<ret_type>(std::move(o));                           \\\n        }                                                                                         \\\n    } while (false)\n\n/** \\rst\n    Macro to populate the virtual method in the trampoline class. This macro tries to look up a\n    method named 'fn' from the Python side, deals with the :ref:`gil` and necessary argument\n    conversions to call this method and return the appropriate type.\n    See :ref:`overriding_virtuals` for more information. This macro should be used when the method\n    name in C is not the same as the method name in Python. For example with `__str__`.\n\n    .. code-block:: cpp\n\n      std::string toString() override {\n        PYBIND11_OVERRIDE_NAME(\n            std::string, // Return type (ret_type)\n            Animal,      // Parent class (cname)\n            \"__str__\",   // Name of method in Python (name)\n            toString,    // Name of function in C++ (fn)\n        );\n      }\n\\endrst */\n#define PYBIND11_OVERRIDE_NAME(ret_type, cname, name, fn, ...)                                    \\\n    do {                                                                                          \\\n        PYBIND11_OVERRIDE_IMPL(PYBIND11_TYPE(ret_type), PYBIND11_TYPE(cname), name, __VA_ARGS__); \\\n        return cname::fn(__VA_ARGS__);                                                            \\\n    } while (false)\n\n/** \\rst\n    Macro for pure virtual functions, this function is identical to\n    :c:macro:`PYBIND11_OVERRIDE_NAME`, except that it throws if no override can be found.\n\\endrst */\n#define PYBIND11_OVERRIDE_PURE_NAME(ret_type, cname, name, fn, ...)                               \\\n    do {                                                                                          \\\n        PYBIND11_OVERRIDE_IMPL(PYBIND11_TYPE(ret_type), PYBIND11_TYPE(cname), name, __VA_ARGS__); \\\n        pybind11::pybind11_fail(                                                                  \\\n            \"Tried to call pure virtual function \\\"\" PYBIND11_STRINGIFY(cname) \"::\" name \"\\\"\");   \\\n    } while (false)\n\n/** \\rst\n    Macro to populate the virtual method in the trampoline class. This macro tries to look up the\n    method from the Python side, deals with the :ref:`gil` and necessary argument conversions to\n    call this method and return the appropriate type. This macro should be used if the method name\n    in C and in Python are identical.\n    See :ref:`overriding_virtuals` for more information.\n\n    .. code-block:: cpp\n\n      class PyAnimal : public Animal {\n      public:\n          // Inherit the constructors\n          using Animal::Animal;\n\n          // Trampoline (need one for each virtual function)\n          std::string go(int n_times) override {\n              PYBIND11_OVERRIDE_PURE(\n                  std::string, // Return type (ret_type)\n                  Animal,      // Parent class (cname)\n                  go,          // Name of function in C++ (must match Python name) (fn)\n                  n_times      // Argument(s) (...)\n              );\n          }\n      };\n\\endrst */\n#define PYBIND11_OVERRIDE(ret_type, cname, fn, ...)                                               \\\n    PYBIND11_OVERRIDE_NAME(PYBIND11_TYPE(ret_type), PYBIND11_TYPE(cname), #fn, fn, __VA_ARGS__)\n\n/** \\rst\n    Macro for pure virtual functions, this function is identical to :c:macro:`PYBIND11_OVERRIDE`,\n    except that it throws if no override can be found.\n\\endrst */\n#define PYBIND11_OVERRIDE_PURE(ret_type, cname, fn, ...)                                          \\\n    PYBIND11_OVERRIDE_PURE_NAME(                                                                  \\\n        PYBIND11_TYPE(ret_type), PYBIND11_TYPE(cname), #fn, fn, __VA_ARGS__)\n\n// Deprecated versions\n\nPYBIND11_DEPRECATED(\"get_type_overload has been deprecated\")\ninline function\nget_type_overload(const void *this_ptr, const detail::type_info *this_type, const char *name) {\n    return detail::get_type_override(this_ptr, this_type, name);\n}\n\ntemplate <class T>\ninline function get_overload(const T *this_ptr, const char *name) {\n    return get_override(this_ptr, name);\n}\n\n#define PYBIND11_OVERLOAD_INT(ret_type, cname, name, ...)                                         \\\n    PYBIND11_OVERRIDE_IMPL(PYBIND11_TYPE(ret_type), PYBIND11_TYPE(cname), name, __VA_ARGS__)\n#define PYBIND11_OVERLOAD_NAME(ret_type, cname, name, fn, ...)                                    \\\n    PYBIND11_OVERRIDE_NAME(PYBIND11_TYPE(ret_type), PYBIND11_TYPE(cname), name, fn, __VA_ARGS__)\n#define PYBIND11_OVERLOAD_PURE_NAME(ret_type, cname, name, fn, ...)                               \\\n    PYBIND11_OVERRIDE_PURE_NAME(                                                                  \\\n        PYBIND11_TYPE(ret_type), PYBIND11_TYPE(cname), name, fn, __VA_ARGS__);\n#define PYBIND11_OVERLOAD(ret_type, cname, fn, ...)                                               \\\n    PYBIND11_OVERRIDE(PYBIND11_TYPE(ret_type), PYBIND11_TYPE(cname), fn, __VA_ARGS__)\n#define PYBIND11_OVERLOAD_PURE(ret_type, cname, fn, ...)                                          \\\n    PYBIND11_OVERRIDE_PURE(PYBIND11_TYPE(ret_type), PYBIND11_TYPE(cname), fn, __VA_ARGS__);\n\nPYBIND11_NAMESPACE_END(PYBIND11_NAMESPACE)\n"
  },
  {
    "path": "libs/pybind11/include/pybind11/pytypes.h",
    "content": "/*\n    pybind11/pytypes.h: Convenience wrapper classes for basic Python types\n\n    Copyright (c) 2016 Wenzel Jakob <wenzel.jakob@epfl.ch>\n\n    All rights reserved. Use of this source code is governed by a\n    BSD-style license that can be found in the LICENSE file.\n*/\n\n#pragma once\n\n#include \"detail/common.h\"\n#include \"buffer_info.h\"\n\n#include <assert.h>\n#include <cstddef>\n#include <exception>\n#include <frameobject.h>\n#include <iterator>\n#include <memory>\n#include <string>\n#include <type_traits>\n#include <typeinfo>\n#include <utility>\n\n#if defined(PYBIND11_HAS_OPTIONAL)\n#    include <optional>\n#endif\n\n#ifdef PYBIND11_HAS_STRING_VIEW\n#    include <string_view>\n#endif\n\nPYBIND11_NAMESPACE_BEGIN(PYBIND11_NAMESPACE)\n\nPYBIND11_WARNING_DISABLE_MSVC(4127)\n\n/* A few forward declarations */\nclass handle;\nclass object;\nclass str;\nclass iterator;\nclass type;\nstruct arg;\nstruct arg_v;\n\nPYBIND11_NAMESPACE_BEGIN(detail)\nclass args_proxy;\nbool isinstance_generic(handle obj, const std::type_info &tp);\n\n// Accessor forward declarations\ntemplate <typename Policy>\nclass accessor;\nnamespace accessor_policies {\nstruct obj_attr;\nstruct str_attr;\nstruct generic_item;\nstruct sequence_item;\nstruct list_item;\nstruct tuple_item;\n} // namespace accessor_policies\n// PLEASE KEEP handle_type_name SPECIALIZATIONS IN SYNC.\nusing obj_attr_accessor = accessor<accessor_policies::obj_attr>;\nusing str_attr_accessor = accessor<accessor_policies::str_attr>;\nusing item_accessor = accessor<accessor_policies::generic_item>;\nusing sequence_accessor = accessor<accessor_policies::sequence_item>;\nusing list_accessor = accessor<accessor_policies::list_item>;\nusing tuple_accessor = accessor<accessor_policies::tuple_item>;\n\n/// Tag and check to identify a class which implements the Python object API\nclass pyobject_tag {};\ntemplate <typename T>\nusing is_pyobject = std::is_base_of<pyobject_tag, remove_reference_t<T>>;\n\n/** \\rst\n    A mixin class which adds common functions to `handle`, `object` and various accessors.\n    The only requirement for `Derived` is to implement ``PyObject *Derived::ptr() const``.\n\\endrst */\ntemplate <typename Derived>\nclass object_api : public pyobject_tag {\n    const Derived &derived() const { return static_cast<const Derived &>(*this); }\n\npublic:\n    /** \\rst\n        Return an iterator equivalent to calling ``iter()`` in Python. The object\n        must be a collection which supports the iteration protocol.\n    \\endrst */\n    iterator begin() const;\n    /// Return a sentinel which ends iteration.\n    iterator end() const;\n\n    /** \\rst\n        Return an internal functor to invoke the object's sequence protocol. Casting\n        the returned ``detail::item_accessor`` instance to a `handle` or `object`\n        subclass causes a corresponding call to ``__getitem__``. Assigning a `handle`\n        or `object` subclass causes a call to ``__setitem__``.\n    \\endrst */\n    item_accessor operator[](handle key) const;\n    /// See above (the only difference is that the key's reference is stolen)\n    item_accessor operator[](object &&key) const;\n    /// See above (the only difference is that the key is provided as a string literal)\n    item_accessor operator[](const char *key) const;\n\n    /** \\rst\n        Return an internal functor to access the object's attributes. Casting the\n        returned ``detail::obj_attr_accessor`` instance to a `handle` or `object`\n        subclass causes a corresponding call to ``getattr``. Assigning a `handle`\n        or `object` subclass causes a call to ``setattr``.\n    \\endrst */\n    obj_attr_accessor attr(handle key) const;\n    /// See above (the only difference is that the key's reference is stolen)\n    obj_attr_accessor attr(object &&key) const;\n    /// See above (the only difference is that the key is provided as a string literal)\n    str_attr_accessor attr(const char *key) const;\n\n    /** \\rst\n        Matches * unpacking in Python, e.g. to unpack arguments out of a ``tuple``\n        or ``list`` for a function call. Applying another * to the result yields\n        ** unpacking, e.g. to unpack a dict as function keyword arguments.\n        See :ref:`calling_python_functions`.\n    \\endrst */\n    args_proxy operator*() const;\n\n    /// Check if the given item is contained within this object, i.e. ``item in obj``.\n    template <typename T>\n    bool contains(T &&item) const;\n\n    /** \\rst\n        Assuming the Python object is a function or implements the ``__call__``\n        protocol, ``operator()`` invokes the underlying function, passing an\n        arbitrary set of parameters. The result is returned as a `object` and\n        may need to be converted back into a Python object using `handle::cast()`.\n\n        When some of the arguments cannot be converted to Python objects, the\n        function will throw a `cast_error` exception. When the Python function\n        call fails, a `error_already_set` exception is thrown.\n    \\endrst */\n    template <return_value_policy policy = return_value_policy::automatic_reference,\n              typename... Args>\n    object operator()(Args &&...args) const;\n    template <return_value_policy policy = return_value_policy::automatic_reference,\n              typename... Args>\n    PYBIND11_DEPRECATED(\"call(...) was deprecated in favor of operator()(...)\")\n    object call(Args &&...args) const;\n\n    /// Equivalent to ``obj is other`` in Python.\n    bool is(object_api const &other) const { return derived().ptr() == other.derived().ptr(); }\n    /// Equivalent to ``obj is None`` in Python.\n    bool is_none() const { return derived().ptr() == Py_None; }\n    /// Equivalent to obj == other in Python\n    bool equal(object_api const &other) const { return rich_compare(other, Py_EQ); }\n    bool not_equal(object_api const &other) const { return rich_compare(other, Py_NE); }\n    bool operator<(object_api const &other) const { return rich_compare(other, Py_LT); }\n    bool operator<=(object_api const &other) const { return rich_compare(other, Py_LE); }\n    bool operator>(object_api const &other) const { return rich_compare(other, Py_GT); }\n    bool operator>=(object_api const &other) const { return rich_compare(other, Py_GE); }\n\n    object operator-() const;\n    object operator~() const;\n    object operator+(object_api const &other) const;\n    object operator+=(object_api const &other);\n    object operator-(object_api const &other) const;\n    object operator-=(object_api const &other);\n    object operator*(object_api const &other) const;\n    object operator*=(object_api const &other);\n    object operator/(object_api const &other) const;\n    object operator/=(object_api const &other);\n    object operator|(object_api const &other) const;\n    object operator|=(object_api const &other);\n    object operator&(object_api const &other) const;\n    object operator&=(object_api const &other);\n    object operator^(object_api const &other) const;\n    object operator^=(object_api const &other);\n    object operator<<(object_api const &other) const;\n    object operator<<=(object_api const &other);\n    object operator>>(object_api const &other) const;\n    object operator>>=(object_api const &other);\n\n    PYBIND11_DEPRECATED(\"Use py::str(obj) instead\")\n    pybind11::str str() const;\n\n    /// Get or set the object's docstring, i.e. ``obj.__doc__``.\n    str_attr_accessor doc() const;\n\n    /// Return the object's current reference count\n    ssize_t ref_count() const {\n#ifdef PYPY_VERSION\n        // PyPy uses the top few bits for REFCNT_FROM_PYPY & REFCNT_FROM_PYPY_LIGHT\n        // Following pybind11 2.12.1 and older behavior and removing this part\n        return static_cast<ssize_t>(static_cast<int>(Py_REFCNT(derived().ptr())));\n#else\n        return Py_REFCNT(derived().ptr());\n#endif\n    }\n\n    // TODO PYBIND11_DEPRECATED(\n    //     \"Call py::type::handle_of(h) or py::type::of(h) instead of h.get_type()\")\n    handle get_type() const;\n\nprivate:\n    bool rich_compare(object_api const &other, int value) const;\n};\n\ntemplate <typename T>\nusing is_pyobj_ptr_or_nullptr_t = detail::any_of<std::is_same<T, PyObject *>,\n                                                 std::is_same<T, PyObject *const>,\n                                                 std::is_same<T, std::nullptr_t>>;\n\nPYBIND11_NAMESPACE_END(detail)\n\n#if !defined(PYBIND11_HANDLE_REF_DEBUG) && !defined(NDEBUG)\n#    define PYBIND11_HANDLE_REF_DEBUG\n#endif\n\n/** \\rst\n    Holds a reference to a Python object (no reference counting)\n\n    The `handle` class is a thin wrapper around an arbitrary Python object (i.e. a\n    ``PyObject *`` in Python's C API). It does not perform any automatic reference\n    counting and merely provides a basic C++ interface to various Python API functions.\n\n    .. seealso::\n        The `object` class inherits from `handle` and adds automatic reference\n        counting features.\n\\endrst */\nclass handle : public detail::object_api<handle> {\npublic:\n    /// The default constructor creates a handle with a ``nullptr``-valued pointer\n    handle() = default;\n\n    /// Enable implicit conversion from ``PyObject *`` and ``nullptr``.\n    /// Not using ``handle(PyObject *ptr)`` to avoid implicit conversion from ``0``.\n    template <typename T,\n              detail::enable_if_t<detail::is_pyobj_ptr_or_nullptr_t<T>::value, int> = 0>\n    // NOLINTNEXTLINE(google-explicit-constructor)\n    handle(T ptr) : m_ptr(ptr) {}\n\n    /// Enable implicit conversion through ``T::operator PyObject *()``.\n    template <\n        typename T,\n        detail::enable_if_t<detail::all_of<detail::none_of<std::is_base_of<handle, T>,\n                                                           detail::is_pyobj_ptr_or_nullptr_t<T>>,\n                                           std::is_convertible<T, PyObject *>>::value,\n                            int>\n        = 0>\n    // NOLINTNEXTLINE(google-explicit-constructor)\n    handle(T &obj) : m_ptr(obj) {}\n\n    /// Return the underlying ``PyObject *`` pointer\n    PyObject *ptr() const { return m_ptr; }\n    PyObject *&ptr() { return m_ptr; }\n\n    /** \\rst\n        Manually increase the reference count of the Python object. Usually, it is\n        preferable to use the `object` class which derives from `handle` and calls\n        this function automatically. Returns a reference to itself.\n    \\endrst */\n    const handle &inc_ref() const & {\n#ifdef PYBIND11_HANDLE_REF_DEBUG\n        inc_ref_counter(1);\n#endif\n#ifdef PYBIND11_ASSERT_GIL_HELD_INCREF_DECREF\n        if (m_ptr != nullptr && !PyGILState_Check()) {\n            throw_gilstate_error(\"pybind11::handle::inc_ref()\");\n        }\n#endif\n        Py_XINCREF(m_ptr);\n        return *this;\n    }\n\n    /** \\rst\n        Manually decrease the reference count of the Python object. Usually, it is\n        preferable to use the `object` class which derives from `handle` and calls\n        this function automatically. Returns a reference to itself.\n    \\endrst */\n    const handle &dec_ref() const & {\n#ifdef PYBIND11_ASSERT_GIL_HELD_INCREF_DECREF\n        if (m_ptr != nullptr && !PyGILState_Check()) {\n            throw_gilstate_error(\"pybind11::handle::dec_ref()\");\n        }\n#endif\n        Py_XDECREF(m_ptr);\n        return *this;\n    }\n\n    /** \\rst\n        Attempt to cast the Python object into the given C++ type. A `cast_error`\n        will be throw upon failure.\n    \\endrst */\n    template <typename T>\n    T cast() const;\n    /// Return ``true`` when the `handle` wraps a valid Python object\n    explicit operator bool() const { return m_ptr != nullptr; }\n    /** \\rst\n        Deprecated: Check that the underlying pointers are the same.\n        Equivalent to ``obj1 is obj2`` in Python.\n    \\endrst */\n    PYBIND11_DEPRECATED(\"Use obj1.is(obj2) instead\")\n    bool operator==(const handle &h) const { return m_ptr == h.m_ptr; }\n    PYBIND11_DEPRECATED(\"Use !obj1.is(obj2) instead\")\n    bool operator!=(const handle &h) const { return m_ptr != h.m_ptr; }\n    PYBIND11_DEPRECATED(\"Use handle::operator bool() instead\")\n    bool check() const { return m_ptr != nullptr; }\n\nprotected:\n    PyObject *m_ptr = nullptr;\n\nprivate:\n#ifdef PYBIND11_ASSERT_GIL_HELD_INCREF_DECREF\n    void throw_gilstate_error(const std::string &function_name) const {\n        fprintf(\n            stderr,\n            \"%s is being called while the GIL is either not held or invalid. Please see \"\n            \"https://pybind11.readthedocs.io/en/stable/advanced/\"\n            \"misc.html#common-sources-of-global-interpreter-lock-errors for debugging advice.\\n\"\n            \"If you are convinced there is no bug in your code, you can #define \"\n            \"PYBIND11_NO_ASSERT_GIL_HELD_INCREF_DECREF \"\n            \"to disable this check. In that case you have to ensure this #define is consistently \"\n            \"used for all translation units linked into a given pybind11 extension, otherwise \"\n            \"there will be ODR violations.\",\n            function_name.c_str());\n        if (Py_TYPE(m_ptr)->tp_name != nullptr) {\n            fprintf(stderr,\n                    \" The failing %s call was triggered on a %s object.\",\n                    function_name.c_str(),\n                    Py_TYPE(m_ptr)->tp_name);\n        }\n        fprintf(stderr, \"\\n\");\n        fflush(stderr);\n        throw std::runtime_error(function_name + \" PyGILState_Check() failure.\");\n    }\n#endif\n\n#ifdef PYBIND11_HANDLE_REF_DEBUG\n    static std::size_t inc_ref_counter(std::size_t add) {\n        thread_local std::size_t counter = 0;\n        counter += add;\n        return counter;\n    }\n\npublic:\n    static std::size_t inc_ref_counter() { return inc_ref_counter(0); }\n#endif\n};\n\ninline void set_error(const handle &type, const char *message) {\n    PyErr_SetString(type.ptr(), message);\n}\n\ninline void set_error(const handle &type, const handle &value) {\n    PyErr_SetObject(type.ptr(), value.ptr());\n}\n\n/** \\rst\n    Holds a reference to a Python object (with reference counting)\n\n    Like `handle`, the `object` class is a thin wrapper around an arbitrary Python\n    object (i.e. a ``PyObject *`` in Python's C API). In contrast to `handle`, it\n    optionally increases the object's reference count upon construction, and it\n    *always* decreases the reference count when the `object` instance goes out of\n    scope and is destructed. When using `object` instances consistently, it is much\n    easier to get reference counting right at the first attempt.\n\\endrst */\nclass object : public handle {\npublic:\n    object() = default;\n    PYBIND11_DEPRECATED(\"Use reinterpret_borrow<object>() or reinterpret_steal<object>()\")\n    object(handle h, bool is_borrowed) : handle(h) {\n        if (is_borrowed) {\n            inc_ref();\n        }\n    }\n    /// Copy constructor; always increases the reference count\n    object(const object &o) : handle(o) { inc_ref(); }\n    /// Move constructor; steals the object from ``other`` and preserves its reference count\n    object(object &&other) noexcept : handle(other) { other.m_ptr = nullptr; }\n    /// Destructor; automatically calls `handle::dec_ref()`\n    ~object() { dec_ref(); }\n\n    /** \\rst\n        Resets the internal pointer to ``nullptr`` without decreasing the\n        object's reference count. The function returns a raw handle to the original\n        Python object.\n    \\endrst */\n    handle release() {\n        PyObject *tmp = m_ptr;\n        m_ptr = nullptr;\n        return handle(tmp);\n    }\n\n    object &operator=(const object &other) {\n        // Skip inc_ref and dec_ref if both objects are the same\n        if (!this->is(other)) {\n            other.inc_ref();\n            // Use temporary variable to ensure `*this` remains valid while\n            // `Py_XDECREF` executes, in case `*this` is accessible from Python.\n            handle temp(m_ptr);\n            m_ptr = other.m_ptr;\n            temp.dec_ref();\n        }\n        return *this;\n    }\n\n    object &operator=(object &&other) noexcept {\n        if (this != &other) {\n            handle temp(m_ptr);\n            m_ptr = other.m_ptr;\n            other.m_ptr = nullptr;\n            temp.dec_ref();\n        }\n        return *this;\n    }\n\n#define PYBIND11_INPLACE_OP(iop)                                                                  \\\n    object iop(object_api const &other) { return operator=(handle::iop(other)); }\n\n    PYBIND11_INPLACE_OP(operator+=)\n    PYBIND11_INPLACE_OP(operator-=)\n    PYBIND11_INPLACE_OP(operator*=)\n    PYBIND11_INPLACE_OP(operator/=)\n    PYBIND11_INPLACE_OP(operator|=)\n    PYBIND11_INPLACE_OP(operator&=)\n    PYBIND11_INPLACE_OP(operator^=)\n    PYBIND11_INPLACE_OP(operator<<=)\n    PYBIND11_INPLACE_OP(operator>>=)\n#undef PYBIND11_INPLACE_OP\n\n    // Calling cast() on an object lvalue just copies (via handle::cast)\n    template <typename T>\n    T cast() const &;\n    // Calling on an object rvalue does a move, if needed and/or possible\n    template <typename T>\n    T cast() &&;\n\nprotected:\n    // Tags for choosing constructors from raw PyObject *\n    struct borrowed_t {};\n    struct stolen_t {};\n\n    /// @cond BROKEN\n    template <typename T>\n    friend T reinterpret_borrow(handle);\n    template <typename T>\n    friend T reinterpret_steal(handle);\n    /// @endcond\n\npublic:\n    // Only accessible from derived classes and the reinterpret_* functions\n    object(handle h, borrowed_t) : handle(h) { inc_ref(); }\n    object(handle h, stolen_t) : handle(h) {}\n};\n\n/** \\rst\n    Declare that a `handle` or ``PyObject *`` is a certain type and borrow the reference.\n    The target type ``T`` must be `object` or one of its derived classes. The function\n    doesn't do any conversions or checks. It's up to the user to make sure that the\n    target type is correct.\n\n    .. code-block:: cpp\n\n        PyObject *p = PyList_GetItem(obj, index);\n        py::object o = reinterpret_borrow<py::object>(p);\n        // or\n        py::tuple t = reinterpret_borrow<py::tuple>(p); // <-- `p` must be already be a `tuple`\n\\endrst */\ntemplate <typename T>\nT reinterpret_borrow(handle h) {\n    return {h, object::borrowed_t{}};\n}\n\n/** \\rst\n    Like `reinterpret_borrow`, but steals the reference.\n\n     .. code-block:: cpp\n\n        PyObject *p = PyObject_Str(obj);\n        py::str s = reinterpret_steal<py::str>(p); // <-- `p` must be already be a `str`\n\\endrst */\ntemplate <typename T>\nT reinterpret_steal(handle h) {\n    return {h, object::stolen_t{}};\n}\n\nPYBIND11_NAMESPACE_BEGIN(detail)\n\n// Equivalent to obj.__class__.__name__ (or obj.__name__ if obj is a class).\ninline const char *obj_class_name(PyObject *obj) {\n    if (PyType_Check(obj)) {\n        return reinterpret_cast<PyTypeObject *>(obj)->tp_name;\n    }\n    return Py_TYPE(obj)->tp_name;\n}\n\nstd::string error_string();\n\n// The code in this struct is very unusual, to minimize the chances of\n// masking bugs (elsewhere) by errors during the error handling (here).\n// This is meant to be a lifeline for troubleshooting long-running processes\n// that crash under conditions that are virtually impossible to reproduce.\n// Low-level implementation alternatives are preferred to higher-level ones\n// that might raise cascading exceptions. Last-ditch-kind-of attempts are made\n// to report as much of the original error as possible, even if there are\n// secondary issues obtaining some of the details.\nstruct error_fetch_and_normalize {\n    // This comment only applies to Python <= 3.11:\n    //     Immediate normalization is long-established behavior (starting with\n    //     https://github.com/pybind/pybind11/commit/135ba8deafb8bf64a15b24d1513899eb600e2011\n    //     from Sep 2016) and safest. Normalization could be deferred, but this could mask\n    //     errors elsewhere, the performance gain is very minor in typical situations\n    //     (usually the dominant bottleneck is EH unwinding), and the implementation here\n    //     would be more complex.\n    // Starting with Python 3.12, PyErr_Fetch() normalizes exceptions immediately.\n    // Any errors during normalization are tracked under __notes__.\n    explicit error_fetch_and_normalize(const char *called) {\n        PyErr_Fetch(&m_type.ptr(), &m_value.ptr(), &m_trace.ptr());\n        if (!m_type) {\n            pybind11_fail(\"Internal error: \" + std::string(called)\n                          + \" called while \"\n                            \"Python error indicator not set.\");\n        }\n        const char *exc_type_name_orig = detail::obj_class_name(m_type.ptr());\n        if (exc_type_name_orig == nullptr) {\n            pybind11_fail(\"Internal error: \" + std::string(called)\n                          + \" failed to obtain the name \"\n                            \"of the original active exception type.\");\n        }\n        m_lazy_error_string = exc_type_name_orig;\n#if PY_VERSION_HEX >= 0x030C0000\n        // The presence of __notes__ is likely due to exception normalization\n        // errors, although that is not necessarily true, therefore insert a\n        // hint only:\n        if (PyObject_HasAttrString(m_value.ptr(), \"__notes__\")) {\n            m_lazy_error_string += \"[WITH __notes__]\";\n        }\n#else\n        // PyErr_NormalizeException() may change the exception type if there are cascading\n        // failures. This can potentially be extremely confusing.\n        PyErr_NormalizeException(&m_type.ptr(), &m_value.ptr(), &m_trace.ptr());\n        if (m_type.ptr() == nullptr) {\n            pybind11_fail(\"Internal error: \" + std::string(called)\n                          + \" failed to normalize the \"\n                            \"active exception.\");\n        }\n        const char *exc_type_name_norm = detail::obj_class_name(m_type.ptr());\n        if (exc_type_name_norm == nullptr) {\n            pybind11_fail(\"Internal error: \" + std::string(called)\n                          + \" failed to obtain the name \"\n                            \"of the normalized active exception type.\");\n        }\n#    if defined(PYPY_VERSION_NUM) && PYPY_VERSION_NUM < 0x07030a00\n        // This behavior runs the risk of masking errors in the error handling, but avoids a\n        // conflict with PyPy, which relies on the normalization here to change OSError to\n        // FileNotFoundError (https://github.com/pybind/pybind11/issues/4075).\n        m_lazy_error_string = exc_type_name_norm;\n#    else\n        if (exc_type_name_norm != m_lazy_error_string) {\n            std::string msg = std::string(called)\n                              + \": MISMATCH of original and normalized \"\n                                \"active exception types: \";\n            msg += \"ORIGINAL \";\n            msg += m_lazy_error_string;\n            msg += \" REPLACED BY \";\n            msg += exc_type_name_norm;\n            msg += \": \" + format_value_and_trace();\n            pybind11_fail(msg);\n        }\n#    endif\n#endif\n    }\n\n    error_fetch_and_normalize(const error_fetch_and_normalize &) = delete;\n    error_fetch_and_normalize(error_fetch_and_normalize &&) = delete;\n\n    std::string format_value_and_trace() const {\n        std::string result;\n        std::string message_error_string;\n        if (m_value) {\n            auto value_str = reinterpret_steal<object>(PyObject_Str(m_value.ptr()));\n            constexpr const char *message_unavailable_exc\n                = \"<MESSAGE UNAVAILABLE DUE TO ANOTHER EXCEPTION>\";\n            if (!value_str) {\n                message_error_string = detail::error_string();\n                result = message_unavailable_exc;\n            } else {\n                // Not using `value_str.cast<std::string>()`, to not potentially throw a secondary\n                // error_already_set that will then result in process termination (#4288).\n                auto value_bytes = reinterpret_steal<object>(\n                    PyUnicode_AsEncodedString(value_str.ptr(), \"utf-8\", \"backslashreplace\"));\n                if (!value_bytes) {\n                    message_error_string = detail::error_string();\n                    result = message_unavailable_exc;\n                } else {\n                    char *buffer = nullptr;\n                    Py_ssize_t length = 0;\n                    if (PyBytes_AsStringAndSize(value_bytes.ptr(), &buffer, &length) == -1) {\n                        message_error_string = detail::error_string();\n                        result = message_unavailable_exc;\n                    } else {\n                        result = std::string(buffer, static_cast<std::size_t>(length));\n                    }\n                }\n            }\n#if PY_VERSION_HEX >= 0x030B0000\n            auto notes\n                = reinterpret_steal<object>(PyObject_GetAttrString(m_value.ptr(), \"__notes__\"));\n            if (!notes) {\n                PyErr_Clear(); // No notes is good news.\n            } else {\n                auto len_notes = PyList_Size(notes.ptr());\n                if (len_notes < 0) {\n                    result += \"\\nFAILURE obtaining len(__notes__): \" + detail::error_string();\n                } else {\n                    result += \"\\n__notes__ (len=\" + std::to_string(len_notes) + \"):\";\n                    for (ssize_t i = 0; i < len_notes; i++) {\n                        PyObject *note = PyList_GET_ITEM(notes.ptr(), i);\n                        auto note_bytes = reinterpret_steal<object>(\n                            PyUnicode_AsEncodedString(note, \"utf-8\", \"backslashreplace\"));\n                        if (!note_bytes) {\n                            result += \"\\nFAILURE obtaining __notes__[\" + std::to_string(i)\n                                      + \"]: \" + detail::error_string();\n                        } else {\n                            char *buffer = nullptr;\n                            Py_ssize_t length = 0;\n                            if (PyBytes_AsStringAndSize(note_bytes.ptr(), &buffer, &length)\n                                == -1) {\n                                result += \"\\nFAILURE formatting __notes__[\" + std::to_string(i)\n                                          + \"]: \" + detail::error_string();\n                            } else {\n                                result += '\\n';\n                                result += std::string(buffer, static_cast<std::size_t>(length));\n                            }\n                        }\n                    }\n                }\n            }\n#endif\n        } else {\n            result = \"<MESSAGE UNAVAILABLE>\";\n        }\n        if (result.empty()) {\n            result = \"<EMPTY MESSAGE>\";\n        }\n\n        bool have_trace = false;\n        if (m_trace) {\n#if !defined(PYPY_VERSION)\n            auto *tb = reinterpret_cast<PyTracebackObject *>(m_trace.ptr());\n\n            // Get the deepest trace possible.\n            while (tb->tb_next) {\n                tb = tb->tb_next;\n            }\n\n            PyFrameObject *frame = tb->tb_frame;\n            Py_XINCREF(frame);\n            result += \"\\n\\nAt:\\n\";\n            while (frame) {\n#    if PY_VERSION_HEX >= 0x030900B1\n                PyCodeObject *f_code = PyFrame_GetCode(frame);\n#    else\n                PyCodeObject *f_code = frame->f_code;\n                Py_INCREF(f_code);\n#    endif\n                int lineno = PyFrame_GetLineNumber(frame);\n                result += \"  \";\n                result += handle(f_code->co_filename).cast<std::string>();\n                result += '(';\n                result += std::to_string(lineno);\n                result += \"): \";\n                result += handle(f_code->co_name).cast<std::string>();\n                result += '\\n';\n                Py_DECREF(f_code);\n#    if PY_VERSION_HEX >= 0x030900B1\n                auto *b_frame = PyFrame_GetBack(frame);\n#    else\n                auto *b_frame = frame->f_back;\n                Py_XINCREF(b_frame);\n#    endif\n                Py_DECREF(frame);\n                frame = b_frame;\n            }\n\n            have_trace = true;\n#endif //! defined(PYPY_VERSION)\n        }\n\n        if (!message_error_string.empty()) {\n            if (!have_trace) {\n                result += '\\n';\n            }\n            result += \"\\nMESSAGE UNAVAILABLE DUE TO EXCEPTION: \" + message_error_string;\n        }\n\n        return result;\n    }\n\n    std::string const &error_string() const {\n        if (!m_lazy_error_string_completed) {\n            m_lazy_error_string += \": \" + format_value_and_trace();\n            m_lazy_error_string_completed = true;\n        }\n        return m_lazy_error_string;\n    }\n\n    void restore() {\n        if (m_restore_called) {\n            pybind11_fail(\"Internal error: pybind11::detail::error_fetch_and_normalize::restore() \"\n                          \"called a second time. ORIGINAL ERROR: \"\n                          + error_string());\n        }\n        PyErr_Restore(m_type.inc_ref().ptr(), m_value.inc_ref().ptr(), m_trace.inc_ref().ptr());\n        m_restore_called = true;\n    }\n\n    bool matches(handle exc) const {\n        return (PyErr_GivenExceptionMatches(m_type.ptr(), exc.ptr()) != 0);\n    }\n\n    // Not protecting these for simplicity.\n    object m_type, m_value, m_trace;\n\nprivate:\n    // Only protecting invariants.\n    mutable std::string m_lazy_error_string;\n    mutable bool m_lazy_error_string_completed = false;\n    mutable bool m_restore_called = false;\n};\n\ninline std::string error_string() {\n    return error_fetch_and_normalize(\"pybind11::detail::error_string\").error_string();\n}\n\nPYBIND11_NAMESPACE_END(detail)\n\n/// Fetch and hold an error which was already set in Python.  An instance of this is typically\n/// thrown to propagate python-side errors back through C++ which can either be caught manually or\n/// else falls back to the function dispatcher (which then raises the captured error back to\n/// python).\nclass PYBIND11_EXPORT_EXCEPTION error_already_set : public std::exception {\npublic:\n    /// Fetches the current Python exception (using PyErr_Fetch()), which will clear the\n    /// current Python error indicator.\n    error_already_set()\n        : m_fetched_error{new detail::error_fetch_and_normalize(\"pybind11::error_already_set\"),\n                          m_fetched_error_deleter} {}\n\n    /// The what() result is built lazily on demand.\n    /// WARNING: This member function needs to acquire the Python GIL. This can lead to\n    ///          crashes (undefined behavior) if the Python interpreter is finalizing.\n    const char *what() const noexcept override;\n\n    /// Restores the currently-held Python error (which will clear the Python error indicator first\n    /// if already set).\n    /// NOTE: This member function will always restore the normalized exception, which may or may\n    ///       not be the original Python exception.\n    /// WARNING: The GIL must be held when this member function is called!\n    void restore() { m_fetched_error->restore(); }\n\n    /// If it is impossible to raise the currently-held error, such as in a destructor, we can\n    /// write it out using Python's unraisable hook (`sys.unraisablehook`). The error context\n    /// should be some object whose `repr()` helps identify the location of the error. Python\n    /// already knows the type and value of the error, so there is no need to repeat that.\n    void discard_as_unraisable(object err_context) {\n        restore();\n        PyErr_WriteUnraisable(err_context.ptr());\n    }\n    /// An alternate version of `discard_as_unraisable()`, where a string provides information on\n    /// the location of the error. For example, `__func__` could be helpful.\n    /// WARNING: The GIL must be held when this member function is called!\n    void discard_as_unraisable(const char *err_context) {\n        discard_as_unraisable(reinterpret_steal<object>(PYBIND11_FROM_STRING(err_context)));\n    }\n\n    // Does nothing; provided for backwards compatibility.\n    PYBIND11_DEPRECATED(\"Use of error_already_set.clear() is deprecated\")\n    void clear() {}\n\n    /// Check if the currently trapped error type matches the given Python exception class (or a\n    /// subclass thereof).  May also be passed a tuple to search for any exception class matches in\n    /// the given tuple.\n    bool matches(handle exc) const { return m_fetched_error->matches(exc); }\n\n    const object &type() const { return m_fetched_error->m_type; }\n    const object &value() const { return m_fetched_error->m_value; }\n    const object &trace() const { return m_fetched_error->m_trace; }\n\nprivate:\n    std::shared_ptr<detail::error_fetch_and_normalize> m_fetched_error;\n\n    /// WARNING: This custom deleter needs to acquire the Python GIL. This can lead to\n    ///          crashes (undefined behavior) if the Python interpreter is finalizing.\n    static void m_fetched_error_deleter(detail::error_fetch_and_normalize *raw_ptr);\n};\n\n/// Replaces the current Python error indicator with the chosen error, performing a\n/// 'raise from' to indicate that the chosen error was caused by the original error.\ninline void raise_from(PyObject *type, const char *message) {\n    // Based on _PyErr_FormatVFromCause:\n    // https://github.com/python/cpython/blob/467ab194fc6189d9f7310c89937c51abeac56839/Python/errors.c#L405\n    // See https://github.com/pybind/pybind11/pull/2112 for details.\n    PyObject *exc = nullptr, *val = nullptr, *val2 = nullptr, *tb = nullptr;\n\n    assert(PyErr_Occurred());\n    PyErr_Fetch(&exc, &val, &tb);\n    PyErr_NormalizeException(&exc, &val, &tb);\n    if (tb != nullptr) {\n        PyException_SetTraceback(val, tb);\n        Py_DECREF(tb);\n    }\n    Py_DECREF(exc);\n    assert(!PyErr_Occurred());\n\n    PyErr_SetString(type, message);\n\n    PyErr_Fetch(&exc, &val2, &tb);\n    PyErr_NormalizeException(&exc, &val2, &tb);\n    Py_INCREF(val);\n    PyException_SetCause(val2, val);\n    PyException_SetContext(val2, val);\n    PyErr_Restore(exc, val2, tb);\n}\n\n/// Sets the current Python error indicator with the chosen error, performing a 'raise from'\n/// from the error contained in error_already_set to indicate that the chosen error was\n/// caused by the original error.\ninline void raise_from(error_already_set &err, PyObject *type, const char *message) {\n    err.restore();\n    raise_from(type, message);\n}\n\n/** \\defgroup python_builtins const_name\n    Unless stated otherwise, the following C++ functions behave the same\n    as their Python counterparts.\n */\n\n/** \\ingroup python_builtins\n    \\rst\n    Return true if ``obj`` is an instance of ``T``. Type ``T`` must be a subclass of\n    `object` or a class which was exposed to Python as ``py::class_<T>``.\n\\endrst */\ntemplate <typename T, detail::enable_if_t<std::is_base_of<object, T>::value, int> = 0>\nbool isinstance(handle obj) {\n    return T::check_(obj);\n}\n\ntemplate <typename T, detail::enable_if_t<!std::is_base_of<object, T>::value, int> = 0>\nbool isinstance(handle obj) {\n    return detail::isinstance_generic(obj, typeid(T));\n}\n\ntemplate <>\ninline bool isinstance<handle>(handle) = delete;\ntemplate <>\ninline bool isinstance<object>(handle obj) {\n    return obj.ptr() != nullptr;\n}\n\n/// \\ingroup python_builtins\n/// Return true if ``obj`` is an instance of the ``type``.\ninline bool isinstance(handle obj, handle type) {\n    const auto result = PyObject_IsInstance(obj.ptr(), type.ptr());\n    if (result == -1) {\n        throw error_already_set();\n    }\n    return result != 0;\n}\n\n/// \\addtogroup python_builtins\n/// @{\ninline bool hasattr(handle obj, handle name) {\n    return PyObject_HasAttr(obj.ptr(), name.ptr()) == 1;\n}\n\ninline bool hasattr(handle obj, const char *name) {\n    return PyObject_HasAttrString(obj.ptr(), name) == 1;\n}\n\ninline void delattr(handle obj, handle name) {\n    if (PyObject_DelAttr(obj.ptr(), name.ptr()) != 0) {\n        throw error_already_set();\n    }\n}\n\ninline void delattr(handle obj, const char *name) {\n    if (PyObject_DelAttrString(obj.ptr(), name) != 0) {\n        throw error_already_set();\n    }\n}\n\ninline object getattr(handle obj, handle name) {\n    PyObject *result = PyObject_GetAttr(obj.ptr(), name.ptr());\n    if (!result) {\n        throw error_already_set();\n    }\n    return reinterpret_steal<object>(result);\n}\n\ninline object getattr(handle obj, const char *name) {\n    PyObject *result = PyObject_GetAttrString(obj.ptr(), name);\n    if (!result) {\n        throw error_already_set();\n    }\n    return reinterpret_steal<object>(result);\n}\n\ninline object getattr(handle obj, handle name, handle default_) {\n    if (PyObject *result = PyObject_GetAttr(obj.ptr(), name.ptr())) {\n        return reinterpret_steal<object>(result);\n    }\n    PyErr_Clear();\n    return reinterpret_borrow<object>(default_);\n}\n\ninline object getattr(handle obj, const char *name, handle default_) {\n    if (PyObject *result = PyObject_GetAttrString(obj.ptr(), name)) {\n        return reinterpret_steal<object>(result);\n    }\n    PyErr_Clear();\n    return reinterpret_borrow<object>(default_);\n}\n\ninline void setattr(handle obj, handle name, handle value) {\n    if (PyObject_SetAttr(obj.ptr(), name.ptr(), value.ptr()) != 0) {\n        throw error_already_set();\n    }\n}\n\ninline void setattr(handle obj, const char *name, handle value) {\n    if (PyObject_SetAttrString(obj.ptr(), name, value.ptr()) != 0) {\n        throw error_already_set();\n    }\n}\n\ninline ssize_t hash(handle obj) {\n    auto h = PyObject_Hash(obj.ptr());\n    if (h == -1) {\n        throw error_already_set();\n    }\n    return h;\n}\n\n/// @} python_builtins\n\nPYBIND11_NAMESPACE_BEGIN(detail)\ninline handle get_function(handle value) {\n    if (value) {\n        if (PyInstanceMethod_Check(value.ptr())) {\n            value = PyInstanceMethod_GET_FUNCTION(value.ptr());\n        } else if (PyMethod_Check(value.ptr())) {\n            value = PyMethod_GET_FUNCTION(value.ptr());\n        }\n    }\n    return value;\n}\n\n// Reimplementation of python's dict helper functions to ensure that exceptions\n// aren't swallowed (see #2862)\n\n// copied from cpython _PyDict_GetItemStringWithError\ninline PyObject *dict_getitemstring(PyObject *v, const char *key) {\n    PyObject *kv = nullptr, *rv = nullptr;\n    kv = PyUnicode_FromString(key);\n    if (kv == nullptr) {\n        throw error_already_set();\n    }\n\n    rv = PyDict_GetItemWithError(v, kv);\n    Py_DECREF(kv);\n    if (rv == nullptr && PyErr_Occurred()) {\n        throw error_already_set();\n    }\n    return rv;\n}\n\ninline PyObject *dict_getitem(PyObject *v, PyObject *key) {\n    PyObject *rv = PyDict_GetItemWithError(v, key);\n    if (rv == nullptr && PyErr_Occurred()) {\n        throw error_already_set();\n    }\n    return rv;\n}\n\ninline PyObject *dict_getitemstringref(PyObject *v, const char *key) {\n#if PY_VERSION_HEX >= 0x030D0000\n    PyObject *rv;\n    if (PyDict_GetItemStringRef(v, key, &rv) < 0) {\n        throw error_already_set();\n    }\n    return rv;\n#else\n    PyObject *rv = dict_getitemstring(v, key);\n    if (rv == nullptr && PyErr_Occurred()) {\n        throw error_already_set();\n    }\n    Py_XINCREF(rv);\n    return rv;\n#endif\n}\n\n// Helper aliases/functions to support implicit casting of values given to python\n// accessors/methods. When given a pyobject, this simply returns the pyobject as-is; for other C++\n// type, the value goes through pybind11::cast(obj) to convert it to an `object`.\ntemplate <typename T, enable_if_t<is_pyobject<T>::value, int> = 0>\nauto object_or_cast(T &&o) -> decltype(std::forward<T>(o)) {\n    return std::forward<T>(o);\n}\n// The following casting version is implemented in cast.h:\ntemplate <typename T, enable_if_t<!is_pyobject<T>::value, int> = 0>\nobject object_or_cast(T &&o);\n// Match a PyObject*, which we want to convert directly to handle via its converting constructor\ninline handle object_or_cast(PyObject *ptr) { return ptr; }\n\nPYBIND11_WARNING_PUSH\nPYBIND11_WARNING_DISABLE_MSVC(4522) // warning C4522: multiple assignment operators specified\ntemplate <typename Policy>\nclass accessor : public object_api<accessor<Policy>> {\n    using key_type = typename Policy::key_type;\n\npublic:\n    accessor(handle obj, key_type key) : obj(obj), key(std::move(key)) {}\n    accessor(const accessor &) = default;\n    accessor(accessor &&) noexcept = default;\n\n    // accessor overload required to override default assignment operator (templates are not\n    // allowed to replace default compiler-generated assignments).\n    void operator=(const accessor &a) && { std::move(*this).operator=(handle(a)); }\n    void operator=(const accessor &a) & { operator=(handle(a)); }\n\n    template <typename T>\n    void operator=(T &&value) && {\n        Policy::set(obj, key, object_or_cast(std::forward<T>(value)));\n    }\n    template <typename T>\n    void operator=(T &&value) & {\n        get_cache() = ensure_object(object_or_cast(std::forward<T>(value)));\n    }\n\n    template <typename T = Policy>\n    PYBIND11_DEPRECATED(\n        \"Use of obj.attr(...) as bool is deprecated in favor of pybind11::hasattr(obj, ...)\")\n    explicit\n    operator enable_if_t<std::is_same<T, accessor_policies::str_attr>::value\n                             || std::is_same<T, accessor_policies::obj_attr>::value,\n                         bool>() const {\n        return hasattr(obj, key);\n    }\n    template <typename T = Policy>\n    PYBIND11_DEPRECATED(\"Use of obj[key] as bool is deprecated in favor of obj.contains(key)\")\n    explicit\n    operator enable_if_t<std::is_same<T, accessor_policies::generic_item>::value, bool>() const {\n        return obj.contains(key);\n    }\n\n    // NOLINTNEXTLINE(google-explicit-constructor)\n    operator object() const { return get_cache(); }\n    PyObject *ptr() const { return get_cache().ptr(); }\n    template <typename T>\n    T cast() const {\n        return get_cache().template cast<T>();\n    }\n\nprivate:\n    static object ensure_object(object &&o) { return std::move(o); }\n    static object ensure_object(handle h) { return reinterpret_borrow<object>(h); }\n\n    object &get_cache() const {\n        if (!cache) {\n            cache = Policy::get(obj, key);\n        }\n        return cache;\n    }\n\nprivate:\n    handle obj;\n    key_type key;\n    mutable object cache;\n};\nPYBIND11_WARNING_POP\n\nPYBIND11_NAMESPACE_BEGIN(accessor_policies)\nstruct obj_attr {\n    using key_type = object;\n    static object get(handle obj, handle key) { return getattr(obj, key); }\n    static void set(handle obj, handle key, handle val) { setattr(obj, key, val); }\n};\n\nstruct str_attr {\n    using key_type = const char *;\n    static object get(handle obj, const char *key) { return getattr(obj, key); }\n    static void set(handle obj, const char *key, handle val) { setattr(obj, key, val); }\n};\n\nstruct generic_item {\n    using key_type = object;\n\n    static object get(handle obj, handle key) {\n        PyObject *result = PyObject_GetItem(obj.ptr(), key.ptr());\n        if (!result) {\n            throw error_already_set();\n        }\n        return reinterpret_steal<object>(result);\n    }\n\n    static void set(handle obj, handle key, handle val) {\n        if (PyObject_SetItem(obj.ptr(), key.ptr(), val.ptr()) != 0) {\n            throw error_already_set();\n        }\n    }\n};\n\nstruct sequence_item {\n    using key_type = size_t;\n\n    template <typename IdxType, detail::enable_if_t<std::is_integral<IdxType>::value, int> = 0>\n    static object get(handle obj, const IdxType &index) {\n        PyObject *result = PySequence_GetItem(obj.ptr(), ssize_t_cast(index));\n        if (!result) {\n            throw error_already_set();\n        }\n        return reinterpret_steal<object>(result);\n    }\n\n    template <typename IdxType, detail::enable_if_t<std::is_integral<IdxType>::value, int> = 0>\n    static void set(handle obj, const IdxType &index, handle val) {\n        // PySequence_SetItem does not steal a reference to 'val'\n        if (PySequence_SetItem(obj.ptr(), ssize_t_cast(index), val.ptr()) != 0) {\n            throw error_already_set();\n        }\n    }\n};\n\nstruct list_item {\n    using key_type = size_t;\n\n    template <typename IdxType, detail::enable_if_t<std::is_integral<IdxType>::value, int> = 0>\n    static object get(handle obj, const IdxType &index) {\n        PyObject *result = PyList_GetItem(obj.ptr(), ssize_t_cast(index));\n        if (!result) {\n            throw error_already_set();\n        }\n        return reinterpret_borrow<object>(result);\n    }\n\n    template <typename IdxType, detail::enable_if_t<std::is_integral<IdxType>::value, int> = 0>\n    static void set(handle obj, const IdxType &index, handle val) {\n        // PyList_SetItem steals a reference to 'val'\n        if (PyList_SetItem(obj.ptr(), ssize_t_cast(index), val.inc_ref().ptr()) != 0) {\n            throw error_already_set();\n        }\n    }\n};\n\nstruct tuple_item {\n    using key_type = size_t;\n\n    template <typename IdxType, detail::enable_if_t<std::is_integral<IdxType>::value, int> = 0>\n    static object get(handle obj, const IdxType &index) {\n        PyObject *result = PyTuple_GetItem(obj.ptr(), ssize_t_cast(index));\n        if (!result) {\n            throw error_already_set();\n        }\n        return reinterpret_borrow<object>(result);\n    }\n\n    template <typename IdxType, detail::enable_if_t<std::is_integral<IdxType>::value, int> = 0>\n    static void set(handle obj, const IdxType &index, handle val) {\n        // PyTuple_SetItem steals a reference to 'val'\n        if (PyTuple_SetItem(obj.ptr(), ssize_t_cast(index), val.inc_ref().ptr()) != 0) {\n            throw error_already_set();\n        }\n    }\n};\nPYBIND11_NAMESPACE_END(accessor_policies)\n\n/// STL iterator template used for tuple, list, sequence and dict\ntemplate <typename Policy>\nclass generic_iterator : public Policy {\n    using It = generic_iterator;\n\npublic:\n    using difference_type = ssize_t;\n    using iterator_category = typename Policy::iterator_category;\n    using value_type = typename Policy::value_type;\n    using reference = typename Policy::reference;\n    using pointer = typename Policy::pointer;\n\n    generic_iterator() = default;\n    generic_iterator(handle seq, ssize_t index) : Policy(seq, index) {}\n\n    // NOLINTNEXTLINE(readability-const-return-type) // PR #3263\n    reference operator*() const { return Policy::dereference(); }\n    // NOLINTNEXTLINE(readability-const-return-type) // PR #3263\n    reference operator[](difference_type n) const { return *(*this + n); }\n    pointer operator->() const { return **this; }\n\n    It &operator++() {\n        Policy::increment();\n        return *this;\n    }\n    It operator++(int) {\n        auto copy = *this;\n        Policy::increment();\n        return copy;\n    }\n    It &operator--() {\n        Policy::decrement();\n        return *this;\n    }\n    It operator--(int) {\n        auto copy = *this;\n        Policy::decrement();\n        return copy;\n    }\n    It &operator+=(difference_type n) {\n        Policy::advance(n);\n        return *this;\n    }\n    It &operator-=(difference_type n) {\n        Policy::advance(-n);\n        return *this;\n    }\n\n    friend It operator+(const It &a, difference_type n) {\n        auto copy = a;\n        return copy += n;\n    }\n    friend It operator+(difference_type n, const It &b) { return b + n; }\n    friend It operator-(const It &a, difference_type n) {\n        auto copy = a;\n        return copy -= n;\n    }\n    friend difference_type operator-(const It &a, const It &b) { return a.distance_to(b); }\n\n    friend bool operator==(const It &a, const It &b) { return a.equal(b); }\n    friend bool operator!=(const It &a, const It &b) { return !(a == b); }\n    friend bool operator<(const It &a, const It &b) { return b - a > 0; }\n    friend bool operator>(const It &a, const It &b) { return b < a; }\n    friend bool operator>=(const It &a, const It &b) { return !(a < b); }\n    friend bool operator<=(const It &a, const It &b) { return !(a > b); }\n};\n\nPYBIND11_NAMESPACE_BEGIN(iterator_policies)\n/// Quick proxy class needed to implement ``operator->`` for iterators which can't return pointers\ntemplate <typename T>\nstruct arrow_proxy {\n    T value;\n\n    // NOLINTNEXTLINE(google-explicit-constructor)\n    arrow_proxy(T &&value) noexcept : value(std::move(value)) {}\n    T *operator->() const { return &value; }\n};\n\n/// Lightweight iterator policy using just a simple pointer: see ``PySequence_Fast_ITEMS``\nclass sequence_fast_readonly {\nprotected:\n    using iterator_category = std::random_access_iterator_tag;\n    using value_type = handle;\n    using reference = const handle; // PR #3263\n    using pointer = arrow_proxy<const handle>;\n\n    sequence_fast_readonly(handle obj, ssize_t n) : ptr(PySequence_Fast_ITEMS(obj.ptr()) + n) {}\n    sequence_fast_readonly() = default;\n\n    // NOLINTNEXTLINE(readability-const-return-type) // PR #3263\n    reference dereference() const { return *ptr; }\n    void increment() { ++ptr; }\n    void decrement() { --ptr; }\n    void advance(ssize_t n) { ptr += n; }\n    bool equal(const sequence_fast_readonly &b) const { return ptr == b.ptr; }\n    ssize_t distance_to(const sequence_fast_readonly &b) const { return ptr - b.ptr; }\n\nprivate:\n    PyObject **ptr;\n};\n\n/// Full read and write access using the sequence protocol: see ``detail::sequence_accessor``\nclass sequence_slow_readwrite {\nprotected:\n    using iterator_category = std::random_access_iterator_tag;\n    using value_type = object;\n    using reference = sequence_accessor;\n    using pointer = arrow_proxy<const sequence_accessor>;\n\n    sequence_slow_readwrite(handle obj, ssize_t index) : obj(obj), index(index) {}\n    sequence_slow_readwrite() = default;\n\n    reference dereference() const { return {obj, static_cast<size_t>(index)}; }\n    void increment() { ++index; }\n    void decrement() { --index; }\n    void advance(ssize_t n) { index += n; }\n    bool equal(const sequence_slow_readwrite &b) const { return index == b.index; }\n    ssize_t distance_to(const sequence_slow_readwrite &b) const { return index - b.index; }\n\nprivate:\n    handle obj;\n    ssize_t index;\n};\n\n/// Python's dictionary protocol permits this to be a forward iterator\nclass dict_readonly {\nprotected:\n    using iterator_category = std::forward_iterator_tag;\n    using value_type = std::pair<handle, handle>;\n    using reference = const value_type; // PR #3263\n    using pointer = arrow_proxy<const value_type>;\n\n    dict_readonly() = default;\n    dict_readonly(handle obj, ssize_t pos) : obj(obj), pos(pos) { increment(); }\n\n    // NOLINTNEXTLINE(readability-const-return-type) // PR #3263\n    reference dereference() const { return {key, value}; }\n    void increment() {\n        if (PyDict_Next(obj.ptr(), &pos, &key, &value) == 0) {\n            pos = -1;\n        }\n    }\n    bool equal(const dict_readonly &b) const { return pos == b.pos; }\n\nprivate:\n    handle obj;\n    PyObject *key = nullptr, *value = nullptr;\n    ssize_t pos = -1;\n};\nPYBIND11_NAMESPACE_END(iterator_policies)\n\n#if !defined(PYPY_VERSION)\nusing tuple_iterator = generic_iterator<iterator_policies::sequence_fast_readonly>;\nusing list_iterator = generic_iterator<iterator_policies::sequence_fast_readonly>;\n#else\nusing tuple_iterator = generic_iterator<iterator_policies::sequence_slow_readwrite>;\nusing list_iterator = generic_iterator<iterator_policies::sequence_slow_readwrite>;\n#endif\n\nusing sequence_iterator = generic_iterator<iterator_policies::sequence_slow_readwrite>;\nusing dict_iterator = generic_iterator<iterator_policies::dict_readonly>;\n\ninline bool PyIterable_Check(PyObject *obj) {\n    PyObject *iter = PyObject_GetIter(obj);\n    if (iter) {\n        Py_DECREF(iter);\n        return true;\n    }\n    PyErr_Clear();\n    return false;\n}\n\ninline bool PyNone_Check(PyObject *o) { return o == Py_None; }\ninline bool PyEllipsis_Check(PyObject *o) { return o == Py_Ellipsis; }\n\n#ifdef PYBIND11_STR_LEGACY_PERMISSIVE\ninline bool PyUnicode_Check_Permissive(PyObject *o) {\n    return PyUnicode_Check(o) || PYBIND11_BYTES_CHECK(o);\n}\n#    define PYBIND11_STR_CHECK_FUN detail::PyUnicode_Check_Permissive\n#else\n#    define PYBIND11_STR_CHECK_FUN PyUnicode_Check\n#endif\n\ninline bool PyStaticMethod_Check(PyObject *o) { return o->ob_type == &PyStaticMethod_Type; }\n\nclass kwargs_proxy : public handle {\npublic:\n    explicit kwargs_proxy(handle h) : handle(h) {}\n};\n\nclass args_proxy : public handle {\npublic:\n    explicit args_proxy(handle h) : handle(h) {}\n    kwargs_proxy operator*() const { return kwargs_proxy(*this); }\n};\n\n/// Python argument categories (using PEP 448 terms)\ntemplate <typename T>\nusing is_keyword = std::is_base_of<arg, T>;\ntemplate <typename T>\nusing is_s_unpacking = std::is_same<args_proxy, T>; // * unpacking\ntemplate <typename T>\nusing is_ds_unpacking = std::is_same<kwargs_proxy, T>; // ** unpacking\ntemplate <typename T>\nusing is_positional = satisfies_none_of<T, is_keyword, is_s_unpacking, is_ds_unpacking>;\ntemplate <typename T>\nusing is_keyword_or_ds = satisfies_any_of<T, is_keyword, is_ds_unpacking>;\n\n// Call argument collector forward declarations\ntemplate <return_value_policy policy = return_value_policy::automatic_reference>\nclass simple_collector;\ntemplate <return_value_policy policy = return_value_policy::automatic_reference>\nclass unpacking_collector;\n\nPYBIND11_NAMESPACE_END(detail)\n\n// TODO: After the deprecated constructors are removed, this macro can be simplified by\n//       inheriting ctors: `using Parent::Parent`. It's not an option right now because\n//       the `using` statement triggers the parent deprecation warning even if the ctor\n//       isn't even used.\n#define PYBIND11_OBJECT_COMMON(Name, Parent, CheckFun)                                            \\\npublic:                                                                                           \\\n    PYBIND11_DEPRECATED(\"Use reinterpret_borrow<\" #Name \">() or reinterpret_steal<\" #Name \">()\")  \\\n    Name(handle h, bool is_borrowed)                                                              \\\n        : Parent(is_borrowed ? Parent(h, borrowed_t{}) : Parent(h, stolen_t{})) {}                \\\n    Name(handle h, borrowed_t) : Parent(h, borrowed_t{}) {}                                       \\\n    Name(handle h, stolen_t) : Parent(h, stolen_t{}) {}                                           \\\n    PYBIND11_DEPRECATED(\"Use py::isinstance<py::python_type>(obj) instead\")                       \\\n    bool check() const { return m_ptr != nullptr && (CheckFun(m_ptr) != 0); }                     \\\n    static bool check_(handle h) { return h.ptr() != nullptr && CheckFun(h.ptr()); }              \\\n    template <typename Policy_> /* NOLINTNEXTLINE(google-explicit-constructor) */                 \\\n    Name(const ::pybind11::detail::accessor<Policy_> &a) : Name(object(a)) {}\n\n#define PYBIND11_OBJECT_CVT(Name, Parent, CheckFun, ConvertFun)                                   \\\n    PYBIND11_OBJECT_COMMON(Name, Parent, CheckFun)                                                \\\n    /* This is deliberately not 'explicit' to allow implicit conversion from object: */           \\\n    /* NOLINTNEXTLINE(google-explicit-constructor) */                                             \\\n    Name(const object &o)                                                                         \\\n        : Parent(check_(o) ? o.inc_ref().ptr() : ConvertFun(o.ptr()), stolen_t{}) {               \\\n        if (!m_ptr)                                                                               \\\n            throw ::pybind11::error_already_set();                                                \\\n    }                                                                                             \\\n    /* NOLINTNEXTLINE(google-explicit-constructor) */                                             \\\n    Name(object &&o) : Parent(check_(o) ? o.release().ptr() : ConvertFun(o.ptr()), stolen_t{}) {  \\\n        if (!m_ptr)                                                                               \\\n            throw ::pybind11::error_already_set();                                                \\\n    }\n\n#define PYBIND11_OBJECT_CVT_DEFAULT(Name, Parent, CheckFun, ConvertFun)                           \\\n    PYBIND11_OBJECT_CVT(Name, Parent, CheckFun, ConvertFun)                                       \\\n    Name() = default;\n\n#define PYBIND11_OBJECT_CHECK_FAILED(Name, o_ptr)                                                 \\\n    ::pybind11::type_error(\"Object of type '\"                                                     \\\n                           + ::pybind11::detail::get_fully_qualified_tp_name(Py_TYPE(o_ptr))      \\\n                           + \"' is not an instance of '\" #Name \"'\")\n\n#define PYBIND11_OBJECT(Name, Parent, CheckFun)                                                   \\\n    PYBIND11_OBJECT_COMMON(Name, Parent, CheckFun)                                                \\\n    /* This is deliberately not 'explicit' to allow implicit conversion from object: */           \\\n    /* NOLINTNEXTLINE(google-explicit-constructor) */                                             \\\n    Name(const object &o) : Parent(o) {                                                           \\\n        if (m_ptr && !check_(m_ptr))                                                              \\\n            throw PYBIND11_OBJECT_CHECK_FAILED(Name, m_ptr);                                      \\\n    }                                                                                             \\\n    /* NOLINTNEXTLINE(google-explicit-constructor) */                                             \\\n    Name(object &&o) : Parent(std::move(o)) {                                                     \\\n        if (m_ptr && !check_(m_ptr))                                                              \\\n            throw PYBIND11_OBJECT_CHECK_FAILED(Name, m_ptr);                                      \\\n    }\n\n#define PYBIND11_OBJECT_DEFAULT(Name, Parent, CheckFun)                                           \\\n    PYBIND11_OBJECT(Name, Parent, CheckFun)                                                       \\\n    Name() = default;\n\n/// \\addtogroup pytypes\n/// @{\n\n/** \\rst\n    Wraps a Python iterator so that it can also be used as a C++ input iterator\n\n    Caveat: copying an iterator does not (and cannot) clone the internal\n    state of the Python iterable. This also applies to the post-increment\n    operator. This iterator should only be used to retrieve the current\n    value using ``operator*()``.\n\\endrst */\nclass iterator : public object {\npublic:\n    using iterator_category = std::input_iterator_tag;\n    using difference_type = ssize_t;\n    using value_type = handle;\n    using reference = const handle; // PR #3263\n    using pointer = const handle *;\n\n    PYBIND11_OBJECT_DEFAULT(iterator, object, PyIter_Check)\n\n    iterator &operator++() {\n        advance();\n        return *this;\n    }\n\n    iterator operator++(int) {\n        auto rv = *this;\n        advance();\n        return rv;\n    }\n\n    // NOLINTNEXTLINE(readability-const-return-type) // PR #3263\n    reference operator*() const {\n        if (m_ptr && !value.ptr()) {\n            auto &self = const_cast<iterator &>(*this);\n            self.advance();\n        }\n        return value;\n    }\n\n    pointer operator->() const {\n        operator*();\n        return &value;\n    }\n\n    /** \\rst\n         The value which marks the end of the iteration. ``it == iterator::sentinel()``\n         is equivalent to catching ``StopIteration`` in Python.\n\n         .. code-block:: cpp\n\n             void foo(py::iterator it) {\n                 while (it != py::iterator::sentinel()) {\n                    // use `*it`\n                    ++it;\n                 }\n             }\n    \\endrst */\n    static iterator sentinel() { return {}; }\n\n    friend bool operator==(const iterator &a, const iterator &b) { return a->ptr() == b->ptr(); }\n    friend bool operator!=(const iterator &a, const iterator &b) { return a->ptr() != b->ptr(); }\n\nprivate:\n    void advance() {\n        value = reinterpret_steal<object>(PyIter_Next(m_ptr));\n        if (value.ptr() == nullptr && PyErr_Occurred()) {\n            throw error_already_set();\n        }\n    }\n\nprivate:\n    object value = {};\n};\n\nclass type : public object {\npublic:\n    PYBIND11_OBJECT(type, object, PyType_Check)\n\n    /// Return a type handle from a handle or an object\n    static handle handle_of(handle h) { return handle((PyObject *) Py_TYPE(h.ptr())); }\n\n    /// Return a type object from a handle or an object\n    static type of(handle h) { return type(type::handle_of(h), borrowed_t{}); }\n\n    // Defined in pybind11/cast.h\n    /// Convert C++ type to handle if previously registered. Does not convert\n    /// standard types, like int, float. etc. yet.\n    /// See https://github.com/pybind/pybind11/issues/2486\n    template <typename T>\n    static handle handle_of();\n\n    /// Convert C++ type to type if previously registered. Does not convert\n    /// standard types, like int, float. etc. yet.\n    /// See https://github.com/pybind/pybind11/issues/2486\n    template <typename T>\n    static type of() {\n        return type(type::handle_of<T>(), borrowed_t{});\n    }\n};\n\nclass iterable : public object {\npublic:\n    PYBIND11_OBJECT_DEFAULT(iterable, object, detail::PyIterable_Check)\n};\n\nclass bytes;\n\nclass str : public object {\npublic:\n    PYBIND11_OBJECT_CVT(str, object, PYBIND11_STR_CHECK_FUN, raw_str)\n\n    template <typename SzType, detail::enable_if_t<std::is_integral<SzType>::value, int> = 0>\n    str(const char *c, const SzType &n)\n        : object(PyUnicode_FromStringAndSize(c, ssize_t_cast(n)), stolen_t{}) {\n        if (!m_ptr) {\n            if (PyErr_Occurred()) {\n                throw error_already_set();\n            }\n            pybind11_fail(\"Could not allocate string object!\");\n        }\n    }\n\n    // 'explicit' is explicitly omitted from the following constructors to allow implicit\n    // conversion to py::str from C++ string-like objects\n    // NOLINTNEXTLINE(google-explicit-constructor)\n    str(const char *c = \"\") : object(PyUnicode_FromString(c), stolen_t{}) {\n        if (!m_ptr) {\n            if (PyErr_Occurred()) {\n                throw error_already_set();\n            }\n            pybind11_fail(\"Could not allocate string object!\");\n        }\n    }\n\n    // NOLINTNEXTLINE(google-explicit-constructor)\n    str(const std::string &s) : str(s.data(), s.size()) {}\n\n#ifdef PYBIND11_HAS_STRING_VIEW\n    // enable_if is needed to avoid \"ambiguous conversion\" errors (see PR #3521).\n    template <typename T, detail::enable_if_t<std::is_same<T, std::string_view>::value, int> = 0>\n    // NOLINTNEXTLINE(google-explicit-constructor)\n    str(T s) : str(s.data(), s.size()) {}\n\n#    ifdef PYBIND11_HAS_U8STRING\n    // reinterpret_cast here is safe (C++20 guarantees char8_t has the same size/alignment as char)\n    // NOLINTNEXTLINE(google-explicit-constructor)\n    str(std::u8string_view s) : str(reinterpret_cast<const char *>(s.data()), s.size()) {}\n#    endif\n\n#endif\n\n    explicit str(const bytes &b);\n\n    /** \\rst\n        Return a string representation of the object. This is analogous to\n        the ``str()`` function in Python.\n    \\endrst */\n    explicit str(handle h) : object(raw_str(h.ptr()), stolen_t{}) {\n        if (!m_ptr) {\n            throw error_already_set();\n        }\n    }\n\n    // NOLINTNEXTLINE(google-explicit-constructor)\n    operator std::string() const {\n        object temp = *this;\n        if (PyUnicode_Check(m_ptr)) {\n            temp = reinterpret_steal<object>(PyUnicode_AsUTF8String(m_ptr));\n            if (!temp) {\n                throw error_already_set();\n            }\n        }\n        char *buffer = nullptr;\n        ssize_t length = 0;\n        if (PyBytes_AsStringAndSize(temp.ptr(), &buffer, &length) != 0) {\n            throw error_already_set();\n        }\n        return std::string(buffer, (size_t) length);\n    }\n\n    template <typename... Args>\n    str format(Args &&...args) const {\n        return attr(\"format\")(std::forward<Args>(args)...);\n    }\n\nprivate:\n    /// Return string representation -- always returns a new reference, even if already a str\n    static PyObject *raw_str(PyObject *op) {\n        PyObject *str_value = PyObject_Str(op);\n        return str_value;\n    }\n};\n/// @} pytypes\n\ninline namespace literals {\n/** \\rst\n    String literal version of `str`\n \\endrst */\ninline str\n#if !defined(__clang__) && defined(__GNUC__) && __GNUC__ < 5\noperator\"\" _s // gcc 4.8.5 insists on having a space (hard error).\n#else\noperator\"\"_s // clang 17 generates a deprecation warning if there is a space.\n#endif\n    (const char *s, size_t size) {\n    return {s, size};\n}\n} // namespace literals\n\n/// \\addtogroup pytypes\n/// @{\nclass bytes : public object {\npublic:\n    PYBIND11_OBJECT(bytes, object, PYBIND11_BYTES_CHECK)\n\n    // Allow implicit conversion:\n    // NOLINTNEXTLINE(google-explicit-constructor)\n    bytes(const char *c = \"\") : object(PYBIND11_BYTES_FROM_STRING(c), stolen_t{}) {\n        if (!m_ptr) {\n            pybind11_fail(\"Could not allocate bytes object!\");\n        }\n    }\n\n    template <typename SzType, detail::enable_if_t<std::is_integral<SzType>::value, int> = 0>\n    bytes(const char *c, const SzType &n)\n        : object(PYBIND11_BYTES_FROM_STRING_AND_SIZE(c, ssize_t_cast(n)), stolen_t{}) {\n        if (!m_ptr) {\n            pybind11_fail(\"Could not allocate bytes object!\");\n        }\n    }\n\n    // Allow implicit conversion:\n    // NOLINTNEXTLINE(google-explicit-constructor)\n    bytes(const std::string &s) : bytes(s.data(), s.size()) {}\n\n    explicit bytes(const pybind11::str &s);\n\n    // NOLINTNEXTLINE(google-explicit-constructor)\n    operator std::string() const { return string_op<std::string>(); }\n\n#ifdef PYBIND11_HAS_STRING_VIEW\n    // enable_if is needed to avoid \"ambiguous conversion\" errors (see PR #3521).\n    template <typename T, detail::enable_if_t<std::is_same<T, std::string_view>::value, int> = 0>\n    // NOLINTNEXTLINE(google-explicit-constructor)\n    bytes(T s) : bytes(s.data(), s.size()) {}\n\n    // Obtain a string view that views the current `bytes` buffer value.  Note that this is only\n    // valid so long as the `bytes` instance remains alive and so generally should not outlive the\n    // lifetime of the `bytes` instance.\n    // NOLINTNEXTLINE(google-explicit-constructor)\n    operator std::string_view() const { return string_op<std::string_view>(); }\n#endif\nprivate:\n    template <typename T>\n    T string_op() const {\n        char *buffer = nullptr;\n        ssize_t length = 0;\n        if (PyBytes_AsStringAndSize(m_ptr, &buffer, &length) != 0) {\n            throw error_already_set();\n        }\n        return {buffer, static_cast<size_t>(length)};\n    }\n};\n// Note: breathe >= 4.17.0 will fail to build docs if the below two constructors\n// are included in the doxygen group; close here and reopen after as a workaround\n/// @} pytypes\n\ninline bytes::bytes(const pybind11::str &s) {\n    object temp = s;\n    if (PyUnicode_Check(s.ptr())) {\n        temp = reinterpret_steal<object>(PyUnicode_AsUTF8String(s.ptr()));\n        if (!temp) {\n            throw error_already_set();\n        }\n    }\n    char *buffer = nullptr;\n    ssize_t length = 0;\n    if (PyBytes_AsStringAndSize(temp.ptr(), &buffer, &length) != 0) {\n        throw error_already_set();\n    }\n    auto obj = reinterpret_steal<object>(PYBIND11_BYTES_FROM_STRING_AND_SIZE(buffer, length));\n    if (!obj) {\n        pybind11_fail(\"Could not allocate bytes object!\");\n    }\n    m_ptr = obj.release().ptr();\n}\n\ninline str::str(const bytes &b) {\n    char *buffer = nullptr;\n    ssize_t length = 0;\n    if (PyBytes_AsStringAndSize(b.ptr(), &buffer, &length) != 0) {\n        throw error_already_set();\n    }\n    auto obj = reinterpret_steal<object>(PyUnicode_FromStringAndSize(buffer, length));\n    if (!obj) {\n        if (PyErr_Occurred()) {\n            throw error_already_set();\n        }\n        pybind11_fail(\"Could not allocate string object!\");\n    }\n    m_ptr = obj.release().ptr();\n}\n\n/// \\addtogroup pytypes\n/// @{\nclass bytearray : public object {\npublic:\n    PYBIND11_OBJECT_CVT(bytearray, object, PyByteArray_Check, PyByteArray_FromObject)\n\n    template <typename SzType, detail::enable_if_t<std::is_integral<SzType>::value, int> = 0>\n    bytearray(const char *c, const SzType &n)\n        : object(PyByteArray_FromStringAndSize(c, ssize_t_cast(n)), stolen_t{}) {\n        if (!m_ptr) {\n            pybind11_fail(\"Could not allocate bytearray object!\");\n        }\n    }\n\n    bytearray() : bytearray(\"\", 0) {}\n\n    explicit bytearray(const std::string &s) : bytearray(s.data(), s.size()) {}\n\n    size_t size() const { return static_cast<size_t>(PyByteArray_Size(m_ptr)); }\n\n    explicit operator std::string() const {\n        char *buffer = PyByteArray_AS_STRING(m_ptr);\n        ssize_t size = PyByteArray_GET_SIZE(m_ptr);\n        return std::string(buffer, static_cast<size_t>(size));\n    }\n};\n// Note: breathe >= 4.17.0 will fail to build docs if the below two constructors\n// are included in the doxygen group; close here and reopen after as a workaround\n/// @} pytypes\n\n/// \\addtogroup pytypes\n/// @{\nclass none : public object {\npublic:\n    PYBIND11_OBJECT(none, object, detail::PyNone_Check)\n    none() : object(Py_None, borrowed_t{}) {}\n};\n\nclass ellipsis : public object {\npublic:\n    PYBIND11_OBJECT(ellipsis, object, detail::PyEllipsis_Check)\n    ellipsis() : object(Py_Ellipsis, borrowed_t{}) {}\n};\n\nclass bool_ : public object {\npublic:\n    PYBIND11_OBJECT_CVT(bool_, object, PyBool_Check, raw_bool)\n    bool_() : object(Py_False, borrowed_t{}) {}\n    // Allow implicit conversion from and to `bool`:\n    // NOLINTNEXTLINE(google-explicit-constructor)\n    bool_(bool value) : object(value ? Py_True : Py_False, borrowed_t{}) {}\n    // NOLINTNEXTLINE(google-explicit-constructor)\n    operator bool() const { return (m_ptr != nullptr) && PyLong_AsLong(m_ptr) != 0; }\n\nprivate:\n    /// Return the truth value of an object -- always returns a new reference\n    static PyObject *raw_bool(PyObject *op) {\n        const auto value = PyObject_IsTrue(op);\n        if (value == -1) {\n            return nullptr;\n        }\n        return handle(value != 0 ? Py_True : Py_False).inc_ref().ptr();\n    }\n};\n\nPYBIND11_NAMESPACE_BEGIN(detail)\n// Converts a value to the given unsigned type.  If an error occurs, you get back (Unsigned) -1;\n// otherwise you get back the unsigned long or unsigned long long value cast to (Unsigned).\n// (The distinction is critically important when casting a returned -1 error value to some other\n// unsigned type: (A)-1 != (B)-1 when A and B are unsigned types of different sizes).\ntemplate <typename Unsigned>\nUnsigned as_unsigned(PyObject *o) {\n    if (sizeof(Unsigned) <= sizeof(unsigned long)) {\n        unsigned long v = PyLong_AsUnsignedLong(o);\n        return v == (unsigned long) -1 && PyErr_Occurred() ? (Unsigned) -1 : (Unsigned) v;\n    }\n    unsigned long long v = PyLong_AsUnsignedLongLong(o);\n    return v == (unsigned long long) -1 && PyErr_Occurred() ? (Unsigned) -1 : (Unsigned) v;\n}\nPYBIND11_NAMESPACE_END(detail)\n\nclass int_ : public object {\npublic:\n    PYBIND11_OBJECT_CVT(int_, object, PYBIND11_LONG_CHECK, PyNumber_Long)\n    int_() : object(PyLong_FromLong(0), stolen_t{}) {}\n    // Allow implicit conversion from C++ integral types:\n    template <typename T, detail::enable_if_t<std::is_integral<T>::value, int> = 0>\n    // NOLINTNEXTLINE(google-explicit-constructor)\n    int_(T value) {\n        if (sizeof(T) <= sizeof(long)) {\n            if (std::is_signed<T>::value) {\n                m_ptr = PyLong_FromLong((long) value);\n            } else {\n                m_ptr = PyLong_FromUnsignedLong((unsigned long) value);\n            }\n        } else {\n            if (std::is_signed<T>::value) {\n                m_ptr = PyLong_FromLongLong((long long) value);\n            } else {\n                m_ptr = PyLong_FromUnsignedLongLong((unsigned long long) value);\n            }\n        }\n        if (!m_ptr) {\n            pybind11_fail(\"Could not allocate int object!\");\n        }\n    }\n\n    template <typename T, detail::enable_if_t<std::is_integral<T>::value, int> = 0>\n    // NOLINTNEXTLINE(google-explicit-constructor)\n    operator T() const {\n        return std::is_unsigned<T>::value  ? detail::as_unsigned<T>(m_ptr)\n               : sizeof(T) <= sizeof(long) ? (T) PyLong_AsLong(m_ptr)\n                                           : (T) PYBIND11_LONG_AS_LONGLONG(m_ptr);\n    }\n};\n\nclass float_ : public object {\npublic:\n    PYBIND11_OBJECT_CVT(float_, object, PyFloat_Check, PyNumber_Float)\n    // Allow implicit conversion from float/double:\n    // NOLINTNEXTLINE(google-explicit-constructor)\n    float_(float value) : object(PyFloat_FromDouble((double) value), stolen_t{}) {\n        if (!m_ptr) {\n            pybind11_fail(\"Could not allocate float object!\");\n        }\n    }\n    // NOLINTNEXTLINE(google-explicit-constructor)\n    float_(double value = .0) : object(PyFloat_FromDouble((double) value), stolen_t{}) {\n        if (!m_ptr) {\n            pybind11_fail(\"Could not allocate float object!\");\n        }\n    }\n    // NOLINTNEXTLINE(google-explicit-constructor)\n    operator float() const { return (float) PyFloat_AsDouble(m_ptr); }\n    // NOLINTNEXTLINE(google-explicit-constructor)\n    operator double() const { return (double) PyFloat_AsDouble(m_ptr); }\n};\n\nclass weakref : public object {\npublic:\n    PYBIND11_OBJECT_CVT_DEFAULT(weakref, object, PyWeakref_Check, raw_weakref)\n    explicit weakref(handle obj, handle callback = {})\n        : object(PyWeakref_NewRef(obj.ptr(), callback.ptr()), stolen_t{}) {\n        if (!m_ptr) {\n            if (PyErr_Occurred()) {\n                throw error_already_set();\n            }\n            pybind11_fail(\"Could not allocate weak reference!\");\n        }\n    }\n\nprivate:\n    static PyObject *raw_weakref(PyObject *o) { return PyWeakref_NewRef(o, nullptr); }\n};\n\nclass slice : public object {\npublic:\n    PYBIND11_OBJECT_DEFAULT(slice, object, PySlice_Check)\n    slice(handle start, handle stop, handle step)\n        : object(PySlice_New(start.ptr(), stop.ptr(), step.ptr()), stolen_t{}) {\n        if (!m_ptr) {\n            pybind11_fail(\"Could not allocate slice object!\");\n        }\n    }\n\n#ifdef PYBIND11_HAS_OPTIONAL\n    slice(std::optional<ssize_t> start, std::optional<ssize_t> stop, std::optional<ssize_t> step)\n        : slice(index_to_object(start), index_to_object(stop), index_to_object(step)) {}\n#else\n    slice(ssize_t start_, ssize_t stop_, ssize_t step_)\n        : slice(int_(start_), int_(stop_), int_(step_)) {}\n#endif\n\n    bool\n    compute(size_t length, size_t *start, size_t *stop, size_t *step, size_t *slicelength) const {\n        return PySlice_GetIndicesEx((PYBIND11_SLICE_OBJECT *) m_ptr,\n                                    (ssize_t) length,\n                                    (ssize_t *) start,\n                                    (ssize_t *) stop,\n                                    (ssize_t *) step,\n                                    (ssize_t *) slicelength)\n               == 0;\n    }\n    bool compute(\n        ssize_t length, ssize_t *start, ssize_t *stop, ssize_t *step, ssize_t *slicelength) const {\n        return PySlice_GetIndicesEx(\n                   (PYBIND11_SLICE_OBJECT *) m_ptr, length, start, stop, step, slicelength)\n               == 0;\n    }\n\nprivate:\n    template <typename T>\n    static object index_to_object(T index) {\n        return index ? object(int_(*index)) : object(none());\n    }\n};\n\nclass capsule : public object {\npublic:\n    PYBIND11_OBJECT_DEFAULT(capsule, object, PyCapsule_CheckExact)\n    PYBIND11_DEPRECATED(\"Use reinterpret_borrow<capsule>() or reinterpret_steal<capsule>()\")\n    capsule(PyObject *ptr, bool is_borrowed)\n        : object(is_borrowed ? object(ptr, borrowed_t{}) : object(ptr, stolen_t{})) {}\n\n    explicit capsule(const void *value,\n                     const char *name = nullptr,\n                     PyCapsule_Destructor destructor = nullptr)\n        : object(PyCapsule_New(const_cast<void *>(value), name, destructor), stolen_t{}) {\n        if (!m_ptr) {\n            throw error_already_set();\n        }\n    }\n\n    PYBIND11_DEPRECATED(\"Please use the ctor with value, name, destructor args\")\n    capsule(const void *value, PyCapsule_Destructor destructor)\n        : object(PyCapsule_New(const_cast<void *>(value), nullptr, destructor), stolen_t{}) {\n        if (!m_ptr) {\n            throw error_already_set();\n        }\n    }\n\n    /// Capsule name is nullptr.\n    capsule(const void *value, void (*destructor)(void *)) {\n        initialize_with_void_ptr_destructor(value, nullptr, destructor);\n    }\n\n    capsule(const void *value, const char *name, void (*destructor)(void *)) {\n        initialize_with_void_ptr_destructor(value, name, destructor);\n    }\n\n    explicit capsule(void (*destructor)()) {\n        m_ptr = PyCapsule_New(reinterpret_cast<void *>(destructor), nullptr, [](PyObject *o) {\n            const char *name = get_name_in_error_scope(o);\n            auto destructor = reinterpret_cast<void (*)()>(PyCapsule_GetPointer(o, name));\n            if (destructor == nullptr) {\n                throw error_already_set();\n            }\n            destructor();\n        });\n\n        if (!m_ptr) {\n            throw error_already_set();\n        }\n    }\n\n    template <typename T>\n    operator T *() const { // NOLINT(google-explicit-constructor)\n        return get_pointer<T>();\n    }\n\n    /// Get the pointer the capsule holds.\n    template <typename T = void>\n    T *get_pointer() const {\n        const auto *name = this->name();\n        T *result = static_cast<T *>(PyCapsule_GetPointer(m_ptr, name));\n        if (!result) {\n            throw error_already_set();\n        }\n        return result;\n    }\n\n    /// Replaces a capsule's pointer *without* calling the destructor on the existing one.\n    void set_pointer(const void *value) {\n        if (PyCapsule_SetPointer(m_ptr, const_cast<void *>(value)) != 0) {\n            throw error_already_set();\n        }\n    }\n\n    const char *name() const {\n        const char *name = PyCapsule_GetName(m_ptr);\n        if ((name == nullptr) && PyErr_Occurred()) {\n            throw error_already_set();\n        }\n        return name;\n    }\n\n    /// Replaces a capsule's name *without* calling the destructor on the existing one.\n    void set_name(const char *new_name) {\n        if (PyCapsule_SetName(m_ptr, new_name) != 0) {\n            throw error_already_set();\n        }\n    }\n\nprivate:\n    static const char *get_name_in_error_scope(PyObject *o) {\n        error_scope error_guard;\n\n        const char *name = PyCapsule_GetName(o);\n        if ((name == nullptr) && PyErr_Occurred()) {\n            // write out and consume error raised by call to PyCapsule_GetName\n            PyErr_WriteUnraisable(o);\n        }\n\n        return name;\n    }\n\n    void initialize_with_void_ptr_destructor(const void *value,\n                                             const char *name,\n                                             void (*destructor)(void *)) {\n        m_ptr = PyCapsule_New(const_cast<void *>(value), name, [](PyObject *o) {\n            // guard if destructor called while err indicator is set\n            error_scope error_guard;\n            auto destructor = reinterpret_cast<void (*)(void *)>(PyCapsule_GetContext(o));\n            if (destructor == nullptr && PyErr_Occurred()) {\n                throw error_already_set();\n            }\n            const char *name = get_name_in_error_scope(o);\n            void *ptr = PyCapsule_GetPointer(o, name);\n            if (ptr == nullptr) {\n                throw error_already_set();\n            }\n\n            if (destructor != nullptr) {\n                destructor(ptr);\n            }\n        });\n\n        if (!m_ptr || PyCapsule_SetContext(m_ptr, reinterpret_cast<void *>(destructor)) != 0) {\n            throw error_already_set();\n        }\n    }\n};\n\nclass tuple : public object {\npublic:\n    PYBIND11_OBJECT_CVT(tuple, object, PyTuple_Check, PySequence_Tuple)\n    template <typename SzType = ssize_t,\n              detail::enable_if_t<std::is_integral<SzType>::value, int> = 0>\n    // Some compilers generate link errors when using `const SzType &` here:\n    explicit tuple(SzType size = 0) : object(PyTuple_New(ssize_t_cast(size)), stolen_t{}) {\n        if (!m_ptr) {\n            pybind11_fail(\"Could not allocate tuple object!\");\n        }\n    }\n    size_t size() const { return (size_t) PyTuple_Size(m_ptr); }\n    bool empty() const { return size() == 0; }\n    detail::tuple_accessor operator[](size_t index) const { return {*this, index}; }\n    template <typename T, detail::enable_if_t<detail::is_pyobject<T>::value, int> = 0>\n    detail::item_accessor operator[](T &&o) const {\n        return object::operator[](std::forward<T>(o));\n    }\n    detail::tuple_iterator begin() const { return {*this, 0}; }\n    detail::tuple_iterator end() const { return {*this, PyTuple_GET_SIZE(m_ptr)}; }\n};\n\n// We need to put this into a separate function because the Intel compiler\n// fails to compile enable_if_t<all_of<is_keyword_or_ds<Args>...>::value> part below\n// (tested with ICC 2021.1 Beta 20200827).\ntemplate <typename... Args>\nconstexpr bool args_are_all_keyword_or_ds() {\n    return detail::all_of<detail::is_keyword_or_ds<Args>...>::value;\n}\n\nclass dict : public object {\npublic:\n    PYBIND11_OBJECT_CVT(dict, object, PyDict_Check, raw_dict)\n    dict() : object(PyDict_New(), stolen_t{}) {\n        if (!m_ptr) {\n            pybind11_fail(\"Could not allocate dict object!\");\n        }\n    }\n    template <typename... Args,\n              typename = detail::enable_if_t<args_are_all_keyword_or_ds<Args...>()>,\n              // MSVC workaround: it can't compile an out-of-line definition, so defer the\n              // collector\n              typename collector = detail::deferred_t<detail::unpacking_collector<>, Args...>>\n    explicit dict(Args &&...args) : dict(collector(std::forward<Args>(args)...).kwargs()) {}\n\n    size_t size() const { return (size_t) PyDict_Size(m_ptr); }\n    bool empty() const { return size() == 0; }\n    detail::dict_iterator begin() const { return {*this, 0}; }\n    detail::dict_iterator end() const { return {}; }\n    void clear() /* py-non-const */ { PyDict_Clear(ptr()); }\n    template <typename T>\n    bool contains(T &&key) const {\n        auto result = PyDict_Contains(m_ptr, detail::object_or_cast(std::forward<T>(key)).ptr());\n        if (result == -1) {\n            throw error_already_set();\n        }\n        return result == 1;\n    }\n\nprivate:\n    /// Call the `dict` Python type -- always returns a new reference\n    static PyObject *raw_dict(PyObject *op) {\n        if (PyDict_Check(op)) {\n            return handle(op).inc_ref().ptr();\n        }\n        return PyObject_CallFunctionObjArgs((PyObject *) &PyDict_Type, op, nullptr);\n    }\n};\n\nclass sequence : public object {\npublic:\n    PYBIND11_OBJECT_DEFAULT(sequence, object, PySequence_Check)\n    size_t size() const {\n        ssize_t result = PySequence_Size(m_ptr);\n        if (result == -1) {\n            throw error_already_set();\n        }\n        return (size_t) result;\n    }\n    bool empty() const { return size() == 0; }\n    detail::sequence_accessor operator[](size_t index) const { return {*this, index}; }\n    template <typename T, detail::enable_if_t<detail::is_pyobject<T>::value, int> = 0>\n    detail::item_accessor operator[](T &&o) const {\n        return object::operator[](std::forward<T>(o));\n    }\n    detail::sequence_iterator begin() const { return {*this, 0}; }\n    detail::sequence_iterator end() const { return {*this, PySequence_Size(m_ptr)}; }\n};\n\nclass list : public object {\npublic:\n    PYBIND11_OBJECT_CVT(list, object, PyList_Check, PySequence_List)\n    template <typename SzType = ssize_t,\n              detail::enable_if_t<std::is_integral<SzType>::value, int> = 0>\n    // Some compilers generate link errors when using `const SzType &` here:\n    explicit list(SzType size = 0) : object(PyList_New(ssize_t_cast(size)), stolen_t{}) {\n        if (!m_ptr) {\n            pybind11_fail(\"Could not allocate list object!\");\n        }\n    }\n    size_t size() const { return (size_t) PyList_Size(m_ptr); }\n    bool empty() const { return size() == 0; }\n    detail::list_accessor operator[](size_t index) const { return {*this, index}; }\n    template <typename T, detail::enable_if_t<detail::is_pyobject<T>::value, int> = 0>\n    detail::item_accessor operator[](T &&o) const {\n        return object::operator[](std::forward<T>(o));\n    }\n    detail::list_iterator begin() const { return {*this, 0}; }\n    detail::list_iterator end() const { return {*this, PyList_GET_SIZE(m_ptr)}; }\n    template <typename T>\n    void append(T &&val) /* py-non-const */ {\n        if (PyList_Append(m_ptr, detail::object_or_cast(std::forward<T>(val)).ptr()) != 0) {\n            throw error_already_set();\n        }\n    }\n    template <typename IdxType,\n              typename ValType,\n              detail::enable_if_t<std::is_integral<IdxType>::value, int> = 0>\n    void insert(const IdxType &index, ValType &&val) /* py-non-const */ {\n        if (PyList_Insert(m_ptr,\n                          ssize_t_cast(index),\n                          detail::object_or_cast(std::forward<ValType>(val)).ptr())\n            != 0) {\n            throw error_already_set();\n        }\n    }\n    void clear() /* py-non-const */ {\n        if (PyList_SetSlice(m_ptr, 0, PyList_Size(m_ptr), nullptr) == -1) {\n            throw error_already_set();\n        }\n    }\n};\n\nclass args : public tuple {\n    PYBIND11_OBJECT_DEFAULT(args, tuple, PyTuple_Check)\n};\nclass kwargs : public dict {\n    PYBIND11_OBJECT_DEFAULT(kwargs, dict, PyDict_Check)\n};\n\nclass anyset : public object {\npublic:\n    PYBIND11_OBJECT(anyset, object, PyAnySet_Check)\n    size_t size() const { return static_cast<size_t>(PySet_Size(m_ptr)); }\n    bool empty() const { return size() == 0; }\n    template <typename T>\n    bool contains(T &&val) const {\n        auto result = PySet_Contains(m_ptr, detail::object_or_cast(std::forward<T>(val)).ptr());\n        if (result == -1) {\n            throw error_already_set();\n        }\n        return result == 1;\n    }\n};\n\nclass set : public anyset {\npublic:\n    PYBIND11_OBJECT_CVT(set, anyset, PySet_Check, PySet_New)\n    set() : anyset(PySet_New(nullptr), stolen_t{}) {\n        if (!m_ptr) {\n            pybind11_fail(\"Could not allocate set object!\");\n        }\n    }\n    template <typename T>\n    bool add(T &&val) /* py-non-const */ {\n        return PySet_Add(m_ptr, detail::object_or_cast(std::forward<T>(val)).ptr()) == 0;\n    }\n    void clear() /* py-non-const */ { PySet_Clear(m_ptr); }\n};\n\nclass frozenset : public anyset {\npublic:\n    PYBIND11_OBJECT_CVT(frozenset, anyset, PyFrozenSet_Check, PyFrozenSet_New)\n};\n\nclass function : public object {\npublic:\n    PYBIND11_OBJECT_DEFAULT(function, object, PyCallable_Check)\n    handle cpp_function() const {\n        handle fun = detail::get_function(m_ptr);\n        if (fun && PyCFunction_Check(fun.ptr())) {\n            return fun;\n        }\n        return handle();\n    }\n    bool is_cpp_function() const { return (bool) cpp_function(); }\n};\n\nclass staticmethod : public object {\npublic:\n    PYBIND11_OBJECT_CVT(staticmethod, object, detail::PyStaticMethod_Check, PyStaticMethod_New)\n};\n\nclass buffer : public object {\npublic:\n    PYBIND11_OBJECT_DEFAULT(buffer, object, PyObject_CheckBuffer)\n\n    buffer_info request(bool writable = false) const {\n        int flags = PyBUF_STRIDES | PyBUF_FORMAT;\n        if (writable) {\n            flags |= PyBUF_WRITABLE;\n        }\n        auto *view = new Py_buffer();\n        if (PyObject_GetBuffer(m_ptr, view, flags) != 0) {\n            delete view;\n            throw error_already_set();\n        }\n        return buffer_info(view);\n    }\n};\n\nclass memoryview : public object {\npublic:\n    PYBIND11_OBJECT_CVT(memoryview, object, PyMemoryView_Check, PyMemoryView_FromObject)\n\n    /** \\rst\n        Creates ``memoryview`` from ``buffer_info``.\n\n        ``buffer_info`` must be created from ``buffer::request()``. Otherwise\n        throws an exception.\n\n        For creating a ``memoryview`` from objects that support buffer protocol,\n        use ``memoryview(const object& obj)`` instead of this constructor.\n     \\endrst */\n    explicit memoryview(const buffer_info &info) {\n        if (!info.view()) {\n            pybind11_fail(\"Prohibited to create memoryview without Py_buffer\");\n        }\n        // Note: PyMemoryView_FromBuffer never increments obj reference.\n        m_ptr = (info.view()->obj) ? PyMemoryView_FromObject(info.view()->obj)\n                                   : PyMemoryView_FromBuffer(info.view());\n        if (!m_ptr) {\n            pybind11_fail(\"Unable to create memoryview from buffer descriptor\");\n        }\n    }\n\n    /** \\rst\n        Creates ``memoryview`` from static buffer.\n\n        This method is meant for providing a ``memoryview`` for C/C++ buffer not\n        managed by Python. The caller is responsible for managing the lifetime\n        of ``ptr`` and ``format``, which MUST outlive the memoryview constructed\n        here.\n\n        See also: Python C API documentation for `PyMemoryView_FromBuffer`_.\n\n        .. _PyMemoryView_FromBuffer:\n           https://docs.python.org/c-api/memoryview.html#c.PyMemoryView_FromBuffer\n\n        :param ptr: Pointer to the buffer.\n        :param itemsize: Byte size of an element.\n        :param format: Pointer to the null-terminated format string. For\n            homogeneous Buffers, this should be set to\n            ``format_descriptor<T>::value``.\n        :param shape: Shape of the tensor (1 entry per dimension).\n        :param strides: Number of bytes between adjacent entries (for each\n            per dimension).\n        :param readonly: Flag to indicate if the underlying storage may be\n            written to.\n     \\endrst */\n    static memoryview from_buffer(void *ptr,\n                                  ssize_t itemsize,\n                                  const char *format,\n                                  detail::any_container<ssize_t> shape,\n                                  detail::any_container<ssize_t> strides,\n                                  bool readonly = false);\n\n    static memoryview from_buffer(const void *ptr,\n                                  ssize_t itemsize,\n                                  const char *format,\n                                  detail::any_container<ssize_t> shape,\n                                  detail::any_container<ssize_t> strides) {\n        return memoryview::from_buffer(\n            const_cast<void *>(ptr), itemsize, format, std::move(shape), std::move(strides), true);\n    }\n\n    template <typename T>\n    static memoryview from_buffer(T *ptr,\n                                  detail::any_container<ssize_t> shape,\n                                  detail::any_container<ssize_t> strides,\n                                  bool readonly = false) {\n        return memoryview::from_buffer(reinterpret_cast<void *>(ptr),\n                                       sizeof(T),\n                                       format_descriptor<T>::value,\n                                       std::move(shape),\n                                       std::move(strides),\n                                       readonly);\n    }\n\n    template <typename T>\n    static memoryview from_buffer(const T *ptr,\n                                  detail::any_container<ssize_t> shape,\n                                  detail::any_container<ssize_t> strides) {\n        return memoryview::from_buffer(\n            const_cast<T *>(ptr), std::move(shape), std::move(strides), true);\n    }\n\n    /** \\rst\n        Creates ``memoryview`` from static memory.\n\n        This method is meant for providing a ``memoryview`` for C/C++ buffer not\n        managed by Python. The caller is responsible for managing the lifetime\n        of ``mem``, which MUST outlive the memoryview constructed here.\n\n        See also: Python C API documentation for `PyMemoryView_FromBuffer`_.\n\n        .. _PyMemoryView_FromMemory:\n           https://docs.python.org/c-api/memoryview.html#c.PyMemoryView_FromMemory\n     \\endrst */\n    static memoryview from_memory(void *mem, ssize_t size, bool readonly = false) {\n        PyObject *ptr = PyMemoryView_FromMemory(\n            reinterpret_cast<char *>(mem), size, (readonly) ? PyBUF_READ : PyBUF_WRITE);\n        if (!ptr) {\n            pybind11_fail(\"Could not allocate memoryview object!\");\n        }\n        return memoryview(object(ptr, stolen_t{}));\n    }\n\n    static memoryview from_memory(const void *mem, ssize_t size) {\n        return memoryview::from_memory(const_cast<void *>(mem), size, true);\n    }\n\n#ifdef PYBIND11_HAS_STRING_VIEW\n    static memoryview from_memory(std::string_view mem) {\n        return from_memory(const_cast<char *>(mem.data()), static_cast<ssize_t>(mem.size()), true);\n    }\n#endif\n};\n\n/// @cond DUPLICATE\ninline memoryview memoryview::from_buffer(void *ptr,\n                                          ssize_t itemsize,\n                                          const char *format,\n                                          detail::any_container<ssize_t> shape,\n                                          detail::any_container<ssize_t> strides,\n                                          bool readonly) {\n    size_t ndim = shape->size();\n    if (ndim != strides->size()) {\n        pybind11_fail(\"memoryview: shape length doesn't match strides length\");\n    }\n    ssize_t size = ndim != 0u ? 1 : 0;\n    for (size_t i = 0; i < ndim; ++i) {\n        size *= (*shape)[i];\n    }\n    Py_buffer view;\n    view.buf = ptr;\n    view.obj = nullptr;\n    view.len = size * itemsize;\n    view.readonly = static_cast<int>(readonly);\n    view.itemsize = itemsize;\n    view.format = const_cast<char *>(format);\n    view.ndim = static_cast<int>(ndim);\n    view.shape = shape->data();\n    view.strides = strides->data();\n    view.suboffsets = nullptr;\n    view.internal = nullptr;\n    PyObject *obj = PyMemoryView_FromBuffer(&view);\n    if (!obj) {\n        throw error_already_set();\n    }\n    return memoryview(object(obj, stolen_t{}));\n}\n/// @endcond\n/// @} pytypes\n\n/// \\addtogroup python_builtins\n/// @{\n\n/// Get the length of a Python object.\ninline size_t len(handle h) {\n    ssize_t result = PyObject_Length(h.ptr());\n    if (result < 0) {\n        throw error_already_set();\n    }\n    return (size_t) result;\n}\n\n/// Get the length hint of a Python object.\n/// Returns 0 when this cannot be determined.\ninline size_t len_hint(handle h) {\n    ssize_t result = PyObject_LengthHint(h.ptr(), 0);\n    if (result < 0) {\n        // Sometimes a length can't be determined at all (eg generators)\n        // In which case simply return 0\n        PyErr_Clear();\n        return 0;\n    }\n    return (size_t) result;\n}\n\ninline str repr(handle h) {\n    PyObject *str_value = PyObject_Repr(h.ptr());\n    if (!str_value) {\n        throw error_already_set();\n    }\n    return reinterpret_steal<str>(str_value);\n}\n\ninline iterator iter(handle obj) {\n    PyObject *result = PyObject_GetIter(obj.ptr());\n    if (!result) {\n        throw error_already_set();\n    }\n    return reinterpret_steal<iterator>(result);\n}\n/// @} python_builtins\n\nPYBIND11_NAMESPACE_BEGIN(detail)\ntemplate <typename D>\niterator object_api<D>::begin() const {\n    return iter(derived());\n}\ntemplate <typename D>\niterator object_api<D>::end() const {\n    return iterator::sentinel();\n}\ntemplate <typename D>\nitem_accessor object_api<D>::operator[](handle key) const {\n    return {derived(), reinterpret_borrow<object>(key)};\n}\ntemplate <typename D>\nitem_accessor object_api<D>::operator[](object &&key) const {\n    return {derived(), std::move(key)};\n}\ntemplate <typename D>\nitem_accessor object_api<D>::operator[](const char *key) const {\n    return {derived(), pybind11::str(key)};\n}\ntemplate <typename D>\nobj_attr_accessor object_api<D>::attr(handle key) const {\n    return {derived(), reinterpret_borrow<object>(key)};\n}\ntemplate <typename D>\nobj_attr_accessor object_api<D>::attr(object &&key) const {\n    return {derived(), std::move(key)};\n}\ntemplate <typename D>\nstr_attr_accessor object_api<D>::attr(const char *key) const {\n    return {derived(), key};\n}\ntemplate <typename D>\nargs_proxy object_api<D>::operator*() const {\n    return args_proxy(derived().ptr());\n}\ntemplate <typename D>\ntemplate <typename T>\nbool object_api<D>::contains(T &&item) const {\n    return attr(\"__contains__\")(std::forward<T>(item)).template cast<bool>();\n}\n\ntemplate <typename D>\npybind11::str object_api<D>::str() const {\n    return pybind11::str(derived());\n}\n\ntemplate <typename D>\nstr_attr_accessor object_api<D>::doc() const {\n    return attr(\"__doc__\");\n}\n\ntemplate <typename D>\nhandle object_api<D>::get_type() const {\n    return type::handle_of(derived());\n}\n\ntemplate <typename D>\nbool object_api<D>::rich_compare(object_api const &other, int value) const {\n    int rv = PyObject_RichCompareBool(derived().ptr(), other.derived().ptr(), value);\n    if (rv == -1) {\n        throw error_already_set();\n    }\n    return rv == 1;\n}\n\n#define PYBIND11_MATH_OPERATOR_UNARY(op, fn)                                                      \\\n    template <typename D>                                                                         \\\n    object object_api<D>::op() const {                                                            \\\n        object result = reinterpret_steal<object>(fn(derived().ptr()));                           \\\n        if (!result.ptr())                                                                        \\\n            throw error_already_set();                                                            \\\n        return result;                                                                            \\\n    }\n\n#define PYBIND11_MATH_OPERATOR_BINARY(op, fn)                                                     \\\n    template <typename D>                                                                         \\\n    object object_api<D>::op(object_api const &other) const {                                     \\\n        object result = reinterpret_steal<object>(fn(derived().ptr(), other.derived().ptr()));    \\\n        if (!result.ptr())                                                                        \\\n            throw error_already_set();                                                            \\\n        return result;                                                                            \\\n    }\n\n#define PYBIND11_MATH_OPERATOR_BINARY_INPLACE(iop, fn)                                            \\\n    template <typename D>                                                                         \\\n    object object_api<D>::iop(object_api const &other) {                                          \\\n        object result = reinterpret_steal<object>(fn(derived().ptr(), other.derived().ptr()));    \\\n        if (!result.ptr())                                                                        \\\n            throw error_already_set();                                                            \\\n        return result;                                                                            \\\n    }\n\nPYBIND11_MATH_OPERATOR_UNARY(operator~, PyNumber_Invert)\nPYBIND11_MATH_OPERATOR_UNARY(operator-, PyNumber_Negative)\nPYBIND11_MATH_OPERATOR_BINARY(operator+, PyNumber_Add)\nPYBIND11_MATH_OPERATOR_BINARY_INPLACE(operator+=, PyNumber_InPlaceAdd)\nPYBIND11_MATH_OPERATOR_BINARY(operator-, PyNumber_Subtract)\nPYBIND11_MATH_OPERATOR_BINARY_INPLACE(operator-=, PyNumber_InPlaceSubtract)\nPYBIND11_MATH_OPERATOR_BINARY(operator*, PyNumber_Multiply)\nPYBIND11_MATH_OPERATOR_BINARY_INPLACE(operator*=, PyNumber_InPlaceMultiply)\nPYBIND11_MATH_OPERATOR_BINARY(operator/, PyNumber_TrueDivide)\nPYBIND11_MATH_OPERATOR_BINARY_INPLACE(operator/=, PyNumber_InPlaceTrueDivide)\nPYBIND11_MATH_OPERATOR_BINARY(operator|, PyNumber_Or)\nPYBIND11_MATH_OPERATOR_BINARY_INPLACE(operator|=, PyNumber_InPlaceOr)\nPYBIND11_MATH_OPERATOR_BINARY(operator&, PyNumber_And)\nPYBIND11_MATH_OPERATOR_BINARY_INPLACE(operator&=, PyNumber_InPlaceAnd)\nPYBIND11_MATH_OPERATOR_BINARY(operator^, PyNumber_Xor)\nPYBIND11_MATH_OPERATOR_BINARY_INPLACE(operator^=, PyNumber_InPlaceXor)\nPYBIND11_MATH_OPERATOR_BINARY(operator<<, PyNumber_Lshift)\nPYBIND11_MATH_OPERATOR_BINARY_INPLACE(operator<<=, PyNumber_InPlaceLshift)\nPYBIND11_MATH_OPERATOR_BINARY(operator>>, PyNumber_Rshift)\nPYBIND11_MATH_OPERATOR_BINARY_INPLACE(operator>>=, PyNumber_InPlaceRshift)\n\n#undef PYBIND11_MATH_OPERATOR_UNARY\n#undef PYBIND11_MATH_OPERATOR_BINARY\n#undef PYBIND11_MATH_OPERATOR_BINARY_INPLACE\n\nPYBIND11_NAMESPACE_END(detail)\nPYBIND11_NAMESPACE_END(PYBIND11_NAMESPACE)\n"
  },
  {
    "path": "libs/pybind11/include/pybind11/stl/filesystem.h",
    "content": "// Copyright (c) 2021 The Pybind Development Team.\n// All rights reserved. Use of this source code is governed by a\n// BSD-style license that can be found in the LICENSE file.\n\n#pragma once\n\n#include <pybind11/cast.h>\n#include <pybind11/detail/common.h>\n#include <pybind11/detail/descr.h>\n#include <pybind11/pybind11.h>\n#include <pybind11/pytypes.h>\n\n#include <string>\n\n#ifdef __has_include\n#    if defined(PYBIND11_CPP17)\n#        if __has_include(<filesystem>)\n#            include <filesystem>\n#            define PYBIND11_HAS_FILESYSTEM 1\n#        elif __has_include(<experimental/filesystem>)\n#            include <experimental/filesystem>\n#            define PYBIND11_HAS_EXPERIMENTAL_FILESYSTEM 1\n#        endif\n#    endif\n#endif\n\n#if !defined(PYBIND11_HAS_FILESYSTEM) && !defined(PYBIND11_HAS_EXPERIMENTAL_FILESYSTEM)           \\\n    && !defined(PYBIND11_HAS_FILESYSTEM_IS_OPTIONAL)\n#    error                                                                                        \\\n        \"Neither #include <filesystem> nor #include <experimental/filesystem is available. (Use -DPYBIND11_HAS_FILESYSTEM_IS_OPTIONAL to ignore.)\"\n#endif\n\nPYBIND11_NAMESPACE_BEGIN(PYBIND11_NAMESPACE)\nPYBIND11_NAMESPACE_BEGIN(detail)\n\n#ifdef PYPY_VERSION\n#    define PYBIND11_REINTERPRET_CAST_VOID_PTR_IF_NOT_PYPY(...) (__VA_ARGS__)\n#else\n#    define PYBIND11_REINTERPRET_CAST_VOID_PTR_IF_NOT_PYPY(...)                                   \\\n        (reinterpret_cast<void *>(__VA_ARGS__))\n#endif\n\n#if defined(PYBIND11_HAS_FILESYSTEM) || defined(PYBIND11_HAS_EXPERIMENTAL_FILESYSTEM)\ntemplate <typename T>\nstruct path_caster {\n\nprivate:\n    static PyObject *unicode_from_fs_native(const std::string &w) {\n#    if !defined(PYPY_VERSION)\n        return PyUnicode_DecodeFSDefaultAndSize(w.c_str(), ssize_t(w.size()));\n#    else\n        // PyPy mistakenly declares the first parameter as non-const.\n        return PyUnicode_DecodeFSDefaultAndSize(const_cast<char *>(w.c_str()), ssize_t(w.size()));\n#    endif\n    }\n\n    static PyObject *unicode_from_fs_native(const std::wstring &w) {\n        return PyUnicode_FromWideChar(w.c_str(), ssize_t(w.size()));\n    }\n\npublic:\n    static handle cast(const T &path, return_value_policy, handle) {\n        if (auto py_str = unicode_from_fs_native(path.native())) {\n            return module_::import(\"pathlib\")\n                .attr(\"Path\")(reinterpret_steal<object>(py_str))\n                .release();\n        }\n        return nullptr;\n    }\n\n    bool load(handle handle, bool) {\n        // PyUnicode_FSConverter and PyUnicode_FSDecoder normally take care of\n        // calling PyOS_FSPath themselves, but that's broken on PyPy (PyPy\n        // issue #3168) so we do it ourselves instead.\n        PyObject *buf = PyOS_FSPath(handle.ptr());\n        if (!buf) {\n            PyErr_Clear();\n            return false;\n        }\n        PyObject *native = nullptr;\n        if constexpr (std::is_same_v<typename T::value_type, char>) {\n            if (PyUnicode_FSConverter(buf, PYBIND11_REINTERPRET_CAST_VOID_PTR_IF_NOT_PYPY(&native))\n                != 0) {\n                if (auto *c_str = PyBytes_AsString(native)) {\n                    // AsString returns a pointer to the internal buffer, which\n                    // must not be free'd.\n                    value = c_str;\n                }\n            }\n        } else if constexpr (std::is_same_v<typename T::value_type, wchar_t>) {\n            if (PyUnicode_FSDecoder(buf, PYBIND11_REINTERPRET_CAST_VOID_PTR_IF_NOT_PYPY(&native))\n                != 0) {\n                if (auto *c_str = PyUnicode_AsWideCharString(native, nullptr)) {\n                    // AsWideCharString returns a new string that must be free'd.\n                    value = c_str; // Copies the string.\n                    PyMem_Free(c_str);\n                }\n            }\n        }\n        Py_XDECREF(native);\n        Py_DECREF(buf);\n        if (PyErr_Occurred()) {\n            PyErr_Clear();\n            return false;\n        }\n        return true;\n    }\n\n    PYBIND11_TYPE_CASTER(T, const_name(\"os.PathLike\"));\n};\n\n#endif // PYBIND11_HAS_FILESYSTEM || defined(PYBIND11_HAS_EXPERIMENTAL_FILESYSTEM)\n\n#if defined(PYBIND11_HAS_FILESYSTEM)\ntemplate <>\nstruct type_caster<std::filesystem::path> : public path_caster<std::filesystem::path> {};\n#elif defined(PYBIND11_HAS_EXPERIMENTAL_FILESYSTEM)\ntemplate <>\nstruct type_caster<std::experimental::filesystem::path>\n    : public path_caster<std::experimental::filesystem::path> {};\n#endif\n\nPYBIND11_NAMESPACE_END(detail)\nPYBIND11_NAMESPACE_END(PYBIND11_NAMESPACE)\n"
  },
  {
    "path": "libs/pybind11/include/pybind11/stl.h",
    "content": "/*\n    pybind11/stl.h: Transparent conversion for STL data types\n\n    Copyright (c) 2016 Wenzel Jakob <wenzel.jakob@epfl.ch>\n\n    All rights reserved. Use of this source code is governed by a\n    BSD-style license that can be found in the LICENSE file.\n*/\n\n#pragma once\n\n#include \"pybind11.h\"\n#include \"detail/common.h\"\n\n#include <deque>\n#include <list>\n#include <map>\n#include <ostream>\n#include <set>\n#include <unordered_map>\n#include <unordered_set>\n#include <valarray>\n\n// See `detail/common.h` for implementation of these guards.\n#if defined(PYBIND11_HAS_OPTIONAL)\n#    include <optional>\n#elif defined(PYBIND11_HAS_EXP_OPTIONAL)\n#    include <experimental/optional>\n#endif\n\n#if defined(PYBIND11_HAS_VARIANT)\n#    include <variant>\n#endif\n\nPYBIND11_NAMESPACE_BEGIN(PYBIND11_NAMESPACE)\nPYBIND11_NAMESPACE_BEGIN(detail)\n\n/// Extracts an const lvalue reference or rvalue reference for U based on the type of T (e.g. for\n/// forwarding a container element).  Typically used indirect via forwarded_type(), below.\ntemplate <typename T, typename U>\nusing forwarded_type = conditional_t<std::is_lvalue_reference<T>::value,\n                                     remove_reference_t<U> &,\n                                     remove_reference_t<U> &&>;\n\n/// Forwards a value U as rvalue or lvalue according to whether T is rvalue or lvalue; typically\n/// used for forwarding a container's elements.\ntemplate <typename T, typename U>\nconstexpr forwarded_type<T, U> forward_like(U &&u) {\n    return std::forward<detail::forwarded_type<T, U>>(std::forward<U>(u));\n}\n\n// Checks if a container has a STL style reserve method.\n// This will only return true for a `reserve()` with a `void` return.\ntemplate <typename C>\nusing has_reserve_method = std::is_same<decltype(std::declval<C>().reserve(0)), void>;\n\ntemplate <typename Type, typename Key>\nstruct set_caster {\n    using type = Type;\n    using key_conv = make_caster<Key>;\n\nprivate:\n    template <typename T = Type, enable_if_t<has_reserve_method<T>::value, int> = 0>\n    void reserve_maybe(const anyset &s, Type *) {\n        value.reserve(s.size());\n    }\n    void reserve_maybe(const anyset &, void *) {}\n\npublic:\n    bool load(handle src, bool convert) {\n        if (!isinstance<anyset>(src)) {\n            return false;\n        }\n        auto s = reinterpret_borrow<anyset>(src);\n        value.clear();\n        reserve_maybe(s, &value);\n        for (auto entry : s) {\n            key_conv conv;\n            if (!conv.load(entry, convert)) {\n                return false;\n            }\n            value.insert(cast_op<Key &&>(std::move(conv)));\n        }\n        return true;\n    }\n\n    template <typename T>\n    static handle cast(T &&src, return_value_policy policy, handle parent) {\n        if (!std::is_lvalue_reference<T>::value) {\n            policy = return_value_policy_override<Key>::policy(policy);\n        }\n        pybind11::set s;\n        for (auto &&value : src) {\n            auto value_ = reinterpret_steal<object>(\n                key_conv::cast(detail::forward_like<T>(value), policy, parent));\n            if (!value_ || !s.add(std::move(value_))) {\n                return handle();\n            }\n        }\n        return s.release();\n    }\n\n    PYBIND11_TYPE_CASTER(type, const_name(\"set[\") + key_conv::name + const_name(\"]\"));\n};\n\ntemplate <typename Type, typename Key, typename Value>\nstruct map_caster {\n    using key_conv = make_caster<Key>;\n    using value_conv = make_caster<Value>;\n\nprivate:\n    template <typename T = Type, enable_if_t<has_reserve_method<T>::value, int> = 0>\n    void reserve_maybe(const dict &d, Type *) {\n        value.reserve(d.size());\n    }\n    void reserve_maybe(const dict &, void *) {}\n\npublic:\n    bool load(handle src, bool convert) {\n        if (!isinstance<dict>(src)) {\n            return false;\n        }\n        auto d = reinterpret_borrow<dict>(src);\n        value.clear();\n        reserve_maybe(d, &value);\n        for (auto it : d) {\n            key_conv kconv;\n            value_conv vconv;\n            if (!kconv.load(it.first.ptr(), convert) || !vconv.load(it.second.ptr(), convert)) {\n                return false;\n            }\n            value.emplace(cast_op<Key &&>(std::move(kconv)), cast_op<Value &&>(std::move(vconv)));\n        }\n        return true;\n    }\n\n    template <typename T>\n    static handle cast(T &&src, return_value_policy policy, handle parent) {\n        dict d;\n        return_value_policy policy_key = policy;\n        return_value_policy policy_value = policy;\n        if (!std::is_lvalue_reference<T>::value) {\n            policy_key = return_value_policy_override<Key>::policy(policy_key);\n            policy_value = return_value_policy_override<Value>::policy(policy_value);\n        }\n        for (auto &&kv : src) {\n            auto key = reinterpret_steal<object>(\n                key_conv::cast(detail::forward_like<T>(kv.first), policy_key, parent));\n            auto value = reinterpret_steal<object>(\n                value_conv::cast(detail::forward_like<T>(kv.second), policy_value, parent));\n            if (!key || !value) {\n                return handle();\n            }\n            d[std::move(key)] = std::move(value);\n        }\n        return d.release();\n    }\n\n    PYBIND11_TYPE_CASTER(Type,\n                         const_name(\"dict[\") + key_conv::name + const_name(\", \") + value_conv::name\n                             + const_name(\"]\"));\n};\n\ntemplate <typename Type, typename Value>\nstruct list_caster {\n    using value_conv = make_caster<Value>;\n\n    bool load(handle src, bool convert) {\n        if (!isinstance<sequence>(src) || isinstance<bytes>(src) || isinstance<str>(src)) {\n            return false;\n        }\n        auto s = reinterpret_borrow<sequence>(src);\n        value.clear();\n        reserve_maybe(s, &value);\n        for (const auto &it : s) {\n            value_conv conv;\n            if (!conv.load(it, convert)) {\n                return false;\n            }\n            value.push_back(cast_op<Value &&>(std::move(conv)));\n        }\n        return true;\n    }\n\nprivate:\n    template <typename T = Type, enable_if_t<has_reserve_method<T>::value, int> = 0>\n    void reserve_maybe(const sequence &s, Type *) {\n        value.reserve(s.size());\n    }\n    void reserve_maybe(const sequence &, void *) {}\n\npublic:\n    template <typename T>\n    static handle cast(T &&src, return_value_policy policy, handle parent) {\n        if (!std::is_lvalue_reference<T>::value) {\n            policy = return_value_policy_override<Value>::policy(policy);\n        }\n        list l(src.size());\n        ssize_t index = 0;\n        for (auto &&value : src) {\n            auto value_ = reinterpret_steal<object>(\n                value_conv::cast(detail::forward_like<T>(value), policy, parent));\n            if (!value_) {\n                return handle();\n            }\n            PyList_SET_ITEM(l.ptr(), index++, value_.release().ptr()); // steals a reference\n        }\n        return l.release();\n    }\n\n    PYBIND11_TYPE_CASTER(Type, const_name(\"list[\") + value_conv::name + const_name(\"]\"));\n};\n\ntemplate <typename Type, typename Alloc>\nstruct type_caster<std::vector<Type, Alloc>> : list_caster<std::vector<Type, Alloc>, Type> {};\n\ntemplate <typename Type, typename Alloc>\nstruct type_caster<std::deque<Type, Alloc>> : list_caster<std::deque<Type, Alloc>, Type> {};\n\ntemplate <typename Type, typename Alloc>\nstruct type_caster<std::list<Type, Alloc>> : list_caster<std::list<Type, Alloc>, Type> {};\n\ntemplate <typename ArrayType, typename Value, bool Resizable, size_t Size = 0>\nstruct array_caster {\n    using value_conv = make_caster<Value>;\n\nprivate:\n    template <bool R = Resizable>\n    bool require_size(enable_if_t<R, size_t> size) {\n        if (value.size() != size) {\n            value.resize(size);\n        }\n        return true;\n    }\n    template <bool R = Resizable>\n    bool require_size(enable_if_t<!R, size_t> size) {\n        return size == Size;\n    }\n\npublic:\n    bool load(handle src, bool convert) {\n        if (!isinstance<sequence>(src)) {\n            return false;\n        }\n        auto l = reinterpret_borrow<sequence>(src);\n        if (!require_size(l.size())) {\n            return false;\n        }\n        size_t ctr = 0;\n        for (const auto &it : l) {\n            value_conv conv;\n            if (!conv.load(it, convert)) {\n                return false;\n            }\n            value[ctr++] = cast_op<Value &&>(std::move(conv));\n        }\n        return true;\n    }\n\n    template <typename T>\n    static handle cast(T &&src, return_value_policy policy, handle parent) {\n        list l(src.size());\n        ssize_t index = 0;\n        for (auto &&value : src) {\n            auto value_ = reinterpret_steal<object>(\n                value_conv::cast(detail::forward_like<T>(value), policy, parent));\n            if (!value_) {\n                return handle();\n            }\n            PyList_SET_ITEM(l.ptr(), index++, value_.release().ptr()); // steals a reference\n        }\n        return l.release();\n    }\n\n    PYBIND11_TYPE_CASTER(ArrayType,\n                         const_name<Resizable>(const_name(\"\"), const_name(\"Annotated[\"))\n                             + const_name(\"list[\") + value_conv::name + const_name(\"]\")\n                             + const_name<Resizable>(const_name(\"\"),\n                                                     const_name(\", FixedSize(\")\n                                                         + const_name<Size>() + const_name(\")]\")));\n};\n\ntemplate <typename Type, size_t Size>\nstruct type_caster<std::array<Type, Size>>\n    : array_caster<std::array<Type, Size>, Type, false, Size> {};\n\ntemplate <typename Type>\nstruct type_caster<std::valarray<Type>> : array_caster<std::valarray<Type>, Type, true> {};\n\ntemplate <typename Key, typename Compare, typename Alloc>\nstruct type_caster<std::set<Key, Compare, Alloc>>\n    : set_caster<std::set<Key, Compare, Alloc>, Key> {};\n\ntemplate <typename Key, typename Hash, typename Equal, typename Alloc>\nstruct type_caster<std::unordered_set<Key, Hash, Equal, Alloc>>\n    : set_caster<std::unordered_set<Key, Hash, Equal, Alloc>, Key> {};\n\ntemplate <typename Key, typename Value, typename Compare, typename Alloc>\nstruct type_caster<std::map<Key, Value, Compare, Alloc>>\n    : map_caster<std::map<Key, Value, Compare, Alloc>, Key, Value> {};\n\ntemplate <typename Key, typename Value, typename Hash, typename Equal, typename Alloc>\nstruct type_caster<std::unordered_map<Key, Value, Hash, Equal, Alloc>>\n    : map_caster<std::unordered_map<Key, Value, Hash, Equal, Alloc>, Key, Value> {};\n\n// This type caster is intended to be used for std::optional and std::experimental::optional\ntemplate <typename Type, typename Value = typename Type::value_type>\nstruct optional_caster {\n    using value_conv = make_caster<Value>;\n\n    template <typename T>\n    static handle cast(T &&src, return_value_policy policy, handle parent) {\n        if (!src) {\n            return none().release();\n        }\n        if (!std::is_lvalue_reference<T>::value) {\n            policy = return_value_policy_override<Value>::policy(policy);\n        }\n        // NOLINTNEXTLINE(bugprone-unchecked-optional-access)\n        return value_conv::cast(*std::forward<T>(src), policy, parent);\n    }\n\n    bool load(handle src, bool convert) {\n        if (!src) {\n            return false;\n        }\n        if (src.is_none()) {\n            return true; // default-constructed value is already empty\n        }\n        value_conv inner_caster;\n        if (!inner_caster.load(src, convert)) {\n            return false;\n        }\n\n        value.emplace(cast_op<Value &&>(std::move(inner_caster)));\n        return true;\n    }\n\n    PYBIND11_TYPE_CASTER(Type, const_name(\"Optional[\") + value_conv::name + const_name(\"]\"));\n};\n\n#if defined(PYBIND11_HAS_OPTIONAL)\ntemplate <typename T>\nstruct type_caster<std::optional<T>> : public optional_caster<std::optional<T>> {};\n\ntemplate <>\nstruct type_caster<std::nullopt_t> : public void_caster<std::nullopt_t> {};\n#endif\n\n#if defined(PYBIND11_HAS_EXP_OPTIONAL)\ntemplate <typename T>\nstruct type_caster<std::experimental::optional<T>>\n    : public optional_caster<std::experimental::optional<T>> {};\n\ntemplate <>\nstruct type_caster<std::experimental::nullopt_t>\n    : public void_caster<std::experimental::nullopt_t> {};\n#endif\n\n/// Visit a variant and cast any found type to Python\nstruct variant_caster_visitor {\n    return_value_policy policy;\n    handle parent;\n\n    using result_type = handle; // required by boost::variant in C++11\n\n    template <typename T>\n    result_type operator()(T &&src) const {\n        return make_caster<T>::cast(std::forward<T>(src), policy, parent);\n    }\n};\n\n/// Helper class which abstracts away variant's `visit` function. `std::variant` and similar\n/// `namespace::variant` types which provide a `namespace::visit()` function are handled here\n/// automatically using argument-dependent lookup. Users can provide specializations for other\n/// variant-like classes, e.g. `boost::variant` and `boost::apply_visitor`.\ntemplate <template <typename...> class Variant>\nstruct visit_helper {\n    template <typename... Args>\n    static auto call(Args &&...args) -> decltype(visit(std::forward<Args>(args)...)) {\n        return visit(std::forward<Args>(args)...);\n    }\n};\n\n/// Generic variant caster\ntemplate <typename Variant>\nstruct variant_caster;\n\ntemplate <template <typename...> class V, typename... Ts>\nstruct variant_caster<V<Ts...>> {\n    static_assert(sizeof...(Ts) > 0, \"Variant must consist of at least one alternative.\");\n\n    template <typename U, typename... Us>\n    bool load_alternative(handle src, bool convert, type_list<U, Us...>) {\n        auto caster = make_caster<U>();\n        if (caster.load(src, convert)) {\n            value = cast_op<U>(std::move(caster));\n            return true;\n        }\n        return load_alternative(src, convert, type_list<Us...>{});\n    }\n\n    bool load_alternative(handle, bool, type_list<>) { return false; }\n\n    bool load(handle src, bool convert) {\n        // Do a first pass without conversions to improve constructor resolution.\n        // E.g. `py::int_(1).cast<variant<double, int>>()` needs to fill the `int`\n        // slot of the variant. Without two-pass loading `double` would be filled\n        // because it appears first and a conversion is possible.\n        if (convert && load_alternative(src, false, type_list<Ts...>{})) {\n            return true;\n        }\n        return load_alternative(src, convert, type_list<Ts...>{});\n    }\n\n    template <typename Variant>\n    static handle cast(Variant &&src, return_value_policy policy, handle parent) {\n        return visit_helper<V>::call(variant_caster_visitor{policy, parent},\n                                     std::forward<Variant>(src));\n    }\n\n    using Type = V<Ts...>;\n    PYBIND11_TYPE_CASTER(Type,\n                         const_name(\"Union[\")\n                             + ::pybind11::detail::concat(make_caster<Ts>::name...)\n                             + const_name(\"]\"));\n};\n\n#if defined(PYBIND11_HAS_VARIANT)\ntemplate <typename... Ts>\nstruct type_caster<std::variant<Ts...>> : variant_caster<std::variant<Ts...>> {};\n\ntemplate <>\nstruct type_caster<std::monostate> : public void_caster<std::monostate> {};\n#endif\n\nPYBIND11_NAMESPACE_END(detail)\n\ninline std::ostream &operator<<(std::ostream &os, const handle &obj) {\n#ifdef PYBIND11_HAS_STRING_VIEW\n    os << str(obj).cast<std::string_view>();\n#else\n    os << (std::string) str(obj);\n#endif\n    return os;\n}\n\nPYBIND11_NAMESPACE_END(PYBIND11_NAMESPACE)\n"
  },
  {
    "path": "libs/pybind11/include/pybind11/stl_bind.h",
    "content": "/*\n    pybind11/std_bind.h: Binding generators for STL data types\n\n    Copyright (c) 2016 Sergey Lyskov and Wenzel Jakob\n\n    All rights reserved. Use of this source code is governed by a\n    BSD-style license that can be found in the LICENSE file.\n*/\n\n#pragma once\n\n#include \"detail/common.h\"\n#include \"detail/type_caster_base.h\"\n#include \"cast.h\"\n#include \"operators.h\"\n\n#include <algorithm>\n#include <sstream>\n#include <type_traits>\n\nPYBIND11_NAMESPACE_BEGIN(PYBIND11_NAMESPACE)\nPYBIND11_NAMESPACE_BEGIN(detail)\n\n/* SFINAE helper class used by 'is_comparable */\ntemplate <typename T>\nstruct container_traits {\n    template <typename T2>\n    static std::true_type\n    test_comparable(decltype(std::declval<const T2 &>() == std::declval<const T2 &>()) *);\n    template <typename T2>\n    static std::false_type test_comparable(...);\n    template <typename T2>\n    static std::true_type test_value(typename T2::value_type *);\n    template <typename T2>\n    static std::false_type test_value(...);\n    template <typename T2>\n    static std::true_type test_pair(typename T2::first_type *, typename T2::second_type *);\n    template <typename T2>\n    static std::false_type test_pair(...);\n\n    static constexpr const bool is_comparable\n        = std::is_same<std::true_type, decltype(test_comparable<T>(nullptr))>::value;\n    static constexpr const bool is_pair\n        = std::is_same<std::true_type, decltype(test_pair<T>(nullptr, nullptr))>::value;\n    static constexpr const bool is_vector\n        = std::is_same<std::true_type, decltype(test_value<T>(nullptr))>::value;\n    static constexpr const bool is_element = !is_pair && !is_vector;\n};\n\n/* Default: is_comparable -> std::false_type */\ntemplate <typename T, typename SFINAE = void>\nstruct is_comparable : std::false_type {};\n\n/* For non-map data structures, check whether operator== can be instantiated */\ntemplate <typename T>\nstruct is_comparable<\n    T,\n    enable_if_t<container_traits<T>::is_element && container_traits<T>::is_comparable>>\n    : std::true_type {};\n\n/* For a vector/map data structure, recursively check the value type\n   (which is std::pair for maps) */\ntemplate <typename T>\nstruct is_comparable<T, enable_if_t<container_traits<T>::is_vector>>\n    : is_comparable<typename recursive_container_traits<T>::type_to_check_recursively> {};\n\ntemplate <>\nstruct is_comparable<recursive_bottom> : std::true_type {};\n\n/* For pairs, recursively check the two data types */\ntemplate <typename T>\nstruct is_comparable<T, enable_if_t<container_traits<T>::is_pair>> {\n    static constexpr const bool value = is_comparable<typename T::first_type>::value\n                                        && is_comparable<typename T::second_type>::value;\n};\n\n/* Fallback functions */\ntemplate <typename, typename, typename... Args>\nvoid vector_if_copy_constructible(const Args &...) {}\ntemplate <typename, typename, typename... Args>\nvoid vector_if_equal_operator(const Args &...) {}\ntemplate <typename, typename, typename... Args>\nvoid vector_if_insertion_operator(const Args &...) {}\ntemplate <typename, typename, typename... Args>\nvoid vector_modifiers(const Args &...) {}\n\ntemplate <typename Vector, typename Class_>\nvoid vector_if_copy_constructible(enable_if_t<is_copy_constructible<Vector>::value, Class_> &cl) {\n    cl.def(init<const Vector &>(), \"Copy constructor\");\n}\n\ntemplate <typename Vector, typename Class_>\nvoid vector_if_equal_operator(enable_if_t<is_comparable<Vector>::value, Class_> &cl) {\n    using T = typename Vector::value_type;\n\n    cl.def(self == self);\n    cl.def(self != self);\n\n    cl.def(\n        \"count\",\n        [](const Vector &v, const T &x) { return std::count(v.begin(), v.end(), x); },\n        arg(\"x\"),\n        \"Return the number of times ``x`` appears in the list\");\n\n    cl.def(\n        \"remove\",\n        [](Vector &v, const T &x) {\n            auto p = std::find(v.begin(), v.end(), x);\n            if (p != v.end()) {\n                v.erase(p);\n            } else {\n                throw value_error();\n            }\n        },\n        arg(\"x\"),\n        \"Remove the first item from the list whose value is x. \"\n        \"It is an error if there is no such item.\");\n\n    cl.def(\n        \"__contains__\",\n        [](const Vector &v, const T &x) { return std::find(v.begin(), v.end(), x) != v.end(); },\n        arg(\"x\"),\n        \"Return true the container contains ``x``\");\n}\n\n// Vector modifiers -- requires a copyable vector_type:\n// (Technically, some of these (pop and __delitem__) don't actually require copyability, but it\n// seems silly to allow deletion but not insertion, so include them here too.)\ntemplate <typename Vector, typename Class_>\nvoid vector_modifiers(\n    enable_if_t<is_copy_constructible<typename Vector::value_type>::value, Class_> &cl) {\n    using T = typename Vector::value_type;\n    using SizeType = typename Vector::size_type;\n    using DiffType = typename Vector::difference_type;\n\n    auto wrap_i = [](DiffType i, SizeType n) {\n        if (i < 0) {\n            i += n;\n        }\n        if (i < 0 || (SizeType) i >= n) {\n            throw index_error();\n        }\n        return i;\n    };\n\n    cl.def(\n        \"append\",\n        [](Vector &v, const T &value) { v.push_back(value); },\n        arg(\"x\"),\n        \"Add an item to the end of the list\");\n\n    cl.def(init([](const iterable &it) {\n        auto v = std::unique_ptr<Vector>(new Vector());\n        v->reserve(len_hint(it));\n        for (handle h : it) {\n            v->push_back(h.cast<T>());\n        }\n        return v.release();\n    }));\n\n    cl.def(\"clear\", [](Vector &v) { v.clear(); }, \"Clear the contents\");\n\n    cl.def(\n        \"extend\",\n        [](Vector &v, const Vector &src) { v.insert(v.end(), src.begin(), src.end()); },\n        arg(\"L\"),\n        \"Extend the list by appending all the items in the given list\");\n\n    cl.def(\n        \"extend\",\n        [](Vector &v, const iterable &it) {\n            const size_t old_size = v.size();\n            v.reserve(old_size + len_hint(it));\n            try {\n                for (handle h : it) {\n                    v.push_back(h.cast<T>());\n                }\n            } catch (const cast_error &) {\n                v.erase(v.begin() + static_cast<typename Vector::difference_type>(old_size),\n                        v.end());\n                try {\n                    v.shrink_to_fit();\n                } catch (const std::exception &) { // NOLINT(bugprone-empty-catch)\n                    // Do nothing\n                }\n                throw;\n            }\n        },\n        arg(\"L\"),\n        \"Extend the list by appending all the items in the given list\");\n\n    cl.def(\n        \"insert\",\n        [](Vector &v, DiffType i, const T &x) {\n            // Can't use wrap_i; i == v.size() is OK\n            if (i < 0) {\n                i += v.size();\n            }\n            if (i < 0 || (SizeType) i > v.size()) {\n                throw index_error();\n            }\n            v.insert(v.begin() + i, x);\n        },\n        arg(\"i\"),\n        arg(\"x\"),\n        \"Insert an item at a given position.\");\n\n    cl.def(\n        \"pop\",\n        [](Vector &v) {\n            if (v.empty()) {\n                throw index_error();\n            }\n            T t = std::move(v.back());\n            v.pop_back();\n            return t;\n        },\n        \"Remove and return the last item\");\n\n    cl.def(\n        \"pop\",\n        [wrap_i](Vector &v, DiffType i) {\n            i = wrap_i(i, v.size());\n            T t = std::move(v[(SizeType) i]);\n            v.erase(std::next(v.begin(), i));\n            return t;\n        },\n        arg(\"i\"),\n        \"Remove and return the item at index ``i``\");\n\n    cl.def(\"__setitem__\", [wrap_i](Vector &v, DiffType i, const T &t) {\n        i = wrap_i(i, v.size());\n        v[(SizeType) i] = t;\n    });\n\n    /// Slicing protocol\n    cl.def(\n        \"__getitem__\",\n        [](const Vector &v, const slice &slice) -> Vector * {\n            size_t start = 0, stop = 0, step = 0, slicelength = 0;\n\n            if (!slice.compute(v.size(), &start, &stop, &step, &slicelength)) {\n                throw error_already_set();\n            }\n\n            auto *seq = new Vector();\n            seq->reserve((size_t) slicelength);\n\n            for (size_t i = 0; i < slicelength; ++i) {\n                seq->push_back(v[start]);\n                start += step;\n            }\n            return seq;\n        },\n        arg(\"s\"),\n        \"Retrieve list elements using a slice object\");\n\n    cl.def(\n        \"__setitem__\",\n        [](Vector &v, const slice &slice, const Vector &value) {\n            size_t start = 0, stop = 0, step = 0, slicelength = 0;\n            if (!slice.compute(v.size(), &start, &stop, &step, &slicelength)) {\n                throw error_already_set();\n            }\n\n            if (slicelength != value.size()) {\n                throw std::runtime_error(\n                    \"Left and right hand size of slice assignment have different sizes!\");\n            }\n\n            for (size_t i = 0; i < slicelength; ++i) {\n                v[start] = value[i];\n                start += step;\n            }\n        },\n        \"Assign list elements using a slice object\");\n\n    cl.def(\n        \"__delitem__\",\n        [wrap_i](Vector &v, DiffType i) {\n            i = wrap_i(i, v.size());\n            v.erase(v.begin() + i);\n        },\n        \"Delete the list elements at index ``i``\");\n\n    cl.def(\n        \"__delitem__\",\n        [](Vector &v, const slice &slice) {\n            size_t start = 0, stop = 0, step = 0, slicelength = 0;\n\n            if (!slice.compute(v.size(), &start, &stop, &step, &slicelength)) {\n                throw error_already_set();\n            }\n\n            if (step == 1 && false) {\n                v.erase(v.begin() + (DiffType) start, v.begin() + DiffType(start + slicelength));\n            } else {\n                for (size_t i = 0; i < slicelength; ++i) {\n                    v.erase(v.begin() + DiffType(start));\n                    start += step - 1;\n                }\n            }\n        },\n        \"Delete list elements using a slice object\");\n}\n\n// If the type has an operator[] that doesn't return a reference (most notably std::vector<bool>),\n// we have to access by copying; otherwise we return by reference.\ntemplate <typename Vector>\nusing vector_needs_copy\n    = negation<std::is_same<decltype(std::declval<Vector>()[typename Vector::size_type()]),\n                            typename Vector::value_type &>>;\n\n// The usual case: access and iterate by reference\ntemplate <typename Vector, typename Class_>\nvoid vector_accessor(enable_if_t<!vector_needs_copy<Vector>::value, Class_> &cl) {\n    using T = typename Vector::value_type;\n    using SizeType = typename Vector::size_type;\n    using DiffType = typename Vector::difference_type;\n    using ItType = typename Vector::iterator;\n\n    auto wrap_i = [](DiffType i, SizeType n) {\n        if (i < 0) {\n            i += n;\n        }\n        if (i < 0 || (SizeType) i >= n) {\n            throw index_error();\n        }\n        return i;\n    };\n\n    cl.def(\n        \"__getitem__\",\n        [wrap_i](Vector &v, DiffType i) -> T & {\n            i = wrap_i(i, v.size());\n            return v[(SizeType) i];\n        },\n        return_value_policy::reference_internal // ref + keepalive\n    );\n\n    cl.def(\n        \"__iter__\",\n        [](Vector &v) {\n            return make_iterator<return_value_policy::reference_internal, ItType, ItType, T &>(\n                v.begin(), v.end());\n        },\n        keep_alive<0, 1>() /* Essential: keep list alive while iterator exists */\n    );\n}\n\n// The case for special objects, like std::vector<bool>, that have to be returned-by-copy:\ntemplate <typename Vector, typename Class_>\nvoid vector_accessor(enable_if_t<vector_needs_copy<Vector>::value, Class_> &cl) {\n    using T = typename Vector::value_type;\n    using SizeType = typename Vector::size_type;\n    using DiffType = typename Vector::difference_type;\n    using ItType = typename Vector::iterator;\n    cl.def(\"__getitem__\", [](const Vector &v, DiffType i) -> T {\n        if (i < 0) {\n            i += v.size();\n            if (i < 0) {\n                throw index_error();\n            }\n        }\n        auto i_st = static_cast<SizeType>(i);\n        if (i_st >= v.size()) {\n            throw index_error();\n        }\n        return v[i_st];\n    });\n\n    cl.def(\n        \"__iter__\",\n        [](Vector &v) {\n            return make_iterator<return_value_policy::copy, ItType, ItType, T>(v.begin(), v.end());\n        },\n        keep_alive<0, 1>() /* Essential: keep list alive while iterator exists */\n    );\n}\n\ntemplate <typename Vector, typename Class_>\nauto vector_if_insertion_operator(Class_ &cl, std::string const &name)\n    -> decltype(std::declval<std::ostream &>() << std::declval<typename Vector::value_type>(),\n                void()) {\n    using size_type = typename Vector::size_type;\n\n    cl.def(\n        \"__repr__\",\n        [name](Vector &v) {\n            std::ostringstream s;\n            s << name << '[';\n            for (size_type i = 0; i < v.size(); ++i) {\n                s << v[i];\n                if (i != v.size() - 1) {\n                    s << \", \";\n                }\n            }\n            s << ']';\n            return s.str();\n        },\n        \"Return the canonical string representation of this list.\");\n}\n\n// Provide the buffer interface for vectors if we have data() and we have a format for it\n// GCC seems to have \"void std::vector<bool>::data()\" - doing SFINAE on the existence of data()\n// is insufficient, we need to check it returns an appropriate pointer\ntemplate <typename Vector, typename = void>\nstruct vector_has_data_and_format : std::false_type {};\ntemplate <typename Vector>\nstruct vector_has_data_and_format<\n    Vector,\n    enable_if_t<std::is_same<decltype(format_descriptor<typename Vector::value_type>::format(),\n                                      std::declval<Vector>().data()),\n                             typename Vector::value_type *>::value>> : std::true_type {};\n\n// [workaround(intel)] Separate function required here\n// Workaround as the Intel compiler does not compile the enable_if_t part below\n// (tested with icc (ICC) 2021.1 Beta 20200827)\ntemplate <typename... Args>\nconstexpr bool args_any_are_buffer() {\n    return detail::any_of<std::is_same<Args, buffer_protocol>...>::value;\n}\n\n// [workaround(intel)] Separate function required here\n// [workaround(msvc)] Can't use constexpr bool in return type\n\n// Add the buffer interface to a vector\ntemplate <typename Vector, typename Class_, typename... Args>\nvoid vector_buffer_impl(Class_ &cl, std::true_type) {\n    using T = typename Vector::value_type;\n\n    static_assert(vector_has_data_and_format<Vector>::value,\n                  \"There is not an appropriate format descriptor for this vector\");\n\n    // numpy.h declares this for arbitrary types, but it may raise an exception and crash hard\n    // at runtime if PYBIND11_NUMPY_DTYPE hasn't been called, so check here\n    format_descriptor<T>::format();\n\n    cl.def_buffer([](Vector &v) -> buffer_info {\n        return buffer_info(v.data(),\n                           static_cast<ssize_t>(sizeof(T)),\n                           format_descriptor<T>::format(),\n                           1,\n                           {v.size()},\n                           {sizeof(T)});\n    });\n\n    cl.def(init([](const buffer &buf) {\n        auto info = buf.request();\n        if (info.ndim != 1 || info.strides[0] % static_cast<ssize_t>(sizeof(T))) {\n            throw type_error(\"Only valid 1D buffers can be copied to a vector\");\n        }\n        if (!detail::compare_buffer_info<T>::compare(info)\n            || (ssize_t) sizeof(T) != info.itemsize) {\n            throw type_error(\"Format mismatch (Python: \" + info.format\n                             + \" C++: \" + format_descriptor<T>::format() + \")\");\n        }\n\n        T *p = static_cast<T *>(info.ptr);\n        ssize_t step = info.strides[0] / static_cast<ssize_t>(sizeof(T));\n        T *end = p + info.shape[0] * step;\n        if (step == 1) {\n            return Vector(p, end);\n        }\n        Vector vec;\n        vec.reserve((size_t) info.shape[0]);\n        for (; p != end; p += step) {\n            vec.push_back(*p);\n        }\n        return vec;\n    }));\n\n    return;\n}\n\ntemplate <typename Vector, typename Class_, typename... Args>\nvoid vector_buffer_impl(Class_ &, std::false_type) {}\n\ntemplate <typename Vector, typename Class_, typename... Args>\nvoid vector_buffer(Class_ &cl) {\n    vector_buffer_impl<Vector, Class_, Args...>(\n        cl, detail::any_of<std::is_same<Args, buffer_protocol>...>{});\n}\n\nPYBIND11_NAMESPACE_END(detail)\n\n//\n// std::vector\n//\ntemplate <typename Vector, typename holder_type = std::unique_ptr<Vector>, typename... Args>\nclass_<Vector, holder_type> bind_vector(handle scope, std::string const &name, Args &&...args) {\n    using Class_ = class_<Vector, holder_type>;\n\n    // If the value_type is unregistered (e.g. a converting type) or is itself registered\n    // module-local then make the vector binding module-local as well:\n    using vtype = typename Vector::value_type;\n    auto *vtype_info = detail::get_type_info(typeid(vtype));\n    bool local = !vtype_info || vtype_info->module_local;\n\n    Class_ cl(scope, name.c_str(), pybind11::module_local(local), std::forward<Args>(args)...);\n\n    // Declare the buffer interface if a buffer_protocol() is passed in\n    detail::vector_buffer<Vector, Class_, Args...>(cl);\n\n    cl.def(init<>());\n\n    // Register copy constructor (if possible)\n    detail::vector_if_copy_constructible<Vector, Class_>(cl);\n\n    // Register comparison-related operators and functions (if possible)\n    detail::vector_if_equal_operator<Vector, Class_>(cl);\n\n    // Register stream insertion operator (if possible)\n    detail::vector_if_insertion_operator<Vector, Class_>(cl, name);\n\n    // Modifiers require copyable vector value type\n    detail::vector_modifiers<Vector, Class_>(cl);\n\n    // Accessor and iterator; return by value if copyable, otherwise we return by ref + keep-alive\n    detail::vector_accessor<Vector, Class_>(cl);\n\n    cl.def(\n        \"__bool__\",\n        [](const Vector &v) -> bool { return !v.empty(); },\n        \"Check whether the list is nonempty\");\n\n    cl.def(\"__len__\", [](const Vector &vec) { return vec.size(); });\n\n#if 0\n    // C++ style functions deprecated, leaving it here as an example\n    cl.def(init<size_type>());\n\n    cl.def(\"resize\",\n         (void (Vector::*) (size_type count)) & Vector::resize,\n         \"changes the number of elements stored\");\n\n    cl.def(\"erase\",\n        [](Vector &v, SizeType i) {\n        if (i >= v.size())\n            throw index_error();\n        v.erase(v.begin() + i);\n    }, \"erases element at index ``i``\");\n\n    cl.def(\"empty\",         &Vector::empty,         \"checks whether the container is empty\");\n    cl.def(\"size\",          &Vector::size,          \"returns the number of elements\");\n    cl.def(\"push_back\", (void (Vector::*)(const T&)) &Vector::push_back, \"adds an element to the end\");\n    cl.def(\"pop_back\",                               &Vector::pop_back, \"removes the last element\");\n\n    cl.def(\"max_size\",      &Vector::max_size,      \"returns the maximum possible number of elements\");\n    cl.def(\"reserve\",       &Vector::reserve,       \"reserves storage\");\n    cl.def(\"capacity\",      &Vector::capacity,      \"returns the number of elements that can be held in currently allocated storage\");\n    cl.def(\"shrink_to_fit\", &Vector::shrink_to_fit, \"reduces memory usage by freeing unused memory\");\n\n    cl.def(\"clear\", &Vector::clear, \"clears the contents\");\n    cl.def(\"swap\",   &Vector::swap, \"swaps the contents\");\n\n    cl.def(\"front\", [](Vector &v) {\n        if (v.size()) return v.front();\n        else throw index_error();\n    }, \"access the first element\");\n\n    cl.def(\"back\", [](Vector &v) {\n        if (v.size()) return v.back();\n        else throw index_error();\n    }, \"access the last element \");\n\n#endif\n\n    return cl;\n}\n\n//\n// std::map, std::unordered_map\n//\n\nPYBIND11_NAMESPACE_BEGIN(detail)\n\n/* Fallback functions */\ntemplate <typename, typename, typename... Args>\nvoid map_if_insertion_operator(const Args &...) {}\ntemplate <typename, typename, typename... Args>\nvoid map_assignment(const Args &...) {}\n\n// Map assignment when copy-assignable: just copy the value\ntemplate <typename Map, typename Class_>\nvoid map_assignment(\n    enable_if_t<is_copy_assignable<typename Map::mapped_type>::value, Class_> &cl) {\n    using KeyType = typename Map::key_type;\n    using MappedType = typename Map::mapped_type;\n\n    cl.def(\"__setitem__\", [](Map &m, const KeyType &k, const MappedType &v) {\n        auto it = m.find(k);\n        if (it != m.end()) {\n            it->second = v;\n        } else {\n            m.emplace(k, v);\n        }\n    });\n}\n\n// Not copy-assignable, but still copy-constructible: we can update the value by erasing and\n// reinserting\ntemplate <typename Map, typename Class_>\nvoid map_assignment(enable_if_t<!is_copy_assignable<typename Map::mapped_type>::value\n                                    && is_copy_constructible<typename Map::mapped_type>::value,\n                                Class_> &cl) {\n    using KeyType = typename Map::key_type;\n    using MappedType = typename Map::mapped_type;\n\n    cl.def(\"__setitem__\", [](Map &m, const KeyType &k, const MappedType &v) {\n        // We can't use m[k] = v; because value type might not be default constructable\n        auto r = m.emplace(k, v);\n        if (!r.second) {\n            // value type is not copy assignable so the only way to insert it is to erase it\n            // first...\n            m.erase(r.first);\n            m.emplace(k, v);\n        }\n    });\n}\n\ntemplate <typename Map, typename Class_>\nauto map_if_insertion_operator(Class_ &cl, std::string const &name)\n    -> decltype(std::declval<std::ostream &>() << std::declval<typename Map::key_type>()\n                                               << std::declval<typename Map::mapped_type>(),\n                void()) {\n\n    cl.def(\n        \"__repr__\",\n        [name](Map &m) {\n            std::ostringstream s;\n            s << name << '{';\n            bool f = false;\n            for (auto const &kv : m) {\n                if (f) {\n                    s << \", \";\n                }\n                s << kv.first << \": \" << kv.second;\n                f = true;\n            }\n            s << '}';\n            return s.str();\n        },\n        \"Return the canonical string representation of this map.\");\n}\n\nstruct keys_view {\n    virtual size_t len() = 0;\n    virtual iterator iter() = 0;\n    virtual bool contains(const handle &k) = 0;\n    virtual ~keys_view() = default;\n};\n\nstruct values_view {\n    virtual size_t len() = 0;\n    virtual iterator iter() = 0;\n    virtual ~values_view() = default;\n};\n\nstruct items_view {\n    virtual size_t len() = 0;\n    virtual iterator iter() = 0;\n    virtual ~items_view() = default;\n};\n\ntemplate <typename Map>\nstruct KeysViewImpl : public detail::keys_view {\n    explicit KeysViewImpl(Map &map) : map(map) {}\n    size_t len() override { return map.size(); }\n    iterator iter() override { return make_key_iterator(map.begin(), map.end()); }\n    bool contains(const handle &k) override {\n        try {\n            return map.find(k.template cast<typename Map::key_type>()) != map.end();\n        } catch (const cast_error &) {\n            return false;\n        }\n    }\n    Map &map;\n};\n\ntemplate <typename Map>\nstruct ValuesViewImpl : public detail::values_view {\n    explicit ValuesViewImpl(Map &map) : map(map) {}\n    size_t len() override { return map.size(); }\n    iterator iter() override { return make_value_iterator(map.begin(), map.end()); }\n    Map &map;\n};\n\ntemplate <typename Map>\nstruct ItemsViewImpl : public detail::items_view {\n    explicit ItemsViewImpl(Map &map) : map(map) {}\n    size_t len() override { return map.size(); }\n    iterator iter() override { return make_iterator(map.begin(), map.end()); }\n    Map &map;\n};\n\nPYBIND11_NAMESPACE_END(detail)\n\ntemplate <typename Map, typename holder_type = std::unique_ptr<Map>, typename... Args>\nclass_<Map, holder_type> bind_map(handle scope, const std::string &name, Args &&...args) {\n    using KeyType = typename Map::key_type;\n    using MappedType = typename Map::mapped_type;\n    using KeysView = detail::keys_view;\n    using ValuesView = detail::values_view;\n    using ItemsView = detail::items_view;\n    using Class_ = class_<Map, holder_type>;\n\n    // If either type is a non-module-local bound type then make the map binding non-local as well;\n    // otherwise (e.g. both types are either module-local or converting) the map will be\n    // module-local.\n    auto *tinfo = detail::get_type_info(typeid(MappedType));\n    bool local = !tinfo || tinfo->module_local;\n    if (local) {\n        tinfo = detail::get_type_info(typeid(KeyType));\n        local = !tinfo || tinfo->module_local;\n    }\n\n    Class_ cl(scope, name.c_str(), pybind11::module_local(local), std::forward<Args>(args)...);\n\n    // Wrap KeysView if it wasn't already wrapped\n    if (!detail::get_type_info(typeid(KeysView))) {\n        class_<KeysView> keys_view(scope, \"KeysView\", pybind11::module_local(local));\n        keys_view.def(\"__len__\", &KeysView::len);\n        keys_view.def(\"__iter__\",\n                      &KeysView::iter,\n                      keep_alive<0, 1>() /* Essential: keep view alive while iterator exists */\n        );\n        keys_view.def(\"__contains__\", &KeysView::contains);\n    }\n    // Similarly for ValuesView:\n    if (!detail::get_type_info(typeid(ValuesView))) {\n        class_<ValuesView> values_view(scope, \"ValuesView\", pybind11::module_local(local));\n        values_view.def(\"__len__\", &ValuesView::len);\n        values_view.def(\"__iter__\",\n                        &ValuesView::iter,\n                        keep_alive<0, 1>() /* Essential: keep view alive while iterator exists */\n        );\n    }\n    // Similarly for ItemsView:\n    if (!detail::get_type_info(typeid(ItemsView))) {\n        class_<ItemsView> items_view(scope, \"ItemsView\", pybind11::module_local(local));\n        items_view.def(\"__len__\", &ItemsView::len);\n        items_view.def(\"__iter__\",\n                       &ItemsView::iter,\n                       keep_alive<0, 1>() /* Essential: keep view alive while iterator exists */\n        );\n    }\n\n    cl.def(init<>());\n\n    // Register stream insertion operator (if possible)\n    detail::map_if_insertion_operator<Map, Class_>(cl, name);\n\n    cl.def(\n        \"__bool__\",\n        [](const Map &m) -> bool { return !m.empty(); },\n        \"Check whether the map is nonempty\");\n\n    cl.def(\n        \"__iter__\",\n        [](Map &m) { return make_key_iterator(m.begin(), m.end()); },\n        keep_alive<0, 1>() /* Essential: keep map alive while iterator exists */\n    );\n\n    cl.def(\n        \"keys\",\n        [](Map &m) { return std::unique_ptr<KeysView>(new detail::KeysViewImpl<Map>(m)); },\n        keep_alive<0, 1>() /* Essential: keep map alive while view exists */\n    );\n\n    cl.def(\n        \"values\",\n        [](Map &m) { return std::unique_ptr<ValuesView>(new detail::ValuesViewImpl<Map>(m)); },\n        keep_alive<0, 1>() /* Essential: keep map alive while view exists */\n    );\n\n    cl.def(\n        \"items\",\n        [](Map &m) { return std::unique_ptr<ItemsView>(new detail::ItemsViewImpl<Map>(m)); },\n        keep_alive<0, 1>() /* Essential: keep map alive while view exists */\n    );\n\n    cl.def(\n        \"__getitem__\",\n        [](Map &m, const KeyType &k) -> MappedType & {\n            auto it = m.find(k);\n            if (it == m.end()) {\n                throw key_error();\n            }\n            return it->second;\n        },\n        return_value_policy::reference_internal // ref + keepalive\n    );\n\n    cl.def(\"__contains__\", [](Map &m, const KeyType &k) -> bool {\n        auto it = m.find(k);\n        if (it == m.end()) {\n            return false;\n        }\n        return true;\n    });\n    // Fallback for when the object is not of the key type\n    cl.def(\"__contains__\", [](Map &, const object &) -> bool { return false; });\n\n    // Assignment provided only if the type is copyable\n    detail::map_assignment<Map, Class_>(cl);\n\n    cl.def(\"__delitem__\", [](Map &m, const KeyType &k) {\n        auto it = m.find(k);\n        if (it == m.end()) {\n            throw key_error();\n        }\n        m.erase(it);\n    });\n\n    // Always use a lambda in case of `using` declaration\n    cl.def(\"__len__\", [](const Map &m) { return m.size(); });\n\n    return cl;\n}\n\nPYBIND11_NAMESPACE_END(PYBIND11_NAMESPACE)\n"
  },
  {
    "path": "libs/pybind11/include/pybind11/type_caster_pyobject_ptr.h",
    "content": "// Copyright (c) 2023 The pybind Community.\n\n#pragma once\n\n#include \"detail/common.h\"\n#include \"detail/descr.h\"\n#include \"cast.h\"\n#include \"pytypes.h\"\n\nPYBIND11_NAMESPACE_BEGIN(PYBIND11_NAMESPACE)\nPYBIND11_NAMESPACE_BEGIN(detail)\n\ntemplate <>\nclass type_caster<PyObject> {\npublic:\n    static constexpr auto name = const_name(\"object\"); // See discussion under PR #4601.\n\n    // This overload is purely to guard against accidents.\n    template <typename T,\n              detail::enable_if_t<!is_same_ignoring_cvref<T, PyObject *>::value, int> = 0>\n    static handle cast(T &&, return_value_policy, handle /*parent*/) {\n        static_assert(is_same_ignoring_cvref<T, PyObject *>::value,\n                      \"Invalid C++ type T for to-Python conversion (type_caster<PyObject>).\");\n        return nullptr; // Unreachable.\n    }\n\n    static handle cast(PyObject *src, return_value_policy policy, handle /*parent*/) {\n        if (src == nullptr) {\n            throw error_already_set();\n        }\n        if (PyErr_Occurred()) {\n            raise_from(PyExc_SystemError, \"src != nullptr but PyErr_Occurred()\");\n            throw error_already_set();\n        }\n        if (policy == return_value_policy::take_ownership) {\n            return src;\n        }\n        if (policy == return_value_policy::reference\n            || policy == return_value_policy::automatic_reference) {\n            return handle(src).inc_ref();\n        }\n        pybind11_fail(\"type_caster<PyObject>::cast(): unsupported return_value_policy: \"\n                      + std::to_string(static_cast<int>(policy)));\n    }\n\n    bool load(handle src, bool) {\n        value = reinterpret_borrow<object>(src);\n        return true;\n    }\n\n    template <typename T>\n    using cast_op_type = PyObject *;\n\n    explicit operator PyObject *() { return value.ptr(); }\n\nprivate:\n    object value;\n};\n\nPYBIND11_NAMESPACE_END(detail)\nPYBIND11_NAMESPACE_END(PYBIND11_NAMESPACE)\n"
  },
  {
    "path": "libs/pybind11/include/pybind11/typing.h",
    "content": "/*\n    pybind11/typing.h: Convenience wrapper classes for basic Python types\n    with more explicit annotations.\n\n    Copyright (c) 2023 Dustin Spicuzza <dustin@virtualroadside.com>\n\n    All rights reserved. Use of this source code is governed by a\n    BSD-style license that can be found in the LICENSE file.\n*/\n\n#pragma once\n\n#include \"detail/common.h\"\n#include \"cast.h\"\n#include \"pytypes.h\"\n\n#include <algorithm>\n\nPYBIND11_NAMESPACE_BEGIN(PYBIND11_NAMESPACE)\nPYBIND11_NAMESPACE_BEGIN(typing)\n\n/*\n    The following types can be used to direct pybind11-generated docstrings\n    to have have more explicit types (e.g., `list[str]` instead of `list`).\n    Just use these in place of existing types.\n\n    There is no additional enforcement of types at runtime.\n*/\n\ntemplate <typename... Types>\nclass Tuple : public tuple {\n    using tuple::tuple;\n};\n\ntemplate <typename K, typename V>\nclass Dict : public dict {\n    using dict::dict;\n};\n\ntemplate <typename T>\nclass List : public list {\n    using list::list;\n};\n\ntemplate <typename T>\nclass Set : public set {\n    using set::set;\n};\n\ntemplate <typename T>\nclass Iterable : public iterable {\n    using iterable::iterable;\n};\n\ntemplate <typename T>\nclass Iterator : public iterator {\n    using iterator::iterator;\n};\n\ntemplate <typename Signature>\nclass Callable;\n\ntemplate <typename Return, typename... Args>\nclass Callable<Return(Args...)> : public function {\n    using function::function;\n};\n\ntemplate <typename T>\nclass Type : public type {\n    using type::type;\n};\n\ntemplate <typename... Types>\nclass Union : public object {\n    PYBIND11_OBJECT_DEFAULT(Union, object, PyObject_Type)\n    using object::object;\n};\n\ntemplate <typename T>\nclass Optional : public object {\n    PYBIND11_OBJECT_DEFAULT(Optional, object, PyObject_Type)\n    using object::object;\n};\n\ntemplate <typename T>\nclass TypeGuard : public bool_ {\n    using bool_::bool_;\n};\n\ntemplate <typename T>\nclass TypeIs : public bool_ {\n    using bool_::bool_;\n};\n\nclass NoReturn : public none {\n    using none::none;\n};\n\nclass Never : public none {\n    using none::none;\n};\n\n#if defined(__cpp_nontype_template_args) && __cpp_nontype_template_args >= 201911L\n#    define PYBIND11_TYPING_H_HAS_STRING_LITERAL\ntemplate <size_t N>\nstruct StringLiteral {\n    constexpr StringLiteral(const char (&str)[N]) { std::copy_n(str, N, name); }\n    char name[N];\n};\n\ntemplate <StringLiteral... StrLits>\nclass Literal : public object {\n    PYBIND11_OBJECT_DEFAULT(Literal, object, PyObject_Type)\n};\n\n// Example syntax for creating a TypeVar.\n// typedef typing::TypeVar<\"T\"> TypeVarT;\ntemplate <StringLiteral>\nclass TypeVar : public object {\n    PYBIND11_OBJECT_DEFAULT(TypeVar, object, PyObject_Type)\n    using object::object;\n};\n#endif\n\nPYBIND11_NAMESPACE_END(typing)\n\nPYBIND11_NAMESPACE_BEGIN(detail)\n\ntemplate <typename... Types>\nstruct handle_type_name<typing::Tuple<Types...>> {\n    static constexpr auto name = const_name(\"tuple[\")\n                                 + ::pybind11::detail::concat(make_caster<Types>::name...)\n                                 + const_name(\"]\");\n};\n\ntemplate <>\nstruct handle_type_name<typing::Tuple<>> {\n    // PEP 484 specifies this syntax for an empty tuple\n    static constexpr auto name = const_name(\"tuple[()]\");\n};\n\ntemplate <typename T>\nstruct handle_type_name<typing::Tuple<T, ellipsis>> {\n    // PEP 484 specifies this syntax for a variable-length tuple\n    static constexpr auto name\n        = const_name(\"tuple[\") + make_caster<T>::name + const_name(\", ...]\");\n};\n\ntemplate <typename K, typename V>\nstruct handle_type_name<typing::Dict<K, V>> {\n    static constexpr auto name = const_name(\"dict[\") + make_caster<K>::name + const_name(\", \")\n                                 + make_caster<V>::name + const_name(\"]\");\n};\n\ntemplate <typename T>\nstruct handle_type_name<typing::List<T>> {\n    static constexpr auto name = const_name(\"list[\") + make_caster<T>::name + const_name(\"]\");\n};\n\ntemplate <typename T>\nstruct handle_type_name<typing::Set<T>> {\n    static constexpr auto name = const_name(\"set[\") + make_caster<T>::name + const_name(\"]\");\n};\n\ntemplate <typename T>\nstruct handle_type_name<typing::Iterable<T>> {\n    static constexpr auto name = const_name(\"Iterable[\") + make_caster<T>::name + const_name(\"]\");\n};\n\ntemplate <typename T>\nstruct handle_type_name<typing::Iterator<T>> {\n    static constexpr auto name = const_name(\"Iterator[\") + make_caster<T>::name + const_name(\"]\");\n};\n\ntemplate <typename Return, typename... Args>\nstruct handle_type_name<typing::Callable<Return(Args...)>> {\n    using retval_type = conditional_t<std::is_same<Return, void>::value, void_type, Return>;\n    static constexpr auto name\n        = const_name(\"Callable[[\") + ::pybind11::detail::concat(make_caster<Args>::name...)\n          + const_name(\"], \") + make_caster<retval_type>::name + const_name(\"]\");\n};\n\ntemplate <typename Return>\nstruct handle_type_name<typing::Callable<Return(ellipsis)>> {\n    // PEP 484 specifies this syntax for defining only return types of callables\n    using retval_type = conditional_t<std::is_same<Return, void>::value, void_type, Return>;\n    static constexpr auto name\n        = const_name(\"Callable[..., \") + make_caster<retval_type>::name + const_name(\"]\");\n};\n\ntemplate <typename T>\nstruct handle_type_name<typing::Type<T>> {\n    static constexpr auto name = const_name(\"type[\") + make_caster<T>::name + const_name(\"]\");\n};\n\ntemplate <typename... Types>\nstruct handle_type_name<typing::Union<Types...>> {\n    static constexpr auto name = const_name(\"Union[\")\n                                 + ::pybind11::detail::concat(make_caster<Types>::name...)\n                                 + const_name(\"]\");\n};\n\ntemplate <typename T>\nstruct handle_type_name<typing::Optional<T>> {\n    static constexpr auto name = const_name(\"Optional[\") + make_caster<T>::name + const_name(\"]\");\n};\n\ntemplate <typename T>\nstruct handle_type_name<typing::TypeGuard<T>> {\n    static constexpr auto name = const_name(\"TypeGuard[\") + make_caster<T>::name + const_name(\"]\");\n};\n\ntemplate <typename T>\nstruct handle_type_name<typing::TypeIs<T>> {\n    static constexpr auto name = const_name(\"TypeIs[\") + make_caster<T>::name + const_name(\"]\");\n};\n\ntemplate <>\nstruct handle_type_name<typing::NoReturn> {\n    static constexpr auto name = const_name(\"NoReturn\");\n};\n\ntemplate <>\nstruct handle_type_name<typing::Never> {\n    static constexpr auto name = const_name(\"Never\");\n};\n\n#if defined(PYBIND11_TYPING_H_HAS_STRING_LITERAL)\ntemplate <typing::StringLiteral... Literals>\nstruct handle_type_name<typing::Literal<Literals...>> {\n    static constexpr auto name = const_name(\"Literal[\")\n                                 + pybind11::detail::concat(const_name(Literals.name)...)\n                                 + const_name(\"]\");\n};\ntemplate <typing::StringLiteral StrLit>\nstruct handle_type_name<typing::TypeVar<StrLit>> {\n    static constexpr auto name = const_name(StrLit.name);\n};\n#endif\n\nPYBIND11_NAMESPACE_END(detail)\nPYBIND11_NAMESPACE_END(PYBIND11_NAMESPACE)\n"
  },
  {
    "path": "libs/pybind11/pybind11/__init__.py",
    "content": "from __future__ import annotations\n\nimport sys\n\nif sys.version_info < (3, 7):  # noqa: UP036\n    msg = \"pybind11 does not support Python < 3.7. v2.12 was the last release supporting Python 3.6.\"\n    raise ImportError(msg)\n\n\nfrom ._version import __version__, version_info\nfrom .commands import get_cmake_dir, get_include, get_pkgconfig_dir\n\n__all__ = (\n    \"version_info\",\n    \"__version__\",\n    \"get_include\",\n    \"get_cmake_dir\",\n    \"get_pkgconfig_dir\",\n)\n"
  },
  {
    "path": "libs/pybind11/pybind11/__main__.py",
    "content": "# pylint: disable=missing-function-docstring\nfrom __future__ import annotations\n\nimport argparse\nimport re\nimport sys\nimport sysconfig\n\nfrom ._version import __version__\nfrom .commands import get_cmake_dir, get_include, get_pkgconfig_dir\n\n# This is the conditional used for os.path being posixpath\nif \"posix\" in sys.builtin_module_names:\n    from shlex import quote\nelif \"nt\" in sys.builtin_module_names:\n    # See https://github.com/mesonbuild/meson/blob/db22551ed9d2dd7889abea01cc1c7bba02bf1c75/mesonbuild/utils/universal.py#L1092-L1121\n    # and the original documents:\n    # https://docs.microsoft.com/en-us/cpp/c-language/parsing-c-command-line-arguments and\n    # https://blogs.msdn.microsoft.com/twistylittlepassagesallalike/2011/04/23/everyone-quotes-command-line-arguments-the-wrong-way/\n    UNSAFE = re.compile(\"[ \\t\\n\\r]\")\n\n    def quote(s: str) -> str:\n        if s and not UNSAFE.search(s):\n            return s\n\n        # Paths cannot contain a '\"' on Windows, so we don't need to worry\n        # about nuanced counting here.\n        return f'\"{s}\\\\\"' if s.endswith(\"\\\\\") else f'\"{s}\"'\nelse:\n\n    def quote(s: str) -> str:\n        return s\n\n\ndef print_includes() -> None:\n    dirs = [\n        sysconfig.get_path(\"include\"),\n        sysconfig.get_path(\"platinclude\"),\n        get_include(),\n    ]\n\n    # Make unique but preserve order\n    unique_dirs = []\n    for d in dirs:\n        if d and d not in unique_dirs:\n            unique_dirs.append(d)\n\n    print(\" \".join(quote(f\"-I{d}\") for d in unique_dirs))\n\n\ndef main() -> None:\n    parser = argparse.ArgumentParser()\n    parser.add_argument(\n        \"--version\",\n        action=\"version\",\n        version=__version__,\n        help=\"Print the version and exit.\",\n    )\n    parser.add_argument(\n        \"--includes\",\n        action=\"store_true\",\n        help=\"Include flags for both pybind11 and Python headers.\",\n    )\n    parser.add_argument(\n        \"--cmakedir\",\n        action=\"store_true\",\n        help=\"Print the CMake module directory, ideal for setting -Dpybind11_ROOT in CMake.\",\n    )\n    parser.add_argument(\n        \"--pkgconfigdir\",\n        action=\"store_true\",\n        help=\"Print the pkgconfig directory, ideal for setting $PKG_CONFIG_PATH.\",\n    )\n    args = parser.parse_args()\n    if not sys.argv[1:]:\n        parser.print_help()\n    if args.includes:\n        print_includes()\n    if args.cmakedir:\n        print(quote(get_cmake_dir()))\n    if args.pkgconfigdir:\n        print(quote(get_pkgconfig_dir()))\n\n\nif __name__ == \"__main__\":\n    main()\n"
  },
  {
    "path": "libs/pybind11/pybind11/_version.py",
    "content": "from __future__ import annotations\n\n\ndef _to_int(s: str) -> int | str:\n    try:\n        return int(s)\n    except ValueError:\n        return s\n\n\n__version__ = \"2.13.6\"\nversion_info = tuple(_to_int(s) for s in __version__.split(\".\"))\n"
  },
  {
    "path": "libs/pybind11/pybind11/commands.py",
    "content": "from __future__ import annotations\n\nimport os\n\nDIR = os.path.abspath(os.path.dirname(__file__))\n\n\ndef get_include(user: bool = False) -> str:  # noqa: ARG001\n    \"\"\"\n    Return the path to the pybind11 include directory. The historical \"user\"\n    argument is unused, and may be removed.\n    \"\"\"\n    installed_path = os.path.join(DIR, \"include\")\n    source_path = os.path.join(os.path.dirname(DIR), \"include\")\n    return installed_path if os.path.exists(installed_path) else source_path\n\n\ndef get_cmake_dir() -> str:\n    \"\"\"\n    Return the path to the pybind11 CMake module directory.\n    \"\"\"\n    cmake_installed_path = os.path.join(DIR, \"share\", \"cmake\", \"pybind11\")\n    if os.path.exists(cmake_installed_path):\n        return cmake_installed_path\n\n    msg = \"pybind11 not installed, installation required to access the CMake files\"\n    raise ImportError(msg)\n\n\ndef get_pkgconfig_dir() -> str:\n    \"\"\"\n    Return the path to the pybind11 pkgconfig directory.\n    \"\"\"\n    pkgconfig_installed_path = os.path.join(DIR, \"share\", \"pkgconfig\")\n    if os.path.exists(pkgconfig_installed_path):\n        return pkgconfig_installed_path\n\n    msg = \"pybind11 not installed, installation required to access the pkgconfig files\"\n    raise ImportError(msg)\n"
  },
  {
    "path": "libs/pybind11/pybind11/py.typed",
    "content": ""
  },
  {
    "path": "libs/pybind11/pybind11/setup_helpers.py",
    "content": "\"\"\"\nThis module provides helpers for C++11+ projects using pybind11.\n\nLICENSE:\n\nCopyright (c) 2016 Wenzel Jakob <wenzel.jakob@epfl.ch>, All rights reserved.\n\nRedistribution and use in source and binary forms, with or without\nmodification, are permitted provided that the following conditions are met:\n\n1. Redistributions of source code must retain the above copyright notice, this\n   list of conditions and the following disclaimer.\n\n2. Redistributions in binary form must reproduce the above copyright notice,\n   this list of conditions and the following disclaimer in the documentation\n   and/or other materials provided with the distribution.\n\n3. Neither the name of the copyright holder nor the names of its contributors\n   may be used to endorse or promote products derived from this software\n   without specific prior written permission.\n\nTHIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS \"AS IS\" AND\nANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED\nWARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE\nDISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE\nFOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL\nDAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR\nSERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER\nCAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,\nOR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE\nOF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.\n\"\"\"\n\n# IMPORTANT: If you change this file in the pybind11 repo, also review\n# setup_helpers.pyi for matching changes.\n#\n# If you copy this file in, you don't\n# need the .pyi file; it's just an interface file for static type checkers.\nfrom __future__ import annotations\n\nimport contextlib\nimport os\nimport platform\nimport shlex\nimport shutil\nimport sys\nimport sysconfig\nimport tempfile\nimport threading\nimport warnings\nfrom functools import lru_cache\nfrom pathlib import Path\nfrom typing import (\n    Any,\n    Callable,\n    Iterable,\n    Iterator,\n    List,\n    Optional,\n    Tuple,\n    TypeVar,\n    Union,\n)\n\ntry:\n    from setuptools import Extension as _Extension\n    from setuptools.command.build_ext import build_ext as _build_ext\nexcept ImportError:\n    from distutils.command.build_ext import (  # type: ignore[assignment]\n        build_ext as _build_ext,\n    )\n    from distutils.extension import Extension as _Extension  # type: ignore[assignment]\n\nimport distutils.ccompiler\nimport distutils.errors\n\nWIN = sys.platform.startswith(\"win32\") and \"mingw\" not in sysconfig.get_platform()\nMACOS = sys.platform.startswith(\"darwin\")\nSTD_TMPL = \"/std:c++{}\" if WIN else \"-std=c++{}\"\n\n\n# It is recommended to use PEP 518 builds if using this module. However, this\n# file explicitly supports being copied into a user's project directory\n# standalone, and pulling pybind11 with the deprecated setup_requires feature.\n# If you copy the file, remember to add it to your MANIFEST.in, and add the current\n# directory into your path if it sits beside your setup.py.\n\n\nclass Pybind11Extension(_Extension):\n    \"\"\"\n    Build a C++11+ Extension module with pybind11. This automatically adds the\n    recommended flags when you init the extension and assumes C++ sources - you\n    can further modify the options yourself.\n\n    The customizations are:\n\n    * ``/EHsc`` and ``/bigobj`` on Windows\n    * ``stdlib=libc++`` on macOS\n    * ``visibility=hidden`` and ``-g0`` on Unix\n\n    Finally, you can set ``cxx_std`` via constructor or afterwards to enable\n    flags for C++ std, and a few extra helper flags related to the C++ standard\n    level. It is _highly_ recommended you either set this, or use the provided\n    ``build_ext``, which will search for the highest supported extension for\n    you if the ``cxx_std`` property is not set. Do not set the ``cxx_std``\n    property more than once, as flags are added when you set it. Set the\n    property to None to disable the addition of C++ standard flags.\n\n    If you want to add pybind11 headers manually, for example for an exact\n    git checkout, then set ``include_pybind11=False``.\n    \"\"\"\n\n    # flags are prepended, so that they can be further overridden, e.g. by\n    # ``extra_compile_args=[\"-g\"]``.\n\n    def _add_cflags(self, flags: list[str]) -> None:\n        self.extra_compile_args[:0] = flags\n\n    def _add_ldflags(self, flags: list[str]) -> None:\n        self.extra_link_args[:0] = flags\n\n    def __init__(self, *args: Any, **kwargs: Any) -> None:\n        self._cxx_level = 0\n        cxx_std = kwargs.pop(\"cxx_std\", 0)\n\n        if \"language\" not in kwargs:\n            kwargs[\"language\"] = \"c++\"\n\n        include_pybind11 = kwargs.pop(\"include_pybind11\", True)\n\n        super().__init__(*args, **kwargs)\n\n        # Include the installed package pybind11 headers\n        if include_pybind11:\n            # If using setup_requires, this fails the first time - that's okay\n            try:\n                import pybind11\n\n                pyinc = pybind11.get_include()\n\n                if pyinc not in self.include_dirs:\n                    self.include_dirs.append(pyinc)\n            except ModuleNotFoundError:\n                pass\n\n        self.cxx_std = cxx_std\n\n        cflags = []\n        if WIN:\n            cflags += [\"/EHsc\", \"/bigobj\"]\n        else:\n            cflags += [\"-fvisibility=hidden\"]\n            env_cflags = os.environ.get(\"CFLAGS\", \"\")\n            env_cppflags = os.environ.get(\"CPPFLAGS\", \"\")\n            c_cpp_flags = shlex.split(env_cflags) + shlex.split(env_cppflags)\n            if not any(opt.startswith(\"-g\") for opt in c_cpp_flags):\n                cflags += [\"-g0\"]\n        self._add_cflags(cflags)\n\n    @property\n    def cxx_std(self) -> int:\n        \"\"\"\n        The CXX standard level. If set, will add the required flags. If left at\n        0, it will trigger an automatic search when pybind11's build_ext is\n        used. If None, will have no effect.  Besides just the flags, this may\n        add a macos-min 10.9 or 10.14 flag if MACOSX_DEPLOYMENT_TARGET is\n        unset.\n        \"\"\"\n        return self._cxx_level\n\n    @cxx_std.setter\n    def cxx_std(self, level: int) -> None:\n        if self._cxx_level:\n            warnings.warn(\n                \"You cannot safely change the cxx_level after setting it!\", stacklevel=2\n            )\n\n        # MSVC 2015 Update 3 and later only have 14 (and later 17) modes, so\n        # force a valid flag here.\n        if WIN and level == 11:\n            level = 14\n\n        self._cxx_level = level\n\n        if not level:\n            return\n\n        cflags = [STD_TMPL.format(level)]\n        ldflags = []\n\n        if MACOS and \"MACOSX_DEPLOYMENT_TARGET\" not in os.environ:\n            # C++17 requires a higher min version of macOS. An earlier version\n            # (10.12 or 10.13) can be set manually via environment variable if\n            # you are careful in your feature usage, but 10.14 is the safest\n            # setting for general use. However, never set higher than the\n            # current macOS version!\n            current_macos = tuple(int(x) for x in platform.mac_ver()[0].split(\".\")[:2])\n            desired_macos = (10, 9) if level < 17 else (10, 14)\n            macos_string = \".\".join(str(x) for x in min(current_macos, desired_macos))\n            macosx_min = f\"-mmacosx-version-min={macos_string}\"\n            cflags += [macosx_min]\n            ldflags += [macosx_min]\n\n        self._add_cflags(cflags)\n        self._add_ldflags(ldflags)\n\n\n# Just in case someone clever tries to multithread\ntmp_chdir_lock = threading.Lock()\n\n\n@contextlib.contextmanager\ndef tmp_chdir() -> Iterator[str]:\n    \"Prepare and enter a temporary directory, cleanup when done\"\n\n    # Threadsafe\n    with tmp_chdir_lock:\n        olddir = os.getcwd()\n        try:\n            tmpdir = tempfile.mkdtemp()\n            os.chdir(tmpdir)\n            yield tmpdir\n        finally:\n            os.chdir(olddir)\n            shutil.rmtree(tmpdir)\n\n\n# cf http://bugs.python.org/issue26689\ndef has_flag(compiler: Any, flag: str) -> bool:\n    \"\"\"\n    Return the flag if a flag name is supported on the\n    specified compiler, otherwise None (can be used as a boolean).\n    If multiple flags are passed, return the first that matches.\n    \"\"\"\n\n    with tmp_chdir():\n        fname = Path(\"flagcheck.cpp\")\n        # Don't trigger -Wunused-parameter.\n        fname.write_text(\"int main (int, char **) { return 0; }\", encoding=\"utf-8\")\n\n        try:\n            compiler.compile([str(fname)], extra_postargs=[flag])\n        except distutils.errors.CompileError:\n            return False\n        return True\n\n\n# Every call will cache the result\ncpp_flag_cache = None\n\n\n@lru_cache()\ndef auto_cpp_level(compiler: Any) -> str | int:\n    \"\"\"\n    Return the max supported C++ std level (17, 14, or 11). Returns latest on Windows.\n    \"\"\"\n\n    if WIN:\n        return \"latest\"\n\n    levels = [17, 14, 11]\n\n    for level in levels:\n        if has_flag(compiler, STD_TMPL.format(level)):\n            return level\n\n    msg = \"Unsupported compiler -- at least C++11 support is needed!\"\n    raise RuntimeError(msg)\n\n\nclass build_ext(_build_ext):  # noqa: N801\n    \"\"\"\n    Customized build_ext that allows an auto-search for the highest supported\n    C++ level for Pybind11Extension. This is only needed for the auto-search\n    for now, and is completely optional otherwise.\n    \"\"\"\n\n    def build_extensions(self) -> None:\n        \"\"\"\n        Build extensions, injecting C++ std for Pybind11Extension if needed.\n        \"\"\"\n\n        for ext in self.extensions:\n            if hasattr(ext, \"_cxx_level\") and ext._cxx_level == 0:\n                ext.cxx_std = auto_cpp_level(self.compiler)\n\n        super().build_extensions()\n\n\ndef intree_extensions(\n    paths: Iterable[str], package_dir: dict[str, str] | None = None\n) -> list[Pybind11Extension]:\n    \"\"\"\n    Generate Pybind11Extensions from source files directly located in a Python\n    source tree.\n\n    ``package_dir`` behaves as in ``setuptools.setup``.  If unset, the Python\n    package root parent is determined as the first parent directory that does\n    not contain an ``__init__.py`` file.\n    \"\"\"\n    exts = []\n\n    if package_dir is None:\n        for path in paths:\n            parent, _ = os.path.split(path)\n            while os.path.exists(os.path.join(parent, \"__init__.py\")):\n                parent, _ = os.path.split(parent)\n            relname, _ = os.path.splitext(os.path.relpath(path, parent))\n            qualified_name = relname.replace(os.path.sep, \".\")\n            exts.append(Pybind11Extension(qualified_name, [path]))\n        return exts\n\n    for path in paths:\n        for prefix, parent in package_dir.items():\n            if path.startswith(parent):\n                relname, _ = os.path.splitext(os.path.relpath(path, parent))\n                qualified_name = relname.replace(os.path.sep, \".\")\n                if prefix:\n                    qualified_name = prefix + \".\" + qualified_name\n                exts.append(Pybind11Extension(qualified_name, [path]))\n                break\n        else:\n            msg = (\n                f\"path {path} is not a child of any of the directories listed \"\n                f\"in 'package_dir' ({package_dir})\"\n            )\n            raise ValueError(msg)\n\n    return exts\n\n\ndef naive_recompile(obj: str, src: str) -> bool:\n    \"\"\"\n    This will recompile only if the source file changes. It does not check\n    header files, so a more advanced function or Ccache is better if you have\n    editable header files in your package.\n    \"\"\"\n    return os.stat(obj).st_mtime < os.stat(src).st_mtime\n\n\ndef no_recompile(obg: str, src: str) -> bool:  # noqa: ARG001\n    \"\"\"\n    This is the safest but slowest choice (and is the default) - will always\n    recompile sources.\n    \"\"\"\n    return True\n\n\nS = TypeVar(\"S\", bound=\"ParallelCompile\")\n\nCCompilerMethod = Callable[\n    [\n        distutils.ccompiler.CCompiler,\n        List[str],\n        Optional[str],\n        Optional[List[Union[Tuple[str], Tuple[str, Optional[str]]]]],\n        Optional[List[str]],\n        bool,\n        Optional[List[str]],\n        Optional[List[str]],\n        Optional[List[str]],\n    ],\n    List[str],\n]\n\n\n# Optional parallel compile utility\n# inspired by: http://stackoverflow.com/questions/11013851/speeding-up-build-process-with-distutils\n# and: https://github.com/tbenthompson/cppimport/blob/stable/cppimport/build_module.py\n# and NumPy's parallel distutils module:\n#              https://github.com/numpy/numpy/blob/master/numpy/distutils/ccompiler.py\nclass ParallelCompile:\n    \"\"\"\n    Make a parallel compile function. Inspired by\n    numpy.distutils.ccompiler.CCompiler.compile and cppimport.\n\n    This takes several arguments that allow you to customize the compile\n    function created:\n\n    envvar:\n        Set an environment variable to control the compilation threads, like\n        NPY_NUM_BUILD_JOBS\n    default:\n        0 will automatically multithread, or 1 will only multithread if the\n        envvar is set.\n    max:\n        The limit for automatic multithreading if non-zero\n    needs_recompile:\n        A function of (obj, src) that returns True when recompile is needed.  No\n        effect in isolated mode; use ccache instead, see\n        https://github.com/matplotlib/matplotlib/issues/1507/\n\n    To use::\n\n        ParallelCompile(\"NPY_NUM_BUILD_JOBS\").install()\n\n    or::\n\n        with ParallelCompile(\"NPY_NUM_BUILD_JOBS\"):\n            setup(...)\n\n    By default, this assumes all files need to be recompiled. A smarter\n    function can be provided via needs_recompile.  If the output has not yet\n    been generated, the compile will always run, and this function is not\n    called.\n    \"\"\"\n\n    __slots__ = (\"envvar\", \"default\", \"max\", \"_old\", \"needs_recompile\")\n\n    def __init__(\n        self,\n        envvar: str | None = None,\n        default: int = 0,\n        max: int = 0,  # pylint: disable=redefined-builtin\n        needs_recompile: Callable[[str, str], bool] = no_recompile,\n    ) -> None:\n        self.envvar = envvar\n        self.default = default\n        self.max = max\n        self.needs_recompile = needs_recompile\n        self._old: list[CCompilerMethod] = []\n\n    def function(self) -> CCompilerMethod:\n        \"\"\"\n        Builds a function object usable as distutils.ccompiler.CCompiler.compile.\n        \"\"\"\n\n        def compile_function(\n            compiler: distutils.ccompiler.CCompiler,\n            sources: list[str],\n            output_dir: str | None = None,\n            macros: list[tuple[str] | tuple[str, str | None]] | None = None,\n            include_dirs: list[str] | None = None,\n            debug: bool = False,\n            extra_preargs: list[str] | None = None,\n            extra_postargs: list[str] | None = None,\n            depends: list[str] | None = None,\n        ) -> Any:\n            # These lines are directly from distutils.ccompiler.CCompiler\n            macros, objects, extra_postargs, pp_opts, build = compiler._setup_compile(  # type: ignore[attr-defined]\n                output_dir, macros, include_dirs, sources, depends, extra_postargs\n            )\n            cc_args = compiler._get_cc_args(pp_opts, debug, extra_preargs)  # type: ignore[attr-defined]\n\n            # The number of threads; start with default.\n            threads = self.default\n\n            # Determine the number of compilation threads, unless set by an environment variable.\n            if self.envvar is not None:\n                threads = int(os.environ.get(self.envvar, self.default))\n\n            def _single_compile(obj: Any) -> None:\n                try:\n                    src, ext = build[obj]\n                except KeyError:\n                    return\n\n                if not os.path.exists(obj) or self.needs_recompile(obj, src):\n                    compiler._compile(obj, src, ext, cc_args, extra_postargs, pp_opts)  # type: ignore[attr-defined]\n\n            try:\n                # Importing .synchronize checks for platforms that have some multiprocessing\n                # capabilities but lack semaphores, such as AWS Lambda and Android Termux.\n                import multiprocessing.synchronize\n                from multiprocessing.pool import ThreadPool\n            except ImportError:\n                threads = 1\n\n            if threads == 0:\n                try:\n                    threads = multiprocessing.cpu_count()\n                    threads = self.max if self.max and self.max < threads else threads\n                except NotImplementedError:\n                    threads = 1\n\n            if threads > 1:\n                with ThreadPool(threads) as pool:\n                    for _ in pool.imap_unordered(_single_compile, objects):\n                        pass\n            else:\n                for ob in objects:\n                    _single_compile(ob)\n\n            return objects\n\n        return compile_function\n\n    def install(self: S) -> S:\n        \"\"\"\n        Installs the compile function into distutils.ccompiler.CCompiler.compile.\n        \"\"\"\n        distutils.ccompiler.CCompiler.compile = self.function()  # type: ignore[assignment]\n        return self\n\n    def __enter__(self: S) -> S:\n        self._old.append(distutils.ccompiler.CCompiler.compile)\n        return self.install()\n\n    def __exit__(self, *args: Any) -> None:\n        distutils.ccompiler.CCompiler.compile = self._old.pop()  # type: ignore[assignment]\n"
  },
  {
    "path": "libs/pybind11/tools/FindCatch.cmake",
    "content": "# - Find the Catch test framework or download it (single header)\n#\n# This is a quick module for internal use. It assumes that Catch is\n# REQUIRED and that a minimum version is provided (not EXACT). If\n# a suitable version isn't found locally, the single header file\n# will be downloaded and placed in the build dir: PROJECT_BINARY_DIR.\n#\n# This code sets the following variables:\n#  CATCH_INCLUDE_DIR      - path to catch.hpp\n#  CATCH_VERSION          - version number\n\noption(DOWNLOAD_CATCH \"Download catch2 if not found\")\n\nif(NOT Catch_FIND_VERSION)\n  message(FATAL_ERROR \"A version number must be specified.\")\nelseif(Catch_FIND_REQUIRED)\n  message(FATAL_ERROR \"This module assumes Catch is not required.\")\nelseif(Catch_FIND_VERSION_EXACT)\n  message(FATAL_ERROR \"Exact version numbers are not supported, only minimum.\")\nendif()\n\n# Extract the version number from catch.hpp\nfunction(_get_catch_version)\n  file(\n    STRINGS \"${CATCH_INCLUDE_DIR}/catch.hpp\" version_line\n    REGEX \"Catch v.*\"\n    LIMIT_COUNT 1)\n  if(version_line MATCHES \"Catch v([0-9]+)\\\\.([0-9]+)\\\\.([0-9]+)\")\n    set(CATCH_VERSION\n        \"${CMAKE_MATCH_1}.${CMAKE_MATCH_2}.${CMAKE_MATCH_3}\"\n        PARENT_SCOPE)\n  endif()\nendfunction()\n\n# Download the single-header version of Catch\nfunction(_download_catch version destination_dir)\n  message(STATUS \"Downloading catch v${version}...\")\n  set(url https://github.com/philsquared/Catch/releases/download/v${version}/catch.hpp)\n  file(\n    DOWNLOAD ${url} \"${destination_dir}/catch.hpp\"\n    STATUS status\n    LOG log)\n  list(GET status 0 error)\n  if(error)\n    string(REPLACE \"\\n\" \"\\n  \" log \"  ${log}\")\n    message(FATAL_ERROR \"Could not download URL:\\n\" \"  ${url}\\n\" \"Log:\\n\" \"${log}\")\n  endif()\n  set(CATCH_INCLUDE_DIR\n      \"${destination_dir}\"\n      CACHE INTERNAL \"\")\nendfunction()\n\n# Look for catch locally\nfind_path(\n  CATCH_INCLUDE_DIR\n  NAMES catch.hpp\n  PATH_SUFFIXES catch2)\nif(CATCH_INCLUDE_DIR)\n  _get_catch_version()\nendif()\n\n# Download the header if it wasn't found or if it's outdated\nif(NOT CATCH_VERSION OR CATCH_VERSION VERSION_LESS ${Catch_FIND_VERSION})\n  if(DOWNLOAD_CATCH)\n    _download_catch(${Catch_FIND_VERSION} \"${PROJECT_BINARY_DIR}/catch/\")\n    _get_catch_version()\n  else()\n    set(CATCH_FOUND FALSE)\n    return()\n  endif()\nendif()\n\nadd_library(Catch2::Catch2 IMPORTED INTERFACE)\nset_property(TARGET Catch2::Catch2 PROPERTY INTERFACE_INCLUDE_DIRECTORIES \"${CATCH_INCLUDE_DIR}\")\n\nset(CATCH_FOUND TRUE)\n"
  },
  {
    "path": "libs/pybind11/tools/FindEigen3.cmake",
    "content": "# - Try to find Eigen3 lib\n#\n# This module supports requiring a minimum version, e.g. you can do\n#   find_package(Eigen3 3.1.2)\n# to require version 3.1.2 or newer of Eigen3.\n#\n# Once done this will define\n#\n#  EIGEN3_FOUND - system has eigen lib with correct version\n#  EIGEN3_INCLUDE_DIR - the eigen include directory\n#  EIGEN3_VERSION - eigen version\n\n# Copyright (c) 2006, 2007 Montel Laurent, <montel@kde.org>\n# Copyright (c) 2008, 2009 Gael Guennebaud, <g.gael@free.fr>\n# Copyright (c) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>\n# Redistribution and use is allowed according to the terms of the 2-clause BSD license.\n\nif(NOT Eigen3_FIND_VERSION)\n  if(NOT Eigen3_FIND_VERSION_MAJOR)\n    set(Eigen3_FIND_VERSION_MAJOR 2)\n  endif(NOT Eigen3_FIND_VERSION_MAJOR)\n  if(NOT Eigen3_FIND_VERSION_MINOR)\n    set(Eigen3_FIND_VERSION_MINOR 91)\n  endif(NOT Eigen3_FIND_VERSION_MINOR)\n  if(NOT Eigen3_FIND_VERSION_PATCH)\n    set(Eigen3_FIND_VERSION_PATCH 0)\n  endif(NOT Eigen3_FIND_VERSION_PATCH)\n\n  set(Eigen3_FIND_VERSION\n      \"${Eigen3_FIND_VERSION_MAJOR}.${Eigen3_FIND_VERSION_MINOR}.${Eigen3_FIND_VERSION_PATCH}\")\nendif(NOT Eigen3_FIND_VERSION)\n\nmacro(_eigen3_check_version)\n  file(READ \"${EIGEN3_INCLUDE_DIR}/Eigen/src/Core/util/Macros.h\" _eigen3_version_header)\n\n  string(REGEX MATCH \"define[ \\t]+EIGEN_WORLD_VERSION[ \\t]+([0-9]+)\" _eigen3_world_version_match\n               \"${_eigen3_version_header}\")\n  set(EIGEN3_WORLD_VERSION \"${CMAKE_MATCH_1}\")\n  string(REGEX MATCH \"define[ \\t]+EIGEN_MAJOR_VERSION[ \\t]+([0-9]+)\" _eigen3_major_version_match\n               \"${_eigen3_version_header}\")\n  set(EIGEN3_MAJOR_VERSION \"${CMAKE_MATCH_1}\")\n  string(REGEX MATCH \"define[ \\t]+EIGEN_MINOR_VERSION[ \\t]+([0-9]+)\" _eigen3_minor_version_match\n               \"${_eigen3_version_header}\")\n  set(EIGEN3_MINOR_VERSION \"${CMAKE_MATCH_1}\")\n\n  set(EIGEN3_VERSION ${EIGEN3_WORLD_VERSION}.${EIGEN3_MAJOR_VERSION}.${EIGEN3_MINOR_VERSION})\n  if(${EIGEN3_VERSION} VERSION_LESS ${Eigen3_FIND_VERSION})\n    set(EIGEN3_VERSION_OK FALSE)\n  else(${EIGEN3_VERSION} VERSION_LESS ${Eigen3_FIND_VERSION})\n    set(EIGEN3_VERSION_OK TRUE)\n  endif(${EIGEN3_VERSION} VERSION_LESS ${Eigen3_FIND_VERSION})\n\n  if(NOT EIGEN3_VERSION_OK)\n\n    message(STATUS \"Eigen3 version ${EIGEN3_VERSION} found in ${EIGEN3_INCLUDE_DIR}, \"\n                   \"but at least version ${Eigen3_FIND_VERSION} is required\")\n  endif(NOT EIGEN3_VERSION_OK)\nendmacro(_eigen3_check_version)\n\nif(EIGEN3_INCLUDE_DIR)\n\n  # in cache already\n  _eigen3_check_version()\n  set(EIGEN3_FOUND ${EIGEN3_VERSION_OK})\n\nelse(EIGEN3_INCLUDE_DIR)\n  if(NOT DEFINED KDE4_INCLUDE_DIR)\n    set(KDE4_INCLUDE_DIR \"\")\n  endif()\n\n  find_path(\n    EIGEN3_INCLUDE_DIR\n    NAMES signature_of_eigen3_matrix_library\n    PATHS ${CMAKE_INSTALL_PREFIX}/include ${KDE4_INCLUDE_DIR}\n    PATH_SUFFIXES eigen3 eigen)\n\n  if(EIGEN3_INCLUDE_DIR)\n    _eigen3_check_version()\n  endif(EIGEN3_INCLUDE_DIR)\n\n  include(FindPackageHandleStandardArgs)\n  find_package_handle_standard_args(Eigen3 DEFAULT_MSG EIGEN3_INCLUDE_DIR EIGEN3_VERSION_OK)\n\n  mark_as_advanced(EIGEN3_INCLUDE_DIR)\n\nendif(EIGEN3_INCLUDE_DIR)\n"
  },
  {
    "path": "libs/pybind11/tools/FindPythonLibsNew.cmake",
    "content": "# - Find python libraries\n# This module finds the libraries corresponding to the Python interpreter\n# FindPythonInterp provides.\n# This code sets the following variables:\n#\n#  PYTHONLIBS_FOUND           - have the Python libs been found\n#  PYTHON_PREFIX              - path to the Python installation\n#  PYTHON_LIBRARIES           - path to the python library\n#  PYTHON_INCLUDE_DIRS        - path to where Python.h is found\n#  PYTHON_MODULE_EXTENSION    - lib extension, e.g. '.so' or '.pyd'\n#  PYTHON_MODULE_PREFIX       - lib name prefix: usually an empty string\n#  PYTHON_SITE_PACKAGES       - path to installation site-packages\n#  PYTHON_IS_DEBUG            - whether the Python interpreter is a debug build\n#\n# Thanks to talljimbo for the patch adding the 'LDVERSION' config\n# variable usage.\n\n#=============================================================================\n# Copyright 2001-2009 Kitware, Inc.\n# Copyright 2012 Continuum Analytics, Inc.\n#\n# All rights reserved.\n#\n# Redistribution and use in source and binary forms, with or without\n# modification, are permitted provided that the following conditions\n# are met:\n#\n# * Redistributions of source code must retain the above copyright\n# notice, this list of conditions and the following disclaimer.\n#\n# * Redistributions in binary form must reproduce the above copyright\n# notice, this list of conditions and the following disclaimer in the\n# documentation and/or other materials provided with the distribution.\n#\n# * Neither the names of Kitware, Inc., the Insight Software Consortium,\n# nor the names of their contributors may be used to endorse or promote\n# products derived from this software without specific prior written\n# permission.\n#\n# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS\n# \"AS IS\" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT\n# LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR\n# # A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT\n# HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,\n# SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT\n# LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,\n# DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY\n# THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT\n# (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE\n# OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.\n#=============================================================================\n\n# Checking for the extension makes sure that `LibsNew` was found and not just `Libs`.\nif(PYTHONLIBS_FOUND AND PYTHON_MODULE_EXTENSION)\n  return()\nendif()\n\nif(PythonLibsNew_FIND_QUIETLY)\n  set(_pythonlibs_quiet QUIET)\nelse()\n  set(_pythonlibs_quiet \"\")\nendif()\n\nif(PythonLibsNew_FIND_REQUIRED)\n  set(_pythonlibs_required REQUIRED)\nendif()\n\n# Check to see if the `python` command is present and from a virtual\n# environment, conda, or GHA activation - if it is, try to use that.\n\nif(NOT DEFINED PYTHON_EXECUTABLE)\n  if(DEFINED ENV{VIRTUAL_ENV})\n    find_program(\n      PYTHON_EXECUTABLE python\n      PATHS \"$ENV{VIRTUAL_ENV}\" \"$ENV{VIRTUAL_ENV}/bin\"\n      NO_DEFAULT_PATH)\n  elseif(DEFINED ENV{CONDA_PREFIX})\n    find_program(\n      PYTHON_EXECUTABLE python\n      PATHS \"$ENV{CONDA_PREFIX}\" \"$ENV{CONDA_PREFIX}/bin\"\n      NO_DEFAULT_PATH)\n  elseif(DEFINED ENV{pythonLocation})\n    find_program(\n      PYTHON_EXECUTABLE python\n      PATHS \"$ENV{pythonLocation}\" \"$ENV{pythonLocation}/bin\"\n      NO_DEFAULT_PATH)\n  endif()\n  if(NOT PYTHON_EXECUTABLE)\n    unset(PYTHON_EXECUTABLE)\n  endif()\nendif()\n\n# Use the Python interpreter to find the libs.\nif(NOT PythonLibsNew_FIND_VERSION)\n  set(PythonLibsNew_FIND_VERSION \"3.7\")\nendif()\n\nif(NOT CMAKE_VERSION VERSION_LESS \"3.27\")\n  cmake_policy(GET CMP0148 _pybind11_cmp0148)\n  if(NOT _pybind11_cmp0148)\n    message(\n      AUTHOR_WARNING\n        \"Policy CMP0148 is not set: The FindPythonInterp and FindPythonLibs \"\n        \"modules are removed.  Run \\\"cmake --help-policy CMP0148\\\" for policy \"\n        \"details.  Use the cmake_policy command to set the policy and suppress \"\n        \"this warning, or preferably upgrade to using FindPython, either by \"\n        \"calling it explicitly before pybind11, or by setting \"\n        \"PYBIND11_FINDPYTHON ON before pybind11.\")\n  endif()\n  cmake_policy(SET CMP0148 OLD)\n  unset(_pybind11_cmp0148)\nendif()\n\nfind_package(PythonInterp ${PythonLibsNew_FIND_VERSION} ${_pythonlibs_required}\n             ${_pythonlibs_quiet})\n\nif(NOT PYTHONINTERP_FOUND)\n  set(PYTHONLIBS_FOUND FALSE)\n  set(PythonLibsNew_FOUND FALSE)\n  return()\nendif()\n\n# According to https://stackoverflow.com/questions/646518/python-how-to-detect-debug-interpreter\n# testing whether sys has the gettotalrefcount function is a reliable, cross-platform\n# way to detect a CPython debug interpreter.\n#\n# The library suffix is from the config var LDVERSION sometimes, otherwise\n# VERSION. VERSION will typically be like \"2.7\" on unix, and \"27\" on windows.\nexecute_process(\n  COMMAND\n    \"${PYTHON_EXECUTABLE}\" \"-c\" \"\nimport sys;import struct;\nimport sysconfig as s\nUSE_SYSCONFIG = sys.version_info >= (3, 10)\nif not USE_SYSCONFIG:\n    from distutils import sysconfig as ds\nprint('.'.join(str(v) for v in sys.version_info));\nprint(sys.prefix);\nif USE_SYSCONFIG:\n    scheme = s.get_default_scheme()\n    if scheme == 'posix_local':\n        # Debian's default scheme installs to /usr/local/ but we want to find headers in /usr/\n        scheme = 'posix_prefix'\n    print(s.get_path('platinclude', scheme))\n    print(s.get_path('platlib'))\n    print(s.get_config_var('EXT_SUFFIX') or s.get_config_var('SO'))\nelse:\n    print(ds.get_python_inc(plat_specific=True));\n    print(ds.get_python_lib(plat_specific=True));\n    print(ds.get_config_var('EXT_SUFFIX') or ds.get_config_var('SO'));\nprint(hasattr(sys, 'gettotalrefcount')+0);\nprint(struct.calcsize('@P'));\nprint(s.get_config_var('LDVERSION') or s.get_config_var('VERSION'));\nprint(s.get_config_var('LIBDIR') or '');\nprint(s.get_config_var('MULTIARCH') or '');\n\"\n  RESULT_VARIABLE _PYTHON_SUCCESS\n  OUTPUT_VARIABLE _PYTHON_VALUES\n  ERROR_VARIABLE _PYTHON_ERROR_VALUE)\n\nif(NOT _PYTHON_SUCCESS MATCHES 0)\n  if(PythonLibsNew_FIND_REQUIRED)\n    message(FATAL_ERROR \"Python config failure:\\n${_PYTHON_ERROR_VALUE}\")\n  endif()\n  set(PYTHONLIBS_FOUND FALSE)\n  set(PythonLibsNew_FOUND FALSE)\n  return()\nendif()\n\noption(\n  PYBIND11_PYTHONLIBS_OVERWRITE\n  \"Overwrite cached values read from Python library (classic search). Turn off if cross-compiling and manually setting these values.\"\n  ON)\n# Can manually set values when cross-compiling\nmacro(_PYBIND11_GET_IF_UNDEF lst index name)\n  if(PYBIND11_PYTHONLIBS_OVERWRITE OR NOT DEFINED \"${name}\")\n    list(GET \"${lst}\" \"${index}\" \"${name}\")\n  endif()\nendmacro()\n\n# Convert the process output into a list\nif(WIN32)\n  string(REGEX REPLACE \"\\\\\\\\\" \"/\" _PYTHON_VALUES ${_PYTHON_VALUES})\nendif()\nstring(REGEX REPLACE \";\" \"\\\\\\\\;\" _PYTHON_VALUES ${_PYTHON_VALUES})\nstring(REGEX REPLACE \"\\n\" \";\" _PYTHON_VALUES ${_PYTHON_VALUES})\n_pybind11_get_if_undef(_PYTHON_VALUES 0 _PYTHON_VERSION_LIST)\n_pybind11_get_if_undef(_PYTHON_VALUES 1 PYTHON_PREFIX)\n_pybind11_get_if_undef(_PYTHON_VALUES 2 PYTHON_INCLUDE_DIR)\n_pybind11_get_if_undef(_PYTHON_VALUES 3 PYTHON_SITE_PACKAGES)\n_pybind11_get_if_undef(_PYTHON_VALUES 5 PYTHON_IS_DEBUG)\n_pybind11_get_if_undef(_PYTHON_VALUES 6 PYTHON_SIZEOF_VOID_P)\n_pybind11_get_if_undef(_PYTHON_VALUES 7 PYTHON_LIBRARY_SUFFIX)\n_pybind11_get_if_undef(_PYTHON_VALUES 8 PYTHON_LIBDIR)\n_pybind11_get_if_undef(_PYTHON_VALUES 9 PYTHON_MULTIARCH)\n\nlist(GET _PYTHON_VALUES 4 _PYTHON_MODULE_EXT_SUFFIX)\nif(PYBIND11_PYTHONLIBS_OVERWRITE OR NOT DEFINED PYTHON_MODULE_DEBUG_POSTFIX)\n  get_filename_component(PYTHON_MODULE_DEBUG_POSTFIX \"${_PYTHON_MODULE_EXT_SUFFIX}\" NAME_WE)\nendif()\nif(PYBIND11_PYTHONLIBS_OVERWRITE OR NOT DEFINED PYTHON_MODULE_EXTENSION)\n  get_filename_component(PYTHON_MODULE_EXTENSION \"${_PYTHON_MODULE_EXT_SUFFIX}\" EXT)\nendif()\n\n# Make sure the Python has the same pointer-size as the chosen compiler\n# Skip if CMAKE_SIZEOF_VOID_P is not defined\n# This should be skipped for (non-Apple) cross-compiles (like EMSCRIPTEN)\nif(NOT _PYBIND11_CROSSCOMPILING\n   AND CMAKE_SIZEOF_VOID_P\n   AND (NOT \"${PYTHON_SIZEOF_VOID_P}\" STREQUAL \"${CMAKE_SIZEOF_VOID_P}\"))\n  if(PythonLibsNew_FIND_REQUIRED)\n    math(EXPR _PYTHON_BITS \"${PYTHON_SIZEOF_VOID_P} * 8\")\n    math(EXPR _CMAKE_BITS \"${CMAKE_SIZEOF_VOID_P} * 8\")\n    message(FATAL_ERROR \"Python config failure: Python is ${_PYTHON_BITS}-bit, \"\n                        \"chosen compiler is  ${_CMAKE_BITS}-bit\")\n  endif()\n  set(PYTHONLIBS_FOUND FALSE)\n  set(PythonLibsNew_FOUND FALSE)\n  return()\nendif()\n\n# The built-in FindPython didn't always give the version numbers\nstring(REGEX REPLACE \"\\\\.\" \";\" _PYTHON_VERSION_LIST ${_PYTHON_VERSION_LIST})\nlist(GET _PYTHON_VERSION_LIST 0 PYTHON_VERSION_MAJOR)\nlist(GET _PYTHON_VERSION_LIST 1 PYTHON_VERSION_MINOR)\nlist(GET _PYTHON_VERSION_LIST 2 PYTHON_VERSION_PATCH)\nset(PYTHON_VERSION \"${PYTHON_VERSION_MAJOR}.${PYTHON_VERSION_MINOR}.${PYTHON_VERSION_PATCH}\")\n\n# Make sure all directory separators are '/'\nstring(REGEX REPLACE \"\\\\\\\\\" \"/\" PYTHON_PREFIX \"${PYTHON_PREFIX}\")\nstring(REGEX REPLACE \"\\\\\\\\\" \"/\" PYTHON_INCLUDE_DIR \"${PYTHON_INCLUDE_DIR}\")\nstring(REGEX REPLACE \"\\\\\\\\\" \"/\" PYTHON_SITE_PACKAGES \"${PYTHON_SITE_PACKAGES}\")\n\nif(DEFINED PYTHON_LIBRARY)\n  # Don't write to PYTHON_LIBRARY if it's already set\nelseif(CMAKE_HOST_WIN32)\n  set(PYTHON_LIBRARY \"${PYTHON_PREFIX}/libs/python${PYTHON_LIBRARY_SUFFIX}.lib\")\n\n  # when run in a venv, PYTHON_PREFIX points to it. But the libraries remain in the\n  # original python installation. They may be found relative to PYTHON_INCLUDE_DIR.\n  if(NOT EXISTS \"${PYTHON_LIBRARY}\")\n    get_filename_component(_PYTHON_ROOT ${PYTHON_INCLUDE_DIR} DIRECTORY)\n    set(PYTHON_LIBRARY \"${_PYTHON_ROOT}/libs/python${PYTHON_LIBRARY_SUFFIX}.lib\")\n  endif()\n\n  # if we are in MSYS & MINGW, and we didn't find windows python lib, look for system python lib\n  if(DEFINED ENV{MSYSTEM}\n     AND MINGW\n     AND NOT EXISTS \"${PYTHON_LIBRARY}\")\n    if(PYTHON_MULTIARCH)\n      set(_PYTHON_LIBS_SEARCH \"${PYTHON_LIBDIR}/${PYTHON_MULTIARCH}\" \"${PYTHON_LIBDIR}\")\n    else()\n      set(_PYTHON_LIBS_SEARCH \"${PYTHON_LIBDIR}\")\n    endif()\n    unset(PYTHON_LIBRARY)\n    find_library(\n      PYTHON_LIBRARY\n      NAMES \"python${PYTHON_LIBRARY_SUFFIX}\"\n      PATHS ${_PYTHON_LIBS_SEARCH}\n      NO_DEFAULT_PATH)\n  endif()\n\n  # raise an error if the python libs are still not found.\n  if(NOT EXISTS \"${PYTHON_LIBRARY}\")\n    message(FATAL_ERROR \"Python libraries not found\")\n  endif()\n\nelse()\n  if(PYTHON_MULTIARCH)\n    set(_PYTHON_LIBS_SEARCH \"${PYTHON_LIBDIR}/${PYTHON_MULTIARCH}\" \"${PYTHON_LIBDIR}\")\n  else()\n    set(_PYTHON_LIBS_SEARCH \"${PYTHON_LIBDIR}\")\n  endif()\n  #message(STATUS \"Searching for Python libs in ${_PYTHON_LIBS_SEARCH}\")\n  # Probably this needs to be more involved. It would be nice if the config\n  # information the python interpreter itself gave us were more complete.\n  find_library(\n    PYTHON_LIBRARY\n    NAMES \"python${PYTHON_LIBRARY_SUFFIX}\"\n    PATHS ${_PYTHON_LIBS_SEARCH}\n    NO_DEFAULT_PATH)\n\n  # If all else fails, just set the name/version and let the linker figure out the path.\n  if(NOT PYTHON_LIBRARY)\n    set(PYTHON_LIBRARY python${PYTHON_LIBRARY_SUFFIX})\n  endif()\nendif()\n\nmark_as_advanced(PYTHON_LIBRARY PYTHON_INCLUDE_DIR)\n\n# We use PYTHON_INCLUDE_DIR, PYTHON_LIBRARY and PYTHON_DEBUG_LIBRARY for the\n# cache entries because they are meant to specify the location of a single\n# library. We now set the variables listed by the documentation for this\n# module.\nset(PYTHON_INCLUDE_DIRS \"${PYTHON_INCLUDE_DIR}\")\nset(PYTHON_LIBRARIES \"${PYTHON_LIBRARY}\")\nif(NOT PYTHON_DEBUG_LIBRARY)\n  set(PYTHON_DEBUG_LIBRARY \"\")\nendif()\nset(PYTHON_DEBUG_LIBRARIES \"${PYTHON_DEBUG_LIBRARY}\")\n\nfind_package_message(PYTHON \"Found PythonLibs: ${PYTHON_LIBRARIES}\"\n                     \"${PYTHON_EXECUTABLE}${PYTHON_VERSION_STRING}\")\n\nset(PYTHONLIBS_FOUND TRUE)\nset(PythonLibsNew_FOUND TRUE)\n\nif(NOT PYTHON_MODULE_PREFIX)\n  set(PYTHON_MODULE_PREFIX \"\")\nendif()\n"
  },
  {
    "path": "libs/pybind11/tools/JoinPaths.cmake",
    "content": "# This module provides function for joining paths\n# known from most languages\n#\n# SPDX-License-Identifier: (MIT OR CC0-1.0)\n# Copyright 2020 Jan Tojnar\n# https://github.com/jtojnar/cmake-snips\n#\n# Modelled after Python’s os.path.join\n# https://docs.python.org/3.7/library/os.path.html#os.path.join\n# Windows not supported\nfunction(join_paths joined_path first_path_segment)\n    set(temp_path \"${first_path_segment}\")\n    foreach(current_segment IN LISTS ARGN)\n        if(NOT (\"${current_segment}\" STREQUAL \"\"))\n            if(IS_ABSOLUTE \"${current_segment}\")\n                set(temp_path \"${current_segment}\")\n            else()\n                set(temp_path \"${temp_path}/${current_segment}\")\n            endif()\n        endif()\n    endforeach()\n    set(${joined_path} \"${temp_path}\" PARENT_SCOPE)\nendfunction()\n"
  },
  {
    "path": "libs/pybind11/tools/check-style.sh",
    "content": "#!/bin/bash\n#\n# Script to check include/test code for common pybind11 code style errors.\n#\n# This script currently checks for\n#\n# 1. missing space between keyword and parenthesis, e.g.: for(, if(, while(\n# 2. Missing space between right parenthesis and brace, e.g. 'for (...){'\n# 3. opening brace on its own line. It should always be on the same line as the\n#    if/while/for/do statement.\n#\n# Invoke as: tools/check-style.sh <filenames>\n#\n\ncheck_style_errors=0\nIFS=$'\\n'\n\n\nfound=\"$(grep '\\<\\(if\\|for\\|while\\|catch\\)(\\|){' \"$@\" -rn --color=always)\"\nif [ -n \"$found\" ]; then\n    echo -e '\\033[31;01mError: found the following coding style problems:\\033[0m'\n    check_style_errors=1\n    echo \"${found//^/    /}\"\nfi\n\nfound=\"$(awk '\nfunction prefix(filename, lineno) {\n    return \"    \\033[35m\" filename \"\\033[36m:\\033[32m\" lineno \"\\033[36m:\\033[0m\"\n}\nfunction mark(pattern, string) { sub(pattern, \"\\033[01;31m&\\033[0m\", string); return string }\nlast && /^\\s*{/ {\n    print prefix(FILENAME, FNR-1) mark(\"\\\\)\\\\s*$\", last)\n    print prefix(FILENAME, FNR)   mark(\"^\\\\s*{\", $0)\n    last=\"\"\n}\n{ last = /(if|for|while|catch|switch)\\s*\\(.*\\)\\s*$/ ? $0 : \"\" }\n' \"$(find include -type f)\" \"$@\")\"\nif [ -n \"$found\" ]; then\n    check_style_errors=1\n    echo -e '\\033[31;01mError: braces should occur on the same line as the if/while/.. statement. Found issues in the following files:\\033[0m'\n    echo \"$found\"\nfi\n\nexit $check_style_errors\n"
  },
  {
    "path": "libs/pybind11/tools/cmake_uninstall.cmake.in",
    "content": "# Source: https://gitlab.kitware.com/cmake/community/-/wikis/FAQ#can-i-do-make-uninstall-with-cmake\n\nif(NOT EXISTS \"@CMAKE_BINARY_DIR@/install_manifest.txt\")\n  message(FATAL_ERROR \"Cannot find install manifest: @CMAKE_BINARY_DIR@/install_manifest.txt\")\nendif()\n\nfile(READ \"@CMAKE_BINARY_DIR@/install_manifest.txt\" files)\nstring(REGEX REPLACE \"\\n\" \";\" files \"${files}\")\nforeach(file ${files})\n  message(STATUS \"Uninstalling $ENV{DESTDIR}${file}\")\n  if(IS_SYMLINK \"$ENV{DESTDIR}${file}\" OR EXISTS \"$ENV{DESTDIR}${file}\")\n    exec_program(\n      \"@CMAKE_COMMAND@\" ARGS\n      \"-E remove \\\"$ENV{DESTDIR}${file}\\\"\"\n      OUTPUT_VARIABLE rm_out\n      RETURN_VALUE rm_retval)\n    if(NOT \"${rm_retval}\" STREQUAL 0)\n      message(FATAL_ERROR \"Problem when removing $ENV{DESTDIR}${file}\")\n    endif()\n  else(IS_SYMLINK \"$ENV{DESTDIR}${file}\" OR EXISTS \"$ENV{DESTDIR}${file}\")\n    message(STATUS \"File $ENV{DESTDIR}${file} does not exist.\")\n  endif()\nendforeach()\n"
  },
  {
    "path": "libs/pybind11/tools/codespell_ignore_lines_from_errors.py",
    "content": "\"\"\"Simple script for rebuilding .codespell-ignore-lines\n\nUsage:\n\ncat < /dev/null > .codespell-ignore-lines\npre-commit run --all-files codespell >& /tmp/codespell_errors.txt\npython3 tools/codespell_ignore_lines_from_errors.py /tmp/codespell_errors.txt > .codespell-ignore-lines\n\ngit diff to review changes, then commit, push.\n\"\"\"\n\nfrom __future__ import annotations\n\nimport sys\n\n\ndef run(args: list[str]) -> None:\n    assert len(args) == 1, \"codespell_errors.txt\"\n    cache = {}\n    done = set()\n    with open(args[0]) as f:\n        lines = f.read().splitlines()\n\n    for line in sorted(lines):\n        i = line.find(\" ==> \")\n        if i > 0:\n            flds = line[:i].split(\":\")\n            if len(flds) >= 2:\n                filename, line_num = flds[:2]\n                if filename not in cache:\n                    with open(filename) as f:\n                        cache[filename] = f.read().splitlines()\n                supp = cache[filename][int(line_num) - 1]\n                if supp not in done:\n                    print(supp)\n                    done.add(supp)\n\n\nif __name__ == \"__main__\":\n    run(args=sys.argv[1:])\n"
  },
  {
    "path": "libs/pybind11/tools/libsize.py",
    "content": "from __future__ import annotations\n\nimport os\nimport sys\n\n# Internal build script for generating debugging test .so size.\n# Usage:\n#     python libsize.py file.so save.txt -- displays the size of file.so and, if save.txt exists, compares it to the\n#                                           size in it, then overwrites save.txt with the new size for future runs.\n\nif len(sys.argv) != 3:\n    sys.exit(\"Invalid arguments: usage: python libsize.py file.so save.txt\")\n\nlib = sys.argv[1]\nsave = sys.argv[2]\n\nif not os.path.exists(lib):\n    sys.exit(f\"Error: requested file ({lib}) does not exist\")\n\nlibsize = os.path.getsize(lib)\n\nprint(\"------\", os.path.basename(lib), \"file size:\", libsize, end=\"\")\n\nif os.path.exists(save):\n    with open(save) as sf:\n        oldsize = int(sf.readline())\n\n    if oldsize > 0:\n        change = libsize - oldsize\n        if change == 0:\n            print(\" (no change)\")\n        else:\n            print(f\" (change of {change:+} bytes = {change / oldsize:+.2%})\")\nelse:\n    print()\n\nwith open(save, \"w\") as sf:\n    sf.write(str(libsize))\n"
  },
  {
    "path": "libs/pybind11/tools/make_changelog.py",
    "content": "#!/usr/bin/env python3\nfrom __future__ import annotations\n\nimport re\n\nimport ghapi.all\nfrom rich import print\nfrom rich.syntax import Syntax\n\nENTRY = re.compile(\n    r\"\"\"\n    Suggested \\s changelog \\s entry:\n    .*\n    ```rst\n    \\s*\n    (.*?)\n    \\s*\n    ```\n\"\"\",\n    re.DOTALL | re.VERBOSE,\n)\n\nprint()\n\n\napi = ghapi.all.GhApi(owner=\"pybind\", repo=\"pybind11\")\n\nissues_pages = ghapi.page.paged(\n    api.issues.list_for_repo, labels=\"needs changelog\", state=\"closed\"\n)\nissues = (issue for page in issues_pages for issue in page)\nmissing = []\ncats_descr = {\n    \"feat\": \"New Features\",\n    \"feat(types)\": \"\",\n    \"feat(cmake)\": \"\",\n    \"fix\": \"Bug fixes\",\n    \"fix(types)\": \"\",\n    \"fix(cmake)\": \"\",\n    \"docs\": \"Documentation\",\n    \"tests\": \"Tests\",\n    \"ci\": \"CI\",\n    \"chore\": \"Other\",\n    \"unknown\": \"Uncategorised\",\n}\ncats: dict[str, list[str]] = {c: [] for c in cats_descr}\n\nfor issue in issues:\n    changelog = ENTRY.findall(issue.body or \"\")\n    if not changelog or not changelog[0]:\n        missing.append(issue)\n    else:\n        (msg,) = changelog\n        if msg.startswith(\"- \"):\n            msg = msg[2:]\n        if not msg.startswith(\"* \"):\n            msg = \"* \" + msg\n        if not msg.endswith(\".\"):\n            msg += \".\"\n\n        msg += f\"\\n  `#{issue.number} <{issue.html_url}>`_\"\n        for cat in cats:\n            if issue.title.lower().startswith(f\"{cat}:\"):\n                cats[cat].append(msg)\n                break\n        else:\n            cats[\"unknown\"].append(msg)\n\nfor cat, msgs in cats.items():\n    if msgs:\n        desc = cats_descr[cat]\n        print(f\"[bold]{desc}:\" if desc else f\".. {cat}\")\n        print()\n        for msg in msgs:\n            print(Syntax(msg, \"rst\", theme=\"ansi_light\", word_wrap=True))\n            print()\n        print()\n\nif missing:\n    print()\n    print(\"[blue]\" + \"-\" * 30)\n    print()\n\n    for issue in missing:\n        print(f\"[red bold]Missing:[/red bold][red] {issue.title}\")\n        print(f\"[red]  {issue.html_url}\\n\")\n\n    print(\"[bold]Template:\\n\")\n    msg = \"## Suggested changelog entry:\\n\\n```rst\\n\\n```\"\n    print(Syntax(msg, \"md\", theme=\"ansi_light\"))\n\nprint()\n"
  },
  {
    "path": "libs/pybind11/tools/pybind11.pc.in",
    "content": "prefix=@prefix_for_pc_file@\nincludedir=@includedir_for_pc_file@\n\nName: @PROJECT_NAME@\nDescription: Seamless operability between C++11 and Python\nVersion: @PROJECT_VERSION@\nCflags: -I${includedir}\n"
  },
  {
    "path": "libs/pybind11/tools/pybind11Common.cmake",
    "content": "#[======================================================[.rst\n\nAdds the following targets::\n\n    pybind11::pybind11 - link to Python headers and pybind11::headers\n    pybind11::module - Adds module links\n    pybind11::embed - Adds embed links\n    pybind11::lto - Link time optimizations (only if CMAKE_INTERPROCEDURAL_OPTIMIZATION is not set)\n    pybind11::thin_lto - Link time optimizations (only if CMAKE_INTERPROCEDURAL_OPTIMIZATION is not set)\n    pybind11::python_link_helper - Adds link to Python libraries\n    pybind11::windows_extras - MSVC bigobj and mp for building multithreaded\n    pybind11::opt_size - avoid optimizations that increase code size\n\nAdds the following functions::\n\n    pybind11_strip(target) - strip target after building on linux/macOS\n    pybind11_find_import(module) - See if a module is installed.\n\n#]======================================================]\n\n# CMake 3.10 has an include_guard command, but we can't use that yet\n# include_guard(global) (pre-CMake 3.10)\nif(TARGET pybind11::pybind11)\n  return()\nendif()\n\n# If we are in subdirectory mode, all IMPORTED targets must be GLOBAL. If we\n# are in CONFIG mode, they should be \"normal\" targets instead.\n# In CMake 3.11+ you can promote a target to global after you create it,\n# which might be simpler than this check.\nget_property(\n  is_config\n  TARGET pybind11::headers\n  PROPERTY IMPORTED)\nif(NOT is_config)\n  set(optional_global GLOBAL)\nendif()\n\n# If not run in Python mode, we still would like this to at least\n# include pybind11's include directory:\nset(pybind11_INCLUDE_DIRS\n    \"${pybind11_INCLUDE_DIR}\"\n    CACHE INTERNAL \"Include directory for pybind11 (Python not requested)\")\n\nif(CMAKE_CROSSCOMPILING AND PYBIND11_USE_CROSSCOMPILING)\n  set(_PYBIND11_CROSSCOMPILING\n      ON\n      CACHE INTERNAL \"\")\nelse()\n  set(_PYBIND11_CROSSCOMPILING\n      OFF\n      CACHE INTERNAL \"\")\nendif()\n\n# --------------------- Shared targets ----------------------------\n\n# Build an interface library target:\nadd_library(pybind11::pybind11 IMPORTED INTERFACE ${optional_global})\nset_property(\n  TARGET pybind11::pybind11\n  APPEND\n  PROPERTY INTERFACE_LINK_LIBRARIES pybind11::headers)\n\n# Build a module target:\nadd_library(pybind11::module IMPORTED INTERFACE ${optional_global})\nset_property(\n  TARGET pybind11::module\n  APPEND\n  PROPERTY INTERFACE_LINK_LIBRARIES pybind11::pybind11)\n\n# Build an embed library target:\nadd_library(pybind11::embed IMPORTED INTERFACE ${optional_global})\nset_property(\n  TARGET pybind11::embed\n  APPEND\n  PROPERTY INTERFACE_LINK_LIBRARIES pybind11::pybind11)\n\n# -------------- emscripten requires exceptions enabled -------------\n# _pybind11_no_exceptions is a private mechanism to disable this addition.\n# Please open an issue if you need to use it; it will be removed if no one\n# needs it.\nif(CMAKE_SYSTEM_NAME MATCHES Emscripten AND NOT _pybind11_no_exceptions)\n  if(CMAKE_VERSION VERSION_LESS 3.13)\n    message(WARNING \"CMake 3.13+ is required to build for Emscripten. Some flags will be missing\")\n  else()\n    if(is_config)\n      set(_tmp_config_target pybind11::pybind11_headers)\n    else()\n      set(_tmp_config_target pybind11_headers)\n    endif()\n\n    set_property(\n      TARGET ${_tmp_config_target}\n      APPEND\n      PROPERTY INTERFACE_LINK_OPTIONS -fexceptions)\n    set_property(\n      TARGET ${_tmp_config_target}\n      APPEND\n      PROPERTY INTERFACE_COMPILE_OPTIONS -fexceptions)\n    unset(_tmp_config_target)\n  endif()\nendif()\n\n# --------------------------- link helper ---------------------------\n\nadd_library(pybind11::python_link_helper IMPORTED INTERFACE ${optional_global})\n\nif(CMAKE_VERSION VERSION_LESS 3.13)\n  # In CMake 3.11+, you can set INTERFACE properties via the normal methods, and\n  # this would be simpler.\n  set_property(\n    TARGET pybind11::python_link_helper\n    APPEND\n    PROPERTY INTERFACE_LINK_LIBRARIES \"$<$<PLATFORM_ID:Darwin>:-undefined dynamic_lookup>\")\nelse()\n  # link_options was added in 3.13+\n  # This is safer, because you are ensured the deduplication pass in CMake will not consider\n  # these separate and remove one but not the other.\n  set_property(\n    TARGET pybind11::python_link_helper\n    APPEND\n    PROPERTY INTERFACE_LINK_OPTIONS \"$<$<PLATFORM_ID:Darwin>:LINKER:-undefined,dynamic_lookup>\")\nendif()\n\n# ------------------------ Windows extras -------------------------\n\nadd_library(pybind11::windows_extras IMPORTED INTERFACE ${optional_global})\n\nif(MSVC) # That's also clang-cl\n  # /bigobj is needed for bigger binding projects due to the limit to 64k\n  # addressable sections\n  set_property(\n    TARGET pybind11::windows_extras\n    APPEND\n    PROPERTY INTERFACE_COMPILE_OPTIONS $<$<COMPILE_LANGUAGE:CXX>:/bigobj>)\n\n  # /MP enables multithreaded builds (relevant when there are many files) for MSVC\n  if(\"${CMAKE_CXX_COMPILER_ID}\" STREQUAL \"MSVC\") # no Clang no Intel\n    if(CMAKE_VERSION VERSION_LESS 3.11)\n      set_property(\n        TARGET pybind11::windows_extras\n        APPEND\n        PROPERTY INTERFACE_COMPILE_OPTIONS $<$<NOT:$<CONFIG:Debug>>:/MP>)\n    else()\n      # Only set these options for C++ files.  This is important so that, for\n      # instance, projects that include other types of source files like CUDA\n      # .cu files don't get these options propagated to nvcc since that would\n      # cause the build to fail.\n      set_property(\n        TARGET pybind11::windows_extras\n        APPEND\n        PROPERTY INTERFACE_COMPILE_OPTIONS\n                 $<$<NOT:$<CONFIG:Debug>>:$<$<COMPILE_LANGUAGE:CXX>:/MP>>)\n    endif()\n  endif()\nendif()\n\n# ----------------------- Optimize binary size --------------------------\n\nadd_library(pybind11::opt_size IMPORTED INTERFACE ${optional_global})\n\nif(MSVC)\n  set(PYBIND11_OPT_SIZE /Os)\nelse()\n  set(PYBIND11_OPT_SIZE -Os)\nendif()\n\nset_property(\n  TARGET pybind11::opt_size\n  APPEND\n  PROPERTY INTERFACE_COMPILE_OPTIONS $<$<CONFIG:Release>:${PYBIND11_OPT_SIZE}>\n           $<$<CONFIG:MinSizeRel>:${PYBIND11_OPT_SIZE}>\n           $<$<CONFIG:RelWithDebInfo>:${PYBIND11_OPT_SIZE}>)\n\n# ----------------------- Legacy option --------------------------\n\n# Warn or error if old variable name used\nif(PYBIND11_CPP_STANDARD)\n  string(REGEX MATCH [[..$]] VAL \"${PYBIND11_CPP_STANDARD}\")\n  if(CMAKE_CXX_STANDARD)\n    if(NOT CMAKE_CXX_STANDARD STREQUAL VAL)\n      message(WARNING \"CMAKE_CXX_STANDARD=${CMAKE_CXX_STANDARD} does not match \"\n                      \"PYBIND11_CPP_STANDARD=${PYBIND11_CPP_STANDARD}, \"\n                      \"please remove PYBIND11_CPP_STANDARD from your cache\")\n    endif()\n  else()\n    set(supported_standards 11 14 17 20)\n    if(\"${VAL}\" IN_LIST supported_standards)\n      message(WARNING \"USE -DCMAKE_CXX_STANDARD=${VAL} instead of PYBIND11_CPP_STANDARD\")\n      set(CMAKE_CXX_STANDARD\n          ${VAL}\n          CACHE STRING \"From PYBIND11_CPP_STANDARD\")\n    else()\n      message(FATAL_ERROR \"PYBIND11_CPP_STANDARD should be replaced with CMAKE_CXX_STANDARD \"\n                          \"(last two chars: ${VAL} not understood as a valid CXX std)\")\n    endif()\n  endif()\nendif()\n\n# --------------------- Python specifics -------------------------\n\n# CMake 3.27 removes the classic FindPythonInterp if CMP0148 is NEW\nif(CMAKE_VERSION VERSION_LESS \"3.27\")\n  set(_pybind11_missing_old_python \"OLD\")\nelse()\n  cmake_policy(GET CMP0148 _pybind11_missing_old_python)\nendif()\n\n# Check to see which Python mode we are in, new, old, or no python\nif(PYBIND11_NOPYTHON)\n  set(_pybind11_nopython ON)\n  # We won't use new FindPython if PYBIND11_FINDPYTHON is defined and falselike\n  # Otherwise, we use if FindPythonLibs is missing or if FindPython was already used\nelseif(\n  (NOT DEFINED PYBIND11_FINDPYTHON OR PYBIND11_FINDPYTHON)\n  AND (_pybind11_missing_old_python STREQUAL \"NEW\"\n       OR PYBIND11_FINDPYTHON\n       OR Python_FOUND\n       OR Python3_FOUND\n      ))\n\n  # New mode\n  include(\"${CMAKE_CURRENT_LIST_DIR}/pybind11NewTools.cmake\")\n\nelse()\n\n  # Classic mode\n  include(\"${CMAKE_CURRENT_LIST_DIR}/pybind11Tools.cmake\")\n\nendif()\n\n# --------------------- pybind11_find_import -------------------------------\n\nif(NOT _pybind11_nopython AND NOT _PYBIND11_CROSSCOMPILING)\n  # Check to see if modules are importable. Use REQUIRED to force an error if\n  # one of the modules is not found. <package_name>_FOUND will be set if the\n  # package was found (underscores replace dashes if present). QUIET will hide\n  # the found message, and VERSION will require a minimum version. A successful\n  # find will cache the result.\n  function(pybind11_find_import PYPI_NAME)\n    # CMake variables need underscores (PyPI doesn't care)\n    string(REPLACE \"-\" \"_\" NORM_PYPI_NAME \"${PYPI_NAME}\")\n\n    # Return if found previously\n    if(${NORM_PYPI_NAME}_FOUND)\n      return()\n    endif()\n\n    set(options \"REQUIRED;QUIET\")\n    set(oneValueArgs \"VERSION\")\n    cmake_parse_arguments(ARG \"${options}\" \"${oneValueArgs}\" \"\" ${ARGN})\n\n    if(ARG_REQUIRED)\n      set(status_level FATAL_ERROR)\n    else()\n      set(status_level WARNING)\n    endif()\n\n    execute_process(\n      COMMAND\n        ${${_Python}_EXECUTABLE} -c \"\ntry:\n    from importlib.metadata import version\nexcept ImportError:\n    from pkg_resources import get_distribution\n    def version(s):\n        return get_distribution(s).version\nprint(version('${PYPI_NAME}'))\n        \"\n      RESULT_VARIABLE RESULT_PRESENT\n      OUTPUT_VARIABLE PKG_VERSION\n      ERROR_QUIET)\n\n    string(STRIP \"${PKG_VERSION}\" PKG_VERSION)\n\n    # If a result is present, this failed\n    if(RESULT_PRESENT)\n      set(${NORM_PYPI_NAME}_FOUND\n          ${NORM_PYPI_NAME}-NOTFOUND\n          CACHE INTERNAL \"\")\n      # Always warn or error\n      message(\n        ${status_level}\n        \"Missing: ${PYPI_NAME} ${ARG_VERSION}\\nTry: ${${_Python}_EXECUTABLE} -m pip install ${PYPI_NAME}\"\n      )\n    else()\n      if(ARG_VERSION AND PKG_VERSION VERSION_LESS ARG_VERSION)\n        message(\n          ${status_level}\n          \"Version incorrect: ${PYPI_NAME} ${PKG_VERSION} found, ${ARG_VERSION} required - try upgrading\"\n        )\n      else()\n        set(${NORM_PYPI_NAME}_FOUND\n            YES\n            CACHE INTERNAL \"\")\n        set(${NORM_PYPI_NAME}_VERSION\n            ${PKG_VERSION}\n            CACHE INTERNAL \"\")\n      endif()\n      if(NOT ARG_QUIET)\n        message(STATUS \"Found ${PYPI_NAME} ${PKG_VERSION}\")\n      endif()\n    endif()\n    if(NOT ARG_VERSION OR (NOT PKG_VERSION VERSION_LESS ARG_VERSION))\n      # We have successfully found a good version, cache to avoid calling again.\n    endif()\n  endfunction()\nendif()\n\n# --------------------- LTO -------------------------------\n\ninclude(CheckCXXCompilerFlag)\n\n# Checks whether the given CXX/linker flags can compile and link a cxx file.\n# cxxflags and linkerflags are lists of flags to use.  The result variable is a\n# unique variable name for each set of flags: the compilation result will be\n# cached base on the result variable.  If the flags work, sets them in\n# cxxflags_out/linkerflags_out internal cache variables (in addition to\n# ${result}).\nfunction(_pybind11_return_if_cxx_and_linker_flags_work result cxxflags linkerflags cxxflags_out\n         linkerflags_out)\n  set(CMAKE_REQUIRED_LIBRARIES ${linkerflags})\n  check_cxx_compiler_flag(\"${cxxflags}\" ${result})\n  if(${result})\n    set(${cxxflags_out}\n        \"${cxxflags}\"\n        PARENT_SCOPE)\n    set(${linkerflags_out}\n        \"${linkerflags}\"\n        PARENT_SCOPE)\n  endif()\nendfunction()\n\nfunction(_pybind11_generate_lto target prefer_thin_lto)\n  if(MINGW)\n    message(STATUS \"${target} disabled (problems with undefined symbols for MinGW for now)\")\n    return()\n  endif()\n\n  if(CMAKE_CXX_COMPILER_ID MATCHES \"GNU|Clang\")\n    set(cxx_append \"\")\n    set(linker_append \"\")\n    if(CMAKE_CXX_COMPILER_ID MATCHES \"Clang\" AND NOT APPLE)\n      # Clang Gold plugin does not support -Os; append -O3 to MinSizeRel builds to override it\n      set(linker_append \";$<$<CONFIG:MinSizeRel>:-O3>\")\n    elseif(CMAKE_CXX_COMPILER_ID MATCHES \"GNU\" AND NOT MINGW)\n      set(cxx_append \";-fno-fat-lto-objects\")\n    endif()\n\n    if(prefer_thin_lto)\n      set(thin \"=thin\")\n    else()\n      set(thin \"\")\n    endif()\n\n    if(CMAKE_SYSTEM_PROCESSOR MATCHES \"ppc64le\" OR CMAKE_SYSTEM_PROCESSOR MATCHES \"mips64\")\n      # Do nothing\n    elseif(CMAKE_SYSTEM_NAME MATCHES Emscripten)\n      # This compile is very costly when cross-compiling, so set this without checking\n      set(PYBIND11_LTO_CXX_FLAGS \"-flto${thin}${cxx_append}\")\n      set(PYBIND11_LTO_LINKER_FLAGS \"-flto${thin}${linker_append}\")\n    elseif(CMAKE_CXX_COMPILER_ID MATCHES \"Clang\")\n      _pybind11_return_if_cxx_and_linker_flags_work(\n        HAS_FLTO_THIN \"-flto${thin}${cxx_append}\" \"-flto${thin}${linker_append}\"\n        PYBIND11_LTO_CXX_FLAGS PYBIND11_LTO_LINKER_FLAGS)\n    endif()\n    if(NOT HAS_FLTO_THIN)\n      _pybind11_return_if_cxx_and_linker_flags_work(\n        HAS_FLTO \"-flto${cxx_append}\" \"-flto${linker_append}\" PYBIND11_LTO_CXX_FLAGS\n        PYBIND11_LTO_LINKER_FLAGS)\n    endif()\n  elseif(CMAKE_CXX_COMPILER_ID MATCHES \"IntelLLVM\")\n    # IntelLLVM equivalent to LTO is called IPO; also IntelLLVM is WIN32/UNIX\n    # WARNING/HELP WANTED: This block of code is currently not covered by pybind11 GitHub Actions!\n    if(WIN32)\n      _pybind11_return_if_cxx_and_linker_flags_work(\n        HAS_INTEL_IPO \"-Qipo\" \"-Qipo\" PYBIND11_LTO_CXX_FLAGS PYBIND11_LTO_LINKER_FLAGS)\n    else()\n      _pybind11_return_if_cxx_and_linker_flags_work(\n        HAS_INTEL_IPO \"-ipo\" \"-ipo\" PYBIND11_LTO_CXX_FLAGS PYBIND11_LTO_LINKER_FLAGS)\n    endif()\n  elseif(CMAKE_CXX_COMPILER_ID MATCHES \"Intel\")\n    # Intel equivalent to LTO is called IPO\n    _pybind11_return_if_cxx_and_linker_flags_work(HAS_INTEL_IPO \"-ipo\" \"-ipo\"\n                                                  PYBIND11_LTO_CXX_FLAGS PYBIND11_LTO_LINKER_FLAGS)\n  elseif(MSVC)\n    # cmake only interprets libraries as linker flags when they start with a - (otherwise it\n    # converts /LTCG to \\LTCG as if it was a Windows path).  Luckily MSVC supports passing flags\n    # with - instead of /, even if it is a bit non-standard:\n    _pybind11_return_if_cxx_and_linker_flags_work(HAS_MSVC_GL_LTCG \"/GL\" \"-LTCG\"\n                                                  PYBIND11_LTO_CXX_FLAGS PYBIND11_LTO_LINKER_FLAGS)\n  endif()\n\n  # Enable LTO flags if found, except for Debug builds\n  if(PYBIND11_LTO_CXX_FLAGS)\n    # CONFIG takes multiple values in CMake 3.19+, until then we have to use OR\n    set(is_debug \"$<OR:$<CONFIG:Debug>,$<CONFIG:RelWithDebInfo>>\")\n    set(not_debug \"$<NOT:${is_debug}>\")\n    set(cxx_lang \"$<COMPILE_LANGUAGE:CXX>\")\n    if(MSVC AND CMAKE_VERSION VERSION_LESS 3.11)\n      set(genex \"${not_debug}\")\n    else()\n      set(genex \"$<AND:${not_debug},${cxx_lang}>\")\n    endif()\n    set_property(\n      TARGET ${target}\n      APPEND\n      PROPERTY INTERFACE_COMPILE_OPTIONS \"$<${genex}:${PYBIND11_LTO_CXX_FLAGS}>\")\n    if(CMAKE_PROJECT_NAME STREQUAL \"pybind11\")\n      message(STATUS \"${target} enabled\")\n    endif()\n  else()\n    if(CMAKE_PROJECT_NAME STREQUAL \"pybind11\")\n      message(STATUS \"${target} disabled (not supported by the compiler and/or linker)\")\n    endif()\n  endif()\n\n  if(PYBIND11_LTO_LINKER_FLAGS)\n    if(CMAKE_VERSION VERSION_LESS 3.11)\n      set_property(\n        TARGET ${target}\n        APPEND\n        PROPERTY INTERFACE_LINK_LIBRARIES \"$<${not_debug}:${PYBIND11_LTO_LINKER_FLAGS}>\")\n    else()\n      set_property(\n        TARGET ${target}\n        APPEND\n        PROPERTY INTERFACE_LINK_OPTIONS \"$<${not_debug}:${PYBIND11_LTO_LINKER_FLAGS}>\")\n    endif()\n  endif()\nendfunction()\n\nif(NOT DEFINED CMAKE_INTERPROCEDURAL_OPTIMIZATION)\n  add_library(pybind11::lto IMPORTED INTERFACE ${optional_global})\n  _pybind11_generate_lto(pybind11::lto FALSE)\n\n  add_library(pybind11::thin_lto IMPORTED INTERFACE ${optional_global})\n  _pybind11_generate_lto(pybind11::thin_lto TRUE)\nendif()\n\n# ---------------------- pybind11_strip -----------------------------\n\nfunction(pybind11_strip target_name)\n  # Strip unnecessary sections of the binary on Linux/macOS\n  if(CMAKE_STRIP)\n    if(APPLE)\n      set(x_opt -x)\n    endif()\n\n    add_custom_command(\n      TARGET ${target_name}\n      POST_BUILD\n      COMMAND ${CMAKE_STRIP} ${x_opt} $<TARGET_FILE:${target_name}>)\n  endif()\nendfunction()\n"
  },
  {
    "path": "libs/pybind11/tools/pybind11Config.cmake.in",
    "content": "#[=============================================================================[.rst:\n\npybind11Config.cmake\n####################\n\nExported variables\n==================\n\nThis module sets the following variables in your project:\n\n``pybind11_FOUND``\n  true if pybind11 and all required components found on the system\n``pybind11_VERSION``\n  pybind11 version in format Major.Minor.Release\n``pybind11_VERSION_TYPE``\n  pybind11 version type (``dev*`` or empty for a release)\n``pybind11_INCLUDE_DIRS``\n  Directories where pybind11 and python headers are located.\n``pybind11_INCLUDE_DIR``\n  Directory where pybind11 headers are located.\n``pybind11_DEFINITIONS``\n  Definitions necessary to use pybind11, namely USING_pybind11.\n``pybind11_LIBRARIES``\n  Compile flags and python libraries (as needed) to link against.\n``pybind11_LIBRARY``\n  Empty.\n\nAvailable components: None\n\n\nExported targets\n================\n\nIf pybind11 is found, this module defines the following ``IMPORTED``\ninterface library targets:\n\n``pybind11::module``\n  for extension modules.\n``pybind11::embed``\n  for embedding the Python interpreter.\n\nPython headers, libraries (as needed by platform), and the C++ standard\nare attached to the target.\n\nAdvanced targets are also supplied - these are primary for users building\ncomplex applications, and they are available in all modes:\n\n``pybind11::headers``\n  Just the pybind11 headers and minimum compile requirements.\n``pybind11::pybind11``\n  Python headers too.\n``pybind11::python_link_helper``\n  Just the \"linking\" part of ``pybind11:module``, for CMake < 3.15.\n``pybind11::thin_lto``\n  An alternative to ``INTERPROCEDURAL_OPTIMIZATION``.\n``pybind11::lto``\n  An alternative to ``INTERPROCEDURAL_OPTIMIZATION`` (also avoids thin LTO on clang).\n``pybind11::windows_extras``\n  Adds bigobj and mp for MSVC.\n\nModes\n=====\n\nThere are two modes provided; classic, which is built on the old Python\ndiscovery packages in CMake, or the new FindPython mode, which uses FindPython\nfrom 3.12+ forward (3.15+ _highly_ recommended). If you set the minimum or\nmaximum version of CMake to 3.27+, then FindPython is the default (since\nFindPythonInterp/FindPythonLibs has been removed via policy `CMP0148`).\n\nNew FindPython mode\n^^^^^^^^^^^^^^^^^^^\n\nTo activate this mode, either call ``find_package(Python COMPONENTS Interpreter Development)``\nbefore finding this package, or set the ``PYBIND11_FINDPYTHON`` variable to ON. In this mode,\nyou can either use the basic targets, or use the FindPython tools:\n\n.. code-block:: cmake\n\n  find_package(Python COMPONENTS Interpreter Development)\n  find_package(pybind11 CONFIG)\n\n  # pybind11 method:\n  pybind11_add_module(MyModule1 src1.cpp)\n\n  # Python method:\n  Python_add_library(MyModule2 src2.cpp)\n  target_link_libraries(MyModule2 PUBLIC pybind11::headers)\n  set_target_properties(MyModule2 PROPERTIES\n                                  INTERPROCEDURAL_OPTIMIZATION ON\n                                  CXX_VISIBILITY_PRESET ON\n                                  VISIBILITY_INLINES_HIDDEN ON)\n\nIf you build targets yourself, you may be interested in stripping the output\nfor reduced size; this is the one other feature that the helper function gives you.\n\nClassic mode\n^^^^^^^^^^^^\n\nSet PythonLibsNew variables to influence python detection and\nCMAKE_CXX_STANDARD to influence standard setting.\n\n.. code-block:: cmake\n\n  find_package(pybind11 CONFIG REQUIRED)\n\n  # Create an extension module\n  add_library(mylib MODULE main.cpp)\n  target_link_libraries(mylib PUBLIC pybind11::module)\n\n  # Or embed the Python interpreter into an executable\n  add_executable(myexe main.cpp)\n  target_link_libraries(myexe PUBLIC pybind11::embed)\n\n\nHints\n=====\n\nThe following variables can be set to guide the search for this package:\n\n``pybind11_DIR``\n  CMake variable, set to directory containing this Config file.\n``CMAKE_PREFIX_PATH``\n  CMake variable, set to root directory of this package.\n``PATH``\n  Environment variable, set to bin directory of this package.\n``CMAKE_DISABLE_FIND_PACKAGE_pybind11``\n  CMake variable, disables ``find_package(pybind11)`` when not ``REQUIRED``,\n  perhaps to force internal build.\n\nCommands\n========\n\npybind11_add_module\n^^^^^^^^^^^^^^^^^^^\n\nThis module defines the following commands to assist with creating Python modules:\n\n.. code-block:: cmake\n\n  pybind11_add_module(<target>\n    [STATIC|SHARED|MODULE]\n    [THIN_LTO] [OPT_SIZE] [NO_EXTRAS] [WITHOUT_SOABI]\n    <files>...\n    )\n\nAdd a module and setup all helpers. You can select the type of the library; the\ndefault is ``MODULE``. There are several options:\n\n``OPT_SIZE``\n  Optimize for size, even if the ``CMAKE_BUILD_TYPE`` is not ``MinSizeRel``.\n``THIN_LTO``\n  Use thin LTO instead of regular if there's a choice (pybind11's selection\n  is disabled if ``CMAKE_INTERPROCEDURAL_OPTIMIZATIONS`` is set).\n``WITHOUT_SOABI``\n  Disable the SOABI component (``PYBIND11_NEWPYTHON`` mode only).\n``NO_EXTRAS``\n  Disable all extras, exit immediately after making the module.\n\npybind11_strip\n^^^^^^^^^^^^^^\n\n.. code-block:: cmake\n\n  pybind11_strip(<target>)\n\nStrip a target after building it (linux/macOS), called by ``pybind11_add_module``.\n\npybind11_extension\n^^^^^^^^^^^^^^^^^^\n\n.. code-block:: cmake\n\n    pybind11_extension(<target>)\n\nSets the Python extension name correctly for Python on your platform, called by\n``pybind11_add_module``.\n\npybind11_find_import(module)\n^^^^^^^^^^^^^^^^^^^^^^^^^^^^\n\n.. code-block:: cmake\n\n    pybind11_find_import(<module> [VERSION <number>] [REQUIRED] [QUIET])\n\nSee if a module is installed. Use the registered name (the one on PyPI). You\ncan specify a ``VERSION``, and you can specify ``REQUIRED`` or ``QUIET``. Only available if\n``NOPYTHON`` mode is not active.  Sets ``module_VERSION`` and ``module_FOUND``. Caches the\nresult once a valid install is found.\n\nSuggested usage\n===============\n\nUsing ``find_package`` with version info is not recommended except for release versions.\n\n.. code-block:: cmake\n\n  find_package(pybind11 CONFIG)\n  find_package(pybind11 2.9 EXACT CONFIG REQUIRED)\n\n#]=============================================================================]\n@PACKAGE_INIT@\n\n# Location of pybind11/pybind11.h\n# This will be relative unless explicitly set as absolute\nset(pybind11_INCLUDE_DIR \"@pybind11_INCLUDEDIR@\")\n\nset(pybind11_LIBRARY \"\")\nset(pybind11_DEFINITIONS USING_pybind11)\nset(pybind11_VERSION_TYPE \"@pybind11_VERSION_TYPE@\")\n\ncheck_required_components(pybind11)\n\nif(TARGET pybind11::python_link_helper)\n  # This has already been setup elsewhere, such as with a previous call or\n  # add_subdirectory\n  return()\nendif()\n\ninclude(\"${CMAKE_CURRENT_LIST_DIR}/pybind11Targets.cmake\")\n\n# Easier to use / remember\nadd_library(pybind11::headers IMPORTED INTERFACE)\nset_target_properties(pybind11::headers PROPERTIES INTERFACE_LINK_LIBRARIES\n                                                   pybind11::pybind11_headers)\n\ninclude(\"${CMAKE_CURRENT_LIST_DIR}/pybind11Common.cmake\")\n\nif(NOT pybind11_FIND_QUIETLY)\n  message(\n    STATUS\n      \"Found pybind11: ${pybind11_INCLUDE_DIR} (found version \\\"${pybind11_VERSION}${pybind11_VERSION_TYPE}\\\")\"\n  )\nendif()\n"
  },
  {
    "path": "libs/pybind11/tools/pybind11GuessPythonExtSuffix.cmake",
    "content": "cmake_minimum_required(VERSION 3.5)\n\nfunction(pybind11_guess_python_module_extension python)\n\n  # The SETUPTOOLS_EXT_SUFFIX environment variable takes precedence:\n  if(NOT DEFINED PYTHON_MODULE_EXT_SUFFIX AND DEFINED ENV{SETUPTOOLS_EXT_SUFFIX})\n    message(\n      STATUS\n        \"Getting Python extension suffix from ENV{SETUPTOOLS_EXT_SUFFIX}: $ENV{SETUPTOOLS_EXT_SUFFIX}\"\n    )\n    set(PYTHON_MODULE_EXT_SUFFIX\n        \"$ENV{SETUPTOOLS_EXT_SUFFIX}\"\n        CACHE\n          STRING\n          \"Extension suffix for Python extension modules (Initialized from SETUPTOOLS_EXT_SUFFIX)\")\n  endif()\n  # If that didn't work, use the Python_SOABI variable:\n  if(NOT DEFINED PYTHON_MODULE_EXT_SUFFIX AND DEFINED ${python}_SOABI)\n    message(\n      STATUS \"Determining Python extension suffix based on ${python}_SOABI: ${${python}_SOABI}\")\n    # The final extension depends on the system\n    set(_PY_BUILD_EXTENSION \"${CMAKE_SHARED_MODULE_SUFFIX}\")\n    if(CMAKE_SYSTEM_NAME STREQUAL \"Windows\")\n      set(_PY_BUILD_EXTENSION \".pyd\")\n    endif()\n    # If the SOABI already has an extension, use it as the full suffix\n    # (used for debug versions of Python on Windows)\n    if(${python}_SOABI MATCHES \"\\\\.\")\n      set(PYTHON_MODULE_EXT_SUFFIX \"${${python}_SOABI}\")\n      # If the SOABI is empty, this is usually a bug, but we generate a\n      # correct extension anyway, which is the best we can do\n    elseif(\"${${python}_SOABI}\" STREQUAL \"\")\n      message(\n        WARNING\n          \"${python}_SOABI is defined but empty. You may want to set PYTHON_MODULE_EXT_SUFFIX explicitly.\"\n      )\n      set(PYTHON_MODULE_EXT_SUFFIX \"${_PY_BUILD_EXTENSION}\")\n      # Otherwise, add the system-dependent extension to it\n    else()\n      set(PYTHON_MODULE_EXT_SUFFIX \".${${python}_SOABI}${_PY_BUILD_EXTENSION}\")\n    endif()\n  endif()\n\n  # If we could not deduce the extension suffix, unset the results:\n  if(NOT DEFINED PYTHON_MODULE_EXT_SUFFIX)\n    unset(PYTHON_MODULE_DEBUG_POSTFIX PARENT_SCOPE)\n    unset(PYTHON_MODULE_EXTENSION PARENT_SCOPE)\n    unset(PYTHON_IS_DEBUG PARENT_SCOPE)\n    return()\n  endif()\n\n  # Sanity checks:\n  if(${python}_SOABI AND NOT (PYTHON_MODULE_EXT_SUFFIX STREQUAL ${python}_SOABI\n                              OR PYTHON_MODULE_EXT_SUFFIX MATCHES \"\\\\.${${python}_SOABI}\\\\.\"))\n    message(\n      WARNING\n        \"Python extension suffix (${PYTHON_MODULE_EXT_SUFFIX}) does not match ${python}_SOABI (${${python}_SOABI}).\"\n    )\n  endif()\n\n  # Separate file name postfix from extension: (https://github.com/pybind/pybind11/issues/4699)\n  get_filename_component(_PYTHON_MODULE_DEBUG_POSTFIX \"${PYTHON_MODULE_EXT_SUFFIX}\" NAME_WE)\n  get_filename_component(_PYTHON_MODULE_EXTENSION \"${PYTHON_MODULE_EXT_SUFFIX}\" EXT)\n\n  # Try to deduce the debug ABI from the extension suffix:\n  if(NOT DEFINED _PYTHON_IS_DEBUG)\n    if(_PYTHON_MODULE_EXTENSION MATCHES \"^\\\\.(cpython-|cp|pypy)[0-9]+dm?-\"\n       OR _PYTHON_MODULE_DEBUG_POSTFIX MATCHES \"^_d\")\n      set(_PYTHON_IS_DEBUG On)\n    else()\n      set(_PYTHON_IS_DEBUG Off)\n    endif()\n  endif()\n\n  # Return results\n  set(PYTHON_MODULE_DEBUG_POSTFIX\n      \"${_PYTHON_MODULE_DEBUG_POSTFIX}\"\n      PARENT_SCOPE)\n  set(PYTHON_MODULE_EXTENSION\n      \"${_PYTHON_MODULE_EXTENSION}\"\n      PARENT_SCOPE)\n  set(PYTHON_IS_DEBUG\n      \"${_PYTHON_IS_DEBUG}\"\n      PARENT_SCOPE)\n\nendfunction()\n"
  },
  {
    "path": "libs/pybind11/tools/pybind11NewTools.cmake",
    "content": "# tools/pybind11NewTools.cmake -- Build system for the pybind11 modules\n#\n# Copyright (c) 2020 Wenzel Jakob <wenzel@inf.ethz.ch> and Henry Schreiner\n#\n# All rights reserved. Use of this source code is governed by a\n# BSD-style license that can be found in the LICENSE file.\n\nif(CMAKE_VERSION VERSION_LESS 3.12)\n  message(FATAL_ERROR \"You cannot use the new FindPython module with CMake < 3.12\")\nendif()\n\ninclude_guard(DIRECTORY)\n\nget_property(\n  is_config\n  TARGET pybind11::headers\n  PROPERTY IMPORTED)\n\nif(pybind11_FIND_QUIETLY)\n  set(_pybind11_quiet QUIET)\nelse()\n  set(_pybind11_quiet \"\")\nendif()\n\nif(NOT Python_FOUND AND NOT Python3_FOUND)\n  if(NOT DEFINED Python_FIND_IMPLEMENTATIONS)\n    set(Python_FIND_IMPLEMENTATIONS CPython PyPy)\n  endif()\n\n  # GitHub Actions like activation\n  if(NOT DEFINED Python_ROOT_DIR AND DEFINED ENV{pythonLocation})\n    set(Python_ROOT_DIR \"$ENV{pythonLocation}\")\n  endif()\n\n  # Interpreter should not be found when cross-compiling\n  if(_PYBIND11_CROSSCOMPILING)\n    set(_pybind11_interp_component \"\")\n  else()\n    set(_pybind11_interp_component Interpreter)\n  endif()\n\n  # Development.Module support (required for manylinux) started in 3.18\n  if(CMAKE_VERSION VERSION_LESS 3.18)\n    set(_pybind11_dev_component Development)\n  else()\n    set(_pybind11_dev_component Development.Module OPTIONAL_COMPONENTS Development.Embed)\n  endif()\n\n  # Callers need to be able to access Python_EXECUTABLE\n  set(_pybind11_global_keyword \"\")\n  if(NOT is_config AND NOT DEFINED Python_ARTIFACTS_INTERACTIVE)\n    set(Python_ARTIFACTS_INTERACTIVE TRUE)\n    if(NOT CMAKE_VERSION VERSION_LESS 3.24)\n      set(_pybind11_global_keyword \"GLOBAL\")\n    endif()\n  endif()\n\n  find_package(\n    Python 3.7 REQUIRED COMPONENTS ${_pybind11_interp_component} ${_pybind11_dev_component}\n                                   ${_pybind11_quiet} ${_pybind11_global_keyword})\n\n  # If we are in submodule mode, export the Python targets to global targets.\n  # If this behavior is not desired, FindPython _before_ pybind11.\n  if(NOT is_config\n     AND Python_ARTIFACTS_INTERACTIVE\n     AND _pybind11_global_keyword STREQUAL \"\")\n    if(TARGET Python::Python)\n      set_property(TARGET Python::Python PROPERTY IMPORTED_GLOBAL TRUE)\n    endif()\n    if(TARGET Python::Interpreter)\n      set_property(TARGET Python::Interpreter PROPERTY IMPORTED_GLOBAL TRUE)\n    endif()\n    if(TARGET Python::Module)\n      set_property(TARGET Python::Module PROPERTY IMPORTED_GLOBAL TRUE)\n    endif()\n  endif()\n\n  # Explicitly export version for callers (including our own functions)\n  if(NOT is_config AND Python_ARTIFACTS_INTERACTIVE)\n    set(Python_VERSION\n        \"${Python_VERSION}\"\n        CACHE INTERNAL \"\")\n    set(Python_VERSION_MAJOR\n        \"${Python_VERSION_MAJOR}\"\n        CACHE INTERNAL \"\")\n    set(Python_VERSION_MINOR\n        \"${Python_VERSION_MINOR}\"\n        CACHE INTERNAL \"\")\n    set(Python_VERSION_PATCH\n        \"${Python_VERSION_PATCH}\"\n        CACHE INTERNAL \"\")\n  endif()\nendif()\n\nif(Python_FOUND)\n  set(_Python\n      Python\n      CACHE INTERNAL \"\" FORCE)\nelseif(Python3_FOUND)\n  set(_Python\n      Python3\n      CACHE INTERNAL \"\" FORCE)\nendif()\n\nif(PYBIND11_MASTER_PROJECT)\n  if(${_Python}_INTERPRETER_ID MATCHES \"PyPy\")\n    message(STATUS \"PyPy ${${_Python}_PyPy_VERSION} (Py ${${_Python}_VERSION})\")\n  else()\n    message(STATUS \"${_Python} ${${_Python}_VERSION}\")\n  endif()\nendif()\n\nif(NOT _PYBIND11_CROSSCOMPILING)\n  # If a user finds Python, they may forget to include the Interpreter component\n  # and the following two steps require it. It is highly recommended by CMake\n  # when finding development libraries anyway, so we will require it.\n  if(NOT DEFINED ${_Python}_EXECUTABLE)\n    message(\n      FATAL_ERROR\n        \"${_Python} was found without the Interpreter component. Pybind11 requires this component.\"\n    )\n\n  endif()\n\n  if(DEFINED PYBIND11_PYTHON_EXECUTABLE_LAST AND NOT ${_Python}_EXECUTABLE STREQUAL\n                                                 PYBIND11_PYTHON_EXECUTABLE_LAST)\n    # Detect changes to the Python version/binary in subsequent CMake runs, and refresh config if needed\n    unset(PYTHON_IS_DEBUG CACHE)\n    unset(PYTHON_MODULE_EXTENSION CACHE)\n  endif()\n\n  set(PYBIND11_PYTHON_EXECUTABLE_LAST\n      \"${${_Python}_EXECUTABLE}\"\n      CACHE INTERNAL \"Python executable during the last CMake run\")\n\n  if(NOT DEFINED PYTHON_IS_DEBUG)\n    # Debug check - see https://stackoverflow.com/questions/646518/python-how-to-detect-debug-Interpreter\n    execute_process(\n      COMMAND \"${${_Python}_EXECUTABLE}\" \"-c\"\n              \"import sys; sys.exit(hasattr(sys, 'gettotalrefcount'))\"\n      RESULT_VARIABLE _PYTHON_IS_DEBUG)\n    set(PYTHON_IS_DEBUG\n        \"${_PYTHON_IS_DEBUG}\"\n        CACHE INTERNAL \"Python debug status\")\n  endif()\n\n  # Get the suffix - SO is deprecated, should use EXT_SUFFIX, but this is\n  # required for PyPy3 (as of 7.3.1)\n  if(NOT DEFINED PYTHON_MODULE_EXTENSION OR NOT DEFINED PYTHON_MODULE_DEBUG_POSTFIX)\n    execute_process(\n      COMMAND\n        \"${${_Python}_EXECUTABLE}\" \"-c\"\n        \"import sys, importlib; s = importlib.import_module('distutils.sysconfig' if sys.version_info < (3, 10) else 'sysconfig'); print(s.get_config_var('EXT_SUFFIX') or s.get_config_var('SO'))\"\n      OUTPUT_VARIABLE _PYTHON_MODULE_EXT_SUFFIX\n      ERROR_VARIABLE _PYTHON_MODULE_EXT_SUFFIX_ERR\n      OUTPUT_STRIP_TRAILING_WHITESPACE)\n\n    if(_PYTHON_MODULE_EXT_SUFFIX STREQUAL \"\")\n      message(\n        FATAL_ERROR\n          \"pybind11 could not query the module file extension, likely the 'distutils'\"\n          \"package is not installed. Full error message:\\n${_PYTHON_MODULE_EXT_SUFFIX_ERR}\")\n    endif()\n\n    # This needs to be available for the pybind11_extension function\n    if(NOT DEFINED PYTHON_MODULE_DEBUG_POSTFIX)\n      get_filename_component(_PYTHON_MODULE_DEBUG_POSTFIX \"${_PYTHON_MODULE_EXT_SUFFIX}\" NAME_WE)\n      set(PYTHON_MODULE_DEBUG_POSTFIX\n          \"${_PYTHON_MODULE_DEBUG_POSTFIX}\"\n          CACHE INTERNAL \"\")\n    endif()\n\n    if(NOT DEFINED PYTHON_MODULE_EXTENSION)\n      get_filename_component(_PYTHON_MODULE_EXTENSION \"${_PYTHON_MODULE_EXT_SUFFIX}\" EXT)\n      set(PYTHON_MODULE_EXTENSION\n          \"${_PYTHON_MODULE_EXTENSION}\"\n          CACHE INTERNAL \"\")\n    endif()\n  endif()\nelse()\n  if(NOT DEFINED PYTHON_IS_DEBUG\n     OR NOT DEFINED PYTHON_MODULE_EXTENSION\n     OR NOT DEFINED PYTHON_MODULE_DEBUG_POSTFIX)\n    include(\"${CMAKE_CURRENT_LIST_DIR}/pybind11GuessPythonExtSuffix.cmake\")\n    pybind11_guess_python_module_extension(\"${_Python}\")\n  endif()\n  # When cross-compiling, we cannot query the Python interpreter, so we require\n  # the user to set these variables explicitly.\n  if(NOT DEFINED PYTHON_IS_DEBUG\n     OR NOT DEFINED PYTHON_MODULE_EXTENSION\n     OR NOT DEFINED PYTHON_MODULE_DEBUG_POSTFIX)\n    message(\n      FATAL_ERROR\n        \"When cross-compiling, you should set the PYTHON_IS_DEBUG, PYTHON_MODULE_EXTENSION and PYTHON_MODULE_DEBUG_POSTFIX \\\n        variables appropriately before loading pybind11 (e.g. in your CMake toolchain file)\")\n  endif()\nendif()\n\n# Python debug libraries expose slightly different objects before 3.8\n# https://docs.python.org/3.6/c-api/intro.html#debugging-builds\n# https://stackoverflow.com/questions/39161202/how-to-work-around-missing-pymodule-create2-in-amd64-win-python35-d-lib\nif(PYTHON_IS_DEBUG)\n  set_property(\n    TARGET pybind11::pybind11\n    APPEND\n    PROPERTY INTERFACE_COMPILE_DEFINITIONS Py_DEBUG)\nendif()\n\n# Check on every access - since Python can change - do nothing in that case.\n\nif(DEFINED ${_Python}_INCLUDE_DIRS)\n  # Only add Python for build - must be added during the import for config\n  # since it has to be re-discovered.\n  #\n  # This needs to be a target to be included after the local pybind11\n  # directory, just in case there there is an installed pybind11 sitting\n  # next to Python's includes. It also ensures Python is a SYSTEM library.\n  add_library(pybind11::python_headers INTERFACE IMPORTED)\n  set_property(\n    TARGET pybind11::python_headers PROPERTY INTERFACE_INCLUDE_DIRECTORIES\n                                             \"$<BUILD_INTERFACE:${${_Python}_INCLUDE_DIRS}>\")\n  set_property(\n    TARGET pybind11::pybind11\n    APPEND\n    PROPERTY INTERFACE_LINK_LIBRARIES pybind11::python_headers)\n  set(pybind11_INCLUDE_DIRS\n      \"${pybind11_INCLUDE_DIR}\" \"${${_Python}_INCLUDE_DIRS}\"\n      CACHE INTERNAL \"Directories where pybind11 and possibly Python headers are located\")\nendif()\n\n# In CMake 3.18+, you can find these separately, so include an if\nif(TARGET ${_Python}::Python)\n  set_property(\n    TARGET pybind11::embed\n    APPEND\n    PROPERTY INTERFACE_LINK_LIBRARIES ${_Python}::Python)\nendif()\n\n# CMake 3.15+ has this\nif(TARGET ${_Python}::Module)\n  set_property(\n    TARGET pybind11::module\n    APPEND\n    PROPERTY INTERFACE_LINK_LIBRARIES ${_Python}::Module)\nelse()\n  set_property(\n    TARGET pybind11::module\n    APPEND\n    PROPERTY INTERFACE_LINK_LIBRARIES pybind11::python_link_helper)\nendif()\n\n# WITHOUT_SOABI and WITH_SOABI will disable the custom extension handling used by pybind11.\n# WITH_SOABI is passed on to python_add_library.\nfunction(pybind11_add_module target_name)\n  cmake_parse_arguments(PARSE_ARGV 1 ARG\n                        \"STATIC;SHARED;MODULE;THIN_LTO;OPT_SIZE;NO_EXTRAS;WITHOUT_SOABI\" \"\" \"\")\n\n  if(ARG_STATIC)\n    set(lib_type STATIC)\n  elseif(ARG_SHARED)\n    set(lib_type SHARED)\n  else()\n    set(lib_type MODULE)\n  endif()\n\n  if(\"${_Python}\" STREQUAL \"Python\")\n    python_add_library(${target_name} ${lib_type} ${ARG_UNPARSED_ARGUMENTS})\n  elseif(\"${_Python}\" STREQUAL \"Python3\")\n    python3_add_library(${target_name} ${lib_type} ${ARG_UNPARSED_ARGUMENTS})\n  else()\n    message(FATAL_ERROR \"Cannot detect FindPython version: ${_Python}\")\n  endif()\n\n  target_link_libraries(${target_name} PRIVATE pybind11::headers)\n\n  if(lib_type STREQUAL \"MODULE\")\n    target_link_libraries(${target_name} PRIVATE pybind11::module)\n  else()\n    target_link_libraries(${target_name} PRIVATE pybind11::embed)\n  endif()\n\n  if(MSVC)\n    target_link_libraries(${target_name} PRIVATE pybind11::windows_extras)\n  endif()\n\n  # -fvisibility=hidden is required to allow multiple modules compiled against\n  # different pybind versions to work properly, and for some features (e.g.\n  # py::module_local).  We force it on everything inside the `pybind11`\n  # namespace; also turning it on for a pybind module compilation here avoids\n  # potential warnings or issues from having mixed hidden/non-hidden types.\n  if(NOT DEFINED CMAKE_CXX_VISIBILITY_PRESET)\n    set_target_properties(${target_name} PROPERTIES CXX_VISIBILITY_PRESET \"hidden\")\n  endif()\n\n  if(NOT DEFINED CMAKE_CUDA_VISIBILITY_PRESET)\n    set_target_properties(${target_name} PROPERTIES CUDA_VISIBILITY_PRESET \"hidden\")\n  endif()\n\n  # If we don't pass a WITH_SOABI or WITHOUT_SOABI, use our own default handling of extensions\n  if(NOT ARG_WITHOUT_SOABI AND NOT \"WITH_SOABI\" IN_LIST ARG_UNPARSED_ARGUMENTS)\n    pybind11_extension(${target_name})\n  endif()\n\n  if(ARG_NO_EXTRAS)\n    return()\n  endif()\n\n  if(NOT DEFINED CMAKE_INTERPROCEDURAL_OPTIMIZATION)\n    if(ARG_THIN_LTO)\n      target_link_libraries(${target_name} PRIVATE pybind11::thin_lto)\n    else()\n      target_link_libraries(${target_name} PRIVATE pybind11::lto)\n    endif()\n  endif()\n\n  if(DEFINED CMAKE_BUILD_TYPE) # see https://github.com/pybind/pybind11/issues/4454\n    # Use case-insensitive comparison to match the result of $<CONFIG:cfgs>\n    string(TOUPPER \"${CMAKE_BUILD_TYPE}\" uppercase_CMAKE_BUILD_TYPE)\n    if(NOT MSVC AND NOT \"${uppercase_CMAKE_BUILD_TYPE}\" MATCHES DEBUG|RELWITHDEBINFO)\n      # Strip unnecessary sections of the binary on Linux/macOS\n      pybind11_strip(${target_name})\n    endif()\n  endif()\n\n  if(MSVC)\n    target_link_libraries(${target_name} PRIVATE pybind11::windows_extras)\n  endif()\n\n  if(ARG_OPT_SIZE)\n    target_link_libraries(${target_name} PRIVATE pybind11::opt_size)\n  endif()\nendfunction()\n\nfunction(pybind11_extension name)\n  # The extension is precomputed\n  set_target_properties(\n    ${name}\n    PROPERTIES PREFIX \"\"\n               DEBUG_POSTFIX \"${PYTHON_MODULE_DEBUG_POSTFIX}\"\n               SUFFIX \"${PYTHON_MODULE_EXTENSION}\")\nendfunction()\n"
  },
  {
    "path": "libs/pybind11/tools/pybind11Tools.cmake",
    "content": "# tools/pybind11Tools.cmake -- Build system for the pybind11 modules\n#\n# Copyright (c) 2020 Wenzel Jakob <wenzel.jakob@epfl.ch>\n#\n# All rights reserved. Use of this source code is governed by a\n# BSD-style license that can be found in the LICENSE file.\n\n# include_guard(global) (pre-CMake 3.10)\nif(TARGET pybind11::python_headers)\n  return()\nendif()\n\n# Built-in in CMake 3.5+\ninclude(CMakeParseArguments)\n\nif(pybind11_FIND_QUIETLY)\n  set(_pybind11_quiet QUIET)\nelse()\n  set(_pybind11_quiet \"\")\nendif()\n\n# If this is the first run, PYTHON_VERSION can stand in for PYBIND11_PYTHON_VERSION\nif(NOT DEFINED PYBIND11_PYTHON_VERSION AND DEFINED PYTHON_VERSION)\n  message(WARNING \"Set PYBIND11_PYTHON_VERSION to search for a specific version, not \"\n                  \"PYTHON_VERSION (which is an output). Assuming that is what you \"\n                  \"meant to do and continuing anyway.\")\n  set(PYBIND11_PYTHON_VERSION\n      \"${PYTHON_VERSION}\"\n      CACHE STRING \"Python version to use for compiling modules\")\n  unset(PYTHON_VERSION)\n  unset(PYTHON_VERSION CACHE)\nelseif(DEFINED PYBIND11_PYTHON_VERSION)\n  # If this is set as a normal variable, promote it\n  set(PYBIND11_PYTHON_VERSION\n      \"${PYBIND11_PYTHON_VERSION}\"\n      CACHE STRING \"Python version to use for compiling modules\")\nelse()\n  # Make an empty cache variable.\n  set(PYBIND11_PYTHON_VERSION\n      \"\"\n      CACHE STRING \"Python version to use for compiling modules\")\nendif()\n\n# A user can set versions manually too\nset(Python_ADDITIONAL_VERSIONS\n    \"3.12;3.11;3.10;3.9;3.8;3.7\"\n    CACHE INTERNAL \"\")\n\nlist(APPEND CMAKE_MODULE_PATH \"${CMAKE_CURRENT_LIST_DIR}\")\nfind_package(PythonLibsNew ${PYBIND11_PYTHON_VERSION} MODULE REQUIRED ${_pybind11_quiet})\nlist(REMOVE_AT CMAKE_MODULE_PATH -1)\n\n# Makes a normal variable a cached variable\nmacro(_PYBIND11_PROMOTE_TO_CACHE NAME)\n  set(_tmp_ptc \"${${NAME}}\")\n  # CMake 3.21 complains if a cached variable is shadowed by a normal one\n  unset(${NAME})\n  set(${NAME}\n      \"${_tmp_ptc}\"\n      CACHE INTERNAL \"\")\nendmacro()\n\n# Cache variables so pybind11_add_module can be used in parent projects\n_pybind11_promote_to_cache(PYTHON_INCLUDE_DIRS)\n_pybind11_promote_to_cache(PYTHON_LIBRARIES)\n_pybind11_promote_to_cache(PYTHON_MODULE_PREFIX)\n_pybind11_promote_to_cache(PYTHON_MODULE_EXTENSION)\n_pybind11_promote_to_cache(PYTHON_MODULE_DEBUG_POSTFIX)\n_pybind11_promote_to_cache(PYTHON_VERSION_MAJOR)\n_pybind11_promote_to_cache(PYTHON_VERSION_MINOR)\n_pybind11_promote_to_cache(PYTHON_VERSION)\n_pybind11_promote_to_cache(PYTHON_IS_DEBUG)\n\nif(PYBIND11_MASTER_PROJECT)\n  if(PYTHON_MODULE_EXTENSION MATCHES \"pypy\")\n    if(NOT DEFINED PYPY_VERSION)\n      execute_process(\n        COMMAND ${PYTHON_EXECUTABLE} -c\n                [=[import sys; sys.stdout.write(\".\".join(map(str, sys.pypy_version_info[:3])))]=]\n        OUTPUT_VARIABLE pypy_version)\n      set(PYPY_VERSION\n          ${pypy_version}\n          CACHE INTERNAL \"\")\n    endif()\n    message(STATUS \"PYPY ${PYPY_VERSION} (Py ${PYTHON_VERSION})\")\n  else()\n    message(STATUS \"PYTHON ${PYTHON_VERSION}\")\n  endif()\nendif()\n\n# Only add Python for build - must be added during the import for config since\n# it has to be re-discovered.\n#\n# This needs to be an target to it is included after the local pybind11\n# directory, just in case there are multiple versions of pybind11, we want the\n# one we expect.\nadd_library(pybind11::python_headers INTERFACE IMPORTED)\nset_property(TARGET pybind11::python_headers PROPERTY INTERFACE_INCLUDE_DIRECTORIES\n                                                      \"$<BUILD_INTERFACE:${PYTHON_INCLUDE_DIRS}>\")\nset_property(\n  TARGET pybind11::pybind11\n  APPEND\n  PROPERTY INTERFACE_LINK_LIBRARIES pybind11::python_headers)\n\nset(pybind11_INCLUDE_DIRS\n    \"${pybind11_INCLUDE_DIR}\" \"${PYTHON_INCLUDE_DIRS}\"\n    CACHE INTERNAL \"Directories where pybind11 and possibly Python headers are located\")\n\n# Python debug libraries expose slightly different objects before 3.8\n# https://docs.python.org/3.6/c-api/intro.html#debugging-builds\n# https://stackoverflow.com/questions/39161202/how-to-work-around-missing-pymodule-create2-in-amd64-win-python35-d-lib\nif(PYTHON_IS_DEBUG)\n  set_property(\n    TARGET pybind11::pybind11\n    APPEND\n    PROPERTY INTERFACE_COMPILE_DEFINITIONS Py_DEBUG)\nendif()\n\n# The <3.11 code here does not support release/debug builds at the same time, like on vcpkg\nif(CMAKE_VERSION VERSION_LESS 3.11)\n  set_property(\n    TARGET pybind11::module\n    APPEND\n    PROPERTY\n      INTERFACE_LINK_LIBRARIES\n      pybind11::python_link_helper\n      \"$<$<OR:$<PLATFORM_ID:Windows>,$<PLATFORM_ID:Cygwin>>:$<BUILD_INTERFACE:${PYTHON_LIBRARIES}>>\"\n  )\n\n  set_property(\n    TARGET pybind11::embed\n    APPEND\n    PROPERTY INTERFACE_LINK_LIBRARIES pybind11::pybind11 $<BUILD_INTERFACE:${PYTHON_LIBRARIES}>)\nelse()\n  # The IMPORTED INTERFACE library here is to ensure that \"debug\" and \"release\" get processed outside\n  # of a generator expression - https://gitlab.kitware.com/cmake/cmake/-/issues/18424, as they are\n  # target_link_library keywords rather than real libraries.\n  add_library(pybind11::_ClassicPythonLibraries IMPORTED INTERFACE)\n  target_link_libraries(pybind11::_ClassicPythonLibraries INTERFACE ${PYTHON_LIBRARIES})\n  target_link_libraries(\n    pybind11::module\n    INTERFACE\n      pybind11::python_link_helper\n      \"$<$<OR:$<PLATFORM_ID:Windows>,$<PLATFORM_ID:Cygwin>>:pybind11::_ClassicPythonLibraries>\")\n\n  target_link_libraries(pybind11::embed INTERFACE pybind11::pybind11\n                                                  pybind11::_ClassicPythonLibraries)\nendif()\n\nfunction(pybind11_extension name)\n  # The prefix and extension are provided by FindPythonLibsNew.cmake\n  set_target_properties(\n    ${name}\n    PROPERTIES PREFIX \"${PYTHON_MODULE_PREFIX}\"\n               DEBUG_POSTFIX \"${PYTHON_MODULE_DEBUG_POSTFIX}\"\n               SUFFIX \"${PYTHON_MODULE_EXTENSION}\")\nendfunction()\n\n# Build a Python extension module:\n# pybind11_add_module(<name> [MODULE | SHARED] [EXCLUDE_FROM_ALL]\n#                     [NO_EXTRAS] [THIN_LTO] [OPT_SIZE] source1 [source2 ...])\n#\nfunction(pybind11_add_module target_name)\n  set(options \"MODULE;SHARED;EXCLUDE_FROM_ALL;NO_EXTRAS;SYSTEM;THIN_LTO;OPT_SIZE\")\n  cmake_parse_arguments(ARG \"${options}\" \"\" \"\" ${ARGN})\n\n  if(ARG_MODULE AND ARG_SHARED)\n    message(FATAL_ERROR \"Can't be both MODULE and SHARED\")\n  elseif(ARG_SHARED)\n    set(lib_type SHARED)\n  else()\n    set(lib_type MODULE)\n  endif()\n\n  if(ARG_EXCLUDE_FROM_ALL)\n    set(exclude_from_all EXCLUDE_FROM_ALL)\n  else()\n    set(exclude_from_all \"\")\n  endif()\n\n  add_library(${target_name} ${lib_type} ${exclude_from_all} ${ARG_UNPARSED_ARGUMENTS})\n\n  target_link_libraries(${target_name} PRIVATE pybind11::module)\n\n  if(ARG_SYSTEM)\n    message(\n      STATUS\n        \"Warning: this does not have an effect - use NO_SYSTEM_FROM_IMPORTED if using imported targets\"\n    )\n  endif()\n\n  pybind11_extension(${target_name})\n\n  # -fvisibility=hidden is required to allow multiple modules compiled against\n  # different pybind versions to work properly, and for some features (e.g.\n  # py::module_local).  We force it on everything inside the `pybind11`\n  # namespace; also turning it on for a pybind module compilation here avoids\n  # potential warnings or issues from having mixed hidden/non-hidden types.\n  if(NOT DEFINED CMAKE_CXX_VISIBILITY_PRESET)\n    set_target_properties(${target_name} PROPERTIES CXX_VISIBILITY_PRESET \"hidden\")\n  endif()\n\n  if(NOT DEFINED CMAKE_CUDA_VISIBILITY_PRESET)\n    set_target_properties(${target_name} PROPERTIES CUDA_VISIBILITY_PRESET \"hidden\")\n  endif()\n\n  if(ARG_NO_EXTRAS)\n    return()\n  endif()\n\n  if(NOT DEFINED CMAKE_INTERPROCEDURAL_OPTIMIZATION)\n    if(ARG_THIN_LTO)\n      target_link_libraries(${target_name} PRIVATE pybind11::thin_lto)\n    else()\n      target_link_libraries(${target_name} PRIVATE pybind11::lto)\n    endif()\n  endif()\n\n  if(DEFINED CMAKE_BUILD_TYPE) # see https://github.com/pybind/pybind11/issues/4454\n    # Use case-insensitive comparison to match the result of $<CONFIG:cfgs>\n    string(TOUPPER \"${CMAKE_BUILD_TYPE}\" uppercase_CMAKE_BUILD_TYPE)\n    if(NOT MSVC AND NOT \"${uppercase_CMAKE_BUILD_TYPE}\" MATCHES DEBUG|RELWITHDEBINFO)\n      pybind11_strip(${target_name})\n    endif()\n  endif()\n\n  if(MSVC)\n    target_link_libraries(${target_name} PRIVATE pybind11::windows_extras)\n  endif()\n\n  if(ARG_OPT_SIZE)\n    target_link_libraries(${target_name} PRIVATE pybind11::opt_size)\n  endif()\nendfunction()\n\n# Provide general way to call common Python commands in \"common\" file.\nset(_Python\n    PYTHON\n    CACHE INTERNAL \"\" FORCE)\n"
  },
  {
    "path": "libs/pybind11/tools/pyproject.toml",
    "content": "[build-system]\nrequires = [\"setuptools>=42\", \"wheel\"]\nbuild-backend = \"setuptools.build_meta\"\n"
  },
  {
    "path": "libs/pybind11/tools/setup_global.py.in",
    "content": "#!/usr/bin/env python3\n\n# Setup script for pybind11-global (in the sdist or in tools/setup_global.py in the repository)\n# This package is targeted for easy use from CMake.\n\nimport glob\nimport os\nimport re\n\n# Setuptools has to be before distutils\nfrom setuptools import setup\n\nfrom distutils.command.install_headers import install_headers\n\nclass InstallHeadersNested(install_headers):\n    def run(self):\n        headers = self.distribution.headers or []\n        for header in headers:\n            # Remove pybind11/include/\n            short_header = header.split(\"/\", 2)[-1]\n\n            dst = os.path.join(self.install_dir, os.path.dirname(short_header))\n            self.mkpath(dst)\n            (out, _) = self.copy_file(header, dst)\n            self.outfiles.append(out)\n\n\nmain_headers = glob.glob(\"pybind11/include/pybind11/*.h\")\ndetail_headers = glob.glob(\"pybind11/include/pybind11/detail/*.h\")\neigen_headers = glob.glob(\"pybind11/include/pybind11/eigen/*.h\")\nstl_headers = glob.glob(\"pybind11/include/pybind11/stl/*.h\")\ncmake_files = glob.glob(\"pybind11/share/cmake/pybind11/*.cmake\")\npkgconfig_files = glob.glob(\"pybind11/share/pkgconfig/*.pc\")\nheaders = main_headers + detail_headers + stl_headers + eigen_headers\n\ncmdclass = {\"install_headers\": InstallHeadersNested}\n$extra_cmd\n\n# This will _not_ affect installing from wheels,\n# only building wheels or installing from SDist.\n# Primarily intended on Windows, where this is sometimes\n# customized (for example, conda-forge uses Library/)\nbase = os.environ.get(\"PYBIND11_GLOBAL_PREFIX\", \"\")\n\n# Must have a separator\nif base and not base.endswith(\"/\"):\n    base += \"/\"\n\nsetup(\n    name=\"pybind11_global\",\n    version=\"$version\",\n    packages=[],\n    headers=headers,\n    data_files=[\n        (base + \"share/cmake/pybind11\", cmake_files),\n        (base + \"share/pkgconfig\", pkgconfig_files),\n        (base + \"include/pybind11\", main_headers),\n        (base + \"include/pybind11/detail\", detail_headers),\n        (base + \"include/pybind11/eigen\", eigen_headers),\n        (base + \"include/pybind11/stl\", stl_headers),\n    ],\n    cmdclass=cmdclass,\n)\n"
  },
  {
    "path": "libs/pybind11/tools/setup_main.py.in",
    "content": "#!/usr/bin/env python3\n\n# Setup script (in the sdist or in tools/setup_main.py in the repository)\n\nfrom setuptools import setup\n\ncmdclass = {}\n$extra_cmd\n\nsetup(\n    name=\"pybind11\",\n    version=\"$version\",\n    download_url='https://github.com/pybind/pybind11/tarball/v$version',\n    packages=[\n        \"pybind11\",\n        \"pybind11.include.pybind11\",\n        \"pybind11.include.pybind11.detail\",\n        \"pybind11.include.pybind11.eigen\",\n        \"pybind11.include.pybind11.stl\",\n        \"pybind11.share.cmake.pybind11\",\n        \"pybind11.share.pkgconfig\",\n    ],\n    package_data={\n        \"pybind11\": [\"py.typed\"],\n        \"pybind11.include.pybind11\": [\"*.h\"],\n        \"pybind11.include.pybind11.detail\": [\"*.h\"],\n        \"pybind11.include.pybind11.eigen\": [\"*.h\"],\n        \"pybind11.include.pybind11.stl\": [\"*.h\"],\n        \"pybind11.share.cmake.pybind11\": [\"*.cmake\"],\n        \"pybind11.share.pkgconfig\": [\"*.pc\"],\n    },\n    extras_require={\n        \"global\": [\"pybind11_global==$version\"]\n        },\n    entry_points={\n        \"console_scripts\": [\n             \"pybind11-config = pybind11.__main__:main\",\n        ],\n        \"pipx.run\": [\n             \"pybind11 = pybind11.__main__:main\",\n        ]\n    },\n    cmdclass=cmdclass\n)\n"
  },
  {
    "path": "libs/pybind11/tools/test-pybind11GuessPythonExtSuffix.cmake",
    "content": "cmake_minimum_required(VERSION 3.5)\n\n# Tests for pybind11_guess_python_module_extension\n# Run using `cmake -P tools/test-pybind11GuessPythonExtSuffix.cmake`\n\ninclude(\"${CMAKE_CURRENT_LIST_DIR}/pybind11GuessPythonExtSuffix.cmake\")\n\nmacro(expect_streq actual expected)\n  if(NOT \"${actual}\" STREQUAL \"${expected}\")\n    message(SEND_ERROR \"Fail\\n *** actual:   '${actual}'\\n *** expected: '${expected}'\")\n  endif()\nendmacro()\n\nmacro(expect_false actual)\n  if(\"${actual}\")\n    message(SEND_ERROR \"Fail\\n *** actual:   '${actual}'\\n *** expected: false\")\n  endif()\nendmacro()\n\nmacro(expect_true actual)\n  if(NOT \"${actual}\")\n    message(SEND_ERROR \"Fail\\n *** actual:   '${actual}'\\n *** expected: true\")\n  endif()\nendmacro()\n\n# Windows\nset(CMAKE_SYSTEM_NAME \"Windows\")\nset(CMAKE_SHARED_MODULE_SUFFIX \".dll\")\n\nset(Python3_SOABI \"\")\npybind11_guess_python_module_extension(\"Python3\")\nexpect_streq(\"${PYTHON_MODULE_EXTENSION}\" \".pyd\")\nexpect_streq(\"${PYTHON_MODULE_DEBUG_POSTFIX}\" \"\")\nexpect_false(\"${PYTHON_IS_DEBUG}\")\nunset(PYTHON_MODULE_EXT_SUFFIX)\nunset(PYTHON_MODULE_EXT_SUFFIX CACHE)\n\nset(Python3_SOABI \"cp311-win_arm64\")\npybind11_guess_python_module_extension(\"Python3\")\nexpect_streq(\"${PYTHON_MODULE_EXTENSION}\" \".cp311-win_arm64.pyd\")\nexpect_streq(\"${PYTHON_MODULE_DEBUG_POSTFIX}\" \"\")\nexpect_false(\"${PYTHON_IS_DEBUG}\")\nunset(PYTHON_MODULE_EXT_SUFFIX)\nunset(PYTHON_MODULE_EXT_SUFFIX CACHE)\n\nset(Python3_SOABI \"cp311d-win_arm64\")\npybind11_guess_python_module_extension(\"Python3\")\nexpect_streq(\"${PYTHON_MODULE_EXTENSION}\" \".cp311d-win_arm64.pyd\")\nexpect_streq(\"${PYTHON_MODULE_DEBUG_POSTFIX}\" \"\")\nexpect_true(\"${PYTHON_IS_DEBUG}\")\nunset(PYTHON_MODULE_EXT_SUFFIX)\nunset(PYTHON_MODULE_EXT_SUFFIX CACHE)\n\nset(Python3_SOABI \"pypy310-pp73-win_amd64\")\npybind11_guess_python_module_extension(\"Python3\")\nexpect_streq(\"${PYTHON_MODULE_EXTENSION}\" \".pypy310-pp73-win_amd64.pyd\")\nexpect_streq(\"${PYTHON_MODULE_DEBUG_POSTFIX}\" \"\")\nexpect_false(\"${PYTHON_IS_DEBUG}\")\nunset(PYTHON_MODULE_EXT_SUFFIX)\nunset(PYTHON_MODULE_EXT_SUFFIX CACHE)\n\nset(Python3_SOABI \"_d.cp311-win_amd64.pyd\") # This is a quirk of FindPython3\npybind11_guess_python_module_extension(\"Python3\")\nexpect_streq(\"${PYTHON_MODULE_EXTENSION}\" \".cp311-win_amd64.pyd\")\nexpect_streq(\"${PYTHON_MODULE_DEBUG_POSTFIX}\" \"_d\")\nexpect_true(\"${PYTHON_IS_DEBUG}\")\nunset(PYTHON_MODULE_EXT_SUFFIX)\nunset(PYTHON_MODULE_EXT_SUFFIX CACHE)\n\nunset(Python3_SOABI)\nset(ENV{SETUPTOOLS_EXT_SUFFIX} \".cp39-win_arm64.pyd\") # Set by cibuildwheel\npybind11_guess_python_module_extension(\"Python3\")\nexpect_streq(\"${PYTHON_MODULE_EXTENSION}\" \".cp39-win_arm64.pyd\")\nexpect_streq(\"${PYTHON_MODULE_DEBUG_POSTFIX}\" \"\")\nexpect_false(\"${PYTHON_IS_DEBUG}\")\nunset(PYTHON_MODULE_EXT_SUFFIX)\nunset(PYTHON_MODULE_EXT_SUFFIX CACHE)\nunset(ENV{SETUPTOOLS_EXT_SUFFIX})\n\nset(Python3_SOABI \"cp311-win_arm64\")\nset(ENV{SETUPTOOLS_EXT_SUFFIX} \"\") # Should not be used\npybind11_guess_python_module_extension(\"Python3\")\nexpect_streq(\"${PYTHON_MODULE_EXTENSION}\" \".cp311-win_arm64.pyd\")\nexpect_streq(\"${PYTHON_MODULE_DEBUG_POSTFIX}\" \"\")\nexpect_false(\"${PYTHON_IS_DEBUG}\")\nunset(PYTHON_MODULE_EXT_SUFFIX)\nunset(PYTHON_MODULE_EXT_SUFFIX CACHE)\nunset(ENV{SETUPTOOLS_EXT_SUFFIX})\n\n# macOS\nset(CMAKE_SYSTEM_NAME \"Darwin\")\nset(CMAKE_SHARED_MODULE_SUFFIX \".so\")\n\nset(Python3_SOABI \"\")\npybind11_guess_python_module_extension(\"Python3\")\nexpect_streq(\"${PYTHON_MODULE_EXTENSION}\" \".so\")\nexpect_streq(\"${PYTHON_MODULE_DEBUG_POSTFIX}\" \"\")\nexpect_false(\"${PYTHON_IS_DEBUG}\")\nunset(PYTHON_MODULE_EXT_SUFFIX)\nunset(PYTHON_MODULE_EXT_SUFFIX CACHE)\n\nset(Python3_SOABI \"cpython-312-darwin\")\npybind11_guess_python_module_extension(\"Python3\")\nexpect_streq(\"${PYTHON_MODULE_EXTENSION}\" \".cpython-312-darwin.so\")\nexpect_streq(\"${PYTHON_MODULE_DEBUG_POSTFIX}\" \"\")\nexpect_false(\"${PYTHON_IS_DEBUG}\")\nunset(PYTHON_MODULE_EXT_SUFFIX)\nunset(PYTHON_MODULE_EXT_SUFFIX CACHE)\n\nset(Python3_SOABI \"cpython-312d-darwin\")\npybind11_guess_python_module_extension(\"Python3\")\nexpect_streq(\"${PYTHON_MODULE_EXTENSION}\" \".cpython-312d-darwin.so\")\nexpect_streq(\"${PYTHON_MODULE_DEBUG_POSTFIX}\" \"\")\nexpect_true(\"${PYTHON_IS_DEBUG}\")\nunset(PYTHON_MODULE_EXT_SUFFIX)\nunset(PYTHON_MODULE_EXT_SUFFIX CACHE)\n\n# Linux\nset(CMAKE_SYSTEM_NAME \"Linux\")\nset(CMAKE_SHARED_MODULE_SUFFIX \".so\")\n\nset(Python3_SOABI \"\")\npybind11_guess_python_module_extension(\"Python3\")\nexpect_streq(\"${PYTHON_MODULE_EXTENSION}\" \".so\")\nexpect_streq(\"${PYTHON_MODULE_DEBUG_POSTFIX}\" \"\")\nexpect_false(\"${PYTHON_IS_DEBUG}\")\nunset(PYTHON_MODULE_EXT_SUFFIX)\nunset(PYTHON_MODULE_EXT_SUFFIX CACHE)\n\nset(Python3_SOABI \"cpython-312-arm-linux-gnueabihf\")\npybind11_guess_python_module_extension(\"Python3\")\nexpect_streq(\"${PYTHON_MODULE_EXTENSION}\" \".cpython-312-arm-linux-gnueabihf.so\")\nexpect_streq(\"${PYTHON_MODULE_DEBUG_POSTFIX}\" \"\")\nexpect_false(\"${PYTHON_IS_DEBUG}\")\nunset(PYTHON_MODULE_EXT_SUFFIX)\nunset(PYTHON_MODULE_EXT_SUFFIX CACHE)\n\nset(Python3_SOABI \"cpython-312d-arm-linux-gnueabihf\")\npybind11_guess_python_module_extension(\"Python3\")\nexpect_streq(\"${PYTHON_MODULE_EXTENSION}\" \".cpython-312d-arm-linux-gnueabihf.so\")\nexpect_streq(\"${PYTHON_MODULE_DEBUG_POSTFIX}\" \"\")\nexpect_true(\"${PYTHON_IS_DEBUG}\")\nunset(PYTHON_MODULE_EXT_SUFFIX)\nunset(PYTHON_MODULE_EXT_SUFFIX CACHE)\n\nset(Python3_SOABI \"pypy310-pp73-x86_64-linux-gnu\")\npybind11_guess_python_module_extension(\"Python3\")\nexpect_streq(\"${PYTHON_MODULE_EXTENSION}\" \".pypy310-pp73-x86_64-linux-gnu.so\")\nexpect_streq(\"${PYTHON_MODULE_DEBUG_POSTFIX}\" \"\")\nexpect_false(\"${PYTHON_IS_DEBUG}\")\nunset(PYTHON_MODULE_EXT_SUFFIX)\nunset(PYTHON_MODULE_EXT_SUFFIX CACHE)\n\nset(Python3_SOABI \"pypy310d-pp73-x86_64-linux-gnu\")\n# TODO: I'm not sure if this is the right SOABI for PyPy debug builds\npybind11_guess_python_module_extension(\"Python3\")\nexpect_streq(\"${PYTHON_MODULE_EXTENSION}\" \".pypy310d-pp73-x86_64-linux-gnu.so\")\nexpect_streq(\"${PYTHON_MODULE_DEBUG_POSTFIX}\" \"\")\nexpect_true(\"${PYTHON_IS_DEBUG}\")\nunset(PYTHON_MODULE_EXT_SUFFIX)\nunset(PYTHON_MODULE_EXT_SUFFIX CACHE)\n"
  },
  {
    "path": "libs/sqlite3/include/sqlite3.h",
    "content": "/*\n** 2001-09-15\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n*************************************************************************\n** This header file defines the interface that the SQLite library\n** presents to client programs.  If a C-function, structure, datatype,\n** or constant definition does not appear in this file, then it is\n** not a published API of SQLite, is subject to change without\n** notice, and should not be referenced by programs that use SQLite.\n**\n** Some of the definitions that are in this file are marked as\n** \"experimental\".  Experimental interfaces are normally new\n** features recently added to SQLite.  We do not anticipate changes\n** to experimental interfaces but reserve the right to make minor changes\n** if experience from use \"in the wild\" suggest such changes are prudent.\n**\n** The official C-language API documentation for SQLite is derived\n** from comments in this file.  This file is the authoritative source\n** on how SQLite interfaces are supposed to operate.\n**\n** The name of this file under configuration management is \"sqlite.h.in\".\n** The makefile makes some minor changes to this file (such as inserting\n** the version number) and changes its name to \"sqlite3.h\" as\n** part of the build process.\n*/\n#ifndef SQLITE3_H\n#define SQLITE3_H\n#include <stdarg.h>     /* Needed for the definition of va_list */\n\n/*\n** Make sure we can call this stuff from C++.\n*/\n#ifdef __cplusplus\nextern \"C\" {\n#endif\n\n\n/*\n** Provide the ability to override linkage features of the interface.\n*/\n#ifndef SQLITE_EXTERN\n# define SQLITE_EXTERN extern\n#endif\n#ifndef SQLITE_API\n# define SQLITE_API\n#endif\n#ifndef SQLITE_CDECL\n# define SQLITE_CDECL\n#endif\n#ifndef SQLITE_APICALL\n# define SQLITE_APICALL\n#endif\n#ifndef SQLITE_STDCALL\n# define SQLITE_STDCALL SQLITE_APICALL\n#endif\n#ifndef SQLITE_CALLBACK\n# define SQLITE_CALLBACK\n#endif\n#ifndef SQLITE_SYSAPI\n# define SQLITE_SYSAPI\n#endif\n\n/*\n** These no-op macros are used in front of interfaces to mark those\n** interfaces as either deprecated or experimental.  New applications\n** should not use deprecated interfaces - they are supported for backwards\n** compatibility only.  Application writers should be aware that\n** experimental interfaces are subject to change in point releases.\n**\n** These macros used to resolve to various kinds of compiler magic that\n** would generate warning messages when they were used.  But that\n** compiler magic ended up generating such a flurry of bug reports\n** that we have taken it all out and gone back to using simple\n** noop macros.\n*/\n#define SQLITE_DEPRECATED\n#define SQLITE_EXPERIMENTAL\n\n/*\n** Ensure these symbols were not defined by some previous header file.\n*/\n#ifdef SQLITE_VERSION\n# undef SQLITE_VERSION\n#endif\n#ifdef SQLITE_VERSION_NUMBER\n# undef SQLITE_VERSION_NUMBER\n#endif\n\n/*\n** CAPI3REF: Compile-Time Library Version Numbers\n**\n** ^(The [SQLITE_VERSION] C preprocessor macro in the sqlite3.h header\n** evaluates to a string literal that is the SQLite version in the\n** format \"X.Y.Z\" where X is the major version number (always 3 for\n** SQLite3) and Y is the minor version number and Z is the release number.)^\n** ^(The [SQLITE_VERSION_NUMBER] C preprocessor macro resolves to an integer\n** with the value (X*1000000 + Y*1000 + Z) where X, Y, and Z are the same\n** numbers used in [SQLITE_VERSION].)^\n** The SQLITE_VERSION_NUMBER for any given release of SQLite will also\n** be larger than the release from which it is derived.  Either Y will\n** be held constant and Z will be incremented or else Y will be incremented\n** and Z will be reset to zero.\n**\n** Since [version 3.6.18] ([dateof:3.6.18]), \n** SQLite source code has been stored in the\n** <a href=\"http://www.fossil-scm.org/\">Fossil configuration management\n** system</a>.  ^The SQLITE_SOURCE_ID macro evaluates to\n** a string which identifies a particular check-in of SQLite\n** within its configuration management system.  ^The SQLITE_SOURCE_ID\n** string contains the date and time of the check-in (UTC) and a SHA1\n** or SHA3-256 hash of the entire source tree.  If the source code has\n** been edited in any way since it was last checked in, then the last\n** four hexadecimal digits of the hash may be modified.\n**\n** See also: [sqlite3_libversion()],\n** [sqlite3_libversion_number()], [sqlite3_sourceid()],\n** [sqlite_version()] and [sqlite_source_id()].\n*/\n#define SQLITE_VERSION        \"3.23.0\"\n#define SQLITE_VERSION_NUMBER 3023000\n#define SQLITE_SOURCE_ID      \"2018-02-27 15:40:59 9a7f02c50e6c8a3dc3addf4e51b7e04bd31670d6ce58d26d55273c43b5ecc8b0\"\n\n/*\n** CAPI3REF: Run-Time Library Version Numbers\n** KEYWORDS: sqlite3_version sqlite3_sourceid\n**\n** These interfaces provide the same information as the [SQLITE_VERSION],\n** [SQLITE_VERSION_NUMBER], and [SQLITE_SOURCE_ID] C preprocessor macros\n** but are associated with the library instead of the header file.  ^(Cautious\n** programmers might include assert() statements in their application to\n** verify that values returned by these interfaces match the macros in\n** the header, and thus ensure that the application is\n** compiled with matching library and header files.\n**\n** <blockquote><pre>\n** assert( sqlite3_libversion_number()==SQLITE_VERSION_NUMBER );\n** assert( strncmp(sqlite3_sourceid(),SQLITE_SOURCE_ID,80)==0 );\n** assert( strcmp(sqlite3_libversion(),SQLITE_VERSION)==0 );\n** </pre></blockquote>)^\n**\n** ^The sqlite3_version[] string constant contains the text of [SQLITE_VERSION]\n** macro.  ^The sqlite3_libversion() function returns a pointer to the\n** to the sqlite3_version[] string constant.  The sqlite3_libversion()\n** function is provided for use in DLLs since DLL users usually do not have\n** direct access to string constants within the DLL.  ^The\n** sqlite3_libversion_number() function returns an integer equal to\n** [SQLITE_VERSION_NUMBER].  ^(The sqlite3_sourceid() function returns \n** a pointer to a string constant whose value is the same as the \n** [SQLITE_SOURCE_ID] C preprocessor macro.  Except if SQLite is built\n** using an edited copy of [the amalgamation], then the last four characters\n** of the hash might be different from [SQLITE_SOURCE_ID].)^\n**\n** See also: [sqlite_version()] and [sqlite_source_id()].\n*/\nSQLITE_API SQLITE_EXTERN const char sqlite3_version[];\nSQLITE_API const char *sqlite3_libversion(void);\nSQLITE_API const char *sqlite3_sourceid(void);\nSQLITE_API int sqlite3_libversion_number(void);\n\n/*\n** CAPI3REF: Run-Time Library Compilation Options Diagnostics\n**\n** ^The sqlite3_compileoption_used() function returns 0 or 1 \n** indicating whether the specified option was defined at \n** compile time.  ^The SQLITE_ prefix may be omitted from the \n** option name passed to sqlite3_compileoption_used().  \n**\n** ^The sqlite3_compileoption_get() function allows iterating\n** over the list of options that were defined at compile time by\n** returning the N-th compile time option string.  ^If N is out of range,\n** sqlite3_compileoption_get() returns a NULL pointer.  ^The SQLITE_ \n** prefix is omitted from any strings returned by \n** sqlite3_compileoption_get().\n**\n** ^Support for the diagnostic functions sqlite3_compileoption_used()\n** and sqlite3_compileoption_get() may be omitted by specifying the \n** [SQLITE_OMIT_COMPILEOPTION_DIAGS] option at compile time.\n**\n** See also: SQL functions [sqlite_compileoption_used()] and\n** [sqlite_compileoption_get()] and the [compile_options pragma].\n*/\n#ifndef SQLITE_OMIT_COMPILEOPTION_DIAGS\nSQLITE_API int sqlite3_compileoption_used(const char *zOptName);\nSQLITE_API const char *sqlite3_compileoption_get(int N);\n#endif\n\n/*\n** CAPI3REF: Test To See If The Library Is Threadsafe\n**\n** ^The sqlite3_threadsafe() function returns zero if and only if\n** SQLite was compiled with mutexing code omitted due to the\n** [SQLITE_THREADSAFE] compile-time option being set to 0.\n**\n** SQLite can be compiled with or without mutexes.  When\n** the [SQLITE_THREADSAFE] C preprocessor macro is 1 or 2, mutexes\n** are enabled and SQLite is threadsafe.  When the\n** [SQLITE_THREADSAFE] macro is 0, \n** the mutexes are omitted.  Without the mutexes, it is not safe\n** to use SQLite concurrently from more than one thread.\n**\n** Enabling mutexes incurs a measurable performance penalty.\n** So if speed is of utmost importance, it makes sense to disable\n** the mutexes.  But for maximum safety, mutexes should be enabled.\n** ^The default behavior is for mutexes to be enabled.\n**\n** This interface can be used by an application to make sure that the\n** version of SQLite that it is linking against was compiled with\n** the desired setting of the [SQLITE_THREADSAFE] macro.\n**\n** This interface only reports on the compile-time mutex setting\n** of the [SQLITE_THREADSAFE] flag.  If SQLite is compiled with\n** SQLITE_THREADSAFE=1 or =2 then mutexes are enabled by default but\n** can be fully or partially disabled using a call to [sqlite3_config()]\n** with the verbs [SQLITE_CONFIG_SINGLETHREAD], [SQLITE_CONFIG_MULTITHREAD],\n** or [SQLITE_CONFIG_SERIALIZED].  ^(The return value of the\n** sqlite3_threadsafe() function shows only the compile-time setting of\n** thread safety, not any run-time changes to that setting made by\n** sqlite3_config(). In other words, the return value from sqlite3_threadsafe()\n** is unchanged by calls to sqlite3_config().)^\n**\n** See the [threading mode] documentation for additional information.\n*/\nSQLITE_API int sqlite3_threadsafe(void);\n\n/*\n** CAPI3REF: Database Connection Handle\n** KEYWORDS: {database connection} {database connections}\n**\n** Each open SQLite database is represented by a pointer to an instance of\n** the opaque structure named \"sqlite3\".  It is useful to think of an sqlite3\n** pointer as an object.  The [sqlite3_open()], [sqlite3_open16()], and\n** [sqlite3_open_v2()] interfaces are its constructors, and [sqlite3_close()]\n** and [sqlite3_close_v2()] are its destructors.  There are many other\n** interfaces (such as\n** [sqlite3_prepare_v2()], [sqlite3_create_function()], and\n** [sqlite3_busy_timeout()] to name but three) that are methods on an\n** sqlite3 object.\n*/\ntypedef struct sqlite3 sqlite3;\n\n/*\n** CAPI3REF: 64-Bit Integer Types\n** KEYWORDS: sqlite_int64 sqlite_uint64\n**\n** Because there is no cross-platform way to specify 64-bit integer types\n** SQLite includes typedefs for 64-bit signed and unsigned integers.\n**\n** The sqlite3_int64 and sqlite3_uint64 are the preferred type definitions.\n** The sqlite_int64 and sqlite_uint64 types are supported for backwards\n** compatibility only.\n**\n** ^The sqlite3_int64 and sqlite_int64 types can store integer values\n** between -9223372036854775808 and +9223372036854775807 inclusive.  ^The\n** sqlite3_uint64 and sqlite_uint64 types can store integer values \n** between 0 and +18446744073709551615 inclusive.\n*/\n#ifdef SQLITE_INT64_TYPE\n  typedef SQLITE_INT64_TYPE sqlite_int64;\n# ifdef SQLITE_UINT64_TYPE\n    typedef SQLITE_UINT64_TYPE sqlite_uint64;\n# else  \n    typedef unsigned SQLITE_INT64_TYPE sqlite_uint64;\n# endif\n#elif defined(_MSC_VER) || defined(__BORLANDC__)\n  typedef __int64 sqlite_int64;\n  typedef unsigned __int64 sqlite_uint64;\n#else\n  typedef long long int sqlite_int64;\n  typedef unsigned long long int sqlite_uint64;\n#endif\ntypedef sqlite_int64 sqlite3_int64;\ntypedef sqlite_uint64 sqlite3_uint64;\n\n/*\n** If compiling for a processor that lacks floating point support,\n** substitute integer for floating-point.\n*/\n#ifdef SQLITE_OMIT_FLOATING_POINT\n# define double sqlite3_int64\n#endif\n\n/*\n** CAPI3REF: Closing A Database Connection\n** DESTRUCTOR: sqlite3\n**\n** ^The sqlite3_close() and sqlite3_close_v2() routines are destructors\n** for the [sqlite3] object.\n** ^Calls to sqlite3_close() and sqlite3_close_v2() return [SQLITE_OK] if\n** the [sqlite3] object is successfully destroyed and all associated\n** resources are deallocated.\n**\n** ^If the database connection is associated with unfinalized prepared\n** statements or unfinished sqlite3_backup objects then sqlite3_close()\n** will leave the database connection open and return [SQLITE_BUSY].\n** ^If sqlite3_close_v2() is called with unfinalized prepared statements\n** and/or unfinished sqlite3_backups, then the database connection becomes\n** an unusable \"zombie\" which will automatically be deallocated when the\n** last prepared statement is finalized or the last sqlite3_backup is\n** finished.  The sqlite3_close_v2() interface is intended for use with\n** host languages that are garbage collected, and where the order in which\n** destructors are called is arbitrary.\n**\n** Applications should [sqlite3_finalize | finalize] all [prepared statements],\n** [sqlite3_blob_close | close] all [BLOB handles], and \n** [sqlite3_backup_finish | finish] all [sqlite3_backup] objects associated\n** with the [sqlite3] object prior to attempting to close the object.  ^If\n** sqlite3_close_v2() is called on a [database connection] that still has\n** outstanding [prepared statements], [BLOB handles], and/or\n** [sqlite3_backup] objects then it returns [SQLITE_OK] and the deallocation\n** of resources is deferred until all [prepared statements], [BLOB handles],\n** and [sqlite3_backup] objects are also destroyed.\n**\n** ^If an [sqlite3] object is destroyed while a transaction is open,\n** the transaction is automatically rolled back.\n**\n** The C parameter to [sqlite3_close(C)] and [sqlite3_close_v2(C)]\n** must be either a NULL\n** pointer or an [sqlite3] object pointer obtained\n** from [sqlite3_open()], [sqlite3_open16()], or\n** [sqlite3_open_v2()], and not previously closed.\n** ^Calling sqlite3_close() or sqlite3_close_v2() with a NULL pointer\n** argument is a harmless no-op.\n*/\nSQLITE_API int sqlite3_close(sqlite3*);\nSQLITE_API int sqlite3_close_v2(sqlite3*);\n\n/*\n** The type for a callback function.\n** This is legacy and deprecated.  It is included for historical\n** compatibility and is not documented.\n*/\ntypedef int (*sqlite3_callback)(void*,int,char**, char**);\n\n/*\n** CAPI3REF: One-Step Query Execution Interface\n** METHOD: sqlite3\n**\n** The sqlite3_exec() interface is a convenience wrapper around\n** [sqlite3_prepare_v2()], [sqlite3_step()], and [sqlite3_finalize()],\n** that allows an application to run multiple statements of SQL\n** without having to use a lot of C code. \n**\n** ^The sqlite3_exec() interface runs zero or more UTF-8 encoded,\n** semicolon-separate SQL statements passed into its 2nd argument,\n** in the context of the [database connection] passed in as its 1st\n** argument.  ^If the callback function of the 3rd argument to\n** sqlite3_exec() is not NULL, then it is invoked for each result row\n** coming out of the evaluated SQL statements.  ^The 4th argument to\n** sqlite3_exec() is relayed through to the 1st argument of each\n** callback invocation.  ^If the callback pointer to sqlite3_exec()\n** is NULL, then no callback is ever invoked and result rows are\n** ignored.\n**\n** ^If an error occurs while evaluating the SQL statements passed into\n** sqlite3_exec(), then execution of the current statement stops and\n** subsequent statements are skipped.  ^If the 5th parameter to sqlite3_exec()\n** is not NULL then any error message is written into memory obtained\n** from [sqlite3_malloc()] and passed back through the 5th parameter.\n** To avoid memory leaks, the application should invoke [sqlite3_free()]\n** on error message strings returned through the 5th parameter of\n** sqlite3_exec() after the error message string is no longer needed.\n** ^If the 5th parameter to sqlite3_exec() is not NULL and no errors\n** occur, then sqlite3_exec() sets the pointer in its 5th parameter to\n** NULL before returning.\n**\n** ^If an sqlite3_exec() callback returns non-zero, the sqlite3_exec()\n** routine returns SQLITE_ABORT without invoking the callback again and\n** without running any subsequent SQL statements.\n**\n** ^The 2nd argument to the sqlite3_exec() callback function is the\n** number of columns in the result.  ^The 3rd argument to the sqlite3_exec()\n** callback is an array of pointers to strings obtained as if from\n** [sqlite3_column_text()], one for each column.  ^If an element of a\n** result row is NULL then the corresponding string pointer for the\n** sqlite3_exec() callback is a NULL pointer.  ^The 4th argument to the\n** sqlite3_exec() callback is an array of pointers to strings where each\n** entry represents the name of corresponding result column as obtained\n** from [sqlite3_column_name()].\n**\n** ^If the 2nd parameter to sqlite3_exec() is a NULL pointer, a pointer\n** to an empty string, or a pointer that contains only whitespace and/or \n** SQL comments, then no SQL statements are evaluated and the database\n** is not changed.\n**\n** Restrictions:\n**\n** <ul>\n** <li> The application must ensure that the 1st parameter to sqlite3_exec()\n**      is a valid and open [database connection].\n** <li> The application must not close the [database connection] specified by\n**      the 1st parameter to sqlite3_exec() while sqlite3_exec() is running.\n** <li> The application must not modify the SQL statement text passed into\n**      the 2nd parameter of sqlite3_exec() while sqlite3_exec() is running.\n** </ul>\n*/\nSQLITE_API int sqlite3_exec(\n  sqlite3*,                                  /* An open database */\n  const char *sql,                           /* SQL to be evaluated */\n  int (*callback)(void*,int,char**,char**),  /* Callback function */\n  void *,                                    /* 1st argument to callback */\n  char **errmsg                              /* Error msg written here */\n);\n\n/*\n** CAPI3REF: Result Codes\n** KEYWORDS: {result code definitions}\n**\n** Many SQLite functions return an integer result code from the set shown\n** here in order to indicate success or failure.\n**\n** New error codes may be added in future versions of SQLite.\n**\n** See also: [extended result code definitions]\n*/\n#define SQLITE_OK           0   /* Successful result */\n/* beginning-of-error-codes */\n#define SQLITE_ERROR        1   /* Generic error */\n#define SQLITE_INTERNAL     2   /* Internal logic error in SQLite */\n#define SQLITE_PERM         3   /* Access permission denied */\n#define SQLITE_ABORT        4   /* Callback routine requested an abort */\n#define SQLITE_BUSY         5   /* The database file is locked */\n#define SQLITE_LOCKED       6   /* A table in the database is locked */\n#define SQLITE_NOMEM        7   /* A malloc() failed */\n#define SQLITE_READONLY     8   /* Attempt to write a readonly database */\n#define SQLITE_INTERRUPT    9   /* Operation terminated by sqlite3_interrupt()*/\n#define SQLITE_IOERR       10   /* Some kind of disk I/O error occurred */\n#define SQLITE_CORRUPT     11   /* The database disk image is malformed */\n#define SQLITE_NOTFOUND    12   /* Unknown opcode in sqlite3_file_control() */\n#define SQLITE_FULL        13   /* Insertion failed because database is full */\n#define SQLITE_CANTOPEN    14   /* Unable to open the database file */\n#define SQLITE_PROTOCOL    15   /* Database lock protocol error */\n#define SQLITE_EMPTY       16   /* Internal use only */\n#define SQLITE_SCHEMA      17   /* The database schema changed */\n#define SQLITE_TOOBIG      18   /* String or BLOB exceeds size limit */\n#define SQLITE_CONSTRAINT  19   /* Abort due to constraint violation */\n#define SQLITE_MISMATCH    20   /* Data type mismatch */\n#define SQLITE_MISUSE      21   /* Library used incorrectly */\n#define SQLITE_NOLFS       22   /* Uses OS features not supported on host */\n#define SQLITE_AUTH        23   /* Authorization denied */\n#define SQLITE_FORMAT      24   /* Not used */\n#define SQLITE_RANGE       25   /* 2nd parameter to sqlite3_bind out of range */\n#define SQLITE_NOTADB      26   /* File opened that is not a database file */\n#define SQLITE_NOTICE      27   /* Notifications from sqlite3_log() */\n#define SQLITE_WARNING     28   /* Warnings from sqlite3_log() */\n#define SQLITE_ROW         100  /* sqlite3_step() has another row ready */\n#define SQLITE_DONE        101  /* sqlite3_step() has finished executing */\n/* end-of-error-codes */\n\n/*\n** CAPI3REF: Extended Result Codes\n** KEYWORDS: {extended result code definitions}\n**\n** In its default configuration, SQLite API routines return one of 30 integer\n** [result codes].  However, experience has shown that many of\n** these result codes are too coarse-grained.  They do not provide as\n** much information about problems as programmers might like.  In an effort to\n** address this, newer versions of SQLite (version 3.3.8 [dateof:3.3.8]\n** and later) include\n** support for additional result codes that provide more detailed information\n** about errors. These [extended result codes] are enabled or disabled\n** on a per database connection basis using the\n** [sqlite3_extended_result_codes()] API.  Or, the extended code for\n** the most recent error can be obtained using\n** [sqlite3_extended_errcode()].\n*/\n#define SQLITE_ERROR_MISSING_COLLSEQ   (SQLITE_ERROR | (1<<8))\n#define SQLITE_ERROR_RETRY             (SQLITE_ERROR | (2<<8))\n#define SQLITE_IOERR_READ              (SQLITE_IOERR | (1<<8))\n#define SQLITE_IOERR_SHORT_READ        (SQLITE_IOERR | (2<<8))\n#define SQLITE_IOERR_WRITE             (SQLITE_IOERR | (3<<8))\n#define SQLITE_IOERR_FSYNC             (SQLITE_IOERR | (4<<8))\n#define SQLITE_IOERR_DIR_FSYNC         (SQLITE_IOERR | (5<<8))\n#define SQLITE_IOERR_TRUNCATE          (SQLITE_IOERR | (6<<8))\n#define SQLITE_IOERR_FSTAT             (SQLITE_IOERR | (7<<8))\n#define SQLITE_IOERR_UNLOCK            (SQLITE_IOERR | (8<<8))\n#define SQLITE_IOERR_RDLOCK            (SQLITE_IOERR | (9<<8))\n#define SQLITE_IOERR_DELETE            (SQLITE_IOERR | (10<<8))\n#define SQLITE_IOERR_BLOCKED           (SQLITE_IOERR | (11<<8))\n#define SQLITE_IOERR_NOMEM             (SQLITE_IOERR | (12<<8))\n#define SQLITE_IOERR_ACCESS            (SQLITE_IOERR | (13<<8))\n#define SQLITE_IOERR_CHECKRESERVEDLOCK (SQLITE_IOERR | (14<<8))\n#define SQLITE_IOERR_LOCK              (SQLITE_IOERR | (15<<8))\n#define SQLITE_IOERR_CLOSE             (SQLITE_IOERR | (16<<8))\n#define SQLITE_IOERR_DIR_CLOSE         (SQLITE_IOERR | (17<<8))\n#define SQLITE_IOERR_SHMOPEN           (SQLITE_IOERR | (18<<8))\n#define SQLITE_IOERR_SHMSIZE           (SQLITE_IOERR | (19<<8))\n#define SQLITE_IOERR_SHMLOCK           (SQLITE_IOERR | (20<<8))\n#define SQLITE_IOERR_SHMMAP            (SQLITE_IOERR | (21<<8))\n#define SQLITE_IOERR_SEEK              (SQLITE_IOERR | (22<<8))\n#define SQLITE_IOERR_DELETE_NOENT      (SQLITE_IOERR | (23<<8))\n#define SQLITE_IOERR_MMAP              (SQLITE_IOERR | (24<<8))\n#define SQLITE_IOERR_GETTEMPPATH       (SQLITE_IOERR | (25<<8))\n#define SQLITE_IOERR_CONVPATH          (SQLITE_IOERR | (26<<8))\n#define SQLITE_IOERR_VNODE             (SQLITE_IOERR | (27<<8))\n#define SQLITE_IOERR_AUTH              (SQLITE_IOERR | (28<<8))\n#define SQLITE_IOERR_BEGIN_ATOMIC      (SQLITE_IOERR | (29<<8))\n#define SQLITE_IOERR_COMMIT_ATOMIC     (SQLITE_IOERR | (30<<8))\n#define SQLITE_IOERR_ROLLBACK_ATOMIC   (SQLITE_IOERR | (31<<8))\n#define SQLITE_LOCKED_SHAREDCACHE      (SQLITE_LOCKED |  (1<<8))\n#define SQLITE_BUSY_RECOVERY           (SQLITE_BUSY   |  (1<<8))\n#define SQLITE_BUSY_SNAPSHOT           (SQLITE_BUSY   |  (2<<8))\n#define SQLITE_CANTOPEN_NOTEMPDIR      (SQLITE_CANTOPEN | (1<<8))\n#define SQLITE_CANTOPEN_ISDIR          (SQLITE_CANTOPEN | (2<<8))\n#define SQLITE_CANTOPEN_FULLPATH       (SQLITE_CANTOPEN | (3<<8))\n#define SQLITE_CANTOPEN_CONVPATH       (SQLITE_CANTOPEN | (4<<8))\n#define SQLITE_CORRUPT_VTAB            (SQLITE_CORRUPT | (1<<8))\n#define SQLITE_READONLY_RECOVERY       (SQLITE_READONLY | (1<<8))\n#define SQLITE_READONLY_CANTLOCK       (SQLITE_READONLY | (2<<8))\n#define SQLITE_READONLY_ROLLBACK       (SQLITE_READONLY | (3<<8))\n#define SQLITE_READONLY_DBMOVED        (SQLITE_READONLY | (4<<8))\n#define SQLITE_READONLY_CANTINIT       (SQLITE_READONLY | (5<<8))\n#define SQLITE_READONLY_DIRECTORY      (SQLITE_READONLY | (6<<8))\n#define SQLITE_ABORT_ROLLBACK          (SQLITE_ABORT | (2<<8))\n#define SQLITE_CONSTRAINT_CHECK        (SQLITE_CONSTRAINT | (1<<8))\n#define SQLITE_CONSTRAINT_COMMITHOOK   (SQLITE_CONSTRAINT | (2<<8))\n#define SQLITE_CONSTRAINT_FOREIGNKEY   (SQLITE_CONSTRAINT | (3<<8))\n#define SQLITE_CONSTRAINT_FUNCTION     (SQLITE_CONSTRAINT | (4<<8))\n#define SQLITE_CONSTRAINT_NOTNULL      (SQLITE_CONSTRAINT | (5<<8))\n#define SQLITE_CONSTRAINT_PRIMARYKEY   (SQLITE_CONSTRAINT | (6<<8))\n#define SQLITE_CONSTRAINT_TRIGGER      (SQLITE_CONSTRAINT | (7<<8))\n#define SQLITE_CONSTRAINT_UNIQUE       (SQLITE_CONSTRAINT | (8<<8))\n#define SQLITE_CONSTRAINT_VTAB         (SQLITE_CONSTRAINT | (9<<8))\n#define SQLITE_CONSTRAINT_ROWID        (SQLITE_CONSTRAINT |(10<<8))\n#define SQLITE_NOTICE_RECOVER_WAL      (SQLITE_NOTICE | (1<<8))\n#define SQLITE_NOTICE_RECOVER_ROLLBACK (SQLITE_NOTICE | (2<<8))\n#define SQLITE_WARNING_AUTOINDEX       (SQLITE_WARNING | (1<<8))\n#define SQLITE_AUTH_USER               (SQLITE_AUTH | (1<<8))\n#define SQLITE_OK_LOAD_PERMANENTLY     (SQLITE_OK | (1<<8))\n\n/*\n** CAPI3REF: Flags For File Open Operations\n**\n** These bit values are intended for use in the\n** 3rd parameter to the [sqlite3_open_v2()] interface and\n** in the 4th parameter to the [sqlite3_vfs.xOpen] method.\n*/\n#define SQLITE_OPEN_READONLY         0x00000001  /* Ok for sqlite3_open_v2() */\n#define SQLITE_OPEN_READWRITE        0x00000002  /* Ok for sqlite3_open_v2() */\n#define SQLITE_OPEN_CREATE           0x00000004  /* Ok for sqlite3_open_v2() */\n#define SQLITE_OPEN_DELETEONCLOSE    0x00000008  /* VFS only */\n#define SQLITE_OPEN_EXCLUSIVE        0x00000010  /* VFS only */\n#define SQLITE_OPEN_AUTOPROXY        0x00000020  /* VFS only */\n#define SQLITE_OPEN_URI              0x00000040  /* Ok for sqlite3_open_v2() */\n#define SQLITE_OPEN_MEMORY           0x00000080  /* Ok for sqlite3_open_v2() */\n#define SQLITE_OPEN_MAIN_DB          0x00000100  /* VFS only */\n#define SQLITE_OPEN_TEMP_DB          0x00000200  /* VFS only */\n#define SQLITE_OPEN_TRANSIENT_DB     0x00000400  /* VFS only */\n#define SQLITE_OPEN_MAIN_JOURNAL     0x00000800  /* VFS only */\n#define SQLITE_OPEN_TEMP_JOURNAL     0x00001000  /* VFS only */\n#define SQLITE_OPEN_SUBJOURNAL       0x00002000  /* VFS only */\n#define SQLITE_OPEN_MASTER_JOURNAL   0x00004000  /* VFS only */\n#define SQLITE_OPEN_NOMUTEX          0x00008000  /* Ok for sqlite3_open_v2() */\n#define SQLITE_OPEN_FULLMUTEX        0x00010000  /* Ok for sqlite3_open_v2() */\n#define SQLITE_OPEN_SHAREDCACHE      0x00020000  /* Ok for sqlite3_open_v2() */\n#define SQLITE_OPEN_PRIVATECACHE     0x00040000  /* Ok for sqlite3_open_v2() */\n#define SQLITE_OPEN_WAL              0x00080000  /* VFS only */\n\n/* Reserved:                         0x00F00000 */\n\n/*\n** CAPI3REF: Device Characteristics\n**\n** The xDeviceCharacteristics method of the [sqlite3_io_methods]\n** object returns an integer which is a vector of these\n** bit values expressing I/O characteristics of the mass storage\n** device that holds the file that the [sqlite3_io_methods]\n** refers to.\n**\n** The SQLITE_IOCAP_ATOMIC property means that all writes of\n** any size are atomic.  The SQLITE_IOCAP_ATOMICnnn values\n** mean that writes of blocks that are nnn bytes in size and\n** are aligned to an address which is an integer multiple of\n** nnn are atomic.  The SQLITE_IOCAP_SAFE_APPEND value means\n** that when data is appended to a file, the data is appended\n** first then the size of the file is extended, never the other\n** way around.  The SQLITE_IOCAP_SEQUENTIAL property means that\n** information is written to disk in the same order as calls\n** to xWrite().  The SQLITE_IOCAP_POWERSAFE_OVERWRITE property means that\n** after reboot following a crash or power loss, the only bytes in a\n** file that were written at the application level might have changed\n** and that adjacent bytes, even bytes within the same sector are\n** guaranteed to be unchanged.  The SQLITE_IOCAP_UNDELETABLE_WHEN_OPEN\n** flag indicates that a file cannot be deleted when open.  The\n** SQLITE_IOCAP_IMMUTABLE flag indicates that the file is on\n** read-only media and cannot be changed even by processes with\n** elevated privileges.\n**\n** The SQLITE_IOCAP_BATCH_ATOMIC property means that the underlying\n** filesystem supports doing multiple write operations atomically when those\n** write operations are bracketed by [SQLITE_FCNTL_BEGIN_ATOMIC_WRITE] and\n** [SQLITE_FCNTL_COMMIT_ATOMIC_WRITE].\n*/\n#define SQLITE_IOCAP_ATOMIC                 0x00000001\n#define SQLITE_IOCAP_ATOMIC512              0x00000002\n#define SQLITE_IOCAP_ATOMIC1K               0x00000004\n#define SQLITE_IOCAP_ATOMIC2K               0x00000008\n#define SQLITE_IOCAP_ATOMIC4K               0x00000010\n#define SQLITE_IOCAP_ATOMIC8K               0x00000020\n#define SQLITE_IOCAP_ATOMIC16K              0x00000040\n#define SQLITE_IOCAP_ATOMIC32K              0x00000080\n#define SQLITE_IOCAP_ATOMIC64K              0x00000100\n#define SQLITE_IOCAP_SAFE_APPEND            0x00000200\n#define SQLITE_IOCAP_SEQUENTIAL             0x00000400\n#define SQLITE_IOCAP_UNDELETABLE_WHEN_OPEN  0x00000800\n#define SQLITE_IOCAP_POWERSAFE_OVERWRITE    0x00001000\n#define SQLITE_IOCAP_IMMUTABLE              0x00002000\n#define SQLITE_IOCAP_BATCH_ATOMIC           0x00004000\n\n/*\n** CAPI3REF: File Locking Levels\n**\n** SQLite uses one of these integer values as the second\n** argument to calls it makes to the xLock() and xUnlock() methods\n** of an [sqlite3_io_methods] object.\n*/\n#define SQLITE_LOCK_NONE          0\n#define SQLITE_LOCK_SHARED        1\n#define SQLITE_LOCK_RESERVED      2\n#define SQLITE_LOCK_PENDING       3\n#define SQLITE_LOCK_EXCLUSIVE     4\n\n/*\n** CAPI3REF: Synchronization Type Flags\n**\n** When SQLite invokes the xSync() method of an\n** [sqlite3_io_methods] object it uses a combination of\n** these integer values as the second argument.\n**\n** When the SQLITE_SYNC_DATAONLY flag is used, it means that the\n** sync operation only needs to flush data to mass storage.  Inode\n** information need not be flushed. If the lower four bits of the flag\n** equal SQLITE_SYNC_NORMAL, that means to use normal fsync() semantics.\n** If the lower four bits equal SQLITE_SYNC_FULL, that means\n** to use Mac OS X style fullsync instead of fsync().\n**\n** Do not confuse the SQLITE_SYNC_NORMAL and SQLITE_SYNC_FULL flags\n** with the [PRAGMA synchronous]=NORMAL and [PRAGMA synchronous]=FULL\n** settings.  The [synchronous pragma] determines when calls to the\n** xSync VFS method occur and applies uniformly across all platforms.\n** The SQLITE_SYNC_NORMAL and SQLITE_SYNC_FULL flags determine how\n** energetic or rigorous or forceful the sync operations are and\n** only make a difference on Mac OSX for the default SQLite code.\n** (Third-party VFS implementations might also make the distinction\n** between SQLITE_SYNC_NORMAL and SQLITE_SYNC_FULL, but among the\n** operating systems natively supported by SQLite, only Mac OSX\n** cares about the difference.)\n*/\n#define SQLITE_SYNC_NORMAL        0x00002\n#define SQLITE_SYNC_FULL          0x00003\n#define SQLITE_SYNC_DATAONLY      0x00010\n\n/*\n** CAPI3REF: OS Interface Open File Handle\n**\n** An [sqlite3_file] object represents an open file in the \n** [sqlite3_vfs | OS interface layer].  Individual OS interface\n** implementations will\n** want to subclass this object by appending additional fields\n** for their own use.  The pMethods entry is a pointer to an\n** [sqlite3_io_methods] object that defines methods for performing\n** I/O operations on the open file.\n*/\ntypedef struct sqlite3_file sqlite3_file;\nstruct sqlite3_file {\n  const struct sqlite3_io_methods *pMethods;  /* Methods for an open file */\n};\n\n/*\n** CAPI3REF: OS Interface File Virtual Methods Object\n**\n** Every file opened by the [sqlite3_vfs.xOpen] method populates an\n** [sqlite3_file] object (or, more commonly, a subclass of the\n** [sqlite3_file] object) with a pointer to an instance of this object.\n** This object defines the methods used to perform various operations\n** against the open file represented by the [sqlite3_file] object.\n**\n** If the [sqlite3_vfs.xOpen] method sets the sqlite3_file.pMethods element \n** to a non-NULL pointer, then the sqlite3_io_methods.xClose method\n** may be invoked even if the [sqlite3_vfs.xOpen] reported that it failed.  The\n** only way to prevent a call to xClose following a failed [sqlite3_vfs.xOpen]\n** is for the [sqlite3_vfs.xOpen] to set the sqlite3_file.pMethods element\n** to NULL.\n**\n** The flags argument to xSync may be one of [SQLITE_SYNC_NORMAL] or\n** [SQLITE_SYNC_FULL].  The first choice is the normal fsync().\n** The second choice is a Mac OS X style fullsync.  The [SQLITE_SYNC_DATAONLY]\n** flag may be ORed in to indicate that only the data of the file\n** and not its inode needs to be synced.\n**\n** The integer values to xLock() and xUnlock() are one of\n** <ul>\n** <li> [SQLITE_LOCK_NONE],\n** <li> [SQLITE_LOCK_SHARED],\n** <li> [SQLITE_LOCK_RESERVED],\n** <li> [SQLITE_LOCK_PENDING], or\n** <li> [SQLITE_LOCK_EXCLUSIVE].\n** </ul>\n** xLock() increases the lock. xUnlock() decreases the lock.\n** The xCheckReservedLock() method checks whether any database connection,\n** either in this process or in some other process, is holding a RESERVED,\n** PENDING, or EXCLUSIVE lock on the file.  It returns true\n** if such a lock exists and false otherwise.\n**\n** The xFileControl() method is a generic interface that allows custom\n** VFS implementations to directly control an open file using the\n** [sqlite3_file_control()] interface.  The second \"op\" argument is an\n** integer opcode.  The third argument is a generic pointer intended to\n** point to a structure that may contain arguments or space in which to\n** write return values.  Potential uses for xFileControl() might be\n** functions to enable blocking locks with timeouts, to change the\n** locking strategy (for example to use dot-file locks), to inquire\n** about the status of a lock, or to break stale locks.  The SQLite\n** core reserves all opcodes less than 100 for its own use.\n** A [file control opcodes | list of opcodes] less than 100 is available.\n** Applications that define a custom xFileControl method should use opcodes\n** greater than 100 to avoid conflicts.  VFS implementations should\n** return [SQLITE_NOTFOUND] for file control opcodes that they do not\n** recognize.\n**\n** The xSectorSize() method returns the sector size of the\n** device that underlies the file.  The sector size is the\n** minimum write that can be performed without disturbing\n** other bytes in the file.  The xDeviceCharacteristics()\n** method returns a bit vector describing behaviors of the\n** underlying device:\n**\n** <ul>\n** <li> [SQLITE_IOCAP_ATOMIC]\n** <li> [SQLITE_IOCAP_ATOMIC512]\n** <li> [SQLITE_IOCAP_ATOMIC1K]\n** <li> [SQLITE_IOCAP_ATOMIC2K]\n** <li> [SQLITE_IOCAP_ATOMIC4K]\n** <li> [SQLITE_IOCAP_ATOMIC8K]\n** <li> [SQLITE_IOCAP_ATOMIC16K]\n** <li> [SQLITE_IOCAP_ATOMIC32K]\n** <li> [SQLITE_IOCAP_ATOMIC64K]\n** <li> [SQLITE_IOCAP_SAFE_APPEND]\n** <li> [SQLITE_IOCAP_SEQUENTIAL]\n** <li> [SQLITE_IOCAP_UNDELETABLE_WHEN_OPEN]\n** <li> [SQLITE_IOCAP_POWERSAFE_OVERWRITE]\n** <li> [SQLITE_IOCAP_IMMUTABLE]\n** <li> [SQLITE_IOCAP_BATCH_ATOMIC]\n** </ul>\n**\n** The SQLITE_IOCAP_ATOMIC property means that all writes of\n** any size are atomic.  The SQLITE_IOCAP_ATOMICnnn values\n** mean that writes of blocks that are nnn bytes in size and\n** are aligned to an address which is an integer multiple of\n** nnn are atomic.  The SQLITE_IOCAP_SAFE_APPEND value means\n** that when data is appended to a file, the data is appended\n** first then the size of the file is extended, never the other\n** way around.  The SQLITE_IOCAP_SEQUENTIAL property means that\n** information is written to disk in the same order as calls\n** to xWrite().\n**\n** If xRead() returns SQLITE_IOERR_SHORT_READ it must also fill\n** in the unread portions of the buffer with zeros.  A VFS that\n** fails to zero-fill short reads might seem to work.  However,\n** failure to zero-fill short reads will eventually lead to\n** database corruption.\n*/\ntypedef struct sqlite3_io_methods sqlite3_io_methods;\nstruct sqlite3_io_methods {\n  int iVersion;\n  int (*xClose)(sqlite3_file*);\n  int (*xRead)(sqlite3_file*, void*, int iAmt, sqlite3_int64 iOfst);\n  int (*xWrite)(sqlite3_file*, const void*, int iAmt, sqlite3_int64 iOfst);\n  int (*xTruncate)(sqlite3_file*, sqlite3_int64 size);\n  int (*xSync)(sqlite3_file*, int flags);\n  int (*xFileSize)(sqlite3_file*, sqlite3_int64 *pSize);\n  int (*xLock)(sqlite3_file*, int);\n  int (*xUnlock)(sqlite3_file*, int);\n  int (*xCheckReservedLock)(sqlite3_file*, int *pResOut);\n  int (*xFileControl)(sqlite3_file*, int op, void *pArg);\n  int (*xSectorSize)(sqlite3_file*);\n  int (*xDeviceCharacteristics)(sqlite3_file*);\n  /* Methods above are valid for version 1 */\n  int (*xShmMap)(sqlite3_file*, int iPg, int pgsz, int, void volatile**);\n  int (*xShmLock)(sqlite3_file*, int offset, int n, int flags);\n  void (*xShmBarrier)(sqlite3_file*);\n  int (*xShmUnmap)(sqlite3_file*, int deleteFlag);\n  /* Methods above are valid for version 2 */\n  int (*xFetch)(sqlite3_file*, sqlite3_int64 iOfst, int iAmt, void **pp);\n  int (*xUnfetch)(sqlite3_file*, sqlite3_int64 iOfst, void *p);\n  /* Methods above are valid for version 3 */\n  /* Additional methods may be added in future releases */\n};\n\n/*\n** CAPI3REF: Standard File Control Opcodes\n** KEYWORDS: {file control opcodes} {file control opcode}\n**\n** These integer constants are opcodes for the xFileControl method\n** of the [sqlite3_io_methods] object and for the [sqlite3_file_control()]\n** interface.\n**\n** <ul>\n** <li>[[SQLITE_FCNTL_LOCKSTATE]]\n** The [SQLITE_FCNTL_LOCKSTATE] opcode is used for debugging.  This\n** opcode causes the xFileControl method to write the current state of\n** the lock (one of [SQLITE_LOCK_NONE], [SQLITE_LOCK_SHARED],\n** [SQLITE_LOCK_RESERVED], [SQLITE_LOCK_PENDING], or [SQLITE_LOCK_EXCLUSIVE])\n** into an integer that the pArg argument points to. This capability\n** is used during testing and is only available when the SQLITE_TEST\n** compile-time option is used.\n**\n** <li>[[SQLITE_FCNTL_SIZE_HINT]]\n** The [SQLITE_FCNTL_SIZE_HINT] opcode is used by SQLite to give the VFS\n** layer a hint of how large the database file will grow to be during the\n** current transaction.  This hint is not guaranteed to be accurate but it\n** is often close.  The underlying VFS might choose to preallocate database\n** file space based on this hint in order to help writes to the database\n** file run faster.\n**\n** <li>[[SQLITE_FCNTL_CHUNK_SIZE]]\n** The [SQLITE_FCNTL_CHUNK_SIZE] opcode is used to request that the VFS\n** extends and truncates the database file in chunks of a size specified\n** by the user. The fourth argument to [sqlite3_file_control()] should \n** point to an integer (type int) containing the new chunk-size to use\n** for the nominated database. Allocating database file space in large\n** chunks (say 1MB at a time), may reduce file-system fragmentation and\n** improve performance on some systems.\n**\n** <li>[[SQLITE_FCNTL_FILE_POINTER]]\n** The [SQLITE_FCNTL_FILE_POINTER] opcode is used to obtain a pointer\n** to the [sqlite3_file] object associated with a particular database\n** connection.  See also [SQLITE_FCNTL_JOURNAL_POINTER].\n**\n** <li>[[SQLITE_FCNTL_JOURNAL_POINTER]]\n** The [SQLITE_FCNTL_JOURNAL_POINTER] opcode is used to obtain a pointer\n** to the [sqlite3_file] object associated with the journal file (either\n** the [rollback journal] or the [write-ahead log]) for a particular database\n** connection.  See also [SQLITE_FCNTL_FILE_POINTER].\n**\n** <li>[[SQLITE_FCNTL_SYNC_OMITTED]]\n** No longer in use.\n**\n** <li>[[SQLITE_FCNTL_SYNC]]\n** The [SQLITE_FCNTL_SYNC] opcode is generated internally by SQLite and\n** sent to the VFS immediately before the xSync method is invoked on a\n** database file descriptor. Or, if the xSync method is not invoked \n** because the user has configured SQLite with \n** [PRAGMA synchronous | PRAGMA synchronous=OFF] it is invoked in place \n** of the xSync method. In most cases, the pointer argument passed with\n** this file-control is NULL. However, if the database file is being synced\n** as part of a multi-database commit, the argument points to a nul-terminated\n** string containing the transactions master-journal file name. VFSes that \n** do not need this signal should silently ignore this opcode. Applications \n** should not call [sqlite3_file_control()] with this opcode as doing so may \n** disrupt the operation of the specialized VFSes that do require it.  \n**\n** <li>[[SQLITE_FCNTL_COMMIT_PHASETWO]]\n** The [SQLITE_FCNTL_COMMIT_PHASETWO] opcode is generated internally by SQLite\n** and sent to the VFS after a transaction has been committed immediately\n** but before the database is unlocked. VFSes that do not need this signal\n** should silently ignore this opcode. Applications should not call\n** [sqlite3_file_control()] with this opcode as doing so may disrupt the \n** operation of the specialized VFSes that do require it.  \n**\n** <li>[[SQLITE_FCNTL_WIN32_AV_RETRY]]\n** ^The [SQLITE_FCNTL_WIN32_AV_RETRY] opcode is used to configure automatic\n** retry counts and intervals for certain disk I/O operations for the\n** windows [VFS] in order to provide robustness in the presence of\n** anti-virus programs.  By default, the windows VFS will retry file read,\n** file write, and file delete operations up to 10 times, with a delay\n** of 25 milliseconds before the first retry and with the delay increasing\n** by an additional 25 milliseconds with each subsequent retry.  This\n** opcode allows these two values (10 retries and 25 milliseconds of delay)\n** to be adjusted.  The values are changed for all database connections\n** within the same process.  The argument is a pointer to an array of two\n** integers where the first integer is the new retry count and the second\n** integer is the delay.  If either integer is negative, then the setting\n** is not changed but instead the prior value of that setting is written\n** into the array entry, allowing the current retry settings to be\n** interrogated.  The zDbName parameter is ignored.\n**\n** <li>[[SQLITE_FCNTL_PERSIST_WAL]]\n** ^The [SQLITE_FCNTL_PERSIST_WAL] opcode is used to set or query the\n** persistent [WAL | Write Ahead Log] setting.  By default, the auxiliary\n** write ahead log and shared memory files used for transaction control\n** are automatically deleted when the latest connection to the database\n** closes.  Setting persistent WAL mode causes those files to persist after\n** close.  Persisting the files is useful when other processes that do not\n** have write permission on the directory containing the database file want\n** to read the database file, as the WAL and shared memory files must exist\n** in order for the database to be readable.  The fourth parameter to\n** [sqlite3_file_control()] for this opcode should be a pointer to an integer.\n** That integer is 0 to disable persistent WAL mode or 1 to enable persistent\n** WAL mode.  If the integer is -1, then it is overwritten with the current\n** WAL persistence setting.\n**\n** <li>[[SQLITE_FCNTL_POWERSAFE_OVERWRITE]]\n** ^The [SQLITE_FCNTL_POWERSAFE_OVERWRITE] opcode is used to set or query the\n** persistent \"powersafe-overwrite\" or \"PSOW\" setting.  The PSOW setting\n** determines the [SQLITE_IOCAP_POWERSAFE_OVERWRITE] bit of the\n** xDeviceCharacteristics methods. The fourth parameter to\n** [sqlite3_file_control()] for this opcode should be a pointer to an integer.\n** That integer is 0 to disable zero-damage mode or 1 to enable zero-damage\n** mode.  If the integer is -1, then it is overwritten with the current\n** zero-damage mode setting.\n**\n** <li>[[SQLITE_FCNTL_OVERWRITE]]\n** ^The [SQLITE_FCNTL_OVERWRITE] opcode is invoked by SQLite after opening\n** a write transaction to indicate that, unless it is rolled back for some\n** reason, the entire database file will be overwritten by the current \n** transaction. This is used by VACUUM operations.\n**\n** <li>[[SQLITE_FCNTL_VFSNAME]]\n** ^The [SQLITE_FCNTL_VFSNAME] opcode can be used to obtain the names of\n** all [VFSes] in the VFS stack.  The names are of all VFS shims and the\n** final bottom-level VFS are written into memory obtained from \n** [sqlite3_malloc()] and the result is stored in the char* variable\n** that the fourth parameter of [sqlite3_file_control()] points to.\n** The caller is responsible for freeing the memory when done.  As with\n** all file-control actions, there is no guarantee that this will actually\n** do anything.  Callers should initialize the char* variable to a NULL\n** pointer in case this file-control is not implemented.  This file-control\n** is intended for diagnostic use only.\n**\n** <li>[[SQLITE_FCNTL_VFS_POINTER]]\n** ^The [SQLITE_FCNTL_VFS_POINTER] opcode finds a pointer to the top-level\n** [VFSes] currently in use.  ^(The argument X in\n** sqlite3_file_control(db,SQLITE_FCNTL_VFS_POINTER,X) must be\n** of type \"[sqlite3_vfs] **\".  This opcodes will set *X\n** to a pointer to the top-level VFS.)^\n** ^When there are multiple VFS shims in the stack, this opcode finds the\n** upper-most shim only.\n**\n** <li>[[SQLITE_FCNTL_PRAGMA]]\n** ^Whenever a [PRAGMA] statement is parsed, an [SQLITE_FCNTL_PRAGMA] \n** file control is sent to the open [sqlite3_file] object corresponding\n** to the database file to which the pragma statement refers. ^The argument\n** to the [SQLITE_FCNTL_PRAGMA] file control is an array of\n** pointers to strings (char**) in which the second element of the array\n** is the name of the pragma and the third element is the argument to the\n** pragma or NULL if the pragma has no argument.  ^The handler for an\n** [SQLITE_FCNTL_PRAGMA] file control can optionally make the first element\n** of the char** argument point to a string obtained from [sqlite3_mprintf()]\n** or the equivalent and that string will become the result of the pragma or\n** the error message if the pragma fails. ^If the\n** [SQLITE_FCNTL_PRAGMA] file control returns [SQLITE_NOTFOUND], then normal \n** [PRAGMA] processing continues.  ^If the [SQLITE_FCNTL_PRAGMA]\n** file control returns [SQLITE_OK], then the parser assumes that the\n** VFS has handled the PRAGMA itself and the parser generates a no-op\n** prepared statement if result string is NULL, or that returns a copy\n** of the result string if the string is non-NULL.\n** ^If the [SQLITE_FCNTL_PRAGMA] file control returns\n** any result code other than [SQLITE_OK] or [SQLITE_NOTFOUND], that means\n** that the VFS encountered an error while handling the [PRAGMA] and the\n** compilation of the PRAGMA fails with an error.  ^The [SQLITE_FCNTL_PRAGMA]\n** file control occurs at the beginning of pragma statement analysis and so\n** it is able to override built-in [PRAGMA] statements.\n**\n** <li>[[SQLITE_FCNTL_BUSYHANDLER]]\n** ^The [SQLITE_FCNTL_BUSYHANDLER]\n** file-control may be invoked by SQLite on the database file handle\n** shortly after it is opened in order to provide a custom VFS with access\n** to the connections busy-handler callback. The argument is of type (void **)\n** - an array of two (void *) values. The first (void *) actually points\n** to a function of type (int (*)(void *)). In order to invoke the connections\n** busy-handler, this function should be invoked with the second (void *) in\n** the array as the only argument. If it returns non-zero, then the operation\n** should be retried. If it returns zero, the custom VFS should abandon the\n** current operation.\n**\n** <li>[[SQLITE_FCNTL_TEMPFILENAME]]\n** ^Application can invoke the [SQLITE_FCNTL_TEMPFILENAME] file-control\n** to have SQLite generate a\n** temporary filename using the same algorithm that is followed to generate\n** temporary filenames for TEMP tables and other internal uses.  The\n** argument should be a char** which will be filled with the filename\n** written into memory obtained from [sqlite3_malloc()].  The caller should\n** invoke [sqlite3_free()] on the result to avoid a memory leak.\n**\n** <li>[[SQLITE_FCNTL_MMAP_SIZE]]\n** The [SQLITE_FCNTL_MMAP_SIZE] file control is used to query or set the\n** maximum number of bytes that will be used for memory-mapped I/O.\n** The argument is a pointer to a value of type sqlite3_int64 that\n** is an advisory maximum number of bytes in the file to memory map.  The\n** pointer is overwritten with the old value.  The limit is not changed if\n** the value originally pointed to is negative, and so the current limit \n** can be queried by passing in a pointer to a negative number.  This\n** file-control is used internally to implement [PRAGMA mmap_size].\n**\n** <li>[[SQLITE_FCNTL_TRACE]]\n** The [SQLITE_FCNTL_TRACE] file control provides advisory information\n** to the VFS about what the higher layers of the SQLite stack are doing.\n** This file control is used by some VFS activity tracing [shims].\n** The argument is a zero-terminated string.  Higher layers in the\n** SQLite stack may generate instances of this file control if\n** the [SQLITE_USE_FCNTL_TRACE] compile-time option is enabled.\n**\n** <li>[[SQLITE_FCNTL_HAS_MOVED]]\n** The [SQLITE_FCNTL_HAS_MOVED] file control interprets its argument as a\n** pointer to an integer and it writes a boolean into that integer depending\n** on whether or not the file has been renamed, moved, or deleted since it\n** was first opened.\n**\n** <li>[[SQLITE_FCNTL_WIN32_GET_HANDLE]]\n** The [SQLITE_FCNTL_WIN32_GET_HANDLE] opcode can be used to obtain the\n** underlying native file handle associated with a file handle.  This file\n** control interprets its argument as a pointer to a native file handle and\n** writes the resulting value there.\n**\n** <li>[[SQLITE_FCNTL_WIN32_SET_HANDLE]]\n** The [SQLITE_FCNTL_WIN32_SET_HANDLE] opcode is used for debugging.  This\n** opcode causes the xFileControl method to swap the file handle with the one\n** pointed to by the pArg argument.  This capability is used during testing\n** and only needs to be supported when SQLITE_TEST is defined.\n**\n** <li>[[SQLITE_FCNTL_WAL_BLOCK]]\n** The [SQLITE_FCNTL_WAL_BLOCK] is a signal to the VFS layer that it might\n** be advantageous to block on the next WAL lock if the lock is not immediately\n** available.  The WAL subsystem issues this signal during rare\n** circumstances in order to fix a problem with priority inversion.\n** Applications should <em>not</em> use this file-control.\n**\n** <li>[[SQLITE_FCNTL_ZIPVFS]]\n** The [SQLITE_FCNTL_ZIPVFS] opcode is implemented by zipvfs only. All other\n** VFS should return SQLITE_NOTFOUND for this opcode.\n**\n** <li>[[SQLITE_FCNTL_RBU]]\n** The [SQLITE_FCNTL_RBU] opcode is implemented by the special VFS used by\n** the RBU extension only.  All other VFS should return SQLITE_NOTFOUND for\n** this opcode.  \n**\n** <li>[[SQLITE_FCNTL_BEGIN_ATOMIC_WRITE]]\n** If the [SQLITE_FCNTL_BEGIN_ATOMIC_WRITE] opcode returns SQLITE_OK, then\n** the file descriptor is placed in \"batch write mode\", which\n** means all subsequent write operations will be deferred and done\n** atomically at the next [SQLITE_FCNTL_COMMIT_ATOMIC_WRITE].  Systems\n** that do not support batch atomic writes will return SQLITE_NOTFOUND.\n** ^Following a successful SQLITE_FCNTL_BEGIN_ATOMIC_WRITE and prior to\n** the closing [SQLITE_FCNTL_COMMIT_ATOMIC_WRITE] or\n** [SQLITE_FCNTL_ROLLBACK_ATOMIC_WRITE], SQLite will make\n** no VFS interface calls on the same [sqlite3_file] file descriptor\n** except for calls to the xWrite method and the xFileControl method\n** with [SQLITE_FCNTL_SIZE_HINT].\n**\n** <li>[[SQLITE_FCNTL_COMMIT_ATOMIC_WRITE]]\n** The [SQLITE_FCNTL_COMMIT_ATOMIC_WRITE] opcode causes all write\n** operations since the previous successful call to \n** [SQLITE_FCNTL_BEGIN_ATOMIC_WRITE] to be performed atomically.\n** This file control returns [SQLITE_OK] if and only if the writes were\n** all performed successfully and have been committed to persistent storage.\n** ^Regardless of whether or not it is successful, this file control takes\n** the file descriptor out of batch write mode so that all subsequent\n** write operations are independent.\n** ^SQLite will never invoke SQLITE_FCNTL_COMMIT_ATOMIC_WRITE without\n** a prior successful call to [SQLITE_FCNTL_BEGIN_ATOMIC_WRITE].\n**\n** <li>[[SQLITE_FCNTL_ROLLBACK_ATOMIC_WRITE]]\n** The [SQLITE_FCNTL_ROLLBACK_ATOMIC_WRITE] opcode causes all write\n** operations since the previous successful call to \n** [SQLITE_FCNTL_BEGIN_ATOMIC_WRITE] to be rolled back.\n** ^This file control takes the file descriptor out of batch write mode\n** so that all subsequent write operations are independent.\n** ^SQLite will never invoke SQLITE_FCNTL_ROLLBACK_ATOMIC_WRITE without\n** a prior successful call to [SQLITE_FCNTL_BEGIN_ATOMIC_WRITE].\n** </ul>\n*/\n#define SQLITE_FCNTL_LOCKSTATE               1\n#define SQLITE_FCNTL_GET_LOCKPROXYFILE       2\n#define SQLITE_FCNTL_SET_LOCKPROXYFILE       3\n#define SQLITE_FCNTL_LAST_ERRNO              4\n#define SQLITE_FCNTL_SIZE_HINT               5\n#define SQLITE_FCNTL_CHUNK_SIZE              6\n#define SQLITE_FCNTL_FILE_POINTER            7\n#define SQLITE_FCNTL_SYNC_OMITTED            8\n#define SQLITE_FCNTL_WIN32_AV_RETRY          9\n#define SQLITE_FCNTL_PERSIST_WAL            10\n#define SQLITE_FCNTL_OVERWRITE              11\n#define SQLITE_FCNTL_VFSNAME                12\n#define SQLITE_FCNTL_POWERSAFE_OVERWRITE    13\n#define SQLITE_FCNTL_PRAGMA                 14\n#define SQLITE_FCNTL_BUSYHANDLER            15\n#define SQLITE_FCNTL_TEMPFILENAME           16\n#define SQLITE_FCNTL_MMAP_SIZE              18\n#define SQLITE_FCNTL_TRACE                  19\n#define SQLITE_FCNTL_HAS_MOVED              20\n#define SQLITE_FCNTL_SYNC                   21\n#define SQLITE_FCNTL_COMMIT_PHASETWO        22\n#define SQLITE_FCNTL_WIN32_SET_HANDLE       23\n#define SQLITE_FCNTL_WAL_BLOCK              24\n#define SQLITE_FCNTL_ZIPVFS                 25\n#define SQLITE_FCNTL_RBU                    26\n#define SQLITE_FCNTL_VFS_POINTER            27\n#define SQLITE_FCNTL_JOURNAL_POINTER        28\n#define SQLITE_FCNTL_WIN32_GET_HANDLE       29\n#define SQLITE_FCNTL_PDB                    30\n#define SQLITE_FCNTL_BEGIN_ATOMIC_WRITE     31\n#define SQLITE_FCNTL_COMMIT_ATOMIC_WRITE    32\n#define SQLITE_FCNTL_ROLLBACK_ATOMIC_WRITE  33\n\n/* deprecated names */\n#define SQLITE_GET_LOCKPROXYFILE      SQLITE_FCNTL_GET_LOCKPROXYFILE\n#define SQLITE_SET_LOCKPROXYFILE      SQLITE_FCNTL_SET_LOCKPROXYFILE\n#define SQLITE_LAST_ERRNO             SQLITE_FCNTL_LAST_ERRNO\n\n\n/*\n** CAPI3REF: Mutex Handle\n**\n** The mutex module within SQLite defines [sqlite3_mutex] to be an\n** abstract type for a mutex object.  The SQLite core never looks\n** at the internal representation of an [sqlite3_mutex].  It only\n** deals with pointers to the [sqlite3_mutex] object.\n**\n** Mutexes are created using [sqlite3_mutex_alloc()].\n*/\ntypedef struct sqlite3_mutex sqlite3_mutex;\n\n/*\n** CAPI3REF: Loadable Extension Thunk\n**\n** A pointer to the opaque sqlite3_api_routines structure is passed as\n** the third parameter to entry points of [loadable extensions].  This\n** structure must be typedefed in order to work around compiler warnings\n** on some platforms.\n*/\ntypedef struct sqlite3_api_routines sqlite3_api_routines;\n\n/*\n** CAPI3REF: OS Interface Object\n**\n** An instance of the sqlite3_vfs object defines the interface between\n** the SQLite core and the underlying operating system.  The \"vfs\"\n** in the name of the object stands for \"virtual file system\".  See\n** the [VFS | VFS documentation] for further information.\n**\n** The VFS interface is sometimes extended by adding new methods onto\n** the end.  Each time such an extension occurs, the iVersion field\n** is incremented.  The iVersion value started out as 1 in\n** SQLite [version 3.5.0] on [dateof:3.5.0], then increased to 2\n** with SQLite [version 3.7.0] on [dateof:3.7.0], and then increased\n** to 3 with SQLite [version 3.7.6] on [dateof:3.7.6].  Additional fields\n** may be appended to the sqlite3_vfs object and the iVersion value\n** may increase again in future versions of SQLite.\n** Note that the structure\n** of the sqlite3_vfs object changes in the transition from\n** SQLite [version 3.5.9] to [version 3.6.0] on [dateof:3.6.0]\n** and yet the iVersion field was not modified.\n**\n** The szOsFile field is the size of the subclassed [sqlite3_file]\n** structure used by this VFS.  mxPathname is the maximum length of\n** a pathname in this VFS.\n**\n** Registered sqlite3_vfs objects are kept on a linked list formed by\n** the pNext pointer.  The [sqlite3_vfs_register()]\n** and [sqlite3_vfs_unregister()] interfaces manage this list\n** in a thread-safe way.  The [sqlite3_vfs_find()] interface\n** searches the list.  Neither the application code nor the VFS\n** implementation should use the pNext pointer.\n**\n** The pNext field is the only field in the sqlite3_vfs\n** structure that SQLite will ever modify.  SQLite will only access\n** or modify this field while holding a particular static mutex.\n** The application should never modify anything within the sqlite3_vfs\n** object once the object has been registered.\n**\n** The zName field holds the name of the VFS module.  The name must\n** be unique across all VFS modules.\n**\n** [[sqlite3_vfs.xOpen]]\n** ^SQLite guarantees that the zFilename parameter to xOpen\n** is either a NULL pointer or string obtained\n** from xFullPathname() with an optional suffix added.\n** ^If a suffix is added to the zFilename parameter, it will\n** consist of a single \"-\" character followed by no more than\n** 11 alphanumeric and/or \"-\" characters.\n** ^SQLite further guarantees that\n** the string will be valid and unchanged until xClose() is\n** called. Because of the previous sentence,\n** the [sqlite3_file] can safely store a pointer to the\n** filename if it needs to remember the filename for some reason.\n** If the zFilename parameter to xOpen is a NULL pointer then xOpen\n** must invent its own temporary name for the file.  ^Whenever the \n** xFilename parameter is NULL it will also be the case that the\n** flags parameter will include [SQLITE_OPEN_DELETEONCLOSE].\n**\n** The flags argument to xOpen() includes all bits set in\n** the flags argument to [sqlite3_open_v2()].  Or if [sqlite3_open()]\n** or [sqlite3_open16()] is used, then flags includes at least\n** [SQLITE_OPEN_READWRITE] | [SQLITE_OPEN_CREATE]. \n** If xOpen() opens a file read-only then it sets *pOutFlags to\n** include [SQLITE_OPEN_READONLY].  Other bits in *pOutFlags may be set.\n**\n** ^(SQLite will also add one of the following flags to the xOpen()\n** call, depending on the object being opened:\n**\n** <ul>\n** <li>  [SQLITE_OPEN_MAIN_DB]\n** <li>  [SQLITE_OPEN_MAIN_JOURNAL]\n** <li>  [SQLITE_OPEN_TEMP_DB]\n** <li>  [SQLITE_OPEN_TEMP_JOURNAL]\n** <li>  [SQLITE_OPEN_TRANSIENT_DB]\n** <li>  [SQLITE_OPEN_SUBJOURNAL]\n** <li>  [SQLITE_OPEN_MASTER_JOURNAL]\n** <li>  [SQLITE_OPEN_WAL]\n** </ul>)^\n**\n** The file I/O implementation can use the object type flags to\n** change the way it deals with files.  For example, an application\n** that does not care about crash recovery or rollback might make\n** the open of a journal file a no-op.  Writes to this journal would\n** also be no-ops, and any attempt to read the journal would return\n** SQLITE_IOERR.  Or the implementation might recognize that a database\n** file will be doing page-aligned sector reads and writes in a random\n** order and set up its I/O subsystem accordingly.\n**\n** SQLite might also add one of the following flags to the xOpen method:\n**\n** <ul>\n** <li> [SQLITE_OPEN_DELETEONCLOSE]\n** <li> [SQLITE_OPEN_EXCLUSIVE]\n** </ul>\n**\n** The [SQLITE_OPEN_DELETEONCLOSE] flag means the file should be\n** deleted when it is closed.  ^The [SQLITE_OPEN_DELETEONCLOSE]\n** will be set for TEMP databases and their journals, transient\n** databases, and subjournals.\n**\n** ^The [SQLITE_OPEN_EXCLUSIVE] flag is always used in conjunction\n** with the [SQLITE_OPEN_CREATE] flag, which are both directly\n** analogous to the O_EXCL and O_CREAT flags of the POSIX open()\n** API.  The SQLITE_OPEN_EXCLUSIVE flag, when paired with the \n** SQLITE_OPEN_CREATE, is used to indicate that file should always\n** be created, and that it is an error if it already exists.\n** It is <i>not</i> used to indicate the file should be opened \n** for exclusive access.\n**\n** ^At least szOsFile bytes of memory are allocated by SQLite\n** to hold the  [sqlite3_file] structure passed as the third\n** argument to xOpen.  The xOpen method does not have to\n** allocate the structure; it should just fill it in.  Note that\n** the xOpen method must set the sqlite3_file.pMethods to either\n** a valid [sqlite3_io_methods] object or to NULL.  xOpen must do\n** this even if the open fails.  SQLite expects that the sqlite3_file.pMethods\n** element will be valid after xOpen returns regardless of the success\n** or failure of the xOpen call.\n**\n** [[sqlite3_vfs.xAccess]]\n** ^The flags argument to xAccess() may be [SQLITE_ACCESS_EXISTS]\n** to test for the existence of a file, or [SQLITE_ACCESS_READWRITE] to\n** test whether a file is readable and writable, or [SQLITE_ACCESS_READ]\n** to test whether a file is at least readable.   The file can be a\n** directory.\n**\n** ^SQLite will always allocate at least mxPathname+1 bytes for the\n** output buffer xFullPathname.  The exact size of the output buffer\n** is also passed as a parameter to both  methods. If the output buffer\n** is not large enough, [SQLITE_CANTOPEN] should be returned. Since this is\n** handled as a fatal error by SQLite, vfs implementations should endeavor\n** to prevent this by setting mxPathname to a sufficiently large value.\n**\n** The xRandomness(), xSleep(), xCurrentTime(), and xCurrentTimeInt64()\n** interfaces are not strictly a part of the filesystem, but they are\n** included in the VFS structure for completeness.\n** The xRandomness() function attempts to return nBytes bytes\n** of good-quality randomness into zOut.  The return value is\n** the actual number of bytes of randomness obtained.\n** The xSleep() method causes the calling thread to sleep for at\n** least the number of microseconds given.  ^The xCurrentTime()\n** method returns a Julian Day Number for the current date and time as\n** a floating point value.\n** ^The xCurrentTimeInt64() method returns, as an integer, the Julian\n** Day Number multiplied by 86400000 (the number of milliseconds in \n** a 24-hour day).  \n** ^SQLite will use the xCurrentTimeInt64() method to get the current\n** date and time if that method is available (if iVersion is 2 or \n** greater and the function pointer is not NULL) and will fall back\n** to xCurrentTime() if xCurrentTimeInt64() is unavailable.\n**\n** ^The xSetSystemCall(), xGetSystemCall(), and xNestSystemCall() interfaces\n** are not used by the SQLite core.  These optional interfaces are provided\n** by some VFSes to facilitate testing of the VFS code. By overriding \n** system calls with functions under its control, a test program can\n** simulate faults and error conditions that would otherwise be difficult\n** or impossible to induce.  The set of system calls that can be overridden\n** varies from one VFS to another, and from one version of the same VFS to the\n** next.  Applications that use these interfaces must be prepared for any\n** or all of these interfaces to be NULL or for their behavior to change\n** from one release to the next.  Applications must not attempt to access\n** any of these methods if the iVersion of the VFS is less than 3.\n*/\ntypedef struct sqlite3_vfs sqlite3_vfs;\ntypedef void (*sqlite3_syscall_ptr)(void);\nstruct sqlite3_vfs {\n  int iVersion;            /* Structure version number (currently 3) */\n  int szOsFile;            /* Size of subclassed sqlite3_file */\n  int mxPathname;          /* Maximum file pathname length */\n  sqlite3_vfs *pNext;      /* Next registered VFS */\n  const char *zName;       /* Name of this virtual file system */\n  void *pAppData;          /* Pointer to application-specific data */\n  int (*xOpen)(sqlite3_vfs*, const char *zName, sqlite3_file*,\n               int flags, int *pOutFlags);\n  int (*xDelete)(sqlite3_vfs*, const char *zName, int syncDir);\n  int (*xAccess)(sqlite3_vfs*, const char *zName, int flags, int *pResOut);\n  int (*xFullPathname)(sqlite3_vfs*, const char *zName, int nOut, char *zOut);\n  void *(*xDlOpen)(sqlite3_vfs*, const char *zFilename);\n  void (*xDlError)(sqlite3_vfs*, int nByte, char *zErrMsg);\n  void (*(*xDlSym)(sqlite3_vfs*,void*, const char *zSymbol))(void);\n  void (*xDlClose)(sqlite3_vfs*, void*);\n  int (*xRandomness)(sqlite3_vfs*, int nByte, char *zOut);\n  int (*xSleep)(sqlite3_vfs*, int microseconds);\n  int (*xCurrentTime)(sqlite3_vfs*, double*);\n  int (*xGetLastError)(sqlite3_vfs*, int, char *);\n  /*\n  ** The methods above are in version 1 of the sqlite_vfs object\n  ** definition.  Those that follow are added in version 2 or later\n  */\n  int (*xCurrentTimeInt64)(sqlite3_vfs*, sqlite3_int64*);\n  /*\n  ** The methods above are in versions 1 and 2 of the sqlite_vfs object.\n  ** Those below are for version 3 and greater.\n  */\n  int (*xSetSystemCall)(sqlite3_vfs*, const char *zName, sqlite3_syscall_ptr);\n  sqlite3_syscall_ptr (*xGetSystemCall)(sqlite3_vfs*, const char *zName);\n  const char *(*xNextSystemCall)(sqlite3_vfs*, const char *zName);\n  /*\n  ** The methods above are in versions 1 through 3 of the sqlite_vfs object.\n  ** New fields may be appended in future versions.  The iVersion\n  ** value will increment whenever this happens. \n  */\n};\n\n/*\n** CAPI3REF: Flags for the xAccess VFS method\n**\n** These integer constants can be used as the third parameter to\n** the xAccess method of an [sqlite3_vfs] object.  They determine\n** what kind of permissions the xAccess method is looking for.\n** With SQLITE_ACCESS_EXISTS, the xAccess method\n** simply checks whether the file exists.\n** With SQLITE_ACCESS_READWRITE, the xAccess method\n** checks whether the named directory is both readable and writable\n** (in other words, if files can be added, removed, and renamed within\n** the directory).\n** The SQLITE_ACCESS_READWRITE constant is currently used only by the\n** [temp_store_directory pragma], though this could change in a future\n** release of SQLite.\n** With SQLITE_ACCESS_READ, the xAccess method\n** checks whether the file is readable.  The SQLITE_ACCESS_READ constant is\n** currently unused, though it might be used in a future release of\n** SQLite.\n*/\n#define SQLITE_ACCESS_EXISTS    0\n#define SQLITE_ACCESS_READWRITE 1   /* Used by PRAGMA temp_store_directory */\n#define SQLITE_ACCESS_READ      2   /* Unused */\n\n/*\n** CAPI3REF: Flags for the xShmLock VFS method\n**\n** These integer constants define the various locking operations\n** allowed by the xShmLock method of [sqlite3_io_methods].  The\n** following are the only legal combinations of flags to the\n** xShmLock method:\n**\n** <ul>\n** <li>  SQLITE_SHM_LOCK | SQLITE_SHM_SHARED\n** <li>  SQLITE_SHM_LOCK | SQLITE_SHM_EXCLUSIVE\n** <li>  SQLITE_SHM_UNLOCK | SQLITE_SHM_SHARED\n** <li>  SQLITE_SHM_UNLOCK | SQLITE_SHM_EXCLUSIVE\n** </ul>\n**\n** When unlocking, the same SHARED or EXCLUSIVE flag must be supplied as\n** was given on the corresponding lock.  \n**\n** The xShmLock method can transition between unlocked and SHARED or\n** between unlocked and EXCLUSIVE.  It cannot transition between SHARED\n** and EXCLUSIVE.\n*/\n#define SQLITE_SHM_UNLOCK       1\n#define SQLITE_SHM_LOCK         2\n#define SQLITE_SHM_SHARED       4\n#define SQLITE_SHM_EXCLUSIVE    8\n\n/*\n** CAPI3REF: Maximum xShmLock index\n**\n** The xShmLock method on [sqlite3_io_methods] may use values\n** between 0 and this upper bound as its \"offset\" argument.\n** The SQLite core will never attempt to acquire or release a\n** lock outside of this range\n*/\n#define SQLITE_SHM_NLOCK        8\n\n\n/*\n** CAPI3REF: Initialize The SQLite Library\n**\n** ^The sqlite3_initialize() routine initializes the\n** SQLite library.  ^The sqlite3_shutdown() routine\n** deallocates any resources that were allocated by sqlite3_initialize().\n** These routines are designed to aid in process initialization and\n** shutdown on embedded systems.  Workstation applications using\n** SQLite normally do not need to invoke either of these routines.\n**\n** A call to sqlite3_initialize() is an \"effective\" call if it is\n** the first time sqlite3_initialize() is invoked during the lifetime of\n** the process, or if it is the first time sqlite3_initialize() is invoked\n** following a call to sqlite3_shutdown().  ^(Only an effective call\n** of sqlite3_initialize() does any initialization.  All other calls\n** are harmless no-ops.)^\n**\n** A call to sqlite3_shutdown() is an \"effective\" call if it is the first\n** call to sqlite3_shutdown() since the last sqlite3_initialize().  ^(Only\n** an effective call to sqlite3_shutdown() does any deinitialization.\n** All other valid calls to sqlite3_shutdown() are harmless no-ops.)^\n**\n** The sqlite3_initialize() interface is threadsafe, but sqlite3_shutdown()\n** is not.  The sqlite3_shutdown() interface must only be called from a\n** single thread.  All open [database connections] must be closed and all\n** other SQLite resources must be deallocated prior to invoking\n** sqlite3_shutdown().\n**\n** Among other things, ^sqlite3_initialize() will invoke\n** sqlite3_os_init().  Similarly, ^sqlite3_shutdown()\n** will invoke sqlite3_os_end().\n**\n** ^The sqlite3_initialize() routine returns [SQLITE_OK] on success.\n** ^If for some reason, sqlite3_initialize() is unable to initialize\n** the library (perhaps it is unable to allocate a needed resource such\n** as a mutex) it returns an [error code] other than [SQLITE_OK].\n**\n** ^The sqlite3_initialize() routine is called internally by many other\n** SQLite interfaces so that an application usually does not need to\n** invoke sqlite3_initialize() directly.  For example, [sqlite3_open()]\n** calls sqlite3_initialize() so the SQLite library will be automatically\n** initialized when [sqlite3_open()] is called if it has not be initialized\n** already.  ^However, if SQLite is compiled with the [SQLITE_OMIT_AUTOINIT]\n** compile-time option, then the automatic calls to sqlite3_initialize()\n** are omitted and the application must call sqlite3_initialize() directly\n** prior to using any other SQLite interface.  For maximum portability,\n** it is recommended that applications always invoke sqlite3_initialize()\n** directly prior to using any other SQLite interface.  Future releases\n** of SQLite may require this.  In other words, the behavior exhibited\n** when SQLite is compiled with [SQLITE_OMIT_AUTOINIT] might become the\n** default behavior in some future release of SQLite.\n**\n** The sqlite3_os_init() routine does operating-system specific\n** initialization of the SQLite library.  The sqlite3_os_end()\n** routine undoes the effect of sqlite3_os_init().  Typical tasks\n** performed by these routines include allocation or deallocation\n** of static resources, initialization of global variables,\n** setting up a default [sqlite3_vfs] module, or setting up\n** a default configuration using [sqlite3_config()].\n**\n** The application should never invoke either sqlite3_os_init()\n** or sqlite3_os_end() directly.  The application should only invoke\n** sqlite3_initialize() and sqlite3_shutdown().  The sqlite3_os_init()\n** interface is called automatically by sqlite3_initialize() and\n** sqlite3_os_end() is called by sqlite3_shutdown().  Appropriate\n** implementations for sqlite3_os_init() and sqlite3_os_end()\n** are built into SQLite when it is compiled for Unix, Windows, or OS/2.\n** When [custom builds | built for other platforms]\n** (using the [SQLITE_OS_OTHER=1] compile-time\n** option) the application must supply a suitable implementation for\n** sqlite3_os_init() and sqlite3_os_end().  An application-supplied\n** implementation of sqlite3_os_init() or sqlite3_os_end()\n** must return [SQLITE_OK] on success and some other [error code] upon\n** failure.\n*/\nSQLITE_API int sqlite3_initialize(void);\nSQLITE_API int sqlite3_shutdown(void);\nSQLITE_API int sqlite3_os_init(void);\nSQLITE_API int sqlite3_os_end(void);\n\n/*\n** CAPI3REF: Configuring The SQLite Library\n**\n** The sqlite3_config() interface is used to make global configuration\n** changes to SQLite in order to tune SQLite to the specific needs of\n** the application.  The default configuration is recommended for most\n** applications and so this routine is usually not necessary.  It is\n** provided to support rare applications with unusual needs.\n**\n** <b>The sqlite3_config() interface is not threadsafe. The application\n** must ensure that no other SQLite interfaces are invoked by other\n** threads while sqlite3_config() is running.</b>\n**\n** The sqlite3_config() interface\n** may only be invoked prior to library initialization using\n** [sqlite3_initialize()] or after shutdown by [sqlite3_shutdown()].\n** ^If sqlite3_config() is called after [sqlite3_initialize()] and before\n** [sqlite3_shutdown()] then it will return SQLITE_MISUSE.\n** Note, however, that ^sqlite3_config() can be called as part of the\n** implementation of an application-defined [sqlite3_os_init()].\n**\n** The first argument to sqlite3_config() is an integer\n** [configuration option] that determines\n** what property of SQLite is to be configured.  Subsequent arguments\n** vary depending on the [configuration option]\n** in the first argument.\n**\n** ^When a configuration option is set, sqlite3_config() returns [SQLITE_OK].\n** ^If the option is unknown or SQLite is unable to set the option\n** then this routine returns a non-zero [error code].\n*/\nSQLITE_API int sqlite3_config(int, ...);\n\n/*\n** CAPI3REF: Configure database connections\n** METHOD: sqlite3\n**\n** The sqlite3_db_config() interface is used to make configuration\n** changes to a [database connection].  The interface is similar to\n** [sqlite3_config()] except that the changes apply to a single\n** [database connection] (specified in the first argument).\n**\n** The second argument to sqlite3_db_config(D,V,...)  is the\n** [SQLITE_DBCONFIG_LOOKASIDE | configuration verb] - an integer code \n** that indicates what aspect of the [database connection] is being configured.\n** Subsequent arguments vary depending on the configuration verb.\n**\n** ^Calls to sqlite3_db_config() return SQLITE_OK if and only if\n** the call is considered successful.\n*/\nSQLITE_API int sqlite3_db_config(sqlite3*, int op, ...);\n\n/*\n** CAPI3REF: Memory Allocation Routines\n**\n** An instance of this object defines the interface between SQLite\n** and low-level memory allocation routines.\n**\n** This object is used in only one place in the SQLite interface.\n** A pointer to an instance of this object is the argument to\n** [sqlite3_config()] when the configuration option is\n** [SQLITE_CONFIG_MALLOC] or [SQLITE_CONFIG_GETMALLOC].  \n** By creating an instance of this object\n** and passing it to [sqlite3_config]([SQLITE_CONFIG_MALLOC])\n** during configuration, an application can specify an alternative\n** memory allocation subsystem for SQLite to use for all of its\n** dynamic memory needs.\n**\n** Note that SQLite comes with several [built-in memory allocators]\n** that are perfectly adequate for the overwhelming majority of applications\n** and that this object is only useful to a tiny minority of applications\n** with specialized memory allocation requirements.  This object is\n** also used during testing of SQLite in order to specify an alternative\n** memory allocator that simulates memory out-of-memory conditions in\n** order to verify that SQLite recovers gracefully from such\n** conditions.\n**\n** The xMalloc, xRealloc, and xFree methods must work like the\n** malloc(), realloc() and free() functions from the standard C library.\n** ^SQLite guarantees that the second argument to\n** xRealloc is always a value returned by a prior call to xRoundup.\n**\n** xSize should return the allocated size of a memory allocation\n** previously obtained from xMalloc or xRealloc.  The allocated size\n** is always at least as big as the requested size but may be larger.\n**\n** The xRoundup method returns what would be the allocated size of\n** a memory allocation given a particular requested size.  Most memory\n** allocators round up memory allocations at least to the next multiple\n** of 8.  Some allocators round up to a larger multiple or to a power of 2.\n** Every memory allocation request coming in through [sqlite3_malloc()]\n** or [sqlite3_realloc()] first calls xRoundup.  If xRoundup returns 0, \n** that causes the corresponding memory allocation to fail.\n**\n** The xInit method initializes the memory allocator.  For example,\n** it might allocate any require mutexes or initialize internal data\n** structures.  The xShutdown method is invoked (indirectly) by\n** [sqlite3_shutdown()] and should deallocate any resources acquired\n** by xInit.  The pAppData pointer is used as the only parameter to\n** xInit and xShutdown.\n**\n** SQLite holds the [SQLITE_MUTEX_STATIC_MASTER] mutex when it invokes\n** the xInit method, so the xInit method need not be threadsafe.  The\n** xShutdown method is only called from [sqlite3_shutdown()] so it does\n** not need to be threadsafe either.  For all other methods, SQLite\n** holds the [SQLITE_MUTEX_STATIC_MEM] mutex as long as the\n** [SQLITE_CONFIG_MEMSTATUS] configuration option is turned on (which\n** it is by default) and so the methods are automatically serialized.\n** However, if [SQLITE_CONFIG_MEMSTATUS] is disabled, then the other\n** methods must be threadsafe or else make their own arrangements for\n** serialization.\n**\n** SQLite will never invoke xInit() more than once without an intervening\n** call to xShutdown().\n*/\ntypedef struct sqlite3_mem_methods sqlite3_mem_methods;\nstruct sqlite3_mem_methods {\n  void *(*xMalloc)(int);         /* Memory allocation function */\n  void (*xFree)(void*);          /* Free a prior allocation */\n  void *(*xRealloc)(void*,int);  /* Resize an allocation */\n  int (*xSize)(void*);           /* Return the size of an allocation */\n  int (*xRoundup)(int);          /* Round up request size to allocation size */\n  int (*xInit)(void*);           /* Initialize the memory allocator */\n  void (*xShutdown)(void*);      /* Deinitialize the memory allocator */\n  void *pAppData;                /* Argument to xInit() and xShutdown() */\n};\n\n/*\n** CAPI3REF: Configuration Options\n** KEYWORDS: {configuration option}\n**\n** These constants are the available integer configuration options that\n** can be passed as the first argument to the [sqlite3_config()] interface.\n**\n** New configuration options may be added in future releases of SQLite.\n** Existing configuration options might be discontinued.  Applications\n** should check the return code from [sqlite3_config()] to make sure that\n** the call worked.  The [sqlite3_config()] interface will return a\n** non-zero [error code] if a discontinued or unsupported configuration option\n** is invoked.\n**\n** <dl>\n** [[SQLITE_CONFIG_SINGLETHREAD]] <dt>SQLITE_CONFIG_SINGLETHREAD</dt>\n** <dd>There are no arguments to this option.  ^This option sets the\n** [threading mode] to Single-thread.  In other words, it disables\n** all mutexing and puts SQLite into a mode where it can only be used\n** by a single thread.   ^If SQLite is compiled with\n** the [SQLITE_THREADSAFE | SQLITE_THREADSAFE=0] compile-time option then\n** it is not possible to change the [threading mode] from its default\n** value of Single-thread and so [sqlite3_config()] will return \n** [SQLITE_ERROR] if called with the SQLITE_CONFIG_SINGLETHREAD\n** configuration option.</dd>\n**\n** [[SQLITE_CONFIG_MULTITHREAD]] <dt>SQLITE_CONFIG_MULTITHREAD</dt>\n** <dd>There are no arguments to this option.  ^This option sets the\n** [threading mode] to Multi-thread.  In other words, it disables\n** mutexing on [database connection] and [prepared statement] objects.\n** The application is responsible for serializing access to\n** [database connections] and [prepared statements].  But other mutexes\n** are enabled so that SQLite will be safe to use in a multi-threaded\n** environment as long as no two threads attempt to use the same\n** [database connection] at the same time.  ^If SQLite is compiled with\n** the [SQLITE_THREADSAFE | SQLITE_THREADSAFE=0] compile-time option then\n** it is not possible to set the Multi-thread [threading mode] and\n** [sqlite3_config()] will return [SQLITE_ERROR] if called with the\n** SQLITE_CONFIG_MULTITHREAD configuration option.</dd>\n**\n** [[SQLITE_CONFIG_SERIALIZED]] <dt>SQLITE_CONFIG_SERIALIZED</dt>\n** <dd>There are no arguments to this option.  ^This option sets the\n** [threading mode] to Serialized. In other words, this option enables\n** all mutexes including the recursive\n** mutexes on [database connection] and [prepared statement] objects.\n** In this mode (which is the default when SQLite is compiled with\n** [SQLITE_THREADSAFE=1]) the SQLite library will itself serialize access\n** to [database connections] and [prepared statements] so that the\n** application is free to use the same [database connection] or the\n** same [prepared statement] in different threads at the same time.\n** ^If SQLite is compiled with\n** the [SQLITE_THREADSAFE | SQLITE_THREADSAFE=0] compile-time option then\n** it is not possible to set the Serialized [threading mode] and\n** [sqlite3_config()] will return [SQLITE_ERROR] if called with the\n** SQLITE_CONFIG_SERIALIZED configuration option.</dd>\n**\n** [[SQLITE_CONFIG_MALLOC]] <dt>SQLITE_CONFIG_MALLOC</dt>\n** <dd> ^(The SQLITE_CONFIG_MALLOC option takes a single argument which is \n** a pointer to an instance of the [sqlite3_mem_methods] structure.\n** The argument specifies\n** alternative low-level memory allocation routines to be used in place of\n** the memory allocation routines built into SQLite.)^ ^SQLite makes\n** its own private copy of the content of the [sqlite3_mem_methods] structure\n** before the [sqlite3_config()] call returns.</dd>\n**\n** [[SQLITE_CONFIG_GETMALLOC]] <dt>SQLITE_CONFIG_GETMALLOC</dt>\n** <dd> ^(The SQLITE_CONFIG_GETMALLOC option takes a single argument which\n** is a pointer to an instance of the [sqlite3_mem_methods] structure.\n** The [sqlite3_mem_methods]\n** structure is filled with the currently defined memory allocation routines.)^\n** This option can be used to overload the default memory allocation\n** routines with a wrapper that simulations memory allocation failure or\n** tracks memory usage, for example. </dd>\n**\n** [[SQLITE_CONFIG_SMALL_MALLOC]] <dt>SQLITE_CONFIG_SMALL_MALLOC</dt>\n** <dd> ^The SQLITE_CONFIG_SMALL_MALLOC option takes single argument of\n** type int, interpreted as a boolean, which if true provides a hint to\n** SQLite that it should avoid large memory allocations if possible.\n** SQLite will run faster if it is free to make large memory allocations,\n** but some application might prefer to run slower in exchange for\n** guarantees about memory fragmentation that are possible if large\n** allocations are avoided.  This hint is normally off.\n** </dd>\n**\n** [[SQLITE_CONFIG_MEMSTATUS]] <dt>SQLITE_CONFIG_MEMSTATUS</dt>\n** <dd> ^The SQLITE_CONFIG_MEMSTATUS option takes single argument of type int,\n** interpreted as a boolean, which enables or disables the collection of\n** memory allocation statistics. ^(When memory allocation statistics are\n** disabled, the following SQLite interfaces become non-operational:\n**   <ul>\n**   <li> [sqlite3_memory_used()]\n**   <li> [sqlite3_memory_highwater()]\n**   <li> [sqlite3_soft_heap_limit64()]\n**   <li> [sqlite3_status64()]\n**   </ul>)^\n** ^Memory allocation statistics are enabled by default unless SQLite is\n** compiled with [SQLITE_DEFAULT_MEMSTATUS]=0 in which case memory\n** allocation statistics are disabled by default.\n** </dd>\n**\n** [[SQLITE_CONFIG_SCRATCH]] <dt>SQLITE_CONFIG_SCRATCH</dt>\n** <dd> The SQLITE_CONFIG_SCRATCH option is no longer used.\n** </dd>\n**\n** [[SQLITE_CONFIG_PAGECACHE]] <dt>SQLITE_CONFIG_PAGECACHE</dt>\n** <dd> ^The SQLITE_CONFIG_PAGECACHE option specifies a memory pool\n** that SQLite can use for the database page cache with the default page\n** cache implementation.  \n** This configuration option is a no-op if an application-define page\n** cache implementation is loaded using the [SQLITE_CONFIG_PCACHE2].\n** ^There are three arguments to SQLITE_CONFIG_PAGECACHE: A pointer to\n** 8-byte aligned memory (pMem), the size of each page cache line (sz),\n** and the number of cache lines (N).\n** The sz argument should be the size of the largest database page\n** (a power of two between 512 and 65536) plus some extra bytes for each\n** page header.  ^The number of extra bytes needed by the page header\n** can be determined using [SQLITE_CONFIG_PCACHE_HDRSZ].\n** ^It is harmless, apart from the wasted memory,\n** for the sz parameter to be larger than necessary.  The pMem\n** argument must be either a NULL pointer or a pointer to an 8-byte\n** aligned block of memory of at least sz*N bytes, otherwise\n** subsequent behavior is undefined.\n** ^When pMem is not NULL, SQLite will strive to use the memory provided\n** to satisfy page cache needs, falling back to [sqlite3_malloc()] if\n** a page cache line is larger than sz bytes or if all of the pMem buffer\n** is exhausted.\n** ^If pMem is NULL and N is non-zero, then each database connection\n** does an initial bulk allocation for page cache memory\n** from [sqlite3_malloc()] sufficient for N cache lines if N is positive or\n** of -1024*N bytes if N is negative, . ^If additional\n** page cache memory is needed beyond what is provided by the initial\n** allocation, then SQLite goes to [sqlite3_malloc()] separately for each\n** additional cache line. </dd>\n**\n** [[SQLITE_CONFIG_HEAP]] <dt>SQLITE_CONFIG_HEAP</dt>\n** <dd> ^The SQLITE_CONFIG_HEAP option specifies a static memory buffer \n** that SQLite will use for all of its dynamic memory allocation needs\n** beyond those provided for by [SQLITE_CONFIG_PAGECACHE].\n** ^The SQLITE_CONFIG_HEAP option is only available if SQLite is compiled\n** with either [SQLITE_ENABLE_MEMSYS3] or [SQLITE_ENABLE_MEMSYS5] and returns\n** [SQLITE_ERROR] if invoked otherwise.\n** ^There are three arguments to SQLITE_CONFIG_HEAP:\n** An 8-byte aligned pointer to the memory,\n** the number of bytes in the memory buffer, and the minimum allocation size.\n** ^If the first pointer (the memory pointer) is NULL, then SQLite reverts\n** to using its default memory allocator (the system malloc() implementation),\n** undoing any prior invocation of [SQLITE_CONFIG_MALLOC].  ^If the\n** memory pointer is not NULL then the alternative memory\n** allocator is engaged to handle all of SQLites memory allocation needs.\n** The first pointer (the memory pointer) must be aligned to an 8-byte\n** boundary or subsequent behavior of SQLite will be undefined.\n** The minimum allocation size is capped at 2**12. Reasonable values\n** for the minimum allocation size are 2**5 through 2**8.</dd>\n**\n** [[SQLITE_CONFIG_MUTEX]] <dt>SQLITE_CONFIG_MUTEX</dt>\n** <dd> ^(The SQLITE_CONFIG_MUTEX option takes a single argument which is a\n** pointer to an instance of the [sqlite3_mutex_methods] structure.\n** The argument specifies alternative low-level mutex routines to be used\n** in place the mutex routines built into SQLite.)^  ^SQLite makes a copy of\n** the content of the [sqlite3_mutex_methods] structure before the call to\n** [sqlite3_config()] returns. ^If SQLite is compiled with\n** the [SQLITE_THREADSAFE | SQLITE_THREADSAFE=0] compile-time option then\n** the entire mutexing subsystem is omitted from the build and hence calls to\n** [sqlite3_config()] with the SQLITE_CONFIG_MUTEX configuration option will\n** return [SQLITE_ERROR].</dd>\n**\n** [[SQLITE_CONFIG_GETMUTEX]] <dt>SQLITE_CONFIG_GETMUTEX</dt>\n** <dd> ^(The SQLITE_CONFIG_GETMUTEX option takes a single argument which\n** is a pointer to an instance of the [sqlite3_mutex_methods] structure.  The\n** [sqlite3_mutex_methods]\n** structure is filled with the currently defined mutex routines.)^\n** This option can be used to overload the default mutex allocation\n** routines with a wrapper used to track mutex usage for performance\n** profiling or testing, for example.   ^If SQLite is compiled with\n** the [SQLITE_THREADSAFE | SQLITE_THREADSAFE=0] compile-time option then\n** the entire mutexing subsystem is omitted from the build and hence calls to\n** [sqlite3_config()] with the SQLITE_CONFIG_GETMUTEX configuration option will\n** return [SQLITE_ERROR].</dd>\n**\n** [[SQLITE_CONFIG_LOOKASIDE]] <dt>SQLITE_CONFIG_LOOKASIDE</dt>\n** <dd> ^(The SQLITE_CONFIG_LOOKASIDE option takes two arguments that determine\n** the default size of lookaside memory on each [database connection].\n** The first argument is the\n** size of each lookaside buffer slot and the second is the number of\n** slots allocated to each database connection.)^  ^(SQLITE_CONFIG_LOOKASIDE\n** sets the <i>default</i> lookaside size. The [SQLITE_DBCONFIG_LOOKASIDE]\n** option to [sqlite3_db_config()] can be used to change the lookaside\n** configuration on individual connections.)^ </dd>\n**\n** [[SQLITE_CONFIG_PCACHE2]] <dt>SQLITE_CONFIG_PCACHE2</dt>\n** <dd> ^(The SQLITE_CONFIG_PCACHE2 option takes a single argument which is \n** a pointer to an [sqlite3_pcache_methods2] object.  This object specifies\n** the interface to a custom page cache implementation.)^\n** ^SQLite makes a copy of the [sqlite3_pcache_methods2] object.</dd>\n**\n** [[SQLITE_CONFIG_GETPCACHE2]] <dt>SQLITE_CONFIG_GETPCACHE2</dt>\n** <dd> ^(The SQLITE_CONFIG_GETPCACHE2 option takes a single argument which\n** is a pointer to an [sqlite3_pcache_methods2] object.  SQLite copies of\n** the current page cache implementation into that object.)^ </dd>\n**\n** [[SQLITE_CONFIG_LOG]] <dt>SQLITE_CONFIG_LOG</dt>\n** <dd> The SQLITE_CONFIG_LOG option is used to configure the SQLite\n** global [error log].\n** (^The SQLITE_CONFIG_LOG option takes two arguments: a pointer to a\n** function with a call signature of void(*)(void*,int,const char*), \n** and a pointer to void. ^If the function pointer is not NULL, it is\n** invoked by [sqlite3_log()] to process each logging event.  ^If the\n** function pointer is NULL, the [sqlite3_log()] interface becomes a no-op.\n** ^The void pointer that is the second argument to SQLITE_CONFIG_LOG is\n** passed through as the first parameter to the application-defined logger\n** function whenever that function is invoked.  ^The second parameter to\n** the logger function is a copy of the first parameter to the corresponding\n** [sqlite3_log()] call and is intended to be a [result code] or an\n** [extended result code].  ^The third parameter passed to the logger is\n** log message after formatting via [sqlite3_snprintf()].\n** The SQLite logging interface is not reentrant; the logger function\n** supplied by the application must not invoke any SQLite interface.\n** In a multi-threaded application, the application-defined logger\n** function must be threadsafe. </dd>\n**\n** [[SQLITE_CONFIG_URI]] <dt>SQLITE_CONFIG_URI\n** <dd>^(The SQLITE_CONFIG_URI option takes a single argument of type int.\n** If non-zero, then URI handling is globally enabled. If the parameter is zero,\n** then URI handling is globally disabled.)^ ^If URI handling is globally\n** enabled, all filenames passed to [sqlite3_open()], [sqlite3_open_v2()],\n** [sqlite3_open16()] or\n** specified as part of [ATTACH] commands are interpreted as URIs, regardless\n** of whether or not the [SQLITE_OPEN_URI] flag is set when the database\n** connection is opened. ^If it is globally disabled, filenames are\n** only interpreted as URIs if the SQLITE_OPEN_URI flag is set when the\n** database connection is opened. ^(By default, URI handling is globally\n** disabled. The default value may be changed by compiling with the\n** [SQLITE_USE_URI] symbol defined.)^\n**\n** [[SQLITE_CONFIG_COVERING_INDEX_SCAN]] <dt>SQLITE_CONFIG_COVERING_INDEX_SCAN\n** <dd>^The SQLITE_CONFIG_COVERING_INDEX_SCAN option takes a single integer\n** argument which is interpreted as a boolean in order to enable or disable\n** the use of covering indices for full table scans in the query optimizer.\n** ^The default setting is determined\n** by the [SQLITE_ALLOW_COVERING_INDEX_SCAN] compile-time option, or is \"on\"\n** if that compile-time option is omitted.\n** The ability to disable the use of covering indices for full table scans\n** is because some incorrectly coded legacy applications might malfunction\n** when the optimization is enabled.  Providing the ability to\n** disable the optimization allows the older, buggy application code to work\n** without change even with newer versions of SQLite.\n**\n** [[SQLITE_CONFIG_PCACHE]] [[SQLITE_CONFIG_GETPCACHE]]\n** <dt>SQLITE_CONFIG_PCACHE and SQLITE_CONFIG_GETPCACHE\n** <dd> These options are obsolete and should not be used by new code.\n** They are retained for backwards compatibility but are now no-ops.\n** </dd>\n**\n** [[SQLITE_CONFIG_SQLLOG]]\n** <dt>SQLITE_CONFIG_SQLLOG\n** <dd>This option is only available if sqlite is compiled with the\n** [SQLITE_ENABLE_SQLLOG] pre-processor macro defined. The first argument should\n** be a pointer to a function of type void(*)(void*,sqlite3*,const char*, int).\n** The second should be of type (void*). The callback is invoked by the library\n** in three separate circumstances, identified by the value passed as the\n** fourth parameter. If the fourth parameter is 0, then the database connection\n** passed as the second argument has just been opened. The third argument\n** points to a buffer containing the name of the main database file. If the\n** fourth parameter is 1, then the SQL statement that the third parameter\n** points to has just been executed. Or, if the fourth parameter is 2, then\n** the connection being passed as the second parameter is being closed. The\n** third parameter is passed NULL In this case.  An example of using this\n** configuration option can be seen in the \"test_sqllog.c\" source file in\n** the canonical SQLite source tree.</dd>\n**\n** [[SQLITE_CONFIG_MMAP_SIZE]]\n** <dt>SQLITE_CONFIG_MMAP_SIZE\n** <dd>^SQLITE_CONFIG_MMAP_SIZE takes two 64-bit integer (sqlite3_int64) values\n** that are the default mmap size limit (the default setting for\n** [PRAGMA mmap_size]) and the maximum allowed mmap size limit.\n** ^The default setting can be overridden by each database connection using\n** either the [PRAGMA mmap_size] command, or by using the\n** [SQLITE_FCNTL_MMAP_SIZE] file control.  ^(The maximum allowed mmap size\n** will be silently truncated if necessary so that it does not exceed the\n** compile-time maximum mmap size set by the\n** [SQLITE_MAX_MMAP_SIZE] compile-time option.)^\n** ^If either argument to this option is negative, then that argument is\n** changed to its compile-time default.\n**\n** [[SQLITE_CONFIG_WIN32_HEAPSIZE]]\n** <dt>SQLITE_CONFIG_WIN32_HEAPSIZE\n** <dd>^The SQLITE_CONFIG_WIN32_HEAPSIZE option is only available if SQLite is\n** compiled for Windows with the [SQLITE_WIN32_MALLOC] pre-processor macro\n** defined. ^SQLITE_CONFIG_WIN32_HEAPSIZE takes a 32-bit unsigned integer value\n** that specifies the maximum size of the created heap.\n**\n** [[SQLITE_CONFIG_PCACHE_HDRSZ]]\n** <dt>SQLITE_CONFIG_PCACHE_HDRSZ\n** <dd>^The SQLITE_CONFIG_PCACHE_HDRSZ option takes a single parameter which\n** is a pointer to an integer and writes into that integer the number of extra\n** bytes per page required for each page in [SQLITE_CONFIG_PAGECACHE].\n** The amount of extra space required can change depending on the compiler,\n** target platform, and SQLite version.\n**\n** [[SQLITE_CONFIG_PMASZ]]\n** <dt>SQLITE_CONFIG_PMASZ\n** <dd>^The SQLITE_CONFIG_PMASZ option takes a single parameter which\n** is an unsigned integer and sets the \"Minimum PMA Size\" for the multithreaded\n** sorter to that integer.  The default minimum PMA Size is set by the\n** [SQLITE_SORTER_PMASZ] compile-time option.  New threads are launched\n** to help with sort operations when multithreaded sorting\n** is enabled (using the [PRAGMA threads] command) and the amount of content\n** to be sorted exceeds the page size times the minimum of the\n** [PRAGMA cache_size] setting and this value.\n**\n** [[SQLITE_CONFIG_STMTJRNL_SPILL]]\n** <dt>SQLITE_CONFIG_STMTJRNL_SPILL\n** <dd>^The SQLITE_CONFIG_STMTJRNL_SPILL option takes a single parameter which\n** becomes the [statement journal] spill-to-disk threshold.  \n** [Statement journals] are held in memory until their size (in bytes)\n** exceeds this threshold, at which point they are written to disk.\n** Or if the threshold is -1, statement journals are always held\n** exclusively in memory.\n** Since many statement journals never become large, setting the spill\n** threshold to a value such as 64KiB can greatly reduce the amount of\n** I/O required to support statement rollback.\n** The default value for this setting is controlled by the\n** [SQLITE_STMTJRNL_SPILL] compile-time option.\n** </dl>\n*/\n#define SQLITE_CONFIG_SINGLETHREAD  1  /* nil */\n#define SQLITE_CONFIG_MULTITHREAD   2  /* nil */\n#define SQLITE_CONFIG_SERIALIZED    3  /* nil */\n#define SQLITE_CONFIG_MALLOC        4  /* sqlite3_mem_methods* */\n#define SQLITE_CONFIG_GETMALLOC     5  /* sqlite3_mem_methods* */\n#define SQLITE_CONFIG_SCRATCH       6  /* No longer used */\n#define SQLITE_CONFIG_PAGECACHE     7  /* void*, int sz, int N */\n#define SQLITE_CONFIG_HEAP          8  /* void*, int nByte, int min */\n#define SQLITE_CONFIG_MEMSTATUS     9  /* boolean */\n#define SQLITE_CONFIG_MUTEX        10  /* sqlite3_mutex_methods* */\n#define SQLITE_CONFIG_GETMUTEX     11  /* sqlite3_mutex_methods* */\n/* previously SQLITE_CONFIG_CHUNKALLOC 12 which is now unused. */ \n#define SQLITE_CONFIG_LOOKASIDE    13  /* int int */\n#define SQLITE_CONFIG_PCACHE       14  /* no-op */\n#define SQLITE_CONFIG_GETPCACHE    15  /* no-op */\n#define SQLITE_CONFIG_LOG          16  /* xFunc, void* */\n#define SQLITE_CONFIG_URI          17  /* int */\n#define SQLITE_CONFIG_PCACHE2      18  /* sqlite3_pcache_methods2* */\n#define SQLITE_CONFIG_GETPCACHE2   19  /* sqlite3_pcache_methods2* */\n#define SQLITE_CONFIG_COVERING_INDEX_SCAN 20  /* int */\n#define SQLITE_CONFIG_SQLLOG       21  /* xSqllog, void* */\n#define SQLITE_CONFIG_MMAP_SIZE    22  /* sqlite3_int64, sqlite3_int64 */\n#define SQLITE_CONFIG_WIN32_HEAPSIZE      23  /* int nByte */\n#define SQLITE_CONFIG_PCACHE_HDRSZ        24  /* int *psz */\n#define SQLITE_CONFIG_PMASZ               25  /* unsigned int szPma */\n#define SQLITE_CONFIG_STMTJRNL_SPILL      26  /* int nByte */\n#define SQLITE_CONFIG_SMALL_MALLOC        27  /* boolean */\n\n/*\n** CAPI3REF: Database Connection Configuration Options\n**\n** These constants are the available integer configuration options that\n** can be passed as the second argument to the [sqlite3_db_config()] interface.\n**\n** New configuration options may be added in future releases of SQLite.\n** Existing configuration options might be discontinued.  Applications\n** should check the return code from [sqlite3_db_config()] to make sure that\n** the call worked.  ^The [sqlite3_db_config()] interface will return a\n** non-zero [error code] if a discontinued or unsupported configuration option\n** is invoked.\n**\n** <dl>\n** <dt>SQLITE_DBCONFIG_LOOKASIDE</dt>\n** <dd> ^This option takes three additional arguments that determine the \n** [lookaside memory allocator] configuration for the [database connection].\n** ^The first argument (the third parameter to [sqlite3_db_config()] is a\n** pointer to a memory buffer to use for lookaside memory.\n** ^The first argument after the SQLITE_DBCONFIG_LOOKASIDE verb\n** may be NULL in which case SQLite will allocate the\n** lookaside buffer itself using [sqlite3_malloc()]. ^The second argument is the\n** size of each lookaside buffer slot.  ^The third argument is the number of\n** slots.  The size of the buffer in the first argument must be greater than\n** or equal to the product of the second and third arguments.  The buffer\n** must be aligned to an 8-byte boundary.  ^If the second argument to\n** SQLITE_DBCONFIG_LOOKASIDE is not a multiple of 8, it is internally\n** rounded down to the next smaller multiple of 8.  ^(The lookaside memory\n** configuration for a database connection can only be changed when that\n** connection is not currently using lookaside memory, or in other words\n** when the \"current value\" returned by\n** [sqlite3_db_status](D,[SQLITE_CONFIG_LOOKASIDE],...) is zero.\n** Any attempt to change the lookaside memory configuration when lookaside\n** memory is in use leaves the configuration unchanged and returns \n** [SQLITE_BUSY].)^</dd>\n**\n** <dt>SQLITE_DBCONFIG_ENABLE_FKEY</dt>\n** <dd> ^This option is used to enable or disable the enforcement of\n** [foreign key constraints].  There should be two additional arguments.\n** The first argument is an integer which is 0 to disable FK enforcement,\n** positive to enable FK enforcement or negative to leave FK enforcement\n** unchanged.  The second parameter is a pointer to an integer into which\n** is written 0 or 1 to indicate whether FK enforcement is off or on\n** following this call.  The second parameter may be a NULL pointer, in\n** which case the FK enforcement setting is not reported back. </dd>\n**\n** <dt>SQLITE_DBCONFIG_ENABLE_TRIGGER</dt>\n** <dd> ^This option is used to enable or disable [CREATE TRIGGER | triggers].\n** There should be two additional arguments.\n** The first argument is an integer which is 0 to disable triggers,\n** positive to enable triggers or negative to leave the setting unchanged.\n** The second parameter is a pointer to an integer into which\n** is written 0 or 1 to indicate whether triggers are disabled or enabled\n** following this call.  The second parameter may be a NULL pointer, in\n** which case the trigger setting is not reported back. </dd>\n**\n** <dt>SQLITE_DBCONFIG_ENABLE_FTS3_TOKENIZER</dt>\n** <dd> ^This option is used to enable or disable the two-argument\n** version of the [fts3_tokenizer()] function which is part of the\n** [FTS3] full-text search engine extension.\n** There should be two additional arguments.\n** The first argument is an integer which is 0 to disable fts3_tokenizer() or\n** positive to enable fts3_tokenizer() or negative to leave the setting\n** unchanged.\n** The second parameter is a pointer to an integer into which\n** is written 0 or 1 to indicate whether fts3_tokenizer is disabled or enabled\n** following this call.  The second parameter may be a NULL pointer, in\n** which case the new setting is not reported back. </dd>\n**\n** <dt>SQLITE_DBCONFIG_ENABLE_LOAD_EXTENSION</dt>\n** <dd> ^This option is used to enable or disable the [sqlite3_load_extension()]\n** interface independently of the [load_extension()] SQL function.\n** The [sqlite3_enable_load_extension()] API enables or disables both the\n** C-API [sqlite3_load_extension()] and the SQL function [load_extension()].\n** There should be two additional arguments.\n** When the first argument to this interface is 1, then only the C-API is\n** enabled and the SQL function remains disabled.  If the first argument to\n** this interface is 0, then both the C-API and the SQL function are disabled.\n** If the first argument is -1, then no changes are made to state of either the\n** C-API or the SQL function.\n** The second parameter is a pointer to an integer into which\n** is written 0 or 1 to indicate whether [sqlite3_load_extension()] interface\n** is disabled or enabled following this call.  The second parameter may\n** be a NULL pointer, in which case the new setting is not reported back.\n** </dd>\n**\n** <dt>SQLITE_DBCONFIG_MAINDBNAME</dt>\n** <dd> ^This option is used to change the name of the \"main\" database\n** schema.  ^The sole argument is a pointer to a constant UTF8 string\n** which will become the new schema name in place of \"main\".  ^SQLite\n** does not make a copy of the new main schema name string, so the application\n** must ensure that the argument passed into this DBCONFIG option is unchanged\n** until after the database connection closes.\n** </dd>\n**\n** <dt>SQLITE_DBCONFIG_NO_CKPT_ON_CLOSE</dt>\n** <dd> Usually, when a database in wal mode is closed or detached from a \n** database handle, SQLite checks if this will mean that there are now no \n** connections at all to the database. If so, it performs a checkpoint \n** operation before closing the connection. This option may be used to\n** override this behaviour. The first parameter passed to this operation\n** is an integer - non-zero to disable checkpoints-on-close, or zero (the\n** default) to enable them. The second parameter is a pointer to an integer\n** into which is written 0 or 1 to indicate whether checkpoints-on-close\n** have been disabled - 0 if they are not disabled, 1 if they are.\n** </dd>\n** <dt>SQLITE_DBCONFIG_ENABLE_QPSG</dt>\n** <dd>^(The SQLITE_DBCONFIG_ENABLE_QPSG option activates or deactivates\n** the [query planner stability guarantee] (QPSG).  When the QPSG is active,\n** a single SQL query statement will always use the same algorithm regardless\n** of values of [bound parameters].)^ The QPSG disables some query optimizations\n** that look at the values of bound parameters, which can make some queries\n** slower.  But the QPSG has the advantage of more predictable behavior.  With\n** the QPSG active, SQLite will always use the same query plan in the field as\n** was used during testing in the lab.\n** </dd>\n** <dt>SQLITE_DBCONFIG_TRIGGER_EQP</dt>\n** <dd> By default, the output of EXPLAIN QUERY PLAN commands does not \n** include output for any operations performed by trigger programs. This\n** option is used to set or clear (the default) a flag that governs this\n** behavior. The first parameter passed to this operation is an integer -\n** non-zero to enable output for trigger programs, or zero to disable it.\n** The second parameter is a pointer to an integer into which is written \n** 0 or 1 to indicate whether output-for-triggers has been disabled - 0 if \n** it is not disabled, 1 if it is.  \n** </dd>\n** </dl>\n*/\n#define SQLITE_DBCONFIG_MAINDBNAME            1000 /* const char* */\n#define SQLITE_DBCONFIG_LOOKASIDE             1001 /* void* int int */\n#define SQLITE_DBCONFIG_ENABLE_FKEY           1002 /* int int* */\n#define SQLITE_DBCONFIG_ENABLE_TRIGGER        1003 /* int int* */\n#define SQLITE_DBCONFIG_ENABLE_FTS3_TOKENIZER 1004 /* int int* */\n#define SQLITE_DBCONFIG_ENABLE_LOAD_EXTENSION 1005 /* int int* */\n#define SQLITE_DBCONFIG_NO_CKPT_ON_CLOSE      1006 /* int int* */\n#define SQLITE_DBCONFIG_ENABLE_QPSG           1007 /* int int* */\n#define SQLITE_DBCONFIG_TRIGGER_EQP           1008 /* int int* */\n#define SQLITE_DBCONFIG_MAX                   1008 /* Largest DBCONFIG */\n\n/*\n** CAPI3REF: Enable Or Disable Extended Result Codes\n** METHOD: sqlite3\n**\n** ^The sqlite3_extended_result_codes() routine enables or disables the\n** [extended result codes] feature of SQLite. ^The extended result\n** codes are disabled by default for historical compatibility.\n*/\nSQLITE_API int sqlite3_extended_result_codes(sqlite3*, int onoff);\n\n/*\n** CAPI3REF: Last Insert Rowid\n** METHOD: sqlite3\n**\n** ^Each entry in most SQLite tables (except for [WITHOUT ROWID] tables)\n** has a unique 64-bit signed\n** integer key called the [ROWID | \"rowid\"]. ^The rowid is always available\n** as an undeclared column named ROWID, OID, or _ROWID_ as long as those\n** names are not also used by explicitly declared columns. ^If\n** the table has a column of type [INTEGER PRIMARY KEY] then that column\n** is another alias for the rowid.\n**\n** ^The sqlite3_last_insert_rowid(D) interface usually returns the [rowid] of\n** the most recent successful [INSERT] into a rowid table or [virtual table]\n** on database connection D. ^Inserts into [WITHOUT ROWID] tables are not\n** recorded. ^If no successful [INSERT]s into rowid tables have ever occurred \n** on the database connection D, then sqlite3_last_insert_rowid(D) returns \n** zero.\n**\n** As well as being set automatically as rows are inserted into database\n** tables, the value returned by this function may be set explicitly by\n** [sqlite3_set_last_insert_rowid()]\n**\n** Some virtual table implementations may INSERT rows into rowid tables as\n** part of committing a transaction (e.g. to flush data accumulated in memory\n** to disk). In this case subsequent calls to this function return the rowid\n** associated with these internal INSERT operations, which leads to \n** unintuitive results. Virtual table implementations that do write to rowid\n** tables in this way can avoid this problem by restoring the original \n** rowid value using [sqlite3_set_last_insert_rowid()] before returning \n** control to the user.\n**\n** ^(If an [INSERT] occurs within a trigger then this routine will \n** return the [rowid] of the inserted row as long as the trigger is \n** running. Once the trigger program ends, the value returned \n** by this routine reverts to what it was before the trigger was fired.)^\n**\n** ^An [INSERT] that fails due to a constraint violation is not a\n** successful [INSERT] and does not change the value returned by this\n** routine.  ^Thus INSERT OR FAIL, INSERT OR IGNORE, INSERT OR ROLLBACK,\n** and INSERT OR ABORT make no changes to the return value of this\n** routine when their insertion fails.  ^(When INSERT OR REPLACE\n** encounters a constraint violation, it does not fail.  The\n** INSERT continues to completion after deleting rows that caused\n** the constraint problem so INSERT OR REPLACE will always change\n** the return value of this interface.)^\n**\n** ^For the purposes of this routine, an [INSERT] is considered to\n** be successful even if it is subsequently rolled back.\n**\n** This function is accessible to SQL statements via the\n** [last_insert_rowid() SQL function].\n**\n** If a separate thread performs a new [INSERT] on the same\n** database connection while the [sqlite3_last_insert_rowid()]\n** function is running and thus changes the last insert [rowid],\n** then the value returned by [sqlite3_last_insert_rowid()] is\n** unpredictable and might not equal either the old or the new\n** last insert [rowid].\n*/\nSQLITE_API sqlite3_int64 sqlite3_last_insert_rowid(sqlite3*);\n\n/*\n** CAPI3REF: Set the Last Insert Rowid value.\n** METHOD: sqlite3\n**\n** The sqlite3_set_last_insert_rowid(D, R) method allows the application to\n** set the value returned by calling sqlite3_last_insert_rowid(D) to R \n** without inserting a row into the database.\n*/\nSQLITE_API void sqlite3_set_last_insert_rowid(sqlite3*,sqlite3_int64);\n\n/*\n** CAPI3REF: Count The Number Of Rows Modified\n** METHOD: sqlite3\n**\n** ^This function returns the number of rows modified, inserted or\n** deleted by the most recently completed INSERT, UPDATE or DELETE\n** statement on the database connection specified by the only parameter.\n** ^Executing any other type of SQL statement does not modify the value\n** returned by this function.\n**\n** ^Only changes made directly by the INSERT, UPDATE or DELETE statement are\n** considered - auxiliary changes caused by [CREATE TRIGGER | triggers], \n** [foreign key actions] or [REPLACE] constraint resolution are not counted.\n** \n** Changes to a view that are intercepted by \n** [INSTEAD OF trigger | INSTEAD OF triggers] are not counted. ^The value \n** returned by sqlite3_changes() immediately after an INSERT, UPDATE or \n** DELETE statement run on a view is always zero. Only changes made to real \n** tables are counted.\n**\n** Things are more complicated if the sqlite3_changes() function is\n** executed while a trigger program is running. This may happen if the\n** program uses the [changes() SQL function], or if some other callback\n** function invokes sqlite3_changes() directly. Essentially:\n** \n** <ul>\n**   <li> ^(Before entering a trigger program the value returned by\n**        sqlite3_changes() function is saved. After the trigger program \n**        has finished, the original value is restored.)^\n** \n**   <li> ^(Within a trigger program each INSERT, UPDATE and DELETE \n**        statement sets the value returned by sqlite3_changes() \n**        upon completion as normal. Of course, this value will not include \n**        any changes performed by sub-triggers, as the sqlite3_changes() \n**        value will be saved and restored after each sub-trigger has run.)^\n** </ul>\n** \n** ^This means that if the changes() SQL function (or similar) is used\n** by the first INSERT, UPDATE or DELETE statement within a trigger, it \n** returns the value as set when the calling statement began executing.\n** ^If it is used by the second or subsequent such statement within a trigger \n** program, the value returned reflects the number of rows modified by the \n** previous INSERT, UPDATE or DELETE statement within the same trigger.\n**\n** See also the [sqlite3_total_changes()] interface, the\n** [count_changes pragma], and the [changes() SQL function].\n**\n** If a separate thread makes changes on the same database connection\n** while [sqlite3_changes()] is running then the value returned\n** is unpredictable and not meaningful.\n*/\nSQLITE_API int sqlite3_changes(sqlite3*);\n\n/*\n** CAPI3REF: Total Number Of Rows Modified\n** METHOD: sqlite3\n**\n** ^This function returns the total number of rows inserted, modified or\n** deleted by all [INSERT], [UPDATE] or [DELETE] statements completed\n** since the database connection was opened, including those executed as\n** part of trigger programs. ^Executing any other type of SQL statement\n** does not affect the value returned by sqlite3_total_changes().\n** \n** ^Changes made as part of [foreign key actions] are included in the\n** count, but those made as part of REPLACE constraint resolution are\n** not. ^Changes to a view that are intercepted by INSTEAD OF triggers \n** are not counted.\n** \n** See also the [sqlite3_changes()] interface, the\n** [count_changes pragma], and the [total_changes() SQL function].\n**\n** If a separate thread makes changes on the same database connection\n** while [sqlite3_total_changes()] is running then the value\n** returned is unpredictable and not meaningful.\n*/\nSQLITE_API int sqlite3_total_changes(sqlite3*);\n\n/*\n** CAPI3REF: Interrupt A Long-Running Query\n** METHOD: sqlite3\n**\n** ^This function causes any pending database operation to abort and\n** return at its earliest opportunity. This routine is typically\n** called in response to a user action such as pressing \"Cancel\"\n** or Ctrl-C where the user wants a long query operation to halt\n** immediately.\n**\n** ^It is safe to call this routine from a thread different from the\n** thread that is currently running the database operation.  But it\n** is not safe to call this routine with a [database connection] that\n** is closed or might close before sqlite3_interrupt() returns.\n**\n** ^If an SQL operation is very nearly finished at the time when\n** sqlite3_interrupt() is called, then it might not have an opportunity\n** to be interrupted and might continue to completion.\n**\n** ^An SQL operation that is interrupted will return [SQLITE_INTERRUPT].\n** ^If the interrupted SQL operation is an INSERT, UPDATE, or DELETE\n** that is inside an explicit transaction, then the entire transaction\n** will be rolled back automatically.\n**\n** ^The sqlite3_interrupt(D) call is in effect until all currently running\n** SQL statements on [database connection] D complete.  ^Any new SQL statements\n** that are started after the sqlite3_interrupt() call and before the \n** running statements reaches zero are interrupted as if they had been\n** running prior to the sqlite3_interrupt() call.  ^New SQL statements\n** that are started after the running statement count reaches zero are\n** not effected by the sqlite3_interrupt().\n** ^A call to sqlite3_interrupt(D) that occurs when there are no running\n** SQL statements is a no-op and has no effect on SQL statements\n** that are started after the sqlite3_interrupt() call returns.\n*/\nSQLITE_API void sqlite3_interrupt(sqlite3*);\n\n/*\n** CAPI3REF: Determine If An SQL Statement Is Complete\n**\n** These routines are useful during command-line input to determine if the\n** currently entered text seems to form a complete SQL statement or\n** if additional input is needed before sending the text into\n** SQLite for parsing.  ^These routines return 1 if the input string\n** appears to be a complete SQL statement.  ^A statement is judged to be\n** complete if it ends with a semicolon token and is not a prefix of a\n** well-formed CREATE TRIGGER statement.  ^Semicolons that are embedded within\n** string literals or quoted identifier names or comments are not\n** independent tokens (they are part of the token in which they are\n** embedded) and thus do not count as a statement terminator.  ^Whitespace\n** and comments that follow the final semicolon are ignored.\n**\n** ^These routines return 0 if the statement is incomplete.  ^If a\n** memory allocation fails, then SQLITE_NOMEM is returned.\n**\n** ^These routines do not parse the SQL statements thus\n** will not detect syntactically incorrect SQL.\n**\n** ^(If SQLite has not been initialized using [sqlite3_initialize()] prior \n** to invoking sqlite3_complete16() then sqlite3_initialize() is invoked\n** automatically by sqlite3_complete16().  If that initialization fails,\n** then the return value from sqlite3_complete16() will be non-zero\n** regardless of whether or not the input SQL is complete.)^\n**\n** The input to [sqlite3_complete()] must be a zero-terminated\n** UTF-8 string.\n**\n** The input to [sqlite3_complete16()] must be a zero-terminated\n** UTF-16 string in native byte order.\n*/\nSQLITE_API int sqlite3_complete(const char *sql);\nSQLITE_API int sqlite3_complete16(const void *sql);\n\n/*\n** CAPI3REF: Register A Callback To Handle SQLITE_BUSY Errors\n** KEYWORDS: {busy-handler callback} {busy handler}\n** METHOD: sqlite3\n**\n** ^The sqlite3_busy_handler(D,X,P) routine sets a callback function X\n** that might be invoked with argument P whenever\n** an attempt is made to access a database table associated with\n** [database connection] D when another thread\n** or process has the table locked.\n** The sqlite3_busy_handler() interface is used to implement\n** [sqlite3_busy_timeout()] and [PRAGMA busy_timeout].\n**\n** ^If the busy callback is NULL, then [SQLITE_BUSY]\n** is returned immediately upon encountering the lock.  ^If the busy callback\n** is not NULL, then the callback might be invoked with two arguments.\n**\n** ^The first argument to the busy handler is a copy of the void* pointer which\n** is the third argument to sqlite3_busy_handler().  ^The second argument to\n** the busy handler callback is the number of times that the busy handler has\n** been invoked previously for the same locking event.  ^If the\n** busy callback returns 0, then no additional attempts are made to\n** access the database and [SQLITE_BUSY] is returned\n** to the application.\n** ^If the callback returns non-zero, then another attempt\n** is made to access the database and the cycle repeats.\n**\n** The presence of a busy handler does not guarantee that it will be invoked\n** when there is lock contention. ^If SQLite determines that invoking the busy\n** handler could result in a deadlock, it will go ahead and return [SQLITE_BUSY]\n** to the application instead of invoking the \n** busy handler.\n** Consider a scenario where one process is holding a read lock that\n** it is trying to promote to a reserved lock and\n** a second process is holding a reserved lock that it is trying\n** to promote to an exclusive lock.  The first process cannot proceed\n** because it is blocked by the second and the second process cannot\n** proceed because it is blocked by the first.  If both processes\n** invoke the busy handlers, neither will make any progress.  Therefore,\n** SQLite returns [SQLITE_BUSY] for the first process, hoping that this\n** will induce the first process to release its read lock and allow\n** the second process to proceed.\n**\n** ^The default busy callback is NULL.\n**\n** ^(There can only be a single busy handler defined for each\n** [database connection].  Setting a new busy handler clears any\n** previously set handler.)^  ^Note that calling [sqlite3_busy_timeout()]\n** or evaluating [PRAGMA busy_timeout=N] will change the\n** busy handler and thus clear any previously set busy handler.\n**\n** The busy callback should not take any actions which modify the\n** database connection that invoked the busy handler.  In other words,\n** the busy handler is not reentrant.  Any such actions\n** result in undefined behavior.\n** \n** A busy handler must not close the database connection\n** or [prepared statement] that invoked the busy handler.\n*/\nSQLITE_API int sqlite3_busy_handler(sqlite3*,int(*)(void*,int),void*);\n\n/*\n** CAPI3REF: Set A Busy Timeout\n** METHOD: sqlite3\n**\n** ^This routine sets a [sqlite3_busy_handler | busy handler] that sleeps\n** for a specified amount of time when a table is locked.  ^The handler\n** will sleep multiple times until at least \"ms\" milliseconds of sleeping\n** have accumulated.  ^After at least \"ms\" milliseconds of sleeping,\n** the handler returns 0 which causes [sqlite3_step()] to return\n** [SQLITE_BUSY].\n**\n** ^Calling this routine with an argument less than or equal to zero\n** turns off all busy handlers.\n**\n** ^(There can only be a single busy handler for a particular\n** [database connection] at any given moment.  If another busy handler\n** was defined  (using [sqlite3_busy_handler()]) prior to calling\n** this routine, that other busy handler is cleared.)^\n**\n** See also:  [PRAGMA busy_timeout]\n*/\nSQLITE_API int sqlite3_busy_timeout(sqlite3*, int ms);\n\n/*\n** CAPI3REF: Convenience Routines For Running Queries\n** METHOD: sqlite3\n**\n** This is a legacy interface that is preserved for backwards compatibility.\n** Use of this interface is not recommended.\n**\n** Definition: A <b>result table</b> is memory data structure created by the\n** [sqlite3_get_table()] interface.  A result table records the\n** complete query results from one or more queries.\n**\n** The table conceptually has a number of rows and columns.  But\n** these numbers are not part of the result table itself.  These\n** numbers are obtained separately.  Let N be the number of rows\n** and M be the number of columns.\n**\n** A result table is an array of pointers to zero-terminated UTF-8 strings.\n** There are (N+1)*M elements in the array.  The first M pointers point\n** to zero-terminated strings that  contain the names of the columns.\n** The remaining entries all point to query results.  NULL values result\n** in NULL pointers.  All other values are in their UTF-8 zero-terminated\n** string representation as returned by [sqlite3_column_text()].\n**\n** A result table might consist of one or more memory allocations.\n** It is not safe to pass a result table directly to [sqlite3_free()].\n** A result table should be deallocated using [sqlite3_free_table()].\n**\n** ^(As an example of the result table format, suppose a query result\n** is as follows:\n**\n** <blockquote><pre>\n**        Name        | Age\n**        -----------------------\n**        Alice       | 43\n**        Bob         | 28\n**        Cindy       | 21\n** </pre></blockquote>\n**\n** There are two column (M==2) and three rows (N==3).  Thus the\n** result table has 8 entries.  Suppose the result table is stored\n** in an array names azResult.  Then azResult holds this content:\n**\n** <blockquote><pre>\n**        azResult&#91;0] = \"Name\";\n**        azResult&#91;1] = \"Age\";\n**        azResult&#91;2] = \"Alice\";\n**        azResult&#91;3] = \"43\";\n**        azResult&#91;4] = \"Bob\";\n**        azResult&#91;5] = \"28\";\n**        azResult&#91;6] = \"Cindy\";\n**        azResult&#91;7] = \"21\";\n** </pre></blockquote>)^\n**\n** ^The sqlite3_get_table() function evaluates one or more\n** semicolon-separated SQL statements in the zero-terminated UTF-8\n** string of its 2nd parameter and returns a result table to the\n** pointer given in its 3rd parameter.\n**\n** After the application has finished with the result from sqlite3_get_table(),\n** it must pass the result table pointer to sqlite3_free_table() in order to\n** release the memory that was malloced.  Because of the way the\n** [sqlite3_malloc()] happens within sqlite3_get_table(), the calling\n** function must not try to call [sqlite3_free()] directly.  Only\n** [sqlite3_free_table()] is able to release the memory properly and safely.\n**\n** The sqlite3_get_table() interface is implemented as a wrapper around\n** [sqlite3_exec()].  The sqlite3_get_table() routine does not have access\n** to any internal data structures of SQLite.  It uses only the public\n** interface defined here.  As a consequence, errors that occur in the\n** wrapper layer outside of the internal [sqlite3_exec()] call are not\n** reflected in subsequent calls to [sqlite3_errcode()] or\n** [sqlite3_errmsg()].\n*/\nSQLITE_API int sqlite3_get_table(\n  sqlite3 *db,          /* An open database */\n  const char *zSql,     /* SQL to be evaluated */\n  char ***pazResult,    /* Results of the query */\n  int *pnRow,           /* Number of result rows written here */\n  int *pnColumn,        /* Number of result columns written here */\n  char **pzErrmsg       /* Error msg written here */\n);\nSQLITE_API void sqlite3_free_table(char **result);\n\n/*\n** CAPI3REF: Formatted String Printing Functions\n**\n** These routines are work-alikes of the \"printf()\" family of functions\n** from the standard C library.\n** These routines understand most of the common formatting options from\n** the standard library printf() \n** plus some additional non-standard formats ([%q], [%Q], [%w], and [%z]).\n** See the [built-in printf()] documentation for details.\n**\n** ^The sqlite3_mprintf() and sqlite3_vmprintf() routines write their\n** results into memory obtained from [sqlite3_malloc64()].\n** The strings returned by these two routines should be\n** released by [sqlite3_free()].  ^Both routines return a\n** NULL pointer if [sqlite3_malloc64()] is unable to allocate enough\n** memory to hold the resulting string.\n**\n** ^(The sqlite3_snprintf() routine is similar to \"snprintf()\" from\n** the standard C library.  The result is written into the\n** buffer supplied as the second parameter whose size is given by\n** the first parameter. Note that the order of the\n** first two parameters is reversed from snprintf().)^  This is an\n** historical accident that cannot be fixed without breaking\n** backwards compatibility.  ^(Note also that sqlite3_snprintf()\n** returns a pointer to its buffer instead of the number of\n** characters actually written into the buffer.)^  We admit that\n** the number of characters written would be a more useful return\n** value but we cannot change the implementation of sqlite3_snprintf()\n** now without breaking compatibility.\n**\n** ^As long as the buffer size is greater than zero, sqlite3_snprintf()\n** guarantees that the buffer is always zero-terminated.  ^The first\n** parameter \"n\" is the total size of the buffer, including space for\n** the zero terminator.  So the longest string that can be completely\n** written will be n-1 characters.\n**\n** ^The sqlite3_vsnprintf() routine is a varargs version of sqlite3_snprintf().\n**\n** See also:  [built-in printf()], [printf() SQL function]\n*/\nSQLITE_API char *sqlite3_mprintf(const char*,...);\nSQLITE_API char *sqlite3_vmprintf(const char*, va_list);\nSQLITE_API char *sqlite3_snprintf(int,char*,const char*, ...);\nSQLITE_API char *sqlite3_vsnprintf(int,char*,const char*, va_list);\n\n/*\n** CAPI3REF: Memory Allocation Subsystem\n**\n** The SQLite core uses these three routines for all of its own\n** internal memory allocation needs. \"Core\" in the previous sentence\n** does not include operating-system specific VFS implementation.  The\n** Windows VFS uses native malloc() and free() for some operations.\n**\n** ^The sqlite3_malloc() routine returns a pointer to a block\n** of memory at least N bytes in length, where N is the parameter.\n** ^If sqlite3_malloc() is unable to obtain sufficient free\n** memory, it returns a NULL pointer.  ^If the parameter N to\n** sqlite3_malloc() is zero or negative then sqlite3_malloc() returns\n** a NULL pointer.\n**\n** ^The sqlite3_malloc64(N) routine works just like\n** sqlite3_malloc(N) except that N is an unsigned 64-bit integer instead\n** of a signed 32-bit integer.\n**\n** ^Calling sqlite3_free() with a pointer previously returned\n** by sqlite3_malloc() or sqlite3_realloc() releases that memory so\n** that it might be reused.  ^The sqlite3_free() routine is\n** a no-op if is called with a NULL pointer.  Passing a NULL pointer\n** to sqlite3_free() is harmless.  After being freed, memory\n** should neither be read nor written.  Even reading previously freed\n** memory might result in a segmentation fault or other severe error.\n** Memory corruption, a segmentation fault, or other severe error\n** might result if sqlite3_free() is called with a non-NULL pointer that\n** was not obtained from sqlite3_malloc() or sqlite3_realloc().\n**\n** ^The sqlite3_realloc(X,N) interface attempts to resize a\n** prior memory allocation X to be at least N bytes.\n** ^If the X parameter to sqlite3_realloc(X,N)\n** is a NULL pointer then its behavior is identical to calling\n** sqlite3_malloc(N).\n** ^If the N parameter to sqlite3_realloc(X,N) is zero or\n** negative then the behavior is exactly the same as calling\n** sqlite3_free(X).\n** ^sqlite3_realloc(X,N) returns a pointer to a memory allocation\n** of at least N bytes in size or NULL if insufficient memory is available.\n** ^If M is the size of the prior allocation, then min(N,M) bytes\n** of the prior allocation are copied into the beginning of buffer returned\n** by sqlite3_realloc(X,N) and the prior allocation is freed.\n** ^If sqlite3_realloc(X,N) returns NULL and N is positive, then the\n** prior allocation is not freed.\n**\n** ^The sqlite3_realloc64(X,N) interfaces works the same as\n** sqlite3_realloc(X,N) except that N is a 64-bit unsigned integer instead\n** of a 32-bit signed integer.\n**\n** ^If X is a memory allocation previously obtained from sqlite3_malloc(),\n** sqlite3_malloc64(), sqlite3_realloc(), or sqlite3_realloc64(), then\n** sqlite3_msize(X) returns the size of that memory allocation in bytes.\n** ^The value returned by sqlite3_msize(X) might be larger than the number\n** of bytes requested when X was allocated.  ^If X is a NULL pointer then\n** sqlite3_msize(X) returns zero.  If X points to something that is not\n** the beginning of memory allocation, or if it points to a formerly\n** valid memory allocation that has now been freed, then the behavior\n** of sqlite3_msize(X) is undefined and possibly harmful.\n**\n** ^The memory returned by sqlite3_malloc(), sqlite3_realloc(),\n** sqlite3_malloc64(), and sqlite3_realloc64()\n** is always aligned to at least an 8 byte boundary, or to a\n** 4 byte boundary if the [SQLITE_4_BYTE_ALIGNED_MALLOC] compile-time\n** option is used.\n**\n** In SQLite version 3.5.0 and 3.5.1, it was possible to define\n** the SQLITE_OMIT_MEMORY_ALLOCATION which would cause the built-in\n** implementation of these routines to be omitted.  That capability\n** is no longer provided.  Only built-in memory allocators can be used.\n**\n** Prior to SQLite version 3.7.10, the Windows OS interface layer called\n** the system malloc() and free() directly when converting\n** filenames between the UTF-8 encoding used by SQLite\n** and whatever filename encoding is used by the particular Windows\n** installation.  Memory allocation errors were detected, but\n** they were reported back as [SQLITE_CANTOPEN] or\n** [SQLITE_IOERR] rather than [SQLITE_NOMEM].\n**\n** The pointer arguments to [sqlite3_free()] and [sqlite3_realloc()]\n** must be either NULL or else pointers obtained from a prior\n** invocation of [sqlite3_malloc()] or [sqlite3_realloc()] that have\n** not yet been released.\n**\n** The application must not read or write any part of\n** a block of memory after it has been released using\n** [sqlite3_free()] or [sqlite3_realloc()].\n*/\nSQLITE_API void *sqlite3_malloc(int);\nSQLITE_API void *sqlite3_malloc64(sqlite3_uint64);\nSQLITE_API void *sqlite3_realloc(void*, int);\nSQLITE_API void *sqlite3_realloc64(void*, sqlite3_uint64);\nSQLITE_API void sqlite3_free(void*);\nSQLITE_API sqlite3_uint64 sqlite3_msize(void*);\n\n/*\n** CAPI3REF: Memory Allocator Statistics\n**\n** SQLite provides these two interfaces for reporting on the status\n** of the [sqlite3_malloc()], [sqlite3_free()], and [sqlite3_realloc()]\n** routines, which form the built-in memory allocation subsystem.\n**\n** ^The [sqlite3_memory_used()] routine returns the number of bytes\n** of memory currently outstanding (malloced but not freed).\n** ^The [sqlite3_memory_highwater()] routine returns the maximum\n** value of [sqlite3_memory_used()] since the high-water mark\n** was last reset.  ^The values returned by [sqlite3_memory_used()] and\n** [sqlite3_memory_highwater()] include any overhead\n** added by SQLite in its implementation of [sqlite3_malloc()],\n** but not overhead added by the any underlying system library\n** routines that [sqlite3_malloc()] may call.\n**\n** ^The memory high-water mark is reset to the current value of\n** [sqlite3_memory_used()] if and only if the parameter to\n** [sqlite3_memory_highwater()] is true.  ^The value returned\n** by [sqlite3_memory_highwater(1)] is the high-water mark\n** prior to the reset.\n*/\nSQLITE_API sqlite3_int64 sqlite3_memory_used(void);\nSQLITE_API sqlite3_int64 sqlite3_memory_highwater(int resetFlag);\n\n/*\n** CAPI3REF: Pseudo-Random Number Generator\n**\n** SQLite contains a high-quality pseudo-random number generator (PRNG) used to\n** select random [ROWID | ROWIDs] when inserting new records into a table that\n** already uses the largest possible [ROWID].  The PRNG is also used for\n** the build-in random() and randomblob() SQL functions.  This interface allows\n** applications to access the same PRNG for other purposes.\n**\n** ^A call to this routine stores N bytes of randomness into buffer P.\n** ^The P parameter can be a NULL pointer.\n**\n** ^If this routine has not been previously called or if the previous\n** call had N less than one or a NULL pointer for P, then the PRNG is\n** seeded using randomness obtained from the xRandomness method of\n** the default [sqlite3_vfs] object.\n** ^If the previous call to this routine had an N of 1 or more and a\n** non-NULL P then the pseudo-randomness is generated\n** internally and without recourse to the [sqlite3_vfs] xRandomness\n** method.\n*/\nSQLITE_API void sqlite3_randomness(int N, void *P);\n\n/*\n** CAPI3REF: Compile-Time Authorization Callbacks\n** METHOD: sqlite3\n** KEYWORDS: {authorizer callback}\n**\n** ^This routine registers an authorizer callback with a particular\n** [database connection], supplied in the first argument.\n** ^The authorizer callback is invoked as SQL statements are being compiled\n** by [sqlite3_prepare()] or its variants [sqlite3_prepare_v2()],\n** [sqlite3_prepare_v3()], [sqlite3_prepare16()], [sqlite3_prepare16_v2()],\n** and [sqlite3_prepare16_v3()].  ^At various\n** points during the compilation process, as logic is being created\n** to perform various actions, the authorizer callback is invoked to\n** see if those actions are allowed.  ^The authorizer callback should\n** return [SQLITE_OK] to allow the action, [SQLITE_IGNORE] to disallow the\n** specific action but allow the SQL statement to continue to be\n** compiled, or [SQLITE_DENY] to cause the entire SQL statement to be\n** rejected with an error.  ^If the authorizer callback returns\n** any value other than [SQLITE_IGNORE], [SQLITE_OK], or [SQLITE_DENY]\n** then the [sqlite3_prepare_v2()] or equivalent call that triggered\n** the authorizer will fail with an error message.\n**\n** When the callback returns [SQLITE_OK], that means the operation\n** requested is ok.  ^When the callback returns [SQLITE_DENY], the\n** [sqlite3_prepare_v2()] or equivalent call that triggered the\n** authorizer will fail with an error message explaining that\n** access is denied. \n**\n** ^The first parameter to the authorizer callback is a copy of the third\n** parameter to the sqlite3_set_authorizer() interface. ^The second parameter\n** to the callback is an integer [SQLITE_COPY | action code] that specifies\n** the particular action to be authorized. ^The third through sixth parameters\n** to the callback are either NULL pointers or zero-terminated strings\n** that contain additional details about the action to be authorized.\n** Applications must always be prepared to encounter a NULL pointer in any\n** of the third through the sixth parameters of the authorization callback.\n**\n** ^If the action code is [SQLITE_READ]\n** and the callback returns [SQLITE_IGNORE] then the\n** [prepared statement] statement is constructed to substitute\n** a NULL value in place of the table column that would have\n** been read if [SQLITE_OK] had been returned.  The [SQLITE_IGNORE]\n** return can be used to deny an untrusted user access to individual\n** columns of a table.\n** ^When a table is referenced by a [SELECT] but no column values are\n** extracted from that table (for example in a query like\n** \"SELECT count(*) FROM tab\") then the [SQLITE_READ] authorizer callback\n** is invoked once for that table with a column name that is an empty string.\n** ^If the action code is [SQLITE_DELETE] and the callback returns\n** [SQLITE_IGNORE] then the [DELETE] operation proceeds but the\n** [truncate optimization] is disabled and all rows are deleted individually.\n**\n** An authorizer is used when [sqlite3_prepare | preparing]\n** SQL statements from an untrusted source, to ensure that the SQL statements\n** do not try to access data they are not allowed to see, or that they do not\n** try to execute malicious statements that damage the database.  For\n** example, an application may allow a user to enter arbitrary\n** SQL queries for evaluation by a database.  But the application does\n** not want the user to be able to make arbitrary changes to the\n** database.  An authorizer could then be put in place while the\n** user-entered SQL is being [sqlite3_prepare | prepared] that\n** disallows everything except [SELECT] statements.\n**\n** Applications that need to process SQL from untrusted sources\n** might also consider lowering resource limits using [sqlite3_limit()]\n** and limiting database size using the [max_page_count] [PRAGMA]\n** in addition to using an authorizer.\n**\n** ^(Only a single authorizer can be in place on a database connection\n** at a time.  Each call to sqlite3_set_authorizer overrides the\n** previous call.)^  ^Disable the authorizer by installing a NULL callback.\n** The authorizer is disabled by default.\n**\n** The authorizer callback must not do anything that will modify\n** the database connection that invoked the authorizer callback.\n** Note that [sqlite3_prepare_v2()] and [sqlite3_step()] both modify their\n** database connections for the meaning of \"modify\" in this paragraph.\n**\n** ^When [sqlite3_prepare_v2()] is used to prepare a statement, the\n** statement might be re-prepared during [sqlite3_step()] due to a \n** schema change.  Hence, the application should ensure that the\n** correct authorizer callback remains in place during the [sqlite3_step()].\n**\n** ^Note that the authorizer callback is invoked only during\n** [sqlite3_prepare()] or its variants.  Authorization is not\n** performed during statement evaluation in [sqlite3_step()], unless\n** as stated in the previous paragraph, sqlite3_step() invokes\n** sqlite3_prepare_v2() to reprepare a statement after a schema change.\n*/\nSQLITE_API int sqlite3_set_authorizer(\n  sqlite3*,\n  int (*xAuth)(void*,int,const char*,const char*,const char*,const char*),\n  void *pUserData\n);\n\n/*\n** CAPI3REF: Authorizer Return Codes\n**\n** The [sqlite3_set_authorizer | authorizer callback function] must\n** return either [SQLITE_OK] or one of these two constants in order\n** to signal SQLite whether or not the action is permitted.  See the\n** [sqlite3_set_authorizer | authorizer documentation] for additional\n** information.\n**\n** Note that SQLITE_IGNORE is also used as a [conflict resolution mode]\n** returned from the [sqlite3_vtab_on_conflict()] interface.\n*/\n#define SQLITE_DENY   1   /* Abort the SQL statement with an error */\n#define SQLITE_IGNORE 2   /* Don't allow access, but don't generate an error */\n\n/*\n** CAPI3REF: Authorizer Action Codes\n**\n** The [sqlite3_set_authorizer()] interface registers a callback function\n** that is invoked to authorize certain SQL statement actions.  The\n** second parameter to the callback is an integer code that specifies\n** what action is being authorized.  These are the integer action codes that\n** the authorizer callback may be passed.\n**\n** These action code values signify what kind of operation is to be\n** authorized.  The 3rd and 4th parameters to the authorization\n** callback function will be parameters or NULL depending on which of these\n** codes is used as the second parameter.  ^(The 5th parameter to the\n** authorizer callback is the name of the database (\"main\", \"temp\",\n** etc.) if applicable.)^  ^The 6th parameter to the authorizer callback\n** is the name of the inner-most trigger or view that is responsible for\n** the access attempt or NULL if this access attempt is directly from\n** top-level SQL code.\n*/\n/******************************************* 3rd ************ 4th ***********/\n#define SQLITE_CREATE_INDEX          1   /* Index Name      Table Name      */\n#define SQLITE_CREATE_TABLE          2   /* Table Name      NULL            */\n#define SQLITE_CREATE_TEMP_INDEX     3   /* Index Name      Table Name      */\n#define SQLITE_CREATE_TEMP_TABLE     4   /* Table Name      NULL            */\n#define SQLITE_CREATE_TEMP_TRIGGER   5   /* Trigger Name    Table Name      */\n#define SQLITE_CREATE_TEMP_VIEW      6   /* View Name       NULL            */\n#define SQLITE_CREATE_TRIGGER        7   /* Trigger Name    Table Name      */\n#define SQLITE_CREATE_VIEW           8   /* View Name       NULL            */\n#define SQLITE_DELETE                9   /* Table Name      NULL            */\n#define SQLITE_DROP_INDEX           10   /* Index Name      Table Name      */\n#define SQLITE_DROP_TABLE           11   /* Table Name      NULL            */\n#define SQLITE_DROP_TEMP_INDEX      12   /* Index Name      Table Name      */\n#define SQLITE_DROP_TEMP_TABLE      13   /* Table Name      NULL            */\n#define SQLITE_DROP_TEMP_TRIGGER    14   /* Trigger Name    Table Name      */\n#define SQLITE_DROP_TEMP_VIEW       15   /* View Name       NULL            */\n#define SQLITE_DROP_TRIGGER         16   /* Trigger Name    Table Name      */\n#define SQLITE_DROP_VIEW            17   /* View Name       NULL            */\n#define SQLITE_INSERT               18   /* Table Name      NULL            */\n#define SQLITE_PRAGMA               19   /* Pragma Name     1st arg or NULL */\n#define SQLITE_READ                 20   /* Table Name      Column Name     */\n#define SQLITE_SELECT               21   /* NULL            NULL            */\n#define SQLITE_TRANSACTION          22   /* Operation       NULL            */\n#define SQLITE_UPDATE               23   /* Table Name      Column Name     */\n#define SQLITE_ATTACH               24   /* Filename        NULL            */\n#define SQLITE_DETACH               25   /* Database Name   NULL            */\n#define SQLITE_ALTER_TABLE          26   /* Database Name   Table Name      */\n#define SQLITE_REINDEX              27   /* Index Name      NULL            */\n#define SQLITE_ANALYZE              28   /* Table Name      NULL            */\n#define SQLITE_CREATE_VTABLE        29   /* Table Name      Module Name     */\n#define SQLITE_DROP_VTABLE          30   /* Table Name      Module Name     */\n#define SQLITE_FUNCTION             31   /* NULL            Function Name   */\n#define SQLITE_SAVEPOINT            32   /* Operation       Savepoint Name  */\n#define SQLITE_COPY                  0   /* No longer used */\n#define SQLITE_RECURSIVE            33   /* NULL            NULL            */\n\n/*\n** CAPI3REF: Tracing And Profiling Functions\n** METHOD: sqlite3\n**\n** These routines are deprecated. Use the [sqlite3_trace_v2()] interface\n** instead of the routines described here.\n**\n** These routines register callback functions that can be used for\n** tracing and profiling the execution of SQL statements.\n**\n** ^The callback function registered by sqlite3_trace() is invoked at\n** various times when an SQL statement is being run by [sqlite3_step()].\n** ^The sqlite3_trace() callback is invoked with a UTF-8 rendering of the\n** SQL statement text as the statement first begins executing.\n** ^(Additional sqlite3_trace() callbacks might occur\n** as each triggered subprogram is entered.  The callbacks for triggers\n** contain a UTF-8 SQL comment that identifies the trigger.)^\n**\n** The [SQLITE_TRACE_SIZE_LIMIT] compile-time option can be used to limit\n** the length of [bound parameter] expansion in the output of sqlite3_trace().\n**\n** ^The callback function registered by sqlite3_profile() is invoked\n** as each SQL statement finishes.  ^The profile callback contains\n** the original statement text and an estimate of wall-clock time\n** of how long that statement took to run.  ^The profile callback\n** time is in units of nanoseconds, however the current implementation\n** is only capable of millisecond resolution so the six least significant\n** digits in the time are meaningless.  Future versions of SQLite\n** might provide greater resolution on the profiler callback.  The\n** sqlite3_profile() function is considered experimental and is\n** subject to change in future versions of SQLite.\n*/\nSQLITE_API SQLITE_DEPRECATED void *sqlite3_trace(sqlite3*,\n   void(*xTrace)(void*,const char*), void*);\nSQLITE_API SQLITE_DEPRECATED void *sqlite3_profile(sqlite3*,\n   void(*xProfile)(void*,const char*,sqlite3_uint64), void*);\n\n/*\n** CAPI3REF: SQL Trace Event Codes\n** KEYWORDS: SQLITE_TRACE\n**\n** These constants identify classes of events that can be monitored\n** using the [sqlite3_trace_v2()] tracing logic.  The M argument\n** to [sqlite3_trace_v2(D,M,X,P)] is an OR-ed combination of one or more of\n** the following constants.  ^The first argument to the trace callback\n** is one of the following constants.\n**\n** New tracing constants may be added in future releases.\n**\n** ^A trace callback has four arguments: xCallback(T,C,P,X).\n** ^The T argument is one of the integer type codes above.\n** ^The C argument is a copy of the context pointer passed in as the\n** fourth argument to [sqlite3_trace_v2()].\n** The P and X arguments are pointers whose meanings depend on T.\n**\n** <dl>\n** [[SQLITE_TRACE_STMT]] <dt>SQLITE_TRACE_STMT</dt>\n** <dd>^An SQLITE_TRACE_STMT callback is invoked when a prepared statement\n** first begins running and possibly at other times during the\n** execution of the prepared statement, such as at the start of each\n** trigger subprogram. ^The P argument is a pointer to the\n** [prepared statement]. ^The X argument is a pointer to a string which\n** is the unexpanded SQL text of the prepared statement or an SQL comment \n** that indicates the invocation of a trigger.  ^The callback can compute\n** the same text that would have been returned by the legacy [sqlite3_trace()]\n** interface by using the X argument when X begins with \"--\" and invoking\n** [sqlite3_expanded_sql(P)] otherwise.\n**\n** [[SQLITE_TRACE_PROFILE]] <dt>SQLITE_TRACE_PROFILE</dt>\n** <dd>^An SQLITE_TRACE_PROFILE callback provides approximately the same\n** information as is provided by the [sqlite3_profile()] callback.\n** ^The P argument is a pointer to the [prepared statement] and the\n** X argument points to a 64-bit integer which is the estimated of\n** the number of nanosecond that the prepared statement took to run.\n** ^The SQLITE_TRACE_PROFILE callback is invoked when the statement finishes.\n**\n** [[SQLITE_TRACE_ROW]] <dt>SQLITE_TRACE_ROW</dt>\n** <dd>^An SQLITE_TRACE_ROW callback is invoked whenever a prepared\n** statement generates a single row of result.  \n** ^The P argument is a pointer to the [prepared statement] and the\n** X argument is unused.\n**\n** [[SQLITE_TRACE_CLOSE]] <dt>SQLITE_TRACE_CLOSE</dt>\n** <dd>^An SQLITE_TRACE_CLOSE callback is invoked when a database\n** connection closes.\n** ^The P argument is a pointer to the [database connection] object\n** and the X argument is unused.\n** </dl>\n*/\n#define SQLITE_TRACE_STMT       0x01\n#define SQLITE_TRACE_PROFILE    0x02\n#define SQLITE_TRACE_ROW        0x04\n#define SQLITE_TRACE_CLOSE      0x08\n\n/*\n** CAPI3REF: SQL Trace Hook\n** METHOD: sqlite3\n**\n** ^The sqlite3_trace_v2(D,M,X,P) interface registers a trace callback\n** function X against [database connection] D, using property mask M\n** and context pointer P.  ^If the X callback is\n** NULL or if the M mask is zero, then tracing is disabled.  The\n** M argument should be the bitwise OR-ed combination of\n** zero or more [SQLITE_TRACE] constants.\n**\n** ^Each call to either sqlite3_trace() or sqlite3_trace_v2() overrides \n** (cancels) any prior calls to sqlite3_trace() or sqlite3_trace_v2().\n**\n** ^The X callback is invoked whenever any of the events identified by \n** mask M occur.  ^The integer return value from the callback is currently\n** ignored, though this may change in future releases.  Callback\n** implementations should return zero to ensure future compatibility.\n**\n** ^A trace callback is invoked with four arguments: callback(T,C,P,X).\n** ^The T argument is one of the [SQLITE_TRACE]\n** constants to indicate why the callback was invoked.\n** ^The C argument is a copy of the context pointer.\n** The P and X arguments are pointers whose meanings depend on T.\n**\n** The sqlite3_trace_v2() interface is intended to replace the legacy\n** interfaces [sqlite3_trace()] and [sqlite3_profile()], both of which\n** are deprecated.\n*/\nSQLITE_API int sqlite3_trace_v2(\n  sqlite3*,\n  unsigned uMask,\n  int(*xCallback)(unsigned,void*,void*,void*),\n  void *pCtx\n);\n\n/*\n** CAPI3REF: Query Progress Callbacks\n** METHOD: sqlite3\n**\n** ^The sqlite3_progress_handler(D,N,X,P) interface causes the callback\n** function X to be invoked periodically during long running calls to\n** [sqlite3_exec()], [sqlite3_step()] and [sqlite3_get_table()] for\n** database connection D.  An example use for this\n** interface is to keep a GUI updated during a large query.\n**\n** ^The parameter P is passed through as the only parameter to the \n** callback function X.  ^The parameter N is the approximate number of \n** [virtual machine instructions] that are evaluated between successive\n** invocations of the callback X.  ^If N is less than one then the progress\n** handler is disabled.\n**\n** ^Only a single progress handler may be defined at one time per\n** [database connection]; setting a new progress handler cancels the\n** old one.  ^Setting parameter X to NULL disables the progress handler.\n** ^The progress handler is also disabled by setting N to a value less\n** than 1.\n**\n** ^If the progress callback returns non-zero, the operation is\n** interrupted.  This feature can be used to implement a\n** \"Cancel\" button on a GUI progress dialog box.\n**\n** The progress handler callback must not do anything that will modify\n** the database connection that invoked the progress handler.\n** Note that [sqlite3_prepare_v2()] and [sqlite3_step()] both modify their\n** database connections for the meaning of \"modify\" in this paragraph.\n**\n*/\nSQLITE_API void sqlite3_progress_handler(sqlite3*, int, int(*)(void*), void*);\n\n/*\n** CAPI3REF: Opening A New Database Connection\n** CONSTRUCTOR: sqlite3\n**\n** ^These routines open an SQLite database file as specified by the \n** filename argument. ^The filename argument is interpreted as UTF-8 for\n** sqlite3_open() and sqlite3_open_v2() and as UTF-16 in the native byte\n** order for sqlite3_open16(). ^(A [database connection] handle is usually\n** returned in *ppDb, even if an error occurs.  The only exception is that\n** if SQLite is unable to allocate memory to hold the [sqlite3] object,\n** a NULL will be written into *ppDb instead of a pointer to the [sqlite3]\n** object.)^ ^(If the database is opened (and/or created) successfully, then\n** [SQLITE_OK] is returned.  Otherwise an [error code] is returned.)^ ^The\n** [sqlite3_errmsg()] or [sqlite3_errmsg16()] routines can be used to obtain\n** an English language description of the error following a failure of any\n** of the sqlite3_open() routines.\n**\n** ^The default encoding will be UTF-8 for databases created using\n** sqlite3_open() or sqlite3_open_v2().  ^The default encoding for databases\n** created using sqlite3_open16() will be UTF-16 in the native byte order.\n**\n** Whether or not an error occurs when it is opened, resources\n** associated with the [database connection] handle should be released by\n** passing it to [sqlite3_close()] when it is no longer required.\n**\n** The sqlite3_open_v2() interface works like sqlite3_open()\n** except that it accepts two additional parameters for additional control\n** over the new database connection.  ^(The flags parameter to\n** sqlite3_open_v2() can take one of\n** the following three values, optionally combined with the \n** [SQLITE_OPEN_NOMUTEX], [SQLITE_OPEN_FULLMUTEX], [SQLITE_OPEN_SHAREDCACHE],\n** [SQLITE_OPEN_PRIVATECACHE], and/or [SQLITE_OPEN_URI] flags:)^\n**\n** <dl>\n** ^(<dt>[SQLITE_OPEN_READONLY]</dt>\n** <dd>The database is opened in read-only mode.  If the database does not\n** already exist, an error is returned.</dd>)^\n**\n** ^(<dt>[SQLITE_OPEN_READWRITE]</dt>\n** <dd>The database is opened for reading and writing if possible, or reading\n** only if the file is write protected by the operating system.  In either\n** case the database must already exist, otherwise an error is returned.</dd>)^\n**\n** ^(<dt>[SQLITE_OPEN_READWRITE] | [SQLITE_OPEN_CREATE]</dt>\n** <dd>The database is opened for reading and writing, and is created if\n** it does not already exist. This is the behavior that is always used for\n** sqlite3_open() and sqlite3_open16().</dd>)^\n** </dl>\n**\n** If the 3rd parameter to sqlite3_open_v2() is not one of the\n** combinations shown above optionally combined with other\n** [SQLITE_OPEN_READONLY | SQLITE_OPEN_* bits]\n** then the behavior is undefined.\n**\n** ^If the [SQLITE_OPEN_NOMUTEX] flag is set, then the database connection\n** opens in the multi-thread [threading mode] as long as the single-thread\n** mode has not been set at compile-time or start-time.  ^If the\n** [SQLITE_OPEN_FULLMUTEX] flag is set then the database connection opens\n** in the serialized [threading mode] unless single-thread was\n** previously selected at compile-time or start-time.\n** ^The [SQLITE_OPEN_SHAREDCACHE] flag causes the database connection to be\n** eligible to use [shared cache mode], regardless of whether or not shared\n** cache is enabled using [sqlite3_enable_shared_cache()].  ^The\n** [SQLITE_OPEN_PRIVATECACHE] flag causes the database connection to not\n** participate in [shared cache mode] even if it is enabled.\n**\n** ^The fourth parameter to sqlite3_open_v2() is the name of the\n** [sqlite3_vfs] object that defines the operating system interface that\n** the new database connection should use.  ^If the fourth parameter is\n** a NULL pointer then the default [sqlite3_vfs] object is used.\n**\n** ^If the filename is \":memory:\", then a private, temporary in-memory database\n** is created for the connection.  ^This in-memory database will vanish when\n** the database connection is closed.  Future versions of SQLite might\n** make use of additional special filenames that begin with the \":\" character.\n** It is recommended that when a database filename actually does begin with\n** a \":\" character you should prefix the filename with a pathname such as\n** \"./\" to avoid ambiguity.\n**\n** ^If the filename is an empty string, then a private, temporary\n** on-disk database will be created.  ^This private database will be\n** automatically deleted as soon as the database connection is closed.\n**\n** [[URI filenames in sqlite3_open()]] <h3>URI Filenames</h3>\n**\n** ^If [URI filename] interpretation is enabled, and the filename argument\n** begins with \"file:\", then the filename is interpreted as a URI. ^URI\n** filename interpretation is enabled if the [SQLITE_OPEN_URI] flag is\n** set in the third argument to sqlite3_open_v2(), or if it has\n** been enabled globally using the [SQLITE_CONFIG_URI] option with the\n** [sqlite3_config()] method or by the [SQLITE_USE_URI] compile-time option.\n** URI filename interpretation is turned off\n** by default, but future releases of SQLite might enable URI filename\n** interpretation by default.  See \"[URI filenames]\" for additional\n** information.\n**\n** URI filenames are parsed according to RFC 3986. ^If the URI contains an\n** authority, then it must be either an empty string or the string \n** \"localhost\". ^If the authority is not an empty string or \"localhost\", an \n** error is returned to the caller. ^The fragment component of a URI, if \n** present, is ignored.\n**\n** ^SQLite uses the path component of the URI as the name of the disk file\n** which contains the database. ^If the path begins with a '/' character, \n** then it is interpreted as an absolute path. ^If the path does not begin \n** with a '/' (meaning that the authority section is omitted from the URI)\n** then the path is interpreted as a relative path. \n** ^(On windows, the first component of an absolute path \n** is a drive specification (e.g. \"C:\").)^\n**\n** [[core URI query parameters]]\n** The query component of a URI may contain parameters that are interpreted\n** either by SQLite itself, or by a [VFS | custom VFS implementation].\n** SQLite and its built-in [VFSes] interpret the\n** following query parameters:\n**\n** <ul>\n**   <li> <b>vfs</b>: ^The \"vfs\" parameter may be used to specify the name of\n**     a VFS object that provides the operating system interface that should\n**     be used to access the database file on disk. ^If this option is set to\n**     an empty string the default VFS object is used. ^Specifying an unknown\n**     VFS is an error. ^If sqlite3_open_v2() is used and the vfs option is\n**     present, then the VFS specified by the option takes precedence over\n**     the value passed as the fourth parameter to sqlite3_open_v2().\n**\n**   <li> <b>mode</b>: ^(The mode parameter may be set to either \"ro\", \"rw\",\n**     \"rwc\", or \"memory\". Attempting to set it to any other value is\n**     an error)^. \n**     ^If \"ro\" is specified, then the database is opened for read-only \n**     access, just as if the [SQLITE_OPEN_READONLY] flag had been set in the \n**     third argument to sqlite3_open_v2(). ^If the mode option is set to \n**     \"rw\", then the database is opened for read-write (but not create) \n**     access, as if SQLITE_OPEN_READWRITE (but not SQLITE_OPEN_CREATE) had \n**     been set. ^Value \"rwc\" is equivalent to setting both \n**     SQLITE_OPEN_READWRITE and SQLITE_OPEN_CREATE.  ^If the mode option is\n**     set to \"memory\" then a pure [in-memory database] that never reads\n**     or writes from disk is used. ^It is an error to specify a value for\n**     the mode parameter that is less restrictive than that specified by\n**     the flags passed in the third parameter to sqlite3_open_v2().\n**\n**   <li> <b>cache</b>: ^The cache parameter may be set to either \"shared\" or\n**     \"private\". ^Setting it to \"shared\" is equivalent to setting the\n**     SQLITE_OPEN_SHAREDCACHE bit in the flags argument passed to\n**     sqlite3_open_v2(). ^Setting the cache parameter to \"private\" is \n**     equivalent to setting the SQLITE_OPEN_PRIVATECACHE bit.\n**     ^If sqlite3_open_v2() is used and the \"cache\" parameter is present in\n**     a URI filename, its value overrides any behavior requested by setting\n**     SQLITE_OPEN_PRIVATECACHE or SQLITE_OPEN_SHAREDCACHE flag.\n**\n**  <li> <b>psow</b>: ^The psow parameter indicates whether or not the\n**     [powersafe overwrite] property does or does not apply to the\n**     storage media on which the database file resides.\n**\n**  <li> <b>nolock</b>: ^The nolock parameter is a boolean query parameter\n**     which if set disables file locking in rollback journal modes.  This\n**     is useful for accessing a database on a filesystem that does not\n**     support locking.  Caution:  Database corruption might result if two\n**     or more processes write to the same database and any one of those\n**     processes uses nolock=1.\n**\n**  <li> <b>immutable</b>: ^The immutable parameter is a boolean query\n**     parameter that indicates that the database file is stored on\n**     read-only media.  ^When immutable is set, SQLite assumes that the\n**     database file cannot be changed, even by a process with higher\n**     privilege, and so the database is opened read-only and all locking\n**     and change detection is disabled.  Caution: Setting the immutable\n**     property on a database file that does in fact change can result\n**     in incorrect query results and/or [SQLITE_CORRUPT] errors.\n**     See also: [SQLITE_IOCAP_IMMUTABLE].\n**       \n** </ul>\n**\n** ^Specifying an unknown parameter in the query component of a URI is not an\n** error.  Future versions of SQLite might understand additional query\n** parameters.  See \"[query parameters with special meaning to SQLite]\" for\n** additional information.\n**\n** [[URI filename examples]] <h3>URI filename examples</h3>\n**\n** <table border=\"1\" align=center cellpadding=5>\n** <tr><th> URI filenames <th> Results\n** <tr><td> file:data.db <td> \n**          Open the file \"data.db\" in the current directory.\n** <tr><td> file:/home/fred/data.db<br>\n**          file:///home/fred/data.db <br> \n**          file://localhost/home/fred/data.db <br> <td> \n**          Open the database file \"/home/fred/data.db\".\n** <tr><td> file://darkstar/home/fred/data.db <td> \n**          An error. \"darkstar\" is not a recognized authority.\n** <tr><td style=\"white-space:nowrap\"> \n**          file:///C:/Documents%20and%20Settings/fred/Desktop/data.db\n**     <td> Windows only: Open the file \"data.db\" on fred's desktop on drive\n**          C:. Note that the %20 escaping in this example is not strictly \n**          necessary - space characters can be used literally\n**          in URI filenames.\n** <tr><td> file:data.db?mode=ro&cache=private <td> \n**          Open file \"data.db\" in the current directory for read-only access.\n**          Regardless of whether or not shared-cache mode is enabled by\n**          default, use a private cache.\n** <tr><td> file:/home/fred/data.db?vfs=unix-dotfile <td>\n**          Open file \"/home/fred/data.db\". Use the special VFS \"unix-dotfile\"\n**          that uses dot-files in place of posix advisory locking.\n** <tr><td> file:data.db?mode=readonly <td> \n**          An error. \"readonly\" is not a valid option for the \"mode\" parameter.\n** </table>\n**\n** ^URI hexadecimal escape sequences (%HH) are supported within the path and\n** query components of a URI. A hexadecimal escape sequence consists of a\n** percent sign - \"%\" - followed by exactly two hexadecimal digits \n** specifying an octet value. ^Before the path or query components of a\n** URI filename are interpreted, they are encoded using UTF-8 and all \n** hexadecimal escape sequences replaced by a single byte containing the\n** corresponding octet. If this process generates an invalid UTF-8 encoding,\n** the results are undefined.\n**\n** <b>Note to Windows users:</b>  The encoding used for the filename argument\n** of sqlite3_open() and sqlite3_open_v2() must be UTF-8, not whatever\n** codepage is currently defined.  Filenames containing international\n** characters must be converted to UTF-8 prior to passing them into\n** sqlite3_open() or sqlite3_open_v2().\n**\n** <b>Note to Windows Runtime users:</b>  The temporary directory must be set\n** prior to calling sqlite3_open() or sqlite3_open_v2().  Otherwise, various\n** features that require the use of temporary files may fail.\n**\n** See also: [sqlite3_temp_directory]\n*/\nSQLITE_API int sqlite3_open(\n  const char *filename,   /* Database filename (UTF-8) */\n  sqlite3 **ppDb          /* OUT: SQLite db handle */\n);\nSQLITE_API int sqlite3_open16(\n  const void *filename,   /* Database filename (UTF-16) */\n  sqlite3 **ppDb          /* OUT: SQLite db handle */\n);\nSQLITE_API int sqlite3_open_v2(\n  const char *filename,   /* Database filename (UTF-8) */\n  sqlite3 **ppDb,         /* OUT: SQLite db handle */\n  int flags,              /* Flags */\n  const char *zVfs        /* Name of VFS module to use */\n);\n\n/*\n** CAPI3REF: Obtain Values For URI Parameters\n**\n** These are utility routines, useful to VFS implementations, that check\n** to see if a database file was a URI that contained a specific query \n** parameter, and if so obtains the value of that query parameter.\n**\n** If F is the database filename pointer passed into the xOpen() method of \n** a VFS implementation when the flags parameter to xOpen() has one or \n** more of the [SQLITE_OPEN_URI] or [SQLITE_OPEN_MAIN_DB] bits set and\n** P is the name of the query parameter, then\n** sqlite3_uri_parameter(F,P) returns the value of the P\n** parameter if it exists or a NULL pointer if P does not appear as a \n** query parameter on F.  If P is a query parameter of F\n** has no explicit value, then sqlite3_uri_parameter(F,P) returns\n** a pointer to an empty string.\n**\n** The sqlite3_uri_boolean(F,P,B) routine assumes that P is a boolean\n** parameter and returns true (1) or false (0) according to the value\n** of P.  The sqlite3_uri_boolean(F,P,B) routine returns true (1) if the\n** value of query parameter P is one of \"yes\", \"true\", or \"on\" in any\n** case or if the value begins with a non-zero number.  The \n** sqlite3_uri_boolean(F,P,B) routines returns false (0) if the value of\n** query parameter P is one of \"no\", \"false\", or \"off\" in any case or\n** if the value begins with a numeric zero.  If P is not a query\n** parameter on F or if the value of P is does not match any of the\n** above, then sqlite3_uri_boolean(F,P,B) returns (B!=0).\n**\n** The sqlite3_uri_int64(F,P,D) routine converts the value of P into a\n** 64-bit signed integer and returns that integer, or D if P does not\n** exist.  If the value of P is something other than an integer, then\n** zero is returned.\n** \n** If F is a NULL pointer, then sqlite3_uri_parameter(F,P) returns NULL and\n** sqlite3_uri_boolean(F,P,B) returns B.  If F is not a NULL pointer and\n** is not a database file pathname pointer that SQLite passed into the xOpen\n** VFS method, then the behavior of this routine is undefined and probably\n** undesirable.\n*/\nSQLITE_API const char *sqlite3_uri_parameter(const char *zFilename, const char *zParam);\nSQLITE_API int sqlite3_uri_boolean(const char *zFile, const char *zParam, int bDefault);\nSQLITE_API sqlite3_int64 sqlite3_uri_int64(const char*, const char*, sqlite3_int64);\n\n\n/*\n** CAPI3REF: Error Codes And Messages\n** METHOD: sqlite3\n**\n** ^If the most recent sqlite3_* API call associated with \n** [database connection] D failed, then the sqlite3_errcode(D) interface\n** returns the numeric [result code] or [extended result code] for that\n** API call.\n** If the most recent API call was successful,\n** then the return value from sqlite3_errcode() is undefined.\n** ^The sqlite3_extended_errcode()\n** interface is the same except that it always returns the \n** [extended result code] even when extended result codes are\n** disabled.\n**\n** ^The sqlite3_errmsg() and sqlite3_errmsg16() return English-language\n** text that describes the error, as either UTF-8 or UTF-16 respectively.\n** ^(Memory to hold the error message string is managed internally.\n** The application does not need to worry about freeing the result.\n** However, the error string might be overwritten or deallocated by\n** subsequent calls to other SQLite interface functions.)^\n**\n** ^The sqlite3_errstr() interface returns the English-language text\n** that describes the [result code], as UTF-8.\n** ^(Memory to hold the error message string is managed internally\n** and must not be freed by the application)^.\n**\n** When the serialized [threading mode] is in use, it might be the\n** case that a second error occurs on a separate thread in between\n** the time of the first error and the call to these interfaces.\n** When that happens, the second error will be reported since these\n** interfaces always report the most recent result.  To avoid\n** this, each thread can obtain exclusive use of the [database connection] D\n** by invoking [sqlite3_mutex_enter]([sqlite3_db_mutex](D)) before beginning\n** to use D and invoking [sqlite3_mutex_leave]([sqlite3_db_mutex](D)) after\n** all calls to the interfaces listed here are completed.\n**\n** If an interface fails with SQLITE_MISUSE, that means the interface\n** was invoked incorrectly by the application.  In that case, the\n** error code and message may or may not be set.\n*/\nSQLITE_API int sqlite3_errcode(sqlite3 *db);\nSQLITE_API int sqlite3_extended_errcode(sqlite3 *db);\nSQLITE_API const char *sqlite3_errmsg(sqlite3*);\nSQLITE_API const void *sqlite3_errmsg16(sqlite3*);\nSQLITE_API const char *sqlite3_errstr(int);\n\n/*\n** CAPI3REF: Prepared Statement Object\n** KEYWORDS: {prepared statement} {prepared statements}\n**\n** An instance of this object represents a single SQL statement that\n** has been compiled into binary form and is ready to be evaluated.\n**\n** Think of each SQL statement as a separate computer program.  The\n** original SQL text is source code.  A prepared statement object \n** is the compiled object code.  All SQL must be converted into a\n** prepared statement before it can be run.\n**\n** The life-cycle of a prepared statement object usually goes like this:\n**\n** <ol>\n** <li> Create the prepared statement object using [sqlite3_prepare_v2()].\n** <li> Bind values to [parameters] using the sqlite3_bind_*()\n**      interfaces.\n** <li> Run the SQL by calling [sqlite3_step()] one or more times.\n** <li> Reset the prepared statement using [sqlite3_reset()] then go back\n**      to step 2.  Do this zero or more times.\n** <li> Destroy the object using [sqlite3_finalize()].\n** </ol>\n*/\ntypedef struct sqlite3_stmt sqlite3_stmt;\n\n/*\n** CAPI3REF: Run-time Limits\n** METHOD: sqlite3\n**\n** ^(This interface allows the size of various constructs to be limited\n** on a connection by connection basis.  The first parameter is the\n** [database connection] whose limit is to be set or queried.  The\n** second parameter is one of the [limit categories] that define a\n** class of constructs to be size limited.  The third parameter is the\n** new limit for that construct.)^\n**\n** ^If the new limit is a negative number, the limit is unchanged.\n** ^(For each limit category SQLITE_LIMIT_<i>NAME</i> there is a \n** [limits | hard upper bound]\n** set at compile-time by a C preprocessor macro called\n** [limits | SQLITE_MAX_<i>NAME</i>].\n** (The \"_LIMIT_\" in the name is changed to \"_MAX_\".))^\n** ^Attempts to increase a limit above its hard upper bound are\n** silently truncated to the hard upper bound.\n**\n** ^Regardless of whether or not the limit was changed, the \n** [sqlite3_limit()] interface returns the prior value of the limit.\n** ^Hence, to find the current value of a limit without changing it,\n** simply invoke this interface with the third parameter set to -1.\n**\n** Run-time limits are intended for use in applications that manage\n** both their own internal database and also databases that are controlled\n** by untrusted external sources.  An example application might be a\n** web browser that has its own databases for storing history and\n** separate databases controlled by JavaScript applications downloaded\n** off the Internet.  The internal databases can be given the\n** large, default limits.  Databases managed by external sources can\n** be given much smaller limits designed to prevent a denial of service\n** attack.  Developers might also want to use the [sqlite3_set_authorizer()]\n** interface to further control untrusted SQL.  The size of the database\n** created by an untrusted script can be contained using the\n** [max_page_count] [PRAGMA].\n**\n** New run-time limit categories may be added in future releases.\n*/\nSQLITE_API int sqlite3_limit(sqlite3*, int id, int newVal);\n\n/*\n** CAPI3REF: Run-Time Limit Categories\n** KEYWORDS: {limit category} {*limit categories}\n**\n** These constants define various performance limits\n** that can be lowered at run-time using [sqlite3_limit()].\n** The synopsis of the meanings of the various limits is shown below.\n** Additional information is available at [limits | Limits in SQLite].\n**\n** <dl>\n** [[SQLITE_LIMIT_LENGTH]] ^(<dt>SQLITE_LIMIT_LENGTH</dt>\n** <dd>The maximum size of any string or BLOB or table row, in bytes.<dd>)^\n**\n** [[SQLITE_LIMIT_SQL_LENGTH]] ^(<dt>SQLITE_LIMIT_SQL_LENGTH</dt>\n** <dd>The maximum length of an SQL statement, in bytes.</dd>)^\n**\n** [[SQLITE_LIMIT_COLUMN]] ^(<dt>SQLITE_LIMIT_COLUMN</dt>\n** <dd>The maximum number of columns in a table definition or in the\n** result set of a [SELECT] or the maximum number of columns in an index\n** or in an ORDER BY or GROUP BY clause.</dd>)^\n**\n** [[SQLITE_LIMIT_EXPR_DEPTH]] ^(<dt>SQLITE_LIMIT_EXPR_DEPTH</dt>\n** <dd>The maximum depth of the parse tree on any expression.</dd>)^\n**\n** [[SQLITE_LIMIT_COMPOUND_SELECT]] ^(<dt>SQLITE_LIMIT_COMPOUND_SELECT</dt>\n** <dd>The maximum number of terms in a compound SELECT statement.</dd>)^\n**\n** [[SQLITE_LIMIT_VDBE_OP]] ^(<dt>SQLITE_LIMIT_VDBE_OP</dt>\n** <dd>The maximum number of instructions in a virtual machine program\n** used to implement an SQL statement.  If [sqlite3_prepare_v2()] or\n** the equivalent tries to allocate space for more than this many opcodes\n** in a single prepared statement, an SQLITE_NOMEM error is returned.</dd>)^\n**\n** [[SQLITE_LIMIT_FUNCTION_ARG]] ^(<dt>SQLITE_LIMIT_FUNCTION_ARG</dt>\n** <dd>The maximum number of arguments on a function.</dd>)^\n**\n** [[SQLITE_LIMIT_ATTACHED]] ^(<dt>SQLITE_LIMIT_ATTACHED</dt>\n** <dd>The maximum number of [ATTACH | attached databases].)^</dd>\n**\n** [[SQLITE_LIMIT_LIKE_PATTERN_LENGTH]]\n** ^(<dt>SQLITE_LIMIT_LIKE_PATTERN_LENGTH</dt>\n** <dd>The maximum length of the pattern argument to the [LIKE] or\n** [GLOB] operators.</dd>)^\n**\n** [[SQLITE_LIMIT_VARIABLE_NUMBER]]\n** ^(<dt>SQLITE_LIMIT_VARIABLE_NUMBER</dt>\n** <dd>The maximum index number of any [parameter] in an SQL statement.)^\n**\n** [[SQLITE_LIMIT_TRIGGER_DEPTH]] ^(<dt>SQLITE_LIMIT_TRIGGER_DEPTH</dt>\n** <dd>The maximum depth of recursion for triggers.</dd>)^\n**\n** [[SQLITE_LIMIT_WORKER_THREADS]] ^(<dt>SQLITE_LIMIT_WORKER_THREADS</dt>\n** <dd>The maximum number of auxiliary worker threads that a single\n** [prepared statement] may start.</dd>)^\n** </dl>\n*/\n#define SQLITE_LIMIT_LENGTH                    0\n#define SQLITE_LIMIT_SQL_LENGTH                1\n#define SQLITE_LIMIT_COLUMN                    2\n#define SQLITE_LIMIT_EXPR_DEPTH                3\n#define SQLITE_LIMIT_COMPOUND_SELECT           4\n#define SQLITE_LIMIT_VDBE_OP                   5\n#define SQLITE_LIMIT_FUNCTION_ARG              6\n#define SQLITE_LIMIT_ATTACHED                  7\n#define SQLITE_LIMIT_LIKE_PATTERN_LENGTH       8\n#define SQLITE_LIMIT_VARIABLE_NUMBER           9\n#define SQLITE_LIMIT_TRIGGER_DEPTH            10\n#define SQLITE_LIMIT_WORKER_THREADS           11\n\n/*\n** CAPI3REF: Prepare Flags\n**\n** These constants define various flags that can be passed into\n** \"prepFlags\" parameter of the [sqlite3_prepare_v3()] and\n** [sqlite3_prepare16_v3()] interfaces.\n**\n** New flags may be added in future releases of SQLite.\n**\n** <dl>\n** [[SQLITE_PREPARE_PERSISTENT]] ^(<dt>SQLITE_PREPARE_PERSISTENT</dt>\n** <dd>The SQLITE_PREPARE_PERSISTENT flag is a hint to the query planner\n** that the prepared statement will be retained for a long time and\n** probably reused many times.)^ ^Without this flag, [sqlite3_prepare_v3()]\n** and [sqlite3_prepare16_v3()] assume that the prepared statement will \n** be used just once or at most a few times and then destroyed using\n** [sqlite3_finalize()] relatively soon. The current implementation acts\n** on this hint by avoiding the use of [lookaside memory] so as not to\n** deplete the limited store of lookaside memory. Future versions of\n** SQLite may act on this hint differently.\n** </dl>\n*/\n#define SQLITE_PREPARE_PERSISTENT              0x01\n\n/*\n** CAPI3REF: Compiling An SQL Statement\n** KEYWORDS: {SQL statement compiler}\n** METHOD: sqlite3\n** CONSTRUCTOR: sqlite3_stmt\n**\n** To execute an SQL statement, it must first be compiled into a byte-code\n** program using one of these routines.  Or, in other words, these routines\n** are constructors for the [prepared statement] object.\n**\n** The preferred routine to use is [sqlite3_prepare_v2()].  The\n** [sqlite3_prepare()] interface is legacy and should be avoided.\n** [sqlite3_prepare_v3()] has an extra \"prepFlags\" option that is used\n** for special purposes.\n**\n** The use of the UTF-8 interfaces is preferred, as SQLite currently\n** does all parsing using UTF-8.  The UTF-16 interfaces are provided\n** as a convenience.  The UTF-16 interfaces work by converting the\n** input text into UTF-8, then invoking the corresponding UTF-8 interface.\n**\n** The first argument, \"db\", is a [database connection] obtained from a\n** prior successful call to [sqlite3_open()], [sqlite3_open_v2()] or\n** [sqlite3_open16()].  The database connection must not have been closed.\n**\n** The second argument, \"zSql\", is the statement to be compiled, encoded\n** as either UTF-8 or UTF-16.  The sqlite3_prepare(), sqlite3_prepare_v2(),\n** and sqlite3_prepare_v3()\n** interfaces use UTF-8, and sqlite3_prepare16(), sqlite3_prepare16_v2(),\n** and sqlite3_prepare16_v3() use UTF-16.\n**\n** ^If the nByte argument is negative, then zSql is read up to the\n** first zero terminator. ^If nByte is positive, then it is the\n** number of bytes read from zSql.  ^If nByte is zero, then no prepared\n** statement is generated.\n** If the caller knows that the supplied string is nul-terminated, then\n** there is a small performance advantage to passing an nByte parameter that\n** is the number of bytes in the input string <i>including</i>\n** the nul-terminator.\n**\n** ^If pzTail is not NULL then *pzTail is made to point to the first byte\n** past the end of the first SQL statement in zSql.  These routines only\n** compile the first statement in zSql, so *pzTail is left pointing to\n** what remains uncompiled.\n**\n** ^*ppStmt is left pointing to a compiled [prepared statement] that can be\n** executed using [sqlite3_step()].  ^If there is an error, *ppStmt is set\n** to NULL.  ^If the input text contains no SQL (if the input is an empty\n** string or a comment) then *ppStmt is set to NULL.\n** The calling procedure is responsible for deleting the compiled\n** SQL statement using [sqlite3_finalize()] after it has finished with it.\n** ppStmt may not be NULL.\n**\n** ^On success, the sqlite3_prepare() family of routines return [SQLITE_OK];\n** otherwise an [error code] is returned.\n**\n** The sqlite3_prepare_v2(), sqlite3_prepare_v3(), sqlite3_prepare16_v2(),\n** and sqlite3_prepare16_v3() interfaces are recommended for all new programs.\n** The older interfaces (sqlite3_prepare() and sqlite3_prepare16())\n** are retained for backwards compatibility, but their use is discouraged.\n** ^In the \"vX\" interfaces, the prepared statement\n** that is returned (the [sqlite3_stmt] object) contains a copy of the\n** original SQL text. This causes the [sqlite3_step()] interface to\n** behave differently in three ways:\n**\n** <ol>\n** <li>\n** ^If the database schema changes, instead of returning [SQLITE_SCHEMA] as it\n** always used to do, [sqlite3_step()] will automatically recompile the SQL\n** statement and try to run it again. As many as [SQLITE_MAX_SCHEMA_RETRY]\n** retries will occur before sqlite3_step() gives up and returns an error.\n** </li>\n**\n** <li>\n** ^When an error occurs, [sqlite3_step()] will return one of the detailed\n** [error codes] or [extended error codes].  ^The legacy behavior was that\n** [sqlite3_step()] would only return a generic [SQLITE_ERROR] result code\n** and the application would have to make a second call to [sqlite3_reset()]\n** in order to find the underlying cause of the problem. With the \"v2\" prepare\n** interfaces, the underlying reason for the error is returned immediately.\n** </li>\n**\n** <li>\n** ^If the specific value bound to [parameter | host parameter] in the \n** WHERE clause might influence the choice of query plan for a statement,\n** then the statement will be automatically recompiled, as if there had been \n** a schema change, on the first  [sqlite3_step()] call following any change\n** to the [sqlite3_bind_text | bindings] of that [parameter]. \n** ^The specific value of WHERE-clause [parameter] might influence the \n** choice of query plan if the parameter is the left-hand side of a [LIKE]\n** or [GLOB] operator or if the parameter is compared to an indexed column\n** and the [SQLITE_ENABLE_STAT3] compile-time option is enabled.\n** </li>\n** </ol>\n**\n** <p>^sqlite3_prepare_v3() differs from sqlite3_prepare_v2() only in having\n** the extra prepFlags parameter, which is a bit array consisting of zero or\n** more of the [SQLITE_PREPARE_PERSISTENT|SQLITE_PREPARE_*] flags.  ^The\n** sqlite3_prepare_v2() interface works exactly the same as\n** sqlite3_prepare_v3() with a zero prepFlags parameter.\n*/\nSQLITE_API int sqlite3_prepare(\n  sqlite3 *db,            /* Database handle */\n  const char *zSql,       /* SQL statement, UTF-8 encoded */\n  int nByte,              /* Maximum length of zSql in bytes. */\n  sqlite3_stmt **ppStmt,  /* OUT: Statement handle */\n  const char **pzTail     /* OUT: Pointer to unused portion of zSql */\n);\nSQLITE_API int sqlite3_prepare_v2(\n  sqlite3 *db,            /* Database handle */\n  const char *zSql,       /* SQL statement, UTF-8 encoded */\n  int nByte,              /* Maximum length of zSql in bytes. */\n  sqlite3_stmt **ppStmt,  /* OUT: Statement handle */\n  const char **pzTail     /* OUT: Pointer to unused portion of zSql */\n);\nSQLITE_API int sqlite3_prepare_v3(\n  sqlite3 *db,            /* Database handle */\n  const char *zSql,       /* SQL statement, UTF-8 encoded */\n  int nByte,              /* Maximum length of zSql in bytes. */\n  unsigned int prepFlags, /* Zero or more SQLITE_PREPARE_ flags */\n  sqlite3_stmt **ppStmt,  /* OUT: Statement handle */\n  const char **pzTail     /* OUT: Pointer to unused portion of zSql */\n);\nSQLITE_API int sqlite3_prepare16(\n  sqlite3 *db,            /* Database handle */\n  const void *zSql,       /* SQL statement, UTF-16 encoded */\n  int nByte,              /* Maximum length of zSql in bytes. */\n  sqlite3_stmt **ppStmt,  /* OUT: Statement handle */\n  const void **pzTail     /* OUT: Pointer to unused portion of zSql */\n);\nSQLITE_API int sqlite3_prepare16_v2(\n  sqlite3 *db,            /* Database handle */\n  const void *zSql,       /* SQL statement, UTF-16 encoded */\n  int nByte,              /* Maximum length of zSql in bytes. */\n  sqlite3_stmt **ppStmt,  /* OUT: Statement handle */\n  const void **pzTail     /* OUT: Pointer to unused portion of zSql */\n);\nSQLITE_API int sqlite3_prepare16_v3(\n  sqlite3 *db,            /* Database handle */\n  const void *zSql,       /* SQL statement, UTF-16 encoded */\n  int nByte,              /* Maximum length of zSql in bytes. */\n  unsigned int prepFlags, /* Zero or more SQLITE_PREPARE_ flags */\n  sqlite3_stmt **ppStmt,  /* OUT: Statement handle */\n  const void **pzTail     /* OUT: Pointer to unused portion of zSql */\n);\n\n/*\n** CAPI3REF: Retrieving Statement SQL\n** METHOD: sqlite3_stmt\n**\n** ^The sqlite3_sql(P) interface returns a pointer to a copy of the UTF-8\n** SQL text used to create [prepared statement] P if P was\n** created by [sqlite3_prepare_v2()], [sqlite3_prepare_v3()],\n** [sqlite3_prepare16_v2()], or [sqlite3_prepare16_v3()].\n** ^The sqlite3_expanded_sql(P) interface returns a pointer to a UTF-8\n** string containing the SQL text of prepared statement P with\n** [bound parameters] expanded.\n**\n** ^(For example, if a prepared statement is created using the SQL\n** text \"SELECT $abc,:xyz\" and if parameter $abc is bound to integer 2345\n** and parameter :xyz is unbound, then sqlite3_sql() will return\n** the original string, \"SELECT $abc,:xyz\" but sqlite3_expanded_sql()\n** will return \"SELECT 2345,NULL\".)^\n**\n** ^The sqlite3_expanded_sql() interface returns NULL if insufficient memory\n** is available to hold the result, or if the result would exceed the\n** the maximum string length determined by the [SQLITE_LIMIT_LENGTH].\n**\n** ^The [SQLITE_TRACE_SIZE_LIMIT] compile-time option limits the size of\n** bound parameter expansions.  ^The [SQLITE_OMIT_TRACE] compile-time\n** option causes sqlite3_expanded_sql() to always return NULL.\n**\n** ^The string returned by sqlite3_sql(P) is managed by SQLite and is\n** automatically freed when the prepared statement is finalized.\n** ^The string returned by sqlite3_expanded_sql(P), on the other hand,\n** is obtained from [sqlite3_malloc()] and must be free by the application\n** by passing it to [sqlite3_free()].\n*/\nSQLITE_API const char *sqlite3_sql(sqlite3_stmt *pStmt);\nSQLITE_API char *sqlite3_expanded_sql(sqlite3_stmt *pStmt);\n\n/*\n** CAPI3REF: Determine If An SQL Statement Writes The Database\n** METHOD: sqlite3_stmt\n**\n** ^The sqlite3_stmt_readonly(X) interface returns true (non-zero) if\n** and only if the [prepared statement] X makes no direct changes to\n** the content of the database file.\n**\n** Note that [application-defined SQL functions] or\n** [virtual tables] might change the database indirectly as a side effect.  \n** ^(For example, if an application defines a function \"eval()\" that \n** calls [sqlite3_exec()], then the following SQL statement would\n** change the database file through side-effects:\n**\n** <blockquote><pre>\n**    SELECT eval('DELETE FROM t1') FROM t2;\n** </pre></blockquote>\n**\n** But because the [SELECT] statement does not change the database file\n** directly, sqlite3_stmt_readonly() would still return true.)^\n**\n** ^Transaction control statements such as [BEGIN], [COMMIT], [ROLLBACK],\n** [SAVEPOINT], and [RELEASE] cause sqlite3_stmt_readonly() to return true,\n** since the statements themselves do not actually modify the database but\n** rather they control the timing of when other statements modify the \n** database.  ^The [ATTACH] and [DETACH] statements also cause\n** sqlite3_stmt_readonly() to return true since, while those statements\n** change the configuration of a database connection, they do not make \n** changes to the content of the database files on disk.\n** ^The sqlite3_stmt_readonly() interface returns true for [BEGIN] since\n** [BEGIN] merely sets internal flags, but the [BEGIN|BEGIN IMMEDIATE] and\n** [BEGIN|BEGIN EXCLUSIVE] commands do touch the database and so\n** sqlite3_stmt_readonly() returns false for those commands.\n*/\nSQLITE_API int sqlite3_stmt_readonly(sqlite3_stmt *pStmt);\n\n/*\n** CAPI3REF: Determine If A Prepared Statement Has Been Reset\n** METHOD: sqlite3_stmt\n**\n** ^The sqlite3_stmt_busy(S) interface returns true (non-zero) if the\n** [prepared statement] S has been stepped at least once using \n** [sqlite3_step(S)] but has neither run to completion (returned\n** [SQLITE_DONE] from [sqlite3_step(S)]) nor\n** been reset using [sqlite3_reset(S)].  ^The sqlite3_stmt_busy(S)\n** interface returns false if S is a NULL pointer.  If S is not a \n** NULL pointer and is not a pointer to a valid [prepared statement]\n** object, then the behavior is undefined and probably undesirable.\n**\n** This interface can be used in combination [sqlite3_next_stmt()]\n** to locate all prepared statements associated with a database \n** connection that are in need of being reset.  This can be used,\n** for example, in diagnostic routines to search for prepared \n** statements that are holding a transaction open.\n*/\nSQLITE_API int sqlite3_stmt_busy(sqlite3_stmt*);\n\n/*\n** CAPI3REF: Dynamically Typed Value Object\n** KEYWORDS: {protected sqlite3_value} {unprotected sqlite3_value}\n**\n** SQLite uses the sqlite3_value object to represent all values\n** that can be stored in a database table. SQLite uses dynamic typing\n** for the values it stores.  ^Values stored in sqlite3_value objects\n** can be integers, floating point values, strings, BLOBs, or NULL.\n**\n** An sqlite3_value object may be either \"protected\" or \"unprotected\".\n** Some interfaces require a protected sqlite3_value.  Other interfaces\n** will accept either a protected or an unprotected sqlite3_value.\n** Every interface that accepts sqlite3_value arguments specifies\n** whether or not it requires a protected sqlite3_value.  The\n** [sqlite3_value_dup()] interface can be used to construct a new \n** protected sqlite3_value from an unprotected sqlite3_value.\n**\n** The terms \"protected\" and \"unprotected\" refer to whether or not\n** a mutex is held.  An internal mutex is held for a protected\n** sqlite3_value object but no mutex is held for an unprotected\n** sqlite3_value object.  If SQLite is compiled to be single-threaded\n** (with [SQLITE_THREADSAFE=0] and with [sqlite3_threadsafe()] returning 0)\n** or if SQLite is run in one of reduced mutex modes \n** [SQLITE_CONFIG_SINGLETHREAD] or [SQLITE_CONFIG_MULTITHREAD]\n** then there is no distinction between protected and unprotected\n** sqlite3_value objects and they can be used interchangeably.  However,\n** for maximum code portability it is recommended that applications\n** still make the distinction between protected and unprotected\n** sqlite3_value objects even when not strictly required.\n**\n** ^The sqlite3_value objects that are passed as parameters into the\n** implementation of [application-defined SQL functions] are protected.\n** ^The sqlite3_value object returned by\n** [sqlite3_column_value()] is unprotected.\n** Unprotected sqlite3_value objects may only be used as arguments\n** to [sqlite3_result_value()], [sqlite3_bind_value()], and\n** [sqlite3_value_dup()].\n** The [sqlite3_value_blob | sqlite3_value_type()] family of\n** interfaces require protected sqlite3_value objects.\n*/\ntypedef struct sqlite3_value sqlite3_value;\n\n/*\n** CAPI3REF: SQL Function Context Object\n**\n** The context in which an SQL function executes is stored in an\n** sqlite3_context object.  ^A pointer to an sqlite3_context object\n** is always first parameter to [application-defined SQL functions].\n** The application-defined SQL function implementation will pass this\n** pointer through into calls to [sqlite3_result_int | sqlite3_result()],\n** [sqlite3_aggregate_context()], [sqlite3_user_data()],\n** [sqlite3_context_db_handle()], [sqlite3_get_auxdata()],\n** and/or [sqlite3_set_auxdata()].\n*/\ntypedef struct sqlite3_context sqlite3_context;\n\n/*\n** CAPI3REF: Binding Values To Prepared Statements\n** KEYWORDS: {host parameter} {host parameters} {host parameter name}\n** KEYWORDS: {SQL parameter} {SQL parameters} {parameter binding}\n** METHOD: sqlite3_stmt\n**\n** ^(In the SQL statement text input to [sqlite3_prepare_v2()] and its variants,\n** literals may be replaced by a [parameter] that matches one of following\n** templates:\n**\n** <ul>\n** <li>  ?\n** <li>  ?NNN\n** <li>  :VVV\n** <li>  @VVV\n** <li>  $VVV\n** </ul>\n**\n** In the templates above, NNN represents an integer literal,\n** and VVV represents an alphanumeric identifier.)^  ^The values of these\n** parameters (also called \"host parameter names\" or \"SQL parameters\")\n** can be set using the sqlite3_bind_*() routines defined here.\n**\n** ^The first argument to the sqlite3_bind_*() routines is always\n** a pointer to the [sqlite3_stmt] object returned from\n** [sqlite3_prepare_v2()] or its variants.\n**\n** ^The second argument is the index of the SQL parameter to be set.\n** ^The leftmost SQL parameter has an index of 1.  ^When the same named\n** SQL parameter is used more than once, second and subsequent\n** occurrences have the same index as the first occurrence.\n** ^The index for named parameters can be looked up using the\n** [sqlite3_bind_parameter_index()] API if desired.  ^The index\n** for \"?NNN\" parameters is the value of NNN.\n** ^The NNN value must be between 1 and the [sqlite3_limit()]\n** parameter [SQLITE_LIMIT_VARIABLE_NUMBER] (default value: 999).\n**\n** ^The third argument is the value to bind to the parameter.\n** ^If the third parameter to sqlite3_bind_text() or sqlite3_bind_text16()\n** or sqlite3_bind_blob() is a NULL pointer then the fourth parameter\n** is ignored and the end result is the same as sqlite3_bind_null().\n**\n** ^(In those routines that have a fourth argument, its value is the\n** number of bytes in the parameter.  To be clear: the value is the\n** number of <u>bytes</u> in the value, not the number of characters.)^\n** ^If the fourth parameter to sqlite3_bind_text() or sqlite3_bind_text16()\n** is negative, then the length of the string is\n** the number of bytes up to the first zero terminator.\n** If the fourth parameter to sqlite3_bind_blob() is negative, then\n** the behavior is undefined.\n** If a non-negative fourth parameter is provided to sqlite3_bind_text()\n** or sqlite3_bind_text16() or sqlite3_bind_text64() then\n** that parameter must be the byte offset\n** where the NUL terminator would occur assuming the string were NUL\n** terminated.  If any NUL characters occur at byte offsets less than \n** the value of the fourth parameter then the resulting string value will\n** contain embedded NULs.  The result of expressions involving strings\n** with embedded NULs is undefined.\n**\n** ^The fifth argument to the BLOB and string binding interfaces\n** is a destructor used to dispose of the BLOB or\n** string after SQLite has finished with it.  ^The destructor is called\n** to dispose of the BLOB or string even if the call to bind API fails.\n** ^If the fifth argument is\n** the special value [SQLITE_STATIC], then SQLite assumes that the\n** information is in static, unmanaged space and does not need to be freed.\n** ^If the fifth argument has the value [SQLITE_TRANSIENT], then\n** SQLite makes its own private copy of the data immediately, before\n** the sqlite3_bind_*() routine returns.\n**\n** ^The sixth argument to sqlite3_bind_text64() must be one of\n** [SQLITE_UTF8], [SQLITE_UTF16], [SQLITE_UTF16BE], or [SQLITE_UTF16LE]\n** to specify the encoding of the text in the third parameter.  If\n** the sixth argument to sqlite3_bind_text64() is not one of the\n** allowed values shown above, or if the text encoding is different\n** from the encoding specified by the sixth parameter, then the behavior\n** is undefined.\n**\n** ^The sqlite3_bind_zeroblob() routine binds a BLOB of length N that\n** is filled with zeroes.  ^A zeroblob uses a fixed amount of memory\n** (just an integer to hold its size) while it is being processed.\n** Zeroblobs are intended to serve as placeholders for BLOBs whose\n** content is later written using\n** [sqlite3_blob_open | incremental BLOB I/O] routines.\n** ^A negative value for the zeroblob results in a zero-length BLOB.\n**\n** ^The sqlite3_bind_pointer(S,I,P,T,D) routine causes the I-th parameter in\n** [prepared statement] S to have an SQL value of NULL, but to also be\n** associated with the pointer P of type T.  ^D is either a NULL pointer or\n** a pointer to a destructor function for P. ^SQLite will invoke the\n** destructor D with a single argument of P when it is finished using\n** P.  The T parameter should be a static string, preferably a string\n** literal. The sqlite3_bind_pointer() routine is part of the\n** [pointer passing interface] added for SQLite 3.20.0.\n**\n** ^If any of the sqlite3_bind_*() routines are called with a NULL pointer\n** for the [prepared statement] or with a prepared statement for which\n** [sqlite3_step()] has been called more recently than [sqlite3_reset()],\n** then the call will return [SQLITE_MISUSE].  If any sqlite3_bind_()\n** routine is passed a [prepared statement] that has been finalized, the\n** result is undefined and probably harmful.\n**\n** ^Bindings are not cleared by the [sqlite3_reset()] routine.\n** ^Unbound parameters are interpreted as NULL.\n**\n** ^The sqlite3_bind_* routines return [SQLITE_OK] on success or an\n** [error code] if anything goes wrong.\n** ^[SQLITE_TOOBIG] might be returned if the size of a string or BLOB\n** exceeds limits imposed by [sqlite3_limit]([SQLITE_LIMIT_LENGTH]) or\n** [SQLITE_MAX_LENGTH].\n** ^[SQLITE_RANGE] is returned if the parameter\n** index is out of range.  ^[SQLITE_NOMEM] is returned if malloc() fails.\n**\n** See also: [sqlite3_bind_parameter_count()],\n** [sqlite3_bind_parameter_name()], and [sqlite3_bind_parameter_index()].\n*/\nSQLITE_API int sqlite3_bind_blob(sqlite3_stmt*, int, const void*, int n, void(*)(void*));\nSQLITE_API int sqlite3_bind_blob64(sqlite3_stmt*, int, const void*, sqlite3_uint64,\n                        void(*)(void*));\nSQLITE_API int sqlite3_bind_double(sqlite3_stmt*, int, double);\nSQLITE_API int sqlite3_bind_int(sqlite3_stmt*, int, int);\nSQLITE_API int sqlite3_bind_int64(sqlite3_stmt*, int, sqlite3_int64);\nSQLITE_API int sqlite3_bind_null(sqlite3_stmt*, int);\nSQLITE_API int sqlite3_bind_text(sqlite3_stmt*,int,const char*,int,void(*)(void*));\nSQLITE_API int sqlite3_bind_text16(sqlite3_stmt*, int, const void*, int, void(*)(void*));\nSQLITE_API int sqlite3_bind_text64(sqlite3_stmt*, int, const char*, sqlite3_uint64,\n                         void(*)(void*), unsigned char encoding);\nSQLITE_API int sqlite3_bind_value(sqlite3_stmt*, int, const sqlite3_value*);\nSQLITE_API int sqlite3_bind_pointer(sqlite3_stmt*, int, void*, const char*,void(*)(void*));\nSQLITE_API int sqlite3_bind_zeroblob(sqlite3_stmt*, int, int n);\nSQLITE_API int sqlite3_bind_zeroblob64(sqlite3_stmt*, int, sqlite3_uint64);\n\n/*\n** CAPI3REF: Number Of SQL Parameters\n** METHOD: sqlite3_stmt\n**\n** ^This routine can be used to find the number of [SQL parameters]\n** in a [prepared statement].  SQL parameters are tokens of the\n** form \"?\", \"?NNN\", \":AAA\", \"$AAA\", or \"@AAA\" that serve as\n** placeholders for values that are [sqlite3_bind_blob | bound]\n** to the parameters at a later time.\n**\n** ^(This routine actually returns the index of the largest (rightmost)\n** parameter. For all forms except ?NNN, this will correspond to the\n** number of unique parameters.  If parameters of the ?NNN form are used,\n** there may be gaps in the list.)^\n**\n** See also: [sqlite3_bind_blob|sqlite3_bind()],\n** [sqlite3_bind_parameter_name()], and\n** [sqlite3_bind_parameter_index()].\n*/\nSQLITE_API int sqlite3_bind_parameter_count(sqlite3_stmt*);\n\n/*\n** CAPI3REF: Name Of A Host Parameter\n** METHOD: sqlite3_stmt\n**\n** ^The sqlite3_bind_parameter_name(P,N) interface returns\n** the name of the N-th [SQL parameter] in the [prepared statement] P.\n** ^(SQL parameters of the form \"?NNN\" or \":AAA\" or \"@AAA\" or \"$AAA\"\n** have a name which is the string \"?NNN\" or \":AAA\" or \"@AAA\" or \"$AAA\"\n** respectively.\n** In other words, the initial \":\" or \"$\" or \"@\" or \"?\"\n** is included as part of the name.)^\n** ^Parameters of the form \"?\" without a following integer have no name\n** and are referred to as \"nameless\" or \"anonymous parameters\".\n**\n** ^The first host parameter has an index of 1, not 0.\n**\n** ^If the value N is out of range or if the N-th parameter is\n** nameless, then NULL is returned.  ^The returned string is\n** always in UTF-8 encoding even if the named parameter was\n** originally specified as UTF-16 in [sqlite3_prepare16()],\n** [sqlite3_prepare16_v2()], or [sqlite3_prepare16_v3()].\n**\n** See also: [sqlite3_bind_blob|sqlite3_bind()],\n** [sqlite3_bind_parameter_count()], and\n** [sqlite3_bind_parameter_index()].\n*/\nSQLITE_API const char *sqlite3_bind_parameter_name(sqlite3_stmt*, int);\n\n/*\n** CAPI3REF: Index Of A Parameter With A Given Name\n** METHOD: sqlite3_stmt\n**\n** ^Return the index of an SQL parameter given its name.  ^The\n** index value returned is suitable for use as the second\n** parameter to [sqlite3_bind_blob|sqlite3_bind()].  ^A zero\n** is returned if no matching parameter is found.  ^The parameter\n** name must be given in UTF-8 even if the original statement\n** was prepared from UTF-16 text using [sqlite3_prepare16_v2()] or\n** [sqlite3_prepare16_v3()].\n**\n** See also: [sqlite3_bind_blob|sqlite3_bind()],\n** [sqlite3_bind_parameter_count()], and\n** [sqlite3_bind_parameter_name()].\n*/\nSQLITE_API int sqlite3_bind_parameter_index(sqlite3_stmt*, const char *zName);\n\n/*\n** CAPI3REF: Reset All Bindings On A Prepared Statement\n** METHOD: sqlite3_stmt\n**\n** ^Contrary to the intuition of many, [sqlite3_reset()] does not reset\n** the [sqlite3_bind_blob | bindings] on a [prepared statement].\n** ^Use this routine to reset all host parameters to NULL.\n*/\nSQLITE_API int sqlite3_clear_bindings(sqlite3_stmt*);\n\n/*\n** CAPI3REF: Number Of Columns In A Result Set\n** METHOD: sqlite3_stmt\n**\n** ^Return the number of columns in the result set returned by the\n** [prepared statement]. ^If this routine returns 0, that means the \n** [prepared statement] returns no data (for example an [UPDATE]).\n** ^However, just because this routine returns a positive number does not\n** mean that one or more rows of data will be returned.  ^A SELECT statement\n** will always have a positive sqlite3_column_count() but depending on the\n** WHERE clause constraints and the table content, it might return no rows.\n**\n** See also: [sqlite3_data_count()]\n*/\nSQLITE_API int sqlite3_column_count(sqlite3_stmt *pStmt);\n\n/*\n** CAPI3REF: Column Names In A Result Set\n** METHOD: sqlite3_stmt\n**\n** ^These routines return the name assigned to a particular column\n** in the result set of a [SELECT] statement.  ^The sqlite3_column_name()\n** interface returns a pointer to a zero-terminated UTF-8 string\n** and sqlite3_column_name16() returns a pointer to a zero-terminated\n** UTF-16 string.  ^The first parameter is the [prepared statement]\n** that implements the [SELECT] statement. ^The second parameter is the\n** column number.  ^The leftmost column is number 0.\n**\n** ^The returned string pointer is valid until either the [prepared statement]\n** is destroyed by [sqlite3_finalize()] or until the statement is automatically\n** reprepared by the first call to [sqlite3_step()] for a particular run\n** or until the next call to\n** sqlite3_column_name() or sqlite3_column_name16() on the same column.\n**\n** ^If sqlite3_malloc() fails during the processing of either routine\n** (for example during a conversion from UTF-8 to UTF-16) then a\n** NULL pointer is returned.\n**\n** ^The name of a result column is the value of the \"AS\" clause for\n** that column, if there is an AS clause.  If there is no AS clause\n** then the name of the column is unspecified and may change from\n** one release of SQLite to the next.\n*/\nSQLITE_API const char *sqlite3_column_name(sqlite3_stmt*, int N);\nSQLITE_API const void *sqlite3_column_name16(sqlite3_stmt*, int N);\n\n/*\n** CAPI3REF: Source Of Data In A Query Result\n** METHOD: sqlite3_stmt\n**\n** ^These routines provide a means to determine the database, table, and\n** table column that is the origin of a particular result column in\n** [SELECT] statement.\n** ^The name of the database or table or column can be returned as\n** either a UTF-8 or UTF-16 string.  ^The _database_ routines return\n** the database name, the _table_ routines return the table name, and\n** the origin_ routines return the column name.\n** ^The returned string is valid until the [prepared statement] is destroyed\n** using [sqlite3_finalize()] or until the statement is automatically\n** reprepared by the first call to [sqlite3_step()] for a particular run\n** or until the same information is requested\n** again in a different encoding.\n**\n** ^The names returned are the original un-aliased names of the\n** database, table, and column.\n**\n** ^The first argument to these interfaces is a [prepared statement].\n** ^These functions return information about the Nth result column returned by\n** the statement, where N is the second function argument.\n** ^The left-most column is column 0 for these routines.\n**\n** ^If the Nth column returned by the statement is an expression or\n** subquery and is not a column value, then all of these functions return\n** NULL.  ^These routine might also return NULL if a memory allocation error\n** occurs.  ^Otherwise, they return the name of the attached database, table,\n** or column that query result column was extracted from.\n**\n** ^As with all other SQLite APIs, those whose names end with \"16\" return\n** UTF-16 encoded strings and the other functions return UTF-8.\n**\n** ^These APIs are only available if the library was compiled with the\n** [SQLITE_ENABLE_COLUMN_METADATA] C-preprocessor symbol.\n**\n** If two or more threads call one or more of these routines against the same\n** prepared statement and column at the same time then the results are\n** undefined.\n**\n** If two or more threads call one or more\n** [sqlite3_column_database_name | column metadata interfaces]\n** for the same [prepared statement] and result column\n** at the same time then the results are undefined.\n*/\nSQLITE_API const char *sqlite3_column_database_name(sqlite3_stmt*,int);\nSQLITE_API const void *sqlite3_column_database_name16(sqlite3_stmt*,int);\nSQLITE_API const char *sqlite3_column_table_name(sqlite3_stmt*,int);\nSQLITE_API const void *sqlite3_column_table_name16(sqlite3_stmt*,int);\nSQLITE_API const char *sqlite3_column_origin_name(sqlite3_stmt*,int);\nSQLITE_API const void *sqlite3_column_origin_name16(sqlite3_stmt*,int);\n\n/*\n** CAPI3REF: Declared Datatype Of A Query Result\n** METHOD: sqlite3_stmt\n**\n** ^(The first parameter is a [prepared statement].\n** If this statement is a [SELECT] statement and the Nth column of the\n** returned result set of that [SELECT] is a table column (not an\n** expression or subquery) then the declared type of the table\n** column is returned.)^  ^If the Nth column of the result set is an\n** expression or subquery, then a NULL pointer is returned.\n** ^The returned string is always UTF-8 encoded.\n**\n** ^(For example, given the database schema:\n**\n** CREATE TABLE t1(c1 VARIANT);\n**\n** and the following statement to be compiled:\n**\n** SELECT c1 + 1, c1 FROM t1;\n**\n** this routine would return the string \"VARIANT\" for the second result\n** column (i==1), and a NULL pointer for the first result column (i==0).)^\n**\n** ^SQLite uses dynamic run-time typing.  ^So just because a column\n** is declared to contain a particular type does not mean that the\n** data stored in that column is of the declared type.  SQLite is\n** strongly typed, but the typing is dynamic not static.  ^Type\n** is associated with individual values, not with the containers\n** used to hold those values.\n*/\nSQLITE_API const char *sqlite3_column_decltype(sqlite3_stmt*,int);\nSQLITE_API const void *sqlite3_column_decltype16(sqlite3_stmt*,int);\n\n/*\n** CAPI3REF: Evaluate An SQL Statement\n** METHOD: sqlite3_stmt\n**\n** After a [prepared statement] has been prepared using any of\n** [sqlite3_prepare_v2()], [sqlite3_prepare_v3()], [sqlite3_prepare16_v2()],\n** or [sqlite3_prepare16_v3()] or one of the legacy\n** interfaces [sqlite3_prepare()] or [sqlite3_prepare16()], this function\n** must be called one or more times to evaluate the statement.\n**\n** The details of the behavior of the sqlite3_step() interface depend\n** on whether the statement was prepared using the newer \"vX\" interfaces\n** [sqlite3_prepare_v3()], [sqlite3_prepare_v2()], [sqlite3_prepare16_v3()],\n** [sqlite3_prepare16_v2()] or the older legacy\n** interfaces [sqlite3_prepare()] and [sqlite3_prepare16()].  The use of the\n** new \"vX\" interface is recommended for new applications but the legacy\n** interface will continue to be supported.\n**\n** ^In the legacy interface, the return value will be either [SQLITE_BUSY],\n** [SQLITE_DONE], [SQLITE_ROW], [SQLITE_ERROR], or [SQLITE_MISUSE].\n** ^With the \"v2\" interface, any of the other [result codes] or\n** [extended result codes] might be returned as well.\n**\n** ^[SQLITE_BUSY] means that the database engine was unable to acquire the\n** database locks it needs to do its job.  ^If the statement is a [COMMIT]\n** or occurs outside of an explicit transaction, then you can retry the\n** statement.  If the statement is not a [COMMIT] and occurs within an\n** explicit transaction then you should rollback the transaction before\n** continuing.\n**\n** ^[SQLITE_DONE] means that the statement has finished executing\n** successfully.  sqlite3_step() should not be called again on this virtual\n** machine without first calling [sqlite3_reset()] to reset the virtual\n** machine back to its initial state.\n**\n** ^If the SQL statement being executed returns any data, then [SQLITE_ROW]\n** is returned each time a new row of data is ready for processing by the\n** caller. The values may be accessed using the [column access functions].\n** sqlite3_step() is called again to retrieve the next row of data.\n**\n** ^[SQLITE_ERROR] means that a run-time error (such as a constraint\n** violation) has occurred.  sqlite3_step() should not be called again on\n** the VM. More information may be found by calling [sqlite3_errmsg()].\n** ^With the legacy interface, a more specific error code (for example,\n** [SQLITE_INTERRUPT], [SQLITE_SCHEMA], [SQLITE_CORRUPT], and so forth)\n** can be obtained by calling [sqlite3_reset()] on the\n** [prepared statement].  ^In the \"v2\" interface,\n** the more specific error code is returned directly by sqlite3_step().\n**\n** [SQLITE_MISUSE] means that the this routine was called inappropriately.\n** Perhaps it was called on a [prepared statement] that has\n** already been [sqlite3_finalize | finalized] or on one that had\n** previously returned [SQLITE_ERROR] or [SQLITE_DONE].  Or it could\n** be the case that the same database connection is being used by two or\n** more threads at the same moment in time.\n**\n** For all versions of SQLite up to and including 3.6.23.1, a call to\n** [sqlite3_reset()] was required after sqlite3_step() returned anything\n** other than [SQLITE_ROW] before any subsequent invocation of\n** sqlite3_step().  Failure to reset the prepared statement using \n** [sqlite3_reset()] would result in an [SQLITE_MISUSE] return from\n** sqlite3_step().  But after [version 3.6.23.1] ([dateof:3.6.23.1],\n** sqlite3_step() began\n** calling [sqlite3_reset()] automatically in this circumstance rather\n** than returning [SQLITE_MISUSE].  This is not considered a compatibility\n** break because any application that ever receives an SQLITE_MISUSE error\n** is broken by definition.  The [SQLITE_OMIT_AUTORESET] compile-time option\n** can be used to restore the legacy behavior.\n**\n** <b>Goofy Interface Alert:</b> In the legacy interface, the sqlite3_step()\n** API always returns a generic error code, [SQLITE_ERROR], following any\n** error other than [SQLITE_BUSY] and [SQLITE_MISUSE].  You must call\n** [sqlite3_reset()] or [sqlite3_finalize()] in order to find one of the\n** specific [error codes] that better describes the error.\n** We admit that this is a goofy design.  The problem has been fixed\n** with the \"v2\" interface.  If you prepare all of your SQL statements\n** using [sqlite3_prepare_v3()] or [sqlite3_prepare_v2()]\n** or [sqlite3_prepare16_v2()] or [sqlite3_prepare16_v3()] instead\n** of the legacy [sqlite3_prepare()] and [sqlite3_prepare16()] interfaces,\n** then the more specific [error codes] are returned directly\n** by sqlite3_step().  The use of the \"vX\" interfaces is recommended.\n*/\nSQLITE_API int sqlite3_step(sqlite3_stmt*);\n\n/*\n** CAPI3REF: Number of columns in a result set\n** METHOD: sqlite3_stmt\n**\n** ^The sqlite3_data_count(P) interface returns the number of columns in the\n** current row of the result set of [prepared statement] P.\n** ^If prepared statement P does not have results ready to return\n** (via calls to the [sqlite3_column_int | sqlite3_column_*()] of\n** interfaces) then sqlite3_data_count(P) returns 0.\n** ^The sqlite3_data_count(P) routine also returns 0 if P is a NULL pointer.\n** ^The sqlite3_data_count(P) routine returns 0 if the previous call to\n** [sqlite3_step](P) returned [SQLITE_DONE].  ^The sqlite3_data_count(P)\n** will return non-zero if previous call to [sqlite3_step](P) returned\n** [SQLITE_ROW], except in the case of the [PRAGMA incremental_vacuum]\n** where it always returns zero since each step of that multi-step\n** pragma returns 0 columns of data.\n**\n** See also: [sqlite3_column_count()]\n*/\nSQLITE_API int sqlite3_data_count(sqlite3_stmt *pStmt);\n\n/*\n** CAPI3REF: Fundamental Datatypes\n** KEYWORDS: SQLITE_TEXT\n**\n** ^(Every value in SQLite has one of five fundamental datatypes:\n**\n** <ul>\n** <li> 64-bit signed integer\n** <li> 64-bit IEEE floating point number\n** <li> string\n** <li> BLOB\n** <li> NULL\n** </ul>)^\n**\n** These constants are codes for each of those types.\n**\n** Note that the SQLITE_TEXT constant was also used in SQLite version 2\n** for a completely different meaning.  Software that links against both\n** SQLite version 2 and SQLite version 3 should use SQLITE3_TEXT, not\n** SQLITE_TEXT.\n*/\n#define SQLITE_INTEGER  1\n#define SQLITE_FLOAT    2\n#define SQLITE_BLOB     4\n#define SQLITE_NULL     5\n#ifdef SQLITE_TEXT\n# undef SQLITE_TEXT\n#else\n# define SQLITE_TEXT     3\n#endif\n#define SQLITE3_TEXT     3\n\n/*\n** CAPI3REF: Result Values From A Query\n** KEYWORDS: {column access functions}\n** METHOD: sqlite3_stmt\n**\n** <b>Summary:</b>\n** <blockquote><table border=0 cellpadding=0 cellspacing=0>\n** <tr><td><b>sqlite3_column_blob</b><td>&rarr;<td>BLOB result\n** <tr><td><b>sqlite3_column_double</b><td>&rarr;<td>REAL result\n** <tr><td><b>sqlite3_column_int</b><td>&rarr;<td>32-bit INTEGER result\n** <tr><td><b>sqlite3_column_int64</b><td>&rarr;<td>64-bit INTEGER result\n** <tr><td><b>sqlite3_column_text</b><td>&rarr;<td>UTF-8 TEXT result\n** <tr><td><b>sqlite3_column_text16</b><td>&rarr;<td>UTF-16 TEXT result\n** <tr><td><b>sqlite3_column_value</b><td>&rarr;<td>The result as an \n** [sqlite3_value|unprotected sqlite3_value] object.\n** <tr><td>&nbsp;<td>&nbsp;<td>&nbsp;\n** <tr><td><b>sqlite3_column_bytes</b><td>&rarr;<td>Size of a BLOB\n** or a UTF-8 TEXT result in bytes\n** <tr><td><b>sqlite3_column_bytes16&nbsp;&nbsp;</b>\n** <td>&rarr;&nbsp;&nbsp;<td>Size of UTF-16\n** TEXT in bytes\n** <tr><td><b>sqlite3_column_type</b><td>&rarr;<td>Default\n** datatype of the result\n** </table></blockquote>\n**\n** <b>Details:</b>\n**\n** ^These routines return information about a single column of the current\n** result row of a query.  ^In every case the first argument is a pointer\n** to the [prepared statement] that is being evaluated (the [sqlite3_stmt*]\n** that was returned from [sqlite3_prepare_v2()] or one of its variants)\n** and the second argument is the index of the column for which information\n** should be returned. ^The leftmost column of the result set has the index 0.\n** ^The number of columns in the result can be determined using\n** [sqlite3_column_count()].\n**\n** If the SQL statement does not currently point to a valid row, or if the\n** column index is out of range, the result is undefined.\n** These routines may only be called when the most recent call to\n** [sqlite3_step()] has returned [SQLITE_ROW] and neither\n** [sqlite3_reset()] nor [sqlite3_finalize()] have been called subsequently.\n** If any of these routines are called after [sqlite3_reset()] or\n** [sqlite3_finalize()] or after [sqlite3_step()] has returned\n** something other than [SQLITE_ROW], the results are undefined.\n** If [sqlite3_step()] or [sqlite3_reset()] or [sqlite3_finalize()]\n** are called from a different thread while any of these routines\n** are pending, then the results are undefined.\n**\n** The first six interfaces (_blob, _double, _int, _int64, _text, and _text16)\n** each return the value of a result column in a specific data format.  If\n** the result column is not initially in the requested format (for example,\n** if the query returns an integer but the sqlite3_column_text() interface\n** is used to extract the value) then an automatic type conversion is performed.\n**\n** ^The sqlite3_column_type() routine returns the\n** [SQLITE_INTEGER | datatype code] for the initial data type\n** of the result column.  ^The returned value is one of [SQLITE_INTEGER],\n** [SQLITE_FLOAT], [SQLITE_TEXT], [SQLITE_BLOB], or [SQLITE_NULL].\n** The return value of sqlite3_column_type() can be used to decide which\n** of the first six interface should be used to extract the column value.\n** The value returned by sqlite3_column_type() is only meaningful if no\n** automatic type conversions have occurred for the value in question.  \n** After a type conversion, the result of calling sqlite3_column_type()\n** is undefined, though harmless.  Future\n** versions of SQLite may change the behavior of sqlite3_column_type()\n** following a type conversion.\n**\n** If the result is a BLOB or a TEXT string, then the sqlite3_column_bytes()\n** or sqlite3_column_bytes16() interfaces can be used to determine the size\n** of that BLOB or string.\n**\n** ^If the result is a BLOB or UTF-8 string then the sqlite3_column_bytes()\n** routine returns the number of bytes in that BLOB or string.\n** ^If the result is a UTF-16 string, then sqlite3_column_bytes() converts\n** the string to UTF-8 and then returns the number of bytes.\n** ^If the result is a numeric value then sqlite3_column_bytes() uses\n** [sqlite3_snprintf()] to convert that value to a UTF-8 string and returns\n** the number of bytes in that string.\n** ^If the result is NULL, then sqlite3_column_bytes() returns zero.\n**\n** ^If the result is a BLOB or UTF-16 string then the sqlite3_column_bytes16()\n** routine returns the number of bytes in that BLOB or string.\n** ^If the result is a UTF-8 string, then sqlite3_column_bytes16() converts\n** the string to UTF-16 and then returns the number of bytes.\n** ^If the result is a numeric value then sqlite3_column_bytes16() uses\n** [sqlite3_snprintf()] to convert that value to a UTF-16 string and returns\n** the number of bytes in that string.\n** ^If the result is NULL, then sqlite3_column_bytes16() returns zero.\n**\n** ^The values returned by [sqlite3_column_bytes()] and \n** [sqlite3_column_bytes16()] do not include the zero terminators at the end\n** of the string.  ^For clarity: the values returned by\n** [sqlite3_column_bytes()] and [sqlite3_column_bytes16()] are the number of\n** bytes in the string, not the number of characters.\n**\n** ^Strings returned by sqlite3_column_text() and sqlite3_column_text16(),\n** even empty strings, are always zero-terminated.  ^The return\n** value from sqlite3_column_blob() for a zero-length BLOB is a NULL pointer.\n**\n** <b>Warning:</b> ^The object returned by [sqlite3_column_value()] is an\n** [unprotected sqlite3_value] object.  In a multithreaded environment,\n** an unprotected sqlite3_value object may only be used safely with\n** [sqlite3_bind_value()] and [sqlite3_result_value()].\n** If the [unprotected sqlite3_value] object returned by\n** [sqlite3_column_value()] is used in any other way, including calls\n** to routines like [sqlite3_value_int()], [sqlite3_value_text()],\n** or [sqlite3_value_bytes()], the behavior is not threadsafe.\n** Hence, the sqlite3_column_value() interface\n** is normally only useful within the implementation of \n** [application-defined SQL functions] or [virtual tables], not within\n** top-level application code.\n**\n** The these routines may attempt to convert the datatype of the result.\n** ^For example, if the internal representation is FLOAT and a text result\n** is requested, [sqlite3_snprintf()] is used internally to perform the\n** conversion automatically.  ^(The following table details the conversions\n** that are applied:\n**\n** <blockquote>\n** <table border=\"1\">\n** <tr><th> Internal<br>Type <th> Requested<br>Type <th>  Conversion\n**\n** <tr><td>  NULL    <td> INTEGER   <td> Result is 0\n** <tr><td>  NULL    <td>  FLOAT    <td> Result is 0.0\n** <tr><td>  NULL    <td>   TEXT    <td> Result is a NULL pointer\n** <tr><td>  NULL    <td>   BLOB    <td> Result is a NULL pointer\n** <tr><td> INTEGER  <td>  FLOAT    <td> Convert from integer to float\n** <tr><td> INTEGER  <td>   TEXT    <td> ASCII rendering of the integer\n** <tr><td> INTEGER  <td>   BLOB    <td> Same as INTEGER->TEXT\n** <tr><td>  FLOAT   <td> INTEGER   <td> [CAST] to INTEGER\n** <tr><td>  FLOAT   <td>   TEXT    <td> ASCII rendering of the float\n** <tr><td>  FLOAT   <td>   BLOB    <td> [CAST] to BLOB\n** <tr><td>  TEXT    <td> INTEGER   <td> [CAST] to INTEGER\n** <tr><td>  TEXT    <td>  FLOAT    <td> [CAST] to REAL\n** <tr><td>  TEXT    <td>   BLOB    <td> No change\n** <tr><td>  BLOB    <td> INTEGER   <td> [CAST] to INTEGER\n** <tr><td>  BLOB    <td>  FLOAT    <td> [CAST] to REAL\n** <tr><td>  BLOB    <td>   TEXT    <td> Add a zero terminator if needed\n** </table>\n** </blockquote>)^\n**\n** Note that when type conversions occur, pointers returned by prior\n** calls to sqlite3_column_blob(), sqlite3_column_text(), and/or\n** sqlite3_column_text16() may be invalidated.\n** Type conversions and pointer invalidations might occur\n** in the following cases:\n**\n** <ul>\n** <li> The initial content is a BLOB and sqlite3_column_text() or\n**      sqlite3_column_text16() is called.  A zero-terminator might\n**      need to be added to the string.</li>\n** <li> The initial content is UTF-8 text and sqlite3_column_bytes16() or\n**      sqlite3_column_text16() is called.  The content must be converted\n**      to UTF-16.</li>\n** <li> The initial content is UTF-16 text and sqlite3_column_bytes() or\n**      sqlite3_column_text() is called.  The content must be converted\n**      to UTF-8.</li>\n** </ul>\n**\n** ^Conversions between UTF-16be and UTF-16le are always done in place and do\n** not invalidate a prior pointer, though of course the content of the buffer\n** that the prior pointer references will have been modified.  Other kinds\n** of conversion are done in place when it is possible, but sometimes they\n** are not possible and in those cases prior pointers are invalidated.\n**\n** The safest policy is to invoke these routines\n** in one of the following ways:\n**\n** <ul>\n**  <li>sqlite3_column_text() followed by sqlite3_column_bytes()</li>\n**  <li>sqlite3_column_blob() followed by sqlite3_column_bytes()</li>\n**  <li>sqlite3_column_text16() followed by sqlite3_column_bytes16()</li>\n** </ul>\n**\n** In other words, you should call sqlite3_column_text(),\n** sqlite3_column_blob(), or sqlite3_column_text16() first to force the result\n** into the desired format, then invoke sqlite3_column_bytes() or\n** sqlite3_column_bytes16() to find the size of the result.  Do not mix calls\n** to sqlite3_column_text() or sqlite3_column_blob() with calls to\n** sqlite3_column_bytes16(), and do not mix calls to sqlite3_column_text16()\n** with calls to sqlite3_column_bytes().\n**\n** ^The pointers returned are valid until a type conversion occurs as\n** described above, or until [sqlite3_step()] or [sqlite3_reset()] or\n** [sqlite3_finalize()] is called.  ^The memory space used to hold strings\n** and BLOBs is freed automatically.  Do not pass the pointers returned\n** from [sqlite3_column_blob()], [sqlite3_column_text()], etc. into\n** [sqlite3_free()].\n**\n** ^(If a memory allocation error occurs during the evaluation of any\n** of these routines, a default value is returned.  The default value\n** is either the integer 0, the floating point number 0.0, or a NULL\n** pointer.  Subsequent calls to [sqlite3_errcode()] will return\n** [SQLITE_NOMEM].)^\n*/\nSQLITE_API const void *sqlite3_column_blob(sqlite3_stmt*, int iCol);\nSQLITE_API double sqlite3_column_double(sqlite3_stmt*, int iCol);\nSQLITE_API int sqlite3_column_int(sqlite3_stmt*, int iCol);\nSQLITE_API sqlite3_int64 sqlite3_column_int64(sqlite3_stmt*, int iCol);\nSQLITE_API const unsigned char *sqlite3_column_text(sqlite3_stmt*, int iCol);\nSQLITE_API const void *sqlite3_column_text16(sqlite3_stmt*, int iCol);\nSQLITE_API sqlite3_value *sqlite3_column_value(sqlite3_stmt*, int iCol);\nSQLITE_API int sqlite3_column_bytes(sqlite3_stmt*, int iCol);\nSQLITE_API int sqlite3_column_bytes16(sqlite3_stmt*, int iCol);\nSQLITE_API int sqlite3_column_type(sqlite3_stmt*, int iCol);\n\n/*\n** CAPI3REF: Destroy A Prepared Statement Object\n** DESTRUCTOR: sqlite3_stmt\n**\n** ^The sqlite3_finalize() function is called to delete a [prepared statement].\n** ^If the most recent evaluation of the statement encountered no errors\n** or if the statement is never been evaluated, then sqlite3_finalize() returns\n** SQLITE_OK.  ^If the most recent evaluation of statement S failed, then\n** sqlite3_finalize(S) returns the appropriate [error code] or\n** [extended error code].\n**\n** ^The sqlite3_finalize(S) routine can be called at any point during\n** the life cycle of [prepared statement] S:\n** before statement S is ever evaluated, after\n** one or more calls to [sqlite3_reset()], or after any call\n** to [sqlite3_step()] regardless of whether or not the statement has\n** completed execution.\n**\n** ^Invoking sqlite3_finalize() on a NULL pointer is a harmless no-op.\n**\n** The application must finalize every [prepared statement] in order to avoid\n** resource leaks.  It is a grievous error for the application to try to use\n** a prepared statement after it has been finalized.  Any use of a prepared\n** statement after it has been finalized can result in undefined and\n** undesirable behavior such as segfaults and heap corruption.\n*/\nSQLITE_API int sqlite3_finalize(sqlite3_stmt *pStmt);\n\n/*\n** CAPI3REF: Reset A Prepared Statement Object\n** METHOD: sqlite3_stmt\n**\n** The sqlite3_reset() function is called to reset a [prepared statement]\n** object back to its initial state, ready to be re-executed.\n** ^Any SQL statement variables that had values bound to them using\n** the [sqlite3_bind_blob | sqlite3_bind_*() API] retain their values.\n** Use [sqlite3_clear_bindings()] to reset the bindings.\n**\n** ^The [sqlite3_reset(S)] interface resets the [prepared statement] S\n** back to the beginning of its program.\n**\n** ^If the most recent call to [sqlite3_step(S)] for the\n** [prepared statement] S returned [SQLITE_ROW] or [SQLITE_DONE],\n** or if [sqlite3_step(S)] has never before been called on S,\n** then [sqlite3_reset(S)] returns [SQLITE_OK].\n**\n** ^If the most recent call to [sqlite3_step(S)] for the\n** [prepared statement] S indicated an error, then\n** [sqlite3_reset(S)] returns an appropriate [error code].\n**\n** ^The [sqlite3_reset(S)] interface does not change the values\n** of any [sqlite3_bind_blob|bindings] on the [prepared statement] S.\n*/\nSQLITE_API int sqlite3_reset(sqlite3_stmt *pStmt);\n\n/*\n** CAPI3REF: Create Or Redefine SQL Functions\n** KEYWORDS: {function creation routines}\n** KEYWORDS: {application-defined SQL function}\n** KEYWORDS: {application-defined SQL functions}\n** METHOD: sqlite3\n**\n** ^These functions (collectively known as \"function creation routines\")\n** are used to add SQL functions or aggregates or to redefine the behavior\n** of existing SQL functions or aggregates.  The only differences between\n** these routines are the text encoding expected for\n** the second parameter (the name of the function being created)\n** and the presence or absence of a destructor callback for\n** the application data pointer.\n**\n** ^The first parameter is the [database connection] to which the SQL\n** function is to be added.  ^If an application uses more than one database\n** connection then application-defined SQL functions must be added\n** to each database connection separately.\n**\n** ^The second parameter is the name of the SQL function to be created or\n** redefined.  ^The length of the name is limited to 255 bytes in a UTF-8\n** representation, exclusive of the zero-terminator.  ^Note that the name\n** length limit is in UTF-8 bytes, not characters nor UTF-16 bytes.  \n** ^Any attempt to create a function with a longer name\n** will result in [SQLITE_MISUSE] being returned.\n**\n** ^The third parameter (nArg)\n** is the number of arguments that the SQL function or\n** aggregate takes. ^If this parameter is -1, then the SQL function or\n** aggregate may take any number of arguments between 0 and the limit\n** set by [sqlite3_limit]([SQLITE_LIMIT_FUNCTION_ARG]).  If the third\n** parameter is less than -1 or greater than 127 then the behavior is\n** undefined.\n**\n** ^The fourth parameter, eTextRep, specifies what\n** [SQLITE_UTF8 | text encoding] this SQL function prefers for\n** its parameters.  The application should set this parameter to\n** [SQLITE_UTF16LE] if the function implementation invokes \n** [sqlite3_value_text16le()] on an input, or [SQLITE_UTF16BE] if the\n** implementation invokes [sqlite3_value_text16be()] on an input, or\n** [SQLITE_UTF16] if [sqlite3_value_text16()] is used, or [SQLITE_UTF8]\n** otherwise.  ^The same SQL function may be registered multiple times using\n** different preferred text encodings, with different implementations for\n** each encoding.\n** ^When multiple implementations of the same function are available, SQLite\n** will pick the one that involves the least amount of data conversion.\n**\n** ^The fourth parameter may optionally be ORed with [SQLITE_DETERMINISTIC]\n** to signal that the function will always return the same result given\n** the same inputs within a single SQL statement.  Most SQL functions are\n** deterministic.  The built-in [random()] SQL function is an example of a\n** function that is not deterministic.  The SQLite query planner is able to\n** perform additional optimizations on deterministic functions, so use\n** of the [SQLITE_DETERMINISTIC] flag is recommended where possible.\n**\n** ^(The fifth parameter is an arbitrary pointer.  The implementation of the\n** function can gain access to this pointer using [sqlite3_user_data()].)^\n**\n** ^The sixth, seventh and eighth parameters, xFunc, xStep and xFinal, are\n** pointers to C-language functions that implement the SQL function or\n** aggregate. ^A scalar SQL function requires an implementation of the xFunc\n** callback only; NULL pointers must be passed as the xStep and xFinal\n** parameters. ^An aggregate SQL function requires an implementation of xStep\n** and xFinal and NULL pointer must be passed for xFunc. ^To delete an existing\n** SQL function or aggregate, pass NULL pointers for all three function\n** callbacks.\n**\n** ^(If the ninth parameter to sqlite3_create_function_v2() is not NULL,\n** then it is destructor for the application data pointer. \n** The destructor is invoked when the function is deleted, either by being\n** overloaded or when the database connection closes.)^\n** ^The destructor is also invoked if the call to\n** sqlite3_create_function_v2() fails.\n** ^When the destructor callback of the tenth parameter is invoked, it\n** is passed a single argument which is a copy of the application data \n** pointer which was the fifth parameter to sqlite3_create_function_v2().\n**\n** ^It is permitted to register multiple implementations of the same\n** functions with the same name but with either differing numbers of\n** arguments or differing preferred text encodings.  ^SQLite will use\n** the implementation that most closely matches the way in which the\n** SQL function is used.  ^A function implementation with a non-negative\n** nArg parameter is a better match than a function implementation with\n** a negative nArg.  ^A function where the preferred text encoding\n** matches the database encoding is a better\n** match than a function where the encoding is different.  \n** ^A function where the encoding difference is between UTF16le and UTF16be\n** is a closer match than a function where the encoding difference is\n** between UTF8 and UTF16.\n**\n** ^Built-in functions may be overloaded by new application-defined functions.\n**\n** ^An application-defined function is permitted to call other\n** SQLite interfaces.  However, such calls must not\n** close the database connection nor finalize or reset the prepared\n** statement in which the function is running.\n*/\nSQLITE_API int sqlite3_create_function(\n  sqlite3 *db,\n  const char *zFunctionName,\n  int nArg,\n  int eTextRep,\n  void *pApp,\n  void (*xFunc)(sqlite3_context*,int,sqlite3_value**),\n  void (*xStep)(sqlite3_context*,int,sqlite3_value**),\n  void (*xFinal)(sqlite3_context*)\n);\nSQLITE_API int sqlite3_create_function16(\n  sqlite3 *db,\n  const void *zFunctionName,\n  int nArg,\n  int eTextRep,\n  void *pApp,\n  void (*xFunc)(sqlite3_context*,int,sqlite3_value**),\n  void (*xStep)(sqlite3_context*,int,sqlite3_value**),\n  void (*xFinal)(sqlite3_context*)\n);\nSQLITE_API int sqlite3_create_function_v2(\n  sqlite3 *db,\n  const char *zFunctionName,\n  int nArg,\n  int eTextRep,\n  void *pApp,\n  void (*xFunc)(sqlite3_context*,int,sqlite3_value**),\n  void (*xStep)(sqlite3_context*,int,sqlite3_value**),\n  void (*xFinal)(sqlite3_context*),\n  void(*xDestroy)(void*)\n);\n\n/*\n** CAPI3REF: Text Encodings\n**\n** These constant define integer codes that represent the various\n** text encodings supported by SQLite.\n*/\n#define SQLITE_UTF8           1    /* IMP: R-37514-35566 */\n#define SQLITE_UTF16LE        2    /* IMP: R-03371-37637 */\n#define SQLITE_UTF16BE        3    /* IMP: R-51971-34154 */\n#define SQLITE_UTF16          4    /* Use native byte order */\n#define SQLITE_ANY            5    /* Deprecated */\n#define SQLITE_UTF16_ALIGNED  8    /* sqlite3_create_collation only */\n\n/*\n** CAPI3REF: Function Flags\n**\n** These constants may be ORed together with the \n** [SQLITE_UTF8 | preferred text encoding] as the fourth argument\n** to [sqlite3_create_function()], [sqlite3_create_function16()], or\n** [sqlite3_create_function_v2()].\n*/\n#define SQLITE_DETERMINISTIC    0x800\n\n/*\n** CAPI3REF: Deprecated Functions\n** DEPRECATED\n**\n** These functions are [deprecated].  In order to maintain\n** backwards compatibility with older code, these functions continue \n** to be supported.  However, new applications should avoid\n** the use of these functions.  To encourage programmers to avoid\n** these functions, we will not explain what they do.\n*/\n#ifndef SQLITE_OMIT_DEPRECATED\nSQLITE_API SQLITE_DEPRECATED int sqlite3_aggregate_count(sqlite3_context*);\nSQLITE_API SQLITE_DEPRECATED int sqlite3_expired(sqlite3_stmt*);\nSQLITE_API SQLITE_DEPRECATED int sqlite3_transfer_bindings(sqlite3_stmt*, sqlite3_stmt*);\nSQLITE_API SQLITE_DEPRECATED int sqlite3_global_recover(void);\nSQLITE_API SQLITE_DEPRECATED void sqlite3_thread_cleanup(void);\nSQLITE_API SQLITE_DEPRECATED int sqlite3_memory_alarm(void(*)(void*,sqlite3_int64,int),\n                      void*,sqlite3_int64);\n#endif\n\n/*\n** CAPI3REF: Obtaining SQL Values\n** METHOD: sqlite3_value\n**\n** <b>Summary:</b>\n** <blockquote><table border=0 cellpadding=0 cellspacing=0>\n** <tr><td><b>sqlite3_value_blob</b><td>&rarr;<td>BLOB value\n** <tr><td><b>sqlite3_value_double</b><td>&rarr;<td>REAL value\n** <tr><td><b>sqlite3_value_int</b><td>&rarr;<td>32-bit INTEGER value\n** <tr><td><b>sqlite3_value_int64</b><td>&rarr;<td>64-bit INTEGER value\n** <tr><td><b>sqlite3_value_pointer</b><td>&rarr;<td>Pointer value\n** <tr><td><b>sqlite3_value_text</b><td>&rarr;<td>UTF-8 TEXT value\n** <tr><td><b>sqlite3_value_text16</b><td>&rarr;<td>UTF-16 TEXT value in\n** the native byteorder\n** <tr><td><b>sqlite3_value_text16be</b><td>&rarr;<td>UTF-16be TEXT value\n** <tr><td><b>sqlite3_value_text16le</b><td>&rarr;<td>UTF-16le TEXT value\n** <tr><td>&nbsp;<td>&nbsp;<td>&nbsp;\n** <tr><td><b>sqlite3_value_bytes</b><td>&rarr;<td>Size of a BLOB\n** or a UTF-8 TEXT in bytes\n** <tr><td><b>sqlite3_value_bytes16&nbsp;&nbsp;</b>\n** <td>&rarr;&nbsp;&nbsp;<td>Size of UTF-16\n** TEXT in bytes\n** <tr><td><b>sqlite3_value_type</b><td>&rarr;<td>Default\n** datatype of the value\n** <tr><td><b>sqlite3_value_numeric_type&nbsp;&nbsp;</b>\n** <td>&rarr;&nbsp;&nbsp;<td>Best numeric datatype of the value\n** <tr><td><b>sqlite3_value_nochange&nbsp;&nbsp;</b>\n** <td>&rarr;&nbsp;&nbsp;<td>True if the column is unchanged in an UPDATE\n** against a virtual table.\n** </table></blockquote>\n**\n** <b>Details:</b>\n**\n** These routines extract type, size, and content information from\n** [protected sqlite3_value] objects.  Protected sqlite3_value objects\n** are used to pass parameter information into implementation of\n** [application-defined SQL functions] and [virtual tables].\n**\n** These routines work only with [protected sqlite3_value] objects.\n** Any attempt to use these routines on an [unprotected sqlite3_value]\n** is not threadsafe.\n**\n** ^These routines work just like the corresponding [column access functions]\n** except that these routines take a single [protected sqlite3_value] object\n** pointer instead of a [sqlite3_stmt*] pointer and an integer column number.\n**\n** ^The sqlite3_value_text16() interface extracts a UTF-16 string\n** in the native byte-order of the host machine.  ^The\n** sqlite3_value_text16be() and sqlite3_value_text16le() interfaces\n** extract UTF-16 strings as big-endian and little-endian respectively.\n**\n** ^If [sqlite3_value] object V was initialized \n** using [sqlite3_bind_pointer(S,I,P,X,D)] or [sqlite3_result_pointer(C,P,X,D)]\n** and if X and Y are strings that compare equal according to strcmp(X,Y),\n** then sqlite3_value_pointer(V,Y) will return the pointer P.  ^Otherwise,\n** sqlite3_value_pointer(V,Y) returns a NULL. The sqlite3_bind_pointer() \n** routine is part of the [pointer passing interface] added for SQLite 3.20.0.\n**\n** ^(The sqlite3_value_type(V) interface returns the\n** [SQLITE_INTEGER | datatype code] for the initial datatype of the\n** [sqlite3_value] object V. The returned value is one of [SQLITE_INTEGER],\n** [SQLITE_FLOAT], [SQLITE_TEXT], [SQLITE_BLOB], or [SQLITE_NULL].)^\n** Other interfaces might change the datatype for an sqlite3_value object.\n** For example, if the datatype is initially SQLITE_INTEGER and\n** sqlite3_value_text(V) is called to extract a text value for that\n** integer, then subsequent calls to sqlite3_value_type(V) might return\n** SQLITE_TEXT.  Whether or not a persistent internal datatype conversion\n** occurs is undefined and may change from one release of SQLite to the next.\n**\n** ^(The sqlite3_value_numeric_type() interface attempts to apply\n** numeric affinity to the value.  This means that an attempt is\n** made to convert the value to an integer or floating point.  If\n** such a conversion is possible without loss of information (in other\n** words, if the value is a string that looks like a number)\n** then the conversion is performed.  Otherwise no conversion occurs.\n** The [SQLITE_INTEGER | datatype] after conversion is returned.)^\n**\n** ^Within the [xUpdate] method of a [virtual table], the\n** sqlite3_value_nochange(X) interface returns true if and only if\n** the column corresponding to X is unchanged by the UPDATE operation\n** that the xUpdate method call was invoked to implement and if\n** and the prior [xColumn] method call that was invoked to extracted\n** the value for that column returned without setting a result (probably\n** because it queried [sqlite3_vtab_nochange()] and found that the column\n** was unchanging).  ^Within an [xUpdate] method, any value for which\n** sqlite3_value_nochange(X) is true will in all other respects appear\n** to be a NULL value.  If sqlite3_value_nochange(X) is invoked anywhere other\n** than within an [xUpdate] method call for an UPDATE statement, then\n** the return value is arbitrary and meaningless.\n**\n** Please pay particular attention to the fact that the pointer returned\n** from [sqlite3_value_blob()], [sqlite3_value_text()], or\n** [sqlite3_value_text16()] can be invalidated by a subsequent call to\n** [sqlite3_value_bytes()], [sqlite3_value_bytes16()], [sqlite3_value_text()],\n** or [sqlite3_value_text16()].\n**\n** These routines must be called from the same thread as\n** the SQL function that supplied the [sqlite3_value*] parameters.\n*/\nSQLITE_API const void *sqlite3_value_blob(sqlite3_value*);\nSQLITE_API double sqlite3_value_double(sqlite3_value*);\nSQLITE_API int sqlite3_value_int(sqlite3_value*);\nSQLITE_API sqlite3_int64 sqlite3_value_int64(sqlite3_value*);\nSQLITE_API void *sqlite3_value_pointer(sqlite3_value*, const char*);\nSQLITE_API const unsigned char *sqlite3_value_text(sqlite3_value*);\nSQLITE_API const void *sqlite3_value_text16(sqlite3_value*);\nSQLITE_API const void *sqlite3_value_text16le(sqlite3_value*);\nSQLITE_API const void *sqlite3_value_text16be(sqlite3_value*);\nSQLITE_API int sqlite3_value_bytes(sqlite3_value*);\nSQLITE_API int sqlite3_value_bytes16(sqlite3_value*);\nSQLITE_API int sqlite3_value_type(sqlite3_value*);\nSQLITE_API int sqlite3_value_numeric_type(sqlite3_value*);\nSQLITE_API int sqlite3_value_nochange(sqlite3_value*);\n\n/*\n** CAPI3REF: Finding The Subtype Of SQL Values\n** METHOD: sqlite3_value\n**\n** The sqlite3_value_subtype(V) function returns the subtype for\n** an [application-defined SQL function] argument V.  The subtype\n** information can be used to pass a limited amount of context from\n** one SQL function to another.  Use the [sqlite3_result_subtype()]\n** routine to set the subtype for the return value of an SQL function.\n*/\nSQLITE_API unsigned int sqlite3_value_subtype(sqlite3_value*);\n\n/*\n** CAPI3REF: Copy And Free SQL Values\n** METHOD: sqlite3_value\n**\n** ^The sqlite3_value_dup(V) interface makes a copy of the [sqlite3_value]\n** object D and returns a pointer to that copy.  ^The [sqlite3_value] returned\n** is a [protected sqlite3_value] object even if the input is not.\n** ^The sqlite3_value_dup(V) interface returns NULL if V is NULL or if a\n** memory allocation fails.\n**\n** ^The sqlite3_value_free(V) interface frees an [sqlite3_value] object\n** previously obtained from [sqlite3_value_dup()].  ^If V is a NULL pointer\n** then sqlite3_value_free(V) is a harmless no-op.\n*/\nSQLITE_API sqlite3_value *sqlite3_value_dup(const sqlite3_value*);\nSQLITE_API void sqlite3_value_free(sqlite3_value*);\n\n/*\n** CAPI3REF: Obtain Aggregate Function Context\n** METHOD: sqlite3_context\n**\n** Implementations of aggregate SQL functions use this\n** routine to allocate memory for storing their state.\n**\n** ^The first time the sqlite3_aggregate_context(C,N) routine is called \n** for a particular aggregate function, SQLite\n** allocates N of memory, zeroes out that memory, and returns a pointer\n** to the new memory. ^On second and subsequent calls to\n** sqlite3_aggregate_context() for the same aggregate function instance,\n** the same buffer is returned.  Sqlite3_aggregate_context() is normally\n** called once for each invocation of the xStep callback and then one\n** last time when the xFinal callback is invoked.  ^(When no rows match\n** an aggregate query, the xStep() callback of the aggregate function\n** implementation is never called and xFinal() is called exactly once.\n** In those cases, sqlite3_aggregate_context() might be called for the\n** first time from within xFinal().)^\n**\n** ^The sqlite3_aggregate_context(C,N) routine returns a NULL pointer \n** when first called if N is less than or equal to zero or if a memory\n** allocate error occurs.\n**\n** ^(The amount of space allocated by sqlite3_aggregate_context(C,N) is\n** determined by the N parameter on first successful call.  Changing the\n** value of N in subsequent call to sqlite3_aggregate_context() within\n** the same aggregate function instance will not resize the memory\n** allocation.)^  Within the xFinal callback, it is customary to set\n** N=0 in calls to sqlite3_aggregate_context(C,N) so that no \n** pointless memory allocations occur.\n**\n** ^SQLite automatically frees the memory allocated by \n** sqlite3_aggregate_context() when the aggregate query concludes.\n**\n** The first parameter must be a copy of the\n** [sqlite3_context | SQL function context] that is the first parameter\n** to the xStep or xFinal callback routine that implements the aggregate\n** function.\n**\n** This routine must be called from the same thread in which\n** the aggregate SQL function is running.\n*/\nSQLITE_API void *sqlite3_aggregate_context(sqlite3_context*, int nBytes);\n\n/*\n** CAPI3REF: User Data For Functions\n** METHOD: sqlite3_context\n**\n** ^The sqlite3_user_data() interface returns a copy of\n** the pointer that was the pUserData parameter (the 5th parameter)\n** of the [sqlite3_create_function()]\n** and [sqlite3_create_function16()] routines that originally\n** registered the application defined function.\n**\n** This routine must be called from the same thread in which\n** the application-defined function is running.\n*/\nSQLITE_API void *sqlite3_user_data(sqlite3_context*);\n\n/*\n** CAPI3REF: Database Connection For Functions\n** METHOD: sqlite3_context\n**\n** ^The sqlite3_context_db_handle() interface returns a copy of\n** the pointer to the [database connection] (the 1st parameter)\n** of the [sqlite3_create_function()]\n** and [sqlite3_create_function16()] routines that originally\n** registered the application defined function.\n*/\nSQLITE_API sqlite3 *sqlite3_context_db_handle(sqlite3_context*);\n\n/*\n** CAPI3REF: Function Auxiliary Data\n** METHOD: sqlite3_context\n**\n** These functions may be used by (non-aggregate) SQL functions to\n** associate metadata with argument values. If the same value is passed to\n** multiple invocations of the same SQL function during query execution, under\n** some circumstances the associated metadata may be preserved.  An example\n** of where this might be useful is in a regular-expression matching\n** function. The compiled version of the regular expression can be stored as\n** metadata associated with the pattern string.  \n** Then as long as the pattern string remains the same,\n** the compiled regular expression can be reused on multiple\n** invocations of the same function.\n**\n** ^The sqlite3_get_auxdata(C,N) interface returns a pointer to the metadata\n** associated by the sqlite3_set_auxdata(C,N,P,X) function with the Nth argument\n** value to the application-defined function.  ^N is zero for the left-most\n** function argument.  ^If there is no metadata\n** associated with the function argument, the sqlite3_get_auxdata(C,N) interface\n** returns a NULL pointer.\n**\n** ^The sqlite3_set_auxdata(C,N,P,X) interface saves P as metadata for the N-th\n** argument of the application-defined function.  ^Subsequent\n** calls to sqlite3_get_auxdata(C,N) return P from the most recent\n** sqlite3_set_auxdata(C,N,P,X) call if the metadata is still valid or\n** NULL if the metadata has been discarded.\n** ^After each call to sqlite3_set_auxdata(C,N,P,X) where X is not NULL,\n** SQLite will invoke the destructor function X with parameter P exactly\n** once, when the metadata is discarded.\n** SQLite is free to discard the metadata at any time, including: <ul>\n** <li> ^(when the corresponding function parameter changes)^, or\n** <li> ^(when [sqlite3_reset()] or [sqlite3_finalize()] is called for the\n**      SQL statement)^, or\n** <li> ^(when sqlite3_set_auxdata() is invoked again on the same\n**       parameter)^, or\n** <li> ^(during the original sqlite3_set_auxdata() call when a memory \n**      allocation error occurs.)^ </ul>\n**\n** Note the last bullet in particular.  The destructor X in \n** sqlite3_set_auxdata(C,N,P,X) might be called immediately, before the\n** sqlite3_set_auxdata() interface even returns.  Hence sqlite3_set_auxdata()\n** should be called near the end of the function implementation and the\n** function implementation should not make any use of P after\n** sqlite3_set_auxdata() has been called.\n**\n** ^(In practice, metadata is preserved between function calls for\n** function parameters that are compile-time constants, including literal\n** values and [parameters] and expressions composed from the same.)^\n**\n** The value of the N parameter to these interfaces should be non-negative.\n** Future enhancements may make use of negative N values to define new\n** kinds of function caching behavior.\n**\n** These routines must be called from the same thread in which\n** the SQL function is running.\n*/\nSQLITE_API void *sqlite3_get_auxdata(sqlite3_context*, int N);\nSQLITE_API void sqlite3_set_auxdata(sqlite3_context*, int N, void*, void (*)(void*));\n\n\n/*\n** CAPI3REF: Constants Defining Special Destructor Behavior\n**\n** These are special values for the destructor that is passed in as the\n** final argument to routines like [sqlite3_result_blob()].  ^If the destructor\n** argument is SQLITE_STATIC, it means that the content pointer is constant\n** and will never change.  It does not need to be destroyed.  ^The\n** SQLITE_TRANSIENT value means that the content will likely change in\n** the near future and that SQLite should make its own private copy of\n** the content before returning.\n**\n** The typedef is necessary to work around problems in certain\n** C++ compilers.\n*/\ntypedef void (*sqlite3_destructor_type)(void*);\n#define SQLITE_STATIC      ((sqlite3_destructor_type)0)\n#define SQLITE_TRANSIENT   ((sqlite3_destructor_type)-1)\n\n/*\n** CAPI3REF: Setting The Result Of An SQL Function\n** METHOD: sqlite3_context\n**\n** These routines are used by the xFunc or xFinal callbacks that\n** implement SQL functions and aggregates.  See\n** [sqlite3_create_function()] and [sqlite3_create_function16()]\n** for additional information.\n**\n** These functions work very much like the [parameter binding] family of\n** functions used to bind values to host parameters in prepared statements.\n** Refer to the [SQL parameter] documentation for additional information.\n**\n** ^The sqlite3_result_blob() interface sets the result from\n** an application-defined function to be the BLOB whose content is pointed\n** to by the second parameter and which is N bytes long where N is the\n** third parameter.\n**\n** ^The sqlite3_result_zeroblob(C,N) and sqlite3_result_zeroblob64(C,N)\n** interfaces set the result of the application-defined function to be\n** a BLOB containing all zero bytes and N bytes in size.\n**\n** ^The sqlite3_result_double() interface sets the result from\n** an application-defined function to be a floating point value specified\n** by its 2nd argument.\n**\n** ^The sqlite3_result_error() and sqlite3_result_error16() functions\n** cause the implemented SQL function to throw an exception.\n** ^SQLite uses the string pointed to by the\n** 2nd parameter of sqlite3_result_error() or sqlite3_result_error16()\n** as the text of an error message.  ^SQLite interprets the error\n** message string from sqlite3_result_error() as UTF-8. ^SQLite\n** interprets the string from sqlite3_result_error16() as UTF-16 in native\n** byte order.  ^If the third parameter to sqlite3_result_error()\n** or sqlite3_result_error16() is negative then SQLite takes as the error\n** message all text up through the first zero character.\n** ^If the third parameter to sqlite3_result_error() or\n** sqlite3_result_error16() is non-negative then SQLite takes that many\n** bytes (not characters) from the 2nd parameter as the error message.\n** ^The sqlite3_result_error() and sqlite3_result_error16()\n** routines make a private copy of the error message text before\n** they return.  Hence, the calling function can deallocate or\n** modify the text after they return without harm.\n** ^The sqlite3_result_error_code() function changes the error code\n** returned by SQLite as a result of an error in a function.  ^By default,\n** the error code is SQLITE_ERROR.  ^A subsequent call to sqlite3_result_error()\n** or sqlite3_result_error16() resets the error code to SQLITE_ERROR.\n**\n** ^The sqlite3_result_error_toobig() interface causes SQLite to throw an\n** error indicating that a string or BLOB is too long to represent.\n**\n** ^The sqlite3_result_error_nomem() interface causes SQLite to throw an\n** error indicating that a memory allocation failed.\n**\n** ^The sqlite3_result_int() interface sets the return value\n** of the application-defined function to be the 32-bit signed integer\n** value given in the 2nd argument.\n** ^The sqlite3_result_int64() interface sets the return value\n** of the application-defined function to be the 64-bit signed integer\n** value given in the 2nd argument.\n**\n** ^The sqlite3_result_null() interface sets the return value\n** of the application-defined function to be NULL.\n**\n** ^The sqlite3_result_text(), sqlite3_result_text16(),\n** sqlite3_result_text16le(), and sqlite3_result_text16be() interfaces\n** set the return value of the application-defined function to be\n** a text string which is represented as UTF-8, UTF-16 native byte order,\n** UTF-16 little endian, or UTF-16 big endian, respectively.\n** ^The sqlite3_result_text64() interface sets the return value of an\n** application-defined function to be a text string in an encoding\n** specified by the fifth (and last) parameter, which must be one\n** of [SQLITE_UTF8], [SQLITE_UTF16], [SQLITE_UTF16BE], or [SQLITE_UTF16LE].\n** ^SQLite takes the text result from the application from\n** the 2nd parameter of the sqlite3_result_text* interfaces.\n** ^If the 3rd parameter to the sqlite3_result_text* interfaces\n** is negative, then SQLite takes result text from the 2nd parameter\n** through the first zero character.\n** ^If the 3rd parameter to the sqlite3_result_text* interfaces\n** is non-negative, then as many bytes (not characters) of the text\n** pointed to by the 2nd parameter are taken as the application-defined\n** function result.  If the 3rd parameter is non-negative, then it\n** must be the byte offset into the string where the NUL terminator would\n** appear if the string where NUL terminated.  If any NUL characters occur\n** in the string at a byte offset that is less than the value of the 3rd\n** parameter, then the resulting string will contain embedded NULs and the\n** result of expressions operating on strings with embedded NULs is undefined.\n** ^If the 4th parameter to the sqlite3_result_text* interfaces\n** or sqlite3_result_blob is a non-NULL pointer, then SQLite calls that\n** function as the destructor on the text or BLOB result when it has\n** finished using that result.\n** ^If the 4th parameter to the sqlite3_result_text* interfaces or to\n** sqlite3_result_blob is the special constant SQLITE_STATIC, then SQLite\n** assumes that the text or BLOB result is in constant space and does not\n** copy the content of the parameter nor call a destructor on the content\n** when it has finished using that result.\n** ^If the 4th parameter to the sqlite3_result_text* interfaces\n** or sqlite3_result_blob is the special constant SQLITE_TRANSIENT\n** then SQLite makes a copy of the result into space obtained\n** from [sqlite3_malloc()] before it returns.\n**\n** ^The sqlite3_result_value() interface sets the result of\n** the application-defined function to be a copy of the\n** [unprotected sqlite3_value] object specified by the 2nd parameter.  ^The\n** sqlite3_result_value() interface makes a copy of the [sqlite3_value]\n** so that the [sqlite3_value] specified in the parameter may change or\n** be deallocated after sqlite3_result_value() returns without harm.\n** ^A [protected sqlite3_value] object may always be used where an\n** [unprotected sqlite3_value] object is required, so either\n** kind of [sqlite3_value] object can be used with this interface.\n**\n** ^The sqlite3_result_pointer(C,P,T,D) interface sets the result to an\n** SQL NULL value, just like [sqlite3_result_null(C)], except that it\n** also associates the host-language pointer P or type T with that \n** NULL value such that the pointer can be retrieved within an\n** [application-defined SQL function] using [sqlite3_value_pointer()].\n** ^If the D parameter is not NULL, then it is a pointer to a destructor\n** for the P parameter.  ^SQLite invokes D with P as its only argument\n** when SQLite is finished with P.  The T parameter should be a static\n** string and preferably a string literal. The sqlite3_result_pointer()\n** routine is part of the [pointer passing interface] added for SQLite 3.20.0.\n**\n** If these routines are called from within the different thread\n** than the one containing the application-defined function that received\n** the [sqlite3_context] pointer, the results are undefined.\n*/\nSQLITE_API void sqlite3_result_blob(sqlite3_context*, const void*, int, void(*)(void*));\nSQLITE_API void sqlite3_result_blob64(sqlite3_context*,const void*,\n                           sqlite3_uint64,void(*)(void*));\nSQLITE_API void sqlite3_result_double(sqlite3_context*, double);\nSQLITE_API void sqlite3_result_error(sqlite3_context*, const char*, int);\nSQLITE_API void sqlite3_result_error16(sqlite3_context*, const void*, int);\nSQLITE_API void sqlite3_result_error_toobig(sqlite3_context*);\nSQLITE_API void sqlite3_result_error_nomem(sqlite3_context*);\nSQLITE_API void sqlite3_result_error_code(sqlite3_context*, int);\nSQLITE_API void sqlite3_result_int(sqlite3_context*, int);\nSQLITE_API void sqlite3_result_int64(sqlite3_context*, sqlite3_int64);\nSQLITE_API void sqlite3_result_null(sqlite3_context*);\nSQLITE_API void sqlite3_result_text(sqlite3_context*, const char*, int, void(*)(void*));\nSQLITE_API void sqlite3_result_text64(sqlite3_context*, const char*,sqlite3_uint64,\n                           void(*)(void*), unsigned char encoding);\nSQLITE_API void sqlite3_result_text16(sqlite3_context*, const void*, int, void(*)(void*));\nSQLITE_API void sqlite3_result_text16le(sqlite3_context*, const void*, int,void(*)(void*));\nSQLITE_API void sqlite3_result_text16be(sqlite3_context*, const void*, int,void(*)(void*));\nSQLITE_API void sqlite3_result_value(sqlite3_context*, sqlite3_value*);\nSQLITE_API void sqlite3_result_pointer(sqlite3_context*, void*,const char*,void(*)(void*));\nSQLITE_API void sqlite3_result_zeroblob(sqlite3_context*, int n);\nSQLITE_API int sqlite3_result_zeroblob64(sqlite3_context*, sqlite3_uint64 n);\n\n\n/*\n** CAPI3REF: Setting The Subtype Of An SQL Function\n** METHOD: sqlite3_context\n**\n** The sqlite3_result_subtype(C,T) function causes the subtype of\n** the result from the [application-defined SQL function] with \n** [sqlite3_context] C to be the value T.  Only the lower 8 bits \n** of the subtype T are preserved in current versions of SQLite;\n** higher order bits are discarded.\n** The number of subtype bytes preserved by SQLite might increase\n** in future releases of SQLite.\n*/\nSQLITE_API void sqlite3_result_subtype(sqlite3_context*,unsigned int);\n\n/*\n** CAPI3REF: Define New Collating Sequences\n** METHOD: sqlite3\n**\n** ^These functions add, remove, or modify a [collation] associated\n** with the [database connection] specified as the first argument.\n**\n** ^The name of the collation is a UTF-8 string\n** for sqlite3_create_collation() and sqlite3_create_collation_v2()\n** and a UTF-16 string in native byte order for sqlite3_create_collation16().\n** ^Collation names that compare equal according to [sqlite3_strnicmp()] are\n** considered to be the same name.\n**\n** ^(The third argument (eTextRep) must be one of the constants:\n** <ul>\n** <li> [SQLITE_UTF8],\n** <li> [SQLITE_UTF16LE],\n** <li> [SQLITE_UTF16BE],\n** <li> [SQLITE_UTF16], or\n** <li> [SQLITE_UTF16_ALIGNED].\n** </ul>)^\n** ^The eTextRep argument determines the encoding of strings passed\n** to the collating function callback, xCallback.\n** ^The [SQLITE_UTF16] and [SQLITE_UTF16_ALIGNED] values for eTextRep\n** force strings to be UTF16 with native byte order.\n** ^The [SQLITE_UTF16_ALIGNED] value for eTextRep forces strings to begin\n** on an even byte address.\n**\n** ^The fourth argument, pArg, is an application data pointer that is passed\n** through as the first argument to the collating function callback.\n**\n** ^The fifth argument, xCallback, is a pointer to the collating function.\n** ^Multiple collating functions can be registered using the same name but\n** with different eTextRep parameters and SQLite will use whichever\n** function requires the least amount of data transformation.\n** ^If the xCallback argument is NULL then the collating function is\n** deleted.  ^When all collating functions having the same name are deleted,\n** that collation is no longer usable.\n**\n** ^The collating function callback is invoked with a copy of the pArg \n** application data pointer and with two strings in the encoding specified\n** by the eTextRep argument.  The collating function must return an\n** integer that is negative, zero, or positive\n** if the first string is less than, equal to, or greater than the second,\n** respectively.  A collating function must always return the same answer\n** given the same inputs.  If two or more collating functions are registered\n** to the same collation name (using different eTextRep values) then all\n** must give an equivalent answer when invoked with equivalent strings.\n** The collating function must obey the following properties for all\n** strings A, B, and C:\n**\n** <ol>\n** <li> If A==B then B==A.\n** <li> If A==B and B==C then A==C.\n** <li> If A&lt;B THEN B&gt;A.\n** <li> If A&lt;B and B&lt;C then A&lt;C.\n** </ol>\n**\n** If a collating function fails any of the above constraints and that\n** collating function is  registered and used, then the behavior of SQLite\n** is undefined.\n**\n** ^The sqlite3_create_collation_v2() works like sqlite3_create_collation()\n** with the addition that the xDestroy callback is invoked on pArg when\n** the collating function is deleted.\n** ^Collating functions are deleted when they are overridden by later\n** calls to the collation creation functions or when the\n** [database connection] is closed using [sqlite3_close()].\n**\n** ^The xDestroy callback is <u>not</u> called if the \n** sqlite3_create_collation_v2() function fails.  Applications that invoke\n** sqlite3_create_collation_v2() with a non-NULL xDestroy argument should \n** check the return code and dispose of the application data pointer\n** themselves rather than expecting SQLite to deal with it for them.\n** This is different from every other SQLite interface.  The inconsistency \n** is unfortunate but cannot be changed without breaking backwards \n** compatibility.\n**\n** See also:  [sqlite3_collation_needed()] and [sqlite3_collation_needed16()].\n*/\nSQLITE_API int sqlite3_create_collation(\n  sqlite3*, \n  const char *zName, \n  int eTextRep, \n  void *pArg,\n  int(*xCompare)(void*,int,const void*,int,const void*)\n);\nSQLITE_API int sqlite3_create_collation_v2(\n  sqlite3*, \n  const char *zName, \n  int eTextRep, \n  void *pArg,\n  int(*xCompare)(void*,int,const void*,int,const void*),\n  void(*xDestroy)(void*)\n);\nSQLITE_API int sqlite3_create_collation16(\n  sqlite3*, \n  const void *zName,\n  int eTextRep, \n  void *pArg,\n  int(*xCompare)(void*,int,const void*,int,const void*)\n);\n\n/*\n** CAPI3REF: Collation Needed Callbacks\n** METHOD: sqlite3\n**\n** ^To avoid having to register all collation sequences before a database\n** can be used, a single callback function may be registered with the\n** [database connection] to be invoked whenever an undefined collation\n** sequence is required.\n**\n** ^If the function is registered using the sqlite3_collation_needed() API,\n** then it is passed the names of undefined collation sequences as strings\n** encoded in UTF-8. ^If sqlite3_collation_needed16() is used,\n** the names are passed as UTF-16 in machine native byte order.\n** ^A call to either function replaces the existing collation-needed callback.\n**\n** ^(When the callback is invoked, the first argument passed is a copy\n** of the second argument to sqlite3_collation_needed() or\n** sqlite3_collation_needed16().  The second argument is the database\n** connection.  The third argument is one of [SQLITE_UTF8], [SQLITE_UTF16BE],\n** or [SQLITE_UTF16LE], indicating the most desirable form of the collation\n** sequence function required.  The fourth parameter is the name of the\n** required collation sequence.)^\n**\n** The callback function should register the desired collation using\n** [sqlite3_create_collation()], [sqlite3_create_collation16()], or\n** [sqlite3_create_collation_v2()].\n*/\nSQLITE_API int sqlite3_collation_needed(\n  sqlite3*, \n  void*, \n  void(*)(void*,sqlite3*,int eTextRep,const char*)\n);\nSQLITE_API int sqlite3_collation_needed16(\n  sqlite3*, \n  void*,\n  void(*)(void*,sqlite3*,int eTextRep,const void*)\n);\n\n#ifdef SQLITE_HAS_CODEC\n/*\n** Specify the key for an encrypted database.  This routine should be\n** called right after sqlite3_open().\n**\n** The code to implement this API is not available in the public release\n** of SQLite.\n*/\nSQLITE_API int sqlite3_key(\n  sqlite3 *db,                   /* Database to be rekeyed */\n  const void *pKey, int nKey     /* The key */\n);\nSQLITE_API int sqlite3_key_v2(\n  sqlite3 *db,                   /* Database to be rekeyed */\n  const char *zDbName,           /* Name of the database */\n  const void *pKey, int nKey     /* The key */\n);\n\n/*\n** Change the key on an open database.  If the current database is not\n** encrypted, this routine will encrypt it.  If pNew==0 or nNew==0, the\n** database is decrypted.\n**\n** The code to implement this API is not available in the public release\n** of SQLite.\n*/\nSQLITE_API int sqlite3_rekey(\n  sqlite3 *db,                   /* Database to be rekeyed */\n  const void *pKey, int nKey     /* The new key */\n);\nSQLITE_API int sqlite3_rekey_v2(\n  sqlite3 *db,                   /* Database to be rekeyed */\n  const char *zDbName,           /* Name of the database */\n  const void *pKey, int nKey     /* The new key */\n);\n\n/*\n** Specify the activation key for a SEE database.  Unless \n** activated, none of the SEE routines will work.\n*/\nSQLITE_API void sqlite3_activate_see(\n  const char *zPassPhrase        /* Activation phrase */\n);\n#endif\n\n#ifdef SQLITE_ENABLE_CEROD\n/*\n** Specify the activation key for a CEROD database.  Unless \n** activated, none of the CEROD routines will work.\n*/\nSQLITE_API void sqlite3_activate_cerod(\n  const char *zPassPhrase        /* Activation phrase */\n);\n#endif\n\n/*\n** CAPI3REF: Suspend Execution For A Short Time\n**\n** The sqlite3_sleep() function causes the current thread to suspend execution\n** for at least a number of milliseconds specified in its parameter.\n**\n** If the operating system does not support sleep requests with\n** millisecond time resolution, then the time will be rounded up to\n** the nearest second. The number of milliseconds of sleep actually\n** requested from the operating system is returned.\n**\n** ^SQLite implements this interface by calling the xSleep()\n** method of the default [sqlite3_vfs] object.  If the xSleep() method\n** of the default VFS is not implemented correctly, or not implemented at\n** all, then the behavior of sqlite3_sleep() may deviate from the description\n** in the previous paragraphs.\n*/\nSQLITE_API int sqlite3_sleep(int);\n\n/*\n** CAPI3REF: Name Of The Folder Holding Temporary Files\n**\n** ^(If this global variable is made to point to a string which is\n** the name of a folder (a.k.a. directory), then all temporary files\n** created by SQLite when using a built-in [sqlite3_vfs | VFS]\n** will be placed in that directory.)^  ^If this variable\n** is a NULL pointer, then SQLite performs a search for an appropriate\n** temporary file directory.\n**\n** Applications are strongly discouraged from using this global variable.\n** It is required to set a temporary folder on Windows Runtime (WinRT).\n** But for all other platforms, it is highly recommended that applications\n** neither read nor write this variable.  This global variable is a relic\n** that exists for backwards compatibility of legacy applications and should\n** be avoided in new projects.\n**\n** It is not safe to read or modify this variable in more than one\n** thread at a time.  It is not safe to read or modify this variable\n** if a [database connection] is being used at the same time in a separate\n** thread.\n** It is intended that this variable be set once\n** as part of process initialization and before any SQLite interface\n** routines have been called and that this variable remain unchanged\n** thereafter.\n**\n** ^The [temp_store_directory pragma] may modify this variable and cause\n** it to point to memory obtained from [sqlite3_malloc].  ^Furthermore,\n** the [temp_store_directory pragma] always assumes that any string\n** that this variable points to is held in memory obtained from \n** [sqlite3_malloc] and the pragma may attempt to free that memory\n** using [sqlite3_free].\n** Hence, if this variable is modified directly, either it should be\n** made NULL or made to point to memory obtained from [sqlite3_malloc]\n** or else the use of the [temp_store_directory pragma] should be avoided.\n** Except when requested by the [temp_store_directory pragma], SQLite\n** does not free the memory that sqlite3_temp_directory points to.  If\n** the application wants that memory to be freed, it must do\n** so itself, taking care to only do so after all [database connection]\n** objects have been destroyed.\n**\n** <b>Note to Windows Runtime users:</b>  The temporary directory must be set\n** prior to calling [sqlite3_open] or [sqlite3_open_v2].  Otherwise, various\n** features that require the use of temporary files may fail.  Here is an\n** example of how to do this using C++ with the Windows Runtime:\n**\n** <blockquote><pre>\n** LPCWSTR zPath = Windows::Storage::ApplicationData::Current->\n** &nbsp;     TemporaryFolder->Path->Data();\n** char zPathBuf&#91;MAX_PATH + 1&#93;;\n** memset(zPathBuf, 0, sizeof(zPathBuf));\n** WideCharToMultiByte(CP_UTF8, 0, zPath, -1, zPathBuf, sizeof(zPathBuf),\n** &nbsp;     NULL, NULL);\n** sqlite3_temp_directory = sqlite3_mprintf(\"%s\", zPathBuf);\n** </pre></blockquote>\n*/\nSQLITE_API SQLITE_EXTERN char *sqlite3_temp_directory;\n\n/*\n** CAPI3REF: Name Of The Folder Holding Database Files\n**\n** ^(If this global variable is made to point to a string which is\n** the name of a folder (a.k.a. directory), then all database files\n** specified with a relative pathname and created or accessed by\n** SQLite when using a built-in windows [sqlite3_vfs | VFS] will be assumed\n** to be relative to that directory.)^ ^If this variable is a NULL\n** pointer, then SQLite assumes that all database files specified\n** with a relative pathname are relative to the current directory\n** for the process.  Only the windows VFS makes use of this global\n** variable; it is ignored by the unix VFS.\n**\n** Changing the value of this variable while a database connection is\n** open can result in a corrupt database.\n**\n** It is not safe to read or modify this variable in more than one\n** thread at a time.  It is not safe to read or modify this variable\n** if a [database connection] is being used at the same time in a separate\n** thread.\n** It is intended that this variable be set once\n** as part of process initialization and before any SQLite interface\n** routines have been called and that this variable remain unchanged\n** thereafter.\n**\n** ^The [data_store_directory pragma] may modify this variable and cause\n** it to point to memory obtained from [sqlite3_malloc].  ^Furthermore,\n** the [data_store_directory pragma] always assumes that any string\n** that this variable points to is held in memory obtained from \n** [sqlite3_malloc] and the pragma may attempt to free that memory\n** using [sqlite3_free].\n** Hence, if this variable is modified directly, either it should be\n** made NULL or made to point to memory obtained from [sqlite3_malloc]\n** or else the use of the [data_store_directory pragma] should be avoided.\n*/\nSQLITE_API SQLITE_EXTERN char *sqlite3_data_directory;\n\n/*\n** CAPI3REF: Test For Auto-Commit Mode\n** KEYWORDS: {autocommit mode}\n** METHOD: sqlite3\n**\n** ^The sqlite3_get_autocommit() interface returns non-zero or\n** zero if the given database connection is or is not in autocommit mode,\n** respectively.  ^Autocommit mode is on by default.\n** ^Autocommit mode is disabled by a [BEGIN] statement.\n** ^Autocommit mode is re-enabled by a [COMMIT] or [ROLLBACK].\n**\n** If certain kinds of errors occur on a statement within a multi-statement\n** transaction (errors including [SQLITE_FULL], [SQLITE_IOERR],\n** [SQLITE_NOMEM], [SQLITE_BUSY], and [SQLITE_INTERRUPT]) then the\n** transaction might be rolled back automatically.  The only way to\n** find out whether SQLite automatically rolled back the transaction after\n** an error is to use this function.\n**\n** If another thread changes the autocommit status of the database\n** connection while this routine is running, then the return value\n** is undefined.\n*/\nSQLITE_API int sqlite3_get_autocommit(sqlite3*);\n\n/*\n** CAPI3REF: Find The Database Handle Of A Prepared Statement\n** METHOD: sqlite3_stmt\n**\n** ^The sqlite3_db_handle interface returns the [database connection] handle\n** to which a [prepared statement] belongs.  ^The [database connection]\n** returned by sqlite3_db_handle is the same [database connection]\n** that was the first argument\n** to the [sqlite3_prepare_v2()] call (or its variants) that was used to\n** create the statement in the first place.\n*/\nSQLITE_API sqlite3 *sqlite3_db_handle(sqlite3_stmt*);\n\n/*\n** CAPI3REF: Return The Filename For A Database Connection\n** METHOD: sqlite3\n**\n** ^The sqlite3_db_filename(D,N) interface returns a pointer to a filename\n** associated with database N of connection D.  ^The main database file\n** has the name \"main\".  If there is no attached database N on the database\n** connection D, or if database N is a temporary or in-memory database, then\n** a NULL pointer is returned.\n**\n** ^The filename returned by this function is the output of the\n** xFullPathname method of the [VFS].  ^In other words, the filename\n** will be an absolute pathname, even if the filename used\n** to open the database originally was a URI or relative pathname.\n*/\nSQLITE_API const char *sqlite3_db_filename(sqlite3 *db, const char *zDbName);\n\n/*\n** CAPI3REF: Determine if a database is read-only\n** METHOD: sqlite3\n**\n** ^The sqlite3_db_readonly(D,N) interface returns 1 if the database N\n** of connection D is read-only, 0 if it is read/write, or -1 if N is not\n** the name of a database on connection D.\n*/\nSQLITE_API int sqlite3_db_readonly(sqlite3 *db, const char *zDbName);\n\n/*\n** CAPI3REF: Find the next prepared statement\n** METHOD: sqlite3\n**\n** ^This interface returns a pointer to the next [prepared statement] after\n** pStmt associated with the [database connection] pDb.  ^If pStmt is NULL\n** then this interface returns a pointer to the first prepared statement\n** associated with the database connection pDb.  ^If no prepared statement\n** satisfies the conditions of this routine, it returns NULL.\n**\n** The [database connection] pointer D in a call to\n** [sqlite3_next_stmt(D,S)] must refer to an open database\n** connection and in particular must not be a NULL pointer.\n*/\nSQLITE_API sqlite3_stmt *sqlite3_next_stmt(sqlite3 *pDb, sqlite3_stmt *pStmt);\n\n/*\n** CAPI3REF: Commit And Rollback Notification Callbacks\n** METHOD: sqlite3\n**\n** ^The sqlite3_commit_hook() interface registers a callback\n** function to be invoked whenever a transaction is [COMMIT | committed].\n** ^Any callback set by a previous call to sqlite3_commit_hook()\n** for the same database connection is overridden.\n** ^The sqlite3_rollback_hook() interface registers a callback\n** function to be invoked whenever a transaction is [ROLLBACK | rolled back].\n** ^Any callback set by a previous call to sqlite3_rollback_hook()\n** for the same database connection is overridden.\n** ^The pArg argument is passed through to the callback.\n** ^If the callback on a commit hook function returns non-zero,\n** then the commit is converted into a rollback.\n**\n** ^The sqlite3_commit_hook(D,C,P) and sqlite3_rollback_hook(D,C,P) functions\n** return the P argument from the previous call of the same function\n** on the same [database connection] D, or NULL for\n** the first call for each function on D.\n**\n** The commit and rollback hook callbacks are not reentrant.\n** The callback implementation must not do anything that will modify\n** the database connection that invoked the callback.  Any actions\n** to modify the database connection must be deferred until after the\n** completion of the [sqlite3_step()] call that triggered the commit\n** or rollback hook in the first place.\n** Note that running any other SQL statements, including SELECT statements,\n** or merely calling [sqlite3_prepare_v2()] and [sqlite3_step()] will modify\n** the database connections for the meaning of \"modify\" in this paragraph.\n**\n** ^Registering a NULL function disables the callback.\n**\n** ^When the commit hook callback routine returns zero, the [COMMIT]\n** operation is allowed to continue normally.  ^If the commit hook\n** returns non-zero, then the [COMMIT] is converted into a [ROLLBACK].\n** ^The rollback hook is invoked on a rollback that results from a commit\n** hook returning non-zero, just as it would be with any other rollback.\n**\n** ^For the purposes of this API, a transaction is said to have been\n** rolled back if an explicit \"ROLLBACK\" statement is executed, or\n** an error or constraint causes an implicit rollback to occur.\n** ^The rollback callback is not invoked if a transaction is\n** automatically rolled back because the database connection is closed.\n**\n** See also the [sqlite3_update_hook()] interface.\n*/\nSQLITE_API void *sqlite3_commit_hook(sqlite3*, int(*)(void*), void*);\nSQLITE_API void *sqlite3_rollback_hook(sqlite3*, void(*)(void *), void*);\n\n/*\n** CAPI3REF: Data Change Notification Callbacks\n** METHOD: sqlite3\n**\n** ^The sqlite3_update_hook() interface registers a callback function\n** with the [database connection] identified by the first argument\n** to be invoked whenever a row is updated, inserted or deleted in\n** a [rowid table].\n** ^Any callback set by a previous call to this function\n** for the same database connection is overridden.\n**\n** ^The second argument is a pointer to the function to invoke when a\n** row is updated, inserted or deleted in a rowid table.\n** ^The first argument to the callback is a copy of the third argument\n** to sqlite3_update_hook().\n** ^The second callback argument is one of [SQLITE_INSERT], [SQLITE_DELETE],\n** or [SQLITE_UPDATE], depending on the operation that caused the callback\n** to be invoked.\n** ^The third and fourth arguments to the callback contain pointers to the\n** database and table name containing the affected row.\n** ^The final callback parameter is the [rowid] of the row.\n** ^In the case of an update, this is the [rowid] after the update takes place.\n**\n** ^(The update hook is not invoked when internal system tables are\n** modified (i.e. sqlite_master and sqlite_sequence).)^\n** ^The update hook is not invoked when [WITHOUT ROWID] tables are modified.\n**\n** ^In the current implementation, the update hook\n** is not invoked when conflicting rows are deleted because of an\n** [ON CONFLICT | ON CONFLICT REPLACE] clause.  ^Nor is the update hook\n** invoked when rows are deleted using the [truncate optimization].\n** The exceptions defined in this paragraph might change in a future\n** release of SQLite.\n**\n** The update hook implementation must not do anything that will modify\n** the database connection that invoked the update hook.  Any actions\n** to modify the database connection must be deferred until after the\n** completion of the [sqlite3_step()] call that triggered the update hook.\n** Note that [sqlite3_prepare_v2()] and [sqlite3_step()] both modify their\n** database connections for the meaning of \"modify\" in this paragraph.\n**\n** ^The sqlite3_update_hook(D,C,P) function\n** returns the P argument from the previous call\n** on the same [database connection] D, or NULL for\n** the first call on D.\n**\n** See also the [sqlite3_commit_hook()], [sqlite3_rollback_hook()],\n** and [sqlite3_preupdate_hook()] interfaces.\n*/\nSQLITE_API void *sqlite3_update_hook(\n  sqlite3*, \n  void(*)(void *,int ,char const *,char const *,sqlite3_int64),\n  void*\n);\n\n/*\n** CAPI3REF: Enable Or Disable Shared Pager Cache\n**\n** ^(This routine enables or disables the sharing of the database cache\n** and schema data structures between [database connection | connections]\n** to the same database. Sharing is enabled if the argument is true\n** and disabled if the argument is false.)^\n**\n** ^Cache sharing is enabled and disabled for an entire process.\n** This is a change as of SQLite [version 3.5.0] ([dateof:3.5.0]). \n** In prior versions of SQLite,\n** sharing was enabled or disabled for each thread separately.\n**\n** ^(The cache sharing mode set by this interface effects all subsequent\n** calls to [sqlite3_open()], [sqlite3_open_v2()], and [sqlite3_open16()].\n** Existing database connections continue use the sharing mode\n** that was in effect at the time they were opened.)^\n**\n** ^(This routine returns [SQLITE_OK] if shared cache was enabled or disabled\n** successfully.  An [error code] is returned otherwise.)^\n**\n** ^Shared cache is disabled by default. But this might change in\n** future releases of SQLite.  Applications that care about shared\n** cache setting should set it explicitly.\n**\n** Note: This method is disabled on MacOS X 10.7 and iOS version 5.0\n** and will always return SQLITE_MISUSE. On those systems, \n** shared cache mode should be enabled per-database connection via \n** [sqlite3_open_v2()] with [SQLITE_OPEN_SHAREDCACHE].\n**\n** This interface is threadsafe on processors where writing a\n** 32-bit integer is atomic.\n**\n** See Also:  [SQLite Shared-Cache Mode]\n*/\nSQLITE_API int sqlite3_enable_shared_cache(int);\n\n/*\n** CAPI3REF: Attempt To Free Heap Memory\n**\n** ^The sqlite3_release_memory() interface attempts to free N bytes\n** of heap memory by deallocating non-essential memory allocations\n** held by the database library.   Memory used to cache database\n** pages to improve performance is an example of non-essential memory.\n** ^sqlite3_release_memory() returns the number of bytes actually freed,\n** which might be more or less than the amount requested.\n** ^The sqlite3_release_memory() routine is a no-op returning zero\n** if SQLite is not compiled with [SQLITE_ENABLE_MEMORY_MANAGEMENT].\n**\n** See also: [sqlite3_db_release_memory()]\n*/\nSQLITE_API int sqlite3_release_memory(int);\n\n/*\n** CAPI3REF: Free Memory Used By A Database Connection\n** METHOD: sqlite3\n**\n** ^The sqlite3_db_release_memory(D) interface attempts to free as much heap\n** memory as possible from database connection D. Unlike the\n** [sqlite3_release_memory()] interface, this interface is in effect even\n** when the [SQLITE_ENABLE_MEMORY_MANAGEMENT] compile-time option is\n** omitted.\n**\n** See also: [sqlite3_release_memory()]\n*/\nSQLITE_API int sqlite3_db_release_memory(sqlite3*);\n\n/*\n** CAPI3REF: Impose A Limit On Heap Size\n**\n** ^The sqlite3_soft_heap_limit64() interface sets and/or queries the\n** soft limit on the amount of heap memory that may be allocated by SQLite.\n** ^SQLite strives to keep heap memory utilization below the soft heap\n** limit by reducing the number of pages held in the page cache\n** as heap memory usages approaches the limit.\n** ^The soft heap limit is \"soft\" because even though SQLite strives to stay\n** below the limit, it will exceed the limit rather than generate\n** an [SQLITE_NOMEM] error.  In other words, the soft heap limit \n** is advisory only.\n**\n** ^The return value from sqlite3_soft_heap_limit64() is the size of\n** the soft heap limit prior to the call, or negative in the case of an\n** error.  ^If the argument N is negative\n** then no change is made to the soft heap limit.  Hence, the current\n** size of the soft heap limit can be determined by invoking\n** sqlite3_soft_heap_limit64() with a negative argument.\n**\n** ^If the argument N is zero then the soft heap limit is disabled.\n**\n** ^(The soft heap limit is not enforced in the current implementation\n** if one or more of following conditions are true:\n**\n** <ul>\n** <li> The soft heap limit is set to zero.\n** <li> Memory accounting is disabled using a combination of the\n**      [sqlite3_config]([SQLITE_CONFIG_MEMSTATUS],...) start-time option and\n**      the [SQLITE_DEFAULT_MEMSTATUS] compile-time option.\n** <li> An alternative page cache implementation is specified using\n**      [sqlite3_config]([SQLITE_CONFIG_PCACHE2],...).\n** <li> The page cache allocates from its own memory pool supplied\n**      by [sqlite3_config]([SQLITE_CONFIG_PAGECACHE],...) rather than\n**      from the heap.\n** </ul>)^\n**\n** Beginning with SQLite [version 3.7.3] ([dateof:3.7.3]), \n** the soft heap limit is enforced\n** regardless of whether or not the [SQLITE_ENABLE_MEMORY_MANAGEMENT]\n** compile-time option is invoked.  With [SQLITE_ENABLE_MEMORY_MANAGEMENT],\n** the soft heap limit is enforced on every memory allocation.  Without\n** [SQLITE_ENABLE_MEMORY_MANAGEMENT], the soft heap limit is only enforced\n** when memory is allocated by the page cache.  Testing suggests that because\n** the page cache is the predominate memory user in SQLite, most\n** applications will achieve adequate soft heap limit enforcement without\n** the use of [SQLITE_ENABLE_MEMORY_MANAGEMENT].\n**\n** The circumstances under which SQLite will enforce the soft heap limit may\n** changes in future releases of SQLite.\n*/\nSQLITE_API sqlite3_int64 sqlite3_soft_heap_limit64(sqlite3_int64 N);\n\n/*\n** CAPI3REF: Deprecated Soft Heap Limit Interface\n** DEPRECATED\n**\n** This is a deprecated version of the [sqlite3_soft_heap_limit64()]\n** interface.  This routine is provided for historical compatibility\n** only.  All new applications should use the\n** [sqlite3_soft_heap_limit64()] interface rather than this one.\n*/\nSQLITE_API SQLITE_DEPRECATED void sqlite3_soft_heap_limit(int N);\n\n\n/*\n** CAPI3REF: Extract Metadata About A Column Of A Table\n** METHOD: sqlite3\n**\n** ^(The sqlite3_table_column_metadata(X,D,T,C,....) routine returns\n** information about column C of table T in database D\n** on [database connection] X.)^  ^The sqlite3_table_column_metadata()\n** interface returns SQLITE_OK and fills in the non-NULL pointers in\n** the final five arguments with appropriate values if the specified\n** column exists.  ^The sqlite3_table_column_metadata() interface returns\n** SQLITE_ERROR and if the specified column does not exist.\n** ^If the column-name parameter to sqlite3_table_column_metadata() is a\n** NULL pointer, then this routine simply checks for the existence of the\n** table and returns SQLITE_OK if the table exists and SQLITE_ERROR if it\n** does not.  If the table name parameter T in a call to\n** sqlite3_table_column_metadata(X,D,T,C,...) is NULL then the result is\n** undefined behavior.\n**\n** ^The column is identified by the second, third and fourth parameters to\n** this function. ^(The second parameter is either the name of the database\n** (i.e. \"main\", \"temp\", or an attached database) containing the specified\n** table or NULL.)^ ^If it is NULL, then all attached databases are searched\n** for the table using the same algorithm used by the database engine to\n** resolve unqualified table references.\n**\n** ^The third and fourth parameters to this function are the table and column\n** name of the desired column, respectively.\n**\n** ^Metadata is returned by writing to the memory locations passed as the 5th\n** and subsequent parameters to this function. ^Any of these arguments may be\n** NULL, in which case the corresponding element of metadata is omitted.\n**\n** ^(<blockquote>\n** <table border=\"1\">\n** <tr><th> Parameter <th> Output<br>Type <th>  Description\n**\n** <tr><td> 5th <td> const char* <td> Data type\n** <tr><td> 6th <td> const char* <td> Name of default collation sequence\n** <tr><td> 7th <td> int         <td> True if column has a NOT NULL constraint\n** <tr><td> 8th <td> int         <td> True if column is part of the PRIMARY KEY\n** <tr><td> 9th <td> int         <td> True if column is [AUTOINCREMENT]\n** </table>\n** </blockquote>)^\n**\n** ^The memory pointed to by the character pointers returned for the\n** declaration type and collation sequence is valid until the next\n** call to any SQLite API function.\n**\n** ^If the specified table is actually a view, an [error code] is returned.\n**\n** ^If the specified column is \"rowid\", \"oid\" or \"_rowid_\" and the table \n** is not a [WITHOUT ROWID] table and an\n** [INTEGER PRIMARY KEY] column has been explicitly declared, then the output\n** parameters are set for the explicitly declared column. ^(If there is no\n** [INTEGER PRIMARY KEY] column, then the outputs\n** for the [rowid] are set as follows:\n**\n** <pre>\n**     data type: \"INTEGER\"\n**     collation sequence: \"BINARY\"\n**     not null: 0\n**     primary key: 1\n**     auto increment: 0\n** </pre>)^\n**\n** ^This function causes all database schemas to be read from disk and\n** parsed, if that has not already been done, and returns an error if\n** any errors are encountered while loading the schema.\n*/\nSQLITE_API int sqlite3_table_column_metadata(\n  sqlite3 *db,                /* Connection handle */\n  const char *zDbName,        /* Database name or NULL */\n  const char *zTableName,     /* Table name */\n  const char *zColumnName,    /* Column name */\n  char const **pzDataType,    /* OUTPUT: Declared data type */\n  char const **pzCollSeq,     /* OUTPUT: Collation sequence name */\n  int *pNotNull,              /* OUTPUT: True if NOT NULL constraint exists */\n  int *pPrimaryKey,           /* OUTPUT: True if column part of PK */\n  int *pAutoinc               /* OUTPUT: True if column is auto-increment */\n);\n\n/*\n** CAPI3REF: Load An Extension\n** METHOD: sqlite3\n**\n** ^This interface loads an SQLite extension library from the named file.\n**\n** ^The sqlite3_load_extension() interface attempts to load an\n** [SQLite extension] library contained in the file zFile.  If\n** the file cannot be loaded directly, attempts are made to load\n** with various operating-system specific extensions added.\n** So for example, if \"samplelib\" cannot be loaded, then names like\n** \"samplelib.so\" or \"samplelib.dylib\" or \"samplelib.dll\" might\n** be tried also.\n**\n** ^The entry point is zProc.\n** ^(zProc may be 0, in which case SQLite will try to come up with an\n** entry point name on its own.  It first tries \"sqlite3_extension_init\".\n** If that does not work, it constructs a name \"sqlite3_X_init\" where the\n** X is consists of the lower-case equivalent of all ASCII alphabetic\n** characters in the filename from the last \"/\" to the first following\n** \".\" and omitting any initial \"lib\".)^\n** ^The sqlite3_load_extension() interface returns\n** [SQLITE_OK] on success and [SQLITE_ERROR] if something goes wrong.\n** ^If an error occurs and pzErrMsg is not 0, then the\n** [sqlite3_load_extension()] interface shall attempt to\n** fill *pzErrMsg with error message text stored in memory\n** obtained from [sqlite3_malloc()]. The calling function\n** should free this memory by calling [sqlite3_free()].\n**\n** ^Extension loading must be enabled using\n** [sqlite3_enable_load_extension()] or\n** [sqlite3_db_config](db,[SQLITE_DBCONFIG_ENABLE_LOAD_EXTENSION],1,NULL)\n** prior to calling this API,\n** otherwise an error will be returned.\n**\n** <b>Security warning:</b> It is recommended that the \n** [SQLITE_DBCONFIG_ENABLE_LOAD_EXTENSION] method be used to enable only this\n** interface.  The use of the [sqlite3_enable_load_extension()] interface\n** should be avoided.  This will keep the SQL function [load_extension()]\n** disabled and prevent SQL injections from giving attackers\n** access to extension loading capabilities.\n**\n** See also the [load_extension() SQL function].\n*/\nSQLITE_API int sqlite3_load_extension(\n  sqlite3 *db,          /* Load the extension into this database connection */\n  const char *zFile,    /* Name of the shared library containing extension */\n  const char *zProc,    /* Entry point.  Derived from zFile if 0 */\n  char **pzErrMsg       /* Put error message here if not 0 */\n);\n\n/*\n** CAPI3REF: Enable Or Disable Extension Loading\n** METHOD: sqlite3\n**\n** ^So as not to open security holes in older applications that are\n** unprepared to deal with [extension loading], and as a means of disabling\n** [extension loading] while evaluating user-entered SQL, the following API\n** is provided to turn the [sqlite3_load_extension()] mechanism on and off.\n**\n** ^Extension loading is off by default.\n** ^Call the sqlite3_enable_load_extension() routine with onoff==1\n** to turn extension loading on and call it with onoff==0 to turn\n** it back off again.\n**\n** ^This interface enables or disables both the C-API\n** [sqlite3_load_extension()] and the SQL function [load_extension()].\n** ^(Use [sqlite3_db_config](db,[SQLITE_DBCONFIG_ENABLE_LOAD_EXTENSION],..)\n** to enable or disable only the C-API.)^\n**\n** <b>Security warning:</b> It is recommended that extension loading\n** be disabled using the [SQLITE_DBCONFIG_ENABLE_LOAD_EXTENSION] method\n** rather than this interface, so the [load_extension()] SQL function\n** remains disabled. This will prevent SQL injections from giving attackers\n** access to extension loading capabilities.\n*/\nSQLITE_API int sqlite3_enable_load_extension(sqlite3 *db, int onoff);\n\n/*\n** CAPI3REF: Automatically Load Statically Linked Extensions\n**\n** ^This interface causes the xEntryPoint() function to be invoked for\n** each new [database connection] that is created.  The idea here is that\n** xEntryPoint() is the entry point for a statically linked [SQLite extension]\n** that is to be automatically loaded into all new database connections.\n**\n** ^(Even though the function prototype shows that xEntryPoint() takes\n** no arguments and returns void, SQLite invokes xEntryPoint() with three\n** arguments and expects an integer result as if the signature of the\n** entry point where as follows:\n**\n** <blockquote><pre>\n** &nbsp;  int xEntryPoint(\n** &nbsp;    sqlite3 *db,\n** &nbsp;    const char **pzErrMsg,\n** &nbsp;    const struct sqlite3_api_routines *pThunk\n** &nbsp;  );\n** </pre></blockquote>)^\n**\n** If the xEntryPoint routine encounters an error, it should make *pzErrMsg\n** point to an appropriate error message (obtained from [sqlite3_mprintf()])\n** and return an appropriate [error code].  ^SQLite ensures that *pzErrMsg\n** is NULL before calling the xEntryPoint().  ^SQLite will invoke\n** [sqlite3_free()] on *pzErrMsg after xEntryPoint() returns.  ^If any\n** xEntryPoint() returns an error, the [sqlite3_open()], [sqlite3_open16()],\n** or [sqlite3_open_v2()] call that provoked the xEntryPoint() will fail.\n**\n** ^Calling sqlite3_auto_extension(X) with an entry point X that is already\n** on the list of automatic extensions is a harmless no-op. ^No entry point\n** will be called more than once for each database connection that is opened.\n**\n** See also: [sqlite3_reset_auto_extension()]\n** and [sqlite3_cancel_auto_extension()]\n*/\nSQLITE_API int sqlite3_auto_extension(void(*xEntryPoint)(void));\n\n/*\n** CAPI3REF: Cancel Automatic Extension Loading\n**\n** ^The [sqlite3_cancel_auto_extension(X)] interface unregisters the\n** initialization routine X that was registered using a prior call to\n** [sqlite3_auto_extension(X)].  ^The [sqlite3_cancel_auto_extension(X)]\n** routine returns 1 if initialization routine X was successfully \n** unregistered and it returns 0 if X was not on the list of initialization\n** routines.\n*/\nSQLITE_API int sqlite3_cancel_auto_extension(void(*xEntryPoint)(void));\n\n/*\n** CAPI3REF: Reset Automatic Extension Loading\n**\n** ^This interface disables all automatic extensions previously\n** registered using [sqlite3_auto_extension()].\n*/\nSQLITE_API void sqlite3_reset_auto_extension(void);\n\n/*\n** The interface to the virtual-table mechanism is currently considered\n** to be experimental.  The interface might change in incompatible ways.\n** If this is a problem for you, do not use the interface at this time.\n**\n** When the virtual-table mechanism stabilizes, we will declare the\n** interface fixed, support it indefinitely, and remove this comment.\n*/\n\n/*\n** Structures used by the virtual table interface\n*/\ntypedef struct sqlite3_vtab sqlite3_vtab;\ntypedef struct sqlite3_index_info sqlite3_index_info;\ntypedef struct sqlite3_vtab_cursor sqlite3_vtab_cursor;\ntypedef struct sqlite3_module sqlite3_module;\n\n/*\n** CAPI3REF: Virtual Table Object\n** KEYWORDS: sqlite3_module {virtual table module}\n**\n** This structure, sometimes called a \"virtual table module\", \n** defines the implementation of a [virtual tables].  \n** This structure consists mostly of methods for the module.\n**\n** ^A virtual table module is created by filling in a persistent\n** instance of this structure and passing a pointer to that instance\n** to [sqlite3_create_module()] or [sqlite3_create_module_v2()].\n** ^The registration remains valid until it is replaced by a different\n** module or until the [database connection] closes.  The content\n** of this structure must not change while it is registered with\n** any database connection.\n*/\nstruct sqlite3_module {\n  int iVersion;\n  int (*xCreate)(sqlite3*, void *pAux,\n               int argc, const char *const*argv,\n               sqlite3_vtab **ppVTab, char**);\n  int (*xConnect)(sqlite3*, void *pAux,\n               int argc, const char *const*argv,\n               sqlite3_vtab **ppVTab, char**);\n  int (*xBestIndex)(sqlite3_vtab *pVTab, sqlite3_index_info*);\n  int (*xDisconnect)(sqlite3_vtab *pVTab);\n  int (*xDestroy)(sqlite3_vtab *pVTab);\n  int (*xOpen)(sqlite3_vtab *pVTab, sqlite3_vtab_cursor **ppCursor);\n  int (*xClose)(sqlite3_vtab_cursor*);\n  int (*xFilter)(sqlite3_vtab_cursor*, int idxNum, const char *idxStr,\n                int argc, sqlite3_value **argv);\n  int (*xNext)(sqlite3_vtab_cursor*);\n  int (*xEof)(sqlite3_vtab_cursor*);\n  int (*xColumn)(sqlite3_vtab_cursor*, sqlite3_context*, int);\n  int (*xRowid)(sqlite3_vtab_cursor*, sqlite3_int64 *pRowid);\n  int (*xUpdate)(sqlite3_vtab *, int, sqlite3_value **, sqlite3_int64 *);\n  int (*xBegin)(sqlite3_vtab *pVTab);\n  int (*xSync)(sqlite3_vtab *pVTab);\n  int (*xCommit)(sqlite3_vtab *pVTab);\n  int (*xRollback)(sqlite3_vtab *pVTab);\n  int (*xFindFunction)(sqlite3_vtab *pVtab, int nArg, const char *zName,\n                       void (**pxFunc)(sqlite3_context*,int,sqlite3_value**),\n                       void **ppArg);\n  int (*xRename)(sqlite3_vtab *pVtab, const char *zNew);\n  /* The methods above are in version 1 of the sqlite_module object. Those \n  ** below are for version 2 and greater. */\n  int (*xSavepoint)(sqlite3_vtab *pVTab, int);\n  int (*xRelease)(sqlite3_vtab *pVTab, int);\n  int (*xRollbackTo)(sqlite3_vtab *pVTab, int);\n};\n\n/*\n** CAPI3REF: Virtual Table Indexing Information\n** KEYWORDS: sqlite3_index_info\n**\n** The sqlite3_index_info structure and its substructures is used as part\n** of the [virtual table] interface to\n** pass information into and receive the reply from the [xBestIndex]\n** method of a [virtual table module].  The fields under **Inputs** are the\n** inputs to xBestIndex and are read-only.  xBestIndex inserts its\n** results into the **Outputs** fields.\n**\n** ^(The aConstraint[] array records WHERE clause constraints of the form:\n**\n** <blockquote>column OP expr</blockquote>\n**\n** where OP is =, &lt;, &lt;=, &gt;, or &gt;=.)^  ^(The particular operator is\n** stored in aConstraint[].op using one of the\n** [SQLITE_INDEX_CONSTRAINT_EQ | SQLITE_INDEX_CONSTRAINT_ values].)^\n** ^(The index of the column is stored in\n** aConstraint[].iColumn.)^  ^(aConstraint[].usable is TRUE if the\n** expr on the right-hand side can be evaluated (and thus the constraint\n** is usable) and false if it cannot.)^\n**\n** ^The optimizer automatically inverts terms of the form \"expr OP column\"\n** and makes other simplifications to the WHERE clause in an attempt to\n** get as many WHERE clause terms into the form shown above as possible.\n** ^The aConstraint[] array only reports WHERE clause terms that are\n** relevant to the particular virtual table being queried.\n**\n** ^Information about the ORDER BY clause is stored in aOrderBy[].\n** ^Each term of aOrderBy records a column of the ORDER BY clause.\n**\n** The colUsed field indicates which columns of the virtual table may be\n** required by the current scan. Virtual table columns are numbered from\n** zero in the order in which they appear within the CREATE TABLE statement\n** passed to sqlite3_declare_vtab(). For the first 63 columns (columns 0-62),\n** the corresponding bit is set within the colUsed mask if the column may be\n** required by SQLite. If the table has at least 64 columns and any column\n** to the right of the first 63 is required, then bit 63 of colUsed is also\n** set. In other words, column iCol may be required if the expression\n** (colUsed & ((sqlite3_uint64)1 << (iCol>=63 ? 63 : iCol))) evaluates to \n** non-zero.\n**\n** The [xBestIndex] method must fill aConstraintUsage[] with information\n** about what parameters to pass to xFilter.  ^If argvIndex>0 then\n** the right-hand side of the corresponding aConstraint[] is evaluated\n** and becomes the argvIndex-th entry in argv.  ^(If aConstraintUsage[].omit\n** is true, then the constraint is assumed to be fully handled by the\n** virtual table and is not checked again by SQLite.)^\n**\n** ^The idxNum and idxPtr values are recorded and passed into the\n** [xFilter] method.\n** ^[sqlite3_free()] is used to free idxPtr if and only if\n** needToFreeIdxPtr is true.\n**\n** ^The orderByConsumed means that output from [xFilter]/[xNext] will occur in\n** the correct order to satisfy the ORDER BY clause so that no separate\n** sorting step is required.\n**\n** ^The estimatedCost value is an estimate of the cost of a particular\n** strategy. A cost of N indicates that the cost of the strategy is similar\n** to a linear scan of an SQLite table with N rows. A cost of log(N) \n** indicates that the expense of the operation is similar to that of a\n** binary search on a unique indexed field of an SQLite table with N rows.\n**\n** ^The estimatedRows value is an estimate of the number of rows that\n** will be returned by the strategy.\n**\n** The xBestIndex method may optionally populate the idxFlags field with a \n** mask of SQLITE_INDEX_SCAN_* flags. Currently there is only one such flag -\n** SQLITE_INDEX_SCAN_UNIQUE. If the xBestIndex method sets this flag, SQLite\n** assumes that the strategy may visit at most one row. \n**\n** Additionally, if xBestIndex sets the SQLITE_INDEX_SCAN_UNIQUE flag, then\n** SQLite also assumes that if a call to the xUpdate() method is made as\n** part of the same statement to delete or update a virtual table row and the\n** implementation returns SQLITE_CONSTRAINT, then there is no need to rollback\n** any database changes. In other words, if the xUpdate() returns\n** SQLITE_CONSTRAINT, the database contents must be exactly as they were\n** before xUpdate was called. By contrast, if SQLITE_INDEX_SCAN_UNIQUE is not\n** set and xUpdate returns SQLITE_CONSTRAINT, any database changes made by\n** the xUpdate method are automatically rolled back by SQLite.\n**\n** IMPORTANT: The estimatedRows field was added to the sqlite3_index_info\n** structure for SQLite [version 3.8.2] ([dateof:3.8.2]). \n** If a virtual table extension is\n** used with an SQLite version earlier than 3.8.2, the results of attempting \n** to read or write the estimatedRows field are undefined (but are likely \n** to included crashing the application). The estimatedRows field should\n** therefore only be used if [sqlite3_libversion_number()] returns a\n** value greater than or equal to 3008002. Similarly, the idxFlags field\n** was added for [version 3.9.0] ([dateof:3.9.0]). \n** It may therefore only be used if\n** sqlite3_libversion_number() returns a value greater than or equal to\n** 3009000.\n*/\nstruct sqlite3_index_info {\n  /* Inputs */\n  int nConstraint;           /* Number of entries in aConstraint */\n  struct sqlite3_index_constraint {\n     int iColumn;              /* Column constrained.  -1 for ROWID */\n     unsigned char op;         /* Constraint operator */\n     unsigned char usable;     /* True if this constraint is usable */\n     int iTermOffset;          /* Used internally - xBestIndex should ignore */\n  } *aConstraint;            /* Table of WHERE clause constraints */\n  int nOrderBy;              /* Number of terms in the ORDER BY clause */\n  struct sqlite3_index_orderby {\n     int iColumn;              /* Column number */\n     unsigned char desc;       /* True for DESC.  False for ASC. */\n  } *aOrderBy;               /* The ORDER BY clause */\n  /* Outputs */\n  struct sqlite3_index_constraint_usage {\n    int argvIndex;           /* if >0, constraint is part of argv to xFilter */\n    unsigned char omit;      /* Do not code a test for this constraint */\n  } *aConstraintUsage;\n  int idxNum;                /* Number used to identify the index */\n  char *idxStr;              /* String, possibly obtained from sqlite3_malloc */\n  int needToFreeIdxStr;      /* Free idxStr using sqlite3_free() if true */\n  int orderByConsumed;       /* True if output is already ordered */\n  double estimatedCost;           /* Estimated cost of using this index */\n  /* Fields below are only available in SQLite 3.8.2 and later */\n  sqlite3_int64 estimatedRows;    /* Estimated number of rows returned */\n  /* Fields below are only available in SQLite 3.9.0 and later */\n  int idxFlags;              /* Mask of SQLITE_INDEX_SCAN_* flags */\n  /* Fields below are only available in SQLite 3.10.0 and later */\n  sqlite3_uint64 colUsed;    /* Input: Mask of columns used by statement */\n};\n\n/*\n** CAPI3REF: Virtual Table Scan Flags\n*/\n#define SQLITE_INDEX_SCAN_UNIQUE      1     /* Scan visits at most 1 row */\n\n/*\n** CAPI3REF: Virtual Table Constraint Operator Codes\n**\n** These macros defined the allowed values for the\n** [sqlite3_index_info].aConstraint[].op field.  Each value represents\n** an operator that is part of a constraint term in the wHERE clause of\n** a query that uses a [virtual table].\n*/\n#define SQLITE_INDEX_CONSTRAINT_EQ         2\n#define SQLITE_INDEX_CONSTRAINT_GT         4\n#define SQLITE_INDEX_CONSTRAINT_LE         8\n#define SQLITE_INDEX_CONSTRAINT_LT        16\n#define SQLITE_INDEX_CONSTRAINT_GE        32\n#define SQLITE_INDEX_CONSTRAINT_MATCH     64\n#define SQLITE_INDEX_CONSTRAINT_LIKE      65\n#define SQLITE_INDEX_CONSTRAINT_GLOB      66\n#define SQLITE_INDEX_CONSTRAINT_REGEXP    67\n#define SQLITE_INDEX_CONSTRAINT_NE        68\n#define SQLITE_INDEX_CONSTRAINT_ISNOT     69\n#define SQLITE_INDEX_CONSTRAINT_ISNOTNULL 70\n#define SQLITE_INDEX_CONSTRAINT_ISNULL    71\n#define SQLITE_INDEX_CONSTRAINT_IS        72\n\n/*\n** CAPI3REF: Register A Virtual Table Implementation\n** METHOD: sqlite3\n**\n** ^These routines are used to register a new [virtual table module] name.\n** ^Module names must be registered before\n** creating a new [virtual table] using the module and before using a\n** preexisting [virtual table] for the module.\n**\n** ^The module name is registered on the [database connection] specified\n** by the first parameter.  ^The name of the module is given by the \n** second parameter.  ^The third parameter is a pointer to\n** the implementation of the [virtual table module].   ^The fourth\n** parameter is an arbitrary client data pointer that is passed through\n** into the [xCreate] and [xConnect] methods of the virtual table module\n** when a new virtual table is be being created or reinitialized.\n**\n** ^The sqlite3_create_module_v2() interface has a fifth parameter which\n** is a pointer to a destructor for the pClientData.  ^SQLite will\n** invoke the destructor function (if it is not NULL) when SQLite\n** no longer needs the pClientData pointer.  ^The destructor will also\n** be invoked if the call to sqlite3_create_module_v2() fails.\n** ^The sqlite3_create_module()\n** interface is equivalent to sqlite3_create_module_v2() with a NULL\n** destructor.\n*/\nSQLITE_API int sqlite3_create_module(\n  sqlite3 *db,               /* SQLite connection to register module with */\n  const char *zName,         /* Name of the module */\n  const sqlite3_module *p,   /* Methods for the module */\n  void *pClientData          /* Client data for xCreate/xConnect */\n);\nSQLITE_API int sqlite3_create_module_v2(\n  sqlite3 *db,               /* SQLite connection to register module with */\n  const char *zName,         /* Name of the module */\n  const sqlite3_module *p,   /* Methods for the module */\n  void *pClientData,         /* Client data for xCreate/xConnect */\n  void(*xDestroy)(void*)     /* Module destructor function */\n);\n\n/*\n** CAPI3REF: Virtual Table Instance Object\n** KEYWORDS: sqlite3_vtab\n**\n** Every [virtual table module] implementation uses a subclass\n** of this object to describe a particular instance\n** of the [virtual table].  Each subclass will\n** be tailored to the specific needs of the module implementation.\n** The purpose of this superclass is to define certain fields that are\n** common to all module implementations.\n**\n** ^Virtual tables methods can set an error message by assigning a\n** string obtained from [sqlite3_mprintf()] to zErrMsg.  The method should\n** take care that any prior string is freed by a call to [sqlite3_free()]\n** prior to assigning a new string to zErrMsg.  ^After the error message\n** is delivered up to the client application, the string will be automatically\n** freed by sqlite3_free() and the zErrMsg field will be zeroed.\n*/\nstruct sqlite3_vtab {\n  const sqlite3_module *pModule;  /* The module for this virtual table */\n  int nRef;                       /* Number of open cursors */\n  char *zErrMsg;                  /* Error message from sqlite3_mprintf() */\n  /* Virtual table implementations will typically add additional fields */\n};\n\n/*\n** CAPI3REF: Virtual Table Cursor Object\n** KEYWORDS: sqlite3_vtab_cursor {virtual table cursor}\n**\n** Every [virtual table module] implementation uses a subclass of the\n** following structure to describe cursors that point into the\n** [virtual table] and are used\n** to loop through the virtual table.  Cursors are created using the\n** [sqlite3_module.xOpen | xOpen] method of the module and are destroyed\n** by the [sqlite3_module.xClose | xClose] method.  Cursors are used\n** by the [xFilter], [xNext], [xEof], [xColumn], and [xRowid] methods\n** of the module.  Each module implementation will define\n** the content of a cursor structure to suit its own needs.\n**\n** This superclass exists in order to define fields of the cursor that\n** are common to all implementations.\n*/\nstruct sqlite3_vtab_cursor {\n  sqlite3_vtab *pVtab;      /* Virtual table of this cursor */\n  /* Virtual table implementations will typically add additional fields */\n};\n\n/*\n** CAPI3REF: Declare The Schema Of A Virtual Table\n**\n** ^The [xCreate] and [xConnect] methods of a\n** [virtual table module] call this interface\n** to declare the format (the names and datatypes of the columns) of\n** the virtual tables they implement.\n*/\nSQLITE_API int sqlite3_declare_vtab(sqlite3*, const char *zSQL);\n\n/*\n** CAPI3REF: Overload A Function For A Virtual Table\n** METHOD: sqlite3\n**\n** ^(Virtual tables can provide alternative implementations of functions\n** using the [xFindFunction] method of the [virtual table module].  \n** But global versions of those functions\n** must exist in order to be overloaded.)^\n**\n** ^(This API makes sure a global version of a function with a particular\n** name and number of parameters exists.  If no such function exists\n** before this API is called, a new function is created.)^  ^The implementation\n** of the new function always causes an exception to be thrown.  So\n** the new function is not good for anything by itself.  Its only\n** purpose is to be a placeholder function that can be overloaded\n** by a [virtual table].\n*/\nSQLITE_API int sqlite3_overload_function(sqlite3*, const char *zFuncName, int nArg);\n\n/*\n** The interface to the virtual-table mechanism defined above (back up\n** to a comment remarkably similar to this one) is currently considered\n** to be experimental.  The interface might change in incompatible ways.\n** If this is a problem for you, do not use the interface at this time.\n**\n** When the virtual-table mechanism stabilizes, we will declare the\n** interface fixed, support it indefinitely, and remove this comment.\n*/\n\n/*\n** CAPI3REF: A Handle To An Open BLOB\n** KEYWORDS: {BLOB handle} {BLOB handles}\n**\n** An instance of this object represents an open BLOB on which\n** [sqlite3_blob_open | incremental BLOB I/O] can be performed.\n** ^Objects of this type are created by [sqlite3_blob_open()]\n** and destroyed by [sqlite3_blob_close()].\n** ^The [sqlite3_blob_read()] and [sqlite3_blob_write()] interfaces\n** can be used to read or write small subsections of the BLOB.\n** ^The [sqlite3_blob_bytes()] interface returns the size of the BLOB in bytes.\n*/\ntypedef struct sqlite3_blob sqlite3_blob;\n\n/*\n** CAPI3REF: Open A BLOB For Incremental I/O\n** METHOD: sqlite3\n** CONSTRUCTOR: sqlite3_blob\n**\n** ^(This interfaces opens a [BLOB handle | handle] to the BLOB located\n** in row iRow, column zColumn, table zTable in database zDb;\n** in other words, the same BLOB that would be selected by:\n**\n** <pre>\n**     SELECT zColumn FROM zDb.zTable WHERE [rowid] = iRow;\n** </pre>)^\n**\n** ^(Parameter zDb is not the filename that contains the database, but \n** rather the symbolic name of the database. For attached databases, this is\n** the name that appears after the AS keyword in the [ATTACH] statement.\n** For the main database file, the database name is \"main\". For TEMP\n** tables, the database name is \"temp\".)^\n**\n** ^If the flags parameter is non-zero, then the BLOB is opened for read\n** and write access. ^If the flags parameter is zero, the BLOB is opened for\n** read-only access.\n**\n** ^(On success, [SQLITE_OK] is returned and the new [BLOB handle] is stored\n** in *ppBlob. Otherwise an [error code] is returned and, unless the error\n** code is SQLITE_MISUSE, *ppBlob is set to NULL.)^ ^This means that, provided\n** the API is not misused, it is always safe to call [sqlite3_blob_close()] \n** on *ppBlob after this function it returns.\n**\n** This function fails with SQLITE_ERROR if any of the following are true:\n** <ul>\n**   <li> ^(Database zDb does not exist)^, \n**   <li> ^(Table zTable does not exist within database zDb)^, \n**   <li> ^(Table zTable is a WITHOUT ROWID table)^, \n**   <li> ^(Column zColumn does not exist)^,\n**   <li> ^(Row iRow is not present in the table)^,\n**   <li> ^(The specified column of row iRow contains a value that is not\n**         a TEXT or BLOB value)^,\n**   <li> ^(Column zColumn is part of an index, PRIMARY KEY or UNIQUE \n**         constraint and the blob is being opened for read/write access)^,\n**   <li> ^([foreign key constraints | Foreign key constraints] are enabled, \n**         column zColumn is part of a [child key] definition and the blob is\n**         being opened for read/write access)^.\n** </ul>\n**\n** ^Unless it returns SQLITE_MISUSE, this function sets the \n** [database connection] error code and message accessible via \n** [sqlite3_errcode()] and [sqlite3_errmsg()] and related functions. \n**\n** A BLOB referenced by sqlite3_blob_open() may be read using the\n** [sqlite3_blob_read()] interface and modified by using\n** [sqlite3_blob_write()].  The [BLOB handle] can be moved to a\n** different row of the same table using the [sqlite3_blob_reopen()]\n** interface.  However, the column, table, or database of a [BLOB handle]\n** cannot be changed after the [BLOB handle] is opened.\n**\n** ^(If the row that a BLOB handle points to is modified by an\n** [UPDATE], [DELETE], or by [ON CONFLICT] side-effects\n** then the BLOB handle is marked as \"expired\".\n** This is true if any column of the row is changed, even a column\n** other than the one the BLOB handle is open on.)^\n** ^Calls to [sqlite3_blob_read()] and [sqlite3_blob_write()] for\n** an expired BLOB handle fail with a return code of [SQLITE_ABORT].\n** ^(Changes written into a BLOB prior to the BLOB expiring are not\n** rolled back by the expiration of the BLOB.  Such changes will eventually\n** commit if the transaction continues to completion.)^\n**\n** ^Use the [sqlite3_blob_bytes()] interface to determine the size of\n** the opened blob.  ^The size of a blob may not be changed by this\n** interface.  Use the [UPDATE] SQL command to change the size of a\n** blob.\n**\n** ^The [sqlite3_bind_zeroblob()] and [sqlite3_result_zeroblob()] interfaces\n** and the built-in [zeroblob] SQL function may be used to create a \n** zero-filled blob to read or write using the incremental-blob interface.\n**\n** To avoid a resource leak, every open [BLOB handle] should eventually\n** be released by a call to [sqlite3_blob_close()].\n**\n** See also: [sqlite3_blob_close()],\n** [sqlite3_blob_reopen()], [sqlite3_blob_read()],\n** [sqlite3_blob_bytes()], [sqlite3_blob_write()].\n*/\nSQLITE_API int sqlite3_blob_open(\n  sqlite3*,\n  const char *zDb,\n  const char *zTable,\n  const char *zColumn,\n  sqlite3_int64 iRow,\n  int flags,\n  sqlite3_blob **ppBlob\n);\n\n/*\n** CAPI3REF: Move a BLOB Handle to a New Row\n** METHOD: sqlite3_blob\n**\n** ^This function is used to move an existing [BLOB handle] so that it points\n** to a different row of the same database table. ^The new row is identified\n** by the rowid value passed as the second argument. Only the row can be\n** changed. ^The database, table and column on which the blob handle is open\n** remain the same. Moving an existing [BLOB handle] to a new row is\n** faster than closing the existing handle and opening a new one.\n**\n** ^(The new row must meet the same criteria as for [sqlite3_blob_open()] -\n** it must exist and there must be either a blob or text value stored in\n** the nominated column.)^ ^If the new row is not present in the table, or if\n** it does not contain a blob or text value, or if another error occurs, an\n** SQLite error code is returned and the blob handle is considered aborted.\n** ^All subsequent calls to [sqlite3_blob_read()], [sqlite3_blob_write()] or\n** [sqlite3_blob_reopen()] on an aborted blob handle immediately return\n** SQLITE_ABORT. ^Calling [sqlite3_blob_bytes()] on an aborted blob handle\n** always returns zero.\n**\n** ^This function sets the database handle error code and message.\n*/\nSQLITE_API int sqlite3_blob_reopen(sqlite3_blob *, sqlite3_int64);\n\n/*\n** CAPI3REF: Close A BLOB Handle\n** DESTRUCTOR: sqlite3_blob\n**\n** ^This function closes an open [BLOB handle]. ^(The BLOB handle is closed\n** unconditionally.  Even if this routine returns an error code, the \n** handle is still closed.)^\n**\n** ^If the blob handle being closed was opened for read-write access, and if\n** the database is in auto-commit mode and there are no other open read-write\n** blob handles or active write statements, the current transaction is\n** committed. ^If an error occurs while committing the transaction, an error\n** code is returned and the transaction rolled back.\n**\n** Calling this function with an argument that is not a NULL pointer or an\n** open blob handle results in undefined behaviour. ^Calling this routine \n** with a null pointer (such as would be returned by a failed call to \n** [sqlite3_blob_open()]) is a harmless no-op. ^Otherwise, if this function\n** is passed a valid open blob handle, the values returned by the \n** sqlite3_errcode() and sqlite3_errmsg() functions are set before returning.\n*/\nSQLITE_API int sqlite3_blob_close(sqlite3_blob *);\n\n/*\n** CAPI3REF: Return The Size Of An Open BLOB\n** METHOD: sqlite3_blob\n**\n** ^Returns the size in bytes of the BLOB accessible via the \n** successfully opened [BLOB handle] in its only argument.  ^The\n** incremental blob I/O routines can only read or overwriting existing\n** blob content; they cannot change the size of a blob.\n**\n** This routine only works on a [BLOB handle] which has been created\n** by a prior successful call to [sqlite3_blob_open()] and which has not\n** been closed by [sqlite3_blob_close()].  Passing any other pointer in\n** to this routine results in undefined and probably undesirable behavior.\n*/\nSQLITE_API int sqlite3_blob_bytes(sqlite3_blob *);\n\n/*\n** CAPI3REF: Read Data From A BLOB Incrementally\n** METHOD: sqlite3_blob\n**\n** ^(This function is used to read data from an open [BLOB handle] into a\n** caller-supplied buffer. N bytes of data are copied into buffer Z\n** from the open BLOB, starting at offset iOffset.)^\n**\n** ^If offset iOffset is less than N bytes from the end of the BLOB,\n** [SQLITE_ERROR] is returned and no data is read.  ^If N or iOffset is\n** less than zero, [SQLITE_ERROR] is returned and no data is read.\n** ^The size of the blob (and hence the maximum value of N+iOffset)\n** can be determined using the [sqlite3_blob_bytes()] interface.\n**\n** ^An attempt to read from an expired [BLOB handle] fails with an\n** error code of [SQLITE_ABORT].\n**\n** ^(On success, sqlite3_blob_read() returns SQLITE_OK.\n** Otherwise, an [error code] or an [extended error code] is returned.)^\n**\n** This routine only works on a [BLOB handle] which has been created\n** by a prior successful call to [sqlite3_blob_open()] and which has not\n** been closed by [sqlite3_blob_close()].  Passing any other pointer in\n** to this routine results in undefined and probably undesirable behavior.\n**\n** See also: [sqlite3_blob_write()].\n*/\nSQLITE_API int sqlite3_blob_read(sqlite3_blob *, void *Z, int N, int iOffset);\n\n/*\n** CAPI3REF: Write Data Into A BLOB Incrementally\n** METHOD: sqlite3_blob\n**\n** ^(This function is used to write data into an open [BLOB handle] from a\n** caller-supplied buffer. N bytes of data are copied from the buffer Z\n** into the open BLOB, starting at offset iOffset.)^\n**\n** ^(On success, sqlite3_blob_write() returns SQLITE_OK.\n** Otherwise, an  [error code] or an [extended error code] is returned.)^\n** ^Unless SQLITE_MISUSE is returned, this function sets the \n** [database connection] error code and message accessible via \n** [sqlite3_errcode()] and [sqlite3_errmsg()] and related functions. \n**\n** ^If the [BLOB handle] passed as the first argument was not opened for\n** writing (the flags parameter to [sqlite3_blob_open()] was zero),\n** this function returns [SQLITE_READONLY].\n**\n** This function may only modify the contents of the BLOB; it is\n** not possible to increase the size of a BLOB using this API.\n** ^If offset iOffset is less than N bytes from the end of the BLOB,\n** [SQLITE_ERROR] is returned and no data is written. The size of the \n** BLOB (and hence the maximum value of N+iOffset) can be determined \n** using the [sqlite3_blob_bytes()] interface. ^If N or iOffset are less \n** than zero [SQLITE_ERROR] is returned and no data is written.\n**\n** ^An attempt to write to an expired [BLOB handle] fails with an\n** error code of [SQLITE_ABORT].  ^Writes to the BLOB that occurred\n** before the [BLOB handle] expired are not rolled back by the\n** expiration of the handle, though of course those changes might\n** have been overwritten by the statement that expired the BLOB handle\n** or by other independent statements.\n**\n** This routine only works on a [BLOB handle] which has been created\n** by a prior successful call to [sqlite3_blob_open()] and which has not\n** been closed by [sqlite3_blob_close()].  Passing any other pointer in\n** to this routine results in undefined and probably undesirable behavior.\n**\n** See also: [sqlite3_blob_read()].\n*/\nSQLITE_API int sqlite3_blob_write(sqlite3_blob *, const void *z, int n, int iOffset);\n\n/*\n** CAPI3REF: Virtual File System Objects\n**\n** A virtual filesystem (VFS) is an [sqlite3_vfs] object\n** that SQLite uses to interact\n** with the underlying operating system.  Most SQLite builds come with a\n** single default VFS that is appropriate for the host computer.\n** New VFSes can be registered and existing VFSes can be unregistered.\n** The following interfaces are provided.\n**\n** ^The sqlite3_vfs_find() interface returns a pointer to a VFS given its name.\n** ^Names are case sensitive.\n** ^Names are zero-terminated UTF-8 strings.\n** ^If there is no match, a NULL pointer is returned.\n** ^If zVfsName is NULL then the default VFS is returned.\n**\n** ^New VFSes are registered with sqlite3_vfs_register().\n** ^Each new VFS becomes the default VFS if the makeDflt flag is set.\n** ^The same VFS can be registered multiple times without injury.\n** ^To make an existing VFS into the default VFS, register it again\n** with the makeDflt flag set.  If two different VFSes with the\n** same name are registered, the behavior is undefined.  If a\n** VFS is registered with a name that is NULL or an empty string,\n** then the behavior is undefined.\n**\n** ^Unregister a VFS with the sqlite3_vfs_unregister() interface.\n** ^(If the default VFS is unregistered, another VFS is chosen as\n** the default.  The choice for the new VFS is arbitrary.)^\n*/\nSQLITE_API sqlite3_vfs *sqlite3_vfs_find(const char *zVfsName);\nSQLITE_API int sqlite3_vfs_register(sqlite3_vfs*, int makeDflt);\nSQLITE_API int sqlite3_vfs_unregister(sqlite3_vfs*);\n\n/*\n** CAPI3REF: Mutexes\n**\n** The SQLite core uses these routines for thread\n** synchronization. Though they are intended for internal\n** use by SQLite, code that links against SQLite is\n** permitted to use any of these routines.\n**\n** The SQLite source code contains multiple implementations\n** of these mutex routines.  An appropriate implementation\n** is selected automatically at compile-time.  The following\n** implementations are available in the SQLite core:\n**\n** <ul>\n** <li>   SQLITE_MUTEX_PTHREADS\n** <li>   SQLITE_MUTEX_W32\n** <li>   SQLITE_MUTEX_NOOP\n** </ul>\n**\n** The SQLITE_MUTEX_NOOP implementation is a set of routines\n** that does no real locking and is appropriate for use in\n** a single-threaded application.  The SQLITE_MUTEX_PTHREADS and\n** SQLITE_MUTEX_W32 implementations are appropriate for use on Unix\n** and Windows.\n**\n** If SQLite is compiled with the SQLITE_MUTEX_APPDEF preprocessor\n** macro defined (with \"-DSQLITE_MUTEX_APPDEF=1\"), then no mutex\n** implementation is included with the library. In this case the\n** application must supply a custom mutex implementation using the\n** [SQLITE_CONFIG_MUTEX] option of the sqlite3_config() function\n** before calling sqlite3_initialize() or any other public sqlite3_\n** function that calls sqlite3_initialize().\n**\n** ^The sqlite3_mutex_alloc() routine allocates a new\n** mutex and returns a pointer to it. ^The sqlite3_mutex_alloc()\n** routine returns NULL if it is unable to allocate the requested\n** mutex.  The argument to sqlite3_mutex_alloc() must one of these\n** integer constants:\n**\n** <ul>\n** <li>  SQLITE_MUTEX_FAST\n** <li>  SQLITE_MUTEX_RECURSIVE\n** <li>  SQLITE_MUTEX_STATIC_MASTER\n** <li>  SQLITE_MUTEX_STATIC_MEM\n** <li>  SQLITE_MUTEX_STATIC_OPEN\n** <li>  SQLITE_MUTEX_STATIC_PRNG\n** <li>  SQLITE_MUTEX_STATIC_LRU\n** <li>  SQLITE_MUTEX_STATIC_PMEM\n** <li>  SQLITE_MUTEX_STATIC_APP1\n** <li>  SQLITE_MUTEX_STATIC_APP2\n** <li>  SQLITE_MUTEX_STATIC_APP3\n** <li>  SQLITE_MUTEX_STATIC_VFS1\n** <li>  SQLITE_MUTEX_STATIC_VFS2\n** <li>  SQLITE_MUTEX_STATIC_VFS3\n** </ul>\n**\n** ^The first two constants (SQLITE_MUTEX_FAST and SQLITE_MUTEX_RECURSIVE)\n** cause sqlite3_mutex_alloc() to create\n** a new mutex.  ^The new mutex is recursive when SQLITE_MUTEX_RECURSIVE\n** is used but not necessarily so when SQLITE_MUTEX_FAST is used.\n** The mutex implementation does not need to make a distinction\n** between SQLITE_MUTEX_RECURSIVE and SQLITE_MUTEX_FAST if it does\n** not want to.  SQLite will only request a recursive mutex in\n** cases where it really needs one.  If a faster non-recursive mutex\n** implementation is available on the host platform, the mutex subsystem\n** might return such a mutex in response to SQLITE_MUTEX_FAST.\n**\n** ^The other allowed parameters to sqlite3_mutex_alloc() (anything other\n** than SQLITE_MUTEX_FAST and SQLITE_MUTEX_RECURSIVE) each return\n** a pointer to a static preexisting mutex.  ^Nine static mutexes are\n** used by the current version of SQLite.  Future versions of SQLite\n** may add additional static mutexes.  Static mutexes are for internal\n** use by SQLite only.  Applications that use SQLite mutexes should\n** use only the dynamic mutexes returned by SQLITE_MUTEX_FAST or\n** SQLITE_MUTEX_RECURSIVE.\n**\n** ^Note that if one of the dynamic mutex parameters (SQLITE_MUTEX_FAST\n** or SQLITE_MUTEX_RECURSIVE) is used then sqlite3_mutex_alloc()\n** returns a different mutex on every call.  ^For the static\n** mutex types, the same mutex is returned on every call that has\n** the same type number.\n**\n** ^The sqlite3_mutex_free() routine deallocates a previously\n** allocated dynamic mutex.  Attempting to deallocate a static\n** mutex results in undefined behavior.\n**\n** ^The sqlite3_mutex_enter() and sqlite3_mutex_try() routines attempt\n** to enter a mutex.  ^If another thread is already within the mutex,\n** sqlite3_mutex_enter() will block and sqlite3_mutex_try() will return\n** SQLITE_BUSY.  ^The sqlite3_mutex_try() interface returns [SQLITE_OK]\n** upon successful entry.  ^(Mutexes created using\n** SQLITE_MUTEX_RECURSIVE can be entered multiple times by the same thread.\n** In such cases, the\n** mutex must be exited an equal number of times before another thread\n** can enter.)^  If the same thread tries to enter any mutex other\n** than an SQLITE_MUTEX_RECURSIVE more than once, the behavior is undefined.\n**\n** ^(Some systems (for example, Windows 95) do not support the operation\n** implemented by sqlite3_mutex_try().  On those systems, sqlite3_mutex_try()\n** will always return SQLITE_BUSY. The SQLite core only ever uses\n** sqlite3_mutex_try() as an optimization so this is acceptable \n** behavior.)^\n**\n** ^The sqlite3_mutex_leave() routine exits a mutex that was\n** previously entered by the same thread.   The behavior\n** is undefined if the mutex is not currently entered by the\n** calling thread or is not currently allocated.\n**\n** ^If the argument to sqlite3_mutex_enter(), sqlite3_mutex_try(), or\n** sqlite3_mutex_leave() is a NULL pointer, then all three routines\n** behave as no-ops.\n**\n** See also: [sqlite3_mutex_held()] and [sqlite3_mutex_notheld()].\n*/\nSQLITE_API sqlite3_mutex *sqlite3_mutex_alloc(int);\nSQLITE_API void sqlite3_mutex_free(sqlite3_mutex*);\nSQLITE_API void sqlite3_mutex_enter(sqlite3_mutex*);\nSQLITE_API int sqlite3_mutex_try(sqlite3_mutex*);\nSQLITE_API void sqlite3_mutex_leave(sqlite3_mutex*);\n\n/*\n** CAPI3REF: Mutex Methods Object\n**\n** An instance of this structure defines the low-level routines\n** used to allocate and use mutexes.\n**\n** Usually, the default mutex implementations provided by SQLite are\n** sufficient, however the application has the option of substituting a custom\n** implementation for specialized deployments or systems for which SQLite\n** does not provide a suitable implementation. In this case, the application\n** creates and populates an instance of this structure to pass\n** to sqlite3_config() along with the [SQLITE_CONFIG_MUTEX] option.\n** Additionally, an instance of this structure can be used as an\n** output variable when querying the system for the current mutex\n** implementation, using the [SQLITE_CONFIG_GETMUTEX] option.\n**\n** ^The xMutexInit method defined by this structure is invoked as\n** part of system initialization by the sqlite3_initialize() function.\n** ^The xMutexInit routine is called by SQLite exactly once for each\n** effective call to [sqlite3_initialize()].\n**\n** ^The xMutexEnd method defined by this structure is invoked as\n** part of system shutdown by the sqlite3_shutdown() function. The\n** implementation of this method is expected to release all outstanding\n** resources obtained by the mutex methods implementation, especially\n** those obtained by the xMutexInit method.  ^The xMutexEnd()\n** interface is invoked exactly once for each call to [sqlite3_shutdown()].\n**\n** ^(The remaining seven methods defined by this structure (xMutexAlloc,\n** xMutexFree, xMutexEnter, xMutexTry, xMutexLeave, xMutexHeld and\n** xMutexNotheld) implement the following interfaces (respectively):\n**\n** <ul>\n**   <li>  [sqlite3_mutex_alloc()] </li>\n**   <li>  [sqlite3_mutex_free()] </li>\n**   <li>  [sqlite3_mutex_enter()] </li>\n**   <li>  [sqlite3_mutex_try()] </li>\n**   <li>  [sqlite3_mutex_leave()] </li>\n**   <li>  [sqlite3_mutex_held()] </li>\n**   <li>  [sqlite3_mutex_notheld()] </li>\n** </ul>)^\n**\n** The only difference is that the public sqlite3_XXX functions enumerated\n** above silently ignore any invocations that pass a NULL pointer instead\n** of a valid mutex handle. The implementations of the methods defined\n** by this structure are not required to handle this case, the results\n** of passing a NULL pointer instead of a valid mutex handle are undefined\n** (i.e. it is acceptable to provide an implementation that segfaults if\n** it is passed a NULL pointer).\n**\n** The xMutexInit() method must be threadsafe.  It must be harmless to\n** invoke xMutexInit() multiple times within the same process and without\n** intervening calls to xMutexEnd().  Second and subsequent calls to\n** xMutexInit() must be no-ops.\n**\n** xMutexInit() must not use SQLite memory allocation ([sqlite3_malloc()]\n** and its associates).  Similarly, xMutexAlloc() must not use SQLite memory\n** allocation for a static mutex.  ^However xMutexAlloc() may use SQLite\n** memory allocation for a fast or recursive mutex.\n**\n** ^SQLite will invoke the xMutexEnd() method when [sqlite3_shutdown()] is\n** called, but only if the prior call to xMutexInit returned SQLITE_OK.\n** If xMutexInit fails in any way, it is expected to clean up after itself\n** prior to returning.\n*/\ntypedef struct sqlite3_mutex_methods sqlite3_mutex_methods;\nstruct sqlite3_mutex_methods {\n  int (*xMutexInit)(void);\n  int (*xMutexEnd)(void);\n  sqlite3_mutex *(*xMutexAlloc)(int);\n  void (*xMutexFree)(sqlite3_mutex *);\n  void (*xMutexEnter)(sqlite3_mutex *);\n  int (*xMutexTry)(sqlite3_mutex *);\n  void (*xMutexLeave)(sqlite3_mutex *);\n  int (*xMutexHeld)(sqlite3_mutex *);\n  int (*xMutexNotheld)(sqlite3_mutex *);\n};\n\n/*\n** CAPI3REF: Mutex Verification Routines\n**\n** The sqlite3_mutex_held() and sqlite3_mutex_notheld() routines\n** are intended for use inside assert() statements.  The SQLite core\n** never uses these routines except inside an assert() and applications\n** are advised to follow the lead of the core.  The SQLite core only\n** provides implementations for these routines when it is compiled\n** with the SQLITE_DEBUG flag.  External mutex implementations\n** are only required to provide these routines if SQLITE_DEBUG is\n** defined and if NDEBUG is not defined.\n**\n** These routines should return true if the mutex in their argument\n** is held or not held, respectively, by the calling thread.\n**\n** The implementation is not required to provide versions of these\n** routines that actually work. If the implementation does not provide working\n** versions of these routines, it should at least provide stubs that always\n** return true so that one does not get spurious assertion failures.\n**\n** If the argument to sqlite3_mutex_held() is a NULL pointer then\n** the routine should return 1.   This seems counter-intuitive since\n** clearly the mutex cannot be held if it does not exist.  But\n** the reason the mutex does not exist is because the build is not\n** using mutexes.  And we do not want the assert() containing the\n** call to sqlite3_mutex_held() to fail, so a non-zero return is\n** the appropriate thing to do.  The sqlite3_mutex_notheld()\n** interface should also return 1 when given a NULL pointer.\n*/\n#ifndef NDEBUG\nSQLITE_API int sqlite3_mutex_held(sqlite3_mutex*);\nSQLITE_API int sqlite3_mutex_notheld(sqlite3_mutex*);\n#endif\n\n/*\n** CAPI3REF: Mutex Types\n**\n** The [sqlite3_mutex_alloc()] interface takes a single argument\n** which is one of these integer constants.\n**\n** The set of static mutexes may change from one SQLite release to the\n** next.  Applications that override the built-in mutex logic must be\n** prepared to accommodate additional static mutexes.\n*/\n#define SQLITE_MUTEX_FAST             0\n#define SQLITE_MUTEX_RECURSIVE        1\n#define SQLITE_MUTEX_STATIC_MASTER    2\n#define SQLITE_MUTEX_STATIC_MEM       3  /* sqlite3_malloc() */\n#define SQLITE_MUTEX_STATIC_MEM2      4  /* NOT USED */\n#define SQLITE_MUTEX_STATIC_OPEN      4  /* sqlite3BtreeOpen() */\n#define SQLITE_MUTEX_STATIC_PRNG      5  /* sqlite3_randomness() */\n#define SQLITE_MUTEX_STATIC_LRU       6  /* lru page list */\n#define SQLITE_MUTEX_STATIC_LRU2      7  /* NOT USED */\n#define SQLITE_MUTEX_STATIC_PMEM      7  /* sqlite3PageMalloc() */\n#define SQLITE_MUTEX_STATIC_APP1      8  /* For use by application */\n#define SQLITE_MUTEX_STATIC_APP2      9  /* For use by application */\n#define SQLITE_MUTEX_STATIC_APP3     10  /* For use by application */\n#define SQLITE_MUTEX_STATIC_VFS1     11  /* For use by built-in VFS */\n#define SQLITE_MUTEX_STATIC_VFS2     12  /* For use by extension VFS */\n#define SQLITE_MUTEX_STATIC_VFS3     13  /* For use by application VFS */\n\n/*\n** CAPI3REF: Retrieve the mutex for a database connection\n** METHOD: sqlite3\n**\n** ^This interface returns a pointer the [sqlite3_mutex] object that \n** serializes access to the [database connection] given in the argument\n** when the [threading mode] is Serialized.\n** ^If the [threading mode] is Single-thread or Multi-thread then this\n** routine returns a NULL pointer.\n*/\nSQLITE_API sqlite3_mutex *sqlite3_db_mutex(sqlite3*);\n\n/*\n** CAPI3REF: Low-Level Control Of Database Files\n** METHOD: sqlite3\n**\n** ^The [sqlite3_file_control()] interface makes a direct call to the\n** xFileControl method for the [sqlite3_io_methods] object associated\n** with a particular database identified by the second argument. ^The\n** name of the database is \"main\" for the main database or \"temp\" for the\n** TEMP database, or the name that appears after the AS keyword for\n** databases that are added using the [ATTACH] SQL command.\n** ^A NULL pointer can be used in place of \"main\" to refer to the\n** main database file.\n** ^The third and fourth parameters to this routine\n** are passed directly through to the second and third parameters of\n** the xFileControl method.  ^The return value of the xFileControl\n** method becomes the return value of this routine.\n**\n** ^The [SQLITE_FCNTL_FILE_POINTER] value for the op parameter causes\n** a pointer to the underlying [sqlite3_file] object to be written into\n** the space pointed to by the 4th parameter.  ^The [SQLITE_FCNTL_FILE_POINTER]\n** case is a short-circuit path which does not actually invoke the\n** underlying sqlite3_io_methods.xFileControl method.\n**\n** ^If the second parameter (zDbName) does not match the name of any\n** open database file, then SQLITE_ERROR is returned.  ^This error\n** code is not remembered and will not be recalled by [sqlite3_errcode()]\n** or [sqlite3_errmsg()].  The underlying xFileControl method might\n** also return SQLITE_ERROR.  There is no way to distinguish between\n** an incorrect zDbName and an SQLITE_ERROR return from the underlying\n** xFileControl method.\n**\n** See also: [file control opcodes]\n*/\nSQLITE_API int sqlite3_file_control(sqlite3*, const char *zDbName, int op, void*);\n\n/*\n** CAPI3REF: Testing Interface\n**\n** ^The sqlite3_test_control() interface is used to read out internal\n** state of SQLite and to inject faults into SQLite for testing\n** purposes.  ^The first parameter is an operation code that determines\n** the number, meaning, and operation of all subsequent parameters.\n**\n** This interface is not for use by applications.  It exists solely\n** for verifying the correct operation of the SQLite library.  Depending\n** on how the SQLite library is compiled, this interface might not exist.\n**\n** The details of the operation codes, their meanings, the parameters\n** they take, and what they do are all subject to change without notice.\n** Unlike most of the SQLite API, this function is not guaranteed to\n** operate consistently from one release to the next.\n*/\nSQLITE_API int sqlite3_test_control(int op, ...);\n\n/*\n** CAPI3REF: Testing Interface Operation Codes\n**\n** These constants are the valid operation code parameters used\n** as the first argument to [sqlite3_test_control()].\n**\n** These parameters and their meanings are subject to change\n** without notice.  These values are for testing purposes only.\n** Applications should not use any of these parameters or the\n** [sqlite3_test_control()] interface.\n*/\n#define SQLITE_TESTCTRL_FIRST                    5\n#define SQLITE_TESTCTRL_PRNG_SAVE                5\n#define SQLITE_TESTCTRL_PRNG_RESTORE             6\n#define SQLITE_TESTCTRL_PRNG_RESET               7\n#define SQLITE_TESTCTRL_BITVEC_TEST              8\n#define SQLITE_TESTCTRL_FAULT_INSTALL            9\n#define SQLITE_TESTCTRL_BENIGN_MALLOC_HOOKS     10\n#define SQLITE_TESTCTRL_PENDING_BYTE            11\n#define SQLITE_TESTCTRL_ASSERT                  12\n#define SQLITE_TESTCTRL_ALWAYS                  13\n#define SQLITE_TESTCTRL_RESERVE                 14\n#define SQLITE_TESTCTRL_OPTIMIZATIONS           15\n#define SQLITE_TESTCTRL_ISKEYWORD               16\n#define SQLITE_TESTCTRL_SCRATCHMALLOC           17  /* NOT USED */\n#define SQLITE_TESTCTRL_LOCALTIME_FAULT         18\n#define SQLITE_TESTCTRL_EXPLAIN_STMT            19  /* NOT USED */\n#define SQLITE_TESTCTRL_ONCE_RESET_THRESHOLD    19\n#define SQLITE_TESTCTRL_NEVER_CORRUPT           20\n#define SQLITE_TESTCTRL_VDBE_COVERAGE           21\n#define SQLITE_TESTCTRL_BYTEORDER               22\n#define SQLITE_TESTCTRL_ISINIT                  23\n#define SQLITE_TESTCTRL_SORTER_MMAP             24\n#define SQLITE_TESTCTRL_IMPOSTER                25\n#define SQLITE_TESTCTRL_PARSER_COVERAGE         26\n#define SQLITE_TESTCTRL_LAST                    26  /* Largest TESTCTRL */\n\n/*\n** CAPI3REF: SQLite Runtime Status\n**\n** ^These interfaces are used to retrieve runtime status information\n** about the performance of SQLite, and optionally to reset various\n** highwater marks.  ^The first argument is an integer code for\n** the specific parameter to measure.  ^(Recognized integer codes\n** are of the form [status parameters | SQLITE_STATUS_...].)^\n** ^The current value of the parameter is returned into *pCurrent.\n** ^The highest recorded value is returned in *pHighwater.  ^If the\n** resetFlag is true, then the highest record value is reset after\n** *pHighwater is written.  ^(Some parameters do not record the highest\n** value.  For those parameters\n** nothing is written into *pHighwater and the resetFlag is ignored.)^\n** ^(Other parameters record only the highwater mark and not the current\n** value.  For these latter parameters nothing is written into *pCurrent.)^\n**\n** ^The sqlite3_status() and sqlite3_status64() routines return\n** SQLITE_OK on success and a non-zero [error code] on failure.\n**\n** If either the current value or the highwater mark is too large to\n** be represented by a 32-bit integer, then the values returned by\n** sqlite3_status() are undefined.\n**\n** See also: [sqlite3_db_status()]\n*/\nSQLITE_API int sqlite3_status(int op, int *pCurrent, int *pHighwater, int resetFlag);\nSQLITE_API int sqlite3_status64(\n  int op,\n  sqlite3_int64 *pCurrent,\n  sqlite3_int64 *pHighwater,\n  int resetFlag\n);\n\n\n/*\n** CAPI3REF: Status Parameters\n** KEYWORDS: {status parameters}\n**\n** These integer constants designate various run-time status parameters\n** that can be returned by [sqlite3_status()].\n**\n** <dl>\n** [[SQLITE_STATUS_MEMORY_USED]] ^(<dt>SQLITE_STATUS_MEMORY_USED</dt>\n** <dd>This parameter is the current amount of memory checked out\n** using [sqlite3_malloc()], either directly or indirectly.  The\n** figure includes calls made to [sqlite3_malloc()] by the application\n** and internal memory usage by the SQLite library.  Auxiliary page-cache\n** memory controlled by [SQLITE_CONFIG_PAGECACHE] is not included in\n** this parameter.  The amount returned is the sum of the allocation\n** sizes as reported by the xSize method in [sqlite3_mem_methods].</dd>)^\n**\n** [[SQLITE_STATUS_MALLOC_SIZE]] ^(<dt>SQLITE_STATUS_MALLOC_SIZE</dt>\n** <dd>This parameter records the largest memory allocation request\n** handed to [sqlite3_malloc()] or [sqlite3_realloc()] (or their\n** internal equivalents).  Only the value returned in the\n** *pHighwater parameter to [sqlite3_status()] is of interest.  \n** The value written into the *pCurrent parameter is undefined.</dd>)^\n**\n** [[SQLITE_STATUS_MALLOC_COUNT]] ^(<dt>SQLITE_STATUS_MALLOC_COUNT</dt>\n** <dd>This parameter records the number of separate memory allocations\n** currently checked out.</dd>)^\n**\n** [[SQLITE_STATUS_PAGECACHE_USED]] ^(<dt>SQLITE_STATUS_PAGECACHE_USED</dt>\n** <dd>This parameter returns the number of pages used out of the\n** [pagecache memory allocator] that was configured using \n** [SQLITE_CONFIG_PAGECACHE].  The\n** value returned is in pages, not in bytes.</dd>)^\n**\n** [[SQLITE_STATUS_PAGECACHE_OVERFLOW]] \n** ^(<dt>SQLITE_STATUS_PAGECACHE_OVERFLOW</dt>\n** <dd>This parameter returns the number of bytes of page cache\n** allocation which could not be satisfied by the [SQLITE_CONFIG_PAGECACHE]\n** buffer and where forced to overflow to [sqlite3_malloc()].  The\n** returned value includes allocations that overflowed because they\n** where too large (they were larger than the \"sz\" parameter to\n** [SQLITE_CONFIG_PAGECACHE]) and allocations that overflowed because\n** no space was left in the page cache.</dd>)^\n**\n** [[SQLITE_STATUS_PAGECACHE_SIZE]] ^(<dt>SQLITE_STATUS_PAGECACHE_SIZE</dt>\n** <dd>This parameter records the largest memory allocation request\n** handed to [pagecache memory allocator].  Only the value returned in the\n** *pHighwater parameter to [sqlite3_status()] is of interest.  \n** The value written into the *pCurrent parameter is undefined.</dd>)^\n**\n** [[SQLITE_STATUS_SCRATCH_USED]] <dt>SQLITE_STATUS_SCRATCH_USED</dt>\n** <dd>No longer used.</dd>\n**\n** [[SQLITE_STATUS_SCRATCH_OVERFLOW]] ^(<dt>SQLITE_STATUS_SCRATCH_OVERFLOW</dt>\n** <dd>No longer used.</dd>\n**\n** [[SQLITE_STATUS_SCRATCH_SIZE]] <dt>SQLITE_STATUS_SCRATCH_SIZE</dt>\n** <dd>No longer used.</dd>\n**\n** [[SQLITE_STATUS_PARSER_STACK]] ^(<dt>SQLITE_STATUS_PARSER_STACK</dt>\n** <dd>The *pHighwater parameter records the deepest parser stack. \n** The *pCurrent value is undefined.  The *pHighwater value is only\n** meaningful if SQLite is compiled with [YYTRACKMAXSTACKDEPTH].</dd>)^\n** </dl>\n**\n** New status parameters may be added from time to time.\n*/\n#define SQLITE_STATUS_MEMORY_USED          0\n#define SQLITE_STATUS_PAGECACHE_USED       1\n#define SQLITE_STATUS_PAGECACHE_OVERFLOW   2\n#define SQLITE_STATUS_SCRATCH_USED         3  /* NOT USED */\n#define SQLITE_STATUS_SCRATCH_OVERFLOW     4  /* NOT USED */\n#define SQLITE_STATUS_MALLOC_SIZE          5\n#define SQLITE_STATUS_PARSER_STACK         6\n#define SQLITE_STATUS_PAGECACHE_SIZE       7\n#define SQLITE_STATUS_SCRATCH_SIZE         8  /* NOT USED */\n#define SQLITE_STATUS_MALLOC_COUNT         9\n\n/*\n** CAPI3REF: Database Connection Status\n** METHOD: sqlite3\n**\n** ^This interface is used to retrieve runtime status information \n** about a single [database connection].  ^The first argument is the\n** database connection object to be interrogated.  ^The second argument\n** is an integer constant, taken from the set of\n** [SQLITE_DBSTATUS options], that\n** determines the parameter to interrogate.  The set of \n** [SQLITE_DBSTATUS options] is likely\n** to grow in future releases of SQLite.\n**\n** ^The current value of the requested parameter is written into *pCur\n** and the highest instantaneous value is written into *pHiwtr.  ^If\n** the resetFlg is true, then the highest instantaneous value is\n** reset back down to the current value.\n**\n** ^The sqlite3_db_status() routine returns SQLITE_OK on success and a\n** non-zero [error code] on failure.\n**\n** See also: [sqlite3_status()] and [sqlite3_stmt_status()].\n*/\nSQLITE_API int sqlite3_db_status(sqlite3*, int op, int *pCur, int *pHiwtr, int resetFlg);\n\n/*\n** CAPI3REF: Status Parameters for database connections\n** KEYWORDS: {SQLITE_DBSTATUS options}\n**\n** These constants are the available integer \"verbs\" that can be passed as\n** the second argument to the [sqlite3_db_status()] interface.\n**\n** New verbs may be added in future releases of SQLite. Existing verbs\n** might be discontinued. Applications should check the return code from\n** [sqlite3_db_status()] to make sure that the call worked.\n** The [sqlite3_db_status()] interface will return a non-zero error code\n** if a discontinued or unsupported verb is invoked.\n**\n** <dl>\n** [[SQLITE_DBSTATUS_LOOKASIDE_USED]] ^(<dt>SQLITE_DBSTATUS_LOOKASIDE_USED</dt>\n** <dd>This parameter returns the number of lookaside memory slots currently\n** checked out.</dd>)^\n**\n** [[SQLITE_DBSTATUS_LOOKASIDE_HIT]] ^(<dt>SQLITE_DBSTATUS_LOOKASIDE_HIT</dt>\n** <dd>This parameter returns the number malloc attempts that were \n** satisfied using lookaside memory. Only the high-water value is meaningful;\n** the current value is always zero.)^\n**\n** [[SQLITE_DBSTATUS_LOOKASIDE_MISS_SIZE]]\n** ^(<dt>SQLITE_DBSTATUS_LOOKASIDE_MISS_SIZE</dt>\n** <dd>This parameter returns the number malloc attempts that might have\n** been satisfied using lookaside memory but failed due to the amount of\n** memory requested being larger than the lookaside slot size.\n** Only the high-water value is meaningful;\n** the current value is always zero.)^\n**\n** [[SQLITE_DBSTATUS_LOOKASIDE_MISS_FULL]]\n** ^(<dt>SQLITE_DBSTATUS_LOOKASIDE_MISS_FULL</dt>\n** <dd>This parameter returns the number malloc attempts that might have\n** been satisfied using lookaside memory but failed due to all lookaside\n** memory already being in use.\n** Only the high-water value is meaningful;\n** the current value is always zero.)^\n**\n** [[SQLITE_DBSTATUS_CACHE_USED]] ^(<dt>SQLITE_DBSTATUS_CACHE_USED</dt>\n** <dd>This parameter returns the approximate number of bytes of heap\n** memory used by all pager caches associated with the database connection.)^\n** ^The highwater mark associated with SQLITE_DBSTATUS_CACHE_USED is always 0.\n**\n** [[SQLITE_DBSTATUS_CACHE_USED_SHARED]] \n** ^(<dt>SQLITE_DBSTATUS_CACHE_USED_SHARED</dt>\n** <dd>This parameter is similar to DBSTATUS_CACHE_USED, except that if a\n** pager cache is shared between two or more connections the bytes of heap\n** memory used by that pager cache is divided evenly between the attached\n** connections.)^  In other words, if none of the pager caches associated\n** with the database connection are shared, this request returns the same\n** value as DBSTATUS_CACHE_USED. Or, if one or more or the pager caches are\n** shared, the value returned by this call will be smaller than that returned\n** by DBSTATUS_CACHE_USED. ^The highwater mark associated with\n** SQLITE_DBSTATUS_CACHE_USED_SHARED is always 0.\n**\n** [[SQLITE_DBSTATUS_SCHEMA_USED]] ^(<dt>SQLITE_DBSTATUS_SCHEMA_USED</dt>\n** <dd>This parameter returns the approximate number of bytes of heap\n** memory used to store the schema for all databases associated\n** with the connection - main, temp, and any [ATTACH]-ed databases.)^ \n** ^The full amount of memory used by the schemas is reported, even if the\n** schema memory is shared with other database connections due to\n** [shared cache mode] being enabled.\n** ^The highwater mark associated with SQLITE_DBSTATUS_SCHEMA_USED is always 0.\n**\n** [[SQLITE_DBSTATUS_STMT_USED]] ^(<dt>SQLITE_DBSTATUS_STMT_USED</dt>\n** <dd>This parameter returns the approximate number of bytes of heap\n** and lookaside memory used by all prepared statements associated with\n** the database connection.)^\n** ^The highwater mark associated with SQLITE_DBSTATUS_STMT_USED is always 0.\n** </dd>\n**\n** [[SQLITE_DBSTATUS_CACHE_HIT]] ^(<dt>SQLITE_DBSTATUS_CACHE_HIT</dt>\n** <dd>This parameter returns the number of pager cache hits that have\n** occurred.)^ ^The highwater mark associated with SQLITE_DBSTATUS_CACHE_HIT \n** is always 0.\n** </dd>\n**\n** [[SQLITE_DBSTATUS_CACHE_MISS]] ^(<dt>SQLITE_DBSTATUS_CACHE_MISS</dt>\n** <dd>This parameter returns the number of pager cache misses that have\n** occurred.)^ ^The highwater mark associated with SQLITE_DBSTATUS_CACHE_MISS \n** is always 0.\n** </dd>\n**\n** [[SQLITE_DBSTATUS_CACHE_WRITE]] ^(<dt>SQLITE_DBSTATUS_CACHE_WRITE</dt>\n** <dd>This parameter returns the number of dirty cache entries that have\n** been written to disk. Specifically, the number of pages written to the\n** wal file in wal mode databases, or the number of pages written to the\n** database file in rollback mode databases. Any pages written as part of\n** transaction rollback or database recovery operations are not included.\n** If an IO or other error occurs while writing a page to disk, the effect\n** on subsequent SQLITE_DBSTATUS_CACHE_WRITE requests is undefined.)^ ^The\n** highwater mark associated with SQLITE_DBSTATUS_CACHE_WRITE is always 0.\n** </dd>\n**\n** [[SQLITE_DBSTATUS_DEFERRED_FKS]] ^(<dt>SQLITE_DBSTATUS_DEFERRED_FKS</dt>\n** <dd>This parameter returns zero for the current value if and only if\n** all foreign key constraints (deferred or immediate) have been\n** resolved.)^  ^The highwater mark is always 0.\n** </dd>\n** </dl>\n*/\n#define SQLITE_DBSTATUS_LOOKASIDE_USED       0\n#define SQLITE_DBSTATUS_CACHE_USED           1\n#define SQLITE_DBSTATUS_SCHEMA_USED          2\n#define SQLITE_DBSTATUS_STMT_USED            3\n#define SQLITE_DBSTATUS_LOOKASIDE_HIT        4\n#define SQLITE_DBSTATUS_LOOKASIDE_MISS_SIZE  5\n#define SQLITE_DBSTATUS_LOOKASIDE_MISS_FULL  6\n#define SQLITE_DBSTATUS_CACHE_HIT            7\n#define SQLITE_DBSTATUS_CACHE_MISS           8\n#define SQLITE_DBSTATUS_CACHE_WRITE          9\n#define SQLITE_DBSTATUS_DEFERRED_FKS        10\n#define SQLITE_DBSTATUS_CACHE_USED_SHARED   11\n#define SQLITE_DBSTATUS_MAX                 11   /* Largest defined DBSTATUS */\n\n\n/*\n** CAPI3REF: Prepared Statement Status\n** METHOD: sqlite3_stmt\n**\n** ^(Each prepared statement maintains various\n** [SQLITE_STMTSTATUS counters] that measure the number\n** of times it has performed specific operations.)^  These counters can\n** be used to monitor the performance characteristics of the prepared\n** statements.  For example, if the number of table steps greatly exceeds\n** the number of table searches or result rows, that would tend to indicate\n** that the prepared statement is using a full table scan rather than\n** an index.  \n**\n** ^(This interface is used to retrieve and reset counter values from\n** a [prepared statement].  The first argument is the prepared statement\n** object to be interrogated.  The second argument\n** is an integer code for a specific [SQLITE_STMTSTATUS counter]\n** to be interrogated.)^\n** ^The current value of the requested counter is returned.\n** ^If the resetFlg is true, then the counter is reset to zero after this\n** interface call returns.\n**\n** See also: [sqlite3_status()] and [sqlite3_db_status()].\n*/\nSQLITE_API int sqlite3_stmt_status(sqlite3_stmt*, int op,int resetFlg);\n\n/*\n** CAPI3REF: Status Parameters for prepared statements\n** KEYWORDS: {SQLITE_STMTSTATUS counter} {SQLITE_STMTSTATUS counters}\n**\n** These preprocessor macros define integer codes that name counter\n** values associated with the [sqlite3_stmt_status()] interface.\n** The meanings of the various counters are as follows:\n**\n** <dl>\n** [[SQLITE_STMTSTATUS_FULLSCAN_STEP]] <dt>SQLITE_STMTSTATUS_FULLSCAN_STEP</dt>\n** <dd>^This is the number of times that SQLite has stepped forward in\n** a table as part of a full table scan.  Large numbers for this counter\n** may indicate opportunities for performance improvement through \n** careful use of indices.</dd>\n**\n** [[SQLITE_STMTSTATUS_SORT]] <dt>SQLITE_STMTSTATUS_SORT</dt>\n** <dd>^This is the number of sort operations that have occurred.\n** A non-zero value in this counter may indicate an opportunity to\n** improvement performance through careful use of indices.</dd>\n**\n** [[SQLITE_STMTSTATUS_AUTOINDEX]] <dt>SQLITE_STMTSTATUS_AUTOINDEX</dt>\n** <dd>^This is the number of rows inserted into transient indices that\n** were created automatically in order to help joins run faster.\n** A non-zero value in this counter may indicate an opportunity to\n** improvement performance by adding permanent indices that do not\n** need to be reinitialized each time the statement is run.</dd>\n**\n** [[SQLITE_STMTSTATUS_VM_STEP]] <dt>SQLITE_STMTSTATUS_VM_STEP</dt>\n** <dd>^This is the number of virtual machine operations executed\n** by the prepared statement if that number is less than or equal\n** to 2147483647.  The number of virtual machine operations can be \n** used as a proxy for the total work done by the prepared statement.\n** If the number of virtual machine operations exceeds 2147483647\n** then the value returned by this statement status code is undefined.\n**\n** [[SQLITE_STMTSTATUS_REPREPARE]] <dt>SQLITE_STMTSTATUS_REPREPARE</dt>\n** <dd>^This is the number of times that the prepare statement has been\n** automatically regenerated due to schema changes or change to \n** [bound parameters] that might affect the query plan.\n**\n** [[SQLITE_STMTSTATUS_RUN]] <dt>SQLITE_STMTSTATUS_RUN</dt>\n** <dd>^This is the number of times that the prepared statement has\n** been run.  A single \"run\" for the purposes of this counter is one\n** or more calls to [sqlite3_step()] followed by a call to [sqlite3_reset()].\n** The counter is incremented on the first [sqlite3_step()] call of each\n** cycle.\n**\n** [[SQLITE_STMTSTATUS_MEMUSED]] <dt>SQLITE_STMTSTATUS_MEMUSED</dt>\n** <dd>^This is the approximate number of bytes of heap memory\n** used to store the prepared statement.  ^This value is not actually\n** a counter, and so the resetFlg parameter to sqlite3_stmt_status()\n** is ignored when the opcode is SQLITE_STMTSTATUS_MEMUSED.\n** </dd>\n** </dl>\n*/\n#define SQLITE_STMTSTATUS_FULLSCAN_STEP     1\n#define SQLITE_STMTSTATUS_SORT              2\n#define SQLITE_STMTSTATUS_AUTOINDEX         3\n#define SQLITE_STMTSTATUS_VM_STEP           4\n#define SQLITE_STMTSTATUS_REPREPARE         5\n#define SQLITE_STMTSTATUS_RUN               6\n#define SQLITE_STMTSTATUS_MEMUSED           99\n\n/*\n** CAPI3REF: Custom Page Cache Object\n**\n** The sqlite3_pcache type is opaque.  It is implemented by\n** the pluggable module.  The SQLite core has no knowledge of\n** its size or internal structure and never deals with the\n** sqlite3_pcache object except by holding and passing pointers\n** to the object.\n**\n** See [sqlite3_pcache_methods2] for additional information.\n*/\ntypedef struct sqlite3_pcache sqlite3_pcache;\n\n/*\n** CAPI3REF: Custom Page Cache Object\n**\n** The sqlite3_pcache_page object represents a single page in the\n** page cache.  The page cache will allocate instances of this\n** object.  Various methods of the page cache use pointers to instances\n** of this object as parameters or as their return value.\n**\n** See [sqlite3_pcache_methods2] for additional information.\n*/\ntypedef struct sqlite3_pcache_page sqlite3_pcache_page;\nstruct sqlite3_pcache_page {\n  void *pBuf;        /* The content of the page */\n  void *pExtra;      /* Extra information associated with the page */\n};\n\n/*\n** CAPI3REF: Application Defined Page Cache.\n** KEYWORDS: {page cache}\n**\n** ^(The [sqlite3_config]([SQLITE_CONFIG_PCACHE2], ...) interface can\n** register an alternative page cache implementation by passing in an \n** instance of the sqlite3_pcache_methods2 structure.)^\n** In many applications, most of the heap memory allocated by \n** SQLite is used for the page cache.\n** By implementing a \n** custom page cache using this API, an application can better control\n** the amount of memory consumed by SQLite, the way in which \n** that memory is allocated and released, and the policies used to \n** determine exactly which parts of a database file are cached and for \n** how long.\n**\n** The alternative page cache mechanism is an\n** extreme measure that is only needed by the most demanding applications.\n** The built-in page cache is recommended for most uses.\n**\n** ^(The contents of the sqlite3_pcache_methods2 structure are copied to an\n** internal buffer by SQLite within the call to [sqlite3_config].  Hence\n** the application may discard the parameter after the call to\n** [sqlite3_config()] returns.)^\n**\n** [[the xInit() page cache method]]\n** ^(The xInit() method is called once for each effective \n** call to [sqlite3_initialize()])^\n** (usually only once during the lifetime of the process). ^(The xInit()\n** method is passed a copy of the sqlite3_pcache_methods2.pArg value.)^\n** The intent of the xInit() method is to set up global data structures \n** required by the custom page cache implementation. \n** ^(If the xInit() method is NULL, then the \n** built-in default page cache is used instead of the application defined\n** page cache.)^\n**\n** [[the xShutdown() page cache method]]\n** ^The xShutdown() method is called by [sqlite3_shutdown()].\n** It can be used to clean up \n** any outstanding resources before process shutdown, if required.\n** ^The xShutdown() method may be NULL.\n**\n** ^SQLite automatically serializes calls to the xInit method,\n** so the xInit method need not be threadsafe.  ^The\n** xShutdown method is only called from [sqlite3_shutdown()] so it does\n** not need to be threadsafe either.  All other methods must be threadsafe\n** in multithreaded applications.\n**\n** ^SQLite will never invoke xInit() more than once without an intervening\n** call to xShutdown().\n**\n** [[the xCreate() page cache methods]]\n** ^SQLite invokes the xCreate() method to construct a new cache instance.\n** SQLite will typically create one cache instance for each open database file,\n** though this is not guaranteed. ^The\n** first parameter, szPage, is the size in bytes of the pages that must\n** be allocated by the cache.  ^szPage will always a power of two.  ^The\n** second parameter szExtra is a number of bytes of extra storage \n** associated with each page cache entry.  ^The szExtra parameter will\n** a number less than 250.  SQLite will use the\n** extra szExtra bytes on each page to store metadata about the underlying\n** database page on disk.  The value passed into szExtra depends\n** on the SQLite version, the target platform, and how SQLite was compiled.\n** ^The third argument to xCreate(), bPurgeable, is true if the cache being\n** created will be used to cache database pages of a file stored on disk, or\n** false if it is used for an in-memory database. The cache implementation\n** does not have to do anything special based with the value of bPurgeable;\n** it is purely advisory.  ^On a cache where bPurgeable is false, SQLite will\n** never invoke xUnpin() except to deliberately delete a page.\n** ^In other words, calls to xUnpin() on a cache with bPurgeable set to\n** false will always have the \"discard\" flag set to true.  \n** ^Hence, a cache created with bPurgeable false will\n** never contain any unpinned pages.\n**\n** [[the xCachesize() page cache method]]\n** ^(The xCachesize() method may be called at any time by SQLite to set the\n** suggested maximum cache-size (number of pages stored by) the cache\n** instance passed as the first argument. This is the value configured using\n** the SQLite \"[PRAGMA cache_size]\" command.)^  As with the bPurgeable\n** parameter, the implementation is not required to do anything with this\n** value; it is advisory only.\n**\n** [[the xPagecount() page cache methods]]\n** The xPagecount() method must return the number of pages currently\n** stored in the cache, both pinned and unpinned.\n** \n** [[the xFetch() page cache methods]]\n** The xFetch() method locates a page in the cache and returns a pointer to \n** an sqlite3_pcache_page object associated with that page, or a NULL pointer.\n** The pBuf element of the returned sqlite3_pcache_page object will be a\n** pointer to a buffer of szPage bytes used to store the content of a \n** single database page.  The pExtra element of sqlite3_pcache_page will be\n** a pointer to the szExtra bytes of extra storage that SQLite has requested\n** for each entry in the page cache.\n**\n** The page to be fetched is determined by the key. ^The minimum key value\n** is 1.  After it has been retrieved using xFetch, the page is considered\n** to be \"pinned\".\n**\n** If the requested page is already in the page cache, then the page cache\n** implementation must return a pointer to the page buffer with its content\n** intact.  If the requested page is not already in the cache, then the\n** cache implementation should use the value of the createFlag\n** parameter to help it determined what action to take:\n**\n** <table border=1 width=85% align=center>\n** <tr><th> createFlag <th> Behavior when page is not already in cache\n** <tr><td> 0 <td> Do not allocate a new page.  Return NULL.\n** <tr><td> 1 <td> Allocate a new page if it easy and convenient to do so.\n**                 Otherwise return NULL.\n** <tr><td> 2 <td> Make every effort to allocate a new page.  Only return\n**                 NULL if allocating a new page is effectively impossible.\n** </table>\n**\n** ^(SQLite will normally invoke xFetch() with a createFlag of 0 or 1.  SQLite\n** will only use a createFlag of 2 after a prior call with a createFlag of 1\n** failed.)^  In between the to xFetch() calls, SQLite may\n** attempt to unpin one or more cache pages by spilling the content of\n** pinned pages to disk and synching the operating system disk cache.\n**\n** [[the xUnpin() page cache method]]\n** ^xUnpin() is called by SQLite with a pointer to a currently pinned page\n** as its second argument.  If the third parameter, discard, is non-zero,\n** then the page must be evicted from the cache.\n** ^If the discard parameter is\n** zero, then the page may be discarded or retained at the discretion of\n** page cache implementation. ^The page cache implementation\n** may choose to evict unpinned pages at any time.\n**\n** The cache must not perform any reference counting. A single \n** call to xUnpin() unpins the page regardless of the number of prior calls \n** to xFetch().\n**\n** [[the xRekey() page cache methods]]\n** The xRekey() method is used to change the key value associated with the\n** page passed as the second argument. If the cache\n** previously contains an entry associated with newKey, it must be\n** discarded. ^Any prior cache entry associated with newKey is guaranteed not\n** to be pinned.\n**\n** When SQLite calls the xTruncate() method, the cache must discard all\n** existing cache entries with page numbers (keys) greater than or equal\n** to the value of the iLimit parameter passed to xTruncate(). If any\n** of these pages are pinned, they are implicitly unpinned, meaning that\n** they can be safely discarded.\n**\n** [[the xDestroy() page cache method]]\n** ^The xDestroy() method is used to delete a cache allocated by xCreate().\n** All resources associated with the specified cache should be freed. ^After\n** calling the xDestroy() method, SQLite considers the [sqlite3_pcache*]\n** handle invalid, and will not use it with any other sqlite3_pcache_methods2\n** functions.\n**\n** [[the xShrink() page cache method]]\n** ^SQLite invokes the xShrink() method when it wants the page cache to\n** free up as much of heap memory as possible.  The page cache implementation\n** is not obligated to free any memory, but well-behaved implementations should\n** do their best.\n*/\ntypedef struct sqlite3_pcache_methods2 sqlite3_pcache_methods2;\nstruct sqlite3_pcache_methods2 {\n  int iVersion;\n  void *pArg;\n  int (*xInit)(void*);\n  void (*xShutdown)(void*);\n  sqlite3_pcache *(*xCreate)(int szPage, int szExtra, int bPurgeable);\n  void (*xCachesize)(sqlite3_pcache*, int nCachesize);\n  int (*xPagecount)(sqlite3_pcache*);\n  sqlite3_pcache_page *(*xFetch)(sqlite3_pcache*, unsigned key, int createFlag);\n  void (*xUnpin)(sqlite3_pcache*, sqlite3_pcache_page*, int discard);\n  void (*xRekey)(sqlite3_pcache*, sqlite3_pcache_page*, \n      unsigned oldKey, unsigned newKey);\n  void (*xTruncate)(sqlite3_pcache*, unsigned iLimit);\n  void (*xDestroy)(sqlite3_pcache*);\n  void (*xShrink)(sqlite3_pcache*);\n};\n\n/*\n** This is the obsolete pcache_methods object that has now been replaced\n** by sqlite3_pcache_methods2.  This object is not used by SQLite.  It is\n** retained in the header file for backwards compatibility only.\n*/\ntypedef struct sqlite3_pcache_methods sqlite3_pcache_methods;\nstruct sqlite3_pcache_methods {\n  void *pArg;\n  int (*xInit)(void*);\n  void (*xShutdown)(void*);\n  sqlite3_pcache *(*xCreate)(int szPage, int bPurgeable);\n  void (*xCachesize)(sqlite3_pcache*, int nCachesize);\n  int (*xPagecount)(sqlite3_pcache*);\n  void *(*xFetch)(sqlite3_pcache*, unsigned key, int createFlag);\n  void (*xUnpin)(sqlite3_pcache*, void*, int discard);\n  void (*xRekey)(sqlite3_pcache*, void*, unsigned oldKey, unsigned newKey);\n  void (*xTruncate)(sqlite3_pcache*, unsigned iLimit);\n  void (*xDestroy)(sqlite3_pcache*);\n};\n\n\n/*\n** CAPI3REF: Online Backup Object\n**\n** The sqlite3_backup object records state information about an ongoing\n** online backup operation.  ^The sqlite3_backup object is created by\n** a call to [sqlite3_backup_init()] and is destroyed by a call to\n** [sqlite3_backup_finish()].\n**\n** See Also: [Using the SQLite Online Backup API]\n*/\ntypedef struct sqlite3_backup sqlite3_backup;\n\n/*\n** CAPI3REF: Online Backup API.\n**\n** The backup API copies the content of one database into another.\n** It is useful either for creating backups of databases or\n** for copying in-memory databases to or from persistent files. \n**\n** See Also: [Using the SQLite Online Backup API]\n**\n** ^SQLite holds a write transaction open on the destination database file\n** for the duration of the backup operation.\n** ^The source database is read-locked only while it is being read;\n** it is not locked continuously for the entire backup operation.\n** ^Thus, the backup may be performed on a live source database without\n** preventing other database connections from\n** reading or writing to the source database while the backup is underway.\n** \n** ^(To perform a backup operation: \n**   <ol>\n**     <li><b>sqlite3_backup_init()</b> is called once to initialize the\n**         backup, \n**     <li><b>sqlite3_backup_step()</b> is called one or more times to transfer \n**         the data between the two databases, and finally\n**     <li><b>sqlite3_backup_finish()</b> is called to release all resources \n**         associated with the backup operation. \n**   </ol>)^\n** There should be exactly one call to sqlite3_backup_finish() for each\n** successful call to sqlite3_backup_init().\n**\n** [[sqlite3_backup_init()]] <b>sqlite3_backup_init()</b>\n**\n** ^The D and N arguments to sqlite3_backup_init(D,N,S,M) are the \n** [database connection] associated with the destination database \n** and the database name, respectively.\n** ^The database name is \"main\" for the main database, \"temp\" for the\n** temporary database, or the name specified after the AS keyword in\n** an [ATTACH] statement for an attached database.\n** ^The S and M arguments passed to \n** sqlite3_backup_init(D,N,S,M) identify the [database connection]\n** and database name of the source database, respectively.\n** ^The source and destination [database connections] (parameters S and D)\n** must be different or else sqlite3_backup_init(D,N,S,M) will fail with\n** an error.\n**\n** ^A call to sqlite3_backup_init() will fail, returning NULL, if \n** there is already a read or read-write transaction open on the \n** destination database.\n**\n** ^If an error occurs within sqlite3_backup_init(D,N,S,M), then NULL is\n** returned and an error code and error message are stored in the\n** destination [database connection] D.\n** ^The error code and message for the failed call to sqlite3_backup_init()\n** can be retrieved using the [sqlite3_errcode()], [sqlite3_errmsg()], and/or\n** [sqlite3_errmsg16()] functions.\n** ^A successful call to sqlite3_backup_init() returns a pointer to an\n** [sqlite3_backup] object.\n** ^The [sqlite3_backup] object may be used with the sqlite3_backup_step() and\n** sqlite3_backup_finish() functions to perform the specified backup \n** operation.\n**\n** [[sqlite3_backup_step()]] <b>sqlite3_backup_step()</b>\n**\n** ^Function sqlite3_backup_step(B,N) will copy up to N pages between \n** the source and destination databases specified by [sqlite3_backup] object B.\n** ^If N is negative, all remaining source pages are copied. \n** ^If sqlite3_backup_step(B,N) successfully copies N pages and there\n** are still more pages to be copied, then the function returns [SQLITE_OK].\n** ^If sqlite3_backup_step(B,N) successfully finishes copying all pages\n** from source to destination, then it returns [SQLITE_DONE].\n** ^If an error occurs while running sqlite3_backup_step(B,N),\n** then an [error code] is returned. ^As well as [SQLITE_OK] and\n** [SQLITE_DONE], a call to sqlite3_backup_step() may return [SQLITE_READONLY],\n** [SQLITE_NOMEM], [SQLITE_BUSY], [SQLITE_LOCKED], or an\n** [SQLITE_IOERR_ACCESS | SQLITE_IOERR_XXX] extended error code.\n**\n** ^(The sqlite3_backup_step() might return [SQLITE_READONLY] if\n** <ol>\n** <li> the destination database was opened read-only, or\n** <li> the destination database is using write-ahead-log journaling\n** and the destination and source page sizes differ, or\n** <li> the destination database is an in-memory database and the\n** destination and source page sizes differ.\n** </ol>)^\n**\n** ^If sqlite3_backup_step() cannot obtain a required file-system lock, then\n** the [sqlite3_busy_handler | busy-handler function]\n** is invoked (if one is specified). ^If the \n** busy-handler returns non-zero before the lock is available, then \n** [SQLITE_BUSY] is returned to the caller. ^In this case the call to\n** sqlite3_backup_step() can be retried later. ^If the source\n** [database connection]\n** is being used to write to the source database when sqlite3_backup_step()\n** is called, then [SQLITE_LOCKED] is returned immediately. ^Again, in this\n** case the call to sqlite3_backup_step() can be retried later on. ^(If\n** [SQLITE_IOERR_ACCESS | SQLITE_IOERR_XXX], [SQLITE_NOMEM], or\n** [SQLITE_READONLY] is returned, then \n** there is no point in retrying the call to sqlite3_backup_step(). These \n** errors are considered fatal.)^  The application must accept \n** that the backup operation has failed and pass the backup operation handle \n** to the sqlite3_backup_finish() to release associated resources.\n**\n** ^The first call to sqlite3_backup_step() obtains an exclusive lock\n** on the destination file. ^The exclusive lock is not released until either \n** sqlite3_backup_finish() is called or the backup operation is complete \n** and sqlite3_backup_step() returns [SQLITE_DONE].  ^Every call to\n** sqlite3_backup_step() obtains a [shared lock] on the source database that\n** lasts for the duration of the sqlite3_backup_step() call.\n** ^Because the source database is not locked between calls to\n** sqlite3_backup_step(), the source database may be modified mid-way\n** through the backup process.  ^If the source database is modified by an\n** external process or via a database connection other than the one being\n** used by the backup operation, then the backup will be automatically\n** restarted by the next call to sqlite3_backup_step(). ^If the source \n** database is modified by the using the same database connection as is used\n** by the backup operation, then the backup database is automatically\n** updated at the same time.\n**\n** [[sqlite3_backup_finish()]] <b>sqlite3_backup_finish()</b>\n**\n** When sqlite3_backup_step() has returned [SQLITE_DONE], or when the \n** application wishes to abandon the backup operation, the application\n** should destroy the [sqlite3_backup] by passing it to sqlite3_backup_finish().\n** ^The sqlite3_backup_finish() interfaces releases all\n** resources associated with the [sqlite3_backup] object. \n** ^If sqlite3_backup_step() has not yet returned [SQLITE_DONE], then any\n** active write-transaction on the destination database is rolled back.\n** The [sqlite3_backup] object is invalid\n** and may not be used following a call to sqlite3_backup_finish().\n**\n** ^The value returned by sqlite3_backup_finish is [SQLITE_OK] if no\n** sqlite3_backup_step() errors occurred, regardless or whether or not\n** sqlite3_backup_step() completed.\n** ^If an out-of-memory condition or IO error occurred during any prior\n** sqlite3_backup_step() call on the same [sqlite3_backup] object, then\n** sqlite3_backup_finish() returns the corresponding [error code].\n**\n** ^A return of [SQLITE_BUSY] or [SQLITE_LOCKED] from sqlite3_backup_step()\n** is not a permanent error and does not affect the return value of\n** sqlite3_backup_finish().\n**\n** [[sqlite3_backup_remaining()]] [[sqlite3_backup_pagecount()]]\n** <b>sqlite3_backup_remaining() and sqlite3_backup_pagecount()</b>\n**\n** ^The sqlite3_backup_remaining() routine returns the number of pages still\n** to be backed up at the conclusion of the most recent sqlite3_backup_step().\n** ^The sqlite3_backup_pagecount() routine returns the total number of pages\n** in the source database at the conclusion of the most recent\n** sqlite3_backup_step().\n** ^(The values returned by these functions are only updated by\n** sqlite3_backup_step(). If the source database is modified in a way that\n** changes the size of the source database or the number of pages remaining,\n** those changes are not reflected in the output of sqlite3_backup_pagecount()\n** and sqlite3_backup_remaining() until after the next\n** sqlite3_backup_step().)^\n**\n** <b>Concurrent Usage of Database Handles</b>\n**\n** ^The source [database connection] may be used by the application for other\n** purposes while a backup operation is underway or being initialized.\n** ^If SQLite is compiled and configured to support threadsafe database\n** connections, then the source database connection may be used concurrently\n** from within other threads.\n**\n** However, the application must guarantee that the destination \n** [database connection] is not passed to any other API (by any thread) after \n** sqlite3_backup_init() is called and before the corresponding call to\n** sqlite3_backup_finish().  SQLite does not currently check to see\n** if the application incorrectly accesses the destination [database connection]\n** and so no error code is reported, but the operations may malfunction\n** nevertheless.  Use of the destination database connection while a\n** backup is in progress might also also cause a mutex deadlock.\n**\n** If running in [shared cache mode], the application must\n** guarantee that the shared cache used by the destination database\n** is not accessed while the backup is running. In practice this means\n** that the application must guarantee that the disk file being \n** backed up to is not accessed by any connection within the process,\n** not just the specific connection that was passed to sqlite3_backup_init().\n**\n** The [sqlite3_backup] object itself is partially threadsafe. Multiple \n** threads may safely make multiple concurrent calls to sqlite3_backup_step().\n** However, the sqlite3_backup_remaining() and sqlite3_backup_pagecount()\n** APIs are not strictly speaking threadsafe. If they are invoked at the\n** same time as another thread is invoking sqlite3_backup_step() it is\n** possible that they return invalid values.\n*/\nSQLITE_API sqlite3_backup *sqlite3_backup_init(\n  sqlite3 *pDest,                        /* Destination database handle */\n  const char *zDestName,                 /* Destination database name */\n  sqlite3 *pSource,                      /* Source database handle */\n  const char *zSourceName                /* Source database name */\n);\nSQLITE_API int sqlite3_backup_step(sqlite3_backup *p, int nPage);\nSQLITE_API int sqlite3_backup_finish(sqlite3_backup *p);\nSQLITE_API int sqlite3_backup_remaining(sqlite3_backup *p);\nSQLITE_API int sqlite3_backup_pagecount(sqlite3_backup *p);\n\n/*\n** CAPI3REF: Unlock Notification\n** METHOD: sqlite3\n**\n** ^When running in shared-cache mode, a database operation may fail with\n** an [SQLITE_LOCKED] error if the required locks on the shared-cache or\n** individual tables within the shared-cache cannot be obtained. See\n** [SQLite Shared-Cache Mode] for a description of shared-cache locking. \n** ^This API may be used to register a callback that SQLite will invoke \n** when the connection currently holding the required lock relinquishes it.\n** ^This API is only available if the library was compiled with the\n** [SQLITE_ENABLE_UNLOCK_NOTIFY] C-preprocessor symbol defined.\n**\n** See Also: [Using the SQLite Unlock Notification Feature].\n**\n** ^Shared-cache locks are released when a database connection concludes\n** its current transaction, either by committing it or rolling it back. \n**\n** ^When a connection (known as the blocked connection) fails to obtain a\n** shared-cache lock and SQLITE_LOCKED is returned to the caller, the\n** identity of the database connection (the blocking connection) that\n** has locked the required resource is stored internally. ^After an \n** application receives an SQLITE_LOCKED error, it may call the\n** sqlite3_unlock_notify() method with the blocked connection handle as \n** the first argument to register for a callback that will be invoked\n** when the blocking connections current transaction is concluded. ^The\n** callback is invoked from within the [sqlite3_step] or [sqlite3_close]\n** call that concludes the blocking connections transaction.\n**\n** ^(If sqlite3_unlock_notify() is called in a multi-threaded application,\n** there is a chance that the blocking connection will have already\n** concluded its transaction by the time sqlite3_unlock_notify() is invoked.\n** If this happens, then the specified callback is invoked immediately,\n** from within the call to sqlite3_unlock_notify().)^\n**\n** ^If the blocked connection is attempting to obtain a write-lock on a\n** shared-cache table, and more than one other connection currently holds\n** a read-lock on the same table, then SQLite arbitrarily selects one of \n** the other connections to use as the blocking connection.\n**\n** ^(There may be at most one unlock-notify callback registered by a \n** blocked connection. If sqlite3_unlock_notify() is called when the\n** blocked connection already has a registered unlock-notify callback,\n** then the new callback replaces the old.)^ ^If sqlite3_unlock_notify() is\n** called with a NULL pointer as its second argument, then any existing\n** unlock-notify callback is canceled. ^The blocked connections \n** unlock-notify callback may also be canceled by closing the blocked\n** connection using [sqlite3_close()].\n**\n** The unlock-notify callback is not reentrant. If an application invokes\n** any sqlite3_xxx API functions from within an unlock-notify callback, a\n** crash or deadlock may be the result.\n**\n** ^Unless deadlock is detected (see below), sqlite3_unlock_notify() always\n** returns SQLITE_OK.\n**\n** <b>Callback Invocation Details</b>\n**\n** When an unlock-notify callback is registered, the application provides a \n** single void* pointer that is passed to the callback when it is invoked.\n** However, the signature of the callback function allows SQLite to pass\n** it an array of void* context pointers. The first argument passed to\n** an unlock-notify callback is a pointer to an array of void* pointers,\n** and the second is the number of entries in the array.\n**\n** When a blocking connections transaction is concluded, there may be\n** more than one blocked connection that has registered for an unlock-notify\n** callback. ^If two or more such blocked connections have specified the\n** same callback function, then instead of invoking the callback function\n** multiple times, it is invoked once with the set of void* context pointers\n** specified by the blocked connections bundled together into an array.\n** This gives the application an opportunity to prioritize any actions \n** related to the set of unblocked database connections.\n**\n** <b>Deadlock Detection</b>\n**\n** Assuming that after registering for an unlock-notify callback a \n** database waits for the callback to be issued before taking any further\n** action (a reasonable assumption), then using this API may cause the\n** application to deadlock. For example, if connection X is waiting for\n** connection Y's transaction to be concluded, and similarly connection\n** Y is waiting on connection X's transaction, then neither connection\n** will proceed and the system may remain deadlocked indefinitely.\n**\n** To avoid this scenario, the sqlite3_unlock_notify() performs deadlock\n** detection. ^If a given call to sqlite3_unlock_notify() would put the\n** system in a deadlocked state, then SQLITE_LOCKED is returned and no\n** unlock-notify callback is registered. The system is said to be in\n** a deadlocked state if connection A has registered for an unlock-notify\n** callback on the conclusion of connection B's transaction, and connection\n** B has itself registered for an unlock-notify callback when connection\n** A's transaction is concluded. ^Indirect deadlock is also detected, so\n** the system is also considered to be deadlocked if connection B has\n** registered for an unlock-notify callback on the conclusion of connection\n** C's transaction, where connection C is waiting on connection A. ^Any\n** number of levels of indirection are allowed.\n**\n** <b>The \"DROP TABLE\" Exception</b>\n**\n** When a call to [sqlite3_step()] returns SQLITE_LOCKED, it is almost \n** always appropriate to call sqlite3_unlock_notify(). There is however,\n** one exception. When executing a \"DROP TABLE\" or \"DROP INDEX\" statement,\n** SQLite checks if there are any currently executing SELECT statements\n** that belong to the same connection. If there are, SQLITE_LOCKED is\n** returned. In this case there is no \"blocking connection\", so invoking\n** sqlite3_unlock_notify() results in the unlock-notify callback being\n** invoked immediately. If the application then re-attempts the \"DROP TABLE\"\n** or \"DROP INDEX\" query, an infinite loop might be the result.\n**\n** One way around this problem is to check the extended error code returned\n** by an sqlite3_step() call. ^(If there is a blocking connection, then the\n** extended error code is set to SQLITE_LOCKED_SHAREDCACHE. Otherwise, in\n** the special \"DROP TABLE/INDEX\" case, the extended error code is just \n** SQLITE_LOCKED.)^\n*/\nSQLITE_API int sqlite3_unlock_notify(\n  sqlite3 *pBlocked,                          /* Waiting connection */\n  void (*xNotify)(void **apArg, int nArg),    /* Callback function to invoke */\n  void *pNotifyArg                            /* Argument to pass to xNotify */\n);\n\n\n/*\n** CAPI3REF: String Comparison\n**\n** ^The [sqlite3_stricmp()] and [sqlite3_strnicmp()] APIs allow applications\n** and extensions to compare the contents of two buffers containing UTF-8\n** strings in a case-independent fashion, using the same definition of \"case\n** independence\" that SQLite uses internally when comparing identifiers.\n*/\nSQLITE_API int sqlite3_stricmp(const char *, const char *);\nSQLITE_API int sqlite3_strnicmp(const char *, const char *, int);\n\n/*\n** CAPI3REF: String Globbing\n*\n** ^The [sqlite3_strglob(P,X)] interface returns zero if and only if\n** string X matches the [GLOB] pattern P.\n** ^The definition of [GLOB] pattern matching used in\n** [sqlite3_strglob(P,X)] is the same as for the \"X GLOB P\" operator in the\n** SQL dialect understood by SQLite.  ^The [sqlite3_strglob(P,X)] function\n** is case sensitive.\n**\n** Note that this routine returns zero on a match and non-zero if the strings\n** do not match, the same as [sqlite3_stricmp()] and [sqlite3_strnicmp()].\n**\n** See also: [sqlite3_strlike()].\n*/\nSQLITE_API int sqlite3_strglob(const char *zGlob, const char *zStr);\n\n/*\n** CAPI3REF: String LIKE Matching\n*\n** ^The [sqlite3_strlike(P,X,E)] interface returns zero if and only if\n** string X matches the [LIKE] pattern P with escape character E.\n** ^The definition of [LIKE] pattern matching used in\n** [sqlite3_strlike(P,X,E)] is the same as for the \"X LIKE P ESCAPE E\"\n** operator in the SQL dialect understood by SQLite.  ^For \"X LIKE P\" without\n** the ESCAPE clause, set the E parameter of [sqlite3_strlike(P,X,E)] to 0.\n** ^As with the LIKE operator, the [sqlite3_strlike(P,X,E)] function is case\n** insensitive - equivalent upper and lower case ASCII characters match\n** one another.\n**\n** ^The [sqlite3_strlike(P,X,E)] function matches Unicode characters, though\n** only ASCII characters are case folded.\n**\n** Note that this routine returns zero on a match and non-zero if the strings\n** do not match, the same as [sqlite3_stricmp()] and [sqlite3_strnicmp()].\n**\n** See also: [sqlite3_strglob()].\n*/\nSQLITE_API int sqlite3_strlike(const char *zGlob, const char *zStr, unsigned int cEsc);\n\n/*\n** CAPI3REF: Error Logging Interface\n**\n** ^The [sqlite3_log()] interface writes a message into the [error log]\n** established by the [SQLITE_CONFIG_LOG] option to [sqlite3_config()].\n** ^If logging is enabled, the zFormat string and subsequent arguments are\n** used with [sqlite3_snprintf()] to generate the final output string.\n**\n** The sqlite3_log() interface is intended for use by extensions such as\n** virtual tables, collating functions, and SQL functions.  While there is\n** nothing to prevent an application from calling sqlite3_log(), doing so\n** is considered bad form.\n**\n** The zFormat string must not be NULL.\n**\n** To avoid deadlocks and other threading problems, the sqlite3_log() routine\n** will not use dynamically allocated memory.  The log message is stored in\n** a fixed-length buffer on the stack.  If the log message is longer than\n** a few hundred characters, it will be truncated to the length of the\n** buffer.\n*/\nSQLITE_API void sqlite3_log(int iErrCode, const char *zFormat, ...);\n\n/*\n** CAPI3REF: Write-Ahead Log Commit Hook\n** METHOD: sqlite3\n**\n** ^The [sqlite3_wal_hook()] function is used to register a callback that\n** is invoked each time data is committed to a database in wal mode.\n**\n** ^(The callback is invoked by SQLite after the commit has taken place and \n** the associated write-lock on the database released)^, so the implementation \n** may read, write or [checkpoint] the database as required.\n**\n** ^The first parameter passed to the callback function when it is invoked\n** is a copy of the third parameter passed to sqlite3_wal_hook() when\n** registering the callback. ^The second is a copy of the database handle.\n** ^The third parameter is the name of the database that was written to -\n** either \"main\" or the name of an [ATTACH]-ed database. ^The fourth parameter\n** is the number of pages currently in the write-ahead log file,\n** including those that were just committed.\n**\n** The callback function should normally return [SQLITE_OK].  ^If an error\n** code is returned, that error will propagate back up through the\n** SQLite code base to cause the statement that provoked the callback\n** to report an error, though the commit will have still occurred. If the\n** callback returns [SQLITE_ROW] or [SQLITE_DONE], or if it returns a value\n** that does not correspond to any valid SQLite error code, the results\n** are undefined.\n**\n** A single database handle may have at most a single write-ahead log callback \n** registered at one time. ^Calling [sqlite3_wal_hook()] replaces any\n** previously registered write-ahead log callback. ^Note that the\n** [sqlite3_wal_autocheckpoint()] interface and the\n** [wal_autocheckpoint pragma] both invoke [sqlite3_wal_hook()] and will\n** overwrite any prior [sqlite3_wal_hook()] settings.\n*/\nSQLITE_API void *sqlite3_wal_hook(\n  sqlite3*, \n  int(*)(void *,sqlite3*,const char*,int),\n  void*\n);\n\n/*\n** CAPI3REF: Configure an auto-checkpoint\n** METHOD: sqlite3\n**\n** ^The [sqlite3_wal_autocheckpoint(D,N)] is a wrapper around\n** [sqlite3_wal_hook()] that causes any database on [database connection] D\n** to automatically [checkpoint]\n** after committing a transaction if there are N or\n** more frames in the [write-ahead log] file.  ^Passing zero or \n** a negative value as the nFrame parameter disables automatic\n** checkpoints entirely.\n**\n** ^The callback registered by this function replaces any existing callback\n** registered using [sqlite3_wal_hook()].  ^Likewise, registering a callback\n** using [sqlite3_wal_hook()] disables the automatic checkpoint mechanism\n** configured by this function.\n**\n** ^The [wal_autocheckpoint pragma] can be used to invoke this interface\n** from SQL.\n**\n** ^Checkpoints initiated by this mechanism are\n** [sqlite3_wal_checkpoint_v2|PASSIVE].\n**\n** ^Every new [database connection] defaults to having the auto-checkpoint\n** enabled with a threshold of 1000 or [SQLITE_DEFAULT_WAL_AUTOCHECKPOINT]\n** pages.  The use of this interface\n** is only necessary if the default setting is found to be suboptimal\n** for a particular application.\n*/\nSQLITE_API int sqlite3_wal_autocheckpoint(sqlite3 *db, int N);\n\n/*\n** CAPI3REF: Checkpoint a database\n** METHOD: sqlite3\n**\n** ^(The sqlite3_wal_checkpoint(D,X) is equivalent to\n** [sqlite3_wal_checkpoint_v2](D,X,[SQLITE_CHECKPOINT_PASSIVE],0,0).)^\n**\n** In brief, sqlite3_wal_checkpoint(D,X) causes the content in the \n** [write-ahead log] for database X on [database connection] D to be\n** transferred into the database file and for the write-ahead log to\n** be reset.  See the [checkpointing] documentation for addition\n** information.\n**\n** This interface used to be the only way to cause a checkpoint to\n** occur.  But then the newer and more powerful [sqlite3_wal_checkpoint_v2()]\n** interface was added.  This interface is retained for backwards\n** compatibility and as a convenience for applications that need to manually\n** start a callback but which do not need the full power (and corresponding\n** complication) of [sqlite3_wal_checkpoint_v2()].\n*/\nSQLITE_API int sqlite3_wal_checkpoint(sqlite3 *db, const char *zDb);\n\n/*\n** CAPI3REF: Checkpoint a database\n** METHOD: sqlite3\n**\n** ^(The sqlite3_wal_checkpoint_v2(D,X,M,L,C) interface runs a checkpoint\n** operation on database X of [database connection] D in mode M.  Status\n** information is written back into integers pointed to by L and C.)^\n** ^(The M parameter must be a valid [checkpoint mode]:)^\n**\n** <dl>\n** <dt>SQLITE_CHECKPOINT_PASSIVE<dd>\n**   ^Checkpoint as many frames as possible without waiting for any database \n**   readers or writers to finish, then sync the database file if all frames \n**   in the log were checkpointed. ^The [busy-handler callback]\n**   is never invoked in the SQLITE_CHECKPOINT_PASSIVE mode.  \n**   ^On the other hand, passive mode might leave the checkpoint unfinished\n**   if there are concurrent readers or writers.\n**\n** <dt>SQLITE_CHECKPOINT_FULL<dd>\n**   ^This mode blocks (it invokes the\n**   [sqlite3_busy_handler|busy-handler callback]) until there is no\n**   database writer and all readers are reading from the most recent database\n**   snapshot. ^It then checkpoints all frames in the log file and syncs the\n**   database file. ^This mode blocks new database writers while it is pending,\n**   but new database readers are allowed to continue unimpeded.\n**\n** <dt>SQLITE_CHECKPOINT_RESTART<dd>\n**   ^This mode works the same way as SQLITE_CHECKPOINT_FULL with the addition\n**   that after checkpointing the log file it blocks (calls the \n**   [busy-handler callback])\n**   until all readers are reading from the database file only. ^This ensures \n**   that the next writer will restart the log file from the beginning.\n**   ^Like SQLITE_CHECKPOINT_FULL, this mode blocks new\n**   database writer attempts while it is pending, but does not impede readers.\n**\n** <dt>SQLITE_CHECKPOINT_TRUNCATE<dd>\n**   ^This mode works the same way as SQLITE_CHECKPOINT_RESTART with the\n**   addition that it also truncates the log file to zero bytes just prior\n**   to a successful return.\n** </dl>\n**\n** ^If pnLog is not NULL, then *pnLog is set to the total number of frames in\n** the log file or to -1 if the checkpoint could not run because\n** of an error or because the database is not in [WAL mode]. ^If pnCkpt is not\n** NULL,then *pnCkpt is set to the total number of checkpointed frames in the\n** log file (including any that were already checkpointed before the function\n** was called) or to -1 if the checkpoint could not run due to an error or\n** because the database is not in WAL mode. ^Note that upon successful\n** completion of an SQLITE_CHECKPOINT_TRUNCATE, the log file will have been\n** truncated to zero bytes and so both *pnLog and *pnCkpt will be set to zero.\n**\n** ^All calls obtain an exclusive \"checkpoint\" lock on the database file. ^If\n** any other process is running a checkpoint operation at the same time, the \n** lock cannot be obtained and SQLITE_BUSY is returned. ^Even if there is a \n** busy-handler configured, it will not be invoked in this case.\n**\n** ^The SQLITE_CHECKPOINT_FULL, RESTART and TRUNCATE modes also obtain the \n** exclusive \"writer\" lock on the database file. ^If the writer lock cannot be\n** obtained immediately, and a busy-handler is configured, it is invoked and\n** the writer lock retried until either the busy-handler returns 0 or the lock\n** is successfully obtained. ^The busy-handler is also invoked while waiting for\n** database readers as described above. ^If the busy-handler returns 0 before\n** the writer lock is obtained or while waiting for database readers, the\n** checkpoint operation proceeds from that point in the same way as \n** SQLITE_CHECKPOINT_PASSIVE - checkpointing as many frames as possible \n** without blocking any further. ^SQLITE_BUSY is returned in this case.\n**\n** ^If parameter zDb is NULL or points to a zero length string, then the\n** specified operation is attempted on all WAL databases [attached] to \n** [database connection] db.  In this case the\n** values written to output parameters *pnLog and *pnCkpt are undefined. ^If \n** an SQLITE_BUSY error is encountered when processing one or more of the \n** attached WAL databases, the operation is still attempted on any remaining \n** attached databases and SQLITE_BUSY is returned at the end. ^If any other \n** error occurs while processing an attached database, processing is abandoned \n** and the error code is returned to the caller immediately. ^If no error \n** (SQLITE_BUSY or otherwise) is encountered while processing the attached \n** databases, SQLITE_OK is returned.\n**\n** ^If database zDb is the name of an attached database that is not in WAL\n** mode, SQLITE_OK is returned and both *pnLog and *pnCkpt set to -1. ^If\n** zDb is not NULL (or a zero length string) and is not the name of any\n** attached database, SQLITE_ERROR is returned to the caller.\n**\n** ^Unless it returns SQLITE_MISUSE,\n** the sqlite3_wal_checkpoint_v2() interface\n** sets the error information that is queried by\n** [sqlite3_errcode()] and [sqlite3_errmsg()].\n**\n** ^The [PRAGMA wal_checkpoint] command can be used to invoke this interface\n** from SQL.\n*/\nSQLITE_API int sqlite3_wal_checkpoint_v2(\n  sqlite3 *db,                    /* Database handle */\n  const char *zDb,                /* Name of attached database (or NULL) */\n  int eMode,                      /* SQLITE_CHECKPOINT_* value */\n  int *pnLog,                     /* OUT: Size of WAL log in frames */\n  int *pnCkpt                     /* OUT: Total number of frames checkpointed */\n);\n\n/*\n** CAPI3REF: Checkpoint Mode Values\n** KEYWORDS: {checkpoint mode}\n**\n** These constants define all valid values for the \"checkpoint mode\" passed\n** as the third parameter to the [sqlite3_wal_checkpoint_v2()] interface.\n** See the [sqlite3_wal_checkpoint_v2()] documentation for details on the\n** meaning of each of these checkpoint modes.\n*/\n#define SQLITE_CHECKPOINT_PASSIVE  0  /* Do as much as possible w/o blocking */\n#define SQLITE_CHECKPOINT_FULL     1  /* Wait for writers, then checkpoint */\n#define SQLITE_CHECKPOINT_RESTART  2  /* Like FULL but wait for for readers */\n#define SQLITE_CHECKPOINT_TRUNCATE 3  /* Like RESTART but also truncate WAL */\n\n/*\n** CAPI3REF: Virtual Table Interface Configuration\n**\n** This function may be called by either the [xConnect] or [xCreate] method\n** of a [virtual table] implementation to configure\n** various facets of the virtual table interface.\n**\n** If this interface is invoked outside the context of an xConnect or\n** xCreate virtual table method then the behavior is undefined.\n**\n** At present, there is only one option that may be configured using\n** this function. (See [SQLITE_VTAB_CONSTRAINT_SUPPORT].)  Further options\n** may be added in the future.\n*/\nSQLITE_API int sqlite3_vtab_config(sqlite3*, int op, ...);\n\n/*\n** CAPI3REF: Virtual Table Configuration Options\n**\n** These macros define the various options to the\n** [sqlite3_vtab_config()] interface that [virtual table] implementations\n** can use to customize and optimize their behavior.\n**\n** <dl>\n** <dt>SQLITE_VTAB_CONSTRAINT_SUPPORT\n** <dd>Calls of the form\n** [sqlite3_vtab_config](db,SQLITE_VTAB_CONSTRAINT_SUPPORT,X) are supported,\n** where X is an integer.  If X is zero, then the [virtual table] whose\n** [xCreate] or [xConnect] method invoked [sqlite3_vtab_config()] does not\n** support constraints.  In this configuration (which is the default) if\n** a call to the [xUpdate] method returns [SQLITE_CONSTRAINT], then the entire\n** statement is rolled back as if [ON CONFLICT | OR ABORT] had been\n** specified as part of the users SQL statement, regardless of the actual\n** ON CONFLICT mode specified.\n**\n** If X is non-zero, then the virtual table implementation guarantees\n** that if [xUpdate] returns [SQLITE_CONSTRAINT], it will do so before\n** any modifications to internal or persistent data structures have been made.\n** If the [ON CONFLICT] mode is ABORT, FAIL, IGNORE or ROLLBACK, SQLite \n** is able to roll back a statement or database transaction, and abandon\n** or continue processing the current SQL statement as appropriate. \n** If the ON CONFLICT mode is REPLACE and the [xUpdate] method returns\n** [SQLITE_CONSTRAINT], SQLite handles this as if the ON CONFLICT mode\n** had been ABORT.\n**\n** Virtual table implementations that are required to handle OR REPLACE\n** must do so within the [xUpdate] method. If a call to the \n** [sqlite3_vtab_on_conflict()] function indicates that the current ON \n** CONFLICT policy is REPLACE, the virtual table implementation should \n** silently replace the appropriate rows within the xUpdate callback and\n** return SQLITE_OK. Or, if this is not possible, it may return\n** SQLITE_CONSTRAINT, in which case SQLite falls back to OR ABORT \n** constraint handling.\n** </dl>\n*/\n#define SQLITE_VTAB_CONSTRAINT_SUPPORT 1\n\n/*\n** CAPI3REF: Determine The Virtual Table Conflict Policy\n**\n** This function may only be called from within a call to the [xUpdate] method\n** of a [virtual table] implementation for an INSERT or UPDATE operation. ^The\n** value returned is one of [SQLITE_ROLLBACK], [SQLITE_IGNORE], [SQLITE_FAIL],\n** [SQLITE_ABORT], or [SQLITE_REPLACE], according to the [ON CONFLICT] mode\n** of the SQL statement that triggered the call to the [xUpdate] method of the\n** [virtual table].\n*/\nSQLITE_API int sqlite3_vtab_on_conflict(sqlite3 *);\n\n/*\n** CAPI3REF: Determine If Virtual Table Column Access Is For UPDATE\n**\n** If the sqlite3_vtab_nochange(X) routine is called within the [xColumn]\n** method of a [virtual table], then it returns true if and only if the\n** column is being fetched as part of an UPDATE operation during which the\n** column value will not change.  Applications might use this to substitute\n** a lighter-weight value to return that the corresponding [xUpdate] method\n** understands as a \"no-change\" value.\n**\n** If the [xColumn] method calls sqlite3_vtab_nochange() and finds that\n** the column is not changed by the UPDATE statement, they the xColumn\n** method can optionally return without setting a result, without calling\n** any of the [sqlite3_result_int|sqlite3_result_xxxxx() interfaces].\n** In that case, [sqlite3_value_nochange(X)] will return true for the\n** same column in the [xUpdate] method.\n*/\nSQLITE_API int sqlite3_vtab_nochange(sqlite3_context*);\n\n/*\n** CAPI3REF: Determine The Collation For a Virtual Table Constraint\n**\n** This function may only be called from within a call to the [xBestIndex]\n** method of a [virtual table]. \n**\n** The first argument must be the sqlite3_index_info object that is the\n** first parameter to the xBestIndex() method. The second argument must be\n** an index into the aConstraint[] array belonging to the sqlite3_index_info\n** structure passed to xBestIndex. This function returns a pointer to a buffer \n** containing the name of the collation sequence for the corresponding\n** constraint.\n*/\nSQLITE_API SQLITE_EXPERIMENTAL const char *sqlite3_vtab_collation(sqlite3_index_info*,int);\n\n/*\n** CAPI3REF: Conflict resolution modes\n** KEYWORDS: {conflict resolution mode}\n**\n** These constants are returned by [sqlite3_vtab_on_conflict()] to\n** inform a [virtual table] implementation what the [ON CONFLICT] mode\n** is for the SQL statement being evaluated.\n**\n** Note that the [SQLITE_IGNORE] constant is also used as a potential\n** return value from the [sqlite3_set_authorizer()] callback and that\n** [SQLITE_ABORT] is also a [result code].\n*/\n#define SQLITE_ROLLBACK 1\n/* #define SQLITE_IGNORE 2 // Also used by sqlite3_authorizer() callback */\n#define SQLITE_FAIL     3\n/* #define SQLITE_ABORT 4  // Also an error code */\n#define SQLITE_REPLACE  5\n\n/*\n** CAPI3REF: Prepared Statement Scan Status Opcodes\n** KEYWORDS: {scanstatus options}\n**\n** The following constants can be used for the T parameter to the\n** [sqlite3_stmt_scanstatus(S,X,T,V)] interface.  Each constant designates a\n** different metric for sqlite3_stmt_scanstatus() to return.\n**\n** When the value returned to V is a string, space to hold that string is\n** managed by the prepared statement S and will be automatically freed when\n** S is finalized.\n**\n** <dl>\n** [[SQLITE_SCANSTAT_NLOOP]] <dt>SQLITE_SCANSTAT_NLOOP</dt>\n** <dd>^The [sqlite3_int64] variable pointed to by the T parameter will be\n** set to the total number of times that the X-th loop has run.</dd>\n**\n** [[SQLITE_SCANSTAT_NVISIT]] <dt>SQLITE_SCANSTAT_NVISIT</dt>\n** <dd>^The [sqlite3_int64] variable pointed to by the T parameter will be set\n** to the total number of rows examined by all iterations of the X-th loop.</dd>\n**\n** [[SQLITE_SCANSTAT_EST]] <dt>SQLITE_SCANSTAT_EST</dt>\n** <dd>^The \"double\" variable pointed to by the T parameter will be set to the\n** query planner's estimate for the average number of rows output from each\n** iteration of the X-th loop.  If the query planner's estimates was accurate,\n** then this value will approximate the quotient NVISIT/NLOOP and the\n** product of this value for all prior loops with the same SELECTID will\n** be the NLOOP value for the current loop.\n**\n** [[SQLITE_SCANSTAT_NAME]] <dt>SQLITE_SCANSTAT_NAME</dt>\n** <dd>^The \"const char *\" variable pointed to by the T parameter will be set\n** to a zero-terminated UTF-8 string containing the name of the index or table\n** used for the X-th loop.\n**\n** [[SQLITE_SCANSTAT_EXPLAIN]] <dt>SQLITE_SCANSTAT_EXPLAIN</dt>\n** <dd>^The \"const char *\" variable pointed to by the T parameter will be set\n** to a zero-terminated UTF-8 string containing the [EXPLAIN QUERY PLAN]\n** description for the X-th loop.\n**\n** [[SQLITE_SCANSTAT_SELECTID]] <dt>SQLITE_SCANSTAT_SELECT</dt>\n** <dd>^The \"int\" variable pointed to by the T parameter will be set to the\n** \"select-id\" for the X-th loop.  The select-id identifies which query or\n** subquery the loop is part of.  The main query has a select-id of zero.\n** The select-id is the same value as is output in the first column\n** of an [EXPLAIN QUERY PLAN] query.\n** </dl>\n*/\n#define SQLITE_SCANSTAT_NLOOP    0\n#define SQLITE_SCANSTAT_NVISIT   1\n#define SQLITE_SCANSTAT_EST      2\n#define SQLITE_SCANSTAT_NAME     3\n#define SQLITE_SCANSTAT_EXPLAIN  4\n#define SQLITE_SCANSTAT_SELECTID 5\n\n/*\n** CAPI3REF: Prepared Statement Scan Status\n** METHOD: sqlite3_stmt\n**\n** This interface returns information about the predicted and measured\n** performance for pStmt.  Advanced applications can use this\n** interface to compare the predicted and the measured performance and\n** issue warnings and/or rerun [ANALYZE] if discrepancies are found.\n**\n** Since this interface is expected to be rarely used, it is only\n** available if SQLite is compiled using the [SQLITE_ENABLE_STMT_SCANSTATUS]\n** compile-time option.\n**\n** The \"iScanStatusOp\" parameter determines which status information to return.\n** The \"iScanStatusOp\" must be one of the [scanstatus options] or the behavior\n** of this interface is undefined.\n** ^The requested measurement is written into a variable pointed to by\n** the \"pOut\" parameter.\n** Parameter \"idx\" identifies the specific loop to retrieve statistics for.\n** Loops are numbered starting from zero. ^If idx is out of range - less than\n** zero or greater than or equal to the total number of loops used to implement\n** the statement - a non-zero value is returned and the variable that pOut\n** points to is unchanged.\n**\n** ^Statistics might not be available for all loops in all statements. ^In cases\n** where there exist loops with no available statistics, this function behaves\n** as if the loop did not exist - it returns non-zero and leave the variable\n** that pOut points to unchanged.\n**\n** See also: [sqlite3_stmt_scanstatus_reset()]\n*/\nSQLITE_API int sqlite3_stmt_scanstatus(\n  sqlite3_stmt *pStmt,      /* Prepared statement for which info desired */\n  int idx,                  /* Index of loop to report on */\n  int iScanStatusOp,        /* Information desired.  SQLITE_SCANSTAT_* */\n  void *pOut                /* Result written here */\n);     \n\n/*\n** CAPI3REF: Zero Scan-Status Counters\n** METHOD: sqlite3_stmt\n**\n** ^Zero all [sqlite3_stmt_scanstatus()] related event counters.\n**\n** This API is only available if the library is built with pre-processor\n** symbol [SQLITE_ENABLE_STMT_SCANSTATUS] defined.\n*/\nSQLITE_API void sqlite3_stmt_scanstatus_reset(sqlite3_stmt*);\n\n/*\n** CAPI3REF: Flush caches to disk mid-transaction\n**\n** ^If a write-transaction is open on [database connection] D when the\n** [sqlite3_db_cacheflush(D)] interface invoked, any dirty\n** pages in the pager-cache that are not currently in use are written out \n** to disk. A dirty page may be in use if a database cursor created by an\n** active SQL statement is reading from it, or if it is page 1 of a database\n** file (page 1 is always \"in use\").  ^The [sqlite3_db_cacheflush(D)]\n** interface flushes caches for all schemas - \"main\", \"temp\", and\n** any [attached] databases.\n**\n** ^If this function needs to obtain extra database locks before dirty pages \n** can be flushed to disk, it does so. ^If those locks cannot be obtained \n** immediately and there is a busy-handler callback configured, it is invoked\n** in the usual manner. ^If the required lock still cannot be obtained, then\n** the database is skipped and an attempt made to flush any dirty pages\n** belonging to the next (if any) database. ^If any databases are skipped\n** because locks cannot be obtained, but no other error occurs, this\n** function returns SQLITE_BUSY.\n**\n** ^If any other error occurs while flushing dirty pages to disk (for\n** example an IO error or out-of-memory condition), then processing is\n** abandoned and an SQLite [error code] is returned to the caller immediately.\n**\n** ^Otherwise, if no error occurs, [sqlite3_db_cacheflush()] returns SQLITE_OK.\n**\n** ^This function does not set the database handle error code or message\n** returned by the [sqlite3_errcode()] and [sqlite3_errmsg()] functions.\n*/\nSQLITE_API int sqlite3_db_cacheflush(sqlite3*);\n\n/*\n** CAPI3REF: The pre-update hook.\n**\n** ^These interfaces are only available if SQLite is compiled using the\n** [SQLITE_ENABLE_PREUPDATE_HOOK] compile-time option.\n**\n** ^The [sqlite3_preupdate_hook()] interface registers a callback function\n** that is invoked prior to each [INSERT], [UPDATE], and [DELETE] operation\n** on a database table.\n** ^At most one preupdate hook may be registered at a time on a single\n** [database connection]; each call to [sqlite3_preupdate_hook()] overrides\n** the previous setting.\n** ^The preupdate hook is disabled by invoking [sqlite3_preupdate_hook()]\n** with a NULL pointer as the second parameter.\n** ^The third parameter to [sqlite3_preupdate_hook()] is passed through as\n** the first parameter to callbacks.\n**\n** ^The preupdate hook only fires for changes to real database tables; the\n** preupdate hook is not invoked for changes to [virtual tables] or to\n** system tables like sqlite_master or sqlite_stat1.\n**\n** ^The second parameter to the preupdate callback is a pointer to\n** the [database connection] that registered the preupdate hook.\n** ^The third parameter to the preupdate callback is one of the constants\n** [SQLITE_INSERT], [SQLITE_DELETE], or [SQLITE_UPDATE] to identify the\n** kind of update operation that is about to occur.\n** ^(The fourth parameter to the preupdate callback is the name of the\n** database within the database connection that is being modified.  This\n** will be \"main\" for the main database or \"temp\" for TEMP tables or \n** the name given after the AS keyword in the [ATTACH] statement for attached\n** databases.)^\n** ^The fifth parameter to the preupdate callback is the name of the\n** table that is being modified.\n**\n** For an UPDATE or DELETE operation on a [rowid table], the sixth\n** parameter passed to the preupdate callback is the initial [rowid] of the \n** row being modified or deleted. For an INSERT operation on a rowid table,\n** or any operation on a WITHOUT ROWID table, the value of the sixth \n** parameter is undefined. For an INSERT or UPDATE on a rowid table the\n** seventh parameter is the final rowid value of the row being inserted\n** or updated. The value of the seventh parameter passed to the callback\n** function is not defined for operations on WITHOUT ROWID tables, or for\n** INSERT operations on rowid tables.\n**\n** The [sqlite3_preupdate_old()], [sqlite3_preupdate_new()],\n** [sqlite3_preupdate_count()], and [sqlite3_preupdate_depth()] interfaces\n** provide additional information about a preupdate event. These routines\n** may only be called from within a preupdate callback.  Invoking any of\n** these routines from outside of a preupdate callback or with a\n** [database connection] pointer that is different from the one supplied\n** to the preupdate callback results in undefined and probably undesirable\n** behavior.\n**\n** ^The [sqlite3_preupdate_count(D)] interface returns the number of columns\n** in the row that is being inserted, updated, or deleted.\n**\n** ^The [sqlite3_preupdate_old(D,N,P)] interface writes into P a pointer to\n** a [protected sqlite3_value] that contains the value of the Nth column of\n** the table row before it is updated.  The N parameter must be between 0\n** and one less than the number of columns or the behavior will be\n** undefined. This must only be used within SQLITE_UPDATE and SQLITE_DELETE\n** preupdate callbacks; if it is used by an SQLITE_INSERT callback then the\n** behavior is undefined.  The [sqlite3_value] that P points to\n** will be destroyed when the preupdate callback returns.\n**\n** ^The [sqlite3_preupdate_new(D,N,P)] interface writes into P a pointer to\n** a [protected sqlite3_value] that contains the value of the Nth column of\n** the table row after it is updated.  The N parameter must be between 0\n** and one less than the number of columns or the behavior will be\n** undefined. This must only be used within SQLITE_INSERT and SQLITE_UPDATE\n** preupdate callbacks; if it is used by an SQLITE_DELETE callback then the\n** behavior is undefined.  The [sqlite3_value] that P points to\n** will be destroyed when the preupdate callback returns.\n**\n** ^The [sqlite3_preupdate_depth(D)] interface returns 0 if the preupdate\n** callback was invoked as a result of a direct insert, update, or delete\n** operation; or 1 for inserts, updates, or deletes invoked by top-level \n** triggers; or 2 for changes resulting from triggers called by top-level\n** triggers; and so forth.\n**\n** See also:  [sqlite3_update_hook()]\n*/\n#if defined(SQLITE_ENABLE_PREUPDATE_HOOK)\nSQLITE_API void *sqlite3_preupdate_hook(\n  sqlite3 *db,\n  void(*xPreUpdate)(\n    void *pCtx,                   /* Copy of third arg to preupdate_hook() */\n    sqlite3 *db,                  /* Database handle */\n    int op,                       /* SQLITE_UPDATE, DELETE or INSERT */\n    char const *zDb,              /* Database name */\n    char const *zName,            /* Table name */\n    sqlite3_int64 iKey1,          /* Rowid of row about to be deleted/updated */\n    sqlite3_int64 iKey2           /* New rowid value (for a rowid UPDATE) */\n  ),\n  void*\n);\nSQLITE_API int sqlite3_preupdate_old(sqlite3 *, int, sqlite3_value **);\nSQLITE_API int sqlite3_preupdate_count(sqlite3 *);\nSQLITE_API int sqlite3_preupdate_depth(sqlite3 *);\nSQLITE_API int sqlite3_preupdate_new(sqlite3 *, int, sqlite3_value **);\n#endif\n\n/*\n** CAPI3REF: Low-level system error code\n**\n** ^Attempt to return the underlying operating system error code or error\n** number that caused the most recent I/O error or failure to open a file.\n** The return value is OS-dependent.  For example, on unix systems, after\n** [sqlite3_open_v2()] returns [SQLITE_CANTOPEN], this interface could be\n** called to get back the underlying \"errno\" that caused the problem, such\n** as ENOSPC, EAUTH, EISDIR, and so forth.  \n*/\nSQLITE_API int sqlite3_system_errno(sqlite3*);\n\n/*\n** CAPI3REF: Database Snapshot\n** KEYWORDS: {snapshot} {sqlite3_snapshot}\n** EXPERIMENTAL\n**\n** An instance of the snapshot object records the state of a [WAL mode]\n** database for some specific point in history.\n**\n** In [WAL mode], multiple [database connections] that are open on the\n** same database file can each be reading a different historical version\n** of the database file.  When a [database connection] begins a read\n** transaction, that connection sees an unchanging copy of the database\n** as it existed for the point in time when the transaction first started.\n** Subsequent changes to the database from other connections are not seen\n** by the reader until a new read transaction is started.\n**\n** The sqlite3_snapshot object records state information about an historical\n** version of the database file so that it is possible to later open a new read\n** transaction that sees that historical version of the database rather than\n** the most recent version.\n**\n** The constructor for this object is [sqlite3_snapshot_get()].  The\n** [sqlite3_snapshot_open()] method causes a fresh read transaction to refer\n** to an historical snapshot (if possible).  The destructor for \n** sqlite3_snapshot objects is [sqlite3_snapshot_free()].\n*/\ntypedef struct sqlite3_snapshot {\n  unsigned char hidden[48];\n} sqlite3_snapshot;\n\n/*\n** CAPI3REF: Record A Database Snapshot\n** EXPERIMENTAL\n**\n** ^The [sqlite3_snapshot_get(D,S,P)] interface attempts to make a\n** new [sqlite3_snapshot] object that records the current state of\n** schema S in database connection D.  ^On success, the\n** [sqlite3_snapshot_get(D,S,P)] interface writes a pointer to the newly\n** created [sqlite3_snapshot] object into *P and returns SQLITE_OK.\n** If there is not already a read-transaction open on schema S when\n** this function is called, one is opened automatically. \n**\n** The following must be true for this function to succeed. If any of\n** the following statements are false when sqlite3_snapshot_get() is\n** called, SQLITE_ERROR is returned. The final value of *P is undefined\n** in this case. \n**\n** <ul>\n**   <li> The database handle must be in [autocommit mode].\n**\n**   <li> Schema S of [database connection] D must be a [WAL mode] database.\n**\n**   <li> There must not be a write transaction open on schema S of database\n**        connection D.\n**\n**   <li> One or more transactions must have been written to the current wal\n**        file since it was created on disk (by any connection). This means\n**        that a snapshot cannot be taken on a wal mode database with no wal \n**        file immediately after it is first opened. At least one transaction\n**        must be written to it first.\n** </ul>\n**\n** This function may also return SQLITE_NOMEM.  If it is called with the\n** database handle in autocommit mode but fails for some other reason, \n** whether or not a read transaction is opened on schema S is undefined.\n**\n** The [sqlite3_snapshot] object returned from a successful call to\n** [sqlite3_snapshot_get()] must be freed using [sqlite3_snapshot_free()]\n** to avoid a memory leak.\n**\n** The [sqlite3_snapshot_get()] interface is only available when the\n** SQLITE_ENABLE_SNAPSHOT compile-time option is used.\n*/\nSQLITE_API SQLITE_EXPERIMENTAL int sqlite3_snapshot_get(\n  sqlite3 *db,\n  const char *zSchema,\n  sqlite3_snapshot **ppSnapshot\n);\n\n/*\n** CAPI3REF: Start a read transaction on an historical snapshot\n** EXPERIMENTAL\n**\n** ^The [sqlite3_snapshot_open(D,S,P)] interface starts a\n** read transaction for schema S of\n** [database connection] D such that the read transaction\n** refers to historical [snapshot] P, rather than the most\n** recent change to the database.\n** ^The [sqlite3_snapshot_open()] interface returns SQLITE_OK on success\n** or an appropriate [error code] if it fails.\n**\n** ^In order to succeed, a call to [sqlite3_snapshot_open(D,S,P)] must be\n** the first operation following the [BEGIN] that takes the schema S\n** out of [autocommit mode].\n** ^In other words, schema S must not currently be in\n** a transaction for [sqlite3_snapshot_open(D,S,P)] to work, but the\n** database connection D must be out of [autocommit mode].\n** ^A [snapshot] will fail to open if it has been overwritten by a\n** [checkpoint].\n** ^(A call to [sqlite3_snapshot_open(D,S,P)] will fail if the\n** database connection D does not know that the database file for\n** schema S is in [WAL mode].  A database connection might not know\n** that the database file is in [WAL mode] if there has been no prior\n** I/O on that database connection, or if the database entered [WAL mode] \n** after the most recent I/O on the database connection.)^\n** (Hint: Run \"[PRAGMA application_id]\" against a newly opened\n** database connection in order to make it ready to use snapshots.)\n**\n** The [sqlite3_snapshot_open()] interface is only available when the\n** SQLITE_ENABLE_SNAPSHOT compile-time option is used.\n*/\nSQLITE_API SQLITE_EXPERIMENTAL int sqlite3_snapshot_open(\n  sqlite3 *db,\n  const char *zSchema,\n  sqlite3_snapshot *pSnapshot\n);\n\n/*\n** CAPI3REF: Destroy a snapshot\n** EXPERIMENTAL\n**\n** ^The [sqlite3_snapshot_free(P)] interface destroys [sqlite3_snapshot] P.\n** The application must eventually free every [sqlite3_snapshot] object\n** using this routine to avoid a memory leak.\n**\n** The [sqlite3_snapshot_free()] interface is only available when the\n** SQLITE_ENABLE_SNAPSHOT compile-time option is used.\n*/\nSQLITE_API SQLITE_EXPERIMENTAL void sqlite3_snapshot_free(sqlite3_snapshot*);\n\n/*\n** CAPI3REF: Compare the ages of two snapshot handles.\n** EXPERIMENTAL\n**\n** The sqlite3_snapshot_cmp(P1, P2) interface is used to compare the ages\n** of two valid snapshot handles. \n**\n** If the two snapshot handles are not associated with the same database \n** file, the result of the comparison is undefined. \n**\n** Additionally, the result of the comparison is only valid if both of the\n** snapshot handles were obtained by calling sqlite3_snapshot_get() since the\n** last time the wal file was deleted. The wal file is deleted when the\n** database is changed back to rollback mode or when the number of database\n** clients drops to zero. If either snapshot handle was obtained before the \n** wal file was last deleted, the value returned by this function \n** is undefined.\n**\n** Otherwise, this API returns a negative value if P1 refers to an older\n** snapshot than P2, zero if the two handles refer to the same database\n** snapshot, and a positive value if P1 is a newer snapshot than P2.\n*/\nSQLITE_API SQLITE_EXPERIMENTAL int sqlite3_snapshot_cmp(\n  sqlite3_snapshot *p1,\n  sqlite3_snapshot *p2\n);\n\n/*\n** CAPI3REF: Recover snapshots from a wal file\n** EXPERIMENTAL\n**\n** If all connections disconnect from a database file but do not perform\n** a checkpoint, the existing wal file is opened along with the database\n** file the next time the database is opened. At this point it is only\n** possible to successfully call sqlite3_snapshot_open() to open the most\n** recent snapshot of the database (the one at the head of the wal file),\n** even though the wal file may contain other valid snapshots for which\n** clients have sqlite3_snapshot handles.\n**\n** This function attempts to scan the wal file associated with database zDb\n** of database handle db and make all valid snapshots available to\n** sqlite3_snapshot_open(). It is an error if there is already a read\n** transaction open on the database, or if the database is not a wal mode\n** database.\n**\n** SQLITE_OK is returned if successful, or an SQLite error code otherwise.\n*/\nSQLITE_API SQLITE_EXPERIMENTAL int sqlite3_snapshot_recover(sqlite3 *db, const char *zDb);\n\n/*\n** Undo the hack that converts floating point types to integer for\n** builds on processors without floating point support.\n*/\n#ifdef SQLITE_OMIT_FLOATING_POINT\n# undef double\n#endif\n\n#ifdef __cplusplus\n}  /* End of the 'extern \"C\"' block */\n#endif\n#endif /* SQLITE3_H */\n\n/******** Begin file sqlite3rtree.h *********/\n/*\n** 2010 August 30\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n*************************************************************************\n*/\n\n#ifndef _SQLITE3RTREE_H_\n#define _SQLITE3RTREE_H_\n\n\n#ifdef __cplusplus\nextern \"C\" {\n#endif\n\ntypedef struct sqlite3_rtree_geometry sqlite3_rtree_geometry;\ntypedef struct sqlite3_rtree_query_info sqlite3_rtree_query_info;\n\n/* The double-precision datatype used by RTree depends on the\n** SQLITE_RTREE_INT_ONLY compile-time option.\n*/\n#ifdef SQLITE_RTREE_INT_ONLY\n  typedef sqlite3_int64 sqlite3_rtree_dbl;\n#else\n  typedef double sqlite3_rtree_dbl;\n#endif\n\n/*\n** Register a geometry callback named zGeom that can be used as part of an\n** R-Tree geometry query as follows:\n**\n**   SELECT ... FROM <rtree> WHERE <rtree col> MATCH $zGeom(... params ...)\n*/\nSQLITE_API int sqlite3_rtree_geometry_callback(\n  sqlite3 *db,\n  const char *zGeom,\n  int (*xGeom)(sqlite3_rtree_geometry*, int, sqlite3_rtree_dbl*,int*),\n  void *pContext\n);\n\n\n/*\n** A pointer to a structure of the following type is passed as the first\n** argument to callbacks registered using rtree_geometry_callback().\n*/\nstruct sqlite3_rtree_geometry {\n  void *pContext;                 /* Copy of pContext passed to s_r_g_c() */\n  int nParam;                     /* Size of array aParam[] */\n  sqlite3_rtree_dbl *aParam;      /* Parameters passed to SQL geom function */\n  void *pUser;                    /* Callback implementation user data */\n  void (*xDelUser)(void *);       /* Called by SQLite to clean up pUser */\n};\n\n/*\n** Register a 2nd-generation geometry callback named zScore that can be \n** used as part of an R-Tree geometry query as follows:\n**\n**   SELECT ... FROM <rtree> WHERE <rtree col> MATCH $zQueryFunc(... params ...)\n*/\nSQLITE_API int sqlite3_rtree_query_callback(\n  sqlite3 *db,\n  const char *zQueryFunc,\n  int (*xQueryFunc)(sqlite3_rtree_query_info*),\n  void *pContext,\n  void (*xDestructor)(void*)\n);\n\n\n/*\n** A pointer to a structure of the following type is passed as the \n** argument to scored geometry callback registered using\n** sqlite3_rtree_query_callback().\n**\n** Note that the first 5 fields of this structure are identical to\n** sqlite3_rtree_geometry.  This structure is a subclass of\n** sqlite3_rtree_geometry.\n*/\nstruct sqlite3_rtree_query_info {\n  void *pContext;                   /* pContext from when function registered */\n  int nParam;                       /* Number of function parameters */\n  sqlite3_rtree_dbl *aParam;        /* value of function parameters */\n  void *pUser;                      /* callback can use this, if desired */\n  void (*xDelUser)(void*);          /* function to free pUser */\n  sqlite3_rtree_dbl *aCoord;        /* Coordinates of node or entry to check */\n  unsigned int *anQueue;            /* Number of pending entries in the queue */\n  int nCoord;                       /* Number of coordinates */\n  int iLevel;                       /* Level of current node or entry */\n  int mxLevel;                      /* The largest iLevel value in the tree */\n  sqlite3_int64 iRowid;             /* Rowid for current entry */\n  sqlite3_rtree_dbl rParentScore;   /* Score of parent node */\n  int eParentWithin;                /* Visibility of parent node */\n  int eWithin;                      /* OUT: Visiblity */\n  sqlite3_rtree_dbl rScore;         /* OUT: Write the score here */\n  /* The following fields are only available in 3.8.11 and later */\n  sqlite3_value **apSqlParam;       /* Original SQL values of parameters */\n};\n\n/*\n** Allowed values for sqlite3_rtree_query.eWithin and .eParentWithin.\n*/\n#define NOT_WITHIN       0   /* Object completely outside of query region */\n#define PARTLY_WITHIN    1   /* Object partially overlaps query region */\n#define FULLY_WITHIN     2   /* Object fully contained within query region */\n\n\n#ifdef __cplusplus\n}  /* end of the 'extern \"C\"' block */\n#endif\n\n#endif  /* ifndef _SQLITE3RTREE_H_ */\n\n/******** End of sqlite3rtree.h *********/\n/******** Begin file sqlite3session.h *********/\n\n#if !defined(__SQLITESESSION_H_) && defined(SQLITE_ENABLE_SESSION)\n#define __SQLITESESSION_H_ 1\n\n/*\n** Make sure we can call this stuff from C++.\n*/\n#ifdef __cplusplus\nextern \"C\" {\n#endif\n\n\n/*\n** CAPI3REF: Session Object Handle\n*/\ntypedef struct sqlite3_session sqlite3_session;\n\n/*\n** CAPI3REF: Changeset Iterator Handle\n*/\ntypedef struct sqlite3_changeset_iter sqlite3_changeset_iter;\n\n/*\n** CAPI3REF: Create A New Session Object\n**\n** Create a new session object attached to database handle db. If successful,\n** a pointer to the new object is written to *ppSession and SQLITE_OK is\n** returned. If an error occurs, *ppSession is set to NULL and an SQLite\n** error code (e.g. SQLITE_NOMEM) is returned.\n**\n** It is possible to create multiple session objects attached to a single\n** database handle.\n**\n** Session objects created using this function should be deleted using the\n** [sqlite3session_delete()] function before the database handle that they\n** are attached to is itself closed. If the database handle is closed before\n** the session object is deleted, then the results of calling any session\n** module function, including [sqlite3session_delete()] on the session object\n** are undefined.\n**\n** Because the session module uses the [sqlite3_preupdate_hook()] API, it\n** is not possible for an application to register a pre-update hook on a\n** database handle that has one or more session objects attached. Nor is\n** it possible to create a session object attached to a database handle for\n** which a pre-update hook is already defined. The results of attempting \n** either of these things are undefined.\n**\n** The session object will be used to create changesets for tables in\n** database zDb, where zDb is either \"main\", or \"temp\", or the name of an\n** attached database. It is not an error if database zDb is not attached\n** to the database when the session object is created.\n*/\nSQLITE_API int sqlite3session_create(\n  sqlite3 *db,                    /* Database handle */\n  const char *zDb,                /* Name of db (e.g. \"main\") */\n  sqlite3_session **ppSession     /* OUT: New session object */\n);\n\n/*\n** CAPI3REF: Delete A Session Object\n**\n** Delete a session object previously allocated using \n** [sqlite3session_create()]. Once a session object has been deleted, the\n** results of attempting to use pSession with any other session module\n** function are undefined.\n**\n** Session objects must be deleted before the database handle to which they\n** are attached is closed. Refer to the documentation for \n** [sqlite3session_create()] for details.\n*/\nSQLITE_API void sqlite3session_delete(sqlite3_session *pSession);\n\n\n/*\n** CAPI3REF: Enable Or Disable A Session Object\n**\n** Enable or disable the recording of changes by a session object. When\n** enabled, a session object records changes made to the database. When\n** disabled - it does not. A newly created session object is enabled.\n** Refer to the documentation for [sqlite3session_changeset()] for further\n** details regarding how enabling and disabling a session object affects\n** the eventual changesets.\n**\n** Passing zero to this function disables the session. Passing a value\n** greater than zero enables it. Passing a value less than zero is a \n** no-op, and may be used to query the current state of the session.\n**\n** The return value indicates the final state of the session object: 0 if \n** the session is disabled, or 1 if it is enabled.\n*/\nSQLITE_API int sqlite3session_enable(sqlite3_session *pSession, int bEnable);\n\n/*\n** CAPI3REF: Set Or Clear the Indirect Change Flag\n**\n** Each change recorded by a session object is marked as either direct or\n** indirect. A change is marked as indirect if either:\n**\n** <ul>\n**   <li> The session object \"indirect\" flag is set when the change is\n**        made, or\n**   <li> The change is made by an SQL trigger or foreign key action \n**        instead of directly as a result of a users SQL statement.\n** </ul>\n**\n** If a single row is affected by more than one operation within a session,\n** then the change is considered indirect if all operations meet the criteria\n** for an indirect change above, or direct otherwise.\n**\n** This function is used to set, clear or query the session object indirect\n** flag.  If the second argument passed to this function is zero, then the\n** indirect flag is cleared. If it is greater than zero, the indirect flag\n** is set. Passing a value less than zero does not modify the current value\n** of the indirect flag, and may be used to query the current state of the \n** indirect flag for the specified session object.\n**\n** The return value indicates the final state of the indirect flag: 0 if \n** it is clear, or 1 if it is set.\n*/\nSQLITE_API int sqlite3session_indirect(sqlite3_session *pSession, int bIndirect);\n\n/*\n** CAPI3REF: Attach A Table To A Session Object\n**\n** If argument zTab is not NULL, then it is the name of a table to attach\n** to the session object passed as the first argument. All subsequent changes \n** made to the table while the session object is enabled will be recorded. See \n** documentation for [sqlite3session_changeset()] for further details.\n**\n** Or, if argument zTab is NULL, then changes are recorded for all tables\n** in the database. If additional tables are added to the database (by \n** executing \"CREATE TABLE\" statements) after this call is made, changes for \n** the new tables are also recorded.\n**\n** Changes can only be recorded for tables that have a PRIMARY KEY explicitly\n** defined as part of their CREATE TABLE statement. It does not matter if the \n** PRIMARY KEY is an \"INTEGER PRIMARY KEY\" (rowid alias) or not. The PRIMARY\n** KEY may consist of a single column, or may be a composite key.\n** \n** It is not an error if the named table does not exist in the database. Nor\n** is it an error if the named table does not have a PRIMARY KEY. However,\n** no changes will be recorded in either of these scenarios.\n**\n** Changes are not recorded for individual rows that have NULL values stored\n** in one or more of their PRIMARY KEY columns.\n**\n** SQLITE_OK is returned if the call completes without error. Or, if an error \n** occurs, an SQLite error code (e.g. SQLITE_NOMEM) is returned.\n**\n** <h3>Special sqlite_stat1 Handling</h3>\n**\n** As of SQLite version 3.22.0, the \"sqlite_stat1\" table is an exception to \n** some of the rules above. In SQLite, the schema of sqlite_stat1 is:\n**  <pre>\n**  &nbsp;     CREATE TABLE sqlite_stat1(tbl,idx,stat)  \n**  </pre>\n**\n** Even though sqlite_stat1 does not have a PRIMARY KEY, changes are \n** recorded for it as if the PRIMARY KEY is (tbl,idx). Additionally, changes \n** are recorded for rows for which (idx IS NULL) is true. However, for such\n** rows a zero-length blob (SQL value X'') is stored in the changeset or\n** patchset instead of a NULL value. This allows such changesets to be\n** manipulated by legacy implementations of sqlite3changeset_invert(),\n** concat() and similar.\n**\n** The sqlite3changeset_apply() function automatically converts the \n** zero-length blob back to a NULL value when updating the sqlite_stat1\n** table. However, if the application calls sqlite3changeset_new(),\n** sqlite3changeset_old() or sqlite3changeset_conflict on a changeset \n** iterator directly (including on a changeset iterator passed to a\n** conflict-handler callback) then the X'' value is returned. The application\n** must translate X'' to NULL itself if required.\n**\n** Legacy (older than 3.22.0) versions of the sessions module cannot capture\n** changes made to the sqlite_stat1 table. Legacy versions of the\n** sqlite3changeset_apply() function silently ignore any modifications to the\n** sqlite_stat1 table that are part of a changeset or patchset.\n*/\nSQLITE_API int sqlite3session_attach(\n  sqlite3_session *pSession,      /* Session object */\n  const char *zTab                /* Table name */\n);\n\n/*\n** CAPI3REF: Set a table filter on a Session Object.\n**\n** The second argument (xFilter) is the \"filter callback\". For changes to rows \n** in tables that are not attached to the Session object, the filter is called\n** to determine whether changes to the table's rows should be tracked or not. \n** If xFilter returns 0, changes is not tracked. Note that once a table is \n** attached, xFilter will not be called again.\n*/\nSQLITE_API void sqlite3session_table_filter(\n  sqlite3_session *pSession,      /* Session object */\n  int(*xFilter)(\n    void *pCtx,                   /* Copy of third arg to _filter_table() */\n    const char *zTab              /* Table name */\n  ),\n  void *pCtx                      /* First argument passed to xFilter */\n);\n\n/*\n** CAPI3REF: Generate A Changeset From A Session Object\n**\n** Obtain a changeset containing changes to the tables attached to the \n** session object passed as the first argument. If successful, \n** set *ppChangeset to point to a buffer containing the changeset \n** and *pnChangeset to the size of the changeset in bytes before returning\n** SQLITE_OK. If an error occurs, set both *ppChangeset and *pnChangeset to\n** zero and return an SQLite error code.\n**\n** A changeset consists of zero or more INSERT, UPDATE and/or DELETE changes,\n** each representing a change to a single row of an attached table. An INSERT\n** change contains the values of each field of a new database row. A DELETE\n** contains the original values of each field of a deleted database row. An\n** UPDATE change contains the original values of each field of an updated\n** database row along with the updated values for each updated non-primary-key\n** column. It is not possible for an UPDATE change to represent a change that\n** modifies the values of primary key columns. If such a change is made, it\n** is represented in a changeset as a DELETE followed by an INSERT.\n**\n** Changes are not recorded for rows that have NULL values stored in one or \n** more of their PRIMARY KEY columns. If such a row is inserted or deleted,\n** no corresponding change is present in the changesets returned by this\n** function. If an existing row with one or more NULL values stored in\n** PRIMARY KEY columns is updated so that all PRIMARY KEY columns are non-NULL,\n** only an INSERT is appears in the changeset. Similarly, if an existing row\n** with non-NULL PRIMARY KEY values is updated so that one or more of its\n** PRIMARY KEY columns are set to NULL, the resulting changeset contains a\n** DELETE change only.\n**\n** The contents of a changeset may be traversed using an iterator created\n** using the [sqlite3changeset_start()] API. A changeset may be applied to\n** a database with a compatible schema using the [sqlite3changeset_apply()]\n** API.\n**\n** Within a changeset generated by this function, all changes related to a\n** single table are grouped together. In other words, when iterating through\n** a changeset or when applying a changeset to a database, all changes related\n** to a single table are processed before moving on to the next table. Tables\n** are sorted in the same order in which they were attached (or auto-attached)\n** to the sqlite3_session object. The order in which the changes related to\n** a single table are stored is undefined.\n**\n** Following a successful call to this function, it is the responsibility of\n** the caller to eventually free the buffer that *ppChangeset points to using\n** [sqlite3_free()].\n**\n** <h3>Changeset Generation</h3>\n**\n** Once a table has been attached to a session object, the session object\n** records the primary key values of all new rows inserted into the table.\n** It also records the original primary key and other column values of any\n** deleted or updated rows. For each unique primary key value, data is only\n** recorded once - the first time a row with said primary key is inserted,\n** updated or deleted in the lifetime of the session.\n**\n** There is one exception to the previous paragraph: when a row is inserted,\n** updated or deleted, if one or more of its primary key columns contain a\n** NULL value, no record of the change is made.\n**\n** The session object therefore accumulates two types of records - those\n** that consist of primary key values only (created when the user inserts\n** a new record) and those that consist of the primary key values and the\n** original values of other table columns (created when the users deletes\n** or updates a record).\n**\n** When this function is called, the requested changeset is created using\n** both the accumulated records and the current contents of the database\n** file. Specifically:\n**\n** <ul>\n**   <li> For each record generated by an insert, the database is queried\n**        for a row with a matching primary key. If one is found, an INSERT\n**        change is added to the changeset. If no such row is found, no change \n**        is added to the changeset.\n**\n**   <li> For each record generated by an update or delete, the database is \n**        queried for a row with a matching primary key. If such a row is\n**        found and one or more of the non-primary key fields have been\n**        modified from their original values, an UPDATE change is added to \n**        the changeset. Or, if no such row is found in the table, a DELETE \n**        change is added to the changeset. If there is a row with a matching\n**        primary key in the database, but all fields contain their original\n**        values, no change is added to the changeset.\n** </ul>\n**\n** This means, amongst other things, that if a row is inserted and then later\n** deleted while a session object is active, neither the insert nor the delete\n** will be present in the changeset. Or if a row is deleted and then later a \n** row with the same primary key values inserted while a session object is\n** active, the resulting changeset will contain an UPDATE change instead of\n** a DELETE and an INSERT.\n**\n** When a session object is disabled (see the [sqlite3session_enable()] API),\n** it does not accumulate records when rows are inserted, updated or deleted.\n** This may appear to have some counter-intuitive effects if a single row\n** is written to more than once during a session. For example, if a row\n** is inserted while a session object is enabled, then later deleted while \n** the same session object is disabled, no INSERT record will appear in the\n** changeset, even though the delete took place while the session was disabled.\n** Or, if one field of a row is updated while a session is disabled, and \n** another field of the same row is updated while the session is enabled, the\n** resulting changeset will contain an UPDATE change that updates both fields.\n*/\nSQLITE_API int sqlite3session_changeset(\n  sqlite3_session *pSession,      /* Session object */\n  int *pnChangeset,               /* OUT: Size of buffer at *ppChangeset */\n  void **ppChangeset              /* OUT: Buffer containing changeset */\n);\n\n/*\n** CAPI3REF: Load The Difference Between Tables Into A Session \n**\n** If it is not already attached to the session object passed as the first\n** argument, this function attaches table zTbl in the same manner as the\n** [sqlite3session_attach()] function. If zTbl does not exist, or if it\n** does not have a primary key, this function is a no-op (but does not return\n** an error).\n**\n** Argument zFromDb must be the name of a database (\"main\", \"temp\" etc.)\n** attached to the same database handle as the session object that contains \n** a table compatible with the table attached to the session by this function.\n** A table is considered compatible if it:\n**\n** <ul>\n**   <li> Has the same name,\n**   <li> Has the same set of columns declared in the same order, and\n**   <li> Has the same PRIMARY KEY definition.\n** </ul>\n**\n** If the tables are not compatible, SQLITE_SCHEMA is returned. If the tables\n** are compatible but do not have any PRIMARY KEY columns, it is not an error\n** but no changes are added to the session object. As with other session\n** APIs, tables without PRIMARY KEYs are simply ignored.\n**\n** This function adds a set of changes to the session object that could be\n** used to update the table in database zFrom (call this the \"from-table\") \n** so that its content is the same as the table attached to the session \n** object (call this the \"to-table\"). Specifically:\n**\n** <ul>\n**   <li> For each row (primary key) that exists in the to-table but not in \n**     the from-table, an INSERT record is added to the session object.\n**\n**   <li> For each row (primary key) that exists in the to-table but not in \n**     the from-table, a DELETE record is added to the session object.\n**\n**   <li> For each row (primary key) that exists in both tables, but features \n**     different non-PK values in each, an UPDATE record is added to the\n**     session.  \n** </ul>\n**\n** To clarify, if this function is called and then a changeset constructed\n** using [sqlite3session_changeset()], then after applying that changeset to \n** database zFrom the contents of the two compatible tables would be \n** identical.\n**\n** It an error if database zFrom does not exist or does not contain the\n** required compatible table.\n**\n** If the operation successful, SQLITE_OK is returned. Otherwise, an SQLite\n** error code. In this case, if argument pzErrMsg is not NULL, *pzErrMsg\n** may be set to point to a buffer containing an English language error \n** message. It is the responsibility of the caller to free this buffer using\n** sqlite3_free().\n*/\nSQLITE_API int sqlite3session_diff(\n  sqlite3_session *pSession,\n  const char *zFromDb,\n  const char *zTbl,\n  char **pzErrMsg\n);\n\n\n/*\n** CAPI3REF: Generate A Patchset From A Session Object\n**\n** The differences between a patchset and a changeset are that:\n**\n** <ul>\n**   <li> DELETE records consist of the primary key fields only. The \n**        original values of other fields are omitted.\n**   <li> The original values of any modified fields are omitted from \n**        UPDATE records.\n** </ul>\n**\n** A patchset blob may be used with up to date versions of all \n** sqlite3changeset_xxx API functions except for sqlite3changeset_invert(), \n** which returns SQLITE_CORRUPT if it is passed a patchset. Similarly,\n** attempting to use a patchset blob with old versions of the\n** sqlite3changeset_xxx APIs also provokes an SQLITE_CORRUPT error. \n**\n** Because the non-primary key \"old.*\" fields are omitted, no \n** SQLITE_CHANGESET_DATA conflicts can be detected or reported if a patchset\n** is passed to the sqlite3changeset_apply() API. Other conflict types work\n** in the same way as for changesets.\n**\n** Changes within a patchset are ordered in the same way as for changesets\n** generated by the sqlite3session_changeset() function (i.e. all changes for\n** a single table are grouped together, tables appear in the order in which\n** they were attached to the session object).\n*/\nSQLITE_API int sqlite3session_patchset(\n  sqlite3_session *pSession,      /* Session object */\n  int *pnPatchset,                /* OUT: Size of buffer at *ppPatchset */\n  void **ppPatchset               /* OUT: Buffer containing patchset */\n);\n\n/*\n** CAPI3REF: Test if a changeset has recorded any changes.\n**\n** Return non-zero if no changes to attached tables have been recorded by \n** the session object passed as the first argument. Otherwise, if one or \n** more changes have been recorded, return zero.\n**\n** Even if this function returns zero, it is possible that calling\n** [sqlite3session_changeset()] on the session handle may still return a\n** changeset that contains no changes. This can happen when a row in \n** an attached table is modified and then later on the original values \n** are restored. However, if this function returns non-zero, then it is\n** guaranteed that a call to sqlite3session_changeset() will return a \n** changeset containing zero changes.\n*/\nSQLITE_API int sqlite3session_isempty(sqlite3_session *pSession);\n\n/*\n** CAPI3REF: Create An Iterator To Traverse A Changeset \n**\n** Create an iterator used to iterate through the contents of a changeset.\n** If successful, *pp is set to point to the iterator handle and SQLITE_OK\n** is returned. Otherwise, if an error occurs, *pp is set to zero and an\n** SQLite error code is returned.\n**\n** The following functions can be used to advance and query a changeset \n** iterator created by this function:\n**\n** <ul>\n**   <li> [sqlite3changeset_next()]\n**   <li> [sqlite3changeset_op()]\n**   <li> [sqlite3changeset_new()]\n**   <li> [sqlite3changeset_old()]\n** </ul>\n**\n** It is the responsibility of the caller to eventually destroy the iterator\n** by passing it to [sqlite3changeset_finalize()]. The buffer containing the\n** changeset (pChangeset) must remain valid until after the iterator is\n** destroyed.\n**\n** Assuming the changeset blob was created by one of the\n** [sqlite3session_changeset()], [sqlite3changeset_concat()] or\n** [sqlite3changeset_invert()] functions, all changes within the changeset \n** that apply to a single table are grouped together. This means that when \n** an application iterates through a changeset using an iterator created by \n** this function, all changes that relate to a single table are visited \n** consecutively. There is no chance that the iterator will visit a change \n** the applies to table X, then one for table Y, and then later on visit \n** another change for table X.\n*/\nSQLITE_API int sqlite3changeset_start(\n  sqlite3_changeset_iter **pp,    /* OUT: New changeset iterator handle */\n  int nChangeset,                 /* Size of changeset blob in bytes */\n  void *pChangeset                /* Pointer to blob containing changeset */\n);\n\n\n/*\n** CAPI3REF: Advance A Changeset Iterator\n**\n** This function may only be used with iterators created by function\n** [sqlite3changeset_start()]. If it is called on an iterator passed to\n** a conflict-handler callback by [sqlite3changeset_apply()], SQLITE_MISUSE\n** is returned and the call has no effect.\n**\n** Immediately after an iterator is created by sqlite3changeset_start(), it\n** does not point to any change in the changeset. Assuming the changeset\n** is not empty, the first call to this function advances the iterator to\n** point to the first change in the changeset. Each subsequent call advances\n** the iterator to point to the next change in the changeset (if any). If\n** no error occurs and the iterator points to a valid change after a call\n** to sqlite3changeset_next() has advanced it, SQLITE_ROW is returned. \n** Otherwise, if all changes in the changeset have already been visited,\n** SQLITE_DONE is returned.\n**\n** If an error occurs, an SQLite error code is returned. Possible error \n** codes include SQLITE_CORRUPT (if the changeset buffer is corrupt) or \n** SQLITE_NOMEM.\n*/\nSQLITE_API int sqlite3changeset_next(sqlite3_changeset_iter *pIter);\n\n/*\n** CAPI3REF: Obtain The Current Operation From A Changeset Iterator\n**\n** The pIter argument passed to this function may either be an iterator\n** passed to a conflict-handler by [sqlite3changeset_apply()], or an iterator\n** created by [sqlite3changeset_start()]. In the latter case, the most recent\n** call to [sqlite3changeset_next()] must have returned [SQLITE_ROW]. If this\n** is not the case, this function returns [SQLITE_MISUSE].\n**\n** If argument pzTab is not NULL, then *pzTab is set to point to a\n** nul-terminated utf-8 encoded string containing the name of the table\n** affected by the current change. The buffer remains valid until either\n** sqlite3changeset_next() is called on the iterator or until the \n** conflict-handler function returns. If pnCol is not NULL, then *pnCol is \n** set to the number of columns in the table affected by the change. If\n** pbIncorrect is not NULL, then *pbIndirect is set to true (1) if the change\n** is an indirect change, or false (0) otherwise. See the documentation for\n** [sqlite3session_indirect()] for a description of direct and indirect\n** changes. Finally, if pOp is not NULL, then *pOp is set to one of \n** [SQLITE_INSERT], [SQLITE_DELETE] or [SQLITE_UPDATE], depending on the \n** type of change that the iterator currently points to.\n**\n** If no error occurs, SQLITE_OK is returned. If an error does occur, an\n** SQLite error code is returned. The values of the output variables may not\n** be trusted in this case.\n*/\nSQLITE_API int sqlite3changeset_op(\n  sqlite3_changeset_iter *pIter,  /* Iterator object */\n  const char **pzTab,             /* OUT: Pointer to table name */\n  int *pnCol,                     /* OUT: Number of columns in table */\n  int *pOp,                       /* OUT: SQLITE_INSERT, DELETE or UPDATE */\n  int *pbIndirect                 /* OUT: True for an 'indirect' change */\n);\n\n/*\n** CAPI3REF: Obtain The Primary Key Definition Of A Table\n**\n** For each modified table, a changeset includes the following:\n**\n** <ul>\n**   <li> The number of columns in the table, and\n**   <li> Which of those columns make up the tables PRIMARY KEY.\n** </ul>\n**\n** This function is used to find which columns comprise the PRIMARY KEY of\n** the table modified by the change that iterator pIter currently points to.\n** If successful, *pabPK is set to point to an array of nCol entries, where\n** nCol is the number of columns in the table. Elements of *pabPK are set to\n** 0x01 if the corresponding column is part of the tables primary key, or\n** 0x00 if it is not.\n**\n** If argument pnCol is not NULL, then *pnCol is set to the number of columns\n** in the table.\n**\n** If this function is called when the iterator does not point to a valid\n** entry, SQLITE_MISUSE is returned and the output variables zeroed. Otherwise,\n** SQLITE_OK is returned and the output variables populated as described\n** above.\n*/\nSQLITE_API int sqlite3changeset_pk(\n  sqlite3_changeset_iter *pIter,  /* Iterator object */\n  unsigned char **pabPK,          /* OUT: Array of boolean - true for PK cols */\n  int *pnCol                      /* OUT: Number of entries in output array */\n);\n\n/*\n** CAPI3REF: Obtain old.* Values From A Changeset Iterator\n**\n** The pIter argument passed to this function may either be an iterator\n** passed to a conflict-handler by [sqlite3changeset_apply()], or an iterator\n** created by [sqlite3changeset_start()]. In the latter case, the most recent\n** call to [sqlite3changeset_next()] must have returned SQLITE_ROW. \n** Furthermore, it may only be called if the type of change that the iterator\n** currently points to is either [SQLITE_DELETE] or [SQLITE_UPDATE]. Otherwise,\n** this function returns [SQLITE_MISUSE] and sets *ppValue to NULL.\n**\n** Argument iVal must be greater than or equal to 0, and less than the number\n** of columns in the table affected by the current change. Otherwise,\n** [SQLITE_RANGE] is returned and *ppValue is set to NULL.\n**\n** If successful, this function sets *ppValue to point to a protected\n** sqlite3_value object containing the iVal'th value from the vector of \n** original row values stored as part of the UPDATE or DELETE change and\n** returns SQLITE_OK. The name of the function comes from the fact that this \n** is similar to the \"old.*\" columns available to update or delete triggers.\n**\n** If some other error occurs (e.g. an OOM condition), an SQLite error code\n** is returned and *ppValue is set to NULL.\n*/\nSQLITE_API int sqlite3changeset_old(\n  sqlite3_changeset_iter *pIter,  /* Changeset iterator */\n  int iVal,                       /* Column number */\n  sqlite3_value **ppValue         /* OUT: Old value (or NULL pointer) */\n);\n\n/*\n** CAPI3REF: Obtain new.* Values From A Changeset Iterator\n**\n** The pIter argument passed to this function may either be an iterator\n** passed to a conflict-handler by [sqlite3changeset_apply()], or an iterator\n** created by [sqlite3changeset_start()]. In the latter case, the most recent\n** call to [sqlite3changeset_next()] must have returned SQLITE_ROW. \n** Furthermore, it may only be called if the type of change that the iterator\n** currently points to is either [SQLITE_UPDATE] or [SQLITE_INSERT]. Otherwise,\n** this function returns [SQLITE_MISUSE] and sets *ppValue to NULL.\n**\n** Argument iVal must be greater than or equal to 0, and less than the number\n** of columns in the table affected by the current change. Otherwise,\n** [SQLITE_RANGE] is returned and *ppValue is set to NULL.\n**\n** If successful, this function sets *ppValue to point to a protected\n** sqlite3_value object containing the iVal'th value from the vector of \n** new row values stored as part of the UPDATE or INSERT change and\n** returns SQLITE_OK. If the change is an UPDATE and does not include\n** a new value for the requested column, *ppValue is set to NULL and \n** SQLITE_OK returned. The name of the function comes from the fact that \n** this is similar to the \"new.*\" columns available to update or delete \n** triggers.\n**\n** If some other error occurs (e.g. an OOM condition), an SQLite error code\n** is returned and *ppValue is set to NULL.\n*/\nSQLITE_API int sqlite3changeset_new(\n  sqlite3_changeset_iter *pIter,  /* Changeset iterator */\n  int iVal,                       /* Column number */\n  sqlite3_value **ppValue         /* OUT: New value (or NULL pointer) */\n);\n\n/*\n** CAPI3REF: Obtain Conflicting Row Values From A Changeset Iterator\n**\n** This function should only be used with iterator objects passed to a\n** conflict-handler callback by [sqlite3changeset_apply()] with either\n** [SQLITE_CHANGESET_DATA] or [SQLITE_CHANGESET_CONFLICT]. If this function\n** is called on any other iterator, [SQLITE_MISUSE] is returned and *ppValue\n** is set to NULL.\n**\n** Argument iVal must be greater than or equal to 0, and less than the number\n** of columns in the table affected by the current change. Otherwise,\n** [SQLITE_RANGE] is returned and *ppValue is set to NULL.\n**\n** If successful, this function sets *ppValue to point to a protected\n** sqlite3_value object containing the iVal'th value from the \n** \"conflicting row\" associated with the current conflict-handler callback\n** and returns SQLITE_OK.\n**\n** If some other error occurs (e.g. an OOM condition), an SQLite error code\n** is returned and *ppValue is set to NULL.\n*/\nSQLITE_API int sqlite3changeset_conflict(\n  sqlite3_changeset_iter *pIter,  /* Changeset iterator */\n  int iVal,                       /* Column number */\n  sqlite3_value **ppValue         /* OUT: Value from conflicting row */\n);\n\n/*\n** CAPI3REF: Determine The Number Of Foreign Key Constraint Violations\n**\n** This function may only be called with an iterator passed to an\n** SQLITE_CHANGESET_FOREIGN_KEY conflict handler callback. In this case\n** it sets the output variable to the total number of known foreign key\n** violations in the destination database and returns SQLITE_OK.\n**\n** In all other cases this function returns SQLITE_MISUSE.\n*/\nSQLITE_API int sqlite3changeset_fk_conflicts(\n  sqlite3_changeset_iter *pIter,  /* Changeset iterator */\n  int *pnOut                      /* OUT: Number of FK violations */\n);\n\n\n/*\n** CAPI3REF: Finalize A Changeset Iterator\n**\n** This function is used to finalize an iterator allocated with\n** [sqlite3changeset_start()].\n**\n** This function should only be called on iterators created using the\n** [sqlite3changeset_start()] function. If an application calls this\n** function with an iterator passed to a conflict-handler by\n** [sqlite3changeset_apply()], [SQLITE_MISUSE] is immediately returned and the\n** call has no effect.\n**\n** If an error was encountered within a call to an sqlite3changeset_xxx()\n** function (for example an [SQLITE_CORRUPT] in [sqlite3changeset_next()] or an \n** [SQLITE_NOMEM] in [sqlite3changeset_new()]) then an error code corresponding\n** to that error is returned by this function. Otherwise, SQLITE_OK is\n** returned. This is to allow the following pattern (pseudo-code):\n**\n**   sqlite3changeset_start();\n**   while( SQLITE_ROW==sqlite3changeset_next() ){\n**     // Do something with change.\n**   }\n**   rc = sqlite3changeset_finalize();\n**   if( rc!=SQLITE_OK ){\n**     // An error has occurred \n**   }\n*/\nSQLITE_API int sqlite3changeset_finalize(sqlite3_changeset_iter *pIter);\n\n/*\n** CAPI3REF: Invert A Changeset\n**\n** This function is used to \"invert\" a changeset object. Applying an inverted\n** changeset to a database reverses the effects of applying the uninverted\n** changeset. Specifically:\n**\n** <ul>\n**   <li> Each DELETE change is changed to an INSERT, and\n**   <li> Each INSERT change is changed to a DELETE, and\n**   <li> For each UPDATE change, the old.* and new.* values are exchanged.\n** </ul>\n**\n** This function does not change the order in which changes appear within\n** the changeset. It merely reverses the sense of each individual change.\n**\n** If successful, a pointer to a buffer containing the inverted changeset\n** is stored in *ppOut, the size of the same buffer is stored in *pnOut, and\n** SQLITE_OK is returned. If an error occurs, both *pnOut and *ppOut are\n** zeroed and an SQLite error code returned.\n**\n** It is the responsibility of the caller to eventually call sqlite3_free()\n** on the *ppOut pointer to free the buffer allocation following a successful \n** call to this function.\n**\n** WARNING/TODO: This function currently assumes that the input is a valid\n** changeset. If it is not, the results are undefined.\n*/\nSQLITE_API int sqlite3changeset_invert(\n  int nIn, const void *pIn,       /* Input changeset */\n  int *pnOut, void **ppOut        /* OUT: Inverse of input */\n);\n\n/*\n** CAPI3REF: Concatenate Two Changeset Objects\n**\n** This function is used to concatenate two changesets, A and B, into a \n** single changeset. The result is a changeset equivalent to applying\n** changeset A followed by changeset B. \n**\n** This function combines the two input changesets using an \n** sqlite3_changegroup object. Calling it produces similar results as the\n** following code fragment:\n**\n**   sqlite3_changegroup *pGrp;\n**   rc = sqlite3_changegroup_new(&pGrp);\n**   if( rc==SQLITE_OK ) rc = sqlite3changegroup_add(pGrp, nA, pA);\n**   if( rc==SQLITE_OK ) rc = sqlite3changegroup_add(pGrp, nB, pB);\n**   if( rc==SQLITE_OK ){\n**     rc = sqlite3changegroup_output(pGrp, pnOut, ppOut);\n**   }else{\n**     *ppOut = 0;\n**     *pnOut = 0;\n**   }\n**\n** Refer to the sqlite3_changegroup documentation below for details.\n*/\nSQLITE_API int sqlite3changeset_concat(\n  int nA,                         /* Number of bytes in buffer pA */\n  void *pA,                       /* Pointer to buffer containing changeset A */\n  int nB,                         /* Number of bytes in buffer pB */\n  void *pB,                       /* Pointer to buffer containing changeset B */\n  int *pnOut,                     /* OUT: Number of bytes in output changeset */\n  void **ppOut                    /* OUT: Buffer containing output changeset */\n);\n\n\n/*\n** CAPI3REF: Changegroup Handle\n*/\ntypedef struct sqlite3_changegroup sqlite3_changegroup;\n\n/*\n** CAPI3REF: Create A New Changegroup Object\n**\n** An sqlite3_changegroup object is used to combine two or more changesets\n** (or patchsets) into a single changeset (or patchset). A single changegroup\n** object may combine changesets or patchsets, but not both. The output is\n** always in the same format as the input.\n**\n** If successful, this function returns SQLITE_OK and populates (*pp) with\n** a pointer to a new sqlite3_changegroup object before returning. The caller\n** should eventually free the returned object using a call to \n** sqlite3changegroup_delete(). If an error occurs, an SQLite error code\n** (i.e. SQLITE_NOMEM) is returned and *pp is set to NULL.\n**\n** The usual usage pattern for an sqlite3_changegroup object is as follows:\n**\n** <ul>\n**   <li> It is created using a call to sqlite3changegroup_new().\n**\n**   <li> Zero or more changesets (or patchsets) are added to the object\n**        by calling sqlite3changegroup_add().\n**\n**   <li> The result of combining all input changesets together is obtained \n**        by the application via a call to sqlite3changegroup_output().\n**\n**   <li> The object is deleted using a call to sqlite3changegroup_delete().\n** </ul>\n**\n** Any number of calls to add() and output() may be made between the calls to\n** new() and delete(), and in any order.\n**\n** As well as the regular sqlite3changegroup_add() and \n** sqlite3changegroup_output() functions, also available are the streaming\n** versions sqlite3changegroup_add_strm() and sqlite3changegroup_output_strm().\n*/\nSQLITE_API int sqlite3changegroup_new(sqlite3_changegroup **pp);\n\n/*\n** CAPI3REF: Add A Changeset To A Changegroup\n**\n** Add all changes within the changeset (or patchset) in buffer pData (size\n** nData bytes) to the changegroup. \n**\n** If the buffer contains a patchset, then all prior calls to this function\n** on the same changegroup object must also have specified patchsets. Or, if\n** the buffer contains a changeset, so must have the earlier calls to this\n** function. Otherwise, SQLITE_ERROR is returned and no changes are added\n** to the changegroup.\n**\n** Rows within the changeset and changegroup are identified by the values in\n** their PRIMARY KEY columns. A change in the changeset is considered to\n** apply to the same row as a change already present in the changegroup if\n** the two rows have the same primary key.\n**\n** Changes to rows that do not already appear in the changegroup are\n** simply copied into it. Or, if both the new changeset and the changegroup\n** contain changes that apply to a single row, the final contents of the\n** changegroup depends on the type of each change, as follows:\n**\n** <table border=1 style=\"margin-left:8ex;margin-right:8ex\">\n**   <tr><th style=\"white-space:pre\">Existing Change  </th>\n**       <th style=\"white-space:pre\">New Change       </th>\n**       <th>Output Change\n**   <tr><td>INSERT <td>INSERT <td>\n**       The new change is ignored. This case does not occur if the new\n**       changeset was recorded immediately after the changesets already\n**       added to the changegroup.\n**   <tr><td>INSERT <td>UPDATE <td>\n**       The INSERT change remains in the changegroup. The values in the \n**       INSERT change are modified as if the row was inserted by the\n**       existing change and then updated according to the new change.\n**   <tr><td>INSERT <td>DELETE <td>\n**       The existing INSERT is removed from the changegroup. The DELETE is\n**       not added.\n**   <tr><td>UPDATE <td>INSERT <td>\n**       The new change is ignored. This case does not occur if the new\n**       changeset was recorded immediately after the changesets already\n**       added to the changegroup.\n**   <tr><td>UPDATE <td>UPDATE <td>\n**       The existing UPDATE remains within the changegroup. It is amended \n**       so that the accompanying values are as if the row was updated once \n**       by the existing change and then again by the new change.\n**   <tr><td>UPDATE <td>DELETE <td>\n**       The existing UPDATE is replaced by the new DELETE within the\n**       changegroup.\n**   <tr><td>DELETE <td>INSERT <td>\n**       If one or more of the column values in the row inserted by the\n**       new change differ from those in the row deleted by the existing \n**       change, the existing DELETE is replaced by an UPDATE within the\n**       changegroup. Otherwise, if the inserted row is exactly the same \n**       as the deleted row, the existing DELETE is simply discarded.\n**   <tr><td>DELETE <td>UPDATE <td>\n**       The new change is ignored. This case does not occur if the new\n**       changeset was recorded immediately after the changesets already\n**       added to the changegroup.\n**   <tr><td>DELETE <td>DELETE <td>\n**       The new change is ignored. This case does not occur if the new\n**       changeset was recorded immediately after the changesets already\n**       added to the changegroup.\n** </table>\n**\n** If the new changeset contains changes to a table that is already present\n** in the changegroup, then the number of columns and the position of the\n** primary key columns for the table must be consistent. If this is not the\n** case, this function fails with SQLITE_SCHEMA. If the input changeset\n** appears to be corrupt and the corruption is detected, SQLITE_CORRUPT is\n** returned. Or, if an out-of-memory condition occurs during processing, this\n** function returns SQLITE_NOMEM. In all cases, if an error occurs the\n** final contents of the changegroup is undefined.\n**\n** If no error occurs, SQLITE_OK is returned.\n*/\nSQLITE_API int sqlite3changegroup_add(sqlite3_changegroup*, int nData, void *pData);\n\n/*\n** CAPI3REF: Obtain A Composite Changeset From A Changegroup\n**\n** Obtain a buffer containing a changeset (or patchset) representing the\n** current contents of the changegroup. If the inputs to the changegroup\n** were themselves changesets, the output is a changeset. Or, if the\n** inputs were patchsets, the output is also a patchset.\n**\n** As with the output of the sqlite3session_changeset() and\n** sqlite3session_patchset() functions, all changes related to a single\n** table are grouped together in the output of this function. Tables appear\n** in the same order as for the very first changeset added to the changegroup.\n** If the second or subsequent changesets added to the changegroup contain\n** changes for tables that do not appear in the first changeset, they are\n** appended onto the end of the output changeset, again in the order in\n** which they are first encountered.\n**\n** If an error occurs, an SQLite error code is returned and the output\n** variables (*pnData) and (*ppData) are set to 0. Otherwise, SQLITE_OK\n** is returned and the output variables are set to the size of and a \n** pointer to the output buffer, respectively. In this case it is the\n** responsibility of the caller to eventually free the buffer using a\n** call to sqlite3_free().\n*/\nSQLITE_API int sqlite3changegroup_output(\n  sqlite3_changegroup*,\n  int *pnData,                    /* OUT: Size of output buffer in bytes */\n  void **ppData                   /* OUT: Pointer to output buffer */\n);\n\n/*\n** CAPI3REF: Delete A Changegroup Object\n*/\nSQLITE_API void sqlite3changegroup_delete(sqlite3_changegroup*);\n\n/*\n** CAPI3REF: Apply A Changeset To A Database\n**\n** Apply a changeset to a database. This function attempts to update the\n** \"main\" database attached to handle db with the changes found in the\n** changeset passed via the second and third arguments.\n**\n** The fourth argument (xFilter) passed to this function is the \"filter\n** callback\". If it is not NULL, then for each table affected by at least one\n** change in the changeset, the filter callback is invoked with\n** the table name as the second argument, and a copy of the context pointer\n** passed as the sixth argument to this function as the first. If the \"filter\n** callback\" returns zero, then no attempt is made to apply any changes to \n** the table. Otherwise, if the return value is non-zero or the xFilter\n** argument to this function is NULL, all changes related to the table are\n** attempted.\n**\n** For each table that is not excluded by the filter callback, this function \n** tests that the target database contains a compatible table. A table is \n** considered compatible if all of the following are true:\n**\n** <ul>\n**   <li> The table has the same name as the name recorded in the \n**        changeset, and\n**   <li> The table has at least as many columns as recorded in the \n**        changeset, and\n**   <li> The table has primary key columns in the same position as \n**        recorded in the changeset.\n** </ul>\n**\n** If there is no compatible table, it is not an error, but none of the\n** changes associated with the table are applied. A warning message is issued\n** via the sqlite3_log() mechanism with the error code SQLITE_SCHEMA. At most\n** one such warning is issued for each table in the changeset.\n**\n** For each change for which there is a compatible table, an attempt is made \n** to modify the table contents according to the UPDATE, INSERT or DELETE \n** change. If a change cannot be applied cleanly, the conflict handler \n** function passed as the fifth argument to sqlite3changeset_apply() may be \n** invoked. A description of exactly when the conflict handler is invoked for \n** each type of change is below.\n**\n** Unlike the xFilter argument, xConflict may not be passed NULL. The results\n** of passing anything other than a valid function pointer as the xConflict\n** argument are undefined.\n**\n** Each time the conflict handler function is invoked, it must return one\n** of [SQLITE_CHANGESET_OMIT], [SQLITE_CHANGESET_ABORT] or \n** [SQLITE_CHANGESET_REPLACE]. SQLITE_CHANGESET_REPLACE may only be returned\n** if the second argument passed to the conflict handler is either\n** SQLITE_CHANGESET_DATA or SQLITE_CHANGESET_CONFLICT. If the conflict-handler\n** returns an illegal value, any changes already made are rolled back and\n** the call to sqlite3changeset_apply() returns SQLITE_MISUSE. Different \n** actions are taken by sqlite3changeset_apply() depending on the value\n** returned by each invocation of the conflict-handler function. Refer to\n** the documentation for the three \n** [SQLITE_CHANGESET_OMIT|available return values] for details.\n**\n** <dl>\n** <dt>DELETE Changes<dd>\n**   For each DELETE change, this function checks if the target database \n**   contains a row with the same primary key value (or values) as the \n**   original row values stored in the changeset. If it does, and the values \n**   stored in all non-primary key columns also match the values stored in \n**   the changeset the row is deleted from the target database.\n**\n**   If a row with matching primary key values is found, but one or more of\n**   the non-primary key fields contains a value different from the original\n**   row value stored in the changeset, the conflict-handler function is\n**   invoked with [SQLITE_CHANGESET_DATA] as the second argument. If the\n**   database table has more columns than are recorded in the changeset,\n**   only the values of those non-primary key fields are compared against\n**   the current database contents - any trailing database table columns\n**   are ignored.\n**\n**   If no row with matching primary key values is found in the database,\n**   the conflict-handler function is invoked with [SQLITE_CHANGESET_NOTFOUND]\n**   passed as the second argument.\n**\n**   If the DELETE operation is attempted, but SQLite returns SQLITE_CONSTRAINT\n**   (which can only happen if a foreign key constraint is violated), the\n**   conflict-handler function is invoked with [SQLITE_CHANGESET_CONSTRAINT]\n**   passed as the second argument. This includes the case where the DELETE\n**   operation is attempted because an earlier call to the conflict handler\n**   function returned [SQLITE_CHANGESET_REPLACE].\n**\n** <dt>INSERT Changes<dd>\n**   For each INSERT change, an attempt is made to insert the new row into\n**   the database. If the changeset row contains fewer fields than the\n**   database table, the trailing fields are populated with their default\n**   values.\n**\n**   If the attempt to insert the row fails because the database already \n**   contains a row with the same primary key values, the conflict handler\n**   function is invoked with the second argument set to \n**   [SQLITE_CHANGESET_CONFLICT].\n**\n**   If the attempt to insert the row fails because of some other constraint\n**   violation (e.g. NOT NULL or UNIQUE), the conflict handler function is \n**   invoked with the second argument set to [SQLITE_CHANGESET_CONSTRAINT].\n**   This includes the case where the INSERT operation is re-attempted because \n**   an earlier call to the conflict handler function returned \n**   [SQLITE_CHANGESET_REPLACE].\n**\n** <dt>UPDATE Changes<dd>\n**   For each UPDATE change, this function checks if the target database \n**   contains a row with the same primary key value (or values) as the \n**   original row values stored in the changeset. If it does, and the values \n**   stored in all modified non-primary key columns also match the values\n**   stored in the changeset the row is updated within the target database.\n**\n**   If a row with matching primary key values is found, but one or more of\n**   the modified non-primary key fields contains a value different from an\n**   original row value stored in the changeset, the conflict-handler function\n**   is invoked with [SQLITE_CHANGESET_DATA] as the second argument. Since\n**   UPDATE changes only contain values for non-primary key fields that are\n**   to be modified, only those fields need to match the original values to\n**   avoid the SQLITE_CHANGESET_DATA conflict-handler callback.\n**\n**   If no row with matching primary key values is found in the database,\n**   the conflict-handler function is invoked with [SQLITE_CHANGESET_NOTFOUND]\n**   passed as the second argument.\n**\n**   If the UPDATE operation is attempted, but SQLite returns \n**   SQLITE_CONSTRAINT, the conflict-handler function is invoked with \n**   [SQLITE_CHANGESET_CONSTRAINT] passed as the second argument.\n**   This includes the case where the UPDATE operation is attempted after \n**   an earlier call to the conflict handler function returned\n**   [SQLITE_CHANGESET_REPLACE].  \n** </dl>\n**\n** It is safe to execute SQL statements, including those that write to the\n** table that the callback related to, from within the xConflict callback.\n** This can be used to further customize the applications conflict\n** resolution strategy.\n**\n** All changes made by this function are enclosed in a savepoint transaction.\n** If any other error (aside from a constraint failure when attempting to\n** write to the target database) occurs, then the savepoint transaction is\n** rolled back, restoring the target database to its original state, and an \n** SQLite error code returned.\n*/\nSQLITE_API int sqlite3changeset_apply(\n  sqlite3 *db,                    /* Apply change to \"main\" db of this handle */\n  int nChangeset,                 /* Size of changeset in bytes */\n  void *pChangeset,               /* Changeset blob */\n  int(*xFilter)(\n    void *pCtx,                   /* Copy of sixth arg to _apply() */\n    const char *zTab              /* Table name */\n  ),\n  int(*xConflict)(\n    void *pCtx,                   /* Copy of sixth arg to _apply() */\n    int eConflict,                /* DATA, MISSING, CONFLICT, CONSTRAINT */\n    sqlite3_changeset_iter *p     /* Handle describing change and conflict */\n  ),\n  void *pCtx                      /* First argument passed to xConflict */\n);\n\n/* \n** CAPI3REF: Constants Passed To The Conflict Handler\n**\n** Values that may be passed as the second argument to a conflict-handler.\n**\n** <dl>\n** <dt>SQLITE_CHANGESET_DATA<dd>\n**   The conflict handler is invoked with CHANGESET_DATA as the second argument\n**   when processing a DELETE or UPDATE change if a row with the required\n**   PRIMARY KEY fields is present in the database, but one or more other \n**   (non primary-key) fields modified by the update do not contain the \n**   expected \"before\" values.\n** \n**   The conflicting row, in this case, is the database row with the matching\n**   primary key.\n** \n** <dt>SQLITE_CHANGESET_NOTFOUND<dd>\n**   The conflict handler is invoked with CHANGESET_NOTFOUND as the second\n**   argument when processing a DELETE or UPDATE change if a row with the\n**   required PRIMARY KEY fields is not present in the database.\n** \n**   There is no conflicting row in this case. The results of invoking the\n**   sqlite3changeset_conflict() API are undefined.\n** \n** <dt>SQLITE_CHANGESET_CONFLICT<dd>\n**   CHANGESET_CONFLICT is passed as the second argument to the conflict\n**   handler while processing an INSERT change if the operation would result \n**   in duplicate primary key values.\n** \n**   The conflicting row in this case is the database row with the matching\n**   primary key.\n**\n** <dt>SQLITE_CHANGESET_FOREIGN_KEY<dd>\n**   If foreign key handling is enabled, and applying a changeset leaves the\n**   database in a state containing foreign key violations, the conflict \n**   handler is invoked with CHANGESET_FOREIGN_KEY as the second argument\n**   exactly once before the changeset is committed. If the conflict handler\n**   returns CHANGESET_OMIT, the changes, including those that caused the\n**   foreign key constraint violation, are committed. Or, if it returns\n**   CHANGESET_ABORT, the changeset is rolled back.\n**\n**   No current or conflicting row information is provided. The only function\n**   it is possible to call on the supplied sqlite3_changeset_iter handle\n**   is sqlite3changeset_fk_conflicts().\n** \n** <dt>SQLITE_CHANGESET_CONSTRAINT<dd>\n**   If any other constraint violation occurs while applying a change (i.e. \n**   a UNIQUE, CHECK or NOT NULL constraint), the conflict handler is \n**   invoked with CHANGESET_CONSTRAINT as the second argument.\n** \n**   There is no conflicting row in this case. The results of invoking the\n**   sqlite3changeset_conflict() API are undefined.\n**\n** </dl>\n*/\n#define SQLITE_CHANGESET_DATA        1\n#define SQLITE_CHANGESET_NOTFOUND    2\n#define SQLITE_CHANGESET_CONFLICT    3\n#define SQLITE_CHANGESET_CONSTRAINT  4\n#define SQLITE_CHANGESET_FOREIGN_KEY 5\n\n/* \n** CAPI3REF: Constants Returned By The Conflict Handler\n**\n** A conflict handler callback must return one of the following three values.\n**\n** <dl>\n** <dt>SQLITE_CHANGESET_OMIT<dd>\n**   If a conflict handler returns this value no special action is taken. The\n**   change that caused the conflict is not applied. The session module \n**   continues to the next change in the changeset.\n**\n** <dt>SQLITE_CHANGESET_REPLACE<dd>\n**   This value may only be returned if the second argument to the conflict\n**   handler was SQLITE_CHANGESET_DATA or SQLITE_CHANGESET_CONFLICT. If this\n**   is not the case, any changes applied so far are rolled back and the \n**   call to sqlite3changeset_apply() returns SQLITE_MISUSE.\n**\n**   If CHANGESET_REPLACE is returned by an SQLITE_CHANGESET_DATA conflict\n**   handler, then the conflicting row is either updated or deleted, depending\n**   on the type of change.\n**\n**   If CHANGESET_REPLACE is returned by an SQLITE_CHANGESET_CONFLICT conflict\n**   handler, then the conflicting row is removed from the database and a\n**   second attempt to apply the change is made. If this second attempt fails,\n**   the original row is restored to the database before continuing.\n**\n** <dt>SQLITE_CHANGESET_ABORT<dd>\n**   If this value is returned, any changes applied so far are rolled back \n**   and the call to sqlite3changeset_apply() returns SQLITE_ABORT.\n** </dl>\n*/\n#define SQLITE_CHANGESET_OMIT       0\n#define SQLITE_CHANGESET_REPLACE    1\n#define SQLITE_CHANGESET_ABORT      2\n\n/*\n** CAPI3REF: Streaming Versions of API functions.\n**\n** The six streaming API xxx_strm() functions serve similar purposes to the \n** corresponding non-streaming API functions:\n**\n** <table border=1 style=\"margin-left:8ex;margin-right:8ex\">\n**   <tr><th>Streaming function<th>Non-streaming equivalent</th>\n**   <tr><td>sqlite3changeset_apply_strm<td>[sqlite3changeset_apply] \n**   <tr><td>sqlite3changeset_concat_strm<td>[sqlite3changeset_concat] \n**   <tr><td>sqlite3changeset_invert_strm<td>[sqlite3changeset_invert] \n**   <tr><td>sqlite3changeset_start_strm<td>[sqlite3changeset_start] \n**   <tr><td>sqlite3session_changeset_strm<td>[sqlite3session_changeset] \n**   <tr><td>sqlite3session_patchset_strm<td>[sqlite3session_patchset] \n** </table>\n**\n** Non-streaming functions that accept changesets (or patchsets) as input\n** require that the entire changeset be stored in a single buffer in memory. \n** Similarly, those that return a changeset or patchset do so by returning \n** a pointer to a single large buffer allocated using sqlite3_malloc(). \n** Normally this is convenient. However, if an application running in a \n** low-memory environment is required to handle very large changesets, the\n** large contiguous memory allocations required can become onerous.\n**\n** In order to avoid this problem, instead of a single large buffer, input\n** is passed to a streaming API functions by way of a callback function that\n** the sessions module invokes to incrementally request input data as it is\n** required. In all cases, a pair of API function parameters such as\n**\n**  <pre>\n**  &nbsp;     int nChangeset,\n**  &nbsp;     void *pChangeset,\n**  </pre>\n**\n** Is replaced by:\n**\n**  <pre>\n**  &nbsp;     int (*xInput)(void *pIn, void *pData, int *pnData),\n**  &nbsp;     void *pIn,\n**  </pre>\n**\n** Each time the xInput callback is invoked by the sessions module, the first\n** argument passed is a copy of the supplied pIn context pointer. The second \n** argument, pData, points to a buffer (*pnData) bytes in size. Assuming no \n** error occurs the xInput method should copy up to (*pnData) bytes of data \n** into the buffer and set (*pnData) to the actual number of bytes copied \n** before returning SQLITE_OK. If the input is completely exhausted, (*pnData) \n** should be set to zero to indicate this. Or, if an error occurs, an SQLite \n** error code should be returned. In all cases, if an xInput callback returns\n** an error, all processing is abandoned and the streaming API function\n** returns a copy of the error code to the caller.\n**\n** In the case of sqlite3changeset_start_strm(), the xInput callback may be\n** invoked by the sessions module at any point during the lifetime of the\n** iterator. If such an xInput callback returns an error, the iterator enters\n** an error state, whereby all subsequent calls to iterator functions \n** immediately fail with the same error code as returned by xInput.\n**\n** Similarly, streaming API functions that return changesets (or patchsets)\n** return them in chunks by way of a callback function instead of via a\n** pointer to a single large buffer. In this case, a pair of parameters such\n** as:\n**\n**  <pre>\n**  &nbsp;     int *pnChangeset,\n**  &nbsp;     void **ppChangeset,\n**  </pre>\n**\n** Is replaced by:\n**\n**  <pre>\n**  &nbsp;     int (*xOutput)(void *pOut, const void *pData, int nData),\n**  &nbsp;     void *pOut\n**  </pre>\n**\n** The xOutput callback is invoked zero or more times to return data to\n** the application. The first parameter passed to each call is a copy of the\n** pOut pointer supplied by the application. The second parameter, pData,\n** points to a buffer nData bytes in size containing the chunk of output\n** data being returned. If the xOutput callback successfully processes the\n** supplied data, it should return SQLITE_OK to indicate success. Otherwise,\n** it should return some other SQLite error code. In this case processing\n** is immediately abandoned and the streaming API function returns a copy\n** of the xOutput error code to the application.\n**\n** The sessions module never invokes an xOutput callback with the third \n** parameter set to a value less than or equal to zero. Other than this,\n** no guarantees are made as to the size of the chunks of data returned.\n*/\nSQLITE_API int sqlite3changeset_apply_strm(\n  sqlite3 *db,                    /* Apply change to \"main\" db of this handle */\n  int (*xInput)(void *pIn, void *pData, int *pnData), /* Input function */\n  void *pIn,                                          /* First arg for xInput */\n  int(*xFilter)(\n    void *pCtx,                   /* Copy of sixth arg to _apply() */\n    const char *zTab              /* Table name */\n  ),\n  int(*xConflict)(\n    void *pCtx,                   /* Copy of sixth arg to _apply() */\n    int eConflict,                /* DATA, MISSING, CONFLICT, CONSTRAINT */\n    sqlite3_changeset_iter *p     /* Handle describing change and conflict */\n  ),\n  void *pCtx                      /* First argument passed to xConflict */\n);\nSQLITE_API int sqlite3changeset_concat_strm(\n  int (*xInputA)(void *pIn, void *pData, int *pnData),\n  void *pInA,\n  int (*xInputB)(void *pIn, void *pData, int *pnData),\n  void *pInB,\n  int (*xOutput)(void *pOut, const void *pData, int nData),\n  void *pOut\n);\nSQLITE_API int sqlite3changeset_invert_strm(\n  int (*xInput)(void *pIn, void *pData, int *pnData),\n  void *pIn,\n  int (*xOutput)(void *pOut, const void *pData, int nData),\n  void *pOut\n);\nSQLITE_API int sqlite3changeset_start_strm(\n  sqlite3_changeset_iter **pp,\n  int (*xInput)(void *pIn, void *pData, int *pnData),\n  void *pIn\n);\nSQLITE_API int sqlite3session_changeset_strm(\n  sqlite3_session *pSession,\n  int (*xOutput)(void *pOut, const void *pData, int nData),\n  void *pOut\n);\nSQLITE_API int sqlite3session_patchset_strm(\n  sqlite3_session *pSession,\n  int (*xOutput)(void *pOut, const void *pData, int nData),\n  void *pOut\n);\nSQLITE_API int sqlite3changegroup_add_strm(sqlite3_changegroup*, \n    int (*xInput)(void *pIn, void *pData, int *pnData),\n    void *pIn\n);\nSQLITE_API int sqlite3changegroup_output_strm(sqlite3_changegroup*,\n    int (*xOutput)(void *pOut, const void *pData, int nData), \n    void *pOut\n);\n\n\n/*\n** Make sure we can call this stuff from C++.\n*/\n#ifdef __cplusplus\n}\n#endif\n\n#endif  /* !defined(__SQLITESESSION_H_) && defined(SQLITE_ENABLE_SESSION) */\n\n/******** End of sqlite3session.h *********/\n/******** Begin file fts5.h *********/\n/*\n** 2014 May 31\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n******************************************************************************\n**\n** Interfaces to extend FTS5. Using the interfaces defined in this file, \n** FTS5 may be extended with:\n**\n**     * custom tokenizers, and\n**     * custom auxiliary functions.\n*/\n\n\n#ifndef _FTS5_H\n#define _FTS5_H\n\n\n#ifdef __cplusplus\nextern \"C\" {\n#endif\n\n/*************************************************************************\n** CUSTOM AUXILIARY FUNCTIONS\n**\n** Virtual table implementations may overload SQL functions by implementing\n** the sqlite3_module.xFindFunction() method.\n*/\n\ntypedef struct Fts5ExtensionApi Fts5ExtensionApi;\ntypedef struct Fts5Context Fts5Context;\ntypedef struct Fts5PhraseIter Fts5PhraseIter;\n\ntypedef void (*fts5_extension_function)(\n  const Fts5ExtensionApi *pApi,   /* API offered by current FTS version */\n  Fts5Context *pFts,              /* First arg to pass to pApi functions */\n  sqlite3_context *pCtx,          /* Context for returning result/error */\n  int nVal,                       /* Number of values in apVal[] array */\n  sqlite3_value **apVal           /* Array of trailing arguments */\n);\n\nstruct Fts5PhraseIter {\n  const unsigned char *a;\n  const unsigned char *b;\n};\n\n/*\n** EXTENSION API FUNCTIONS\n**\n** xUserData(pFts):\n**   Return a copy of the context pointer the extension function was \n**   registered with.\n**\n** xColumnTotalSize(pFts, iCol, pnToken):\n**   If parameter iCol is less than zero, set output variable *pnToken\n**   to the total number of tokens in the FTS5 table. Or, if iCol is\n**   non-negative but less than the number of columns in the table, return\n**   the total number of tokens in column iCol, considering all rows in \n**   the FTS5 table.\n**\n**   If parameter iCol is greater than or equal to the number of columns\n**   in the table, SQLITE_RANGE is returned. Or, if an error occurs (e.g.\n**   an OOM condition or IO error), an appropriate SQLite error code is \n**   returned.\n**\n** xColumnCount(pFts):\n**   Return the number of columns in the table.\n**\n** xColumnSize(pFts, iCol, pnToken):\n**   If parameter iCol is less than zero, set output variable *pnToken\n**   to the total number of tokens in the current row. Or, if iCol is\n**   non-negative but less than the number of columns in the table, set\n**   *pnToken to the number of tokens in column iCol of the current row.\n**\n**   If parameter iCol is greater than or equal to the number of columns\n**   in the table, SQLITE_RANGE is returned. Or, if an error occurs (e.g.\n**   an OOM condition or IO error), an appropriate SQLite error code is \n**   returned.\n**\n**   This function may be quite inefficient if used with an FTS5 table\n**   created with the \"columnsize=0\" option.\n**\n** xColumnText:\n**   This function attempts to retrieve the text of column iCol of the\n**   current document. If successful, (*pz) is set to point to a buffer\n**   containing the text in utf-8 encoding, (*pn) is set to the size in bytes\n**   (not characters) of the buffer and SQLITE_OK is returned. Otherwise,\n**   if an error occurs, an SQLite error code is returned and the final values\n**   of (*pz) and (*pn) are undefined.\n**\n** xPhraseCount:\n**   Returns the number of phrases in the current query expression.\n**\n** xPhraseSize:\n**   Returns the number of tokens in phrase iPhrase of the query. Phrases\n**   are numbered starting from zero.\n**\n** xInstCount:\n**   Set *pnInst to the total number of occurrences of all phrases within\n**   the query within the current row. Return SQLITE_OK if successful, or\n**   an error code (i.e. SQLITE_NOMEM) if an error occurs.\n**\n**   This API can be quite slow if used with an FTS5 table created with the\n**   \"detail=none\" or \"detail=column\" option. If the FTS5 table is created \n**   with either \"detail=none\" or \"detail=column\" and \"content=\" option \n**   (i.e. if it is a contentless table), then this API always returns 0.\n**\n** xInst:\n**   Query for the details of phrase match iIdx within the current row.\n**   Phrase matches are numbered starting from zero, so the iIdx argument\n**   should be greater than or equal to zero and smaller than the value\n**   output by xInstCount().\n**\n**   Usually, output parameter *piPhrase is set to the phrase number, *piCol\n**   to the column in which it occurs and *piOff the token offset of the\n**   first token of the phrase. The exception is if the table was created\n**   with the offsets=0 option specified. In this case *piOff is always\n**   set to -1.\n**\n**   Returns SQLITE_OK if successful, or an error code (i.e. SQLITE_NOMEM) \n**   if an error occurs.\n**\n**   This API can be quite slow if used with an FTS5 table created with the\n**   \"detail=none\" or \"detail=column\" option. \n**\n** xRowid:\n**   Returns the rowid of the current row.\n**\n** xTokenize:\n**   Tokenize text using the tokenizer belonging to the FTS5 table.\n**\n** xQueryPhrase(pFts5, iPhrase, pUserData, xCallback):\n**   This API function is used to query the FTS table for phrase iPhrase\n**   of the current query. Specifically, a query equivalent to:\n**\n**       ... FROM ftstable WHERE ftstable MATCH $p ORDER BY rowid\n**\n**   with $p set to a phrase equivalent to the phrase iPhrase of the\n**   current query is executed. Any column filter that applies to\n**   phrase iPhrase of the current query is included in $p. For each \n**   row visited, the callback function passed as the fourth argument \n**   is invoked. The context and API objects passed to the callback \n**   function may be used to access the properties of each matched row.\n**   Invoking Api.xUserData() returns a copy of the pointer passed as \n**   the third argument to pUserData.\n**\n**   If the callback function returns any value other than SQLITE_OK, the\n**   query is abandoned and the xQueryPhrase function returns immediately.\n**   If the returned value is SQLITE_DONE, xQueryPhrase returns SQLITE_OK.\n**   Otherwise, the error code is propagated upwards.\n**\n**   If the query runs to completion without incident, SQLITE_OK is returned.\n**   Or, if some error occurs before the query completes or is aborted by\n**   the callback, an SQLite error code is returned.\n**\n**\n** xSetAuxdata(pFts5, pAux, xDelete)\n**\n**   Save the pointer passed as the second argument as the extension functions \n**   \"auxiliary data\". The pointer may then be retrieved by the current or any\n**   future invocation of the same fts5 extension function made as part of\n**   of the same MATCH query using the xGetAuxdata() API.\n**\n**   Each extension function is allocated a single auxiliary data slot for\n**   each FTS query (MATCH expression). If the extension function is invoked \n**   more than once for a single FTS query, then all invocations share a \n**   single auxiliary data context.\n**\n**   If there is already an auxiliary data pointer when this function is\n**   invoked, then it is replaced by the new pointer. If an xDelete callback\n**   was specified along with the original pointer, it is invoked at this\n**   point.\n**\n**   The xDelete callback, if one is specified, is also invoked on the\n**   auxiliary data pointer after the FTS5 query has finished.\n**\n**   If an error (e.g. an OOM condition) occurs within this function, an\n**   the auxiliary data is set to NULL and an error code returned. If the\n**   xDelete parameter was not NULL, it is invoked on the auxiliary data\n**   pointer before returning.\n**\n**\n** xGetAuxdata(pFts5, bClear)\n**\n**   Returns the current auxiliary data pointer for the fts5 extension \n**   function. See the xSetAuxdata() method for details.\n**\n**   If the bClear argument is non-zero, then the auxiliary data is cleared\n**   (set to NULL) before this function returns. In this case the xDelete,\n**   if any, is not invoked.\n**\n**\n** xRowCount(pFts5, pnRow)\n**\n**   This function is used to retrieve the total number of rows in the table.\n**   In other words, the same value that would be returned by:\n**\n**        SELECT count(*) FROM ftstable;\n**\n** xPhraseFirst()\n**   This function is used, along with type Fts5PhraseIter and the xPhraseNext\n**   method, to iterate through all instances of a single query phrase within\n**   the current row. This is the same information as is accessible via the\n**   xInstCount/xInst APIs. While the xInstCount/xInst APIs are more convenient\n**   to use, this API may be faster under some circumstances. To iterate \n**   through instances of phrase iPhrase, use the following code:\n**\n**       Fts5PhraseIter iter;\n**       int iCol, iOff;\n**       for(pApi->xPhraseFirst(pFts, iPhrase, &iter, &iCol, &iOff);\n**           iCol>=0;\n**           pApi->xPhraseNext(pFts, &iter, &iCol, &iOff)\n**       ){\n**         // An instance of phrase iPhrase at offset iOff of column iCol\n**       }\n**\n**   The Fts5PhraseIter structure is defined above. Applications should not\n**   modify this structure directly - it should only be used as shown above\n**   with the xPhraseFirst() and xPhraseNext() API methods (and by\n**   xPhraseFirstColumn() and xPhraseNextColumn() as illustrated below).\n**\n**   This API can be quite slow if used with an FTS5 table created with the\n**   \"detail=none\" or \"detail=column\" option. If the FTS5 table is created \n**   with either \"detail=none\" or \"detail=column\" and \"content=\" option \n**   (i.e. if it is a contentless table), then this API always iterates\n**   through an empty set (all calls to xPhraseFirst() set iCol to -1).\n**\n** xPhraseNext()\n**   See xPhraseFirst above.\n**\n** xPhraseFirstColumn()\n**   This function and xPhraseNextColumn() are similar to the xPhraseFirst()\n**   and xPhraseNext() APIs described above. The difference is that instead\n**   of iterating through all instances of a phrase in the current row, these\n**   APIs are used to iterate through the set of columns in the current row\n**   that contain one or more instances of a specified phrase. For example:\n**\n**       Fts5PhraseIter iter;\n**       int iCol;\n**       for(pApi->xPhraseFirstColumn(pFts, iPhrase, &iter, &iCol);\n**           iCol>=0;\n**           pApi->xPhraseNextColumn(pFts, &iter, &iCol)\n**       ){\n**         // Column iCol contains at least one instance of phrase iPhrase\n**       }\n**\n**   This API can be quite slow if used with an FTS5 table created with the\n**   \"detail=none\" option. If the FTS5 table is created with either \n**   \"detail=none\" \"content=\" option (i.e. if it is a contentless table), \n**   then this API always iterates through an empty set (all calls to \n**   xPhraseFirstColumn() set iCol to -1).\n**\n**   The information accessed using this API and its companion\n**   xPhraseFirstColumn() may also be obtained using xPhraseFirst/xPhraseNext\n**   (or xInst/xInstCount). The chief advantage of this API is that it is\n**   significantly more efficient than those alternatives when used with\n**   \"detail=column\" tables.  \n**\n** xPhraseNextColumn()\n**   See xPhraseFirstColumn above.\n*/\nstruct Fts5ExtensionApi {\n  int iVersion;                   /* Currently always set to 3 */\n\n  void *(*xUserData)(Fts5Context*);\n\n  int (*xColumnCount)(Fts5Context*);\n  int (*xRowCount)(Fts5Context*, sqlite3_int64 *pnRow);\n  int (*xColumnTotalSize)(Fts5Context*, int iCol, sqlite3_int64 *pnToken);\n\n  int (*xTokenize)(Fts5Context*, \n    const char *pText, int nText, /* Text to tokenize */\n    void *pCtx,                   /* Context passed to xToken() */\n    int (*xToken)(void*, int, const char*, int, int, int)       /* Callback */\n  );\n\n  int (*xPhraseCount)(Fts5Context*);\n  int (*xPhraseSize)(Fts5Context*, int iPhrase);\n\n  int (*xInstCount)(Fts5Context*, int *pnInst);\n  int (*xInst)(Fts5Context*, int iIdx, int *piPhrase, int *piCol, int *piOff);\n\n  sqlite3_int64 (*xRowid)(Fts5Context*);\n  int (*xColumnText)(Fts5Context*, int iCol, const char **pz, int *pn);\n  int (*xColumnSize)(Fts5Context*, int iCol, int *pnToken);\n\n  int (*xQueryPhrase)(Fts5Context*, int iPhrase, void *pUserData,\n    int(*)(const Fts5ExtensionApi*,Fts5Context*,void*)\n  );\n  int (*xSetAuxdata)(Fts5Context*, void *pAux, void(*xDelete)(void*));\n  void *(*xGetAuxdata)(Fts5Context*, int bClear);\n\n  int (*xPhraseFirst)(Fts5Context*, int iPhrase, Fts5PhraseIter*, int*, int*);\n  void (*xPhraseNext)(Fts5Context*, Fts5PhraseIter*, int *piCol, int *piOff);\n\n  int (*xPhraseFirstColumn)(Fts5Context*, int iPhrase, Fts5PhraseIter*, int*);\n  void (*xPhraseNextColumn)(Fts5Context*, Fts5PhraseIter*, int *piCol);\n};\n\n/* \n** CUSTOM AUXILIARY FUNCTIONS\n*************************************************************************/\n\n/*************************************************************************\n** CUSTOM TOKENIZERS\n**\n** Applications may also register custom tokenizer types. A tokenizer \n** is registered by providing fts5 with a populated instance of the \n** following structure. All structure methods must be defined, setting\n** any member of the fts5_tokenizer struct to NULL leads to undefined\n** behaviour. The structure methods are expected to function as follows:\n**\n** xCreate:\n**   This function is used to allocate and initialize a tokenizer instance.\n**   A tokenizer instance is required to actually tokenize text.\n**\n**   The first argument passed to this function is a copy of the (void*)\n**   pointer provided by the application when the fts5_tokenizer object\n**   was registered with FTS5 (the third argument to xCreateTokenizer()). \n**   The second and third arguments are an array of nul-terminated strings\n**   containing the tokenizer arguments, if any, specified following the\n**   tokenizer name as part of the CREATE VIRTUAL TABLE statement used\n**   to create the FTS5 table.\n**\n**   The final argument is an output variable. If successful, (*ppOut) \n**   should be set to point to the new tokenizer handle and SQLITE_OK\n**   returned. If an error occurs, some value other than SQLITE_OK should\n**   be returned. In this case, fts5 assumes that the final value of *ppOut \n**   is undefined.\n**\n** xDelete:\n**   This function is invoked to delete a tokenizer handle previously\n**   allocated using xCreate(). Fts5 guarantees that this function will\n**   be invoked exactly once for each successful call to xCreate().\n**\n** xTokenize:\n**   This function is expected to tokenize the nText byte string indicated \n**   by argument pText. pText may or may not be nul-terminated. The first\n**   argument passed to this function is a pointer to an Fts5Tokenizer object\n**   returned by an earlier call to xCreate().\n**\n**   The second argument indicates the reason that FTS5 is requesting\n**   tokenization of the supplied text. This is always one of the following\n**   four values:\n**\n**   <ul><li> <b>FTS5_TOKENIZE_DOCUMENT</b> - A document is being inserted into\n**            or removed from the FTS table. The tokenizer is being invoked to\n**            determine the set of tokens to add to (or delete from) the\n**            FTS index.\n**\n**       <li> <b>FTS5_TOKENIZE_QUERY</b> - A MATCH query is being executed \n**            against the FTS index. The tokenizer is being called to tokenize \n**            a bareword or quoted string specified as part of the query.\n**\n**       <li> <b>(FTS5_TOKENIZE_QUERY | FTS5_TOKENIZE_PREFIX)</b> - Same as\n**            FTS5_TOKENIZE_QUERY, except that the bareword or quoted string is\n**            followed by a \"*\" character, indicating that the last token\n**            returned by the tokenizer will be treated as a token prefix.\n**\n**       <li> <b>FTS5_TOKENIZE_AUX</b> - The tokenizer is being invoked to \n**            satisfy an fts5_api.xTokenize() request made by an auxiliary\n**            function. Or an fts5_api.xColumnSize() request made by the same\n**            on a columnsize=0 database.  \n**   </ul>\n**\n**   For each token in the input string, the supplied callback xToken() must\n**   be invoked. The first argument to it should be a copy of the pointer\n**   passed as the second argument to xTokenize(). The third and fourth\n**   arguments are a pointer to a buffer containing the token text, and the\n**   size of the token in bytes. The 4th and 5th arguments are the byte offsets\n**   of the first byte of and first byte immediately following the text from\n**   which the token is derived within the input.\n**\n**   The second argument passed to the xToken() callback (\"tflags\") should\n**   normally be set to 0. The exception is if the tokenizer supports \n**   synonyms. In this case see the discussion below for details.\n**\n**   FTS5 assumes the xToken() callback is invoked for each token in the \n**   order that they occur within the input text.\n**\n**   If an xToken() callback returns any value other than SQLITE_OK, then\n**   the tokenization should be abandoned and the xTokenize() method should\n**   immediately return a copy of the xToken() return value. Or, if the\n**   input buffer is exhausted, xTokenize() should return SQLITE_OK. Finally,\n**   if an error occurs with the xTokenize() implementation itself, it\n**   may abandon the tokenization and return any error code other than\n**   SQLITE_OK or SQLITE_DONE.\n**\n** SYNONYM SUPPORT\n**\n**   Custom tokenizers may also support synonyms. Consider a case in which a\n**   user wishes to query for a phrase such as \"first place\". Using the \n**   built-in tokenizers, the FTS5 query 'first + place' will match instances\n**   of \"first place\" within the document set, but not alternative forms\n**   such as \"1st place\". In some applications, it would be better to match\n**   all instances of \"first place\" or \"1st place\" regardless of which form\n**   the user specified in the MATCH query text.\n**\n**   There are several ways to approach this in FTS5:\n**\n**   <ol><li> By mapping all synonyms to a single token. In this case, the \n**            In the above example, this means that the tokenizer returns the\n**            same token for inputs \"first\" and \"1st\". Say that token is in\n**            fact \"first\", so that when the user inserts the document \"I won\n**            1st place\" entries are added to the index for tokens \"i\", \"won\",\n**            \"first\" and \"place\". If the user then queries for '1st + place',\n**            the tokenizer substitutes \"first\" for \"1st\" and the query works\n**            as expected.\n**\n**       <li> By adding multiple synonyms for a single term to the FTS index.\n**            In this case, when tokenizing query text, the tokenizer may \n**            provide multiple synonyms for a single term within the document.\n**            FTS5 then queries the index for each synonym individually. For\n**            example, faced with the query:\n**\n**   <codeblock>\n**     ... MATCH 'first place'</codeblock>\n**\n**            the tokenizer offers both \"1st\" and \"first\" as synonyms for the\n**            first token in the MATCH query and FTS5 effectively runs a query \n**            similar to:\n**\n**   <codeblock>\n**     ... MATCH '(first OR 1st) place'</codeblock>\n**\n**            except that, for the purposes of auxiliary functions, the query\n**            still appears to contain just two phrases - \"(first OR 1st)\" \n**            being treated as a single phrase.\n**\n**       <li> By adding multiple synonyms for a single term to the FTS index.\n**            Using this method, when tokenizing document text, the tokenizer\n**            provides multiple synonyms for each token. So that when a \n**            document such as \"I won first place\" is tokenized, entries are\n**            added to the FTS index for \"i\", \"won\", \"first\", \"1st\" and\n**            \"place\".\n**\n**            This way, even if the tokenizer does not provide synonyms\n**            when tokenizing query text (it should not - to do would be\n**            inefficient), it doesn't matter if the user queries for \n**            'first + place' or '1st + place', as there are entires in the\n**            FTS index corresponding to both forms of the first token.\n**   </ol>\n**\n**   Whether it is parsing document or query text, any call to xToken that\n**   specifies a <i>tflags</i> argument with the FTS5_TOKEN_COLOCATED bit\n**   is considered to supply a synonym for the previous token. For example,\n**   when parsing the document \"I won first place\", a tokenizer that supports\n**   synonyms would call xToken() 5 times, as follows:\n**\n**   <codeblock>\n**       xToken(pCtx, 0, \"i\",                      1,  0,  1);\n**       xToken(pCtx, 0, \"won\",                    3,  2,  5);\n**       xToken(pCtx, 0, \"first\",                  5,  6, 11);\n**       xToken(pCtx, FTS5_TOKEN_COLOCATED, \"1st\", 3,  6, 11);\n**       xToken(pCtx, 0, \"place\",                  5, 12, 17);\n**</codeblock>\n**\n**   It is an error to specify the FTS5_TOKEN_COLOCATED flag the first time\n**   xToken() is called. Multiple synonyms may be specified for a single token\n**   by making multiple calls to xToken(FTS5_TOKEN_COLOCATED) in sequence. \n**   There is no limit to the number of synonyms that may be provided for a\n**   single token.\n**\n**   In many cases, method (1) above is the best approach. It does not add \n**   extra data to the FTS index or require FTS5 to query for multiple terms,\n**   so it is efficient in terms of disk space and query speed. However, it\n**   does not support prefix queries very well. If, as suggested above, the\n**   token \"first\" is subsituted for \"1st\" by the tokenizer, then the query:\n**\n**   <codeblock>\n**     ... MATCH '1s*'</codeblock>\n**\n**   will not match documents that contain the token \"1st\" (as the tokenizer\n**   will probably not map \"1s\" to any prefix of \"first\").\n**\n**   For full prefix support, method (3) may be preferred. In this case, \n**   because the index contains entries for both \"first\" and \"1st\", prefix\n**   queries such as 'fi*' or '1s*' will match correctly. However, because\n**   extra entries are added to the FTS index, this method uses more space\n**   within the database.\n**\n**   Method (2) offers a midpoint between (1) and (3). Using this method,\n**   a query such as '1s*' will match documents that contain the literal \n**   token \"1st\", but not \"first\" (assuming the tokenizer is not able to\n**   provide synonyms for prefixes). However, a non-prefix query like '1st'\n**   will match against \"1st\" and \"first\". This method does not require\n**   extra disk space, as no extra entries are added to the FTS index. \n**   On the other hand, it may require more CPU cycles to run MATCH queries,\n**   as separate queries of the FTS index are required for each synonym.\n**\n**   When using methods (2) or (3), it is important that the tokenizer only\n**   provide synonyms when tokenizing document text (method (2)) or query\n**   text (method (3)), not both. Doing so will not cause any errors, but is\n**   inefficient.\n*/\ntypedef struct Fts5Tokenizer Fts5Tokenizer;\ntypedef struct fts5_tokenizer fts5_tokenizer;\nstruct fts5_tokenizer {\n  int (*xCreate)(void*, const char **azArg, int nArg, Fts5Tokenizer **ppOut);\n  void (*xDelete)(Fts5Tokenizer*);\n  int (*xTokenize)(Fts5Tokenizer*, \n      void *pCtx,\n      int flags,            /* Mask of FTS5_TOKENIZE_* flags */\n      const char *pText, int nText, \n      int (*xToken)(\n        void *pCtx,         /* Copy of 2nd argument to xTokenize() */\n        int tflags,         /* Mask of FTS5_TOKEN_* flags */\n        const char *pToken, /* Pointer to buffer containing token */\n        int nToken,         /* Size of token in bytes */\n        int iStart,         /* Byte offset of token within input text */\n        int iEnd            /* Byte offset of end of token within input text */\n      )\n  );\n};\n\n/* Flags that may be passed as the third argument to xTokenize() */\n#define FTS5_TOKENIZE_QUERY     0x0001\n#define FTS5_TOKENIZE_PREFIX    0x0002\n#define FTS5_TOKENIZE_DOCUMENT  0x0004\n#define FTS5_TOKENIZE_AUX       0x0008\n\n/* Flags that may be passed by the tokenizer implementation back to FTS5\n** as the third argument to the supplied xToken callback. */\n#define FTS5_TOKEN_COLOCATED    0x0001      /* Same position as prev. token */\n\n/*\n** END OF CUSTOM TOKENIZERS\n*************************************************************************/\n\n/*************************************************************************\n** FTS5 EXTENSION REGISTRATION API\n*/\ntypedef struct fts5_api fts5_api;\nstruct fts5_api {\n  int iVersion;                   /* Currently always set to 2 */\n\n  /* Create a new tokenizer */\n  int (*xCreateTokenizer)(\n    fts5_api *pApi,\n    const char *zName,\n    void *pContext,\n    fts5_tokenizer *pTokenizer,\n    void (*xDestroy)(void*)\n  );\n\n  /* Find an existing tokenizer */\n  int (*xFindTokenizer)(\n    fts5_api *pApi,\n    const char *zName,\n    void **ppContext,\n    fts5_tokenizer *pTokenizer\n  );\n\n  /* Create a new auxiliary function */\n  int (*xCreateFunction)(\n    fts5_api *pApi,\n    const char *zName,\n    void *pContext,\n    fts5_extension_function xFunction,\n    void (*xDestroy)(void*)\n  );\n};\n\n/*\n** END OF REGISTRATION API\n*************************************************************************/\n\n#ifdef __cplusplus\n}  /* end of the 'extern \"C\"' block */\n#endif\n\n#endif /* _FTS5_H */\n\n/******** End of fts5.h *********/\n"
  },
  {
    "path": "libs/sqlite3/sqlite3.c",
    "content": "/******************************************************************************\n** This file is an amalgamation of many separate C source files from SQLite\n** version 3.23.0.  By combining all the individual C code files into this\n** single large file, the entire code can be compiled as a single translation\n** unit.  This allows many compilers to do optimizations that would not be\n** possible if the files were compiled separately.  Performance improvements\n** of 5% or more are commonly seen when SQLite is compiled as a single\n** translation unit.\n**\n** This file is all you need to compile SQLite.  To use SQLite in other\n** programs, you need this file and the \"sqlite3.h\" header file that defines\n** the programming interface to the SQLite library.  (If you do not have\n** the \"sqlite3.h\" header file at hand, you will find a copy embedded within\n** the text of this file.  Search for \"Begin file sqlite3.h\" to find the start\n** of the embedded sqlite3.h header file.) Additional code files may be needed\n** if you want a wrapper to interface SQLite with your choice of programming\n** language. The code for the \"sqlite3\" command-line shell is also in a\n** separate file. This file contains only code for the core SQLite library.\n*/\n#define SQLITE_CORE 1\n#define SQLITE_AMALGAMATION 1\n#ifndef SQLITE_PRIVATE\n# define SQLITE_PRIVATE static\n#endif\n/************** Begin file ctime.c *******************************************/\n/*\n** 2010 February 23\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n*************************************************************************\n**\n** This file implements routines used to report what compile-time options\n** SQLite was built with.\n*/\n\n#ifndef SQLITE_OMIT_COMPILEOPTION_DIAGS\n\n/*\n** Include the configuration header output by 'configure' if we're using the\n** autoconf-based build\n*/\n#if defined(_HAVE_SQLITE_CONFIG_H) && !defined(SQLITECONFIG_H)\n#include \"config.h\"\n#define SQLITECONFIG_H 1\n#endif\n\n/* These macros are provided to \"stringify\" the value of the define\n** for those options in which the value is meaningful. */\n#define CTIMEOPT_VAL_(opt) #opt\n#define CTIMEOPT_VAL(opt) CTIMEOPT_VAL_(opt)\n\n/*\n** An array of names of all compile-time options.  This array should \n** be sorted A-Z.\n**\n** This array looks large, but in a typical installation actually uses\n** only a handful of compile-time options, so most times this array is usually\n** rather short and uses little memory space.\n*/\nstatic const char * const sqlite3azCompileOpt[] = {\n\n/* \n** BEGIN CODE GENERATED BY tool/mkctime.tcl \n*/\n#if SQLITE_32BIT_ROWID\n  \"32BIT_ROWID\",\n#endif\n#if SQLITE_4_BYTE_ALIGNED_MALLOC\n  \"4_BYTE_ALIGNED_MALLOC\",\n#endif\n#if SQLITE_64BIT_STATS\n  \"64BIT_STATS\",\n#endif\n#if SQLITE_ALLOW_COVERING_INDEX_SCAN\n  \"ALLOW_COVERING_INDEX_SCAN\",\n#endif\n#if SQLITE_ALLOW_URI_AUTHORITY\n  \"ALLOW_URI_AUTHORITY\",\n#endif\n#ifdef SQLITE_BITMASK_TYPE\n  \"BITMASK_TYPE=\" CTIMEOPT_VAL(SQLITE_BITMASK_TYPE),\n#endif\n#if SQLITE_BUG_COMPATIBLE_20160819\n  \"BUG_COMPATIBLE_20160819\",\n#endif\n#if SQLITE_CASE_SENSITIVE_LIKE\n  \"CASE_SENSITIVE_LIKE\",\n#endif\n#if SQLITE_CHECK_PAGES\n  \"CHECK_PAGES\",\n#endif\n#if defined(__clang__) && defined(__clang_major__)\n  \"COMPILER=clang-\" CTIMEOPT_VAL(__clang_major__) \".\"\n                    CTIMEOPT_VAL(__clang_minor__) \".\"\n                    CTIMEOPT_VAL(__clang_patchlevel__),\n#elif defined(_MSC_VER)\n  \"COMPILER=msvc-\" CTIMEOPT_VAL(_MSC_VER),\n#elif defined(__GNUC__) && defined(__VERSION__)\n  \"COMPILER=gcc-\" __VERSION__,\n#endif\n#if SQLITE_COVERAGE_TEST\n  \"COVERAGE_TEST\",\n#endif\n#if SQLITE_DEBUG\n  \"DEBUG\",\n#endif\n#if SQLITE_DEFAULT_AUTOMATIC_INDEX\n  \"DEFAULT_AUTOMATIC_INDEX\",\n#endif\n#if SQLITE_DEFAULT_AUTOVACUUM\n  \"DEFAULT_AUTOVACUUM\",\n#endif\n#ifdef SQLITE_DEFAULT_CACHE_SIZE\n  \"DEFAULT_CACHE_SIZE=\" CTIMEOPT_VAL(SQLITE_DEFAULT_CACHE_SIZE),\n#endif\n#if SQLITE_DEFAULT_CKPTFULLFSYNC\n  \"DEFAULT_CKPTFULLFSYNC\",\n#endif\n#ifdef SQLITE_DEFAULT_FILE_FORMAT\n  \"DEFAULT_FILE_FORMAT=\" CTIMEOPT_VAL(SQLITE_DEFAULT_FILE_FORMAT),\n#endif\n#ifdef SQLITE_DEFAULT_FILE_PERMISSIONS\n  \"DEFAULT_FILE_PERMISSIONS=\" CTIMEOPT_VAL(SQLITE_DEFAULT_FILE_PERMISSIONS),\n#endif\n#if SQLITE_DEFAULT_FOREIGN_KEYS\n  \"DEFAULT_FOREIGN_KEYS\",\n#endif\n#ifdef SQLITE_DEFAULT_JOURNAL_SIZE_LIMIT\n  \"DEFAULT_JOURNAL_SIZE_LIMIT=\" CTIMEOPT_VAL(SQLITE_DEFAULT_JOURNAL_SIZE_LIMIT),\n#endif\n#ifdef SQLITE_DEFAULT_LOCKING_MODE\n  \"DEFAULT_LOCKING_MODE=\" CTIMEOPT_VAL(SQLITE_DEFAULT_LOCKING_MODE),\n#endif\n#ifdef SQLITE_DEFAULT_LOOKASIDE\n  \"DEFAULT_LOOKASIDE=\" CTIMEOPT_VAL(SQLITE_DEFAULT_LOOKASIDE),\n#endif\n#if SQLITE_DEFAULT_MEMSTATUS\n  \"DEFAULT_MEMSTATUS\",\n#endif\n#ifdef SQLITE_DEFAULT_MMAP_SIZE\n  \"DEFAULT_MMAP_SIZE=\" CTIMEOPT_VAL(SQLITE_DEFAULT_MMAP_SIZE),\n#endif\n#ifdef SQLITE_DEFAULT_PAGE_SIZE\n  \"DEFAULT_PAGE_SIZE=\" CTIMEOPT_VAL(SQLITE_DEFAULT_PAGE_SIZE),\n#endif\n#ifdef SQLITE_DEFAULT_PCACHE_INITSZ\n  \"DEFAULT_PCACHE_INITSZ=\" CTIMEOPT_VAL(SQLITE_DEFAULT_PCACHE_INITSZ),\n#endif\n#ifdef SQLITE_DEFAULT_PROXYDIR_PERMISSIONS\n  \"DEFAULT_PROXYDIR_PERMISSIONS=\" CTIMEOPT_VAL(SQLITE_DEFAULT_PROXYDIR_PERMISSIONS),\n#endif\n#if SQLITE_DEFAULT_RECURSIVE_TRIGGERS\n  \"DEFAULT_RECURSIVE_TRIGGERS\",\n#endif\n#ifdef SQLITE_DEFAULT_ROWEST\n  \"DEFAULT_ROWEST=\" CTIMEOPT_VAL(SQLITE_DEFAULT_ROWEST),\n#endif\n#ifdef SQLITE_DEFAULT_SECTOR_SIZE\n  \"DEFAULT_SECTOR_SIZE=\" CTIMEOPT_VAL(SQLITE_DEFAULT_SECTOR_SIZE),\n#endif\n#ifdef SQLITE_DEFAULT_SYNCHRONOUS\n  \"DEFAULT_SYNCHRONOUS=\" CTIMEOPT_VAL(SQLITE_DEFAULT_SYNCHRONOUS),\n#endif\n#ifdef SQLITE_DEFAULT_WAL_AUTOCHECKPOINT\n  \"DEFAULT_WAL_AUTOCHECKPOINT=\" CTIMEOPT_VAL(SQLITE_DEFAULT_WAL_AUTOCHECKPOINT),\n#endif\n#ifdef SQLITE_DEFAULT_WAL_SYNCHRONOUS\n  \"DEFAULT_WAL_SYNCHRONOUS=\" CTIMEOPT_VAL(SQLITE_DEFAULT_WAL_SYNCHRONOUS),\n#endif\n#ifdef SQLITE_DEFAULT_WORKER_THREADS\n  \"DEFAULT_WORKER_THREADS=\" CTIMEOPT_VAL(SQLITE_DEFAULT_WORKER_THREADS),\n#endif\n#if SQLITE_DIRECT_OVERFLOW_READ\n  \"DIRECT_OVERFLOW_READ\",\n#endif\n#if SQLITE_DISABLE_DIRSYNC\n  \"DISABLE_DIRSYNC\",\n#endif\n#if SQLITE_DISABLE_FTS3_UNICODE\n  \"DISABLE_FTS3_UNICODE\",\n#endif\n#if SQLITE_DISABLE_FTS4_DEFERRED\n  \"DISABLE_FTS4_DEFERRED\",\n#endif\n#if SQLITE_DISABLE_INTRINSIC\n  \"DISABLE_INTRINSIC\",\n#endif\n#if SQLITE_DISABLE_LFS\n  \"DISABLE_LFS\",\n#endif\n#if SQLITE_DISABLE_PAGECACHE_OVERFLOW_STATS\n  \"DISABLE_PAGECACHE_OVERFLOW_STATS\",\n#endif\n#if SQLITE_DISABLE_SKIPAHEAD_DISTINCT\n  \"DISABLE_SKIPAHEAD_DISTINCT\",\n#endif\n#ifdef SQLITE_ENABLE_8_3_NAMES\n  \"ENABLE_8_3_NAMES=\" CTIMEOPT_VAL(SQLITE_ENABLE_8_3_NAMES),\n#endif\n#if SQLITE_ENABLE_API_ARMOR\n  \"ENABLE_API_ARMOR\",\n#endif\n#if SQLITE_ENABLE_ATOMIC_WRITE\n  \"ENABLE_ATOMIC_WRITE\",\n#endif\n#if SQLITE_ENABLE_BATCH_ATOMIC_WRITE\n  \"ENABLE_BATCH_ATOMIC_WRITE\",\n#endif\n#if SQLITE_ENABLE_CEROD\n  \"ENABLE_CEROD\",\n#endif\n#if SQLITE_ENABLE_COLUMN_METADATA\n  \"ENABLE_COLUMN_METADATA\",\n#endif\n#if SQLITE_ENABLE_COLUMN_USED_MASK\n  \"ENABLE_COLUMN_USED_MASK\",\n#endif\n#if SQLITE_ENABLE_COSTMULT\n  \"ENABLE_COSTMULT\",\n#endif\n#if SQLITE_ENABLE_CURSOR_HINTS\n  \"ENABLE_CURSOR_HINTS\",\n#endif\n#if SQLITE_ENABLE_DBSTAT_VTAB\n  \"ENABLE_DBSTAT_VTAB\",\n#endif\n#if SQLITE_ENABLE_EXPENSIVE_ASSERT\n  \"ENABLE_EXPENSIVE_ASSERT\",\n#endif\n#if SQLITE_ENABLE_FTS1\n  \"ENABLE_FTS1\",\n#endif\n#if SQLITE_ENABLE_FTS2\n  \"ENABLE_FTS2\",\n#endif\n#if SQLITE_ENABLE_FTS3\n  \"ENABLE_FTS3\",\n#endif\n#if SQLITE_ENABLE_FTS3_PARENTHESIS\n  \"ENABLE_FTS3_PARENTHESIS\",\n#endif\n#if SQLITE_ENABLE_FTS3_TOKENIZER\n  \"ENABLE_FTS3_TOKENIZER\",\n#endif\n#if SQLITE_ENABLE_FTS4\n  \"ENABLE_FTS4\",\n#endif\n#if SQLITE_ENABLE_FTS5\n  \"ENABLE_FTS5\",\n#endif\n#if SQLITE_ENABLE_HIDDEN_COLUMNS\n  \"ENABLE_HIDDEN_COLUMNS\",\n#endif\n#if SQLITE_ENABLE_ICU\n  \"ENABLE_ICU\",\n#endif\n#if SQLITE_ENABLE_IOTRACE\n  \"ENABLE_IOTRACE\",\n#endif\n#if SQLITE_ENABLE_JSON1\n  \"ENABLE_JSON1\",\n#endif\n#if SQLITE_ENABLE_LOAD_EXTENSION\n  \"ENABLE_LOAD_EXTENSION\",\n#endif\n#ifdef SQLITE_ENABLE_LOCKING_STYLE\n  \"ENABLE_LOCKING_STYLE=\" CTIMEOPT_VAL(SQLITE_ENABLE_LOCKING_STYLE),\n#endif\n#if SQLITE_ENABLE_MEMORY_MANAGEMENT\n  \"ENABLE_MEMORY_MANAGEMENT\",\n#endif\n#if SQLITE_ENABLE_MEMSYS3\n  \"ENABLE_MEMSYS3\",\n#endif\n#if SQLITE_ENABLE_MEMSYS5\n  \"ENABLE_MEMSYS5\",\n#endif\n#if SQLITE_ENABLE_MULTIPLEX\n  \"ENABLE_MULTIPLEX\",\n#endif\n#if SQLITE_ENABLE_NULL_TRIM\n  \"ENABLE_NULL_TRIM\",\n#endif\n#if SQLITE_ENABLE_OVERSIZE_CELL_CHECK\n  \"ENABLE_OVERSIZE_CELL_CHECK\",\n#endif\n#if SQLITE_ENABLE_PREUPDATE_HOOK\n  \"ENABLE_PREUPDATE_HOOK\",\n#endif\n#if SQLITE_ENABLE_QPSG\n  \"ENABLE_QPSG\",\n#endif\n#if SQLITE_ENABLE_RBU\n  \"ENABLE_RBU\",\n#endif\n#if SQLITE_ENABLE_RTREE\n  \"ENABLE_RTREE\",\n#endif\n#if SQLITE_ENABLE_SELECTTRACE\n  \"ENABLE_SELECTTRACE\",\n#endif\n#if SQLITE_ENABLE_SESSION\n  \"ENABLE_SESSION\",\n#endif\n#if SQLITE_ENABLE_SNAPSHOT\n  \"ENABLE_SNAPSHOT\",\n#endif\n#if SQLITE_ENABLE_SQLLOG\n  \"ENABLE_SQLLOG\",\n#endif\n#if defined(SQLITE_ENABLE_STAT4)\n  \"ENABLE_STAT4\",\n#elif defined(SQLITE_ENABLE_STAT3)\n  \"ENABLE_STAT3\",\n#endif\n#if SQLITE_ENABLE_STMTVTAB\n  \"ENABLE_STMTVTAB\",\n#endif\n#if SQLITE_ENABLE_STMT_SCANSTATUS\n  \"ENABLE_STMT_SCANSTATUS\",\n#endif\n#if SQLITE_ENABLE_UNKNOWN_SQL_FUNCTION\n  \"ENABLE_UNKNOWN_SQL_FUNCTION\",\n#endif\n#if SQLITE_ENABLE_UNLOCK_NOTIFY\n  \"ENABLE_UNLOCK_NOTIFY\",\n#endif\n#if SQLITE_ENABLE_UPDATE_DELETE_LIMIT\n  \"ENABLE_UPDATE_DELETE_LIMIT\",\n#endif\n#if SQLITE_ENABLE_URI_00_ERROR\n  \"ENABLE_URI_00_ERROR\",\n#endif\n#if SQLITE_ENABLE_VFSTRACE\n  \"ENABLE_VFSTRACE\",\n#endif\n#if SQLITE_ENABLE_WHERETRACE\n  \"ENABLE_WHERETRACE\",\n#endif\n#if SQLITE_ENABLE_ZIPVFS\n  \"ENABLE_ZIPVFS\",\n#endif\n#if SQLITE_EXPLAIN_ESTIMATED_ROWS\n  \"EXPLAIN_ESTIMATED_ROWS\",\n#endif\n#if SQLITE_EXTRA_IFNULLROW\n  \"EXTRA_IFNULLROW\",\n#endif\n#ifdef SQLITE_EXTRA_INIT\n  \"EXTRA_INIT=\" CTIMEOPT_VAL(SQLITE_EXTRA_INIT),\n#endif\n#ifdef SQLITE_EXTRA_SHUTDOWN\n  \"EXTRA_SHUTDOWN=\" CTIMEOPT_VAL(SQLITE_EXTRA_SHUTDOWN),\n#endif\n#ifdef SQLITE_FTS3_MAX_EXPR_DEPTH\n  \"FTS3_MAX_EXPR_DEPTH=\" CTIMEOPT_VAL(SQLITE_FTS3_MAX_EXPR_DEPTH),\n#endif\n#if SQLITE_FTS5_ENABLE_TEST_MI\n  \"FTS5_ENABLE_TEST_MI\",\n#endif\n#if SQLITE_FTS5_NO_WITHOUT_ROWID\n  \"FTS5_NO_WITHOUT_ROWID\",\n#endif\n#if SQLITE_HAS_CODEC\n  \"HAS_CODEC\",\n#endif\n#if HAVE_ISNAN || SQLITE_HAVE_ISNAN\n  \"HAVE_ISNAN\",\n#endif\n#if SQLITE_HOMEGROWN_RECURSIVE_MUTEX\n  \"HOMEGROWN_RECURSIVE_MUTEX\",\n#endif\n#if SQLITE_IGNORE_AFP_LOCK_ERRORS\n  \"IGNORE_AFP_LOCK_ERRORS\",\n#endif\n#if SQLITE_IGNORE_FLOCK_LOCK_ERRORS\n  \"IGNORE_FLOCK_LOCK_ERRORS\",\n#endif\n#if SQLITE_INLINE_MEMCPY\n  \"INLINE_MEMCPY\",\n#endif\n#if SQLITE_INT64_TYPE\n  \"INT64_TYPE\",\n#endif\n#ifdef SQLITE_INTEGRITY_CHECK_ERROR_MAX\n  \"INTEGRITY_CHECK_ERROR_MAX=\" CTIMEOPT_VAL(SQLITE_INTEGRITY_CHECK_ERROR_MAX),\n#endif\n#if SQLITE_LIKE_DOESNT_MATCH_BLOBS\n  \"LIKE_DOESNT_MATCH_BLOBS\",\n#endif\n#if SQLITE_LOCK_TRACE\n  \"LOCK_TRACE\",\n#endif\n#if SQLITE_LOG_CACHE_SPILL\n  \"LOG_CACHE_SPILL\",\n#endif\n#ifdef SQLITE_MALLOC_SOFT_LIMIT\n  \"MALLOC_SOFT_LIMIT=\" CTIMEOPT_VAL(SQLITE_MALLOC_SOFT_LIMIT),\n#endif\n#ifdef SQLITE_MAX_ATTACHED\n  \"MAX_ATTACHED=\" CTIMEOPT_VAL(SQLITE_MAX_ATTACHED),\n#endif\n#ifdef SQLITE_MAX_COLUMN\n  \"MAX_COLUMN=\" CTIMEOPT_VAL(SQLITE_MAX_COLUMN),\n#endif\n#ifdef SQLITE_MAX_COMPOUND_SELECT\n  \"MAX_COMPOUND_SELECT=\" CTIMEOPT_VAL(SQLITE_MAX_COMPOUND_SELECT),\n#endif\n#ifdef SQLITE_MAX_DEFAULT_PAGE_SIZE\n  \"MAX_DEFAULT_PAGE_SIZE=\" CTIMEOPT_VAL(SQLITE_MAX_DEFAULT_PAGE_SIZE),\n#endif\n#ifdef SQLITE_MAX_EXPR_DEPTH\n  \"MAX_EXPR_DEPTH=\" CTIMEOPT_VAL(SQLITE_MAX_EXPR_DEPTH),\n#endif\n#ifdef SQLITE_MAX_FUNCTION_ARG\n  \"MAX_FUNCTION_ARG=\" CTIMEOPT_VAL(SQLITE_MAX_FUNCTION_ARG),\n#endif\n#ifdef SQLITE_MAX_LENGTH\n  \"MAX_LENGTH=\" CTIMEOPT_VAL(SQLITE_MAX_LENGTH),\n#endif\n#ifdef SQLITE_MAX_LIKE_PATTERN_LENGTH\n  \"MAX_LIKE_PATTERN_LENGTH=\" CTIMEOPT_VAL(SQLITE_MAX_LIKE_PATTERN_LENGTH),\n#endif\n#ifdef SQLITE_MAX_MEMORY\n  \"MAX_MEMORY=\" CTIMEOPT_VAL(SQLITE_MAX_MEMORY),\n#endif\n#ifdef SQLITE_MAX_MMAP_SIZE\n  \"MAX_MMAP_SIZE=\" CTIMEOPT_VAL(SQLITE_MAX_MMAP_SIZE),\n#endif\n#ifdef SQLITE_MAX_MMAP_SIZE_\n  \"MAX_MMAP_SIZE_=\" CTIMEOPT_VAL(SQLITE_MAX_MMAP_SIZE_),\n#endif\n#ifdef SQLITE_MAX_PAGE_COUNT\n  \"MAX_PAGE_COUNT=\" CTIMEOPT_VAL(SQLITE_MAX_PAGE_COUNT),\n#endif\n#ifdef SQLITE_MAX_PAGE_SIZE\n  \"MAX_PAGE_SIZE=\" CTIMEOPT_VAL(SQLITE_MAX_PAGE_SIZE),\n#endif\n#ifdef SQLITE_MAX_SCHEMA_RETRY\n  \"MAX_SCHEMA_RETRY=\" CTIMEOPT_VAL(SQLITE_MAX_SCHEMA_RETRY),\n#endif\n#ifdef SQLITE_MAX_SQL_LENGTH\n  \"MAX_SQL_LENGTH=\" CTIMEOPT_VAL(SQLITE_MAX_SQL_LENGTH),\n#endif\n#ifdef SQLITE_MAX_TRIGGER_DEPTH\n  \"MAX_TRIGGER_DEPTH=\" CTIMEOPT_VAL(SQLITE_MAX_TRIGGER_DEPTH),\n#endif\n#ifdef SQLITE_MAX_VARIABLE_NUMBER\n  \"MAX_VARIABLE_NUMBER=\" CTIMEOPT_VAL(SQLITE_MAX_VARIABLE_NUMBER),\n#endif\n#ifdef SQLITE_MAX_VDBE_OP\n  \"MAX_VDBE_OP=\" CTIMEOPT_VAL(SQLITE_MAX_VDBE_OP),\n#endif\n#ifdef SQLITE_MAX_WORKER_THREADS\n  \"MAX_WORKER_THREADS=\" CTIMEOPT_VAL(SQLITE_MAX_WORKER_THREADS),\n#endif\n#if SQLITE_MEMDEBUG\n  \"MEMDEBUG\",\n#endif\n#if SQLITE_MIXED_ENDIAN_64BIT_FLOAT\n  \"MIXED_ENDIAN_64BIT_FLOAT\",\n#endif\n#if SQLITE_MMAP_READWRITE\n  \"MMAP_READWRITE\",\n#endif\n#if SQLITE_MUTEX_NOOP\n  \"MUTEX_NOOP\",\n#endif\n#if SQLITE_MUTEX_NREF\n  \"MUTEX_NREF\",\n#endif\n#if SQLITE_MUTEX_OMIT\n  \"MUTEX_OMIT\",\n#endif\n#if SQLITE_MUTEX_PTHREADS\n  \"MUTEX_PTHREADS\",\n#endif\n#if SQLITE_MUTEX_W32\n  \"MUTEX_W32\",\n#endif\n#if SQLITE_NEED_ERR_NAME\n  \"NEED_ERR_NAME\",\n#endif\n#if SQLITE_NOINLINE\n  \"NOINLINE\",\n#endif\n#if SQLITE_NO_SYNC\n  \"NO_SYNC\",\n#endif\n#if SQLITE_OMIT_ALTERTABLE\n  \"OMIT_ALTERTABLE\",\n#endif\n#if SQLITE_OMIT_ANALYZE\n  \"OMIT_ANALYZE\",\n#endif\n#if SQLITE_OMIT_ATTACH\n  \"OMIT_ATTACH\",\n#endif\n#if SQLITE_OMIT_AUTHORIZATION\n  \"OMIT_AUTHORIZATION\",\n#endif\n#if SQLITE_OMIT_AUTOINCREMENT\n  \"OMIT_AUTOINCREMENT\",\n#endif\n#if SQLITE_OMIT_AUTOINIT\n  \"OMIT_AUTOINIT\",\n#endif\n#if SQLITE_OMIT_AUTOMATIC_INDEX\n  \"OMIT_AUTOMATIC_INDEX\",\n#endif\n#if SQLITE_OMIT_AUTORESET\n  \"OMIT_AUTORESET\",\n#endif\n#if SQLITE_OMIT_AUTOVACUUM\n  \"OMIT_AUTOVACUUM\",\n#endif\n#if SQLITE_OMIT_BETWEEN_OPTIMIZATION\n  \"OMIT_BETWEEN_OPTIMIZATION\",\n#endif\n#if SQLITE_OMIT_BLOB_LITERAL\n  \"OMIT_BLOB_LITERAL\",\n#endif\n#if SQLITE_OMIT_BTREECOUNT\n  \"OMIT_BTREECOUNT\",\n#endif\n#if SQLITE_OMIT_CAST\n  \"OMIT_CAST\",\n#endif\n#if SQLITE_OMIT_CHECK\n  \"OMIT_CHECK\",\n#endif\n#if SQLITE_OMIT_COMPLETE\n  \"OMIT_COMPLETE\",\n#endif\n#if SQLITE_OMIT_COMPOUND_SELECT\n  \"OMIT_COMPOUND_SELECT\",\n#endif\n#if SQLITE_OMIT_CONFLICT_CLAUSE\n  \"OMIT_CONFLICT_CLAUSE\",\n#endif\n#if SQLITE_OMIT_CTE\n  \"OMIT_CTE\",\n#endif\n#if SQLITE_OMIT_DATETIME_FUNCS\n  \"OMIT_DATETIME_FUNCS\",\n#endif\n#if SQLITE_OMIT_DECLTYPE\n  \"OMIT_DECLTYPE\",\n#endif\n#if SQLITE_OMIT_DEPRECATED\n  \"OMIT_DEPRECATED\",\n#endif\n#if SQLITE_OMIT_DISKIO\n  \"OMIT_DISKIO\",\n#endif\n#if SQLITE_OMIT_EXPLAIN\n  \"OMIT_EXPLAIN\",\n#endif\n#if SQLITE_OMIT_FLAG_PRAGMAS\n  \"OMIT_FLAG_PRAGMAS\",\n#endif\n#if SQLITE_OMIT_FLOATING_POINT\n  \"OMIT_FLOATING_POINT\",\n#endif\n#if SQLITE_OMIT_FOREIGN_KEY\n  \"OMIT_FOREIGN_KEY\",\n#endif\n#if SQLITE_OMIT_GET_TABLE\n  \"OMIT_GET_TABLE\",\n#endif\n#if SQLITE_OMIT_HEX_INTEGER\n  \"OMIT_HEX_INTEGER\",\n#endif\n#if SQLITE_OMIT_INCRBLOB\n  \"OMIT_INCRBLOB\",\n#endif\n#if SQLITE_OMIT_INTEGRITY_CHECK\n  \"OMIT_INTEGRITY_CHECK\",\n#endif\n#if SQLITE_OMIT_LIKE_OPTIMIZATION\n  \"OMIT_LIKE_OPTIMIZATION\",\n#endif\n#if SQLITE_OMIT_LOAD_EXTENSION\n  \"OMIT_LOAD_EXTENSION\",\n#endif\n#if SQLITE_OMIT_LOCALTIME\n  \"OMIT_LOCALTIME\",\n#endif\n#if SQLITE_OMIT_LOOKASIDE\n  \"OMIT_LOOKASIDE\",\n#endif\n#if SQLITE_OMIT_MEMORYDB\n  \"OMIT_MEMORYDB\",\n#endif\n#if SQLITE_OMIT_OR_OPTIMIZATION\n  \"OMIT_OR_OPTIMIZATION\",\n#endif\n#if SQLITE_OMIT_PAGER_PRAGMAS\n  \"OMIT_PAGER_PRAGMAS\",\n#endif\n#if SQLITE_OMIT_PARSER_TRACE\n  \"OMIT_PARSER_TRACE\",\n#endif\n#if SQLITE_OMIT_POPEN\n  \"OMIT_POPEN\",\n#endif\n#if SQLITE_OMIT_PRAGMA\n  \"OMIT_PRAGMA\",\n#endif\n#if SQLITE_OMIT_PROGRESS_CALLBACK\n  \"OMIT_PROGRESS_CALLBACK\",\n#endif\n#if SQLITE_OMIT_QUICKBALANCE\n  \"OMIT_QUICKBALANCE\",\n#endif\n#if SQLITE_OMIT_REINDEX\n  \"OMIT_REINDEX\",\n#endif\n#if SQLITE_OMIT_SCHEMA_PRAGMAS\n  \"OMIT_SCHEMA_PRAGMAS\",\n#endif\n#if SQLITE_OMIT_SCHEMA_VERSION_PRAGMAS\n  \"OMIT_SCHEMA_VERSION_PRAGMAS\",\n#endif\n#if SQLITE_OMIT_SHARED_CACHE\n  \"OMIT_SHARED_CACHE\",\n#endif\n#if SQLITE_OMIT_SHUTDOWN_DIRECTORIES\n  \"OMIT_SHUTDOWN_DIRECTORIES\",\n#endif\n#if SQLITE_OMIT_SUBQUERY\n  \"OMIT_SUBQUERY\",\n#endif\n#if SQLITE_OMIT_TCL_VARIABLE\n  \"OMIT_TCL_VARIABLE\",\n#endif\n#if SQLITE_OMIT_TEMPDB\n  \"OMIT_TEMPDB\",\n#endif\n#if SQLITE_OMIT_TEST_CONTROL\n  \"OMIT_TEST_CONTROL\",\n#endif\n#if SQLITE_OMIT_TRACE\n  \"OMIT_TRACE\",\n#endif\n#if SQLITE_OMIT_TRIGGER\n  \"OMIT_TRIGGER\",\n#endif\n#if SQLITE_OMIT_TRUNCATE_OPTIMIZATION\n  \"OMIT_TRUNCATE_OPTIMIZATION\",\n#endif\n#if SQLITE_OMIT_UTF16\n  \"OMIT_UTF16\",\n#endif\n#if SQLITE_OMIT_VACUUM\n  \"OMIT_VACUUM\",\n#endif\n#if SQLITE_OMIT_VIEW\n  \"OMIT_VIEW\",\n#endif\n#if SQLITE_OMIT_VIRTUALTABLE\n  \"OMIT_VIRTUALTABLE\",\n#endif\n#if SQLITE_OMIT_WAL\n  \"OMIT_WAL\",\n#endif\n#if SQLITE_OMIT_WSD\n  \"OMIT_WSD\",\n#endif\n#if SQLITE_OMIT_XFER_OPT\n  \"OMIT_XFER_OPT\",\n#endif\n#if SQLITE_PCACHE_SEPARATE_HEADER\n  \"PCACHE_SEPARATE_HEADER\",\n#endif\n#if SQLITE_PERFORMANCE_TRACE\n  \"PERFORMANCE_TRACE\",\n#endif\n#if SQLITE_POWERSAFE_OVERWRITE\n  \"POWERSAFE_OVERWRITE\",\n#endif\n#if SQLITE_PREFER_PROXY_LOCKING\n  \"PREFER_PROXY_LOCKING\",\n#endif\n#if SQLITE_PROXY_DEBUG\n  \"PROXY_DEBUG\",\n#endif\n#if SQLITE_REVERSE_UNORDERED_SELECTS\n  \"REVERSE_UNORDERED_SELECTS\",\n#endif\n#if SQLITE_RTREE_INT_ONLY\n  \"RTREE_INT_ONLY\",\n#endif\n#if SQLITE_SECURE_DELETE\n  \"SECURE_DELETE\",\n#endif\n#if SQLITE_SMALL_STACK\n  \"SMALL_STACK\",\n#endif\n#ifdef SQLITE_SORTER_PMASZ\n  \"SORTER_PMASZ=\" CTIMEOPT_VAL(SQLITE_SORTER_PMASZ),\n#endif\n#if SQLITE_SOUNDEX\n  \"SOUNDEX\",\n#endif\n#ifdef SQLITE_STAT4_SAMPLES\n  \"STAT4_SAMPLES=\" CTIMEOPT_VAL(SQLITE_STAT4_SAMPLES),\n#endif\n#ifdef SQLITE_STMTJRNL_SPILL\n  \"STMTJRNL_SPILL=\" CTIMEOPT_VAL(SQLITE_STMTJRNL_SPILL),\n#endif\n#if SQLITE_SUBSTR_COMPATIBILITY\n  \"SUBSTR_COMPATIBILITY\",\n#endif\n#if SQLITE_SYSTEM_MALLOC\n  \"SYSTEM_MALLOC\",\n#endif\n#if SQLITE_TCL\n  \"TCL\",\n#endif\n#ifdef SQLITE_TEMP_STORE\n  \"TEMP_STORE=\" CTIMEOPT_VAL(SQLITE_TEMP_STORE),\n#endif\n#if SQLITE_TEST\n  \"TEST\",\n#endif\n#if defined(SQLITE_THREADSAFE)\n  \"THREADSAFE=\" CTIMEOPT_VAL(SQLITE_THREADSAFE),\n#elif defined(THREADSAFE)\n  \"THREADSAFE=\" CTIMEOPT_VAL(THREADSAFE),\n#else\n  \"THREADSAFE=1\",\n#endif\n#if SQLITE_UNLINK_AFTER_CLOSE\n  \"UNLINK_AFTER_CLOSE\",\n#endif\n#if SQLITE_UNTESTABLE\n  \"UNTESTABLE\",\n#endif\n#if SQLITE_USER_AUTHENTICATION\n  \"USER_AUTHENTICATION\",\n#endif\n#if SQLITE_USE_ALLOCA\n  \"USE_ALLOCA\",\n#endif\n#if SQLITE_USE_FCNTL_TRACE\n  \"USE_FCNTL_TRACE\",\n#endif\n#if SQLITE_USE_URI\n  \"USE_URI\",\n#endif\n#if SQLITE_VDBE_COVERAGE\n  \"VDBE_COVERAGE\",\n#endif\n#if SQLITE_WIN32_MALLOC\n  \"WIN32_MALLOC\",\n#endif\n#if SQLITE_ZERO_MALLOC\n  \"ZERO_MALLOC\",\n#endif\n/* \n** END CODE GENERATED BY tool/mkctime.tcl \n*/\n};\n\nSQLITE_PRIVATE const char **sqlite3CompileOptions(int *pnOpt){\n  *pnOpt = sizeof(sqlite3azCompileOpt) / sizeof(sqlite3azCompileOpt[0]);\n  return (const char**)sqlite3azCompileOpt;\n}\n\n#endif /* SQLITE_OMIT_COMPILEOPTION_DIAGS */\n\n/************** End of ctime.c ***********************************************/\n/************** Begin file sqliteInt.h ***************************************/\n/*\n** 2001 September 15\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n*************************************************************************\n** Internal interface definitions for SQLite.\n**\n*/\n#ifndef SQLITEINT_H\n#define SQLITEINT_H\n\n/* Special Comments:\n**\n** Some comments have special meaning to the tools that measure test\n** coverage:\n**\n**    NO_TEST                     - The branches on this line are not\n**                                  measured by branch coverage.  This is\n**                                  used on lines of code that actually\n**                                  implement parts of coverage testing.\n**\n**    OPTIMIZATION-IF-TRUE        - This branch is allowed to alway be false\n**                                  and the correct answer is still obtained,\n**                                  though perhaps more slowly.\n**\n**    OPTIMIZATION-IF-FALSE       - This branch is allowed to alway be true\n**                                  and the correct answer is still obtained,\n**                                  though perhaps more slowly.\n**\n**    PREVENTS-HARMLESS-OVERREAD  - This branch prevents a buffer overread\n**                                  that would be harmless and undetectable\n**                                  if it did occur.  \n**\n** In all cases, the special comment must be enclosed in the usual\n** slash-asterisk...asterisk-slash comment marks, with no spaces between the \n** asterisks and the comment text.\n*/\n\n/*\n** Make sure the Tcl calling convention macro is defined.  This macro is\n** only used by test code and Tcl integration code.\n*/\n#ifndef SQLITE_TCLAPI\n#  define SQLITE_TCLAPI\n#endif\n\n/*\n** Include the header file used to customize the compiler options for MSVC.\n** This should be done first so that it can successfully prevent spurious\n** compiler warnings due to subsequent content in this file and other files\n** that are included by this file.\n*/\n/************** Include msvc.h in the middle of sqliteInt.h ******************/\n/************** Begin file msvc.h ********************************************/\n/*\n** 2015 January 12\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n******************************************************************************\n**\n** This file contains code that is specific to MSVC.\n*/\n#ifndef SQLITE_MSVC_H\n#define SQLITE_MSVC_H\n\n#if defined(_MSC_VER)\n#pragma warning(disable : 4054)\n#pragma warning(disable : 4055)\n#pragma warning(disable : 4100)\n#pragma warning(disable : 4127)\n#pragma warning(disable : 4130)\n#pragma warning(disable : 4152)\n#pragma warning(disable : 4189)\n#pragma warning(disable : 4206)\n#pragma warning(disable : 4210)\n#pragma warning(disable : 4232)\n#pragma warning(disable : 4244)\n#pragma warning(disable : 4305)\n#pragma warning(disable : 4306)\n#pragma warning(disable : 4702)\n#pragma warning(disable : 4706)\n#endif /* defined(_MSC_VER) */\n\n#endif /* SQLITE_MSVC_H */\n\n/************** End of msvc.h ************************************************/\n/************** Continuing where we left off in sqliteInt.h ******************/\n\n/*\n** Special setup for VxWorks\n*/\n/************** Include vxworks.h in the middle of sqliteInt.h ***************/\n/************** Begin file vxworks.h *****************************************/\n/*\n** 2015-03-02\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n******************************************************************************\n**\n** This file contains code that is specific to Wind River's VxWorks\n*/\n#if defined(__RTP__) || defined(_WRS_KERNEL)\n/* This is VxWorks.  Set up things specially for that OS\n*/\n#include <vxWorks.h>\n#include <pthread.h>  /* amalgamator: dontcache */\n#define OS_VXWORKS 1\n#define SQLITE_OS_OTHER 0\n#define SQLITE_HOMEGROWN_RECURSIVE_MUTEX 1\n#define SQLITE_OMIT_LOAD_EXTENSION 1\n#define SQLITE_ENABLE_LOCKING_STYLE 0\n#define HAVE_UTIME 1\n#else\n/* This is not VxWorks. */\n#define OS_VXWORKS 0\n#define HAVE_FCHOWN 1\n#define HAVE_READLINK 1\n#define HAVE_LSTAT 1\n#endif /* defined(_WRS_KERNEL) */\n\n/************** End of vxworks.h *********************************************/\n/************** Continuing where we left off in sqliteInt.h ******************/\n\n/*\n** These #defines should enable >2GB file support on POSIX if the\n** underlying operating system supports it.  If the OS lacks\n** large file support, or if the OS is windows, these should be no-ops.\n**\n** Ticket #2739:  The _LARGEFILE_SOURCE macro must appear before any\n** system #includes.  Hence, this block of code must be the very first\n** code in all source files.\n**\n** Large file support can be disabled using the -DSQLITE_DISABLE_LFS switch\n** on the compiler command line.  This is necessary if you are compiling\n** on a recent machine (ex: Red Hat 7.2) but you want your code to work\n** on an older machine (ex: Red Hat 6.0).  If you compile on Red Hat 7.2\n** without this option, LFS is enable.  But LFS does not exist in the kernel\n** in Red Hat 6.0, so the code won't work.  Hence, for maximum binary\n** portability you should omit LFS.\n**\n** The previous paragraph was written in 2005.  (This paragraph is written\n** on 2008-11-28.) These days, all Linux kernels support large files, so\n** you should probably leave LFS enabled.  But some embedded platforms might\n** lack LFS in which case the SQLITE_DISABLE_LFS macro might still be useful.\n**\n** Similar is true for Mac OS X.  LFS is only supported on Mac OS X 9 and later.\n*/\n#ifndef SQLITE_DISABLE_LFS\n# define _LARGE_FILE       1\n# ifndef _FILE_OFFSET_BITS\n#   define _FILE_OFFSET_BITS 64\n# endif\n# define _LARGEFILE_SOURCE 1\n#endif\n\n/* The GCC_VERSION and MSVC_VERSION macros are used to\n** conditionally include optimizations for each of these compilers.  A\n** value of 0 means that compiler is not being used.  The\n** SQLITE_DISABLE_INTRINSIC macro means do not use any compiler-specific\n** optimizations, and hence set all compiler macros to 0\n**\n** There was once also a CLANG_VERSION macro.  However, we learn that the\n** version numbers in clang are for \"marketing\" only and are inconsistent\n** and unreliable.  Fortunately, all versions of clang also recognize the\n** gcc version numbers and have reasonable settings for gcc version numbers,\n** so the GCC_VERSION macro will be set to a correct non-zero value even\n** when compiling with clang.\n*/\n#if defined(__GNUC__) && !defined(SQLITE_DISABLE_INTRINSIC)\n# define GCC_VERSION (__GNUC__*1000000+__GNUC_MINOR__*1000+__GNUC_PATCHLEVEL__)\n#else\n# define GCC_VERSION 0\n#endif\n#if defined(_MSC_VER) && !defined(SQLITE_DISABLE_INTRINSIC)\n# define MSVC_VERSION _MSC_VER\n#else\n# define MSVC_VERSION 0\n#endif\n\n/* Needed for various definitions... */\n#if defined(__GNUC__) && !defined(_GNU_SOURCE)\n# define _GNU_SOURCE\n#endif\n\n#if defined(__OpenBSD__) && !defined(_BSD_SOURCE)\n# define _BSD_SOURCE\n#endif\n\n/*\n** For MinGW, check to see if we can include the header file containing its\n** version information, among other things.  Normally, this internal MinGW\n** header file would [only] be included automatically by other MinGW header\n** files; however, the contained version information is now required by this\n** header file to work around binary compatibility issues (see below) and\n** this is the only known way to reliably obtain it.  This entire #if block\n** would be completely unnecessary if there was any other way of detecting\n** MinGW via their preprocessor (e.g. if they customized their GCC to define\n** some MinGW-specific macros).  When compiling for MinGW, either the\n** _HAVE_MINGW_H or _HAVE__MINGW_H (note the extra underscore) macro must be\n** defined; otherwise, detection of conditions specific to MinGW will be\n** disabled.\n*/\n#if defined(_HAVE_MINGW_H)\n# include \"mingw.h\"\n#elif defined(_HAVE__MINGW_H)\n# include \"_mingw.h\"\n#endif\n\n/*\n** For MinGW version 4.x (and higher), check to see if the _USE_32BIT_TIME_T\n** define is required to maintain binary compatibility with the MSVC runtime\n** library in use (e.g. for Windows XP).\n*/\n#if !defined(_USE_32BIT_TIME_T) && !defined(_USE_64BIT_TIME_T) && \\\n    defined(_WIN32) && !defined(_WIN64) && \\\n    defined(__MINGW_MAJOR_VERSION) && __MINGW_MAJOR_VERSION >= 4 && \\\n    defined(__MSVCRT__)\n# define _USE_32BIT_TIME_T\n#endif\n\n/* The public SQLite interface.  The _FILE_OFFSET_BITS macro must appear\n** first in QNX.  Also, the _USE_32BIT_TIME_T macro must appear first for\n** MinGW.\n*/\n/************** Include sqlite3.h in the middle of sqliteInt.h ***************/\n/************** Begin file sqlite3.h *****************************************/\n/*\n** 2001-09-15\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n*************************************************************************\n** This header file defines the interface that the SQLite library\n** presents to client programs.  If a C-function, structure, datatype,\n** or constant definition does not appear in this file, then it is\n** not a published API of SQLite, is subject to change without\n** notice, and should not be referenced by programs that use SQLite.\n**\n** Some of the definitions that are in this file are marked as\n** \"experimental\".  Experimental interfaces are normally new\n** features recently added to SQLite.  We do not anticipate changes\n** to experimental interfaces but reserve the right to make minor changes\n** if experience from use \"in the wild\" suggest such changes are prudent.\n**\n** The official C-language API documentation for SQLite is derived\n** from comments in this file.  This file is the authoritative source\n** on how SQLite interfaces are supposed to operate.\n**\n** The name of this file under configuration management is \"sqlite.h.in\".\n** The makefile makes some minor changes to this file (such as inserting\n** the version number) and changes its name to \"sqlite3.h\" as\n** part of the build process.\n*/\n#ifndef SQLITE3_H\n#define SQLITE3_H\n#include <stdarg.h>     /* Needed for the definition of va_list */\n\n/*\n** Make sure we can call this stuff from C++.\n*/\n#if 0\nextern \"C\" {\n#endif\n\n\n/*\n** Provide the ability to override linkage features of the interface.\n*/\n#ifndef SQLITE_EXTERN\n# define SQLITE_EXTERN extern\n#endif\n#ifndef SQLITE_API\n# define SQLITE_API\n#endif\n#ifndef SQLITE_CDECL\n# define SQLITE_CDECL\n#endif\n#ifndef SQLITE_APICALL\n# define SQLITE_APICALL\n#endif\n#ifndef SQLITE_STDCALL\n# define SQLITE_STDCALL SQLITE_APICALL\n#endif\n#ifndef SQLITE_CALLBACK\n# define SQLITE_CALLBACK\n#endif\n#ifndef SQLITE_SYSAPI\n# define SQLITE_SYSAPI\n#endif\n\n/*\n** These no-op macros are used in front of interfaces to mark those\n** interfaces as either deprecated or experimental.  New applications\n** should not use deprecated interfaces - they are supported for backwards\n** compatibility only.  Application writers should be aware that\n** experimental interfaces are subject to change in point releases.\n**\n** These macros used to resolve to various kinds of compiler magic that\n** would generate warning messages when they were used.  But that\n** compiler magic ended up generating such a flurry of bug reports\n** that we have taken it all out and gone back to using simple\n** noop macros.\n*/\n#define SQLITE_DEPRECATED\n#define SQLITE_EXPERIMENTAL\n\n/*\n** Ensure these symbols were not defined by some previous header file.\n*/\n#ifdef SQLITE_VERSION\n# undef SQLITE_VERSION\n#endif\n#ifdef SQLITE_VERSION_NUMBER\n# undef SQLITE_VERSION_NUMBER\n#endif\n\n/*\n** CAPI3REF: Compile-Time Library Version Numbers\n**\n** ^(The [SQLITE_VERSION] C preprocessor macro in the sqlite3.h header\n** evaluates to a string literal that is the SQLite version in the\n** format \"X.Y.Z\" where X is the major version number (always 3 for\n** SQLite3) and Y is the minor version number and Z is the release number.)^\n** ^(The [SQLITE_VERSION_NUMBER] C preprocessor macro resolves to an integer\n** with the value (X*1000000 + Y*1000 + Z) where X, Y, and Z are the same\n** numbers used in [SQLITE_VERSION].)^\n** The SQLITE_VERSION_NUMBER for any given release of SQLite will also\n** be larger than the release from which it is derived.  Either Y will\n** be held constant and Z will be incremented or else Y will be incremented\n** and Z will be reset to zero.\n**\n** Since [version 3.6.18] ([dateof:3.6.18]), \n** SQLite source code has been stored in the\n** <a href=\"http://www.fossil-scm.org/\">Fossil configuration management\n** system</a>.  ^The SQLITE_SOURCE_ID macro evaluates to\n** a string which identifies a particular check-in of SQLite\n** within its configuration management system.  ^The SQLITE_SOURCE_ID\n** string contains the date and time of the check-in (UTC) and a SHA1\n** or SHA3-256 hash of the entire source tree.  If the source code has\n** been edited in any way since it was last checked in, then the last\n** four hexadecimal digits of the hash may be modified.\n**\n** See also: [sqlite3_libversion()],\n** [sqlite3_libversion_number()], [sqlite3_sourceid()],\n** [sqlite_version()] and [sqlite_source_id()].\n*/\n#define SQLITE_VERSION        \"3.23.0\"\n#define SQLITE_VERSION_NUMBER 3023000\n#define SQLITE_SOURCE_ID      \"2018-02-27 15:40:59 9a7f02c50e6c8a3dc3addf4e51b7e04bd31670d6ce58d26d55273c43b5ecc8b0\"\n\n/*\n** CAPI3REF: Run-Time Library Version Numbers\n** KEYWORDS: sqlite3_version sqlite3_sourceid\n**\n** These interfaces provide the same information as the [SQLITE_VERSION],\n** [SQLITE_VERSION_NUMBER], and [SQLITE_SOURCE_ID] C preprocessor macros\n** but are associated with the library instead of the header file.  ^(Cautious\n** programmers might include assert() statements in their application to\n** verify that values returned by these interfaces match the macros in\n** the header, and thus ensure that the application is\n** compiled with matching library and header files.\n**\n** <blockquote><pre>\n** assert( sqlite3_libversion_number()==SQLITE_VERSION_NUMBER );\n** assert( strncmp(sqlite3_sourceid(),SQLITE_SOURCE_ID,80)==0 );\n** assert( strcmp(sqlite3_libversion(),SQLITE_VERSION)==0 );\n** </pre></blockquote>)^\n**\n** ^The sqlite3_version[] string constant contains the text of [SQLITE_VERSION]\n** macro.  ^The sqlite3_libversion() function returns a pointer to the\n** to the sqlite3_version[] string constant.  The sqlite3_libversion()\n** function is provided for use in DLLs since DLL users usually do not have\n** direct access to string constants within the DLL.  ^The\n** sqlite3_libversion_number() function returns an integer equal to\n** [SQLITE_VERSION_NUMBER].  ^(The sqlite3_sourceid() function returns \n** a pointer to a string constant whose value is the same as the \n** [SQLITE_SOURCE_ID] C preprocessor macro.  Except if SQLite is built\n** using an edited copy of [the amalgamation], then the last four characters\n** of the hash might be different from [SQLITE_SOURCE_ID].)^\n**\n** See also: [sqlite_version()] and [sqlite_source_id()].\n*/\nSQLITE_API const char sqlite3_version[] = SQLITE_VERSION;\nSQLITE_API const char *sqlite3_libversion(void);\nSQLITE_API const char *sqlite3_sourceid(void);\nSQLITE_API int sqlite3_libversion_number(void);\n\n/*\n** CAPI3REF: Run-Time Library Compilation Options Diagnostics\n**\n** ^The sqlite3_compileoption_used() function returns 0 or 1 \n** indicating whether the specified option was defined at \n** compile time.  ^The SQLITE_ prefix may be omitted from the \n** option name passed to sqlite3_compileoption_used().  \n**\n** ^The sqlite3_compileoption_get() function allows iterating\n** over the list of options that were defined at compile time by\n** returning the N-th compile time option string.  ^If N is out of range,\n** sqlite3_compileoption_get() returns a NULL pointer.  ^The SQLITE_ \n** prefix is omitted from any strings returned by \n** sqlite3_compileoption_get().\n**\n** ^Support for the diagnostic functions sqlite3_compileoption_used()\n** and sqlite3_compileoption_get() may be omitted by specifying the \n** [SQLITE_OMIT_COMPILEOPTION_DIAGS] option at compile time.\n**\n** See also: SQL functions [sqlite_compileoption_used()] and\n** [sqlite_compileoption_get()] and the [compile_options pragma].\n*/\n#ifndef SQLITE_OMIT_COMPILEOPTION_DIAGS\nSQLITE_API int sqlite3_compileoption_used(const char *zOptName);\nSQLITE_API const char *sqlite3_compileoption_get(int N);\n#endif\n\n/*\n** CAPI3REF: Test To See If The Library Is Threadsafe\n**\n** ^The sqlite3_threadsafe() function returns zero if and only if\n** SQLite was compiled with mutexing code omitted due to the\n** [SQLITE_THREADSAFE] compile-time option being set to 0.\n**\n** SQLite can be compiled with or without mutexes.  When\n** the [SQLITE_THREADSAFE] C preprocessor macro is 1 or 2, mutexes\n** are enabled and SQLite is threadsafe.  When the\n** [SQLITE_THREADSAFE] macro is 0, \n** the mutexes are omitted.  Without the mutexes, it is not safe\n** to use SQLite concurrently from more than one thread.\n**\n** Enabling mutexes incurs a measurable performance penalty.\n** So if speed is of utmost importance, it makes sense to disable\n** the mutexes.  But for maximum safety, mutexes should be enabled.\n** ^The default behavior is for mutexes to be enabled.\n**\n** This interface can be used by an application to make sure that the\n** version of SQLite that it is linking against was compiled with\n** the desired setting of the [SQLITE_THREADSAFE] macro.\n**\n** This interface only reports on the compile-time mutex setting\n** of the [SQLITE_THREADSAFE] flag.  If SQLite is compiled with\n** SQLITE_THREADSAFE=1 or =2 then mutexes are enabled by default but\n** can be fully or partially disabled using a call to [sqlite3_config()]\n** with the verbs [SQLITE_CONFIG_SINGLETHREAD], [SQLITE_CONFIG_MULTITHREAD],\n** or [SQLITE_CONFIG_SERIALIZED].  ^(The return value of the\n** sqlite3_threadsafe() function shows only the compile-time setting of\n** thread safety, not any run-time changes to that setting made by\n** sqlite3_config(). In other words, the return value from sqlite3_threadsafe()\n** is unchanged by calls to sqlite3_config().)^\n**\n** See the [threading mode] documentation for additional information.\n*/\nSQLITE_API int sqlite3_threadsafe(void);\n\n/*\n** CAPI3REF: Database Connection Handle\n** KEYWORDS: {database connection} {database connections}\n**\n** Each open SQLite database is represented by a pointer to an instance of\n** the opaque structure named \"sqlite3\".  It is useful to think of an sqlite3\n** pointer as an object.  The [sqlite3_open()], [sqlite3_open16()], and\n** [sqlite3_open_v2()] interfaces are its constructors, and [sqlite3_close()]\n** and [sqlite3_close_v2()] are its destructors.  There are many other\n** interfaces (such as\n** [sqlite3_prepare_v2()], [sqlite3_create_function()], and\n** [sqlite3_busy_timeout()] to name but three) that are methods on an\n** sqlite3 object.\n*/\ntypedef struct sqlite3 sqlite3;\n\n/*\n** CAPI3REF: 64-Bit Integer Types\n** KEYWORDS: sqlite_int64 sqlite_uint64\n**\n** Because there is no cross-platform way to specify 64-bit integer types\n** SQLite includes typedefs for 64-bit signed and unsigned integers.\n**\n** The sqlite3_int64 and sqlite3_uint64 are the preferred type definitions.\n** The sqlite_int64 and sqlite_uint64 types are supported for backwards\n** compatibility only.\n**\n** ^The sqlite3_int64 and sqlite_int64 types can store integer values\n** between -9223372036854775808 and +9223372036854775807 inclusive.  ^The\n** sqlite3_uint64 and sqlite_uint64 types can store integer values \n** between 0 and +18446744073709551615 inclusive.\n*/\n#ifdef SQLITE_INT64_TYPE\n  typedef SQLITE_INT64_TYPE sqlite_int64;\n# ifdef SQLITE_UINT64_TYPE\n    typedef SQLITE_UINT64_TYPE sqlite_uint64;\n# else  \n    typedef unsigned SQLITE_INT64_TYPE sqlite_uint64;\n# endif\n#elif defined(_MSC_VER) || defined(__BORLANDC__)\n  typedef __int64 sqlite_int64;\n  typedef unsigned __int64 sqlite_uint64;\n#else\n  typedef long long int sqlite_int64;\n  typedef unsigned long long int sqlite_uint64;\n#endif\ntypedef sqlite_int64 sqlite3_int64;\ntypedef sqlite_uint64 sqlite3_uint64;\n\n/*\n** If compiling for a processor that lacks floating point support,\n** substitute integer for floating-point.\n*/\n#ifdef SQLITE_OMIT_FLOATING_POINT\n# define double sqlite3_int64\n#endif\n\n/*\n** CAPI3REF: Closing A Database Connection\n** DESTRUCTOR: sqlite3\n**\n** ^The sqlite3_close() and sqlite3_close_v2() routines are destructors\n** for the [sqlite3] object.\n** ^Calls to sqlite3_close() and sqlite3_close_v2() return [SQLITE_OK] if\n** the [sqlite3] object is successfully destroyed and all associated\n** resources are deallocated.\n**\n** ^If the database connection is associated with unfinalized prepared\n** statements or unfinished sqlite3_backup objects then sqlite3_close()\n** will leave the database connection open and return [SQLITE_BUSY].\n** ^If sqlite3_close_v2() is called with unfinalized prepared statements\n** and/or unfinished sqlite3_backups, then the database connection becomes\n** an unusable \"zombie\" which will automatically be deallocated when the\n** last prepared statement is finalized or the last sqlite3_backup is\n** finished.  The sqlite3_close_v2() interface is intended for use with\n** host languages that are garbage collected, and where the order in which\n** destructors are called is arbitrary.\n**\n** Applications should [sqlite3_finalize | finalize] all [prepared statements],\n** [sqlite3_blob_close | close] all [BLOB handles], and \n** [sqlite3_backup_finish | finish] all [sqlite3_backup] objects associated\n** with the [sqlite3] object prior to attempting to close the object.  ^If\n** sqlite3_close_v2() is called on a [database connection] that still has\n** outstanding [prepared statements], [BLOB handles], and/or\n** [sqlite3_backup] objects then it returns [SQLITE_OK] and the deallocation\n** of resources is deferred until all [prepared statements], [BLOB handles],\n** and [sqlite3_backup] objects are also destroyed.\n**\n** ^If an [sqlite3] object is destroyed while a transaction is open,\n** the transaction is automatically rolled back.\n**\n** The C parameter to [sqlite3_close(C)] and [sqlite3_close_v2(C)]\n** must be either a NULL\n** pointer or an [sqlite3] object pointer obtained\n** from [sqlite3_open()], [sqlite3_open16()], or\n** [sqlite3_open_v2()], and not previously closed.\n** ^Calling sqlite3_close() or sqlite3_close_v2() with a NULL pointer\n** argument is a harmless no-op.\n*/\nSQLITE_API int sqlite3_close(sqlite3*);\nSQLITE_API int sqlite3_close_v2(sqlite3*);\n\n/*\n** The type for a callback function.\n** This is legacy and deprecated.  It is included for historical\n** compatibility and is not documented.\n*/\ntypedef int (*sqlite3_callback)(void*,int,char**, char**);\n\n/*\n** CAPI3REF: One-Step Query Execution Interface\n** METHOD: sqlite3\n**\n** The sqlite3_exec() interface is a convenience wrapper around\n** [sqlite3_prepare_v2()], [sqlite3_step()], and [sqlite3_finalize()],\n** that allows an application to run multiple statements of SQL\n** without having to use a lot of C code. \n**\n** ^The sqlite3_exec() interface runs zero or more UTF-8 encoded,\n** semicolon-separate SQL statements passed into its 2nd argument,\n** in the context of the [database connection] passed in as its 1st\n** argument.  ^If the callback function of the 3rd argument to\n** sqlite3_exec() is not NULL, then it is invoked for each result row\n** coming out of the evaluated SQL statements.  ^The 4th argument to\n** sqlite3_exec() is relayed through to the 1st argument of each\n** callback invocation.  ^If the callback pointer to sqlite3_exec()\n** is NULL, then no callback is ever invoked and result rows are\n** ignored.\n**\n** ^If an error occurs while evaluating the SQL statements passed into\n** sqlite3_exec(), then execution of the current statement stops and\n** subsequent statements are skipped.  ^If the 5th parameter to sqlite3_exec()\n** is not NULL then any error message is written into memory obtained\n** from [sqlite3_malloc()] and passed back through the 5th parameter.\n** To avoid memory leaks, the application should invoke [sqlite3_free()]\n** on error message strings returned through the 5th parameter of\n** sqlite3_exec() after the error message string is no longer needed.\n** ^If the 5th parameter to sqlite3_exec() is not NULL and no errors\n** occur, then sqlite3_exec() sets the pointer in its 5th parameter to\n** NULL before returning.\n**\n** ^If an sqlite3_exec() callback returns non-zero, the sqlite3_exec()\n** routine returns SQLITE_ABORT without invoking the callback again and\n** without running any subsequent SQL statements.\n**\n** ^The 2nd argument to the sqlite3_exec() callback function is the\n** number of columns in the result.  ^The 3rd argument to the sqlite3_exec()\n** callback is an array of pointers to strings obtained as if from\n** [sqlite3_column_text()], one for each column.  ^If an element of a\n** result row is NULL then the corresponding string pointer for the\n** sqlite3_exec() callback is a NULL pointer.  ^The 4th argument to the\n** sqlite3_exec() callback is an array of pointers to strings where each\n** entry represents the name of corresponding result column as obtained\n** from [sqlite3_column_name()].\n**\n** ^If the 2nd parameter to sqlite3_exec() is a NULL pointer, a pointer\n** to an empty string, or a pointer that contains only whitespace and/or \n** SQL comments, then no SQL statements are evaluated and the database\n** is not changed.\n**\n** Restrictions:\n**\n** <ul>\n** <li> The application must ensure that the 1st parameter to sqlite3_exec()\n**      is a valid and open [database connection].\n** <li> The application must not close the [database connection] specified by\n**      the 1st parameter to sqlite3_exec() while sqlite3_exec() is running.\n** <li> The application must not modify the SQL statement text passed into\n**      the 2nd parameter of sqlite3_exec() while sqlite3_exec() is running.\n** </ul>\n*/\nSQLITE_API int sqlite3_exec(\n  sqlite3*,                                  /* An open database */\n  const char *sql,                           /* SQL to be evaluated */\n  int (*callback)(void*,int,char**,char**),  /* Callback function */\n  void *,                                    /* 1st argument to callback */\n  char **errmsg                              /* Error msg written here */\n);\n\n/*\n** CAPI3REF: Result Codes\n** KEYWORDS: {result code definitions}\n**\n** Many SQLite functions return an integer result code from the set shown\n** here in order to indicate success or failure.\n**\n** New error codes may be added in future versions of SQLite.\n**\n** See also: [extended result code definitions]\n*/\n#define SQLITE_OK           0   /* Successful result */\n/* beginning-of-error-codes */\n#define SQLITE_ERROR        1   /* Generic error */\n#define SQLITE_INTERNAL     2   /* Internal logic error in SQLite */\n#define SQLITE_PERM         3   /* Access permission denied */\n#define SQLITE_ABORT        4   /* Callback routine requested an abort */\n#define SQLITE_BUSY         5   /* The database file is locked */\n#define SQLITE_LOCKED       6   /* A table in the database is locked */\n#define SQLITE_NOMEM        7   /* A malloc() failed */\n#define SQLITE_READONLY     8   /* Attempt to write a readonly database */\n#define SQLITE_INTERRUPT    9   /* Operation terminated by sqlite3_interrupt()*/\n#define SQLITE_IOERR       10   /* Some kind of disk I/O error occurred */\n#define SQLITE_CORRUPT     11   /* The database disk image is malformed */\n#define SQLITE_NOTFOUND    12   /* Unknown opcode in sqlite3_file_control() */\n#define SQLITE_FULL        13   /* Insertion failed because database is full */\n#define SQLITE_CANTOPEN    14   /* Unable to open the database file */\n#define SQLITE_PROTOCOL    15   /* Database lock protocol error */\n#define SQLITE_EMPTY       16   /* Internal use only */\n#define SQLITE_SCHEMA      17   /* The database schema changed */\n#define SQLITE_TOOBIG      18   /* String or BLOB exceeds size limit */\n#define SQLITE_CONSTRAINT  19   /* Abort due to constraint violation */\n#define SQLITE_MISMATCH    20   /* Data type mismatch */\n#define SQLITE_MISUSE      21   /* Library used incorrectly */\n#define SQLITE_NOLFS       22   /* Uses OS features not supported on host */\n#define SQLITE_AUTH        23   /* Authorization denied */\n#define SQLITE_FORMAT      24   /* Not used */\n#define SQLITE_RANGE       25   /* 2nd parameter to sqlite3_bind out of range */\n#define SQLITE_NOTADB      26   /* File opened that is not a database file */\n#define SQLITE_NOTICE      27   /* Notifications from sqlite3_log() */\n#define SQLITE_WARNING     28   /* Warnings from sqlite3_log() */\n#define SQLITE_ROW         100  /* sqlite3_step() has another row ready */\n#define SQLITE_DONE        101  /* sqlite3_step() has finished executing */\n/* end-of-error-codes */\n\n/*\n** CAPI3REF: Extended Result Codes\n** KEYWORDS: {extended result code definitions}\n**\n** In its default configuration, SQLite API routines return one of 30 integer\n** [result codes].  However, experience has shown that many of\n** these result codes are too coarse-grained.  They do not provide as\n** much information about problems as programmers might like.  In an effort to\n** address this, newer versions of SQLite (version 3.3.8 [dateof:3.3.8]\n** and later) include\n** support for additional result codes that provide more detailed information\n** about errors. These [extended result codes] are enabled or disabled\n** on a per database connection basis using the\n** [sqlite3_extended_result_codes()] API.  Or, the extended code for\n** the most recent error can be obtained using\n** [sqlite3_extended_errcode()].\n*/\n#define SQLITE_ERROR_MISSING_COLLSEQ   (SQLITE_ERROR | (1<<8))\n#define SQLITE_ERROR_RETRY             (SQLITE_ERROR | (2<<8))\n#define SQLITE_IOERR_READ              (SQLITE_IOERR | (1<<8))\n#define SQLITE_IOERR_SHORT_READ        (SQLITE_IOERR | (2<<8))\n#define SQLITE_IOERR_WRITE             (SQLITE_IOERR | (3<<8))\n#define SQLITE_IOERR_FSYNC             (SQLITE_IOERR | (4<<8))\n#define SQLITE_IOERR_DIR_FSYNC         (SQLITE_IOERR | (5<<8))\n#define SQLITE_IOERR_TRUNCATE          (SQLITE_IOERR | (6<<8))\n#define SQLITE_IOERR_FSTAT             (SQLITE_IOERR | (7<<8))\n#define SQLITE_IOERR_UNLOCK            (SQLITE_IOERR | (8<<8))\n#define SQLITE_IOERR_RDLOCK            (SQLITE_IOERR | (9<<8))\n#define SQLITE_IOERR_DELETE            (SQLITE_IOERR | (10<<8))\n#define SQLITE_IOERR_BLOCKED           (SQLITE_IOERR | (11<<8))\n#define SQLITE_IOERR_NOMEM             (SQLITE_IOERR | (12<<8))\n#define SQLITE_IOERR_ACCESS            (SQLITE_IOERR | (13<<8))\n#define SQLITE_IOERR_CHECKRESERVEDLOCK (SQLITE_IOERR | (14<<8))\n#define SQLITE_IOERR_LOCK              (SQLITE_IOERR | (15<<8))\n#define SQLITE_IOERR_CLOSE             (SQLITE_IOERR | (16<<8))\n#define SQLITE_IOERR_DIR_CLOSE         (SQLITE_IOERR | (17<<8))\n#define SQLITE_IOERR_SHMOPEN           (SQLITE_IOERR | (18<<8))\n#define SQLITE_IOERR_SHMSIZE           (SQLITE_IOERR | (19<<8))\n#define SQLITE_IOERR_SHMLOCK           (SQLITE_IOERR | (20<<8))\n#define SQLITE_IOERR_SHMMAP            (SQLITE_IOERR | (21<<8))\n#define SQLITE_IOERR_SEEK              (SQLITE_IOERR | (22<<8))\n#define SQLITE_IOERR_DELETE_NOENT      (SQLITE_IOERR | (23<<8))\n#define SQLITE_IOERR_MMAP              (SQLITE_IOERR | (24<<8))\n#define SQLITE_IOERR_GETTEMPPATH       (SQLITE_IOERR | (25<<8))\n#define SQLITE_IOERR_CONVPATH          (SQLITE_IOERR | (26<<8))\n#define SQLITE_IOERR_VNODE             (SQLITE_IOERR | (27<<8))\n#define SQLITE_IOERR_AUTH              (SQLITE_IOERR | (28<<8))\n#define SQLITE_IOERR_BEGIN_ATOMIC      (SQLITE_IOERR | (29<<8))\n#define SQLITE_IOERR_COMMIT_ATOMIC     (SQLITE_IOERR | (30<<8))\n#define SQLITE_IOERR_ROLLBACK_ATOMIC   (SQLITE_IOERR | (31<<8))\n#define SQLITE_LOCKED_SHAREDCACHE      (SQLITE_LOCKED |  (1<<8))\n#define SQLITE_BUSY_RECOVERY           (SQLITE_BUSY   |  (1<<8))\n#define SQLITE_BUSY_SNAPSHOT           (SQLITE_BUSY   |  (2<<8))\n#define SQLITE_CANTOPEN_NOTEMPDIR      (SQLITE_CANTOPEN | (1<<8))\n#define SQLITE_CANTOPEN_ISDIR          (SQLITE_CANTOPEN | (2<<8))\n#define SQLITE_CANTOPEN_FULLPATH       (SQLITE_CANTOPEN | (3<<8))\n#define SQLITE_CANTOPEN_CONVPATH       (SQLITE_CANTOPEN | (4<<8))\n#define SQLITE_CORRUPT_VTAB            (SQLITE_CORRUPT | (1<<8))\n#define SQLITE_READONLY_RECOVERY       (SQLITE_READONLY | (1<<8))\n#define SQLITE_READONLY_CANTLOCK       (SQLITE_READONLY | (2<<8))\n#define SQLITE_READONLY_ROLLBACK       (SQLITE_READONLY | (3<<8))\n#define SQLITE_READONLY_DBMOVED        (SQLITE_READONLY | (4<<8))\n#define SQLITE_READONLY_CANTINIT       (SQLITE_READONLY | (5<<8))\n#define SQLITE_READONLY_DIRECTORY      (SQLITE_READONLY | (6<<8))\n#define SQLITE_ABORT_ROLLBACK          (SQLITE_ABORT | (2<<8))\n#define SQLITE_CONSTRAINT_CHECK        (SQLITE_CONSTRAINT | (1<<8))\n#define SQLITE_CONSTRAINT_COMMITHOOK   (SQLITE_CONSTRAINT | (2<<8))\n#define SQLITE_CONSTRAINT_FOREIGNKEY   (SQLITE_CONSTRAINT | (3<<8))\n#define SQLITE_CONSTRAINT_FUNCTION     (SQLITE_CONSTRAINT | (4<<8))\n#define SQLITE_CONSTRAINT_NOTNULL      (SQLITE_CONSTRAINT | (5<<8))\n#define SQLITE_CONSTRAINT_PRIMARYKEY   (SQLITE_CONSTRAINT | (6<<8))\n#define SQLITE_CONSTRAINT_TRIGGER      (SQLITE_CONSTRAINT | (7<<8))\n#define SQLITE_CONSTRAINT_UNIQUE       (SQLITE_CONSTRAINT | (8<<8))\n#define SQLITE_CONSTRAINT_VTAB         (SQLITE_CONSTRAINT | (9<<8))\n#define SQLITE_CONSTRAINT_ROWID        (SQLITE_CONSTRAINT |(10<<8))\n#define SQLITE_NOTICE_RECOVER_WAL      (SQLITE_NOTICE | (1<<8))\n#define SQLITE_NOTICE_RECOVER_ROLLBACK (SQLITE_NOTICE | (2<<8))\n#define SQLITE_WARNING_AUTOINDEX       (SQLITE_WARNING | (1<<8))\n#define SQLITE_AUTH_USER               (SQLITE_AUTH | (1<<8))\n#define SQLITE_OK_LOAD_PERMANENTLY     (SQLITE_OK | (1<<8))\n\n/*\n** CAPI3REF: Flags For File Open Operations\n**\n** These bit values are intended for use in the\n** 3rd parameter to the [sqlite3_open_v2()] interface and\n** in the 4th parameter to the [sqlite3_vfs.xOpen] method.\n*/\n#define SQLITE_OPEN_READONLY         0x00000001  /* Ok for sqlite3_open_v2() */\n#define SQLITE_OPEN_READWRITE        0x00000002  /* Ok for sqlite3_open_v2() */\n#define SQLITE_OPEN_CREATE           0x00000004  /* Ok for sqlite3_open_v2() */\n#define SQLITE_OPEN_DELETEONCLOSE    0x00000008  /* VFS only */\n#define SQLITE_OPEN_EXCLUSIVE        0x00000010  /* VFS only */\n#define SQLITE_OPEN_AUTOPROXY        0x00000020  /* VFS only */\n#define SQLITE_OPEN_URI              0x00000040  /* Ok for sqlite3_open_v2() */\n#define SQLITE_OPEN_MEMORY           0x00000080  /* Ok for sqlite3_open_v2() */\n#define SQLITE_OPEN_MAIN_DB          0x00000100  /* VFS only */\n#define SQLITE_OPEN_TEMP_DB          0x00000200  /* VFS only */\n#define SQLITE_OPEN_TRANSIENT_DB     0x00000400  /* VFS only */\n#define SQLITE_OPEN_MAIN_JOURNAL     0x00000800  /* VFS only */\n#define SQLITE_OPEN_TEMP_JOURNAL     0x00001000  /* VFS only */\n#define SQLITE_OPEN_SUBJOURNAL       0x00002000  /* VFS only */\n#define SQLITE_OPEN_MASTER_JOURNAL   0x00004000  /* VFS only */\n#define SQLITE_OPEN_NOMUTEX          0x00008000  /* Ok for sqlite3_open_v2() */\n#define SQLITE_OPEN_FULLMUTEX        0x00010000  /* Ok for sqlite3_open_v2() */\n#define SQLITE_OPEN_SHAREDCACHE      0x00020000  /* Ok for sqlite3_open_v2() */\n#define SQLITE_OPEN_PRIVATECACHE     0x00040000  /* Ok for sqlite3_open_v2() */\n#define SQLITE_OPEN_WAL              0x00080000  /* VFS only */\n\n/* Reserved:                         0x00F00000 */\n\n/*\n** CAPI3REF: Device Characteristics\n**\n** The xDeviceCharacteristics method of the [sqlite3_io_methods]\n** object returns an integer which is a vector of these\n** bit values expressing I/O characteristics of the mass storage\n** device that holds the file that the [sqlite3_io_methods]\n** refers to.\n**\n** The SQLITE_IOCAP_ATOMIC property means that all writes of\n** any size are atomic.  The SQLITE_IOCAP_ATOMICnnn values\n** mean that writes of blocks that are nnn bytes in size and\n** are aligned to an address which is an integer multiple of\n** nnn are atomic.  The SQLITE_IOCAP_SAFE_APPEND value means\n** that when data is appended to a file, the data is appended\n** first then the size of the file is extended, never the other\n** way around.  The SQLITE_IOCAP_SEQUENTIAL property means that\n** information is written to disk in the same order as calls\n** to xWrite().  The SQLITE_IOCAP_POWERSAFE_OVERWRITE property means that\n** after reboot following a crash or power loss, the only bytes in a\n** file that were written at the application level might have changed\n** and that adjacent bytes, even bytes within the same sector are\n** guaranteed to be unchanged.  The SQLITE_IOCAP_UNDELETABLE_WHEN_OPEN\n** flag indicates that a file cannot be deleted when open.  The\n** SQLITE_IOCAP_IMMUTABLE flag indicates that the file is on\n** read-only media and cannot be changed even by processes with\n** elevated privileges.\n**\n** The SQLITE_IOCAP_BATCH_ATOMIC property means that the underlying\n** filesystem supports doing multiple write operations atomically when those\n** write operations are bracketed by [SQLITE_FCNTL_BEGIN_ATOMIC_WRITE] and\n** [SQLITE_FCNTL_COMMIT_ATOMIC_WRITE].\n*/\n#define SQLITE_IOCAP_ATOMIC                 0x00000001\n#define SQLITE_IOCAP_ATOMIC512              0x00000002\n#define SQLITE_IOCAP_ATOMIC1K               0x00000004\n#define SQLITE_IOCAP_ATOMIC2K               0x00000008\n#define SQLITE_IOCAP_ATOMIC4K               0x00000010\n#define SQLITE_IOCAP_ATOMIC8K               0x00000020\n#define SQLITE_IOCAP_ATOMIC16K              0x00000040\n#define SQLITE_IOCAP_ATOMIC32K              0x00000080\n#define SQLITE_IOCAP_ATOMIC64K              0x00000100\n#define SQLITE_IOCAP_SAFE_APPEND            0x00000200\n#define SQLITE_IOCAP_SEQUENTIAL             0x00000400\n#define SQLITE_IOCAP_UNDELETABLE_WHEN_OPEN  0x00000800\n#define SQLITE_IOCAP_POWERSAFE_OVERWRITE    0x00001000\n#define SQLITE_IOCAP_IMMUTABLE              0x00002000\n#define SQLITE_IOCAP_BATCH_ATOMIC           0x00004000\n\n/*\n** CAPI3REF: File Locking Levels\n**\n** SQLite uses one of these integer values as the second\n** argument to calls it makes to the xLock() and xUnlock() methods\n** of an [sqlite3_io_methods] object.\n*/\n#define SQLITE_LOCK_NONE          0\n#define SQLITE_LOCK_SHARED        1\n#define SQLITE_LOCK_RESERVED      2\n#define SQLITE_LOCK_PENDING       3\n#define SQLITE_LOCK_EXCLUSIVE     4\n\n/*\n** CAPI3REF: Synchronization Type Flags\n**\n** When SQLite invokes the xSync() method of an\n** [sqlite3_io_methods] object it uses a combination of\n** these integer values as the second argument.\n**\n** When the SQLITE_SYNC_DATAONLY flag is used, it means that the\n** sync operation only needs to flush data to mass storage.  Inode\n** information need not be flushed. If the lower four bits of the flag\n** equal SQLITE_SYNC_NORMAL, that means to use normal fsync() semantics.\n** If the lower four bits equal SQLITE_SYNC_FULL, that means\n** to use Mac OS X style fullsync instead of fsync().\n**\n** Do not confuse the SQLITE_SYNC_NORMAL and SQLITE_SYNC_FULL flags\n** with the [PRAGMA synchronous]=NORMAL and [PRAGMA synchronous]=FULL\n** settings.  The [synchronous pragma] determines when calls to the\n** xSync VFS method occur and applies uniformly across all platforms.\n** The SQLITE_SYNC_NORMAL and SQLITE_SYNC_FULL flags determine how\n** energetic or rigorous or forceful the sync operations are and\n** only make a difference on Mac OSX for the default SQLite code.\n** (Third-party VFS implementations might also make the distinction\n** between SQLITE_SYNC_NORMAL and SQLITE_SYNC_FULL, but among the\n** operating systems natively supported by SQLite, only Mac OSX\n** cares about the difference.)\n*/\n#define SQLITE_SYNC_NORMAL        0x00002\n#define SQLITE_SYNC_FULL          0x00003\n#define SQLITE_SYNC_DATAONLY      0x00010\n\n/*\n** CAPI3REF: OS Interface Open File Handle\n**\n** An [sqlite3_file] object represents an open file in the \n** [sqlite3_vfs | OS interface layer].  Individual OS interface\n** implementations will\n** want to subclass this object by appending additional fields\n** for their own use.  The pMethods entry is a pointer to an\n** [sqlite3_io_methods] object that defines methods for performing\n** I/O operations on the open file.\n*/\ntypedef struct sqlite3_file sqlite3_file;\nstruct sqlite3_file {\n  const struct sqlite3_io_methods *pMethods;  /* Methods for an open file */\n};\n\n/*\n** CAPI3REF: OS Interface File Virtual Methods Object\n**\n** Every file opened by the [sqlite3_vfs.xOpen] method populates an\n** [sqlite3_file] object (or, more commonly, a subclass of the\n** [sqlite3_file] object) with a pointer to an instance of this object.\n** This object defines the methods used to perform various operations\n** against the open file represented by the [sqlite3_file] object.\n**\n** If the [sqlite3_vfs.xOpen] method sets the sqlite3_file.pMethods element \n** to a non-NULL pointer, then the sqlite3_io_methods.xClose method\n** may be invoked even if the [sqlite3_vfs.xOpen] reported that it failed.  The\n** only way to prevent a call to xClose following a failed [sqlite3_vfs.xOpen]\n** is for the [sqlite3_vfs.xOpen] to set the sqlite3_file.pMethods element\n** to NULL.\n**\n** The flags argument to xSync may be one of [SQLITE_SYNC_NORMAL] or\n** [SQLITE_SYNC_FULL].  The first choice is the normal fsync().\n** The second choice is a Mac OS X style fullsync.  The [SQLITE_SYNC_DATAONLY]\n** flag may be ORed in to indicate that only the data of the file\n** and not its inode needs to be synced.\n**\n** The integer values to xLock() and xUnlock() are one of\n** <ul>\n** <li> [SQLITE_LOCK_NONE],\n** <li> [SQLITE_LOCK_SHARED],\n** <li> [SQLITE_LOCK_RESERVED],\n** <li> [SQLITE_LOCK_PENDING], or\n** <li> [SQLITE_LOCK_EXCLUSIVE].\n** </ul>\n** xLock() increases the lock. xUnlock() decreases the lock.\n** The xCheckReservedLock() method checks whether any database connection,\n** either in this process or in some other process, is holding a RESERVED,\n** PENDING, or EXCLUSIVE lock on the file.  It returns true\n** if such a lock exists and false otherwise.\n**\n** The xFileControl() method is a generic interface that allows custom\n** VFS implementations to directly control an open file using the\n** [sqlite3_file_control()] interface.  The second \"op\" argument is an\n** integer opcode.  The third argument is a generic pointer intended to\n** point to a structure that may contain arguments or space in which to\n** write return values.  Potential uses for xFileControl() might be\n** functions to enable blocking locks with timeouts, to change the\n** locking strategy (for example to use dot-file locks), to inquire\n** about the status of a lock, or to break stale locks.  The SQLite\n** core reserves all opcodes less than 100 for its own use.\n** A [file control opcodes | list of opcodes] less than 100 is available.\n** Applications that define a custom xFileControl method should use opcodes\n** greater than 100 to avoid conflicts.  VFS implementations should\n** return [SQLITE_NOTFOUND] for file control opcodes that they do not\n** recognize.\n**\n** The xSectorSize() method returns the sector size of the\n** device that underlies the file.  The sector size is the\n** minimum write that can be performed without disturbing\n** other bytes in the file.  The xDeviceCharacteristics()\n** method returns a bit vector describing behaviors of the\n** underlying device:\n**\n** <ul>\n** <li> [SQLITE_IOCAP_ATOMIC]\n** <li> [SQLITE_IOCAP_ATOMIC512]\n** <li> [SQLITE_IOCAP_ATOMIC1K]\n** <li> [SQLITE_IOCAP_ATOMIC2K]\n** <li> [SQLITE_IOCAP_ATOMIC4K]\n** <li> [SQLITE_IOCAP_ATOMIC8K]\n** <li> [SQLITE_IOCAP_ATOMIC16K]\n** <li> [SQLITE_IOCAP_ATOMIC32K]\n** <li> [SQLITE_IOCAP_ATOMIC64K]\n** <li> [SQLITE_IOCAP_SAFE_APPEND]\n** <li> [SQLITE_IOCAP_SEQUENTIAL]\n** <li> [SQLITE_IOCAP_UNDELETABLE_WHEN_OPEN]\n** <li> [SQLITE_IOCAP_POWERSAFE_OVERWRITE]\n** <li> [SQLITE_IOCAP_IMMUTABLE]\n** <li> [SQLITE_IOCAP_BATCH_ATOMIC]\n** </ul>\n**\n** The SQLITE_IOCAP_ATOMIC property means that all writes of\n** any size are atomic.  The SQLITE_IOCAP_ATOMICnnn values\n** mean that writes of blocks that are nnn bytes in size and\n** are aligned to an address which is an integer multiple of\n** nnn are atomic.  The SQLITE_IOCAP_SAFE_APPEND value means\n** that when data is appended to a file, the data is appended\n** first then the size of the file is extended, never the other\n** way around.  The SQLITE_IOCAP_SEQUENTIAL property means that\n** information is written to disk in the same order as calls\n** to xWrite().\n**\n** If xRead() returns SQLITE_IOERR_SHORT_READ it must also fill\n** in the unread portions of the buffer with zeros.  A VFS that\n** fails to zero-fill short reads might seem to work.  However,\n** failure to zero-fill short reads will eventually lead to\n** database corruption.\n*/\ntypedef struct sqlite3_io_methods sqlite3_io_methods;\nstruct sqlite3_io_methods {\n  int iVersion;\n  int (*xClose)(sqlite3_file*);\n  int (*xRead)(sqlite3_file*, void*, int iAmt, sqlite3_int64 iOfst);\n  int (*xWrite)(sqlite3_file*, const void*, int iAmt, sqlite3_int64 iOfst);\n  int (*xTruncate)(sqlite3_file*, sqlite3_int64 size);\n  int (*xSync)(sqlite3_file*, int flags);\n  int (*xFileSize)(sqlite3_file*, sqlite3_int64 *pSize);\n  int (*xLock)(sqlite3_file*, int);\n  int (*xUnlock)(sqlite3_file*, int);\n  int (*xCheckReservedLock)(sqlite3_file*, int *pResOut);\n  int (*xFileControl)(sqlite3_file*, int op, void *pArg);\n  int (*xSectorSize)(sqlite3_file*);\n  int (*xDeviceCharacteristics)(sqlite3_file*);\n  /* Methods above are valid for version 1 */\n  int (*xShmMap)(sqlite3_file*, int iPg, int pgsz, int, void volatile**);\n  int (*xShmLock)(sqlite3_file*, int offset, int n, int flags);\n  void (*xShmBarrier)(sqlite3_file*);\n  int (*xShmUnmap)(sqlite3_file*, int deleteFlag);\n  /* Methods above are valid for version 2 */\n  int (*xFetch)(sqlite3_file*, sqlite3_int64 iOfst, int iAmt, void **pp);\n  int (*xUnfetch)(sqlite3_file*, sqlite3_int64 iOfst, void *p);\n  /* Methods above are valid for version 3 */\n  /* Additional methods may be added in future releases */\n};\n\n/*\n** CAPI3REF: Standard File Control Opcodes\n** KEYWORDS: {file control opcodes} {file control opcode}\n**\n** These integer constants are opcodes for the xFileControl method\n** of the [sqlite3_io_methods] object and for the [sqlite3_file_control()]\n** interface.\n**\n** <ul>\n** <li>[[SQLITE_FCNTL_LOCKSTATE]]\n** The [SQLITE_FCNTL_LOCKSTATE] opcode is used for debugging.  This\n** opcode causes the xFileControl method to write the current state of\n** the lock (one of [SQLITE_LOCK_NONE], [SQLITE_LOCK_SHARED],\n** [SQLITE_LOCK_RESERVED], [SQLITE_LOCK_PENDING], or [SQLITE_LOCK_EXCLUSIVE])\n** into an integer that the pArg argument points to. This capability\n** is used during testing and is only available when the SQLITE_TEST\n** compile-time option is used.\n**\n** <li>[[SQLITE_FCNTL_SIZE_HINT]]\n** The [SQLITE_FCNTL_SIZE_HINT] opcode is used by SQLite to give the VFS\n** layer a hint of how large the database file will grow to be during the\n** current transaction.  This hint is not guaranteed to be accurate but it\n** is often close.  The underlying VFS might choose to preallocate database\n** file space based on this hint in order to help writes to the database\n** file run faster.\n**\n** <li>[[SQLITE_FCNTL_CHUNK_SIZE]]\n** The [SQLITE_FCNTL_CHUNK_SIZE] opcode is used to request that the VFS\n** extends and truncates the database file in chunks of a size specified\n** by the user. The fourth argument to [sqlite3_file_control()] should \n** point to an integer (type int) containing the new chunk-size to use\n** for the nominated database. Allocating database file space in large\n** chunks (say 1MB at a time), may reduce file-system fragmentation and\n** improve performance on some systems.\n**\n** <li>[[SQLITE_FCNTL_FILE_POINTER]]\n** The [SQLITE_FCNTL_FILE_POINTER] opcode is used to obtain a pointer\n** to the [sqlite3_file] object associated with a particular database\n** connection.  See also [SQLITE_FCNTL_JOURNAL_POINTER].\n**\n** <li>[[SQLITE_FCNTL_JOURNAL_POINTER]]\n** The [SQLITE_FCNTL_JOURNAL_POINTER] opcode is used to obtain a pointer\n** to the [sqlite3_file] object associated with the journal file (either\n** the [rollback journal] or the [write-ahead log]) for a particular database\n** connection.  See also [SQLITE_FCNTL_FILE_POINTER].\n**\n** <li>[[SQLITE_FCNTL_SYNC_OMITTED]]\n** No longer in use.\n**\n** <li>[[SQLITE_FCNTL_SYNC]]\n** The [SQLITE_FCNTL_SYNC] opcode is generated internally by SQLite and\n** sent to the VFS immediately before the xSync method is invoked on a\n** database file descriptor. Or, if the xSync method is not invoked \n** because the user has configured SQLite with \n** [PRAGMA synchronous | PRAGMA synchronous=OFF] it is invoked in place \n** of the xSync method. In most cases, the pointer argument passed with\n** this file-control is NULL. However, if the database file is being synced\n** as part of a multi-database commit, the argument points to a nul-terminated\n** string containing the transactions master-journal file name. VFSes that \n** do not need this signal should silently ignore this opcode. Applications \n** should not call [sqlite3_file_control()] with this opcode as doing so may \n** disrupt the operation of the specialized VFSes that do require it.  \n**\n** <li>[[SQLITE_FCNTL_COMMIT_PHASETWO]]\n** The [SQLITE_FCNTL_COMMIT_PHASETWO] opcode is generated internally by SQLite\n** and sent to the VFS after a transaction has been committed immediately\n** but before the database is unlocked. VFSes that do not need this signal\n** should silently ignore this opcode. Applications should not call\n** [sqlite3_file_control()] with this opcode as doing so may disrupt the \n** operation of the specialized VFSes that do require it.  \n**\n** <li>[[SQLITE_FCNTL_WIN32_AV_RETRY]]\n** ^The [SQLITE_FCNTL_WIN32_AV_RETRY] opcode is used to configure automatic\n** retry counts and intervals for certain disk I/O operations for the\n** windows [VFS] in order to provide robustness in the presence of\n** anti-virus programs.  By default, the windows VFS will retry file read,\n** file write, and file delete operations up to 10 times, with a delay\n** of 25 milliseconds before the first retry and with the delay increasing\n** by an additional 25 milliseconds with each subsequent retry.  This\n** opcode allows these two values (10 retries and 25 milliseconds of delay)\n** to be adjusted.  The values are changed for all database connections\n** within the same process.  The argument is a pointer to an array of two\n** integers where the first integer is the new retry count and the second\n** integer is the delay.  If either integer is negative, then the setting\n** is not changed but instead the prior value of that setting is written\n** into the array entry, allowing the current retry settings to be\n** interrogated.  The zDbName parameter is ignored.\n**\n** <li>[[SQLITE_FCNTL_PERSIST_WAL]]\n** ^The [SQLITE_FCNTL_PERSIST_WAL] opcode is used to set or query the\n** persistent [WAL | Write Ahead Log] setting.  By default, the auxiliary\n** write ahead log and shared memory files used for transaction control\n** are automatically deleted when the latest connection to the database\n** closes.  Setting persistent WAL mode causes those files to persist after\n** close.  Persisting the files is useful when other processes that do not\n** have write permission on the directory containing the database file want\n** to read the database file, as the WAL and shared memory files must exist\n** in order for the database to be readable.  The fourth parameter to\n** [sqlite3_file_control()] for this opcode should be a pointer to an integer.\n** That integer is 0 to disable persistent WAL mode or 1 to enable persistent\n** WAL mode.  If the integer is -1, then it is overwritten with the current\n** WAL persistence setting.\n**\n** <li>[[SQLITE_FCNTL_POWERSAFE_OVERWRITE]]\n** ^The [SQLITE_FCNTL_POWERSAFE_OVERWRITE] opcode is used to set or query the\n** persistent \"powersafe-overwrite\" or \"PSOW\" setting.  The PSOW setting\n** determines the [SQLITE_IOCAP_POWERSAFE_OVERWRITE] bit of the\n** xDeviceCharacteristics methods. The fourth parameter to\n** [sqlite3_file_control()] for this opcode should be a pointer to an integer.\n** That integer is 0 to disable zero-damage mode or 1 to enable zero-damage\n** mode.  If the integer is -1, then it is overwritten with the current\n** zero-damage mode setting.\n**\n** <li>[[SQLITE_FCNTL_OVERWRITE]]\n** ^The [SQLITE_FCNTL_OVERWRITE] opcode is invoked by SQLite after opening\n** a write transaction to indicate that, unless it is rolled back for some\n** reason, the entire database file will be overwritten by the current \n** transaction. This is used by VACUUM operations.\n**\n** <li>[[SQLITE_FCNTL_VFSNAME]]\n** ^The [SQLITE_FCNTL_VFSNAME] opcode can be used to obtain the names of\n** all [VFSes] in the VFS stack.  The names are of all VFS shims and the\n** final bottom-level VFS are written into memory obtained from \n** [sqlite3_malloc()] and the result is stored in the char* variable\n** that the fourth parameter of [sqlite3_file_control()] points to.\n** The caller is responsible for freeing the memory when done.  As with\n** all file-control actions, there is no guarantee that this will actually\n** do anything.  Callers should initialize the char* variable to a NULL\n** pointer in case this file-control is not implemented.  This file-control\n** is intended for diagnostic use only.\n**\n** <li>[[SQLITE_FCNTL_VFS_POINTER]]\n** ^The [SQLITE_FCNTL_VFS_POINTER] opcode finds a pointer to the top-level\n** [VFSes] currently in use.  ^(The argument X in\n** sqlite3_file_control(db,SQLITE_FCNTL_VFS_POINTER,X) must be\n** of type \"[sqlite3_vfs] **\".  This opcodes will set *X\n** to a pointer to the top-level VFS.)^\n** ^When there are multiple VFS shims in the stack, this opcode finds the\n** upper-most shim only.\n**\n** <li>[[SQLITE_FCNTL_PRAGMA]]\n** ^Whenever a [PRAGMA] statement is parsed, an [SQLITE_FCNTL_PRAGMA] \n** file control is sent to the open [sqlite3_file] object corresponding\n** to the database file to which the pragma statement refers. ^The argument\n** to the [SQLITE_FCNTL_PRAGMA] file control is an array of\n** pointers to strings (char**) in which the second element of the array\n** is the name of the pragma and the third element is the argument to the\n** pragma or NULL if the pragma has no argument.  ^The handler for an\n** [SQLITE_FCNTL_PRAGMA] file control can optionally make the first element\n** of the char** argument point to a string obtained from [sqlite3_mprintf()]\n** or the equivalent and that string will become the result of the pragma or\n** the error message if the pragma fails. ^If the\n** [SQLITE_FCNTL_PRAGMA] file control returns [SQLITE_NOTFOUND], then normal \n** [PRAGMA] processing continues.  ^If the [SQLITE_FCNTL_PRAGMA]\n** file control returns [SQLITE_OK], then the parser assumes that the\n** VFS has handled the PRAGMA itself and the parser generates a no-op\n** prepared statement if result string is NULL, or that returns a copy\n** of the result string if the string is non-NULL.\n** ^If the [SQLITE_FCNTL_PRAGMA] file control returns\n** any result code other than [SQLITE_OK] or [SQLITE_NOTFOUND], that means\n** that the VFS encountered an error while handling the [PRAGMA] and the\n** compilation of the PRAGMA fails with an error.  ^The [SQLITE_FCNTL_PRAGMA]\n** file control occurs at the beginning of pragma statement analysis and so\n** it is able to override built-in [PRAGMA] statements.\n**\n** <li>[[SQLITE_FCNTL_BUSYHANDLER]]\n** ^The [SQLITE_FCNTL_BUSYHANDLER]\n** file-control may be invoked by SQLite on the database file handle\n** shortly after it is opened in order to provide a custom VFS with access\n** to the connections busy-handler callback. The argument is of type (void **)\n** - an array of two (void *) values. The first (void *) actually points\n** to a function of type (int (*)(void *)). In order to invoke the connections\n** busy-handler, this function should be invoked with the second (void *) in\n** the array as the only argument. If it returns non-zero, then the operation\n** should be retried. If it returns zero, the custom VFS should abandon the\n** current operation.\n**\n** <li>[[SQLITE_FCNTL_TEMPFILENAME]]\n** ^Application can invoke the [SQLITE_FCNTL_TEMPFILENAME] file-control\n** to have SQLite generate a\n** temporary filename using the same algorithm that is followed to generate\n** temporary filenames for TEMP tables and other internal uses.  The\n** argument should be a char** which will be filled with the filename\n** written into memory obtained from [sqlite3_malloc()].  The caller should\n** invoke [sqlite3_free()] on the result to avoid a memory leak.\n**\n** <li>[[SQLITE_FCNTL_MMAP_SIZE]]\n** The [SQLITE_FCNTL_MMAP_SIZE] file control is used to query or set the\n** maximum number of bytes that will be used for memory-mapped I/O.\n** The argument is a pointer to a value of type sqlite3_int64 that\n** is an advisory maximum number of bytes in the file to memory map.  The\n** pointer is overwritten with the old value.  The limit is not changed if\n** the value originally pointed to is negative, and so the current limit \n** can be queried by passing in a pointer to a negative number.  This\n** file-control is used internally to implement [PRAGMA mmap_size].\n**\n** <li>[[SQLITE_FCNTL_TRACE]]\n** The [SQLITE_FCNTL_TRACE] file control provides advisory information\n** to the VFS about what the higher layers of the SQLite stack are doing.\n** This file control is used by some VFS activity tracing [shims].\n** The argument is a zero-terminated string.  Higher layers in the\n** SQLite stack may generate instances of this file control if\n** the [SQLITE_USE_FCNTL_TRACE] compile-time option is enabled.\n**\n** <li>[[SQLITE_FCNTL_HAS_MOVED]]\n** The [SQLITE_FCNTL_HAS_MOVED] file control interprets its argument as a\n** pointer to an integer and it writes a boolean into that integer depending\n** on whether or not the file has been renamed, moved, or deleted since it\n** was first opened.\n**\n** <li>[[SQLITE_FCNTL_WIN32_GET_HANDLE]]\n** The [SQLITE_FCNTL_WIN32_GET_HANDLE] opcode can be used to obtain the\n** underlying native file handle associated with a file handle.  This file\n** control interprets its argument as a pointer to a native file handle and\n** writes the resulting value there.\n**\n** <li>[[SQLITE_FCNTL_WIN32_SET_HANDLE]]\n** The [SQLITE_FCNTL_WIN32_SET_HANDLE] opcode is used for debugging.  This\n** opcode causes the xFileControl method to swap the file handle with the one\n** pointed to by the pArg argument.  This capability is used during testing\n** and only needs to be supported when SQLITE_TEST is defined.\n**\n** <li>[[SQLITE_FCNTL_WAL_BLOCK]]\n** The [SQLITE_FCNTL_WAL_BLOCK] is a signal to the VFS layer that it might\n** be advantageous to block on the next WAL lock if the lock is not immediately\n** available.  The WAL subsystem issues this signal during rare\n** circumstances in order to fix a problem with priority inversion.\n** Applications should <em>not</em> use this file-control.\n**\n** <li>[[SQLITE_FCNTL_ZIPVFS]]\n** The [SQLITE_FCNTL_ZIPVFS] opcode is implemented by zipvfs only. All other\n** VFS should return SQLITE_NOTFOUND for this opcode.\n**\n** <li>[[SQLITE_FCNTL_RBU]]\n** The [SQLITE_FCNTL_RBU] opcode is implemented by the special VFS used by\n** the RBU extension only.  All other VFS should return SQLITE_NOTFOUND for\n** this opcode.  \n**\n** <li>[[SQLITE_FCNTL_BEGIN_ATOMIC_WRITE]]\n** If the [SQLITE_FCNTL_BEGIN_ATOMIC_WRITE] opcode returns SQLITE_OK, then\n** the file descriptor is placed in \"batch write mode\", which\n** means all subsequent write operations will be deferred and done\n** atomically at the next [SQLITE_FCNTL_COMMIT_ATOMIC_WRITE].  Systems\n** that do not support batch atomic writes will return SQLITE_NOTFOUND.\n** ^Following a successful SQLITE_FCNTL_BEGIN_ATOMIC_WRITE and prior to\n** the closing [SQLITE_FCNTL_COMMIT_ATOMIC_WRITE] or\n** [SQLITE_FCNTL_ROLLBACK_ATOMIC_WRITE], SQLite will make\n** no VFS interface calls on the same [sqlite3_file] file descriptor\n** except for calls to the xWrite method and the xFileControl method\n** with [SQLITE_FCNTL_SIZE_HINT].\n**\n** <li>[[SQLITE_FCNTL_COMMIT_ATOMIC_WRITE]]\n** The [SQLITE_FCNTL_COMMIT_ATOMIC_WRITE] opcode causes all write\n** operations since the previous successful call to \n** [SQLITE_FCNTL_BEGIN_ATOMIC_WRITE] to be performed atomically.\n** This file control returns [SQLITE_OK] if and only if the writes were\n** all performed successfully and have been committed to persistent storage.\n** ^Regardless of whether or not it is successful, this file control takes\n** the file descriptor out of batch write mode so that all subsequent\n** write operations are independent.\n** ^SQLite will never invoke SQLITE_FCNTL_COMMIT_ATOMIC_WRITE without\n** a prior successful call to [SQLITE_FCNTL_BEGIN_ATOMIC_WRITE].\n**\n** <li>[[SQLITE_FCNTL_ROLLBACK_ATOMIC_WRITE]]\n** The [SQLITE_FCNTL_ROLLBACK_ATOMIC_WRITE] opcode causes all write\n** operations since the previous successful call to \n** [SQLITE_FCNTL_BEGIN_ATOMIC_WRITE] to be rolled back.\n** ^This file control takes the file descriptor out of batch write mode\n** so that all subsequent write operations are independent.\n** ^SQLite will never invoke SQLITE_FCNTL_ROLLBACK_ATOMIC_WRITE without\n** a prior successful call to [SQLITE_FCNTL_BEGIN_ATOMIC_WRITE].\n** </ul>\n*/\n#define SQLITE_FCNTL_LOCKSTATE               1\n#define SQLITE_FCNTL_GET_LOCKPROXYFILE       2\n#define SQLITE_FCNTL_SET_LOCKPROXYFILE       3\n#define SQLITE_FCNTL_LAST_ERRNO              4\n#define SQLITE_FCNTL_SIZE_HINT               5\n#define SQLITE_FCNTL_CHUNK_SIZE              6\n#define SQLITE_FCNTL_FILE_POINTER            7\n#define SQLITE_FCNTL_SYNC_OMITTED            8\n#define SQLITE_FCNTL_WIN32_AV_RETRY          9\n#define SQLITE_FCNTL_PERSIST_WAL            10\n#define SQLITE_FCNTL_OVERWRITE              11\n#define SQLITE_FCNTL_VFSNAME                12\n#define SQLITE_FCNTL_POWERSAFE_OVERWRITE    13\n#define SQLITE_FCNTL_PRAGMA                 14\n#define SQLITE_FCNTL_BUSYHANDLER            15\n#define SQLITE_FCNTL_TEMPFILENAME           16\n#define SQLITE_FCNTL_MMAP_SIZE              18\n#define SQLITE_FCNTL_TRACE                  19\n#define SQLITE_FCNTL_HAS_MOVED              20\n#define SQLITE_FCNTL_SYNC                   21\n#define SQLITE_FCNTL_COMMIT_PHASETWO        22\n#define SQLITE_FCNTL_WIN32_SET_HANDLE       23\n#define SQLITE_FCNTL_WAL_BLOCK              24\n#define SQLITE_FCNTL_ZIPVFS                 25\n#define SQLITE_FCNTL_RBU                    26\n#define SQLITE_FCNTL_VFS_POINTER            27\n#define SQLITE_FCNTL_JOURNAL_POINTER        28\n#define SQLITE_FCNTL_WIN32_GET_HANDLE       29\n#define SQLITE_FCNTL_PDB                    30\n#define SQLITE_FCNTL_BEGIN_ATOMIC_WRITE     31\n#define SQLITE_FCNTL_COMMIT_ATOMIC_WRITE    32\n#define SQLITE_FCNTL_ROLLBACK_ATOMIC_WRITE  33\n\n/* deprecated names */\n#define SQLITE_GET_LOCKPROXYFILE      SQLITE_FCNTL_GET_LOCKPROXYFILE\n#define SQLITE_SET_LOCKPROXYFILE      SQLITE_FCNTL_SET_LOCKPROXYFILE\n#define SQLITE_LAST_ERRNO             SQLITE_FCNTL_LAST_ERRNO\n\n\n/*\n** CAPI3REF: Mutex Handle\n**\n** The mutex module within SQLite defines [sqlite3_mutex] to be an\n** abstract type for a mutex object.  The SQLite core never looks\n** at the internal representation of an [sqlite3_mutex].  It only\n** deals with pointers to the [sqlite3_mutex] object.\n**\n** Mutexes are created using [sqlite3_mutex_alloc()].\n*/\ntypedef struct sqlite3_mutex sqlite3_mutex;\n\n/*\n** CAPI3REF: Loadable Extension Thunk\n**\n** A pointer to the opaque sqlite3_api_routines structure is passed as\n** the third parameter to entry points of [loadable extensions].  This\n** structure must be typedefed in order to work around compiler warnings\n** on some platforms.\n*/\ntypedef struct sqlite3_api_routines sqlite3_api_routines;\n\n/*\n** CAPI3REF: OS Interface Object\n**\n** An instance of the sqlite3_vfs object defines the interface between\n** the SQLite core and the underlying operating system.  The \"vfs\"\n** in the name of the object stands for \"virtual file system\".  See\n** the [VFS | VFS documentation] for further information.\n**\n** The VFS interface is sometimes extended by adding new methods onto\n** the end.  Each time such an extension occurs, the iVersion field\n** is incremented.  The iVersion value started out as 1 in\n** SQLite [version 3.5.0] on [dateof:3.5.0], then increased to 2\n** with SQLite [version 3.7.0] on [dateof:3.7.0], and then increased\n** to 3 with SQLite [version 3.7.6] on [dateof:3.7.6].  Additional fields\n** may be appended to the sqlite3_vfs object and the iVersion value\n** may increase again in future versions of SQLite.\n** Note that the structure\n** of the sqlite3_vfs object changes in the transition from\n** SQLite [version 3.5.9] to [version 3.6.0] on [dateof:3.6.0]\n** and yet the iVersion field was not modified.\n**\n** The szOsFile field is the size of the subclassed [sqlite3_file]\n** structure used by this VFS.  mxPathname is the maximum length of\n** a pathname in this VFS.\n**\n** Registered sqlite3_vfs objects are kept on a linked list formed by\n** the pNext pointer.  The [sqlite3_vfs_register()]\n** and [sqlite3_vfs_unregister()] interfaces manage this list\n** in a thread-safe way.  The [sqlite3_vfs_find()] interface\n** searches the list.  Neither the application code nor the VFS\n** implementation should use the pNext pointer.\n**\n** The pNext field is the only field in the sqlite3_vfs\n** structure that SQLite will ever modify.  SQLite will only access\n** or modify this field while holding a particular static mutex.\n** The application should never modify anything within the sqlite3_vfs\n** object once the object has been registered.\n**\n** The zName field holds the name of the VFS module.  The name must\n** be unique across all VFS modules.\n**\n** [[sqlite3_vfs.xOpen]]\n** ^SQLite guarantees that the zFilename parameter to xOpen\n** is either a NULL pointer or string obtained\n** from xFullPathname() with an optional suffix added.\n** ^If a suffix is added to the zFilename parameter, it will\n** consist of a single \"-\" character followed by no more than\n** 11 alphanumeric and/or \"-\" characters.\n** ^SQLite further guarantees that\n** the string will be valid and unchanged until xClose() is\n** called. Because of the previous sentence,\n** the [sqlite3_file] can safely store a pointer to the\n** filename if it needs to remember the filename for some reason.\n** If the zFilename parameter to xOpen is a NULL pointer then xOpen\n** must invent its own temporary name for the file.  ^Whenever the \n** xFilename parameter is NULL it will also be the case that the\n** flags parameter will include [SQLITE_OPEN_DELETEONCLOSE].\n**\n** The flags argument to xOpen() includes all bits set in\n** the flags argument to [sqlite3_open_v2()].  Or if [sqlite3_open()]\n** or [sqlite3_open16()] is used, then flags includes at least\n** [SQLITE_OPEN_READWRITE] | [SQLITE_OPEN_CREATE]. \n** If xOpen() opens a file read-only then it sets *pOutFlags to\n** include [SQLITE_OPEN_READONLY].  Other bits in *pOutFlags may be set.\n**\n** ^(SQLite will also add one of the following flags to the xOpen()\n** call, depending on the object being opened:\n**\n** <ul>\n** <li>  [SQLITE_OPEN_MAIN_DB]\n** <li>  [SQLITE_OPEN_MAIN_JOURNAL]\n** <li>  [SQLITE_OPEN_TEMP_DB]\n** <li>  [SQLITE_OPEN_TEMP_JOURNAL]\n** <li>  [SQLITE_OPEN_TRANSIENT_DB]\n** <li>  [SQLITE_OPEN_SUBJOURNAL]\n** <li>  [SQLITE_OPEN_MASTER_JOURNAL]\n** <li>  [SQLITE_OPEN_WAL]\n** </ul>)^\n**\n** The file I/O implementation can use the object type flags to\n** change the way it deals with files.  For example, an application\n** that does not care about crash recovery or rollback might make\n** the open of a journal file a no-op.  Writes to this journal would\n** also be no-ops, and any attempt to read the journal would return\n** SQLITE_IOERR.  Or the implementation might recognize that a database\n** file will be doing page-aligned sector reads and writes in a random\n** order and set up its I/O subsystem accordingly.\n**\n** SQLite might also add one of the following flags to the xOpen method:\n**\n** <ul>\n** <li> [SQLITE_OPEN_DELETEONCLOSE]\n** <li> [SQLITE_OPEN_EXCLUSIVE]\n** </ul>\n**\n** The [SQLITE_OPEN_DELETEONCLOSE] flag means the file should be\n** deleted when it is closed.  ^The [SQLITE_OPEN_DELETEONCLOSE]\n** will be set for TEMP databases and their journals, transient\n** databases, and subjournals.\n**\n** ^The [SQLITE_OPEN_EXCLUSIVE] flag is always used in conjunction\n** with the [SQLITE_OPEN_CREATE] flag, which are both directly\n** analogous to the O_EXCL and O_CREAT flags of the POSIX open()\n** API.  The SQLITE_OPEN_EXCLUSIVE flag, when paired with the \n** SQLITE_OPEN_CREATE, is used to indicate that file should always\n** be created, and that it is an error if it already exists.\n** It is <i>not</i> used to indicate the file should be opened \n** for exclusive access.\n**\n** ^At least szOsFile bytes of memory are allocated by SQLite\n** to hold the  [sqlite3_file] structure passed as the third\n** argument to xOpen.  The xOpen method does not have to\n** allocate the structure; it should just fill it in.  Note that\n** the xOpen method must set the sqlite3_file.pMethods to either\n** a valid [sqlite3_io_methods] object or to NULL.  xOpen must do\n** this even if the open fails.  SQLite expects that the sqlite3_file.pMethods\n** element will be valid after xOpen returns regardless of the success\n** or failure of the xOpen call.\n**\n** [[sqlite3_vfs.xAccess]]\n** ^The flags argument to xAccess() may be [SQLITE_ACCESS_EXISTS]\n** to test for the existence of a file, or [SQLITE_ACCESS_READWRITE] to\n** test whether a file is readable and writable, or [SQLITE_ACCESS_READ]\n** to test whether a file is at least readable.   The file can be a\n** directory.\n**\n** ^SQLite will always allocate at least mxPathname+1 bytes for the\n** output buffer xFullPathname.  The exact size of the output buffer\n** is also passed as a parameter to both  methods. If the output buffer\n** is not large enough, [SQLITE_CANTOPEN] should be returned. Since this is\n** handled as a fatal error by SQLite, vfs implementations should endeavor\n** to prevent this by setting mxPathname to a sufficiently large value.\n**\n** The xRandomness(), xSleep(), xCurrentTime(), and xCurrentTimeInt64()\n** interfaces are not strictly a part of the filesystem, but they are\n** included in the VFS structure for completeness.\n** The xRandomness() function attempts to return nBytes bytes\n** of good-quality randomness into zOut.  The return value is\n** the actual number of bytes of randomness obtained.\n** The xSleep() method causes the calling thread to sleep for at\n** least the number of microseconds given.  ^The xCurrentTime()\n** method returns a Julian Day Number for the current date and time as\n** a floating point value.\n** ^The xCurrentTimeInt64() method returns, as an integer, the Julian\n** Day Number multiplied by 86400000 (the number of milliseconds in \n** a 24-hour day).  \n** ^SQLite will use the xCurrentTimeInt64() method to get the current\n** date and time if that method is available (if iVersion is 2 or \n** greater and the function pointer is not NULL) and will fall back\n** to xCurrentTime() if xCurrentTimeInt64() is unavailable.\n**\n** ^The xSetSystemCall(), xGetSystemCall(), and xNestSystemCall() interfaces\n** are not used by the SQLite core.  These optional interfaces are provided\n** by some VFSes to facilitate testing of the VFS code. By overriding \n** system calls with functions under its control, a test program can\n** simulate faults and error conditions that would otherwise be difficult\n** or impossible to induce.  The set of system calls that can be overridden\n** varies from one VFS to another, and from one version of the same VFS to the\n** next.  Applications that use these interfaces must be prepared for any\n** or all of these interfaces to be NULL or for their behavior to change\n** from one release to the next.  Applications must not attempt to access\n** any of these methods if the iVersion of the VFS is less than 3.\n*/\ntypedef struct sqlite3_vfs sqlite3_vfs;\ntypedef void (*sqlite3_syscall_ptr)(void);\nstruct sqlite3_vfs {\n  int iVersion;            /* Structure version number (currently 3) */\n  int szOsFile;            /* Size of subclassed sqlite3_file */\n  int mxPathname;          /* Maximum file pathname length */\n  sqlite3_vfs *pNext;      /* Next registered VFS */\n  const char *zName;       /* Name of this virtual file system */\n  void *pAppData;          /* Pointer to application-specific data */\n  int (*xOpen)(sqlite3_vfs*, const char *zName, sqlite3_file*,\n               int flags, int *pOutFlags);\n  int (*xDelete)(sqlite3_vfs*, const char *zName, int syncDir);\n  int (*xAccess)(sqlite3_vfs*, const char *zName, int flags, int *pResOut);\n  int (*xFullPathname)(sqlite3_vfs*, const char *zName, int nOut, char *zOut);\n  void *(*xDlOpen)(sqlite3_vfs*, const char *zFilename);\n  void (*xDlError)(sqlite3_vfs*, int nByte, char *zErrMsg);\n  void (*(*xDlSym)(sqlite3_vfs*,void*, const char *zSymbol))(void);\n  void (*xDlClose)(sqlite3_vfs*, void*);\n  int (*xRandomness)(sqlite3_vfs*, int nByte, char *zOut);\n  int (*xSleep)(sqlite3_vfs*, int microseconds);\n  int (*xCurrentTime)(sqlite3_vfs*, double*);\n  int (*xGetLastError)(sqlite3_vfs*, int, char *);\n  /*\n  ** The methods above are in version 1 of the sqlite_vfs object\n  ** definition.  Those that follow are added in version 2 or later\n  */\n  int (*xCurrentTimeInt64)(sqlite3_vfs*, sqlite3_int64*);\n  /*\n  ** The methods above are in versions 1 and 2 of the sqlite_vfs object.\n  ** Those below are for version 3 and greater.\n  */\n  int (*xSetSystemCall)(sqlite3_vfs*, const char *zName, sqlite3_syscall_ptr);\n  sqlite3_syscall_ptr (*xGetSystemCall)(sqlite3_vfs*, const char *zName);\n  const char *(*xNextSystemCall)(sqlite3_vfs*, const char *zName);\n  /*\n  ** The methods above are in versions 1 through 3 of the sqlite_vfs object.\n  ** New fields may be appended in future versions.  The iVersion\n  ** value will increment whenever this happens. \n  */\n};\n\n/*\n** CAPI3REF: Flags for the xAccess VFS method\n**\n** These integer constants can be used as the third parameter to\n** the xAccess method of an [sqlite3_vfs] object.  They determine\n** what kind of permissions the xAccess method is looking for.\n** With SQLITE_ACCESS_EXISTS, the xAccess method\n** simply checks whether the file exists.\n** With SQLITE_ACCESS_READWRITE, the xAccess method\n** checks whether the named directory is both readable and writable\n** (in other words, if files can be added, removed, and renamed within\n** the directory).\n** The SQLITE_ACCESS_READWRITE constant is currently used only by the\n** [temp_store_directory pragma], though this could change in a future\n** release of SQLite.\n** With SQLITE_ACCESS_READ, the xAccess method\n** checks whether the file is readable.  The SQLITE_ACCESS_READ constant is\n** currently unused, though it might be used in a future release of\n** SQLite.\n*/\n#define SQLITE_ACCESS_EXISTS    0\n#define SQLITE_ACCESS_READWRITE 1   /* Used by PRAGMA temp_store_directory */\n#define SQLITE_ACCESS_READ      2   /* Unused */\n\n/*\n** CAPI3REF: Flags for the xShmLock VFS method\n**\n** These integer constants define the various locking operations\n** allowed by the xShmLock method of [sqlite3_io_methods].  The\n** following are the only legal combinations of flags to the\n** xShmLock method:\n**\n** <ul>\n** <li>  SQLITE_SHM_LOCK | SQLITE_SHM_SHARED\n** <li>  SQLITE_SHM_LOCK | SQLITE_SHM_EXCLUSIVE\n** <li>  SQLITE_SHM_UNLOCK | SQLITE_SHM_SHARED\n** <li>  SQLITE_SHM_UNLOCK | SQLITE_SHM_EXCLUSIVE\n** </ul>\n**\n** When unlocking, the same SHARED or EXCLUSIVE flag must be supplied as\n** was given on the corresponding lock.  \n**\n** The xShmLock method can transition between unlocked and SHARED or\n** between unlocked and EXCLUSIVE.  It cannot transition between SHARED\n** and EXCLUSIVE.\n*/\n#define SQLITE_SHM_UNLOCK       1\n#define SQLITE_SHM_LOCK         2\n#define SQLITE_SHM_SHARED       4\n#define SQLITE_SHM_EXCLUSIVE    8\n\n/*\n** CAPI3REF: Maximum xShmLock index\n**\n** The xShmLock method on [sqlite3_io_methods] may use values\n** between 0 and this upper bound as its \"offset\" argument.\n** The SQLite core will never attempt to acquire or release a\n** lock outside of this range\n*/\n#define SQLITE_SHM_NLOCK        8\n\n\n/*\n** CAPI3REF: Initialize The SQLite Library\n**\n** ^The sqlite3_initialize() routine initializes the\n** SQLite library.  ^The sqlite3_shutdown() routine\n** deallocates any resources that were allocated by sqlite3_initialize().\n** These routines are designed to aid in process initialization and\n** shutdown on embedded systems.  Workstation applications using\n** SQLite normally do not need to invoke either of these routines.\n**\n** A call to sqlite3_initialize() is an \"effective\" call if it is\n** the first time sqlite3_initialize() is invoked during the lifetime of\n** the process, or if it is the first time sqlite3_initialize() is invoked\n** following a call to sqlite3_shutdown().  ^(Only an effective call\n** of sqlite3_initialize() does any initialization.  All other calls\n** are harmless no-ops.)^\n**\n** A call to sqlite3_shutdown() is an \"effective\" call if it is the first\n** call to sqlite3_shutdown() since the last sqlite3_initialize().  ^(Only\n** an effective call to sqlite3_shutdown() does any deinitialization.\n** All other valid calls to sqlite3_shutdown() are harmless no-ops.)^\n**\n** The sqlite3_initialize() interface is threadsafe, but sqlite3_shutdown()\n** is not.  The sqlite3_shutdown() interface must only be called from a\n** single thread.  All open [database connections] must be closed and all\n** other SQLite resources must be deallocated prior to invoking\n** sqlite3_shutdown().\n**\n** Among other things, ^sqlite3_initialize() will invoke\n** sqlite3_os_init().  Similarly, ^sqlite3_shutdown()\n** will invoke sqlite3_os_end().\n**\n** ^The sqlite3_initialize() routine returns [SQLITE_OK] on success.\n** ^If for some reason, sqlite3_initialize() is unable to initialize\n** the library (perhaps it is unable to allocate a needed resource such\n** as a mutex) it returns an [error code] other than [SQLITE_OK].\n**\n** ^The sqlite3_initialize() routine is called internally by many other\n** SQLite interfaces so that an application usually does not need to\n** invoke sqlite3_initialize() directly.  For example, [sqlite3_open()]\n** calls sqlite3_initialize() so the SQLite library will be automatically\n** initialized when [sqlite3_open()] is called if it has not be initialized\n** already.  ^However, if SQLite is compiled with the [SQLITE_OMIT_AUTOINIT]\n** compile-time option, then the automatic calls to sqlite3_initialize()\n** are omitted and the application must call sqlite3_initialize() directly\n** prior to using any other SQLite interface.  For maximum portability,\n** it is recommended that applications always invoke sqlite3_initialize()\n** directly prior to using any other SQLite interface.  Future releases\n** of SQLite may require this.  In other words, the behavior exhibited\n** when SQLite is compiled with [SQLITE_OMIT_AUTOINIT] might become the\n** default behavior in some future release of SQLite.\n**\n** The sqlite3_os_init() routine does operating-system specific\n** initialization of the SQLite library.  The sqlite3_os_end()\n** routine undoes the effect of sqlite3_os_init().  Typical tasks\n** performed by these routines include allocation or deallocation\n** of static resources, initialization of global variables,\n** setting up a default [sqlite3_vfs] module, or setting up\n** a default configuration using [sqlite3_config()].\n**\n** The application should never invoke either sqlite3_os_init()\n** or sqlite3_os_end() directly.  The application should only invoke\n** sqlite3_initialize() and sqlite3_shutdown().  The sqlite3_os_init()\n** interface is called automatically by sqlite3_initialize() and\n** sqlite3_os_end() is called by sqlite3_shutdown().  Appropriate\n** implementations for sqlite3_os_init() and sqlite3_os_end()\n** are built into SQLite when it is compiled for Unix, Windows, or OS/2.\n** When [custom builds | built for other platforms]\n** (using the [SQLITE_OS_OTHER=1] compile-time\n** option) the application must supply a suitable implementation for\n** sqlite3_os_init() and sqlite3_os_end().  An application-supplied\n** implementation of sqlite3_os_init() or sqlite3_os_end()\n** must return [SQLITE_OK] on success and some other [error code] upon\n** failure.\n*/\nSQLITE_API int sqlite3_initialize(void);\nSQLITE_API int sqlite3_shutdown(void);\nSQLITE_API int sqlite3_os_init(void);\nSQLITE_API int sqlite3_os_end(void);\n\n/*\n** CAPI3REF: Configuring The SQLite Library\n**\n** The sqlite3_config() interface is used to make global configuration\n** changes to SQLite in order to tune SQLite to the specific needs of\n** the application.  The default configuration is recommended for most\n** applications and so this routine is usually not necessary.  It is\n** provided to support rare applications with unusual needs.\n**\n** <b>The sqlite3_config() interface is not threadsafe. The application\n** must ensure that no other SQLite interfaces are invoked by other\n** threads while sqlite3_config() is running.</b>\n**\n** The sqlite3_config() interface\n** may only be invoked prior to library initialization using\n** [sqlite3_initialize()] or after shutdown by [sqlite3_shutdown()].\n** ^If sqlite3_config() is called after [sqlite3_initialize()] and before\n** [sqlite3_shutdown()] then it will return SQLITE_MISUSE.\n** Note, however, that ^sqlite3_config() can be called as part of the\n** implementation of an application-defined [sqlite3_os_init()].\n**\n** The first argument to sqlite3_config() is an integer\n** [configuration option] that determines\n** what property of SQLite is to be configured.  Subsequent arguments\n** vary depending on the [configuration option]\n** in the first argument.\n**\n** ^When a configuration option is set, sqlite3_config() returns [SQLITE_OK].\n** ^If the option is unknown or SQLite is unable to set the option\n** then this routine returns a non-zero [error code].\n*/\nSQLITE_API int sqlite3_config(int, ...);\n\n/*\n** CAPI3REF: Configure database connections\n** METHOD: sqlite3\n**\n** The sqlite3_db_config() interface is used to make configuration\n** changes to a [database connection].  The interface is similar to\n** [sqlite3_config()] except that the changes apply to a single\n** [database connection] (specified in the first argument).\n**\n** The second argument to sqlite3_db_config(D,V,...)  is the\n** [SQLITE_DBCONFIG_LOOKASIDE | configuration verb] - an integer code \n** that indicates what aspect of the [database connection] is being configured.\n** Subsequent arguments vary depending on the configuration verb.\n**\n** ^Calls to sqlite3_db_config() return SQLITE_OK if and only if\n** the call is considered successful.\n*/\nSQLITE_API int sqlite3_db_config(sqlite3*, int op, ...);\n\n/*\n** CAPI3REF: Memory Allocation Routines\n**\n** An instance of this object defines the interface between SQLite\n** and low-level memory allocation routines.\n**\n** This object is used in only one place in the SQLite interface.\n** A pointer to an instance of this object is the argument to\n** [sqlite3_config()] when the configuration option is\n** [SQLITE_CONFIG_MALLOC] or [SQLITE_CONFIG_GETMALLOC].  \n** By creating an instance of this object\n** and passing it to [sqlite3_config]([SQLITE_CONFIG_MALLOC])\n** during configuration, an application can specify an alternative\n** memory allocation subsystem for SQLite to use for all of its\n** dynamic memory needs.\n**\n** Note that SQLite comes with several [built-in memory allocators]\n** that are perfectly adequate for the overwhelming majority of applications\n** and that this object is only useful to a tiny minority of applications\n** with specialized memory allocation requirements.  This object is\n** also used during testing of SQLite in order to specify an alternative\n** memory allocator that simulates memory out-of-memory conditions in\n** order to verify that SQLite recovers gracefully from such\n** conditions.\n**\n** The xMalloc, xRealloc, and xFree methods must work like the\n** malloc(), realloc() and free() functions from the standard C library.\n** ^SQLite guarantees that the second argument to\n** xRealloc is always a value returned by a prior call to xRoundup.\n**\n** xSize should return the allocated size of a memory allocation\n** previously obtained from xMalloc or xRealloc.  The allocated size\n** is always at least as big as the requested size but may be larger.\n**\n** The xRoundup method returns what would be the allocated size of\n** a memory allocation given a particular requested size.  Most memory\n** allocators round up memory allocations at least to the next multiple\n** of 8.  Some allocators round up to a larger multiple or to a power of 2.\n** Every memory allocation request coming in through [sqlite3_malloc()]\n** or [sqlite3_realloc()] first calls xRoundup.  If xRoundup returns 0, \n** that causes the corresponding memory allocation to fail.\n**\n** The xInit method initializes the memory allocator.  For example,\n** it might allocate any require mutexes or initialize internal data\n** structures.  The xShutdown method is invoked (indirectly) by\n** [sqlite3_shutdown()] and should deallocate any resources acquired\n** by xInit.  The pAppData pointer is used as the only parameter to\n** xInit and xShutdown.\n**\n** SQLite holds the [SQLITE_MUTEX_STATIC_MASTER] mutex when it invokes\n** the xInit method, so the xInit method need not be threadsafe.  The\n** xShutdown method is only called from [sqlite3_shutdown()] so it does\n** not need to be threadsafe either.  For all other methods, SQLite\n** holds the [SQLITE_MUTEX_STATIC_MEM] mutex as long as the\n** [SQLITE_CONFIG_MEMSTATUS] configuration option is turned on (which\n** it is by default) and so the methods are automatically serialized.\n** However, if [SQLITE_CONFIG_MEMSTATUS] is disabled, then the other\n** methods must be threadsafe or else make their own arrangements for\n** serialization.\n**\n** SQLite will never invoke xInit() more than once without an intervening\n** call to xShutdown().\n*/\ntypedef struct sqlite3_mem_methods sqlite3_mem_methods;\nstruct sqlite3_mem_methods {\n  void *(*xMalloc)(int);         /* Memory allocation function */\n  void (*xFree)(void*);          /* Free a prior allocation */\n  void *(*xRealloc)(void*,int);  /* Resize an allocation */\n  int (*xSize)(void*);           /* Return the size of an allocation */\n  int (*xRoundup)(int);          /* Round up request size to allocation size */\n  int (*xInit)(void*);           /* Initialize the memory allocator */\n  void (*xShutdown)(void*);      /* Deinitialize the memory allocator */\n  void *pAppData;                /* Argument to xInit() and xShutdown() */\n};\n\n/*\n** CAPI3REF: Configuration Options\n** KEYWORDS: {configuration option}\n**\n** These constants are the available integer configuration options that\n** can be passed as the first argument to the [sqlite3_config()] interface.\n**\n** New configuration options may be added in future releases of SQLite.\n** Existing configuration options might be discontinued.  Applications\n** should check the return code from [sqlite3_config()] to make sure that\n** the call worked.  The [sqlite3_config()] interface will return a\n** non-zero [error code] if a discontinued or unsupported configuration option\n** is invoked.\n**\n** <dl>\n** [[SQLITE_CONFIG_SINGLETHREAD]] <dt>SQLITE_CONFIG_SINGLETHREAD</dt>\n** <dd>There are no arguments to this option.  ^This option sets the\n** [threading mode] to Single-thread.  In other words, it disables\n** all mutexing and puts SQLite into a mode where it can only be used\n** by a single thread.   ^If SQLite is compiled with\n** the [SQLITE_THREADSAFE | SQLITE_THREADSAFE=0] compile-time option then\n** it is not possible to change the [threading mode] from its default\n** value of Single-thread and so [sqlite3_config()] will return \n** [SQLITE_ERROR] if called with the SQLITE_CONFIG_SINGLETHREAD\n** configuration option.</dd>\n**\n** [[SQLITE_CONFIG_MULTITHREAD]] <dt>SQLITE_CONFIG_MULTITHREAD</dt>\n** <dd>There are no arguments to this option.  ^This option sets the\n** [threading mode] to Multi-thread.  In other words, it disables\n** mutexing on [database connection] and [prepared statement] objects.\n** The application is responsible for serializing access to\n** [database connections] and [prepared statements].  But other mutexes\n** are enabled so that SQLite will be safe to use in a multi-threaded\n** environment as long as no two threads attempt to use the same\n** [database connection] at the same time.  ^If SQLite is compiled with\n** the [SQLITE_THREADSAFE | SQLITE_THREADSAFE=0] compile-time option then\n** it is not possible to set the Multi-thread [threading mode] and\n** [sqlite3_config()] will return [SQLITE_ERROR] if called with the\n** SQLITE_CONFIG_MULTITHREAD configuration option.</dd>\n**\n** [[SQLITE_CONFIG_SERIALIZED]] <dt>SQLITE_CONFIG_SERIALIZED</dt>\n** <dd>There are no arguments to this option.  ^This option sets the\n** [threading mode] to Serialized. In other words, this option enables\n** all mutexes including the recursive\n** mutexes on [database connection] and [prepared statement] objects.\n** In this mode (which is the default when SQLite is compiled with\n** [SQLITE_THREADSAFE=1]) the SQLite library will itself serialize access\n** to [database connections] and [prepared statements] so that the\n** application is free to use the same [database connection] or the\n** same [prepared statement] in different threads at the same time.\n** ^If SQLite is compiled with\n** the [SQLITE_THREADSAFE | SQLITE_THREADSAFE=0] compile-time option then\n** it is not possible to set the Serialized [threading mode] and\n** [sqlite3_config()] will return [SQLITE_ERROR] if called with the\n** SQLITE_CONFIG_SERIALIZED configuration option.</dd>\n**\n** [[SQLITE_CONFIG_MALLOC]] <dt>SQLITE_CONFIG_MALLOC</dt>\n** <dd> ^(The SQLITE_CONFIG_MALLOC option takes a single argument which is \n** a pointer to an instance of the [sqlite3_mem_methods] structure.\n** The argument specifies\n** alternative low-level memory allocation routines to be used in place of\n** the memory allocation routines built into SQLite.)^ ^SQLite makes\n** its own private copy of the content of the [sqlite3_mem_methods] structure\n** before the [sqlite3_config()] call returns.</dd>\n**\n** [[SQLITE_CONFIG_GETMALLOC]] <dt>SQLITE_CONFIG_GETMALLOC</dt>\n** <dd> ^(The SQLITE_CONFIG_GETMALLOC option takes a single argument which\n** is a pointer to an instance of the [sqlite3_mem_methods] structure.\n** The [sqlite3_mem_methods]\n** structure is filled with the currently defined memory allocation routines.)^\n** This option can be used to overload the default memory allocation\n** routines with a wrapper that simulations memory allocation failure or\n** tracks memory usage, for example. </dd>\n**\n** [[SQLITE_CONFIG_SMALL_MALLOC]] <dt>SQLITE_CONFIG_SMALL_MALLOC</dt>\n** <dd> ^The SQLITE_CONFIG_SMALL_MALLOC option takes single argument of\n** type int, interpreted as a boolean, which if true provides a hint to\n** SQLite that it should avoid large memory allocations if possible.\n** SQLite will run faster if it is free to make large memory allocations,\n** but some application might prefer to run slower in exchange for\n** guarantees about memory fragmentation that are possible if large\n** allocations are avoided.  This hint is normally off.\n** </dd>\n**\n** [[SQLITE_CONFIG_MEMSTATUS]] <dt>SQLITE_CONFIG_MEMSTATUS</dt>\n** <dd> ^The SQLITE_CONFIG_MEMSTATUS option takes single argument of type int,\n** interpreted as a boolean, which enables or disables the collection of\n** memory allocation statistics. ^(When memory allocation statistics are\n** disabled, the following SQLite interfaces become non-operational:\n**   <ul>\n**   <li> [sqlite3_memory_used()]\n**   <li> [sqlite3_memory_highwater()]\n**   <li> [sqlite3_soft_heap_limit64()]\n**   <li> [sqlite3_status64()]\n**   </ul>)^\n** ^Memory allocation statistics are enabled by default unless SQLite is\n** compiled with [SQLITE_DEFAULT_MEMSTATUS]=0 in which case memory\n** allocation statistics are disabled by default.\n** </dd>\n**\n** [[SQLITE_CONFIG_SCRATCH]] <dt>SQLITE_CONFIG_SCRATCH</dt>\n** <dd> The SQLITE_CONFIG_SCRATCH option is no longer used.\n** </dd>\n**\n** [[SQLITE_CONFIG_PAGECACHE]] <dt>SQLITE_CONFIG_PAGECACHE</dt>\n** <dd> ^The SQLITE_CONFIG_PAGECACHE option specifies a memory pool\n** that SQLite can use for the database page cache with the default page\n** cache implementation.  \n** This configuration option is a no-op if an application-define page\n** cache implementation is loaded using the [SQLITE_CONFIG_PCACHE2].\n** ^There are three arguments to SQLITE_CONFIG_PAGECACHE: A pointer to\n** 8-byte aligned memory (pMem), the size of each page cache line (sz),\n** and the number of cache lines (N).\n** The sz argument should be the size of the largest database page\n** (a power of two between 512 and 65536) plus some extra bytes for each\n** page header.  ^The number of extra bytes needed by the page header\n** can be determined using [SQLITE_CONFIG_PCACHE_HDRSZ].\n** ^It is harmless, apart from the wasted memory,\n** for the sz parameter to be larger than necessary.  The pMem\n** argument must be either a NULL pointer or a pointer to an 8-byte\n** aligned block of memory of at least sz*N bytes, otherwise\n** subsequent behavior is undefined.\n** ^When pMem is not NULL, SQLite will strive to use the memory provided\n** to satisfy page cache needs, falling back to [sqlite3_malloc()] if\n** a page cache line is larger than sz bytes or if all of the pMem buffer\n** is exhausted.\n** ^If pMem is NULL and N is non-zero, then each database connection\n** does an initial bulk allocation for page cache memory\n** from [sqlite3_malloc()] sufficient for N cache lines if N is positive or\n** of -1024*N bytes if N is negative, . ^If additional\n** page cache memory is needed beyond what is provided by the initial\n** allocation, then SQLite goes to [sqlite3_malloc()] separately for each\n** additional cache line. </dd>\n**\n** [[SQLITE_CONFIG_HEAP]] <dt>SQLITE_CONFIG_HEAP</dt>\n** <dd> ^The SQLITE_CONFIG_HEAP option specifies a static memory buffer \n** that SQLite will use for all of its dynamic memory allocation needs\n** beyond those provided for by [SQLITE_CONFIG_PAGECACHE].\n** ^The SQLITE_CONFIG_HEAP option is only available if SQLite is compiled\n** with either [SQLITE_ENABLE_MEMSYS3] or [SQLITE_ENABLE_MEMSYS5] and returns\n** [SQLITE_ERROR] if invoked otherwise.\n** ^There are three arguments to SQLITE_CONFIG_HEAP:\n** An 8-byte aligned pointer to the memory,\n** the number of bytes in the memory buffer, and the minimum allocation size.\n** ^If the first pointer (the memory pointer) is NULL, then SQLite reverts\n** to using its default memory allocator (the system malloc() implementation),\n** undoing any prior invocation of [SQLITE_CONFIG_MALLOC].  ^If the\n** memory pointer is not NULL then the alternative memory\n** allocator is engaged to handle all of SQLites memory allocation needs.\n** The first pointer (the memory pointer) must be aligned to an 8-byte\n** boundary or subsequent behavior of SQLite will be undefined.\n** The minimum allocation size is capped at 2**12. Reasonable values\n** for the minimum allocation size are 2**5 through 2**8.</dd>\n**\n** [[SQLITE_CONFIG_MUTEX]] <dt>SQLITE_CONFIG_MUTEX</dt>\n** <dd> ^(The SQLITE_CONFIG_MUTEX option takes a single argument which is a\n** pointer to an instance of the [sqlite3_mutex_methods] structure.\n** The argument specifies alternative low-level mutex routines to be used\n** in place the mutex routines built into SQLite.)^  ^SQLite makes a copy of\n** the content of the [sqlite3_mutex_methods] structure before the call to\n** [sqlite3_config()] returns. ^If SQLite is compiled with\n** the [SQLITE_THREADSAFE | SQLITE_THREADSAFE=0] compile-time option then\n** the entire mutexing subsystem is omitted from the build and hence calls to\n** [sqlite3_config()] with the SQLITE_CONFIG_MUTEX configuration option will\n** return [SQLITE_ERROR].</dd>\n**\n** [[SQLITE_CONFIG_GETMUTEX]] <dt>SQLITE_CONFIG_GETMUTEX</dt>\n** <dd> ^(The SQLITE_CONFIG_GETMUTEX option takes a single argument which\n** is a pointer to an instance of the [sqlite3_mutex_methods] structure.  The\n** [sqlite3_mutex_methods]\n** structure is filled with the currently defined mutex routines.)^\n** This option can be used to overload the default mutex allocation\n** routines with a wrapper used to track mutex usage for performance\n** profiling or testing, for example.   ^If SQLite is compiled with\n** the [SQLITE_THREADSAFE | SQLITE_THREADSAFE=0] compile-time option then\n** the entire mutexing subsystem is omitted from the build and hence calls to\n** [sqlite3_config()] with the SQLITE_CONFIG_GETMUTEX configuration option will\n** return [SQLITE_ERROR].</dd>\n**\n** [[SQLITE_CONFIG_LOOKASIDE]] <dt>SQLITE_CONFIG_LOOKASIDE</dt>\n** <dd> ^(The SQLITE_CONFIG_LOOKASIDE option takes two arguments that determine\n** the default size of lookaside memory on each [database connection].\n** The first argument is the\n** size of each lookaside buffer slot and the second is the number of\n** slots allocated to each database connection.)^  ^(SQLITE_CONFIG_LOOKASIDE\n** sets the <i>default</i> lookaside size. The [SQLITE_DBCONFIG_LOOKASIDE]\n** option to [sqlite3_db_config()] can be used to change the lookaside\n** configuration on individual connections.)^ </dd>\n**\n** [[SQLITE_CONFIG_PCACHE2]] <dt>SQLITE_CONFIG_PCACHE2</dt>\n** <dd> ^(The SQLITE_CONFIG_PCACHE2 option takes a single argument which is \n** a pointer to an [sqlite3_pcache_methods2] object.  This object specifies\n** the interface to a custom page cache implementation.)^\n** ^SQLite makes a copy of the [sqlite3_pcache_methods2] object.</dd>\n**\n** [[SQLITE_CONFIG_GETPCACHE2]] <dt>SQLITE_CONFIG_GETPCACHE2</dt>\n** <dd> ^(The SQLITE_CONFIG_GETPCACHE2 option takes a single argument which\n** is a pointer to an [sqlite3_pcache_methods2] object.  SQLite copies of\n** the current page cache implementation into that object.)^ </dd>\n**\n** [[SQLITE_CONFIG_LOG]] <dt>SQLITE_CONFIG_LOG</dt>\n** <dd> The SQLITE_CONFIG_LOG option is used to configure the SQLite\n** global [error log].\n** (^The SQLITE_CONFIG_LOG option takes two arguments: a pointer to a\n** function with a call signature of void(*)(void*,int,const char*), \n** and a pointer to void. ^If the function pointer is not NULL, it is\n** invoked by [sqlite3_log()] to process each logging event.  ^If the\n** function pointer is NULL, the [sqlite3_log()] interface becomes a no-op.\n** ^The void pointer that is the second argument to SQLITE_CONFIG_LOG is\n** passed through as the first parameter to the application-defined logger\n** function whenever that function is invoked.  ^The second parameter to\n** the logger function is a copy of the first parameter to the corresponding\n** [sqlite3_log()] call and is intended to be a [result code] or an\n** [extended result code].  ^The third parameter passed to the logger is\n** log message after formatting via [sqlite3_snprintf()].\n** The SQLite logging interface is not reentrant; the logger function\n** supplied by the application must not invoke any SQLite interface.\n** In a multi-threaded application, the application-defined logger\n** function must be threadsafe. </dd>\n**\n** [[SQLITE_CONFIG_URI]] <dt>SQLITE_CONFIG_URI\n** <dd>^(The SQLITE_CONFIG_URI option takes a single argument of type int.\n** If non-zero, then URI handling is globally enabled. If the parameter is zero,\n** then URI handling is globally disabled.)^ ^If URI handling is globally\n** enabled, all filenames passed to [sqlite3_open()], [sqlite3_open_v2()],\n** [sqlite3_open16()] or\n** specified as part of [ATTACH] commands are interpreted as URIs, regardless\n** of whether or not the [SQLITE_OPEN_URI] flag is set when the database\n** connection is opened. ^If it is globally disabled, filenames are\n** only interpreted as URIs if the SQLITE_OPEN_URI flag is set when the\n** database connection is opened. ^(By default, URI handling is globally\n** disabled. The default value may be changed by compiling with the\n** [SQLITE_USE_URI] symbol defined.)^\n**\n** [[SQLITE_CONFIG_COVERING_INDEX_SCAN]] <dt>SQLITE_CONFIG_COVERING_INDEX_SCAN\n** <dd>^The SQLITE_CONFIG_COVERING_INDEX_SCAN option takes a single integer\n** argument which is interpreted as a boolean in order to enable or disable\n** the use of covering indices for full table scans in the query optimizer.\n** ^The default setting is determined\n** by the [SQLITE_ALLOW_COVERING_INDEX_SCAN] compile-time option, or is \"on\"\n** if that compile-time option is omitted.\n** The ability to disable the use of covering indices for full table scans\n** is because some incorrectly coded legacy applications might malfunction\n** when the optimization is enabled.  Providing the ability to\n** disable the optimization allows the older, buggy application code to work\n** without change even with newer versions of SQLite.\n**\n** [[SQLITE_CONFIG_PCACHE]] [[SQLITE_CONFIG_GETPCACHE]]\n** <dt>SQLITE_CONFIG_PCACHE and SQLITE_CONFIG_GETPCACHE\n** <dd> These options are obsolete and should not be used by new code.\n** They are retained for backwards compatibility but are now no-ops.\n** </dd>\n**\n** [[SQLITE_CONFIG_SQLLOG]]\n** <dt>SQLITE_CONFIG_SQLLOG\n** <dd>This option is only available if sqlite is compiled with the\n** [SQLITE_ENABLE_SQLLOG] pre-processor macro defined. The first argument should\n** be a pointer to a function of type void(*)(void*,sqlite3*,const char*, int).\n** The second should be of type (void*). The callback is invoked by the library\n** in three separate circumstances, identified by the value passed as the\n** fourth parameter. If the fourth parameter is 0, then the database connection\n** passed as the second argument has just been opened. The third argument\n** points to a buffer containing the name of the main database file. If the\n** fourth parameter is 1, then the SQL statement that the third parameter\n** points to has just been executed. Or, if the fourth parameter is 2, then\n** the connection being passed as the second parameter is being closed. The\n** third parameter is passed NULL In this case.  An example of using this\n** configuration option can be seen in the \"test_sqllog.c\" source file in\n** the canonical SQLite source tree.</dd>\n**\n** [[SQLITE_CONFIG_MMAP_SIZE]]\n** <dt>SQLITE_CONFIG_MMAP_SIZE\n** <dd>^SQLITE_CONFIG_MMAP_SIZE takes two 64-bit integer (sqlite3_int64) values\n** that are the default mmap size limit (the default setting for\n** [PRAGMA mmap_size]) and the maximum allowed mmap size limit.\n** ^The default setting can be overridden by each database connection using\n** either the [PRAGMA mmap_size] command, or by using the\n** [SQLITE_FCNTL_MMAP_SIZE] file control.  ^(The maximum allowed mmap size\n** will be silently truncated if necessary so that it does not exceed the\n** compile-time maximum mmap size set by the\n** [SQLITE_MAX_MMAP_SIZE] compile-time option.)^\n** ^If either argument to this option is negative, then that argument is\n** changed to its compile-time default.\n**\n** [[SQLITE_CONFIG_WIN32_HEAPSIZE]]\n** <dt>SQLITE_CONFIG_WIN32_HEAPSIZE\n** <dd>^The SQLITE_CONFIG_WIN32_HEAPSIZE option is only available if SQLite is\n** compiled for Windows with the [SQLITE_WIN32_MALLOC] pre-processor macro\n** defined. ^SQLITE_CONFIG_WIN32_HEAPSIZE takes a 32-bit unsigned integer value\n** that specifies the maximum size of the created heap.\n**\n** [[SQLITE_CONFIG_PCACHE_HDRSZ]]\n** <dt>SQLITE_CONFIG_PCACHE_HDRSZ\n** <dd>^The SQLITE_CONFIG_PCACHE_HDRSZ option takes a single parameter which\n** is a pointer to an integer and writes into that integer the number of extra\n** bytes per page required for each page in [SQLITE_CONFIG_PAGECACHE].\n** The amount of extra space required can change depending on the compiler,\n** target platform, and SQLite version.\n**\n** [[SQLITE_CONFIG_PMASZ]]\n** <dt>SQLITE_CONFIG_PMASZ\n** <dd>^The SQLITE_CONFIG_PMASZ option takes a single parameter which\n** is an unsigned integer and sets the \"Minimum PMA Size\" for the multithreaded\n** sorter to that integer.  The default minimum PMA Size is set by the\n** [SQLITE_SORTER_PMASZ] compile-time option.  New threads are launched\n** to help with sort operations when multithreaded sorting\n** is enabled (using the [PRAGMA threads] command) and the amount of content\n** to be sorted exceeds the page size times the minimum of the\n** [PRAGMA cache_size] setting and this value.\n**\n** [[SQLITE_CONFIG_STMTJRNL_SPILL]]\n** <dt>SQLITE_CONFIG_STMTJRNL_SPILL\n** <dd>^The SQLITE_CONFIG_STMTJRNL_SPILL option takes a single parameter which\n** becomes the [statement journal] spill-to-disk threshold.  \n** [Statement journals] are held in memory until their size (in bytes)\n** exceeds this threshold, at which point they are written to disk.\n** Or if the threshold is -1, statement journals are always held\n** exclusively in memory.\n** Since many statement journals never become large, setting the spill\n** threshold to a value such as 64KiB can greatly reduce the amount of\n** I/O required to support statement rollback.\n** The default value for this setting is controlled by the\n** [SQLITE_STMTJRNL_SPILL] compile-time option.\n** </dl>\n*/\n#define SQLITE_CONFIG_SINGLETHREAD  1  /* nil */\n#define SQLITE_CONFIG_MULTITHREAD   2  /* nil */\n#define SQLITE_CONFIG_SERIALIZED    3  /* nil */\n#define SQLITE_CONFIG_MALLOC        4  /* sqlite3_mem_methods* */\n#define SQLITE_CONFIG_GETMALLOC     5  /* sqlite3_mem_methods* */\n#define SQLITE_CONFIG_SCRATCH       6  /* No longer used */\n#define SQLITE_CONFIG_PAGECACHE     7  /* void*, int sz, int N */\n#define SQLITE_CONFIG_HEAP          8  /* void*, int nByte, int min */\n#define SQLITE_CONFIG_MEMSTATUS     9  /* boolean */\n#define SQLITE_CONFIG_MUTEX        10  /* sqlite3_mutex_methods* */\n#define SQLITE_CONFIG_GETMUTEX     11  /* sqlite3_mutex_methods* */\n/* previously SQLITE_CONFIG_CHUNKALLOC 12 which is now unused. */ \n#define SQLITE_CONFIG_LOOKASIDE    13  /* int int */\n#define SQLITE_CONFIG_PCACHE       14  /* no-op */\n#define SQLITE_CONFIG_GETPCACHE    15  /* no-op */\n#define SQLITE_CONFIG_LOG          16  /* xFunc, void* */\n#define SQLITE_CONFIG_URI          17  /* int */\n#define SQLITE_CONFIG_PCACHE2      18  /* sqlite3_pcache_methods2* */\n#define SQLITE_CONFIG_GETPCACHE2   19  /* sqlite3_pcache_methods2* */\n#define SQLITE_CONFIG_COVERING_INDEX_SCAN 20  /* int */\n#define SQLITE_CONFIG_SQLLOG       21  /* xSqllog, void* */\n#define SQLITE_CONFIG_MMAP_SIZE    22  /* sqlite3_int64, sqlite3_int64 */\n#define SQLITE_CONFIG_WIN32_HEAPSIZE      23  /* int nByte */\n#define SQLITE_CONFIG_PCACHE_HDRSZ        24  /* int *psz */\n#define SQLITE_CONFIG_PMASZ               25  /* unsigned int szPma */\n#define SQLITE_CONFIG_STMTJRNL_SPILL      26  /* int nByte */\n#define SQLITE_CONFIG_SMALL_MALLOC        27  /* boolean */\n\n/*\n** CAPI3REF: Database Connection Configuration Options\n**\n** These constants are the available integer configuration options that\n** can be passed as the second argument to the [sqlite3_db_config()] interface.\n**\n** New configuration options may be added in future releases of SQLite.\n** Existing configuration options might be discontinued.  Applications\n** should check the return code from [sqlite3_db_config()] to make sure that\n** the call worked.  ^The [sqlite3_db_config()] interface will return a\n** non-zero [error code] if a discontinued or unsupported configuration option\n** is invoked.\n**\n** <dl>\n** <dt>SQLITE_DBCONFIG_LOOKASIDE</dt>\n** <dd> ^This option takes three additional arguments that determine the \n** [lookaside memory allocator] configuration for the [database connection].\n** ^The first argument (the third parameter to [sqlite3_db_config()] is a\n** pointer to a memory buffer to use for lookaside memory.\n** ^The first argument after the SQLITE_DBCONFIG_LOOKASIDE verb\n** may be NULL in which case SQLite will allocate the\n** lookaside buffer itself using [sqlite3_malloc()]. ^The second argument is the\n** size of each lookaside buffer slot.  ^The third argument is the number of\n** slots.  The size of the buffer in the first argument must be greater than\n** or equal to the product of the second and third arguments.  The buffer\n** must be aligned to an 8-byte boundary.  ^If the second argument to\n** SQLITE_DBCONFIG_LOOKASIDE is not a multiple of 8, it is internally\n** rounded down to the next smaller multiple of 8.  ^(The lookaside memory\n** configuration for a database connection can only be changed when that\n** connection is not currently using lookaside memory, or in other words\n** when the \"current value\" returned by\n** [sqlite3_db_status](D,[SQLITE_CONFIG_LOOKASIDE],...) is zero.\n** Any attempt to change the lookaside memory configuration when lookaside\n** memory is in use leaves the configuration unchanged and returns \n** [SQLITE_BUSY].)^</dd>\n**\n** <dt>SQLITE_DBCONFIG_ENABLE_FKEY</dt>\n** <dd> ^This option is used to enable or disable the enforcement of\n** [foreign key constraints].  There should be two additional arguments.\n** The first argument is an integer which is 0 to disable FK enforcement,\n** positive to enable FK enforcement or negative to leave FK enforcement\n** unchanged.  The second parameter is a pointer to an integer into which\n** is written 0 or 1 to indicate whether FK enforcement is off or on\n** following this call.  The second parameter may be a NULL pointer, in\n** which case the FK enforcement setting is not reported back. </dd>\n**\n** <dt>SQLITE_DBCONFIG_ENABLE_TRIGGER</dt>\n** <dd> ^This option is used to enable or disable [CREATE TRIGGER | triggers].\n** There should be two additional arguments.\n** The first argument is an integer which is 0 to disable triggers,\n** positive to enable triggers or negative to leave the setting unchanged.\n** The second parameter is a pointer to an integer into which\n** is written 0 or 1 to indicate whether triggers are disabled or enabled\n** following this call.  The second parameter may be a NULL pointer, in\n** which case the trigger setting is not reported back. </dd>\n**\n** <dt>SQLITE_DBCONFIG_ENABLE_FTS3_TOKENIZER</dt>\n** <dd> ^This option is used to enable or disable the two-argument\n** version of the [fts3_tokenizer()] function which is part of the\n** [FTS3] full-text search engine extension.\n** There should be two additional arguments.\n** The first argument is an integer which is 0 to disable fts3_tokenizer() or\n** positive to enable fts3_tokenizer() or negative to leave the setting\n** unchanged.\n** The second parameter is a pointer to an integer into which\n** is written 0 or 1 to indicate whether fts3_tokenizer is disabled or enabled\n** following this call.  The second parameter may be a NULL pointer, in\n** which case the new setting is not reported back. </dd>\n**\n** <dt>SQLITE_DBCONFIG_ENABLE_LOAD_EXTENSION</dt>\n** <dd> ^This option is used to enable or disable the [sqlite3_load_extension()]\n** interface independently of the [load_extension()] SQL function.\n** The [sqlite3_enable_load_extension()] API enables or disables both the\n** C-API [sqlite3_load_extension()] and the SQL function [load_extension()].\n** There should be two additional arguments.\n** When the first argument to this interface is 1, then only the C-API is\n** enabled and the SQL function remains disabled.  If the first argument to\n** this interface is 0, then both the C-API and the SQL function are disabled.\n** If the first argument is -1, then no changes are made to state of either the\n** C-API or the SQL function.\n** The second parameter is a pointer to an integer into which\n** is written 0 or 1 to indicate whether [sqlite3_load_extension()] interface\n** is disabled or enabled following this call.  The second parameter may\n** be a NULL pointer, in which case the new setting is not reported back.\n** </dd>\n**\n** <dt>SQLITE_DBCONFIG_MAINDBNAME</dt>\n** <dd> ^This option is used to change the name of the \"main\" database\n** schema.  ^The sole argument is a pointer to a constant UTF8 string\n** which will become the new schema name in place of \"main\".  ^SQLite\n** does not make a copy of the new main schema name string, so the application\n** must ensure that the argument passed into this DBCONFIG option is unchanged\n** until after the database connection closes.\n** </dd>\n**\n** <dt>SQLITE_DBCONFIG_NO_CKPT_ON_CLOSE</dt>\n** <dd> Usually, when a database in wal mode is closed or detached from a \n** database handle, SQLite checks if this will mean that there are now no \n** connections at all to the database. If so, it performs a checkpoint \n** operation before closing the connection. This option may be used to\n** override this behaviour. The first parameter passed to this operation\n** is an integer - non-zero to disable checkpoints-on-close, or zero (the\n** default) to enable them. The second parameter is a pointer to an integer\n** into which is written 0 or 1 to indicate whether checkpoints-on-close\n** have been disabled - 0 if they are not disabled, 1 if they are.\n** </dd>\n** <dt>SQLITE_DBCONFIG_ENABLE_QPSG</dt>\n** <dd>^(The SQLITE_DBCONFIG_ENABLE_QPSG option activates or deactivates\n** the [query planner stability guarantee] (QPSG).  When the QPSG is active,\n** a single SQL query statement will always use the same algorithm regardless\n** of values of [bound parameters].)^ The QPSG disables some query optimizations\n** that look at the values of bound parameters, which can make some queries\n** slower.  But the QPSG has the advantage of more predictable behavior.  With\n** the QPSG active, SQLite will always use the same query plan in the field as\n** was used during testing in the lab.\n** </dd>\n** <dt>SQLITE_DBCONFIG_TRIGGER_EQP</dt>\n** <dd> By default, the output of EXPLAIN QUERY PLAN commands does not \n** include output for any operations performed by trigger programs. This\n** option is used to set or clear (the default) a flag that governs this\n** behavior. The first parameter passed to this operation is an integer -\n** non-zero to enable output for trigger programs, or zero to disable it.\n** The second parameter is a pointer to an integer into which is written \n** 0 or 1 to indicate whether output-for-triggers has been disabled - 0 if \n** it is not disabled, 1 if it is.  \n** </dd>\n** </dl>\n*/\n#define SQLITE_DBCONFIG_MAINDBNAME            1000 /* const char* */\n#define SQLITE_DBCONFIG_LOOKASIDE             1001 /* void* int int */\n#define SQLITE_DBCONFIG_ENABLE_FKEY           1002 /* int int* */\n#define SQLITE_DBCONFIG_ENABLE_TRIGGER        1003 /* int int* */\n#define SQLITE_DBCONFIG_ENABLE_FTS3_TOKENIZER 1004 /* int int* */\n#define SQLITE_DBCONFIG_ENABLE_LOAD_EXTENSION 1005 /* int int* */\n#define SQLITE_DBCONFIG_NO_CKPT_ON_CLOSE      1006 /* int int* */\n#define SQLITE_DBCONFIG_ENABLE_QPSG           1007 /* int int* */\n#define SQLITE_DBCONFIG_TRIGGER_EQP           1008 /* int int* */\n#define SQLITE_DBCONFIG_MAX                   1008 /* Largest DBCONFIG */\n\n/*\n** CAPI3REF: Enable Or Disable Extended Result Codes\n** METHOD: sqlite3\n**\n** ^The sqlite3_extended_result_codes() routine enables or disables the\n** [extended result codes] feature of SQLite. ^The extended result\n** codes are disabled by default for historical compatibility.\n*/\nSQLITE_API int sqlite3_extended_result_codes(sqlite3*, int onoff);\n\n/*\n** CAPI3REF: Last Insert Rowid\n** METHOD: sqlite3\n**\n** ^Each entry in most SQLite tables (except for [WITHOUT ROWID] tables)\n** has a unique 64-bit signed\n** integer key called the [ROWID | \"rowid\"]. ^The rowid is always available\n** as an undeclared column named ROWID, OID, or _ROWID_ as long as those\n** names are not also used by explicitly declared columns. ^If\n** the table has a column of type [INTEGER PRIMARY KEY] then that column\n** is another alias for the rowid.\n**\n** ^The sqlite3_last_insert_rowid(D) interface usually returns the [rowid] of\n** the most recent successful [INSERT] into a rowid table or [virtual table]\n** on database connection D. ^Inserts into [WITHOUT ROWID] tables are not\n** recorded. ^If no successful [INSERT]s into rowid tables have ever occurred \n** on the database connection D, then sqlite3_last_insert_rowid(D) returns \n** zero.\n**\n** As well as being set automatically as rows are inserted into database\n** tables, the value returned by this function may be set explicitly by\n** [sqlite3_set_last_insert_rowid()]\n**\n** Some virtual table implementations may INSERT rows into rowid tables as\n** part of committing a transaction (e.g. to flush data accumulated in memory\n** to disk). In this case subsequent calls to this function return the rowid\n** associated with these internal INSERT operations, which leads to \n** unintuitive results. Virtual table implementations that do write to rowid\n** tables in this way can avoid this problem by restoring the original \n** rowid value using [sqlite3_set_last_insert_rowid()] before returning \n** control to the user.\n**\n** ^(If an [INSERT] occurs within a trigger then this routine will \n** return the [rowid] of the inserted row as long as the trigger is \n** running. Once the trigger program ends, the value returned \n** by this routine reverts to what it was before the trigger was fired.)^\n**\n** ^An [INSERT] that fails due to a constraint violation is not a\n** successful [INSERT] and does not change the value returned by this\n** routine.  ^Thus INSERT OR FAIL, INSERT OR IGNORE, INSERT OR ROLLBACK,\n** and INSERT OR ABORT make no changes to the return value of this\n** routine when their insertion fails.  ^(When INSERT OR REPLACE\n** encounters a constraint violation, it does not fail.  The\n** INSERT continues to completion after deleting rows that caused\n** the constraint problem so INSERT OR REPLACE will always change\n** the return value of this interface.)^\n**\n** ^For the purposes of this routine, an [INSERT] is considered to\n** be successful even if it is subsequently rolled back.\n**\n** This function is accessible to SQL statements via the\n** [last_insert_rowid() SQL function].\n**\n** If a separate thread performs a new [INSERT] on the same\n** database connection while the [sqlite3_last_insert_rowid()]\n** function is running and thus changes the last insert [rowid],\n** then the value returned by [sqlite3_last_insert_rowid()] is\n** unpredictable and might not equal either the old or the new\n** last insert [rowid].\n*/\nSQLITE_API sqlite3_int64 sqlite3_last_insert_rowid(sqlite3*);\n\n/*\n** CAPI3REF: Set the Last Insert Rowid value.\n** METHOD: sqlite3\n**\n** The sqlite3_set_last_insert_rowid(D, R) method allows the application to\n** set the value returned by calling sqlite3_last_insert_rowid(D) to R \n** without inserting a row into the database.\n*/\nSQLITE_API void sqlite3_set_last_insert_rowid(sqlite3*,sqlite3_int64);\n\n/*\n** CAPI3REF: Count The Number Of Rows Modified\n** METHOD: sqlite3\n**\n** ^This function returns the number of rows modified, inserted or\n** deleted by the most recently completed INSERT, UPDATE or DELETE\n** statement on the database connection specified by the only parameter.\n** ^Executing any other type of SQL statement does not modify the value\n** returned by this function.\n**\n** ^Only changes made directly by the INSERT, UPDATE or DELETE statement are\n** considered - auxiliary changes caused by [CREATE TRIGGER | triggers], \n** [foreign key actions] or [REPLACE] constraint resolution are not counted.\n** \n** Changes to a view that are intercepted by \n** [INSTEAD OF trigger | INSTEAD OF triggers] are not counted. ^The value \n** returned by sqlite3_changes() immediately after an INSERT, UPDATE or \n** DELETE statement run on a view is always zero. Only changes made to real \n** tables are counted.\n**\n** Things are more complicated if the sqlite3_changes() function is\n** executed while a trigger program is running. This may happen if the\n** program uses the [changes() SQL function], or if some other callback\n** function invokes sqlite3_changes() directly. Essentially:\n** \n** <ul>\n**   <li> ^(Before entering a trigger program the value returned by\n**        sqlite3_changes() function is saved. After the trigger program \n**        has finished, the original value is restored.)^\n** \n**   <li> ^(Within a trigger program each INSERT, UPDATE and DELETE \n**        statement sets the value returned by sqlite3_changes() \n**        upon completion as normal. Of course, this value will not include \n**        any changes performed by sub-triggers, as the sqlite3_changes() \n**        value will be saved and restored after each sub-trigger has run.)^\n** </ul>\n** \n** ^This means that if the changes() SQL function (or similar) is used\n** by the first INSERT, UPDATE or DELETE statement within a trigger, it \n** returns the value as set when the calling statement began executing.\n** ^If it is used by the second or subsequent such statement within a trigger \n** program, the value returned reflects the number of rows modified by the \n** previous INSERT, UPDATE or DELETE statement within the same trigger.\n**\n** See also the [sqlite3_total_changes()] interface, the\n** [count_changes pragma], and the [changes() SQL function].\n**\n** If a separate thread makes changes on the same database connection\n** while [sqlite3_changes()] is running then the value returned\n** is unpredictable and not meaningful.\n*/\nSQLITE_API int sqlite3_changes(sqlite3*);\n\n/*\n** CAPI3REF: Total Number Of Rows Modified\n** METHOD: sqlite3\n**\n** ^This function returns the total number of rows inserted, modified or\n** deleted by all [INSERT], [UPDATE] or [DELETE] statements completed\n** since the database connection was opened, including those executed as\n** part of trigger programs. ^Executing any other type of SQL statement\n** does not affect the value returned by sqlite3_total_changes().\n** \n** ^Changes made as part of [foreign key actions] are included in the\n** count, but those made as part of REPLACE constraint resolution are\n** not. ^Changes to a view that are intercepted by INSTEAD OF triggers \n** are not counted.\n** \n** See also the [sqlite3_changes()] interface, the\n** [count_changes pragma], and the [total_changes() SQL function].\n**\n** If a separate thread makes changes on the same database connection\n** while [sqlite3_total_changes()] is running then the value\n** returned is unpredictable and not meaningful.\n*/\nSQLITE_API int sqlite3_total_changes(sqlite3*);\n\n/*\n** CAPI3REF: Interrupt A Long-Running Query\n** METHOD: sqlite3\n**\n** ^This function causes any pending database operation to abort and\n** return at its earliest opportunity. This routine is typically\n** called in response to a user action such as pressing \"Cancel\"\n** or Ctrl-C where the user wants a long query operation to halt\n** immediately.\n**\n** ^It is safe to call this routine from a thread different from the\n** thread that is currently running the database operation.  But it\n** is not safe to call this routine with a [database connection] that\n** is closed or might close before sqlite3_interrupt() returns.\n**\n** ^If an SQL operation is very nearly finished at the time when\n** sqlite3_interrupt() is called, then it might not have an opportunity\n** to be interrupted and might continue to completion.\n**\n** ^An SQL operation that is interrupted will return [SQLITE_INTERRUPT].\n** ^If the interrupted SQL operation is an INSERT, UPDATE, or DELETE\n** that is inside an explicit transaction, then the entire transaction\n** will be rolled back automatically.\n**\n** ^The sqlite3_interrupt(D) call is in effect until all currently running\n** SQL statements on [database connection] D complete.  ^Any new SQL statements\n** that are started after the sqlite3_interrupt() call and before the \n** running statements reaches zero are interrupted as if they had been\n** running prior to the sqlite3_interrupt() call.  ^New SQL statements\n** that are started after the running statement count reaches zero are\n** not effected by the sqlite3_interrupt().\n** ^A call to sqlite3_interrupt(D) that occurs when there are no running\n** SQL statements is a no-op and has no effect on SQL statements\n** that are started after the sqlite3_interrupt() call returns.\n*/\nSQLITE_API void sqlite3_interrupt(sqlite3*);\n\n/*\n** CAPI3REF: Determine If An SQL Statement Is Complete\n**\n** These routines are useful during command-line input to determine if the\n** currently entered text seems to form a complete SQL statement or\n** if additional input is needed before sending the text into\n** SQLite for parsing.  ^These routines return 1 if the input string\n** appears to be a complete SQL statement.  ^A statement is judged to be\n** complete if it ends with a semicolon token and is not a prefix of a\n** well-formed CREATE TRIGGER statement.  ^Semicolons that are embedded within\n** string literals or quoted identifier names or comments are not\n** independent tokens (they are part of the token in which they are\n** embedded) and thus do not count as a statement terminator.  ^Whitespace\n** and comments that follow the final semicolon are ignored.\n**\n** ^These routines return 0 if the statement is incomplete.  ^If a\n** memory allocation fails, then SQLITE_NOMEM is returned.\n**\n** ^These routines do not parse the SQL statements thus\n** will not detect syntactically incorrect SQL.\n**\n** ^(If SQLite has not been initialized using [sqlite3_initialize()] prior \n** to invoking sqlite3_complete16() then sqlite3_initialize() is invoked\n** automatically by sqlite3_complete16().  If that initialization fails,\n** then the return value from sqlite3_complete16() will be non-zero\n** regardless of whether or not the input SQL is complete.)^\n**\n** The input to [sqlite3_complete()] must be a zero-terminated\n** UTF-8 string.\n**\n** The input to [sqlite3_complete16()] must be a zero-terminated\n** UTF-16 string in native byte order.\n*/\nSQLITE_API int sqlite3_complete(const char *sql);\nSQLITE_API int sqlite3_complete16(const void *sql);\n\n/*\n** CAPI3REF: Register A Callback To Handle SQLITE_BUSY Errors\n** KEYWORDS: {busy-handler callback} {busy handler}\n** METHOD: sqlite3\n**\n** ^The sqlite3_busy_handler(D,X,P) routine sets a callback function X\n** that might be invoked with argument P whenever\n** an attempt is made to access a database table associated with\n** [database connection] D when another thread\n** or process has the table locked.\n** The sqlite3_busy_handler() interface is used to implement\n** [sqlite3_busy_timeout()] and [PRAGMA busy_timeout].\n**\n** ^If the busy callback is NULL, then [SQLITE_BUSY]\n** is returned immediately upon encountering the lock.  ^If the busy callback\n** is not NULL, then the callback might be invoked with two arguments.\n**\n** ^The first argument to the busy handler is a copy of the void* pointer which\n** is the third argument to sqlite3_busy_handler().  ^The second argument to\n** the busy handler callback is the number of times that the busy handler has\n** been invoked previously for the same locking event.  ^If the\n** busy callback returns 0, then no additional attempts are made to\n** access the database and [SQLITE_BUSY] is returned\n** to the application.\n** ^If the callback returns non-zero, then another attempt\n** is made to access the database and the cycle repeats.\n**\n** The presence of a busy handler does not guarantee that it will be invoked\n** when there is lock contention. ^If SQLite determines that invoking the busy\n** handler could result in a deadlock, it will go ahead and return [SQLITE_BUSY]\n** to the application instead of invoking the \n** busy handler.\n** Consider a scenario where one process is holding a read lock that\n** it is trying to promote to a reserved lock and\n** a second process is holding a reserved lock that it is trying\n** to promote to an exclusive lock.  The first process cannot proceed\n** because it is blocked by the second and the second process cannot\n** proceed because it is blocked by the first.  If both processes\n** invoke the busy handlers, neither will make any progress.  Therefore,\n** SQLite returns [SQLITE_BUSY] for the first process, hoping that this\n** will induce the first process to release its read lock and allow\n** the second process to proceed.\n**\n** ^The default busy callback is NULL.\n**\n** ^(There can only be a single busy handler defined for each\n** [database connection].  Setting a new busy handler clears any\n** previously set handler.)^  ^Note that calling [sqlite3_busy_timeout()]\n** or evaluating [PRAGMA busy_timeout=N] will change the\n** busy handler and thus clear any previously set busy handler.\n**\n** The busy callback should not take any actions which modify the\n** database connection that invoked the busy handler.  In other words,\n** the busy handler is not reentrant.  Any such actions\n** result in undefined behavior.\n** \n** A busy handler must not close the database connection\n** or [prepared statement] that invoked the busy handler.\n*/\nSQLITE_API int sqlite3_busy_handler(sqlite3*,int(*)(void*,int),void*);\n\n/*\n** CAPI3REF: Set A Busy Timeout\n** METHOD: sqlite3\n**\n** ^This routine sets a [sqlite3_busy_handler | busy handler] that sleeps\n** for a specified amount of time when a table is locked.  ^The handler\n** will sleep multiple times until at least \"ms\" milliseconds of sleeping\n** have accumulated.  ^After at least \"ms\" milliseconds of sleeping,\n** the handler returns 0 which causes [sqlite3_step()] to return\n** [SQLITE_BUSY].\n**\n** ^Calling this routine with an argument less than or equal to zero\n** turns off all busy handlers.\n**\n** ^(There can only be a single busy handler for a particular\n** [database connection] at any given moment.  If another busy handler\n** was defined  (using [sqlite3_busy_handler()]) prior to calling\n** this routine, that other busy handler is cleared.)^\n**\n** See also:  [PRAGMA busy_timeout]\n*/\nSQLITE_API int sqlite3_busy_timeout(sqlite3*, int ms);\n\n/*\n** CAPI3REF: Convenience Routines For Running Queries\n** METHOD: sqlite3\n**\n** This is a legacy interface that is preserved for backwards compatibility.\n** Use of this interface is not recommended.\n**\n** Definition: A <b>result table</b> is memory data structure created by the\n** [sqlite3_get_table()] interface.  A result table records the\n** complete query results from one or more queries.\n**\n** The table conceptually has a number of rows and columns.  But\n** these numbers are not part of the result table itself.  These\n** numbers are obtained separately.  Let N be the number of rows\n** and M be the number of columns.\n**\n** A result table is an array of pointers to zero-terminated UTF-8 strings.\n** There are (N+1)*M elements in the array.  The first M pointers point\n** to zero-terminated strings that  contain the names of the columns.\n** The remaining entries all point to query results.  NULL values result\n** in NULL pointers.  All other values are in their UTF-8 zero-terminated\n** string representation as returned by [sqlite3_column_text()].\n**\n** A result table might consist of one or more memory allocations.\n** It is not safe to pass a result table directly to [sqlite3_free()].\n** A result table should be deallocated using [sqlite3_free_table()].\n**\n** ^(As an example of the result table format, suppose a query result\n** is as follows:\n**\n** <blockquote><pre>\n**        Name        | Age\n**        -----------------------\n**        Alice       | 43\n**        Bob         | 28\n**        Cindy       | 21\n** </pre></blockquote>\n**\n** There are two column (M==2) and three rows (N==3).  Thus the\n** result table has 8 entries.  Suppose the result table is stored\n** in an array names azResult.  Then azResult holds this content:\n**\n** <blockquote><pre>\n**        azResult&#91;0] = \"Name\";\n**        azResult&#91;1] = \"Age\";\n**        azResult&#91;2] = \"Alice\";\n**        azResult&#91;3] = \"43\";\n**        azResult&#91;4] = \"Bob\";\n**        azResult&#91;5] = \"28\";\n**        azResult&#91;6] = \"Cindy\";\n**        azResult&#91;7] = \"21\";\n** </pre></blockquote>)^\n**\n** ^The sqlite3_get_table() function evaluates one or more\n** semicolon-separated SQL statements in the zero-terminated UTF-8\n** string of its 2nd parameter and returns a result table to the\n** pointer given in its 3rd parameter.\n**\n** After the application has finished with the result from sqlite3_get_table(),\n** it must pass the result table pointer to sqlite3_free_table() in order to\n** release the memory that was malloced.  Because of the way the\n** [sqlite3_malloc()] happens within sqlite3_get_table(), the calling\n** function must not try to call [sqlite3_free()] directly.  Only\n** [sqlite3_free_table()] is able to release the memory properly and safely.\n**\n** The sqlite3_get_table() interface is implemented as a wrapper around\n** [sqlite3_exec()].  The sqlite3_get_table() routine does not have access\n** to any internal data structures of SQLite.  It uses only the public\n** interface defined here.  As a consequence, errors that occur in the\n** wrapper layer outside of the internal [sqlite3_exec()] call are not\n** reflected in subsequent calls to [sqlite3_errcode()] or\n** [sqlite3_errmsg()].\n*/\nSQLITE_API int sqlite3_get_table(\n  sqlite3 *db,          /* An open database */\n  const char *zSql,     /* SQL to be evaluated */\n  char ***pazResult,    /* Results of the query */\n  int *pnRow,           /* Number of result rows written here */\n  int *pnColumn,        /* Number of result columns written here */\n  char **pzErrmsg       /* Error msg written here */\n);\nSQLITE_API void sqlite3_free_table(char **result);\n\n/*\n** CAPI3REF: Formatted String Printing Functions\n**\n** These routines are work-alikes of the \"printf()\" family of functions\n** from the standard C library.\n** These routines understand most of the common formatting options from\n** the standard library printf() \n** plus some additional non-standard formats ([%q], [%Q], [%w], and [%z]).\n** See the [built-in printf()] documentation for details.\n**\n** ^The sqlite3_mprintf() and sqlite3_vmprintf() routines write their\n** results into memory obtained from [sqlite3_malloc64()].\n** The strings returned by these two routines should be\n** released by [sqlite3_free()].  ^Both routines return a\n** NULL pointer if [sqlite3_malloc64()] is unable to allocate enough\n** memory to hold the resulting string.\n**\n** ^(The sqlite3_snprintf() routine is similar to \"snprintf()\" from\n** the standard C library.  The result is written into the\n** buffer supplied as the second parameter whose size is given by\n** the first parameter. Note that the order of the\n** first two parameters is reversed from snprintf().)^  This is an\n** historical accident that cannot be fixed without breaking\n** backwards compatibility.  ^(Note also that sqlite3_snprintf()\n** returns a pointer to its buffer instead of the number of\n** characters actually written into the buffer.)^  We admit that\n** the number of characters written would be a more useful return\n** value but we cannot change the implementation of sqlite3_snprintf()\n** now without breaking compatibility.\n**\n** ^As long as the buffer size is greater than zero, sqlite3_snprintf()\n** guarantees that the buffer is always zero-terminated.  ^The first\n** parameter \"n\" is the total size of the buffer, including space for\n** the zero terminator.  So the longest string that can be completely\n** written will be n-1 characters.\n**\n** ^The sqlite3_vsnprintf() routine is a varargs version of sqlite3_snprintf().\n**\n** See also:  [built-in printf()], [printf() SQL function]\n*/\nSQLITE_API char *sqlite3_mprintf(const char*,...);\nSQLITE_API char *sqlite3_vmprintf(const char*, va_list);\nSQLITE_API char *sqlite3_snprintf(int,char*,const char*, ...);\nSQLITE_API char *sqlite3_vsnprintf(int,char*,const char*, va_list);\n\n/*\n** CAPI3REF: Memory Allocation Subsystem\n**\n** The SQLite core uses these three routines for all of its own\n** internal memory allocation needs. \"Core\" in the previous sentence\n** does not include operating-system specific VFS implementation.  The\n** Windows VFS uses native malloc() and free() for some operations.\n**\n** ^The sqlite3_malloc() routine returns a pointer to a block\n** of memory at least N bytes in length, where N is the parameter.\n** ^If sqlite3_malloc() is unable to obtain sufficient free\n** memory, it returns a NULL pointer.  ^If the parameter N to\n** sqlite3_malloc() is zero or negative then sqlite3_malloc() returns\n** a NULL pointer.\n**\n** ^The sqlite3_malloc64(N) routine works just like\n** sqlite3_malloc(N) except that N is an unsigned 64-bit integer instead\n** of a signed 32-bit integer.\n**\n** ^Calling sqlite3_free() with a pointer previously returned\n** by sqlite3_malloc() or sqlite3_realloc() releases that memory so\n** that it might be reused.  ^The sqlite3_free() routine is\n** a no-op if is called with a NULL pointer.  Passing a NULL pointer\n** to sqlite3_free() is harmless.  After being freed, memory\n** should neither be read nor written.  Even reading previously freed\n** memory might result in a segmentation fault or other severe error.\n** Memory corruption, a segmentation fault, or other severe error\n** might result if sqlite3_free() is called with a non-NULL pointer that\n** was not obtained from sqlite3_malloc() or sqlite3_realloc().\n**\n** ^The sqlite3_realloc(X,N) interface attempts to resize a\n** prior memory allocation X to be at least N bytes.\n** ^If the X parameter to sqlite3_realloc(X,N)\n** is a NULL pointer then its behavior is identical to calling\n** sqlite3_malloc(N).\n** ^If the N parameter to sqlite3_realloc(X,N) is zero or\n** negative then the behavior is exactly the same as calling\n** sqlite3_free(X).\n** ^sqlite3_realloc(X,N) returns a pointer to a memory allocation\n** of at least N bytes in size or NULL if insufficient memory is available.\n** ^If M is the size of the prior allocation, then min(N,M) bytes\n** of the prior allocation are copied into the beginning of buffer returned\n** by sqlite3_realloc(X,N) and the prior allocation is freed.\n** ^If sqlite3_realloc(X,N) returns NULL and N is positive, then the\n** prior allocation is not freed.\n**\n** ^The sqlite3_realloc64(X,N) interfaces works the same as\n** sqlite3_realloc(X,N) except that N is a 64-bit unsigned integer instead\n** of a 32-bit signed integer.\n**\n** ^If X is a memory allocation previously obtained from sqlite3_malloc(),\n** sqlite3_malloc64(), sqlite3_realloc(), or sqlite3_realloc64(), then\n** sqlite3_msize(X) returns the size of that memory allocation in bytes.\n** ^The value returned by sqlite3_msize(X) might be larger than the number\n** of bytes requested when X was allocated.  ^If X is a NULL pointer then\n** sqlite3_msize(X) returns zero.  If X points to something that is not\n** the beginning of memory allocation, or if it points to a formerly\n** valid memory allocation that has now been freed, then the behavior\n** of sqlite3_msize(X) is undefined and possibly harmful.\n**\n** ^The memory returned by sqlite3_malloc(), sqlite3_realloc(),\n** sqlite3_malloc64(), and sqlite3_realloc64()\n** is always aligned to at least an 8 byte boundary, or to a\n** 4 byte boundary if the [SQLITE_4_BYTE_ALIGNED_MALLOC] compile-time\n** option is used.\n**\n** In SQLite version 3.5.0 and 3.5.1, it was possible to define\n** the SQLITE_OMIT_MEMORY_ALLOCATION which would cause the built-in\n** implementation of these routines to be omitted.  That capability\n** is no longer provided.  Only built-in memory allocators can be used.\n**\n** Prior to SQLite version 3.7.10, the Windows OS interface layer called\n** the system malloc() and free() directly when converting\n** filenames between the UTF-8 encoding used by SQLite\n** and whatever filename encoding is used by the particular Windows\n** installation.  Memory allocation errors were detected, but\n** they were reported back as [SQLITE_CANTOPEN] or\n** [SQLITE_IOERR] rather than [SQLITE_NOMEM].\n**\n** The pointer arguments to [sqlite3_free()] and [sqlite3_realloc()]\n** must be either NULL or else pointers obtained from a prior\n** invocation of [sqlite3_malloc()] or [sqlite3_realloc()] that have\n** not yet been released.\n**\n** The application must not read or write any part of\n** a block of memory after it has been released using\n** [sqlite3_free()] or [sqlite3_realloc()].\n*/\nSQLITE_API void *sqlite3_malloc(int);\nSQLITE_API void *sqlite3_malloc64(sqlite3_uint64);\nSQLITE_API void *sqlite3_realloc(void*, int);\nSQLITE_API void *sqlite3_realloc64(void*, sqlite3_uint64);\nSQLITE_API void sqlite3_free(void*);\nSQLITE_API sqlite3_uint64 sqlite3_msize(void*);\n\n/*\n** CAPI3REF: Memory Allocator Statistics\n**\n** SQLite provides these two interfaces for reporting on the status\n** of the [sqlite3_malloc()], [sqlite3_free()], and [sqlite3_realloc()]\n** routines, which form the built-in memory allocation subsystem.\n**\n** ^The [sqlite3_memory_used()] routine returns the number of bytes\n** of memory currently outstanding (malloced but not freed).\n** ^The [sqlite3_memory_highwater()] routine returns the maximum\n** value of [sqlite3_memory_used()] since the high-water mark\n** was last reset.  ^The values returned by [sqlite3_memory_used()] and\n** [sqlite3_memory_highwater()] include any overhead\n** added by SQLite in its implementation of [sqlite3_malloc()],\n** but not overhead added by the any underlying system library\n** routines that [sqlite3_malloc()] may call.\n**\n** ^The memory high-water mark is reset to the current value of\n** [sqlite3_memory_used()] if and only if the parameter to\n** [sqlite3_memory_highwater()] is true.  ^The value returned\n** by [sqlite3_memory_highwater(1)] is the high-water mark\n** prior to the reset.\n*/\nSQLITE_API sqlite3_int64 sqlite3_memory_used(void);\nSQLITE_API sqlite3_int64 sqlite3_memory_highwater(int resetFlag);\n\n/*\n** CAPI3REF: Pseudo-Random Number Generator\n**\n** SQLite contains a high-quality pseudo-random number generator (PRNG) used to\n** select random [ROWID | ROWIDs] when inserting new records into a table that\n** already uses the largest possible [ROWID].  The PRNG is also used for\n** the build-in random() and randomblob() SQL functions.  This interface allows\n** applications to access the same PRNG for other purposes.\n**\n** ^A call to this routine stores N bytes of randomness into buffer P.\n** ^The P parameter can be a NULL pointer.\n**\n** ^If this routine has not been previously called or if the previous\n** call had N less than one or a NULL pointer for P, then the PRNG is\n** seeded using randomness obtained from the xRandomness method of\n** the default [sqlite3_vfs] object.\n** ^If the previous call to this routine had an N of 1 or more and a\n** non-NULL P then the pseudo-randomness is generated\n** internally and without recourse to the [sqlite3_vfs] xRandomness\n** method.\n*/\nSQLITE_API void sqlite3_randomness(int N, void *P);\n\n/*\n** CAPI3REF: Compile-Time Authorization Callbacks\n** METHOD: sqlite3\n** KEYWORDS: {authorizer callback}\n**\n** ^This routine registers an authorizer callback with a particular\n** [database connection], supplied in the first argument.\n** ^The authorizer callback is invoked as SQL statements are being compiled\n** by [sqlite3_prepare()] or its variants [sqlite3_prepare_v2()],\n** [sqlite3_prepare_v3()], [sqlite3_prepare16()], [sqlite3_prepare16_v2()],\n** and [sqlite3_prepare16_v3()].  ^At various\n** points during the compilation process, as logic is being created\n** to perform various actions, the authorizer callback is invoked to\n** see if those actions are allowed.  ^The authorizer callback should\n** return [SQLITE_OK] to allow the action, [SQLITE_IGNORE] to disallow the\n** specific action but allow the SQL statement to continue to be\n** compiled, or [SQLITE_DENY] to cause the entire SQL statement to be\n** rejected with an error.  ^If the authorizer callback returns\n** any value other than [SQLITE_IGNORE], [SQLITE_OK], or [SQLITE_DENY]\n** then the [sqlite3_prepare_v2()] or equivalent call that triggered\n** the authorizer will fail with an error message.\n**\n** When the callback returns [SQLITE_OK], that means the operation\n** requested is ok.  ^When the callback returns [SQLITE_DENY], the\n** [sqlite3_prepare_v2()] or equivalent call that triggered the\n** authorizer will fail with an error message explaining that\n** access is denied. \n**\n** ^The first parameter to the authorizer callback is a copy of the third\n** parameter to the sqlite3_set_authorizer() interface. ^The second parameter\n** to the callback is an integer [SQLITE_COPY | action code] that specifies\n** the particular action to be authorized. ^The third through sixth parameters\n** to the callback are either NULL pointers or zero-terminated strings\n** that contain additional details about the action to be authorized.\n** Applications must always be prepared to encounter a NULL pointer in any\n** of the third through the sixth parameters of the authorization callback.\n**\n** ^If the action code is [SQLITE_READ]\n** and the callback returns [SQLITE_IGNORE] then the\n** [prepared statement] statement is constructed to substitute\n** a NULL value in place of the table column that would have\n** been read if [SQLITE_OK] had been returned.  The [SQLITE_IGNORE]\n** return can be used to deny an untrusted user access to individual\n** columns of a table.\n** ^When a table is referenced by a [SELECT] but no column values are\n** extracted from that table (for example in a query like\n** \"SELECT count(*) FROM tab\") then the [SQLITE_READ] authorizer callback\n** is invoked once for that table with a column name that is an empty string.\n** ^If the action code is [SQLITE_DELETE] and the callback returns\n** [SQLITE_IGNORE] then the [DELETE] operation proceeds but the\n** [truncate optimization] is disabled and all rows are deleted individually.\n**\n** An authorizer is used when [sqlite3_prepare | preparing]\n** SQL statements from an untrusted source, to ensure that the SQL statements\n** do not try to access data they are not allowed to see, or that they do not\n** try to execute malicious statements that damage the database.  For\n** example, an application may allow a user to enter arbitrary\n** SQL queries for evaluation by a database.  But the application does\n** not want the user to be able to make arbitrary changes to the\n** database.  An authorizer could then be put in place while the\n** user-entered SQL is being [sqlite3_prepare | prepared] that\n** disallows everything except [SELECT] statements.\n**\n** Applications that need to process SQL from untrusted sources\n** might also consider lowering resource limits using [sqlite3_limit()]\n** and limiting database size using the [max_page_count] [PRAGMA]\n** in addition to using an authorizer.\n**\n** ^(Only a single authorizer can be in place on a database connection\n** at a time.  Each call to sqlite3_set_authorizer overrides the\n** previous call.)^  ^Disable the authorizer by installing a NULL callback.\n** The authorizer is disabled by default.\n**\n** The authorizer callback must not do anything that will modify\n** the database connection that invoked the authorizer callback.\n** Note that [sqlite3_prepare_v2()] and [sqlite3_step()] both modify their\n** database connections for the meaning of \"modify\" in this paragraph.\n**\n** ^When [sqlite3_prepare_v2()] is used to prepare a statement, the\n** statement might be re-prepared during [sqlite3_step()] due to a \n** schema change.  Hence, the application should ensure that the\n** correct authorizer callback remains in place during the [sqlite3_step()].\n**\n** ^Note that the authorizer callback is invoked only during\n** [sqlite3_prepare()] or its variants.  Authorization is not\n** performed during statement evaluation in [sqlite3_step()], unless\n** as stated in the previous paragraph, sqlite3_step() invokes\n** sqlite3_prepare_v2() to reprepare a statement after a schema change.\n*/\nSQLITE_API int sqlite3_set_authorizer(\n  sqlite3*,\n  int (*xAuth)(void*,int,const char*,const char*,const char*,const char*),\n  void *pUserData\n);\n\n/*\n** CAPI3REF: Authorizer Return Codes\n**\n** The [sqlite3_set_authorizer | authorizer callback function] must\n** return either [SQLITE_OK] or one of these two constants in order\n** to signal SQLite whether or not the action is permitted.  See the\n** [sqlite3_set_authorizer | authorizer documentation] for additional\n** information.\n**\n** Note that SQLITE_IGNORE is also used as a [conflict resolution mode]\n** returned from the [sqlite3_vtab_on_conflict()] interface.\n*/\n#define SQLITE_DENY   1   /* Abort the SQL statement with an error */\n#define SQLITE_IGNORE 2   /* Don't allow access, but don't generate an error */\n\n/*\n** CAPI3REF: Authorizer Action Codes\n**\n** The [sqlite3_set_authorizer()] interface registers a callback function\n** that is invoked to authorize certain SQL statement actions.  The\n** second parameter to the callback is an integer code that specifies\n** what action is being authorized.  These are the integer action codes that\n** the authorizer callback may be passed.\n**\n** These action code values signify what kind of operation is to be\n** authorized.  The 3rd and 4th parameters to the authorization\n** callback function will be parameters or NULL depending on which of these\n** codes is used as the second parameter.  ^(The 5th parameter to the\n** authorizer callback is the name of the database (\"main\", \"temp\",\n** etc.) if applicable.)^  ^The 6th parameter to the authorizer callback\n** is the name of the inner-most trigger or view that is responsible for\n** the access attempt or NULL if this access attempt is directly from\n** top-level SQL code.\n*/\n/******************************************* 3rd ************ 4th ***********/\n#define SQLITE_CREATE_INDEX          1   /* Index Name      Table Name      */\n#define SQLITE_CREATE_TABLE          2   /* Table Name      NULL            */\n#define SQLITE_CREATE_TEMP_INDEX     3   /* Index Name      Table Name      */\n#define SQLITE_CREATE_TEMP_TABLE     4   /* Table Name      NULL            */\n#define SQLITE_CREATE_TEMP_TRIGGER   5   /* Trigger Name    Table Name      */\n#define SQLITE_CREATE_TEMP_VIEW      6   /* View Name       NULL            */\n#define SQLITE_CREATE_TRIGGER        7   /* Trigger Name    Table Name      */\n#define SQLITE_CREATE_VIEW           8   /* View Name       NULL            */\n#define SQLITE_DELETE                9   /* Table Name      NULL            */\n#define SQLITE_DROP_INDEX           10   /* Index Name      Table Name      */\n#define SQLITE_DROP_TABLE           11   /* Table Name      NULL            */\n#define SQLITE_DROP_TEMP_INDEX      12   /* Index Name      Table Name      */\n#define SQLITE_DROP_TEMP_TABLE      13   /* Table Name      NULL            */\n#define SQLITE_DROP_TEMP_TRIGGER    14   /* Trigger Name    Table Name      */\n#define SQLITE_DROP_TEMP_VIEW       15   /* View Name       NULL            */\n#define SQLITE_DROP_TRIGGER         16   /* Trigger Name    Table Name      */\n#define SQLITE_DROP_VIEW            17   /* View Name       NULL            */\n#define SQLITE_INSERT               18   /* Table Name      NULL            */\n#define SQLITE_PRAGMA               19   /* Pragma Name     1st arg or NULL */\n#define SQLITE_READ                 20   /* Table Name      Column Name     */\n#define SQLITE_SELECT               21   /* NULL            NULL            */\n#define SQLITE_TRANSACTION          22   /* Operation       NULL            */\n#define SQLITE_UPDATE               23   /* Table Name      Column Name     */\n#define SQLITE_ATTACH               24   /* Filename        NULL            */\n#define SQLITE_DETACH               25   /* Database Name   NULL            */\n#define SQLITE_ALTER_TABLE          26   /* Database Name   Table Name      */\n#define SQLITE_REINDEX              27   /* Index Name      NULL            */\n#define SQLITE_ANALYZE              28   /* Table Name      NULL            */\n#define SQLITE_CREATE_VTABLE        29   /* Table Name      Module Name     */\n#define SQLITE_DROP_VTABLE          30   /* Table Name      Module Name     */\n#define SQLITE_FUNCTION             31   /* NULL            Function Name   */\n#define SQLITE_SAVEPOINT            32   /* Operation       Savepoint Name  */\n#define SQLITE_COPY                  0   /* No longer used */\n#define SQLITE_RECURSIVE            33   /* NULL            NULL            */\n\n/*\n** CAPI3REF: Tracing And Profiling Functions\n** METHOD: sqlite3\n**\n** These routines are deprecated. Use the [sqlite3_trace_v2()] interface\n** instead of the routines described here.\n**\n** These routines register callback functions that can be used for\n** tracing and profiling the execution of SQL statements.\n**\n** ^The callback function registered by sqlite3_trace() is invoked at\n** various times when an SQL statement is being run by [sqlite3_step()].\n** ^The sqlite3_trace() callback is invoked with a UTF-8 rendering of the\n** SQL statement text as the statement first begins executing.\n** ^(Additional sqlite3_trace() callbacks might occur\n** as each triggered subprogram is entered.  The callbacks for triggers\n** contain a UTF-8 SQL comment that identifies the trigger.)^\n**\n** The [SQLITE_TRACE_SIZE_LIMIT] compile-time option can be used to limit\n** the length of [bound parameter] expansion in the output of sqlite3_trace().\n**\n** ^The callback function registered by sqlite3_profile() is invoked\n** as each SQL statement finishes.  ^The profile callback contains\n** the original statement text and an estimate of wall-clock time\n** of how long that statement took to run.  ^The profile callback\n** time is in units of nanoseconds, however the current implementation\n** is only capable of millisecond resolution so the six least significant\n** digits in the time are meaningless.  Future versions of SQLite\n** might provide greater resolution on the profiler callback.  The\n** sqlite3_profile() function is considered experimental and is\n** subject to change in future versions of SQLite.\n*/\nSQLITE_API SQLITE_DEPRECATED void *sqlite3_trace(sqlite3*,\n   void(*xTrace)(void*,const char*), void*);\nSQLITE_API SQLITE_DEPRECATED void *sqlite3_profile(sqlite3*,\n   void(*xProfile)(void*,const char*,sqlite3_uint64), void*);\n\n/*\n** CAPI3REF: SQL Trace Event Codes\n** KEYWORDS: SQLITE_TRACE\n**\n** These constants identify classes of events that can be monitored\n** using the [sqlite3_trace_v2()] tracing logic.  The M argument\n** to [sqlite3_trace_v2(D,M,X,P)] is an OR-ed combination of one or more of\n** the following constants.  ^The first argument to the trace callback\n** is one of the following constants.\n**\n** New tracing constants may be added in future releases.\n**\n** ^A trace callback has four arguments: xCallback(T,C,P,X).\n** ^The T argument is one of the integer type codes above.\n** ^The C argument is a copy of the context pointer passed in as the\n** fourth argument to [sqlite3_trace_v2()].\n** The P and X arguments are pointers whose meanings depend on T.\n**\n** <dl>\n** [[SQLITE_TRACE_STMT]] <dt>SQLITE_TRACE_STMT</dt>\n** <dd>^An SQLITE_TRACE_STMT callback is invoked when a prepared statement\n** first begins running and possibly at other times during the\n** execution of the prepared statement, such as at the start of each\n** trigger subprogram. ^The P argument is a pointer to the\n** [prepared statement]. ^The X argument is a pointer to a string which\n** is the unexpanded SQL text of the prepared statement or an SQL comment \n** that indicates the invocation of a trigger.  ^The callback can compute\n** the same text that would have been returned by the legacy [sqlite3_trace()]\n** interface by using the X argument when X begins with \"--\" and invoking\n** [sqlite3_expanded_sql(P)] otherwise.\n**\n** [[SQLITE_TRACE_PROFILE]] <dt>SQLITE_TRACE_PROFILE</dt>\n** <dd>^An SQLITE_TRACE_PROFILE callback provides approximately the same\n** information as is provided by the [sqlite3_profile()] callback.\n** ^The P argument is a pointer to the [prepared statement] and the\n** X argument points to a 64-bit integer which is the estimated of\n** the number of nanosecond that the prepared statement took to run.\n** ^The SQLITE_TRACE_PROFILE callback is invoked when the statement finishes.\n**\n** [[SQLITE_TRACE_ROW]] <dt>SQLITE_TRACE_ROW</dt>\n** <dd>^An SQLITE_TRACE_ROW callback is invoked whenever a prepared\n** statement generates a single row of result.  \n** ^The P argument is a pointer to the [prepared statement] and the\n** X argument is unused.\n**\n** [[SQLITE_TRACE_CLOSE]] <dt>SQLITE_TRACE_CLOSE</dt>\n** <dd>^An SQLITE_TRACE_CLOSE callback is invoked when a database\n** connection closes.\n** ^The P argument is a pointer to the [database connection] object\n** and the X argument is unused.\n** </dl>\n*/\n#define SQLITE_TRACE_STMT       0x01\n#define SQLITE_TRACE_PROFILE    0x02\n#define SQLITE_TRACE_ROW        0x04\n#define SQLITE_TRACE_CLOSE      0x08\n\n/*\n** CAPI3REF: SQL Trace Hook\n** METHOD: sqlite3\n**\n** ^The sqlite3_trace_v2(D,M,X,P) interface registers a trace callback\n** function X against [database connection] D, using property mask M\n** and context pointer P.  ^If the X callback is\n** NULL or if the M mask is zero, then tracing is disabled.  The\n** M argument should be the bitwise OR-ed combination of\n** zero or more [SQLITE_TRACE] constants.\n**\n** ^Each call to either sqlite3_trace() or sqlite3_trace_v2() overrides \n** (cancels) any prior calls to sqlite3_trace() or sqlite3_trace_v2().\n**\n** ^The X callback is invoked whenever any of the events identified by \n** mask M occur.  ^The integer return value from the callback is currently\n** ignored, though this may change in future releases.  Callback\n** implementations should return zero to ensure future compatibility.\n**\n** ^A trace callback is invoked with four arguments: callback(T,C,P,X).\n** ^The T argument is one of the [SQLITE_TRACE]\n** constants to indicate why the callback was invoked.\n** ^The C argument is a copy of the context pointer.\n** The P and X arguments are pointers whose meanings depend on T.\n**\n** The sqlite3_trace_v2() interface is intended to replace the legacy\n** interfaces [sqlite3_trace()] and [sqlite3_profile()], both of which\n** are deprecated.\n*/\nSQLITE_API int sqlite3_trace_v2(\n  sqlite3*,\n  unsigned uMask,\n  int(*xCallback)(unsigned,void*,void*,void*),\n  void *pCtx\n);\n\n/*\n** CAPI3REF: Query Progress Callbacks\n** METHOD: sqlite3\n**\n** ^The sqlite3_progress_handler(D,N,X,P) interface causes the callback\n** function X to be invoked periodically during long running calls to\n** [sqlite3_exec()], [sqlite3_step()] and [sqlite3_get_table()] for\n** database connection D.  An example use for this\n** interface is to keep a GUI updated during a large query.\n**\n** ^The parameter P is passed through as the only parameter to the \n** callback function X.  ^The parameter N is the approximate number of \n** [virtual machine instructions] that are evaluated between successive\n** invocations of the callback X.  ^If N is less than one then the progress\n** handler is disabled.\n**\n** ^Only a single progress handler may be defined at one time per\n** [database connection]; setting a new progress handler cancels the\n** old one.  ^Setting parameter X to NULL disables the progress handler.\n** ^The progress handler is also disabled by setting N to a value less\n** than 1.\n**\n** ^If the progress callback returns non-zero, the operation is\n** interrupted.  This feature can be used to implement a\n** \"Cancel\" button on a GUI progress dialog box.\n**\n** The progress handler callback must not do anything that will modify\n** the database connection that invoked the progress handler.\n** Note that [sqlite3_prepare_v2()] and [sqlite3_step()] both modify their\n** database connections for the meaning of \"modify\" in this paragraph.\n**\n*/\nSQLITE_API void sqlite3_progress_handler(sqlite3*, int, int(*)(void*), void*);\n\n/*\n** CAPI3REF: Opening A New Database Connection\n** CONSTRUCTOR: sqlite3\n**\n** ^These routines open an SQLite database file as specified by the \n** filename argument. ^The filename argument is interpreted as UTF-8 for\n** sqlite3_open() and sqlite3_open_v2() and as UTF-16 in the native byte\n** order for sqlite3_open16(). ^(A [database connection] handle is usually\n** returned in *ppDb, even if an error occurs.  The only exception is that\n** if SQLite is unable to allocate memory to hold the [sqlite3] object,\n** a NULL will be written into *ppDb instead of a pointer to the [sqlite3]\n** object.)^ ^(If the database is opened (and/or created) successfully, then\n** [SQLITE_OK] is returned.  Otherwise an [error code] is returned.)^ ^The\n** [sqlite3_errmsg()] or [sqlite3_errmsg16()] routines can be used to obtain\n** an English language description of the error following a failure of any\n** of the sqlite3_open() routines.\n**\n** ^The default encoding will be UTF-8 for databases created using\n** sqlite3_open() or sqlite3_open_v2().  ^The default encoding for databases\n** created using sqlite3_open16() will be UTF-16 in the native byte order.\n**\n** Whether or not an error occurs when it is opened, resources\n** associated with the [database connection] handle should be released by\n** passing it to [sqlite3_close()] when it is no longer required.\n**\n** The sqlite3_open_v2() interface works like sqlite3_open()\n** except that it accepts two additional parameters for additional control\n** over the new database connection.  ^(The flags parameter to\n** sqlite3_open_v2() can take one of\n** the following three values, optionally combined with the \n** [SQLITE_OPEN_NOMUTEX], [SQLITE_OPEN_FULLMUTEX], [SQLITE_OPEN_SHAREDCACHE],\n** [SQLITE_OPEN_PRIVATECACHE], and/or [SQLITE_OPEN_URI] flags:)^\n**\n** <dl>\n** ^(<dt>[SQLITE_OPEN_READONLY]</dt>\n** <dd>The database is opened in read-only mode.  If the database does not\n** already exist, an error is returned.</dd>)^\n**\n** ^(<dt>[SQLITE_OPEN_READWRITE]</dt>\n** <dd>The database is opened for reading and writing if possible, or reading\n** only if the file is write protected by the operating system.  In either\n** case the database must already exist, otherwise an error is returned.</dd>)^\n**\n** ^(<dt>[SQLITE_OPEN_READWRITE] | [SQLITE_OPEN_CREATE]</dt>\n** <dd>The database is opened for reading and writing, and is created if\n** it does not already exist. This is the behavior that is always used for\n** sqlite3_open() and sqlite3_open16().</dd>)^\n** </dl>\n**\n** If the 3rd parameter to sqlite3_open_v2() is not one of the\n** combinations shown above optionally combined with other\n** [SQLITE_OPEN_READONLY | SQLITE_OPEN_* bits]\n** then the behavior is undefined.\n**\n** ^If the [SQLITE_OPEN_NOMUTEX] flag is set, then the database connection\n** opens in the multi-thread [threading mode] as long as the single-thread\n** mode has not been set at compile-time or start-time.  ^If the\n** [SQLITE_OPEN_FULLMUTEX] flag is set then the database connection opens\n** in the serialized [threading mode] unless single-thread was\n** previously selected at compile-time or start-time.\n** ^The [SQLITE_OPEN_SHAREDCACHE] flag causes the database connection to be\n** eligible to use [shared cache mode], regardless of whether or not shared\n** cache is enabled using [sqlite3_enable_shared_cache()].  ^The\n** [SQLITE_OPEN_PRIVATECACHE] flag causes the database connection to not\n** participate in [shared cache mode] even if it is enabled.\n**\n** ^The fourth parameter to sqlite3_open_v2() is the name of the\n** [sqlite3_vfs] object that defines the operating system interface that\n** the new database connection should use.  ^If the fourth parameter is\n** a NULL pointer then the default [sqlite3_vfs] object is used.\n**\n** ^If the filename is \":memory:\", then a private, temporary in-memory database\n** is created for the connection.  ^This in-memory database will vanish when\n** the database connection is closed.  Future versions of SQLite might\n** make use of additional special filenames that begin with the \":\" character.\n** It is recommended that when a database filename actually does begin with\n** a \":\" character you should prefix the filename with a pathname such as\n** \"./\" to avoid ambiguity.\n**\n** ^If the filename is an empty string, then a private, temporary\n** on-disk database will be created.  ^This private database will be\n** automatically deleted as soon as the database connection is closed.\n**\n** [[URI filenames in sqlite3_open()]] <h3>URI Filenames</h3>\n**\n** ^If [URI filename] interpretation is enabled, and the filename argument\n** begins with \"file:\", then the filename is interpreted as a URI. ^URI\n** filename interpretation is enabled if the [SQLITE_OPEN_URI] flag is\n** set in the third argument to sqlite3_open_v2(), or if it has\n** been enabled globally using the [SQLITE_CONFIG_URI] option with the\n** [sqlite3_config()] method or by the [SQLITE_USE_URI] compile-time option.\n** URI filename interpretation is turned off\n** by default, but future releases of SQLite might enable URI filename\n** interpretation by default.  See \"[URI filenames]\" for additional\n** information.\n**\n** URI filenames are parsed according to RFC 3986. ^If the URI contains an\n** authority, then it must be either an empty string or the string \n** \"localhost\". ^If the authority is not an empty string or \"localhost\", an \n** error is returned to the caller. ^The fragment component of a URI, if \n** present, is ignored.\n**\n** ^SQLite uses the path component of the URI as the name of the disk file\n** which contains the database. ^If the path begins with a '/' character, \n** then it is interpreted as an absolute path. ^If the path does not begin \n** with a '/' (meaning that the authority section is omitted from the URI)\n** then the path is interpreted as a relative path. \n** ^(On windows, the first component of an absolute path \n** is a drive specification (e.g. \"C:\").)^\n**\n** [[core URI query parameters]]\n** The query component of a URI may contain parameters that are interpreted\n** either by SQLite itself, or by a [VFS | custom VFS implementation].\n** SQLite and its built-in [VFSes] interpret the\n** following query parameters:\n**\n** <ul>\n**   <li> <b>vfs</b>: ^The \"vfs\" parameter may be used to specify the name of\n**     a VFS object that provides the operating system interface that should\n**     be used to access the database file on disk. ^If this option is set to\n**     an empty string the default VFS object is used. ^Specifying an unknown\n**     VFS is an error. ^If sqlite3_open_v2() is used and the vfs option is\n**     present, then the VFS specified by the option takes precedence over\n**     the value passed as the fourth parameter to sqlite3_open_v2().\n**\n**   <li> <b>mode</b>: ^(The mode parameter may be set to either \"ro\", \"rw\",\n**     \"rwc\", or \"memory\". Attempting to set it to any other value is\n**     an error)^. \n**     ^If \"ro\" is specified, then the database is opened for read-only \n**     access, just as if the [SQLITE_OPEN_READONLY] flag had been set in the \n**     third argument to sqlite3_open_v2(). ^If the mode option is set to \n**     \"rw\", then the database is opened for read-write (but not create) \n**     access, as if SQLITE_OPEN_READWRITE (but not SQLITE_OPEN_CREATE) had \n**     been set. ^Value \"rwc\" is equivalent to setting both \n**     SQLITE_OPEN_READWRITE and SQLITE_OPEN_CREATE.  ^If the mode option is\n**     set to \"memory\" then a pure [in-memory database] that never reads\n**     or writes from disk is used. ^It is an error to specify a value for\n**     the mode parameter that is less restrictive than that specified by\n**     the flags passed in the third parameter to sqlite3_open_v2().\n**\n**   <li> <b>cache</b>: ^The cache parameter may be set to either \"shared\" or\n**     \"private\". ^Setting it to \"shared\" is equivalent to setting the\n**     SQLITE_OPEN_SHAREDCACHE bit in the flags argument passed to\n**     sqlite3_open_v2(). ^Setting the cache parameter to \"private\" is \n**     equivalent to setting the SQLITE_OPEN_PRIVATECACHE bit.\n**     ^If sqlite3_open_v2() is used and the \"cache\" parameter is present in\n**     a URI filename, its value overrides any behavior requested by setting\n**     SQLITE_OPEN_PRIVATECACHE or SQLITE_OPEN_SHAREDCACHE flag.\n**\n**  <li> <b>psow</b>: ^The psow parameter indicates whether or not the\n**     [powersafe overwrite] property does or does not apply to the\n**     storage media on which the database file resides.\n**\n**  <li> <b>nolock</b>: ^The nolock parameter is a boolean query parameter\n**     which if set disables file locking in rollback journal modes.  This\n**     is useful for accessing a database on a filesystem that does not\n**     support locking.  Caution:  Database corruption might result if two\n**     or more processes write to the same database and any one of those\n**     processes uses nolock=1.\n**\n**  <li> <b>immutable</b>: ^The immutable parameter is a boolean query\n**     parameter that indicates that the database file is stored on\n**     read-only media.  ^When immutable is set, SQLite assumes that the\n**     database file cannot be changed, even by a process with higher\n**     privilege, and so the database is opened read-only and all locking\n**     and change detection is disabled.  Caution: Setting the immutable\n**     property on a database file that does in fact change can result\n**     in incorrect query results and/or [SQLITE_CORRUPT] errors.\n**     See also: [SQLITE_IOCAP_IMMUTABLE].\n**       \n** </ul>\n**\n** ^Specifying an unknown parameter in the query component of a URI is not an\n** error.  Future versions of SQLite might understand additional query\n** parameters.  See \"[query parameters with special meaning to SQLite]\" for\n** additional information.\n**\n** [[URI filename examples]] <h3>URI filename examples</h3>\n**\n** <table border=\"1\" align=center cellpadding=5>\n** <tr><th> URI filenames <th> Results\n** <tr><td> file:data.db <td> \n**          Open the file \"data.db\" in the current directory.\n** <tr><td> file:/home/fred/data.db<br>\n**          file:///home/fred/data.db <br> \n**          file://localhost/home/fred/data.db <br> <td> \n**          Open the database file \"/home/fred/data.db\".\n** <tr><td> file://darkstar/home/fred/data.db <td> \n**          An error. \"darkstar\" is not a recognized authority.\n** <tr><td style=\"white-space:nowrap\"> \n**          file:///C:/Documents%20and%20Settings/fred/Desktop/data.db\n**     <td> Windows only: Open the file \"data.db\" on fred's desktop on drive\n**          C:. Note that the %20 escaping in this example is not strictly \n**          necessary - space characters can be used literally\n**          in URI filenames.\n** <tr><td> file:data.db?mode=ro&cache=private <td> \n**          Open file \"data.db\" in the current directory for read-only access.\n**          Regardless of whether or not shared-cache mode is enabled by\n**          default, use a private cache.\n** <tr><td> file:/home/fred/data.db?vfs=unix-dotfile <td>\n**          Open file \"/home/fred/data.db\". Use the special VFS \"unix-dotfile\"\n**          that uses dot-files in place of posix advisory locking.\n** <tr><td> file:data.db?mode=readonly <td> \n**          An error. \"readonly\" is not a valid option for the \"mode\" parameter.\n** </table>\n**\n** ^URI hexadecimal escape sequences (%HH) are supported within the path and\n** query components of a URI. A hexadecimal escape sequence consists of a\n** percent sign - \"%\" - followed by exactly two hexadecimal digits \n** specifying an octet value. ^Before the path or query components of a\n** URI filename are interpreted, they are encoded using UTF-8 and all \n** hexadecimal escape sequences replaced by a single byte containing the\n** corresponding octet. If this process generates an invalid UTF-8 encoding,\n** the results are undefined.\n**\n** <b>Note to Windows users:</b>  The encoding used for the filename argument\n** of sqlite3_open() and sqlite3_open_v2() must be UTF-8, not whatever\n** codepage is currently defined.  Filenames containing international\n** characters must be converted to UTF-8 prior to passing them into\n** sqlite3_open() or sqlite3_open_v2().\n**\n** <b>Note to Windows Runtime users:</b>  The temporary directory must be set\n** prior to calling sqlite3_open() or sqlite3_open_v2().  Otherwise, various\n** features that require the use of temporary files may fail.\n**\n** See also: [sqlite3_temp_directory]\n*/\nSQLITE_API int sqlite3_open(\n  const char *filename,   /* Database filename (UTF-8) */\n  sqlite3 **ppDb          /* OUT: SQLite db handle */\n);\nSQLITE_API int sqlite3_open16(\n  const void *filename,   /* Database filename (UTF-16) */\n  sqlite3 **ppDb          /* OUT: SQLite db handle */\n);\nSQLITE_API int sqlite3_open_v2(\n  const char *filename,   /* Database filename (UTF-8) */\n  sqlite3 **ppDb,         /* OUT: SQLite db handle */\n  int flags,              /* Flags */\n  const char *zVfs        /* Name of VFS module to use */\n);\n\n/*\n** CAPI3REF: Obtain Values For URI Parameters\n**\n** These are utility routines, useful to VFS implementations, that check\n** to see if a database file was a URI that contained a specific query \n** parameter, and if so obtains the value of that query parameter.\n**\n** If F is the database filename pointer passed into the xOpen() method of \n** a VFS implementation when the flags parameter to xOpen() has one or \n** more of the [SQLITE_OPEN_URI] or [SQLITE_OPEN_MAIN_DB] bits set and\n** P is the name of the query parameter, then\n** sqlite3_uri_parameter(F,P) returns the value of the P\n** parameter if it exists or a NULL pointer if P does not appear as a \n** query parameter on F.  If P is a query parameter of F\n** has no explicit value, then sqlite3_uri_parameter(F,P) returns\n** a pointer to an empty string.\n**\n** The sqlite3_uri_boolean(F,P,B) routine assumes that P is a boolean\n** parameter and returns true (1) or false (0) according to the value\n** of P.  The sqlite3_uri_boolean(F,P,B) routine returns true (1) if the\n** value of query parameter P is one of \"yes\", \"true\", or \"on\" in any\n** case or if the value begins with a non-zero number.  The \n** sqlite3_uri_boolean(F,P,B) routines returns false (0) if the value of\n** query parameter P is one of \"no\", \"false\", or \"off\" in any case or\n** if the value begins with a numeric zero.  If P is not a query\n** parameter on F or if the value of P is does not match any of the\n** above, then sqlite3_uri_boolean(F,P,B) returns (B!=0).\n**\n** The sqlite3_uri_int64(F,P,D) routine converts the value of P into a\n** 64-bit signed integer and returns that integer, or D if P does not\n** exist.  If the value of P is something other than an integer, then\n** zero is returned.\n** \n** If F is a NULL pointer, then sqlite3_uri_parameter(F,P) returns NULL and\n** sqlite3_uri_boolean(F,P,B) returns B.  If F is not a NULL pointer and\n** is not a database file pathname pointer that SQLite passed into the xOpen\n** VFS method, then the behavior of this routine is undefined and probably\n** undesirable.\n*/\nSQLITE_API const char *sqlite3_uri_parameter(const char *zFilename, const char *zParam);\nSQLITE_API int sqlite3_uri_boolean(const char *zFile, const char *zParam, int bDefault);\nSQLITE_API sqlite3_int64 sqlite3_uri_int64(const char*, const char*, sqlite3_int64);\n\n\n/*\n** CAPI3REF: Error Codes And Messages\n** METHOD: sqlite3\n**\n** ^If the most recent sqlite3_* API call associated with \n** [database connection] D failed, then the sqlite3_errcode(D) interface\n** returns the numeric [result code] or [extended result code] for that\n** API call.\n** If the most recent API call was successful,\n** then the return value from sqlite3_errcode() is undefined.\n** ^The sqlite3_extended_errcode()\n** interface is the same except that it always returns the \n** [extended result code] even when extended result codes are\n** disabled.\n**\n** ^The sqlite3_errmsg() and sqlite3_errmsg16() return English-language\n** text that describes the error, as either UTF-8 or UTF-16 respectively.\n** ^(Memory to hold the error message string is managed internally.\n** The application does not need to worry about freeing the result.\n** However, the error string might be overwritten or deallocated by\n** subsequent calls to other SQLite interface functions.)^\n**\n** ^The sqlite3_errstr() interface returns the English-language text\n** that describes the [result code], as UTF-8.\n** ^(Memory to hold the error message string is managed internally\n** and must not be freed by the application)^.\n**\n** When the serialized [threading mode] is in use, it might be the\n** case that a second error occurs on a separate thread in between\n** the time of the first error and the call to these interfaces.\n** When that happens, the second error will be reported since these\n** interfaces always report the most recent result.  To avoid\n** this, each thread can obtain exclusive use of the [database connection] D\n** by invoking [sqlite3_mutex_enter]([sqlite3_db_mutex](D)) before beginning\n** to use D and invoking [sqlite3_mutex_leave]([sqlite3_db_mutex](D)) after\n** all calls to the interfaces listed here are completed.\n**\n** If an interface fails with SQLITE_MISUSE, that means the interface\n** was invoked incorrectly by the application.  In that case, the\n** error code and message may or may not be set.\n*/\nSQLITE_API int sqlite3_errcode(sqlite3 *db);\nSQLITE_API int sqlite3_extended_errcode(sqlite3 *db);\nSQLITE_API const char *sqlite3_errmsg(sqlite3*);\nSQLITE_API const void *sqlite3_errmsg16(sqlite3*);\nSQLITE_API const char *sqlite3_errstr(int);\n\n/*\n** CAPI3REF: Prepared Statement Object\n** KEYWORDS: {prepared statement} {prepared statements}\n**\n** An instance of this object represents a single SQL statement that\n** has been compiled into binary form and is ready to be evaluated.\n**\n** Think of each SQL statement as a separate computer program.  The\n** original SQL text is source code.  A prepared statement object \n** is the compiled object code.  All SQL must be converted into a\n** prepared statement before it can be run.\n**\n** The life-cycle of a prepared statement object usually goes like this:\n**\n** <ol>\n** <li> Create the prepared statement object using [sqlite3_prepare_v2()].\n** <li> Bind values to [parameters] using the sqlite3_bind_*()\n**      interfaces.\n** <li> Run the SQL by calling [sqlite3_step()] one or more times.\n** <li> Reset the prepared statement using [sqlite3_reset()] then go back\n**      to step 2.  Do this zero or more times.\n** <li> Destroy the object using [sqlite3_finalize()].\n** </ol>\n*/\ntypedef struct sqlite3_stmt sqlite3_stmt;\n\n/*\n** CAPI3REF: Run-time Limits\n** METHOD: sqlite3\n**\n** ^(This interface allows the size of various constructs to be limited\n** on a connection by connection basis.  The first parameter is the\n** [database connection] whose limit is to be set or queried.  The\n** second parameter is one of the [limit categories] that define a\n** class of constructs to be size limited.  The third parameter is the\n** new limit for that construct.)^\n**\n** ^If the new limit is a negative number, the limit is unchanged.\n** ^(For each limit category SQLITE_LIMIT_<i>NAME</i> there is a \n** [limits | hard upper bound]\n** set at compile-time by a C preprocessor macro called\n** [limits | SQLITE_MAX_<i>NAME</i>].\n** (The \"_LIMIT_\" in the name is changed to \"_MAX_\".))^\n** ^Attempts to increase a limit above its hard upper bound are\n** silently truncated to the hard upper bound.\n**\n** ^Regardless of whether or not the limit was changed, the \n** [sqlite3_limit()] interface returns the prior value of the limit.\n** ^Hence, to find the current value of a limit without changing it,\n** simply invoke this interface with the third parameter set to -1.\n**\n** Run-time limits are intended for use in applications that manage\n** both their own internal database and also databases that are controlled\n** by untrusted external sources.  An example application might be a\n** web browser that has its own databases for storing history and\n** separate databases controlled by JavaScript applications downloaded\n** off the Internet.  The internal databases can be given the\n** large, default limits.  Databases managed by external sources can\n** be given much smaller limits designed to prevent a denial of service\n** attack.  Developers might also want to use the [sqlite3_set_authorizer()]\n** interface to further control untrusted SQL.  The size of the database\n** created by an untrusted script can be contained using the\n** [max_page_count] [PRAGMA].\n**\n** New run-time limit categories may be added in future releases.\n*/\nSQLITE_API int sqlite3_limit(sqlite3*, int id, int newVal);\n\n/*\n** CAPI3REF: Run-Time Limit Categories\n** KEYWORDS: {limit category} {*limit categories}\n**\n** These constants define various performance limits\n** that can be lowered at run-time using [sqlite3_limit()].\n** The synopsis of the meanings of the various limits is shown below.\n** Additional information is available at [limits | Limits in SQLite].\n**\n** <dl>\n** [[SQLITE_LIMIT_LENGTH]] ^(<dt>SQLITE_LIMIT_LENGTH</dt>\n** <dd>The maximum size of any string or BLOB or table row, in bytes.<dd>)^\n**\n** [[SQLITE_LIMIT_SQL_LENGTH]] ^(<dt>SQLITE_LIMIT_SQL_LENGTH</dt>\n** <dd>The maximum length of an SQL statement, in bytes.</dd>)^\n**\n** [[SQLITE_LIMIT_COLUMN]] ^(<dt>SQLITE_LIMIT_COLUMN</dt>\n** <dd>The maximum number of columns in a table definition or in the\n** result set of a [SELECT] or the maximum number of columns in an index\n** or in an ORDER BY or GROUP BY clause.</dd>)^\n**\n** [[SQLITE_LIMIT_EXPR_DEPTH]] ^(<dt>SQLITE_LIMIT_EXPR_DEPTH</dt>\n** <dd>The maximum depth of the parse tree on any expression.</dd>)^\n**\n** [[SQLITE_LIMIT_COMPOUND_SELECT]] ^(<dt>SQLITE_LIMIT_COMPOUND_SELECT</dt>\n** <dd>The maximum number of terms in a compound SELECT statement.</dd>)^\n**\n** [[SQLITE_LIMIT_VDBE_OP]] ^(<dt>SQLITE_LIMIT_VDBE_OP</dt>\n** <dd>The maximum number of instructions in a virtual machine program\n** used to implement an SQL statement.  If [sqlite3_prepare_v2()] or\n** the equivalent tries to allocate space for more than this many opcodes\n** in a single prepared statement, an SQLITE_NOMEM error is returned.</dd>)^\n**\n** [[SQLITE_LIMIT_FUNCTION_ARG]] ^(<dt>SQLITE_LIMIT_FUNCTION_ARG</dt>\n** <dd>The maximum number of arguments on a function.</dd>)^\n**\n** [[SQLITE_LIMIT_ATTACHED]] ^(<dt>SQLITE_LIMIT_ATTACHED</dt>\n** <dd>The maximum number of [ATTACH | attached databases].)^</dd>\n**\n** [[SQLITE_LIMIT_LIKE_PATTERN_LENGTH]]\n** ^(<dt>SQLITE_LIMIT_LIKE_PATTERN_LENGTH</dt>\n** <dd>The maximum length of the pattern argument to the [LIKE] or\n** [GLOB] operators.</dd>)^\n**\n** [[SQLITE_LIMIT_VARIABLE_NUMBER]]\n** ^(<dt>SQLITE_LIMIT_VARIABLE_NUMBER</dt>\n** <dd>The maximum index number of any [parameter] in an SQL statement.)^\n**\n** [[SQLITE_LIMIT_TRIGGER_DEPTH]] ^(<dt>SQLITE_LIMIT_TRIGGER_DEPTH</dt>\n** <dd>The maximum depth of recursion for triggers.</dd>)^\n**\n** [[SQLITE_LIMIT_WORKER_THREADS]] ^(<dt>SQLITE_LIMIT_WORKER_THREADS</dt>\n** <dd>The maximum number of auxiliary worker threads that a single\n** [prepared statement] may start.</dd>)^\n** </dl>\n*/\n#define SQLITE_LIMIT_LENGTH                    0\n#define SQLITE_LIMIT_SQL_LENGTH                1\n#define SQLITE_LIMIT_COLUMN                    2\n#define SQLITE_LIMIT_EXPR_DEPTH                3\n#define SQLITE_LIMIT_COMPOUND_SELECT           4\n#define SQLITE_LIMIT_VDBE_OP                   5\n#define SQLITE_LIMIT_FUNCTION_ARG              6\n#define SQLITE_LIMIT_ATTACHED                  7\n#define SQLITE_LIMIT_LIKE_PATTERN_LENGTH       8\n#define SQLITE_LIMIT_VARIABLE_NUMBER           9\n#define SQLITE_LIMIT_TRIGGER_DEPTH            10\n#define SQLITE_LIMIT_WORKER_THREADS           11\n\n/*\n** CAPI3REF: Prepare Flags\n**\n** These constants define various flags that can be passed into\n** \"prepFlags\" parameter of the [sqlite3_prepare_v3()] and\n** [sqlite3_prepare16_v3()] interfaces.\n**\n** New flags may be added in future releases of SQLite.\n**\n** <dl>\n** [[SQLITE_PREPARE_PERSISTENT]] ^(<dt>SQLITE_PREPARE_PERSISTENT</dt>\n** <dd>The SQLITE_PREPARE_PERSISTENT flag is a hint to the query planner\n** that the prepared statement will be retained for a long time and\n** probably reused many times.)^ ^Without this flag, [sqlite3_prepare_v3()]\n** and [sqlite3_prepare16_v3()] assume that the prepared statement will \n** be used just once or at most a few times and then destroyed using\n** [sqlite3_finalize()] relatively soon. The current implementation acts\n** on this hint by avoiding the use of [lookaside memory] so as not to\n** deplete the limited store of lookaside memory. Future versions of\n** SQLite may act on this hint differently.\n** </dl>\n*/\n#define SQLITE_PREPARE_PERSISTENT              0x01\n\n/*\n** CAPI3REF: Compiling An SQL Statement\n** KEYWORDS: {SQL statement compiler}\n** METHOD: sqlite3\n** CONSTRUCTOR: sqlite3_stmt\n**\n** To execute an SQL statement, it must first be compiled into a byte-code\n** program using one of these routines.  Or, in other words, these routines\n** are constructors for the [prepared statement] object.\n**\n** The preferred routine to use is [sqlite3_prepare_v2()].  The\n** [sqlite3_prepare()] interface is legacy and should be avoided.\n** [sqlite3_prepare_v3()] has an extra \"prepFlags\" option that is used\n** for special purposes.\n**\n** The use of the UTF-8 interfaces is preferred, as SQLite currently\n** does all parsing using UTF-8.  The UTF-16 interfaces are provided\n** as a convenience.  The UTF-16 interfaces work by converting the\n** input text into UTF-8, then invoking the corresponding UTF-8 interface.\n**\n** The first argument, \"db\", is a [database connection] obtained from a\n** prior successful call to [sqlite3_open()], [sqlite3_open_v2()] or\n** [sqlite3_open16()].  The database connection must not have been closed.\n**\n** The second argument, \"zSql\", is the statement to be compiled, encoded\n** as either UTF-8 or UTF-16.  The sqlite3_prepare(), sqlite3_prepare_v2(),\n** and sqlite3_prepare_v3()\n** interfaces use UTF-8, and sqlite3_prepare16(), sqlite3_prepare16_v2(),\n** and sqlite3_prepare16_v3() use UTF-16.\n**\n** ^If the nByte argument is negative, then zSql is read up to the\n** first zero terminator. ^If nByte is positive, then it is the\n** number of bytes read from zSql.  ^If nByte is zero, then no prepared\n** statement is generated.\n** If the caller knows that the supplied string is nul-terminated, then\n** there is a small performance advantage to passing an nByte parameter that\n** is the number of bytes in the input string <i>including</i>\n** the nul-terminator.\n**\n** ^If pzTail is not NULL then *pzTail is made to point to the first byte\n** past the end of the first SQL statement in zSql.  These routines only\n** compile the first statement in zSql, so *pzTail is left pointing to\n** what remains uncompiled.\n**\n** ^*ppStmt is left pointing to a compiled [prepared statement] that can be\n** executed using [sqlite3_step()].  ^If there is an error, *ppStmt is set\n** to NULL.  ^If the input text contains no SQL (if the input is an empty\n** string or a comment) then *ppStmt is set to NULL.\n** The calling procedure is responsible for deleting the compiled\n** SQL statement using [sqlite3_finalize()] after it has finished with it.\n** ppStmt may not be NULL.\n**\n** ^On success, the sqlite3_prepare() family of routines return [SQLITE_OK];\n** otherwise an [error code] is returned.\n**\n** The sqlite3_prepare_v2(), sqlite3_prepare_v3(), sqlite3_prepare16_v2(),\n** and sqlite3_prepare16_v3() interfaces are recommended for all new programs.\n** The older interfaces (sqlite3_prepare() and sqlite3_prepare16())\n** are retained for backwards compatibility, but their use is discouraged.\n** ^In the \"vX\" interfaces, the prepared statement\n** that is returned (the [sqlite3_stmt] object) contains a copy of the\n** original SQL text. This causes the [sqlite3_step()] interface to\n** behave differently in three ways:\n**\n** <ol>\n** <li>\n** ^If the database schema changes, instead of returning [SQLITE_SCHEMA] as it\n** always used to do, [sqlite3_step()] will automatically recompile the SQL\n** statement and try to run it again. As many as [SQLITE_MAX_SCHEMA_RETRY]\n** retries will occur before sqlite3_step() gives up and returns an error.\n** </li>\n**\n** <li>\n** ^When an error occurs, [sqlite3_step()] will return one of the detailed\n** [error codes] or [extended error codes].  ^The legacy behavior was that\n** [sqlite3_step()] would only return a generic [SQLITE_ERROR] result code\n** and the application would have to make a second call to [sqlite3_reset()]\n** in order to find the underlying cause of the problem. With the \"v2\" prepare\n** interfaces, the underlying reason for the error is returned immediately.\n** </li>\n**\n** <li>\n** ^If the specific value bound to [parameter | host parameter] in the \n** WHERE clause might influence the choice of query plan for a statement,\n** then the statement will be automatically recompiled, as if there had been \n** a schema change, on the first  [sqlite3_step()] call following any change\n** to the [sqlite3_bind_text | bindings] of that [parameter]. \n** ^The specific value of WHERE-clause [parameter] might influence the \n** choice of query plan if the parameter is the left-hand side of a [LIKE]\n** or [GLOB] operator or if the parameter is compared to an indexed column\n** and the [SQLITE_ENABLE_STAT3] compile-time option is enabled.\n** </li>\n** </ol>\n**\n** <p>^sqlite3_prepare_v3() differs from sqlite3_prepare_v2() only in having\n** the extra prepFlags parameter, which is a bit array consisting of zero or\n** more of the [SQLITE_PREPARE_PERSISTENT|SQLITE_PREPARE_*] flags.  ^The\n** sqlite3_prepare_v2() interface works exactly the same as\n** sqlite3_prepare_v3() with a zero prepFlags parameter.\n*/\nSQLITE_API int sqlite3_prepare(\n  sqlite3 *db,            /* Database handle */\n  const char *zSql,       /* SQL statement, UTF-8 encoded */\n  int nByte,              /* Maximum length of zSql in bytes. */\n  sqlite3_stmt **ppStmt,  /* OUT: Statement handle */\n  const char **pzTail     /* OUT: Pointer to unused portion of zSql */\n);\nSQLITE_API int sqlite3_prepare_v2(\n  sqlite3 *db,            /* Database handle */\n  const char *zSql,       /* SQL statement, UTF-8 encoded */\n  int nByte,              /* Maximum length of zSql in bytes. */\n  sqlite3_stmt **ppStmt,  /* OUT: Statement handle */\n  const char **pzTail     /* OUT: Pointer to unused portion of zSql */\n);\nSQLITE_API int sqlite3_prepare_v3(\n  sqlite3 *db,            /* Database handle */\n  const char *zSql,       /* SQL statement, UTF-8 encoded */\n  int nByte,              /* Maximum length of zSql in bytes. */\n  unsigned int prepFlags, /* Zero or more SQLITE_PREPARE_ flags */\n  sqlite3_stmt **ppStmt,  /* OUT: Statement handle */\n  const char **pzTail     /* OUT: Pointer to unused portion of zSql */\n);\nSQLITE_API int sqlite3_prepare16(\n  sqlite3 *db,            /* Database handle */\n  const void *zSql,       /* SQL statement, UTF-16 encoded */\n  int nByte,              /* Maximum length of zSql in bytes. */\n  sqlite3_stmt **ppStmt,  /* OUT: Statement handle */\n  const void **pzTail     /* OUT: Pointer to unused portion of zSql */\n);\nSQLITE_API int sqlite3_prepare16_v2(\n  sqlite3 *db,            /* Database handle */\n  const void *zSql,       /* SQL statement, UTF-16 encoded */\n  int nByte,              /* Maximum length of zSql in bytes. */\n  sqlite3_stmt **ppStmt,  /* OUT: Statement handle */\n  const void **pzTail     /* OUT: Pointer to unused portion of zSql */\n);\nSQLITE_API int sqlite3_prepare16_v3(\n  sqlite3 *db,            /* Database handle */\n  const void *zSql,       /* SQL statement, UTF-16 encoded */\n  int nByte,              /* Maximum length of zSql in bytes. */\n  unsigned int prepFlags, /* Zero or more SQLITE_PREPARE_ flags */\n  sqlite3_stmt **ppStmt,  /* OUT: Statement handle */\n  const void **pzTail     /* OUT: Pointer to unused portion of zSql */\n);\n\n/*\n** CAPI3REF: Retrieving Statement SQL\n** METHOD: sqlite3_stmt\n**\n** ^The sqlite3_sql(P) interface returns a pointer to a copy of the UTF-8\n** SQL text used to create [prepared statement] P if P was\n** created by [sqlite3_prepare_v2()], [sqlite3_prepare_v3()],\n** [sqlite3_prepare16_v2()], or [sqlite3_prepare16_v3()].\n** ^The sqlite3_expanded_sql(P) interface returns a pointer to a UTF-8\n** string containing the SQL text of prepared statement P with\n** [bound parameters] expanded.\n**\n** ^(For example, if a prepared statement is created using the SQL\n** text \"SELECT $abc,:xyz\" and if parameter $abc is bound to integer 2345\n** and parameter :xyz is unbound, then sqlite3_sql() will return\n** the original string, \"SELECT $abc,:xyz\" but sqlite3_expanded_sql()\n** will return \"SELECT 2345,NULL\".)^\n**\n** ^The sqlite3_expanded_sql() interface returns NULL if insufficient memory\n** is available to hold the result, or if the result would exceed the\n** the maximum string length determined by the [SQLITE_LIMIT_LENGTH].\n**\n** ^The [SQLITE_TRACE_SIZE_LIMIT] compile-time option limits the size of\n** bound parameter expansions.  ^The [SQLITE_OMIT_TRACE] compile-time\n** option causes sqlite3_expanded_sql() to always return NULL.\n**\n** ^The string returned by sqlite3_sql(P) is managed by SQLite and is\n** automatically freed when the prepared statement is finalized.\n** ^The string returned by sqlite3_expanded_sql(P), on the other hand,\n** is obtained from [sqlite3_malloc()] and must be free by the application\n** by passing it to [sqlite3_free()].\n*/\nSQLITE_API const char *sqlite3_sql(sqlite3_stmt *pStmt);\nSQLITE_API char *sqlite3_expanded_sql(sqlite3_stmt *pStmt);\n\n/*\n** CAPI3REF: Determine If An SQL Statement Writes The Database\n** METHOD: sqlite3_stmt\n**\n** ^The sqlite3_stmt_readonly(X) interface returns true (non-zero) if\n** and only if the [prepared statement] X makes no direct changes to\n** the content of the database file.\n**\n** Note that [application-defined SQL functions] or\n** [virtual tables] might change the database indirectly as a side effect.  \n** ^(For example, if an application defines a function \"eval()\" that \n** calls [sqlite3_exec()], then the following SQL statement would\n** change the database file through side-effects:\n**\n** <blockquote><pre>\n**    SELECT eval('DELETE FROM t1') FROM t2;\n** </pre></blockquote>\n**\n** But because the [SELECT] statement does not change the database file\n** directly, sqlite3_stmt_readonly() would still return true.)^\n**\n** ^Transaction control statements such as [BEGIN], [COMMIT], [ROLLBACK],\n** [SAVEPOINT], and [RELEASE] cause sqlite3_stmt_readonly() to return true,\n** since the statements themselves do not actually modify the database but\n** rather they control the timing of when other statements modify the \n** database.  ^The [ATTACH] and [DETACH] statements also cause\n** sqlite3_stmt_readonly() to return true since, while those statements\n** change the configuration of a database connection, they do not make \n** changes to the content of the database files on disk.\n** ^The sqlite3_stmt_readonly() interface returns true for [BEGIN] since\n** [BEGIN] merely sets internal flags, but the [BEGIN|BEGIN IMMEDIATE] and\n** [BEGIN|BEGIN EXCLUSIVE] commands do touch the database and so\n** sqlite3_stmt_readonly() returns false for those commands.\n*/\nSQLITE_API int sqlite3_stmt_readonly(sqlite3_stmt *pStmt);\n\n/*\n** CAPI3REF: Determine If A Prepared Statement Has Been Reset\n** METHOD: sqlite3_stmt\n**\n** ^The sqlite3_stmt_busy(S) interface returns true (non-zero) if the\n** [prepared statement] S has been stepped at least once using \n** [sqlite3_step(S)] but has neither run to completion (returned\n** [SQLITE_DONE] from [sqlite3_step(S)]) nor\n** been reset using [sqlite3_reset(S)].  ^The sqlite3_stmt_busy(S)\n** interface returns false if S is a NULL pointer.  If S is not a \n** NULL pointer and is not a pointer to a valid [prepared statement]\n** object, then the behavior is undefined and probably undesirable.\n**\n** This interface can be used in combination [sqlite3_next_stmt()]\n** to locate all prepared statements associated with a database \n** connection that are in need of being reset.  This can be used,\n** for example, in diagnostic routines to search for prepared \n** statements that are holding a transaction open.\n*/\nSQLITE_API int sqlite3_stmt_busy(sqlite3_stmt*);\n\n/*\n** CAPI3REF: Dynamically Typed Value Object\n** KEYWORDS: {protected sqlite3_value} {unprotected sqlite3_value}\n**\n** SQLite uses the sqlite3_value object to represent all values\n** that can be stored in a database table. SQLite uses dynamic typing\n** for the values it stores.  ^Values stored in sqlite3_value objects\n** can be integers, floating point values, strings, BLOBs, or NULL.\n**\n** An sqlite3_value object may be either \"protected\" or \"unprotected\".\n** Some interfaces require a protected sqlite3_value.  Other interfaces\n** will accept either a protected or an unprotected sqlite3_value.\n** Every interface that accepts sqlite3_value arguments specifies\n** whether or not it requires a protected sqlite3_value.  The\n** [sqlite3_value_dup()] interface can be used to construct a new \n** protected sqlite3_value from an unprotected sqlite3_value.\n**\n** The terms \"protected\" and \"unprotected\" refer to whether or not\n** a mutex is held.  An internal mutex is held for a protected\n** sqlite3_value object but no mutex is held for an unprotected\n** sqlite3_value object.  If SQLite is compiled to be single-threaded\n** (with [SQLITE_THREADSAFE=0] and with [sqlite3_threadsafe()] returning 0)\n** or if SQLite is run in one of reduced mutex modes \n** [SQLITE_CONFIG_SINGLETHREAD] or [SQLITE_CONFIG_MULTITHREAD]\n** then there is no distinction between protected and unprotected\n** sqlite3_value objects and they can be used interchangeably.  However,\n** for maximum code portability it is recommended that applications\n** still make the distinction between protected and unprotected\n** sqlite3_value objects even when not strictly required.\n**\n** ^The sqlite3_value objects that are passed as parameters into the\n** implementation of [application-defined SQL functions] are protected.\n** ^The sqlite3_value object returned by\n** [sqlite3_column_value()] is unprotected.\n** Unprotected sqlite3_value objects may only be used as arguments\n** to [sqlite3_result_value()], [sqlite3_bind_value()], and\n** [sqlite3_value_dup()].\n** The [sqlite3_value_blob | sqlite3_value_type()] family of\n** interfaces require protected sqlite3_value objects.\n*/\ntypedef struct sqlite3_value sqlite3_value;\n\n/*\n** CAPI3REF: SQL Function Context Object\n**\n** The context in which an SQL function executes is stored in an\n** sqlite3_context object.  ^A pointer to an sqlite3_context object\n** is always first parameter to [application-defined SQL functions].\n** The application-defined SQL function implementation will pass this\n** pointer through into calls to [sqlite3_result_int | sqlite3_result()],\n** [sqlite3_aggregate_context()], [sqlite3_user_data()],\n** [sqlite3_context_db_handle()], [sqlite3_get_auxdata()],\n** and/or [sqlite3_set_auxdata()].\n*/\ntypedef struct sqlite3_context sqlite3_context;\n\n/*\n** CAPI3REF: Binding Values To Prepared Statements\n** KEYWORDS: {host parameter} {host parameters} {host parameter name}\n** KEYWORDS: {SQL parameter} {SQL parameters} {parameter binding}\n** METHOD: sqlite3_stmt\n**\n** ^(In the SQL statement text input to [sqlite3_prepare_v2()] and its variants,\n** literals may be replaced by a [parameter] that matches one of following\n** templates:\n**\n** <ul>\n** <li>  ?\n** <li>  ?NNN\n** <li>  :VVV\n** <li>  @VVV\n** <li>  $VVV\n** </ul>\n**\n** In the templates above, NNN represents an integer literal,\n** and VVV represents an alphanumeric identifier.)^  ^The values of these\n** parameters (also called \"host parameter names\" or \"SQL parameters\")\n** can be set using the sqlite3_bind_*() routines defined here.\n**\n** ^The first argument to the sqlite3_bind_*() routines is always\n** a pointer to the [sqlite3_stmt] object returned from\n** [sqlite3_prepare_v2()] or its variants.\n**\n** ^The second argument is the index of the SQL parameter to be set.\n** ^The leftmost SQL parameter has an index of 1.  ^When the same named\n** SQL parameter is used more than once, second and subsequent\n** occurrences have the same index as the first occurrence.\n** ^The index for named parameters can be looked up using the\n** [sqlite3_bind_parameter_index()] API if desired.  ^The index\n** for \"?NNN\" parameters is the value of NNN.\n** ^The NNN value must be between 1 and the [sqlite3_limit()]\n** parameter [SQLITE_LIMIT_VARIABLE_NUMBER] (default value: 999).\n**\n** ^The third argument is the value to bind to the parameter.\n** ^If the third parameter to sqlite3_bind_text() or sqlite3_bind_text16()\n** or sqlite3_bind_blob() is a NULL pointer then the fourth parameter\n** is ignored and the end result is the same as sqlite3_bind_null().\n**\n** ^(In those routines that have a fourth argument, its value is the\n** number of bytes in the parameter.  To be clear: the value is the\n** number of <u>bytes</u> in the value, not the number of characters.)^\n** ^If the fourth parameter to sqlite3_bind_text() or sqlite3_bind_text16()\n** is negative, then the length of the string is\n** the number of bytes up to the first zero terminator.\n** If the fourth parameter to sqlite3_bind_blob() is negative, then\n** the behavior is undefined.\n** If a non-negative fourth parameter is provided to sqlite3_bind_text()\n** or sqlite3_bind_text16() or sqlite3_bind_text64() then\n** that parameter must be the byte offset\n** where the NUL terminator would occur assuming the string were NUL\n** terminated.  If any NUL characters occur at byte offsets less than \n** the value of the fourth parameter then the resulting string value will\n** contain embedded NULs.  The result of expressions involving strings\n** with embedded NULs is undefined.\n**\n** ^The fifth argument to the BLOB and string binding interfaces\n** is a destructor used to dispose of the BLOB or\n** string after SQLite has finished with it.  ^The destructor is called\n** to dispose of the BLOB or string even if the call to bind API fails.\n** ^If the fifth argument is\n** the special value [SQLITE_STATIC], then SQLite assumes that the\n** information is in static, unmanaged space and does not need to be freed.\n** ^If the fifth argument has the value [SQLITE_TRANSIENT], then\n** SQLite makes its own private copy of the data immediately, before\n** the sqlite3_bind_*() routine returns.\n**\n** ^The sixth argument to sqlite3_bind_text64() must be one of\n** [SQLITE_UTF8], [SQLITE_UTF16], [SQLITE_UTF16BE], or [SQLITE_UTF16LE]\n** to specify the encoding of the text in the third parameter.  If\n** the sixth argument to sqlite3_bind_text64() is not one of the\n** allowed values shown above, or if the text encoding is different\n** from the encoding specified by the sixth parameter, then the behavior\n** is undefined.\n**\n** ^The sqlite3_bind_zeroblob() routine binds a BLOB of length N that\n** is filled with zeroes.  ^A zeroblob uses a fixed amount of memory\n** (just an integer to hold its size) while it is being processed.\n** Zeroblobs are intended to serve as placeholders for BLOBs whose\n** content is later written using\n** [sqlite3_blob_open | incremental BLOB I/O] routines.\n** ^A negative value for the zeroblob results in a zero-length BLOB.\n**\n** ^The sqlite3_bind_pointer(S,I,P,T,D) routine causes the I-th parameter in\n** [prepared statement] S to have an SQL value of NULL, but to also be\n** associated with the pointer P of type T.  ^D is either a NULL pointer or\n** a pointer to a destructor function for P. ^SQLite will invoke the\n** destructor D with a single argument of P when it is finished using\n** P.  The T parameter should be a static string, preferably a string\n** literal. The sqlite3_bind_pointer() routine is part of the\n** [pointer passing interface] added for SQLite 3.20.0.\n**\n** ^If any of the sqlite3_bind_*() routines are called with a NULL pointer\n** for the [prepared statement] or with a prepared statement for which\n** [sqlite3_step()] has been called more recently than [sqlite3_reset()],\n** then the call will return [SQLITE_MISUSE].  If any sqlite3_bind_()\n** routine is passed a [prepared statement] that has been finalized, the\n** result is undefined and probably harmful.\n**\n** ^Bindings are not cleared by the [sqlite3_reset()] routine.\n** ^Unbound parameters are interpreted as NULL.\n**\n** ^The sqlite3_bind_* routines return [SQLITE_OK] on success or an\n** [error code] if anything goes wrong.\n** ^[SQLITE_TOOBIG] might be returned if the size of a string or BLOB\n** exceeds limits imposed by [sqlite3_limit]([SQLITE_LIMIT_LENGTH]) or\n** [SQLITE_MAX_LENGTH].\n** ^[SQLITE_RANGE] is returned if the parameter\n** index is out of range.  ^[SQLITE_NOMEM] is returned if malloc() fails.\n**\n** See also: [sqlite3_bind_parameter_count()],\n** [sqlite3_bind_parameter_name()], and [sqlite3_bind_parameter_index()].\n*/\nSQLITE_API int sqlite3_bind_blob(sqlite3_stmt*, int, const void*, int n, void(*)(void*));\nSQLITE_API int sqlite3_bind_blob64(sqlite3_stmt*, int, const void*, sqlite3_uint64,\n                        void(*)(void*));\nSQLITE_API int sqlite3_bind_double(sqlite3_stmt*, int, double);\nSQLITE_API int sqlite3_bind_int(sqlite3_stmt*, int, int);\nSQLITE_API int sqlite3_bind_int64(sqlite3_stmt*, int, sqlite3_int64);\nSQLITE_API int sqlite3_bind_null(sqlite3_stmt*, int);\nSQLITE_API int sqlite3_bind_text(sqlite3_stmt*,int,const char*,int,void(*)(void*));\nSQLITE_API int sqlite3_bind_text16(sqlite3_stmt*, int, const void*, int, void(*)(void*));\nSQLITE_API int sqlite3_bind_text64(sqlite3_stmt*, int, const char*, sqlite3_uint64,\n                         void(*)(void*), unsigned char encoding);\nSQLITE_API int sqlite3_bind_value(sqlite3_stmt*, int, const sqlite3_value*);\nSQLITE_API int sqlite3_bind_pointer(sqlite3_stmt*, int, void*, const char*,void(*)(void*));\nSQLITE_API int sqlite3_bind_zeroblob(sqlite3_stmt*, int, int n);\nSQLITE_API int sqlite3_bind_zeroblob64(sqlite3_stmt*, int, sqlite3_uint64);\n\n/*\n** CAPI3REF: Number Of SQL Parameters\n** METHOD: sqlite3_stmt\n**\n** ^This routine can be used to find the number of [SQL parameters]\n** in a [prepared statement].  SQL parameters are tokens of the\n** form \"?\", \"?NNN\", \":AAA\", \"$AAA\", or \"@AAA\" that serve as\n** placeholders for values that are [sqlite3_bind_blob | bound]\n** to the parameters at a later time.\n**\n** ^(This routine actually returns the index of the largest (rightmost)\n** parameter. For all forms except ?NNN, this will correspond to the\n** number of unique parameters.  If parameters of the ?NNN form are used,\n** there may be gaps in the list.)^\n**\n** See also: [sqlite3_bind_blob|sqlite3_bind()],\n** [sqlite3_bind_parameter_name()], and\n** [sqlite3_bind_parameter_index()].\n*/\nSQLITE_API int sqlite3_bind_parameter_count(sqlite3_stmt*);\n\n/*\n** CAPI3REF: Name Of A Host Parameter\n** METHOD: sqlite3_stmt\n**\n** ^The sqlite3_bind_parameter_name(P,N) interface returns\n** the name of the N-th [SQL parameter] in the [prepared statement] P.\n** ^(SQL parameters of the form \"?NNN\" or \":AAA\" or \"@AAA\" or \"$AAA\"\n** have a name which is the string \"?NNN\" or \":AAA\" or \"@AAA\" or \"$AAA\"\n** respectively.\n** In other words, the initial \":\" or \"$\" or \"@\" or \"?\"\n** is included as part of the name.)^\n** ^Parameters of the form \"?\" without a following integer have no name\n** and are referred to as \"nameless\" or \"anonymous parameters\".\n**\n** ^The first host parameter has an index of 1, not 0.\n**\n** ^If the value N is out of range or if the N-th parameter is\n** nameless, then NULL is returned.  ^The returned string is\n** always in UTF-8 encoding even if the named parameter was\n** originally specified as UTF-16 in [sqlite3_prepare16()],\n** [sqlite3_prepare16_v2()], or [sqlite3_prepare16_v3()].\n**\n** See also: [sqlite3_bind_blob|sqlite3_bind()],\n** [sqlite3_bind_parameter_count()], and\n** [sqlite3_bind_parameter_index()].\n*/\nSQLITE_API const char *sqlite3_bind_parameter_name(sqlite3_stmt*, int);\n\n/*\n** CAPI3REF: Index Of A Parameter With A Given Name\n** METHOD: sqlite3_stmt\n**\n** ^Return the index of an SQL parameter given its name.  ^The\n** index value returned is suitable for use as the second\n** parameter to [sqlite3_bind_blob|sqlite3_bind()].  ^A zero\n** is returned if no matching parameter is found.  ^The parameter\n** name must be given in UTF-8 even if the original statement\n** was prepared from UTF-16 text using [sqlite3_prepare16_v2()] or\n** [sqlite3_prepare16_v3()].\n**\n** See also: [sqlite3_bind_blob|sqlite3_bind()],\n** [sqlite3_bind_parameter_count()], and\n** [sqlite3_bind_parameter_name()].\n*/\nSQLITE_API int sqlite3_bind_parameter_index(sqlite3_stmt*, const char *zName);\n\n/*\n** CAPI3REF: Reset All Bindings On A Prepared Statement\n** METHOD: sqlite3_stmt\n**\n** ^Contrary to the intuition of many, [sqlite3_reset()] does not reset\n** the [sqlite3_bind_blob | bindings] on a [prepared statement].\n** ^Use this routine to reset all host parameters to NULL.\n*/\nSQLITE_API int sqlite3_clear_bindings(sqlite3_stmt*);\n\n/*\n** CAPI3REF: Number Of Columns In A Result Set\n** METHOD: sqlite3_stmt\n**\n** ^Return the number of columns in the result set returned by the\n** [prepared statement]. ^If this routine returns 0, that means the \n** [prepared statement] returns no data (for example an [UPDATE]).\n** ^However, just because this routine returns a positive number does not\n** mean that one or more rows of data will be returned.  ^A SELECT statement\n** will always have a positive sqlite3_column_count() but depending on the\n** WHERE clause constraints and the table content, it might return no rows.\n**\n** See also: [sqlite3_data_count()]\n*/\nSQLITE_API int sqlite3_column_count(sqlite3_stmt *pStmt);\n\n/*\n** CAPI3REF: Column Names In A Result Set\n** METHOD: sqlite3_stmt\n**\n** ^These routines return the name assigned to a particular column\n** in the result set of a [SELECT] statement.  ^The sqlite3_column_name()\n** interface returns a pointer to a zero-terminated UTF-8 string\n** and sqlite3_column_name16() returns a pointer to a zero-terminated\n** UTF-16 string.  ^The first parameter is the [prepared statement]\n** that implements the [SELECT] statement. ^The second parameter is the\n** column number.  ^The leftmost column is number 0.\n**\n** ^The returned string pointer is valid until either the [prepared statement]\n** is destroyed by [sqlite3_finalize()] or until the statement is automatically\n** reprepared by the first call to [sqlite3_step()] for a particular run\n** or until the next call to\n** sqlite3_column_name() or sqlite3_column_name16() on the same column.\n**\n** ^If sqlite3_malloc() fails during the processing of either routine\n** (for example during a conversion from UTF-8 to UTF-16) then a\n** NULL pointer is returned.\n**\n** ^The name of a result column is the value of the \"AS\" clause for\n** that column, if there is an AS clause.  If there is no AS clause\n** then the name of the column is unspecified and may change from\n** one release of SQLite to the next.\n*/\nSQLITE_API const char *sqlite3_column_name(sqlite3_stmt*, int N);\nSQLITE_API const void *sqlite3_column_name16(sqlite3_stmt*, int N);\n\n/*\n** CAPI3REF: Source Of Data In A Query Result\n** METHOD: sqlite3_stmt\n**\n** ^These routines provide a means to determine the database, table, and\n** table column that is the origin of a particular result column in\n** [SELECT] statement.\n** ^The name of the database or table or column can be returned as\n** either a UTF-8 or UTF-16 string.  ^The _database_ routines return\n** the database name, the _table_ routines return the table name, and\n** the origin_ routines return the column name.\n** ^The returned string is valid until the [prepared statement] is destroyed\n** using [sqlite3_finalize()] or until the statement is automatically\n** reprepared by the first call to [sqlite3_step()] for a particular run\n** or until the same information is requested\n** again in a different encoding.\n**\n** ^The names returned are the original un-aliased names of the\n** database, table, and column.\n**\n** ^The first argument to these interfaces is a [prepared statement].\n** ^These functions return information about the Nth result column returned by\n** the statement, where N is the second function argument.\n** ^The left-most column is column 0 for these routines.\n**\n** ^If the Nth column returned by the statement is an expression or\n** subquery and is not a column value, then all of these functions return\n** NULL.  ^These routine might also return NULL if a memory allocation error\n** occurs.  ^Otherwise, they return the name of the attached database, table,\n** or column that query result column was extracted from.\n**\n** ^As with all other SQLite APIs, those whose names end with \"16\" return\n** UTF-16 encoded strings and the other functions return UTF-8.\n**\n** ^These APIs are only available if the library was compiled with the\n** [SQLITE_ENABLE_COLUMN_METADATA] C-preprocessor symbol.\n**\n** If two or more threads call one or more of these routines against the same\n** prepared statement and column at the same time then the results are\n** undefined.\n**\n** If two or more threads call one or more\n** [sqlite3_column_database_name | column metadata interfaces]\n** for the same [prepared statement] and result column\n** at the same time then the results are undefined.\n*/\nSQLITE_API const char *sqlite3_column_database_name(sqlite3_stmt*,int);\nSQLITE_API const void *sqlite3_column_database_name16(sqlite3_stmt*,int);\nSQLITE_API const char *sqlite3_column_table_name(sqlite3_stmt*,int);\nSQLITE_API const void *sqlite3_column_table_name16(sqlite3_stmt*,int);\nSQLITE_API const char *sqlite3_column_origin_name(sqlite3_stmt*,int);\nSQLITE_API const void *sqlite3_column_origin_name16(sqlite3_stmt*,int);\n\n/*\n** CAPI3REF: Declared Datatype Of A Query Result\n** METHOD: sqlite3_stmt\n**\n** ^(The first parameter is a [prepared statement].\n** If this statement is a [SELECT] statement and the Nth column of the\n** returned result set of that [SELECT] is a table column (not an\n** expression or subquery) then the declared type of the table\n** column is returned.)^  ^If the Nth column of the result set is an\n** expression or subquery, then a NULL pointer is returned.\n** ^The returned string is always UTF-8 encoded.\n**\n** ^(For example, given the database schema:\n**\n** CREATE TABLE t1(c1 VARIANT);\n**\n** and the following statement to be compiled:\n**\n** SELECT c1 + 1, c1 FROM t1;\n**\n** this routine would return the string \"VARIANT\" for the second result\n** column (i==1), and a NULL pointer for the first result column (i==0).)^\n**\n** ^SQLite uses dynamic run-time typing.  ^So just because a column\n** is declared to contain a particular type does not mean that the\n** data stored in that column is of the declared type.  SQLite is\n** strongly typed, but the typing is dynamic not static.  ^Type\n** is associated with individual values, not with the containers\n** used to hold those values.\n*/\nSQLITE_API const char *sqlite3_column_decltype(sqlite3_stmt*,int);\nSQLITE_API const void *sqlite3_column_decltype16(sqlite3_stmt*,int);\n\n/*\n** CAPI3REF: Evaluate An SQL Statement\n** METHOD: sqlite3_stmt\n**\n** After a [prepared statement] has been prepared using any of\n** [sqlite3_prepare_v2()], [sqlite3_prepare_v3()], [sqlite3_prepare16_v2()],\n** or [sqlite3_prepare16_v3()] or one of the legacy\n** interfaces [sqlite3_prepare()] or [sqlite3_prepare16()], this function\n** must be called one or more times to evaluate the statement.\n**\n** The details of the behavior of the sqlite3_step() interface depend\n** on whether the statement was prepared using the newer \"vX\" interfaces\n** [sqlite3_prepare_v3()], [sqlite3_prepare_v2()], [sqlite3_prepare16_v3()],\n** [sqlite3_prepare16_v2()] or the older legacy\n** interfaces [sqlite3_prepare()] and [sqlite3_prepare16()].  The use of the\n** new \"vX\" interface is recommended for new applications but the legacy\n** interface will continue to be supported.\n**\n** ^In the legacy interface, the return value will be either [SQLITE_BUSY],\n** [SQLITE_DONE], [SQLITE_ROW], [SQLITE_ERROR], or [SQLITE_MISUSE].\n** ^With the \"v2\" interface, any of the other [result codes] or\n** [extended result codes] might be returned as well.\n**\n** ^[SQLITE_BUSY] means that the database engine was unable to acquire the\n** database locks it needs to do its job.  ^If the statement is a [COMMIT]\n** or occurs outside of an explicit transaction, then you can retry the\n** statement.  If the statement is not a [COMMIT] and occurs within an\n** explicit transaction then you should rollback the transaction before\n** continuing.\n**\n** ^[SQLITE_DONE] means that the statement has finished executing\n** successfully.  sqlite3_step() should not be called again on this virtual\n** machine without first calling [sqlite3_reset()] to reset the virtual\n** machine back to its initial state.\n**\n** ^If the SQL statement being executed returns any data, then [SQLITE_ROW]\n** is returned each time a new row of data is ready for processing by the\n** caller. The values may be accessed using the [column access functions].\n** sqlite3_step() is called again to retrieve the next row of data.\n**\n** ^[SQLITE_ERROR] means that a run-time error (such as a constraint\n** violation) has occurred.  sqlite3_step() should not be called again on\n** the VM. More information may be found by calling [sqlite3_errmsg()].\n** ^With the legacy interface, a more specific error code (for example,\n** [SQLITE_INTERRUPT], [SQLITE_SCHEMA], [SQLITE_CORRUPT], and so forth)\n** can be obtained by calling [sqlite3_reset()] on the\n** [prepared statement].  ^In the \"v2\" interface,\n** the more specific error code is returned directly by sqlite3_step().\n**\n** [SQLITE_MISUSE] means that the this routine was called inappropriately.\n** Perhaps it was called on a [prepared statement] that has\n** already been [sqlite3_finalize | finalized] or on one that had\n** previously returned [SQLITE_ERROR] or [SQLITE_DONE].  Or it could\n** be the case that the same database connection is being used by two or\n** more threads at the same moment in time.\n**\n** For all versions of SQLite up to and including 3.6.23.1, a call to\n** [sqlite3_reset()] was required after sqlite3_step() returned anything\n** other than [SQLITE_ROW] before any subsequent invocation of\n** sqlite3_step().  Failure to reset the prepared statement using \n** [sqlite3_reset()] would result in an [SQLITE_MISUSE] return from\n** sqlite3_step().  But after [version 3.6.23.1] ([dateof:3.6.23.1],\n** sqlite3_step() began\n** calling [sqlite3_reset()] automatically in this circumstance rather\n** than returning [SQLITE_MISUSE].  This is not considered a compatibility\n** break because any application that ever receives an SQLITE_MISUSE error\n** is broken by definition.  The [SQLITE_OMIT_AUTORESET] compile-time option\n** can be used to restore the legacy behavior.\n**\n** <b>Goofy Interface Alert:</b> In the legacy interface, the sqlite3_step()\n** API always returns a generic error code, [SQLITE_ERROR], following any\n** error other than [SQLITE_BUSY] and [SQLITE_MISUSE].  You must call\n** [sqlite3_reset()] or [sqlite3_finalize()] in order to find one of the\n** specific [error codes] that better describes the error.\n** We admit that this is a goofy design.  The problem has been fixed\n** with the \"v2\" interface.  If you prepare all of your SQL statements\n** using [sqlite3_prepare_v3()] or [sqlite3_prepare_v2()]\n** or [sqlite3_prepare16_v2()] or [sqlite3_prepare16_v3()] instead\n** of the legacy [sqlite3_prepare()] and [sqlite3_prepare16()] interfaces,\n** then the more specific [error codes] are returned directly\n** by sqlite3_step().  The use of the \"vX\" interfaces is recommended.\n*/\nSQLITE_API int sqlite3_step(sqlite3_stmt*);\n\n/*\n** CAPI3REF: Number of columns in a result set\n** METHOD: sqlite3_stmt\n**\n** ^The sqlite3_data_count(P) interface returns the number of columns in the\n** current row of the result set of [prepared statement] P.\n** ^If prepared statement P does not have results ready to return\n** (via calls to the [sqlite3_column_int | sqlite3_column_*()] of\n** interfaces) then sqlite3_data_count(P) returns 0.\n** ^The sqlite3_data_count(P) routine also returns 0 if P is a NULL pointer.\n** ^The sqlite3_data_count(P) routine returns 0 if the previous call to\n** [sqlite3_step](P) returned [SQLITE_DONE].  ^The sqlite3_data_count(P)\n** will return non-zero if previous call to [sqlite3_step](P) returned\n** [SQLITE_ROW], except in the case of the [PRAGMA incremental_vacuum]\n** where it always returns zero since each step of that multi-step\n** pragma returns 0 columns of data.\n**\n** See also: [sqlite3_column_count()]\n*/\nSQLITE_API int sqlite3_data_count(sqlite3_stmt *pStmt);\n\n/*\n** CAPI3REF: Fundamental Datatypes\n** KEYWORDS: SQLITE_TEXT\n**\n** ^(Every value in SQLite has one of five fundamental datatypes:\n**\n** <ul>\n** <li> 64-bit signed integer\n** <li> 64-bit IEEE floating point number\n** <li> string\n** <li> BLOB\n** <li> NULL\n** </ul>)^\n**\n** These constants are codes for each of those types.\n**\n** Note that the SQLITE_TEXT constant was also used in SQLite version 2\n** for a completely different meaning.  Software that links against both\n** SQLite version 2 and SQLite version 3 should use SQLITE3_TEXT, not\n** SQLITE_TEXT.\n*/\n#define SQLITE_INTEGER  1\n#define SQLITE_FLOAT    2\n#define SQLITE_BLOB     4\n#define SQLITE_NULL     5\n#ifdef SQLITE_TEXT\n# undef SQLITE_TEXT\n#else\n# define SQLITE_TEXT     3\n#endif\n#define SQLITE3_TEXT     3\n\n/*\n** CAPI3REF: Result Values From A Query\n** KEYWORDS: {column access functions}\n** METHOD: sqlite3_stmt\n**\n** <b>Summary:</b>\n** <blockquote><table border=0 cellpadding=0 cellspacing=0>\n** <tr><td><b>sqlite3_column_blob</b><td>&rarr;<td>BLOB result\n** <tr><td><b>sqlite3_column_double</b><td>&rarr;<td>REAL result\n** <tr><td><b>sqlite3_column_int</b><td>&rarr;<td>32-bit INTEGER result\n** <tr><td><b>sqlite3_column_int64</b><td>&rarr;<td>64-bit INTEGER result\n** <tr><td><b>sqlite3_column_text</b><td>&rarr;<td>UTF-8 TEXT result\n** <tr><td><b>sqlite3_column_text16</b><td>&rarr;<td>UTF-16 TEXT result\n** <tr><td><b>sqlite3_column_value</b><td>&rarr;<td>The result as an \n** [sqlite3_value|unprotected sqlite3_value] object.\n** <tr><td>&nbsp;<td>&nbsp;<td>&nbsp;\n** <tr><td><b>sqlite3_column_bytes</b><td>&rarr;<td>Size of a BLOB\n** or a UTF-8 TEXT result in bytes\n** <tr><td><b>sqlite3_column_bytes16&nbsp;&nbsp;</b>\n** <td>&rarr;&nbsp;&nbsp;<td>Size of UTF-16\n** TEXT in bytes\n** <tr><td><b>sqlite3_column_type</b><td>&rarr;<td>Default\n** datatype of the result\n** </table></blockquote>\n**\n** <b>Details:</b>\n**\n** ^These routines return information about a single column of the current\n** result row of a query.  ^In every case the first argument is a pointer\n** to the [prepared statement] that is being evaluated (the [sqlite3_stmt*]\n** that was returned from [sqlite3_prepare_v2()] or one of its variants)\n** and the second argument is the index of the column for which information\n** should be returned. ^The leftmost column of the result set has the index 0.\n** ^The number of columns in the result can be determined using\n** [sqlite3_column_count()].\n**\n** If the SQL statement does not currently point to a valid row, or if the\n** column index is out of range, the result is undefined.\n** These routines may only be called when the most recent call to\n** [sqlite3_step()] has returned [SQLITE_ROW] and neither\n** [sqlite3_reset()] nor [sqlite3_finalize()] have been called subsequently.\n** If any of these routines are called after [sqlite3_reset()] or\n** [sqlite3_finalize()] or after [sqlite3_step()] has returned\n** something other than [SQLITE_ROW], the results are undefined.\n** If [sqlite3_step()] or [sqlite3_reset()] or [sqlite3_finalize()]\n** are called from a different thread while any of these routines\n** are pending, then the results are undefined.\n**\n** The first six interfaces (_blob, _double, _int, _int64, _text, and _text16)\n** each return the value of a result column in a specific data format.  If\n** the result column is not initially in the requested format (for example,\n** if the query returns an integer but the sqlite3_column_text() interface\n** is used to extract the value) then an automatic type conversion is performed.\n**\n** ^The sqlite3_column_type() routine returns the\n** [SQLITE_INTEGER | datatype code] for the initial data type\n** of the result column.  ^The returned value is one of [SQLITE_INTEGER],\n** [SQLITE_FLOAT], [SQLITE_TEXT], [SQLITE_BLOB], or [SQLITE_NULL].\n** The return value of sqlite3_column_type() can be used to decide which\n** of the first six interface should be used to extract the column value.\n** The value returned by sqlite3_column_type() is only meaningful if no\n** automatic type conversions have occurred for the value in question.  \n** After a type conversion, the result of calling sqlite3_column_type()\n** is undefined, though harmless.  Future\n** versions of SQLite may change the behavior of sqlite3_column_type()\n** following a type conversion.\n**\n** If the result is a BLOB or a TEXT string, then the sqlite3_column_bytes()\n** or sqlite3_column_bytes16() interfaces can be used to determine the size\n** of that BLOB or string.\n**\n** ^If the result is a BLOB or UTF-8 string then the sqlite3_column_bytes()\n** routine returns the number of bytes in that BLOB or string.\n** ^If the result is a UTF-16 string, then sqlite3_column_bytes() converts\n** the string to UTF-8 and then returns the number of bytes.\n** ^If the result is a numeric value then sqlite3_column_bytes() uses\n** [sqlite3_snprintf()] to convert that value to a UTF-8 string and returns\n** the number of bytes in that string.\n** ^If the result is NULL, then sqlite3_column_bytes() returns zero.\n**\n** ^If the result is a BLOB or UTF-16 string then the sqlite3_column_bytes16()\n** routine returns the number of bytes in that BLOB or string.\n** ^If the result is a UTF-8 string, then sqlite3_column_bytes16() converts\n** the string to UTF-16 and then returns the number of bytes.\n** ^If the result is a numeric value then sqlite3_column_bytes16() uses\n** [sqlite3_snprintf()] to convert that value to a UTF-16 string and returns\n** the number of bytes in that string.\n** ^If the result is NULL, then sqlite3_column_bytes16() returns zero.\n**\n** ^The values returned by [sqlite3_column_bytes()] and \n** [sqlite3_column_bytes16()] do not include the zero terminators at the end\n** of the string.  ^For clarity: the values returned by\n** [sqlite3_column_bytes()] and [sqlite3_column_bytes16()] are the number of\n** bytes in the string, not the number of characters.\n**\n** ^Strings returned by sqlite3_column_text() and sqlite3_column_text16(),\n** even empty strings, are always zero-terminated.  ^The return\n** value from sqlite3_column_blob() for a zero-length BLOB is a NULL pointer.\n**\n** <b>Warning:</b> ^The object returned by [sqlite3_column_value()] is an\n** [unprotected sqlite3_value] object.  In a multithreaded environment,\n** an unprotected sqlite3_value object may only be used safely with\n** [sqlite3_bind_value()] and [sqlite3_result_value()].\n** If the [unprotected sqlite3_value] object returned by\n** [sqlite3_column_value()] is used in any other way, including calls\n** to routines like [sqlite3_value_int()], [sqlite3_value_text()],\n** or [sqlite3_value_bytes()], the behavior is not threadsafe.\n** Hence, the sqlite3_column_value() interface\n** is normally only useful within the implementation of \n** [application-defined SQL functions] or [virtual tables], not within\n** top-level application code.\n**\n** The these routines may attempt to convert the datatype of the result.\n** ^For example, if the internal representation is FLOAT and a text result\n** is requested, [sqlite3_snprintf()] is used internally to perform the\n** conversion automatically.  ^(The following table details the conversions\n** that are applied:\n**\n** <blockquote>\n** <table border=\"1\">\n** <tr><th> Internal<br>Type <th> Requested<br>Type <th>  Conversion\n**\n** <tr><td>  NULL    <td> INTEGER   <td> Result is 0\n** <tr><td>  NULL    <td>  FLOAT    <td> Result is 0.0\n** <tr><td>  NULL    <td>   TEXT    <td> Result is a NULL pointer\n** <tr><td>  NULL    <td>   BLOB    <td> Result is a NULL pointer\n** <tr><td> INTEGER  <td>  FLOAT    <td> Convert from integer to float\n** <tr><td> INTEGER  <td>   TEXT    <td> ASCII rendering of the integer\n** <tr><td> INTEGER  <td>   BLOB    <td> Same as INTEGER->TEXT\n** <tr><td>  FLOAT   <td> INTEGER   <td> [CAST] to INTEGER\n** <tr><td>  FLOAT   <td>   TEXT    <td> ASCII rendering of the float\n** <tr><td>  FLOAT   <td>   BLOB    <td> [CAST] to BLOB\n** <tr><td>  TEXT    <td> INTEGER   <td> [CAST] to INTEGER\n** <tr><td>  TEXT    <td>  FLOAT    <td> [CAST] to REAL\n** <tr><td>  TEXT    <td>   BLOB    <td> No change\n** <tr><td>  BLOB    <td> INTEGER   <td> [CAST] to INTEGER\n** <tr><td>  BLOB    <td>  FLOAT    <td> [CAST] to REAL\n** <tr><td>  BLOB    <td>   TEXT    <td> Add a zero terminator if needed\n** </table>\n** </blockquote>)^\n**\n** Note that when type conversions occur, pointers returned by prior\n** calls to sqlite3_column_blob(), sqlite3_column_text(), and/or\n** sqlite3_column_text16() may be invalidated.\n** Type conversions and pointer invalidations might occur\n** in the following cases:\n**\n** <ul>\n** <li> The initial content is a BLOB and sqlite3_column_text() or\n**      sqlite3_column_text16() is called.  A zero-terminator might\n**      need to be added to the string.</li>\n** <li> The initial content is UTF-8 text and sqlite3_column_bytes16() or\n**      sqlite3_column_text16() is called.  The content must be converted\n**      to UTF-16.</li>\n** <li> The initial content is UTF-16 text and sqlite3_column_bytes() or\n**      sqlite3_column_text() is called.  The content must be converted\n**      to UTF-8.</li>\n** </ul>\n**\n** ^Conversions between UTF-16be and UTF-16le are always done in place and do\n** not invalidate a prior pointer, though of course the content of the buffer\n** that the prior pointer references will have been modified.  Other kinds\n** of conversion are done in place when it is possible, but sometimes they\n** are not possible and in those cases prior pointers are invalidated.\n**\n** The safest policy is to invoke these routines\n** in one of the following ways:\n**\n** <ul>\n**  <li>sqlite3_column_text() followed by sqlite3_column_bytes()</li>\n**  <li>sqlite3_column_blob() followed by sqlite3_column_bytes()</li>\n**  <li>sqlite3_column_text16() followed by sqlite3_column_bytes16()</li>\n** </ul>\n**\n** In other words, you should call sqlite3_column_text(),\n** sqlite3_column_blob(), or sqlite3_column_text16() first to force the result\n** into the desired format, then invoke sqlite3_column_bytes() or\n** sqlite3_column_bytes16() to find the size of the result.  Do not mix calls\n** to sqlite3_column_text() or sqlite3_column_blob() with calls to\n** sqlite3_column_bytes16(), and do not mix calls to sqlite3_column_text16()\n** with calls to sqlite3_column_bytes().\n**\n** ^The pointers returned are valid until a type conversion occurs as\n** described above, or until [sqlite3_step()] or [sqlite3_reset()] or\n** [sqlite3_finalize()] is called.  ^The memory space used to hold strings\n** and BLOBs is freed automatically.  Do not pass the pointers returned\n** from [sqlite3_column_blob()], [sqlite3_column_text()], etc. into\n** [sqlite3_free()].\n**\n** ^(If a memory allocation error occurs during the evaluation of any\n** of these routines, a default value is returned.  The default value\n** is either the integer 0, the floating point number 0.0, or a NULL\n** pointer.  Subsequent calls to [sqlite3_errcode()] will return\n** [SQLITE_NOMEM].)^\n*/\nSQLITE_API const void *sqlite3_column_blob(sqlite3_stmt*, int iCol);\nSQLITE_API double sqlite3_column_double(sqlite3_stmt*, int iCol);\nSQLITE_API int sqlite3_column_int(sqlite3_stmt*, int iCol);\nSQLITE_API sqlite3_int64 sqlite3_column_int64(sqlite3_stmt*, int iCol);\nSQLITE_API const unsigned char *sqlite3_column_text(sqlite3_stmt*, int iCol);\nSQLITE_API const void *sqlite3_column_text16(sqlite3_stmt*, int iCol);\nSQLITE_API sqlite3_value *sqlite3_column_value(sqlite3_stmt*, int iCol);\nSQLITE_API int sqlite3_column_bytes(sqlite3_stmt*, int iCol);\nSQLITE_API int sqlite3_column_bytes16(sqlite3_stmt*, int iCol);\nSQLITE_API int sqlite3_column_type(sqlite3_stmt*, int iCol);\n\n/*\n** CAPI3REF: Destroy A Prepared Statement Object\n** DESTRUCTOR: sqlite3_stmt\n**\n** ^The sqlite3_finalize() function is called to delete a [prepared statement].\n** ^If the most recent evaluation of the statement encountered no errors\n** or if the statement is never been evaluated, then sqlite3_finalize() returns\n** SQLITE_OK.  ^If the most recent evaluation of statement S failed, then\n** sqlite3_finalize(S) returns the appropriate [error code] or\n** [extended error code].\n**\n** ^The sqlite3_finalize(S) routine can be called at any point during\n** the life cycle of [prepared statement] S:\n** before statement S is ever evaluated, after\n** one or more calls to [sqlite3_reset()], or after any call\n** to [sqlite3_step()] regardless of whether or not the statement has\n** completed execution.\n**\n** ^Invoking sqlite3_finalize() on a NULL pointer is a harmless no-op.\n**\n** The application must finalize every [prepared statement] in order to avoid\n** resource leaks.  It is a grievous error for the application to try to use\n** a prepared statement after it has been finalized.  Any use of a prepared\n** statement after it has been finalized can result in undefined and\n** undesirable behavior such as segfaults and heap corruption.\n*/\nSQLITE_API int sqlite3_finalize(sqlite3_stmt *pStmt);\n\n/*\n** CAPI3REF: Reset A Prepared Statement Object\n** METHOD: sqlite3_stmt\n**\n** The sqlite3_reset() function is called to reset a [prepared statement]\n** object back to its initial state, ready to be re-executed.\n** ^Any SQL statement variables that had values bound to them using\n** the [sqlite3_bind_blob | sqlite3_bind_*() API] retain their values.\n** Use [sqlite3_clear_bindings()] to reset the bindings.\n**\n** ^The [sqlite3_reset(S)] interface resets the [prepared statement] S\n** back to the beginning of its program.\n**\n** ^If the most recent call to [sqlite3_step(S)] for the\n** [prepared statement] S returned [SQLITE_ROW] or [SQLITE_DONE],\n** or if [sqlite3_step(S)] has never before been called on S,\n** then [sqlite3_reset(S)] returns [SQLITE_OK].\n**\n** ^If the most recent call to [sqlite3_step(S)] for the\n** [prepared statement] S indicated an error, then\n** [sqlite3_reset(S)] returns an appropriate [error code].\n**\n** ^The [sqlite3_reset(S)] interface does not change the values\n** of any [sqlite3_bind_blob|bindings] on the [prepared statement] S.\n*/\nSQLITE_API int sqlite3_reset(sqlite3_stmt *pStmt);\n\n/*\n** CAPI3REF: Create Or Redefine SQL Functions\n** KEYWORDS: {function creation routines}\n** KEYWORDS: {application-defined SQL function}\n** KEYWORDS: {application-defined SQL functions}\n** METHOD: sqlite3\n**\n** ^These functions (collectively known as \"function creation routines\")\n** are used to add SQL functions or aggregates or to redefine the behavior\n** of existing SQL functions or aggregates.  The only differences between\n** these routines are the text encoding expected for\n** the second parameter (the name of the function being created)\n** and the presence or absence of a destructor callback for\n** the application data pointer.\n**\n** ^The first parameter is the [database connection] to which the SQL\n** function is to be added.  ^If an application uses more than one database\n** connection then application-defined SQL functions must be added\n** to each database connection separately.\n**\n** ^The second parameter is the name of the SQL function to be created or\n** redefined.  ^The length of the name is limited to 255 bytes in a UTF-8\n** representation, exclusive of the zero-terminator.  ^Note that the name\n** length limit is in UTF-8 bytes, not characters nor UTF-16 bytes.  \n** ^Any attempt to create a function with a longer name\n** will result in [SQLITE_MISUSE] being returned.\n**\n** ^The third parameter (nArg)\n** is the number of arguments that the SQL function or\n** aggregate takes. ^If this parameter is -1, then the SQL function or\n** aggregate may take any number of arguments between 0 and the limit\n** set by [sqlite3_limit]([SQLITE_LIMIT_FUNCTION_ARG]).  If the third\n** parameter is less than -1 or greater than 127 then the behavior is\n** undefined.\n**\n** ^The fourth parameter, eTextRep, specifies what\n** [SQLITE_UTF8 | text encoding] this SQL function prefers for\n** its parameters.  The application should set this parameter to\n** [SQLITE_UTF16LE] if the function implementation invokes \n** [sqlite3_value_text16le()] on an input, or [SQLITE_UTF16BE] if the\n** implementation invokes [sqlite3_value_text16be()] on an input, or\n** [SQLITE_UTF16] if [sqlite3_value_text16()] is used, or [SQLITE_UTF8]\n** otherwise.  ^The same SQL function may be registered multiple times using\n** different preferred text encodings, with different implementations for\n** each encoding.\n** ^When multiple implementations of the same function are available, SQLite\n** will pick the one that involves the least amount of data conversion.\n**\n** ^The fourth parameter may optionally be ORed with [SQLITE_DETERMINISTIC]\n** to signal that the function will always return the same result given\n** the same inputs within a single SQL statement.  Most SQL functions are\n** deterministic.  The built-in [random()] SQL function is an example of a\n** function that is not deterministic.  The SQLite query planner is able to\n** perform additional optimizations on deterministic functions, so use\n** of the [SQLITE_DETERMINISTIC] flag is recommended where possible.\n**\n** ^(The fifth parameter is an arbitrary pointer.  The implementation of the\n** function can gain access to this pointer using [sqlite3_user_data()].)^\n**\n** ^The sixth, seventh and eighth parameters, xFunc, xStep and xFinal, are\n** pointers to C-language functions that implement the SQL function or\n** aggregate. ^A scalar SQL function requires an implementation of the xFunc\n** callback only; NULL pointers must be passed as the xStep and xFinal\n** parameters. ^An aggregate SQL function requires an implementation of xStep\n** and xFinal and NULL pointer must be passed for xFunc. ^To delete an existing\n** SQL function or aggregate, pass NULL pointers for all three function\n** callbacks.\n**\n** ^(If the ninth parameter to sqlite3_create_function_v2() is not NULL,\n** then it is destructor for the application data pointer. \n** The destructor is invoked when the function is deleted, either by being\n** overloaded or when the database connection closes.)^\n** ^The destructor is also invoked if the call to\n** sqlite3_create_function_v2() fails.\n** ^When the destructor callback of the tenth parameter is invoked, it\n** is passed a single argument which is a copy of the application data \n** pointer which was the fifth parameter to sqlite3_create_function_v2().\n**\n** ^It is permitted to register multiple implementations of the same\n** functions with the same name but with either differing numbers of\n** arguments or differing preferred text encodings.  ^SQLite will use\n** the implementation that most closely matches the way in which the\n** SQL function is used.  ^A function implementation with a non-negative\n** nArg parameter is a better match than a function implementation with\n** a negative nArg.  ^A function where the preferred text encoding\n** matches the database encoding is a better\n** match than a function where the encoding is different.  \n** ^A function where the encoding difference is between UTF16le and UTF16be\n** is a closer match than a function where the encoding difference is\n** between UTF8 and UTF16.\n**\n** ^Built-in functions may be overloaded by new application-defined functions.\n**\n** ^An application-defined function is permitted to call other\n** SQLite interfaces.  However, such calls must not\n** close the database connection nor finalize or reset the prepared\n** statement in which the function is running.\n*/\nSQLITE_API int sqlite3_create_function(\n  sqlite3 *db,\n  const char *zFunctionName,\n  int nArg,\n  int eTextRep,\n  void *pApp,\n  void (*xFunc)(sqlite3_context*,int,sqlite3_value**),\n  void (*xStep)(sqlite3_context*,int,sqlite3_value**),\n  void (*xFinal)(sqlite3_context*)\n);\nSQLITE_API int sqlite3_create_function16(\n  sqlite3 *db,\n  const void *zFunctionName,\n  int nArg,\n  int eTextRep,\n  void *pApp,\n  void (*xFunc)(sqlite3_context*,int,sqlite3_value**),\n  void (*xStep)(sqlite3_context*,int,sqlite3_value**),\n  void (*xFinal)(sqlite3_context*)\n);\nSQLITE_API int sqlite3_create_function_v2(\n  sqlite3 *db,\n  const char *zFunctionName,\n  int nArg,\n  int eTextRep,\n  void *pApp,\n  void (*xFunc)(sqlite3_context*,int,sqlite3_value**),\n  void (*xStep)(sqlite3_context*,int,sqlite3_value**),\n  void (*xFinal)(sqlite3_context*),\n  void(*xDestroy)(void*)\n);\n\n/*\n** CAPI3REF: Text Encodings\n**\n** These constant define integer codes that represent the various\n** text encodings supported by SQLite.\n*/\n#define SQLITE_UTF8           1    /* IMP: R-37514-35566 */\n#define SQLITE_UTF16LE        2    /* IMP: R-03371-37637 */\n#define SQLITE_UTF16BE        3    /* IMP: R-51971-34154 */\n#define SQLITE_UTF16          4    /* Use native byte order */\n#define SQLITE_ANY            5    /* Deprecated */\n#define SQLITE_UTF16_ALIGNED  8    /* sqlite3_create_collation only */\n\n/*\n** CAPI3REF: Function Flags\n**\n** These constants may be ORed together with the \n** [SQLITE_UTF8 | preferred text encoding] as the fourth argument\n** to [sqlite3_create_function()], [sqlite3_create_function16()], or\n** [sqlite3_create_function_v2()].\n*/\n#define SQLITE_DETERMINISTIC    0x800\n\n/*\n** CAPI3REF: Deprecated Functions\n** DEPRECATED\n**\n** These functions are [deprecated].  In order to maintain\n** backwards compatibility with older code, these functions continue \n** to be supported.  However, new applications should avoid\n** the use of these functions.  To encourage programmers to avoid\n** these functions, we will not explain what they do.\n*/\n#ifndef SQLITE_OMIT_DEPRECATED\nSQLITE_API SQLITE_DEPRECATED int sqlite3_aggregate_count(sqlite3_context*);\nSQLITE_API SQLITE_DEPRECATED int sqlite3_expired(sqlite3_stmt*);\nSQLITE_API SQLITE_DEPRECATED int sqlite3_transfer_bindings(sqlite3_stmt*, sqlite3_stmt*);\nSQLITE_API SQLITE_DEPRECATED int sqlite3_global_recover(void);\nSQLITE_API SQLITE_DEPRECATED void sqlite3_thread_cleanup(void);\nSQLITE_API SQLITE_DEPRECATED int sqlite3_memory_alarm(void(*)(void*,sqlite3_int64,int),\n                      void*,sqlite3_int64);\n#endif\n\n/*\n** CAPI3REF: Obtaining SQL Values\n** METHOD: sqlite3_value\n**\n** <b>Summary:</b>\n** <blockquote><table border=0 cellpadding=0 cellspacing=0>\n** <tr><td><b>sqlite3_value_blob</b><td>&rarr;<td>BLOB value\n** <tr><td><b>sqlite3_value_double</b><td>&rarr;<td>REAL value\n** <tr><td><b>sqlite3_value_int</b><td>&rarr;<td>32-bit INTEGER value\n** <tr><td><b>sqlite3_value_int64</b><td>&rarr;<td>64-bit INTEGER value\n** <tr><td><b>sqlite3_value_pointer</b><td>&rarr;<td>Pointer value\n** <tr><td><b>sqlite3_value_text</b><td>&rarr;<td>UTF-8 TEXT value\n** <tr><td><b>sqlite3_value_text16</b><td>&rarr;<td>UTF-16 TEXT value in\n** the native byteorder\n** <tr><td><b>sqlite3_value_text16be</b><td>&rarr;<td>UTF-16be TEXT value\n** <tr><td><b>sqlite3_value_text16le</b><td>&rarr;<td>UTF-16le TEXT value\n** <tr><td>&nbsp;<td>&nbsp;<td>&nbsp;\n** <tr><td><b>sqlite3_value_bytes</b><td>&rarr;<td>Size of a BLOB\n** or a UTF-8 TEXT in bytes\n** <tr><td><b>sqlite3_value_bytes16&nbsp;&nbsp;</b>\n** <td>&rarr;&nbsp;&nbsp;<td>Size of UTF-16\n** TEXT in bytes\n** <tr><td><b>sqlite3_value_type</b><td>&rarr;<td>Default\n** datatype of the value\n** <tr><td><b>sqlite3_value_numeric_type&nbsp;&nbsp;</b>\n** <td>&rarr;&nbsp;&nbsp;<td>Best numeric datatype of the value\n** <tr><td><b>sqlite3_value_nochange&nbsp;&nbsp;</b>\n** <td>&rarr;&nbsp;&nbsp;<td>True if the column is unchanged in an UPDATE\n** against a virtual table.\n** </table></blockquote>\n**\n** <b>Details:</b>\n**\n** These routines extract type, size, and content information from\n** [protected sqlite3_value] objects.  Protected sqlite3_value objects\n** are used to pass parameter information into implementation of\n** [application-defined SQL functions] and [virtual tables].\n**\n** These routines work only with [protected sqlite3_value] objects.\n** Any attempt to use these routines on an [unprotected sqlite3_value]\n** is not threadsafe.\n**\n** ^These routines work just like the corresponding [column access functions]\n** except that these routines take a single [protected sqlite3_value] object\n** pointer instead of a [sqlite3_stmt*] pointer and an integer column number.\n**\n** ^The sqlite3_value_text16() interface extracts a UTF-16 string\n** in the native byte-order of the host machine.  ^The\n** sqlite3_value_text16be() and sqlite3_value_text16le() interfaces\n** extract UTF-16 strings as big-endian and little-endian respectively.\n**\n** ^If [sqlite3_value] object V was initialized \n** using [sqlite3_bind_pointer(S,I,P,X,D)] or [sqlite3_result_pointer(C,P,X,D)]\n** and if X and Y are strings that compare equal according to strcmp(X,Y),\n** then sqlite3_value_pointer(V,Y) will return the pointer P.  ^Otherwise,\n** sqlite3_value_pointer(V,Y) returns a NULL. The sqlite3_bind_pointer() \n** routine is part of the [pointer passing interface] added for SQLite 3.20.0.\n**\n** ^(The sqlite3_value_type(V) interface returns the\n** [SQLITE_INTEGER | datatype code] for the initial datatype of the\n** [sqlite3_value] object V. The returned value is one of [SQLITE_INTEGER],\n** [SQLITE_FLOAT], [SQLITE_TEXT], [SQLITE_BLOB], or [SQLITE_NULL].)^\n** Other interfaces might change the datatype for an sqlite3_value object.\n** For example, if the datatype is initially SQLITE_INTEGER and\n** sqlite3_value_text(V) is called to extract a text value for that\n** integer, then subsequent calls to sqlite3_value_type(V) might return\n** SQLITE_TEXT.  Whether or not a persistent internal datatype conversion\n** occurs is undefined and may change from one release of SQLite to the next.\n**\n** ^(The sqlite3_value_numeric_type() interface attempts to apply\n** numeric affinity to the value.  This means that an attempt is\n** made to convert the value to an integer or floating point.  If\n** such a conversion is possible without loss of information (in other\n** words, if the value is a string that looks like a number)\n** then the conversion is performed.  Otherwise no conversion occurs.\n** The [SQLITE_INTEGER | datatype] after conversion is returned.)^\n**\n** ^Within the [xUpdate] method of a [virtual table], the\n** sqlite3_value_nochange(X) interface returns true if and only if\n** the column corresponding to X is unchanged by the UPDATE operation\n** that the xUpdate method call was invoked to implement and if\n** and the prior [xColumn] method call that was invoked to extracted\n** the value for that column returned without setting a result (probably\n** because it queried [sqlite3_vtab_nochange()] and found that the column\n** was unchanging).  ^Within an [xUpdate] method, any value for which\n** sqlite3_value_nochange(X) is true will in all other respects appear\n** to be a NULL value.  If sqlite3_value_nochange(X) is invoked anywhere other\n** than within an [xUpdate] method call for an UPDATE statement, then\n** the return value is arbitrary and meaningless.\n**\n** Please pay particular attention to the fact that the pointer returned\n** from [sqlite3_value_blob()], [sqlite3_value_text()], or\n** [sqlite3_value_text16()] can be invalidated by a subsequent call to\n** [sqlite3_value_bytes()], [sqlite3_value_bytes16()], [sqlite3_value_text()],\n** or [sqlite3_value_text16()].\n**\n** These routines must be called from the same thread as\n** the SQL function that supplied the [sqlite3_value*] parameters.\n*/\nSQLITE_API const void *sqlite3_value_blob(sqlite3_value*);\nSQLITE_API double sqlite3_value_double(sqlite3_value*);\nSQLITE_API int sqlite3_value_int(sqlite3_value*);\nSQLITE_API sqlite3_int64 sqlite3_value_int64(sqlite3_value*);\nSQLITE_API void *sqlite3_value_pointer(sqlite3_value*, const char*);\nSQLITE_API const unsigned char *sqlite3_value_text(sqlite3_value*);\nSQLITE_API const void *sqlite3_value_text16(sqlite3_value*);\nSQLITE_API const void *sqlite3_value_text16le(sqlite3_value*);\nSQLITE_API const void *sqlite3_value_text16be(sqlite3_value*);\nSQLITE_API int sqlite3_value_bytes(sqlite3_value*);\nSQLITE_API int sqlite3_value_bytes16(sqlite3_value*);\nSQLITE_API int sqlite3_value_type(sqlite3_value*);\nSQLITE_API int sqlite3_value_numeric_type(sqlite3_value*);\nSQLITE_API int sqlite3_value_nochange(sqlite3_value*);\n\n/*\n** CAPI3REF: Finding The Subtype Of SQL Values\n** METHOD: sqlite3_value\n**\n** The sqlite3_value_subtype(V) function returns the subtype for\n** an [application-defined SQL function] argument V.  The subtype\n** information can be used to pass a limited amount of context from\n** one SQL function to another.  Use the [sqlite3_result_subtype()]\n** routine to set the subtype for the return value of an SQL function.\n*/\nSQLITE_API unsigned int sqlite3_value_subtype(sqlite3_value*);\n\n/*\n** CAPI3REF: Copy And Free SQL Values\n** METHOD: sqlite3_value\n**\n** ^The sqlite3_value_dup(V) interface makes a copy of the [sqlite3_value]\n** object D and returns a pointer to that copy.  ^The [sqlite3_value] returned\n** is a [protected sqlite3_value] object even if the input is not.\n** ^The sqlite3_value_dup(V) interface returns NULL if V is NULL or if a\n** memory allocation fails.\n**\n** ^The sqlite3_value_free(V) interface frees an [sqlite3_value] object\n** previously obtained from [sqlite3_value_dup()].  ^If V is a NULL pointer\n** then sqlite3_value_free(V) is a harmless no-op.\n*/\nSQLITE_API sqlite3_value *sqlite3_value_dup(const sqlite3_value*);\nSQLITE_API void sqlite3_value_free(sqlite3_value*);\n\n/*\n** CAPI3REF: Obtain Aggregate Function Context\n** METHOD: sqlite3_context\n**\n** Implementations of aggregate SQL functions use this\n** routine to allocate memory for storing their state.\n**\n** ^The first time the sqlite3_aggregate_context(C,N) routine is called \n** for a particular aggregate function, SQLite\n** allocates N of memory, zeroes out that memory, and returns a pointer\n** to the new memory. ^On second and subsequent calls to\n** sqlite3_aggregate_context() for the same aggregate function instance,\n** the same buffer is returned.  Sqlite3_aggregate_context() is normally\n** called once for each invocation of the xStep callback and then one\n** last time when the xFinal callback is invoked.  ^(When no rows match\n** an aggregate query, the xStep() callback of the aggregate function\n** implementation is never called and xFinal() is called exactly once.\n** In those cases, sqlite3_aggregate_context() might be called for the\n** first time from within xFinal().)^\n**\n** ^The sqlite3_aggregate_context(C,N) routine returns a NULL pointer \n** when first called if N is less than or equal to zero or if a memory\n** allocate error occurs.\n**\n** ^(The amount of space allocated by sqlite3_aggregate_context(C,N) is\n** determined by the N parameter on first successful call.  Changing the\n** value of N in subsequent call to sqlite3_aggregate_context() within\n** the same aggregate function instance will not resize the memory\n** allocation.)^  Within the xFinal callback, it is customary to set\n** N=0 in calls to sqlite3_aggregate_context(C,N) so that no \n** pointless memory allocations occur.\n**\n** ^SQLite automatically frees the memory allocated by \n** sqlite3_aggregate_context() when the aggregate query concludes.\n**\n** The first parameter must be a copy of the\n** [sqlite3_context | SQL function context] that is the first parameter\n** to the xStep or xFinal callback routine that implements the aggregate\n** function.\n**\n** This routine must be called from the same thread in which\n** the aggregate SQL function is running.\n*/\nSQLITE_API void *sqlite3_aggregate_context(sqlite3_context*, int nBytes);\n\n/*\n** CAPI3REF: User Data For Functions\n** METHOD: sqlite3_context\n**\n** ^The sqlite3_user_data() interface returns a copy of\n** the pointer that was the pUserData parameter (the 5th parameter)\n** of the [sqlite3_create_function()]\n** and [sqlite3_create_function16()] routines that originally\n** registered the application defined function.\n**\n** This routine must be called from the same thread in which\n** the application-defined function is running.\n*/\nSQLITE_API void *sqlite3_user_data(sqlite3_context*);\n\n/*\n** CAPI3REF: Database Connection For Functions\n** METHOD: sqlite3_context\n**\n** ^The sqlite3_context_db_handle() interface returns a copy of\n** the pointer to the [database connection] (the 1st parameter)\n** of the [sqlite3_create_function()]\n** and [sqlite3_create_function16()] routines that originally\n** registered the application defined function.\n*/\nSQLITE_API sqlite3 *sqlite3_context_db_handle(sqlite3_context*);\n\n/*\n** CAPI3REF: Function Auxiliary Data\n** METHOD: sqlite3_context\n**\n** These functions may be used by (non-aggregate) SQL functions to\n** associate metadata with argument values. If the same value is passed to\n** multiple invocations of the same SQL function during query execution, under\n** some circumstances the associated metadata may be preserved.  An example\n** of where this might be useful is in a regular-expression matching\n** function. The compiled version of the regular expression can be stored as\n** metadata associated with the pattern string.  \n** Then as long as the pattern string remains the same,\n** the compiled regular expression can be reused on multiple\n** invocations of the same function.\n**\n** ^The sqlite3_get_auxdata(C,N) interface returns a pointer to the metadata\n** associated by the sqlite3_set_auxdata(C,N,P,X) function with the Nth argument\n** value to the application-defined function.  ^N is zero for the left-most\n** function argument.  ^If there is no metadata\n** associated with the function argument, the sqlite3_get_auxdata(C,N) interface\n** returns a NULL pointer.\n**\n** ^The sqlite3_set_auxdata(C,N,P,X) interface saves P as metadata for the N-th\n** argument of the application-defined function.  ^Subsequent\n** calls to sqlite3_get_auxdata(C,N) return P from the most recent\n** sqlite3_set_auxdata(C,N,P,X) call if the metadata is still valid or\n** NULL if the metadata has been discarded.\n** ^After each call to sqlite3_set_auxdata(C,N,P,X) where X is not NULL,\n** SQLite will invoke the destructor function X with parameter P exactly\n** once, when the metadata is discarded.\n** SQLite is free to discard the metadata at any time, including: <ul>\n** <li> ^(when the corresponding function parameter changes)^, or\n** <li> ^(when [sqlite3_reset()] or [sqlite3_finalize()] is called for the\n**      SQL statement)^, or\n** <li> ^(when sqlite3_set_auxdata() is invoked again on the same\n**       parameter)^, or\n** <li> ^(during the original sqlite3_set_auxdata() call when a memory \n**      allocation error occurs.)^ </ul>\n**\n** Note the last bullet in particular.  The destructor X in \n** sqlite3_set_auxdata(C,N,P,X) might be called immediately, before the\n** sqlite3_set_auxdata() interface even returns.  Hence sqlite3_set_auxdata()\n** should be called near the end of the function implementation and the\n** function implementation should not make any use of P after\n** sqlite3_set_auxdata() has been called.\n**\n** ^(In practice, metadata is preserved between function calls for\n** function parameters that are compile-time constants, including literal\n** values and [parameters] and expressions composed from the same.)^\n**\n** The value of the N parameter to these interfaces should be non-negative.\n** Future enhancements may make use of negative N values to define new\n** kinds of function caching behavior.\n**\n** These routines must be called from the same thread in which\n** the SQL function is running.\n*/\nSQLITE_API void *sqlite3_get_auxdata(sqlite3_context*, int N);\nSQLITE_API void sqlite3_set_auxdata(sqlite3_context*, int N, void*, void (*)(void*));\n\n\n/*\n** CAPI3REF: Constants Defining Special Destructor Behavior\n**\n** These are special values for the destructor that is passed in as the\n** final argument to routines like [sqlite3_result_blob()].  ^If the destructor\n** argument is SQLITE_STATIC, it means that the content pointer is constant\n** and will never change.  It does not need to be destroyed.  ^The\n** SQLITE_TRANSIENT value means that the content will likely change in\n** the near future and that SQLite should make its own private copy of\n** the content before returning.\n**\n** The typedef is necessary to work around problems in certain\n** C++ compilers.\n*/\ntypedef void (*sqlite3_destructor_type)(void*);\n#define SQLITE_STATIC      ((sqlite3_destructor_type)0)\n#define SQLITE_TRANSIENT   ((sqlite3_destructor_type)-1)\n\n/*\n** CAPI3REF: Setting The Result Of An SQL Function\n** METHOD: sqlite3_context\n**\n** These routines are used by the xFunc or xFinal callbacks that\n** implement SQL functions and aggregates.  See\n** [sqlite3_create_function()] and [sqlite3_create_function16()]\n** for additional information.\n**\n** These functions work very much like the [parameter binding] family of\n** functions used to bind values to host parameters in prepared statements.\n** Refer to the [SQL parameter] documentation for additional information.\n**\n** ^The sqlite3_result_blob() interface sets the result from\n** an application-defined function to be the BLOB whose content is pointed\n** to by the second parameter and which is N bytes long where N is the\n** third parameter.\n**\n** ^The sqlite3_result_zeroblob(C,N) and sqlite3_result_zeroblob64(C,N)\n** interfaces set the result of the application-defined function to be\n** a BLOB containing all zero bytes and N bytes in size.\n**\n** ^The sqlite3_result_double() interface sets the result from\n** an application-defined function to be a floating point value specified\n** by its 2nd argument.\n**\n** ^The sqlite3_result_error() and sqlite3_result_error16() functions\n** cause the implemented SQL function to throw an exception.\n** ^SQLite uses the string pointed to by the\n** 2nd parameter of sqlite3_result_error() or sqlite3_result_error16()\n** as the text of an error message.  ^SQLite interprets the error\n** message string from sqlite3_result_error() as UTF-8. ^SQLite\n** interprets the string from sqlite3_result_error16() as UTF-16 in native\n** byte order.  ^If the third parameter to sqlite3_result_error()\n** or sqlite3_result_error16() is negative then SQLite takes as the error\n** message all text up through the first zero character.\n** ^If the third parameter to sqlite3_result_error() or\n** sqlite3_result_error16() is non-negative then SQLite takes that many\n** bytes (not characters) from the 2nd parameter as the error message.\n** ^The sqlite3_result_error() and sqlite3_result_error16()\n** routines make a private copy of the error message text before\n** they return.  Hence, the calling function can deallocate or\n** modify the text after they return without harm.\n** ^The sqlite3_result_error_code() function changes the error code\n** returned by SQLite as a result of an error in a function.  ^By default,\n** the error code is SQLITE_ERROR.  ^A subsequent call to sqlite3_result_error()\n** or sqlite3_result_error16() resets the error code to SQLITE_ERROR.\n**\n** ^The sqlite3_result_error_toobig() interface causes SQLite to throw an\n** error indicating that a string or BLOB is too long to represent.\n**\n** ^The sqlite3_result_error_nomem() interface causes SQLite to throw an\n** error indicating that a memory allocation failed.\n**\n** ^The sqlite3_result_int() interface sets the return value\n** of the application-defined function to be the 32-bit signed integer\n** value given in the 2nd argument.\n** ^The sqlite3_result_int64() interface sets the return value\n** of the application-defined function to be the 64-bit signed integer\n** value given in the 2nd argument.\n**\n** ^The sqlite3_result_null() interface sets the return value\n** of the application-defined function to be NULL.\n**\n** ^The sqlite3_result_text(), sqlite3_result_text16(),\n** sqlite3_result_text16le(), and sqlite3_result_text16be() interfaces\n** set the return value of the application-defined function to be\n** a text string which is represented as UTF-8, UTF-16 native byte order,\n** UTF-16 little endian, or UTF-16 big endian, respectively.\n** ^The sqlite3_result_text64() interface sets the return value of an\n** application-defined function to be a text string in an encoding\n** specified by the fifth (and last) parameter, which must be one\n** of [SQLITE_UTF8], [SQLITE_UTF16], [SQLITE_UTF16BE], or [SQLITE_UTF16LE].\n** ^SQLite takes the text result from the application from\n** the 2nd parameter of the sqlite3_result_text* interfaces.\n** ^If the 3rd parameter to the sqlite3_result_text* interfaces\n** is negative, then SQLite takes result text from the 2nd parameter\n** through the first zero character.\n** ^If the 3rd parameter to the sqlite3_result_text* interfaces\n** is non-negative, then as many bytes (not characters) of the text\n** pointed to by the 2nd parameter are taken as the application-defined\n** function result.  If the 3rd parameter is non-negative, then it\n** must be the byte offset into the string where the NUL terminator would\n** appear if the string where NUL terminated.  If any NUL characters occur\n** in the string at a byte offset that is less than the value of the 3rd\n** parameter, then the resulting string will contain embedded NULs and the\n** result of expressions operating on strings with embedded NULs is undefined.\n** ^If the 4th parameter to the sqlite3_result_text* interfaces\n** or sqlite3_result_blob is a non-NULL pointer, then SQLite calls that\n** function as the destructor on the text or BLOB result when it has\n** finished using that result.\n** ^If the 4th parameter to the sqlite3_result_text* interfaces or to\n** sqlite3_result_blob is the special constant SQLITE_STATIC, then SQLite\n** assumes that the text or BLOB result is in constant space and does not\n** copy the content of the parameter nor call a destructor on the content\n** when it has finished using that result.\n** ^If the 4th parameter to the sqlite3_result_text* interfaces\n** or sqlite3_result_blob is the special constant SQLITE_TRANSIENT\n** then SQLite makes a copy of the result into space obtained\n** from [sqlite3_malloc()] before it returns.\n**\n** ^The sqlite3_result_value() interface sets the result of\n** the application-defined function to be a copy of the\n** [unprotected sqlite3_value] object specified by the 2nd parameter.  ^The\n** sqlite3_result_value() interface makes a copy of the [sqlite3_value]\n** so that the [sqlite3_value] specified in the parameter may change or\n** be deallocated after sqlite3_result_value() returns without harm.\n** ^A [protected sqlite3_value] object may always be used where an\n** [unprotected sqlite3_value] object is required, so either\n** kind of [sqlite3_value] object can be used with this interface.\n**\n** ^The sqlite3_result_pointer(C,P,T,D) interface sets the result to an\n** SQL NULL value, just like [sqlite3_result_null(C)], except that it\n** also associates the host-language pointer P or type T with that \n** NULL value such that the pointer can be retrieved within an\n** [application-defined SQL function] using [sqlite3_value_pointer()].\n** ^If the D parameter is not NULL, then it is a pointer to a destructor\n** for the P parameter.  ^SQLite invokes D with P as its only argument\n** when SQLite is finished with P.  The T parameter should be a static\n** string and preferably a string literal. The sqlite3_result_pointer()\n** routine is part of the [pointer passing interface] added for SQLite 3.20.0.\n**\n** If these routines are called from within the different thread\n** than the one containing the application-defined function that received\n** the [sqlite3_context] pointer, the results are undefined.\n*/\nSQLITE_API void sqlite3_result_blob(sqlite3_context*, const void*, int, void(*)(void*));\nSQLITE_API void sqlite3_result_blob64(sqlite3_context*,const void*,\n                           sqlite3_uint64,void(*)(void*));\nSQLITE_API void sqlite3_result_double(sqlite3_context*, double);\nSQLITE_API void sqlite3_result_error(sqlite3_context*, const char*, int);\nSQLITE_API void sqlite3_result_error16(sqlite3_context*, const void*, int);\nSQLITE_API void sqlite3_result_error_toobig(sqlite3_context*);\nSQLITE_API void sqlite3_result_error_nomem(sqlite3_context*);\nSQLITE_API void sqlite3_result_error_code(sqlite3_context*, int);\nSQLITE_API void sqlite3_result_int(sqlite3_context*, int);\nSQLITE_API void sqlite3_result_int64(sqlite3_context*, sqlite3_int64);\nSQLITE_API void sqlite3_result_null(sqlite3_context*);\nSQLITE_API void sqlite3_result_text(sqlite3_context*, const char*, int, void(*)(void*));\nSQLITE_API void sqlite3_result_text64(sqlite3_context*, const char*,sqlite3_uint64,\n                           void(*)(void*), unsigned char encoding);\nSQLITE_API void sqlite3_result_text16(sqlite3_context*, const void*, int, void(*)(void*));\nSQLITE_API void sqlite3_result_text16le(sqlite3_context*, const void*, int,void(*)(void*));\nSQLITE_API void sqlite3_result_text16be(sqlite3_context*, const void*, int,void(*)(void*));\nSQLITE_API void sqlite3_result_value(sqlite3_context*, sqlite3_value*);\nSQLITE_API void sqlite3_result_pointer(sqlite3_context*, void*,const char*,void(*)(void*));\nSQLITE_API void sqlite3_result_zeroblob(sqlite3_context*, int n);\nSQLITE_API int sqlite3_result_zeroblob64(sqlite3_context*, sqlite3_uint64 n);\n\n\n/*\n** CAPI3REF: Setting The Subtype Of An SQL Function\n** METHOD: sqlite3_context\n**\n** The sqlite3_result_subtype(C,T) function causes the subtype of\n** the result from the [application-defined SQL function] with \n** [sqlite3_context] C to be the value T.  Only the lower 8 bits \n** of the subtype T are preserved in current versions of SQLite;\n** higher order bits are discarded.\n** The number of subtype bytes preserved by SQLite might increase\n** in future releases of SQLite.\n*/\nSQLITE_API void sqlite3_result_subtype(sqlite3_context*,unsigned int);\n\n/*\n** CAPI3REF: Define New Collating Sequences\n** METHOD: sqlite3\n**\n** ^These functions add, remove, or modify a [collation] associated\n** with the [database connection] specified as the first argument.\n**\n** ^The name of the collation is a UTF-8 string\n** for sqlite3_create_collation() and sqlite3_create_collation_v2()\n** and a UTF-16 string in native byte order for sqlite3_create_collation16().\n** ^Collation names that compare equal according to [sqlite3_strnicmp()] are\n** considered to be the same name.\n**\n** ^(The third argument (eTextRep) must be one of the constants:\n** <ul>\n** <li> [SQLITE_UTF8],\n** <li> [SQLITE_UTF16LE],\n** <li> [SQLITE_UTF16BE],\n** <li> [SQLITE_UTF16], or\n** <li> [SQLITE_UTF16_ALIGNED].\n** </ul>)^\n** ^The eTextRep argument determines the encoding of strings passed\n** to the collating function callback, xCallback.\n** ^The [SQLITE_UTF16] and [SQLITE_UTF16_ALIGNED] values for eTextRep\n** force strings to be UTF16 with native byte order.\n** ^The [SQLITE_UTF16_ALIGNED] value for eTextRep forces strings to begin\n** on an even byte address.\n**\n** ^The fourth argument, pArg, is an application data pointer that is passed\n** through as the first argument to the collating function callback.\n**\n** ^The fifth argument, xCallback, is a pointer to the collating function.\n** ^Multiple collating functions can be registered using the same name but\n** with different eTextRep parameters and SQLite will use whichever\n** function requires the least amount of data transformation.\n** ^If the xCallback argument is NULL then the collating function is\n** deleted.  ^When all collating functions having the same name are deleted,\n** that collation is no longer usable.\n**\n** ^The collating function callback is invoked with a copy of the pArg \n** application data pointer and with two strings in the encoding specified\n** by the eTextRep argument.  The collating function must return an\n** integer that is negative, zero, or positive\n** if the first string is less than, equal to, or greater than the second,\n** respectively.  A collating function must always return the same answer\n** given the same inputs.  If two or more collating functions are registered\n** to the same collation name (using different eTextRep values) then all\n** must give an equivalent answer when invoked with equivalent strings.\n** The collating function must obey the following properties for all\n** strings A, B, and C:\n**\n** <ol>\n** <li> If A==B then B==A.\n** <li> If A==B and B==C then A==C.\n** <li> If A&lt;B THEN B&gt;A.\n** <li> If A&lt;B and B&lt;C then A&lt;C.\n** </ol>\n**\n** If a collating function fails any of the above constraints and that\n** collating function is  registered and used, then the behavior of SQLite\n** is undefined.\n**\n** ^The sqlite3_create_collation_v2() works like sqlite3_create_collation()\n** with the addition that the xDestroy callback is invoked on pArg when\n** the collating function is deleted.\n** ^Collating functions are deleted when they are overridden by later\n** calls to the collation creation functions or when the\n** [database connection] is closed using [sqlite3_close()].\n**\n** ^The xDestroy callback is <u>not</u> called if the \n** sqlite3_create_collation_v2() function fails.  Applications that invoke\n** sqlite3_create_collation_v2() with a non-NULL xDestroy argument should \n** check the return code and dispose of the application data pointer\n** themselves rather than expecting SQLite to deal with it for them.\n** This is different from every other SQLite interface.  The inconsistency \n** is unfortunate but cannot be changed without breaking backwards \n** compatibility.\n**\n** See also:  [sqlite3_collation_needed()] and [sqlite3_collation_needed16()].\n*/\nSQLITE_API int sqlite3_create_collation(\n  sqlite3*, \n  const char *zName, \n  int eTextRep, \n  void *pArg,\n  int(*xCompare)(void*,int,const void*,int,const void*)\n);\nSQLITE_API int sqlite3_create_collation_v2(\n  sqlite3*, \n  const char *zName, \n  int eTextRep, \n  void *pArg,\n  int(*xCompare)(void*,int,const void*,int,const void*),\n  void(*xDestroy)(void*)\n);\nSQLITE_API int sqlite3_create_collation16(\n  sqlite3*, \n  const void *zName,\n  int eTextRep, \n  void *pArg,\n  int(*xCompare)(void*,int,const void*,int,const void*)\n);\n\n/*\n** CAPI3REF: Collation Needed Callbacks\n** METHOD: sqlite3\n**\n** ^To avoid having to register all collation sequences before a database\n** can be used, a single callback function may be registered with the\n** [database connection] to be invoked whenever an undefined collation\n** sequence is required.\n**\n** ^If the function is registered using the sqlite3_collation_needed() API,\n** then it is passed the names of undefined collation sequences as strings\n** encoded in UTF-8. ^If sqlite3_collation_needed16() is used,\n** the names are passed as UTF-16 in machine native byte order.\n** ^A call to either function replaces the existing collation-needed callback.\n**\n** ^(When the callback is invoked, the first argument passed is a copy\n** of the second argument to sqlite3_collation_needed() or\n** sqlite3_collation_needed16().  The second argument is the database\n** connection.  The third argument is one of [SQLITE_UTF8], [SQLITE_UTF16BE],\n** or [SQLITE_UTF16LE], indicating the most desirable form of the collation\n** sequence function required.  The fourth parameter is the name of the\n** required collation sequence.)^\n**\n** The callback function should register the desired collation using\n** [sqlite3_create_collation()], [sqlite3_create_collation16()], or\n** [sqlite3_create_collation_v2()].\n*/\nSQLITE_API int sqlite3_collation_needed(\n  sqlite3*, \n  void*, \n  void(*)(void*,sqlite3*,int eTextRep,const char*)\n);\nSQLITE_API int sqlite3_collation_needed16(\n  sqlite3*, \n  void*,\n  void(*)(void*,sqlite3*,int eTextRep,const void*)\n);\n\n#ifdef SQLITE_HAS_CODEC\n/*\n** Specify the key for an encrypted database.  This routine should be\n** called right after sqlite3_open().\n**\n** The code to implement this API is not available in the public release\n** of SQLite.\n*/\nSQLITE_API int sqlite3_key(\n  sqlite3 *db,                   /* Database to be rekeyed */\n  const void *pKey, int nKey     /* The key */\n);\nSQLITE_API int sqlite3_key_v2(\n  sqlite3 *db,                   /* Database to be rekeyed */\n  const char *zDbName,           /* Name of the database */\n  const void *pKey, int nKey     /* The key */\n);\n\n/*\n** Change the key on an open database.  If the current database is not\n** encrypted, this routine will encrypt it.  If pNew==0 or nNew==0, the\n** database is decrypted.\n**\n** The code to implement this API is not available in the public release\n** of SQLite.\n*/\nSQLITE_API int sqlite3_rekey(\n  sqlite3 *db,                   /* Database to be rekeyed */\n  const void *pKey, int nKey     /* The new key */\n);\nSQLITE_API int sqlite3_rekey_v2(\n  sqlite3 *db,                   /* Database to be rekeyed */\n  const char *zDbName,           /* Name of the database */\n  const void *pKey, int nKey     /* The new key */\n);\n\n/*\n** Specify the activation key for a SEE database.  Unless \n** activated, none of the SEE routines will work.\n*/\nSQLITE_API void sqlite3_activate_see(\n  const char *zPassPhrase        /* Activation phrase */\n);\n#endif\n\n#ifdef SQLITE_ENABLE_CEROD\n/*\n** Specify the activation key for a CEROD database.  Unless \n** activated, none of the CEROD routines will work.\n*/\nSQLITE_API void sqlite3_activate_cerod(\n  const char *zPassPhrase        /* Activation phrase */\n);\n#endif\n\n/*\n** CAPI3REF: Suspend Execution For A Short Time\n**\n** The sqlite3_sleep() function causes the current thread to suspend execution\n** for at least a number of milliseconds specified in its parameter.\n**\n** If the operating system does not support sleep requests with\n** millisecond time resolution, then the time will be rounded up to\n** the nearest second. The number of milliseconds of sleep actually\n** requested from the operating system is returned.\n**\n** ^SQLite implements this interface by calling the xSleep()\n** method of the default [sqlite3_vfs] object.  If the xSleep() method\n** of the default VFS is not implemented correctly, or not implemented at\n** all, then the behavior of sqlite3_sleep() may deviate from the description\n** in the previous paragraphs.\n*/\nSQLITE_API int sqlite3_sleep(int);\n\n/*\n** CAPI3REF: Name Of The Folder Holding Temporary Files\n**\n** ^(If this global variable is made to point to a string which is\n** the name of a folder (a.k.a. directory), then all temporary files\n** created by SQLite when using a built-in [sqlite3_vfs | VFS]\n** will be placed in that directory.)^  ^If this variable\n** is a NULL pointer, then SQLite performs a search for an appropriate\n** temporary file directory.\n**\n** Applications are strongly discouraged from using this global variable.\n** It is required to set a temporary folder on Windows Runtime (WinRT).\n** But for all other platforms, it is highly recommended that applications\n** neither read nor write this variable.  This global variable is a relic\n** that exists for backwards compatibility of legacy applications and should\n** be avoided in new projects.\n**\n** It is not safe to read or modify this variable in more than one\n** thread at a time.  It is not safe to read or modify this variable\n** if a [database connection] is being used at the same time in a separate\n** thread.\n** It is intended that this variable be set once\n** as part of process initialization and before any SQLite interface\n** routines have been called and that this variable remain unchanged\n** thereafter.\n**\n** ^The [temp_store_directory pragma] may modify this variable and cause\n** it to point to memory obtained from [sqlite3_malloc].  ^Furthermore,\n** the [temp_store_directory pragma] always assumes that any string\n** that this variable points to is held in memory obtained from \n** [sqlite3_malloc] and the pragma may attempt to free that memory\n** using [sqlite3_free].\n** Hence, if this variable is modified directly, either it should be\n** made NULL or made to point to memory obtained from [sqlite3_malloc]\n** or else the use of the [temp_store_directory pragma] should be avoided.\n** Except when requested by the [temp_store_directory pragma], SQLite\n** does not free the memory that sqlite3_temp_directory points to.  If\n** the application wants that memory to be freed, it must do\n** so itself, taking care to only do so after all [database connection]\n** objects have been destroyed.\n**\n** <b>Note to Windows Runtime users:</b>  The temporary directory must be set\n** prior to calling [sqlite3_open] or [sqlite3_open_v2].  Otherwise, various\n** features that require the use of temporary files may fail.  Here is an\n** example of how to do this using C++ with the Windows Runtime:\n**\n** <blockquote><pre>\n** LPCWSTR zPath = Windows::Storage::ApplicationData::Current->\n** &nbsp;     TemporaryFolder->Path->Data();\n** char zPathBuf&#91;MAX_PATH + 1&#93;;\n** memset(zPathBuf, 0, sizeof(zPathBuf));\n** WideCharToMultiByte(CP_UTF8, 0, zPath, -1, zPathBuf, sizeof(zPathBuf),\n** &nbsp;     NULL, NULL);\n** sqlite3_temp_directory = sqlite3_mprintf(\"%s\", zPathBuf);\n** </pre></blockquote>\n*/\nSQLITE_API char *sqlite3_temp_directory;\n\n/*\n** CAPI3REF: Name Of The Folder Holding Database Files\n**\n** ^(If this global variable is made to point to a string which is\n** the name of a folder (a.k.a. directory), then all database files\n** specified with a relative pathname and created or accessed by\n** SQLite when using a built-in windows [sqlite3_vfs | VFS] will be assumed\n** to be relative to that directory.)^ ^If this variable is a NULL\n** pointer, then SQLite assumes that all database files specified\n** with a relative pathname are relative to the current directory\n** for the process.  Only the windows VFS makes use of this global\n** variable; it is ignored by the unix VFS.\n**\n** Changing the value of this variable while a database connection is\n** open can result in a corrupt database.\n**\n** It is not safe to read or modify this variable in more than one\n** thread at a time.  It is not safe to read or modify this variable\n** if a [database connection] is being used at the same time in a separate\n** thread.\n** It is intended that this variable be set once\n** as part of process initialization and before any SQLite interface\n** routines have been called and that this variable remain unchanged\n** thereafter.\n**\n** ^The [data_store_directory pragma] may modify this variable and cause\n** it to point to memory obtained from [sqlite3_malloc].  ^Furthermore,\n** the [data_store_directory pragma] always assumes that any string\n** that this variable points to is held in memory obtained from \n** [sqlite3_malloc] and the pragma may attempt to free that memory\n** using [sqlite3_free].\n** Hence, if this variable is modified directly, either it should be\n** made NULL or made to point to memory obtained from [sqlite3_malloc]\n** or else the use of the [data_store_directory pragma] should be avoided.\n*/\nSQLITE_API char *sqlite3_data_directory;\n\n/*\n** CAPI3REF: Test For Auto-Commit Mode\n** KEYWORDS: {autocommit mode}\n** METHOD: sqlite3\n**\n** ^The sqlite3_get_autocommit() interface returns non-zero or\n** zero if the given database connection is or is not in autocommit mode,\n** respectively.  ^Autocommit mode is on by default.\n** ^Autocommit mode is disabled by a [BEGIN] statement.\n** ^Autocommit mode is re-enabled by a [COMMIT] or [ROLLBACK].\n**\n** If certain kinds of errors occur on a statement within a multi-statement\n** transaction (errors including [SQLITE_FULL], [SQLITE_IOERR],\n** [SQLITE_NOMEM], [SQLITE_BUSY], and [SQLITE_INTERRUPT]) then the\n** transaction might be rolled back automatically.  The only way to\n** find out whether SQLite automatically rolled back the transaction after\n** an error is to use this function.\n**\n** If another thread changes the autocommit status of the database\n** connection while this routine is running, then the return value\n** is undefined.\n*/\nSQLITE_API int sqlite3_get_autocommit(sqlite3*);\n\n/*\n** CAPI3REF: Find The Database Handle Of A Prepared Statement\n** METHOD: sqlite3_stmt\n**\n** ^The sqlite3_db_handle interface returns the [database connection] handle\n** to which a [prepared statement] belongs.  ^The [database connection]\n** returned by sqlite3_db_handle is the same [database connection]\n** that was the first argument\n** to the [sqlite3_prepare_v2()] call (or its variants) that was used to\n** create the statement in the first place.\n*/\nSQLITE_API sqlite3 *sqlite3_db_handle(sqlite3_stmt*);\n\n/*\n** CAPI3REF: Return The Filename For A Database Connection\n** METHOD: sqlite3\n**\n** ^The sqlite3_db_filename(D,N) interface returns a pointer to a filename\n** associated with database N of connection D.  ^The main database file\n** has the name \"main\".  If there is no attached database N on the database\n** connection D, or if database N is a temporary or in-memory database, then\n** a NULL pointer is returned.\n**\n** ^The filename returned by this function is the output of the\n** xFullPathname method of the [VFS].  ^In other words, the filename\n** will be an absolute pathname, even if the filename used\n** to open the database originally was a URI or relative pathname.\n*/\nSQLITE_API const char *sqlite3_db_filename(sqlite3 *db, const char *zDbName);\n\n/*\n** CAPI3REF: Determine if a database is read-only\n** METHOD: sqlite3\n**\n** ^The sqlite3_db_readonly(D,N) interface returns 1 if the database N\n** of connection D is read-only, 0 if it is read/write, or -1 if N is not\n** the name of a database on connection D.\n*/\nSQLITE_API int sqlite3_db_readonly(sqlite3 *db, const char *zDbName);\n\n/*\n** CAPI3REF: Find the next prepared statement\n** METHOD: sqlite3\n**\n** ^This interface returns a pointer to the next [prepared statement] after\n** pStmt associated with the [database connection] pDb.  ^If pStmt is NULL\n** then this interface returns a pointer to the first prepared statement\n** associated with the database connection pDb.  ^If no prepared statement\n** satisfies the conditions of this routine, it returns NULL.\n**\n** The [database connection] pointer D in a call to\n** [sqlite3_next_stmt(D,S)] must refer to an open database\n** connection and in particular must not be a NULL pointer.\n*/\nSQLITE_API sqlite3_stmt *sqlite3_next_stmt(sqlite3 *pDb, sqlite3_stmt *pStmt);\n\n/*\n** CAPI3REF: Commit And Rollback Notification Callbacks\n** METHOD: sqlite3\n**\n** ^The sqlite3_commit_hook() interface registers a callback\n** function to be invoked whenever a transaction is [COMMIT | committed].\n** ^Any callback set by a previous call to sqlite3_commit_hook()\n** for the same database connection is overridden.\n** ^The sqlite3_rollback_hook() interface registers a callback\n** function to be invoked whenever a transaction is [ROLLBACK | rolled back].\n** ^Any callback set by a previous call to sqlite3_rollback_hook()\n** for the same database connection is overridden.\n** ^The pArg argument is passed through to the callback.\n** ^If the callback on a commit hook function returns non-zero,\n** then the commit is converted into a rollback.\n**\n** ^The sqlite3_commit_hook(D,C,P) and sqlite3_rollback_hook(D,C,P) functions\n** return the P argument from the previous call of the same function\n** on the same [database connection] D, or NULL for\n** the first call for each function on D.\n**\n** The commit and rollback hook callbacks are not reentrant.\n** The callback implementation must not do anything that will modify\n** the database connection that invoked the callback.  Any actions\n** to modify the database connection must be deferred until after the\n** completion of the [sqlite3_step()] call that triggered the commit\n** or rollback hook in the first place.\n** Note that running any other SQL statements, including SELECT statements,\n** or merely calling [sqlite3_prepare_v2()] and [sqlite3_step()] will modify\n** the database connections for the meaning of \"modify\" in this paragraph.\n**\n** ^Registering a NULL function disables the callback.\n**\n** ^When the commit hook callback routine returns zero, the [COMMIT]\n** operation is allowed to continue normally.  ^If the commit hook\n** returns non-zero, then the [COMMIT] is converted into a [ROLLBACK].\n** ^The rollback hook is invoked on a rollback that results from a commit\n** hook returning non-zero, just as it would be with any other rollback.\n**\n** ^For the purposes of this API, a transaction is said to have been\n** rolled back if an explicit \"ROLLBACK\" statement is executed, or\n** an error or constraint causes an implicit rollback to occur.\n** ^The rollback callback is not invoked if a transaction is\n** automatically rolled back because the database connection is closed.\n**\n** See also the [sqlite3_update_hook()] interface.\n*/\nSQLITE_API void *sqlite3_commit_hook(sqlite3*, int(*)(void*), void*);\nSQLITE_API void *sqlite3_rollback_hook(sqlite3*, void(*)(void *), void*);\n\n/*\n** CAPI3REF: Data Change Notification Callbacks\n** METHOD: sqlite3\n**\n** ^The sqlite3_update_hook() interface registers a callback function\n** with the [database connection] identified by the first argument\n** to be invoked whenever a row is updated, inserted or deleted in\n** a [rowid table].\n** ^Any callback set by a previous call to this function\n** for the same database connection is overridden.\n**\n** ^The second argument is a pointer to the function to invoke when a\n** row is updated, inserted or deleted in a rowid table.\n** ^The first argument to the callback is a copy of the third argument\n** to sqlite3_update_hook().\n** ^The second callback argument is one of [SQLITE_INSERT], [SQLITE_DELETE],\n** or [SQLITE_UPDATE], depending on the operation that caused the callback\n** to be invoked.\n** ^The third and fourth arguments to the callback contain pointers to the\n** database and table name containing the affected row.\n** ^The final callback parameter is the [rowid] of the row.\n** ^In the case of an update, this is the [rowid] after the update takes place.\n**\n** ^(The update hook is not invoked when internal system tables are\n** modified (i.e. sqlite_master and sqlite_sequence).)^\n** ^The update hook is not invoked when [WITHOUT ROWID] tables are modified.\n**\n** ^In the current implementation, the update hook\n** is not invoked when conflicting rows are deleted because of an\n** [ON CONFLICT | ON CONFLICT REPLACE] clause.  ^Nor is the update hook\n** invoked when rows are deleted using the [truncate optimization].\n** The exceptions defined in this paragraph might change in a future\n** release of SQLite.\n**\n** The update hook implementation must not do anything that will modify\n** the database connection that invoked the update hook.  Any actions\n** to modify the database connection must be deferred until after the\n** completion of the [sqlite3_step()] call that triggered the update hook.\n** Note that [sqlite3_prepare_v2()] and [sqlite3_step()] both modify their\n** database connections for the meaning of \"modify\" in this paragraph.\n**\n** ^The sqlite3_update_hook(D,C,P) function\n** returns the P argument from the previous call\n** on the same [database connection] D, or NULL for\n** the first call on D.\n**\n** See also the [sqlite3_commit_hook()], [sqlite3_rollback_hook()],\n** and [sqlite3_preupdate_hook()] interfaces.\n*/\nSQLITE_API void *sqlite3_update_hook(\n  sqlite3*, \n  void(*)(void *,int ,char const *,char const *,sqlite3_int64),\n  void*\n);\n\n/*\n** CAPI3REF: Enable Or Disable Shared Pager Cache\n**\n** ^(This routine enables or disables the sharing of the database cache\n** and schema data structures between [database connection | connections]\n** to the same database. Sharing is enabled if the argument is true\n** and disabled if the argument is false.)^\n**\n** ^Cache sharing is enabled and disabled for an entire process.\n** This is a change as of SQLite [version 3.5.0] ([dateof:3.5.0]). \n** In prior versions of SQLite,\n** sharing was enabled or disabled for each thread separately.\n**\n** ^(The cache sharing mode set by this interface effects all subsequent\n** calls to [sqlite3_open()], [sqlite3_open_v2()], and [sqlite3_open16()].\n** Existing database connections continue use the sharing mode\n** that was in effect at the time they were opened.)^\n**\n** ^(This routine returns [SQLITE_OK] if shared cache was enabled or disabled\n** successfully.  An [error code] is returned otherwise.)^\n**\n** ^Shared cache is disabled by default. But this might change in\n** future releases of SQLite.  Applications that care about shared\n** cache setting should set it explicitly.\n**\n** Note: This method is disabled on MacOS X 10.7 and iOS version 5.0\n** and will always return SQLITE_MISUSE. On those systems, \n** shared cache mode should be enabled per-database connection via \n** [sqlite3_open_v2()] with [SQLITE_OPEN_SHAREDCACHE].\n**\n** This interface is threadsafe on processors where writing a\n** 32-bit integer is atomic.\n**\n** See Also:  [SQLite Shared-Cache Mode]\n*/\nSQLITE_API int sqlite3_enable_shared_cache(int);\n\n/*\n** CAPI3REF: Attempt To Free Heap Memory\n**\n** ^The sqlite3_release_memory() interface attempts to free N bytes\n** of heap memory by deallocating non-essential memory allocations\n** held by the database library.   Memory used to cache database\n** pages to improve performance is an example of non-essential memory.\n** ^sqlite3_release_memory() returns the number of bytes actually freed,\n** which might be more or less than the amount requested.\n** ^The sqlite3_release_memory() routine is a no-op returning zero\n** if SQLite is not compiled with [SQLITE_ENABLE_MEMORY_MANAGEMENT].\n**\n** See also: [sqlite3_db_release_memory()]\n*/\nSQLITE_API int sqlite3_release_memory(int);\n\n/*\n** CAPI3REF: Free Memory Used By A Database Connection\n** METHOD: sqlite3\n**\n** ^The sqlite3_db_release_memory(D) interface attempts to free as much heap\n** memory as possible from database connection D. Unlike the\n** [sqlite3_release_memory()] interface, this interface is in effect even\n** when the [SQLITE_ENABLE_MEMORY_MANAGEMENT] compile-time option is\n** omitted.\n**\n** See also: [sqlite3_release_memory()]\n*/\nSQLITE_API int sqlite3_db_release_memory(sqlite3*);\n\n/*\n** CAPI3REF: Impose A Limit On Heap Size\n**\n** ^The sqlite3_soft_heap_limit64() interface sets and/or queries the\n** soft limit on the amount of heap memory that may be allocated by SQLite.\n** ^SQLite strives to keep heap memory utilization below the soft heap\n** limit by reducing the number of pages held in the page cache\n** as heap memory usages approaches the limit.\n** ^The soft heap limit is \"soft\" because even though SQLite strives to stay\n** below the limit, it will exceed the limit rather than generate\n** an [SQLITE_NOMEM] error.  In other words, the soft heap limit \n** is advisory only.\n**\n** ^The return value from sqlite3_soft_heap_limit64() is the size of\n** the soft heap limit prior to the call, or negative in the case of an\n** error.  ^If the argument N is negative\n** then no change is made to the soft heap limit.  Hence, the current\n** size of the soft heap limit can be determined by invoking\n** sqlite3_soft_heap_limit64() with a negative argument.\n**\n** ^If the argument N is zero then the soft heap limit is disabled.\n**\n** ^(The soft heap limit is not enforced in the current implementation\n** if one or more of following conditions are true:\n**\n** <ul>\n** <li> The soft heap limit is set to zero.\n** <li> Memory accounting is disabled using a combination of the\n**      [sqlite3_config]([SQLITE_CONFIG_MEMSTATUS],...) start-time option and\n**      the [SQLITE_DEFAULT_MEMSTATUS] compile-time option.\n** <li> An alternative page cache implementation is specified using\n**      [sqlite3_config]([SQLITE_CONFIG_PCACHE2],...).\n** <li> The page cache allocates from its own memory pool supplied\n**      by [sqlite3_config]([SQLITE_CONFIG_PAGECACHE],...) rather than\n**      from the heap.\n** </ul>)^\n**\n** Beginning with SQLite [version 3.7.3] ([dateof:3.7.3]), \n** the soft heap limit is enforced\n** regardless of whether or not the [SQLITE_ENABLE_MEMORY_MANAGEMENT]\n** compile-time option is invoked.  With [SQLITE_ENABLE_MEMORY_MANAGEMENT],\n** the soft heap limit is enforced on every memory allocation.  Without\n** [SQLITE_ENABLE_MEMORY_MANAGEMENT], the soft heap limit is only enforced\n** when memory is allocated by the page cache.  Testing suggests that because\n** the page cache is the predominate memory user in SQLite, most\n** applications will achieve adequate soft heap limit enforcement without\n** the use of [SQLITE_ENABLE_MEMORY_MANAGEMENT].\n**\n** The circumstances under which SQLite will enforce the soft heap limit may\n** changes in future releases of SQLite.\n*/\nSQLITE_API sqlite3_int64 sqlite3_soft_heap_limit64(sqlite3_int64 N);\n\n/*\n** CAPI3REF: Deprecated Soft Heap Limit Interface\n** DEPRECATED\n**\n** This is a deprecated version of the [sqlite3_soft_heap_limit64()]\n** interface.  This routine is provided for historical compatibility\n** only.  All new applications should use the\n** [sqlite3_soft_heap_limit64()] interface rather than this one.\n*/\nSQLITE_API SQLITE_DEPRECATED void sqlite3_soft_heap_limit(int N);\n\n\n/*\n** CAPI3REF: Extract Metadata About A Column Of A Table\n** METHOD: sqlite3\n**\n** ^(The sqlite3_table_column_metadata(X,D,T,C,....) routine returns\n** information about column C of table T in database D\n** on [database connection] X.)^  ^The sqlite3_table_column_metadata()\n** interface returns SQLITE_OK and fills in the non-NULL pointers in\n** the final five arguments with appropriate values if the specified\n** column exists.  ^The sqlite3_table_column_metadata() interface returns\n** SQLITE_ERROR and if the specified column does not exist.\n** ^If the column-name parameter to sqlite3_table_column_metadata() is a\n** NULL pointer, then this routine simply checks for the existence of the\n** table and returns SQLITE_OK if the table exists and SQLITE_ERROR if it\n** does not.  If the table name parameter T in a call to\n** sqlite3_table_column_metadata(X,D,T,C,...) is NULL then the result is\n** undefined behavior.\n**\n** ^The column is identified by the second, third and fourth parameters to\n** this function. ^(The second parameter is either the name of the database\n** (i.e. \"main\", \"temp\", or an attached database) containing the specified\n** table or NULL.)^ ^If it is NULL, then all attached databases are searched\n** for the table using the same algorithm used by the database engine to\n** resolve unqualified table references.\n**\n** ^The third and fourth parameters to this function are the table and column\n** name of the desired column, respectively.\n**\n** ^Metadata is returned by writing to the memory locations passed as the 5th\n** and subsequent parameters to this function. ^Any of these arguments may be\n** NULL, in which case the corresponding element of metadata is omitted.\n**\n** ^(<blockquote>\n** <table border=\"1\">\n** <tr><th> Parameter <th> Output<br>Type <th>  Description\n**\n** <tr><td> 5th <td> const char* <td> Data type\n** <tr><td> 6th <td> const char* <td> Name of default collation sequence\n** <tr><td> 7th <td> int         <td> True if column has a NOT NULL constraint\n** <tr><td> 8th <td> int         <td> True if column is part of the PRIMARY KEY\n** <tr><td> 9th <td> int         <td> True if column is [AUTOINCREMENT]\n** </table>\n** </blockquote>)^\n**\n** ^The memory pointed to by the character pointers returned for the\n** declaration type and collation sequence is valid until the next\n** call to any SQLite API function.\n**\n** ^If the specified table is actually a view, an [error code] is returned.\n**\n** ^If the specified column is \"rowid\", \"oid\" or \"_rowid_\" and the table \n** is not a [WITHOUT ROWID] table and an\n** [INTEGER PRIMARY KEY] column has been explicitly declared, then the output\n** parameters are set for the explicitly declared column. ^(If there is no\n** [INTEGER PRIMARY KEY] column, then the outputs\n** for the [rowid] are set as follows:\n**\n** <pre>\n**     data type: \"INTEGER\"\n**     collation sequence: \"BINARY\"\n**     not null: 0\n**     primary key: 1\n**     auto increment: 0\n** </pre>)^\n**\n** ^This function causes all database schemas to be read from disk and\n** parsed, if that has not already been done, and returns an error if\n** any errors are encountered while loading the schema.\n*/\nSQLITE_API int sqlite3_table_column_metadata(\n  sqlite3 *db,                /* Connection handle */\n  const char *zDbName,        /* Database name or NULL */\n  const char *zTableName,     /* Table name */\n  const char *zColumnName,    /* Column name */\n  char const **pzDataType,    /* OUTPUT: Declared data type */\n  char const **pzCollSeq,     /* OUTPUT: Collation sequence name */\n  int *pNotNull,              /* OUTPUT: True if NOT NULL constraint exists */\n  int *pPrimaryKey,           /* OUTPUT: True if column part of PK */\n  int *pAutoinc               /* OUTPUT: True if column is auto-increment */\n);\n\n/*\n** CAPI3REF: Load An Extension\n** METHOD: sqlite3\n**\n** ^This interface loads an SQLite extension library from the named file.\n**\n** ^The sqlite3_load_extension() interface attempts to load an\n** [SQLite extension] library contained in the file zFile.  If\n** the file cannot be loaded directly, attempts are made to load\n** with various operating-system specific extensions added.\n** So for example, if \"samplelib\" cannot be loaded, then names like\n** \"samplelib.so\" or \"samplelib.dylib\" or \"samplelib.dll\" might\n** be tried also.\n**\n** ^The entry point is zProc.\n** ^(zProc may be 0, in which case SQLite will try to come up with an\n** entry point name on its own.  It first tries \"sqlite3_extension_init\".\n** If that does not work, it constructs a name \"sqlite3_X_init\" where the\n** X is consists of the lower-case equivalent of all ASCII alphabetic\n** characters in the filename from the last \"/\" to the first following\n** \".\" and omitting any initial \"lib\".)^\n** ^The sqlite3_load_extension() interface returns\n** [SQLITE_OK] on success and [SQLITE_ERROR] if something goes wrong.\n** ^If an error occurs and pzErrMsg is not 0, then the\n** [sqlite3_load_extension()] interface shall attempt to\n** fill *pzErrMsg with error message text stored in memory\n** obtained from [sqlite3_malloc()]. The calling function\n** should free this memory by calling [sqlite3_free()].\n**\n** ^Extension loading must be enabled using\n** [sqlite3_enable_load_extension()] or\n** [sqlite3_db_config](db,[SQLITE_DBCONFIG_ENABLE_LOAD_EXTENSION],1,NULL)\n** prior to calling this API,\n** otherwise an error will be returned.\n**\n** <b>Security warning:</b> It is recommended that the \n** [SQLITE_DBCONFIG_ENABLE_LOAD_EXTENSION] method be used to enable only this\n** interface.  The use of the [sqlite3_enable_load_extension()] interface\n** should be avoided.  This will keep the SQL function [load_extension()]\n** disabled and prevent SQL injections from giving attackers\n** access to extension loading capabilities.\n**\n** See also the [load_extension() SQL function].\n*/\nSQLITE_API int sqlite3_load_extension(\n  sqlite3 *db,          /* Load the extension into this database connection */\n  const char *zFile,    /* Name of the shared library containing extension */\n  const char *zProc,    /* Entry point.  Derived from zFile if 0 */\n  char **pzErrMsg       /* Put error message here if not 0 */\n);\n\n/*\n** CAPI3REF: Enable Or Disable Extension Loading\n** METHOD: sqlite3\n**\n** ^So as not to open security holes in older applications that are\n** unprepared to deal with [extension loading], and as a means of disabling\n** [extension loading] while evaluating user-entered SQL, the following API\n** is provided to turn the [sqlite3_load_extension()] mechanism on and off.\n**\n** ^Extension loading is off by default.\n** ^Call the sqlite3_enable_load_extension() routine with onoff==1\n** to turn extension loading on and call it with onoff==0 to turn\n** it back off again.\n**\n** ^This interface enables or disables both the C-API\n** [sqlite3_load_extension()] and the SQL function [load_extension()].\n** ^(Use [sqlite3_db_config](db,[SQLITE_DBCONFIG_ENABLE_LOAD_EXTENSION],..)\n** to enable or disable only the C-API.)^\n**\n** <b>Security warning:</b> It is recommended that extension loading\n** be disabled using the [SQLITE_DBCONFIG_ENABLE_LOAD_EXTENSION] method\n** rather than this interface, so the [load_extension()] SQL function\n** remains disabled. This will prevent SQL injections from giving attackers\n** access to extension loading capabilities.\n*/\nSQLITE_API int sqlite3_enable_load_extension(sqlite3 *db, int onoff);\n\n/*\n** CAPI3REF: Automatically Load Statically Linked Extensions\n**\n** ^This interface causes the xEntryPoint() function to be invoked for\n** each new [database connection] that is created.  The idea here is that\n** xEntryPoint() is the entry point for a statically linked [SQLite extension]\n** that is to be automatically loaded into all new database connections.\n**\n** ^(Even though the function prototype shows that xEntryPoint() takes\n** no arguments and returns void, SQLite invokes xEntryPoint() with three\n** arguments and expects an integer result as if the signature of the\n** entry point where as follows:\n**\n** <blockquote><pre>\n** &nbsp;  int xEntryPoint(\n** &nbsp;    sqlite3 *db,\n** &nbsp;    const char **pzErrMsg,\n** &nbsp;    const struct sqlite3_api_routines *pThunk\n** &nbsp;  );\n** </pre></blockquote>)^\n**\n** If the xEntryPoint routine encounters an error, it should make *pzErrMsg\n** point to an appropriate error message (obtained from [sqlite3_mprintf()])\n** and return an appropriate [error code].  ^SQLite ensures that *pzErrMsg\n** is NULL before calling the xEntryPoint().  ^SQLite will invoke\n** [sqlite3_free()] on *pzErrMsg after xEntryPoint() returns.  ^If any\n** xEntryPoint() returns an error, the [sqlite3_open()], [sqlite3_open16()],\n** or [sqlite3_open_v2()] call that provoked the xEntryPoint() will fail.\n**\n** ^Calling sqlite3_auto_extension(X) with an entry point X that is already\n** on the list of automatic extensions is a harmless no-op. ^No entry point\n** will be called more than once for each database connection that is opened.\n**\n** See also: [sqlite3_reset_auto_extension()]\n** and [sqlite3_cancel_auto_extension()]\n*/\nSQLITE_API int sqlite3_auto_extension(void(*xEntryPoint)(void));\n\n/*\n** CAPI3REF: Cancel Automatic Extension Loading\n**\n** ^The [sqlite3_cancel_auto_extension(X)] interface unregisters the\n** initialization routine X that was registered using a prior call to\n** [sqlite3_auto_extension(X)].  ^The [sqlite3_cancel_auto_extension(X)]\n** routine returns 1 if initialization routine X was successfully \n** unregistered and it returns 0 if X was not on the list of initialization\n** routines.\n*/\nSQLITE_API int sqlite3_cancel_auto_extension(void(*xEntryPoint)(void));\n\n/*\n** CAPI3REF: Reset Automatic Extension Loading\n**\n** ^This interface disables all automatic extensions previously\n** registered using [sqlite3_auto_extension()].\n*/\nSQLITE_API void sqlite3_reset_auto_extension(void);\n\n/*\n** The interface to the virtual-table mechanism is currently considered\n** to be experimental.  The interface might change in incompatible ways.\n** If this is a problem for you, do not use the interface at this time.\n**\n** When the virtual-table mechanism stabilizes, we will declare the\n** interface fixed, support it indefinitely, and remove this comment.\n*/\n\n/*\n** Structures used by the virtual table interface\n*/\ntypedef struct sqlite3_vtab sqlite3_vtab;\ntypedef struct sqlite3_index_info sqlite3_index_info;\ntypedef struct sqlite3_vtab_cursor sqlite3_vtab_cursor;\ntypedef struct sqlite3_module sqlite3_module;\n\n/*\n** CAPI3REF: Virtual Table Object\n** KEYWORDS: sqlite3_module {virtual table module}\n**\n** This structure, sometimes called a \"virtual table module\", \n** defines the implementation of a [virtual tables].  \n** This structure consists mostly of methods for the module.\n**\n** ^A virtual table module is created by filling in a persistent\n** instance of this structure and passing a pointer to that instance\n** to [sqlite3_create_module()] or [sqlite3_create_module_v2()].\n** ^The registration remains valid until it is replaced by a different\n** module or until the [database connection] closes.  The content\n** of this structure must not change while it is registered with\n** any database connection.\n*/\nstruct sqlite3_module {\n  int iVersion;\n  int (*xCreate)(sqlite3*, void *pAux,\n               int argc, const char *const*argv,\n               sqlite3_vtab **ppVTab, char**);\n  int (*xConnect)(sqlite3*, void *pAux,\n               int argc, const char *const*argv,\n               sqlite3_vtab **ppVTab, char**);\n  int (*xBestIndex)(sqlite3_vtab *pVTab, sqlite3_index_info*);\n  int (*xDisconnect)(sqlite3_vtab *pVTab);\n  int (*xDestroy)(sqlite3_vtab *pVTab);\n  int (*xOpen)(sqlite3_vtab *pVTab, sqlite3_vtab_cursor **ppCursor);\n  int (*xClose)(sqlite3_vtab_cursor*);\n  int (*xFilter)(sqlite3_vtab_cursor*, int idxNum, const char *idxStr,\n                int argc, sqlite3_value **argv);\n  int (*xNext)(sqlite3_vtab_cursor*);\n  int (*xEof)(sqlite3_vtab_cursor*);\n  int (*xColumn)(sqlite3_vtab_cursor*, sqlite3_context*, int);\n  int (*xRowid)(sqlite3_vtab_cursor*, sqlite3_int64 *pRowid);\n  int (*xUpdate)(sqlite3_vtab *, int, sqlite3_value **, sqlite3_int64 *);\n  int (*xBegin)(sqlite3_vtab *pVTab);\n  int (*xSync)(sqlite3_vtab *pVTab);\n  int (*xCommit)(sqlite3_vtab *pVTab);\n  int (*xRollback)(sqlite3_vtab *pVTab);\n  int (*xFindFunction)(sqlite3_vtab *pVtab, int nArg, const char *zName,\n                       void (**pxFunc)(sqlite3_context*,int,sqlite3_value**),\n                       void **ppArg);\n  int (*xRename)(sqlite3_vtab *pVtab, const char *zNew);\n  /* The methods above are in version 1 of the sqlite_module object. Those \n  ** below are for version 2 and greater. */\n  int (*xSavepoint)(sqlite3_vtab *pVTab, int);\n  int (*xRelease)(sqlite3_vtab *pVTab, int);\n  int (*xRollbackTo)(sqlite3_vtab *pVTab, int);\n};\n\n/*\n** CAPI3REF: Virtual Table Indexing Information\n** KEYWORDS: sqlite3_index_info\n**\n** The sqlite3_index_info structure and its substructures is used as part\n** of the [virtual table] interface to\n** pass information into and receive the reply from the [xBestIndex]\n** method of a [virtual table module].  The fields under **Inputs** are the\n** inputs to xBestIndex and are read-only.  xBestIndex inserts its\n** results into the **Outputs** fields.\n**\n** ^(The aConstraint[] array records WHERE clause constraints of the form:\n**\n** <blockquote>column OP expr</blockquote>\n**\n** where OP is =, &lt;, &lt;=, &gt;, or &gt;=.)^  ^(The particular operator is\n** stored in aConstraint[].op using one of the\n** [SQLITE_INDEX_CONSTRAINT_EQ | SQLITE_INDEX_CONSTRAINT_ values].)^\n** ^(The index of the column is stored in\n** aConstraint[].iColumn.)^  ^(aConstraint[].usable is TRUE if the\n** expr on the right-hand side can be evaluated (and thus the constraint\n** is usable) and false if it cannot.)^\n**\n** ^The optimizer automatically inverts terms of the form \"expr OP column\"\n** and makes other simplifications to the WHERE clause in an attempt to\n** get as many WHERE clause terms into the form shown above as possible.\n** ^The aConstraint[] array only reports WHERE clause terms that are\n** relevant to the particular virtual table being queried.\n**\n** ^Information about the ORDER BY clause is stored in aOrderBy[].\n** ^Each term of aOrderBy records a column of the ORDER BY clause.\n**\n** The colUsed field indicates which columns of the virtual table may be\n** required by the current scan. Virtual table columns are numbered from\n** zero in the order in which they appear within the CREATE TABLE statement\n** passed to sqlite3_declare_vtab(). For the first 63 columns (columns 0-62),\n** the corresponding bit is set within the colUsed mask if the column may be\n** required by SQLite. If the table has at least 64 columns and any column\n** to the right of the first 63 is required, then bit 63 of colUsed is also\n** set. In other words, column iCol may be required if the expression\n** (colUsed & ((sqlite3_uint64)1 << (iCol>=63 ? 63 : iCol))) evaluates to \n** non-zero.\n**\n** The [xBestIndex] method must fill aConstraintUsage[] with information\n** about what parameters to pass to xFilter.  ^If argvIndex>0 then\n** the right-hand side of the corresponding aConstraint[] is evaluated\n** and becomes the argvIndex-th entry in argv.  ^(If aConstraintUsage[].omit\n** is true, then the constraint is assumed to be fully handled by the\n** virtual table and is not checked again by SQLite.)^\n**\n** ^The idxNum and idxPtr values are recorded and passed into the\n** [xFilter] method.\n** ^[sqlite3_free()] is used to free idxPtr if and only if\n** needToFreeIdxPtr is true.\n**\n** ^The orderByConsumed means that output from [xFilter]/[xNext] will occur in\n** the correct order to satisfy the ORDER BY clause so that no separate\n** sorting step is required.\n**\n** ^The estimatedCost value is an estimate of the cost of a particular\n** strategy. A cost of N indicates that the cost of the strategy is similar\n** to a linear scan of an SQLite table with N rows. A cost of log(N) \n** indicates that the expense of the operation is similar to that of a\n** binary search on a unique indexed field of an SQLite table with N rows.\n**\n** ^The estimatedRows value is an estimate of the number of rows that\n** will be returned by the strategy.\n**\n** The xBestIndex method may optionally populate the idxFlags field with a \n** mask of SQLITE_INDEX_SCAN_* flags. Currently there is only one such flag -\n** SQLITE_INDEX_SCAN_UNIQUE. If the xBestIndex method sets this flag, SQLite\n** assumes that the strategy may visit at most one row. \n**\n** Additionally, if xBestIndex sets the SQLITE_INDEX_SCAN_UNIQUE flag, then\n** SQLite also assumes that if a call to the xUpdate() method is made as\n** part of the same statement to delete or update a virtual table row and the\n** implementation returns SQLITE_CONSTRAINT, then there is no need to rollback\n** any database changes. In other words, if the xUpdate() returns\n** SQLITE_CONSTRAINT, the database contents must be exactly as they were\n** before xUpdate was called. By contrast, if SQLITE_INDEX_SCAN_UNIQUE is not\n** set and xUpdate returns SQLITE_CONSTRAINT, any database changes made by\n** the xUpdate method are automatically rolled back by SQLite.\n**\n** IMPORTANT: The estimatedRows field was added to the sqlite3_index_info\n** structure for SQLite [version 3.8.2] ([dateof:3.8.2]). \n** If a virtual table extension is\n** used with an SQLite version earlier than 3.8.2, the results of attempting \n** to read or write the estimatedRows field are undefined (but are likely \n** to included crashing the application). The estimatedRows field should\n** therefore only be used if [sqlite3_libversion_number()] returns a\n** value greater than or equal to 3008002. Similarly, the idxFlags field\n** was added for [version 3.9.0] ([dateof:3.9.0]). \n** It may therefore only be used if\n** sqlite3_libversion_number() returns a value greater than or equal to\n** 3009000.\n*/\nstruct sqlite3_index_info {\n  /* Inputs */\n  int nConstraint;           /* Number of entries in aConstraint */\n  struct sqlite3_index_constraint {\n     int iColumn;              /* Column constrained.  -1 for ROWID */\n     unsigned char op;         /* Constraint operator */\n     unsigned char usable;     /* True if this constraint is usable */\n     int iTermOffset;          /* Used internally - xBestIndex should ignore */\n  } *aConstraint;            /* Table of WHERE clause constraints */\n  int nOrderBy;              /* Number of terms in the ORDER BY clause */\n  struct sqlite3_index_orderby {\n     int iColumn;              /* Column number */\n     unsigned char desc;       /* True for DESC.  False for ASC. */\n  } *aOrderBy;               /* The ORDER BY clause */\n  /* Outputs */\n  struct sqlite3_index_constraint_usage {\n    int argvIndex;           /* if >0, constraint is part of argv to xFilter */\n    unsigned char omit;      /* Do not code a test for this constraint */\n  } *aConstraintUsage;\n  int idxNum;                /* Number used to identify the index */\n  char *idxStr;              /* String, possibly obtained from sqlite3_malloc */\n  int needToFreeIdxStr;      /* Free idxStr using sqlite3_free() if true */\n  int orderByConsumed;       /* True if output is already ordered */\n  double estimatedCost;           /* Estimated cost of using this index */\n  /* Fields below are only available in SQLite 3.8.2 and later */\n  sqlite3_int64 estimatedRows;    /* Estimated number of rows returned */\n  /* Fields below are only available in SQLite 3.9.0 and later */\n  int idxFlags;              /* Mask of SQLITE_INDEX_SCAN_* flags */\n  /* Fields below are only available in SQLite 3.10.0 and later */\n  sqlite3_uint64 colUsed;    /* Input: Mask of columns used by statement */\n};\n\n/*\n** CAPI3REF: Virtual Table Scan Flags\n*/\n#define SQLITE_INDEX_SCAN_UNIQUE      1     /* Scan visits at most 1 row */\n\n/*\n** CAPI3REF: Virtual Table Constraint Operator Codes\n**\n** These macros defined the allowed values for the\n** [sqlite3_index_info].aConstraint[].op field.  Each value represents\n** an operator that is part of a constraint term in the wHERE clause of\n** a query that uses a [virtual table].\n*/\n#define SQLITE_INDEX_CONSTRAINT_EQ         2\n#define SQLITE_INDEX_CONSTRAINT_GT         4\n#define SQLITE_INDEX_CONSTRAINT_LE         8\n#define SQLITE_INDEX_CONSTRAINT_LT        16\n#define SQLITE_INDEX_CONSTRAINT_GE        32\n#define SQLITE_INDEX_CONSTRAINT_MATCH     64\n#define SQLITE_INDEX_CONSTRAINT_LIKE      65\n#define SQLITE_INDEX_CONSTRAINT_GLOB      66\n#define SQLITE_INDEX_CONSTRAINT_REGEXP    67\n#define SQLITE_INDEX_CONSTRAINT_NE        68\n#define SQLITE_INDEX_CONSTRAINT_ISNOT     69\n#define SQLITE_INDEX_CONSTRAINT_ISNOTNULL 70\n#define SQLITE_INDEX_CONSTRAINT_ISNULL    71\n#define SQLITE_INDEX_CONSTRAINT_IS        72\n\n/*\n** CAPI3REF: Register A Virtual Table Implementation\n** METHOD: sqlite3\n**\n** ^These routines are used to register a new [virtual table module] name.\n** ^Module names must be registered before\n** creating a new [virtual table] using the module and before using a\n** preexisting [virtual table] for the module.\n**\n** ^The module name is registered on the [database connection] specified\n** by the first parameter.  ^The name of the module is given by the \n** second parameter.  ^The third parameter is a pointer to\n** the implementation of the [virtual table module].   ^The fourth\n** parameter is an arbitrary client data pointer that is passed through\n** into the [xCreate] and [xConnect] methods of the virtual table module\n** when a new virtual table is be being created or reinitialized.\n**\n** ^The sqlite3_create_module_v2() interface has a fifth parameter which\n** is a pointer to a destructor for the pClientData.  ^SQLite will\n** invoke the destructor function (if it is not NULL) when SQLite\n** no longer needs the pClientData pointer.  ^The destructor will also\n** be invoked if the call to sqlite3_create_module_v2() fails.\n** ^The sqlite3_create_module()\n** interface is equivalent to sqlite3_create_module_v2() with a NULL\n** destructor.\n*/\nSQLITE_API int sqlite3_create_module(\n  sqlite3 *db,               /* SQLite connection to register module with */\n  const char *zName,         /* Name of the module */\n  const sqlite3_module *p,   /* Methods for the module */\n  void *pClientData          /* Client data for xCreate/xConnect */\n);\nSQLITE_API int sqlite3_create_module_v2(\n  sqlite3 *db,               /* SQLite connection to register module with */\n  const char *zName,         /* Name of the module */\n  const sqlite3_module *p,   /* Methods for the module */\n  void *pClientData,         /* Client data for xCreate/xConnect */\n  void(*xDestroy)(void*)     /* Module destructor function */\n);\n\n/*\n** CAPI3REF: Virtual Table Instance Object\n** KEYWORDS: sqlite3_vtab\n**\n** Every [virtual table module] implementation uses a subclass\n** of this object to describe a particular instance\n** of the [virtual table].  Each subclass will\n** be tailored to the specific needs of the module implementation.\n** The purpose of this superclass is to define certain fields that are\n** common to all module implementations.\n**\n** ^Virtual tables methods can set an error message by assigning a\n** string obtained from [sqlite3_mprintf()] to zErrMsg.  The method should\n** take care that any prior string is freed by a call to [sqlite3_free()]\n** prior to assigning a new string to zErrMsg.  ^After the error message\n** is delivered up to the client application, the string will be automatically\n** freed by sqlite3_free() and the zErrMsg field will be zeroed.\n*/\nstruct sqlite3_vtab {\n  const sqlite3_module *pModule;  /* The module for this virtual table */\n  int nRef;                       /* Number of open cursors */\n  char *zErrMsg;                  /* Error message from sqlite3_mprintf() */\n  /* Virtual table implementations will typically add additional fields */\n};\n\n/*\n** CAPI3REF: Virtual Table Cursor Object\n** KEYWORDS: sqlite3_vtab_cursor {virtual table cursor}\n**\n** Every [virtual table module] implementation uses a subclass of the\n** following structure to describe cursors that point into the\n** [virtual table] and are used\n** to loop through the virtual table.  Cursors are created using the\n** [sqlite3_module.xOpen | xOpen] method of the module and are destroyed\n** by the [sqlite3_module.xClose | xClose] method.  Cursors are used\n** by the [xFilter], [xNext], [xEof], [xColumn], and [xRowid] methods\n** of the module.  Each module implementation will define\n** the content of a cursor structure to suit its own needs.\n**\n** This superclass exists in order to define fields of the cursor that\n** are common to all implementations.\n*/\nstruct sqlite3_vtab_cursor {\n  sqlite3_vtab *pVtab;      /* Virtual table of this cursor */\n  /* Virtual table implementations will typically add additional fields */\n};\n\n/*\n** CAPI3REF: Declare The Schema Of A Virtual Table\n**\n** ^The [xCreate] and [xConnect] methods of a\n** [virtual table module] call this interface\n** to declare the format (the names and datatypes of the columns) of\n** the virtual tables they implement.\n*/\nSQLITE_API int sqlite3_declare_vtab(sqlite3*, const char *zSQL);\n\n/*\n** CAPI3REF: Overload A Function For A Virtual Table\n** METHOD: sqlite3\n**\n** ^(Virtual tables can provide alternative implementations of functions\n** using the [xFindFunction] method of the [virtual table module].  \n** But global versions of those functions\n** must exist in order to be overloaded.)^\n**\n** ^(This API makes sure a global version of a function with a particular\n** name and number of parameters exists.  If no such function exists\n** before this API is called, a new function is created.)^  ^The implementation\n** of the new function always causes an exception to be thrown.  So\n** the new function is not good for anything by itself.  Its only\n** purpose is to be a placeholder function that can be overloaded\n** by a [virtual table].\n*/\nSQLITE_API int sqlite3_overload_function(sqlite3*, const char *zFuncName, int nArg);\n\n/*\n** The interface to the virtual-table mechanism defined above (back up\n** to a comment remarkably similar to this one) is currently considered\n** to be experimental.  The interface might change in incompatible ways.\n** If this is a problem for you, do not use the interface at this time.\n**\n** When the virtual-table mechanism stabilizes, we will declare the\n** interface fixed, support it indefinitely, and remove this comment.\n*/\n\n/*\n** CAPI3REF: A Handle To An Open BLOB\n** KEYWORDS: {BLOB handle} {BLOB handles}\n**\n** An instance of this object represents an open BLOB on which\n** [sqlite3_blob_open | incremental BLOB I/O] can be performed.\n** ^Objects of this type are created by [sqlite3_blob_open()]\n** and destroyed by [sqlite3_blob_close()].\n** ^The [sqlite3_blob_read()] and [sqlite3_blob_write()] interfaces\n** can be used to read or write small subsections of the BLOB.\n** ^The [sqlite3_blob_bytes()] interface returns the size of the BLOB in bytes.\n*/\ntypedef struct sqlite3_blob sqlite3_blob;\n\n/*\n** CAPI3REF: Open A BLOB For Incremental I/O\n** METHOD: sqlite3\n** CONSTRUCTOR: sqlite3_blob\n**\n** ^(This interfaces opens a [BLOB handle | handle] to the BLOB located\n** in row iRow, column zColumn, table zTable in database zDb;\n** in other words, the same BLOB that would be selected by:\n**\n** <pre>\n**     SELECT zColumn FROM zDb.zTable WHERE [rowid] = iRow;\n** </pre>)^\n**\n** ^(Parameter zDb is not the filename that contains the database, but \n** rather the symbolic name of the database. For attached databases, this is\n** the name that appears after the AS keyword in the [ATTACH] statement.\n** For the main database file, the database name is \"main\". For TEMP\n** tables, the database name is \"temp\".)^\n**\n** ^If the flags parameter is non-zero, then the BLOB is opened for read\n** and write access. ^If the flags parameter is zero, the BLOB is opened for\n** read-only access.\n**\n** ^(On success, [SQLITE_OK] is returned and the new [BLOB handle] is stored\n** in *ppBlob. Otherwise an [error code] is returned and, unless the error\n** code is SQLITE_MISUSE, *ppBlob is set to NULL.)^ ^This means that, provided\n** the API is not misused, it is always safe to call [sqlite3_blob_close()] \n** on *ppBlob after this function it returns.\n**\n** This function fails with SQLITE_ERROR if any of the following are true:\n** <ul>\n**   <li> ^(Database zDb does not exist)^, \n**   <li> ^(Table zTable does not exist within database zDb)^, \n**   <li> ^(Table zTable is a WITHOUT ROWID table)^, \n**   <li> ^(Column zColumn does not exist)^,\n**   <li> ^(Row iRow is not present in the table)^,\n**   <li> ^(The specified column of row iRow contains a value that is not\n**         a TEXT or BLOB value)^,\n**   <li> ^(Column zColumn is part of an index, PRIMARY KEY or UNIQUE \n**         constraint and the blob is being opened for read/write access)^,\n**   <li> ^([foreign key constraints | Foreign key constraints] are enabled, \n**         column zColumn is part of a [child key] definition and the blob is\n**         being opened for read/write access)^.\n** </ul>\n**\n** ^Unless it returns SQLITE_MISUSE, this function sets the \n** [database connection] error code and message accessible via \n** [sqlite3_errcode()] and [sqlite3_errmsg()] and related functions. \n**\n** A BLOB referenced by sqlite3_blob_open() may be read using the\n** [sqlite3_blob_read()] interface and modified by using\n** [sqlite3_blob_write()].  The [BLOB handle] can be moved to a\n** different row of the same table using the [sqlite3_blob_reopen()]\n** interface.  However, the column, table, or database of a [BLOB handle]\n** cannot be changed after the [BLOB handle] is opened.\n**\n** ^(If the row that a BLOB handle points to is modified by an\n** [UPDATE], [DELETE], or by [ON CONFLICT] side-effects\n** then the BLOB handle is marked as \"expired\".\n** This is true if any column of the row is changed, even a column\n** other than the one the BLOB handle is open on.)^\n** ^Calls to [sqlite3_blob_read()] and [sqlite3_blob_write()] for\n** an expired BLOB handle fail with a return code of [SQLITE_ABORT].\n** ^(Changes written into a BLOB prior to the BLOB expiring are not\n** rolled back by the expiration of the BLOB.  Such changes will eventually\n** commit if the transaction continues to completion.)^\n**\n** ^Use the [sqlite3_blob_bytes()] interface to determine the size of\n** the opened blob.  ^The size of a blob may not be changed by this\n** interface.  Use the [UPDATE] SQL command to change the size of a\n** blob.\n**\n** ^The [sqlite3_bind_zeroblob()] and [sqlite3_result_zeroblob()] interfaces\n** and the built-in [zeroblob] SQL function may be used to create a \n** zero-filled blob to read or write using the incremental-blob interface.\n**\n** To avoid a resource leak, every open [BLOB handle] should eventually\n** be released by a call to [sqlite3_blob_close()].\n**\n** See also: [sqlite3_blob_close()],\n** [sqlite3_blob_reopen()], [sqlite3_blob_read()],\n** [sqlite3_blob_bytes()], [sqlite3_blob_write()].\n*/\nSQLITE_API int sqlite3_blob_open(\n  sqlite3*,\n  const char *zDb,\n  const char *zTable,\n  const char *zColumn,\n  sqlite3_int64 iRow,\n  int flags,\n  sqlite3_blob **ppBlob\n);\n\n/*\n** CAPI3REF: Move a BLOB Handle to a New Row\n** METHOD: sqlite3_blob\n**\n** ^This function is used to move an existing [BLOB handle] so that it points\n** to a different row of the same database table. ^The new row is identified\n** by the rowid value passed as the second argument. Only the row can be\n** changed. ^The database, table and column on which the blob handle is open\n** remain the same. Moving an existing [BLOB handle] to a new row is\n** faster than closing the existing handle and opening a new one.\n**\n** ^(The new row must meet the same criteria as for [sqlite3_blob_open()] -\n** it must exist and there must be either a blob or text value stored in\n** the nominated column.)^ ^If the new row is not present in the table, or if\n** it does not contain a blob or text value, or if another error occurs, an\n** SQLite error code is returned and the blob handle is considered aborted.\n** ^All subsequent calls to [sqlite3_blob_read()], [sqlite3_blob_write()] or\n** [sqlite3_blob_reopen()] on an aborted blob handle immediately return\n** SQLITE_ABORT. ^Calling [sqlite3_blob_bytes()] on an aborted blob handle\n** always returns zero.\n**\n** ^This function sets the database handle error code and message.\n*/\nSQLITE_API int sqlite3_blob_reopen(sqlite3_blob *, sqlite3_int64);\n\n/*\n** CAPI3REF: Close A BLOB Handle\n** DESTRUCTOR: sqlite3_blob\n**\n** ^This function closes an open [BLOB handle]. ^(The BLOB handle is closed\n** unconditionally.  Even if this routine returns an error code, the \n** handle is still closed.)^\n**\n** ^If the blob handle being closed was opened for read-write access, and if\n** the database is in auto-commit mode and there are no other open read-write\n** blob handles or active write statements, the current transaction is\n** committed. ^If an error occurs while committing the transaction, an error\n** code is returned and the transaction rolled back.\n**\n** Calling this function with an argument that is not a NULL pointer or an\n** open blob handle results in undefined behaviour. ^Calling this routine \n** with a null pointer (such as would be returned by a failed call to \n** [sqlite3_blob_open()]) is a harmless no-op. ^Otherwise, if this function\n** is passed a valid open blob handle, the values returned by the \n** sqlite3_errcode() and sqlite3_errmsg() functions are set before returning.\n*/\nSQLITE_API int sqlite3_blob_close(sqlite3_blob *);\n\n/*\n** CAPI3REF: Return The Size Of An Open BLOB\n** METHOD: sqlite3_blob\n**\n** ^Returns the size in bytes of the BLOB accessible via the \n** successfully opened [BLOB handle] in its only argument.  ^The\n** incremental blob I/O routines can only read or overwriting existing\n** blob content; they cannot change the size of a blob.\n**\n** This routine only works on a [BLOB handle] which has been created\n** by a prior successful call to [sqlite3_blob_open()] and which has not\n** been closed by [sqlite3_blob_close()].  Passing any other pointer in\n** to this routine results in undefined and probably undesirable behavior.\n*/\nSQLITE_API int sqlite3_blob_bytes(sqlite3_blob *);\n\n/*\n** CAPI3REF: Read Data From A BLOB Incrementally\n** METHOD: sqlite3_blob\n**\n** ^(This function is used to read data from an open [BLOB handle] into a\n** caller-supplied buffer. N bytes of data are copied into buffer Z\n** from the open BLOB, starting at offset iOffset.)^\n**\n** ^If offset iOffset is less than N bytes from the end of the BLOB,\n** [SQLITE_ERROR] is returned and no data is read.  ^If N or iOffset is\n** less than zero, [SQLITE_ERROR] is returned and no data is read.\n** ^The size of the blob (and hence the maximum value of N+iOffset)\n** can be determined using the [sqlite3_blob_bytes()] interface.\n**\n** ^An attempt to read from an expired [BLOB handle] fails with an\n** error code of [SQLITE_ABORT].\n**\n** ^(On success, sqlite3_blob_read() returns SQLITE_OK.\n** Otherwise, an [error code] or an [extended error code] is returned.)^\n**\n** This routine only works on a [BLOB handle] which has been created\n** by a prior successful call to [sqlite3_blob_open()] and which has not\n** been closed by [sqlite3_blob_close()].  Passing any other pointer in\n** to this routine results in undefined and probably undesirable behavior.\n**\n** See also: [sqlite3_blob_write()].\n*/\nSQLITE_API int sqlite3_blob_read(sqlite3_blob *, void *Z, int N, int iOffset);\n\n/*\n** CAPI3REF: Write Data Into A BLOB Incrementally\n** METHOD: sqlite3_blob\n**\n** ^(This function is used to write data into an open [BLOB handle] from a\n** caller-supplied buffer. N bytes of data are copied from the buffer Z\n** into the open BLOB, starting at offset iOffset.)^\n**\n** ^(On success, sqlite3_blob_write() returns SQLITE_OK.\n** Otherwise, an  [error code] or an [extended error code] is returned.)^\n** ^Unless SQLITE_MISUSE is returned, this function sets the \n** [database connection] error code and message accessible via \n** [sqlite3_errcode()] and [sqlite3_errmsg()] and related functions. \n**\n** ^If the [BLOB handle] passed as the first argument was not opened for\n** writing (the flags parameter to [sqlite3_blob_open()] was zero),\n** this function returns [SQLITE_READONLY].\n**\n** This function may only modify the contents of the BLOB; it is\n** not possible to increase the size of a BLOB using this API.\n** ^If offset iOffset is less than N bytes from the end of the BLOB,\n** [SQLITE_ERROR] is returned and no data is written. The size of the \n** BLOB (and hence the maximum value of N+iOffset) can be determined \n** using the [sqlite3_blob_bytes()] interface. ^If N or iOffset are less \n** than zero [SQLITE_ERROR] is returned and no data is written.\n**\n** ^An attempt to write to an expired [BLOB handle] fails with an\n** error code of [SQLITE_ABORT].  ^Writes to the BLOB that occurred\n** before the [BLOB handle] expired are not rolled back by the\n** expiration of the handle, though of course those changes might\n** have been overwritten by the statement that expired the BLOB handle\n** or by other independent statements.\n**\n** This routine only works on a [BLOB handle] which has been created\n** by a prior successful call to [sqlite3_blob_open()] and which has not\n** been closed by [sqlite3_blob_close()].  Passing any other pointer in\n** to this routine results in undefined and probably undesirable behavior.\n**\n** See also: [sqlite3_blob_read()].\n*/\nSQLITE_API int sqlite3_blob_write(sqlite3_blob *, const void *z, int n, int iOffset);\n\n/*\n** CAPI3REF: Virtual File System Objects\n**\n** A virtual filesystem (VFS) is an [sqlite3_vfs] object\n** that SQLite uses to interact\n** with the underlying operating system.  Most SQLite builds come with a\n** single default VFS that is appropriate for the host computer.\n** New VFSes can be registered and existing VFSes can be unregistered.\n** The following interfaces are provided.\n**\n** ^The sqlite3_vfs_find() interface returns a pointer to a VFS given its name.\n** ^Names are case sensitive.\n** ^Names are zero-terminated UTF-8 strings.\n** ^If there is no match, a NULL pointer is returned.\n** ^If zVfsName is NULL then the default VFS is returned.\n**\n** ^New VFSes are registered with sqlite3_vfs_register().\n** ^Each new VFS becomes the default VFS if the makeDflt flag is set.\n** ^The same VFS can be registered multiple times without injury.\n** ^To make an existing VFS into the default VFS, register it again\n** with the makeDflt flag set.  If two different VFSes with the\n** same name are registered, the behavior is undefined.  If a\n** VFS is registered with a name that is NULL or an empty string,\n** then the behavior is undefined.\n**\n** ^Unregister a VFS with the sqlite3_vfs_unregister() interface.\n** ^(If the default VFS is unregistered, another VFS is chosen as\n** the default.  The choice for the new VFS is arbitrary.)^\n*/\nSQLITE_API sqlite3_vfs *sqlite3_vfs_find(const char *zVfsName);\nSQLITE_API int sqlite3_vfs_register(sqlite3_vfs*, int makeDflt);\nSQLITE_API int sqlite3_vfs_unregister(sqlite3_vfs*);\n\n/*\n** CAPI3REF: Mutexes\n**\n** The SQLite core uses these routines for thread\n** synchronization. Though they are intended for internal\n** use by SQLite, code that links against SQLite is\n** permitted to use any of these routines.\n**\n** The SQLite source code contains multiple implementations\n** of these mutex routines.  An appropriate implementation\n** is selected automatically at compile-time.  The following\n** implementations are available in the SQLite core:\n**\n** <ul>\n** <li>   SQLITE_MUTEX_PTHREADS\n** <li>   SQLITE_MUTEX_W32\n** <li>   SQLITE_MUTEX_NOOP\n** </ul>\n**\n** The SQLITE_MUTEX_NOOP implementation is a set of routines\n** that does no real locking and is appropriate for use in\n** a single-threaded application.  The SQLITE_MUTEX_PTHREADS and\n** SQLITE_MUTEX_W32 implementations are appropriate for use on Unix\n** and Windows.\n**\n** If SQLite is compiled with the SQLITE_MUTEX_APPDEF preprocessor\n** macro defined (with \"-DSQLITE_MUTEX_APPDEF=1\"), then no mutex\n** implementation is included with the library. In this case the\n** application must supply a custom mutex implementation using the\n** [SQLITE_CONFIG_MUTEX] option of the sqlite3_config() function\n** before calling sqlite3_initialize() or any other public sqlite3_\n** function that calls sqlite3_initialize().\n**\n** ^The sqlite3_mutex_alloc() routine allocates a new\n** mutex and returns a pointer to it. ^The sqlite3_mutex_alloc()\n** routine returns NULL if it is unable to allocate the requested\n** mutex.  The argument to sqlite3_mutex_alloc() must one of these\n** integer constants:\n**\n** <ul>\n** <li>  SQLITE_MUTEX_FAST\n** <li>  SQLITE_MUTEX_RECURSIVE\n** <li>  SQLITE_MUTEX_STATIC_MASTER\n** <li>  SQLITE_MUTEX_STATIC_MEM\n** <li>  SQLITE_MUTEX_STATIC_OPEN\n** <li>  SQLITE_MUTEX_STATIC_PRNG\n** <li>  SQLITE_MUTEX_STATIC_LRU\n** <li>  SQLITE_MUTEX_STATIC_PMEM\n** <li>  SQLITE_MUTEX_STATIC_APP1\n** <li>  SQLITE_MUTEX_STATIC_APP2\n** <li>  SQLITE_MUTEX_STATIC_APP3\n** <li>  SQLITE_MUTEX_STATIC_VFS1\n** <li>  SQLITE_MUTEX_STATIC_VFS2\n** <li>  SQLITE_MUTEX_STATIC_VFS3\n** </ul>\n**\n** ^The first two constants (SQLITE_MUTEX_FAST and SQLITE_MUTEX_RECURSIVE)\n** cause sqlite3_mutex_alloc() to create\n** a new mutex.  ^The new mutex is recursive when SQLITE_MUTEX_RECURSIVE\n** is used but not necessarily so when SQLITE_MUTEX_FAST is used.\n** The mutex implementation does not need to make a distinction\n** between SQLITE_MUTEX_RECURSIVE and SQLITE_MUTEX_FAST if it does\n** not want to.  SQLite will only request a recursive mutex in\n** cases where it really needs one.  If a faster non-recursive mutex\n** implementation is available on the host platform, the mutex subsystem\n** might return such a mutex in response to SQLITE_MUTEX_FAST.\n**\n** ^The other allowed parameters to sqlite3_mutex_alloc() (anything other\n** than SQLITE_MUTEX_FAST and SQLITE_MUTEX_RECURSIVE) each return\n** a pointer to a static preexisting mutex.  ^Nine static mutexes are\n** used by the current version of SQLite.  Future versions of SQLite\n** may add additional static mutexes.  Static mutexes are for internal\n** use by SQLite only.  Applications that use SQLite mutexes should\n** use only the dynamic mutexes returned by SQLITE_MUTEX_FAST or\n** SQLITE_MUTEX_RECURSIVE.\n**\n** ^Note that if one of the dynamic mutex parameters (SQLITE_MUTEX_FAST\n** or SQLITE_MUTEX_RECURSIVE) is used then sqlite3_mutex_alloc()\n** returns a different mutex on every call.  ^For the static\n** mutex types, the same mutex is returned on every call that has\n** the same type number.\n**\n** ^The sqlite3_mutex_free() routine deallocates a previously\n** allocated dynamic mutex.  Attempting to deallocate a static\n** mutex results in undefined behavior.\n**\n** ^The sqlite3_mutex_enter() and sqlite3_mutex_try() routines attempt\n** to enter a mutex.  ^If another thread is already within the mutex,\n** sqlite3_mutex_enter() will block and sqlite3_mutex_try() will return\n** SQLITE_BUSY.  ^The sqlite3_mutex_try() interface returns [SQLITE_OK]\n** upon successful entry.  ^(Mutexes created using\n** SQLITE_MUTEX_RECURSIVE can be entered multiple times by the same thread.\n** In such cases, the\n** mutex must be exited an equal number of times before another thread\n** can enter.)^  If the same thread tries to enter any mutex other\n** than an SQLITE_MUTEX_RECURSIVE more than once, the behavior is undefined.\n**\n** ^(Some systems (for example, Windows 95) do not support the operation\n** implemented by sqlite3_mutex_try().  On those systems, sqlite3_mutex_try()\n** will always return SQLITE_BUSY. The SQLite core only ever uses\n** sqlite3_mutex_try() as an optimization so this is acceptable \n** behavior.)^\n**\n** ^The sqlite3_mutex_leave() routine exits a mutex that was\n** previously entered by the same thread.   The behavior\n** is undefined if the mutex is not currently entered by the\n** calling thread or is not currently allocated.\n**\n** ^If the argument to sqlite3_mutex_enter(), sqlite3_mutex_try(), or\n** sqlite3_mutex_leave() is a NULL pointer, then all three routines\n** behave as no-ops.\n**\n** See also: [sqlite3_mutex_held()] and [sqlite3_mutex_notheld()].\n*/\nSQLITE_API sqlite3_mutex *sqlite3_mutex_alloc(int);\nSQLITE_API void sqlite3_mutex_free(sqlite3_mutex*);\nSQLITE_API void sqlite3_mutex_enter(sqlite3_mutex*);\nSQLITE_API int sqlite3_mutex_try(sqlite3_mutex*);\nSQLITE_API void sqlite3_mutex_leave(sqlite3_mutex*);\n\n/*\n** CAPI3REF: Mutex Methods Object\n**\n** An instance of this structure defines the low-level routines\n** used to allocate and use mutexes.\n**\n** Usually, the default mutex implementations provided by SQLite are\n** sufficient, however the application has the option of substituting a custom\n** implementation for specialized deployments or systems for which SQLite\n** does not provide a suitable implementation. In this case, the application\n** creates and populates an instance of this structure to pass\n** to sqlite3_config() along with the [SQLITE_CONFIG_MUTEX] option.\n** Additionally, an instance of this structure can be used as an\n** output variable when querying the system for the current mutex\n** implementation, using the [SQLITE_CONFIG_GETMUTEX] option.\n**\n** ^The xMutexInit method defined by this structure is invoked as\n** part of system initialization by the sqlite3_initialize() function.\n** ^The xMutexInit routine is called by SQLite exactly once for each\n** effective call to [sqlite3_initialize()].\n**\n** ^The xMutexEnd method defined by this structure is invoked as\n** part of system shutdown by the sqlite3_shutdown() function. The\n** implementation of this method is expected to release all outstanding\n** resources obtained by the mutex methods implementation, especially\n** those obtained by the xMutexInit method.  ^The xMutexEnd()\n** interface is invoked exactly once for each call to [sqlite3_shutdown()].\n**\n** ^(The remaining seven methods defined by this structure (xMutexAlloc,\n** xMutexFree, xMutexEnter, xMutexTry, xMutexLeave, xMutexHeld and\n** xMutexNotheld) implement the following interfaces (respectively):\n**\n** <ul>\n**   <li>  [sqlite3_mutex_alloc()] </li>\n**   <li>  [sqlite3_mutex_free()] </li>\n**   <li>  [sqlite3_mutex_enter()] </li>\n**   <li>  [sqlite3_mutex_try()] </li>\n**   <li>  [sqlite3_mutex_leave()] </li>\n**   <li>  [sqlite3_mutex_held()] </li>\n**   <li>  [sqlite3_mutex_notheld()] </li>\n** </ul>)^\n**\n** The only difference is that the public sqlite3_XXX functions enumerated\n** above silently ignore any invocations that pass a NULL pointer instead\n** of a valid mutex handle. The implementations of the methods defined\n** by this structure are not required to handle this case, the results\n** of passing a NULL pointer instead of a valid mutex handle are undefined\n** (i.e. it is acceptable to provide an implementation that segfaults if\n** it is passed a NULL pointer).\n**\n** The xMutexInit() method must be threadsafe.  It must be harmless to\n** invoke xMutexInit() multiple times within the same process and without\n** intervening calls to xMutexEnd().  Second and subsequent calls to\n** xMutexInit() must be no-ops.\n**\n** xMutexInit() must not use SQLite memory allocation ([sqlite3_malloc()]\n** and its associates).  Similarly, xMutexAlloc() must not use SQLite memory\n** allocation for a static mutex.  ^However xMutexAlloc() may use SQLite\n** memory allocation for a fast or recursive mutex.\n**\n** ^SQLite will invoke the xMutexEnd() method when [sqlite3_shutdown()] is\n** called, but only if the prior call to xMutexInit returned SQLITE_OK.\n** If xMutexInit fails in any way, it is expected to clean up after itself\n** prior to returning.\n*/\ntypedef struct sqlite3_mutex_methods sqlite3_mutex_methods;\nstruct sqlite3_mutex_methods {\n  int (*xMutexInit)(void);\n  int (*xMutexEnd)(void);\n  sqlite3_mutex *(*xMutexAlloc)(int);\n  void (*xMutexFree)(sqlite3_mutex *);\n  void (*xMutexEnter)(sqlite3_mutex *);\n  int (*xMutexTry)(sqlite3_mutex *);\n  void (*xMutexLeave)(sqlite3_mutex *);\n  int (*xMutexHeld)(sqlite3_mutex *);\n  int (*xMutexNotheld)(sqlite3_mutex *);\n};\n\n/*\n** CAPI3REF: Mutex Verification Routines\n**\n** The sqlite3_mutex_held() and sqlite3_mutex_notheld() routines\n** are intended for use inside assert() statements.  The SQLite core\n** never uses these routines except inside an assert() and applications\n** are advised to follow the lead of the core.  The SQLite core only\n** provides implementations for these routines when it is compiled\n** with the SQLITE_DEBUG flag.  External mutex implementations\n** are only required to provide these routines if SQLITE_DEBUG is\n** defined and if NDEBUG is not defined.\n**\n** These routines should return true if the mutex in their argument\n** is held or not held, respectively, by the calling thread.\n**\n** The implementation is not required to provide versions of these\n** routines that actually work. If the implementation does not provide working\n** versions of these routines, it should at least provide stubs that always\n** return true so that one does not get spurious assertion failures.\n**\n** If the argument to sqlite3_mutex_held() is a NULL pointer then\n** the routine should return 1.   This seems counter-intuitive since\n** clearly the mutex cannot be held if it does not exist.  But\n** the reason the mutex does not exist is because the build is not\n** using mutexes.  And we do not want the assert() containing the\n** call to sqlite3_mutex_held() to fail, so a non-zero return is\n** the appropriate thing to do.  The sqlite3_mutex_notheld()\n** interface should also return 1 when given a NULL pointer.\n*/\n#ifndef NDEBUG\nSQLITE_API int sqlite3_mutex_held(sqlite3_mutex*);\nSQLITE_API int sqlite3_mutex_notheld(sqlite3_mutex*);\n#endif\n\n/*\n** CAPI3REF: Mutex Types\n**\n** The [sqlite3_mutex_alloc()] interface takes a single argument\n** which is one of these integer constants.\n**\n** The set of static mutexes may change from one SQLite release to the\n** next.  Applications that override the built-in mutex logic must be\n** prepared to accommodate additional static mutexes.\n*/\n#define SQLITE_MUTEX_FAST             0\n#define SQLITE_MUTEX_RECURSIVE        1\n#define SQLITE_MUTEX_STATIC_MASTER    2\n#define SQLITE_MUTEX_STATIC_MEM       3  /* sqlite3_malloc() */\n#define SQLITE_MUTEX_STATIC_MEM2      4  /* NOT USED */\n#define SQLITE_MUTEX_STATIC_OPEN      4  /* sqlite3BtreeOpen() */\n#define SQLITE_MUTEX_STATIC_PRNG      5  /* sqlite3_randomness() */\n#define SQLITE_MUTEX_STATIC_LRU       6  /* lru page list */\n#define SQLITE_MUTEX_STATIC_LRU2      7  /* NOT USED */\n#define SQLITE_MUTEX_STATIC_PMEM      7  /* sqlite3PageMalloc() */\n#define SQLITE_MUTEX_STATIC_APP1      8  /* For use by application */\n#define SQLITE_MUTEX_STATIC_APP2      9  /* For use by application */\n#define SQLITE_MUTEX_STATIC_APP3     10  /* For use by application */\n#define SQLITE_MUTEX_STATIC_VFS1     11  /* For use by built-in VFS */\n#define SQLITE_MUTEX_STATIC_VFS2     12  /* For use by extension VFS */\n#define SQLITE_MUTEX_STATIC_VFS3     13  /* For use by application VFS */\n\n/*\n** CAPI3REF: Retrieve the mutex for a database connection\n** METHOD: sqlite3\n**\n** ^This interface returns a pointer the [sqlite3_mutex] object that \n** serializes access to the [database connection] given in the argument\n** when the [threading mode] is Serialized.\n** ^If the [threading mode] is Single-thread or Multi-thread then this\n** routine returns a NULL pointer.\n*/\nSQLITE_API sqlite3_mutex *sqlite3_db_mutex(sqlite3*);\n\n/*\n** CAPI3REF: Low-Level Control Of Database Files\n** METHOD: sqlite3\n**\n** ^The [sqlite3_file_control()] interface makes a direct call to the\n** xFileControl method for the [sqlite3_io_methods] object associated\n** with a particular database identified by the second argument. ^The\n** name of the database is \"main\" for the main database or \"temp\" for the\n** TEMP database, or the name that appears after the AS keyword for\n** databases that are added using the [ATTACH] SQL command.\n** ^A NULL pointer can be used in place of \"main\" to refer to the\n** main database file.\n** ^The third and fourth parameters to this routine\n** are passed directly through to the second and third parameters of\n** the xFileControl method.  ^The return value of the xFileControl\n** method becomes the return value of this routine.\n**\n** ^The [SQLITE_FCNTL_FILE_POINTER] value for the op parameter causes\n** a pointer to the underlying [sqlite3_file] object to be written into\n** the space pointed to by the 4th parameter.  ^The [SQLITE_FCNTL_FILE_POINTER]\n** case is a short-circuit path which does not actually invoke the\n** underlying sqlite3_io_methods.xFileControl method.\n**\n** ^If the second parameter (zDbName) does not match the name of any\n** open database file, then SQLITE_ERROR is returned.  ^This error\n** code is not remembered and will not be recalled by [sqlite3_errcode()]\n** or [sqlite3_errmsg()].  The underlying xFileControl method might\n** also return SQLITE_ERROR.  There is no way to distinguish between\n** an incorrect zDbName and an SQLITE_ERROR return from the underlying\n** xFileControl method.\n**\n** See also: [file control opcodes]\n*/\nSQLITE_API int sqlite3_file_control(sqlite3*, const char *zDbName, int op, void*);\n\n/*\n** CAPI3REF: Testing Interface\n**\n** ^The sqlite3_test_control() interface is used to read out internal\n** state of SQLite and to inject faults into SQLite for testing\n** purposes.  ^The first parameter is an operation code that determines\n** the number, meaning, and operation of all subsequent parameters.\n**\n** This interface is not for use by applications.  It exists solely\n** for verifying the correct operation of the SQLite library.  Depending\n** on how the SQLite library is compiled, this interface might not exist.\n**\n** The details of the operation codes, their meanings, the parameters\n** they take, and what they do are all subject to change without notice.\n** Unlike most of the SQLite API, this function is not guaranteed to\n** operate consistently from one release to the next.\n*/\nSQLITE_API int sqlite3_test_control(int op, ...);\n\n/*\n** CAPI3REF: Testing Interface Operation Codes\n**\n** These constants are the valid operation code parameters used\n** as the first argument to [sqlite3_test_control()].\n**\n** These parameters and their meanings are subject to change\n** without notice.  These values are for testing purposes only.\n** Applications should not use any of these parameters or the\n** [sqlite3_test_control()] interface.\n*/\n#define SQLITE_TESTCTRL_FIRST                    5\n#define SQLITE_TESTCTRL_PRNG_SAVE                5\n#define SQLITE_TESTCTRL_PRNG_RESTORE             6\n#define SQLITE_TESTCTRL_PRNG_RESET               7\n#define SQLITE_TESTCTRL_BITVEC_TEST              8\n#define SQLITE_TESTCTRL_FAULT_INSTALL            9\n#define SQLITE_TESTCTRL_BENIGN_MALLOC_HOOKS     10\n#define SQLITE_TESTCTRL_PENDING_BYTE            11\n#define SQLITE_TESTCTRL_ASSERT                  12\n#define SQLITE_TESTCTRL_ALWAYS                  13\n#define SQLITE_TESTCTRL_RESERVE                 14\n#define SQLITE_TESTCTRL_OPTIMIZATIONS           15\n#define SQLITE_TESTCTRL_ISKEYWORD               16\n#define SQLITE_TESTCTRL_SCRATCHMALLOC           17  /* NOT USED */\n#define SQLITE_TESTCTRL_LOCALTIME_FAULT         18\n#define SQLITE_TESTCTRL_EXPLAIN_STMT            19  /* NOT USED */\n#define SQLITE_TESTCTRL_ONCE_RESET_THRESHOLD    19\n#define SQLITE_TESTCTRL_NEVER_CORRUPT           20\n#define SQLITE_TESTCTRL_VDBE_COVERAGE           21\n#define SQLITE_TESTCTRL_BYTEORDER               22\n#define SQLITE_TESTCTRL_ISINIT                  23\n#define SQLITE_TESTCTRL_SORTER_MMAP             24\n#define SQLITE_TESTCTRL_IMPOSTER                25\n#define SQLITE_TESTCTRL_PARSER_COVERAGE         26\n#define SQLITE_TESTCTRL_LAST                    26  /* Largest TESTCTRL */\n\n/*\n** CAPI3REF: SQLite Runtime Status\n**\n** ^These interfaces are used to retrieve runtime status information\n** about the performance of SQLite, and optionally to reset various\n** highwater marks.  ^The first argument is an integer code for\n** the specific parameter to measure.  ^(Recognized integer codes\n** are of the form [status parameters | SQLITE_STATUS_...].)^\n** ^The current value of the parameter is returned into *pCurrent.\n** ^The highest recorded value is returned in *pHighwater.  ^If the\n** resetFlag is true, then the highest record value is reset after\n** *pHighwater is written.  ^(Some parameters do not record the highest\n** value.  For those parameters\n** nothing is written into *pHighwater and the resetFlag is ignored.)^\n** ^(Other parameters record only the highwater mark and not the current\n** value.  For these latter parameters nothing is written into *pCurrent.)^\n**\n** ^The sqlite3_status() and sqlite3_status64() routines return\n** SQLITE_OK on success and a non-zero [error code] on failure.\n**\n** If either the current value or the highwater mark is too large to\n** be represented by a 32-bit integer, then the values returned by\n** sqlite3_status() are undefined.\n**\n** See also: [sqlite3_db_status()]\n*/\nSQLITE_API int sqlite3_status(int op, int *pCurrent, int *pHighwater, int resetFlag);\nSQLITE_API int sqlite3_status64(\n  int op,\n  sqlite3_int64 *pCurrent,\n  sqlite3_int64 *pHighwater,\n  int resetFlag\n);\n\n\n/*\n** CAPI3REF: Status Parameters\n** KEYWORDS: {status parameters}\n**\n** These integer constants designate various run-time status parameters\n** that can be returned by [sqlite3_status()].\n**\n** <dl>\n** [[SQLITE_STATUS_MEMORY_USED]] ^(<dt>SQLITE_STATUS_MEMORY_USED</dt>\n** <dd>This parameter is the current amount of memory checked out\n** using [sqlite3_malloc()], either directly or indirectly.  The\n** figure includes calls made to [sqlite3_malloc()] by the application\n** and internal memory usage by the SQLite library.  Auxiliary page-cache\n** memory controlled by [SQLITE_CONFIG_PAGECACHE] is not included in\n** this parameter.  The amount returned is the sum of the allocation\n** sizes as reported by the xSize method in [sqlite3_mem_methods].</dd>)^\n**\n** [[SQLITE_STATUS_MALLOC_SIZE]] ^(<dt>SQLITE_STATUS_MALLOC_SIZE</dt>\n** <dd>This parameter records the largest memory allocation request\n** handed to [sqlite3_malloc()] or [sqlite3_realloc()] (or their\n** internal equivalents).  Only the value returned in the\n** *pHighwater parameter to [sqlite3_status()] is of interest.  \n** The value written into the *pCurrent parameter is undefined.</dd>)^\n**\n** [[SQLITE_STATUS_MALLOC_COUNT]] ^(<dt>SQLITE_STATUS_MALLOC_COUNT</dt>\n** <dd>This parameter records the number of separate memory allocations\n** currently checked out.</dd>)^\n**\n** [[SQLITE_STATUS_PAGECACHE_USED]] ^(<dt>SQLITE_STATUS_PAGECACHE_USED</dt>\n** <dd>This parameter returns the number of pages used out of the\n** [pagecache memory allocator] that was configured using \n** [SQLITE_CONFIG_PAGECACHE].  The\n** value returned is in pages, not in bytes.</dd>)^\n**\n** [[SQLITE_STATUS_PAGECACHE_OVERFLOW]] \n** ^(<dt>SQLITE_STATUS_PAGECACHE_OVERFLOW</dt>\n** <dd>This parameter returns the number of bytes of page cache\n** allocation which could not be satisfied by the [SQLITE_CONFIG_PAGECACHE]\n** buffer and where forced to overflow to [sqlite3_malloc()].  The\n** returned value includes allocations that overflowed because they\n** where too large (they were larger than the \"sz\" parameter to\n** [SQLITE_CONFIG_PAGECACHE]) and allocations that overflowed because\n** no space was left in the page cache.</dd>)^\n**\n** [[SQLITE_STATUS_PAGECACHE_SIZE]] ^(<dt>SQLITE_STATUS_PAGECACHE_SIZE</dt>\n** <dd>This parameter records the largest memory allocation request\n** handed to [pagecache memory allocator].  Only the value returned in the\n** *pHighwater parameter to [sqlite3_status()] is of interest.  \n** The value written into the *pCurrent parameter is undefined.</dd>)^\n**\n** [[SQLITE_STATUS_SCRATCH_USED]] <dt>SQLITE_STATUS_SCRATCH_USED</dt>\n** <dd>No longer used.</dd>\n**\n** [[SQLITE_STATUS_SCRATCH_OVERFLOW]] ^(<dt>SQLITE_STATUS_SCRATCH_OVERFLOW</dt>\n** <dd>No longer used.</dd>\n**\n** [[SQLITE_STATUS_SCRATCH_SIZE]] <dt>SQLITE_STATUS_SCRATCH_SIZE</dt>\n** <dd>No longer used.</dd>\n**\n** [[SQLITE_STATUS_PARSER_STACK]] ^(<dt>SQLITE_STATUS_PARSER_STACK</dt>\n** <dd>The *pHighwater parameter records the deepest parser stack. \n** The *pCurrent value is undefined.  The *pHighwater value is only\n** meaningful if SQLite is compiled with [YYTRACKMAXSTACKDEPTH].</dd>)^\n** </dl>\n**\n** New status parameters may be added from time to time.\n*/\n#define SQLITE_STATUS_MEMORY_USED          0\n#define SQLITE_STATUS_PAGECACHE_USED       1\n#define SQLITE_STATUS_PAGECACHE_OVERFLOW   2\n#define SQLITE_STATUS_SCRATCH_USED         3  /* NOT USED */\n#define SQLITE_STATUS_SCRATCH_OVERFLOW     4  /* NOT USED */\n#define SQLITE_STATUS_MALLOC_SIZE          5\n#define SQLITE_STATUS_PARSER_STACK         6\n#define SQLITE_STATUS_PAGECACHE_SIZE       7\n#define SQLITE_STATUS_SCRATCH_SIZE         8  /* NOT USED */\n#define SQLITE_STATUS_MALLOC_COUNT         9\n\n/*\n** CAPI3REF: Database Connection Status\n** METHOD: sqlite3\n**\n** ^This interface is used to retrieve runtime status information \n** about a single [database connection].  ^The first argument is the\n** database connection object to be interrogated.  ^The second argument\n** is an integer constant, taken from the set of\n** [SQLITE_DBSTATUS options], that\n** determines the parameter to interrogate.  The set of \n** [SQLITE_DBSTATUS options] is likely\n** to grow in future releases of SQLite.\n**\n** ^The current value of the requested parameter is written into *pCur\n** and the highest instantaneous value is written into *pHiwtr.  ^If\n** the resetFlg is true, then the highest instantaneous value is\n** reset back down to the current value.\n**\n** ^The sqlite3_db_status() routine returns SQLITE_OK on success and a\n** non-zero [error code] on failure.\n**\n** See also: [sqlite3_status()] and [sqlite3_stmt_status()].\n*/\nSQLITE_API int sqlite3_db_status(sqlite3*, int op, int *pCur, int *pHiwtr, int resetFlg);\n\n/*\n** CAPI3REF: Status Parameters for database connections\n** KEYWORDS: {SQLITE_DBSTATUS options}\n**\n** These constants are the available integer \"verbs\" that can be passed as\n** the second argument to the [sqlite3_db_status()] interface.\n**\n** New verbs may be added in future releases of SQLite. Existing verbs\n** might be discontinued. Applications should check the return code from\n** [sqlite3_db_status()] to make sure that the call worked.\n** The [sqlite3_db_status()] interface will return a non-zero error code\n** if a discontinued or unsupported verb is invoked.\n**\n** <dl>\n** [[SQLITE_DBSTATUS_LOOKASIDE_USED]] ^(<dt>SQLITE_DBSTATUS_LOOKASIDE_USED</dt>\n** <dd>This parameter returns the number of lookaside memory slots currently\n** checked out.</dd>)^\n**\n** [[SQLITE_DBSTATUS_LOOKASIDE_HIT]] ^(<dt>SQLITE_DBSTATUS_LOOKASIDE_HIT</dt>\n** <dd>This parameter returns the number malloc attempts that were \n** satisfied using lookaside memory. Only the high-water value is meaningful;\n** the current value is always zero.)^\n**\n** [[SQLITE_DBSTATUS_LOOKASIDE_MISS_SIZE]]\n** ^(<dt>SQLITE_DBSTATUS_LOOKASIDE_MISS_SIZE</dt>\n** <dd>This parameter returns the number malloc attempts that might have\n** been satisfied using lookaside memory but failed due to the amount of\n** memory requested being larger than the lookaside slot size.\n** Only the high-water value is meaningful;\n** the current value is always zero.)^\n**\n** [[SQLITE_DBSTATUS_LOOKASIDE_MISS_FULL]]\n** ^(<dt>SQLITE_DBSTATUS_LOOKASIDE_MISS_FULL</dt>\n** <dd>This parameter returns the number malloc attempts that might have\n** been satisfied using lookaside memory but failed due to all lookaside\n** memory already being in use.\n** Only the high-water value is meaningful;\n** the current value is always zero.)^\n**\n** [[SQLITE_DBSTATUS_CACHE_USED]] ^(<dt>SQLITE_DBSTATUS_CACHE_USED</dt>\n** <dd>This parameter returns the approximate number of bytes of heap\n** memory used by all pager caches associated with the database connection.)^\n** ^The highwater mark associated with SQLITE_DBSTATUS_CACHE_USED is always 0.\n**\n** [[SQLITE_DBSTATUS_CACHE_USED_SHARED]] \n** ^(<dt>SQLITE_DBSTATUS_CACHE_USED_SHARED</dt>\n** <dd>This parameter is similar to DBSTATUS_CACHE_USED, except that if a\n** pager cache is shared between two or more connections the bytes of heap\n** memory used by that pager cache is divided evenly between the attached\n** connections.)^  In other words, if none of the pager caches associated\n** with the database connection are shared, this request returns the same\n** value as DBSTATUS_CACHE_USED. Or, if one or more or the pager caches are\n** shared, the value returned by this call will be smaller than that returned\n** by DBSTATUS_CACHE_USED. ^The highwater mark associated with\n** SQLITE_DBSTATUS_CACHE_USED_SHARED is always 0.\n**\n** [[SQLITE_DBSTATUS_SCHEMA_USED]] ^(<dt>SQLITE_DBSTATUS_SCHEMA_USED</dt>\n** <dd>This parameter returns the approximate number of bytes of heap\n** memory used to store the schema for all databases associated\n** with the connection - main, temp, and any [ATTACH]-ed databases.)^ \n** ^The full amount of memory used by the schemas is reported, even if the\n** schema memory is shared with other database connections due to\n** [shared cache mode] being enabled.\n** ^The highwater mark associated with SQLITE_DBSTATUS_SCHEMA_USED is always 0.\n**\n** [[SQLITE_DBSTATUS_STMT_USED]] ^(<dt>SQLITE_DBSTATUS_STMT_USED</dt>\n** <dd>This parameter returns the approximate number of bytes of heap\n** and lookaside memory used by all prepared statements associated with\n** the database connection.)^\n** ^The highwater mark associated with SQLITE_DBSTATUS_STMT_USED is always 0.\n** </dd>\n**\n** [[SQLITE_DBSTATUS_CACHE_HIT]] ^(<dt>SQLITE_DBSTATUS_CACHE_HIT</dt>\n** <dd>This parameter returns the number of pager cache hits that have\n** occurred.)^ ^The highwater mark associated with SQLITE_DBSTATUS_CACHE_HIT \n** is always 0.\n** </dd>\n**\n** [[SQLITE_DBSTATUS_CACHE_MISS]] ^(<dt>SQLITE_DBSTATUS_CACHE_MISS</dt>\n** <dd>This parameter returns the number of pager cache misses that have\n** occurred.)^ ^The highwater mark associated with SQLITE_DBSTATUS_CACHE_MISS \n** is always 0.\n** </dd>\n**\n** [[SQLITE_DBSTATUS_CACHE_WRITE]] ^(<dt>SQLITE_DBSTATUS_CACHE_WRITE</dt>\n** <dd>This parameter returns the number of dirty cache entries that have\n** been written to disk. Specifically, the number of pages written to the\n** wal file in wal mode databases, or the number of pages written to the\n** database file in rollback mode databases. Any pages written as part of\n** transaction rollback or database recovery operations are not included.\n** If an IO or other error occurs while writing a page to disk, the effect\n** on subsequent SQLITE_DBSTATUS_CACHE_WRITE requests is undefined.)^ ^The\n** highwater mark associated with SQLITE_DBSTATUS_CACHE_WRITE is always 0.\n** </dd>\n**\n** [[SQLITE_DBSTATUS_DEFERRED_FKS]] ^(<dt>SQLITE_DBSTATUS_DEFERRED_FKS</dt>\n** <dd>This parameter returns zero for the current value if and only if\n** all foreign key constraints (deferred or immediate) have been\n** resolved.)^  ^The highwater mark is always 0.\n** </dd>\n** </dl>\n*/\n#define SQLITE_DBSTATUS_LOOKASIDE_USED       0\n#define SQLITE_DBSTATUS_CACHE_USED           1\n#define SQLITE_DBSTATUS_SCHEMA_USED          2\n#define SQLITE_DBSTATUS_STMT_USED            3\n#define SQLITE_DBSTATUS_LOOKASIDE_HIT        4\n#define SQLITE_DBSTATUS_LOOKASIDE_MISS_SIZE  5\n#define SQLITE_DBSTATUS_LOOKASIDE_MISS_FULL  6\n#define SQLITE_DBSTATUS_CACHE_HIT            7\n#define SQLITE_DBSTATUS_CACHE_MISS           8\n#define SQLITE_DBSTATUS_CACHE_WRITE          9\n#define SQLITE_DBSTATUS_DEFERRED_FKS        10\n#define SQLITE_DBSTATUS_CACHE_USED_SHARED   11\n#define SQLITE_DBSTATUS_MAX                 11   /* Largest defined DBSTATUS */\n\n\n/*\n** CAPI3REF: Prepared Statement Status\n** METHOD: sqlite3_stmt\n**\n** ^(Each prepared statement maintains various\n** [SQLITE_STMTSTATUS counters] that measure the number\n** of times it has performed specific operations.)^  These counters can\n** be used to monitor the performance characteristics of the prepared\n** statements.  For example, if the number of table steps greatly exceeds\n** the number of table searches or result rows, that would tend to indicate\n** that the prepared statement is using a full table scan rather than\n** an index.  \n**\n** ^(This interface is used to retrieve and reset counter values from\n** a [prepared statement].  The first argument is the prepared statement\n** object to be interrogated.  The second argument\n** is an integer code for a specific [SQLITE_STMTSTATUS counter]\n** to be interrogated.)^\n** ^The current value of the requested counter is returned.\n** ^If the resetFlg is true, then the counter is reset to zero after this\n** interface call returns.\n**\n** See also: [sqlite3_status()] and [sqlite3_db_status()].\n*/\nSQLITE_API int sqlite3_stmt_status(sqlite3_stmt*, int op,int resetFlg);\n\n/*\n** CAPI3REF: Status Parameters for prepared statements\n** KEYWORDS: {SQLITE_STMTSTATUS counter} {SQLITE_STMTSTATUS counters}\n**\n** These preprocessor macros define integer codes that name counter\n** values associated with the [sqlite3_stmt_status()] interface.\n** The meanings of the various counters are as follows:\n**\n** <dl>\n** [[SQLITE_STMTSTATUS_FULLSCAN_STEP]] <dt>SQLITE_STMTSTATUS_FULLSCAN_STEP</dt>\n** <dd>^This is the number of times that SQLite has stepped forward in\n** a table as part of a full table scan.  Large numbers for this counter\n** may indicate opportunities for performance improvement through \n** careful use of indices.</dd>\n**\n** [[SQLITE_STMTSTATUS_SORT]] <dt>SQLITE_STMTSTATUS_SORT</dt>\n** <dd>^This is the number of sort operations that have occurred.\n** A non-zero value in this counter may indicate an opportunity to\n** improvement performance through careful use of indices.</dd>\n**\n** [[SQLITE_STMTSTATUS_AUTOINDEX]] <dt>SQLITE_STMTSTATUS_AUTOINDEX</dt>\n** <dd>^This is the number of rows inserted into transient indices that\n** were created automatically in order to help joins run faster.\n** A non-zero value in this counter may indicate an opportunity to\n** improvement performance by adding permanent indices that do not\n** need to be reinitialized each time the statement is run.</dd>\n**\n** [[SQLITE_STMTSTATUS_VM_STEP]] <dt>SQLITE_STMTSTATUS_VM_STEP</dt>\n** <dd>^This is the number of virtual machine operations executed\n** by the prepared statement if that number is less than or equal\n** to 2147483647.  The number of virtual machine operations can be \n** used as a proxy for the total work done by the prepared statement.\n** If the number of virtual machine operations exceeds 2147483647\n** then the value returned by this statement status code is undefined.\n**\n** [[SQLITE_STMTSTATUS_REPREPARE]] <dt>SQLITE_STMTSTATUS_REPREPARE</dt>\n** <dd>^This is the number of times that the prepare statement has been\n** automatically regenerated due to schema changes or change to \n** [bound parameters] that might affect the query plan.\n**\n** [[SQLITE_STMTSTATUS_RUN]] <dt>SQLITE_STMTSTATUS_RUN</dt>\n** <dd>^This is the number of times that the prepared statement has\n** been run.  A single \"run\" for the purposes of this counter is one\n** or more calls to [sqlite3_step()] followed by a call to [sqlite3_reset()].\n** The counter is incremented on the first [sqlite3_step()] call of each\n** cycle.\n**\n** [[SQLITE_STMTSTATUS_MEMUSED]] <dt>SQLITE_STMTSTATUS_MEMUSED</dt>\n** <dd>^This is the approximate number of bytes of heap memory\n** used to store the prepared statement.  ^This value is not actually\n** a counter, and so the resetFlg parameter to sqlite3_stmt_status()\n** is ignored when the opcode is SQLITE_STMTSTATUS_MEMUSED.\n** </dd>\n** </dl>\n*/\n#define SQLITE_STMTSTATUS_FULLSCAN_STEP     1\n#define SQLITE_STMTSTATUS_SORT              2\n#define SQLITE_STMTSTATUS_AUTOINDEX         3\n#define SQLITE_STMTSTATUS_VM_STEP           4\n#define SQLITE_STMTSTATUS_REPREPARE         5\n#define SQLITE_STMTSTATUS_RUN               6\n#define SQLITE_STMTSTATUS_MEMUSED           99\n\n/*\n** CAPI3REF: Custom Page Cache Object\n**\n** The sqlite3_pcache type is opaque.  It is implemented by\n** the pluggable module.  The SQLite core has no knowledge of\n** its size or internal structure and never deals with the\n** sqlite3_pcache object except by holding and passing pointers\n** to the object.\n**\n** See [sqlite3_pcache_methods2] for additional information.\n*/\ntypedef struct sqlite3_pcache sqlite3_pcache;\n\n/*\n** CAPI3REF: Custom Page Cache Object\n**\n** The sqlite3_pcache_page object represents a single page in the\n** page cache.  The page cache will allocate instances of this\n** object.  Various methods of the page cache use pointers to instances\n** of this object as parameters or as their return value.\n**\n** See [sqlite3_pcache_methods2] for additional information.\n*/\ntypedef struct sqlite3_pcache_page sqlite3_pcache_page;\nstruct sqlite3_pcache_page {\n  void *pBuf;        /* The content of the page */\n  void *pExtra;      /* Extra information associated with the page */\n};\n\n/*\n** CAPI3REF: Application Defined Page Cache.\n** KEYWORDS: {page cache}\n**\n** ^(The [sqlite3_config]([SQLITE_CONFIG_PCACHE2], ...) interface can\n** register an alternative page cache implementation by passing in an \n** instance of the sqlite3_pcache_methods2 structure.)^\n** In many applications, most of the heap memory allocated by \n** SQLite is used for the page cache.\n** By implementing a \n** custom page cache using this API, an application can better control\n** the amount of memory consumed by SQLite, the way in which \n** that memory is allocated and released, and the policies used to \n** determine exactly which parts of a database file are cached and for \n** how long.\n**\n** The alternative page cache mechanism is an\n** extreme measure that is only needed by the most demanding applications.\n** The built-in page cache is recommended for most uses.\n**\n** ^(The contents of the sqlite3_pcache_methods2 structure are copied to an\n** internal buffer by SQLite within the call to [sqlite3_config].  Hence\n** the application may discard the parameter after the call to\n** [sqlite3_config()] returns.)^\n**\n** [[the xInit() page cache method]]\n** ^(The xInit() method is called once for each effective \n** call to [sqlite3_initialize()])^\n** (usually only once during the lifetime of the process). ^(The xInit()\n** method is passed a copy of the sqlite3_pcache_methods2.pArg value.)^\n** The intent of the xInit() method is to set up global data structures \n** required by the custom page cache implementation. \n** ^(If the xInit() method is NULL, then the \n** built-in default page cache is used instead of the application defined\n** page cache.)^\n**\n** [[the xShutdown() page cache method]]\n** ^The xShutdown() method is called by [sqlite3_shutdown()].\n** It can be used to clean up \n** any outstanding resources before process shutdown, if required.\n** ^The xShutdown() method may be NULL.\n**\n** ^SQLite automatically serializes calls to the xInit method,\n** so the xInit method need not be threadsafe.  ^The\n** xShutdown method is only called from [sqlite3_shutdown()] so it does\n** not need to be threadsafe either.  All other methods must be threadsafe\n** in multithreaded applications.\n**\n** ^SQLite will never invoke xInit() more than once without an intervening\n** call to xShutdown().\n**\n** [[the xCreate() page cache methods]]\n** ^SQLite invokes the xCreate() method to construct a new cache instance.\n** SQLite will typically create one cache instance for each open database file,\n** though this is not guaranteed. ^The\n** first parameter, szPage, is the size in bytes of the pages that must\n** be allocated by the cache.  ^szPage will always a power of two.  ^The\n** second parameter szExtra is a number of bytes of extra storage \n** associated with each page cache entry.  ^The szExtra parameter will\n** a number less than 250.  SQLite will use the\n** extra szExtra bytes on each page to store metadata about the underlying\n** database page on disk.  The value passed into szExtra depends\n** on the SQLite version, the target platform, and how SQLite was compiled.\n** ^The third argument to xCreate(), bPurgeable, is true if the cache being\n** created will be used to cache database pages of a file stored on disk, or\n** false if it is used for an in-memory database. The cache implementation\n** does not have to do anything special based with the value of bPurgeable;\n** it is purely advisory.  ^On a cache where bPurgeable is false, SQLite will\n** never invoke xUnpin() except to deliberately delete a page.\n** ^In other words, calls to xUnpin() on a cache with bPurgeable set to\n** false will always have the \"discard\" flag set to true.  \n** ^Hence, a cache created with bPurgeable false will\n** never contain any unpinned pages.\n**\n** [[the xCachesize() page cache method]]\n** ^(The xCachesize() method may be called at any time by SQLite to set the\n** suggested maximum cache-size (number of pages stored by) the cache\n** instance passed as the first argument. This is the value configured using\n** the SQLite \"[PRAGMA cache_size]\" command.)^  As with the bPurgeable\n** parameter, the implementation is not required to do anything with this\n** value; it is advisory only.\n**\n** [[the xPagecount() page cache methods]]\n** The xPagecount() method must return the number of pages currently\n** stored in the cache, both pinned and unpinned.\n** \n** [[the xFetch() page cache methods]]\n** The xFetch() method locates a page in the cache and returns a pointer to \n** an sqlite3_pcache_page object associated with that page, or a NULL pointer.\n** The pBuf element of the returned sqlite3_pcache_page object will be a\n** pointer to a buffer of szPage bytes used to store the content of a \n** single database page.  The pExtra element of sqlite3_pcache_page will be\n** a pointer to the szExtra bytes of extra storage that SQLite has requested\n** for each entry in the page cache.\n**\n** The page to be fetched is determined by the key. ^The minimum key value\n** is 1.  After it has been retrieved using xFetch, the page is considered\n** to be \"pinned\".\n**\n** If the requested page is already in the page cache, then the page cache\n** implementation must return a pointer to the page buffer with its content\n** intact.  If the requested page is not already in the cache, then the\n** cache implementation should use the value of the createFlag\n** parameter to help it determined what action to take:\n**\n** <table border=1 width=85% align=center>\n** <tr><th> createFlag <th> Behavior when page is not already in cache\n** <tr><td> 0 <td> Do not allocate a new page.  Return NULL.\n** <tr><td> 1 <td> Allocate a new page if it easy and convenient to do so.\n**                 Otherwise return NULL.\n** <tr><td> 2 <td> Make every effort to allocate a new page.  Only return\n**                 NULL if allocating a new page is effectively impossible.\n** </table>\n**\n** ^(SQLite will normally invoke xFetch() with a createFlag of 0 or 1.  SQLite\n** will only use a createFlag of 2 after a prior call with a createFlag of 1\n** failed.)^  In between the to xFetch() calls, SQLite may\n** attempt to unpin one or more cache pages by spilling the content of\n** pinned pages to disk and synching the operating system disk cache.\n**\n** [[the xUnpin() page cache method]]\n** ^xUnpin() is called by SQLite with a pointer to a currently pinned page\n** as its second argument.  If the third parameter, discard, is non-zero,\n** then the page must be evicted from the cache.\n** ^If the discard parameter is\n** zero, then the page may be discarded or retained at the discretion of\n** page cache implementation. ^The page cache implementation\n** may choose to evict unpinned pages at any time.\n**\n** The cache must not perform any reference counting. A single \n** call to xUnpin() unpins the page regardless of the number of prior calls \n** to xFetch().\n**\n** [[the xRekey() page cache methods]]\n** The xRekey() method is used to change the key value associated with the\n** page passed as the second argument. If the cache\n** previously contains an entry associated with newKey, it must be\n** discarded. ^Any prior cache entry associated with newKey is guaranteed not\n** to be pinned.\n**\n** When SQLite calls the xTruncate() method, the cache must discard all\n** existing cache entries with page numbers (keys) greater than or equal\n** to the value of the iLimit parameter passed to xTruncate(). If any\n** of these pages are pinned, they are implicitly unpinned, meaning that\n** they can be safely discarded.\n**\n** [[the xDestroy() page cache method]]\n** ^The xDestroy() method is used to delete a cache allocated by xCreate().\n** All resources associated with the specified cache should be freed. ^After\n** calling the xDestroy() method, SQLite considers the [sqlite3_pcache*]\n** handle invalid, and will not use it with any other sqlite3_pcache_methods2\n** functions.\n**\n** [[the xShrink() page cache method]]\n** ^SQLite invokes the xShrink() method when it wants the page cache to\n** free up as much of heap memory as possible.  The page cache implementation\n** is not obligated to free any memory, but well-behaved implementations should\n** do their best.\n*/\ntypedef struct sqlite3_pcache_methods2 sqlite3_pcache_methods2;\nstruct sqlite3_pcache_methods2 {\n  int iVersion;\n  void *pArg;\n  int (*xInit)(void*);\n  void (*xShutdown)(void*);\n  sqlite3_pcache *(*xCreate)(int szPage, int szExtra, int bPurgeable);\n  void (*xCachesize)(sqlite3_pcache*, int nCachesize);\n  int (*xPagecount)(sqlite3_pcache*);\n  sqlite3_pcache_page *(*xFetch)(sqlite3_pcache*, unsigned key, int createFlag);\n  void (*xUnpin)(sqlite3_pcache*, sqlite3_pcache_page*, int discard);\n  void (*xRekey)(sqlite3_pcache*, sqlite3_pcache_page*, \n      unsigned oldKey, unsigned newKey);\n  void (*xTruncate)(sqlite3_pcache*, unsigned iLimit);\n  void (*xDestroy)(sqlite3_pcache*);\n  void (*xShrink)(sqlite3_pcache*);\n};\n\n/*\n** This is the obsolete pcache_methods object that has now been replaced\n** by sqlite3_pcache_methods2.  This object is not used by SQLite.  It is\n** retained in the header file for backwards compatibility only.\n*/\ntypedef struct sqlite3_pcache_methods sqlite3_pcache_methods;\nstruct sqlite3_pcache_methods {\n  void *pArg;\n  int (*xInit)(void*);\n  void (*xShutdown)(void*);\n  sqlite3_pcache *(*xCreate)(int szPage, int bPurgeable);\n  void (*xCachesize)(sqlite3_pcache*, int nCachesize);\n  int (*xPagecount)(sqlite3_pcache*);\n  void *(*xFetch)(sqlite3_pcache*, unsigned key, int createFlag);\n  void (*xUnpin)(sqlite3_pcache*, void*, int discard);\n  void (*xRekey)(sqlite3_pcache*, void*, unsigned oldKey, unsigned newKey);\n  void (*xTruncate)(sqlite3_pcache*, unsigned iLimit);\n  void (*xDestroy)(sqlite3_pcache*);\n};\n\n\n/*\n** CAPI3REF: Online Backup Object\n**\n** The sqlite3_backup object records state information about an ongoing\n** online backup operation.  ^The sqlite3_backup object is created by\n** a call to [sqlite3_backup_init()] and is destroyed by a call to\n** [sqlite3_backup_finish()].\n**\n** See Also: [Using the SQLite Online Backup API]\n*/\ntypedef struct sqlite3_backup sqlite3_backup;\n\n/*\n** CAPI3REF: Online Backup API.\n**\n** The backup API copies the content of one database into another.\n** It is useful either for creating backups of databases or\n** for copying in-memory databases to or from persistent files. \n**\n** See Also: [Using the SQLite Online Backup API]\n**\n** ^SQLite holds a write transaction open on the destination database file\n** for the duration of the backup operation.\n** ^The source database is read-locked only while it is being read;\n** it is not locked continuously for the entire backup operation.\n** ^Thus, the backup may be performed on a live source database without\n** preventing other database connections from\n** reading or writing to the source database while the backup is underway.\n** \n** ^(To perform a backup operation: \n**   <ol>\n**     <li><b>sqlite3_backup_init()</b> is called once to initialize the\n**         backup, \n**     <li><b>sqlite3_backup_step()</b> is called one or more times to transfer \n**         the data between the two databases, and finally\n**     <li><b>sqlite3_backup_finish()</b> is called to release all resources \n**         associated with the backup operation. \n**   </ol>)^\n** There should be exactly one call to sqlite3_backup_finish() for each\n** successful call to sqlite3_backup_init().\n**\n** [[sqlite3_backup_init()]] <b>sqlite3_backup_init()</b>\n**\n** ^The D and N arguments to sqlite3_backup_init(D,N,S,M) are the \n** [database connection] associated with the destination database \n** and the database name, respectively.\n** ^The database name is \"main\" for the main database, \"temp\" for the\n** temporary database, or the name specified after the AS keyword in\n** an [ATTACH] statement for an attached database.\n** ^The S and M arguments passed to \n** sqlite3_backup_init(D,N,S,M) identify the [database connection]\n** and database name of the source database, respectively.\n** ^The source and destination [database connections] (parameters S and D)\n** must be different or else sqlite3_backup_init(D,N,S,M) will fail with\n** an error.\n**\n** ^A call to sqlite3_backup_init() will fail, returning NULL, if \n** there is already a read or read-write transaction open on the \n** destination database.\n**\n** ^If an error occurs within sqlite3_backup_init(D,N,S,M), then NULL is\n** returned and an error code and error message are stored in the\n** destination [database connection] D.\n** ^The error code and message for the failed call to sqlite3_backup_init()\n** can be retrieved using the [sqlite3_errcode()], [sqlite3_errmsg()], and/or\n** [sqlite3_errmsg16()] functions.\n** ^A successful call to sqlite3_backup_init() returns a pointer to an\n** [sqlite3_backup] object.\n** ^The [sqlite3_backup] object may be used with the sqlite3_backup_step() and\n** sqlite3_backup_finish() functions to perform the specified backup \n** operation.\n**\n** [[sqlite3_backup_step()]] <b>sqlite3_backup_step()</b>\n**\n** ^Function sqlite3_backup_step(B,N) will copy up to N pages between \n** the source and destination databases specified by [sqlite3_backup] object B.\n** ^If N is negative, all remaining source pages are copied. \n** ^If sqlite3_backup_step(B,N) successfully copies N pages and there\n** are still more pages to be copied, then the function returns [SQLITE_OK].\n** ^If sqlite3_backup_step(B,N) successfully finishes copying all pages\n** from source to destination, then it returns [SQLITE_DONE].\n** ^If an error occurs while running sqlite3_backup_step(B,N),\n** then an [error code] is returned. ^As well as [SQLITE_OK] and\n** [SQLITE_DONE], a call to sqlite3_backup_step() may return [SQLITE_READONLY],\n** [SQLITE_NOMEM], [SQLITE_BUSY], [SQLITE_LOCKED], or an\n** [SQLITE_IOERR_ACCESS | SQLITE_IOERR_XXX] extended error code.\n**\n** ^(The sqlite3_backup_step() might return [SQLITE_READONLY] if\n** <ol>\n** <li> the destination database was opened read-only, or\n** <li> the destination database is using write-ahead-log journaling\n** and the destination and source page sizes differ, or\n** <li> the destination database is an in-memory database and the\n** destination and source page sizes differ.\n** </ol>)^\n**\n** ^If sqlite3_backup_step() cannot obtain a required file-system lock, then\n** the [sqlite3_busy_handler | busy-handler function]\n** is invoked (if one is specified). ^If the \n** busy-handler returns non-zero before the lock is available, then \n** [SQLITE_BUSY] is returned to the caller. ^In this case the call to\n** sqlite3_backup_step() can be retried later. ^If the source\n** [database connection]\n** is being used to write to the source database when sqlite3_backup_step()\n** is called, then [SQLITE_LOCKED] is returned immediately. ^Again, in this\n** case the call to sqlite3_backup_step() can be retried later on. ^(If\n** [SQLITE_IOERR_ACCESS | SQLITE_IOERR_XXX], [SQLITE_NOMEM], or\n** [SQLITE_READONLY] is returned, then \n** there is no point in retrying the call to sqlite3_backup_step(). These \n** errors are considered fatal.)^  The application must accept \n** that the backup operation has failed and pass the backup operation handle \n** to the sqlite3_backup_finish() to release associated resources.\n**\n** ^The first call to sqlite3_backup_step() obtains an exclusive lock\n** on the destination file. ^The exclusive lock is not released until either \n** sqlite3_backup_finish() is called or the backup operation is complete \n** and sqlite3_backup_step() returns [SQLITE_DONE].  ^Every call to\n** sqlite3_backup_step() obtains a [shared lock] on the source database that\n** lasts for the duration of the sqlite3_backup_step() call.\n** ^Because the source database is not locked between calls to\n** sqlite3_backup_step(), the source database may be modified mid-way\n** through the backup process.  ^If the source database is modified by an\n** external process or via a database connection other than the one being\n** used by the backup operation, then the backup will be automatically\n** restarted by the next call to sqlite3_backup_step(). ^If the source \n** database is modified by the using the same database connection as is used\n** by the backup operation, then the backup database is automatically\n** updated at the same time.\n**\n** [[sqlite3_backup_finish()]] <b>sqlite3_backup_finish()</b>\n**\n** When sqlite3_backup_step() has returned [SQLITE_DONE], or when the \n** application wishes to abandon the backup operation, the application\n** should destroy the [sqlite3_backup] by passing it to sqlite3_backup_finish().\n** ^The sqlite3_backup_finish() interfaces releases all\n** resources associated with the [sqlite3_backup] object. \n** ^If sqlite3_backup_step() has not yet returned [SQLITE_DONE], then any\n** active write-transaction on the destination database is rolled back.\n** The [sqlite3_backup] object is invalid\n** and may not be used following a call to sqlite3_backup_finish().\n**\n** ^The value returned by sqlite3_backup_finish is [SQLITE_OK] if no\n** sqlite3_backup_step() errors occurred, regardless or whether or not\n** sqlite3_backup_step() completed.\n** ^If an out-of-memory condition or IO error occurred during any prior\n** sqlite3_backup_step() call on the same [sqlite3_backup] object, then\n** sqlite3_backup_finish() returns the corresponding [error code].\n**\n** ^A return of [SQLITE_BUSY] or [SQLITE_LOCKED] from sqlite3_backup_step()\n** is not a permanent error and does not affect the return value of\n** sqlite3_backup_finish().\n**\n** [[sqlite3_backup_remaining()]] [[sqlite3_backup_pagecount()]]\n** <b>sqlite3_backup_remaining() and sqlite3_backup_pagecount()</b>\n**\n** ^The sqlite3_backup_remaining() routine returns the number of pages still\n** to be backed up at the conclusion of the most recent sqlite3_backup_step().\n** ^The sqlite3_backup_pagecount() routine returns the total number of pages\n** in the source database at the conclusion of the most recent\n** sqlite3_backup_step().\n** ^(The values returned by these functions are only updated by\n** sqlite3_backup_step(). If the source database is modified in a way that\n** changes the size of the source database or the number of pages remaining,\n** those changes are not reflected in the output of sqlite3_backup_pagecount()\n** and sqlite3_backup_remaining() until after the next\n** sqlite3_backup_step().)^\n**\n** <b>Concurrent Usage of Database Handles</b>\n**\n** ^The source [database connection] may be used by the application for other\n** purposes while a backup operation is underway or being initialized.\n** ^If SQLite is compiled and configured to support threadsafe database\n** connections, then the source database connection may be used concurrently\n** from within other threads.\n**\n** However, the application must guarantee that the destination \n** [database connection] is not passed to any other API (by any thread) after \n** sqlite3_backup_init() is called and before the corresponding call to\n** sqlite3_backup_finish().  SQLite does not currently check to see\n** if the application incorrectly accesses the destination [database connection]\n** and so no error code is reported, but the operations may malfunction\n** nevertheless.  Use of the destination database connection while a\n** backup is in progress might also also cause a mutex deadlock.\n**\n** If running in [shared cache mode], the application must\n** guarantee that the shared cache used by the destination database\n** is not accessed while the backup is running. In practice this means\n** that the application must guarantee that the disk file being \n** backed up to is not accessed by any connection within the process,\n** not just the specific connection that was passed to sqlite3_backup_init().\n**\n** The [sqlite3_backup] object itself is partially threadsafe. Multiple \n** threads may safely make multiple concurrent calls to sqlite3_backup_step().\n** However, the sqlite3_backup_remaining() and sqlite3_backup_pagecount()\n** APIs are not strictly speaking threadsafe. If they are invoked at the\n** same time as another thread is invoking sqlite3_backup_step() it is\n** possible that they return invalid values.\n*/\nSQLITE_API sqlite3_backup *sqlite3_backup_init(\n  sqlite3 *pDest,                        /* Destination database handle */\n  const char *zDestName,                 /* Destination database name */\n  sqlite3 *pSource,                      /* Source database handle */\n  const char *zSourceName                /* Source database name */\n);\nSQLITE_API int sqlite3_backup_step(sqlite3_backup *p, int nPage);\nSQLITE_API int sqlite3_backup_finish(sqlite3_backup *p);\nSQLITE_API int sqlite3_backup_remaining(sqlite3_backup *p);\nSQLITE_API int sqlite3_backup_pagecount(sqlite3_backup *p);\n\n/*\n** CAPI3REF: Unlock Notification\n** METHOD: sqlite3\n**\n** ^When running in shared-cache mode, a database operation may fail with\n** an [SQLITE_LOCKED] error if the required locks on the shared-cache or\n** individual tables within the shared-cache cannot be obtained. See\n** [SQLite Shared-Cache Mode] for a description of shared-cache locking. \n** ^This API may be used to register a callback that SQLite will invoke \n** when the connection currently holding the required lock relinquishes it.\n** ^This API is only available if the library was compiled with the\n** [SQLITE_ENABLE_UNLOCK_NOTIFY] C-preprocessor symbol defined.\n**\n** See Also: [Using the SQLite Unlock Notification Feature].\n**\n** ^Shared-cache locks are released when a database connection concludes\n** its current transaction, either by committing it or rolling it back. \n**\n** ^When a connection (known as the blocked connection) fails to obtain a\n** shared-cache lock and SQLITE_LOCKED is returned to the caller, the\n** identity of the database connection (the blocking connection) that\n** has locked the required resource is stored internally. ^After an \n** application receives an SQLITE_LOCKED error, it may call the\n** sqlite3_unlock_notify() method with the blocked connection handle as \n** the first argument to register for a callback that will be invoked\n** when the blocking connections current transaction is concluded. ^The\n** callback is invoked from within the [sqlite3_step] or [sqlite3_close]\n** call that concludes the blocking connections transaction.\n**\n** ^(If sqlite3_unlock_notify() is called in a multi-threaded application,\n** there is a chance that the blocking connection will have already\n** concluded its transaction by the time sqlite3_unlock_notify() is invoked.\n** If this happens, then the specified callback is invoked immediately,\n** from within the call to sqlite3_unlock_notify().)^\n**\n** ^If the blocked connection is attempting to obtain a write-lock on a\n** shared-cache table, and more than one other connection currently holds\n** a read-lock on the same table, then SQLite arbitrarily selects one of \n** the other connections to use as the blocking connection.\n**\n** ^(There may be at most one unlock-notify callback registered by a \n** blocked connection. If sqlite3_unlock_notify() is called when the\n** blocked connection already has a registered unlock-notify callback,\n** then the new callback replaces the old.)^ ^If sqlite3_unlock_notify() is\n** called with a NULL pointer as its second argument, then any existing\n** unlock-notify callback is canceled. ^The blocked connections \n** unlock-notify callback may also be canceled by closing the blocked\n** connection using [sqlite3_close()].\n**\n** The unlock-notify callback is not reentrant. If an application invokes\n** any sqlite3_xxx API functions from within an unlock-notify callback, a\n** crash or deadlock may be the result.\n**\n** ^Unless deadlock is detected (see below), sqlite3_unlock_notify() always\n** returns SQLITE_OK.\n**\n** <b>Callback Invocation Details</b>\n**\n** When an unlock-notify callback is registered, the application provides a \n** single void* pointer that is passed to the callback when it is invoked.\n** However, the signature of the callback function allows SQLite to pass\n** it an array of void* context pointers. The first argument passed to\n** an unlock-notify callback is a pointer to an array of void* pointers,\n** and the second is the number of entries in the array.\n**\n** When a blocking connections transaction is concluded, there may be\n** more than one blocked connection that has registered for an unlock-notify\n** callback. ^If two or more such blocked connections have specified the\n** same callback function, then instead of invoking the callback function\n** multiple times, it is invoked once with the set of void* context pointers\n** specified by the blocked connections bundled together into an array.\n** This gives the application an opportunity to prioritize any actions \n** related to the set of unblocked database connections.\n**\n** <b>Deadlock Detection</b>\n**\n** Assuming that after registering for an unlock-notify callback a \n** database waits for the callback to be issued before taking any further\n** action (a reasonable assumption), then using this API may cause the\n** application to deadlock. For example, if connection X is waiting for\n** connection Y's transaction to be concluded, and similarly connection\n** Y is waiting on connection X's transaction, then neither connection\n** will proceed and the system may remain deadlocked indefinitely.\n**\n** To avoid this scenario, the sqlite3_unlock_notify() performs deadlock\n** detection. ^If a given call to sqlite3_unlock_notify() would put the\n** system in a deadlocked state, then SQLITE_LOCKED is returned and no\n** unlock-notify callback is registered. The system is said to be in\n** a deadlocked state if connection A has registered for an unlock-notify\n** callback on the conclusion of connection B's transaction, and connection\n** B has itself registered for an unlock-notify callback when connection\n** A's transaction is concluded. ^Indirect deadlock is also detected, so\n** the system is also considered to be deadlocked if connection B has\n** registered for an unlock-notify callback on the conclusion of connection\n** C's transaction, where connection C is waiting on connection A. ^Any\n** number of levels of indirection are allowed.\n**\n** <b>The \"DROP TABLE\" Exception</b>\n**\n** When a call to [sqlite3_step()] returns SQLITE_LOCKED, it is almost \n** always appropriate to call sqlite3_unlock_notify(). There is however,\n** one exception. When executing a \"DROP TABLE\" or \"DROP INDEX\" statement,\n** SQLite checks if there are any currently executing SELECT statements\n** that belong to the same connection. If there are, SQLITE_LOCKED is\n** returned. In this case there is no \"blocking connection\", so invoking\n** sqlite3_unlock_notify() results in the unlock-notify callback being\n** invoked immediately. If the application then re-attempts the \"DROP TABLE\"\n** or \"DROP INDEX\" query, an infinite loop might be the result.\n**\n** One way around this problem is to check the extended error code returned\n** by an sqlite3_step() call. ^(If there is a blocking connection, then the\n** extended error code is set to SQLITE_LOCKED_SHAREDCACHE. Otherwise, in\n** the special \"DROP TABLE/INDEX\" case, the extended error code is just \n** SQLITE_LOCKED.)^\n*/\nSQLITE_API int sqlite3_unlock_notify(\n  sqlite3 *pBlocked,                          /* Waiting connection */\n  void (*xNotify)(void **apArg, int nArg),    /* Callback function to invoke */\n  void *pNotifyArg                            /* Argument to pass to xNotify */\n);\n\n\n/*\n** CAPI3REF: String Comparison\n**\n** ^The [sqlite3_stricmp()] and [sqlite3_strnicmp()] APIs allow applications\n** and extensions to compare the contents of two buffers containing UTF-8\n** strings in a case-independent fashion, using the same definition of \"case\n** independence\" that SQLite uses internally when comparing identifiers.\n*/\nSQLITE_API int sqlite3_stricmp(const char *, const char *);\nSQLITE_API int sqlite3_strnicmp(const char *, const char *, int);\n\n/*\n** CAPI3REF: String Globbing\n*\n** ^The [sqlite3_strglob(P,X)] interface returns zero if and only if\n** string X matches the [GLOB] pattern P.\n** ^The definition of [GLOB] pattern matching used in\n** [sqlite3_strglob(P,X)] is the same as for the \"X GLOB P\" operator in the\n** SQL dialect understood by SQLite.  ^The [sqlite3_strglob(P,X)] function\n** is case sensitive.\n**\n** Note that this routine returns zero on a match and non-zero if the strings\n** do not match, the same as [sqlite3_stricmp()] and [sqlite3_strnicmp()].\n**\n** See also: [sqlite3_strlike()].\n*/\nSQLITE_API int sqlite3_strglob(const char *zGlob, const char *zStr);\n\n/*\n** CAPI3REF: String LIKE Matching\n*\n** ^The [sqlite3_strlike(P,X,E)] interface returns zero if and only if\n** string X matches the [LIKE] pattern P with escape character E.\n** ^The definition of [LIKE] pattern matching used in\n** [sqlite3_strlike(P,X,E)] is the same as for the \"X LIKE P ESCAPE E\"\n** operator in the SQL dialect understood by SQLite.  ^For \"X LIKE P\" without\n** the ESCAPE clause, set the E parameter of [sqlite3_strlike(P,X,E)] to 0.\n** ^As with the LIKE operator, the [sqlite3_strlike(P,X,E)] function is case\n** insensitive - equivalent upper and lower case ASCII characters match\n** one another.\n**\n** ^The [sqlite3_strlike(P,X,E)] function matches Unicode characters, though\n** only ASCII characters are case folded.\n**\n** Note that this routine returns zero on a match and non-zero if the strings\n** do not match, the same as [sqlite3_stricmp()] and [sqlite3_strnicmp()].\n**\n** See also: [sqlite3_strglob()].\n*/\nSQLITE_API int sqlite3_strlike(const char *zGlob, const char *zStr, unsigned int cEsc);\n\n/*\n** CAPI3REF: Error Logging Interface\n**\n** ^The [sqlite3_log()] interface writes a message into the [error log]\n** established by the [SQLITE_CONFIG_LOG] option to [sqlite3_config()].\n** ^If logging is enabled, the zFormat string and subsequent arguments are\n** used with [sqlite3_snprintf()] to generate the final output string.\n**\n** The sqlite3_log() interface is intended for use by extensions such as\n** virtual tables, collating functions, and SQL functions.  While there is\n** nothing to prevent an application from calling sqlite3_log(), doing so\n** is considered bad form.\n**\n** The zFormat string must not be NULL.\n**\n** To avoid deadlocks and other threading problems, the sqlite3_log() routine\n** will not use dynamically allocated memory.  The log message is stored in\n** a fixed-length buffer on the stack.  If the log message is longer than\n** a few hundred characters, it will be truncated to the length of the\n** buffer.\n*/\nSQLITE_API void sqlite3_log(int iErrCode, const char *zFormat, ...);\n\n/*\n** CAPI3REF: Write-Ahead Log Commit Hook\n** METHOD: sqlite3\n**\n** ^The [sqlite3_wal_hook()] function is used to register a callback that\n** is invoked each time data is committed to a database in wal mode.\n**\n** ^(The callback is invoked by SQLite after the commit has taken place and \n** the associated write-lock on the database released)^, so the implementation \n** may read, write or [checkpoint] the database as required.\n**\n** ^The first parameter passed to the callback function when it is invoked\n** is a copy of the third parameter passed to sqlite3_wal_hook() when\n** registering the callback. ^The second is a copy of the database handle.\n** ^The third parameter is the name of the database that was written to -\n** either \"main\" or the name of an [ATTACH]-ed database. ^The fourth parameter\n** is the number of pages currently in the write-ahead log file,\n** including those that were just committed.\n**\n** The callback function should normally return [SQLITE_OK].  ^If an error\n** code is returned, that error will propagate back up through the\n** SQLite code base to cause the statement that provoked the callback\n** to report an error, though the commit will have still occurred. If the\n** callback returns [SQLITE_ROW] or [SQLITE_DONE], or if it returns a value\n** that does not correspond to any valid SQLite error code, the results\n** are undefined.\n**\n** A single database handle may have at most a single write-ahead log callback \n** registered at one time. ^Calling [sqlite3_wal_hook()] replaces any\n** previously registered write-ahead log callback. ^Note that the\n** [sqlite3_wal_autocheckpoint()] interface and the\n** [wal_autocheckpoint pragma] both invoke [sqlite3_wal_hook()] and will\n** overwrite any prior [sqlite3_wal_hook()] settings.\n*/\nSQLITE_API void *sqlite3_wal_hook(\n  sqlite3*, \n  int(*)(void *,sqlite3*,const char*,int),\n  void*\n);\n\n/*\n** CAPI3REF: Configure an auto-checkpoint\n** METHOD: sqlite3\n**\n** ^The [sqlite3_wal_autocheckpoint(D,N)] is a wrapper around\n** [sqlite3_wal_hook()] that causes any database on [database connection] D\n** to automatically [checkpoint]\n** after committing a transaction if there are N or\n** more frames in the [write-ahead log] file.  ^Passing zero or \n** a negative value as the nFrame parameter disables automatic\n** checkpoints entirely.\n**\n** ^The callback registered by this function replaces any existing callback\n** registered using [sqlite3_wal_hook()].  ^Likewise, registering a callback\n** using [sqlite3_wal_hook()] disables the automatic checkpoint mechanism\n** configured by this function.\n**\n** ^The [wal_autocheckpoint pragma] can be used to invoke this interface\n** from SQL.\n**\n** ^Checkpoints initiated by this mechanism are\n** [sqlite3_wal_checkpoint_v2|PASSIVE].\n**\n** ^Every new [database connection] defaults to having the auto-checkpoint\n** enabled with a threshold of 1000 or [SQLITE_DEFAULT_WAL_AUTOCHECKPOINT]\n** pages.  The use of this interface\n** is only necessary if the default setting is found to be suboptimal\n** for a particular application.\n*/\nSQLITE_API int sqlite3_wal_autocheckpoint(sqlite3 *db, int N);\n\n/*\n** CAPI3REF: Checkpoint a database\n** METHOD: sqlite3\n**\n** ^(The sqlite3_wal_checkpoint(D,X) is equivalent to\n** [sqlite3_wal_checkpoint_v2](D,X,[SQLITE_CHECKPOINT_PASSIVE],0,0).)^\n**\n** In brief, sqlite3_wal_checkpoint(D,X) causes the content in the \n** [write-ahead log] for database X on [database connection] D to be\n** transferred into the database file and for the write-ahead log to\n** be reset.  See the [checkpointing] documentation for addition\n** information.\n**\n** This interface used to be the only way to cause a checkpoint to\n** occur.  But then the newer and more powerful [sqlite3_wal_checkpoint_v2()]\n** interface was added.  This interface is retained for backwards\n** compatibility and as a convenience for applications that need to manually\n** start a callback but which do not need the full power (and corresponding\n** complication) of [sqlite3_wal_checkpoint_v2()].\n*/\nSQLITE_API int sqlite3_wal_checkpoint(sqlite3 *db, const char *zDb);\n\n/*\n** CAPI3REF: Checkpoint a database\n** METHOD: sqlite3\n**\n** ^(The sqlite3_wal_checkpoint_v2(D,X,M,L,C) interface runs a checkpoint\n** operation on database X of [database connection] D in mode M.  Status\n** information is written back into integers pointed to by L and C.)^\n** ^(The M parameter must be a valid [checkpoint mode]:)^\n**\n** <dl>\n** <dt>SQLITE_CHECKPOINT_PASSIVE<dd>\n**   ^Checkpoint as many frames as possible without waiting for any database \n**   readers or writers to finish, then sync the database file if all frames \n**   in the log were checkpointed. ^The [busy-handler callback]\n**   is never invoked in the SQLITE_CHECKPOINT_PASSIVE mode.  \n**   ^On the other hand, passive mode might leave the checkpoint unfinished\n**   if there are concurrent readers or writers.\n**\n** <dt>SQLITE_CHECKPOINT_FULL<dd>\n**   ^This mode blocks (it invokes the\n**   [sqlite3_busy_handler|busy-handler callback]) until there is no\n**   database writer and all readers are reading from the most recent database\n**   snapshot. ^It then checkpoints all frames in the log file and syncs the\n**   database file. ^This mode blocks new database writers while it is pending,\n**   but new database readers are allowed to continue unimpeded.\n**\n** <dt>SQLITE_CHECKPOINT_RESTART<dd>\n**   ^This mode works the same way as SQLITE_CHECKPOINT_FULL with the addition\n**   that after checkpointing the log file it blocks (calls the \n**   [busy-handler callback])\n**   until all readers are reading from the database file only. ^This ensures \n**   that the next writer will restart the log file from the beginning.\n**   ^Like SQLITE_CHECKPOINT_FULL, this mode blocks new\n**   database writer attempts while it is pending, but does not impede readers.\n**\n** <dt>SQLITE_CHECKPOINT_TRUNCATE<dd>\n**   ^This mode works the same way as SQLITE_CHECKPOINT_RESTART with the\n**   addition that it also truncates the log file to zero bytes just prior\n**   to a successful return.\n** </dl>\n**\n** ^If pnLog is not NULL, then *pnLog is set to the total number of frames in\n** the log file or to -1 if the checkpoint could not run because\n** of an error or because the database is not in [WAL mode]. ^If pnCkpt is not\n** NULL,then *pnCkpt is set to the total number of checkpointed frames in the\n** log file (including any that were already checkpointed before the function\n** was called) or to -1 if the checkpoint could not run due to an error or\n** because the database is not in WAL mode. ^Note that upon successful\n** completion of an SQLITE_CHECKPOINT_TRUNCATE, the log file will have been\n** truncated to zero bytes and so both *pnLog and *pnCkpt will be set to zero.\n**\n** ^All calls obtain an exclusive \"checkpoint\" lock on the database file. ^If\n** any other process is running a checkpoint operation at the same time, the \n** lock cannot be obtained and SQLITE_BUSY is returned. ^Even if there is a \n** busy-handler configured, it will not be invoked in this case.\n**\n** ^The SQLITE_CHECKPOINT_FULL, RESTART and TRUNCATE modes also obtain the \n** exclusive \"writer\" lock on the database file. ^If the writer lock cannot be\n** obtained immediately, and a busy-handler is configured, it is invoked and\n** the writer lock retried until either the busy-handler returns 0 or the lock\n** is successfully obtained. ^The busy-handler is also invoked while waiting for\n** database readers as described above. ^If the busy-handler returns 0 before\n** the writer lock is obtained or while waiting for database readers, the\n** checkpoint operation proceeds from that point in the same way as \n** SQLITE_CHECKPOINT_PASSIVE - checkpointing as many frames as possible \n** without blocking any further. ^SQLITE_BUSY is returned in this case.\n**\n** ^If parameter zDb is NULL or points to a zero length string, then the\n** specified operation is attempted on all WAL databases [attached] to \n** [database connection] db.  In this case the\n** values written to output parameters *pnLog and *pnCkpt are undefined. ^If \n** an SQLITE_BUSY error is encountered when processing one or more of the \n** attached WAL databases, the operation is still attempted on any remaining \n** attached databases and SQLITE_BUSY is returned at the end. ^If any other \n** error occurs while processing an attached database, processing is abandoned \n** and the error code is returned to the caller immediately. ^If no error \n** (SQLITE_BUSY or otherwise) is encountered while processing the attached \n** databases, SQLITE_OK is returned.\n**\n** ^If database zDb is the name of an attached database that is not in WAL\n** mode, SQLITE_OK is returned and both *pnLog and *pnCkpt set to -1. ^If\n** zDb is not NULL (or a zero length string) and is not the name of any\n** attached database, SQLITE_ERROR is returned to the caller.\n**\n** ^Unless it returns SQLITE_MISUSE,\n** the sqlite3_wal_checkpoint_v2() interface\n** sets the error information that is queried by\n** [sqlite3_errcode()] and [sqlite3_errmsg()].\n**\n** ^The [PRAGMA wal_checkpoint] command can be used to invoke this interface\n** from SQL.\n*/\nSQLITE_API int sqlite3_wal_checkpoint_v2(\n  sqlite3 *db,                    /* Database handle */\n  const char *zDb,                /* Name of attached database (or NULL) */\n  int eMode,                      /* SQLITE_CHECKPOINT_* value */\n  int *pnLog,                     /* OUT: Size of WAL log in frames */\n  int *pnCkpt                     /* OUT: Total number of frames checkpointed */\n);\n\n/*\n** CAPI3REF: Checkpoint Mode Values\n** KEYWORDS: {checkpoint mode}\n**\n** These constants define all valid values for the \"checkpoint mode\" passed\n** as the third parameter to the [sqlite3_wal_checkpoint_v2()] interface.\n** See the [sqlite3_wal_checkpoint_v2()] documentation for details on the\n** meaning of each of these checkpoint modes.\n*/\n#define SQLITE_CHECKPOINT_PASSIVE  0  /* Do as much as possible w/o blocking */\n#define SQLITE_CHECKPOINT_FULL     1  /* Wait for writers, then checkpoint */\n#define SQLITE_CHECKPOINT_RESTART  2  /* Like FULL but wait for for readers */\n#define SQLITE_CHECKPOINT_TRUNCATE 3  /* Like RESTART but also truncate WAL */\n\n/*\n** CAPI3REF: Virtual Table Interface Configuration\n**\n** This function may be called by either the [xConnect] or [xCreate] method\n** of a [virtual table] implementation to configure\n** various facets of the virtual table interface.\n**\n** If this interface is invoked outside the context of an xConnect or\n** xCreate virtual table method then the behavior is undefined.\n**\n** At present, there is only one option that may be configured using\n** this function. (See [SQLITE_VTAB_CONSTRAINT_SUPPORT].)  Further options\n** may be added in the future.\n*/\nSQLITE_API int sqlite3_vtab_config(sqlite3*, int op, ...);\n\n/*\n** CAPI3REF: Virtual Table Configuration Options\n**\n** These macros define the various options to the\n** [sqlite3_vtab_config()] interface that [virtual table] implementations\n** can use to customize and optimize their behavior.\n**\n** <dl>\n** <dt>SQLITE_VTAB_CONSTRAINT_SUPPORT\n** <dd>Calls of the form\n** [sqlite3_vtab_config](db,SQLITE_VTAB_CONSTRAINT_SUPPORT,X) are supported,\n** where X is an integer.  If X is zero, then the [virtual table] whose\n** [xCreate] or [xConnect] method invoked [sqlite3_vtab_config()] does not\n** support constraints.  In this configuration (which is the default) if\n** a call to the [xUpdate] method returns [SQLITE_CONSTRAINT], then the entire\n** statement is rolled back as if [ON CONFLICT | OR ABORT] had been\n** specified as part of the users SQL statement, regardless of the actual\n** ON CONFLICT mode specified.\n**\n** If X is non-zero, then the virtual table implementation guarantees\n** that if [xUpdate] returns [SQLITE_CONSTRAINT], it will do so before\n** any modifications to internal or persistent data structures have been made.\n** If the [ON CONFLICT] mode is ABORT, FAIL, IGNORE or ROLLBACK, SQLite \n** is able to roll back a statement or database transaction, and abandon\n** or continue processing the current SQL statement as appropriate. \n** If the ON CONFLICT mode is REPLACE and the [xUpdate] method returns\n** [SQLITE_CONSTRAINT], SQLite handles this as if the ON CONFLICT mode\n** had been ABORT.\n**\n** Virtual table implementations that are required to handle OR REPLACE\n** must do so within the [xUpdate] method. If a call to the \n** [sqlite3_vtab_on_conflict()] function indicates that the current ON \n** CONFLICT policy is REPLACE, the virtual table implementation should \n** silently replace the appropriate rows within the xUpdate callback and\n** return SQLITE_OK. Or, if this is not possible, it may return\n** SQLITE_CONSTRAINT, in which case SQLite falls back to OR ABORT \n** constraint handling.\n** </dl>\n*/\n#define SQLITE_VTAB_CONSTRAINT_SUPPORT 1\n\n/*\n** CAPI3REF: Determine The Virtual Table Conflict Policy\n**\n** This function may only be called from within a call to the [xUpdate] method\n** of a [virtual table] implementation for an INSERT or UPDATE operation. ^The\n** value returned is one of [SQLITE_ROLLBACK], [SQLITE_IGNORE], [SQLITE_FAIL],\n** [SQLITE_ABORT], or [SQLITE_REPLACE], according to the [ON CONFLICT] mode\n** of the SQL statement that triggered the call to the [xUpdate] method of the\n** [virtual table].\n*/\nSQLITE_API int sqlite3_vtab_on_conflict(sqlite3 *);\n\n/*\n** CAPI3REF: Determine If Virtual Table Column Access Is For UPDATE\n**\n** If the sqlite3_vtab_nochange(X) routine is called within the [xColumn]\n** method of a [virtual table], then it returns true if and only if the\n** column is being fetched as part of an UPDATE operation during which the\n** column value will not change.  Applications might use this to substitute\n** a lighter-weight value to return that the corresponding [xUpdate] method\n** understands as a \"no-change\" value.\n**\n** If the [xColumn] method calls sqlite3_vtab_nochange() and finds that\n** the column is not changed by the UPDATE statement, they the xColumn\n** method can optionally return without setting a result, without calling\n** any of the [sqlite3_result_int|sqlite3_result_xxxxx() interfaces].\n** In that case, [sqlite3_value_nochange(X)] will return true for the\n** same column in the [xUpdate] method.\n*/\nSQLITE_API int sqlite3_vtab_nochange(sqlite3_context*);\n\n/*\n** CAPI3REF: Determine The Collation For a Virtual Table Constraint\n**\n** This function may only be called from within a call to the [xBestIndex]\n** method of a [virtual table]. \n**\n** The first argument must be the sqlite3_index_info object that is the\n** first parameter to the xBestIndex() method. The second argument must be\n** an index into the aConstraint[] array belonging to the sqlite3_index_info\n** structure passed to xBestIndex. This function returns a pointer to a buffer \n** containing the name of the collation sequence for the corresponding\n** constraint.\n*/\nSQLITE_API SQLITE_EXPERIMENTAL const char *sqlite3_vtab_collation(sqlite3_index_info*,int);\n\n/*\n** CAPI3REF: Conflict resolution modes\n** KEYWORDS: {conflict resolution mode}\n**\n** These constants are returned by [sqlite3_vtab_on_conflict()] to\n** inform a [virtual table] implementation what the [ON CONFLICT] mode\n** is for the SQL statement being evaluated.\n**\n** Note that the [SQLITE_IGNORE] constant is also used as a potential\n** return value from the [sqlite3_set_authorizer()] callback and that\n** [SQLITE_ABORT] is also a [result code].\n*/\n#define SQLITE_ROLLBACK 1\n/* #define SQLITE_IGNORE 2 // Also used by sqlite3_authorizer() callback */\n#define SQLITE_FAIL     3\n/* #define SQLITE_ABORT 4  // Also an error code */\n#define SQLITE_REPLACE  5\n\n/*\n** CAPI3REF: Prepared Statement Scan Status Opcodes\n** KEYWORDS: {scanstatus options}\n**\n** The following constants can be used for the T parameter to the\n** [sqlite3_stmt_scanstatus(S,X,T,V)] interface.  Each constant designates a\n** different metric for sqlite3_stmt_scanstatus() to return.\n**\n** When the value returned to V is a string, space to hold that string is\n** managed by the prepared statement S and will be automatically freed when\n** S is finalized.\n**\n** <dl>\n** [[SQLITE_SCANSTAT_NLOOP]] <dt>SQLITE_SCANSTAT_NLOOP</dt>\n** <dd>^The [sqlite3_int64] variable pointed to by the T parameter will be\n** set to the total number of times that the X-th loop has run.</dd>\n**\n** [[SQLITE_SCANSTAT_NVISIT]] <dt>SQLITE_SCANSTAT_NVISIT</dt>\n** <dd>^The [sqlite3_int64] variable pointed to by the T parameter will be set\n** to the total number of rows examined by all iterations of the X-th loop.</dd>\n**\n** [[SQLITE_SCANSTAT_EST]] <dt>SQLITE_SCANSTAT_EST</dt>\n** <dd>^The \"double\" variable pointed to by the T parameter will be set to the\n** query planner's estimate for the average number of rows output from each\n** iteration of the X-th loop.  If the query planner's estimates was accurate,\n** then this value will approximate the quotient NVISIT/NLOOP and the\n** product of this value for all prior loops with the same SELECTID will\n** be the NLOOP value for the current loop.\n**\n** [[SQLITE_SCANSTAT_NAME]] <dt>SQLITE_SCANSTAT_NAME</dt>\n** <dd>^The \"const char *\" variable pointed to by the T parameter will be set\n** to a zero-terminated UTF-8 string containing the name of the index or table\n** used for the X-th loop.\n**\n** [[SQLITE_SCANSTAT_EXPLAIN]] <dt>SQLITE_SCANSTAT_EXPLAIN</dt>\n** <dd>^The \"const char *\" variable pointed to by the T parameter will be set\n** to a zero-terminated UTF-8 string containing the [EXPLAIN QUERY PLAN]\n** description for the X-th loop.\n**\n** [[SQLITE_SCANSTAT_SELECTID]] <dt>SQLITE_SCANSTAT_SELECT</dt>\n** <dd>^The \"int\" variable pointed to by the T parameter will be set to the\n** \"select-id\" for the X-th loop.  The select-id identifies which query or\n** subquery the loop is part of.  The main query has a select-id of zero.\n** The select-id is the same value as is output in the first column\n** of an [EXPLAIN QUERY PLAN] query.\n** </dl>\n*/\n#define SQLITE_SCANSTAT_NLOOP    0\n#define SQLITE_SCANSTAT_NVISIT   1\n#define SQLITE_SCANSTAT_EST      2\n#define SQLITE_SCANSTAT_NAME     3\n#define SQLITE_SCANSTAT_EXPLAIN  4\n#define SQLITE_SCANSTAT_SELECTID 5\n\n/*\n** CAPI3REF: Prepared Statement Scan Status\n** METHOD: sqlite3_stmt\n**\n** This interface returns information about the predicted and measured\n** performance for pStmt.  Advanced applications can use this\n** interface to compare the predicted and the measured performance and\n** issue warnings and/or rerun [ANALYZE] if discrepancies are found.\n**\n** Since this interface is expected to be rarely used, it is only\n** available if SQLite is compiled using the [SQLITE_ENABLE_STMT_SCANSTATUS]\n** compile-time option.\n**\n** The \"iScanStatusOp\" parameter determines which status information to return.\n** The \"iScanStatusOp\" must be one of the [scanstatus options] or the behavior\n** of this interface is undefined.\n** ^The requested measurement is written into a variable pointed to by\n** the \"pOut\" parameter.\n** Parameter \"idx\" identifies the specific loop to retrieve statistics for.\n** Loops are numbered starting from zero. ^If idx is out of range - less than\n** zero or greater than or equal to the total number of loops used to implement\n** the statement - a non-zero value is returned and the variable that pOut\n** points to is unchanged.\n**\n** ^Statistics might not be available for all loops in all statements. ^In cases\n** where there exist loops with no available statistics, this function behaves\n** as if the loop did not exist - it returns non-zero and leave the variable\n** that pOut points to unchanged.\n**\n** See also: [sqlite3_stmt_scanstatus_reset()]\n*/\nSQLITE_API int sqlite3_stmt_scanstatus(\n  sqlite3_stmt *pStmt,      /* Prepared statement for which info desired */\n  int idx,                  /* Index of loop to report on */\n  int iScanStatusOp,        /* Information desired.  SQLITE_SCANSTAT_* */\n  void *pOut                /* Result written here */\n);     \n\n/*\n** CAPI3REF: Zero Scan-Status Counters\n** METHOD: sqlite3_stmt\n**\n** ^Zero all [sqlite3_stmt_scanstatus()] related event counters.\n**\n** This API is only available if the library is built with pre-processor\n** symbol [SQLITE_ENABLE_STMT_SCANSTATUS] defined.\n*/\nSQLITE_API void sqlite3_stmt_scanstatus_reset(sqlite3_stmt*);\n\n/*\n** CAPI3REF: Flush caches to disk mid-transaction\n**\n** ^If a write-transaction is open on [database connection] D when the\n** [sqlite3_db_cacheflush(D)] interface invoked, any dirty\n** pages in the pager-cache that are not currently in use are written out \n** to disk. A dirty page may be in use if a database cursor created by an\n** active SQL statement is reading from it, or if it is page 1 of a database\n** file (page 1 is always \"in use\").  ^The [sqlite3_db_cacheflush(D)]\n** interface flushes caches for all schemas - \"main\", \"temp\", and\n** any [attached] databases.\n**\n** ^If this function needs to obtain extra database locks before dirty pages \n** can be flushed to disk, it does so. ^If those locks cannot be obtained \n** immediately and there is a busy-handler callback configured, it is invoked\n** in the usual manner. ^If the required lock still cannot be obtained, then\n** the database is skipped and an attempt made to flush any dirty pages\n** belonging to the next (if any) database. ^If any databases are skipped\n** because locks cannot be obtained, but no other error occurs, this\n** function returns SQLITE_BUSY.\n**\n** ^If any other error occurs while flushing dirty pages to disk (for\n** example an IO error or out-of-memory condition), then processing is\n** abandoned and an SQLite [error code] is returned to the caller immediately.\n**\n** ^Otherwise, if no error occurs, [sqlite3_db_cacheflush()] returns SQLITE_OK.\n**\n** ^This function does not set the database handle error code or message\n** returned by the [sqlite3_errcode()] and [sqlite3_errmsg()] functions.\n*/\nSQLITE_API int sqlite3_db_cacheflush(sqlite3*);\n\n/*\n** CAPI3REF: The pre-update hook.\n**\n** ^These interfaces are only available if SQLite is compiled using the\n** [SQLITE_ENABLE_PREUPDATE_HOOK] compile-time option.\n**\n** ^The [sqlite3_preupdate_hook()] interface registers a callback function\n** that is invoked prior to each [INSERT], [UPDATE], and [DELETE] operation\n** on a database table.\n** ^At most one preupdate hook may be registered at a time on a single\n** [database connection]; each call to [sqlite3_preupdate_hook()] overrides\n** the previous setting.\n** ^The preupdate hook is disabled by invoking [sqlite3_preupdate_hook()]\n** with a NULL pointer as the second parameter.\n** ^The third parameter to [sqlite3_preupdate_hook()] is passed through as\n** the first parameter to callbacks.\n**\n** ^The preupdate hook only fires for changes to real database tables; the\n** preupdate hook is not invoked for changes to [virtual tables] or to\n** system tables like sqlite_master or sqlite_stat1.\n**\n** ^The second parameter to the preupdate callback is a pointer to\n** the [database connection] that registered the preupdate hook.\n** ^The third parameter to the preupdate callback is one of the constants\n** [SQLITE_INSERT], [SQLITE_DELETE], or [SQLITE_UPDATE] to identify the\n** kind of update operation that is about to occur.\n** ^(The fourth parameter to the preupdate callback is the name of the\n** database within the database connection that is being modified.  This\n** will be \"main\" for the main database or \"temp\" for TEMP tables or \n** the name given after the AS keyword in the [ATTACH] statement for attached\n** databases.)^\n** ^The fifth parameter to the preupdate callback is the name of the\n** table that is being modified.\n**\n** For an UPDATE or DELETE operation on a [rowid table], the sixth\n** parameter passed to the preupdate callback is the initial [rowid] of the \n** row being modified or deleted. For an INSERT operation on a rowid table,\n** or any operation on a WITHOUT ROWID table, the value of the sixth \n** parameter is undefined. For an INSERT or UPDATE on a rowid table the\n** seventh parameter is the final rowid value of the row being inserted\n** or updated. The value of the seventh parameter passed to the callback\n** function is not defined for operations on WITHOUT ROWID tables, or for\n** INSERT operations on rowid tables.\n**\n** The [sqlite3_preupdate_old()], [sqlite3_preupdate_new()],\n** [sqlite3_preupdate_count()], and [sqlite3_preupdate_depth()] interfaces\n** provide additional information about a preupdate event. These routines\n** may only be called from within a preupdate callback.  Invoking any of\n** these routines from outside of a preupdate callback or with a\n** [database connection] pointer that is different from the one supplied\n** to the preupdate callback results in undefined and probably undesirable\n** behavior.\n**\n** ^The [sqlite3_preupdate_count(D)] interface returns the number of columns\n** in the row that is being inserted, updated, or deleted.\n**\n** ^The [sqlite3_preupdate_old(D,N,P)] interface writes into P a pointer to\n** a [protected sqlite3_value] that contains the value of the Nth column of\n** the table row before it is updated.  The N parameter must be between 0\n** and one less than the number of columns or the behavior will be\n** undefined. This must only be used within SQLITE_UPDATE and SQLITE_DELETE\n** preupdate callbacks; if it is used by an SQLITE_INSERT callback then the\n** behavior is undefined.  The [sqlite3_value] that P points to\n** will be destroyed when the preupdate callback returns.\n**\n** ^The [sqlite3_preupdate_new(D,N,P)] interface writes into P a pointer to\n** a [protected sqlite3_value] that contains the value of the Nth column of\n** the table row after it is updated.  The N parameter must be between 0\n** and one less than the number of columns or the behavior will be\n** undefined. This must only be used within SQLITE_INSERT and SQLITE_UPDATE\n** preupdate callbacks; if it is used by an SQLITE_DELETE callback then the\n** behavior is undefined.  The [sqlite3_value] that P points to\n** will be destroyed when the preupdate callback returns.\n**\n** ^The [sqlite3_preupdate_depth(D)] interface returns 0 if the preupdate\n** callback was invoked as a result of a direct insert, update, or delete\n** operation; or 1 for inserts, updates, or deletes invoked by top-level \n** triggers; or 2 for changes resulting from triggers called by top-level\n** triggers; and so forth.\n**\n** See also:  [sqlite3_update_hook()]\n*/\n#if defined(SQLITE_ENABLE_PREUPDATE_HOOK)\nSQLITE_API void *sqlite3_preupdate_hook(\n  sqlite3 *db,\n  void(*xPreUpdate)(\n    void *pCtx,                   /* Copy of third arg to preupdate_hook() */\n    sqlite3 *db,                  /* Database handle */\n    int op,                       /* SQLITE_UPDATE, DELETE or INSERT */\n    char const *zDb,              /* Database name */\n    char const *zName,            /* Table name */\n    sqlite3_int64 iKey1,          /* Rowid of row about to be deleted/updated */\n    sqlite3_int64 iKey2           /* New rowid value (for a rowid UPDATE) */\n  ),\n  void*\n);\nSQLITE_API int sqlite3_preupdate_old(sqlite3 *, int, sqlite3_value **);\nSQLITE_API int sqlite3_preupdate_count(sqlite3 *);\nSQLITE_API int sqlite3_preupdate_depth(sqlite3 *);\nSQLITE_API int sqlite3_preupdate_new(sqlite3 *, int, sqlite3_value **);\n#endif\n\n/*\n** CAPI3REF: Low-level system error code\n**\n** ^Attempt to return the underlying operating system error code or error\n** number that caused the most recent I/O error or failure to open a file.\n** The return value is OS-dependent.  For example, on unix systems, after\n** [sqlite3_open_v2()] returns [SQLITE_CANTOPEN], this interface could be\n** called to get back the underlying \"errno\" that caused the problem, such\n** as ENOSPC, EAUTH, EISDIR, and so forth.  \n*/\nSQLITE_API int sqlite3_system_errno(sqlite3*);\n\n/*\n** CAPI3REF: Database Snapshot\n** KEYWORDS: {snapshot} {sqlite3_snapshot}\n** EXPERIMENTAL\n**\n** An instance of the snapshot object records the state of a [WAL mode]\n** database for some specific point in history.\n**\n** In [WAL mode], multiple [database connections] that are open on the\n** same database file can each be reading a different historical version\n** of the database file.  When a [database connection] begins a read\n** transaction, that connection sees an unchanging copy of the database\n** as it existed for the point in time when the transaction first started.\n** Subsequent changes to the database from other connections are not seen\n** by the reader until a new read transaction is started.\n**\n** The sqlite3_snapshot object records state information about an historical\n** version of the database file so that it is possible to later open a new read\n** transaction that sees that historical version of the database rather than\n** the most recent version.\n**\n** The constructor for this object is [sqlite3_snapshot_get()].  The\n** [sqlite3_snapshot_open()] method causes a fresh read transaction to refer\n** to an historical snapshot (if possible).  The destructor for \n** sqlite3_snapshot objects is [sqlite3_snapshot_free()].\n*/\ntypedef struct sqlite3_snapshot {\n  unsigned char hidden[48];\n} sqlite3_snapshot;\n\n/*\n** CAPI3REF: Record A Database Snapshot\n** EXPERIMENTAL\n**\n** ^The [sqlite3_snapshot_get(D,S,P)] interface attempts to make a\n** new [sqlite3_snapshot] object that records the current state of\n** schema S in database connection D.  ^On success, the\n** [sqlite3_snapshot_get(D,S,P)] interface writes a pointer to the newly\n** created [sqlite3_snapshot] object into *P and returns SQLITE_OK.\n** If there is not already a read-transaction open on schema S when\n** this function is called, one is opened automatically. \n**\n** The following must be true for this function to succeed. If any of\n** the following statements are false when sqlite3_snapshot_get() is\n** called, SQLITE_ERROR is returned. The final value of *P is undefined\n** in this case. \n**\n** <ul>\n**   <li> The database handle must be in [autocommit mode].\n**\n**   <li> Schema S of [database connection] D must be a [WAL mode] database.\n**\n**   <li> There must not be a write transaction open on schema S of database\n**        connection D.\n**\n**   <li> One or more transactions must have been written to the current wal\n**        file since it was created on disk (by any connection). This means\n**        that a snapshot cannot be taken on a wal mode database with no wal \n**        file immediately after it is first opened. At least one transaction\n**        must be written to it first.\n** </ul>\n**\n** This function may also return SQLITE_NOMEM.  If it is called with the\n** database handle in autocommit mode but fails for some other reason, \n** whether or not a read transaction is opened on schema S is undefined.\n**\n** The [sqlite3_snapshot] object returned from a successful call to\n** [sqlite3_snapshot_get()] must be freed using [sqlite3_snapshot_free()]\n** to avoid a memory leak.\n**\n** The [sqlite3_snapshot_get()] interface is only available when the\n** SQLITE_ENABLE_SNAPSHOT compile-time option is used.\n*/\nSQLITE_API SQLITE_EXPERIMENTAL int sqlite3_snapshot_get(\n  sqlite3 *db,\n  const char *zSchema,\n  sqlite3_snapshot **ppSnapshot\n);\n\n/*\n** CAPI3REF: Start a read transaction on an historical snapshot\n** EXPERIMENTAL\n**\n** ^The [sqlite3_snapshot_open(D,S,P)] interface starts a\n** read transaction for schema S of\n** [database connection] D such that the read transaction\n** refers to historical [snapshot] P, rather than the most\n** recent change to the database.\n** ^The [sqlite3_snapshot_open()] interface returns SQLITE_OK on success\n** or an appropriate [error code] if it fails.\n**\n** ^In order to succeed, a call to [sqlite3_snapshot_open(D,S,P)] must be\n** the first operation following the [BEGIN] that takes the schema S\n** out of [autocommit mode].\n** ^In other words, schema S must not currently be in\n** a transaction for [sqlite3_snapshot_open(D,S,P)] to work, but the\n** database connection D must be out of [autocommit mode].\n** ^A [snapshot] will fail to open if it has been overwritten by a\n** [checkpoint].\n** ^(A call to [sqlite3_snapshot_open(D,S,P)] will fail if the\n** database connection D does not know that the database file for\n** schema S is in [WAL mode].  A database connection might not know\n** that the database file is in [WAL mode] if there has been no prior\n** I/O on that database connection, or if the database entered [WAL mode] \n** after the most recent I/O on the database connection.)^\n** (Hint: Run \"[PRAGMA application_id]\" against a newly opened\n** database connection in order to make it ready to use snapshots.)\n**\n** The [sqlite3_snapshot_open()] interface is only available when the\n** SQLITE_ENABLE_SNAPSHOT compile-time option is used.\n*/\nSQLITE_API SQLITE_EXPERIMENTAL int sqlite3_snapshot_open(\n  sqlite3 *db,\n  const char *zSchema,\n  sqlite3_snapshot *pSnapshot\n);\n\n/*\n** CAPI3REF: Destroy a snapshot\n** EXPERIMENTAL\n**\n** ^The [sqlite3_snapshot_free(P)] interface destroys [sqlite3_snapshot] P.\n** The application must eventually free every [sqlite3_snapshot] object\n** using this routine to avoid a memory leak.\n**\n** The [sqlite3_snapshot_free()] interface is only available when the\n** SQLITE_ENABLE_SNAPSHOT compile-time option is used.\n*/\nSQLITE_API SQLITE_EXPERIMENTAL void sqlite3_snapshot_free(sqlite3_snapshot*);\n\n/*\n** CAPI3REF: Compare the ages of two snapshot handles.\n** EXPERIMENTAL\n**\n** The sqlite3_snapshot_cmp(P1, P2) interface is used to compare the ages\n** of two valid snapshot handles. \n**\n** If the two snapshot handles are not associated with the same database \n** file, the result of the comparison is undefined. \n**\n** Additionally, the result of the comparison is only valid if both of the\n** snapshot handles were obtained by calling sqlite3_snapshot_get() since the\n** last time the wal file was deleted. The wal file is deleted when the\n** database is changed back to rollback mode or when the number of database\n** clients drops to zero. If either snapshot handle was obtained before the \n** wal file was last deleted, the value returned by this function \n** is undefined.\n**\n** Otherwise, this API returns a negative value if P1 refers to an older\n** snapshot than P2, zero if the two handles refer to the same database\n** snapshot, and a positive value if P1 is a newer snapshot than P2.\n*/\nSQLITE_API SQLITE_EXPERIMENTAL int sqlite3_snapshot_cmp(\n  sqlite3_snapshot *p1,\n  sqlite3_snapshot *p2\n);\n\n/*\n** CAPI3REF: Recover snapshots from a wal file\n** EXPERIMENTAL\n**\n** If all connections disconnect from a database file but do not perform\n** a checkpoint, the existing wal file is opened along with the database\n** file the next time the database is opened. At this point it is only\n** possible to successfully call sqlite3_snapshot_open() to open the most\n** recent snapshot of the database (the one at the head of the wal file),\n** even though the wal file may contain other valid snapshots for which\n** clients have sqlite3_snapshot handles.\n**\n** This function attempts to scan the wal file associated with database zDb\n** of database handle db and make all valid snapshots available to\n** sqlite3_snapshot_open(). It is an error if there is already a read\n** transaction open on the database, or if the database is not a wal mode\n** database.\n**\n** SQLITE_OK is returned if successful, or an SQLite error code otherwise.\n*/\nSQLITE_API SQLITE_EXPERIMENTAL int sqlite3_snapshot_recover(sqlite3 *db, const char *zDb);\n\n/*\n** Undo the hack that converts floating point types to integer for\n** builds on processors without floating point support.\n*/\n#ifdef SQLITE_OMIT_FLOATING_POINT\n# undef double\n#endif\n\n#if 0\n}  /* End of the 'extern \"C\"' block */\n#endif\n#endif /* SQLITE3_H */\n\n/******** Begin file sqlite3rtree.h *********/\n/*\n** 2010 August 30\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n*************************************************************************\n*/\n\n#ifndef _SQLITE3RTREE_H_\n#define _SQLITE3RTREE_H_\n\n\n#if 0\nextern \"C\" {\n#endif\n\ntypedef struct sqlite3_rtree_geometry sqlite3_rtree_geometry;\ntypedef struct sqlite3_rtree_query_info sqlite3_rtree_query_info;\n\n/* The double-precision datatype used by RTree depends on the\n** SQLITE_RTREE_INT_ONLY compile-time option.\n*/\n#ifdef SQLITE_RTREE_INT_ONLY\n  typedef sqlite3_int64 sqlite3_rtree_dbl;\n#else\n  typedef double sqlite3_rtree_dbl;\n#endif\n\n/*\n** Register a geometry callback named zGeom that can be used as part of an\n** R-Tree geometry query as follows:\n**\n**   SELECT ... FROM <rtree> WHERE <rtree col> MATCH $zGeom(... params ...)\n*/\nSQLITE_API int sqlite3_rtree_geometry_callback(\n  sqlite3 *db,\n  const char *zGeom,\n  int (*xGeom)(sqlite3_rtree_geometry*, int, sqlite3_rtree_dbl*,int*),\n  void *pContext\n);\n\n\n/*\n** A pointer to a structure of the following type is passed as the first\n** argument to callbacks registered using rtree_geometry_callback().\n*/\nstruct sqlite3_rtree_geometry {\n  void *pContext;                 /* Copy of pContext passed to s_r_g_c() */\n  int nParam;                     /* Size of array aParam[] */\n  sqlite3_rtree_dbl *aParam;      /* Parameters passed to SQL geom function */\n  void *pUser;                    /* Callback implementation user data */\n  void (*xDelUser)(void *);       /* Called by SQLite to clean up pUser */\n};\n\n/*\n** Register a 2nd-generation geometry callback named zScore that can be \n** used as part of an R-Tree geometry query as follows:\n**\n**   SELECT ... FROM <rtree> WHERE <rtree col> MATCH $zQueryFunc(... params ...)\n*/\nSQLITE_API int sqlite3_rtree_query_callback(\n  sqlite3 *db,\n  const char *zQueryFunc,\n  int (*xQueryFunc)(sqlite3_rtree_query_info*),\n  void *pContext,\n  void (*xDestructor)(void*)\n);\n\n\n/*\n** A pointer to a structure of the following type is passed as the \n** argument to scored geometry callback registered using\n** sqlite3_rtree_query_callback().\n**\n** Note that the first 5 fields of this structure are identical to\n** sqlite3_rtree_geometry.  This structure is a subclass of\n** sqlite3_rtree_geometry.\n*/\nstruct sqlite3_rtree_query_info {\n  void *pContext;                   /* pContext from when function registered */\n  int nParam;                       /* Number of function parameters */\n  sqlite3_rtree_dbl *aParam;        /* value of function parameters */\n  void *pUser;                      /* callback can use this, if desired */\n  void (*xDelUser)(void*);          /* function to free pUser */\n  sqlite3_rtree_dbl *aCoord;        /* Coordinates of node or entry to check */\n  unsigned int *anQueue;            /* Number of pending entries in the queue */\n  int nCoord;                       /* Number of coordinates */\n  int iLevel;                       /* Level of current node or entry */\n  int mxLevel;                      /* The largest iLevel value in the tree */\n  sqlite3_int64 iRowid;             /* Rowid for current entry */\n  sqlite3_rtree_dbl rParentScore;   /* Score of parent node */\n  int eParentWithin;                /* Visibility of parent node */\n  int eWithin;                      /* OUT: Visiblity */\n  sqlite3_rtree_dbl rScore;         /* OUT: Write the score here */\n  /* The following fields are only available in 3.8.11 and later */\n  sqlite3_value **apSqlParam;       /* Original SQL values of parameters */\n};\n\n/*\n** Allowed values for sqlite3_rtree_query.eWithin and .eParentWithin.\n*/\n#define NOT_WITHIN       0   /* Object completely outside of query region */\n#define PARTLY_WITHIN    1   /* Object partially overlaps query region */\n#define FULLY_WITHIN     2   /* Object fully contained within query region */\n\n\n#if 0\n}  /* end of the 'extern \"C\"' block */\n#endif\n\n#endif  /* ifndef _SQLITE3RTREE_H_ */\n\n/******** End of sqlite3rtree.h *********/\n/******** Begin file sqlite3session.h *********/\n\n#if !defined(__SQLITESESSION_H_) && defined(SQLITE_ENABLE_SESSION)\n#define __SQLITESESSION_H_ 1\n\n/*\n** Make sure we can call this stuff from C++.\n*/\n#if 0\nextern \"C\" {\n#endif\n\n\n/*\n** CAPI3REF: Session Object Handle\n*/\ntypedef struct sqlite3_session sqlite3_session;\n\n/*\n** CAPI3REF: Changeset Iterator Handle\n*/\ntypedef struct sqlite3_changeset_iter sqlite3_changeset_iter;\n\n/*\n** CAPI3REF: Create A New Session Object\n**\n** Create a new session object attached to database handle db. If successful,\n** a pointer to the new object is written to *ppSession and SQLITE_OK is\n** returned. If an error occurs, *ppSession is set to NULL and an SQLite\n** error code (e.g. SQLITE_NOMEM) is returned.\n**\n** It is possible to create multiple session objects attached to a single\n** database handle.\n**\n** Session objects created using this function should be deleted using the\n** [sqlite3session_delete()] function before the database handle that they\n** are attached to is itself closed. If the database handle is closed before\n** the session object is deleted, then the results of calling any session\n** module function, including [sqlite3session_delete()] on the session object\n** are undefined.\n**\n** Because the session module uses the [sqlite3_preupdate_hook()] API, it\n** is not possible for an application to register a pre-update hook on a\n** database handle that has one or more session objects attached. Nor is\n** it possible to create a session object attached to a database handle for\n** which a pre-update hook is already defined. The results of attempting \n** either of these things are undefined.\n**\n** The session object will be used to create changesets for tables in\n** database zDb, where zDb is either \"main\", or \"temp\", or the name of an\n** attached database. It is not an error if database zDb is not attached\n** to the database when the session object is created.\n*/\nSQLITE_API int sqlite3session_create(\n  sqlite3 *db,                    /* Database handle */\n  const char *zDb,                /* Name of db (e.g. \"main\") */\n  sqlite3_session **ppSession     /* OUT: New session object */\n);\n\n/*\n** CAPI3REF: Delete A Session Object\n**\n** Delete a session object previously allocated using \n** [sqlite3session_create()]. Once a session object has been deleted, the\n** results of attempting to use pSession with any other session module\n** function are undefined.\n**\n** Session objects must be deleted before the database handle to which they\n** are attached is closed. Refer to the documentation for \n** [sqlite3session_create()] for details.\n*/\nSQLITE_API void sqlite3session_delete(sqlite3_session *pSession);\n\n\n/*\n** CAPI3REF: Enable Or Disable A Session Object\n**\n** Enable or disable the recording of changes by a session object. When\n** enabled, a session object records changes made to the database. When\n** disabled - it does not. A newly created session object is enabled.\n** Refer to the documentation for [sqlite3session_changeset()] for further\n** details regarding how enabling and disabling a session object affects\n** the eventual changesets.\n**\n** Passing zero to this function disables the session. Passing a value\n** greater than zero enables it. Passing a value less than zero is a \n** no-op, and may be used to query the current state of the session.\n**\n** The return value indicates the final state of the session object: 0 if \n** the session is disabled, or 1 if it is enabled.\n*/\nSQLITE_API int sqlite3session_enable(sqlite3_session *pSession, int bEnable);\n\n/*\n** CAPI3REF: Set Or Clear the Indirect Change Flag\n**\n** Each change recorded by a session object is marked as either direct or\n** indirect. A change is marked as indirect if either:\n**\n** <ul>\n**   <li> The session object \"indirect\" flag is set when the change is\n**        made, or\n**   <li> The change is made by an SQL trigger or foreign key action \n**        instead of directly as a result of a users SQL statement.\n** </ul>\n**\n** If a single row is affected by more than one operation within a session,\n** then the change is considered indirect if all operations meet the criteria\n** for an indirect change above, or direct otherwise.\n**\n** This function is used to set, clear or query the session object indirect\n** flag.  If the second argument passed to this function is zero, then the\n** indirect flag is cleared. If it is greater than zero, the indirect flag\n** is set. Passing a value less than zero does not modify the current value\n** of the indirect flag, and may be used to query the current state of the \n** indirect flag for the specified session object.\n**\n** The return value indicates the final state of the indirect flag: 0 if \n** it is clear, or 1 if it is set.\n*/\nSQLITE_API int sqlite3session_indirect(sqlite3_session *pSession, int bIndirect);\n\n/*\n** CAPI3REF: Attach A Table To A Session Object\n**\n** If argument zTab is not NULL, then it is the name of a table to attach\n** to the session object passed as the first argument. All subsequent changes \n** made to the table while the session object is enabled will be recorded. See \n** documentation for [sqlite3session_changeset()] for further details.\n**\n** Or, if argument zTab is NULL, then changes are recorded for all tables\n** in the database. If additional tables are added to the database (by \n** executing \"CREATE TABLE\" statements) after this call is made, changes for \n** the new tables are also recorded.\n**\n** Changes can only be recorded for tables that have a PRIMARY KEY explicitly\n** defined as part of their CREATE TABLE statement. It does not matter if the \n** PRIMARY KEY is an \"INTEGER PRIMARY KEY\" (rowid alias) or not. The PRIMARY\n** KEY may consist of a single column, or may be a composite key.\n** \n** It is not an error if the named table does not exist in the database. Nor\n** is it an error if the named table does not have a PRIMARY KEY. However,\n** no changes will be recorded in either of these scenarios.\n**\n** Changes are not recorded for individual rows that have NULL values stored\n** in one or more of their PRIMARY KEY columns.\n**\n** SQLITE_OK is returned if the call completes without error. Or, if an error \n** occurs, an SQLite error code (e.g. SQLITE_NOMEM) is returned.\n**\n** <h3>Special sqlite_stat1 Handling</h3>\n**\n** As of SQLite version 3.22.0, the \"sqlite_stat1\" table is an exception to \n** some of the rules above. In SQLite, the schema of sqlite_stat1 is:\n**  <pre>\n**  &nbsp;     CREATE TABLE sqlite_stat1(tbl,idx,stat)  \n**  </pre>\n**\n** Even though sqlite_stat1 does not have a PRIMARY KEY, changes are \n** recorded for it as if the PRIMARY KEY is (tbl,idx). Additionally, changes \n** are recorded for rows for which (idx IS NULL) is true. However, for such\n** rows a zero-length blob (SQL value X'') is stored in the changeset or\n** patchset instead of a NULL value. This allows such changesets to be\n** manipulated by legacy implementations of sqlite3changeset_invert(),\n** concat() and similar.\n**\n** The sqlite3changeset_apply() function automatically converts the \n** zero-length blob back to a NULL value when updating the sqlite_stat1\n** table. However, if the application calls sqlite3changeset_new(),\n** sqlite3changeset_old() or sqlite3changeset_conflict on a changeset \n** iterator directly (including on a changeset iterator passed to a\n** conflict-handler callback) then the X'' value is returned. The application\n** must translate X'' to NULL itself if required.\n**\n** Legacy (older than 3.22.0) versions of the sessions module cannot capture\n** changes made to the sqlite_stat1 table. Legacy versions of the\n** sqlite3changeset_apply() function silently ignore any modifications to the\n** sqlite_stat1 table that are part of a changeset or patchset.\n*/\nSQLITE_API int sqlite3session_attach(\n  sqlite3_session *pSession,      /* Session object */\n  const char *zTab                /* Table name */\n);\n\n/*\n** CAPI3REF: Set a table filter on a Session Object.\n**\n** The second argument (xFilter) is the \"filter callback\". For changes to rows \n** in tables that are not attached to the Session object, the filter is called\n** to determine whether changes to the table's rows should be tracked or not. \n** If xFilter returns 0, changes is not tracked. Note that once a table is \n** attached, xFilter will not be called again.\n*/\nSQLITE_API void sqlite3session_table_filter(\n  sqlite3_session *pSession,      /* Session object */\n  int(*xFilter)(\n    void *pCtx,                   /* Copy of third arg to _filter_table() */\n    const char *zTab              /* Table name */\n  ),\n  void *pCtx                      /* First argument passed to xFilter */\n);\n\n/*\n** CAPI3REF: Generate A Changeset From A Session Object\n**\n** Obtain a changeset containing changes to the tables attached to the \n** session object passed as the first argument. If successful, \n** set *ppChangeset to point to a buffer containing the changeset \n** and *pnChangeset to the size of the changeset in bytes before returning\n** SQLITE_OK. If an error occurs, set both *ppChangeset and *pnChangeset to\n** zero and return an SQLite error code.\n**\n** A changeset consists of zero or more INSERT, UPDATE and/or DELETE changes,\n** each representing a change to a single row of an attached table. An INSERT\n** change contains the values of each field of a new database row. A DELETE\n** contains the original values of each field of a deleted database row. An\n** UPDATE change contains the original values of each field of an updated\n** database row along with the updated values for each updated non-primary-key\n** column. It is not possible for an UPDATE change to represent a change that\n** modifies the values of primary key columns. If such a change is made, it\n** is represented in a changeset as a DELETE followed by an INSERT.\n**\n** Changes are not recorded for rows that have NULL values stored in one or \n** more of their PRIMARY KEY columns. If such a row is inserted or deleted,\n** no corresponding change is present in the changesets returned by this\n** function. If an existing row with one or more NULL values stored in\n** PRIMARY KEY columns is updated so that all PRIMARY KEY columns are non-NULL,\n** only an INSERT is appears in the changeset. Similarly, if an existing row\n** with non-NULL PRIMARY KEY values is updated so that one or more of its\n** PRIMARY KEY columns are set to NULL, the resulting changeset contains a\n** DELETE change only.\n**\n** The contents of a changeset may be traversed using an iterator created\n** using the [sqlite3changeset_start()] API. A changeset may be applied to\n** a database with a compatible schema using the [sqlite3changeset_apply()]\n** API.\n**\n** Within a changeset generated by this function, all changes related to a\n** single table are grouped together. In other words, when iterating through\n** a changeset or when applying a changeset to a database, all changes related\n** to a single table are processed before moving on to the next table. Tables\n** are sorted in the same order in which they were attached (or auto-attached)\n** to the sqlite3_session object. The order in which the changes related to\n** a single table are stored is undefined.\n**\n** Following a successful call to this function, it is the responsibility of\n** the caller to eventually free the buffer that *ppChangeset points to using\n** [sqlite3_free()].\n**\n** <h3>Changeset Generation</h3>\n**\n** Once a table has been attached to a session object, the session object\n** records the primary key values of all new rows inserted into the table.\n** It also records the original primary key and other column values of any\n** deleted or updated rows. For each unique primary key value, data is only\n** recorded once - the first time a row with said primary key is inserted,\n** updated or deleted in the lifetime of the session.\n**\n** There is one exception to the previous paragraph: when a row is inserted,\n** updated or deleted, if one or more of its primary key columns contain a\n** NULL value, no record of the change is made.\n**\n** The session object therefore accumulates two types of records - those\n** that consist of primary key values only (created when the user inserts\n** a new record) and those that consist of the primary key values and the\n** original values of other table columns (created when the users deletes\n** or updates a record).\n**\n** When this function is called, the requested changeset is created using\n** both the accumulated records and the current contents of the database\n** file. Specifically:\n**\n** <ul>\n**   <li> For each record generated by an insert, the database is queried\n**        for a row with a matching primary key. If one is found, an INSERT\n**        change is added to the changeset. If no such row is found, no change \n**        is added to the changeset.\n**\n**   <li> For each record generated by an update or delete, the database is \n**        queried for a row with a matching primary key. If such a row is\n**        found and one or more of the non-primary key fields have been\n**        modified from their original values, an UPDATE change is added to \n**        the changeset. Or, if no such row is found in the table, a DELETE \n**        change is added to the changeset. If there is a row with a matching\n**        primary key in the database, but all fields contain their original\n**        values, no change is added to the changeset.\n** </ul>\n**\n** This means, amongst other things, that if a row is inserted and then later\n** deleted while a session object is active, neither the insert nor the delete\n** will be present in the changeset. Or if a row is deleted and then later a \n** row with the same primary key values inserted while a session object is\n** active, the resulting changeset will contain an UPDATE change instead of\n** a DELETE and an INSERT.\n**\n** When a session object is disabled (see the [sqlite3session_enable()] API),\n** it does not accumulate records when rows are inserted, updated or deleted.\n** This may appear to have some counter-intuitive effects if a single row\n** is written to more than once during a session. For example, if a row\n** is inserted while a session object is enabled, then later deleted while \n** the same session object is disabled, no INSERT record will appear in the\n** changeset, even though the delete took place while the session was disabled.\n** Or, if one field of a row is updated while a session is disabled, and \n** another field of the same row is updated while the session is enabled, the\n** resulting changeset will contain an UPDATE change that updates both fields.\n*/\nSQLITE_API int sqlite3session_changeset(\n  sqlite3_session *pSession,      /* Session object */\n  int *pnChangeset,               /* OUT: Size of buffer at *ppChangeset */\n  void **ppChangeset              /* OUT: Buffer containing changeset */\n);\n\n/*\n** CAPI3REF: Load The Difference Between Tables Into A Session \n**\n** If it is not already attached to the session object passed as the first\n** argument, this function attaches table zTbl in the same manner as the\n** [sqlite3session_attach()] function. If zTbl does not exist, or if it\n** does not have a primary key, this function is a no-op (but does not return\n** an error).\n**\n** Argument zFromDb must be the name of a database (\"main\", \"temp\" etc.)\n** attached to the same database handle as the session object that contains \n** a table compatible with the table attached to the session by this function.\n** A table is considered compatible if it:\n**\n** <ul>\n**   <li> Has the same name,\n**   <li> Has the same set of columns declared in the same order, and\n**   <li> Has the same PRIMARY KEY definition.\n** </ul>\n**\n** If the tables are not compatible, SQLITE_SCHEMA is returned. If the tables\n** are compatible but do not have any PRIMARY KEY columns, it is not an error\n** but no changes are added to the session object. As with other session\n** APIs, tables without PRIMARY KEYs are simply ignored.\n**\n** This function adds a set of changes to the session object that could be\n** used to update the table in database zFrom (call this the \"from-table\") \n** so that its content is the same as the table attached to the session \n** object (call this the \"to-table\"). Specifically:\n**\n** <ul>\n**   <li> For each row (primary key) that exists in the to-table but not in \n**     the from-table, an INSERT record is added to the session object.\n**\n**   <li> For each row (primary key) that exists in the to-table but not in \n**     the from-table, a DELETE record is added to the session object.\n**\n**   <li> For each row (primary key) that exists in both tables, but features \n**     different non-PK values in each, an UPDATE record is added to the\n**     session.  \n** </ul>\n**\n** To clarify, if this function is called and then a changeset constructed\n** using [sqlite3session_changeset()], then after applying that changeset to \n** database zFrom the contents of the two compatible tables would be \n** identical.\n**\n** It an error if database zFrom does not exist or does not contain the\n** required compatible table.\n**\n** If the operation successful, SQLITE_OK is returned. Otherwise, an SQLite\n** error code. In this case, if argument pzErrMsg is not NULL, *pzErrMsg\n** may be set to point to a buffer containing an English language error \n** message. It is the responsibility of the caller to free this buffer using\n** sqlite3_free().\n*/\nSQLITE_API int sqlite3session_diff(\n  sqlite3_session *pSession,\n  const char *zFromDb,\n  const char *zTbl,\n  char **pzErrMsg\n);\n\n\n/*\n** CAPI3REF: Generate A Patchset From A Session Object\n**\n** The differences between a patchset and a changeset are that:\n**\n** <ul>\n**   <li> DELETE records consist of the primary key fields only. The \n**        original values of other fields are omitted.\n**   <li> The original values of any modified fields are omitted from \n**        UPDATE records.\n** </ul>\n**\n** A patchset blob may be used with up to date versions of all \n** sqlite3changeset_xxx API functions except for sqlite3changeset_invert(), \n** which returns SQLITE_CORRUPT if it is passed a patchset. Similarly,\n** attempting to use a patchset blob with old versions of the\n** sqlite3changeset_xxx APIs also provokes an SQLITE_CORRUPT error. \n**\n** Because the non-primary key \"old.*\" fields are omitted, no \n** SQLITE_CHANGESET_DATA conflicts can be detected or reported if a patchset\n** is passed to the sqlite3changeset_apply() API. Other conflict types work\n** in the same way as for changesets.\n**\n** Changes within a patchset are ordered in the same way as for changesets\n** generated by the sqlite3session_changeset() function (i.e. all changes for\n** a single table are grouped together, tables appear in the order in which\n** they were attached to the session object).\n*/\nSQLITE_API int sqlite3session_patchset(\n  sqlite3_session *pSession,      /* Session object */\n  int *pnPatchset,                /* OUT: Size of buffer at *ppPatchset */\n  void **ppPatchset               /* OUT: Buffer containing patchset */\n);\n\n/*\n** CAPI3REF: Test if a changeset has recorded any changes.\n**\n** Return non-zero if no changes to attached tables have been recorded by \n** the session object passed as the first argument. Otherwise, if one or \n** more changes have been recorded, return zero.\n**\n** Even if this function returns zero, it is possible that calling\n** [sqlite3session_changeset()] on the session handle may still return a\n** changeset that contains no changes. This can happen when a row in \n** an attached table is modified and then later on the original values \n** are restored. However, if this function returns non-zero, then it is\n** guaranteed that a call to sqlite3session_changeset() will return a \n** changeset containing zero changes.\n*/\nSQLITE_API int sqlite3session_isempty(sqlite3_session *pSession);\n\n/*\n** CAPI3REF: Create An Iterator To Traverse A Changeset \n**\n** Create an iterator used to iterate through the contents of a changeset.\n** If successful, *pp is set to point to the iterator handle and SQLITE_OK\n** is returned. Otherwise, if an error occurs, *pp is set to zero and an\n** SQLite error code is returned.\n**\n** The following functions can be used to advance and query a changeset \n** iterator created by this function:\n**\n** <ul>\n**   <li> [sqlite3changeset_next()]\n**   <li> [sqlite3changeset_op()]\n**   <li> [sqlite3changeset_new()]\n**   <li> [sqlite3changeset_old()]\n** </ul>\n**\n** It is the responsibility of the caller to eventually destroy the iterator\n** by passing it to [sqlite3changeset_finalize()]. The buffer containing the\n** changeset (pChangeset) must remain valid until after the iterator is\n** destroyed.\n**\n** Assuming the changeset blob was created by one of the\n** [sqlite3session_changeset()], [sqlite3changeset_concat()] or\n** [sqlite3changeset_invert()] functions, all changes within the changeset \n** that apply to a single table are grouped together. This means that when \n** an application iterates through a changeset using an iterator created by \n** this function, all changes that relate to a single table are visited \n** consecutively. There is no chance that the iterator will visit a change \n** the applies to table X, then one for table Y, and then later on visit \n** another change for table X.\n*/\nSQLITE_API int sqlite3changeset_start(\n  sqlite3_changeset_iter **pp,    /* OUT: New changeset iterator handle */\n  int nChangeset,                 /* Size of changeset blob in bytes */\n  void *pChangeset                /* Pointer to blob containing changeset */\n);\n\n\n/*\n** CAPI3REF: Advance A Changeset Iterator\n**\n** This function may only be used with iterators created by function\n** [sqlite3changeset_start()]. If it is called on an iterator passed to\n** a conflict-handler callback by [sqlite3changeset_apply()], SQLITE_MISUSE\n** is returned and the call has no effect.\n**\n** Immediately after an iterator is created by sqlite3changeset_start(), it\n** does not point to any change in the changeset. Assuming the changeset\n** is not empty, the first call to this function advances the iterator to\n** point to the first change in the changeset. Each subsequent call advances\n** the iterator to point to the next change in the changeset (if any). If\n** no error occurs and the iterator points to a valid change after a call\n** to sqlite3changeset_next() has advanced it, SQLITE_ROW is returned. \n** Otherwise, if all changes in the changeset have already been visited,\n** SQLITE_DONE is returned.\n**\n** If an error occurs, an SQLite error code is returned. Possible error \n** codes include SQLITE_CORRUPT (if the changeset buffer is corrupt) or \n** SQLITE_NOMEM.\n*/\nSQLITE_API int sqlite3changeset_next(sqlite3_changeset_iter *pIter);\n\n/*\n** CAPI3REF: Obtain The Current Operation From A Changeset Iterator\n**\n** The pIter argument passed to this function may either be an iterator\n** passed to a conflict-handler by [sqlite3changeset_apply()], or an iterator\n** created by [sqlite3changeset_start()]. In the latter case, the most recent\n** call to [sqlite3changeset_next()] must have returned [SQLITE_ROW]. If this\n** is not the case, this function returns [SQLITE_MISUSE].\n**\n** If argument pzTab is not NULL, then *pzTab is set to point to a\n** nul-terminated utf-8 encoded string containing the name of the table\n** affected by the current change. The buffer remains valid until either\n** sqlite3changeset_next() is called on the iterator or until the \n** conflict-handler function returns. If pnCol is not NULL, then *pnCol is \n** set to the number of columns in the table affected by the change. If\n** pbIncorrect is not NULL, then *pbIndirect is set to true (1) if the change\n** is an indirect change, or false (0) otherwise. See the documentation for\n** [sqlite3session_indirect()] for a description of direct and indirect\n** changes. Finally, if pOp is not NULL, then *pOp is set to one of \n** [SQLITE_INSERT], [SQLITE_DELETE] or [SQLITE_UPDATE], depending on the \n** type of change that the iterator currently points to.\n**\n** If no error occurs, SQLITE_OK is returned. If an error does occur, an\n** SQLite error code is returned. The values of the output variables may not\n** be trusted in this case.\n*/\nSQLITE_API int sqlite3changeset_op(\n  sqlite3_changeset_iter *pIter,  /* Iterator object */\n  const char **pzTab,             /* OUT: Pointer to table name */\n  int *pnCol,                     /* OUT: Number of columns in table */\n  int *pOp,                       /* OUT: SQLITE_INSERT, DELETE or UPDATE */\n  int *pbIndirect                 /* OUT: True for an 'indirect' change */\n);\n\n/*\n** CAPI3REF: Obtain The Primary Key Definition Of A Table\n**\n** For each modified table, a changeset includes the following:\n**\n** <ul>\n**   <li> The number of columns in the table, and\n**   <li> Which of those columns make up the tables PRIMARY KEY.\n** </ul>\n**\n** This function is used to find which columns comprise the PRIMARY KEY of\n** the table modified by the change that iterator pIter currently points to.\n** If successful, *pabPK is set to point to an array of nCol entries, where\n** nCol is the number of columns in the table. Elements of *pabPK are set to\n** 0x01 if the corresponding column is part of the tables primary key, or\n** 0x00 if it is not.\n**\n** If argument pnCol is not NULL, then *pnCol is set to the number of columns\n** in the table.\n**\n** If this function is called when the iterator does not point to a valid\n** entry, SQLITE_MISUSE is returned and the output variables zeroed. Otherwise,\n** SQLITE_OK is returned and the output variables populated as described\n** above.\n*/\nSQLITE_API int sqlite3changeset_pk(\n  sqlite3_changeset_iter *pIter,  /* Iterator object */\n  unsigned char **pabPK,          /* OUT: Array of boolean - true for PK cols */\n  int *pnCol                      /* OUT: Number of entries in output array */\n);\n\n/*\n** CAPI3REF: Obtain old.* Values From A Changeset Iterator\n**\n** The pIter argument passed to this function may either be an iterator\n** passed to a conflict-handler by [sqlite3changeset_apply()], or an iterator\n** created by [sqlite3changeset_start()]. In the latter case, the most recent\n** call to [sqlite3changeset_next()] must have returned SQLITE_ROW. \n** Furthermore, it may only be called if the type of change that the iterator\n** currently points to is either [SQLITE_DELETE] or [SQLITE_UPDATE]. Otherwise,\n** this function returns [SQLITE_MISUSE] and sets *ppValue to NULL.\n**\n** Argument iVal must be greater than or equal to 0, and less than the number\n** of columns in the table affected by the current change. Otherwise,\n** [SQLITE_RANGE] is returned and *ppValue is set to NULL.\n**\n** If successful, this function sets *ppValue to point to a protected\n** sqlite3_value object containing the iVal'th value from the vector of \n** original row values stored as part of the UPDATE or DELETE change and\n** returns SQLITE_OK. The name of the function comes from the fact that this \n** is similar to the \"old.*\" columns available to update or delete triggers.\n**\n** If some other error occurs (e.g. an OOM condition), an SQLite error code\n** is returned and *ppValue is set to NULL.\n*/\nSQLITE_API int sqlite3changeset_old(\n  sqlite3_changeset_iter *pIter,  /* Changeset iterator */\n  int iVal,                       /* Column number */\n  sqlite3_value **ppValue         /* OUT: Old value (or NULL pointer) */\n);\n\n/*\n** CAPI3REF: Obtain new.* Values From A Changeset Iterator\n**\n** The pIter argument passed to this function may either be an iterator\n** passed to a conflict-handler by [sqlite3changeset_apply()], or an iterator\n** created by [sqlite3changeset_start()]. In the latter case, the most recent\n** call to [sqlite3changeset_next()] must have returned SQLITE_ROW. \n** Furthermore, it may only be called if the type of change that the iterator\n** currently points to is either [SQLITE_UPDATE] or [SQLITE_INSERT]. Otherwise,\n** this function returns [SQLITE_MISUSE] and sets *ppValue to NULL.\n**\n** Argument iVal must be greater than or equal to 0, and less than the number\n** of columns in the table affected by the current change. Otherwise,\n** [SQLITE_RANGE] is returned and *ppValue is set to NULL.\n**\n** If successful, this function sets *ppValue to point to a protected\n** sqlite3_value object containing the iVal'th value from the vector of \n** new row values stored as part of the UPDATE or INSERT change and\n** returns SQLITE_OK. If the change is an UPDATE and does not include\n** a new value for the requested column, *ppValue is set to NULL and \n** SQLITE_OK returned. The name of the function comes from the fact that \n** this is similar to the \"new.*\" columns available to update or delete \n** triggers.\n**\n** If some other error occurs (e.g. an OOM condition), an SQLite error code\n** is returned and *ppValue is set to NULL.\n*/\nSQLITE_API int sqlite3changeset_new(\n  sqlite3_changeset_iter *pIter,  /* Changeset iterator */\n  int iVal,                       /* Column number */\n  sqlite3_value **ppValue         /* OUT: New value (or NULL pointer) */\n);\n\n/*\n** CAPI3REF: Obtain Conflicting Row Values From A Changeset Iterator\n**\n** This function should only be used with iterator objects passed to a\n** conflict-handler callback by [sqlite3changeset_apply()] with either\n** [SQLITE_CHANGESET_DATA] or [SQLITE_CHANGESET_CONFLICT]. If this function\n** is called on any other iterator, [SQLITE_MISUSE] is returned and *ppValue\n** is set to NULL.\n**\n** Argument iVal must be greater than or equal to 0, and less than the number\n** of columns in the table affected by the current change. Otherwise,\n** [SQLITE_RANGE] is returned and *ppValue is set to NULL.\n**\n** If successful, this function sets *ppValue to point to a protected\n** sqlite3_value object containing the iVal'th value from the \n** \"conflicting row\" associated with the current conflict-handler callback\n** and returns SQLITE_OK.\n**\n** If some other error occurs (e.g. an OOM condition), an SQLite error code\n** is returned and *ppValue is set to NULL.\n*/\nSQLITE_API int sqlite3changeset_conflict(\n  sqlite3_changeset_iter *pIter,  /* Changeset iterator */\n  int iVal,                       /* Column number */\n  sqlite3_value **ppValue         /* OUT: Value from conflicting row */\n);\n\n/*\n** CAPI3REF: Determine The Number Of Foreign Key Constraint Violations\n**\n** This function may only be called with an iterator passed to an\n** SQLITE_CHANGESET_FOREIGN_KEY conflict handler callback. In this case\n** it sets the output variable to the total number of known foreign key\n** violations in the destination database and returns SQLITE_OK.\n**\n** In all other cases this function returns SQLITE_MISUSE.\n*/\nSQLITE_API int sqlite3changeset_fk_conflicts(\n  sqlite3_changeset_iter *pIter,  /* Changeset iterator */\n  int *pnOut                      /* OUT: Number of FK violations */\n);\n\n\n/*\n** CAPI3REF: Finalize A Changeset Iterator\n**\n** This function is used to finalize an iterator allocated with\n** [sqlite3changeset_start()].\n**\n** This function should only be called on iterators created using the\n** [sqlite3changeset_start()] function. If an application calls this\n** function with an iterator passed to a conflict-handler by\n** [sqlite3changeset_apply()], [SQLITE_MISUSE] is immediately returned and the\n** call has no effect.\n**\n** If an error was encountered within a call to an sqlite3changeset_xxx()\n** function (for example an [SQLITE_CORRUPT] in [sqlite3changeset_next()] or an \n** [SQLITE_NOMEM] in [sqlite3changeset_new()]) then an error code corresponding\n** to that error is returned by this function. Otherwise, SQLITE_OK is\n** returned. This is to allow the following pattern (pseudo-code):\n**\n**   sqlite3changeset_start();\n**   while( SQLITE_ROW==sqlite3changeset_next() ){\n**     // Do something with change.\n**   }\n**   rc = sqlite3changeset_finalize();\n**   if( rc!=SQLITE_OK ){\n**     // An error has occurred \n**   }\n*/\nSQLITE_API int sqlite3changeset_finalize(sqlite3_changeset_iter *pIter);\n\n/*\n** CAPI3REF: Invert A Changeset\n**\n** This function is used to \"invert\" a changeset object. Applying an inverted\n** changeset to a database reverses the effects of applying the uninverted\n** changeset. Specifically:\n**\n** <ul>\n**   <li> Each DELETE change is changed to an INSERT, and\n**   <li> Each INSERT change is changed to a DELETE, and\n**   <li> For each UPDATE change, the old.* and new.* values are exchanged.\n** </ul>\n**\n** This function does not change the order in which changes appear within\n** the changeset. It merely reverses the sense of each individual change.\n**\n** If successful, a pointer to a buffer containing the inverted changeset\n** is stored in *ppOut, the size of the same buffer is stored in *pnOut, and\n** SQLITE_OK is returned. If an error occurs, both *pnOut and *ppOut are\n** zeroed and an SQLite error code returned.\n**\n** It is the responsibility of the caller to eventually call sqlite3_free()\n** on the *ppOut pointer to free the buffer allocation following a successful \n** call to this function.\n**\n** WARNING/TODO: This function currently assumes that the input is a valid\n** changeset. If it is not, the results are undefined.\n*/\nSQLITE_API int sqlite3changeset_invert(\n  int nIn, const void *pIn,       /* Input changeset */\n  int *pnOut, void **ppOut        /* OUT: Inverse of input */\n);\n\n/*\n** CAPI3REF: Concatenate Two Changeset Objects\n**\n** This function is used to concatenate two changesets, A and B, into a \n** single changeset. The result is a changeset equivalent to applying\n** changeset A followed by changeset B. \n**\n** This function combines the two input changesets using an \n** sqlite3_changegroup object. Calling it produces similar results as the\n** following code fragment:\n**\n**   sqlite3_changegroup *pGrp;\n**   rc = sqlite3_changegroup_new(&pGrp);\n**   if( rc==SQLITE_OK ) rc = sqlite3changegroup_add(pGrp, nA, pA);\n**   if( rc==SQLITE_OK ) rc = sqlite3changegroup_add(pGrp, nB, pB);\n**   if( rc==SQLITE_OK ){\n**     rc = sqlite3changegroup_output(pGrp, pnOut, ppOut);\n**   }else{\n**     *ppOut = 0;\n**     *pnOut = 0;\n**   }\n**\n** Refer to the sqlite3_changegroup documentation below for details.\n*/\nSQLITE_API int sqlite3changeset_concat(\n  int nA,                         /* Number of bytes in buffer pA */\n  void *pA,                       /* Pointer to buffer containing changeset A */\n  int nB,                         /* Number of bytes in buffer pB */\n  void *pB,                       /* Pointer to buffer containing changeset B */\n  int *pnOut,                     /* OUT: Number of bytes in output changeset */\n  void **ppOut                    /* OUT: Buffer containing output changeset */\n);\n\n\n/*\n** CAPI3REF: Changegroup Handle\n*/\ntypedef struct sqlite3_changegroup sqlite3_changegroup;\n\n/*\n** CAPI3REF: Create A New Changegroup Object\n**\n** An sqlite3_changegroup object is used to combine two or more changesets\n** (or patchsets) into a single changeset (or patchset). A single changegroup\n** object may combine changesets or patchsets, but not both. The output is\n** always in the same format as the input.\n**\n** If successful, this function returns SQLITE_OK and populates (*pp) with\n** a pointer to a new sqlite3_changegroup object before returning. The caller\n** should eventually free the returned object using a call to \n** sqlite3changegroup_delete(). If an error occurs, an SQLite error code\n** (i.e. SQLITE_NOMEM) is returned and *pp is set to NULL.\n**\n** The usual usage pattern for an sqlite3_changegroup object is as follows:\n**\n** <ul>\n**   <li> It is created using a call to sqlite3changegroup_new().\n**\n**   <li> Zero or more changesets (or patchsets) are added to the object\n**        by calling sqlite3changegroup_add().\n**\n**   <li> The result of combining all input changesets together is obtained \n**        by the application via a call to sqlite3changegroup_output().\n**\n**   <li> The object is deleted using a call to sqlite3changegroup_delete().\n** </ul>\n**\n** Any number of calls to add() and output() may be made between the calls to\n** new() and delete(), and in any order.\n**\n** As well as the regular sqlite3changegroup_add() and \n** sqlite3changegroup_output() functions, also available are the streaming\n** versions sqlite3changegroup_add_strm() and sqlite3changegroup_output_strm().\n*/\nSQLITE_API int sqlite3changegroup_new(sqlite3_changegroup **pp);\n\n/*\n** CAPI3REF: Add A Changeset To A Changegroup\n**\n** Add all changes within the changeset (or patchset) in buffer pData (size\n** nData bytes) to the changegroup. \n**\n** If the buffer contains a patchset, then all prior calls to this function\n** on the same changegroup object must also have specified patchsets. Or, if\n** the buffer contains a changeset, so must have the earlier calls to this\n** function. Otherwise, SQLITE_ERROR is returned and no changes are added\n** to the changegroup.\n**\n** Rows within the changeset and changegroup are identified by the values in\n** their PRIMARY KEY columns. A change in the changeset is considered to\n** apply to the same row as a change already present in the changegroup if\n** the two rows have the same primary key.\n**\n** Changes to rows that do not already appear in the changegroup are\n** simply copied into it. Or, if both the new changeset and the changegroup\n** contain changes that apply to a single row, the final contents of the\n** changegroup depends on the type of each change, as follows:\n**\n** <table border=1 style=\"margin-left:8ex;margin-right:8ex\">\n**   <tr><th style=\"white-space:pre\">Existing Change  </th>\n**       <th style=\"white-space:pre\">New Change       </th>\n**       <th>Output Change\n**   <tr><td>INSERT <td>INSERT <td>\n**       The new change is ignored. This case does not occur if the new\n**       changeset was recorded immediately after the changesets already\n**       added to the changegroup.\n**   <tr><td>INSERT <td>UPDATE <td>\n**       The INSERT change remains in the changegroup. The values in the \n**       INSERT change are modified as if the row was inserted by the\n**       existing change and then updated according to the new change.\n**   <tr><td>INSERT <td>DELETE <td>\n**       The existing INSERT is removed from the changegroup. The DELETE is\n**       not added.\n**   <tr><td>UPDATE <td>INSERT <td>\n**       The new change is ignored. This case does not occur if the new\n**       changeset was recorded immediately after the changesets already\n**       added to the changegroup.\n**   <tr><td>UPDATE <td>UPDATE <td>\n**       The existing UPDATE remains within the changegroup. It is amended \n**       so that the accompanying values are as if the row was updated once \n**       by the existing change and then again by the new change.\n**   <tr><td>UPDATE <td>DELETE <td>\n**       The existing UPDATE is replaced by the new DELETE within the\n**       changegroup.\n**   <tr><td>DELETE <td>INSERT <td>\n**       If one or more of the column values in the row inserted by the\n**       new change differ from those in the row deleted by the existing \n**       change, the existing DELETE is replaced by an UPDATE within the\n**       changegroup. Otherwise, if the inserted row is exactly the same \n**       as the deleted row, the existing DELETE is simply discarded.\n**   <tr><td>DELETE <td>UPDATE <td>\n**       The new change is ignored. This case does not occur if the new\n**       changeset was recorded immediately after the changesets already\n**       added to the changegroup.\n**   <tr><td>DELETE <td>DELETE <td>\n**       The new change is ignored. This case does not occur if the new\n**       changeset was recorded immediately after the changesets already\n**       added to the changegroup.\n** </table>\n**\n** If the new changeset contains changes to a table that is already present\n** in the changegroup, then the number of columns and the position of the\n** primary key columns for the table must be consistent. If this is not the\n** case, this function fails with SQLITE_SCHEMA. If the input changeset\n** appears to be corrupt and the corruption is detected, SQLITE_CORRUPT is\n** returned. Or, if an out-of-memory condition occurs during processing, this\n** function returns SQLITE_NOMEM. In all cases, if an error occurs the\n** final contents of the changegroup is undefined.\n**\n** If no error occurs, SQLITE_OK is returned.\n*/\nSQLITE_API int sqlite3changegroup_add(sqlite3_changegroup*, int nData, void *pData);\n\n/*\n** CAPI3REF: Obtain A Composite Changeset From A Changegroup\n**\n** Obtain a buffer containing a changeset (or patchset) representing the\n** current contents of the changegroup. If the inputs to the changegroup\n** were themselves changesets, the output is a changeset. Or, if the\n** inputs were patchsets, the output is also a patchset.\n**\n** As with the output of the sqlite3session_changeset() and\n** sqlite3session_patchset() functions, all changes related to a single\n** table are grouped together in the output of this function. Tables appear\n** in the same order as for the very first changeset added to the changegroup.\n** If the second or subsequent changesets added to the changegroup contain\n** changes for tables that do not appear in the first changeset, they are\n** appended onto the end of the output changeset, again in the order in\n** which they are first encountered.\n**\n** If an error occurs, an SQLite error code is returned and the output\n** variables (*pnData) and (*ppData) are set to 0. Otherwise, SQLITE_OK\n** is returned and the output variables are set to the size of and a \n** pointer to the output buffer, respectively. In this case it is the\n** responsibility of the caller to eventually free the buffer using a\n** call to sqlite3_free().\n*/\nSQLITE_API int sqlite3changegroup_output(\n  sqlite3_changegroup*,\n  int *pnData,                    /* OUT: Size of output buffer in bytes */\n  void **ppData                   /* OUT: Pointer to output buffer */\n);\n\n/*\n** CAPI3REF: Delete A Changegroup Object\n*/\nSQLITE_API void sqlite3changegroup_delete(sqlite3_changegroup*);\n\n/*\n** CAPI3REF: Apply A Changeset To A Database\n**\n** Apply a changeset to a database. This function attempts to update the\n** \"main\" database attached to handle db with the changes found in the\n** changeset passed via the second and third arguments.\n**\n** The fourth argument (xFilter) passed to this function is the \"filter\n** callback\". If it is not NULL, then for each table affected by at least one\n** change in the changeset, the filter callback is invoked with\n** the table name as the second argument, and a copy of the context pointer\n** passed as the sixth argument to this function as the first. If the \"filter\n** callback\" returns zero, then no attempt is made to apply any changes to \n** the table. Otherwise, if the return value is non-zero or the xFilter\n** argument to this function is NULL, all changes related to the table are\n** attempted.\n**\n** For each table that is not excluded by the filter callback, this function \n** tests that the target database contains a compatible table. A table is \n** considered compatible if all of the following are true:\n**\n** <ul>\n**   <li> The table has the same name as the name recorded in the \n**        changeset, and\n**   <li> The table has at least as many columns as recorded in the \n**        changeset, and\n**   <li> The table has primary key columns in the same position as \n**        recorded in the changeset.\n** </ul>\n**\n** If there is no compatible table, it is not an error, but none of the\n** changes associated with the table are applied. A warning message is issued\n** via the sqlite3_log() mechanism with the error code SQLITE_SCHEMA. At most\n** one such warning is issued for each table in the changeset.\n**\n** For each change for which there is a compatible table, an attempt is made \n** to modify the table contents according to the UPDATE, INSERT or DELETE \n** change. If a change cannot be applied cleanly, the conflict handler \n** function passed as the fifth argument to sqlite3changeset_apply() may be \n** invoked. A description of exactly when the conflict handler is invoked for \n** each type of change is below.\n**\n** Unlike the xFilter argument, xConflict may not be passed NULL. The results\n** of passing anything other than a valid function pointer as the xConflict\n** argument are undefined.\n**\n** Each time the conflict handler function is invoked, it must return one\n** of [SQLITE_CHANGESET_OMIT], [SQLITE_CHANGESET_ABORT] or \n** [SQLITE_CHANGESET_REPLACE]. SQLITE_CHANGESET_REPLACE may only be returned\n** if the second argument passed to the conflict handler is either\n** SQLITE_CHANGESET_DATA or SQLITE_CHANGESET_CONFLICT. If the conflict-handler\n** returns an illegal value, any changes already made are rolled back and\n** the call to sqlite3changeset_apply() returns SQLITE_MISUSE. Different \n** actions are taken by sqlite3changeset_apply() depending on the value\n** returned by each invocation of the conflict-handler function. Refer to\n** the documentation for the three \n** [SQLITE_CHANGESET_OMIT|available return values] for details.\n**\n** <dl>\n** <dt>DELETE Changes<dd>\n**   For each DELETE change, this function checks if the target database \n**   contains a row with the same primary key value (or values) as the \n**   original row values stored in the changeset. If it does, and the values \n**   stored in all non-primary key columns also match the values stored in \n**   the changeset the row is deleted from the target database.\n**\n**   If a row with matching primary key values is found, but one or more of\n**   the non-primary key fields contains a value different from the original\n**   row value stored in the changeset, the conflict-handler function is\n**   invoked with [SQLITE_CHANGESET_DATA] as the second argument. If the\n**   database table has more columns than are recorded in the changeset,\n**   only the values of those non-primary key fields are compared against\n**   the current database contents - any trailing database table columns\n**   are ignored.\n**\n**   If no row with matching primary key values is found in the database,\n**   the conflict-handler function is invoked with [SQLITE_CHANGESET_NOTFOUND]\n**   passed as the second argument.\n**\n**   If the DELETE operation is attempted, but SQLite returns SQLITE_CONSTRAINT\n**   (which can only happen if a foreign key constraint is violated), the\n**   conflict-handler function is invoked with [SQLITE_CHANGESET_CONSTRAINT]\n**   passed as the second argument. This includes the case where the DELETE\n**   operation is attempted because an earlier call to the conflict handler\n**   function returned [SQLITE_CHANGESET_REPLACE].\n**\n** <dt>INSERT Changes<dd>\n**   For each INSERT change, an attempt is made to insert the new row into\n**   the database. If the changeset row contains fewer fields than the\n**   database table, the trailing fields are populated with their default\n**   values.\n**\n**   If the attempt to insert the row fails because the database already \n**   contains a row with the same primary key values, the conflict handler\n**   function is invoked with the second argument set to \n**   [SQLITE_CHANGESET_CONFLICT].\n**\n**   If the attempt to insert the row fails because of some other constraint\n**   violation (e.g. NOT NULL or UNIQUE), the conflict handler function is \n**   invoked with the second argument set to [SQLITE_CHANGESET_CONSTRAINT].\n**   This includes the case where the INSERT operation is re-attempted because \n**   an earlier call to the conflict handler function returned \n**   [SQLITE_CHANGESET_REPLACE].\n**\n** <dt>UPDATE Changes<dd>\n**   For each UPDATE change, this function checks if the target database \n**   contains a row with the same primary key value (or values) as the \n**   original row values stored in the changeset. If it does, and the values \n**   stored in all modified non-primary key columns also match the values\n**   stored in the changeset the row is updated within the target database.\n**\n**   If a row with matching primary key values is found, but one or more of\n**   the modified non-primary key fields contains a value different from an\n**   original row value stored in the changeset, the conflict-handler function\n**   is invoked with [SQLITE_CHANGESET_DATA] as the second argument. Since\n**   UPDATE changes only contain values for non-primary key fields that are\n**   to be modified, only those fields need to match the original values to\n**   avoid the SQLITE_CHANGESET_DATA conflict-handler callback.\n**\n**   If no row with matching primary key values is found in the database,\n**   the conflict-handler function is invoked with [SQLITE_CHANGESET_NOTFOUND]\n**   passed as the second argument.\n**\n**   If the UPDATE operation is attempted, but SQLite returns \n**   SQLITE_CONSTRAINT, the conflict-handler function is invoked with \n**   [SQLITE_CHANGESET_CONSTRAINT] passed as the second argument.\n**   This includes the case where the UPDATE operation is attempted after \n**   an earlier call to the conflict handler function returned\n**   [SQLITE_CHANGESET_REPLACE].  \n** </dl>\n**\n** It is safe to execute SQL statements, including those that write to the\n** table that the callback related to, from within the xConflict callback.\n** This can be used to further customize the applications conflict\n** resolution strategy.\n**\n** All changes made by this function are enclosed in a savepoint transaction.\n** If any other error (aside from a constraint failure when attempting to\n** write to the target database) occurs, then the savepoint transaction is\n** rolled back, restoring the target database to its original state, and an \n** SQLite error code returned.\n*/\nSQLITE_API int sqlite3changeset_apply(\n  sqlite3 *db,                    /* Apply change to \"main\" db of this handle */\n  int nChangeset,                 /* Size of changeset in bytes */\n  void *pChangeset,               /* Changeset blob */\n  int(*xFilter)(\n    void *pCtx,                   /* Copy of sixth arg to _apply() */\n    const char *zTab              /* Table name */\n  ),\n  int(*xConflict)(\n    void *pCtx,                   /* Copy of sixth arg to _apply() */\n    int eConflict,                /* DATA, MISSING, CONFLICT, CONSTRAINT */\n    sqlite3_changeset_iter *p     /* Handle describing change and conflict */\n  ),\n  void *pCtx                      /* First argument passed to xConflict */\n);\n\n/* \n** CAPI3REF: Constants Passed To The Conflict Handler\n**\n** Values that may be passed as the second argument to a conflict-handler.\n**\n** <dl>\n** <dt>SQLITE_CHANGESET_DATA<dd>\n**   The conflict handler is invoked with CHANGESET_DATA as the second argument\n**   when processing a DELETE or UPDATE change if a row with the required\n**   PRIMARY KEY fields is present in the database, but one or more other \n**   (non primary-key) fields modified by the update do not contain the \n**   expected \"before\" values.\n** \n**   The conflicting row, in this case, is the database row with the matching\n**   primary key.\n** \n** <dt>SQLITE_CHANGESET_NOTFOUND<dd>\n**   The conflict handler is invoked with CHANGESET_NOTFOUND as the second\n**   argument when processing a DELETE or UPDATE change if a row with the\n**   required PRIMARY KEY fields is not present in the database.\n** \n**   There is no conflicting row in this case. The results of invoking the\n**   sqlite3changeset_conflict() API are undefined.\n** \n** <dt>SQLITE_CHANGESET_CONFLICT<dd>\n**   CHANGESET_CONFLICT is passed as the second argument to the conflict\n**   handler while processing an INSERT change if the operation would result \n**   in duplicate primary key values.\n** \n**   The conflicting row in this case is the database row with the matching\n**   primary key.\n**\n** <dt>SQLITE_CHANGESET_FOREIGN_KEY<dd>\n**   If foreign key handling is enabled, and applying a changeset leaves the\n**   database in a state containing foreign key violations, the conflict \n**   handler is invoked with CHANGESET_FOREIGN_KEY as the second argument\n**   exactly once before the changeset is committed. If the conflict handler\n**   returns CHANGESET_OMIT, the changes, including those that caused the\n**   foreign key constraint violation, are committed. Or, if it returns\n**   CHANGESET_ABORT, the changeset is rolled back.\n**\n**   No current or conflicting row information is provided. The only function\n**   it is possible to call on the supplied sqlite3_changeset_iter handle\n**   is sqlite3changeset_fk_conflicts().\n** \n** <dt>SQLITE_CHANGESET_CONSTRAINT<dd>\n**   If any other constraint violation occurs while applying a change (i.e. \n**   a UNIQUE, CHECK or NOT NULL constraint), the conflict handler is \n**   invoked with CHANGESET_CONSTRAINT as the second argument.\n** \n**   There is no conflicting row in this case. The results of invoking the\n**   sqlite3changeset_conflict() API are undefined.\n**\n** </dl>\n*/\n#define SQLITE_CHANGESET_DATA        1\n#define SQLITE_CHANGESET_NOTFOUND    2\n#define SQLITE_CHANGESET_CONFLICT    3\n#define SQLITE_CHANGESET_CONSTRAINT  4\n#define SQLITE_CHANGESET_FOREIGN_KEY 5\n\n/* \n** CAPI3REF: Constants Returned By The Conflict Handler\n**\n** A conflict handler callback must return one of the following three values.\n**\n** <dl>\n** <dt>SQLITE_CHANGESET_OMIT<dd>\n**   If a conflict handler returns this value no special action is taken. The\n**   change that caused the conflict is not applied. The session module \n**   continues to the next change in the changeset.\n**\n** <dt>SQLITE_CHANGESET_REPLACE<dd>\n**   This value may only be returned if the second argument to the conflict\n**   handler was SQLITE_CHANGESET_DATA or SQLITE_CHANGESET_CONFLICT. If this\n**   is not the case, any changes applied so far are rolled back and the \n**   call to sqlite3changeset_apply() returns SQLITE_MISUSE.\n**\n**   If CHANGESET_REPLACE is returned by an SQLITE_CHANGESET_DATA conflict\n**   handler, then the conflicting row is either updated or deleted, depending\n**   on the type of change.\n**\n**   If CHANGESET_REPLACE is returned by an SQLITE_CHANGESET_CONFLICT conflict\n**   handler, then the conflicting row is removed from the database and a\n**   second attempt to apply the change is made. If this second attempt fails,\n**   the original row is restored to the database before continuing.\n**\n** <dt>SQLITE_CHANGESET_ABORT<dd>\n**   If this value is returned, any changes applied so far are rolled back \n**   and the call to sqlite3changeset_apply() returns SQLITE_ABORT.\n** </dl>\n*/\n#define SQLITE_CHANGESET_OMIT       0\n#define SQLITE_CHANGESET_REPLACE    1\n#define SQLITE_CHANGESET_ABORT      2\n\n/*\n** CAPI3REF: Streaming Versions of API functions.\n**\n** The six streaming API xxx_strm() functions serve similar purposes to the \n** corresponding non-streaming API functions:\n**\n** <table border=1 style=\"margin-left:8ex;margin-right:8ex\">\n**   <tr><th>Streaming function<th>Non-streaming equivalent</th>\n**   <tr><td>sqlite3changeset_apply_strm<td>[sqlite3changeset_apply] \n**   <tr><td>sqlite3changeset_concat_strm<td>[sqlite3changeset_concat] \n**   <tr><td>sqlite3changeset_invert_strm<td>[sqlite3changeset_invert] \n**   <tr><td>sqlite3changeset_start_strm<td>[sqlite3changeset_start] \n**   <tr><td>sqlite3session_changeset_strm<td>[sqlite3session_changeset] \n**   <tr><td>sqlite3session_patchset_strm<td>[sqlite3session_patchset] \n** </table>\n**\n** Non-streaming functions that accept changesets (or patchsets) as input\n** require that the entire changeset be stored in a single buffer in memory. \n** Similarly, those that return a changeset or patchset do so by returning \n** a pointer to a single large buffer allocated using sqlite3_malloc(). \n** Normally this is convenient. However, if an application running in a \n** low-memory environment is required to handle very large changesets, the\n** large contiguous memory allocations required can become onerous.\n**\n** In order to avoid this problem, instead of a single large buffer, input\n** is passed to a streaming API functions by way of a callback function that\n** the sessions module invokes to incrementally request input data as it is\n** required. In all cases, a pair of API function parameters such as\n**\n**  <pre>\n**  &nbsp;     int nChangeset,\n**  &nbsp;     void *pChangeset,\n**  </pre>\n**\n** Is replaced by:\n**\n**  <pre>\n**  &nbsp;     int (*xInput)(void *pIn, void *pData, int *pnData),\n**  &nbsp;     void *pIn,\n**  </pre>\n**\n** Each time the xInput callback is invoked by the sessions module, the first\n** argument passed is a copy of the supplied pIn context pointer. The second \n** argument, pData, points to a buffer (*pnData) bytes in size. Assuming no \n** error occurs the xInput method should copy up to (*pnData) bytes of data \n** into the buffer and set (*pnData) to the actual number of bytes copied \n** before returning SQLITE_OK. If the input is completely exhausted, (*pnData) \n** should be set to zero to indicate this. Or, if an error occurs, an SQLite \n** error code should be returned. In all cases, if an xInput callback returns\n** an error, all processing is abandoned and the streaming API function\n** returns a copy of the error code to the caller.\n**\n** In the case of sqlite3changeset_start_strm(), the xInput callback may be\n** invoked by the sessions module at any point during the lifetime of the\n** iterator. If such an xInput callback returns an error, the iterator enters\n** an error state, whereby all subsequent calls to iterator functions \n** immediately fail with the same error code as returned by xInput.\n**\n** Similarly, streaming API functions that return changesets (or patchsets)\n** return them in chunks by way of a callback function instead of via a\n** pointer to a single large buffer. In this case, a pair of parameters such\n** as:\n**\n**  <pre>\n**  &nbsp;     int *pnChangeset,\n**  &nbsp;     void **ppChangeset,\n**  </pre>\n**\n** Is replaced by:\n**\n**  <pre>\n**  &nbsp;     int (*xOutput)(void *pOut, const void *pData, int nData),\n**  &nbsp;     void *pOut\n**  </pre>\n**\n** The xOutput callback is invoked zero or more times to return data to\n** the application. The first parameter passed to each call is a copy of the\n** pOut pointer supplied by the application. The second parameter, pData,\n** points to a buffer nData bytes in size containing the chunk of output\n** data being returned. If the xOutput callback successfully processes the\n** supplied data, it should return SQLITE_OK to indicate success. Otherwise,\n** it should return some other SQLite error code. In this case processing\n** is immediately abandoned and the streaming API function returns a copy\n** of the xOutput error code to the application.\n**\n** The sessions module never invokes an xOutput callback with the third \n** parameter set to a value less than or equal to zero. Other than this,\n** no guarantees are made as to the size of the chunks of data returned.\n*/\nSQLITE_API int sqlite3changeset_apply_strm(\n  sqlite3 *db,                    /* Apply change to \"main\" db of this handle */\n  int (*xInput)(void *pIn, void *pData, int *pnData), /* Input function */\n  void *pIn,                                          /* First arg for xInput */\n  int(*xFilter)(\n    void *pCtx,                   /* Copy of sixth arg to _apply() */\n    const char *zTab              /* Table name */\n  ),\n  int(*xConflict)(\n    void *pCtx,                   /* Copy of sixth arg to _apply() */\n    int eConflict,                /* DATA, MISSING, CONFLICT, CONSTRAINT */\n    sqlite3_changeset_iter *p     /* Handle describing change and conflict */\n  ),\n  void *pCtx                      /* First argument passed to xConflict */\n);\nSQLITE_API int sqlite3changeset_concat_strm(\n  int (*xInputA)(void *pIn, void *pData, int *pnData),\n  void *pInA,\n  int (*xInputB)(void *pIn, void *pData, int *pnData),\n  void *pInB,\n  int (*xOutput)(void *pOut, const void *pData, int nData),\n  void *pOut\n);\nSQLITE_API int sqlite3changeset_invert_strm(\n  int (*xInput)(void *pIn, void *pData, int *pnData),\n  void *pIn,\n  int (*xOutput)(void *pOut, const void *pData, int nData),\n  void *pOut\n);\nSQLITE_API int sqlite3changeset_start_strm(\n  sqlite3_changeset_iter **pp,\n  int (*xInput)(void *pIn, void *pData, int *pnData),\n  void *pIn\n);\nSQLITE_API int sqlite3session_changeset_strm(\n  sqlite3_session *pSession,\n  int (*xOutput)(void *pOut, const void *pData, int nData),\n  void *pOut\n);\nSQLITE_API int sqlite3session_patchset_strm(\n  sqlite3_session *pSession,\n  int (*xOutput)(void *pOut, const void *pData, int nData),\n  void *pOut\n);\nSQLITE_API int sqlite3changegroup_add_strm(sqlite3_changegroup*, \n    int (*xInput)(void *pIn, void *pData, int *pnData),\n    void *pIn\n);\nSQLITE_API int sqlite3changegroup_output_strm(sqlite3_changegroup*,\n    int (*xOutput)(void *pOut, const void *pData, int nData), \n    void *pOut\n);\n\n\n/*\n** Make sure we can call this stuff from C++.\n*/\n#if 0\n}\n#endif\n\n#endif  /* !defined(__SQLITESESSION_H_) && defined(SQLITE_ENABLE_SESSION) */\n\n/******** End of sqlite3session.h *********/\n/******** Begin file fts5.h *********/\n/*\n** 2014 May 31\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n******************************************************************************\n**\n** Interfaces to extend FTS5. Using the interfaces defined in this file, \n** FTS5 may be extended with:\n**\n**     * custom tokenizers, and\n**     * custom auxiliary functions.\n*/\n\n\n#ifndef _FTS5_H\n#define _FTS5_H\n\n\n#if 0\nextern \"C\" {\n#endif\n\n/*************************************************************************\n** CUSTOM AUXILIARY FUNCTIONS\n**\n** Virtual table implementations may overload SQL functions by implementing\n** the sqlite3_module.xFindFunction() method.\n*/\n\ntypedef struct Fts5ExtensionApi Fts5ExtensionApi;\ntypedef struct Fts5Context Fts5Context;\ntypedef struct Fts5PhraseIter Fts5PhraseIter;\n\ntypedef void (*fts5_extension_function)(\n  const Fts5ExtensionApi *pApi,   /* API offered by current FTS version */\n  Fts5Context *pFts,              /* First arg to pass to pApi functions */\n  sqlite3_context *pCtx,          /* Context for returning result/error */\n  int nVal,                       /* Number of values in apVal[] array */\n  sqlite3_value **apVal           /* Array of trailing arguments */\n);\n\nstruct Fts5PhraseIter {\n  const unsigned char *a;\n  const unsigned char *b;\n};\n\n/*\n** EXTENSION API FUNCTIONS\n**\n** xUserData(pFts):\n**   Return a copy of the context pointer the extension function was \n**   registered with.\n**\n** xColumnTotalSize(pFts, iCol, pnToken):\n**   If parameter iCol is less than zero, set output variable *pnToken\n**   to the total number of tokens in the FTS5 table. Or, if iCol is\n**   non-negative but less than the number of columns in the table, return\n**   the total number of tokens in column iCol, considering all rows in \n**   the FTS5 table.\n**\n**   If parameter iCol is greater than or equal to the number of columns\n**   in the table, SQLITE_RANGE is returned. Or, if an error occurs (e.g.\n**   an OOM condition or IO error), an appropriate SQLite error code is \n**   returned.\n**\n** xColumnCount(pFts):\n**   Return the number of columns in the table.\n**\n** xColumnSize(pFts, iCol, pnToken):\n**   If parameter iCol is less than zero, set output variable *pnToken\n**   to the total number of tokens in the current row. Or, if iCol is\n**   non-negative but less than the number of columns in the table, set\n**   *pnToken to the number of tokens in column iCol of the current row.\n**\n**   If parameter iCol is greater than or equal to the number of columns\n**   in the table, SQLITE_RANGE is returned. Or, if an error occurs (e.g.\n**   an OOM condition or IO error), an appropriate SQLite error code is \n**   returned.\n**\n**   This function may be quite inefficient if used with an FTS5 table\n**   created with the \"columnsize=0\" option.\n**\n** xColumnText:\n**   This function attempts to retrieve the text of column iCol of the\n**   current document. If successful, (*pz) is set to point to a buffer\n**   containing the text in utf-8 encoding, (*pn) is set to the size in bytes\n**   (not characters) of the buffer and SQLITE_OK is returned. Otherwise,\n**   if an error occurs, an SQLite error code is returned and the final values\n**   of (*pz) and (*pn) are undefined.\n**\n** xPhraseCount:\n**   Returns the number of phrases in the current query expression.\n**\n** xPhraseSize:\n**   Returns the number of tokens in phrase iPhrase of the query. Phrases\n**   are numbered starting from zero.\n**\n** xInstCount:\n**   Set *pnInst to the total number of occurrences of all phrases within\n**   the query within the current row. Return SQLITE_OK if successful, or\n**   an error code (i.e. SQLITE_NOMEM) if an error occurs.\n**\n**   This API can be quite slow if used with an FTS5 table created with the\n**   \"detail=none\" or \"detail=column\" option. If the FTS5 table is created \n**   with either \"detail=none\" or \"detail=column\" and \"content=\" option \n**   (i.e. if it is a contentless table), then this API always returns 0.\n**\n** xInst:\n**   Query for the details of phrase match iIdx within the current row.\n**   Phrase matches are numbered starting from zero, so the iIdx argument\n**   should be greater than or equal to zero and smaller than the value\n**   output by xInstCount().\n**\n**   Usually, output parameter *piPhrase is set to the phrase number, *piCol\n**   to the column in which it occurs and *piOff the token offset of the\n**   first token of the phrase. The exception is if the table was created\n**   with the offsets=0 option specified. In this case *piOff is always\n**   set to -1.\n**\n**   Returns SQLITE_OK if successful, or an error code (i.e. SQLITE_NOMEM) \n**   if an error occurs.\n**\n**   This API can be quite slow if used with an FTS5 table created with the\n**   \"detail=none\" or \"detail=column\" option. \n**\n** xRowid:\n**   Returns the rowid of the current row.\n**\n** xTokenize:\n**   Tokenize text using the tokenizer belonging to the FTS5 table.\n**\n** xQueryPhrase(pFts5, iPhrase, pUserData, xCallback):\n**   This API function is used to query the FTS table for phrase iPhrase\n**   of the current query. Specifically, a query equivalent to:\n**\n**       ... FROM ftstable WHERE ftstable MATCH $p ORDER BY rowid\n**\n**   with $p set to a phrase equivalent to the phrase iPhrase of the\n**   current query is executed. Any column filter that applies to\n**   phrase iPhrase of the current query is included in $p. For each \n**   row visited, the callback function passed as the fourth argument \n**   is invoked. The context and API objects passed to the callback \n**   function may be used to access the properties of each matched row.\n**   Invoking Api.xUserData() returns a copy of the pointer passed as \n**   the third argument to pUserData.\n**\n**   If the callback function returns any value other than SQLITE_OK, the\n**   query is abandoned and the xQueryPhrase function returns immediately.\n**   If the returned value is SQLITE_DONE, xQueryPhrase returns SQLITE_OK.\n**   Otherwise, the error code is propagated upwards.\n**\n**   If the query runs to completion without incident, SQLITE_OK is returned.\n**   Or, if some error occurs before the query completes or is aborted by\n**   the callback, an SQLite error code is returned.\n**\n**\n** xSetAuxdata(pFts5, pAux, xDelete)\n**\n**   Save the pointer passed as the second argument as the extension functions \n**   \"auxiliary data\". The pointer may then be retrieved by the current or any\n**   future invocation of the same fts5 extension function made as part of\n**   of the same MATCH query using the xGetAuxdata() API.\n**\n**   Each extension function is allocated a single auxiliary data slot for\n**   each FTS query (MATCH expression). If the extension function is invoked \n**   more than once for a single FTS query, then all invocations share a \n**   single auxiliary data context.\n**\n**   If there is already an auxiliary data pointer when this function is\n**   invoked, then it is replaced by the new pointer. If an xDelete callback\n**   was specified along with the original pointer, it is invoked at this\n**   point.\n**\n**   The xDelete callback, if one is specified, is also invoked on the\n**   auxiliary data pointer after the FTS5 query has finished.\n**\n**   If an error (e.g. an OOM condition) occurs within this function, an\n**   the auxiliary data is set to NULL and an error code returned. If the\n**   xDelete parameter was not NULL, it is invoked on the auxiliary data\n**   pointer before returning.\n**\n**\n** xGetAuxdata(pFts5, bClear)\n**\n**   Returns the current auxiliary data pointer for the fts5 extension \n**   function. See the xSetAuxdata() method for details.\n**\n**   If the bClear argument is non-zero, then the auxiliary data is cleared\n**   (set to NULL) before this function returns. In this case the xDelete,\n**   if any, is not invoked.\n**\n**\n** xRowCount(pFts5, pnRow)\n**\n**   This function is used to retrieve the total number of rows in the table.\n**   In other words, the same value that would be returned by:\n**\n**        SELECT count(*) FROM ftstable;\n**\n** xPhraseFirst()\n**   This function is used, along with type Fts5PhraseIter and the xPhraseNext\n**   method, to iterate through all instances of a single query phrase within\n**   the current row. This is the same information as is accessible via the\n**   xInstCount/xInst APIs. While the xInstCount/xInst APIs are more convenient\n**   to use, this API may be faster under some circumstances. To iterate \n**   through instances of phrase iPhrase, use the following code:\n**\n**       Fts5PhraseIter iter;\n**       int iCol, iOff;\n**       for(pApi->xPhraseFirst(pFts, iPhrase, &iter, &iCol, &iOff);\n**           iCol>=0;\n**           pApi->xPhraseNext(pFts, &iter, &iCol, &iOff)\n**       ){\n**         // An instance of phrase iPhrase at offset iOff of column iCol\n**       }\n**\n**   The Fts5PhraseIter structure is defined above. Applications should not\n**   modify this structure directly - it should only be used as shown above\n**   with the xPhraseFirst() and xPhraseNext() API methods (and by\n**   xPhraseFirstColumn() and xPhraseNextColumn() as illustrated below).\n**\n**   This API can be quite slow if used with an FTS5 table created with the\n**   \"detail=none\" or \"detail=column\" option. If the FTS5 table is created \n**   with either \"detail=none\" or \"detail=column\" and \"content=\" option \n**   (i.e. if it is a contentless table), then this API always iterates\n**   through an empty set (all calls to xPhraseFirst() set iCol to -1).\n**\n** xPhraseNext()\n**   See xPhraseFirst above.\n**\n** xPhraseFirstColumn()\n**   This function and xPhraseNextColumn() are similar to the xPhraseFirst()\n**   and xPhraseNext() APIs described above. The difference is that instead\n**   of iterating through all instances of a phrase in the current row, these\n**   APIs are used to iterate through the set of columns in the current row\n**   that contain one or more instances of a specified phrase. For example:\n**\n**       Fts5PhraseIter iter;\n**       int iCol;\n**       for(pApi->xPhraseFirstColumn(pFts, iPhrase, &iter, &iCol);\n**           iCol>=0;\n**           pApi->xPhraseNextColumn(pFts, &iter, &iCol)\n**       ){\n**         // Column iCol contains at least one instance of phrase iPhrase\n**       }\n**\n**   This API can be quite slow if used with an FTS5 table created with the\n**   \"detail=none\" option. If the FTS5 table is created with either \n**   \"detail=none\" \"content=\" option (i.e. if it is a contentless table), \n**   then this API always iterates through an empty set (all calls to \n**   xPhraseFirstColumn() set iCol to -1).\n**\n**   The information accessed using this API and its companion\n**   xPhraseFirstColumn() may also be obtained using xPhraseFirst/xPhraseNext\n**   (or xInst/xInstCount). The chief advantage of this API is that it is\n**   significantly more efficient than those alternatives when used with\n**   \"detail=column\" tables.  \n**\n** xPhraseNextColumn()\n**   See xPhraseFirstColumn above.\n*/\nstruct Fts5ExtensionApi {\n  int iVersion;                   /* Currently always set to 3 */\n\n  void *(*xUserData)(Fts5Context*);\n\n  int (*xColumnCount)(Fts5Context*);\n  int (*xRowCount)(Fts5Context*, sqlite3_int64 *pnRow);\n  int (*xColumnTotalSize)(Fts5Context*, int iCol, sqlite3_int64 *pnToken);\n\n  int (*xTokenize)(Fts5Context*, \n    const char *pText, int nText, /* Text to tokenize */\n    void *pCtx,                   /* Context passed to xToken() */\n    int (*xToken)(void*, int, const char*, int, int, int)       /* Callback */\n  );\n\n  int (*xPhraseCount)(Fts5Context*);\n  int (*xPhraseSize)(Fts5Context*, int iPhrase);\n\n  int (*xInstCount)(Fts5Context*, int *pnInst);\n  int (*xInst)(Fts5Context*, int iIdx, int *piPhrase, int *piCol, int *piOff);\n\n  sqlite3_int64 (*xRowid)(Fts5Context*);\n  int (*xColumnText)(Fts5Context*, int iCol, const char **pz, int *pn);\n  int (*xColumnSize)(Fts5Context*, int iCol, int *pnToken);\n\n  int (*xQueryPhrase)(Fts5Context*, int iPhrase, void *pUserData,\n    int(*)(const Fts5ExtensionApi*,Fts5Context*,void*)\n  );\n  int (*xSetAuxdata)(Fts5Context*, void *pAux, void(*xDelete)(void*));\n  void *(*xGetAuxdata)(Fts5Context*, int bClear);\n\n  int (*xPhraseFirst)(Fts5Context*, int iPhrase, Fts5PhraseIter*, int*, int*);\n  void (*xPhraseNext)(Fts5Context*, Fts5PhraseIter*, int *piCol, int *piOff);\n\n  int (*xPhraseFirstColumn)(Fts5Context*, int iPhrase, Fts5PhraseIter*, int*);\n  void (*xPhraseNextColumn)(Fts5Context*, Fts5PhraseIter*, int *piCol);\n};\n\n/* \n** CUSTOM AUXILIARY FUNCTIONS\n*************************************************************************/\n\n/*************************************************************************\n** CUSTOM TOKENIZERS\n**\n** Applications may also register custom tokenizer types. A tokenizer \n** is registered by providing fts5 with a populated instance of the \n** following structure. All structure methods must be defined, setting\n** any member of the fts5_tokenizer struct to NULL leads to undefined\n** behaviour. The structure methods are expected to function as follows:\n**\n** xCreate:\n**   This function is used to allocate and initialize a tokenizer instance.\n**   A tokenizer instance is required to actually tokenize text.\n**\n**   The first argument passed to this function is a copy of the (void*)\n**   pointer provided by the application when the fts5_tokenizer object\n**   was registered with FTS5 (the third argument to xCreateTokenizer()). \n**   The second and third arguments are an array of nul-terminated strings\n**   containing the tokenizer arguments, if any, specified following the\n**   tokenizer name as part of the CREATE VIRTUAL TABLE statement used\n**   to create the FTS5 table.\n**\n**   The final argument is an output variable. If successful, (*ppOut) \n**   should be set to point to the new tokenizer handle and SQLITE_OK\n**   returned. If an error occurs, some value other than SQLITE_OK should\n**   be returned. In this case, fts5 assumes that the final value of *ppOut \n**   is undefined.\n**\n** xDelete:\n**   This function is invoked to delete a tokenizer handle previously\n**   allocated using xCreate(). Fts5 guarantees that this function will\n**   be invoked exactly once for each successful call to xCreate().\n**\n** xTokenize:\n**   This function is expected to tokenize the nText byte string indicated \n**   by argument pText. pText may or may not be nul-terminated. The first\n**   argument passed to this function is a pointer to an Fts5Tokenizer object\n**   returned by an earlier call to xCreate().\n**\n**   The second argument indicates the reason that FTS5 is requesting\n**   tokenization of the supplied text. This is always one of the following\n**   four values:\n**\n**   <ul><li> <b>FTS5_TOKENIZE_DOCUMENT</b> - A document is being inserted into\n**            or removed from the FTS table. The tokenizer is being invoked to\n**            determine the set of tokens to add to (or delete from) the\n**            FTS index.\n**\n**       <li> <b>FTS5_TOKENIZE_QUERY</b> - A MATCH query is being executed \n**            against the FTS index. The tokenizer is being called to tokenize \n**            a bareword or quoted string specified as part of the query.\n**\n**       <li> <b>(FTS5_TOKENIZE_QUERY | FTS5_TOKENIZE_PREFIX)</b> - Same as\n**            FTS5_TOKENIZE_QUERY, except that the bareword or quoted string is\n**            followed by a \"*\" character, indicating that the last token\n**            returned by the tokenizer will be treated as a token prefix.\n**\n**       <li> <b>FTS5_TOKENIZE_AUX</b> - The tokenizer is being invoked to \n**            satisfy an fts5_api.xTokenize() request made by an auxiliary\n**            function. Or an fts5_api.xColumnSize() request made by the same\n**            on a columnsize=0 database.  \n**   </ul>\n**\n**   For each token in the input string, the supplied callback xToken() must\n**   be invoked. The first argument to it should be a copy of the pointer\n**   passed as the second argument to xTokenize(). The third and fourth\n**   arguments are a pointer to a buffer containing the token text, and the\n**   size of the token in bytes. The 4th and 5th arguments are the byte offsets\n**   of the first byte of and first byte immediately following the text from\n**   which the token is derived within the input.\n**\n**   The second argument passed to the xToken() callback (\"tflags\") should\n**   normally be set to 0. The exception is if the tokenizer supports \n**   synonyms. In this case see the discussion below for details.\n**\n**   FTS5 assumes the xToken() callback is invoked for each token in the \n**   order that they occur within the input text.\n**\n**   If an xToken() callback returns any value other than SQLITE_OK, then\n**   the tokenization should be abandoned and the xTokenize() method should\n**   immediately return a copy of the xToken() return value. Or, if the\n**   input buffer is exhausted, xTokenize() should return SQLITE_OK. Finally,\n**   if an error occurs with the xTokenize() implementation itself, it\n**   may abandon the tokenization and return any error code other than\n**   SQLITE_OK or SQLITE_DONE.\n**\n** SYNONYM SUPPORT\n**\n**   Custom tokenizers may also support synonyms. Consider a case in which a\n**   user wishes to query for a phrase such as \"first place\". Using the \n**   built-in tokenizers, the FTS5 query 'first + place' will match instances\n**   of \"first place\" within the document set, but not alternative forms\n**   such as \"1st place\". In some applications, it would be better to match\n**   all instances of \"first place\" or \"1st place\" regardless of which form\n**   the user specified in the MATCH query text.\n**\n**   There are several ways to approach this in FTS5:\n**\n**   <ol><li> By mapping all synonyms to a single token. In this case, the \n**            In the above example, this means that the tokenizer returns the\n**            same token for inputs \"first\" and \"1st\". Say that token is in\n**            fact \"first\", so that when the user inserts the document \"I won\n**            1st place\" entries are added to the index for tokens \"i\", \"won\",\n**            \"first\" and \"place\". If the user then queries for '1st + place',\n**            the tokenizer substitutes \"first\" for \"1st\" and the query works\n**            as expected.\n**\n**       <li> By adding multiple synonyms for a single term to the FTS index.\n**            In this case, when tokenizing query text, the tokenizer may \n**            provide multiple synonyms for a single term within the document.\n**            FTS5 then queries the index for each synonym individually. For\n**            example, faced with the query:\n**\n**   <codeblock>\n**     ... MATCH 'first place'</codeblock>\n**\n**            the tokenizer offers both \"1st\" and \"first\" as synonyms for the\n**            first token in the MATCH query and FTS5 effectively runs a query \n**            similar to:\n**\n**   <codeblock>\n**     ... MATCH '(first OR 1st) place'</codeblock>\n**\n**            except that, for the purposes of auxiliary functions, the query\n**            still appears to contain just two phrases - \"(first OR 1st)\" \n**            being treated as a single phrase.\n**\n**       <li> By adding multiple synonyms for a single term to the FTS index.\n**            Using this method, when tokenizing document text, the tokenizer\n**            provides multiple synonyms for each token. So that when a \n**            document such as \"I won first place\" is tokenized, entries are\n**            added to the FTS index for \"i\", \"won\", \"first\", \"1st\" and\n**            \"place\".\n**\n**            This way, even if the tokenizer does not provide synonyms\n**            when tokenizing query text (it should not - to do would be\n**            inefficient), it doesn't matter if the user queries for \n**            'first + place' or '1st + place', as there are entires in the\n**            FTS index corresponding to both forms of the first token.\n**   </ol>\n**\n**   Whether it is parsing document or query text, any call to xToken that\n**   specifies a <i>tflags</i> argument with the FTS5_TOKEN_COLOCATED bit\n**   is considered to supply a synonym for the previous token. For example,\n**   when parsing the document \"I won first place\", a tokenizer that supports\n**   synonyms would call xToken() 5 times, as follows:\n**\n**   <codeblock>\n**       xToken(pCtx, 0, \"i\",                      1,  0,  1);\n**       xToken(pCtx, 0, \"won\",                    3,  2,  5);\n**       xToken(pCtx, 0, \"first\",                  5,  6, 11);\n**       xToken(pCtx, FTS5_TOKEN_COLOCATED, \"1st\", 3,  6, 11);\n**       xToken(pCtx, 0, \"place\",                  5, 12, 17);\n**</codeblock>\n**\n**   It is an error to specify the FTS5_TOKEN_COLOCATED flag the first time\n**   xToken() is called. Multiple synonyms may be specified for a single token\n**   by making multiple calls to xToken(FTS5_TOKEN_COLOCATED) in sequence. \n**   There is no limit to the number of synonyms that may be provided for a\n**   single token.\n**\n**   In many cases, method (1) above is the best approach. It does not add \n**   extra data to the FTS index or require FTS5 to query for multiple terms,\n**   so it is efficient in terms of disk space and query speed. However, it\n**   does not support prefix queries very well. If, as suggested above, the\n**   token \"first\" is subsituted for \"1st\" by the tokenizer, then the query:\n**\n**   <codeblock>\n**     ... MATCH '1s*'</codeblock>\n**\n**   will not match documents that contain the token \"1st\" (as the tokenizer\n**   will probably not map \"1s\" to any prefix of \"first\").\n**\n**   For full prefix support, method (3) may be preferred. In this case, \n**   because the index contains entries for both \"first\" and \"1st\", prefix\n**   queries such as 'fi*' or '1s*' will match correctly. However, because\n**   extra entries are added to the FTS index, this method uses more space\n**   within the database.\n**\n**   Method (2) offers a midpoint between (1) and (3). Using this method,\n**   a query such as '1s*' will match documents that contain the literal \n**   token \"1st\", but not \"first\" (assuming the tokenizer is not able to\n**   provide synonyms for prefixes). However, a non-prefix query like '1st'\n**   will match against \"1st\" and \"first\". This method does not require\n**   extra disk space, as no extra entries are added to the FTS index. \n**   On the other hand, it may require more CPU cycles to run MATCH queries,\n**   as separate queries of the FTS index are required for each synonym.\n**\n**   When using methods (2) or (3), it is important that the tokenizer only\n**   provide synonyms when tokenizing document text (method (2)) or query\n**   text (method (3)), not both. Doing so will not cause any errors, but is\n**   inefficient.\n*/\ntypedef struct Fts5Tokenizer Fts5Tokenizer;\ntypedef struct fts5_tokenizer fts5_tokenizer;\nstruct fts5_tokenizer {\n  int (*xCreate)(void*, const char **azArg, int nArg, Fts5Tokenizer **ppOut);\n  void (*xDelete)(Fts5Tokenizer*);\n  int (*xTokenize)(Fts5Tokenizer*, \n      void *pCtx,\n      int flags,            /* Mask of FTS5_TOKENIZE_* flags */\n      const char *pText, int nText, \n      int (*xToken)(\n        void *pCtx,         /* Copy of 2nd argument to xTokenize() */\n        int tflags,         /* Mask of FTS5_TOKEN_* flags */\n        const char *pToken, /* Pointer to buffer containing token */\n        int nToken,         /* Size of token in bytes */\n        int iStart,         /* Byte offset of token within input text */\n        int iEnd            /* Byte offset of end of token within input text */\n      )\n  );\n};\n\n/* Flags that may be passed as the third argument to xTokenize() */\n#define FTS5_TOKENIZE_QUERY     0x0001\n#define FTS5_TOKENIZE_PREFIX    0x0002\n#define FTS5_TOKENIZE_DOCUMENT  0x0004\n#define FTS5_TOKENIZE_AUX       0x0008\n\n/* Flags that may be passed by the tokenizer implementation back to FTS5\n** as the third argument to the supplied xToken callback. */\n#define FTS5_TOKEN_COLOCATED    0x0001      /* Same position as prev. token */\n\n/*\n** END OF CUSTOM TOKENIZERS\n*************************************************************************/\n\n/*************************************************************************\n** FTS5 EXTENSION REGISTRATION API\n*/\ntypedef struct fts5_api fts5_api;\nstruct fts5_api {\n  int iVersion;                   /* Currently always set to 2 */\n\n  /* Create a new tokenizer */\n  int (*xCreateTokenizer)(\n    fts5_api *pApi,\n    const char *zName,\n    void *pContext,\n    fts5_tokenizer *pTokenizer,\n    void (*xDestroy)(void*)\n  );\n\n  /* Find an existing tokenizer */\n  int (*xFindTokenizer)(\n    fts5_api *pApi,\n    const char *zName,\n    void **ppContext,\n    fts5_tokenizer *pTokenizer\n  );\n\n  /* Create a new auxiliary function */\n  int (*xCreateFunction)(\n    fts5_api *pApi,\n    const char *zName,\n    void *pContext,\n    fts5_extension_function xFunction,\n    void (*xDestroy)(void*)\n  );\n};\n\n/*\n** END OF REGISTRATION API\n*************************************************************************/\n\n#if 0\n}  /* end of the 'extern \"C\"' block */\n#endif\n\n#endif /* _FTS5_H */\n\n/******** End of fts5.h *********/\n\n/************** End of sqlite3.h *********************************************/\n/************** Continuing where we left off in sqliteInt.h ******************/\n\n/*\n** Include the configuration header output by 'configure' if we're using the\n** autoconf-based build\n*/\n#if defined(_HAVE_SQLITE_CONFIG_H) && !defined(SQLITECONFIG_H)\n/* #include \"config.h\" */\n#define SQLITECONFIG_H 1\n#endif\n\n/************** Include sqliteLimit.h in the middle of sqliteInt.h ***********/\n/************** Begin file sqliteLimit.h *************************************/\n/*\n** 2007 May 7\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n*************************************************************************\n** \n** This file defines various limits of what SQLite can process.\n*/\n\n/*\n** The maximum length of a TEXT or BLOB in bytes.   This also\n** limits the size of a row in a table or index.\n**\n** The hard limit is the ability of a 32-bit signed integer\n** to count the size: 2^31-1 or 2147483647.\n*/\n#ifndef SQLITE_MAX_LENGTH\n# define SQLITE_MAX_LENGTH 1000000000\n#endif\n\n/*\n** This is the maximum number of\n**\n**    * Columns in a table\n**    * Columns in an index\n**    * Columns in a view\n**    * Terms in the SET clause of an UPDATE statement\n**    * Terms in the result set of a SELECT statement\n**    * Terms in the GROUP BY or ORDER BY clauses of a SELECT statement.\n**    * Terms in the VALUES clause of an INSERT statement\n**\n** The hard upper limit here is 32676.  Most database people will\n** tell you that in a well-normalized database, you usually should\n** not have more than a dozen or so columns in any table.  And if\n** that is the case, there is no point in having more than a few\n** dozen values in any of the other situations described above.\n*/\n#ifndef SQLITE_MAX_COLUMN\n# define SQLITE_MAX_COLUMN 2000\n#endif\n\n/*\n** The maximum length of a single SQL statement in bytes.\n**\n** It used to be the case that setting this value to zero would\n** turn the limit off.  That is no longer true.  It is not possible\n** to turn this limit off.\n*/\n#ifndef SQLITE_MAX_SQL_LENGTH\n# define SQLITE_MAX_SQL_LENGTH 1000000000\n#endif\n\n/*\n** The maximum depth of an expression tree. This is limited to \n** some extent by SQLITE_MAX_SQL_LENGTH. But sometime you might \n** want to place more severe limits on the complexity of an \n** expression.\n**\n** A value of 0 used to mean that the limit was not enforced.\n** But that is no longer true.  The limit is now strictly enforced\n** at all times.\n*/\n#ifndef SQLITE_MAX_EXPR_DEPTH\n# define SQLITE_MAX_EXPR_DEPTH 1000\n#endif\n\n/*\n** The maximum number of terms in a compound SELECT statement.\n** The code generator for compound SELECT statements does one\n** level of recursion for each term.  A stack overflow can result\n** if the number of terms is too large.  In practice, most SQL\n** never has more than 3 or 4 terms.  Use a value of 0 to disable\n** any limit on the number of terms in a compount SELECT.\n*/\n#ifndef SQLITE_MAX_COMPOUND_SELECT\n# define SQLITE_MAX_COMPOUND_SELECT 500\n#endif\n\n/*\n** The maximum number of opcodes in a VDBE program.\n** Not currently enforced.\n*/\n#ifndef SQLITE_MAX_VDBE_OP\n# define SQLITE_MAX_VDBE_OP 250000000\n#endif\n\n/*\n** The maximum number of arguments to an SQL function.\n*/\n#ifndef SQLITE_MAX_FUNCTION_ARG\n# define SQLITE_MAX_FUNCTION_ARG 127\n#endif\n\n/*\n** The suggested maximum number of in-memory pages to use for\n** the main database table and for temporary tables.\n**\n** IMPLEMENTATION-OF: R-30185-15359 The default suggested cache size is -2000,\n** which means the cache size is limited to 2048000 bytes of memory.\n** IMPLEMENTATION-OF: R-48205-43578 The default suggested cache size can be\n** altered using the SQLITE_DEFAULT_CACHE_SIZE compile-time options.\n*/\n#ifndef SQLITE_DEFAULT_CACHE_SIZE\n# define SQLITE_DEFAULT_CACHE_SIZE  -2000\n#endif\n\n/*\n** The default number of frames to accumulate in the log file before\n** checkpointing the database in WAL mode.\n*/\n#ifndef SQLITE_DEFAULT_WAL_AUTOCHECKPOINT\n# define SQLITE_DEFAULT_WAL_AUTOCHECKPOINT  1000\n#endif\n\n/*\n** The maximum number of attached databases.  This must be between 0\n** and 125.  The upper bound of 125 is because the attached databases are\n** counted using a signed 8-bit integer which has a maximum value of 127\n** and we have to allow 2 extra counts for the \"main\" and \"temp\" databases.\n*/\n#ifndef SQLITE_MAX_ATTACHED\n# define SQLITE_MAX_ATTACHED 10\n#endif\n\n\n/*\n** The maximum value of a ?nnn wildcard that the parser will accept.\n*/\n#ifndef SQLITE_MAX_VARIABLE_NUMBER\n# define SQLITE_MAX_VARIABLE_NUMBER 999\n#endif\n\n/* Maximum page size.  The upper bound on this value is 65536.  This a limit\n** imposed by the use of 16-bit offsets within each page.\n**\n** Earlier versions of SQLite allowed the user to change this value at\n** compile time. This is no longer permitted, on the grounds that it creates\n** a library that is technically incompatible with an SQLite library \n** compiled with a different limit. If a process operating on a database \n** with a page-size of 65536 bytes crashes, then an instance of SQLite \n** compiled with the default page-size limit will not be able to rollback \n** the aborted transaction. This could lead to database corruption.\n*/\n#ifdef SQLITE_MAX_PAGE_SIZE\n# undef SQLITE_MAX_PAGE_SIZE\n#endif\n#define SQLITE_MAX_PAGE_SIZE 65536\n\n\n/*\n** The default size of a database page.\n*/\n#ifndef SQLITE_DEFAULT_PAGE_SIZE\n# define SQLITE_DEFAULT_PAGE_SIZE 4096\n#endif\n#if SQLITE_DEFAULT_PAGE_SIZE>SQLITE_MAX_PAGE_SIZE\n# undef SQLITE_DEFAULT_PAGE_SIZE\n# define SQLITE_DEFAULT_PAGE_SIZE SQLITE_MAX_PAGE_SIZE\n#endif\n\n/*\n** Ordinarily, if no value is explicitly provided, SQLite creates databases\n** with page size SQLITE_DEFAULT_PAGE_SIZE. However, based on certain\n** device characteristics (sector-size and atomic write() support),\n** SQLite may choose a larger value. This constant is the maximum value\n** SQLite will choose on its own.\n*/\n#ifndef SQLITE_MAX_DEFAULT_PAGE_SIZE\n# define SQLITE_MAX_DEFAULT_PAGE_SIZE 8192\n#endif\n#if SQLITE_MAX_DEFAULT_PAGE_SIZE>SQLITE_MAX_PAGE_SIZE\n# undef SQLITE_MAX_DEFAULT_PAGE_SIZE\n# define SQLITE_MAX_DEFAULT_PAGE_SIZE SQLITE_MAX_PAGE_SIZE\n#endif\n\n\n/*\n** Maximum number of pages in one database file.\n**\n** This is really just the default value for the max_page_count pragma.\n** This value can be lowered (or raised) at run-time using that the\n** max_page_count macro.\n*/\n#ifndef SQLITE_MAX_PAGE_COUNT\n# define SQLITE_MAX_PAGE_COUNT 1073741823\n#endif\n\n/*\n** Maximum length (in bytes) of the pattern in a LIKE or GLOB\n** operator.\n*/\n#ifndef SQLITE_MAX_LIKE_PATTERN_LENGTH\n# define SQLITE_MAX_LIKE_PATTERN_LENGTH 50000\n#endif\n\n/*\n** Maximum depth of recursion for triggers.\n**\n** A value of 1 means that a trigger program will not be able to itself\n** fire any triggers. A value of 0 means that no trigger programs at all \n** may be executed.\n*/\n#ifndef SQLITE_MAX_TRIGGER_DEPTH\n# define SQLITE_MAX_TRIGGER_DEPTH 1000\n#endif\n\n/************** End of sqliteLimit.h *****************************************/\n/************** Continuing where we left off in sqliteInt.h ******************/\n\n/* Disable nuisance warnings on Borland compilers */\n#if defined(__BORLANDC__)\n#pragma warn -rch /* unreachable code */\n#pragma warn -ccc /* Condition is always true or false */\n#pragma warn -aus /* Assigned value is never used */\n#pragma warn -csu /* Comparing signed and unsigned */\n#pragma warn -spa /* Suspicious pointer arithmetic */\n#endif\n\n/*\n** Include standard header files as necessary\n*/\n#ifdef HAVE_STDINT_H\n#include <stdint.h>\n#endif\n#ifdef HAVE_INTTYPES_H\n#include <inttypes.h>\n#endif\n\n/*\n** The following macros are used to cast pointers to integers and\n** integers to pointers.  The way you do this varies from one compiler\n** to the next, so we have developed the following set of #if statements\n** to generate appropriate macros for a wide range of compilers.\n**\n** The correct \"ANSI\" way to do this is to use the intptr_t type.\n** Unfortunately, that typedef is not available on all compilers, or\n** if it is available, it requires an #include of specific headers\n** that vary from one machine to the next.\n**\n** Ticket #3860:  The llvm-gcc-4.2 compiler from Apple chokes on\n** the ((void*)&((char*)0)[X]) construct.  But MSVC chokes on ((void*)(X)).\n** So we have to define the macros in different ways depending on the\n** compiler.\n*/\n#if defined(__PTRDIFF_TYPE__)  /* This case should work for GCC */\n# define SQLITE_INT_TO_PTR(X)  ((void*)(__PTRDIFF_TYPE__)(X))\n# define SQLITE_PTR_TO_INT(X)  ((int)(__PTRDIFF_TYPE__)(X))\n#elif !defined(__GNUC__)       /* Works for compilers other than LLVM */\n# define SQLITE_INT_TO_PTR(X)  ((void*)&((char*)0)[X])\n# define SQLITE_PTR_TO_INT(X)  ((int)(((char*)X)-(char*)0))\n#elif defined(HAVE_STDINT_H)   /* Use this case if we have ANSI headers */\n# define SQLITE_INT_TO_PTR(X)  ((void*)(intptr_t)(X))\n# define SQLITE_PTR_TO_INT(X)  ((int)(intptr_t)(X))\n#else                          /* Generates a warning - but it always works */\n# define SQLITE_INT_TO_PTR(X)  ((void*)(X))\n# define SQLITE_PTR_TO_INT(X)  ((int)(X))\n#endif\n\n/*\n** A macro to hint to the compiler that a function should not be\n** inlined.\n*/\n#if defined(__GNUC__)\n#  define SQLITE_NOINLINE  __attribute__((noinline))\n#elif defined(_MSC_VER) && _MSC_VER>=1310\n#  define SQLITE_NOINLINE  __declspec(noinline)\n#else\n#  define SQLITE_NOINLINE\n#endif\n\n/*\n** Make sure that the compiler intrinsics we desire are enabled when\n** compiling with an appropriate version of MSVC unless prevented by\n** the SQLITE_DISABLE_INTRINSIC define.\n*/\n#if !defined(SQLITE_DISABLE_INTRINSIC)\n#  if defined(_MSC_VER) && _MSC_VER>=1400\n#    if !defined(_WIN32_WCE)\n#      include <intrin.h>\n#      pragma intrinsic(_byteswap_ushort)\n#      pragma intrinsic(_byteswap_ulong)\n#      pragma intrinsic(_byteswap_uint64)\n#      pragma intrinsic(_ReadWriteBarrier)\n#    else\n#      include <cmnintrin.h>\n#    endif\n#  endif\n#endif\n\n/*\n** The SQLITE_THREADSAFE macro must be defined as 0, 1, or 2.\n** 0 means mutexes are permanently disable and the library is never\n** threadsafe.  1 means the library is serialized which is the highest\n** level of threadsafety.  2 means the library is multithreaded - multiple\n** threads can use SQLite as long as no two threads try to use the same\n** database connection at the same time.\n**\n** Older versions of SQLite used an optional THREADSAFE macro.\n** We support that for legacy.\n**\n** To ensure that the correct value of \"THREADSAFE\" is reported when querying\n** for compile-time options at runtime (e.g. \"PRAGMA compile_options\"), this\n** logic is partially replicated in ctime.c. If it is updated here, it should\n** also be updated there.\n*/\n#if !defined(SQLITE_THREADSAFE)\n# if defined(THREADSAFE)\n#   define SQLITE_THREADSAFE THREADSAFE\n# else\n#   define SQLITE_THREADSAFE 1 /* IMP: R-07272-22309 */\n# endif\n#endif\n\n/*\n** Powersafe overwrite is on by default.  But can be turned off using\n** the -DSQLITE_POWERSAFE_OVERWRITE=0 command-line option.\n*/\n#ifndef SQLITE_POWERSAFE_OVERWRITE\n# define SQLITE_POWERSAFE_OVERWRITE 1\n#endif\n\n/*\n** EVIDENCE-OF: R-25715-37072 Memory allocation statistics are enabled by\n** default unless SQLite is compiled with SQLITE_DEFAULT_MEMSTATUS=0 in\n** which case memory allocation statistics are disabled by default.\n*/\n#if !defined(SQLITE_DEFAULT_MEMSTATUS)\n# define SQLITE_DEFAULT_MEMSTATUS 1\n#endif\n\n/*\n** Exactly one of the following macros must be defined in order to\n** specify which memory allocation subsystem to use.\n**\n**     SQLITE_SYSTEM_MALLOC          // Use normal system malloc()\n**     SQLITE_WIN32_MALLOC           // Use Win32 native heap API\n**     SQLITE_ZERO_MALLOC            // Use a stub allocator that always fails\n**     SQLITE_MEMDEBUG               // Debugging version of system malloc()\n**\n** On Windows, if the SQLITE_WIN32_MALLOC_VALIDATE macro is defined and the\n** assert() macro is enabled, each call into the Win32 native heap subsystem\n** will cause HeapValidate to be called.  If heap validation should fail, an\n** assertion will be triggered.\n**\n** If none of the above are defined, then set SQLITE_SYSTEM_MALLOC as\n** the default.\n*/\n#if defined(SQLITE_SYSTEM_MALLOC) \\\n  + defined(SQLITE_WIN32_MALLOC) \\\n  + defined(SQLITE_ZERO_MALLOC) \\\n  + defined(SQLITE_MEMDEBUG)>1\n# error \"Two or more of the following compile-time configuration options\\\n are defined but at most one is allowed:\\\n SQLITE_SYSTEM_MALLOC, SQLITE_WIN32_MALLOC, SQLITE_MEMDEBUG,\\\n SQLITE_ZERO_MALLOC\"\n#endif\n#if defined(SQLITE_SYSTEM_MALLOC) \\\n  + defined(SQLITE_WIN32_MALLOC) \\\n  + defined(SQLITE_ZERO_MALLOC) \\\n  + defined(SQLITE_MEMDEBUG)==0\n# define SQLITE_SYSTEM_MALLOC 1\n#endif\n\n/*\n** If SQLITE_MALLOC_SOFT_LIMIT is not zero, then try to keep the\n** sizes of memory allocations below this value where possible.\n*/\n#if !defined(SQLITE_MALLOC_SOFT_LIMIT)\n# define SQLITE_MALLOC_SOFT_LIMIT 1024\n#endif\n\n/*\n** We need to define _XOPEN_SOURCE as follows in order to enable\n** recursive mutexes on most Unix systems and fchmod() on OpenBSD.\n** But _XOPEN_SOURCE define causes problems for Mac OS X, so omit\n** it.\n*/\n#if !defined(_XOPEN_SOURCE) && !defined(__DARWIN__) && !defined(__APPLE__)\n#  define _XOPEN_SOURCE 600\n#endif\n\n/*\n** NDEBUG and SQLITE_DEBUG are opposites.  It should always be true that\n** defined(NDEBUG)==!defined(SQLITE_DEBUG).  If this is not currently true,\n** make it true by defining or undefining NDEBUG.\n**\n** Setting NDEBUG makes the code smaller and faster by disabling the\n** assert() statements in the code.  So we want the default action\n** to be for NDEBUG to be set and NDEBUG to be undefined only if SQLITE_DEBUG\n** is set.  Thus NDEBUG becomes an opt-in rather than an opt-out\n** feature.\n*/\n#if !defined(NDEBUG) && !defined(SQLITE_DEBUG)\n# define NDEBUG 1\n#endif\n#if defined(NDEBUG) && defined(SQLITE_DEBUG)\n# undef NDEBUG\n#endif\n\n/*\n** Enable SQLITE_ENABLE_EXPLAIN_COMMENTS if SQLITE_DEBUG is turned on.\n*/\n#if !defined(SQLITE_ENABLE_EXPLAIN_COMMENTS) && defined(SQLITE_DEBUG)\n# define SQLITE_ENABLE_EXPLAIN_COMMENTS 1\n#endif\n\n/*\n** The testcase() macro is used to aid in coverage testing.  When\n** doing coverage testing, the condition inside the argument to\n** testcase() must be evaluated both true and false in order to\n** get full branch coverage.  The testcase() macro is inserted\n** to help ensure adequate test coverage in places where simple\n** condition/decision coverage is inadequate.  For example, testcase()\n** can be used to make sure boundary values are tested.  For\n** bitmask tests, testcase() can be used to make sure each bit\n** is significant and used at least once.  On switch statements\n** where multiple cases go to the same block of code, testcase()\n** can insure that all cases are evaluated.\n**\n*/\n#ifdef SQLITE_COVERAGE_TEST\nSQLITE_PRIVATE   void sqlite3Coverage(int);\n# define testcase(X)  if( X ){ sqlite3Coverage(__LINE__); }\n#else\n# define testcase(X)\n#endif\n\n/*\n** The TESTONLY macro is used to enclose variable declarations or\n** other bits of code that are needed to support the arguments\n** within testcase() and assert() macros.\n*/\n#if !defined(NDEBUG) || defined(SQLITE_COVERAGE_TEST)\n# define TESTONLY(X)  X\n#else\n# define TESTONLY(X)\n#endif\n\n/*\n** Sometimes we need a small amount of code such as a variable initialization\n** to setup for a later assert() statement.  We do not want this code to\n** appear when assert() is disabled.  The following macro is therefore\n** used to contain that setup code.  The \"VVA\" acronym stands for\n** \"Verification, Validation, and Accreditation\".  In other words, the\n** code within VVA_ONLY() will only run during verification processes.\n*/\n#ifndef NDEBUG\n# define VVA_ONLY(X)  X\n#else\n# define VVA_ONLY(X)\n#endif\n\n/*\n** The ALWAYS and NEVER macros surround boolean expressions which\n** are intended to always be true or false, respectively.  Such\n** expressions could be omitted from the code completely.  But they\n** are included in a few cases in order to enhance the resilience\n** of SQLite to unexpected behavior - to make the code \"self-healing\"\n** or \"ductile\" rather than being \"brittle\" and crashing at the first\n** hint of unplanned behavior.\n**\n** In other words, ALWAYS and NEVER are added for defensive code.\n**\n** When doing coverage testing ALWAYS and NEVER are hard-coded to\n** be true and false so that the unreachable code they specify will\n** not be counted as untested code.\n*/\n#if defined(SQLITE_COVERAGE_TEST) || defined(SQLITE_MUTATION_TEST)\n# define ALWAYS(X)      (1)\n# define NEVER(X)       (0)\n#elif !defined(NDEBUG)\n# define ALWAYS(X)      ((X)?1:(assert(0),0))\n# define NEVER(X)       ((X)?(assert(0),1):0)\n#else\n# define ALWAYS(X)      (X)\n# define NEVER(X)       (X)\n#endif\n\n/*\n** Some conditionals are optimizations only.  In other words, if the\n** conditionals are replaced with a constant 1 (true) or 0 (false) then\n** the correct answer is still obtained, though perhaps not as quickly.\n**\n** The following macros mark these optimizations conditionals.\n*/\n#if defined(SQLITE_MUTATION_TEST)\n# define OK_IF_ALWAYS_TRUE(X)  (1)\n# define OK_IF_ALWAYS_FALSE(X) (0)\n#else\n# define OK_IF_ALWAYS_TRUE(X)  (X)\n# define OK_IF_ALWAYS_FALSE(X) (X)\n#endif\n\n/*\n** Some malloc failures are only possible if SQLITE_TEST_REALLOC_STRESS is\n** defined.  We need to defend against those failures when testing with\n** SQLITE_TEST_REALLOC_STRESS, but we don't want the unreachable branches\n** during a normal build.  The following macro can be used to disable tests\n** that are always false except when SQLITE_TEST_REALLOC_STRESS is set.\n*/\n#if defined(SQLITE_TEST_REALLOC_STRESS)\n# define ONLY_IF_REALLOC_STRESS(X)  (X)\n#elif !defined(NDEBUG)\n# define ONLY_IF_REALLOC_STRESS(X)  ((X)?(assert(0),1):0)\n#else\n# define ONLY_IF_REALLOC_STRESS(X)  (0)\n#endif\n\n/*\n** Declarations used for tracing the operating system interfaces.\n*/\n#if defined(SQLITE_FORCE_OS_TRACE) || defined(SQLITE_TEST) || \\\n    (defined(SQLITE_DEBUG) && SQLITE_OS_WIN)\n  extern int sqlite3OSTrace;\n# define OSTRACE(X)          if( sqlite3OSTrace ) sqlite3DebugPrintf X\n# define SQLITE_HAVE_OS_TRACE\n#else\n# define OSTRACE(X)\n# undef  SQLITE_HAVE_OS_TRACE\n#endif\n\n/*\n** Is the sqlite3ErrName() function needed in the build?  Currently,\n** it is needed by \"mutex_w32.c\" (when debugging), \"os_win.c\" (when\n** OSTRACE is enabled), and by several \"test*.c\" files (which are\n** compiled using SQLITE_TEST).\n*/\n#if defined(SQLITE_HAVE_OS_TRACE) || defined(SQLITE_TEST) || \\\n    (defined(SQLITE_DEBUG) && SQLITE_OS_WIN)\n# define SQLITE_NEED_ERR_NAME\n#else\n# undef  SQLITE_NEED_ERR_NAME\n#endif\n\n/*\n** SQLITE_ENABLE_EXPLAIN_COMMENTS is incompatible with SQLITE_OMIT_EXPLAIN\n*/\n#ifdef SQLITE_OMIT_EXPLAIN\n# undef SQLITE_ENABLE_EXPLAIN_COMMENTS\n#endif\n\n/*\n** Return true (non-zero) if the input is an integer that is too large\n** to fit in 32-bits.  This macro is used inside of various testcase()\n** macros to verify that we have tested SQLite for large-file support.\n*/\n#define IS_BIG_INT(X)  (((X)&~(i64)0xffffffff)!=0)\n\n/*\n** The macro unlikely() is a hint that surrounds a boolean\n** expression that is usually false.  Macro likely() surrounds\n** a boolean expression that is usually true.  These hints could,\n** in theory, be used by the compiler to generate better code, but\n** currently they are just comments for human readers.\n*/\n#define likely(X)    (X)\n#define unlikely(X)  (X)\n\n/************** Include hash.h in the middle of sqliteInt.h ******************/\n/************** Begin file hash.h ********************************************/\n/*\n** 2001 September 22\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n*************************************************************************\n** This is the header file for the generic hash-table implementation\n** used in SQLite.\n*/\n#ifndef SQLITE_HASH_H\n#define SQLITE_HASH_H\n\n/* Forward declarations of structures. */\ntypedef struct Hash Hash;\ntypedef struct HashElem HashElem;\n\n/* A complete hash table is an instance of the following structure.\n** The internals of this structure are intended to be opaque -- client\n** code should not attempt to access or modify the fields of this structure\n** directly.  Change this structure only by using the routines below.\n** However, some of the \"procedures\" and \"functions\" for modifying and\n** accessing this structure are really macros, so we can't really make\n** this structure opaque.\n**\n** All elements of the hash table are on a single doubly-linked list.\n** Hash.first points to the head of this list.\n**\n** There are Hash.htsize buckets.  Each bucket points to a spot in\n** the global doubly-linked list.  The contents of the bucket are the\n** element pointed to plus the next _ht.count-1 elements in the list.\n**\n** Hash.htsize and Hash.ht may be zero.  In that case lookup is done\n** by a linear search of the global list.  For small tables, the \n** Hash.ht table is never allocated because if there are few elements\n** in the table, it is faster to do a linear search than to manage\n** the hash table.\n*/\nstruct Hash {\n  unsigned int htsize;      /* Number of buckets in the hash table */\n  unsigned int count;       /* Number of entries in this table */\n  HashElem *first;          /* The first element of the array */\n  struct _ht {              /* the hash table */\n    int count;                 /* Number of entries with this hash */\n    HashElem *chain;           /* Pointer to first entry with this hash */\n  } *ht;\n};\n\n/* Each element in the hash table is an instance of the following \n** structure.  All elements are stored on a single doubly-linked list.\n**\n** Again, this structure is intended to be opaque, but it can't really\n** be opaque because it is used by macros.\n*/\nstruct HashElem {\n  HashElem *next, *prev;       /* Next and previous elements in the table */\n  void *data;                  /* Data associated with this element */\n  const char *pKey;            /* Key associated with this element */\n};\n\n/*\n** Access routines.  To delete, insert a NULL pointer.\n*/\nSQLITE_PRIVATE void sqlite3HashInit(Hash*);\nSQLITE_PRIVATE void *sqlite3HashInsert(Hash*, const char *pKey, void *pData);\nSQLITE_PRIVATE void *sqlite3HashFind(const Hash*, const char *pKey);\nSQLITE_PRIVATE void sqlite3HashClear(Hash*);\n\n/*\n** Macros for looping over all elements of a hash table.  The idiom is\n** like this:\n**\n**   Hash h;\n**   HashElem *p;\n**   ...\n**   for(p=sqliteHashFirst(&h); p; p=sqliteHashNext(p)){\n**     SomeStructure *pData = sqliteHashData(p);\n**     // do something with pData\n**   }\n*/\n#define sqliteHashFirst(H)  ((H)->first)\n#define sqliteHashNext(E)   ((E)->next)\n#define sqliteHashData(E)   ((E)->data)\n/* #define sqliteHashKey(E)    ((E)->pKey) // NOT USED */\n/* #define sqliteHashKeysize(E) ((E)->nKey)  // NOT USED */\n\n/*\n** Number of entries in a hash table\n*/\n/* #define sqliteHashCount(H)  ((H)->count) // NOT USED */\n\n#endif /* SQLITE_HASH_H */\n\n/************** End of hash.h ************************************************/\n/************** Continuing where we left off in sqliteInt.h ******************/\n/************** Include parse.h in the middle of sqliteInt.h *****************/\n/************** Begin file parse.h *******************************************/\n#define TK_SEMI                             1\n#define TK_EXPLAIN                          2\n#define TK_QUERY                            3\n#define TK_PLAN                             4\n#define TK_BEGIN                            5\n#define TK_TRANSACTION                      6\n#define TK_DEFERRED                         7\n#define TK_IMMEDIATE                        8\n#define TK_EXCLUSIVE                        9\n#define TK_COMMIT                          10\n#define TK_END                             11\n#define TK_ROLLBACK                        12\n#define TK_SAVEPOINT                       13\n#define TK_RELEASE                         14\n#define TK_TO                              15\n#define TK_TABLE                           16\n#define TK_CREATE                          17\n#define TK_IF                              18\n#define TK_NOT                             19\n#define TK_EXISTS                          20\n#define TK_TEMP                            21\n#define TK_LP                              22\n#define TK_RP                              23\n#define TK_AS                              24\n#define TK_WITHOUT                         25\n#define TK_COMMA                           26\n#define TK_ABORT                           27\n#define TK_ACTION                          28\n#define TK_AFTER                           29\n#define TK_ANALYZE                         30\n#define TK_ASC                             31\n#define TK_ATTACH                          32\n#define TK_BEFORE                          33\n#define TK_BY                              34\n#define TK_CASCADE                         35\n#define TK_CAST                            36\n#define TK_CONFLICT                        37\n#define TK_DATABASE                        38\n#define TK_DESC                            39\n#define TK_DETACH                          40\n#define TK_EACH                            41\n#define TK_FAIL                            42\n#define TK_OR                              43\n#define TK_AND                             44\n#define TK_IS                              45\n#define TK_MATCH                           46\n#define TK_LIKE_KW                         47\n#define TK_BETWEEN                         48\n#define TK_IN                              49\n#define TK_ISNULL                          50\n#define TK_NOTNULL                         51\n#define TK_NE                              52\n#define TK_EQ                              53\n#define TK_GT                              54\n#define TK_LE                              55\n#define TK_LT                              56\n#define TK_GE                              57\n#define TK_ESCAPE                          58\n#define TK_ID                              59\n#define TK_COLUMNKW                        60\n#define TK_FOR                             61\n#define TK_IGNORE                          62\n#define TK_INITIALLY                       63\n#define TK_INSTEAD                         64\n#define TK_NO                              65\n#define TK_KEY                             66\n#define TK_OF                              67\n#define TK_OFFSET                          68\n#define TK_PRAGMA                          69\n#define TK_RAISE                           70\n#define TK_RECURSIVE                       71\n#define TK_REPLACE                         72\n#define TK_RESTRICT                        73\n#define TK_ROW                             74\n#define TK_TRIGGER                         75\n#define TK_VACUUM                          76\n#define TK_VIEW                            77\n#define TK_VIRTUAL                         78\n#define TK_WITH                            79\n#define TK_REINDEX                         80\n#define TK_RENAME                          81\n#define TK_CTIME_KW                        82\n#define TK_ANY                             83\n#define TK_BITAND                          84\n#define TK_BITOR                           85\n#define TK_LSHIFT                          86\n#define TK_RSHIFT                          87\n#define TK_PLUS                            88\n#define TK_MINUS                           89\n#define TK_STAR                            90\n#define TK_SLASH                           91\n#define TK_REM                             92\n#define TK_CONCAT                          93\n#define TK_COLLATE                         94\n#define TK_BITNOT                          95\n#define TK_INDEXED                         96\n#define TK_STRING                          97\n#define TK_JOIN_KW                         98\n#define TK_CONSTRAINT                      99\n#define TK_DEFAULT                        100\n#define TK_NULL                           101\n#define TK_PRIMARY                        102\n#define TK_UNIQUE                         103\n#define TK_CHECK                          104\n#define TK_REFERENCES                     105\n#define TK_AUTOINCR                       106\n#define TK_ON                             107\n#define TK_INSERT                         108\n#define TK_DELETE                         109\n#define TK_UPDATE                         110\n#define TK_SET                            111\n#define TK_DEFERRABLE                     112\n#define TK_FOREIGN                        113\n#define TK_DROP                           114\n#define TK_UNION                          115\n#define TK_ALL                            116\n#define TK_EXCEPT                         117\n#define TK_INTERSECT                      118\n#define TK_SELECT                         119\n#define TK_VALUES                         120\n#define TK_DISTINCT                       121\n#define TK_DOT                            122\n#define TK_FROM                           123\n#define TK_JOIN                           124\n#define TK_USING                          125\n#define TK_ORDER                          126\n#define TK_GROUP                          127\n#define TK_HAVING                         128\n#define TK_LIMIT                          129\n#define TK_WHERE                          130\n#define TK_INTO                           131\n#define TK_FLOAT                          132\n#define TK_BLOB                           133\n#define TK_INTEGER                        134\n#define TK_VARIABLE                       135\n#define TK_CASE                           136\n#define TK_WHEN                           137\n#define TK_THEN                           138\n#define TK_ELSE                           139\n#define TK_INDEX                          140\n#define TK_ALTER                          141\n#define TK_ADD                            142\n#define TK_TRUEFALSE                      143\n#define TK_ISNOT                          144\n#define TK_FUNCTION                       145\n#define TK_COLUMN                         146\n#define TK_AGG_FUNCTION                   147\n#define TK_AGG_COLUMN                     148\n#define TK_UMINUS                         149\n#define TK_UPLUS                          150\n#define TK_TRUTH                          151\n#define TK_REGISTER                       152\n#define TK_VECTOR                         153\n#define TK_SELECT_COLUMN                  154\n#define TK_IF_NULL_ROW                    155\n#define TK_ASTERISK                       156\n#define TK_SPAN                           157\n#define TK_END_OF_FILE                    158\n#define TK_UNCLOSED_STRING                159\n#define TK_SPACE                          160\n#define TK_ILLEGAL                        161\n\n/* The token codes above must all fit in 8 bits */\n#define TKFLG_MASK           0xff  \n\n/* Flags that can be added to a token code when it is not\n** being stored in a u8: */\n#define TKFLG_DONTFOLD       0x100  /* Omit constant folding optimizations */\n\n/************** End of parse.h ***********************************************/\n/************** Continuing where we left off in sqliteInt.h ******************/\n#include <stdio.h>\n#include <stdlib.h>\n#include <string.h>\n#include <assert.h>\n#include <stddef.h>\n\n/*\n** Use a macro to replace memcpy() if compiled with SQLITE_INLINE_MEMCPY.\n** This allows better measurements of where memcpy() is used when running\n** cachegrind.  But this macro version of memcpy() is very slow so it\n** should not be used in production.  This is a performance measurement\n** hack only.\n*/\n#ifdef SQLITE_INLINE_MEMCPY\n# define memcpy(D,S,N) {char*xxd=(char*)(D);const char*xxs=(const char*)(S);\\\n                        int xxn=(N);while(xxn-->0)*(xxd++)=*(xxs++);}\n#endif\n\n/*\n** If compiling for a processor that lacks floating point support,\n** substitute integer for floating-point\n*/\n#ifdef SQLITE_OMIT_FLOATING_POINT\n# define double sqlite_int64\n# define float sqlite_int64\n# define LONGDOUBLE_TYPE sqlite_int64\n# ifndef SQLITE_BIG_DBL\n#   define SQLITE_BIG_DBL (((sqlite3_int64)1)<<50)\n# endif\n# define SQLITE_OMIT_DATETIME_FUNCS 1\n# define SQLITE_OMIT_TRACE 1\n# undef SQLITE_MIXED_ENDIAN_64BIT_FLOAT\n# undef SQLITE_HAVE_ISNAN\n#endif\n#ifndef SQLITE_BIG_DBL\n# define SQLITE_BIG_DBL (1e99)\n#endif\n\n/*\n** OMIT_TEMPDB is set to 1 if SQLITE_OMIT_TEMPDB is defined, or 0\n** afterward. Having this macro allows us to cause the C compiler\n** to omit code used by TEMP tables without messy #ifndef statements.\n*/\n#ifdef SQLITE_OMIT_TEMPDB\n#define OMIT_TEMPDB 1\n#else\n#define OMIT_TEMPDB 0\n#endif\n\n/*\n** The \"file format\" number is an integer that is incremented whenever\n** the VDBE-level file format changes.  The following macros define the\n** the default file format for new databases and the maximum file format\n** that the library can read.\n*/\n#define SQLITE_MAX_FILE_FORMAT 4\n#ifndef SQLITE_DEFAULT_FILE_FORMAT\n# define SQLITE_DEFAULT_FILE_FORMAT 4\n#endif\n\n/*\n** Determine whether triggers are recursive by default.  This can be\n** changed at run-time using a pragma.\n*/\n#ifndef SQLITE_DEFAULT_RECURSIVE_TRIGGERS\n# define SQLITE_DEFAULT_RECURSIVE_TRIGGERS 0\n#endif\n\n/*\n** Provide a default value for SQLITE_TEMP_STORE in case it is not specified\n** on the command-line\n*/\n#ifndef SQLITE_TEMP_STORE\n# define SQLITE_TEMP_STORE 1\n#endif\n\n/*\n** If no value has been provided for SQLITE_MAX_WORKER_THREADS, or if\n** SQLITE_TEMP_STORE is set to 3 (never use temporary files), set it\n** to zero.\n*/\n#if SQLITE_TEMP_STORE==3 || SQLITE_THREADSAFE==0\n# undef SQLITE_MAX_WORKER_THREADS\n# define SQLITE_MAX_WORKER_THREADS 0\n#endif\n#ifndef SQLITE_MAX_WORKER_THREADS\n# define SQLITE_MAX_WORKER_THREADS 8\n#endif\n#ifndef SQLITE_DEFAULT_WORKER_THREADS\n# define SQLITE_DEFAULT_WORKER_THREADS 0\n#endif\n#if SQLITE_DEFAULT_WORKER_THREADS>SQLITE_MAX_WORKER_THREADS\n# undef SQLITE_MAX_WORKER_THREADS\n# define SQLITE_MAX_WORKER_THREADS SQLITE_DEFAULT_WORKER_THREADS\n#endif\n\n/*\n** The default initial allocation for the pagecache when using separate\n** pagecaches for each database connection.  A positive number is the\n** number of pages.  A negative number N translations means that a buffer\n** of -1024*N bytes is allocated and used for as many pages as it will hold.\n**\n** The default value of \"20\" was choosen to minimize the run-time of the\n** speedtest1 test program with options: --shrink-memory --reprepare\n*/\n#ifndef SQLITE_DEFAULT_PCACHE_INITSZ\n# define SQLITE_DEFAULT_PCACHE_INITSZ 20\n#endif\n\n/*\n** The compile-time options SQLITE_MMAP_READWRITE and \n** SQLITE_ENABLE_BATCH_ATOMIC_WRITE are not compatible with one another.\n** You must choose one or the other (or neither) but not both.\n*/\n#if defined(SQLITE_MMAP_READWRITE) && defined(SQLITE_ENABLE_BATCH_ATOMIC_WRITE)\n#error Cannot use both SQLITE_MMAP_READWRITE and SQLITE_ENABLE_BATCH_ATOMIC_WRITE\n#endif\n\n/*\n** GCC does not define the offsetof() macro so we'll have to do it\n** ourselves.\n*/\n#ifndef offsetof\n#define offsetof(STRUCTURE,FIELD) ((int)((char*)&((STRUCTURE*)0)->FIELD))\n#endif\n\n/*\n** Macros to compute minimum and maximum of two numbers.\n*/\n#ifndef MIN\n# define MIN(A,B) ((A)<(B)?(A):(B))\n#endif\n#ifndef MAX\n# define MAX(A,B) ((A)>(B)?(A):(B))\n#endif\n\n/*\n** Swap two objects of type TYPE.\n*/\n#define SWAP(TYPE,A,B) {TYPE t=A; A=B; B=t;}\n\n/*\n** Check to see if this machine uses EBCDIC.  (Yes, believe it or\n** not, there are still machines out there that use EBCDIC.)\n*/\n#if 'A' == '\\301'\n# define SQLITE_EBCDIC 1\n#else\n# define SQLITE_ASCII 1\n#endif\n\n/*\n** Integers of known sizes.  These typedefs might change for architectures\n** where the sizes very.  Preprocessor macros are available so that the\n** types can be conveniently redefined at compile-type.  Like this:\n**\n**         cc '-DUINTPTR_TYPE=long long int' ...\n*/\n#ifndef UINT32_TYPE\n# ifdef HAVE_UINT32_T\n#  define UINT32_TYPE uint32_t\n# else\n#  define UINT32_TYPE unsigned int\n# endif\n#endif\n#ifndef UINT16_TYPE\n# ifdef HAVE_UINT16_T\n#  define UINT16_TYPE uint16_t\n# else\n#  define UINT16_TYPE unsigned short int\n# endif\n#endif\n#ifndef INT16_TYPE\n# ifdef HAVE_INT16_T\n#  define INT16_TYPE int16_t\n# else\n#  define INT16_TYPE short int\n# endif\n#endif\n#ifndef UINT8_TYPE\n# ifdef HAVE_UINT8_T\n#  define UINT8_TYPE uint8_t\n# else\n#  define UINT8_TYPE unsigned char\n# endif\n#endif\n#ifndef INT8_TYPE\n# ifdef HAVE_INT8_T\n#  define INT8_TYPE int8_t\n# else\n#  define INT8_TYPE signed char\n# endif\n#endif\n#ifndef LONGDOUBLE_TYPE\n# define LONGDOUBLE_TYPE long double\n#endif\ntypedef sqlite_int64 i64;          /* 8-byte signed integer */\ntypedef sqlite_uint64 u64;         /* 8-byte unsigned integer */\ntypedef UINT32_TYPE u32;           /* 4-byte unsigned integer */\ntypedef UINT16_TYPE u16;           /* 2-byte unsigned integer */\ntypedef INT16_TYPE i16;            /* 2-byte signed integer */\ntypedef UINT8_TYPE u8;             /* 1-byte unsigned integer */\ntypedef INT8_TYPE i8;              /* 1-byte signed integer */\n\n/*\n** SQLITE_MAX_U32 is a u64 constant that is the maximum u64 value\n** that can be stored in a u32 without loss of data.  The value\n** is 0x00000000ffffffff.  But because of quirks of some compilers, we\n** have to specify the value in the less intuitive manner shown:\n*/\n#define SQLITE_MAX_U32  ((((u64)1)<<32)-1)\n\n/*\n** The datatype used to store estimates of the number of rows in a\n** table or index.  This is an unsigned integer type.  For 99.9% of\n** the world, a 32-bit integer is sufficient.  But a 64-bit integer\n** can be used at compile-time if desired.\n*/\n#ifdef SQLITE_64BIT_STATS\n typedef u64 tRowcnt;    /* 64-bit only if requested at compile-time */\n#else\n typedef u32 tRowcnt;    /* 32-bit is the default */\n#endif\n\n/*\n** Estimated quantities used for query planning are stored as 16-bit\n** logarithms.  For quantity X, the value stored is 10*log2(X).  This\n** gives a possible range of values of approximately 1.0e986 to 1e-986.\n** But the allowed values are \"grainy\".  Not every value is representable.\n** For example, quantities 16 and 17 are both represented by a LogEst\n** of 40.  However, since LogEst quantities are suppose to be estimates,\n** not exact values, this imprecision is not a problem.\n**\n** \"LogEst\" is short for \"Logarithmic Estimate\".\n**\n** Examples:\n**      1 -> 0              20 -> 43          10000 -> 132\n**      2 -> 10             25 -> 46          25000 -> 146\n**      3 -> 16            100 -> 66        1000000 -> 199\n**      4 -> 20           1000 -> 99        1048576 -> 200\n**     10 -> 33           1024 -> 100    4294967296 -> 320\n**\n** The LogEst can be negative to indicate fractional values.\n** Examples:\n**\n**    0.5 -> -10           0.1 -> -33        0.0625 -> -40\n*/\ntypedef INT16_TYPE LogEst;\n\n/*\n** Set the SQLITE_PTRSIZE macro to the number of bytes in a pointer\n*/\n#ifndef SQLITE_PTRSIZE\n# if defined(__SIZEOF_POINTER__)\n#   define SQLITE_PTRSIZE __SIZEOF_POINTER__\n# elif defined(i386)     || defined(__i386__)   || defined(_M_IX86) ||    \\\n       defined(_M_ARM)   || defined(__arm__)    || defined(__x86)\n#   define SQLITE_PTRSIZE 4\n# else\n#   define SQLITE_PTRSIZE 8\n# endif\n#endif\n\n/* The uptr type is an unsigned integer large enough to hold a pointer\n*/\n#if defined(HAVE_STDINT_H)\n  typedef uintptr_t uptr;\n#elif SQLITE_PTRSIZE==4\n  typedef u32 uptr;\n#else\n  typedef u64 uptr;\n#endif\n\n/*\n** The SQLITE_WITHIN(P,S,E) macro checks to see if pointer P points to\n** something between S (inclusive) and E (exclusive).\n**\n** In other words, S is a buffer and E is a pointer to the first byte after\n** the end of buffer S.  This macro returns true if P points to something\n** contained within the buffer S.\n*/\n#define SQLITE_WITHIN(P,S,E) (((uptr)(P)>=(uptr)(S))&&((uptr)(P)<(uptr)(E)))\n\n\n/*\n** Macros to determine whether the machine is big or little endian,\n** and whether or not that determination is run-time or compile-time.\n**\n** For best performance, an attempt is made to guess at the byte-order\n** using C-preprocessor macros.  If that is unsuccessful, or if\n** -DSQLITE_BYTEORDER=0 is set, then byte-order is determined\n** at run-time.\n*/\n#ifndef SQLITE_BYTEORDER\n# if defined(i386)     || defined(__i386__)   || defined(_M_IX86) ||    \\\n     defined(__x86_64) || defined(__x86_64__) || defined(_M_X64)  ||    \\\n     defined(_M_AMD64) || defined(_M_ARM)     || defined(__x86)   ||    \\\n     defined(__arm__)\n#   define SQLITE_BYTEORDER    1234\n# elif defined(sparc)    || defined(__ppc__)\n#   define SQLITE_BYTEORDER    4321\n# else\n#   define SQLITE_BYTEORDER 0\n# endif\n#endif\n#if SQLITE_BYTEORDER==4321\n# define SQLITE_BIGENDIAN    1\n# define SQLITE_LITTLEENDIAN 0\n# define SQLITE_UTF16NATIVE  SQLITE_UTF16BE\n#elif SQLITE_BYTEORDER==1234\n# define SQLITE_BIGENDIAN    0\n# define SQLITE_LITTLEENDIAN 1\n# define SQLITE_UTF16NATIVE  SQLITE_UTF16LE\n#else\n# ifdef SQLITE_AMALGAMATION\n  const int sqlite3one = 1;\n# else\n  extern const int sqlite3one;\n# endif\n# define SQLITE_BIGENDIAN    (*(char *)(&sqlite3one)==0)\n# define SQLITE_LITTLEENDIAN (*(char *)(&sqlite3one)==1)\n# define SQLITE_UTF16NATIVE  (SQLITE_BIGENDIAN?SQLITE_UTF16BE:SQLITE_UTF16LE)\n#endif\n\n/*\n** Constants for the largest and smallest possible 64-bit signed integers.\n** These macros are designed to work correctly on both 32-bit and 64-bit\n** compilers.\n*/\n#define LARGEST_INT64  (0xffffffff|(((i64)0x7fffffff)<<32))\n#define SMALLEST_INT64 (((i64)-1) - LARGEST_INT64)\n\n/*\n** Round up a number to the next larger multiple of 8.  This is used\n** to force 8-byte alignment on 64-bit architectures.\n*/\n#define ROUND8(x)     (((x)+7)&~7)\n\n/*\n** Round down to the nearest multiple of 8\n*/\n#define ROUNDDOWN8(x) ((x)&~7)\n\n/*\n** Assert that the pointer X is aligned to an 8-byte boundary.  This\n** macro is used only within assert() to verify that the code gets\n** all alignment restrictions correct.\n**\n** Except, if SQLITE_4_BYTE_ALIGNED_MALLOC is defined, then the\n** underlying malloc() implementation might return us 4-byte aligned\n** pointers.  In that case, only verify 4-byte alignment.\n*/\n#ifdef SQLITE_4_BYTE_ALIGNED_MALLOC\n# define EIGHT_BYTE_ALIGNMENT(X)   ((((char*)(X) - (char*)0)&3)==0)\n#else\n# define EIGHT_BYTE_ALIGNMENT(X)   ((((char*)(X) - (char*)0)&7)==0)\n#endif\n\n/*\n** Disable MMAP on platforms where it is known to not work\n*/\n#if defined(__OpenBSD__) || defined(__QNXNTO__)\n# undef SQLITE_MAX_MMAP_SIZE\n# define SQLITE_MAX_MMAP_SIZE 0\n#endif\n\n/*\n** Default maximum size of memory used by memory-mapped I/O in the VFS\n*/\n#ifdef __APPLE__\n# include <TargetConditionals.h>\n#endif\n#ifndef SQLITE_MAX_MMAP_SIZE\n# if defined(__linux__) \\\n  || defined(_WIN32) \\\n  || (defined(__APPLE__) && defined(__MACH__)) \\\n  || defined(__sun) \\\n  || defined(__FreeBSD__) \\\n  || defined(__DragonFly__)\n#   define SQLITE_MAX_MMAP_SIZE 0x7fff0000  /* 2147418112 */\n# else\n#   define SQLITE_MAX_MMAP_SIZE 0\n# endif\n#endif\n\n/*\n** The default MMAP_SIZE is zero on all platforms.  Or, even if a larger\n** default MMAP_SIZE is specified at compile-time, make sure that it does\n** not exceed the maximum mmap size.\n*/\n#ifndef SQLITE_DEFAULT_MMAP_SIZE\n# define SQLITE_DEFAULT_MMAP_SIZE 0\n#endif\n#if SQLITE_DEFAULT_MMAP_SIZE>SQLITE_MAX_MMAP_SIZE\n# undef SQLITE_DEFAULT_MMAP_SIZE\n# define SQLITE_DEFAULT_MMAP_SIZE SQLITE_MAX_MMAP_SIZE\n#endif\n\n/*\n** Only one of SQLITE_ENABLE_STAT3 or SQLITE_ENABLE_STAT4 can be defined.\n** Priority is given to SQLITE_ENABLE_STAT4.  If either are defined, also\n** define SQLITE_ENABLE_STAT3_OR_STAT4\n*/\n#ifdef SQLITE_ENABLE_STAT4\n# undef SQLITE_ENABLE_STAT3\n# define SQLITE_ENABLE_STAT3_OR_STAT4 1\n#elif SQLITE_ENABLE_STAT3\n# define SQLITE_ENABLE_STAT3_OR_STAT4 1\n#elif SQLITE_ENABLE_STAT3_OR_STAT4\n# undef SQLITE_ENABLE_STAT3_OR_STAT4\n#endif\n\n/*\n** SELECTTRACE_ENABLED will be either 1 or 0 depending on whether or not\n** the Select query generator tracing logic is turned on.\n*/\n#if defined(SQLITE_ENABLE_SELECTTRACE)\n# define SELECTTRACE_ENABLED 1\n#else\n# define SELECTTRACE_ENABLED 0\n#endif\n\n/*\n** An instance of the following structure is used to store the busy-handler\n** callback for a given sqlite handle.\n**\n** The sqlite.busyHandler member of the sqlite struct contains the busy\n** callback for the database handle. Each pager opened via the sqlite\n** handle is passed a pointer to sqlite.busyHandler. The busy-handler\n** callback is currently invoked only from within pager.c.\n*/\ntypedef struct BusyHandler BusyHandler;\nstruct BusyHandler {\n  int (*xFunc)(void *,int);  /* The busy callback */\n  void *pArg;                /* First arg to busy callback */\n  int nBusy;                 /* Incremented with each busy call */\n};\n\n/*\n** Name of the master database table.  The master database table\n** is a special table that holds the names and attributes of all\n** user tables and indices.\n*/\n#define MASTER_NAME       \"sqlite_master\"\n#define TEMP_MASTER_NAME  \"sqlite_temp_master\"\n\n/*\n** The root-page of the master database table.\n*/\n#define MASTER_ROOT       1\n\n/*\n** The name of the schema table.\n*/\n#define SCHEMA_TABLE(x)  ((!OMIT_TEMPDB)&&(x==1)?TEMP_MASTER_NAME:MASTER_NAME)\n\n/*\n** A convenience macro that returns the number of elements in\n** an array.\n*/\n#define ArraySize(X)    ((int)(sizeof(X)/sizeof(X[0])))\n\n/*\n** Determine if the argument is a power of two\n*/\n#define IsPowerOfTwo(X) (((X)&((X)-1))==0)\n\n/*\n** The following value as a destructor means to use sqlite3DbFree().\n** The sqlite3DbFree() routine requires two parameters instead of the\n** one parameter that destructors normally want.  So we have to introduce\n** this magic value that the code knows to handle differently.  Any\n** pointer will work here as long as it is distinct from SQLITE_STATIC\n** and SQLITE_TRANSIENT.\n*/\n#define SQLITE_DYNAMIC   ((sqlite3_destructor_type)sqlite3MallocSize)\n\n/*\n** When SQLITE_OMIT_WSD is defined, it means that the target platform does\n** not support Writable Static Data (WSD) such as global and static variables.\n** All variables must either be on the stack or dynamically allocated from\n** the heap.  When WSD is unsupported, the variable declarations scattered\n** throughout the SQLite code must become constants instead.  The SQLITE_WSD\n** macro is used for this purpose.  And instead of referencing the variable\n** directly, we use its constant as a key to lookup the run-time allocated\n** buffer that holds real variable.  The constant is also the initializer\n** for the run-time allocated buffer.\n**\n** In the usual case where WSD is supported, the SQLITE_WSD and GLOBAL\n** macros become no-ops and have zero performance impact.\n*/\n#ifdef SQLITE_OMIT_WSD\n  #define SQLITE_WSD const\n  #define GLOBAL(t,v) (*(t*)sqlite3_wsd_find((void*)&(v), sizeof(v)))\n  #define sqlite3GlobalConfig GLOBAL(struct Sqlite3Config, sqlite3Config)\nSQLITE_API int sqlite3_wsd_init(int N, int J);\nSQLITE_API void *sqlite3_wsd_find(void *K, int L);\n#else\n  #define SQLITE_WSD\n  #define GLOBAL(t,v) v\n  #define sqlite3GlobalConfig sqlite3Config\n#endif\n\n/*\n** The following macros are used to suppress compiler warnings and to\n** make it clear to human readers when a function parameter is deliberately\n** left unused within the body of a function. This usually happens when\n** a function is called via a function pointer. For example the\n** implementation of an SQL aggregate step callback may not use the\n** parameter indicating the number of arguments passed to the aggregate,\n** if it knows that this is enforced elsewhere.\n**\n** When a function parameter is not used at all within the body of a function,\n** it is generally named \"NotUsed\" or \"NotUsed2\" to make things even clearer.\n** However, these macros may also be used to suppress warnings related to\n** parameters that may or may not be used depending on compilation options.\n** For example those parameters only used in assert() statements. In these\n** cases the parameters are named as per the usual conventions.\n*/\n#define UNUSED_PARAMETER(x) (void)(x)\n#define UNUSED_PARAMETER2(x,y) UNUSED_PARAMETER(x),UNUSED_PARAMETER(y)\n\n/*\n** Forward references to structures\n*/\ntypedef struct AggInfo AggInfo;\ntypedef struct AuthContext AuthContext;\ntypedef struct AutoincInfo AutoincInfo;\ntypedef struct Bitvec Bitvec;\ntypedef struct CollSeq CollSeq;\ntypedef struct Column Column;\ntypedef struct Db Db;\ntypedef struct Schema Schema;\ntypedef struct Expr Expr;\ntypedef struct ExprList ExprList;\ntypedef struct FKey FKey;\ntypedef struct FuncDestructor FuncDestructor;\ntypedef struct FuncDef FuncDef;\ntypedef struct FuncDefHash FuncDefHash;\ntypedef struct IdList IdList;\ntypedef struct Index Index;\ntypedef struct IndexSample IndexSample;\ntypedef struct KeyClass KeyClass;\ntypedef struct KeyInfo KeyInfo;\ntypedef struct Lookaside Lookaside;\ntypedef struct LookasideSlot LookasideSlot;\ntypedef struct Module Module;\ntypedef struct NameContext NameContext;\ntypedef struct Parse Parse;\ntypedef struct PreUpdate PreUpdate;\ntypedef struct PrintfArguments PrintfArguments;\ntypedef struct RowSet RowSet;\ntypedef struct Savepoint Savepoint;\ntypedef struct Select Select;\ntypedef struct SQLiteThread SQLiteThread;\ntypedef struct SelectDest SelectDest;\ntypedef struct SrcList SrcList;\ntypedef struct StrAccum StrAccum;\ntypedef struct Table Table;\ntypedef struct TableLock TableLock;\ntypedef struct Token Token;\ntypedef struct TreeView TreeView;\ntypedef struct Trigger Trigger;\ntypedef struct TriggerPrg TriggerPrg;\ntypedef struct TriggerStep TriggerStep;\ntypedef struct UnpackedRecord UnpackedRecord;\ntypedef struct VTable VTable;\ntypedef struct VtabCtx VtabCtx;\ntypedef struct Walker Walker;\ntypedef struct WhereInfo WhereInfo;\ntypedef struct With With;\n\n/* A VList object records a mapping between parameters/variables/wildcards\n** in the SQL statement (such as $abc, @pqr, or :xyz) and the integer\n** variable number associated with that parameter.  See the format description\n** on the sqlite3VListAdd() routine for more information.  A VList is really\n** just an array of integers.\n*/\ntypedef int VList;\n\n/*\n** Defer sourcing vdbe.h and btree.h until after the \"u8\" and\n** \"BusyHandler\" typedefs. vdbe.h also requires a few of the opaque\n** pointer types (i.e. FuncDef) defined above.\n*/\n/************** Include btree.h in the middle of sqliteInt.h *****************/\n/************** Begin file btree.h *******************************************/\n/*\n** 2001 September 15\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n*************************************************************************\n** This header file defines the interface that the sqlite B-Tree file\n** subsystem.  See comments in the source code for a detailed description\n** of what each interface routine does.\n*/\n#ifndef SQLITE_BTREE_H\n#define SQLITE_BTREE_H\n\n/* TODO: This definition is just included so other modules compile. It\n** needs to be revisited.\n*/\n#define SQLITE_N_BTREE_META 16\n\n/*\n** If defined as non-zero, auto-vacuum is enabled by default. Otherwise\n** it must be turned on for each database using \"PRAGMA auto_vacuum = 1\".\n*/\n#ifndef SQLITE_DEFAULT_AUTOVACUUM\n  #define SQLITE_DEFAULT_AUTOVACUUM 0\n#endif\n\n#define BTREE_AUTOVACUUM_NONE 0        /* Do not do auto-vacuum */\n#define BTREE_AUTOVACUUM_FULL 1        /* Do full auto-vacuum */\n#define BTREE_AUTOVACUUM_INCR 2        /* Incremental vacuum */\n\n/*\n** Forward declarations of structure\n*/\ntypedef struct Btree Btree;\ntypedef struct BtCursor BtCursor;\ntypedef struct BtShared BtShared;\ntypedef struct BtreePayload BtreePayload;\n\n\nSQLITE_PRIVATE int sqlite3BtreeOpen(\n  sqlite3_vfs *pVfs,       /* VFS to use with this b-tree */\n  const char *zFilename,   /* Name of database file to open */\n  sqlite3 *db,             /* Associated database connection */\n  Btree **ppBtree,         /* Return open Btree* here */\n  int flags,               /* Flags */\n  int vfsFlags             /* Flags passed through to VFS open */\n);\n\n/* The flags parameter to sqlite3BtreeOpen can be the bitwise or of the\n** following values.\n**\n** NOTE:  These values must match the corresponding PAGER_ values in\n** pager.h.\n*/\n#define BTREE_OMIT_JOURNAL  1  /* Do not create or use a rollback journal */\n#define BTREE_MEMORY        2  /* This is an in-memory DB */\n#define BTREE_SINGLE        4  /* The file contains at most 1 b-tree */\n#define BTREE_UNORDERED     8  /* Use of a hash implementation is OK */\n\nSQLITE_PRIVATE int sqlite3BtreeClose(Btree*);\nSQLITE_PRIVATE int sqlite3BtreeSetCacheSize(Btree*,int);\nSQLITE_PRIVATE int sqlite3BtreeSetSpillSize(Btree*,int);\n#if SQLITE_MAX_MMAP_SIZE>0\nSQLITE_PRIVATE   int sqlite3BtreeSetMmapLimit(Btree*,sqlite3_int64);\n#endif\nSQLITE_PRIVATE int sqlite3BtreeSetPagerFlags(Btree*,unsigned);\nSQLITE_PRIVATE int sqlite3BtreeSetPageSize(Btree *p, int nPagesize, int nReserve, int eFix);\nSQLITE_PRIVATE int sqlite3BtreeGetPageSize(Btree*);\nSQLITE_PRIVATE int sqlite3BtreeMaxPageCount(Btree*,int);\nSQLITE_PRIVATE u32 sqlite3BtreeLastPage(Btree*);\nSQLITE_PRIVATE int sqlite3BtreeSecureDelete(Btree*,int);\nSQLITE_PRIVATE int sqlite3BtreeGetOptimalReserve(Btree*);\nSQLITE_PRIVATE int sqlite3BtreeGetReserveNoMutex(Btree *p);\nSQLITE_PRIVATE int sqlite3BtreeSetAutoVacuum(Btree *, int);\nSQLITE_PRIVATE int sqlite3BtreeGetAutoVacuum(Btree *);\nSQLITE_PRIVATE int sqlite3BtreeBeginTrans(Btree*,int);\nSQLITE_PRIVATE int sqlite3BtreeCommitPhaseOne(Btree*, const char *zMaster);\nSQLITE_PRIVATE int sqlite3BtreeCommitPhaseTwo(Btree*, int);\nSQLITE_PRIVATE int sqlite3BtreeCommit(Btree*);\nSQLITE_PRIVATE int sqlite3BtreeRollback(Btree*,int,int);\nSQLITE_PRIVATE int sqlite3BtreeBeginStmt(Btree*,int);\nSQLITE_PRIVATE int sqlite3BtreeCreateTable(Btree*, int*, int flags);\nSQLITE_PRIVATE int sqlite3BtreeIsInTrans(Btree*);\nSQLITE_PRIVATE int sqlite3BtreeIsInReadTrans(Btree*);\nSQLITE_PRIVATE int sqlite3BtreeIsInBackup(Btree*);\nSQLITE_PRIVATE void *sqlite3BtreeSchema(Btree *, int, void(*)(void *));\nSQLITE_PRIVATE int sqlite3BtreeSchemaLocked(Btree *pBtree);\n#ifndef SQLITE_OMIT_SHARED_CACHE\nSQLITE_PRIVATE int sqlite3BtreeLockTable(Btree *pBtree, int iTab, u8 isWriteLock);\n#endif\nSQLITE_PRIVATE int sqlite3BtreeSavepoint(Btree *, int, int);\n\nSQLITE_PRIVATE const char *sqlite3BtreeGetFilename(Btree *);\nSQLITE_PRIVATE const char *sqlite3BtreeGetJournalname(Btree *);\nSQLITE_PRIVATE int sqlite3BtreeCopyFile(Btree *, Btree *);\n\nSQLITE_PRIVATE int sqlite3BtreeIncrVacuum(Btree *);\n\n/* The flags parameter to sqlite3BtreeCreateTable can be the bitwise OR\n** of the flags shown below.\n**\n** Every SQLite table must have either BTREE_INTKEY or BTREE_BLOBKEY set.\n** With BTREE_INTKEY, the table key is a 64-bit integer and arbitrary data\n** is stored in the leaves.  (BTREE_INTKEY is used for SQL tables.)  With\n** BTREE_BLOBKEY, the key is an arbitrary BLOB and no content is stored\n** anywhere - the key is the content.  (BTREE_BLOBKEY is used for SQL\n** indices.)\n*/\n#define BTREE_INTKEY     1    /* Table has only 64-bit signed integer keys */\n#define BTREE_BLOBKEY    2    /* Table has keys only - no data */\n\nSQLITE_PRIVATE int sqlite3BtreeDropTable(Btree*, int, int*);\nSQLITE_PRIVATE int sqlite3BtreeClearTable(Btree*, int, int*);\nSQLITE_PRIVATE int sqlite3BtreeClearTableOfCursor(BtCursor*);\nSQLITE_PRIVATE int sqlite3BtreeTripAllCursors(Btree*, int, int);\n\nSQLITE_PRIVATE void sqlite3BtreeGetMeta(Btree *pBtree, int idx, u32 *pValue);\nSQLITE_PRIVATE int sqlite3BtreeUpdateMeta(Btree*, int idx, u32 value);\n\nSQLITE_PRIVATE int sqlite3BtreeNewDb(Btree *p);\n\n/*\n** The second parameter to sqlite3BtreeGetMeta or sqlite3BtreeUpdateMeta\n** should be one of the following values. The integer values are assigned \n** to constants so that the offset of the corresponding field in an\n** SQLite database header may be found using the following formula:\n**\n**   offset = 36 + (idx * 4)\n**\n** For example, the free-page-count field is located at byte offset 36 of\n** the database file header. The incr-vacuum-flag field is located at\n** byte offset 64 (== 36+4*7).\n**\n** The BTREE_DATA_VERSION value is not really a value stored in the header.\n** It is a read-only number computed by the pager.  But we merge it with\n** the header value access routines since its access pattern is the same.\n** Call it a \"virtual meta value\".\n*/\n#define BTREE_FREE_PAGE_COUNT     0\n#define BTREE_SCHEMA_VERSION      1\n#define BTREE_FILE_FORMAT         2\n#define BTREE_DEFAULT_CACHE_SIZE  3\n#define BTREE_LARGEST_ROOT_PAGE   4\n#define BTREE_TEXT_ENCODING       5\n#define BTREE_USER_VERSION        6\n#define BTREE_INCR_VACUUM         7\n#define BTREE_APPLICATION_ID      8\n#define BTREE_DATA_VERSION        15  /* A virtual meta-value */\n\n/*\n** Kinds of hints that can be passed into the sqlite3BtreeCursorHint()\n** interface.\n**\n** BTREE_HINT_RANGE  (arguments: Expr*, Mem*)\n**\n**     The first argument is an Expr* (which is guaranteed to be constant for\n**     the lifetime of the cursor) that defines constraints on which rows\n**     might be fetched with this cursor.  The Expr* tree may contain\n**     TK_REGISTER nodes that refer to values stored in the array of registers\n**     passed as the second parameter.  In other words, if Expr.op==TK_REGISTER\n**     then the value of the node is the value in Mem[pExpr.iTable].  Any\n**     TK_COLUMN node in the expression tree refers to the Expr.iColumn-th\n**     column of the b-tree of the cursor.  The Expr tree will not contain\n**     any function calls nor subqueries nor references to b-trees other than\n**     the cursor being hinted.\n**\n**     The design of the _RANGE hint is aid b-tree implementations that try\n**     to prefetch content from remote machines - to provide those\n**     implementations with limits on what needs to be prefetched and thereby\n**     reduce network bandwidth.\n**\n** Note that BTREE_HINT_FLAGS with BTREE_BULKLOAD is the only hint used by\n** standard SQLite.  The other hints are provided for extentions that use\n** the SQLite parser and code generator but substitute their own storage\n** engine.\n*/\n#define BTREE_HINT_RANGE 0       /* Range constraints on queries */\n\n/*\n** Values that may be OR'd together to form the argument to the\n** BTREE_HINT_FLAGS hint for sqlite3BtreeCursorHint():\n**\n** The BTREE_BULKLOAD flag is set on index cursors when the index is going\n** to be filled with content that is already in sorted order.\n**\n** The BTREE_SEEK_EQ flag is set on cursors that will get OP_SeekGE or\n** OP_SeekLE opcodes for a range search, but where the range of entries\n** selected will all have the same key.  In other words, the cursor will\n** be used only for equality key searches.\n**\n*/\n#define BTREE_BULKLOAD 0x00000001  /* Used to full index in sorted order */\n#define BTREE_SEEK_EQ  0x00000002  /* EQ seeks only - no range seeks */\n\n/* \n** Flags passed as the third argument to sqlite3BtreeCursor().\n**\n** For read-only cursors the wrFlag argument is always zero. For read-write\n** cursors it may be set to either (BTREE_WRCSR|BTREE_FORDELETE) or just\n** (BTREE_WRCSR). If the BTREE_FORDELETE bit is set, then the cursor will\n** only be used by SQLite for the following:\n**\n**   * to seek to and then delete specific entries, and/or\n**\n**   * to read values that will be used to create keys that other\n**     BTREE_FORDELETE cursors will seek to and delete.\n**\n** The BTREE_FORDELETE flag is an optimization hint.  It is not used by\n** by this, the native b-tree engine of SQLite, but it is available to\n** alternative storage engines that might be substituted in place of this\n** b-tree system.  For alternative storage engines in which a delete of\n** the main table row automatically deletes corresponding index rows,\n** the FORDELETE flag hint allows those alternative storage engines to\n** skip a lot of work.  Namely:  FORDELETE cursors may treat all SEEK\n** and DELETE operations as no-ops, and any READ operation against a\n** FORDELETE cursor may return a null row: 0x01 0x00.\n*/\n#define BTREE_WRCSR     0x00000004     /* read-write cursor */\n#define BTREE_FORDELETE 0x00000008     /* Cursor is for seek/delete only */\n\nSQLITE_PRIVATE int sqlite3BtreeCursor(\n  Btree*,                              /* BTree containing table to open */\n  int iTable,                          /* Index of root page */\n  int wrFlag,                          /* 1 for writing.  0 for read-only */\n  struct KeyInfo*,                     /* First argument to compare function */\n  BtCursor *pCursor                    /* Space to write cursor structure */\n);\nSQLITE_PRIVATE BtCursor *sqlite3BtreeFakeValidCursor(void);\nSQLITE_PRIVATE int sqlite3BtreeCursorSize(void);\nSQLITE_PRIVATE void sqlite3BtreeCursorZero(BtCursor*);\nSQLITE_PRIVATE void sqlite3BtreeCursorHintFlags(BtCursor*, unsigned);\n#ifdef SQLITE_ENABLE_CURSOR_HINTS\nSQLITE_PRIVATE void sqlite3BtreeCursorHint(BtCursor*, int, ...);\n#endif\n\nSQLITE_PRIVATE int sqlite3BtreeCloseCursor(BtCursor*);\nSQLITE_PRIVATE int sqlite3BtreeMovetoUnpacked(\n  BtCursor*,\n  UnpackedRecord *pUnKey,\n  i64 intKey,\n  int bias,\n  int *pRes\n);\nSQLITE_PRIVATE int sqlite3BtreeCursorHasMoved(BtCursor*);\nSQLITE_PRIVATE int sqlite3BtreeCursorRestore(BtCursor*, int*);\nSQLITE_PRIVATE int sqlite3BtreeDelete(BtCursor*, u8 flags);\n\n/* Allowed flags for sqlite3BtreeDelete() and sqlite3BtreeInsert() */\n#define BTREE_SAVEPOSITION 0x02  /* Leave cursor pointing at NEXT or PREV */\n#define BTREE_AUXDELETE    0x04  /* not the primary delete operation */\n#define BTREE_APPEND       0x08  /* Insert is likely an append */\n\n/* An instance of the BtreePayload object describes the content of a single\n** entry in either an index or table btree.\n**\n** Index btrees (used for indexes and also WITHOUT ROWID tables) contain\n** an arbitrary key and no data.  These btrees have pKey,nKey set to their\n** key and pData,nData,nZero set to zero.\n**\n** Table btrees (used for rowid tables) contain an integer rowid used as\n** the key and passed in the nKey field.  The pKey field is zero.  \n** pData,nData hold the content of the new entry.  nZero extra zero bytes\n** are appended to the end of the content when constructing the entry.\n**\n** This object is used to pass information into sqlite3BtreeInsert().  The\n** same information used to be passed as five separate parameters.  But placing\n** the information into this object helps to keep the interface more \n** organized and understandable, and it also helps the resulting code to\n** run a little faster by using fewer registers for parameter passing.\n*/\nstruct BtreePayload {\n  const void *pKey;       /* Key content for indexes.  NULL for tables */\n  sqlite3_int64 nKey;     /* Size of pKey for indexes.  PRIMARY KEY for tabs */\n  const void *pData;      /* Data for tables.  NULL for indexes */\n  sqlite3_value *aMem;    /* First of nMem value in the unpacked pKey */\n  u16 nMem;               /* Number of aMem[] value.  Might be zero */\n  int nData;              /* Size of pData.  0 if none. */\n  int nZero;              /* Extra zero data appended after pData,nData */\n};\n\nSQLITE_PRIVATE int sqlite3BtreeInsert(BtCursor*, const BtreePayload *pPayload,\n                       int flags, int seekResult);\nSQLITE_PRIVATE int sqlite3BtreeFirst(BtCursor*, int *pRes);\nSQLITE_PRIVATE int sqlite3BtreeLast(BtCursor*, int *pRes);\nSQLITE_PRIVATE int sqlite3BtreeNext(BtCursor*, int flags);\nSQLITE_PRIVATE int sqlite3BtreeEof(BtCursor*);\nSQLITE_PRIVATE int sqlite3BtreePrevious(BtCursor*, int flags);\nSQLITE_PRIVATE i64 sqlite3BtreeIntegerKey(BtCursor*);\n#ifdef SQLITE_ENABLE_OFFSET_SQL_FUNC\nSQLITE_PRIVATE i64 sqlite3BtreeOffset(BtCursor*);\n#endif\nSQLITE_PRIVATE int sqlite3BtreePayload(BtCursor*, u32 offset, u32 amt, void*);\nSQLITE_PRIVATE const void *sqlite3BtreePayloadFetch(BtCursor*, u32 *pAmt);\nSQLITE_PRIVATE u32 sqlite3BtreePayloadSize(BtCursor*);\n\nSQLITE_PRIVATE char *sqlite3BtreeIntegrityCheck(Btree*, int *aRoot, int nRoot, int, int*);\nSQLITE_PRIVATE struct Pager *sqlite3BtreePager(Btree*);\nSQLITE_PRIVATE i64 sqlite3BtreeRowCountEst(BtCursor*);\n\n#ifndef SQLITE_OMIT_INCRBLOB\nSQLITE_PRIVATE int sqlite3BtreePayloadChecked(BtCursor*, u32 offset, u32 amt, void*);\nSQLITE_PRIVATE int sqlite3BtreePutData(BtCursor*, u32 offset, u32 amt, void*);\nSQLITE_PRIVATE void sqlite3BtreeIncrblobCursor(BtCursor *);\n#endif\nSQLITE_PRIVATE void sqlite3BtreeClearCursor(BtCursor *);\nSQLITE_PRIVATE int sqlite3BtreeSetVersion(Btree *pBt, int iVersion);\nSQLITE_PRIVATE int sqlite3BtreeCursorHasHint(BtCursor*, unsigned int mask);\nSQLITE_PRIVATE int sqlite3BtreeIsReadonly(Btree *pBt);\nSQLITE_PRIVATE int sqlite3HeaderSizeBtree(void);\n\n#ifndef NDEBUG\nSQLITE_PRIVATE int sqlite3BtreeCursorIsValid(BtCursor*);\n#endif\nSQLITE_PRIVATE int sqlite3BtreeCursorIsValidNN(BtCursor*);\n\n#ifndef SQLITE_OMIT_BTREECOUNT\nSQLITE_PRIVATE int sqlite3BtreeCount(BtCursor *, i64 *);\n#endif\n\n#ifdef SQLITE_TEST\nSQLITE_PRIVATE int sqlite3BtreeCursorInfo(BtCursor*, int*, int);\nSQLITE_PRIVATE void sqlite3BtreeCursorList(Btree*);\n#endif\n\n#ifndef SQLITE_OMIT_WAL\nSQLITE_PRIVATE   int sqlite3BtreeCheckpoint(Btree*, int, int *, int *);\n#endif\n\n/*\n** If we are not using shared cache, then there is no need to\n** use mutexes to access the BtShared structures.  So make the\n** Enter and Leave procedures no-ops.\n*/\n#ifndef SQLITE_OMIT_SHARED_CACHE\nSQLITE_PRIVATE   void sqlite3BtreeEnter(Btree*);\nSQLITE_PRIVATE   void sqlite3BtreeEnterAll(sqlite3*);\nSQLITE_PRIVATE   int sqlite3BtreeSharable(Btree*);\nSQLITE_PRIVATE   void sqlite3BtreeEnterCursor(BtCursor*);\nSQLITE_PRIVATE   int sqlite3BtreeConnectionCount(Btree*);\n#else\n# define sqlite3BtreeEnter(X) \n# define sqlite3BtreeEnterAll(X)\n# define sqlite3BtreeSharable(X) 0\n# define sqlite3BtreeEnterCursor(X)\n# define sqlite3BtreeConnectionCount(X) 1\n#endif\n\n#if !defined(SQLITE_OMIT_SHARED_CACHE) && SQLITE_THREADSAFE\nSQLITE_PRIVATE   void sqlite3BtreeLeave(Btree*);\nSQLITE_PRIVATE   void sqlite3BtreeLeaveCursor(BtCursor*);\nSQLITE_PRIVATE   void sqlite3BtreeLeaveAll(sqlite3*);\n#ifndef NDEBUG\n  /* These routines are used inside assert() statements only. */\nSQLITE_PRIVATE   int sqlite3BtreeHoldsMutex(Btree*);\nSQLITE_PRIVATE   int sqlite3BtreeHoldsAllMutexes(sqlite3*);\nSQLITE_PRIVATE   int sqlite3SchemaMutexHeld(sqlite3*,int,Schema*);\n#endif\n#else\n\n# define sqlite3BtreeLeave(X)\n# define sqlite3BtreeLeaveCursor(X)\n# define sqlite3BtreeLeaveAll(X)\n\n# define sqlite3BtreeHoldsMutex(X) 1\n# define sqlite3BtreeHoldsAllMutexes(X) 1\n# define sqlite3SchemaMutexHeld(X,Y,Z) 1\n#endif\n\n\n#endif /* SQLITE_BTREE_H */\n\n/************** End of btree.h ***********************************************/\n/************** Continuing where we left off in sqliteInt.h ******************/\n/************** Include vdbe.h in the middle of sqliteInt.h ******************/\n/************** Begin file vdbe.h ********************************************/\n/*\n** 2001 September 15\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n*************************************************************************\n** Header file for the Virtual DataBase Engine (VDBE)\n**\n** This header defines the interface to the virtual database engine\n** or VDBE.  The VDBE implements an abstract machine that runs a\n** simple program to access and modify the underlying database.\n*/\n#ifndef SQLITE_VDBE_H\n#define SQLITE_VDBE_H\n/* #include <stdio.h> */\n\n/*\n** A single VDBE is an opaque structure named \"Vdbe\".  Only routines\n** in the source file sqliteVdbe.c are allowed to see the insides\n** of this structure.\n*/\ntypedef struct Vdbe Vdbe;\n\n/*\n** The names of the following types declared in vdbeInt.h are required\n** for the VdbeOp definition.\n*/\ntypedef struct sqlite3_value Mem;\ntypedef struct SubProgram SubProgram;\n\n/*\n** A single instruction of the virtual machine has an opcode\n** and as many as three operands.  The instruction is recorded\n** as an instance of the following structure:\n*/\nstruct VdbeOp {\n  u8 opcode;          /* What operation to perform */\n  signed char p4type; /* One of the P4_xxx constants for p4 */\n  u16 p5;             /* Fifth parameter is an unsigned 16-bit integer */\n  int p1;             /* First operand */\n  int p2;             /* Second parameter (often the jump destination) */\n  int p3;             /* The third parameter */\n  union p4union {     /* fourth parameter */\n    int i;                 /* Integer value if p4type==P4_INT32 */\n    void *p;               /* Generic pointer */\n    char *z;               /* Pointer to data for string (char array) types */\n    i64 *pI64;             /* Used when p4type is P4_INT64 */\n    double *pReal;         /* Used when p4type is P4_REAL */\n    FuncDef *pFunc;        /* Used when p4type is P4_FUNCDEF */\n    sqlite3_context *pCtx; /* Used when p4type is P4_FUNCCTX */\n    CollSeq *pColl;        /* Used when p4type is P4_COLLSEQ */\n    Mem *pMem;             /* Used when p4type is P4_MEM */\n    VTable *pVtab;         /* Used when p4type is P4_VTAB */\n    KeyInfo *pKeyInfo;     /* Used when p4type is P4_KEYINFO */\n    int *ai;               /* Used when p4type is P4_INTARRAY */\n    SubProgram *pProgram;  /* Used when p4type is P4_SUBPROGRAM */\n    Table *pTab;           /* Used when p4type is P4_TABLE */\n#ifdef SQLITE_ENABLE_CURSOR_HINTS\n    Expr *pExpr;           /* Used when p4type is P4_EXPR */\n#endif\n    int (*xAdvance)(BtCursor *, int);\n  } p4;\n#ifdef SQLITE_ENABLE_EXPLAIN_COMMENTS\n  char *zComment;          /* Comment to improve readability */\n#endif\n#ifdef VDBE_PROFILE\n  u32 cnt;                 /* Number of times this instruction was executed */\n  u64 cycles;              /* Total time spent executing this instruction */\n#endif\n#ifdef SQLITE_VDBE_COVERAGE\n  int iSrcLine;            /* Source-code line that generated this opcode */\n#endif\n};\ntypedef struct VdbeOp VdbeOp;\n\n\n/*\n** A sub-routine used to implement a trigger program.\n*/\nstruct SubProgram {\n  VdbeOp *aOp;                  /* Array of opcodes for sub-program */\n  int nOp;                      /* Elements in aOp[] */\n  int nMem;                     /* Number of memory cells required */\n  int nCsr;                     /* Number of cursors required */\n  u8 *aOnce;                    /* Array of OP_Once flags */\n  void *token;                  /* id that may be used to recursive triggers */\n  SubProgram *pNext;            /* Next sub-program already visited */\n};\n\n/*\n** A smaller version of VdbeOp used for the VdbeAddOpList() function because\n** it takes up less space.\n*/\nstruct VdbeOpList {\n  u8 opcode;          /* What operation to perform */\n  signed char p1;     /* First operand */\n  signed char p2;     /* Second parameter (often the jump destination) */\n  signed char p3;     /* Third parameter */\n};\ntypedef struct VdbeOpList VdbeOpList;\n\n/*\n** Allowed values of VdbeOp.p4type\n*/\n#define P4_NOTUSED      0   /* The P4 parameter is not used */\n#define P4_TRANSIENT    0   /* P4 is a pointer to a transient string */\n#define P4_STATIC     (-1)  /* Pointer to a static string */\n#define P4_COLLSEQ    (-2)  /* P4 is a pointer to a CollSeq structure */\n#define P4_INT32      (-3)  /* P4 is a 32-bit signed integer */\n#define P4_SUBPROGRAM (-4)  /* P4 is a pointer to a SubProgram structure */\n#define P4_ADVANCE    (-5)  /* P4 is a pointer to BtreeNext() or BtreePrev() */\n#define P4_TABLE      (-6)  /* P4 is a pointer to a Table structure */\n/* Above do not own any resources.  Must free those below */\n#define P4_FREE_IF_LE (-7)\n#define P4_DYNAMIC    (-7)  /* Pointer to memory from sqliteMalloc() */\n#define P4_FUNCDEF    (-8)  /* P4 is a pointer to a FuncDef structure */\n#define P4_KEYINFO    (-9)  /* P4 is a pointer to a KeyInfo structure */\n#define P4_EXPR       (-10) /* P4 is a pointer to an Expr tree */\n#define P4_MEM        (-11) /* P4 is a pointer to a Mem*    structure */\n#define P4_VTAB       (-12) /* P4 is a pointer to an sqlite3_vtab structure */\n#define P4_REAL       (-13) /* P4 is a 64-bit floating point value */\n#define P4_INT64      (-14) /* P4 is a 64-bit signed integer */\n#define P4_INTARRAY   (-15) /* P4 is a vector of 32-bit integers */\n#define P4_FUNCCTX    (-16) /* P4 is a pointer to an sqlite3_context object */\n#define P4_DYNBLOB    (-17) /* Pointer to memory from sqliteMalloc() */\n\n/* Error message codes for OP_Halt */\n#define P5_ConstraintNotNull 1\n#define P5_ConstraintUnique  2\n#define P5_ConstraintCheck   3\n#define P5_ConstraintFK      4\n\n/*\n** The Vdbe.aColName array contains 5n Mem structures, where n is the \n** number of columns of data returned by the statement.\n*/\n#define COLNAME_NAME     0\n#define COLNAME_DECLTYPE 1\n#define COLNAME_DATABASE 2\n#define COLNAME_TABLE    3\n#define COLNAME_COLUMN   4\n#ifdef SQLITE_ENABLE_COLUMN_METADATA\n# define COLNAME_N        5      /* Number of COLNAME_xxx symbols */\n#else\n# ifdef SQLITE_OMIT_DECLTYPE\n#   define COLNAME_N      1      /* Store only the name */\n# else\n#   define COLNAME_N      2      /* Store the name and decltype */\n# endif\n#endif\n\n/*\n** The following macro converts a relative address in the p2 field\n** of a VdbeOp structure into a negative number so that \n** sqlite3VdbeAddOpList() knows that the address is relative.  Calling\n** the macro again restores the address.\n*/\n#define ADDR(X)  (-1-(X))\n\n/*\n** The makefile scans the vdbe.c source file and creates the \"opcodes.h\"\n** header file that defines a number for each opcode used by the VDBE.\n*/\n/************** Include opcodes.h in the middle of vdbe.h ********************/\n/************** Begin file opcodes.h *****************************************/\n/* Automatically generated.  Do not edit */\n/* See the tool/mkopcodeh.tcl script for details */\n#define OP_Savepoint       0\n#define OP_AutoCommit      1\n#define OP_Transaction     2\n#define OP_SorterNext      3 /* jump                                       */\n#define OP_PrevIfOpen      4 /* jump                                       */\n#define OP_NextIfOpen      5 /* jump                                       */\n#define OP_Prev            6 /* jump                                       */\n#define OP_Next            7 /* jump                                       */\n#define OP_Checkpoint      8\n#define OP_JournalMode     9\n#define OP_Vacuum         10\n#define OP_VFilter        11 /* jump, synopsis: iplan=r[P3] zplan='P4'     */\n#define OP_VUpdate        12 /* synopsis: data=r[P3@P2]                    */\n#define OP_Goto           13 /* jump                                       */\n#define OP_Gosub          14 /* jump                                       */\n#define OP_InitCoroutine  15 /* jump                                       */\n#define OP_Yield          16 /* jump                                       */\n#define OP_MustBeInt      17 /* jump                                       */\n#define OP_Jump           18 /* jump                                       */\n#define OP_Not            19 /* same as TK_NOT, synopsis: r[P2]= !r[P1]    */\n#define OP_Once           20 /* jump                                       */\n#define OP_If             21 /* jump                                       */\n#define OP_IfNot          22 /* jump                                       */\n#define OP_IfNullRow      23 /* jump, synopsis: if P1.nullRow then r[P3]=NULL, goto P2 */\n#define OP_SeekLT         24 /* jump, synopsis: key=r[P3@P4]               */\n#define OP_SeekLE         25 /* jump, synopsis: key=r[P3@P4]               */\n#define OP_SeekGE         26 /* jump, synopsis: key=r[P3@P4]               */\n#define OP_SeekGT         27 /* jump, synopsis: key=r[P3@P4]               */\n#define OP_NoConflict     28 /* jump, synopsis: key=r[P3@P4]               */\n#define OP_NotFound       29 /* jump, synopsis: key=r[P3@P4]               */\n#define OP_Found          30 /* jump, synopsis: key=r[P3@P4]               */\n#define OP_SeekRowid      31 /* jump, synopsis: intkey=r[P3]               */\n#define OP_NotExists      32 /* jump, synopsis: intkey=r[P3]               */\n#define OP_Last           33 /* jump                                       */\n#define OP_IfSmaller      34 /* jump                                       */\n#define OP_SorterSort     35 /* jump                                       */\n#define OP_Sort           36 /* jump                                       */\n#define OP_Rewind         37 /* jump                                       */\n#define OP_IdxLE          38 /* jump, synopsis: key=r[P3@P4]               */\n#define OP_IdxGT          39 /* jump, synopsis: key=r[P3@P4]               */\n#define OP_IdxLT          40 /* jump, synopsis: key=r[P3@P4]               */\n#define OP_IdxGE          41 /* jump, synopsis: key=r[P3@P4]               */\n#define OP_RowSetRead     42 /* jump, synopsis: r[P3]=rowset(P1)           */\n#define OP_Or             43 /* same as TK_OR, synopsis: r[P3]=(r[P1] || r[P2]) */\n#define OP_And            44 /* same as TK_AND, synopsis: r[P3]=(r[P1] && r[P2]) */\n#define OP_RowSetTest     45 /* jump, synopsis: if r[P3] in rowset(P1) goto P2 */\n#define OP_Program        46 /* jump                                       */\n#define OP_FkIfZero       47 /* jump, synopsis: if fkctr[P1]==0 goto P2    */\n#define OP_IfPos          48 /* jump, synopsis: if r[P1]>0 then r[P1]-=P3, goto P2 */\n#define OP_IfNotZero      49 /* jump, synopsis: if r[P1]!=0 then r[P1]--, goto P2 */\n#define OP_IsNull         50 /* jump, same as TK_ISNULL, synopsis: if r[P1]==NULL goto P2 */\n#define OP_NotNull        51 /* jump, same as TK_NOTNULL, synopsis: if r[P1]!=NULL goto P2 */\n#define OP_Ne             52 /* jump, same as TK_NE, synopsis: IF r[P3]!=r[P1] */\n#define OP_Eq             53 /* jump, same as TK_EQ, synopsis: IF r[P3]==r[P1] */\n#define OP_Gt             54 /* jump, same as TK_GT, synopsis: IF r[P3]>r[P1] */\n#define OP_Le             55 /* jump, same as TK_LE, synopsis: IF r[P3]<=r[P1] */\n#define OP_Lt             56 /* jump, same as TK_LT, synopsis: IF r[P3]<r[P1] */\n#define OP_Ge             57 /* jump, same as TK_GE, synopsis: IF r[P3]>=r[P1] */\n#define OP_ElseNotEq      58 /* jump, same as TK_ESCAPE                    */\n#define OP_DecrJumpZero   59 /* jump, synopsis: if (--r[P1])==0 goto P2    */\n#define OP_IncrVacuum     60 /* jump                                       */\n#define OP_VNext          61 /* jump                                       */\n#define OP_Init           62 /* jump, synopsis: Start at P2                */\n#define OP_Return         63\n#define OP_EndCoroutine   64\n#define OP_HaltIfNull     65 /* synopsis: if r[P3]=null halt               */\n#define OP_Halt           66\n#define OP_Integer        67 /* synopsis: r[P2]=P1                         */\n#define OP_Int64          68 /* synopsis: r[P2]=P4                         */\n#define OP_String         69 /* synopsis: r[P2]='P4' (len=P1)              */\n#define OP_Null           70 /* synopsis: r[P2..P3]=NULL                   */\n#define OP_SoftNull       71 /* synopsis: r[P1]=NULL                       */\n#define OP_Blob           72 /* synopsis: r[P2]=P4 (len=P1)                */\n#define OP_Variable       73 /* synopsis: r[P2]=parameter(P1,P4)           */\n#define OP_Move           74 /* synopsis: r[P2@P3]=r[P1@P3]                */\n#define OP_Copy           75 /* synopsis: r[P2@P3+1]=r[P1@P3+1]            */\n#define OP_SCopy          76 /* synopsis: r[P2]=r[P1]                      */\n#define OP_IntCopy        77 /* synopsis: r[P2]=r[P1]                      */\n#define OP_ResultRow      78 /* synopsis: output=r[P1@P2]                  */\n#define OP_CollSeq        79\n#define OP_AddImm         80 /* synopsis: r[P1]=r[P1]+P2                   */\n#define OP_RealAffinity   81\n#define OP_Cast           82 /* synopsis: affinity(r[P1])                  */\n#define OP_Permutation    83\n#define OP_BitAnd         84 /* same as TK_BITAND, synopsis: r[P3]=r[P1]&r[P2] */\n#define OP_BitOr          85 /* same as TK_BITOR, synopsis: r[P3]=r[P1]|r[P2] */\n#define OP_ShiftLeft      86 /* same as TK_LSHIFT, synopsis: r[P3]=r[P2]<<r[P1] */\n#define OP_ShiftRight     87 /* same as TK_RSHIFT, synopsis: r[P3]=r[P2]>>r[P1] */\n#define OP_Add            88 /* same as TK_PLUS, synopsis: r[P3]=r[P1]+r[P2] */\n#define OP_Subtract       89 /* same as TK_MINUS, synopsis: r[P3]=r[P2]-r[P1] */\n#define OP_Multiply       90 /* same as TK_STAR, synopsis: r[P3]=r[P1]*r[P2] */\n#define OP_Divide         91 /* same as TK_SLASH, synopsis: r[P3]=r[P2]/r[P1] */\n#define OP_Remainder      92 /* same as TK_REM, synopsis: r[P3]=r[P2]%r[P1] */\n#define OP_Concat         93 /* same as TK_CONCAT, synopsis: r[P3]=r[P2]+r[P1] */\n#define OP_Compare        94 /* synopsis: r[P1@P3] <-> r[P2@P3]            */\n#define OP_BitNot         95 /* same as TK_BITNOT, synopsis: r[P1]= ~r[P1] */\n#define OP_IsTrue         96 /* synopsis: r[P2] = coalesce(r[P1]==TRUE,P3) ^ P4 */\n#define OP_String8        97 /* same as TK_STRING, synopsis: r[P2]='P4'    */\n#define OP_Offset         98 /* synopsis: r[P3] = sqlite_offset(P1)        */\n#define OP_Column         99 /* synopsis: r[P3]=PX                         */\n#define OP_Affinity      100 /* synopsis: affinity(r[P1@P2])               */\n#define OP_MakeRecord    101 /* synopsis: r[P3]=mkrec(r[P1@P2])            */\n#define OP_Count         102 /* synopsis: r[P2]=count()                    */\n#define OP_ReadCookie    103\n#define OP_SetCookie     104\n#define OP_ReopenIdx     105 /* synopsis: root=P2 iDb=P3                   */\n#define OP_OpenRead      106 /* synopsis: root=P2 iDb=P3                   */\n#define OP_OpenWrite     107 /* synopsis: root=P2 iDb=P3                   */\n#define OP_OpenDup       108\n#define OP_OpenAutoindex 109 /* synopsis: nColumn=P2                       */\n#define OP_OpenEphemeral 110 /* synopsis: nColumn=P2                       */\n#define OP_SorterOpen    111\n#define OP_SequenceTest  112 /* synopsis: if( cursor[P1].ctr++ ) pc = P2   */\n#define OP_OpenPseudo    113 /* synopsis: P3 columns in r[P2]              */\n#define OP_Close         114\n#define OP_ColumnsUsed   115\n#define OP_Sequence      116 /* synopsis: r[P2]=cursor[P1].ctr++           */\n#define OP_NewRowid      117 /* synopsis: r[P2]=rowid                      */\n#define OP_Insert        118 /* synopsis: intkey=r[P3] data=r[P2]          */\n#define OP_InsertInt     119 /* synopsis: intkey=P3 data=r[P2]             */\n#define OP_Delete        120\n#define OP_ResetCount    121\n#define OP_SorterCompare 122 /* synopsis: if key(P1)!=trim(r[P3],P4) goto P2 */\n#define OP_SorterData    123 /* synopsis: r[P2]=data                       */\n#define OP_RowData       124 /* synopsis: r[P2]=data                       */\n#define OP_Rowid         125 /* synopsis: r[P2]=rowid                      */\n#define OP_NullRow       126\n#define OP_SeekEnd       127\n#define OP_SorterInsert  128 /* synopsis: key=r[P2]                        */\n#define OP_IdxInsert     129 /* synopsis: key=r[P2]                        */\n#define OP_IdxDelete     130 /* synopsis: key=r[P2@P3]                     */\n#define OP_DeferredSeek  131 /* synopsis: Move P3 to P1.rowid if needed    */\n#define OP_Real          132 /* same as TK_FLOAT, synopsis: r[P2]=P4       */\n#define OP_IdxRowid      133 /* synopsis: r[P2]=rowid                      */\n#define OP_Destroy       134\n#define OP_Clear         135\n#define OP_ResetSorter   136\n#define OP_CreateBtree   137 /* synopsis: r[P2]=root iDb=P1 flags=P3       */\n#define OP_SqlExec       138\n#define OP_ParseSchema   139\n#define OP_LoadAnalysis  140\n#define OP_DropTable     141\n#define OP_DropIndex     142\n#define OP_DropTrigger   143\n#define OP_IntegrityCk   144\n#define OP_RowSetAdd     145 /* synopsis: rowset(P1)=r[P2]                 */\n#define OP_Param         146\n#define OP_FkCounter     147 /* synopsis: fkctr[P1]+=P2                    */\n#define OP_MemMax        148 /* synopsis: r[P1]=max(r[P1],r[P2])           */\n#define OP_OffsetLimit   149 /* synopsis: if r[P1]>0 then r[P2]=r[P1]+max(0,r[P3]) else r[P2]=(-1) */\n#define OP_AggStep0      150 /* synopsis: accum=r[P3] step(r[P2@P5])       */\n#define OP_AggStep       151 /* synopsis: accum=r[P3] step(r[P2@P5])       */\n#define OP_AggFinal      152 /* synopsis: accum=r[P1] N=P2                 */\n#define OP_Expire        153\n#define OP_TableLock     154 /* synopsis: iDb=P1 root=P2 write=P3          */\n#define OP_VBegin        155\n#define OP_VCreate       156\n#define OP_VDestroy      157\n#define OP_VOpen         158\n#define OP_VColumn       159 /* synopsis: r[P3]=vcolumn(P2)                */\n#define OP_VRename       160\n#define OP_Pagecount     161\n#define OP_MaxPgcnt      162\n#define OP_PureFunc0     163\n#define OP_Function0     164 /* synopsis: r[P3]=func(r[P2@P5])             */\n#define OP_PureFunc      165\n#define OP_Function      166 /* synopsis: r[P3]=func(r[P2@P5])             */\n#define OP_Trace         167\n#define OP_CursorHint    168\n#define OP_Noop          169\n#define OP_Explain       170\n\n/* Properties such as \"out2\" or \"jump\" that are specified in\n** comments following the \"case\" for each opcode in the vdbe.c\n** are encoded into bitvectors as follows:\n*/\n#define OPFLG_JUMP        0x01  /* jump:  P2 holds jmp target */\n#define OPFLG_IN1         0x02  /* in1:   P1 is an input */\n#define OPFLG_IN2         0x04  /* in2:   P2 is an input */\n#define OPFLG_IN3         0x08  /* in3:   P3 is an input */\n#define OPFLG_OUT2        0x10  /* out2:  P2 is an output */\n#define OPFLG_OUT3        0x20  /* out3:  P3 is an output */\n#define OPFLG_INITIALIZER {\\\n/*   0 */ 0x00, 0x00, 0x00, 0x01, 0x01, 0x01, 0x01, 0x01,\\\n/*   8 */ 0x00, 0x10, 0x00, 0x01, 0x00, 0x01, 0x01, 0x01,\\\n/*  16 */ 0x03, 0x03, 0x01, 0x12, 0x01, 0x03, 0x03, 0x01,\\\n/*  24 */ 0x09, 0x09, 0x09, 0x09, 0x09, 0x09, 0x09, 0x09,\\\n/*  32 */ 0x09, 0x01, 0x01, 0x01, 0x01, 0x01, 0x01, 0x01,\\\n/*  40 */ 0x01, 0x01, 0x23, 0x26, 0x26, 0x0b, 0x01, 0x01,\\\n/*  48 */ 0x03, 0x03, 0x03, 0x03, 0x0b, 0x0b, 0x0b, 0x0b,\\\n/*  56 */ 0x0b, 0x0b, 0x01, 0x03, 0x01, 0x01, 0x01, 0x02,\\\n/*  64 */ 0x02, 0x08, 0x00, 0x10, 0x10, 0x10, 0x10, 0x00,\\\n/*  72 */ 0x10, 0x10, 0x00, 0x00, 0x10, 0x10, 0x00, 0x00,\\\n/*  80 */ 0x02, 0x02, 0x02, 0x00, 0x26, 0x26, 0x26, 0x26,\\\n/*  88 */ 0x26, 0x26, 0x26, 0x26, 0x26, 0x26, 0x00, 0x12,\\\n/*  96 */ 0x12, 0x10, 0x20, 0x00, 0x00, 0x00, 0x10, 0x10,\\\n/* 104 */ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,\\\n/* 112 */ 0x00, 0x00, 0x00, 0x00, 0x10, 0x10, 0x00, 0x00,\\\n/* 120 */ 0x00, 0x00, 0x00, 0x00, 0x00, 0x10, 0x00, 0x00,\\\n/* 128 */ 0x04, 0x04, 0x00, 0x00, 0x10, 0x10, 0x10, 0x00,\\\n/* 136 */ 0x00, 0x10, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,\\\n/* 144 */ 0x00, 0x06, 0x10, 0x00, 0x04, 0x1a, 0x00, 0x00,\\\n/* 152 */ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,\\\n/* 160 */ 0x00, 0x10, 0x10, 0x00, 0x00, 0x00, 0x00, 0x00,\\\n/* 168 */ 0x00, 0x00, 0x00,}\n\n/* The sqlite3P2Values() routine is able to run faster if it knows\n** the value of the largest JUMP opcode.  The smaller the maximum\n** JUMP opcode the better, so the mkopcodeh.tcl script that\n** generated this include file strives to group all JUMP opcodes\n** together near the beginning of the list.\n*/\n#define SQLITE_MX_JUMP_OPCODE  62  /* Maximum JUMP opcode */\n\n/************** End of opcodes.h *********************************************/\n/************** Continuing where we left off in vdbe.h ***********************/\n\n/*\n** Additional non-public SQLITE_PREPARE_* flags\n*/\n#define SQLITE_PREPARE_SAVESQL  0x80  /* Preserve SQL text */\n#define SQLITE_PREPARE_MASK     0x0f  /* Mask of public flags */\n\n/*\n** Prototypes for the VDBE interface.  See comments on the implementation\n** for a description of what each of these routines does.\n*/\nSQLITE_PRIVATE Vdbe *sqlite3VdbeCreate(Parse*);\nSQLITE_PRIVATE int sqlite3VdbeAddOp0(Vdbe*,int);\nSQLITE_PRIVATE int sqlite3VdbeAddOp1(Vdbe*,int,int);\nSQLITE_PRIVATE int sqlite3VdbeAddOp2(Vdbe*,int,int,int);\nSQLITE_PRIVATE int sqlite3VdbeGoto(Vdbe*,int);\nSQLITE_PRIVATE int sqlite3VdbeLoadString(Vdbe*,int,const char*);\nSQLITE_PRIVATE void sqlite3VdbeMultiLoad(Vdbe*,int,const char*,...);\nSQLITE_PRIVATE int sqlite3VdbeAddOp3(Vdbe*,int,int,int,int);\nSQLITE_PRIVATE int sqlite3VdbeAddOp4(Vdbe*,int,int,int,int,const char *zP4,int);\nSQLITE_PRIVATE int sqlite3VdbeAddOp4Dup8(Vdbe*,int,int,int,int,const u8*,int);\nSQLITE_PRIVATE int sqlite3VdbeAddOp4Int(Vdbe*,int,int,int,int,int);\nSQLITE_PRIVATE void sqlite3VdbeEndCoroutine(Vdbe*,int);\n#if defined(SQLITE_DEBUG) && !defined(SQLITE_TEST_REALLOC_STRESS)\nSQLITE_PRIVATE   void sqlite3VdbeVerifyNoMallocRequired(Vdbe *p, int N);\nSQLITE_PRIVATE   void sqlite3VdbeVerifyNoResultRow(Vdbe *p);\n#else\n# define sqlite3VdbeVerifyNoMallocRequired(A,B)\n# define sqlite3VdbeVerifyNoResultRow(A)\n#endif\nSQLITE_PRIVATE VdbeOp *sqlite3VdbeAddOpList(Vdbe*, int nOp, VdbeOpList const *aOp, int iLineno);\nSQLITE_PRIVATE void sqlite3VdbeAddParseSchemaOp(Vdbe*,int,char*);\nSQLITE_PRIVATE void sqlite3VdbeChangeOpcode(Vdbe*, u32 addr, u8);\nSQLITE_PRIVATE void sqlite3VdbeChangeP1(Vdbe*, u32 addr, int P1);\nSQLITE_PRIVATE void sqlite3VdbeChangeP2(Vdbe*, u32 addr, int P2);\nSQLITE_PRIVATE void sqlite3VdbeChangeP3(Vdbe*, u32 addr, int P3);\nSQLITE_PRIVATE void sqlite3VdbeChangeP5(Vdbe*, u16 P5);\nSQLITE_PRIVATE void sqlite3VdbeJumpHere(Vdbe*, int addr);\nSQLITE_PRIVATE int sqlite3VdbeChangeToNoop(Vdbe*, int addr);\nSQLITE_PRIVATE int sqlite3VdbeDeletePriorOpcode(Vdbe*, u8 op);\nSQLITE_PRIVATE void sqlite3VdbeChangeP4(Vdbe*, int addr, const char *zP4, int N);\nSQLITE_PRIVATE void sqlite3VdbeAppendP4(Vdbe*, void *pP4, int p4type);\nSQLITE_PRIVATE void sqlite3VdbeSetP4KeyInfo(Parse*, Index*);\nSQLITE_PRIVATE void sqlite3VdbeUsesBtree(Vdbe*, int);\nSQLITE_PRIVATE VdbeOp *sqlite3VdbeGetOp(Vdbe*, int);\nSQLITE_PRIVATE int sqlite3VdbeMakeLabel(Vdbe*);\nSQLITE_PRIVATE void sqlite3VdbeRunOnlyOnce(Vdbe*);\nSQLITE_PRIVATE void sqlite3VdbeReusable(Vdbe*);\nSQLITE_PRIVATE void sqlite3VdbeDelete(Vdbe*);\nSQLITE_PRIVATE void sqlite3VdbeClearObject(sqlite3*,Vdbe*);\nSQLITE_PRIVATE void sqlite3VdbeMakeReady(Vdbe*,Parse*);\nSQLITE_PRIVATE int sqlite3VdbeFinalize(Vdbe*);\nSQLITE_PRIVATE void sqlite3VdbeResolveLabel(Vdbe*, int);\nSQLITE_PRIVATE int sqlite3VdbeCurrentAddr(Vdbe*);\n#ifdef SQLITE_DEBUG\nSQLITE_PRIVATE   int sqlite3VdbeAssertMayAbort(Vdbe *, int);\n#endif\nSQLITE_PRIVATE void sqlite3VdbeResetStepResult(Vdbe*);\nSQLITE_PRIVATE void sqlite3VdbeRewind(Vdbe*);\nSQLITE_PRIVATE int sqlite3VdbeReset(Vdbe*);\nSQLITE_PRIVATE void sqlite3VdbeSetNumCols(Vdbe*,int);\nSQLITE_PRIVATE int sqlite3VdbeSetColName(Vdbe*, int, int, const char *, void(*)(void*));\nSQLITE_PRIVATE void sqlite3VdbeCountChanges(Vdbe*);\nSQLITE_PRIVATE sqlite3 *sqlite3VdbeDb(Vdbe*);\nSQLITE_PRIVATE u8 sqlite3VdbePrepareFlags(Vdbe*);\nSQLITE_PRIVATE void sqlite3VdbeSetSql(Vdbe*, const char *z, int n, u8);\nSQLITE_PRIVATE void sqlite3VdbeSwap(Vdbe*,Vdbe*);\nSQLITE_PRIVATE VdbeOp *sqlite3VdbeTakeOpArray(Vdbe*, int*, int*);\nSQLITE_PRIVATE sqlite3_value *sqlite3VdbeGetBoundValue(Vdbe*, int, u8);\nSQLITE_PRIVATE void sqlite3VdbeSetVarmask(Vdbe*, int);\n#ifndef SQLITE_OMIT_TRACE\nSQLITE_PRIVATE   char *sqlite3VdbeExpandSql(Vdbe*, const char*);\n#endif\nSQLITE_PRIVATE int sqlite3MemCompare(const Mem*, const Mem*, const CollSeq*);\n\nSQLITE_PRIVATE void sqlite3VdbeRecordUnpack(KeyInfo*,int,const void*,UnpackedRecord*);\nSQLITE_PRIVATE int sqlite3VdbeRecordCompare(int,const void*,UnpackedRecord*);\nSQLITE_PRIVATE int sqlite3VdbeRecordCompareWithSkip(int, const void *, UnpackedRecord *, int);\nSQLITE_PRIVATE UnpackedRecord *sqlite3VdbeAllocUnpackedRecord(KeyInfo*);\n\ntypedef int (*RecordCompare)(int,const void*,UnpackedRecord*);\nSQLITE_PRIVATE RecordCompare sqlite3VdbeFindCompare(UnpackedRecord*);\n\n#ifndef SQLITE_OMIT_TRIGGER\nSQLITE_PRIVATE void sqlite3VdbeLinkSubProgram(Vdbe *, SubProgram *);\n#endif\n\nSQLITE_PRIVATE int sqlite3NotPureFunc(sqlite3_context*);\n\n/* Use SQLITE_ENABLE_COMMENTS to enable generation of extra comments on\n** each VDBE opcode.\n**\n** Use the SQLITE_ENABLE_MODULE_COMMENTS macro to see some extra no-op\n** comments in VDBE programs that show key decision points in the code\n** generator.\n*/\n#ifdef SQLITE_ENABLE_EXPLAIN_COMMENTS\nSQLITE_PRIVATE   void sqlite3VdbeComment(Vdbe*, const char*, ...);\n# define VdbeComment(X)  sqlite3VdbeComment X\nSQLITE_PRIVATE   void sqlite3VdbeNoopComment(Vdbe*, const char*, ...);\n# define VdbeNoopComment(X)  sqlite3VdbeNoopComment X\n# ifdef SQLITE_ENABLE_MODULE_COMMENTS\n#   define VdbeModuleComment(X)  sqlite3VdbeNoopComment X\n# else\n#   define VdbeModuleComment(X)\n# endif\n#else\n# define VdbeComment(X)\n# define VdbeNoopComment(X)\n# define VdbeModuleComment(X)\n#endif\n\n/*\n** The VdbeCoverage macros are used to set a coverage testing point\n** for VDBE branch instructions.  The coverage testing points are line\n** numbers in the sqlite3.c source file.  VDBE branch coverage testing\n** only works with an amalagmation build.  That's ok since a VDBE branch\n** coverage build designed for testing the test suite only.  No application\n** should ever ship with VDBE branch coverage measuring turned on.\n**\n**    VdbeCoverage(v)                  // Mark the previously coded instruction\n**                                     // as a branch\n**\n**    VdbeCoverageIf(v, conditional)   // Mark previous if conditional true\n**\n**    VdbeCoverageAlwaysTaken(v)       // Previous branch is always taken\n**\n**    VdbeCoverageNeverTaken(v)        // Previous branch is never taken\n**\n** Every VDBE branch operation must be tagged with one of the macros above.\n** If not, then when \"make test\" is run with -DSQLITE_VDBE_COVERAGE and\n** -DSQLITE_DEBUG then an ALWAYS() will fail in the vdbeTakeBranch()\n** routine in vdbe.c, alerting the developer to the missed tag.\n*/\n#ifdef SQLITE_VDBE_COVERAGE\nSQLITE_PRIVATE   void sqlite3VdbeSetLineNumber(Vdbe*,int);\n# define VdbeCoverage(v) sqlite3VdbeSetLineNumber(v,__LINE__)\n# define VdbeCoverageIf(v,x) if(x)sqlite3VdbeSetLineNumber(v,__LINE__)\n# define VdbeCoverageAlwaysTaken(v) sqlite3VdbeSetLineNumber(v,2);\n# define VdbeCoverageNeverTaken(v) sqlite3VdbeSetLineNumber(v,1);\n# define VDBE_OFFSET_LINENO(x) (__LINE__+x)\n#else\n# define VdbeCoverage(v)\n# define VdbeCoverageIf(v,x)\n# define VdbeCoverageAlwaysTaken(v)\n# define VdbeCoverageNeverTaken(v)\n# define VDBE_OFFSET_LINENO(x) 0\n#endif\n\n#ifdef SQLITE_ENABLE_STMT_SCANSTATUS\nSQLITE_PRIVATE void sqlite3VdbeScanStatus(Vdbe*, int, int, int, LogEst, const char*);\n#else\n# define sqlite3VdbeScanStatus(a,b,c,d,e)\n#endif\n\n#endif /* SQLITE_VDBE_H */\n\n/************** End of vdbe.h ************************************************/\n/************** Continuing where we left off in sqliteInt.h ******************/\n/************** Include pager.h in the middle of sqliteInt.h *****************/\n/************** Begin file pager.h *******************************************/\n/*\n** 2001 September 15\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n*************************************************************************\n** This header file defines the interface that the sqlite page cache\n** subsystem.  The page cache subsystem reads and writes a file a page\n** at a time and provides a journal for rollback.\n*/\n\n#ifndef SQLITE_PAGER_H\n#define SQLITE_PAGER_H\n\n/*\n** Default maximum size for persistent journal files. A negative \n** value means no limit. This value may be overridden using the \n** sqlite3PagerJournalSizeLimit() API. See also \"PRAGMA journal_size_limit\".\n*/\n#ifndef SQLITE_DEFAULT_JOURNAL_SIZE_LIMIT\n  #define SQLITE_DEFAULT_JOURNAL_SIZE_LIMIT -1\n#endif\n\n/*\n** The type used to represent a page number.  The first page in a file\n** is called page 1.  0 is used to represent \"not a page\".\n*/\ntypedef u32 Pgno;\n\n/*\n** Each open file is managed by a separate instance of the \"Pager\" structure.\n*/\ntypedef struct Pager Pager;\n\n/*\n** Handle type for pages.\n*/\ntypedef struct PgHdr DbPage;\n\n/*\n** Page number PAGER_MJ_PGNO is never used in an SQLite database (it is\n** reserved for working around a windows/posix incompatibility). It is\n** used in the journal to signify that the remainder of the journal file \n** is devoted to storing a master journal name - there are no more pages to\n** roll back. See comments for function writeMasterJournal() in pager.c \n** for details.\n*/\n#define PAGER_MJ_PGNO(x) ((Pgno)((PENDING_BYTE/((x)->pageSize))+1))\n\n/*\n** Allowed values for the flags parameter to sqlite3PagerOpen().\n**\n** NOTE: These values must match the corresponding BTREE_ values in btree.h.\n*/\n#define PAGER_OMIT_JOURNAL  0x0001    /* Do not use a rollback journal */\n#define PAGER_MEMORY        0x0002    /* In-memory database */\n\n/*\n** Valid values for the second argument to sqlite3PagerLockingMode().\n*/\n#define PAGER_LOCKINGMODE_QUERY      -1\n#define PAGER_LOCKINGMODE_NORMAL      0\n#define PAGER_LOCKINGMODE_EXCLUSIVE   1\n\n/*\n** Numeric constants that encode the journalmode.\n**\n** The numeric values encoded here (other than PAGER_JOURNALMODE_QUERY)\n** are exposed in the API via the \"PRAGMA journal_mode\" command and\n** therefore cannot be changed without a compatibility break.\n*/\n#define PAGER_JOURNALMODE_QUERY     (-1)  /* Query the value of journalmode */\n#define PAGER_JOURNALMODE_DELETE      0   /* Commit by deleting journal file */\n#define PAGER_JOURNALMODE_PERSIST     1   /* Commit by zeroing journal header */\n#define PAGER_JOURNALMODE_OFF         2   /* Journal omitted.  */\n#define PAGER_JOURNALMODE_TRUNCATE    3   /* Commit by truncating journal */\n#define PAGER_JOURNALMODE_MEMORY      4   /* In-memory journal file */\n#define PAGER_JOURNALMODE_WAL         5   /* Use write-ahead logging */\n\n/*\n** Flags that make up the mask passed to sqlite3PagerGet().\n*/\n#define PAGER_GET_NOCONTENT     0x01  /* Do not load data from disk */\n#define PAGER_GET_READONLY      0x02  /* Read-only page is acceptable */\n\n/*\n** Flags for sqlite3PagerSetFlags()\n**\n** Value constraints (enforced via assert()):\n**    PAGER_FULLFSYNC      == SQLITE_FullFSync\n**    PAGER_CKPT_FULLFSYNC == SQLITE_CkptFullFSync\n**    PAGER_CACHE_SPILL    == SQLITE_CacheSpill\n*/\n#define PAGER_SYNCHRONOUS_OFF       0x01  /* PRAGMA synchronous=OFF */\n#define PAGER_SYNCHRONOUS_NORMAL    0x02  /* PRAGMA synchronous=NORMAL */\n#define PAGER_SYNCHRONOUS_FULL      0x03  /* PRAGMA synchronous=FULL */\n#define PAGER_SYNCHRONOUS_EXTRA     0x04  /* PRAGMA synchronous=EXTRA */\n#define PAGER_SYNCHRONOUS_MASK      0x07  /* Mask for four values above */\n#define PAGER_FULLFSYNC             0x08  /* PRAGMA fullfsync=ON */\n#define PAGER_CKPT_FULLFSYNC        0x10  /* PRAGMA checkpoint_fullfsync=ON */\n#define PAGER_CACHESPILL            0x20  /* PRAGMA cache_spill=ON */\n#define PAGER_FLAGS_MASK            0x38  /* All above except SYNCHRONOUS */\n\n/*\n** The remainder of this file contains the declarations of the functions\n** that make up the Pager sub-system API. See source code comments for \n** a detailed description of each routine.\n*/\n\n/* Open and close a Pager connection. */ \nSQLITE_PRIVATE int sqlite3PagerOpen(\n  sqlite3_vfs*,\n  Pager **ppPager,\n  const char*,\n  int,\n  int,\n  int,\n  void(*)(DbPage*)\n);\nSQLITE_PRIVATE int sqlite3PagerClose(Pager *pPager, sqlite3*);\nSQLITE_PRIVATE int sqlite3PagerReadFileheader(Pager*, int, unsigned char*);\n\n/* Functions used to configure a Pager object. */\nSQLITE_PRIVATE void sqlite3PagerSetBusyhandler(Pager*, int(*)(void *), void *);\nSQLITE_PRIVATE int sqlite3PagerSetPagesize(Pager*, u32*, int);\n#ifdef SQLITE_HAS_CODEC\nSQLITE_PRIVATE void sqlite3PagerAlignReserve(Pager*,Pager*);\n#endif\nSQLITE_PRIVATE int sqlite3PagerMaxPageCount(Pager*, int);\nSQLITE_PRIVATE void sqlite3PagerSetCachesize(Pager*, int);\nSQLITE_PRIVATE int sqlite3PagerSetSpillsize(Pager*, int);\nSQLITE_PRIVATE void sqlite3PagerSetMmapLimit(Pager *, sqlite3_int64);\nSQLITE_PRIVATE void sqlite3PagerShrink(Pager*);\nSQLITE_PRIVATE void sqlite3PagerSetFlags(Pager*,unsigned);\nSQLITE_PRIVATE int sqlite3PagerLockingMode(Pager *, int);\nSQLITE_PRIVATE int sqlite3PagerSetJournalMode(Pager *, int);\nSQLITE_PRIVATE int sqlite3PagerGetJournalMode(Pager*);\nSQLITE_PRIVATE int sqlite3PagerOkToChangeJournalMode(Pager*);\nSQLITE_PRIVATE i64 sqlite3PagerJournalSizeLimit(Pager *, i64);\nSQLITE_PRIVATE sqlite3_backup **sqlite3PagerBackupPtr(Pager*);\nSQLITE_PRIVATE int sqlite3PagerFlush(Pager*);\n\n/* Functions used to obtain and release page references. */ \nSQLITE_PRIVATE int sqlite3PagerGet(Pager *pPager, Pgno pgno, DbPage **ppPage, int clrFlag);\nSQLITE_PRIVATE DbPage *sqlite3PagerLookup(Pager *pPager, Pgno pgno);\nSQLITE_PRIVATE void sqlite3PagerRef(DbPage*);\nSQLITE_PRIVATE void sqlite3PagerUnref(DbPage*);\nSQLITE_PRIVATE void sqlite3PagerUnrefNotNull(DbPage*);\nSQLITE_PRIVATE void sqlite3PagerUnrefPageOne(DbPage*);\n\n/* Operations on page references. */\nSQLITE_PRIVATE int sqlite3PagerWrite(DbPage*);\nSQLITE_PRIVATE void sqlite3PagerDontWrite(DbPage*);\nSQLITE_PRIVATE int sqlite3PagerMovepage(Pager*,DbPage*,Pgno,int);\nSQLITE_PRIVATE int sqlite3PagerPageRefcount(DbPage*);\nSQLITE_PRIVATE void *sqlite3PagerGetData(DbPage *); \nSQLITE_PRIVATE void *sqlite3PagerGetExtra(DbPage *); \n\n/* Functions used to manage pager transactions and savepoints. */\nSQLITE_PRIVATE void sqlite3PagerPagecount(Pager*, int*);\nSQLITE_PRIVATE int sqlite3PagerBegin(Pager*, int exFlag, int);\nSQLITE_PRIVATE int sqlite3PagerCommitPhaseOne(Pager*,const char *zMaster, int);\nSQLITE_PRIVATE int sqlite3PagerExclusiveLock(Pager*);\nSQLITE_PRIVATE int sqlite3PagerSync(Pager *pPager, const char *zMaster);\nSQLITE_PRIVATE int sqlite3PagerCommitPhaseTwo(Pager*);\nSQLITE_PRIVATE int sqlite3PagerRollback(Pager*);\nSQLITE_PRIVATE int sqlite3PagerOpenSavepoint(Pager *pPager, int n);\nSQLITE_PRIVATE int sqlite3PagerSavepoint(Pager *pPager, int op, int iSavepoint);\nSQLITE_PRIVATE int sqlite3PagerSharedLock(Pager *pPager);\n\n#ifndef SQLITE_OMIT_WAL\nSQLITE_PRIVATE   int sqlite3PagerCheckpoint(Pager *pPager, sqlite3*, int, int*, int*);\nSQLITE_PRIVATE   int sqlite3PagerWalSupported(Pager *pPager);\nSQLITE_PRIVATE   int sqlite3PagerWalCallback(Pager *pPager);\nSQLITE_PRIVATE   int sqlite3PagerOpenWal(Pager *pPager, int *pisOpen);\nSQLITE_PRIVATE   int sqlite3PagerCloseWal(Pager *pPager, sqlite3*);\n# ifdef SQLITE_DIRECT_OVERFLOW_READ\nSQLITE_PRIVATE   int sqlite3PagerUseWal(Pager *pPager, Pgno);\n# endif\n# ifdef SQLITE_ENABLE_SNAPSHOT\nSQLITE_PRIVATE   int sqlite3PagerSnapshotGet(Pager *pPager, sqlite3_snapshot **ppSnapshot);\nSQLITE_PRIVATE   int sqlite3PagerSnapshotOpen(Pager *pPager, sqlite3_snapshot *pSnapshot);\nSQLITE_PRIVATE   int sqlite3PagerSnapshotRecover(Pager *pPager);\n# endif\n#else\n# define sqlite3PagerUseWal(x,y) 0\n#endif\n\n#ifdef SQLITE_ENABLE_ZIPVFS\nSQLITE_PRIVATE   int sqlite3PagerWalFramesize(Pager *pPager);\n#endif\n\n/* Functions used to query pager state and configuration. */\nSQLITE_PRIVATE u8 sqlite3PagerIsreadonly(Pager*);\nSQLITE_PRIVATE u32 sqlite3PagerDataVersion(Pager*);\n#ifdef SQLITE_DEBUG\nSQLITE_PRIVATE   int sqlite3PagerRefcount(Pager*);\n#endif\nSQLITE_PRIVATE int sqlite3PagerMemUsed(Pager*);\nSQLITE_PRIVATE const char *sqlite3PagerFilename(Pager*, int);\nSQLITE_PRIVATE sqlite3_vfs *sqlite3PagerVfs(Pager*);\nSQLITE_PRIVATE sqlite3_file *sqlite3PagerFile(Pager*);\nSQLITE_PRIVATE sqlite3_file *sqlite3PagerJrnlFile(Pager*);\nSQLITE_PRIVATE const char *sqlite3PagerJournalname(Pager*);\nSQLITE_PRIVATE void *sqlite3PagerTempSpace(Pager*);\nSQLITE_PRIVATE int sqlite3PagerIsMemdb(Pager*);\nSQLITE_PRIVATE void sqlite3PagerCacheStat(Pager *, int, int, int *);\nSQLITE_PRIVATE void sqlite3PagerClearCache(Pager*);\nSQLITE_PRIVATE int sqlite3SectorSize(sqlite3_file *);\n\n/* Functions used to truncate the database file. */\nSQLITE_PRIVATE void sqlite3PagerTruncateImage(Pager*,Pgno);\n\nSQLITE_PRIVATE void sqlite3PagerRekey(DbPage*, Pgno, u16);\n\n#if defined(SQLITE_HAS_CODEC) && !defined(SQLITE_OMIT_WAL)\nSQLITE_PRIVATE void *sqlite3PagerCodec(DbPage *);\n#endif\n\n/* Functions to support testing and debugging. */\n#if !defined(NDEBUG) || defined(SQLITE_TEST)\nSQLITE_PRIVATE   Pgno sqlite3PagerPagenumber(DbPage*);\nSQLITE_PRIVATE   int sqlite3PagerIswriteable(DbPage*);\n#endif\n#ifdef SQLITE_TEST\nSQLITE_PRIVATE   int *sqlite3PagerStats(Pager*);\nSQLITE_PRIVATE   void sqlite3PagerRefdump(Pager*);\n  void disable_simulated_io_errors(void);\n  void enable_simulated_io_errors(void);\n#else\n# define disable_simulated_io_errors()\n# define enable_simulated_io_errors()\n#endif\n\n#endif /* SQLITE_PAGER_H */\n\n/************** End of pager.h ***********************************************/\n/************** Continuing where we left off in sqliteInt.h ******************/\n/************** Include pcache.h in the middle of sqliteInt.h ****************/\n/************** Begin file pcache.h ******************************************/\n/*\n** 2008 August 05\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n*************************************************************************\n** This header file defines the interface that the sqlite page cache\n** subsystem. \n*/\n\n#ifndef _PCACHE_H_\n\ntypedef struct PgHdr PgHdr;\ntypedef struct PCache PCache;\n\n/*\n** Every page in the cache is controlled by an instance of the following\n** structure.\n*/\nstruct PgHdr {\n  sqlite3_pcache_page *pPage;    /* Pcache object page handle */\n  void *pData;                   /* Page data */\n  void *pExtra;                  /* Extra content */\n  PCache *pCache;                /* PRIVATE: Cache that owns this page */\n  PgHdr *pDirty;                 /* Transient list of dirty sorted by pgno */\n  Pager *pPager;                 /* The pager this page is part of */\n  Pgno pgno;                     /* Page number for this page */\n#ifdef SQLITE_CHECK_PAGES\n  u32 pageHash;                  /* Hash of page content */\n#endif\n  u16 flags;                     /* PGHDR flags defined below */\n\n  /**********************************************************************\n  ** Elements above, except pCache, are public.  All that follow are \n  ** private to pcache.c and should not be accessed by other modules.\n  ** pCache is grouped with the public elements for efficiency.\n  */\n  i16 nRef;                      /* Number of users of this page */\n  PgHdr *pDirtyNext;             /* Next element in list of dirty pages */\n  PgHdr *pDirtyPrev;             /* Previous element in list of dirty pages */\n                          /* NB: pDirtyNext and pDirtyPrev are undefined if the\n                          ** PgHdr object is not dirty */\n};\n\n/* Bit values for PgHdr.flags */\n#define PGHDR_CLEAN           0x001  /* Page not on the PCache.pDirty list */\n#define PGHDR_DIRTY           0x002  /* Page is on the PCache.pDirty list */\n#define PGHDR_WRITEABLE       0x004  /* Journaled and ready to modify */\n#define PGHDR_NEED_SYNC       0x008  /* Fsync the rollback journal before\n                                     ** writing this page to the database */\n#define PGHDR_DONT_WRITE      0x010  /* Do not write content to disk */\n#define PGHDR_MMAP            0x020  /* This is an mmap page object */\n\n#define PGHDR_WAL_APPEND      0x040  /* Appended to wal file */\n\n/* Initialize and shutdown the page cache subsystem */\nSQLITE_PRIVATE int sqlite3PcacheInitialize(void);\nSQLITE_PRIVATE void sqlite3PcacheShutdown(void);\n\n/* Page cache buffer management:\n** These routines implement SQLITE_CONFIG_PAGECACHE.\n*/\nSQLITE_PRIVATE void sqlite3PCacheBufferSetup(void *, int sz, int n);\n\n/* Create a new pager cache.\n** Under memory stress, invoke xStress to try to make pages clean.\n** Only clean and unpinned pages can be reclaimed.\n*/\nSQLITE_PRIVATE int sqlite3PcacheOpen(\n  int szPage,                    /* Size of every page */\n  int szExtra,                   /* Extra space associated with each page */\n  int bPurgeable,                /* True if pages are on backing store */\n  int (*xStress)(void*, PgHdr*), /* Call to try to make pages clean */\n  void *pStress,                 /* Argument to xStress */\n  PCache *pToInit                /* Preallocated space for the PCache */\n);\n\n/* Modify the page-size after the cache has been created. */\nSQLITE_PRIVATE int sqlite3PcacheSetPageSize(PCache *, int);\n\n/* Return the size in bytes of a PCache object.  Used to preallocate\n** storage space.\n*/\nSQLITE_PRIVATE int sqlite3PcacheSize(void);\n\n/* One release per successful fetch.  Page is pinned until released.\n** Reference counted. \n*/\nSQLITE_PRIVATE sqlite3_pcache_page *sqlite3PcacheFetch(PCache*, Pgno, int createFlag);\nSQLITE_PRIVATE int sqlite3PcacheFetchStress(PCache*, Pgno, sqlite3_pcache_page**);\nSQLITE_PRIVATE PgHdr *sqlite3PcacheFetchFinish(PCache*, Pgno, sqlite3_pcache_page *pPage);\nSQLITE_PRIVATE void sqlite3PcacheRelease(PgHdr*);\n\nSQLITE_PRIVATE void sqlite3PcacheDrop(PgHdr*);         /* Remove page from cache */\nSQLITE_PRIVATE void sqlite3PcacheMakeDirty(PgHdr*);    /* Make sure page is marked dirty */\nSQLITE_PRIVATE void sqlite3PcacheMakeClean(PgHdr*);    /* Mark a single page as clean */\nSQLITE_PRIVATE void sqlite3PcacheCleanAll(PCache*);    /* Mark all dirty list pages as clean */\nSQLITE_PRIVATE void sqlite3PcacheClearWritable(PCache*);\n\n/* Change a page number.  Used by incr-vacuum. */\nSQLITE_PRIVATE void sqlite3PcacheMove(PgHdr*, Pgno);\n\n/* Remove all pages with pgno>x.  Reset the cache if x==0 */\nSQLITE_PRIVATE void sqlite3PcacheTruncate(PCache*, Pgno x);\n\n/* Get a list of all dirty pages in the cache, sorted by page number */\nSQLITE_PRIVATE PgHdr *sqlite3PcacheDirtyList(PCache*);\n\n/* Reset and close the cache object */\nSQLITE_PRIVATE void sqlite3PcacheClose(PCache*);\n\n/* Clear flags from pages of the page cache */\nSQLITE_PRIVATE void sqlite3PcacheClearSyncFlags(PCache *);\n\n/* Discard the contents of the cache */\nSQLITE_PRIVATE void sqlite3PcacheClear(PCache*);\n\n/* Return the total number of outstanding page references */\nSQLITE_PRIVATE int sqlite3PcacheRefCount(PCache*);\n\n/* Increment the reference count of an existing page */\nSQLITE_PRIVATE void sqlite3PcacheRef(PgHdr*);\n\nSQLITE_PRIVATE int sqlite3PcachePageRefcount(PgHdr*);\n\n/* Return the total number of pages stored in the cache */\nSQLITE_PRIVATE int sqlite3PcachePagecount(PCache*);\n\n#if defined(SQLITE_CHECK_PAGES) || defined(SQLITE_DEBUG)\n/* Iterate through all dirty pages currently stored in the cache. This\n** interface is only available if SQLITE_CHECK_PAGES is defined when the \n** library is built.\n*/\nSQLITE_PRIVATE void sqlite3PcacheIterateDirty(PCache *pCache, void (*xIter)(PgHdr *));\n#endif\n\n#if defined(SQLITE_DEBUG)\n/* Check invariants on a PgHdr object */\nSQLITE_PRIVATE int sqlite3PcachePageSanity(PgHdr*);\n#endif\n\n/* Set and get the suggested cache-size for the specified pager-cache.\n**\n** If no global maximum is configured, then the system attempts to limit\n** the total number of pages cached by purgeable pager-caches to the sum\n** of the suggested cache-sizes.\n*/\nSQLITE_PRIVATE void sqlite3PcacheSetCachesize(PCache *, int);\n#ifdef SQLITE_TEST\nSQLITE_PRIVATE int sqlite3PcacheGetCachesize(PCache *);\n#endif\n\n/* Set or get the suggested spill-size for the specified pager-cache.\n**\n** The spill-size is the minimum number of pages in cache before the cache\n** will attempt to spill dirty pages by calling xStress.\n*/\nSQLITE_PRIVATE int sqlite3PcacheSetSpillsize(PCache *, int);\n\n/* Free up as much memory as possible from the page cache */\nSQLITE_PRIVATE void sqlite3PcacheShrink(PCache*);\n\n#ifdef SQLITE_ENABLE_MEMORY_MANAGEMENT\n/* Try to return memory used by the pcache module to the main memory heap */\nSQLITE_PRIVATE int sqlite3PcacheReleaseMemory(int);\n#endif\n\n#ifdef SQLITE_TEST\nSQLITE_PRIVATE void sqlite3PcacheStats(int*,int*,int*,int*);\n#endif\n\nSQLITE_PRIVATE void sqlite3PCacheSetDefault(void);\n\n/* Return the header size */\nSQLITE_PRIVATE int sqlite3HeaderSizePcache(void);\nSQLITE_PRIVATE int sqlite3HeaderSizePcache1(void);\n\n/* Number of dirty pages as a percentage of the configured cache size */\nSQLITE_PRIVATE int sqlite3PCachePercentDirty(PCache*);\n\n#endif /* _PCACHE_H_ */\n\n/************** End of pcache.h **********************************************/\n/************** Continuing where we left off in sqliteInt.h ******************/\n/************** Include os.h in the middle of sqliteInt.h ********************/\n/************** Begin file os.h **********************************************/\n/*\n** 2001 September 16\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n******************************************************************************\n**\n** This header file (together with is companion C source-code file\n** \"os.c\") attempt to abstract the underlying operating system so that\n** the SQLite library will work on both POSIX and windows systems.\n**\n** This header file is #include-ed by sqliteInt.h and thus ends up\n** being included by every source file.\n*/\n#ifndef _SQLITE_OS_H_\n#define _SQLITE_OS_H_\n\n/*\n** Attempt to automatically detect the operating system and setup the\n** necessary pre-processor macros for it.\n*/\n/************** Include os_setup.h in the middle of os.h *********************/\n/************** Begin file os_setup.h ****************************************/\n/*\n** 2013 November 25\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n******************************************************************************\n**\n** This file contains pre-processor directives related to operating system\n** detection and/or setup.\n*/\n#ifndef SQLITE_OS_SETUP_H\n#define SQLITE_OS_SETUP_H\n\n/*\n** Figure out if we are dealing with Unix, Windows, or some other operating\n** system.\n**\n** After the following block of preprocess macros, all of SQLITE_OS_UNIX,\n** SQLITE_OS_WIN, and SQLITE_OS_OTHER will defined to either 1 or 0.  One of\n** the three will be 1.  The other two will be 0.\n*/\n#if defined(SQLITE_OS_OTHER)\n#  if SQLITE_OS_OTHER==1\n#    undef SQLITE_OS_UNIX\n#    define SQLITE_OS_UNIX 0\n#    undef SQLITE_OS_WIN\n#    define SQLITE_OS_WIN 0\n#  else\n#    undef SQLITE_OS_OTHER\n#  endif\n#endif\n#if !defined(SQLITE_OS_UNIX) && !defined(SQLITE_OS_OTHER)\n#  define SQLITE_OS_OTHER 0\n#  ifndef SQLITE_OS_WIN\n#    if defined(_WIN32) || defined(WIN32) || defined(__CYGWIN__) || \\\n        defined(__MINGW32__) || defined(__BORLANDC__)\n#      define SQLITE_OS_WIN 1\n#      define SQLITE_OS_UNIX 0\n#    else\n#      define SQLITE_OS_WIN 0\n#      define SQLITE_OS_UNIX 1\n#    endif\n#  else\n#    define SQLITE_OS_UNIX 0\n#  endif\n#else\n#  ifndef SQLITE_OS_WIN\n#    define SQLITE_OS_WIN 0\n#  endif\n#endif\n\n#endif /* SQLITE_OS_SETUP_H */\n\n/************** End of os_setup.h ********************************************/\n/************** Continuing where we left off in os.h *************************/\n\n/* If the SET_FULLSYNC macro is not defined above, then make it\n** a no-op\n*/\n#ifndef SET_FULLSYNC\n# define SET_FULLSYNC(x,y)\n#endif\n\n/*\n** The default size of a disk sector\n*/\n#ifndef SQLITE_DEFAULT_SECTOR_SIZE\n# define SQLITE_DEFAULT_SECTOR_SIZE 4096\n#endif\n\n/*\n** Temporary files are named starting with this prefix followed by 16 random\n** alphanumeric characters, and no file extension. They are stored in the\n** OS's standard temporary file directory, and are deleted prior to exit.\n** If sqlite is being embedded in another program, you may wish to change the\n** prefix to reflect your program's name, so that if your program exits\n** prematurely, old temporary files can be easily identified. This can be done\n** using -DSQLITE_TEMP_FILE_PREFIX=myprefix_ on the compiler command line.\n**\n** 2006-10-31:  The default prefix used to be \"sqlite_\".  But then\n** Mcafee started using SQLite in their anti-virus product and it\n** started putting files with the \"sqlite\" name in the c:/temp folder.\n** This annoyed many windows users.  Those users would then do a \n** Google search for \"sqlite\", find the telephone numbers of the\n** developers and call to wake them up at night and complain.\n** For this reason, the default name prefix is changed to be \"sqlite\" \n** spelled backwards.  So the temp files are still identified, but\n** anybody smart enough to figure out the code is also likely smart\n** enough to know that calling the developer will not help get rid\n** of the file.\n*/\n#ifndef SQLITE_TEMP_FILE_PREFIX\n# define SQLITE_TEMP_FILE_PREFIX \"etilqs_\"\n#endif\n\n/*\n** The following values may be passed as the second argument to\n** sqlite3OsLock(). The various locks exhibit the following semantics:\n**\n** SHARED:    Any number of processes may hold a SHARED lock simultaneously.\n** RESERVED:  A single process may hold a RESERVED lock on a file at\n**            any time. Other processes may hold and obtain new SHARED locks.\n** PENDING:   A single process may hold a PENDING lock on a file at\n**            any one time. Existing SHARED locks may persist, but no new\n**            SHARED locks may be obtained by other processes.\n** EXCLUSIVE: An EXCLUSIVE lock precludes all other locks.\n**\n** PENDING_LOCK may not be passed directly to sqlite3OsLock(). Instead, a\n** process that requests an EXCLUSIVE lock may actually obtain a PENDING\n** lock. This can be upgraded to an EXCLUSIVE lock by a subsequent call to\n** sqlite3OsLock().\n*/\n#define NO_LOCK         0\n#define SHARED_LOCK     1\n#define RESERVED_LOCK   2\n#define PENDING_LOCK    3\n#define EXCLUSIVE_LOCK  4\n\n/*\n** File Locking Notes:  (Mostly about windows but also some info for Unix)\n**\n** We cannot use LockFileEx() or UnlockFileEx() on Win95/98/ME because\n** those functions are not available.  So we use only LockFile() and\n** UnlockFile().\n**\n** LockFile() prevents not just writing but also reading by other processes.\n** A SHARED_LOCK is obtained by locking a single randomly-chosen \n** byte out of a specific range of bytes. The lock byte is obtained at \n** random so two separate readers can probably access the file at the \n** same time, unless they are unlucky and choose the same lock byte.\n** An EXCLUSIVE_LOCK is obtained by locking all bytes in the range.\n** There can only be one writer.  A RESERVED_LOCK is obtained by locking\n** a single byte of the file that is designated as the reserved lock byte.\n** A PENDING_LOCK is obtained by locking a designated byte different from\n** the RESERVED_LOCK byte.\n**\n** On WinNT/2K/XP systems, LockFileEx() and UnlockFileEx() are available,\n** which means we can use reader/writer locks.  When reader/writer locks\n** are used, the lock is placed on the same range of bytes that is used\n** for probabilistic locking in Win95/98/ME.  Hence, the locking scheme\n** will support two or more Win95 readers or two or more WinNT readers.\n** But a single Win95 reader will lock out all WinNT readers and a single\n** WinNT reader will lock out all other Win95 readers.\n**\n** The following #defines specify the range of bytes used for locking.\n** SHARED_SIZE is the number of bytes available in the pool from which\n** a random byte is selected for a shared lock.  The pool of bytes for\n** shared locks begins at SHARED_FIRST. \n**\n** The same locking strategy and\n** byte ranges are used for Unix.  This leaves open the possibility of having\n** clients on win95, winNT, and unix all talking to the same shared file\n** and all locking correctly.  To do so would require that samba (or whatever\n** tool is being used for file sharing) implements locks correctly between\n** windows and unix.  I'm guessing that isn't likely to happen, but by\n** using the same locking range we are at least open to the possibility.\n**\n** Locking in windows is manditory.  For this reason, we cannot store\n** actual data in the bytes used for locking.  The pager never allocates\n** the pages involved in locking therefore.  SHARED_SIZE is selected so\n** that all locks will fit on a single page even at the minimum page size.\n** PENDING_BYTE defines the beginning of the locks.  By default PENDING_BYTE\n** is set high so that we don't have to allocate an unused page except\n** for very large databases.  But one should test the page skipping logic \n** by setting PENDING_BYTE low and running the entire regression suite.\n**\n** Changing the value of PENDING_BYTE results in a subtly incompatible\n** file format.  Depending on how it is changed, you might not notice\n** the incompatibility right away, even running a full regression test.\n** The default location of PENDING_BYTE is the first byte past the\n** 1GB boundary.\n**\n*/\n#ifdef SQLITE_OMIT_WSD\n# define PENDING_BYTE     (0x40000000)\n#else\n# define PENDING_BYTE      sqlite3PendingByte\n#endif\n#define RESERVED_BYTE     (PENDING_BYTE+1)\n#define SHARED_FIRST      (PENDING_BYTE+2)\n#define SHARED_SIZE       510\n\n/*\n** Wrapper around OS specific sqlite3_os_init() function.\n*/\nSQLITE_PRIVATE int sqlite3OsInit(void);\n\n/* \n** Functions for accessing sqlite3_file methods \n*/\nSQLITE_PRIVATE void sqlite3OsClose(sqlite3_file*);\nSQLITE_PRIVATE int sqlite3OsRead(sqlite3_file*, void*, int amt, i64 offset);\nSQLITE_PRIVATE int sqlite3OsWrite(sqlite3_file*, const void*, int amt, i64 offset);\nSQLITE_PRIVATE int sqlite3OsTruncate(sqlite3_file*, i64 size);\nSQLITE_PRIVATE int sqlite3OsSync(sqlite3_file*, int);\nSQLITE_PRIVATE int sqlite3OsFileSize(sqlite3_file*, i64 *pSize);\nSQLITE_PRIVATE int sqlite3OsLock(sqlite3_file*, int);\nSQLITE_PRIVATE int sqlite3OsUnlock(sqlite3_file*, int);\nSQLITE_PRIVATE int sqlite3OsCheckReservedLock(sqlite3_file *id, int *pResOut);\nSQLITE_PRIVATE int sqlite3OsFileControl(sqlite3_file*,int,void*);\nSQLITE_PRIVATE void sqlite3OsFileControlHint(sqlite3_file*,int,void*);\n#define SQLITE_FCNTL_DB_UNCHANGED 0xca093fa0\nSQLITE_PRIVATE int sqlite3OsSectorSize(sqlite3_file *id);\nSQLITE_PRIVATE int sqlite3OsDeviceCharacteristics(sqlite3_file *id);\n#ifndef SQLITE_OMIT_WAL\nSQLITE_PRIVATE int sqlite3OsShmMap(sqlite3_file *,int,int,int,void volatile **);\nSQLITE_PRIVATE int sqlite3OsShmLock(sqlite3_file *id, int, int, int);\nSQLITE_PRIVATE void sqlite3OsShmBarrier(sqlite3_file *id);\nSQLITE_PRIVATE int sqlite3OsShmUnmap(sqlite3_file *id, int);\n#endif /* SQLITE_OMIT_WAL */\nSQLITE_PRIVATE int sqlite3OsFetch(sqlite3_file *id, i64, int, void **);\nSQLITE_PRIVATE int sqlite3OsUnfetch(sqlite3_file *, i64, void *);\n\n\n/* \n** Functions for accessing sqlite3_vfs methods \n*/\nSQLITE_PRIVATE int sqlite3OsOpen(sqlite3_vfs *, const char *, sqlite3_file*, int, int *);\nSQLITE_PRIVATE int sqlite3OsDelete(sqlite3_vfs *, const char *, int);\nSQLITE_PRIVATE int sqlite3OsAccess(sqlite3_vfs *, const char *, int, int *pResOut);\nSQLITE_PRIVATE int sqlite3OsFullPathname(sqlite3_vfs *, const char *, int, char *);\n#ifndef SQLITE_OMIT_LOAD_EXTENSION\nSQLITE_PRIVATE void *sqlite3OsDlOpen(sqlite3_vfs *, const char *);\nSQLITE_PRIVATE void sqlite3OsDlError(sqlite3_vfs *, int, char *);\nSQLITE_PRIVATE void (*sqlite3OsDlSym(sqlite3_vfs *, void *, const char *))(void);\nSQLITE_PRIVATE void sqlite3OsDlClose(sqlite3_vfs *, void *);\n#endif /* SQLITE_OMIT_LOAD_EXTENSION */\nSQLITE_PRIVATE int sqlite3OsRandomness(sqlite3_vfs *, int, char *);\nSQLITE_PRIVATE int sqlite3OsSleep(sqlite3_vfs *, int);\nSQLITE_PRIVATE int sqlite3OsGetLastError(sqlite3_vfs*);\nSQLITE_PRIVATE int sqlite3OsCurrentTimeInt64(sqlite3_vfs *, sqlite3_int64*);\n\n/*\n** Convenience functions for opening and closing files using \n** sqlite3_malloc() to obtain space for the file-handle structure.\n*/\nSQLITE_PRIVATE int sqlite3OsOpenMalloc(sqlite3_vfs *, const char *, sqlite3_file **, int,int*);\nSQLITE_PRIVATE void sqlite3OsCloseFree(sqlite3_file *);\n\n#endif /* _SQLITE_OS_H_ */\n\n/************** End of os.h **************************************************/\n/************** Continuing where we left off in sqliteInt.h ******************/\n/************** Include mutex.h in the middle of sqliteInt.h *****************/\n/************** Begin file mutex.h *******************************************/\n/*\n** 2007 August 28\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n*************************************************************************\n**\n** This file contains the common header for all mutex implementations.\n** The sqliteInt.h header #includes this file so that it is available\n** to all source files.  We break it out in an effort to keep the code\n** better organized.\n**\n** NOTE:  source files should *not* #include this header file directly.\n** Source files should #include the sqliteInt.h file and let that file\n** include this one indirectly.\n*/\n\n\n/*\n** Figure out what version of the code to use.  The choices are\n**\n**   SQLITE_MUTEX_OMIT         No mutex logic.  Not even stubs.  The\n**                             mutexes implementation cannot be overridden\n**                             at start-time.\n**\n**   SQLITE_MUTEX_NOOP         For single-threaded applications.  No\n**                             mutual exclusion is provided.  But this\n**                             implementation can be overridden at\n**                             start-time.\n**\n**   SQLITE_MUTEX_PTHREADS     For multi-threaded applications on Unix.\n**\n**   SQLITE_MUTEX_W32          For multi-threaded applications on Win32.\n*/\n#if !SQLITE_THREADSAFE\n# define SQLITE_MUTEX_OMIT\n#endif\n#if SQLITE_THREADSAFE && !defined(SQLITE_MUTEX_NOOP)\n#  if SQLITE_OS_UNIX\n#    define SQLITE_MUTEX_PTHREADS\n#  elif SQLITE_OS_WIN\n#    define SQLITE_MUTEX_W32\n#  else\n#    define SQLITE_MUTEX_NOOP\n#  endif\n#endif\n\n#ifdef SQLITE_MUTEX_OMIT\n/*\n** If this is a no-op implementation, implement everything as macros.\n*/\n#define sqlite3_mutex_alloc(X)    ((sqlite3_mutex*)8)\n#define sqlite3_mutex_free(X)\n#define sqlite3_mutex_enter(X)    \n#define sqlite3_mutex_try(X)      SQLITE_OK\n#define sqlite3_mutex_leave(X)    \n#define sqlite3_mutex_held(X)     ((void)(X),1)\n#define sqlite3_mutex_notheld(X)  ((void)(X),1)\n#define sqlite3MutexAlloc(X)      ((sqlite3_mutex*)8)\n#define sqlite3MutexInit()        SQLITE_OK\n#define sqlite3MutexEnd()\n#define MUTEX_LOGIC(X)\n#else\n#define MUTEX_LOGIC(X)            X\n#endif /* defined(SQLITE_MUTEX_OMIT) */\n\n/************** End of mutex.h ***********************************************/\n/************** Continuing where we left off in sqliteInt.h ******************/\n\n/* The SQLITE_EXTRA_DURABLE compile-time option used to set the default\n** synchronous setting to EXTRA.  It is no longer supported.\n*/\n#ifdef SQLITE_EXTRA_DURABLE\n# warning Use SQLITE_DEFAULT_SYNCHRONOUS=3 instead of SQLITE_EXTRA_DURABLE\n# define SQLITE_DEFAULT_SYNCHRONOUS 3\n#endif\n\n/*\n** Default synchronous levels.\n**\n** Note that (for historcal reasons) the PAGER_SYNCHRONOUS_* macros differ\n** from the SQLITE_DEFAULT_SYNCHRONOUS value by 1.\n**\n**           PAGER_SYNCHRONOUS       DEFAULT_SYNCHRONOUS\n**   OFF           1                         0\n**   NORMAL        2                         1\n**   FULL          3                         2\n**   EXTRA         4                         3\n**\n** The \"PRAGMA synchronous\" statement also uses the zero-based numbers.\n** In other words, the zero-based numbers are used for all external interfaces\n** and the one-based values are used internally.\n*/\n#ifndef SQLITE_DEFAULT_SYNCHRONOUS\n# define SQLITE_DEFAULT_SYNCHRONOUS 2\n#endif\n#ifndef SQLITE_DEFAULT_WAL_SYNCHRONOUS\n# define SQLITE_DEFAULT_WAL_SYNCHRONOUS SQLITE_DEFAULT_SYNCHRONOUS\n#endif\n\n/*\n** Each database file to be accessed by the system is an instance\n** of the following structure.  There are normally two of these structures\n** in the sqlite.aDb[] array.  aDb[0] is the main database file and\n** aDb[1] is the database file used to hold temporary tables.  Additional\n** databases may be attached.\n*/\nstruct Db {\n  char *zDbSName;      /* Name of this database. (schema name, not filename) */\n  Btree *pBt;          /* The B*Tree structure for this database file */\n  u8 safety_level;     /* How aggressive at syncing data to disk */\n  u8 bSyncSet;         /* True if \"PRAGMA synchronous=N\" has been run */\n  Schema *pSchema;     /* Pointer to database schema (possibly shared) */\n};\n\n/*\n** An instance of the following structure stores a database schema.\n**\n** Most Schema objects are associated with a Btree.  The exception is\n** the Schema for the TEMP databaes (sqlite3.aDb[1]) which is free-standing.\n** In shared cache mode, a single Schema object can be shared by multiple\n** Btrees that refer to the same underlying BtShared object.\n**\n** Schema objects are automatically deallocated when the last Btree that\n** references them is destroyed.   The TEMP Schema is manually freed by\n** sqlite3_close().\n*\n** A thread must be holding a mutex on the corresponding Btree in order\n** to access Schema content.  This implies that the thread must also be\n** holding a mutex on the sqlite3 connection pointer that owns the Btree.\n** For a TEMP Schema, only the connection mutex is required.\n*/\nstruct Schema {\n  int schema_cookie;   /* Database schema version number for this file */\n  int iGeneration;     /* Generation counter.  Incremented with each change */\n  Hash tblHash;        /* All tables indexed by name */\n  Hash idxHash;        /* All (named) indices indexed by name */\n  Hash trigHash;       /* All triggers indexed by name */\n  Hash fkeyHash;       /* All foreign keys by referenced table name */\n  Table *pSeqTab;      /* The sqlite_sequence table used by AUTOINCREMENT */\n  u8 file_format;      /* Schema format version for this file */\n  u8 enc;              /* Text encoding used by this database */\n  u16 schemaFlags;     /* Flags associated with this schema */\n  int cache_size;      /* Number of pages to use in the cache */\n};\n\n/*\n** These macros can be used to test, set, or clear bits in the\n** Db.pSchema->flags field.\n*/\n#define DbHasProperty(D,I,P)     (((D)->aDb[I].pSchema->schemaFlags&(P))==(P))\n#define DbHasAnyProperty(D,I,P)  (((D)->aDb[I].pSchema->schemaFlags&(P))!=0)\n#define DbSetProperty(D,I,P)     (D)->aDb[I].pSchema->schemaFlags|=(P)\n#define DbClearProperty(D,I,P)   (D)->aDb[I].pSchema->schemaFlags&=~(P)\n\n/*\n** Allowed values for the DB.pSchema->flags field.\n**\n** The DB_SchemaLoaded flag is set after the database schema has been\n** read into internal hash tables.\n**\n** DB_UnresetViews means that one or more views have column names that\n** have been filled out.  If the schema changes, these column names might\n** changes and so the view will need to be reset.\n*/\n#define DB_SchemaLoaded    0x0001  /* The schema has been loaded */\n#define DB_UnresetViews    0x0002  /* Some views have defined column names */\n#define DB_Empty           0x0004  /* The file is empty (length 0 bytes) */\n#define DB_ResetWanted     0x0008  /* Reset the schema when nSchemaLock==0 */\n\n/*\n** The number of different kinds of things that can be limited\n** using the sqlite3_limit() interface.\n*/\n#define SQLITE_N_LIMIT (SQLITE_LIMIT_WORKER_THREADS+1)\n\n/*\n** Lookaside malloc is a set of fixed-size buffers that can be used\n** to satisfy small transient memory allocation requests for objects\n** associated with a particular database connection.  The use of\n** lookaside malloc provides a significant performance enhancement\n** (approx 10%) by avoiding numerous malloc/free requests while parsing\n** SQL statements.\n**\n** The Lookaside structure holds configuration information about the\n** lookaside malloc subsystem.  Each available memory allocation in\n** the lookaside subsystem is stored on a linked list of LookasideSlot\n** objects.\n**\n** Lookaside allocations are only allowed for objects that are associated\n** with a particular database connection.  Hence, schema information cannot\n** be stored in lookaside because in shared cache mode the schema information\n** is shared by multiple database connections.  Therefore, while parsing\n** schema information, the Lookaside.bEnabled flag is cleared so that\n** lookaside allocations are not used to construct the schema objects.\n*/\nstruct Lookaside {\n  u32 bDisable;           /* Only operate the lookaside when zero */\n  u16 sz;                 /* Size of each buffer in bytes */\n  u8 bMalloced;           /* True if pStart obtained from sqlite3_malloc() */\n  u32 nSlot;              /* Number of lookaside slots allocated */\n  u32 anStat[3];          /* 0: hits.  1: size misses.  2: full misses */\n  LookasideSlot *pInit;   /* List of buffers not previously used */\n  LookasideSlot *pFree;   /* List of available buffers */\n  void *pStart;           /* First byte of available memory space */\n  void *pEnd;             /* First byte past end of available space */\n};\nstruct LookasideSlot {\n  LookasideSlot *pNext;    /* Next buffer in the list of free buffers */\n};\n\n/*\n** A hash table for built-in function definitions.  (Application-defined\n** functions use a regular table table from hash.h.)\n**\n** Hash each FuncDef structure into one of the FuncDefHash.a[] slots.\n** Collisions are on the FuncDef.u.pHash chain.\n*/\n#define SQLITE_FUNC_HASH_SZ 23\nstruct FuncDefHash {\n  FuncDef *a[SQLITE_FUNC_HASH_SZ];       /* Hash table for functions */\n};\n\n#ifdef SQLITE_USER_AUTHENTICATION\n/*\n** Information held in the \"sqlite3\" database connection object and used\n** to manage user authentication.\n*/\ntypedef struct sqlite3_userauth sqlite3_userauth;\nstruct sqlite3_userauth {\n  u8 authLevel;                 /* Current authentication level */\n  int nAuthPW;                  /* Size of the zAuthPW in bytes */\n  char *zAuthPW;                /* Password used to authenticate */\n  char *zAuthUser;              /* User name used to authenticate */\n};\n\n/* Allowed values for sqlite3_userauth.authLevel */\n#define UAUTH_Unknown     0     /* Authentication not yet checked */\n#define UAUTH_Fail        1     /* User authentication failed */\n#define UAUTH_User        2     /* Authenticated as a normal user */\n#define UAUTH_Admin       3     /* Authenticated as an administrator */\n\n/* Functions used only by user authorization logic */\nSQLITE_PRIVATE int sqlite3UserAuthTable(const char*);\nSQLITE_PRIVATE int sqlite3UserAuthCheckLogin(sqlite3*,const char*,u8*);\nSQLITE_PRIVATE void sqlite3UserAuthInit(sqlite3*);\nSQLITE_PRIVATE void sqlite3CryptFunc(sqlite3_context*,int,sqlite3_value**);\n\n#endif /* SQLITE_USER_AUTHENTICATION */\n\n/*\n** typedef for the authorization callback function.\n*/\n#ifdef SQLITE_USER_AUTHENTICATION\n  typedef int (*sqlite3_xauth)(void*,int,const char*,const char*,const char*,\n                               const char*, const char*);\n#else\n  typedef int (*sqlite3_xauth)(void*,int,const char*,const char*,const char*,\n                               const char*);\n#endif\n\n#ifndef SQLITE_OMIT_DEPRECATED\n/* This is an extra SQLITE_TRACE macro that indicates \"legacy\" tracing\n** in the style of sqlite3_trace()\n*/\n#define SQLITE_TRACE_LEGACY  0x80\n#else\n#define SQLITE_TRACE_LEGACY  0\n#endif /* SQLITE_OMIT_DEPRECATED */\n\n\n/*\n** Each database connection is an instance of the following structure.\n*/\nstruct sqlite3 {\n  sqlite3_vfs *pVfs;            /* OS Interface */\n  struct Vdbe *pVdbe;           /* List of active virtual machines */\n  CollSeq *pDfltColl;           /* The default collating sequence (BINARY) */\n  sqlite3_mutex *mutex;         /* Connection mutex */\n  Db *aDb;                      /* All backends */\n  int nDb;                      /* Number of backends currently in use */\n  u32 mDbFlags;                 /* flags recording internal state */\n  u32 flags;                    /* flags settable by pragmas. See below */\n  i64 lastRowid;                /* ROWID of most recent insert (see above) */\n  i64 szMmap;                   /* Default mmap_size setting */\n  u32 nSchemaLock;              /* Do not reset the schema when non-zero */\n  unsigned int openFlags;       /* Flags passed to sqlite3_vfs.xOpen() */\n  int errCode;                  /* Most recent error code (SQLITE_*) */\n  int errMask;                  /* & result codes with this before returning */\n  int iSysErrno;                /* Errno value from last system error */\n  u16 dbOptFlags;               /* Flags to enable/disable optimizations */\n  u8 enc;                       /* Text encoding */\n  u8 autoCommit;                /* The auto-commit flag. */\n  u8 temp_store;                /* 1: file 2: memory 0: default */\n  u8 mallocFailed;              /* True if we have seen a malloc failure */\n  u8 bBenignMalloc;             /* Do not require OOMs if true */\n  u8 dfltLockMode;              /* Default locking-mode for attached dbs */\n  signed char nextAutovac;      /* Autovac setting after VACUUM if >=0 */\n  u8 suppressErr;               /* Do not issue error messages if true */\n  u8 vtabOnConflict;            /* Value to return for s3_vtab_on_conflict() */\n  u8 isTransactionSavepoint;    /* True if the outermost savepoint is a TS */\n  u8 mTrace;                    /* zero or more SQLITE_TRACE flags */\n  u8 skipBtreeMutex;            /* True if no shared-cache backends */\n  u8 nSqlExec;                  /* Number of pending OP_SqlExec opcodes */\n  int nextPagesize;             /* Pagesize after VACUUM if >0 */\n  u32 magic;                    /* Magic number for detect library misuse */\n  int nChange;                  /* Value returned by sqlite3_changes() */\n  int nTotalChange;             /* Value returned by sqlite3_total_changes() */\n  int aLimit[SQLITE_N_LIMIT];   /* Limits */\n  int nMaxSorterMmap;           /* Maximum size of regions mapped by sorter */\n  struct sqlite3InitInfo {      /* Information used during initialization */\n    int newTnum;                /* Rootpage of table being initialized */\n    u8 iDb;                     /* Which db file is being initialized */\n    u8 busy;                    /* TRUE if currently initializing */\n    u8 orphanTrigger;           /* Last statement is orphaned TEMP trigger */\n    u8 imposterTable;           /* Building an imposter table */\n  } init;\n  int nVdbeActive;              /* Number of VDBEs currently running */\n  int nVdbeRead;                /* Number of active VDBEs that read or write */\n  int nVdbeWrite;               /* Number of active VDBEs that read and write */\n  int nVdbeExec;                /* Number of nested calls to VdbeExec() */\n  int nVDestroy;                /* Number of active OP_VDestroy operations */\n  int nExtension;               /* Number of loaded extensions */\n  void **aExtension;            /* Array of shared library handles */\n  int (*xTrace)(u32,void*,void*,void*);     /* Trace function */\n  void *pTraceArg;                          /* Argument to the trace function */\n  void (*xProfile)(void*,const char*,u64);  /* Profiling function */\n  void *pProfileArg;                        /* Argument to profile function */\n  void *pCommitArg;                 /* Argument to xCommitCallback() */\n  int (*xCommitCallback)(void*);    /* Invoked at every commit. */\n  void *pRollbackArg;               /* Argument to xRollbackCallback() */\n  void (*xRollbackCallback)(void*); /* Invoked at every commit. */\n  void *pUpdateArg;\n  void (*xUpdateCallback)(void*,int, const char*,const char*,sqlite_int64);\n#ifdef SQLITE_ENABLE_PREUPDATE_HOOK\n  void *pPreUpdateArg;          /* First argument to xPreUpdateCallback */\n  void (*xPreUpdateCallback)(   /* Registered using sqlite3_preupdate_hook() */\n    void*,sqlite3*,int,char const*,char const*,sqlite3_int64,sqlite3_int64\n  );\n  PreUpdate *pPreUpdate;        /* Context for active pre-update callback */\n#endif /* SQLITE_ENABLE_PREUPDATE_HOOK */\n#ifndef SQLITE_OMIT_WAL\n  int (*xWalCallback)(void *, sqlite3 *, const char *, int);\n  void *pWalArg;\n#endif\n  void(*xCollNeeded)(void*,sqlite3*,int eTextRep,const char*);\n  void(*xCollNeeded16)(void*,sqlite3*,int eTextRep,const void*);\n  void *pCollNeededArg;\n  sqlite3_value *pErr;          /* Most recent error message */\n  union {\n    volatile int isInterrupted; /* True if sqlite3_interrupt has been called */\n    double notUsed1;            /* Spacer */\n  } u1;\n  Lookaside lookaside;          /* Lookaside malloc configuration */\n#ifndef SQLITE_OMIT_AUTHORIZATION\n  sqlite3_xauth xAuth;          /* Access authorization function */\n  void *pAuthArg;               /* 1st argument to the access auth function */\n#endif\n#ifndef SQLITE_OMIT_PROGRESS_CALLBACK\n  int (*xProgress)(void *);     /* The progress callback */\n  void *pProgressArg;           /* Argument to the progress callback */\n  unsigned nProgressOps;        /* Number of opcodes for progress callback */\n#endif\n#ifndef SQLITE_OMIT_VIRTUALTABLE\n  int nVTrans;                  /* Allocated size of aVTrans */\n  Hash aModule;                 /* populated by sqlite3_create_module() */\n  VtabCtx *pVtabCtx;            /* Context for active vtab connect/create */\n  VTable **aVTrans;             /* Virtual tables with open transactions */\n  VTable *pDisconnect;          /* Disconnect these in next sqlite3_prepare() */\n#endif\n  Hash aFunc;                   /* Hash table of connection functions */\n  Hash aCollSeq;                /* All collating sequences */\n  BusyHandler busyHandler;      /* Busy callback */\n  Db aDbStatic[2];              /* Static space for the 2 default backends */\n  Savepoint *pSavepoint;        /* List of active savepoints */\n  int busyTimeout;              /* Busy handler timeout, in msec */\n  int nSavepoint;               /* Number of non-transaction savepoints */\n  int nStatement;               /* Number of nested statement-transactions  */\n  i64 nDeferredCons;            /* Net deferred constraints this transaction. */\n  i64 nDeferredImmCons;         /* Net deferred immediate constraints */\n  int *pnBytesFreed;            /* If not NULL, increment this in DbFree() */\n#ifdef SQLITE_ENABLE_UNLOCK_NOTIFY\n  /* The following variables are all protected by the STATIC_MASTER\n  ** mutex, not by sqlite3.mutex. They are used by code in notify.c.\n  **\n  ** When X.pUnlockConnection==Y, that means that X is waiting for Y to\n  ** unlock so that it can proceed.\n  **\n  ** When X.pBlockingConnection==Y, that means that something that X tried\n  ** tried to do recently failed with an SQLITE_LOCKED error due to locks\n  ** held by Y.\n  */\n  sqlite3 *pBlockingConnection; /* Connection that caused SQLITE_LOCKED */\n  sqlite3 *pUnlockConnection;           /* Connection to watch for unlock */\n  void *pUnlockArg;                     /* Argument to xUnlockNotify */\n  void (*xUnlockNotify)(void **, int);  /* Unlock notify callback */\n  sqlite3 *pNextBlocked;        /* Next in list of all blocked connections */\n#endif\n#ifdef SQLITE_USER_AUTHENTICATION\n  sqlite3_userauth auth;        /* User authentication information */\n#endif\n};\n\n/*\n** A macro to discover the encoding of a database.\n*/\n#define SCHEMA_ENC(db) ((db)->aDb[0].pSchema->enc)\n#define ENC(db)        ((db)->enc)\n\n/*\n** Possible values for the sqlite3.flags.\n**\n** Value constraints (enforced via assert()):\n**      SQLITE_FullFSync     == PAGER_FULLFSYNC\n**      SQLITE_CkptFullFSync == PAGER_CKPT_FULLFSYNC\n**      SQLITE_CacheSpill    == PAGER_CACHE_SPILL\n*/\n#define SQLITE_WriteSchema    0x00000001  /* OK to update SQLITE_MASTER */\n#define SQLITE_LegacyFileFmt  0x00000002  /* Create new databases in format 1 */\n#define SQLITE_FullColNames   0x00000004  /* Show full column names on SELECT */\n#define SQLITE_FullFSync      0x00000008  /* Use full fsync on the backend */\n#define SQLITE_CkptFullFSync  0x00000010  /* Use full fsync for checkpoint */\n#define SQLITE_CacheSpill     0x00000020  /* OK to spill pager cache */\n#define SQLITE_ShortColNames  0x00000040  /* Show short columns names */\n#define SQLITE_CountRows      0x00000080  /* Count rows changed by INSERT, */\n                                          /*   DELETE, or UPDATE and return */\n                                          /*   the count using a callback. */\n#define SQLITE_NullCallback   0x00000100  /* Invoke the callback once if the */\n                                          /*   result set is empty */\n#define SQLITE_IgnoreChecks   0x00000200  /* Do not enforce check constraints */\n#define SQLITE_ReadUncommit   0x00000400  /* READ UNCOMMITTED in shared-cache */\n#define SQLITE_NoCkptOnClose  0x00000800  /* No checkpoint on close()/DETACH */\n#define SQLITE_ReverseOrder   0x00001000  /* Reverse unordered SELECTs */\n#define SQLITE_RecTriggers    0x00002000  /* Enable recursive triggers */\n#define SQLITE_ForeignKeys    0x00004000  /* Enforce foreign key constraints  */\n#define SQLITE_AutoIndex      0x00008000  /* Enable automatic indexes */\n#define SQLITE_LoadExtension  0x00010000  /* Enable load_extension */\n#define SQLITE_LoadExtFunc    0x00020000  /* Enable load_extension() SQL func */\n#define SQLITE_EnableTrigger  0x00040000  /* True to enable triggers */\n#define SQLITE_DeferFKs       0x00080000  /* Defer all FK constraints */\n#define SQLITE_QueryOnly      0x00100000  /* Disable database changes */\n#define SQLITE_CellSizeCk     0x00200000  /* Check btree cell sizes on load */\n#define SQLITE_Fts3Tokenizer  0x00400000  /* Enable fts3_tokenizer(2) */\n#define SQLITE_EnableQPSG     0x00800000  /* Query Planner Stability Guarantee*/\n#define SQLITE_TriggerEQP     0x01000000  /* Show trigger EXPLAIN QUERY PLAN */\n\n/* Flags used only if debugging */\n#ifdef SQLITE_DEBUG\n#define SQLITE_SqlTrace       0x08000000  /* Debug print SQL as it executes */\n#define SQLITE_VdbeListing    0x10000000  /* Debug listings of VDBE programs */\n#define SQLITE_VdbeTrace      0x20000000  /* True to trace VDBE execution */\n#define SQLITE_VdbeAddopTrace 0x40000000  /* Trace sqlite3VdbeAddOp() calls */\n#define SQLITE_VdbeEQP        0x80000000  /* Debug EXPLAIN QUERY PLAN */\n#endif\n\n/*\n** Allowed values for sqlite3.mDbFlags\n*/\n#define DBFLAG_SchemaChange   0x0001  /* Uncommitted Hash table changes */\n#define DBFLAG_PreferBuiltin  0x0002  /* Preference to built-in funcs */\n#define DBFLAG_Vacuum         0x0004  /* Currently in a VACUUM */\n\n/*\n** Bits of the sqlite3.dbOptFlags field that are used by the\n** sqlite3_test_control(SQLITE_TESTCTRL_OPTIMIZATIONS,...) interface to\n** selectively disable various optimizations.\n*/\n#define SQLITE_QueryFlattener 0x0001   /* Query flattening */\n#define SQLITE_ColumnCache    0x0002   /* Column cache */\n#define SQLITE_GroupByOrder   0x0004   /* GROUPBY cover of ORDERBY */\n#define SQLITE_FactorOutConst 0x0008   /* Constant factoring */\n#define SQLITE_DistinctOpt    0x0010   /* DISTINCT using indexes */\n#define SQLITE_CoverIdxScan   0x0020   /* Covering index scans */\n#define SQLITE_OrderByIdxJoin 0x0040   /* ORDER BY of joins via index */\n#define SQLITE_Transitive     0x0080   /* Transitive constraints */\n#define SQLITE_OmitNoopJoin   0x0100   /* Omit unused tables in joins */\n#define SQLITE_CountOfView    0x0200   /* The count-of-view optimization */\n#define SQLITE_CursorHints    0x0400   /* Add OP_CursorHint opcodes */\n#define SQLITE_Stat34         0x0800   /* Use STAT3 or STAT4 data */\n   /* TH3 expects the Stat34  ^^^^^^ value to be 0x0800.  Don't change it */\n#define SQLITE_AllOpts        0xffff   /* All optimizations */\n\n/*\n** Macros for testing whether or not optimizations are enabled or disabled.\n*/\n#define OptimizationDisabled(db, mask)  (((db)->dbOptFlags&(mask))!=0)\n#define OptimizationEnabled(db, mask)   (((db)->dbOptFlags&(mask))==0)\n\n/*\n** Return true if it OK to factor constant expressions into the initialization\n** code. The argument is a Parse object for the code generator.\n*/\n#define ConstFactorOk(P) ((P)->okConstFactor)\n\n/*\n** Possible values for the sqlite.magic field.\n** The numbers are obtained at random and have no special meaning, other\n** than being distinct from one another.\n*/\n#define SQLITE_MAGIC_OPEN     0xa029a697  /* Database is open */\n#define SQLITE_MAGIC_CLOSED   0x9f3c2d33  /* Database is closed */\n#define SQLITE_MAGIC_SICK     0x4b771290  /* Error and awaiting close */\n#define SQLITE_MAGIC_BUSY     0xf03b7906  /* Database currently in use */\n#define SQLITE_MAGIC_ERROR    0xb5357930  /* An SQLITE_MISUSE error occurred */\n#define SQLITE_MAGIC_ZOMBIE   0x64cffc7f  /* Close with last statement close */\n\n/*\n** Each SQL function is defined by an instance of the following\n** structure.  For global built-in functions (ex: substr(), max(), count())\n** a pointer to this structure is held in the sqlite3BuiltinFunctions object.\n** For per-connection application-defined functions, a pointer to this\n** structure is held in the db->aHash hash table.\n**\n** The u.pHash field is used by the global built-ins.  The u.pDestructor\n** field is used by per-connection app-def functions.\n*/\nstruct FuncDef {\n  i8 nArg;             /* Number of arguments.  -1 means unlimited */\n  u16 funcFlags;       /* Some combination of SQLITE_FUNC_* */\n  void *pUserData;     /* User data parameter */\n  FuncDef *pNext;      /* Next function with same name */\n  void (*xSFunc)(sqlite3_context*,int,sqlite3_value**); /* func or agg-step */\n  void (*xFinalize)(sqlite3_context*);                  /* Agg finalizer */\n  const char *zName;   /* SQL name of the function. */\n  union {\n    FuncDef *pHash;      /* Next with a different name but the same hash */\n    FuncDestructor *pDestructor;   /* Reference counted destructor function */\n  } u;\n};\n\n/*\n** This structure encapsulates a user-function destructor callback (as\n** configured using create_function_v2()) and a reference counter. When\n** create_function_v2() is called to create a function with a destructor,\n** a single object of this type is allocated. FuncDestructor.nRef is set to\n** the number of FuncDef objects created (either 1 or 3, depending on whether\n** or not the specified encoding is SQLITE_ANY). The FuncDef.pDestructor\n** member of each of the new FuncDef objects is set to point to the allocated\n** FuncDestructor.\n**\n** Thereafter, when one of the FuncDef objects is deleted, the reference\n** count on this object is decremented. When it reaches 0, the destructor\n** is invoked and the FuncDestructor structure freed.\n*/\nstruct FuncDestructor {\n  int nRef;\n  void (*xDestroy)(void *);\n  void *pUserData;\n};\n\n/*\n** Possible values for FuncDef.flags.  Note that the _LENGTH and _TYPEOF\n** values must correspond to OPFLAG_LENGTHARG and OPFLAG_TYPEOFARG.  And\n** SQLITE_FUNC_CONSTANT must be the same as SQLITE_DETERMINISTIC.  There\n** are assert() statements in the code to verify this.\n**\n** Value constraints (enforced via assert()):\n**     SQLITE_FUNC_MINMAX    ==  NC_MinMaxAgg      == SF_MinMaxAgg\n**     SQLITE_FUNC_LENGTH    ==  OPFLAG_LENGTHARG\n**     SQLITE_FUNC_TYPEOF    ==  OPFLAG_TYPEOFARG\n**     SQLITE_FUNC_CONSTANT  ==  SQLITE_DETERMINISTIC from the API\n**     SQLITE_FUNC_ENCMASK   depends on SQLITE_UTF* macros in the API\n*/\n#define SQLITE_FUNC_ENCMASK  0x0003 /* SQLITE_UTF8, SQLITE_UTF16BE or UTF16LE */\n#define SQLITE_FUNC_LIKE     0x0004 /* Candidate for the LIKE optimization */\n#define SQLITE_FUNC_CASE     0x0008 /* Case-sensitive LIKE-type function */\n#define SQLITE_FUNC_EPHEM    0x0010 /* Ephemeral.  Delete with VDBE */\n#define SQLITE_FUNC_NEEDCOLL 0x0020 /* sqlite3GetFuncCollSeq() might be called*/\n#define SQLITE_FUNC_LENGTH   0x0040 /* Built-in length() function */\n#define SQLITE_FUNC_TYPEOF   0x0080 /* Built-in typeof() function */\n#define SQLITE_FUNC_COUNT    0x0100 /* Built-in count(*) aggregate */\n#define SQLITE_FUNC_COALESCE 0x0200 /* Built-in coalesce() or ifnull() */\n#define SQLITE_FUNC_UNLIKELY 0x0400 /* Built-in unlikely() function */\n#define SQLITE_FUNC_CONSTANT 0x0800 /* Constant inputs give a constant output */\n#define SQLITE_FUNC_MINMAX   0x1000 /* True for min() and max() aggregates */\n#define SQLITE_FUNC_SLOCHNG  0x2000 /* \"Slow Change\". Value constant during a\n                                    ** single query - might change over time */\n#define SQLITE_FUNC_AFFINITY 0x4000 /* Built-in affinity() function */\n#define SQLITE_FUNC_OFFSET   0x8000 /* Built-in sqlite_offset() function */\n\n/*\n** The following three macros, FUNCTION(), LIKEFUNC() and AGGREGATE() are\n** used to create the initializers for the FuncDef structures.\n**\n**   FUNCTION(zName, nArg, iArg, bNC, xFunc)\n**     Used to create a scalar function definition of a function zName\n**     implemented by C function xFunc that accepts nArg arguments. The\n**     value passed as iArg is cast to a (void*) and made available\n**     as the user-data (sqlite3_user_data()) for the function. If\n**     argument bNC is true, then the SQLITE_FUNC_NEEDCOLL flag is set.\n**\n**   VFUNCTION(zName, nArg, iArg, bNC, xFunc)\n**     Like FUNCTION except it omits the SQLITE_FUNC_CONSTANT flag.\n**\n**   DFUNCTION(zName, nArg, iArg, bNC, xFunc)\n**     Like FUNCTION except it omits the SQLITE_FUNC_CONSTANT flag and\n**     adds the SQLITE_FUNC_SLOCHNG flag.  Used for date & time functions\n**     and functions like sqlite_version() that can change, but not during\n**     a single query.  The iArg is ignored.  The user-data is always set\n**     to a NULL pointer.  The bNC parameter is not used.\n**\n**   PURE_DATE(zName, nArg, iArg, bNC, xFunc)\n**     Used for \"pure\" date/time functions, this macro is like DFUNCTION\n**     except that it does set the SQLITE_FUNC_CONSTANT flags.  iArg is\n**     ignored and the user-data for these functions is set to an \n**     arbitrary non-NULL pointer.  The bNC parameter is not used.\n**\n**   AGGREGATE(zName, nArg, iArg, bNC, xStep, xFinal)\n**     Used to create an aggregate function definition implemented by\n**     the C functions xStep and xFinal. The first four parameters\n**     are interpreted in the same way as the first 4 parameters to\n**     FUNCTION().\n**\n**   LIKEFUNC(zName, nArg, pArg, flags)\n**     Used to create a scalar function definition of a function zName\n**     that accepts nArg arguments and is implemented by a call to C\n**     function likeFunc. Argument pArg is cast to a (void *) and made\n**     available as the function user-data (sqlite3_user_data()). The\n**     FuncDef.flags variable is set to the value passed as the flags\n**     parameter.\n*/\n#define FUNCTION(zName, nArg, iArg, bNC, xFunc) \\\n  {nArg, SQLITE_FUNC_CONSTANT|SQLITE_UTF8|(bNC*SQLITE_FUNC_NEEDCOLL), \\\n   SQLITE_INT_TO_PTR(iArg), 0, xFunc, 0, #zName, {0} }\n#define VFUNCTION(zName, nArg, iArg, bNC, xFunc) \\\n  {nArg, SQLITE_UTF8|(bNC*SQLITE_FUNC_NEEDCOLL), \\\n   SQLITE_INT_TO_PTR(iArg), 0, xFunc, 0, #zName, {0} }\n#define DFUNCTION(zName, nArg, iArg, bNC, xFunc) \\\n  {nArg, SQLITE_FUNC_SLOCHNG|SQLITE_UTF8, \\\n   0, 0, xFunc, 0, #zName, {0} }\n#define PURE_DATE(zName, nArg, iArg, bNC, xFunc) \\\n  {nArg, SQLITE_FUNC_SLOCHNG|SQLITE_UTF8|SQLITE_FUNC_CONSTANT, \\\n   (void*)&sqlite3Config, 0, xFunc, 0, #zName, {0} }\n#define FUNCTION2(zName, nArg, iArg, bNC, xFunc, extraFlags) \\\n  {nArg,SQLITE_FUNC_CONSTANT|SQLITE_UTF8|(bNC*SQLITE_FUNC_NEEDCOLL)|extraFlags,\\\n   SQLITE_INT_TO_PTR(iArg), 0, xFunc, 0, #zName, {0} }\n#define STR_FUNCTION(zName, nArg, pArg, bNC, xFunc) \\\n  {nArg, SQLITE_FUNC_SLOCHNG|SQLITE_UTF8|(bNC*SQLITE_FUNC_NEEDCOLL), \\\n   pArg, 0, xFunc, 0, #zName, }\n#define LIKEFUNC(zName, nArg, arg, flags) \\\n  {nArg, SQLITE_FUNC_CONSTANT|SQLITE_UTF8|flags, \\\n   (void *)arg, 0, likeFunc, 0, #zName, {0} }\n#define AGGREGATE(zName, nArg, arg, nc, xStep, xFinal) \\\n  {nArg, SQLITE_UTF8|(nc*SQLITE_FUNC_NEEDCOLL), \\\n   SQLITE_INT_TO_PTR(arg), 0, xStep,xFinal,#zName, {0}}\n#define AGGREGATE2(zName, nArg, arg, nc, xStep, xFinal, extraFlags) \\\n  {nArg, SQLITE_UTF8|(nc*SQLITE_FUNC_NEEDCOLL)|extraFlags, \\\n   SQLITE_INT_TO_PTR(arg), 0, xStep,xFinal,#zName, {0}}\n\n/*\n** All current savepoints are stored in a linked list starting at\n** sqlite3.pSavepoint. The first element in the list is the most recently\n** opened savepoint. Savepoints are added to the list by the vdbe\n** OP_Savepoint instruction.\n*/\nstruct Savepoint {\n  char *zName;                        /* Savepoint name (nul-terminated) */\n  i64 nDeferredCons;                  /* Number of deferred fk violations */\n  i64 nDeferredImmCons;               /* Number of deferred imm fk. */\n  Savepoint *pNext;                   /* Parent savepoint (if any) */\n};\n\n/*\n** The following are used as the second parameter to sqlite3Savepoint(),\n** and as the P1 argument to the OP_Savepoint instruction.\n*/\n#define SAVEPOINT_BEGIN      0\n#define SAVEPOINT_RELEASE    1\n#define SAVEPOINT_ROLLBACK   2\n\n\n/*\n** Each SQLite module (virtual table definition) is defined by an\n** instance of the following structure, stored in the sqlite3.aModule\n** hash table.\n*/\nstruct Module {\n  const sqlite3_module *pModule;       /* Callback pointers */\n  const char *zName;                   /* Name passed to create_module() */\n  void *pAux;                          /* pAux passed to create_module() */\n  void (*xDestroy)(void *);            /* Module destructor function */\n  Table *pEpoTab;                      /* Eponymous table for this module */\n};\n\n/*\n** information about each column of an SQL table is held in an instance\n** of this structure.\n*/\nstruct Column {\n  char *zName;     /* Name of this column, \\000, then the type */\n  Expr *pDflt;     /* Default value of this column */\n  char *zColl;     /* Collating sequence.  If NULL, use the default */\n  u8 notNull;      /* An OE_ code for handling a NOT NULL constraint */\n  char affinity;   /* One of the SQLITE_AFF_... values */\n  u8 szEst;        /* Estimated size of value in this column. sizeof(INT)==1 */\n  u8 colFlags;     /* Boolean properties.  See COLFLAG_ defines below */\n};\n\n/* Allowed values for Column.colFlags:\n*/\n#define COLFLAG_PRIMKEY  0x0001    /* Column is part of the primary key */\n#define COLFLAG_HIDDEN   0x0002    /* A hidden column in a virtual table */\n#define COLFLAG_HASTYPE  0x0004    /* Type name follows column name */\n#define COLFLAG_UNIQUE   0x0008    /* Column def contains \"UNIQUE\" or \"PK\" */\n\n/*\n** A \"Collating Sequence\" is defined by an instance of the following\n** structure. Conceptually, a collating sequence consists of a name and\n** a comparison routine that defines the order of that sequence.\n**\n** If CollSeq.xCmp is NULL, it means that the\n** collating sequence is undefined.  Indices built on an undefined\n** collating sequence may not be read or written.\n*/\nstruct CollSeq {\n  char *zName;          /* Name of the collating sequence, UTF-8 encoded */\n  u8 enc;               /* Text encoding handled by xCmp() */\n  void *pUser;          /* First argument to xCmp() */\n  int (*xCmp)(void*,int, const void*, int, const void*);\n  void (*xDel)(void*);  /* Destructor for pUser */\n};\n\n/*\n** A sort order can be either ASC or DESC.\n*/\n#define SQLITE_SO_ASC       0  /* Sort in ascending order */\n#define SQLITE_SO_DESC      1  /* Sort in ascending order */\n#define SQLITE_SO_UNDEFINED -1 /* No sort order specified */\n\n/*\n** Column affinity types.\n**\n** These used to have mnemonic name like 'i' for SQLITE_AFF_INTEGER and\n** 't' for SQLITE_AFF_TEXT.  But we can save a little space and improve\n** the speed a little by numbering the values consecutively.\n**\n** But rather than start with 0 or 1, we begin with 'A'.  That way,\n** when multiple affinity types are concatenated into a string and\n** used as the P4 operand, they will be more readable.\n**\n** Note also that the numeric types are grouped together so that testing\n** for a numeric type is a single comparison.  And the BLOB type is first.\n*/\n#define SQLITE_AFF_BLOB     'A'\n#define SQLITE_AFF_TEXT     'B'\n#define SQLITE_AFF_NUMERIC  'C'\n#define SQLITE_AFF_INTEGER  'D'\n#define SQLITE_AFF_REAL     'E'\n\n#define sqlite3IsNumericAffinity(X)  ((X)>=SQLITE_AFF_NUMERIC)\n\n/*\n** The SQLITE_AFF_MASK values masks off the significant bits of an\n** affinity value.\n*/\n#define SQLITE_AFF_MASK     0x47\n\n/*\n** Additional bit values that can be ORed with an affinity without\n** changing the affinity.\n**\n** The SQLITE_NOTNULL flag is a combination of NULLEQ and JUMPIFNULL.\n** It causes an assert() to fire if either operand to a comparison\n** operator is NULL.  It is added to certain comparison operators to\n** prove that the operands are always NOT NULL.\n*/\n#define SQLITE_KEEPNULL     0x08  /* Used by vector == or <> */\n#define SQLITE_JUMPIFNULL   0x10  /* jumps if either operand is NULL */\n#define SQLITE_STOREP2      0x20  /* Store result in reg[P2] rather than jump */\n#define SQLITE_NULLEQ       0x80  /* NULL=NULL */\n#define SQLITE_NOTNULL      0x90  /* Assert that operands are never NULL */\n\n/*\n** An object of this type is created for each virtual table present in\n** the database schema.\n**\n** If the database schema is shared, then there is one instance of this\n** structure for each database connection (sqlite3*) that uses the shared\n** schema. This is because each database connection requires its own unique\n** instance of the sqlite3_vtab* handle used to access the virtual table\n** implementation. sqlite3_vtab* handles can not be shared between\n** database connections, even when the rest of the in-memory database\n** schema is shared, as the implementation often stores the database\n** connection handle passed to it via the xConnect() or xCreate() method\n** during initialization internally. This database connection handle may\n** then be used by the virtual table implementation to access real tables\n** within the database. So that they appear as part of the callers\n** transaction, these accesses need to be made via the same database\n** connection as that used to execute SQL operations on the virtual table.\n**\n** All VTable objects that correspond to a single table in a shared\n** database schema are initially stored in a linked-list pointed to by\n** the Table.pVTable member variable of the corresponding Table object.\n** When an sqlite3_prepare() operation is required to access the virtual\n** table, it searches the list for the VTable that corresponds to the\n** database connection doing the preparing so as to use the correct\n** sqlite3_vtab* handle in the compiled query.\n**\n** When an in-memory Table object is deleted (for example when the\n** schema is being reloaded for some reason), the VTable objects are not\n** deleted and the sqlite3_vtab* handles are not xDisconnect()ed\n** immediately. Instead, they are moved from the Table.pVTable list to\n** another linked list headed by the sqlite3.pDisconnect member of the\n** corresponding sqlite3 structure. They are then deleted/xDisconnected\n** next time a statement is prepared using said sqlite3*. This is done\n** to avoid deadlock issues involving multiple sqlite3.mutex mutexes.\n** Refer to comments above function sqlite3VtabUnlockList() for an\n** explanation as to why it is safe to add an entry to an sqlite3.pDisconnect\n** list without holding the corresponding sqlite3.mutex mutex.\n**\n** The memory for objects of this type is always allocated by\n** sqlite3DbMalloc(), using the connection handle stored in VTable.db as\n** the first argument.\n*/\nstruct VTable {\n  sqlite3 *db;              /* Database connection associated with this table */\n  Module *pMod;             /* Pointer to module implementation */\n  sqlite3_vtab *pVtab;      /* Pointer to vtab instance */\n  int nRef;                 /* Number of pointers to this structure */\n  u8 bConstraint;           /* True if constraints are supported */\n  int iSavepoint;           /* Depth of the SAVEPOINT stack */\n  VTable *pNext;            /* Next in linked list (see above) */\n};\n\n/*\n** The schema for each SQL table and view is represented in memory\n** by an instance of the following structure.\n*/\nstruct Table {\n  char *zName;         /* Name of the table or view */\n  Column *aCol;        /* Information about each column */\n  Index *pIndex;       /* List of SQL indexes on this table. */\n  Select *pSelect;     /* NULL for tables.  Points to definition if a view. */\n  FKey *pFKey;         /* Linked list of all foreign keys in this table */\n  char *zColAff;       /* String defining the affinity of each column */\n  ExprList *pCheck;    /* All CHECK constraints */\n                       /*   ... also used as column name list in a VIEW */\n  int tnum;            /* Root BTree page for this table */\n  u32 nTabRef;         /* Number of pointers to this Table */\n  u32 tabFlags;        /* Mask of TF_* values */\n  i16 iPKey;           /* If not negative, use aCol[iPKey] as the rowid */\n  i16 nCol;            /* Number of columns in this table */\n  LogEst nRowLogEst;   /* Estimated rows in table - from sqlite_stat1 table */\n  LogEst szTabRow;     /* Estimated size of each table row in bytes */\n#ifdef SQLITE_ENABLE_COSTMULT\n  LogEst costMult;     /* Cost multiplier for using this table */\n#endif\n  u8 keyConf;          /* What to do in case of uniqueness conflict on iPKey */\n#ifndef SQLITE_OMIT_ALTERTABLE\n  int addColOffset;    /* Offset in CREATE TABLE stmt to add a new column */\n#endif\n#ifndef SQLITE_OMIT_VIRTUALTABLE\n  int nModuleArg;      /* Number of arguments to the module */\n  char **azModuleArg;  /* 0: module 1: schema 2: vtab name 3...: args */\n  VTable *pVTable;     /* List of VTable objects. */\n#endif\n  Trigger *pTrigger;   /* List of triggers stored in pSchema */\n  Schema *pSchema;     /* Schema that contains this table */\n  Table *pNextZombie;  /* Next on the Parse.pZombieTab list */\n};\n\n/*\n** Allowed values for Table.tabFlags.\n**\n** TF_OOOHidden applies to tables or view that have hidden columns that are\n** followed by non-hidden columns.  Example:  \"CREATE VIRTUAL TABLE x USING\n** vtab1(a HIDDEN, b);\".  Since \"b\" is a non-hidden column but \"a\" is hidden,\n** the TF_OOOHidden attribute would apply in this case.  Such tables require\n** special handling during INSERT processing.\n*/\n#define TF_Readonly        0x0001    /* Read-only system table */\n#define TF_Ephemeral       0x0002    /* An ephemeral table */\n#define TF_HasPrimaryKey   0x0004    /* Table has a primary key */\n#define TF_Autoincrement   0x0008    /* Integer primary key is autoincrement */\n#define TF_HasStat1        0x0010    /* nRowLogEst set from sqlite_stat1 */\n#define TF_WithoutRowid    0x0020    /* No rowid.  PRIMARY KEY is the key */\n#define TF_NoVisibleRowid  0x0040    /* No user-visible \"rowid\" column */\n#define TF_OOOHidden       0x0080    /* Out-of-Order hidden columns */\n#define TF_StatsUsed       0x0100    /* Query planner decisions affected by\n                                     ** Index.aiRowLogEst[] values */\n#define TF_HasNotNull      0x0200    /* Contains NOT NULL constraints */\n\n/*\n** Test to see whether or not a table is a virtual table.  This is\n** done as a macro so that it will be optimized out when virtual\n** table support is omitted from the build.\n*/\n#ifndef SQLITE_OMIT_VIRTUALTABLE\n#  define IsVirtual(X)      ((X)->nModuleArg)\n#else\n#  define IsVirtual(X)      0\n#endif\n\n/*\n** Macros to determine if a column is hidden.  IsOrdinaryHiddenColumn()\n** only works for non-virtual tables (ordinary tables and views) and is\n** always false unless SQLITE_ENABLE_HIDDEN_COLUMNS is defined.  The\n** IsHiddenColumn() macro is general purpose.\n*/\n#if defined(SQLITE_ENABLE_HIDDEN_COLUMNS)\n#  define IsHiddenColumn(X)         (((X)->colFlags & COLFLAG_HIDDEN)!=0)\n#  define IsOrdinaryHiddenColumn(X) (((X)->colFlags & COLFLAG_HIDDEN)!=0)\n#elif !defined(SQLITE_OMIT_VIRTUALTABLE)\n#  define IsHiddenColumn(X)         (((X)->colFlags & COLFLAG_HIDDEN)!=0)\n#  define IsOrdinaryHiddenColumn(X) 0\n#else\n#  define IsHiddenColumn(X)         0\n#  define IsOrdinaryHiddenColumn(X) 0\n#endif\n\n\n/* Does the table have a rowid */\n#define HasRowid(X)     (((X)->tabFlags & TF_WithoutRowid)==0)\n#define VisibleRowid(X) (((X)->tabFlags & TF_NoVisibleRowid)==0)\n\n/*\n** Each foreign key constraint is an instance of the following structure.\n**\n** A foreign key is associated with two tables.  The \"from\" table is\n** the table that contains the REFERENCES clause that creates the foreign\n** key.  The \"to\" table is the table that is named in the REFERENCES clause.\n** Consider this example:\n**\n**     CREATE TABLE ex1(\n**       a INTEGER PRIMARY KEY,\n**       b INTEGER CONSTRAINT fk1 REFERENCES ex2(x)\n**     );\n**\n** For foreign key \"fk1\", the from-table is \"ex1\" and the to-table is \"ex2\".\n** Equivalent names:\n**\n**     from-table == child-table\n**       to-table == parent-table\n**\n** Each REFERENCES clause generates an instance of the following structure\n** which is attached to the from-table.  The to-table need not exist when\n** the from-table is created.  The existence of the to-table is not checked.\n**\n** The list of all parents for child Table X is held at X.pFKey.\n**\n** A list of all children for a table named Z (which might not even exist)\n** is held in Schema.fkeyHash with a hash key of Z.\n*/\nstruct FKey {\n  Table *pFrom;     /* Table containing the REFERENCES clause (aka: Child) */\n  FKey *pNextFrom;  /* Next FKey with the same in pFrom. Next parent of pFrom */\n  char *zTo;        /* Name of table that the key points to (aka: Parent) */\n  FKey *pNextTo;    /* Next with the same zTo. Next child of zTo. */\n  FKey *pPrevTo;    /* Previous with the same zTo */\n  int nCol;         /* Number of columns in this key */\n  /* EV: R-30323-21917 */\n  u8 isDeferred;       /* True if constraint checking is deferred till COMMIT */\n  u8 aAction[2];        /* ON DELETE and ON UPDATE actions, respectively */\n  Trigger *apTrigger[2];/* Triggers for aAction[] actions */\n  struct sColMap {      /* Mapping of columns in pFrom to columns in zTo */\n    int iFrom;            /* Index of column in pFrom */\n    char *zCol;           /* Name of column in zTo.  If NULL use PRIMARY KEY */\n  } aCol[1];            /* One entry for each of nCol columns */\n};\n\n/*\n** SQLite supports many different ways to resolve a constraint\n** error.  ROLLBACK processing means that a constraint violation\n** causes the operation in process to fail and for the current transaction\n** to be rolled back.  ABORT processing means the operation in process\n** fails and any prior changes from that one operation are backed out,\n** but the transaction is not rolled back.  FAIL processing means that\n** the operation in progress stops and returns an error code.  But prior\n** changes due to the same operation are not backed out and no rollback\n** occurs.  IGNORE means that the particular row that caused the constraint\n** error is not inserted or updated.  Processing continues and no error\n** is returned.  REPLACE means that preexisting database rows that caused\n** a UNIQUE constraint violation are removed so that the new insert or\n** update can proceed.  Processing continues and no error is reported.\n**\n** RESTRICT, SETNULL, and CASCADE actions apply only to foreign keys.\n** RESTRICT is the same as ABORT for IMMEDIATE foreign keys and the\n** same as ROLLBACK for DEFERRED keys.  SETNULL means that the foreign\n** key is set to NULL.  CASCADE means that a DELETE or UPDATE of the\n** referenced table row is propagated into the row that holds the\n** foreign key.\n**\n** The following symbolic values are used to record which type\n** of action to take.\n*/\n#define OE_None     0   /* There is no constraint to check */\n#define OE_Rollback 1   /* Fail the operation and rollback the transaction */\n#define OE_Abort    2   /* Back out changes but do no rollback transaction */\n#define OE_Fail     3   /* Stop the operation but leave all prior changes */\n#define OE_Ignore   4   /* Ignore the error. Do not do the INSERT or UPDATE */\n#define OE_Replace  5   /* Delete existing record, then do INSERT or UPDATE */\n\n#define OE_Restrict 6   /* OE_Abort for IMMEDIATE, OE_Rollback for DEFERRED */\n#define OE_SetNull  7   /* Set the foreign key value to NULL */\n#define OE_SetDflt  8   /* Set the foreign key value to its default */\n#define OE_Cascade  9   /* Cascade the changes */\n\n#define OE_Default  10  /* Do whatever the default action is */\n\n\n/*\n** An instance of the following structure is passed as the first\n** argument to sqlite3VdbeKeyCompare and is used to control the\n** comparison of the two index keys.\n**\n** Note that aSortOrder[] and aColl[] have nField+1 slots.  There\n** are nField slots for the columns of an index then one extra slot\n** for the rowid at the end.\n*/\nstruct KeyInfo {\n  u32 nRef;           /* Number of references to this KeyInfo object */\n  u8 enc;             /* Text encoding - one of the SQLITE_UTF* values */\n  u16 nKeyField;      /* Number of key columns in the index */\n  u16 nAllField;      /* Total columns, including key plus others */\n  sqlite3 *db;        /* The database connection */\n  u8 *aSortOrder;     /* Sort order for each column. */\n  CollSeq *aColl[1];  /* Collating sequence for each term of the key */\n};\n\n/*\n** This object holds a record which has been parsed out into individual\n** fields, for the purposes of doing a comparison.\n**\n** A record is an object that contains one or more fields of data.\n** Records are used to store the content of a table row and to store\n** the key of an index.  A blob encoding of a record is created by\n** the OP_MakeRecord opcode of the VDBE and is disassembled by the\n** OP_Column opcode.\n**\n** An instance of this object serves as a \"key\" for doing a search on\n** an index b+tree. The goal of the search is to find the entry that\n** is closed to the key described by this object.  This object might hold\n** just a prefix of the key.  The number of fields is given by\n** pKeyInfo->nField.\n**\n** The r1 and r2 fields are the values to return if this key is less than\n** or greater than a key in the btree, respectively.  These are normally\n** -1 and +1 respectively, but might be inverted to +1 and -1 if the b-tree\n** is in DESC order.\n**\n** The key comparison functions actually return default_rc when they find\n** an equals comparison.  default_rc can be -1, 0, or +1.  If there are\n** multiple entries in the b-tree with the same key (when only looking\n** at the first pKeyInfo->nFields,) then default_rc can be set to -1 to\n** cause the search to find the last match, or +1 to cause the search to\n** find the first match.\n**\n** The key comparison functions will set eqSeen to true if they ever\n** get and equal results when comparing this structure to a b-tree record.\n** When default_rc!=0, the search might end up on the record immediately\n** before the first match or immediately after the last match.  The\n** eqSeen field will indicate whether or not an exact match exists in the\n** b-tree.\n*/\nstruct UnpackedRecord {\n  KeyInfo *pKeyInfo;  /* Collation and sort-order information */\n  Mem *aMem;          /* Values */\n  u16 nField;         /* Number of entries in apMem[] */\n  i8 default_rc;      /* Comparison result if keys are equal */\n  u8 errCode;         /* Error detected by xRecordCompare (CORRUPT or NOMEM) */\n  i8 r1;              /* Value to return if (lhs < rhs) */\n  i8 r2;              /* Value to return if (lhs > rhs) */\n  u8 eqSeen;          /* True if an equality comparison has been seen */\n};\n\n\n/*\n** Each SQL index is represented in memory by an\n** instance of the following structure.\n**\n** The columns of the table that are to be indexed are described\n** by the aiColumn[] field of this structure.  For example, suppose\n** we have the following table and index:\n**\n**     CREATE TABLE Ex1(c1 int, c2 int, c3 text);\n**     CREATE INDEX Ex2 ON Ex1(c3,c1);\n**\n** In the Table structure describing Ex1, nCol==3 because there are\n** three columns in the table.  In the Index structure describing\n** Ex2, nColumn==2 since 2 of the 3 columns of Ex1 are indexed.\n** The value of aiColumn is {2, 0}.  aiColumn[0]==2 because the\n** first column to be indexed (c3) has an index of 2 in Ex1.aCol[].\n** The second column to be indexed (c1) has an index of 0 in\n** Ex1.aCol[], hence Ex2.aiColumn[1]==0.\n**\n** The Index.onError field determines whether or not the indexed columns\n** must be unique and what to do if they are not.  When Index.onError=OE_None,\n** it means this is not a unique index.  Otherwise it is a unique index\n** and the value of Index.onError indicate the which conflict resolution\n** algorithm to employ whenever an attempt is made to insert a non-unique\n** element.\n**\n** While parsing a CREATE TABLE or CREATE INDEX statement in order to\n** generate VDBE code (as opposed to parsing one read from an sqlite_master\n** table as part of parsing an existing database schema), transient instances\n** of this structure may be created. In this case the Index.tnum variable is\n** used to store the address of a VDBE instruction, not a database page\n** number (it cannot - the database page is not allocated until the VDBE\n** program is executed). See convertToWithoutRowidTable() for details.\n*/\nstruct Index {\n  char *zName;             /* Name of this index */\n  i16 *aiColumn;           /* Which columns are used by this index.  1st is 0 */\n  LogEst *aiRowLogEst;     /* From ANALYZE: Est. rows selected by each column */\n  Table *pTable;           /* The SQL table being indexed */\n  char *zColAff;           /* String defining the affinity of each column */\n  Index *pNext;            /* The next index associated with the same table */\n  Schema *pSchema;         /* Schema containing this index */\n  u8 *aSortOrder;          /* for each column: True==DESC, False==ASC */\n  const char **azColl;     /* Array of collation sequence names for index */\n  Expr *pPartIdxWhere;     /* WHERE clause for partial indices */\n  ExprList *aColExpr;      /* Column expressions */\n  int tnum;                /* DB Page containing root of this index */\n  LogEst szIdxRow;         /* Estimated average row size in bytes */\n  u16 nKeyCol;             /* Number of columns forming the key */\n  u16 nColumn;             /* Number of columns stored in the index */\n  u8 onError;              /* OE_Abort, OE_Ignore, OE_Replace, or OE_None */\n  unsigned idxType:2;      /* 1==UNIQUE, 2==PRIMARY KEY, 0==CREATE INDEX */\n  unsigned bUnordered:1;   /* Use this index for == or IN queries only */\n  unsigned uniqNotNull:1;  /* True if UNIQUE and NOT NULL for all columns */\n  unsigned isResized:1;    /* True if resizeIndexObject() has been called */\n  unsigned isCovering:1;   /* True if this is a covering index */\n  unsigned noSkipScan:1;   /* Do not try to use skip-scan if true */\n  unsigned hasStat1:1;     /* aiRowLogEst values come from sqlite_stat1 */\n  unsigned bNoQuery:1;     /* Do not use this index to optimize queries */\n#ifdef SQLITE_ENABLE_STAT3_OR_STAT4\n  int nSample;             /* Number of elements in aSample[] */\n  int nSampleCol;          /* Size of IndexSample.anEq[] and so on */\n  tRowcnt *aAvgEq;         /* Average nEq values for keys not in aSample */\n  IndexSample *aSample;    /* Samples of the left-most key */\n  tRowcnt *aiRowEst;       /* Non-logarithmic stat1 data for this index */\n  tRowcnt nRowEst0;        /* Non-logarithmic number of rows in the index */\n#endif\n};\n\n/*\n** Allowed values for Index.idxType\n*/\n#define SQLITE_IDXTYPE_APPDEF      0   /* Created using CREATE INDEX */\n#define SQLITE_IDXTYPE_UNIQUE      1   /* Implements a UNIQUE constraint */\n#define SQLITE_IDXTYPE_PRIMARYKEY  2   /* Is the PRIMARY KEY for the table */\n\n/* Return true if index X is a PRIMARY KEY index */\n#define IsPrimaryKeyIndex(X)  ((X)->idxType==SQLITE_IDXTYPE_PRIMARYKEY)\n\n/* Return true if index X is a UNIQUE index */\n#define IsUniqueIndex(X)      ((X)->onError!=OE_None)\n\n/* The Index.aiColumn[] values are normally positive integer.  But\n** there are some negative values that have special meaning:\n*/\n#define XN_ROWID     (-1)     /* Indexed column is the rowid */\n#define XN_EXPR      (-2)     /* Indexed column is an expression */\n\n/*\n** Each sample stored in the sqlite_stat3 table is represented in memory\n** using a structure of this type.  See documentation at the top of the\n** analyze.c source file for additional information.\n*/\nstruct IndexSample {\n  void *p;          /* Pointer to sampled record */\n  int n;            /* Size of record in bytes */\n  tRowcnt *anEq;    /* Est. number of rows where the key equals this sample */\n  tRowcnt *anLt;    /* Est. number of rows where key is less than this sample */\n  tRowcnt *anDLt;   /* Est. number of distinct keys less than this sample */\n};\n\n/*\n** Each token coming out of the lexer is an instance of\n** this structure.  Tokens are also used as part of an expression.\n**\n** Note if Token.z==0 then Token.dyn and Token.n are undefined and\n** may contain random values.  Do not make any assumptions about Token.dyn\n** and Token.n when Token.z==0.\n*/\nstruct Token {\n  const char *z;     /* Text of the token.  Not NULL-terminated! */\n  unsigned int n;    /* Number of characters in this token */\n};\n\n/*\n** An instance of this structure contains information needed to generate\n** code for a SELECT that contains aggregate functions.\n**\n** If Expr.op==TK_AGG_COLUMN or TK_AGG_FUNCTION then Expr.pAggInfo is a\n** pointer to this structure.  The Expr.iColumn field is the index in\n** AggInfo.aCol[] or AggInfo.aFunc[] of information needed to generate\n** code for that node.\n**\n** AggInfo.pGroupBy and AggInfo.aFunc.pExpr point to fields within the\n** original Select structure that describes the SELECT statement.  These\n** fields do not need to be freed when deallocating the AggInfo structure.\n*/\nstruct AggInfo {\n  u8 directMode;          /* Direct rendering mode means take data directly\n                          ** from source tables rather than from accumulators */\n  u8 useSortingIdx;       /* In direct mode, reference the sorting index rather\n                          ** than the source table */\n  int sortingIdx;         /* Cursor number of the sorting index */\n  int sortingIdxPTab;     /* Cursor number of pseudo-table */\n  int nSortingColumn;     /* Number of columns in the sorting index */\n  int mnReg, mxReg;       /* Range of registers allocated for aCol and aFunc */\n  ExprList *pGroupBy;     /* The group by clause */\n  struct AggInfo_col {    /* For each column used in source tables */\n    Table *pTab;             /* Source table */\n    int iTable;              /* Cursor number of the source table */\n    int iColumn;             /* Column number within the source table */\n    int iSorterColumn;       /* Column number in the sorting index */\n    int iMem;                /* Memory location that acts as accumulator */\n    Expr *pExpr;             /* The original expression */\n  } *aCol;\n  int nColumn;            /* Number of used entries in aCol[] */\n  int nAccumulator;       /* Number of columns that show through to the output.\n                          ** Additional columns are used only as parameters to\n                          ** aggregate functions */\n  struct AggInfo_func {   /* For each aggregate function */\n    Expr *pExpr;             /* Expression encoding the function */\n    FuncDef *pFunc;          /* The aggregate function implementation */\n    int iMem;                /* Memory location that acts as accumulator */\n    int iDistinct;           /* Ephemeral table used to enforce DISTINCT */\n  } *aFunc;\n  int nFunc;              /* Number of entries in aFunc[] */\n};\n\n/*\n** The datatype ynVar is a signed integer, either 16-bit or 32-bit.\n** Usually it is 16-bits.  But if SQLITE_MAX_VARIABLE_NUMBER is greater\n** than 32767 we have to make it 32-bit.  16-bit is preferred because\n** it uses less memory in the Expr object, which is a big memory user\n** in systems with lots of prepared statements.  And few applications\n** need more than about 10 or 20 variables.  But some extreme users want\n** to have prepared statements with over 32767 variables, and for them\n** the option is available (at compile-time).\n*/\n#if SQLITE_MAX_VARIABLE_NUMBER<=32767\ntypedef i16 ynVar;\n#else\ntypedef int ynVar;\n#endif\n\n/*\n** Each node of an expression in the parse tree is an instance\n** of this structure.\n**\n** Expr.op is the opcode. The integer parser token codes are reused\n** as opcodes here. For example, the parser defines TK_GE to be an integer\n** code representing the \">=\" operator. This same integer code is reused\n** to represent the greater-than-or-equal-to operator in the expression\n** tree.\n**\n** If the expression is an SQL literal (TK_INTEGER, TK_FLOAT, TK_BLOB,\n** or TK_STRING), then Expr.token contains the text of the SQL literal. If\n** the expression is a variable (TK_VARIABLE), then Expr.token contains the\n** variable name. Finally, if the expression is an SQL function (TK_FUNCTION),\n** then Expr.token contains the name of the function.\n**\n** Expr.pRight and Expr.pLeft are the left and right subexpressions of a\n** binary operator. Either or both may be NULL.\n**\n** Expr.x.pList is a list of arguments if the expression is an SQL function,\n** a CASE expression or an IN expression of the form \"<lhs> IN (<y>, <z>...)\".\n** Expr.x.pSelect is used if the expression is a sub-select or an expression of\n** the form \"<lhs> IN (SELECT ...)\". If the EP_xIsSelect bit is set in the\n** Expr.flags mask, then Expr.x.pSelect is valid. Otherwise, Expr.x.pList is\n** valid.\n**\n** An expression of the form ID or ID.ID refers to a column in a table.\n** For such expressions, Expr.op is set to TK_COLUMN and Expr.iTable is\n** the integer cursor number of a VDBE cursor pointing to that table and\n** Expr.iColumn is the column number for the specific column.  If the\n** expression is used as a result in an aggregate SELECT, then the\n** value is also stored in the Expr.iAgg column in the aggregate so that\n** it can be accessed after all aggregates are computed.\n**\n** If the expression is an unbound variable marker (a question mark\n** character '?' in the original SQL) then the Expr.iTable holds the index\n** number for that variable.\n**\n** If the expression is a subquery then Expr.iColumn holds an integer\n** register number containing the result of the subquery.  If the\n** subquery gives a constant result, then iTable is -1.  If the subquery\n** gives a different answer at different times during statement processing\n** then iTable is the address of a subroutine that computes the subquery.\n**\n** If the Expr is of type OP_Column, and the table it is selecting from\n** is a disk table or the \"old.*\" pseudo-table, then pTab points to the\n** corresponding table definition.\n**\n** ALLOCATION NOTES:\n**\n** Expr objects can use a lot of memory space in database schema.  To\n** help reduce memory requirements, sometimes an Expr object will be\n** truncated.  And to reduce the number of memory allocations, sometimes\n** two or more Expr objects will be stored in a single memory allocation,\n** together with Expr.zToken strings.\n**\n** If the EP_Reduced and EP_TokenOnly flags are set when\n** an Expr object is truncated.  When EP_Reduced is set, then all\n** the child Expr objects in the Expr.pLeft and Expr.pRight subtrees\n** are contained within the same memory allocation.  Note, however, that\n** the subtrees in Expr.x.pList or Expr.x.pSelect are always separately\n** allocated, regardless of whether or not EP_Reduced is set.\n*/\nstruct Expr {\n  u8 op;                 /* Operation performed by this node */\n  char affinity;         /* The affinity of the column or 0 if not a column */\n  u32 flags;             /* Various flags.  EP_* See below */\n  union {\n    char *zToken;          /* Token value. Zero terminated and dequoted */\n    int iValue;            /* Non-negative integer value if EP_IntValue */\n  } u;\n\n  /* If the EP_TokenOnly flag is set in the Expr.flags mask, then no\n  ** space is allocated for the fields below this point. An attempt to\n  ** access them will result in a segfault or malfunction.\n  *********************************************************************/\n\n  Expr *pLeft;           /* Left subnode */\n  Expr *pRight;          /* Right subnode */\n  union {\n    ExprList *pList;     /* op = IN, EXISTS, SELECT, CASE, FUNCTION, BETWEEN */\n    Select *pSelect;     /* EP_xIsSelect and op = IN, EXISTS, SELECT */\n  } x;\n\n  /* If the EP_Reduced flag is set in the Expr.flags mask, then no\n  ** space is allocated for the fields below this point. An attempt to\n  ** access them will result in a segfault or malfunction.\n  *********************************************************************/\n\n#if SQLITE_MAX_EXPR_DEPTH>0\n  int nHeight;           /* Height of the tree headed by this node */\n#endif\n  int iTable;            /* TK_COLUMN: cursor number of table holding column\n                         ** TK_REGISTER: register number\n                         ** TK_TRIGGER: 1 -> new, 0 -> old\n                         ** EP_Unlikely:  134217728 times likelihood\n                         ** TK_SELECT: 1st register of result vector */\n  ynVar iColumn;         /* TK_COLUMN: column index.  -1 for rowid.\n                         ** TK_VARIABLE: variable number (always >= 1).\n                         ** TK_SELECT_COLUMN: column of the result vector */\n  i16 iAgg;              /* Which entry in pAggInfo->aCol[] or ->aFunc[] */\n  i16 iRightJoinTable;   /* If EP_FromJoin, the right table of the join */\n  u8 op2;                /* TK_REGISTER: original value of Expr.op\n                         ** TK_COLUMN: the value of p5 for OP_Column\n                         ** TK_AGG_FUNCTION: nesting depth */\n  AggInfo *pAggInfo;     /* Used by TK_AGG_COLUMN and TK_AGG_FUNCTION */\n  Table *pTab;           /* Table for TK_COLUMN expressions.  Can be NULL\n                         ** for a column of an index on an expression */\n};\n\n/*\n** The following are the meanings of bits in the Expr.flags field.\n*/\n#define EP_FromJoin  0x000001 /* Originates in ON/USING clause of outer join */\n#define EP_Agg       0x000002 /* Contains one or more aggregate functions */\n#define EP_HasFunc   0x000004 /* Contains one or more functions of any kind */\n                  /* 0x000008 // available for use */\n#define EP_Distinct  0x000010 /* Aggregate function with DISTINCT keyword */\n#define EP_VarSelect 0x000020 /* pSelect is correlated, not constant */\n#define EP_DblQuoted 0x000040 /* token.z was originally in \"...\" */\n#define EP_InfixFunc 0x000080 /* True for an infix function: LIKE, GLOB, etc */\n#define EP_Collate   0x000100 /* Tree contains a TK_COLLATE operator */\n#define EP_Generic   0x000200 /* Ignore COLLATE or affinity on this tree */\n#define EP_IntValue  0x000400 /* Integer value contained in u.iValue */\n#define EP_xIsSelect 0x000800 /* x.pSelect is valid (otherwise x.pList is) */\n#define EP_Skip      0x001000 /* COLLATE, AS, or UNLIKELY */\n#define EP_Reduced   0x002000 /* Expr struct EXPR_REDUCEDSIZE bytes only */\n#define EP_TokenOnly 0x004000 /* Expr struct EXPR_TOKENONLYSIZE bytes only */\n#define EP_Static    0x008000 /* Held in memory not obtained from malloc() */\n#define EP_MemToken  0x010000 /* Need to sqlite3DbFree() Expr.zToken */\n#define EP_NoReduce  0x020000 /* Cannot EXPRDUP_REDUCE this Expr */\n#define EP_Unlikely  0x040000 /* unlikely() or likelihood() function */\n#define EP_ConstFunc 0x080000 /* A SQLITE_FUNC_CONSTANT or _SLOCHNG function */\n#define EP_CanBeNull 0x100000 /* Can be null despite NOT NULL constraint */\n#define EP_Subquery  0x200000 /* Tree contains a TK_SELECT operator */\n#define EP_Alias     0x400000 /* Is an alias for a result set column */\n#define EP_Leaf      0x800000 /* Expr.pLeft, .pRight, .u.pSelect all NULL */\n\n/*\n** The EP_Propagate mask is a set of properties that automatically propagate\n** upwards into parent nodes.\n*/\n#define EP_Propagate (EP_Collate|EP_Subquery|EP_HasFunc)\n\n/*\n** These macros can be used to test, set, or clear bits in the\n** Expr.flags field.\n*/\n#define ExprHasProperty(E,P)     (((E)->flags&(P))!=0)\n#define ExprHasAllProperty(E,P)  (((E)->flags&(P))==(P))\n#define ExprSetProperty(E,P)     (E)->flags|=(P)\n#define ExprClearProperty(E,P)   (E)->flags&=~(P)\n\n/* The ExprSetVVAProperty() macro is used for Verification, Validation,\n** and Accreditation only.  It works like ExprSetProperty() during VVA\n** processes but is a no-op for delivery.\n*/\n#ifdef SQLITE_DEBUG\n# define ExprSetVVAProperty(E,P)  (E)->flags|=(P)\n#else\n# define ExprSetVVAProperty(E,P)\n#endif\n\n/*\n** Macros to determine the number of bytes required by a normal Expr\n** struct, an Expr struct with the EP_Reduced flag set in Expr.flags\n** and an Expr struct with the EP_TokenOnly flag set.\n*/\n#define EXPR_FULLSIZE           sizeof(Expr)           /* Full size */\n#define EXPR_REDUCEDSIZE        offsetof(Expr,iTable)  /* Common features */\n#define EXPR_TOKENONLYSIZE      offsetof(Expr,pLeft)   /* Fewer features */\n\n/*\n** Flags passed to the sqlite3ExprDup() function. See the header comment\n** above sqlite3ExprDup() for details.\n*/\n#define EXPRDUP_REDUCE         0x0001  /* Used reduced-size Expr nodes */\n\n/*\n** A list of expressions.  Each expression may optionally have a\n** name.  An expr/name combination can be used in several ways, such\n** as the list of \"expr AS ID\" fields following a \"SELECT\" or in the\n** list of \"ID = expr\" items in an UPDATE.  A list of expressions can\n** also be used as the argument to a function, in which case the a.zName\n** field is not used.\n**\n** By default the Expr.zSpan field holds a human-readable description of\n** the expression that is used in the generation of error messages and\n** column labels.  In this case, Expr.zSpan is typically the text of a\n** column expression as it exists in a SELECT statement.  However, if\n** the bSpanIsTab flag is set, then zSpan is overloaded to mean the name\n** of the result column in the form: DATABASE.TABLE.COLUMN.  This later\n** form is used for name resolution with nested FROM clauses.\n*/\nstruct ExprList {\n  int nExpr;             /* Number of expressions on the list */\n  struct ExprList_item { /* For each expression in the list */\n    Expr *pExpr;            /* The parse tree for this expression */\n    char *zName;            /* Token associated with this expression */\n    char *zSpan;            /* Original text of the expression */\n    u8 sortOrder;           /* 1 for DESC or 0 for ASC */\n    unsigned done :1;       /* A flag to indicate when processing is finished */\n    unsigned bSpanIsTab :1; /* zSpan holds DB.TABLE.COLUMN */\n    unsigned reusable :1;   /* Constant expression is reusable */\n    union {\n      struct {\n        u16 iOrderByCol;      /* For ORDER BY, column number in result set */\n        u16 iAlias;           /* Index into Parse.aAlias[] for zName */\n      } x;\n      int iConstExprReg;      /* Register in which Expr value is cached */\n    } u;\n  } a[1];                  /* One slot for each expression in the list */\n};\n\n/*\n** An instance of this structure can hold a simple list of identifiers,\n** such as the list \"a,b,c\" in the following statements:\n**\n**      INSERT INTO t(a,b,c) VALUES ...;\n**      CREATE INDEX idx ON t(a,b,c);\n**      CREATE TRIGGER trig BEFORE UPDATE ON t(a,b,c) ...;\n**\n** The IdList.a.idx field is used when the IdList represents the list of\n** column names after a table name in an INSERT statement.  In the statement\n**\n**     INSERT INTO t(a,b,c) ...\n**\n** If \"a\" is the k-th column of table \"t\", then IdList.a[0].idx==k.\n*/\nstruct IdList {\n  struct IdList_item {\n    char *zName;      /* Name of the identifier */\n    int idx;          /* Index in some Table.aCol[] of a column named zName */\n  } *a;\n  int nId;         /* Number of identifiers on the list */\n};\n\n/*\n** The bitmask datatype defined below is used for various optimizations.\n**\n** Changing this from a 64-bit to a 32-bit type limits the number of\n** tables in a join to 32 instead of 64.  But it also reduces the size\n** of the library by 738 bytes on ix86.\n*/\n#ifdef SQLITE_BITMASK_TYPE\n  typedef SQLITE_BITMASK_TYPE Bitmask;\n#else\n  typedef u64 Bitmask;\n#endif\n\n/*\n** The number of bits in a Bitmask.  \"BMS\" means \"BitMask Size\".\n*/\n#define BMS  ((int)(sizeof(Bitmask)*8))\n\n/*\n** A bit in a Bitmask\n*/\n#define MASKBIT(n)   (((Bitmask)1)<<(n))\n#define MASKBIT32(n) (((unsigned int)1)<<(n))\n#define ALLBITS      ((Bitmask)-1)\n\n/*\n** The following structure describes the FROM clause of a SELECT statement.\n** Each table or subquery in the FROM clause is a separate element of\n** the SrcList.a[] array.\n**\n** With the addition of multiple database support, the following structure\n** can also be used to describe a particular table such as the table that\n** is modified by an INSERT, DELETE, or UPDATE statement.  In standard SQL,\n** such a table must be a simple name: ID.  But in SQLite, the table can\n** now be identified by a database name, a dot, then the table name: ID.ID.\n**\n** The jointype starts out showing the join type between the current table\n** and the next table on the list.  The parser builds the list this way.\n** But sqlite3SrcListShiftJoinType() later shifts the jointypes so that each\n** jointype expresses the join between the table and the previous table.\n**\n** In the colUsed field, the high-order bit (bit 63) is set if the table\n** contains more than 63 columns and the 64-th or later column is used.\n*/\nstruct SrcList {\n  int nSrc;        /* Number of tables or subqueries in the FROM clause */\n  u32 nAlloc;      /* Number of entries allocated in a[] below */\n  struct SrcList_item {\n    Schema *pSchema;  /* Schema to which this item is fixed */\n    char *zDatabase;  /* Name of database holding this table */\n    char *zName;      /* Name of the table */\n    char *zAlias;     /* The \"B\" part of a \"A AS B\" phrase.  zName is the \"A\" */\n    Table *pTab;      /* An SQL table corresponding to zName */\n    Select *pSelect;  /* A SELECT statement used in place of a table name */\n    int addrFillSub;  /* Address of subroutine to manifest a subquery */\n    int regReturn;    /* Register holding return address of addrFillSub */\n    int regResult;    /* Registers holding results of a co-routine */\n    struct {\n      u8 jointype;      /* Type of join between this table and the previous */\n      unsigned notIndexed :1;    /* True if there is a NOT INDEXED clause */\n      unsigned isIndexedBy :1;   /* True if there is an INDEXED BY clause */\n      unsigned isTabFunc :1;     /* True if table-valued-function syntax */\n      unsigned isCorrelated :1;  /* True if sub-query is correlated */\n      unsigned viaCoroutine :1;  /* Implemented as a co-routine */\n      unsigned isRecursive :1;   /* True for recursive reference in WITH */\n    } fg;\n#ifndef SQLITE_OMIT_EXPLAIN\n    u8 iSelectId;     /* If pSelect!=0, the id of the sub-select in EQP */\n#endif\n    int iCursor;      /* The VDBE cursor number used to access this table */\n    Expr *pOn;        /* The ON clause of a join */\n    IdList *pUsing;   /* The USING clause of a join */\n    Bitmask colUsed;  /* Bit N (1<<N) set if column N of pTab is used */\n    union {\n      char *zIndexedBy;    /* Identifier from \"INDEXED BY <zIndex>\" clause */\n      ExprList *pFuncArg;  /* Arguments to table-valued-function */\n    } u1;\n    Index *pIBIndex;  /* Index structure corresponding to u1.zIndexedBy */\n  } a[1];             /* One entry for each identifier on the list */\n};\n\n/*\n** Permitted values of the SrcList.a.jointype field\n*/\n#define JT_INNER     0x0001    /* Any kind of inner or cross join */\n#define JT_CROSS     0x0002    /* Explicit use of the CROSS keyword */\n#define JT_NATURAL   0x0004    /* True for a \"natural\" join */\n#define JT_LEFT      0x0008    /* Left outer join */\n#define JT_RIGHT     0x0010    /* Right outer join */\n#define JT_OUTER     0x0020    /* The \"OUTER\" keyword is present */\n#define JT_ERROR     0x0040    /* unknown or unsupported join type */\n\n\n/*\n** Flags appropriate for the wctrlFlags parameter of sqlite3WhereBegin()\n** and the WhereInfo.wctrlFlags member.\n**\n** Value constraints (enforced via assert()):\n**     WHERE_USE_LIMIT  == SF_FixedLimit\n*/\n#define WHERE_ORDERBY_NORMAL   0x0000 /* No-op */\n#define WHERE_ORDERBY_MIN      0x0001 /* ORDER BY processing for min() func */\n#define WHERE_ORDERBY_MAX      0x0002 /* ORDER BY processing for max() func */\n#define WHERE_ONEPASS_DESIRED  0x0004 /* Want to do one-pass UPDATE/DELETE */\n#define WHERE_ONEPASS_MULTIROW 0x0008 /* ONEPASS is ok with multiple rows */\n#define WHERE_DUPLICATES_OK    0x0010 /* Ok to return a row more than once */\n#define WHERE_OR_SUBCLAUSE     0x0020 /* Processing a sub-WHERE as part of\n                                      ** the OR optimization  */\n#define WHERE_GROUPBY          0x0040 /* pOrderBy is really a GROUP BY */\n#define WHERE_DISTINCTBY       0x0080 /* pOrderby is really a DISTINCT clause */\n#define WHERE_WANT_DISTINCT    0x0100 /* All output needs to be distinct */\n#define WHERE_SORTBYGROUP      0x0200 /* Support sqlite3WhereIsSorted() */\n#define WHERE_SEEK_TABLE       0x0400 /* Do not defer seeks on main table */\n#define WHERE_ORDERBY_LIMIT    0x0800 /* ORDERBY+LIMIT on the inner loop */\n#define WHERE_SEEK_UNIQ_TABLE  0x1000 /* Do not defer seeks if unique */\n                        /*     0x2000    not currently used */\n#define WHERE_USE_LIMIT        0x4000 /* Use the LIMIT in cost estimates */\n                        /*     0x8000    not currently used */\n\n/* Allowed return values from sqlite3WhereIsDistinct()\n*/\n#define WHERE_DISTINCT_NOOP      0  /* DISTINCT keyword not used */\n#define WHERE_DISTINCT_UNIQUE    1  /* No duplicates */\n#define WHERE_DISTINCT_ORDERED   2  /* All duplicates are adjacent */\n#define WHERE_DISTINCT_UNORDERED 3  /* Duplicates are scattered */\n\n/*\n** A NameContext defines a context in which to resolve table and column\n** names.  The context consists of a list of tables (the pSrcList) field and\n** a list of named expression (pEList).  The named expression list may\n** be NULL.  The pSrc corresponds to the FROM clause of a SELECT or\n** to the table being operated on by INSERT, UPDATE, or DELETE.  The\n** pEList corresponds to the result set of a SELECT and is NULL for\n** other statements.\n**\n** NameContexts can be nested.  When resolving names, the inner-most\n** context is searched first.  If no match is found, the next outer\n** context is checked.  If there is still no match, the next context\n** is checked.  This process continues until either a match is found\n** or all contexts are check.  When a match is found, the nRef member of\n** the context containing the match is incremented.\n**\n** Each subquery gets a new NameContext.  The pNext field points to the\n** NameContext in the parent query.  Thus the process of scanning the\n** NameContext list corresponds to searching through successively outer\n** subqueries looking for a match.\n*/\nstruct NameContext {\n  Parse *pParse;       /* The parser */\n  SrcList *pSrcList;   /* One or more tables used to resolve names */\n  ExprList *pEList;    /* Optional list of result-set columns */\n  AggInfo *pAggInfo;   /* Information about aggregates at this level */\n  NameContext *pNext;  /* Next outer name context.  NULL for outermost */\n  int nRef;            /* Number of names resolved by this context */\n  int nErr;            /* Number of errors encountered while resolving names */\n  u16 ncFlags;         /* Zero or more NC_* flags defined below */\n};\n\n/*\n** Allowed values for the NameContext, ncFlags field.\n**\n** Value constraints (all checked via assert()):\n**    NC_HasAgg    == SF_HasAgg\n**    NC_MinMaxAgg == SF_MinMaxAgg == SQLITE_FUNC_MINMAX\n**\n*/\n#define NC_AllowAgg  0x0001  /* Aggregate functions are allowed here */\n#define NC_PartIdx   0x0002  /* True if resolving a partial index WHERE */\n#define NC_IsCheck   0x0004  /* True if resolving names in a CHECK constraint */\n#define NC_InAggFunc 0x0008  /* True if analyzing arguments to an agg func */\n#define NC_HasAgg    0x0010  /* One or more aggregate functions seen */\n#define NC_IdxExpr   0x0020  /* True if resolving columns of CREATE INDEX */\n#define NC_VarSelect 0x0040  /* A correlated subquery has been seen */\n#define NC_MinMaxAgg 0x1000  /* min/max aggregates seen.  See note above */\n#define NC_Complex   0x2000  /* True if a function or subquery seen */\n\n/*\n** An instance of the following structure contains all information\n** needed to generate code for a single SELECT statement.\n**\n** nLimit is set to -1 if there is no LIMIT clause.  nOffset is set to 0.\n** If there is a LIMIT clause, the parser sets nLimit to the value of the\n** limit and nOffset to the value of the offset (or 0 if there is not\n** offset).  But later on, nLimit and nOffset become the memory locations\n** in the VDBE that record the limit and offset counters.\n**\n** addrOpenEphm[] entries contain the address of OP_OpenEphemeral opcodes.\n** These addresses must be stored so that we can go back and fill in\n** the P4_KEYINFO and P2 parameters later.  Neither the KeyInfo nor\n** the number of columns in P2 can be computed at the same time\n** as the OP_OpenEphm instruction is coded because not\n** enough information about the compound query is known at that point.\n** The KeyInfo for addrOpenTran[0] and [1] contains collating sequences\n** for the result set.  The KeyInfo for addrOpenEphm[2] contains collating\n** sequences for the ORDER BY clause.\n*/\nstruct Select {\n  ExprList *pEList;      /* The fields of the result */\n  u8 op;                 /* One of: TK_UNION TK_ALL TK_INTERSECT TK_EXCEPT */\n  LogEst nSelectRow;     /* Estimated number of result rows */\n  u32 selFlags;          /* Various SF_* values */\n  int iLimit, iOffset;   /* Memory registers holding LIMIT & OFFSET counters */\n#if SELECTTRACE_ENABLED\n  char zSelName[12];     /* Symbolic name of this SELECT use for debugging */\n#endif\n  int addrOpenEphm[2];   /* OP_OpenEphem opcodes related to this select */\n  SrcList *pSrc;         /* The FROM clause */\n  Expr *pWhere;          /* The WHERE clause */\n  ExprList *pGroupBy;    /* The GROUP BY clause */\n  Expr *pHaving;         /* The HAVING clause */\n  ExprList *pOrderBy;    /* The ORDER BY clause */\n  Select *pPrior;        /* Prior select in a compound select statement */\n  Select *pNext;         /* Next select to the left in a compound */\n  Expr *pLimit;          /* LIMIT expression. NULL means not used. */\n  With *pWith;           /* WITH clause attached to this select. Or NULL. */\n};\n\n/*\n** Allowed values for Select.selFlags.  The \"SF\" prefix stands for\n** \"Select Flag\".\n**\n** Value constraints (all checked via assert())\n**     SF_HasAgg     == NC_HasAgg\n**     SF_MinMaxAgg  == NC_MinMaxAgg     == SQLITE_FUNC_MINMAX\n**     SF_FixedLimit == WHERE_USE_LIMIT\n*/\n#define SF_Distinct       0x00001  /* Output should be DISTINCT */\n#define SF_All            0x00002  /* Includes the ALL keyword */\n#define SF_Resolved       0x00004  /* Identifiers have been resolved */\n#define SF_Aggregate      0x00008  /* Contains agg functions or a GROUP BY */\n#define SF_HasAgg         0x00010  /* Contains aggregate functions */\n#define SF_UsesEphemeral  0x00020  /* Uses the OpenEphemeral opcode */\n#define SF_Expanded       0x00040  /* sqlite3SelectExpand() called on this */\n#define SF_HasTypeInfo    0x00080  /* FROM subqueries have Table metadata */\n#define SF_Compound       0x00100  /* Part of a compound query */\n#define SF_Values         0x00200  /* Synthesized from VALUES clause */\n#define SF_MultiValue     0x00400  /* Single VALUES term with multiple rows */\n#define SF_NestedFrom     0x00800  /* Part of a parenthesized FROM clause */\n#define SF_MinMaxAgg      0x01000  /* Aggregate containing min() or max() */\n#define SF_Recursive      0x02000  /* The recursive part of a recursive CTE */\n#define SF_FixedLimit     0x04000  /* nSelectRow set by a constant LIMIT */\n#define SF_MaybeConvert   0x08000  /* Need convertCompoundSelectToSubquery() */\n#define SF_Converted      0x10000  /* By convertCompoundSelectToSubquery() */\n#define SF_IncludeHidden  0x20000  /* Include hidden columns in output */\n#define SF_ComplexResult  0x40000  /* Result set contains subquery or function */\n\n\n/*\n** The results of a SELECT can be distributed in several ways, as defined\n** by one of the following macros.  The \"SRT\" prefix means \"SELECT Result\n** Type\".\n**\n**     SRT_Union       Store results as a key in a temporary index\n**                     identified by pDest->iSDParm.\n**\n**     SRT_Except      Remove results from the temporary index pDest->iSDParm.\n**\n**     SRT_Exists      Store a 1 in memory cell pDest->iSDParm if the result\n**                     set is not empty.\n**\n**     SRT_Discard     Throw the results away.  This is used by SELECT\n**                     statements within triggers whose only purpose is\n**                     the side-effects of functions.\n**\n** All of the above are free to ignore their ORDER BY clause. Those that\n** follow must honor the ORDER BY clause.\n**\n**     SRT_Output      Generate a row of output (using the OP_ResultRow\n**                     opcode) for each row in the result set.\n**\n**     SRT_Mem         Only valid if the result is a single column.\n**                     Store the first column of the first result row\n**                     in register pDest->iSDParm then abandon the rest\n**                     of the query.  This destination implies \"LIMIT 1\".\n**\n**     SRT_Set         The result must be a single column.  Store each\n**                     row of result as the key in table pDest->iSDParm.\n**                     Apply the affinity pDest->affSdst before storing\n**                     results.  Used to implement \"IN (SELECT ...)\".\n**\n**     SRT_EphemTab    Create an temporary table pDest->iSDParm and store\n**                     the result there. The cursor is left open after\n**                     returning.  This is like SRT_Table except that\n**                     this destination uses OP_OpenEphemeral to create\n**                     the table first.\n**\n**     SRT_Coroutine   Generate a co-routine that returns a new row of\n**                     results each time it is invoked.  The entry point\n**                     of the co-routine is stored in register pDest->iSDParm\n**                     and the result row is stored in pDest->nDest registers\n**                     starting with pDest->iSdst.\n**\n**     SRT_Table       Store results in temporary table pDest->iSDParm.\n**     SRT_Fifo        This is like SRT_EphemTab except that the table\n**                     is assumed to already be open.  SRT_Fifo has\n**                     the additional property of being able to ignore\n**                     the ORDER BY clause.\n**\n**     SRT_DistFifo    Store results in a temporary table pDest->iSDParm.\n**                     But also use temporary table pDest->iSDParm+1 as\n**                     a record of all prior results and ignore any duplicate\n**                     rows.  Name means:  \"Distinct Fifo\".\n**\n**     SRT_Queue       Store results in priority queue pDest->iSDParm (really\n**                     an index).  Append a sequence number so that all entries\n**                     are distinct.\n**\n**     SRT_DistQueue   Store results in priority queue pDest->iSDParm only if\n**                     the same record has never been stored before.  The\n**                     index at pDest->iSDParm+1 hold all prior stores.\n*/\n#define SRT_Union        1  /* Store result as keys in an index */\n#define SRT_Except       2  /* Remove result from a UNION index */\n#define SRT_Exists       3  /* Store 1 if the result is not empty */\n#define SRT_Discard      4  /* Do not save the results anywhere */\n#define SRT_Fifo         5  /* Store result as data with an automatic rowid */\n#define SRT_DistFifo     6  /* Like SRT_Fifo, but unique results only */\n#define SRT_Queue        7  /* Store result in an queue */\n#define SRT_DistQueue    8  /* Like SRT_Queue, but unique results only */\n\n/* The ORDER BY clause is ignored for all of the above */\n#define IgnorableOrderby(X) ((X->eDest)<=SRT_DistQueue)\n\n#define SRT_Output       9  /* Output each row of result */\n#define SRT_Mem         10  /* Store result in a memory cell */\n#define SRT_Set         11  /* Store results as keys in an index */\n#define SRT_EphemTab    12  /* Create transient tab and store like SRT_Table */\n#define SRT_Coroutine   13  /* Generate a single row of result */\n#define SRT_Table       14  /* Store result as data with an automatic rowid */\n\n/*\n** An instance of this object describes where to put of the results of\n** a SELECT statement.\n*/\nstruct SelectDest {\n  u8 eDest;            /* How to dispose of the results.  On of SRT_* above. */\n  int iSDParm;         /* A parameter used by the eDest disposal method */\n  int iSdst;           /* Base register where results are written */\n  int nSdst;           /* Number of registers allocated */\n  char *zAffSdst;      /* Affinity used when eDest==SRT_Set */\n  ExprList *pOrderBy;  /* Key columns for SRT_Queue and SRT_DistQueue */\n};\n\n/*\n** During code generation of statements that do inserts into AUTOINCREMENT\n** tables, the following information is attached to the Table.u.autoInc.p\n** pointer of each autoincrement table to record some side information that\n** the code generator needs.  We have to keep per-table autoincrement\n** information in case inserts are done within triggers.  Triggers do not\n** normally coordinate their activities, but we do need to coordinate the\n** loading and saving of autoincrement information.\n*/\nstruct AutoincInfo {\n  AutoincInfo *pNext;   /* Next info block in a list of them all */\n  Table *pTab;          /* Table this info block refers to */\n  int iDb;              /* Index in sqlite3.aDb[] of database holding pTab */\n  int regCtr;           /* Memory register holding the rowid counter */\n};\n\n/*\n** Size of the column cache\n*/\n#ifndef SQLITE_N_COLCACHE\n# define SQLITE_N_COLCACHE 10\n#endif\n\n/*\n** At least one instance of the following structure is created for each\n** trigger that may be fired while parsing an INSERT, UPDATE or DELETE\n** statement. All such objects are stored in the linked list headed at\n** Parse.pTriggerPrg and deleted once statement compilation has been\n** completed.\n**\n** A Vdbe sub-program that implements the body and WHEN clause of trigger\n** TriggerPrg.pTrigger, assuming a default ON CONFLICT clause of\n** TriggerPrg.orconf, is stored in the TriggerPrg.pProgram variable.\n** The Parse.pTriggerPrg list never contains two entries with the same\n** values for both pTrigger and orconf.\n**\n** The TriggerPrg.aColmask[0] variable is set to a mask of old.* columns\n** accessed (or set to 0 for triggers fired as a result of INSERT\n** statements). Similarly, the TriggerPrg.aColmask[1] variable is set to\n** a mask of new.* columns used by the program.\n*/\nstruct TriggerPrg {\n  Trigger *pTrigger;      /* Trigger this program was coded from */\n  TriggerPrg *pNext;      /* Next entry in Parse.pTriggerPrg list */\n  SubProgram *pProgram;   /* Program implementing pTrigger/orconf */\n  int orconf;             /* Default ON CONFLICT policy */\n  u32 aColmask[2];        /* Masks of old.*, new.* columns accessed */\n};\n\n/*\n** The yDbMask datatype for the bitmask of all attached databases.\n*/\n#if SQLITE_MAX_ATTACHED>30\n  typedef unsigned char yDbMask[(SQLITE_MAX_ATTACHED+9)/8];\n# define DbMaskTest(M,I)    (((M)[(I)/8]&(1<<((I)&7)))!=0)\n# define DbMaskZero(M)      memset((M),0,sizeof(M))\n# define DbMaskSet(M,I)     (M)[(I)/8]|=(1<<((I)&7))\n# define DbMaskAllZero(M)   sqlite3DbMaskAllZero(M)\n# define DbMaskNonZero(M)   (sqlite3DbMaskAllZero(M)==0)\n#else\n  typedef unsigned int yDbMask;\n# define DbMaskTest(M,I)    (((M)&(((yDbMask)1)<<(I)))!=0)\n# define DbMaskZero(M)      (M)=0\n# define DbMaskSet(M,I)     (M)|=(((yDbMask)1)<<(I))\n# define DbMaskAllZero(M)   (M)==0\n# define DbMaskNonZero(M)   (M)!=0\n#endif\n\n/*\n** An SQL parser context.  A copy of this structure is passed through\n** the parser and down into all the parser action routine in order to\n** carry around information that is global to the entire parse.\n**\n** The structure is divided into two parts.  When the parser and code\n** generate call themselves recursively, the first part of the structure\n** is constant but the second part is reset at the beginning and end of\n** each recursion.\n**\n** The nTableLock and aTableLock variables are only used if the shared-cache\n** feature is enabled (if sqlite3Tsd()->useSharedData is true). They are\n** used to store the set of table-locks required by the statement being\n** compiled. Function sqlite3TableLock() is used to add entries to the\n** list.\n*/\nstruct Parse {\n  sqlite3 *db;         /* The main database structure */\n  char *zErrMsg;       /* An error message */\n  Vdbe *pVdbe;         /* An engine for executing database bytecode */\n  int rc;              /* Return code from execution */\n  u8 colNamesSet;      /* TRUE after OP_ColumnName has been issued to pVdbe */\n  u8 checkSchema;      /* Causes schema cookie check after an error */\n  u8 nested;           /* Number of nested calls to the parser/code generator */\n  u8 nTempReg;         /* Number of temporary registers in aTempReg[] */\n  u8 isMultiWrite;     /* True if statement may modify/insert multiple rows */\n  u8 mayAbort;         /* True if statement may throw an ABORT exception */\n  u8 hasCompound;      /* Need to invoke convertCompoundSelectToSubquery() */\n  u8 okConstFactor;    /* OK to factor out constants */\n  u8 disableLookaside; /* Number of times lookaside has been disabled */\n  u8 nColCache;        /* Number of entries in aColCache[] */\n  int nRangeReg;       /* Size of the temporary register block */\n  int iRangeReg;       /* First register in temporary register block */\n  int nErr;            /* Number of errors seen */\n  int nTab;            /* Number of previously allocated VDBE cursors */\n  int nMem;            /* Number of memory cells used so far */\n  int nOpAlloc;        /* Number of slots allocated for Vdbe.aOp[] */\n  int szOpAlloc;       /* Bytes of memory space allocated for Vdbe.aOp[] */\n  int iSelfTab;        /* Table associated with an index on expr, or negative\n                       ** of the base register during check-constraint eval */\n  int iCacheLevel;     /* ColCache valid when aColCache[].iLevel<=iCacheLevel */\n  int iCacheCnt;       /* Counter used to generate aColCache[].lru values */\n  int nLabel;          /* Number of labels used */\n  int *aLabel;         /* Space to hold the labels */\n  ExprList *pConstExpr;/* Constant expressions */\n  Token constraintName;/* Name of the constraint currently being parsed */\n  yDbMask writeMask;   /* Start a write transaction on these databases */\n  yDbMask cookieMask;  /* Bitmask of schema verified databases */\n  int regRowid;        /* Register holding rowid of CREATE TABLE entry */\n  int regRoot;         /* Register holding root page number for new objects */\n  int nMaxArg;         /* Max args passed to user function by sub-program */\n#if SELECTTRACE_ENABLED\n  int nSelect;         /* Number of SELECT statements seen */\n  int nSelectIndent;   /* How far to indent SELECTTRACE() output */\n#endif\n#ifndef SQLITE_OMIT_SHARED_CACHE\n  int nTableLock;        /* Number of locks in aTableLock */\n  TableLock *aTableLock; /* Required table locks for shared-cache mode */\n#endif\n  AutoincInfo *pAinc;  /* Information about AUTOINCREMENT counters */\n  Parse *pToplevel;    /* Parse structure for main program (or NULL) */\n  Table *pTriggerTab;  /* Table triggers are being coded for */\n  int addrCrTab;       /* Address of OP_CreateBtree opcode on CREATE TABLE */\n  u32 nQueryLoop;      /* Est number of iterations of a query (10*log2(N)) */\n  u32 oldmask;         /* Mask of old.* columns referenced */\n  u32 newmask;         /* Mask of new.* columns referenced */\n  u8 eTriggerOp;       /* TK_UPDATE, TK_INSERT or TK_DELETE */\n  u8 eOrconf;          /* Default ON CONFLICT policy for trigger steps */\n  u8 disableTriggers;  /* True to disable triggers */\n\n  /**************************************************************************\n  ** Fields above must be initialized to zero.  The fields that follow,\n  ** down to the beginning of the recursive section, do not need to be\n  ** initialized as they will be set before being used.  The boundary is\n  ** determined by offsetof(Parse,aColCache).\n  **************************************************************************/\n\n  struct yColCache {\n    int iTable;           /* Table cursor number */\n    i16 iColumn;          /* Table column number */\n    u8 tempReg;           /* iReg is a temp register that needs to be freed */\n    int iLevel;           /* Nesting level */\n    int iReg;             /* Reg with value of this column. 0 means none. */\n    int lru;              /* Least recently used entry has the smallest value */\n  } aColCache[SQLITE_N_COLCACHE];  /* One for each column cache entry */\n  int aTempReg[8];        /* Holding area for temporary registers */\n  Token sNameToken;       /* Token with unqualified schema object name */\n\n  /************************************************************************\n  ** Above is constant between recursions.  Below is reset before and after\n  ** each recursion.  The boundary between these two regions is determined\n  ** using offsetof(Parse,sLastToken) so the sLastToken field must be the\n  ** first field in the recursive region.\n  ************************************************************************/\n\n  Token sLastToken;       /* The last token parsed */\n  ynVar nVar;               /* Number of '?' variables seen in the SQL so far */\n  u8 iPkSortOrder;          /* ASC or DESC for INTEGER PRIMARY KEY */\n  u8 explain;               /* True if the EXPLAIN flag is found on the query */\n#ifndef SQLITE_OMIT_VIRTUALTABLE\n  u8 declareVtab;           /* True if inside sqlite3_declare_vtab() */\n  int nVtabLock;            /* Number of virtual tables to lock */\n#endif\n  int nHeight;              /* Expression tree height of current sub-select */\n#ifndef SQLITE_OMIT_EXPLAIN\n  int iSelectId;            /* ID of current select for EXPLAIN output */\n  int iNextSelectId;        /* Next available select ID for EXPLAIN output */\n#endif\n  VList *pVList;            /* Mapping between variable names and numbers */\n  Vdbe *pReprepare;         /* VM being reprepared (sqlite3Reprepare()) */\n  const char *zTail;        /* All SQL text past the last semicolon parsed */\n  Table *pNewTable;         /* A table being constructed by CREATE TABLE */\n  Trigger *pNewTrigger;     /* Trigger under construct by a CREATE TRIGGER */\n  const char *zAuthContext; /* The 6th parameter to db->xAuth callbacks */\n#ifndef SQLITE_OMIT_VIRTUALTABLE\n  Token sArg;               /* Complete text of a module argument */\n  Table **apVtabLock;       /* Pointer to virtual tables needing locking */\n#endif\n  Table *pZombieTab;        /* List of Table objects to delete after code gen */\n  TriggerPrg *pTriggerPrg;  /* Linked list of coded triggers */\n  With *pWith;              /* Current WITH clause, or NULL */\n  With *pWithToFree;        /* Free this WITH object at the end of the parse */\n};\n\n/*\n** Sizes and pointers of various parts of the Parse object.\n*/\n#define PARSE_HDR_SZ offsetof(Parse,aColCache) /* Recursive part w/o aColCache*/\n#define PARSE_RECURSE_SZ offsetof(Parse,sLastToken)    /* Recursive part */\n#define PARSE_TAIL_SZ (sizeof(Parse)-PARSE_RECURSE_SZ) /* Non-recursive part */\n#define PARSE_TAIL(X) (((char*)(X))+PARSE_RECURSE_SZ)  /* Pointer to tail */\n\n/*\n** Return true if currently inside an sqlite3_declare_vtab() call.\n*/\n#ifdef SQLITE_OMIT_VIRTUALTABLE\n  #define IN_DECLARE_VTAB 0\n#else\n  #define IN_DECLARE_VTAB (pParse->declareVtab)\n#endif\n\n/*\n** An instance of the following structure can be declared on a stack and used\n** to save the Parse.zAuthContext value so that it can be restored later.\n*/\nstruct AuthContext {\n  const char *zAuthContext;   /* Put saved Parse.zAuthContext here */\n  Parse *pParse;              /* The Parse structure */\n};\n\n/*\n** Bitfield flags for P5 value in various opcodes.\n**\n** Value constraints (enforced via assert()):\n**    OPFLAG_LENGTHARG    == SQLITE_FUNC_LENGTH\n**    OPFLAG_TYPEOFARG    == SQLITE_FUNC_TYPEOF\n**    OPFLAG_BULKCSR      == BTREE_BULKLOAD\n**    OPFLAG_SEEKEQ       == BTREE_SEEK_EQ\n**    OPFLAG_FORDELETE    == BTREE_FORDELETE\n**    OPFLAG_SAVEPOSITION == BTREE_SAVEPOSITION\n**    OPFLAG_AUXDELETE    == BTREE_AUXDELETE\n*/\n#define OPFLAG_NCHANGE       0x01    /* OP_Insert: Set to update db->nChange */\n                                     /* Also used in P2 (not P5) of OP_Delete */\n#define OPFLAG_EPHEM         0x01    /* OP_Column: Ephemeral output is ok */\n#define OPFLAG_LASTROWID     0x20    /* Set to update db->lastRowid */\n#define OPFLAG_ISUPDATE      0x04    /* This OP_Insert is an sql UPDATE */\n#define OPFLAG_APPEND        0x08    /* This is likely to be an append */\n#define OPFLAG_USESEEKRESULT 0x10    /* Try to avoid a seek in BtreeInsert() */\n#define OPFLAG_ISNOOP        0x40    /* OP_Delete does pre-update-hook only */\n#define OPFLAG_LENGTHARG     0x40    /* OP_Column only used for length() */\n#define OPFLAG_TYPEOFARG     0x80    /* OP_Column only used for typeof() */\n#define OPFLAG_BULKCSR       0x01    /* OP_Open** used to open bulk cursor */\n#define OPFLAG_SEEKEQ        0x02    /* OP_Open** cursor uses EQ seek only */\n#define OPFLAG_FORDELETE     0x08    /* OP_Open should use BTREE_FORDELETE */\n#define OPFLAG_P2ISREG       0x10    /* P2 to OP_Open** is a register number */\n#define OPFLAG_PERMUTE       0x01    /* OP_Compare: use the permutation */\n#define OPFLAG_SAVEPOSITION  0x02    /* OP_Delete/Insert: save cursor pos */\n#define OPFLAG_AUXDELETE     0x04    /* OP_Delete: index in a DELETE op */\n#define OPFLAG_NOCHNG_MAGIC  0x6d    /* OP_MakeRecord: serialtype 10 is ok */\n\n/*\n * Each trigger present in the database schema is stored as an instance of\n * struct Trigger.\n *\n * Pointers to instances of struct Trigger are stored in two ways.\n * 1. In the \"trigHash\" hash table (part of the sqlite3* that represents the\n *    database). This allows Trigger structures to be retrieved by name.\n * 2. All triggers associated with a single table form a linked list, using the\n *    pNext member of struct Trigger. A pointer to the first element of the\n *    linked list is stored as the \"pTrigger\" member of the associated\n *    struct Table.\n *\n * The \"step_list\" member points to the first element of a linked list\n * containing the SQL statements specified as the trigger program.\n */\nstruct Trigger {\n  char *zName;            /* The name of the trigger                        */\n  char *table;            /* The table or view to which the trigger applies */\n  u8 op;                  /* One of TK_DELETE, TK_UPDATE, TK_INSERT         */\n  u8 tr_tm;               /* One of TRIGGER_BEFORE, TRIGGER_AFTER */\n  Expr *pWhen;            /* The WHEN clause of the expression (may be NULL) */\n  IdList *pColumns;       /* If this is an UPDATE OF <column-list> trigger,\n                             the <column-list> is stored here */\n  Schema *pSchema;        /* Schema containing the trigger */\n  Schema *pTabSchema;     /* Schema containing the table */\n  TriggerStep *step_list; /* Link list of trigger program steps             */\n  Trigger *pNext;         /* Next trigger associated with the table */\n};\n\n/*\n** A trigger is either a BEFORE or an AFTER trigger.  The following constants\n** determine which.\n**\n** If there are multiple triggers, you might of some BEFORE and some AFTER.\n** In that cases, the constants below can be ORed together.\n*/\n#define TRIGGER_BEFORE  1\n#define TRIGGER_AFTER   2\n\n/*\n * An instance of struct TriggerStep is used to store a single SQL statement\n * that is a part of a trigger-program.\n *\n * Instances of struct TriggerStep are stored in a singly linked list (linked\n * using the \"pNext\" member) referenced by the \"step_list\" member of the\n * associated struct Trigger instance. The first element of the linked list is\n * the first step of the trigger-program.\n *\n * The \"op\" member indicates whether this is a \"DELETE\", \"INSERT\", \"UPDATE\" or\n * \"SELECT\" statement. The meanings of the other members is determined by the\n * value of \"op\" as follows:\n *\n * (op == TK_INSERT)\n * orconf    -> stores the ON CONFLICT algorithm\n * pSelect   -> If this is an INSERT INTO ... SELECT ... statement, then\n *              this stores a pointer to the SELECT statement. Otherwise NULL.\n * zTarget   -> Dequoted name of the table to insert into.\n * pExprList -> If this is an INSERT INTO ... VALUES ... statement, then\n *              this stores values to be inserted. Otherwise NULL.\n * pIdList   -> If this is an INSERT INTO ... (<column-names>) VALUES ...\n *              statement, then this stores the column-names to be\n *              inserted into.\n *\n * (op == TK_DELETE)\n * zTarget   -> Dequoted name of the table to delete from.\n * pWhere    -> The WHERE clause of the DELETE statement if one is specified.\n *              Otherwise NULL.\n *\n * (op == TK_UPDATE)\n * zTarget   -> Dequoted name of the table to update.\n * pWhere    -> The WHERE clause of the UPDATE statement if one is specified.\n *              Otherwise NULL.\n * pExprList -> A list of the columns to update and the expressions to update\n *              them to. See sqlite3Update() documentation of \"pChanges\"\n *              argument.\n *\n */\nstruct TriggerStep {\n  u8 op;               /* One of TK_DELETE, TK_UPDATE, TK_INSERT, TK_SELECT */\n  u8 orconf;           /* OE_Rollback etc. */\n  Trigger *pTrig;      /* The trigger that this step is a part of */\n  Select *pSelect;     /* SELECT statement or RHS of INSERT INTO SELECT ... */\n  char *zTarget;       /* Target table for DELETE, UPDATE, INSERT */\n  Expr *pWhere;        /* The WHERE clause for DELETE or UPDATE steps */\n  ExprList *pExprList; /* SET clause for UPDATE. */\n  IdList *pIdList;     /* Column names for INSERT */\n  char *zSpan;         /* Original SQL text of this command */\n  TriggerStep *pNext;  /* Next in the link-list */\n  TriggerStep *pLast;  /* Last element in link-list. Valid for 1st elem only */\n};\n\n/*\n** The following structure contains information used by the sqliteFix...\n** routines as they walk the parse tree to make database references\n** explicit.\n*/\ntypedef struct DbFixer DbFixer;\nstruct DbFixer {\n  Parse *pParse;      /* The parsing context.  Error messages written here */\n  Schema *pSchema;    /* Fix items to this schema */\n  int bVarOnly;       /* Check for variable references only */\n  const char *zDb;    /* Make sure all objects are contained in this database */\n  const char *zType;  /* Type of the container - used for error messages */\n  const Token *pName; /* Name of the container - used for error messages */\n};\n\n/*\n** An objected used to accumulate the text of a string where we\n** do not necessarily know how big the string will be in the end.\n*/\nstruct StrAccum {\n  sqlite3 *db;         /* Optional database for lookaside.  Can be NULL */\n  char *zText;         /* The string collected so far */\n  u32  nAlloc;         /* Amount of space allocated in zText */\n  u32  mxAlloc;        /* Maximum allowed allocation.  0 for no malloc usage */\n  u32  nChar;          /* Length of the string so far */\n  u8   accError;       /* STRACCUM_NOMEM or STRACCUM_TOOBIG */\n  u8   printfFlags;    /* SQLITE_PRINTF flags below */\n};\n#define STRACCUM_NOMEM   1\n#define STRACCUM_TOOBIG  2\n#define SQLITE_PRINTF_INTERNAL 0x01  /* Internal-use-only converters allowed */\n#define SQLITE_PRINTF_SQLFUNC  0x02  /* SQL function arguments to VXPrintf */\n#define SQLITE_PRINTF_MALLOCED 0x04  /* True if xText is allocated space */\n\n#define isMalloced(X)  (((X)->printfFlags & SQLITE_PRINTF_MALLOCED)!=0)\n\n\n/*\n** A pointer to this structure is used to communicate information\n** from sqlite3Init and OP_ParseSchema into the sqlite3InitCallback.\n*/\ntypedef struct {\n  sqlite3 *db;        /* The database being initialized */\n  char **pzErrMsg;    /* Error message stored here */\n  int iDb;            /* 0 for main database.  1 for TEMP, 2.. for ATTACHed */\n  int rc;             /* Result code stored here */\n} InitData;\n\n/*\n** Structure containing global configuration data for the SQLite library.\n**\n** This structure also contains some state information.\n*/\nstruct Sqlite3Config {\n  int bMemstat;                     /* True to enable memory status */\n  int bCoreMutex;                   /* True to enable core mutexing */\n  int bFullMutex;                   /* True to enable full mutexing */\n  int bOpenUri;                     /* True to interpret filenames as URIs */\n  int bUseCis;                      /* Use covering indices for full-scans */\n  int bSmallMalloc;                 /* Avoid large memory allocations if true */\n  int mxStrlen;                     /* Maximum string length */\n  int neverCorrupt;                 /* Database is always well-formed */\n  int szLookaside;                  /* Default lookaside buffer size */\n  int nLookaside;                   /* Default lookaside buffer count */\n  int nStmtSpill;                   /* Stmt-journal spill-to-disk threshold */\n  sqlite3_mem_methods m;            /* Low-level memory allocation interface */\n  sqlite3_mutex_methods mutex;      /* Low-level mutex interface */\n  sqlite3_pcache_methods2 pcache2;  /* Low-level page-cache interface */\n  void *pHeap;                      /* Heap storage space */\n  int nHeap;                        /* Size of pHeap[] */\n  int mnReq, mxReq;                 /* Min and max heap requests sizes */\n  sqlite3_int64 szMmap;             /* mmap() space per open file */\n  sqlite3_int64 mxMmap;             /* Maximum value for szMmap */\n  void *pPage;                      /* Page cache memory */\n  int szPage;                       /* Size of each page in pPage[] */\n  int nPage;                        /* Number of pages in pPage[] */\n  int mxParserStack;                /* maximum depth of the parser stack */\n  int sharedCacheEnabled;           /* true if shared-cache mode enabled */\n  u32 szPma;                        /* Maximum Sorter PMA size */\n  /* The above might be initialized to non-zero.  The following need to always\n  ** initially be zero, however. */\n  int isInit;                       /* True after initialization has finished */\n  int inProgress;                   /* True while initialization in progress */\n  int isMutexInit;                  /* True after mutexes are initialized */\n  int isMallocInit;                 /* True after malloc is initialized */\n  int isPCacheInit;                 /* True after malloc is initialized */\n  int nRefInitMutex;                /* Number of users of pInitMutex */\n  sqlite3_mutex *pInitMutex;        /* Mutex used by sqlite3_initialize() */\n  void (*xLog)(void*,int,const char*); /* Function for logging */\n  void *pLogArg;                       /* First argument to xLog() */\n#ifdef SQLITE_ENABLE_SQLLOG\n  void(*xSqllog)(void*,sqlite3*,const char*, int);\n  void *pSqllogArg;\n#endif\n#ifdef SQLITE_VDBE_COVERAGE\n  /* The following callback (if not NULL) is invoked on every VDBE branch\n  ** operation.  Set the callback using SQLITE_TESTCTRL_VDBE_COVERAGE.\n  */\n  void (*xVdbeBranch)(void*,int iSrcLine,u8 eThis,u8 eMx);  /* Callback */\n  void *pVdbeBranchArg;                                     /* 1st argument */\n#endif\n#ifndef SQLITE_UNTESTABLE\n  int (*xTestCallback)(int);        /* Invoked by sqlite3FaultSim() */\n#endif\n  int bLocaltimeFault;              /* True to fail localtime() calls */\n  int iOnceResetThreshold;          /* When to reset OP_Once counters */\n};\n\n/*\n** This macro is used inside of assert() statements to indicate that\n** the assert is only valid on a well-formed database.  Instead of:\n**\n**     assert( X );\n**\n** One writes:\n**\n**     assert( X || CORRUPT_DB );\n**\n** CORRUPT_DB is true during normal operation.  CORRUPT_DB does not indicate\n** that the database is definitely corrupt, only that it might be corrupt.\n** For most test cases, CORRUPT_DB is set to false using a special\n** sqlite3_test_control().  This enables assert() statements to prove\n** things that are always true for well-formed databases.\n*/\n#define CORRUPT_DB  (sqlite3Config.neverCorrupt==0)\n\n/*\n** Context pointer passed down through the tree-walk.\n*/\nstruct Walker {\n  Parse *pParse;                            /* Parser context.  */\n  int (*xExprCallback)(Walker*, Expr*);     /* Callback for expressions */\n  int (*xSelectCallback)(Walker*,Select*);  /* Callback for SELECTs */\n  void (*xSelectCallback2)(Walker*,Select*);/* Second callback for SELECTs */\n  int walkerDepth;                          /* Number of subqueries */\n  u8 eCode;                                 /* A small processing code */\n  union {                                   /* Extra data for callback */\n    NameContext *pNC;                         /* Naming context */\n    int n;                                    /* A counter */\n    int iCur;                                 /* A cursor number */\n    SrcList *pSrcList;                        /* FROM clause */\n    struct SrcCount *pSrcCount;               /* Counting column references */\n    struct CCurHint *pCCurHint;               /* Used by codeCursorHint() */\n    int *aiCol;                               /* array of column indexes */\n    struct IdxCover *pIdxCover;               /* Check for index coverage */\n    struct IdxExprTrans *pIdxTrans;           /* Convert indexed expr to column */\n    ExprList *pGroupBy;                       /* GROUP BY clause */\n    struct HavingToWhereCtx *pHavingCtx;      /* HAVING to WHERE clause ctx */\n  } u;\n};\n\n/* Forward declarations */\nSQLITE_PRIVATE int sqlite3WalkExpr(Walker*, Expr*);\nSQLITE_PRIVATE int sqlite3WalkExprList(Walker*, ExprList*);\nSQLITE_PRIVATE int sqlite3WalkSelect(Walker*, Select*);\nSQLITE_PRIVATE int sqlite3WalkSelectExpr(Walker*, Select*);\nSQLITE_PRIVATE int sqlite3WalkSelectFrom(Walker*, Select*);\nSQLITE_PRIVATE int sqlite3ExprWalkNoop(Walker*, Expr*);\nSQLITE_PRIVATE int sqlite3SelectWalkNoop(Walker*, Select*);\nSQLITE_PRIVATE int sqlite3SelectWalkFail(Walker*, Select*);\n#ifdef SQLITE_DEBUG\nSQLITE_PRIVATE void sqlite3SelectWalkAssert2(Walker*, Select*);\n#endif\n\n/*\n** Return code from the parse-tree walking primitives and their\n** callbacks.\n*/\n#define WRC_Continue    0   /* Continue down into children */\n#define WRC_Prune       1   /* Omit children but continue walking siblings */\n#define WRC_Abort       2   /* Abandon the tree walk */\n\n/*\n** An instance of this structure represents a set of one or more CTEs\n** (common table expressions) created by a single WITH clause.\n*/\nstruct With {\n  int nCte;                       /* Number of CTEs in the WITH clause */\n  With *pOuter;                   /* Containing WITH clause, or NULL */\n  struct Cte {                    /* For each CTE in the WITH clause.... */\n    char *zName;                    /* Name of this CTE */\n    ExprList *pCols;                /* List of explicit column names, or NULL */\n    Select *pSelect;                /* The definition of this CTE */\n    const char *zCteErr;            /* Error message for circular references */\n  } a[1];\n};\n\n#ifdef SQLITE_DEBUG\n/*\n** An instance of the TreeView object is used for printing the content of\n** data structures on sqlite3DebugPrintf() using a tree-like view.\n*/\nstruct TreeView {\n  int iLevel;             /* Which level of the tree we are on */\n  u8  bLine[100];         /* Draw vertical in column i if bLine[i] is true */\n};\n#endif /* SQLITE_DEBUG */\n\n/*\n** Assuming zIn points to the first byte of a UTF-8 character,\n** advance zIn to point to the first byte of the next UTF-8 character.\n*/\n#define SQLITE_SKIP_UTF8(zIn) {                        \\\n  if( (*(zIn++))>=0xc0 ){                              \\\n    while( (*zIn & 0xc0)==0x80 ){ zIn++; }             \\\n  }                                                    \\\n}\n\n/*\n** The SQLITE_*_BKPT macros are substitutes for the error codes with\n** the same name but without the _BKPT suffix.  These macros invoke\n** routines that report the line-number on which the error originated\n** using sqlite3_log().  The routines also provide a convenient place\n** to set a debugger breakpoint.\n*/\nSQLITE_PRIVATE int sqlite3ReportError(int iErr, int lineno, const char *zType);\nSQLITE_PRIVATE int sqlite3CorruptError(int);\nSQLITE_PRIVATE int sqlite3MisuseError(int);\nSQLITE_PRIVATE int sqlite3CantopenError(int);\n#define SQLITE_CORRUPT_BKPT sqlite3CorruptError(__LINE__)\n#define SQLITE_MISUSE_BKPT sqlite3MisuseError(__LINE__)\n#define SQLITE_CANTOPEN_BKPT sqlite3CantopenError(__LINE__)\n#ifdef SQLITE_DEBUG\nSQLITE_PRIVATE   int sqlite3NomemError(int);\nSQLITE_PRIVATE   int sqlite3IoerrnomemError(int);\nSQLITE_PRIVATE   int sqlite3CorruptPgnoError(int,Pgno);\n# define SQLITE_NOMEM_BKPT sqlite3NomemError(__LINE__)\n# define SQLITE_IOERR_NOMEM_BKPT sqlite3IoerrnomemError(__LINE__)\n# define SQLITE_CORRUPT_PGNO(P) sqlite3CorruptPgnoError(__LINE__,(P))\n#else\n# define SQLITE_NOMEM_BKPT SQLITE_NOMEM\n# define SQLITE_IOERR_NOMEM_BKPT SQLITE_IOERR_NOMEM\n# define SQLITE_CORRUPT_PGNO(P) sqlite3CorruptError(__LINE__)\n#endif\n\n/*\n** FTS3 and FTS4 both require virtual table support\n*/\n#if defined(SQLITE_OMIT_VIRTUALTABLE)\n# undef SQLITE_ENABLE_FTS3\n# undef SQLITE_ENABLE_FTS4\n#endif\n\n/*\n** FTS4 is really an extension for FTS3.  It is enabled using the\n** SQLITE_ENABLE_FTS3 macro.  But to avoid confusion we also call\n** the SQLITE_ENABLE_FTS4 macro to serve as an alias for SQLITE_ENABLE_FTS3.\n*/\n#if defined(SQLITE_ENABLE_FTS4) && !defined(SQLITE_ENABLE_FTS3)\n# define SQLITE_ENABLE_FTS3 1\n#endif\n\n/*\n** The ctype.h header is needed for non-ASCII systems.  It is also\n** needed by FTS3 when FTS3 is included in the amalgamation.\n*/\n#if !defined(SQLITE_ASCII) || \\\n    (defined(SQLITE_ENABLE_FTS3) && defined(SQLITE_AMALGAMATION))\n# include <ctype.h>\n#endif\n\n/*\n** The following macros mimic the standard library functions toupper(),\n** isspace(), isalnum(), isdigit() and isxdigit(), respectively. The\n** sqlite versions only work for ASCII characters, regardless of locale.\n*/\n#ifdef SQLITE_ASCII\n# define sqlite3Toupper(x)  ((x)&~(sqlite3CtypeMap[(unsigned char)(x)]&0x20))\n# define sqlite3Isspace(x)   (sqlite3CtypeMap[(unsigned char)(x)]&0x01)\n# define sqlite3Isalnum(x)   (sqlite3CtypeMap[(unsigned char)(x)]&0x06)\n# define sqlite3Isalpha(x)   (sqlite3CtypeMap[(unsigned char)(x)]&0x02)\n# define sqlite3Isdigit(x)   (sqlite3CtypeMap[(unsigned char)(x)]&0x04)\n# define sqlite3Isxdigit(x)  (sqlite3CtypeMap[(unsigned char)(x)]&0x08)\n# define sqlite3Tolower(x)   (sqlite3UpperToLower[(unsigned char)(x)])\n# define sqlite3Isquote(x)   (sqlite3CtypeMap[(unsigned char)(x)]&0x80)\n#else\n# define sqlite3Toupper(x)   toupper((unsigned char)(x))\n# define sqlite3Isspace(x)   isspace((unsigned char)(x))\n# define sqlite3Isalnum(x)   isalnum((unsigned char)(x))\n# define sqlite3Isalpha(x)   isalpha((unsigned char)(x))\n# define sqlite3Isdigit(x)   isdigit((unsigned char)(x))\n# define sqlite3Isxdigit(x)  isxdigit((unsigned char)(x))\n# define sqlite3Tolower(x)   tolower((unsigned char)(x))\n# define sqlite3Isquote(x)   ((x)=='\"'||(x)=='\\''||(x)=='['||(x)=='`')\n#endif\n#ifndef SQLITE_OMIT_COMPILEOPTION_DIAGS\nSQLITE_PRIVATE int sqlite3IsIdChar(u8);\n#endif\n\n/*\n** Internal function prototypes\n*/\nSQLITE_PRIVATE int sqlite3StrICmp(const char*,const char*);\nSQLITE_PRIVATE int sqlite3Strlen30(const char*);\nSQLITE_PRIVATE char *sqlite3ColumnType(Column*,char*);\n#define sqlite3StrNICmp sqlite3_strnicmp\n\nSQLITE_PRIVATE int sqlite3MallocInit(void);\nSQLITE_PRIVATE void sqlite3MallocEnd(void);\nSQLITE_PRIVATE void *sqlite3Malloc(u64);\nSQLITE_PRIVATE void *sqlite3MallocZero(u64);\nSQLITE_PRIVATE void *sqlite3DbMallocZero(sqlite3*, u64);\nSQLITE_PRIVATE void *sqlite3DbMallocRaw(sqlite3*, u64);\nSQLITE_PRIVATE void *sqlite3DbMallocRawNN(sqlite3*, u64);\nSQLITE_PRIVATE char *sqlite3DbStrDup(sqlite3*,const char*);\nSQLITE_PRIVATE char *sqlite3DbStrNDup(sqlite3*,const char*, u64);\nSQLITE_PRIVATE char *sqlite3DbSpanDup(sqlite3*,const char*,const char*);\nSQLITE_PRIVATE void *sqlite3Realloc(void*, u64);\nSQLITE_PRIVATE void *sqlite3DbReallocOrFree(sqlite3 *, void *, u64);\nSQLITE_PRIVATE void *sqlite3DbRealloc(sqlite3 *, void *, u64);\nSQLITE_PRIVATE void sqlite3DbFree(sqlite3*, void*);\nSQLITE_PRIVATE void sqlite3DbFreeNN(sqlite3*, void*);\nSQLITE_PRIVATE int sqlite3MallocSize(void*);\nSQLITE_PRIVATE int sqlite3DbMallocSize(sqlite3*, void*);\nSQLITE_PRIVATE void *sqlite3PageMalloc(int);\nSQLITE_PRIVATE void sqlite3PageFree(void*);\nSQLITE_PRIVATE void sqlite3MemSetDefault(void);\n#ifndef SQLITE_UNTESTABLE\nSQLITE_PRIVATE void sqlite3BenignMallocHooks(void (*)(void), void (*)(void));\n#endif\nSQLITE_PRIVATE int sqlite3HeapNearlyFull(void);\n\n/*\n** On systems with ample stack space and that support alloca(), make\n** use of alloca() to obtain space for large automatic objects.  By default,\n** obtain space from malloc().\n**\n** The alloca() routine never returns NULL.  This will cause code paths\n** that deal with sqlite3StackAlloc() failures to be unreachable.\n*/\n#ifdef SQLITE_USE_ALLOCA\n# define sqlite3StackAllocRaw(D,N)   alloca(N)\n# define sqlite3StackAllocZero(D,N)  memset(alloca(N), 0, N)\n# define sqlite3StackFree(D,P)\n#else\n# define sqlite3StackAllocRaw(D,N)   sqlite3DbMallocRaw(D,N)\n# define sqlite3StackAllocZero(D,N)  sqlite3DbMallocZero(D,N)\n# define sqlite3StackFree(D,P)       sqlite3DbFree(D,P)\n#endif\n\n/* Do not allow both MEMSYS5 and MEMSYS3 to be defined together.  If they\n** are, disable MEMSYS3\n*/\n#ifdef SQLITE_ENABLE_MEMSYS5\nSQLITE_PRIVATE const sqlite3_mem_methods *sqlite3MemGetMemsys5(void);\n#undef SQLITE_ENABLE_MEMSYS3\n#endif\n#ifdef SQLITE_ENABLE_MEMSYS3\nSQLITE_PRIVATE const sqlite3_mem_methods *sqlite3MemGetMemsys3(void);\n#endif\n\n\n#ifndef SQLITE_MUTEX_OMIT\nSQLITE_PRIVATE   sqlite3_mutex_methods const *sqlite3DefaultMutex(void);\nSQLITE_PRIVATE   sqlite3_mutex_methods const *sqlite3NoopMutex(void);\nSQLITE_PRIVATE   sqlite3_mutex *sqlite3MutexAlloc(int);\nSQLITE_PRIVATE   int sqlite3MutexInit(void);\nSQLITE_PRIVATE   int sqlite3MutexEnd(void);\n#endif\n#if !defined(SQLITE_MUTEX_OMIT) && !defined(SQLITE_MUTEX_NOOP)\nSQLITE_PRIVATE   void sqlite3MemoryBarrier(void);\n#else\n# define sqlite3MemoryBarrier()\n#endif\n\nSQLITE_PRIVATE sqlite3_int64 sqlite3StatusValue(int);\nSQLITE_PRIVATE void sqlite3StatusUp(int, int);\nSQLITE_PRIVATE void sqlite3StatusDown(int, int);\nSQLITE_PRIVATE void sqlite3StatusHighwater(int, int);\nSQLITE_PRIVATE int sqlite3LookasideUsed(sqlite3*,int*);\n\n/* Access to mutexes used by sqlite3_status() */\nSQLITE_PRIVATE sqlite3_mutex *sqlite3Pcache1Mutex(void);\nSQLITE_PRIVATE sqlite3_mutex *sqlite3MallocMutex(void);\n\n#if defined(SQLITE_ENABLE_MULTITHREADED_CHECKS) && !defined(SQLITE_MUTEX_OMIT)\nSQLITE_PRIVATE void sqlite3MutexWarnOnContention(sqlite3_mutex*);\n#else\n# define sqlite3MutexWarnOnContention(x)\n#endif\n\n#ifndef SQLITE_OMIT_FLOATING_POINT\nSQLITE_PRIVATE   int sqlite3IsNaN(double);\n#else\n# define sqlite3IsNaN(X)  0\n#endif\n\n/*\n** An instance of the following structure holds information about SQL\n** functions arguments that are the parameters to the printf() function.\n*/\nstruct PrintfArguments {\n  int nArg;                /* Total number of arguments */\n  int nUsed;               /* Number of arguments used so far */\n  sqlite3_value **apArg;   /* The argument values */\n};\n\nSQLITE_PRIVATE void sqlite3VXPrintf(StrAccum*, const char*, va_list);\nSQLITE_PRIVATE void sqlite3XPrintf(StrAccum*, const char*, ...);\nSQLITE_PRIVATE char *sqlite3MPrintf(sqlite3*,const char*, ...);\nSQLITE_PRIVATE char *sqlite3VMPrintf(sqlite3*,const char*, va_list);\n#if defined(SQLITE_DEBUG) || defined(SQLITE_HAVE_OS_TRACE)\nSQLITE_PRIVATE   void sqlite3DebugPrintf(const char*, ...);\n#endif\n#if defined(SQLITE_TEST)\nSQLITE_PRIVATE   void *sqlite3TestTextToPtr(const char*);\n#endif\n\n#if defined(SQLITE_DEBUG)\nSQLITE_PRIVATE   void sqlite3TreeViewExpr(TreeView*, const Expr*, u8);\nSQLITE_PRIVATE   void sqlite3TreeViewBareExprList(TreeView*, const ExprList*, const char*);\nSQLITE_PRIVATE   void sqlite3TreeViewExprList(TreeView*, const ExprList*, u8, const char*);\nSQLITE_PRIVATE   void sqlite3TreeViewSelect(TreeView*, const Select*, u8);\nSQLITE_PRIVATE   void sqlite3TreeViewWith(TreeView*, const With*, u8);\n#endif\n\n\nSQLITE_PRIVATE void sqlite3SetString(char **, sqlite3*, const char*);\nSQLITE_PRIVATE void sqlite3ErrorMsg(Parse*, const char*, ...);\nSQLITE_PRIVATE void sqlite3Dequote(char*);\nSQLITE_PRIVATE void sqlite3TokenInit(Token*,char*);\nSQLITE_PRIVATE int sqlite3KeywordCode(const unsigned char*, int);\nSQLITE_PRIVATE int sqlite3RunParser(Parse*, const char*, char **);\nSQLITE_PRIVATE void sqlite3FinishCoding(Parse*);\nSQLITE_PRIVATE int sqlite3GetTempReg(Parse*);\nSQLITE_PRIVATE void sqlite3ReleaseTempReg(Parse*,int);\nSQLITE_PRIVATE int sqlite3GetTempRange(Parse*,int);\nSQLITE_PRIVATE void sqlite3ReleaseTempRange(Parse*,int,int);\nSQLITE_PRIVATE void sqlite3ClearTempRegCache(Parse*);\n#ifdef SQLITE_DEBUG\nSQLITE_PRIVATE int sqlite3NoTempsInRange(Parse*,int,int);\n#endif\nSQLITE_PRIVATE Expr *sqlite3ExprAlloc(sqlite3*,int,const Token*,int);\nSQLITE_PRIVATE Expr *sqlite3Expr(sqlite3*,int,const char*);\nSQLITE_PRIVATE void sqlite3ExprAttachSubtrees(sqlite3*,Expr*,Expr*,Expr*);\nSQLITE_PRIVATE Expr *sqlite3PExpr(Parse*, int, Expr*, Expr*);\nSQLITE_PRIVATE void sqlite3PExprAddSelect(Parse*, Expr*, Select*);\nSQLITE_PRIVATE Expr *sqlite3ExprAnd(sqlite3*,Expr*, Expr*);\nSQLITE_PRIVATE Expr *sqlite3ExprFunction(Parse*,ExprList*, Token*);\nSQLITE_PRIVATE void sqlite3ExprAssignVarNumber(Parse*, Expr*, u32);\nSQLITE_PRIVATE void sqlite3ExprDelete(sqlite3*, Expr*);\nSQLITE_PRIVATE ExprList *sqlite3ExprListAppend(Parse*,ExprList*,Expr*);\nSQLITE_PRIVATE ExprList *sqlite3ExprListAppendVector(Parse*,ExprList*,IdList*,Expr*);\nSQLITE_PRIVATE void sqlite3ExprListSetSortOrder(ExprList*,int);\nSQLITE_PRIVATE void sqlite3ExprListSetName(Parse*,ExprList*,Token*,int);\nSQLITE_PRIVATE void sqlite3ExprListSetSpan(Parse*,ExprList*,const char*,const char*);\nSQLITE_PRIVATE void sqlite3ExprListDelete(sqlite3*, ExprList*);\nSQLITE_PRIVATE u32 sqlite3ExprListFlags(const ExprList*);\nSQLITE_PRIVATE int sqlite3Init(sqlite3*, char**);\nSQLITE_PRIVATE int sqlite3InitCallback(void*, int, char**, char**);\nSQLITE_PRIVATE void sqlite3Pragma(Parse*,Token*,Token*,Token*,int);\n#ifndef SQLITE_OMIT_VIRTUALTABLE\nSQLITE_PRIVATE Module *sqlite3PragmaVtabRegister(sqlite3*,const char *zName);\n#endif\nSQLITE_PRIVATE void sqlite3ResetAllSchemasOfConnection(sqlite3*);\nSQLITE_PRIVATE void sqlite3ResetOneSchema(sqlite3*,int);\nSQLITE_PRIVATE void sqlite3CollapseDatabaseArray(sqlite3*);\nSQLITE_PRIVATE void sqlite3CommitInternalChanges(sqlite3*);\nSQLITE_PRIVATE void sqlite3DeleteColumnNames(sqlite3*,Table*);\nSQLITE_PRIVATE int sqlite3ColumnsFromExprList(Parse*,ExprList*,i16*,Column**);\nSQLITE_PRIVATE void sqlite3SelectAddColumnTypeAndCollation(Parse*,Table*,Select*);\nSQLITE_PRIVATE Table *sqlite3ResultSetOfSelect(Parse*,Select*);\nSQLITE_PRIVATE void sqlite3OpenMasterTable(Parse *, int);\nSQLITE_PRIVATE Index *sqlite3PrimaryKeyIndex(Table*);\nSQLITE_PRIVATE i16 sqlite3ColumnOfIndex(Index*, i16);\nSQLITE_PRIVATE void sqlite3StartTable(Parse*,Token*,Token*,int,int,int,int);\n#if SQLITE_ENABLE_HIDDEN_COLUMNS\nSQLITE_PRIVATE   void sqlite3ColumnPropertiesFromName(Table*, Column*);\n#else\n# define sqlite3ColumnPropertiesFromName(T,C) /* no-op */\n#endif\nSQLITE_PRIVATE void sqlite3AddColumn(Parse*,Token*,Token*);\nSQLITE_PRIVATE void sqlite3AddNotNull(Parse*, int);\nSQLITE_PRIVATE void sqlite3AddPrimaryKey(Parse*, ExprList*, int, int, int);\nSQLITE_PRIVATE void sqlite3AddCheckConstraint(Parse*, Expr*);\nSQLITE_PRIVATE void sqlite3AddDefaultValue(Parse*,Expr*,const char*,const char*);\nSQLITE_PRIVATE void sqlite3AddCollateType(Parse*, Token*);\nSQLITE_PRIVATE void sqlite3EndTable(Parse*,Token*,Token*,u8,Select*);\nSQLITE_PRIVATE int sqlite3ParseUri(const char*,const char*,unsigned int*,\n                    sqlite3_vfs**,char**,char **);\nSQLITE_PRIVATE Btree *sqlite3DbNameToBtree(sqlite3*,const char*);\n\n#ifdef SQLITE_UNTESTABLE\n# define sqlite3FaultSim(X) SQLITE_OK\n#else\nSQLITE_PRIVATE   int sqlite3FaultSim(int);\n#endif\n\nSQLITE_PRIVATE Bitvec *sqlite3BitvecCreate(u32);\nSQLITE_PRIVATE int sqlite3BitvecTest(Bitvec*, u32);\nSQLITE_PRIVATE int sqlite3BitvecTestNotNull(Bitvec*, u32);\nSQLITE_PRIVATE int sqlite3BitvecSet(Bitvec*, u32);\nSQLITE_PRIVATE void sqlite3BitvecClear(Bitvec*, u32, void*);\nSQLITE_PRIVATE void sqlite3BitvecDestroy(Bitvec*);\nSQLITE_PRIVATE u32 sqlite3BitvecSize(Bitvec*);\n#ifndef SQLITE_UNTESTABLE\nSQLITE_PRIVATE int sqlite3BitvecBuiltinTest(int,int*);\n#endif\n\nSQLITE_PRIVATE RowSet *sqlite3RowSetInit(sqlite3*, void*, unsigned int);\nSQLITE_PRIVATE void sqlite3RowSetClear(RowSet*);\nSQLITE_PRIVATE void sqlite3RowSetInsert(RowSet*, i64);\nSQLITE_PRIVATE int sqlite3RowSetTest(RowSet*, int iBatch, i64);\nSQLITE_PRIVATE int sqlite3RowSetNext(RowSet*, i64*);\n\nSQLITE_PRIVATE void sqlite3CreateView(Parse*,Token*,Token*,Token*,ExprList*,Select*,int,int);\n\n#if !defined(SQLITE_OMIT_VIEW) || !defined(SQLITE_OMIT_VIRTUALTABLE)\nSQLITE_PRIVATE   int sqlite3ViewGetColumnNames(Parse*,Table*);\n#else\n# define sqlite3ViewGetColumnNames(A,B) 0\n#endif\n\n#if SQLITE_MAX_ATTACHED>30\nSQLITE_PRIVATE   int sqlite3DbMaskAllZero(yDbMask);\n#endif\nSQLITE_PRIVATE void sqlite3DropTable(Parse*, SrcList*, int, int);\nSQLITE_PRIVATE void sqlite3CodeDropTable(Parse*, Table*, int, int);\nSQLITE_PRIVATE void sqlite3DeleteTable(sqlite3*, Table*);\n#ifndef SQLITE_OMIT_AUTOINCREMENT\nSQLITE_PRIVATE   void sqlite3AutoincrementBegin(Parse *pParse);\nSQLITE_PRIVATE   void sqlite3AutoincrementEnd(Parse *pParse);\n#else\n# define sqlite3AutoincrementBegin(X)\n# define sqlite3AutoincrementEnd(X)\n#endif\nSQLITE_PRIVATE void sqlite3Insert(Parse*, SrcList*, Select*, IdList*, int);\nSQLITE_PRIVATE void *sqlite3ArrayAllocate(sqlite3*,void*,int,int*,int*);\nSQLITE_PRIVATE IdList *sqlite3IdListAppend(sqlite3*, IdList*, Token*);\nSQLITE_PRIVATE int sqlite3IdListIndex(IdList*,const char*);\nSQLITE_PRIVATE SrcList *sqlite3SrcListEnlarge(sqlite3*, SrcList*, int, int);\nSQLITE_PRIVATE SrcList *sqlite3SrcListAppend(sqlite3*, SrcList*, Token*, Token*);\nSQLITE_PRIVATE SrcList *sqlite3SrcListAppendFromTerm(Parse*, SrcList*, Token*, Token*,\n                                      Token*, Select*, Expr*, IdList*);\nSQLITE_PRIVATE void sqlite3SrcListIndexedBy(Parse *, SrcList *, Token *);\nSQLITE_PRIVATE void sqlite3SrcListFuncArgs(Parse*, SrcList*, ExprList*);\nSQLITE_PRIVATE int sqlite3IndexedByLookup(Parse *, struct SrcList_item *);\nSQLITE_PRIVATE void sqlite3SrcListShiftJoinType(SrcList*);\nSQLITE_PRIVATE void sqlite3SrcListAssignCursors(Parse*, SrcList*);\nSQLITE_PRIVATE void sqlite3IdListDelete(sqlite3*, IdList*);\nSQLITE_PRIVATE void sqlite3SrcListDelete(sqlite3*, SrcList*);\nSQLITE_PRIVATE Index *sqlite3AllocateIndexObject(sqlite3*,i16,int,char**);\nSQLITE_PRIVATE void sqlite3CreateIndex(Parse*,Token*,Token*,SrcList*,ExprList*,int,Token*,\n                          Expr*, int, int, u8);\nSQLITE_PRIVATE void sqlite3DropIndex(Parse*, SrcList*, int);\nSQLITE_PRIVATE int sqlite3Select(Parse*, Select*, SelectDest*);\nSQLITE_PRIVATE Select *sqlite3SelectNew(Parse*,ExprList*,SrcList*,Expr*,ExprList*,\n                         Expr*,ExprList*,u32,Expr*);\nSQLITE_PRIVATE void sqlite3SelectDelete(sqlite3*, Select*);\nSQLITE_PRIVATE Table *sqlite3SrcListLookup(Parse*, SrcList*);\nSQLITE_PRIVATE int sqlite3IsReadOnly(Parse*, Table*, int);\nSQLITE_PRIVATE void sqlite3OpenTable(Parse*, int iCur, int iDb, Table*, int);\n#if defined(SQLITE_ENABLE_UPDATE_DELETE_LIMIT) && !defined(SQLITE_OMIT_SUBQUERY)\nSQLITE_PRIVATE Expr *sqlite3LimitWhere(Parse*,SrcList*,Expr*,ExprList*,Expr*,char*);\n#endif\nSQLITE_PRIVATE void sqlite3DeleteFrom(Parse*, SrcList*, Expr*, ExprList*, Expr*);\nSQLITE_PRIVATE void sqlite3Update(Parse*, SrcList*, ExprList*,Expr*,int,ExprList*,Expr*);\nSQLITE_PRIVATE WhereInfo *sqlite3WhereBegin(Parse*,SrcList*,Expr*,ExprList*,ExprList*,u16,int);\nSQLITE_PRIVATE void sqlite3WhereEnd(WhereInfo*);\nSQLITE_PRIVATE LogEst sqlite3WhereOutputRowCount(WhereInfo*);\nSQLITE_PRIVATE int sqlite3WhereIsDistinct(WhereInfo*);\nSQLITE_PRIVATE int sqlite3WhereIsOrdered(WhereInfo*);\nSQLITE_PRIVATE int sqlite3WhereOrderedInnerLoop(WhereInfo*);\nSQLITE_PRIVATE int sqlite3WhereIsSorted(WhereInfo*);\nSQLITE_PRIVATE int sqlite3WhereContinueLabel(WhereInfo*);\nSQLITE_PRIVATE int sqlite3WhereBreakLabel(WhereInfo*);\nSQLITE_PRIVATE int sqlite3WhereOkOnePass(WhereInfo*, int*);\n#define ONEPASS_OFF      0        /* Use of ONEPASS not allowed */\n#define ONEPASS_SINGLE   1        /* ONEPASS valid for a single row update */\n#define ONEPASS_MULTI    2        /* ONEPASS is valid for multiple rows */\nSQLITE_PRIVATE void sqlite3ExprCodeLoadIndexColumn(Parse*, Index*, int, int, int);\nSQLITE_PRIVATE int sqlite3ExprCodeGetColumn(Parse*, Table*, int, int, int, u8);\nSQLITE_PRIVATE void sqlite3ExprCodeGetColumnToReg(Parse*, Table*, int, int, int);\nSQLITE_PRIVATE void sqlite3ExprCodeGetColumnOfTable(Vdbe*, Table*, int, int, int);\nSQLITE_PRIVATE void sqlite3ExprCodeMove(Parse*, int, int, int);\nSQLITE_PRIVATE void sqlite3ExprCacheStore(Parse*, int, int, int);\nSQLITE_PRIVATE void sqlite3ExprCachePush(Parse*);\nSQLITE_PRIVATE void sqlite3ExprCachePop(Parse*);\nSQLITE_PRIVATE void sqlite3ExprCacheRemove(Parse*, int, int);\nSQLITE_PRIVATE void sqlite3ExprCacheClear(Parse*);\nSQLITE_PRIVATE void sqlite3ExprCacheAffinityChange(Parse*, int, int);\nSQLITE_PRIVATE void sqlite3ExprCode(Parse*, Expr*, int);\nSQLITE_PRIVATE void sqlite3ExprCodeCopy(Parse*, Expr*, int);\nSQLITE_PRIVATE void sqlite3ExprCodeFactorable(Parse*, Expr*, int);\nSQLITE_PRIVATE int sqlite3ExprCodeAtInit(Parse*, Expr*, int);\nSQLITE_PRIVATE int sqlite3ExprCodeTemp(Parse*, Expr*, int*);\nSQLITE_PRIVATE int sqlite3ExprCodeTarget(Parse*, Expr*, int);\nSQLITE_PRIVATE void sqlite3ExprCodeAndCache(Parse*, Expr*, int);\nSQLITE_PRIVATE int sqlite3ExprCodeExprList(Parse*, ExprList*, int, int, u8);\n#define SQLITE_ECEL_DUP      0x01  /* Deep, not shallow copies */\n#define SQLITE_ECEL_FACTOR   0x02  /* Factor out constant terms */\n#define SQLITE_ECEL_REF      0x04  /* Use ExprList.u.x.iOrderByCol */\n#define SQLITE_ECEL_OMITREF  0x08  /* Omit if ExprList.u.x.iOrderByCol */\nSQLITE_PRIVATE void sqlite3ExprIfTrue(Parse*, Expr*, int, int);\nSQLITE_PRIVATE void sqlite3ExprIfFalse(Parse*, Expr*, int, int);\nSQLITE_PRIVATE void sqlite3ExprIfFalseDup(Parse*, Expr*, int, int);\nSQLITE_PRIVATE Table *sqlite3FindTable(sqlite3*,const char*, const char*);\n#define LOCATE_VIEW    0x01\n#define LOCATE_NOERR   0x02\nSQLITE_PRIVATE Table *sqlite3LocateTable(Parse*,u32 flags,const char*, const char*);\nSQLITE_PRIVATE Table *sqlite3LocateTableItem(Parse*,u32 flags,struct SrcList_item *);\nSQLITE_PRIVATE Index *sqlite3FindIndex(sqlite3*,const char*, const char*);\nSQLITE_PRIVATE void sqlite3UnlinkAndDeleteTable(sqlite3*,int,const char*);\nSQLITE_PRIVATE void sqlite3UnlinkAndDeleteIndex(sqlite3*,int,const char*);\nSQLITE_PRIVATE void sqlite3Vacuum(Parse*,Token*);\nSQLITE_PRIVATE int sqlite3RunVacuum(char**, sqlite3*, int);\nSQLITE_PRIVATE char *sqlite3NameFromToken(sqlite3*, Token*);\nSQLITE_PRIVATE int sqlite3ExprCompare(Parse*,Expr*, Expr*, int);\nSQLITE_PRIVATE int sqlite3ExprCompareSkip(Expr*, Expr*, int);\nSQLITE_PRIVATE int sqlite3ExprListCompare(ExprList*, ExprList*, int);\nSQLITE_PRIVATE int sqlite3ExprImpliesExpr(Parse*,Expr*, Expr*, int);\nSQLITE_PRIVATE void sqlite3ExprAnalyzeAggregates(NameContext*, Expr*);\nSQLITE_PRIVATE void sqlite3ExprAnalyzeAggList(NameContext*,ExprList*);\nSQLITE_PRIVATE int sqlite3ExprCoveredByIndex(Expr*, int iCur, Index *pIdx);\nSQLITE_PRIVATE int sqlite3FunctionUsesThisSrc(Expr*, SrcList*);\nSQLITE_PRIVATE Vdbe *sqlite3GetVdbe(Parse*);\n#ifndef SQLITE_UNTESTABLE\nSQLITE_PRIVATE void sqlite3PrngSaveState(void);\nSQLITE_PRIVATE void sqlite3PrngRestoreState(void);\n#endif\nSQLITE_PRIVATE void sqlite3RollbackAll(sqlite3*,int);\nSQLITE_PRIVATE void sqlite3CodeVerifySchema(Parse*, int);\nSQLITE_PRIVATE void sqlite3CodeVerifyNamedSchema(Parse*, const char *zDb);\nSQLITE_PRIVATE void sqlite3BeginTransaction(Parse*, int);\nSQLITE_PRIVATE void sqlite3EndTransaction(Parse*,int);\nSQLITE_PRIVATE void sqlite3Savepoint(Parse*, int, Token*);\nSQLITE_PRIVATE void sqlite3CloseSavepoints(sqlite3 *);\nSQLITE_PRIVATE void sqlite3LeaveMutexAndCloseZombie(sqlite3*);\nSQLITE_PRIVATE int sqlite3ExprIdToTrueFalse(Expr*);\nSQLITE_PRIVATE int sqlite3ExprTruthValue(const Expr*);\nSQLITE_PRIVATE int sqlite3ExprIsConstant(Expr*);\nSQLITE_PRIVATE int sqlite3ExprIsConstantNotJoin(Expr*);\nSQLITE_PRIVATE int sqlite3ExprIsConstantOrFunction(Expr*, u8);\nSQLITE_PRIVATE int sqlite3ExprIsConstantOrGroupBy(Parse*, Expr*, ExprList*);\nSQLITE_PRIVATE int sqlite3ExprIsTableConstant(Expr*,int);\n#ifdef SQLITE_ENABLE_CURSOR_HINTS\nSQLITE_PRIVATE int sqlite3ExprContainsSubquery(Expr*);\n#endif\nSQLITE_PRIVATE int sqlite3ExprIsInteger(Expr*, int*);\nSQLITE_PRIVATE int sqlite3ExprCanBeNull(const Expr*);\nSQLITE_PRIVATE int sqlite3ExprNeedsNoAffinityChange(const Expr*, char);\nSQLITE_PRIVATE int sqlite3IsRowid(const char*);\nSQLITE_PRIVATE void sqlite3GenerateRowDelete(\n    Parse*,Table*,Trigger*,int,int,int,i16,u8,u8,u8,int);\nSQLITE_PRIVATE void sqlite3GenerateRowIndexDelete(Parse*, Table*, int, int, int*, int);\nSQLITE_PRIVATE int sqlite3GenerateIndexKey(Parse*, Index*, int, int, int, int*,Index*,int);\nSQLITE_PRIVATE void sqlite3ResolvePartIdxLabel(Parse*,int);\nSQLITE_PRIVATE void sqlite3GenerateConstraintChecks(Parse*,Table*,int*,int,int,int,int,\n                                     u8,u8,int,int*,int*);\n#ifdef SQLITE_ENABLE_NULL_TRIM\nSQLITE_PRIVATE   void sqlite3SetMakeRecordP5(Vdbe*,Table*);\n#else\n# define sqlite3SetMakeRecordP5(A,B)\n#endif\nSQLITE_PRIVATE void sqlite3CompleteInsertion(Parse*,Table*,int,int,int,int*,int,int,int);\nSQLITE_PRIVATE int sqlite3OpenTableAndIndices(Parse*, Table*, int, u8, int, u8*, int*, int*);\nSQLITE_PRIVATE void sqlite3BeginWriteOperation(Parse*, int, int);\nSQLITE_PRIVATE void sqlite3MultiWrite(Parse*);\nSQLITE_PRIVATE void sqlite3MayAbort(Parse*);\nSQLITE_PRIVATE void sqlite3HaltConstraint(Parse*, int, int, char*, i8, u8);\nSQLITE_PRIVATE void sqlite3UniqueConstraint(Parse*, int, Index*);\nSQLITE_PRIVATE void sqlite3RowidConstraint(Parse*, int, Table*);\nSQLITE_PRIVATE Expr *sqlite3ExprDup(sqlite3*,Expr*,int);\nSQLITE_PRIVATE ExprList *sqlite3ExprListDup(sqlite3*,ExprList*,int);\nSQLITE_PRIVATE SrcList *sqlite3SrcListDup(sqlite3*,SrcList*,int);\nSQLITE_PRIVATE IdList *sqlite3IdListDup(sqlite3*,IdList*);\nSQLITE_PRIVATE Select *sqlite3SelectDup(sqlite3*,Select*,int);\n#if SELECTTRACE_ENABLED\nSQLITE_PRIVATE void sqlite3SelectSetName(Select*,const char*);\n#else\n# define sqlite3SelectSetName(A,B)\n#endif\nSQLITE_PRIVATE void sqlite3InsertBuiltinFuncs(FuncDef*,int);\nSQLITE_PRIVATE FuncDef *sqlite3FindFunction(sqlite3*,const char*,int,u8,u8);\nSQLITE_PRIVATE void sqlite3RegisterBuiltinFunctions(void);\nSQLITE_PRIVATE void sqlite3RegisterDateTimeFunctions(void);\nSQLITE_PRIVATE void sqlite3RegisterPerConnectionBuiltinFunctions(sqlite3*);\nSQLITE_PRIVATE int sqlite3SafetyCheckOk(sqlite3*);\nSQLITE_PRIVATE int sqlite3SafetyCheckSickOrOk(sqlite3*);\nSQLITE_PRIVATE void sqlite3ChangeCookie(Parse*, int);\n\n#if !defined(SQLITE_OMIT_VIEW) && !defined(SQLITE_OMIT_TRIGGER)\nSQLITE_PRIVATE void sqlite3MaterializeView(Parse*, Table*, Expr*, ExprList*,Expr*,int);\n#endif\n\n#ifndef SQLITE_OMIT_TRIGGER\nSQLITE_PRIVATE   void sqlite3BeginTrigger(Parse*, Token*,Token*,int,int,IdList*,SrcList*,\n                           Expr*,int, int);\nSQLITE_PRIVATE   void sqlite3FinishTrigger(Parse*, TriggerStep*, Token*);\nSQLITE_PRIVATE   void sqlite3DropTrigger(Parse*, SrcList*, int);\nSQLITE_PRIVATE   void sqlite3DropTriggerPtr(Parse*, Trigger*);\nSQLITE_PRIVATE   Trigger *sqlite3TriggersExist(Parse *, Table*, int, ExprList*, int *pMask);\nSQLITE_PRIVATE   Trigger *sqlite3TriggerList(Parse *, Table *);\nSQLITE_PRIVATE   void sqlite3CodeRowTrigger(Parse*, Trigger *, int, ExprList*, int, Table *,\n                            int, int, int);\nSQLITE_PRIVATE   void sqlite3CodeRowTriggerDirect(Parse *, Trigger *, Table *, int, int, int);\n  void sqliteViewTriggers(Parse*, Table*, Expr*, int, ExprList*);\nSQLITE_PRIVATE   void sqlite3DeleteTriggerStep(sqlite3*, TriggerStep*);\nSQLITE_PRIVATE   TriggerStep *sqlite3TriggerSelectStep(sqlite3*,Select*,\n                                        const char*,const char*);\nSQLITE_PRIVATE   TriggerStep *sqlite3TriggerInsertStep(sqlite3*,Token*, IdList*,\n                                        Select*,u8,const char*,const char*);\nSQLITE_PRIVATE   TriggerStep *sqlite3TriggerUpdateStep(sqlite3*,Token*,ExprList*, Expr*, u8,\n                                        const char*,const char*);\nSQLITE_PRIVATE   TriggerStep *sqlite3TriggerDeleteStep(sqlite3*,Token*, Expr*,\n                                        const char*,const char*);\nSQLITE_PRIVATE   void sqlite3DeleteTrigger(sqlite3*, Trigger*);\nSQLITE_PRIVATE   void sqlite3UnlinkAndDeleteTrigger(sqlite3*,int,const char*);\nSQLITE_PRIVATE   u32 sqlite3TriggerColmask(Parse*,Trigger*,ExprList*,int,int,Table*,int);\n# define sqlite3ParseToplevel(p) ((p)->pToplevel ? (p)->pToplevel : (p))\n# define sqlite3IsToplevel(p) ((p)->pToplevel==0)\n#else\n# define sqlite3TriggersExist(B,C,D,E,F) 0\n# define sqlite3DeleteTrigger(A,B)\n# define sqlite3DropTriggerPtr(A,B)\n# define sqlite3UnlinkAndDeleteTrigger(A,B,C)\n# define sqlite3CodeRowTrigger(A,B,C,D,E,F,G,H,I)\n# define sqlite3CodeRowTriggerDirect(A,B,C,D,E,F)\n# define sqlite3TriggerList(X, Y) 0\n# define sqlite3ParseToplevel(p) p\n# define sqlite3IsToplevel(p) 1\n# define sqlite3TriggerColmask(A,B,C,D,E,F,G) 0\n#endif\n\nSQLITE_PRIVATE int sqlite3JoinType(Parse*, Token*, Token*, Token*);\nSQLITE_PRIVATE void sqlite3CreateForeignKey(Parse*, ExprList*, Token*, ExprList*, int);\nSQLITE_PRIVATE void sqlite3DeferForeignKey(Parse*, int);\n#ifndef SQLITE_OMIT_AUTHORIZATION\nSQLITE_PRIVATE   void sqlite3AuthRead(Parse*,Expr*,Schema*,SrcList*);\nSQLITE_PRIVATE   int sqlite3AuthCheck(Parse*,int, const char*, const char*, const char*);\nSQLITE_PRIVATE   void sqlite3AuthContextPush(Parse*, AuthContext*, const char*);\nSQLITE_PRIVATE   void sqlite3AuthContextPop(AuthContext*);\nSQLITE_PRIVATE   int sqlite3AuthReadCol(Parse*, const char *, const char *, int);\n#else\n# define sqlite3AuthRead(a,b,c,d)\n# define sqlite3AuthCheck(a,b,c,d,e)    SQLITE_OK\n# define sqlite3AuthContextPush(a,b,c)\n# define sqlite3AuthContextPop(a)  ((void)(a))\n#endif\nSQLITE_PRIVATE void sqlite3Attach(Parse*, Expr*, Expr*, Expr*);\nSQLITE_PRIVATE void sqlite3Detach(Parse*, Expr*);\nSQLITE_PRIVATE void sqlite3FixInit(DbFixer*, Parse*, int, const char*, const Token*);\nSQLITE_PRIVATE int sqlite3FixSrcList(DbFixer*, SrcList*);\nSQLITE_PRIVATE int sqlite3FixSelect(DbFixer*, Select*);\nSQLITE_PRIVATE int sqlite3FixExpr(DbFixer*, Expr*);\nSQLITE_PRIVATE int sqlite3FixExprList(DbFixer*, ExprList*);\nSQLITE_PRIVATE int sqlite3FixTriggerStep(DbFixer*, TriggerStep*);\nSQLITE_PRIVATE int sqlite3AtoF(const char *z, double*, int, u8);\nSQLITE_PRIVATE int sqlite3GetInt32(const char *, int*);\nSQLITE_PRIVATE int sqlite3Atoi(const char*);\n#ifndef SQLITE_OMIT_UTF16\nSQLITE_PRIVATE int sqlite3Utf16ByteLen(const void *pData, int nChar);\n#endif\nSQLITE_PRIVATE int sqlite3Utf8CharLen(const char *pData, int nByte);\nSQLITE_PRIVATE u32 sqlite3Utf8Read(const u8**);\nSQLITE_PRIVATE LogEst sqlite3LogEst(u64);\nSQLITE_PRIVATE LogEst sqlite3LogEstAdd(LogEst,LogEst);\n#ifndef SQLITE_OMIT_VIRTUALTABLE\nSQLITE_PRIVATE LogEst sqlite3LogEstFromDouble(double);\n#endif\n#if defined(SQLITE_ENABLE_STMT_SCANSTATUS) || \\\n    defined(SQLITE_ENABLE_STAT3_OR_STAT4) || \\\n    defined(SQLITE_EXPLAIN_ESTIMATED_ROWS)\nSQLITE_PRIVATE u64 sqlite3LogEstToInt(LogEst);\n#endif\nSQLITE_PRIVATE VList *sqlite3VListAdd(sqlite3*,VList*,const char*,int,int);\nSQLITE_PRIVATE const char *sqlite3VListNumToName(VList*,int);\nSQLITE_PRIVATE int sqlite3VListNameToNum(VList*,const char*,int);\n\n/*\n** Routines to read and write variable-length integers.  These used to\n** be defined locally, but now we use the varint routines in the util.c\n** file.\n*/\nSQLITE_PRIVATE int sqlite3PutVarint(unsigned char*, u64);\nSQLITE_PRIVATE u8 sqlite3GetVarint(const unsigned char *, u64 *);\nSQLITE_PRIVATE u8 sqlite3GetVarint32(const unsigned char *, u32 *);\nSQLITE_PRIVATE int sqlite3VarintLen(u64 v);\n\n/*\n** The common case is for a varint to be a single byte.  They following\n** macros handle the common case without a procedure call, but then call\n** the procedure for larger varints.\n*/\n#define getVarint32(A,B)  \\\n  (u8)((*(A)<(u8)0x80)?((B)=(u32)*(A)),1:sqlite3GetVarint32((A),(u32 *)&(B)))\n#define putVarint32(A,B)  \\\n  (u8)(((u32)(B)<(u32)0x80)?(*(A)=(unsigned char)(B)),1:\\\n  sqlite3PutVarint((A),(B)))\n#define getVarint    sqlite3GetVarint\n#define putVarint    sqlite3PutVarint\n\n\nSQLITE_PRIVATE const char *sqlite3IndexAffinityStr(sqlite3*, Index*);\nSQLITE_PRIVATE void sqlite3TableAffinity(Vdbe*, Table*, int);\nSQLITE_PRIVATE char sqlite3CompareAffinity(Expr *pExpr, char aff2);\nSQLITE_PRIVATE int sqlite3IndexAffinityOk(Expr *pExpr, char idx_affinity);\nSQLITE_PRIVATE char sqlite3TableColumnAffinity(Table*,int);\nSQLITE_PRIVATE char sqlite3ExprAffinity(Expr *pExpr);\nSQLITE_PRIVATE int sqlite3Atoi64(const char*, i64*, int, u8);\nSQLITE_PRIVATE int sqlite3DecOrHexToI64(const char*, i64*);\nSQLITE_PRIVATE void sqlite3ErrorWithMsg(sqlite3*, int, const char*,...);\nSQLITE_PRIVATE void sqlite3Error(sqlite3*,int);\nSQLITE_PRIVATE void sqlite3SystemError(sqlite3*,int);\nSQLITE_PRIVATE void *sqlite3HexToBlob(sqlite3*, const char *z, int n);\nSQLITE_PRIVATE u8 sqlite3HexToInt(int h);\nSQLITE_PRIVATE int sqlite3TwoPartName(Parse *, Token *, Token *, Token **);\n\n#if defined(SQLITE_NEED_ERR_NAME)\nSQLITE_PRIVATE const char *sqlite3ErrName(int);\n#endif\n\nSQLITE_PRIVATE const char *sqlite3ErrStr(int);\nSQLITE_PRIVATE int sqlite3ReadSchema(Parse *pParse);\nSQLITE_PRIVATE CollSeq *sqlite3FindCollSeq(sqlite3*,u8 enc, const char*,int);\nSQLITE_PRIVATE CollSeq *sqlite3LocateCollSeq(Parse *pParse, const char*zName);\nSQLITE_PRIVATE CollSeq *sqlite3ExprCollSeq(Parse *pParse, Expr *pExpr);\nSQLITE_PRIVATE CollSeq *sqlite3ExprNNCollSeq(Parse *pParse, Expr *pExpr);\nSQLITE_PRIVATE int sqlite3ExprCollSeqMatch(Parse*,Expr*,Expr*);\nSQLITE_PRIVATE Expr *sqlite3ExprAddCollateToken(Parse *pParse, Expr*, const Token*, int);\nSQLITE_PRIVATE Expr *sqlite3ExprAddCollateString(Parse*,Expr*,const char*);\nSQLITE_PRIVATE Expr *sqlite3ExprSkipCollate(Expr*);\nSQLITE_PRIVATE int sqlite3CheckCollSeq(Parse *, CollSeq *);\nSQLITE_PRIVATE int sqlite3CheckObjectName(Parse *, const char *);\nSQLITE_PRIVATE void sqlite3VdbeSetChanges(sqlite3 *, int);\nSQLITE_PRIVATE int sqlite3AddInt64(i64*,i64);\nSQLITE_PRIVATE int sqlite3SubInt64(i64*,i64);\nSQLITE_PRIVATE int sqlite3MulInt64(i64*,i64);\nSQLITE_PRIVATE int sqlite3AbsInt32(int);\n#ifdef SQLITE_ENABLE_8_3_NAMES\nSQLITE_PRIVATE void sqlite3FileSuffix3(const char*, char*);\n#else\n# define sqlite3FileSuffix3(X,Y)\n#endif\nSQLITE_PRIVATE u8 sqlite3GetBoolean(const char *z,u8);\n\nSQLITE_PRIVATE const void *sqlite3ValueText(sqlite3_value*, u8);\nSQLITE_PRIVATE int sqlite3ValueBytes(sqlite3_value*, u8);\nSQLITE_PRIVATE void sqlite3ValueSetStr(sqlite3_value*, int, const void *,u8,\n                        void(*)(void*));\nSQLITE_PRIVATE void sqlite3ValueSetNull(sqlite3_value*);\nSQLITE_PRIVATE void sqlite3ValueFree(sqlite3_value*);\nSQLITE_PRIVATE sqlite3_value *sqlite3ValueNew(sqlite3 *);\n#ifndef SQLITE_OMIT_UTF16\nSQLITE_PRIVATE char *sqlite3Utf16to8(sqlite3 *, const void*, int, u8);\n#endif\nSQLITE_PRIVATE int sqlite3ValueFromExpr(sqlite3 *, Expr *, u8, u8, sqlite3_value **);\nSQLITE_PRIVATE void sqlite3ValueApplyAffinity(sqlite3_value *, u8, u8);\n#ifndef SQLITE_AMALGAMATION\nSQLITE_PRIVATE const unsigned char sqlite3OpcodeProperty[];\nSQLITE_PRIVATE const char sqlite3StrBINARY[];\nSQLITE_PRIVATE const unsigned char sqlite3UpperToLower[];\nSQLITE_PRIVATE const unsigned char sqlite3CtypeMap[];\nSQLITE_PRIVATE const Token sqlite3IntTokens[];\nSQLITE_PRIVATE SQLITE_WSD struct Sqlite3Config sqlite3Config;\nSQLITE_PRIVATE FuncDefHash sqlite3BuiltinFunctions;\n#ifndef SQLITE_OMIT_WSD\nSQLITE_PRIVATE int sqlite3PendingByte;\n#endif\n#endif\n#ifdef VDBE_PROFILE\nSQLITE_PRIVATE sqlite3_uint64 sqlite3NProfileCnt;\n#endif\nSQLITE_PRIVATE void sqlite3RootPageMoved(sqlite3*, int, int, int);\nSQLITE_PRIVATE void sqlite3Reindex(Parse*, Token*, Token*);\nSQLITE_PRIVATE void sqlite3AlterFunctions(void);\nSQLITE_PRIVATE void sqlite3AlterRenameTable(Parse*, SrcList*, Token*);\nSQLITE_PRIVATE int sqlite3GetToken(const unsigned char *, int *);\nSQLITE_PRIVATE void sqlite3NestedParse(Parse*, const char*, ...);\nSQLITE_PRIVATE void sqlite3ExpirePreparedStatements(sqlite3*);\nSQLITE_PRIVATE int sqlite3CodeSubselect(Parse*, Expr *, int, int);\nSQLITE_PRIVATE void sqlite3SelectPrep(Parse*, Select*, NameContext*);\nSQLITE_PRIVATE void sqlite3SelectWrongNumTermsError(Parse *pParse, Select *p);\nSQLITE_PRIVATE int sqlite3MatchSpanName(const char*, const char*, const char*, const char*);\nSQLITE_PRIVATE int sqlite3ResolveExprNames(NameContext*, Expr*);\nSQLITE_PRIVATE int sqlite3ResolveExprListNames(NameContext*, ExprList*);\nSQLITE_PRIVATE void sqlite3ResolveSelectNames(Parse*, Select*, NameContext*);\nSQLITE_PRIVATE void sqlite3ResolveSelfReference(Parse*,Table*,int,Expr*,ExprList*);\nSQLITE_PRIVATE int sqlite3ResolveOrderGroupBy(Parse*, Select*, ExprList*, const char*);\nSQLITE_PRIVATE void sqlite3ColumnDefault(Vdbe *, Table *, int, int);\nSQLITE_PRIVATE void sqlite3AlterFinishAddColumn(Parse *, Token *);\nSQLITE_PRIVATE void sqlite3AlterBeginAddColumn(Parse *, SrcList *);\nSQLITE_PRIVATE CollSeq *sqlite3GetCollSeq(Parse*, u8, CollSeq *, const char*);\nSQLITE_PRIVATE char sqlite3AffinityType(const char*, u8*);\nSQLITE_PRIVATE void sqlite3Analyze(Parse*, Token*, Token*);\nSQLITE_PRIVATE int sqlite3InvokeBusyHandler(BusyHandler*);\nSQLITE_PRIVATE int sqlite3FindDb(sqlite3*, Token*);\nSQLITE_PRIVATE int sqlite3FindDbName(sqlite3 *, const char *);\nSQLITE_PRIVATE int sqlite3AnalysisLoad(sqlite3*,int iDB);\nSQLITE_PRIVATE void sqlite3DeleteIndexSamples(sqlite3*,Index*);\nSQLITE_PRIVATE void sqlite3DefaultRowEst(Index*);\nSQLITE_PRIVATE void sqlite3RegisterLikeFunctions(sqlite3*, int);\nSQLITE_PRIVATE int sqlite3IsLikeFunction(sqlite3*,Expr*,int*,char*);\nSQLITE_PRIVATE void sqlite3SchemaClear(void *);\nSQLITE_PRIVATE Schema *sqlite3SchemaGet(sqlite3 *, Btree *);\nSQLITE_PRIVATE int sqlite3SchemaToIndex(sqlite3 *db, Schema *);\nSQLITE_PRIVATE KeyInfo *sqlite3KeyInfoAlloc(sqlite3*,int,int);\nSQLITE_PRIVATE void sqlite3KeyInfoUnref(KeyInfo*);\nSQLITE_PRIVATE KeyInfo *sqlite3KeyInfoRef(KeyInfo*);\nSQLITE_PRIVATE KeyInfo *sqlite3KeyInfoOfIndex(Parse*, Index*);\n#ifdef SQLITE_DEBUG\nSQLITE_PRIVATE int sqlite3KeyInfoIsWriteable(KeyInfo*);\n#endif\nSQLITE_PRIVATE int sqlite3CreateFunc(sqlite3 *, const char *, int, int, void *,\n  void (*)(sqlite3_context*,int,sqlite3_value **),\n  void (*)(sqlite3_context*,int,sqlite3_value **), void (*)(sqlite3_context*),\n  FuncDestructor *pDestructor\n);\nSQLITE_PRIVATE void sqlite3OomFault(sqlite3*);\nSQLITE_PRIVATE void sqlite3OomClear(sqlite3*);\nSQLITE_PRIVATE int sqlite3ApiExit(sqlite3 *db, int);\nSQLITE_PRIVATE int sqlite3OpenTempDatabase(Parse *);\n\nSQLITE_PRIVATE void sqlite3StrAccumInit(StrAccum*, sqlite3*, char*, int, int);\nSQLITE_PRIVATE void sqlite3StrAccumAppend(StrAccum*,const char*,int);\nSQLITE_PRIVATE void sqlite3StrAccumAppendAll(StrAccum*,const char*);\nSQLITE_PRIVATE void sqlite3AppendChar(StrAccum*,int,char);\nSQLITE_PRIVATE char *sqlite3StrAccumFinish(StrAccum*);\nSQLITE_PRIVATE void sqlite3StrAccumReset(StrAccum*);\nSQLITE_PRIVATE void sqlite3SelectDestInit(SelectDest*,int,int);\nSQLITE_PRIVATE Expr *sqlite3CreateColumnExpr(sqlite3 *, SrcList *, int, int);\n\nSQLITE_PRIVATE void sqlite3BackupRestart(sqlite3_backup *);\nSQLITE_PRIVATE void sqlite3BackupUpdate(sqlite3_backup *, Pgno, const u8 *);\n\n#ifndef SQLITE_OMIT_SUBQUERY\nSQLITE_PRIVATE int sqlite3ExprCheckIN(Parse*, Expr*);\n#else\n# define sqlite3ExprCheckIN(x,y) SQLITE_OK\n#endif\n\n#ifdef SQLITE_ENABLE_STAT3_OR_STAT4\nSQLITE_PRIVATE void sqlite3AnalyzeFunctions(void);\nSQLITE_PRIVATE int sqlite3Stat4ProbeSetValue(\n    Parse*,Index*,UnpackedRecord**,Expr*,int,int,int*);\nSQLITE_PRIVATE int sqlite3Stat4ValueFromExpr(Parse*, Expr*, u8, sqlite3_value**);\nSQLITE_PRIVATE void sqlite3Stat4ProbeFree(UnpackedRecord*);\nSQLITE_PRIVATE int sqlite3Stat4Column(sqlite3*, const void*, int, int, sqlite3_value**);\nSQLITE_PRIVATE char sqlite3IndexColumnAffinity(sqlite3*, Index*, int);\n#endif\n\n/*\n** The interface to the LEMON-generated parser\n*/\n#ifndef SQLITE_AMALGAMATION\nSQLITE_PRIVATE   void *sqlite3ParserAlloc(void*(*)(u64));\nSQLITE_PRIVATE   void sqlite3ParserFree(void*, void(*)(void*));\n#endif\nSQLITE_PRIVATE void sqlite3Parser(void*, int, Token, Parse*);\n#ifdef YYTRACKMAXSTACKDEPTH\nSQLITE_PRIVATE   int sqlite3ParserStackPeak(void*);\n#endif\n\nSQLITE_PRIVATE void sqlite3AutoLoadExtensions(sqlite3*);\n#ifndef SQLITE_OMIT_LOAD_EXTENSION\nSQLITE_PRIVATE   void sqlite3CloseExtensions(sqlite3*);\n#else\n# define sqlite3CloseExtensions(X)\n#endif\n\n#ifndef SQLITE_OMIT_SHARED_CACHE\nSQLITE_PRIVATE   void sqlite3TableLock(Parse *, int, int, u8, const char *);\n#else\n  #define sqlite3TableLock(v,w,x,y,z)\n#endif\n\n#ifdef SQLITE_TEST\nSQLITE_PRIVATE   int sqlite3Utf8To8(unsigned char*);\n#endif\n\n#ifdef SQLITE_OMIT_VIRTUALTABLE\n#  define sqlite3VtabClear(Y)\n#  define sqlite3VtabSync(X,Y) SQLITE_OK\n#  define sqlite3VtabRollback(X)\n#  define sqlite3VtabCommit(X)\n#  define sqlite3VtabInSync(db) 0\n#  define sqlite3VtabLock(X)\n#  define sqlite3VtabUnlock(X)\n#  define sqlite3VtabUnlockList(X)\n#  define sqlite3VtabSavepoint(X, Y, Z) SQLITE_OK\n#  define sqlite3GetVTable(X,Y)  ((VTable*)0)\n#else\nSQLITE_PRIVATE    void sqlite3VtabClear(sqlite3 *db, Table*);\nSQLITE_PRIVATE    void sqlite3VtabDisconnect(sqlite3 *db, Table *p);\nSQLITE_PRIVATE    int sqlite3VtabSync(sqlite3 *db, Vdbe*);\nSQLITE_PRIVATE    int sqlite3VtabRollback(sqlite3 *db);\nSQLITE_PRIVATE    int sqlite3VtabCommit(sqlite3 *db);\nSQLITE_PRIVATE    void sqlite3VtabLock(VTable *);\nSQLITE_PRIVATE    void sqlite3VtabUnlock(VTable *);\nSQLITE_PRIVATE    void sqlite3VtabUnlockList(sqlite3*);\nSQLITE_PRIVATE    int sqlite3VtabSavepoint(sqlite3 *, int, int);\nSQLITE_PRIVATE    void sqlite3VtabImportErrmsg(Vdbe*, sqlite3_vtab*);\nSQLITE_PRIVATE    VTable *sqlite3GetVTable(sqlite3*, Table*);\nSQLITE_PRIVATE    Module *sqlite3VtabCreateModule(\n     sqlite3*,\n     const char*,\n     const sqlite3_module*,\n     void*,\n     void(*)(void*)\n   );\n#  define sqlite3VtabInSync(db) ((db)->nVTrans>0 && (db)->aVTrans==0)\n#endif\nSQLITE_PRIVATE int sqlite3VtabEponymousTableInit(Parse*,Module*);\nSQLITE_PRIVATE void sqlite3VtabEponymousTableClear(sqlite3*,Module*);\nSQLITE_PRIVATE void sqlite3VtabMakeWritable(Parse*,Table*);\nSQLITE_PRIVATE void sqlite3VtabBeginParse(Parse*, Token*, Token*, Token*, int);\nSQLITE_PRIVATE void sqlite3VtabFinishParse(Parse*, Token*);\nSQLITE_PRIVATE void sqlite3VtabArgInit(Parse*);\nSQLITE_PRIVATE void sqlite3VtabArgExtend(Parse*, Token*);\nSQLITE_PRIVATE int sqlite3VtabCallCreate(sqlite3*, int, const char *, char **);\nSQLITE_PRIVATE int sqlite3VtabCallConnect(Parse*, Table*);\nSQLITE_PRIVATE int sqlite3VtabCallDestroy(sqlite3*, int, const char *);\nSQLITE_PRIVATE int sqlite3VtabBegin(sqlite3 *, VTable *);\nSQLITE_PRIVATE FuncDef *sqlite3VtabOverloadFunction(sqlite3 *,FuncDef*, int nArg, Expr*);\nSQLITE_PRIVATE void sqlite3InvalidFunction(sqlite3_context*,int,sqlite3_value**);\nSQLITE_PRIVATE sqlite3_int64 sqlite3StmtCurrentTime(sqlite3_context*);\nSQLITE_PRIVATE int sqlite3VdbeParameterIndex(Vdbe*, const char*, int);\nSQLITE_PRIVATE int sqlite3TransferBindings(sqlite3_stmt *, sqlite3_stmt *);\nSQLITE_PRIVATE void sqlite3ParserReset(Parse*);\nSQLITE_PRIVATE int sqlite3Reprepare(Vdbe*);\nSQLITE_PRIVATE void sqlite3ExprListCheckLength(Parse*, ExprList*, const char*);\nSQLITE_PRIVATE CollSeq *sqlite3BinaryCompareCollSeq(Parse *, Expr *, Expr *);\nSQLITE_PRIVATE int sqlite3TempInMemory(const sqlite3*);\nSQLITE_PRIVATE const char *sqlite3JournalModename(int);\n#ifndef SQLITE_OMIT_WAL\nSQLITE_PRIVATE   int sqlite3Checkpoint(sqlite3*, int, int, int*, int*);\nSQLITE_PRIVATE   int sqlite3WalDefaultHook(void*,sqlite3*,const char*,int);\n#endif\n#ifndef SQLITE_OMIT_CTE\nSQLITE_PRIVATE   With *sqlite3WithAdd(Parse*,With*,Token*,ExprList*,Select*);\nSQLITE_PRIVATE   void sqlite3WithDelete(sqlite3*,With*);\nSQLITE_PRIVATE   void sqlite3WithPush(Parse*, With*, u8);\n#else\n#define sqlite3WithPush(x,y,z)\n#define sqlite3WithDelete(x,y)\n#endif\n\n/* Declarations for functions in fkey.c. All of these are replaced by\n** no-op macros if OMIT_FOREIGN_KEY is defined. In this case no foreign\n** key functionality is available. If OMIT_TRIGGER is defined but\n** OMIT_FOREIGN_KEY is not, only some of the functions are no-oped. In\n** this case foreign keys are parsed, but no other functionality is\n** provided (enforcement of FK constraints requires the triggers sub-system).\n*/\n#if !defined(SQLITE_OMIT_FOREIGN_KEY) && !defined(SQLITE_OMIT_TRIGGER)\nSQLITE_PRIVATE   void sqlite3FkCheck(Parse*, Table*, int, int, int*, int);\nSQLITE_PRIVATE   void sqlite3FkDropTable(Parse*, SrcList *, Table*);\nSQLITE_PRIVATE   void sqlite3FkActions(Parse*, Table*, ExprList*, int, int*, int);\nSQLITE_PRIVATE   int sqlite3FkRequired(Parse*, Table*, int*, int);\nSQLITE_PRIVATE   u32 sqlite3FkOldmask(Parse*, Table*);\nSQLITE_PRIVATE   FKey *sqlite3FkReferences(Table *);\n#else\n  #define sqlite3FkActions(a,b,c,d,e,f)\n  #define sqlite3FkCheck(a,b,c,d,e,f)\n  #define sqlite3FkDropTable(a,b,c)\n  #define sqlite3FkOldmask(a,b)         0\n  #define sqlite3FkRequired(a,b,c,d)    0\n  #define sqlite3FkReferences(a)        0\n#endif\n#ifndef SQLITE_OMIT_FOREIGN_KEY\nSQLITE_PRIVATE   void sqlite3FkDelete(sqlite3 *, Table*);\nSQLITE_PRIVATE   int sqlite3FkLocateIndex(Parse*,Table*,FKey*,Index**,int**);\n#else\n  #define sqlite3FkDelete(a,b)\n  #define sqlite3FkLocateIndex(a,b,c,d,e)\n#endif\n\n\n/*\n** Available fault injectors.  Should be numbered beginning with 0.\n*/\n#define SQLITE_FAULTINJECTOR_MALLOC     0\n#define SQLITE_FAULTINJECTOR_COUNT      1\n\n/*\n** The interface to the code in fault.c used for identifying \"benign\"\n** malloc failures. This is only present if SQLITE_UNTESTABLE\n** is not defined.\n*/\n#ifndef SQLITE_UNTESTABLE\nSQLITE_PRIVATE   void sqlite3BeginBenignMalloc(void);\nSQLITE_PRIVATE   void sqlite3EndBenignMalloc(void);\n#else\n  #define sqlite3BeginBenignMalloc()\n  #define sqlite3EndBenignMalloc()\n#endif\n\n/*\n** Allowed return values from sqlite3FindInIndex()\n*/\n#define IN_INDEX_ROWID        1   /* Search the rowid of the table */\n#define IN_INDEX_EPH          2   /* Search an ephemeral b-tree */\n#define IN_INDEX_INDEX_ASC    3   /* Existing index ASCENDING */\n#define IN_INDEX_INDEX_DESC   4   /* Existing index DESCENDING */\n#define IN_INDEX_NOOP         5   /* No table available. Use comparisons */\n/*\n** Allowed flags for the 3rd parameter to sqlite3FindInIndex().\n*/\n#define IN_INDEX_NOOP_OK     0x0001  /* OK to return IN_INDEX_NOOP */\n#define IN_INDEX_MEMBERSHIP  0x0002  /* IN operator used for membership test */\n#define IN_INDEX_LOOP        0x0004  /* IN operator used as a loop */\nSQLITE_PRIVATE int sqlite3FindInIndex(Parse *, Expr *, u32, int*, int*);\n\nSQLITE_PRIVATE int sqlite3JournalOpen(sqlite3_vfs *, const char *, sqlite3_file *, int, int);\nSQLITE_PRIVATE int sqlite3JournalSize(sqlite3_vfs *);\n#if defined(SQLITE_ENABLE_ATOMIC_WRITE) \\\n || defined(SQLITE_ENABLE_BATCH_ATOMIC_WRITE)\nSQLITE_PRIVATE   int sqlite3JournalCreate(sqlite3_file *);\n#endif\n\nSQLITE_PRIVATE int sqlite3JournalIsInMemory(sqlite3_file *p);\nSQLITE_PRIVATE void sqlite3MemJournalOpen(sqlite3_file *);\n\nSQLITE_PRIVATE void sqlite3ExprSetHeightAndFlags(Parse *pParse, Expr *p);\n#if SQLITE_MAX_EXPR_DEPTH>0\nSQLITE_PRIVATE   int sqlite3SelectExprHeight(Select *);\nSQLITE_PRIVATE   int sqlite3ExprCheckHeight(Parse*, int);\n#else\n  #define sqlite3SelectExprHeight(x) 0\n  #define sqlite3ExprCheckHeight(x,y)\n#endif\n\nSQLITE_PRIVATE u32 sqlite3Get4byte(const u8*);\nSQLITE_PRIVATE void sqlite3Put4byte(u8*, u32);\n\n#ifdef SQLITE_ENABLE_UNLOCK_NOTIFY\nSQLITE_PRIVATE   void sqlite3ConnectionBlocked(sqlite3 *, sqlite3 *);\nSQLITE_PRIVATE   void sqlite3ConnectionUnlocked(sqlite3 *db);\nSQLITE_PRIVATE   void sqlite3ConnectionClosed(sqlite3 *db);\n#else\n  #define sqlite3ConnectionBlocked(x,y)\n  #define sqlite3ConnectionUnlocked(x)\n  #define sqlite3ConnectionClosed(x)\n#endif\n\n#ifdef SQLITE_DEBUG\nSQLITE_PRIVATE   void sqlite3ParserTrace(FILE*, char *);\n#endif\n#if defined(YYCOVERAGE)\nSQLITE_PRIVATE   int sqlite3ParserCoverage(FILE*);\n#endif\n\n/*\n** If the SQLITE_ENABLE IOTRACE exists then the global variable\n** sqlite3IoTrace is a pointer to a printf-like routine used to\n** print I/O tracing messages.\n*/\n#ifdef SQLITE_ENABLE_IOTRACE\n# define IOTRACE(A)  if( sqlite3IoTrace ){ sqlite3IoTrace A; }\nSQLITE_PRIVATE   void sqlite3VdbeIOTraceSql(Vdbe*);\nSQLITE_API SQLITE_EXTERN void (SQLITE_CDECL *sqlite3IoTrace)(const char*,...);\n#else\n# define IOTRACE(A)\n# define sqlite3VdbeIOTraceSql(X)\n#endif\n\n/*\n** These routines are available for the mem2.c debugging memory allocator\n** only.  They are used to verify that different \"types\" of memory\n** allocations are properly tracked by the system.\n**\n** sqlite3MemdebugSetType() sets the \"type\" of an allocation to one of\n** the MEMTYPE_* macros defined below.  The type must be a bitmask with\n** a single bit set.\n**\n** sqlite3MemdebugHasType() returns true if any of the bits in its second\n** argument match the type set by the previous sqlite3MemdebugSetType().\n** sqlite3MemdebugHasType() is intended for use inside assert() statements.\n**\n** sqlite3MemdebugNoType() returns true if none of the bits in its second\n** argument match the type set by the previous sqlite3MemdebugSetType().\n**\n** Perhaps the most important point is the difference between MEMTYPE_HEAP\n** and MEMTYPE_LOOKASIDE.  If an allocation is MEMTYPE_LOOKASIDE, that means\n** it might have been allocated by lookaside, except the allocation was\n** too large or lookaside was already full.  It is important to verify\n** that allocations that might have been satisfied by lookaside are not\n** passed back to non-lookaside free() routines.  Asserts such as the\n** example above are placed on the non-lookaside free() routines to verify\n** this constraint.\n**\n** All of this is no-op for a production build.  It only comes into\n** play when the SQLITE_MEMDEBUG compile-time option is used.\n*/\n#ifdef SQLITE_MEMDEBUG\nSQLITE_PRIVATE   void sqlite3MemdebugSetType(void*,u8);\nSQLITE_PRIVATE   int sqlite3MemdebugHasType(void*,u8);\nSQLITE_PRIVATE   int sqlite3MemdebugNoType(void*,u8);\n#else\n# define sqlite3MemdebugSetType(X,Y)  /* no-op */\n# define sqlite3MemdebugHasType(X,Y)  1\n# define sqlite3MemdebugNoType(X,Y)   1\n#endif\n#define MEMTYPE_HEAP       0x01  /* General heap allocations */\n#define MEMTYPE_LOOKASIDE  0x02  /* Heap that might have been lookaside */\n#define MEMTYPE_PCACHE     0x04  /* Page cache allocations */\n\n/*\n** Threading interface\n*/\n#if SQLITE_MAX_WORKER_THREADS>0\nSQLITE_PRIVATE int sqlite3ThreadCreate(SQLiteThread**,void*(*)(void*),void*);\nSQLITE_PRIVATE int sqlite3ThreadJoin(SQLiteThread*, void**);\n#endif\n\n#if defined(SQLITE_ENABLE_DBPAGE_VTAB) || defined(SQLITE_TEST)\nSQLITE_PRIVATE int sqlite3DbpageRegister(sqlite3*);\n#endif\n#if defined(SQLITE_ENABLE_DBSTAT_VTAB) || defined(SQLITE_TEST)\nSQLITE_PRIVATE int sqlite3DbstatRegister(sqlite3*);\n#endif\n\nSQLITE_PRIVATE int sqlite3ExprVectorSize(Expr *pExpr);\nSQLITE_PRIVATE int sqlite3ExprIsVector(Expr *pExpr);\nSQLITE_PRIVATE Expr *sqlite3VectorFieldSubexpr(Expr*, int);\nSQLITE_PRIVATE Expr *sqlite3ExprForVectorField(Parse*,Expr*,int);\nSQLITE_PRIVATE void sqlite3VectorErrorMsg(Parse*, Expr*);\n\n#ifndef SQLITE_OMIT_COMPILEOPTION_DIAGS\nSQLITE_PRIVATE const char **sqlite3CompileOptions(int *pnOpt);\n#endif\n\n#endif /* SQLITEINT_H */\n\n/************** End of sqliteInt.h *******************************************/\n/************** Begin file global.c ******************************************/\n/*\n** 2008 June 13\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n*************************************************************************\n**\n** This file contains definitions of global variables and constants.\n*/\n/* #include \"sqliteInt.h\" */\n\n/* An array to map all upper-case characters into their corresponding\n** lower-case character. \n**\n** SQLite only considers US-ASCII (or EBCDIC) characters.  We do not\n** handle case conversions for the UTF character set since the tables\n** involved are nearly as big or bigger than SQLite itself.\n*/\nSQLITE_PRIVATE const unsigned char sqlite3UpperToLower[] = {\n#ifdef SQLITE_ASCII\n      0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17,\n     18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35,\n     36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53,\n     54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 97, 98, 99,100,101,102,103,\n    104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,\n    122, 91, 92, 93, 94, 95, 96, 97, 98, 99,100,101,102,103,104,105,106,107,\n    108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,\n    126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,\n    144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,\n    162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,\n    180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,\n    198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,\n    216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,\n    234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,\n    252,253,254,255\n#endif\n#ifdef SQLITE_EBCDIC\n      0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, /* 0x */\n     16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, /* 1x */\n     32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, /* 2x */\n     48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, /* 3x */\n     64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, /* 4x */\n     80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, /* 5x */\n     96, 97, 98, 99,100,101,102,103,104,105,106,107,108,109,110,111, /* 6x */\n    112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127, /* 7x */\n    128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143, /* 8x */\n    144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159, /* 9x */\n    160,161,162,163,164,165,166,167,168,169,170,171,140,141,142,175, /* Ax */\n    176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191, /* Bx */\n    192,129,130,131,132,133,134,135,136,137,202,203,204,205,206,207, /* Cx */\n    208,145,146,147,148,149,150,151,152,153,218,219,220,221,222,223, /* Dx */\n    224,225,162,163,164,165,166,167,168,169,234,235,236,237,238,239, /* Ex */\n    240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255, /* Fx */\n#endif\n};\n\n/*\n** The following 256 byte lookup table is used to support SQLites built-in\n** equivalents to the following standard library functions:\n**\n**   isspace()                        0x01\n**   isalpha()                        0x02\n**   isdigit()                        0x04\n**   isalnum()                        0x06\n**   isxdigit()                       0x08\n**   toupper()                        0x20\n**   SQLite identifier character      0x40\n**   Quote character                  0x80\n**\n** Bit 0x20 is set if the mapped character requires translation to upper\n** case. i.e. if the character is a lower-case ASCII character.\n** If x is a lower-case ASCII character, then its upper-case equivalent\n** is (x - 0x20). Therefore toupper() can be implemented as:\n**\n**   (x & ~(map[x]&0x20))\n**\n** The equivalent of tolower() is implemented using the sqlite3UpperToLower[]\n** array. tolower() is used more often than toupper() by SQLite.\n**\n** Bit 0x40 is set if the character is non-alphanumeric and can be used in an \n** SQLite identifier.  Identifiers are alphanumerics, \"_\", \"$\", and any\n** non-ASCII UTF character. Hence the test for whether or not a character is\n** part of an identifier is 0x46.\n*/\n#ifdef SQLITE_ASCII\nSQLITE_PRIVATE const unsigned char sqlite3CtypeMap[256] = {\n  0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,  /* 00..07    ........ */\n  0x00, 0x01, 0x01, 0x01, 0x01, 0x01, 0x00, 0x00,  /* 08..0f    ........ */\n  0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,  /* 10..17    ........ */\n  0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,  /* 18..1f    ........ */\n  0x01, 0x00, 0x80, 0x00, 0x40, 0x00, 0x00, 0x80,  /* 20..27     !\"#$%&' */\n  0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,  /* 28..2f    ()*+,-./ */\n  0x0c, 0x0c, 0x0c, 0x0c, 0x0c, 0x0c, 0x0c, 0x0c,  /* 30..37    01234567 */\n  0x0c, 0x0c, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,  /* 38..3f    89:;<=>? */\n\n  0x00, 0x0a, 0x0a, 0x0a, 0x0a, 0x0a, 0x0a, 0x02,  /* 40..47    @ABCDEFG */\n  0x02, 0x02, 0x02, 0x02, 0x02, 0x02, 0x02, 0x02,  /* 48..4f    HIJKLMNO */\n  0x02, 0x02, 0x02, 0x02, 0x02, 0x02, 0x02, 0x02,  /* 50..57    PQRSTUVW */\n  0x02, 0x02, 0x02, 0x80, 0x00, 0x00, 0x00, 0x40,  /* 58..5f    XYZ[\\]^_ */\n  0x80, 0x2a, 0x2a, 0x2a, 0x2a, 0x2a, 0x2a, 0x22,  /* 60..67    `abcdefg */\n  0x22, 0x22, 0x22, 0x22, 0x22, 0x22, 0x22, 0x22,  /* 68..6f    hijklmno */\n  0x22, 0x22, 0x22, 0x22, 0x22, 0x22, 0x22, 0x22,  /* 70..77    pqrstuvw */\n  0x22, 0x22, 0x22, 0x00, 0x00, 0x00, 0x00, 0x00,  /* 78..7f    xyz{|}~. */\n\n  0x40, 0x40, 0x40, 0x40, 0x40, 0x40, 0x40, 0x40,  /* 80..87    ........ */\n  0x40, 0x40, 0x40, 0x40, 0x40, 0x40, 0x40, 0x40,  /* 88..8f    ........ */\n  0x40, 0x40, 0x40, 0x40, 0x40, 0x40, 0x40, 0x40,  /* 90..97    ........ */\n  0x40, 0x40, 0x40, 0x40, 0x40, 0x40, 0x40, 0x40,  /* 98..9f    ........ */\n  0x40, 0x40, 0x40, 0x40, 0x40, 0x40, 0x40, 0x40,  /* a0..a7    ........ */\n  0x40, 0x40, 0x40, 0x40, 0x40, 0x40, 0x40, 0x40,  /* a8..af    ........ */\n  0x40, 0x40, 0x40, 0x40, 0x40, 0x40, 0x40, 0x40,  /* b0..b7    ........ */\n  0x40, 0x40, 0x40, 0x40, 0x40, 0x40, 0x40, 0x40,  /* b8..bf    ........ */\n\n  0x40, 0x40, 0x40, 0x40, 0x40, 0x40, 0x40, 0x40,  /* c0..c7    ........ */\n  0x40, 0x40, 0x40, 0x40, 0x40, 0x40, 0x40, 0x40,  /* c8..cf    ........ */\n  0x40, 0x40, 0x40, 0x40, 0x40, 0x40, 0x40, 0x40,  /* d0..d7    ........ */\n  0x40, 0x40, 0x40, 0x40, 0x40, 0x40, 0x40, 0x40,  /* d8..df    ........ */\n  0x40, 0x40, 0x40, 0x40, 0x40, 0x40, 0x40, 0x40,  /* e0..e7    ........ */\n  0x40, 0x40, 0x40, 0x40, 0x40, 0x40, 0x40, 0x40,  /* e8..ef    ........ */\n  0x40, 0x40, 0x40, 0x40, 0x40, 0x40, 0x40, 0x40,  /* f0..f7    ........ */\n  0x40, 0x40, 0x40, 0x40, 0x40, 0x40, 0x40, 0x40   /* f8..ff    ........ */\n};\n#endif\n\n/* EVIDENCE-OF: R-02982-34736 In order to maintain full backwards\n** compatibility for legacy applications, the URI filename capability is\n** disabled by default.\n**\n** EVIDENCE-OF: R-38799-08373 URI filenames can be enabled or disabled\n** using the SQLITE_USE_URI=1 or SQLITE_USE_URI=0 compile-time options.\n**\n** EVIDENCE-OF: R-43642-56306 By default, URI handling is globally\n** disabled. The default value may be changed by compiling with the\n** SQLITE_USE_URI symbol defined.\n**\n** URI filenames are enabled by default if SQLITE_HAS_CODEC is\n** enabled.\n*/\n#ifndef SQLITE_USE_URI\n# ifdef SQLITE_HAS_CODEC\n#  define SQLITE_USE_URI 1\n# else\n#  define SQLITE_USE_URI 0\n# endif\n#endif\n\n/* EVIDENCE-OF: R-38720-18127 The default setting is determined by the\n** SQLITE_ALLOW_COVERING_INDEX_SCAN compile-time option, or is \"on\" if\n** that compile-time option is omitted.\n*/\n#ifndef SQLITE_ALLOW_COVERING_INDEX_SCAN\n# define SQLITE_ALLOW_COVERING_INDEX_SCAN 1\n#endif\n\n/* The minimum PMA size is set to this value multiplied by the database\n** page size in bytes.\n*/\n#ifndef SQLITE_SORTER_PMASZ\n# define SQLITE_SORTER_PMASZ 250\n#endif\n\n/* Statement journals spill to disk when their size exceeds the following\n** threshold (in bytes). 0 means that statement journals are created and\n** written to disk immediately (the default behavior for SQLite versions\n** before 3.12.0).  -1 means always keep the entire statement journal in\n** memory.  (The statement journal is also always held entirely in memory\n** if journal_mode=MEMORY or if temp_store=MEMORY, regardless of this\n** setting.)\n*/\n#ifndef SQLITE_STMTJRNL_SPILL \n# define SQLITE_STMTJRNL_SPILL (64*1024)\n#endif\n\n/*\n** The default lookaside-configuration, the format \"SZ,N\".  SZ is the\n** number of bytes in each lookaside slot (should be a multiple of 8)\n** and N is the number of slots.  The lookaside-configuration can be\n** changed as start-time using sqlite3_config(SQLITE_CONFIG_LOOKASIDE)\n** or at run-time for an individual database connection using\n** sqlite3_db_config(db, SQLITE_DBCONFIG_LOOKASIDE);\n*/\n#ifndef SQLITE_DEFAULT_LOOKASIDE\n# define SQLITE_DEFAULT_LOOKASIDE 1200,100\n#endif\n\n\n/*\n** The following singleton contains the global configuration for\n** the SQLite library.\n*/\nSQLITE_PRIVATE SQLITE_WSD struct Sqlite3Config sqlite3Config = {\n   SQLITE_DEFAULT_MEMSTATUS,  /* bMemstat */\n   1,                         /* bCoreMutex */\n   SQLITE_THREADSAFE==1,      /* bFullMutex */\n   SQLITE_USE_URI,            /* bOpenUri */\n   SQLITE_ALLOW_COVERING_INDEX_SCAN,   /* bUseCis */\n   0,                         /* bSmallMalloc */\n   0x7ffffffe,                /* mxStrlen */\n   0,                         /* neverCorrupt */\n   SQLITE_DEFAULT_LOOKASIDE,  /* szLookaside, nLookaside */\n   SQLITE_STMTJRNL_SPILL,     /* nStmtSpill */\n   {0,0,0,0,0,0,0,0},         /* m */\n   {0,0,0,0,0,0,0,0,0},       /* mutex */\n   {0,0,0,0,0,0,0,0,0,0,0,0,0},/* pcache2 */\n   (void*)0,                  /* pHeap */\n   0,                         /* nHeap */\n   0, 0,                      /* mnHeap, mxHeap */\n   SQLITE_DEFAULT_MMAP_SIZE,  /* szMmap */\n   SQLITE_MAX_MMAP_SIZE,      /* mxMmap */\n   (void*)0,                  /* pPage */\n   0,                         /* szPage */\n   SQLITE_DEFAULT_PCACHE_INITSZ, /* nPage */\n   0,                         /* mxParserStack */\n   0,                         /* sharedCacheEnabled */\n   SQLITE_SORTER_PMASZ,       /* szPma */\n   /* All the rest should always be initialized to zero */\n   0,                         /* isInit */\n   0,                         /* inProgress */\n   0,                         /* isMutexInit */\n   0,                         /* isMallocInit */\n   0,                         /* isPCacheInit */\n   0,                         /* nRefInitMutex */\n   0,                         /* pInitMutex */\n   0,                         /* xLog */\n   0,                         /* pLogArg */\n#ifdef SQLITE_ENABLE_SQLLOG\n   0,                         /* xSqllog */\n   0,                         /* pSqllogArg */\n#endif\n#ifdef SQLITE_VDBE_COVERAGE\n   0,                         /* xVdbeBranch */\n   0,                         /* pVbeBranchArg */\n#endif\n#ifndef SQLITE_UNTESTABLE\n   0,                         /* xTestCallback */\n#endif\n   0,                         /* bLocaltimeFault */\n   0x7ffffffe                 /* iOnceResetThreshold */\n};\n\n/*\n** Hash table for global functions - functions common to all\n** database connections.  After initialization, this table is\n** read-only.\n*/\nSQLITE_PRIVATE FuncDefHash sqlite3BuiltinFunctions;\n\n/*\n** Constant tokens for values 0 and 1.\n*/\nSQLITE_PRIVATE const Token sqlite3IntTokens[] = {\n   { \"0\", 1 },\n   { \"1\", 1 }\n};\n\n#ifdef VDBE_PROFILE\n/*\n** The following performance counter can be used in place of\n** sqlite3Hwtime() for profiling.  This is a no-op on standard builds.\n*/\nSQLITE_PRIVATE sqlite3_uint64 sqlite3NProfileCnt = 0;\n#endif\n\n/*\n** The value of the \"pending\" byte must be 0x40000000 (1 byte past the\n** 1-gibabyte boundary) in a compatible database.  SQLite never uses\n** the database page that contains the pending byte.  It never attempts\n** to read or write that page.  The pending byte page is set aside\n** for use by the VFS layers as space for managing file locks.\n**\n** During testing, it is often desirable to move the pending byte to\n** a different position in the file.  This allows code that has to\n** deal with the pending byte to run on files that are much smaller\n** than 1 GiB.  The sqlite3_test_control() interface can be used to\n** move the pending byte.\n**\n** IMPORTANT:  Changing the pending byte to any value other than\n** 0x40000000 results in an incompatible database file format!\n** Changing the pending byte during operation will result in undefined\n** and incorrect behavior.\n*/\n#ifndef SQLITE_OMIT_WSD\nSQLITE_PRIVATE int sqlite3PendingByte = 0x40000000;\n#endif\n\n/* #include \"opcodes.h\" */\n/*\n** Properties of opcodes.  The OPFLG_INITIALIZER macro is\n** created by mkopcodeh.awk during compilation.  Data is obtained\n** from the comments following the \"case OP_xxxx:\" statements in\n** the vdbe.c file.  \n*/\nSQLITE_PRIVATE const unsigned char sqlite3OpcodeProperty[] = OPFLG_INITIALIZER;\n\n/*\n** Name of the default collating sequence\n*/\nSQLITE_PRIVATE const char sqlite3StrBINARY[] = \"BINARY\";\n\n/************** End of global.c **********************************************/\n/************** Begin file status.c ******************************************/\n/*\n** 2008 June 18\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n*************************************************************************\n**\n** This module implements the sqlite3_status() interface and related\n** functionality.\n*/\n/* #include \"sqliteInt.h\" */\n/************** Include vdbeInt.h in the middle of status.c ******************/\n/************** Begin file vdbeInt.h *****************************************/\n/*\n** 2003 September 6\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n*************************************************************************\n** This is the header file for information that is private to the\n** VDBE.  This information used to all be at the top of the single\n** source code file \"vdbe.c\".  When that file became too big (over\n** 6000 lines long) it was split up into several smaller files and\n** this header information was factored out.\n*/\n#ifndef SQLITE_VDBEINT_H\n#define SQLITE_VDBEINT_H\n\n/*\n** The maximum number of times that a statement will try to reparse\n** itself before giving up and returning SQLITE_SCHEMA.\n*/\n#ifndef SQLITE_MAX_SCHEMA_RETRY\n# define SQLITE_MAX_SCHEMA_RETRY 50\n#endif\n\n/*\n** VDBE_DISPLAY_P4 is true or false depending on whether or not the\n** \"explain\" P4 display logic is enabled.\n*/\n#if !defined(SQLITE_OMIT_EXPLAIN) || !defined(NDEBUG) \\\n     || defined(VDBE_PROFILE) || defined(SQLITE_DEBUG)\n# define VDBE_DISPLAY_P4 1\n#else\n# define VDBE_DISPLAY_P4 0\n#endif\n\n/*\n** SQL is translated into a sequence of instructions to be\n** executed by a virtual machine.  Each instruction is an instance\n** of the following structure.\n*/\ntypedef struct VdbeOp Op;\n\n/*\n** Boolean values\n*/\ntypedef unsigned Bool;\n\n/* Opaque type used by code in vdbesort.c */\ntypedef struct VdbeSorter VdbeSorter;\n\n/* Elements of the linked list at Vdbe.pAuxData */\ntypedef struct AuxData AuxData;\n\n/* Types of VDBE cursors */\n#define CURTYPE_BTREE       0\n#define CURTYPE_SORTER      1\n#define CURTYPE_VTAB        2\n#define CURTYPE_PSEUDO      3\n\n/*\n** A VdbeCursor is an superclass (a wrapper) for various cursor objects:\n**\n**      * A b-tree cursor\n**          -  In the main database or in an ephemeral database\n**          -  On either an index or a table\n**      * A sorter\n**      * A virtual table\n**      * A one-row \"pseudotable\" stored in a single register\n*/\ntypedef struct VdbeCursor VdbeCursor;\nstruct VdbeCursor {\n  u8 eCurType;            /* One of the CURTYPE_* values above */\n  i8 iDb;                 /* Index of cursor database in db->aDb[] (or -1) */\n  u8 nullRow;             /* True if pointing to a row with no data */\n  u8 deferredMoveto;      /* A call to sqlite3BtreeMoveto() is needed */\n  u8 isTable;             /* True for rowid tables.  False for indexes */\n#ifdef SQLITE_DEBUG\n  u8 seekOp;              /* Most recent seek operation on this cursor */\n  u8 wrFlag;              /* The wrFlag argument to sqlite3BtreeCursor() */\n#endif\n  Bool isEphemeral:1;     /* True for an ephemeral table */\n  Bool useRandomRowid:1;  /* Generate new record numbers semi-randomly */\n  Bool isOrdered:1;       /* True if the table is not BTREE_UNORDERED */\n  Btree *pBtx;            /* Separate file holding temporary table */\n  i64 seqCount;           /* Sequence counter */\n  int *aAltMap;           /* Mapping from table to index column numbers */\n\n  /* Cached OP_Column parse information is only valid if cacheStatus matches\n  ** Vdbe.cacheCtr.  Vdbe.cacheCtr will never take on the value of\n  ** CACHE_STALE (0) and so setting cacheStatus=CACHE_STALE guarantees that\n  ** the cache is out of date. */\n  u32 cacheStatus;        /* Cache is valid if this matches Vdbe.cacheCtr */\n  int seekResult;         /* Result of previous sqlite3BtreeMoveto() or 0\n                          ** if there have been no prior seeks on the cursor. */\n  /* seekResult does not distinguish between \"no seeks have ever occurred\n  ** on this cursor\" and \"the most recent seek was an exact match\".\n  ** For CURTYPE_PSEUDO, seekResult is the register holding the record */\n\n  /* When a new VdbeCursor is allocated, only the fields above are zeroed.\n  ** The fields that follow are uninitialized, and must be individually\n  ** initialized prior to first use. */\n  VdbeCursor *pAltCursor; /* Associated index cursor from which to read */\n  union {\n    BtCursor *pCursor;          /* CURTYPE_BTREE or _PSEUDO.  Btree cursor */\n    sqlite3_vtab_cursor *pVCur; /* CURTYPE_VTAB.              Vtab cursor */\n    VdbeSorter *pSorter;        /* CURTYPE_SORTER.            Sorter object */\n  } uc;\n  KeyInfo *pKeyInfo;      /* Info about index keys needed by index cursors */\n  u32 iHdrOffset;         /* Offset to next unparsed byte of the header */\n  Pgno pgnoRoot;          /* Root page of the open btree cursor */\n  i16 nField;             /* Number of fields in the header */\n  u16 nHdrParsed;         /* Number of header fields parsed so far */\n  i64 movetoTarget;       /* Argument to the deferred sqlite3BtreeMoveto() */\n  u32 *aOffset;           /* Pointer to aType[nField] */\n  const u8 *aRow;         /* Data for the current row, if all on one page */\n  u32 payloadSize;        /* Total number of bytes in the record */\n  u32 szRow;              /* Byte available in aRow */\n#ifdef SQLITE_ENABLE_COLUMN_USED_MASK\n  u64 maskUsed;           /* Mask of columns used by this cursor */\n#endif\n\n  /* 2*nField extra array elements allocated for aType[], beyond the one\n  ** static element declared in the structure.  nField total array slots for\n  ** aType[] and nField+1 array slots for aOffset[] */\n  u32 aType[1];           /* Type values record decode.  MUST BE LAST */\n};\n\n\n/*\n** A value for VdbeCursor.cacheStatus that means the cache is always invalid.\n*/\n#define CACHE_STALE 0\n\n/*\n** When a sub-program is executed (OP_Program), a structure of this type\n** is allocated to store the current value of the program counter, as\n** well as the current memory cell array and various other frame specific\n** values stored in the Vdbe struct. When the sub-program is finished, \n** these values are copied back to the Vdbe from the VdbeFrame structure,\n** restoring the state of the VM to as it was before the sub-program\n** began executing.\n**\n** The memory for a VdbeFrame object is allocated and managed by a memory\n** cell in the parent (calling) frame. When the memory cell is deleted or\n** overwritten, the VdbeFrame object is not freed immediately. Instead, it\n** is linked into the Vdbe.pDelFrame list. The contents of the Vdbe.pDelFrame\n** list is deleted when the VM is reset in VdbeHalt(). The reason for doing\n** this instead of deleting the VdbeFrame immediately is to avoid recursive\n** calls to sqlite3VdbeMemRelease() when the memory cells belonging to the\n** child frame are released.\n**\n** The currently executing frame is stored in Vdbe.pFrame. Vdbe.pFrame is\n** set to NULL if the currently executing frame is the main program.\n*/\ntypedef struct VdbeFrame VdbeFrame;\nstruct VdbeFrame {\n  Vdbe *v;                /* VM this frame belongs to */\n  VdbeFrame *pParent;     /* Parent of this frame, or NULL if parent is main */\n  Op *aOp;                /* Program instructions for parent frame */\n  i64 *anExec;            /* Event counters from parent frame */\n  Mem *aMem;              /* Array of memory cells for parent frame */\n  VdbeCursor **apCsr;     /* Array of Vdbe cursors for parent frame */\n  u8 *aOnce;              /* Bitmask used by OP_Once */\n  void *token;            /* Copy of SubProgram.token */\n  i64 lastRowid;          /* Last insert rowid (sqlite3.lastRowid) */\n  AuxData *pAuxData;      /* Linked list of auxdata allocations */\n  int nCursor;            /* Number of entries in apCsr */\n  int pc;                 /* Program Counter in parent (calling) frame */\n  int nOp;                /* Size of aOp array */\n  int nMem;               /* Number of entries in aMem */\n  int nChildMem;          /* Number of memory cells for child frame */\n  int nChildCsr;          /* Number of cursors for child frame */\n  int nChange;            /* Statement changes (Vdbe.nChange)     */\n  int nDbChange;          /* Value of db->nChange */\n};\n\n#define VdbeFrameMem(p) ((Mem *)&((u8 *)p)[ROUND8(sizeof(VdbeFrame))])\n\n/*\n** Internally, the vdbe manipulates nearly all SQL values as Mem\n** structures. Each Mem struct may cache multiple representations (string,\n** integer etc.) of the same value.\n*/\nstruct sqlite3_value {\n  union MemValue {\n    double r;           /* Real value used when MEM_Real is set in flags */\n    i64 i;              /* Integer value used when MEM_Int is set in flags */\n    int nZero;          /* Extra zero bytes when MEM_Zero and MEM_Blob set */\n    const char *zPType; /* Pointer type when MEM_Term|MEM_Subtype|MEM_Null */\n    FuncDef *pDef;      /* Used only when flags==MEM_Agg */\n    RowSet *pRowSet;    /* Used only when flags==MEM_RowSet */\n    VdbeFrame *pFrame;  /* Used when flags==MEM_Frame */\n  } u;\n  u16 flags;          /* Some combination of MEM_Null, MEM_Str, MEM_Dyn, etc. */\n  u8  enc;            /* SQLITE_UTF8, SQLITE_UTF16BE, SQLITE_UTF16LE */\n  u8  eSubtype;       /* Subtype for this value */\n  int n;              /* Number of characters in string value, excluding '\\0' */\n  char *z;            /* String or BLOB value */\n  /* ShallowCopy only needs to copy the information above */\n  char *zMalloc;      /* Space to hold MEM_Str or MEM_Blob if szMalloc>0 */\n  int szMalloc;       /* Size of the zMalloc allocation */\n  u32 uTemp;          /* Transient storage for serial_type in OP_MakeRecord */\n  sqlite3 *db;        /* The associated database connection */\n  void (*xDel)(void*);/* Destructor for Mem.z - only valid if MEM_Dyn */\n#ifdef SQLITE_DEBUG\n  Mem *pScopyFrom;    /* This Mem is a shallow copy of pScopyFrom */\n  void *pFiller;      /* So that sizeof(Mem) is a multiple of 8 */\n#endif\n};\n\n/*\n** Size of struct Mem not including the Mem.zMalloc member or anything that\n** follows.\n*/\n#define MEMCELLSIZE offsetof(Mem,zMalloc)\n\n/* One or more of the following flags are set to indicate the validOK\n** representations of the value stored in the Mem struct.\n**\n** If the MEM_Null flag is set, then the value is an SQL NULL value.\n** For a pointer type created using sqlite3_bind_pointer() or\n** sqlite3_result_pointer() the MEM_Term and MEM_Subtype flags are also set.\n**\n** If the MEM_Str flag is set then Mem.z points at a string representation.\n** Usually this is encoded in the same unicode encoding as the main\n** database (see below for exceptions). If the MEM_Term flag is also\n** set, then the string is nul terminated. The MEM_Int and MEM_Real \n** flags may coexist with the MEM_Str flag.\n*/\n#define MEM_Null      0x0001   /* Value is NULL (or a pointer) */\n#define MEM_Str       0x0002   /* Value is a string */\n#define MEM_Int       0x0004   /* Value is an integer */\n#define MEM_Real      0x0008   /* Value is a real number */\n#define MEM_Blob      0x0010   /* Value is a BLOB */\n#define MEM_AffMask   0x001f   /* Mask of affinity bits */\n#define MEM_RowSet    0x0020   /* Value is a RowSet object */\n#define MEM_Frame     0x0040   /* Value is a VdbeFrame object */\n#define MEM_Undefined 0x0080   /* Value is undefined */\n#define MEM_Cleared   0x0100   /* NULL set by OP_Null, not from data */\n#define MEM_TypeMask  0xc1ff   /* Mask of type bits */\n\n\n/* Whenever Mem contains a valid string or blob representation, one of\n** the following flags must be set to determine the memory management\n** policy for Mem.z.  The MEM_Term flag tells us whether or not the\n** string is \\000 or \\u0000 terminated\n*/\n#define MEM_Term      0x0200   /* String in Mem.z is zero terminated */\n#define MEM_Dyn       0x0400   /* Need to call Mem.xDel() on Mem.z */\n#define MEM_Static    0x0800   /* Mem.z points to a static string */\n#define MEM_Ephem     0x1000   /* Mem.z points to an ephemeral string */\n#define MEM_Agg       0x2000   /* Mem.z points to an agg function context */\n#define MEM_Zero      0x4000   /* Mem.i contains count of 0s appended to blob */\n#define MEM_Subtype   0x8000   /* Mem.eSubtype is valid */\n#ifdef SQLITE_OMIT_INCRBLOB\n  #undef MEM_Zero\n  #define MEM_Zero 0x0000\n#endif\n\n/* Return TRUE if Mem X contains dynamically allocated content - anything\n** that needs to be deallocated to avoid a leak.\n*/\n#define VdbeMemDynamic(X)  \\\n  (((X)->flags&(MEM_Agg|MEM_Dyn|MEM_RowSet|MEM_Frame))!=0)\n\n/*\n** Clear any existing type flags from a Mem and replace them with f\n*/\n#define MemSetTypeFlag(p, f) \\\n   ((p)->flags = ((p)->flags&~(MEM_TypeMask|MEM_Zero))|f)\n\n/*\n** Return true if a memory cell is not marked as invalid.  This macro\n** is for use inside assert() statements only.\n*/\n#ifdef SQLITE_DEBUG\n#define memIsValid(M)  ((M)->flags & MEM_Undefined)==0\n#endif\n\n/*\n** Each auxiliary data pointer stored by a user defined function \n** implementation calling sqlite3_set_auxdata() is stored in an instance\n** of this structure. All such structures associated with a single VM\n** are stored in a linked list headed at Vdbe.pAuxData. All are destroyed\n** when the VM is halted (if not before).\n*/\nstruct AuxData {\n  int iAuxOp;                     /* Instruction number of OP_Function opcode */\n  int iAuxArg;                    /* Index of function argument. */\n  void *pAux;                     /* Aux data pointer */\n  void (*xDeleteAux)(void*);      /* Destructor for the aux data */\n  AuxData *pNextAux;              /* Next element in list */\n};\n\n/*\n** The \"context\" argument for an installable function.  A pointer to an\n** instance of this structure is the first argument to the routines used\n** implement the SQL functions.\n**\n** There is a typedef for this structure in sqlite.h.  So all routines,\n** even the public interface to SQLite, can use a pointer to this structure.\n** But this file is the only place where the internal details of this\n** structure are known.\n**\n** This structure is defined inside of vdbeInt.h because it uses substructures\n** (Mem) which are only defined there.\n*/\nstruct sqlite3_context {\n  Mem *pOut;              /* The return value is stored here */\n  FuncDef *pFunc;         /* Pointer to function information */\n  Mem *pMem;              /* Memory cell used to store aggregate context */\n  Vdbe *pVdbe;            /* The VM that owns this context */\n  int iOp;                /* Instruction number of OP_Function */\n  int isError;            /* Error code returned by the function. */\n  u8 skipFlag;            /* Skip accumulator loading if true */\n  u8 argc;                /* Number of arguments */\n  sqlite3_value *argv[1]; /* Argument set */\n};\n\n/* A bitfield type for use inside of structures.  Always follow with :N where\n** N is the number of bits.\n*/\ntypedef unsigned bft;  /* Bit Field Type */\n\ntypedef struct ScanStatus ScanStatus;\nstruct ScanStatus {\n  int addrExplain;                /* OP_Explain for loop */\n  int addrLoop;                   /* Address of \"loops\" counter */\n  int addrVisit;                  /* Address of \"rows visited\" counter */\n  int iSelectID;                  /* The \"Select-ID\" for this loop */\n  LogEst nEst;                    /* Estimated output rows per loop */\n  char *zName;                    /* Name of table or index */\n};\n\n/*\n** An instance of the virtual machine.  This structure contains the complete\n** state of the virtual machine.\n**\n** The \"sqlite3_stmt\" structure pointer that is returned by sqlite3_prepare()\n** is really a pointer to an instance of this structure.\n*/\nstruct Vdbe {\n  sqlite3 *db;            /* The database connection that owns this statement */\n  Vdbe *pPrev,*pNext;     /* Linked list of VDBEs with the same Vdbe.db */\n  Parse *pParse;          /* Parsing context used to create this Vdbe */\n  ynVar nVar;             /* Number of entries in aVar[] */\n  u32 magic;              /* Magic number for sanity checking */\n  int nMem;               /* Number of memory locations currently allocated */\n  int nCursor;            /* Number of slots in apCsr[] */\n  u32 cacheCtr;           /* VdbeCursor row cache generation counter */\n  int pc;                 /* The program counter */\n  int rc;                 /* Value to return */\n  int nChange;            /* Number of db changes made since last reset */\n  int iStatement;         /* Statement number (or 0 if has not opened stmt) */\n  i64 iCurrentTime;       /* Value of julianday('now') for this statement */\n  i64 nFkConstraint;      /* Number of imm. FK constraints this VM */\n  i64 nStmtDefCons;       /* Number of def. constraints when stmt started */\n  i64 nStmtDefImmCons;    /* Number of def. imm constraints when stmt started */\n\n  /* When allocating a new Vdbe object, all of the fields below should be\n  ** initialized to zero or NULL */\n\n  Op *aOp;                /* Space to hold the virtual machine's program */\n  Mem *aMem;              /* The memory locations */\n  Mem **apArg;            /* Arguments to currently executing user function */\n  Mem *aColName;          /* Column names to return */\n  Mem *pResultSet;        /* Pointer to an array of results */\n  char *zErrMsg;          /* Error message written here */\n  VdbeCursor **apCsr;     /* One element of this array for each open cursor */\n  Mem *aVar;              /* Values for the OP_Variable opcode. */\n  VList *pVList;          /* Name of variables */\n#ifndef SQLITE_OMIT_TRACE\n  i64 startTime;          /* Time when query started - used for profiling */\n#endif\n  int nOp;                /* Number of instructions in the program */\n#ifdef SQLITE_DEBUG\n  int rcApp;              /* errcode set by sqlite3_result_error_code() */\n#endif\n  u16 nResColumn;         /* Number of columns in one row of the result set */\n  u8 errorAction;         /* Recovery action to do in case of an error */\n  u8 minWriteFileFormat;  /* Minimum file format for writable database files */\n  u8 prepFlags;           /* SQLITE_PREPARE_* flags */\n  bft expired:1;          /* True if the VM needs to be recompiled */\n  bft doingRerun:1;       /* True if rerunning after an auto-reprepare */\n  bft explain:2;          /* True if EXPLAIN present on SQL command */\n  bft changeCntOn:1;      /* True to update the change-counter */\n  bft runOnlyOnce:1;      /* Automatically expire on reset */\n  bft usesStmtJournal:1;  /* True if uses a statement journal */\n  bft readOnly:1;         /* True for statements that do not write */\n  bft bIsReader:1;        /* True for statements that read */\n  yDbMask btreeMask;      /* Bitmask of db->aDb[] entries referenced */\n  yDbMask lockMask;       /* Subset of btreeMask that requires a lock */\n  u32 aCounter[7];        /* Counters used by sqlite3_stmt_status() */\n  char *zSql;             /* Text of the SQL statement that generated this */\n  void *pFree;            /* Free this when deleting the vdbe */\n  VdbeFrame *pFrame;      /* Parent frame */\n  VdbeFrame *pDelFrame;   /* List of frame objects to free on VM reset */\n  int nFrame;             /* Number of frames in pFrame list */\n  u32 expmask;            /* Binding to these vars invalidates VM */\n  SubProgram *pProgram;   /* Linked list of all sub-programs used by VM */\n  AuxData *pAuxData;      /* Linked list of auxdata allocations */\n#ifdef SQLITE_ENABLE_STMT_SCANSTATUS\n  i64 *anExec;            /* Number of times each op has been executed */\n  int nScan;              /* Entries in aScan[] */\n  ScanStatus *aScan;      /* Scan definitions for sqlite3_stmt_scanstatus() */\n#endif\n};\n\n/*\n** The following are allowed values for Vdbe.magic\n*/\n#define VDBE_MAGIC_INIT     0x16bceaa5    /* Building a VDBE program */\n#define VDBE_MAGIC_RUN      0x2df20da3    /* VDBE is ready to execute */\n#define VDBE_MAGIC_HALT     0x319c2973    /* VDBE has completed execution */\n#define VDBE_MAGIC_RESET    0x48fa9f76    /* Reset and ready to run again */\n#define VDBE_MAGIC_DEAD     0x5606c3c8    /* The VDBE has been deallocated */\n\n/*\n** Structure used to store the context required by the \n** sqlite3_preupdate_*() API functions.\n*/\nstruct PreUpdate {\n  Vdbe *v;\n  VdbeCursor *pCsr;               /* Cursor to read old values from */\n  int op;                         /* One of SQLITE_INSERT, UPDATE, DELETE */\n  u8 *aRecord;                    /* old.* database record */\n  KeyInfo keyinfo;\n  UnpackedRecord *pUnpacked;      /* Unpacked version of aRecord[] */\n  UnpackedRecord *pNewUnpacked;   /* Unpacked version of new.* record */\n  int iNewReg;                    /* Register for new.* values */\n  i64 iKey1;                      /* First key value passed to hook */\n  i64 iKey2;                      /* Second key value passed to hook */\n  Mem *aNew;                      /* Array of new.* values */\n  Table *pTab;                    /* Schema object being upated */          \n  Index *pPk;                     /* PK index if pTab is WITHOUT ROWID */\n};\n\n/*\n** Function prototypes\n*/\nSQLITE_PRIVATE void sqlite3VdbeError(Vdbe*, const char *, ...);\nSQLITE_PRIVATE void sqlite3VdbeFreeCursor(Vdbe *, VdbeCursor*);\nvoid sqliteVdbePopStack(Vdbe*,int);\nSQLITE_PRIVATE int sqlite3VdbeCursorMoveto(VdbeCursor**, int*);\nSQLITE_PRIVATE int sqlite3VdbeCursorRestore(VdbeCursor*);\n#if defined(SQLITE_DEBUG) || defined(VDBE_PROFILE)\nSQLITE_PRIVATE void sqlite3VdbePrintOp(FILE*, int, Op*);\n#endif\nSQLITE_PRIVATE u32 sqlite3VdbeSerialTypeLen(u32);\nSQLITE_PRIVATE u8 sqlite3VdbeOneByteSerialTypeLen(u8);\nSQLITE_PRIVATE u32 sqlite3VdbeSerialType(Mem*, int, u32*);\nSQLITE_PRIVATE u32 sqlite3VdbeSerialPut(unsigned char*, Mem*, u32);\nSQLITE_PRIVATE u32 sqlite3VdbeSerialGet(const unsigned char*, u32, Mem*);\nSQLITE_PRIVATE void sqlite3VdbeDeleteAuxData(sqlite3*, AuxData**, int, int);\n\nint sqlite2BtreeKeyCompare(BtCursor *, const void *, int, int, int *);\nSQLITE_PRIVATE int sqlite3VdbeIdxKeyCompare(sqlite3*,VdbeCursor*,UnpackedRecord*,int*);\nSQLITE_PRIVATE int sqlite3VdbeIdxRowid(sqlite3*, BtCursor*, i64*);\nSQLITE_PRIVATE int sqlite3VdbeExec(Vdbe*);\nSQLITE_PRIVATE int sqlite3VdbeList(Vdbe*);\nSQLITE_PRIVATE int sqlite3VdbeHalt(Vdbe*);\nSQLITE_PRIVATE int sqlite3VdbeChangeEncoding(Mem *, int);\nSQLITE_PRIVATE int sqlite3VdbeMemTooBig(Mem*);\nSQLITE_PRIVATE int sqlite3VdbeMemCopy(Mem*, const Mem*);\nSQLITE_PRIVATE void sqlite3VdbeMemShallowCopy(Mem*, const Mem*, int);\nSQLITE_PRIVATE void sqlite3VdbeMemMove(Mem*, Mem*);\nSQLITE_PRIVATE int sqlite3VdbeMemNulTerminate(Mem*);\nSQLITE_PRIVATE int sqlite3VdbeMemSetStr(Mem*, const char*, int, u8, void(*)(void*));\nSQLITE_PRIVATE void sqlite3VdbeMemSetInt64(Mem*, i64);\n#ifdef SQLITE_OMIT_FLOATING_POINT\n# define sqlite3VdbeMemSetDouble sqlite3VdbeMemSetInt64\n#else\nSQLITE_PRIVATE   void sqlite3VdbeMemSetDouble(Mem*, double);\n#endif\nSQLITE_PRIVATE void sqlite3VdbeMemSetPointer(Mem*, void*, const char*, void(*)(void*));\nSQLITE_PRIVATE void sqlite3VdbeMemInit(Mem*,sqlite3*,u16);\nSQLITE_PRIVATE void sqlite3VdbeMemSetNull(Mem*);\nSQLITE_PRIVATE void sqlite3VdbeMemSetZeroBlob(Mem*,int);\nSQLITE_PRIVATE void sqlite3VdbeMemSetRowSet(Mem*);\nSQLITE_PRIVATE int sqlite3VdbeMemMakeWriteable(Mem*);\nSQLITE_PRIVATE int sqlite3VdbeMemStringify(Mem*, u8, u8);\nSQLITE_PRIVATE i64 sqlite3VdbeIntValue(Mem*);\nSQLITE_PRIVATE int sqlite3VdbeMemIntegerify(Mem*);\nSQLITE_PRIVATE double sqlite3VdbeRealValue(Mem*);\nSQLITE_PRIVATE int sqlite3VdbeBooleanValue(Mem*, int ifNull);\nSQLITE_PRIVATE void sqlite3VdbeIntegerAffinity(Mem*);\nSQLITE_PRIVATE int sqlite3VdbeMemRealify(Mem*);\nSQLITE_PRIVATE int sqlite3VdbeMemNumerify(Mem*);\nSQLITE_PRIVATE void sqlite3VdbeMemCast(Mem*,u8,u8);\nSQLITE_PRIVATE int sqlite3VdbeMemFromBtree(BtCursor*,u32,u32,Mem*);\nSQLITE_PRIVATE void sqlite3VdbeMemRelease(Mem *p);\nSQLITE_PRIVATE int sqlite3VdbeMemFinalize(Mem*, FuncDef*);\nSQLITE_PRIVATE const char *sqlite3OpcodeName(int);\nSQLITE_PRIVATE int sqlite3VdbeMemGrow(Mem *pMem, int n, int preserve);\nSQLITE_PRIVATE int sqlite3VdbeMemClearAndResize(Mem *pMem, int n);\nSQLITE_PRIVATE int sqlite3VdbeCloseStatement(Vdbe *, int);\nSQLITE_PRIVATE void sqlite3VdbeFrameDelete(VdbeFrame*);\nSQLITE_PRIVATE int sqlite3VdbeFrameRestore(VdbeFrame *);\n#ifdef SQLITE_ENABLE_PREUPDATE_HOOK\nSQLITE_PRIVATE void sqlite3VdbePreUpdateHook(Vdbe*,VdbeCursor*,int,const char*,Table*,i64,int);\n#endif\nSQLITE_PRIVATE int sqlite3VdbeTransferError(Vdbe *p);\n\nSQLITE_PRIVATE int sqlite3VdbeSorterInit(sqlite3 *, int, VdbeCursor *);\nSQLITE_PRIVATE void sqlite3VdbeSorterReset(sqlite3 *, VdbeSorter *);\nSQLITE_PRIVATE void sqlite3VdbeSorterClose(sqlite3 *, VdbeCursor *);\nSQLITE_PRIVATE int sqlite3VdbeSorterRowkey(const VdbeCursor *, Mem *);\nSQLITE_PRIVATE int sqlite3VdbeSorterNext(sqlite3 *, const VdbeCursor *);\nSQLITE_PRIVATE int sqlite3VdbeSorterRewind(const VdbeCursor *, int *);\nSQLITE_PRIVATE int sqlite3VdbeSorterWrite(const VdbeCursor *, Mem *);\nSQLITE_PRIVATE int sqlite3VdbeSorterCompare(const VdbeCursor *, Mem *, int, int *);\n\n#if !defined(SQLITE_OMIT_SHARED_CACHE) \nSQLITE_PRIVATE   void sqlite3VdbeEnter(Vdbe*);\n#else\n# define sqlite3VdbeEnter(X)\n#endif\n\n#if !defined(SQLITE_OMIT_SHARED_CACHE) && SQLITE_THREADSAFE>0\nSQLITE_PRIVATE   void sqlite3VdbeLeave(Vdbe*);\n#else\n# define sqlite3VdbeLeave(X)\n#endif\n\n#ifdef SQLITE_DEBUG\nSQLITE_PRIVATE void sqlite3VdbeMemAboutToChange(Vdbe*,Mem*);\nSQLITE_PRIVATE int sqlite3VdbeCheckMemInvariants(Mem*);\n#endif\n\n#ifndef SQLITE_OMIT_FOREIGN_KEY\nSQLITE_PRIVATE int sqlite3VdbeCheckFk(Vdbe *, int);\n#else\n# define sqlite3VdbeCheckFk(p,i) 0\n#endif\n\n#ifdef SQLITE_DEBUG\nSQLITE_PRIVATE   void sqlite3VdbePrintSql(Vdbe*);\nSQLITE_PRIVATE   void sqlite3VdbeMemPrettyPrint(Mem *pMem, char *zBuf);\n#endif\n#ifndef SQLITE_OMIT_UTF16\nSQLITE_PRIVATE   int sqlite3VdbeMemTranslate(Mem*, u8);\nSQLITE_PRIVATE   int sqlite3VdbeMemHandleBom(Mem *pMem);\n#endif\n\n#ifndef SQLITE_OMIT_INCRBLOB\nSQLITE_PRIVATE   int sqlite3VdbeMemExpandBlob(Mem *);\n  #define ExpandBlob(P) (((P)->flags&MEM_Zero)?sqlite3VdbeMemExpandBlob(P):0)\n#else\n  #define sqlite3VdbeMemExpandBlob(x) SQLITE_OK\n  #define ExpandBlob(P) SQLITE_OK\n#endif\n\n#endif /* !defined(SQLITE_VDBEINT_H) */\n\n/************** End of vdbeInt.h *********************************************/\n/************** Continuing where we left off in status.c *********************/\n\n/*\n** Variables in which to record status information.\n*/\n#if SQLITE_PTRSIZE>4\ntypedef sqlite3_int64 sqlite3StatValueType;\n#else\ntypedef u32 sqlite3StatValueType;\n#endif\ntypedef struct sqlite3StatType sqlite3StatType;\nstatic SQLITE_WSD struct sqlite3StatType {\n  sqlite3StatValueType nowValue[10];  /* Current value */\n  sqlite3StatValueType mxValue[10];   /* Maximum value */\n} sqlite3Stat = { {0,}, {0,} };\n\n/*\n** Elements of sqlite3Stat[] are protected by either the memory allocator\n** mutex, or by the pcache1 mutex.  The following array determines which.\n*/\nstatic const char statMutex[] = {\n  0,  /* SQLITE_STATUS_MEMORY_USED */\n  1,  /* SQLITE_STATUS_PAGECACHE_USED */\n  1,  /* SQLITE_STATUS_PAGECACHE_OVERFLOW */\n  0,  /* SQLITE_STATUS_SCRATCH_USED */\n  0,  /* SQLITE_STATUS_SCRATCH_OVERFLOW */\n  0,  /* SQLITE_STATUS_MALLOC_SIZE */\n  0,  /* SQLITE_STATUS_PARSER_STACK */\n  1,  /* SQLITE_STATUS_PAGECACHE_SIZE */\n  0,  /* SQLITE_STATUS_SCRATCH_SIZE */\n  0,  /* SQLITE_STATUS_MALLOC_COUNT */\n};\n\n\n/* The \"wsdStat\" macro will resolve to the status information\n** state vector.  If writable static data is unsupported on the target,\n** we have to locate the state vector at run-time.  In the more common\n** case where writable static data is supported, wsdStat can refer directly\n** to the \"sqlite3Stat\" state vector declared above.\n*/\n#ifdef SQLITE_OMIT_WSD\n# define wsdStatInit  sqlite3StatType *x = &GLOBAL(sqlite3StatType,sqlite3Stat)\n# define wsdStat x[0]\n#else\n# define wsdStatInit\n# define wsdStat sqlite3Stat\n#endif\n\n/*\n** Return the current value of a status parameter.  The caller must\n** be holding the appropriate mutex.\n*/\nSQLITE_PRIVATE sqlite3_int64 sqlite3StatusValue(int op){\n  wsdStatInit;\n  assert( op>=0 && op<ArraySize(wsdStat.nowValue) );\n  assert( op>=0 && op<ArraySize(statMutex) );\n  assert( sqlite3_mutex_held(statMutex[op] ? sqlite3Pcache1Mutex()\n                                           : sqlite3MallocMutex()) );\n  return wsdStat.nowValue[op];\n}\n\n/*\n** Add N to the value of a status record.  The caller must hold the\n** appropriate mutex.  (Locking is checked by assert()).\n**\n** The StatusUp() routine can accept positive or negative values for N.\n** The value of N is added to the current status value and the high-water\n** mark is adjusted if necessary.\n**\n** The StatusDown() routine lowers the current value by N.  The highwater\n** mark is unchanged.  N must be non-negative for StatusDown().\n*/\nSQLITE_PRIVATE void sqlite3StatusUp(int op, int N){\n  wsdStatInit;\n  assert( op>=0 && op<ArraySize(wsdStat.nowValue) );\n  assert( op>=0 && op<ArraySize(statMutex) );\n  assert( sqlite3_mutex_held(statMutex[op] ? sqlite3Pcache1Mutex()\n                                           : sqlite3MallocMutex()) );\n  wsdStat.nowValue[op] += N;\n  if( wsdStat.nowValue[op]>wsdStat.mxValue[op] ){\n    wsdStat.mxValue[op] = wsdStat.nowValue[op];\n  }\n}\nSQLITE_PRIVATE void sqlite3StatusDown(int op, int N){\n  wsdStatInit;\n  assert( N>=0 );\n  assert( op>=0 && op<ArraySize(statMutex) );\n  assert( sqlite3_mutex_held(statMutex[op] ? sqlite3Pcache1Mutex()\n                                           : sqlite3MallocMutex()) );\n  assert( op>=0 && op<ArraySize(wsdStat.nowValue) );\n  wsdStat.nowValue[op] -= N;\n}\n\n/*\n** Adjust the highwater mark if necessary.\n** The caller must hold the appropriate mutex.\n*/\nSQLITE_PRIVATE void sqlite3StatusHighwater(int op, int X){\n  sqlite3StatValueType newValue;\n  wsdStatInit;\n  assert( X>=0 );\n  newValue = (sqlite3StatValueType)X;\n  assert( op>=0 && op<ArraySize(wsdStat.nowValue) );\n  assert( op>=0 && op<ArraySize(statMutex) );\n  assert( sqlite3_mutex_held(statMutex[op] ? sqlite3Pcache1Mutex()\n                                           : sqlite3MallocMutex()) );\n  assert( op==SQLITE_STATUS_MALLOC_SIZE\n          || op==SQLITE_STATUS_PAGECACHE_SIZE\n          || op==SQLITE_STATUS_PARSER_STACK );\n  if( newValue>wsdStat.mxValue[op] ){\n    wsdStat.mxValue[op] = newValue;\n  }\n}\n\n/*\n** Query status information.\n*/\nSQLITE_API int sqlite3_status64(\n  int op,\n  sqlite3_int64 *pCurrent,\n  sqlite3_int64 *pHighwater,\n  int resetFlag\n){\n  sqlite3_mutex *pMutex;\n  wsdStatInit;\n  if( op<0 || op>=ArraySize(wsdStat.nowValue) ){\n    return SQLITE_MISUSE_BKPT;\n  }\n#ifdef SQLITE_ENABLE_API_ARMOR\n  if( pCurrent==0 || pHighwater==0 ) return SQLITE_MISUSE_BKPT;\n#endif\n  pMutex = statMutex[op] ? sqlite3Pcache1Mutex() : sqlite3MallocMutex();\n  sqlite3_mutex_enter(pMutex);\n  *pCurrent = wsdStat.nowValue[op];\n  *pHighwater = wsdStat.mxValue[op];\n  if( resetFlag ){\n    wsdStat.mxValue[op] = wsdStat.nowValue[op];\n  }\n  sqlite3_mutex_leave(pMutex);\n  (void)pMutex;  /* Prevent warning when SQLITE_THREADSAFE=0 */\n  return SQLITE_OK;\n}\nSQLITE_API int sqlite3_status(int op, int *pCurrent, int *pHighwater, int resetFlag){\n  sqlite3_int64 iCur = 0, iHwtr = 0;\n  int rc;\n#ifdef SQLITE_ENABLE_API_ARMOR\n  if( pCurrent==0 || pHighwater==0 ) return SQLITE_MISUSE_BKPT;\n#endif\n  rc = sqlite3_status64(op, &iCur, &iHwtr, resetFlag);\n  if( rc==0 ){\n    *pCurrent = (int)iCur;\n    *pHighwater = (int)iHwtr;\n  }\n  return rc;\n}\n\n/*\n** Return the number of LookasideSlot elements on the linked list\n*/\nstatic u32 countLookasideSlots(LookasideSlot *p){\n  u32 cnt = 0;\n  while( p ){\n    p = p->pNext;\n    cnt++;\n  }\n  return cnt;\n}\n\n/*\n** Count the number of slots of lookaside memory that are outstanding\n*/\nSQLITE_PRIVATE int sqlite3LookasideUsed(sqlite3 *db, int *pHighwater){\n  u32 nInit = countLookasideSlots(db->lookaside.pInit);\n  u32 nFree = countLookasideSlots(db->lookaside.pFree);\n  if( pHighwater ) *pHighwater = db->lookaside.nSlot - nInit;\n  return db->lookaside.nSlot - (nInit+nFree);\n}\n\n/*\n** Query status information for a single database connection\n*/\nSQLITE_API int sqlite3_db_status(\n  sqlite3 *db,          /* The database connection whose status is desired */\n  int op,               /* Status verb */\n  int *pCurrent,        /* Write current value here */\n  int *pHighwater,      /* Write high-water mark here */\n  int resetFlag         /* Reset high-water mark if true */\n){\n  int rc = SQLITE_OK;   /* Return code */\n#ifdef SQLITE_ENABLE_API_ARMOR\n  if( !sqlite3SafetyCheckOk(db) || pCurrent==0|| pHighwater==0 ){\n    return SQLITE_MISUSE_BKPT;\n  }\n#endif\n  sqlite3_mutex_enter(db->mutex);\n  switch( op ){\n    case SQLITE_DBSTATUS_LOOKASIDE_USED: {\n      *pCurrent = sqlite3LookasideUsed(db, pHighwater);\n      if( resetFlag ){\n        LookasideSlot *p = db->lookaside.pFree;\n        if( p ){\n          while( p->pNext ) p = p->pNext;\n          p->pNext = db->lookaside.pInit;\n          db->lookaside.pInit = db->lookaside.pFree;\n          db->lookaside.pFree = 0;\n        }\n      }\n      break;\n    }\n\n    case SQLITE_DBSTATUS_LOOKASIDE_HIT:\n    case SQLITE_DBSTATUS_LOOKASIDE_MISS_SIZE:\n    case SQLITE_DBSTATUS_LOOKASIDE_MISS_FULL: {\n      testcase( op==SQLITE_DBSTATUS_LOOKASIDE_HIT );\n      testcase( op==SQLITE_DBSTATUS_LOOKASIDE_MISS_SIZE );\n      testcase( op==SQLITE_DBSTATUS_LOOKASIDE_MISS_FULL );\n      assert( (op-SQLITE_DBSTATUS_LOOKASIDE_HIT)>=0 );\n      assert( (op-SQLITE_DBSTATUS_LOOKASIDE_HIT)<3 );\n      *pCurrent = 0;\n      *pHighwater = db->lookaside.anStat[op - SQLITE_DBSTATUS_LOOKASIDE_HIT];\n      if( resetFlag ){\n        db->lookaside.anStat[op - SQLITE_DBSTATUS_LOOKASIDE_HIT] = 0;\n      }\n      break;\n    }\n\n    /* \n    ** Return an approximation for the amount of memory currently used\n    ** by all pagers associated with the given database connection.  The\n    ** highwater mark is meaningless and is returned as zero.\n    */\n    case SQLITE_DBSTATUS_CACHE_USED_SHARED:\n    case SQLITE_DBSTATUS_CACHE_USED: {\n      int totalUsed = 0;\n      int i;\n      sqlite3BtreeEnterAll(db);\n      for(i=0; i<db->nDb; i++){\n        Btree *pBt = db->aDb[i].pBt;\n        if( pBt ){\n          Pager *pPager = sqlite3BtreePager(pBt);\n          int nByte = sqlite3PagerMemUsed(pPager);\n          if( op==SQLITE_DBSTATUS_CACHE_USED_SHARED ){\n            nByte = nByte / sqlite3BtreeConnectionCount(pBt);\n          }\n          totalUsed += nByte;\n        }\n      }\n      sqlite3BtreeLeaveAll(db);\n      *pCurrent = totalUsed;\n      *pHighwater = 0;\n      break;\n    }\n\n    /*\n    ** *pCurrent gets an accurate estimate of the amount of memory used\n    ** to store the schema for all databases (main, temp, and any ATTACHed\n    ** databases.  *pHighwater is set to zero.\n    */\n    case SQLITE_DBSTATUS_SCHEMA_USED: {\n      int i;                      /* Used to iterate through schemas */\n      int nByte = 0;              /* Used to accumulate return value */\n\n      sqlite3BtreeEnterAll(db);\n      db->pnBytesFreed = &nByte;\n      for(i=0; i<db->nDb; i++){\n        Schema *pSchema = db->aDb[i].pSchema;\n        if( ALWAYS(pSchema!=0) ){\n          HashElem *p;\n\n          nByte += sqlite3GlobalConfig.m.xRoundup(sizeof(HashElem)) * (\n              pSchema->tblHash.count \n            + pSchema->trigHash.count\n            + pSchema->idxHash.count\n            + pSchema->fkeyHash.count\n          );\n          nByte += sqlite3_msize(pSchema->tblHash.ht);\n          nByte += sqlite3_msize(pSchema->trigHash.ht);\n          nByte += sqlite3_msize(pSchema->idxHash.ht);\n          nByte += sqlite3_msize(pSchema->fkeyHash.ht);\n\n          for(p=sqliteHashFirst(&pSchema->trigHash); p; p=sqliteHashNext(p)){\n            sqlite3DeleteTrigger(db, (Trigger*)sqliteHashData(p));\n          }\n          for(p=sqliteHashFirst(&pSchema->tblHash); p; p=sqliteHashNext(p)){\n            sqlite3DeleteTable(db, (Table *)sqliteHashData(p));\n          }\n        }\n      }\n      db->pnBytesFreed = 0;\n      sqlite3BtreeLeaveAll(db);\n\n      *pHighwater = 0;\n      *pCurrent = nByte;\n      break;\n    }\n\n    /*\n    ** *pCurrent gets an accurate estimate of the amount of memory used\n    ** to store all prepared statements.\n    ** *pHighwater is set to zero.\n    */\n    case SQLITE_DBSTATUS_STMT_USED: {\n      struct Vdbe *pVdbe;         /* Used to iterate through VMs */\n      int nByte = 0;              /* Used to accumulate return value */\n\n      db->pnBytesFreed = &nByte;\n      for(pVdbe=db->pVdbe; pVdbe; pVdbe=pVdbe->pNext){\n        sqlite3VdbeClearObject(db, pVdbe);\n        sqlite3DbFree(db, pVdbe);\n      }\n      db->pnBytesFreed = 0;\n\n      *pHighwater = 0;  /* IMP: R-64479-57858 */\n      *pCurrent = nByte;\n\n      break;\n    }\n\n    /*\n    ** Set *pCurrent to the total cache hits or misses encountered by all\n    ** pagers the database handle is connected to. *pHighwater is always set \n    ** to zero.\n    */\n    case SQLITE_DBSTATUS_CACHE_HIT:\n    case SQLITE_DBSTATUS_CACHE_MISS:\n    case SQLITE_DBSTATUS_CACHE_WRITE:{\n      int i;\n      int nRet = 0;\n      assert( SQLITE_DBSTATUS_CACHE_MISS==SQLITE_DBSTATUS_CACHE_HIT+1 );\n      assert( SQLITE_DBSTATUS_CACHE_WRITE==SQLITE_DBSTATUS_CACHE_HIT+2 );\n\n      for(i=0; i<db->nDb; i++){\n        if( db->aDb[i].pBt ){\n          Pager *pPager = sqlite3BtreePager(db->aDb[i].pBt);\n          sqlite3PagerCacheStat(pPager, op, resetFlag, &nRet);\n        }\n      }\n      *pHighwater = 0; /* IMP: R-42420-56072 */\n                       /* IMP: R-54100-20147 */\n                       /* IMP: R-29431-39229 */\n      *pCurrent = nRet;\n      break;\n    }\n\n    /* Set *pCurrent to non-zero if there are unresolved deferred foreign\n    ** key constraints.  Set *pCurrent to zero if all foreign key constraints\n    ** have been satisfied.  The *pHighwater is always set to zero.\n    */\n    case SQLITE_DBSTATUS_DEFERRED_FKS: {\n      *pHighwater = 0;  /* IMP: R-11967-56545 */\n      *pCurrent = db->nDeferredImmCons>0 || db->nDeferredCons>0;\n      break;\n    }\n\n    default: {\n      rc = SQLITE_ERROR;\n    }\n  }\n  sqlite3_mutex_leave(db->mutex);\n  return rc;\n}\n\n/************** End of status.c **********************************************/\n/************** Begin file date.c ********************************************/\n/*\n** 2003 October 31\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n*************************************************************************\n** This file contains the C functions that implement date and time\n** functions for SQLite.  \n**\n** There is only one exported symbol in this file - the function\n** sqlite3RegisterDateTimeFunctions() found at the bottom of the file.\n** All other code has file scope.\n**\n** SQLite processes all times and dates as julian day numbers.  The\n** dates and times are stored as the number of days since noon\n** in Greenwich on November 24, 4714 B.C. according to the Gregorian\n** calendar system. \n**\n** 1970-01-01 00:00:00 is JD 2440587.5\n** 2000-01-01 00:00:00 is JD 2451544.5\n**\n** This implementation requires years to be expressed as a 4-digit number\n** which means that only dates between 0000-01-01 and 9999-12-31 can\n** be represented, even though julian day numbers allow a much wider\n** range of dates.\n**\n** The Gregorian calendar system is used for all dates and times,\n** even those that predate the Gregorian calendar.  Historians usually\n** use the julian calendar for dates prior to 1582-10-15 and for some\n** dates afterwards, depending on locale.  Beware of this difference.\n**\n** The conversion algorithms are implemented based on descriptions\n** in the following text:\n**\n**      Jean Meeus\n**      Astronomical Algorithms, 2nd Edition, 1998\n**      ISBN 0-943396-61-1\n**      Willmann-Bell, Inc\n**      Richmond, Virginia (USA)\n*/\n/* #include \"sqliteInt.h\" */\n/* #include <stdlib.h> */\n/* #include <assert.h> */\n#include <time.h>\n\n#ifndef SQLITE_OMIT_DATETIME_FUNCS\n\n/*\n** The MSVC CRT on Windows CE may not have a localtime() function.\n** So declare a substitute.  The substitute function itself is\n** defined in \"os_win.c\".\n*/\n#if !defined(SQLITE_OMIT_LOCALTIME) && defined(_WIN32_WCE) && \\\n    (!defined(SQLITE_MSVC_LOCALTIME_API) || !SQLITE_MSVC_LOCALTIME_API)\nstruct tm *__cdecl localtime(const time_t *);\n#endif\n\n/*\n** A structure for holding a single date and time.\n*/\ntypedef struct DateTime DateTime;\nstruct DateTime {\n  sqlite3_int64 iJD;  /* The julian day number times 86400000 */\n  int Y, M, D;        /* Year, month, and day */\n  int h, m;           /* Hour and minutes */\n  int tz;             /* Timezone offset in minutes */\n  double s;           /* Seconds */\n  char validJD;       /* True (1) if iJD is valid */\n  char rawS;          /* Raw numeric value stored in s */\n  char validYMD;      /* True (1) if Y,M,D are valid */\n  char validHMS;      /* True (1) if h,m,s are valid */\n  char validTZ;       /* True (1) if tz is valid */\n  char tzSet;         /* Timezone was set explicitly */\n  char isError;       /* An overflow has occurred */\n};\n\n\n/*\n** Convert zDate into one or more integers according to the conversion\n** specifier zFormat.\n**\n** zFormat[] contains 4 characters for each integer converted, except for\n** the last integer which is specified by three characters.  The meaning\n** of a four-character format specifiers ABCD is:\n**\n**    A:   number of digits to convert.  Always \"2\" or \"4\".\n**    B:   minimum value.  Always \"0\" or \"1\".\n**    C:   maximum value, decoded as:\n**           a:  12\n**           b:  14\n**           c:  24\n**           d:  31\n**           e:  59\n**           f:  9999\n**    D:   the separator character, or \\000 to indicate this is the\n**         last number to convert.\n**\n** Example:  To translate an ISO-8601 date YYYY-MM-DD, the format would\n** be \"40f-21a-20c\".  The \"40f-\" indicates the 4-digit year followed by \"-\".\n** The \"21a-\" indicates the 2-digit month followed by \"-\".  The \"20c\" indicates\n** the 2-digit day which is the last integer in the set.\n**\n** The function returns the number of successful conversions.\n*/\nstatic int getDigits(const char *zDate, const char *zFormat, ...){\n  /* The aMx[] array translates the 3rd character of each format\n  ** spec into a max size:    a   b   c   d   e     f */\n  static const u16 aMx[] = { 12, 14, 24, 31, 59, 9999 };\n  va_list ap;\n  int cnt = 0;\n  char nextC;\n  va_start(ap, zFormat);\n  do{\n    char N = zFormat[0] - '0';\n    char min = zFormat[1] - '0';\n    int val = 0;\n    u16 max;\n\n    assert( zFormat[2]>='a' && zFormat[2]<='f' );\n    max = aMx[zFormat[2] - 'a'];\n    nextC = zFormat[3];\n    val = 0;\n    while( N-- ){\n      if( !sqlite3Isdigit(*zDate) ){\n        goto end_getDigits;\n      }\n      val = val*10 + *zDate - '0';\n      zDate++;\n    }\n    if( val<(int)min || val>(int)max || (nextC!=0 && nextC!=*zDate) ){\n      goto end_getDigits;\n    }\n    *va_arg(ap,int*) = val;\n    zDate++;\n    cnt++;\n    zFormat += 4;\n  }while( nextC );\nend_getDigits:\n  va_end(ap);\n  return cnt;\n}\n\n/*\n** Parse a timezone extension on the end of a date-time.\n** The extension is of the form:\n**\n**        (+/-)HH:MM\n**\n** Or the \"zulu\" notation:\n**\n**        Z\n**\n** If the parse is successful, write the number of minutes\n** of change in p->tz and return 0.  If a parser error occurs,\n** return non-zero.\n**\n** A missing specifier is not considered an error.\n*/\nstatic int parseTimezone(const char *zDate, DateTime *p){\n  int sgn = 0;\n  int nHr, nMn;\n  int c;\n  while( sqlite3Isspace(*zDate) ){ zDate++; }\n  p->tz = 0;\n  c = *zDate;\n  if( c=='-' ){\n    sgn = -1;\n  }else if( c=='+' ){\n    sgn = +1;\n  }else if( c=='Z' || c=='z' ){\n    zDate++;\n    goto zulu_time;\n  }else{\n    return c!=0;\n  }\n  zDate++;\n  if( getDigits(zDate, \"20b:20e\", &nHr, &nMn)!=2 ){\n    return 1;\n  }\n  zDate += 5;\n  p->tz = sgn*(nMn + nHr*60);\nzulu_time:\n  while( sqlite3Isspace(*zDate) ){ zDate++; }\n  p->tzSet = 1;\n  return *zDate!=0;\n}\n\n/*\n** Parse times of the form HH:MM or HH:MM:SS or HH:MM:SS.FFFF.\n** The HH, MM, and SS must each be exactly 2 digits.  The\n** fractional seconds FFFF can be one or more digits.\n**\n** Return 1 if there is a parsing error and 0 on success.\n*/\nstatic int parseHhMmSs(const char *zDate, DateTime *p){\n  int h, m, s;\n  double ms = 0.0;\n  if( getDigits(zDate, \"20c:20e\", &h, &m)!=2 ){\n    return 1;\n  }\n  zDate += 5;\n  if( *zDate==':' ){\n    zDate++;\n    if( getDigits(zDate, \"20e\", &s)!=1 ){\n      return 1;\n    }\n    zDate += 2;\n    if( *zDate=='.' && sqlite3Isdigit(zDate[1]) ){\n      double rScale = 1.0;\n      zDate++;\n      while( sqlite3Isdigit(*zDate) ){\n        ms = ms*10.0 + *zDate - '0';\n        rScale *= 10.0;\n        zDate++;\n      }\n      ms /= rScale;\n    }\n  }else{\n    s = 0;\n  }\n  p->validJD = 0;\n  p->rawS = 0;\n  p->validHMS = 1;\n  p->h = h;\n  p->m = m;\n  p->s = s + ms;\n  if( parseTimezone(zDate, p) ) return 1;\n  p->validTZ = (p->tz!=0)?1:0;\n  return 0;\n}\n\n/*\n** Put the DateTime object into its error state.\n*/\nstatic void datetimeError(DateTime *p){\n  memset(p, 0, sizeof(*p));\n  p->isError = 1;\n}\n\n/*\n** Convert from YYYY-MM-DD HH:MM:SS to julian day.  We always assume\n** that the YYYY-MM-DD is according to the Gregorian calendar.\n**\n** Reference:  Meeus page 61\n*/\nstatic void computeJD(DateTime *p){\n  int Y, M, D, A, B, X1, X2;\n\n  if( p->validJD ) return;\n  if( p->validYMD ){\n    Y = p->Y;\n    M = p->M;\n    D = p->D;\n  }else{\n    Y = 2000;  /* If no YMD specified, assume 2000-Jan-01 */\n    M = 1;\n    D = 1;\n  }\n  if( Y<-4713 || Y>9999 || p->rawS ){\n    datetimeError(p);\n    return;\n  }\n  if( M<=2 ){\n    Y--;\n    M += 12;\n  }\n  A = Y/100;\n  B = 2 - A + (A/4);\n  X1 = 36525*(Y+4716)/100;\n  X2 = 306001*(M+1)/10000;\n  p->iJD = (sqlite3_int64)((X1 + X2 + D + B - 1524.5 ) * 86400000);\n  p->validJD = 1;\n  if( p->validHMS ){\n    p->iJD += p->h*3600000 + p->m*60000 + (sqlite3_int64)(p->s*1000);\n    if( p->validTZ ){\n      p->iJD -= p->tz*60000;\n      p->validYMD = 0;\n      p->validHMS = 0;\n      p->validTZ = 0;\n    }\n  }\n}\n\n/*\n** Parse dates of the form\n**\n**     YYYY-MM-DD HH:MM:SS.FFF\n**     YYYY-MM-DD HH:MM:SS\n**     YYYY-MM-DD HH:MM\n**     YYYY-MM-DD\n**\n** Write the result into the DateTime structure and return 0\n** on success and 1 if the input string is not a well-formed\n** date.\n*/\nstatic int parseYyyyMmDd(const char *zDate, DateTime *p){\n  int Y, M, D, neg;\n\n  if( zDate[0]=='-' ){\n    zDate++;\n    neg = 1;\n  }else{\n    neg = 0;\n  }\n  if( getDigits(zDate, \"40f-21a-21d\", &Y, &M, &D)!=3 ){\n    return 1;\n  }\n  zDate += 10;\n  while( sqlite3Isspace(*zDate) || 'T'==*(u8*)zDate ){ zDate++; }\n  if( parseHhMmSs(zDate, p)==0 ){\n    /* We got the time */\n  }else if( *zDate==0 ){\n    p->validHMS = 0;\n  }else{\n    return 1;\n  }\n  p->validJD = 0;\n  p->validYMD = 1;\n  p->Y = neg ? -Y : Y;\n  p->M = M;\n  p->D = D;\n  if( p->validTZ ){\n    computeJD(p);\n  }\n  return 0;\n}\n\n/*\n** Set the time to the current time reported by the VFS.\n**\n** Return the number of errors.\n*/\nstatic int setDateTimeToCurrent(sqlite3_context *context, DateTime *p){\n  p->iJD = sqlite3StmtCurrentTime(context);\n  if( p->iJD>0 ){\n    p->validJD = 1;\n    return 0;\n  }else{\n    return 1;\n  }\n}\n\n/*\n** Input \"r\" is a numeric quantity which might be a julian day number,\n** or the number of seconds since 1970.  If the value if r is within\n** range of a julian day number, install it as such and set validJD.\n** If the value is a valid unix timestamp, put it in p->s and set p->rawS.\n*/\nstatic void setRawDateNumber(DateTime *p, double r){\n  p->s = r;\n  p->rawS = 1;\n  if( r>=0.0 && r<5373484.5 ){\n    p->iJD = (sqlite3_int64)(r*86400000.0 + 0.5);\n    p->validJD = 1;\n  }\n}\n\n/*\n** Attempt to parse the given string into a julian day number.  Return\n** the number of errors.\n**\n** The following are acceptable forms for the input string:\n**\n**      YYYY-MM-DD HH:MM:SS.FFF  +/-HH:MM\n**      DDDD.DD \n**      now\n**\n** In the first form, the +/-HH:MM is always optional.  The fractional\n** seconds extension (the \".FFF\") is optional.  The seconds portion\n** (\":SS.FFF\") is option.  The year and date can be omitted as long\n** as there is a time string.  The time string can be omitted as long\n** as there is a year and date.\n*/\nstatic int parseDateOrTime(\n  sqlite3_context *context, \n  const char *zDate, \n  DateTime *p\n){\n  double r;\n  if( parseYyyyMmDd(zDate,p)==0 ){\n    return 0;\n  }else if( parseHhMmSs(zDate, p)==0 ){\n    return 0;\n  }else if( sqlite3StrICmp(zDate,\"now\")==0 && sqlite3NotPureFunc(context) ){\n    return setDateTimeToCurrent(context, p);\n  }else if( sqlite3AtoF(zDate, &r, sqlite3Strlen30(zDate), SQLITE_UTF8) ){\n    setRawDateNumber(p, r);\n    return 0;\n  }\n  return 1;\n}\n\n/* The julian day number for 9999-12-31 23:59:59.999 is 5373484.4999999.\n** Multiplying this by 86400000 gives 464269060799999 as the maximum value\n** for DateTime.iJD.\n**\n** But some older compilers (ex: gcc 4.2.1 on older Macs) cannot deal with \n** such a large integer literal, so we have to encode it.\n*/\n#define INT_464269060799999  ((((i64)0x1a640)<<32)|0x1072fdff)\n\n/*\n** Return TRUE if the given julian day number is within range.\n**\n** The input is the JulianDay times 86400000.\n*/\nstatic int validJulianDay(sqlite3_int64 iJD){\n  return iJD>=0 && iJD<=INT_464269060799999;\n}\n\n/*\n** Compute the Year, Month, and Day from the julian day number.\n*/\nstatic void computeYMD(DateTime *p){\n  int Z, A, B, C, D, E, X1;\n  if( p->validYMD ) return;\n  if( !p->validJD ){\n    p->Y = 2000;\n    p->M = 1;\n    p->D = 1;\n  }else if( !validJulianDay(p->iJD) ){\n    datetimeError(p);\n    return;\n  }else{\n    Z = (int)((p->iJD + 43200000)/86400000);\n    A = (int)((Z - 1867216.25)/36524.25);\n    A = Z + 1 + A - (A/4);\n    B = A + 1524;\n    C = (int)((B - 122.1)/365.25);\n    D = (36525*(C&32767))/100;\n    E = (int)((B-D)/30.6001);\n    X1 = (int)(30.6001*E);\n    p->D = B - D - X1;\n    p->M = E<14 ? E-1 : E-13;\n    p->Y = p->M>2 ? C - 4716 : C - 4715;\n  }\n  p->validYMD = 1;\n}\n\n/*\n** Compute the Hour, Minute, and Seconds from the julian day number.\n*/\nstatic void computeHMS(DateTime *p){\n  int s;\n  if( p->validHMS ) return;\n  computeJD(p);\n  s = (int)((p->iJD + 43200000) % 86400000);\n  p->s = s/1000.0;\n  s = (int)p->s;\n  p->s -= s;\n  p->h = s/3600;\n  s -= p->h*3600;\n  p->m = s/60;\n  p->s += s - p->m*60;\n  p->rawS = 0;\n  p->validHMS = 1;\n}\n\n/*\n** Compute both YMD and HMS\n*/\nstatic void computeYMD_HMS(DateTime *p){\n  computeYMD(p);\n  computeHMS(p);\n}\n\n/*\n** Clear the YMD and HMS and the TZ\n*/\nstatic void clearYMD_HMS_TZ(DateTime *p){\n  p->validYMD = 0;\n  p->validHMS = 0;\n  p->validTZ = 0;\n}\n\n#ifndef SQLITE_OMIT_LOCALTIME\n/*\n** On recent Windows platforms, the localtime_s() function is available\n** as part of the \"Secure CRT\". It is essentially equivalent to \n** localtime_r() available under most POSIX platforms, except that the \n** order of the parameters is reversed.\n**\n** See http://msdn.microsoft.com/en-us/library/a442x3ye(VS.80).aspx.\n**\n** If the user has not indicated to use localtime_r() or localtime_s()\n** already, check for an MSVC build environment that provides \n** localtime_s().\n*/\n#if !HAVE_LOCALTIME_R && !HAVE_LOCALTIME_S \\\n    && defined(_MSC_VER) && defined(_CRT_INSECURE_DEPRECATE)\n#undef  HAVE_LOCALTIME_S\n#define HAVE_LOCALTIME_S 1\n#endif\n\n/*\n** The following routine implements the rough equivalent of localtime_r()\n** using whatever operating-system specific localtime facility that\n** is available.  This routine returns 0 on success and\n** non-zero on any kind of error.\n**\n** If the sqlite3GlobalConfig.bLocaltimeFault variable is true then this\n** routine will always fail.\n**\n** EVIDENCE-OF: R-62172-00036 In this implementation, the standard C\n** library function localtime_r() is used to assist in the calculation of\n** local time.\n*/\nstatic int osLocaltime(time_t *t, struct tm *pTm){\n  int rc;\n#if !HAVE_LOCALTIME_R && !HAVE_LOCALTIME_S\n  struct tm *pX;\n#if SQLITE_THREADSAFE>0\n  sqlite3_mutex *mutex = sqlite3MutexAlloc(SQLITE_MUTEX_STATIC_MASTER);\n#endif\n  sqlite3_mutex_enter(mutex);\n  pX = localtime(t);\n#ifndef SQLITE_UNTESTABLE\n  if( sqlite3GlobalConfig.bLocaltimeFault ) pX = 0;\n#endif\n  if( pX ) *pTm = *pX;\n  sqlite3_mutex_leave(mutex);\n  rc = pX==0;\n#else\n#ifndef SQLITE_UNTESTABLE\n  if( sqlite3GlobalConfig.bLocaltimeFault ) return 1;\n#endif\n#if HAVE_LOCALTIME_R\n  rc = localtime_r(t, pTm)==0;\n#else\n  rc = localtime_s(pTm, t);\n#endif /* HAVE_LOCALTIME_R */\n#endif /* HAVE_LOCALTIME_R || HAVE_LOCALTIME_S */\n  return rc;\n}\n#endif /* SQLITE_OMIT_LOCALTIME */\n\n\n#ifndef SQLITE_OMIT_LOCALTIME\n/*\n** Compute the difference (in milliseconds) between localtime and UTC\n** (a.k.a. GMT) for the time value p where p is in UTC. If no error occurs,\n** return this value and set *pRc to SQLITE_OK. \n**\n** Or, if an error does occur, set *pRc to SQLITE_ERROR. The returned value\n** is undefined in this case.\n*/\nstatic sqlite3_int64 localtimeOffset(\n  DateTime *p,                    /* Date at which to calculate offset */\n  sqlite3_context *pCtx,          /* Write error here if one occurs */\n  int *pRc                        /* OUT: Error code. SQLITE_OK or ERROR */\n){\n  DateTime x, y;\n  time_t t;\n  struct tm sLocal;\n\n  /* Initialize the contents of sLocal to avoid a compiler warning. */\n  memset(&sLocal, 0, sizeof(sLocal));\n\n  x = *p;\n  computeYMD_HMS(&x);\n  if( x.Y<1971 || x.Y>=2038 ){\n    /* EVIDENCE-OF: R-55269-29598 The localtime_r() C function normally only\n    ** works for years between 1970 and 2037. For dates outside this range,\n    ** SQLite attempts to map the year into an equivalent year within this\n    ** range, do the calculation, then map the year back.\n    */\n    x.Y = 2000;\n    x.M = 1;\n    x.D = 1;\n    x.h = 0;\n    x.m = 0;\n    x.s = 0.0;\n  } else {\n    int s = (int)(x.s + 0.5);\n    x.s = s;\n  }\n  x.tz = 0;\n  x.validJD = 0;\n  computeJD(&x);\n  t = (time_t)(x.iJD/1000 - 21086676*(i64)10000);\n  if( osLocaltime(&t, &sLocal) ){\n    sqlite3_result_error(pCtx, \"local time unavailable\", -1);\n    *pRc = SQLITE_ERROR;\n    return 0;\n  }\n  y.Y = sLocal.tm_year + 1900;\n  y.M = sLocal.tm_mon + 1;\n  y.D = sLocal.tm_mday;\n  y.h = sLocal.tm_hour;\n  y.m = sLocal.tm_min;\n  y.s = sLocal.tm_sec;\n  y.validYMD = 1;\n  y.validHMS = 1;\n  y.validJD = 0;\n  y.rawS = 0;\n  y.validTZ = 0;\n  y.isError = 0;\n  computeJD(&y);\n  *pRc = SQLITE_OK;\n  return y.iJD - x.iJD;\n}\n#endif /* SQLITE_OMIT_LOCALTIME */\n\n/*\n** The following table defines various date transformations of the form\n**\n**            'NNN days'\n**\n** Where NNN is an arbitrary floating-point number and \"days\" can be one\n** of several units of time.\n*/\nstatic const struct {\n  u8 eType;           /* Transformation type code */\n  u8 nName;           /* Length of th name */\n  char *zName;        /* Name of the transformation */\n  double rLimit;      /* Maximum NNN value for this transform */\n  double rXform;      /* Constant used for this transform */\n} aXformType[] = {\n  { 0, 6, \"second\", 464269060800.0, 86400000.0/(24.0*60.0*60.0) },\n  { 0, 6, \"minute\", 7737817680.0,   86400000.0/(24.0*60.0)      },\n  { 0, 4, \"hour\",   128963628.0,    86400000.0/24.0             },\n  { 0, 3, \"day\",    5373485.0,      86400000.0                  },\n  { 1, 5, \"month\",  176546.0,       30.0*86400000.0             },\n  { 2, 4, \"year\",   14713.0,        365.0*86400000.0            },\n};\n\n/*\n** Process a modifier to a date-time stamp.  The modifiers are\n** as follows:\n**\n**     NNN days\n**     NNN hours\n**     NNN minutes\n**     NNN.NNNN seconds\n**     NNN months\n**     NNN years\n**     start of month\n**     start of year\n**     start of week\n**     start of day\n**     weekday N\n**     unixepoch\n**     localtime\n**     utc\n**\n** Return 0 on success and 1 if there is any kind of error. If the error\n** is in a system call (i.e. localtime()), then an error message is written\n** to context pCtx. If the error is an unrecognized modifier, no error is\n** written to pCtx.\n*/\nstatic int parseModifier(\n  sqlite3_context *pCtx,      /* Function context */\n  const char *z,              /* The text of the modifier */\n  int n,                      /* Length of zMod in bytes */\n  DateTime *p                 /* The date/time value to be modified */\n){\n  int rc = 1;\n  double r;\n  switch(sqlite3UpperToLower[(u8)z[0]] ){\n#ifndef SQLITE_OMIT_LOCALTIME\n    case 'l': {\n      /*    localtime\n      **\n      ** Assuming the current time value is UTC (a.k.a. GMT), shift it to\n      ** show local time.\n      */\n      if( sqlite3_stricmp(z, \"localtime\")==0 && sqlite3NotPureFunc(pCtx) ){\n        computeJD(p);\n        p->iJD += localtimeOffset(p, pCtx, &rc);\n        clearYMD_HMS_TZ(p);\n      }\n      break;\n    }\n#endif\n    case 'u': {\n      /*\n      **    unixepoch\n      **\n      ** Treat the current value of p->s as the number of\n      ** seconds since 1970.  Convert to a real julian day number.\n      */\n      if( sqlite3_stricmp(z, \"unixepoch\")==0 && p->rawS ){\n        r = p->s*1000.0 + 210866760000000.0;\n        if( r>=0.0 && r<464269060800000.0 ){\n          clearYMD_HMS_TZ(p);\n          p->iJD = (sqlite3_int64)r;\n          p->validJD = 1;\n          p->rawS = 0;\n          rc = 0;\n        }\n      }\n#ifndef SQLITE_OMIT_LOCALTIME\n      else if( sqlite3_stricmp(z, \"utc\")==0 && sqlite3NotPureFunc(pCtx) ){\n        if( p->tzSet==0 ){\n          sqlite3_int64 c1;\n          computeJD(p);\n          c1 = localtimeOffset(p, pCtx, &rc);\n          if( rc==SQLITE_OK ){\n            p->iJD -= c1;\n            clearYMD_HMS_TZ(p);\n            p->iJD += c1 - localtimeOffset(p, pCtx, &rc);\n          }\n          p->tzSet = 1;\n        }else{\n          rc = SQLITE_OK;\n        }\n      }\n#endif\n      break;\n    }\n    case 'w': {\n      /*\n      **    weekday N\n      **\n      ** Move the date to the same time on the next occurrence of\n      ** weekday N where 0==Sunday, 1==Monday, and so forth.  If the\n      ** date is already on the appropriate weekday, this is a no-op.\n      */\n      if( sqlite3_strnicmp(z, \"weekday \", 8)==0\n               && sqlite3AtoF(&z[8], &r, sqlite3Strlen30(&z[8]), SQLITE_UTF8)\n               && (n=(int)r)==r && n>=0 && r<7 ){\n        sqlite3_int64 Z;\n        computeYMD_HMS(p);\n        p->validTZ = 0;\n        p->validJD = 0;\n        computeJD(p);\n        Z = ((p->iJD + 129600000)/86400000) % 7;\n        if( Z>n ) Z -= 7;\n        p->iJD += (n - Z)*86400000;\n        clearYMD_HMS_TZ(p);\n        rc = 0;\n      }\n      break;\n    }\n    case 's': {\n      /*\n      **    start of TTTTT\n      **\n      ** Move the date backwards to the beginning of the current day,\n      ** or month or year.\n      */\n      if( sqlite3_strnicmp(z, \"start of \", 9)!=0 ) break;\n      if( !p->validJD && !p->validYMD && !p->validHMS ) break;\n      z += 9;\n      computeYMD(p);\n      p->validHMS = 1;\n      p->h = p->m = 0;\n      p->s = 0.0;\n      p->rawS = 0;\n      p->validTZ = 0;\n      p->validJD = 0;\n      if( sqlite3_stricmp(z,\"month\")==0 ){\n        p->D = 1;\n        rc = 0;\n      }else if( sqlite3_stricmp(z,\"year\")==0 ){\n        p->M = 1;\n        p->D = 1;\n        rc = 0;\n      }else if( sqlite3_stricmp(z,\"day\")==0 ){\n        rc = 0;\n      }\n      break;\n    }\n    case '+':\n    case '-':\n    case '0':\n    case '1':\n    case '2':\n    case '3':\n    case '4':\n    case '5':\n    case '6':\n    case '7':\n    case '8':\n    case '9': {\n      double rRounder;\n      int i;\n      for(n=1; z[n] && z[n]!=':' && !sqlite3Isspace(z[n]); n++){}\n      if( !sqlite3AtoF(z, &r, n, SQLITE_UTF8) ){\n        rc = 1;\n        break;\n      }\n      if( z[n]==':' ){\n        /* A modifier of the form (+|-)HH:MM:SS.FFF adds (or subtracts) the\n        ** specified number of hours, minutes, seconds, and fractional seconds\n        ** to the time.  The \".FFF\" may be omitted.  The \":SS.FFF\" may be\n        ** omitted.\n        */\n        const char *z2 = z;\n        DateTime tx;\n        sqlite3_int64 day;\n        if( !sqlite3Isdigit(*z2) ) z2++;\n        memset(&tx, 0, sizeof(tx));\n        if( parseHhMmSs(z2, &tx) ) break;\n        computeJD(&tx);\n        tx.iJD -= 43200000;\n        day = tx.iJD/86400000;\n        tx.iJD -= day*86400000;\n        if( z[0]=='-' ) tx.iJD = -tx.iJD;\n        computeJD(p);\n        clearYMD_HMS_TZ(p);\n        p->iJD += tx.iJD;\n        rc = 0;\n        break;\n      }\n\n      /* If control reaches this point, it means the transformation is\n      ** one of the forms like \"+NNN days\".  */\n      z += n;\n      while( sqlite3Isspace(*z) ) z++;\n      n = sqlite3Strlen30(z);\n      if( n>10 || n<3 ) break;\n      if( sqlite3UpperToLower[(u8)z[n-1]]=='s' ) n--;\n      computeJD(p);\n      rc = 1;\n      rRounder = r<0 ? -0.5 : +0.5;\n      for(i=0; i<ArraySize(aXformType); i++){\n        if( aXformType[i].nName==n\n         && sqlite3_strnicmp(aXformType[i].zName, z, n)==0\n         && r>-aXformType[i].rLimit && r<aXformType[i].rLimit\n        ){\n          switch( aXformType[i].eType ){\n            case 1: { /* Special processing to add months */\n              int x;\n              computeYMD_HMS(p);\n              p->M += (int)r;\n              x = p->M>0 ? (p->M-1)/12 : (p->M-12)/12;\n              p->Y += x;\n              p->M -= x*12;\n              p->validJD = 0;\n              r -= (int)r;\n              break;\n            }\n            case 2: { /* Special processing to add years */\n              int y = (int)r;\n              computeYMD_HMS(p);\n              p->Y += y;\n              p->validJD = 0;\n              r -= (int)r;\n              break;\n            }\n          }\n          computeJD(p);\n          p->iJD += (sqlite3_int64)(r*aXformType[i].rXform + rRounder);\n          rc = 0;\n          break;\n        }\n      }\n      clearYMD_HMS_TZ(p);\n      break;\n    }\n    default: {\n      break;\n    }\n  }\n  return rc;\n}\n\n/*\n** Process time function arguments.  argv[0] is a date-time stamp.\n** argv[1] and following are modifiers.  Parse them all and write\n** the resulting time into the DateTime structure p.  Return 0\n** on success and 1 if there are any errors.\n**\n** If there are zero parameters (if even argv[0] is undefined)\n** then assume a default value of \"now\" for argv[0].\n*/\nstatic int isDate(\n  sqlite3_context *context, \n  int argc, \n  sqlite3_value **argv, \n  DateTime *p\n){\n  int i, n;\n  const unsigned char *z;\n  int eType;\n  memset(p, 0, sizeof(*p));\n  if( argc==0 ){\n    return setDateTimeToCurrent(context, p);\n  }\n  if( (eType = sqlite3_value_type(argv[0]))==SQLITE_FLOAT\n                   || eType==SQLITE_INTEGER ){\n    setRawDateNumber(p, sqlite3_value_double(argv[0]));\n  }else{\n    z = sqlite3_value_text(argv[0]);\n    if( !z || parseDateOrTime(context, (char*)z, p) ){\n      return 1;\n    }\n  }\n  for(i=1; i<argc; i++){\n    z = sqlite3_value_text(argv[i]);\n    n = sqlite3_value_bytes(argv[i]);\n    if( z==0 || parseModifier(context, (char*)z, n, p) ) return 1;\n  }\n  computeJD(p);\n  if( p->isError || !validJulianDay(p->iJD) ) return 1;\n  return 0;\n}\n\n\n/*\n** The following routines implement the various date and time functions\n** of SQLite.\n*/\n\n/*\n**    julianday( TIMESTRING, MOD, MOD, ...)\n**\n** Return the julian day number of the date specified in the arguments\n*/\nstatic void juliandayFunc(\n  sqlite3_context *context,\n  int argc,\n  sqlite3_value **argv\n){\n  DateTime x;\n  if( isDate(context, argc, argv, &x)==0 ){\n    computeJD(&x);\n    sqlite3_result_double(context, x.iJD/86400000.0);\n  }\n}\n\n/*\n**    datetime( TIMESTRING, MOD, MOD, ...)\n**\n** Return YYYY-MM-DD HH:MM:SS\n*/\nstatic void datetimeFunc(\n  sqlite3_context *context,\n  int argc,\n  sqlite3_value **argv\n){\n  DateTime x;\n  if( isDate(context, argc, argv, &x)==0 ){\n    char zBuf[100];\n    computeYMD_HMS(&x);\n    sqlite3_snprintf(sizeof(zBuf), zBuf, \"%04d-%02d-%02d %02d:%02d:%02d\",\n                     x.Y, x.M, x.D, x.h, x.m, (int)(x.s));\n    sqlite3_result_text(context, zBuf, -1, SQLITE_TRANSIENT);\n  }\n}\n\n/*\n**    time( TIMESTRING, MOD, MOD, ...)\n**\n** Return HH:MM:SS\n*/\nstatic void timeFunc(\n  sqlite3_context *context,\n  int argc,\n  sqlite3_value **argv\n){\n  DateTime x;\n  if( isDate(context, argc, argv, &x)==0 ){\n    char zBuf[100];\n    computeHMS(&x);\n    sqlite3_snprintf(sizeof(zBuf), zBuf, \"%02d:%02d:%02d\", x.h, x.m, (int)x.s);\n    sqlite3_result_text(context, zBuf, -1, SQLITE_TRANSIENT);\n  }\n}\n\n/*\n**    date( TIMESTRING, MOD, MOD, ...)\n**\n** Return YYYY-MM-DD\n*/\nstatic void dateFunc(\n  sqlite3_context *context,\n  int argc,\n  sqlite3_value **argv\n){\n  DateTime x;\n  if( isDate(context, argc, argv, &x)==0 ){\n    char zBuf[100];\n    computeYMD(&x);\n    sqlite3_snprintf(sizeof(zBuf), zBuf, \"%04d-%02d-%02d\", x.Y, x.M, x.D);\n    sqlite3_result_text(context, zBuf, -1, SQLITE_TRANSIENT);\n  }\n}\n\n/*\n**    strftime( FORMAT, TIMESTRING, MOD, MOD, ...)\n**\n** Return a string described by FORMAT.  Conversions as follows:\n**\n**   %d  day of month\n**   %f  ** fractional seconds  SS.SSS\n**   %H  hour 00-24\n**   %j  day of year 000-366\n**   %J  ** julian day number\n**   %m  month 01-12\n**   %M  minute 00-59\n**   %s  seconds since 1970-01-01\n**   %S  seconds 00-59\n**   %w  day of week 0-6  sunday==0\n**   %W  week of year 00-53\n**   %Y  year 0000-9999\n**   %%  %\n*/\nstatic void strftimeFunc(\n  sqlite3_context *context,\n  int argc,\n  sqlite3_value **argv\n){\n  DateTime x;\n  u64 n;\n  size_t i,j;\n  char *z;\n  sqlite3 *db;\n  const char *zFmt;\n  char zBuf[100];\n  if( argc==0 ) return;\n  zFmt = (const char*)sqlite3_value_text(argv[0]);\n  if( zFmt==0 || isDate(context, argc-1, argv+1, &x) ) return;\n  db = sqlite3_context_db_handle(context);\n  for(i=0, n=1; zFmt[i]; i++, n++){\n    if( zFmt[i]=='%' ){\n      switch( zFmt[i+1] ){\n        case 'd':\n        case 'H':\n        case 'm':\n        case 'M':\n        case 'S':\n        case 'W':\n          n++;\n          /* fall thru */\n        case 'w':\n        case '%':\n          break;\n        case 'f':\n          n += 8;\n          break;\n        case 'j':\n          n += 3;\n          break;\n        case 'Y':\n          n += 8;\n          break;\n        case 's':\n        case 'J':\n          n += 50;\n          break;\n        default:\n          return;  /* ERROR.  return a NULL */\n      }\n      i++;\n    }\n  }\n  testcase( n==sizeof(zBuf)-1 );\n  testcase( n==sizeof(zBuf) );\n  testcase( n==(u64)db->aLimit[SQLITE_LIMIT_LENGTH]+1 );\n  testcase( n==(u64)db->aLimit[SQLITE_LIMIT_LENGTH] );\n  if( n<sizeof(zBuf) ){\n    z = zBuf;\n  }else if( n>(u64)db->aLimit[SQLITE_LIMIT_LENGTH] ){\n    sqlite3_result_error_toobig(context);\n    return;\n  }else{\n    z = sqlite3DbMallocRawNN(db, (int)n);\n    if( z==0 ){\n      sqlite3_result_error_nomem(context);\n      return;\n    }\n  }\n  computeJD(&x);\n  computeYMD_HMS(&x);\n  for(i=j=0; zFmt[i]; i++){\n    if( zFmt[i]!='%' ){\n      z[j++] = zFmt[i];\n    }else{\n      i++;\n      switch( zFmt[i] ){\n        case 'd':  sqlite3_snprintf(3, &z[j],\"%02d\",x.D); j+=2; break;\n        case 'f': {\n          double s = x.s;\n          if( s>59.999 ) s = 59.999;\n          sqlite3_snprintf(7, &z[j],\"%06.3f\", s);\n          j += sqlite3Strlen30(&z[j]);\n          break;\n        }\n        case 'H':  sqlite3_snprintf(3, &z[j],\"%02d\",x.h); j+=2; break;\n        case 'W': /* Fall thru */\n        case 'j': {\n          int nDay;             /* Number of days since 1st day of year */\n          DateTime y = x;\n          y.validJD = 0;\n          y.M = 1;\n          y.D = 1;\n          computeJD(&y);\n          nDay = (int)((x.iJD-y.iJD+43200000)/86400000);\n          if( zFmt[i]=='W' ){\n            int wd;   /* 0=Monday, 1=Tuesday, ... 6=Sunday */\n            wd = (int)(((x.iJD+43200000)/86400000)%7);\n            sqlite3_snprintf(3, &z[j],\"%02d\",(nDay+7-wd)/7);\n            j += 2;\n          }else{\n            sqlite3_snprintf(4, &z[j],\"%03d\",nDay+1);\n            j += 3;\n          }\n          break;\n        }\n        case 'J': {\n          sqlite3_snprintf(20, &z[j],\"%.16g\",x.iJD/86400000.0);\n          j+=sqlite3Strlen30(&z[j]);\n          break;\n        }\n        case 'm':  sqlite3_snprintf(3, &z[j],\"%02d\",x.M); j+=2; break;\n        case 'M':  sqlite3_snprintf(3, &z[j],\"%02d\",x.m); j+=2; break;\n        case 's': {\n          sqlite3_snprintf(30,&z[j],\"%lld\",\n                           (i64)(x.iJD/1000 - 21086676*(i64)10000));\n          j += sqlite3Strlen30(&z[j]);\n          break;\n        }\n        case 'S':  sqlite3_snprintf(3,&z[j],\"%02d\",(int)x.s); j+=2; break;\n        case 'w': {\n          z[j++] = (char)(((x.iJD+129600000)/86400000) % 7) + '0';\n          break;\n        }\n        case 'Y': {\n          sqlite3_snprintf(5,&z[j],\"%04d\",x.Y); j+=sqlite3Strlen30(&z[j]);\n          break;\n        }\n        default:   z[j++] = '%'; break;\n      }\n    }\n  }\n  z[j] = 0;\n  sqlite3_result_text(context, z, -1,\n                      z==zBuf ? SQLITE_TRANSIENT : SQLITE_DYNAMIC);\n}\n\n/*\n** current_time()\n**\n** This function returns the same value as time('now').\n*/\nstatic void ctimeFunc(\n  sqlite3_context *context,\n  int NotUsed,\n  sqlite3_value **NotUsed2\n){\n  UNUSED_PARAMETER2(NotUsed, NotUsed2);\n  timeFunc(context, 0, 0);\n}\n\n/*\n** current_date()\n**\n** This function returns the same value as date('now').\n*/\nstatic void cdateFunc(\n  sqlite3_context *context,\n  int NotUsed,\n  sqlite3_value **NotUsed2\n){\n  UNUSED_PARAMETER2(NotUsed, NotUsed2);\n  dateFunc(context, 0, 0);\n}\n\n/*\n** current_timestamp()\n**\n** This function returns the same value as datetime('now').\n*/\nstatic void ctimestampFunc(\n  sqlite3_context *context,\n  int NotUsed,\n  sqlite3_value **NotUsed2\n){\n  UNUSED_PARAMETER2(NotUsed, NotUsed2);\n  datetimeFunc(context, 0, 0);\n}\n#endif /* !defined(SQLITE_OMIT_DATETIME_FUNCS) */\n\n#ifdef SQLITE_OMIT_DATETIME_FUNCS\n/*\n** If the library is compiled to omit the full-scale date and time\n** handling (to get a smaller binary), the following minimal version\n** of the functions current_time(), current_date() and current_timestamp()\n** are included instead. This is to support column declarations that\n** include \"DEFAULT CURRENT_TIME\" etc.\n**\n** This function uses the C-library functions time(), gmtime()\n** and strftime(). The format string to pass to strftime() is supplied\n** as the user-data for the function.\n*/\nstatic void currentTimeFunc(\n  sqlite3_context *context,\n  int argc,\n  sqlite3_value **argv\n){\n  time_t t;\n  char *zFormat = (char *)sqlite3_user_data(context);\n  sqlite3_int64 iT;\n  struct tm *pTm;\n  struct tm sNow;\n  char zBuf[20];\n\n  UNUSED_PARAMETER(argc);\n  UNUSED_PARAMETER(argv);\n\n  iT = sqlite3StmtCurrentTime(context);\n  if( iT<=0 ) return;\n  t = iT/1000 - 10000*(sqlite3_int64)21086676;\n#if HAVE_GMTIME_R\n  pTm = gmtime_r(&t, &sNow);\n#else\n  sqlite3_mutex_enter(sqlite3MutexAlloc(SQLITE_MUTEX_STATIC_MASTER));\n  pTm = gmtime(&t);\n  if( pTm ) memcpy(&sNow, pTm, sizeof(sNow));\n  sqlite3_mutex_leave(sqlite3MutexAlloc(SQLITE_MUTEX_STATIC_MASTER));\n#endif\n  if( pTm ){\n    strftime(zBuf, 20, zFormat, &sNow);\n    sqlite3_result_text(context, zBuf, -1, SQLITE_TRANSIENT);\n  }\n}\n#endif\n\n/*\n** This function registered all of the above C functions as SQL\n** functions.  This should be the only routine in this file with\n** external linkage.\n*/\nSQLITE_PRIVATE void sqlite3RegisterDateTimeFunctions(void){\n  static FuncDef aDateTimeFuncs[] = {\n#ifndef SQLITE_OMIT_DATETIME_FUNCS\n    PURE_DATE(julianday,        -1, 0, 0, juliandayFunc ),\n    PURE_DATE(date,             -1, 0, 0, dateFunc      ),\n    PURE_DATE(time,             -1, 0, 0, timeFunc      ),\n    PURE_DATE(datetime,         -1, 0, 0, datetimeFunc  ),\n    PURE_DATE(strftime,         -1, 0, 0, strftimeFunc  ),\n    DFUNCTION(current_time,      0, 0, 0, ctimeFunc     ),\n    DFUNCTION(current_timestamp, 0, 0, 0, ctimestampFunc),\n    DFUNCTION(current_date,      0, 0, 0, cdateFunc     ),\n#else\n    STR_FUNCTION(current_time,      0, \"%H:%M:%S\",          0, currentTimeFunc),\n    STR_FUNCTION(current_date,      0, \"%Y-%m-%d\",          0, currentTimeFunc),\n    STR_FUNCTION(current_timestamp, 0, \"%Y-%m-%d %H:%M:%S\", 0, currentTimeFunc),\n#endif\n  };\n  sqlite3InsertBuiltinFuncs(aDateTimeFuncs, ArraySize(aDateTimeFuncs));\n}\n\n/************** End of date.c ************************************************/\n/************** Begin file os.c **********************************************/\n/*\n** 2005 November 29\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n******************************************************************************\n**\n** This file contains OS interface code that is common to all\n** architectures.\n*/\n/* #include \"sqliteInt.h\" */\n\n/*\n** If we compile with the SQLITE_TEST macro set, then the following block\n** of code will give us the ability to simulate a disk I/O error.  This\n** is used for testing the I/O recovery logic.\n*/\n#if defined(SQLITE_TEST)\nSQLITE_API int sqlite3_io_error_hit = 0;            /* Total number of I/O Errors */\nSQLITE_API int sqlite3_io_error_hardhit = 0;        /* Number of non-benign errors */\nSQLITE_API int sqlite3_io_error_pending = 0;        /* Count down to first I/O error */\nSQLITE_API int sqlite3_io_error_persist = 0;        /* True if I/O errors persist */\nSQLITE_API int sqlite3_io_error_benign = 0;         /* True if errors are benign */\nSQLITE_API int sqlite3_diskfull_pending = 0;\nSQLITE_API int sqlite3_diskfull = 0;\n#endif /* defined(SQLITE_TEST) */\n\n/*\n** When testing, also keep a count of the number of open files.\n*/\n#if defined(SQLITE_TEST)\nSQLITE_API int sqlite3_open_file_count = 0;\n#endif /* defined(SQLITE_TEST) */\n\n/*\n** The default SQLite sqlite3_vfs implementations do not allocate\n** memory (actually, os_unix.c allocates a small amount of memory\n** from within OsOpen()), but some third-party implementations may.\n** So we test the effects of a malloc() failing and the sqlite3OsXXX()\n** function returning SQLITE_IOERR_NOMEM using the DO_OS_MALLOC_TEST macro.\n**\n** The following functions are instrumented for malloc() failure\n** testing:\n**\n**     sqlite3OsRead()\n**     sqlite3OsWrite()\n**     sqlite3OsSync()\n**     sqlite3OsFileSize()\n**     sqlite3OsLock()\n**     sqlite3OsCheckReservedLock()\n**     sqlite3OsFileControl()\n**     sqlite3OsShmMap()\n**     sqlite3OsOpen()\n**     sqlite3OsDelete()\n**     sqlite3OsAccess()\n**     sqlite3OsFullPathname()\n**\n*/\n#if defined(SQLITE_TEST)\nSQLITE_API int sqlite3_memdebug_vfs_oom_test = 1;\n  #define DO_OS_MALLOC_TEST(x)                                       \\\n  if (sqlite3_memdebug_vfs_oom_test && (!x || !sqlite3JournalIsInMemory(x))) { \\\n    void *pTstAlloc = sqlite3Malloc(10);                             \\\n    if (!pTstAlloc) return SQLITE_IOERR_NOMEM_BKPT;                  \\\n    sqlite3_free(pTstAlloc);                                         \\\n  }\n#else\n  #define DO_OS_MALLOC_TEST(x)\n#endif\n\n/*\n** The following routines are convenience wrappers around methods\n** of the sqlite3_file object.  This is mostly just syntactic sugar. All\n** of this would be completely automatic if SQLite were coded using\n** C++ instead of plain old C.\n*/\nSQLITE_PRIVATE void sqlite3OsClose(sqlite3_file *pId){\n  if( pId->pMethods ){\n    pId->pMethods->xClose(pId);\n    pId->pMethods = 0;\n  }\n}\nSQLITE_PRIVATE int sqlite3OsRead(sqlite3_file *id, void *pBuf, int amt, i64 offset){\n  DO_OS_MALLOC_TEST(id);\n  return id->pMethods->xRead(id, pBuf, amt, offset);\n}\nSQLITE_PRIVATE int sqlite3OsWrite(sqlite3_file *id, const void *pBuf, int amt, i64 offset){\n  DO_OS_MALLOC_TEST(id);\n  return id->pMethods->xWrite(id, pBuf, amt, offset);\n}\nSQLITE_PRIVATE int sqlite3OsTruncate(sqlite3_file *id, i64 size){\n  return id->pMethods->xTruncate(id, size);\n}\nSQLITE_PRIVATE int sqlite3OsSync(sqlite3_file *id, int flags){\n  DO_OS_MALLOC_TEST(id);\n  return flags ? id->pMethods->xSync(id, flags) : SQLITE_OK;\n}\nSQLITE_PRIVATE int sqlite3OsFileSize(sqlite3_file *id, i64 *pSize){\n  DO_OS_MALLOC_TEST(id);\n  return id->pMethods->xFileSize(id, pSize);\n}\nSQLITE_PRIVATE int sqlite3OsLock(sqlite3_file *id, int lockType){\n  DO_OS_MALLOC_TEST(id);\n  return id->pMethods->xLock(id, lockType);\n}\nSQLITE_PRIVATE int sqlite3OsUnlock(sqlite3_file *id, int lockType){\n  return id->pMethods->xUnlock(id, lockType);\n}\nSQLITE_PRIVATE int sqlite3OsCheckReservedLock(sqlite3_file *id, int *pResOut){\n  DO_OS_MALLOC_TEST(id);\n  return id->pMethods->xCheckReservedLock(id, pResOut);\n}\n\n/*\n** Use sqlite3OsFileControl() when we are doing something that might fail\n** and we need to know about the failures.  Use sqlite3OsFileControlHint()\n** when simply tossing information over the wall to the VFS and we do not\n** really care if the VFS receives and understands the information since it\n** is only a hint and can be safely ignored.  The sqlite3OsFileControlHint()\n** routine has no return value since the return value would be meaningless.\n*/\nSQLITE_PRIVATE int sqlite3OsFileControl(sqlite3_file *id, int op, void *pArg){\n#ifdef SQLITE_TEST\n  if( op!=SQLITE_FCNTL_COMMIT_PHASETWO ){\n    /* Faults are not injected into COMMIT_PHASETWO because, assuming SQLite\n    ** is using a regular VFS, it is called after the corresponding\n    ** transaction has been committed. Injecting a fault at this point\n    ** confuses the test scripts - the COMMIT comand returns SQLITE_NOMEM\n    ** but the transaction is committed anyway.\n    **\n    ** The core must call OsFileControl() though, not OsFileControlHint(),\n    ** as if a custom VFS (e.g. zipvfs) returns an error here, it probably\n    ** means the commit really has failed and an error should be returned\n    ** to the user.  */\n    DO_OS_MALLOC_TEST(id);\n  }\n#endif\n  return id->pMethods->xFileControl(id, op, pArg);\n}\nSQLITE_PRIVATE void sqlite3OsFileControlHint(sqlite3_file *id, int op, void *pArg){\n  (void)id->pMethods->xFileControl(id, op, pArg);\n}\n\nSQLITE_PRIVATE int sqlite3OsSectorSize(sqlite3_file *id){\n  int (*xSectorSize)(sqlite3_file*) = id->pMethods->xSectorSize;\n  return (xSectorSize ? xSectorSize(id) : SQLITE_DEFAULT_SECTOR_SIZE);\n}\nSQLITE_PRIVATE int sqlite3OsDeviceCharacteristics(sqlite3_file *id){\n  return id->pMethods->xDeviceCharacteristics(id);\n}\n#ifndef SQLITE_OMIT_WAL\nSQLITE_PRIVATE int sqlite3OsShmLock(sqlite3_file *id, int offset, int n, int flags){\n  return id->pMethods->xShmLock(id, offset, n, flags);\n}\nSQLITE_PRIVATE void sqlite3OsShmBarrier(sqlite3_file *id){\n  id->pMethods->xShmBarrier(id);\n}\nSQLITE_PRIVATE int sqlite3OsShmUnmap(sqlite3_file *id, int deleteFlag){\n  return id->pMethods->xShmUnmap(id, deleteFlag);\n}\nSQLITE_PRIVATE int sqlite3OsShmMap(\n  sqlite3_file *id,               /* Database file handle */\n  int iPage,\n  int pgsz,\n  int bExtend,                    /* True to extend file if necessary */\n  void volatile **pp              /* OUT: Pointer to mapping */\n){\n  DO_OS_MALLOC_TEST(id);\n  return id->pMethods->xShmMap(id, iPage, pgsz, bExtend, pp);\n}\n#endif /* SQLITE_OMIT_WAL */\n\n#if SQLITE_MAX_MMAP_SIZE>0\n/* The real implementation of xFetch and xUnfetch */\nSQLITE_PRIVATE int sqlite3OsFetch(sqlite3_file *id, i64 iOff, int iAmt, void **pp){\n  DO_OS_MALLOC_TEST(id);\n  return id->pMethods->xFetch(id, iOff, iAmt, pp);\n}\nSQLITE_PRIVATE int sqlite3OsUnfetch(sqlite3_file *id, i64 iOff, void *p){\n  return id->pMethods->xUnfetch(id, iOff, p);\n}\n#else\n/* No-op stubs to use when memory-mapped I/O is disabled */\nSQLITE_PRIVATE int sqlite3OsFetch(sqlite3_file *id, i64 iOff, int iAmt, void **pp){\n  *pp = 0;\n  return SQLITE_OK;\n}\nSQLITE_PRIVATE int sqlite3OsUnfetch(sqlite3_file *id, i64 iOff, void *p){\n  return SQLITE_OK;\n}\n#endif\n\n/*\n** The next group of routines are convenience wrappers around the\n** VFS methods.\n*/\nSQLITE_PRIVATE int sqlite3OsOpen(\n  sqlite3_vfs *pVfs,\n  const char *zPath,\n  sqlite3_file *pFile,\n  int flags,\n  int *pFlagsOut\n){\n  int rc;\n  DO_OS_MALLOC_TEST(0);\n  /* 0x87f7f is a mask of SQLITE_OPEN_ flags that are valid to be passed\n  ** down into the VFS layer.  Some SQLITE_OPEN_ flags (for example,\n  ** SQLITE_OPEN_FULLMUTEX or SQLITE_OPEN_SHAREDCACHE) are blocked before\n  ** reaching the VFS. */\n  rc = pVfs->xOpen(pVfs, zPath, pFile, flags & 0x87f7f, pFlagsOut);\n  assert( rc==SQLITE_OK || pFile->pMethods==0 );\n  return rc;\n}\nSQLITE_PRIVATE int sqlite3OsDelete(sqlite3_vfs *pVfs, const char *zPath, int dirSync){\n  DO_OS_MALLOC_TEST(0);\n  assert( dirSync==0 || dirSync==1 );\n  return pVfs->xDelete(pVfs, zPath, dirSync);\n}\nSQLITE_PRIVATE int sqlite3OsAccess(\n  sqlite3_vfs *pVfs,\n  const char *zPath,\n  int flags,\n  int *pResOut\n){\n  DO_OS_MALLOC_TEST(0);\n  return pVfs->xAccess(pVfs, zPath, flags, pResOut);\n}\nSQLITE_PRIVATE int sqlite3OsFullPathname(\n  sqlite3_vfs *pVfs,\n  const char *zPath,\n  int nPathOut,\n  char *zPathOut\n){\n  DO_OS_MALLOC_TEST(0);\n  zPathOut[0] = 0;\n  return pVfs->xFullPathname(pVfs, zPath, nPathOut, zPathOut);\n}\n#ifndef SQLITE_OMIT_LOAD_EXTENSION\nSQLITE_PRIVATE void *sqlite3OsDlOpen(sqlite3_vfs *pVfs, const char *zPath){\n  return pVfs->xDlOpen(pVfs, zPath);\n}\nSQLITE_PRIVATE void sqlite3OsDlError(sqlite3_vfs *pVfs, int nByte, char *zBufOut){\n  pVfs->xDlError(pVfs, nByte, zBufOut);\n}\nSQLITE_PRIVATE void (*sqlite3OsDlSym(sqlite3_vfs *pVfs, void *pHdle, const char *zSym))(void){\n  return pVfs->xDlSym(pVfs, pHdle, zSym);\n}\nSQLITE_PRIVATE void sqlite3OsDlClose(sqlite3_vfs *pVfs, void *pHandle){\n  pVfs->xDlClose(pVfs, pHandle);\n}\n#endif /* SQLITE_OMIT_LOAD_EXTENSION */\nSQLITE_PRIVATE int sqlite3OsRandomness(sqlite3_vfs *pVfs, int nByte, char *zBufOut){\n  return pVfs->xRandomness(pVfs, nByte, zBufOut);\n}\nSQLITE_PRIVATE int sqlite3OsSleep(sqlite3_vfs *pVfs, int nMicro){\n  return pVfs->xSleep(pVfs, nMicro);\n}\nSQLITE_PRIVATE int sqlite3OsGetLastError(sqlite3_vfs *pVfs){\n  return pVfs->xGetLastError ? pVfs->xGetLastError(pVfs, 0, 0) : 0;\n}\nSQLITE_PRIVATE int sqlite3OsCurrentTimeInt64(sqlite3_vfs *pVfs, sqlite3_int64 *pTimeOut){\n  int rc;\n  /* IMPLEMENTATION-OF: R-49045-42493 SQLite will use the xCurrentTimeInt64()\n  ** method to get the current date and time if that method is available\n  ** (if iVersion is 2 or greater and the function pointer is not NULL) and\n  ** will fall back to xCurrentTime() if xCurrentTimeInt64() is\n  ** unavailable.\n  */\n  if( pVfs->iVersion>=2 && pVfs->xCurrentTimeInt64 ){\n    rc = pVfs->xCurrentTimeInt64(pVfs, pTimeOut);\n  }else{\n    double r;\n    rc = pVfs->xCurrentTime(pVfs, &r);\n    *pTimeOut = (sqlite3_int64)(r*86400000.0);\n  }\n  return rc;\n}\n\nSQLITE_PRIVATE int sqlite3OsOpenMalloc(\n  sqlite3_vfs *pVfs,\n  const char *zFile,\n  sqlite3_file **ppFile,\n  int flags,\n  int *pOutFlags\n){\n  int rc;\n  sqlite3_file *pFile;\n  pFile = (sqlite3_file *)sqlite3MallocZero(pVfs->szOsFile);\n  if( pFile ){\n    rc = sqlite3OsOpen(pVfs, zFile, pFile, flags, pOutFlags);\n    if( rc!=SQLITE_OK ){\n      sqlite3_free(pFile);\n    }else{\n      *ppFile = pFile;\n    }\n  }else{\n    rc = SQLITE_NOMEM_BKPT;\n  }\n  return rc;\n}\nSQLITE_PRIVATE void sqlite3OsCloseFree(sqlite3_file *pFile){\n  assert( pFile );\n  sqlite3OsClose(pFile);\n  sqlite3_free(pFile);\n}\n\n/*\n** This function is a wrapper around the OS specific implementation of\n** sqlite3_os_init(). The purpose of the wrapper is to provide the\n** ability to simulate a malloc failure, so that the handling of an\n** error in sqlite3_os_init() by the upper layers can be tested.\n*/\nSQLITE_PRIVATE int sqlite3OsInit(void){\n  void *p = sqlite3_malloc(10);\n  if( p==0 ) return SQLITE_NOMEM_BKPT;\n  sqlite3_free(p);\n  return sqlite3_os_init();\n}\n\n/*\n** The list of all registered VFS implementations.\n*/\nstatic sqlite3_vfs * SQLITE_WSD vfsList = 0;\n#define vfsList GLOBAL(sqlite3_vfs *, vfsList)\n\n/*\n** Locate a VFS by name.  If no name is given, simply return the\n** first VFS on the list.\n*/\nSQLITE_API sqlite3_vfs *sqlite3_vfs_find(const char *zVfs){\n  sqlite3_vfs *pVfs = 0;\n#if SQLITE_THREADSAFE\n  sqlite3_mutex *mutex;\n#endif\n#ifndef SQLITE_OMIT_AUTOINIT\n  int rc = sqlite3_initialize();\n  if( rc ) return 0;\n#endif\n#if SQLITE_THREADSAFE\n  mutex = sqlite3MutexAlloc(SQLITE_MUTEX_STATIC_MASTER);\n#endif\n  sqlite3_mutex_enter(mutex);\n  for(pVfs = vfsList; pVfs; pVfs=pVfs->pNext){\n    if( zVfs==0 ) break;\n    if( strcmp(zVfs, pVfs->zName)==0 ) break;\n  }\n  sqlite3_mutex_leave(mutex);\n  return pVfs;\n}\n\n/*\n** Unlink a VFS from the linked list\n*/\nstatic void vfsUnlink(sqlite3_vfs *pVfs){\n  assert( sqlite3_mutex_held(sqlite3MutexAlloc(SQLITE_MUTEX_STATIC_MASTER)) );\n  if( pVfs==0 ){\n    /* No-op */\n  }else if( vfsList==pVfs ){\n    vfsList = pVfs->pNext;\n  }else if( vfsList ){\n    sqlite3_vfs *p = vfsList;\n    while( p->pNext && p->pNext!=pVfs ){\n      p = p->pNext;\n    }\n    if( p->pNext==pVfs ){\n      p->pNext = pVfs->pNext;\n    }\n  }\n}\n\n/*\n** Register a VFS with the system.  It is harmless to register the same\n** VFS multiple times.  The new VFS becomes the default if makeDflt is\n** true.\n*/\nSQLITE_API int sqlite3_vfs_register(sqlite3_vfs *pVfs, int makeDflt){\n  MUTEX_LOGIC(sqlite3_mutex *mutex;)\n#ifndef SQLITE_OMIT_AUTOINIT\n  int rc = sqlite3_initialize();\n  if( rc ) return rc;\n#endif\n#ifdef SQLITE_ENABLE_API_ARMOR\n  if( pVfs==0 ) return SQLITE_MISUSE_BKPT;\n#endif\n\n  MUTEX_LOGIC( mutex = sqlite3MutexAlloc(SQLITE_MUTEX_STATIC_MASTER); )\n  sqlite3_mutex_enter(mutex);\n  vfsUnlink(pVfs);\n  if( makeDflt || vfsList==0 ){\n    pVfs->pNext = vfsList;\n    vfsList = pVfs;\n  }else{\n    pVfs->pNext = vfsList->pNext;\n    vfsList->pNext = pVfs;\n  }\n  assert(vfsList);\n  sqlite3_mutex_leave(mutex);\n  return SQLITE_OK;\n}\n\n/*\n** Unregister a VFS so that it is no longer accessible.\n*/\nSQLITE_API int sqlite3_vfs_unregister(sqlite3_vfs *pVfs){\n#if SQLITE_THREADSAFE\n  sqlite3_mutex *mutex = sqlite3MutexAlloc(SQLITE_MUTEX_STATIC_MASTER);\n#endif\n  sqlite3_mutex_enter(mutex);\n  vfsUnlink(pVfs);\n  sqlite3_mutex_leave(mutex);\n  return SQLITE_OK;\n}\n\n/************** End of os.c **************************************************/\n/************** Begin file fault.c *******************************************/\n/*\n** 2008 Jan 22\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n*************************************************************************\n**\n** This file contains code to support the concept of \"benign\" \n** malloc failures (when the xMalloc() or xRealloc() method of the\n** sqlite3_mem_methods structure fails to allocate a block of memory\n** and returns 0). \n**\n** Most malloc failures are non-benign. After they occur, SQLite\n** abandons the current operation and returns an error code (usually\n** SQLITE_NOMEM) to the user. However, sometimes a fault is not necessarily\n** fatal. For example, if a malloc fails while resizing a hash table, this \n** is completely recoverable simply by not carrying out the resize. The \n** hash table will continue to function normally.  So a malloc failure \n** during a hash table resize is a benign fault.\n*/\n\n/* #include \"sqliteInt.h\" */\n\n#ifndef SQLITE_UNTESTABLE\n\n/*\n** Global variables.\n*/\ntypedef struct BenignMallocHooks BenignMallocHooks;\nstatic SQLITE_WSD struct BenignMallocHooks {\n  void (*xBenignBegin)(void);\n  void (*xBenignEnd)(void);\n} sqlite3Hooks = { 0, 0 };\n\n/* The \"wsdHooks\" macro will resolve to the appropriate BenignMallocHooks\n** structure.  If writable static data is unsupported on the target,\n** we have to locate the state vector at run-time.  In the more common\n** case where writable static data is supported, wsdHooks can refer directly\n** to the \"sqlite3Hooks\" state vector declared above.\n*/\n#ifdef SQLITE_OMIT_WSD\n# define wsdHooksInit \\\n  BenignMallocHooks *x = &GLOBAL(BenignMallocHooks,sqlite3Hooks)\n# define wsdHooks x[0]\n#else\n# define wsdHooksInit\n# define wsdHooks sqlite3Hooks\n#endif\n\n\n/*\n** Register hooks to call when sqlite3BeginBenignMalloc() and\n** sqlite3EndBenignMalloc() are called, respectively.\n*/\nSQLITE_PRIVATE void sqlite3BenignMallocHooks(\n  void (*xBenignBegin)(void),\n  void (*xBenignEnd)(void)\n){\n  wsdHooksInit;\n  wsdHooks.xBenignBegin = xBenignBegin;\n  wsdHooks.xBenignEnd = xBenignEnd;\n}\n\n/*\n** This (sqlite3EndBenignMalloc()) is called by SQLite code to indicate that\n** subsequent malloc failures are benign. A call to sqlite3EndBenignMalloc()\n** indicates that subsequent malloc failures are non-benign.\n*/\nSQLITE_PRIVATE void sqlite3BeginBenignMalloc(void){\n  wsdHooksInit;\n  if( wsdHooks.xBenignBegin ){\n    wsdHooks.xBenignBegin();\n  }\n}\nSQLITE_PRIVATE void sqlite3EndBenignMalloc(void){\n  wsdHooksInit;\n  if( wsdHooks.xBenignEnd ){\n    wsdHooks.xBenignEnd();\n  }\n}\n\n#endif   /* #ifndef SQLITE_UNTESTABLE */\n\n/************** End of fault.c ***********************************************/\n/************** Begin file mem0.c ********************************************/\n/*\n** 2008 October 28\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n*************************************************************************\n**\n** This file contains a no-op memory allocation drivers for use when\n** SQLITE_ZERO_MALLOC is defined.  The allocation drivers implemented\n** here always fail.  SQLite will not operate with these drivers.  These\n** are merely placeholders.  Real drivers must be substituted using\n** sqlite3_config() before SQLite will operate.\n*/\n/* #include \"sqliteInt.h\" */\n\n/*\n** This version of the memory allocator is the default.  It is\n** used when no other memory allocator is specified using compile-time\n** macros.\n*/\n#ifdef SQLITE_ZERO_MALLOC\n\n/*\n** No-op versions of all memory allocation routines\n*/\nstatic void *sqlite3MemMalloc(int nByte){ return 0; }\nstatic void sqlite3MemFree(void *pPrior){ return; }\nstatic void *sqlite3MemRealloc(void *pPrior, int nByte){ return 0; }\nstatic int sqlite3MemSize(void *pPrior){ return 0; }\nstatic int sqlite3MemRoundup(int n){ return n; }\nstatic int sqlite3MemInit(void *NotUsed){ return SQLITE_OK; }\nstatic void sqlite3MemShutdown(void *NotUsed){ return; }\n\n/*\n** This routine is the only routine in this file with external linkage.\n**\n** Populate the low-level memory allocation function pointers in\n** sqlite3GlobalConfig.m with pointers to the routines in this file.\n*/\nSQLITE_PRIVATE void sqlite3MemSetDefault(void){\n  static const sqlite3_mem_methods defaultMethods = {\n     sqlite3MemMalloc,\n     sqlite3MemFree,\n     sqlite3MemRealloc,\n     sqlite3MemSize,\n     sqlite3MemRoundup,\n     sqlite3MemInit,\n     sqlite3MemShutdown,\n     0\n  };\n  sqlite3_config(SQLITE_CONFIG_MALLOC, &defaultMethods);\n}\n\n#endif /* SQLITE_ZERO_MALLOC */\n\n/************** End of mem0.c ************************************************/\n/************** Begin file mem1.c ********************************************/\n/*\n** 2007 August 14\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n*************************************************************************\n**\n** This file contains low-level memory allocation drivers for when\n** SQLite will use the standard C-library malloc/realloc/free interface\n** to obtain the memory it needs.\n**\n** This file contains implementations of the low-level memory allocation\n** routines specified in the sqlite3_mem_methods object.  The content of\n** this file is only used if SQLITE_SYSTEM_MALLOC is defined.  The\n** SQLITE_SYSTEM_MALLOC macro is defined automatically if neither the\n** SQLITE_MEMDEBUG nor the SQLITE_WIN32_MALLOC macros are defined.  The\n** default configuration is to use memory allocation routines in this\n** file.\n**\n** C-preprocessor macro summary:\n**\n**    HAVE_MALLOC_USABLE_SIZE     The configure script sets this symbol if\n**                                the malloc_usable_size() interface exists\n**                                on the target platform.  Or, this symbol\n**                                can be set manually, if desired.\n**                                If an equivalent interface exists by\n**                                a different name, using a separate -D\n**                                option to rename it.\n**\n**    SQLITE_WITHOUT_ZONEMALLOC   Some older macs lack support for the zone\n**                                memory allocator.  Set this symbol to enable\n**                                building on older macs.\n**\n**    SQLITE_WITHOUT_MSIZE        Set this symbol to disable the use of\n**                                _msize() on windows systems.  This might\n**                                be necessary when compiling for Delphi,\n**                                for example.\n*/\n/* #include \"sqliteInt.h\" */\n\n/*\n** This version of the memory allocator is the default.  It is\n** used when no other memory allocator is specified using compile-time\n** macros.\n*/\n#ifdef SQLITE_SYSTEM_MALLOC\n#if defined(__APPLE__) && !defined(SQLITE_WITHOUT_ZONEMALLOC)\n\n/*\n** Use the zone allocator available on apple products unless the\n** SQLITE_WITHOUT_ZONEMALLOC symbol is defined.\n*/\n#include <sys/sysctl.h>\n#include <malloc/malloc.h>\n#ifdef SQLITE_MIGHT_BE_SINGLE_CORE\n#include <libkern/OSAtomic.h>\n#endif /* SQLITE_MIGHT_BE_SINGLE_CORE */\nstatic malloc_zone_t* _sqliteZone_;\n#define SQLITE_MALLOC(x) malloc_zone_malloc(_sqliteZone_, (x))\n#define SQLITE_FREE(x) malloc_zone_free(_sqliteZone_, (x));\n#define SQLITE_REALLOC(x,y) malloc_zone_realloc(_sqliteZone_, (x), (y))\n#define SQLITE_MALLOCSIZE(x) \\\n        (_sqliteZone_ ? _sqliteZone_->size(_sqliteZone_,x) : malloc_size(x))\n\n#else /* if not __APPLE__ */\n\n/*\n** Use standard C library malloc and free on non-Apple systems.  \n** Also used by Apple systems if SQLITE_WITHOUT_ZONEMALLOC is defined.\n*/\n#define SQLITE_MALLOC(x)             malloc(x)\n#define SQLITE_FREE(x)               free(x)\n#define SQLITE_REALLOC(x,y)          realloc((x),(y))\n\n/*\n** The malloc.h header file is needed for malloc_usable_size() function\n** on some systems (e.g. Linux).\n*/\n#if HAVE_MALLOC_H && HAVE_MALLOC_USABLE_SIZE\n#  define SQLITE_USE_MALLOC_H 1\n#  define SQLITE_USE_MALLOC_USABLE_SIZE 1\n/*\n** The MSVCRT has malloc_usable_size(), but it is called _msize().  The\n** use of _msize() is automatic, but can be disabled by compiling with\n** -DSQLITE_WITHOUT_MSIZE.  Using the _msize() function also requires\n** the malloc.h header file.\n*/\n#elif defined(_MSC_VER) && !defined(SQLITE_WITHOUT_MSIZE)\n#  define SQLITE_USE_MALLOC_H\n#  define SQLITE_USE_MSIZE\n#endif\n\n/*\n** Include the malloc.h header file, if necessary.  Also set define macro\n** SQLITE_MALLOCSIZE to the appropriate function name, which is _msize()\n** for MSVC and malloc_usable_size() for most other systems (e.g. Linux).\n** The memory size function can always be overridden manually by defining\n** the macro SQLITE_MALLOCSIZE to the desired function name.\n*/\n#if defined(SQLITE_USE_MALLOC_H)\n#  include <malloc.h>\n#  if defined(SQLITE_USE_MALLOC_USABLE_SIZE)\n#    if !defined(SQLITE_MALLOCSIZE)\n#      define SQLITE_MALLOCSIZE(x)   malloc_usable_size(x)\n#    endif\n#  elif defined(SQLITE_USE_MSIZE)\n#    if !defined(SQLITE_MALLOCSIZE)\n#      define SQLITE_MALLOCSIZE      _msize\n#    endif\n#  endif\n#endif /* defined(SQLITE_USE_MALLOC_H) */\n\n#endif /* __APPLE__ or not __APPLE__ */\n\n/*\n** Like malloc(), but remember the size of the allocation\n** so that we can find it later using sqlite3MemSize().\n**\n** For this low-level routine, we are guaranteed that nByte>0 because\n** cases of nByte<=0 will be intercepted and dealt with by higher level\n** routines.\n*/\nstatic void *sqlite3MemMalloc(int nByte){\n#ifdef SQLITE_MALLOCSIZE\n  void *p;\n  testcase( ROUND8(nByte)==nByte );\n  p = SQLITE_MALLOC( nByte );\n  if( p==0 ){\n    testcase( sqlite3GlobalConfig.xLog!=0 );\n    sqlite3_log(SQLITE_NOMEM, \"failed to allocate %u bytes of memory\", nByte);\n  }\n  return p;\n#else\n  sqlite3_int64 *p;\n  assert( nByte>0 );\n  testcase( ROUND8(nByte)!=nByte );\n  p = SQLITE_MALLOC( nByte+8 );\n  if( p ){\n    p[0] = nByte;\n    p++;\n  }else{\n    testcase( sqlite3GlobalConfig.xLog!=0 );\n    sqlite3_log(SQLITE_NOMEM, \"failed to allocate %u bytes of memory\", nByte);\n  }\n  return (void *)p;\n#endif\n}\n\n/*\n** Like free() but works for allocations obtained from sqlite3MemMalloc()\n** or sqlite3MemRealloc().\n**\n** For this low-level routine, we already know that pPrior!=0 since\n** cases where pPrior==0 will have been intecepted and dealt with\n** by higher-level routines.\n*/\nstatic void sqlite3MemFree(void *pPrior){\n#ifdef SQLITE_MALLOCSIZE\n  SQLITE_FREE(pPrior);\n#else\n  sqlite3_int64 *p = (sqlite3_int64*)pPrior;\n  assert( pPrior!=0 );\n  p--;\n  SQLITE_FREE(p);\n#endif\n}\n\n/*\n** Report the allocated size of a prior return from xMalloc()\n** or xRealloc().\n*/\nstatic int sqlite3MemSize(void *pPrior){\n#ifdef SQLITE_MALLOCSIZE\n  assert( pPrior!=0 );\n  return (int)SQLITE_MALLOCSIZE(pPrior);\n#else\n  sqlite3_int64 *p;\n  assert( pPrior!=0 );\n  p = (sqlite3_int64*)pPrior;\n  p--;\n  return (int)p[0];\n#endif\n}\n\n/*\n** Like realloc().  Resize an allocation previously obtained from\n** sqlite3MemMalloc().\n**\n** For this low-level interface, we know that pPrior!=0.  Cases where\n** pPrior==0 while have been intercepted by higher-level routine and\n** redirected to xMalloc.  Similarly, we know that nByte>0 because\n** cases where nByte<=0 will have been intercepted by higher-level\n** routines and redirected to xFree.\n*/\nstatic void *sqlite3MemRealloc(void *pPrior, int nByte){\n#ifdef SQLITE_MALLOCSIZE\n  void *p = SQLITE_REALLOC(pPrior, nByte);\n  if( p==0 ){\n    testcase( sqlite3GlobalConfig.xLog!=0 );\n    sqlite3_log(SQLITE_NOMEM,\n      \"failed memory resize %u to %u bytes\",\n      SQLITE_MALLOCSIZE(pPrior), nByte);\n  }\n  return p;\n#else\n  sqlite3_int64 *p = (sqlite3_int64*)pPrior;\n  assert( pPrior!=0 && nByte>0 );\n  assert( nByte==ROUND8(nByte) ); /* EV: R-46199-30249 */\n  p--;\n  p = SQLITE_REALLOC(p, nByte+8 );\n  if( p ){\n    p[0] = nByte;\n    p++;\n  }else{\n    testcase( sqlite3GlobalConfig.xLog!=0 );\n    sqlite3_log(SQLITE_NOMEM,\n      \"failed memory resize %u to %u bytes\",\n      sqlite3MemSize(pPrior), nByte);\n  }\n  return (void*)p;\n#endif\n}\n\n/*\n** Round up a request size to the next valid allocation size.\n*/\nstatic int sqlite3MemRoundup(int n){\n  return ROUND8(n);\n}\n\n/*\n** Initialize this module.\n*/\nstatic int sqlite3MemInit(void *NotUsed){\n#if defined(__APPLE__) && !defined(SQLITE_WITHOUT_ZONEMALLOC)\n  int cpuCount;\n  size_t len;\n  if( _sqliteZone_ ){\n    return SQLITE_OK;\n  }\n  len = sizeof(cpuCount);\n  /* One usually wants to use hw.acctivecpu for MT decisions, but not here */\n  sysctlbyname(\"hw.ncpu\", &cpuCount, &len, NULL, 0);\n  if( cpuCount>1 ){\n    /* defer MT decisions to system malloc */\n    _sqliteZone_ = malloc_default_zone();\n  }else{\n    /* only 1 core, use our own zone to contention over global locks, \n    ** e.g. we have our own dedicated locks */\n    _sqliteZone_ = malloc_create_zone(4096, 0);\n    malloc_set_zone_name(_sqliteZone_, \"Sqlite_Heap\");\n  }\n#endif /*  defined(__APPLE__) && !defined(SQLITE_WITHOUT_ZONEMALLOC) */\n  UNUSED_PARAMETER(NotUsed);\n  return SQLITE_OK;\n}\n\n/*\n** Deinitialize this module.\n*/\nstatic void sqlite3MemShutdown(void *NotUsed){\n  UNUSED_PARAMETER(NotUsed);\n  return;\n}\n\n/*\n** This routine is the only routine in this file with external linkage.\n**\n** Populate the low-level memory allocation function pointers in\n** sqlite3GlobalConfig.m with pointers to the routines in this file.\n*/\nSQLITE_PRIVATE void sqlite3MemSetDefault(void){\n  static const sqlite3_mem_methods defaultMethods = {\n     sqlite3MemMalloc,\n     sqlite3MemFree,\n     sqlite3MemRealloc,\n     sqlite3MemSize,\n     sqlite3MemRoundup,\n     sqlite3MemInit,\n     sqlite3MemShutdown,\n     0\n  };\n  sqlite3_config(SQLITE_CONFIG_MALLOC, &defaultMethods);\n}\n\n#endif /* SQLITE_SYSTEM_MALLOC */\n\n/************** End of mem1.c ************************************************/\n/************** Begin file mem2.c ********************************************/\n/*\n** 2007 August 15\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n*************************************************************************\n**\n** This file contains low-level memory allocation drivers for when\n** SQLite will use the standard C-library malloc/realloc/free interface\n** to obtain the memory it needs while adding lots of additional debugging\n** information to each allocation in order to help detect and fix memory\n** leaks and memory usage errors.\n**\n** This file contains implementations of the low-level memory allocation\n** routines specified in the sqlite3_mem_methods object.\n*/\n/* #include \"sqliteInt.h\" */\n\n/*\n** This version of the memory allocator is used only if the\n** SQLITE_MEMDEBUG macro is defined\n*/\n#ifdef SQLITE_MEMDEBUG\n\n/*\n** The backtrace functionality is only available with GLIBC\n*/\n#ifdef __GLIBC__\n  extern int backtrace(void**,int);\n  extern void backtrace_symbols_fd(void*const*,int,int);\n#else\n# define backtrace(A,B) 1\n# define backtrace_symbols_fd(A,B,C)\n#endif\n/* #include <stdio.h> */\n\n/*\n** Each memory allocation looks like this:\n**\n**  ------------------------------------------------------------------------\n**  | Title |  backtrace pointers |  MemBlockHdr |  allocation |  EndGuard |\n**  ------------------------------------------------------------------------\n**\n** The application code sees only a pointer to the allocation.  We have\n** to back up from the allocation pointer to find the MemBlockHdr.  The\n** MemBlockHdr tells us the size of the allocation and the number of\n** backtrace pointers.  There is also a guard word at the end of the\n** MemBlockHdr.\n*/\nstruct MemBlockHdr {\n  i64 iSize;                          /* Size of this allocation */\n  struct MemBlockHdr *pNext, *pPrev;  /* Linked list of all unfreed memory */\n  char nBacktrace;                    /* Number of backtraces on this alloc */\n  char nBacktraceSlots;               /* Available backtrace slots */\n  u8 nTitle;                          /* Bytes of title; includes '\\0' */\n  u8 eType;                           /* Allocation type code */\n  int iForeGuard;                     /* Guard word for sanity */\n};\n\n/*\n** Guard words\n*/\n#define FOREGUARD 0x80F5E153\n#define REARGUARD 0xE4676B53\n\n/*\n** Number of malloc size increments to track.\n*/\n#define NCSIZE  1000\n\n/*\n** All of the static variables used by this module are collected\n** into a single structure named \"mem\".  This is to keep the\n** static variables organized and to reduce namespace pollution\n** when this module is combined with other in the amalgamation.\n*/\nstatic struct {\n  \n  /*\n  ** Mutex to control access to the memory allocation subsystem.\n  */\n  sqlite3_mutex *mutex;\n\n  /*\n  ** Head and tail of a linked list of all outstanding allocations\n  */\n  struct MemBlockHdr *pFirst;\n  struct MemBlockHdr *pLast;\n  \n  /*\n  ** The number of levels of backtrace to save in new allocations.\n  */\n  int nBacktrace;\n  void (*xBacktrace)(int, int, void **);\n\n  /*\n  ** Title text to insert in front of each block\n  */\n  int nTitle;        /* Bytes of zTitle to save.  Includes '\\0' and padding */\n  char zTitle[100];  /* The title text */\n\n  /* \n  ** sqlite3MallocDisallow() increments the following counter.\n  ** sqlite3MallocAllow() decrements it.\n  */\n  int disallow; /* Do not allow memory allocation */\n\n  /*\n  ** Gather statistics on the sizes of memory allocations.\n  ** nAlloc[i] is the number of allocation attempts of i*8\n  ** bytes.  i==NCSIZE is the number of allocation attempts for\n  ** sizes more than NCSIZE*8 bytes.\n  */\n  int nAlloc[NCSIZE];      /* Total number of allocations */\n  int nCurrent[NCSIZE];    /* Current number of allocations */\n  int mxCurrent[NCSIZE];   /* Highwater mark for nCurrent */\n\n} mem;\n\n\n/*\n** Adjust memory usage statistics\n*/\nstatic void adjustStats(int iSize, int increment){\n  int i = ROUND8(iSize)/8;\n  if( i>NCSIZE-1 ){\n    i = NCSIZE - 1;\n  }\n  if( increment>0 ){\n    mem.nAlloc[i]++;\n    mem.nCurrent[i]++;\n    if( mem.nCurrent[i]>mem.mxCurrent[i] ){\n      mem.mxCurrent[i] = mem.nCurrent[i];\n    }\n  }else{\n    mem.nCurrent[i]--;\n    assert( mem.nCurrent[i]>=0 );\n  }\n}\n\n/*\n** Given an allocation, find the MemBlockHdr for that allocation.\n**\n** This routine checks the guards at either end of the allocation and\n** if they are incorrect it asserts.\n*/\nstatic struct MemBlockHdr *sqlite3MemsysGetHeader(void *pAllocation){\n  struct MemBlockHdr *p;\n  int *pInt;\n  u8 *pU8;\n  int nReserve;\n\n  p = (struct MemBlockHdr*)pAllocation;\n  p--;\n  assert( p->iForeGuard==(int)FOREGUARD );\n  nReserve = ROUND8(p->iSize);\n  pInt = (int*)pAllocation;\n  pU8 = (u8*)pAllocation;\n  assert( pInt[nReserve/sizeof(int)]==(int)REARGUARD );\n  /* This checks any of the \"extra\" bytes allocated due\n  ** to rounding up to an 8 byte boundary to ensure \n  ** they haven't been overwritten.\n  */\n  while( nReserve-- > p->iSize ) assert( pU8[nReserve]==0x65 );\n  return p;\n}\n\n/*\n** Return the number of bytes currently allocated at address p.\n*/\nstatic int sqlite3MemSize(void *p){\n  struct MemBlockHdr *pHdr;\n  if( !p ){\n    return 0;\n  }\n  pHdr = sqlite3MemsysGetHeader(p);\n  return (int)pHdr->iSize;\n}\n\n/*\n** Initialize the memory allocation subsystem.\n*/\nstatic int sqlite3MemInit(void *NotUsed){\n  UNUSED_PARAMETER(NotUsed);\n  assert( (sizeof(struct MemBlockHdr)&7) == 0 );\n  if( !sqlite3GlobalConfig.bMemstat ){\n    /* If memory status is enabled, then the malloc.c wrapper will already\n    ** hold the STATIC_MEM mutex when the routines here are invoked. */\n    mem.mutex = sqlite3MutexAlloc(SQLITE_MUTEX_STATIC_MEM);\n  }\n  return SQLITE_OK;\n}\n\n/*\n** Deinitialize the memory allocation subsystem.\n*/\nstatic void sqlite3MemShutdown(void *NotUsed){\n  UNUSED_PARAMETER(NotUsed);\n  mem.mutex = 0;\n}\n\n/*\n** Round up a request size to the next valid allocation size.\n*/\nstatic int sqlite3MemRoundup(int n){\n  return ROUND8(n);\n}\n\n/*\n** Fill a buffer with pseudo-random bytes.  This is used to preset\n** the content of a new memory allocation to unpredictable values and\n** to clear the content of a freed allocation to unpredictable values.\n*/\nstatic void randomFill(char *pBuf, int nByte){\n  unsigned int x, y, r;\n  x = SQLITE_PTR_TO_INT(pBuf);\n  y = nByte | 1;\n  while( nByte >= 4 ){\n    x = (x>>1) ^ (-(int)(x&1) & 0xd0000001);\n    y = y*1103515245 + 12345;\n    r = x ^ y;\n    *(int*)pBuf = r;\n    pBuf += 4;\n    nByte -= 4;\n  }\n  while( nByte-- > 0 ){\n    x = (x>>1) ^ (-(int)(x&1) & 0xd0000001);\n    y = y*1103515245 + 12345;\n    r = x ^ y;\n    *(pBuf++) = r & 0xff;\n  }\n}\n\n/*\n** Allocate nByte bytes of memory.\n*/\nstatic void *sqlite3MemMalloc(int nByte){\n  struct MemBlockHdr *pHdr;\n  void **pBt;\n  char *z;\n  int *pInt;\n  void *p = 0;\n  int totalSize;\n  int nReserve;\n  sqlite3_mutex_enter(mem.mutex);\n  assert( mem.disallow==0 );\n  nReserve = ROUND8(nByte);\n  totalSize = nReserve + sizeof(*pHdr) + sizeof(int) +\n               mem.nBacktrace*sizeof(void*) + mem.nTitle;\n  p = malloc(totalSize);\n  if( p ){\n    z = p;\n    pBt = (void**)&z[mem.nTitle];\n    pHdr = (struct MemBlockHdr*)&pBt[mem.nBacktrace];\n    pHdr->pNext = 0;\n    pHdr->pPrev = mem.pLast;\n    if( mem.pLast ){\n      mem.pLast->pNext = pHdr;\n    }else{\n      mem.pFirst = pHdr;\n    }\n    mem.pLast = pHdr;\n    pHdr->iForeGuard = FOREGUARD;\n    pHdr->eType = MEMTYPE_HEAP;\n    pHdr->nBacktraceSlots = mem.nBacktrace;\n    pHdr->nTitle = mem.nTitle;\n    if( mem.nBacktrace ){\n      void *aAddr[40];\n      pHdr->nBacktrace = backtrace(aAddr, mem.nBacktrace+1)-1;\n      memcpy(pBt, &aAddr[1], pHdr->nBacktrace*sizeof(void*));\n      assert(pBt[0]);\n      if( mem.xBacktrace ){\n        mem.xBacktrace(nByte, pHdr->nBacktrace-1, &aAddr[1]);\n      }\n    }else{\n      pHdr->nBacktrace = 0;\n    }\n    if( mem.nTitle ){\n      memcpy(z, mem.zTitle, mem.nTitle);\n    }\n    pHdr->iSize = nByte;\n    adjustStats(nByte, +1);\n    pInt = (int*)&pHdr[1];\n    pInt[nReserve/sizeof(int)] = REARGUARD;\n    randomFill((char*)pInt, nByte);\n    memset(((char*)pInt)+nByte, 0x65, nReserve-nByte);\n    p = (void*)pInt;\n  }\n  sqlite3_mutex_leave(mem.mutex);\n  return p; \n}\n\n/*\n** Free memory.\n*/\nstatic void sqlite3MemFree(void *pPrior){\n  struct MemBlockHdr *pHdr;\n  void **pBt;\n  char *z;\n  assert( sqlite3GlobalConfig.bMemstat || sqlite3GlobalConfig.bCoreMutex==0 \n       || mem.mutex!=0 );\n  pHdr = sqlite3MemsysGetHeader(pPrior);\n  pBt = (void**)pHdr;\n  pBt -= pHdr->nBacktraceSlots;\n  sqlite3_mutex_enter(mem.mutex);\n  if( pHdr->pPrev ){\n    assert( pHdr->pPrev->pNext==pHdr );\n    pHdr->pPrev->pNext = pHdr->pNext;\n  }else{\n    assert( mem.pFirst==pHdr );\n    mem.pFirst = pHdr->pNext;\n  }\n  if( pHdr->pNext ){\n    assert( pHdr->pNext->pPrev==pHdr );\n    pHdr->pNext->pPrev = pHdr->pPrev;\n  }else{\n    assert( mem.pLast==pHdr );\n    mem.pLast = pHdr->pPrev;\n  }\n  z = (char*)pBt;\n  z -= pHdr->nTitle;\n  adjustStats((int)pHdr->iSize, -1);\n  randomFill(z, sizeof(void*)*pHdr->nBacktraceSlots + sizeof(*pHdr) +\n                (int)pHdr->iSize + sizeof(int) + pHdr->nTitle);\n  free(z);\n  sqlite3_mutex_leave(mem.mutex);  \n}\n\n/*\n** Change the size of an existing memory allocation.\n**\n** For this debugging implementation, we *always* make a copy of the\n** allocation into a new place in memory.  In this way, if the \n** higher level code is using pointer to the old allocation, it is \n** much more likely to break and we are much more liking to find\n** the error.\n*/\nstatic void *sqlite3MemRealloc(void *pPrior, int nByte){\n  struct MemBlockHdr *pOldHdr;\n  void *pNew;\n  assert( mem.disallow==0 );\n  assert( (nByte & 7)==0 );     /* EV: R-46199-30249 */\n  pOldHdr = sqlite3MemsysGetHeader(pPrior);\n  pNew = sqlite3MemMalloc(nByte);\n  if( pNew ){\n    memcpy(pNew, pPrior, (int)(nByte<pOldHdr->iSize ? nByte : pOldHdr->iSize));\n    if( nByte>pOldHdr->iSize ){\n      randomFill(&((char*)pNew)[pOldHdr->iSize], nByte - (int)pOldHdr->iSize);\n    }\n    sqlite3MemFree(pPrior);\n  }\n  return pNew;\n}\n\n/*\n** Populate the low-level memory allocation function pointers in\n** sqlite3GlobalConfig.m with pointers to the routines in this file.\n*/\nSQLITE_PRIVATE void sqlite3MemSetDefault(void){\n  static const sqlite3_mem_methods defaultMethods = {\n     sqlite3MemMalloc,\n     sqlite3MemFree,\n     sqlite3MemRealloc,\n     sqlite3MemSize,\n     sqlite3MemRoundup,\n     sqlite3MemInit,\n     sqlite3MemShutdown,\n     0\n  };\n  sqlite3_config(SQLITE_CONFIG_MALLOC, &defaultMethods);\n}\n\n/*\n** Set the \"type\" of an allocation.\n*/\nSQLITE_PRIVATE void sqlite3MemdebugSetType(void *p, u8 eType){\n  if( p && sqlite3GlobalConfig.m.xMalloc==sqlite3MemMalloc ){\n    struct MemBlockHdr *pHdr;\n    pHdr = sqlite3MemsysGetHeader(p);\n    assert( pHdr->iForeGuard==FOREGUARD );\n    pHdr->eType = eType;\n  }\n}\n\n/*\n** Return TRUE if the mask of type in eType matches the type of the\n** allocation p.  Also return true if p==NULL.\n**\n** This routine is designed for use within an assert() statement, to\n** verify the type of an allocation.  For example:\n**\n**     assert( sqlite3MemdebugHasType(p, MEMTYPE_HEAP) );\n*/\nSQLITE_PRIVATE int sqlite3MemdebugHasType(void *p, u8 eType){\n  int rc = 1;\n  if( p && sqlite3GlobalConfig.m.xMalloc==sqlite3MemMalloc ){\n    struct MemBlockHdr *pHdr;\n    pHdr = sqlite3MemsysGetHeader(p);\n    assert( pHdr->iForeGuard==FOREGUARD );         /* Allocation is valid */\n    if( (pHdr->eType&eType)==0 ){\n      rc = 0;\n    }\n  }\n  return rc;\n}\n\n/*\n** Return TRUE if the mask of type in eType matches no bits of the type of the\n** allocation p.  Also return true if p==NULL.\n**\n** This routine is designed for use within an assert() statement, to\n** verify the type of an allocation.  For example:\n**\n**     assert( sqlite3MemdebugNoType(p, MEMTYPE_LOOKASIDE) );\n*/\nSQLITE_PRIVATE int sqlite3MemdebugNoType(void *p, u8 eType){\n  int rc = 1;\n  if( p && sqlite3GlobalConfig.m.xMalloc==sqlite3MemMalloc ){\n    struct MemBlockHdr *pHdr;\n    pHdr = sqlite3MemsysGetHeader(p);\n    assert( pHdr->iForeGuard==FOREGUARD );         /* Allocation is valid */\n    if( (pHdr->eType&eType)!=0 ){\n      rc = 0;\n    }\n  }\n  return rc;\n}\n\n/*\n** Set the number of backtrace levels kept for each allocation.\n** A value of zero turns off backtracing.  The number is always rounded\n** up to a multiple of 2.\n*/\nSQLITE_PRIVATE void sqlite3MemdebugBacktrace(int depth){\n  if( depth<0 ){ depth = 0; }\n  if( depth>20 ){ depth = 20; }\n  depth = (depth+1)&0xfe;\n  mem.nBacktrace = depth;\n}\n\nSQLITE_PRIVATE void sqlite3MemdebugBacktraceCallback(void (*xBacktrace)(int, int, void **)){\n  mem.xBacktrace = xBacktrace;\n}\n\n/*\n** Set the title string for subsequent allocations.\n*/\nSQLITE_PRIVATE void sqlite3MemdebugSettitle(const char *zTitle){\n  unsigned int n = sqlite3Strlen30(zTitle) + 1;\n  sqlite3_mutex_enter(mem.mutex);\n  if( n>=sizeof(mem.zTitle) ) n = sizeof(mem.zTitle)-1;\n  memcpy(mem.zTitle, zTitle, n);\n  mem.zTitle[n] = 0;\n  mem.nTitle = ROUND8(n);\n  sqlite3_mutex_leave(mem.mutex);\n}\n\nSQLITE_PRIVATE void sqlite3MemdebugSync(){\n  struct MemBlockHdr *pHdr;\n  for(pHdr=mem.pFirst; pHdr; pHdr=pHdr->pNext){\n    void **pBt = (void**)pHdr;\n    pBt -= pHdr->nBacktraceSlots;\n    mem.xBacktrace((int)pHdr->iSize, pHdr->nBacktrace-1, &pBt[1]);\n  }\n}\n\n/*\n** Open the file indicated and write a log of all unfreed memory \n** allocations into that log.\n*/\nSQLITE_PRIVATE void sqlite3MemdebugDump(const char *zFilename){\n  FILE *out;\n  struct MemBlockHdr *pHdr;\n  void **pBt;\n  int i;\n  out = fopen(zFilename, \"w\");\n  if( out==0 ){\n    fprintf(stderr, \"** Unable to output memory debug output log: %s **\\n\",\n                    zFilename);\n    return;\n  }\n  for(pHdr=mem.pFirst; pHdr; pHdr=pHdr->pNext){\n    char *z = (char*)pHdr;\n    z -= pHdr->nBacktraceSlots*sizeof(void*) + pHdr->nTitle;\n    fprintf(out, \"**** %lld bytes at %p from %s ****\\n\", \n            pHdr->iSize, &pHdr[1], pHdr->nTitle ? z : \"???\");\n    if( pHdr->nBacktrace ){\n      fflush(out);\n      pBt = (void**)pHdr;\n      pBt -= pHdr->nBacktraceSlots;\n      backtrace_symbols_fd(pBt, pHdr->nBacktrace, fileno(out));\n      fprintf(out, \"\\n\");\n    }\n  }\n  fprintf(out, \"COUNTS:\\n\");\n  for(i=0; i<NCSIZE-1; i++){\n    if( mem.nAlloc[i] ){\n      fprintf(out, \"   %5d: %10d %10d %10d\\n\", \n            i*8, mem.nAlloc[i], mem.nCurrent[i], mem.mxCurrent[i]);\n    }\n  }\n  if( mem.nAlloc[NCSIZE-1] ){\n    fprintf(out, \"   %5d: %10d %10d %10d\\n\",\n             NCSIZE*8-8, mem.nAlloc[NCSIZE-1],\n             mem.nCurrent[NCSIZE-1], mem.mxCurrent[NCSIZE-1]);\n  }\n  fclose(out);\n}\n\n/*\n** Return the number of times sqlite3MemMalloc() has been called.\n*/\nSQLITE_PRIVATE int sqlite3MemdebugMallocCount(){\n  int i;\n  int nTotal = 0;\n  for(i=0; i<NCSIZE; i++){\n    nTotal += mem.nAlloc[i];\n  }\n  return nTotal;\n}\n\n\n#endif /* SQLITE_MEMDEBUG */\n\n/************** End of mem2.c ************************************************/\n/************** Begin file mem3.c ********************************************/\n/*\n** 2007 October 14\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n*************************************************************************\n** This file contains the C functions that implement a memory\n** allocation subsystem for use by SQLite. \n**\n** This version of the memory allocation subsystem omits all\n** use of malloc(). The SQLite user supplies a block of memory\n** before calling sqlite3_initialize() from which allocations\n** are made and returned by the xMalloc() and xRealloc() \n** implementations. Once sqlite3_initialize() has been called,\n** the amount of memory available to SQLite is fixed and cannot\n** be changed.\n**\n** This version of the memory allocation subsystem is included\n** in the build only if SQLITE_ENABLE_MEMSYS3 is defined.\n*/\n/* #include \"sqliteInt.h\" */\n\n/*\n** This version of the memory allocator is only built into the library\n** SQLITE_ENABLE_MEMSYS3 is defined. Defining this symbol does not\n** mean that the library will use a memory-pool by default, just that\n** it is available. The mempool allocator is activated by calling\n** sqlite3_config().\n*/\n#ifdef SQLITE_ENABLE_MEMSYS3\n\n/*\n** Maximum size (in Mem3Blocks) of a \"small\" chunk.\n*/\n#define MX_SMALL 10\n\n\n/*\n** Number of freelist hash slots\n*/\n#define N_HASH  61\n\n/*\n** A memory allocation (also called a \"chunk\") consists of two or \n** more blocks where each block is 8 bytes.  The first 8 bytes are \n** a header that is not returned to the user.\n**\n** A chunk is two or more blocks that is either checked out or\n** free.  The first block has format u.hdr.  u.hdr.size4x is 4 times the\n** size of the allocation in blocks if the allocation is free.\n** The u.hdr.size4x&1 bit is true if the chunk is checked out and\n** false if the chunk is on the freelist.  The u.hdr.size4x&2 bit\n** is true if the previous chunk is checked out and false if the\n** previous chunk is free.  The u.hdr.prevSize field is the size of\n** the previous chunk in blocks if the previous chunk is on the\n** freelist. If the previous chunk is checked out, then\n** u.hdr.prevSize can be part of the data for that chunk and should\n** not be read or written.\n**\n** We often identify a chunk by its index in mem3.aPool[].  When\n** this is done, the chunk index refers to the second block of\n** the chunk.  In this way, the first chunk has an index of 1.\n** A chunk index of 0 means \"no such chunk\" and is the equivalent\n** of a NULL pointer.\n**\n** The second block of free chunks is of the form u.list.  The\n** two fields form a double-linked list of chunks of related sizes.\n** Pointers to the head of the list are stored in mem3.aiSmall[] \n** for smaller chunks and mem3.aiHash[] for larger chunks.\n**\n** The second block of a chunk is user data if the chunk is checked \n** out.  If a chunk is checked out, the user data may extend into\n** the u.hdr.prevSize value of the following chunk.\n*/\ntypedef struct Mem3Block Mem3Block;\nstruct Mem3Block {\n  union {\n    struct {\n      u32 prevSize;   /* Size of previous chunk in Mem3Block elements */\n      u32 size4x;     /* 4x the size of current chunk in Mem3Block elements */\n    } hdr;\n    struct {\n      u32 next;       /* Index in mem3.aPool[] of next free chunk */\n      u32 prev;       /* Index in mem3.aPool[] of previous free chunk */\n    } list;\n  } u;\n};\n\n/*\n** All of the static variables used by this module are collected\n** into a single structure named \"mem3\".  This is to keep the\n** static variables organized and to reduce namespace pollution\n** when this module is combined with other in the amalgamation.\n*/\nstatic SQLITE_WSD struct Mem3Global {\n  /*\n  ** Memory available for allocation. nPool is the size of the array\n  ** (in Mem3Blocks) pointed to by aPool less 2.\n  */\n  u32 nPool;\n  Mem3Block *aPool;\n\n  /*\n  ** True if we are evaluating an out-of-memory callback.\n  */\n  int alarmBusy;\n  \n  /*\n  ** Mutex to control access to the memory allocation subsystem.\n  */\n  sqlite3_mutex *mutex;\n  \n  /*\n  ** The minimum amount of free space that we have seen.\n  */\n  u32 mnMaster;\n\n  /*\n  ** iMaster is the index of the master chunk.  Most new allocations\n  ** occur off of this chunk.  szMaster is the size (in Mem3Blocks)\n  ** of the current master.  iMaster is 0 if there is not master chunk.\n  ** The master chunk is not in either the aiHash[] or aiSmall[].\n  */\n  u32 iMaster;\n  u32 szMaster;\n\n  /*\n  ** Array of lists of free blocks according to the block size \n  ** for smaller chunks, or a hash on the block size for larger\n  ** chunks.\n  */\n  u32 aiSmall[MX_SMALL-1];   /* For sizes 2 through MX_SMALL, inclusive */\n  u32 aiHash[N_HASH];        /* For sizes MX_SMALL+1 and larger */\n} mem3 = { 97535575 };\n\n#define mem3 GLOBAL(struct Mem3Global, mem3)\n\n/*\n** Unlink the chunk at mem3.aPool[i] from list it is currently\n** on.  *pRoot is the list that i is a member of.\n*/\nstatic void memsys3UnlinkFromList(u32 i, u32 *pRoot){\n  u32 next = mem3.aPool[i].u.list.next;\n  u32 prev = mem3.aPool[i].u.list.prev;\n  assert( sqlite3_mutex_held(mem3.mutex) );\n  if( prev==0 ){\n    *pRoot = next;\n  }else{\n    mem3.aPool[prev].u.list.next = next;\n  }\n  if( next ){\n    mem3.aPool[next].u.list.prev = prev;\n  }\n  mem3.aPool[i].u.list.next = 0;\n  mem3.aPool[i].u.list.prev = 0;\n}\n\n/*\n** Unlink the chunk at index i from \n** whatever list is currently a member of.\n*/\nstatic void memsys3Unlink(u32 i){\n  u32 size, hash;\n  assert( sqlite3_mutex_held(mem3.mutex) );\n  assert( (mem3.aPool[i-1].u.hdr.size4x & 1)==0 );\n  assert( i>=1 );\n  size = mem3.aPool[i-1].u.hdr.size4x/4;\n  assert( size==mem3.aPool[i+size-1].u.hdr.prevSize );\n  assert( size>=2 );\n  if( size <= MX_SMALL ){\n    memsys3UnlinkFromList(i, &mem3.aiSmall[size-2]);\n  }else{\n    hash = size % N_HASH;\n    memsys3UnlinkFromList(i, &mem3.aiHash[hash]);\n  }\n}\n\n/*\n** Link the chunk at mem3.aPool[i] so that is on the list rooted\n** at *pRoot.\n*/\nstatic void memsys3LinkIntoList(u32 i, u32 *pRoot){\n  assert( sqlite3_mutex_held(mem3.mutex) );\n  mem3.aPool[i].u.list.next = *pRoot;\n  mem3.aPool[i].u.list.prev = 0;\n  if( *pRoot ){\n    mem3.aPool[*pRoot].u.list.prev = i;\n  }\n  *pRoot = i;\n}\n\n/*\n** Link the chunk at index i into either the appropriate\n** small chunk list, or into the large chunk hash table.\n*/\nstatic void memsys3Link(u32 i){\n  u32 size, hash;\n  assert( sqlite3_mutex_held(mem3.mutex) );\n  assert( i>=1 );\n  assert( (mem3.aPool[i-1].u.hdr.size4x & 1)==0 );\n  size = mem3.aPool[i-1].u.hdr.size4x/4;\n  assert( size==mem3.aPool[i+size-1].u.hdr.prevSize );\n  assert( size>=2 );\n  if( size <= MX_SMALL ){\n    memsys3LinkIntoList(i, &mem3.aiSmall[size-2]);\n  }else{\n    hash = size % N_HASH;\n    memsys3LinkIntoList(i, &mem3.aiHash[hash]);\n  }\n}\n\n/*\n** If the STATIC_MEM mutex is not already held, obtain it now. The mutex\n** will already be held (obtained by code in malloc.c) if\n** sqlite3GlobalConfig.bMemStat is true.\n*/\nstatic void memsys3Enter(void){\n  if( sqlite3GlobalConfig.bMemstat==0 && mem3.mutex==0 ){\n    mem3.mutex = sqlite3MutexAlloc(SQLITE_MUTEX_STATIC_MEM);\n  }\n  sqlite3_mutex_enter(mem3.mutex);\n}\nstatic void memsys3Leave(void){\n  sqlite3_mutex_leave(mem3.mutex);\n}\n\n/*\n** Called when we are unable to satisfy an allocation of nBytes.\n*/\nstatic void memsys3OutOfMemory(int nByte){\n  if( !mem3.alarmBusy ){\n    mem3.alarmBusy = 1;\n    assert( sqlite3_mutex_held(mem3.mutex) );\n    sqlite3_mutex_leave(mem3.mutex);\n    sqlite3_release_memory(nByte);\n    sqlite3_mutex_enter(mem3.mutex);\n    mem3.alarmBusy = 0;\n  }\n}\n\n\n/*\n** Chunk i is a free chunk that has been unlinked.  Adjust its \n** size parameters for check-out and return a pointer to the \n** user portion of the chunk.\n*/\nstatic void *memsys3Checkout(u32 i, u32 nBlock){\n  u32 x;\n  assert( sqlite3_mutex_held(mem3.mutex) );\n  assert( i>=1 );\n  assert( mem3.aPool[i-1].u.hdr.size4x/4==nBlock );\n  assert( mem3.aPool[i+nBlock-1].u.hdr.prevSize==nBlock );\n  x = mem3.aPool[i-1].u.hdr.size4x;\n  mem3.aPool[i-1].u.hdr.size4x = nBlock*4 | 1 | (x&2);\n  mem3.aPool[i+nBlock-1].u.hdr.prevSize = nBlock;\n  mem3.aPool[i+nBlock-1].u.hdr.size4x |= 2;\n  return &mem3.aPool[i];\n}\n\n/*\n** Carve a piece off of the end of the mem3.iMaster free chunk.\n** Return a pointer to the new allocation.  Or, if the master chunk\n** is not large enough, return 0.\n*/\nstatic void *memsys3FromMaster(u32 nBlock){\n  assert( sqlite3_mutex_held(mem3.mutex) );\n  assert( mem3.szMaster>=nBlock );\n  if( nBlock>=mem3.szMaster-1 ){\n    /* Use the entire master */\n    void *p = memsys3Checkout(mem3.iMaster, mem3.szMaster);\n    mem3.iMaster = 0;\n    mem3.szMaster = 0;\n    mem3.mnMaster = 0;\n    return p;\n  }else{\n    /* Split the master block.  Return the tail. */\n    u32 newi, x;\n    newi = mem3.iMaster + mem3.szMaster - nBlock;\n    assert( newi > mem3.iMaster+1 );\n    mem3.aPool[mem3.iMaster+mem3.szMaster-1].u.hdr.prevSize = nBlock;\n    mem3.aPool[mem3.iMaster+mem3.szMaster-1].u.hdr.size4x |= 2;\n    mem3.aPool[newi-1].u.hdr.size4x = nBlock*4 + 1;\n    mem3.szMaster -= nBlock;\n    mem3.aPool[newi-1].u.hdr.prevSize = mem3.szMaster;\n    x = mem3.aPool[mem3.iMaster-1].u.hdr.size4x & 2;\n    mem3.aPool[mem3.iMaster-1].u.hdr.size4x = mem3.szMaster*4 | x;\n    if( mem3.szMaster < mem3.mnMaster ){\n      mem3.mnMaster = mem3.szMaster;\n    }\n    return (void*)&mem3.aPool[newi];\n  }\n}\n\n/*\n** *pRoot is the head of a list of free chunks of the same size\n** or same size hash.  In other words, *pRoot is an entry in either\n** mem3.aiSmall[] or mem3.aiHash[].  \n**\n** This routine examines all entries on the given list and tries\n** to coalesce each entries with adjacent free chunks.  \n**\n** If it sees a chunk that is larger than mem3.iMaster, it replaces \n** the current mem3.iMaster with the new larger chunk.  In order for\n** this mem3.iMaster replacement to work, the master chunk must be\n** linked into the hash tables.  That is not the normal state of\n** affairs, of course.  The calling routine must link the master\n** chunk before invoking this routine, then must unlink the (possibly\n** changed) master chunk once this routine has finished.\n*/\nstatic void memsys3Merge(u32 *pRoot){\n  u32 iNext, prev, size, i, x;\n\n  assert( sqlite3_mutex_held(mem3.mutex) );\n  for(i=*pRoot; i>0; i=iNext){\n    iNext = mem3.aPool[i].u.list.next;\n    size = mem3.aPool[i-1].u.hdr.size4x;\n    assert( (size&1)==0 );\n    if( (size&2)==0 ){\n      memsys3UnlinkFromList(i, pRoot);\n      assert( i > mem3.aPool[i-1].u.hdr.prevSize );\n      prev = i - mem3.aPool[i-1].u.hdr.prevSize;\n      if( prev==iNext ){\n        iNext = mem3.aPool[prev].u.list.next;\n      }\n      memsys3Unlink(prev);\n      size = i + size/4 - prev;\n      x = mem3.aPool[prev-1].u.hdr.size4x & 2;\n      mem3.aPool[prev-1].u.hdr.size4x = size*4 | x;\n      mem3.aPool[prev+size-1].u.hdr.prevSize = size;\n      memsys3Link(prev);\n      i = prev;\n    }else{\n      size /= 4;\n    }\n    if( size>mem3.szMaster ){\n      mem3.iMaster = i;\n      mem3.szMaster = size;\n    }\n  }\n}\n\n/*\n** Return a block of memory of at least nBytes in size.\n** Return NULL if unable.\n**\n** This function assumes that the necessary mutexes, if any, are\n** already held by the caller. Hence \"Unsafe\".\n*/\nstatic void *memsys3MallocUnsafe(int nByte){\n  u32 i;\n  u32 nBlock;\n  u32 toFree;\n\n  assert( sqlite3_mutex_held(mem3.mutex) );\n  assert( sizeof(Mem3Block)==8 );\n  if( nByte<=12 ){\n    nBlock = 2;\n  }else{\n    nBlock = (nByte + 11)/8;\n  }\n  assert( nBlock>=2 );\n\n  /* STEP 1:\n  ** Look for an entry of the correct size in either the small\n  ** chunk table or in the large chunk hash table.  This is\n  ** successful most of the time (about 9 times out of 10).\n  */\n  if( nBlock <= MX_SMALL ){\n    i = mem3.aiSmall[nBlock-2];\n    if( i>0 ){\n      memsys3UnlinkFromList(i, &mem3.aiSmall[nBlock-2]);\n      return memsys3Checkout(i, nBlock);\n    }\n  }else{\n    int hash = nBlock % N_HASH;\n    for(i=mem3.aiHash[hash]; i>0; i=mem3.aPool[i].u.list.next){\n      if( mem3.aPool[i-1].u.hdr.size4x/4==nBlock ){\n        memsys3UnlinkFromList(i, &mem3.aiHash[hash]);\n        return memsys3Checkout(i, nBlock);\n      }\n    }\n  }\n\n  /* STEP 2:\n  ** Try to satisfy the allocation by carving a piece off of the end\n  ** of the master chunk.  This step usually works if step 1 fails.\n  */\n  if( mem3.szMaster>=nBlock ){\n    return memsys3FromMaster(nBlock);\n  }\n\n\n  /* STEP 3:  \n  ** Loop through the entire memory pool.  Coalesce adjacent free\n  ** chunks.  Recompute the master chunk as the largest free chunk.\n  ** Then try again to satisfy the allocation by carving a piece off\n  ** of the end of the master chunk.  This step happens very\n  ** rarely (we hope!)\n  */\n  for(toFree=nBlock*16; toFree<(mem3.nPool*16); toFree *= 2){\n    memsys3OutOfMemory(toFree);\n    if( mem3.iMaster ){\n      memsys3Link(mem3.iMaster);\n      mem3.iMaster = 0;\n      mem3.szMaster = 0;\n    }\n    for(i=0; i<N_HASH; i++){\n      memsys3Merge(&mem3.aiHash[i]);\n    }\n    for(i=0; i<MX_SMALL-1; i++){\n      memsys3Merge(&mem3.aiSmall[i]);\n    }\n    if( mem3.szMaster ){\n      memsys3Unlink(mem3.iMaster);\n      if( mem3.szMaster>=nBlock ){\n        return memsys3FromMaster(nBlock);\n      }\n    }\n  }\n\n  /* If none of the above worked, then we fail. */\n  return 0;\n}\n\n/*\n** Free an outstanding memory allocation.\n**\n** This function assumes that the necessary mutexes, if any, are\n** already held by the caller. Hence \"Unsafe\".\n*/\nstatic void memsys3FreeUnsafe(void *pOld){\n  Mem3Block *p = (Mem3Block*)pOld;\n  int i;\n  u32 size, x;\n  assert( sqlite3_mutex_held(mem3.mutex) );\n  assert( p>mem3.aPool && p<&mem3.aPool[mem3.nPool] );\n  i = p - mem3.aPool;\n  assert( (mem3.aPool[i-1].u.hdr.size4x&1)==1 );\n  size = mem3.aPool[i-1].u.hdr.size4x/4;\n  assert( i+size<=mem3.nPool+1 );\n  mem3.aPool[i-1].u.hdr.size4x &= ~1;\n  mem3.aPool[i+size-1].u.hdr.prevSize = size;\n  mem3.aPool[i+size-1].u.hdr.size4x &= ~2;\n  memsys3Link(i);\n\n  /* Try to expand the master using the newly freed chunk */\n  if( mem3.iMaster ){\n    while( (mem3.aPool[mem3.iMaster-1].u.hdr.size4x&2)==0 ){\n      size = mem3.aPool[mem3.iMaster-1].u.hdr.prevSize;\n      mem3.iMaster -= size;\n      mem3.szMaster += size;\n      memsys3Unlink(mem3.iMaster);\n      x = mem3.aPool[mem3.iMaster-1].u.hdr.size4x & 2;\n      mem3.aPool[mem3.iMaster-1].u.hdr.size4x = mem3.szMaster*4 | x;\n      mem3.aPool[mem3.iMaster+mem3.szMaster-1].u.hdr.prevSize = mem3.szMaster;\n    }\n    x = mem3.aPool[mem3.iMaster-1].u.hdr.size4x & 2;\n    while( (mem3.aPool[mem3.iMaster+mem3.szMaster-1].u.hdr.size4x&1)==0 ){\n      memsys3Unlink(mem3.iMaster+mem3.szMaster);\n      mem3.szMaster += mem3.aPool[mem3.iMaster+mem3.szMaster-1].u.hdr.size4x/4;\n      mem3.aPool[mem3.iMaster-1].u.hdr.size4x = mem3.szMaster*4 | x;\n      mem3.aPool[mem3.iMaster+mem3.szMaster-1].u.hdr.prevSize = mem3.szMaster;\n    }\n  }\n}\n\n/*\n** Return the size of an outstanding allocation, in bytes.  The\n** size returned omits the 8-byte header overhead.  This only\n** works for chunks that are currently checked out.\n*/\nstatic int memsys3Size(void *p){\n  Mem3Block *pBlock;\n  assert( p!=0 );\n  pBlock = (Mem3Block*)p;\n  assert( (pBlock[-1].u.hdr.size4x&1)!=0 );\n  return (pBlock[-1].u.hdr.size4x&~3)*2 - 4;\n}\n\n/*\n** Round up a request size to the next valid allocation size.\n*/\nstatic int memsys3Roundup(int n){\n  if( n<=12 ){\n    return 12;\n  }else{\n    return ((n+11)&~7) - 4;\n  }\n}\n\n/*\n** Allocate nBytes of memory.\n*/\nstatic void *memsys3Malloc(int nBytes){\n  sqlite3_int64 *p;\n  assert( nBytes>0 );          /* malloc.c filters out 0 byte requests */\n  memsys3Enter();\n  p = memsys3MallocUnsafe(nBytes);\n  memsys3Leave();\n  return (void*)p; \n}\n\n/*\n** Free memory.\n*/\nstatic void memsys3Free(void *pPrior){\n  assert( pPrior );\n  memsys3Enter();\n  memsys3FreeUnsafe(pPrior);\n  memsys3Leave();\n}\n\n/*\n** Change the size of an existing memory allocation\n*/\nstatic void *memsys3Realloc(void *pPrior, int nBytes){\n  int nOld;\n  void *p;\n  if( pPrior==0 ){\n    return sqlite3_malloc(nBytes);\n  }\n  if( nBytes<=0 ){\n    sqlite3_free(pPrior);\n    return 0;\n  }\n  nOld = memsys3Size(pPrior);\n  if( nBytes<=nOld && nBytes>=nOld-128 ){\n    return pPrior;\n  }\n  memsys3Enter();\n  p = memsys3MallocUnsafe(nBytes);\n  if( p ){\n    if( nOld<nBytes ){\n      memcpy(p, pPrior, nOld);\n    }else{\n      memcpy(p, pPrior, nBytes);\n    }\n    memsys3FreeUnsafe(pPrior);\n  }\n  memsys3Leave();\n  return p;\n}\n\n/*\n** Initialize this module.\n*/\nstatic int memsys3Init(void *NotUsed){\n  UNUSED_PARAMETER(NotUsed);\n  if( !sqlite3GlobalConfig.pHeap ){\n    return SQLITE_ERROR;\n  }\n\n  /* Store a pointer to the memory block in global structure mem3. */\n  assert( sizeof(Mem3Block)==8 );\n  mem3.aPool = (Mem3Block *)sqlite3GlobalConfig.pHeap;\n  mem3.nPool = (sqlite3GlobalConfig.nHeap / sizeof(Mem3Block)) - 2;\n\n  /* Initialize the master block. */\n  mem3.szMaster = mem3.nPool;\n  mem3.mnMaster = mem3.szMaster;\n  mem3.iMaster = 1;\n  mem3.aPool[0].u.hdr.size4x = (mem3.szMaster<<2) + 2;\n  mem3.aPool[mem3.nPool].u.hdr.prevSize = mem3.nPool;\n  mem3.aPool[mem3.nPool].u.hdr.size4x = 1;\n\n  return SQLITE_OK;\n}\n\n/*\n** Deinitialize this module.\n*/\nstatic void memsys3Shutdown(void *NotUsed){\n  UNUSED_PARAMETER(NotUsed);\n  mem3.mutex = 0;\n  return;\n}\n\n\n\n/*\n** Open the file indicated and write a log of all unfreed memory \n** allocations into that log.\n*/\nSQLITE_PRIVATE void sqlite3Memsys3Dump(const char *zFilename){\n#ifdef SQLITE_DEBUG\n  FILE *out;\n  u32 i, j;\n  u32 size;\n  if( zFilename==0 || zFilename[0]==0 ){\n    out = stdout;\n  }else{\n    out = fopen(zFilename, \"w\");\n    if( out==0 ){\n      fprintf(stderr, \"** Unable to output memory debug output log: %s **\\n\",\n                      zFilename);\n      return;\n    }\n  }\n  memsys3Enter();\n  fprintf(out, \"CHUNKS:\\n\");\n  for(i=1; i<=mem3.nPool; i+=size/4){\n    size = mem3.aPool[i-1].u.hdr.size4x;\n    if( size/4<=1 ){\n      fprintf(out, \"%p size error\\n\", &mem3.aPool[i]);\n      assert( 0 );\n      break;\n    }\n    if( (size&1)==0 && mem3.aPool[i+size/4-1].u.hdr.prevSize!=size/4 ){\n      fprintf(out, \"%p tail size does not match\\n\", &mem3.aPool[i]);\n      assert( 0 );\n      break;\n    }\n    if( ((mem3.aPool[i+size/4-1].u.hdr.size4x&2)>>1)!=(size&1) ){\n      fprintf(out, \"%p tail checkout bit is incorrect\\n\", &mem3.aPool[i]);\n      assert( 0 );\n      break;\n    }\n    if( size&1 ){\n      fprintf(out, \"%p %6d bytes checked out\\n\", &mem3.aPool[i], (size/4)*8-8);\n    }else{\n      fprintf(out, \"%p %6d bytes free%s\\n\", &mem3.aPool[i], (size/4)*8-8,\n                  i==mem3.iMaster ? \" **master**\" : \"\");\n    }\n  }\n  for(i=0; i<MX_SMALL-1; i++){\n    if( mem3.aiSmall[i]==0 ) continue;\n    fprintf(out, \"small(%2d):\", i);\n    for(j = mem3.aiSmall[i]; j>0; j=mem3.aPool[j].u.list.next){\n      fprintf(out, \" %p(%d)\", &mem3.aPool[j],\n              (mem3.aPool[j-1].u.hdr.size4x/4)*8-8);\n    }\n    fprintf(out, \"\\n\"); \n  }\n  for(i=0; i<N_HASH; i++){\n    if( mem3.aiHash[i]==0 ) continue;\n    fprintf(out, \"hash(%2d):\", i);\n    for(j = mem3.aiHash[i]; j>0; j=mem3.aPool[j].u.list.next){\n      fprintf(out, \" %p(%d)\", &mem3.aPool[j],\n              (mem3.aPool[j-1].u.hdr.size4x/4)*8-8);\n    }\n    fprintf(out, \"\\n\"); \n  }\n  fprintf(out, \"master=%d\\n\", mem3.iMaster);\n  fprintf(out, \"nowUsed=%d\\n\", mem3.nPool*8 - mem3.szMaster*8);\n  fprintf(out, \"mxUsed=%d\\n\", mem3.nPool*8 - mem3.mnMaster*8);\n  sqlite3_mutex_leave(mem3.mutex);\n  if( out==stdout ){\n    fflush(stdout);\n  }else{\n    fclose(out);\n  }\n#else\n  UNUSED_PARAMETER(zFilename);\n#endif\n}\n\n/*\n** This routine is the only routine in this file with external \n** linkage.\n**\n** Populate the low-level memory allocation function pointers in\n** sqlite3GlobalConfig.m with pointers to the routines in this file. The\n** arguments specify the block of memory to manage.\n**\n** This routine is only called by sqlite3_config(), and therefore\n** is not required to be threadsafe (it is not).\n*/\nSQLITE_PRIVATE const sqlite3_mem_methods *sqlite3MemGetMemsys3(void){\n  static const sqlite3_mem_methods mempoolMethods = {\n     memsys3Malloc,\n     memsys3Free,\n     memsys3Realloc,\n     memsys3Size,\n     memsys3Roundup,\n     memsys3Init,\n     memsys3Shutdown,\n     0\n  };\n  return &mempoolMethods;\n}\n\n#endif /* SQLITE_ENABLE_MEMSYS3 */\n\n/************** End of mem3.c ************************************************/\n/************** Begin file mem5.c ********************************************/\n/*\n** 2007 October 14\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n*************************************************************************\n** This file contains the C functions that implement a memory\n** allocation subsystem for use by SQLite. \n**\n** This version of the memory allocation subsystem omits all\n** use of malloc(). The application gives SQLite a block of memory\n** before calling sqlite3_initialize() from which allocations\n** are made and returned by the xMalloc() and xRealloc() \n** implementations. Once sqlite3_initialize() has been called,\n** the amount of memory available to SQLite is fixed and cannot\n** be changed.\n**\n** This version of the memory allocation subsystem is included\n** in the build only if SQLITE_ENABLE_MEMSYS5 is defined.\n**\n** This memory allocator uses the following algorithm:\n**\n**   1.  All memory allocation sizes are rounded up to a power of 2.\n**\n**   2.  If two adjacent free blocks are the halves of a larger block,\n**       then the two blocks are coalesced into the single larger block.\n**\n**   3.  New memory is allocated from the first available free block.\n**\n** This algorithm is described in: J. M. Robson. \"Bounds for Some Functions\n** Concerning Dynamic Storage Allocation\". Journal of the Association for\n** Computing Machinery, Volume 21, Number 8, July 1974, pages 491-499.\n** \n** Let n be the size of the largest allocation divided by the minimum\n** allocation size (after rounding all sizes up to a power of 2.)  Let M\n** be the maximum amount of memory ever outstanding at one time.  Let\n** N be the total amount of memory available for allocation.  Robson\n** proved that this memory allocator will never breakdown due to \n** fragmentation as long as the following constraint holds:\n**\n**      N >=  M*(1 + log2(n)/2) - n + 1\n**\n** The sqlite3_status() logic tracks the maximum values of n and M so\n** that an application can, at any time, verify this constraint.\n*/\n/* #include \"sqliteInt.h\" */\n\n/*\n** This version of the memory allocator is used only when \n** SQLITE_ENABLE_MEMSYS5 is defined.\n*/\n#ifdef SQLITE_ENABLE_MEMSYS5\n\n/*\n** A minimum allocation is an instance of the following structure.\n** Larger allocations are an array of these structures where the\n** size of the array is a power of 2.\n**\n** The size of this object must be a power of two.  That fact is\n** verified in memsys5Init().\n*/\ntypedef struct Mem5Link Mem5Link;\nstruct Mem5Link {\n  int next;       /* Index of next free chunk */\n  int prev;       /* Index of previous free chunk */\n};\n\n/*\n** Maximum size of any allocation is ((1<<LOGMAX)*mem5.szAtom). Since\n** mem5.szAtom is always at least 8 and 32-bit integers are used,\n** it is not actually possible to reach this limit.\n*/\n#define LOGMAX 30\n\n/*\n** Masks used for mem5.aCtrl[] elements.\n*/\n#define CTRL_LOGSIZE  0x1f    /* Log2 Size of this block */\n#define CTRL_FREE     0x20    /* True if not checked out */\n\n/*\n** All of the static variables used by this module are collected\n** into a single structure named \"mem5\".  This is to keep the\n** static variables organized and to reduce namespace pollution\n** when this module is combined with other in the amalgamation.\n*/\nstatic SQLITE_WSD struct Mem5Global {\n  /*\n  ** Memory available for allocation\n  */\n  int szAtom;      /* Smallest possible allocation in bytes */\n  int nBlock;      /* Number of szAtom sized blocks in zPool */\n  u8 *zPool;       /* Memory available to be allocated */\n  \n  /*\n  ** Mutex to control access to the memory allocation subsystem.\n  */\n  sqlite3_mutex *mutex;\n\n#if defined(SQLITE_DEBUG) || defined(SQLITE_TEST)\n  /*\n  ** Performance statistics\n  */\n  u64 nAlloc;         /* Total number of calls to malloc */\n  u64 totalAlloc;     /* Total of all malloc calls - includes internal frag */\n  u64 totalExcess;    /* Total internal fragmentation */\n  u32 currentOut;     /* Current checkout, including internal fragmentation */\n  u32 currentCount;   /* Current number of distinct checkouts */\n  u32 maxOut;         /* Maximum instantaneous currentOut */\n  u32 maxCount;       /* Maximum instantaneous currentCount */\n  u32 maxRequest;     /* Largest allocation (exclusive of internal frag) */\n#endif\n  \n  /*\n  ** Lists of free blocks.  aiFreelist[0] is a list of free blocks of\n  ** size mem5.szAtom.  aiFreelist[1] holds blocks of size szAtom*2.\n  ** aiFreelist[2] holds free blocks of size szAtom*4.  And so forth.\n  */\n  int aiFreelist[LOGMAX+1];\n\n  /*\n  ** Space for tracking which blocks are checked out and the size\n  ** of each block.  One byte per block.\n  */\n  u8 *aCtrl;\n\n} mem5;\n\n/*\n** Access the static variable through a macro for SQLITE_OMIT_WSD.\n*/\n#define mem5 GLOBAL(struct Mem5Global, mem5)\n\n/*\n** Assuming mem5.zPool is divided up into an array of Mem5Link\n** structures, return a pointer to the idx-th such link.\n*/\n#define MEM5LINK(idx) ((Mem5Link *)(&mem5.zPool[(idx)*mem5.szAtom]))\n\n/*\n** Unlink the chunk at mem5.aPool[i] from list it is currently\n** on.  It should be found on mem5.aiFreelist[iLogsize].\n*/\nstatic void memsys5Unlink(int i, int iLogsize){\n  int next, prev;\n  assert( i>=0 && i<mem5.nBlock );\n  assert( iLogsize>=0 && iLogsize<=LOGMAX );\n  assert( (mem5.aCtrl[i] & CTRL_LOGSIZE)==iLogsize );\n\n  next = MEM5LINK(i)->next;\n  prev = MEM5LINK(i)->prev;\n  if( prev<0 ){\n    mem5.aiFreelist[iLogsize] = next;\n  }else{\n    MEM5LINK(prev)->next = next;\n  }\n  if( next>=0 ){\n    MEM5LINK(next)->prev = prev;\n  }\n}\n\n/*\n** Link the chunk at mem5.aPool[i] so that is on the iLogsize\n** free list.\n*/\nstatic void memsys5Link(int i, int iLogsize){\n  int x;\n  assert( sqlite3_mutex_held(mem5.mutex) );\n  assert( i>=0 && i<mem5.nBlock );\n  assert( iLogsize>=0 && iLogsize<=LOGMAX );\n  assert( (mem5.aCtrl[i] & CTRL_LOGSIZE)==iLogsize );\n\n  x = MEM5LINK(i)->next = mem5.aiFreelist[iLogsize];\n  MEM5LINK(i)->prev = -1;\n  if( x>=0 ){\n    assert( x<mem5.nBlock );\n    MEM5LINK(x)->prev = i;\n  }\n  mem5.aiFreelist[iLogsize] = i;\n}\n\n/*\n** Obtain or release the mutex needed to access global data structures.\n*/\nstatic void memsys5Enter(void){\n  sqlite3_mutex_enter(mem5.mutex);\n}\nstatic void memsys5Leave(void){\n  sqlite3_mutex_leave(mem5.mutex);\n}\n\n/*\n** Return the size of an outstanding allocation, in bytes.\n** This only works for chunks that are currently checked out.\n*/\nstatic int memsys5Size(void *p){\n  int iSize, i;\n  assert( p!=0 );\n  i = (int)(((u8 *)p-mem5.zPool)/mem5.szAtom);\n  assert( i>=0 && i<mem5.nBlock );\n  iSize = mem5.szAtom * (1 << (mem5.aCtrl[i]&CTRL_LOGSIZE));\n  return iSize;\n}\n\n/*\n** Return a block of memory of at least nBytes in size.\n** Return NULL if unable.  Return NULL if nBytes==0.\n**\n** The caller guarantees that nByte is positive.\n**\n** The caller has obtained a mutex prior to invoking this\n** routine so there is never any chance that two or more\n** threads can be in this routine at the same time.\n*/\nstatic void *memsys5MallocUnsafe(int nByte){\n  int i;           /* Index of a mem5.aPool[] slot */\n  int iBin;        /* Index into mem5.aiFreelist[] */\n  int iFullSz;     /* Size of allocation rounded up to power of 2 */\n  int iLogsize;    /* Log2 of iFullSz/POW2_MIN */\n\n  /* nByte must be a positive */\n  assert( nByte>0 );\n\n  /* No more than 1GiB per allocation */\n  if( nByte > 0x40000000 ) return 0;\n\n#if defined(SQLITE_DEBUG) || defined(SQLITE_TEST)\n  /* Keep track of the maximum allocation request.  Even unfulfilled\n  ** requests are counted */\n  if( (u32)nByte>mem5.maxRequest ){\n    mem5.maxRequest = nByte;\n  }\n#endif\n\n\n  /* Round nByte up to the next valid power of two */\n  for(iFullSz=mem5.szAtom,iLogsize=0; iFullSz<nByte; iFullSz*=2,iLogsize++){}\n\n  /* Make sure mem5.aiFreelist[iLogsize] contains at least one free\n  ** block.  If not, then split a block of the next larger power of\n  ** two in order to create a new free block of size iLogsize.\n  */\n  for(iBin=iLogsize; iBin<=LOGMAX && mem5.aiFreelist[iBin]<0; iBin++){}\n  if( iBin>LOGMAX ){\n    testcase( sqlite3GlobalConfig.xLog!=0 );\n    sqlite3_log(SQLITE_NOMEM, \"failed to allocate %u bytes\", nByte);\n    return 0;\n  }\n  i = mem5.aiFreelist[iBin];\n  memsys5Unlink(i, iBin);\n  while( iBin>iLogsize ){\n    int newSize;\n\n    iBin--;\n    newSize = 1 << iBin;\n    mem5.aCtrl[i+newSize] = CTRL_FREE | iBin;\n    memsys5Link(i+newSize, iBin);\n  }\n  mem5.aCtrl[i] = iLogsize;\n\n#if defined(SQLITE_DEBUG) || defined(SQLITE_TEST)\n  /* Update allocator performance statistics. */\n  mem5.nAlloc++;\n  mem5.totalAlloc += iFullSz;\n  mem5.totalExcess += iFullSz - nByte;\n  mem5.currentCount++;\n  mem5.currentOut += iFullSz;\n  if( mem5.maxCount<mem5.currentCount ) mem5.maxCount = mem5.currentCount;\n  if( mem5.maxOut<mem5.currentOut ) mem5.maxOut = mem5.currentOut;\n#endif\n\n#ifdef SQLITE_DEBUG\n  /* Make sure the allocated memory does not assume that it is set to zero\n  ** or retains a value from a previous allocation */\n  memset(&mem5.zPool[i*mem5.szAtom], 0xAA, iFullSz);\n#endif\n\n  /* Return a pointer to the allocated memory. */\n  return (void*)&mem5.zPool[i*mem5.szAtom];\n}\n\n/*\n** Free an outstanding memory allocation.\n*/\nstatic void memsys5FreeUnsafe(void *pOld){\n  u32 size, iLogsize;\n  int iBlock;\n\n  /* Set iBlock to the index of the block pointed to by pOld in \n  ** the array of mem5.szAtom byte blocks pointed to by mem5.zPool.\n  */\n  iBlock = (int)(((u8 *)pOld-mem5.zPool)/mem5.szAtom);\n\n  /* Check that the pointer pOld points to a valid, non-free block. */\n  assert( iBlock>=0 && iBlock<mem5.nBlock );\n  assert( ((u8 *)pOld-mem5.zPool)%mem5.szAtom==0 );\n  assert( (mem5.aCtrl[iBlock] & CTRL_FREE)==0 );\n\n  iLogsize = mem5.aCtrl[iBlock] & CTRL_LOGSIZE;\n  size = 1<<iLogsize;\n  assert( iBlock+size-1<(u32)mem5.nBlock );\n\n  mem5.aCtrl[iBlock] |= CTRL_FREE;\n  mem5.aCtrl[iBlock+size-1] |= CTRL_FREE;\n\n#if defined(SQLITE_DEBUG) || defined(SQLITE_TEST)\n  assert( mem5.currentCount>0 );\n  assert( mem5.currentOut>=(size*mem5.szAtom) );\n  mem5.currentCount--;\n  mem5.currentOut -= size*mem5.szAtom;\n  assert( mem5.currentOut>0 || mem5.currentCount==0 );\n  assert( mem5.currentCount>0 || mem5.currentOut==0 );\n#endif\n\n  mem5.aCtrl[iBlock] = CTRL_FREE | iLogsize;\n  while( ALWAYS(iLogsize<LOGMAX) ){\n    int iBuddy;\n    if( (iBlock>>iLogsize) & 1 ){\n      iBuddy = iBlock - size;\n      assert( iBuddy>=0 );\n    }else{\n      iBuddy = iBlock + size;\n      if( iBuddy>=mem5.nBlock ) break;\n    }\n    if( mem5.aCtrl[iBuddy]!=(CTRL_FREE | iLogsize) ) break;\n    memsys5Unlink(iBuddy, iLogsize);\n    iLogsize++;\n    if( iBuddy<iBlock ){\n      mem5.aCtrl[iBuddy] = CTRL_FREE | iLogsize;\n      mem5.aCtrl[iBlock] = 0;\n      iBlock = iBuddy;\n    }else{\n      mem5.aCtrl[iBlock] = CTRL_FREE | iLogsize;\n      mem5.aCtrl[iBuddy] = 0;\n    }\n    size *= 2;\n  }\n\n#ifdef SQLITE_DEBUG\n  /* Overwrite freed memory with the 0x55 bit pattern to verify that it is\n  ** not used after being freed */\n  memset(&mem5.zPool[iBlock*mem5.szAtom], 0x55, size);\n#endif\n\n  memsys5Link(iBlock, iLogsize);\n}\n\n/*\n** Allocate nBytes of memory.\n*/\nstatic void *memsys5Malloc(int nBytes){\n  sqlite3_int64 *p = 0;\n  if( nBytes>0 ){\n    memsys5Enter();\n    p = memsys5MallocUnsafe(nBytes);\n    memsys5Leave();\n  }\n  return (void*)p; \n}\n\n/*\n** Free memory.\n**\n** The outer layer memory allocator prevents this routine from\n** being called with pPrior==0.\n*/\nstatic void memsys5Free(void *pPrior){\n  assert( pPrior!=0 );\n  memsys5Enter();\n  memsys5FreeUnsafe(pPrior);\n  memsys5Leave();  \n}\n\n/*\n** Change the size of an existing memory allocation.\n**\n** The outer layer memory allocator prevents this routine from\n** being called with pPrior==0.  \n**\n** nBytes is always a value obtained from a prior call to\n** memsys5Round().  Hence nBytes is always a non-negative power\n** of two.  If nBytes==0 that means that an oversize allocation\n** (an allocation larger than 0x40000000) was requested and this\n** routine should return 0 without freeing pPrior.\n*/\nstatic void *memsys5Realloc(void *pPrior, int nBytes){\n  int nOld;\n  void *p;\n  assert( pPrior!=0 );\n  assert( (nBytes&(nBytes-1))==0 );  /* EV: R-46199-30249 */\n  assert( nBytes>=0 );\n  if( nBytes==0 ){\n    return 0;\n  }\n  nOld = memsys5Size(pPrior);\n  if( nBytes<=nOld ){\n    return pPrior;\n  }\n  p = memsys5Malloc(nBytes);\n  if( p ){\n    memcpy(p, pPrior, nOld);\n    memsys5Free(pPrior);\n  }\n  return p;\n}\n\n/*\n** Round up a request size to the next valid allocation size.  If\n** the allocation is too large to be handled by this allocation system,\n** return 0.\n**\n** All allocations must be a power of two and must be expressed by a\n** 32-bit signed integer.  Hence the largest allocation is 0x40000000\n** or 1073741824 bytes.\n*/\nstatic int memsys5Roundup(int n){\n  int iFullSz;\n  if( n > 0x40000000 ) return 0;\n  for(iFullSz=mem5.szAtom; iFullSz<n; iFullSz *= 2);\n  return iFullSz;\n}\n\n/*\n** Return the ceiling of the logarithm base 2 of iValue.\n**\n** Examples:   memsys5Log(1) -> 0\n**             memsys5Log(2) -> 1\n**             memsys5Log(4) -> 2\n**             memsys5Log(5) -> 3\n**             memsys5Log(8) -> 3\n**             memsys5Log(9) -> 4\n*/\nstatic int memsys5Log(int iValue){\n  int iLog;\n  for(iLog=0; (iLog<(int)((sizeof(int)*8)-1)) && (1<<iLog)<iValue; iLog++);\n  return iLog;\n}\n\n/*\n** Initialize the memory allocator.\n**\n** This routine is not threadsafe.  The caller must be holding a mutex\n** to prevent multiple threads from entering at the same time.\n*/\nstatic int memsys5Init(void *NotUsed){\n  int ii;            /* Loop counter */\n  int nByte;         /* Number of bytes of memory available to this allocator */\n  u8 *zByte;         /* Memory usable by this allocator */\n  int nMinLog;       /* Log base 2 of minimum allocation size in bytes */\n  int iOffset;       /* An offset into mem5.aCtrl[] */\n\n  UNUSED_PARAMETER(NotUsed);\n\n  /* For the purposes of this routine, disable the mutex */\n  mem5.mutex = 0;\n\n  /* The size of a Mem5Link object must be a power of two.  Verify that\n  ** this is case.\n  */\n  assert( (sizeof(Mem5Link)&(sizeof(Mem5Link)-1))==0 );\n\n  nByte = sqlite3GlobalConfig.nHeap;\n  zByte = (u8*)sqlite3GlobalConfig.pHeap;\n  assert( zByte!=0 );  /* sqlite3_config() does not allow otherwise */\n\n  /* boundaries on sqlite3GlobalConfig.mnReq are enforced in sqlite3_config() */\n  nMinLog = memsys5Log(sqlite3GlobalConfig.mnReq);\n  mem5.szAtom = (1<<nMinLog);\n  while( (int)sizeof(Mem5Link)>mem5.szAtom ){\n    mem5.szAtom = mem5.szAtom << 1;\n  }\n\n  mem5.nBlock = (nByte / (mem5.szAtom+sizeof(u8)));\n  mem5.zPool = zByte;\n  mem5.aCtrl = (u8 *)&mem5.zPool[mem5.nBlock*mem5.szAtom];\n\n  for(ii=0; ii<=LOGMAX; ii++){\n    mem5.aiFreelist[ii] = -1;\n  }\n\n  iOffset = 0;\n  for(ii=LOGMAX; ii>=0; ii--){\n    int nAlloc = (1<<ii);\n    if( (iOffset+nAlloc)<=mem5.nBlock ){\n      mem5.aCtrl[iOffset] = ii | CTRL_FREE;\n      memsys5Link(iOffset, ii);\n      iOffset += nAlloc;\n    }\n    assert((iOffset+nAlloc)>mem5.nBlock);\n  }\n\n  /* If a mutex is required for normal operation, allocate one */\n  if( sqlite3GlobalConfig.bMemstat==0 ){\n    mem5.mutex = sqlite3MutexAlloc(SQLITE_MUTEX_STATIC_MEM);\n  }\n\n  return SQLITE_OK;\n}\n\n/*\n** Deinitialize this module.\n*/\nstatic void memsys5Shutdown(void *NotUsed){\n  UNUSED_PARAMETER(NotUsed);\n  mem5.mutex = 0;\n  return;\n}\n\n#ifdef SQLITE_TEST\n/*\n** Open the file indicated and write a log of all unfreed memory \n** allocations into that log.\n*/\nSQLITE_PRIVATE void sqlite3Memsys5Dump(const char *zFilename){\n  FILE *out;\n  int i, j, n;\n  int nMinLog;\n\n  if( zFilename==0 || zFilename[0]==0 ){\n    out = stdout;\n  }else{\n    out = fopen(zFilename, \"w\");\n    if( out==0 ){\n      fprintf(stderr, \"** Unable to output memory debug output log: %s **\\n\",\n                      zFilename);\n      return;\n    }\n  }\n  memsys5Enter();\n  nMinLog = memsys5Log(mem5.szAtom);\n  for(i=0; i<=LOGMAX && i+nMinLog<32; i++){\n    for(n=0, j=mem5.aiFreelist[i]; j>=0; j = MEM5LINK(j)->next, n++){}\n    fprintf(out, \"freelist items of size %d: %d\\n\", mem5.szAtom << i, n);\n  }\n  fprintf(out, \"mem5.nAlloc       = %llu\\n\", mem5.nAlloc);\n  fprintf(out, \"mem5.totalAlloc   = %llu\\n\", mem5.totalAlloc);\n  fprintf(out, \"mem5.totalExcess  = %llu\\n\", mem5.totalExcess);\n  fprintf(out, \"mem5.currentOut   = %u\\n\", mem5.currentOut);\n  fprintf(out, \"mem5.currentCount = %u\\n\", mem5.currentCount);\n  fprintf(out, \"mem5.maxOut       = %u\\n\", mem5.maxOut);\n  fprintf(out, \"mem5.maxCount     = %u\\n\", mem5.maxCount);\n  fprintf(out, \"mem5.maxRequest   = %u\\n\", mem5.maxRequest);\n  memsys5Leave();\n  if( out==stdout ){\n    fflush(stdout);\n  }else{\n    fclose(out);\n  }\n}\n#endif\n\n/*\n** This routine is the only routine in this file with external \n** linkage. It returns a pointer to a static sqlite3_mem_methods\n** struct populated with the memsys5 methods.\n*/\nSQLITE_PRIVATE const sqlite3_mem_methods *sqlite3MemGetMemsys5(void){\n  static const sqlite3_mem_methods memsys5Methods = {\n     memsys5Malloc,\n     memsys5Free,\n     memsys5Realloc,\n     memsys5Size,\n     memsys5Roundup,\n     memsys5Init,\n     memsys5Shutdown,\n     0\n  };\n  return &memsys5Methods;\n}\n\n#endif /* SQLITE_ENABLE_MEMSYS5 */\n\n/************** End of mem5.c ************************************************/\n/************** Begin file mutex.c *******************************************/\n/*\n** 2007 August 14\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n*************************************************************************\n** This file contains the C functions that implement mutexes.\n**\n** This file contains code that is common across all mutex implementations.\n*/\n/* #include \"sqliteInt.h\" */\n\n#if defined(SQLITE_DEBUG) && !defined(SQLITE_MUTEX_OMIT)\n/*\n** For debugging purposes, record when the mutex subsystem is initialized\n** and uninitialized so that we can assert() if there is an attempt to\n** allocate a mutex while the system is uninitialized.\n*/\nstatic SQLITE_WSD int mutexIsInit = 0;\n#endif /* SQLITE_DEBUG && !defined(SQLITE_MUTEX_OMIT) */\n\n\n#ifndef SQLITE_MUTEX_OMIT\n\n#ifdef SQLITE_ENABLE_MULTITHREADED_CHECKS\n/*\n** This block (enclosed by SQLITE_ENABLE_MULTITHREADED_CHECKS) contains\n** the implementation of a wrapper around the system default mutex\n** implementation (sqlite3DefaultMutex()). \n**\n** Most calls are passed directly through to the underlying default\n** mutex implementation. Except, if a mutex is configured by calling\n** sqlite3MutexWarnOnContention() on it, then if contention is ever\n** encountered within xMutexEnter() a warning is emitted via sqlite3_log().\n**\n** This type of mutex is used as the database handle mutex when testing\n** apps that usually use SQLITE_CONFIG_MULTITHREAD mode.\n*/\n\n/* \n** Type for all mutexes used when SQLITE_ENABLE_MULTITHREADED_CHECKS\n** is defined. Variable CheckMutex.mutex is a pointer to the real mutex\n** allocated by the system mutex implementation. Variable iType is usually set\n** to the type of mutex requested - SQLITE_MUTEX_RECURSIVE, SQLITE_MUTEX_FAST\n** or one of the static mutex identifiers. Or, if this is a recursive mutex\n** that has been configured using sqlite3MutexWarnOnContention(), it is\n** set to SQLITE_MUTEX_WARNONCONTENTION.\n*/\ntypedef struct CheckMutex CheckMutex;\nstruct CheckMutex {\n  int iType;\n  sqlite3_mutex *mutex;\n};\n\n#define SQLITE_MUTEX_WARNONCONTENTION  (-1)\n\n/* \n** Pointer to real mutex methods object used by the CheckMutex\n** implementation. Set by checkMutexInit(). \n*/\nstatic SQLITE_WSD const sqlite3_mutex_methods *pGlobalMutexMethods;\n\n#ifdef SQLITE_DEBUG\nstatic int checkMutexHeld(sqlite3_mutex *p){\n  return pGlobalMutexMethods->xMutexHeld(((CheckMutex*)p)->mutex);\n}\nstatic int checkMutexNotheld(sqlite3_mutex *p){\n  return pGlobalMutexMethods->xMutexNotheld(((CheckMutex*)p)->mutex);\n}\n#endif\n\n/*\n** Initialize and deinitialize the mutex subsystem.\n*/\nstatic int checkMutexInit(void){ \n  pGlobalMutexMethods = sqlite3DefaultMutex();\n  return SQLITE_OK; \n}\nstatic int checkMutexEnd(void){ \n  pGlobalMutexMethods = 0;\n  return SQLITE_OK; \n}\n\n/*\n** Allocate a mutex.\n*/\nstatic sqlite3_mutex *checkMutexAlloc(int iType){\n  static CheckMutex staticMutexes[] = {\n    {2, 0}, {3, 0}, {4, 0}, {5, 0},\n    {6, 0}, {7, 0}, {8, 0}, {9, 0},\n    {10, 0}, {11, 0}, {12, 0}, {13, 0}\n  };\n  CheckMutex *p = 0;\n\n  assert( SQLITE_MUTEX_RECURSIVE==1 && SQLITE_MUTEX_FAST==0 );\n  if( iType<2 ){\n    p = sqlite3MallocZero(sizeof(CheckMutex));\n    if( p==0 ) return 0;\n    p->iType = iType;\n  }else{\n#ifdef SQLITE_ENABLE_API_ARMOR\n    if( iType-2>=ArraySize(staticMutexes) ){\n      (void)SQLITE_MISUSE_BKPT;\n      return 0;\n    }\n#endif\n    p = &staticMutexes[iType-2];\n  }\n\n  if( p->mutex==0 ){\n    p->mutex = pGlobalMutexMethods->xMutexAlloc(iType);\n    if( p->mutex==0 ){\n      if( iType<2 ){\n        sqlite3_free(p);\n      }\n      p = 0;\n    }\n  }\n\n  return (sqlite3_mutex*)p;\n}\n\n/*\n** Free a mutex.\n*/\nstatic void checkMutexFree(sqlite3_mutex *p){\n  assert( SQLITE_MUTEX_RECURSIVE<2 );\n  assert( SQLITE_MUTEX_FAST<2 );\n  assert( SQLITE_MUTEX_WARNONCONTENTION<2 );\n\n#if SQLITE_ENABLE_API_ARMOR\n  if( ((CheckMutex*)p)->iType<2 )\n#endif\n  {\n    CheckMutex *pCheck = (CheckMutex*)p;\n    pGlobalMutexMethods->xMutexFree(pCheck->mutex);\n    sqlite3_free(pCheck);\n  }\n#ifdef SQLITE_ENABLE_API_ARMOR\n  else{\n    (void)SQLITE_MISUSE_BKPT;\n  }\n#endif\n}\n\n/*\n** Enter the mutex.\n*/\nstatic void checkMutexEnter(sqlite3_mutex *p){\n  CheckMutex *pCheck = (CheckMutex*)p;\n  if( pCheck->iType==SQLITE_MUTEX_WARNONCONTENTION ){\n    if( SQLITE_OK==pGlobalMutexMethods->xMutexTry(pCheck->mutex) ){\n      return;\n    }\n    sqlite3_log(SQLITE_MISUSE, \n        \"illegal multi-threaded access to database connection\"\n    );\n  }\n  pGlobalMutexMethods->xMutexEnter(pCheck->mutex);\n}\n\n/*\n** Enter the mutex (do not block).\n*/\nstatic int checkMutexTry(sqlite3_mutex *p){\n  CheckMutex *pCheck = (CheckMutex*)p;\n  return pGlobalMutexMethods->xMutexTry(pCheck->mutex);\n}\n\n/*\n** Leave the mutex.\n*/\nstatic void checkMutexLeave(sqlite3_mutex *p){\n  CheckMutex *pCheck = (CheckMutex*)p;\n  pGlobalMutexMethods->xMutexLeave(pCheck->mutex);\n}\n\nsqlite3_mutex_methods const *multiThreadedCheckMutex(void){\n  static const sqlite3_mutex_methods sMutex = {\n    checkMutexInit,\n    checkMutexEnd,\n    checkMutexAlloc,\n    checkMutexFree,\n    checkMutexEnter,\n    checkMutexTry,\n    checkMutexLeave,\n#ifdef SQLITE_DEBUG\n    checkMutexHeld,\n    checkMutexNotheld\n#else\n    0,\n    0\n#endif\n  };\n  return &sMutex;\n}\n\n/*\n** Mark the SQLITE_MUTEX_RECURSIVE mutex passed as the only argument as\n** one on which there should be no contention.\n*/\nSQLITE_PRIVATE void sqlite3MutexWarnOnContention(sqlite3_mutex *p){\n  if( sqlite3GlobalConfig.mutex.xMutexAlloc==checkMutexAlloc ){\n    CheckMutex *pCheck = (CheckMutex*)p;\n    assert( pCheck->iType==SQLITE_MUTEX_RECURSIVE );\n    pCheck->iType = SQLITE_MUTEX_WARNONCONTENTION;\n  }\n}\n#endif   /* ifdef SQLITE_ENABLE_MULTITHREADED_CHECKS */\n\n/*\n** Initialize the mutex system.\n*/\nSQLITE_PRIVATE int sqlite3MutexInit(void){ \n  int rc = SQLITE_OK;\n  if( !sqlite3GlobalConfig.mutex.xMutexAlloc ){\n    /* If the xMutexAlloc method has not been set, then the user did not\n    ** install a mutex implementation via sqlite3_config() prior to \n    ** sqlite3_initialize() being called. This block copies pointers to\n    ** the default implementation into the sqlite3GlobalConfig structure.\n    */\n    sqlite3_mutex_methods const *pFrom;\n    sqlite3_mutex_methods *pTo = &sqlite3GlobalConfig.mutex;\n\n    if( sqlite3GlobalConfig.bCoreMutex ){\n#ifdef SQLITE_ENABLE_MULTITHREADED_CHECKS\n      pFrom = multiThreadedCheckMutex();\n#else\n      pFrom = sqlite3DefaultMutex();\n#endif\n    }else{\n      pFrom = sqlite3NoopMutex();\n    }\n    pTo->xMutexInit = pFrom->xMutexInit;\n    pTo->xMutexEnd = pFrom->xMutexEnd;\n    pTo->xMutexFree = pFrom->xMutexFree;\n    pTo->xMutexEnter = pFrom->xMutexEnter;\n    pTo->xMutexTry = pFrom->xMutexTry;\n    pTo->xMutexLeave = pFrom->xMutexLeave;\n    pTo->xMutexHeld = pFrom->xMutexHeld;\n    pTo->xMutexNotheld = pFrom->xMutexNotheld;\n    sqlite3MemoryBarrier();\n    pTo->xMutexAlloc = pFrom->xMutexAlloc;\n  }\n  assert( sqlite3GlobalConfig.mutex.xMutexInit );\n  rc = sqlite3GlobalConfig.mutex.xMutexInit();\n\n#ifdef SQLITE_DEBUG\n  GLOBAL(int, mutexIsInit) = 1;\n#endif\n\n  return rc;\n}\n\n/*\n** Shutdown the mutex system. This call frees resources allocated by\n** sqlite3MutexInit().\n*/\nSQLITE_PRIVATE int sqlite3MutexEnd(void){\n  int rc = SQLITE_OK;\n  if( sqlite3GlobalConfig.mutex.xMutexEnd ){\n    rc = sqlite3GlobalConfig.mutex.xMutexEnd();\n  }\n\n#ifdef SQLITE_DEBUG\n  GLOBAL(int, mutexIsInit) = 0;\n#endif\n\n  return rc;\n}\n\n/*\n** Retrieve a pointer to a static mutex or allocate a new dynamic one.\n*/\nSQLITE_API sqlite3_mutex *sqlite3_mutex_alloc(int id){\n#ifndef SQLITE_OMIT_AUTOINIT\n  if( id<=SQLITE_MUTEX_RECURSIVE && sqlite3_initialize() ) return 0;\n  if( id>SQLITE_MUTEX_RECURSIVE && sqlite3MutexInit() ) return 0;\n#endif\n  assert( sqlite3GlobalConfig.mutex.xMutexAlloc );\n  return sqlite3GlobalConfig.mutex.xMutexAlloc(id);\n}\n\nSQLITE_PRIVATE sqlite3_mutex *sqlite3MutexAlloc(int id){\n  if( !sqlite3GlobalConfig.bCoreMutex ){\n    return 0;\n  }\n  assert( GLOBAL(int, mutexIsInit) );\n  assert( sqlite3GlobalConfig.mutex.xMutexAlloc );\n  return sqlite3GlobalConfig.mutex.xMutexAlloc(id);\n}\n\n/*\n** Free a dynamic mutex.\n*/\nSQLITE_API void sqlite3_mutex_free(sqlite3_mutex *p){\n  if( p ){\n    assert( sqlite3GlobalConfig.mutex.xMutexFree );\n    sqlite3GlobalConfig.mutex.xMutexFree(p);\n  }\n}\n\n/*\n** Obtain the mutex p. If some other thread already has the mutex, block\n** until it can be obtained.\n*/\nSQLITE_API void sqlite3_mutex_enter(sqlite3_mutex *p){\n  if( p ){\n    assert( sqlite3GlobalConfig.mutex.xMutexEnter );\n    sqlite3GlobalConfig.mutex.xMutexEnter(p);\n  }\n}\n\n/*\n** Obtain the mutex p. If successful, return SQLITE_OK. Otherwise, if another\n** thread holds the mutex and it cannot be obtained, return SQLITE_BUSY.\n*/\nSQLITE_API int sqlite3_mutex_try(sqlite3_mutex *p){\n  int rc = SQLITE_OK;\n  if( p ){\n    assert( sqlite3GlobalConfig.mutex.xMutexTry );\n    return sqlite3GlobalConfig.mutex.xMutexTry(p);\n  }\n  return rc;\n}\n\n/*\n** The sqlite3_mutex_leave() routine exits a mutex that was previously\n** entered by the same thread.  The behavior is undefined if the mutex \n** is not currently entered. If a NULL pointer is passed as an argument\n** this function is a no-op.\n*/\nSQLITE_API void sqlite3_mutex_leave(sqlite3_mutex *p){\n  if( p ){\n    assert( sqlite3GlobalConfig.mutex.xMutexLeave );\n    sqlite3GlobalConfig.mutex.xMutexLeave(p);\n  }\n}\n\n#ifndef NDEBUG\n/*\n** The sqlite3_mutex_held() and sqlite3_mutex_notheld() routine are\n** intended for use inside assert() statements.\n*/\nSQLITE_API int sqlite3_mutex_held(sqlite3_mutex *p){\n  assert( p==0 || sqlite3GlobalConfig.mutex.xMutexHeld );\n  return p==0 || sqlite3GlobalConfig.mutex.xMutexHeld(p);\n}\nSQLITE_API int sqlite3_mutex_notheld(sqlite3_mutex *p){\n  assert( p==0 || sqlite3GlobalConfig.mutex.xMutexNotheld );\n  return p==0 || sqlite3GlobalConfig.mutex.xMutexNotheld(p);\n}\n#endif\n\n#endif /* !defined(SQLITE_MUTEX_OMIT) */\n\n\n/************** End of mutex.c ***********************************************/\n/************** Begin file mutex_noop.c **************************************/\n/*\n** 2008 October 07\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n*************************************************************************\n** This file contains the C functions that implement mutexes.\n**\n** This implementation in this file does not provide any mutual\n** exclusion and is thus suitable for use only in applications\n** that use SQLite in a single thread.  The routines defined\n** here are place-holders.  Applications can substitute working\n** mutex routines at start-time using the\n**\n**     sqlite3_config(SQLITE_CONFIG_MUTEX,...)\n**\n** interface.\n**\n** If compiled with SQLITE_DEBUG, then additional logic is inserted\n** that does error checking on mutexes to make sure they are being\n** called correctly.\n*/\n/* #include \"sqliteInt.h\" */\n\n#ifndef SQLITE_MUTEX_OMIT\n\n#ifndef SQLITE_DEBUG\n/*\n** Stub routines for all mutex methods.\n**\n** This routines provide no mutual exclusion or error checking.\n*/\nstatic int noopMutexInit(void){ return SQLITE_OK; }\nstatic int noopMutexEnd(void){ return SQLITE_OK; }\nstatic sqlite3_mutex *noopMutexAlloc(int id){ \n  UNUSED_PARAMETER(id);\n  return (sqlite3_mutex*)8; \n}\nstatic void noopMutexFree(sqlite3_mutex *p){ UNUSED_PARAMETER(p); return; }\nstatic void noopMutexEnter(sqlite3_mutex *p){ UNUSED_PARAMETER(p); return; }\nstatic int noopMutexTry(sqlite3_mutex *p){\n  UNUSED_PARAMETER(p);\n  return SQLITE_OK;\n}\nstatic void noopMutexLeave(sqlite3_mutex *p){ UNUSED_PARAMETER(p); return; }\n\nSQLITE_PRIVATE sqlite3_mutex_methods const *sqlite3NoopMutex(void){\n  static const sqlite3_mutex_methods sMutex = {\n    noopMutexInit,\n    noopMutexEnd,\n    noopMutexAlloc,\n    noopMutexFree,\n    noopMutexEnter,\n    noopMutexTry,\n    noopMutexLeave,\n\n    0,\n    0,\n  };\n\n  return &sMutex;\n}\n#endif /* !SQLITE_DEBUG */\n\n#ifdef SQLITE_DEBUG\n/*\n** In this implementation, error checking is provided for testing\n** and debugging purposes.  The mutexes still do not provide any\n** mutual exclusion.\n*/\n\n/*\n** The mutex object\n*/\ntypedef struct sqlite3_debug_mutex {\n  int id;     /* The mutex type */\n  int cnt;    /* Number of entries without a matching leave */\n} sqlite3_debug_mutex;\n\n/*\n** The sqlite3_mutex_held() and sqlite3_mutex_notheld() routine are\n** intended for use inside assert() statements.\n*/\nstatic int debugMutexHeld(sqlite3_mutex *pX){\n  sqlite3_debug_mutex *p = (sqlite3_debug_mutex*)pX;\n  return p==0 || p->cnt>0;\n}\nstatic int debugMutexNotheld(sqlite3_mutex *pX){\n  sqlite3_debug_mutex *p = (sqlite3_debug_mutex*)pX;\n  return p==0 || p->cnt==0;\n}\n\n/*\n** Initialize and deinitialize the mutex subsystem.\n*/\nstatic int debugMutexInit(void){ return SQLITE_OK; }\nstatic int debugMutexEnd(void){ return SQLITE_OK; }\n\n/*\n** The sqlite3_mutex_alloc() routine allocates a new\n** mutex and returns a pointer to it.  If it returns NULL\n** that means that a mutex could not be allocated. \n*/\nstatic sqlite3_mutex *debugMutexAlloc(int id){\n  static sqlite3_debug_mutex aStatic[SQLITE_MUTEX_STATIC_VFS3 - 1];\n  sqlite3_debug_mutex *pNew = 0;\n  switch( id ){\n    case SQLITE_MUTEX_FAST:\n    case SQLITE_MUTEX_RECURSIVE: {\n      pNew = sqlite3Malloc(sizeof(*pNew));\n      if( pNew ){\n        pNew->id = id;\n        pNew->cnt = 0;\n      }\n      break;\n    }\n    default: {\n#ifdef SQLITE_ENABLE_API_ARMOR\n      if( id-2<0 || id-2>=ArraySize(aStatic) ){\n        (void)SQLITE_MISUSE_BKPT;\n        return 0;\n      }\n#endif\n      pNew = &aStatic[id-2];\n      pNew->id = id;\n      break;\n    }\n  }\n  return (sqlite3_mutex*)pNew;\n}\n\n/*\n** This routine deallocates a previously allocated mutex.\n*/\nstatic void debugMutexFree(sqlite3_mutex *pX){\n  sqlite3_debug_mutex *p = (sqlite3_debug_mutex*)pX;\n  assert( p->cnt==0 );\n  if( p->id==SQLITE_MUTEX_RECURSIVE || p->id==SQLITE_MUTEX_FAST ){\n    sqlite3_free(p);\n  }else{\n#ifdef SQLITE_ENABLE_API_ARMOR\n    (void)SQLITE_MISUSE_BKPT;\n#endif\n  }\n}\n\n/*\n** The sqlite3_mutex_enter() and sqlite3_mutex_try() routines attempt\n** to enter a mutex.  If another thread is already within the mutex,\n** sqlite3_mutex_enter() will block and sqlite3_mutex_try() will return\n** SQLITE_BUSY.  The sqlite3_mutex_try() interface returns SQLITE_OK\n** upon successful entry.  Mutexes created using SQLITE_MUTEX_RECURSIVE can\n** be entered multiple times by the same thread.  In such cases the,\n** mutex must be exited an equal number of times before another thread\n** can enter.  If the same thread tries to enter any other kind of mutex\n** more than once, the behavior is undefined.\n*/\nstatic void debugMutexEnter(sqlite3_mutex *pX){\n  sqlite3_debug_mutex *p = (sqlite3_debug_mutex*)pX;\n  assert( p->id==SQLITE_MUTEX_RECURSIVE || debugMutexNotheld(pX) );\n  p->cnt++;\n}\nstatic int debugMutexTry(sqlite3_mutex *pX){\n  sqlite3_debug_mutex *p = (sqlite3_debug_mutex*)pX;\n  assert( p->id==SQLITE_MUTEX_RECURSIVE || debugMutexNotheld(pX) );\n  p->cnt++;\n  return SQLITE_OK;\n}\n\n/*\n** The sqlite3_mutex_leave() routine exits a mutex that was\n** previously entered by the same thread.  The behavior\n** is undefined if the mutex is not currently entered or\n** is not currently allocated.  SQLite will never do either.\n*/\nstatic void debugMutexLeave(sqlite3_mutex *pX){\n  sqlite3_debug_mutex *p = (sqlite3_debug_mutex*)pX;\n  assert( debugMutexHeld(pX) );\n  p->cnt--;\n  assert( p->id==SQLITE_MUTEX_RECURSIVE || debugMutexNotheld(pX) );\n}\n\nSQLITE_PRIVATE sqlite3_mutex_methods const *sqlite3NoopMutex(void){\n  static const sqlite3_mutex_methods sMutex = {\n    debugMutexInit,\n    debugMutexEnd,\n    debugMutexAlloc,\n    debugMutexFree,\n    debugMutexEnter,\n    debugMutexTry,\n    debugMutexLeave,\n\n    debugMutexHeld,\n    debugMutexNotheld\n  };\n\n  return &sMutex;\n}\n#endif /* SQLITE_DEBUG */\n\n/*\n** If compiled with SQLITE_MUTEX_NOOP, then the no-op mutex implementation\n** is used regardless of the run-time threadsafety setting.\n*/\n#ifdef SQLITE_MUTEX_NOOP\nSQLITE_PRIVATE sqlite3_mutex_methods const *sqlite3DefaultMutex(void){\n  return sqlite3NoopMutex();\n}\n#endif /* defined(SQLITE_MUTEX_NOOP) */\n#endif /* !defined(SQLITE_MUTEX_OMIT) */\n\n/************** End of mutex_noop.c ******************************************/\n/************** Begin file mutex_unix.c **************************************/\n/*\n** 2007 August 28\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n*************************************************************************\n** This file contains the C functions that implement mutexes for pthreads\n*/\n/* #include \"sqliteInt.h\" */\n\n/*\n** The code in this file is only used if we are compiling threadsafe\n** under unix with pthreads.\n**\n** Note that this implementation requires a version of pthreads that\n** supports recursive mutexes.\n*/\n#ifdef SQLITE_MUTEX_PTHREADS\n\n#include <pthread.h>\n\n/*\n** The sqlite3_mutex.id, sqlite3_mutex.nRef, and sqlite3_mutex.owner fields\n** are necessary under two condidtions:  (1) Debug builds and (2) using\n** home-grown mutexes.  Encapsulate these conditions into a single #define.\n*/\n#if defined(SQLITE_DEBUG) || defined(SQLITE_HOMEGROWN_RECURSIVE_MUTEX)\n# define SQLITE_MUTEX_NREF 1\n#else\n# define SQLITE_MUTEX_NREF 0\n#endif\n\n/*\n** Each recursive mutex is an instance of the following structure.\n*/\nstruct sqlite3_mutex {\n  pthread_mutex_t mutex;     /* Mutex controlling the lock */\n#if SQLITE_MUTEX_NREF || defined(SQLITE_ENABLE_API_ARMOR)\n  int id;                    /* Mutex type */\n#endif\n#if SQLITE_MUTEX_NREF\n  volatile int nRef;         /* Number of entrances */\n  volatile pthread_t owner;  /* Thread that is within this mutex */\n  int trace;                 /* True to trace changes */\n#endif\n};\n#if SQLITE_MUTEX_NREF\n# define SQLITE3_MUTEX_INITIALIZER(id) \\\n     {PTHREAD_MUTEX_INITIALIZER,id,0,(pthread_t)0,0}\n#elif defined(SQLITE_ENABLE_API_ARMOR)\n# define SQLITE3_MUTEX_INITIALIZER(id) { PTHREAD_MUTEX_INITIALIZER, id }\n#else\n#define SQLITE3_MUTEX_INITIALIZER(id) { PTHREAD_MUTEX_INITIALIZER }\n#endif\n\n/*\n** The sqlite3_mutex_held() and sqlite3_mutex_notheld() routine are\n** intended for use only inside assert() statements.  On some platforms,\n** there might be race conditions that can cause these routines to\n** deliver incorrect results.  In particular, if pthread_equal() is\n** not an atomic operation, then these routines might delivery\n** incorrect results.  On most platforms, pthread_equal() is a \n** comparison of two integers and is therefore atomic.  But we are\n** told that HPUX is not such a platform.  If so, then these routines\n** will not always work correctly on HPUX.\n**\n** On those platforms where pthread_equal() is not atomic, SQLite\n** should be compiled without -DSQLITE_DEBUG and with -DNDEBUG to\n** make sure no assert() statements are evaluated and hence these\n** routines are never called.\n*/\n#if !defined(NDEBUG) || defined(SQLITE_DEBUG)\nstatic int pthreadMutexHeld(sqlite3_mutex *p){\n  return (p->nRef!=0 && pthread_equal(p->owner, pthread_self()));\n}\nstatic int pthreadMutexNotheld(sqlite3_mutex *p){\n  return p->nRef==0 || pthread_equal(p->owner, pthread_self())==0;\n}\n#endif\n\n/*\n** Try to provide a memory barrier operation, needed for initialization\n** and also for the implementation of xShmBarrier in the VFS in cases\n** where SQLite is compiled without mutexes.\n*/\nSQLITE_PRIVATE void sqlite3MemoryBarrier(void){\n#if defined(SQLITE_MEMORY_BARRIER)\n  SQLITE_MEMORY_BARRIER;\n#elif defined(__GNUC__) && GCC_VERSION>=4001000\n  __sync_synchronize();\n#endif\n}\n\n/*\n** Initialize and deinitialize the mutex subsystem.\n*/\nstatic int pthreadMutexInit(void){ return SQLITE_OK; }\nstatic int pthreadMutexEnd(void){ return SQLITE_OK; }\n\n/*\n** The sqlite3_mutex_alloc() routine allocates a new\n** mutex and returns a pointer to it.  If it returns NULL\n** that means that a mutex could not be allocated.  SQLite\n** will unwind its stack and return an error.  The argument\n** to sqlite3_mutex_alloc() is one of these integer constants:\n**\n** <ul>\n** <li>  SQLITE_MUTEX_FAST\n** <li>  SQLITE_MUTEX_RECURSIVE\n** <li>  SQLITE_MUTEX_STATIC_MASTER\n** <li>  SQLITE_MUTEX_STATIC_MEM\n** <li>  SQLITE_MUTEX_STATIC_OPEN\n** <li>  SQLITE_MUTEX_STATIC_PRNG\n** <li>  SQLITE_MUTEX_STATIC_LRU\n** <li>  SQLITE_MUTEX_STATIC_PMEM\n** <li>  SQLITE_MUTEX_STATIC_APP1\n** <li>  SQLITE_MUTEX_STATIC_APP2\n** <li>  SQLITE_MUTEX_STATIC_APP3\n** <li>  SQLITE_MUTEX_STATIC_VFS1\n** <li>  SQLITE_MUTEX_STATIC_VFS2\n** <li>  SQLITE_MUTEX_STATIC_VFS3\n** </ul>\n**\n** The first two constants cause sqlite3_mutex_alloc() to create\n** a new mutex.  The new mutex is recursive when SQLITE_MUTEX_RECURSIVE\n** is used but not necessarily so when SQLITE_MUTEX_FAST is used.\n** The mutex implementation does not need to make a distinction\n** between SQLITE_MUTEX_RECURSIVE and SQLITE_MUTEX_FAST if it does\n** not want to.  But SQLite will only request a recursive mutex in\n** cases where it really needs one.  If a faster non-recursive mutex\n** implementation is available on the host platform, the mutex subsystem\n** might return such a mutex in response to SQLITE_MUTEX_FAST.\n**\n** The other allowed parameters to sqlite3_mutex_alloc() each return\n** a pointer to a static preexisting mutex.  Six static mutexes are\n** used by the current version of SQLite.  Future versions of SQLite\n** may add additional static mutexes.  Static mutexes are for internal\n** use by SQLite only.  Applications that use SQLite mutexes should\n** use only the dynamic mutexes returned by SQLITE_MUTEX_FAST or\n** SQLITE_MUTEX_RECURSIVE.\n**\n** Note that if one of the dynamic mutex parameters (SQLITE_MUTEX_FAST\n** or SQLITE_MUTEX_RECURSIVE) is used then sqlite3_mutex_alloc()\n** returns a different mutex on every call.  But for the static \n** mutex types, the same mutex is returned on every call that has\n** the same type number.\n*/\nstatic sqlite3_mutex *pthreadMutexAlloc(int iType){\n  static sqlite3_mutex staticMutexes[] = {\n    SQLITE3_MUTEX_INITIALIZER(2),\n    SQLITE3_MUTEX_INITIALIZER(3),\n    SQLITE3_MUTEX_INITIALIZER(4),\n    SQLITE3_MUTEX_INITIALIZER(5),\n    SQLITE3_MUTEX_INITIALIZER(6),\n    SQLITE3_MUTEX_INITIALIZER(7),\n    SQLITE3_MUTEX_INITIALIZER(8),\n    SQLITE3_MUTEX_INITIALIZER(9),\n    SQLITE3_MUTEX_INITIALIZER(10),\n    SQLITE3_MUTEX_INITIALIZER(11),\n    SQLITE3_MUTEX_INITIALIZER(12),\n    SQLITE3_MUTEX_INITIALIZER(13)\n  };\n  sqlite3_mutex *p;\n  switch( iType ){\n    case SQLITE_MUTEX_RECURSIVE: {\n      p = sqlite3MallocZero( sizeof(*p) );\n      if( p ){\n#ifdef SQLITE_HOMEGROWN_RECURSIVE_MUTEX\n        /* If recursive mutexes are not available, we will have to\n        ** build our own.  See below. */\n        pthread_mutex_init(&p->mutex, 0);\n#else\n        /* Use a recursive mutex if it is available */\n        pthread_mutexattr_t recursiveAttr;\n        pthread_mutexattr_init(&recursiveAttr);\n        pthread_mutexattr_settype(&recursiveAttr, PTHREAD_MUTEX_RECURSIVE);\n        pthread_mutex_init(&p->mutex, &recursiveAttr);\n        pthread_mutexattr_destroy(&recursiveAttr);\n#endif\n#if SQLITE_MUTEX_NREF || defined(SQLITE_ENABLE_API_ARMOR)\n        p->id = SQLITE_MUTEX_RECURSIVE;\n#endif\n      }\n      break;\n    }\n    case SQLITE_MUTEX_FAST: {\n      p = sqlite3MallocZero( sizeof(*p) );\n      if( p ){\n        pthread_mutex_init(&p->mutex, 0);\n#if SQLITE_MUTEX_NREF || defined(SQLITE_ENABLE_API_ARMOR)\n        p->id = SQLITE_MUTEX_FAST;\n#endif\n      }\n      break;\n    }\n    default: {\n#ifdef SQLITE_ENABLE_API_ARMOR\n      if( iType-2<0 || iType-2>=ArraySize(staticMutexes) ){\n        (void)SQLITE_MISUSE_BKPT;\n        return 0;\n      }\n#endif\n      p = &staticMutexes[iType-2];\n      break;\n    }\n  }\n#if SQLITE_MUTEX_NREF || defined(SQLITE_ENABLE_API_ARMOR)\n  assert( p==0 || p->id==iType );\n#endif\n  return p;\n}\n\n\n/*\n** This routine deallocates a previously\n** allocated mutex.  SQLite is careful to deallocate every\n** mutex that it allocates.\n*/\nstatic void pthreadMutexFree(sqlite3_mutex *p){\n  assert( p->nRef==0 );\n#if SQLITE_ENABLE_API_ARMOR\n  if( p->id==SQLITE_MUTEX_FAST || p->id==SQLITE_MUTEX_RECURSIVE )\n#endif\n  {\n    pthread_mutex_destroy(&p->mutex);\n    sqlite3_free(p);\n  }\n#ifdef SQLITE_ENABLE_API_ARMOR\n  else{\n    (void)SQLITE_MISUSE_BKPT;\n  }\n#endif\n}\n\n/*\n** The sqlite3_mutex_enter() and sqlite3_mutex_try() routines attempt\n** to enter a mutex.  If another thread is already within the mutex,\n** sqlite3_mutex_enter() will block and sqlite3_mutex_try() will return\n** SQLITE_BUSY.  The sqlite3_mutex_try() interface returns SQLITE_OK\n** upon successful entry.  Mutexes created using SQLITE_MUTEX_RECURSIVE can\n** be entered multiple times by the same thread.  In such cases the,\n** mutex must be exited an equal number of times before another thread\n** can enter.  If the same thread tries to enter any other kind of mutex\n** more than once, the behavior is undefined.\n*/\nstatic void pthreadMutexEnter(sqlite3_mutex *p){\n  assert( p->id==SQLITE_MUTEX_RECURSIVE || pthreadMutexNotheld(p) );\n\n#ifdef SQLITE_HOMEGROWN_RECURSIVE_MUTEX\n  /* If recursive mutexes are not available, then we have to grow\n  ** our own.  This implementation assumes that pthread_equal()\n  ** is atomic - that it cannot be deceived into thinking self\n  ** and p->owner are equal if p->owner changes between two values\n  ** that are not equal to self while the comparison is taking place.\n  ** This implementation also assumes a coherent cache - that \n  ** separate processes cannot read different values from the same\n  ** address at the same time.  If either of these two conditions\n  ** are not met, then the mutexes will fail and problems will result.\n  */\n  {\n    pthread_t self = pthread_self();\n    if( p->nRef>0 && pthread_equal(p->owner, self) ){\n      p->nRef++;\n    }else{\n      pthread_mutex_lock(&p->mutex);\n      assert( p->nRef==0 );\n      p->owner = self;\n      p->nRef = 1;\n    }\n  }\n#else\n  /* Use the built-in recursive mutexes if they are available.\n  */\n  pthread_mutex_lock(&p->mutex);\n#if SQLITE_MUTEX_NREF\n  assert( p->nRef>0 || p->owner==0 );\n  p->owner = pthread_self();\n  p->nRef++;\n#endif\n#endif\n\n#ifdef SQLITE_DEBUG\n  if( p->trace ){\n    printf(\"enter mutex %p (%d) with nRef=%d\\n\", p, p->trace, p->nRef);\n  }\n#endif\n}\nstatic int pthreadMutexTry(sqlite3_mutex *p){\n  int rc;\n  assert( p->id==SQLITE_MUTEX_RECURSIVE || pthreadMutexNotheld(p) );\n\n#ifdef SQLITE_HOMEGROWN_RECURSIVE_MUTEX\n  /* If recursive mutexes are not available, then we have to grow\n  ** our own.  This implementation assumes that pthread_equal()\n  ** is atomic - that it cannot be deceived into thinking self\n  ** and p->owner are equal if p->owner changes between two values\n  ** that are not equal to self while the comparison is taking place.\n  ** This implementation also assumes a coherent cache - that \n  ** separate processes cannot read different values from the same\n  ** address at the same time.  If either of these two conditions\n  ** are not met, then the mutexes will fail and problems will result.\n  */\n  {\n    pthread_t self = pthread_self();\n    if( p->nRef>0 && pthread_equal(p->owner, self) ){\n      p->nRef++;\n      rc = SQLITE_OK;\n    }else if( pthread_mutex_trylock(&p->mutex)==0 ){\n      assert( p->nRef==0 );\n      p->owner = self;\n      p->nRef = 1;\n      rc = SQLITE_OK;\n    }else{\n      rc = SQLITE_BUSY;\n    }\n  }\n#else\n  /* Use the built-in recursive mutexes if they are available.\n  */\n  if( pthread_mutex_trylock(&p->mutex)==0 ){\n#if SQLITE_MUTEX_NREF\n    p->owner = pthread_self();\n    p->nRef++;\n#endif\n    rc = SQLITE_OK;\n  }else{\n    rc = SQLITE_BUSY;\n  }\n#endif\n\n#ifdef SQLITE_DEBUG\n  if( rc==SQLITE_OK && p->trace ){\n    printf(\"enter mutex %p (%d) with nRef=%d\\n\", p, p->trace, p->nRef);\n  }\n#endif\n  return rc;\n}\n\n/*\n** The sqlite3_mutex_leave() routine exits a mutex that was\n** previously entered by the same thread.  The behavior\n** is undefined if the mutex is not currently entered or\n** is not currently allocated.  SQLite will never do either.\n*/\nstatic void pthreadMutexLeave(sqlite3_mutex *p){\n  assert( pthreadMutexHeld(p) );\n#if SQLITE_MUTEX_NREF\n  p->nRef--;\n  if( p->nRef==0 ) p->owner = 0;\n#endif\n  assert( p->nRef==0 || p->id==SQLITE_MUTEX_RECURSIVE );\n\n#ifdef SQLITE_HOMEGROWN_RECURSIVE_MUTEX\n  if( p->nRef==0 ){\n    pthread_mutex_unlock(&p->mutex);\n  }\n#else\n  pthread_mutex_unlock(&p->mutex);\n#endif\n\n#ifdef SQLITE_DEBUG\n  if( p->trace ){\n    printf(\"leave mutex %p (%d) with nRef=%d\\n\", p, p->trace, p->nRef);\n  }\n#endif\n}\n\nSQLITE_PRIVATE sqlite3_mutex_methods const *sqlite3DefaultMutex(void){\n  static const sqlite3_mutex_methods sMutex = {\n    pthreadMutexInit,\n    pthreadMutexEnd,\n    pthreadMutexAlloc,\n    pthreadMutexFree,\n    pthreadMutexEnter,\n    pthreadMutexTry,\n    pthreadMutexLeave,\n#ifdef SQLITE_DEBUG\n    pthreadMutexHeld,\n    pthreadMutexNotheld\n#else\n    0,\n    0\n#endif\n  };\n\n  return &sMutex;\n}\n\n#endif /* SQLITE_MUTEX_PTHREADS */\n\n/************** End of mutex_unix.c ******************************************/\n/************** Begin file mutex_w32.c ***************************************/\n/*\n** 2007 August 14\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n*************************************************************************\n** This file contains the C functions that implement mutexes for Win32.\n*/\n/* #include \"sqliteInt.h\" */\n\n#if SQLITE_OS_WIN\n/*\n** Include code that is common to all os_*.c files\n*/\n/************** Include os_common.h in the middle of mutex_w32.c *************/\n/************** Begin file os_common.h ***************************************/\n/*\n** 2004 May 22\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n******************************************************************************\n**\n** This file contains macros and a little bit of code that is common to\n** all of the platform-specific files (os_*.c) and is #included into those\n** files.\n**\n** This file should be #included by the os_*.c files only.  It is not a\n** general purpose header file.\n*/\n#ifndef _OS_COMMON_H_\n#define _OS_COMMON_H_\n\n/*\n** At least two bugs have slipped in because we changed the MEMORY_DEBUG\n** macro to SQLITE_DEBUG and some older makefiles have not yet made the\n** switch.  The following code should catch this problem at compile-time.\n*/\n#ifdef MEMORY_DEBUG\n# error \"The MEMORY_DEBUG macro is obsolete.  Use SQLITE_DEBUG instead.\"\n#endif\n\n/*\n** Macros for performance tracing.  Normally turned off.  Only works\n** on i486 hardware.\n*/\n#ifdef SQLITE_PERFORMANCE_TRACE\n\n/*\n** hwtime.h contains inline assembler code for implementing\n** high-performance timing routines.\n*/\n/************** Include hwtime.h in the middle of os_common.h ****************/\n/************** Begin file hwtime.h ******************************************/\n/*\n** 2008 May 27\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n******************************************************************************\n**\n** This file contains inline asm code for retrieving \"high-performance\"\n** counters for x86 class CPUs.\n*/\n#ifndef SQLITE_HWTIME_H\n#define SQLITE_HWTIME_H\n\n/*\n** The following routine only works on pentium-class (or newer) processors.\n** It uses the RDTSC opcode to read the cycle count value out of the\n** processor and returns that value.  This can be used for high-res\n** profiling.\n*/\n#if (defined(__GNUC__) || defined(_MSC_VER)) && \\\n      (defined(i386) || defined(__i386__) || defined(_M_IX86))\n\n  #if defined(__GNUC__)\n\n  __inline__ sqlite_uint64 sqlite3Hwtime(void){\n     unsigned int lo, hi;\n     __asm__ __volatile__ (\"rdtsc\" : \"=a\" (lo), \"=d\" (hi));\n     return (sqlite_uint64)hi << 32 | lo;\n  }\n\n  #elif defined(_MSC_VER)\n\n  __declspec(naked) __inline sqlite_uint64 __cdecl sqlite3Hwtime(void){\n     __asm {\n        rdtsc\n        ret       ; return value at EDX:EAX\n     }\n  }\n\n  #endif\n\n#elif (defined(__GNUC__) && defined(__x86_64__))\n\n  __inline__ sqlite_uint64 sqlite3Hwtime(void){\n      unsigned long val;\n      __asm__ __volatile__ (\"rdtsc\" : \"=A\" (val));\n      return val;\n  }\n \n#elif (defined(__GNUC__) && defined(__ppc__))\n\n  __inline__ sqlite_uint64 sqlite3Hwtime(void){\n      unsigned long long retval;\n      unsigned long junk;\n      __asm__ __volatile__ (\"\\n\\\n          1:      mftbu   %1\\n\\\n                  mftb    %L0\\n\\\n                  mftbu   %0\\n\\\n                  cmpw    %0,%1\\n\\\n                  bne     1b\"\n                  : \"=r\" (retval), \"=r\" (junk));\n      return retval;\n  }\n\n#else\n\n  #error Need implementation of sqlite3Hwtime() for your platform.\n\n  /*\n  ** To compile without implementing sqlite3Hwtime() for your platform,\n  ** you can remove the above #error and use the following\n  ** stub function.  You will lose timing support for many\n  ** of the debugging and testing utilities, but it should at\n  ** least compile and run.\n  */\nSQLITE_PRIVATE   sqlite_uint64 sqlite3Hwtime(void){ return ((sqlite_uint64)0); }\n\n#endif\n\n#endif /* !defined(SQLITE_HWTIME_H) */\n\n/************** End of hwtime.h **********************************************/\n/************** Continuing where we left off in os_common.h ******************/\n\nstatic sqlite_uint64 g_start;\nstatic sqlite_uint64 g_elapsed;\n#define TIMER_START       g_start=sqlite3Hwtime()\n#define TIMER_END         g_elapsed=sqlite3Hwtime()-g_start\n#define TIMER_ELAPSED     g_elapsed\n#else\n#define TIMER_START\n#define TIMER_END\n#define TIMER_ELAPSED     ((sqlite_uint64)0)\n#endif\n\n/*\n** If we compile with the SQLITE_TEST macro set, then the following block\n** of code will give us the ability to simulate a disk I/O error.  This\n** is used for testing the I/O recovery logic.\n*/\n#if defined(SQLITE_TEST)\nSQLITE_API extern int sqlite3_io_error_hit;\nSQLITE_API extern int sqlite3_io_error_hardhit;\nSQLITE_API extern int sqlite3_io_error_pending;\nSQLITE_API extern int sqlite3_io_error_persist;\nSQLITE_API extern int sqlite3_io_error_benign;\nSQLITE_API extern int sqlite3_diskfull_pending;\nSQLITE_API extern int sqlite3_diskfull;\n#define SimulateIOErrorBenign(X) sqlite3_io_error_benign=(X)\n#define SimulateIOError(CODE)  \\\n  if( (sqlite3_io_error_persist && sqlite3_io_error_hit) \\\n       || sqlite3_io_error_pending-- == 1 )  \\\n              { local_ioerr(); CODE; }\nstatic void local_ioerr(){\n  IOTRACE((\"IOERR\\n\"));\n  sqlite3_io_error_hit++;\n  if( !sqlite3_io_error_benign ) sqlite3_io_error_hardhit++;\n}\n#define SimulateDiskfullError(CODE) \\\n   if( sqlite3_diskfull_pending ){ \\\n     if( sqlite3_diskfull_pending == 1 ){ \\\n       local_ioerr(); \\\n       sqlite3_diskfull = 1; \\\n       sqlite3_io_error_hit = 1; \\\n       CODE; \\\n     }else{ \\\n       sqlite3_diskfull_pending--; \\\n     } \\\n   }\n#else\n#define SimulateIOErrorBenign(X)\n#define SimulateIOError(A)\n#define SimulateDiskfullError(A)\n#endif /* defined(SQLITE_TEST) */\n\n/*\n** When testing, keep a count of the number of open files.\n*/\n#if defined(SQLITE_TEST)\nSQLITE_API extern int sqlite3_open_file_count;\n#define OpenCounter(X)  sqlite3_open_file_count+=(X)\n#else\n#define OpenCounter(X)\n#endif /* defined(SQLITE_TEST) */\n\n#endif /* !defined(_OS_COMMON_H_) */\n\n/************** End of os_common.h *******************************************/\n/************** Continuing where we left off in mutex_w32.c ******************/\n\n/*\n** Include the header file for the Windows VFS.\n*/\n/************** Include os_win.h in the middle of mutex_w32.c ****************/\n/************** Begin file os_win.h ******************************************/\n/*\n** 2013 November 25\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n******************************************************************************\n**\n** This file contains code that is specific to Windows.\n*/\n#ifndef SQLITE_OS_WIN_H\n#define SQLITE_OS_WIN_H\n\n/*\n** Include the primary Windows SDK header file.\n*/\n#include \"windows.h\"\n\n#ifdef __CYGWIN__\n# include <sys/cygwin.h>\n# include <errno.h> /* amalgamator: dontcache */\n#endif\n\n/*\n** Determine if we are dealing with Windows NT.\n**\n** We ought to be able to determine if we are compiling for Windows 9x or\n** Windows NT using the _WIN32_WINNT macro as follows:\n**\n** #if defined(_WIN32_WINNT)\n** # define SQLITE_OS_WINNT 1\n** #else\n** # define SQLITE_OS_WINNT 0\n** #endif\n**\n** However, Visual Studio 2005 does not set _WIN32_WINNT by default, as\n** it ought to, so the above test does not work.  We'll just assume that\n** everything is Windows NT unless the programmer explicitly says otherwise\n** by setting SQLITE_OS_WINNT to 0.\n*/\n#if SQLITE_OS_WIN && !defined(SQLITE_OS_WINNT)\n# define SQLITE_OS_WINNT 1\n#endif\n\n/*\n** Determine if we are dealing with Windows CE - which has a much reduced\n** API.\n*/\n#if defined(_WIN32_WCE)\n# define SQLITE_OS_WINCE 1\n#else\n# define SQLITE_OS_WINCE 0\n#endif\n\n/*\n** Determine if we are dealing with WinRT, which provides only a subset of\n** the full Win32 API.\n*/\n#if !defined(SQLITE_OS_WINRT)\n# define SQLITE_OS_WINRT 0\n#endif\n\n/*\n** For WinCE, some API function parameters do not appear to be declared as\n** volatile.\n*/\n#if SQLITE_OS_WINCE\n# define SQLITE_WIN32_VOLATILE\n#else\n# define SQLITE_WIN32_VOLATILE volatile\n#endif\n\n/*\n** For some Windows sub-platforms, the _beginthreadex() / _endthreadex()\n** functions are not available (e.g. those not using MSVC, Cygwin, etc).\n*/\n#if SQLITE_OS_WIN && !SQLITE_OS_WINCE && !SQLITE_OS_WINRT && \\\n    SQLITE_THREADSAFE>0 && !defined(__CYGWIN__)\n# define SQLITE_OS_WIN_THREADS 1\n#else\n# define SQLITE_OS_WIN_THREADS 0\n#endif\n\n#endif /* SQLITE_OS_WIN_H */\n\n/************** End of os_win.h **********************************************/\n/************** Continuing where we left off in mutex_w32.c ******************/\n#endif\n\n/*\n** The code in this file is only used if we are compiling multithreaded\n** on a Win32 system.\n*/\n#ifdef SQLITE_MUTEX_W32\n\n/*\n** Each recursive mutex is an instance of the following structure.\n*/\nstruct sqlite3_mutex {\n  CRITICAL_SECTION mutex;    /* Mutex controlling the lock */\n  int id;                    /* Mutex type */\n#ifdef SQLITE_DEBUG\n  volatile int nRef;         /* Number of enterances */\n  volatile DWORD owner;      /* Thread holding this mutex */\n  volatile LONG trace;       /* True to trace changes */\n#endif\n};\n\n/*\n** These are the initializer values used when declaring a \"static\" mutex\n** on Win32.  It should be noted that all mutexes require initialization\n** on the Win32 platform.\n*/\n#define SQLITE_W32_MUTEX_INITIALIZER { 0 }\n\n#ifdef SQLITE_DEBUG\n#define SQLITE3_MUTEX_INITIALIZER(id) { SQLITE_W32_MUTEX_INITIALIZER, id, \\\n                                    0L, (DWORD)0, 0 }\n#else\n#define SQLITE3_MUTEX_INITIALIZER(id) { SQLITE_W32_MUTEX_INITIALIZER, id }\n#endif\n\n#ifdef SQLITE_DEBUG\n/*\n** The sqlite3_mutex_held() and sqlite3_mutex_notheld() routine are\n** intended for use only inside assert() statements.\n*/\nstatic int winMutexHeld(sqlite3_mutex *p){\n  return p->nRef!=0 && p->owner==GetCurrentThreadId();\n}\n\nstatic int winMutexNotheld2(sqlite3_mutex *p, DWORD tid){\n  return p->nRef==0 || p->owner!=tid;\n}\n\nstatic int winMutexNotheld(sqlite3_mutex *p){\n  DWORD tid = GetCurrentThreadId();\n  return winMutexNotheld2(p, tid);\n}\n#endif\n\n/*\n** Try to provide a memory barrier operation, needed for initialization\n** and also for the xShmBarrier method of the VFS in cases when SQLite is\n** compiled without mutexes (SQLITE_THREADSAFE=0).\n*/\nSQLITE_PRIVATE void sqlite3MemoryBarrier(void){\n#if defined(SQLITE_MEMORY_BARRIER)\n  SQLITE_MEMORY_BARRIER;\n#elif defined(__GNUC__)\n  __sync_synchronize();\n#elif MSVC_VERSION>=1300\n  _ReadWriteBarrier();\n#elif defined(MemoryBarrier)\n  MemoryBarrier();\n#endif\n}\n\n/*\n** Initialize and deinitialize the mutex subsystem.\n*/\nstatic sqlite3_mutex winMutex_staticMutexes[] = {\n  SQLITE3_MUTEX_INITIALIZER(2),\n  SQLITE3_MUTEX_INITIALIZER(3),\n  SQLITE3_MUTEX_INITIALIZER(4),\n  SQLITE3_MUTEX_INITIALIZER(5),\n  SQLITE3_MUTEX_INITIALIZER(6),\n  SQLITE3_MUTEX_INITIALIZER(7),\n  SQLITE3_MUTEX_INITIALIZER(8),\n  SQLITE3_MUTEX_INITIALIZER(9),\n  SQLITE3_MUTEX_INITIALIZER(10),\n  SQLITE3_MUTEX_INITIALIZER(11),\n  SQLITE3_MUTEX_INITIALIZER(12),\n  SQLITE3_MUTEX_INITIALIZER(13)\n};\n\nstatic int winMutex_isInit = 0;\nstatic int winMutex_isNt = -1; /* <0 means \"need to query\" */\n\n/* As the winMutexInit() and winMutexEnd() functions are called as part\n** of the sqlite3_initialize() and sqlite3_shutdown() processing, the\n** \"interlocked\" magic used here is probably not strictly necessary.\n*/\nstatic LONG SQLITE_WIN32_VOLATILE winMutex_lock = 0;\n\nSQLITE_API int sqlite3_win32_is_nt(void); /* os_win.c */\nSQLITE_API void sqlite3_win32_sleep(DWORD milliseconds); /* os_win.c */\n\nstatic int winMutexInit(void){\n  /* The first to increment to 1 does actual initialization */\n  if( InterlockedCompareExchange(&winMutex_lock, 1, 0)==0 ){\n    int i;\n    for(i=0; i<ArraySize(winMutex_staticMutexes); i++){\n#if SQLITE_OS_WINRT\n      InitializeCriticalSectionEx(&winMutex_staticMutexes[i].mutex, 0, 0);\n#else\n      InitializeCriticalSection(&winMutex_staticMutexes[i].mutex);\n#endif\n    }\n    winMutex_isInit = 1;\n  }else{\n    /* Another thread is (in the process of) initializing the static\n    ** mutexes */\n    while( !winMutex_isInit ){\n      sqlite3_win32_sleep(1);\n    }\n  }\n  return SQLITE_OK;\n}\n\nstatic int winMutexEnd(void){\n  /* The first to decrement to 0 does actual shutdown\n  ** (which should be the last to shutdown.) */\n  if( InterlockedCompareExchange(&winMutex_lock, 0, 1)==1 ){\n    if( winMutex_isInit==1 ){\n      int i;\n      for(i=0; i<ArraySize(winMutex_staticMutexes); i++){\n        DeleteCriticalSection(&winMutex_staticMutexes[i].mutex);\n      }\n      winMutex_isInit = 0;\n    }\n  }\n  return SQLITE_OK;\n}\n\n/*\n** The sqlite3_mutex_alloc() routine allocates a new\n** mutex and returns a pointer to it.  If it returns NULL\n** that means that a mutex could not be allocated.  SQLite\n** will unwind its stack and return an error.  The argument\n** to sqlite3_mutex_alloc() is one of these integer constants:\n**\n** <ul>\n** <li>  SQLITE_MUTEX_FAST\n** <li>  SQLITE_MUTEX_RECURSIVE\n** <li>  SQLITE_MUTEX_STATIC_MASTER\n** <li>  SQLITE_MUTEX_STATIC_MEM\n** <li>  SQLITE_MUTEX_STATIC_OPEN\n** <li>  SQLITE_MUTEX_STATIC_PRNG\n** <li>  SQLITE_MUTEX_STATIC_LRU\n** <li>  SQLITE_MUTEX_STATIC_PMEM\n** <li>  SQLITE_MUTEX_STATIC_APP1\n** <li>  SQLITE_MUTEX_STATIC_APP2\n** <li>  SQLITE_MUTEX_STATIC_APP3\n** <li>  SQLITE_MUTEX_STATIC_VFS1\n** <li>  SQLITE_MUTEX_STATIC_VFS2\n** <li>  SQLITE_MUTEX_STATIC_VFS3\n** </ul>\n**\n** The first two constants cause sqlite3_mutex_alloc() to create\n** a new mutex.  The new mutex is recursive when SQLITE_MUTEX_RECURSIVE\n** is used but not necessarily so when SQLITE_MUTEX_FAST is used.\n** The mutex implementation does not need to make a distinction\n** between SQLITE_MUTEX_RECURSIVE and SQLITE_MUTEX_FAST if it does\n** not want to.  But SQLite will only request a recursive mutex in\n** cases where it really needs one.  If a faster non-recursive mutex\n** implementation is available on the host platform, the mutex subsystem\n** might return such a mutex in response to SQLITE_MUTEX_FAST.\n**\n** The other allowed parameters to sqlite3_mutex_alloc() each return\n** a pointer to a static preexisting mutex.  Six static mutexes are\n** used by the current version of SQLite.  Future versions of SQLite\n** may add additional static mutexes.  Static mutexes are for internal\n** use by SQLite only.  Applications that use SQLite mutexes should\n** use only the dynamic mutexes returned by SQLITE_MUTEX_FAST or\n** SQLITE_MUTEX_RECURSIVE.\n**\n** Note that if one of the dynamic mutex parameters (SQLITE_MUTEX_FAST\n** or SQLITE_MUTEX_RECURSIVE) is used then sqlite3_mutex_alloc()\n** returns a different mutex on every call.  But for the static\n** mutex types, the same mutex is returned on every call that has\n** the same type number.\n*/\nstatic sqlite3_mutex *winMutexAlloc(int iType){\n  sqlite3_mutex *p;\n\n  switch( iType ){\n    case SQLITE_MUTEX_FAST:\n    case SQLITE_MUTEX_RECURSIVE: {\n      p = sqlite3MallocZero( sizeof(*p) );\n      if( p ){\n        p->id = iType;\n#ifdef SQLITE_DEBUG\n#ifdef SQLITE_WIN32_MUTEX_TRACE_DYNAMIC\n        p->trace = 1;\n#endif\n#endif\n#if SQLITE_OS_WINRT\n        InitializeCriticalSectionEx(&p->mutex, 0, 0);\n#else\n        InitializeCriticalSection(&p->mutex);\n#endif\n      }\n      break;\n    }\n    default: {\n#ifdef SQLITE_ENABLE_API_ARMOR\n      if( iType-2<0 || iType-2>=ArraySize(winMutex_staticMutexes) ){\n        (void)SQLITE_MISUSE_BKPT;\n        return 0;\n      }\n#endif\n      p = &winMutex_staticMutexes[iType-2];\n#ifdef SQLITE_DEBUG\n#ifdef SQLITE_WIN32_MUTEX_TRACE_STATIC\n      InterlockedCompareExchange(&p->trace, 1, 0);\n#endif\n#endif\n      break;\n    }\n  }\n  assert( p==0 || p->id==iType );\n  return p;\n}\n\n\n/*\n** This routine deallocates a previously\n** allocated mutex.  SQLite is careful to deallocate every\n** mutex that it allocates.\n*/\nstatic void winMutexFree(sqlite3_mutex *p){\n  assert( p );\n  assert( p->nRef==0 && p->owner==0 );\n  if( p->id==SQLITE_MUTEX_FAST || p->id==SQLITE_MUTEX_RECURSIVE ){\n    DeleteCriticalSection(&p->mutex);\n    sqlite3_free(p);\n  }else{\n#ifdef SQLITE_ENABLE_API_ARMOR\n    (void)SQLITE_MISUSE_BKPT;\n#endif\n  }\n}\n\n/*\n** The sqlite3_mutex_enter() and sqlite3_mutex_try() routines attempt\n** to enter a mutex.  If another thread is already within the mutex,\n** sqlite3_mutex_enter() will block and sqlite3_mutex_try() will return\n** SQLITE_BUSY.  The sqlite3_mutex_try() interface returns SQLITE_OK\n** upon successful entry.  Mutexes created using SQLITE_MUTEX_RECURSIVE can\n** be entered multiple times by the same thread.  In such cases the,\n** mutex must be exited an equal number of times before another thread\n** can enter.  If the same thread tries to enter any other kind of mutex\n** more than once, the behavior is undefined.\n*/\nstatic void winMutexEnter(sqlite3_mutex *p){\n#if defined(SQLITE_DEBUG) || defined(SQLITE_TEST)\n  DWORD tid = GetCurrentThreadId();\n#endif\n#ifdef SQLITE_DEBUG\n  assert( p );\n  assert( p->id==SQLITE_MUTEX_RECURSIVE || winMutexNotheld2(p, tid) );\n#else\n  assert( p );\n#endif\n  assert( winMutex_isInit==1 );\n  EnterCriticalSection(&p->mutex);\n#ifdef SQLITE_DEBUG\n  assert( p->nRef>0 || p->owner==0 );\n  p->owner = tid;\n  p->nRef++;\n  if( p->trace ){\n    OSTRACE((\"ENTER-MUTEX tid=%lu, mutex(%d)=%p (%d), nRef=%d\\n\",\n             tid, p->id, p, p->trace, p->nRef));\n  }\n#endif\n}\n\nstatic int winMutexTry(sqlite3_mutex *p){\n#if defined(SQLITE_DEBUG) || defined(SQLITE_TEST)\n  DWORD tid = GetCurrentThreadId();\n#endif\n  int rc = SQLITE_BUSY;\n  assert( p );\n  assert( p->id==SQLITE_MUTEX_RECURSIVE || winMutexNotheld2(p, tid) );\n  /*\n  ** The sqlite3_mutex_try() routine is very rarely used, and when it\n  ** is used it is merely an optimization.  So it is OK for it to always\n  ** fail.\n  **\n  ** The TryEnterCriticalSection() interface is only available on WinNT.\n  ** And some windows compilers complain if you try to use it without\n  ** first doing some #defines that prevent SQLite from building on Win98.\n  ** For that reason, we will omit this optimization for now.  See\n  ** ticket #2685.\n  */\n#if defined(_WIN32_WINNT) && _WIN32_WINNT >= 0x0400\n  assert( winMutex_isInit==1 );\n  assert( winMutex_isNt>=-1 && winMutex_isNt<=1 );\n  if( winMutex_isNt<0 ){\n    winMutex_isNt = sqlite3_win32_is_nt();\n  }\n  assert( winMutex_isNt==0 || winMutex_isNt==1 );\n  if( winMutex_isNt && TryEnterCriticalSection(&p->mutex) ){\n#ifdef SQLITE_DEBUG\n    p->owner = tid;\n    p->nRef++;\n#endif\n    rc = SQLITE_OK;\n  }\n#else\n  UNUSED_PARAMETER(p);\n#endif\n#ifdef SQLITE_DEBUG\n  if( p->trace ){\n    OSTRACE((\"TRY-MUTEX tid=%lu, mutex(%d)=%p (%d), owner=%lu, nRef=%d, rc=%s\\n\",\n             tid, p->id, p, p->trace, p->owner, p->nRef, sqlite3ErrName(rc)));\n  }\n#endif\n  return rc;\n}\n\n/*\n** The sqlite3_mutex_leave() routine exits a mutex that was\n** previously entered by the same thread.  The behavior\n** is undefined if the mutex is not currently entered or\n** is not currently allocated.  SQLite will never do either.\n*/\nstatic void winMutexLeave(sqlite3_mutex *p){\n#if defined(SQLITE_DEBUG) || defined(SQLITE_TEST)\n  DWORD tid = GetCurrentThreadId();\n#endif\n  assert( p );\n#ifdef SQLITE_DEBUG\n  assert( p->nRef>0 );\n  assert( p->owner==tid );\n  p->nRef--;\n  if( p->nRef==0 ) p->owner = 0;\n  assert( p->nRef==0 || p->id==SQLITE_MUTEX_RECURSIVE );\n#endif\n  assert( winMutex_isInit==1 );\n  LeaveCriticalSection(&p->mutex);\n#ifdef SQLITE_DEBUG\n  if( p->trace ){\n    OSTRACE((\"LEAVE-MUTEX tid=%lu, mutex(%d)=%p (%d), nRef=%d\\n\",\n             tid, p->id, p, p->trace, p->nRef));\n  }\n#endif\n}\n\nSQLITE_PRIVATE sqlite3_mutex_methods const *sqlite3DefaultMutex(void){\n  static const sqlite3_mutex_methods sMutex = {\n    winMutexInit,\n    winMutexEnd,\n    winMutexAlloc,\n    winMutexFree,\n    winMutexEnter,\n    winMutexTry,\n    winMutexLeave,\n#ifdef SQLITE_DEBUG\n    winMutexHeld,\n    winMutexNotheld\n#else\n    0,\n    0\n#endif\n  };\n  return &sMutex;\n}\n\n#endif /* SQLITE_MUTEX_W32 */\n\n/************** End of mutex_w32.c *******************************************/\n/************** Begin file malloc.c ******************************************/\n/*\n** 2001 September 15\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n*************************************************************************\n**\n** Memory allocation functions used throughout sqlite.\n*/\n/* #include \"sqliteInt.h\" */\n/* #include <stdarg.h> */\n\n/*\n** Attempt to release up to n bytes of non-essential memory currently\n** held by SQLite. An example of non-essential memory is memory used to\n** cache database pages that are not currently in use.\n*/\nSQLITE_API int sqlite3_release_memory(int n){\n#ifdef SQLITE_ENABLE_MEMORY_MANAGEMENT\n  return sqlite3PcacheReleaseMemory(n);\n#else\n  /* IMPLEMENTATION-OF: R-34391-24921 The sqlite3_release_memory() routine\n  ** is a no-op returning zero if SQLite is not compiled with\n  ** SQLITE_ENABLE_MEMORY_MANAGEMENT. */\n  UNUSED_PARAMETER(n);\n  return 0;\n#endif\n}\n\n/*\n** State information local to the memory allocation subsystem.\n*/\nstatic SQLITE_WSD struct Mem0Global {\n  sqlite3_mutex *mutex;         /* Mutex to serialize access */\n  sqlite3_int64 alarmThreshold; /* The soft heap limit */\n\n  /*\n  ** True if heap is nearly \"full\" where \"full\" is defined by the\n  ** sqlite3_soft_heap_limit() setting.\n  */\n  int nearlyFull;\n} mem0 = { 0, 0, 0 };\n\n#define mem0 GLOBAL(struct Mem0Global, mem0)\n\n/*\n** Return the memory allocator mutex. sqlite3_status() needs it.\n*/\nSQLITE_PRIVATE sqlite3_mutex *sqlite3MallocMutex(void){\n  return mem0.mutex;\n}\n\n#ifndef SQLITE_OMIT_DEPRECATED\n/*\n** Deprecated external interface.  It used to set an alarm callback\n** that was invoked when memory usage grew too large.  Now it is a\n** no-op.\n*/\nSQLITE_API int sqlite3_memory_alarm(\n  void(*xCallback)(void *pArg, sqlite3_int64 used,int N),\n  void *pArg,\n  sqlite3_int64 iThreshold\n){\n  (void)xCallback;\n  (void)pArg;\n  (void)iThreshold;\n  return SQLITE_OK;\n}\n#endif\n\n/*\n** Set the soft heap-size limit for the library. Passing a zero or \n** negative value indicates no limit.\n*/\nSQLITE_API sqlite3_int64 sqlite3_soft_heap_limit64(sqlite3_int64 n){\n  sqlite3_int64 priorLimit;\n  sqlite3_int64 excess;\n  sqlite3_int64 nUsed;\n#ifndef SQLITE_OMIT_AUTOINIT\n  int rc = sqlite3_initialize();\n  if( rc ) return -1;\n#endif\n  sqlite3_mutex_enter(mem0.mutex);\n  priorLimit = mem0.alarmThreshold;\n  if( n<0 ){\n    sqlite3_mutex_leave(mem0.mutex);\n    return priorLimit;\n  }\n  mem0.alarmThreshold = n;\n  nUsed = sqlite3StatusValue(SQLITE_STATUS_MEMORY_USED);\n  mem0.nearlyFull = (n>0 && n<=nUsed);\n  sqlite3_mutex_leave(mem0.mutex);\n  excess = sqlite3_memory_used() - n;\n  if( excess>0 ) sqlite3_release_memory((int)(excess & 0x7fffffff));\n  return priorLimit;\n}\nSQLITE_API void sqlite3_soft_heap_limit(int n){\n  if( n<0 ) n = 0;\n  sqlite3_soft_heap_limit64(n);\n}\n\n/*\n** Initialize the memory allocation subsystem.\n*/\nSQLITE_PRIVATE int sqlite3MallocInit(void){\n  int rc;\n  if( sqlite3GlobalConfig.m.xMalloc==0 ){\n    sqlite3MemSetDefault();\n  }\n  memset(&mem0, 0, sizeof(mem0));\n  mem0.mutex = sqlite3MutexAlloc(SQLITE_MUTEX_STATIC_MEM);\n  if( sqlite3GlobalConfig.pPage==0 || sqlite3GlobalConfig.szPage<512\n      || sqlite3GlobalConfig.nPage<=0 ){\n    sqlite3GlobalConfig.pPage = 0;\n    sqlite3GlobalConfig.szPage = 0;\n  }\n  rc = sqlite3GlobalConfig.m.xInit(sqlite3GlobalConfig.m.pAppData);\n  if( rc!=SQLITE_OK ) memset(&mem0, 0, sizeof(mem0));\n  return rc;\n}\n\n/*\n** Return true if the heap is currently under memory pressure - in other\n** words if the amount of heap used is close to the limit set by\n** sqlite3_soft_heap_limit().\n*/\nSQLITE_PRIVATE int sqlite3HeapNearlyFull(void){\n  return mem0.nearlyFull;\n}\n\n/*\n** Deinitialize the memory allocation subsystem.\n*/\nSQLITE_PRIVATE void sqlite3MallocEnd(void){\n  if( sqlite3GlobalConfig.m.xShutdown ){\n    sqlite3GlobalConfig.m.xShutdown(sqlite3GlobalConfig.m.pAppData);\n  }\n  memset(&mem0, 0, sizeof(mem0));\n}\n\n/*\n** Return the amount of memory currently checked out.\n*/\nSQLITE_API sqlite3_int64 sqlite3_memory_used(void){\n  sqlite3_int64 res, mx;\n  sqlite3_status64(SQLITE_STATUS_MEMORY_USED, &res, &mx, 0);\n  return res;\n}\n\n/*\n** Return the maximum amount of memory that has ever been\n** checked out since either the beginning of this process\n** or since the most recent reset.\n*/\nSQLITE_API sqlite3_int64 sqlite3_memory_highwater(int resetFlag){\n  sqlite3_int64 res, mx;\n  sqlite3_status64(SQLITE_STATUS_MEMORY_USED, &res, &mx, resetFlag);\n  return mx;\n}\n\n/*\n** Trigger the alarm \n*/\nstatic void sqlite3MallocAlarm(int nByte){\n  if( mem0.alarmThreshold<=0 ) return;\n  sqlite3_mutex_leave(mem0.mutex);\n  sqlite3_release_memory(nByte);\n  sqlite3_mutex_enter(mem0.mutex);\n}\n\n/*\n** Do a memory allocation with statistics and alarms.  Assume the\n** lock is already held.\n*/\nstatic void mallocWithAlarm(int n, void **pp){\n  void *p;\n  int nFull;\n  assert( sqlite3_mutex_held(mem0.mutex) );\n  assert( n>0 );\n\n  /* In Firefox (circa 2017-02-08), xRoundup() is remapped to an internal\n  ** implementation of malloc_good_size(), which must be called in debug\n  ** mode and specifically when the DMD \"Dark Matter Detector\" is enabled\n  ** or else a crash results.  Hence, do not attempt to optimize out the\n  ** following xRoundup() call. */\n  nFull = sqlite3GlobalConfig.m.xRoundup(n);\n\n#ifdef SQLITE_MAX_MEMORY\n  if( sqlite3StatusValue(SQLITE_STATUS_MEMORY_USED)+nFull>SQLITE_MAX_MEMORY ){\n    *pp = 0;\n    return;\n  }\n#endif\n\n  sqlite3StatusHighwater(SQLITE_STATUS_MALLOC_SIZE, n);\n  if( mem0.alarmThreshold>0 ){\n    sqlite3_int64 nUsed = sqlite3StatusValue(SQLITE_STATUS_MEMORY_USED);\n    if( nUsed >= mem0.alarmThreshold - nFull ){\n      mem0.nearlyFull = 1;\n      sqlite3MallocAlarm(nFull);\n    }else{\n      mem0.nearlyFull = 0;\n    }\n  }\n  p = sqlite3GlobalConfig.m.xMalloc(nFull);\n#ifdef SQLITE_ENABLE_MEMORY_MANAGEMENT\n  if( p==0 && mem0.alarmThreshold>0 ){\n    sqlite3MallocAlarm(nFull);\n    p = sqlite3GlobalConfig.m.xMalloc(nFull);\n  }\n#endif\n  if( p ){\n    nFull = sqlite3MallocSize(p);\n    sqlite3StatusUp(SQLITE_STATUS_MEMORY_USED, nFull);\n    sqlite3StatusUp(SQLITE_STATUS_MALLOC_COUNT, 1);\n  }\n  *pp = p;\n}\n\n/*\n** Allocate memory.  This routine is like sqlite3_malloc() except that it\n** assumes the memory subsystem has already been initialized.\n*/\nSQLITE_PRIVATE void *sqlite3Malloc(u64 n){\n  void *p;\n  if( n==0 || n>=0x7fffff00 ){\n    /* A memory allocation of a number of bytes which is near the maximum\n    ** signed integer value might cause an integer overflow inside of the\n    ** xMalloc().  Hence we limit the maximum size to 0x7fffff00, giving\n    ** 255 bytes of overhead.  SQLite itself will never use anything near\n    ** this amount.  The only way to reach the limit is with sqlite3_malloc() */\n    p = 0;\n  }else if( sqlite3GlobalConfig.bMemstat ){\n    sqlite3_mutex_enter(mem0.mutex);\n    mallocWithAlarm((int)n, &p);\n    sqlite3_mutex_leave(mem0.mutex);\n  }else{\n    p = sqlite3GlobalConfig.m.xMalloc((int)n);\n  }\n  assert( EIGHT_BYTE_ALIGNMENT(p) );  /* IMP: R-11148-40995 */\n  return p;\n}\n\n/*\n** This version of the memory allocation is for use by the application.\n** First make sure the memory subsystem is initialized, then do the\n** allocation.\n*/\nSQLITE_API void *sqlite3_malloc(int n){\n#ifndef SQLITE_OMIT_AUTOINIT\n  if( sqlite3_initialize() ) return 0;\n#endif\n  return n<=0 ? 0 : sqlite3Malloc(n);\n}\nSQLITE_API void *sqlite3_malloc64(sqlite3_uint64 n){\n#ifndef SQLITE_OMIT_AUTOINIT\n  if( sqlite3_initialize() ) return 0;\n#endif\n  return sqlite3Malloc(n);\n}\n\n/*\n** TRUE if p is a lookaside memory allocation from db\n*/\n#ifndef SQLITE_OMIT_LOOKASIDE\nstatic int isLookaside(sqlite3 *db, void *p){\n  return SQLITE_WITHIN(p, db->lookaside.pStart, db->lookaside.pEnd);\n}\n#else\n#define isLookaside(A,B) 0\n#endif\n\n/*\n** Return the size of a memory allocation previously obtained from\n** sqlite3Malloc() or sqlite3_malloc().\n*/\nSQLITE_PRIVATE int sqlite3MallocSize(void *p){\n  assert( sqlite3MemdebugHasType(p, MEMTYPE_HEAP) );\n  return sqlite3GlobalConfig.m.xSize(p);\n}\nSQLITE_PRIVATE int sqlite3DbMallocSize(sqlite3 *db, void *p){\n  assert( p!=0 );\n  if( db==0 || !isLookaside(db,p) ){\n#ifdef SQLITE_DEBUG\n    if( db==0 ){\n      assert( sqlite3MemdebugNoType(p, (u8)~MEMTYPE_HEAP) );\n      assert( sqlite3MemdebugHasType(p, MEMTYPE_HEAP) );\n    }else{\n      assert( sqlite3MemdebugHasType(p, (MEMTYPE_LOOKASIDE|MEMTYPE_HEAP)) );\n      assert( sqlite3MemdebugNoType(p, (u8)~(MEMTYPE_LOOKASIDE|MEMTYPE_HEAP)) );\n    }\n#endif\n    return sqlite3GlobalConfig.m.xSize(p);\n  }else{\n    assert( sqlite3_mutex_held(db->mutex) );\n    return db->lookaside.sz;\n  }\n}\nSQLITE_API sqlite3_uint64 sqlite3_msize(void *p){\n  assert( sqlite3MemdebugNoType(p, (u8)~MEMTYPE_HEAP) );\n  assert( sqlite3MemdebugHasType(p, MEMTYPE_HEAP) );\n  return p ? sqlite3GlobalConfig.m.xSize(p) : 0;\n}\n\n/*\n** Free memory previously obtained from sqlite3Malloc().\n*/\nSQLITE_API void sqlite3_free(void *p){\n  if( p==0 ) return;  /* IMP: R-49053-54554 */\n  assert( sqlite3MemdebugHasType(p, MEMTYPE_HEAP) );\n  assert( sqlite3MemdebugNoType(p, (u8)~MEMTYPE_HEAP) );\n  if( sqlite3GlobalConfig.bMemstat ){\n    sqlite3_mutex_enter(mem0.mutex);\n    sqlite3StatusDown(SQLITE_STATUS_MEMORY_USED, sqlite3MallocSize(p));\n    sqlite3StatusDown(SQLITE_STATUS_MALLOC_COUNT, 1);\n    sqlite3GlobalConfig.m.xFree(p);\n    sqlite3_mutex_leave(mem0.mutex);\n  }else{\n    sqlite3GlobalConfig.m.xFree(p);\n  }\n}\n\n/*\n** Add the size of memory allocation \"p\" to the count in\n** *db->pnBytesFreed.\n*/\nstatic SQLITE_NOINLINE void measureAllocationSize(sqlite3 *db, void *p){\n  *db->pnBytesFreed += sqlite3DbMallocSize(db,p);\n}\n\n/*\n** Free memory that might be associated with a particular database\n** connection.  Calling sqlite3DbFree(D,X) for X==0 is a harmless no-op.\n** The sqlite3DbFreeNN(D,X) version requires that X be non-NULL.\n*/\nSQLITE_PRIVATE void sqlite3DbFreeNN(sqlite3 *db, void *p){\n  assert( db==0 || sqlite3_mutex_held(db->mutex) );\n  assert( p!=0 );\n  if( db ){\n    if( db->pnBytesFreed ){\n      measureAllocationSize(db, p);\n      return;\n    }\n    if( isLookaside(db, p) ){\n      LookasideSlot *pBuf = (LookasideSlot*)p;\n#ifdef SQLITE_DEBUG\n      /* Trash all content in the buffer being freed */\n      memset(p, 0xaa, db->lookaside.sz);\n#endif\n      pBuf->pNext = db->lookaside.pFree;\n      db->lookaside.pFree = pBuf;\n      return;\n    }\n  }\n  assert( sqlite3MemdebugHasType(p, (MEMTYPE_LOOKASIDE|MEMTYPE_HEAP)) );\n  assert( sqlite3MemdebugNoType(p, (u8)~(MEMTYPE_LOOKASIDE|MEMTYPE_HEAP)) );\n  assert( db!=0 || sqlite3MemdebugNoType(p, MEMTYPE_LOOKASIDE) );\n  sqlite3MemdebugSetType(p, MEMTYPE_HEAP);\n  sqlite3_free(p);\n}\nSQLITE_PRIVATE void sqlite3DbFree(sqlite3 *db, void *p){\n  assert( db==0 || sqlite3_mutex_held(db->mutex) );\n  if( p ) sqlite3DbFreeNN(db, p);\n}\n\n/*\n** Change the size of an existing memory allocation\n*/\nSQLITE_PRIVATE void *sqlite3Realloc(void *pOld, u64 nBytes){\n  int nOld, nNew, nDiff;\n  void *pNew;\n  assert( sqlite3MemdebugHasType(pOld, MEMTYPE_HEAP) );\n  assert( sqlite3MemdebugNoType(pOld, (u8)~MEMTYPE_HEAP) );\n  if( pOld==0 ){\n    return sqlite3Malloc(nBytes); /* IMP: R-04300-56712 */\n  }\n  if( nBytes==0 ){\n    sqlite3_free(pOld); /* IMP: R-26507-47431 */\n    return 0;\n  }\n  if( nBytes>=0x7fffff00 ){\n    /* The 0x7ffff00 limit term is explained in comments on sqlite3Malloc() */\n    return 0;\n  }\n  nOld = sqlite3MallocSize(pOld);\n  /* IMPLEMENTATION-OF: R-46199-30249 SQLite guarantees that the second\n  ** argument to xRealloc is always a value returned by a prior call to\n  ** xRoundup. */\n  nNew = sqlite3GlobalConfig.m.xRoundup((int)nBytes);\n  if( nOld==nNew ){\n    pNew = pOld;\n  }else if( sqlite3GlobalConfig.bMemstat ){\n    sqlite3_mutex_enter(mem0.mutex);\n    sqlite3StatusHighwater(SQLITE_STATUS_MALLOC_SIZE, (int)nBytes);\n    nDiff = nNew - nOld;\n    if( nDiff>0 && sqlite3StatusValue(SQLITE_STATUS_MEMORY_USED) >= \n          mem0.alarmThreshold-nDiff ){\n      sqlite3MallocAlarm(nDiff);\n    }\n    pNew = sqlite3GlobalConfig.m.xRealloc(pOld, nNew);\n    if( pNew==0 && mem0.alarmThreshold>0 ){\n      sqlite3MallocAlarm((int)nBytes);\n      pNew = sqlite3GlobalConfig.m.xRealloc(pOld, nNew);\n    }\n    if( pNew ){\n      nNew = sqlite3MallocSize(pNew);\n      sqlite3StatusUp(SQLITE_STATUS_MEMORY_USED, nNew-nOld);\n    }\n    sqlite3_mutex_leave(mem0.mutex);\n  }else{\n    pNew = sqlite3GlobalConfig.m.xRealloc(pOld, nNew);\n  }\n  assert( EIGHT_BYTE_ALIGNMENT(pNew) ); /* IMP: R-11148-40995 */\n  return pNew;\n}\n\n/*\n** The public interface to sqlite3Realloc.  Make sure that the memory\n** subsystem is initialized prior to invoking sqliteRealloc.\n*/\nSQLITE_API void *sqlite3_realloc(void *pOld, int n){\n#ifndef SQLITE_OMIT_AUTOINIT\n  if( sqlite3_initialize() ) return 0;\n#endif\n  if( n<0 ) n = 0;  /* IMP: R-26507-47431 */\n  return sqlite3Realloc(pOld, n);\n}\nSQLITE_API void *sqlite3_realloc64(void *pOld, sqlite3_uint64 n){\n#ifndef SQLITE_OMIT_AUTOINIT\n  if( sqlite3_initialize() ) return 0;\n#endif\n  return sqlite3Realloc(pOld, n);\n}\n\n\n/*\n** Allocate and zero memory.\n*/ \nSQLITE_PRIVATE void *sqlite3MallocZero(u64 n){\n  void *p = sqlite3Malloc(n);\n  if( p ){\n    memset(p, 0, (size_t)n);\n  }\n  return p;\n}\n\n/*\n** Allocate and zero memory.  If the allocation fails, make\n** the mallocFailed flag in the connection pointer.\n*/\nSQLITE_PRIVATE void *sqlite3DbMallocZero(sqlite3 *db, u64 n){\n  void *p;\n  testcase( db==0 );\n  p = sqlite3DbMallocRaw(db, n);\n  if( p ) memset(p, 0, (size_t)n);\n  return p;\n}\n\n\n/* Finish the work of sqlite3DbMallocRawNN for the unusual and\n** slower case when the allocation cannot be fulfilled using lookaside.\n*/\nstatic SQLITE_NOINLINE void *dbMallocRawFinish(sqlite3 *db, u64 n){\n  void *p;\n  assert( db!=0 );\n  p = sqlite3Malloc(n);\n  if( !p ) sqlite3OomFault(db);\n  sqlite3MemdebugSetType(p, \n         (db->lookaside.bDisable==0) ? MEMTYPE_LOOKASIDE : MEMTYPE_HEAP);\n  return p;\n}\n\n/*\n** Allocate memory, either lookaside (if possible) or heap.  \n** If the allocation fails, set the mallocFailed flag in\n** the connection pointer.\n**\n** If db!=0 and db->mallocFailed is true (indicating a prior malloc\n** failure on the same database connection) then always return 0.\n** Hence for a particular database connection, once malloc starts\n** failing, it fails consistently until mallocFailed is reset.\n** This is an important assumption.  There are many places in the\n** code that do things like this:\n**\n**         int *a = (int*)sqlite3DbMallocRaw(db, 100);\n**         int *b = (int*)sqlite3DbMallocRaw(db, 200);\n**         if( b ) a[10] = 9;\n**\n** In other words, if a subsequent malloc (ex: \"b\") worked, it is assumed\n** that all prior mallocs (ex: \"a\") worked too.\n**\n** The sqlite3MallocRawNN() variant guarantees that the \"db\" parameter is\n** not a NULL pointer.\n*/\nSQLITE_PRIVATE void *sqlite3DbMallocRaw(sqlite3 *db, u64 n){\n  void *p;\n  if( db ) return sqlite3DbMallocRawNN(db, n);\n  p = sqlite3Malloc(n);\n  sqlite3MemdebugSetType(p, MEMTYPE_HEAP);\n  return p;\n}\nSQLITE_PRIVATE void *sqlite3DbMallocRawNN(sqlite3 *db, u64 n){\n#ifndef SQLITE_OMIT_LOOKASIDE\n  LookasideSlot *pBuf;\n  assert( db!=0 );\n  assert( sqlite3_mutex_held(db->mutex) );\n  assert( db->pnBytesFreed==0 );\n  if( db->lookaside.bDisable==0 ){\n    assert( db->mallocFailed==0 );\n    if( n>db->lookaside.sz ){\n      db->lookaside.anStat[1]++;\n    }else if( (pBuf = db->lookaside.pFree)!=0 ){\n      db->lookaside.pFree = pBuf->pNext;\n      db->lookaside.anStat[0]++;\n      return (void*)pBuf;\n    }else if( (pBuf = db->lookaside.pInit)!=0 ){\n      db->lookaside.pInit = pBuf->pNext;\n      db->lookaside.anStat[0]++;\n      return (void*)pBuf;\n    }else{\n      db->lookaside.anStat[2]++;\n    }\n  }else if( db->mallocFailed ){\n    return 0;\n  }\n#else\n  assert( db!=0 );\n  assert( sqlite3_mutex_held(db->mutex) );\n  assert( db->pnBytesFreed==0 );\n  if( db->mallocFailed ){\n    return 0;\n  }\n#endif\n  return dbMallocRawFinish(db, n);\n}\n\n/* Forward declaration */\nstatic SQLITE_NOINLINE void *dbReallocFinish(sqlite3 *db, void *p, u64 n);\n\n/*\n** Resize the block of memory pointed to by p to n bytes. If the\n** resize fails, set the mallocFailed flag in the connection object.\n*/\nSQLITE_PRIVATE void *sqlite3DbRealloc(sqlite3 *db, void *p, u64 n){\n  assert( db!=0 );\n  if( p==0 ) return sqlite3DbMallocRawNN(db, n);\n  assert( sqlite3_mutex_held(db->mutex) );\n  if( isLookaside(db,p) && n<=db->lookaside.sz ) return p;\n  return dbReallocFinish(db, p, n);\n}\nstatic SQLITE_NOINLINE void *dbReallocFinish(sqlite3 *db, void *p, u64 n){\n  void *pNew = 0;\n  assert( db!=0 );\n  assert( p!=0 );\n  if( db->mallocFailed==0 ){\n    if( isLookaside(db, p) ){\n      pNew = sqlite3DbMallocRawNN(db, n);\n      if( pNew ){\n        memcpy(pNew, p, db->lookaside.sz);\n        sqlite3DbFree(db, p);\n      }\n    }else{\n      assert( sqlite3MemdebugHasType(p, (MEMTYPE_LOOKASIDE|MEMTYPE_HEAP)) );\n      assert( sqlite3MemdebugNoType(p, (u8)~(MEMTYPE_LOOKASIDE|MEMTYPE_HEAP)) );\n      sqlite3MemdebugSetType(p, MEMTYPE_HEAP);\n      pNew = sqlite3_realloc64(p, n);\n      if( !pNew ){\n        sqlite3OomFault(db);\n      }\n      sqlite3MemdebugSetType(pNew,\n            (db->lookaside.bDisable==0 ? MEMTYPE_LOOKASIDE : MEMTYPE_HEAP));\n    }\n  }\n  return pNew;\n}\n\n/*\n** Attempt to reallocate p.  If the reallocation fails, then free p\n** and set the mallocFailed flag in the database connection.\n*/\nSQLITE_PRIVATE void *sqlite3DbReallocOrFree(sqlite3 *db, void *p, u64 n){\n  void *pNew;\n  pNew = sqlite3DbRealloc(db, p, n);\n  if( !pNew ){\n    sqlite3DbFree(db, p);\n  }\n  return pNew;\n}\n\n/*\n** Make a copy of a string in memory obtained from sqliteMalloc(). These \n** functions call sqlite3MallocRaw() directly instead of sqliteMalloc(). This\n** is because when memory debugging is turned on, these two functions are \n** called via macros that record the current file and line number in the\n** ThreadData structure.\n*/\nSQLITE_PRIVATE char *sqlite3DbStrDup(sqlite3 *db, const char *z){\n  char *zNew;\n  size_t n;\n  if( z==0 ){\n    return 0;\n  }\n  n = strlen(z) + 1;\n  zNew = sqlite3DbMallocRaw(db, n);\n  if( zNew ){\n    memcpy(zNew, z, n);\n  }\n  return zNew;\n}\nSQLITE_PRIVATE char *sqlite3DbStrNDup(sqlite3 *db, const char *z, u64 n){\n  char *zNew;\n  assert( db!=0 );\n  if( z==0 ){\n    return 0;\n  }\n  assert( (n&0x7fffffff)==n );\n  zNew = sqlite3DbMallocRawNN(db, n+1);\n  if( zNew ){\n    memcpy(zNew, z, (size_t)n);\n    zNew[n] = 0;\n  }\n  return zNew;\n}\n\n/*\n** The text between zStart and zEnd represents a phrase within a larger\n** SQL statement.  Make a copy of this phrase in space obtained form\n** sqlite3DbMalloc().  Omit leading and trailing whitespace.\n*/\nSQLITE_PRIVATE char *sqlite3DbSpanDup(sqlite3 *db, const char *zStart, const char *zEnd){\n  int n;\n  while( sqlite3Isspace(zStart[0]) ) zStart++;\n  n = (int)(zEnd - zStart);\n  while( ALWAYS(n>0) && sqlite3Isspace(zStart[n-1]) ) n--;\n  return sqlite3DbStrNDup(db, zStart, n);\n}\n\n/*\n** Free any prior content in *pz and replace it with a copy of zNew.\n*/\nSQLITE_PRIVATE void sqlite3SetString(char **pz, sqlite3 *db, const char *zNew){\n  sqlite3DbFree(db, *pz);\n  *pz = sqlite3DbStrDup(db, zNew);\n}\n\n/*\n** Call this routine to record the fact that an OOM (out-of-memory) error\n** has happened.  This routine will set db->mallocFailed, and also\n** temporarily disable the lookaside memory allocator and interrupt\n** any running VDBEs.\n*/\nSQLITE_PRIVATE void sqlite3OomFault(sqlite3 *db){\n  if( db->mallocFailed==0 && db->bBenignMalloc==0 ){\n    db->mallocFailed = 1;\n    if( db->nVdbeExec>0 ){\n      db->u1.isInterrupted = 1;\n    }\n    db->lookaside.bDisable++;\n  }\n}\n\n/*\n** This routine reactivates the memory allocator and clears the\n** db->mallocFailed flag as necessary.\n**\n** The memory allocator is not restarted if there are running\n** VDBEs.\n*/\nSQLITE_PRIVATE void sqlite3OomClear(sqlite3 *db){\n  if( db->mallocFailed && db->nVdbeExec==0 ){\n    db->mallocFailed = 0;\n    db->u1.isInterrupted = 0;\n    assert( db->lookaside.bDisable>0 );\n    db->lookaside.bDisable--;\n  }\n}\n\n/*\n** Take actions at the end of an API call to indicate an OOM error\n*/\nstatic SQLITE_NOINLINE int apiOomError(sqlite3 *db){\n  sqlite3OomClear(db);\n  sqlite3Error(db, SQLITE_NOMEM);\n  return SQLITE_NOMEM_BKPT;\n}\n\n/*\n** This function must be called before exiting any API function (i.e. \n** returning control to the user) that has called sqlite3_malloc or\n** sqlite3_realloc.\n**\n** The returned value is normally a copy of the second argument to this\n** function. However, if a malloc() failure has occurred since the previous\n** invocation SQLITE_NOMEM is returned instead. \n**\n** If an OOM as occurred, then the connection error-code (the value\n** returned by sqlite3_errcode()) is set to SQLITE_NOMEM.\n*/\nSQLITE_PRIVATE int sqlite3ApiExit(sqlite3* db, int rc){\n  /* If the db handle must hold the connection handle mutex here.\n  ** Otherwise the read (and possible write) of db->mallocFailed \n  ** is unsafe, as is the call to sqlite3Error().\n  */\n  assert( db!=0 );\n  assert( sqlite3_mutex_held(db->mutex) );\n  if( db->mallocFailed || rc==SQLITE_IOERR_NOMEM ){\n    return apiOomError(db);\n  }\n  return rc & db->errMask;\n}\n\n/************** End of malloc.c **********************************************/\n/************** Begin file printf.c ******************************************/\n/*\n** The \"printf\" code that follows dates from the 1980's.  It is in\n** the public domain. \n**\n**************************************************************************\n**\n** This file contains code for a set of \"printf\"-like routines.  These\n** routines format strings much like the printf() from the standard C\n** library, though the implementation here has enhancements to support\n** SQLite.\n*/\n/* #include \"sqliteInt.h\" */\n\n/*\n** Conversion types fall into various categories as defined by the\n** following enumeration.\n*/\n#define etRADIX       0 /* non-decimal integer types.  %x %o */\n#define etFLOAT       1 /* Floating point.  %f */\n#define etEXP         2 /* Exponentional notation. %e and %E */\n#define etGENERIC     3 /* Floating or exponential, depending on exponent. %g */\n#define etSIZE        4 /* Return number of characters processed so far. %n */\n#define etSTRING      5 /* Strings. %s */\n#define etDYNSTRING   6 /* Dynamically allocated strings. %z */\n#define etPERCENT     7 /* Percent symbol. %% */\n#define etCHARX       8 /* Characters. %c */\n/* The rest are extensions, not normally found in printf() */\n#define etSQLESCAPE   9 /* Strings with '\\'' doubled.  %q */\n#define etSQLESCAPE2 10 /* Strings with '\\'' doubled and enclosed in '',\n                          NULL pointers replaced by SQL NULL.  %Q */\n#define etTOKEN      11 /* a pointer to a Token structure */\n#define etSRCLIST    12 /* a pointer to a SrcList */\n#define etPOINTER    13 /* The %p conversion */\n#define etSQLESCAPE3 14 /* %w -> Strings with '\\\"' doubled */\n#define etORDINAL    15 /* %r -> 1st, 2nd, 3rd, 4th, etc.  English only */\n#define etDECIMAL    16 /* %d or %u, but not %x, %o */\n\n#define etINVALID    17 /* Any unrecognized conversion type */\n\n\n/*\n** An \"etByte\" is an 8-bit unsigned value.\n*/\ntypedef unsigned char etByte;\n\n/*\n** Each builtin conversion character (ex: the 'd' in \"%d\") is described\n** by an instance of the following structure\n*/\ntypedef struct et_info {   /* Information about each format field */\n  char fmttype;            /* The format field code letter */\n  etByte base;             /* The base for radix conversion */\n  etByte flags;            /* One or more of FLAG_ constants below */\n  etByte type;             /* Conversion paradigm */\n  etByte charset;          /* Offset into aDigits[] of the digits string */\n  etByte prefix;           /* Offset into aPrefix[] of the prefix string */\n} et_info;\n\n/*\n** Allowed values for et_info.flags\n*/\n#define FLAG_SIGNED    1     /* True if the value to convert is signed */\n#define FLAG_STRING    4     /* Allow infinite precision */\n\n\n/*\n** The following table is searched linearly, so it is good to put the\n** most frequently used conversion types first.\n*/\nstatic const char aDigits[] = \"0123456789ABCDEF0123456789abcdef\";\nstatic const char aPrefix[] = \"-x0\\000X0\";\nstatic const et_info fmtinfo[] = {\n  {  'd', 10, 1, etDECIMAL,    0,  0 },\n  {  's',  0, 4, etSTRING,     0,  0 },\n  {  'g',  0, 1, etGENERIC,    30, 0 },\n  {  'z',  0, 4, etDYNSTRING,  0,  0 },\n  {  'q',  0, 4, etSQLESCAPE,  0,  0 },\n  {  'Q',  0, 4, etSQLESCAPE2, 0,  0 },\n  {  'w',  0, 4, etSQLESCAPE3, 0,  0 },\n  {  'c',  0, 0, etCHARX,      0,  0 },\n  {  'o',  8, 0, etRADIX,      0,  2 },\n  {  'u', 10, 0, etDECIMAL,    0,  0 },\n  {  'x', 16, 0, etRADIX,      16, 1 },\n  {  'X', 16, 0, etRADIX,      0,  4 },\n#ifndef SQLITE_OMIT_FLOATING_POINT\n  {  'f',  0, 1, etFLOAT,      0,  0 },\n  {  'e',  0, 1, etEXP,        30, 0 },\n  {  'E',  0, 1, etEXP,        14, 0 },\n  {  'G',  0, 1, etGENERIC,    14, 0 },\n#endif\n  {  'i', 10, 1, etDECIMAL,    0,  0 },\n  {  'n',  0, 0, etSIZE,       0,  0 },\n  {  '%',  0, 0, etPERCENT,    0,  0 },\n  {  'p', 16, 0, etPOINTER,    0,  1 },\n\n  /* All the rest are undocumented and are for internal use only */\n  {  'T',  0, 0, etTOKEN,      0,  0 },\n  {  'S',  0, 0, etSRCLIST,    0,  0 },\n  {  'r', 10, 1, etORDINAL,    0,  0 },\n};\n\n/*\n** If SQLITE_OMIT_FLOATING_POINT is defined, then none of the floating point\n** conversions will work.\n*/\n#ifndef SQLITE_OMIT_FLOATING_POINT\n/*\n** \"*val\" is a double such that 0.1 <= *val < 10.0\n** Return the ascii code for the leading digit of *val, then\n** multiply \"*val\" by 10.0 to renormalize.\n**\n** Example:\n**     input:     *val = 3.14159\n**     output:    *val = 1.4159    function return = '3'\n**\n** The counter *cnt is incremented each time.  After counter exceeds\n** 16 (the number of significant digits in a 64-bit float) '0' is\n** always returned.\n*/\nstatic char et_getdigit(LONGDOUBLE_TYPE *val, int *cnt){\n  int digit;\n  LONGDOUBLE_TYPE d;\n  if( (*cnt)<=0 ) return '0';\n  (*cnt)--;\n  digit = (int)*val;\n  d = digit;\n  digit += '0';\n  *val = (*val - d)*10.0;\n  return (char)digit;\n}\n#endif /* SQLITE_OMIT_FLOATING_POINT */\n\n/*\n** Set the StrAccum object to an error mode.\n*/\nstatic void setStrAccumError(StrAccum *p, u8 eError){\n  assert( eError==STRACCUM_NOMEM || eError==STRACCUM_TOOBIG );\n  p->accError = eError;\n  p->nAlloc = 0;\n}\n\n/*\n** Extra argument values from a PrintfArguments object\n*/\nstatic sqlite3_int64 getIntArg(PrintfArguments *p){\n  if( p->nArg<=p->nUsed ) return 0;\n  return sqlite3_value_int64(p->apArg[p->nUsed++]);\n}\nstatic double getDoubleArg(PrintfArguments *p){\n  if( p->nArg<=p->nUsed ) return 0.0;\n  return sqlite3_value_double(p->apArg[p->nUsed++]);\n}\nstatic char *getTextArg(PrintfArguments *p){\n  if( p->nArg<=p->nUsed ) return 0;\n  return (char*)sqlite3_value_text(p->apArg[p->nUsed++]);\n}\n\n\n/*\n** On machines with a small stack size, you can redefine the\n** SQLITE_PRINT_BUF_SIZE to be something smaller, if desired.\n*/\n#ifndef SQLITE_PRINT_BUF_SIZE\n# define SQLITE_PRINT_BUF_SIZE 70\n#endif\n#define etBUFSIZE SQLITE_PRINT_BUF_SIZE  /* Size of the output buffer */\n\n/*\n** Render a string given by \"fmt\" into the StrAccum object.\n*/\nSQLITE_PRIVATE void sqlite3VXPrintf(\n  StrAccum *pAccum,          /* Accumulate results here */\n  const char *fmt,           /* Format string */\n  va_list ap                 /* arguments */\n){\n  int c;                     /* Next character in the format string */\n  char *bufpt;               /* Pointer to the conversion buffer */\n  int precision;             /* Precision of the current field */\n  int length;                /* Length of the field */\n  int idx;                   /* A general purpose loop counter */\n  int width;                 /* Width of the current field */\n  etByte flag_leftjustify;   /* True if \"-\" flag is present */\n  etByte flag_prefix;        /* '+' or ' ' or 0 for prefix */\n  etByte flag_alternateform; /* True if \"#\" flag is present */\n  etByte flag_altform2;      /* True if \"!\" flag is present */\n  etByte flag_zeropad;       /* True if field width constant starts with zero */\n  etByte flag_long;          /* 1 for the \"l\" flag, 2 for \"ll\", 0 by default */\n  etByte done;               /* Loop termination flag */\n  etByte cThousand;          /* Thousands separator for %d and %u */\n  etByte xtype = etINVALID;  /* Conversion paradigm */\n  u8 bArgList;               /* True for SQLITE_PRINTF_SQLFUNC */\n  char prefix;               /* Prefix character.  \"+\" or \"-\" or \" \" or '\\0'. */\n  sqlite_uint64 longvalue;   /* Value for integer types */\n  LONGDOUBLE_TYPE realvalue; /* Value for real types */\n  const et_info *infop;      /* Pointer to the appropriate info structure */\n  char *zOut;                /* Rendering buffer */\n  int nOut;                  /* Size of the rendering buffer */\n  char *zExtra = 0;          /* Malloced memory used by some conversion */\n#ifndef SQLITE_OMIT_FLOATING_POINT\n  int  exp, e2;              /* exponent of real numbers */\n  int nsd;                   /* Number of significant digits returned */\n  double rounder;            /* Used for rounding floating point values */\n  etByte flag_dp;            /* True if decimal point should be shown */\n  etByte flag_rtz;           /* True if trailing zeros should be removed */\n#endif\n  PrintfArguments *pArgList = 0; /* Arguments for SQLITE_PRINTF_SQLFUNC */\n  char buf[etBUFSIZE];       /* Conversion buffer */\n\n  /* pAccum never starts out with an empty buffer that was obtained from \n  ** malloc().  This precondition is required by the mprintf(\"%z...\")\n  ** optimization. */\n  assert( pAccum->nChar>0 || (pAccum->printfFlags&SQLITE_PRINTF_MALLOCED)==0 );\n\n  bufpt = 0;\n  if( (pAccum->printfFlags & SQLITE_PRINTF_SQLFUNC)!=0 ){\n    pArgList = va_arg(ap, PrintfArguments*);\n    bArgList = 1;\n  }else{\n    bArgList = 0;\n  }\n  for(; (c=(*fmt))!=0; ++fmt){\n    if( c!='%' ){\n      bufpt = (char *)fmt;\n#if HAVE_STRCHRNUL\n      fmt = strchrnul(fmt, '%');\n#else\n      do{ fmt++; }while( *fmt && *fmt != '%' );\n#endif\n      sqlite3StrAccumAppend(pAccum, bufpt, (int)(fmt - bufpt));\n      if( *fmt==0 ) break;\n    }\n    if( (c=(*++fmt))==0 ){\n      sqlite3StrAccumAppend(pAccum, \"%\", 1);\n      break;\n    }\n    /* Find out what flags are present */\n    flag_leftjustify = flag_prefix = cThousand =\n     flag_alternateform = flag_altform2 = flag_zeropad = 0;\n    done = 0;\n    do{\n      switch( c ){\n        case '-':   flag_leftjustify = 1;     break;\n        case '+':   flag_prefix = '+';        break;\n        case ' ':   flag_prefix = ' ';        break;\n        case '#':   flag_alternateform = 1;   break;\n        case '!':   flag_altform2 = 1;        break;\n        case '0':   flag_zeropad = 1;         break;\n        case ',':   cThousand = ',';          break;\n        default:    done = 1;                 break;\n      }\n    }while( !done && (c=(*++fmt))!=0 );\n    /* Get the field width */\n    if( c=='*' ){\n      if( bArgList ){\n        width = (int)getIntArg(pArgList);\n      }else{\n        width = va_arg(ap,int);\n      }\n      if( width<0 ){\n        flag_leftjustify = 1;\n        width = width >= -2147483647 ? -width : 0;\n      }\n      c = *++fmt;\n    }else{\n      unsigned wx = 0;\n      while( c>='0' && c<='9' ){\n        wx = wx*10 + c - '0';\n        c = *++fmt;\n      }\n      testcase( wx>0x7fffffff );\n      width = wx & 0x7fffffff;\n    }\n    assert( width>=0 );\n#ifdef SQLITE_PRINTF_PRECISION_LIMIT\n    if( width>SQLITE_PRINTF_PRECISION_LIMIT ){\n      width = SQLITE_PRINTF_PRECISION_LIMIT;\n    }\n#endif\n\n    /* Get the precision */\n    if( c=='.' ){\n      c = *++fmt;\n      if( c=='*' ){\n        if( bArgList ){\n          precision = (int)getIntArg(pArgList);\n        }else{\n          precision = va_arg(ap,int);\n        }\n        c = *++fmt;\n        if( precision<0 ){\n          precision = precision >= -2147483647 ? -precision : -1;\n        }\n      }else{\n        unsigned px = 0;\n        while( c>='0' && c<='9' ){\n          px = px*10 + c - '0';\n          c = *++fmt;\n        }\n        testcase( px>0x7fffffff );\n        precision = px & 0x7fffffff;\n      }\n    }else{\n      precision = -1;\n    }\n    assert( precision>=(-1) );\n#ifdef SQLITE_PRINTF_PRECISION_LIMIT\n    if( precision>SQLITE_PRINTF_PRECISION_LIMIT ){\n      precision = SQLITE_PRINTF_PRECISION_LIMIT;\n    }\n#endif\n\n\n    /* Get the conversion type modifier */\n    if( c=='l' ){\n      flag_long = 1;\n      c = *++fmt;\n      if( c=='l' ){\n        flag_long = 2;\n        c = *++fmt;\n      }\n    }else{\n      flag_long = 0;\n    }\n    /* Fetch the info entry for the field */\n    infop = &fmtinfo[0];\n    xtype = etINVALID;\n    for(idx=0; idx<ArraySize(fmtinfo); idx++){\n      if( c==fmtinfo[idx].fmttype ){\n        infop = &fmtinfo[idx];\n        xtype = infop->type;\n        break;\n      }\n    }\n\n    /*\n    ** At this point, variables are initialized as follows:\n    **\n    **   flag_alternateform          TRUE if a '#' is present.\n    **   flag_altform2               TRUE if a '!' is present.\n    **   flag_prefix                 '+' or ' ' or zero\n    **   flag_leftjustify            TRUE if a '-' is present or if the\n    **                               field width was negative.\n    **   flag_zeropad                TRUE if the width began with 0.\n    **   flag_long                   1 for \"l\", 2 for \"ll\"\n    **   width                       The specified field width.  This is\n    **                               always non-negative.  Zero is the default.\n    **   precision                   The specified precision.  The default\n    **                               is -1.\n    **   xtype                       The class of the conversion.\n    **   infop                       Pointer to the appropriate info struct.\n    */\n    switch( xtype ){\n      case etPOINTER:\n        flag_long = sizeof(char*)==sizeof(i64) ? 2 :\n                     sizeof(char*)==sizeof(long int) ? 1 : 0;\n        /* Fall through into the next case */\n      case etORDINAL:\n      case etRADIX:      \n        cThousand = 0;\n        /* Fall through into the next case */\n      case etDECIMAL:\n        if( infop->flags & FLAG_SIGNED ){\n          i64 v;\n          if( bArgList ){\n            v = getIntArg(pArgList);\n          }else if( flag_long ){\n            if( flag_long==2 ){\n              v = va_arg(ap,i64) ;\n            }else{\n              v = va_arg(ap,long int);\n            }\n          }else{\n            v = va_arg(ap,int);\n          }\n          if( v<0 ){\n            if( v==SMALLEST_INT64 ){\n              longvalue = ((u64)1)<<63;\n            }else{\n              longvalue = -v;\n            }\n            prefix = '-';\n          }else{\n            longvalue = v;\n            prefix = flag_prefix;\n          }\n        }else{\n          if( bArgList ){\n            longvalue = (u64)getIntArg(pArgList);\n          }else if( flag_long ){\n            if( flag_long==2 ){\n              longvalue = va_arg(ap,u64);\n            }else{\n              longvalue = va_arg(ap,unsigned long int);\n            }\n          }else{\n            longvalue = va_arg(ap,unsigned int);\n          }\n          prefix = 0;\n        }\n        if( longvalue==0 ) flag_alternateform = 0;\n        if( flag_zeropad && precision<width-(prefix!=0) ){\n          precision = width-(prefix!=0);\n        }\n        if( precision<etBUFSIZE-10-etBUFSIZE/3 ){\n          nOut = etBUFSIZE;\n          zOut = buf;\n        }else{\n          u64 n = (u64)precision + 10 + precision/3;\n          zOut = zExtra = sqlite3Malloc( n );\n          if( zOut==0 ){\n            setStrAccumError(pAccum, STRACCUM_NOMEM);\n            return;\n          }\n          nOut = (int)n;\n        }\n        bufpt = &zOut[nOut-1];\n        if( xtype==etORDINAL ){\n          static const char zOrd[] = \"thstndrd\";\n          int x = (int)(longvalue % 10);\n          if( x>=4 || (longvalue/10)%10==1 ){\n            x = 0;\n          }\n          *(--bufpt) = zOrd[x*2+1];\n          *(--bufpt) = zOrd[x*2];\n        }\n        {\n          const char *cset = &aDigits[infop->charset];\n          u8 base = infop->base;\n          do{                                           /* Convert to ascii */\n            *(--bufpt) = cset[longvalue%base];\n            longvalue = longvalue/base;\n          }while( longvalue>0 );\n        }\n        length = (int)(&zOut[nOut-1]-bufpt);\n        while( precision>length ){\n          *(--bufpt) = '0';                             /* Zero pad */\n          length++;\n        }\n        if( cThousand ){\n          int nn = (length - 1)/3;  /* Number of \",\" to insert */\n          int ix = (length - 1)%3 + 1;\n          bufpt -= nn;\n          for(idx=0; nn>0; idx++){\n            bufpt[idx] = bufpt[idx+nn];\n            ix--;\n            if( ix==0 ){\n              bufpt[++idx] = cThousand;\n              nn--;\n              ix = 3;\n            }\n          }\n        }\n        if( prefix ) *(--bufpt) = prefix;               /* Add sign */\n        if( flag_alternateform && infop->prefix ){      /* Add \"0\" or \"0x\" */\n          const char *pre;\n          char x;\n          pre = &aPrefix[infop->prefix];\n          for(; (x=(*pre))!=0; pre++) *(--bufpt) = x;\n        }\n        length = (int)(&zOut[nOut-1]-bufpt);\n        break;\n      case etFLOAT:\n      case etEXP:\n      case etGENERIC:\n        if( bArgList ){\n          realvalue = getDoubleArg(pArgList);\n        }else{\n          realvalue = va_arg(ap,double);\n        }\n#ifdef SQLITE_OMIT_FLOATING_POINT\n        length = 0;\n#else\n        if( precision<0 ) precision = 6;         /* Set default precision */\n        if( realvalue<0.0 ){\n          realvalue = -realvalue;\n          prefix = '-';\n        }else{\n          prefix = flag_prefix;\n        }\n        if( xtype==etGENERIC && precision>0 ) precision--;\n        testcase( precision>0xfff );\n        for(idx=precision&0xfff, rounder=0.5; idx>0; idx--, rounder*=0.1){}\n        if( xtype==etFLOAT ) realvalue += rounder;\n        /* Normalize realvalue to within 10.0 > realvalue >= 1.0 */\n        exp = 0;\n        if( sqlite3IsNaN((double)realvalue) ){\n          bufpt = \"NaN\";\n          length = 3;\n          break;\n        }\n        if( realvalue>0.0 ){\n          LONGDOUBLE_TYPE scale = 1.0;\n          while( realvalue>=1e100*scale && exp<=350 ){ scale *= 1e100;exp+=100;}\n          while( realvalue>=1e10*scale && exp<=350 ){ scale *= 1e10; exp+=10; }\n          while( realvalue>=10.0*scale && exp<=350 ){ scale *= 10.0; exp++; }\n          realvalue /= scale;\n          while( realvalue<1e-8 ){ realvalue *= 1e8; exp-=8; }\n          while( realvalue<1.0 ){ realvalue *= 10.0; exp--; }\n          if( exp>350 ){\n            bufpt = buf;\n            buf[0] = prefix;\n            memcpy(buf+(prefix!=0),\"Inf\",4);\n            length = 3+(prefix!=0);\n            break;\n          }\n        }\n        bufpt = buf;\n        /*\n        ** If the field type is etGENERIC, then convert to either etEXP\n        ** or etFLOAT, as appropriate.\n        */\n        if( xtype!=etFLOAT ){\n          realvalue += rounder;\n          if( realvalue>=10.0 ){ realvalue *= 0.1; exp++; }\n        }\n        if( xtype==etGENERIC ){\n          flag_rtz = !flag_alternateform;\n          if( exp<-4 || exp>precision ){\n            xtype = etEXP;\n          }else{\n            precision = precision - exp;\n            xtype = etFLOAT;\n          }\n        }else{\n          flag_rtz = flag_altform2;\n        }\n        if( xtype==etEXP ){\n          e2 = 0;\n        }else{\n          e2 = exp;\n        }\n        if( MAX(e2,0)+(i64)precision+(i64)width > etBUFSIZE - 15 ){\n          bufpt = zExtra \n              = sqlite3Malloc( MAX(e2,0)+(i64)precision+(i64)width+15 );\n          if( bufpt==0 ){\n            setStrAccumError(pAccum, STRACCUM_NOMEM);\n            return;\n          }\n        }\n        zOut = bufpt;\n        nsd = 16 + flag_altform2*10;\n        flag_dp = (precision>0 ?1:0) | flag_alternateform | flag_altform2;\n        /* The sign in front of the number */\n        if( prefix ){\n          *(bufpt++) = prefix;\n        }\n        /* Digits prior to the decimal point */\n        if( e2<0 ){\n          *(bufpt++) = '0';\n        }else{\n          for(; e2>=0; e2--){\n            *(bufpt++) = et_getdigit(&realvalue,&nsd);\n          }\n        }\n        /* The decimal point */\n        if( flag_dp ){\n          *(bufpt++) = '.';\n        }\n        /* \"0\" digits after the decimal point but before the first\n        ** significant digit of the number */\n        for(e2++; e2<0; precision--, e2++){\n          assert( precision>0 );\n          *(bufpt++) = '0';\n        }\n        /* Significant digits after the decimal point */\n        while( (precision--)>0 ){\n          *(bufpt++) = et_getdigit(&realvalue,&nsd);\n        }\n        /* Remove trailing zeros and the \".\" if no digits follow the \".\" */\n        if( flag_rtz && flag_dp ){\n          while( bufpt[-1]=='0' ) *(--bufpt) = 0;\n          assert( bufpt>zOut );\n          if( bufpt[-1]=='.' ){\n            if( flag_altform2 ){\n              *(bufpt++) = '0';\n            }else{\n              *(--bufpt) = 0;\n            }\n          }\n        }\n        /* Add the \"eNNN\" suffix */\n        if( xtype==etEXP ){\n          *(bufpt++) = aDigits[infop->charset];\n          if( exp<0 ){\n            *(bufpt++) = '-'; exp = -exp;\n          }else{\n            *(bufpt++) = '+';\n          }\n          if( exp>=100 ){\n            *(bufpt++) = (char)((exp/100)+'0');        /* 100's digit */\n            exp %= 100;\n          }\n          *(bufpt++) = (char)(exp/10+'0');             /* 10's digit */\n          *(bufpt++) = (char)(exp%10+'0');             /* 1's digit */\n        }\n        *bufpt = 0;\n\n        /* The converted number is in buf[] and zero terminated. Output it.\n        ** Note that the number is in the usual order, not reversed as with\n        ** integer conversions. */\n        length = (int)(bufpt-zOut);\n        bufpt = zOut;\n\n        /* Special case:  Add leading zeros if the flag_zeropad flag is\n        ** set and we are not left justified */\n        if( flag_zeropad && !flag_leftjustify && length < width){\n          int i;\n          int nPad = width - length;\n          for(i=width; i>=nPad; i--){\n            bufpt[i] = bufpt[i-nPad];\n          }\n          i = prefix!=0;\n          while( nPad-- ) bufpt[i++] = '0';\n          length = width;\n        }\n#endif /* !defined(SQLITE_OMIT_FLOATING_POINT) */\n        break;\n      case etSIZE:\n        if( !bArgList ){\n          *(va_arg(ap,int*)) = pAccum->nChar;\n        }\n        length = width = 0;\n        break;\n      case etPERCENT:\n        buf[0] = '%';\n        bufpt = buf;\n        length = 1;\n        break;\n      case etCHARX:\n        if( bArgList ){\n          bufpt = getTextArg(pArgList);\n          length = 1;\n          if( bufpt ){\n            buf[0] = c = *(bufpt++);\n            if( (c&0xc0)==0xc0 ){\n              while( length<4 && (bufpt[0]&0xc0)==0x80 ){\n                buf[length++] = *(bufpt++);\n              }\n            }\n          }else{\n            buf[0] = 0;\n          }\n        }else{\n          unsigned int ch = va_arg(ap,unsigned int);\n          if( ch<0x00080 ){\n            buf[0] = ch & 0xff;\n            length = 1;\n          }else if( ch<0x00800 ){\n            buf[0] = 0xc0 + (u8)((ch>>6)&0x1f);\n            buf[1] = 0x80 + (u8)(ch & 0x3f);\n            length = 2;\n          }else if( ch<0x10000 ){\n            buf[0] = 0xe0 + (u8)((ch>>12)&0x0f);\n            buf[1] = 0x80 + (u8)((ch>>6) & 0x3f);\n            buf[2] = 0x80 + (u8)(ch & 0x3f);\n            length = 3;\n          }else{\n            buf[0] = 0xf0 + (u8)((ch>>18) & 0x07);\n            buf[1] = 0x80 + (u8)((ch>>12) & 0x3f);\n            buf[2] = 0x80 + (u8)((ch>>6) & 0x3f);\n            buf[3] = 0x80 + (u8)(ch & 0x3f);\n            length = 4;\n          }\n        }\n        if( precision>1 ){\n          width -= precision-1;\n          if( width>1 && !flag_leftjustify ){\n            sqlite3AppendChar(pAccum, width-1, ' ');\n            width = 0;\n          }\n          while( precision-- > 1 ){\n            sqlite3StrAccumAppend(pAccum, buf, length);\n          }\n        }\n        bufpt = buf;\n        flag_altform2 = 1;\n        goto adjust_width_for_utf8;\n      case etSTRING:\n      case etDYNSTRING:\n        if( bArgList ){\n          bufpt = getTextArg(pArgList);\n          xtype = etSTRING;\n        }else{\n          bufpt = va_arg(ap,char*);\n        }\n        if( bufpt==0 ){\n          bufpt = \"\";\n        }else if( xtype==etDYNSTRING ){\n          if( pAccum->nChar==0 && pAccum->mxAlloc && width==0 && precision<0 ){\n            /* Special optimization for sqlite3_mprintf(\"%z...\"):\n            ** Extend an existing memory allocation rather than creating\n            ** a new one. */\n            assert( (pAccum->printfFlags&SQLITE_PRINTF_MALLOCED)==0 );\n            pAccum->zText = bufpt;\n            pAccum->nAlloc = sqlite3DbMallocSize(pAccum->db, bufpt);\n            pAccum->nChar = 0x7fffffff & (int)strlen(bufpt);\n            pAccum->printfFlags |= SQLITE_PRINTF_MALLOCED;\n            length = 0;\n            break;\n          }\n          zExtra = bufpt;\n        }\n        if( precision>=0 ){\n          if( flag_altform2 ){\n            /* Set length to the number of bytes needed in order to display\n            ** precision characters */\n            unsigned char *z = (unsigned char*)bufpt;\n            while( precision-- > 0 && z[0] ){\n              SQLITE_SKIP_UTF8(z);\n            }\n            length = (int)(z - (unsigned char*)bufpt);\n          }else{\n            for(length=0; length<precision && bufpt[length]; length++){}\n          }\n        }else{\n          length = 0x7fffffff & (int)strlen(bufpt);\n        }\n      adjust_width_for_utf8:\n        if( flag_altform2 && width>0 ){\n          /* Adjust width to account for extra bytes in UTF-8 characters */\n          int ii = length - 1;\n          while( ii>=0 ) if( (bufpt[ii--] & 0xc0)==0x80 ) width++;\n        }\n        break;\n      case etSQLESCAPE:           /* %q: Escape ' characters */\n      case etSQLESCAPE2:          /* %Q: Escape ' and enclose in '...' */\n      case etSQLESCAPE3: {        /* %w: Escape \" characters */\n        int i, j, k, n, isnull;\n        int needQuote;\n        char ch;\n        char q = ((xtype==etSQLESCAPE3)?'\"':'\\'');   /* Quote character */\n        char *escarg;\n\n        if( bArgList ){\n          escarg = getTextArg(pArgList);\n        }else{\n          escarg = va_arg(ap,char*);\n        }\n        isnull = escarg==0;\n        if( isnull ) escarg = (xtype==etSQLESCAPE2 ? \"NULL\" : \"(NULL)\");\n        /* For %q, %Q, and %w, the precision is the number of byte (or\n        ** characters if the ! flags is present) to use from the input.\n        ** Because of the extra quoting characters inserted, the number\n        ** of output characters may be larger than the precision.\n        */\n        k = precision;\n        for(i=n=0; k!=0 && (ch=escarg[i])!=0; i++, k--){\n          if( ch==q )  n++;\n          if( flag_altform2 && (ch&0xc0)==0xc0 ){\n            while( (escarg[i+1]&0xc0)==0x80 ){ i++; }\n          }\n        }\n        needQuote = !isnull && xtype==etSQLESCAPE2;\n        n += i + 3;\n        if( n>etBUFSIZE ){\n          bufpt = zExtra = sqlite3Malloc( n );\n          if( bufpt==0 ){\n            setStrAccumError(pAccum, STRACCUM_NOMEM);\n            return;\n          }\n        }else{\n          bufpt = buf;\n        }\n        j = 0;\n        if( needQuote ) bufpt[j++] = q;\n        k = i;\n        for(i=0; i<k; i++){\n          bufpt[j++] = ch = escarg[i];\n          if( ch==q ) bufpt[j++] = ch;\n        }\n        if( needQuote ) bufpt[j++] = q;\n        bufpt[j] = 0;\n        length = j;\n        goto adjust_width_for_utf8;\n      }\n      case etTOKEN: {\n        Token *pToken;\n        if( (pAccum->printfFlags & SQLITE_PRINTF_INTERNAL)==0 ) return;\n        pToken = va_arg(ap, Token*);\n        assert( bArgList==0 );\n        if( pToken && pToken->n ){\n          sqlite3StrAccumAppend(pAccum, (const char*)pToken->z, pToken->n);\n        }\n        length = width = 0;\n        break;\n      }\n      case etSRCLIST: {\n        SrcList *pSrc;\n        int k;\n        struct SrcList_item *pItem;\n        if( (pAccum->printfFlags & SQLITE_PRINTF_INTERNAL)==0 ) return;\n        pSrc = va_arg(ap, SrcList*);\n        k = va_arg(ap, int);\n        pItem = &pSrc->a[k];\n        assert( bArgList==0 );\n        assert( k>=0 && k<pSrc->nSrc );\n        if( pItem->zDatabase ){\n          sqlite3StrAccumAppendAll(pAccum, pItem->zDatabase);\n          sqlite3StrAccumAppend(pAccum, \".\", 1);\n        }\n        sqlite3StrAccumAppendAll(pAccum, pItem->zName);\n        length = width = 0;\n        break;\n      }\n      default: {\n        assert( xtype==etINVALID );\n        return;\n      }\n    }/* End switch over the format type */\n    /*\n    ** The text of the conversion is pointed to by \"bufpt\" and is\n    ** \"length\" characters long.  The field width is \"width\".  Do\n    ** the output.  Both length and width are in bytes, not characters,\n    ** at this point.  If the \"!\" flag was present on string conversions\n    ** indicating that width and precision should be expressed in characters,\n    ** then the values have been translated prior to reaching this point.\n    */\n    width -= length;\n    if( width>0 ){\n      if( !flag_leftjustify ) sqlite3AppendChar(pAccum, width, ' ');\n      sqlite3StrAccumAppend(pAccum, bufpt, length);\n      if( flag_leftjustify ) sqlite3AppendChar(pAccum, width, ' ');\n    }else{\n      sqlite3StrAccumAppend(pAccum, bufpt, length);\n    }\n\n    if( zExtra ){\n      sqlite3DbFree(pAccum->db, zExtra);\n      zExtra = 0;\n    }\n  }/* End for loop over the format string */\n} /* End of function */\n\n/*\n** Enlarge the memory allocation on a StrAccum object so that it is\n** able to accept at least N more bytes of text.\n**\n** Return the number of bytes of text that StrAccum is able to accept\n** after the attempted enlargement.  The value returned might be zero.\n*/\nstatic int sqlite3StrAccumEnlarge(StrAccum *p, int N){\n  char *zNew;\n  assert( p->nChar+(i64)N >= p->nAlloc ); /* Only called if really needed */\n  if( p->accError ){\n    testcase(p->accError==STRACCUM_TOOBIG);\n    testcase(p->accError==STRACCUM_NOMEM);\n    return 0;\n  }\n  if( p->mxAlloc==0 ){\n    N = p->nAlloc - p->nChar - 1;\n    setStrAccumError(p, STRACCUM_TOOBIG);\n    return N;\n  }else{\n    char *zOld = isMalloced(p) ? p->zText : 0;\n    i64 szNew = p->nChar;\n    szNew += N + 1;\n    if( szNew+p->nChar<=p->mxAlloc ){\n      /* Force exponential buffer size growth as long as it does not overflow,\n      ** to avoid having to call this routine too often */\n      szNew += p->nChar;\n    }\n    if( szNew > p->mxAlloc ){\n      sqlite3StrAccumReset(p);\n      setStrAccumError(p, STRACCUM_TOOBIG);\n      return 0;\n    }else{\n      p->nAlloc = (int)szNew;\n    }\n    if( p->db ){\n      zNew = sqlite3DbRealloc(p->db, zOld, p->nAlloc);\n    }else{\n      zNew = sqlite3_realloc64(zOld, p->nAlloc);\n    }\n    if( zNew ){\n      assert( p->zText!=0 || p->nChar==0 );\n      if( !isMalloced(p) && p->nChar>0 ) memcpy(zNew, p->zText, p->nChar);\n      p->zText = zNew;\n      p->nAlloc = sqlite3DbMallocSize(p->db, zNew);\n      p->printfFlags |= SQLITE_PRINTF_MALLOCED;\n    }else{\n      sqlite3StrAccumReset(p);\n      setStrAccumError(p, STRACCUM_NOMEM);\n      return 0;\n    }\n  }\n  return N;\n}\n\n/*\n** Append N copies of character c to the given string buffer.\n*/\nSQLITE_PRIVATE void sqlite3AppendChar(StrAccum *p, int N, char c){\n  testcase( p->nChar + (i64)N > 0x7fffffff );\n  if( p->nChar+(i64)N >= p->nAlloc && (N = sqlite3StrAccumEnlarge(p, N))<=0 ){\n    return;\n  }\n  while( (N--)>0 ) p->zText[p->nChar++] = c;\n}\n\n/*\n** The StrAccum \"p\" is not large enough to accept N new bytes of z[].\n** So enlarge if first, then do the append.\n**\n** This is a helper routine to sqlite3StrAccumAppend() that does special-case\n** work (enlarging the buffer) using tail recursion, so that the\n** sqlite3StrAccumAppend() routine can use fast calling semantics.\n*/\nstatic void SQLITE_NOINLINE enlargeAndAppend(StrAccum *p, const char *z, int N){\n  N = sqlite3StrAccumEnlarge(p, N);\n  if( N>0 ){\n    memcpy(&p->zText[p->nChar], z, N);\n    p->nChar += N;\n  }\n}\n\n/*\n** Append N bytes of text from z to the StrAccum object.  Increase the\n** size of the memory allocation for StrAccum if necessary.\n*/\nSQLITE_PRIVATE void sqlite3StrAccumAppend(StrAccum *p, const char *z, int N){\n  assert( z!=0 || N==0 );\n  assert( p->zText!=0 || p->nChar==0 || p->accError );\n  assert( N>=0 );\n  assert( p->accError==0 || p->nAlloc==0 );\n  if( p->nChar+N >= p->nAlloc ){\n    enlargeAndAppend(p,z,N);\n  }else if( N ){\n    assert( p->zText );\n    p->nChar += N;\n    memcpy(&p->zText[p->nChar-N], z, N);\n  }\n}\n\n/*\n** Append the complete text of zero-terminated string z[] to the p string.\n*/\nSQLITE_PRIVATE void sqlite3StrAccumAppendAll(StrAccum *p, const char *z){\n  sqlite3StrAccumAppend(p, z, sqlite3Strlen30(z));\n}\n\n\n/*\n** Finish off a string by making sure it is zero-terminated.\n** Return a pointer to the resulting string.  Return a NULL\n** pointer if any kind of error was encountered.\n*/\nstatic SQLITE_NOINLINE char *strAccumFinishRealloc(StrAccum *p){\n  char *zText;\n  assert( p->mxAlloc>0 && !isMalloced(p) );\n  zText = sqlite3DbMallocRaw(p->db, p->nChar+1 );\n  if( zText ){\n    memcpy(zText, p->zText, p->nChar+1);\n    p->printfFlags |= SQLITE_PRINTF_MALLOCED;\n  }else{\n    setStrAccumError(p, STRACCUM_NOMEM);\n  }\n  p->zText = zText;\n  return zText;\n}\nSQLITE_PRIVATE char *sqlite3StrAccumFinish(StrAccum *p){\n  if( p->zText ){\n    p->zText[p->nChar] = 0;\n    if( p->mxAlloc>0 && !isMalloced(p) ){\n      return strAccumFinishRealloc(p);\n    }\n  }\n  return p->zText;\n}\n\n/*\n** Reset an StrAccum string.  Reclaim all malloced memory.\n*/\nSQLITE_PRIVATE void sqlite3StrAccumReset(StrAccum *p){\n  if( isMalloced(p) ){\n    sqlite3DbFree(p->db, p->zText);\n    p->printfFlags &= ~SQLITE_PRINTF_MALLOCED;\n  }\n  p->zText = 0;\n}\n\n/*\n** Initialize a string accumulator.\n**\n** p:     The accumulator to be initialized.\n** db:    Pointer to a database connection.  May be NULL.  Lookaside\n**        memory is used if not NULL. db->mallocFailed is set appropriately\n**        when not NULL.\n** zBase: An initial buffer.  May be NULL in which case the initial buffer\n**        is malloced.\n** n:     Size of zBase in bytes.  If total space requirements never exceed\n**        n then no memory allocations ever occur.\n** mx:    Maximum number of bytes to accumulate.  If mx==0 then no memory\n**        allocations will ever occur.\n*/\nSQLITE_PRIVATE void sqlite3StrAccumInit(StrAccum *p, sqlite3 *db, char *zBase, int n, int mx){\n  p->zText = zBase;\n  p->db = db;\n  p->nAlloc = n;\n  p->mxAlloc = mx;\n  p->nChar = 0;\n  p->accError = 0;\n  p->printfFlags = 0;\n}\n\n/*\n** Print into memory obtained from sqliteMalloc().  Use the internal\n** %-conversion extensions.\n*/\nSQLITE_PRIVATE char *sqlite3VMPrintf(sqlite3 *db, const char *zFormat, va_list ap){\n  char *z;\n  char zBase[SQLITE_PRINT_BUF_SIZE];\n  StrAccum acc;\n  assert( db!=0 );\n  sqlite3StrAccumInit(&acc, db, zBase, sizeof(zBase),\n                      db->aLimit[SQLITE_LIMIT_LENGTH]);\n  acc.printfFlags = SQLITE_PRINTF_INTERNAL;\n  sqlite3VXPrintf(&acc, zFormat, ap);\n  z = sqlite3StrAccumFinish(&acc);\n  if( acc.accError==STRACCUM_NOMEM ){\n    sqlite3OomFault(db);\n  }\n  return z;\n}\n\n/*\n** Print into memory obtained from sqliteMalloc().  Use the internal\n** %-conversion extensions.\n*/\nSQLITE_PRIVATE char *sqlite3MPrintf(sqlite3 *db, const char *zFormat, ...){\n  va_list ap;\n  char *z;\n  va_start(ap, zFormat);\n  z = sqlite3VMPrintf(db, zFormat, ap);\n  va_end(ap);\n  return z;\n}\n\n/*\n** Print into memory obtained from sqlite3_malloc().  Omit the internal\n** %-conversion extensions.\n*/\nSQLITE_API char *sqlite3_vmprintf(const char *zFormat, va_list ap){\n  char *z;\n  char zBase[SQLITE_PRINT_BUF_SIZE];\n  StrAccum acc;\n\n#ifdef SQLITE_ENABLE_API_ARMOR  \n  if( zFormat==0 ){\n    (void)SQLITE_MISUSE_BKPT;\n    return 0;\n  }\n#endif\n#ifndef SQLITE_OMIT_AUTOINIT\n  if( sqlite3_initialize() ) return 0;\n#endif\n  sqlite3StrAccumInit(&acc, 0, zBase, sizeof(zBase), SQLITE_MAX_LENGTH);\n  sqlite3VXPrintf(&acc, zFormat, ap);\n  z = sqlite3StrAccumFinish(&acc);\n  return z;\n}\n\n/*\n** Print into memory obtained from sqlite3_malloc()().  Omit the internal\n** %-conversion extensions.\n*/\nSQLITE_API char *sqlite3_mprintf(const char *zFormat, ...){\n  va_list ap;\n  char *z;\n#ifndef SQLITE_OMIT_AUTOINIT\n  if( sqlite3_initialize() ) return 0;\n#endif\n  va_start(ap, zFormat);\n  z = sqlite3_vmprintf(zFormat, ap);\n  va_end(ap);\n  return z;\n}\n\n/*\n** sqlite3_snprintf() works like snprintf() except that it ignores the\n** current locale settings.  This is important for SQLite because we\n** are not able to use a \",\" as the decimal point in place of \".\" as\n** specified by some locales.\n**\n** Oops:  The first two arguments of sqlite3_snprintf() are backwards\n** from the snprintf() standard.  Unfortunately, it is too late to change\n** this without breaking compatibility, so we just have to live with the\n** mistake.\n**\n** sqlite3_vsnprintf() is the varargs version.\n*/\nSQLITE_API char *sqlite3_vsnprintf(int n, char *zBuf, const char *zFormat, va_list ap){\n  StrAccum acc;\n  if( n<=0 ) return zBuf;\n#ifdef SQLITE_ENABLE_API_ARMOR\n  if( zBuf==0 || zFormat==0 ) {\n    (void)SQLITE_MISUSE_BKPT;\n    if( zBuf ) zBuf[0] = 0;\n    return zBuf;\n  }\n#endif\n  sqlite3StrAccumInit(&acc, 0, zBuf, n, 0);\n  sqlite3VXPrintf(&acc, zFormat, ap);\n  zBuf[acc.nChar] = 0;\n  return zBuf;\n}\nSQLITE_API char *sqlite3_snprintf(int n, char *zBuf, const char *zFormat, ...){\n  char *z;\n  va_list ap;\n  va_start(ap,zFormat);\n  z = sqlite3_vsnprintf(n, zBuf, zFormat, ap);\n  va_end(ap);\n  return z;\n}\n\n/*\n** This is the routine that actually formats the sqlite3_log() message.\n** We house it in a separate routine from sqlite3_log() to avoid using\n** stack space on small-stack systems when logging is disabled.\n**\n** sqlite3_log() must render into a static buffer.  It cannot dynamically\n** allocate memory because it might be called while the memory allocator\n** mutex is held.\n**\n** sqlite3VXPrintf() might ask for *temporary* memory allocations for\n** certain format characters (%q) or for very large precisions or widths.\n** Care must be taken that any sqlite3_log() calls that occur while the\n** memory mutex is held do not use these mechanisms.\n*/\nstatic void renderLogMsg(int iErrCode, const char *zFormat, va_list ap){\n  StrAccum acc;                          /* String accumulator */\n  char zMsg[SQLITE_PRINT_BUF_SIZE*3];    /* Complete log message */\n\n  sqlite3StrAccumInit(&acc, 0, zMsg, sizeof(zMsg), 0);\n  sqlite3VXPrintf(&acc, zFormat, ap);\n  sqlite3GlobalConfig.xLog(sqlite3GlobalConfig.pLogArg, iErrCode,\n                           sqlite3StrAccumFinish(&acc));\n}\n\n/*\n** Format and write a message to the log if logging is enabled.\n*/\nSQLITE_API void sqlite3_log(int iErrCode, const char *zFormat, ...){\n  va_list ap;                             /* Vararg list */\n  if( sqlite3GlobalConfig.xLog ){\n    va_start(ap, zFormat);\n    renderLogMsg(iErrCode, zFormat, ap);\n    va_end(ap);\n  }\n}\n\n#if defined(SQLITE_DEBUG) || defined(SQLITE_HAVE_OS_TRACE)\n/*\n** A version of printf() that understands %lld.  Used for debugging.\n** The printf() built into some versions of windows does not understand %lld\n** and segfaults if you give it a long long int.\n*/\nSQLITE_PRIVATE void sqlite3DebugPrintf(const char *zFormat, ...){\n  va_list ap;\n  StrAccum acc;\n  char zBuf[500];\n  sqlite3StrAccumInit(&acc, 0, zBuf, sizeof(zBuf), 0);\n  va_start(ap,zFormat);\n  sqlite3VXPrintf(&acc, zFormat, ap);\n  va_end(ap);\n  sqlite3StrAccumFinish(&acc);\n#ifdef SQLITE_OS_TRACE_PROC\n  {\n    extern void SQLITE_OS_TRACE_PROC(const char *zBuf, int nBuf);\n    SQLITE_OS_TRACE_PROC(zBuf, sizeof(zBuf));\n  }\n#else\n  fprintf(stdout,\"%s\", zBuf);\n  fflush(stdout);\n#endif\n}\n#endif\n\n\n/*\n** variable-argument wrapper around sqlite3VXPrintf().  The bFlags argument\n** can contain the bit SQLITE_PRINTF_INTERNAL enable internal formats.\n*/\nSQLITE_PRIVATE void sqlite3XPrintf(StrAccum *p, const char *zFormat, ...){\n  va_list ap;\n  va_start(ap,zFormat);\n  sqlite3VXPrintf(p, zFormat, ap);\n  va_end(ap);\n}\n\n/************** End of printf.c **********************************************/\n/************** Begin file treeview.c ****************************************/\n/*\n** 2015-06-08\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n*************************************************************************\n**\n** This file contains C code to implement the TreeView debugging routines.\n** These routines print a parse tree to standard output for debugging and\n** analysis. \n**\n** The interfaces in this file is only available when compiling\n** with SQLITE_DEBUG.\n*/\n/* #include \"sqliteInt.h\" */\n#ifdef SQLITE_DEBUG\n\n/*\n** Add a new subitem to the tree.  The moreToFollow flag indicates that this\n** is not the last item in the tree.\n*/\nstatic TreeView *sqlite3TreeViewPush(TreeView *p, u8 moreToFollow){\n  if( p==0 ){\n    p = sqlite3_malloc64( sizeof(*p) );\n    if( p==0 ) return 0;\n    memset(p, 0, sizeof(*p));\n  }else{\n    p->iLevel++;\n  }\n  assert( moreToFollow==0 || moreToFollow==1 );\n  if( p->iLevel<sizeof(p->bLine) ) p->bLine[p->iLevel] = moreToFollow;\n  return p;\n}\n\n/*\n** Finished with one layer of the tree\n*/\nstatic void sqlite3TreeViewPop(TreeView *p){\n  if( p==0 ) return;\n  p->iLevel--;\n  if( p->iLevel<0 ) sqlite3_free(p);\n}\n\n/*\n** Generate a single line of output for the tree, with a prefix that contains\n** all the appropriate tree lines\n*/\nstatic void sqlite3TreeViewLine(TreeView *p, const char *zFormat, ...){\n  va_list ap;\n  int i;\n  StrAccum acc;\n  char zBuf[500];\n  sqlite3StrAccumInit(&acc, 0, zBuf, sizeof(zBuf), 0);\n  if( p ){\n    for(i=0; i<p->iLevel && i<sizeof(p->bLine)-1; i++){\n      sqlite3StrAccumAppend(&acc, p->bLine[i] ? \"|   \" : \"    \", 4);\n    }\n    sqlite3StrAccumAppend(&acc, p->bLine[i] ? \"|-- \" : \"'-- \", 4);\n  }\n  va_start(ap, zFormat);\n  sqlite3VXPrintf(&acc, zFormat, ap);\n  va_end(ap);\n  assert( acc.nChar>0 );\n  if( zBuf[acc.nChar-1]!='\\n' ) sqlite3StrAccumAppend(&acc, \"\\n\", 1);\n  sqlite3StrAccumFinish(&acc);\n  fprintf(stdout,\"%s\", zBuf);\n  fflush(stdout);\n}\n\n/*\n** Shorthand for starting a new tree item that consists of a single label\n*/\nstatic void sqlite3TreeViewItem(TreeView *p, const char *zLabel,u8 moreFollows){\n  p = sqlite3TreeViewPush(p, moreFollows);\n  sqlite3TreeViewLine(p, \"%s\", zLabel);\n}\n\n/*\n** Generate a human-readable description of a WITH clause.\n*/\nSQLITE_PRIVATE void sqlite3TreeViewWith(TreeView *pView, const With *pWith, u8 moreToFollow){\n  int i;\n  if( pWith==0 ) return;\n  if( pWith->nCte==0 ) return;\n  if( pWith->pOuter ){\n    sqlite3TreeViewLine(pView, \"WITH (0x%p, pOuter=0x%p)\",pWith,pWith->pOuter);\n  }else{\n    sqlite3TreeViewLine(pView, \"WITH (0x%p)\", pWith);\n  }\n  if( pWith->nCte>0 ){\n    pView = sqlite3TreeViewPush(pView, 1);\n    for(i=0; i<pWith->nCte; i++){\n      StrAccum x;\n      char zLine[1000];\n      const struct Cte *pCte = &pWith->a[i];\n      sqlite3StrAccumInit(&x, 0, zLine, sizeof(zLine), 0);\n      sqlite3XPrintf(&x, \"%s\", pCte->zName);\n      if( pCte->pCols && pCte->pCols->nExpr>0 ){\n        char cSep = '(';\n        int j;\n        for(j=0; j<pCte->pCols->nExpr; j++){\n          sqlite3XPrintf(&x, \"%c%s\", cSep, pCte->pCols->a[j].zName);\n          cSep = ',';\n        }\n        sqlite3XPrintf(&x, \")\");\n      }\n      sqlite3XPrintf(&x, \" AS\");\n      sqlite3StrAccumFinish(&x);\n      sqlite3TreeViewItem(pView, zLine, i<pWith->nCte-1);\n      sqlite3TreeViewSelect(pView, pCte->pSelect, 0);\n      sqlite3TreeViewPop(pView);\n    }\n    sqlite3TreeViewPop(pView);\n  }\n}\n\n\n/*\n** Generate a human-readable description of a Select object.\n*/\nSQLITE_PRIVATE void sqlite3TreeViewSelect(TreeView *pView, const Select *p, u8 moreToFollow){\n  int n = 0;\n  int cnt = 0;\n  if( p==0 ){\n    sqlite3TreeViewLine(pView, \"nil-SELECT\");\n    return;\n  } \n  pView = sqlite3TreeViewPush(pView, moreToFollow);\n  if( p->pWith ){\n    sqlite3TreeViewWith(pView, p->pWith, 1);\n    cnt = 1;\n    sqlite3TreeViewPush(pView, 1);\n  }\n  do{\n    sqlite3TreeViewLine(pView, \"SELECT%s%s (0x%p) selFlags=0x%x nSelectRow=%d\",\n      ((p->selFlags & SF_Distinct) ? \" DISTINCT\" : \"\"),\n      ((p->selFlags & SF_Aggregate) ? \" agg_flag\" : \"\"), p, p->selFlags,\n      (int)p->nSelectRow\n    );\n    if( cnt++ ) sqlite3TreeViewPop(pView);\n    if( p->pPrior ){\n      n = 1000;\n    }else{\n      n = 0;\n      if( p->pSrc && p->pSrc->nSrc ) n++;\n      if( p->pWhere ) n++;\n      if( p->pGroupBy ) n++;\n      if( p->pHaving ) n++;\n      if( p->pOrderBy ) n++;\n      if( p->pLimit ) n++;\n    }\n    sqlite3TreeViewExprList(pView, p->pEList, (n--)>0, \"result-set\");\n    if( p->pSrc && p->pSrc->nSrc ){\n      int i;\n      pView = sqlite3TreeViewPush(pView, (n--)>0);\n      sqlite3TreeViewLine(pView, \"FROM\");\n      for(i=0; i<p->pSrc->nSrc; i++){\n        struct SrcList_item *pItem = &p->pSrc->a[i];\n        StrAccum x;\n        char zLine[100];\n        sqlite3StrAccumInit(&x, 0, zLine, sizeof(zLine), 0);\n        sqlite3XPrintf(&x, \"{%d,*}\", pItem->iCursor);\n        if( pItem->zDatabase ){\n          sqlite3XPrintf(&x, \" %s.%s\", pItem->zDatabase, pItem->zName);\n        }else if( pItem->zName ){\n          sqlite3XPrintf(&x, \" %s\", pItem->zName);\n        }\n        if( pItem->pTab ){\n          sqlite3XPrintf(&x, \" tabname=%Q\", pItem->pTab->zName);\n        }\n        if( pItem->zAlias ){\n          sqlite3XPrintf(&x, \" (AS %s)\", pItem->zAlias);\n        }\n        if( pItem->fg.jointype & JT_LEFT ){\n          sqlite3XPrintf(&x, \" LEFT-JOIN\");\n        }\n        sqlite3StrAccumFinish(&x);\n        sqlite3TreeViewItem(pView, zLine, i<p->pSrc->nSrc-1); \n        if( pItem->pSelect ){\n          sqlite3TreeViewSelect(pView, pItem->pSelect, 0);\n        }\n        if( pItem->fg.isTabFunc ){\n          sqlite3TreeViewExprList(pView, pItem->u1.pFuncArg, 0, \"func-args:\");\n        }\n        sqlite3TreeViewPop(pView);\n      }\n      sqlite3TreeViewPop(pView);\n    }\n    if( p->pWhere ){\n      sqlite3TreeViewItem(pView, \"WHERE\", (n--)>0);\n      sqlite3TreeViewExpr(pView, p->pWhere, 0);\n      sqlite3TreeViewPop(pView);\n    }\n    if( p->pGroupBy ){\n      sqlite3TreeViewExprList(pView, p->pGroupBy, (n--)>0, \"GROUPBY\");\n    }\n    if( p->pHaving ){\n      sqlite3TreeViewItem(pView, \"HAVING\", (n--)>0);\n      sqlite3TreeViewExpr(pView, p->pHaving, 0);\n      sqlite3TreeViewPop(pView);\n    }\n    if( p->pOrderBy ){\n      sqlite3TreeViewExprList(pView, p->pOrderBy, (n--)>0, \"ORDERBY\");\n    }\n    if( p->pLimit ){\n      sqlite3TreeViewItem(pView, \"LIMIT\", (n--)>0);\n      sqlite3TreeViewExpr(pView, p->pLimit->pLeft, p->pLimit->pRight!=0);\n      if( p->pLimit->pRight ){\n        sqlite3TreeViewItem(pView, \"OFFSET\", (n--)>0);\n        sqlite3TreeViewExpr(pView, p->pLimit->pRight, 0);\n        sqlite3TreeViewPop(pView);\n      }\n      sqlite3TreeViewPop(pView);\n    }\n    if( p->pPrior ){\n      const char *zOp = \"UNION\";\n      switch( p->op ){\n        case TK_ALL:         zOp = \"UNION ALL\";  break;\n        case TK_INTERSECT:   zOp = \"INTERSECT\";  break;\n        case TK_EXCEPT:      zOp = \"EXCEPT\";     break;\n      }\n      sqlite3TreeViewItem(pView, zOp, 1);\n    }\n    p = p->pPrior;\n  }while( p!=0 );\n  sqlite3TreeViewPop(pView);\n}\n\n/*\n** Generate a human-readable explanation of an expression tree.\n*/\nSQLITE_PRIVATE void sqlite3TreeViewExpr(TreeView *pView, const Expr *pExpr, u8 moreToFollow){\n  const char *zBinOp = 0;   /* Binary operator */\n  const char *zUniOp = 0;   /* Unary operator */\n  char zFlgs[60];\n  pView = sqlite3TreeViewPush(pView, moreToFollow);\n  if( pExpr==0 ){\n    sqlite3TreeViewLine(pView, \"nil\");\n    sqlite3TreeViewPop(pView);\n    return;\n  }\n  if( pExpr->flags ){\n    if( ExprHasProperty(pExpr, EP_FromJoin) ){\n      sqlite3_snprintf(sizeof(zFlgs),zFlgs,\"  flags=0x%x iRJT=%d\",\n                       pExpr->flags, pExpr->iRightJoinTable);\n    }else{\n      sqlite3_snprintf(sizeof(zFlgs),zFlgs,\"  flags=0x%x\",pExpr->flags);\n    }\n  }else{\n    zFlgs[0] = 0;\n  }\n  switch( pExpr->op ){\n    case TK_AGG_COLUMN: {\n      sqlite3TreeViewLine(pView, \"AGG{%d:%d}%s\",\n            pExpr->iTable, pExpr->iColumn, zFlgs);\n      break;\n    }\n    case TK_COLUMN: {\n      if( pExpr->iTable<0 ){\n        /* This only happens when coding check constraints */\n        sqlite3TreeViewLine(pView, \"COLUMN(%d)%s\", pExpr->iColumn, zFlgs);\n      }else{\n        sqlite3TreeViewLine(pView, \"{%d:%d}%s\",\n                             pExpr->iTable, pExpr->iColumn, zFlgs);\n      }\n      break;\n    }\n    case TK_INTEGER: {\n      if( pExpr->flags & EP_IntValue ){\n        sqlite3TreeViewLine(pView, \"%d\", pExpr->u.iValue);\n      }else{\n        sqlite3TreeViewLine(pView, \"%s\", pExpr->u.zToken);\n      }\n      break;\n    }\n#ifndef SQLITE_OMIT_FLOATING_POINT\n    case TK_FLOAT: {\n      sqlite3TreeViewLine(pView,\"%s\", pExpr->u.zToken);\n      break;\n    }\n#endif\n    case TK_STRING: {\n      sqlite3TreeViewLine(pView,\"%Q\", pExpr->u.zToken);\n      break;\n    }\n    case TK_NULL: {\n      sqlite3TreeViewLine(pView,\"NULL\");\n      break;\n    }\n    case TK_TRUEFALSE: {\n      sqlite3TreeViewLine(pView,\n         sqlite3ExprTruthValue(pExpr) ? \"TRUE\" : \"FALSE\");\n      break;\n    }\n#ifndef SQLITE_OMIT_BLOB_LITERAL\n    case TK_BLOB: {\n      sqlite3TreeViewLine(pView,\"%s\", pExpr->u.zToken);\n      break;\n    }\n#endif\n    case TK_VARIABLE: {\n      sqlite3TreeViewLine(pView,\"VARIABLE(%s,%d)\",\n                          pExpr->u.zToken, pExpr->iColumn);\n      break;\n    }\n    case TK_REGISTER: {\n      sqlite3TreeViewLine(pView,\"REGISTER(%d)\", pExpr->iTable);\n      break;\n    }\n    case TK_ID: {\n      sqlite3TreeViewLine(pView,\"ID \\\"%w\\\"\", pExpr->u.zToken);\n      break;\n    }\n#ifndef SQLITE_OMIT_CAST\n    case TK_CAST: {\n      /* Expressions of the form:   CAST(pLeft AS token) */\n      sqlite3TreeViewLine(pView,\"CAST %Q\", pExpr->u.zToken);\n      sqlite3TreeViewExpr(pView, pExpr->pLeft, 0);\n      break;\n    }\n#endif /* SQLITE_OMIT_CAST */\n    case TK_LT:      zBinOp = \"LT\";     break;\n    case TK_LE:      zBinOp = \"LE\";     break;\n    case TK_GT:      zBinOp = \"GT\";     break;\n    case TK_GE:      zBinOp = \"GE\";     break;\n    case TK_NE:      zBinOp = \"NE\";     break;\n    case TK_EQ:      zBinOp = \"EQ\";     break;\n    case TK_IS:      zBinOp = \"IS\";     break;\n    case TK_ISNOT:   zBinOp = \"ISNOT\";  break;\n    case TK_AND:     zBinOp = \"AND\";    break;\n    case TK_OR:      zBinOp = \"OR\";     break;\n    case TK_PLUS:    zBinOp = \"ADD\";    break;\n    case TK_STAR:    zBinOp = \"MUL\";    break;\n    case TK_MINUS:   zBinOp = \"SUB\";    break;\n    case TK_REM:     zBinOp = \"REM\";    break;\n    case TK_BITAND:  zBinOp = \"BITAND\"; break;\n    case TK_BITOR:   zBinOp = \"BITOR\";  break;\n    case TK_SLASH:   zBinOp = \"DIV\";    break;\n    case TK_LSHIFT:  zBinOp = \"LSHIFT\"; break;\n    case TK_RSHIFT:  zBinOp = \"RSHIFT\"; break;\n    case TK_CONCAT:  zBinOp = \"CONCAT\"; break;\n    case TK_DOT:     zBinOp = \"DOT\";    break;\n\n    case TK_UMINUS:  zUniOp = \"UMINUS\"; break;\n    case TK_UPLUS:   zUniOp = \"UPLUS\";  break;\n    case TK_BITNOT:  zUniOp = \"BITNOT\"; break;\n    case TK_NOT:     zUniOp = \"NOT\";    break;\n    case TK_ISNULL:  zUniOp = \"ISNULL\"; break;\n    case TK_NOTNULL: zUniOp = \"NOTNULL\"; break;\n\n    case TK_TRUTH: {\n      int x;\n      const char *azOp[] = {\n         \"IS-FALSE\", \"IS-TRUE\", \"IS-NOT-FALSE\", \"IS-NOT-TRUE\"\n      };\n      assert( pExpr->op2==TK_IS || pExpr->op2==TK_ISNOT );\n      assert( pExpr->pRight );\n      assert( pExpr->pRight->op==TK_TRUEFALSE );\n      x = (pExpr->op2==TK_ISNOT)*2 + sqlite3ExprTruthValue(pExpr->pRight);\n      zUniOp = azOp[x];\n      break;\n    }\n\n    case TK_SPAN: {\n      sqlite3TreeViewLine(pView, \"SPAN %Q\", pExpr->u.zToken);\n      sqlite3TreeViewExpr(pView, pExpr->pLeft, 0);\n      break;\n    }\n\n    case TK_COLLATE: {\n      sqlite3TreeViewLine(pView, \"COLLATE %Q\", pExpr->u.zToken);\n      sqlite3TreeViewExpr(pView, pExpr->pLeft, 0);\n      break;\n    }\n\n    case TK_AGG_FUNCTION:\n    case TK_FUNCTION: {\n      ExprList *pFarg;       /* List of function arguments */\n      if( ExprHasProperty(pExpr, EP_TokenOnly) ){\n        pFarg = 0;\n      }else{\n        pFarg = pExpr->x.pList;\n      }\n      if( pExpr->op==TK_AGG_FUNCTION ){\n        sqlite3TreeViewLine(pView, \"AGG_FUNCTION%d %Q\",\n                             pExpr->op2, pExpr->u.zToken);\n      }else{\n        sqlite3TreeViewLine(pView, \"FUNCTION %Q\", pExpr->u.zToken);\n      }\n      if( pFarg ){\n        sqlite3TreeViewExprList(pView, pFarg, 0, 0);\n      }\n      break;\n    }\n#ifndef SQLITE_OMIT_SUBQUERY\n    case TK_EXISTS: {\n      sqlite3TreeViewLine(pView, \"EXISTS-expr flags=0x%x\", pExpr->flags);\n      sqlite3TreeViewSelect(pView, pExpr->x.pSelect, 0);\n      break;\n    }\n    case TK_SELECT: {\n      sqlite3TreeViewLine(pView, \"SELECT-expr flags=0x%x\", pExpr->flags);\n      sqlite3TreeViewSelect(pView, pExpr->x.pSelect, 0);\n      break;\n    }\n    case TK_IN: {\n      sqlite3TreeViewLine(pView, \"IN flags=0x%x\", pExpr->flags);\n      sqlite3TreeViewExpr(pView, pExpr->pLeft, 1);\n      if( ExprHasProperty(pExpr, EP_xIsSelect) ){\n        sqlite3TreeViewSelect(pView, pExpr->x.pSelect, 0);\n      }else{\n        sqlite3TreeViewExprList(pView, pExpr->x.pList, 0, 0);\n      }\n      break;\n    }\n#endif /* SQLITE_OMIT_SUBQUERY */\n\n    /*\n    **    x BETWEEN y AND z\n    **\n    ** This is equivalent to\n    **\n    **    x>=y AND x<=z\n    **\n    ** X is stored in pExpr->pLeft.\n    ** Y is stored in pExpr->pList->a[0].pExpr.\n    ** Z is stored in pExpr->pList->a[1].pExpr.\n    */\n    case TK_BETWEEN: {\n      Expr *pX = pExpr->pLeft;\n      Expr *pY = pExpr->x.pList->a[0].pExpr;\n      Expr *pZ = pExpr->x.pList->a[1].pExpr;\n      sqlite3TreeViewLine(pView, \"BETWEEN\");\n      sqlite3TreeViewExpr(pView, pX, 1);\n      sqlite3TreeViewExpr(pView, pY, 1);\n      sqlite3TreeViewExpr(pView, pZ, 0);\n      break;\n    }\n    case TK_TRIGGER: {\n      /* If the opcode is TK_TRIGGER, then the expression is a reference\n      ** to a column in the new.* or old.* pseudo-tables available to\n      ** trigger programs. In this case Expr.iTable is set to 1 for the\n      ** new.* pseudo-table, or 0 for the old.* pseudo-table. Expr.iColumn\n      ** is set to the column of the pseudo-table to read, or to -1 to\n      ** read the rowid field.\n      */\n      sqlite3TreeViewLine(pView, \"%s(%d)\", \n          pExpr->iTable ? \"NEW\" : \"OLD\", pExpr->iColumn);\n      break;\n    }\n    case TK_CASE: {\n      sqlite3TreeViewLine(pView, \"CASE\");\n      sqlite3TreeViewExpr(pView, pExpr->pLeft, 1);\n      sqlite3TreeViewExprList(pView, pExpr->x.pList, 0, 0);\n      break;\n    }\n#ifndef SQLITE_OMIT_TRIGGER\n    case TK_RAISE: {\n      const char *zType = \"unk\";\n      switch( pExpr->affinity ){\n        case OE_Rollback:   zType = \"rollback\";  break;\n        case OE_Abort:      zType = \"abort\";     break;\n        case OE_Fail:       zType = \"fail\";      break;\n        case OE_Ignore:     zType = \"ignore\";    break;\n      }\n      sqlite3TreeViewLine(pView, \"RAISE %s(%Q)\", zType, pExpr->u.zToken);\n      break;\n    }\n#endif\n    case TK_MATCH: {\n      sqlite3TreeViewLine(pView, \"MATCH {%d:%d}%s\",\n                          pExpr->iTable, pExpr->iColumn, zFlgs);\n      sqlite3TreeViewExpr(pView, pExpr->pRight, 0);\n      break;\n    }\n    case TK_VECTOR: {\n      sqlite3TreeViewBareExprList(pView, pExpr->x.pList, \"VECTOR\");\n      break;\n    }\n    case TK_SELECT_COLUMN: {\n      sqlite3TreeViewLine(pView, \"SELECT-COLUMN %d\", pExpr->iColumn);\n      sqlite3TreeViewSelect(pView, pExpr->pLeft->x.pSelect, 0);\n      break;\n    }\n    case TK_IF_NULL_ROW: {\n      sqlite3TreeViewLine(pView, \"IF-NULL-ROW %d\", pExpr->iTable);\n      sqlite3TreeViewExpr(pView, pExpr->pLeft, 0);\n      break;\n    }\n    default: {\n      sqlite3TreeViewLine(pView, \"op=%d\", pExpr->op);\n      break;\n    }\n  }\n  if( zBinOp ){\n    sqlite3TreeViewLine(pView, \"%s%s\", zBinOp, zFlgs);\n    sqlite3TreeViewExpr(pView, pExpr->pLeft, 1);\n    sqlite3TreeViewExpr(pView, pExpr->pRight, 0);\n  }else if( zUniOp ){\n    sqlite3TreeViewLine(pView, \"%s%s\", zUniOp, zFlgs);\n    sqlite3TreeViewExpr(pView, pExpr->pLeft, 0);\n  }\n  sqlite3TreeViewPop(pView);\n}\n\n\n/*\n** Generate a human-readable explanation of an expression list.\n*/\nSQLITE_PRIVATE void sqlite3TreeViewBareExprList(\n  TreeView *pView,\n  const ExprList *pList,\n  const char *zLabel\n){\n  if( zLabel==0 || zLabel[0]==0 ) zLabel = \"LIST\";\n  if( pList==0 ){\n    sqlite3TreeViewLine(pView, \"%s (empty)\", zLabel);\n  }else{\n    int i;\n    sqlite3TreeViewLine(pView, \"%s\", zLabel);\n    for(i=0; i<pList->nExpr; i++){\n      int j = pList->a[i].u.x.iOrderByCol;\n      char *zName = pList->a[i].zName;\n      if( j || zName ){\n        sqlite3TreeViewPush(pView, 0);\n      }\n      if( zName ){\n        sqlite3TreeViewLine(pView, \"AS %s\", zName);\n      }\n      if( j ){\n        sqlite3TreeViewLine(pView, \"iOrderByCol=%d\", j);\n      }\n      sqlite3TreeViewExpr(pView, pList->a[i].pExpr, i<pList->nExpr-1);\n      if( j || zName ){\n        sqlite3TreeViewPop(pView);\n      }\n    }\n  }\n}\nSQLITE_PRIVATE void sqlite3TreeViewExprList(\n  TreeView *pView,\n  const ExprList *pList,\n  u8 moreToFollow,\n  const char *zLabel\n){\n  pView = sqlite3TreeViewPush(pView, moreToFollow);\n  sqlite3TreeViewBareExprList(pView, pList, zLabel);\n  sqlite3TreeViewPop(pView);\n}\n\n#endif /* SQLITE_DEBUG */\n\n/************** End of treeview.c ********************************************/\n/************** Begin file random.c ******************************************/\n/*\n** 2001 September 15\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n*************************************************************************\n** This file contains code to implement a pseudo-random number\n** generator (PRNG) for SQLite.\n**\n** Random numbers are used by some of the database backends in order\n** to generate random integer keys for tables or random filenames.\n*/\n/* #include \"sqliteInt.h\" */\n\n\n/* All threads share a single random number generator.\n** This structure is the current state of the generator.\n*/\nstatic SQLITE_WSD struct sqlite3PrngType {\n  unsigned char isInit;          /* True if initialized */\n  unsigned char i, j;            /* State variables */\n  unsigned char s[256];          /* State variables */\n} sqlite3Prng;\n\n/*\n** Return N random bytes.\n*/\nSQLITE_API void sqlite3_randomness(int N, void *pBuf){\n  unsigned char t;\n  unsigned char *zBuf = pBuf;\n\n  /* The \"wsdPrng\" macro will resolve to the pseudo-random number generator\n  ** state vector.  If writable static data is unsupported on the target,\n  ** we have to locate the state vector at run-time.  In the more common\n  ** case where writable static data is supported, wsdPrng can refer directly\n  ** to the \"sqlite3Prng\" state vector declared above.\n  */\n#ifdef SQLITE_OMIT_WSD\n  struct sqlite3PrngType *p = &GLOBAL(struct sqlite3PrngType, sqlite3Prng);\n# define wsdPrng p[0]\n#else\n# define wsdPrng sqlite3Prng\n#endif\n\n#if SQLITE_THREADSAFE\n  sqlite3_mutex *mutex;\n#endif\n\n#ifndef SQLITE_OMIT_AUTOINIT\n  if( sqlite3_initialize() ) return;\n#endif\n\n#if SQLITE_THREADSAFE\n  mutex = sqlite3MutexAlloc(SQLITE_MUTEX_STATIC_PRNG);\n#endif\n\n  sqlite3_mutex_enter(mutex);\n  if( N<=0 || pBuf==0 ){\n    wsdPrng.isInit = 0;\n    sqlite3_mutex_leave(mutex);\n    return;\n  }\n\n  /* Initialize the state of the random number generator once,\n  ** the first time this routine is called.  The seed value does\n  ** not need to contain a lot of randomness since we are not\n  ** trying to do secure encryption or anything like that...\n  **\n  ** Nothing in this file or anywhere else in SQLite does any kind of\n  ** encryption.  The RC4 algorithm is being used as a PRNG (pseudo-random\n  ** number generator) not as an encryption device.\n  */\n  if( !wsdPrng.isInit ){\n    int i;\n    char k[256];\n    wsdPrng.j = 0;\n    wsdPrng.i = 0;\n    sqlite3OsRandomness(sqlite3_vfs_find(0), 256, k);\n    for(i=0; i<256; i++){\n      wsdPrng.s[i] = (u8)i;\n    }\n    for(i=0; i<256; i++){\n      wsdPrng.j += wsdPrng.s[i] + k[i];\n      t = wsdPrng.s[wsdPrng.j];\n      wsdPrng.s[wsdPrng.j] = wsdPrng.s[i];\n      wsdPrng.s[i] = t;\n    }\n    wsdPrng.isInit = 1;\n  }\n\n  assert( N>0 );\n  do{\n    wsdPrng.i++;\n    t = wsdPrng.s[wsdPrng.i];\n    wsdPrng.j += t;\n    wsdPrng.s[wsdPrng.i] = wsdPrng.s[wsdPrng.j];\n    wsdPrng.s[wsdPrng.j] = t;\n    t += wsdPrng.s[wsdPrng.i];\n    *(zBuf++) = wsdPrng.s[t];\n  }while( --N );\n  sqlite3_mutex_leave(mutex);\n}\n\n#ifndef SQLITE_UNTESTABLE\n/*\n** For testing purposes, we sometimes want to preserve the state of\n** PRNG and restore the PRNG to its saved state at a later time, or\n** to reset the PRNG to its initial state.  These routines accomplish\n** those tasks.\n**\n** The sqlite3_test_control() interface calls these routines to\n** control the PRNG.\n*/\nstatic SQLITE_WSD struct sqlite3PrngType sqlite3SavedPrng;\nSQLITE_PRIVATE void sqlite3PrngSaveState(void){\n  memcpy(\n    &GLOBAL(struct sqlite3PrngType, sqlite3SavedPrng),\n    &GLOBAL(struct sqlite3PrngType, sqlite3Prng),\n    sizeof(sqlite3Prng)\n  );\n}\nSQLITE_PRIVATE void sqlite3PrngRestoreState(void){\n  memcpy(\n    &GLOBAL(struct sqlite3PrngType, sqlite3Prng),\n    &GLOBAL(struct sqlite3PrngType, sqlite3SavedPrng),\n    sizeof(sqlite3Prng)\n  );\n}\n#endif /* SQLITE_UNTESTABLE */\n\n/************** End of random.c **********************************************/\n/************** Begin file threads.c *****************************************/\n/*\n** 2012 July 21\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n******************************************************************************\n**\n** This file presents a simple cross-platform threading interface for\n** use internally by SQLite.\n**\n** A \"thread\" can be created using sqlite3ThreadCreate().  This thread\n** runs independently of its creator until it is joined using\n** sqlite3ThreadJoin(), at which point it terminates.\n**\n** Threads do not have to be real.  It could be that the work of the\n** \"thread\" is done by the main thread at either the sqlite3ThreadCreate()\n** or sqlite3ThreadJoin() call.  This is, in fact, what happens in\n** single threaded systems.  Nothing in SQLite requires multiple threads.\n** This interface exists so that applications that want to take advantage\n** of multiple cores can do so, while also allowing applications to stay\n** single-threaded if desired.\n*/\n/* #include \"sqliteInt.h\" */\n#if SQLITE_OS_WIN\n/* #  include \"os_win.h\" */\n#endif\n\n#if SQLITE_MAX_WORKER_THREADS>0\n\n/********************************* Unix Pthreads ****************************/\n#if SQLITE_OS_UNIX && defined(SQLITE_MUTEX_PTHREADS) && SQLITE_THREADSAFE>0\n\n#define SQLITE_THREADS_IMPLEMENTED 1  /* Prevent the single-thread code below */\n/* #include <pthread.h> */\n\n/* A running thread */\nstruct SQLiteThread {\n  pthread_t tid;                 /* Thread ID */\n  int done;                      /* Set to true when thread finishes */\n  void *pOut;                    /* Result returned by the thread */\n  void *(*xTask)(void*);         /* The thread routine */\n  void *pIn;                     /* Argument to the thread */\n};\n\n/* Create a new thread */\nSQLITE_PRIVATE int sqlite3ThreadCreate(\n  SQLiteThread **ppThread,  /* OUT: Write the thread object here */\n  void *(*xTask)(void*),    /* Routine to run in a separate thread */\n  void *pIn                 /* Argument passed into xTask() */\n){\n  SQLiteThread *p;\n  int rc;\n\n  assert( ppThread!=0 );\n  assert( xTask!=0 );\n  /* This routine is never used in single-threaded mode */\n  assert( sqlite3GlobalConfig.bCoreMutex!=0 );\n\n  *ppThread = 0;\n  p = sqlite3Malloc(sizeof(*p));\n  if( p==0 ) return SQLITE_NOMEM_BKPT;\n  memset(p, 0, sizeof(*p));\n  p->xTask = xTask;\n  p->pIn = pIn;\n  /* If the SQLITE_TESTCTRL_FAULT_INSTALL callback is registered to a \n  ** function that returns SQLITE_ERROR when passed the argument 200, that\n  ** forces worker threads to run sequentially and deterministically \n  ** for testing purposes. */\n  if( sqlite3FaultSim(200) ){\n    rc = 1;\n  }else{    \n    rc = pthread_create(&p->tid, 0, xTask, pIn);\n  }\n  if( rc ){\n    p->done = 1;\n    p->pOut = xTask(pIn);\n  }\n  *ppThread = p;\n  return SQLITE_OK;\n}\n\n/* Get the results of the thread */\nSQLITE_PRIVATE int sqlite3ThreadJoin(SQLiteThread *p, void **ppOut){\n  int rc;\n\n  assert( ppOut!=0 );\n  if( NEVER(p==0) ) return SQLITE_NOMEM_BKPT;\n  if( p->done ){\n    *ppOut = p->pOut;\n    rc = SQLITE_OK;\n  }else{\n    rc = pthread_join(p->tid, ppOut) ? SQLITE_ERROR : SQLITE_OK;\n  }\n  sqlite3_free(p);\n  return rc;\n}\n\n#endif /* SQLITE_OS_UNIX && defined(SQLITE_MUTEX_PTHREADS) */\n/******************************** End Unix Pthreads *************************/\n\n\n/********************************* Win32 Threads ****************************/\n#if SQLITE_OS_WIN_THREADS\n\n#define SQLITE_THREADS_IMPLEMENTED 1  /* Prevent the single-thread code below */\n#include <process.h>\n\n/* A running thread */\nstruct SQLiteThread {\n  void *tid;               /* The thread handle */\n  unsigned id;             /* The thread identifier */\n  void *(*xTask)(void*);   /* The routine to run as a thread */\n  void *pIn;               /* Argument to xTask */\n  void *pResult;           /* Result of xTask */\n};\n\n/* Thread procedure Win32 compatibility shim */\nstatic unsigned __stdcall sqlite3ThreadProc(\n  void *pArg  /* IN: Pointer to the SQLiteThread structure */\n){\n  SQLiteThread *p = (SQLiteThread *)pArg;\n\n  assert( p!=0 );\n#if 0\n  /*\n  ** This assert appears to trigger spuriously on certain\n  ** versions of Windows, possibly due to _beginthreadex()\n  ** and/or CreateThread() not fully setting their thread\n  ** ID parameter before starting the thread.\n  */\n  assert( p->id==GetCurrentThreadId() );\n#endif\n  assert( p->xTask!=0 );\n  p->pResult = p->xTask(p->pIn);\n\n  _endthreadex(0);\n  return 0; /* NOT REACHED */\n}\n\n/* Create a new thread */\nSQLITE_PRIVATE int sqlite3ThreadCreate(\n  SQLiteThread **ppThread,  /* OUT: Write the thread object here */\n  void *(*xTask)(void*),    /* Routine to run in a separate thread */\n  void *pIn                 /* Argument passed into xTask() */\n){\n  SQLiteThread *p;\n\n  assert( ppThread!=0 );\n  assert( xTask!=0 );\n  *ppThread = 0;\n  p = sqlite3Malloc(sizeof(*p));\n  if( p==0 ) return SQLITE_NOMEM_BKPT;\n  /* If the SQLITE_TESTCTRL_FAULT_INSTALL callback is registered to a \n  ** function that returns SQLITE_ERROR when passed the argument 200, that\n  ** forces worker threads to run sequentially and deterministically \n  ** (via the sqlite3FaultSim() term of the conditional) for testing\n  ** purposes. */\n  if( sqlite3GlobalConfig.bCoreMutex==0 || sqlite3FaultSim(200) ){\n    memset(p, 0, sizeof(*p));\n  }else{\n    p->xTask = xTask;\n    p->pIn = pIn;\n    p->tid = (void*)_beginthreadex(0, 0, sqlite3ThreadProc, p, 0, &p->id);\n    if( p->tid==0 ){\n      memset(p, 0, sizeof(*p));\n    }\n  }\n  if( p->xTask==0 ){\n    p->id = GetCurrentThreadId();\n    p->pResult = xTask(pIn);\n  }\n  *ppThread = p;\n  return SQLITE_OK;\n}\n\nSQLITE_PRIVATE DWORD sqlite3Win32Wait(HANDLE hObject); /* os_win.c */\n\n/* Get the results of the thread */\nSQLITE_PRIVATE int sqlite3ThreadJoin(SQLiteThread *p, void **ppOut){\n  DWORD rc;\n  BOOL bRc;\n\n  assert( ppOut!=0 );\n  if( NEVER(p==0) ) return SQLITE_NOMEM_BKPT;\n  if( p->xTask==0 ){\n    /* assert( p->id==GetCurrentThreadId() ); */\n    rc = WAIT_OBJECT_0;\n    assert( p->tid==0 );\n  }else{\n    assert( p->id!=0 && p->id!=GetCurrentThreadId() );\n    rc = sqlite3Win32Wait((HANDLE)p->tid);\n    assert( rc!=WAIT_IO_COMPLETION );\n    bRc = CloseHandle((HANDLE)p->tid);\n    assert( bRc );\n  }\n  if( rc==WAIT_OBJECT_0 ) *ppOut = p->pResult;\n  sqlite3_free(p);\n  return (rc==WAIT_OBJECT_0) ? SQLITE_OK : SQLITE_ERROR;\n}\n\n#endif /* SQLITE_OS_WIN_THREADS */\n/******************************** End Win32 Threads *************************/\n\n\n/********************************* Single-Threaded **************************/\n#ifndef SQLITE_THREADS_IMPLEMENTED\n/*\n** This implementation does not actually create a new thread.  It does the\n** work of the thread in the main thread, when either the thread is created\n** or when it is joined\n*/\n\n/* A running thread */\nstruct SQLiteThread {\n  void *(*xTask)(void*);   /* The routine to run as a thread */\n  void *pIn;               /* Argument to xTask */\n  void *pResult;           /* Result of xTask */\n};\n\n/* Create a new thread */\nSQLITE_PRIVATE int sqlite3ThreadCreate(\n  SQLiteThread **ppThread,  /* OUT: Write the thread object here */\n  void *(*xTask)(void*),    /* Routine to run in a separate thread */\n  void *pIn                 /* Argument passed into xTask() */\n){\n  SQLiteThread *p;\n\n  assert( ppThread!=0 );\n  assert( xTask!=0 );\n  *ppThread = 0;\n  p = sqlite3Malloc(sizeof(*p));\n  if( p==0 ) return SQLITE_NOMEM_BKPT;\n  if( (SQLITE_PTR_TO_INT(p)/17)&1 ){\n    p->xTask = xTask;\n    p->pIn = pIn;\n  }else{\n    p->xTask = 0;\n    p->pResult = xTask(pIn);\n  }\n  *ppThread = p;\n  return SQLITE_OK;\n}\n\n/* Get the results of the thread */\nSQLITE_PRIVATE int sqlite3ThreadJoin(SQLiteThread *p, void **ppOut){\n\n  assert( ppOut!=0 );\n  if( NEVER(p==0) ) return SQLITE_NOMEM_BKPT;\n  if( p->xTask ){\n    *ppOut = p->xTask(p->pIn);\n  }else{\n    *ppOut = p->pResult;\n  }\n  sqlite3_free(p);\n\n#if defined(SQLITE_TEST)\n  {\n    void *pTstAlloc = sqlite3Malloc(10);\n    if (!pTstAlloc) return SQLITE_NOMEM_BKPT;\n    sqlite3_free(pTstAlloc);\n  }\n#endif\n\n  return SQLITE_OK;\n}\n\n#endif /* !defined(SQLITE_THREADS_IMPLEMENTED) */\n/****************************** End Single-Threaded *************************/\n#endif /* SQLITE_MAX_WORKER_THREADS>0 */\n\n/************** End of threads.c *********************************************/\n/************** Begin file utf.c *********************************************/\n/*\n** 2004 April 13\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n*************************************************************************\n** This file contains routines used to translate between UTF-8, \n** UTF-16, UTF-16BE, and UTF-16LE.\n**\n** Notes on UTF-8:\n**\n**   Byte-0    Byte-1    Byte-2    Byte-3    Value\n**  0xxxxxxx                                 00000000 00000000 0xxxxxxx\n**  110yyyyy  10xxxxxx                       00000000 00000yyy yyxxxxxx\n**  1110zzzz  10yyyyyy  10xxxxxx             00000000 zzzzyyyy yyxxxxxx\n**  11110uuu  10uuzzzz  10yyyyyy  10xxxxxx   000uuuuu zzzzyyyy yyxxxxxx\n**\n**\n** Notes on UTF-16:  (with wwww+1==uuuuu)\n**\n**      Word-0               Word-1          Value\n**  110110ww wwzzzzyy   110111yy yyxxxxxx    000uuuuu zzzzyyyy yyxxxxxx\n**  zzzzyyyy yyxxxxxx                        00000000 zzzzyyyy yyxxxxxx\n**\n**\n** BOM or Byte Order Mark:\n**     0xff 0xfe   little-endian utf-16 follows\n**     0xfe 0xff   big-endian utf-16 follows\n**\n*/\n/* #include \"sqliteInt.h\" */\n/* #include <assert.h> */\n/* #include \"vdbeInt.h\" */\n\n#if !defined(SQLITE_AMALGAMATION) && SQLITE_BYTEORDER==0\n/*\n** The following constant value is used by the SQLITE_BIGENDIAN and\n** SQLITE_LITTLEENDIAN macros.\n*/\nSQLITE_PRIVATE const int sqlite3one = 1;\n#endif /* SQLITE_AMALGAMATION && SQLITE_BYTEORDER==0 */\n\n/*\n** This lookup table is used to help decode the first byte of\n** a multi-byte UTF8 character.\n*/\nstatic const unsigned char sqlite3Utf8Trans1[] = {\n  0x00, 0x01, 0x02, 0x03, 0x04, 0x05, 0x06, 0x07,\n  0x08, 0x09, 0x0a, 0x0b, 0x0c, 0x0d, 0x0e, 0x0f,\n  0x10, 0x11, 0x12, 0x13, 0x14, 0x15, 0x16, 0x17,\n  0x18, 0x19, 0x1a, 0x1b, 0x1c, 0x1d, 0x1e, 0x1f,\n  0x00, 0x01, 0x02, 0x03, 0x04, 0x05, 0x06, 0x07,\n  0x08, 0x09, 0x0a, 0x0b, 0x0c, 0x0d, 0x0e, 0x0f,\n  0x00, 0x01, 0x02, 0x03, 0x04, 0x05, 0x06, 0x07,\n  0x00, 0x01, 0x02, 0x03, 0x00, 0x01, 0x00, 0x00,\n};\n\n\n#define WRITE_UTF8(zOut, c) {                          \\\n  if( c<0x00080 ){                                     \\\n    *zOut++ = (u8)(c&0xFF);                            \\\n  }                                                    \\\n  else if( c<0x00800 ){                                \\\n    *zOut++ = 0xC0 + (u8)((c>>6)&0x1F);                \\\n    *zOut++ = 0x80 + (u8)(c & 0x3F);                   \\\n  }                                                    \\\n  else if( c<0x10000 ){                                \\\n    *zOut++ = 0xE0 + (u8)((c>>12)&0x0F);               \\\n    *zOut++ = 0x80 + (u8)((c>>6) & 0x3F);              \\\n    *zOut++ = 0x80 + (u8)(c & 0x3F);                   \\\n  }else{                                               \\\n    *zOut++ = 0xF0 + (u8)((c>>18) & 0x07);             \\\n    *zOut++ = 0x80 + (u8)((c>>12) & 0x3F);             \\\n    *zOut++ = 0x80 + (u8)((c>>6) & 0x3F);              \\\n    *zOut++ = 0x80 + (u8)(c & 0x3F);                   \\\n  }                                                    \\\n}\n\n#define WRITE_UTF16LE(zOut, c) {                                    \\\n  if( c<=0xFFFF ){                                                  \\\n    *zOut++ = (u8)(c&0x00FF);                                       \\\n    *zOut++ = (u8)((c>>8)&0x00FF);                                  \\\n  }else{                                                            \\\n    *zOut++ = (u8)(((c>>10)&0x003F) + (((c-0x10000)>>10)&0x00C0));  \\\n    *zOut++ = (u8)(0x00D8 + (((c-0x10000)>>18)&0x03));              \\\n    *zOut++ = (u8)(c&0x00FF);                                       \\\n    *zOut++ = (u8)(0x00DC + ((c>>8)&0x03));                         \\\n  }                                                                 \\\n}\n\n#define WRITE_UTF16BE(zOut, c) {                                    \\\n  if( c<=0xFFFF ){                                                  \\\n    *zOut++ = (u8)((c>>8)&0x00FF);                                  \\\n    *zOut++ = (u8)(c&0x00FF);                                       \\\n  }else{                                                            \\\n    *zOut++ = (u8)(0x00D8 + (((c-0x10000)>>18)&0x03));              \\\n    *zOut++ = (u8)(((c>>10)&0x003F) + (((c-0x10000)>>10)&0x00C0));  \\\n    *zOut++ = (u8)(0x00DC + ((c>>8)&0x03));                         \\\n    *zOut++ = (u8)(c&0x00FF);                                       \\\n  }                                                                 \\\n}\n\n#define READ_UTF16LE(zIn, TERM, c){                                   \\\n  c = (*zIn++);                                                       \\\n  c += ((*zIn++)<<8);                                                 \\\n  if( c>=0xD800 && c<0xE000 && TERM ){                                \\\n    int c2 = (*zIn++);                                                \\\n    c2 += ((*zIn++)<<8);                                              \\\n    c = (c2&0x03FF) + ((c&0x003F)<<10) + (((c&0x03C0)+0x0040)<<10);   \\\n  }                                                                   \\\n}\n\n#define READ_UTF16BE(zIn, TERM, c){                                   \\\n  c = ((*zIn++)<<8);                                                  \\\n  c += (*zIn++);                                                      \\\n  if( c>=0xD800 && c<0xE000 && TERM ){                                \\\n    int c2 = ((*zIn++)<<8);                                           \\\n    c2 += (*zIn++);                                                   \\\n    c = (c2&0x03FF) + ((c&0x003F)<<10) + (((c&0x03C0)+0x0040)<<10);   \\\n  }                                                                   \\\n}\n\n/*\n** Translate a single UTF-8 character.  Return the unicode value.\n**\n** During translation, assume that the byte that zTerm points\n** is a 0x00.\n**\n** Write a pointer to the next unread byte back into *pzNext.\n**\n** Notes On Invalid UTF-8:\n**\n**  *  This routine never allows a 7-bit character (0x00 through 0x7f) to\n**     be encoded as a multi-byte character.  Any multi-byte character that\n**     attempts to encode a value between 0x00 and 0x7f is rendered as 0xfffd.\n**\n**  *  This routine never allows a UTF16 surrogate value to be encoded.\n**     If a multi-byte character attempts to encode a value between\n**     0xd800 and 0xe000 then it is rendered as 0xfffd.\n**\n**  *  Bytes in the range of 0x80 through 0xbf which occur as the first\n**     byte of a character are interpreted as single-byte characters\n**     and rendered as themselves even though they are technically\n**     invalid characters.\n**\n**  *  This routine accepts over-length UTF8 encodings\n**     for unicode values 0x80 and greater.  It does not change over-length\n**     encodings to 0xfffd as some systems recommend.\n*/\n#define READ_UTF8(zIn, zTerm, c)                           \\\n  c = *(zIn++);                                            \\\n  if( c>=0xc0 ){                                           \\\n    c = sqlite3Utf8Trans1[c-0xc0];                         \\\n    while( zIn!=zTerm && (*zIn & 0xc0)==0x80 ){            \\\n      c = (c<<6) + (0x3f & *(zIn++));                      \\\n    }                                                      \\\n    if( c<0x80                                             \\\n        || (c&0xFFFFF800)==0xD800                          \\\n        || (c&0xFFFFFFFE)==0xFFFE ){  c = 0xFFFD; }        \\\n  }\nSQLITE_PRIVATE u32 sqlite3Utf8Read(\n  const unsigned char **pz    /* Pointer to string from which to read char */\n){\n  unsigned int c;\n\n  /* Same as READ_UTF8() above but without the zTerm parameter.\n  ** For this routine, we assume the UTF8 string is always zero-terminated.\n  */\n  c = *((*pz)++);\n  if( c>=0xc0 ){\n    c = sqlite3Utf8Trans1[c-0xc0];\n    while( (*(*pz) & 0xc0)==0x80 ){\n      c = (c<<6) + (0x3f & *((*pz)++));\n    }\n    if( c<0x80\n        || (c&0xFFFFF800)==0xD800\n        || (c&0xFFFFFFFE)==0xFFFE ){  c = 0xFFFD; }\n  }\n  return c;\n}\n\n\n\n\n/*\n** If the TRANSLATE_TRACE macro is defined, the value of each Mem is\n** printed on stderr on the way into and out of sqlite3VdbeMemTranslate().\n*/ \n/* #define TRANSLATE_TRACE 1 */\n\n#ifndef SQLITE_OMIT_UTF16\n/*\n** This routine transforms the internal text encoding used by pMem to\n** desiredEnc. It is an error if the string is already of the desired\n** encoding, or if *pMem does not contain a string value.\n*/\nSQLITE_PRIVATE SQLITE_NOINLINE int sqlite3VdbeMemTranslate(Mem *pMem, u8 desiredEnc){\n  int len;                    /* Maximum length of output string in bytes */\n  unsigned char *zOut;                  /* Output buffer */\n  unsigned char *zIn;                   /* Input iterator */\n  unsigned char *zTerm;                 /* End of input */\n  unsigned char *z;                     /* Output iterator */\n  unsigned int c;\n\n  assert( pMem->db==0 || sqlite3_mutex_held(pMem->db->mutex) );\n  assert( pMem->flags&MEM_Str );\n  assert( pMem->enc!=desiredEnc );\n  assert( pMem->enc!=0 );\n  assert( pMem->n>=0 );\n\n#if defined(TRANSLATE_TRACE) && defined(SQLITE_DEBUG)\n  {\n    char zBuf[100];\n    sqlite3VdbeMemPrettyPrint(pMem, zBuf);\n    fprintf(stderr, \"INPUT:  %s\\n\", zBuf);\n  }\n#endif\n\n  /* If the translation is between UTF-16 little and big endian, then \n  ** all that is required is to swap the byte order. This case is handled\n  ** differently from the others.\n  */\n  if( pMem->enc!=SQLITE_UTF8 && desiredEnc!=SQLITE_UTF8 ){\n    u8 temp;\n    int rc;\n    rc = sqlite3VdbeMemMakeWriteable(pMem);\n    if( rc!=SQLITE_OK ){\n      assert( rc==SQLITE_NOMEM );\n      return SQLITE_NOMEM_BKPT;\n    }\n    zIn = (u8*)pMem->z;\n    zTerm = &zIn[pMem->n&~1];\n    while( zIn<zTerm ){\n      temp = *zIn;\n      *zIn = *(zIn+1);\n      zIn++;\n      *zIn++ = temp;\n    }\n    pMem->enc = desiredEnc;\n    goto translate_out;\n  }\n\n  /* Set len to the maximum number of bytes required in the output buffer. */\n  if( desiredEnc==SQLITE_UTF8 ){\n    /* When converting from UTF-16, the maximum growth results from\n    ** translating a 2-byte character to a 4-byte UTF-8 character.\n    ** A single byte is required for the output string\n    ** nul-terminator.\n    */\n    pMem->n &= ~1;\n    len = pMem->n * 2 + 1;\n  }else{\n    /* When converting from UTF-8 to UTF-16 the maximum growth is caused\n    ** when a 1-byte UTF-8 character is translated into a 2-byte UTF-16\n    ** character. Two bytes are required in the output buffer for the\n    ** nul-terminator.\n    */\n    len = pMem->n * 2 + 2;\n  }\n\n  /* Set zIn to point at the start of the input buffer and zTerm to point 1\n  ** byte past the end.\n  **\n  ** Variable zOut is set to point at the output buffer, space obtained\n  ** from sqlite3_malloc().\n  */\n  zIn = (u8*)pMem->z;\n  zTerm = &zIn[pMem->n];\n  zOut = sqlite3DbMallocRaw(pMem->db, len);\n  if( !zOut ){\n    return SQLITE_NOMEM_BKPT;\n  }\n  z = zOut;\n\n  if( pMem->enc==SQLITE_UTF8 ){\n    if( desiredEnc==SQLITE_UTF16LE ){\n      /* UTF-8 -> UTF-16 Little-endian */\n      while( zIn<zTerm ){\n        READ_UTF8(zIn, zTerm, c);\n        WRITE_UTF16LE(z, c);\n      }\n    }else{\n      assert( desiredEnc==SQLITE_UTF16BE );\n      /* UTF-8 -> UTF-16 Big-endian */\n      while( zIn<zTerm ){\n        READ_UTF8(zIn, zTerm, c);\n        WRITE_UTF16BE(z, c);\n      }\n    }\n    pMem->n = (int)(z - zOut);\n    *z++ = 0;\n  }else{\n    assert( desiredEnc==SQLITE_UTF8 );\n    if( pMem->enc==SQLITE_UTF16LE ){\n      /* UTF-16 Little-endian -> UTF-8 */\n      while( zIn<zTerm ){\n        READ_UTF16LE(zIn, zIn<zTerm, c); \n        WRITE_UTF8(z, c);\n      }\n    }else{\n      /* UTF-16 Big-endian -> UTF-8 */\n      while( zIn<zTerm ){\n        READ_UTF16BE(zIn, zIn<zTerm, c); \n        WRITE_UTF8(z, c);\n      }\n    }\n    pMem->n = (int)(z - zOut);\n  }\n  *z = 0;\n  assert( (pMem->n+(desiredEnc==SQLITE_UTF8?1:2))<=len );\n\n  c = pMem->flags;\n  sqlite3VdbeMemRelease(pMem);\n  pMem->flags = MEM_Str|MEM_Term|(c&(MEM_AffMask|MEM_Subtype));\n  pMem->enc = desiredEnc;\n  pMem->z = (char*)zOut;\n  pMem->zMalloc = pMem->z;\n  pMem->szMalloc = sqlite3DbMallocSize(pMem->db, pMem->z);\n\ntranslate_out:\n#if defined(TRANSLATE_TRACE) && defined(SQLITE_DEBUG)\n  {\n    char zBuf[100];\n    sqlite3VdbeMemPrettyPrint(pMem, zBuf);\n    fprintf(stderr, \"OUTPUT: %s\\n\", zBuf);\n  }\n#endif\n  return SQLITE_OK;\n}\n#endif /* SQLITE_OMIT_UTF16 */\n\n#ifndef SQLITE_OMIT_UTF16\n/*\n** This routine checks for a byte-order mark at the beginning of the \n** UTF-16 string stored in *pMem. If one is present, it is removed and\n** the encoding of the Mem adjusted. This routine does not do any\n** byte-swapping, it just sets Mem.enc appropriately.\n**\n** The allocation (static, dynamic etc.) and encoding of the Mem may be\n** changed by this function.\n*/\nSQLITE_PRIVATE int sqlite3VdbeMemHandleBom(Mem *pMem){\n  int rc = SQLITE_OK;\n  u8 bom = 0;\n\n  assert( pMem->n>=0 );\n  if( pMem->n>1 ){\n    u8 b1 = *(u8 *)pMem->z;\n    u8 b2 = *(((u8 *)pMem->z) + 1);\n    if( b1==0xFE && b2==0xFF ){\n      bom = SQLITE_UTF16BE;\n    }\n    if( b1==0xFF && b2==0xFE ){\n      bom = SQLITE_UTF16LE;\n    }\n  }\n  \n  if( bom ){\n    rc = sqlite3VdbeMemMakeWriteable(pMem);\n    if( rc==SQLITE_OK ){\n      pMem->n -= 2;\n      memmove(pMem->z, &pMem->z[2], pMem->n);\n      pMem->z[pMem->n] = '\\0';\n      pMem->z[pMem->n+1] = '\\0';\n      pMem->flags |= MEM_Term;\n      pMem->enc = bom;\n    }\n  }\n  return rc;\n}\n#endif /* SQLITE_OMIT_UTF16 */\n\n/*\n** pZ is a UTF-8 encoded unicode string. If nByte is less than zero,\n** return the number of unicode characters in pZ up to (but not including)\n** the first 0x00 byte. If nByte is not less than zero, return the\n** number of unicode characters in the first nByte of pZ (or up to \n** the first 0x00, whichever comes first).\n*/\nSQLITE_PRIVATE int sqlite3Utf8CharLen(const char *zIn, int nByte){\n  int r = 0;\n  const u8 *z = (const u8*)zIn;\n  const u8 *zTerm;\n  if( nByte>=0 ){\n    zTerm = &z[nByte];\n  }else{\n    zTerm = (const u8*)(-1);\n  }\n  assert( z<=zTerm );\n  while( *z!=0 && z<zTerm ){\n    SQLITE_SKIP_UTF8(z);\n    r++;\n  }\n  return r;\n}\n\n/* This test function is not currently used by the automated test-suite. \n** Hence it is only available in debug builds.\n*/\n#if defined(SQLITE_TEST) && defined(SQLITE_DEBUG)\n/*\n** Translate UTF-8 to UTF-8.\n**\n** This has the effect of making sure that the string is well-formed\n** UTF-8.  Miscoded characters are removed.\n**\n** The translation is done in-place and aborted if the output\n** overruns the input.\n*/\nSQLITE_PRIVATE int sqlite3Utf8To8(unsigned char *zIn){\n  unsigned char *zOut = zIn;\n  unsigned char *zStart = zIn;\n  u32 c;\n\n  while( zIn[0] && zOut<=zIn ){\n    c = sqlite3Utf8Read((const u8**)&zIn);\n    if( c!=0xfffd ){\n      WRITE_UTF8(zOut, c);\n    }\n  }\n  *zOut = 0;\n  return (int)(zOut - zStart);\n}\n#endif\n\n#ifndef SQLITE_OMIT_UTF16\n/*\n** Convert a UTF-16 string in the native encoding into a UTF-8 string.\n** Memory to hold the UTF-8 string is obtained from sqlite3_malloc and must\n** be freed by the calling function.\n**\n** NULL is returned if there is an allocation error.\n*/\nSQLITE_PRIVATE char *sqlite3Utf16to8(sqlite3 *db, const void *z, int nByte, u8 enc){\n  Mem m;\n  memset(&m, 0, sizeof(m));\n  m.db = db;\n  sqlite3VdbeMemSetStr(&m, z, nByte, enc, SQLITE_STATIC);\n  sqlite3VdbeChangeEncoding(&m, SQLITE_UTF8);\n  if( db->mallocFailed ){\n    sqlite3VdbeMemRelease(&m);\n    m.z = 0;\n  }\n  assert( (m.flags & MEM_Term)!=0 || db->mallocFailed );\n  assert( (m.flags & MEM_Str)!=0 || db->mallocFailed );\n  assert( m.z || db->mallocFailed );\n  return m.z;\n}\n\n/*\n** zIn is a UTF-16 encoded unicode string at least nChar characters long.\n** Return the number of bytes in the first nChar unicode characters\n** in pZ.  nChar must be non-negative.\n*/\nSQLITE_PRIVATE int sqlite3Utf16ByteLen(const void *zIn, int nChar){\n  int c;\n  unsigned char const *z = zIn;\n  int n = 0;\n  \n  if( SQLITE_UTF16NATIVE==SQLITE_UTF16BE ){\n    while( n<nChar ){\n      READ_UTF16BE(z, 1, c);\n      n++;\n    }\n  }else{\n    while( n<nChar ){\n      READ_UTF16LE(z, 1, c);\n      n++;\n    }\n  }\n  return (int)(z-(unsigned char const *)zIn);\n}\n\n#if defined(SQLITE_TEST)\n/*\n** This routine is called from the TCL test function \"translate_selftest\".\n** It checks that the primitives for serializing and deserializing\n** characters in each encoding are inverses of each other.\n*/\nSQLITE_PRIVATE void sqlite3UtfSelfTest(void){\n  unsigned int i, t;\n  unsigned char zBuf[20];\n  unsigned char *z;\n  int n;\n  unsigned int c;\n\n  for(i=0; i<0x00110000; i++){\n    z = zBuf;\n    WRITE_UTF8(z, i);\n    n = (int)(z-zBuf);\n    assert( n>0 && n<=4 );\n    z[0] = 0;\n    z = zBuf;\n    c = sqlite3Utf8Read((const u8**)&z);\n    t = i;\n    if( i>=0xD800 && i<=0xDFFF ) t = 0xFFFD;\n    if( (i&0xFFFFFFFE)==0xFFFE ) t = 0xFFFD;\n    assert( c==t );\n    assert( (z-zBuf)==n );\n  }\n  for(i=0; i<0x00110000; i++){\n    if( i>=0xD800 && i<0xE000 ) continue;\n    z = zBuf;\n    WRITE_UTF16LE(z, i);\n    n = (int)(z-zBuf);\n    assert( n>0 && n<=4 );\n    z[0] = 0;\n    z = zBuf;\n    READ_UTF16LE(z, 1, c);\n    assert( c==i );\n    assert( (z-zBuf)==n );\n  }\n  for(i=0; i<0x00110000; i++){\n    if( i>=0xD800 && i<0xE000 ) continue;\n    z = zBuf;\n    WRITE_UTF16BE(z, i);\n    n = (int)(z-zBuf);\n    assert( n>0 && n<=4 );\n    z[0] = 0;\n    z = zBuf;\n    READ_UTF16BE(z, 1, c);\n    assert( c==i );\n    assert( (z-zBuf)==n );\n  }\n}\n#endif /* SQLITE_TEST */\n#endif /* SQLITE_OMIT_UTF16 */\n\n/************** End of utf.c *************************************************/\n/************** Begin file util.c ********************************************/\n/*\n** 2001 September 15\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n*************************************************************************\n** Utility functions used throughout sqlite.\n**\n** This file contains functions for allocating memory, comparing\n** strings, and stuff like that.\n**\n*/\n/* #include \"sqliteInt.h\" */\n/* #include <stdarg.h> */\n#if HAVE_ISNAN || SQLITE_HAVE_ISNAN\n# include <math.h>\n#endif\n\n/*\n** Routine needed to support the testcase() macro.\n*/\n#ifdef SQLITE_COVERAGE_TEST\nSQLITE_PRIVATE void sqlite3Coverage(int x){\n  static unsigned dummy = 0;\n  dummy += (unsigned)x;\n}\n#endif\n\n/*\n** Give a callback to the test harness that can be used to simulate faults\n** in places where it is difficult or expensive to do so purely by means\n** of inputs.\n**\n** The intent of the integer argument is to let the fault simulator know\n** which of multiple sqlite3FaultSim() calls has been hit.\n**\n** Return whatever integer value the test callback returns, or return\n** SQLITE_OK if no test callback is installed.\n*/\n#ifndef SQLITE_UNTESTABLE\nSQLITE_PRIVATE int sqlite3FaultSim(int iTest){\n  int (*xCallback)(int) = sqlite3GlobalConfig.xTestCallback;\n  return xCallback ? xCallback(iTest) : SQLITE_OK;\n}\n#endif\n\n#ifndef SQLITE_OMIT_FLOATING_POINT\n/*\n** Return true if the floating point value is Not a Number (NaN).\n**\n** Use the math library isnan() function if compiled with SQLITE_HAVE_ISNAN.\n** Otherwise, we have our own implementation that works on most systems.\n*/\nSQLITE_PRIVATE int sqlite3IsNaN(double x){\n  int rc;   /* The value return */\n#if !SQLITE_HAVE_ISNAN && !HAVE_ISNAN\n  /*\n  ** Systems that support the isnan() library function should probably\n  ** make use of it by compiling with -DSQLITE_HAVE_ISNAN.  But we have\n  ** found that many systems do not have a working isnan() function so\n  ** this implementation is provided as an alternative.\n  **\n  ** This NaN test sometimes fails if compiled on GCC with -ffast-math.\n  ** On the other hand, the use of -ffast-math comes with the following\n  ** warning:\n  **\n  **      This option [-ffast-math] should never be turned on by any\n  **      -O option since it can result in incorrect output for programs\n  **      which depend on an exact implementation of IEEE or ISO \n  **      rules/specifications for math functions.\n  **\n  ** Under MSVC, this NaN test may fail if compiled with a floating-\n  ** point precision mode other than /fp:precise.  From the MSDN \n  ** documentation:\n  **\n  **      The compiler [with /fp:precise] will properly handle comparisons \n  **      involving NaN. For example, x != x evaluates to true if x is NaN \n  **      ...\n  */\n#ifdef __FAST_MATH__\n# error SQLite will not work correctly with the -ffast-math option of GCC.\n#endif\n  volatile double y = x;\n  volatile double z = y;\n  rc = (y!=z);\n#else  /* if HAVE_ISNAN */\n  rc = isnan(x);\n#endif /* HAVE_ISNAN */\n  testcase( rc );\n  return rc;\n}\n#endif /* SQLITE_OMIT_FLOATING_POINT */\n\n/*\n** Compute a string length that is limited to what can be stored in\n** lower 30 bits of a 32-bit signed integer.\n**\n** The value returned will never be negative.  Nor will it ever be greater\n** than the actual length of the string.  For very long strings (greater\n** than 1GiB) the value returned might be less than the true string length.\n*/\nSQLITE_PRIVATE int sqlite3Strlen30(const char *z){\n  if( z==0 ) return 0;\n  return 0x3fffffff & (int)strlen(z);\n}\n\n/*\n** Return the declared type of a column.  Or return zDflt if the column \n** has no declared type.\n**\n** The column type is an extra string stored after the zero-terminator on\n** the column name if and only if the COLFLAG_HASTYPE flag is set.\n*/\nSQLITE_PRIVATE char *sqlite3ColumnType(Column *pCol, char *zDflt){\n  if( (pCol->colFlags & COLFLAG_HASTYPE)==0 ) return zDflt;\n  return pCol->zName + strlen(pCol->zName) + 1;\n}\n\n/*\n** Helper function for sqlite3Error() - called rarely.  Broken out into\n** a separate routine to avoid unnecessary register saves on entry to\n** sqlite3Error().\n*/\nstatic SQLITE_NOINLINE void  sqlite3ErrorFinish(sqlite3 *db, int err_code){\n  if( db->pErr ) sqlite3ValueSetNull(db->pErr);\n  sqlite3SystemError(db, err_code);\n}\n\n/*\n** Set the current error code to err_code and clear any prior error message.\n** Also set iSysErrno (by calling sqlite3System) if the err_code indicates\n** that would be appropriate.\n*/\nSQLITE_PRIVATE void sqlite3Error(sqlite3 *db, int err_code){\n  assert( db!=0 );\n  db->errCode = err_code;\n  if( err_code || db->pErr ) sqlite3ErrorFinish(db, err_code);\n}\n\n/*\n** Load the sqlite3.iSysErrno field if that is an appropriate thing\n** to do based on the SQLite error code in rc.\n*/\nSQLITE_PRIVATE void sqlite3SystemError(sqlite3 *db, int rc){\n  if( rc==SQLITE_IOERR_NOMEM ) return;\n  rc &= 0xff;\n  if( rc==SQLITE_CANTOPEN || rc==SQLITE_IOERR ){\n    db->iSysErrno = sqlite3OsGetLastError(db->pVfs);\n  }\n}\n\n/*\n** Set the most recent error code and error string for the sqlite\n** handle \"db\". The error code is set to \"err_code\".\n**\n** If it is not NULL, string zFormat specifies the format of the\n** error string in the style of the printf functions: The following\n** format characters are allowed:\n**\n**      %s      Insert a string\n**      %z      A string that should be freed after use\n**      %d      Insert an integer\n**      %T      Insert a token\n**      %S      Insert the first element of a SrcList\n**\n** zFormat and any string tokens that follow it are assumed to be\n** encoded in UTF-8.\n**\n** To clear the most recent error for sqlite handle \"db\", sqlite3Error\n** should be called with err_code set to SQLITE_OK and zFormat set\n** to NULL.\n*/\nSQLITE_PRIVATE void sqlite3ErrorWithMsg(sqlite3 *db, int err_code, const char *zFormat, ...){\n  assert( db!=0 );\n  db->errCode = err_code;\n  sqlite3SystemError(db, err_code);\n  if( zFormat==0 ){\n    sqlite3Error(db, err_code);\n  }else if( db->pErr || (db->pErr = sqlite3ValueNew(db))!=0 ){\n    char *z;\n    va_list ap;\n    va_start(ap, zFormat);\n    z = sqlite3VMPrintf(db, zFormat, ap);\n    va_end(ap);\n    sqlite3ValueSetStr(db->pErr, -1, z, SQLITE_UTF8, SQLITE_DYNAMIC);\n  }\n}\n\n/*\n** Add an error message to pParse->zErrMsg and increment pParse->nErr.\n** The following formatting characters are allowed:\n**\n**      %s      Insert a string\n**      %z      A string that should be freed after use\n**      %d      Insert an integer\n**      %T      Insert a token\n**      %S      Insert the first element of a SrcList\n**\n** This function should be used to report any error that occurs while\n** compiling an SQL statement (i.e. within sqlite3_prepare()). The\n** last thing the sqlite3_prepare() function does is copy the error\n** stored by this function into the database handle using sqlite3Error().\n** Functions sqlite3Error() or sqlite3ErrorWithMsg() should be used\n** during statement execution (sqlite3_step() etc.).\n*/\nSQLITE_PRIVATE void sqlite3ErrorMsg(Parse *pParse, const char *zFormat, ...){\n  char *zMsg;\n  va_list ap;\n  sqlite3 *db = pParse->db;\n  va_start(ap, zFormat);\n  zMsg = sqlite3VMPrintf(db, zFormat, ap);\n  va_end(ap);\n  if( db->suppressErr ){\n    sqlite3DbFree(db, zMsg);\n  }else{\n    pParse->nErr++;\n    sqlite3DbFree(db, pParse->zErrMsg);\n    pParse->zErrMsg = zMsg;\n    pParse->rc = SQLITE_ERROR;\n  }\n}\n\n/*\n** Convert an SQL-style quoted string into a normal string by removing\n** the quote characters.  The conversion is done in-place.  If the\n** input does not begin with a quote character, then this routine\n** is a no-op.\n**\n** The input string must be zero-terminated.  A new zero-terminator\n** is added to the dequoted string.\n**\n** The return value is -1 if no dequoting occurs or the length of the\n** dequoted string, exclusive of the zero terminator, if dequoting does\n** occur.\n**\n** 2002-Feb-14: This routine is extended to remove MS-Access style\n** brackets from around identifiers.  For example:  \"[a-b-c]\" becomes\n** \"a-b-c\".\n*/\nSQLITE_PRIVATE void sqlite3Dequote(char *z){\n  char quote;\n  int i, j;\n  if( z==0 ) return;\n  quote = z[0];\n  if( !sqlite3Isquote(quote) ) return;\n  if( quote=='[' ) quote = ']';\n  for(i=1, j=0;; i++){\n    assert( z[i] );\n    if( z[i]==quote ){\n      if( z[i+1]==quote ){\n        z[j++] = quote;\n        i++;\n      }else{\n        break;\n      }\n    }else{\n      z[j++] = z[i];\n    }\n  }\n  z[j] = 0;\n}\n\n/*\n** Generate a Token object from a string\n*/\nSQLITE_PRIVATE void sqlite3TokenInit(Token *p, char *z){\n  p->z = z;\n  p->n = sqlite3Strlen30(z);\n}\n\n/* Convenient short-hand */\n#define UpperToLower sqlite3UpperToLower\n\n/*\n** Some systems have stricmp().  Others have strcasecmp().  Because\n** there is no consistency, we will define our own.\n**\n** IMPLEMENTATION-OF: R-30243-02494 The sqlite3_stricmp() and\n** sqlite3_strnicmp() APIs allow applications and extensions to compare\n** the contents of two buffers containing UTF-8 strings in a\n** case-independent fashion, using the same definition of \"case\n** independence\" that SQLite uses internally when comparing identifiers.\n*/\nSQLITE_API int sqlite3_stricmp(const char *zLeft, const char *zRight){\n  if( zLeft==0 ){\n    return zRight ? -1 : 0;\n  }else if( zRight==0 ){\n    return 1;\n  }\n  return sqlite3StrICmp(zLeft, zRight);\n}\nSQLITE_PRIVATE int sqlite3StrICmp(const char *zLeft, const char *zRight){\n  unsigned char *a, *b;\n  int c;\n  a = (unsigned char *)zLeft;\n  b = (unsigned char *)zRight;\n  for(;;){\n    c = (int)UpperToLower[*a] - (int)UpperToLower[*b];\n    if( c || *a==0 ) break;\n    a++;\n    b++;\n  }\n  return c;\n}\nSQLITE_API int sqlite3_strnicmp(const char *zLeft, const char *zRight, int N){\n  register unsigned char *a, *b;\n  if( zLeft==0 ){\n    return zRight ? -1 : 0;\n  }else if( zRight==0 ){\n    return 1;\n  }\n  a = (unsigned char *)zLeft;\n  b = (unsigned char *)zRight;\n  while( N-- > 0 && *a!=0 && UpperToLower[*a]==UpperToLower[*b]){ a++; b++; }\n  return N<0 ? 0 : UpperToLower[*a] - UpperToLower[*b];\n}\n\n/*\n** Compute 10 to the E-th power.  Examples:  E==1 results in 10.\n** E==2 results in 100.  E==50 results in 1.0e50.\n**\n** This routine only works for values of E between 1 and 341.\n*/\nstatic LONGDOUBLE_TYPE sqlite3Pow10(int E){\n#if defined(_MSC_VER)\n  static const LONGDOUBLE_TYPE x[] = {\n    1.0e+001,\n    1.0e+002,\n    1.0e+004,\n    1.0e+008,\n    1.0e+016,\n    1.0e+032,\n    1.0e+064,\n    1.0e+128,\n    1.0e+256\n  };\n  LONGDOUBLE_TYPE r = 1.0;\n  int i;\n  assert( E>=0 && E<=307 );\n  for(i=0; E!=0; i++, E >>=1){\n    if( E & 1 ) r *= x[i];\n  }\n  return r;\n#else\n  LONGDOUBLE_TYPE x = 10.0;\n  LONGDOUBLE_TYPE r = 1.0;\n  while(1){\n    if( E & 1 ) r *= x;\n    E >>= 1;\n    if( E==0 ) break;\n    x *= x;\n  }\n  return r; \n#endif\n}\n\n/*\n** The string z[] is an text representation of a real number.\n** Convert this string to a double and write it into *pResult.\n**\n** The string z[] is length bytes in length (bytes, not characters) and\n** uses the encoding enc.  The string is not necessarily zero-terminated.\n**\n** Return TRUE if the result is a valid real number (or integer) and FALSE\n** if the string is empty or contains extraneous text.  Valid numbers\n** are in one of these formats:\n**\n**    [+-]digits[E[+-]digits]\n**    [+-]digits.[digits][E[+-]digits]\n**    [+-].digits[E[+-]digits]\n**\n** Leading and trailing whitespace is ignored for the purpose of determining\n** validity.\n**\n** If some prefix of the input string is a valid number, this routine\n** returns FALSE but it still converts the prefix and writes the result\n** into *pResult.\n*/\nSQLITE_PRIVATE int sqlite3AtoF(const char *z, double *pResult, int length, u8 enc){\n#ifndef SQLITE_OMIT_FLOATING_POINT\n  int incr;\n  const char *zEnd = z + length;\n  /* sign * significand * (10 ^ (esign * exponent)) */\n  int sign = 1;    /* sign of significand */\n  i64 s = 0;       /* significand */\n  int d = 0;       /* adjust exponent for shifting decimal point */\n  int esign = 1;   /* sign of exponent */\n  int e = 0;       /* exponent */\n  int eValid = 1;  /* True exponent is either not used or is well-formed */\n  double result;\n  int nDigits = 0;\n  int nonNum = 0;  /* True if input contains UTF16 with high byte non-zero */\n\n  assert( enc==SQLITE_UTF8 || enc==SQLITE_UTF16LE || enc==SQLITE_UTF16BE );\n  *pResult = 0.0;   /* Default return value, in case of an error */\n\n  if( enc==SQLITE_UTF8 ){\n    incr = 1;\n  }else{\n    int i;\n    incr = 2;\n    assert( SQLITE_UTF16LE==2 && SQLITE_UTF16BE==3 );\n    for(i=3-enc; i<length && z[i]==0; i+=2){}\n    nonNum = i<length;\n    zEnd = &z[i^1];\n    z += (enc&1);\n  }\n\n  /* skip leading spaces */\n  while( z<zEnd && sqlite3Isspace(*z) ) z+=incr;\n  if( z>=zEnd ) return 0;\n\n  /* get sign of significand */\n  if( *z=='-' ){\n    sign = -1;\n    z+=incr;\n  }else if( *z=='+' ){\n    z+=incr;\n  }\n\n  /* copy max significant digits to significand */\n  while( z<zEnd && sqlite3Isdigit(*z) && s<((LARGEST_INT64-9)/10) ){\n    s = s*10 + (*z - '0');\n    z+=incr; nDigits++;\n  }\n\n  /* skip non-significant significand digits\n  ** (increase exponent by d to shift decimal left) */\n  while( z<zEnd && sqlite3Isdigit(*z) ){ z+=incr; nDigits++; d++; }\n  if( z>=zEnd ) goto do_atof_calc;\n\n  /* if decimal point is present */\n  if( *z=='.' ){\n    z+=incr;\n    /* copy digits from after decimal to significand\n    ** (decrease exponent by d to shift decimal right) */\n    while( z<zEnd && sqlite3Isdigit(*z) ){\n      if( s<((LARGEST_INT64-9)/10) ){\n        s = s*10 + (*z - '0');\n        d--;\n      }\n      z+=incr; nDigits++;\n    }\n  }\n  if( z>=zEnd ) goto do_atof_calc;\n\n  /* if exponent is present */\n  if( *z=='e' || *z=='E' ){\n    z+=incr;\n    eValid = 0;\n\n    /* This branch is needed to avoid a (harmless) buffer overread.  The \n    ** special comment alerts the mutation tester that the correct answer\n    ** is obtained even if the branch is omitted */\n    if( z>=zEnd ) goto do_atof_calc;              /*PREVENTS-HARMLESS-OVERREAD*/\n\n    /* get sign of exponent */\n    if( *z=='-' ){\n      esign = -1;\n      z+=incr;\n    }else if( *z=='+' ){\n      z+=incr;\n    }\n    /* copy digits to exponent */\n    while( z<zEnd && sqlite3Isdigit(*z) ){\n      e = e<10000 ? (e*10 + (*z - '0')) : 10000;\n      z+=incr;\n      eValid = 1;\n    }\n  }\n\n  /* skip trailing spaces */\n  while( z<zEnd && sqlite3Isspace(*z) ) z+=incr;\n\ndo_atof_calc:\n  /* adjust exponent by d, and update sign */\n  e = (e*esign) + d;\n  if( e<0 ) {\n    esign = -1;\n    e *= -1;\n  } else {\n    esign = 1;\n  }\n\n  if( s==0 ) {\n    /* In the IEEE 754 standard, zero is signed. */\n    result = sign<0 ? -(double)0 : (double)0;\n  } else {\n    /* Attempt to reduce exponent.\n    **\n    ** Branches that are not required for the correct answer but which only\n    ** help to obtain the correct answer faster are marked with special\n    ** comments, as a hint to the mutation tester.\n    */\n    while( e>0 ){                                       /*OPTIMIZATION-IF-TRUE*/\n      if( esign>0 ){\n        if( s>=(LARGEST_INT64/10) ) break;             /*OPTIMIZATION-IF-FALSE*/\n        s *= 10;\n      }else{\n        if( s%10!=0 ) break;                           /*OPTIMIZATION-IF-FALSE*/\n        s /= 10;\n      }\n      e--;\n    }\n\n    /* adjust the sign of significand */\n    s = sign<0 ? -s : s;\n\n    if( e==0 ){                                         /*OPTIMIZATION-IF-TRUE*/\n      result = (double)s;\n    }else{\n      /* attempt to handle extremely small/large numbers better */\n      if( e>307 ){                                      /*OPTIMIZATION-IF-TRUE*/\n        if( e<342 ){                                    /*OPTIMIZATION-IF-TRUE*/\n          LONGDOUBLE_TYPE scale = sqlite3Pow10(e-308);\n          if( esign<0 ){\n            result = s / scale;\n            result /= 1.0e+308;\n          }else{\n            result = s * scale;\n            result *= 1.0e+308;\n          }\n        }else{ assert( e>=342 );\n          if( esign<0 ){\n            result = 0.0*s;\n          }else{\n#ifdef INFINITY\n            result = INFINITY*s;\n#else\n            result = 1e308*1e308*s;  /* Infinity */\n#endif\n          }\n        }\n      }else{\n        LONGDOUBLE_TYPE scale = sqlite3Pow10(e);\n        if( esign<0 ){\n          result = s / scale;\n        }else{\n          result = s * scale;\n        }\n      }\n    }\n  }\n\n  /* store the result */\n  *pResult = result;\n\n  /* return true if number and no extra non-whitespace chracters after */\n  return z==zEnd && nDigits>0 && eValid && nonNum==0;\n#else\n  return !sqlite3Atoi64(z, pResult, length, enc);\n#endif /* SQLITE_OMIT_FLOATING_POINT */\n}\n\n/*\n** Compare the 19-character string zNum against the text representation\n** value 2^63:  9223372036854775808.  Return negative, zero, or positive\n** if zNum is less than, equal to, or greater than the string.\n** Note that zNum must contain exactly 19 characters.\n**\n** Unlike memcmp() this routine is guaranteed to return the difference\n** in the values of the last digit if the only difference is in the\n** last digit.  So, for example,\n**\n**      compare2pow63(\"9223372036854775800\", 1)\n**\n** will return -8.\n*/\nstatic int compare2pow63(const char *zNum, int incr){\n  int c = 0;\n  int i;\n                    /* 012345678901234567 */\n  const char *pow63 = \"922337203685477580\";\n  for(i=0; c==0 && i<18; i++){\n    c = (zNum[i*incr]-pow63[i])*10;\n  }\n  if( c==0 ){\n    c = zNum[18*incr] - '8';\n    testcase( c==(-1) );\n    testcase( c==0 );\n    testcase( c==(+1) );\n  }\n  return c;\n}\n\n/*\n** Convert zNum to a 64-bit signed integer.  zNum must be decimal. This\n** routine does *not* accept hexadecimal notation.\n**\n** Returns:\n**\n**     0    Successful transformation.  Fits in a 64-bit signed integer.\n**     1    Excess non-space text after the integer value\n**     2    Integer too large for a 64-bit signed integer or is malformed\n**     3    Special case of 9223372036854775808\n**\n** length is the number of bytes in the string (bytes, not characters).\n** The string is not necessarily zero-terminated.  The encoding is\n** given by enc.\n*/\nSQLITE_PRIVATE int sqlite3Atoi64(const char *zNum, i64 *pNum, int length, u8 enc){\n  int incr;\n  u64 u = 0;\n  int neg = 0; /* assume positive */\n  int i;\n  int c = 0;\n  int nonNum = 0;  /* True if input contains UTF16 with high byte non-zero */\n  int rc;          /* Baseline return code */\n  const char *zStart;\n  const char *zEnd = zNum + length;\n  assert( enc==SQLITE_UTF8 || enc==SQLITE_UTF16LE || enc==SQLITE_UTF16BE );\n  if( enc==SQLITE_UTF8 ){\n    incr = 1;\n  }else{\n    incr = 2;\n    assert( SQLITE_UTF16LE==2 && SQLITE_UTF16BE==3 );\n    for(i=3-enc; i<length && zNum[i]==0; i+=2){}\n    nonNum = i<length;\n    zEnd = &zNum[i^1];\n    zNum += (enc&1);\n  }\n  while( zNum<zEnd && sqlite3Isspace(*zNum) ) zNum+=incr;\n  if( zNum<zEnd ){\n    if( *zNum=='-' ){\n      neg = 1;\n      zNum+=incr;\n    }else if( *zNum=='+' ){\n      zNum+=incr;\n    }\n  }\n  zStart = zNum;\n  while( zNum<zEnd && zNum[0]=='0' ){ zNum+=incr; } /* Skip leading zeros. */\n  for(i=0; &zNum[i]<zEnd && (c=zNum[i])>='0' && c<='9'; i+=incr){\n    u = u*10 + c - '0';\n  }\n  testcase( i==18*incr );\n  testcase( i==19*incr );\n  testcase( i==20*incr );\n  if( u>LARGEST_INT64 ){\n    /* This test and assignment is needed only to suppress UB warnings\n    ** from clang and -fsanitize=undefined.  This test and assignment make\n    ** the code a little larger and slower, and no harm comes from omitting\n    ** them, but we must appaise the undefined-behavior pharisees. */\n    *pNum = neg ? SMALLEST_INT64 : LARGEST_INT64;\n  }else if( neg ){\n    *pNum = -(i64)u;\n  }else{\n    *pNum = (i64)u;\n  }\n  rc = 0;\n  if( (i==0 && zStart==zNum)     /* No digits */\n   || nonNum                     /* UTF16 with high-order bytes non-zero */\n  ){\n    rc = 1;\n  }else if( &zNum[i]<zEnd ){     /* Extra bytes at the end */\n    int jj = i;\n    do{\n      if( !sqlite3Isspace(zNum[jj]) ){\n        rc = 1;          /* Extra non-space text after the integer */\n        break;\n      }\n      jj += incr;\n    }while( &zNum[jj]<zEnd );\n  }\n  if( i<19*incr ){\n    /* Less than 19 digits, so we know that it fits in 64 bits */\n    assert( u<=LARGEST_INT64 );\n    return rc;\n  }else{\n    /* zNum is a 19-digit numbers.  Compare it against 9223372036854775808. */\n    c = i>19*incr ? 1 : compare2pow63(zNum, incr);\n    if( c<0 ){\n      /* zNum is less than 9223372036854775808 so it fits */\n      assert( u<=LARGEST_INT64 );\n      return rc;\n    }else{\n      *pNum = neg ? SMALLEST_INT64 : LARGEST_INT64;\n      if( c>0 ){\n        /* zNum is greater than 9223372036854775808 so it overflows */\n        return 2;\n      }else{\n        /* zNum is exactly 9223372036854775808.  Fits if negative.  The\n        ** special case 2 overflow if positive */\n        assert( u-1==LARGEST_INT64 );\n        return neg ? rc : 3;\n      }\n    }\n  }\n}\n\n/*\n** Transform a UTF-8 integer literal, in either decimal or hexadecimal,\n** into a 64-bit signed integer.  This routine accepts hexadecimal literals,\n** whereas sqlite3Atoi64() does not.\n**\n** Returns:\n**\n**     0    Successful transformation.  Fits in a 64-bit signed integer.\n**     1    Excess text after the integer value\n**     2    Integer too large for a 64-bit signed integer or is malformed\n**     3    Special case of 9223372036854775808\n*/\nSQLITE_PRIVATE int sqlite3DecOrHexToI64(const char *z, i64 *pOut){\n#ifndef SQLITE_OMIT_HEX_INTEGER\n  if( z[0]=='0'\n   && (z[1]=='x' || z[1]=='X')\n  ){\n    u64 u = 0;\n    int i, k;\n    for(i=2; z[i]=='0'; i++){}\n    for(k=i; sqlite3Isxdigit(z[k]); k++){\n      u = u*16 + sqlite3HexToInt(z[k]);\n    }\n    memcpy(pOut, &u, 8);\n    return (z[k]==0 && k-i<=16) ? 0 : 2;\n  }else\n#endif /* SQLITE_OMIT_HEX_INTEGER */\n  {\n    return sqlite3Atoi64(z, pOut, sqlite3Strlen30(z), SQLITE_UTF8);\n  }\n}\n\n/*\n** If zNum represents an integer that will fit in 32-bits, then set\n** *pValue to that integer and return true.  Otherwise return false.\n**\n** This routine accepts both decimal and hexadecimal notation for integers.\n**\n** Any non-numeric characters that following zNum are ignored.\n** This is different from sqlite3Atoi64() which requires the\n** input number to be zero-terminated.\n*/\nSQLITE_PRIVATE int sqlite3GetInt32(const char *zNum, int *pValue){\n  sqlite_int64 v = 0;\n  int i, c;\n  int neg = 0;\n  if( zNum[0]=='-' ){\n    neg = 1;\n    zNum++;\n  }else if( zNum[0]=='+' ){\n    zNum++;\n  }\n#ifndef SQLITE_OMIT_HEX_INTEGER\n  else if( zNum[0]=='0'\n        && (zNum[1]=='x' || zNum[1]=='X')\n        && sqlite3Isxdigit(zNum[2])\n  ){\n    u32 u = 0;\n    zNum += 2;\n    while( zNum[0]=='0' ) zNum++;\n    for(i=0; sqlite3Isxdigit(zNum[i]) && i<8; i++){\n      u = u*16 + sqlite3HexToInt(zNum[i]);\n    }\n    if( (u&0x80000000)==0 && sqlite3Isxdigit(zNum[i])==0 ){\n      memcpy(pValue, &u, 4);\n      return 1;\n    }else{\n      return 0;\n    }\n  }\n#endif\n  if( !sqlite3Isdigit(zNum[0]) ) return 0;\n  while( zNum[0]=='0' ) zNum++;\n  for(i=0; i<11 && (c = zNum[i] - '0')>=0 && c<=9; i++){\n    v = v*10 + c;\n  }\n\n  /* The longest decimal representation of a 32 bit integer is 10 digits:\n  **\n  **             1234567890\n  **     2^31 -> 2147483648\n  */\n  testcase( i==10 );\n  if( i>10 ){\n    return 0;\n  }\n  testcase( v-neg==2147483647 );\n  if( v-neg>2147483647 ){\n    return 0;\n  }\n  if( neg ){\n    v = -v;\n  }\n  *pValue = (int)v;\n  return 1;\n}\n\n/*\n** Return a 32-bit integer value extracted from a string.  If the\n** string is not an integer, just return 0.\n*/\nSQLITE_PRIVATE int sqlite3Atoi(const char *z){\n  int x = 0;\n  if( z ) sqlite3GetInt32(z, &x);\n  return x;\n}\n\n/*\n** The variable-length integer encoding is as follows:\n**\n** KEY:\n**         A = 0xxxxxxx    7 bits of data and one flag bit\n**         B = 1xxxxxxx    7 bits of data and one flag bit\n**         C = xxxxxxxx    8 bits of data\n**\n**  7 bits - A\n** 14 bits - BA\n** 21 bits - BBA\n** 28 bits - BBBA\n** 35 bits - BBBBA\n** 42 bits - BBBBBA\n** 49 bits - BBBBBBA\n** 56 bits - BBBBBBBA\n** 64 bits - BBBBBBBBC\n*/\n\n/*\n** Write a 64-bit variable-length integer to memory starting at p[0].\n** The length of data write will be between 1 and 9 bytes.  The number\n** of bytes written is returned.\n**\n** A variable-length integer consists of the lower 7 bits of each byte\n** for all bytes that have the 8th bit set and one byte with the 8th\n** bit clear.  Except, if we get to the 9th byte, it stores the full\n** 8 bits and is the last byte.\n*/\nstatic int SQLITE_NOINLINE putVarint64(unsigned char *p, u64 v){\n  int i, j, n;\n  u8 buf[10];\n  if( v & (((u64)0xff000000)<<32) ){\n    p[8] = (u8)v;\n    v >>= 8;\n    for(i=7; i>=0; i--){\n      p[i] = (u8)((v & 0x7f) | 0x80);\n      v >>= 7;\n    }\n    return 9;\n  }    \n  n = 0;\n  do{\n    buf[n++] = (u8)((v & 0x7f) | 0x80);\n    v >>= 7;\n  }while( v!=0 );\n  buf[0] &= 0x7f;\n  assert( n<=9 );\n  for(i=0, j=n-1; j>=0; j--, i++){\n    p[i] = buf[j];\n  }\n  return n;\n}\nSQLITE_PRIVATE int sqlite3PutVarint(unsigned char *p, u64 v){\n  if( v<=0x7f ){\n    p[0] = v&0x7f;\n    return 1;\n  }\n  if( v<=0x3fff ){\n    p[0] = ((v>>7)&0x7f)|0x80;\n    p[1] = v&0x7f;\n    return 2;\n  }\n  return putVarint64(p,v);\n}\n\n/*\n** Bitmasks used by sqlite3GetVarint().  These precomputed constants\n** are defined here rather than simply putting the constant expressions\n** inline in order to work around bugs in the RVT compiler.\n**\n** SLOT_2_0     A mask for  (0x7f<<14) | 0x7f\n**\n** SLOT_4_2_0   A mask for  (0x7f<<28) | SLOT_2_0\n*/\n#define SLOT_2_0     0x001fc07f\n#define SLOT_4_2_0   0xf01fc07f\n\n\n/*\n** Read a 64-bit variable-length integer from memory starting at p[0].\n** Return the number of bytes read.  The value is stored in *v.\n*/\nSQLITE_PRIVATE u8 sqlite3GetVarint(const unsigned char *p, u64 *v){\n  u32 a,b,s;\n\n  a = *p;\n  /* a: p0 (unmasked) */\n  if (!(a&0x80))\n  {\n    *v = a;\n    return 1;\n  }\n\n  p++;\n  b = *p;\n  /* b: p1 (unmasked) */\n  if (!(b&0x80))\n  {\n    a &= 0x7f;\n    a = a<<7;\n    a |= b;\n    *v = a;\n    return 2;\n  }\n\n  /* Verify that constants are precomputed correctly */\n  assert( SLOT_2_0 == ((0x7f<<14) | (0x7f)) );\n  assert( SLOT_4_2_0 == ((0xfU<<28) | (0x7f<<14) | (0x7f)) );\n\n  p++;\n  a = a<<14;\n  a |= *p;\n  /* a: p0<<14 | p2 (unmasked) */\n  if (!(a&0x80))\n  {\n    a &= SLOT_2_0;\n    b &= 0x7f;\n    b = b<<7;\n    a |= b;\n    *v = a;\n    return 3;\n  }\n\n  /* CSE1 from below */\n  a &= SLOT_2_0;\n  p++;\n  b = b<<14;\n  b |= *p;\n  /* b: p1<<14 | p3 (unmasked) */\n  if (!(b&0x80))\n  {\n    b &= SLOT_2_0;\n    /* moved CSE1 up */\n    /* a &= (0x7f<<14)|(0x7f); */\n    a = a<<7;\n    a |= b;\n    *v = a;\n    return 4;\n  }\n\n  /* a: p0<<14 | p2 (masked) */\n  /* b: p1<<14 | p3 (unmasked) */\n  /* 1:save off p0<<21 | p1<<14 | p2<<7 | p3 (masked) */\n  /* moved CSE1 up */\n  /* a &= (0x7f<<14)|(0x7f); */\n  b &= SLOT_2_0;\n  s = a;\n  /* s: p0<<14 | p2 (masked) */\n\n  p++;\n  a = a<<14;\n  a |= *p;\n  /* a: p0<<28 | p2<<14 | p4 (unmasked) */\n  if (!(a&0x80))\n  {\n    /* we can skip these cause they were (effectively) done above\n    ** while calculating s */\n    /* a &= (0x7f<<28)|(0x7f<<14)|(0x7f); */\n    /* b &= (0x7f<<14)|(0x7f); */\n    b = b<<7;\n    a |= b;\n    s = s>>18;\n    *v = ((u64)s)<<32 | a;\n    return 5;\n  }\n\n  /* 2:save off p0<<21 | p1<<14 | p2<<7 | p3 (masked) */\n  s = s<<7;\n  s |= b;\n  /* s: p0<<21 | p1<<14 | p2<<7 | p3 (masked) */\n\n  p++;\n  b = b<<14;\n  b |= *p;\n  /* b: p1<<28 | p3<<14 | p5 (unmasked) */\n  if (!(b&0x80))\n  {\n    /* we can skip this cause it was (effectively) done above in calc'ing s */\n    /* b &= (0x7f<<28)|(0x7f<<14)|(0x7f); */\n    a &= SLOT_2_0;\n    a = a<<7;\n    a |= b;\n    s = s>>18;\n    *v = ((u64)s)<<32 | a;\n    return 6;\n  }\n\n  p++;\n  a = a<<14;\n  a |= *p;\n  /* a: p2<<28 | p4<<14 | p6 (unmasked) */\n  if (!(a&0x80))\n  {\n    a &= SLOT_4_2_0;\n    b &= SLOT_2_0;\n    b = b<<7;\n    a |= b;\n    s = s>>11;\n    *v = ((u64)s)<<32 | a;\n    return 7;\n  }\n\n  /* CSE2 from below */\n  a &= SLOT_2_0;\n  p++;\n  b = b<<14;\n  b |= *p;\n  /* b: p3<<28 | p5<<14 | p7 (unmasked) */\n  if (!(b&0x80))\n  {\n    b &= SLOT_4_2_0;\n    /* moved CSE2 up */\n    /* a &= (0x7f<<14)|(0x7f); */\n    a = a<<7;\n    a |= b;\n    s = s>>4;\n    *v = ((u64)s)<<32 | a;\n    return 8;\n  }\n\n  p++;\n  a = a<<15;\n  a |= *p;\n  /* a: p4<<29 | p6<<15 | p8 (unmasked) */\n\n  /* moved CSE2 up */\n  /* a &= (0x7f<<29)|(0x7f<<15)|(0xff); */\n  b &= SLOT_2_0;\n  b = b<<8;\n  a |= b;\n\n  s = s<<4;\n  b = p[-4];\n  b &= 0x7f;\n  b = b>>3;\n  s |= b;\n\n  *v = ((u64)s)<<32 | a;\n\n  return 9;\n}\n\n/*\n** Read a 32-bit variable-length integer from memory starting at p[0].\n** Return the number of bytes read.  The value is stored in *v.\n**\n** If the varint stored in p[0] is larger than can fit in a 32-bit unsigned\n** integer, then set *v to 0xffffffff.\n**\n** A MACRO version, getVarint32, is provided which inlines the \n** single-byte case.  All code should use the MACRO version as \n** this function assumes the single-byte case has already been handled.\n*/\nSQLITE_PRIVATE u8 sqlite3GetVarint32(const unsigned char *p, u32 *v){\n  u32 a,b;\n\n  /* The 1-byte case.  Overwhelmingly the most common.  Handled inline\n  ** by the getVarin32() macro */\n  a = *p;\n  /* a: p0 (unmasked) */\n#ifndef getVarint32\n  if (!(a&0x80))\n  {\n    /* Values between 0 and 127 */\n    *v = a;\n    return 1;\n  }\n#endif\n\n  /* The 2-byte case */\n  p++;\n  b = *p;\n  /* b: p1 (unmasked) */\n  if (!(b&0x80))\n  {\n    /* Values between 128 and 16383 */\n    a &= 0x7f;\n    a = a<<7;\n    *v = a | b;\n    return 2;\n  }\n\n  /* The 3-byte case */\n  p++;\n  a = a<<14;\n  a |= *p;\n  /* a: p0<<14 | p2 (unmasked) */\n  if (!(a&0x80))\n  {\n    /* Values between 16384 and 2097151 */\n    a &= (0x7f<<14)|(0x7f);\n    b &= 0x7f;\n    b = b<<7;\n    *v = a | b;\n    return 3;\n  }\n\n  /* A 32-bit varint is used to store size information in btrees.\n  ** Objects are rarely larger than 2MiB limit of a 3-byte varint.\n  ** A 3-byte varint is sufficient, for example, to record the size\n  ** of a 1048569-byte BLOB or string.\n  **\n  ** We only unroll the first 1-, 2-, and 3- byte cases.  The very\n  ** rare larger cases can be handled by the slower 64-bit varint\n  ** routine.\n  */\n#if 1\n  {\n    u64 v64;\n    u8 n;\n\n    p -= 2;\n    n = sqlite3GetVarint(p, &v64);\n    assert( n>3 && n<=9 );\n    if( (v64 & SQLITE_MAX_U32)!=v64 ){\n      *v = 0xffffffff;\n    }else{\n      *v = (u32)v64;\n    }\n    return n;\n  }\n\n#else\n  /* For following code (kept for historical record only) shows an\n  ** unrolling for the 3- and 4-byte varint cases.  This code is\n  ** slightly faster, but it is also larger and much harder to test.\n  */\n  p++;\n  b = b<<14;\n  b |= *p;\n  /* b: p1<<14 | p3 (unmasked) */\n  if (!(b&0x80))\n  {\n    /* Values between 2097152 and 268435455 */\n    b &= (0x7f<<14)|(0x7f);\n    a &= (0x7f<<14)|(0x7f);\n    a = a<<7;\n    *v = a | b;\n    return 4;\n  }\n\n  p++;\n  a = a<<14;\n  a |= *p;\n  /* a: p0<<28 | p2<<14 | p4 (unmasked) */\n  if (!(a&0x80))\n  {\n    /* Values  between 268435456 and 34359738367 */\n    a &= SLOT_4_2_0;\n    b &= SLOT_4_2_0;\n    b = b<<7;\n    *v = a | b;\n    return 5;\n  }\n\n  /* We can only reach this point when reading a corrupt database\n  ** file.  In that case we are not in any hurry.  Use the (relatively\n  ** slow) general-purpose sqlite3GetVarint() routine to extract the\n  ** value. */\n  {\n    u64 v64;\n    u8 n;\n\n    p -= 4;\n    n = sqlite3GetVarint(p, &v64);\n    assert( n>5 && n<=9 );\n    *v = (u32)v64;\n    return n;\n  }\n#endif\n}\n\n/*\n** Return the number of bytes that will be needed to store the given\n** 64-bit integer.\n*/\nSQLITE_PRIVATE int sqlite3VarintLen(u64 v){\n  int i;\n  for(i=1; (v >>= 7)!=0; i++){ assert( i<10 ); }\n  return i;\n}\n\n\n/*\n** Read or write a four-byte big-endian integer value.\n*/\nSQLITE_PRIVATE u32 sqlite3Get4byte(const u8 *p){\n#if SQLITE_BYTEORDER==4321\n  u32 x;\n  memcpy(&x,p,4);\n  return x;\n#elif SQLITE_BYTEORDER==1234 && GCC_VERSION>=4003000\n  u32 x;\n  memcpy(&x,p,4);\n  return __builtin_bswap32(x);\n#elif SQLITE_BYTEORDER==1234 && MSVC_VERSION>=1300\n  u32 x;\n  memcpy(&x,p,4);\n  return _byteswap_ulong(x);\n#else\n  testcase( p[0]&0x80 );\n  return ((unsigned)p[0]<<24) | (p[1]<<16) | (p[2]<<8) | p[3];\n#endif\n}\nSQLITE_PRIVATE void sqlite3Put4byte(unsigned char *p, u32 v){\n#if SQLITE_BYTEORDER==4321\n  memcpy(p,&v,4);\n#elif SQLITE_BYTEORDER==1234 && GCC_VERSION>=4003000\n  u32 x = __builtin_bswap32(v);\n  memcpy(p,&x,4);\n#elif SQLITE_BYTEORDER==1234 && MSVC_VERSION>=1300\n  u32 x = _byteswap_ulong(v);\n  memcpy(p,&x,4);\n#else\n  p[0] = (u8)(v>>24);\n  p[1] = (u8)(v>>16);\n  p[2] = (u8)(v>>8);\n  p[3] = (u8)v;\n#endif\n}\n\n\n\n/*\n** Translate a single byte of Hex into an integer.\n** This routine only works if h really is a valid hexadecimal\n** character:  0..9a..fA..F\n*/\nSQLITE_PRIVATE u8 sqlite3HexToInt(int h){\n  assert( (h>='0' && h<='9') ||  (h>='a' && h<='f') ||  (h>='A' && h<='F') );\n#ifdef SQLITE_ASCII\n  h += 9*(1&(h>>6));\n#endif\n#ifdef SQLITE_EBCDIC\n  h += 9*(1&~(h>>4));\n#endif\n  return (u8)(h & 0xf);\n}\n\n#if !defined(SQLITE_OMIT_BLOB_LITERAL) || defined(SQLITE_HAS_CODEC)\n/*\n** Convert a BLOB literal of the form \"x'hhhhhh'\" into its binary\n** value.  Return a pointer to its binary value.  Space to hold the\n** binary value has been obtained from malloc and must be freed by\n** the calling routine.\n*/\nSQLITE_PRIVATE void *sqlite3HexToBlob(sqlite3 *db, const char *z, int n){\n  char *zBlob;\n  int i;\n\n  zBlob = (char *)sqlite3DbMallocRawNN(db, n/2 + 1);\n  n--;\n  if( zBlob ){\n    for(i=0; i<n; i+=2){\n      zBlob[i/2] = (sqlite3HexToInt(z[i])<<4) | sqlite3HexToInt(z[i+1]);\n    }\n    zBlob[i/2] = 0;\n  }\n  return zBlob;\n}\n#endif /* !SQLITE_OMIT_BLOB_LITERAL || SQLITE_HAS_CODEC */\n\n/*\n** Log an error that is an API call on a connection pointer that should\n** not have been used.  The \"type\" of connection pointer is given as the\n** argument.  The zType is a word like \"NULL\" or \"closed\" or \"invalid\".\n*/\nstatic void logBadConnection(const char *zType){\n  sqlite3_log(SQLITE_MISUSE, \n     \"API call with %s database connection pointer\",\n     zType\n  );\n}\n\n/*\n** Check to make sure we have a valid db pointer.  This test is not\n** foolproof but it does provide some measure of protection against\n** misuse of the interface such as passing in db pointers that are\n** NULL or which have been previously closed.  If this routine returns\n** 1 it means that the db pointer is valid and 0 if it should not be\n** dereferenced for any reason.  The calling function should invoke\n** SQLITE_MISUSE immediately.\n**\n** sqlite3SafetyCheckOk() requires that the db pointer be valid for\n** use.  sqlite3SafetyCheckSickOrOk() allows a db pointer that failed to\n** open properly and is not fit for general use but which can be\n** used as an argument to sqlite3_errmsg() or sqlite3_close().\n*/\nSQLITE_PRIVATE int sqlite3SafetyCheckOk(sqlite3 *db){\n  u32 magic;\n  if( db==0 ){\n    logBadConnection(\"NULL\");\n    return 0;\n  }\n  magic = db->magic;\n  if( magic!=SQLITE_MAGIC_OPEN ){\n    if( sqlite3SafetyCheckSickOrOk(db) ){\n      testcase( sqlite3GlobalConfig.xLog!=0 );\n      logBadConnection(\"unopened\");\n    }\n    return 0;\n  }else{\n    return 1;\n  }\n}\nSQLITE_PRIVATE int sqlite3SafetyCheckSickOrOk(sqlite3 *db){\n  u32 magic;\n  magic = db->magic;\n  if( magic!=SQLITE_MAGIC_SICK &&\n      magic!=SQLITE_MAGIC_OPEN &&\n      magic!=SQLITE_MAGIC_BUSY ){\n    testcase( sqlite3GlobalConfig.xLog!=0 );\n    logBadConnection(\"invalid\");\n    return 0;\n  }else{\n    return 1;\n  }\n}\n\n/*\n** Attempt to add, substract, or multiply the 64-bit signed value iB against\n** the other 64-bit signed integer at *pA and store the result in *pA.\n** Return 0 on success.  Or if the operation would have resulted in an\n** overflow, leave *pA unchanged and return 1.\n*/\nSQLITE_PRIVATE int sqlite3AddInt64(i64 *pA, i64 iB){\n#if GCC_VERSION>=5004000 && !defined(__INTEL_COMPILER)\n  return __builtin_add_overflow(*pA, iB, pA);\n#else\n  i64 iA = *pA;\n  testcase( iA==0 ); testcase( iA==1 );\n  testcase( iB==-1 ); testcase( iB==0 );\n  if( iB>=0 ){\n    testcase( iA>0 && LARGEST_INT64 - iA == iB );\n    testcase( iA>0 && LARGEST_INT64 - iA == iB - 1 );\n    if( iA>0 && LARGEST_INT64 - iA < iB ) return 1;\n  }else{\n    testcase( iA<0 && -(iA + LARGEST_INT64) == iB + 1 );\n    testcase( iA<0 && -(iA + LARGEST_INT64) == iB + 2 );\n    if( iA<0 && -(iA + LARGEST_INT64) > iB + 1 ) return 1;\n  }\n  *pA += iB;\n  return 0; \n#endif\n}\nSQLITE_PRIVATE int sqlite3SubInt64(i64 *pA, i64 iB){\n#if GCC_VERSION>=5004000 && !defined(__INTEL_COMPILER)\n  return __builtin_sub_overflow(*pA, iB, pA);\n#else\n  testcase( iB==SMALLEST_INT64+1 );\n  if( iB==SMALLEST_INT64 ){\n    testcase( (*pA)==(-1) ); testcase( (*pA)==0 );\n    if( (*pA)>=0 ) return 1;\n    *pA -= iB;\n    return 0;\n  }else{\n    return sqlite3AddInt64(pA, -iB);\n  }\n#endif\n}\nSQLITE_PRIVATE int sqlite3MulInt64(i64 *pA, i64 iB){\n#if GCC_VERSION>=5004000 && !defined(__INTEL_COMPILER)\n  return __builtin_mul_overflow(*pA, iB, pA);\n#else\n  i64 iA = *pA;\n  if( iB>0 ){\n    if( iA>LARGEST_INT64/iB ) return 1;\n    if( iA<SMALLEST_INT64/iB ) return 1;\n  }else if( iB<0 ){\n    if( iA>0 ){\n      if( iB<SMALLEST_INT64/iA ) return 1;\n    }else if( iA<0 ){\n      if( iB==SMALLEST_INT64 ) return 1;\n      if( iA==SMALLEST_INT64 ) return 1;\n      if( -iA>LARGEST_INT64/-iB ) return 1;\n    }\n  }\n  *pA = iA*iB;\n  return 0;\n#endif\n}\n\n/*\n** Compute the absolute value of a 32-bit signed integer, of possible.  Or \n** if the integer has a value of -2147483648, return +2147483647\n*/\nSQLITE_PRIVATE int sqlite3AbsInt32(int x){\n  if( x>=0 ) return x;\n  if( x==(int)0x80000000 ) return 0x7fffffff;\n  return -x;\n}\n\n#ifdef SQLITE_ENABLE_8_3_NAMES\n/*\n** If SQLITE_ENABLE_8_3_NAMES is set at compile-time and if the database\n** filename in zBaseFilename is a URI with the \"8_3_names=1\" parameter and\n** if filename in z[] has a suffix (a.k.a. \"extension\") that is longer than\n** three characters, then shorten the suffix on z[] to be the last three\n** characters of the original suffix.\n**\n** If SQLITE_ENABLE_8_3_NAMES is set to 2 at compile-time, then always\n** do the suffix shortening regardless of URI parameter.\n**\n** Examples:\n**\n**     test.db-journal    =>   test.nal\n**     test.db-wal        =>   test.wal\n**     test.db-shm        =>   test.shm\n**     test.db-mj7f3319fa =>   test.9fa\n*/\nSQLITE_PRIVATE void sqlite3FileSuffix3(const char *zBaseFilename, char *z){\n#if SQLITE_ENABLE_8_3_NAMES<2\n  if( sqlite3_uri_boolean(zBaseFilename, \"8_3_names\", 0) )\n#endif\n  {\n    int i, sz;\n    sz = sqlite3Strlen30(z);\n    for(i=sz-1; i>0 && z[i]!='/' && z[i]!='.'; i--){}\n    if( z[i]=='.' && ALWAYS(sz>i+4) ) memmove(&z[i+1], &z[sz-3], 4);\n  }\n}\n#endif\n\n/* \n** Find (an approximate) sum of two LogEst values.  This computation is\n** not a simple \"+\" operator because LogEst is stored as a logarithmic\n** value.\n** \n*/\nSQLITE_PRIVATE LogEst sqlite3LogEstAdd(LogEst a, LogEst b){\n  static const unsigned char x[] = {\n     10, 10,                         /* 0,1 */\n      9, 9,                          /* 2,3 */\n      8, 8,                          /* 4,5 */\n      7, 7, 7,                       /* 6,7,8 */\n      6, 6, 6,                       /* 9,10,11 */\n      5, 5, 5,                       /* 12-14 */\n      4, 4, 4, 4,                    /* 15-18 */\n      3, 3, 3, 3, 3, 3,              /* 19-24 */\n      2, 2, 2, 2, 2, 2, 2,           /* 25-31 */\n  };\n  if( a>=b ){\n    if( a>b+49 ) return a;\n    if( a>b+31 ) return a+1;\n    return a+x[a-b];\n  }else{\n    if( b>a+49 ) return b;\n    if( b>a+31 ) return b+1;\n    return b+x[b-a];\n  }\n}\n\n/*\n** Convert an integer into a LogEst.  In other words, compute an\n** approximation for 10*log2(x).\n*/\nSQLITE_PRIVATE LogEst sqlite3LogEst(u64 x){\n  static LogEst a[] = { 0, 2, 3, 5, 6, 7, 8, 9 };\n  LogEst y = 40;\n  if( x<8 ){\n    if( x<2 ) return 0;\n    while( x<8 ){  y -= 10; x <<= 1; }\n  }else{\n#if GCC_VERSION>=5004000\n    int i = 60 - __builtin_clzll(x);\n    y += i*10;\n    x >>= i;\n#else\n    while( x>255 ){ y += 40; x >>= 4; }  /*OPTIMIZATION-IF-TRUE*/\n    while( x>15 ){  y += 10; x >>= 1; }\n#endif\n  }\n  return a[x&7] + y - 10;\n}\n\n#ifndef SQLITE_OMIT_VIRTUALTABLE\n/*\n** Convert a double into a LogEst\n** In other words, compute an approximation for 10*log2(x).\n*/\nSQLITE_PRIVATE LogEst sqlite3LogEstFromDouble(double x){\n  u64 a;\n  LogEst e;\n  assert( sizeof(x)==8 && sizeof(a)==8 );\n  if( x<=1 ) return 0;\n  if( x<=2000000000 ) return sqlite3LogEst((u64)x);\n  memcpy(&a, &x, 8);\n  e = (a>>52) - 1022;\n  return e*10;\n}\n#endif /* SQLITE_OMIT_VIRTUALTABLE */\n\n#if defined(SQLITE_ENABLE_STMT_SCANSTATUS) || \\\n    defined(SQLITE_ENABLE_STAT3_OR_STAT4) || \\\n    defined(SQLITE_EXPLAIN_ESTIMATED_ROWS)\n/*\n** Convert a LogEst into an integer.\n**\n** Note that this routine is only used when one or more of various\n** non-standard compile-time options is enabled.\n*/\nSQLITE_PRIVATE u64 sqlite3LogEstToInt(LogEst x){\n  u64 n;\n  n = x%10;\n  x /= 10;\n  if( n>=5 ) n -= 2;\n  else if( n>=1 ) n -= 1;\n#if defined(SQLITE_ENABLE_STMT_SCANSTATUS) || \\\n    defined(SQLITE_EXPLAIN_ESTIMATED_ROWS)\n  if( x>60 ) return (u64)LARGEST_INT64;\n#else\n  /* If only SQLITE_ENABLE_STAT3_OR_STAT4 is on, then the largest input\n  ** possible to this routine is 310, resulting in a maximum x of 31 */\n  assert( x<=60 );\n#endif\n  return x>=3 ? (n+8)<<(x-3) : (n+8)>>(3-x);\n}\n#endif /* defined SCANSTAT or STAT4 or ESTIMATED_ROWS */\n\n/*\n** Add a new name/number pair to a VList.  This might require that the\n** VList object be reallocated, so return the new VList.  If an OOM\n** error occurs, the original VList returned and the\n** db->mallocFailed flag is set.\n**\n** A VList is really just an array of integers.  To destroy a VList,\n** simply pass it to sqlite3DbFree().\n**\n** The first integer is the number of integers allocated for the whole\n** VList.  The second integer is the number of integers actually used.\n** Each name/number pair is encoded by subsequent groups of 3 or more\n** integers.\n**\n** Each name/number pair starts with two integers which are the numeric\n** value for the pair and the size of the name/number pair, respectively.\n** The text name overlays one or more following integers.  The text name\n** is always zero-terminated.\n**\n** Conceptually:\n**\n**    struct VList {\n**      int nAlloc;   // Number of allocated slots \n**      int nUsed;    // Number of used slots \n**      struct VListEntry {\n**        int iValue;    // Value for this entry\n**        int nSlot;     // Slots used by this entry\n**        // ... variable name goes here\n**      } a[0];\n**    }\n**\n** During code generation, pointers to the variable names within the\n** VList are taken.  When that happens, nAlloc is set to zero as an \n** indication that the VList may never again be enlarged, since the\n** accompanying realloc() would invalidate the pointers.\n*/\nSQLITE_PRIVATE VList *sqlite3VListAdd(\n  sqlite3 *db,           /* The database connection used for malloc() */\n  VList *pIn,            /* The input VList.  Might be NULL */\n  const char *zName,     /* Name of symbol to add */\n  int nName,             /* Bytes of text in zName */\n  int iVal               /* Value to associate with zName */\n){\n  int nInt;              /* number of sizeof(int) objects needed for zName */\n  char *z;               /* Pointer to where zName will be stored */\n  int i;                 /* Index in pIn[] where zName is stored */\n\n  nInt = nName/4 + 3;\n  assert( pIn==0 || pIn[0]>=3 );  /* Verify ok to add new elements */\n  if( pIn==0 || pIn[1]+nInt > pIn[0] ){\n    /* Enlarge the allocation */\n    int nAlloc = (pIn ? pIn[0]*2 : 10) + nInt;\n    VList *pOut = sqlite3DbRealloc(db, pIn, nAlloc*sizeof(int));\n    if( pOut==0 ) return pIn;\n    if( pIn==0 ) pOut[1] = 2;\n    pIn = pOut;\n    pIn[0] = nAlloc;\n  }\n  i = pIn[1];\n  pIn[i] = iVal;\n  pIn[i+1] = nInt;\n  z = (char*)&pIn[i+2];\n  pIn[1] = i+nInt;\n  assert( pIn[1]<=pIn[0] );\n  memcpy(z, zName, nName);\n  z[nName] = 0;\n  return pIn;\n}\n\n/*\n** Return a pointer to the name of a variable in the given VList that\n** has the value iVal.  Or return a NULL if there is no such variable in\n** the list\n*/\nSQLITE_PRIVATE const char *sqlite3VListNumToName(VList *pIn, int iVal){\n  int i, mx;\n  if( pIn==0 ) return 0;\n  mx = pIn[1];\n  i = 2;\n  do{\n    if( pIn[i]==iVal ) return (char*)&pIn[i+2];\n    i += pIn[i+1];\n  }while( i<mx );\n  return 0;\n}\n\n/*\n** Return the number of the variable named zName, if it is in VList.\n** or return 0 if there is no such variable.\n*/\nSQLITE_PRIVATE int sqlite3VListNameToNum(VList *pIn, const char *zName, int nName){\n  int i, mx;\n  if( pIn==0 ) return 0;\n  mx = pIn[1];\n  i = 2;\n  do{\n    const char *z = (const char*)&pIn[i+2];\n    if( strncmp(z,zName,nName)==0 && z[nName]==0 ) return pIn[i];\n    i += pIn[i+1];\n  }while( i<mx );\n  return 0;\n}\n\n/************** End of util.c ************************************************/\n/************** Begin file hash.c ********************************************/\n/*\n** 2001 September 22\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n*************************************************************************\n** This is the implementation of generic hash-tables\n** used in SQLite.\n*/\n/* #include \"sqliteInt.h\" */\n/* #include <assert.h> */\n\n/* Turn bulk memory into a hash table object by initializing the\n** fields of the Hash structure.\n**\n** \"pNew\" is a pointer to the hash table that is to be initialized.\n*/\nSQLITE_PRIVATE void sqlite3HashInit(Hash *pNew){\n  assert( pNew!=0 );\n  pNew->first = 0;\n  pNew->count = 0;\n  pNew->htsize = 0;\n  pNew->ht = 0;\n}\n\n/* Remove all entries from a hash table.  Reclaim all memory.\n** Call this routine to delete a hash table or to reset a hash table\n** to the empty state.\n*/\nSQLITE_PRIVATE void sqlite3HashClear(Hash *pH){\n  HashElem *elem;         /* For looping over all elements of the table */\n\n  assert( pH!=0 );\n  elem = pH->first;\n  pH->first = 0;\n  sqlite3_free(pH->ht);\n  pH->ht = 0;\n  pH->htsize = 0;\n  while( elem ){\n    HashElem *next_elem = elem->next;\n    sqlite3_free(elem);\n    elem = next_elem;\n  }\n  pH->count = 0;\n}\n\n/*\n** The hashing function.\n*/\nstatic unsigned int strHash(const char *z){\n  unsigned int h = 0;\n  unsigned char c;\n  while( (c = (unsigned char)*z++)!=0 ){     /*OPTIMIZATION-IF-TRUE*/\n    /* Knuth multiplicative hashing.  (Sorting & Searching, p. 510).\n    ** 0x9e3779b1 is 2654435761 which is the closest prime number to\n    ** (2**32)*golden_ratio, where golden_ratio = (sqrt(5) - 1)/2. */\n    h += sqlite3UpperToLower[c];\n    h *= 0x9e3779b1;\n  }\n  return h;\n}\n\n\n/* Link pNew element into the hash table pH.  If pEntry!=0 then also\n** insert pNew into the pEntry hash bucket.\n*/\nstatic void insertElement(\n  Hash *pH,              /* The complete hash table */\n  struct _ht *pEntry,    /* The entry into which pNew is inserted */\n  HashElem *pNew         /* The element to be inserted */\n){\n  HashElem *pHead;       /* First element already in pEntry */\n  if( pEntry ){\n    pHead = pEntry->count ? pEntry->chain : 0;\n    pEntry->count++;\n    pEntry->chain = pNew;\n  }else{\n    pHead = 0;\n  }\n  if( pHead ){\n    pNew->next = pHead;\n    pNew->prev = pHead->prev;\n    if( pHead->prev ){ pHead->prev->next = pNew; }\n    else             { pH->first = pNew; }\n    pHead->prev = pNew;\n  }else{\n    pNew->next = pH->first;\n    if( pH->first ){ pH->first->prev = pNew; }\n    pNew->prev = 0;\n    pH->first = pNew;\n  }\n}\n\n\n/* Resize the hash table so that it cantains \"new_size\" buckets.\n**\n** The hash table might fail to resize if sqlite3_malloc() fails or\n** if the new size is the same as the prior size.\n** Return TRUE if the resize occurs and false if not.\n*/\nstatic int rehash(Hash *pH, unsigned int new_size){\n  struct _ht *new_ht;            /* The new hash table */\n  HashElem *elem, *next_elem;    /* For looping over existing elements */\n\n#if SQLITE_MALLOC_SOFT_LIMIT>0\n  if( new_size*sizeof(struct _ht)>SQLITE_MALLOC_SOFT_LIMIT ){\n    new_size = SQLITE_MALLOC_SOFT_LIMIT/sizeof(struct _ht);\n  }\n  if( new_size==pH->htsize ) return 0;\n#endif\n\n  /* The inability to allocates space for a larger hash table is\n  ** a performance hit but it is not a fatal error.  So mark the\n  ** allocation as a benign. Use sqlite3Malloc()/memset(0) instead of \n  ** sqlite3MallocZero() to make the allocation, as sqlite3MallocZero()\n  ** only zeroes the requested number of bytes whereas this module will\n  ** use the actual amount of space allocated for the hash table (which\n  ** may be larger than the requested amount).\n  */\n  sqlite3BeginBenignMalloc();\n  new_ht = (struct _ht *)sqlite3Malloc( new_size*sizeof(struct _ht) );\n  sqlite3EndBenignMalloc();\n\n  if( new_ht==0 ) return 0;\n  sqlite3_free(pH->ht);\n  pH->ht = new_ht;\n  pH->htsize = new_size = sqlite3MallocSize(new_ht)/sizeof(struct _ht);\n  memset(new_ht, 0, new_size*sizeof(struct _ht));\n  for(elem=pH->first, pH->first=0; elem; elem = next_elem){\n    unsigned int h = strHash(elem->pKey) % new_size;\n    next_elem = elem->next;\n    insertElement(pH, &new_ht[h], elem);\n  }\n  return 1;\n}\n\n/* This function (for internal use only) locates an element in an\n** hash table that matches the given key.  If no element is found,\n** a pointer to a static null element with HashElem.data==0 is returned.\n** If pH is not NULL, then the hash for this key is written to *pH.\n*/\nstatic HashElem *findElementWithHash(\n  const Hash *pH,     /* The pH to be searched */\n  const char *pKey,   /* The key we are searching for */\n  unsigned int *pHash /* Write the hash value here */\n){\n  HashElem *elem;                /* Used to loop thru the element list */\n  int count;                     /* Number of elements left to test */\n  unsigned int h;                /* The computed hash */\n  static HashElem nullElement = { 0, 0, 0, 0 };\n\n  if( pH->ht ){   /*OPTIMIZATION-IF-TRUE*/\n    struct _ht *pEntry;\n    h = strHash(pKey) % pH->htsize;\n    pEntry = &pH->ht[h];\n    elem = pEntry->chain;\n    count = pEntry->count;\n  }else{\n    h = 0;\n    elem = pH->first;\n    count = pH->count;\n  }\n  if( pHash ) *pHash = h;\n  while( count-- ){\n    assert( elem!=0 );\n    if( sqlite3StrICmp(elem->pKey,pKey)==0 ){ \n      return elem;\n    }\n    elem = elem->next;\n  }\n  return &nullElement;\n}\n\n/* Remove a single entry from the hash table given a pointer to that\n** element and a hash on the element's key.\n*/\nstatic void removeElementGivenHash(\n  Hash *pH,         /* The pH containing \"elem\" */\n  HashElem* elem,   /* The element to be removed from the pH */\n  unsigned int h    /* Hash value for the element */\n){\n  struct _ht *pEntry;\n  if( elem->prev ){\n    elem->prev->next = elem->next; \n  }else{\n    pH->first = elem->next;\n  }\n  if( elem->next ){\n    elem->next->prev = elem->prev;\n  }\n  if( pH->ht ){\n    pEntry = &pH->ht[h];\n    if( pEntry->chain==elem ){\n      pEntry->chain = elem->next;\n    }\n    pEntry->count--;\n    assert( pEntry->count>=0 );\n  }\n  sqlite3_free( elem );\n  pH->count--;\n  if( pH->count==0 ){\n    assert( pH->first==0 );\n    assert( pH->count==0 );\n    sqlite3HashClear(pH);\n  }\n}\n\n/* Attempt to locate an element of the hash table pH with a key\n** that matches pKey.  Return the data for this element if it is\n** found, or NULL if there is no match.\n*/\nSQLITE_PRIVATE void *sqlite3HashFind(const Hash *pH, const char *pKey){\n  assert( pH!=0 );\n  assert( pKey!=0 );\n  return findElementWithHash(pH, pKey, 0)->data;\n}\n\n/* Insert an element into the hash table pH.  The key is pKey\n** and the data is \"data\".\n**\n** If no element exists with a matching key, then a new\n** element is created and NULL is returned.\n**\n** If another element already exists with the same key, then the\n** new data replaces the old data and the old data is returned.\n** The key is not copied in this instance.  If a malloc fails, then\n** the new data is returned and the hash table is unchanged.\n**\n** If the \"data\" parameter to this function is NULL, then the\n** element corresponding to \"key\" is removed from the hash table.\n*/\nSQLITE_PRIVATE void *sqlite3HashInsert(Hash *pH, const char *pKey, void *data){\n  unsigned int h;       /* the hash of the key modulo hash table size */\n  HashElem *elem;       /* Used to loop thru the element list */\n  HashElem *new_elem;   /* New element added to the pH */\n\n  assert( pH!=0 );\n  assert( pKey!=0 );\n  elem = findElementWithHash(pH,pKey,&h);\n  if( elem->data ){\n    void *old_data = elem->data;\n    if( data==0 ){\n      removeElementGivenHash(pH,elem,h);\n    }else{\n      elem->data = data;\n      elem->pKey = pKey;\n    }\n    return old_data;\n  }\n  if( data==0 ) return 0;\n  new_elem = (HashElem*)sqlite3Malloc( sizeof(HashElem) );\n  if( new_elem==0 ) return data;\n  new_elem->pKey = pKey;\n  new_elem->data = data;\n  pH->count++;\n  if( pH->count>=10 && pH->count > 2*pH->htsize ){\n    if( rehash(pH, pH->count*2) ){\n      assert( pH->htsize>0 );\n      h = strHash(pKey) % pH->htsize;\n    }\n  }\n  insertElement(pH, pH->ht ? &pH->ht[h] : 0, new_elem);\n  return 0;\n}\n\n/************** End of hash.c ************************************************/\n/************** Begin file opcodes.c *****************************************/\n/* Automatically generated.  Do not edit */\n/* See the tool/mkopcodec.tcl script for details. */\n#if !defined(SQLITE_OMIT_EXPLAIN) \\\n || defined(VDBE_PROFILE) \\\n || defined(SQLITE_DEBUG)\n#if defined(SQLITE_ENABLE_EXPLAIN_COMMENTS) || defined(SQLITE_DEBUG)\n# define OpHelp(X) \"\\0\" X\n#else\n# define OpHelp(X)\n#endif\nSQLITE_PRIVATE const char *sqlite3OpcodeName(int i){\n static const char *const azName[] = {\n    /*   0 */ \"Savepoint\"        OpHelp(\"\"),\n    /*   1 */ \"AutoCommit\"       OpHelp(\"\"),\n    /*   2 */ \"Transaction\"      OpHelp(\"\"),\n    /*   3 */ \"SorterNext\"       OpHelp(\"\"),\n    /*   4 */ \"PrevIfOpen\"       OpHelp(\"\"),\n    /*   5 */ \"NextIfOpen\"       OpHelp(\"\"),\n    /*   6 */ \"Prev\"             OpHelp(\"\"),\n    /*   7 */ \"Next\"             OpHelp(\"\"),\n    /*   8 */ \"Checkpoint\"       OpHelp(\"\"),\n    /*   9 */ \"JournalMode\"      OpHelp(\"\"),\n    /*  10 */ \"Vacuum\"           OpHelp(\"\"),\n    /*  11 */ \"VFilter\"          OpHelp(\"iplan=r[P3] zplan='P4'\"),\n    /*  12 */ \"VUpdate\"          OpHelp(\"data=r[P3@P2]\"),\n    /*  13 */ \"Goto\"             OpHelp(\"\"),\n    /*  14 */ \"Gosub\"            OpHelp(\"\"),\n    /*  15 */ \"InitCoroutine\"    OpHelp(\"\"),\n    /*  16 */ \"Yield\"            OpHelp(\"\"),\n    /*  17 */ \"MustBeInt\"        OpHelp(\"\"),\n    /*  18 */ \"Jump\"             OpHelp(\"\"),\n    /*  19 */ \"Not\"              OpHelp(\"r[P2]= !r[P1]\"),\n    /*  20 */ \"Once\"             OpHelp(\"\"),\n    /*  21 */ \"If\"               OpHelp(\"\"),\n    /*  22 */ \"IfNot\"            OpHelp(\"\"),\n    /*  23 */ \"IfNullRow\"        OpHelp(\"if P1.nullRow then r[P3]=NULL, goto P2\"),\n    /*  24 */ \"SeekLT\"           OpHelp(\"key=r[P3@P4]\"),\n    /*  25 */ \"SeekLE\"           OpHelp(\"key=r[P3@P4]\"),\n    /*  26 */ \"SeekGE\"           OpHelp(\"key=r[P3@P4]\"),\n    /*  27 */ \"SeekGT\"           OpHelp(\"key=r[P3@P4]\"),\n    /*  28 */ \"NoConflict\"       OpHelp(\"key=r[P3@P4]\"),\n    /*  29 */ \"NotFound\"         OpHelp(\"key=r[P3@P4]\"),\n    /*  30 */ \"Found\"            OpHelp(\"key=r[P3@P4]\"),\n    /*  31 */ \"SeekRowid\"        OpHelp(\"intkey=r[P3]\"),\n    /*  32 */ \"NotExists\"        OpHelp(\"intkey=r[P3]\"),\n    /*  33 */ \"Last\"             OpHelp(\"\"),\n    /*  34 */ \"IfSmaller\"        OpHelp(\"\"),\n    /*  35 */ \"SorterSort\"       OpHelp(\"\"),\n    /*  36 */ \"Sort\"             OpHelp(\"\"),\n    /*  37 */ \"Rewind\"           OpHelp(\"\"),\n    /*  38 */ \"IdxLE\"            OpHelp(\"key=r[P3@P4]\"),\n    /*  39 */ \"IdxGT\"            OpHelp(\"key=r[P3@P4]\"),\n    /*  40 */ \"IdxLT\"            OpHelp(\"key=r[P3@P4]\"),\n    /*  41 */ \"IdxGE\"            OpHelp(\"key=r[P3@P4]\"),\n    /*  42 */ \"RowSetRead\"       OpHelp(\"r[P3]=rowset(P1)\"),\n    /*  43 */ \"Or\"               OpHelp(\"r[P3]=(r[P1] || r[P2])\"),\n    /*  44 */ \"And\"              OpHelp(\"r[P3]=(r[P1] && r[P2])\"),\n    /*  45 */ \"RowSetTest\"       OpHelp(\"if r[P3] in rowset(P1) goto P2\"),\n    /*  46 */ \"Program\"          OpHelp(\"\"),\n    /*  47 */ \"FkIfZero\"         OpHelp(\"if fkctr[P1]==0 goto P2\"),\n    /*  48 */ \"IfPos\"            OpHelp(\"if r[P1]>0 then r[P1]-=P3, goto P2\"),\n    /*  49 */ \"IfNotZero\"        OpHelp(\"if r[P1]!=0 then r[P1]--, goto P2\"),\n    /*  50 */ \"IsNull\"           OpHelp(\"if r[P1]==NULL goto P2\"),\n    /*  51 */ \"NotNull\"          OpHelp(\"if r[P1]!=NULL goto P2\"),\n    /*  52 */ \"Ne\"               OpHelp(\"IF r[P3]!=r[P1]\"),\n    /*  53 */ \"Eq\"               OpHelp(\"IF r[P3]==r[P1]\"),\n    /*  54 */ \"Gt\"               OpHelp(\"IF r[P3]>r[P1]\"),\n    /*  55 */ \"Le\"               OpHelp(\"IF r[P3]<=r[P1]\"),\n    /*  56 */ \"Lt\"               OpHelp(\"IF r[P3]<r[P1]\"),\n    /*  57 */ \"Ge\"               OpHelp(\"IF r[P3]>=r[P1]\"),\n    /*  58 */ \"ElseNotEq\"        OpHelp(\"\"),\n    /*  59 */ \"DecrJumpZero\"     OpHelp(\"if (--r[P1])==0 goto P2\"),\n    /*  60 */ \"IncrVacuum\"       OpHelp(\"\"),\n    /*  61 */ \"VNext\"            OpHelp(\"\"),\n    /*  62 */ \"Init\"             OpHelp(\"Start at P2\"),\n    /*  63 */ \"Return\"           OpHelp(\"\"),\n    /*  64 */ \"EndCoroutine\"     OpHelp(\"\"),\n    /*  65 */ \"HaltIfNull\"       OpHelp(\"if r[P3]=null halt\"),\n    /*  66 */ \"Halt\"             OpHelp(\"\"),\n    /*  67 */ \"Integer\"          OpHelp(\"r[P2]=P1\"),\n    /*  68 */ \"Int64\"            OpHelp(\"r[P2]=P4\"),\n    /*  69 */ \"String\"           OpHelp(\"r[P2]='P4' (len=P1)\"),\n    /*  70 */ \"Null\"             OpHelp(\"r[P2..P3]=NULL\"),\n    /*  71 */ \"SoftNull\"         OpHelp(\"r[P1]=NULL\"),\n    /*  72 */ \"Blob\"             OpHelp(\"r[P2]=P4 (len=P1)\"),\n    /*  73 */ \"Variable\"         OpHelp(\"r[P2]=parameter(P1,P4)\"),\n    /*  74 */ \"Move\"             OpHelp(\"r[P2@P3]=r[P1@P3]\"),\n    /*  75 */ \"Copy\"             OpHelp(\"r[P2@P3+1]=r[P1@P3+1]\"),\n    /*  76 */ \"SCopy\"            OpHelp(\"r[P2]=r[P1]\"),\n    /*  77 */ \"IntCopy\"          OpHelp(\"r[P2]=r[P1]\"),\n    /*  78 */ \"ResultRow\"        OpHelp(\"output=r[P1@P2]\"),\n    /*  79 */ \"CollSeq\"          OpHelp(\"\"),\n    /*  80 */ \"AddImm\"           OpHelp(\"r[P1]=r[P1]+P2\"),\n    /*  81 */ \"RealAffinity\"     OpHelp(\"\"),\n    /*  82 */ \"Cast\"             OpHelp(\"affinity(r[P1])\"),\n    /*  83 */ \"Permutation\"      OpHelp(\"\"),\n    /*  84 */ \"BitAnd\"           OpHelp(\"r[P3]=r[P1]&r[P2]\"),\n    /*  85 */ \"BitOr\"            OpHelp(\"r[P3]=r[P1]|r[P2]\"),\n    /*  86 */ \"ShiftLeft\"        OpHelp(\"r[P3]=r[P2]<<r[P1]\"),\n    /*  87 */ \"ShiftRight\"       OpHelp(\"r[P3]=r[P2]>>r[P1]\"),\n    /*  88 */ \"Add\"              OpHelp(\"r[P3]=r[P1]+r[P2]\"),\n    /*  89 */ \"Subtract\"         OpHelp(\"r[P3]=r[P2]-r[P1]\"),\n    /*  90 */ \"Multiply\"         OpHelp(\"r[P3]=r[P1]*r[P2]\"),\n    /*  91 */ \"Divide\"           OpHelp(\"r[P3]=r[P2]/r[P1]\"),\n    /*  92 */ \"Remainder\"        OpHelp(\"r[P3]=r[P2]%r[P1]\"),\n    /*  93 */ \"Concat\"           OpHelp(\"r[P3]=r[P2]+r[P1]\"),\n    /*  94 */ \"Compare\"          OpHelp(\"r[P1@P3] <-> r[P2@P3]\"),\n    /*  95 */ \"BitNot\"           OpHelp(\"r[P1]= ~r[P1]\"),\n    /*  96 */ \"IsTrue\"           OpHelp(\"r[P2] = coalesce(r[P1]==TRUE,P3) ^ P4\"),\n    /*  97 */ \"String8\"          OpHelp(\"r[P2]='P4'\"),\n    /*  98 */ \"Offset\"           OpHelp(\"r[P3] = sqlite_offset(P1)\"),\n    /*  99 */ \"Column\"           OpHelp(\"r[P3]=PX\"),\n    /* 100 */ \"Affinity\"         OpHelp(\"affinity(r[P1@P2])\"),\n    /* 101 */ \"MakeRecord\"       OpHelp(\"r[P3]=mkrec(r[P1@P2])\"),\n    /* 102 */ \"Count\"            OpHelp(\"r[P2]=count()\"),\n    /* 103 */ \"ReadCookie\"       OpHelp(\"\"),\n    /* 104 */ \"SetCookie\"        OpHelp(\"\"),\n    /* 105 */ \"ReopenIdx\"        OpHelp(\"root=P2 iDb=P3\"),\n    /* 106 */ \"OpenRead\"         OpHelp(\"root=P2 iDb=P3\"),\n    /* 107 */ \"OpenWrite\"        OpHelp(\"root=P2 iDb=P3\"),\n    /* 108 */ \"OpenDup\"          OpHelp(\"\"),\n    /* 109 */ \"OpenAutoindex\"    OpHelp(\"nColumn=P2\"),\n    /* 110 */ \"OpenEphemeral\"    OpHelp(\"nColumn=P2\"),\n    /* 111 */ \"SorterOpen\"       OpHelp(\"\"),\n    /* 112 */ \"SequenceTest\"     OpHelp(\"if( cursor[P1].ctr++ ) pc = P2\"),\n    /* 113 */ \"OpenPseudo\"       OpHelp(\"P3 columns in r[P2]\"),\n    /* 114 */ \"Close\"            OpHelp(\"\"),\n    /* 115 */ \"ColumnsUsed\"      OpHelp(\"\"),\n    /* 116 */ \"Sequence\"         OpHelp(\"r[P2]=cursor[P1].ctr++\"),\n    /* 117 */ \"NewRowid\"         OpHelp(\"r[P2]=rowid\"),\n    /* 118 */ \"Insert\"           OpHelp(\"intkey=r[P3] data=r[P2]\"),\n    /* 119 */ \"InsertInt\"        OpHelp(\"intkey=P3 data=r[P2]\"),\n    /* 120 */ \"Delete\"           OpHelp(\"\"),\n    /* 121 */ \"ResetCount\"       OpHelp(\"\"),\n    /* 122 */ \"SorterCompare\"    OpHelp(\"if key(P1)!=trim(r[P3],P4) goto P2\"),\n    /* 123 */ \"SorterData\"       OpHelp(\"r[P2]=data\"),\n    /* 124 */ \"RowData\"          OpHelp(\"r[P2]=data\"),\n    /* 125 */ \"Rowid\"            OpHelp(\"r[P2]=rowid\"),\n    /* 126 */ \"NullRow\"          OpHelp(\"\"),\n    /* 127 */ \"SeekEnd\"          OpHelp(\"\"),\n    /* 128 */ \"SorterInsert\"     OpHelp(\"key=r[P2]\"),\n    /* 129 */ \"IdxInsert\"        OpHelp(\"key=r[P2]\"),\n    /* 130 */ \"IdxDelete\"        OpHelp(\"key=r[P2@P3]\"),\n    /* 131 */ \"DeferredSeek\"     OpHelp(\"Move P3 to P1.rowid if needed\"),\n    /* 132 */ \"Real\"             OpHelp(\"r[P2]=P4\"),\n    /* 133 */ \"IdxRowid\"         OpHelp(\"r[P2]=rowid\"),\n    /* 134 */ \"Destroy\"          OpHelp(\"\"),\n    /* 135 */ \"Clear\"            OpHelp(\"\"),\n    /* 136 */ \"ResetSorter\"      OpHelp(\"\"),\n    /* 137 */ \"CreateBtree\"      OpHelp(\"r[P2]=root iDb=P1 flags=P3\"),\n    /* 138 */ \"SqlExec\"          OpHelp(\"\"),\n    /* 139 */ \"ParseSchema\"      OpHelp(\"\"),\n    /* 140 */ \"LoadAnalysis\"     OpHelp(\"\"),\n    /* 141 */ \"DropTable\"        OpHelp(\"\"),\n    /* 142 */ \"DropIndex\"        OpHelp(\"\"),\n    /* 143 */ \"DropTrigger\"      OpHelp(\"\"),\n    /* 144 */ \"IntegrityCk\"      OpHelp(\"\"),\n    /* 145 */ \"RowSetAdd\"        OpHelp(\"rowset(P1)=r[P2]\"),\n    /* 146 */ \"Param\"            OpHelp(\"\"),\n    /* 147 */ \"FkCounter\"        OpHelp(\"fkctr[P1]+=P2\"),\n    /* 148 */ \"MemMax\"           OpHelp(\"r[P1]=max(r[P1],r[P2])\"),\n    /* 149 */ \"OffsetLimit\"      OpHelp(\"if r[P1]>0 then r[P2]=r[P1]+max(0,r[P3]) else r[P2]=(-1)\"),\n    /* 150 */ \"AggStep0\"         OpHelp(\"accum=r[P3] step(r[P2@P5])\"),\n    /* 151 */ \"AggStep\"          OpHelp(\"accum=r[P3] step(r[P2@P5])\"),\n    /* 152 */ \"AggFinal\"         OpHelp(\"accum=r[P1] N=P2\"),\n    /* 153 */ \"Expire\"           OpHelp(\"\"),\n    /* 154 */ \"TableLock\"        OpHelp(\"iDb=P1 root=P2 write=P3\"),\n    /* 155 */ \"VBegin\"           OpHelp(\"\"),\n    /* 156 */ \"VCreate\"          OpHelp(\"\"),\n    /* 157 */ \"VDestroy\"         OpHelp(\"\"),\n    /* 158 */ \"VOpen\"            OpHelp(\"\"),\n    /* 159 */ \"VColumn\"          OpHelp(\"r[P3]=vcolumn(P2)\"),\n    /* 160 */ \"VRename\"          OpHelp(\"\"),\n    /* 161 */ \"Pagecount\"        OpHelp(\"\"),\n    /* 162 */ \"MaxPgcnt\"         OpHelp(\"\"),\n    /* 163 */ \"PureFunc0\"        OpHelp(\"\"),\n    /* 164 */ \"Function0\"        OpHelp(\"r[P3]=func(r[P2@P5])\"),\n    /* 165 */ \"PureFunc\"         OpHelp(\"\"),\n    /* 166 */ \"Function\"         OpHelp(\"r[P3]=func(r[P2@P5])\"),\n    /* 167 */ \"Trace\"            OpHelp(\"\"),\n    /* 168 */ \"CursorHint\"       OpHelp(\"\"),\n    /* 169 */ \"Noop\"             OpHelp(\"\"),\n    /* 170 */ \"Explain\"          OpHelp(\"\"),\n  };\n  return azName[i];\n}\n#endif\n\n/************** End of opcodes.c *********************************************/\n/************** Begin file os_unix.c *****************************************/\n/*\n** 2004 May 22\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n******************************************************************************\n**\n** This file contains the VFS implementation for unix-like operating systems\n** include Linux, MacOSX, *BSD, QNX, VxWorks, AIX, HPUX, and others.\n**\n** There are actually several different VFS implementations in this file.\n** The differences are in the way that file locking is done.  The default\n** implementation uses Posix Advisory Locks.  Alternative implementations\n** use flock(), dot-files, various proprietary locking schemas, or simply\n** skip locking all together.\n**\n** This source file is organized into divisions where the logic for various\n** subfunctions is contained within the appropriate division.  PLEASE\n** KEEP THE STRUCTURE OF THIS FILE INTACT.  New code should be placed\n** in the correct division and should be clearly labeled.\n**\n** The layout of divisions is as follows:\n**\n**   *  General-purpose declarations and utility functions.\n**   *  Unique file ID logic used by VxWorks.\n**   *  Various locking primitive implementations (all except proxy locking):\n**      + for Posix Advisory Locks\n**      + for no-op locks\n**      + for dot-file locks\n**      + for flock() locking\n**      + for named semaphore locks (VxWorks only)\n**      + for AFP filesystem locks (MacOSX only)\n**   *  sqlite3_file methods not associated with locking.\n**   *  Definitions of sqlite3_io_methods objects for all locking\n**      methods plus \"finder\" functions for each locking method.\n**   *  sqlite3_vfs method implementations.\n**   *  Locking primitives for the proxy uber-locking-method. (MacOSX only)\n**   *  Definitions of sqlite3_vfs objects for all locking methods\n**      plus implementations of sqlite3_os_init() and sqlite3_os_end().\n*/\n/* #include \"sqliteInt.h\" */\n#if SQLITE_OS_UNIX              /* This file is used on unix only */\n\n/*\n** There are various methods for file locking used for concurrency\n** control:\n**\n**   1. POSIX locking (the default),\n**   2. No locking,\n**   3. Dot-file locking,\n**   4. flock() locking,\n**   5. AFP locking (OSX only),\n**   6. Named POSIX semaphores (VXWorks only),\n**   7. proxy locking. (OSX only)\n**\n** Styles 4, 5, and 7 are only available of SQLITE_ENABLE_LOCKING_STYLE\n** is defined to 1.  The SQLITE_ENABLE_LOCKING_STYLE also enables automatic\n** selection of the appropriate locking style based on the filesystem\n** where the database is located.  \n*/\n#if !defined(SQLITE_ENABLE_LOCKING_STYLE)\n#  if defined(__APPLE__)\n#    define SQLITE_ENABLE_LOCKING_STYLE 1\n#  else\n#    define SQLITE_ENABLE_LOCKING_STYLE 0\n#  endif\n#endif\n\n/* Use pread() and pwrite() if they are available */\n#if defined(__APPLE__)\n# define HAVE_PREAD 1\n# define HAVE_PWRITE 1\n#endif\n#if defined(HAVE_PREAD64) && defined(HAVE_PWRITE64)\n# undef USE_PREAD\n# define USE_PREAD64 1\n#elif defined(HAVE_PREAD) && defined(HAVE_PWRITE)\n# undef USE_PREAD64\n# define USE_PREAD 1\n#endif\n\n/*\n** standard include files.\n*/\n#include <sys/types.h>\n#include <sys/stat.h>\n#include <fcntl.h>\n#include <sys/ioctl.h>\n#include <unistd.h>\n/* #include <time.h> */\n#include <sys/time.h>\n#include <errno.h>\n#if !defined(SQLITE_OMIT_WAL) || SQLITE_MAX_MMAP_SIZE>0\n# include <sys/mman.h>\n#endif\n\n#if SQLITE_ENABLE_LOCKING_STYLE\n/* # include <sys/ioctl.h> */\n# include <sys/file.h>\n# include <sys/param.h>\n#endif /* SQLITE_ENABLE_LOCKING_STYLE */\n\n#if defined(__APPLE__) && ((__MAC_OS_X_VERSION_MIN_REQUIRED > 1050) || \\\n                           (__IPHONE_OS_VERSION_MIN_REQUIRED > 2000))\n#  if (!defined(TARGET_OS_EMBEDDED) || (TARGET_OS_EMBEDDED==0)) \\\n       && (!defined(TARGET_IPHONE_SIMULATOR) || (TARGET_IPHONE_SIMULATOR==0))\n#    define HAVE_GETHOSTUUID 1\n#  else\n#    warning \"gethostuuid() is disabled.\"\n#  endif\n#endif\n\n\n#if OS_VXWORKS\n/* # include <sys/ioctl.h> */\n# include <semaphore.h>\n# include <limits.h>\n#endif /* OS_VXWORKS */\n\n#if defined(__APPLE__) || SQLITE_ENABLE_LOCKING_STYLE\n# include <sys/mount.h>\n#endif\n\n#ifdef HAVE_UTIME\n# include <utime.h>\n#endif\n\n/*\n** Allowed values of unixFile.fsFlags\n*/\n#define SQLITE_FSFLAGS_IS_MSDOS     0x1\n\n/*\n** If we are to be thread-safe, include the pthreads header and define\n** the SQLITE_UNIX_THREADS macro.\n*/\n#if SQLITE_THREADSAFE\n/* # include <pthread.h> */\n# define SQLITE_UNIX_THREADS 1\n#endif\n\n/*\n** Default permissions when creating a new file\n*/\n#ifndef SQLITE_DEFAULT_FILE_PERMISSIONS\n# define SQLITE_DEFAULT_FILE_PERMISSIONS 0644\n#endif\n\n/*\n** Default permissions when creating auto proxy dir\n*/\n#ifndef SQLITE_DEFAULT_PROXYDIR_PERMISSIONS\n# define SQLITE_DEFAULT_PROXYDIR_PERMISSIONS 0755\n#endif\n\n/*\n** Maximum supported path-length.\n*/\n#define MAX_PATHNAME 512\n\n/*\n** Maximum supported symbolic links\n*/\n#define SQLITE_MAX_SYMLINKS 100\n\n/* Always cast the getpid() return type for compatibility with\n** kernel modules in VxWorks. */\n#define osGetpid(X) (pid_t)getpid()\n\n/*\n** Only set the lastErrno if the error code is a real error and not \n** a normal expected return code of SQLITE_BUSY or SQLITE_OK\n*/\n#define IS_LOCK_ERROR(x)  ((x != SQLITE_OK) && (x != SQLITE_BUSY))\n\n/* Forward references */\ntypedef struct unixShm unixShm;               /* Connection shared memory */\ntypedef struct unixShmNode unixShmNode;       /* Shared memory instance */\ntypedef struct unixInodeInfo unixInodeInfo;   /* An i-node */\ntypedef struct UnixUnusedFd UnixUnusedFd;     /* An unused file descriptor */\n\n/*\n** Sometimes, after a file handle is closed by SQLite, the file descriptor\n** cannot be closed immediately. In these cases, instances of the following\n** structure are used to store the file descriptor while waiting for an\n** opportunity to either close or reuse it.\n*/\nstruct UnixUnusedFd {\n  int fd;                   /* File descriptor to close */\n  int flags;                /* Flags this file descriptor was opened with */\n  UnixUnusedFd *pNext;      /* Next unused file descriptor on same file */\n};\n\n/*\n** The unixFile structure is subclass of sqlite3_file specific to the unix\n** VFS implementations.\n*/\ntypedef struct unixFile unixFile;\nstruct unixFile {\n  sqlite3_io_methods const *pMethod;  /* Always the first entry */\n  sqlite3_vfs *pVfs;                  /* The VFS that created this unixFile */\n  unixInodeInfo *pInode;              /* Info about locks on this inode */\n  int h;                              /* The file descriptor */\n  unsigned char eFileLock;            /* The type of lock held on this fd */\n  unsigned short int ctrlFlags;       /* Behavioral bits.  UNIXFILE_* flags */\n  int lastErrno;                      /* The unix errno from last I/O error */\n  void *lockingContext;               /* Locking style specific state */\n  UnixUnusedFd *pPreallocatedUnused;  /* Pre-allocated UnixUnusedFd */\n  const char *zPath;                  /* Name of the file */\n  unixShm *pShm;                      /* Shared memory segment information */\n  int szChunk;                        /* Configured by FCNTL_CHUNK_SIZE */\n#if SQLITE_MAX_MMAP_SIZE>0\n  int nFetchOut;                      /* Number of outstanding xFetch refs */\n  sqlite3_int64 mmapSize;             /* Usable size of mapping at pMapRegion */\n  sqlite3_int64 mmapSizeActual;       /* Actual size of mapping at pMapRegion */\n  sqlite3_int64 mmapSizeMax;          /* Configured FCNTL_MMAP_SIZE value */\n  void *pMapRegion;                   /* Memory mapped region */\n#endif\n  int sectorSize;                     /* Device sector size */\n  int deviceCharacteristics;          /* Precomputed device characteristics */\n#if SQLITE_ENABLE_LOCKING_STYLE\n  int openFlags;                      /* The flags specified at open() */\n#endif\n#if SQLITE_ENABLE_LOCKING_STYLE || defined(__APPLE__)\n  unsigned fsFlags;                   /* cached details from statfs() */\n#endif\n#if OS_VXWORKS\n  struct vxworksFileId *pId;          /* Unique file ID */\n#endif\n#ifdef SQLITE_DEBUG\n  /* The next group of variables are used to track whether or not the\n  ** transaction counter in bytes 24-27 of database files are updated\n  ** whenever any part of the database changes.  An assertion fault will\n  ** occur if a file is updated without also updating the transaction\n  ** counter.  This test is made to avoid new problems similar to the\n  ** one described by ticket #3584. \n  */\n  unsigned char transCntrChng;   /* True if the transaction counter changed */\n  unsigned char dbUpdate;        /* True if any part of database file changed */\n  unsigned char inNormalWrite;   /* True if in a normal write operation */\n\n#endif\n\n#ifdef SQLITE_TEST\n  /* In test mode, increase the size of this structure a bit so that \n  ** it is larger than the struct CrashFile defined in test6.c.\n  */\n  char aPadding[32];\n#endif\n};\n\n/* This variable holds the process id (pid) from when the xRandomness()\n** method was called.  If xOpen() is called from a different process id,\n** indicating that a fork() has occurred, the PRNG will be reset.\n*/\nstatic pid_t randomnessPid = 0;\n\n/*\n** Allowed values for the unixFile.ctrlFlags bitmask:\n*/\n#define UNIXFILE_EXCL        0x01     /* Connections from one process only */\n#define UNIXFILE_RDONLY      0x02     /* Connection is read only */\n#define UNIXFILE_PERSIST_WAL 0x04     /* Persistent WAL mode */\n#ifndef SQLITE_DISABLE_DIRSYNC\n# define UNIXFILE_DIRSYNC    0x08     /* Directory sync needed */\n#else\n# define UNIXFILE_DIRSYNC    0x00\n#endif\n#define UNIXFILE_PSOW        0x10     /* SQLITE_IOCAP_POWERSAFE_OVERWRITE */\n#define UNIXFILE_DELETE      0x20     /* Delete on close */\n#define UNIXFILE_URI         0x40     /* Filename might have query parameters */\n#define UNIXFILE_NOLOCK      0x80     /* Do no file locking */\n\n/*\n** Include code that is common to all os_*.c files\n*/\n/************** Include os_common.h in the middle of os_unix.c ***************/\n/************** Begin file os_common.h ***************************************/\n/*\n** 2004 May 22\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n******************************************************************************\n**\n** This file contains macros and a little bit of code that is common to\n** all of the platform-specific files (os_*.c) and is #included into those\n** files.\n**\n** This file should be #included by the os_*.c files only.  It is not a\n** general purpose header file.\n*/\n#ifndef _OS_COMMON_H_\n#define _OS_COMMON_H_\n\n/*\n** At least two bugs have slipped in because we changed the MEMORY_DEBUG\n** macro to SQLITE_DEBUG and some older makefiles have not yet made the\n** switch.  The following code should catch this problem at compile-time.\n*/\n#ifdef MEMORY_DEBUG\n# error \"The MEMORY_DEBUG macro is obsolete.  Use SQLITE_DEBUG instead.\"\n#endif\n\n/*\n** Macros for performance tracing.  Normally turned off.  Only works\n** on i486 hardware.\n*/\n#ifdef SQLITE_PERFORMANCE_TRACE\n\n/*\n** hwtime.h contains inline assembler code for implementing\n** high-performance timing routines.\n*/\n/************** Include hwtime.h in the middle of os_common.h ****************/\n/************** Begin file hwtime.h ******************************************/\n/*\n** 2008 May 27\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n******************************************************************************\n**\n** This file contains inline asm code for retrieving \"high-performance\"\n** counters for x86 class CPUs.\n*/\n#ifndef SQLITE_HWTIME_H\n#define SQLITE_HWTIME_H\n\n/*\n** The following routine only works on pentium-class (or newer) processors.\n** It uses the RDTSC opcode to read the cycle count value out of the\n** processor and returns that value.  This can be used for high-res\n** profiling.\n*/\n#if (defined(__GNUC__) || defined(_MSC_VER)) && \\\n      (defined(i386) || defined(__i386__) || defined(_M_IX86))\n\n  #if defined(__GNUC__)\n\n  __inline__ sqlite_uint64 sqlite3Hwtime(void){\n     unsigned int lo, hi;\n     __asm__ __volatile__ (\"rdtsc\" : \"=a\" (lo), \"=d\" (hi));\n     return (sqlite_uint64)hi << 32 | lo;\n  }\n\n  #elif defined(_MSC_VER)\n\n  __declspec(naked) __inline sqlite_uint64 __cdecl sqlite3Hwtime(void){\n     __asm {\n        rdtsc\n        ret       ; return value at EDX:EAX\n     }\n  }\n\n  #endif\n\n#elif (defined(__GNUC__) && defined(__x86_64__))\n\n  __inline__ sqlite_uint64 sqlite3Hwtime(void){\n      unsigned long val;\n      __asm__ __volatile__ (\"rdtsc\" : \"=A\" (val));\n      return val;\n  }\n \n#elif (defined(__GNUC__) && defined(__ppc__))\n\n  __inline__ sqlite_uint64 sqlite3Hwtime(void){\n      unsigned long long retval;\n      unsigned long junk;\n      __asm__ __volatile__ (\"\\n\\\n          1:      mftbu   %1\\n\\\n                  mftb    %L0\\n\\\n                  mftbu   %0\\n\\\n                  cmpw    %0,%1\\n\\\n                  bne     1b\"\n                  : \"=r\" (retval), \"=r\" (junk));\n      return retval;\n  }\n\n#else\n\n  #error Need implementation of sqlite3Hwtime() for your platform.\n\n  /*\n  ** To compile without implementing sqlite3Hwtime() for your platform,\n  ** you can remove the above #error and use the following\n  ** stub function.  You will lose timing support for many\n  ** of the debugging and testing utilities, but it should at\n  ** least compile and run.\n  */\nSQLITE_PRIVATE   sqlite_uint64 sqlite3Hwtime(void){ return ((sqlite_uint64)0); }\n\n#endif\n\n#endif /* !defined(SQLITE_HWTIME_H) */\n\n/************** End of hwtime.h **********************************************/\n/************** Continuing where we left off in os_common.h ******************/\n\nstatic sqlite_uint64 g_start;\nstatic sqlite_uint64 g_elapsed;\n#define TIMER_START       g_start=sqlite3Hwtime()\n#define TIMER_END         g_elapsed=sqlite3Hwtime()-g_start\n#define TIMER_ELAPSED     g_elapsed\n#else\n#define TIMER_START\n#define TIMER_END\n#define TIMER_ELAPSED     ((sqlite_uint64)0)\n#endif\n\n/*\n** If we compile with the SQLITE_TEST macro set, then the following block\n** of code will give us the ability to simulate a disk I/O error.  This\n** is used for testing the I/O recovery logic.\n*/\n#if defined(SQLITE_TEST)\nSQLITE_API extern int sqlite3_io_error_hit;\nSQLITE_API extern int sqlite3_io_error_hardhit;\nSQLITE_API extern int sqlite3_io_error_pending;\nSQLITE_API extern int sqlite3_io_error_persist;\nSQLITE_API extern int sqlite3_io_error_benign;\nSQLITE_API extern int sqlite3_diskfull_pending;\nSQLITE_API extern int sqlite3_diskfull;\n#define SimulateIOErrorBenign(X) sqlite3_io_error_benign=(X)\n#define SimulateIOError(CODE)  \\\n  if( (sqlite3_io_error_persist && sqlite3_io_error_hit) \\\n       || sqlite3_io_error_pending-- == 1 )  \\\n              { local_ioerr(); CODE; }\nstatic void local_ioerr(){\n  IOTRACE((\"IOERR\\n\"));\n  sqlite3_io_error_hit++;\n  if( !sqlite3_io_error_benign ) sqlite3_io_error_hardhit++;\n}\n#define SimulateDiskfullError(CODE) \\\n   if( sqlite3_diskfull_pending ){ \\\n     if( sqlite3_diskfull_pending == 1 ){ \\\n       local_ioerr(); \\\n       sqlite3_diskfull = 1; \\\n       sqlite3_io_error_hit = 1; \\\n       CODE; \\\n     }else{ \\\n       sqlite3_diskfull_pending--; \\\n     } \\\n   }\n#else\n#define SimulateIOErrorBenign(X)\n#define SimulateIOError(A)\n#define SimulateDiskfullError(A)\n#endif /* defined(SQLITE_TEST) */\n\n/*\n** When testing, keep a count of the number of open files.\n*/\n#if defined(SQLITE_TEST)\nSQLITE_API extern int sqlite3_open_file_count;\n#define OpenCounter(X)  sqlite3_open_file_count+=(X)\n#else\n#define OpenCounter(X)\n#endif /* defined(SQLITE_TEST) */\n\n#endif /* !defined(_OS_COMMON_H_) */\n\n/************** End of os_common.h *******************************************/\n/************** Continuing where we left off in os_unix.c ********************/\n\n/*\n** Define various macros that are missing from some systems.\n*/\n#ifndef O_LARGEFILE\n# define O_LARGEFILE 0\n#endif\n#ifdef SQLITE_DISABLE_LFS\n# undef O_LARGEFILE\n# define O_LARGEFILE 0\n#endif\n#ifndef O_NOFOLLOW\n# define O_NOFOLLOW 0\n#endif\n#ifndef O_BINARY\n# define O_BINARY 0\n#endif\n\n/*\n** The threadid macro resolves to the thread-id or to 0.  Used for\n** testing and debugging only.\n*/\n#if SQLITE_THREADSAFE\n#define threadid pthread_self()\n#else\n#define threadid 0\n#endif\n\n/*\n** HAVE_MREMAP defaults to true on Linux and false everywhere else.\n*/\n#if !defined(HAVE_MREMAP)\n# if defined(__linux__) && defined(_GNU_SOURCE)\n#  define HAVE_MREMAP 1\n# else\n#  define HAVE_MREMAP 0\n# endif\n#endif\n\n/*\n** Explicitly call the 64-bit version of lseek() on Android. Otherwise, lseek()\n** is the 32-bit version, even if _FILE_OFFSET_BITS=64 is defined.\n*/\n#ifdef __ANDROID__\n# define lseek lseek64\n#endif\n\n#ifdef __linux__\n/*\n** Linux-specific IOCTL magic numbers used for controlling F2FS\n*/\n#define F2FS_IOCTL_MAGIC        0xf5\n#define F2FS_IOC_START_ATOMIC_WRITE     _IO(F2FS_IOCTL_MAGIC, 1)\n#define F2FS_IOC_COMMIT_ATOMIC_WRITE    _IO(F2FS_IOCTL_MAGIC, 2)\n#define F2FS_IOC_START_VOLATILE_WRITE   _IO(F2FS_IOCTL_MAGIC, 3)\n#define F2FS_IOC_ABORT_VOLATILE_WRITE   _IO(F2FS_IOCTL_MAGIC, 5)\n#define F2FS_IOC_GET_FEATURES           _IOR(F2FS_IOCTL_MAGIC, 12, u32)\n#define F2FS_FEATURE_ATOMIC_WRITE 0x0004\n#endif /* __linux__ */\n\n\n/*\n** Different Unix systems declare open() in different ways.  Same use\n** open(const char*,int,mode_t).  Others use open(const char*,int,...).\n** The difference is important when using a pointer to the function.\n**\n** The safest way to deal with the problem is to always use this wrapper\n** which always has the same well-defined interface.\n*/\nstatic int posixOpen(const char *zFile, int flags, int mode){\n  return open(zFile, flags, mode);\n}\n\n/* Forward reference */\nstatic int openDirectory(const char*, int*);\nstatic int unixGetpagesize(void);\n\n/*\n** Many system calls are accessed through pointer-to-functions so that\n** they may be overridden at runtime to facilitate fault injection during\n** testing and sandboxing.  The following array holds the names and pointers\n** to all overrideable system calls.\n*/\nstatic struct unix_syscall {\n  const char *zName;            /* Name of the system call */\n  sqlite3_syscall_ptr pCurrent; /* Current value of the system call */\n  sqlite3_syscall_ptr pDefault; /* Default value */\n} aSyscall[] = {\n  { \"open\",         (sqlite3_syscall_ptr)posixOpen,  0  },\n#define osOpen      ((int(*)(const char*,int,int))aSyscall[0].pCurrent)\n\n  { \"close\",        (sqlite3_syscall_ptr)close,      0  },\n#define osClose     ((int(*)(int))aSyscall[1].pCurrent)\n\n  { \"access\",       (sqlite3_syscall_ptr)access,     0  },\n#define osAccess    ((int(*)(const char*,int))aSyscall[2].pCurrent)\n\n  { \"getcwd\",       (sqlite3_syscall_ptr)getcwd,     0  },\n#define osGetcwd    ((char*(*)(char*,size_t))aSyscall[3].pCurrent)\n\n  { \"stat\",         (sqlite3_syscall_ptr)stat,       0  },\n#define osStat      ((int(*)(const char*,struct stat*))aSyscall[4].pCurrent)\n\n/*\n** The DJGPP compiler environment looks mostly like Unix, but it\n** lacks the fcntl() system call.  So redefine fcntl() to be something\n** that always succeeds.  This means that locking does not occur under\n** DJGPP.  But it is DOS - what did you expect?\n*/\n#ifdef __DJGPP__\n  { \"fstat\",        0,                 0  },\n#define osFstat(a,b,c)    0\n#else     \n  { \"fstat\",        (sqlite3_syscall_ptr)fstat,      0  },\n#define osFstat     ((int(*)(int,struct stat*))aSyscall[5].pCurrent)\n#endif\n\n  { \"ftruncate\",    (sqlite3_syscall_ptr)ftruncate,  0  },\n#define osFtruncate ((int(*)(int,off_t))aSyscall[6].pCurrent)\n\n  { \"fcntl\",        (sqlite3_syscall_ptr)fcntl,      0  },\n#define osFcntl     ((int(*)(int,int,...))aSyscall[7].pCurrent)\n\n  { \"read\",         (sqlite3_syscall_ptr)read,       0  },\n#define osRead      ((ssize_t(*)(int,void*,size_t))aSyscall[8].pCurrent)\n\n#if defined(USE_PREAD) || SQLITE_ENABLE_LOCKING_STYLE\n  { \"pread\",        (sqlite3_syscall_ptr)pread,      0  },\n#else\n  { \"pread\",        (sqlite3_syscall_ptr)0,          0  },\n#endif\n#define osPread     ((ssize_t(*)(int,void*,size_t,off_t))aSyscall[9].pCurrent)\n\n#if defined(USE_PREAD64)\n  { \"pread64\",      (sqlite3_syscall_ptr)pread64,    0  },\n#else\n  { \"pread64\",      (sqlite3_syscall_ptr)0,          0  },\n#endif\n#define osPread64 ((ssize_t(*)(int,void*,size_t,off64_t))aSyscall[10].pCurrent)\n\n  { \"write\",        (sqlite3_syscall_ptr)write,      0  },\n#define osWrite     ((ssize_t(*)(int,const void*,size_t))aSyscall[11].pCurrent)\n\n#if defined(USE_PREAD) || SQLITE_ENABLE_LOCKING_STYLE\n  { \"pwrite\",       (sqlite3_syscall_ptr)pwrite,     0  },\n#else\n  { \"pwrite\",       (sqlite3_syscall_ptr)0,          0  },\n#endif\n#define osPwrite    ((ssize_t(*)(int,const void*,size_t,off_t))\\\n                    aSyscall[12].pCurrent)\n\n#if defined(USE_PREAD64)\n  { \"pwrite64\",     (sqlite3_syscall_ptr)pwrite64,   0  },\n#else\n  { \"pwrite64\",     (sqlite3_syscall_ptr)0,          0  },\n#endif\n#define osPwrite64  ((ssize_t(*)(int,const void*,size_t,off64_t))\\\n                    aSyscall[13].pCurrent)\n\n  { \"fchmod\",       (sqlite3_syscall_ptr)fchmod,          0  },\n#define osFchmod    ((int(*)(int,mode_t))aSyscall[14].pCurrent)\n\n#if defined(HAVE_POSIX_FALLOCATE) && HAVE_POSIX_FALLOCATE\n  { \"fallocate\",    (sqlite3_syscall_ptr)posix_fallocate,  0 },\n#else\n  { \"fallocate\",    (sqlite3_syscall_ptr)0,                0 },\n#endif\n#define osFallocate ((int(*)(int,off_t,off_t))aSyscall[15].pCurrent)\n\n  { \"unlink\",       (sqlite3_syscall_ptr)unlink,           0 },\n#define osUnlink    ((int(*)(const char*))aSyscall[16].pCurrent)\n\n  { \"openDirectory\",    (sqlite3_syscall_ptr)openDirectory,      0 },\n#define osOpenDirectory ((int(*)(const char*,int*))aSyscall[17].pCurrent)\n\n  { \"mkdir\",        (sqlite3_syscall_ptr)mkdir,           0 },\n#define osMkdir     ((int(*)(const char*,mode_t))aSyscall[18].pCurrent)\n\n  { \"rmdir\",        (sqlite3_syscall_ptr)rmdir,           0 },\n#define osRmdir     ((int(*)(const char*))aSyscall[19].pCurrent)\n\n#if defined(HAVE_FCHOWN)\n  { \"fchown\",       (sqlite3_syscall_ptr)fchown,          0 },\n#else\n  { \"fchown\",       (sqlite3_syscall_ptr)0,               0 },\n#endif\n#define osFchown    ((int(*)(int,uid_t,gid_t))aSyscall[20].pCurrent)\n\n#if defined(HAVE_FCHOWN)\n  { \"geteuid\",      (sqlite3_syscall_ptr)geteuid,         0 },\n#else\n  { \"geteuid\",      (sqlite3_syscall_ptr)0,               0 },\n#endif\n#define osGeteuid   ((uid_t(*)(void))aSyscall[21].pCurrent)\n\n#if !defined(SQLITE_OMIT_WAL) || SQLITE_MAX_MMAP_SIZE>0\n  { \"mmap\",         (sqlite3_syscall_ptr)mmap,            0 },\n#else\n  { \"mmap\",         (sqlite3_syscall_ptr)0,               0 },\n#endif\n#define osMmap ((void*(*)(void*,size_t,int,int,int,off_t))aSyscall[22].pCurrent)\n\n#if !defined(SQLITE_OMIT_WAL) || SQLITE_MAX_MMAP_SIZE>0\n  { \"munmap\",       (sqlite3_syscall_ptr)munmap,          0 },\n#else\n  { \"munmap\",       (sqlite3_syscall_ptr)0,               0 },\n#endif\n#define osMunmap ((int(*)(void*,size_t))aSyscall[23].pCurrent)\n\n#if HAVE_MREMAP && (!defined(SQLITE_OMIT_WAL) || SQLITE_MAX_MMAP_SIZE>0)\n  { \"mremap\",       (sqlite3_syscall_ptr)mremap,          0 },\n#else\n  { \"mremap\",       (sqlite3_syscall_ptr)0,               0 },\n#endif\n#define osMremap ((void*(*)(void*,size_t,size_t,int,...))aSyscall[24].pCurrent)\n\n#if !defined(SQLITE_OMIT_WAL) || SQLITE_MAX_MMAP_SIZE>0\n  { \"getpagesize\",  (sqlite3_syscall_ptr)unixGetpagesize, 0 },\n#else\n  { \"getpagesize\",  (sqlite3_syscall_ptr)0,               0 },\n#endif\n#define osGetpagesize ((int(*)(void))aSyscall[25].pCurrent)\n\n#if defined(HAVE_READLINK)\n  { \"readlink\",     (sqlite3_syscall_ptr)readlink,        0 },\n#else\n  { \"readlink\",     (sqlite3_syscall_ptr)0,               0 },\n#endif\n#define osReadlink ((ssize_t(*)(const char*,char*,size_t))aSyscall[26].pCurrent)\n\n#if defined(HAVE_LSTAT)\n  { \"lstat\",         (sqlite3_syscall_ptr)lstat,          0 },\n#else\n  { \"lstat\",         (sqlite3_syscall_ptr)0,              0 },\n#endif\n#define osLstat      ((int(*)(const char*,struct stat*))aSyscall[27].pCurrent)\n\n#if defined(__linux__) && defined(SQLITE_ENABLE_BATCH_ATOMIC_WRITE)\n  { \"ioctl\",         (sqlite3_syscall_ptr)ioctl,          0 },\n#else\n  { \"ioctl\",         (sqlite3_syscall_ptr)0,              0 },\n#endif\n#define osIoctl ((int(*)(int,int,...))aSyscall[28].pCurrent)\n\n}; /* End of the overrideable system calls */\n\n\n/*\n** On some systems, calls to fchown() will trigger a message in a security\n** log if they come from non-root processes.  So avoid calling fchown() if\n** we are not running as root.\n*/\nstatic int robustFchown(int fd, uid_t uid, gid_t gid){\n#if defined(HAVE_FCHOWN)\n  return osGeteuid() ? 0 : osFchown(fd,uid,gid);\n#else\n  return 0;\n#endif\n}\n\n/*\n** This is the xSetSystemCall() method of sqlite3_vfs for all of the\n** \"unix\" VFSes.  Return SQLITE_OK opon successfully updating the\n** system call pointer, or SQLITE_NOTFOUND if there is no configurable\n** system call named zName.\n*/\nstatic int unixSetSystemCall(\n  sqlite3_vfs *pNotUsed,        /* The VFS pointer.  Not used */\n  const char *zName,            /* Name of system call to override */\n  sqlite3_syscall_ptr pNewFunc  /* Pointer to new system call value */\n){\n  unsigned int i;\n  int rc = SQLITE_NOTFOUND;\n\n  UNUSED_PARAMETER(pNotUsed);\n  if( zName==0 ){\n    /* If no zName is given, restore all system calls to their default\n    ** settings and return NULL\n    */\n    rc = SQLITE_OK;\n    for(i=0; i<sizeof(aSyscall)/sizeof(aSyscall[0]); i++){\n      if( aSyscall[i].pDefault ){\n        aSyscall[i].pCurrent = aSyscall[i].pDefault;\n      }\n    }\n  }else{\n    /* If zName is specified, operate on only the one system call\n    ** specified.\n    */\n    for(i=0; i<sizeof(aSyscall)/sizeof(aSyscall[0]); i++){\n      if( strcmp(zName, aSyscall[i].zName)==0 ){\n        if( aSyscall[i].pDefault==0 ){\n          aSyscall[i].pDefault = aSyscall[i].pCurrent;\n        }\n        rc = SQLITE_OK;\n        if( pNewFunc==0 ) pNewFunc = aSyscall[i].pDefault;\n        aSyscall[i].pCurrent = pNewFunc;\n        break;\n      }\n    }\n  }\n  return rc;\n}\n\n/*\n** Return the value of a system call.  Return NULL if zName is not a\n** recognized system call name.  NULL is also returned if the system call\n** is currently undefined.\n*/\nstatic sqlite3_syscall_ptr unixGetSystemCall(\n  sqlite3_vfs *pNotUsed,\n  const char *zName\n){\n  unsigned int i;\n\n  UNUSED_PARAMETER(pNotUsed);\n  for(i=0; i<sizeof(aSyscall)/sizeof(aSyscall[0]); i++){\n    if( strcmp(zName, aSyscall[i].zName)==0 ) return aSyscall[i].pCurrent;\n  }\n  return 0;\n}\n\n/*\n** Return the name of the first system call after zName.  If zName==NULL\n** then return the name of the first system call.  Return NULL if zName\n** is the last system call or if zName is not the name of a valid\n** system call.\n*/\nstatic const char *unixNextSystemCall(sqlite3_vfs *p, const char *zName){\n  int i = -1;\n\n  UNUSED_PARAMETER(p);\n  if( zName ){\n    for(i=0; i<ArraySize(aSyscall)-1; i++){\n      if( strcmp(zName, aSyscall[i].zName)==0 ) break;\n    }\n  }\n  for(i++; i<ArraySize(aSyscall); i++){\n    if( aSyscall[i].pCurrent!=0 ) return aSyscall[i].zName;\n  }\n  return 0;\n}\n\n/*\n** Do not accept any file descriptor less than this value, in order to avoid\n** opening database file using file descriptors that are commonly used for \n** standard input, output, and error.\n*/\n#ifndef SQLITE_MINIMUM_FILE_DESCRIPTOR\n# define SQLITE_MINIMUM_FILE_DESCRIPTOR 3\n#endif\n\n/*\n** Invoke open().  Do so multiple times, until it either succeeds or\n** fails for some reason other than EINTR.\n**\n** If the file creation mode \"m\" is 0 then set it to the default for\n** SQLite.  The default is SQLITE_DEFAULT_FILE_PERMISSIONS (normally\n** 0644) as modified by the system umask.  If m is not 0, then\n** make the file creation mode be exactly m ignoring the umask.\n**\n** The m parameter will be non-zero only when creating -wal, -journal,\n** and -shm files.  We want those files to have *exactly* the same\n** permissions as their original database, unadulterated by the umask.\n** In that way, if a database file is -rw-rw-rw or -rw-rw-r-, and a\n** transaction crashes and leaves behind hot journals, then any\n** process that is able to write to the database will also be able to\n** recover the hot journals.\n*/\nstatic int robust_open(const char *z, int f, mode_t m){\n  int fd;\n  mode_t m2 = m ? m : SQLITE_DEFAULT_FILE_PERMISSIONS;\n  while(1){\n#if defined(O_CLOEXEC)\n    fd = osOpen(z,f|O_CLOEXEC,m2);\n#else\n    fd = osOpen(z,f,m2);\n#endif\n    if( fd<0 ){\n      if( errno==EINTR ) continue;\n      break;\n    }\n    if( fd>=SQLITE_MINIMUM_FILE_DESCRIPTOR ) break;\n    osClose(fd);\n    sqlite3_log(SQLITE_WARNING, \n                \"attempt to open \\\"%s\\\" as file descriptor %d\", z, fd);\n    fd = -1;\n    if( osOpen(\"/dev/null\", f, m)<0 ) break;\n  }\n  if( fd>=0 ){\n    if( m!=0 ){\n      struct stat statbuf;\n      if( osFstat(fd, &statbuf)==0 \n       && statbuf.st_size==0\n       && (statbuf.st_mode&0777)!=m \n      ){\n        osFchmod(fd, m);\n      }\n    }\n#if defined(FD_CLOEXEC) && (!defined(O_CLOEXEC) || O_CLOEXEC==0)\n    osFcntl(fd, F_SETFD, osFcntl(fd, F_GETFD, 0) | FD_CLOEXEC);\n#endif\n  }\n  return fd;\n}\n\n/*\n** Helper functions to obtain and relinquish the global mutex. The\n** global mutex is used to protect the unixInodeInfo and\n** vxworksFileId objects used by this file, all of which may be \n** shared by multiple threads.\n**\n** Function unixMutexHeld() is used to assert() that the global mutex \n** is held when required. This function is only used as part of assert() \n** statements. e.g.\n**\n**   unixEnterMutex()\n**     assert( unixMutexHeld() );\n**   unixEnterLeave()\n*/\nstatic sqlite3_mutex *unixBigLock = 0;\nstatic void unixEnterMutex(void){\n  sqlite3_mutex_enter(unixBigLock);\n}\nstatic void unixLeaveMutex(void){\n  sqlite3_mutex_leave(unixBigLock);\n}\n#ifdef SQLITE_DEBUG\nstatic int unixMutexHeld(void) {\n  return sqlite3_mutex_held(unixBigLock);\n}\n#endif\n\n\n#ifdef SQLITE_HAVE_OS_TRACE\n/*\n** Helper function for printing out trace information from debugging\n** binaries. This returns the string representation of the supplied\n** integer lock-type.\n*/\nstatic const char *azFileLock(int eFileLock){\n  switch( eFileLock ){\n    case NO_LOCK: return \"NONE\";\n    case SHARED_LOCK: return \"SHARED\";\n    case RESERVED_LOCK: return \"RESERVED\";\n    case PENDING_LOCK: return \"PENDING\";\n    case EXCLUSIVE_LOCK: return \"EXCLUSIVE\";\n  }\n  return \"ERROR\";\n}\n#endif\n\n#ifdef SQLITE_LOCK_TRACE\n/*\n** Print out information about all locking operations.\n**\n** This routine is used for troubleshooting locks on multithreaded\n** platforms.  Enable by compiling with the -DSQLITE_LOCK_TRACE\n** command-line option on the compiler.  This code is normally\n** turned off.\n*/\nstatic int lockTrace(int fd, int op, struct flock *p){\n  char *zOpName, *zType;\n  int s;\n  int savedErrno;\n  if( op==F_GETLK ){\n    zOpName = \"GETLK\";\n  }else if( op==F_SETLK ){\n    zOpName = \"SETLK\";\n  }else{\n    s = osFcntl(fd, op, p);\n    sqlite3DebugPrintf(\"fcntl unknown %d %d %d\\n\", fd, op, s);\n    return s;\n  }\n  if( p->l_type==F_RDLCK ){\n    zType = \"RDLCK\";\n  }else if( p->l_type==F_WRLCK ){\n    zType = \"WRLCK\";\n  }else if( p->l_type==F_UNLCK ){\n    zType = \"UNLCK\";\n  }else{\n    assert( 0 );\n  }\n  assert( p->l_whence==SEEK_SET );\n  s = osFcntl(fd, op, p);\n  savedErrno = errno;\n  sqlite3DebugPrintf(\"fcntl %d %d %s %s %d %d %d %d\\n\",\n     threadid, fd, zOpName, zType, (int)p->l_start, (int)p->l_len,\n     (int)p->l_pid, s);\n  if( s==(-1) && op==F_SETLK && (p->l_type==F_RDLCK || p->l_type==F_WRLCK) ){\n    struct flock l2;\n    l2 = *p;\n    osFcntl(fd, F_GETLK, &l2);\n    if( l2.l_type==F_RDLCK ){\n      zType = \"RDLCK\";\n    }else if( l2.l_type==F_WRLCK ){\n      zType = \"WRLCK\";\n    }else if( l2.l_type==F_UNLCK ){\n      zType = \"UNLCK\";\n    }else{\n      assert( 0 );\n    }\n    sqlite3DebugPrintf(\"fcntl-failure-reason: %s %d %d %d\\n\",\n       zType, (int)l2.l_start, (int)l2.l_len, (int)l2.l_pid);\n  }\n  errno = savedErrno;\n  return s;\n}\n#undef osFcntl\n#define osFcntl lockTrace\n#endif /* SQLITE_LOCK_TRACE */\n\n/*\n** Retry ftruncate() calls that fail due to EINTR\n**\n** All calls to ftruncate() within this file should be made through\n** this wrapper.  On the Android platform, bypassing the logic below\n** could lead to a corrupt database.\n*/\nstatic int robust_ftruncate(int h, sqlite3_int64 sz){\n  int rc;\n#ifdef __ANDROID__\n  /* On Android, ftruncate() always uses 32-bit offsets, even if \n  ** _FILE_OFFSET_BITS=64 is defined. This means it is unsafe to attempt to\n  ** truncate a file to any size larger than 2GiB. Silently ignore any\n  ** such attempts.  */\n  if( sz>(sqlite3_int64)0x7FFFFFFF ){\n    rc = SQLITE_OK;\n  }else\n#endif\n  do{ rc = osFtruncate(h,sz); }while( rc<0 && errno==EINTR );\n  return rc;\n}\n\n/*\n** This routine translates a standard POSIX errno code into something\n** useful to the clients of the sqlite3 functions.  Specifically, it is\n** intended to translate a variety of \"try again\" errors into SQLITE_BUSY\n** and a variety of \"please close the file descriptor NOW\" errors into \n** SQLITE_IOERR\n** \n** Errors during initialization of locks, or file system support for locks,\n** should handle ENOLCK, ENOTSUP, EOPNOTSUPP separately.\n*/\nstatic int sqliteErrorFromPosixError(int posixError, int sqliteIOErr) {\n  assert( (sqliteIOErr == SQLITE_IOERR_LOCK) || \n          (sqliteIOErr == SQLITE_IOERR_UNLOCK) || \n          (sqliteIOErr == SQLITE_IOERR_RDLOCK) ||\n          (sqliteIOErr == SQLITE_IOERR_CHECKRESERVEDLOCK) );\n  switch (posixError) {\n  case EACCES: \n  case EAGAIN:\n  case ETIMEDOUT:\n  case EBUSY:\n  case EINTR:\n  case ENOLCK:  \n    /* random NFS retry error, unless during file system support \n     * introspection, in which it actually means what it says */\n    return SQLITE_BUSY;\n    \n  case EPERM: \n    return SQLITE_PERM;\n    \n  default: \n    return sqliteIOErr;\n  }\n}\n\n\n/******************************************************************************\n****************** Begin Unique File ID Utility Used By VxWorks ***************\n**\n** On most versions of unix, we can get a unique ID for a file by concatenating\n** the device number and the inode number.  But this does not work on VxWorks.\n** On VxWorks, a unique file id must be based on the canonical filename.\n**\n** A pointer to an instance of the following structure can be used as a\n** unique file ID in VxWorks.  Each instance of this structure contains\n** a copy of the canonical filename.  There is also a reference count.  \n** The structure is reclaimed when the number of pointers to it drops to\n** zero.\n**\n** There are never very many files open at one time and lookups are not\n** a performance-critical path, so it is sufficient to put these\n** structures on a linked list.\n*/\nstruct vxworksFileId {\n  struct vxworksFileId *pNext;  /* Next in a list of them all */\n  int nRef;                     /* Number of references to this one */\n  int nName;                    /* Length of the zCanonicalName[] string */\n  char *zCanonicalName;         /* Canonical filename */\n};\n\n#if OS_VXWORKS\n/* \n** All unique filenames are held on a linked list headed by this\n** variable:\n*/\nstatic struct vxworksFileId *vxworksFileList = 0;\n\n/*\n** Simplify a filename into its canonical form\n** by making the following changes:\n**\n**  * removing any trailing and duplicate /\n**  * convert /./ into just /\n**  * convert /A/../ where A is any simple name into just /\n**\n** Changes are made in-place.  Return the new name length.\n**\n** The original filename is in z[0..n-1].  Return the number of\n** characters in the simplified name.\n*/\nstatic int vxworksSimplifyName(char *z, int n){\n  int i, j;\n  while( n>1 && z[n-1]=='/' ){ n--; }\n  for(i=j=0; i<n; i++){\n    if( z[i]=='/' ){\n      if( z[i+1]=='/' ) continue;\n      if( z[i+1]=='.' && i+2<n && z[i+2]=='/' ){\n        i += 1;\n        continue;\n      }\n      if( z[i+1]=='.' && i+3<n && z[i+2]=='.' && z[i+3]=='/' ){\n        while( j>0 && z[j-1]!='/' ){ j--; }\n        if( j>0 ){ j--; }\n        i += 2;\n        continue;\n      }\n    }\n    z[j++] = z[i];\n  }\n  z[j] = 0;\n  return j;\n}\n\n/*\n** Find a unique file ID for the given absolute pathname.  Return\n** a pointer to the vxworksFileId object.  This pointer is the unique\n** file ID.\n**\n** The nRef field of the vxworksFileId object is incremented before\n** the object is returned.  A new vxworksFileId object is created\n** and added to the global list if necessary.\n**\n** If a memory allocation error occurs, return NULL.\n*/\nstatic struct vxworksFileId *vxworksFindFileId(const char *zAbsoluteName){\n  struct vxworksFileId *pNew;         /* search key and new file ID */\n  struct vxworksFileId *pCandidate;   /* For looping over existing file IDs */\n  int n;                              /* Length of zAbsoluteName string */\n\n  assert( zAbsoluteName[0]=='/' );\n  n = (int)strlen(zAbsoluteName);\n  pNew = sqlite3_malloc64( sizeof(*pNew) + (n+1) );\n  if( pNew==0 ) return 0;\n  pNew->zCanonicalName = (char*)&pNew[1];\n  memcpy(pNew->zCanonicalName, zAbsoluteName, n+1);\n  n = vxworksSimplifyName(pNew->zCanonicalName, n);\n\n  /* Search for an existing entry that matching the canonical name.\n  ** If found, increment the reference count and return a pointer to\n  ** the existing file ID.\n  */\n  unixEnterMutex();\n  for(pCandidate=vxworksFileList; pCandidate; pCandidate=pCandidate->pNext){\n    if( pCandidate->nName==n \n     && memcmp(pCandidate->zCanonicalName, pNew->zCanonicalName, n)==0\n    ){\n       sqlite3_free(pNew);\n       pCandidate->nRef++;\n       unixLeaveMutex();\n       return pCandidate;\n    }\n  }\n\n  /* No match was found.  We will make a new file ID */\n  pNew->nRef = 1;\n  pNew->nName = n;\n  pNew->pNext = vxworksFileList;\n  vxworksFileList = pNew;\n  unixLeaveMutex();\n  return pNew;\n}\n\n/*\n** Decrement the reference count on a vxworksFileId object.  Free\n** the object when the reference count reaches zero.\n*/\nstatic void vxworksReleaseFileId(struct vxworksFileId *pId){\n  unixEnterMutex();\n  assert( pId->nRef>0 );\n  pId->nRef--;\n  if( pId->nRef==0 ){\n    struct vxworksFileId **pp;\n    for(pp=&vxworksFileList; *pp && *pp!=pId; pp = &((*pp)->pNext)){}\n    assert( *pp==pId );\n    *pp = pId->pNext;\n    sqlite3_free(pId);\n  }\n  unixLeaveMutex();\n}\n#endif /* OS_VXWORKS */\n/*************** End of Unique File ID Utility Used By VxWorks ****************\n******************************************************************************/\n\n\n/******************************************************************************\n*************************** Posix Advisory Locking ****************************\n**\n** POSIX advisory locks are broken by design.  ANSI STD 1003.1 (1996)\n** section 6.5.2.2 lines 483 through 490 specify that when a process\n** sets or clears a lock, that operation overrides any prior locks set\n** by the same process.  It does not explicitly say so, but this implies\n** that it overrides locks set by the same process using a different\n** file descriptor.  Consider this test case:\n**\n**       int fd1 = open(\"./file1\", O_RDWR|O_CREAT, 0644);\n**       int fd2 = open(\"./file2\", O_RDWR|O_CREAT, 0644);\n**\n** Suppose ./file1 and ./file2 are really the same file (because\n** one is a hard or symbolic link to the other) then if you set\n** an exclusive lock on fd1, then try to get an exclusive lock\n** on fd2, it works.  I would have expected the second lock to\n** fail since there was already a lock on the file due to fd1.\n** But not so.  Since both locks came from the same process, the\n** second overrides the first, even though they were on different\n** file descriptors opened on different file names.\n**\n** This means that we cannot use POSIX locks to synchronize file access\n** among competing threads of the same process.  POSIX locks will work fine\n** to synchronize access for threads in separate processes, but not\n** threads within the same process.\n**\n** To work around the problem, SQLite has to manage file locks internally\n** on its own.  Whenever a new database is opened, we have to find the\n** specific inode of the database file (the inode is determined by the\n** st_dev and st_ino fields of the stat structure that fstat() fills in)\n** and check for locks already existing on that inode.  When locks are\n** created or removed, we have to look at our own internal record of the\n** locks to see if another thread has previously set a lock on that same\n** inode.\n**\n** (Aside: The use of inode numbers as unique IDs does not work on VxWorks.\n** For VxWorks, we have to use the alternative unique ID system based on\n** canonical filename and implemented in the previous division.)\n**\n** The sqlite3_file structure for POSIX is no longer just an integer file\n** descriptor.  It is now a structure that holds the integer file\n** descriptor and a pointer to a structure that describes the internal\n** locks on the corresponding inode.  There is one locking structure\n** per inode, so if the same inode is opened twice, both unixFile structures\n** point to the same locking structure.  The locking structure keeps\n** a reference count (so we will know when to delete it) and a \"cnt\"\n** field that tells us its internal lock status.  cnt==0 means the\n** file is unlocked.  cnt==-1 means the file has an exclusive lock.\n** cnt>0 means there are cnt shared locks on the file.\n**\n** Any attempt to lock or unlock a file first checks the locking\n** structure.  The fcntl() system call is only invoked to set a \n** POSIX lock if the internal lock structure transitions between\n** a locked and an unlocked state.\n**\n** But wait:  there are yet more problems with POSIX advisory locks.\n**\n** If you close a file descriptor that points to a file that has locks,\n** all locks on that file that are owned by the current process are\n** released.  To work around this problem, each unixInodeInfo object\n** maintains a count of the number of pending locks on tha inode.\n** When an attempt is made to close an unixFile, if there are\n** other unixFile open on the same inode that are holding locks, the call\n** to close() the file descriptor is deferred until all of the locks clear.\n** The unixInodeInfo structure keeps a list of file descriptors that need to\n** be closed and that list is walked (and cleared) when the last lock\n** clears.\n**\n** Yet another problem:  LinuxThreads do not play well with posix locks.\n**\n** Many older versions of linux use the LinuxThreads library which is\n** not posix compliant.  Under LinuxThreads, a lock created by thread\n** A cannot be modified or overridden by a different thread B.\n** Only thread A can modify the lock.  Locking behavior is correct\n** if the appliation uses the newer Native Posix Thread Library (NPTL)\n** on linux - with NPTL a lock created by thread A can override locks\n** in thread B.  But there is no way to know at compile-time which\n** threading library is being used.  So there is no way to know at\n** compile-time whether or not thread A can override locks on thread B.\n** One has to do a run-time check to discover the behavior of the\n** current process.\n**\n** SQLite used to support LinuxThreads.  But support for LinuxThreads\n** was dropped beginning with version 3.7.0.  SQLite will still work with\n** LinuxThreads provided that (1) there is no more than one connection \n** per database file in the same process and (2) database connections\n** do not move across threads.\n*/\n\n/*\n** An instance of the following structure serves as the key used\n** to locate a particular unixInodeInfo object.\n*/\nstruct unixFileId {\n  dev_t dev;                  /* Device number */\n#if OS_VXWORKS\n  struct vxworksFileId *pId;  /* Unique file ID for vxworks. */\n#else\n  /* We are told that some versions of Android contain a bug that\n  ** sizes ino_t at only 32-bits instead of 64-bits. (See\n  ** https://android-review.googlesource.com/#/c/115351/3/dist/sqlite3.c)\n  ** To work around this, always allocate 64-bits for the inode number.  \n  ** On small machines that only have 32-bit inodes, this wastes 4 bytes,\n  ** but that should not be a big deal. */\n  /* WAS:  ino_t ino;   */\n  u64 ino;                   /* Inode number */\n#endif\n};\n\n/*\n** An instance of the following structure is allocated for each open\n** inode.  Or, on LinuxThreads, there is one of these structures for\n** each inode opened by each thread.\n**\n** A single inode can have multiple file descriptors, so each unixFile\n** structure contains a pointer to an instance of this object and this\n** object keeps a count of the number of unixFile pointing to it.\n*/\nstruct unixInodeInfo {\n  struct unixFileId fileId;       /* The lookup key */\n  int nShared;                    /* Number of SHARED locks held */\n  unsigned char eFileLock;        /* One of SHARED_LOCK, RESERVED_LOCK etc. */\n  unsigned char bProcessLock;     /* An exclusive process lock is held */\n  int nRef;                       /* Number of pointers to this structure */\n  unixShmNode *pShmNode;          /* Shared memory associated with this inode */\n  int nLock;                      /* Number of outstanding file locks */\n  UnixUnusedFd *pUnused;          /* Unused file descriptors to close */\n  unixInodeInfo *pNext;           /* List of all unixInodeInfo objects */\n  unixInodeInfo *pPrev;           /*    .... doubly linked */\n#if SQLITE_ENABLE_LOCKING_STYLE\n  unsigned long long sharedByte;  /* for AFP simulated shared lock */\n#endif\n#if OS_VXWORKS\n  sem_t *pSem;                    /* Named POSIX semaphore */\n  char aSemName[MAX_PATHNAME+2];  /* Name of that semaphore */\n#endif\n};\n\n/*\n** A lists of all unixInodeInfo objects.\n*/\nstatic unixInodeInfo *inodeList = 0;  /* All unixInodeInfo objects */\nstatic unsigned int nUnusedFd = 0;    /* Total unused file descriptors */\n\n/*\n**\n** This function - unixLogErrorAtLine(), is only ever called via the macro\n** unixLogError().\n**\n** It is invoked after an error occurs in an OS function and errno has been\n** set. It logs a message using sqlite3_log() containing the current value of\n** errno and, if possible, the human-readable equivalent from strerror() or\n** strerror_r().\n**\n** The first argument passed to the macro should be the error code that\n** will be returned to SQLite (e.g. SQLITE_IOERR_DELETE, SQLITE_CANTOPEN). \n** The two subsequent arguments should be the name of the OS function that\n** failed (e.g. \"unlink\", \"open\") and the associated file-system path,\n** if any.\n*/\n#define unixLogError(a,b,c)     unixLogErrorAtLine(a,b,c,__LINE__)\nstatic int unixLogErrorAtLine(\n  int errcode,                    /* SQLite error code */\n  const char *zFunc,              /* Name of OS function that failed */\n  const char *zPath,              /* File path associated with error */\n  int iLine                       /* Source line number where error occurred */\n){\n  char *zErr;                     /* Message from strerror() or equivalent */\n  int iErrno = errno;             /* Saved syscall error number */\n\n  /* If this is not a threadsafe build (SQLITE_THREADSAFE==0), then use\n  ** the strerror() function to obtain the human-readable error message\n  ** equivalent to errno. Otherwise, use strerror_r().\n  */ \n#if SQLITE_THREADSAFE && defined(HAVE_STRERROR_R)\n  char aErr[80];\n  memset(aErr, 0, sizeof(aErr));\n  zErr = aErr;\n\n  /* If STRERROR_R_CHAR_P (set by autoconf scripts) or __USE_GNU is defined,\n  ** assume that the system provides the GNU version of strerror_r() that\n  ** returns a pointer to a buffer containing the error message. That pointer \n  ** may point to aErr[], or it may point to some static storage somewhere. \n  ** Otherwise, assume that the system provides the POSIX version of \n  ** strerror_r(), which always writes an error message into aErr[].\n  **\n  ** If the code incorrectly assumes that it is the POSIX version that is\n  ** available, the error message will often be an empty string. Not a\n  ** huge problem. Incorrectly concluding that the GNU version is available \n  ** could lead to a segfault though.\n  */\n#if defined(STRERROR_R_CHAR_P) || defined(__USE_GNU)\n  zErr = \n# endif\n  strerror_r(iErrno, aErr, sizeof(aErr)-1);\n\n#elif SQLITE_THREADSAFE\n  /* This is a threadsafe build, but strerror_r() is not available. */\n  zErr = \"\";\n#else\n  /* Non-threadsafe build, use strerror(). */\n  zErr = strerror(iErrno);\n#endif\n\n  if( zPath==0 ) zPath = \"\";\n  sqlite3_log(errcode,\n      \"os_unix.c:%d: (%d) %s(%s) - %s\",\n      iLine, iErrno, zFunc, zPath, zErr\n  );\n\n  return errcode;\n}\n\n/*\n** Close a file descriptor.\n**\n** We assume that close() almost always works, since it is only in a\n** very sick application or on a very sick platform that it might fail.\n** If it does fail, simply leak the file descriptor, but do log the\n** error.\n**\n** Note that it is not safe to retry close() after EINTR since the\n** file descriptor might have already been reused by another thread.\n** So we don't even try to recover from an EINTR.  Just log the error\n** and move on.\n*/\nstatic void robust_close(unixFile *pFile, int h, int lineno){\n  if( osClose(h) ){\n    unixLogErrorAtLine(SQLITE_IOERR_CLOSE, \"close\",\n                       pFile ? pFile->zPath : 0, lineno);\n  }\n}\n\n/*\n** Set the pFile->lastErrno.  Do this in a subroutine as that provides\n** a convenient place to set a breakpoint.\n*/\nstatic void storeLastErrno(unixFile *pFile, int error){\n  pFile->lastErrno = error;\n}\n\n/*\n** Close all file descriptors accumuated in the unixInodeInfo->pUnused list.\n*/ \nstatic void closePendingFds(unixFile *pFile){\n  unixInodeInfo *pInode = pFile->pInode;\n  UnixUnusedFd *p;\n  UnixUnusedFd *pNext;\n  for(p=pInode->pUnused; p; p=pNext){\n    pNext = p->pNext;\n    robust_close(pFile, p->fd, __LINE__);\n    sqlite3_free(p);\n    nUnusedFd--;\n  }\n  pInode->pUnused = 0;\n}\n\n/*\n** Release a unixInodeInfo structure previously allocated by findInodeInfo().\n**\n** The mutex entered using the unixEnterMutex() function must be held\n** when this function is called.\n*/\nstatic void releaseInodeInfo(unixFile *pFile){\n  unixInodeInfo *pInode = pFile->pInode;\n  assert( unixMutexHeld() );\n  if( ALWAYS(pInode) ){\n    pInode->nRef--;\n    if( pInode->nRef==0 ){\n      assert( pInode->pShmNode==0 );\n      closePendingFds(pFile);\n      if( pInode->pPrev ){\n        assert( pInode->pPrev->pNext==pInode );\n        pInode->pPrev->pNext = pInode->pNext;\n      }else{\n        assert( inodeList==pInode );\n        inodeList = pInode->pNext;\n      }\n      if( pInode->pNext ){\n        assert( pInode->pNext->pPrev==pInode );\n        pInode->pNext->pPrev = pInode->pPrev;\n      }\n      sqlite3_free(pInode);\n    }\n  }\n  assert( inodeList!=0 || nUnusedFd==0 );\n}\n\n/*\n** Given a file descriptor, locate the unixInodeInfo object that\n** describes that file descriptor.  Create a new one if necessary.  The\n** return value might be uninitialized if an error occurs.\n**\n** The mutex entered using the unixEnterMutex() function must be held\n** when this function is called.\n**\n** Return an appropriate error code.\n*/\nstatic int findInodeInfo(\n  unixFile *pFile,               /* Unix file with file desc used in the key */\n  unixInodeInfo **ppInode        /* Return the unixInodeInfo object here */\n){\n  int rc;                        /* System call return code */\n  int fd;                        /* The file descriptor for pFile */\n  struct unixFileId fileId;      /* Lookup key for the unixInodeInfo */\n  struct stat statbuf;           /* Low-level file information */\n  unixInodeInfo *pInode = 0;     /* Candidate unixInodeInfo object */\n\n  assert( unixMutexHeld() );\n\n  /* Get low-level information about the file that we can used to\n  ** create a unique name for the file.\n  */\n  fd = pFile->h;\n  rc = osFstat(fd, &statbuf);\n  if( rc!=0 ){\n    storeLastErrno(pFile, errno);\n#if defined(EOVERFLOW) && defined(SQLITE_DISABLE_LFS)\n    if( pFile->lastErrno==EOVERFLOW ) return SQLITE_NOLFS;\n#endif\n    return SQLITE_IOERR;\n  }\n\n#ifdef __APPLE__\n  /* On OS X on an msdos filesystem, the inode number is reported\n  ** incorrectly for zero-size files.  See ticket #3260.  To work\n  ** around this problem (we consider it a bug in OS X, not SQLite)\n  ** we always increase the file size to 1 by writing a single byte\n  ** prior to accessing the inode number.  The one byte written is\n  ** an ASCII 'S' character which also happens to be the first byte\n  ** in the header of every SQLite database.  In this way, if there\n  ** is a race condition such that another thread has already populated\n  ** the first page of the database, no damage is done.\n  */\n  if( statbuf.st_size==0 && (pFile->fsFlags & SQLITE_FSFLAGS_IS_MSDOS)!=0 ){\n    do{ rc = osWrite(fd, \"S\", 1); }while( rc<0 && errno==EINTR );\n    if( rc!=1 ){\n      storeLastErrno(pFile, errno);\n      return SQLITE_IOERR;\n    }\n    rc = osFstat(fd, &statbuf);\n    if( rc!=0 ){\n      storeLastErrno(pFile, errno);\n      return SQLITE_IOERR;\n    }\n  }\n#endif\n\n  memset(&fileId, 0, sizeof(fileId));\n  fileId.dev = statbuf.st_dev;\n#if OS_VXWORKS\n  fileId.pId = pFile->pId;\n#else\n  fileId.ino = (u64)statbuf.st_ino;\n#endif\n  assert( inodeList!=0 || nUnusedFd==0 );\n  pInode = inodeList;\n  while( pInode && memcmp(&fileId, &pInode->fileId, sizeof(fileId)) ){\n    pInode = pInode->pNext;\n  }\n  if( pInode==0 ){\n    pInode = sqlite3_malloc64( sizeof(*pInode) );\n    if( pInode==0 ){\n      return SQLITE_NOMEM_BKPT;\n    }\n    memset(pInode, 0, sizeof(*pInode));\n    memcpy(&pInode->fileId, &fileId, sizeof(fileId));\n    pInode->nRef = 1;\n    pInode->pNext = inodeList;\n    pInode->pPrev = 0;\n    if( inodeList ) inodeList->pPrev = pInode;\n    inodeList = pInode;\n  }else{\n    pInode->nRef++;\n  }\n  *ppInode = pInode;\n  return SQLITE_OK;\n}\n\n/*\n** Return TRUE if pFile has been renamed or unlinked since it was first opened.\n*/\nstatic int fileHasMoved(unixFile *pFile){\n#if OS_VXWORKS\n  return pFile->pInode!=0 && pFile->pId!=pFile->pInode->fileId.pId;\n#else\n  struct stat buf;\n  return pFile->pInode!=0 &&\n      (osStat(pFile->zPath, &buf)!=0 \n         || (u64)buf.st_ino!=pFile->pInode->fileId.ino);\n#endif\n}\n\n\n/*\n** Check a unixFile that is a database.  Verify the following:\n**\n** (1) There is exactly one hard link on the file\n** (2) The file is not a symbolic link\n** (3) The file has not been renamed or unlinked\n**\n** Issue sqlite3_log(SQLITE_WARNING,...) messages if anything is not right.\n*/\nstatic void verifyDbFile(unixFile *pFile){\n  struct stat buf;\n  int rc;\n\n  /* These verifications occurs for the main database only */\n  if( pFile->ctrlFlags & UNIXFILE_NOLOCK ) return;\n\n  rc = osFstat(pFile->h, &buf);\n  if( rc!=0 ){\n    sqlite3_log(SQLITE_WARNING, \"cannot fstat db file %s\", pFile->zPath);\n    return;\n  }\n  if( buf.st_nlink==0 ){\n    sqlite3_log(SQLITE_WARNING, \"file unlinked while open: %s\", pFile->zPath);\n    return;\n  }\n  if( buf.st_nlink>1 ){\n    sqlite3_log(SQLITE_WARNING, \"multiple links to file: %s\", pFile->zPath);\n    return;\n  }\n  if( fileHasMoved(pFile) ){\n    sqlite3_log(SQLITE_WARNING, \"file renamed while open: %s\", pFile->zPath);\n    return;\n  }\n}\n\n\n/*\n** This routine checks if there is a RESERVED lock held on the specified\n** file by this or any other process. If such a lock is held, set *pResOut\n** to a non-zero value otherwise *pResOut is set to zero.  The return value\n** is set to SQLITE_OK unless an I/O error occurs during lock checking.\n*/\nstatic int unixCheckReservedLock(sqlite3_file *id, int *pResOut){\n  int rc = SQLITE_OK;\n  int reserved = 0;\n  unixFile *pFile = (unixFile*)id;\n\n  SimulateIOError( return SQLITE_IOERR_CHECKRESERVEDLOCK; );\n\n  assert( pFile );\n  assert( pFile->eFileLock<=SHARED_LOCK );\n  unixEnterMutex(); /* Because pFile->pInode is shared across threads */\n\n  /* Check if a thread in this process holds such a lock */\n  if( pFile->pInode->eFileLock>SHARED_LOCK ){\n    reserved = 1;\n  }\n\n  /* Otherwise see if some other process holds it.\n  */\n#ifndef __DJGPP__\n  if( !reserved && !pFile->pInode->bProcessLock ){\n    struct flock lock;\n    lock.l_whence = SEEK_SET;\n    lock.l_start = RESERVED_BYTE;\n    lock.l_len = 1;\n    lock.l_type = F_WRLCK;\n    if( osFcntl(pFile->h, F_GETLK, &lock) ){\n      rc = SQLITE_IOERR_CHECKRESERVEDLOCK;\n      storeLastErrno(pFile, errno);\n    } else if( lock.l_type!=F_UNLCK ){\n      reserved = 1;\n    }\n  }\n#endif\n  \n  unixLeaveMutex();\n  OSTRACE((\"TEST WR-LOCK %d %d %d (unix)\\n\", pFile->h, rc, reserved));\n\n  *pResOut = reserved;\n  return rc;\n}\n\n/*\n** Attempt to set a system-lock on the file pFile.  The lock is \n** described by pLock.\n**\n** If the pFile was opened read/write from unix-excl, then the only lock\n** ever obtained is an exclusive lock, and it is obtained exactly once\n** the first time any lock is attempted.  All subsequent system locking\n** operations become no-ops.  Locking operations still happen internally,\n** in order to coordinate access between separate database connections\n** within this process, but all of that is handled in memory and the\n** operating system does not participate.\n**\n** This function is a pass-through to fcntl(F_SETLK) if pFile is using\n** any VFS other than \"unix-excl\" or if pFile is opened on \"unix-excl\"\n** and is read-only.\n**\n** Zero is returned if the call completes successfully, or -1 if a call\n** to fcntl() fails. In this case, errno is set appropriately (by fcntl()).\n*/\nstatic int unixFileLock(unixFile *pFile, struct flock *pLock){\n  int rc;\n  unixInodeInfo *pInode = pFile->pInode;\n  assert( unixMutexHeld() );\n  assert( pInode!=0 );\n  if( (pFile->ctrlFlags & (UNIXFILE_EXCL|UNIXFILE_RDONLY))==UNIXFILE_EXCL ){\n    if( pInode->bProcessLock==0 ){\n      struct flock lock;\n      assert( pInode->nLock==0 );\n      lock.l_whence = SEEK_SET;\n      lock.l_start = SHARED_FIRST;\n      lock.l_len = SHARED_SIZE;\n      lock.l_type = F_WRLCK;\n      rc = osFcntl(pFile->h, F_SETLK, &lock);\n      if( rc<0 ) return rc;\n      pInode->bProcessLock = 1;\n      pInode->nLock++;\n    }else{\n      rc = 0;\n    }\n  }else{\n    rc = osFcntl(pFile->h, F_SETLK, pLock);\n  }\n  return rc;\n}\n\n/*\n** Lock the file with the lock specified by parameter eFileLock - one\n** of the following:\n**\n**     (1) SHARED_LOCK\n**     (2) RESERVED_LOCK\n**     (3) PENDING_LOCK\n**     (4) EXCLUSIVE_LOCK\n**\n** Sometimes when requesting one lock state, additional lock states\n** are inserted in between.  The locking might fail on one of the later\n** transitions leaving the lock state different from what it started but\n** still short of its goal.  The following chart shows the allowed\n** transitions and the inserted intermediate states:\n**\n**    UNLOCKED -> SHARED\n**    SHARED -> RESERVED\n**    SHARED -> (PENDING) -> EXCLUSIVE\n**    RESERVED -> (PENDING) -> EXCLUSIVE\n**    PENDING -> EXCLUSIVE\n**\n** This routine will only increase a lock.  Use the sqlite3OsUnlock()\n** routine to lower a locking level.\n*/\nstatic int unixLock(sqlite3_file *id, int eFileLock){\n  /* The following describes the implementation of the various locks and\n  ** lock transitions in terms of the POSIX advisory shared and exclusive\n  ** lock primitives (called read-locks and write-locks below, to avoid\n  ** confusion with SQLite lock names). The algorithms are complicated\n  ** slightly in order to be compatible with Windows95 systems simultaneously\n  ** accessing the same database file, in case that is ever required.\n  **\n  ** Symbols defined in os.h indentify the 'pending byte' and the 'reserved\n  ** byte', each single bytes at well known offsets, and the 'shared byte\n  ** range', a range of 510 bytes at a well known offset.\n  **\n  ** To obtain a SHARED lock, a read-lock is obtained on the 'pending\n  ** byte'.  If this is successful, 'shared byte range' is read-locked\n  ** and the lock on the 'pending byte' released.  (Legacy note:  When\n  ** SQLite was first developed, Windows95 systems were still very common,\n  ** and Widnows95 lacks a shared-lock capability.  So on Windows95, a\n  ** single randomly selected by from the 'shared byte range' is locked.\n  ** Windows95 is now pretty much extinct, but this work-around for the\n  ** lack of shared-locks on Windows95 lives on, for backwards\n  ** compatibility.)\n  **\n  ** A process may only obtain a RESERVED lock after it has a SHARED lock.\n  ** A RESERVED lock is implemented by grabbing a write-lock on the\n  ** 'reserved byte'. \n  **\n  ** A process may only obtain a PENDING lock after it has obtained a\n  ** SHARED lock. A PENDING lock is implemented by obtaining a write-lock\n  ** on the 'pending byte'. This ensures that no new SHARED locks can be\n  ** obtained, but existing SHARED locks are allowed to persist. A process\n  ** does not have to obtain a RESERVED lock on the way to a PENDING lock.\n  ** This property is used by the algorithm for rolling back a journal file\n  ** after a crash.\n  **\n  ** An EXCLUSIVE lock, obtained after a PENDING lock is held, is\n  ** implemented by obtaining a write-lock on the entire 'shared byte\n  ** range'. Since all other locks require a read-lock on one of the bytes\n  ** within this range, this ensures that no other locks are held on the\n  ** database. \n  */\n  int rc = SQLITE_OK;\n  unixFile *pFile = (unixFile*)id;\n  unixInodeInfo *pInode;\n  struct flock lock;\n  int tErrno = 0;\n\n  assert( pFile );\n  OSTRACE((\"LOCK    %d %s was %s(%s,%d) pid=%d (unix)\\n\", pFile->h,\n      azFileLock(eFileLock), azFileLock(pFile->eFileLock),\n      azFileLock(pFile->pInode->eFileLock), pFile->pInode->nShared,\n      osGetpid(0)));\n\n  /* If there is already a lock of this type or more restrictive on the\n  ** unixFile, do nothing. Don't use the end_lock: exit path, as\n  ** unixEnterMutex() hasn't been called yet.\n  */\n  if( pFile->eFileLock>=eFileLock ){\n    OSTRACE((\"LOCK    %d %s ok (already held) (unix)\\n\", pFile->h,\n            azFileLock(eFileLock)));\n    return SQLITE_OK;\n  }\n\n  /* Make sure the locking sequence is correct.\n  **  (1) We never move from unlocked to anything higher than shared lock.\n  **  (2) SQLite never explicitly requests a pendig lock.\n  **  (3) A shared lock is always held when a reserve lock is requested.\n  */\n  assert( pFile->eFileLock!=NO_LOCK || eFileLock==SHARED_LOCK );\n  assert( eFileLock!=PENDING_LOCK );\n  assert( eFileLock!=RESERVED_LOCK || pFile->eFileLock==SHARED_LOCK );\n\n  /* This mutex is needed because pFile->pInode is shared across threads\n  */\n  unixEnterMutex();\n  pInode = pFile->pInode;\n\n  /* If some thread using this PID has a lock via a different unixFile*\n  ** handle that precludes the requested lock, return BUSY.\n  */\n  if( (pFile->eFileLock!=pInode->eFileLock && \n          (pInode->eFileLock>=PENDING_LOCK || eFileLock>SHARED_LOCK))\n  ){\n    rc = SQLITE_BUSY;\n    goto end_lock;\n  }\n\n  /* If a SHARED lock is requested, and some thread using this PID already\n  ** has a SHARED or RESERVED lock, then increment reference counts and\n  ** return SQLITE_OK.\n  */\n  if( eFileLock==SHARED_LOCK && \n      (pInode->eFileLock==SHARED_LOCK || pInode->eFileLock==RESERVED_LOCK) ){\n    assert( eFileLock==SHARED_LOCK );\n    assert( pFile->eFileLock==0 );\n    assert( pInode->nShared>0 );\n    pFile->eFileLock = SHARED_LOCK;\n    pInode->nShared++;\n    pInode->nLock++;\n    goto end_lock;\n  }\n\n\n  /* A PENDING lock is needed before acquiring a SHARED lock and before\n  ** acquiring an EXCLUSIVE lock.  For the SHARED lock, the PENDING will\n  ** be released.\n  */\n  lock.l_len = 1L;\n  lock.l_whence = SEEK_SET;\n  if( eFileLock==SHARED_LOCK \n      || (eFileLock==EXCLUSIVE_LOCK && pFile->eFileLock<PENDING_LOCK)\n  ){\n    lock.l_type = (eFileLock==SHARED_LOCK?F_RDLCK:F_WRLCK);\n    lock.l_start = PENDING_BYTE;\n    if( unixFileLock(pFile, &lock) ){\n      tErrno = errno;\n      rc = sqliteErrorFromPosixError(tErrno, SQLITE_IOERR_LOCK);\n      if( rc!=SQLITE_BUSY ){\n        storeLastErrno(pFile, tErrno);\n      }\n      goto end_lock;\n    }\n  }\n\n\n  /* If control gets to this point, then actually go ahead and make\n  ** operating system calls for the specified lock.\n  */\n  if( eFileLock==SHARED_LOCK ){\n    assert( pInode->nShared==0 );\n    assert( pInode->eFileLock==0 );\n    assert( rc==SQLITE_OK );\n\n    /* Now get the read-lock */\n    lock.l_start = SHARED_FIRST;\n    lock.l_len = SHARED_SIZE;\n    if( unixFileLock(pFile, &lock) ){\n      tErrno = errno;\n      rc = sqliteErrorFromPosixError(tErrno, SQLITE_IOERR_LOCK);\n    }\n\n    /* Drop the temporary PENDING lock */\n    lock.l_start = PENDING_BYTE;\n    lock.l_len = 1L;\n    lock.l_type = F_UNLCK;\n    if( unixFileLock(pFile, &lock) && rc==SQLITE_OK ){\n      /* This could happen with a network mount */\n      tErrno = errno;\n      rc = SQLITE_IOERR_UNLOCK; \n    }\n\n    if( rc ){\n      if( rc!=SQLITE_BUSY ){\n        storeLastErrno(pFile, tErrno);\n      }\n      goto end_lock;\n    }else{\n      pFile->eFileLock = SHARED_LOCK;\n      pInode->nLock++;\n      pInode->nShared = 1;\n    }\n  }else if( eFileLock==EXCLUSIVE_LOCK && pInode->nShared>1 ){\n    /* We are trying for an exclusive lock but another thread in this\n    ** same process is still holding a shared lock. */\n    rc = SQLITE_BUSY;\n  }else{\n    /* The request was for a RESERVED or EXCLUSIVE lock.  It is\n    ** assumed that there is a SHARED or greater lock on the file\n    ** already.\n    */\n    assert( 0!=pFile->eFileLock );\n    lock.l_type = F_WRLCK;\n\n    assert( eFileLock==RESERVED_LOCK || eFileLock==EXCLUSIVE_LOCK );\n    if( eFileLock==RESERVED_LOCK ){\n      lock.l_start = RESERVED_BYTE;\n      lock.l_len = 1L;\n    }else{\n      lock.l_start = SHARED_FIRST;\n      lock.l_len = SHARED_SIZE;\n    }\n\n    if( unixFileLock(pFile, &lock) ){\n      tErrno = errno;\n      rc = sqliteErrorFromPosixError(tErrno, SQLITE_IOERR_LOCK);\n      if( rc!=SQLITE_BUSY ){\n        storeLastErrno(pFile, tErrno);\n      }\n    }\n  }\n  \n\n#ifdef SQLITE_DEBUG\n  /* Set up the transaction-counter change checking flags when\n  ** transitioning from a SHARED to a RESERVED lock.  The change\n  ** from SHARED to RESERVED marks the beginning of a normal\n  ** write operation (not a hot journal rollback).\n  */\n  if( rc==SQLITE_OK\n   && pFile->eFileLock<=SHARED_LOCK\n   && eFileLock==RESERVED_LOCK\n  ){\n    pFile->transCntrChng = 0;\n    pFile->dbUpdate = 0;\n    pFile->inNormalWrite = 1;\n  }\n#endif\n\n\n  if( rc==SQLITE_OK ){\n    pFile->eFileLock = eFileLock;\n    pInode->eFileLock = eFileLock;\n  }else if( eFileLock==EXCLUSIVE_LOCK ){\n    pFile->eFileLock = PENDING_LOCK;\n    pInode->eFileLock = PENDING_LOCK;\n  }\n\nend_lock:\n  unixLeaveMutex();\n  OSTRACE((\"LOCK    %d %s %s (unix)\\n\", pFile->h, azFileLock(eFileLock), \n      rc==SQLITE_OK ? \"ok\" : \"failed\"));\n  return rc;\n}\n\n/*\n** Add the file descriptor used by file handle pFile to the corresponding\n** pUnused list.\n*/\nstatic void setPendingFd(unixFile *pFile){\n  unixInodeInfo *pInode = pFile->pInode;\n  UnixUnusedFd *p = pFile->pPreallocatedUnused;\n  p->pNext = pInode->pUnused;\n  pInode->pUnused = p;\n  pFile->h = -1;\n  pFile->pPreallocatedUnused = 0;\n  nUnusedFd++;\n}\n\n/*\n** Lower the locking level on file descriptor pFile to eFileLock.  eFileLock\n** must be either NO_LOCK or SHARED_LOCK.\n**\n** If the locking level of the file descriptor is already at or below\n** the requested locking level, this routine is a no-op.\n** \n** If handleNFSUnlock is true, then on downgrading an EXCLUSIVE_LOCK to SHARED\n** the byte range is divided into 2 parts and the first part is unlocked then\n** set to a read lock, then the other part is simply unlocked.  This works \n** around a bug in BSD NFS lockd (also seen on MacOSX 10.3+) that fails to \n** remove the write lock on a region when a read lock is set.\n*/\nstatic int posixUnlock(sqlite3_file *id, int eFileLock, int handleNFSUnlock){\n  unixFile *pFile = (unixFile*)id;\n  unixInodeInfo *pInode;\n  struct flock lock;\n  int rc = SQLITE_OK;\n\n  assert( pFile );\n  OSTRACE((\"UNLOCK  %d %d was %d(%d,%d) pid=%d (unix)\\n\", pFile->h, eFileLock,\n      pFile->eFileLock, pFile->pInode->eFileLock, pFile->pInode->nShared,\n      osGetpid(0)));\n\n  assert( eFileLock<=SHARED_LOCK );\n  if( pFile->eFileLock<=eFileLock ){\n    return SQLITE_OK;\n  }\n  unixEnterMutex();\n  pInode = pFile->pInode;\n  assert( pInode->nShared!=0 );\n  if( pFile->eFileLock>SHARED_LOCK ){\n    assert( pInode->eFileLock==pFile->eFileLock );\n\n#ifdef SQLITE_DEBUG\n    /* When reducing a lock such that other processes can start\n    ** reading the database file again, make sure that the\n    ** transaction counter was updated if any part of the database\n    ** file changed.  If the transaction counter is not updated,\n    ** other connections to the same file might not realize that\n    ** the file has changed and hence might not know to flush their\n    ** cache.  The use of a stale cache can lead to database corruption.\n    */\n    pFile->inNormalWrite = 0;\n#endif\n\n    /* downgrading to a shared lock on NFS involves clearing the write lock\n    ** before establishing the readlock - to avoid a race condition we downgrade\n    ** the lock in 2 blocks, so that part of the range will be covered by a \n    ** write lock until the rest is covered by a read lock:\n    **  1:   [WWWWW]\n    **  2:   [....W]\n    **  3:   [RRRRW]\n    **  4:   [RRRR.]\n    */\n    if( eFileLock==SHARED_LOCK ){\n#if !defined(__APPLE__) || !SQLITE_ENABLE_LOCKING_STYLE\n      (void)handleNFSUnlock;\n      assert( handleNFSUnlock==0 );\n#endif\n#if defined(__APPLE__) && SQLITE_ENABLE_LOCKING_STYLE\n      if( handleNFSUnlock ){\n        int tErrno;               /* Error code from system call errors */\n        off_t divSize = SHARED_SIZE - 1;\n        \n        lock.l_type = F_UNLCK;\n        lock.l_whence = SEEK_SET;\n        lock.l_start = SHARED_FIRST;\n        lock.l_len = divSize;\n        if( unixFileLock(pFile, &lock)==(-1) ){\n          tErrno = errno;\n          rc = SQLITE_IOERR_UNLOCK;\n          storeLastErrno(pFile, tErrno);\n          goto end_unlock;\n        }\n        lock.l_type = F_RDLCK;\n        lock.l_whence = SEEK_SET;\n        lock.l_start = SHARED_FIRST;\n        lock.l_len = divSize;\n        if( unixFileLock(pFile, &lock)==(-1) ){\n          tErrno = errno;\n          rc = sqliteErrorFromPosixError(tErrno, SQLITE_IOERR_RDLOCK);\n          if( IS_LOCK_ERROR(rc) ){\n            storeLastErrno(pFile, tErrno);\n          }\n          goto end_unlock;\n        }\n        lock.l_type = F_UNLCK;\n        lock.l_whence = SEEK_SET;\n        lock.l_start = SHARED_FIRST+divSize;\n        lock.l_len = SHARED_SIZE-divSize;\n        if( unixFileLock(pFile, &lock)==(-1) ){\n          tErrno = errno;\n          rc = SQLITE_IOERR_UNLOCK;\n          storeLastErrno(pFile, tErrno);\n          goto end_unlock;\n        }\n      }else\n#endif /* defined(__APPLE__) && SQLITE_ENABLE_LOCKING_STYLE */\n      {\n        lock.l_type = F_RDLCK;\n        lock.l_whence = SEEK_SET;\n        lock.l_start = SHARED_FIRST;\n        lock.l_len = SHARED_SIZE;\n        if( unixFileLock(pFile, &lock) ){\n          /* In theory, the call to unixFileLock() cannot fail because another\n          ** process is holding an incompatible lock. If it does, this \n          ** indicates that the other process is not following the locking\n          ** protocol. If this happens, return SQLITE_IOERR_RDLOCK. Returning\n          ** SQLITE_BUSY would confuse the upper layer (in practice it causes \n          ** an assert to fail). */ \n          rc = SQLITE_IOERR_RDLOCK;\n          storeLastErrno(pFile, errno);\n          goto end_unlock;\n        }\n      }\n    }\n    lock.l_type = F_UNLCK;\n    lock.l_whence = SEEK_SET;\n    lock.l_start = PENDING_BYTE;\n    lock.l_len = 2L;  assert( PENDING_BYTE+1==RESERVED_BYTE );\n    if( unixFileLock(pFile, &lock)==0 ){\n      pInode->eFileLock = SHARED_LOCK;\n    }else{\n      rc = SQLITE_IOERR_UNLOCK;\n      storeLastErrno(pFile, errno);\n      goto end_unlock;\n    }\n  }\n  if( eFileLock==NO_LOCK ){\n    /* Decrement the shared lock counter.  Release the lock using an\n    ** OS call only when all threads in this same process have released\n    ** the lock.\n    */\n    pInode->nShared--;\n    if( pInode->nShared==0 ){\n      lock.l_type = F_UNLCK;\n      lock.l_whence = SEEK_SET;\n      lock.l_start = lock.l_len = 0L;\n      if( unixFileLock(pFile, &lock)==0 ){\n        pInode->eFileLock = NO_LOCK;\n      }else{\n        rc = SQLITE_IOERR_UNLOCK;\n        storeLastErrno(pFile, errno);\n        pInode->eFileLock = NO_LOCK;\n        pFile->eFileLock = NO_LOCK;\n      }\n    }\n\n    /* Decrement the count of locks against this same file.  When the\n    ** count reaches zero, close any other file descriptors whose close\n    ** was deferred because of outstanding locks.\n    */\n    pInode->nLock--;\n    assert( pInode->nLock>=0 );\n    if( pInode->nLock==0 ){\n      closePendingFds(pFile);\n    }\n  }\n\nend_unlock:\n  unixLeaveMutex();\n  if( rc==SQLITE_OK ) pFile->eFileLock = eFileLock;\n  return rc;\n}\n\n/*\n** Lower the locking level on file descriptor pFile to eFileLock.  eFileLock\n** must be either NO_LOCK or SHARED_LOCK.\n**\n** If the locking level of the file descriptor is already at or below\n** the requested locking level, this routine is a no-op.\n*/\nstatic int unixUnlock(sqlite3_file *id, int eFileLock){\n#if SQLITE_MAX_MMAP_SIZE>0\n  assert( eFileLock==SHARED_LOCK || ((unixFile *)id)->nFetchOut==0 );\n#endif\n  return posixUnlock(id, eFileLock, 0);\n}\n\n#if SQLITE_MAX_MMAP_SIZE>0\nstatic int unixMapfile(unixFile *pFd, i64 nByte);\nstatic void unixUnmapfile(unixFile *pFd);\n#endif\n\n/*\n** This function performs the parts of the \"close file\" operation \n** common to all locking schemes. It closes the directory and file\n** handles, if they are valid, and sets all fields of the unixFile\n** structure to 0.\n**\n** It is *not* necessary to hold the mutex when this routine is called,\n** even on VxWorks.  A mutex will be acquired on VxWorks by the\n** vxworksReleaseFileId() routine.\n*/\nstatic int closeUnixFile(sqlite3_file *id){\n  unixFile *pFile = (unixFile*)id;\n#if SQLITE_MAX_MMAP_SIZE>0\n  unixUnmapfile(pFile);\n#endif\n  if( pFile->h>=0 ){\n    robust_close(pFile, pFile->h, __LINE__);\n    pFile->h = -1;\n  }\n#if OS_VXWORKS\n  if( pFile->pId ){\n    if( pFile->ctrlFlags & UNIXFILE_DELETE ){\n      osUnlink(pFile->pId->zCanonicalName);\n    }\n    vxworksReleaseFileId(pFile->pId);\n    pFile->pId = 0;\n  }\n#endif\n#ifdef SQLITE_UNLINK_AFTER_CLOSE\n  if( pFile->ctrlFlags & UNIXFILE_DELETE ){\n    osUnlink(pFile->zPath);\n    sqlite3_free(*(char**)&pFile->zPath);\n    pFile->zPath = 0;\n  }\n#endif\n  OSTRACE((\"CLOSE   %-3d\\n\", pFile->h));\n  OpenCounter(-1);\n  sqlite3_free(pFile->pPreallocatedUnused);\n  memset(pFile, 0, sizeof(unixFile));\n  return SQLITE_OK;\n}\n\n/*\n** Close a file.\n*/\nstatic int unixClose(sqlite3_file *id){\n  int rc = SQLITE_OK;\n  unixFile *pFile = (unixFile *)id;\n  verifyDbFile(pFile);\n  unixUnlock(id, NO_LOCK);\n  unixEnterMutex();\n\n  /* unixFile.pInode is always valid here. Otherwise, a different close\n  ** routine (e.g. nolockClose()) would be called instead.\n  */\n  assert( pFile->pInode->nLock>0 || pFile->pInode->bProcessLock==0 );\n  if( ALWAYS(pFile->pInode) && pFile->pInode->nLock ){\n    /* If there are outstanding locks, do not actually close the file just\n    ** yet because that would clear those locks.  Instead, add the file\n    ** descriptor to pInode->pUnused list.  It will be automatically closed \n    ** when the last lock is cleared.\n    */\n    setPendingFd(pFile);\n  }\n  releaseInodeInfo(pFile);\n  rc = closeUnixFile(id);\n  unixLeaveMutex();\n  return rc;\n}\n\n/************** End of the posix advisory lock implementation *****************\n******************************************************************************/\n\n/******************************************************************************\n****************************** No-op Locking **********************************\n**\n** Of the various locking implementations available, this is by far the\n** simplest:  locking is ignored.  No attempt is made to lock the database\n** file for reading or writing.\n**\n** This locking mode is appropriate for use on read-only databases\n** (ex: databases that are burned into CD-ROM, for example.)  It can\n** also be used if the application employs some external mechanism to\n** prevent simultaneous access of the same database by two or more\n** database connections.  But there is a serious risk of database\n** corruption if this locking mode is used in situations where multiple\n** database connections are accessing the same database file at the same\n** time and one or more of those connections are writing.\n*/\n\nstatic int nolockCheckReservedLock(sqlite3_file *NotUsed, int *pResOut){\n  UNUSED_PARAMETER(NotUsed);\n  *pResOut = 0;\n  return SQLITE_OK;\n}\nstatic int nolockLock(sqlite3_file *NotUsed, int NotUsed2){\n  UNUSED_PARAMETER2(NotUsed, NotUsed2);\n  return SQLITE_OK;\n}\nstatic int nolockUnlock(sqlite3_file *NotUsed, int NotUsed2){\n  UNUSED_PARAMETER2(NotUsed, NotUsed2);\n  return SQLITE_OK;\n}\n\n/*\n** Close the file.\n*/\nstatic int nolockClose(sqlite3_file *id) {\n  return closeUnixFile(id);\n}\n\n/******************* End of the no-op lock implementation *********************\n******************************************************************************/\n\n/******************************************************************************\n************************* Begin dot-file Locking ******************************\n**\n** The dotfile locking implementation uses the existence of separate lock\n** files (really a directory) to control access to the database.  This works\n** on just about every filesystem imaginable.  But there are serious downsides:\n**\n**    (1)  There is zero concurrency.  A single reader blocks all other\n**         connections from reading or writing the database.\n**\n**    (2)  An application crash or power loss can leave stale lock files\n**         sitting around that need to be cleared manually.\n**\n** Nevertheless, a dotlock is an appropriate locking mode for use if no\n** other locking strategy is available.\n**\n** Dotfile locking works by creating a subdirectory in the same directory as\n** the database and with the same name but with a \".lock\" extension added.\n** The existence of a lock directory implies an EXCLUSIVE lock.  All other\n** lock types (SHARED, RESERVED, PENDING) are mapped into EXCLUSIVE.\n*/\n\n/*\n** The file suffix added to the data base filename in order to create the\n** lock directory.\n*/\n#define DOTLOCK_SUFFIX \".lock\"\n\n/*\n** This routine checks if there is a RESERVED lock held on the specified\n** file by this or any other process. If such a lock is held, set *pResOut\n** to a non-zero value otherwise *pResOut is set to zero.  The return value\n** is set to SQLITE_OK unless an I/O error occurs during lock checking.\n**\n** In dotfile locking, either a lock exists or it does not.  So in this\n** variation of CheckReservedLock(), *pResOut is set to true if any lock\n** is held on the file and false if the file is unlocked.\n*/\nstatic int dotlockCheckReservedLock(sqlite3_file *id, int *pResOut) {\n  int rc = SQLITE_OK;\n  int reserved = 0;\n  unixFile *pFile = (unixFile*)id;\n\n  SimulateIOError( return SQLITE_IOERR_CHECKRESERVEDLOCK; );\n  \n  assert( pFile );\n  reserved = osAccess((const char*)pFile->lockingContext, 0)==0;\n  OSTRACE((\"TEST WR-LOCK %d %d %d (dotlock)\\n\", pFile->h, rc, reserved));\n  *pResOut = reserved;\n  return rc;\n}\n\n/*\n** Lock the file with the lock specified by parameter eFileLock - one\n** of the following:\n**\n**     (1) SHARED_LOCK\n**     (2) RESERVED_LOCK\n**     (3) PENDING_LOCK\n**     (4) EXCLUSIVE_LOCK\n**\n** Sometimes when requesting one lock state, additional lock states\n** are inserted in between.  The locking might fail on one of the later\n** transitions leaving the lock state different from what it started but\n** still short of its goal.  The following chart shows the allowed\n** transitions and the inserted intermediate states:\n**\n**    UNLOCKED -> SHARED\n**    SHARED -> RESERVED\n**    SHARED -> (PENDING) -> EXCLUSIVE\n**    RESERVED -> (PENDING) -> EXCLUSIVE\n**    PENDING -> EXCLUSIVE\n**\n** This routine will only increase a lock.  Use the sqlite3OsUnlock()\n** routine to lower a locking level.\n**\n** With dotfile locking, we really only support state (4): EXCLUSIVE.\n** But we track the other locking levels internally.\n*/\nstatic int dotlockLock(sqlite3_file *id, int eFileLock) {\n  unixFile *pFile = (unixFile*)id;\n  char *zLockFile = (char *)pFile->lockingContext;\n  int rc = SQLITE_OK;\n\n\n  /* If we have any lock, then the lock file already exists.  All we have\n  ** to do is adjust our internal record of the lock level.\n  */\n  if( pFile->eFileLock > NO_LOCK ){\n    pFile->eFileLock = eFileLock;\n    /* Always update the timestamp on the old file */\n#ifdef HAVE_UTIME\n    utime(zLockFile, NULL);\n#else\n    utimes(zLockFile, NULL);\n#endif\n    return SQLITE_OK;\n  }\n  \n  /* grab an exclusive lock */\n  rc = osMkdir(zLockFile, 0777);\n  if( rc<0 ){\n    /* failed to open/create the lock directory */\n    int tErrno = errno;\n    if( EEXIST == tErrno ){\n      rc = SQLITE_BUSY;\n    } else {\n      rc = sqliteErrorFromPosixError(tErrno, SQLITE_IOERR_LOCK);\n      if( rc!=SQLITE_BUSY ){\n        storeLastErrno(pFile, tErrno);\n      }\n    }\n    return rc;\n  } \n  \n  /* got it, set the type and return ok */\n  pFile->eFileLock = eFileLock;\n  return rc;\n}\n\n/*\n** Lower the locking level on file descriptor pFile to eFileLock.  eFileLock\n** must be either NO_LOCK or SHARED_LOCK.\n**\n** If the locking level of the file descriptor is already at or below\n** the requested locking level, this routine is a no-op.\n**\n** When the locking level reaches NO_LOCK, delete the lock file.\n*/\nstatic int dotlockUnlock(sqlite3_file *id, int eFileLock) {\n  unixFile *pFile = (unixFile*)id;\n  char *zLockFile = (char *)pFile->lockingContext;\n  int rc;\n\n  assert( pFile );\n  OSTRACE((\"UNLOCK  %d %d was %d pid=%d (dotlock)\\n\", pFile->h, eFileLock,\n           pFile->eFileLock, osGetpid(0)));\n  assert( eFileLock<=SHARED_LOCK );\n  \n  /* no-op if possible */\n  if( pFile->eFileLock==eFileLock ){\n    return SQLITE_OK;\n  }\n\n  /* To downgrade to shared, simply update our internal notion of the\n  ** lock state.  No need to mess with the file on disk.\n  */\n  if( eFileLock==SHARED_LOCK ){\n    pFile->eFileLock = SHARED_LOCK;\n    return SQLITE_OK;\n  }\n  \n  /* To fully unlock the database, delete the lock file */\n  assert( eFileLock==NO_LOCK );\n  rc = osRmdir(zLockFile);\n  if( rc<0 ){\n    int tErrno = errno;\n    if( tErrno==ENOENT ){\n      rc = SQLITE_OK;\n    }else{\n      rc = SQLITE_IOERR_UNLOCK;\n      storeLastErrno(pFile, tErrno);\n    }\n    return rc; \n  }\n  pFile->eFileLock = NO_LOCK;\n  return SQLITE_OK;\n}\n\n/*\n** Close a file.  Make sure the lock has been released before closing.\n*/\nstatic int dotlockClose(sqlite3_file *id) {\n  unixFile *pFile = (unixFile*)id;\n  assert( id!=0 );\n  dotlockUnlock(id, NO_LOCK);\n  sqlite3_free(pFile->lockingContext);\n  return closeUnixFile(id);\n}\n/****************** End of the dot-file lock implementation *******************\n******************************************************************************/\n\n/******************************************************************************\n************************** Begin flock Locking ********************************\n**\n** Use the flock() system call to do file locking.\n**\n** flock() locking is like dot-file locking in that the various\n** fine-grain locking levels supported by SQLite are collapsed into\n** a single exclusive lock.  In other words, SHARED, RESERVED, and\n** PENDING locks are the same thing as an EXCLUSIVE lock.  SQLite\n** still works when you do this, but concurrency is reduced since\n** only a single process can be reading the database at a time.\n**\n** Omit this section if SQLITE_ENABLE_LOCKING_STYLE is turned off\n*/\n#if SQLITE_ENABLE_LOCKING_STYLE\n\n/*\n** Retry flock() calls that fail with EINTR\n*/\n#ifdef EINTR\nstatic int robust_flock(int fd, int op){\n  int rc;\n  do{ rc = flock(fd,op); }while( rc<0 && errno==EINTR );\n  return rc;\n}\n#else\n# define robust_flock(a,b) flock(a,b)\n#endif\n     \n\n/*\n** This routine checks if there is a RESERVED lock held on the specified\n** file by this or any other process. If such a lock is held, set *pResOut\n** to a non-zero value otherwise *pResOut is set to zero.  The return value\n** is set to SQLITE_OK unless an I/O error occurs during lock checking.\n*/\nstatic int flockCheckReservedLock(sqlite3_file *id, int *pResOut){\n  int rc = SQLITE_OK;\n  int reserved = 0;\n  unixFile *pFile = (unixFile*)id;\n  \n  SimulateIOError( return SQLITE_IOERR_CHECKRESERVEDLOCK; );\n  \n  assert( pFile );\n  \n  /* Check if a thread in this process holds such a lock */\n  if( pFile->eFileLock>SHARED_LOCK ){\n    reserved = 1;\n  }\n  \n  /* Otherwise see if some other process holds it. */\n  if( !reserved ){\n    /* attempt to get the lock */\n    int lrc = robust_flock(pFile->h, LOCK_EX | LOCK_NB);\n    if( !lrc ){\n      /* got the lock, unlock it */\n      lrc = robust_flock(pFile->h, LOCK_UN);\n      if ( lrc ) {\n        int tErrno = errno;\n        /* unlock failed with an error */\n        lrc = SQLITE_IOERR_UNLOCK; \n        storeLastErrno(pFile, tErrno);\n        rc = lrc;\n      }\n    } else {\n      int tErrno = errno;\n      reserved = 1;\n      /* someone else might have it reserved */\n      lrc = sqliteErrorFromPosixError(tErrno, SQLITE_IOERR_LOCK); \n      if( IS_LOCK_ERROR(lrc) ){\n        storeLastErrno(pFile, tErrno);\n        rc = lrc;\n      }\n    }\n  }\n  OSTRACE((\"TEST WR-LOCK %d %d %d (flock)\\n\", pFile->h, rc, reserved));\n\n#ifdef SQLITE_IGNORE_FLOCK_LOCK_ERRORS\n  if( (rc & 0xff) == SQLITE_IOERR ){\n    rc = SQLITE_OK;\n    reserved=1;\n  }\n#endif /* SQLITE_IGNORE_FLOCK_LOCK_ERRORS */\n  *pResOut = reserved;\n  return rc;\n}\n\n/*\n** Lock the file with the lock specified by parameter eFileLock - one\n** of the following:\n**\n**     (1) SHARED_LOCK\n**     (2) RESERVED_LOCK\n**     (3) PENDING_LOCK\n**     (4) EXCLUSIVE_LOCK\n**\n** Sometimes when requesting one lock state, additional lock states\n** are inserted in between.  The locking might fail on one of the later\n** transitions leaving the lock state different from what it started but\n** still short of its goal.  The following chart shows the allowed\n** transitions and the inserted intermediate states:\n**\n**    UNLOCKED -> SHARED\n**    SHARED -> RESERVED\n**    SHARED -> (PENDING) -> EXCLUSIVE\n**    RESERVED -> (PENDING) -> EXCLUSIVE\n**    PENDING -> EXCLUSIVE\n**\n** flock() only really support EXCLUSIVE locks.  We track intermediate\n** lock states in the sqlite3_file structure, but all locks SHARED or\n** above are really EXCLUSIVE locks and exclude all other processes from\n** access the file.\n**\n** This routine will only increase a lock.  Use the sqlite3OsUnlock()\n** routine to lower a locking level.\n*/\nstatic int flockLock(sqlite3_file *id, int eFileLock) {\n  int rc = SQLITE_OK;\n  unixFile *pFile = (unixFile*)id;\n\n  assert( pFile );\n\n  /* if we already have a lock, it is exclusive.  \n  ** Just adjust level and punt on outta here. */\n  if (pFile->eFileLock > NO_LOCK) {\n    pFile->eFileLock = eFileLock;\n    return SQLITE_OK;\n  }\n  \n  /* grab an exclusive lock */\n  \n  if (robust_flock(pFile->h, LOCK_EX | LOCK_NB)) {\n    int tErrno = errno;\n    /* didn't get, must be busy */\n    rc = sqliteErrorFromPosixError(tErrno, SQLITE_IOERR_LOCK);\n    if( IS_LOCK_ERROR(rc) ){\n      storeLastErrno(pFile, tErrno);\n    }\n  } else {\n    /* got it, set the type and return ok */\n    pFile->eFileLock = eFileLock;\n  }\n  OSTRACE((\"LOCK    %d %s %s (flock)\\n\", pFile->h, azFileLock(eFileLock), \n           rc==SQLITE_OK ? \"ok\" : \"failed\"));\n#ifdef SQLITE_IGNORE_FLOCK_LOCK_ERRORS\n  if( (rc & 0xff) == SQLITE_IOERR ){\n    rc = SQLITE_BUSY;\n  }\n#endif /* SQLITE_IGNORE_FLOCK_LOCK_ERRORS */\n  return rc;\n}\n\n\n/*\n** Lower the locking level on file descriptor pFile to eFileLock.  eFileLock\n** must be either NO_LOCK or SHARED_LOCK.\n**\n** If the locking level of the file descriptor is already at or below\n** the requested locking level, this routine is a no-op.\n*/\nstatic int flockUnlock(sqlite3_file *id, int eFileLock) {\n  unixFile *pFile = (unixFile*)id;\n  \n  assert( pFile );\n  OSTRACE((\"UNLOCK  %d %d was %d pid=%d (flock)\\n\", pFile->h, eFileLock,\n           pFile->eFileLock, osGetpid(0)));\n  assert( eFileLock<=SHARED_LOCK );\n  \n  /* no-op if possible */\n  if( pFile->eFileLock==eFileLock ){\n    return SQLITE_OK;\n  }\n  \n  /* shared can just be set because we always have an exclusive */\n  if (eFileLock==SHARED_LOCK) {\n    pFile->eFileLock = eFileLock;\n    return SQLITE_OK;\n  }\n  \n  /* no, really, unlock. */\n  if( robust_flock(pFile->h, LOCK_UN) ){\n#ifdef SQLITE_IGNORE_FLOCK_LOCK_ERRORS\n    return SQLITE_OK;\n#endif /* SQLITE_IGNORE_FLOCK_LOCK_ERRORS */\n    return SQLITE_IOERR_UNLOCK;\n  }else{\n    pFile->eFileLock = NO_LOCK;\n    return SQLITE_OK;\n  }\n}\n\n/*\n** Close a file.\n*/\nstatic int flockClose(sqlite3_file *id) {\n  assert( id!=0 );\n  flockUnlock(id, NO_LOCK);\n  return closeUnixFile(id);\n}\n\n#endif /* SQLITE_ENABLE_LOCKING_STYLE && !OS_VXWORK */\n\n/******************* End of the flock lock implementation *********************\n******************************************************************************/\n\n/******************************************************************************\n************************ Begin Named Semaphore Locking ************************\n**\n** Named semaphore locking is only supported on VxWorks.\n**\n** Semaphore locking is like dot-lock and flock in that it really only\n** supports EXCLUSIVE locking.  Only a single process can read or write\n** the database file at a time.  This reduces potential concurrency, but\n** makes the lock implementation much easier.\n*/\n#if OS_VXWORKS\n\n/*\n** This routine checks if there is a RESERVED lock held on the specified\n** file by this or any other process. If such a lock is held, set *pResOut\n** to a non-zero value otherwise *pResOut is set to zero.  The return value\n** is set to SQLITE_OK unless an I/O error occurs during lock checking.\n*/\nstatic int semXCheckReservedLock(sqlite3_file *id, int *pResOut) {\n  int rc = SQLITE_OK;\n  int reserved = 0;\n  unixFile *pFile = (unixFile*)id;\n\n  SimulateIOError( return SQLITE_IOERR_CHECKRESERVEDLOCK; );\n  \n  assert( pFile );\n\n  /* Check if a thread in this process holds such a lock */\n  if( pFile->eFileLock>SHARED_LOCK ){\n    reserved = 1;\n  }\n  \n  /* Otherwise see if some other process holds it. */\n  if( !reserved ){\n    sem_t *pSem = pFile->pInode->pSem;\n\n    if( sem_trywait(pSem)==-1 ){\n      int tErrno = errno;\n      if( EAGAIN != tErrno ){\n        rc = sqliteErrorFromPosixError(tErrno, SQLITE_IOERR_CHECKRESERVEDLOCK);\n        storeLastErrno(pFile, tErrno);\n      } else {\n        /* someone else has the lock when we are in NO_LOCK */\n        reserved = (pFile->eFileLock < SHARED_LOCK);\n      }\n    }else{\n      /* we could have it if we want it */\n      sem_post(pSem);\n    }\n  }\n  OSTRACE((\"TEST WR-LOCK %d %d %d (sem)\\n\", pFile->h, rc, reserved));\n\n  *pResOut = reserved;\n  return rc;\n}\n\n/*\n** Lock the file with the lock specified by parameter eFileLock - one\n** of the following:\n**\n**     (1) SHARED_LOCK\n**     (2) RESERVED_LOCK\n**     (3) PENDING_LOCK\n**     (4) EXCLUSIVE_LOCK\n**\n** Sometimes when requesting one lock state, additional lock states\n** are inserted in between.  The locking might fail on one of the later\n** transitions leaving the lock state different from what it started but\n** still short of its goal.  The following chart shows the allowed\n** transitions and the inserted intermediate states:\n**\n**    UNLOCKED -> SHARED\n**    SHARED -> RESERVED\n**    SHARED -> (PENDING) -> EXCLUSIVE\n**    RESERVED -> (PENDING) -> EXCLUSIVE\n**    PENDING -> EXCLUSIVE\n**\n** Semaphore locks only really support EXCLUSIVE locks.  We track intermediate\n** lock states in the sqlite3_file structure, but all locks SHARED or\n** above are really EXCLUSIVE locks and exclude all other processes from\n** access the file.\n**\n** This routine will only increase a lock.  Use the sqlite3OsUnlock()\n** routine to lower a locking level.\n*/\nstatic int semXLock(sqlite3_file *id, int eFileLock) {\n  unixFile *pFile = (unixFile*)id;\n  sem_t *pSem = pFile->pInode->pSem;\n  int rc = SQLITE_OK;\n\n  /* if we already have a lock, it is exclusive.  \n  ** Just adjust level and punt on outta here. */\n  if (pFile->eFileLock > NO_LOCK) {\n    pFile->eFileLock = eFileLock;\n    rc = SQLITE_OK;\n    goto sem_end_lock;\n  }\n  \n  /* lock semaphore now but bail out when already locked. */\n  if( sem_trywait(pSem)==-1 ){\n    rc = SQLITE_BUSY;\n    goto sem_end_lock;\n  }\n\n  /* got it, set the type and return ok */\n  pFile->eFileLock = eFileLock;\n\n sem_end_lock:\n  return rc;\n}\n\n/*\n** Lower the locking level on file descriptor pFile to eFileLock.  eFileLock\n** must be either NO_LOCK or SHARED_LOCK.\n**\n** If the locking level of the file descriptor is already at or below\n** the requested locking level, this routine is a no-op.\n*/\nstatic int semXUnlock(sqlite3_file *id, int eFileLock) {\n  unixFile *pFile = (unixFile*)id;\n  sem_t *pSem = pFile->pInode->pSem;\n\n  assert( pFile );\n  assert( pSem );\n  OSTRACE((\"UNLOCK  %d %d was %d pid=%d (sem)\\n\", pFile->h, eFileLock,\n           pFile->eFileLock, osGetpid(0)));\n  assert( eFileLock<=SHARED_LOCK );\n  \n  /* no-op if possible */\n  if( pFile->eFileLock==eFileLock ){\n    return SQLITE_OK;\n  }\n  \n  /* shared can just be set because we always have an exclusive */\n  if (eFileLock==SHARED_LOCK) {\n    pFile->eFileLock = eFileLock;\n    return SQLITE_OK;\n  }\n  \n  /* no, really unlock. */\n  if ( sem_post(pSem)==-1 ) {\n    int rc, tErrno = errno;\n    rc = sqliteErrorFromPosixError(tErrno, SQLITE_IOERR_UNLOCK);\n    if( IS_LOCK_ERROR(rc) ){\n      storeLastErrno(pFile, tErrno);\n    }\n    return rc; \n  }\n  pFile->eFileLock = NO_LOCK;\n  return SQLITE_OK;\n}\n\n/*\n ** Close a file.\n */\nstatic int semXClose(sqlite3_file *id) {\n  if( id ){\n    unixFile *pFile = (unixFile*)id;\n    semXUnlock(id, NO_LOCK);\n    assert( pFile );\n    unixEnterMutex();\n    releaseInodeInfo(pFile);\n    unixLeaveMutex();\n    closeUnixFile(id);\n  }\n  return SQLITE_OK;\n}\n\n#endif /* OS_VXWORKS */\n/*\n** Named semaphore locking is only available on VxWorks.\n**\n*************** End of the named semaphore lock implementation ****************\n******************************************************************************/\n\n\n/******************************************************************************\n*************************** Begin AFP Locking *********************************\n**\n** AFP is the Apple Filing Protocol.  AFP is a network filesystem found\n** on Apple Macintosh computers - both OS9 and OSX.\n**\n** Third-party implementations of AFP are available.  But this code here\n** only works on OSX.\n*/\n\n#if defined(__APPLE__) && SQLITE_ENABLE_LOCKING_STYLE\n/*\n** The afpLockingContext structure contains all afp lock specific state\n*/\ntypedef struct afpLockingContext afpLockingContext;\nstruct afpLockingContext {\n  int reserved;\n  const char *dbPath;             /* Name of the open file */\n};\n\nstruct ByteRangeLockPB2\n{\n  unsigned long long offset;        /* offset to first byte to lock */\n  unsigned long long length;        /* nbr of bytes to lock */\n  unsigned long long retRangeStart; /* nbr of 1st byte locked if successful */\n  unsigned char unLockFlag;         /* 1 = unlock, 0 = lock */\n  unsigned char startEndFlag;       /* 1=rel to end of fork, 0=rel to start */\n  int fd;                           /* file desc to assoc this lock with */\n};\n\n#define afpfsByteRangeLock2FSCTL        _IOWR('z', 23, struct ByteRangeLockPB2)\n\n/*\n** This is a utility for setting or clearing a bit-range lock on an\n** AFP filesystem.\n** \n** Return SQLITE_OK on success, SQLITE_BUSY on failure.\n*/\nstatic int afpSetLock(\n  const char *path,              /* Name of the file to be locked or unlocked */\n  unixFile *pFile,               /* Open file descriptor on path */\n  unsigned long long offset,     /* First byte to be locked */\n  unsigned long long length,     /* Number of bytes to lock */\n  int setLockFlag                /* True to set lock.  False to clear lock */\n){\n  struct ByteRangeLockPB2 pb;\n  int err;\n  \n  pb.unLockFlag = setLockFlag ? 0 : 1;\n  pb.startEndFlag = 0;\n  pb.offset = offset;\n  pb.length = length; \n  pb.fd = pFile->h;\n  \n  OSTRACE((\"AFPSETLOCK [%s] for %d%s in range %llx:%llx\\n\", \n    (setLockFlag?\"ON\":\"OFF\"), pFile->h, (pb.fd==-1?\"[testval-1]\":\"\"),\n    offset, length));\n  err = fsctl(path, afpfsByteRangeLock2FSCTL, &pb, 0);\n  if ( err==-1 ) {\n    int rc;\n    int tErrno = errno;\n    OSTRACE((\"AFPSETLOCK failed to fsctl() '%s' %d %s\\n\",\n             path, tErrno, strerror(tErrno)));\n#ifdef SQLITE_IGNORE_AFP_LOCK_ERRORS\n    rc = SQLITE_BUSY;\n#else\n    rc = sqliteErrorFromPosixError(tErrno,\n                    setLockFlag ? SQLITE_IOERR_LOCK : SQLITE_IOERR_UNLOCK);\n#endif /* SQLITE_IGNORE_AFP_LOCK_ERRORS */\n    if( IS_LOCK_ERROR(rc) ){\n      storeLastErrno(pFile, tErrno);\n    }\n    return rc;\n  } else {\n    return SQLITE_OK;\n  }\n}\n\n/*\n** This routine checks if there is a RESERVED lock held on the specified\n** file by this or any other process. If such a lock is held, set *pResOut\n** to a non-zero value otherwise *pResOut is set to zero.  The return value\n** is set to SQLITE_OK unless an I/O error occurs during lock checking.\n*/\nstatic int afpCheckReservedLock(sqlite3_file *id, int *pResOut){\n  int rc = SQLITE_OK;\n  int reserved = 0;\n  unixFile *pFile = (unixFile*)id;\n  afpLockingContext *context;\n  \n  SimulateIOError( return SQLITE_IOERR_CHECKRESERVEDLOCK; );\n  \n  assert( pFile );\n  context = (afpLockingContext *) pFile->lockingContext;\n  if( context->reserved ){\n    *pResOut = 1;\n    return SQLITE_OK;\n  }\n  unixEnterMutex(); /* Because pFile->pInode is shared across threads */\n  \n  /* Check if a thread in this process holds such a lock */\n  if( pFile->pInode->eFileLock>SHARED_LOCK ){\n    reserved = 1;\n  }\n  \n  /* Otherwise see if some other process holds it.\n   */\n  if( !reserved ){\n    /* lock the RESERVED byte */\n    int lrc = afpSetLock(context->dbPath, pFile, RESERVED_BYTE, 1,1);  \n    if( SQLITE_OK==lrc ){\n      /* if we succeeded in taking the reserved lock, unlock it to restore\n      ** the original state */\n      lrc = afpSetLock(context->dbPath, pFile, RESERVED_BYTE, 1, 0);\n    } else {\n      /* if we failed to get the lock then someone else must have it */\n      reserved = 1;\n    }\n    if( IS_LOCK_ERROR(lrc) ){\n      rc=lrc;\n    }\n  }\n  \n  unixLeaveMutex();\n  OSTRACE((\"TEST WR-LOCK %d %d %d (afp)\\n\", pFile->h, rc, reserved));\n  \n  *pResOut = reserved;\n  return rc;\n}\n\n/*\n** Lock the file with the lock specified by parameter eFileLock - one\n** of the following:\n**\n**     (1) SHARED_LOCK\n**     (2) RESERVED_LOCK\n**     (3) PENDING_LOCK\n**     (4) EXCLUSIVE_LOCK\n**\n** Sometimes when requesting one lock state, additional lock states\n** are inserted in between.  The locking might fail on one of the later\n** transitions leaving the lock state different from what it started but\n** still short of its goal.  The following chart shows the allowed\n** transitions and the inserted intermediate states:\n**\n**    UNLOCKED -> SHARED\n**    SHARED -> RESERVED\n**    SHARED -> (PENDING) -> EXCLUSIVE\n**    RESERVED -> (PENDING) -> EXCLUSIVE\n**    PENDING -> EXCLUSIVE\n**\n** This routine will only increase a lock.  Use the sqlite3OsUnlock()\n** routine to lower a locking level.\n*/\nstatic int afpLock(sqlite3_file *id, int eFileLock){\n  int rc = SQLITE_OK;\n  unixFile *pFile = (unixFile*)id;\n  unixInodeInfo *pInode = pFile->pInode;\n  afpLockingContext *context = (afpLockingContext *) pFile->lockingContext;\n  \n  assert( pFile );\n  OSTRACE((\"LOCK    %d %s was %s(%s,%d) pid=%d (afp)\\n\", pFile->h,\n           azFileLock(eFileLock), azFileLock(pFile->eFileLock),\n           azFileLock(pInode->eFileLock), pInode->nShared , osGetpid(0)));\n\n  /* If there is already a lock of this type or more restrictive on the\n  ** unixFile, do nothing. Don't use the afp_end_lock: exit path, as\n  ** unixEnterMutex() hasn't been called yet.\n  */\n  if( pFile->eFileLock>=eFileLock ){\n    OSTRACE((\"LOCK    %d %s ok (already held) (afp)\\n\", pFile->h,\n           azFileLock(eFileLock)));\n    return SQLITE_OK;\n  }\n\n  /* Make sure the locking sequence is correct\n  **  (1) We never move from unlocked to anything higher than shared lock.\n  **  (2) SQLite never explicitly requests a pendig lock.\n  **  (3) A shared lock is always held when a reserve lock is requested.\n  */\n  assert( pFile->eFileLock!=NO_LOCK || eFileLock==SHARED_LOCK );\n  assert( eFileLock!=PENDING_LOCK );\n  assert( eFileLock!=RESERVED_LOCK || pFile->eFileLock==SHARED_LOCK );\n  \n  /* This mutex is needed because pFile->pInode is shared across threads\n  */\n  unixEnterMutex();\n  pInode = pFile->pInode;\n\n  /* If some thread using this PID has a lock via a different unixFile*\n  ** handle that precludes the requested lock, return BUSY.\n  */\n  if( (pFile->eFileLock!=pInode->eFileLock && \n       (pInode->eFileLock>=PENDING_LOCK || eFileLock>SHARED_LOCK))\n     ){\n    rc = SQLITE_BUSY;\n    goto afp_end_lock;\n  }\n  \n  /* If a SHARED lock is requested, and some thread using this PID already\n  ** has a SHARED or RESERVED lock, then increment reference counts and\n  ** return SQLITE_OK.\n  */\n  if( eFileLock==SHARED_LOCK && \n     (pInode->eFileLock==SHARED_LOCK || pInode->eFileLock==RESERVED_LOCK) ){\n    assert( eFileLock==SHARED_LOCK );\n    assert( pFile->eFileLock==0 );\n    assert( pInode->nShared>0 );\n    pFile->eFileLock = SHARED_LOCK;\n    pInode->nShared++;\n    pInode->nLock++;\n    goto afp_end_lock;\n  }\n    \n  /* A PENDING lock is needed before acquiring a SHARED lock and before\n  ** acquiring an EXCLUSIVE lock.  For the SHARED lock, the PENDING will\n  ** be released.\n  */\n  if( eFileLock==SHARED_LOCK \n      || (eFileLock==EXCLUSIVE_LOCK && pFile->eFileLock<PENDING_LOCK)\n  ){\n    int failed;\n    failed = afpSetLock(context->dbPath, pFile, PENDING_BYTE, 1, 1);\n    if (failed) {\n      rc = failed;\n      goto afp_end_lock;\n    }\n  }\n  \n  /* If control gets to this point, then actually go ahead and make\n  ** operating system calls for the specified lock.\n  */\n  if( eFileLock==SHARED_LOCK ){\n    int lrc1, lrc2, lrc1Errno = 0;\n    long lk, mask;\n    \n    assert( pInode->nShared==0 );\n    assert( pInode->eFileLock==0 );\n        \n    mask = (sizeof(long)==8) ? LARGEST_INT64 : 0x7fffffff;\n    /* Now get the read-lock SHARED_LOCK */\n    /* note that the quality of the randomness doesn't matter that much */\n    lk = random(); \n    pInode->sharedByte = (lk & mask)%(SHARED_SIZE - 1);\n    lrc1 = afpSetLock(context->dbPath, pFile, \n          SHARED_FIRST+pInode->sharedByte, 1, 1);\n    if( IS_LOCK_ERROR(lrc1) ){\n      lrc1Errno = pFile->lastErrno;\n    }\n    /* Drop the temporary PENDING lock */\n    lrc2 = afpSetLock(context->dbPath, pFile, PENDING_BYTE, 1, 0);\n    \n    if( IS_LOCK_ERROR(lrc1) ) {\n      storeLastErrno(pFile, lrc1Errno);\n      rc = lrc1;\n      goto afp_end_lock;\n    } else if( IS_LOCK_ERROR(lrc2) ){\n      rc = lrc2;\n      goto afp_end_lock;\n    } else if( lrc1 != SQLITE_OK ) {\n      rc = lrc1;\n    } else {\n      pFile->eFileLock = SHARED_LOCK;\n      pInode->nLock++;\n      pInode->nShared = 1;\n    }\n  }else if( eFileLock==EXCLUSIVE_LOCK && pInode->nShared>1 ){\n    /* We are trying for an exclusive lock but another thread in this\n     ** same process is still holding a shared lock. */\n    rc = SQLITE_BUSY;\n  }else{\n    /* The request was for a RESERVED or EXCLUSIVE lock.  It is\n    ** assumed that there is a SHARED or greater lock on the file\n    ** already.\n    */\n    int failed = 0;\n    assert( 0!=pFile->eFileLock );\n    if (eFileLock >= RESERVED_LOCK && pFile->eFileLock < RESERVED_LOCK) {\n        /* Acquire a RESERVED lock */\n        failed = afpSetLock(context->dbPath, pFile, RESERVED_BYTE, 1,1);\n      if( !failed ){\n        context->reserved = 1;\n      }\n    }\n    if (!failed && eFileLock == EXCLUSIVE_LOCK) {\n      /* Acquire an EXCLUSIVE lock */\n        \n      /* Remove the shared lock before trying the range.  we'll need to \n      ** reestablish the shared lock if we can't get the  afpUnlock\n      */\n      if( !(failed = afpSetLock(context->dbPath, pFile, SHARED_FIRST +\n                         pInode->sharedByte, 1, 0)) ){\n        int failed2 = SQLITE_OK;\n        /* now attemmpt to get the exclusive lock range */\n        failed = afpSetLock(context->dbPath, pFile, SHARED_FIRST, \n                               SHARED_SIZE, 1);\n        if( failed && (failed2 = afpSetLock(context->dbPath, pFile, \n                       SHARED_FIRST + pInode->sharedByte, 1, 1)) ){\n          /* Can't reestablish the shared lock.  Sqlite can't deal, this is\n          ** a critical I/O error\n          */\n          rc = ((failed & 0xff) == SQLITE_IOERR) ? failed2 : \n               SQLITE_IOERR_LOCK;\n          goto afp_end_lock;\n        } \n      }else{\n        rc = failed; \n      }\n    }\n    if( failed ){\n      rc = failed;\n    }\n  }\n  \n  if( rc==SQLITE_OK ){\n    pFile->eFileLock = eFileLock;\n    pInode->eFileLock = eFileLock;\n  }else if( eFileLock==EXCLUSIVE_LOCK ){\n    pFile->eFileLock = PENDING_LOCK;\n    pInode->eFileLock = PENDING_LOCK;\n  }\n  \nafp_end_lock:\n  unixLeaveMutex();\n  OSTRACE((\"LOCK    %d %s %s (afp)\\n\", pFile->h, azFileLock(eFileLock), \n         rc==SQLITE_OK ? \"ok\" : \"failed\"));\n  return rc;\n}\n\n/*\n** Lower the locking level on file descriptor pFile to eFileLock.  eFileLock\n** must be either NO_LOCK or SHARED_LOCK.\n**\n** If the locking level of the file descriptor is already at or below\n** the requested locking level, this routine is a no-op.\n*/\nstatic int afpUnlock(sqlite3_file *id, int eFileLock) {\n  int rc = SQLITE_OK;\n  unixFile *pFile = (unixFile*)id;\n  unixInodeInfo *pInode;\n  afpLockingContext *context = (afpLockingContext *) pFile->lockingContext;\n  int skipShared = 0;\n#ifdef SQLITE_TEST\n  int h = pFile->h;\n#endif\n\n  assert( pFile );\n  OSTRACE((\"UNLOCK  %d %d was %d(%d,%d) pid=%d (afp)\\n\", pFile->h, eFileLock,\n           pFile->eFileLock, pFile->pInode->eFileLock, pFile->pInode->nShared,\n           osGetpid(0)));\n\n  assert( eFileLock<=SHARED_LOCK );\n  if( pFile->eFileLock<=eFileLock ){\n    return SQLITE_OK;\n  }\n  unixEnterMutex();\n  pInode = pFile->pInode;\n  assert( pInode->nShared!=0 );\n  if( pFile->eFileLock>SHARED_LOCK ){\n    assert( pInode->eFileLock==pFile->eFileLock );\n    SimulateIOErrorBenign(1);\n    SimulateIOError( h=(-1) )\n    SimulateIOErrorBenign(0);\n    \n#ifdef SQLITE_DEBUG\n    /* When reducing a lock such that other processes can start\n    ** reading the database file again, make sure that the\n    ** transaction counter was updated if any part of the database\n    ** file changed.  If the transaction counter is not updated,\n    ** other connections to the same file might not realize that\n    ** the file has changed and hence might not know to flush their\n    ** cache.  The use of a stale cache can lead to database corruption.\n    */\n    assert( pFile->inNormalWrite==0\n           || pFile->dbUpdate==0\n           || pFile->transCntrChng==1 );\n    pFile->inNormalWrite = 0;\n#endif\n    \n    if( pFile->eFileLock==EXCLUSIVE_LOCK ){\n      rc = afpSetLock(context->dbPath, pFile, SHARED_FIRST, SHARED_SIZE, 0);\n      if( rc==SQLITE_OK && (eFileLock==SHARED_LOCK || pInode->nShared>1) ){\n        /* only re-establish the shared lock if necessary */\n        int sharedLockByte = SHARED_FIRST+pInode->sharedByte;\n        rc = afpSetLock(context->dbPath, pFile, sharedLockByte, 1, 1);\n      } else {\n        skipShared = 1;\n      }\n    }\n    if( rc==SQLITE_OK && pFile->eFileLock>=PENDING_LOCK ){\n      rc = afpSetLock(context->dbPath, pFile, PENDING_BYTE, 1, 0);\n    } \n    if( rc==SQLITE_OK && pFile->eFileLock>=RESERVED_LOCK && context->reserved ){\n      rc = afpSetLock(context->dbPath, pFile, RESERVED_BYTE, 1, 0);\n      if( !rc ){ \n        context->reserved = 0; \n      }\n    }\n    if( rc==SQLITE_OK && (eFileLock==SHARED_LOCK || pInode->nShared>1)){\n      pInode->eFileLock = SHARED_LOCK;\n    }\n  }\n  if( rc==SQLITE_OK && eFileLock==NO_LOCK ){\n\n    /* Decrement the shared lock counter.  Release the lock using an\n    ** OS call only when all threads in this same process have released\n    ** the lock.\n    */\n    unsigned long long sharedLockByte = SHARED_FIRST+pInode->sharedByte;\n    pInode->nShared--;\n    if( pInode->nShared==0 ){\n      SimulateIOErrorBenign(1);\n      SimulateIOError( h=(-1) )\n      SimulateIOErrorBenign(0);\n      if( !skipShared ){\n        rc = afpSetLock(context->dbPath, pFile, sharedLockByte, 1, 0);\n      }\n      if( !rc ){\n        pInode->eFileLock = NO_LOCK;\n        pFile->eFileLock = NO_LOCK;\n      }\n    }\n    if( rc==SQLITE_OK ){\n      pInode->nLock--;\n      assert( pInode->nLock>=0 );\n      if( pInode->nLock==0 ){\n        closePendingFds(pFile);\n      }\n    }\n  }\n  \n  unixLeaveMutex();\n  if( rc==SQLITE_OK ) pFile->eFileLock = eFileLock;\n  return rc;\n}\n\n/*\n** Close a file & cleanup AFP specific locking context \n*/\nstatic int afpClose(sqlite3_file *id) {\n  int rc = SQLITE_OK;\n  unixFile *pFile = (unixFile*)id;\n  assert( id!=0 );\n  afpUnlock(id, NO_LOCK);\n  unixEnterMutex();\n  if( pFile->pInode && pFile->pInode->nLock ){\n    /* If there are outstanding locks, do not actually close the file just\n    ** yet because that would clear those locks.  Instead, add the file\n    ** descriptor to pInode->aPending.  It will be automatically closed when\n    ** the last lock is cleared.\n    */\n    setPendingFd(pFile);\n  }\n  releaseInodeInfo(pFile);\n  sqlite3_free(pFile->lockingContext);\n  rc = closeUnixFile(id);\n  unixLeaveMutex();\n  return rc;\n}\n\n#endif /* defined(__APPLE__) && SQLITE_ENABLE_LOCKING_STYLE */\n/*\n** The code above is the AFP lock implementation.  The code is specific\n** to MacOSX and does not work on other unix platforms.  No alternative\n** is available.  If you don't compile for a mac, then the \"unix-afp\"\n** VFS is not available.\n**\n********************* End of the AFP lock implementation **********************\n******************************************************************************/\n\n/******************************************************************************\n*************************** Begin NFS Locking ********************************/\n\n#if defined(__APPLE__) && SQLITE_ENABLE_LOCKING_STYLE\n/*\n ** Lower the locking level on file descriptor pFile to eFileLock.  eFileLock\n ** must be either NO_LOCK or SHARED_LOCK.\n **\n ** If the locking level of the file descriptor is already at or below\n ** the requested locking level, this routine is a no-op.\n */\nstatic int nfsUnlock(sqlite3_file *id, int eFileLock){\n  return posixUnlock(id, eFileLock, 1);\n}\n\n#endif /* defined(__APPLE__) && SQLITE_ENABLE_LOCKING_STYLE */\n/*\n** The code above is the NFS lock implementation.  The code is specific\n** to MacOSX and does not work on other unix platforms.  No alternative\n** is available.  \n**\n********************* End of the NFS lock implementation **********************\n******************************************************************************/\n\n/******************************************************************************\n**************** Non-locking sqlite3_file methods *****************************\n**\n** The next division contains implementations for all methods of the \n** sqlite3_file object other than the locking methods.  The locking\n** methods were defined in divisions above (one locking method per\n** division).  Those methods that are common to all locking modes\n** are gather together into this division.\n*/\n\n/*\n** Seek to the offset passed as the second argument, then read cnt \n** bytes into pBuf. Return the number of bytes actually read.\n**\n** NB:  If you define USE_PREAD or USE_PREAD64, then it might also\n** be necessary to define _XOPEN_SOURCE to be 500.  This varies from\n** one system to another.  Since SQLite does not define USE_PREAD\n** in any form by default, we will not attempt to define _XOPEN_SOURCE.\n** See tickets #2741 and #2681.\n**\n** To avoid stomping the errno value on a failed read the lastErrno value\n** is set before returning.\n*/\nstatic int seekAndRead(unixFile *id, sqlite3_int64 offset, void *pBuf, int cnt){\n  int got;\n  int prior = 0;\n#if (!defined(USE_PREAD) && !defined(USE_PREAD64))\n  i64 newOffset;\n#endif\n  TIMER_START;\n  assert( cnt==(cnt&0x1ffff) );\n  assert( id->h>2 );\n  do{\n#if defined(USE_PREAD)\n    got = osPread(id->h, pBuf, cnt, offset);\n    SimulateIOError( got = -1 );\n#elif defined(USE_PREAD64)\n    got = osPread64(id->h, pBuf, cnt, offset);\n    SimulateIOError( got = -1 );\n#else\n    newOffset = lseek(id->h, offset, SEEK_SET);\n    SimulateIOError( newOffset = -1 );\n    if( newOffset<0 ){\n      storeLastErrno((unixFile*)id, errno);\n      return -1;\n    }\n    got = osRead(id->h, pBuf, cnt);\n#endif\n    if( got==cnt ) break;\n    if( got<0 ){\n      if( errno==EINTR ){ got = 1; continue; }\n      prior = 0;\n      storeLastErrno((unixFile*)id,  errno);\n      break;\n    }else if( got>0 ){\n      cnt -= got;\n      offset += got;\n      prior += got;\n      pBuf = (void*)(got + (char*)pBuf);\n    }\n  }while( got>0 );\n  TIMER_END;\n  OSTRACE((\"READ    %-3d %5d %7lld %llu\\n\",\n            id->h, got+prior, offset-prior, TIMER_ELAPSED));\n  return got+prior;\n}\n\n/*\n** Read data from a file into a buffer.  Return SQLITE_OK if all\n** bytes were read successfully and SQLITE_IOERR if anything goes\n** wrong.\n*/\nstatic int unixRead(\n  sqlite3_file *id, \n  void *pBuf, \n  int amt,\n  sqlite3_int64 offset\n){\n  unixFile *pFile = (unixFile *)id;\n  int got;\n  assert( id );\n  assert( offset>=0 );\n  assert( amt>0 );\n\n  /* If this is a database file (not a journal, master-journal or temp\n  ** file), the bytes in the locking range should never be read or written. */\n#if 0\n  assert( pFile->pPreallocatedUnused==0\n       || offset>=PENDING_BYTE+512\n       || offset+amt<=PENDING_BYTE \n  );\n#endif\n\n#if SQLITE_MAX_MMAP_SIZE>0\n  /* Deal with as much of this read request as possible by transfering\n  ** data from the memory mapping using memcpy().  */\n  if( offset<pFile->mmapSize ){\n    if( offset+amt <= pFile->mmapSize ){\n      memcpy(pBuf, &((u8 *)(pFile->pMapRegion))[offset], amt);\n      return SQLITE_OK;\n    }else{\n      int nCopy = pFile->mmapSize - offset;\n      memcpy(pBuf, &((u8 *)(pFile->pMapRegion))[offset], nCopy);\n      pBuf = &((u8 *)pBuf)[nCopy];\n      amt -= nCopy;\n      offset += nCopy;\n    }\n  }\n#endif\n\n  got = seekAndRead(pFile, offset, pBuf, amt);\n  if( got==amt ){\n    return SQLITE_OK;\n  }else if( got<0 ){\n    /* lastErrno set by seekAndRead */\n    return SQLITE_IOERR_READ;\n  }else{\n    storeLastErrno(pFile, 0);   /* not a system error */\n    /* Unread parts of the buffer must be zero-filled */\n    memset(&((char*)pBuf)[got], 0, amt-got);\n    return SQLITE_IOERR_SHORT_READ;\n  }\n}\n\n/*\n** Attempt to seek the file-descriptor passed as the first argument to\n** absolute offset iOff, then attempt to write nBuf bytes of data from\n** pBuf to it. If an error occurs, return -1 and set *piErrno. Otherwise, \n** return the actual number of bytes written (which may be less than\n** nBuf).\n*/\nstatic int seekAndWriteFd(\n  int fd,                         /* File descriptor to write to */\n  i64 iOff,                       /* File offset to begin writing at */\n  const void *pBuf,               /* Copy data from this buffer to the file */\n  int nBuf,                       /* Size of buffer pBuf in bytes */\n  int *piErrno                    /* OUT: Error number if error occurs */\n){\n  int rc = 0;                     /* Value returned by system call */\n\n  assert( nBuf==(nBuf&0x1ffff) );\n  assert( fd>2 );\n  assert( piErrno!=0 );\n  nBuf &= 0x1ffff;\n  TIMER_START;\n\n#if defined(USE_PREAD)\n  do{ rc = (int)osPwrite(fd, pBuf, nBuf, iOff); }while( rc<0 && errno==EINTR );\n#elif defined(USE_PREAD64)\n  do{ rc = (int)osPwrite64(fd, pBuf, nBuf, iOff);}while( rc<0 && errno==EINTR);\n#else\n  do{\n    i64 iSeek = lseek(fd, iOff, SEEK_SET);\n    SimulateIOError( iSeek = -1 );\n    if( iSeek<0 ){\n      rc = -1;\n      break;\n    }\n    rc = osWrite(fd, pBuf, nBuf);\n  }while( rc<0 && errno==EINTR );\n#endif\n\n  TIMER_END;\n  OSTRACE((\"WRITE   %-3d %5d %7lld %llu\\n\", fd, rc, iOff, TIMER_ELAPSED));\n\n  if( rc<0 ) *piErrno = errno;\n  return rc;\n}\n\n\n/*\n** Seek to the offset in id->offset then read cnt bytes into pBuf.\n** Return the number of bytes actually read.  Update the offset.\n**\n** To avoid stomping the errno value on a failed write the lastErrno value\n** is set before returning.\n*/\nstatic int seekAndWrite(unixFile *id, i64 offset, const void *pBuf, int cnt){\n  return seekAndWriteFd(id->h, offset, pBuf, cnt, &id->lastErrno);\n}\n\n\n/*\n** Write data from a buffer into a file.  Return SQLITE_OK on success\n** or some other error code on failure.\n*/\nstatic int unixWrite(\n  sqlite3_file *id, \n  const void *pBuf, \n  int amt,\n  sqlite3_int64 offset \n){\n  unixFile *pFile = (unixFile*)id;\n  int wrote = 0;\n  assert( id );\n  assert( amt>0 );\n\n  /* If this is a database file (not a journal, master-journal or temp\n  ** file), the bytes in the locking range should never be read or written. */\n#if 0\n  assert( pFile->pPreallocatedUnused==0\n       || offset>=PENDING_BYTE+512\n       || offset+amt<=PENDING_BYTE \n  );\n#endif\n\n#ifdef SQLITE_DEBUG\n  /* If we are doing a normal write to a database file (as opposed to\n  ** doing a hot-journal rollback or a write to some file other than a\n  ** normal database file) then record the fact that the database\n  ** has changed.  If the transaction counter is modified, record that\n  ** fact too.\n  */\n  if( pFile->inNormalWrite ){\n    pFile->dbUpdate = 1;  /* The database has been modified */\n    if( offset<=24 && offset+amt>=27 ){\n      int rc;\n      char oldCntr[4];\n      SimulateIOErrorBenign(1);\n      rc = seekAndRead(pFile, 24, oldCntr, 4);\n      SimulateIOErrorBenign(0);\n      if( rc!=4 || memcmp(oldCntr, &((char*)pBuf)[24-offset], 4)!=0 ){\n        pFile->transCntrChng = 1;  /* The transaction counter has changed */\n      }\n    }\n  }\n#endif\n\n#if defined(SQLITE_MMAP_READWRITE) && SQLITE_MAX_MMAP_SIZE>0\n  /* Deal with as much of this write request as possible by transfering\n  ** data from the memory mapping using memcpy().  */\n  if( offset<pFile->mmapSize ){\n    if( offset+amt <= pFile->mmapSize ){\n      memcpy(&((u8 *)(pFile->pMapRegion))[offset], pBuf, amt);\n      return SQLITE_OK;\n    }else{\n      int nCopy = pFile->mmapSize - offset;\n      memcpy(&((u8 *)(pFile->pMapRegion))[offset], pBuf, nCopy);\n      pBuf = &((u8 *)pBuf)[nCopy];\n      amt -= nCopy;\n      offset += nCopy;\n    }\n  }\n#endif\n \n  while( (wrote = seekAndWrite(pFile, offset, pBuf, amt))<amt && wrote>0 ){\n    amt -= wrote;\n    offset += wrote;\n    pBuf = &((char*)pBuf)[wrote];\n  }\n  SimulateIOError(( wrote=(-1), amt=1 ));\n  SimulateDiskfullError(( wrote=0, amt=1 ));\n\n  if( amt>wrote ){\n    if( wrote<0 && pFile->lastErrno!=ENOSPC ){\n      /* lastErrno set by seekAndWrite */\n      return SQLITE_IOERR_WRITE;\n    }else{\n      storeLastErrno(pFile, 0); /* not a system error */\n      return SQLITE_FULL;\n    }\n  }\n\n  return SQLITE_OK;\n}\n\n#ifdef SQLITE_TEST\n/*\n** Count the number of fullsyncs and normal syncs.  This is used to test\n** that syncs and fullsyncs are occurring at the right times.\n*/\nSQLITE_API int sqlite3_sync_count = 0;\nSQLITE_API int sqlite3_fullsync_count = 0;\n#endif\n\n/*\n** We do not trust systems to provide a working fdatasync().  Some do.\n** Others do no.  To be safe, we will stick with the (slightly slower)\n** fsync(). If you know that your system does support fdatasync() correctly,\n** then simply compile with -Dfdatasync=fdatasync or -DHAVE_FDATASYNC\n*/\n#if !defined(fdatasync) && !HAVE_FDATASYNC\n# define fdatasync fsync\n#endif\n\n/*\n** Define HAVE_FULLFSYNC to 0 or 1 depending on whether or not\n** the F_FULLFSYNC macro is defined.  F_FULLFSYNC is currently\n** only available on Mac OS X.  But that could change.\n*/\n#ifdef F_FULLFSYNC\n# define HAVE_FULLFSYNC 1\n#else\n# define HAVE_FULLFSYNC 0\n#endif\n\n\n/*\n** The fsync() system call does not work as advertised on many\n** unix systems.  The following procedure is an attempt to make\n** it work better.\n**\n** The SQLITE_NO_SYNC macro disables all fsync()s.  This is useful\n** for testing when we want to run through the test suite quickly.\n** You are strongly advised *not* to deploy with SQLITE_NO_SYNC\n** enabled, however, since with SQLITE_NO_SYNC enabled, an OS crash\n** or power failure will likely corrupt the database file.\n**\n** SQLite sets the dataOnly flag if the size of the file is unchanged.\n** The idea behind dataOnly is that it should only write the file content\n** to disk, not the inode.  We only set dataOnly if the file size is \n** unchanged since the file size is part of the inode.  However, \n** Ted Ts'o tells us that fdatasync() will also write the inode if the\n** file size has changed.  The only real difference between fdatasync()\n** and fsync(), Ted tells us, is that fdatasync() will not flush the\n** inode if the mtime or owner or other inode attributes have changed.\n** We only care about the file size, not the other file attributes, so\n** as far as SQLite is concerned, an fdatasync() is always adequate.\n** So, we always use fdatasync() if it is available, regardless of\n** the value of the dataOnly flag.\n*/\nstatic int full_fsync(int fd, int fullSync, int dataOnly){\n  int rc;\n\n  /* The following \"ifdef/elif/else/\" block has the same structure as\n  ** the one below. It is replicated here solely to avoid cluttering \n  ** up the real code with the UNUSED_PARAMETER() macros.\n  */\n#ifdef SQLITE_NO_SYNC\n  UNUSED_PARAMETER(fd);\n  UNUSED_PARAMETER(fullSync);\n  UNUSED_PARAMETER(dataOnly);\n#elif HAVE_FULLFSYNC\n  UNUSED_PARAMETER(dataOnly);\n#else\n  UNUSED_PARAMETER(fullSync);\n  UNUSED_PARAMETER(dataOnly);\n#endif\n\n  /* Record the number of times that we do a normal fsync() and \n  ** FULLSYNC.  This is used during testing to verify that this procedure\n  ** gets called with the correct arguments.\n  */\n#ifdef SQLITE_TEST\n  if( fullSync ) sqlite3_fullsync_count++;\n  sqlite3_sync_count++;\n#endif\n\n  /* If we compiled with the SQLITE_NO_SYNC flag, then syncing is a\n  ** no-op.  But go ahead and call fstat() to validate the file\n  ** descriptor as we need a method to provoke a failure during\n  ** coverate testing.\n  */\n#ifdef SQLITE_NO_SYNC\n  {\n    struct stat buf;\n    rc = osFstat(fd, &buf);\n  }\n#elif HAVE_FULLFSYNC\n  if( fullSync ){\n    rc = osFcntl(fd, F_FULLFSYNC, 0);\n  }else{\n    rc = 1;\n  }\n  /* If the FULLFSYNC failed, fall back to attempting an fsync().\n  ** It shouldn't be possible for fullfsync to fail on the local \n  ** file system (on OSX), so failure indicates that FULLFSYNC\n  ** isn't supported for this file system. So, attempt an fsync \n  ** and (for now) ignore the overhead of a superfluous fcntl call.  \n  ** It'd be better to detect fullfsync support once and avoid \n  ** the fcntl call every time sync is called.\n  */\n  if( rc ) rc = fsync(fd);\n\n#elif defined(__APPLE__)\n  /* fdatasync() on HFS+ doesn't yet flush the file size if it changed correctly\n  ** so currently we default to the macro that redefines fdatasync to fsync\n  */\n  rc = fsync(fd);\n#else \n  rc = fdatasync(fd);\n#if OS_VXWORKS\n  if( rc==-1 && errno==ENOTSUP ){\n    rc = fsync(fd);\n  }\n#endif /* OS_VXWORKS */\n#endif /* ifdef SQLITE_NO_SYNC elif HAVE_FULLFSYNC */\n\n  if( OS_VXWORKS && rc!= -1 ){\n    rc = 0;\n  }\n  return rc;\n}\n\n/*\n** Open a file descriptor to the directory containing file zFilename.\n** If successful, *pFd is set to the opened file descriptor and\n** SQLITE_OK is returned. If an error occurs, either SQLITE_NOMEM\n** or SQLITE_CANTOPEN is returned and *pFd is set to an undefined\n** value.\n**\n** The directory file descriptor is used for only one thing - to\n** fsync() a directory to make sure file creation and deletion events\n** are flushed to disk.  Such fsyncs are not needed on newer\n** journaling filesystems, but are required on older filesystems.\n**\n** This routine can be overridden using the xSetSysCall interface.\n** The ability to override this routine was added in support of the\n** chromium sandbox.  Opening a directory is a security risk (we are\n** told) so making it overrideable allows the chromium sandbox to\n** replace this routine with a harmless no-op.  To make this routine\n** a no-op, replace it with a stub that returns SQLITE_OK but leaves\n** *pFd set to a negative number.\n**\n** If SQLITE_OK is returned, the caller is responsible for closing\n** the file descriptor *pFd using close().\n*/\nstatic int openDirectory(const char *zFilename, int *pFd){\n  int ii;\n  int fd = -1;\n  char zDirname[MAX_PATHNAME+1];\n\n  sqlite3_snprintf(MAX_PATHNAME, zDirname, \"%s\", zFilename);\n  for(ii=(int)strlen(zDirname); ii>0 && zDirname[ii]!='/'; ii--);\n  if( ii>0 ){\n    zDirname[ii] = '\\0';\n  }else{\n    if( zDirname[0]!='/' ) zDirname[0] = '.';\n    zDirname[1] = 0;\n  }\n  fd = robust_open(zDirname, O_RDONLY|O_BINARY, 0);\n  if( fd>=0 ){\n    OSTRACE((\"OPENDIR %-3d %s\\n\", fd, zDirname));\n  }\n  *pFd = fd;\n  if( fd>=0 ) return SQLITE_OK;\n  return unixLogError(SQLITE_CANTOPEN_BKPT, \"openDirectory\", zDirname);\n}\n\n/*\n** Make sure all writes to a particular file are committed to disk.\n**\n** If dataOnly==0 then both the file itself and its metadata (file\n** size, access time, etc) are synced.  If dataOnly!=0 then only the\n** file data is synced.\n**\n** Under Unix, also make sure that the directory entry for the file\n** has been created by fsync-ing the directory that contains the file.\n** If we do not do this and we encounter a power failure, the directory\n** entry for the journal might not exist after we reboot.  The next\n** SQLite to access the file will not know that the journal exists (because\n** the directory entry for the journal was never created) and the transaction\n** will not roll back - possibly leading to database corruption.\n*/\nstatic int unixSync(sqlite3_file *id, int flags){\n  int rc;\n  unixFile *pFile = (unixFile*)id;\n\n  int isDataOnly = (flags&SQLITE_SYNC_DATAONLY);\n  int isFullsync = (flags&0x0F)==SQLITE_SYNC_FULL;\n\n  /* Check that one of SQLITE_SYNC_NORMAL or FULL was passed */\n  assert((flags&0x0F)==SQLITE_SYNC_NORMAL\n      || (flags&0x0F)==SQLITE_SYNC_FULL\n  );\n\n  /* Unix cannot, but some systems may return SQLITE_FULL from here. This\n  ** line is to test that doing so does not cause any problems.\n  */\n  SimulateDiskfullError( return SQLITE_FULL );\n\n  assert( pFile );\n  OSTRACE((\"SYNC    %-3d\\n\", pFile->h));\n  rc = full_fsync(pFile->h, isFullsync, isDataOnly);\n  SimulateIOError( rc=1 );\n  if( rc ){\n    storeLastErrno(pFile, errno);\n    return unixLogError(SQLITE_IOERR_FSYNC, \"full_fsync\", pFile->zPath);\n  }\n\n  /* Also fsync the directory containing the file if the DIRSYNC flag\n  ** is set.  This is a one-time occurrence.  Many systems (examples: AIX)\n  ** are unable to fsync a directory, so ignore errors on the fsync.\n  */\n  if( pFile->ctrlFlags & UNIXFILE_DIRSYNC ){\n    int dirfd;\n    OSTRACE((\"DIRSYNC %s (have_fullfsync=%d fullsync=%d)\\n\", pFile->zPath,\n            HAVE_FULLFSYNC, isFullsync));\n    rc = osOpenDirectory(pFile->zPath, &dirfd);\n    if( rc==SQLITE_OK ){\n      full_fsync(dirfd, 0, 0);\n      robust_close(pFile, dirfd, __LINE__);\n    }else{\n      assert( rc==SQLITE_CANTOPEN );\n      rc = SQLITE_OK;\n    }\n    pFile->ctrlFlags &= ~UNIXFILE_DIRSYNC;\n  }\n  return rc;\n}\n\n/*\n** Truncate an open file to a specified size\n*/\nstatic int unixTruncate(sqlite3_file *id, i64 nByte){\n  unixFile *pFile = (unixFile *)id;\n  int rc;\n  assert( pFile );\n  SimulateIOError( return SQLITE_IOERR_TRUNCATE );\n\n  /* If the user has configured a chunk-size for this file, truncate the\n  ** file so that it consists of an integer number of chunks (i.e. the\n  ** actual file size after the operation may be larger than the requested\n  ** size).\n  */\n  if( pFile->szChunk>0 ){\n    nByte = ((nByte + pFile->szChunk - 1)/pFile->szChunk) * pFile->szChunk;\n  }\n\n  rc = robust_ftruncate(pFile->h, nByte);\n  if( rc ){\n    storeLastErrno(pFile, errno);\n    return unixLogError(SQLITE_IOERR_TRUNCATE, \"ftruncate\", pFile->zPath);\n  }else{\n#ifdef SQLITE_DEBUG\n    /* If we are doing a normal write to a database file (as opposed to\n    ** doing a hot-journal rollback or a write to some file other than a\n    ** normal database file) and we truncate the file to zero length,\n    ** that effectively updates the change counter.  This might happen\n    ** when restoring a database using the backup API from a zero-length\n    ** source.\n    */\n    if( pFile->inNormalWrite && nByte==0 ){\n      pFile->transCntrChng = 1;\n    }\n#endif\n\n#if SQLITE_MAX_MMAP_SIZE>0\n    /* If the file was just truncated to a size smaller than the currently\n    ** mapped region, reduce the effective mapping size as well. SQLite will\n    ** use read() and write() to access data beyond this point from now on.  \n    */\n    if( nByte<pFile->mmapSize ){\n      pFile->mmapSize = nByte;\n    }\n#endif\n\n    return SQLITE_OK;\n  }\n}\n\n/*\n** Determine the current size of a file in bytes\n*/\nstatic int unixFileSize(sqlite3_file *id, i64 *pSize){\n  int rc;\n  struct stat buf;\n  assert( id );\n  rc = osFstat(((unixFile*)id)->h, &buf);\n  SimulateIOError( rc=1 );\n  if( rc!=0 ){\n    storeLastErrno((unixFile*)id, errno);\n    return SQLITE_IOERR_FSTAT;\n  }\n  *pSize = buf.st_size;\n\n  /* When opening a zero-size database, the findInodeInfo() procedure\n  ** writes a single byte into that file in order to work around a bug\n  ** in the OS-X msdos filesystem.  In order to avoid problems with upper\n  ** layers, we need to report this file size as zero even though it is\n  ** really 1.   Ticket #3260.\n  */\n  if( *pSize==1 ) *pSize = 0;\n\n\n  return SQLITE_OK;\n}\n\n#if SQLITE_ENABLE_LOCKING_STYLE && defined(__APPLE__)\n/*\n** Handler for proxy-locking file-control verbs.  Defined below in the\n** proxying locking division.\n*/\nstatic int proxyFileControl(sqlite3_file*,int,void*);\n#endif\n\n/* \n** This function is called to handle the SQLITE_FCNTL_SIZE_HINT \n** file-control operation.  Enlarge the database to nBytes in size\n** (rounded up to the next chunk-size).  If the database is already\n** nBytes or larger, this routine is a no-op.\n*/\nstatic int fcntlSizeHint(unixFile *pFile, i64 nByte){\n  if( pFile->szChunk>0 ){\n    i64 nSize;                    /* Required file size */\n    struct stat buf;              /* Used to hold return values of fstat() */\n   \n    if( osFstat(pFile->h, &buf) ){\n      return SQLITE_IOERR_FSTAT;\n    }\n\n    nSize = ((nByte+pFile->szChunk-1) / pFile->szChunk) * pFile->szChunk;\n    if( nSize>(i64)buf.st_size ){\n\n#if defined(HAVE_POSIX_FALLOCATE) && HAVE_POSIX_FALLOCATE\n      /* The code below is handling the return value of osFallocate() \n      ** correctly. posix_fallocate() is defined to \"returns zero on success, \n      ** or an error number on  failure\". See the manpage for details. */\n      int err;\n      do{\n        err = osFallocate(pFile->h, buf.st_size, nSize-buf.st_size);\n      }while( err==EINTR );\n      if( err ) return SQLITE_IOERR_WRITE;\n#else\n      /* If the OS does not have posix_fallocate(), fake it. Write a \n      ** single byte to the last byte in each block that falls entirely\n      ** within the extended region. Then, if required, a single byte\n      ** at offset (nSize-1), to set the size of the file correctly.\n      ** This is a similar technique to that used by glibc on systems\n      ** that do not have a real fallocate() call.\n      */\n      int nBlk = buf.st_blksize;  /* File-system block size */\n      int nWrite = 0;             /* Number of bytes written by seekAndWrite */\n      i64 iWrite;                 /* Next offset to write to */\n\n      iWrite = (buf.st_size/nBlk)*nBlk + nBlk - 1;\n      assert( iWrite>=buf.st_size );\n      assert( ((iWrite+1)%nBlk)==0 );\n      for(/*no-op*/; iWrite<nSize+nBlk-1; iWrite+=nBlk ){\n        if( iWrite>=nSize ) iWrite = nSize - 1;\n        nWrite = seekAndWrite(pFile, iWrite, \"\", 1);\n        if( nWrite!=1 ) return SQLITE_IOERR_WRITE;\n      }\n#endif\n    }\n  }\n\n#if SQLITE_MAX_MMAP_SIZE>0\n  if( pFile->mmapSizeMax>0 && nByte>pFile->mmapSize ){\n    int rc;\n    if( pFile->szChunk<=0 ){\n      if( robust_ftruncate(pFile->h, nByte) ){\n        storeLastErrno(pFile, errno);\n        return unixLogError(SQLITE_IOERR_TRUNCATE, \"ftruncate\", pFile->zPath);\n      }\n    }\n\n    rc = unixMapfile(pFile, nByte);\n    return rc;\n  }\n#endif\n\n  return SQLITE_OK;\n}\n\n/*\n** If *pArg is initially negative then this is a query.  Set *pArg to\n** 1 or 0 depending on whether or not bit mask of pFile->ctrlFlags is set.\n**\n** If *pArg is 0 or 1, then clear or set the mask bit of pFile->ctrlFlags.\n*/\nstatic void unixModeBit(unixFile *pFile, unsigned char mask, int *pArg){\n  if( *pArg<0 ){\n    *pArg = (pFile->ctrlFlags & mask)!=0;\n  }else if( (*pArg)==0 ){\n    pFile->ctrlFlags &= ~mask;\n  }else{\n    pFile->ctrlFlags |= mask;\n  }\n}\n\n/* Forward declaration */\nstatic int unixGetTempname(int nBuf, char *zBuf);\n\n/*\n** Information and control of an open file handle.\n*/\nstatic int unixFileControl(sqlite3_file *id, int op, void *pArg){\n  unixFile *pFile = (unixFile*)id;\n  switch( op ){\n#if defined(__linux__) && defined(SQLITE_ENABLE_BATCH_ATOMIC_WRITE)\n    case SQLITE_FCNTL_BEGIN_ATOMIC_WRITE: {\n      int rc = osIoctl(pFile->h, F2FS_IOC_START_ATOMIC_WRITE);\n      return rc ? SQLITE_IOERR_BEGIN_ATOMIC : SQLITE_OK;\n    }\n    case SQLITE_FCNTL_COMMIT_ATOMIC_WRITE: {\n      int rc = osIoctl(pFile->h, F2FS_IOC_COMMIT_ATOMIC_WRITE);\n      return rc ? SQLITE_IOERR_COMMIT_ATOMIC : SQLITE_OK;\n    }\n    case SQLITE_FCNTL_ROLLBACK_ATOMIC_WRITE: {\n      int rc = osIoctl(pFile->h, F2FS_IOC_ABORT_VOLATILE_WRITE);\n      return rc ? SQLITE_IOERR_ROLLBACK_ATOMIC : SQLITE_OK;\n    }\n#endif /* __linux__ && SQLITE_ENABLE_BATCH_ATOMIC_WRITE */\n\n    case SQLITE_FCNTL_LOCKSTATE: {\n      *(int*)pArg = pFile->eFileLock;\n      return SQLITE_OK;\n    }\n    case SQLITE_FCNTL_LAST_ERRNO: {\n      *(int*)pArg = pFile->lastErrno;\n      return SQLITE_OK;\n    }\n    case SQLITE_FCNTL_CHUNK_SIZE: {\n      pFile->szChunk = *(int *)pArg;\n      return SQLITE_OK;\n    }\n    case SQLITE_FCNTL_SIZE_HINT: {\n      int rc;\n      SimulateIOErrorBenign(1);\n      rc = fcntlSizeHint(pFile, *(i64 *)pArg);\n      SimulateIOErrorBenign(0);\n      return rc;\n    }\n    case SQLITE_FCNTL_PERSIST_WAL: {\n      unixModeBit(pFile, UNIXFILE_PERSIST_WAL, (int*)pArg);\n      return SQLITE_OK;\n    }\n    case SQLITE_FCNTL_POWERSAFE_OVERWRITE: {\n      unixModeBit(pFile, UNIXFILE_PSOW, (int*)pArg);\n      return SQLITE_OK;\n    }\n    case SQLITE_FCNTL_VFSNAME: {\n      *(char**)pArg = sqlite3_mprintf(\"%s\", pFile->pVfs->zName);\n      return SQLITE_OK;\n    }\n    case SQLITE_FCNTL_TEMPFILENAME: {\n      char *zTFile = sqlite3_malloc64( pFile->pVfs->mxPathname );\n      if( zTFile ){\n        unixGetTempname(pFile->pVfs->mxPathname, zTFile);\n        *(char**)pArg = zTFile;\n      }\n      return SQLITE_OK;\n    }\n    case SQLITE_FCNTL_HAS_MOVED: {\n      *(int*)pArg = fileHasMoved(pFile);\n      return SQLITE_OK;\n    }\n#if SQLITE_MAX_MMAP_SIZE>0\n    case SQLITE_FCNTL_MMAP_SIZE: {\n      i64 newLimit = *(i64*)pArg;\n      int rc = SQLITE_OK;\n      if( newLimit>sqlite3GlobalConfig.mxMmap ){\n        newLimit = sqlite3GlobalConfig.mxMmap;\n      }\n\n      /* The value of newLimit may be eventually cast to (size_t) and passed\n      ** to mmap(). Restrict its value to 2GB if (size_t) is not at least a\n      ** 64-bit type. */\n      if( newLimit>0 && sizeof(size_t)<8 ){\n        newLimit = (newLimit & 0x7FFFFFFF);\n      }\n\n      *(i64*)pArg = pFile->mmapSizeMax;\n      if( newLimit>=0 && newLimit!=pFile->mmapSizeMax && pFile->nFetchOut==0 ){\n        pFile->mmapSizeMax = newLimit;\n        if( pFile->mmapSize>0 ){\n          unixUnmapfile(pFile);\n          rc = unixMapfile(pFile, -1);\n        }\n      }\n      return rc;\n    }\n#endif\n#ifdef SQLITE_DEBUG\n    /* The pager calls this method to signal that it has done\n    ** a rollback and that the database is therefore unchanged and\n    ** it hence it is OK for the transaction change counter to be\n    ** unchanged.\n    */\n    case SQLITE_FCNTL_DB_UNCHANGED: {\n      ((unixFile*)id)->dbUpdate = 0;\n      return SQLITE_OK;\n    }\n#endif\n#if SQLITE_ENABLE_LOCKING_STYLE && defined(__APPLE__)\n    case SQLITE_FCNTL_SET_LOCKPROXYFILE:\n    case SQLITE_FCNTL_GET_LOCKPROXYFILE: {\n      return proxyFileControl(id,op,pArg);\n    }\n#endif /* SQLITE_ENABLE_LOCKING_STYLE && defined(__APPLE__) */\n  }\n  return SQLITE_NOTFOUND;\n}\n\n/*\n** If pFd->sectorSize is non-zero when this function is called, it is a\n** no-op. Otherwise, the values of pFd->sectorSize and \n** pFd->deviceCharacteristics are set according to the file-system \n** characteristics. \n**\n** There are two versions of this function. One for QNX and one for all\n** other systems.\n*/\n#ifndef __QNXNTO__\nstatic void setDeviceCharacteristics(unixFile *pFd){\n  assert( pFd->deviceCharacteristics==0 || pFd->sectorSize!=0 );\n  if( pFd->sectorSize==0 ){\n#if defined(__linux__) && defined(SQLITE_ENABLE_BATCH_ATOMIC_WRITE)\n    int res;\n    u32 f = 0;\n\n    /* Check for support for F2FS atomic batch writes. */\n    res = osIoctl(pFd->h, F2FS_IOC_GET_FEATURES, &f);\n    if( res==0 && (f & F2FS_FEATURE_ATOMIC_WRITE) ){\n      pFd->deviceCharacteristics = SQLITE_IOCAP_BATCH_ATOMIC;\n    }\n#endif /* __linux__ && SQLITE_ENABLE_BATCH_ATOMIC_WRITE */\n\n    /* Set the POWERSAFE_OVERWRITE flag if requested. */\n    if( pFd->ctrlFlags & UNIXFILE_PSOW ){\n      pFd->deviceCharacteristics |= SQLITE_IOCAP_POWERSAFE_OVERWRITE;\n    }\n\n    pFd->sectorSize = SQLITE_DEFAULT_SECTOR_SIZE;\n  }\n}\n#else\n#include <sys/dcmd_blk.h>\n#include <sys/statvfs.h>\nstatic void setDeviceCharacteristics(unixFile *pFile){\n  if( pFile->sectorSize == 0 ){\n    struct statvfs fsInfo;\n       \n    /* Set defaults for non-supported filesystems */\n    pFile->sectorSize = SQLITE_DEFAULT_SECTOR_SIZE;\n    pFile->deviceCharacteristics = 0;\n    if( fstatvfs(pFile->h, &fsInfo) == -1 ) {\n      return;\n    }\n\n    if( !strcmp(fsInfo.f_basetype, \"tmp\") ) {\n      pFile->sectorSize = fsInfo.f_bsize;\n      pFile->deviceCharacteristics =\n        SQLITE_IOCAP_ATOMIC4K |       /* All ram filesystem writes are atomic */\n        SQLITE_IOCAP_SAFE_APPEND |    /* growing the file does not occur until\n                                      ** the write succeeds */\n        SQLITE_IOCAP_SEQUENTIAL |     /* The ram filesystem has no write behind\n                                      ** so it is ordered */\n        0;\n    }else if( strstr(fsInfo.f_basetype, \"etfs\") ){\n      pFile->sectorSize = fsInfo.f_bsize;\n      pFile->deviceCharacteristics =\n        /* etfs cluster size writes are atomic */\n        (pFile->sectorSize / 512 * SQLITE_IOCAP_ATOMIC512) |\n        SQLITE_IOCAP_SAFE_APPEND |    /* growing the file does not occur until\n                                      ** the write succeeds */\n        SQLITE_IOCAP_SEQUENTIAL |     /* The ram filesystem has no write behind\n                                      ** so it is ordered */\n        0;\n    }else if( !strcmp(fsInfo.f_basetype, \"qnx6\") ){\n      pFile->sectorSize = fsInfo.f_bsize;\n      pFile->deviceCharacteristics =\n        SQLITE_IOCAP_ATOMIC |         /* All filesystem writes are atomic */\n        SQLITE_IOCAP_SAFE_APPEND |    /* growing the file does not occur until\n                                      ** the write succeeds */\n        SQLITE_IOCAP_SEQUENTIAL |     /* The ram filesystem has no write behind\n                                      ** so it is ordered */\n        0;\n    }else if( !strcmp(fsInfo.f_basetype, \"qnx4\") ){\n      pFile->sectorSize = fsInfo.f_bsize;\n      pFile->deviceCharacteristics =\n        /* full bitset of atomics from max sector size and smaller */\n        ((pFile->sectorSize / 512 * SQLITE_IOCAP_ATOMIC512) << 1) - 2 |\n        SQLITE_IOCAP_SEQUENTIAL |     /* The ram filesystem has no write behind\n                                      ** so it is ordered */\n        0;\n    }else if( strstr(fsInfo.f_basetype, \"dos\") ){\n      pFile->sectorSize = fsInfo.f_bsize;\n      pFile->deviceCharacteristics =\n        /* full bitset of atomics from max sector size and smaller */\n        ((pFile->sectorSize / 512 * SQLITE_IOCAP_ATOMIC512) << 1) - 2 |\n        SQLITE_IOCAP_SEQUENTIAL |     /* The ram filesystem has no write behind\n                                      ** so it is ordered */\n        0;\n    }else{\n      pFile->deviceCharacteristics =\n        SQLITE_IOCAP_ATOMIC512 |      /* blocks are atomic */\n        SQLITE_IOCAP_SAFE_APPEND |    /* growing the file does not occur until\n                                      ** the write succeeds */\n        0;\n    }\n  }\n  /* Last chance verification.  If the sector size isn't a multiple of 512\n  ** then it isn't valid.*/\n  if( pFile->sectorSize % 512 != 0 ){\n    pFile->deviceCharacteristics = 0;\n    pFile->sectorSize = SQLITE_DEFAULT_SECTOR_SIZE;\n  }\n}\n#endif\n\n/*\n** Return the sector size in bytes of the underlying block device for\n** the specified file. This is almost always 512 bytes, but may be\n** larger for some devices.\n**\n** SQLite code assumes this function cannot fail. It also assumes that\n** if two files are created in the same file-system directory (i.e.\n** a database and its journal file) that the sector size will be the\n** same for both.\n*/\nstatic int unixSectorSize(sqlite3_file *id){\n  unixFile *pFd = (unixFile*)id;\n  setDeviceCharacteristics(pFd);\n  return pFd->sectorSize;\n}\n\n/*\n** Return the device characteristics for the file.\n**\n** This VFS is set up to return SQLITE_IOCAP_POWERSAFE_OVERWRITE by default.\n** However, that choice is controversial since technically the underlying\n** file system does not always provide powersafe overwrites.  (In other\n** words, after a power-loss event, parts of the file that were never\n** written might end up being altered.)  However, non-PSOW behavior is very,\n** very rare.  And asserting PSOW makes a large reduction in the amount\n** of required I/O for journaling, since a lot of padding is eliminated.\n**  Hence, while POWERSAFE_OVERWRITE is on by default, there is a file-control\n** available to turn it off and URI query parameter available to turn it off.\n*/\nstatic int unixDeviceCharacteristics(sqlite3_file *id){\n  unixFile *pFd = (unixFile*)id;\n  setDeviceCharacteristics(pFd);\n  return pFd->deviceCharacteristics;\n}\n\n#if !defined(SQLITE_OMIT_WAL) || SQLITE_MAX_MMAP_SIZE>0\n\n/*\n** Return the system page size.\n**\n** This function should not be called directly by other code in this file. \n** Instead, it should be called via macro osGetpagesize().\n*/\nstatic int unixGetpagesize(void){\n#if OS_VXWORKS\n  return 1024;\n#elif defined(_BSD_SOURCE)\n  return getpagesize();\n#else\n  return (int)sysconf(_SC_PAGESIZE);\n#endif\n}\n\n#endif /* !defined(SQLITE_OMIT_WAL) || SQLITE_MAX_MMAP_SIZE>0 */\n\n#ifndef SQLITE_OMIT_WAL\n\n/*\n** Object used to represent an shared memory buffer.  \n**\n** When multiple threads all reference the same wal-index, each thread\n** has its own unixShm object, but they all point to a single instance\n** of this unixShmNode object.  In other words, each wal-index is opened\n** only once per process.\n**\n** Each unixShmNode object is connected to a single unixInodeInfo object.\n** We could coalesce this object into unixInodeInfo, but that would mean\n** every open file that does not use shared memory (in other words, most\n** open files) would have to carry around this extra information.  So\n** the unixInodeInfo object contains a pointer to this unixShmNode object\n** and the unixShmNode object is created only when needed.\n**\n** unixMutexHeld() must be true when creating or destroying\n** this object or while reading or writing the following fields:\n**\n**      nRef\n**\n** The following fields are read-only after the object is created:\n** \n**      fid\n**      zFilename\n**\n** Either unixShmNode.mutex must be held or unixShmNode.nRef==0 and\n** unixMutexHeld() is true when reading or writing any other field\n** in this structure.\n*/\nstruct unixShmNode {\n  unixInodeInfo *pInode;     /* unixInodeInfo that owns this SHM node */\n  sqlite3_mutex *mutex;      /* Mutex to access this object */\n  char *zFilename;           /* Name of the mmapped file */\n  int h;                     /* Open file descriptor */\n  int szRegion;              /* Size of shared-memory regions */\n  u16 nRegion;               /* Size of array apRegion */\n  u8 isReadonly;             /* True if read-only */\n  u8 isUnlocked;             /* True if no DMS lock held */\n  char **apRegion;           /* Array of mapped shared-memory regions */\n  int nRef;                  /* Number of unixShm objects pointing to this */\n  unixShm *pFirst;           /* All unixShm objects pointing to this */\n#ifdef SQLITE_DEBUG\n  u8 exclMask;               /* Mask of exclusive locks held */\n  u8 sharedMask;             /* Mask of shared locks held */\n  u8 nextShmId;              /* Next available unixShm.id value */\n#endif\n};\n\n/*\n** Structure used internally by this VFS to record the state of an\n** open shared memory connection.\n**\n** The following fields are initialized when this object is created and\n** are read-only thereafter:\n**\n**    unixShm.pFile\n**    unixShm.id\n**\n** All other fields are read/write.  The unixShm.pFile->mutex must be held\n** while accessing any read/write fields.\n*/\nstruct unixShm {\n  unixShmNode *pShmNode;     /* The underlying unixShmNode object */\n  unixShm *pNext;            /* Next unixShm with the same unixShmNode */\n  u8 hasMutex;               /* True if holding the unixShmNode mutex */\n  u8 id;                     /* Id of this connection within its unixShmNode */\n  u16 sharedMask;            /* Mask of shared locks held */\n  u16 exclMask;              /* Mask of exclusive locks held */\n};\n\n/*\n** Constants used for locking\n*/\n#define UNIX_SHM_BASE   ((22+SQLITE_SHM_NLOCK)*4)         /* first lock byte */\n#define UNIX_SHM_DMS    (UNIX_SHM_BASE+SQLITE_SHM_NLOCK)  /* deadman switch */\n\n/*\n** Apply posix advisory locks for all bytes from ofst through ofst+n-1.\n**\n** Locks block if the mask is exactly UNIX_SHM_C and are non-blocking\n** otherwise.\n*/\nstatic int unixShmSystemLock(\n  unixFile *pFile,       /* Open connection to the WAL file */\n  int lockType,          /* F_UNLCK, F_RDLCK, or F_WRLCK */\n  int ofst,              /* First byte of the locking range */\n  int n                  /* Number of bytes to lock */\n){\n  unixShmNode *pShmNode; /* Apply locks to this open shared-memory segment */\n  struct flock f;        /* The posix advisory locking structure */\n  int rc = SQLITE_OK;    /* Result code form fcntl() */\n\n  /* Access to the unixShmNode object is serialized by the caller */\n  pShmNode = pFile->pInode->pShmNode;\n  assert( pShmNode->nRef==0 || sqlite3_mutex_held(pShmNode->mutex) );\n\n  /* Shared locks never span more than one byte */\n  assert( n==1 || lockType!=F_RDLCK );\n\n  /* Locks are within range */\n  assert( n>=1 && n<=SQLITE_SHM_NLOCK );\n\n  if( pShmNode->h>=0 ){\n    /* Initialize the locking parameters */\n    f.l_type = lockType;\n    f.l_whence = SEEK_SET;\n    f.l_start = ofst;\n    f.l_len = n;\n    rc = osFcntl(pShmNode->h, F_SETLK, &f);\n    rc = (rc!=(-1)) ? SQLITE_OK : SQLITE_BUSY;\n  }\n\n  /* Update the global lock state and do debug tracing */\n#ifdef SQLITE_DEBUG\n  { u16 mask;\n  OSTRACE((\"SHM-LOCK \"));\n  mask = ofst>31 ? 0xffff : (1<<(ofst+n)) - (1<<ofst);\n  if( rc==SQLITE_OK ){\n    if( lockType==F_UNLCK ){\n      OSTRACE((\"unlock %d ok\", ofst));\n      pShmNode->exclMask &= ~mask;\n      pShmNode->sharedMask &= ~mask;\n    }else if( lockType==F_RDLCK ){\n      OSTRACE((\"read-lock %d ok\", ofst));\n      pShmNode->exclMask &= ~mask;\n      pShmNode->sharedMask |= mask;\n    }else{\n      assert( lockType==F_WRLCK );\n      OSTRACE((\"write-lock %d ok\", ofst));\n      pShmNode->exclMask |= mask;\n      pShmNode->sharedMask &= ~mask;\n    }\n  }else{\n    if( lockType==F_UNLCK ){\n      OSTRACE((\"unlock %d failed\", ofst));\n    }else if( lockType==F_RDLCK ){\n      OSTRACE((\"read-lock failed\"));\n    }else{\n      assert( lockType==F_WRLCK );\n      OSTRACE((\"write-lock %d failed\", ofst));\n    }\n  }\n  OSTRACE((\" - afterwards %03x,%03x\\n\",\n           pShmNode->sharedMask, pShmNode->exclMask));\n  }\n#endif\n\n  return rc;        \n}\n\n/*\n** Return the minimum number of 32KB shm regions that should be mapped at\n** a time, assuming that each mapping must be an integer multiple of the\n** current system page-size.\n**\n** Usually, this is 1. The exception seems to be systems that are configured\n** to use 64KB pages - in this case each mapping must cover at least two\n** shm regions.\n*/\nstatic int unixShmRegionPerMap(void){\n  int shmsz = 32*1024;            /* SHM region size */\n  int pgsz = osGetpagesize();   /* System page size */\n  assert( ((pgsz-1)&pgsz)==0 );   /* Page size must be a power of 2 */\n  if( pgsz<shmsz ) return 1;\n  return pgsz/shmsz;\n}\n\n/*\n** Purge the unixShmNodeList list of all entries with unixShmNode.nRef==0.\n**\n** This is not a VFS shared-memory method; it is a utility function called\n** by VFS shared-memory methods.\n*/\nstatic void unixShmPurge(unixFile *pFd){\n  unixShmNode *p = pFd->pInode->pShmNode;\n  assert( unixMutexHeld() );\n  if( p && ALWAYS(p->nRef==0) ){\n    int nShmPerMap = unixShmRegionPerMap();\n    int i;\n    assert( p->pInode==pFd->pInode );\n    sqlite3_mutex_free(p->mutex);\n    for(i=0; i<p->nRegion; i+=nShmPerMap){\n      if( p->h>=0 ){\n        osMunmap(p->apRegion[i], p->szRegion);\n      }else{\n        sqlite3_free(p->apRegion[i]);\n      }\n    }\n    sqlite3_free(p->apRegion);\n    if( p->h>=0 ){\n      robust_close(pFd, p->h, __LINE__);\n      p->h = -1;\n    }\n    p->pInode->pShmNode = 0;\n    sqlite3_free(p);\n  }\n}\n\n/*\n** The DMS lock has not yet been taken on shm file pShmNode. Attempt to\n** take it now. Return SQLITE_OK if successful, or an SQLite error\n** code otherwise.\n**\n** If the DMS cannot be locked because this is a readonly_shm=1 \n** connection and no other process already holds a lock, return\n** SQLITE_READONLY_CANTINIT and set pShmNode->isUnlocked=1.\n*/\nstatic int unixLockSharedMemory(unixFile *pDbFd, unixShmNode *pShmNode){\n  struct flock lock;\n  int rc = SQLITE_OK;\n\n  /* Use F_GETLK to determine the locks other processes are holding\n  ** on the DMS byte. If it indicates that another process is holding\n  ** a SHARED lock, then this process may also take a SHARED lock\n  ** and proceed with opening the *-shm file. \n  **\n  ** Or, if no other process is holding any lock, then this process\n  ** is the first to open it. In this case take an EXCLUSIVE lock on the\n  ** DMS byte and truncate the *-shm file to zero bytes in size. Then\n  ** downgrade to a SHARED lock on the DMS byte.\n  **\n  ** If another process is holding an EXCLUSIVE lock on the DMS byte,\n  ** return SQLITE_BUSY to the caller (it will try again). An earlier\n  ** version of this code attempted the SHARED lock at this point. But\n  ** this introduced a subtle race condition: if the process holding\n  ** EXCLUSIVE failed just before truncating the *-shm file, then this\n  ** process might open and use the *-shm file without truncating it.\n  ** And if the *-shm file has been corrupted by a power failure or\n  ** system crash, the database itself may also become corrupt.  */\n  lock.l_whence = SEEK_SET;\n  lock.l_start = UNIX_SHM_DMS;\n  lock.l_len = 1;\n  lock.l_type = F_WRLCK;\n  if( osFcntl(pShmNode->h, F_GETLK, &lock)!=0 ) {\n    rc = SQLITE_IOERR_LOCK;\n  }else if( lock.l_type==F_UNLCK ){\n    if( pShmNode->isReadonly ){\n      pShmNode->isUnlocked = 1;\n      rc = SQLITE_READONLY_CANTINIT;\n    }else{\n      rc = unixShmSystemLock(pDbFd, F_WRLCK, UNIX_SHM_DMS, 1);\n      if( rc==SQLITE_OK && robust_ftruncate(pShmNode->h, 0) ){\n        rc = unixLogError(SQLITE_IOERR_SHMOPEN,\"ftruncate\",pShmNode->zFilename);\n      }\n    }\n  }else if( lock.l_type==F_WRLCK ){\n    rc = SQLITE_BUSY;\n  }\n\n  if( rc==SQLITE_OK ){\n    assert( lock.l_type==F_UNLCK || lock.l_type==F_RDLCK );\n    rc = unixShmSystemLock(pDbFd, F_RDLCK, UNIX_SHM_DMS, 1);\n  }\n  return rc;\n}\n\n/*\n** Open a shared-memory area associated with open database file pDbFd.  \n** This particular implementation uses mmapped files.\n**\n** The file used to implement shared-memory is in the same directory\n** as the open database file and has the same name as the open database\n** file with the \"-shm\" suffix added.  For example, if the database file\n** is \"/home/user1/config.db\" then the file that is created and mmapped\n** for shared memory will be called \"/home/user1/config.db-shm\".  \n**\n** Another approach to is to use files in /dev/shm or /dev/tmp or an\n** some other tmpfs mount. But if a file in a different directory\n** from the database file is used, then differing access permissions\n** or a chroot() might cause two different processes on the same\n** database to end up using different files for shared memory - \n** meaning that their memory would not really be shared - resulting\n** in database corruption.  Nevertheless, this tmpfs file usage\n** can be enabled at compile-time using -DSQLITE_SHM_DIRECTORY=\"/dev/shm\"\n** or the equivalent.  The use of the SQLITE_SHM_DIRECTORY compile-time\n** option results in an incompatible build of SQLite;  builds of SQLite\n** that with differing SQLITE_SHM_DIRECTORY settings attempt to use the\n** same database file at the same time, database corruption will likely\n** result. The SQLITE_SHM_DIRECTORY compile-time option is considered\n** \"unsupported\" and may go away in a future SQLite release.\n**\n** When opening a new shared-memory file, if no other instances of that\n** file are currently open, in this process or in other processes, then\n** the file must be truncated to zero length or have its header cleared.\n**\n** If the original database file (pDbFd) is using the \"unix-excl\" VFS\n** that means that an exclusive lock is held on the database file and\n** that no other processes are able to read or write the database.  In\n** that case, we do not really need shared memory.  No shared memory\n** file is created.  The shared memory will be simulated with heap memory.\n*/\nstatic int unixOpenSharedMemory(unixFile *pDbFd){\n  struct unixShm *p = 0;          /* The connection to be opened */\n  struct unixShmNode *pShmNode;   /* The underlying mmapped file */\n  int rc = SQLITE_OK;             /* Result code */\n  unixInodeInfo *pInode;          /* The inode of fd */\n  char *zShm;             /* Name of the file used for SHM */\n  int nShmFilename;               /* Size of the SHM filename in bytes */\n\n  /* Allocate space for the new unixShm object. */\n  p = sqlite3_malloc64( sizeof(*p) );\n  if( p==0 ) return SQLITE_NOMEM_BKPT;\n  memset(p, 0, sizeof(*p));\n  assert( pDbFd->pShm==0 );\n\n  /* Check to see if a unixShmNode object already exists. Reuse an existing\n  ** one if present. Create a new one if necessary.\n  */\n  unixEnterMutex();\n  pInode = pDbFd->pInode;\n  pShmNode = pInode->pShmNode;\n  if( pShmNode==0 ){\n    struct stat sStat;                 /* fstat() info for database file */\n#ifndef SQLITE_SHM_DIRECTORY\n    const char *zBasePath = pDbFd->zPath;\n#endif\n\n    /* Call fstat() to figure out the permissions on the database file. If\n    ** a new *-shm file is created, an attempt will be made to create it\n    ** with the same permissions.\n    */\n    if( osFstat(pDbFd->h, &sStat) ){\n      rc = SQLITE_IOERR_FSTAT;\n      goto shm_open_err;\n    }\n\n#ifdef SQLITE_SHM_DIRECTORY\n    nShmFilename = sizeof(SQLITE_SHM_DIRECTORY) + 31;\n#else\n    nShmFilename = 6 + (int)strlen(zBasePath);\n#endif\n    pShmNode = sqlite3_malloc64( sizeof(*pShmNode) + nShmFilename );\n    if( pShmNode==0 ){\n      rc = SQLITE_NOMEM_BKPT;\n      goto shm_open_err;\n    }\n    memset(pShmNode, 0, sizeof(*pShmNode)+nShmFilename);\n    zShm = pShmNode->zFilename = (char*)&pShmNode[1];\n#ifdef SQLITE_SHM_DIRECTORY\n    sqlite3_snprintf(nShmFilename, zShm, \n                     SQLITE_SHM_DIRECTORY \"/sqlite-shm-%x-%x\",\n                     (u32)sStat.st_ino, (u32)sStat.st_dev);\n#else\n    sqlite3_snprintf(nShmFilename, zShm, \"%s-shm\", zBasePath);\n    sqlite3FileSuffix3(pDbFd->zPath, zShm);\n#endif\n    pShmNode->h = -1;\n    pDbFd->pInode->pShmNode = pShmNode;\n    pShmNode->pInode = pDbFd->pInode;\n    if( sqlite3GlobalConfig.bCoreMutex ){\n      pShmNode->mutex = sqlite3_mutex_alloc(SQLITE_MUTEX_FAST);\n      if( pShmNode->mutex==0 ){\n        rc = SQLITE_NOMEM_BKPT;\n        goto shm_open_err;\n      }\n    }\n\n    if( pInode->bProcessLock==0 ){\n      if( 0==sqlite3_uri_boolean(pDbFd->zPath, \"readonly_shm\", 0) ){\n        pShmNode->h = robust_open(zShm, O_RDWR|O_CREAT, (sStat.st_mode&0777));\n      }\n      if( pShmNode->h<0 ){\n        pShmNode->h = robust_open(zShm, O_RDONLY, (sStat.st_mode&0777));\n        if( pShmNode->h<0 ){\n          rc = unixLogError(SQLITE_CANTOPEN_BKPT, \"open\", zShm);\n          goto shm_open_err;\n        }\n        pShmNode->isReadonly = 1;\n      }\n\n      /* If this process is running as root, make sure that the SHM file\n      ** is owned by the same user that owns the original database.  Otherwise,\n      ** the original owner will not be able to connect.\n      */\n      robustFchown(pShmNode->h, sStat.st_uid, sStat.st_gid);\n\n      rc = unixLockSharedMemory(pDbFd, pShmNode);\n      if( rc!=SQLITE_OK && rc!=SQLITE_READONLY_CANTINIT ) goto shm_open_err;\n    }\n  }\n\n  /* Make the new connection a child of the unixShmNode */\n  p->pShmNode = pShmNode;\n#ifdef SQLITE_DEBUG\n  p->id = pShmNode->nextShmId++;\n#endif\n  pShmNode->nRef++;\n  pDbFd->pShm = p;\n  unixLeaveMutex();\n\n  /* The reference count on pShmNode has already been incremented under\n  ** the cover of the unixEnterMutex() mutex and the pointer from the\n  ** new (struct unixShm) object to the pShmNode has been set. All that is\n  ** left to do is to link the new object into the linked list starting\n  ** at pShmNode->pFirst. This must be done while holding the pShmNode->mutex \n  ** mutex.\n  */\n  sqlite3_mutex_enter(pShmNode->mutex);\n  p->pNext = pShmNode->pFirst;\n  pShmNode->pFirst = p;\n  sqlite3_mutex_leave(pShmNode->mutex);\n  return rc;\n\n  /* Jump here on any error */\nshm_open_err:\n  unixShmPurge(pDbFd);       /* This call frees pShmNode if required */\n  sqlite3_free(p);\n  unixLeaveMutex();\n  return rc;\n}\n\n/*\n** This function is called to obtain a pointer to region iRegion of the \n** shared-memory associated with the database file fd. Shared-memory regions \n** are numbered starting from zero. Each shared-memory region is szRegion \n** bytes in size.\n**\n** If an error occurs, an error code is returned and *pp is set to NULL.\n**\n** Otherwise, if the bExtend parameter is 0 and the requested shared-memory\n** region has not been allocated (by any client, including one running in a\n** separate process), then *pp is set to NULL and SQLITE_OK returned. If \n** bExtend is non-zero and the requested shared-memory region has not yet \n** been allocated, it is allocated by this function.\n**\n** If the shared-memory region has already been allocated or is allocated by\n** this call as described above, then it is mapped into this processes \n** address space (if it is not already), *pp is set to point to the mapped \n** memory and SQLITE_OK returned.\n*/\nstatic int unixShmMap(\n  sqlite3_file *fd,               /* Handle open on database file */\n  int iRegion,                    /* Region to retrieve */\n  int szRegion,                   /* Size of regions */\n  int bExtend,                    /* True to extend file if necessary */\n  void volatile **pp              /* OUT: Mapped memory */\n){\n  unixFile *pDbFd = (unixFile*)fd;\n  unixShm *p;\n  unixShmNode *pShmNode;\n  int rc = SQLITE_OK;\n  int nShmPerMap = unixShmRegionPerMap();\n  int nReqRegion;\n\n  /* If the shared-memory file has not yet been opened, open it now. */\n  if( pDbFd->pShm==0 ){\n    rc = unixOpenSharedMemory(pDbFd);\n    if( rc!=SQLITE_OK ) return rc;\n  }\n\n  p = pDbFd->pShm;\n  pShmNode = p->pShmNode;\n  sqlite3_mutex_enter(pShmNode->mutex);\n  if( pShmNode->isUnlocked ){\n    rc = unixLockSharedMemory(pDbFd, pShmNode);\n    if( rc!=SQLITE_OK ) goto shmpage_out;\n    pShmNode->isUnlocked = 0;\n  }\n  assert( szRegion==pShmNode->szRegion || pShmNode->nRegion==0 );\n  assert( pShmNode->pInode==pDbFd->pInode );\n  assert( pShmNode->h>=0 || pDbFd->pInode->bProcessLock==1 );\n  assert( pShmNode->h<0 || pDbFd->pInode->bProcessLock==0 );\n\n  /* Minimum number of regions required to be mapped. */\n  nReqRegion = ((iRegion+nShmPerMap) / nShmPerMap) * nShmPerMap;\n\n  if( pShmNode->nRegion<nReqRegion ){\n    char **apNew;                      /* New apRegion[] array */\n    int nByte = nReqRegion*szRegion;   /* Minimum required file size */\n    struct stat sStat;                 /* Used by fstat() */\n\n    pShmNode->szRegion = szRegion;\n\n    if( pShmNode->h>=0 ){\n      /* The requested region is not mapped into this processes address space.\n      ** Check to see if it has been allocated (i.e. if the wal-index file is\n      ** large enough to contain the requested region).\n      */\n      if( osFstat(pShmNode->h, &sStat) ){\n        rc = SQLITE_IOERR_SHMSIZE;\n        goto shmpage_out;\n      }\n  \n      if( sStat.st_size<nByte ){\n        /* The requested memory region does not exist. If bExtend is set to\n        ** false, exit early. *pp will be set to NULL and SQLITE_OK returned.\n        */\n        if( !bExtend ){\n          goto shmpage_out;\n        }\n\n        /* Alternatively, if bExtend is true, extend the file. Do this by\n        ** writing a single byte to the end of each (OS) page being\n        ** allocated or extended. Technically, we need only write to the\n        ** last page in order to extend the file. But writing to all new\n        ** pages forces the OS to allocate them immediately, which reduces\n        ** the chances of SIGBUS while accessing the mapped region later on.\n        */\n        else{\n          static const int pgsz = 4096;\n          int iPg;\n\n          /* Write to the last byte of each newly allocated or extended page */\n          assert( (nByte % pgsz)==0 );\n          for(iPg=(sStat.st_size/pgsz); iPg<(nByte/pgsz); iPg++){\n            int x = 0;\n            if( seekAndWriteFd(pShmNode->h, iPg*pgsz + pgsz-1, \"\", 1, &x)!=1 ){\n              const char *zFile = pShmNode->zFilename;\n              rc = unixLogError(SQLITE_IOERR_SHMSIZE, \"write\", zFile);\n              goto shmpage_out;\n            }\n          }\n        }\n      }\n    }\n\n    /* Map the requested memory region into this processes address space. */\n    apNew = (char **)sqlite3_realloc(\n        pShmNode->apRegion, nReqRegion*sizeof(char *)\n    );\n    if( !apNew ){\n      rc = SQLITE_IOERR_NOMEM_BKPT;\n      goto shmpage_out;\n    }\n    pShmNode->apRegion = apNew;\n    while( pShmNode->nRegion<nReqRegion ){\n      int nMap = szRegion*nShmPerMap;\n      int i;\n      void *pMem;\n      if( pShmNode->h>=0 ){\n        pMem = osMmap(0, nMap,\n            pShmNode->isReadonly ? PROT_READ : PROT_READ|PROT_WRITE, \n            MAP_SHARED, pShmNode->h, szRegion*(i64)pShmNode->nRegion\n        );\n        if( pMem==MAP_FAILED ){\n          rc = unixLogError(SQLITE_IOERR_SHMMAP, \"mmap\", pShmNode->zFilename);\n          goto shmpage_out;\n        }\n      }else{\n        pMem = sqlite3_malloc64(szRegion);\n        if( pMem==0 ){\n          rc = SQLITE_NOMEM_BKPT;\n          goto shmpage_out;\n        }\n        memset(pMem, 0, szRegion);\n      }\n\n      for(i=0; i<nShmPerMap; i++){\n        pShmNode->apRegion[pShmNode->nRegion+i] = &((char*)pMem)[szRegion*i];\n      }\n      pShmNode->nRegion += nShmPerMap;\n    }\n  }\n\nshmpage_out:\n  if( pShmNode->nRegion>iRegion ){\n    *pp = pShmNode->apRegion[iRegion];\n  }else{\n    *pp = 0;\n  }\n  if( pShmNode->isReadonly && rc==SQLITE_OK ) rc = SQLITE_READONLY;\n  sqlite3_mutex_leave(pShmNode->mutex);\n  return rc;\n}\n\n/*\n** Change the lock state for a shared-memory segment.\n**\n** Note that the relationship between SHAREd and EXCLUSIVE locks is a little\n** different here than in posix.  In xShmLock(), one can go from unlocked\n** to shared and back or from unlocked to exclusive and back.  But one may\n** not go from shared to exclusive or from exclusive to shared.\n*/\nstatic int unixShmLock(\n  sqlite3_file *fd,          /* Database file holding the shared memory */\n  int ofst,                  /* First lock to acquire or release */\n  int n,                     /* Number of locks to acquire or release */\n  int flags                  /* What to do with the lock */\n){\n  unixFile *pDbFd = (unixFile*)fd;      /* Connection holding shared memory */\n  unixShm *p = pDbFd->pShm;             /* The shared memory being locked */\n  unixShm *pX;                          /* For looping over all siblings */\n  unixShmNode *pShmNode = p->pShmNode;  /* The underlying file iNode */\n  int rc = SQLITE_OK;                   /* Result code */\n  u16 mask;                             /* Mask of locks to take or release */\n\n  assert( pShmNode==pDbFd->pInode->pShmNode );\n  assert( pShmNode->pInode==pDbFd->pInode );\n  assert( ofst>=0 && ofst+n<=SQLITE_SHM_NLOCK );\n  assert( n>=1 );\n  assert( flags==(SQLITE_SHM_LOCK | SQLITE_SHM_SHARED)\n       || flags==(SQLITE_SHM_LOCK | SQLITE_SHM_EXCLUSIVE)\n       || flags==(SQLITE_SHM_UNLOCK | SQLITE_SHM_SHARED)\n       || flags==(SQLITE_SHM_UNLOCK | SQLITE_SHM_EXCLUSIVE) );\n  assert( n==1 || (flags & SQLITE_SHM_EXCLUSIVE)!=0 );\n  assert( pShmNode->h>=0 || pDbFd->pInode->bProcessLock==1 );\n  assert( pShmNode->h<0 || pDbFd->pInode->bProcessLock==0 );\n\n  mask = (1<<(ofst+n)) - (1<<ofst);\n  assert( n>1 || mask==(1<<ofst) );\n  sqlite3_mutex_enter(pShmNode->mutex);\n  if( flags & SQLITE_SHM_UNLOCK ){\n    u16 allMask = 0; /* Mask of locks held by siblings */\n\n    /* See if any siblings hold this same lock */\n    for(pX=pShmNode->pFirst; pX; pX=pX->pNext){\n      if( pX==p ) continue;\n      assert( (pX->exclMask & (p->exclMask|p->sharedMask))==0 );\n      allMask |= pX->sharedMask;\n    }\n\n    /* Unlock the system-level locks */\n    if( (mask & allMask)==0 ){\n      rc = unixShmSystemLock(pDbFd, F_UNLCK, ofst+UNIX_SHM_BASE, n);\n    }else{\n      rc = SQLITE_OK;\n    }\n\n    /* Undo the local locks */\n    if( rc==SQLITE_OK ){\n      p->exclMask &= ~mask;\n      p->sharedMask &= ~mask;\n    } \n  }else if( flags & SQLITE_SHM_SHARED ){\n    u16 allShared = 0;  /* Union of locks held by connections other than \"p\" */\n\n    /* Find out which shared locks are already held by sibling connections.\n    ** If any sibling already holds an exclusive lock, go ahead and return\n    ** SQLITE_BUSY.\n    */\n    for(pX=pShmNode->pFirst; pX; pX=pX->pNext){\n      if( (pX->exclMask & mask)!=0 ){\n        rc = SQLITE_BUSY;\n        break;\n      }\n      allShared |= pX->sharedMask;\n    }\n\n    /* Get shared locks at the system level, if necessary */\n    if( rc==SQLITE_OK ){\n      if( (allShared & mask)==0 ){\n        rc = unixShmSystemLock(pDbFd, F_RDLCK, ofst+UNIX_SHM_BASE, n);\n      }else{\n        rc = SQLITE_OK;\n      }\n    }\n\n    /* Get the local shared locks */\n    if( rc==SQLITE_OK ){\n      p->sharedMask |= mask;\n    }\n  }else{\n    /* Make sure no sibling connections hold locks that will block this\n    ** lock.  If any do, return SQLITE_BUSY right away.\n    */\n    for(pX=pShmNode->pFirst; pX; pX=pX->pNext){\n      if( (pX->exclMask & mask)!=0 || (pX->sharedMask & mask)!=0 ){\n        rc = SQLITE_BUSY;\n        break;\n      }\n    }\n  \n    /* Get the exclusive locks at the system level.  Then if successful\n    ** also mark the local connection as being locked.\n    */\n    if( rc==SQLITE_OK ){\n      rc = unixShmSystemLock(pDbFd, F_WRLCK, ofst+UNIX_SHM_BASE, n);\n      if( rc==SQLITE_OK ){\n        assert( (p->sharedMask & mask)==0 );\n        p->exclMask |= mask;\n      }\n    }\n  }\n  sqlite3_mutex_leave(pShmNode->mutex);\n  OSTRACE((\"SHM-LOCK shmid-%d, pid-%d got %03x,%03x\\n\",\n           p->id, osGetpid(0), p->sharedMask, p->exclMask));\n  return rc;\n}\n\n/*\n** Implement a memory barrier or memory fence on shared memory.  \n**\n** All loads and stores begun before the barrier must complete before\n** any load or store begun after the barrier.\n*/\nstatic void unixShmBarrier(\n  sqlite3_file *fd                /* Database file holding the shared memory */\n){\n  UNUSED_PARAMETER(fd);\n  sqlite3MemoryBarrier();         /* compiler-defined memory barrier */\n  unixEnterMutex();               /* Also mutex, for redundancy */\n  unixLeaveMutex();\n}\n\n/*\n** Close a connection to shared-memory.  Delete the underlying \n** storage if deleteFlag is true.\n**\n** If there is no shared memory associated with the connection then this\n** routine is a harmless no-op.\n*/\nstatic int unixShmUnmap(\n  sqlite3_file *fd,               /* The underlying database file */\n  int deleteFlag                  /* Delete shared-memory if true */\n){\n  unixShm *p;                     /* The connection to be closed */\n  unixShmNode *pShmNode;          /* The underlying shared-memory file */\n  unixShm **pp;                   /* For looping over sibling connections */\n  unixFile *pDbFd;                /* The underlying database file */\n\n  pDbFd = (unixFile*)fd;\n  p = pDbFd->pShm;\n  if( p==0 ) return SQLITE_OK;\n  pShmNode = p->pShmNode;\n\n  assert( pShmNode==pDbFd->pInode->pShmNode );\n  assert( pShmNode->pInode==pDbFd->pInode );\n\n  /* Remove connection p from the set of connections associated\n  ** with pShmNode */\n  sqlite3_mutex_enter(pShmNode->mutex);\n  for(pp=&pShmNode->pFirst; (*pp)!=p; pp = &(*pp)->pNext){}\n  *pp = p->pNext;\n\n  /* Free the connection p */\n  sqlite3_free(p);\n  pDbFd->pShm = 0;\n  sqlite3_mutex_leave(pShmNode->mutex);\n\n  /* If pShmNode->nRef has reached 0, then close the underlying\n  ** shared-memory file, too */\n  unixEnterMutex();\n  assert( pShmNode->nRef>0 );\n  pShmNode->nRef--;\n  if( pShmNode->nRef==0 ){\n    if( deleteFlag && pShmNode->h>=0 ){\n      osUnlink(pShmNode->zFilename);\n    }\n    unixShmPurge(pDbFd);\n  }\n  unixLeaveMutex();\n\n  return SQLITE_OK;\n}\n\n\n#else\n# define unixShmMap     0\n# define unixShmLock    0\n# define unixShmBarrier 0\n# define unixShmUnmap   0\n#endif /* #ifndef SQLITE_OMIT_WAL */\n\n#if SQLITE_MAX_MMAP_SIZE>0\n/*\n** If it is currently memory mapped, unmap file pFd.\n*/\nstatic void unixUnmapfile(unixFile *pFd){\n  assert( pFd->nFetchOut==0 );\n  if( pFd->pMapRegion ){\n    osMunmap(pFd->pMapRegion, pFd->mmapSizeActual);\n    pFd->pMapRegion = 0;\n    pFd->mmapSize = 0;\n    pFd->mmapSizeActual = 0;\n  }\n}\n\n/*\n** Attempt to set the size of the memory mapping maintained by file \n** descriptor pFd to nNew bytes. Any existing mapping is discarded.\n**\n** If successful, this function sets the following variables:\n**\n**       unixFile.pMapRegion\n**       unixFile.mmapSize\n**       unixFile.mmapSizeActual\n**\n** If unsuccessful, an error message is logged via sqlite3_log() and\n** the three variables above are zeroed. In this case SQLite should\n** continue accessing the database using the xRead() and xWrite()\n** methods.\n*/\nstatic void unixRemapfile(\n  unixFile *pFd,                  /* File descriptor object */\n  i64 nNew                        /* Required mapping size */\n){\n  const char *zErr = \"mmap\";\n  int h = pFd->h;                      /* File descriptor open on db file */\n  u8 *pOrig = (u8 *)pFd->pMapRegion;   /* Pointer to current file mapping */\n  i64 nOrig = pFd->mmapSizeActual;     /* Size of pOrig region in bytes */\n  u8 *pNew = 0;                        /* Location of new mapping */\n  int flags = PROT_READ;               /* Flags to pass to mmap() */\n\n  assert( pFd->nFetchOut==0 );\n  assert( nNew>pFd->mmapSize );\n  assert( nNew<=pFd->mmapSizeMax );\n  assert( nNew>0 );\n  assert( pFd->mmapSizeActual>=pFd->mmapSize );\n  assert( MAP_FAILED!=0 );\n\n#ifdef SQLITE_MMAP_READWRITE\n  if( (pFd->ctrlFlags & UNIXFILE_RDONLY)==0 ) flags |= PROT_WRITE;\n#endif\n\n  if( pOrig ){\n#if HAVE_MREMAP\n    i64 nReuse = pFd->mmapSize;\n#else\n    const int szSyspage = osGetpagesize();\n    i64 nReuse = (pFd->mmapSize & ~(szSyspage-1));\n#endif\n    u8 *pReq = &pOrig[nReuse];\n\n    /* Unmap any pages of the existing mapping that cannot be reused. */\n    if( nReuse!=nOrig ){\n      osMunmap(pReq, nOrig-nReuse);\n    }\n\n#if HAVE_MREMAP\n    pNew = osMremap(pOrig, nReuse, nNew, MREMAP_MAYMOVE);\n    zErr = \"mremap\";\n#else\n    pNew = osMmap(pReq, nNew-nReuse, flags, MAP_SHARED, h, nReuse);\n    if( pNew!=MAP_FAILED ){\n      if( pNew!=pReq ){\n        osMunmap(pNew, nNew - nReuse);\n        pNew = 0;\n      }else{\n        pNew = pOrig;\n      }\n    }\n#endif\n\n    /* The attempt to extend the existing mapping failed. Free it. */\n    if( pNew==MAP_FAILED || pNew==0 ){\n      osMunmap(pOrig, nReuse);\n    }\n  }\n\n  /* If pNew is still NULL, try to create an entirely new mapping. */\n  if( pNew==0 ){\n    pNew = osMmap(0, nNew, flags, MAP_SHARED, h, 0);\n  }\n\n  if( pNew==MAP_FAILED ){\n    pNew = 0;\n    nNew = 0;\n    unixLogError(SQLITE_OK, zErr, pFd->zPath);\n\n    /* If the mmap() above failed, assume that all subsequent mmap() calls\n    ** will probably fail too. Fall back to using xRead/xWrite exclusively\n    ** in this case.  */\n    pFd->mmapSizeMax = 0;\n  }\n  pFd->pMapRegion = (void *)pNew;\n  pFd->mmapSize = pFd->mmapSizeActual = nNew;\n}\n\n/*\n** Memory map or remap the file opened by file-descriptor pFd (if the file\n** is already mapped, the existing mapping is replaced by the new). Or, if \n** there already exists a mapping for this file, and there are still \n** outstanding xFetch() references to it, this function is a no-op.\n**\n** If parameter nByte is non-negative, then it is the requested size of \n** the mapping to create. Otherwise, if nByte is less than zero, then the \n** requested size is the size of the file on disk. The actual size of the\n** created mapping is either the requested size or the value configured \n** using SQLITE_FCNTL_MMAP_LIMIT, whichever is smaller.\n**\n** SQLITE_OK is returned if no error occurs (even if the mapping is not\n** recreated as a result of outstanding references) or an SQLite error\n** code otherwise.\n*/\nstatic int unixMapfile(unixFile *pFd, i64 nMap){\n  assert( nMap>=0 || pFd->nFetchOut==0 );\n  assert( nMap>0 || (pFd->mmapSize==0 && pFd->pMapRegion==0) );\n  if( pFd->nFetchOut>0 ) return SQLITE_OK;\n\n  if( nMap<0 ){\n    struct stat statbuf;          /* Low-level file information */\n    if( osFstat(pFd->h, &statbuf) ){\n      return SQLITE_IOERR_FSTAT;\n    }\n    nMap = statbuf.st_size;\n  }\n  if( nMap>pFd->mmapSizeMax ){\n    nMap = pFd->mmapSizeMax;\n  }\n\n  assert( nMap>0 || (pFd->mmapSize==0 && pFd->pMapRegion==0) );\n  if( nMap!=pFd->mmapSize ){\n    unixRemapfile(pFd, nMap);\n  }\n\n  return SQLITE_OK;\n}\n#endif /* SQLITE_MAX_MMAP_SIZE>0 */\n\n/*\n** If possible, return a pointer to a mapping of file fd starting at offset\n** iOff. The mapping must be valid for at least nAmt bytes.\n**\n** If such a pointer can be obtained, store it in *pp and return SQLITE_OK.\n** Or, if one cannot but no error occurs, set *pp to 0 and return SQLITE_OK.\n** Finally, if an error does occur, return an SQLite error code. The final\n** value of *pp is undefined in this case.\n**\n** If this function does return a pointer, the caller must eventually \n** release the reference by calling unixUnfetch().\n*/\nstatic int unixFetch(sqlite3_file *fd, i64 iOff, int nAmt, void **pp){\n#if SQLITE_MAX_MMAP_SIZE>0\n  unixFile *pFd = (unixFile *)fd;   /* The underlying database file */\n#endif\n  *pp = 0;\n\n#if SQLITE_MAX_MMAP_SIZE>0\n  if( pFd->mmapSizeMax>0 ){\n    if( pFd->pMapRegion==0 ){\n      int rc = unixMapfile(pFd, -1);\n      if( rc!=SQLITE_OK ) return rc;\n    }\n    if( pFd->mmapSize >= iOff+nAmt ){\n      *pp = &((u8 *)pFd->pMapRegion)[iOff];\n      pFd->nFetchOut++;\n    }\n  }\n#endif\n  return SQLITE_OK;\n}\n\n/*\n** If the third argument is non-NULL, then this function releases a \n** reference obtained by an earlier call to unixFetch(). The second\n** argument passed to this function must be the same as the corresponding\n** argument that was passed to the unixFetch() invocation. \n**\n** Or, if the third argument is NULL, then this function is being called \n** to inform the VFS layer that, according to POSIX, any existing mapping \n** may now be invalid and should be unmapped.\n*/\nstatic int unixUnfetch(sqlite3_file *fd, i64 iOff, void *p){\n#if SQLITE_MAX_MMAP_SIZE>0\n  unixFile *pFd = (unixFile *)fd;   /* The underlying database file */\n  UNUSED_PARAMETER(iOff);\n\n  /* If p==0 (unmap the entire file) then there must be no outstanding \n  ** xFetch references. Or, if p!=0 (meaning it is an xFetch reference),\n  ** then there must be at least one outstanding.  */\n  assert( (p==0)==(pFd->nFetchOut==0) );\n\n  /* If p!=0, it must match the iOff value. */\n  assert( p==0 || p==&((u8 *)pFd->pMapRegion)[iOff] );\n\n  if( p ){\n    pFd->nFetchOut--;\n  }else{\n    unixUnmapfile(pFd);\n  }\n\n  assert( pFd->nFetchOut>=0 );\n#else\n  UNUSED_PARAMETER(fd);\n  UNUSED_PARAMETER(p);\n  UNUSED_PARAMETER(iOff);\n#endif\n  return SQLITE_OK;\n}\n\n/*\n** Here ends the implementation of all sqlite3_file methods.\n**\n********************** End sqlite3_file Methods *******************************\n******************************************************************************/\n\n/*\n** This division contains definitions of sqlite3_io_methods objects that\n** implement various file locking strategies.  It also contains definitions\n** of \"finder\" functions.  A finder-function is used to locate the appropriate\n** sqlite3_io_methods object for a particular database file.  The pAppData\n** field of the sqlite3_vfs VFS objects are initialized to be pointers to\n** the correct finder-function for that VFS.\n**\n** Most finder functions return a pointer to a fixed sqlite3_io_methods\n** object.  The only interesting finder-function is autolockIoFinder, which\n** looks at the filesystem type and tries to guess the best locking\n** strategy from that.\n**\n** For finder-function F, two objects are created:\n**\n**    (1) The real finder-function named \"FImpt()\".\n**\n**    (2) A constant pointer to this function named just \"F\".\n**\n**\n** A pointer to the F pointer is used as the pAppData value for VFS\n** objects.  We have to do this instead of letting pAppData point\n** directly at the finder-function since C90 rules prevent a void*\n** from be cast into a function pointer.\n**\n**\n** Each instance of this macro generates two objects:\n**\n**   *  A constant sqlite3_io_methods object call METHOD that has locking\n**      methods CLOSE, LOCK, UNLOCK, CKRESLOCK.\n**\n**   *  An I/O method finder function called FINDER that returns a pointer\n**      to the METHOD object in the previous bullet.\n*/\n#define IOMETHODS(FINDER,METHOD,VERSION,CLOSE,LOCK,UNLOCK,CKLOCK,SHMMAP)     \\\nstatic const sqlite3_io_methods METHOD = {                                   \\\n   VERSION,                    /* iVersion */                                \\\n   CLOSE,                      /* xClose */                                  \\\n   unixRead,                   /* xRead */                                   \\\n   unixWrite,                  /* xWrite */                                  \\\n   unixTruncate,               /* xTruncate */                               \\\n   unixSync,                   /* xSync */                                   \\\n   unixFileSize,               /* xFileSize */                               \\\n   LOCK,                       /* xLock */                                   \\\n   UNLOCK,                     /* xUnlock */                                 \\\n   CKLOCK,                     /* xCheckReservedLock */                      \\\n   unixFileControl,            /* xFileControl */                            \\\n   unixSectorSize,             /* xSectorSize */                             \\\n   unixDeviceCharacteristics,  /* xDeviceCapabilities */                     \\\n   SHMMAP,                     /* xShmMap */                                 \\\n   unixShmLock,                /* xShmLock */                                \\\n   unixShmBarrier,             /* xShmBarrier */                             \\\n   unixShmUnmap,               /* xShmUnmap */                               \\\n   unixFetch,                  /* xFetch */                                  \\\n   unixUnfetch,                /* xUnfetch */                                \\\n};                                                                           \\\nstatic const sqlite3_io_methods *FINDER##Impl(const char *z, unixFile *p){   \\\n  UNUSED_PARAMETER(z); UNUSED_PARAMETER(p);                                  \\\n  return &METHOD;                                                            \\\n}                                                                            \\\nstatic const sqlite3_io_methods *(*const FINDER)(const char*,unixFile *p)    \\\n    = FINDER##Impl;\n\n/*\n** Here are all of the sqlite3_io_methods objects for each of the\n** locking strategies.  Functions that return pointers to these methods\n** are also created.\n*/\nIOMETHODS(\n  posixIoFinder,            /* Finder function name */\n  posixIoMethods,           /* sqlite3_io_methods object name */\n  3,                        /* shared memory and mmap are enabled */\n  unixClose,                /* xClose method */\n  unixLock,                 /* xLock method */\n  unixUnlock,               /* xUnlock method */\n  unixCheckReservedLock,    /* xCheckReservedLock method */\n  unixShmMap                /* xShmMap method */\n)\nIOMETHODS(\n  nolockIoFinder,           /* Finder function name */\n  nolockIoMethods,          /* sqlite3_io_methods object name */\n  3,                        /* shared memory is disabled */\n  nolockClose,              /* xClose method */\n  nolockLock,               /* xLock method */\n  nolockUnlock,             /* xUnlock method */\n  nolockCheckReservedLock,  /* xCheckReservedLock method */\n  0                         /* xShmMap method */\n)\nIOMETHODS(\n  dotlockIoFinder,          /* Finder function name */\n  dotlockIoMethods,         /* sqlite3_io_methods object name */\n  1,                        /* shared memory is disabled */\n  dotlockClose,             /* xClose method */\n  dotlockLock,              /* xLock method */\n  dotlockUnlock,            /* xUnlock method */\n  dotlockCheckReservedLock, /* xCheckReservedLock method */\n  0                         /* xShmMap method */\n)\n\n#if SQLITE_ENABLE_LOCKING_STYLE\nIOMETHODS(\n  flockIoFinder,            /* Finder function name */\n  flockIoMethods,           /* sqlite3_io_methods object name */\n  1,                        /* shared memory is disabled */\n  flockClose,               /* xClose method */\n  flockLock,                /* xLock method */\n  flockUnlock,              /* xUnlock method */\n  flockCheckReservedLock,   /* xCheckReservedLock method */\n  0                         /* xShmMap method */\n)\n#endif\n\n#if OS_VXWORKS\nIOMETHODS(\n  semIoFinder,              /* Finder function name */\n  semIoMethods,             /* sqlite3_io_methods object name */\n  1,                        /* shared memory is disabled */\n  semXClose,                /* xClose method */\n  semXLock,                 /* xLock method */\n  semXUnlock,               /* xUnlock method */\n  semXCheckReservedLock,    /* xCheckReservedLock method */\n  0                         /* xShmMap method */\n)\n#endif\n\n#if defined(__APPLE__) && SQLITE_ENABLE_LOCKING_STYLE\nIOMETHODS(\n  afpIoFinder,              /* Finder function name */\n  afpIoMethods,             /* sqlite3_io_methods object name */\n  1,                        /* shared memory is disabled */\n  afpClose,                 /* xClose method */\n  afpLock,                  /* xLock method */\n  afpUnlock,                /* xUnlock method */\n  afpCheckReservedLock,     /* xCheckReservedLock method */\n  0                         /* xShmMap method */\n)\n#endif\n\n/*\n** The proxy locking method is a \"super-method\" in the sense that it\n** opens secondary file descriptors for the conch and lock files and\n** it uses proxy, dot-file, AFP, and flock() locking methods on those\n** secondary files.  For this reason, the division that implements\n** proxy locking is located much further down in the file.  But we need\n** to go ahead and define the sqlite3_io_methods and finder function\n** for proxy locking here.  So we forward declare the I/O methods.\n*/\n#if defined(__APPLE__) && SQLITE_ENABLE_LOCKING_STYLE\nstatic int proxyClose(sqlite3_file*);\nstatic int proxyLock(sqlite3_file*, int);\nstatic int proxyUnlock(sqlite3_file*, int);\nstatic int proxyCheckReservedLock(sqlite3_file*, int*);\nIOMETHODS(\n  proxyIoFinder,            /* Finder function name */\n  proxyIoMethods,           /* sqlite3_io_methods object name */\n  1,                        /* shared memory is disabled */\n  proxyClose,               /* xClose method */\n  proxyLock,                /* xLock method */\n  proxyUnlock,              /* xUnlock method */\n  proxyCheckReservedLock,   /* xCheckReservedLock method */\n  0                         /* xShmMap method */\n)\n#endif\n\n/* nfs lockd on OSX 10.3+ doesn't clear write locks when a read lock is set */\n#if defined(__APPLE__) && SQLITE_ENABLE_LOCKING_STYLE\nIOMETHODS(\n  nfsIoFinder,               /* Finder function name */\n  nfsIoMethods,              /* sqlite3_io_methods object name */\n  1,                         /* shared memory is disabled */\n  unixClose,                 /* xClose method */\n  unixLock,                  /* xLock method */\n  nfsUnlock,                 /* xUnlock method */\n  unixCheckReservedLock,     /* xCheckReservedLock method */\n  0                          /* xShmMap method */\n)\n#endif\n\n#if defined(__APPLE__) && SQLITE_ENABLE_LOCKING_STYLE\n/* \n** This \"finder\" function attempts to determine the best locking strategy \n** for the database file \"filePath\".  It then returns the sqlite3_io_methods\n** object that implements that strategy.\n**\n** This is for MacOSX only.\n*/\nstatic const sqlite3_io_methods *autolockIoFinderImpl(\n  const char *filePath,    /* name of the database file */\n  unixFile *pNew           /* open file object for the database file */\n){\n  static const struct Mapping {\n    const char *zFilesystem;              /* Filesystem type name */\n    const sqlite3_io_methods *pMethods;   /* Appropriate locking method */\n  } aMap[] = {\n    { \"hfs\",    &posixIoMethods },\n    { \"ufs\",    &posixIoMethods },\n    { \"afpfs\",  &afpIoMethods },\n    { \"smbfs\",  &afpIoMethods },\n    { \"webdav\", &nolockIoMethods },\n    { 0, 0 }\n  };\n  int i;\n  struct statfs fsInfo;\n  struct flock lockInfo;\n\n  if( !filePath ){\n    /* If filePath==NULL that means we are dealing with a transient file\n    ** that does not need to be locked. */\n    return &nolockIoMethods;\n  }\n  if( statfs(filePath, &fsInfo) != -1 ){\n    if( fsInfo.f_flags & MNT_RDONLY ){\n      return &nolockIoMethods;\n    }\n    for(i=0; aMap[i].zFilesystem; i++){\n      if( strcmp(fsInfo.f_fstypename, aMap[i].zFilesystem)==0 ){\n        return aMap[i].pMethods;\n      }\n    }\n  }\n\n  /* Default case. Handles, amongst others, \"nfs\".\n  ** Test byte-range lock using fcntl(). If the call succeeds, \n  ** assume that the file-system supports POSIX style locks. \n  */\n  lockInfo.l_len = 1;\n  lockInfo.l_start = 0;\n  lockInfo.l_whence = SEEK_SET;\n  lockInfo.l_type = F_RDLCK;\n  if( osFcntl(pNew->h, F_GETLK, &lockInfo)!=-1 ) {\n    if( strcmp(fsInfo.f_fstypename, \"nfs\")==0 ){\n      return &nfsIoMethods;\n    } else {\n      return &posixIoMethods;\n    }\n  }else{\n    return &dotlockIoMethods;\n  }\n}\nstatic const sqlite3_io_methods \n  *(*const autolockIoFinder)(const char*,unixFile*) = autolockIoFinderImpl;\n\n#endif /* defined(__APPLE__) && SQLITE_ENABLE_LOCKING_STYLE */\n\n#if OS_VXWORKS\n/*\n** This \"finder\" function for VxWorks checks to see if posix advisory\n** locking works.  If it does, then that is what is used.  If it does not\n** work, then fallback to named semaphore locking.\n*/\nstatic const sqlite3_io_methods *vxworksIoFinderImpl(\n  const char *filePath,    /* name of the database file */\n  unixFile *pNew           /* the open file object */\n){\n  struct flock lockInfo;\n\n  if( !filePath ){\n    /* If filePath==NULL that means we are dealing with a transient file\n    ** that does not need to be locked. */\n    return &nolockIoMethods;\n  }\n\n  /* Test if fcntl() is supported and use POSIX style locks.\n  ** Otherwise fall back to the named semaphore method.\n  */\n  lockInfo.l_len = 1;\n  lockInfo.l_start = 0;\n  lockInfo.l_whence = SEEK_SET;\n  lockInfo.l_type = F_RDLCK;\n  if( osFcntl(pNew->h, F_GETLK, &lockInfo)!=-1 ) {\n    return &posixIoMethods;\n  }else{\n    return &semIoMethods;\n  }\n}\nstatic const sqlite3_io_methods \n  *(*const vxworksIoFinder)(const char*,unixFile*) = vxworksIoFinderImpl;\n\n#endif /* OS_VXWORKS */\n\n/*\n** An abstract type for a pointer to an IO method finder function:\n*/\ntypedef const sqlite3_io_methods *(*finder_type)(const char*,unixFile*);\n\n\n/****************************************************************************\n**************************** sqlite3_vfs methods ****************************\n**\n** This division contains the implementation of methods on the\n** sqlite3_vfs object.\n*/\n\n/*\n** Initialize the contents of the unixFile structure pointed to by pId.\n*/\nstatic int fillInUnixFile(\n  sqlite3_vfs *pVfs,      /* Pointer to vfs object */\n  int h,                  /* Open file descriptor of file being opened */\n  sqlite3_file *pId,      /* Write to the unixFile structure here */\n  const char *zFilename,  /* Name of the file being opened */\n  int ctrlFlags           /* Zero or more UNIXFILE_* values */\n){\n  const sqlite3_io_methods *pLockingStyle;\n  unixFile *pNew = (unixFile *)pId;\n  int rc = SQLITE_OK;\n\n  assert( pNew->pInode==NULL );\n\n  /* No locking occurs in temporary files */\n  assert( zFilename!=0 || (ctrlFlags & UNIXFILE_NOLOCK)!=0 );\n\n  OSTRACE((\"OPEN    %-3d %s\\n\", h, zFilename));\n  pNew->h = h;\n  pNew->pVfs = pVfs;\n  pNew->zPath = zFilename;\n  pNew->ctrlFlags = (u8)ctrlFlags;\n#if SQLITE_MAX_MMAP_SIZE>0\n  pNew->mmapSizeMax = sqlite3GlobalConfig.szMmap;\n#endif\n  if( sqlite3_uri_boolean(((ctrlFlags & UNIXFILE_URI) ? zFilename : 0),\n                           \"psow\", SQLITE_POWERSAFE_OVERWRITE) ){\n    pNew->ctrlFlags |= UNIXFILE_PSOW;\n  }\n  if( strcmp(pVfs->zName,\"unix-excl\")==0 ){\n    pNew->ctrlFlags |= UNIXFILE_EXCL;\n  }\n\n#if OS_VXWORKS\n  pNew->pId = vxworksFindFileId(zFilename);\n  if( pNew->pId==0 ){\n    ctrlFlags |= UNIXFILE_NOLOCK;\n    rc = SQLITE_NOMEM_BKPT;\n  }\n#endif\n\n  if( ctrlFlags & UNIXFILE_NOLOCK ){\n    pLockingStyle = &nolockIoMethods;\n  }else{\n    pLockingStyle = (**(finder_type*)pVfs->pAppData)(zFilename, pNew);\n#if SQLITE_ENABLE_LOCKING_STYLE\n    /* Cache zFilename in the locking context (AFP and dotlock override) for\n    ** proxyLock activation is possible (remote proxy is based on db name)\n    ** zFilename remains valid until file is closed, to support */\n    pNew->lockingContext = (void*)zFilename;\n#endif\n  }\n\n  if( pLockingStyle == &posixIoMethods\n#if defined(__APPLE__) && SQLITE_ENABLE_LOCKING_STYLE\n    || pLockingStyle == &nfsIoMethods\n#endif\n  ){\n    unixEnterMutex();\n    rc = findInodeInfo(pNew, &pNew->pInode);\n    if( rc!=SQLITE_OK ){\n      /* If an error occurred in findInodeInfo(), close the file descriptor\n      ** immediately, before releasing the mutex. findInodeInfo() may fail\n      ** in two scenarios:\n      **\n      **   (a) A call to fstat() failed.\n      **   (b) A malloc failed.\n      **\n      ** Scenario (b) may only occur if the process is holding no other\n      ** file descriptors open on the same file. If there were other file\n      ** descriptors on this file, then no malloc would be required by\n      ** findInodeInfo(). If this is the case, it is quite safe to close\n      ** handle h - as it is guaranteed that no posix locks will be released\n      ** by doing so.\n      **\n      ** If scenario (a) caused the error then things are not so safe. The\n      ** implicit assumption here is that if fstat() fails, things are in\n      ** such bad shape that dropping a lock or two doesn't matter much.\n      */\n      robust_close(pNew, h, __LINE__);\n      h = -1;\n    }\n    unixLeaveMutex();\n  }\n\n#if SQLITE_ENABLE_LOCKING_STYLE && defined(__APPLE__)\n  else if( pLockingStyle == &afpIoMethods ){\n    /* AFP locking uses the file path so it needs to be included in\n    ** the afpLockingContext.\n    */\n    afpLockingContext *pCtx;\n    pNew->lockingContext = pCtx = sqlite3_malloc64( sizeof(*pCtx) );\n    if( pCtx==0 ){\n      rc = SQLITE_NOMEM_BKPT;\n    }else{\n      /* NB: zFilename exists and remains valid until the file is closed\n      ** according to requirement F11141.  So we do not need to make a\n      ** copy of the filename. */\n      pCtx->dbPath = zFilename;\n      pCtx->reserved = 0;\n      srandomdev();\n      unixEnterMutex();\n      rc = findInodeInfo(pNew, &pNew->pInode);\n      if( rc!=SQLITE_OK ){\n        sqlite3_free(pNew->lockingContext);\n        robust_close(pNew, h, __LINE__);\n        h = -1;\n      }\n      unixLeaveMutex();        \n    }\n  }\n#endif\n\n  else if( pLockingStyle == &dotlockIoMethods ){\n    /* Dotfile locking uses the file path so it needs to be included in\n    ** the dotlockLockingContext \n    */\n    char *zLockFile;\n    int nFilename;\n    assert( zFilename!=0 );\n    nFilename = (int)strlen(zFilename) + 6;\n    zLockFile = (char *)sqlite3_malloc64(nFilename);\n    if( zLockFile==0 ){\n      rc = SQLITE_NOMEM_BKPT;\n    }else{\n      sqlite3_snprintf(nFilename, zLockFile, \"%s\" DOTLOCK_SUFFIX, zFilename);\n    }\n    pNew->lockingContext = zLockFile;\n  }\n\n#if OS_VXWORKS\n  else if( pLockingStyle == &semIoMethods ){\n    /* Named semaphore locking uses the file path so it needs to be\n    ** included in the semLockingContext\n    */\n    unixEnterMutex();\n    rc = findInodeInfo(pNew, &pNew->pInode);\n    if( (rc==SQLITE_OK) && (pNew->pInode->pSem==NULL) ){\n      char *zSemName = pNew->pInode->aSemName;\n      int n;\n      sqlite3_snprintf(MAX_PATHNAME, zSemName, \"/%s.sem\",\n                       pNew->pId->zCanonicalName);\n      for( n=1; zSemName[n]; n++ )\n        if( zSemName[n]=='/' ) zSemName[n] = '_';\n      pNew->pInode->pSem = sem_open(zSemName, O_CREAT, 0666, 1);\n      if( pNew->pInode->pSem == SEM_FAILED ){\n        rc = SQLITE_NOMEM_BKPT;\n        pNew->pInode->aSemName[0] = '\\0';\n      }\n    }\n    unixLeaveMutex();\n  }\n#endif\n  \n  storeLastErrno(pNew, 0);\n#if OS_VXWORKS\n  if( rc!=SQLITE_OK ){\n    if( h>=0 ) robust_close(pNew, h, __LINE__);\n    h = -1;\n    osUnlink(zFilename);\n    pNew->ctrlFlags |= UNIXFILE_DELETE;\n  }\n#endif\n  if( rc!=SQLITE_OK ){\n    if( h>=0 ) robust_close(pNew, h, __LINE__);\n  }else{\n    pNew->pMethod = pLockingStyle;\n    OpenCounter(+1);\n    verifyDbFile(pNew);\n  }\n  return rc;\n}\n\n/*\n** Return the name of a directory in which to put temporary files.\n** If no suitable temporary file directory can be found, return NULL.\n*/\nstatic const char *unixTempFileDir(void){\n  static const char *azDirs[] = {\n     0,\n     0,\n     \"/var/tmp\",\n     \"/usr/tmp\",\n     \"/tmp\",\n     \".\"\n  };\n  unsigned int i = 0;\n  struct stat buf;\n  const char *zDir = sqlite3_temp_directory;\n\n  if( !azDirs[0] ) azDirs[0] = getenv(\"SQLITE_TMPDIR\");\n  if( !azDirs[1] ) azDirs[1] = getenv(\"TMPDIR\");\n  while(1){\n    if( zDir!=0\n     && osStat(zDir, &buf)==0\n     && S_ISDIR(buf.st_mode)\n     && osAccess(zDir, 03)==0\n    ){\n      return zDir;\n    }\n    if( i>=sizeof(azDirs)/sizeof(azDirs[0]) ) break;\n    zDir = azDirs[i++];\n  }\n  return 0;\n}\n\n/*\n** Create a temporary file name in zBuf.  zBuf must be allocated\n** by the calling process and must be big enough to hold at least\n** pVfs->mxPathname bytes.\n*/\nstatic int unixGetTempname(int nBuf, char *zBuf){\n  const char *zDir;\n  int iLimit = 0;\n\n  /* It's odd to simulate an io-error here, but really this is just\n  ** using the io-error infrastructure to test that SQLite handles this\n  ** function failing. \n  */\n  zBuf[0] = 0;\n  SimulateIOError( return SQLITE_IOERR );\n\n  zDir = unixTempFileDir();\n  if( zDir==0 ) return SQLITE_IOERR_GETTEMPPATH;\n  do{\n    u64 r;\n    sqlite3_randomness(sizeof(r), &r);\n    assert( nBuf>2 );\n    zBuf[nBuf-2] = 0;\n    sqlite3_snprintf(nBuf, zBuf, \"%s/\"SQLITE_TEMP_FILE_PREFIX\"%llx%c\",\n                     zDir, r, 0);\n    if( zBuf[nBuf-2]!=0 || (iLimit++)>10 ) return SQLITE_ERROR;\n  }while( osAccess(zBuf,0)==0 );\n  return SQLITE_OK;\n}\n\n#if SQLITE_ENABLE_LOCKING_STYLE && defined(__APPLE__)\n/*\n** Routine to transform a unixFile into a proxy-locking unixFile.\n** Implementation in the proxy-lock division, but used by unixOpen()\n** if SQLITE_PREFER_PROXY_LOCKING is defined.\n*/\nstatic int proxyTransformUnixFile(unixFile*, const char*);\n#endif\n\n/*\n** Search for an unused file descriptor that was opened on the database \n** file (not a journal or master-journal file) identified by pathname\n** zPath with SQLITE_OPEN_XXX flags matching those passed as the second\n** argument to this function.\n**\n** Such a file descriptor may exist if a database connection was closed\n** but the associated file descriptor could not be closed because some\n** other file descriptor open on the same file is holding a file-lock.\n** Refer to comments in the unixClose() function and the lengthy comment\n** describing \"Posix Advisory Locking\" at the start of this file for \n** further details. Also, ticket #4018.\n**\n** If a suitable file descriptor is found, then it is returned. If no\n** such file descriptor is located, -1 is returned.\n*/\nstatic UnixUnusedFd *findReusableFd(const char *zPath, int flags){\n  UnixUnusedFd *pUnused = 0;\n\n  /* Do not search for an unused file descriptor on vxworks. Not because\n  ** vxworks would not benefit from the change (it might, we're not sure),\n  ** but because no way to test it is currently available. It is better \n  ** not to risk breaking vxworks support for the sake of such an obscure \n  ** feature.  */\n#if !OS_VXWORKS\n  struct stat sStat;                   /* Results of stat() call */\n\n  unixEnterMutex();\n\n  /* A stat() call may fail for various reasons. If this happens, it is\n  ** almost certain that an open() call on the same path will also fail.\n  ** For this reason, if an error occurs in the stat() call here, it is\n  ** ignored and -1 is returned. The caller will try to open a new file\n  ** descriptor on the same path, fail, and return an error to SQLite.\n  **\n  ** Even if a subsequent open() call does succeed, the consequences of\n  ** not searching for a reusable file descriptor are not dire.  */\n  if( nUnusedFd>0 && 0==osStat(zPath, &sStat) ){\n    unixInodeInfo *pInode;\n\n    pInode = inodeList;\n    while( pInode && (pInode->fileId.dev!=sStat.st_dev\n                     || pInode->fileId.ino!=(u64)sStat.st_ino) ){\n       pInode = pInode->pNext;\n    }\n    if( pInode ){\n      UnixUnusedFd **pp;\n      for(pp=&pInode->pUnused; *pp && (*pp)->flags!=flags; pp=&((*pp)->pNext));\n      pUnused = *pp;\n      if( pUnused ){\n        nUnusedFd--;\n        *pp = pUnused->pNext;\n      }\n    }\n  }\n  unixLeaveMutex();\n#endif    /* if !OS_VXWORKS */\n  return pUnused;\n}\n\n/*\n** Find the mode, uid and gid of file zFile. \n*/\nstatic int getFileMode(\n  const char *zFile,              /* File name */\n  mode_t *pMode,                  /* OUT: Permissions of zFile */\n  uid_t *pUid,                    /* OUT: uid of zFile. */\n  gid_t *pGid                     /* OUT: gid of zFile. */\n){\n  struct stat sStat;              /* Output of stat() on database file */\n  int rc = SQLITE_OK;\n  if( 0==osStat(zFile, &sStat) ){\n    *pMode = sStat.st_mode & 0777;\n    *pUid = sStat.st_uid;\n    *pGid = sStat.st_gid;\n  }else{\n    rc = SQLITE_IOERR_FSTAT;\n  }\n  return rc;\n}\n\n/*\n** This function is called by unixOpen() to determine the unix permissions\n** to create new files with. If no error occurs, then SQLITE_OK is returned\n** and a value suitable for passing as the third argument to open(2) is\n** written to *pMode. If an IO error occurs, an SQLite error code is \n** returned and the value of *pMode is not modified.\n**\n** In most cases, this routine sets *pMode to 0, which will become\n** an indication to robust_open() to create the file using\n** SQLITE_DEFAULT_FILE_PERMISSIONS adjusted by the umask.\n** But if the file being opened is a WAL or regular journal file, then \n** this function queries the file-system for the permissions on the \n** corresponding database file and sets *pMode to this value. Whenever \n** possible, WAL and journal files are created using the same permissions \n** as the associated database file.\n**\n** If the SQLITE_ENABLE_8_3_NAMES option is enabled, then the\n** original filename is unavailable.  But 8_3_NAMES is only used for\n** FAT filesystems and permissions do not matter there, so just use\n** the default permissions.\n*/\nstatic int findCreateFileMode(\n  const char *zPath,              /* Path of file (possibly) being created */\n  int flags,                      /* Flags passed as 4th argument to xOpen() */\n  mode_t *pMode,                  /* OUT: Permissions to open file with */\n  uid_t *pUid,                    /* OUT: uid to set on the file */\n  gid_t *pGid                     /* OUT: gid to set on the file */\n){\n  int rc = SQLITE_OK;             /* Return Code */\n  *pMode = 0;\n  *pUid = 0;\n  *pGid = 0;\n  if( flags & (SQLITE_OPEN_WAL|SQLITE_OPEN_MAIN_JOURNAL) ){\n    char zDb[MAX_PATHNAME+1];     /* Database file path */\n    int nDb;                      /* Number of valid bytes in zDb */\n\n    /* zPath is a path to a WAL or journal file. The following block derives\n    ** the path to the associated database file from zPath. This block handles\n    ** the following naming conventions:\n    **\n    **   \"<path to db>-journal\"\n    **   \"<path to db>-wal\"\n    **   \"<path to db>-journalNN\"\n    **   \"<path to db>-walNN\"\n    **\n    ** where NN is a decimal number. The NN naming schemes are \n    ** used by the test_multiplex.c module.\n    */\n    nDb = sqlite3Strlen30(zPath) - 1; \n    while( zPath[nDb]!='-' ){\n      /* In normal operation, the journal file name will always contain\n      ** a '-' character.  However in 8+3 filename mode, or if a corrupt\n      ** rollback journal specifies a master journal with a goofy name, then\n      ** the '-' might be missing. */\n      if( nDb==0 || zPath[nDb]=='.' ) return SQLITE_OK;\n      nDb--;\n    }\n    memcpy(zDb, zPath, nDb);\n    zDb[nDb] = '\\0';\n\n    rc = getFileMode(zDb, pMode, pUid, pGid);\n  }else if( flags & SQLITE_OPEN_DELETEONCLOSE ){\n    *pMode = 0600;\n  }else if( flags & SQLITE_OPEN_URI ){\n    /* If this is a main database file and the file was opened using a URI\n    ** filename, check for the \"modeof\" parameter. If present, interpret\n    ** its value as a filename and try to copy the mode, uid and gid from\n    ** that file.  */\n    const char *z = sqlite3_uri_parameter(zPath, \"modeof\");\n    if( z ){\n      rc = getFileMode(z, pMode, pUid, pGid);\n    }\n  }\n  return rc;\n}\n\n/*\n** Open the file zPath.\n** \n** Previously, the SQLite OS layer used three functions in place of this\n** one:\n**\n**     sqlite3OsOpenReadWrite();\n**     sqlite3OsOpenReadOnly();\n**     sqlite3OsOpenExclusive();\n**\n** These calls correspond to the following combinations of flags:\n**\n**     ReadWrite() ->     (READWRITE | CREATE)\n**     ReadOnly()  ->     (READONLY) \n**     OpenExclusive() -> (READWRITE | CREATE | EXCLUSIVE)\n**\n** The old OpenExclusive() accepted a boolean argument - \"delFlag\". If\n** true, the file was configured to be automatically deleted when the\n** file handle closed. To achieve the same effect using this new \n** interface, add the DELETEONCLOSE flag to those specified above for \n** OpenExclusive().\n*/\nstatic int unixOpen(\n  sqlite3_vfs *pVfs,           /* The VFS for which this is the xOpen method */\n  const char *zPath,           /* Pathname of file to be opened */\n  sqlite3_file *pFile,         /* The file descriptor to be filled in */\n  int flags,                   /* Input flags to control the opening */\n  int *pOutFlags               /* Output flags returned to SQLite core */\n){\n  unixFile *p = (unixFile *)pFile;\n  int fd = -1;                   /* File descriptor returned by open() */\n  int openFlags = 0;             /* Flags to pass to open() */\n  int eType = flags&0xFFFFFF00;  /* Type of file to open */\n  int noLock;                    /* True to omit locking primitives */\n  int rc = SQLITE_OK;            /* Function Return Code */\n  int ctrlFlags = 0;             /* UNIXFILE_* flags */\n\n  int isExclusive  = (flags & SQLITE_OPEN_EXCLUSIVE);\n  int isDelete     = (flags & SQLITE_OPEN_DELETEONCLOSE);\n  int isCreate     = (flags & SQLITE_OPEN_CREATE);\n  int isReadonly   = (flags & SQLITE_OPEN_READONLY);\n  int isReadWrite  = (flags & SQLITE_OPEN_READWRITE);\n#if SQLITE_ENABLE_LOCKING_STYLE\n  int isAutoProxy  = (flags & SQLITE_OPEN_AUTOPROXY);\n#endif\n#if defined(__APPLE__) || SQLITE_ENABLE_LOCKING_STYLE\n  struct statfs fsInfo;\n#endif\n\n  /* If creating a master or main-file journal, this function will open\n  ** a file-descriptor on the directory too. The first time unixSync()\n  ** is called the directory file descriptor will be fsync()ed and close()d.\n  */\n  int isNewJrnl = (isCreate && (\n        eType==SQLITE_OPEN_MASTER_JOURNAL \n     || eType==SQLITE_OPEN_MAIN_JOURNAL \n     || eType==SQLITE_OPEN_WAL\n  ));\n\n  /* If argument zPath is a NULL pointer, this function is required to open\n  ** a temporary file. Use this buffer to store the file name in.\n  */\n  char zTmpname[MAX_PATHNAME+2];\n  const char *zName = zPath;\n\n  /* Check the following statements are true: \n  **\n  **   (a) Exactly one of the READWRITE and READONLY flags must be set, and \n  **   (b) if CREATE is set, then READWRITE must also be set, and\n  **   (c) if EXCLUSIVE is set, then CREATE must also be set.\n  **   (d) if DELETEONCLOSE is set, then CREATE must also be set.\n  */\n  assert((isReadonly==0 || isReadWrite==0) && (isReadWrite || isReadonly));\n  assert(isCreate==0 || isReadWrite);\n  assert(isExclusive==0 || isCreate);\n  assert(isDelete==0 || isCreate);\n\n  /* The main DB, main journal, WAL file and master journal are never \n  ** automatically deleted. Nor are they ever temporary files.  */\n  assert( (!isDelete && zName) || eType!=SQLITE_OPEN_MAIN_DB );\n  assert( (!isDelete && zName) || eType!=SQLITE_OPEN_MAIN_JOURNAL );\n  assert( (!isDelete && zName) || eType!=SQLITE_OPEN_MASTER_JOURNAL );\n  assert( (!isDelete && zName) || eType!=SQLITE_OPEN_WAL );\n\n  /* Assert that the upper layer has set one of the \"file-type\" flags. */\n  assert( eType==SQLITE_OPEN_MAIN_DB      || eType==SQLITE_OPEN_TEMP_DB \n       || eType==SQLITE_OPEN_MAIN_JOURNAL || eType==SQLITE_OPEN_TEMP_JOURNAL \n       || eType==SQLITE_OPEN_SUBJOURNAL   || eType==SQLITE_OPEN_MASTER_JOURNAL \n       || eType==SQLITE_OPEN_TRANSIENT_DB || eType==SQLITE_OPEN_WAL\n  );\n\n  /* Detect a pid change and reset the PRNG.  There is a race condition\n  ** here such that two or more threads all trying to open databases at\n  ** the same instant might all reset the PRNG.  But multiple resets\n  ** are harmless.\n  */\n  if( randomnessPid!=osGetpid(0) ){\n    randomnessPid = osGetpid(0);\n    sqlite3_randomness(0,0);\n  }\n  memset(p, 0, sizeof(unixFile));\n\n  if( eType==SQLITE_OPEN_MAIN_DB ){\n    UnixUnusedFd *pUnused;\n    pUnused = findReusableFd(zName, flags);\n    if( pUnused ){\n      fd = pUnused->fd;\n    }else{\n      pUnused = sqlite3_malloc64(sizeof(*pUnused));\n      if( !pUnused ){\n        return SQLITE_NOMEM_BKPT;\n      }\n    }\n    p->pPreallocatedUnused = pUnused;\n\n    /* Database filenames are double-zero terminated if they are not\n    ** URIs with parameters.  Hence, they can always be passed into\n    ** sqlite3_uri_parameter(). */\n    assert( (flags & SQLITE_OPEN_URI) || zName[strlen(zName)+1]==0 );\n\n  }else if( !zName ){\n    /* If zName is NULL, the upper layer is requesting a temp file. */\n    assert(isDelete && !isNewJrnl);\n    rc = unixGetTempname(pVfs->mxPathname, zTmpname);\n    if( rc!=SQLITE_OK ){\n      return rc;\n    }\n    zName = zTmpname;\n\n    /* Generated temporary filenames are always double-zero terminated\n    ** for use by sqlite3_uri_parameter(). */\n    assert( zName[strlen(zName)+1]==0 );\n  }\n\n  /* Determine the value of the flags parameter passed to POSIX function\n  ** open(). These must be calculated even if open() is not called, as\n  ** they may be stored as part of the file handle and used by the \n  ** 'conch file' locking functions later on.  */\n  if( isReadonly )  openFlags |= O_RDONLY;\n  if( isReadWrite ) openFlags |= O_RDWR;\n  if( isCreate )    openFlags |= O_CREAT;\n  if( isExclusive ) openFlags |= (O_EXCL|O_NOFOLLOW);\n  openFlags |= (O_LARGEFILE|O_BINARY);\n\n  if( fd<0 ){\n    mode_t openMode;              /* Permissions to create file with */\n    uid_t uid;                    /* Userid for the file */\n    gid_t gid;                    /* Groupid for the file */\n    rc = findCreateFileMode(zName, flags, &openMode, &uid, &gid);\n    if( rc!=SQLITE_OK ){\n      assert( !p->pPreallocatedUnused );\n      assert( eType==SQLITE_OPEN_WAL || eType==SQLITE_OPEN_MAIN_JOURNAL );\n      return rc;\n    }\n    fd = robust_open(zName, openFlags, openMode);\n    OSTRACE((\"OPENX   %-3d %s 0%o\\n\", fd, zName, openFlags));\n    assert( !isExclusive || (openFlags & O_CREAT)!=0 );\n    if( fd<0 ){\n      if( isNewJrnl && errno==EACCES && osAccess(zName, F_OK) ){\n        /* If unable to create a journal because the directory is not\n        ** writable, change the error code to indicate that. */\n        rc = SQLITE_READONLY_DIRECTORY;\n      }else if( errno!=EISDIR && isReadWrite ){\n        /* Failed to open the file for read/write access. Try read-only. */\n        flags &= ~(SQLITE_OPEN_READWRITE|SQLITE_OPEN_CREATE);\n        openFlags &= ~(O_RDWR|O_CREAT);\n        flags |= SQLITE_OPEN_READONLY;\n        openFlags |= O_RDONLY;\n        isReadonly = 1;\n        fd = robust_open(zName, openFlags, openMode);\n      }\n    }\n    if( fd<0 ){\n      int rc2 = unixLogError(SQLITE_CANTOPEN_BKPT, \"open\", zName);\n      if( rc==SQLITE_OK ) rc = rc2;\n      goto open_finished;\n    }\n\n    /* If this process is running as root and if creating a new rollback\n    ** journal or WAL file, set the ownership of the journal or WAL to be\n    ** the same as the original database.\n    */\n    if( flags & (SQLITE_OPEN_WAL|SQLITE_OPEN_MAIN_JOURNAL) ){\n      robustFchown(fd, uid, gid);\n    }\n  }\n  assert( fd>=0 );\n  if( pOutFlags ){\n    *pOutFlags = flags;\n  }\n\n  if( p->pPreallocatedUnused ){\n    p->pPreallocatedUnused->fd = fd;\n    p->pPreallocatedUnused->flags = flags;\n  }\n\n  if( isDelete ){\n#if OS_VXWORKS\n    zPath = zName;\n#elif defined(SQLITE_UNLINK_AFTER_CLOSE)\n    zPath = sqlite3_mprintf(\"%s\", zName);\n    if( zPath==0 ){\n      robust_close(p, fd, __LINE__);\n      return SQLITE_NOMEM_BKPT;\n    }\n#else\n    osUnlink(zName);\n#endif\n  }\n#if SQLITE_ENABLE_LOCKING_STYLE\n  else{\n    p->openFlags = openFlags;\n  }\n#endif\n  \n#if defined(__APPLE__) || SQLITE_ENABLE_LOCKING_STYLE\n  if( fstatfs(fd, &fsInfo) == -1 ){\n    storeLastErrno(p, errno);\n    robust_close(p, fd, __LINE__);\n    return SQLITE_IOERR_ACCESS;\n  }\n  if (0 == strncmp(\"msdos\", fsInfo.f_fstypename, 5)) {\n    ((unixFile*)pFile)->fsFlags |= SQLITE_FSFLAGS_IS_MSDOS;\n  }\n  if (0 == strncmp(\"exfat\", fsInfo.f_fstypename, 5)) {\n    ((unixFile*)pFile)->fsFlags |= SQLITE_FSFLAGS_IS_MSDOS;\n  }\n#endif\n\n  /* Set up appropriate ctrlFlags */\n  if( isDelete )                ctrlFlags |= UNIXFILE_DELETE;\n  if( isReadonly )              ctrlFlags |= UNIXFILE_RDONLY;\n  noLock = eType!=SQLITE_OPEN_MAIN_DB;\n  if( noLock )                  ctrlFlags |= UNIXFILE_NOLOCK;\n  if( isNewJrnl )               ctrlFlags |= UNIXFILE_DIRSYNC;\n  if( flags & SQLITE_OPEN_URI ) ctrlFlags |= UNIXFILE_URI;\n\n#if SQLITE_ENABLE_LOCKING_STYLE\n#if SQLITE_PREFER_PROXY_LOCKING\n  isAutoProxy = 1;\n#endif\n  if( isAutoProxy && (zPath!=NULL) && (!noLock) && pVfs->xOpen ){\n    char *envforce = getenv(\"SQLITE_FORCE_PROXY_LOCKING\");\n    int useProxy = 0;\n\n    /* SQLITE_FORCE_PROXY_LOCKING==1 means force always use proxy, 0 means \n    ** never use proxy, NULL means use proxy for non-local files only.  */\n    if( envforce!=NULL ){\n      useProxy = atoi(envforce)>0;\n    }else{\n      useProxy = !(fsInfo.f_flags&MNT_LOCAL);\n    }\n    if( useProxy ){\n      rc = fillInUnixFile(pVfs, fd, pFile, zPath, ctrlFlags);\n      if( rc==SQLITE_OK ){\n        rc = proxyTransformUnixFile((unixFile*)pFile, \":auto:\");\n        if( rc!=SQLITE_OK ){\n          /* Use unixClose to clean up the resources added in fillInUnixFile \n          ** and clear all the structure's references.  Specifically, \n          ** pFile->pMethods will be NULL so sqlite3OsClose will be a no-op \n          */\n          unixClose(pFile);\n          return rc;\n        }\n      }\n      goto open_finished;\n    }\n  }\n#endif\n  \n  assert( zPath==0 || zPath[0]=='/' \n      || eType==SQLITE_OPEN_MASTER_JOURNAL || eType==SQLITE_OPEN_MAIN_JOURNAL \n  );\n  rc = fillInUnixFile(pVfs, fd, pFile, zPath, ctrlFlags);\n\nopen_finished:\n  if( rc!=SQLITE_OK ){\n    sqlite3_free(p->pPreallocatedUnused);\n  }\n  return rc;\n}\n\n\n/*\n** Delete the file at zPath. If the dirSync argument is true, fsync()\n** the directory after deleting the file.\n*/\nstatic int unixDelete(\n  sqlite3_vfs *NotUsed,     /* VFS containing this as the xDelete method */\n  const char *zPath,        /* Name of file to be deleted */\n  int dirSync               /* If true, fsync() directory after deleting file */\n){\n  int rc = SQLITE_OK;\n  UNUSED_PARAMETER(NotUsed);\n  SimulateIOError(return SQLITE_IOERR_DELETE);\n  if( osUnlink(zPath)==(-1) ){\n    if( errno==ENOENT\n#if OS_VXWORKS\n        || osAccess(zPath,0)!=0\n#endif\n    ){\n      rc = SQLITE_IOERR_DELETE_NOENT;\n    }else{\n      rc = unixLogError(SQLITE_IOERR_DELETE, \"unlink\", zPath);\n    }\n    return rc;\n  }\n#ifndef SQLITE_DISABLE_DIRSYNC\n  if( (dirSync & 1)!=0 ){\n    int fd;\n    rc = osOpenDirectory(zPath, &fd);\n    if( rc==SQLITE_OK ){\n      if( full_fsync(fd,0,0) ){\n        rc = unixLogError(SQLITE_IOERR_DIR_FSYNC, \"fsync\", zPath);\n      }\n      robust_close(0, fd, __LINE__);\n    }else{\n      assert( rc==SQLITE_CANTOPEN );\n      rc = SQLITE_OK;\n    }\n  }\n#endif\n  return rc;\n}\n\n/*\n** Test the existence of or access permissions of file zPath. The\n** test performed depends on the value of flags:\n**\n**     SQLITE_ACCESS_EXISTS: Return 1 if the file exists\n**     SQLITE_ACCESS_READWRITE: Return 1 if the file is read and writable.\n**     SQLITE_ACCESS_READONLY: Return 1 if the file is readable.\n**\n** Otherwise return 0.\n*/\nstatic int unixAccess(\n  sqlite3_vfs *NotUsed,   /* The VFS containing this xAccess method */\n  const char *zPath,      /* Path of the file to examine */\n  int flags,              /* What do we want to learn about the zPath file? */\n  int *pResOut            /* Write result boolean here */\n){\n  UNUSED_PARAMETER(NotUsed);\n  SimulateIOError( return SQLITE_IOERR_ACCESS; );\n  assert( pResOut!=0 );\n\n  /* The spec says there are three possible values for flags.  But only\n  ** two of them are actually used */\n  assert( flags==SQLITE_ACCESS_EXISTS || flags==SQLITE_ACCESS_READWRITE );\n\n  if( flags==SQLITE_ACCESS_EXISTS ){\n    struct stat buf;\n    *pResOut = (0==osStat(zPath, &buf) && buf.st_size>0);\n  }else{\n    *pResOut = osAccess(zPath, W_OK|R_OK)==0;\n  }\n  return SQLITE_OK;\n}\n\n/*\n**\n*/\nstatic int mkFullPathname(\n  const char *zPath,              /* Input path */\n  char *zOut,                     /* Output buffer */\n  int nOut                        /* Allocated size of buffer zOut */\n){\n  int nPath = sqlite3Strlen30(zPath);\n  int iOff = 0;\n  if( zPath[0]!='/' ){\n    if( osGetcwd(zOut, nOut-2)==0 ){\n      return unixLogError(SQLITE_CANTOPEN_BKPT, \"getcwd\", zPath);\n    }\n    iOff = sqlite3Strlen30(zOut);\n    zOut[iOff++] = '/';\n  }\n  if( (iOff+nPath+1)>nOut ){\n    /* SQLite assumes that xFullPathname() nul-terminates the output buffer\n    ** even if it returns an error.  */\n    zOut[iOff] = '\\0';\n    return SQLITE_CANTOPEN_BKPT;\n  }\n  sqlite3_snprintf(nOut-iOff, &zOut[iOff], \"%s\", zPath);\n  return SQLITE_OK;\n}\n\n/*\n** Turn a relative pathname into a full pathname. The relative path\n** is stored as a nul-terminated string in the buffer pointed to by\n** zPath. \n**\n** zOut points to a buffer of at least sqlite3_vfs.mxPathname bytes \n** (in this case, MAX_PATHNAME bytes). The full-path is written to\n** this buffer before returning.\n*/\nstatic int unixFullPathname(\n  sqlite3_vfs *pVfs,            /* Pointer to vfs object */\n  const char *zPath,            /* Possibly relative input path */\n  int nOut,                     /* Size of output buffer in bytes */\n  char *zOut                    /* Output buffer */\n){\n#if !defined(HAVE_READLINK) || !defined(HAVE_LSTAT)\n  return mkFullPathname(zPath, zOut, nOut);\n#else\n  int rc = SQLITE_OK;\n  int nByte;\n  int nLink = 1;                /* Number of symbolic links followed so far */\n  const char *zIn = zPath;      /* Input path for each iteration of loop */\n  char *zDel = 0;\n\n  assert( pVfs->mxPathname==MAX_PATHNAME );\n  UNUSED_PARAMETER(pVfs);\n\n  /* It's odd to simulate an io-error here, but really this is just\n  ** using the io-error infrastructure to test that SQLite handles this\n  ** function failing. This function could fail if, for example, the\n  ** current working directory has been unlinked.\n  */\n  SimulateIOError( return SQLITE_ERROR );\n\n  do {\n\n    /* Call stat() on path zIn. Set bLink to true if the path is a symbolic\n    ** link, or false otherwise.  */\n    int bLink = 0;\n    struct stat buf;\n    if( osLstat(zIn, &buf)!=0 ){\n      if( errno!=ENOENT ){\n        rc = unixLogError(SQLITE_CANTOPEN_BKPT, \"lstat\", zIn);\n      }\n    }else{\n      bLink = S_ISLNK(buf.st_mode);\n    }\n\n    if( bLink ){\n      if( zDel==0 ){\n        zDel = sqlite3_malloc(nOut);\n        if( zDel==0 ) rc = SQLITE_NOMEM_BKPT;\n      }else if( ++nLink>SQLITE_MAX_SYMLINKS ){\n        rc = SQLITE_CANTOPEN_BKPT;\n      }\n\n      if( rc==SQLITE_OK ){\n        nByte = osReadlink(zIn, zDel, nOut-1);\n        if( nByte<0 ){\n          rc = unixLogError(SQLITE_CANTOPEN_BKPT, \"readlink\", zIn);\n        }else{\n          if( zDel[0]!='/' ){\n            int n;\n            for(n = sqlite3Strlen30(zIn); n>0 && zIn[n-1]!='/'; n--);\n            if( nByte+n+1>nOut ){\n              rc = SQLITE_CANTOPEN_BKPT;\n            }else{\n              memmove(&zDel[n], zDel, nByte+1);\n              memcpy(zDel, zIn, n);\n              nByte += n;\n            }\n          }\n          zDel[nByte] = '\\0';\n        }\n      }\n\n      zIn = zDel;\n    }\n\n    assert( rc!=SQLITE_OK || zIn!=zOut || zIn[0]=='/' );\n    if( rc==SQLITE_OK && zIn!=zOut ){\n      rc = mkFullPathname(zIn, zOut, nOut);\n    }\n    if( bLink==0 ) break;\n    zIn = zOut;\n  }while( rc==SQLITE_OK );\n\n  sqlite3_free(zDel);\n  return rc;\n#endif   /* HAVE_READLINK && HAVE_LSTAT */\n}\n\n\n#ifndef SQLITE_OMIT_LOAD_EXTENSION\n/*\n** Interfaces for opening a shared library, finding entry points\n** within the shared library, and closing the shared library.\n*/\n#include <dlfcn.h>\nstatic void *unixDlOpen(sqlite3_vfs *NotUsed, const char *zFilename){\n  UNUSED_PARAMETER(NotUsed);\n  return dlopen(zFilename, RTLD_NOW | RTLD_GLOBAL);\n}\n\n/*\n** SQLite calls this function immediately after a call to unixDlSym() or\n** unixDlOpen() fails (returns a null pointer). If a more detailed error\n** message is available, it is written to zBufOut. If no error message\n** is available, zBufOut is left unmodified and SQLite uses a default\n** error message.\n*/\nstatic void unixDlError(sqlite3_vfs *NotUsed, int nBuf, char *zBufOut){\n  const char *zErr;\n  UNUSED_PARAMETER(NotUsed);\n  unixEnterMutex();\n  zErr = dlerror();\n  if( zErr ){\n    sqlite3_snprintf(nBuf, zBufOut, \"%s\", zErr);\n  }\n  unixLeaveMutex();\n}\nstatic void (*unixDlSym(sqlite3_vfs *NotUsed, void *p, const char*zSym))(void){\n  /* \n  ** GCC with -pedantic-errors says that C90 does not allow a void* to be\n  ** cast into a pointer to a function.  And yet the library dlsym() routine\n  ** returns a void* which is really a pointer to a function.  So how do we\n  ** use dlsym() with -pedantic-errors?\n  **\n  ** Variable x below is defined to be a pointer to a function taking\n  ** parameters void* and const char* and returning a pointer to a function.\n  ** We initialize x by assigning it a pointer to the dlsym() function.\n  ** (That assignment requires a cast.)  Then we call the function that\n  ** x points to.  \n  **\n  ** This work-around is unlikely to work correctly on any system where\n  ** you really cannot cast a function pointer into void*.  But then, on the\n  ** other hand, dlsym() will not work on such a system either, so we have\n  ** not really lost anything.\n  */\n  void (*(*x)(void*,const char*))(void);\n  UNUSED_PARAMETER(NotUsed);\n  x = (void(*(*)(void*,const char*))(void))dlsym;\n  return (*x)(p, zSym);\n}\nstatic void unixDlClose(sqlite3_vfs *NotUsed, void *pHandle){\n  UNUSED_PARAMETER(NotUsed);\n  dlclose(pHandle);\n}\n#else /* if SQLITE_OMIT_LOAD_EXTENSION is defined: */\n  #define unixDlOpen  0\n  #define unixDlError 0\n  #define unixDlSym   0\n  #define unixDlClose 0\n#endif\n\n/*\n** Write nBuf bytes of random data to the supplied buffer zBuf.\n*/\nstatic int unixRandomness(sqlite3_vfs *NotUsed, int nBuf, char *zBuf){\n  UNUSED_PARAMETER(NotUsed);\n  assert((size_t)nBuf>=(sizeof(time_t)+sizeof(int)));\n\n  /* We have to initialize zBuf to prevent valgrind from reporting\n  ** errors.  The reports issued by valgrind are incorrect - we would\n  ** prefer that the randomness be increased by making use of the\n  ** uninitialized space in zBuf - but valgrind errors tend to worry\n  ** some users.  Rather than argue, it seems easier just to initialize\n  ** the whole array and silence valgrind, even if that means less randomness\n  ** in the random seed.\n  **\n  ** When testing, initializing zBuf[] to zero is all we do.  That means\n  ** that we always use the same random number sequence.  This makes the\n  ** tests repeatable.\n  */\n  memset(zBuf, 0, nBuf);\n  randomnessPid = osGetpid(0);  \n#if !defined(SQLITE_TEST) && !defined(SQLITE_OMIT_RANDOMNESS)\n  {\n    int fd, got;\n    fd = robust_open(\"/dev/urandom\", O_RDONLY, 0);\n    if( fd<0 ){\n      time_t t;\n      time(&t);\n      memcpy(zBuf, &t, sizeof(t));\n      memcpy(&zBuf[sizeof(t)], &randomnessPid, sizeof(randomnessPid));\n      assert( sizeof(t)+sizeof(randomnessPid)<=(size_t)nBuf );\n      nBuf = sizeof(t) + sizeof(randomnessPid);\n    }else{\n      do{ got = osRead(fd, zBuf, nBuf); }while( got<0 && errno==EINTR );\n      robust_close(0, fd, __LINE__);\n    }\n  }\n#endif\n  return nBuf;\n}\n\n\n/*\n** Sleep for a little while.  Return the amount of time slept.\n** The argument is the number of microseconds we want to sleep.\n** The return value is the number of microseconds of sleep actually\n** requested from the underlying operating system, a number which\n** might be greater than or equal to the argument, but not less\n** than the argument.\n*/\nstatic int unixSleep(sqlite3_vfs *NotUsed, int microseconds){\n#if OS_VXWORKS\n  struct timespec sp;\n\n  sp.tv_sec = microseconds / 1000000;\n  sp.tv_nsec = (microseconds % 1000000) * 1000;\n  nanosleep(&sp, NULL);\n  UNUSED_PARAMETER(NotUsed);\n  return microseconds;\n#elif defined(HAVE_USLEEP) && HAVE_USLEEP\n  usleep(microseconds);\n  UNUSED_PARAMETER(NotUsed);\n  return microseconds;\n#else\n  int seconds = (microseconds+999999)/1000000;\n  sleep(seconds);\n  UNUSED_PARAMETER(NotUsed);\n  return seconds*1000000;\n#endif\n}\n\n/*\n** The following variable, if set to a non-zero value, is interpreted as\n** the number of seconds since 1970 and is used to set the result of\n** sqlite3OsCurrentTime() during testing.\n*/\n#ifdef SQLITE_TEST\nSQLITE_API int sqlite3_current_time = 0;  /* Fake system time in seconds since 1970. */\n#endif\n\n/*\n** Find the current time (in Universal Coordinated Time).  Write into *piNow\n** the current time and date as a Julian Day number times 86_400_000.  In\n** other words, write into *piNow the number of milliseconds since the Julian\n** epoch of noon in Greenwich on November 24, 4714 B.C according to the\n** proleptic Gregorian calendar.\n**\n** On success, return SQLITE_OK.  Return SQLITE_ERROR if the time and date \n** cannot be found.\n*/\nstatic int unixCurrentTimeInt64(sqlite3_vfs *NotUsed, sqlite3_int64 *piNow){\n  static const sqlite3_int64 unixEpoch = 24405875*(sqlite3_int64)8640000;\n  int rc = SQLITE_OK;\n#if defined(NO_GETTOD)\n  time_t t;\n  time(&t);\n  *piNow = ((sqlite3_int64)t)*1000 + unixEpoch;\n#elif OS_VXWORKS\n  struct timespec sNow;\n  clock_gettime(CLOCK_REALTIME, &sNow);\n  *piNow = unixEpoch + 1000*(sqlite3_int64)sNow.tv_sec + sNow.tv_nsec/1000000;\n#else\n  struct timeval sNow;\n  (void)gettimeofday(&sNow, 0);  /* Cannot fail given valid arguments */\n  *piNow = unixEpoch + 1000*(sqlite3_int64)sNow.tv_sec + sNow.tv_usec/1000;\n#endif\n\n#ifdef SQLITE_TEST\n  if( sqlite3_current_time ){\n    *piNow = 1000*(sqlite3_int64)sqlite3_current_time + unixEpoch;\n  }\n#endif\n  UNUSED_PARAMETER(NotUsed);\n  return rc;\n}\n\n#ifndef SQLITE_OMIT_DEPRECATED\n/*\n** Find the current time (in Universal Coordinated Time).  Write the\n** current time and date as a Julian Day number into *prNow and\n** return 0.  Return 1 if the time and date cannot be found.\n*/\nstatic int unixCurrentTime(sqlite3_vfs *NotUsed, double *prNow){\n  sqlite3_int64 i = 0;\n  int rc;\n  UNUSED_PARAMETER(NotUsed);\n  rc = unixCurrentTimeInt64(0, &i);\n  *prNow = i/86400000.0;\n  return rc;\n}\n#else\n# define unixCurrentTime 0\n#endif\n\n/*\n** The xGetLastError() method is designed to return a better\n** low-level error message when operating-system problems come up\n** during SQLite operation.  Only the integer return code is currently\n** used.\n*/\nstatic int unixGetLastError(sqlite3_vfs *NotUsed, int NotUsed2, char *NotUsed3){\n  UNUSED_PARAMETER(NotUsed);\n  UNUSED_PARAMETER(NotUsed2);\n  UNUSED_PARAMETER(NotUsed3);\n  return errno;\n}\n\n\n/*\n************************ End of sqlite3_vfs methods ***************************\n******************************************************************************/\n\n/******************************************************************************\n************************** Begin Proxy Locking ********************************\n**\n** Proxy locking is a \"uber-locking-method\" in this sense:  It uses the\n** other locking methods on secondary lock files.  Proxy locking is a\n** meta-layer over top of the primitive locking implemented above.  For\n** this reason, the division that implements of proxy locking is deferred\n** until late in the file (here) after all of the other I/O methods have\n** been defined - so that the primitive locking methods are available\n** as services to help with the implementation of proxy locking.\n**\n****\n**\n** The default locking schemes in SQLite use byte-range locks on the\n** database file to coordinate safe, concurrent access by multiple readers\n** and writers [http://sqlite.org/lockingv3.html].  The five file locking\n** states (UNLOCKED, PENDING, SHARED, RESERVED, EXCLUSIVE) are implemented\n** as POSIX read & write locks over fixed set of locations (via fsctl),\n** on AFP and SMB only exclusive byte-range locks are available via fsctl\n** with _IOWR('z', 23, struct ByteRangeLockPB2) to track the same 5 states.\n** To simulate a F_RDLCK on the shared range, on AFP a randomly selected\n** address in the shared range is taken for a SHARED lock, the entire\n** shared range is taken for an EXCLUSIVE lock):\n**\n**      PENDING_BYTE        0x40000000\n**      RESERVED_BYTE       0x40000001\n**      SHARED_RANGE        0x40000002 -> 0x40000200\n**\n** This works well on the local file system, but shows a nearly 100x\n** slowdown in read performance on AFP because the AFP client disables\n** the read cache when byte-range locks are present.  Enabling the read\n** cache exposes a cache coherency problem that is present on all OS X\n** supported network file systems.  NFS and AFP both observe the\n** close-to-open semantics for ensuring cache coherency\n** [http://nfs.sourceforge.net/#faq_a8], which does not effectively\n** address the requirements for concurrent database access by multiple\n** readers and writers\n** [http://www.nabble.com/SQLite-on-NFS-cache-coherency-td15655701.html].\n**\n** To address the performance and cache coherency issues, proxy file locking\n** changes the way database access is controlled by limiting access to a\n** single host at a time and moving file locks off of the database file\n** and onto a proxy file on the local file system.  \n**\n**\n** Using proxy locks\n** -----------------\n**\n** C APIs\n**\n**  sqlite3_file_control(db, dbname, SQLITE_FCNTL_SET_LOCKPROXYFILE,\n**                       <proxy_path> | \":auto:\");\n**  sqlite3_file_control(db, dbname, SQLITE_FCNTL_GET_LOCKPROXYFILE,\n**                       &<proxy_path>);\n**\n**\n** SQL pragmas\n**\n**  PRAGMA [database.]lock_proxy_file=<proxy_path> | :auto:\n**  PRAGMA [database.]lock_proxy_file\n**\n** Specifying \":auto:\" means that if there is a conch file with a matching\n** host ID in it, the proxy path in the conch file will be used, otherwise\n** a proxy path based on the user's temp dir\n** (via confstr(_CS_DARWIN_USER_TEMP_DIR,...)) will be used and the\n** actual proxy file name is generated from the name and path of the\n** database file.  For example:\n**\n**       For database path \"/Users/me/foo.db\" \n**       The lock path will be \"<tmpdir>/sqliteplocks/_Users_me_foo.db:auto:\")\n**\n** Once a lock proxy is configured for a database connection, it can not\n** be removed, however it may be switched to a different proxy path via\n** the above APIs (assuming the conch file is not being held by another\n** connection or process). \n**\n**\n** How proxy locking works\n** -----------------------\n**\n** Proxy file locking relies primarily on two new supporting files: \n**\n**   *  conch file to limit access to the database file to a single host\n**      at a time\n**\n**   *  proxy file to act as a proxy for the advisory locks normally\n**      taken on the database\n**\n** The conch file - to use a proxy file, sqlite must first \"hold the conch\"\n** by taking an sqlite-style shared lock on the conch file, reading the\n** contents and comparing the host's unique host ID (see below) and lock\n** proxy path against the values stored in the conch.  The conch file is\n** stored in the same directory as the database file and the file name\n** is patterned after the database file name as \".<databasename>-conch\".\n** If the conch file does not exist, or its contents do not match the\n** host ID and/or proxy path, then the lock is escalated to an exclusive\n** lock and the conch file contents is updated with the host ID and proxy\n** path and the lock is downgraded to a shared lock again.  If the conch\n** is held by another process (with a shared lock), the exclusive lock\n** will fail and SQLITE_BUSY is returned.\n**\n** The proxy file - a single-byte file used for all advisory file locks\n** normally taken on the database file.   This allows for safe sharing\n** of the database file for multiple readers and writers on the same\n** host (the conch ensures that they all use the same local lock file).\n**\n** Requesting the lock proxy does not immediately take the conch, it is\n** only taken when the first request to lock database file is made.  \n** This matches the semantics of the traditional locking behavior, where\n** opening a connection to a database file does not take a lock on it.\n** The shared lock and an open file descriptor are maintained until \n** the connection to the database is closed. \n**\n** The proxy file and the lock file are never deleted so they only need\n** to be created the first time they are used.\n**\n** Configuration options\n** ---------------------\n**\n**  SQLITE_PREFER_PROXY_LOCKING\n**\n**       Database files accessed on non-local file systems are\n**       automatically configured for proxy locking, lock files are\n**       named automatically using the same logic as\n**       PRAGMA lock_proxy_file=\":auto:\"\n**    \n**  SQLITE_PROXY_DEBUG\n**\n**       Enables the logging of error messages during host id file\n**       retrieval and creation\n**\n**  LOCKPROXYDIR\n**\n**       Overrides the default directory used for lock proxy files that\n**       are named automatically via the \":auto:\" setting\n**\n**  SQLITE_DEFAULT_PROXYDIR_PERMISSIONS\n**\n**       Permissions to use when creating a directory for storing the\n**       lock proxy files, only used when LOCKPROXYDIR is not set.\n**    \n**    \n** As mentioned above, when compiled with SQLITE_PREFER_PROXY_LOCKING,\n** setting the environment variable SQLITE_FORCE_PROXY_LOCKING to 1 will\n** force proxy locking to be used for every database file opened, and 0\n** will force automatic proxy locking to be disabled for all database\n** files (explicitly calling the SQLITE_FCNTL_SET_LOCKPROXYFILE pragma or\n** sqlite_file_control API is not affected by SQLITE_FORCE_PROXY_LOCKING).\n*/\n\n/*\n** Proxy locking is only available on MacOSX \n*/\n#if defined(__APPLE__) && SQLITE_ENABLE_LOCKING_STYLE\n\n/*\n** The proxyLockingContext has the path and file structures for the remote \n** and local proxy files in it\n*/\ntypedef struct proxyLockingContext proxyLockingContext;\nstruct proxyLockingContext {\n  unixFile *conchFile;         /* Open conch file */\n  char *conchFilePath;         /* Name of the conch file */\n  unixFile *lockProxy;         /* Open proxy lock file */\n  char *lockProxyPath;         /* Name of the proxy lock file */\n  char *dbPath;                /* Name of the open file */\n  int conchHeld;               /* 1 if the conch is held, -1 if lockless */\n  int nFails;                  /* Number of conch taking failures */\n  void *oldLockingContext;     /* Original lockingcontext to restore on close */\n  sqlite3_io_methods const *pOldMethod;     /* Original I/O methods for close */\n};\n\n/* \n** The proxy lock file path for the database at dbPath is written into lPath, \n** which must point to valid, writable memory large enough for a maxLen length\n** file path. \n*/\nstatic int proxyGetLockPath(const char *dbPath, char *lPath, size_t maxLen){\n  int len;\n  int dbLen;\n  int i;\n\n#ifdef LOCKPROXYDIR\n  len = strlcpy(lPath, LOCKPROXYDIR, maxLen);\n#else\n# ifdef _CS_DARWIN_USER_TEMP_DIR\n  {\n    if( !confstr(_CS_DARWIN_USER_TEMP_DIR, lPath, maxLen) ){\n      OSTRACE((\"GETLOCKPATH  failed %s errno=%d pid=%d\\n\",\n               lPath, errno, osGetpid(0)));\n      return SQLITE_IOERR_LOCK;\n    }\n    len = strlcat(lPath, \"sqliteplocks\", maxLen);    \n  }\n# else\n  len = strlcpy(lPath, \"/tmp/\", maxLen);\n# endif\n#endif\n\n  if( lPath[len-1]!='/' ){\n    len = strlcat(lPath, \"/\", maxLen);\n  }\n  \n  /* transform the db path to a unique cache name */\n  dbLen = (int)strlen(dbPath);\n  for( i=0; i<dbLen && (i+len+7)<(int)maxLen; i++){\n    char c = dbPath[i];\n    lPath[i+len] = (c=='/')?'_':c;\n  }\n  lPath[i+len]='\\0';\n  strlcat(lPath, \":auto:\", maxLen);\n  OSTRACE((\"GETLOCKPATH  proxy lock path=%s pid=%d\\n\", lPath, osGetpid(0)));\n  return SQLITE_OK;\n}\n\n/* \n ** Creates the lock file and any missing directories in lockPath\n */\nstatic int proxyCreateLockPath(const char *lockPath){\n  int i, len;\n  char buf[MAXPATHLEN];\n  int start = 0;\n  \n  assert(lockPath!=NULL);\n  /* try to create all the intermediate directories */\n  len = (int)strlen(lockPath);\n  buf[0] = lockPath[0];\n  for( i=1; i<len; i++ ){\n    if( lockPath[i] == '/' && (i - start > 0) ){\n      /* only mkdir if leaf dir != \".\" or \"/\" or \"..\" */\n      if( i-start>2 || (i-start==1 && buf[start] != '.' && buf[start] != '/') \n         || (i-start==2 && buf[start] != '.' && buf[start+1] != '.') ){\n        buf[i]='\\0';\n        if( osMkdir(buf, SQLITE_DEFAULT_PROXYDIR_PERMISSIONS) ){\n          int err=errno;\n          if( err!=EEXIST ) {\n            OSTRACE((\"CREATELOCKPATH  FAILED creating %s, \"\n                     \"'%s' proxy lock path=%s pid=%d\\n\",\n                     buf, strerror(err), lockPath, osGetpid(0)));\n            return err;\n          }\n        }\n      }\n      start=i+1;\n    }\n    buf[i] = lockPath[i];\n  }\n  OSTRACE((\"CREATELOCKPATH  proxy lock path=%s pid=%d\\n\",lockPath,osGetpid(0)));\n  return 0;\n}\n\n/*\n** Create a new VFS file descriptor (stored in memory obtained from\n** sqlite3_malloc) and open the file named \"path\" in the file descriptor.\n**\n** The caller is responsible not only for closing the file descriptor\n** but also for freeing the memory associated with the file descriptor.\n*/\nstatic int proxyCreateUnixFile(\n    const char *path,        /* path for the new unixFile */\n    unixFile **ppFile,       /* unixFile created and returned by ref */\n    int islockfile           /* if non zero missing dirs will be created */\n) {\n  int fd = -1;\n  unixFile *pNew;\n  int rc = SQLITE_OK;\n  int openFlags = O_RDWR | O_CREAT;\n  sqlite3_vfs dummyVfs;\n  int terrno = 0;\n  UnixUnusedFd *pUnused = NULL;\n\n  /* 1. first try to open/create the file\n  ** 2. if that fails, and this is a lock file (not-conch), try creating\n  ** the parent directories and then try again.\n  ** 3. if that fails, try to open the file read-only\n  ** otherwise return BUSY (if lock file) or CANTOPEN for the conch file\n  */\n  pUnused = findReusableFd(path, openFlags);\n  if( pUnused ){\n    fd = pUnused->fd;\n  }else{\n    pUnused = sqlite3_malloc64(sizeof(*pUnused));\n    if( !pUnused ){\n      return SQLITE_NOMEM_BKPT;\n    }\n  }\n  if( fd<0 ){\n    fd = robust_open(path, openFlags, 0);\n    terrno = errno;\n    if( fd<0 && errno==ENOENT && islockfile ){\n      if( proxyCreateLockPath(path) == SQLITE_OK ){\n        fd = robust_open(path, openFlags, 0);\n      }\n    }\n  }\n  if( fd<0 ){\n    openFlags = O_RDONLY;\n    fd = robust_open(path, openFlags, 0);\n    terrno = errno;\n  }\n  if( fd<0 ){\n    if( islockfile ){\n      return SQLITE_BUSY;\n    }\n    switch (terrno) {\n      case EACCES:\n        return SQLITE_PERM;\n      case EIO: \n        return SQLITE_IOERR_LOCK; /* even though it is the conch */\n      default:\n        return SQLITE_CANTOPEN_BKPT;\n    }\n  }\n  \n  pNew = (unixFile *)sqlite3_malloc64(sizeof(*pNew));\n  if( pNew==NULL ){\n    rc = SQLITE_NOMEM_BKPT;\n    goto end_create_proxy;\n  }\n  memset(pNew, 0, sizeof(unixFile));\n  pNew->openFlags = openFlags;\n  memset(&dummyVfs, 0, sizeof(dummyVfs));\n  dummyVfs.pAppData = (void*)&autolockIoFinder;\n  dummyVfs.zName = \"dummy\";\n  pUnused->fd = fd;\n  pUnused->flags = openFlags;\n  pNew->pPreallocatedUnused = pUnused;\n  \n  rc = fillInUnixFile(&dummyVfs, fd, (sqlite3_file*)pNew, path, 0);\n  if( rc==SQLITE_OK ){\n    *ppFile = pNew;\n    return SQLITE_OK;\n  }\nend_create_proxy:    \n  robust_close(pNew, fd, __LINE__);\n  sqlite3_free(pNew);\n  sqlite3_free(pUnused);\n  return rc;\n}\n\n#ifdef SQLITE_TEST\n/* simulate multiple hosts by creating unique hostid file paths */\nSQLITE_API int sqlite3_hostid_num = 0;\n#endif\n\n#define PROXY_HOSTIDLEN    16  /* conch file host id length */\n\n#ifdef HAVE_GETHOSTUUID\n/* Not always defined in the headers as it ought to be */\nextern int gethostuuid(uuid_t id, const struct timespec *wait);\n#endif\n\n/* get the host ID via gethostuuid(), pHostID must point to PROXY_HOSTIDLEN \n** bytes of writable memory.\n*/\nstatic int proxyGetHostID(unsigned char *pHostID, int *pError){\n  assert(PROXY_HOSTIDLEN == sizeof(uuid_t));\n  memset(pHostID, 0, PROXY_HOSTIDLEN);\n#ifdef HAVE_GETHOSTUUID\n  {\n    struct timespec timeout = {1, 0}; /* 1 sec timeout */\n    if( gethostuuid(pHostID, &timeout) ){\n      int err = errno;\n      if( pError ){\n        *pError = err;\n      }\n      return SQLITE_IOERR;\n    }\n  }\n#else\n  UNUSED_PARAMETER(pError);\n#endif\n#ifdef SQLITE_TEST\n  /* simulate multiple hosts by creating unique hostid file paths */\n  if( sqlite3_hostid_num != 0){\n    pHostID[0] = (char)(pHostID[0] + (char)(sqlite3_hostid_num & 0xFF));\n  }\n#endif\n  \n  return SQLITE_OK;\n}\n\n/* The conch file contains the header, host id and lock file path\n */\n#define PROXY_CONCHVERSION 2   /* 1-byte header, 16-byte host id, path */\n#define PROXY_HEADERLEN    1   /* conch file header length */\n#define PROXY_PATHINDEX    (PROXY_HEADERLEN+PROXY_HOSTIDLEN)\n#define PROXY_MAXCONCHLEN  (PROXY_HEADERLEN+PROXY_HOSTIDLEN+MAXPATHLEN)\n\n/* \n** Takes an open conch file, copies the contents to a new path and then moves \n** it back.  The newly created file's file descriptor is assigned to the\n** conch file structure and finally the original conch file descriptor is \n** closed.  Returns zero if successful.\n*/\nstatic int proxyBreakConchLock(unixFile *pFile, uuid_t myHostID){\n  proxyLockingContext *pCtx = (proxyLockingContext *)pFile->lockingContext; \n  unixFile *conchFile = pCtx->conchFile;\n  char tPath[MAXPATHLEN];\n  char buf[PROXY_MAXCONCHLEN];\n  char *cPath = pCtx->conchFilePath;\n  size_t readLen = 0;\n  size_t pathLen = 0;\n  char errmsg[64] = \"\";\n  int fd = -1;\n  int rc = -1;\n  UNUSED_PARAMETER(myHostID);\n\n  /* create a new path by replace the trailing '-conch' with '-break' */\n  pathLen = strlcpy(tPath, cPath, MAXPATHLEN);\n  if( pathLen>MAXPATHLEN || pathLen<6 || \n     (strlcpy(&tPath[pathLen-5], \"break\", 6) != 5) ){\n    sqlite3_snprintf(sizeof(errmsg),errmsg,\"path error (len %d)\",(int)pathLen);\n    goto end_breaklock;\n  }\n  /* read the conch content */\n  readLen = osPread(conchFile->h, buf, PROXY_MAXCONCHLEN, 0);\n  if( readLen<PROXY_PATHINDEX ){\n    sqlite3_snprintf(sizeof(errmsg),errmsg,\"read error (len %d)\",(int)readLen);\n    goto end_breaklock;\n  }\n  /* write it out to the temporary break file */\n  fd = robust_open(tPath, (O_RDWR|O_CREAT|O_EXCL), 0);\n  if( fd<0 ){\n    sqlite3_snprintf(sizeof(errmsg), errmsg, \"create failed (%d)\", errno);\n    goto end_breaklock;\n  }\n  if( osPwrite(fd, buf, readLen, 0) != (ssize_t)readLen ){\n    sqlite3_snprintf(sizeof(errmsg), errmsg, \"write failed (%d)\", errno);\n    goto end_breaklock;\n  }\n  if( rename(tPath, cPath) ){\n    sqlite3_snprintf(sizeof(errmsg), errmsg, \"rename failed (%d)\", errno);\n    goto end_breaklock;\n  }\n  rc = 0;\n  fprintf(stderr, \"broke stale lock on %s\\n\", cPath);\n  robust_close(pFile, conchFile->h, __LINE__);\n  conchFile->h = fd;\n  conchFile->openFlags = O_RDWR | O_CREAT;\n\nend_breaklock:\n  if( rc ){\n    if( fd>=0 ){\n      osUnlink(tPath);\n      robust_close(pFile, fd, __LINE__);\n    }\n    fprintf(stderr, \"failed to break stale lock on %s, %s\\n\", cPath, errmsg);\n  }\n  return rc;\n}\n\n/* Take the requested lock on the conch file and break a stale lock if the \n** host id matches.\n*/\nstatic int proxyConchLock(unixFile *pFile, uuid_t myHostID, int lockType){\n  proxyLockingContext *pCtx = (proxyLockingContext *)pFile->lockingContext; \n  unixFile *conchFile = pCtx->conchFile;\n  int rc = SQLITE_OK;\n  int nTries = 0;\n  struct timespec conchModTime;\n  \n  memset(&conchModTime, 0, sizeof(conchModTime));\n  do {\n    rc = conchFile->pMethod->xLock((sqlite3_file*)conchFile, lockType);\n    nTries ++;\n    if( rc==SQLITE_BUSY ){\n      /* If the lock failed (busy):\n       * 1st try: get the mod time of the conch, wait 0.5s and try again. \n       * 2nd try: fail if the mod time changed or host id is different, wait \n       *           10 sec and try again\n       * 3rd try: break the lock unless the mod time has changed.\n       */\n      struct stat buf;\n      if( osFstat(conchFile->h, &buf) ){\n        storeLastErrno(pFile, errno);\n        return SQLITE_IOERR_LOCK;\n      }\n      \n      if( nTries==1 ){\n        conchModTime = buf.st_mtimespec;\n        usleep(500000); /* wait 0.5 sec and try the lock again*/\n        continue;  \n      }\n\n      assert( nTries>1 );\n      if( conchModTime.tv_sec != buf.st_mtimespec.tv_sec || \n         conchModTime.tv_nsec != buf.st_mtimespec.tv_nsec ){\n        return SQLITE_BUSY;\n      }\n      \n      if( nTries==2 ){  \n        char tBuf[PROXY_MAXCONCHLEN];\n        int len = osPread(conchFile->h, tBuf, PROXY_MAXCONCHLEN, 0);\n        if( len<0 ){\n          storeLastErrno(pFile, errno);\n          return SQLITE_IOERR_LOCK;\n        }\n        if( len>PROXY_PATHINDEX && tBuf[0]==(char)PROXY_CONCHVERSION){\n          /* don't break the lock if the host id doesn't match */\n          if( 0!=memcmp(&tBuf[PROXY_HEADERLEN], myHostID, PROXY_HOSTIDLEN) ){\n            return SQLITE_BUSY;\n          }\n        }else{\n          /* don't break the lock on short read or a version mismatch */\n          return SQLITE_BUSY;\n        }\n        usleep(10000000); /* wait 10 sec and try the lock again */\n        continue; \n      }\n      \n      assert( nTries==3 );\n      if( 0==proxyBreakConchLock(pFile, myHostID) ){\n        rc = SQLITE_OK;\n        if( lockType==EXCLUSIVE_LOCK ){\n          rc = conchFile->pMethod->xLock((sqlite3_file*)conchFile, SHARED_LOCK);\n        }\n        if( !rc ){\n          rc = conchFile->pMethod->xLock((sqlite3_file*)conchFile, lockType);\n        }\n      }\n    }\n  } while( rc==SQLITE_BUSY && nTries<3 );\n  \n  return rc;\n}\n\n/* Takes the conch by taking a shared lock and read the contents conch, if \n** lockPath is non-NULL, the host ID and lock file path must match.  A NULL \n** lockPath means that the lockPath in the conch file will be used if the \n** host IDs match, or a new lock path will be generated automatically \n** and written to the conch file.\n*/\nstatic int proxyTakeConch(unixFile *pFile){\n  proxyLockingContext *pCtx = (proxyLockingContext *)pFile->lockingContext; \n  \n  if( pCtx->conchHeld!=0 ){\n    return SQLITE_OK;\n  }else{\n    unixFile *conchFile = pCtx->conchFile;\n    uuid_t myHostID;\n    int pError = 0;\n    char readBuf[PROXY_MAXCONCHLEN];\n    char lockPath[MAXPATHLEN];\n    char *tempLockPath = NULL;\n    int rc = SQLITE_OK;\n    int createConch = 0;\n    int hostIdMatch = 0;\n    int readLen = 0;\n    int tryOldLockPath = 0;\n    int forceNewLockPath = 0;\n    \n    OSTRACE((\"TAKECONCH  %d for %s pid=%d\\n\", conchFile->h,\n             (pCtx->lockProxyPath ? pCtx->lockProxyPath : \":auto:\"),\n             osGetpid(0)));\n\n    rc = proxyGetHostID(myHostID, &pError);\n    if( (rc&0xff)==SQLITE_IOERR ){\n      storeLastErrno(pFile, pError);\n      goto end_takeconch;\n    }\n    rc = proxyConchLock(pFile, myHostID, SHARED_LOCK);\n    if( rc!=SQLITE_OK ){\n      goto end_takeconch;\n    }\n    /* read the existing conch file */\n    readLen = seekAndRead((unixFile*)conchFile, 0, readBuf, PROXY_MAXCONCHLEN);\n    if( readLen<0 ){\n      /* I/O error: lastErrno set by seekAndRead */\n      storeLastErrno(pFile, conchFile->lastErrno);\n      rc = SQLITE_IOERR_READ;\n      goto end_takeconch;\n    }else if( readLen<=(PROXY_HEADERLEN+PROXY_HOSTIDLEN) || \n             readBuf[0]!=(char)PROXY_CONCHVERSION ){\n      /* a short read or version format mismatch means we need to create a new \n      ** conch file. \n      */\n      createConch = 1;\n    }\n    /* if the host id matches and the lock path already exists in the conch\n    ** we'll try to use the path there, if we can't open that path, we'll \n    ** retry with a new auto-generated path \n    */\n    do { /* in case we need to try again for an :auto: named lock file */\n\n      if( !createConch && !forceNewLockPath ){\n        hostIdMatch = !memcmp(&readBuf[PROXY_HEADERLEN], myHostID, \n                                  PROXY_HOSTIDLEN);\n        /* if the conch has data compare the contents */\n        if( !pCtx->lockProxyPath ){\n          /* for auto-named local lock file, just check the host ID and we'll\n           ** use the local lock file path that's already in there\n           */\n          if( hostIdMatch ){\n            size_t pathLen = (readLen - PROXY_PATHINDEX);\n            \n            if( pathLen>=MAXPATHLEN ){\n              pathLen=MAXPATHLEN-1;\n            }\n            memcpy(lockPath, &readBuf[PROXY_PATHINDEX], pathLen);\n            lockPath[pathLen] = 0;\n            tempLockPath = lockPath;\n            tryOldLockPath = 1;\n            /* create a copy of the lock path if the conch is taken */\n            goto end_takeconch;\n          }\n        }else if( hostIdMatch\n               && !strncmp(pCtx->lockProxyPath, &readBuf[PROXY_PATHINDEX],\n                           readLen-PROXY_PATHINDEX)\n        ){\n          /* conch host and lock path match */\n          goto end_takeconch; \n        }\n      }\n      \n      /* if the conch isn't writable and doesn't match, we can't take it */\n      if( (conchFile->openFlags&O_RDWR) == 0 ){\n        rc = SQLITE_BUSY;\n        goto end_takeconch;\n      }\n      \n      /* either the conch didn't match or we need to create a new one */\n      if( !pCtx->lockProxyPath ){\n        proxyGetLockPath(pCtx->dbPath, lockPath, MAXPATHLEN);\n        tempLockPath = lockPath;\n        /* create a copy of the lock path _only_ if the conch is taken */\n      }\n      \n      /* update conch with host and path (this will fail if other process\n      ** has a shared lock already), if the host id matches, use the big\n      ** stick.\n      */\n      futimes(conchFile->h, NULL);\n      if( hostIdMatch && !createConch ){\n        if( conchFile->pInode && conchFile->pInode->nShared>1 ){\n          /* We are trying for an exclusive lock but another thread in this\n           ** same process is still holding a shared lock. */\n          rc = SQLITE_BUSY;\n        } else {          \n          rc = proxyConchLock(pFile, myHostID, EXCLUSIVE_LOCK);\n        }\n      }else{\n        rc = proxyConchLock(pFile, myHostID, EXCLUSIVE_LOCK);\n      }\n      if( rc==SQLITE_OK ){\n        char writeBuffer[PROXY_MAXCONCHLEN];\n        int writeSize = 0;\n        \n        writeBuffer[0] = (char)PROXY_CONCHVERSION;\n        memcpy(&writeBuffer[PROXY_HEADERLEN], myHostID, PROXY_HOSTIDLEN);\n        if( pCtx->lockProxyPath!=NULL ){\n          strlcpy(&writeBuffer[PROXY_PATHINDEX], pCtx->lockProxyPath,\n                  MAXPATHLEN);\n        }else{\n          strlcpy(&writeBuffer[PROXY_PATHINDEX], tempLockPath, MAXPATHLEN);\n        }\n        writeSize = PROXY_PATHINDEX + strlen(&writeBuffer[PROXY_PATHINDEX]);\n        robust_ftruncate(conchFile->h, writeSize);\n        rc = unixWrite((sqlite3_file *)conchFile, writeBuffer, writeSize, 0);\n        full_fsync(conchFile->h,0,0);\n        /* If we created a new conch file (not just updated the contents of a \n         ** valid conch file), try to match the permissions of the database \n         */\n        if( rc==SQLITE_OK && createConch ){\n          struct stat buf;\n          int err = osFstat(pFile->h, &buf);\n          if( err==0 ){\n            mode_t cmode = buf.st_mode&(S_IRUSR|S_IWUSR | S_IRGRP|S_IWGRP |\n                                        S_IROTH|S_IWOTH);\n            /* try to match the database file R/W permissions, ignore failure */\n#ifndef SQLITE_PROXY_DEBUG\n            osFchmod(conchFile->h, cmode);\n#else\n            do{\n              rc = osFchmod(conchFile->h, cmode);\n            }while( rc==(-1) && errno==EINTR );\n            if( rc!=0 ){\n              int code = errno;\n              fprintf(stderr, \"fchmod %o FAILED with %d %s\\n\",\n                      cmode, code, strerror(code));\n            } else {\n              fprintf(stderr, \"fchmod %o SUCCEDED\\n\",cmode);\n            }\n          }else{\n            int code = errno;\n            fprintf(stderr, \"STAT FAILED[%d] with %d %s\\n\", \n                    err, code, strerror(code));\n#endif\n          }\n        }\n      }\n      conchFile->pMethod->xUnlock((sqlite3_file*)conchFile, SHARED_LOCK);\n      \n    end_takeconch:\n      OSTRACE((\"TRANSPROXY: CLOSE  %d\\n\", pFile->h));\n      if( rc==SQLITE_OK && pFile->openFlags ){\n        int fd;\n        if( pFile->h>=0 ){\n          robust_close(pFile, pFile->h, __LINE__);\n        }\n        pFile->h = -1;\n        fd = robust_open(pCtx->dbPath, pFile->openFlags, 0);\n        OSTRACE((\"TRANSPROXY: OPEN  %d\\n\", fd));\n        if( fd>=0 ){\n          pFile->h = fd;\n        }else{\n          rc=SQLITE_CANTOPEN_BKPT; /* SQLITE_BUSY? proxyTakeConch called\n           during locking */\n        }\n      }\n      if( rc==SQLITE_OK && !pCtx->lockProxy ){\n        char *path = tempLockPath ? tempLockPath : pCtx->lockProxyPath;\n        rc = proxyCreateUnixFile(path, &pCtx->lockProxy, 1);\n        if( rc!=SQLITE_OK && rc!=SQLITE_NOMEM && tryOldLockPath ){\n          /* we couldn't create the proxy lock file with the old lock file path\n           ** so try again via auto-naming \n           */\n          forceNewLockPath = 1;\n          tryOldLockPath = 0;\n          continue; /* go back to the do {} while start point, try again */\n        }\n      }\n      if( rc==SQLITE_OK ){\n        /* Need to make a copy of path if we extracted the value\n         ** from the conch file or the path was allocated on the stack\n         */\n        if( tempLockPath ){\n          pCtx->lockProxyPath = sqlite3DbStrDup(0, tempLockPath);\n          if( !pCtx->lockProxyPath ){\n            rc = SQLITE_NOMEM_BKPT;\n          }\n        }\n      }\n      if( rc==SQLITE_OK ){\n        pCtx->conchHeld = 1;\n        \n        if( pCtx->lockProxy->pMethod == &afpIoMethods ){\n          afpLockingContext *afpCtx;\n          afpCtx = (afpLockingContext *)pCtx->lockProxy->lockingContext;\n          afpCtx->dbPath = pCtx->lockProxyPath;\n        }\n      } else {\n        conchFile->pMethod->xUnlock((sqlite3_file*)conchFile, NO_LOCK);\n      }\n      OSTRACE((\"TAKECONCH  %d %s\\n\", conchFile->h,\n               rc==SQLITE_OK?\"ok\":\"failed\"));\n      return rc;\n    } while (1); /* in case we need to retry the :auto: lock file - \n                 ** we should never get here except via the 'continue' call. */\n  }\n}\n\n/*\n** If pFile holds a lock on a conch file, then release that lock.\n*/\nstatic int proxyReleaseConch(unixFile *pFile){\n  int rc = SQLITE_OK;         /* Subroutine return code */\n  proxyLockingContext *pCtx;  /* The locking context for the proxy lock */\n  unixFile *conchFile;        /* Name of the conch file */\n\n  pCtx = (proxyLockingContext *)pFile->lockingContext;\n  conchFile = pCtx->conchFile;\n  OSTRACE((\"RELEASECONCH  %d for %s pid=%d\\n\", conchFile->h,\n           (pCtx->lockProxyPath ? pCtx->lockProxyPath : \":auto:\"), \n           osGetpid(0)));\n  if( pCtx->conchHeld>0 ){\n    rc = conchFile->pMethod->xUnlock((sqlite3_file*)conchFile, NO_LOCK);\n  }\n  pCtx->conchHeld = 0;\n  OSTRACE((\"RELEASECONCH  %d %s\\n\", conchFile->h,\n           (rc==SQLITE_OK ? \"ok\" : \"failed\")));\n  return rc;\n}\n\n/*\n** Given the name of a database file, compute the name of its conch file.\n** Store the conch filename in memory obtained from sqlite3_malloc64().\n** Make *pConchPath point to the new name.  Return SQLITE_OK on success\n** or SQLITE_NOMEM if unable to obtain memory.\n**\n** The caller is responsible for ensuring that the allocated memory\n** space is eventually freed.\n**\n** *pConchPath is set to NULL if a memory allocation error occurs.\n*/\nstatic int proxyCreateConchPathname(char *dbPath, char **pConchPath){\n  int i;                        /* Loop counter */\n  int len = (int)strlen(dbPath); /* Length of database filename - dbPath */\n  char *conchPath;              /* buffer in which to construct conch name */\n\n  /* Allocate space for the conch filename and initialize the name to\n  ** the name of the original database file. */  \n  *pConchPath = conchPath = (char *)sqlite3_malloc64(len + 8);\n  if( conchPath==0 ){\n    return SQLITE_NOMEM_BKPT;\n  }\n  memcpy(conchPath, dbPath, len+1);\n  \n  /* now insert a \".\" before the last / character */\n  for( i=(len-1); i>=0; i-- ){\n    if( conchPath[i]=='/' ){\n      i++;\n      break;\n    }\n  }\n  conchPath[i]='.';\n  while ( i<len ){\n    conchPath[i+1]=dbPath[i];\n    i++;\n  }\n\n  /* append the \"-conch\" suffix to the file */\n  memcpy(&conchPath[i+1], \"-conch\", 7);\n  assert( (int)strlen(conchPath) == len+7 );\n\n  return SQLITE_OK;\n}\n\n\n/* Takes a fully configured proxy locking-style unix file and switches\n** the local lock file path \n*/\nstatic int switchLockProxyPath(unixFile *pFile, const char *path) {\n  proxyLockingContext *pCtx = (proxyLockingContext*)pFile->lockingContext;\n  char *oldPath = pCtx->lockProxyPath;\n  int rc = SQLITE_OK;\n\n  if( pFile->eFileLock!=NO_LOCK ){\n    return SQLITE_BUSY;\n  }  \n\n  /* nothing to do if the path is NULL, :auto: or matches the existing path */\n  if( !path || path[0]=='\\0' || !strcmp(path, \":auto:\") ||\n    (oldPath && !strncmp(oldPath, path, MAXPATHLEN)) ){\n    return SQLITE_OK;\n  }else{\n    unixFile *lockProxy = pCtx->lockProxy;\n    pCtx->lockProxy=NULL;\n    pCtx->conchHeld = 0;\n    if( lockProxy!=NULL ){\n      rc=lockProxy->pMethod->xClose((sqlite3_file *)lockProxy);\n      if( rc ) return rc;\n      sqlite3_free(lockProxy);\n    }\n    sqlite3_free(oldPath);\n    pCtx->lockProxyPath = sqlite3DbStrDup(0, path);\n  }\n  \n  return rc;\n}\n\n/*\n** pFile is a file that has been opened by a prior xOpen call.  dbPath\n** is a string buffer at least MAXPATHLEN+1 characters in size.\n**\n** This routine find the filename associated with pFile and writes it\n** int dbPath.\n*/\nstatic int proxyGetDbPathForUnixFile(unixFile *pFile, char *dbPath){\n#if defined(__APPLE__)\n  if( pFile->pMethod == &afpIoMethods ){\n    /* afp style keeps a reference to the db path in the filePath field \n    ** of the struct */\n    assert( (int)strlen((char*)pFile->lockingContext)<=MAXPATHLEN );\n    strlcpy(dbPath, ((afpLockingContext *)pFile->lockingContext)->dbPath,\n            MAXPATHLEN);\n  } else\n#endif\n  if( pFile->pMethod == &dotlockIoMethods ){\n    /* dot lock style uses the locking context to store the dot lock\n    ** file path */\n    int len = strlen((char *)pFile->lockingContext) - strlen(DOTLOCK_SUFFIX);\n    memcpy(dbPath, (char *)pFile->lockingContext, len + 1);\n  }else{\n    /* all other styles use the locking context to store the db file path */\n    assert( strlen((char*)pFile->lockingContext)<=MAXPATHLEN );\n    strlcpy(dbPath, (char *)pFile->lockingContext, MAXPATHLEN);\n  }\n  return SQLITE_OK;\n}\n\n/*\n** Takes an already filled in unix file and alters it so all file locking \n** will be performed on the local proxy lock file.  The following fields\n** are preserved in the locking context so that they can be restored and \n** the unix structure properly cleaned up at close time:\n**  ->lockingContext\n**  ->pMethod\n*/\nstatic int proxyTransformUnixFile(unixFile *pFile, const char *path) {\n  proxyLockingContext *pCtx;\n  char dbPath[MAXPATHLEN+1];       /* Name of the database file */\n  char *lockPath=NULL;\n  int rc = SQLITE_OK;\n  \n  if( pFile->eFileLock!=NO_LOCK ){\n    return SQLITE_BUSY;\n  }\n  proxyGetDbPathForUnixFile(pFile, dbPath);\n  if( !path || path[0]=='\\0' || !strcmp(path, \":auto:\") ){\n    lockPath=NULL;\n  }else{\n    lockPath=(char *)path;\n  }\n  \n  OSTRACE((\"TRANSPROXY  %d for %s pid=%d\\n\", pFile->h,\n           (lockPath ? lockPath : \":auto:\"), osGetpid(0)));\n\n  pCtx = sqlite3_malloc64( sizeof(*pCtx) );\n  if( pCtx==0 ){\n    return SQLITE_NOMEM_BKPT;\n  }\n  memset(pCtx, 0, sizeof(*pCtx));\n\n  rc = proxyCreateConchPathname(dbPath, &pCtx->conchFilePath);\n  if( rc==SQLITE_OK ){\n    rc = proxyCreateUnixFile(pCtx->conchFilePath, &pCtx->conchFile, 0);\n    if( rc==SQLITE_CANTOPEN && ((pFile->openFlags&O_RDWR) == 0) ){\n      /* if (a) the open flags are not O_RDWR, (b) the conch isn't there, and\n      ** (c) the file system is read-only, then enable no-locking access.\n      ** Ugh, since O_RDONLY==0x0000 we test for !O_RDWR since unixOpen asserts\n      ** that openFlags will have only one of O_RDONLY or O_RDWR.\n      */\n      struct statfs fsInfo;\n      struct stat conchInfo;\n      int goLockless = 0;\n\n      if( osStat(pCtx->conchFilePath, &conchInfo) == -1 ) {\n        int err = errno;\n        if( (err==ENOENT) && (statfs(dbPath, &fsInfo) != -1) ){\n          goLockless = (fsInfo.f_flags&MNT_RDONLY) == MNT_RDONLY;\n        }\n      }\n      if( goLockless ){\n        pCtx->conchHeld = -1; /* read only FS/ lockless */\n        rc = SQLITE_OK;\n      }\n    }\n  }  \n  if( rc==SQLITE_OK && lockPath ){\n    pCtx->lockProxyPath = sqlite3DbStrDup(0, lockPath);\n  }\n\n  if( rc==SQLITE_OK ){\n    pCtx->dbPath = sqlite3DbStrDup(0, dbPath);\n    if( pCtx->dbPath==NULL ){\n      rc = SQLITE_NOMEM_BKPT;\n    }\n  }\n  if( rc==SQLITE_OK ){\n    /* all memory is allocated, proxys are created and assigned, \n    ** switch the locking context and pMethod then return.\n    */\n    pCtx->oldLockingContext = pFile->lockingContext;\n    pFile->lockingContext = pCtx;\n    pCtx->pOldMethod = pFile->pMethod;\n    pFile->pMethod = &proxyIoMethods;\n  }else{\n    if( pCtx->conchFile ){ \n      pCtx->conchFile->pMethod->xClose((sqlite3_file *)pCtx->conchFile);\n      sqlite3_free(pCtx->conchFile);\n    }\n    sqlite3DbFree(0, pCtx->lockProxyPath);\n    sqlite3_free(pCtx->conchFilePath); \n    sqlite3_free(pCtx);\n  }\n  OSTRACE((\"TRANSPROXY  %d %s\\n\", pFile->h,\n           (rc==SQLITE_OK ? \"ok\" : \"failed\")));\n  return rc;\n}\n\n\n/*\n** This routine handles sqlite3_file_control() calls that are specific\n** to proxy locking.\n*/\nstatic int proxyFileControl(sqlite3_file *id, int op, void *pArg){\n  switch( op ){\n    case SQLITE_FCNTL_GET_LOCKPROXYFILE: {\n      unixFile *pFile = (unixFile*)id;\n      if( pFile->pMethod == &proxyIoMethods ){\n        proxyLockingContext *pCtx = (proxyLockingContext*)pFile->lockingContext;\n        proxyTakeConch(pFile);\n        if( pCtx->lockProxyPath ){\n          *(const char **)pArg = pCtx->lockProxyPath;\n        }else{\n          *(const char **)pArg = \":auto: (not held)\";\n        }\n      } else {\n        *(const char **)pArg = NULL;\n      }\n      return SQLITE_OK;\n    }\n    case SQLITE_FCNTL_SET_LOCKPROXYFILE: {\n      unixFile *pFile = (unixFile*)id;\n      int rc = SQLITE_OK;\n      int isProxyStyle = (pFile->pMethod == &proxyIoMethods);\n      if( pArg==NULL || (const char *)pArg==0 ){\n        if( isProxyStyle ){\n          /* turn off proxy locking - not supported.  If support is added for\n          ** switching proxy locking mode off then it will need to fail if\n          ** the journal mode is WAL mode. \n          */\n          rc = SQLITE_ERROR /*SQLITE_PROTOCOL? SQLITE_MISUSE?*/;\n        }else{\n          /* turn off proxy locking - already off - NOOP */\n          rc = SQLITE_OK;\n        }\n      }else{\n        const char *proxyPath = (const char *)pArg;\n        if( isProxyStyle ){\n          proxyLockingContext *pCtx = \n            (proxyLockingContext*)pFile->lockingContext;\n          if( !strcmp(pArg, \":auto:\") \n           || (pCtx->lockProxyPath &&\n               !strncmp(pCtx->lockProxyPath, proxyPath, MAXPATHLEN))\n          ){\n            rc = SQLITE_OK;\n          }else{\n            rc = switchLockProxyPath(pFile, proxyPath);\n          }\n        }else{\n          /* turn on proxy file locking */\n          rc = proxyTransformUnixFile(pFile, proxyPath);\n        }\n      }\n      return rc;\n    }\n    default: {\n      assert( 0 );  /* The call assures that only valid opcodes are sent */\n    }\n  }\n  /*NOTREACHED*/\n  return SQLITE_ERROR;\n}\n\n/*\n** Within this division (the proxying locking implementation) the procedures\n** above this point are all utilities.  The lock-related methods of the\n** proxy-locking sqlite3_io_method object follow.\n*/\n\n\n/*\n** This routine checks if there is a RESERVED lock held on the specified\n** file by this or any other process. If such a lock is held, set *pResOut\n** to a non-zero value otherwise *pResOut is set to zero.  The return value\n** is set to SQLITE_OK unless an I/O error occurs during lock checking.\n*/\nstatic int proxyCheckReservedLock(sqlite3_file *id, int *pResOut) {\n  unixFile *pFile = (unixFile*)id;\n  int rc = proxyTakeConch(pFile);\n  if( rc==SQLITE_OK ){\n    proxyLockingContext *pCtx = (proxyLockingContext *)pFile->lockingContext;\n    if( pCtx->conchHeld>0 ){\n      unixFile *proxy = pCtx->lockProxy;\n      return proxy->pMethod->xCheckReservedLock((sqlite3_file*)proxy, pResOut);\n    }else{ /* conchHeld < 0 is lockless */\n      pResOut=0;\n    }\n  }\n  return rc;\n}\n\n/*\n** Lock the file with the lock specified by parameter eFileLock - one\n** of the following:\n**\n**     (1) SHARED_LOCK\n**     (2) RESERVED_LOCK\n**     (3) PENDING_LOCK\n**     (4) EXCLUSIVE_LOCK\n**\n** Sometimes when requesting one lock state, additional lock states\n** are inserted in between.  The locking might fail on one of the later\n** transitions leaving the lock state different from what it started but\n** still short of its goal.  The following chart shows the allowed\n** transitions and the inserted intermediate states:\n**\n**    UNLOCKED -> SHARED\n**    SHARED -> RESERVED\n**    SHARED -> (PENDING) -> EXCLUSIVE\n**    RESERVED -> (PENDING) -> EXCLUSIVE\n**    PENDING -> EXCLUSIVE\n**\n** This routine will only increase a lock.  Use the sqlite3OsUnlock()\n** routine to lower a locking level.\n*/\nstatic int proxyLock(sqlite3_file *id, int eFileLock) {\n  unixFile *pFile = (unixFile*)id;\n  int rc = proxyTakeConch(pFile);\n  if( rc==SQLITE_OK ){\n    proxyLockingContext *pCtx = (proxyLockingContext *)pFile->lockingContext;\n    if( pCtx->conchHeld>0 ){\n      unixFile *proxy = pCtx->lockProxy;\n      rc = proxy->pMethod->xLock((sqlite3_file*)proxy, eFileLock);\n      pFile->eFileLock = proxy->eFileLock;\n    }else{\n      /* conchHeld < 0 is lockless */\n    }\n  }\n  return rc;\n}\n\n\n/*\n** Lower the locking level on file descriptor pFile to eFileLock.  eFileLock\n** must be either NO_LOCK or SHARED_LOCK.\n**\n** If the locking level of the file descriptor is already at or below\n** the requested locking level, this routine is a no-op.\n*/\nstatic int proxyUnlock(sqlite3_file *id, int eFileLock) {\n  unixFile *pFile = (unixFile*)id;\n  int rc = proxyTakeConch(pFile);\n  if( rc==SQLITE_OK ){\n    proxyLockingContext *pCtx = (proxyLockingContext *)pFile->lockingContext;\n    if( pCtx->conchHeld>0 ){\n      unixFile *proxy = pCtx->lockProxy;\n      rc = proxy->pMethod->xUnlock((sqlite3_file*)proxy, eFileLock);\n      pFile->eFileLock = proxy->eFileLock;\n    }else{\n      /* conchHeld < 0 is lockless */\n    }\n  }\n  return rc;\n}\n\n/*\n** Close a file that uses proxy locks.\n*/\nstatic int proxyClose(sqlite3_file *id) {\n  if( ALWAYS(id) ){\n    unixFile *pFile = (unixFile*)id;\n    proxyLockingContext *pCtx = (proxyLockingContext *)pFile->lockingContext;\n    unixFile *lockProxy = pCtx->lockProxy;\n    unixFile *conchFile = pCtx->conchFile;\n    int rc = SQLITE_OK;\n    \n    if( lockProxy ){\n      rc = lockProxy->pMethod->xUnlock((sqlite3_file*)lockProxy, NO_LOCK);\n      if( rc ) return rc;\n      rc = lockProxy->pMethod->xClose((sqlite3_file*)lockProxy);\n      if( rc ) return rc;\n      sqlite3_free(lockProxy);\n      pCtx->lockProxy = 0;\n    }\n    if( conchFile ){\n      if( pCtx->conchHeld ){\n        rc = proxyReleaseConch(pFile);\n        if( rc ) return rc;\n      }\n      rc = conchFile->pMethod->xClose((sqlite3_file*)conchFile);\n      if( rc ) return rc;\n      sqlite3_free(conchFile);\n    }\n    sqlite3DbFree(0, pCtx->lockProxyPath);\n    sqlite3_free(pCtx->conchFilePath);\n    sqlite3DbFree(0, pCtx->dbPath);\n    /* restore the original locking context and pMethod then close it */\n    pFile->lockingContext = pCtx->oldLockingContext;\n    pFile->pMethod = pCtx->pOldMethod;\n    sqlite3_free(pCtx);\n    return pFile->pMethod->xClose(id);\n  }\n  return SQLITE_OK;\n}\n\n\n\n#endif /* defined(__APPLE__) && SQLITE_ENABLE_LOCKING_STYLE */\n/*\n** The proxy locking style is intended for use with AFP filesystems.\n** And since AFP is only supported on MacOSX, the proxy locking is also\n** restricted to MacOSX.\n** \n**\n******************* End of the proxy lock implementation **********************\n******************************************************************************/\n\n/*\n** Initialize the operating system interface.\n**\n** This routine registers all VFS implementations for unix-like operating\n** systems.  This routine, and the sqlite3_os_end() routine that follows,\n** should be the only routines in this file that are visible from other\n** files.\n**\n** This routine is called once during SQLite initialization and by a\n** single thread.  The memory allocation and mutex subsystems have not\n** necessarily been initialized when this routine is called, and so they\n** should not be used.\n*/\nSQLITE_API int sqlite3_os_init(void){ \n  /* \n  ** The following macro defines an initializer for an sqlite3_vfs object.\n  ** The name of the VFS is NAME.  The pAppData is a pointer to a pointer\n  ** to the \"finder\" function.  (pAppData is a pointer to a pointer because\n  ** silly C90 rules prohibit a void* from being cast to a function pointer\n  ** and so we have to go through the intermediate pointer to avoid problems\n  ** when compiling with -pedantic-errors on GCC.)\n  **\n  ** The FINDER parameter to this macro is the name of the pointer to the\n  ** finder-function.  The finder-function returns a pointer to the\n  ** sqlite_io_methods object that implements the desired locking\n  ** behaviors.  See the division above that contains the IOMETHODS\n  ** macro for addition information on finder-functions.\n  **\n  ** Most finders simply return a pointer to a fixed sqlite3_io_methods\n  ** object.  But the \"autolockIoFinder\" available on MacOSX does a little\n  ** more than that; it looks at the filesystem type that hosts the \n  ** database file and tries to choose an locking method appropriate for\n  ** that filesystem time.\n  */\n  #define UNIXVFS(VFSNAME, FINDER) {                        \\\n    3,                    /* iVersion */                    \\\n    sizeof(unixFile),     /* szOsFile */                    \\\n    MAX_PATHNAME,         /* mxPathname */                  \\\n    0,                    /* pNext */                       \\\n    VFSNAME,              /* zName */                       \\\n    (void*)&FINDER,       /* pAppData */                    \\\n    unixOpen,             /* xOpen */                       \\\n    unixDelete,           /* xDelete */                     \\\n    unixAccess,           /* xAccess */                     \\\n    unixFullPathname,     /* xFullPathname */               \\\n    unixDlOpen,           /* xDlOpen */                     \\\n    unixDlError,          /* xDlError */                    \\\n    unixDlSym,            /* xDlSym */                      \\\n    unixDlClose,          /* xDlClose */                    \\\n    unixRandomness,       /* xRandomness */                 \\\n    unixSleep,            /* xSleep */                      \\\n    unixCurrentTime,      /* xCurrentTime */                \\\n    unixGetLastError,     /* xGetLastError */               \\\n    unixCurrentTimeInt64, /* xCurrentTimeInt64 */           \\\n    unixSetSystemCall,    /* xSetSystemCall */              \\\n    unixGetSystemCall,    /* xGetSystemCall */              \\\n    unixNextSystemCall,   /* xNextSystemCall */             \\\n  }\n\n  /*\n  ** All default VFSes for unix are contained in the following array.\n  **\n  ** Note that the sqlite3_vfs.pNext field of the VFS object is modified\n  ** by the SQLite core when the VFS is registered.  So the following\n  ** array cannot be const.\n  */\n  static sqlite3_vfs aVfs[] = {\n#if SQLITE_ENABLE_LOCKING_STYLE && defined(__APPLE__)\n    UNIXVFS(\"unix\",          autolockIoFinder ),\n#elif OS_VXWORKS\n    UNIXVFS(\"unix\",          vxworksIoFinder ),\n#else\n    UNIXVFS(\"unix\",          posixIoFinder ),\n#endif\n    UNIXVFS(\"unix-none\",     nolockIoFinder ),\n    UNIXVFS(\"unix-dotfile\",  dotlockIoFinder ),\n    UNIXVFS(\"unix-excl\",     posixIoFinder ),\n#if OS_VXWORKS\n    UNIXVFS(\"unix-namedsem\", semIoFinder ),\n#endif\n#if SQLITE_ENABLE_LOCKING_STYLE || OS_VXWORKS\n    UNIXVFS(\"unix-posix\",    posixIoFinder ),\n#endif\n#if SQLITE_ENABLE_LOCKING_STYLE\n    UNIXVFS(\"unix-flock\",    flockIoFinder ),\n#endif\n#if SQLITE_ENABLE_LOCKING_STYLE && defined(__APPLE__)\n    UNIXVFS(\"unix-afp\",      afpIoFinder ),\n    UNIXVFS(\"unix-nfs\",      nfsIoFinder ),\n    UNIXVFS(\"unix-proxy\",    proxyIoFinder ),\n#endif\n  };\n  unsigned int i;          /* Loop counter */\n\n  /* Double-check that the aSyscall[] array has been constructed\n  ** correctly.  See ticket [bb3a86e890c8e96ab] */\n  assert( ArraySize(aSyscall)==29 );\n\n  /* Register all VFSes defined in the aVfs[] array */\n  for(i=0; i<(sizeof(aVfs)/sizeof(sqlite3_vfs)); i++){\n    sqlite3_vfs_register(&aVfs[i], i==0);\n  }\n  unixBigLock = sqlite3MutexAlloc(SQLITE_MUTEX_STATIC_VFS1);\n  return SQLITE_OK; \n}\n\n/*\n** Shutdown the operating system interface.\n**\n** Some operating systems might need to do some cleanup in this routine,\n** to release dynamically allocated objects.  But not on unix.\n** This routine is a no-op for unix.\n*/\nSQLITE_API int sqlite3_os_end(void){ \n  unixBigLock = 0;\n  return SQLITE_OK; \n}\n \n#endif /* SQLITE_OS_UNIX */\n\n/************** End of os_unix.c *********************************************/\n/************** Begin file os_win.c ******************************************/\n/*\n** 2004 May 22\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n******************************************************************************\n**\n** This file contains code that is specific to Windows.\n*/\n/* #include \"sqliteInt.h\" */\n#if SQLITE_OS_WIN               /* This file is used for Windows only */\n\n/*\n** Include code that is common to all os_*.c files\n*/\n/************** Include os_common.h in the middle of os_win.c ****************/\n/************** Begin file os_common.h ***************************************/\n/*\n** 2004 May 22\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n******************************************************************************\n**\n** This file contains macros and a little bit of code that is common to\n** all of the platform-specific files (os_*.c) and is #included into those\n** files.\n**\n** This file should be #included by the os_*.c files only.  It is not a\n** general purpose header file.\n*/\n#ifndef _OS_COMMON_H_\n#define _OS_COMMON_H_\n\n/*\n** At least two bugs have slipped in because we changed the MEMORY_DEBUG\n** macro to SQLITE_DEBUG and some older makefiles have not yet made the\n** switch.  The following code should catch this problem at compile-time.\n*/\n#ifdef MEMORY_DEBUG\n# error \"The MEMORY_DEBUG macro is obsolete.  Use SQLITE_DEBUG instead.\"\n#endif\n\n/*\n** Macros for performance tracing.  Normally turned off.  Only works\n** on i486 hardware.\n*/\n#ifdef SQLITE_PERFORMANCE_TRACE\n\n/*\n** hwtime.h contains inline assembler code for implementing\n** high-performance timing routines.\n*/\n/************** Include hwtime.h in the middle of os_common.h ****************/\n/************** Begin file hwtime.h ******************************************/\n/*\n** 2008 May 27\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n******************************************************************************\n**\n** This file contains inline asm code for retrieving \"high-performance\"\n** counters for x86 class CPUs.\n*/\n#ifndef SQLITE_HWTIME_H\n#define SQLITE_HWTIME_H\n\n/*\n** The following routine only works on pentium-class (or newer) processors.\n** It uses the RDTSC opcode to read the cycle count value out of the\n** processor and returns that value.  This can be used for high-res\n** profiling.\n*/\n#if (defined(__GNUC__) || defined(_MSC_VER)) && \\\n      (defined(i386) || defined(__i386__) || defined(_M_IX86))\n\n  #if defined(__GNUC__)\n\n  __inline__ sqlite_uint64 sqlite3Hwtime(void){\n     unsigned int lo, hi;\n     __asm__ __volatile__ (\"rdtsc\" : \"=a\" (lo), \"=d\" (hi));\n     return (sqlite_uint64)hi << 32 | lo;\n  }\n\n  #elif defined(_MSC_VER)\n\n  __declspec(naked) __inline sqlite_uint64 __cdecl sqlite3Hwtime(void){\n     __asm {\n        rdtsc\n        ret       ; return value at EDX:EAX\n     }\n  }\n\n  #endif\n\n#elif (defined(__GNUC__) && defined(__x86_64__))\n\n  __inline__ sqlite_uint64 sqlite3Hwtime(void){\n      unsigned long val;\n      __asm__ __volatile__ (\"rdtsc\" : \"=A\" (val));\n      return val;\n  }\n \n#elif (defined(__GNUC__) && defined(__ppc__))\n\n  __inline__ sqlite_uint64 sqlite3Hwtime(void){\n      unsigned long long retval;\n      unsigned long junk;\n      __asm__ __volatile__ (\"\\n\\\n          1:      mftbu   %1\\n\\\n                  mftb    %L0\\n\\\n                  mftbu   %0\\n\\\n                  cmpw    %0,%1\\n\\\n                  bne     1b\"\n                  : \"=r\" (retval), \"=r\" (junk));\n      return retval;\n  }\n\n#else\n\n  #error Need implementation of sqlite3Hwtime() for your platform.\n\n  /*\n  ** To compile without implementing sqlite3Hwtime() for your platform,\n  ** you can remove the above #error and use the following\n  ** stub function.  You will lose timing support for many\n  ** of the debugging and testing utilities, but it should at\n  ** least compile and run.\n  */\nSQLITE_PRIVATE   sqlite_uint64 sqlite3Hwtime(void){ return ((sqlite_uint64)0); }\n\n#endif\n\n#endif /* !defined(SQLITE_HWTIME_H) */\n\n/************** End of hwtime.h **********************************************/\n/************** Continuing where we left off in os_common.h ******************/\n\nstatic sqlite_uint64 g_start;\nstatic sqlite_uint64 g_elapsed;\n#define TIMER_START       g_start=sqlite3Hwtime()\n#define TIMER_END         g_elapsed=sqlite3Hwtime()-g_start\n#define TIMER_ELAPSED     g_elapsed\n#else\n#define TIMER_START\n#define TIMER_END\n#define TIMER_ELAPSED     ((sqlite_uint64)0)\n#endif\n\n/*\n** If we compile with the SQLITE_TEST macro set, then the following block\n** of code will give us the ability to simulate a disk I/O error.  This\n** is used for testing the I/O recovery logic.\n*/\n#if defined(SQLITE_TEST)\nSQLITE_API extern int sqlite3_io_error_hit;\nSQLITE_API extern int sqlite3_io_error_hardhit;\nSQLITE_API extern int sqlite3_io_error_pending;\nSQLITE_API extern int sqlite3_io_error_persist;\nSQLITE_API extern int sqlite3_io_error_benign;\nSQLITE_API extern int sqlite3_diskfull_pending;\nSQLITE_API extern int sqlite3_diskfull;\n#define SimulateIOErrorBenign(X) sqlite3_io_error_benign=(X)\n#define SimulateIOError(CODE)  \\\n  if( (sqlite3_io_error_persist && sqlite3_io_error_hit) \\\n       || sqlite3_io_error_pending-- == 1 )  \\\n              { local_ioerr(); CODE; }\nstatic void local_ioerr(){\n  IOTRACE((\"IOERR\\n\"));\n  sqlite3_io_error_hit++;\n  if( !sqlite3_io_error_benign ) sqlite3_io_error_hardhit++;\n}\n#define SimulateDiskfullError(CODE) \\\n   if( sqlite3_diskfull_pending ){ \\\n     if( sqlite3_diskfull_pending == 1 ){ \\\n       local_ioerr(); \\\n       sqlite3_diskfull = 1; \\\n       sqlite3_io_error_hit = 1; \\\n       CODE; \\\n     }else{ \\\n       sqlite3_diskfull_pending--; \\\n     } \\\n   }\n#else\n#define SimulateIOErrorBenign(X)\n#define SimulateIOError(A)\n#define SimulateDiskfullError(A)\n#endif /* defined(SQLITE_TEST) */\n\n/*\n** When testing, keep a count of the number of open files.\n*/\n#if defined(SQLITE_TEST)\nSQLITE_API extern int sqlite3_open_file_count;\n#define OpenCounter(X)  sqlite3_open_file_count+=(X)\n#else\n#define OpenCounter(X)\n#endif /* defined(SQLITE_TEST) */\n\n#endif /* !defined(_OS_COMMON_H_) */\n\n/************** End of os_common.h *******************************************/\n/************** Continuing where we left off in os_win.c *********************/\n\n/*\n** Include the header file for the Windows VFS.\n*/\n/* #include \"os_win.h\" */\n\n/*\n** Compiling and using WAL mode requires several APIs that are only\n** available in Windows platforms based on the NT kernel.\n*/\n#if !SQLITE_OS_WINNT && !defined(SQLITE_OMIT_WAL)\n#  error \"WAL mode requires support from the Windows NT kernel, compile\\\n with SQLITE_OMIT_WAL.\"\n#endif\n\n#if !SQLITE_OS_WINNT && SQLITE_MAX_MMAP_SIZE>0\n#  error \"Memory mapped files require support from the Windows NT kernel,\\\n compile with SQLITE_MAX_MMAP_SIZE=0.\"\n#endif\n\n/*\n** Are most of the Win32 ANSI APIs available (i.e. with certain exceptions\n** based on the sub-platform)?\n*/\n#if !SQLITE_OS_WINCE && !SQLITE_OS_WINRT && !defined(SQLITE_WIN32_NO_ANSI)\n#  define SQLITE_WIN32_HAS_ANSI\n#endif\n\n/*\n** Are most of the Win32 Unicode APIs available (i.e. with certain exceptions\n** based on the sub-platform)?\n*/\n#if (SQLITE_OS_WINCE || SQLITE_OS_WINNT || SQLITE_OS_WINRT) && \\\n    !defined(SQLITE_WIN32_NO_WIDE)\n#  define SQLITE_WIN32_HAS_WIDE\n#endif\n\n/*\n** Make sure at least one set of Win32 APIs is available.\n*/\n#if !defined(SQLITE_WIN32_HAS_ANSI) && !defined(SQLITE_WIN32_HAS_WIDE)\n#  error \"At least one of SQLITE_WIN32_HAS_ANSI and SQLITE_WIN32_HAS_WIDE\\\n must be defined.\"\n#endif\n\n/*\n** Define the required Windows SDK version constants if they are not\n** already available.\n*/\n#ifndef NTDDI_WIN8\n#  define NTDDI_WIN8                        0x06020000\n#endif\n\n#ifndef NTDDI_WINBLUE\n#  define NTDDI_WINBLUE                     0x06030000\n#endif\n\n#ifndef NTDDI_WINTHRESHOLD\n#  define NTDDI_WINTHRESHOLD                0x06040000\n#endif\n\n/*\n** Check to see if the GetVersionEx[AW] functions are deprecated on the\n** target system.  GetVersionEx was first deprecated in Win8.1.\n*/\n#ifndef SQLITE_WIN32_GETVERSIONEX\n#  if defined(NTDDI_VERSION) && NTDDI_VERSION >= NTDDI_WINBLUE\n#    define SQLITE_WIN32_GETVERSIONEX   0   /* GetVersionEx() is deprecated */\n#  else\n#    define SQLITE_WIN32_GETVERSIONEX   1   /* GetVersionEx() is current */\n#  endif\n#endif\n\n/*\n** Check to see if the CreateFileMappingA function is supported on the\n** target system.  It is unavailable when using \"mincore.lib\" on Win10.\n** When compiling for Windows 10, always assume \"mincore.lib\" is in use.\n*/\n#ifndef SQLITE_WIN32_CREATEFILEMAPPINGA\n#  if defined(NTDDI_VERSION) && NTDDI_VERSION >= NTDDI_WINTHRESHOLD\n#    define SQLITE_WIN32_CREATEFILEMAPPINGA   0\n#  else\n#    define SQLITE_WIN32_CREATEFILEMAPPINGA   1\n#  endif\n#endif\n\n/*\n** This constant should already be defined (in the \"WinDef.h\" SDK file).\n*/\n#ifndef MAX_PATH\n#  define MAX_PATH                      (260)\n#endif\n\n/*\n** Maximum pathname length (in chars) for Win32.  This should normally be\n** MAX_PATH.\n*/\n#ifndef SQLITE_WIN32_MAX_PATH_CHARS\n#  define SQLITE_WIN32_MAX_PATH_CHARS   (MAX_PATH)\n#endif\n\n/*\n** This constant should already be defined (in the \"WinNT.h\" SDK file).\n*/\n#ifndef UNICODE_STRING_MAX_CHARS\n#  define UNICODE_STRING_MAX_CHARS      (32767)\n#endif\n\n/*\n** Maximum pathname length (in chars) for WinNT.  This should normally be\n** UNICODE_STRING_MAX_CHARS.\n*/\n#ifndef SQLITE_WINNT_MAX_PATH_CHARS\n#  define SQLITE_WINNT_MAX_PATH_CHARS   (UNICODE_STRING_MAX_CHARS)\n#endif\n\n/*\n** Maximum pathname length (in bytes) for Win32.  The MAX_PATH macro is in\n** characters, so we allocate 4 bytes per character assuming worst-case of\n** 4-bytes-per-character for UTF8.\n*/\n#ifndef SQLITE_WIN32_MAX_PATH_BYTES\n#  define SQLITE_WIN32_MAX_PATH_BYTES   (SQLITE_WIN32_MAX_PATH_CHARS*4)\n#endif\n\n/*\n** Maximum pathname length (in bytes) for WinNT.  This should normally be\n** UNICODE_STRING_MAX_CHARS * sizeof(WCHAR).\n*/\n#ifndef SQLITE_WINNT_MAX_PATH_BYTES\n#  define SQLITE_WINNT_MAX_PATH_BYTES   \\\n                            (sizeof(WCHAR) * SQLITE_WINNT_MAX_PATH_CHARS)\n#endif\n\n/*\n** Maximum error message length (in chars) for WinRT.\n*/\n#ifndef SQLITE_WIN32_MAX_ERRMSG_CHARS\n#  define SQLITE_WIN32_MAX_ERRMSG_CHARS (1024)\n#endif\n\n/*\n** Returns non-zero if the character should be treated as a directory\n** separator.\n*/\n#ifndef winIsDirSep\n#  define winIsDirSep(a)                (((a) == '/') || ((a) == '\\\\'))\n#endif\n\n/*\n** This macro is used when a local variable is set to a value that is\n** [sometimes] not used by the code (e.g. via conditional compilation).\n*/\n#ifndef UNUSED_VARIABLE_VALUE\n#  define UNUSED_VARIABLE_VALUE(x)      (void)(x)\n#endif\n\n/*\n** Returns the character that should be used as the directory separator.\n*/\n#ifndef winGetDirSep\n#  define winGetDirSep()                '\\\\'\n#endif\n\n/*\n** Do we need to manually define the Win32 file mapping APIs for use with WAL\n** mode or memory mapped files (e.g. these APIs are available in the Windows\n** CE SDK; however, they are not present in the header file)?\n*/\n#if SQLITE_WIN32_FILEMAPPING_API && \\\n        (!defined(SQLITE_OMIT_WAL) || SQLITE_MAX_MMAP_SIZE>0)\n/*\n** Two of the file mapping APIs are different under WinRT.  Figure out which\n** set we need.\n*/\n#if SQLITE_OS_WINRT\nWINBASEAPI HANDLE WINAPI CreateFileMappingFromApp(HANDLE, \\\n        LPSECURITY_ATTRIBUTES, ULONG, ULONG64, LPCWSTR);\n\nWINBASEAPI LPVOID WINAPI MapViewOfFileFromApp(HANDLE, ULONG, ULONG64, SIZE_T);\n#else\n#if defined(SQLITE_WIN32_HAS_ANSI)\nWINBASEAPI HANDLE WINAPI CreateFileMappingA(HANDLE, LPSECURITY_ATTRIBUTES, \\\n        DWORD, DWORD, DWORD, LPCSTR);\n#endif /* defined(SQLITE_WIN32_HAS_ANSI) */\n\n#if defined(SQLITE_WIN32_HAS_WIDE)\nWINBASEAPI HANDLE WINAPI CreateFileMappingW(HANDLE, LPSECURITY_ATTRIBUTES, \\\n        DWORD, DWORD, DWORD, LPCWSTR);\n#endif /* defined(SQLITE_WIN32_HAS_WIDE) */\n\nWINBASEAPI LPVOID WINAPI MapViewOfFile(HANDLE, DWORD, DWORD, DWORD, SIZE_T);\n#endif /* SQLITE_OS_WINRT */\n\n/*\n** These file mapping APIs are common to both Win32 and WinRT.\n*/\n\nWINBASEAPI BOOL WINAPI FlushViewOfFile(LPCVOID, SIZE_T);\nWINBASEAPI BOOL WINAPI UnmapViewOfFile(LPCVOID);\n#endif /* SQLITE_WIN32_FILEMAPPING_API */\n\n/*\n** Some Microsoft compilers lack this definition.\n*/\n#ifndef INVALID_FILE_ATTRIBUTES\n# define INVALID_FILE_ATTRIBUTES ((DWORD)-1)\n#endif\n\n#ifndef FILE_FLAG_MASK\n# define FILE_FLAG_MASK          (0xFF3C0000)\n#endif\n\n#ifndef FILE_ATTRIBUTE_MASK\n# define FILE_ATTRIBUTE_MASK     (0x0003FFF7)\n#endif\n\n#ifndef SQLITE_OMIT_WAL\n/* Forward references to structures used for WAL */\ntypedef struct winShm winShm;           /* A connection to shared-memory */\ntypedef struct winShmNode winShmNode;   /* A region of shared-memory */\n#endif\n\n/*\n** WinCE lacks native support for file locking so we have to fake it\n** with some code of our own.\n*/\n#if SQLITE_OS_WINCE\ntypedef struct winceLock {\n  int nReaders;       /* Number of reader locks obtained */\n  BOOL bPending;      /* Indicates a pending lock has been obtained */\n  BOOL bReserved;     /* Indicates a reserved lock has been obtained */\n  BOOL bExclusive;    /* Indicates an exclusive lock has been obtained */\n} winceLock;\n#endif\n\n/*\n** The winFile structure is a subclass of sqlite3_file* specific to the win32\n** portability layer.\n*/\ntypedef struct winFile winFile;\nstruct winFile {\n  const sqlite3_io_methods *pMethod; /*** Must be first ***/\n  sqlite3_vfs *pVfs;      /* The VFS used to open this file */\n  HANDLE h;               /* Handle for accessing the file */\n  u8 locktype;            /* Type of lock currently held on this file */\n  short sharedLockByte;   /* Randomly chosen byte used as a shared lock */\n  u8 ctrlFlags;           /* Flags.  See WINFILE_* below */\n  DWORD lastErrno;        /* The Windows errno from the last I/O error */\n#ifndef SQLITE_OMIT_WAL\n  winShm *pShm;           /* Instance of shared memory on this file */\n#endif\n  const char *zPath;      /* Full pathname of this file */\n  int szChunk;            /* Chunk size configured by FCNTL_CHUNK_SIZE */\n#if SQLITE_OS_WINCE\n  LPWSTR zDeleteOnClose;  /* Name of file to delete when closing */\n  HANDLE hMutex;          /* Mutex used to control access to shared lock */\n  HANDLE hShared;         /* Shared memory segment used for locking */\n  winceLock local;        /* Locks obtained by this instance of winFile */\n  winceLock *shared;      /* Global shared lock memory for the file  */\n#endif\n#if SQLITE_MAX_MMAP_SIZE>0\n  int nFetchOut;                /* Number of outstanding xFetch references */\n  HANDLE hMap;                  /* Handle for accessing memory mapping */\n  void *pMapRegion;             /* Area memory mapped */\n  sqlite3_int64 mmapSize;       /* Usable size of mapped region */\n  sqlite3_int64 mmapSizeActual; /* Actual size of mapped region */\n  sqlite3_int64 mmapSizeMax;    /* Configured FCNTL_MMAP_SIZE value */\n#endif\n};\n\n/*\n** The winVfsAppData structure is used for the pAppData member for all of the\n** Win32 VFS variants.\n*/\ntypedef struct winVfsAppData winVfsAppData;\nstruct winVfsAppData {\n  const sqlite3_io_methods *pMethod; /* The file I/O methods to use. */\n  void *pAppData;                    /* The extra pAppData, if any. */\n  BOOL bNoLock;                      /* Non-zero if locking is disabled. */\n};\n\n/*\n** Allowed values for winFile.ctrlFlags\n*/\n#define WINFILE_RDONLY          0x02   /* Connection is read only */\n#define WINFILE_PERSIST_WAL     0x04   /* Persistent WAL mode */\n#define WINFILE_PSOW            0x10   /* SQLITE_IOCAP_POWERSAFE_OVERWRITE */\n\n/*\n * The size of the buffer used by sqlite3_win32_write_debug().\n */\n#ifndef SQLITE_WIN32_DBG_BUF_SIZE\n#  define SQLITE_WIN32_DBG_BUF_SIZE   ((int)(4096-sizeof(DWORD)))\n#endif\n\n/*\n * The value used with sqlite3_win32_set_directory() to specify that\n * the data directory should be changed.\n */\n#ifndef SQLITE_WIN32_DATA_DIRECTORY_TYPE\n#  define SQLITE_WIN32_DATA_DIRECTORY_TYPE (1)\n#endif\n\n/*\n * The value used with sqlite3_win32_set_directory() to specify that\n * the temporary directory should be changed.\n */\n#ifndef SQLITE_WIN32_TEMP_DIRECTORY_TYPE\n#  define SQLITE_WIN32_TEMP_DIRECTORY_TYPE (2)\n#endif\n\n/*\n * If compiled with SQLITE_WIN32_MALLOC on Windows, we will use the\n * various Win32 API heap functions instead of our own.\n */\n#ifdef SQLITE_WIN32_MALLOC\n\n/*\n * If this is non-zero, an isolated heap will be created by the native Win32\n * allocator subsystem; otherwise, the default process heap will be used.  This\n * setting has no effect when compiling for WinRT.  By default, this is enabled\n * and an isolated heap will be created to store all allocated data.\n *\n ******************************************************************************\n * WARNING: It is important to note that when this setting is non-zero and the\n *          winMemShutdown function is called (e.g. by the sqlite3_shutdown\n *          function), all data that was allocated using the isolated heap will\n *          be freed immediately and any attempt to access any of that freed\n *          data will almost certainly result in an immediate access violation.\n ******************************************************************************\n */\n#ifndef SQLITE_WIN32_HEAP_CREATE\n#  define SQLITE_WIN32_HEAP_CREATE        (TRUE)\n#endif\n\n/*\n * This is the maximum possible initial size of the Win32-specific heap, in\n * bytes.\n */\n#ifndef SQLITE_WIN32_HEAP_MAX_INIT_SIZE\n#  define SQLITE_WIN32_HEAP_MAX_INIT_SIZE (4294967295U)\n#endif\n\n/*\n * This is the extra space for the initial size of the Win32-specific heap,\n * in bytes.  This value may be zero.\n */\n#ifndef SQLITE_WIN32_HEAP_INIT_EXTRA\n#  define SQLITE_WIN32_HEAP_INIT_EXTRA  (4194304)\n#endif\n\n/*\n * Calculate the maximum legal cache size, in pages, based on the maximum\n * possible initial heap size and the default page size, setting aside the\n * needed extra space.\n */\n#ifndef SQLITE_WIN32_MAX_CACHE_SIZE\n#  define SQLITE_WIN32_MAX_CACHE_SIZE   (((SQLITE_WIN32_HEAP_MAX_INIT_SIZE) - \\\n                                          (SQLITE_WIN32_HEAP_INIT_EXTRA)) / \\\n                                         (SQLITE_DEFAULT_PAGE_SIZE))\n#endif\n\n/*\n * This is cache size used in the calculation of the initial size of the\n * Win32-specific heap.  It cannot be negative.\n */\n#ifndef SQLITE_WIN32_CACHE_SIZE\n#  if SQLITE_DEFAULT_CACHE_SIZE>=0\n#    define SQLITE_WIN32_CACHE_SIZE     (SQLITE_DEFAULT_CACHE_SIZE)\n#  else\n#    define SQLITE_WIN32_CACHE_SIZE     (-(SQLITE_DEFAULT_CACHE_SIZE))\n#  endif\n#endif\n\n/*\n * Make sure that the calculated cache size, in pages, cannot cause the\n * initial size of the Win32-specific heap to exceed the maximum amount\n * of memory that can be specified in the call to HeapCreate.\n */\n#if SQLITE_WIN32_CACHE_SIZE>SQLITE_WIN32_MAX_CACHE_SIZE\n#  undef SQLITE_WIN32_CACHE_SIZE\n#  define SQLITE_WIN32_CACHE_SIZE       (2000)\n#endif\n\n/*\n * The initial size of the Win32-specific heap.  This value may be zero.\n */\n#ifndef SQLITE_WIN32_HEAP_INIT_SIZE\n#  define SQLITE_WIN32_HEAP_INIT_SIZE   ((SQLITE_WIN32_CACHE_SIZE) * \\\n                                         (SQLITE_DEFAULT_PAGE_SIZE) + \\\n                                         (SQLITE_WIN32_HEAP_INIT_EXTRA))\n#endif\n\n/*\n * The maximum size of the Win32-specific heap.  This value may be zero.\n */\n#ifndef SQLITE_WIN32_HEAP_MAX_SIZE\n#  define SQLITE_WIN32_HEAP_MAX_SIZE    (0)\n#endif\n\n/*\n * The extra flags to use in calls to the Win32 heap APIs.  This value may be\n * zero for the default behavior.\n */\n#ifndef SQLITE_WIN32_HEAP_FLAGS\n#  define SQLITE_WIN32_HEAP_FLAGS       (0)\n#endif\n\n\n/*\n** The winMemData structure stores information required by the Win32-specific\n** sqlite3_mem_methods implementation.\n*/\ntypedef struct winMemData winMemData;\nstruct winMemData {\n#ifndef NDEBUG\n  u32 magic1;   /* Magic number to detect structure corruption. */\n#endif\n  HANDLE hHeap; /* The handle to our heap. */\n  BOOL bOwned;  /* Do we own the heap (i.e. destroy it on shutdown)? */\n#ifndef NDEBUG\n  u32 magic2;   /* Magic number to detect structure corruption. */\n#endif\n};\n\n#ifndef NDEBUG\n#define WINMEM_MAGIC1     0x42b2830b\n#define WINMEM_MAGIC2     0xbd4d7cf4\n#endif\n\nstatic struct winMemData win_mem_data = {\n#ifndef NDEBUG\n  WINMEM_MAGIC1,\n#endif\n  NULL, FALSE\n#ifndef NDEBUG\n  ,WINMEM_MAGIC2\n#endif\n};\n\n#ifndef NDEBUG\n#define winMemAssertMagic1() assert( win_mem_data.magic1==WINMEM_MAGIC1 )\n#define winMemAssertMagic2() assert( win_mem_data.magic2==WINMEM_MAGIC2 )\n#define winMemAssertMagic()  winMemAssertMagic1(); winMemAssertMagic2();\n#else\n#define winMemAssertMagic()\n#endif\n\n#define winMemGetDataPtr()  &win_mem_data\n#define winMemGetHeap()     win_mem_data.hHeap\n#define winMemGetOwned()    win_mem_data.bOwned\n\nstatic void *winMemMalloc(int nBytes);\nstatic void winMemFree(void *pPrior);\nstatic void *winMemRealloc(void *pPrior, int nBytes);\nstatic int winMemSize(void *p);\nstatic int winMemRoundup(int n);\nstatic int winMemInit(void *pAppData);\nstatic void winMemShutdown(void *pAppData);\n\nSQLITE_PRIVATE const sqlite3_mem_methods *sqlite3MemGetWin32(void);\n#endif /* SQLITE_WIN32_MALLOC */\n\n/*\n** The following variable is (normally) set once and never changes\n** thereafter.  It records whether the operating system is Win9x\n** or WinNT.\n**\n** 0:   Operating system unknown.\n** 1:   Operating system is Win9x.\n** 2:   Operating system is WinNT.\n**\n** In order to facilitate testing on a WinNT system, the test fixture\n** can manually set this value to 1 to emulate Win98 behavior.\n*/\n#ifdef SQLITE_TEST\nSQLITE_API LONG SQLITE_WIN32_VOLATILE sqlite3_os_type = 0;\n#else\nstatic LONG SQLITE_WIN32_VOLATILE sqlite3_os_type = 0;\n#endif\n\n#ifndef SYSCALL\n#  define SYSCALL sqlite3_syscall_ptr\n#endif\n\n/*\n** This function is not available on Windows CE or WinRT.\n */\n\n#if SQLITE_OS_WINCE || SQLITE_OS_WINRT\n#  define osAreFileApisANSI()       1\n#endif\n\n/*\n** Many system calls are accessed through pointer-to-functions so that\n** they may be overridden at runtime to facilitate fault injection during\n** testing and sandboxing.  The following array holds the names and pointers\n** to all overrideable system calls.\n*/\nstatic struct win_syscall {\n  const char *zName;            /* Name of the system call */\n  sqlite3_syscall_ptr pCurrent; /* Current value of the system call */\n  sqlite3_syscall_ptr pDefault; /* Default value */\n} aSyscall[] = {\n#if !SQLITE_OS_WINCE && !SQLITE_OS_WINRT\n  { \"AreFileApisANSI\",         (SYSCALL)AreFileApisANSI,         0 },\n#else\n  { \"AreFileApisANSI\",         (SYSCALL)0,                       0 },\n#endif\n\n#ifndef osAreFileApisANSI\n#define osAreFileApisANSI ((BOOL(WINAPI*)(VOID))aSyscall[0].pCurrent)\n#endif\n\n#if SQLITE_OS_WINCE && defined(SQLITE_WIN32_HAS_WIDE)\n  { \"CharLowerW\",              (SYSCALL)CharLowerW,              0 },\n#else\n  { \"CharLowerW\",              (SYSCALL)0,                       0 },\n#endif\n\n#define osCharLowerW ((LPWSTR(WINAPI*)(LPWSTR))aSyscall[1].pCurrent)\n\n#if SQLITE_OS_WINCE && defined(SQLITE_WIN32_HAS_WIDE)\n  { \"CharUpperW\",              (SYSCALL)CharUpperW,              0 },\n#else\n  { \"CharUpperW\",              (SYSCALL)0,                       0 },\n#endif\n\n#define osCharUpperW ((LPWSTR(WINAPI*)(LPWSTR))aSyscall[2].pCurrent)\n\n  { \"CloseHandle\",             (SYSCALL)CloseHandle,             0 },\n\n#define osCloseHandle ((BOOL(WINAPI*)(HANDLE))aSyscall[3].pCurrent)\n\n#if defined(SQLITE_WIN32_HAS_ANSI)\n  { \"CreateFileA\",             (SYSCALL)CreateFileA,             0 },\n#else\n  { \"CreateFileA\",             (SYSCALL)0,                       0 },\n#endif\n\n#define osCreateFileA ((HANDLE(WINAPI*)(LPCSTR,DWORD,DWORD, \\\n        LPSECURITY_ATTRIBUTES,DWORD,DWORD,HANDLE))aSyscall[4].pCurrent)\n\n#if !SQLITE_OS_WINRT && defined(SQLITE_WIN32_HAS_WIDE)\n  { \"CreateFileW\",             (SYSCALL)CreateFileW,             0 },\n#else\n  { \"CreateFileW\",             (SYSCALL)0,                       0 },\n#endif\n\n#define osCreateFileW ((HANDLE(WINAPI*)(LPCWSTR,DWORD,DWORD, \\\n        LPSECURITY_ATTRIBUTES,DWORD,DWORD,HANDLE))aSyscall[5].pCurrent)\n\n#if !SQLITE_OS_WINRT && defined(SQLITE_WIN32_HAS_ANSI) && \\\n        (!defined(SQLITE_OMIT_WAL) || SQLITE_MAX_MMAP_SIZE>0) && \\\n        SQLITE_WIN32_CREATEFILEMAPPINGA\n  { \"CreateFileMappingA\",      (SYSCALL)CreateFileMappingA,      0 },\n#else\n  { \"CreateFileMappingA\",      (SYSCALL)0,                       0 },\n#endif\n\n#define osCreateFileMappingA ((HANDLE(WINAPI*)(HANDLE,LPSECURITY_ATTRIBUTES, \\\n        DWORD,DWORD,DWORD,LPCSTR))aSyscall[6].pCurrent)\n\n#if SQLITE_OS_WINCE || (!SQLITE_OS_WINRT && defined(SQLITE_WIN32_HAS_WIDE) && \\\n        (!defined(SQLITE_OMIT_WAL) || SQLITE_MAX_MMAP_SIZE>0))\n  { \"CreateFileMappingW\",      (SYSCALL)CreateFileMappingW,      0 },\n#else\n  { \"CreateFileMappingW\",      (SYSCALL)0,                       0 },\n#endif\n\n#define osCreateFileMappingW ((HANDLE(WINAPI*)(HANDLE,LPSECURITY_ATTRIBUTES, \\\n        DWORD,DWORD,DWORD,LPCWSTR))aSyscall[7].pCurrent)\n\n#if !SQLITE_OS_WINRT && defined(SQLITE_WIN32_HAS_WIDE)\n  { \"CreateMutexW\",            (SYSCALL)CreateMutexW,            0 },\n#else\n  { \"CreateMutexW\",            (SYSCALL)0,                       0 },\n#endif\n\n#define osCreateMutexW ((HANDLE(WINAPI*)(LPSECURITY_ATTRIBUTES,BOOL, \\\n        LPCWSTR))aSyscall[8].pCurrent)\n\n#if defined(SQLITE_WIN32_HAS_ANSI)\n  { \"DeleteFileA\",             (SYSCALL)DeleteFileA,             0 },\n#else\n  { \"DeleteFileA\",             (SYSCALL)0,                       0 },\n#endif\n\n#define osDeleteFileA ((BOOL(WINAPI*)(LPCSTR))aSyscall[9].pCurrent)\n\n#if defined(SQLITE_WIN32_HAS_WIDE)\n  { \"DeleteFileW\",             (SYSCALL)DeleteFileW,             0 },\n#else\n  { \"DeleteFileW\",             (SYSCALL)0,                       0 },\n#endif\n\n#define osDeleteFileW ((BOOL(WINAPI*)(LPCWSTR))aSyscall[10].pCurrent)\n\n#if SQLITE_OS_WINCE\n  { \"FileTimeToLocalFileTime\", (SYSCALL)FileTimeToLocalFileTime, 0 },\n#else\n  { \"FileTimeToLocalFileTime\", (SYSCALL)0,                       0 },\n#endif\n\n#define osFileTimeToLocalFileTime ((BOOL(WINAPI*)(CONST FILETIME*, \\\n        LPFILETIME))aSyscall[11].pCurrent)\n\n#if SQLITE_OS_WINCE\n  { \"FileTimeToSystemTime\",    (SYSCALL)FileTimeToSystemTime,    0 },\n#else\n  { \"FileTimeToSystemTime\",    (SYSCALL)0,                       0 },\n#endif\n\n#define osFileTimeToSystemTime ((BOOL(WINAPI*)(CONST FILETIME*, \\\n        LPSYSTEMTIME))aSyscall[12].pCurrent)\n\n  { \"FlushFileBuffers\",        (SYSCALL)FlushFileBuffers,        0 },\n\n#define osFlushFileBuffers ((BOOL(WINAPI*)(HANDLE))aSyscall[13].pCurrent)\n\n#if defined(SQLITE_WIN32_HAS_ANSI)\n  { \"FormatMessageA\",          (SYSCALL)FormatMessageA,          0 },\n#else\n  { \"FormatMessageA\",          (SYSCALL)0,                       0 },\n#endif\n\n#define osFormatMessageA ((DWORD(WINAPI*)(DWORD,LPCVOID,DWORD,DWORD,LPSTR, \\\n        DWORD,va_list*))aSyscall[14].pCurrent)\n\n#if defined(SQLITE_WIN32_HAS_WIDE)\n  { \"FormatMessageW\",          (SYSCALL)FormatMessageW,          0 },\n#else\n  { \"FormatMessageW\",          (SYSCALL)0,                       0 },\n#endif\n\n#define osFormatMessageW ((DWORD(WINAPI*)(DWORD,LPCVOID,DWORD,DWORD,LPWSTR, \\\n        DWORD,va_list*))aSyscall[15].pCurrent)\n\n#if !defined(SQLITE_OMIT_LOAD_EXTENSION)\n  { \"FreeLibrary\",             (SYSCALL)FreeLibrary,             0 },\n#else\n  { \"FreeLibrary\",             (SYSCALL)0,                       0 },\n#endif\n\n#define osFreeLibrary ((BOOL(WINAPI*)(HMODULE))aSyscall[16].pCurrent)\n\n  { \"GetCurrentProcessId\",     (SYSCALL)GetCurrentProcessId,     0 },\n\n#define osGetCurrentProcessId ((DWORD(WINAPI*)(VOID))aSyscall[17].pCurrent)\n\n#if !SQLITE_OS_WINCE && defined(SQLITE_WIN32_HAS_ANSI)\n  { \"GetDiskFreeSpaceA\",       (SYSCALL)GetDiskFreeSpaceA,       0 },\n#else\n  { \"GetDiskFreeSpaceA\",       (SYSCALL)0,                       0 },\n#endif\n\n#define osGetDiskFreeSpaceA ((BOOL(WINAPI*)(LPCSTR,LPDWORD,LPDWORD,LPDWORD, \\\n        LPDWORD))aSyscall[18].pCurrent)\n\n#if !SQLITE_OS_WINCE && !SQLITE_OS_WINRT && defined(SQLITE_WIN32_HAS_WIDE)\n  { \"GetDiskFreeSpaceW\",       (SYSCALL)GetDiskFreeSpaceW,       0 },\n#else\n  { \"GetDiskFreeSpaceW\",       (SYSCALL)0,                       0 },\n#endif\n\n#define osGetDiskFreeSpaceW ((BOOL(WINAPI*)(LPCWSTR,LPDWORD,LPDWORD,LPDWORD, \\\n        LPDWORD))aSyscall[19].pCurrent)\n\n#if defined(SQLITE_WIN32_HAS_ANSI)\n  { \"GetFileAttributesA\",      (SYSCALL)GetFileAttributesA,      0 },\n#else\n  { \"GetFileAttributesA\",      (SYSCALL)0,                       0 },\n#endif\n\n#define osGetFileAttributesA ((DWORD(WINAPI*)(LPCSTR))aSyscall[20].pCurrent)\n\n#if !SQLITE_OS_WINRT && defined(SQLITE_WIN32_HAS_WIDE)\n  { \"GetFileAttributesW\",      (SYSCALL)GetFileAttributesW,      0 },\n#else\n  { \"GetFileAttributesW\",      (SYSCALL)0,                       0 },\n#endif\n\n#define osGetFileAttributesW ((DWORD(WINAPI*)(LPCWSTR))aSyscall[21].pCurrent)\n\n#if defined(SQLITE_WIN32_HAS_WIDE)\n  { \"GetFileAttributesExW\",    (SYSCALL)GetFileAttributesExW,    0 },\n#else\n  { \"GetFileAttributesExW\",    (SYSCALL)0,                       0 },\n#endif\n\n#define osGetFileAttributesExW ((BOOL(WINAPI*)(LPCWSTR,GET_FILEEX_INFO_LEVELS, \\\n        LPVOID))aSyscall[22].pCurrent)\n\n#if !SQLITE_OS_WINRT\n  { \"GetFileSize\",             (SYSCALL)GetFileSize,             0 },\n#else\n  { \"GetFileSize\",             (SYSCALL)0,                       0 },\n#endif\n\n#define osGetFileSize ((DWORD(WINAPI*)(HANDLE,LPDWORD))aSyscall[23].pCurrent)\n\n#if !SQLITE_OS_WINCE && defined(SQLITE_WIN32_HAS_ANSI)\n  { \"GetFullPathNameA\",        (SYSCALL)GetFullPathNameA,        0 },\n#else\n  { \"GetFullPathNameA\",        (SYSCALL)0,                       0 },\n#endif\n\n#define osGetFullPathNameA ((DWORD(WINAPI*)(LPCSTR,DWORD,LPSTR, \\\n        LPSTR*))aSyscall[24].pCurrent)\n\n#if !SQLITE_OS_WINCE && !SQLITE_OS_WINRT && defined(SQLITE_WIN32_HAS_WIDE)\n  { \"GetFullPathNameW\",        (SYSCALL)GetFullPathNameW,        0 },\n#else\n  { \"GetFullPathNameW\",        (SYSCALL)0,                       0 },\n#endif\n\n#define osGetFullPathNameW ((DWORD(WINAPI*)(LPCWSTR,DWORD,LPWSTR, \\\n        LPWSTR*))aSyscall[25].pCurrent)\n\n  { \"GetLastError\",            (SYSCALL)GetLastError,            0 },\n\n#define osGetLastError ((DWORD(WINAPI*)(VOID))aSyscall[26].pCurrent)\n\n#if !defined(SQLITE_OMIT_LOAD_EXTENSION)\n#if SQLITE_OS_WINCE\n  /* The GetProcAddressA() routine is only available on Windows CE. */\n  { \"GetProcAddressA\",         (SYSCALL)GetProcAddressA,         0 },\n#else\n  /* All other Windows platforms expect GetProcAddress() to take\n  ** an ANSI string regardless of the _UNICODE setting */\n  { \"GetProcAddressA\",         (SYSCALL)GetProcAddress,          0 },\n#endif\n#else\n  { \"GetProcAddressA\",         (SYSCALL)0,                       0 },\n#endif\n\n#define osGetProcAddressA ((FARPROC(WINAPI*)(HMODULE, \\\n        LPCSTR))aSyscall[27].pCurrent)\n\n#if !SQLITE_OS_WINRT\n  { \"GetSystemInfo\",           (SYSCALL)GetSystemInfo,           0 },\n#else\n  { \"GetSystemInfo\",           (SYSCALL)0,                       0 },\n#endif\n\n#define osGetSystemInfo ((VOID(WINAPI*)(LPSYSTEM_INFO))aSyscall[28].pCurrent)\n\n  { \"GetSystemTime\",           (SYSCALL)GetSystemTime,           0 },\n\n#define osGetSystemTime ((VOID(WINAPI*)(LPSYSTEMTIME))aSyscall[29].pCurrent)\n\n#if !SQLITE_OS_WINCE\n  { \"GetSystemTimeAsFileTime\", (SYSCALL)GetSystemTimeAsFileTime, 0 },\n#else\n  { \"GetSystemTimeAsFileTime\", (SYSCALL)0,                       0 },\n#endif\n\n#define osGetSystemTimeAsFileTime ((VOID(WINAPI*)( \\\n        LPFILETIME))aSyscall[30].pCurrent)\n\n#if defined(SQLITE_WIN32_HAS_ANSI)\n  { \"GetTempPathA\",            (SYSCALL)GetTempPathA,            0 },\n#else\n  { \"GetTempPathA\",            (SYSCALL)0,                       0 },\n#endif\n\n#define osGetTempPathA ((DWORD(WINAPI*)(DWORD,LPSTR))aSyscall[31].pCurrent)\n\n#if !SQLITE_OS_WINRT && defined(SQLITE_WIN32_HAS_WIDE)\n  { \"GetTempPathW\",            (SYSCALL)GetTempPathW,            0 },\n#else\n  { \"GetTempPathW\",            (SYSCALL)0,                       0 },\n#endif\n\n#define osGetTempPathW ((DWORD(WINAPI*)(DWORD,LPWSTR))aSyscall[32].pCurrent)\n\n#if !SQLITE_OS_WINRT\n  { \"GetTickCount\",            (SYSCALL)GetTickCount,            0 },\n#else\n  { \"GetTickCount\",            (SYSCALL)0,                       0 },\n#endif\n\n#define osGetTickCount ((DWORD(WINAPI*)(VOID))aSyscall[33].pCurrent)\n\n#if defined(SQLITE_WIN32_HAS_ANSI) && SQLITE_WIN32_GETVERSIONEX\n  { \"GetVersionExA\",           (SYSCALL)GetVersionExA,           0 },\n#else\n  { \"GetVersionExA\",           (SYSCALL)0,                       0 },\n#endif\n\n#define osGetVersionExA ((BOOL(WINAPI*)( \\\n        LPOSVERSIONINFOA))aSyscall[34].pCurrent)\n\n#if !SQLITE_OS_WINRT && defined(SQLITE_WIN32_HAS_WIDE) && \\\n        SQLITE_WIN32_GETVERSIONEX\n  { \"GetVersionExW\",           (SYSCALL)GetVersionExW,           0 },\n#else\n  { \"GetVersionExW\",           (SYSCALL)0,                       0 },\n#endif\n\n#define osGetVersionExW ((BOOL(WINAPI*)( \\\n        LPOSVERSIONINFOW))aSyscall[35].pCurrent)\n\n  { \"HeapAlloc\",               (SYSCALL)HeapAlloc,               0 },\n\n#define osHeapAlloc ((LPVOID(WINAPI*)(HANDLE,DWORD, \\\n        SIZE_T))aSyscall[36].pCurrent)\n\n#if !SQLITE_OS_WINRT\n  { \"HeapCreate\",              (SYSCALL)HeapCreate,              0 },\n#else\n  { \"HeapCreate\",              (SYSCALL)0,                       0 },\n#endif\n\n#define osHeapCreate ((HANDLE(WINAPI*)(DWORD,SIZE_T, \\\n        SIZE_T))aSyscall[37].pCurrent)\n\n#if !SQLITE_OS_WINRT\n  { \"HeapDestroy\",             (SYSCALL)HeapDestroy,             0 },\n#else\n  { \"HeapDestroy\",             (SYSCALL)0,                       0 },\n#endif\n\n#define osHeapDestroy ((BOOL(WINAPI*)(HANDLE))aSyscall[38].pCurrent)\n\n  { \"HeapFree\",                (SYSCALL)HeapFree,                0 },\n\n#define osHeapFree ((BOOL(WINAPI*)(HANDLE,DWORD,LPVOID))aSyscall[39].pCurrent)\n\n  { \"HeapReAlloc\",             (SYSCALL)HeapReAlloc,             0 },\n\n#define osHeapReAlloc ((LPVOID(WINAPI*)(HANDLE,DWORD,LPVOID, \\\n        SIZE_T))aSyscall[40].pCurrent)\n\n  { \"HeapSize\",                (SYSCALL)HeapSize,                0 },\n\n#define osHeapSize ((SIZE_T(WINAPI*)(HANDLE,DWORD, \\\n        LPCVOID))aSyscall[41].pCurrent)\n\n#if !SQLITE_OS_WINRT\n  { \"HeapValidate\",            (SYSCALL)HeapValidate,            0 },\n#else\n  { \"HeapValidate\",            (SYSCALL)0,                       0 },\n#endif\n\n#define osHeapValidate ((BOOL(WINAPI*)(HANDLE,DWORD, \\\n        LPCVOID))aSyscall[42].pCurrent)\n\n#if !SQLITE_OS_WINCE && !SQLITE_OS_WINRT\n  { \"HeapCompact\",             (SYSCALL)HeapCompact,             0 },\n#else\n  { \"HeapCompact\",             (SYSCALL)0,                       0 },\n#endif\n\n#define osHeapCompact ((UINT(WINAPI*)(HANDLE,DWORD))aSyscall[43].pCurrent)\n\n#if defined(SQLITE_WIN32_HAS_ANSI) && !defined(SQLITE_OMIT_LOAD_EXTENSION)\n  { \"LoadLibraryA\",            (SYSCALL)LoadLibraryA,            0 },\n#else\n  { \"LoadLibraryA\",            (SYSCALL)0,                       0 },\n#endif\n\n#define osLoadLibraryA ((HMODULE(WINAPI*)(LPCSTR))aSyscall[44].pCurrent)\n\n#if !SQLITE_OS_WINRT && defined(SQLITE_WIN32_HAS_WIDE) && \\\n        !defined(SQLITE_OMIT_LOAD_EXTENSION)\n  { \"LoadLibraryW\",            (SYSCALL)LoadLibraryW,            0 },\n#else\n  { \"LoadLibraryW\",            (SYSCALL)0,                       0 },\n#endif\n\n#define osLoadLibraryW ((HMODULE(WINAPI*)(LPCWSTR))aSyscall[45].pCurrent)\n\n#if !SQLITE_OS_WINRT\n  { \"LocalFree\",               (SYSCALL)LocalFree,               0 },\n#else\n  { \"LocalFree\",               (SYSCALL)0,                       0 },\n#endif\n\n#define osLocalFree ((HLOCAL(WINAPI*)(HLOCAL))aSyscall[46].pCurrent)\n\n#if !SQLITE_OS_WINCE && !SQLITE_OS_WINRT\n  { \"LockFile\",                (SYSCALL)LockFile,                0 },\n#else\n  { \"LockFile\",                (SYSCALL)0,                       0 },\n#endif\n\n#ifndef osLockFile\n#define osLockFile ((BOOL(WINAPI*)(HANDLE,DWORD,DWORD,DWORD, \\\n        DWORD))aSyscall[47].pCurrent)\n#endif\n\n#if !SQLITE_OS_WINCE\n  { \"LockFileEx\",              (SYSCALL)LockFileEx,              0 },\n#else\n  { \"LockFileEx\",              (SYSCALL)0,                       0 },\n#endif\n\n#ifndef osLockFileEx\n#define osLockFileEx ((BOOL(WINAPI*)(HANDLE,DWORD,DWORD,DWORD,DWORD, \\\n        LPOVERLAPPED))aSyscall[48].pCurrent)\n#endif\n\n#if SQLITE_OS_WINCE || (!SQLITE_OS_WINRT && \\\n        (!defined(SQLITE_OMIT_WAL) || SQLITE_MAX_MMAP_SIZE>0))\n  { \"MapViewOfFile\",           (SYSCALL)MapViewOfFile,           0 },\n#else\n  { \"MapViewOfFile\",           (SYSCALL)0,                       0 },\n#endif\n\n#define osMapViewOfFile ((LPVOID(WINAPI*)(HANDLE,DWORD,DWORD,DWORD, \\\n        SIZE_T))aSyscall[49].pCurrent)\n\n  { \"MultiByteToWideChar\",     (SYSCALL)MultiByteToWideChar,     0 },\n\n#define osMultiByteToWideChar ((int(WINAPI*)(UINT,DWORD,LPCSTR,int,LPWSTR, \\\n        int))aSyscall[50].pCurrent)\n\n  { \"QueryPerformanceCounter\", (SYSCALL)QueryPerformanceCounter, 0 },\n\n#define osQueryPerformanceCounter ((BOOL(WINAPI*)( \\\n        LARGE_INTEGER*))aSyscall[51].pCurrent)\n\n  { \"ReadFile\",                (SYSCALL)ReadFile,                0 },\n\n#define osReadFile ((BOOL(WINAPI*)(HANDLE,LPVOID,DWORD,LPDWORD, \\\n        LPOVERLAPPED))aSyscall[52].pCurrent)\n\n  { \"SetEndOfFile\",            (SYSCALL)SetEndOfFile,            0 },\n\n#define osSetEndOfFile ((BOOL(WINAPI*)(HANDLE))aSyscall[53].pCurrent)\n\n#if !SQLITE_OS_WINRT\n  { \"SetFilePointer\",          (SYSCALL)SetFilePointer,          0 },\n#else\n  { \"SetFilePointer\",          (SYSCALL)0,                       0 },\n#endif\n\n#define osSetFilePointer ((DWORD(WINAPI*)(HANDLE,LONG,PLONG, \\\n        DWORD))aSyscall[54].pCurrent)\n\n#if !SQLITE_OS_WINRT\n  { \"Sleep\",                   (SYSCALL)Sleep,                   0 },\n#else\n  { \"Sleep\",                   (SYSCALL)0,                       0 },\n#endif\n\n#define osSleep ((VOID(WINAPI*)(DWORD))aSyscall[55].pCurrent)\n\n  { \"SystemTimeToFileTime\",    (SYSCALL)SystemTimeToFileTime,    0 },\n\n#define osSystemTimeToFileTime ((BOOL(WINAPI*)(CONST SYSTEMTIME*, \\\n        LPFILETIME))aSyscall[56].pCurrent)\n\n#if !SQLITE_OS_WINCE && !SQLITE_OS_WINRT\n  { \"UnlockFile\",              (SYSCALL)UnlockFile,              0 },\n#else\n  { \"UnlockFile\",              (SYSCALL)0,                       0 },\n#endif\n\n#ifndef osUnlockFile\n#define osUnlockFile ((BOOL(WINAPI*)(HANDLE,DWORD,DWORD,DWORD, \\\n        DWORD))aSyscall[57].pCurrent)\n#endif\n\n#if !SQLITE_OS_WINCE\n  { \"UnlockFileEx\",            (SYSCALL)UnlockFileEx,            0 },\n#else\n  { \"UnlockFileEx\",            (SYSCALL)0,                       0 },\n#endif\n\n#define osUnlockFileEx ((BOOL(WINAPI*)(HANDLE,DWORD,DWORD,DWORD, \\\n        LPOVERLAPPED))aSyscall[58].pCurrent)\n\n#if SQLITE_OS_WINCE || !defined(SQLITE_OMIT_WAL) || SQLITE_MAX_MMAP_SIZE>0\n  { \"UnmapViewOfFile\",         (SYSCALL)UnmapViewOfFile,         0 },\n#else\n  { \"UnmapViewOfFile\",         (SYSCALL)0,                       0 },\n#endif\n\n#define osUnmapViewOfFile ((BOOL(WINAPI*)(LPCVOID))aSyscall[59].pCurrent)\n\n  { \"WideCharToMultiByte\",     (SYSCALL)WideCharToMultiByte,     0 },\n\n#define osWideCharToMultiByte ((int(WINAPI*)(UINT,DWORD,LPCWSTR,int,LPSTR,int, \\\n        LPCSTR,LPBOOL))aSyscall[60].pCurrent)\n\n  { \"WriteFile\",               (SYSCALL)WriteFile,               0 },\n\n#define osWriteFile ((BOOL(WINAPI*)(HANDLE,LPCVOID,DWORD,LPDWORD, \\\n        LPOVERLAPPED))aSyscall[61].pCurrent)\n\n#if SQLITE_OS_WINRT\n  { \"CreateEventExW\",          (SYSCALL)CreateEventExW,          0 },\n#else\n  { \"CreateEventExW\",          (SYSCALL)0,                       0 },\n#endif\n\n#define osCreateEventExW ((HANDLE(WINAPI*)(LPSECURITY_ATTRIBUTES,LPCWSTR, \\\n        DWORD,DWORD))aSyscall[62].pCurrent)\n\n#if !SQLITE_OS_WINRT\n  { \"WaitForSingleObject\",     (SYSCALL)WaitForSingleObject,     0 },\n#else\n  { \"WaitForSingleObject\",     (SYSCALL)0,                       0 },\n#endif\n\n#define osWaitForSingleObject ((DWORD(WINAPI*)(HANDLE, \\\n        DWORD))aSyscall[63].pCurrent)\n\n#if !SQLITE_OS_WINCE\n  { \"WaitForSingleObjectEx\",   (SYSCALL)WaitForSingleObjectEx,   0 },\n#else\n  { \"WaitForSingleObjectEx\",   (SYSCALL)0,                       0 },\n#endif\n\n#define osWaitForSingleObjectEx ((DWORD(WINAPI*)(HANDLE,DWORD, \\\n        BOOL))aSyscall[64].pCurrent)\n\n#if SQLITE_OS_WINRT\n  { \"SetFilePointerEx\",        (SYSCALL)SetFilePointerEx,        0 },\n#else\n  { \"SetFilePointerEx\",        (SYSCALL)0,                       0 },\n#endif\n\n#define osSetFilePointerEx ((BOOL(WINAPI*)(HANDLE,LARGE_INTEGER, \\\n        PLARGE_INTEGER,DWORD))aSyscall[65].pCurrent)\n\n#if SQLITE_OS_WINRT\n  { \"GetFileInformationByHandleEx\", (SYSCALL)GetFileInformationByHandleEx, 0 },\n#else\n  { \"GetFileInformationByHandleEx\", (SYSCALL)0,                  0 },\n#endif\n\n#define osGetFileInformationByHandleEx ((BOOL(WINAPI*)(HANDLE, \\\n        FILE_INFO_BY_HANDLE_CLASS,LPVOID,DWORD))aSyscall[66].pCurrent)\n\n#if SQLITE_OS_WINRT && (!defined(SQLITE_OMIT_WAL) || SQLITE_MAX_MMAP_SIZE>0)\n  { \"MapViewOfFileFromApp\",    (SYSCALL)MapViewOfFileFromApp,    0 },\n#else\n  { \"MapViewOfFileFromApp\",    (SYSCALL)0,                       0 },\n#endif\n\n#define osMapViewOfFileFromApp ((LPVOID(WINAPI*)(HANDLE,ULONG,ULONG64, \\\n        SIZE_T))aSyscall[67].pCurrent)\n\n#if SQLITE_OS_WINRT\n  { \"CreateFile2\",             (SYSCALL)CreateFile2,             0 },\n#else\n  { \"CreateFile2\",             (SYSCALL)0,                       0 },\n#endif\n\n#define osCreateFile2 ((HANDLE(WINAPI*)(LPCWSTR,DWORD,DWORD,DWORD, \\\n        LPCREATEFILE2_EXTENDED_PARAMETERS))aSyscall[68].pCurrent)\n\n#if SQLITE_OS_WINRT && !defined(SQLITE_OMIT_LOAD_EXTENSION)\n  { \"LoadPackagedLibrary\",     (SYSCALL)LoadPackagedLibrary,     0 },\n#else\n  { \"LoadPackagedLibrary\",     (SYSCALL)0,                       0 },\n#endif\n\n#define osLoadPackagedLibrary ((HMODULE(WINAPI*)(LPCWSTR, \\\n        DWORD))aSyscall[69].pCurrent)\n\n#if SQLITE_OS_WINRT\n  { \"GetTickCount64\",          (SYSCALL)GetTickCount64,          0 },\n#else\n  { \"GetTickCount64\",          (SYSCALL)0,                       0 },\n#endif\n\n#define osGetTickCount64 ((ULONGLONG(WINAPI*)(VOID))aSyscall[70].pCurrent)\n\n#if SQLITE_OS_WINRT\n  { \"GetNativeSystemInfo\",     (SYSCALL)GetNativeSystemInfo,     0 },\n#else\n  { \"GetNativeSystemInfo\",     (SYSCALL)0,                       0 },\n#endif\n\n#define osGetNativeSystemInfo ((VOID(WINAPI*)( \\\n        LPSYSTEM_INFO))aSyscall[71].pCurrent)\n\n#if defined(SQLITE_WIN32_HAS_ANSI)\n  { \"OutputDebugStringA\",      (SYSCALL)OutputDebugStringA,      0 },\n#else\n  { \"OutputDebugStringA\",      (SYSCALL)0,                       0 },\n#endif\n\n#define osOutputDebugStringA ((VOID(WINAPI*)(LPCSTR))aSyscall[72].pCurrent)\n\n#if defined(SQLITE_WIN32_HAS_WIDE)\n  { \"OutputDebugStringW\",      (SYSCALL)OutputDebugStringW,      0 },\n#else\n  { \"OutputDebugStringW\",      (SYSCALL)0,                       0 },\n#endif\n\n#define osOutputDebugStringW ((VOID(WINAPI*)(LPCWSTR))aSyscall[73].pCurrent)\n\n  { \"GetProcessHeap\",          (SYSCALL)GetProcessHeap,          0 },\n\n#define osGetProcessHeap ((HANDLE(WINAPI*)(VOID))aSyscall[74].pCurrent)\n\n#if SQLITE_OS_WINRT && (!defined(SQLITE_OMIT_WAL) || SQLITE_MAX_MMAP_SIZE>0)\n  { \"CreateFileMappingFromApp\", (SYSCALL)CreateFileMappingFromApp, 0 },\n#else\n  { \"CreateFileMappingFromApp\", (SYSCALL)0,                      0 },\n#endif\n\n#define osCreateFileMappingFromApp ((HANDLE(WINAPI*)(HANDLE, \\\n        LPSECURITY_ATTRIBUTES,ULONG,ULONG64,LPCWSTR))aSyscall[75].pCurrent)\n\n/*\n** NOTE: On some sub-platforms, the InterlockedCompareExchange \"function\"\n**       is really just a macro that uses a compiler intrinsic (e.g. x64).\n**       So do not try to make this is into a redefinable interface.\n*/\n#if defined(InterlockedCompareExchange)\n  { \"InterlockedCompareExchange\", (SYSCALL)0,                    0 },\n\n#define osInterlockedCompareExchange InterlockedCompareExchange\n#else\n  { \"InterlockedCompareExchange\", (SYSCALL)InterlockedCompareExchange, 0 },\n\n#define osInterlockedCompareExchange ((LONG(WINAPI*)(LONG \\\n        SQLITE_WIN32_VOLATILE*, LONG,LONG))aSyscall[76].pCurrent)\n#endif /* defined(InterlockedCompareExchange) */\n\n#if !SQLITE_OS_WINCE && !SQLITE_OS_WINRT && SQLITE_WIN32_USE_UUID\n  { \"UuidCreate\",               (SYSCALL)UuidCreate,             0 },\n#else\n  { \"UuidCreate\",               (SYSCALL)0,                      0 },\n#endif\n\n#define osUuidCreate ((RPC_STATUS(RPC_ENTRY*)(UUID*))aSyscall[77].pCurrent)\n\n#if !SQLITE_OS_WINCE && !SQLITE_OS_WINRT && SQLITE_WIN32_USE_UUID\n  { \"UuidCreateSequential\",     (SYSCALL)UuidCreateSequential,   0 },\n#else\n  { \"UuidCreateSequential\",     (SYSCALL)0,                      0 },\n#endif\n\n#define osUuidCreateSequential \\\n        ((RPC_STATUS(RPC_ENTRY*)(UUID*))aSyscall[78].pCurrent)\n\n#if !defined(SQLITE_NO_SYNC) && SQLITE_MAX_MMAP_SIZE>0\n  { \"FlushViewOfFile\",          (SYSCALL)FlushViewOfFile,        0 },\n#else\n  { \"FlushViewOfFile\",          (SYSCALL)0,                      0 },\n#endif\n\n#define osFlushViewOfFile \\\n        ((BOOL(WINAPI*)(LPCVOID,SIZE_T))aSyscall[79].pCurrent)\n\n}; /* End of the overrideable system calls */\n\n/*\n** This is the xSetSystemCall() method of sqlite3_vfs for all of the\n** \"win32\" VFSes.  Return SQLITE_OK opon successfully updating the\n** system call pointer, or SQLITE_NOTFOUND if there is no configurable\n** system call named zName.\n*/\nstatic int winSetSystemCall(\n  sqlite3_vfs *pNotUsed,        /* The VFS pointer.  Not used */\n  const char *zName,            /* Name of system call to override */\n  sqlite3_syscall_ptr pNewFunc  /* Pointer to new system call value */\n){\n  unsigned int i;\n  int rc = SQLITE_NOTFOUND;\n\n  UNUSED_PARAMETER(pNotUsed);\n  if( zName==0 ){\n    /* If no zName is given, restore all system calls to their default\n    ** settings and return NULL\n    */\n    rc = SQLITE_OK;\n    for(i=0; i<sizeof(aSyscall)/sizeof(aSyscall[0]); i++){\n      if( aSyscall[i].pDefault ){\n        aSyscall[i].pCurrent = aSyscall[i].pDefault;\n      }\n    }\n  }else{\n    /* If zName is specified, operate on only the one system call\n    ** specified.\n    */\n    for(i=0; i<sizeof(aSyscall)/sizeof(aSyscall[0]); i++){\n      if( strcmp(zName, aSyscall[i].zName)==0 ){\n        if( aSyscall[i].pDefault==0 ){\n          aSyscall[i].pDefault = aSyscall[i].pCurrent;\n        }\n        rc = SQLITE_OK;\n        if( pNewFunc==0 ) pNewFunc = aSyscall[i].pDefault;\n        aSyscall[i].pCurrent = pNewFunc;\n        break;\n      }\n    }\n  }\n  return rc;\n}\n\n/*\n** Return the value of a system call.  Return NULL if zName is not a\n** recognized system call name.  NULL is also returned if the system call\n** is currently undefined.\n*/\nstatic sqlite3_syscall_ptr winGetSystemCall(\n  sqlite3_vfs *pNotUsed,\n  const char *zName\n){\n  unsigned int i;\n\n  UNUSED_PARAMETER(pNotUsed);\n  for(i=0; i<sizeof(aSyscall)/sizeof(aSyscall[0]); i++){\n    if( strcmp(zName, aSyscall[i].zName)==0 ) return aSyscall[i].pCurrent;\n  }\n  return 0;\n}\n\n/*\n** Return the name of the first system call after zName.  If zName==NULL\n** then return the name of the first system call.  Return NULL if zName\n** is the last system call or if zName is not the name of a valid\n** system call.\n*/\nstatic const char *winNextSystemCall(sqlite3_vfs *p, const char *zName){\n  int i = -1;\n\n  UNUSED_PARAMETER(p);\n  if( zName ){\n    for(i=0; i<ArraySize(aSyscall)-1; i++){\n      if( strcmp(zName, aSyscall[i].zName)==0 ) break;\n    }\n  }\n  for(i++; i<ArraySize(aSyscall); i++){\n    if( aSyscall[i].pCurrent!=0 ) return aSyscall[i].zName;\n  }\n  return 0;\n}\n\n#ifdef SQLITE_WIN32_MALLOC\n/*\n** If a Win32 native heap has been configured, this function will attempt to\n** compact it.  Upon success, SQLITE_OK will be returned.  Upon failure, one\n** of SQLITE_NOMEM, SQLITE_ERROR, or SQLITE_NOTFOUND will be returned.  The\n** \"pnLargest\" argument, if non-zero, will be used to return the size of the\n** largest committed free block in the heap, in bytes.\n*/\nSQLITE_API int sqlite3_win32_compact_heap(LPUINT pnLargest){\n  int rc = SQLITE_OK;\n  UINT nLargest = 0;\n  HANDLE hHeap;\n\n  winMemAssertMagic();\n  hHeap = winMemGetHeap();\n  assert( hHeap!=0 );\n  assert( hHeap!=INVALID_HANDLE_VALUE );\n#if !SQLITE_OS_WINRT && defined(SQLITE_WIN32_MALLOC_VALIDATE)\n  assert( osHeapValidate(hHeap, SQLITE_WIN32_HEAP_FLAGS, NULL) );\n#endif\n#if !SQLITE_OS_WINCE && !SQLITE_OS_WINRT\n  if( (nLargest=osHeapCompact(hHeap, SQLITE_WIN32_HEAP_FLAGS))==0 ){\n    DWORD lastErrno = osGetLastError();\n    if( lastErrno==NO_ERROR ){\n      sqlite3_log(SQLITE_NOMEM, \"failed to HeapCompact (no space), heap=%p\",\n                  (void*)hHeap);\n      rc = SQLITE_NOMEM_BKPT;\n    }else{\n      sqlite3_log(SQLITE_ERROR, \"failed to HeapCompact (%lu), heap=%p\",\n                  osGetLastError(), (void*)hHeap);\n      rc = SQLITE_ERROR;\n    }\n  }\n#else\n  sqlite3_log(SQLITE_NOTFOUND, \"failed to HeapCompact, heap=%p\",\n              (void*)hHeap);\n  rc = SQLITE_NOTFOUND;\n#endif\n  if( pnLargest ) *pnLargest = nLargest;\n  return rc;\n}\n\n/*\n** If a Win32 native heap has been configured, this function will attempt to\n** destroy and recreate it.  If the Win32 native heap is not isolated and/or\n** the sqlite3_memory_used() function does not return zero, SQLITE_BUSY will\n** be returned and no changes will be made to the Win32 native heap.\n*/\nSQLITE_API int sqlite3_win32_reset_heap(){\n  int rc;\n  MUTEX_LOGIC( sqlite3_mutex *pMaster; ) /* The main static mutex */\n  MUTEX_LOGIC( sqlite3_mutex *pMem; )    /* The memsys static mutex */\n  MUTEX_LOGIC( pMaster = sqlite3MutexAlloc(SQLITE_MUTEX_STATIC_MASTER); )\n  MUTEX_LOGIC( pMem = sqlite3MutexAlloc(SQLITE_MUTEX_STATIC_MEM); )\n  sqlite3_mutex_enter(pMaster);\n  sqlite3_mutex_enter(pMem);\n  winMemAssertMagic();\n  if( winMemGetHeap()!=NULL && winMemGetOwned() && sqlite3_memory_used()==0 ){\n    /*\n    ** At this point, there should be no outstanding memory allocations on\n    ** the heap.  Also, since both the master and memsys locks are currently\n    ** being held by us, no other function (i.e. from another thread) should\n    ** be able to even access the heap.  Attempt to destroy and recreate our\n    ** isolated Win32 native heap now.\n    */\n    assert( winMemGetHeap()!=NULL );\n    assert( winMemGetOwned() );\n    assert( sqlite3_memory_used()==0 );\n    winMemShutdown(winMemGetDataPtr());\n    assert( winMemGetHeap()==NULL );\n    assert( !winMemGetOwned() );\n    assert( sqlite3_memory_used()==0 );\n    rc = winMemInit(winMemGetDataPtr());\n    assert( rc!=SQLITE_OK || winMemGetHeap()!=NULL );\n    assert( rc!=SQLITE_OK || winMemGetOwned() );\n    assert( rc!=SQLITE_OK || sqlite3_memory_used()==0 );\n  }else{\n    /*\n    ** The Win32 native heap cannot be modified because it may be in use.\n    */\n    rc = SQLITE_BUSY;\n  }\n  sqlite3_mutex_leave(pMem);\n  sqlite3_mutex_leave(pMaster);\n  return rc;\n}\n#endif /* SQLITE_WIN32_MALLOC */\n\n/*\n** This function outputs the specified (ANSI) string to the Win32 debugger\n** (if available).\n*/\n\nSQLITE_API void sqlite3_win32_write_debug(const char *zBuf, int nBuf){\n  char zDbgBuf[SQLITE_WIN32_DBG_BUF_SIZE];\n  int nMin = MIN(nBuf, (SQLITE_WIN32_DBG_BUF_SIZE - 1)); /* may be negative. */\n  if( nMin<-1 ) nMin = -1; /* all negative values become -1. */\n  assert( nMin==-1 || nMin==0 || nMin<SQLITE_WIN32_DBG_BUF_SIZE );\n#ifdef SQLITE_ENABLE_API_ARMOR\n  if( !zBuf ){\n    (void)SQLITE_MISUSE_BKPT;\n    return;\n  }\n#endif\n#if defined(SQLITE_WIN32_HAS_ANSI)\n  if( nMin>0 ){\n    memset(zDbgBuf, 0, SQLITE_WIN32_DBG_BUF_SIZE);\n    memcpy(zDbgBuf, zBuf, nMin);\n    osOutputDebugStringA(zDbgBuf);\n  }else{\n    osOutputDebugStringA(zBuf);\n  }\n#elif defined(SQLITE_WIN32_HAS_WIDE)\n  memset(zDbgBuf, 0, SQLITE_WIN32_DBG_BUF_SIZE);\n  if ( osMultiByteToWideChar(\n          osAreFileApisANSI() ? CP_ACP : CP_OEMCP, 0, zBuf,\n          nMin, (LPWSTR)zDbgBuf, SQLITE_WIN32_DBG_BUF_SIZE/sizeof(WCHAR))<=0 ){\n    return;\n  }\n  osOutputDebugStringW((LPCWSTR)zDbgBuf);\n#else\n  if( nMin>0 ){\n    memset(zDbgBuf, 0, SQLITE_WIN32_DBG_BUF_SIZE);\n    memcpy(zDbgBuf, zBuf, nMin);\n    fprintf(stderr, \"%s\", zDbgBuf);\n  }else{\n    fprintf(stderr, \"%s\", zBuf);\n  }\n#endif\n}\n\n/*\n** The following routine suspends the current thread for at least ms\n** milliseconds.  This is equivalent to the Win32 Sleep() interface.\n*/\n#if SQLITE_OS_WINRT\nstatic HANDLE sleepObj = NULL;\n#endif\n\nSQLITE_API void sqlite3_win32_sleep(DWORD milliseconds){\n#if SQLITE_OS_WINRT\n  if ( sleepObj==NULL ){\n    sleepObj = osCreateEventExW(NULL, NULL, CREATE_EVENT_MANUAL_RESET,\n                                SYNCHRONIZE);\n  }\n  assert( sleepObj!=NULL );\n  osWaitForSingleObjectEx(sleepObj, milliseconds, FALSE);\n#else\n  osSleep(milliseconds);\n#endif\n}\n\n#if SQLITE_MAX_WORKER_THREADS>0 && !SQLITE_OS_WINCE && !SQLITE_OS_WINRT && \\\n        SQLITE_THREADSAFE>0\nSQLITE_PRIVATE DWORD sqlite3Win32Wait(HANDLE hObject){\n  DWORD rc;\n  while( (rc = osWaitForSingleObjectEx(hObject, INFINITE,\n                                       TRUE))==WAIT_IO_COMPLETION ){}\n  return rc;\n}\n#endif\n\n/*\n** Return true (non-zero) if we are running under WinNT, Win2K, WinXP,\n** or WinCE.  Return false (zero) for Win95, Win98, or WinME.\n**\n** Here is an interesting observation:  Win95, Win98, and WinME lack\n** the LockFileEx() API.  But we can still statically link against that\n** API as long as we don't call it when running Win95/98/ME.  A call to\n** this routine is used to determine if the host is Win95/98/ME or\n** WinNT/2K/XP so that we will know whether or not we can safely call\n** the LockFileEx() API.\n*/\n\n#if !SQLITE_WIN32_GETVERSIONEX\n# define osIsNT()  (1)\n#elif SQLITE_OS_WINCE || SQLITE_OS_WINRT || !defined(SQLITE_WIN32_HAS_ANSI)\n# define osIsNT()  (1)\n#elif !defined(SQLITE_WIN32_HAS_WIDE)\n# define osIsNT()  (0)\n#else\n# define osIsNT()  ((sqlite3_os_type==2) || sqlite3_win32_is_nt())\n#endif\n\n/*\n** This function determines if the machine is running a version of Windows\n** based on the NT kernel.\n*/\nSQLITE_API int sqlite3_win32_is_nt(void){\n#if SQLITE_OS_WINRT\n  /*\n  ** NOTE: The WinRT sub-platform is always assumed to be based on the NT\n  **       kernel.\n  */\n  return 1;\n#elif SQLITE_WIN32_GETVERSIONEX\n  if( osInterlockedCompareExchange(&sqlite3_os_type, 0, 0)==0 ){\n#if defined(SQLITE_WIN32_HAS_ANSI)\n    OSVERSIONINFOA sInfo;\n    sInfo.dwOSVersionInfoSize = sizeof(sInfo);\n    osGetVersionExA(&sInfo);\n    osInterlockedCompareExchange(&sqlite3_os_type,\n        (sInfo.dwPlatformId == VER_PLATFORM_WIN32_NT) ? 2 : 1, 0);\n#elif defined(SQLITE_WIN32_HAS_WIDE)\n    OSVERSIONINFOW sInfo;\n    sInfo.dwOSVersionInfoSize = sizeof(sInfo);\n    osGetVersionExW(&sInfo);\n    osInterlockedCompareExchange(&sqlite3_os_type,\n        (sInfo.dwPlatformId == VER_PLATFORM_WIN32_NT) ? 2 : 1, 0);\n#endif\n  }\n  return osInterlockedCompareExchange(&sqlite3_os_type, 2, 2)==2;\n#elif SQLITE_TEST\n  return osInterlockedCompareExchange(&sqlite3_os_type, 2, 2)==2;\n#else\n  /*\n  ** NOTE: All sub-platforms where the GetVersionEx[AW] functions are\n  **       deprecated are always assumed to be based on the NT kernel.\n  */\n  return 1;\n#endif\n}\n\n#ifdef SQLITE_WIN32_MALLOC\n/*\n** Allocate nBytes of memory.\n*/\nstatic void *winMemMalloc(int nBytes){\n  HANDLE hHeap;\n  void *p;\n\n  winMemAssertMagic();\n  hHeap = winMemGetHeap();\n  assert( hHeap!=0 );\n  assert( hHeap!=INVALID_HANDLE_VALUE );\n#if !SQLITE_OS_WINRT && defined(SQLITE_WIN32_MALLOC_VALIDATE)\n  assert( osHeapValidate(hHeap, SQLITE_WIN32_HEAP_FLAGS, NULL) );\n#endif\n  assert( nBytes>=0 );\n  p = osHeapAlloc(hHeap, SQLITE_WIN32_HEAP_FLAGS, (SIZE_T)nBytes);\n  if( !p ){\n    sqlite3_log(SQLITE_NOMEM, \"failed to HeapAlloc %u bytes (%lu), heap=%p\",\n                nBytes, osGetLastError(), (void*)hHeap);\n  }\n  return p;\n}\n\n/*\n** Free memory.\n*/\nstatic void winMemFree(void *pPrior){\n  HANDLE hHeap;\n\n  winMemAssertMagic();\n  hHeap = winMemGetHeap();\n  assert( hHeap!=0 );\n  assert( hHeap!=INVALID_HANDLE_VALUE );\n#if !SQLITE_OS_WINRT && defined(SQLITE_WIN32_MALLOC_VALIDATE)\n  assert( osHeapValidate(hHeap, SQLITE_WIN32_HEAP_FLAGS, pPrior) );\n#endif\n  if( !pPrior ) return; /* Passing NULL to HeapFree is undefined. */\n  if( !osHeapFree(hHeap, SQLITE_WIN32_HEAP_FLAGS, pPrior) ){\n    sqlite3_log(SQLITE_NOMEM, \"failed to HeapFree block %p (%lu), heap=%p\",\n                pPrior, osGetLastError(), (void*)hHeap);\n  }\n}\n\n/*\n** Change the size of an existing memory allocation\n*/\nstatic void *winMemRealloc(void *pPrior, int nBytes){\n  HANDLE hHeap;\n  void *p;\n\n  winMemAssertMagic();\n  hHeap = winMemGetHeap();\n  assert( hHeap!=0 );\n  assert( hHeap!=INVALID_HANDLE_VALUE );\n#if !SQLITE_OS_WINRT && defined(SQLITE_WIN32_MALLOC_VALIDATE)\n  assert( osHeapValidate(hHeap, SQLITE_WIN32_HEAP_FLAGS, pPrior) );\n#endif\n  assert( nBytes>=0 );\n  if( !pPrior ){\n    p = osHeapAlloc(hHeap, SQLITE_WIN32_HEAP_FLAGS, (SIZE_T)nBytes);\n  }else{\n    p = osHeapReAlloc(hHeap, SQLITE_WIN32_HEAP_FLAGS, pPrior, (SIZE_T)nBytes);\n  }\n  if( !p ){\n    sqlite3_log(SQLITE_NOMEM, \"failed to %s %u bytes (%lu), heap=%p\",\n                pPrior ? \"HeapReAlloc\" : \"HeapAlloc\", nBytes, osGetLastError(),\n                (void*)hHeap);\n  }\n  return p;\n}\n\n/*\n** Return the size of an outstanding allocation, in bytes.\n*/\nstatic int winMemSize(void *p){\n  HANDLE hHeap;\n  SIZE_T n;\n\n  winMemAssertMagic();\n  hHeap = winMemGetHeap();\n  assert( hHeap!=0 );\n  assert( hHeap!=INVALID_HANDLE_VALUE );\n#if !SQLITE_OS_WINRT && defined(SQLITE_WIN32_MALLOC_VALIDATE)\n  assert( osHeapValidate(hHeap, SQLITE_WIN32_HEAP_FLAGS, p) );\n#endif\n  if( !p ) return 0;\n  n = osHeapSize(hHeap, SQLITE_WIN32_HEAP_FLAGS, p);\n  if( n==(SIZE_T)-1 ){\n    sqlite3_log(SQLITE_NOMEM, \"failed to HeapSize block %p (%lu), heap=%p\",\n                p, osGetLastError(), (void*)hHeap);\n    return 0;\n  }\n  return (int)n;\n}\n\n/*\n** Round up a request size to the next valid allocation size.\n*/\nstatic int winMemRoundup(int n){\n  return n;\n}\n\n/*\n** Initialize this module.\n*/\nstatic int winMemInit(void *pAppData){\n  winMemData *pWinMemData = (winMemData *)pAppData;\n\n  if( !pWinMemData ) return SQLITE_ERROR;\n  assert( pWinMemData->magic1==WINMEM_MAGIC1 );\n  assert( pWinMemData->magic2==WINMEM_MAGIC2 );\n\n#if !SQLITE_OS_WINRT && SQLITE_WIN32_HEAP_CREATE\n  if( !pWinMemData->hHeap ){\n    DWORD dwInitialSize = SQLITE_WIN32_HEAP_INIT_SIZE;\n    DWORD dwMaximumSize = (DWORD)sqlite3GlobalConfig.nHeap;\n    if( dwMaximumSize==0 ){\n      dwMaximumSize = SQLITE_WIN32_HEAP_MAX_SIZE;\n    }else if( dwInitialSize>dwMaximumSize ){\n      dwInitialSize = dwMaximumSize;\n    }\n    pWinMemData->hHeap = osHeapCreate(SQLITE_WIN32_HEAP_FLAGS,\n                                      dwInitialSize, dwMaximumSize);\n    if( !pWinMemData->hHeap ){\n      sqlite3_log(SQLITE_NOMEM,\n          \"failed to HeapCreate (%lu), flags=%u, initSize=%lu, maxSize=%lu\",\n          osGetLastError(), SQLITE_WIN32_HEAP_FLAGS, dwInitialSize,\n          dwMaximumSize);\n      return SQLITE_NOMEM_BKPT;\n    }\n    pWinMemData->bOwned = TRUE;\n    assert( pWinMemData->bOwned );\n  }\n#else\n  pWinMemData->hHeap = osGetProcessHeap();\n  if( !pWinMemData->hHeap ){\n    sqlite3_log(SQLITE_NOMEM,\n        \"failed to GetProcessHeap (%lu)\", osGetLastError());\n    return SQLITE_NOMEM_BKPT;\n  }\n  pWinMemData->bOwned = FALSE;\n  assert( !pWinMemData->bOwned );\n#endif\n  assert( pWinMemData->hHeap!=0 );\n  assert( pWinMemData->hHeap!=INVALID_HANDLE_VALUE );\n#if !SQLITE_OS_WINRT && defined(SQLITE_WIN32_MALLOC_VALIDATE)\n  assert( osHeapValidate(pWinMemData->hHeap, SQLITE_WIN32_HEAP_FLAGS, NULL) );\n#endif\n  return SQLITE_OK;\n}\n\n/*\n** Deinitialize this module.\n*/\nstatic void winMemShutdown(void *pAppData){\n  winMemData *pWinMemData = (winMemData *)pAppData;\n\n  if( !pWinMemData ) return;\n  assert( pWinMemData->magic1==WINMEM_MAGIC1 );\n  assert( pWinMemData->magic2==WINMEM_MAGIC2 );\n\n  if( pWinMemData->hHeap ){\n    assert( pWinMemData->hHeap!=INVALID_HANDLE_VALUE );\n#if !SQLITE_OS_WINRT && defined(SQLITE_WIN32_MALLOC_VALIDATE)\n    assert( osHeapValidate(pWinMemData->hHeap, SQLITE_WIN32_HEAP_FLAGS, NULL) );\n#endif\n    if( pWinMemData->bOwned ){\n      if( !osHeapDestroy(pWinMemData->hHeap) ){\n        sqlite3_log(SQLITE_NOMEM, \"failed to HeapDestroy (%lu), heap=%p\",\n                    osGetLastError(), (void*)pWinMemData->hHeap);\n      }\n      pWinMemData->bOwned = FALSE;\n    }\n    pWinMemData->hHeap = NULL;\n  }\n}\n\n/*\n** Populate the low-level memory allocation function pointers in\n** sqlite3GlobalConfig.m with pointers to the routines in this file. The\n** arguments specify the block of memory to manage.\n**\n** This routine is only called by sqlite3_config(), and therefore\n** is not required to be threadsafe (it is not).\n*/\nSQLITE_PRIVATE const sqlite3_mem_methods *sqlite3MemGetWin32(void){\n  static const sqlite3_mem_methods winMemMethods = {\n    winMemMalloc,\n    winMemFree,\n    winMemRealloc,\n    winMemSize,\n    winMemRoundup,\n    winMemInit,\n    winMemShutdown,\n    &win_mem_data\n  };\n  return &winMemMethods;\n}\n\nSQLITE_PRIVATE void sqlite3MemSetDefault(void){\n  sqlite3_config(SQLITE_CONFIG_MALLOC, sqlite3MemGetWin32());\n}\n#endif /* SQLITE_WIN32_MALLOC */\n\n/*\n** Convert a UTF-8 string to Microsoft Unicode.\n**\n** Space to hold the returned string is obtained from sqlite3_malloc().\n*/\nstatic LPWSTR winUtf8ToUnicode(const char *zText){\n  int nChar;\n  LPWSTR zWideText;\n\n  nChar = osMultiByteToWideChar(CP_UTF8, 0, zText, -1, NULL, 0);\n  if( nChar==0 ){\n    return 0;\n  }\n  zWideText = sqlite3MallocZero( nChar*sizeof(WCHAR) );\n  if( zWideText==0 ){\n    return 0;\n  }\n  nChar = osMultiByteToWideChar(CP_UTF8, 0, zText, -1, zWideText,\n                                nChar);\n  if( nChar==0 ){\n    sqlite3_free(zWideText);\n    zWideText = 0;\n  }\n  return zWideText;\n}\n\n/*\n** Convert a Microsoft Unicode string to UTF-8.\n**\n** Space to hold the returned string is obtained from sqlite3_malloc().\n*/\nstatic char *winUnicodeToUtf8(LPCWSTR zWideText){\n  int nByte;\n  char *zText;\n\n  nByte = osWideCharToMultiByte(CP_UTF8, 0, zWideText, -1, 0, 0, 0, 0);\n  if( nByte == 0 ){\n    return 0;\n  }\n  zText = sqlite3MallocZero( nByte );\n  if( zText==0 ){\n    return 0;\n  }\n  nByte = osWideCharToMultiByte(CP_UTF8, 0, zWideText, -1, zText, nByte,\n                                0, 0);\n  if( nByte == 0 ){\n    sqlite3_free(zText);\n    zText = 0;\n  }\n  return zText;\n}\n\n/*\n** Convert an ANSI string to Microsoft Unicode, using the ANSI or OEM\n** code page.\n**\n** Space to hold the returned string is obtained from sqlite3_malloc().\n*/\nstatic LPWSTR winMbcsToUnicode(const char *zText, int useAnsi){\n  int nByte;\n  LPWSTR zMbcsText;\n  int codepage = useAnsi ? CP_ACP : CP_OEMCP;\n\n  nByte = osMultiByteToWideChar(codepage, 0, zText, -1, NULL,\n                                0)*sizeof(WCHAR);\n  if( nByte==0 ){\n    return 0;\n  }\n  zMbcsText = sqlite3MallocZero( nByte*sizeof(WCHAR) );\n  if( zMbcsText==0 ){\n    return 0;\n  }\n  nByte = osMultiByteToWideChar(codepage, 0, zText, -1, zMbcsText,\n                                nByte);\n  if( nByte==0 ){\n    sqlite3_free(zMbcsText);\n    zMbcsText = 0;\n  }\n  return zMbcsText;\n}\n\n/*\n** Convert a Microsoft Unicode string to a multi-byte character string,\n** using the ANSI or OEM code page.\n**\n** Space to hold the returned string is obtained from sqlite3_malloc().\n*/\nstatic char *winUnicodeToMbcs(LPCWSTR zWideText, int useAnsi){\n  int nByte;\n  char *zText;\n  int codepage = useAnsi ? CP_ACP : CP_OEMCP;\n\n  nByte = osWideCharToMultiByte(codepage, 0, zWideText, -1, 0, 0, 0, 0);\n  if( nByte == 0 ){\n    return 0;\n  }\n  zText = sqlite3MallocZero( nByte );\n  if( zText==0 ){\n    return 0;\n  }\n  nByte = osWideCharToMultiByte(codepage, 0, zWideText, -1, zText,\n                                nByte, 0, 0);\n  if( nByte == 0 ){\n    sqlite3_free(zText);\n    zText = 0;\n  }\n  return zText;\n}\n\n/*\n** Convert a multi-byte character string to UTF-8.\n**\n** Space to hold the returned string is obtained from sqlite3_malloc().\n*/\nstatic char *winMbcsToUtf8(const char *zText, int useAnsi){\n  char *zTextUtf8;\n  LPWSTR zTmpWide;\n\n  zTmpWide = winMbcsToUnicode(zText, useAnsi);\n  if( zTmpWide==0 ){\n    return 0;\n  }\n  zTextUtf8 = winUnicodeToUtf8(zTmpWide);\n  sqlite3_free(zTmpWide);\n  return zTextUtf8;\n}\n\n/*\n** Convert a UTF-8 string to a multi-byte character string.\n**\n** Space to hold the returned string is obtained from sqlite3_malloc().\n*/\nstatic char *winUtf8ToMbcs(const char *zText, int useAnsi){\n  char *zTextMbcs;\n  LPWSTR zTmpWide;\n\n  zTmpWide = winUtf8ToUnicode(zText);\n  if( zTmpWide==0 ){\n    return 0;\n  }\n  zTextMbcs = winUnicodeToMbcs(zTmpWide, useAnsi);\n  sqlite3_free(zTmpWide);\n  return zTextMbcs;\n}\n\n/*\n** This is a public wrapper for the winUtf8ToUnicode() function.\n*/\nSQLITE_API LPWSTR sqlite3_win32_utf8_to_unicode(const char *zText){\n#ifdef SQLITE_ENABLE_API_ARMOR\n  if( !zText ){\n    (void)SQLITE_MISUSE_BKPT;\n    return 0;\n  }\n#endif\n#ifndef SQLITE_OMIT_AUTOINIT\n  if( sqlite3_initialize() ) return 0;\n#endif\n  return winUtf8ToUnicode(zText);\n}\n\n/*\n** This is a public wrapper for the winUnicodeToUtf8() function.\n*/\nSQLITE_API char *sqlite3_win32_unicode_to_utf8(LPCWSTR zWideText){\n#ifdef SQLITE_ENABLE_API_ARMOR\n  if( !zWideText ){\n    (void)SQLITE_MISUSE_BKPT;\n    return 0;\n  }\n#endif\n#ifndef SQLITE_OMIT_AUTOINIT\n  if( sqlite3_initialize() ) return 0;\n#endif\n  return winUnicodeToUtf8(zWideText);\n}\n\n/*\n** This is a public wrapper for the winMbcsToUtf8() function.\n*/\nSQLITE_API char *sqlite3_win32_mbcs_to_utf8(const char *zText){\n#ifdef SQLITE_ENABLE_API_ARMOR\n  if( !zText ){\n    (void)SQLITE_MISUSE_BKPT;\n    return 0;\n  }\n#endif\n#ifndef SQLITE_OMIT_AUTOINIT\n  if( sqlite3_initialize() ) return 0;\n#endif\n  return winMbcsToUtf8(zText, osAreFileApisANSI());\n}\n\n/*\n** This is a public wrapper for the winMbcsToUtf8() function.\n*/\nSQLITE_API char *sqlite3_win32_mbcs_to_utf8_v2(const char *zText, int useAnsi){\n#ifdef SQLITE_ENABLE_API_ARMOR\n  if( !zText ){\n    (void)SQLITE_MISUSE_BKPT;\n    return 0;\n  }\n#endif\n#ifndef SQLITE_OMIT_AUTOINIT\n  if( sqlite3_initialize() ) return 0;\n#endif\n  return winMbcsToUtf8(zText, useAnsi);\n}\n\n/*\n** This is a public wrapper for the winUtf8ToMbcs() function.\n*/\nSQLITE_API char *sqlite3_win32_utf8_to_mbcs(const char *zText){\n#ifdef SQLITE_ENABLE_API_ARMOR\n  if( !zText ){\n    (void)SQLITE_MISUSE_BKPT;\n    return 0;\n  }\n#endif\n#ifndef SQLITE_OMIT_AUTOINIT\n  if( sqlite3_initialize() ) return 0;\n#endif\n  return winUtf8ToMbcs(zText, osAreFileApisANSI());\n}\n\n/*\n** This is a public wrapper for the winUtf8ToMbcs() function.\n*/\nSQLITE_API char *sqlite3_win32_utf8_to_mbcs_v2(const char *zText, int useAnsi){\n#ifdef SQLITE_ENABLE_API_ARMOR\n  if( !zText ){\n    (void)SQLITE_MISUSE_BKPT;\n    return 0;\n  }\n#endif\n#ifndef SQLITE_OMIT_AUTOINIT\n  if( sqlite3_initialize() ) return 0;\n#endif\n  return winUtf8ToMbcs(zText, useAnsi);\n}\n\n/*\n** This function sets the data directory or the temporary directory based on\n** the provided arguments.  The type argument must be 1 in order to set the\n** data directory or 2 in order to set the temporary directory.  The zValue\n** argument is the name of the directory to use.  The return value will be\n** SQLITE_OK if successful.\n*/\nSQLITE_API int sqlite3_win32_set_directory(DWORD type, LPCWSTR zValue){\n  char **ppDirectory = 0;\n#ifndef SQLITE_OMIT_AUTOINIT\n  int rc = sqlite3_initialize();\n  if( rc ) return rc;\n#endif\n  if( type==SQLITE_WIN32_DATA_DIRECTORY_TYPE ){\n    ppDirectory = &sqlite3_data_directory;\n  }else if( type==SQLITE_WIN32_TEMP_DIRECTORY_TYPE ){\n    ppDirectory = &sqlite3_temp_directory;\n  }\n  assert( !ppDirectory || type==SQLITE_WIN32_DATA_DIRECTORY_TYPE\n          || type==SQLITE_WIN32_TEMP_DIRECTORY_TYPE\n  );\n  assert( !ppDirectory || sqlite3MemdebugHasType(*ppDirectory, MEMTYPE_HEAP) );\n  if( ppDirectory ){\n    char *zValueUtf8 = 0;\n    if( zValue && zValue[0] ){\n      zValueUtf8 = winUnicodeToUtf8(zValue);\n      if ( zValueUtf8==0 ){\n        return SQLITE_NOMEM_BKPT;\n      }\n    }\n    sqlite3_free(*ppDirectory);\n    *ppDirectory = zValueUtf8;\n    return SQLITE_OK;\n  }\n  return SQLITE_ERROR;\n}\n\n/*\n** The return value of winGetLastErrorMsg\n** is zero if the error message fits in the buffer, or non-zero\n** otherwise (if the message was truncated).\n*/\nstatic int winGetLastErrorMsg(DWORD lastErrno, int nBuf, char *zBuf){\n  /* FormatMessage returns 0 on failure.  Otherwise it\n  ** returns the number of TCHARs written to the output\n  ** buffer, excluding the terminating null char.\n  */\n  DWORD dwLen = 0;\n  char *zOut = 0;\n\n  if( osIsNT() ){\n#if SQLITE_OS_WINRT\n    WCHAR zTempWide[SQLITE_WIN32_MAX_ERRMSG_CHARS+1];\n    dwLen = osFormatMessageW(FORMAT_MESSAGE_FROM_SYSTEM |\n                             FORMAT_MESSAGE_IGNORE_INSERTS,\n                             NULL,\n                             lastErrno,\n                             0,\n                             zTempWide,\n                             SQLITE_WIN32_MAX_ERRMSG_CHARS,\n                             0);\n#else\n    LPWSTR zTempWide = NULL;\n    dwLen = osFormatMessageW(FORMAT_MESSAGE_ALLOCATE_BUFFER |\n                             FORMAT_MESSAGE_FROM_SYSTEM |\n                             FORMAT_MESSAGE_IGNORE_INSERTS,\n                             NULL,\n                             lastErrno,\n                             0,\n                             (LPWSTR) &zTempWide,\n                             0,\n                             0);\n#endif\n    if( dwLen > 0 ){\n      /* allocate a buffer and convert to UTF8 */\n      sqlite3BeginBenignMalloc();\n      zOut = winUnicodeToUtf8(zTempWide);\n      sqlite3EndBenignMalloc();\n#if !SQLITE_OS_WINRT\n      /* free the system buffer allocated by FormatMessage */\n      osLocalFree(zTempWide);\n#endif\n    }\n  }\n#ifdef SQLITE_WIN32_HAS_ANSI\n  else{\n    char *zTemp = NULL;\n    dwLen = osFormatMessageA(FORMAT_MESSAGE_ALLOCATE_BUFFER |\n                             FORMAT_MESSAGE_FROM_SYSTEM |\n                             FORMAT_MESSAGE_IGNORE_INSERTS,\n                             NULL,\n                             lastErrno,\n                             0,\n                             (LPSTR) &zTemp,\n                             0,\n                             0);\n    if( dwLen > 0 ){\n      /* allocate a buffer and convert to UTF8 */\n      sqlite3BeginBenignMalloc();\n      zOut = winMbcsToUtf8(zTemp, osAreFileApisANSI());\n      sqlite3EndBenignMalloc();\n      /* free the system buffer allocated by FormatMessage */\n      osLocalFree(zTemp);\n    }\n  }\n#endif\n  if( 0 == dwLen ){\n    sqlite3_snprintf(nBuf, zBuf, \"OsError 0x%lx (%lu)\", lastErrno, lastErrno);\n  }else{\n    /* copy a maximum of nBuf chars to output buffer */\n    sqlite3_snprintf(nBuf, zBuf, \"%s\", zOut);\n    /* free the UTF8 buffer */\n    sqlite3_free(zOut);\n  }\n  return 0;\n}\n\n/*\n**\n** This function - winLogErrorAtLine() - is only ever called via the macro\n** winLogError().\n**\n** This routine is invoked after an error occurs in an OS function.\n** It logs a message using sqlite3_log() containing the current value of\n** error code and, if possible, the human-readable equivalent from\n** FormatMessage.\n**\n** The first argument passed to the macro should be the error code that\n** will be returned to SQLite (e.g. SQLITE_IOERR_DELETE, SQLITE_CANTOPEN).\n** The two subsequent arguments should be the name of the OS function that\n** failed and the associated file-system path, if any.\n*/\n#define winLogError(a,b,c,d)   winLogErrorAtLine(a,b,c,d,__LINE__)\nstatic int winLogErrorAtLine(\n  int errcode,                    /* SQLite error code */\n  DWORD lastErrno,                /* Win32 last error */\n  const char *zFunc,              /* Name of OS function that failed */\n  const char *zPath,              /* File path associated with error */\n  int iLine                       /* Source line number where error occurred */\n){\n  char zMsg[500];                 /* Human readable error text */\n  int i;                          /* Loop counter */\n\n  zMsg[0] = 0;\n  winGetLastErrorMsg(lastErrno, sizeof(zMsg), zMsg);\n  assert( errcode!=SQLITE_OK );\n  if( zPath==0 ) zPath = \"\";\n  for(i=0; zMsg[i] && zMsg[i]!='\\r' && zMsg[i]!='\\n'; i++){}\n  zMsg[i] = 0;\n  sqlite3_log(errcode,\n      \"os_win.c:%d: (%lu) %s(%s) - %s\",\n      iLine, lastErrno, zFunc, zPath, zMsg\n  );\n\n  return errcode;\n}\n\n/*\n** The number of times that a ReadFile(), WriteFile(), and DeleteFile()\n** will be retried following a locking error - probably caused by\n** antivirus software.  Also the initial delay before the first retry.\n** The delay increases linearly with each retry.\n*/\n#ifndef SQLITE_WIN32_IOERR_RETRY\n# define SQLITE_WIN32_IOERR_RETRY 10\n#endif\n#ifndef SQLITE_WIN32_IOERR_RETRY_DELAY\n# define SQLITE_WIN32_IOERR_RETRY_DELAY 25\n#endif\nstatic int winIoerrRetry = SQLITE_WIN32_IOERR_RETRY;\nstatic int winIoerrRetryDelay = SQLITE_WIN32_IOERR_RETRY_DELAY;\n\n/*\n** The \"winIoerrCanRetry1\" macro is used to determine if a particular I/O\n** error code obtained via GetLastError() is eligible to be retried.  It\n** must accept the error code DWORD as its only argument and should return\n** non-zero if the error code is transient in nature and the operation\n** responsible for generating the original error might succeed upon being\n** retried.  The argument to this macro should be a variable.\n**\n** Additionally, a macro named \"winIoerrCanRetry2\" may be defined.  If it\n** is defined, it will be consulted only when the macro \"winIoerrCanRetry1\"\n** returns zero.  The \"winIoerrCanRetry2\" macro is completely optional and\n** may be used to include additional error codes in the set that should\n** result in the failing I/O operation being retried by the caller.  If\n** defined, the \"winIoerrCanRetry2\" macro must exhibit external semantics\n** identical to those of the \"winIoerrCanRetry1\" macro.\n*/\n#if !defined(winIoerrCanRetry1)\n#define winIoerrCanRetry1(a) (((a)==ERROR_ACCESS_DENIED)        || \\\n                              ((a)==ERROR_SHARING_VIOLATION)    || \\\n                              ((a)==ERROR_LOCK_VIOLATION)       || \\\n                              ((a)==ERROR_DEV_NOT_EXIST)        || \\\n                              ((a)==ERROR_NETNAME_DELETED)      || \\\n                              ((a)==ERROR_SEM_TIMEOUT)          || \\\n                              ((a)==ERROR_NETWORK_UNREACHABLE))\n#endif\n\n/*\n** If a ReadFile() or WriteFile() error occurs, invoke this routine\n** to see if it should be retried.  Return TRUE to retry.  Return FALSE\n** to give up with an error.\n*/\nstatic int winRetryIoerr(int *pnRetry, DWORD *pError){\n  DWORD e = osGetLastError();\n  if( *pnRetry>=winIoerrRetry ){\n    if( pError ){\n      *pError = e;\n    }\n    return 0;\n  }\n  if( winIoerrCanRetry1(e) ){\n    sqlite3_win32_sleep(winIoerrRetryDelay*(1+*pnRetry));\n    ++*pnRetry;\n    return 1;\n  }\n#if defined(winIoerrCanRetry2)\n  else if( winIoerrCanRetry2(e) ){\n    sqlite3_win32_sleep(winIoerrRetryDelay*(1+*pnRetry));\n    ++*pnRetry;\n    return 1;\n  }\n#endif\n  if( pError ){\n    *pError = e;\n  }\n  return 0;\n}\n\n/*\n** Log a I/O error retry episode.\n*/\nstatic void winLogIoerr(int nRetry, int lineno){\n  if( nRetry ){\n    sqlite3_log(SQLITE_NOTICE,\n      \"delayed %dms for lock/sharing conflict at line %d\",\n      winIoerrRetryDelay*nRetry*(nRetry+1)/2, lineno\n    );\n  }\n}\n\n/*\n** This #if does not rely on the SQLITE_OS_WINCE define because the\n** corresponding section in \"date.c\" cannot use it.\n*/\n#if !defined(SQLITE_OMIT_LOCALTIME) && defined(_WIN32_WCE) && \\\n    (!defined(SQLITE_MSVC_LOCALTIME_API) || !SQLITE_MSVC_LOCALTIME_API)\n/*\n** The MSVC CRT on Windows CE may not have a localtime() function.\n** So define a substitute.\n*/\n/* #  include <time.h> */\nstruct tm *__cdecl localtime(const time_t *t)\n{\n  static struct tm y;\n  FILETIME uTm, lTm;\n  SYSTEMTIME pTm;\n  sqlite3_int64 t64;\n  t64 = *t;\n  t64 = (t64 + 11644473600)*10000000;\n  uTm.dwLowDateTime = (DWORD)(t64 & 0xFFFFFFFF);\n  uTm.dwHighDateTime= (DWORD)(t64 >> 32);\n  osFileTimeToLocalFileTime(&uTm,&lTm);\n  osFileTimeToSystemTime(&lTm,&pTm);\n  y.tm_year = pTm.wYear - 1900;\n  y.tm_mon = pTm.wMonth - 1;\n  y.tm_wday = pTm.wDayOfWeek;\n  y.tm_mday = pTm.wDay;\n  y.tm_hour = pTm.wHour;\n  y.tm_min = pTm.wMinute;\n  y.tm_sec = pTm.wSecond;\n  return &y;\n}\n#endif\n\n#if SQLITE_OS_WINCE\n/*************************************************************************\n** This section contains code for WinCE only.\n*/\n#define HANDLE_TO_WINFILE(a) (winFile*)&((char*)a)[-(int)offsetof(winFile,h)]\n\n/*\n** Acquire a lock on the handle h\n*/\nstatic void winceMutexAcquire(HANDLE h){\n   DWORD dwErr;\n   do {\n     dwErr = osWaitForSingleObject(h, INFINITE);\n   } while (dwErr != WAIT_OBJECT_0 && dwErr != WAIT_ABANDONED);\n}\n/*\n** Release a lock acquired by winceMutexAcquire()\n*/\n#define winceMutexRelease(h) ReleaseMutex(h)\n\n/*\n** Create the mutex and shared memory used for locking in the file\n** descriptor pFile\n*/\nstatic int winceCreateLock(const char *zFilename, winFile *pFile){\n  LPWSTR zTok;\n  LPWSTR zName;\n  DWORD lastErrno;\n  BOOL bLogged = FALSE;\n  BOOL bInit = TRUE;\n\n  zName = winUtf8ToUnicode(zFilename);\n  if( zName==0 ){\n    /* out of memory */\n    return SQLITE_IOERR_NOMEM_BKPT;\n  }\n\n  /* Initialize the local lockdata */\n  memset(&pFile->local, 0, sizeof(pFile->local));\n\n  /* Replace the backslashes from the filename and lowercase it\n  ** to derive a mutex name. */\n  zTok = osCharLowerW(zName);\n  for (;*zTok;zTok++){\n    if (*zTok == '\\\\') *zTok = '_';\n  }\n\n  /* Create/open the named mutex */\n  pFile->hMutex = osCreateMutexW(NULL, FALSE, zName);\n  if (!pFile->hMutex){\n    pFile->lastErrno = osGetLastError();\n    sqlite3_free(zName);\n    return winLogError(SQLITE_IOERR, pFile->lastErrno,\n                       \"winceCreateLock1\", zFilename);\n  }\n\n  /* Acquire the mutex before continuing */\n  winceMutexAcquire(pFile->hMutex);\n\n  /* Since the names of named mutexes, semaphores, file mappings etc are\n  ** case-sensitive, take advantage of that by uppercasing the mutex name\n  ** and using that as the shared filemapping name.\n  */\n  osCharUpperW(zName);\n  pFile->hShared = osCreateFileMappingW(INVALID_HANDLE_VALUE, NULL,\n                                        PAGE_READWRITE, 0, sizeof(winceLock),\n                                        zName);\n\n  /* Set a flag that indicates we're the first to create the memory so it\n  ** must be zero-initialized */\n  lastErrno = osGetLastError();\n  if (lastErrno == ERROR_ALREADY_EXISTS){\n    bInit = FALSE;\n  }\n\n  sqlite3_free(zName);\n\n  /* If we succeeded in making the shared memory handle, map it. */\n  if( pFile->hShared ){\n    pFile->shared = (winceLock*)osMapViewOfFile(pFile->hShared,\n             FILE_MAP_READ|FILE_MAP_WRITE, 0, 0, sizeof(winceLock));\n    /* If mapping failed, close the shared memory handle and erase it */\n    if( !pFile->shared ){\n      pFile->lastErrno = osGetLastError();\n      winLogError(SQLITE_IOERR, pFile->lastErrno,\n                  \"winceCreateLock2\", zFilename);\n      bLogged = TRUE;\n      osCloseHandle(pFile->hShared);\n      pFile->hShared = NULL;\n    }\n  }\n\n  /* If shared memory could not be created, then close the mutex and fail */\n  if( pFile->hShared==NULL ){\n    if( !bLogged ){\n      pFile->lastErrno = lastErrno;\n      winLogError(SQLITE_IOERR, pFile->lastErrno,\n                  \"winceCreateLock3\", zFilename);\n      bLogged = TRUE;\n    }\n    winceMutexRelease(pFile->hMutex);\n    osCloseHandle(pFile->hMutex);\n    pFile->hMutex = NULL;\n    return SQLITE_IOERR;\n  }\n\n  /* Initialize the shared memory if we're supposed to */\n  if( bInit ){\n    memset(pFile->shared, 0, sizeof(winceLock));\n  }\n\n  winceMutexRelease(pFile->hMutex);\n  return SQLITE_OK;\n}\n\n/*\n** Destroy the part of winFile that deals with wince locks\n*/\nstatic void winceDestroyLock(winFile *pFile){\n  if (pFile->hMutex){\n    /* Acquire the mutex */\n    winceMutexAcquire(pFile->hMutex);\n\n    /* The following blocks should probably assert in debug mode, but they\n       are to cleanup in case any locks remained open */\n    if (pFile->local.nReaders){\n      pFile->shared->nReaders --;\n    }\n    if (pFile->local.bReserved){\n      pFile->shared->bReserved = FALSE;\n    }\n    if (pFile->local.bPending){\n      pFile->shared->bPending = FALSE;\n    }\n    if (pFile->local.bExclusive){\n      pFile->shared->bExclusive = FALSE;\n    }\n\n    /* De-reference and close our copy of the shared memory handle */\n    osUnmapViewOfFile(pFile->shared);\n    osCloseHandle(pFile->hShared);\n\n    /* Done with the mutex */\n    winceMutexRelease(pFile->hMutex);\n    osCloseHandle(pFile->hMutex);\n    pFile->hMutex = NULL;\n  }\n}\n\n/*\n** An implementation of the LockFile() API of Windows for CE\n*/\nstatic BOOL winceLockFile(\n  LPHANDLE phFile,\n  DWORD dwFileOffsetLow,\n  DWORD dwFileOffsetHigh,\n  DWORD nNumberOfBytesToLockLow,\n  DWORD nNumberOfBytesToLockHigh\n){\n  winFile *pFile = HANDLE_TO_WINFILE(phFile);\n  BOOL bReturn = FALSE;\n\n  UNUSED_PARAMETER(dwFileOffsetHigh);\n  UNUSED_PARAMETER(nNumberOfBytesToLockHigh);\n\n  if (!pFile->hMutex) return TRUE;\n  winceMutexAcquire(pFile->hMutex);\n\n  /* Wanting an exclusive lock? */\n  if (dwFileOffsetLow == (DWORD)SHARED_FIRST\n       && nNumberOfBytesToLockLow == (DWORD)SHARED_SIZE){\n    if (pFile->shared->nReaders == 0 && pFile->shared->bExclusive == 0){\n       pFile->shared->bExclusive = TRUE;\n       pFile->local.bExclusive = TRUE;\n       bReturn = TRUE;\n    }\n  }\n\n  /* Want a read-only lock? */\n  else if (dwFileOffsetLow == (DWORD)SHARED_FIRST &&\n           nNumberOfBytesToLockLow == 1){\n    if (pFile->shared->bExclusive == 0){\n      pFile->local.nReaders ++;\n      if (pFile->local.nReaders == 1){\n        pFile->shared->nReaders ++;\n      }\n      bReturn = TRUE;\n    }\n  }\n\n  /* Want a pending lock? */\n  else if (dwFileOffsetLow == (DWORD)PENDING_BYTE\n           && nNumberOfBytesToLockLow == 1){\n    /* If no pending lock has been acquired, then acquire it */\n    if (pFile->shared->bPending == 0) {\n      pFile->shared->bPending = TRUE;\n      pFile->local.bPending = TRUE;\n      bReturn = TRUE;\n    }\n  }\n\n  /* Want a reserved lock? */\n  else if (dwFileOffsetLow == (DWORD)RESERVED_BYTE\n           && nNumberOfBytesToLockLow == 1){\n    if (pFile->shared->bReserved == 0) {\n      pFile->shared->bReserved = TRUE;\n      pFile->local.bReserved = TRUE;\n      bReturn = TRUE;\n    }\n  }\n\n  winceMutexRelease(pFile->hMutex);\n  return bReturn;\n}\n\n/*\n** An implementation of the UnlockFile API of Windows for CE\n*/\nstatic BOOL winceUnlockFile(\n  LPHANDLE phFile,\n  DWORD dwFileOffsetLow,\n  DWORD dwFileOffsetHigh,\n  DWORD nNumberOfBytesToUnlockLow,\n  DWORD nNumberOfBytesToUnlockHigh\n){\n  winFile *pFile = HANDLE_TO_WINFILE(phFile);\n  BOOL bReturn = FALSE;\n\n  UNUSED_PARAMETER(dwFileOffsetHigh);\n  UNUSED_PARAMETER(nNumberOfBytesToUnlockHigh);\n\n  if (!pFile->hMutex) return TRUE;\n  winceMutexAcquire(pFile->hMutex);\n\n  /* Releasing a reader lock or an exclusive lock */\n  if (dwFileOffsetLow == (DWORD)SHARED_FIRST){\n    /* Did we have an exclusive lock? */\n    if (pFile->local.bExclusive){\n      assert(nNumberOfBytesToUnlockLow == (DWORD)SHARED_SIZE);\n      pFile->local.bExclusive = FALSE;\n      pFile->shared->bExclusive = FALSE;\n      bReturn = TRUE;\n    }\n\n    /* Did we just have a reader lock? */\n    else if (pFile->local.nReaders){\n      assert(nNumberOfBytesToUnlockLow == (DWORD)SHARED_SIZE\n             || nNumberOfBytesToUnlockLow == 1);\n      pFile->local.nReaders --;\n      if (pFile->local.nReaders == 0)\n      {\n        pFile->shared->nReaders --;\n      }\n      bReturn = TRUE;\n    }\n  }\n\n  /* Releasing a pending lock */\n  else if (dwFileOffsetLow == (DWORD)PENDING_BYTE\n           && nNumberOfBytesToUnlockLow == 1){\n    if (pFile->local.bPending){\n      pFile->local.bPending = FALSE;\n      pFile->shared->bPending = FALSE;\n      bReturn = TRUE;\n    }\n  }\n  /* Releasing a reserved lock */\n  else if (dwFileOffsetLow == (DWORD)RESERVED_BYTE\n           && nNumberOfBytesToUnlockLow == 1){\n    if (pFile->local.bReserved) {\n      pFile->local.bReserved = FALSE;\n      pFile->shared->bReserved = FALSE;\n      bReturn = TRUE;\n    }\n  }\n\n  winceMutexRelease(pFile->hMutex);\n  return bReturn;\n}\n/*\n** End of the special code for wince\n*****************************************************************************/\n#endif /* SQLITE_OS_WINCE */\n\n/*\n** Lock a file region.\n*/\nstatic BOOL winLockFile(\n  LPHANDLE phFile,\n  DWORD flags,\n  DWORD offsetLow,\n  DWORD offsetHigh,\n  DWORD numBytesLow,\n  DWORD numBytesHigh\n){\n#if SQLITE_OS_WINCE\n  /*\n  ** NOTE: Windows CE is handled differently here due its lack of the Win32\n  **       API LockFile.\n  */\n  return winceLockFile(phFile, offsetLow, offsetHigh,\n                       numBytesLow, numBytesHigh);\n#else\n  if( osIsNT() ){\n    OVERLAPPED ovlp;\n    memset(&ovlp, 0, sizeof(OVERLAPPED));\n    ovlp.Offset = offsetLow;\n    ovlp.OffsetHigh = offsetHigh;\n    return osLockFileEx(*phFile, flags, 0, numBytesLow, numBytesHigh, &ovlp);\n  }else{\n    return osLockFile(*phFile, offsetLow, offsetHigh, numBytesLow,\n                      numBytesHigh);\n  }\n#endif\n}\n\n/*\n** Unlock a file region.\n */\nstatic BOOL winUnlockFile(\n  LPHANDLE phFile,\n  DWORD offsetLow,\n  DWORD offsetHigh,\n  DWORD numBytesLow,\n  DWORD numBytesHigh\n){\n#if SQLITE_OS_WINCE\n  /*\n  ** NOTE: Windows CE is handled differently here due its lack of the Win32\n  **       API UnlockFile.\n  */\n  return winceUnlockFile(phFile, offsetLow, offsetHigh,\n                         numBytesLow, numBytesHigh);\n#else\n  if( osIsNT() ){\n    OVERLAPPED ovlp;\n    memset(&ovlp, 0, sizeof(OVERLAPPED));\n    ovlp.Offset = offsetLow;\n    ovlp.OffsetHigh = offsetHigh;\n    return osUnlockFileEx(*phFile, 0, numBytesLow, numBytesHigh, &ovlp);\n  }else{\n    return osUnlockFile(*phFile, offsetLow, offsetHigh, numBytesLow,\n                        numBytesHigh);\n  }\n#endif\n}\n\n/*****************************************************************************\n** The next group of routines implement the I/O methods specified\n** by the sqlite3_io_methods object.\n******************************************************************************/\n\n/*\n** Some Microsoft compilers lack this definition.\n*/\n#ifndef INVALID_SET_FILE_POINTER\n# define INVALID_SET_FILE_POINTER ((DWORD)-1)\n#endif\n\n/*\n** Move the current position of the file handle passed as the first\n** argument to offset iOffset within the file. If successful, return 0.\n** Otherwise, set pFile->lastErrno and return non-zero.\n*/\nstatic int winSeekFile(winFile *pFile, sqlite3_int64 iOffset){\n#if !SQLITE_OS_WINRT\n  LONG upperBits;                 /* Most sig. 32 bits of new offset */\n  LONG lowerBits;                 /* Least sig. 32 bits of new offset */\n  DWORD dwRet;                    /* Value returned by SetFilePointer() */\n  DWORD lastErrno;                /* Value returned by GetLastError() */\n\n  OSTRACE((\"SEEK file=%p, offset=%lld\\n\", pFile->h, iOffset));\n\n  upperBits = (LONG)((iOffset>>32) & 0x7fffffff);\n  lowerBits = (LONG)(iOffset & 0xffffffff);\n\n  /* API oddity: If successful, SetFilePointer() returns a dword\n  ** containing the lower 32-bits of the new file-offset. Or, if it fails,\n  ** it returns INVALID_SET_FILE_POINTER. However according to MSDN,\n  ** INVALID_SET_FILE_POINTER may also be a valid new offset. So to determine\n  ** whether an error has actually occurred, it is also necessary to call\n  ** GetLastError().\n  */\n  dwRet = osSetFilePointer(pFile->h, lowerBits, &upperBits, FILE_BEGIN);\n\n  if( (dwRet==INVALID_SET_FILE_POINTER\n      && ((lastErrno = osGetLastError())!=NO_ERROR)) ){\n    pFile->lastErrno = lastErrno;\n    winLogError(SQLITE_IOERR_SEEK, pFile->lastErrno,\n                \"winSeekFile\", pFile->zPath);\n    OSTRACE((\"SEEK file=%p, rc=SQLITE_IOERR_SEEK\\n\", pFile->h));\n    return 1;\n  }\n\n  OSTRACE((\"SEEK file=%p, rc=SQLITE_OK\\n\", pFile->h));\n  return 0;\n#else\n  /*\n  ** Same as above, except that this implementation works for WinRT.\n  */\n\n  LARGE_INTEGER x;                /* The new offset */\n  BOOL bRet;                      /* Value returned by SetFilePointerEx() */\n\n  x.QuadPart = iOffset;\n  bRet = osSetFilePointerEx(pFile->h, x, 0, FILE_BEGIN);\n\n  if(!bRet){\n    pFile->lastErrno = osGetLastError();\n    winLogError(SQLITE_IOERR_SEEK, pFile->lastErrno,\n                \"winSeekFile\", pFile->zPath);\n    OSTRACE((\"SEEK file=%p, rc=SQLITE_IOERR_SEEK\\n\", pFile->h));\n    return 1;\n  }\n\n  OSTRACE((\"SEEK file=%p, rc=SQLITE_OK\\n\", pFile->h));\n  return 0;\n#endif\n}\n\n#if SQLITE_MAX_MMAP_SIZE>0\n/* Forward references to VFS helper methods used for memory mapped files */\nstatic int winMapfile(winFile*, sqlite3_int64);\nstatic int winUnmapfile(winFile*);\n#endif\n\n/*\n** Close a file.\n**\n** It is reported that an attempt to close a handle might sometimes\n** fail.  This is a very unreasonable result, but Windows is notorious\n** for being unreasonable so I do not doubt that it might happen.  If\n** the close fails, we pause for 100 milliseconds and try again.  As\n** many as MX_CLOSE_ATTEMPT attempts to close the handle are made before\n** giving up and returning an error.\n*/\n#define MX_CLOSE_ATTEMPT 3\nstatic int winClose(sqlite3_file *id){\n  int rc, cnt = 0;\n  winFile *pFile = (winFile*)id;\n\n  assert( id!=0 );\n#ifndef SQLITE_OMIT_WAL\n  assert( pFile->pShm==0 );\n#endif\n  assert( pFile->h!=NULL && pFile->h!=INVALID_HANDLE_VALUE );\n  OSTRACE((\"CLOSE pid=%lu, pFile=%p, file=%p\\n\",\n           osGetCurrentProcessId(), pFile, pFile->h));\n\n#if SQLITE_MAX_MMAP_SIZE>0\n  winUnmapfile(pFile);\n#endif\n\n  do{\n    rc = osCloseHandle(pFile->h);\n    /* SimulateIOError( rc=0; cnt=MX_CLOSE_ATTEMPT; ); */\n  }while( rc==0 && ++cnt < MX_CLOSE_ATTEMPT && (sqlite3_win32_sleep(100), 1) );\n#if SQLITE_OS_WINCE\n#define WINCE_DELETION_ATTEMPTS 3\n  {\n    winVfsAppData *pAppData = (winVfsAppData*)pFile->pVfs->pAppData;\n    if( pAppData==NULL || !pAppData->bNoLock ){\n      winceDestroyLock(pFile);\n    }\n  }\n  if( pFile->zDeleteOnClose ){\n    int cnt = 0;\n    while(\n           osDeleteFileW(pFile->zDeleteOnClose)==0\n        && osGetFileAttributesW(pFile->zDeleteOnClose)!=0xffffffff\n        && cnt++ < WINCE_DELETION_ATTEMPTS\n    ){\n       sqlite3_win32_sleep(100);  /* Wait a little before trying again */\n    }\n    sqlite3_free(pFile->zDeleteOnClose);\n  }\n#endif\n  if( rc ){\n    pFile->h = NULL;\n  }\n  OpenCounter(-1);\n  OSTRACE((\"CLOSE pid=%lu, pFile=%p, file=%p, rc=%s\\n\",\n           osGetCurrentProcessId(), pFile, pFile->h, rc ? \"ok\" : \"failed\"));\n  return rc ? SQLITE_OK\n            : winLogError(SQLITE_IOERR_CLOSE, osGetLastError(),\n                          \"winClose\", pFile->zPath);\n}\n\n/*\n** Read data from a file into a buffer.  Return SQLITE_OK if all\n** bytes were read successfully and SQLITE_IOERR if anything goes\n** wrong.\n*/\nstatic int winRead(\n  sqlite3_file *id,          /* File to read from */\n  void *pBuf,                /* Write content into this buffer */\n  int amt,                   /* Number of bytes to read */\n  sqlite3_int64 offset       /* Begin reading at this offset */\n){\n#if !SQLITE_OS_WINCE && !defined(SQLITE_WIN32_NO_OVERLAPPED)\n  OVERLAPPED overlapped;          /* The offset for ReadFile. */\n#endif\n  winFile *pFile = (winFile*)id;  /* file handle */\n  DWORD nRead;                    /* Number of bytes actually read from file */\n  int nRetry = 0;                 /* Number of retrys */\n\n  assert( id!=0 );\n  assert( amt>0 );\n  assert( offset>=0 );\n  SimulateIOError(return SQLITE_IOERR_READ);\n  OSTRACE((\"READ pid=%lu, pFile=%p, file=%p, buffer=%p, amount=%d, \"\n           \"offset=%lld, lock=%d\\n\", osGetCurrentProcessId(), pFile,\n           pFile->h, pBuf, amt, offset, pFile->locktype));\n\n#if SQLITE_MAX_MMAP_SIZE>0\n  /* Deal with as much of this read request as possible by transfering\n  ** data from the memory mapping using memcpy().  */\n  if( offset<pFile->mmapSize ){\n    if( offset+amt <= pFile->mmapSize ){\n      memcpy(pBuf, &((u8 *)(pFile->pMapRegion))[offset], amt);\n      OSTRACE((\"READ-MMAP pid=%lu, pFile=%p, file=%p, rc=SQLITE_OK\\n\",\n               osGetCurrentProcessId(), pFile, pFile->h));\n      return SQLITE_OK;\n    }else{\n      int nCopy = (int)(pFile->mmapSize - offset);\n      memcpy(pBuf, &((u8 *)(pFile->pMapRegion))[offset], nCopy);\n      pBuf = &((u8 *)pBuf)[nCopy];\n      amt -= nCopy;\n      offset += nCopy;\n    }\n  }\n#endif\n\n#if SQLITE_OS_WINCE || defined(SQLITE_WIN32_NO_OVERLAPPED)\n  if( winSeekFile(pFile, offset) ){\n    OSTRACE((\"READ pid=%lu, pFile=%p, file=%p, rc=SQLITE_FULL\\n\",\n             osGetCurrentProcessId(), pFile, pFile->h));\n    return SQLITE_FULL;\n  }\n  while( !osReadFile(pFile->h, pBuf, amt, &nRead, 0) ){\n#else\n  memset(&overlapped, 0, sizeof(OVERLAPPED));\n  overlapped.Offset = (LONG)(offset & 0xffffffff);\n  overlapped.OffsetHigh = (LONG)((offset>>32) & 0x7fffffff);\n  while( !osReadFile(pFile->h, pBuf, amt, &nRead, &overlapped) &&\n         osGetLastError()!=ERROR_HANDLE_EOF ){\n#endif\n    DWORD lastErrno;\n    if( winRetryIoerr(&nRetry, &lastErrno) ) continue;\n    pFile->lastErrno = lastErrno;\n    OSTRACE((\"READ pid=%lu, pFile=%p, file=%p, rc=SQLITE_IOERR_READ\\n\",\n             osGetCurrentProcessId(), pFile, pFile->h));\n    return winLogError(SQLITE_IOERR_READ, pFile->lastErrno,\n                       \"winRead\", pFile->zPath);\n  }\n  winLogIoerr(nRetry, __LINE__);\n  if( nRead<(DWORD)amt ){\n    /* Unread parts of the buffer must be zero-filled */\n    memset(&((char*)pBuf)[nRead], 0, amt-nRead);\n    OSTRACE((\"READ pid=%lu, pFile=%p, file=%p, rc=SQLITE_IOERR_SHORT_READ\\n\",\n             osGetCurrentProcessId(), pFile, pFile->h));\n    return SQLITE_IOERR_SHORT_READ;\n  }\n\n  OSTRACE((\"READ pid=%lu, pFile=%p, file=%p, rc=SQLITE_OK\\n\",\n           osGetCurrentProcessId(), pFile, pFile->h));\n  return SQLITE_OK;\n}\n\n/*\n** Write data from a buffer into a file.  Return SQLITE_OK on success\n** or some other error code on failure.\n*/\nstatic int winWrite(\n  sqlite3_file *id,               /* File to write into */\n  const void *pBuf,               /* The bytes to be written */\n  int amt,                        /* Number of bytes to write */\n  sqlite3_int64 offset            /* Offset into the file to begin writing at */\n){\n  int rc = 0;                     /* True if error has occurred, else false */\n  winFile *pFile = (winFile*)id;  /* File handle */\n  int nRetry = 0;                 /* Number of retries */\n\n  assert( amt>0 );\n  assert( pFile );\n  SimulateIOError(return SQLITE_IOERR_WRITE);\n  SimulateDiskfullError(return SQLITE_FULL);\n\n  OSTRACE((\"WRITE pid=%lu, pFile=%p, file=%p, buffer=%p, amount=%d, \"\n           \"offset=%lld, lock=%d\\n\", osGetCurrentProcessId(), pFile,\n           pFile->h, pBuf, amt, offset, pFile->locktype));\n\n#if defined(SQLITE_MMAP_READWRITE) && SQLITE_MAX_MMAP_SIZE>0\n  /* Deal with as much of this write request as possible by transfering\n  ** data from the memory mapping using memcpy().  */\n  if( offset<pFile->mmapSize ){\n    if( offset+amt <= pFile->mmapSize ){\n      memcpy(&((u8 *)(pFile->pMapRegion))[offset], pBuf, amt);\n      OSTRACE((\"WRITE-MMAP pid=%lu, pFile=%p, file=%p, rc=SQLITE_OK\\n\",\n               osGetCurrentProcessId(), pFile, pFile->h));\n      return SQLITE_OK;\n    }else{\n      int nCopy = (int)(pFile->mmapSize - offset);\n      memcpy(&((u8 *)(pFile->pMapRegion))[offset], pBuf, nCopy);\n      pBuf = &((u8 *)pBuf)[nCopy];\n      amt -= nCopy;\n      offset += nCopy;\n    }\n  }\n#endif\n\n#if SQLITE_OS_WINCE || defined(SQLITE_WIN32_NO_OVERLAPPED)\n  rc = winSeekFile(pFile, offset);\n  if( rc==0 ){\n#else\n  {\n#endif\n#if !SQLITE_OS_WINCE && !defined(SQLITE_WIN32_NO_OVERLAPPED)\n    OVERLAPPED overlapped;        /* The offset for WriteFile. */\n#endif\n    u8 *aRem = (u8 *)pBuf;        /* Data yet to be written */\n    int nRem = amt;               /* Number of bytes yet to be written */\n    DWORD nWrite;                 /* Bytes written by each WriteFile() call */\n    DWORD lastErrno = NO_ERROR;   /* Value returned by GetLastError() */\n\n#if !SQLITE_OS_WINCE && !defined(SQLITE_WIN32_NO_OVERLAPPED)\n    memset(&overlapped, 0, sizeof(OVERLAPPED));\n    overlapped.Offset = (LONG)(offset & 0xffffffff);\n    overlapped.OffsetHigh = (LONG)((offset>>32) & 0x7fffffff);\n#endif\n\n    while( nRem>0 ){\n#if SQLITE_OS_WINCE || defined(SQLITE_WIN32_NO_OVERLAPPED)\n      if( !osWriteFile(pFile->h, aRem, nRem, &nWrite, 0) ){\n#else\n      if( !osWriteFile(pFile->h, aRem, nRem, &nWrite, &overlapped) ){\n#endif\n        if( winRetryIoerr(&nRetry, &lastErrno) ) continue;\n        break;\n      }\n      assert( nWrite==0 || nWrite<=(DWORD)nRem );\n      if( nWrite==0 || nWrite>(DWORD)nRem ){\n        lastErrno = osGetLastError();\n        break;\n      }\n#if !SQLITE_OS_WINCE && !defined(SQLITE_WIN32_NO_OVERLAPPED)\n      offset += nWrite;\n      overlapped.Offset = (LONG)(offset & 0xffffffff);\n      overlapped.OffsetHigh = (LONG)((offset>>32) & 0x7fffffff);\n#endif\n      aRem += nWrite;\n      nRem -= nWrite;\n    }\n    if( nRem>0 ){\n      pFile->lastErrno = lastErrno;\n      rc = 1;\n    }\n  }\n\n  if( rc ){\n    if(   ( pFile->lastErrno==ERROR_HANDLE_DISK_FULL )\n       || ( pFile->lastErrno==ERROR_DISK_FULL )){\n      OSTRACE((\"WRITE pid=%lu, pFile=%p, file=%p, rc=SQLITE_FULL\\n\",\n               osGetCurrentProcessId(), pFile, pFile->h));\n      return winLogError(SQLITE_FULL, pFile->lastErrno,\n                         \"winWrite1\", pFile->zPath);\n    }\n    OSTRACE((\"WRITE pid=%lu, pFile=%p, file=%p, rc=SQLITE_IOERR_WRITE\\n\",\n             osGetCurrentProcessId(), pFile, pFile->h));\n    return winLogError(SQLITE_IOERR_WRITE, pFile->lastErrno,\n                       \"winWrite2\", pFile->zPath);\n  }else{\n    winLogIoerr(nRetry, __LINE__);\n  }\n  OSTRACE((\"WRITE pid=%lu, pFile=%p, file=%p, rc=SQLITE_OK\\n\",\n           osGetCurrentProcessId(), pFile, pFile->h));\n  return SQLITE_OK;\n}\n\n/*\n** Truncate an open file to a specified size\n*/\nstatic int winTruncate(sqlite3_file *id, sqlite3_int64 nByte){\n  winFile *pFile = (winFile*)id;  /* File handle object */\n  int rc = SQLITE_OK;             /* Return code for this function */\n  DWORD lastErrno;\n\n  assert( pFile );\n  SimulateIOError(return SQLITE_IOERR_TRUNCATE);\n  OSTRACE((\"TRUNCATE pid=%lu, pFile=%p, file=%p, size=%lld, lock=%d\\n\",\n           osGetCurrentProcessId(), pFile, pFile->h, nByte, pFile->locktype));\n\n  /* If the user has configured a chunk-size for this file, truncate the\n  ** file so that it consists of an integer number of chunks (i.e. the\n  ** actual file size after the operation may be larger than the requested\n  ** size).\n  */\n  if( pFile->szChunk>0 ){\n    nByte = ((nByte + pFile->szChunk - 1)/pFile->szChunk) * pFile->szChunk;\n  }\n\n  /* SetEndOfFile() returns non-zero when successful, or zero when it fails. */\n  if( winSeekFile(pFile, nByte) ){\n    rc = winLogError(SQLITE_IOERR_TRUNCATE, pFile->lastErrno,\n                     \"winTruncate1\", pFile->zPath);\n  }else if( 0==osSetEndOfFile(pFile->h) &&\n            ((lastErrno = osGetLastError())!=ERROR_USER_MAPPED_FILE) ){\n    pFile->lastErrno = lastErrno;\n    rc = winLogError(SQLITE_IOERR_TRUNCATE, pFile->lastErrno,\n                     \"winTruncate2\", pFile->zPath);\n  }\n\n#if SQLITE_MAX_MMAP_SIZE>0\n  /* If the file was truncated to a size smaller than the currently\n  ** mapped region, reduce the effective mapping size as well. SQLite will\n  ** use read() and write() to access data beyond this point from now on.\n  */\n  if( pFile->pMapRegion && nByte<pFile->mmapSize ){\n    pFile->mmapSize = nByte;\n  }\n#endif\n\n  OSTRACE((\"TRUNCATE pid=%lu, pFile=%p, file=%p, rc=%s\\n\",\n           osGetCurrentProcessId(), pFile, pFile->h, sqlite3ErrName(rc)));\n  return rc;\n}\n\n#ifdef SQLITE_TEST\n/*\n** Count the number of fullsyncs and normal syncs.  This is used to test\n** that syncs and fullsyncs are occuring at the right times.\n*/\nSQLITE_API int sqlite3_sync_count = 0;\nSQLITE_API int sqlite3_fullsync_count = 0;\n#endif\n\n/*\n** Make sure all writes to a particular file are committed to disk.\n*/\nstatic int winSync(sqlite3_file *id, int flags){\n#ifndef SQLITE_NO_SYNC\n  /*\n  ** Used only when SQLITE_NO_SYNC is not defined.\n   */\n  BOOL rc;\n#endif\n#if !defined(NDEBUG) || !defined(SQLITE_NO_SYNC) || \\\n    defined(SQLITE_HAVE_OS_TRACE)\n  /*\n  ** Used when SQLITE_NO_SYNC is not defined and by the assert() and/or\n  ** OSTRACE() macros.\n   */\n  winFile *pFile = (winFile*)id;\n#else\n  UNUSED_PARAMETER(id);\n#endif\n\n  assert( pFile );\n  /* Check that one of SQLITE_SYNC_NORMAL or FULL was passed */\n  assert((flags&0x0F)==SQLITE_SYNC_NORMAL\n      || (flags&0x0F)==SQLITE_SYNC_FULL\n  );\n\n  /* Unix cannot, but some systems may return SQLITE_FULL from here. This\n  ** line is to test that doing so does not cause any problems.\n  */\n  SimulateDiskfullError( return SQLITE_FULL );\n\n  OSTRACE((\"SYNC pid=%lu, pFile=%p, file=%p, flags=%x, lock=%d\\n\",\n           osGetCurrentProcessId(), pFile, pFile->h, flags,\n           pFile->locktype));\n\n#ifndef SQLITE_TEST\n  UNUSED_PARAMETER(flags);\n#else\n  if( (flags&0x0F)==SQLITE_SYNC_FULL ){\n    sqlite3_fullsync_count++;\n  }\n  sqlite3_sync_count++;\n#endif\n\n  /* If we compiled with the SQLITE_NO_SYNC flag, then syncing is a\n  ** no-op\n  */\n#ifdef SQLITE_NO_SYNC\n  OSTRACE((\"SYNC-NOP pid=%lu, pFile=%p, file=%p, rc=SQLITE_OK\\n\",\n           osGetCurrentProcessId(), pFile, pFile->h));\n  return SQLITE_OK;\n#else\n#if SQLITE_MAX_MMAP_SIZE>0\n  if( pFile->pMapRegion ){\n    if( osFlushViewOfFile(pFile->pMapRegion, 0) ){\n      OSTRACE((\"SYNC-MMAP pid=%lu, pFile=%p, pMapRegion=%p, \"\n               \"rc=SQLITE_OK\\n\", osGetCurrentProcessId(),\n               pFile, pFile->pMapRegion));\n    }else{\n      pFile->lastErrno = osGetLastError();\n      OSTRACE((\"SYNC-MMAP pid=%lu, pFile=%p, pMapRegion=%p, \"\n               \"rc=SQLITE_IOERR_MMAP\\n\", osGetCurrentProcessId(),\n               pFile, pFile->pMapRegion));\n      return winLogError(SQLITE_IOERR_MMAP, pFile->lastErrno,\n                         \"winSync1\", pFile->zPath);\n    }\n  }\n#endif\n  rc = osFlushFileBuffers(pFile->h);\n  SimulateIOError( rc=FALSE );\n  if( rc ){\n    OSTRACE((\"SYNC pid=%lu, pFile=%p, file=%p, rc=SQLITE_OK\\n\",\n             osGetCurrentProcessId(), pFile, pFile->h));\n    return SQLITE_OK;\n  }else{\n    pFile->lastErrno = osGetLastError();\n    OSTRACE((\"SYNC pid=%lu, pFile=%p, file=%p, rc=SQLITE_IOERR_FSYNC\\n\",\n             osGetCurrentProcessId(), pFile, pFile->h));\n    return winLogError(SQLITE_IOERR_FSYNC, pFile->lastErrno,\n                       \"winSync2\", pFile->zPath);\n  }\n#endif\n}\n\n/*\n** Determine the current size of a file in bytes\n*/\nstatic int winFileSize(sqlite3_file *id, sqlite3_int64 *pSize){\n  winFile *pFile = (winFile*)id;\n  int rc = SQLITE_OK;\n\n  assert( id!=0 );\n  assert( pSize!=0 );\n  SimulateIOError(return SQLITE_IOERR_FSTAT);\n  OSTRACE((\"SIZE file=%p, pSize=%p\\n\", pFile->h, pSize));\n\n#if SQLITE_OS_WINRT\n  {\n    FILE_STANDARD_INFO info;\n    if( osGetFileInformationByHandleEx(pFile->h, FileStandardInfo,\n                                     &info, sizeof(info)) ){\n      *pSize = info.EndOfFile.QuadPart;\n    }else{\n      pFile->lastErrno = osGetLastError();\n      rc = winLogError(SQLITE_IOERR_FSTAT, pFile->lastErrno,\n                       \"winFileSize\", pFile->zPath);\n    }\n  }\n#else\n  {\n    DWORD upperBits;\n    DWORD lowerBits;\n    DWORD lastErrno;\n\n    lowerBits = osGetFileSize(pFile->h, &upperBits);\n    *pSize = (((sqlite3_int64)upperBits)<<32) + lowerBits;\n    if(   (lowerBits == INVALID_FILE_SIZE)\n       && ((lastErrno = osGetLastError())!=NO_ERROR) ){\n      pFile->lastErrno = lastErrno;\n      rc = winLogError(SQLITE_IOERR_FSTAT, pFile->lastErrno,\n                       \"winFileSize\", pFile->zPath);\n    }\n  }\n#endif\n  OSTRACE((\"SIZE file=%p, pSize=%p, *pSize=%lld, rc=%s\\n\",\n           pFile->h, pSize, *pSize, sqlite3ErrName(rc)));\n  return rc;\n}\n\n/*\n** LOCKFILE_FAIL_IMMEDIATELY is undefined on some Windows systems.\n*/\n#ifndef LOCKFILE_FAIL_IMMEDIATELY\n# define LOCKFILE_FAIL_IMMEDIATELY 1\n#endif\n\n#ifndef LOCKFILE_EXCLUSIVE_LOCK\n# define LOCKFILE_EXCLUSIVE_LOCK 2\n#endif\n\n/*\n** Historically, SQLite has used both the LockFile and LockFileEx functions.\n** When the LockFile function was used, it was always expected to fail\n** immediately if the lock could not be obtained.  Also, it always expected to\n** obtain an exclusive lock.  These flags are used with the LockFileEx function\n** and reflect those expectations; therefore, they should not be changed.\n*/\n#ifndef SQLITE_LOCKFILE_FLAGS\n# define SQLITE_LOCKFILE_FLAGS   (LOCKFILE_FAIL_IMMEDIATELY | \\\n                                  LOCKFILE_EXCLUSIVE_LOCK)\n#endif\n\n/*\n** Currently, SQLite never calls the LockFileEx function without wanting the\n** call to fail immediately if the lock cannot be obtained.\n*/\n#ifndef SQLITE_LOCKFILEEX_FLAGS\n# define SQLITE_LOCKFILEEX_FLAGS (LOCKFILE_FAIL_IMMEDIATELY)\n#endif\n\n/*\n** Acquire a reader lock.\n** Different API routines are called depending on whether or not this\n** is Win9x or WinNT.\n*/\nstatic int winGetReadLock(winFile *pFile){\n  int res;\n  OSTRACE((\"READ-LOCK file=%p, lock=%d\\n\", pFile->h, pFile->locktype));\n  if( osIsNT() ){\n#if SQLITE_OS_WINCE\n    /*\n    ** NOTE: Windows CE is handled differently here due its lack of the Win32\n    **       API LockFileEx.\n    */\n    res = winceLockFile(&pFile->h, SHARED_FIRST, 0, 1, 0);\n#else\n    res = winLockFile(&pFile->h, SQLITE_LOCKFILEEX_FLAGS, SHARED_FIRST, 0,\n                      SHARED_SIZE, 0);\n#endif\n  }\n#ifdef SQLITE_WIN32_HAS_ANSI\n  else{\n    int lk;\n    sqlite3_randomness(sizeof(lk), &lk);\n    pFile->sharedLockByte = (short)((lk & 0x7fffffff)%(SHARED_SIZE - 1));\n    res = winLockFile(&pFile->h, SQLITE_LOCKFILE_FLAGS,\n                      SHARED_FIRST+pFile->sharedLockByte, 0, 1, 0);\n  }\n#endif\n  if( res == 0 ){\n    pFile->lastErrno = osGetLastError();\n    /* No need to log a failure to lock */\n  }\n  OSTRACE((\"READ-LOCK file=%p, result=%d\\n\", pFile->h, res));\n  return res;\n}\n\n/*\n** Undo a readlock\n*/\nstatic int winUnlockReadLock(winFile *pFile){\n  int res;\n  DWORD lastErrno;\n  OSTRACE((\"READ-UNLOCK file=%p, lock=%d\\n\", pFile->h, pFile->locktype));\n  if( osIsNT() ){\n    res = winUnlockFile(&pFile->h, SHARED_FIRST, 0, SHARED_SIZE, 0);\n  }\n#ifdef SQLITE_WIN32_HAS_ANSI\n  else{\n    res = winUnlockFile(&pFile->h, SHARED_FIRST+pFile->sharedLockByte, 0, 1, 0);\n  }\n#endif\n  if( res==0 && ((lastErrno = osGetLastError())!=ERROR_NOT_LOCKED) ){\n    pFile->lastErrno = lastErrno;\n    winLogError(SQLITE_IOERR_UNLOCK, pFile->lastErrno,\n                \"winUnlockReadLock\", pFile->zPath);\n  }\n  OSTRACE((\"READ-UNLOCK file=%p, result=%d\\n\", pFile->h, res));\n  return res;\n}\n\n/*\n** Lock the file with the lock specified by parameter locktype - one\n** of the following:\n**\n**     (1) SHARED_LOCK\n**     (2) RESERVED_LOCK\n**     (3) PENDING_LOCK\n**     (4) EXCLUSIVE_LOCK\n**\n** Sometimes when requesting one lock state, additional lock states\n** are inserted in between.  The locking might fail on one of the later\n** transitions leaving the lock state different from what it started but\n** still short of its goal.  The following chart shows the allowed\n** transitions and the inserted intermediate states:\n**\n**    UNLOCKED -> SHARED\n**    SHARED -> RESERVED\n**    SHARED -> (PENDING) -> EXCLUSIVE\n**    RESERVED -> (PENDING) -> EXCLUSIVE\n**    PENDING -> EXCLUSIVE\n**\n** This routine will only increase a lock.  The winUnlock() routine\n** erases all locks at once and returns us immediately to locking level 0.\n** It is not possible to lower the locking level one step at a time.  You\n** must go straight to locking level 0.\n*/\nstatic int winLock(sqlite3_file *id, int locktype){\n  int rc = SQLITE_OK;    /* Return code from subroutines */\n  int res = 1;           /* Result of a Windows lock call */\n  int newLocktype;       /* Set pFile->locktype to this value before exiting */\n  int gotPendingLock = 0;/* True if we acquired a PENDING lock this time */\n  winFile *pFile = (winFile*)id;\n  DWORD lastErrno = NO_ERROR;\n\n  assert( id!=0 );\n  OSTRACE((\"LOCK file=%p, oldLock=%d(%d), newLock=%d\\n\",\n           pFile->h, pFile->locktype, pFile->sharedLockByte, locktype));\n\n  /* If there is already a lock of this type or more restrictive on the\n  ** OsFile, do nothing. Don't use the end_lock: exit path, as\n  ** sqlite3OsEnterMutex() hasn't been called yet.\n  */\n  if( pFile->locktype>=locktype ){\n    OSTRACE((\"LOCK-HELD file=%p, rc=SQLITE_OK\\n\", pFile->h));\n    return SQLITE_OK;\n  }\n\n  /* Do not allow any kind of write-lock on a read-only database\n  */\n  if( (pFile->ctrlFlags & WINFILE_RDONLY)!=0 && locktype>=RESERVED_LOCK ){\n    return SQLITE_IOERR_LOCK;\n  }\n\n  /* Make sure the locking sequence is correct\n  */\n  assert( pFile->locktype!=NO_LOCK || locktype==SHARED_LOCK );\n  assert( locktype!=PENDING_LOCK );\n  assert( locktype!=RESERVED_LOCK || pFile->locktype==SHARED_LOCK );\n\n  /* Lock the PENDING_LOCK byte if we need to acquire a PENDING lock or\n  ** a SHARED lock.  If we are acquiring a SHARED lock, the acquisition of\n  ** the PENDING_LOCK byte is temporary.\n  */\n  newLocktype = pFile->locktype;\n  if( pFile->locktype==NO_LOCK\n   || (locktype==EXCLUSIVE_LOCK && pFile->locktype<=RESERVED_LOCK)\n  ){\n    int cnt = 3;\n    while( cnt-->0 && (res = winLockFile(&pFile->h, SQLITE_LOCKFILE_FLAGS,\n                                         PENDING_BYTE, 0, 1, 0))==0 ){\n      /* Try 3 times to get the pending lock.  This is needed to work\n      ** around problems caused by indexing and/or anti-virus software on\n      ** Windows systems.\n      ** If you are using this code as a model for alternative VFSes, do not\n      ** copy this retry logic.  It is a hack intended for Windows only.\n      */\n      lastErrno = osGetLastError();\n      OSTRACE((\"LOCK-PENDING-FAIL file=%p, count=%d, result=%d\\n\",\n               pFile->h, cnt, res));\n      if( lastErrno==ERROR_INVALID_HANDLE ){\n        pFile->lastErrno = lastErrno;\n        rc = SQLITE_IOERR_LOCK;\n        OSTRACE((\"LOCK-FAIL file=%p, count=%d, rc=%s\\n\",\n                 pFile->h, cnt, sqlite3ErrName(rc)));\n        return rc;\n      }\n      if( cnt ) sqlite3_win32_sleep(1);\n    }\n    gotPendingLock = res;\n    if( !res ){\n      lastErrno = osGetLastError();\n    }\n  }\n\n  /* Acquire a shared lock\n  */\n  if( locktype==SHARED_LOCK && res ){\n    assert( pFile->locktype==NO_LOCK );\n    res = winGetReadLock(pFile);\n    if( res ){\n      newLocktype = SHARED_LOCK;\n    }else{\n      lastErrno = osGetLastError();\n    }\n  }\n\n  /* Acquire a RESERVED lock\n  */\n  if( locktype==RESERVED_LOCK && res ){\n    assert( pFile->locktype==SHARED_LOCK );\n    res = winLockFile(&pFile->h, SQLITE_LOCKFILE_FLAGS, RESERVED_BYTE, 0, 1, 0);\n    if( res ){\n      newLocktype = RESERVED_LOCK;\n    }else{\n      lastErrno = osGetLastError();\n    }\n  }\n\n  /* Acquire a PENDING lock\n  */\n  if( locktype==EXCLUSIVE_LOCK && res ){\n    newLocktype = PENDING_LOCK;\n    gotPendingLock = 0;\n  }\n\n  /* Acquire an EXCLUSIVE lock\n  */\n  if( locktype==EXCLUSIVE_LOCK && res ){\n    assert( pFile->locktype>=SHARED_LOCK );\n    res = winUnlockReadLock(pFile);\n    res = winLockFile(&pFile->h, SQLITE_LOCKFILE_FLAGS, SHARED_FIRST, 0,\n                      SHARED_SIZE, 0);\n    if( res ){\n      newLocktype = EXCLUSIVE_LOCK;\n    }else{\n      lastErrno = osGetLastError();\n      winGetReadLock(pFile);\n    }\n  }\n\n  /* If we are holding a PENDING lock that ought to be released, then\n  ** release it now.\n  */\n  if( gotPendingLock && locktype==SHARED_LOCK ){\n    winUnlockFile(&pFile->h, PENDING_BYTE, 0, 1, 0);\n  }\n\n  /* Update the state of the lock has held in the file descriptor then\n  ** return the appropriate result code.\n  */\n  if( res ){\n    rc = SQLITE_OK;\n  }else{\n    pFile->lastErrno = lastErrno;\n    rc = SQLITE_BUSY;\n    OSTRACE((\"LOCK-FAIL file=%p, wanted=%d, got=%d\\n\",\n             pFile->h, locktype, newLocktype));\n  }\n  pFile->locktype = (u8)newLocktype;\n  OSTRACE((\"LOCK file=%p, lock=%d, rc=%s\\n\",\n           pFile->h, pFile->locktype, sqlite3ErrName(rc)));\n  return rc;\n}\n\n/*\n** This routine checks if there is a RESERVED lock held on the specified\n** file by this or any other process. If such a lock is held, return\n** non-zero, otherwise zero.\n*/\nstatic int winCheckReservedLock(sqlite3_file *id, int *pResOut){\n  int res;\n  winFile *pFile = (winFile*)id;\n\n  SimulateIOError( return SQLITE_IOERR_CHECKRESERVEDLOCK; );\n  OSTRACE((\"TEST-WR-LOCK file=%p, pResOut=%p\\n\", pFile->h, pResOut));\n\n  assert( id!=0 );\n  if( pFile->locktype>=RESERVED_LOCK ){\n    res = 1;\n    OSTRACE((\"TEST-WR-LOCK file=%p, result=%d (local)\\n\", pFile->h, res));\n  }else{\n    res = winLockFile(&pFile->h, SQLITE_LOCKFILEEX_FLAGS,RESERVED_BYTE,0,1,0);\n    if( res ){\n      winUnlockFile(&pFile->h, RESERVED_BYTE, 0, 1, 0);\n    }\n    res = !res;\n    OSTRACE((\"TEST-WR-LOCK file=%p, result=%d (remote)\\n\", pFile->h, res));\n  }\n  *pResOut = res;\n  OSTRACE((\"TEST-WR-LOCK file=%p, pResOut=%p, *pResOut=%d, rc=SQLITE_OK\\n\",\n           pFile->h, pResOut, *pResOut));\n  return SQLITE_OK;\n}\n\n/*\n** Lower the locking level on file descriptor id to locktype.  locktype\n** must be either NO_LOCK or SHARED_LOCK.\n**\n** If the locking level of the file descriptor is already at or below\n** the requested locking level, this routine is a no-op.\n**\n** It is not possible for this routine to fail if the second argument\n** is NO_LOCK.  If the second argument is SHARED_LOCK then this routine\n** might return SQLITE_IOERR;\n*/\nstatic int winUnlock(sqlite3_file *id, int locktype){\n  int type;\n  winFile *pFile = (winFile*)id;\n  int rc = SQLITE_OK;\n  assert( pFile!=0 );\n  assert( locktype<=SHARED_LOCK );\n  OSTRACE((\"UNLOCK file=%p, oldLock=%d(%d), newLock=%d\\n\",\n           pFile->h, pFile->locktype, pFile->sharedLockByte, locktype));\n  type = pFile->locktype;\n  if( type>=EXCLUSIVE_LOCK ){\n    winUnlockFile(&pFile->h, SHARED_FIRST, 0, SHARED_SIZE, 0);\n    if( locktype==SHARED_LOCK && !winGetReadLock(pFile) ){\n      /* This should never happen.  We should always be able to\n      ** reacquire the read lock */\n      rc = winLogError(SQLITE_IOERR_UNLOCK, osGetLastError(),\n                       \"winUnlock\", pFile->zPath);\n    }\n  }\n  if( type>=RESERVED_LOCK ){\n    winUnlockFile(&pFile->h, RESERVED_BYTE, 0, 1, 0);\n  }\n  if( locktype==NO_LOCK && type>=SHARED_LOCK ){\n    winUnlockReadLock(pFile);\n  }\n  if( type>=PENDING_LOCK ){\n    winUnlockFile(&pFile->h, PENDING_BYTE, 0, 1, 0);\n  }\n  pFile->locktype = (u8)locktype;\n  OSTRACE((\"UNLOCK file=%p, lock=%d, rc=%s\\n\",\n           pFile->h, pFile->locktype, sqlite3ErrName(rc)));\n  return rc;\n}\n\n/******************************************************************************\n****************************** No-op Locking **********************************\n**\n** Of the various locking implementations available, this is by far the\n** simplest:  locking is ignored.  No attempt is made to lock the database\n** file for reading or writing.\n**\n** This locking mode is appropriate for use on read-only databases\n** (ex: databases that are burned into CD-ROM, for example.)  It can\n** also be used if the application employs some external mechanism to\n** prevent simultaneous access of the same database by two or more\n** database connections.  But there is a serious risk of database\n** corruption if this locking mode is used in situations where multiple\n** database connections are accessing the same database file at the same\n** time and one or more of those connections are writing.\n*/\n\nstatic int winNolockLock(sqlite3_file *id, int locktype){\n  UNUSED_PARAMETER(id);\n  UNUSED_PARAMETER(locktype);\n  return SQLITE_OK;\n}\n\nstatic int winNolockCheckReservedLock(sqlite3_file *id, int *pResOut){\n  UNUSED_PARAMETER(id);\n  UNUSED_PARAMETER(pResOut);\n  return SQLITE_OK;\n}\n\nstatic int winNolockUnlock(sqlite3_file *id, int locktype){\n  UNUSED_PARAMETER(id);\n  UNUSED_PARAMETER(locktype);\n  return SQLITE_OK;\n}\n\n/******************* End of the no-op lock implementation *********************\n******************************************************************************/\n\n/*\n** If *pArg is initially negative then this is a query.  Set *pArg to\n** 1 or 0 depending on whether or not bit mask of pFile->ctrlFlags is set.\n**\n** If *pArg is 0 or 1, then clear or set the mask bit of pFile->ctrlFlags.\n*/\nstatic void winModeBit(winFile *pFile, unsigned char mask, int *pArg){\n  if( *pArg<0 ){\n    *pArg = (pFile->ctrlFlags & mask)!=0;\n  }else if( (*pArg)==0 ){\n    pFile->ctrlFlags &= ~mask;\n  }else{\n    pFile->ctrlFlags |= mask;\n  }\n}\n\n/* Forward references to VFS helper methods used for temporary files */\nstatic int winGetTempname(sqlite3_vfs *, char **);\nstatic int winIsDir(const void *);\nstatic BOOL winIsDriveLetterAndColon(const char *);\n\n/*\n** Control and query of the open file handle.\n*/\nstatic int winFileControl(sqlite3_file *id, int op, void *pArg){\n  winFile *pFile = (winFile*)id;\n  OSTRACE((\"FCNTL file=%p, op=%d, pArg=%p\\n\", pFile->h, op, pArg));\n  switch( op ){\n    case SQLITE_FCNTL_LOCKSTATE: {\n      *(int*)pArg = pFile->locktype;\n      OSTRACE((\"FCNTL file=%p, rc=SQLITE_OK\\n\", pFile->h));\n      return SQLITE_OK;\n    }\n    case SQLITE_FCNTL_LAST_ERRNO: {\n      *(int*)pArg = (int)pFile->lastErrno;\n      OSTRACE((\"FCNTL file=%p, rc=SQLITE_OK\\n\", pFile->h));\n      return SQLITE_OK;\n    }\n    case SQLITE_FCNTL_CHUNK_SIZE: {\n      pFile->szChunk = *(int *)pArg;\n      OSTRACE((\"FCNTL file=%p, rc=SQLITE_OK\\n\", pFile->h));\n      return SQLITE_OK;\n    }\n    case SQLITE_FCNTL_SIZE_HINT: {\n      if( pFile->szChunk>0 ){\n        sqlite3_int64 oldSz;\n        int rc = winFileSize(id, &oldSz);\n        if( rc==SQLITE_OK ){\n          sqlite3_int64 newSz = *(sqlite3_int64*)pArg;\n          if( newSz>oldSz ){\n            SimulateIOErrorBenign(1);\n            rc = winTruncate(id, newSz);\n            SimulateIOErrorBenign(0);\n          }\n        }\n        OSTRACE((\"FCNTL file=%p, rc=%s\\n\", pFile->h, sqlite3ErrName(rc)));\n        return rc;\n      }\n      OSTRACE((\"FCNTL file=%p, rc=SQLITE_OK\\n\", pFile->h));\n      return SQLITE_OK;\n    }\n    case SQLITE_FCNTL_PERSIST_WAL: {\n      winModeBit(pFile, WINFILE_PERSIST_WAL, (int*)pArg);\n      OSTRACE((\"FCNTL file=%p, rc=SQLITE_OK\\n\", pFile->h));\n      return SQLITE_OK;\n    }\n    case SQLITE_FCNTL_POWERSAFE_OVERWRITE: {\n      winModeBit(pFile, WINFILE_PSOW, (int*)pArg);\n      OSTRACE((\"FCNTL file=%p, rc=SQLITE_OK\\n\", pFile->h));\n      return SQLITE_OK;\n    }\n    case SQLITE_FCNTL_VFSNAME: {\n      *(char**)pArg = sqlite3_mprintf(\"%s\", pFile->pVfs->zName);\n      OSTRACE((\"FCNTL file=%p, rc=SQLITE_OK\\n\", pFile->h));\n      return SQLITE_OK;\n    }\n    case SQLITE_FCNTL_WIN32_AV_RETRY: {\n      int *a = (int*)pArg;\n      if( a[0]>0 ){\n        winIoerrRetry = a[0];\n      }else{\n        a[0] = winIoerrRetry;\n      }\n      if( a[1]>0 ){\n        winIoerrRetryDelay = a[1];\n      }else{\n        a[1] = winIoerrRetryDelay;\n      }\n      OSTRACE((\"FCNTL file=%p, rc=SQLITE_OK\\n\", pFile->h));\n      return SQLITE_OK;\n    }\n    case SQLITE_FCNTL_WIN32_GET_HANDLE: {\n      LPHANDLE phFile = (LPHANDLE)pArg;\n      *phFile = pFile->h;\n      OSTRACE((\"FCNTL file=%p, rc=SQLITE_OK\\n\", pFile->h));\n      return SQLITE_OK;\n    }\n#ifdef SQLITE_TEST\n    case SQLITE_FCNTL_WIN32_SET_HANDLE: {\n      LPHANDLE phFile = (LPHANDLE)pArg;\n      HANDLE hOldFile = pFile->h;\n      pFile->h = *phFile;\n      *phFile = hOldFile;\n      OSTRACE((\"FCNTL oldFile=%p, newFile=%p, rc=SQLITE_OK\\n\",\n               hOldFile, pFile->h));\n      return SQLITE_OK;\n    }\n#endif\n    case SQLITE_FCNTL_TEMPFILENAME: {\n      char *zTFile = 0;\n      int rc = winGetTempname(pFile->pVfs, &zTFile);\n      if( rc==SQLITE_OK ){\n        *(char**)pArg = zTFile;\n      }\n      OSTRACE((\"FCNTL file=%p, rc=%s\\n\", pFile->h, sqlite3ErrName(rc)));\n      return rc;\n    }\n#if SQLITE_MAX_MMAP_SIZE>0\n    case SQLITE_FCNTL_MMAP_SIZE: {\n      i64 newLimit = *(i64*)pArg;\n      int rc = SQLITE_OK;\n      if( newLimit>sqlite3GlobalConfig.mxMmap ){\n        newLimit = sqlite3GlobalConfig.mxMmap;\n      }\n\n      /* The value of newLimit may be eventually cast to (SIZE_T) and passed\n      ** to MapViewOfFile(). Restrict its value to 2GB if (SIZE_T) is not at\n      ** least a 64-bit type. */\n      if( newLimit>0 && sizeof(SIZE_T)<8 ){\n        newLimit = (newLimit & 0x7FFFFFFF);\n      }\n\n      *(i64*)pArg = pFile->mmapSizeMax;\n      if( newLimit>=0 && newLimit!=pFile->mmapSizeMax && pFile->nFetchOut==0 ){\n        pFile->mmapSizeMax = newLimit;\n        if( pFile->mmapSize>0 ){\n          winUnmapfile(pFile);\n          rc = winMapfile(pFile, -1);\n        }\n      }\n      OSTRACE((\"FCNTL file=%p, rc=%s\\n\", pFile->h, sqlite3ErrName(rc)));\n      return rc;\n    }\n#endif\n  }\n  OSTRACE((\"FCNTL file=%p, rc=SQLITE_NOTFOUND\\n\", pFile->h));\n  return SQLITE_NOTFOUND;\n}\n\n/*\n** Return the sector size in bytes of the underlying block device for\n** the specified file. This is almost always 512 bytes, but may be\n** larger for some devices.\n**\n** SQLite code assumes this function cannot fail. It also assumes that\n** if two files are created in the same file-system directory (i.e.\n** a database and its journal file) that the sector size will be the\n** same for both.\n*/\nstatic int winSectorSize(sqlite3_file *id){\n  (void)id;\n  return SQLITE_DEFAULT_SECTOR_SIZE;\n}\n\n/*\n** Return a vector of device characteristics.\n*/\nstatic int winDeviceCharacteristics(sqlite3_file *id){\n  winFile *p = (winFile*)id;\n  return SQLITE_IOCAP_UNDELETABLE_WHEN_OPEN |\n         ((p->ctrlFlags & WINFILE_PSOW)?SQLITE_IOCAP_POWERSAFE_OVERWRITE:0);\n}\n\n/*\n** Windows will only let you create file view mappings\n** on allocation size granularity boundaries.\n** During sqlite3_os_init() we do a GetSystemInfo()\n** to get the granularity size.\n*/\nstatic SYSTEM_INFO winSysInfo;\n\n#ifndef SQLITE_OMIT_WAL\n\n/*\n** Helper functions to obtain and relinquish the global mutex. The\n** global mutex is used to protect the winLockInfo objects used by\n** this file, all of which may be shared by multiple threads.\n**\n** Function winShmMutexHeld() is used to assert() that the global mutex\n** is held when required. This function is only used as part of assert()\n** statements. e.g.\n**\n**   winShmEnterMutex()\n**     assert( winShmMutexHeld() );\n**   winShmLeaveMutex()\n*/\nstatic sqlite3_mutex *winBigLock = 0;\nstatic void winShmEnterMutex(void){\n  sqlite3_mutex_enter(winBigLock);\n}\nstatic void winShmLeaveMutex(void){\n  sqlite3_mutex_leave(winBigLock);\n}\n#ifndef NDEBUG\nstatic int winShmMutexHeld(void) {\n  return sqlite3_mutex_held(winBigLock);\n}\n#endif\n\n/*\n** Object used to represent a single file opened and mmapped to provide\n** shared memory.  When multiple threads all reference the same\n** log-summary, each thread has its own winFile object, but they all\n** point to a single instance of this object.  In other words, each\n** log-summary is opened only once per process.\n**\n** winShmMutexHeld() must be true when creating or destroying\n** this object or while reading or writing the following fields:\n**\n**      nRef\n**      pNext\n**\n** The following fields are read-only after the object is created:\n**\n**      fid\n**      zFilename\n**\n** Either winShmNode.mutex must be held or winShmNode.nRef==0 and\n** winShmMutexHeld() is true when reading or writing any other field\n** in this structure.\n**\n*/\nstruct winShmNode {\n  sqlite3_mutex *mutex;      /* Mutex to access this object */\n  char *zFilename;           /* Name of the file */\n  winFile hFile;             /* File handle from winOpen */\n\n  int szRegion;              /* Size of shared-memory regions */\n  int nRegion;               /* Size of array apRegion */\n  u8 isReadonly;             /* True if read-only */\n  u8 isUnlocked;             /* True if no DMS lock held */\n\n  struct ShmRegion {\n    HANDLE hMap;             /* File handle from CreateFileMapping */\n    void *pMap;\n  } *aRegion;\n  DWORD lastErrno;           /* The Windows errno from the last I/O error */\n\n  int nRef;                  /* Number of winShm objects pointing to this */\n  winShm *pFirst;            /* All winShm objects pointing to this */\n  winShmNode *pNext;         /* Next in list of all winShmNode objects */\n#if defined(SQLITE_DEBUG) || defined(SQLITE_HAVE_OS_TRACE)\n  u8 nextShmId;              /* Next available winShm.id value */\n#endif\n};\n\n/*\n** A global array of all winShmNode objects.\n**\n** The winShmMutexHeld() must be true while reading or writing this list.\n*/\nstatic winShmNode *winShmNodeList = 0;\n\n/*\n** Structure used internally by this VFS to record the state of an\n** open shared memory connection.\n**\n** The following fields are initialized when this object is created and\n** are read-only thereafter:\n**\n**    winShm.pShmNode\n**    winShm.id\n**\n** All other fields are read/write.  The winShm.pShmNode->mutex must be held\n** while accessing any read/write fields.\n*/\nstruct winShm {\n  winShmNode *pShmNode;      /* The underlying winShmNode object */\n  winShm *pNext;             /* Next winShm with the same winShmNode */\n  u8 hasMutex;               /* True if holding the winShmNode mutex */\n  u16 sharedMask;            /* Mask of shared locks held */\n  u16 exclMask;              /* Mask of exclusive locks held */\n#if defined(SQLITE_DEBUG) || defined(SQLITE_HAVE_OS_TRACE)\n  u8 id;                     /* Id of this connection with its winShmNode */\n#endif\n};\n\n/*\n** Constants used for locking\n*/\n#define WIN_SHM_BASE   ((22+SQLITE_SHM_NLOCK)*4)        /* first lock byte */\n#define WIN_SHM_DMS    (WIN_SHM_BASE+SQLITE_SHM_NLOCK)  /* deadman switch */\n\n/*\n** Apply advisory locks for all n bytes beginning at ofst.\n*/\n#define WINSHM_UNLCK  1\n#define WINSHM_RDLCK  2\n#define WINSHM_WRLCK  3\nstatic int winShmSystemLock(\n  winShmNode *pFile,    /* Apply locks to this open shared-memory segment */\n  int lockType,         /* WINSHM_UNLCK, WINSHM_RDLCK, or WINSHM_WRLCK */\n  int ofst,             /* Offset to first byte to be locked/unlocked */\n  int nByte             /* Number of bytes to lock or unlock */\n){\n  int rc = 0;           /* Result code form Lock/UnlockFileEx() */\n\n  /* Access to the winShmNode object is serialized by the caller */\n  assert( pFile->nRef==0 || sqlite3_mutex_held(pFile->mutex) );\n\n  OSTRACE((\"SHM-LOCK file=%p, lock=%d, offset=%d, size=%d\\n\",\n           pFile->hFile.h, lockType, ofst, nByte));\n\n  /* Release/Acquire the system-level lock */\n  if( lockType==WINSHM_UNLCK ){\n    rc = winUnlockFile(&pFile->hFile.h, ofst, 0, nByte, 0);\n  }else{\n    /* Initialize the locking parameters */\n    DWORD dwFlags = LOCKFILE_FAIL_IMMEDIATELY;\n    if( lockType == WINSHM_WRLCK ) dwFlags |= LOCKFILE_EXCLUSIVE_LOCK;\n    rc = winLockFile(&pFile->hFile.h, dwFlags, ofst, 0, nByte, 0);\n  }\n\n  if( rc!= 0 ){\n    rc = SQLITE_OK;\n  }else{\n    pFile->lastErrno =  osGetLastError();\n    rc = SQLITE_BUSY;\n  }\n\n  OSTRACE((\"SHM-LOCK file=%p, func=%s, errno=%lu, rc=%s\\n\",\n           pFile->hFile.h, (lockType == WINSHM_UNLCK) ? \"winUnlockFile\" :\n           \"winLockFile\", pFile->lastErrno, sqlite3ErrName(rc)));\n\n  return rc;\n}\n\n/* Forward references to VFS methods */\nstatic int winOpen(sqlite3_vfs*,const char*,sqlite3_file*,int,int*);\nstatic int winDelete(sqlite3_vfs *,const char*,int);\n\n/*\n** Purge the winShmNodeList list of all entries with winShmNode.nRef==0.\n**\n** This is not a VFS shared-memory method; it is a utility function called\n** by VFS shared-memory methods.\n*/\nstatic void winShmPurge(sqlite3_vfs *pVfs, int deleteFlag){\n  winShmNode **pp;\n  winShmNode *p;\n  assert( winShmMutexHeld() );\n  OSTRACE((\"SHM-PURGE pid=%lu, deleteFlag=%d\\n\",\n           osGetCurrentProcessId(), deleteFlag));\n  pp = &winShmNodeList;\n  while( (p = *pp)!=0 ){\n    if( p->nRef==0 ){\n      int i;\n      if( p->mutex ){ sqlite3_mutex_free(p->mutex); }\n      for(i=0; i<p->nRegion; i++){\n        BOOL bRc = osUnmapViewOfFile(p->aRegion[i].pMap);\n        OSTRACE((\"SHM-PURGE-UNMAP pid=%lu, region=%d, rc=%s\\n\",\n                 osGetCurrentProcessId(), i, bRc ? \"ok\" : \"failed\"));\n        UNUSED_VARIABLE_VALUE(bRc);\n        bRc = osCloseHandle(p->aRegion[i].hMap);\n        OSTRACE((\"SHM-PURGE-CLOSE pid=%lu, region=%d, rc=%s\\n\",\n                 osGetCurrentProcessId(), i, bRc ? \"ok\" : \"failed\"));\n        UNUSED_VARIABLE_VALUE(bRc);\n      }\n      if( p->hFile.h!=NULL && p->hFile.h!=INVALID_HANDLE_VALUE ){\n        SimulateIOErrorBenign(1);\n        winClose((sqlite3_file *)&p->hFile);\n        SimulateIOErrorBenign(0);\n      }\n      if( deleteFlag ){\n        SimulateIOErrorBenign(1);\n        sqlite3BeginBenignMalloc();\n        winDelete(pVfs, p->zFilename, 0);\n        sqlite3EndBenignMalloc();\n        SimulateIOErrorBenign(0);\n      }\n      *pp = p->pNext;\n      sqlite3_free(p->aRegion);\n      sqlite3_free(p);\n    }else{\n      pp = &p->pNext;\n    }\n  }\n}\n\n/*\n** The DMS lock has not yet been taken on shm file pShmNode. Attempt to\n** take it now. Return SQLITE_OK if successful, or an SQLite error\n** code otherwise.\n**\n** If the DMS cannot be locked because this is a readonly_shm=1\n** connection and no other process already holds a lock, return\n** SQLITE_READONLY_CANTINIT and set pShmNode->isUnlocked=1.\n*/\nstatic int winLockSharedMemory(winShmNode *pShmNode){\n  int rc = winShmSystemLock(pShmNode, WINSHM_WRLCK, WIN_SHM_DMS, 1);\n\n  if( rc==SQLITE_OK ){\n    if( pShmNode->isReadonly ){\n      pShmNode->isUnlocked = 1;\n      winShmSystemLock(pShmNode, WINSHM_UNLCK, WIN_SHM_DMS, 1);\n      return SQLITE_READONLY_CANTINIT;\n    }else if( winTruncate((sqlite3_file*)&pShmNode->hFile, 0) ){\n      winShmSystemLock(pShmNode, WINSHM_UNLCK, WIN_SHM_DMS, 1);\n      return winLogError(SQLITE_IOERR_SHMOPEN, osGetLastError(),\n                         \"winLockSharedMemory\", pShmNode->zFilename);\n    }\n  }\n\n  if( rc==SQLITE_OK ){\n    winShmSystemLock(pShmNode, WINSHM_UNLCK, WIN_SHM_DMS, 1);\n  }\n\n  return winShmSystemLock(pShmNode, WINSHM_RDLCK, WIN_SHM_DMS, 1);\n}\n\n/*\n** Open the shared-memory area associated with database file pDbFd.\n**\n** When opening a new shared-memory file, if no other instances of that\n** file are currently open, in this process or in other processes, then\n** the file must be truncated to zero length or have its header cleared.\n*/\nstatic int winOpenSharedMemory(winFile *pDbFd){\n  struct winShm *p;                  /* The connection to be opened */\n  winShmNode *pShmNode = 0;          /* The underlying mmapped file */\n  int rc = SQLITE_OK;                /* Result code */\n  winShmNode *pNew;                  /* Newly allocated winShmNode */\n  int nName;                         /* Size of zName in bytes */\n\n  assert( pDbFd->pShm==0 );    /* Not previously opened */\n\n  /* Allocate space for the new sqlite3_shm object.  Also speculatively\n  ** allocate space for a new winShmNode and filename.\n  */\n  p = sqlite3MallocZero( sizeof(*p) );\n  if( p==0 ) return SQLITE_IOERR_NOMEM_BKPT;\n  nName = sqlite3Strlen30(pDbFd->zPath);\n  pNew = sqlite3MallocZero( sizeof(*pShmNode) + nName + 17 );\n  if( pNew==0 ){\n    sqlite3_free(p);\n    return SQLITE_IOERR_NOMEM_BKPT;\n  }\n  pNew->zFilename = (char*)&pNew[1];\n  sqlite3_snprintf(nName+15, pNew->zFilename, \"%s-shm\", pDbFd->zPath);\n  sqlite3FileSuffix3(pDbFd->zPath, pNew->zFilename);\n\n  /* Look to see if there is an existing winShmNode that can be used.\n  ** If no matching winShmNode currently exists, create a new one.\n  */\n  winShmEnterMutex();\n  for(pShmNode = winShmNodeList; pShmNode; pShmNode=pShmNode->pNext){\n    /* TBD need to come up with better match here.  Perhaps\n    ** use FILE_ID_BOTH_DIR_INFO Structure.\n    */\n    if( sqlite3StrICmp(pShmNode->zFilename, pNew->zFilename)==0 ) break;\n  }\n  if( pShmNode ){\n    sqlite3_free(pNew);\n  }else{\n    int inFlags = SQLITE_OPEN_WAL;\n    int outFlags = 0;\n\n    pShmNode = pNew;\n    pNew = 0;\n    ((winFile*)(&pShmNode->hFile))->h = INVALID_HANDLE_VALUE;\n    pShmNode->pNext = winShmNodeList;\n    winShmNodeList = pShmNode;\n\n    if( sqlite3GlobalConfig.bCoreMutex ){\n      pShmNode->mutex = sqlite3_mutex_alloc(SQLITE_MUTEX_FAST);\n      if( pShmNode->mutex==0 ){\n        rc = SQLITE_IOERR_NOMEM_BKPT;\n        goto shm_open_err;\n      }\n    }\n\n    if( 0==sqlite3_uri_boolean(pDbFd->zPath, \"readonly_shm\", 0) ){\n      inFlags |= SQLITE_OPEN_READWRITE | SQLITE_OPEN_CREATE;\n    }else{\n      inFlags |= SQLITE_OPEN_READONLY;\n    }\n    rc = winOpen(pDbFd->pVfs, pShmNode->zFilename,\n                 (sqlite3_file*)&pShmNode->hFile,\n                 inFlags, &outFlags);\n    if( rc!=SQLITE_OK ){\n      rc = winLogError(rc, osGetLastError(), \"winOpenShm\",\n                       pShmNode->zFilename);\n      goto shm_open_err;\n    }\n    if( outFlags==SQLITE_OPEN_READONLY ) pShmNode->isReadonly = 1;\n\n    rc = winLockSharedMemory(pShmNode);\n    if( rc!=SQLITE_OK && rc!=SQLITE_READONLY_CANTINIT ) goto shm_open_err;\n  }\n\n  /* Make the new connection a child of the winShmNode */\n  p->pShmNode = pShmNode;\n#if defined(SQLITE_DEBUG) || defined(SQLITE_HAVE_OS_TRACE)\n  p->id = pShmNode->nextShmId++;\n#endif\n  pShmNode->nRef++;\n  pDbFd->pShm = p;\n  winShmLeaveMutex();\n\n  /* The reference count on pShmNode has already been incremented under\n  ** the cover of the winShmEnterMutex() mutex and the pointer from the\n  ** new (struct winShm) object to the pShmNode has been set. All that is\n  ** left to do is to link the new object into the linked list starting\n  ** at pShmNode->pFirst. This must be done while holding the pShmNode->mutex\n  ** mutex.\n  */\n  sqlite3_mutex_enter(pShmNode->mutex);\n  p->pNext = pShmNode->pFirst;\n  pShmNode->pFirst = p;\n  sqlite3_mutex_leave(pShmNode->mutex);\n  return rc;\n\n  /* Jump here on any error */\nshm_open_err:\n  winShmSystemLock(pShmNode, WINSHM_UNLCK, WIN_SHM_DMS, 1);\n  winShmPurge(pDbFd->pVfs, 0);      /* This call frees pShmNode if required */\n  sqlite3_free(p);\n  sqlite3_free(pNew);\n  winShmLeaveMutex();\n  return rc;\n}\n\n/*\n** Close a connection to shared-memory.  Delete the underlying\n** storage if deleteFlag is true.\n*/\nstatic int winShmUnmap(\n  sqlite3_file *fd,          /* Database holding shared memory */\n  int deleteFlag             /* Delete after closing if true */\n){\n  winFile *pDbFd;       /* Database holding shared-memory */\n  winShm *p;            /* The connection to be closed */\n  winShmNode *pShmNode; /* The underlying shared-memory file */\n  winShm **pp;          /* For looping over sibling connections */\n\n  pDbFd = (winFile*)fd;\n  p = pDbFd->pShm;\n  if( p==0 ) return SQLITE_OK;\n  pShmNode = p->pShmNode;\n\n  /* Remove connection p from the set of connections associated\n  ** with pShmNode */\n  sqlite3_mutex_enter(pShmNode->mutex);\n  for(pp=&pShmNode->pFirst; (*pp)!=p; pp = &(*pp)->pNext){}\n  *pp = p->pNext;\n\n  /* Free the connection p */\n  sqlite3_free(p);\n  pDbFd->pShm = 0;\n  sqlite3_mutex_leave(pShmNode->mutex);\n\n  /* If pShmNode->nRef has reached 0, then close the underlying\n  ** shared-memory file, too */\n  winShmEnterMutex();\n  assert( pShmNode->nRef>0 );\n  pShmNode->nRef--;\n  if( pShmNode->nRef==0 ){\n    winShmPurge(pDbFd->pVfs, deleteFlag);\n  }\n  winShmLeaveMutex();\n\n  return SQLITE_OK;\n}\n\n/*\n** Change the lock state for a shared-memory segment.\n*/\nstatic int winShmLock(\n  sqlite3_file *fd,          /* Database file holding the shared memory */\n  int ofst,                  /* First lock to acquire or release */\n  int n,                     /* Number of locks to acquire or release */\n  int flags                  /* What to do with the lock */\n){\n  winFile *pDbFd = (winFile*)fd;        /* Connection holding shared memory */\n  winShm *p = pDbFd->pShm;              /* The shared memory being locked */\n  winShm *pX;                           /* For looping over all siblings */\n  winShmNode *pShmNode = p->pShmNode;\n  int rc = SQLITE_OK;                   /* Result code */\n  u16 mask;                             /* Mask of locks to take or release */\n\n  assert( ofst>=0 && ofst+n<=SQLITE_SHM_NLOCK );\n  assert( n>=1 );\n  assert( flags==(SQLITE_SHM_LOCK | SQLITE_SHM_SHARED)\n       || flags==(SQLITE_SHM_LOCK | SQLITE_SHM_EXCLUSIVE)\n       || flags==(SQLITE_SHM_UNLOCK | SQLITE_SHM_SHARED)\n       || flags==(SQLITE_SHM_UNLOCK | SQLITE_SHM_EXCLUSIVE) );\n  assert( n==1 || (flags & SQLITE_SHM_EXCLUSIVE)!=0 );\n\n  mask = (u16)((1U<<(ofst+n)) - (1U<<ofst));\n  assert( n>1 || mask==(1<<ofst) );\n  sqlite3_mutex_enter(pShmNode->mutex);\n  if( flags & SQLITE_SHM_UNLOCK ){\n    u16 allMask = 0; /* Mask of locks held by siblings */\n\n    /* See if any siblings hold this same lock */\n    for(pX=pShmNode->pFirst; pX; pX=pX->pNext){\n      if( pX==p ) continue;\n      assert( (pX->exclMask & (p->exclMask|p->sharedMask))==0 );\n      allMask |= pX->sharedMask;\n    }\n\n    /* Unlock the system-level locks */\n    if( (mask & allMask)==0 ){\n      rc = winShmSystemLock(pShmNode, WINSHM_UNLCK, ofst+WIN_SHM_BASE, n);\n    }else{\n      rc = SQLITE_OK;\n    }\n\n    /* Undo the local locks */\n    if( rc==SQLITE_OK ){\n      p->exclMask &= ~mask;\n      p->sharedMask &= ~mask;\n    }\n  }else if( flags & SQLITE_SHM_SHARED ){\n    u16 allShared = 0;  /* Union of locks held by connections other than \"p\" */\n\n    /* Find out which shared locks are already held by sibling connections.\n    ** If any sibling already holds an exclusive lock, go ahead and return\n    ** SQLITE_BUSY.\n    */\n    for(pX=pShmNode->pFirst; pX; pX=pX->pNext){\n      if( (pX->exclMask & mask)!=0 ){\n        rc = SQLITE_BUSY;\n        break;\n      }\n      allShared |= pX->sharedMask;\n    }\n\n    /* Get shared locks at the system level, if necessary */\n    if( rc==SQLITE_OK ){\n      if( (allShared & mask)==0 ){\n        rc = winShmSystemLock(pShmNode, WINSHM_RDLCK, ofst+WIN_SHM_BASE, n);\n      }else{\n        rc = SQLITE_OK;\n      }\n    }\n\n    /* Get the local shared locks */\n    if( rc==SQLITE_OK ){\n      p->sharedMask |= mask;\n    }\n  }else{\n    /* Make sure no sibling connections hold locks that will block this\n    ** lock.  If any do, return SQLITE_BUSY right away.\n    */\n    for(pX=pShmNode->pFirst; pX; pX=pX->pNext){\n      if( (pX->exclMask & mask)!=0 || (pX->sharedMask & mask)!=0 ){\n        rc = SQLITE_BUSY;\n        break;\n      }\n    }\n\n    /* Get the exclusive locks at the system level.  Then if successful\n    ** also mark the local connection as being locked.\n    */\n    if( rc==SQLITE_OK ){\n      rc = winShmSystemLock(pShmNode, WINSHM_WRLCK, ofst+WIN_SHM_BASE, n);\n      if( rc==SQLITE_OK ){\n        assert( (p->sharedMask & mask)==0 );\n        p->exclMask |= mask;\n      }\n    }\n  }\n  sqlite3_mutex_leave(pShmNode->mutex);\n  OSTRACE((\"SHM-LOCK pid=%lu, id=%d, sharedMask=%03x, exclMask=%03x, rc=%s\\n\",\n           osGetCurrentProcessId(), p->id, p->sharedMask, p->exclMask,\n           sqlite3ErrName(rc)));\n  return rc;\n}\n\n/*\n** Implement a memory barrier or memory fence on shared memory.\n**\n** All loads and stores begun before the barrier must complete before\n** any load or store begun after the barrier.\n*/\nstatic void winShmBarrier(\n  sqlite3_file *fd          /* Database holding the shared memory */\n){\n  UNUSED_PARAMETER(fd);\n  sqlite3MemoryBarrier();   /* compiler-defined memory barrier */\n  winShmEnterMutex();       /* Also mutex, for redundancy */\n  winShmLeaveMutex();\n}\n\n/*\n** This function is called to obtain a pointer to region iRegion of the\n** shared-memory associated with the database file fd. Shared-memory regions\n** are numbered starting from zero. Each shared-memory region is szRegion\n** bytes in size.\n**\n** If an error occurs, an error code is returned and *pp is set to NULL.\n**\n** Otherwise, if the isWrite parameter is 0 and the requested shared-memory\n** region has not been allocated (by any client, including one running in a\n** separate process), then *pp is set to NULL and SQLITE_OK returned. If\n** isWrite is non-zero and the requested shared-memory region has not yet\n** been allocated, it is allocated by this function.\n**\n** If the shared-memory region has already been allocated or is allocated by\n** this call as described above, then it is mapped into this processes\n** address space (if it is not already), *pp is set to point to the mapped\n** memory and SQLITE_OK returned.\n*/\nstatic int winShmMap(\n  sqlite3_file *fd,               /* Handle open on database file */\n  int iRegion,                    /* Region to retrieve */\n  int szRegion,                   /* Size of regions */\n  int isWrite,                    /* True to extend file if necessary */\n  void volatile **pp              /* OUT: Mapped memory */\n){\n  winFile *pDbFd = (winFile*)fd;\n  winShm *pShm = pDbFd->pShm;\n  winShmNode *pShmNode;\n  DWORD protect = PAGE_READWRITE;\n  DWORD flags = FILE_MAP_WRITE | FILE_MAP_READ;\n  int rc = SQLITE_OK;\n\n  if( !pShm ){\n    rc = winOpenSharedMemory(pDbFd);\n    if( rc!=SQLITE_OK ) return rc;\n    pShm = pDbFd->pShm;\n  }\n  pShmNode = pShm->pShmNode;\n\n  sqlite3_mutex_enter(pShmNode->mutex);\n  if( pShmNode->isUnlocked ){\n    rc = winLockSharedMemory(pShmNode);\n    if( rc!=SQLITE_OK ) goto shmpage_out;\n    pShmNode->isUnlocked = 0;\n  }\n  assert( szRegion==pShmNode->szRegion || pShmNode->nRegion==0 );\n\n  if( pShmNode->nRegion<=iRegion ){\n    struct ShmRegion *apNew;           /* New aRegion[] array */\n    int nByte = (iRegion+1)*szRegion;  /* Minimum required file size */\n    sqlite3_int64 sz;                  /* Current size of wal-index file */\n\n    pShmNode->szRegion = szRegion;\n\n    /* The requested region is not mapped into this processes address space.\n    ** Check to see if it has been allocated (i.e. if the wal-index file is\n    ** large enough to contain the requested region).\n    */\n    rc = winFileSize((sqlite3_file *)&pShmNode->hFile, &sz);\n    if( rc!=SQLITE_OK ){\n      rc = winLogError(SQLITE_IOERR_SHMSIZE, osGetLastError(),\n                       \"winShmMap1\", pDbFd->zPath);\n      goto shmpage_out;\n    }\n\n    if( sz<nByte ){\n      /* The requested memory region does not exist. If isWrite is set to\n      ** zero, exit early. *pp will be set to NULL and SQLITE_OK returned.\n      **\n      ** Alternatively, if isWrite is non-zero, use ftruncate() to allocate\n      ** the requested memory region.\n      */\n      if( !isWrite ) goto shmpage_out;\n      rc = winTruncate((sqlite3_file *)&pShmNode->hFile, nByte);\n      if( rc!=SQLITE_OK ){\n        rc = winLogError(SQLITE_IOERR_SHMSIZE, osGetLastError(),\n                         \"winShmMap2\", pDbFd->zPath);\n        goto shmpage_out;\n      }\n    }\n\n    /* Map the requested memory region into this processes address space. */\n    apNew = (struct ShmRegion *)sqlite3_realloc64(\n        pShmNode->aRegion, (iRegion+1)*sizeof(apNew[0])\n    );\n    if( !apNew ){\n      rc = SQLITE_IOERR_NOMEM_BKPT;\n      goto shmpage_out;\n    }\n    pShmNode->aRegion = apNew;\n\n    if( pShmNode->isReadonly ){\n      protect = PAGE_READONLY;\n      flags = FILE_MAP_READ;\n    }\n\n    while( pShmNode->nRegion<=iRegion ){\n      HANDLE hMap = NULL;         /* file-mapping handle */\n      void *pMap = 0;             /* Mapped memory region */\n\n#if SQLITE_OS_WINRT\n      hMap = osCreateFileMappingFromApp(pShmNode->hFile.h,\n          NULL, protect, nByte, NULL\n      );\n#elif defined(SQLITE_WIN32_HAS_WIDE)\n      hMap = osCreateFileMappingW(pShmNode->hFile.h,\n          NULL, protect, 0, nByte, NULL\n      );\n#elif defined(SQLITE_WIN32_HAS_ANSI) && SQLITE_WIN32_CREATEFILEMAPPINGA\n      hMap = osCreateFileMappingA(pShmNode->hFile.h,\n          NULL, protect, 0, nByte, NULL\n      );\n#endif\n      OSTRACE((\"SHM-MAP-CREATE pid=%lu, region=%d, size=%d, rc=%s\\n\",\n               osGetCurrentProcessId(), pShmNode->nRegion, nByte,\n               hMap ? \"ok\" : \"failed\"));\n      if( hMap ){\n        int iOffset = pShmNode->nRegion*szRegion;\n        int iOffsetShift = iOffset % winSysInfo.dwAllocationGranularity;\n#if SQLITE_OS_WINRT\n        pMap = osMapViewOfFileFromApp(hMap, flags,\n            iOffset - iOffsetShift, szRegion + iOffsetShift\n        );\n#else\n        pMap = osMapViewOfFile(hMap, flags,\n            0, iOffset - iOffsetShift, szRegion + iOffsetShift\n        );\n#endif\n        OSTRACE((\"SHM-MAP-MAP pid=%lu, region=%d, offset=%d, size=%d, rc=%s\\n\",\n                 osGetCurrentProcessId(), pShmNode->nRegion, iOffset,\n                 szRegion, pMap ? \"ok\" : \"failed\"));\n      }\n      if( !pMap ){\n        pShmNode->lastErrno = osGetLastError();\n        rc = winLogError(SQLITE_IOERR_SHMMAP, pShmNode->lastErrno,\n                         \"winShmMap3\", pDbFd->zPath);\n        if( hMap ) osCloseHandle(hMap);\n        goto shmpage_out;\n      }\n\n      pShmNode->aRegion[pShmNode->nRegion].pMap = pMap;\n      pShmNode->aRegion[pShmNode->nRegion].hMap = hMap;\n      pShmNode->nRegion++;\n    }\n  }\n\nshmpage_out:\n  if( pShmNode->nRegion>iRegion ){\n    int iOffset = iRegion*szRegion;\n    int iOffsetShift = iOffset % winSysInfo.dwAllocationGranularity;\n    char *p = (char *)pShmNode->aRegion[iRegion].pMap;\n    *pp = (void *)&p[iOffsetShift];\n  }else{\n    *pp = 0;\n  }\n  if( pShmNode->isReadonly && rc==SQLITE_OK ) rc = SQLITE_READONLY;\n  sqlite3_mutex_leave(pShmNode->mutex);\n  return rc;\n}\n\n#else\n# define winShmMap     0\n# define winShmLock    0\n# define winShmBarrier 0\n# define winShmUnmap   0\n#endif /* #ifndef SQLITE_OMIT_WAL */\n\n/*\n** Cleans up the mapped region of the specified file, if any.\n*/\n#if SQLITE_MAX_MMAP_SIZE>0\nstatic int winUnmapfile(winFile *pFile){\n  assert( pFile!=0 );\n  OSTRACE((\"UNMAP-FILE pid=%lu, pFile=%p, hMap=%p, pMapRegion=%p, \"\n           \"mmapSize=%lld, mmapSizeActual=%lld, mmapSizeMax=%lld\\n\",\n           osGetCurrentProcessId(), pFile, pFile->hMap, pFile->pMapRegion,\n           pFile->mmapSize, pFile->mmapSizeActual, pFile->mmapSizeMax));\n  if( pFile->pMapRegion ){\n    if( !osUnmapViewOfFile(pFile->pMapRegion) ){\n      pFile->lastErrno = osGetLastError();\n      OSTRACE((\"UNMAP-FILE pid=%lu, pFile=%p, pMapRegion=%p, \"\n               \"rc=SQLITE_IOERR_MMAP\\n\", osGetCurrentProcessId(), pFile,\n               pFile->pMapRegion));\n      return winLogError(SQLITE_IOERR_MMAP, pFile->lastErrno,\n                         \"winUnmapfile1\", pFile->zPath);\n    }\n    pFile->pMapRegion = 0;\n    pFile->mmapSize = 0;\n    pFile->mmapSizeActual = 0;\n  }\n  if( pFile->hMap!=NULL ){\n    if( !osCloseHandle(pFile->hMap) ){\n      pFile->lastErrno = osGetLastError();\n      OSTRACE((\"UNMAP-FILE pid=%lu, pFile=%p, hMap=%p, rc=SQLITE_IOERR_MMAP\\n\",\n               osGetCurrentProcessId(), pFile, pFile->hMap));\n      return winLogError(SQLITE_IOERR_MMAP, pFile->lastErrno,\n                         \"winUnmapfile2\", pFile->zPath);\n    }\n    pFile->hMap = NULL;\n  }\n  OSTRACE((\"UNMAP-FILE pid=%lu, pFile=%p, rc=SQLITE_OK\\n\",\n           osGetCurrentProcessId(), pFile));\n  return SQLITE_OK;\n}\n\n/*\n** Memory map or remap the file opened by file-descriptor pFd (if the file\n** is already mapped, the existing mapping is replaced by the new). Or, if\n** there already exists a mapping for this file, and there are still\n** outstanding xFetch() references to it, this function is a no-op.\n**\n** If parameter nByte is non-negative, then it is the requested size of\n** the mapping to create. Otherwise, if nByte is less than zero, then the\n** requested size is the size of the file on disk. The actual size of the\n** created mapping is either the requested size or the value configured\n** using SQLITE_FCNTL_MMAP_SIZE, whichever is smaller.\n**\n** SQLITE_OK is returned if no error occurs (even if the mapping is not\n** recreated as a result of outstanding references) or an SQLite error\n** code otherwise.\n*/\nstatic int winMapfile(winFile *pFd, sqlite3_int64 nByte){\n  sqlite3_int64 nMap = nByte;\n  int rc;\n\n  assert( nMap>=0 || pFd->nFetchOut==0 );\n  OSTRACE((\"MAP-FILE pid=%lu, pFile=%p, size=%lld\\n\",\n           osGetCurrentProcessId(), pFd, nByte));\n\n  if( pFd->nFetchOut>0 ) return SQLITE_OK;\n\n  if( nMap<0 ){\n    rc = winFileSize((sqlite3_file*)pFd, &nMap);\n    if( rc ){\n      OSTRACE((\"MAP-FILE pid=%lu, pFile=%p, rc=SQLITE_IOERR_FSTAT\\n\",\n               osGetCurrentProcessId(), pFd));\n      return SQLITE_IOERR_FSTAT;\n    }\n  }\n  if( nMap>pFd->mmapSizeMax ){\n    nMap = pFd->mmapSizeMax;\n  }\n  nMap &= ~(sqlite3_int64)(winSysInfo.dwPageSize - 1);\n\n  if( nMap==0 && pFd->mmapSize>0 ){\n    winUnmapfile(pFd);\n  }\n  if( nMap!=pFd->mmapSize ){\n    void *pNew = 0;\n    DWORD protect = PAGE_READONLY;\n    DWORD flags = FILE_MAP_READ;\n\n    winUnmapfile(pFd);\n#ifdef SQLITE_MMAP_READWRITE\n    if( (pFd->ctrlFlags & WINFILE_RDONLY)==0 ){\n      protect = PAGE_READWRITE;\n      flags |= FILE_MAP_WRITE;\n    }\n#endif\n#if SQLITE_OS_WINRT\n    pFd->hMap = osCreateFileMappingFromApp(pFd->h, NULL, protect, nMap, NULL);\n#elif defined(SQLITE_WIN32_HAS_WIDE)\n    pFd->hMap = osCreateFileMappingW(pFd->h, NULL, protect,\n                                (DWORD)((nMap>>32) & 0xffffffff),\n                                (DWORD)(nMap & 0xffffffff), NULL);\n#elif defined(SQLITE_WIN32_HAS_ANSI) && SQLITE_WIN32_CREATEFILEMAPPINGA\n    pFd->hMap = osCreateFileMappingA(pFd->h, NULL, protect,\n                                (DWORD)((nMap>>32) & 0xffffffff),\n                                (DWORD)(nMap & 0xffffffff), NULL);\n#endif\n    if( pFd->hMap==NULL ){\n      pFd->lastErrno = osGetLastError();\n      rc = winLogError(SQLITE_IOERR_MMAP, pFd->lastErrno,\n                       \"winMapfile1\", pFd->zPath);\n      /* Log the error, but continue normal operation using xRead/xWrite */\n      OSTRACE((\"MAP-FILE-CREATE pid=%lu, pFile=%p, rc=%s\\n\",\n               osGetCurrentProcessId(), pFd, sqlite3ErrName(rc)));\n      return SQLITE_OK;\n    }\n    assert( (nMap % winSysInfo.dwPageSize)==0 );\n    assert( sizeof(SIZE_T)==sizeof(sqlite3_int64) || nMap<=0xffffffff );\n#if SQLITE_OS_WINRT\n    pNew = osMapViewOfFileFromApp(pFd->hMap, flags, 0, (SIZE_T)nMap);\n#else\n    pNew = osMapViewOfFile(pFd->hMap, flags, 0, 0, (SIZE_T)nMap);\n#endif\n    if( pNew==NULL ){\n      osCloseHandle(pFd->hMap);\n      pFd->hMap = NULL;\n      pFd->lastErrno = osGetLastError();\n      rc = winLogError(SQLITE_IOERR_MMAP, pFd->lastErrno,\n                       \"winMapfile2\", pFd->zPath);\n      /* Log the error, but continue normal operation using xRead/xWrite */\n      OSTRACE((\"MAP-FILE-MAP pid=%lu, pFile=%p, rc=%s\\n\",\n               osGetCurrentProcessId(), pFd, sqlite3ErrName(rc)));\n      return SQLITE_OK;\n    }\n    pFd->pMapRegion = pNew;\n    pFd->mmapSize = nMap;\n    pFd->mmapSizeActual = nMap;\n  }\n\n  OSTRACE((\"MAP-FILE pid=%lu, pFile=%p, rc=SQLITE_OK\\n\",\n           osGetCurrentProcessId(), pFd));\n  return SQLITE_OK;\n}\n#endif /* SQLITE_MAX_MMAP_SIZE>0 */\n\n/*\n** If possible, return a pointer to a mapping of file fd starting at offset\n** iOff. The mapping must be valid for at least nAmt bytes.\n**\n** If such a pointer can be obtained, store it in *pp and return SQLITE_OK.\n** Or, if one cannot but no error occurs, set *pp to 0 and return SQLITE_OK.\n** Finally, if an error does occur, return an SQLite error code. The final\n** value of *pp is undefined in this case.\n**\n** If this function does return a pointer, the caller must eventually\n** release the reference by calling winUnfetch().\n*/\nstatic int winFetch(sqlite3_file *fd, i64 iOff, int nAmt, void **pp){\n#if SQLITE_MAX_MMAP_SIZE>0\n  winFile *pFd = (winFile*)fd;   /* The underlying database file */\n#endif\n  *pp = 0;\n\n  OSTRACE((\"FETCH pid=%lu, pFile=%p, offset=%lld, amount=%d, pp=%p\\n\",\n           osGetCurrentProcessId(), fd, iOff, nAmt, pp));\n\n#if SQLITE_MAX_MMAP_SIZE>0\n  if( pFd->mmapSizeMax>0 ){\n    if( pFd->pMapRegion==0 ){\n      int rc = winMapfile(pFd, -1);\n      if( rc!=SQLITE_OK ){\n        OSTRACE((\"FETCH pid=%lu, pFile=%p, rc=%s\\n\",\n                 osGetCurrentProcessId(), pFd, sqlite3ErrName(rc)));\n        return rc;\n      }\n    }\n    if( pFd->mmapSize >= iOff+nAmt ){\n      *pp = &((u8 *)pFd->pMapRegion)[iOff];\n      pFd->nFetchOut++;\n    }\n  }\n#endif\n\n  OSTRACE((\"FETCH pid=%lu, pFile=%p, pp=%p, *pp=%p, rc=SQLITE_OK\\n\",\n           osGetCurrentProcessId(), fd, pp, *pp));\n  return SQLITE_OK;\n}\n\n/*\n** If the third argument is non-NULL, then this function releases a\n** reference obtained by an earlier call to winFetch(). The second\n** argument passed to this function must be the same as the corresponding\n** argument that was passed to the winFetch() invocation.\n**\n** Or, if the third argument is NULL, then this function is being called\n** to inform the VFS layer that, according to POSIX, any existing mapping\n** may now be invalid and should be unmapped.\n*/\nstatic int winUnfetch(sqlite3_file *fd, i64 iOff, void *p){\n#if SQLITE_MAX_MMAP_SIZE>0\n  winFile *pFd = (winFile*)fd;   /* The underlying database file */\n\n  /* If p==0 (unmap the entire file) then there must be no outstanding\n  ** xFetch references. Or, if p!=0 (meaning it is an xFetch reference),\n  ** then there must be at least one outstanding.  */\n  assert( (p==0)==(pFd->nFetchOut==0) );\n\n  /* If p!=0, it must match the iOff value. */\n  assert( p==0 || p==&((u8 *)pFd->pMapRegion)[iOff] );\n\n  OSTRACE((\"UNFETCH pid=%lu, pFile=%p, offset=%lld, p=%p\\n\",\n           osGetCurrentProcessId(), pFd, iOff, p));\n\n  if( p ){\n    pFd->nFetchOut--;\n  }else{\n    /* FIXME:  If Windows truly always prevents truncating or deleting a\n    ** file while a mapping is held, then the following winUnmapfile() call\n    ** is unnecessary can be omitted - potentially improving\n    ** performance.  */\n    winUnmapfile(pFd);\n  }\n\n  assert( pFd->nFetchOut>=0 );\n#endif\n\n  OSTRACE((\"UNFETCH pid=%lu, pFile=%p, rc=SQLITE_OK\\n\",\n           osGetCurrentProcessId(), fd));\n  return SQLITE_OK;\n}\n\n/*\n** Here ends the implementation of all sqlite3_file methods.\n**\n********************** End sqlite3_file Methods *******************************\n******************************************************************************/\n\n/*\n** This vector defines all the methods that can operate on an\n** sqlite3_file for win32.\n*/\nstatic const sqlite3_io_methods winIoMethod = {\n  3,                              /* iVersion */\n  winClose,                       /* xClose */\n  winRead,                        /* xRead */\n  winWrite,                       /* xWrite */\n  winTruncate,                    /* xTruncate */\n  winSync,                        /* xSync */\n  winFileSize,                    /* xFileSize */\n  winLock,                        /* xLock */\n  winUnlock,                      /* xUnlock */\n  winCheckReservedLock,           /* xCheckReservedLock */\n  winFileControl,                 /* xFileControl */\n  winSectorSize,                  /* xSectorSize */\n  winDeviceCharacteristics,       /* xDeviceCharacteristics */\n  winShmMap,                      /* xShmMap */\n  winShmLock,                     /* xShmLock */\n  winShmBarrier,                  /* xShmBarrier */\n  winShmUnmap,                    /* xShmUnmap */\n  winFetch,                       /* xFetch */\n  winUnfetch                      /* xUnfetch */\n};\n\n/*\n** This vector defines all the methods that can operate on an\n** sqlite3_file for win32 without performing any locking.\n*/\nstatic const sqlite3_io_methods winIoNolockMethod = {\n  3,                              /* iVersion */\n  winClose,                       /* xClose */\n  winRead,                        /* xRead */\n  winWrite,                       /* xWrite */\n  winTruncate,                    /* xTruncate */\n  winSync,                        /* xSync */\n  winFileSize,                    /* xFileSize */\n  winNolockLock,                  /* xLock */\n  winNolockUnlock,                /* xUnlock */\n  winNolockCheckReservedLock,     /* xCheckReservedLock */\n  winFileControl,                 /* xFileControl */\n  winSectorSize,                  /* xSectorSize */\n  winDeviceCharacteristics,       /* xDeviceCharacteristics */\n  winShmMap,                      /* xShmMap */\n  winShmLock,                     /* xShmLock */\n  winShmBarrier,                  /* xShmBarrier */\n  winShmUnmap,                    /* xShmUnmap */\n  winFetch,                       /* xFetch */\n  winUnfetch                      /* xUnfetch */\n};\n\nstatic winVfsAppData winAppData = {\n  &winIoMethod,       /* pMethod */\n  0,                  /* pAppData */\n  0                   /* bNoLock */\n};\n\nstatic winVfsAppData winNolockAppData = {\n  &winIoNolockMethod, /* pMethod */\n  0,                  /* pAppData */\n  1                   /* bNoLock */\n};\n\n/****************************************************************************\n**************************** sqlite3_vfs methods ****************************\n**\n** This division contains the implementation of methods on the\n** sqlite3_vfs object.\n*/\n\n#if defined(__CYGWIN__)\n/*\n** Convert a filename from whatever the underlying operating system\n** supports for filenames into UTF-8.  Space to hold the result is\n** obtained from malloc and must be freed by the calling function.\n*/\nstatic char *winConvertToUtf8Filename(const void *zFilename){\n  char *zConverted = 0;\n  if( osIsNT() ){\n    zConverted = winUnicodeToUtf8(zFilename);\n  }\n#ifdef SQLITE_WIN32_HAS_ANSI\n  else{\n    zConverted = winMbcsToUtf8(zFilename, osAreFileApisANSI());\n  }\n#endif\n  /* caller will handle out of memory */\n  return zConverted;\n}\n#endif\n\n/*\n** Convert a UTF-8 filename into whatever form the underlying\n** operating system wants filenames in.  Space to hold the result\n** is obtained from malloc and must be freed by the calling\n** function.\n*/\nstatic void *winConvertFromUtf8Filename(const char *zFilename){\n  void *zConverted = 0;\n  if( osIsNT() ){\n    zConverted = winUtf8ToUnicode(zFilename);\n  }\n#ifdef SQLITE_WIN32_HAS_ANSI\n  else{\n    zConverted = winUtf8ToMbcs(zFilename, osAreFileApisANSI());\n  }\n#endif\n  /* caller will handle out of memory */\n  return zConverted;\n}\n\n/*\n** This function returns non-zero if the specified UTF-8 string buffer\n** ends with a directory separator character or one was successfully\n** added to it.\n*/\nstatic int winMakeEndInDirSep(int nBuf, char *zBuf){\n  if( zBuf ){\n    int nLen = sqlite3Strlen30(zBuf);\n    if( nLen>0 ){\n      if( winIsDirSep(zBuf[nLen-1]) ){\n        return 1;\n      }else if( nLen+1<nBuf ){\n        zBuf[nLen] = winGetDirSep();\n        zBuf[nLen+1] = '\\0';\n        return 1;\n      }\n    }\n  }\n  return 0;\n}\n\n/*\n** Create a temporary file name and store the resulting pointer into pzBuf.\n** The pointer returned in pzBuf must be freed via sqlite3_free().\n*/\nstatic int winGetTempname(sqlite3_vfs *pVfs, char **pzBuf){\n  static char zChars[] =\n    \"abcdefghijklmnopqrstuvwxyz\"\n    \"ABCDEFGHIJKLMNOPQRSTUVWXYZ\"\n    \"0123456789\";\n  size_t i, j;\n  int nPre = sqlite3Strlen30(SQLITE_TEMP_FILE_PREFIX);\n  int nMax, nBuf, nDir, nLen;\n  char *zBuf;\n\n  /* It's odd to simulate an io-error here, but really this is just\n  ** using the io-error infrastructure to test that SQLite handles this\n  ** function failing.\n  */\n  SimulateIOError( return SQLITE_IOERR );\n\n  /* Allocate a temporary buffer to store the fully qualified file\n  ** name for the temporary file.  If this fails, we cannot continue.\n  */\n  nMax = pVfs->mxPathname; nBuf = nMax + 2;\n  zBuf = sqlite3MallocZero( nBuf );\n  if( !zBuf ){\n    OSTRACE((\"TEMP-FILENAME rc=SQLITE_IOERR_NOMEM\\n\"));\n    return SQLITE_IOERR_NOMEM_BKPT;\n  }\n\n  /* Figure out the effective temporary directory.  First, check if one\n  ** has been explicitly set by the application; otherwise, use the one\n  ** configured by the operating system.\n  */\n  nDir = nMax - (nPre + 15);\n  assert( nDir>0 );\n  if( sqlite3_temp_directory ){\n    int nDirLen = sqlite3Strlen30(sqlite3_temp_directory);\n    if( nDirLen>0 ){\n      if( !winIsDirSep(sqlite3_temp_directory[nDirLen-1]) ){\n        nDirLen++;\n      }\n      if( nDirLen>nDir ){\n        sqlite3_free(zBuf);\n        OSTRACE((\"TEMP-FILENAME rc=SQLITE_ERROR\\n\"));\n        return winLogError(SQLITE_ERROR, 0, \"winGetTempname1\", 0);\n      }\n      sqlite3_snprintf(nMax, zBuf, \"%s\", sqlite3_temp_directory);\n    }\n  }\n#if defined(__CYGWIN__)\n  else{\n    static const char *azDirs[] = {\n       0, /* getenv(\"SQLITE_TMPDIR\") */\n       0, /* getenv(\"TMPDIR\") */\n       0, /* getenv(\"TMP\") */\n       0, /* getenv(\"TEMP\") */\n       0, /* getenv(\"USERPROFILE\") */\n       \"/var/tmp\",\n       \"/usr/tmp\",\n       \"/tmp\",\n       \".\",\n       0        /* List terminator */\n    };\n    unsigned int i;\n    const char *zDir = 0;\n\n    if( !azDirs[0] ) azDirs[0] = getenv(\"SQLITE_TMPDIR\");\n    if( !azDirs[1] ) azDirs[1] = getenv(\"TMPDIR\");\n    if( !azDirs[2] ) azDirs[2] = getenv(\"TMP\");\n    if( !azDirs[3] ) azDirs[3] = getenv(\"TEMP\");\n    if( !azDirs[4] ) azDirs[4] = getenv(\"USERPROFILE\");\n    for(i=0; i<sizeof(azDirs)/sizeof(azDirs[0]); zDir=azDirs[i++]){\n      void *zConverted;\n      if( zDir==0 ) continue;\n      /* If the path starts with a drive letter followed by the colon\n      ** character, assume it is already a native Win32 path; otherwise,\n      ** it must be converted to a native Win32 path via the Cygwin API\n      ** prior to using it.\n      */\n      if( winIsDriveLetterAndColon(zDir) ){\n        zConverted = winConvertFromUtf8Filename(zDir);\n        if( !zConverted ){\n          sqlite3_free(zBuf);\n          OSTRACE((\"TEMP-FILENAME rc=SQLITE_IOERR_NOMEM\\n\"));\n          return SQLITE_IOERR_NOMEM_BKPT;\n        }\n        if( winIsDir(zConverted) ){\n          sqlite3_snprintf(nMax, zBuf, \"%s\", zDir);\n          sqlite3_free(zConverted);\n          break;\n        }\n        sqlite3_free(zConverted);\n      }else{\n        zConverted = sqlite3MallocZero( nMax+1 );\n        if( !zConverted ){\n          sqlite3_free(zBuf);\n          OSTRACE((\"TEMP-FILENAME rc=SQLITE_IOERR_NOMEM\\n\"));\n          return SQLITE_IOERR_NOMEM_BKPT;\n        }\n        if( cygwin_conv_path(\n                osIsNT() ? CCP_POSIX_TO_WIN_W : CCP_POSIX_TO_WIN_A, zDir,\n                zConverted, nMax+1)<0 ){\n          sqlite3_free(zConverted);\n          sqlite3_free(zBuf);\n          OSTRACE((\"TEMP-FILENAME rc=SQLITE_IOERR_CONVPATH\\n\"));\n          return winLogError(SQLITE_IOERR_CONVPATH, (DWORD)errno,\n                             \"winGetTempname2\", zDir);\n        }\n        if( winIsDir(zConverted) ){\n          /* At this point, we know the candidate directory exists and should\n          ** be used.  However, we may need to convert the string containing\n          ** its name into UTF-8 (i.e. if it is UTF-16 right now).\n          */\n          char *zUtf8 = winConvertToUtf8Filename(zConverted);\n          if( !zUtf8 ){\n            sqlite3_free(zConverted);\n            sqlite3_free(zBuf);\n            OSTRACE((\"TEMP-FILENAME rc=SQLITE_IOERR_NOMEM\\n\"));\n            return SQLITE_IOERR_NOMEM_BKPT;\n          }\n          sqlite3_snprintf(nMax, zBuf, \"%s\", zUtf8);\n          sqlite3_free(zUtf8);\n          sqlite3_free(zConverted);\n          break;\n        }\n        sqlite3_free(zConverted);\n      }\n    }\n  }\n#elif !SQLITE_OS_WINRT && !defined(__CYGWIN__)\n  else if( osIsNT() ){\n    char *zMulti;\n    LPWSTR zWidePath = sqlite3MallocZero( nMax*sizeof(WCHAR) );\n    if( !zWidePath ){\n      sqlite3_free(zBuf);\n      OSTRACE((\"TEMP-FILENAME rc=SQLITE_IOERR_NOMEM\\n\"));\n      return SQLITE_IOERR_NOMEM_BKPT;\n    }\n    if( osGetTempPathW(nMax, zWidePath)==0 ){\n      sqlite3_free(zWidePath);\n      sqlite3_free(zBuf);\n      OSTRACE((\"TEMP-FILENAME rc=SQLITE_IOERR_GETTEMPPATH\\n\"));\n      return winLogError(SQLITE_IOERR_GETTEMPPATH, osGetLastError(),\n                         \"winGetTempname2\", 0);\n    }\n    zMulti = winUnicodeToUtf8(zWidePath);\n    if( zMulti ){\n      sqlite3_snprintf(nMax, zBuf, \"%s\", zMulti);\n      sqlite3_free(zMulti);\n      sqlite3_free(zWidePath);\n    }else{\n      sqlite3_free(zWidePath);\n      sqlite3_free(zBuf);\n      OSTRACE((\"TEMP-FILENAME rc=SQLITE_IOERR_NOMEM\\n\"));\n      return SQLITE_IOERR_NOMEM_BKPT;\n    }\n  }\n#ifdef SQLITE_WIN32_HAS_ANSI\n  else{\n    char *zUtf8;\n    char *zMbcsPath = sqlite3MallocZero( nMax );\n    if( !zMbcsPath ){\n      sqlite3_free(zBuf);\n      OSTRACE((\"TEMP-FILENAME rc=SQLITE_IOERR_NOMEM\\n\"));\n      return SQLITE_IOERR_NOMEM_BKPT;\n    }\n    if( osGetTempPathA(nMax, zMbcsPath)==0 ){\n      sqlite3_free(zBuf);\n      OSTRACE((\"TEMP-FILENAME rc=SQLITE_IOERR_GETTEMPPATH\\n\"));\n      return winLogError(SQLITE_IOERR_GETTEMPPATH, osGetLastError(),\n                         \"winGetTempname3\", 0);\n    }\n    zUtf8 = winMbcsToUtf8(zMbcsPath, osAreFileApisANSI());\n    if( zUtf8 ){\n      sqlite3_snprintf(nMax, zBuf, \"%s\", zUtf8);\n      sqlite3_free(zUtf8);\n    }else{\n      sqlite3_free(zBuf);\n      OSTRACE((\"TEMP-FILENAME rc=SQLITE_IOERR_NOMEM\\n\"));\n      return SQLITE_IOERR_NOMEM_BKPT;\n    }\n  }\n#endif /* SQLITE_WIN32_HAS_ANSI */\n#endif /* !SQLITE_OS_WINRT */\n\n  /*\n  ** Check to make sure the temporary directory ends with an appropriate\n  ** separator.  If it does not and there is not enough space left to add\n  ** one, fail.\n  */\n  if( !winMakeEndInDirSep(nDir+1, zBuf) ){\n    sqlite3_free(zBuf);\n    OSTRACE((\"TEMP-FILENAME rc=SQLITE_ERROR\\n\"));\n    return winLogError(SQLITE_ERROR, 0, \"winGetTempname4\", 0);\n  }\n\n  /*\n  ** Check that the output buffer is large enough for the temporary file\n  ** name in the following format:\n  **\n  **   \"<temporary_directory>/etilqs_XXXXXXXXXXXXXXX\\0\\0\"\n  **\n  ** If not, return SQLITE_ERROR.  The number 17 is used here in order to\n  ** account for the space used by the 15 character random suffix and the\n  ** two trailing NUL characters.  The final directory separator character\n  ** has already added if it was not already present.\n  */\n  nLen = sqlite3Strlen30(zBuf);\n  if( (nLen + nPre + 17) > nBuf ){\n    sqlite3_free(zBuf);\n    OSTRACE((\"TEMP-FILENAME rc=SQLITE_ERROR\\n\"));\n    return winLogError(SQLITE_ERROR, 0, \"winGetTempname5\", 0);\n  }\n\n  sqlite3_snprintf(nBuf-16-nLen, zBuf+nLen, SQLITE_TEMP_FILE_PREFIX);\n\n  j = sqlite3Strlen30(zBuf);\n  sqlite3_randomness(15, &zBuf[j]);\n  for(i=0; i<15; i++, j++){\n    zBuf[j] = (char)zChars[ ((unsigned char)zBuf[j])%(sizeof(zChars)-1) ];\n  }\n  zBuf[j] = 0;\n  zBuf[j+1] = 0;\n  *pzBuf = zBuf;\n\n  OSTRACE((\"TEMP-FILENAME name=%s, rc=SQLITE_OK\\n\", zBuf));\n  return SQLITE_OK;\n}\n\n/*\n** Return TRUE if the named file is really a directory.  Return false if\n** it is something other than a directory, or if there is any kind of memory\n** allocation failure.\n*/\nstatic int winIsDir(const void *zConverted){\n  DWORD attr;\n  int rc = 0;\n  DWORD lastErrno;\n\n  if( osIsNT() ){\n    int cnt = 0;\n    WIN32_FILE_ATTRIBUTE_DATA sAttrData;\n    memset(&sAttrData, 0, sizeof(sAttrData));\n    while( !(rc = osGetFileAttributesExW((LPCWSTR)zConverted,\n                             GetFileExInfoStandard,\n                             &sAttrData)) && winRetryIoerr(&cnt, &lastErrno) ){}\n    if( !rc ){\n      return 0; /* Invalid name? */\n    }\n    attr = sAttrData.dwFileAttributes;\n#if SQLITE_OS_WINCE==0\n  }else{\n    attr = osGetFileAttributesA((char*)zConverted);\n#endif\n  }\n  return (attr!=INVALID_FILE_ATTRIBUTES) && (attr&FILE_ATTRIBUTE_DIRECTORY);\n}\n\n/* forward reference */\nstatic int winAccess(\n  sqlite3_vfs *pVfs,         /* Not used on win32 */\n  const char *zFilename,     /* Name of file to check */\n  int flags,                 /* Type of test to make on this file */\n  int *pResOut               /* OUT: Result */\n);\n\n/*\n** Open a file.\n*/\nstatic int winOpen(\n  sqlite3_vfs *pVfs,        /* Used to get maximum path length and AppData */\n  const char *zName,        /* Name of the file (UTF-8) */\n  sqlite3_file *id,         /* Write the SQLite file handle here */\n  int flags,                /* Open mode flags */\n  int *pOutFlags            /* Status return flags */\n){\n  HANDLE h;\n  DWORD lastErrno = 0;\n  DWORD dwDesiredAccess;\n  DWORD dwShareMode;\n  DWORD dwCreationDisposition;\n  DWORD dwFlagsAndAttributes = 0;\n#if SQLITE_OS_WINCE\n  int isTemp = 0;\n#endif\n  winVfsAppData *pAppData;\n  winFile *pFile = (winFile*)id;\n  void *zConverted;              /* Filename in OS encoding */\n  const char *zUtf8Name = zName; /* Filename in UTF-8 encoding */\n  int cnt = 0;\n\n  /* If argument zPath is a NULL pointer, this function is required to open\n  ** a temporary file. Use this buffer to store the file name in.\n  */\n  char *zTmpname = 0; /* For temporary filename, if necessary. */\n\n  int rc = SQLITE_OK;            /* Function Return Code */\n#if !defined(NDEBUG) || SQLITE_OS_WINCE\n  int eType = flags&0xFFFFFF00;  /* Type of file to open */\n#endif\n\n  int isExclusive  = (flags & SQLITE_OPEN_EXCLUSIVE);\n  int isDelete     = (flags & SQLITE_OPEN_DELETEONCLOSE);\n  int isCreate     = (flags & SQLITE_OPEN_CREATE);\n  int isReadonly   = (flags & SQLITE_OPEN_READONLY);\n  int isReadWrite  = (flags & SQLITE_OPEN_READWRITE);\n\n#ifndef NDEBUG\n  int isOpenJournal = (isCreate && (\n        eType==SQLITE_OPEN_MASTER_JOURNAL\n     || eType==SQLITE_OPEN_MAIN_JOURNAL\n     || eType==SQLITE_OPEN_WAL\n  ));\n#endif\n\n  OSTRACE((\"OPEN name=%s, pFile=%p, flags=%x, pOutFlags=%p\\n\",\n           zUtf8Name, id, flags, pOutFlags));\n\n  /* Check the following statements are true:\n  **\n  **   (a) Exactly one of the READWRITE and READONLY flags must be set, and\n  **   (b) if CREATE is set, then READWRITE must also be set, and\n  **   (c) if EXCLUSIVE is set, then CREATE must also be set.\n  **   (d) if DELETEONCLOSE is set, then CREATE must also be set.\n  */\n  assert((isReadonly==0 || isReadWrite==0) && (isReadWrite || isReadonly));\n  assert(isCreate==0 || isReadWrite);\n  assert(isExclusive==0 || isCreate);\n  assert(isDelete==0 || isCreate);\n\n  /* The main DB, main journal, WAL file and master journal are never\n  ** automatically deleted. Nor are they ever temporary files.  */\n  assert( (!isDelete && zName) || eType!=SQLITE_OPEN_MAIN_DB );\n  assert( (!isDelete && zName) || eType!=SQLITE_OPEN_MAIN_JOURNAL );\n  assert( (!isDelete && zName) || eType!=SQLITE_OPEN_MASTER_JOURNAL );\n  assert( (!isDelete && zName) || eType!=SQLITE_OPEN_WAL );\n\n  /* Assert that the upper layer has set one of the \"file-type\" flags. */\n  assert( eType==SQLITE_OPEN_MAIN_DB      || eType==SQLITE_OPEN_TEMP_DB\n       || eType==SQLITE_OPEN_MAIN_JOURNAL || eType==SQLITE_OPEN_TEMP_JOURNAL\n       || eType==SQLITE_OPEN_SUBJOURNAL   || eType==SQLITE_OPEN_MASTER_JOURNAL\n       || eType==SQLITE_OPEN_TRANSIENT_DB || eType==SQLITE_OPEN_WAL\n  );\n\n  assert( pFile!=0 );\n  memset(pFile, 0, sizeof(winFile));\n  pFile->h = INVALID_HANDLE_VALUE;\n\n#if SQLITE_OS_WINRT\n  if( !zUtf8Name && !sqlite3_temp_directory ){\n    sqlite3_log(SQLITE_ERROR,\n        \"sqlite3_temp_directory variable should be set for WinRT\");\n  }\n#endif\n\n  /* If the second argument to this function is NULL, generate a\n  ** temporary file name to use\n  */\n  if( !zUtf8Name ){\n    assert( isDelete && !isOpenJournal );\n    rc = winGetTempname(pVfs, &zTmpname);\n    if( rc!=SQLITE_OK ){\n      OSTRACE((\"OPEN name=%s, rc=%s\", zUtf8Name, sqlite3ErrName(rc)));\n      return rc;\n    }\n    zUtf8Name = zTmpname;\n  }\n\n  /* Database filenames are double-zero terminated if they are not\n  ** URIs with parameters.  Hence, they can always be passed into\n  ** sqlite3_uri_parameter().\n  */\n  assert( (eType!=SQLITE_OPEN_MAIN_DB) || (flags & SQLITE_OPEN_URI) ||\n       zUtf8Name[sqlite3Strlen30(zUtf8Name)+1]==0 );\n\n  /* Convert the filename to the system encoding. */\n  zConverted = winConvertFromUtf8Filename(zUtf8Name);\n  if( zConverted==0 ){\n    sqlite3_free(zTmpname);\n    OSTRACE((\"OPEN name=%s, rc=SQLITE_IOERR_NOMEM\", zUtf8Name));\n    return SQLITE_IOERR_NOMEM_BKPT;\n  }\n\n  if( winIsDir(zConverted) ){\n    sqlite3_free(zConverted);\n    sqlite3_free(zTmpname);\n    OSTRACE((\"OPEN name=%s, rc=SQLITE_CANTOPEN_ISDIR\", zUtf8Name));\n    return SQLITE_CANTOPEN_ISDIR;\n  }\n\n  if( isReadWrite ){\n    dwDesiredAccess = GENERIC_READ | GENERIC_WRITE;\n  }else{\n    dwDesiredAccess = GENERIC_READ;\n  }\n\n  /* SQLITE_OPEN_EXCLUSIVE is used to make sure that a new file is\n  ** created. SQLite doesn't use it to indicate \"exclusive access\"\n  ** as it is usually understood.\n  */\n  if( isExclusive ){\n    /* Creates a new file, only if it does not already exist. */\n    /* If the file exists, it fails. */\n    dwCreationDisposition = CREATE_NEW;\n  }else if( isCreate ){\n    /* Open existing file, or create if it doesn't exist */\n    dwCreationDisposition = OPEN_ALWAYS;\n  }else{\n    /* Opens a file, only if it exists. */\n    dwCreationDisposition = OPEN_EXISTING;\n  }\n\n  dwShareMode = FILE_SHARE_READ | FILE_SHARE_WRITE;\n\n  if( isDelete ){\n#if SQLITE_OS_WINCE\n    dwFlagsAndAttributes = FILE_ATTRIBUTE_HIDDEN;\n    isTemp = 1;\n#else\n    dwFlagsAndAttributes = FILE_ATTRIBUTE_TEMPORARY\n                               | FILE_ATTRIBUTE_HIDDEN\n                               | FILE_FLAG_DELETE_ON_CLOSE;\n#endif\n  }else{\n    dwFlagsAndAttributes = FILE_ATTRIBUTE_NORMAL;\n  }\n  /* Reports from the internet are that performance is always\n  ** better if FILE_FLAG_RANDOM_ACCESS is used.  Ticket #2699. */\n#if SQLITE_OS_WINCE\n  dwFlagsAndAttributes |= FILE_FLAG_RANDOM_ACCESS;\n#endif\n\n  if( osIsNT() ){\n#if SQLITE_OS_WINRT\n    CREATEFILE2_EXTENDED_PARAMETERS extendedParameters;\n    extendedParameters.dwSize = sizeof(CREATEFILE2_EXTENDED_PARAMETERS);\n    extendedParameters.dwFileAttributes =\n            dwFlagsAndAttributes & FILE_ATTRIBUTE_MASK;\n    extendedParameters.dwFileFlags = dwFlagsAndAttributes & FILE_FLAG_MASK;\n    extendedParameters.dwSecurityQosFlags = SECURITY_ANONYMOUS;\n    extendedParameters.lpSecurityAttributes = NULL;\n    extendedParameters.hTemplateFile = NULL;\n    do{\n      h = osCreateFile2((LPCWSTR)zConverted,\n                        dwDesiredAccess,\n                        dwShareMode,\n                        dwCreationDisposition,\n                        &extendedParameters);\n      if( h!=INVALID_HANDLE_VALUE ) break;\n      if( isReadWrite ){\n        int rc2, isRO = 0;\n        sqlite3BeginBenignMalloc();\n        rc2 = winAccess(pVfs, zName, SQLITE_ACCESS_READ, &isRO);\n        sqlite3EndBenignMalloc();\n        if( rc2==SQLITE_OK && isRO ) break;\n      }\n    }while( winRetryIoerr(&cnt, &lastErrno) );\n#else\n    do{\n      h = osCreateFileW((LPCWSTR)zConverted,\n                        dwDesiredAccess,\n                        dwShareMode, NULL,\n                        dwCreationDisposition,\n                        dwFlagsAndAttributes,\n                        NULL);\n      if( h!=INVALID_HANDLE_VALUE ) break;\n      if( isReadWrite ){\n        int rc2, isRO = 0;\n        sqlite3BeginBenignMalloc();\n        rc2 = winAccess(pVfs, zName, SQLITE_ACCESS_READ, &isRO);\n        sqlite3EndBenignMalloc();\n        if( rc2==SQLITE_OK && isRO ) break;\n      }\n    }while( winRetryIoerr(&cnt, &lastErrno) );\n#endif\n  }\n#ifdef SQLITE_WIN32_HAS_ANSI\n  else{\n    do{\n      h = osCreateFileA((LPCSTR)zConverted,\n                        dwDesiredAccess,\n                        dwShareMode, NULL,\n                        dwCreationDisposition,\n                        dwFlagsAndAttributes,\n                        NULL);\n      if( h!=INVALID_HANDLE_VALUE ) break;\n      if( isReadWrite ){\n        int rc2, isRO = 0;\n        sqlite3BeginBenignMalloc();\n        rc2 = winAccess(pVfs, zName, SQLITE_ACCESS_READ, &isRO);\n        sqlite3EndBenignMalloc();\n        if( rc2==SQLITE_OK && isRO ) break;\n      }\n    }while( winRetryIoerr(&cnt, &lastErrno) );\n  }\n#endif\n  winLogIoerr(cnt, __LINE__);\n\n  OSTRACE((\"OPEN file=%p, name=%s, access=%lx, rc=%s\\n\", h, zUtf8Name,\n           dwDesiredAccess, (h==INVALID_HANDLE_VALUE) ? \"failed\" : \"ok\"));\n\n  if( h==INVALID_HANDLE_VALUE ){\n    sqlite3_free(zConverted);\n    sqlite3_free(zTmpname);\n    if( isReadWrite && !isExclusive ){\n      return winOpen(pVfs, zName, id,\n         ((flags|SQLITE_OPEN_READONLY) &\n                     ~(SQLITE_OPEN_CREATE|SQLITE_OPEN_READWRITE)),\n         pOutFlags);\n    }else{\n      pFile->lastErrno = lastErrno;\n      winLogError(SQLITE_CANTOPEN, pFile->lastErrno, \"winOpen\", zUtf8Name);\n      return SQLITE_CANTOPEN_BKPT;\n    }\n  }\n\n  if( pOutFlags ){\n    if( isReadWrite ){\n      *pOutFlags = SQLITE_OPEN_READWRITE;\n    }else{\n      *pOutFlags = SQLITE_OPEN_READONLY;\n    }\n  }\n\n  OSTRACE((\"OPEN file=%p, name=%s, access=%lx, pOutFlags=%p, *pOutFlags=%d, \"\n           \"rc=%s\\n\", h, zUtf8Name, dwDesiredAccess, pOutFlags, pOutFlags ?\n           *pOutFlags : 0, (h==INVALID_HANDLE_VALUE) ? \"failed\" : \"ok\"));\n\n  pAppData = (winVfsAppData*)pVfs->pAppData;\n\n#if SQLITE_OS_WINCE\n  {\n    if( isReadWrite && eType==SQLITE_OPEN_MAIN_DB\n         && ((pAppData==NULL) || !pAppData->bNoLock)\n         && (rc = winceCreateLock(zName, pFile))!=SQLITE_OK\n    ){\n      osCloseHandle(h);\n      sqlite3_free(zConverted);\n      sqlite3_free(zTmpname);\n      OSTRACE((\"OPEN-CE-LOCK name=%s, rc=%s\\n\", zName, sqlite3ErrName(rc)));\n      return rc;\n    }\n  }\n  if( isTemp ){\n    pFile->zDeleteOnClose = zConverted;\n  }else\n#endif\n  {\n    sqlite3_free(zConverted);\n  }\n\n  sqlite3_free(zTmpname);\n  pFile->pMethod = pAppData ? pAppData->pMethod : &winIoMethod;\n  pFile->pVfs = pVfs;\n  pFile->h = h;\n  if( isReadonly ){\n    pFile->ctrlFlags |= WINFILE_RDONLY;\n  }\n  if( sqlite3_uri_boolean(zName, \"psow\", SQLITE_POWERSAFE_OVERWRITE) ){\n    pFile->ctrlFlags |= WINFILE_PSOW;\n  }\n  pFile->lastErrno = NO_ERROR;\n  pFile->zPath = zName;\n#if SQLITE_MAX_MMAP_SIZE>0\n  pFile->hMap = NULL;\n  pFile->pMapRegion = 0;\n  pFile->mmapSize = 0;\n  pFile->mmapSizeActual = 0;\n  pFile->mmapSizeMax = sqlite3GlobalConfig.szMmap;\n#endif\n\n  OpenCounter(+1);\n  return rc;\n}\n\n/*\n** Delete the named file.\n**\n** Note that Windows does not allow a file to be deleted if some other\n** process has it open.  Sometimes a virus scanner or indexing program\n** will open a journal file shortly after it is created in order to do\n** whatever it does.  While this other process is holding the\n** file open, we will be unable to delete it.  To work around this\n** problem, we delay 100 milliseconds and try to delete again.  Up\n** to MX_DELETION_ATTEMPTs deletion attempts are run before giving\n** up and returning an error.\n*/\nstatic int winDelete(\n  sqlite3_vfs *pVfs,          /* Not used on win32 */\n  const char *zFilename,      /* Name of file to delete */\n  int syncDir                 /* Not used on win32 */\n){\n  int cnt = 0;\n  int rc;\n  DWORD attr;\n  DWORD lastErrno = 0;\n  void *zConverted;\n  UNUSED_PARAMETER(pVfs);\n  UNUSED_PARAMETER(syncDir);\n\n  SimulateIOError(return SQLITE_IOERR_DELETE);\n  OSTRACE((\"DELETE name=%s, syncDir=%d\\n\", zFilename, syncDir));\n\n  zConverted = winConvertFromUtf8Filename(zFilename);\n  if( zConverted==0 ){\n    OSTRACE((\"DELETE name=%s, rc=SQLITE_IOERR_NOMEM\\n\", zFilename));\n    return SQLITE_IOERR_NOMEM_BKPT;\n  }\n  if( osIsNT() ){\n    do {\n#if SQLITE_OS_WINRT\n      WIN32_FILE_ATTRIBUTE_DATA sAttrData;\n      memset(&sAttrData, 0, sizeof(sAttrData));\n      if ( osGetFileAttributesExW(zConverted, GetFileExInfoStandard,\n                                  &sAttrData) ){\n        attr = sAttrData.dwFileAttributes;\n      }else{\n        lastErrno = osGetLastError();\n        if( lastErrno==ERROR_FILE_NOT_FOUND\n         || lastErrno==ERROR_PATH_NOT_FOUND ){\n          rc = SQLITE_IOERR_DELETE_NOENT; /* Already gone? */\n        }else{\n          rc = SQLITE_ERROR;\n        }\n        break;\n      }\n#else\n      attr = osGetFileAttributesW(zConverted);\n#endif\n      if ( attr==INVALID_FILE_ATTRIBUTES ){\n        lastErrno = osGetLastError();\n        if( lastErrno==ERROR_FILE_NOT_FOUND\n         || lastErrno==ERROR_PATH_NOT_FOUND ){\n          rc = SQLITE_IOERR_DELETE_NOENT; /* Already gone? */\n        }else{\n          rc = SQLITE_ERROR;\n        }\n        break;\n      }\n      if ( attr&FILE_ATTRIBUTE_DIRECTORY ){\n        rc = SQLITE_ERROR; /* Files only. */\n        break;\n      }\n      if ( osDeleteFileW(zConverted) ){\n        rc = SQLITE_OK; /* Deleted OK. */\n        break;\n      }\n      if ( !winRetryIoerr(&cnt, &lastErrno) ){\n        rc = SQLITE_ERROR; /* No more retries. */\n        break;\n      }\n    } while(1);\n  }\n#ifdef SQLITE_WIN32_HAS_ANSI\n  else{\n    do {\n      attr = osGetFileAttributesA(zConverted);\n      if ( attr==INVALID_FILE_ATTRIBUTES ){\n        lastErrno = osGetLastError();\n        if( lastErrno==ERROR_FILE_NOT_FOUND\n         || lastErrno==ERROR_PATH_NOT_FOUND ){\n          rc = SQLITE_IOERR_DELETE_NOENT; /* Already gone? */\n        }else{\n          rc = SQLITE_ERROR;\n        }\n        break;\n      }\n      if ( attr&FILE_ATTRIBUTE_DIRECTORY ){\n        rc = SQLITE_ERROR; /* Files only. */\n        break;\n      }\n      if ( osDeleteFileA(zConverted) ){\n        rc = SQLITE_OK; /* Deleted OK. */\n        break;\n      }\n      if ( !winRetryIoerr(&cnt, &lastErrno) ){\n        rc = SQLITE_ERROR; /* No more retries. */\n        break;\n      }\n    } while(1);\n  }\n#endif\n  if( rc && rc!=SQLITE_IOERR_DELETE_NOENT ){\n    rc = winLogError(SQLITE_IOERR_DELETE, lastErrno, \"winDelete\", zFilename);\n  }else{\n    winLogIoerr(cnt, __LINE__);\n  }\n  sqlite3_free(zConverted);\n  OSTRACE((\"DELETE name=%s, rc=%s\\n\", zFilename, sqlite3ErrName(rc)));\n  return rc;\n}\n\n/*\n** Check the existence and status of a file.\n*/\nstatic int winAccess(\n  sqlite3_vfs *pVfs,         /* Not used on win32 */\n  const char *zFilename,     /* Name of file to check */\n  int flags,                 /* Type of test to make on this file */\n  int *pResOut               /* OUT: Result */\n){\n  DWORD attr;\n  int rc = 0;\n  DWORD lastErrno = 0;\n  void *zConverted;\n  UNUSED_PARAMETER(pVfs);\n\n  SimulateIOError( return SQLITE_IOERR_ACCESS; );\n  OSTRACE((\"ACCESS name=%s, flags=%x, pResOut=%p\\n\",\n           zFilename, flags, pResOut));\n\n  zConverted = winConvertFromUtf8Filename(zFilename);\n  if( zConverted==0 ){\n    OSTRACE((\"ACCESS name=%s, rc=SQLITE_IOERR_NOMEM\\n\", zFilename));\n    return SQLITE_IOERR_NOMEM_BKPT;\n  }\n  if( osIsNT() ){\n    int cnt = 0;\n    WIN32_FILE_ATTRIBUTE_DATA sAttrData;\n    memset(&sAttrData, 0, sizeof(sAttrData));\n    while( !(rc = osGetFileAttributesExW((LPCWSTR)zConverted,\n                             GetFileExInfoStandard,\n                             &sAttrData)) && winRetryIoerr(&cnt, &lastErrno) ){}\n    if( rc ){\n      /* For an SQLITE_ACCESS_EXISTS query, treat a zero-length file\n      ** as if it does not exist.\n      */\n      if(    flags==SQLITE_ACCESS_EXISTS\n          && sAttrData.nFileSizeHigh==0\n          && sAttrData.nFileSizeLow==0 ){\n        attr = INVALID_FILE_ATTRIBUTES;\n      }else{\n        attr = sAttrData.dwFileAttributes;\n      }\n    }else{\n      winLogIoerr(cnt, __LINE__);\n      if( lastErrno!=ERROR_FILE_NOT_FOUND && lastErrno!=ERROR_PATH_NOT_FOUND ){\n        sqlite3_free(zConverted);\n        return winLogError(SQLITE_IOERR_ACCESS, lastErrno, \"winAccess\",\n                           zFilename);\n      }else{\n        attr = INVALID_FILE_ATTRIBUTES;\n      }\n    }\n  }\n#ifdef SQLITE_WIN32_HAS_ANSI\n  else{\n    attr = osGetFileAttributesA((char*)zConverted);\n  }\n#endif\n  sqlite3_free(zConverted);\n  switch( flags ){\n    case SQLITE_ACCESS_READ:\n    case SQLITE_ACCESS_EXISTS:\n      rc = attr!=INVALID_FILE_ATTRIBUTES;\n      break;\n    case SQLITE_ACCESS_READWRITE:\n      rc = attr!=INVALID_FILE_ATTRIBUTES &&\n             (attr & FILE_ATTRIBUTE_READONLY)==0;\n      break;\n    default:\n      assert(!\"Invalid flags argument\");\n  }\n  *pResOut = rc;\n  OSTRACE((\"ACCESS name=%s, pResOut=%p, *pResOut=%d, rc=SQLITE_OK\\n\",\n           zFilename, pResOut, *pResOut));\n  return SQLITE_OK;\n}\n\n/*\n** Returns non-zero if the specified path name starts with a drive letter\n** followed by a colon character.\n*/\nstatic BOOL winIsDriveLetterAndColon(\n  const char *zPathname\n){\n  return ( sqlite3Isalpha(zPathname[0]) && zPathname[1]==':' );\n}\n\n/*\n** Returns non-zero if the specified path name should be used verbatim.  If\n** non-zero is returned from this function, the calling function must simply\n** use the provided path name verbatim -OR- resolve it into a full path name\n** using the GetFullPathName Win32 API function (if available).\n*/\nstatic BOOL winIsVerbatimPathname(\n  const char *zPathname\n){\n  /*\n  ** If the path name starts with a forward slash or a backslash, it is either\n  ** a legal UNC name, a volume relative path, or an absolute path name in the\n  ** \"Unix\" format on Windows.  There is no easy way to differentiate between\n  ** the final two cases; therefore, we return the safer return value of TRUE\n  ** so that callers of this function will simply use it verbatim.\n  */\n  if ( winIsDirSep(zPathname[0]) ){\n    return TRUE;\n  }\n\n  /*\n  ** If the path name starts with a letter and a colon it is either a volume\n  ** relative path or an absolute path.  Callers of this function must not\n  ** attempt to treat it as a relative path name (i.e. they should simply use\n  ** it verbatim).\n  */\n  if ( winIsDriveLetterAndColon(zPathname) ){\n    return TRUE;\n  }\n\n  /*\n  ** If we get to this point, the path name should almost certainly be a purely\n  ** relative one (i.e. not a UNC name, not absolute, and not volume relative).\n  */\n  return FALSE;\n}\n\n/*\n** Turn a relative pathname into a full pathname.  Write the full\n** pathname into zOut[].  zOut[] will be at least pVfs->mxPathname\n** bytes in size.\n*/\nstatic int winFullPathname(\n  sqlite3_vfs *pVfs,            /* Pointer to vfs object */\n  const char *zRelative,        /* Possibly relative input path */\n  int nFull,                    /* Size of output buffer in bytes */\n  char *zFull                   /* Output buffer */\n){\n#if !SQLITE_OS_WINCE && !SQLITE_OS_WINRT && !defined(__CYGWIN__)\n  DWORD nByte;\n  void *zConverted;\n  char *zOut;\n#endif\n\n  /* If this path name begins with \"/X:\", where \"X\" is any alphabetic\n  ** character, discard the initial \"/\" from the pathname.\n  */\n  if( zRelative[0]=='/' && winIsDriveLetterAndColon(zRelative+1) ){\n    zRelative++;\n  }\n\n#if defined(__CYGWIN__)\n  SimulateIOError( return SQLITE_ERROR );\n  UNUSED_PARAMETER(nFull);\n  assert( nFull>=pVfs->mxPathname );\n  if ( sqlite3_data_directory && !winIsVerbatimPathname(zRelative) ){\n    /*\n    ** NOTE: We are dealing with a relative path name and the data\n    **       directory has been set.  Therefore, use it as the basis\n    **       for converting the relative path name to an absolute\n    **       one by prepending the data directory and a slash.\n    */\n    char *zOut = sqlite3MallocZero( pVfs->mxPathname+1 );\n    if( !zOut ){\n      return SQLITE_IOERR_NOMEM_BKPT;\n    }\n    if( cygwin_conv_path(\n            (osIsNT() ? CCP_POSIX_TO_WIN_W : CCP_POSIX_TO_WIN_A) |\n            CCP_RELATIVE, zRelative, zOut, pVfs->mxPathname+1)<0 ){\n      sqlite3_free(zOut);\n      return winLogError(SQLITE_CANTOPEN_CONVPATH, (DWORD)errno,\n                         \"winFullPathname1\", zRelative);\n    }else{\n      char *zUtf8 = winConvertToUtf8Filename(zOut);\n      if( !zUtf8 ){\n        sqlite3_free(zOut);\n        return SQLITE_IOERR_NOMEM_BKPT;\n      }\n      sqlite3_snprintf(MIN(nFull, pVfs->mxPathname), zFull, \"%s%c%s\",\n                       sqlite3_data_directory, winGetDirSep(), zUtf8);\n      sqlite3_free(zUtf8);\n      sqlite3_free(zOut);\n    }\n  }else{\n    char *zOut = sqlite3MallocZero( pVfs->mxPathname+1 );\n    if( !zOut ){\n      return SQLITE_IOERR_NOMEM_BKPT;\n    }\n    if( cygwin_conv_path(\n            (osIsNT() ? CCP_POSIX_TO_WIN_W : CCP_POSIX_TO_WIN_A),\n            zRelative, zOut, pVfs->mxPathname+1)<0 ){\n      sqlite3_free(zOut);\n      return winLogError(SQLITE_CANTOPEN_CONVPATH, (DWORD)errno,\n                         \"winFullPathname2\", zRelative);\n    }else{\n      char *zUtf8 = winConvertToUtf8Filename(zOut);\n      if( !zUtf8 ){\n        sqlite3_free(zOut);\n        return SQLITE_IOERR_NOMEM_BKPT;\n      }\n      sqlite3_snprintf(MIN(nFull, pVfs->mxPathname), zFull, \"%s\", zUtf8);\n      sqlite3_free(zUtf8);\n      sqlite3_free(zOut);\n    }\n  }\n  return SQLITE_OK;\n#endif\n\n#if (SQLITE_OS_WINCE || SQLITE_OS_WINRT) && !defined(__CYGWIN__)\n  SimulateIOError( return SQLITE_ERROR );\n  /* WinCE has no concept of a relative pathname, or so I am told. */\n  /* WinRT has no way to convert a relative path to an absolute one. */\n  if ( sqlite3_data_directory && !winIsVerbatimPathname(zRelative) ){\n    /*\n    ** NOTE: We are dealing with a relative path name and the data\n    **       directory has been set.  Therefore, use it as the basis\n    **       for converting the relative path name to an absolute\n    **       one by prepending the data directory and a backslash.\n    */\n    sqlite3_snprintf(MIN(nFull, pVfs->mxPathname), zFull, \"%s%c%s\",\n                     sqlite3_data_directory, winGetDirSep(), zRelative);\n  }else{\n    sqlite3_snprintf(MIN(nFull, pVfs->mxPathname), zFull, \"%s\", zRelative);\n  }\n  return SQLITE_OK;\n#endif\n\n#if !SQLITE_OS_WINCE && !SQLITE_OS_WINRT && !defined(__CYGWIN__)\n  /* It's odd to simulate an io-error here, but really this is just\n  ** using the io-error infrastructure to test that SQLite handles this\n  ** function failing. This function could fail if, for example, the\n  ** current working directory has been unlinked.\n  */\n  SimulateIOError( return SQLITE_ERROR );\n  if ( sqlite3_data_directory && !winIsVerbatimPathname(zRelative) ){\n    /*\n    ** NOTE: We are dealing with a relative path name and the data\n    **       directory has been set.  Therefore, use it as the basis\n    **       for converting the relative path name to an absolute\n    **       one by prepending the data directory and a backslash.\n    */\n    sqlite3_snprintf(MIN(nFull, pVfs->mxPathname), zFull, \"%s%c%s\",\n                     sqlite3_data_directory, winGetDirSep(), zRelative);\n    return SQLITE_OK;\n  }\n  zConverted = winConvertFromUtf8Filename(zRelative);\n  if( zConverted==0 ){\n    return SQLITE_IOERR_NOMEM_BKPT;\n  }\n  if( osIsNT() ){\n    LPWSTR zTemp;\n    nByte = osGetFullPathNameW((LPCWSTR)zConverted, 0, 0, 0);\n    if( nByte==0 ){\n      sqlite3_free(zConverted);\n      return winLogError(SQLITE_CANTOPEN_FULLPATH, osGetLastError(),\n                         \"winFullPathname1\", zRelative);\n    }\n    nByte += 3;\n    zTemp = sqlite3MallocZero( nByte*sizeof(zTemp[0]) );\n    if( zTemp==0 ){\n      sqlite3_free(zConverted);\n      return SQLITE_IOERR_NOMEM_BKPT;\n    }\n    nByte = osGetFullPathNameW((LPCWSTR)zConverted, nByte, zTemp, 0);\n    if( nByte==0 ){\n      sqlite3_free(zConverted);\n      sqlite3_free(zTemp);\n      return winLogError(SQLITE_CANTOPEN_FULLPATH, osGetLastError(),\n                         \"winFullPathname2\", zRelative);\n    }\n    sqlite3_free(zConverted);\n    zOut = winUnicodeToUtf8(zTemp);\n    sqlite3_free(zTemp);\n  }\n#ifdef SQLITE_WIN32_HAS_ANSI\n  else{\n    char *zTemp;\n    nByte = osGetFullPathNameA((char*)zConverted, 0, 0, 0);\n    if( nByte==0 ){\n      sqlite3_free(zConverted);\n      return winLogError(SQLITE_CANTOPEN_FULLPATH, osGetLastError(),\n                         \"winFullPathname3\", zRelative);\n    }\n    nByte += 3;\n    zTemp = sqlite3MallocZero( nByte*sizeof(zTemp[0]) );\n    if( zTemp==0 ){\n      sqlite3_free(zConverted);\n      return SQLITE_IOERR_NOMEM_BKPT;\n    }\n    nByte = osGetFullPathNameA((char*)zConverted, nByte, zTemp, 0);\n    if( nByte==0 ){\n      sqlite3_free(zConverted);\n      sqlite3_free(zTemp);\n      return winLogError(SQLITE_CANTOPEN_FULLPATH, osGetLastError(),\n                         \"winFullPathname4\", zRelative);\n    }\n    sqlite3_free(zConverted);\n    zOut = winMbcsToUtf8(zTemp, osAreFileApisANSI());\n    sqlite3_free(zTemp);\n  }\n#endif\n  if( zOut ){\n    sqlite3_snprintf(MIN(nFull, pVfs->mxPathname), zFull, \"%s\", zOut);\n    sqlite3_free(zOut);\n    return SQLITE_OK;\n  }else{\n    return SQLITE_IOERR_NOMEM_BKPT;\n  }\n#endif\n}\n\n#ifndef SQLITE_OMIT_LOAD_EXTENSION\n/*\n** Interfaces for opening a shared library, finding entry points\n** within the shared library, and closing the shared library.\n*/\nstatic void *winDlOpen(sqlite3_vfs *pVfs, const char *zFilename){\n  HANDLE h;\n#if defined(__CYGWIN__)\n  int nFull = pVfs->mxPathname+1;\n  char *zFull = sqlite3MallocZero( nFull );\n  void *zConverted = 0;\n  if( zFull==0 ){\n    OSTRACE((\"DLOPEN name=%s, handle=%p\\n\", zFilename, (void*)0));\n    return 0;\n  }\n  if( winFullPathname(pVfs, zFilename, nFull, zFull)!=SQLITE_OK ){\n    sqlite3_free(zFull);\n    OSTRACE((\"DLOPEN name=%s, handle=%p\\n\", zFilename, (void*)0));\n    return 0;\n  }\n  zConverted = winConvertFromUtf8Filename(zFull);\n  sqlite3_free(zFull);\n#else\n  void *zConverted = winConvertFromUtf8Filename(zFilename);\n  UNUSED_PARAMETER(pVfs);\n#endif\n  if( zConverted==0 ){\n    OSTRACE((\"DLOPEN name=%s, handle=%p\\n\", zFilename, (void*)0));\n    return 0;\n  }\n  if( osIsNT() ){\n#if SQLITE_OS_WINRT\n    h = osLoadPackagedLibrary((LPCWSTR)zConverted, 0);\n#else\n    h = osLoadLibraryW((LPCWSTR)zConverted);\n#endif\n  }\n#ifdef SQLITE_WIN32_HAS_ANSI\n  else{\n    h = osLoadLibraryA((char*)zConverted);\n  }\n#endif\n  OSTRACE((\"DLOPEN name=%s, handle=%p\\n\", zFilename, (void*)h));\n  sqlite3_free(zConverted);\n  return (void*)h;\n}\nstatic void winDlError(sqlite3_vfs *pVfs, int nBuf, char *zBufOut){\n  UNUSED_PARAMETER(pVfs);\n  winGetLastErrorMsg(osGetLastError(), nBuf, zBufOut);\n}\nstatic void (*winDlSym(sqlite3_vfs *pVfs,void *pH,const char *zSym))(void){\n  FARPROC proc;\n  UNUSED_PARAMETER(pVfs);\n  proc = osGetProcAddressA((HANDLE)pH, zSym);\n  OSTRACE((\"DLSYM handle=%p, symbol=%s, address=%p\\n\",\n           (void*)pH, zSym, (void*)proc));\n  return (void(*)(void))proc;\n}\nstatic void winDlClose(sqlite3_vfs *pVfs, void *pHandle){\n  UNUSED_PARAMETER(pVfs);\n  osFreeLibrary((HANDLE)pHandle);\n  OSTRACE((\"DLCLOSE handle=%p\\n\", (void*)pHandle));\n}\n#else /* if SQLITE_OMIT_LOAD_EXTENSION is defined: */\n  #define winDlOpen  0\n  #define winDlError 0\n  #define winDlSym   0\n  #define winDlClose 0\n#endif\n\n/* State information for the randomness gatherer. */\ntypedef struct EntropyGatherer EntropyGatherer;\nstruct EntropyGatherer {\n  unsigned char *a;   /* Gather entropy into this buffer */\n  int na;             /* Size of a[] in bytes */\n  int i;              /* XOR next input into a[i] */\n  int nXor;           /* Number of XOR operations done */\n};\n\n#if !defined(SQLITE_TEST) && !defined(SQLITE_OMIT_RANDOMNESS)\n/* Mix sz bytes of entropy into p. */\nstatic void xorMemory(EntropyGatherer *p, unsigned char *x, int sz){\n  int j, k;\n  for(j=0, k=p->i; j<sz; j++){\n    p->a[k++] ^= x[j];\n    if( k>=p->na ) k = 0;\n  }\n  p->i = k;\n  p->nXor += sz;\n}\n#endif /* !defined(SQLITE_TEST) && !defined(SQLITE_OMIT_RANDOMNESS) */\n\n/*\n** Write up to nBuf bytes of randomness into zBuf.\n*/\nstatic int winRandomness(sqlite3_vfs *pVfs, int nBuf, char *zBuf){\n#if defined(SQLITE_TEST) || defined(SQLITE_OMIT_RANDOMNESS)\n  UNUSED_PARAMETER(pVfs);\n  memset(zBuf, 0, nBuf);\n  return nBuf;\n#else\n  EntropyGatherer e;\n  UNUSED_PARAMETER(pVfs);\n  memset(zBuf, 0, nBuf);\n  e.a = (unsigned char*)zBuf;\n  e.na = nBuf;\n  e.nXor = 0;\n  e.i = 0;\n  {\n    SYSTEMTIME x;\n    osGetSystemTime(&x);\n    xorMemory(&e, (unsigned char*)&x, sizeof(SYSTEMTIME));\n  }\n  {\n    DWORD pid = osGetCurrentProcessId();\n    xorMemory(&e, (unsigned char*)&pid, sizeof(DWORD));\n  }\n#if SQLITE_OS_WINRT\n  {\n    ULONGLONG cnt = osGetTickCount64();\n    xorMemory(&e, (unsigned char*)&cnt, sizeof(ULONGLONG));\n  }\n#else\n  {\n    DWORD cnt = osGetTickCount();\n    xorMemory(&e, (unsigned char*)&cnt, sizeof(DWORD));\n  }\n#endif /* SQLITE_OS_WINRT */\n  {\n    LARGE_INTEGER i;\n    osQueryPerformanceCounter(&i);\n    xorMemory(&e, (unsigned char*)&i, sizeof(LARGE_INTEGER));\n  }\n#if !SQLITE_OS_WINCE && !SQLITE_OS_WINRT && SQLITE_WIN32_USE_UUID\n  {\n    UUID id;\n    memset(&id, 0, sizeof(UUID));\n    osUuidCreate(&id);\n    xorMemory(&e, (unsigned char*)&id, sizeof(UUID));\n    memset(&id, 0, sizeof(UUID));\n    osUuidCreateSequential(&id);\n    xorMemory(&e, (unsigned char*)&id, sizeof(UUID));\n  }\n#endif /* !SQLITE_OS_WINCE && !SQLITE_OS_WINRT && SQLITE_WIN32_USE_UUID */\n  return e.nXor>nBuf ? nBuf : e.nXor;\n#endif /* defined(SQLITE_TEST) || defined(SQLITE_OMIT_RANDOMNESS) */\n}\n\n\n/*\n** Sleep for a little while.  Return the amount of time slept.\n*/\nstatic int winSleep(sqlite3_vfs *pVfs, int microsec){\n  sqlite3_win32_sleep((microsec+999)/1000);\n  UNUSED_PARAMETER(pVfs);\n  return ((microsec+999)/1000)*1000;\n}\n\n/*\n** The following variable, if set to a non-zero value, is interpreted as\n** the number of seconds since 1970 and is used to set the result of\n** sqlite3OsCurrentTime() during testing.\n*/\n#ifdef SQLITE_TEST\nSQLITE_API int sqlite3_current_time = 0;  /* Fake system time in seconds since 1970. */\n#endif\n\n/*\n** Find the current time (in Universal Coordinated Time).  Write into *piNow\n** the current time and date as a Julian Day number times 86_400_000.  In\n** other words, write into *piNow the number of milliseconds since the Julian\n** epoch of noon in Greenwich on November 24, 4714 B.C according to the\n** proleptic Gregorian calendar.\n**\n** On success, return SQLITE_OK.  Return SQLITE_ERROR if the time and date\n** cannot be found.\n*/\nstatic int winCurrentTimeInt64(sqlite3_vfs *pVfs, sqlite3_int64 *piNow){\n  /* FILETIME structure is a 64-bit value representing the number of\n     100-nanosecond intervals since January 1, 1601 (= JD 2305813.5).\n  */\n  FILETIME ft;\n  static const sqlite3_int64 winFiletimeEpoch = 23058135*(sqlite3_int64)8640000;\n#ifdef SQLITE_TEST\n  static const sqlite3_int64 unixEpoch = 24405875*(sqlite3_int64)8640000;\n#endif\n  /* 2^32 - to avoid use of LL and warnings in gcc */\n  static const sqlite3_int64 max32BitValue =\n      (sqlite3_int64)2000000000 + (sqlite3_int64)2000000000 +\n      (sqlite3_int64)294967296;\n\n#if SQLITE_OS_WINCE\n  SYSTEMTIME time;\n  osGetSystemTime(&time);\n  /* if SystemTimeToFileTime() fails, it returns zero. */\n  if (!osSystemTimeToFileTime(&time,&ft)){\n    return SQLITE_ERROR;\n  }\n#else\n  osGetSystemTimeAsFileTime( &ft );\n#endif\n\n  *piNow = winFiletimeEpoch +\n            ((((sqlite3_int64)ft.dwHighDateTime)*max32BitValue) +\n               (sqlite3_int64)ft.dwLowDateTime)/(sqlite3_int64)10000;\n\n#ifdef SQLITE_TEST\n  if( sqlite3_current_time ){\n    *piNow = 1000*(sqlite3_int64)sqlite3_current_time + unixEpoch;\n  }\n#endif\n  UNUSED_PARAMETER(pVfs);\n  return SQLITE_OK;\n}\n\n/*\n** Find the current time (in Universal Coordinated Time).  Write the\n** current time and date as a Julian Day number into *prNow and\n** return 0.  Return 1 if the time and date cannot be found.\n*/\nstatic int winCurrentTime(sqlite3_vfs *pVfs, double *prNow){\n  int rc;\n  sqlite3_int64 i;\n  rc = winCurrentTimeInt64(pVfs, &i);\n  if( !rc ){\n    *prNow = i/86400000.0;\n  }\n  return rc;\n}\n\n/*\n** The idea is that this function works like a combination of\n** GetLastError() and FormatMessage() on Windows (or errno and\n** strerror_r() on Unix). After an error is returned by an OS\n** function, SQLite calls this function with zBuf pointing to\n** a buffer of nBuf bytes. The OS layer should populate the\n** buffer with a nul-terminated UTF-8 encoded error message\n** describing the last IO error to have occurred within the calling\n** thread.\n**\n** If the error message is too large for the supplied buffer,\n** it should be truncated. The return value of xGetLastError\n** is zero if the error message fits in the buffer, or non-zero\n** otherwise (if the message was truncated). If non-zero is returned,\n** then it is not necessary to include the nul-terminator character\n** in the output buffer.\n**\n** Not supplying an error message will have no adverse effect\n** on SQLite. It is fine to have an implementation that never\n** returns an error message:\n**\n**   int xGetLastError(sqlite3_vfs *pVfs, int nBuf, char *zBuf){\n**     assert(zBuf[0]=='\\0');\n**     return 0;\n**   }\n**\n** However if an error message is supplied, it will be incorporated\n** by sqlite into the error message available to the user using\n** sqlite3_errmsg(), possibly making IO errors easier to debug.\n*/\nstatic int winGetLastError(sqlite3_vfs *pVfs, int nBuf, char *zBuf){\n  DWORD e = osGetLastError();\n  UNUSED_PARAMETER(pVfs);\n  if( nBuf>0 ) winGetLastErrorMsg(e, nBuf, zBuf);\n  return e;\n}\n\n/*\n** Initialize and deinitialize the operating system interface.\n*/\nSQLITE_API int sqlite3_os_init(void){\n  static sqlite3_vfs winVfs = {\n    3,                     /* iVersion */\n    sizeof(winFile),       /* szOsFile */\n    SQLITE_WIN32_MAX_PATH_BYTES, /* mxPathname */\n    0,                     /* pNext */\n    \"win32\",               /* zName */\n    &winAppData,           /* pAppData */\n    winOpen,               /* xOpen */\n    winDelete,             /* xDelete */\n    winAccess,             /* xAccess */\n    winFullPathname,       /* xFullPathname */\n    winDlOpen,             /* xDlOpen */\n    winDlError,            /* xDlError */\n    winDlSym,              /* xDlSym */\n    winDlClose,            /* xDlClose */\n    winRandomness,         /* xRandomness */\n    winSleep,              /* xSleep */\n    winCurrentTime,        /* xCurrentTime */\n    winGetLastError,       /* xGetLastError */\n    winCurrentTimeInt64,   /* xCurrentTimeInt64 */\n    winSetSystemCall,      /* xSetSystemCall */\n    winGetSystemCall,      /* xGetSystemCall */\n    winNextSystemCall,     /* xNextSystemCall */\n  };\n#if defined(SQLITE_WIN32_HAS_WIDE)\n  static sqlite3_vfs winLongPathVfs = {\n    3,                     /* iVersion */\n    sizeof(winFile),       /* szOsFile */\n    SQLITE_WINNT_MAX_PATH_BYTES, /* mxPathname */\n    0,                     /* pNext */\n    \"win32-longpath\",      /* zName */\n    &winAppData,           /* pAppData */\n    winOpen,               /* xOpen */\n    winDelete,             /* xDelete */\n    winAccess,             /* xAccess */\n    winFullPathname,       /* xFullPathname */\n    winDlOpen,             /* xDlOpen */\n    winDlError,            /* xDlError */\n    winDlSym,              /* xDlSym */\n    winDlClose,            /* xDlClose */\n    winRandomness,         /* xRandomness */\n    winSleep,              /* xSleep */\n    winCurrentTime,        /* xCurrentTime */\n    winGetLastError,       /* xGetLastError */\n    winCurrentTimeInt64,   /* xCurrentTimeInt64 */\n    winSetSystemCall,      /* xSetSystemCall */\n    winGetSystemCall,      /* xGetSystemCall */\n    winNextSystemCall,     /* xNextSystemCall */\n  };\n#endif\n  static sqlite3_vfs winNolockVfs = {\n    3,                     /* iVersion */\n    sizeof(winFile),       /* szOsFile */\n    SQLITE_WIN32_MAX_PATH_BYTES, /* mxPathname */\n    0,                     /* pNext */\n    \"win32-none\",          /* zName */\n    &winNolockAppData,     /* pAppData */\n    winOpen,               /* xOpen */\n    winDelete,             /* xDelete */\n    winAccess,             /* xAccess */\n    winFullPathname,       /* xFullPathname */\n    winDlOpen,             /* xDlOpen */\n    winDlError,            /* xDlError */\n    winDlSym,              /* xDlSym */\n    winDlClose,            /* xDlClose */\n    winRandomness,         /* xRandomness */\n    winSleep,              /* xSleep */\n    winCurrentTime,        /* xCurrentTime */\n    winGetLastError,       /* xGetLastError */\n    winCurrentTimeInt64,   /* xCurrentTimeInt64 */\n    winSetSystemCall,      /* xSetSystemCall */\n    winGetSystemCall,      /* xGetSystemCall */\n    winNextSystemCall,     /* xNextSystemCall */\n  };\n#if defined(SQLITE_WIN32_HAS_WIDE)\n  static sqlite3_vfs winLongPathNolockVfs = {\n    3,                     /* iVersion */\n    sizeof(winFile),       /* szOsFile */\n    SQLITE_WINNT_MAX_PATH_BYTES, /* mxPathname */\n    0,                     /* pNext */\n    \"win32-longpath-none\", /* zName */\n    &winNolockAppData,     /* pAppData */\n    winOpen,               /* xOpen */\n    winDelete,             /* xDelete */\n    winAccess,             /* xAccess */\n    winFullPathname,       /* xFullPathname */\n    winDlOpen,             /* xDlOpen */\n    winDlError,            /* xDlError */\n    winDlSym,              /* xDlSym */\n    winDlClose,            /* xDlClose */\n    winRandomness,         /* xRandomness */\n    winSleep,              /* xSleep */\n    winCurrentTime,        /* xCurrentTime */\n    winGetLastError,       /* xGetLastError */\n    winCurrentTimeInt64,   /* xCurrentTimeInt64 */\n    winSetSystemCall,      /* xSetSystemCall */\n    winGetSystemCall,      /* xGetSystemCall */\n    winNextSystemCall,     /* xNextSystemCall */\n  };\n#endif\n\n  /* Double-check that the aSyscall[] array has been constructed\n  ** correctly.  See ticket [bb3a86e890c8e96ab] */\n  assert( ArraySize(aSyscall)==80 );\n\n  /* get memory map allocation granularity */\n  memset(&winSysInfo, 0, sizeof(SYSTEM_INFO));\n#if SQLITE_OS_WINRT\n  osGetNativeSystemInfo(&winSysInfo);\n#else\n  osGetSystemInfo(&winSysInfo);\n#endif\n  assert( winSysInfo.dwAllocationGranularity>0 );\n  assert( winSysInfo.dwPageSize>0 );\n\n  sqlite3_vfs_register(&winVfs, 1);\n\n#if defined(SQLITE_WIN32_HAS_WIDE)\n  sqlite3_vfs_register(&winLongPathVfs, 0);\n#endif\n\n  sqlite3_vfs_register(&winNolockVfs, 0);\n\n#if defined(SQLITE_WIN32_HAS_WIDE)\n  sqlite3_vfs_register(&winLongPathNolockVfs, 0);\n#endif\n\n#ifndef SQLITE_OMIT_WAL\n  winBigLock = sqlite3MutexAlloc(SQLITE_MUTEX_STATIC_VFS1);\n#endif\n\n  return SQLITE_OK;\n}\n\nSQLITE_API int sqlite3_os_end(void){\n#if SQLITE_OS_WINRT\n  if( sleepObj!=NULL ){\n    osCloseHandle(sleepObj);\n    sleepObj = NULL;\n  }\n#endif\n\n#ifndef SQLITE_OMIT_WAL\n  winBigLock = 0;\n#endif\n\n  return SQLITE_OK;\n}\n\n#endif /* SQLITE_OS_WIN */\n\n/************** End of os_win.c **********************************************/\n/************** Begin file bitvec.c ******************************************/\n/*\n** 2008 February 16\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n*************************************************************************\n** This file implements an object that represents a fixed-length\n** bitmap.  Bits are numbered starting with 1.\n**\n** A bitmap is used to record which pages of a database file have been\n** journalled during a transaction, or which pages have the \"dont-write\"\n** property.  Usually only a few pages are meet either condition.\n** So the bitmap is usually sparse and has low cardinality.\n** But sometimes (for example when during a DROP of a large table) most\n** or all of the pages in a database can get journalled.  In those cases, \n** the bitmap becomes dense with high cardinality.  The algorithm needs \n** to handle both cases well.\n**\n** The size of the bitmap is fixed when the object is created.\n**\n** All bits are clear when the bitmap is created.  Individual bits\n** may be set or cleared one at a time.\n**\n** Test operations are about 100 times more common that set operations.\n** Clear operations are exceedingly rare.  There are usually between\n** 5 and 500 set operations per Bitvec object, though the number of sets can\n** sometimes grow into tens of thousands or larger.  The size of the\n** Bitvec object is the number of pages in the database file at the\n** start of a transaction, and is thus usually less than a few thousand,\n** but can be as large as 2 billion for a really big database.\n*/\n/* #include \"sqliteInt.h\" */\n\n/* Size of the Bitvec structure in bytes. */\n#define BITVEC_SZ        512\n\n/* Round the union size down to the nearest pointer boundary, since that's how \n** it will be aligned within the Bitvec struct. */\n#define BITVEC_USIZE \\\n    (((BITVEC_SZ-(3*sizeof(u32)))/sizeof(Bitvec*))*sizeof(Bitvec*))\n\n/* Type of the array \"element\" for the bitmap representation. \n** Should be a power of 2, and ideally, evenly divide into BITVEC_USIZE. \n** Setting this to the \"natural word\" size of your CPU may improve\n** performance. */\n#define BITVEC_TELEM     u8\n/* Size, in bits, of the bitmap element. */\n#define BITVEC_SZELEM    8\n/* Number of elements in a bitmap array. */\n#define BITVEC_NELEM     (BITVEC_USIZE/sizeof(BITVEC_TELEM))\n/* Number of bits in the bitmap array. */\n#define BITVEC_NBIT      (BITVEC_NELEM*BITVEC_SZELEM)\n\n/* Number of u32 values in hash table. */\n#define BITVEC_NINT      (BITVEC_USIZE/sizeof(u32))\n/* Maximum number of entries in hash table before \n** sub-dividing and re-hashing. */\n#define BITVEC_MXHASH    (BITVEC_NINT/2)\n/* Hashing function for the aHash representation.\n** Empirical testing showed that the *37 multiplier \n** (an arbitrary prime)in the hash function provided \n** no fewer collisions than the no-op *1. */\n#define BITVEC_HASH(X)   (((X)*1)%BITVEC_NINT)\n\n#define BITVEC_NPTR      (BITVEC_USIZE/sizeof(Bitvec *))\n\n\n/*\n** A bitmap is an instance of the following structure.\n**\n** This bitmap records the existence of zero or more bits\n** with values between 1 and iSize, inclusive.\n**\n** There are three possible representations of the bitmap.\n** If iSize<=BITVEC_NBIT, then Bitvec.u.aBitmap[] is a straight\n** bitmap.  The least significant bit is bit 1.\n**\n** If iSize>BITVEC_NBIT and iDivisor==0 then Bitvec.u.aHash[] is\n** a hash table that will hold up to BITVEC_MXHASH distinct values.\n**\n** Otherwise, the value i is redirected into one of BITVEC_NPTR\n** sub-bitmaps pointed to by Bitvec.u.apSub[].  Each subbitmap\n** handles up to iDivisor separate values of i.  apSub[0] holds\n** values between 1 and iDivisor.  apSub[1] holds values between\n** iDivisor+1 and 2*iDivisor.  apSub[N] holds values between\n** N*iDivisor+1 and (N+1)*iDivisor.  Each subbitmap is normalized\n** to hold deal with values between 1 and iDivisor.\n*/\nstruct Bitvec {\n  u32 iSize;      /* Maximum bit index.  Max iSize is 4,294,967,296. */\n  u32 nSet;       /* Number of bits that are set - only valid for aHash\n                  ** element.  Max is BITVEC_NINT.  For BITVEC_SZ of 512,\n                  ** this would be 125. */\n  u32 iDivisor;   /* Number of bits handled by each apSub[] entry. */\n                  /* Should >=0 for apSub element. */\n                  /* Max iDivisor is max(u32) / BITVEC_NPTR + 1.  */\n                  /* For a BITVEC_SZ of 512, this would be 34,359,739. */\n  union {\n    BITVEC_TELEM aBitmap[BITVEC_NELEM];    /* Bitmap representation */\n    u32 aHash[BITVEC_NINT];      /* Hash table representation */\n    Bitvec *apSub[BITVEC_NPTR];  /* Recursive representation */\n  } u;\n};\n\n/*\n** Create a new bitmap object able to handle bits between 0 and iSize,\n** inclusive.  Return a pointer to the new object.  Return NULL if \n** malloc fails.\n*/\nSQLITE_PRIVATE Bitvec *sqlite3BitvecCreate(u32 iSize){\n  Bitvec *p;\n  assert( sizeof(*p)==BITVEC_SZ );\n  p = sqlite3MallocZero( sizeof(*p) );\n  if( p ){\n    p->iSize = iSize;\n  }\n  return p;\n}\n\n/*\n** Check to see if the i-th bit is set.  Return true or false.\n** If p is NULL (if the bitmap has not been created) or if\n** i is out of range, then return false.\n*/\nSQLITE_PRIVATE int sqlite3BitvecTestNotNull(Bitvec *p, u32 i){\n  assert( p!=0 );\n  i--;\n  if( i>=p->iSize ) return 0;\n  while( p->iDivisor ){\n    u32 bin = i/p->iDivisor;\n    i = i%p->iDivisor;\n    p = p->u.apSub[bin];\n    if (!p) {\n      return 0;\n    }\n  }\n  if( p->iSize<=BITVEC_NBIT ){\n    return (p->u.aBitmap[i/BITVEC_SZELEM] & (1<<(i&(BITVEC_SZELEM-1))))!=0;\n  } else{\n    u32 h = BITVEC_HASH(i++);\n    while( p->u.aHash[h] ){\n      if( p->u.aHash[h]==i ) return 1;\n      h = (h+1) % BITVEC_NINT;\n    }\n    return 0;\n  }\n}\nSQLITE_PRIVATE int sqlite3BitvecTest(Bitvec *p, u32 i){\n  return p!=0 && sqlite3BitvecTestNotNull(p,i);\n}\n\n/*\n** Set the i-th bit.  Return 0 on success and an error code if\n** anything goes wrong.\n**\n** This routine might cause sub-bitmaps to be allocated.  Failing\n** to get the memory needed to hold the sub-bitmap is the only\n** that can go wrong with an insert, assuming p and i are valid.\n**\n** The calling function must ensure that p is a valid Bitvec object\n** and that the value for \"i\" is within range of the Bitvec object.\n** Otherwise the behavior is undefined.\n*/\nSQLITE_PRIVATE int sqlite3BitvecSet(Bitvec *p, u32 i){\n  u32 h;\n  if( p==0 ) return SQLITE_OK;\n  assert( i>0 );\n  assert( i<=p->iSize );\n  i--;\n  while((p->iSize > BITVEC_NBIT) && p->iDivisor) {\n    u32 bin = i/p->iDivisor;\n    i = i%p->iDivisor;\n    if( p->u.apSub[bin]==0 ){\n      p->u.apSub[bin] = sqlite3BitvecCreate( p->iDivisor );\n      if( p->u.apSub[bin]==0 ) return SQLITE_NOMEM_BKPT;\n    }\n    p = p->u.apSub[bin];\n  }\n  if( p->iSize<=BITVEC_NBIT ){\n    p->u.aBitmap[i/BITVEC_SZELEM] |= 1 << (i&(BITVEC_SZELEM-1));\n    return SQLITE_OK;\n  }\n  h = BITVEC_HASH(i++);\n  /* if there wasn't a hash collision, and this doesn't */\n  /* completely fill the hash, then just add it without */\n  /* worring about sub-dividing and re-hashing. */\n  if( !p->u.aHash[h] ){\n    if (p->nSet<(BITVEC_NINT-1)) {\n      goto bitvec_set_end;\n    } else {\n      goto bitvec_set_rehash;\n    }\n  }\n  /* there was a collision, check to see if it's already */\n  /* in hash, if not, try to find a spot for it */\n  do {\n    if( p->u.aHash[h]==i ) return SQLITE_OK;\n    h++;\n    if( h>=BITVEC_NINT ) h = 0;\n  } while( p->u.aHash[h] );\n  /* we didn't find it in the hash.  h points to the first */\n  /* available free spot. check to see if this is going to */\n  /* make our hash too \"full\".  */\nbitvec_set_rehash:\n  if( p->nSet>=BITVEC_MXHASH ){\n    unsigned int j;\n    int rc;\n    u32 *aiValues = sqlite3StackAllocRaw(0, sizeof(p->u.aHash));\n    if( aiValues==0 ){\n      return SQLITE_NOMEM_BKPT;\n    }else{\n      memcpy(aiValues, p->u.aHash, sizeof(p->u.aHash));\n      memset(p->u.apSub, 0, sizeof(p->u.apSub));\n      p->iDivisor = (p->iSize + BITVEC_NPTR - 1)/BITVEC_NPTR;\n      rc = sqlite3BitvecSet(p, i);\n      for(j=0; j<BITVEC_NINT; j++){\n        if( aiValues[j] ) rc |= sqlite3BitvecSet(p, aiValues[j]);\n      }\n      sqlite3StackFree(0, aiValues);\n      return rc;\n    }\n  }\nbitvec_set_end:\n  p->nSet++;\n  p->u.aHash[h] = i;\n  return SQLITE_OK;\n}\n\n/*\n** Clear the i-th bit.\n**\n** pBuf must be a pointer to at least BITVEC_SZ bytes of temporary storage\n** that BitvecClear can use to rebuilt its hash table.\n*/\nSQLITE_PRIVATE void sqlite3BitvecClear(Bitvec *p, u32 i, void *pBuf){\n  if( p==0 ) return;\n  assert( i>0 );\n  i--;\n  while( p->iDivisor ){\n    u32 bin = i/p->iDivisor;\n    i = i%p->iDivisor;\n    p = p->u.apSub[bin];\n    if (!p) {\n      return;\n    }\n  }\n  if( p->iSize<=BITVEC_NBIT ){\n    p->u.aBitmap[i/BITVEC_SZELEM] &= ~(1 << (i&(BITVEC_SZELEM-1)));\n  }else{\n    unsigned int j;\n    u32 *aiValues = pBuf;\n    memcpy(aiValues, p->u.aHash, sizeof(p->u.aHash));\n    memset(p->u.aHash, 0, sizeof(p->u.aHash));\n    p->nSet = 0;\n    for(j=0; j<BITVEC_NINT; j++){\n      if( aiValues[j] && aiValues[j]!=(i+1) ){\n        u32 h = BITVEC_HASH(aiValues[j]-1);\n        p->nSet++;\n        while( p->u.aHash[h] ){\n          h++;\n          if( h>=BITVEC_NINT ) h = 0;\n        }\n        p->u.aHash[h] = aiValues[j];\n      }\n    }\n  }\n}\n\n/*\n** Destroy a bitmap object.  Reclaim all memory used.\n*/\nSQLITE_PRIVATE void sqlite3BitvecDestroy(Bitvec *p){\n  if( p==0 ) return;\n  if( p->iDivisor ){\n    unsigned int i;\n    for(i=0; i<BITVEC_NPTR; i++){\n      sqlite3BitvecDestroy(p->u.apSub[i]);\n    }\n  }\n  sqlite3_free(p);\n}\n\n/*\n** Return the value of the iSize parameter specified when Bitvec *p\n** was created.\n*/\nSQLITE_PRIVATE u32 sqlite3BitvecSize(Bitvec *p){\n  return p->iSize;\n}\n\n#ifndef SQLITE_UNTESTABLE\n/*\n** Let V[] be an array of unsigned characters sufficient to hold\n** up to N bits.  Let I be an integer between 0 and N.  0<=I<N.\n** Then the following macros can be used to set, clear, or test\n** individual bits within V.\n*/\n#define SETBIT(V,I)      V[I>>3] |= (1<<(I&7))\n#define CLEARBIT(V,I)    V[I>>3] &= ~(1<<(I&7))\n#define TESTBIT(V,I)     (V[I>>3]&(1<<(I&7)))!=0\n\n/*\n** This routine runs an extensive test of the Bitvec code.\n**\n** The input is an array of integers that acts as a program\n** to test the Bitvec.  The integers are opcodes followed\n** by 0, 1, or 3 operands, depending on the opcode.  Another\n** opcode follows immediately after the last operand.\n**\n** There are 6 opcodes numbered from 0 through 5.  0 is the\n** \"halt\" opcode and causes the test to end.\n**\n**    0          Halt and return the number of errors\n**    1 N S X    Set N bits beginning with S and incrementing by X\n**    2 N S X    Clear N bits beginning with S and incrementing by X\n**    3 N        Set N randomly chosen bits\n**    4 N        Clear N randomly chosen bits\n**    5 N S X    Set N bits from S increment X in array only, not in bitvec\n**\n** The opcodes 1 through 4 perform set and clear operations are performed\n** on both a Bitvec object and on a linear array of bits obtained from malloc.\n** Opcode 5 works on the linear array only, not on the Bitvec.\n** Opcode 5 is used to deliberately induce a fault in order to\n** confirm that error detection works.\n**\n** At the conclusion of the test the linear array is compared\n** against the Bitvec object.  If there are any differences,\n** an error is returned.  If they are the same, zero is returned.\n**\n** If a memory allocation error occurs, return -1.\n*/\nSQLITE_PRIVATE int sqlite3BitvecBuiltinTest(int sz, int *aOp){\n  Bitvec *pBitvec = 0;\n  unsigned char *pV = 0;\n  int rc = -1;\n  int i, nx, pc, op;\n  void *pTmpSpace;\n\n  /* Allocate the Bitvec to be tested and a linear array of\n  ** bits to act as the reference */\n  pBitvec = sqlite3BitvecCreate( sz );\n  pV = sqlite3MallocZero( (sz+7)/8 + 1 );\n  pTmpSpace = sqlite3_malloc64(BITVEC_SZ);\n  if( pBitvec==0 || pV==0 || pTmpSpace==0  ) goto bitvec_end;\n\n  /* NULL pBitvec tests */\n  sqlite3BitvecSet(0, 1);\n  sqlite3BitvecClear(0, 1, pTmpSpace);\n\n  /* Run the program */\n  pc = 0;\n  while( (op = aOp[pc])!=0 ){\n    switch( op ){\n      case 1:\n      case 2:\n      case 5: {\n        nx = 4;\n        i = aOp[pc+2] - 1;\n        aOp[pc+2] += aOp[pc+3];\n        break;\n      }\n      case 3:\n      case 4: \n      default: {\n        nx = 2;\n        sqlite3_randomness(sizeof(i), &i);\n        break;\n      }\n    }\n    if( (--aOp[pc+1]) > 0 ) nx = 0;\n    pc += nx;\n    i = (i & 0x7fffffff)%sz;\n    if( (op & 1)!=0 ){\n      SETBIT(pV, (i+1));\n      if( op!=5 ){\n        if( sqlite3BitvecSet(pBitvec, i+1) ) goto bitvec_end;\n      }\n    }else{\n      CLEARBIT(pV, (i+1));\n      sqlite3BitvecClear(pBitvec, i+1, pTmpSpace);\n    }\n  }\n\n  /* Test to make sure the linear array exactly matches the\n  ** Bitvec object.  Start with the assumption that they do\n  ** match (rc==0).  Change rc to non-zero if a discrepancy\n  ** is found.\n  */\n  rc = sqlite3BitvecTest(0,0) + sqlite3BitvecTest(pBitvec, sz+1)\n          + sqlite3BitvecTest(pBitvec, 0)\n          + (sqlite3BitvecSize(pBitvec) - sz);\n  for(i=1; i<=sz; i++){\n    if(  (TESTBIT(pV,i))!=sqlite3BitvecTest(pBitvec,i) ){\n      rc = i;\n      break;\n    }\n  }\n\n  /* Free allocated structure */\nbitvec_end:\n  sqlite3_free(pTmpSpace);\n  sqlite3_free(pV);\n  sqlite3BitvecDestroy(pBitvec);\n  return rc;\n}\n#endif /* SQLITE_UNTESTABLE */\n\n/************** End of bitvec.c **********************************************/\n/************** Begin file pcache.c ******************************************/\n/*\n** 2008 August 05\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n*************************************************************************\n** This file implements that page cache.\n*/\n/* #include \"sqliteInt.h\" */\n\n/*\n** A complete page cache is an instance of this structure.  Every\n** entry in the cache holds a single page of the database file.  The\n** btree layer only operates on the cached copy of the database pages.\n**\n** A page cache entry is \"clean\" if it exactly matches what is currently\n** on disk.  A page is \"dirty\" if it has been modified and needs to be\n** persisted to disk.\n**\n** pDirty, pDirtyTail, pSynced:\n**   All dirty pages are linked into the doubly linked list using\n**   PgHdr.pDirtyNext and pDirtyPrev. The list is maintained in LRU order\n**   such that p was added to the list more recently than p->pDirtyNext.\n**   PCache.pDirty points to the first (newest) element in the list and\n**   pDirtyTail to the last (oldest).\n**\n**   The PCache.pSynced variable is used to optimize searching for a dirty\n**   page to eject from the cache mid-transaction. It is better to eject\n**   a page that does not require a journal sync than one that does. \n**   Therefore, pSynced is maintained to that it *almost* always points\n**   to either the oldest page in the pDirty/pDirtyTail list that has a\n**   clear PGHDR_NEED_SYNC flag or to a page that is older than this one\n**   (so that the right page to eject can be found by following pDirtyPrev\n**   pointers).\n*/\nstruct PCache {\n  PgHdr *pDirty, *pDirtyTail;         /* List of dirty pages in LRU order */\n  PgHdr *pSynced;                     /* Last synced page in dirty page list */\n  int nRefSum;                        /* Sum of ref counts over all pages */\n  int szCache;                        /* Configured cache size */\n  int szSpill;                        /* Size before spilling occurs */\n  int szPage;                         /* Size of every page in this cache */\n  int szExtra;                        /* Size of extra space for each page */\n  u8 bPurgeable;                      /* True if pages are on backing store */\n  u8 eCreate;                         /* eCreate value for for xFetch() */\n  int (*xStress)(void*,PgHdr*);       /* Call to try make a page clean */\n  void *pStress;                      /* Argument to xStress */\n  sqlite3_pcache *pCache;             /* Pluggable cache module */\n};\n\n/********************************** Test and Debug Logic **********************/\n/*\n** Debug tracing macros.  Enable by by changing the \"0\" to \"1\" and\n** recompiling.\n**\n** When sqlite3PcacheTrace is 1, single line trace messages are issued.\n** When sqlite3PcacheTrace is 2, a dump of the pcache showing all cache entries\n** is displayed for many operations, resulting in a lot of output.\n*/\n#if defined(SQLITE_DEBUG) && 0\n  int sqlite3PcacheTrace = 2;       /* 0: off  1: simple  2: cache dumps */\n  int sqlite3PcacheMxDump = 9999;   /* Max cache entries for pcacheDump() */\n# define pcacheTrace(X) if(sqlite3PcacheTrace){sqlite3DebugPrintf X;}\n  void pcacheDump(PCache *pCache){\n    int N;\n    int i, j;\n    sqlite3_pcache_page *pLower;\n    PgHdr *pPg;\n    unsigned char *a;\n  \n    if( sqlite3PcacheTrace<2 ) return;\n    if( pCache->pCache==0 ) return;\n    N = sqlite3PcachePagecount(pCache);\n    if( N>sqlite3PcacheMxDump ) N = sqlite3PcacheMxDump;\n    for(i=1; i<=N; i++){\n       pLower = sqlite3GlobalConfig.pcache2.xFetch(pCache->pCache, i, 0);\n       if( pLower==0 ) continue;\n       pPg = (PgHdr*)pLower->pExtra;\n       printf(\"%3d: nRef %2d flgs %02x data \", i, pPg->nRef, pPg->flags);\n       a = (unsigned char *)pLower->pBuf;\n       for(j=0; j<12; j++) printf(\"%02x\", a[j]);\n       printf(\"\\n\");\n       if( pPg->pPage==0 ){\n         sqlite3GlobalConfig.pcache2.xUnpin(pCache->pCache, pLower, 0);\n       }\n    }\n  }\n  #else\n# define pcacheTrace(X)\n# define pcacheDump(X)\n#endif\n\n/*\n** Check invariants on a PgHdr entry.  Return true if everything is OK.\n** Return false if any invariant is violated.\n**\n** This routine is for use inside of assert() statements only.  For\n** example:\n**\n**          assert( sqlite3PcachePageSanity(pPg) );\n*/\n#ifdef SQLITE_DEBUG\nSQLITE_PRIVATE int sqlite3PcachePageSanity(PgHdr *pPg){\n  PCache *pCache;\n  assert( pPg!=0 );\n  assert( pPg->pgno>0 || pPg->pPager==0 );    /* Page number is 1 or more */\n  pCache = pPg->pCache;\n  assert( pCache!=0 );      /* Every page has an associated PCache */\n  if( pPg->flags & PGHDR_CLEAN ){\n    assert( (pPg->flags & PGHDR_DIRTY)==0 );/* Cannot be both CLEAN and DIRTY */\n    assert( pCache->pDirty!=pPg );          /* CLEAN pages not on dirty list */\n    assert( pCache->pDirtyTail!=pPg );\n  }\n  /* WRITEABLE pages must also be DIRTY */\n  if( pPg->flags & PGHDR_WRITEABLE ){\n    assert( pPg->flags & PGHDR_DIRTY );     /* WRITEABLE implies DIRTY */\n  }\n  /* NEED_SYNC can be set independently of WRITEABLE.  This can happen,\n  ** for example, when using the sqlite3PagerDontWrite() optimization:\n  **    (1)  Page X is journalled, and gets WRITEABLE and NEED_SEEK.\n  **    (2)  Page X moved to freelist, WRITEABLE is cleared\n  **    (3)  Page X reused, WRITEABLE is set again\n  ** If NEED_SYNC had been cleared in step 2, then it would not be reset\n  ** in step 3, and page might be written into the database without first\n  ** syncing the rollback journal, which might cause corruption on a power\n  ** loss.\n  **\n  ** Another example is when the database page size is smaller than the\n  ** disk sector size.  When any page of a sector is journalled, all pages\n  ** in that sector are marked NEED_SYNC even if they are still CLEAN, just\n  ** in case they are later modified, since all pages in the same sector\n  ** must be journalled and synced before any of those pages can be safely\n  ** written.\n  */\n  return 1;\n}\n#endif /* SQLITE_DEBUG */\n\n\n/********************************** Linked List Management ********************/\n\n/* Allowed values for second argument to pcacheManageDirtyList() */\n#define PCACHE_DIRTYLIST_REMOVE   1    /* Remove pPage from dirty list */\n#define PCACHE_DIRTYLIST_ADD      2    /* Add pPage to the dirty list */\n#define PCACHE_DIRTYLIST_FRONT    3    /* Move pPage to the front of the list */\n\n/*\n** Manage pPage's participation on the dirty list.  Bits of the addRemove\n** argument determines what operation to do.  The 0x01 bit means first\n** remove pPage from the dirty list.  The 0x02 means add pPage back to\n** the dirty list.  Doing both moves pPage to the front of the dirty list.\n*/\nstatic void pcacheManageDirtyList(PgHdr *pPage, u8 addRemove){\n  PCache *p = pPage->pCache;\n\n  pcacheTrace((\"%p.DIRTYLIST.%s %d\\n\", p,\n                addRemove==1 ? \"REMOVE\" : addRemove==2 ? \"ADD\" : \"FRONT\",\n                pPage->pgno));\n  if( addRemove & PCACHE_DIRTYLIST_REMOVE ){\n    assert( pPage->pDirtyNext || pPage==p->pDirtyTail );\n    assert( pPage->pDirtyPrev || pPage==p->pDirty );\n  \n    /* Update the PCache1.pSynced variable if necessary. */\n    if( p->pSynced==pPage ){\n      p->pSynced = pPage->pDirtyPrev;\n    }\n  \n    if( pPage->pDirtyNext ){\n      pPage->pDirtyNext->pDirtyPrev = pPage->pDirtyPrev;\n    }else{\n      assert( pPage==p->pDirtyTail );\n      p->pDirtyTail = pPage->pDirtyPrev;\n    }\n    if( pPage->pDirtyPrev ){\n      pPage->pDirtyPrev->pDirtyNext = pPage->pDirtyNext;\n    }else{\n      /* If there are now no dirty pages in the cache, set eCreate to 2. \n      ** This is an optimization that allows sqlite3PcacheFetch() to skip\n      ** searching for a dirty page to eject from the cache when it might\n      ** otherwise have to.  */\n      assert( pPage==p->pDirty );\n      p->pDirty = pPage->pDirtyNext;\n      assert( p->bPurgeable || p->eCreate==2 );\n      if( p->pDirty==0 ){         /*OPTIMIZATION-IF-TRUE*/\n        assert( p->bPurgeable==0 || p->eCreate==1 );\n        p->eCreate = 2;\n      }\n    }\n  }\n  if( addRemove & PCACHE_DIRTYLIST_ADD ){\n    pPage->pDirtyPrev = 0;\n    pPage->pDirtyNext = p->pDirty;\n    if( pPage->pDirtyNext ){\n      assert( pPage->pDirtyNext->pDirtyPrev==0 );\n      pPage->pDirtyNext->pDirtyPrev = pPage;\n    }else{\n      p->pDirtyTail = pPage;\n      if( p->bPurgeable ){\n        assert( p->eCreate==2 );\n        p->eCreate = 1;\n      }\n    }\n    p->pDirty = pPage;\n\n    /* If pSynced is NULL and this page has a clear NEED_SYNC flag, set\n    ** pSynced to point to it. Checking the NEED_SYNC flag is an \n    ** optimization, as if pSynced points to a page with the NEED_SYNC\n    ** flag set sqlite3PcacheFetchStress() searches through all newer \n    ** entries of the dirty-list for a page with NEED_SYNC clear anyway.  */\n    if( !p->pSynced \n     && 0==(pPage->flags&PGHDR_NEED_SYNC)   /*OPTIMIZATION-IF-FALSE*/\n    ){\n      p->pSynced = pPage;\n    }\n  }\n  pcacheDump(p);\n}\n\n/*\n** Wrapper around the pluggable caches xUnpin method. If the cache is\n** being used for an in-memory database, this function is a no-op.\n*/\nstatic void pcacheUnpin(PgHdr *p){\n  if( p->pCache->bPurgeable ){\n    pcacheTrace((\"%p.UNPIN %d\\n\", p->pCache, p->pgno));\n    sqlite3GlobalConfig.pcache2.xUnpin(p->pCache->pCache, p->pPage, 0);\n    pcacheDump(p->pCache);\n  }\n}\n\n/*\n** Compute the number of pages of cache requested.   p->szCache is the\n** cache size requested by the \"PRAGMA cache_size\" statement.\n*/\nstatic int numberOfCachePages(PCache *p){\n  if( p->szCache>=0 ){\n    /* IMPLEMENTATION-OF: R-42059-47211 If the argument N is positive then the\n    ** suggested cache size is set to N. */\n    return p->szCache;\n  }else{\n    /* IMPLEMENTATION-OF: R-61436-13639 If the argument N is negative, then\n    ** the number of cache pages is adjusted to use approximately abs(N*1024)\n    ** bytes of memory. */\n    return (int)((-1024*(i64)p->szCache)/(p->szPage+p->szExtra));\n  }\n}\n\n/*************************************************** General Interfaces ******\n**\n** Initialize and shutdown the page cache subsystem. Neither of these \n** functions are threadsafe.\n*/\nSQLITE_PRIVATE int sqlite3PcacheInitialize(void){\n  if( sqlite3GlobalConfig.pcache2.xInit==0 ){\n    /* IMPLEMENTATION-OF: R-26801-64137 If the xInit() method is NULL, then the\n    ** built-in default page cache is used instead of the application defined\n    ** page cache. */\n    sqlite3PCacheSetDefault();\n  }\n  return sqlite3GlobalConfig.pcache2.xInit(sqlite3GlobalConfig.pcache2.pArg);\n}\nSQLITE_PRIVATE void sqlite3PcacheShutdown(void){\n  if( sqlite3GlobalConfig.pcache2.xShutdown ){\n    /* IMPLEMENTATION-OF: R-26000-56589 The xShutdown() method may be NULL. */\n    sqlite3GlobalConfig.pcache2.xShutdown(sqlite3GlobalConfig.pcache2.pArg);\n  }\n}\n\n/*\n** Return the size in bytes of a PCache object.\n*/\nSQLITE_PRIVATE int sqlite3PcacheSize(void){ return sizeof(PCache); }\n\n/*\n** Create a new PCache object. Storage space to hold the object\n** has already been allocated and is passed in as the p pointer. \n** The caller discovers how much space needs to be allocated by \n** calling sqlite3PcacheSize().\n**\n** szExtra is some extra space allocated for each page.  The first\n** 8 bytes of the extra space will be zeroed as the page is allocated,\n** but remaining content will be uninitialized.  Though it is opaque\n** to this module, the extra space really ends up being the MemPage\n** structure in the pager.\n*/\nSQLITE_PRIVATE int sqlite3PcacheOpen(\n  int szPage,                  /* Size of every page */\n  int szExtra,                 /* Extra space associated with each page */\n  int bPurgeable,              /* True if pages are on backing store */\n  int (*xStress)(void*,PgHdr*),/* Call to try to make pages clean */\n  void *pStress,               /* Argument to xStress */\n  PCache *p                    /* Preallocated space for the PCache */\n){\n  memset(p, 0, sizeof(PCache));\n  p->szPage = 1;\n  p->szExtra = szExtra;\n  assert( szExtra>=8 );  /* First 8 bytes will be zeroed */\n  p->bPurgeable = bPurgeable;\n  p->eCreate = 2;\n  p->xStress = xStress;\n  p->pStress = pStress;\n  p->szCache = 100;\n  p->szSpill = 1;\n  pcacheTrace((\"%p.OPEN szPage %d bPurgeable %d\\n\",p,szPage,bPurgeable));\n  return sqlite3PcacheSetPageSize(p, szPage);\n}\n\n/*\n** Change the page size for PCache object. The caller must ensure that there\n** are no outstanding page references when this function is called.\n*/\nSQLITE_PRIVATE int sqlite3PcacheSetPageSize(PCache *pCache, int szPage){\n  assert( pCache->nRefSum==0 && pCache->pDirty==0 );\n  if( pCache->szPage ){\n    sqlite3_pcache *pNew;\n    pNew = sqlite3GlobalConfig.pcache2.xCreate(\n                szPage, pCache->szExtra + ROUND8(sizeof(PgHdr)),\n                pCache->bPurgeable\n    );\n    if( pNew==0 ) return SQLITE_NOMEM_BKPT;\n    sqlite3GlobalConfig.pcache2.xCachesize(pNew, numberOfCachePages(pCache));\n    if( pCache->pCache ){\n      sqlite3GlobalConfig.pcache2.xDestroy(pCache->pCache);\n    }\n    pCache->pCache = pNew;\n    pCache->szPage = szPage;\n    pcacheTrace((\"%p.PAGESIZE %d\\n\",pCache,szPage));\n  }\n  return SQLITE_OK;\n}\n\n/*\n** Try to obtain a page from the cache.\n**\n** This routine returns a pointer to an sqlite3_pcache_page object if\n** such an object is already in cache, or if a new one is created.\n** This routine returns a NULL pointer if the object was not in cache\n** and could not be created.\n**\n** The createFlags should be 0 to check for existing pages and should\n** be 3 (not 1, but 3) to try to create a new page.\n**\n** If the createFlag is 0, then NULL is always returned if the page\n** is not already in the cache.  If createFlag is 1, then a new page\n** is created only if that can be done without spilling dirty pages\n** and without exceeding the cache size limit.\n**\n** The caller needs to invoke sqlite3PcacheFetchFinish() to properly\n** initialize the sqlite3_pcache_page object and convert it into a\n** PgHdr object.  The sqlite3PcacheFetch() and sqlite3PcacheFetchFinish()\n** routines are split this way for performance reasons. When separated\n** they can both (usually) operate without having to push values to\n** the stack on entry and pop them back off on exit, which saves a\n** lot of pushing and popping.\n*/\nSQLITE_PRIVATE sqlite3_pcache_page *sqlite3PcacheFetch(\n  PCache *pCache,       /* Obtain the page from this cache */\n  Pgno pgno,            /* Page number to obtain */\n  int createFlag        /* If true, create page if it does not exist already */\n){\n  int eCreate;\n  sqlite3_pcache_page *pRes;\n\n  assert( pCache!=0 );\n  assert( pCache->pCache!=0 );\n  assert( createFlag==3 || createFlag==0 );\n  assert( pCache->eCreate==((pCache->bPurgeable && pCache->pDirty) ? 1 : 2) );\n\n  /* eCreate defines what to do if the page does not exist.\n  **    0     Do not allocate a new page.  (createFlag==0)\n  **    1     Allocate a new page if doing so is inexpensive.\n  **          (createFlag==1 AND bPurgeable AND pDirty)\n  **    2     Allocate a new page even it doing so is difficult.\n  **          (createFlag==1 AND !(bPurgeable AND pDirty)\n  */\n  eCreate = createFlag & pCache->eCreate;\n  assert( eCreate==0 || eCreate==1 || eCreate==2 );\n  assert( createFlag==0 || pCache->eCreate==eCreate );\n  assert( createFlag==0 || eCreate==1+(!pCache->bPurgeable||!pCache->pDirty) );\n  pRes = sqlite3GlobalConfig.pcache2.xFetch(pCache->pCache, pgno, eCreate);\n  pcacheTrace((\"%p.FETCH %d%s (result: %p)\\n\",pCache,pgno,\n               createFlag?\" create\":\"\",pRes));\n  return pRes;\n}\n\n/*\n** If the sqlite3PcacheFetch() routine is unable to allocate a new\n** page because no clean pages are available for reuse and the cache\n** size limit has been reached, then this routine can be invoked to \n** try harder to allocate a page.  This routine might invoke the stress\n** callback to spill dirty pages to the journal.  It will then try to\n** allocate the new page and will only fail to allocate a new page on\n** an OOM error.\n**\n** This routine should be invoked only after sqlite3PcacheFetch() fails.\n*/\nSQLITE_PRIVATE int sqlite3PcacheFetchStress(\n  PCache *pCache,                 /* Obtain the page from this cache */\n  Pgno pgno,                      /* Page number to obtain */\n  sqlite3_pcache_page **ppPage    /* Write result here */\n){\n  PgHdr *pPg;\n  if( pCache->eCreate==2 ) return 0;\n\n  if( sqlite3PcachePagecount(pCache)>pCache->szSpill ){\n    /* Find a dirty page to write-out and recycle. First try to find a \n    ** page that does not require a journal-sync (one with PGHDR_NEED_SYNC\n    ** cleared), but if that is not possible settle for any other \n    ** unreferenced dirty page.\n    **\n    ** If the LRU page in the dirty list that has a clear PGHDR_NEED_SYNC\n    ** flag is currently referenced, then the following may leave pSynced\n    ** set incorrectly (pointing to other than the LRU page with NEED_SYNC\n    ** cleared). This is Ok, as pSynced is just an optimization.  */\n    for(pPg=pCache->pSynced; \n        pPg && (pPg->nRef || (pPg->flags&PGHDR_NEED_SYNC)); \n        pPg=pPg->pDirtyPrev\n    );\n    pCache->pSynced = pPg;\n    if( !pPg ){\n      for(pPg=pCache->pDirtyTail; pPg && pPg->nRef; pPg=pPg->pDirtyPrev);\n    }\n    if( pPg ){\n      int rc;\n#ifdef SQLITE_LOG_CACHE_SPILL\n      sqlite3_log(SQLITE_FULL, \n                  \"spill page %d making room for %d - cache used: %d/%d\",\n                  pPg->pgno, pgno,\n                  sqlite3GlobalConfig.pcache.xPagecount(pCache->pCache),\n                numberOfCachePages(pCache));\n#endif\n      pcacheTrace((\"%p.SPILL %d\\n\",pCache,pPg->pgno));\n      rc = pCache->xStress(pCache->pStress, pPg);\n      pcacheDump(pCache);\n      if( rc!=SQLITE_OK && rc!=SQLITE_BUSY ){\n        return rc;\n      }\n    }\n  }\n  *ppPage = sqlite3GlobalConfig.pcache2.xFetch(pCache->pCache, pgno, 2);\n  return *ppPage==0 ? SQLITE_NOMEM_BKPT : SQLITE_OK;\n}\n\n/*\n** This is a helper routine for sqlite3PcacheFetchFinish()\n**\n** In the uncommon case where the page being fetched has not been\n** initialized, this routine is invoked to do the initialization.\n** This routine is broken out into a separate function since it\n** requires extra stack manipulation that can be avoided in the common\n** case.\n*/\nstatic SQLITE_NOINLINE PgHdr *pcacheFetchFinishWithInit(\n  PCache *pCache,             /* Obtain the page from this cache */\n  Pgno pgno,                  /* Page number obtained */\n  sqlite3_pcache_page *pPage  /* Page obtained by prior PcacheFetch() call */\n){\n  PgHdr *pPgHdr;\n  assert( pPage!=0 );\n  pPgHdr = (PgHdr*)pPage->pExtra;\n  assert( pPgHdr->pPage==0 );\n  memset(&pPgHdr->pDirty, 0, sizeof(PgHdr) - offsetof(PgHdr,pDirty));\n  pPgHdr->pPage = pPage;\n  pPgHdr->pData = pPage->pBuf;\n  pPgHdr->pExtra = (void *)&pPgHdr[1];\n  memset(pPgHdr->pExtra, 0, 8);\n  pPgHdr->pCache = pCache;\n  pPgHdr->pgno = pgno;\n  pPgHdr->flags = PGHDR_CLEAN;\n  return sqlite3PcacheFetchFinish(pCache,pgno,pPage);\n}\n\n/*\n** This routine converts the sqlite3_pcache_page object returned by\n** sqlite3PcacheFetch() into an initialized PgHdr object.  This routine\n** must be called after sqlite3PcacheFetch() in order to get a usable\n** result.\n*/\nSQLITE_PRIVATE PgHdr *sqlite3PcacheFetchFinish(\n  PCache *pCache,             /* Obtain the page from this cache */\n  Pgno pgno,                  /* Page number obtained */\n  sqlite3_pcache_page *pPage  /* Page obtained by prior PcacheFetch() call */\n){\n  PgHdr *pPgHdr;\n\n  assert( pPage!=0 );\n  pPgHdr = (PgHdr *)pPage->pExtra;\n\n  if( !pPgHdr->pPage ){\n    return pcacheFetchFinishWithInit(pCache, pgno, pPage);\n  }\n  pCache->nRefSum++;\n  pPgHdr->nRef++;\n  assert( sqlite3PcachePageSanity(pPgHdr) );\n  return pPgHdr;\n}\n\n/*\n** Decrement the reference count on a page. If the page is clean and the\n** reference count drops to 0, then it is made eligible for recycling.\n*/\nSQLITE_PRIVATE void SQLITE_NOINLINE sqlite3PcacheRelease(PgHdr *p){\n  assert( p->nRef>0 );\n  p->pCache->nRefSum--;\n  if( (--p->nRef)==0 ){\n    if( p->flags&PGHDR_CLEAN ){\n      pcacheUnpin(p);\n    }else{\n      pcacheManageDirtyList(p, PCACHE_DIRTYLIST_FRONT);\n    }\n  }\n}\n\n/*\n** Increase the reference count of a supplied page by 1.\n*/\nSQLITE_PRIVATE void sqlite3PcacheRef(PgHdr *p){\n  assert(p->nRef>0);\n  assert( sqlite3PcachePageSanity(p) );\n  p->nRef++;\n  p->pCache->nRefSum++;\n}\n\n/*\n** Drop a page from the cache. There must be exactly one reference to the\n** page. This function deletes that reference, so after it returns the\n** page pointed to by p is invalid.\n*/\nSQLITE_PRIVATE void sqlite3PcacheDrop(PgHdr *p){\n  assert( p->nRef==1 );\n  assert( sqlite3PcachePageSanity(p) );\n  if( p->flags&PGHDR_DIRTY ){\n    pcacheManageDirtyList(p, PCACHE_DIRTYLIST_REMOVE);\n  }\n  p->pCache->nRefSum--;\n  sqlite3GlobalConfig.pcache2.xUnpin(p->pCache->pCache, p->pPage, 1);\n}\n\n/*\n** Make sure the page is marked as dirty. If it isn't dirty already,\n** make it so.\n*/\nSQLITE_PRIVATE void sqlite3PcacheMakeDirty(PgHdr *p){\n  assert( p->nRef>0 );\n  assert( sqlite3PcachePageSanity(p) );\n  if( p->flags & (PGHDR_CLEAN|PGHDR_DONT_WRITE) ){    /*OPTIMIZATION-IF-FALSE*/\n    p->flags &= ~PGHDR_DONT_WRITE;\n    if( p->flags & PGHDR_CLEAN ){\n      p->flags ^= (PGHDR_DIRTY|PGHDR_CLEAN);\n      pcacheTrace((\"%p.DIRTY %d\\n\",p->pCache,p->pgno));\n      assert( (p->flags & (PGHDR_DIRTY|PGHDR_CLEAN))==PGHDR_DIRTY );\n      pcacheManageDirtyList(p, PCACHE_DIRTYLIST_ADD);\n    }\n    assert( sqlite3PcachePageSanity(p) );\n  }\n}\n\n/*\n** Make sure the page is marked as clean. If it isn't clean already,\n** make it so.\n*/\nSQLITE_PRIVATE void sqlite3PcacheMakeClean(PgHdr *p){\n  assert( sqlite3PcachePageSanity(p) );\n  assert( (p->flags & PGHDR_DIRTY)!=0 );\n  assert( (p->flags & PGHDR_CLEAN)==0 );\n  pcacheManageDirtyList(p, PCACHE_DIRTYLIST_REMOVE);\n  p->flags &= ~(PGHDR_DIRTY|PGHDR_NEED_SYNC|PGHDR_WRITEABLE);\n  p->flags |= PGHDR_CLEAN;\n  pcacheTrace((\"%p.CLEAN %d\\n\",p->pCache,p->pgno));\n  assert( sqlite3PcachePageSanity(p) );\n  if( p->nRef==0 ){\n    pcacheUnpin(p);\n  }\n}\n\n/*\n** Make every page in the cache clean.\n*/\nSQLITE_PRIVATE void sqlite3PcacheCleanAll(PCache *pCache){\n  PgHdr *p;\n  pcacheTrace((\"%p.CLEAN-ALL\\n\",pCache));\n  while( (p = pCache->pDirty)!=0 ){\n    sqlite3PcacheMakeClean(p);\n  }\n}\n\n/*\n** Clear the PGHDR_NEED_SYNC and PGHDR_WRITEABLE flag from all dirty pages.\n*/\nSQLITE_PRIVATE void sqlite3PcacheClearWritable(PCache *pCache){\n  PgHdr *p;\n  pcacheTrace((\"%p.CLEAR-WRITEABLE\\n\",pCache));\n  for(p=pCache->pDirty; p; p=p->pDirtyNext){\n    p->flags &= ~(PGHDR_NEED_SYNC|PGHDR_WRITEABLE);\n  }\n  pCache->pSynced = pCache->pDirtyTail;\n}\n\n/*\n** Clear the PGHDR_NEED_SYNC flag from all dirty pages.\n*/\nSQLITE_PRIVATE void sqlite3PcacheClearSyncFlags(PCache *pCache){\n  PgHdr *p;\n  for(p=pCache->pDirty; p; p=p->pDirtyNext){\n    p->flags &= ~PGHDR_NEED_SYNC;\n  }\n  pCache->pSynced = pCache->pDirtyTail;\n}\n\n/*\n** Change the page number of page p to newPgno. \n*/\nSQLITE_PRIVATE void sqlite3PcacheMove(PgHdr *p, Pgno newPgno){\n  PCache *pCache = p->pCache;\n  assert( p->nRef>0 );\n  assert( newPgno>0 );\n  assert( sqlite3PcachePageSanity(p) );\n  pcacheTrace((\"%p.MOVE %d -> %d\\n\",pCache,p->pgno,newPgno));\n  sqlite3GlobalConfig.pcache2.xRekey(pCache->pCache, p->pPage, p->pgno,newPgno);\n  p->pgno = newPgno;\n  if( (p->flags&PGHDR_DIRTY) && (p->flags&PGHDR_NEED_SYNC) ){\n    pcacheManageDirtyList(p, PCACHE_DIRTYLIST_FRONT);\n  }\n}\n\n/*\n** Drop every cache entry whose page number is greater than \"pgno\". The\n** caller must ensure that there are no outstanding references to any pages\n** other than page 1 with a page number greater than pgno.\n**\n** If there is a reference to page 1 and the pgno parameter passed to this\n** function is 0, then the data area associated with page 1 is zeroed, but\n** the page object is not dropped.\n*/\nSQLITE_PRIVATE void sqlite3PcacheTruncate(PCache *pCache, Pgno pgno){\n  if( pCache->pCache ){\n    PgHdr *p;\n    PgHdr *pNext;\n    pcacheTrace((\"%p.TRUNCATE %d\\n\",pCache,pgno));\n    for(p=pCache->pDirty; p; p=pNext){\n      pNext = p->pDirtyNext;\n      /* This routine never gets call with a positive pgno except right\n      ** after sqlite3PcacheCleanAll().  So if there are dirty pages,\n      ** it must be that pgno==0.\n      */\n      assert( p->pgno>0 );\n      if( p->pgno>pgno ){\n        assert( p->flags&PGHDR_DIRTY );\n        sqlite3PcacheMakeClean(p);\n      }\n    }\n    if( pgno==0 && pCache->nRefSum ){\n      sqlite3_pcache_page *pPage1;\n      pPage1 = sqlite3GlobalConfig.pcache2.xFetch(pCache->pCache,1,0);\n      if( ALWAYS(pPage1) ){  /* Page 1 is always available in cache, because\n                             ** pCache->nRefSum>0 */\n        memset(pPage1->pBuf, 0, pCache->szPage);\n        pgno = 1;\n      }\n    }\n    sqlite3GlobalConfig.pcache2.xTruncate(pCache->pCache, pgno+1);\n  }\n}\n\n/*\n** Close a cache.\n*/\nSQLITE_PRIVATE void sqlite3PcacheClose(PCache *pCache){\n  assert( pCache->pCache!=0 );\n  pcacheTrace((\"%p.CLOSE\\n\",pCache));\n  sqlite3GlobalConfig.pcache2.xDestroy(pCache->pCache);\n}\n\n/* \n** Discard the contents of the cache.\n*/\nSQLITE_PRIVATE void sqlite3PcacheClear(PCache *pCache){\n  sqlite3PcacheTruncate(pCache, 0);\n}\n\n/*\n** Merge two lists of pages connected by pDirty and in pgno order.\n** Do not bother fixing the pDirtyPrev pointers.\n*/\nstatic PgHdr *pcacheMergeDirtyList(PgHdr *pA, PgHdr *pB){\n  PgHdr result, *pTail;\n  pTail = &result;\n  assert( pA!=0 && pB!=0 );\n  for(;;){\n    if( pA->pgno<pB->pgno ){\n      pTail->pDirty = pA;\n      pTail = pA;\n      pA = pA->pDirty;\n      if( pA==0 ){\n        pTail->pDirty = pB;\n        break;\n      }\n    }else{\n      pTail->pDirty = pB;\n      pTail = pB;\n      pB = pB->pDirty;\n      if( pB==0 ){\n        pTail->pDirty = pA;\n        break;\n      }\n    }\n  }\n  return result.pDirty;\n}\n\n/*\n** Sort the list of pages in accending order by pgno.  Pages are\n** connected by pDirty pointers.  The pDirtyPrev pointers are\n** corrupted by this sort.\n**\n** Since there cannot be more than 2^31 distinct pages in a database,\n** there cannot be more than 31 buckets required by the merge sorter.\n** One extra bucket is added to catch overflow in case something\n** ever changes to make the previous sentence incorrect.\n*/\n#define N_SORT_BUCKET  32\nstatic PgHdr *pcacheSortDirtyList(PgHdr *pIn){\n  PgHdr *a[N_SORT_BUCKET], *p;\n  int i;\n  memset(a, 0, sizeof(a));\n  while( pIn ){\n    p = pIn;\n    pIn = p->pDirty;\n    p->pDirty = 0;\n    for(i=0; ALWAYS(i<N_SORT_BUCKET-1); i++){\n      if( a[i]==0 ){\n        a[i] = p;\n        break;\n      }else{\n        p = pcacheMergeDirtyList(a[i], p);\n        a[i] = 0;\n      }\n    }\n    if( NEVER(i==N_SORT_BUCKET-1) ){\n      /* To get here, there need to be 2^(N_SORT_BUCKET) elements in\n      ** the input list.  But that is impossible.\n      */\n      a[i] = pcacheMergeDirtyList(a[i], p);\n    }\n  }\n  p = a[0];\n  for(i=1; i<N_SORT_BUCKET; i++){\n    if( a[i]==0 ) continue;\n    p = p ? pcacheMergeDirtyList(p, a[i]) : a[i];\n  }\n  return p;\n}\n\n/*\n** Return a list of all dirty pages in the cache, sorted by page number.\n*/\nSQLITE_PRIVATE PgHdr *sqlite3PcacheDirtyList(PCache *pCache){\n  PgHdr *p;\n  for(p=pCache->pDirty; p; p=p->pDirtyNext){\n    p->pDirty = p->pDirtyNext;\n  }\n  return pcacheSortDirtyList(pCache->pDirty);\n}\n\n/* \n** Return the total number of references to all pages held by the cache.\n**\n** This is not the total number of pages referenced, but the sum of the\n** reference count for all pages.\n*/\nSQLITE_PRIVATE int sqlite3PcacheRefCount(PCache *pCache){\n  return pCache->nRefSum;\n}\n\n/*\n** Return the number of references to the page supplied as an argument.\n*/\nSQLITE_PRIVATE int sqlite3PcachePageRefcount(PgHdr *p){\n  return p->nRef;\n}\n\n/* \n** Return the total number of pages in the cache.\n*/\nSQLITE_PRIVATE int sqlite3PcachePagecount(PCache *pCache){\n  assert( pCache->pCache!=0 );\n  return sqlite3GlobalConfig.pcache2.xPagecount(pCache->pCache);\n}\n\n#ifdef SQLITE_TEST\n/*\n** Get the suggested cache-size value.\n*/\nSQLITE_PRIVATE int sqlite3PcacheGetCachesize(PCache *pCache){\n  return numberOfCachePages(pCache);\n}\n#endif\n\n/*\n** Set the suggested cache-size value.\n*/\nSQLITE_PRIVATE void sqlite3PcacheSetCachesize(PCache *pCache, int mxPage){\n  assert( pCache->pCache!=0 );\n  pCache->szCache = mxPage;\n  sqlite3GlobalConfig.pcache2.xCachesize(pCache->pCache,\n                                         numberOfCachePages(pCache));\n}\n\n/*\n** Set the suggested cache-spill value.  Make no changes if if the\n** argument is zero.  Return the effective cache-spill size, which will\n** be the larger of the szSpill and szCache.\n*/\nSQLITE_PRIVATE int sqlite3PcacheSetSpillsize(PCache *p, int mxPage){\n  int res;\n  assert( p->pCache!=0 );\n  if( mxPage ){\n    if( mxPage<0 ){\n      mxPage = (int)((-1024*(i64)mxPage)/(p->szPage+p->szExtra));\n    }\n    p->szSpill = mxPage;\n  }\n  res = numberOfCachePages(p);\n  if( res<p->szSpill ) res = p->szSpill; \n  return res;\n}\n\n/*\n** Free up as much memory as possible from the page cache.\n*/\nSQLITE_PRIVATE void sqlite3PcacheShrink(PCache *pCache){\n  assert( pCache->pCache!=0 );\n  sqlite3GlobalConfig.pcache2.xShrink(pCache->pCache);\n}\n\n/*\n** Return the size of the header added by this middleware layer\n** in the page-cache hierarchy.\n*/\nSQLITE_PRIVATE int sqlite3HeaderSizePcache(void){ return ROUND8(sizeof(PgHdr)); }\n\n/*\n** Return the number of dirty pages currently in the cache, as a percentage\n** of the configured cache size.\n*/\nSQLITE_PRIVATE int sqlite3PCachePercentDirty(PCache *pCache){\n  PgHdr *pDirty;\n  int nDirty = 0;\n  int nCache = numberOfCachePages(pCache);\n  for(pDirty=pCache->pDirty; pDirty; pDirty=pDirty->pDirtyNext) nDirty++;\n  return nCache ? (int)(((i64)nDirty * 100) / nCache) : 0;\n}\n\n#if defined(SQLITE_CHECK_PAGES) || defined(SQLITE_DEBUG)\n/*\n** For all dirty pages currently in the cache, invoke the specified\n** callback. This is only used if the SQLITE_CHECK_PAGES macro is\n** defined.\n*/\nSQLITE_PRIVATE void sqlite3PcacheIterateDirty(PCache *pCache, void (*xIter)(PgHdr *)){\n  PgHdr *pDirty;\n  for(pDirty=pCache->pDirty; pDirty; pDirty=pDirty->pDirtyNext){\n    xIter(pDirty);\n  }\n}\n#endif\n\n/************** End of pcache.c **********************************************/\n/************** Begin file pcache1.c *****************************************/\n/*\n** 2008 November 05\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n*************************************************************************\n**\n** This file implements the default page cache implementation (the\n** sqlite3_pcache interface). It also contains part of the implementation\n** of the SQLITE_CONFIG_PAGECACHE and sqlite3_release_memory() features.\n** If the default page cache implementation is overridden, then neither of\n** these two features are available.\n**\n** A Page cache line looks like this:\n**\n**  -------------------------------------------------------------\n**  |  database page content   |  PgHdr1  |  MemPage  |  PgHdr  |\n**  -------------------------------------------------------------\n**\n** The database page content is up front (so that buffer overreads tend to\n** flow harmlessly into the PgHdr1, MemPage, and PgHdr extensions).   MemPage\n** is the extension added by the btree.c module containing information such\n** as the database page number and how that database page is used.  PgHdr\n** is added by the pcache.c layer and contains information used to keep track\n** of which pages are \"dirty\".  PgHdr1 is an extension added by this\n** module (pcache1.c).  The PgHdr1 header is a subclass of sqlite3_pcache_page.\n** PgHdr1 contains information needed to look up a page by its page number.\n** The superclass sqlite3_pcache_page.pBuf points to the start of the\n** database page content and sqlite3_pcache_page.pExtra points to PgHdr.\n**\n** The size of the extension (MemPage+PgHdr+PgHdr1) can be determined at\n** runtime using sqlite3_config(SQLITE_CONFIG_PCACHE_HDRSZ, &size).  The\n** sizes of the extensions sum to 272 bytes on x64 for 3.8.10, but this\n** size can vary according to architecture, compile-time options, and\n** SQLite library version number.\n**\n** If SQLITE_PCACHE_SEPARATE_HEADER is defined, then the extension is obtained\n** using a separate memory allocation from the database page content.  This\n** seeks to overcome the \"clownshoe\" problem (also called \"internal\n** fragmentation\" in academic literature) of allocating a few bytes more\n** than a power of two with the memory allocator rounding up to the next\n** power of two, and leaving the rounded-up space unused.\n**\n** This module tracks pointers to PgHdr1 objects.  Only pcache.c communicates\n** with this module.  Information is passed back and forth as PgHdr1 pointers.\n**\n** The pcache.c and pager.c modules deal pointers to PgHdr objects.\n** The btree.c module deals with pointers to MemPage objects.\n**\n** SOURCE OF PAGE CACHE MEMORY:\n**\n** Memory for a page might come from any of three sources:\n**\n**    (1)  The general-purpose memory allocator - sqlite3Malloc()\n**    (2)  Global page-cache memory provided using sqlite3_config() with\n**         SQLITE_CONFIG_PAGECACHE.\n**    (3)  PCache-local bulk allocation.\n**\n** The third case is a chunk of heap memory (defaulting to 100 pages worth)\n** that is allocated when the page cache is created.  The size of the local\n** bulk allocation can be adjusted using \n**\n**     sqlite3_config(SQLITE_CONFIG_PAGECACHE, (void*)0, 0, N).\n**\n** If N is positive, then N pages worth of memory are allocated using a single\n** sqlite3Malloc() call and that memory is used for the first N pages allocated.\n** Or if N is negative, then -1024*N bytes of memory are allocated and used\n** for as many pages as can be accomodated.\n**\n** Only one of (2) or (3) can be used.  Once the memory available to (2) or\n** (3) is exhausted, subsequent allocations fail over to the general-purpose\n** memory allocator (1).\n**\n** Earlier versions of SQLite used only methods (1) and (2).  But experiments\n** show that method (3) with N==100 provides about a 5% performance boost for\n** common workloads.\n*/\n/* #include \"sqliteInt.h\" */\n\ntypedef struct PCache1 PCache1;\ntypedef struct PgHdr1 PgHdr1;\ntypedef struct PgFreeslot PgFreeslot;\ntypedef struct PGroup PGroup;\n\n/*\n** Each cache entry is represented by an instance of the following \n** structure. Unless SQLITE_PCACHE_SEPARATE_HEADER is defined, a buffer of\n** PgHdr1.pCache->szPage bytes is allocated directly before this structure \n** in memory.\n*/\nstruct PgHdr1 {\n  sqlite3_pcache_page page;      /* Base class. Must be first. pBuf & pExtra */\n  unsigned int iKey;             /* Key value (page number) */\n  u8 isBulkLocal;                /* This page from bulk local storage */\n  u8 isAnchor;                   /* This is the PGroup.lru element */\n  PgHdr1 *pNext;                 /* Next in hash table chain */\n  PCache1 *pCache;               /* Cache that currently owns this page */\n  PgHdr1 *pLruNext;              /* Next in LRU list of unpinned pages */\n  PgHdr1 *pLruPrev;              /* Previous in LRU list of unpinned pages */\n};\n\n/*\n** A page is pinned if it is no on the LRU list\n*/\n#define PAGE_IS_PINNED(p)    ((p)->pLruNext==0)\n#define PAGE_IS_UNPINNED(p)  ((p)->pLruNext!=0)\n\n/* Each page cache (or PCache) belongs to a PGroup.  A PGroup is a set \n** of one or more PCaches that are able to recycle each other's unpinned\n** pages when they are under memory pressure.  A PGroup is an instance of\n** the following object.\n**\n** This page cache implementation works in one of two modes:\n**\n**   (1)  Every PCache is the sole member of its own PGroup.  There is\n**        one PGroup per PCache.\n**\n**   (2)  There is a single global PGroup that all PCaches are a member\n**        of.\n**\n** Mode 1 uses more memory (since PCache instances are not able to rob\n** unused pages from other PCaches) but it also operates without a mutex,\n** and is therefore often faster.  Mode 2 requires a mutex in order to be\n** threadsafe, but recycles pages more efficiently.\n**\n** For mode (1), PGroup.mutex is NULL.  For mode (2) there is only a single\n** PGroup which is the pcache1.grp global variable and its mutex is\n** SQLITE_MUTEX_STATIC_LRU.\n*/\nstruct PGroup {\n  sqlite3_mutex *mutex;          /* MUTEX_STATIC_LRU or NULL */\n  unsigned int nMaxPage;         /* Sum of nMax for purgeable caches */\n  unsigned int nMinPage;         /* Sum of nMin for purgeable caches */\n  unsigned int mxPinned;         /* nMaxpage + 10 - nMinPage */\n  unsigned int nPurgeable;       /* Number of purgeable pages allocated */\n  PgHdr1 lru;                    /* The beginning and end of the LRU list */\n};\n\n/* Each page cache is an instance of the following object.  Every\n** open database file (including each in-memory database and each\n** temporary or transient database) has a single page cache which\n** is an instance of this object.\n**\n** Pointers to structures of this type are cast and returned as \n** opaque sqlite3_pcache* handles.\n*/\nstruct PCache1 {\n  /* Cache configuration parameters. Page size (szPage) and the purgeable\n  ** flag (bPurgeable) and the pnPurgeable pointer are all set when the\n  ** cache is created and are never changed thereafter. nMax may be \n  ** modified at any time by a call to the pcache1Cachesize() method.\n  ** The PGroup mutex must be held when accessing nMax.\n  */\n  PGroup *pGroup;                     /* PGroup this cache belongs to */\n  unsigned int *pnPurgeable;          /* Pointer to pGroup->nPurgeable */\n  int szPage;                         /* Size of database content section */\n  int szExtra;                        /* sizeof(MemPage)+sizeof(PgHdr) */\n  int szAlloc;                        /* Total size of one pcache line */\n  int bPurgeable;                     /* True if cache is purgeable */\n  unsigned int nMin;                  /* Minimum number of pages reserved */\n  unsigned int nMax;                  /* Configured \"cache_size\" value */\n  unsigned int n90pct;                /* nMax*9/10 */\n  unsigned int iMaxKey;               /* Largest key seen since xTruncate() */\n\n  /* Hash table of all pages. The following variables may only be accessed\n  ** when the accessor is holding the PGroup mutex.\n  */\n  unsigned int nRecyclable;           /* Number of pages in the LRU list */\n  unsigned int nPage;                 /* Total number of pages in apHash */\n  unsigned int nHash;                 /* Number of slots in apHash[] */\n  PgHdr1 **apHash;                    /* Hash table for fast lookup by key */\n  PgHdr1 *pFree;                      /* List of unused pcache-local pages */\n  void *pBulk;                        /* Bulk memory used by pcache-local */\n};\n\n/*\n** Free slots in the allocator used to divide up the global page cache\n** buffer provided using the SQLITE_CONFIG_PAGECACHE mechanism.\n*/\nstruct PgFreeslot {\n  PgFreeslot *pNext;  /* Next free slot */\n};\n\n/*\n** Global data used by this cache.\n*/\nstatic SQLITE_WSD struct PCacheGlobal {\n  PGroup grp;                    /* The global PGroup for mode (2) */\n\n  /* Variables related to SQLITE_CONFIG_PAGECACHE settings.  The\n  ** szSlot, nSlot, pStart, pEnd, nReserve, and isInit values are all\n  ** fixed at sqlite3_initialize() time and do not require mutex protection.\n  ** The nFreeSlot and pFree values do require mutex protection.\n  */\n  int isInit;                    /* True if initialized */\n  int separateCache;             /* Use a new PGroup for each PCache */\n  int nInitPage;                 /* Initial bulk allocation size */   \n  int szSlot;                    /* Size of each free slot */\n  int nSlot;                     /* The number of pcache slots */\n  int nReserve;                  /* Try to keep nFreeSlot above this */\n  void *pStart, *pEnd;           /* Bounds of global page cache memory */\n  /* Above requires no mutex.  Use mutex below for variable that follow. */\n  sqlite3_mutex *mutex;          /* Mutex for accessing the following: */\n  PgFreeslot *pFree;             /* Free page blocks */\n  int nFreeSlot;                 /* Number of unused pcache slots */\n  /* The following value requires a mutex to change.  We skip the mutex on\n  ** reading because (1) most platforms read a 32-bit integer atomically and\n  ** (2) even if an incorrect value is read, no great harm is done since this\n  ** is really just an optimization. */\n  int bUnderPressure;            /* True if low on PAGECACHE memory */\n} pcache1_g;\n\n/*\n** All code in this file should access the global structure above via the\n** alias \"pcache1\". This ensures that the WSD emulation is used when\n** compiling for systems that do not support real WSD.\n*/\n#define pcache1 (GLOBAL(struct PCacheGlobal, pcache1_g))\n\n/*\n** Macros to enter and leave the PCache LRU mutex.\n*/\n#if !defined(SQLITE_ENABLE_MEMORY_MANAGEMENT) || SQLITE_THREADSAFE==0\n# define pcache1EnterMutex(X)  assert((X)->mutex==0)\n# define pcache1LeaveMutex(X)  assert((X)->mutex==0)\n# define PCACHE1_MIGHT_USE_GROUP_MUTEX 0\n#else\n# define pcache1EnterMutex(X) sqlite3_mutex_enter((X)->mutex)\n# define pcache1LeaveMutex(X) sqlite3_mutex_leave((X)->mutex)\n# define PCACHE1_MIGHT_USE_GROUP_MUTEX 1\n#endif\n\n/******************************************************************************/\n/******** Page Allocation/SQLITE_CONFIG_PCACHE Related Functions **************/\n\n\n/*\n** This function is called during initialization if a static buffer is \n** supplied to use for the page-cache by passing the SQLITE_CONFIG_PAGECACHE\n** verb to sqlite3_config(). Parameter pBuf points to an allocation large\n** enough to contain 'n' buffers of 'sz' bytes each.\n**\n** This routine is called from sqlite3_initialize() and so it is guaranteed\n** to be serialized already.  There is no need for further mutexing.\n*/\nSQLITE_PRIVATE void sqlite3PCacheBufferSetup(void *pBuf, int sz, int n){\n  if( pcache1.isInit ){\n    PgFreeslot *p;\n    if( pBuf==0 ) sz = n = 0;\n    if( n==0 ) sz = 0;\n    sz = ROUNDDOWN8(sz);\n    pcache1.szSlot = sz;\n    pcache1.nSlot = pcache1.nFreeSlot = n;\n    pcache1.nReserve = n>90 ? 10 : (n/10 + 1);\n    pcache1.pStart = pBuf;\n    pcache1.pFree = 0;\n    pcache1.bUnderPressure = 0;\n    while( n-- ){\n      p = (PgFreeslot*)pBuf;\n      p->pNext = pcache1.pFree;\n      pcache1.pFree = p;\n      pBuf = (void*)&((char*)pBuf)[sz];\n    }\n    pcache1.pEnd = pBuf;\n  }\n}\n\n/*\n** Try to initialize the pCache->pFree and pCache->pBulk fields.  Return\n** true if pCache->pFree ends up containing one or more free pages.\n*/\nstatic int pcache1InitBulk(PCache1 *pCache){\n  i64 szBulk;\n  char *zBulk;\n  if( pcache1.nInitPage==0 ) return 0;\n  /* Do not bother with a bulk allocation if the cache size very small */\n  if( pCache->nMax<3 ) return 0;\n  sqlite3BeginBenignMalloc();\n  if( pcache1.nInitPage>0 ){\n    szBulk = pCache->szAlloc * (i64)pcache1.nInitPage;\n  }else{\n    szBulk = -1024 * (i64)pcache1.nInitPage;\n  }\n  if( szBulk > pCache->szAlloc*(i64)pCache->nMax ){\n    szBulk = pCache->szAlloc*(i64)pCache->nMax;\n  }\n  zBulk = pCache->pBulk = sqlite3Malloc( szBulk );\n  sqlite3EndBenignMalloc();\n  if( zBulk ){\n    int nBulk = sqlite3MallocSize(zBulk)/pCache->szAlloc;\n    do{\n      PgHdr1 *pX = (PgHdr1*)&zBulk[pCache->szPage];\n      pX->page.pBuf = zBulk;\n      pX->page.pExtra = &pX[1];\n      pX->isBulkLocal = 1;\n      pX->isAnchor = 0;\n      pX->pNext = pCache->pFree;\n      pCache->pFree = pX;\n      zBulk += pCache->szAlloc;\n    }while( --nBulk );\n  }\n  return pCache->pFree!=0;\n}\n\n/*\n** Malloc function used within this file to allocate space from the buffer\n** configured using sqlite3_config(SQLITE_CONFIG_PAGECACHE) option. If no \n** such buffer exists or there is no space left in it, this function falls \n** back to sqlite3Malloc().\n**\n** Multiple threads can run this routine at the same time.  Global variables\n** in pcache1 need to be protected via mutex.\n*/\nstatic void *pcache1Alloc(int nByte){\n  void *p = 0;\n  assert( sqlite3_mutex_notheld(pcache1.grp.mutex) );\n  if( nByte<=pcache1.szSlot ){\n    sqlite3_mutex_enter(pcache1.mutex);\n    p = (PgHdr1 *)pcache1.pFree;\n    if( p ){\n      pcache1.pFree = pcache1.pFree->pNext;\n      pcache1.nFreeSlot--;\n      pcache1.bUnderPressure = pcache1.nFreeSlot<pcache1.nReserve;\n      assert( pcache1.nFreeSlot>=0 );\n      sqlite3StatusHighwater(SQLITE_STATUS_PAGECACHE_SIZE, nByte);\n      sqlite3StatusUp(SQLITE_STATUS_PAGECACHE_USED, 1);\n    }\n    sqlite3_mutex_leave(pcache1.mutex);\n  }\n  if( p==0 ){\n    /* Memory is not available in the SQLITE_CONFIG_PAGECACHE pool.  Get\n    ** it from sqlite3Malloc instead.\n    */\n    p = sqlite3Malloc(nByte);\n#ifndef SQLITE_DISABLE_PAGECACHE_OVERFLOW_STATS\n    if( p ){\n      int sz = sqlite3MallocSize(p);\n      sqlite3_mutex_enter(pcache1.mutex);\n      sqlite3StatusHighwater(SQLITE_STATUS_PAGECACHE_SIZE, nByte);\n      sqlite3StatusUp(SQLITE_STATUS_PAGECACHE_OVERFLOW, sz);\n      sqlite3_mutex_leave(pcache1.mutex);\n    }\n#endif\n    sqlite3MemdebugSetType(p, MEMTYPE_PCACHE);\n  }\n  return p;\n}\n\n/*\n** Free an allocated buffer obtained from pcache1Alloc().\n*/\nstatic void pcache1Free(void *p){\n  if( p==0 ) return;\n  if( SQLITE_WITHIN(p, pcache1.pStart, pcache1.pEnd) ){\n    PgFreeslot *pSlot;\n    sqlite3_mutex_enter(pcache1.mutex);\n    sqlite3StatusDown(SQLITE_STATUS_PAGECACHE_USED, 1);\n    pSlot = (PgFreeslot*)p;\n    pSlot->pNext = pcache1.pFree;\n    pcache1.pFree = pSlot;\n    pcache1.nFreeSlot++;\n    pcache1.bUnderPressure = pcache1.nFreeSlot<pcache1.nReserve;\n    assert( pcache1.nFreeSlot<=pcache1.nSlot );\n    sqlite3_mutex_leave(pcache1.mutex);\n  }else{\n    assert( sqlite3MemdebugHasType(p, MEMTYPE_PCACHE) );\n    sqlite3MemdebugSetType(p, MEMTYPE_HEAP);\n#ifndef SQLITE_DISABLE_PAGECACHE_OVERFLOW_STATS\n    {\n      int nFreed = 0;\n      nFreed = sqlite3MallocSize(p);\n      sqlite3_mutex_enter(pcache1.mutex);\n      sqlite3StatusDown(SQLITE_STATUS_PAGECACHE_OVERFLOW, nFreed);\n      sqlite3_mutex_leave(pcache1.mutex);\n    }\n#endif\n    sqlite3_free(p);\n  }\n}\n\n#ifdef SQLITE_ENABLE_MEMORY_MANAGEMENT\n/*\n** Return the size of a pcache allocation\n*/\nstatic int pcache1MemSize(void *p){\n  if( p>=pcache1.pStart && p<pcache1.pEnd ){\n    return pcache1.szSlot;\n  }else{\n    int iSize;\n    assert( sqlite3MemdebugHasType(p, MEMTYPE_PCACHE) );\n    sqlite3MemdebugSetType(p, MEMTYPE_HEAP);\n    iSize = sqlite3MallocSize(p);\n    sqlite3MemdebugSetType(p, MEMTYPE_PCACHE);\n    return iSize;\n  }\n}\n#endif /* SQLITE_ENABLE_MEMORY_MANAGEMENT */\n\n/*\n** Allocate a new page object initially associated with cache pCache.\n*/\nstatic PgHdr1 *pcache1AllocPage(PCache1 *pCache, int benignMalloc){\n  PgHdr1 *p = 0;\n  void *pPg;\n\n  assert( sqlite3_mutex_held(pCache->pGroup->mutex) );\n  if( pCache->pFree || (pCache->nPage==0 && pcache1InitBulk(pCache)) ){\n    p = pCache->pFree;\n    pCache->pFree = p->pNext;\n    p->pNext = 0;\n  }else{\n#ifdef SQLITE_ENABLE_MEMORY_MANAGEMENT\n    /* The group mutex must be released before pcache1Alloc() is called. This\n    ** is because it might call sqlite3_release_memory(), which assumes that \n    ** this mutex is not held. */\n    assert( pcache1.separateCache==0 );\n    assert( pCache->pGroup==&pcache1.grp );\n    pcache1LeaveMutex(pCache->pGroup);\n#endif\n    if( benignMalloc ){ sqlite3BeginBenignMalloc(); }\n#ifdef SQLITE_PCACHE_SEPARATE_HEADER\n    pPg = pcache1Alloc(pCache->szPage);\n    p = sqlite3Malloc(sizeof(PgHdr1) + pCache->szExtra);\n    if( !pPg || !p ){\n      pcache1Free(pPg);\n      sqlite3_free(p);\n      pPg = 0;\n    }\n#else\n    pPg = pcache1Alloc(pCache->szAlloc);\n    p = (PgHdr1 *)&((u8 *)pPg)[pCache->szPage];\n#endif\n    if( benignMalloc ){ sqlite3EndBenignMalloc(); }\n#ifdef SQLITE_ENABLE_MEMORY_MANAGEMENT\n    pcache1EnterMutex(pCache->pGroup);\n#endif\n    if( pPg==0 ) return 0;\n    p->page.pBuf = pPg;\n    p->page.pExtra = &p[1];\n    p->isBulkLocal = 0;\n    p->isAnchor = 0;\n  }\n  (*pCache->pnPurgeable)++;\n  return p;\n}\n\n/*\n** Free a page object allocated by pcache1AllocPage().\n*/\nstatic void pcache1FreePage(PgHdr1 *p){\n  PCache1 *pCache;\n  assert( p!=0 );\n  pCache = p->pCache;\n  assert( sqlite3_mutex_held(p->pCache->pGroup->mutex) );\n  if( p->isBulkLocal ){\n    p->pNext = pCache->pFree;\n    pCache->pFree = p;\n  }else{\n    pcache1Free(p->page.pBuf);\n#ifdef SQLITE_PCACHE_SEPARATE_HEADER\n    sqlite3_free(p);\n#endif\n  }\n  (*pCache->pnPurgeable)--;\n}\n\n/*\n** Malloc function used by SQLite to obtain space from the buffer configured\n** using sqlite3_config(SQLITE_CONFIG_PAGECACHE) option. If no such buffer\n** exists, this function falls back to sqlite3Malloc().\n*/\nSQLITE_PRIVATE void *sqlite3PageMalloc(int sz){\n  return pcache1Alloc(sz);\n}\n\n/*\n** Free an allocated buffer obtained from sqlite3PageMalloc().\n*/\nSQLITE_PRIVATE void sqlite3PageFree(void *p){\n  pcache1Free(p);\n}\n\n\n/*\n** Return true if it desirable to avoid allocating a new page cache\n** entry.\n**\n** If memory was allocated specifically to the page cache using\n** SQLITE_CONFIG_PAGECACHE but that memory has all been used, then\n** it is desirable to avoid allocating a new page cache entry because\n** presumably SQLITE_CONFIG_PAGECACHE was suppose to be sufficient\n** for all page cache needs and we should not need to spill the\n** allocation onto the heap.\n**\n** Or, the heap is used for all page cache memory but the heap is\n** under memory pressure, then again it is desirable to avoid\n** allocating a new page cache entry in order to avoid stressing\n** the heap even further.\n*/\nstatic int pcache1UnderMemoryPressure(PCache1 *pCache){\n  if( pcache1.nSlot && (pCache->szPage+pCache->szExtra)<=pcache1.szSlot ){\n    return pcache1.bUnderPressure;\n  }else{\n    return sqlite3HeapNearlyFull();\n  }\n}\n\n/******************************************************************************/\n/******** General Implementation Functions ************************************/\n\n/*\n** This function is used to resize the hash table used by the cache passed\n** as the first argument.\n**\n** The PCache mutex must be held when this function is called.\n*/\nstatic void pcache1ResizeHash(PCache1 *p){\n  PgHdr1 **apNew;\n  unsigned int nNew;\n  unsigned int i;\n\n  assert( sqlite3_mutex_held(p->pGroup->mutex) );\n\n  nNew = p->nHash*2;\n  if( nNew<256 ){\n    nNew = 256;\n  }\n\n  pcache1LeaveMutex(p->pGroup);\n  if( p->nHash ){ sqlite3BeginBenignMalloc(); }\n  apNew = (PgHdr1 **)sqlite3MallocZero(sizeof(PgHdr1 *)*nNew);\n  if( p->nHash ){ sqlite3EndBenignMalloc(); }\n  pcache1EnterMutex(p->pGroup);\n  if( apNew ){\n    for(i=0; i<p->nHash; i++){\n      PgHdr1 *pPage;\n      PgHdr1 *pNext = p->apHash[i];\n      while( (pPage = pNext)!=0 ){\n        unsigned int h = pPage->iKey % nNew;\n        pNext = pPage->pNext;\n        pPage->pNext = apNew[h];\n        apNew[h] = pPage;\n      }\n    }\n    sqlite3_free(p->apHash);\n    p->apHash = apNew;\n    p->nHash = nNew;\n  }\n}\n\n/*\n** This function is used internally to remove the page pPage from the \n** PGroup LRU list, if is part of it. If pPage is not part of the PGroup\n** LRU list, then this function is a no-op.\n**\n** The PGroup mutex must be held when this function is called.\n*/\nstatic PgHdr1 *pcache1PinPage(PgHdr1 *pPage){\n  assert( pPage!=0 );\n  assert( PAGE_IS_UNPINNED(pPage) );\n  assert( pPage->pLruNext );\n  assert( pPage->pLruPrev );\n  assert( sqlite3_mutex_held(pPage->pCache->pGroup->mutex) );\n  pPage->pLruPrev->pLruNext = pPage->pLruNext;\n  pPage->pLruNext->pLruPrev = pPage->pLruPrev;\n  pPage->pLruNext = 0;\n  pPage->pLruPrev = 0;\n  assert( pPage->isAnchor==0 );\n  assert( pPage->pCache->pGroup->lru.isAnchor==1 );\n  pPage->pCache->nRecyclable--;\n  return pPage;\n}\n\n\n/*\n** Remove the page supplied as an argument from the hash table \n** (PCache1.apHash structure) that it is currently stored in.\n** Also free the page if freePage is true.\n**\n** The PGroup mutex must be held when this function is called.\n*/\nstatic void pcache1RemoveFromHash(PgHdr1 *pPage, int freeFlag){\n  unsigned int h;\n  PCache1 *pCache = pPage->pCache;\n  PgHdr1 **pp;\n\n  assert( sqlite3_mutex_held(pCache->pGroup->mutex) );\n  h = pPage->iKey % pCache->nHash;\n  for(pp=&pCache->apHash[h]; (*pp)!=pPage; pp=&(*pp)->pNext);\n  *pp = (*pp)->pNext;\n\n  pCache->nPage--;\n  if( freeFlag ) pcache1FreePage(pPage);\n}\n\n/*\n** If there are currently more than nMaxPage pages allocated, try\n** to recycle pages to reduce the number allocated to nMaxPage.\n*/\nstatic void pcache1EnforceMaxPage(PCache1 *pCache){\n  PGroup *pGroup = pCache->pGroup;\n  PgHdr1 *p;\n  assert( sqlite3_mutex_held(pGroup->mutex) );\n  while( pGroup->nPurgeable>pGroup->nMaxPage\n      && (p=pGroup->lru.pLruPrev)->isAnchor==0\n  ){\n    assert( p->pCache->pGroup==pGroup );\n    assert( PAGE_IS_UNPINNED(p) );\n    pcache1PinPage(p);\n    pcache1RemoveFromHash(p, 1);\n  }\n  if( pCache->nPage==0 && pCache->pBulk ){\n    sqlite3_free(pCache->pBulk);\n    pCache->pBulk = pCache->pFree = 0;\n  }\n}\n\n/*\n** Discard all pages from cache pCache with a page number (key value) \n** greater than or equal to iLimit. Any pinned pages that meet this \n** criteria are unpinned before they are discarded.\n**\n** The PCache mutex must be held when this function is called.\n*/\nstatic void pcache1TruncateUnsafe(\n  PCache1 *pCache,             /* The cache to truncate */\n  unsigned int iLimit          /* Drop pages with this pgno or larger */\n){\n  TESTONLY( int nPage = 0; )  /* To assert pCache->nPage is correct */\n  unsigned int h, iStop;\n  assert( sqlite3_mutex_held(pCache->pGroup->mutex) );\n  assert( pCache->iMaxKey >= iLimit );\n  assert( pCache->nHash > 0 );\n  if( pCache->iMaxKey - iLimit < pCache->nHash ){\n    /* If we are just shaving the last few pages off the end of the\n    ** cache, then there is no point in scanning the entire hash table.\n    ** Only scan those hash slots that might contain pages that need to\n    ** be removed. */\n    h = iLimit % pCache->nHash;\n    iStop = pCache->iMaxKey % pCache->nHash;\n    TESTONLY( nPage = -10; )  /* Disable the pCache->nPage validity check */\n  }else{\n    /* This is the general case where many pages are being removed.\n    ** It is necessary to scan the entire hash table */\n    h = pCache->nHash/2;\n    iStop = h - 1;\n  }\n  for(;;){\n    PgHdr1 **pp;\n    PgHdr1 *pPage;\n    assert( h<pCache->nHash );\n    pp = &pCache->apHash[h]; \n    while( (pPage = *pp)!=0 ){\n      if( pPage->iKey>=iLimit ){\n        pCache->nPage--;\n        *pp = pPage->pNext;\n        if( PAGE_IS_UNPINNED(pPage) ) pcache1PinPage(pPage);\n        pcache1FreePage(pPage);\n      }else{\n        pp = &pPage->pNext;\n        TESTONLY( if( nPage>=0 ) nPage++; )\n      }\n    }\n    if( h==iStop ) break;\n    h = (h+1) % pCache->nHash;\n  }\n  assert( nPage<0 || pCache->nPage==(unsigned)nPage );\n}\n\n/******************************************************************************/\n/******** sqlite3_pcache Methods **********************************************/\n\n/*\n** Implementation of the sqlite3_pcache.xInit method.\n*/\nstatic int pcache1Init(void *NotUsed){\n  UNUSED_PARAMETER(NotUsed);\n  assert( pcache1.isInit==0 );\n  memset(&pcache1, 0, sizeof(pcache1));\n\n\n  /*\n  ** The pcache1.separateCache variable is true if each PCache has its own\n  ** private PGroup (mode-1).  pcache1.separateCache is false if the single\n  ** PGroup in pcache1.grp is used for all page caches (mode-2).\n  **\n  **   *  Always use a unified cache (mode-2) if ENABLE_MEMORY_MANAGEMENT\n  **\n  **   *  Use a unified cache in single-threaded applications that have\n  **      configured a start-time buffer for use as page-cache memory using\n  **      sqlite3_config(SQLITE_CONFIG_PAGECACHE, pBuf, sz, N) with non-NULL \n  **      pBuf argument.\n  **\n  **   *  Otherwise use separate caches (mode-1)\n  */\n#if defined(SQLITE_ENABLE_MEMORY_MANAGEMENT)\n  pcache1.separateCache = 0;\n#elif SQLITE_THREADSAFE\n  pcache1.separateCache = sqlite3GlobalConfig.pPage==0\n                          || sqlite3GlobalConfig.bCoreMutex>0;\n#else\n  pcache1.separateCache = sqlite3GlobalConfig.pPage==0;\n#endif\n\n#if SQLITE_THREADSAFE\n  if( sqlite3GlobalConfig.bCoreMutex ){\n    pcache1.grp.mutex = sqlite3MutexAlloc(SQLITE_MUTEX_STATIC_LRU);\n    pcache1.mutex = sqlite3MutexAlloc(SQLITE_MUTEX_STATIC_PMEM);\n  }\n#endif\n  if( pcache1.separateCache\n   && sqlite3GlobalConfig.nPage!=0\n   && sqlite3GlobalConfig.pPage==0\n  ){\n    pcache1.nInitPage = sqlite3GlobalConfig.nPage;\n  }else{\n    pcache1.nInitPage = 0;\n  }\n  pcache1.grp.mxPinned = 10;\n  pcache1.isInit = 1;\n  return SQLITE_OK;\n}\n\n/*\n** Implementation of the sqlite3_pcache.xShutdown method.\n** Note that the static mutex allocated in xInit does \n** not need to be freed.\n*/\nstatic void pcache1Shutdown(void *NotUsed){\n  UNUSED_PARAMETER(NotUsed);\n  assert( pcache1.isInit!=0 );\n  memset(&pcache1, 0, sizeof(pcache1));\n}\n\n/* forward declaration */\nstatic void pcache1Destroy(sqlite3_pcache *p);\n\n/*\n** Implementation of the sqlite3_pcache.xCreate method.\n**\n** Allocate a new cache.\n*/\nstatic sqlite3_pcache *pcache1Create(int szPage, int szExtra, int bPurgeable){\n  PCache1 *pCache;      /* The newly created page cache */\n  PGroup *pGroup;       /* The group the new page cache will belong to */\n  int sz;               /* Bytes of memory required to allocate the new cache */\n\n  assert( (szPage & (szPage-1))==0 && szPage>=512 && szPage<=65536 );\n  assert( szExtra < 300 );\n\n  sz = sizeof(PCache1) + sizeof(PGroup)*pcache1.separateCache;\n  pCache = (PCache1 *)sqlite3MallocZero(sz);\n  if( pCache ){\n    if( pcache1.separateCache ){\n      pGroup = (PGroup*)&pCache[1];\n      pGroup->mxPinned = 10;\n    }else{\n      pGroup = &pcache1.grp;\n    }\n    if( pGroup->lru.isAnchor==0 ){\n      pGroup->lru.isAnchor = 1;\n      pGroup->lru.pLruPrev = pGroup->lru.pLruNext = &pGroup->lru;\n    }\n    pCache->pGroup = pGroup;\n    pCache->szPage = szPage;\n    pCache->szExtra = szExtra;\n    pCache->szAlloc = szPage + szExtra + ROUND8(sizeof(PgHdr1));\n    pCache->bPurgeable = (bPurgeable ? 1 : 0);\n    pcache1EnterMutex(pGroup);\n    pcache1ResizeHash(pCache);\n    if( bPurgeable ){\n      pCache->nMin = 10;\n      pGroup->nMinPage += pCache->nMin;\n      pGroup->mxPinned = pGroup->nMaxPage + 10 - pGroup->nMinPage;\n      pCache->pnPurgeable = &pGroup->nPurgeable;\n    }else{\n      static unsigned int dummyCurrentPage;\n      pCache->pnPurgeable = &dummyCurrentPage;\n    }\n    pcache1LeaveMutex(pGroup);\n    if( pCache->nHash==0 ){\n      pcache1Destroy((sqlite3_pcache*)pCache);\n      pCache = 0;\n    }\n  }\n  return (sqlite3_pcache *)pCache;\n}\n\n/*\n** Implementation of the sqlite3_pcache.xCachesize method. \n**\n** Configure the cache_size limit for a cache.\n*/\nstatic void pcache1Cachesize(sqlite3_pcache *p, int nMax){\n  PCache1 *pCache = (PCache1 *)p;\n  if( pCache->bPurgeable ){\n    PGroup *pGroup = pCache->pGroup;\n    pcache1EnterMutex(pGroup);\n    pGroup->nMaxPage += (nMax - pCache->nMax);\n    pGroup->mxPinned = pGroup->nMaxPage + 10 - pGroup->nMinPage;\n    pCache->nMax = nMax;\n    pCache->n90pct = pCache->nMax*9/10;\n    pcache1EnforceMaxPage(pCache);\n    pcache1LeaveMutex(pGroup);\n  }\n}\n\n/*\n** Implementation of the sqlite3_pcache.xShrink method. \n**\n** Free up as much memory as possible.\n*/\nstatic void pcache1Shrink(sqlite3_pcache *p){\n  PCache1 *pCache = (PCache1*)p;\n  if( pCache->bPurgeable ){\n    PGroup *pGroup = pCache->pGroup;\n    int savedMaxPage;\n    pcache1EnterMutex(pGroup);\n    savedMaxPage = pGroup->nMaxPage;\n    pGroup->nMaxPage = 0;\n    pcache1EnforceMaxPage(pCache);\n    pGroup->nMaxPage = savedMaxPage;\n    pcache1LeaveMutex(pGroup);\n  }\n}\n\n/*\n** Implementation of the sqlite3_pcache.xPagecount method. \n*/\nstatic int pcache1Pagecount(sqlite3_pcache *p){\n  int n;\n  PCache1 *pCache = (PCache1*)p;\n  pcache1EnterMutex(pCache->pGroup);\n  n = pCache->nPage;\n  pcache1LeaveMutex(pCache->pGroup);\n  return n;\n}\n\n\n/*\n** Implement steps 3, 4, and 5 of the pcache1Fetch() algorithm described\n** in the header of the pcache1Fetch() procedure.\n**\n** This steps are broken out into a separate procedure because they are\n** usually not needed, and by avoiding the stack initialization required\n** for these steps, the main pcache1Fetch() procedure can run faster.\n*/\nstatic SQLITE_NOINLINE PgHdr1 *pcache1FetchStage2(\n  PCache1 *pCache, \n  unsigned int iKey, \n  int createFlag\n){\n  unsigned int nPinned;\n  PGroup *pGroup = pCache->pGroup;\n  PgHdr1 *pPage = 0;\n\n  /* Step 3: Abort if createFlag is 1 but the cache is nearly full */\n  assert( pCache->nPage >= pCache->nRecyclable );\n  nPinned = pCache->nPage - pCache->nRecyclable;\n  assert( pGroup->mxPinned == pGroup->nMaxPage + 10 - pGroup->nMinPage );\n  assert( pCache->n90pct == pCache->nMax*9/10 );\n  if( createFlag==1 && (\n        nPinned>=pGroup->mxPinned\n     || nPinned>=pCache->n90pct\n     || (pcache1UnderMemoryPressure(pCache) && pCache->nRecyclable<nPinned)\n  )){\n    return 0;\n  }\n\n  if( pCache->nPage>=pCache->nHash ) pcache1ResizeHash(pCache);\n  assert( pCache->nHash>0 && pCache->apHash );\n\n  /* Step 4. Try to recycle a page. */\n  if( pCache->bPurgeable\n   && !pGroup->lru.pLruPrev->isAnchor\n   && ((pCache->nPage+1>=pCache->nMax) || pcache1UnderMemoryPressure(pCache))\n  ){\n    PCache1 *pOther;\n    pPage = pGroup->lru.pLruPrev;\n    assert( PAGE_IS_UNPINNED(pPage) );\n    pcache1RemoveFromHash(pPage, 0);\n    pcache1PinPage(pPage);\n    pOther = pPage->pCache;\n    if( pOther->szAlloc != pCache->szAlloc ){\n      pcache1FreePage(pPage);\n      pPage = 0;\n    }else{\n      pGroup->nPurgeable -= (pOther->bPurgeable - pCache->bPurgeable);\n    }\n  }\n\n  /* Step 5. If a usable page buffer has still not been found, \n  ** attempt to allocate a new one. \n  */\n  if( !pPage ){\n    pPage = pcache1AllocPage(pCache, createFlag==1);\n  }\n\n  if( pPage ){\n    unsigned int h = iKey % pCache->nHash;\n    pCache->nPage++;\n    pPage->iKey = iKey;\n    pPage->pNext = pCache->apHash[h];\n    pPage->pCache = pCache;\n    pPage->pLruPrev = 0;\n    pPage->pLruNext = 0;\n    *(void **)pPage->page.pExtra = 0;\n    pCache->apHash[h] = pPage;\n    if( iKey>pCache->iMaxKey ){\n      pCache->iMaxKey = iKey;\n    }\n  }\n  return pPage;\n}\n\n/*\n** Implementation of the sqlite3_pcache.xFetch method. \n**\n** Fetch a page by key value.\n**\n** Whether or not a new page may be allocated by this function depends on\n** the value of the createFlag argument.  0 means do not allocate a new\n** page.  1 means allocate a new page if space is easily available.  2 \n** means to try really hard to allocate a new page.\n**\n** For a non-purgeable cache (a cache used as the storage for an in-memory\n** database) there is really no difference between createFlag 1 and 2.  So\n** the calling function (pcache.c) will never have a createFlag of 1 on\n** a non-purgeable cache.\n**\n** There are three different approaches to obtaining space for a page,\n** depending on the value of parameter createFlag (which may be 0, 1 or 2).\n**\n**   1. Regardless of the value of createFlag, the cache is searched for a \n**      copy of the requested page. If one is found, it is returned.\n**\n**   2. If createFlag==0 and the page is not already in the cache, NULL is\n**      returned.\n**\n**   3. If createFlag is 1, and the page is not already in the cache, then\n**      return NULL (do not allocate a new page) if any of the following\n**      conditions are true:\n**\n**       (a) the number of pages pinned by the cache is greater than\n**           PCache1.nMax, or\n**\n**       (b) the number of pages pinned by the cache is greater than\n**           the sum of nMax for all purgeable caches, less the sum of \n**           nMin for all other purgeable caches, or\n**\n**   4. If none of the first three conditions apply and the cache is marked\n**      as purgeable, and if one of the following is true:\n**\n**       (a) The number of pages allocated for the cache is already \n**           PCache1.nMax, or\n**\n**       (b) The number of pages allocated for all purgeable caches is\n**           already equal to or greater than the sum of nMax for all\n**           purgeable caches,\n**\n**       (c) The system is under memory pressure and wants to avoid\n**           unnecessary pages cache entry allocations\n**\n**      then attempt to recycle a page from the LRU list. If it is the right\n**      size, return the recycled buffer. Otherwise, free the buffer and\n**      proceed to step 5. \n**\n**   5. Otherwise, allocate and return a new page buffer.\n**\n** There are two versions of this routine.  pcache1FetchWithMutex() is\n** the general case.  pcache1FetchNoMutex() is a faster implementation for\n** the common case where pGroup->mutex is NULL.  The pcache1Fetch() wrapper\n** invokes the appropriate routine.\n*/\nstatic PgHdr1 *pcache1FetchNoMutex(\n  sqlite3_pcache *p, \n  unsigned int iKey, \n  int createFlag\n){\n  PCache1 *pCache = (PCache1 *)p;\n  PgHdr1 *pPage = 0;\n\n  /* Step 1: Search the hash table for an existing entry. */\n  pPage = pCache->apHash[iKey % pCache->nHash];\n  while( pPage && pPage->iKey!=iKey ){ pPage = pPage->pNext; }\n\n  /* Step 2: If the page was found in the hash table, then return it.\n  ** If the page was not in the hash table and createFlag is 0, abort.\n  ** Otherwise (page not in hash and createFlag!=0) continue with\n  ** subsequent steps to try to create the page. */\n  if( pPage ){\n    if( PAGE_IS_UNPINNED(pPage) ){\n      return pcache1PinPage(pPage);\n    }else{\n      return pPage;\n    }\n  }else if( createFlag ){\n    /* Steps 3, 4, and 5 implemented by this subroutine */\n    return pcache1FetchStage2(pCache, iKey, createFlag);\n  }else{\n    return 0;\n  }\n}\n#if PCACHE1_MIGHT_USE_GROUP_MUTEX\nstatic PgHdr1 *pcache1FetchWithMutex(\n  sqlite3_pcache *p, \n  unsigned int iKey, \n  int createFlag\n){\n  PCache1 *pCache = (PCache1 *)p;\n  PgHdr1 *pPage;\n\n  pcache1EnterMutex(pCache->pGroup);\n  pPage = pcache1FetchNoMutex(p, iKey, createFlag);\n  assert( pPage==0 || pCache->iMaxKey>=iKey );\n  pcache1LeaveMutex(pCache->pGroup);\n  return pPage;\n}\n#endif\nstatic sqlite3_pcache_page *pcache1Fetch(\n  sqlite3_pcache *p, \n  unsigned int iKey, \n  int createFlag\n){\n#if PCACHE1_MIGHT_USE_GROUP_MUTEX || defined(SQLITE_DEBUG)\n  PCache1 *pCache = (PCache1 *)p;\n#endif\n\n  assert( offsetof(PgHdr1,page)==0 );\n  assert( pCache->bPurgeable || createFlag!=1 );\n  assert( pCache->bPurgeable || pCache->nMin==0 );\n  assert( pCache->bPurgeable==0 || pCache->nMin==10 );\n  assert( pCache->nMin==0 || pCache->bPurgeable );\n  assert( pCache->nHash>0 );\n#if PCACHE1_MIGHT_USE_GROUP_MUTEX\n  if( pCache->pGroup->mutex ){\n    return (sqlite3_pcache_page*)pcache1FetchWithMutex(p, iKey, createFlag);\n  }else\n#endif\n  {\n    return (sqlite3_pcache_page*)pcache1FetchNoMutex(p, iKey, createFlag);\n  }\n}\n\n\n/*\n** Implementation of the sqlite3_pcache.xUnpin method.\n**\n** Mark a page as unpinned (eligible for asynchronous recycling).\n*/\nstatic void pcache1Unpin(\n  sqlite3_pcache *p, \n  sqlite3_pcache_page *pPg, \n  int reuseUnlikely\n){\n  PCache1 *pCache = (PCache1 *)p;\n  PgHdr1 *pPage = (PgHdr1 *)pPg;\n  PGroup *pGroup = pCache->pGroup;\n \n  assert( pPage->pCache==pCache );\n  pcache1EnterMutex(pGroup);\n\n  /* It is an error to call this function if the page is already \n  ** part of the PGroup LRU list.\n  */\n  assert( pPage->pLruPrev==0 && pPage->pLruNext==0 );\n  assert( PAGE_IS_PINNED(pPage) );\n\n  if( reuseUnlikely || pGroup->nPurgeable>pGroup->nMaxPage ){\n    pcache1RemoveFromHash(pPage, 1);\n  }else{\n    /* Add the page to the PGroup LRU list. */\n    PgHdr1 **ppFirst = &pGroup->lru.pLruNext;\n    pPage->pLruPrev = &pGroup->lru;\n    (pPage->pLruNext = *ppFirst)->pLruPrev = pPage;\n    *ppFirst = pPage;\n    pCache->nRecyclable++;\n  }\n\n  pcache1LeaveMutex(pCache->pGroup);\n}\n\n/*\n** Implementation of the sqlite3_pcache.xRekey method. \n*/\nstatic void pcache1Rekey(\n  sqlite3_pcache *p,\n  sqlite3_pcache_page *pPg,\n  unsigned int iOld,\n  unsigned int iNew\n){\n  PCache1 *pCache = (PCache1 *)p;\n  PgHdr1 *pPage = (PgHdr1 *)pPg;\n  PgHdr1 **pp;\n  unsigned int h; \n  assert( pPage->iKey==iOld );\n  assert( pPage->pCache==pCache );\n\n  pcache1EnterMutex(pCache->pGroup);\n\n  h = iOld%pCache->nHash;\n  pp = &pCache->apHash[h];\n  while( (*pp)!=pPage ){\n    pp = &(*pp)->pNext;\n  }\n  *pp = pPage->pNext;\n\n  h = iNew%pCache->nHash;\n  pPage->iKey = iNew;\n  pPage->pNext = pCache->apHash[h];\n  pCache->apHash[h] = pPage;\n  if( iNew>pCache->iMaxKey ){\n    pCache->iMaxKey = iNew;\n  }\n\n  pcache1LeaveMutex(pCache->pGroup);\n}\n\n/*\n** Implementation of the sqlite3_pcache.xTruncate method. \n**\n** Discard all unpinned pages in the cache with a page number equal to\n** or greater than parameter iLimit. Any pinned pages with a page number\n** equal to or greater than iLimit are implicitly unpinned.\n*/\nstatic void pcache1Truncate(sqlite3_pcache *p, unsigned int iLimit){\n  PCache1 *pCache = (PCache1 *)p;\n  pcache1EnterMutex(pCache->pGroup);\n  if( iLimit<=pCache->iMaxKey ){\n    pcache1TruncateUnsafe(pCache, iLimit);\n    pCache->iMaxKey = iLimit-1;\n  }\n  pcache1LeaveMutex(pCache->pGroup);\n}\n\n/*\n** Implementation of the sqlite3_pcache.xDestroy method. \n**\n** Destroy a cache allocated using pcache1Create().\n*/\nstatic void pcache1Destroy(sqlite3_pcache *p){\n  PCache1 *pCache = (PCache1 *)p;\n  PGroup *pGroup = pCache->pGroup;\n  assert( pCache->bPurgeable || (pCache->nMax==0 && pCache->nMin==0) );\n  pcache1EnterMutex(pGroup);\n  if( pCache->nPage ) pcache1TruncateUnsafe(pCache, 0);\n  assert( pGroup->nMaxPage >= pCache->nMax );\n  pGroup->nMaxPage -= pCache->nMax;\n  assert( pGroup->nMinPage >= pCache->nMin );\n  pGroup->nMinPage -= pCache->nMin;\n  pGroup->mxPinned = pGroup->nMaxPage + 10 - pGroup->nMinPage;\n  pcache1EnforceMaxPage(pCache);\n  pcache1LeaveMutex(pGroup);\n  sqlite3_free(pCache->pBulk);\n  sqlite3_free(pCache->apHash);\n  sqlite3_free(pCache);\n}\n\n/*\n** This function is called during initialization (sqlite3_initialize()) to\n** install the default pluggable cache module, assuming the user has not\n** already provided an alternative.\n*/\nSQLITE_PRIVATE void sqlite3PCacheSetDefault(void){\n  static const sqlite3_pcache_methods2 defaultMethods = {\n    1,                       /* iVersion */\n    0,                       /* pArg */\n    pcache1Init,             /* xInit */\n    pcache1Shutdown,         /* xShutdown */\n    pcache1Create,           /* xCreate */\n    pcache1Cachesize,        /* xCachesize */\n    pcache1Pagecount,        /* xPagecount */\n    pcache1Fetch,            /* xFetch */\n    pcache1Unpin,            /* xUnpin */\n    pcache1Rekey,            /* xRekey */\n    pcache1Truncate,         /* xTruncate */\n    pcache1Destroy,          /* xDestroy */\n    pcache1Shrink            /* xShrink */\n  };\n  sqlite3_config(SQLITE_CONFIG_PCACHE2, &defaultMethods);\n}\n\n/*\n** Return the size of the header on each page of this PCACHE implementation.\n*/\nSQLITE_PRIVATE int sqlite3HeaderSizePcache1(void){ return ROUND8(sizeof(PgHdr1)); }\n\n/*\n** Return the global mutex used by this PCACHE implementation.  The\n** sqlite3_status() routine needs access to this mutex.\n*/\nSQLITE_PRIVATE sqlite3_mutex *sqlite3Pcache1Mutex(void){\n  return pcache1.mutex;\n}\n\n#ifdef SQLITE_ENABLE_MEMORY_MANAGEMENT\n/*\n** This function is called to free superfluous dynamically allocated memory\n** held by the pager system. Memory in use by any SQLite pager allocated\n** by the current thread may be sqlite3_free()ed.\n**\n** nReq is the number of bytes of memory required. Once this much has\n** been released, the function returns. The return value is the total number \n** of bytes of memory released.\n*/\nSQLITE_PRIVATE int sqlite3PcacheReleaseMemory(int nReq){\n  int nFree = 0;\n  assert( sqlite3_mutex_notheld(pcache1.grp.mutex) );\n  assert( sqlite3_mutex_notheld(pcache1.mutex) );\n  if( sqlite3GlobalConfig.pPage==0 ){\n    PgHdr1 *p;\n    pcache1EnterMutex(&pcache1.grp);\n    while( (nReq<0 || nFree<nReq)\n       &&  (p=pcache1.grp.lru.pLruPrev)!=0\n       &&  p->isAnchor==0\n    ){\n      nFree += pcache1MemSize(p->page.pBuf);\n#ifdef SQLITE_PCACHE_SEPARATE_HEADER\n      nFree += sqlite3MemSize(p);\n#endif\n      assert( PAGE_IS_UNPINNED(p) );\n      pcache1PinPage(p);\n      pcache1RemoveFromHash(p, 1);\n    }\n    pcache1LeaveMutex(&pcache1.grp);\n  }\n  return nFree;\n}\n#endif /* SQLITE_ENABLE_MEMORY_MANAGEMENT */\n\n#ifdef SQLITE_TEST\n/*\n** This function is used by test procedures to inspect the internal state\n** of the global cache.\n*/\nSQLITE_PRIVATE void sqlite3PcacheStats(\n  int *pnCurrent,      /* OUT: Total number of pages cached */\n  int *pnMax,          /* OUT: Global maximum cache size */\n  int *pnMin,          /* OUT: Sum of PCache1.nMin for purgeable caches */\n  int *pnRecyclable    /* OUT: Total number of pages available for recycling */\n){\n  PgHdr1 *p;\n  int nRecyclable = 0;\n  for(p=pcache1.grp.lru.pLruNext; p && !p->isAnchor; p=p->pLruNext){\n    assert( PAGE_IS_UNPINNED(p) );\n    nRecyclable++;\n  }\n  *pnCurrent = pcache1.grp.nPurgeable;\n  *pnMax = (int)pcache1.grp.nMaxPage;\n  *pnMin = (int)pcache1.grp.nMinPage;\n  *pnRecyclable = nRecyclable;\n}\n#endif\n\n/************** End of pcache1.c *********************************************/\n/************** Begin file rowset.c ******************************************/\n/*\n** 2008 December 3\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n*************************************************************************\n**\n** This module implements an object we call a \"RowSet\".\n**\n** The RowSet object is a collection of rowids.  Rowids\n** are inserted into the RowSet in an arbitrary order.  Inserts\n** can be intermixed with tests to see if a given rowid has been\n** previously inserted into the RowSet.\n**\n** After all inserts are finished, it is possible to extract the\n** elements of the RowSet in sorted order.  Once this extraction\n** process has started, no new elements may be inserted.\n**\n** Hence, the primitive operations for a RowSet are:\n**\n**    CREATE\n**    INSERT\n**    TEST\n**    SMALLEST\n**    DESTROY\n**\n** The CREATE and DESTROY primitives are the constructor and destructor,\n** obviously.  The INSERT primitive adds a new element to the RowSet.\n** TEST checks to see if an element is already in the RowSet.  SMALLEST\n** extracts the least value from the RowSet.\n**\n** The INSERT primitive might allocate additional memory.  Memory is\n** allocated in chunks so most INSERTs do no allocation.  There is an \n** upper bound on the size of allocated memory.  No memory is freed\n** until DESTROY.\n**\n** The TEST primitive includes a \"batch\" number.  The TEST primitive\n** will only see elements that were inserted before the last change\n** in the batch number.  In other words, if an INSERT occurs between\n** two TESTs where the TESTs have the same batch nubmer, then the\n** value added by the INSERT will not be visible to the second TEST.\n** The initial batch number is zero, so if the very first TEST contains\n** a non-zero batch number, it will see all prior INSERTs.\n**\n** No INSERTs may occurs after a SMALLEST.  An assertion will fail if\n** that is attempted.\n**\n** The cost of an INSERT is roughly constant.  (Sometimes new memory\n** has to be allocated on an INSERT.)  The cost of a TEST with a new\n** batch number is O(NlogN) where N is the number of elements in the RowSet.\n** The cost of a TEST using the same batch number is O(logN).  The cost\n** of the first SMALLEST is O(NlogN).  Second and subsequent SMALLEST\n** primitives are constant time.  The cost of DESTROY is O(N).\n**\n** TEST and SMALLEST may not be used by the same RowSet.  This used to\n** be possible, but the feature was not used, so it was removed in order\n** to simplify the code.\n*/\n/* #include \"sqliteInt.h\" */\n\n\n/*\n** Target size for allocation chunks.\n*/\n#define ROWSET_ALLOCATION_SIZE 1024\n\n/*\n** The number of rowset entries per allocation chunk.\n*/\n#define ROWSET_ENTRY_PER_CHUNK  \\\n                       ((ROWSET_ALLOCATION_SIZE-8)/sizeof(struct RowSetEntry))\n\n/*\n** Each entry in a RowSet is an instance of the following object.\n**\n** This same object is reused to store a linked list of trees of RowSetEntry\n** objects.  In that alternative use, pRight points to the next entry\n** in the list, pLeft points to the tree, and v is unused.  The\n** RowSet.pForest value points to the head of this forest list.\n*/\nstruct RowSetEntry {            \n  i64 v;                        /* ROWID value for this entry */\n  struct RowSetEntry *pRight;   /* Right subtree (larger entries) or list */\n  struct RowSetEntry *pLeft;    /* Left subtree (smaller entries) */\n};\n\n/*\n** RowSetEntry objects are allocated in large chunks (instances of the\n** following structure) to reduce memory allocation overhead.  The\n** chunks are kept on a linked list so that they can be deallocated\n** when the RowSet is destroyed.\n*/\nstruct RowSetChunk {\n  struct RowSetChunk *pNextChunk;        /* Next chunk on list of them all */\n  struct RowSetEntry aEntry[ROWSET_ENTRY_PER_CHUNK]; /* Allocated entries */\n};\n\n/*\n** A RowSet in an instance of the following structure.\n**\n** A typedef of this structure if found in sqliteInt.h.\n*/\nstruct RowSet {\n  struct RowSetChunk *pChunk;    /* List of all chunk allocations */\n  sqlite3 *db;                   /* The database connection */\n  struct RowSetEntry *pEntry;    /* List of entries using pRight */\n  struct RowSetEntry *pLast;     /* Last entry on the pEntry list */\n  struct RowSetEntry *pFresh;    /* Source of new entry objects */\n  struct RowSetEntry *pForest;   /* List of binary trees of entries */\n  u16 nFresh;                    /* Number of objects on pFresh */\n  u16 rsFlags;                   /* Various flags */\n  int iBatch;                    /* Current insert batch */\n};\n\n/*\n** Allowed values for RowSet.rsFlags\n*/\n#define ROWSET_SORTED  0x01   /* True if RowSet.pEntry is sorted */\n#define ROWSET_NEXT    0x02   /* True if sqlite3RowSetNext() has been called */\n\n/*\n** Turn bulk memory into a RowSet object.  N bytes of memory\n** are available at pSpace.  The db pointer is used as a memory context\n** for any subsequent allocations that need to occur.\n** Return a pointer to the new RowSet object.\n**\n** It must be the case that N is sufficient to make a Rowset.  If not\n** an assertion fault occurs.\n** \n** If N is larger than the minimum, use the surplus as an initial\n** allocation of entries available to be filled.\n*/\nSQLITE_PRIVATE RowSet *sqlite3RowSetInit(sqlite3 *db, void *pSpace, unsigned int N){\n  RowSet *p;\n  assert( N >= ROUND8(sizeof(*p)) );\n  p = pSpace;\n  p->pChunk = 0;\n  p->db = db;\n  p->pEntry = 0;\n  p->pLast = 0;\n  p->pForest = 0;\n  p->pFresh = (struct RowSetEntry*)(ROUND8(sizeof(*p)) + (char*)p);\n  p->nFresh = (u16)((N - ROUND8(sizeof(*p)))/sizeof(struct RowSetEntry));\n  p->rsFlags = ROWSET_SORTED;\n  p->iBatch = 0;\n  return p;\n}\n\n/*\n** Deallocate all chunks from a RowSet.  This frees all memory that\n** the RowSet has allocated over its lifetime.  This routine is\n** the destructor for the RowSet.\n*/\nSQLITE_PRIVATE void sqlite3RowSetClear(RowSet *p){\n  struct RowSetChunk *pChunk, *pNextChunk;\n  for(pChunk=p->pChunk; pChunk; pChunk = pNextChunk){\n    pNextChunk = pChunk->pNextChunk;\n    sqlite3DbFree(p->db, pChunk);\n  }\n  p->pChunk = 0;\n  p->nFresh = 0;\n  p->pEntry = 0;\n  p->pLast = 0;\n  p->pForest = 0;\n  p->rsFlags = ROWSET_SORTED;\n}\n\n/*\n** Allocate a new RowSetEntry object that is associated with the\n** given RowSet.  Return a pointer to the new and completely uninitialized\n** objected.\n**\n** In an OOM situation, the RowSet.db->mallocFailed flag is set and this\n** routine returns NULL.\n*/\nstatic struct RowSetEntry *rowSetEntryAlloc(RowSet *p){\n  assert( p!=0 );\n  if( p->nFresh==0 ){  /*OPTIMIZATION-IF-FALSE*/\n    /* We could allocate a fresh RowSetEntry each time one is needed, but it\n    ** is more efficient to pull a preallocated entry from the pool */\n    struct RowSetChunk *pNew;\n    pNew = sqlite3DbMallocRawNN(p->db, sizeof(*pNew));\n    if( pNew==0 ){\n      return 0;\n    }\n    pNew->pNextChunk = p->pChunk;\n    p->pChunk = pNew;\n    p->pFresh = pNew->aEntry;\n    p->nFresh = ROWSET_ENTRY_PER_CHUNK;\n  }\n  p->nFresh--;\n  return p->pFresh++;\n}\n\n/*\n** Insert a new value into a RowSet.\n**\n** The mallocFailed flag of the database connection is set if a\n** memory allocation fails.\n*/\nSQLITE_PRIVATE void sqlite3RowSetInsert(RowSet *p, i64 rowid){\n  struct RowSetEntry *pEntry;  /* The new entry */\n  struct RowSetEntry *pLast;   /* The last prior entry */\n\n  /* This routine is never called after sqlite3RowSetNext() */\n  assert( p!=0 && (p->rsFlags & ROWSET_NEXT)==0 );\n\n  pEntry = rowSetEntryAlloc(p);\n  if( pEntry==0 ) return;\n  pEntry->v = rowid;\n  pEntry->pRight = 0;\n  pLast = p->pLast;\n  if( pLast ){\n    if( rowid<=pLast->v ){  /*OPTIMIZATION-IF-FALSE*/\n      /* Avoid unnecessary sorts by preserving the ROWSET_SORTED flags\n      ** where possible */\n      p->rsFlags &= ~ROWSET_SORTED;\n    }\n    pLast->pRight = pEntry;\n  }else{\n    p->pEntry = pEntry;\n  }\n  p->pLast = pEntry;\n}\n\n/*\n** Merge two lists of RowSetEntry objects.  Remove duplicates.\n**\n** The input lists are connected via pRight pointers and are \n** assumed to each already be in sorted order.\n*/\nstatic struct RowSetEntry *rowSetEntryMerge(\n  struct RowSetEntry *pA,    /* First sorted list to be merged */\n  struct RowSetEntry *pB     /* Second sorted list to be merged */\n){\n  struct RowSetEntry head;\n  struct RowSetEntry *pTail;\n\n  pTail = &head;\n  assert( pA!=0 && pB!=0 );\n  for(;;){\n    assert( pA->pRight==0 || pA->v<=pA->pRight->v );\n    assert( pB->pRight==0 || pB->v<=pB->pRight->v );\n    if( pA->v<=pB->v ){\n      if( pA->v<pB->v ) pTail = pTail->pRight = pA;\n      pA = pA->pRight;\n      if( pA==0 ){\n        pTail->pRight = pB;\n        break;\n      }\n    }else{\n      pTail = pTail->pRight = pB;\n      pB = pB->pRight;\n      if( pB==0 ){\n        pTail->pRight = pA;\n        break;\n      }\n    }\n  }\n  return head.pRight;\n}\n\n/*\n** Sort all elements on the list of RowSetEntry objects into order of\n** increasing v.\n*/ \nstatic struct RowSetEntry *rowSetEntrySort(struct RowSetEntry *pIn){\n  unsigned int i;\n  struct RowSetEntry *pNext, *aBucket[40];\n\n  memset(aBucket, 0, sizeof(aBucket));\n  while( pIn ){\n    pNext = pIn->pRight;\n    pIn->pRight = 0;\n    for(i=0; aBucket[i]; i++){\n      pIn = rowSetEntryMerge(aBucket[i], pIn);\n      aBucket[i] = 0;\n    }\n    aBucket[i] = pIn;\n    pIn = pNext;\n  }\n  pIn = aBucket[0];\n  for(i=1; i<sizeof(aBucket)/sizeof(aBucket[0]); i++){\n    if( aBucket[i]==0 ) continue;\n    pIn = pIn ? rowSetEntryMerge(pIn, aBucket[i]) : aBucket[i];\n  }\n  return pIn;\n}\n\n\n/*\n** The input, pIn, is a binary tree (or subtree) of RowSetEntry objects.\n** Convert this tree into a linked list connected by the pRight pointers\n** and return pointers to the first and last elements of the new list.\n*/\nstatic void rowSetTreeToList(\n  struct RowSetEntry *pIn,         /* Root of the input tree */\n  struct RowSetEntry **ppFirst,    /* Write head of the output list here */\n  struct RowSetEntry **ppLast      /* Write tail of the output list here */\n){\n  assert( pIn!=0 );\n  if( pIn->pLeft ){\n    struct RowSetEntry *p;\n    rowSetTreeToList(pIn->pLeft, ppFirst, &p);\n    p->pRight = pIn;\n  }else{\n    *ppFirst = pIn;\n  }\n  if( pIn->pRight ){\n    rowSetTreeToList(pIn->pRight, &pIn->pRight, ppLast);\n  }else{\n    *ppLast = pIn;\n  }\n  assert( (*ppLast)->pRight==0 );\n}\n\n\n/*\n** Convert a sorted list of elements (connected by pRight) into a binary\n** tree with depth of iDepth.  A depth of 1 means the tree contains a single\n** node taken from the head of *ppList.  A depth of 2 means a tree with\n** three nodes.  And so forth.\n**\n** Use as many entries from the input list as required and update the\n** *ppList to point to the unused elements of the list.  If the input\n** list contains too few elements, then construct an incomplete tree\n** and leave *ppList set to NULL.\n**\n** Return a pointer to the root of the constructed binary tree.\n*/\nstatic struct RowSetEntry *rowSetNDeepTree(\n  struct RowSetEntry **ppList,\n  int iDepth\n){\n  struct RowSetEntry *p;         /* Root of the new tree */\n  struct RowSetEntry *pLeft;     /* Left subtree */\n  if( *ppList==0 ){ /*OPTIMIZATION-IF-TRUE*/\n    /* Prevent unnecessary deep recursion when we run out of entries */\n    return 0; \n  }\n  if( iDepth>1 ){   /*OPTIMIZATION-IF-TRUE*/\n    /* This branch causes a *balanced* tree to be generated.  A valid tree\n    ** is still generated without this branch, but the tree is wildly\n    ** unbalanced and inefficient. */\n    pLeft = rowSetNDeepTree(ppList, iDepth-1);\n    p = *ppList;\n    if( p==0 ){     /*OPTIMIZATION-IF-FALSE*/\n      /* It is safe to always return here, but the resulting tree\n      ** would be unbalanced */\n      return pLeft;\n    }\n    p->pLeft = pLeft;\n    *ppList = p->pRight;\n    p->pRight = rowSetNDeepTree(ppList, iDepth-1);\n  }else{\n    p = *ppList;\n    *ppList = p->pRight;\n    p->pLeft = p->pRight = 0;\n  }\n  return p;\n}\n\n/*\n** Convert a sorted list of elements into a binary tree. Make the tree\n** as deep as it needs to be in order to contain the entire list.\n*/\nstatic struct RowSetEntry *rowSetListToTree(struct RowSetEntry *pList){\n  int iDepth;           /* Depth of the tree so far */\n  struct RowSetEntry *p;       /* Current tree root */\n  struct RowSetEntry *pLeft;   /* Left subtree */\n\n  assert( pList!=0 );\n  p = pList;\n  pList = p->pRight;\n  p->pLeft = p->pRight = 0;\n  for(iDepth=1; pList; iDepth++){\n    pLeft = p;\n    p = pList;\n    pList = p->pRight;\n    p->pLeft = pLeft;\n    p->pRight = rowSetNDeepTree(&pList, iDepth);\n  }\n  return p;\n}\n\n/*\n** Extract the smallest element from the RowSet.\n** Write the element into *pRowid.  Return 1 on success.  Return\n** 0 if the RowSet is already empty.\n**\n** After this routine has been called, the sqlite3RowSetInsert()\n** routine may not be called again.\n**\n** This routine may not be called after sqlite3RowSetTest() has\n** been used.  Older versions of RowSet allowed that, but as the\n** capability was not used by the code generator, it was removed\n** for code economy.\n*/\nSQLITE_PRIVATE int sqlite3RowSetNext(RowSet *p, i64 *pRowid){\n  assert( p!=0 );\n  assert( p->pForest==0 );  /* Cannot be used with sqlite3RowSetText() */\n\n  /* Merge the forest into a single sorted list on first call */\n  if( (p->rsFlags & ROWSET_NEXT)==0 ){  /*OPTIMIZATION-IF-FALSE*/\n    if( (p->rsFlags & ROWSET_SORTED)==0 ){  /*OPTIMIZATION-IF-FALSE*/\n      p->pEntry = rowSetEntrySort(p->pEntry);\n    }\n    p->rsFlags |= ROWSET_SORTED|ROWSET_NEXT;\n  }\n\n  /* Return the next entry on the list */\n  if( p->pEntry ){\n    *pRowid = p->pEntry->v;\n    p->pEntry = p->pEntry->pRight;\n    if( p->pEntry==0 ){ /*OPTIMIZATION-IF-TRUE*/\n      /* Free memory immediately, rather than waiting on sqlite3_finalize() */\n      sqlite3RowSetClear(p);\n    }\n    return 1;\n  }else{\n    return 0;\n  }\n}\n\n/*\n** Check to see if element iRowid was inserted into the rowset as\n** part of any insert batch prior to iBatch.  Return 1 or 0.\n**\n** If this is the first test of a new batch and if there exist entries\n** on pRowSet->pEntry, then sort those entries into the forest at\n** pRowSet->pForest so that they can be tested.\n*/\nSQLITE_PRIVATE int sqlite3RowSetTest(RowSet *pRowSet, int iBatch, sqlite3_int64 iRowid){\n  struct RowSetEntry *p, *pTree;\n\n  /* This routine is never called after sqlite3RowSetNext() */\n  assert( pRowSet!=0 && (pRowSet->rsFlags & ROWSET_NEXT)==0 );\n\n  /* Sort entries into the forest on the first test of a new batch.\n  ** To save unnecessary work, only do this when the batch number changes.\n  */\n  if( iBatch!=pRowSet->iBatch ){  /*OPTIMIZATION-IF-FALSE*/\n    p = pRowSet->pEntry;\n    if( p ){\n      struct RowSetEntry **ppPrevTree = &pRowSet->pForest;\n      if( (pRowSet->rsFlags & ROWSET_SORTED)==0 ){ /*OPTIMIZATION-IF-FALSE*/\n        /* Only sort the current set of entiries if they need it */\n        p = rowSetEntrySort(p);\n      }\n      for(pTree = pRowSet->pForest; pTree; pTree=pTree->pRight){\n        ppPrevTree = &pTree->pRight;\n        if( pTree->pLeft==0 ){\n          pTree->pLeft = rowSetListToTree(p);\n          break;\n        }else{\n          struct RowSetEntry *pAux, *pTail;\n          rowSetTreeToList(pTree->pLeft, &pAux, &pTail);\n          pTree->pLeft = 0;\n          p = rowSetEntryMerge(pAux, p);\n        }\n      }\n      if( pTree==0 ){\n        *ppPrevTree = pTree = rowSetEntryAlloc(pRowSet);\n        if( pTree ){\n          pTree->v = 0;\n          pTree->pRight = 0;\n          pTree->pLeft = rowSetListToTree(p);\n        }\n      }\n      pRowSet->pEntry = 0;\n      pRowSet->pLast = 0;\n      pRowSet->rsFlags |= ROWSET_SORTED;\n    }\n    pRowSet->iBatch = iBatch;\n  }\n\n  /* Test to see if the iRowid value appears anywhere in the forest.\n  ** Return 1 if it does and 0 if not.\n  */\n  for(pTree = pRowSet->pForest; pTree; pTree=pTree->pRight){\n    p = pTree->pLeft;\n    while( p ){\n      if( p->v<iRowid ){\n        p = p->pRight;\n      }else if( p->v>iRowid ){\n        p = p->pLeft;\n      }else{\n        return 1;\n      }\n    }\n  }\n  return 0;\n}\n\n/************** End of rowset.c **********************************************/\n/************** Begin file pager.c *******************************************/\n/*\n** 2001 September 15\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n*************************************************************************\n** This is the implementation of the page cache subsystem or \"pager\".\n** \n** The pager is used to access a database disk file.  It implements\n** atomic commit and rollback through the use of a journal file that\n** is separate from the database file.  The pager also implements file\n** locking to prevent two processes from writing the same database\n** file simultaneously, or one process from reading the database while\n** another is writing.\n*/\n#ifndef SQLITE_OMIT_DISKIO\n/* #include \"sqliteInt.h\" */\n/************** Include wal.h in the middle of pager.c ***********************/\n/************** Begin file wal.h *********************************************/\n/*\n** 2010 February 1\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n*************************************************************************\n** This header file defines the interface to the write-ahead logging \n** system. Refer to the comments below and the header comment attached to \n** the implementation of each function in log.c for further details.\n*/\n\n#ifndef SQLITE_WAL_H\n#define SQLITE_WAL_H\n\n/* #include \"sqliteInt.h\" */\n\n/* Macros for extracting appropriate sync flags for either transaction\n** commits (WAL_SYNC_FLAGS(X)) or for checkpoint ops (CKPT_SYNC_FLAGS(X)):\n*/\n#define WAL_SYNC_FLAGS(X)   ((X)&0x03)\n#define CKPT_SYNC_FLAGS(X)  (((X)>>2)&0x03)\n\n#ifdef SQLITE_OMIT_WAL\n# define sqlite3WalOpen(x,y,z)                   0\n# define sqlite3WalLimit(x,y)\n# define sqlite3WalClose(v,w,x,y,z)              0\n# define sqlite3WalBeginReadTransaction(y,z)     0\n# define sqlite3WalEndReadTransaction(z)\n# define sqlite3WalDbsize(y)                     0\n# define sqlite3WalBeginWriteTransaction(y)      0\n# define sqlite3WalEndWriteTransaction(x)        0\n# define sqlite3WalUndo(x,y,z)                   0\n# define sqlite3WalSavepoint(y,z)\n# define sqlite3WalSavepointUndo(y,z)            0\n# define sqlite3WalFrames(u,v,w,x,y,z)           0\n# define sqlite3WalCheckpoint(q,r,s,t,u,v,w,x,y,z) 0\n# define sqlite3WalCallback(z)                   0\n# define sqlite3WalExclusiveMode(y,z)            0\n# define sqlite3WalHeapMemory(z)                 0\n# define sqlite3WalFramesize(z)                  0\n# define sqlite3WalFindFrame(x,y,z)              0\n# define sqlite3WalFile(x)                       0\n#else\n\n#define WAL_SAVEPOINT_NDATA 4\n\n/* Connection to a write-ahead log (WAL) file. \n** There is one object of this type for each pager. \n*/\ntypedef struct Wal Wal;\n\n/* Open and close a connection to a write-ahead log. */\nSQLITE_PRIVATE int sqlite3WalOpen(sqlite3_vfs*, sqlite3_file*, const char *, int, i64, Wal**);\nSQLITE_PRIVATE int sqlite3WalClose(Wal *pWal, sqlite3*, int sync_flags, int, u8 *);\n\n/* Set the limiting size of a WAL file. */\nSQLITE_PRIVATE void sqlite3WalLimit(Wal*, i64);\n\n/* Used by readers to open (lock) and close (unlock) a snapshot.  A \n** snapshot is like a read-transaction.  It is the state of the database\n** at an instant in time.  sqlite3WalOpenSnapshot gets a read lock and\n** preserves the current state even if the other threads or processes\n** write to or checkpoint the WAL.  sqlite3WalCloseSnapshot() closes the\n** transaction and releases the lock.\n*/\nSQLITE_PRIVATE int sqlite3WalBeginReadTransaction(Wal *pWal, int *);\nSQLITE_PRIVATE void sqlite3WalEndReadTransaction(Wal *pWal);\n\n/* Read a page from the write-ahead log, if it is present. */\nSQLITE_PRIVATE int sqlite3WalFindFrame(Wal *, Pgno, u32 *);\nSQLITE_PRIVATE int sqlite3WalReadFrame(Wal *, u32, int, u8 *);\n\n/* If the WAL is not empty, return the size of the database. */\nSQLITE_PRIVATE Pgno sqlite3WalDbsize(Wal *pWal);\n\n/* Obtain or release the WRITER lock. */\nSQLITE_PRIVATE int sqlite3WalBeginWriteTransaction(Wal *pWal);\nSQLITE_PRIVATE int sqlite3WalEndWriteTransaction(Wal *pWal);\n\n/* Undo any frames written (but not committed) to the log */\nSQLITE_PRIVATE int sqlite3WalUndo(Wal *pWal, int (*xUndo)(void *, Pgno), void *pUndoCtx);\n\n/* Return an integer that records the current (uncommitted) write\n** position in the WAL */\nSQLITE_PRIVATE void sqlite3WalSavepoint(Wal *pWal, u32 *aWalData);\n\n/* Move the write position of the WAL back to iFrame.  Called in\n** response to a ROLLBACK TO command. */\nSQLITE_PRIVATE int sqlite3WalSavepointUndo(Wal *pWal, u32 *aWalData);\n\n/* Write a frame or frames to the log. */\nSQLITE_PRIVATE int sqlite3WalFrames(Wal *pWal, int, PgHdr *, Pgno, int, int);\n\n/* Copy pages from the log to the database file */ \nSQLITE_PRIVATE int sqlite3WalCheckpoint(\n  Wal *pWal,                      /* Write-ahead log connection */\n  sqlite3 *db,                    /* Check this handle's interrupt flag */\n  int eMode,                      /* One of PASSIVE, FULL and RESTART */\n  int (*xBusy)(void*),            /* Function to call when busy */\n  void *pBusyArg,                 /* Context argument for xBusyHandler */\n  int sync_flags,                 /* Flags to sync db file with (or 0) */\n  int nBuf,                       /* Size of buffer nBuf */\n  u8 *zBuf,                       /* Temporary buffer to use */\n  int *pnLog,                     /* OUT: Number of frames in WAL */\n  int *pnCkpt                     /* OUT: Number of backfilled frames in WAL */\n);\n\n/* Return the value to pass to a sqlite3_wal_hook callback, the\n** number of frames in the WAL at the point of the last commit since\n** sqlite3WalCallback() was called.  If no commits have occurred since\n** the last call, then return 0.\n*/\nSQLITE_PRIVATE int sqlite3WalCallback(Wal *pWal);\n\n/* Tell the wal layer that an EXCLUSIVE lock has been obtained (or released)\n** by the pager layer on the database file.\n*/\nSQLITE_PRIVATE int sqlite3WalExclusiveMode(Wal *pWal, int op);\n\n/* Return true if the argument is non-NULL and the WAL module is using\n** heap-memory for the wal-index. Otherwise, if the argument is NULL or the\n** WAL module is using shared-memory, return false. \n*/\nSQLITE_PRIVATE int sqlite3WalHeapMemory(Wal *pWal);\n\n#ifdef SQLITE_ENABLE_SNAPSHOT\nSQLITE_PRIVATE int sqlite3WalSnapshotGet(Wal *pWal, sqlite3_snapshot **ppSnapshot);\nSQLITE_PRIVATE void sqlite3WalSnapshotOpen(Wal *pWal, sqlite3_snapshot *pSnapshot);\nSQLITE_PRIVATE int sqlite3WalSnapshotRecover(Wal *pWal);\n#endif\n\n#ifdef SQLITE_ENABLE_ZIPVFS\n/* If the WAL file is not empty, return the number of bytes of content\n** stored in each frame (i.e. the db page-size when the WAL was created).\n*/\nSQLITE_PRIVATE int sqlite3WalFramesize(Wal *pWal);\n#endif\n\n/* Return the sqlite3_file object for the WAL file */\nSQLITE_PRIVATE sqlite3_file *sqlite3WalFile(Wal *pWal);\n\n#endif /* ifndef SQLITE_OMIT_WAL */\n#endif /* SQLITE_WAL_H */\n\n/************** End of wal.h *************************************************/\n/************** Continuing where we left off in pager.c **********************/\n\n\n/******************* NOTES ON THE DESIGN OF THE PAGER ************************\n**\n** This comment block describes invariants that hold when using a rollback\n** journal.  These invariants do not apply for journal_mode=WAL,\n** journal_mode=MEMORY, or journal_mode=OFF.\n**\n** Within this comment block, a page is deemed to have been synced\n** automatically as soon as it is written when PRAGMA synchronous=OFF.\n** Otherwise, the page is not synced until the xSync method of the VFS\n** is called successfully on the file containing the page.\n**\n** Definition:  A page of the database file is said to be \"overwriteable\" if\n** one or more of the following are true about the page:\n** \n**     (a)  The original content of the page as it was at the beginning of\n**          the transaction has been written into the rollback journal and\n**          synced.\n** \n**     (b)  The page was a freelist leaf page at the start of the transaction.\n** \n**     (c)  The page number is greater than the largest page that existed in\n**          the database file at the start of the transaction.\n** \n** (1) A page of the database file is never overwritten unless one of the\n**     following are true:\n** \n**     (a) The page and all other pages on the same sector are overwriteable.\n** \n**     (b) The atomic page write optimization is enabled, and the entire\n**         transaction other than the update of the transaction sequence\n**         number consists of a single page change.\n** \n** (2) The content of a page written into the rollback journal exactly matches\n**     both the content in the database when the rollback journal was written\n**     and the content in the database at the beginning of the current\n**     transaction.\n** \n** (3) Writes to the database file are an integer multiple of the page size\n**     in length and are aligned on a page boundary.\n** \n** (4) Reads from the database file are either aligned on a page boundary and\n**     an integer multiple of the page size in length or are taken from the\n**     first 100 bytes of the database file.\n** \n** (5) All writes to the database file are synced prior to the rollback journal\n**     being deleted, truncated, or zeroed.\n** \n** (6) If a master journal file is used, then all writes to the database file\n**     are synced prior to the master journal being deleted.\n** \n** Definition: Two databases (or the same database at two points it time)\n** are said to be \"logically equivalent\" if they give the same answer to\n** all queries.  Note in particular the content of freelist leaf\n** pages can be changed arbitrarily without affecting the logical equivalence\n** of the database.\n** \n** (7) At any time, if any subset, including the empty set and the total set,\n**     of the unsynced changes to a rollback journal are removed and the \n**     journal is rolled back, the resulting database file will be logically\n**     equivalent to the database file at the beginning of the transaction.\n** \n** (8) When a transaction is rolled back, the xTruncate method of the VFS\n**     is called to restore the database file to the same size it was at\n**     the beginning of the transaction.  (In some VFSes, the xTruncate\n**     method is a no-op, but that does not change the fact the SQLite will\n**     invoke it.)\n** \n** (9) Whenever the database file is modified, at least one bit in the range\n**     of bytes from 24 through 39 inclusive will be changed prior to releasing\n**     the EXCLUSIVE lock, thus signaling other connections on the same\n**     database to flush their caches.\n**\n** (10) The pattern of bits in bytes 24 through 39 shall not repeat in less\n**      than one billion transactions.\n**\n** (11) A database file is well-formed at the beginning and at the conclusion\n**      of every transaction.\n**\n** (12) An EXCLUSIVE lock is held on the database file when writing to\n**      the database file.\n**\n** (13) A SHARED lock is held on the database file while reading any\n**      content out of the database file.\n**\n******************************************************************************/\n\n/*\n** Macros for troubleshooting.  Normally turned off\n*/\n#if 0\nint sqlite3PagerTrace=1;  /* True to enable tracing */\n#define sqlite3DebugPrintf printf\n#define PAGERTRACE(X)     if( sqlite3PagerTrace ){ sqlite3DebugPrintf X; }\n#else\n#define PAGERTRACE(X)\n#endif\n\n/*\n** The following two macros are used within the PAGERTRACE() macros above\n** to print out file-descriptors. \n**\n** PAGERID() takes a pointer to a Pager struct as its argument. The\n** associated file-descriptor is returned. FILEHANDLEID() takes an sqlite3_file\n** struct as its argument.\n*/\n#define PAGERID(p) (SQLITE_PTR_TO_INT(p->fd))\n#define FILEHANDLEID(fd) (SQLITE_PTR_TO_INT(fd))\n\n/*\n** The Pager.eState variable stores the current 'state' of a pager. A\n** pager may be in any one of the seven states shown in the following\n** state diagram.\n**\n**                            OPEN <------+------+\n**                              |         |      |\n**                              V         |      |\n**               +---------> READER-------+      |\n**               |              |                |\n**               |              V                |\n**               |<-------WRITER_LOCKED------> ERROR\n**               |              |                ^  \n**               |              V                |\n**               |<------WRITER_CACHEMOD-------->|\n**               |              |                |\n**               |              V                |\n**               |<-------WRITER_DBMOD---------->|\n**               |              |                |\n**               |              V                |\n**               +<------WRITER_FINISHED-------->+\n**\n**\n** List of state transitions and the C [function] that performs each:\n** \n**   OPEN              -> READER              [sqlite3PagerSharedLock]\n**   READER            -> OPEN                [pager_unlock]\n**\n**   READER            -> WRITER_LOCKED       [sqlite3PagerBegin]\n**   WRITER_LOCKED     -> WRITER_CACHEMOD     [pager_open_journal]\n**   WRITER_CACHEMOD   -> WRITER_DBMOD        [syncJournal]\n**   WRITER_DBMOD      -> WRITER_FINISHED     [sqlite3PagerCommitPhaseOne]\n**   WRITER_***        -> READER              [pager_end_transaction]\n**\n**   WRITER_***        -> ERROR               [pager_error]\n**   ERROR             -> OPEN                [pager_unlock]\n** \n**\n**  OPEN:\n**\n**    The pager starts up in this state. Nothing is guaranteed in this\n**    state - the file may or may not be locked and the database size is\n**    unknown. The database may not be read or written.\n**\n**    * No read or write transaction is active.\n**    * Any lock, or no lock at all, may be held on the database file.\n**    * The dbSize, dbOrigSize and dbFileSize variables may not be trusted.\n**\n**  READER:\n**\n**    In this state all the requirements for reading the database in \n**    rollback (non-WAL) mode are met. Unless the pager is (or recently\n**    was) in exclusive-locking mode, a user-level read transaction is \n**    open. The database size is known in this state.\n**\n**    A connection running with locking_mode=normal enters this state when\n**    it opens a read-transaction on the database and returns to state\n**    OPEN after the read-transaction is completed. However a connection\n**    running in locking_mode=exclusive (including temp databases) remains in\n**    this state even after the read-transaction is closed. The only way\n**    a locking_mode=exclusive connection can transition from READER to OPEN\n**    is via the ERROR state (see below).\n** \n**    * A read transaction may be active (but a write-transaction cannot).\n**    * A SHARED or greater lock is held on the database file.\n**    * The dbSize variable may be trusted (even if a user-level read \n**      transaction is not active). The dbOrigSize and dbFileSize variables\n**      may not be trusted at this point.\n**    * If the database is a WAL database, then the WAL connection is open.\n**    * Even if a read-transaction is not open, it is guaranteed that \n**      there is no hot-journal in the file-system.\n**\n**  WRITER_LOCKED:\n**\n**    The pager moves to this state from READER when a write-transaction\n**    is first opened on the database. In WRITER_LOCKED state, all locks \n**    required to start a write-transaction are held, but no actual \n**    modifications to the cache or database have taken place.\n**\n**    In rollback mode, a RESERVED or (if the transaction was opened with \n**    BEGIN EXCLUSIVE) EXCLUSIVE lock is obtained on the database file when\n**    moving to this state, but the journal file is not written to or opened \n**    to in this state. If the transaction is committed or rolled back while \n**    in WRITER_LOCKED state, all that is required is to unlock the database \n**    file.\n**\n**    IN WAL mode, WalBeginWriteTransaction() is called to lock the log file.\n**    If the connection is running with locking_mode=exclusive, an attempt\n**    is made to obtain an EXCLUSIVE lock on the database file.\n**\n**    * A write transaction is active.\n**    * If the connection is open in rollback-mode, a RESERVED or greater \n**      lock is held on the database file.\n**    * If the connection is open in WAL-mode, a WAL write transaction\n**      is open (i.e. sqlite3WalBeginWriteTransaction() has been successfully\n**      called).\n**    * The dbSize, dbOrigSize and dbFileSize variables are all valid.\n**    * The contents of the pager cache have not been modified.\n**    * The journal file may or may not be open.\n**    * Nothing (not even the first header) has been written to the journal.\n**\n**  WRITER_CACHEMOD:\n**\n**    A pager moves from WRITER_LOCKED state to this state when a page is\n**    first modified by the upper layer. In rollback mode the journal file\n**    is opened (if it is not already open) and a header written to the\n**    start of it. The database file on disk has not been modified.\n**\n**    * A write transaction is active.\n**    * A RESERVED or greater lock is held on the database file.\n**    * The journal file is open and the first header has been written \n**      to it, but the header has not been synced to disk.\n**    * The contents of the page cache have been modified.\n**\n**  WRITER_DBMOD:\n**\n**    The pager transitions from WRITER_CACHEMOD into WRITER_DBMOD state\n**    when it modifies the contents of the database file. WAL connections\n**    never enter this state (since they do not modify the database file,\n**    just the log file).\n**\n**    * A write transaction is active.\n**    * An EXCLUSIVE or greater lock is held on the database file.\n**    * The journal file is open and the first header has been written \n**      and synced to disk.\n**    * The contents of the page cache have been modified (and possibly\n**      written to disk).\n**\n**  WRITER_FINISHED:\n**\n**    It is not possible for a WAL connection to enter this state.\n**\n**    A rollback-mode pager changes to WRITER_FINISHED state from WRITER_DBMOD\n**    state after the entire transaction has been successfully written into the\n**    database file. In this state the transaction may be committed simply\n**    by finalizing the journal file. Once in WRITER_FINISHED state, it is \n**    not possible to modify the database further. At this point, the upper \n**    layer must either commit or rollback the transaction.\n**\n**    * A write transaction is active.\n**    * An EXCLUSIVE or greater lock is held on the database file.\n**    * All writing and syncing of journal and database data has finished.\n**      If no error occurred, all that remains is to finalize the journal to\n**      commit the transaction. If an error did occur, the caller will need\n**      to rollback the transaction. \n**\n**  ERROR:\n**\n**    The ERROR state is entered when an IO or disk-full error (including\n**    SQLITE_IOERR_NOMEM) occurs at a point in the code that makes it \n**    difficult to be sure that the in-memory pager state (cache contents, \n**    db size etc.) are consistent with the contents of the file-system.\n**\n**    Temporary pager files may enter the ERROR state, but in-memory pagers\n**    cannot.\n**\n**    For example, if an IO error occurs while performing a rollback, \n**    the contents of the page-cache may be left in an inconsistent state.\n**    At this point it would be dangerous to change back to READER state\n**    (as usually happens after a rollback). Any subsequent readers might\n**    report database corruption (due to the inconsistent cache), and if\n**    they upgrade to writers, they may inadvertently corrupt the database\n**    file. To avoid this hazard, the pager switches into the ERROR state\n**    instead of READER following such an error.\n**\n**    Once it has entered the ERROR state, any attempt to use the pager\n**    to read or write data returns an error. Eventually, once all \n**    outstanding transactions have been abandoned, the pager is able to\n**    transition back to OPEN state, discarding the contents of the \n**    page-cache and any other in-memory state at the same time. Everything\n**    is reloaded from disk (and, if necessary, hot-journal rollback peformed)\n**    when a read-transaction is next opened on the pager (transitioning\n**    the pager into READER state). At that point the system has recovered \n**    from the error.\n**\n**    Specifically, the pager jumps into the ERROR state if:\n**\n**      1. An error occurs while attempting a rollback. This happens in\n**         function sqlite3PagerRollback().\n**\n**      2. An error occurs while attempting to finalize a journal file\n**         following a commit in function sqlite3PagerCommitPhaseTwo().\n**\n**      3. An error occurs while attempting to write to the journal or\n**         database file in function pagerStress() in order to free up\n**         memory.\n**\n**    In other cases, the error is returned to the b-tree layer. The b-tree\n**    layer then attempts a rollback operation. If the error condition \n**    persists, the pager enters the ERROR state via condition (1) above.\n**\n**    Condition (3) is necessary because it can be triggered by a read-only\n**    statement executed within a transaction. In this case, if the error\n**    code were simply returned to the user, the b-tree layer would not\n**    automatically attempt a rollback, as it assumes that an error in a\n**    read-only statement cannot leave the pager in an internally inconsistent \n**    state.\n**\n**    * The Pager.errCode variable is set to something other than SQLITE_OK.\n**    * There are one or more outstanding references to pages (after the\n**      last reference is dropped the pager should move back to OPEN state).\n**    * The pager is not an in-memory pager.\n**    \n**\n** Notes:\n**\n**   * A pager is never in WRITER_DBMOD or WRITER_FINISHED state if the\n**     connection is open in WAL mode. A WAL connection is always in one\n**     of the first four states.\n**\n**   * Normally, a connection open in exclusive mode is never in PAGER_OPEN\n**     state. There are two exceptions: immediately after exclusive-mode has\n**     been turned on (and before any read or write transactions are \n**     executed), and when the pager is leaving the \"error state\".\n**\n**   * See also: assert_pager_state().\n*/\n#define PAGER_OPEN                  0\n#define PAGER_READER                1\n#define PAGER_WRITER_LOCKED         2\n#define PAGER_WRITER_CACHEMOD       3\n#define PAGER_WRITER_DBMOD          4\n#define PAGER_WRITER_FINISHED       5\n#define PAGER_ERROR                 6\n\n/*\n** The Pager.eLock variable is almost always set to one of the \n** following locking-states, according to the lock currently held on\n** the database file: NO_LOCK, SHARED_LOCK, RESERVED_LOCK or EXCLUSIVE_LOCK.\n** This variable is kept up to date as locks are taken and released by\n** the pagerLockDb() and pagerUnlockDb() wrappers.\n**\n** If the VFS xLock() or xUnlock() returns an error other than SQLITE_BUSY\n** (i.e. one of the SQLITE_IOERR subtypes), it is not clear whether or not\n** the operation was successful. In these circumstances pagerLockDb() and\n** pagerUnlockDb() take a conservative approach - eLock is always updated\n** when unlocking the file, and only updated when locking the file if the\n** VFS call is successful. This way, the Pager.eLock variable may be set\n** to a less exclusive (lower) value than the lock that is actually held\n** at the system level, but it is never set to a more exclusive value.\n**\n** This is usually safe. If an xUnlock fails or appears to fail, there may \n** be a few redundant xLock() calls or a lock may be held for longer than\n** required, but nothing really goes wrong.\n**\n** The exception is when the database file is unlocked as the pager moves\n** from ERROR to OPEN state. At this point there may be a hot-journal file \n** in the file-system that needs to be rolled back (as part of an OPEN->SHARED\n** transition, by the same pager or any other). If the call to xUnlock()\n** fails at this point and the pager is left holding an EXCLUSIVE lock, this\n** can confuse the call to xCheckReservedLock() call made later as part\n** of hot-journal detection.\n**\n** xCheckReservedLock() is defined as returning true \"if there is a RESERVED \n** lock held by this process or any others\". So xCheckReservedLock may \n** return true because the caller itself is holding an EXCLUSIVE lock (but\n** doesn't know it because of a previous error in xUnlock). If this happens\n** a hot-journal may be mistaken for a journal being created by an active\n** transaction in another process, causing SQLite to read from the database\n** without rolling it back.\n**\n** To work around this, if a call to xUnlock() fails when unlocking the\n** database in the ERROR state, Pager.eLock is set to UNKNOWN_LOCK. It\n** is only changed back to a real locking state after a successful call\n** to xLock(EXCLUSIVE). Also, the code to do the OPEN->SHARED state transition\n** omits the check for a hot-journal if Pager.eLock is set to UNKNOWN_LOCK \n** lock. Instead, it assumes a hot-journal exists and obtains an EXCLUSIVE\n** lock on the database file before attempting to roll it back. See function\n** PagerSharedLock() for more detail.\n**\n** Pager.eLock may only be set to UNKNOWN_LOCK when the pager is in \n** PAGER_OPEN state.\n*/\n#define UNKNOWN_LOCK                (EXCLUSIVE_LOCK+1)\n\n/*\n** A macro used for invoking the codec if there is one\n*/\n#ifdef SQLITE_HAS_CODEC\n# define CODEC1(P,D,N,X,E) \\\n    if( P->xCodec && P->xCodec(P->pCodec,D,N,X)==0 ){ E; }\n# define CODEC2(P,D,N,X,E,O) \\\n    if( P->xCodec==0 ){ O=(char*)D; }else \\\n    if( (O=(char*)(P->xCodec(P->pCodec,D,N,X)))==0 ){ E; }\n#else\n# define CODEC1(P,D,N,X,E)   /* NO-OP */\n# define CODEC2(P,D,N,X,E,O) O=(char*)D\n#endif\n\n/*\n** The maximum allowed sector size. 64KiB. If the xSectorsize() method \n** returns a value larger than this, then MAX_SECTOR_SIZE is used instead.\n** This could conceivably cause corruption following a power failure on\n** such a system. This is currently an undocumented limit.\n*/\n#define MAX_SECTOR_SIZE 0x10000\n\n\n/*\n** An instance of the following structure is allocated for each active\n** savepoint and statement transaction in the system. All such structures\n** are stored in the Pager.aSavepoint[] array, which is allocated and\n** resized using sqlite3Realloc().\n**\n** When a savepoint is created, the PagerSavepoint.iHdrOffset field is\n** set to 0. If a journal-header is written into the main journal while\n** the savepoint is active, then iHdrOffset is set to the byte offset \n** immediately following the last journal record written into the main\n** journal before the journal-header. This is required during savepoint\n** rollback (see pagerPlaybackSavepoint()).\n*/\ntypedef struct PagerSavepoint PagerSavepoint;\nstruct PagerSavepoint {\n  i64 iOffset;                 /* Starting offset in main journal */\n  i64 iHdrOffset;              /* See above */\n  Bitvec *pInSavepoint;        /* Set of pages in this savepoint */\n  Pgno nOrig;                  /* Original number of pages in file */\n  Pgno iSubRec;                /* Index of first record in sub-journal */\n#ifndef SQLITE_OMIT_WAL\n  u32 aWalData[WAL_SAVEPOINT_NDATA];        /* WAL savepoint context */\n#endif\n};\n\n/*\n** Bits of the Pager.doNotSpill flag.  See further description below.\n*/\n#define SPILLFLAG_OFF         0x01 /* Never spill cache.  Set via pragma */\n#define SPILLFLAG_ROLLBACK    0x02 /* Current rolling back, so do not spill */\n#define SPILLFLAG_NOSYNC      0x04 /* Spill is ok, but do not sync */\n\n/*\n** An open page cache is an instance of struct Pager. A description of\n** some of the more important member variables follows:\n**\n** eState\n**\n**   The current 'state' of the pager object. See the comment and state\n**   diagram above for a description of the pager state.\n**\n** eLock\n**\n**   For a real on-disk database, the current lock held on the database file -\n**   NO_LOCK, SHARED_LOCK, RESERVED_LOCK or EXCLUSIVE_LOCK.\n**\n**   For a temporary or in-memory database (neither of which require any\n**   locks), this variable is always set to EXCLUSIVE_LOCK. Since such\n**   databases always have Pager.exclusiveMode==1, this tricks the pager\n**   logic into thinking that it already has all the locks it will ever\n**   need (and no reason to release them).\n**\n**   In some (obscure) circumstances, this variable may also be set to\n**   UNKNOWN_LOCK. See the comment above the #define of UNKNOWN_LOCK for\n**   details.\n**\n** changeCountDone\n**\n**   This boolean variable is used to make sure that the change-counter \n**   (the 4-byte header field at byte offset 24 of the database file) is \n**   not updated more often than necessary. \n**\n**   It is set to true when the change-counter field is updated, which \n**   can only happen if an exclusive lock is held on the database file.\n**   It is cleared (set to false) whenever an exclusive lock is \n**   relinquished on the database file. Each time a transaction is committed,\n**   The changeCountDone flag is inspected. If it is true, the work of\n**   updating the change-counter is omitted for the current transaction.\n**\n**   This mechanism means that when running in exclusive mode, a connection \n**   need only update the change-counter once, for the first transaction\n**   committed.\n**\n** setMaster\n**\n**   When PagerCommitPhaseOne() is called to commit a transaction, it may\n**   (or may not) specify a master-journal name to be written into the \n**   journal file before it is synced to disk.\n**\n**   Whether or not a journal file contains a master-journal pointer affects \n**   the way in which the journal file is finalized after the transaction is \n**   committed or rolled back when running in \"journal_mode=PERSIST\" mode.\n**   If a journal file does not contain a master-journal pointer, it is\n**   finalized by overwriting the first journal header with zeroes. If\n**   it does contain a master-journal pointer the journal file is finalized \n**   by truncating it to zero bytes, just as if the connection were \n**   running in \"journal_mode=truncate\" mode.\n**\n**   Journal files that contain master journal pointers cannot be finalized\n**   simply by overwriting the first journal-header with zeroes, as the\n**   master journal pointer could interfere with hot-journal rollback of any\n**   subsequently interrupted transaction that reuses the journal file.\n**\n**   The flag is cleared as soon as the journal file is finalized (either\n**   by PagerCommitPhaseTwo or PagerRollback). If an IO error prevents the\n**   journal file from being successfully finalized, the setMaster flag\n**   is cleared anyway (and the pager will move to ERROR state).\n**\n** doNotSpill\n**\n**   This variables control the behavior of cache-spills  (calls made by\n**   the pcache module to the pagerStress() routine to write cached data\n**   to the file-system in order to free up memory).\n**\n**   When bits SPILLFLAG_OFF or SPILLFLAG_ROLLBACK of doNotSpill are set,\n**   writing to the database from pagerStress() is disabled altogether.\n**   The SPILLFLAG_ROLLBACK case is done in a very obscure case that\n**   comes up during savepoint rollback that requires the pcache module\n**   to allocate a new page to prevent the journal file from being written\n**   while it is being traversed by code in pager_playback().  The SPILLFLAG_OFF\n**   case is a user preference.\n** \n**   If the SPILLFLAG_NOSYNC bit is set, writing to the database from\n**   pagerStress() is permitted, but syncing the journal file is not.\n**   This flag is set by sqlite3PagerWrite() when the file-system sector-size\n**   is larger than the database page-size in order to prevent a journal sync\n**   from happening in between the journalling of two pages on the same sector. \n**\n** subjInMemory\n**\n**   This is a boolean variable. If true, then any required sub-journal\n**   is opened as an in-memory journal file. If false, then in-memory\n**   sub-journals are only used for in-memory pager files.\n**\n**   This variable is updated by the upper layer each time a new \n**   write-transaction is opened.\n**\n** dbSize, dbOrigSize, dbFileSize\n**\n**   Variable dbSize is set to the number of pages in the database file.\n**   It is valid in PAGER_READER and higher states (all states except for\n**   OPEN and ERROR). \n**\n**   dbSize is set based on the size of the database file, which may be \n**   larger than the size of the database (the value stored at offset\n**   28 of the database header by the btree). If the size of the file\n**   is not an integer multiple of the page-size, the value stored in\n**   dbSize is rounded down (i.e. a 5KB file with 2K page-size has dbSize==2).\n**   Except, any file that is greater than 0 bytes in size is considered\n**   to have at least one page. (i.e. a 1KB file with 2K page-size leads\n**   to dbSize==1).\n**\n**   During a write-transaction, if pages with page-numbers greater than\n**   dbSize are modified in the cache, dbSize is updated accordingly.\n**   Similarly, if the database is truncated using PagerTruncateImage(), \n**   dbSize is updated.\n**\n**   Variables dbOrigSize and dbFileSize are valid in states \n**   PAGER_WRITER_LOCKED and higher. dbOrigSize is a copy of the dbSize\n**   variable at the start of the transaction. It is used during rollback,\n**   and to determine whether or not pages need to be journalled before\n**   being modified.\n**\n**   Throughout a write-transaction, dbFileSize contains the size of\n**   the file on disk in pages. It is set to a copy of dbSize when the\n**   write-transaction is first opened, and updated when VFS calls are made\n**   to write or truncate the database file on disk. \n**\n**   The only reason the dbFileSize variable is required is to suppress \n**   unnecessary calls to xTruncate() after committing a transaction. If, \n**   when a transaction is committed, the dbFileSize variable indicates \n**   that the database file is larger than the database image (Pager.dbSize), \n**   pager_truncate() is called. The pager_truncate() call uses xFilesize()\n**   to measure the database file on disk, and then truncates it if required.\n**   dbFileSize is not used when rolling back a transaction. In this case\n**   pager_truncate() is called unconditionally (which means there may be\n**   a call to xFilesize() that is not strictly required). In either case,\n**   pager_truncate() may cause the file to become smaller or larger.\n**\n** dbHintSize\n**\n**   The dbHintSize variable is used to limit the number of calls made to\n**   the VFS xFileControl(FCNTL_SIZE_HINT) method. \n**\n**   dbHintSize is set to a copy of the dbSize variable when a\n**   write-transaction is opened (at the same time as dbFileSize and\n**   dbOrigSize). If the xFileControl(FCNTL_SIZE_HINT) method is called,\n**   dbHintSize is increased to the number of pages that correspond to the\n**   size-hint passed to the method call. See pager_write_pagelist() for \n**   details.\n**\n** errCode\n**\n**   The Pager.errCode variable is only ever used in PAGER_ERROR state. It\n**   is set to zero in all other states. In PAGER_ERROR state, Pager.errCode \n**   is always set to SQLITE_FULL, SQLITE_IOERR or one of the SQLITE_IOERR_XXX \n**   sub-codes.\n**\n** syncFlags, walSyncFlags\n**\n**   syncFlags is either SQLITE_SYNC_NORMAL (0x02) or SQLITE_SYNC_FULL (0x03).\n**   syncFlags is used for rollback mode.  walSyncFlags is used for WAL mode\n**   and contains the flags used to sync the checkpoint operations in the\n**   lower two bits, and sync flags used for transaction commits in the WAL\n**   file in bits 0x04 and 0x08.  In other words, to get the correct sync flags\n**   for checkpoint operations, use (walSyncFlags&0x03) and to get the correct\n**   sync flags for transaction commit, use ((walSyncFlags>>2)&0x03).  Note\n**   that with synchronous=NORMAL in WAL mode, transaction commit is not synced\n**   meaning that the 0x04 and 0x08 bits are both zero.\n*/\nstruct Pager {\n  sqlite3_vfs *pVfs;          /* OS functions to use for IO */\n  u8 exclusiveMode;           /* Boolean. True if locking_mode==EXCLUSIVE */\n  u8 journalMode;             /* One of the PAGER_JOURNALMODE_* values */\n  u8 useJournal;              /* Use a rollback journal on this file */\n  u8 noSync;                  /* Do not sync the journal if true */\n  u8 fullSync;                /* Do extra syncs of the journal for robustness */\n  u8 extraSync;               /* sync directory after journal delete */\n  u8 syncFlags;               /* SYNC_NORMAL or SYNC_FULL otherwise */\n  u8 walSyncFlags;            /* See description above */\n  u8 tempFile;                /* zFilename is a temporary or immutable file */\n  u8 noLock;                  /* Do not lock (except in WAL mode) */\n  u8 readOnly;                /* True for a read-only database */\n  u8 memDb;                   /* True to inhibit all file I/O */\n\n  /**************************************************************************\n  ** The following block contains those class members that change during\n  ** routine operation.  Class members not in this block are either fixed\n  ** when the pager is first created or else only change when there is a\n  ** significant mode change (such as changing the page_size, locking_mode,\n  ** or the journal_mode).  From another view, these class members describe\n  ** the \"state\" of the pager, while other class members describe the\n  ** \"configuration\" of the pager.\n  */\n  u8 eState;                  /* Pager state (OPEN, READER, WRITER_LOCKED..) */\n  u8 eLock;                   /* Current lock held on database file */\n  u8 changeCountDone;         /* Set after incrementing the change-counter */\n  u8 setMaster;               /* True if a m-j name has been written to jrnl */\n  u8 doNotSpill;              /* Do not spill the cache when non-zero */\n  u8 subjInMemory;            /* True to use in-memory sub-journals */\n  u8 bUseFetch;               /* True to use xFetch() */\n  u8 hasHeldSharedLock;       /* True if a shared lock has ever been held */\n  Pgno dbSize;                /* Number of pages in the database */\n  Pgno dbOrigSize;            /* dbSize before the current transaction */\n  Pgno dbFileSize;            /* Number of pages in the database file */\n  Pgno dbHintSize;            /* Value passed to FCNTL_SIZE_HINT call */\n  int errCode;                /* One of several kinds of errors */\n  int nRec;                   /* Pages journalled since last j-header written */\n  u32 cksumInit;              /* Quasi-random value added to every checksum */\n  u32 nSubRec;                /* Number of records written to sub-journal */\n  Bitvec *pInJournal;         /* One bit for each page in the database file */\n  sqlite3_file *fd;           /* File descriptor for database */\n  sqlite3_file *jfd;          /* File descriptor for main journal */\n  sqlite3_file *sjfd;         /* File descriptor for sub-journal */\n  i64 journalOff;             /* Current write offset in the journal file */\n  i64 journalHdr;             /* Byte offset to previous journal header */\n  sqlite3_backup *pBackup;    /* Pointer to list of ongoing backup processes */\n  PagerSavepoint *aSavepoint; /* Array of active savepoints */\n  int nSavepoint;             /* Number of elements in aSavepoint[] */\n  u32 iDataVersion;           /* Changes whenever database content changes */\n  char dbFileVers[16];        /* Changes whenever database file changes */\n\n  int nMmapOut;               /* Number of mmap pages currently outstanding */\n  sqlite3_int64 szMmap;       /* Desired maximum mmap size */\n  PgHdr *pMmapFreelist;       /* List of free mmap page headers (pDirty) */\n  /*\n  ** End of the routinely-changing class members\n  ***************************************************************************/\n\n  u16 nExtra;                 /* Add this many bytes to each in-memory page */\n  i16 nReserve;               /* Number of unused bytes at end of each page */\n  u32 vfsFlags;               /* Flags for sqlite3_vfs.xOpen() */\n  u32 sectorSize;             /* Assumed sector size during rollback */\n  int pageSize;               /* Number of bytes in a page */\n  Pgno mxPgno;                /* Maximum allowed size of the database */\n  i64 journalSizeLimit;       /* Size limit for persistent journal files */\n  char *zFilename;            /* Name of the database file */\n  char *zJournal;             /* Name of the journal file */\n  int (*xBusyHandler)(void*); /* Function to call when busy */\n  void *pBusyHandlerArg;      /* Context argument for xBusyHandler */\n  int aStat[3];               /* Total cache hits, misses and writes */\n#ifdef SQLITE_TEST\n  int nRead;                  /* Database pages read */\n#endif\n  void (*xReiniter)(DbPage*); /* Call this routine when reloading pages */\n  int (*xGet)(Pager*,Pgno,DbPage**,int); /* Routine to fetch a patch */\n#ifdef SQLITE_HAS_CODEC\n  void *(*xCodec)(void*,void*,Pgno,int); /* Routine for en/decoding data */\n  void (*xCodecSizeChng)(void*,int,int); /* Notify of page size changes */\n  void (*xCodecFree)(void*);             /* Destructor for the codec */\n  void *pCodec;               /* First argument to xCodec... methods */\n#endif\n  char *pTmpSpace;            /* Pager.pageSize bytes of space for tmp use */\n  PCache *pPCache;            /* Pointer to page cache object */\n#ifndef SQLITE_OMIT_WAL\n  Wal *pWal;                  /* Write-ahead log used by \"journal_mode=wal\" */\n  char *zWal;                 /* File name for write-ahead log */\n#endif\n};\n\n/*\n** Indexes for use with Pager.aStat[]. The Pager.aStat[] array contains\n** the values accessed by passing SQLITE_DBSTATUS_CACHE_HIT, CACHE_MISS \n** or CACHE_WRITE to sqlite3_db_status().\n*/\n#define PAGER_STAT_HIT   0\n#define PAGER_STAT_MISS  1\n#define PAGER_STAT_WRITE 2\n\n/*\n** The following global variables hold counters used for\n** testing purposes only.  These variables do not exist in\n** a non-testing build.  These variables are not thread-safe.\n*/\n#ifdef SQLITE_TEST\nSQLITE_API int sqlite3_pager_readdb_count = 0;    /* Number of full pages read from DB */\nSQLITE_API int sqlite3_pager_writedb_count = 0;   /* Number of full pages written to DB */\nSQLITE_API int sqlite3_pager_writej_count = 0;    /* Number of pages written to journal */\n# define PAGER_INCR(v)  v++\n#else\n# define PAGER_INCR(v)\n#endif\n\n\n\n/*\n** Journal files begin with the following magic string.  The data\n** was obtained from /dev/random.  It is used only as a sanity check.\n**\n** Since version 2.8.0, the journal format contains additional sanity\n** checking information.  If the power fails while the journal is being\n** written, semi-random garbage data might appear in the journal\n** file after power is restored.  If an attempt is then made\n** to roll the journal back, the database could be corrupted.  The additional\n** sanity checking data is an attempt to discover the garbage in the\n** journal and ignore it.\n**\n** The sanity checking information for the new journal format consists\n** of a 32-bit checksum on each page of data.  The checksum covers both\n** the page number and the pPager->pageSize bytes of data for the page.\n** This cksum is initialized to a 32-bit random value that appears in the\n** journal file right after the header.  The random initializer is important,\n** because garbage data that appears at the end of a journal is likely\n** data that was once in other files that have now been deleted.  If the\n** garbage data came from an obsolete journal file, the checksums might\n** be correct.  But by initializing the checksum to random value which\n** is different for every journal, we minimize that risk.\n*/\nstatic const unsigned char aJournalMagic[] = {\n  0xd9, 0xd5, 0x05, 0xf9, 0x20, 0xa1, 0x63, 0xd7,\n};\n\n/*\n** The size of the of each page record in the journal is given by\n** the following macro.\n*/\n#define JOURNAL_PG_SZ(pPager)  ((pPager->pageSize) + 8)\n\n/*\n** The journal header size for this pager. This is usually the same \n** size as a single disk sector. See also setSectorSize().\n*/\n#define JOURNAL_HDR_SZ(pPager) (pPager->sectorSize)\n\n/*\n** The macro MEMDB is true if we are dealing with an in-memory database.\n** We do this as a macro so that if the SQLITE_OMIT_MEMORYDB macro is set,\n** the value of MEMDB will be a constant and the compiler will optimize\n** out code that would never execute.\n*/\n#ifdef SQLITE_OMIT_MEMORYDB\n# define MEMDB 0\n#else\n# define MEMDB pPager->memDb\n#endif\n\n/*\n** The macro USEFETCH is true if we are allowed to use the xFetch and xUnfetch\n** interfaces to access the database using memory-mapped I/O.\n*/\n#if SQLITE_MAX_MMAP_SIZE>0\n# define USEFETCH(x) ((x)->bUseFetch)\n#else\n# define USEFETCH(x) 0\n#endif\n\n/*\n** The maximum legal page number is (2^31 - 1).\n*/\n#define PAGER_MAX_PGNO 2147483647\n\n/*\n** The argument to this macro is a file descriptor (type sqlite3_file*).\n** Return 0 if it is not open, or non-zero (but not 1) if it is.\n**\n** This is so that expressions can be written as:\n**\n**   if( isOpen(pPager->jfd) ){ ...\n**\n** instead of\n**\n**   if( pPager->jfd->pMethods ){ ...\n*/\n#define isOpen(pFd) ((pFd)->pMethods!=0)\n\n/*\n** Return true if this pager uses a write-ahead log to read page pgno.\n** Return false if the pager reads pgno directly from the database.\n*/\n#if !defined(SQLITE_OMIT_WAL) && defined(SQLITE_DIRECT_OVERFLOW_READ)\nSQLITE_PRIVATE int sqlite3PagerUseWal(Pager *pPager, Pgno pgno){\n  u32 iRead = 0;\n  int rc;\n  if( pPager->pWal==0 ) return 0;\n  rc = sqlite3WalFindFrame(pPager->pWal, pgno, &iRead);\n  return rc || iRead;\n}\n#endif\n#ifndef SQLITE_OMIT_WAL\n# define pagerUseWal(x) ((x)->pWal!=0)\n#else\n# define pagerUseWal(x) 0\n# define pagerRollbackWal(x) 0\n# define pagerWalFrames(v,w,x,y) 0\n# define pagerOpenWalIfPresent(z) SQLITE_OK\n# define pagerBeginReadTransaction(z) SQLITE_OK\n#endif\n\n#ifndef NDEBUG \n/*\n** Usage:\n**\n**   assert( assert_pager_state(pPager) );\n**\n** This function runs many asserts to try to find inconsistencies in\n** the internal state of the Pager object.\n*/\nstatic int assert_pager_state(Pager *p){\n  Pager *pPager = p;\n\n  /* State must be valid. */\n  assert( p->eState==PAGER_OPEN\n       || p->eState==PAGER_READER\n       || p->eState==PAGER_WRITER_LOCKED\n       || p->eState==PAGER_WRITER_CACHEMOD\n       || p->eState==PAGER_WRITER_DBMOD\n       || p->eState==PAGER_WRITER_FINISHED\n       || p->eState==PAGER_ERROR\n  );\n\n  /* Regardless of the current state, a temp-file connection always behaves\n  ** as if it has an exclusive lock on the database file. It never updates\n  ** the change-counter field, so the changeCountDone flag is always set.\n  */\n  assert( p->tempFile==0 || p->eLock==EXCLUSIVE_LOCK );\n  assert( p->tempFile==0 || pPager->changeCountDone );\n\n  /* If the useJournal flag is clear, the journal-mode must be \"OFF\". \n  ** And if the journal-mode is \"OFF\", the journal file must not be open.\n  */\n  assert( p->journalMode==PAGER_JOURNALMODE_OFF || p->useJournal );\n  assert( p->journalMode!=PAGER_JOURNALMODE_OFF || !isOpen(p->jfd) );\n\n  /* Check that MEMDB implies noSync. And an in-memory journal. Since \n  ** this means an in-memory pager performs no IO at all, it cannot encounter \n  ** either SQLITE_IOERR or SQLITE_FULL during rollback or while finalizing \n  ** a journal file. (although the in-memory journal implementation may \n  ** return SQLITE_IOERR_NOMEM while the journal file is being written). It \n  ** is therefore not possible for an in-memory pager to enter the ERROR \n  ** state.\n  */\n  if( MEMDB ){\n    assert( !isOpen(p->fd) );\n    assert( p->noSync );\n    assert( p->journalMode==PAGER_JOURNALMODE_OFF \n         || p->journalMode==PAGER_JOURNALMODE_MEMORY \n    );\n    assert( p->eState!=PAGER_ERROR && p->eState!=PAGER_OPEN );\n    assert( pagerUseWal(p)==0 );\n  }\n\n  /* If changeCountDone is set, a RESERVED lock or greater must be held\n  ** on the file.\n  */\n  assert( pPager->changeCountDone==0 || pPager->eLock>=RESERVED_LOCK );\n  assert( p->eLock!=PENDING_LOCK );\n\n  switch( p->eState ){\n    case PAGER_OPEN:\n      assert( !MEMDB );\n      assert( pPager->errCode==SQLITE_OK );\n      assert( sqlite3PcacheRefCount(pPager->pPCache)==0 || pPager->tempFile );\n      break;\n\n    case PAGER_READER:\n      assert( pPager->errCode==SQLITE_OK );\n      assert( p->eLock!=UNKNOWN_LOCK );\n      assert( p->eLock>=SHARED_LOCK );\n      break;\n\n    case PAGER_WRITER_LOCKED:\n      assert( p->eLock!=UNKNOWN_LOCK );\n      assert( pPager->errCode==SQLITE_OK );\n      if( !pagerUseWal(pPager) ){\n        assert( p->eLock>=RESERVED_LOCK );\n      }\n      assert( pPager->dbSize==pPager->dbOrigSize );\n      assert( pPager->dbOrigSize==pPager->dbFileSize );\n      assert( pPager->dbOrigSize==pPager->dbHintSize );\n      assert( pPager->setMaster==0 );\n      break;\n\n    case PAGER_WRITER_CACHEMOD:\n      assert( p->eLock!=UNKNOWN_LOCK );\n      assert( pPager->errCode==SQLITE_OK );\n      if( !pagerUseWal(pPager) ){\n        /* It is possible that if journal_mode=wal here that neither the\n        ** journal file nor the WAL file are open. This happens during\n        ** a rollback transaction that switches from journal_mode=off\n        ** to journal_mode=wal.\n        */\n        assert( p->eLock>=RESERVED_LOCK );\n        assert( isOpen(p->jfd) \n             || p->journalMode==PAGER_JOURNALMODE_OFF \n             || p->journalMode==PAGER_JOURNALMODE_WAL \n        );\n      }\n      assert( pPager->dbOrigSize==pPager->dbFileSize );\n      assert( pPager->dbOrigSize==pPager->dbHintSize );\n      break;\n\n    case PAGER_WRITER_DBMOD:\n      assert( p->eLock==EXCLUSIVE_LOCK );\n      assert( pPager->errCode==SQLITE_OK );\n      assert( !pagerUseWal(pPager) );\n      assert( p->eLock>=EXCLUSIVE_LOCK );\n      assert( isOpen(p->jfd) \n           || p->journalMode==PAGER_JOURNALMODE_OFF \n           || p->journalMode==PAGER_JOURNALMODE_WAL \n           || (sqlite3OsDeviceCharacteristics(p->fd)&SQLITE_IOCAP_BATCH_ATOMIC)\n      );\n      assert( pPager->dbOrigSize<=pPager->dbHintSize );\n      break;\n\n    case PAGER_WRITER_FINISHED:\n      assert( p->eLock==EXCLUSIVE_LOCK );\n      assert( pPager->errCode==SQLITE_OK );\n      assert( !pagerUseWal(pPager) );\n      assert( isOpen(p->jfd) \n           || p->journalMode==PAGER_JOURNALMODE_OFF \n           || p->journalMode==PAGER_JOURNALMODE_WAL \n           || (sqlite3OsDeviceCharacteristics(p->fd)&SQLITE_IOCAP_BATCH_ATOMIC)\n      );\n      break;\n\n    case PAGER_ERROR:\n      /* There must be at least one outstanding reference to the pager if\n      ** in ERROR state. Otherwise the pager should have already dropped\n      ** back to OPEN state.\n      */\n      assert( pPager->errCode!=SQLITE_OK );\n      assert( sqlite3PcacheRefCount(pPager->pPCache)>0 || pPager->tempFile );\n      break;\n  }\n\n  return 1;\n}\n#endif /* ifndef NDEBUG */\n\n#ifdef SQLITE_DEBUG \n/*\n** Return a pointer to a human readable string in a static buffer\n** containing the state of the Pager object passed as an argument. This\n** is intended to be used within debuggers. For example, as an alternative\n** to \"print *pPager\" in gdb:\n**\n** (gdb) printf \"%s\", print_pager_state(pPager)\n*/\nstatic char *print_pager_state(Pager *p){\n  static char zRet[1024];\n\n  sqlite3_snprintf(1024, zRet,\n      \"Filename:      %s\\n\"\n      \"State:         %s errCode=%d\\n\"\n      \"Lock:          %s\\n\"\n      \"Locking mode:  locking_mode=%s\\n\"\n      \"Journal mode:  journal_mode=%s\\n\"\n      \"Backing store: tempFile=%d memDb=%d useJournal=%d\\n\"\n      \"Journal:       journalOff=%lld journalHdr=%lld\\n\"\n      \"Size:          dbsize=%d dbOrigSize=%d dbFileSize=%d\\n\"\n      , p->zFilename\n      , p->eState==PAGER_OPEN            ? \"OPEN\" :\n        p->eState==PAGER_READER          ? \"READER\" :\n        p->eState==PAGER_WRITER_LOCKED   ? \"WRITER_LOCKED\" :\n        p->eState==PAGER_WRITER_CACHEMOD ? \"WRITER_CACHEMOD\" :\n        p->eState==PAGER_WRITER_DBMOD    ? \"WRITER_DBMOD\" :\n        p->eState==PAGER_WRITER_FINISHED ? \"WRITER_FINISHED\" :\n        p->eState==PAGER_ERROR           ? \"ERROR\" : \"?error?\"\n      , (int)p->errCode\n      , p->eLock==NO_LOCK         ? \"NO_LOCK\" :\n        p->eLock==RESERVED_LOCK   ? \"RESERVED\" :\n        p->eLock==EXCLUSIVE_LOCK  ? \"EXCLUSIVE\" :\n        p->eLock==SHARED_LOCK     ? \"SHARED\" :\n        p->eLock==UNKNOWN_LOCK    ? \"UNKNOWN\" : \"?error?\"\n      , p->exclusiveMode ? \"exclusive\" : \"normal\"\n      , p->journalMode==PAGER_JOURNALMODE_MEMORY   ? \"memory\" :\n        p->journalMode==PAGER_JOURNALMODE_OFF      ? \"off\" :\n        p->journalMode==PAGER_JOURNALMODE_DELETE   ? \"delete\" :\n        p->journalMode==PAGER_JOURNALMODE_PERSIST  ? \"persist\" :\n        p->journalMode==PAGER_JOURNALMODE_TRUNCATE ? \"truncate\" :\n        p->journalMode==PAGER_JOURNALMODE_WAL      ? \"wal\" : \"?error?\"\n      , (int)p->tempFile, (int)p->memDb, (int)p->useJournal\n      , p->journalOff, p->journalHdr\n      , (int)p->dbSize, (int)p->dbOrigSize, (int)p->dbFileSize\n  );\n\n  return zRet;\n}\n#endif\n\n/* Forward references to the various page getters */\nstatic int getPageNormal(Pager*,Pgno,DbPage**,int);\nstatic int getPageError(Pager*,Pgno,DbPage**,int);\n#if SQLITE_MAX_MMAP_SIZE>0\nstatic int getPageMMap(Pager*,Pgno,DbPage**,int);\n#endif\n\n/*\n** Set the Pager.xGet method for the appropriate routine used to fetch\n** content from the pager.\n*/\nstatic void setGetterMethod(Pager *pPager){\n  if( pPager->errCode ){\n    pPager->xGet = getPageError;\n#if SQLITE_MAX_MMAP_SIZE>0\n  }else if( USEFETCH(pPager)\n#ifdef SQLITE_HAS_CODEC\n   && pPager->xCodec==0\n#endif\n  ){\n    pPager->xGet = getPageMMap;\n#endif /* SQLITE_MAX_MMAP_SIZE>0 */\n  }else{\n    pPager->xGet = getPageNormal;\n  }\n}\n\n/*\n** Return true if it is necessary to write page *pPg into the sub-journal.\n** A page needs to be written into the sub-journal if there exists one\n** or more open savepoints for which:\n**\n**   * The page-number is less than or equal to PagerSavepoint.nOrig, and\n**   * The bit corresponding to the page-number is not set in\n**     PagerSavepoint.pInSavepoint.\n*/\nstatic int subjRequiresPage(PgHdr *pPg){\n  Pager *pPager = pPg->pPager;\n  PagerSavepoint *p;\n  Pgno pgno = pPg->pgno;\n  int i;\n  for(i=0; i<pPager->nSavepoint; i++){\n    p = &pPager->aSavepoint[i];\n    if( p->nOrig>=pgno && 0==sqlite3BitvecTestNotNull(p->pInSavepoint, pgno) ){\n      return 1;\n    }\n  }\n  return 0;\n}\n\n#ifdef SQLITE_DEBUG\n/*\n** Return true if the page is already in the journal file.\n*/\nstatic int pageInJournal(Pager *pPager, PgHdr *pPg){\n  return sqlite3BitvecTest(pPager->pInJournal, pPg->pgno);\n}\n#endif\n\n/*\n** Read a 32-bit integer from the given file descriptor.  Store the integer\n** that is read in *pRes.  Return SQLITE_OK if everything worked, or an\n** error code is something goes wrong.\n**\n** All values are stored on disk as big-endian.\n*/\nstatic int read32bits(sqlite3_file *fd, i64 offset, u32 *pRes){\n  unsigned char ac[4];\n  int rc = sqlite3OsRead(fd, ac, sizeof(ac), offset);\n  if( rc==SQLITE_OK ){\n    *pRes = sqlite3Get4byte(ac);\n  }\n  return rc;\n}\n\n/*\n** Write a 32-bit integer into a string buffer in big-endian byte order.\n*/\n#define put32bits(A,B)  sqlite3Put4byte((u8*)A,B)\n\n\n/*\n** Write a 32-bit integer into the given file descriptor.  Return SQLITE_OK\n** on success or an error code is something goes wrong.\n*/\nstatic int write32bits(sqlite3_file *fd, i64 offset, u32 val){\n  char ac[4];\n  put32bits(ac, val);\n  return sqlite3OsWrite(fd, ac, 4, offset);\n}\n\n/*\n** Unlock the database file to level eLock, which must be either NO_LOCK\n** or SHARED_LOCK. Regardless of whether or not the call to xUnlock()\n** succeeds, set the Pager.eLock variable to match the (attempted) new lock.\n**\n** Except, if Pager.eLock is set to UNKNOWN_LOCK when this function is\n** called, do not modify it. See the comment above the #define of \n** UNKNOWN_LOCK for an explanation of this.\n*/\nstatic int pagerUnlockDb(Pager *pPager, int eLock){\n  int rc = SQLITE_OK;\n\n  assert( !pPager->exclusiveMode || pPager->eLock==eLock );\n  assert( eLock==NO_LOCK || eLock==SHARED_LOCK );\n  assert( eLock!=NO_LOCK || pagerUseWal(pPager)==0 );\n  if( isOpen(pPager->fd) ){\n    assert( pPager->eLock>=eLock );\n    rc = pPager->noLock ? SQLITE_OK : sqlite3OsUnlock(pPager->fd, eLock);\n    if( pPager->eLock!=UNKNOWN_LOCK ){\n      pPager->eLock = (u8)eLock;\n    }\n    IOTRACE((\"UNLOCK %p %d\\n\", pPager, eLock))\n  }\n  return rc;\n}\n\n/*\n** Lock the database file to level eLock, which must be either SHARED_LOCK,\n** RESERVED_LOCK or EXCLUSIVE_LOCK. If the caller is successful, set the\n** Pager.eLock variable to the new locking state. \n**\n** Except, if Pager.eLock is set to UNKNOWN_LOCK when this function is \n** called, do not modify it unless the new locking state is EXCLUSIVE_LOCK. \n** See the comment above the #define of UNKNOWN_LOCK for an explanation \n** of this.\n*/\nstatic int pagerLockDb(Pager *pPager, int eLock){\n  int rc = SQLITE_OK;\n\n  assert( eLock==SHARED_LOCK || eLock==RESERVED_LOCK || eLock==EXCLUSIVE_LOCK );\n  if( pPager->eLock<eLock || pPager->eLock==UNKNOWN_LOCK ){\n    rc = pPager->noLock ? SQLITE_OK : sqlite3OsLock(pPager->fd, eLock);\n    if( rc==SQLITE_OK && (pPager->eLock!=UNKNOWN_LOCK||eLock==EXCLUSIVE_LOCK) ){\n      pPager->eLock = (u8)eLock;\n      IOTRACE((\"LOCK %p %d\\n\", pPager, eLock))\n    }\n  }\n  return rc;\n}\n\n/*\n** This function determines whether or not the atomic-write or\n** atomic-batch-write optimizations can be used with this pager. The\n** atomic-write optimization can be used if:\n**\n**  (a) the value returned by OsDeviceCharacteristics() indicates that\n**      a database page may be written atomically, and\n**  (b) the value returned by OsSectorSize() is less than or equal\n**      to the page size.\n**\n** If it can be used, then the value returned is the size of the journal \n** file when it contains rollback data for exactly one page.\n**\n** The atomic-batch-write optimization can be used if OsDeviceCharacteristics()\n** returns a value with the SQLITE_IOCAP_BATCH_ATOMIC bit set. -1 is\n** returned in this case.\n**\n** If neither optimization can be used, 0 is returned.\n*/\nstatic int jrnlBufferSize(Pager *pPager){\n  assert( !MEMDB );\n\n#if defined(SQLITE_ENABLE_ATOMIC_WRITE) \\\n || defined(SQLITE_ENABLE_BATCH_ATOMIC_WRITE)\n  int dc;                           /* Device characteristics */\n\n  assert( isOpen(pPager->fd) );\n  dc = sqlite3OsDeviceCharacteristics(pPager->fd);\n#else\n  UNUSED_PARAMETER(pPager);\n#endif\n\n#ifdef SQLITE_ENABLE_BATCH_ATOMIC_WRITE\n  if( pPager->dbSize>0 && (dc&SQLITE_IOCAP_BATCH_ATOMIC) ){\n    return -1;\n  }\n#endif\n\n#ifdef SQLITE_ENABLE_ATOMIC_WRITE\n  {\n    int nSector = pPager->sectorSize;\n    int szPage = pPager->pageSize;\n\n    assert(SQLITE_IOCAP_ATOMIC512==(512>>8));\n    assert(SQLITE_IOCAP_ATOMIC64K==(65536>>8));\n    if( 0==(dc&(SQLITE_IOCAP_ATOMIC|(szPage>>8)) || nSector>szPage) ){\n      return 0;\n    }\n  }\n\n  return JOURNAL_HDR_SZ(pPager) + JOURNAL_PG_SZ(pPager);\n#endif\n\n  return 0;\n}\n\n/*\n** If SQLITE_CHECK_PAGES is defined then we do some sanity checking\n** on the cache using a hash function.  This is used for testing\n** and debugging only.\n*/\n#ifdef SQLITE_CHECK_PAGES\n/*\n** Return a 32-bit hash of the page data for pPage.\n*/\nstatic u32 pager_datahash(int nByte, unsigned char *pData){\n  u32 hash = 0;\n  int i;\n  for(i=0; i<nByte; i++){\n    hash = (hash*1039) + pData[i];\n  }\n  return hash;\n}\nstatic u32 pager_pagehash(PgHdr *pPage){\n  return pager_datahash(pPage->pPager->pageSize, (unsigned char *)pPage->pData);\n}\nstatic void pager_set_pagehash(PgHdr *pPage){\n  pPage->pageHash = pager_pagehash(pPage);\n}\n\n/*\n** The CHECK_PAGE macro takes a PgHdr* as an argument. If SQLITE_CHECK_PAGES\n** is defined, and NDEBUG is not defined, an assert() statement checks\n** that the page is either dirty or still matches the calculated page-hash.\n*/\n#define CHECK_PAGE(x) checkPage(x)\nstatic void checkPage(PgHdr *pPg){\n  Pager *pPager = pPg->pPager;\n  assert( pPager->eState!=PAGER_ERROR );\n  assert( (pPg->flags&PGHDR_DIRTY) || pPg->pageHash==pager_pagehash(pPg) );\n}\n\n#else\n#define pager_datahash(X,Y)  0\n#define pager_pagehash(X)  0\n#define pager_set_pagehash(X)\n#define CHECK_PAGE(x)\n#endif  /* SQLITE_CHECK_PAGES */\n\n/*\n** When this is called the journal file for pager pPager must be open.\n** This function attempts to read a master journal file name from the \n** end of the file and, if successful, copies it into memory supplied \n** by the caller. See comments above writeMasterJournal() for the format\n** used to store a master journal file name at the end of a journal file.\n**\n** zMaster must point to a buffer of at least nMaster bytes allocated by\n** the caller. This should be sqlite3_vfs.mxPathname+1 (to ensure there is\n** enough space to write the master journal name). If the master journal\n** name in the journal is longer than nMaster bytes (including a\n** nul-terminator), then this is handled as if no master journal name\n** were present in the journal.\n**\n** If a master journal file name is present at the end of the journal\n** file, then it is copied into the buffer pointed to by zMaster. A\n** nul-terminator byte is appended to the buffer following the master\n** journal file name.\n**\n** If it is determined that no master journal file name is present \n** zMaster[0] is set to 0 and SQLITE_OK returned.\n**\n** If an error occurs while reading from the journal file, an SQLite\n** error code is returned.\n*/\nstatic int readMasterJournal(sqlite3_file *pJrnl, char *zMaster, u32 nMaster){\n  int rc;                    /* Return code */\n  u32 len;                   /* Length in bytes of master journal name */\n  i64 szJ;                   /* Total size in bytes of journal file pJrnl */\n  u32 cksum;                 /* MJ checksum value read from journal */\n  u32 u;                     /* Unsigned loop counter */\n  unsigned char aMagic[8];   /* A buffer to hold the magic header */\n  zMaster[0] = '\\0';\n\n  if( SQLITE_OK!=(rc = sqlite3OsFileSize(pJrnl, &szJ))\n   || szJ<16\n   || SQLITE_OK!=(rc = read32bits(pJrnl, szJ-16, &len))\n   || len>=nMaster \n   || len>szJ-16\n   || len==0 \n   || SQLITE_OK!=(rc = read32bits(pJrnl, szJ-12, &cksum))\n   || SQLITE_OK!=(rc = sqlite3OsRead(pJrnl, aMagic, 8, szJ-8))\n   || memcmp(aMagic, aJournalMagic, 8)\n   || SQLITE_OK!=(rc = sqlite3OsRead(pJrnl, zMaster, len, szJ-16-len))\n  ){\n    return rc;\n  }\n\n  /* See if the checksum matches the master journal name */\n  for(u=0; u<len; u++){\n    cksum -= zMaster[u];\n  }\n  if( cksum ){\n    /* If the checksum doesn't add up, then one or more of the disk sectors\n    ** containing the master journal filename is corrupted. This means\n    ** definitely roll back, so just return SQLITE_OK and report a (nul)\n    ** master-journal filename.\n    */\n    len = 0;\n  }\n  zMaster[len] = '\\0';\n   \n  return SQLITE_OK;\n}\n\n/*\n** Return the offset of the sector boundary at or immediately \n** following the value in pPager->journalOff, assuming a sector \n** size of pPager->sectorSize bytes.\n**\n** i.e for a sector size of 512:\n**\n**   Pager.journalOff          Return value\n**   ---------------------------------------\n**   0                         0\n**   512                       512\n**   100                       512\n**   2000                      2048\n** \n*/\nstatic i64 journalHdrOffset(Pager *pPager){\n  i64 offset = 0;\n  i64 c = pPager->journalOff;\n  if( c ){\n    offset = ((c-1)/JOURNAL_HDR_SZ(pPager) + 1) * JOURNAL_HDR_SZ(pPager);\n  }\n  assert( offset%JOURNAL_HDR_SZ(pPager)==0 );\n  assert( offset>=c );\n  assert( (offset-c)<JOURNAL_HDR_SZ(pPager) );\n  return offset;\n}\n\n/*\n** The journal file must be open when this function is called.\n**\n** This function is a no-op if the journal file has not been written to\n** within the current transaction (i.e. if Pager.journalOff==0).\n**\n** If doTruncate is non-zero or the Pager.journalSizeLimit variable is\n** set to 0, then truncate the journal file to zero bytes in size. Otherwise,\n** zero the 28-byte header at the start of the journal file. In either case, \n** if the pager is not in no-sync mode, sync the journal file immediately \n** after writing or truncating it.\n**\n** If Pager.journalSizeLimit is set to a positive, non-zero value, and\n** following the truncation or zeroing described above the size of the \n** journal file in bytes is larger than this value, then truncate the\n** journal file to Pager.journalSizeLimit bytes. The journal file does\n** not need to be synced following this operation.\n**\n** If an IO error occurs, abandon processing and return the IO error code.\n** Otherwise, return SQLITE_OK.\n*/\nstatic int zeroJournalHdr(Pager *pPager, int doTruncate){\n  int rc = SQLITE_OK;                               /* Return code */\n  assert( isOpen(pPager->jfd) );\n  assert( !sqlite3JournalIsInMemory(pPager->jfd) );\n  if( pPager->journalOff ){\n    const i64 iLimit = pPager->journalSizeLimit;    /* Local cache of jsl */\n\n    IOTRACE((\"JZEROHDR %p\\n\", pPager))\n    if( doTruncate || iLimit==0 ){\n      rc = sqlite3OsTruncate(pPager->jfd, 0);\n    }else{\n      static const char zeroHdr[28] = {0};\n      rc = sqlite3OsWrite(pPager->jfd, zeroHdr, sizeof(zeroHdr), 0);\n    }\n    if( rc==SQLITE_OK && !pPager->noSync ){\n      rc = sqlite3OsSync(pPager->jfd, SQLITE_SYNC_DATAONLY|pPager->syncFlags);\n    }\n\n    /* At this point the transaction is committed but the write lock \n    ** is still held on the file. If there is a size limit configured for \n    ** the persistent journal and the journal file currently consumes more\n    ** space than that limit allows for, truncate it now. There is no need\n    ** to sync the file following this operation.\n    */\n    if( rc==SQLITE_OK && iLimit>0 ){\n      i64 sz;\n      rc = sqlite3OsFileSize(pPager->jfd, &sz);\n      if( rc==SQLITE_OK && sz>iLimit ){\n        rc = sqlite3OsTruncate(pPager->jfd, iLimit);\n      }\n    }\n  }\n  return rc;\n}\n\n/*\n** The journal file must be open when this routine is called. A journal\n** header (JOURNAL_HDR_SZ bytes) is written into the journal file at the\n** current location.\n**\n** The format for the journal header is as follows:\n** - 8 bytes: Magic identifying journal format.\n** - 4 bytes: Number of records in journal, or -1 no-sync mode is on.\n** - 4 bytes: Random number used for page hash.\n** - 4 bytes: Initial database page count.\n** - 4 bytes: Sector size used by the process that wrote this journal.\n** - 4 bytes: Database page size.\n** \n** Followed by (JOURNAL_HDR_SZ - 28) bytes of unused space.\n*/\nstatic int writeJournalHdr(Pager *pPager){\n  int rc = SQLITE_OK;                 /* Return code */\n  char *zHeader = pPager->pTmpSpace;  /* Temporary space used to build header */\n  u32 nHeader = (u32)pPager->pageSize;/* Size of buffer pointed to by zHeader */\n  u32 nWrite;                         /* Bytes of header sector written */\n  int ii;                             /* Loop counter */\n\n  assert( isOpen(pPager->jfd) );      /* Journal file must be open. */\n\n  if( nHeader>JOURNAL_HDR_SZ(pPager) ){\n    nHeader = JOURNAL_HDR_SZ(pPager);\n  }\n\n  /* If there are active savepoints and any of them were created \n  ** since the most recent journal header was written, update the \n  ** PagerSavepoint.iHdrOffset fields now.\n  */\n  for(ii=0; ii<pPager->nSavepoint; ii++){\n    if( pPager->aSavepoint[ii].iHdrOffset==0 ){\n      pPager->aSavepoint[ii].iHdrOffset = pPager->journalOff;\n    }\n  }\n\n  pPager->journalHdr = pPager->journalOff = journalHdrOffset(pPager);\n\n  /* \n  ** Write the nRec Field - the number of page records that follow this\n  ** journal header. Normally, zero is written to this value at this time.\n  ** After the records are added to the journal (and the journal synced, \n  ** if in full-sync mode), the zero is overwritten with the true number\n  ** of records (see syncJournal()).\n  **\n  ** A faster alternative is to write 0xFFFFFFFF to the nRec field. When\n  ** reading the journal this value tells SQLite to assume that the\n  ** rest of the journal file contains valid page records. This assumption\n  ** is dangerous, as if a failure occurred whilst writing to the journal\n  ** file it may contain some garbage data. There are two scenarios\n  ** where this risk can be ignored:\n  **\n  **   * When the pager is in no-sync mode. Corruption can follow a\n  **     power failure in this case anyway.\n  **\n  **   * When the SQLITE_IOCAP_SAFE_APPEND flag is set. This guarantees\n  **     that garbage data is never appended to the journal file.\n  */\n  assert( isOpen(pPager->fd) || pPager->noSync );\n  if( pPager->noSync || (pPager->journalMode==PAGER_JOURNALMODE_MEMORY)\n   || (sqlite3OsDeviceCharacteristics(pPager->fd)&SQLITE_IOCAP_SAFE_APPEND) \n  ){\n    memcpy(zHeader, aJournalMagic, sizeof(aJournalMagic));\n    put32bits(&zHeader[sizeof(aJournalMagic)], 0xffffffff);\n  }else{\n    memset(zHeader, 0, sizeof(aJournalMagic)+4);\n  }\n\n  /* The random check-hash initializer */ \n  sqlite3_randomness(sizeof(pPager->cksumInit), &pPager->cksumInit);\n  put32bits(&zHeader[sizeof(aJournalMagic)+4], pPager->cksumInit);\n  /* The initial database size */\n  put32bits(&zHeader[sizeof(aJournalMagic)+8], pPager->dbOrigSize);\n  /* The assumed sector size for this process */\n  put32bits(&zHeader[sizeof(aJournalMagic)+12], pPager->sectorSize);\n\n  /* The page size */\n  put32bits(&zHeader[sizeof(aJournalMagic)+16], pPager->pageSize);\n\n  /* Initializing the tail of the buffer is not necessary.  Everything\n  ** works find if the following memset() is omitted.  But initializing\n  ** the memory prevents valgrind from complaining, so we are willing to\n  ** take the performance hit.\n  */\n  memset(&zHeader[sizeof(aJournalMagic)+20], 0,\n         nHeader-(sizeof(aJournalMagic)+20));\n\n  /* In theory, it is only necessary to write the 28 bytes that the \n  ** journal header consumes to the journal file here. Then increment the \n  ** Pager.journalOff variable by JOURNAL_HDR_SZ so that the next \n  ** record is written to the following sector (leaving a gap in the file\n  ** that will be implicitly filled in by the OS).\n  **\n  ** However it has been discovered that on some systems this pattern can \n  ** be significantly slower than contiguously writing data to the file,\n  ** even if that means explicitly writing data to the block of \n  ** (JOURNAL_HDR_SZ - 28) bytes that will not be used. So that is what\n  ** is done. \n  **\n  ** The loop is required here in case the sector-size is larger than the \n  ** database page size. Since the zHeader buffer is only Pager.pageSize\n  ** bytes in size, more than one call to sqlite3OsWrite() may be required\n  ** to populate the entire journal header sector.\n  */ \n  for(nWrite=0; rc==SQLITE_OK&&nWrite<JOURNAL_HDR_SZ(pPager); nWrite+=nHeader){\n    IOTRACE((\"JHDR %p %lld %d\\n\", pPager, pPager->journalHdr, nHeader))\n    rc = sqlite3OsWrite(pPager->jfd, zHeader, nHeader, pPager->journalOff);\n    assert( pPager->journalHdr <= pPager->journalOff );\n    pPager->journalOff += nHeader;\n  }\n\n  return rc;\n}\n\n/*\n** The journal file must be open when this is called. A journal header file\n** (JOURNAL_HDR_SZ bytes) is read from the current location in the journal\n** file. The current location in the journal file is given by\n** pPager->journalOff. See comments above function writeJournalHdr() for\n** a description of the journal header format.\n**\n** If the header is read successfully, *pNRec is set to the number of\n** page records following this header and *pDbSize is set to the size of the\n** database before the transaction began, in pages. Also, pPager->cksumInit\n** is set to the value read from the journal header. SQLITE_OK is returned\n** in this case.\n**\n** If the journal header file appears to be corrupted, SQLITE_DONE is\n** returned and *pNRec and *PDbSize are undefined.  If JOURNAL_HDR_SZ bytes\n** cannot be read from the journal file an error code is returned.\n*/\nstatic int readJournalHdr(\n  Pager *pPager,               /* Pager object */\n  int isHot,\n  i64 journalSize,             /* Size of the open journal file in bytes */\n  u32 *pNRec,                  /* OUT: Value read from the nRec field */\n  u32 *pDbSize                 /* OUT: Value of original database size field */\n){\n  int rc;                      /* Return code */\n  unsigned char aMagic[8];     /* A buffer to hold the magic header */\n  i64 iHdrOff;                 /* Offset of journal header being read */\n\n  assert( isOpen(pPager->jfd) );      /* Journal file must be open. */\n\n  /* Advance Pager.journalOff to the start of the next sector. If the\n  ** journal file is too small for there to be a header stored at this\n  ** point, return SQLITE_DONE.\n  */\n  pPager->journalOff = journalHdrOffset(pPager);\n  if( pPager->journalOff+JOURNAL_HDR_SZ(pPager) > journalSize ){\n    return SQLITE_DONE;\n  }\n  iHdrOff = pPager->journalOff;\n\n  /* Read in the first 8 bytes of the journal header. If they do not match\n  ** the  magic string found at the start of each journal header, return\n  ** SQLITE_DONE. If an IO error occurs, return an error code. Otherwise,\n  ** proceed.\n  */\n  if( isHot || iHdrOff!=pPager->journalHdr ){\n    rc = sqlite3OsRead(pPager->jfd, aMagic, sizeof(aMagic), iHdrOff);\n    if( rc ){\n      return rc;\n    }\n    if( memcmp(aMagic, aJournalMagic, sizeof(aMagic))!=0 ){\n      return SQLITE_DONE;\n    }\n  }\n\n  /* Read the first three 32-bit fields of the journal header: The nRec\n  ** field, the checksum-initializer and the database size at the start\n  ** of the transaction. Return an error code if anything goes wrong.\n  */\n  if( SQLITE_OK!=(rc = read32bits(pPager->jfd, iHdrOff+8, pNRec))\n   || SQLITE_OK!=(rc = read32bits(pPager->jfd, iHdrOff+12, &pPager->cksumInit))\n   || SQLITE_OK!=(rc = read32bits(pPager->jfd, iHdrOff+16, pDbSize))\n  ){\n    return rc;\n  }\n\n  if( pPager->journalOff==0 ){\n    u32 iPageSize;               /* Page-size field of journal header */\n    u32 iSectorSize;             /* Sector-size field of journal header */\n\n    /* Read the page-size and sector-size journal header fields. */\n    if( SQLITE_OK!=(rc = read32bits(pPager->jfd, iHdrOff+20, &iSectorSize))\n     || SQLITE_OK!=(rc = read32bits(pPager->jfd, iHdrOff+24, &iPageSize))\n    ){\n      return rc;\n    }\n\n    /* Versions of SQLite prior to 3.5.8 set the page-size field of the\n    ** journal header to zero. In this case, assume that the Pager.pageSize\n    ** variable is already set to the correct page size.\n    */\n    if( iPageSize==0 ){\n      iPageSize = pPager->pageSize;\n    }\n\n    /* Check that the values read from the page-size and sector-size fields\n    ** are within range. To be 'in range', both values need to be a power\n    ** of two greater than or equal to 512 or 32, and not greater than their \n    ** respective compile time maximum limits.\n    */\n    if( iPageSize<512                  || iSectorSize<32\n     || iPageSize>SQLITE_MAX_PAGE_SIZE || iSectorSize>MAX_SECTOR_SIZE\n     || ((iPageSize-1)&iPageSize)!=0   || ((iSectorSize-1)&iSectorSize)!=0 \n    ){\n      /* If the either the page-size or sector-size in the journal-header is \n      ** invalid, then the process that wrote the journal-header must have \n      ** crashed before the header was synced. In this case stop reading \n      ** the journal file here.\n      */\n      return SQLITE_DONE;\n    }\n\n    /* Update the page-size to match the value read from the journal. \n    ** Use a testcase() macro to make sure that malloc failure within \n    ** PagerSetPagesize() is tested.\n    */\n    rc = sqlite3PagerSetPagesize(pPager, &iPageSize, -1);\n    testcase( rc!=SQLITE_OK );\n\n    /* Update the assumed sector-size to match the value used by \n    ** the process that created this journal. If this journal was\n    ** created by a process other than this one, then this routine\n    ** is being called from within pager_playback(). The local value\n    ** of Pager.sectorSize is restored at the end of that routine.\n    */\n    pPager->sectorSize = iSectorSize;\n  }\n\n  pPager->journalOff += JOURNAL_HDR_SZ(pPager);\n  return rc;\n}\n\n\n/*\n** Write the supplied master journal name into the journal file for pager\n** pPager at the current location. The master journal name must be the last\n** thing written to a journal file. If the pager is in full-sync mode, the\n** journal file descriptor is advanced to the next sector boundary before\n** anything is written. The format is:\n**\n**   + 4 bytes: PAGER_MJ_PGNO.\n**   + N bytes: Master journal filename in utf-8.\n**   + 4 bytes: N (length of master journal name in bytes, no nul-terminator).\n**   + 4 bytes: Master journal name checksum.\n**   + 8 bytes: aJournalMagic[].\n**\n** The master journal page checksum is the sum of the bytes in the master\n** journal name, where each byte is interpreted as a signed 8-bit integer.\n**\n** If zMaster is a NULL pointer (occurs for a single database transaction), \n** this call is a no-op.\n*/\nstatic int writeMasterJournal(Pager *pPager, const char *zMaster){\n  int rc;                          /* Return code */\n  int nMaster;                     /* Length of string zMaster */\n  i64 iHdrOff;                     /* Offset of header in journal file */\n  i64 jrnlSize;                    /* Size of journal file on disk */\n  u32 cksum = 0;                   /* Checksum of string zMaster */\n\n  assert( pPager->setMaster==0 );\n  assert( !pagerUseWal(pPager) );\n\n  if( !zMaster \n   || pPager->journalMode==PAGER_JOURNALMODE_MEMORY \n   || !isOpen(pPager->jfd)\n  ){\n    return SQLITE_OK;\n  }\n  pPager->setMaster = 1;\n  assert( pPager->journalHdr <= pPager->journalOff );\n\n  /* Calculate the length in bytes and the checksum of zMaster */\n  for(nMaster=0; zMaster[nMaster]; nMaster++){\n    cksum += zMaster[nMaster];\n  }\n\n  /* If in full-sync mode, advance to the next disk sector before writing\n  ** the master journal name. This is in case the previous page written to\n  ** the journal has already been synced.\n  */\n  if( pPager->fullSync ){\n    pPager->journalOff = journalHdrOffset(pPager);\n  }\n  iHdrOff = pPager->journalOff;\n\n  /* Write the master journal data to the end of the journal file. If\n  ** an error occurs, return the error code to the caller.\n  */\n  if( (0 != (rc = write32bits(pPager->jfd, iHdrOff, PAGER_MJ_PGNO(pPager))))\n   || (0 != (rc = sqlite3OsWrite(pPager->jfd, zMaster, nMaster, iHdrOff+4)))\n   || (0 != (rc = write32bits(pPager->jfd, iHdrOff+4+nMaster, nMaster)))\n   || (0 != (rc = write32bits(pPager->jfd, iHdrOff+4+nMaster+4, cksum)))\n   || (0 != (rc = sqlite3OsWrite(pPager->jfd, aJournalMagic, 8,\n                                 iHdrOff+4+nMaster+8)))\n  ){\n    return rc;\n  }\n  pPager->journalOff += (nMaster+20);\n\n  /* If the pager is in peristent-journal mode, then the physical \n  ** journal-file may extend past the end of the master-journal name\n  ** and 8 bytes of magic data just written to the file. This is \n  ** dangerous because the code to rollback a hot-journal file\n  ** will not be able to find the master-journal name to determine \n  ** whether or not the journal is hot. \n  **\n  ** Easiest thing to do in this scenario is to truncate the journal \n  ** file to the required size.\n  */ \n  if( SQLITE_OK==(rc = sqlite3OsFileSize(pPager->jfd, &jrnlSize))\n   && jrnlSize>pPager->journalOff\n  ){\n    rc = sqlite3OsTruncate(pPager->jfd, pPager->journalOff);\n  }\n  return rc;\n}\n\n/*\n** Discard the entire contents of the in-memory page-cache.\n*/\nstatic void pager_reset(Pager *pPager){\n  pPager->iDataVersion++;\n  sqlite3BackupRestart(pPager->pBackup);\n  sqlite3PcacheClear(pPager->pPCache);\n}\n\n/*\n** Return the pPager->iDataVersion value\n*/\nSQLITE_PRIVATE u32 sqlite3PagerDataVersion(Pager *pPager){\n  assert( pPager->eState>PAGER_OPEN );\n  return pPager->iDataVersion;\n}\n\n/*\n** Free all structures in the Pager.aSavepoint[] array and set both\n** Pager.aSavepoint and Pager.nSavepoint to zero. Close the sub-journal\n** if it is open and the pager is not in exclusive mode.\n*/\nstatic void releaseAllSavepoints(Pager *pPager){\n  int ii;               /* Iterator for looping through Pager.aSavepoint */\n  for(ii=0; ii<pPager->nSavepoint; ii++){\n    sqlite3BitvecDestroy(pPager->aSavepoint[ii].pInSavepoint);\n  }\n  if( !pPager->exclusiveMode || sqlite3JournalIsInMemory(pPager->sjfd) ){\n    sqlite3OsClose(pPager->sjfd);\n  }\n  sqlite3_free(pPager->aSavepoint);\n  pPager->aSavepoint = 0;\n  pPager->nSavepoint = 0;\n  pPager->nSubRec = 0;\n}\n\n/*\n** Set the bit number pgno in the PagerSavepoint.pInSavepoint \n** bitvecs of all open savepoints. Return SQLITE_OK if successful\n** or SQLITE_NOMEM if a malloc failure occurs.\n*/\nstatic int addToSavepointBitvecs(Pager *pPager, Pgno pgno){\n  int ii;                   /* Loop counter */\n  int rc = SQLITE_OK;       /* Result code */\n\n  for(ii=0; ii<pPager->nSavepoint; ii++){\n    PagerSavepoint *p = &pPager->aSavepoint[ii];\n    if( pgno<=p->nOrig ){\n      rc |= sqlite3BitvecSet(p->pInSavepoint, pgno);\n      testcase( rc==SQLITE_NOMEM );\n      assert( rc==SQLITE_OK || rc==SQLITE_NOMEM );\n    }\n  }\n  return rc;\n}\n\n/*\n** This function is a no-op if the pager is in exclusive mode and not\n** in the ERROR state. Otherwise, it switches the pager to PAGER_OPEN\n** state.\n**\n** If the pager is not in exclusive-access mode, the database file is\n** completely unlocked. If the file is unlocked and the file-system does\n** not exhibit the UNDELETABLE_WHEN_OPEN property, the journal file is\n** closed (if it is open).\n**\n** If the pager is in ERROR state when this function is called, the \n** contents of the pager cache are discarded before switching back to \n** the OPEN state. Regardless of whether the pager is in exclusive-mode\n** or not, any journal file left in the file-system will be treated\n** as a hot-journal and rolled back the next time a read-transaction\n** is opened (by this or by any other connection).\n*/\nstatic void pager_unlock(Pager *pPager){\n\n  assert( pPager->eState==PAGER_READER \n       || pPager->eState==PAGER_OPEN \n       || pPager->eState==PAGER_ERROR \n  );\n\n  sqlite3BitvecDestroy(pPager->pInJournal);\n  pPager->pInJournal = 0;\n  releaseAllSavepoints(pPager);\n\n  if( pagerUseWal(pPager) ){\n    assert( !isOpen(pPager->jfd) );\n    sqlite3WalEndReadTransaction(pPager->pWal);\n    pPager->eState = PAGER_OPEN;\n  }else if( !pPager->exclusiveMode ){\n    int rc;                       /* Error code returned by pagerUnlockDb() */\n    int iDc = isOpen(pPager->fd)?sqlite3OsDeviceCharacteristics(pPager->fd):0;\n\n    /* If the operating system support deletion of open files, then\n    ** close the journal file when dropping the database lock.  Otherwise\n    ** another connection with journal_mode=delete might delete the file\n    ** out from under us.\n    */\n    assert( (PAGER_JOURNALMODE_MEMORY   & 5)!=1 );\n    assert( (PAGER_JOURNALMODE_OFF      & 5)!=1 );\n    assert( (PAGER_JOURNALMODE_WAL      & 5)!=1 );\n    assert( (PAGER_JOURNALMODE_DELETE   & 5)!=1 );\n    assert( (PAGER_JOURNALMODE_TRUNCATE & 5)==1 );\n    assert( (PAGER_JOURNALMODE_PERSIST  & 5)==1 );\n    if( 0==(iDc & SQLITE_IOCAP_UNDELETABLE_WHEN_OPEN)\n     || 1!=(pPager->journalMode & 5)\n    ){\n      sqlite3OsClose(pPager->jfd);\n    }\n\n    /* If the pager is in the ERROR state and the call to unlock the database\n    ** file fails, set the current lock to UNKNOWN_LOCK. See the comment\n    ** above the #define for UNKNOWN_LOCK for an explanation of why this\n    ** is necessary.\n    */\n    rc = pagerUnlockDb(pPager, NO_LOCK);\n    if( rc!=SQLITE_OK && pPager->eState==PAGER_ERROR ){\n      pPager->eLock = UNKNOWN_LOCK;\n    }\n\n    /* The pager state may be changed from PAGER_ERROR to PAGER_OPEN here\n    ** without clearing the error code. This is intentional - the error\n    ** code is cleared and the cache reset in the block below.\n    */\n    assert( pPager->errCode || pPager->eState!=PAGER_ERROR );\n    pPager->changeCountDone = 0;\n    pPager->eState = PAGER_OPEN;\n  }\n\n  /* If Pager.errCode is set, the contents of the pager cache cannot be\n  ** trusted. Now that there are no outstanding references to the pager,\n  ** it can safely move back to PAGER_OPEN state. This happens in both\n  ** normal and exclusive-locking mode.\n  */\n  assert( pPager->errCode==SQLITE_OK || !MEMDB );\n  if( pPager->errCode ){\n    if( pPager->tempFile==0 ){\n      pager_reset(pPager);\n      pPager->changeCountDone = 0;\n      pPager->eState = PAGER_OPEN;\n    }else{\n      pPager->eState = (isOpen(pPager->jfd) ? PAGER_OPEN : PAGER_READER);\n    }\n    if( USEFETCH(pPager) ) sqlite3OsUnfetch(pPager->fd, 0, 0);\n    pPager->errCode = SQLITE_OK;\n    setGetterMethod(pPager);\n  }\n\n  pPager->journalOff = 0;\n  pPager->journalHdr = 0;\n  pPager->setMaster = 0;\n}\n\n/*\n** This function is called whenever an IOERR or FULL error that requires\n** the pager to transition into the ERROR state may ahve occurred.\n** The first argument is a pointer to the pager structure, the second \n** the error-code about to be returned by a pager API function. The \n** value returned is a copy of the second argument to this function. \n**\n** If the second argument is SQLITE_FULL, SQLITE_IOERR or one of the\n** IOERR sub-codes, the pager enters the ERROR state and the error code\n** is stored in Pager.errCode. While the pager remains in the ERROR state,\n** all major API calls on the Pager will immediately return Pager.errCode.\n**\n** The ERROR state indicates that the contents of the pager-cache \n** cannot be trusted. This state can be cleared by completely discarding \n** the contents of the pager-cache. If a transaction was active when\n** the persistent error occurred, then the rollback journal may need\n** to be replayed to restore the contents of the database file (as if\n** it were a hot-journal).\n*/\nstatic int pager_error(Pager *pPager, int rc){\n  int rc2 = rc & 0xff;\n  assert( rc==SQLITE_OK || !MEMDB );\n  assert(\n       pPager->errCode==SQLITE_FULL ||\n       pPager->errCode==SQLITE_OK ||\n       (pPager->errCode & 0xff)==SQLITE_IOERR\n  );\n  if( rc2==SQLITE_FULL || rc2==SQLITE_IOERR ){\n    pPager->errCode = rc;\n    pPager->eState = PAGER_ERROR;\n    setGetterMethod(pPager);\n  }\n  return rc;\n}\n\nstatic int pager_truncate(Pager *pPager, Pgno nPage);\n\n/*\n** The write transaction open on pPager is being committed (bCommit==1)\n** or rolled back (bCommit==0).\n**\n** Return TRUE if and only if all dirty pages should be flushed to disk.\n**\n** Rules:\n**\n**   *  For non-TEMP databases, always sync to disk.  This is necessary\n**      for transactions to be durable.\n**\n**   *  Sync TEMP database only on a COMMIT (not a ROLLBACK) when the backing\n**      file has been created already (via a spill on pagerStress()) and\n**      when the number of dirty pages in memory exceeds 25% of the total\n**      cache size.\n*/\nstatic int pagerFlushOnCommit(Pager *pPager, int bCommit){\n  if( pPager->tempFile==0 ) return 1;\n  if( !bCommit ) return 0;\n  if( !isOpen(pPager->fd) ) return 0;\n  return (sqlite3PCachePercentDirty(pPager->pPCache)>=25);\n}\n\n/*\n** This routine ends a transaction. A transaction is usually ended by \n** either a COMMIT or a ROLLBACK operation. This routine may be called \n** after rollback of a hot-journal, or if an error occurs while opening\n** the journal file or writing the very first journal-header of a\n** database transaction.\n** \n** This routine is never called in PAGER_ERROR state. If it is called\n** in PAGER_NONE or PAGER_SHARED state and the lock held is less\n** exclusive than a RESERVED lock, it is a no-op.\n**\n** Otherwise, any active savepoints are released.\n**\n** If the journal file is open, then it is \"finalized\". Once a journal \n** file has been finalized it is not possible to use it to roll back a \n** transaction. Nor will it be considered to be a hot-journal by this\n** or any other database connection. Exactly how a journal is finalized\n** depends on whether or not the pager is running in exclusive mode and\n** the current journal-mode (Pager.journalMode value), as follows:\n**\n**   journalMode==MEMORY\n**     Journal file descriptor is simply closed. This destroys an \n**     in-memory journal.\n**\n**   journalMode==TRUNCATE\n**     Journal file is truncated to zero bytes in size.\n**\n**   journalMode==PERSIST\n**     The first 28 bytes of the journal file are zeroed. This invalidates\n**     the first journal header in the file, and hence the entire journal\n**     file. An invalid journal file cannot be rolled back.\n**\n**   journalMode==DELETE\n**     The journal file is closed and deleted using sqlite3OsDelete().\n**\n**     If the pager is running in exclusive mode, this method of finalizing\n**     the journal file is never used. Instead, if the journalMode is\n**     DELETE and the pager is in exclusive mode, the method described under\n**     journalMode==PERSIST is used instead.\n**\n** After the journal is finalized, the pager moves to PAGER_READER state.\n** If running in non-exclusive rollback mode, the lock on the file is \n** downgraded to a SHARED_LOCK.\n**\n** SQLITE_OK is returned if no error occurs. If an error occurs during\n** any of the IO operations to finalize the journal file or unlock the\n** database then the IO error code is returned to the user. If the \n** operation to finalize the journal file fails, then the code still\n** tries to unlock the database file if not in exclusive mode. If the\n** unlock operation fails as well, then the first error code related\n** to the first error encountered (the journal finalization one) is\n** returned.\n*/\nstatic int pager_end_transaction(Pager *pPager, int hasMaster, int bCommit){\n  int rc = SQLITE_OK;      /* Error code from journal finalization operation */\n  int rc2 = SQLITE_OK;     /* Error code from db file unlock operation */\n\n  /* Do nothing if the pager does not have an open write transaction\n  ** or at least a RESERVED lock. This function may be called when there\n  ** is no write-transaction active but a RESERVED or greater lock is\n  ** held under two circumstances:\n  **\n  **   1. After a successful hot-journal rollback, it is called with\n  **      eState==PAGER_NONE and eLock==EXCLUSIVE_LOCK.\n  **\n  **   2. If a connection with locking_mode=exclusive holding an EXCLUSIVE \n  **      lock switches back to locking_mode=normal and then executes a\n  **      read-transaction, this function is called with eState==PAGER_READER \n  **      and eLock==EXCLUSIVE_LOCK when the read-transaction is closed.\n  */\n  assert( assert_pager_state(pPager) );\n  assert( pPager->eState!=PAGER_ERROR );\n  if( pPager->eState<PAGER_WRITER_LOCKED && pPager->eLock<RESERVED_LOCK ){\n    return SQLITE_OK;\n  }\n\n  releaseAllSavepoints(pPager);\n  assert( isOpen(pPager->jfd) || pPager->pInJournal==0 \n      || (sqlite3OsDeviceCharacteristics(pPager->fd)&SQLITE_IOCAP_BATCH_ATOMIC)\n  );\n  if( isOpen(pPager->jfd) ){\n    assert( !pagerUseWal(pPager) );\n\n    /* Finalize the journal file. */\n    if( sqlite3JournalIsInMemory(pPager->jfd) ){\n      /* assert( pPager->journalMode==PAGER_JOURNALMODE_MEMORY ); */\n      sqlite3OsClose(pPager->jfd);\n    }else if( pPager->journalMode==PAGER_JOURNALMODE_TRUNCATE ){\n      if( pPager->journalOff==0 ){\n        rc = SQLITE_OK;\n      }else{\n        rc = sqlite3OsTruncate(pPager->jfd, 0);\n        if( rc==SQLITE_OK && pPager->fullSync ){\n          /* Make sure the new file size is written into the inode right away.\n          ** Otherwise the journal might resurrect following a power loss and\n          ** cause the last transaction to roll back.  See\n          ** https://bugzilla.mozilla.org/show_bug.cgi?id=1072773\n          */\n          rc = sqlite3OsSync(pPager->jfd, pPager->syncFlags);\n        }\n      }\n      pPager->journalOff = 0;\n    }else if( pPager->journalMode==PAGER_JOURNALMODE_PERSIST\n      || (pPager->exclusiveMode && pPager->journalMode!=PAGER_JOURNALMODE_WAL)\n    ){\n      rc = zeroJournalHdr(pPager, hasMaster||pPager->tempFile);\n      pPager->journalOff = 0;\n    }else{\n      /* This branch may be executed with Pager.journalMode==MEMORY if\n      ** a hot-journal was just rolled back. In this case the journal\n      ** file should be closed and deleted. If this connection writes to\n      ** the database file, it will do so using an in-memory journal.\n      */\n      int bDelete = !pPager->tempFile;\n      assert( sqlite3JournalIsInMemory(pPager->jfd)==0 );\n      assert( pPager->journalMode==PAGER_JOURNALMODE_DELETE \n           || pPager->journalMode==PAGER_JOURNALMODE_MEMORY \n           || pPager->journalMode==PAGER_JOURNALMODE_WAL \n      );\n      sqlite3OsClose(pPager->jfd);\n      if( bDelete ){\n        rc = sqlite3OsDelete(pPager->pVfs, pPager->zJournal, pPager->extraSync);\n      }\n    }\n  }\n\n#ifdef SQLITE_CHECK_PAGES\n  sqlite3PcacheIterateDirty(pPager->pPCache, pager_set_pagehash);\n  if( pPager->dbSize==0 && sqlite3PcacheRefCount(pPager->pPCache)>0 ){\n    PgHdr *p = sqlite3PagerLookup(pPager, 1);\n    if( p ){\n      p->pageHash = 0;\n      sqlite3PagerUnrefNotNull(p);\n    }\n  }\n#endif\n\n  sqlite3BitvecDestroy(pPager->pInJournal);\n  pPager->pInJournal = 0;\n  pPager->nRec = 0;\n  if( rc==SQLITE_OK ){\n    if( MEMDB || pagerFlushOnCommit(pPager, bCommit) ){\n      sqlite3PcacheCleanAll(pPager->pPCache);\n    }else{\n      sqlite3PcacheClearWritable(pPager->pPCache);\n    }\n    sqlite3PcacheTruncate(pPager->pPCache, pPager->dbSize);\n  }\n\n  if( pagerUseWal(pPager) ){\n    /* Drop the WAL write-lock, if any. Also, if the connection was in \n    ** locking_mode=exclusive mode but is no longer, drop the EXCLUSIVE \n    ** lock held on the database file.\n    */\n    rc2 = sqlite3WalEndWriteTransaction(pPager->pWal);\n    assert( rc2==SQLITE_OK );\n  }else if( rc==SQLITE_OK && bCommit && pPager->dbFileSize>pPager->dbSize ){\n    /* This branch is taken when committing a transaction in rollback-journal\n    ** mode if the database file on disk is larger than the database image.\n    ** At this point the journal has been finalized and the transaction \n    ** successfully committed, but the EXCLUSIVE lock is still held on the\n    ** file. So it is safe to truncate the database file to its minimum\n    ** required size.  */\n    assert( pPager->eLock==EXCLUSIVE_LOCK );\n    rc = pager_truncate(pPager, pPager->dbSize);\n  }\n\n  if( rc==SQLITE_OK && bCommit && isOpen(pPager->fd) ){\n    rc = sqlite3OsFileControl(pPager->fd, SQLITE_FCNTL_COMMIT_PHASETWO, 0);\n    if( rc==SQLITE_NOTFOUND ) rc = SQLITE_OK;\n  }\n\n  if( !pPager->exclusiveMode \n   && (!pagerUseWal(pPager) || sqlite3WalExclusiveMode(pPager->pWal, 0))\n  ){\n    rc2 = pagerUnlockDb(pPager, SHARED_LOCK);\n    pPager->changeCountDone = 0;\n  }\n  pPager->eState = PAGER_READER;\n  pPager->setMaster = 0;\n\n  return (rc==SQLITE_OK?rc2:rc);\n}\n\n/*\n** Execute a rollback if a transaction is active and unlock the \n** database file. \n**\n** If the pager has already entered the ERROR state, do not attempt \n** the rollback at this time. Instead, pager_unlock() is called. The\n** call to pager_unlock() will discard all in-memory pages, unlock\n** the database file and move the pager back to OPEN state. If this \n** means that there is a hot-journal left in the file-system, the next \n** connection to obtain a shared lock on the pager (which may be this one) \n** will roll it back.\n**\n** If the pager has not already entered the ERROR state, but an IO or\n** malloc error occurs during a rollback, then this will itself cause \n** the pager to enter the ERROR state. Which will be cleared by the\n** call to pager_unlock(), as described above.\n*/\nstatic void pagerUnlockAndRollback(Pager *pPager){\n  if( pPager->eState!=PAGER_ERROR && pPager->eState!=PAGER_OPEN ){\n    assert( assert_pager_state(pPager) );\n    if( pPager->eState>=PAGER_WRITER_LOCKED ){\n      sqlite3BeginBenignMalloc();\n      sqlite3PagerRollback(pPager);\n      sqlite3EndBenignMalloc();\n    }else if( !pPager->exclusiveMode ){\n      assert( pPager->eState==PAGER_READER );\n      pager_end_transaction(pPager, 0, 0);\n    }\n  }\n  pager_unlock(pPager);\n}\n\n/*\n** Parameter aData must point to a buffer of pPager->pageSize bytes\n** of data. Compute and return a checksum based ont the contents of the \n** page of data and the current value of pPager->cksumInit.\n**\n** This is not a real checksum. It is really just the sum of the \n** random initial value (pPager->cksumInit) and every 200th byte\n** of the page data, starting with byte offset (pPager->pageSize%200).\n** Each byte is interpreted as an 8-bit unsigned integer.\n**\n** Changing the formula used to compute this checksum results in an\n** incompatible journal file format.\n**\n** If journal corruption occurs due to a power failure, the most likely \n** scenario is that one end or the other of the record will be changed. \n** It is much less likely that the two ends of the journal record will be\n** correct and the middle be corrupt.  Thus, this \"checksum\" scheme,\n** though fast and simple, catches the mostly likely kind of corruption.\n*/\nstatic u32 pager_cksum(Pager *pPager, const u8 *aData){\n  u32 cksum = pPager->cksumInit;         /* Checksum value to return */\n  int i = pPager->pageSize-200;          /* Loop counter */\n  while( i>0 ){\n    cksum += aData[i];\n    i -= 200;\n  }\n  return cksum;\n}\n\n/*\n** Report the current page size and number of reserved bytes back\n** to the codec.\n*/\n#ifdef SQLITE_HAS_CODEC\nstatic void pagerReportSize(Pager *pPager){\n  if( pPager->xCodecSizeChng ){\n    pPager->xCodecSizeChng(pPager->pCodec, pPager->pageSize,\n                           (int)pPager->nReserve);\n  }\n}\n#else\n# define pagerReportSize(X)     /* No-op if we do not support a codec */\n#endif\n\n#ifdef SQLITE_HAS_CODEC\n/*\n** Make sure the number of reserved bits is the same in the destination\n** pager as it is in the source.  This comes up when a VACUUM changes the\n** number of reserved bits to the \"optimal\" amount.\n*/\nSQLITE_PRIVATE void sqlite3PagerAlignReserve(Pager *pDest, Pager *pSrc){\n  if( pDest->nReserve!=pSrc->nReserve ){\n    pDest->nReserve = pSrc->nReserve;\n    pagerReportSize(pDest);\n  }\n}\n#endif\n\n/*\n** Read a single page from either the journal file (if isMainJrnl==1) or\n** from the sub-journal (if isMainJrnl==0) and playback that page.\n** The page begins at offset *pOffset into the file. The *pOffset\n** value is increased to the start of the next page in the journal.\n**\n** The main rollback journal uses checksums - the statement journal does \n** not.\n**\n** If the page number of the page record read from the (sub-)journal file\n** is greater than the current value of Pager.dbSize, then playback is\n** skipped and SQLITE_OK is returned.\n**\n** If pDone is not NULL, then it is a record of pages that have already\n** been played back.  If the page at *pOffset has already been played back\n** (if the corresponding pDone bit is set) then skip the playback.\n** Make sure the pDone bit corresponding to the *pOffset page is set\n** prior to returning.\n**\n** If the page record is successfully read from the (sub-)journal file\n** and played back, then SQLITE_OK is returned. If an IO error occurs\n** while reading the record from the (sub-)journal file or while writing\n** to the database file, then the IO error code is returned. If data\n** is successfully read from the (sub-)journal file but appears to be\n** corrupted, SQLITE_DONE is returned. Data is considered corrupted in\n** two circumstances:\n** \n**   * If the record page-number is illegal (0 or PAGER_MJ_PGNO), or\n**   * If the record is being rolled back from the main journal file\n**     and the checksum field does not match the record content.\n**\n** Neither of these two scenarios are possible during a savepoint rollback.\n**\n** If this is a savepoint rollback, then memory may have to be dynamically\n** allocated by this function. If this is the case and an allocation fails,\n** SQLITE_NOMEM is returned.\n*/\nstatic int pager_playback_one_page(\n  Pager *pPager,                /* The pager being played back */\n  i64 *pOffset,                 /* Offset of record to playback */\n  Bitvec *pDone,                /* Bitvec of pages already played back */\n  int isMainJrnl,               /* 1 -> main journal. 0 -> sub-journal. */\n  int isSavepnt                 /* True for a savepoint rollback */\n){\n  int rc;\n  PgHdr *pPg;                   /* An existing page in the cache */\n  Pgno pgno;                    /* The page number of a page in journal */\n  u32 cksum;                    /* Checksum used for sanity checking */\n  char *aData;                  /* Temporary storage for the page */\n  sqlite3_file *jfd;            /* The file descriptor for the journal file */\n  int isSynced;                 /* True if journal page is synced */\n#ifdef SQLITE_HAS_CODEC\n  /* The jrnlEnc flag is true if Journal pages should be passed through\n  ** the codec.  It is false for pure in-memory journals. */\n  const int jrnlEnc = (isMainJrnl || pPager->subjInMemory==0);\n#endif\n\n  assert( (isMainJrnl&~1)==0 );      /* isMainJrnl is 0 or 1 */\n  assert( (isSavepnt&~1)==0 );       /* isSavepnt is 0 or 1 */\n  assert( isMainJrnl || pDone );     /* pDone always used on sub-journals */\n  assert( isSavepnt || pDone==0 );   /* pDone never used on non-savepoint */\n\n  aData = pPager->pTmpSpace;\n  assert( aData );         /* Temp storage must have already been allocated */\n  assert( pagerUseWal(pPager)==0 || (!isMainJrnl && isSavepnt) );\n\n  /* Either the state is greater than PAGER_WRITER_CACHEMOD (a transaction \n  ** or savepoint rollback done at the request of the caller) or this is\n  ** a hot-journal rollback. If it is a hot-journal rollback, the pager\n  ** is in state OPEN and holds an EXCLUSIVE lock. Hot-journal rollback\n  ** only reads from the main journal, not the sub-journal.\n  */\n  assert( pPager->eState>=PAGER_WRITER_CACHEMOD\n       || (pPager->eState==PAGER_OPEN && pPager->eLock==EXCLUSIVE_LOCK)\n  );\n  assert( pPager->eState>=PAGER_WRITER_CACHEMOD || isMainJrnl );\n\n  /* Read the page number and page data from the journal or sub-journal\n  ** file. Return an error code to the caller if an IO error occurs.\n  */\n  jfd = isMainJrnl ? pPager->jfd : pPager->sjfd;\n  rc = read32bits(jfd, *pOffset, &pgno);\n  if( rc!=SQLITE_OK ) return rc;\n  rc = sqlite3OsRead(jfd, (u8*)aData, pPager->pageSize, (*pOffset)+4);\n  if( rc!=SQLITE_OK ) return rc;\n  *pOffset += pPager->pageSize + 4 + isMainJrnl*4;\n\n  /* Sanity checking on the page.  This is more important that I originally\n  ** thought.  If a power failure occurs while the journal is being written,\n  ** it could cause invalid data to be written into the journal.  We need to\n  ** detect this invalid data (with high probability) and ignore it.\n  */\n  if( pgno==0 || pgno==PAGER_MJ_PGNO(pPager) ){\n    assert( !isSavepnt );\n    return SQLITE_DONE;\n  }\n  if( pgno>(Pgno)pPager->dbSize || sqlite3BitvecTest(pDone, pgno) ){\n    return SQLITE_OK;\n  }\n  if( isMainJrnl ){\n    rc = read32bits(jfd, (*pOffset)-4, &cksum);\n    if( rc ) return rc;\n    if( !isSavepnt && pager_cksum(pPager, (u8*)aData)!=cksum ){\n      return SQLITE_DONE;\n    }\n  }\n\n  /* If this page has already been played back before during the current\n  ** rollback, then don't bother to play it back again.\n  */\n  if( pDone && (rc = sqlite3BitvecSet(pDone, pgno))!=SQLITE_OK ){\n    return rc;\n  }\n\n  /* When playing back page 1, restore the nReserve setting\n  */\n  if( pgno==1 && pPager->nReserve!=((u8*)aData)[20] ){\n    pPager->nReserve = ((u8*)aData)[20];\n    pagerReportSize(pPager);\n  }\n\n  /* If the pager is in CACHEMOD state, then there must be a copy of this\n  ** page in the pager cache. In this case just update the pager cache,\n  ** not the database file. The page is left marked dirty in this case.\n  **\n  ** An exception to the above rule: If the database is in no-sync mode\n  ** and a page is moved during an incremental vacuum then the page may\n  ** not be in the pager cache. Later: if a malloc() or IO error occurs\n  ** during a Movepage() call, then the page may not be in the cache\n  ** either. So the condition described in the above paragraph is not\n  ** assert()able.\n  **\n  ** If in WRITER_DBMOD, WRITER_FINISHED or OPEN state, then we update the\n  ** pager cache if it exists and the main file. The page is then marked \n  ** not dirty. Since this code is only executed in PAGER_OPEN state for\n  ** a hot-journal rollback, it is guaranteed that the page-cache is empty\n  ** if the pager is in OPEN state.\n  **\n  ** Ticket #1171:  The statement journal might contain page content that is\n  ** different from the page content at the start of the transaction.\n  ** This occurs when a page is changed prior to the start of a statement\n  ** then changed again within the statement.  When rolling back such a\n  ** statement we must not write to the original database unless we know\n  ** for certain that original page contents are synced into the main rollback\n  ** journal.  Otherwise, a power loss might leave modified data in the\n  ** database file without an entry in the rollback journal that can\n  ** restore the database to its original form.  Two conditions must be\n  ** met before writing to the database files. (1) the database must be\n  ** locked.  (2) we know that the original page content is fully synced\n  ** in the main journal either because the page is not in cache or else\n  ** the page is marked as needSync==0.\n  **\n  ** 2008-04-14:  When attempting to vacuum a corrupt database file, it\n  ** is possible to fail a statement on a database that does not yet exist.\n  ** Do not attempt to write if database file has never been opened.\n  */\n  if( pagerUseWal(pPager) ){\n    pPg = 0;\n  }else{\n    pPg = sqlite3PagerLookup(pPager, pgno);\n  }\n  assert( pPg || !MEMDB );\n  assert( pPager->eState!=PAGER_OPEN || pPg==0 || pPager->tempFile );\n  PAGERTRACE((\"PLAYBACK %d page %d hash(%08x) %s\\n\",\n           PAGERID(pPager), pgno, pager_datahash(pPager->pageSize, (u8*)aData),\n           (isMainJrnl?\"main-journal\":\"sub-journal\")\n  ));\n  if( isMainJrnl ){\n    isSynced = pPager->noSync || (*pOffset <= pPager->journalHdr);\n  }else{\n    isSynced = (pPg==0 || 0==(pPg->flags & PGHDR_NEED_SYNC));\n  }\n  if( isOpen(pPager->fd)\n   && (pPager->eState>=PAGER_WRITER_DBMOD || pPager->eState==PAGER_OPEN)\n   && isSynced\n  ){\n    i64 ofst = (pgno-1)*(i64)pPager->pageSize;\n    testcase( !isSavepnt && pPg!=0 && (pPg->flags&PGHDR_NEED_SYNC)!=0 );\n    assert( !pagerUseWal(pPager) );\n\n    /* Write the data read from the journal back into the database file.\n    ** This is usually safe even for an encrypted database - as the data\n    ** was encrypted before it was written to the journal file. The exception\n    ** is if the data was just read from an in-memory sub-journal. In that\n    ** case it must be encrypted here before it is copied into the database\n    ** file.  */\n#ifdef SQLITE_HAS_CODEC\n    if( !jrnlEnc ){\n      CODEC2(pPager, aData, pgno, 7, rc=SQLITE_NOMEM_BKPT, aData);\n      rc = sqlite3OsWrite(pPager->fd, (u8 *)aData, pPager->pageSize, ofst);\n      CODEC1(pPager, aData, pgno, 3, rc=SQLITE_NOMEM_BKPT);\n    }else\n#endif\n    rc = sqlite3OsWrite(pPager->fd, (u8 *)aData, pPager->pageSize, ofst);\n\n    if( pgno>pPager->dbFileSize ){\n      pPager->dbFileSize = pgno;\n    }\n    if( pPager->pBackup ){\n#ifdef SQLITE_HAS_CODEC\n      if( jrnlEnc ){\n        CODEC1(pPager, aData, pgno, 3, rc=SQLITE_NOMEM_BKPT);\n        sqlite3BackupUpdate(pPager->pBackup, pgno, (u8*)aData);\n        CODEC2(pPager, aData, pgno, 7, rc=SQLITE_NOMEM_BKPT,aData);\n      }else\n#endif\n      sqlite3BackupUpdate(pPager->pBackup, pgno, (u8*)aData);\n    }\n  }else if( !isMainJrnl && pPg==0 ){\n    /* If this is a rollback of a savepoint and data was not written to\n    ** the database and the page is not in-memory, there is a potential\n    ** problem. When the page is next fetched by the b-tree layer, it \n    ** will be read from the database file, which may or may not be \n    ** current. \n    **\n    ** There are a couple of different ways this can happen. All are quite\n    ** obscure. When running in synchronous mode, this can only happen \n    ** if the page is on the free-list at the start of the transaction, then\n    ** populated, then moved using sqlite3PagerMovepage().\n    **\n    ** The solution is to add an in-memory page to the cache containing\n    ** the data just read from the sub-journal. Mark the page as dirty \n    ** and if the pager requires a journal-sync, then mark the page as \n    ** requiring a journal-sync before it is written.\n    */\n    assert( isSavepnt );\n    assert( (pPager->doNotSpill & SPILLFLAG_ROLLBACK)==0 );\n    pPager->doNotSpill |= SPILLFLAG_ROLLBACK;\n    rc = sqlite3PagerGet(pPager, pgno, &pPg, 1);\n    assert( (pPager->doNotSpill & SPILLFLAG_ROLLBACK)!=0 );\n    pPager->doNotSpill &= ~SPILLFLAG_ROLLBACK;\n    if( rc!=SQLITE_OK ) return rc;\n    sqlite3PcacheMakeDirty(pPg);\n  }\n  if( pPg ){\n    /* No page should ever be explicitly rolled back that is in use, except\n    ** for page 1 which is held in use in order to keep the lock on the\n    ** database active. However such a page may be rolled back as a result\n    ** of an internal error resulting in an automatic call to\n    ** sqlite3PagerRollback().\n    */\n    void *pData;\n    pData = pPg->pData;\n    memcpy(pData, (u8*)aData, pPager->pageSize);\n    pPager->xReiniter(pPg);\n    /* It used to be that sqlite3PcacheMakeClean(pPg) was called here.  But\n    ** that call was dangerous and had no detectable benefit since the cache\n    ** is normally cleaned by sqlite3PcacheCleanAll() after rollback and so\n    ** has been removed. */\n    pager_set_pagehash(pPg);\n\n    /* If this was page 1, then restore the value of Pager.dbFileVers.\n    ** Do this before any decoding. */\n    if( pgno==1 ){\n      memcpy(&pPager->dbFileVers, &((u8*)pData)[24],sizeof(pPager->dbFileVers));\n    }\n\n    /* Decode the page just read from disk */\n#if SQLITE_HAS_CODEC\n    if( jrnlEnc ){ CODEC1(pPager, pData, pPg->pgno, 3, rc=SQLITE_NOMEM_BKPT); }\n#endif\n    sqlite3PcacheRelease(pPg);\n  }\n  return rc;\n}\n\n/*\n** Parameter zMaster is the name of a master journal file. A single journal\n** file that referred to the master journal file has just been rolled back.\n** This routine checks if it is possible to delete the master journal file,\n** and does so if it is.\n**\n** Argument zMaster may point to Pager.pTmpSpace. So that buffer is not \n** available for use within this function.\n**\n** When a master journal file is created, it is populated with the names \n** of all of its child journals, one after another, formatted as utf-8 \n** encoded text. The end of each child journal file is marked with a \n** nul-terminator byte (0x00). i.e. the entire contents of a master journal\n** file for a transaction involving two databases might be:\n**\n**   \"/home/bill/a.db-journal\\x00/home/bill/b.db-journal\\x00\"\n**\n** A master journal file may only be deleted once all of its child \n** journals have been rolled back.\n**\n** This function reads the contents of the master-journal file into \n** memory and loops through each of the child journal names. For\n** each child journal, it checks if:\n**\n**   * if the child journal exists, and if so\n**   * if the child journal contains a reference to master journal \n**     file zMaster\n**\n** If a child journal can be found that matches both of the criteria\n** above, this function returns without doing anything. Otherwise, if\n** no such child journal can be found, file zMaster is deleted from\n** the file-system using sqlite3OsDelete().\n**\n** If an IO error within this function, an error code is returned. This\n** function allocates memory by calling sqlite3Malloc(). If an allocation\n** fails, SQLITE_NOMEM is returned. Otherwise, if no IO or malloc errors \n** occur, SQLITE_OK is returned.\n**\n** TODO: This function allocates a single block of memory to load\n** the entire contents of the master journal file. This could be\n** a couple of kilobytes or so - potentially larger than the page \n** size.\n*/\nstatic int pager_delmaster(Pager *pPager, const char *zMaster){\n  sqlite3_vfs *pVfs = pPager->pVfs;\n  int rc;                   /* Return code */\n  sqlite3_file *pMaster;    /* Malloc'd master-journal file descriptor */\n  sqlite3_file *pJournal;   /* Malloc'd child-journal file descriptor */\n  char *zMasterJournal = 0; /* Contents of master journal file */\n  i64 nMasterJournal;       /* Size of master journal file */\n  char *zJournal;           /* Pointer to one journal within MJ file */\n  char *zMasterPtr;         /* Space to hold MJ filename from a journal file */\n  int nMasterPtr;           /* Amount of space allocated to zMasterPtr[] */\n\n  /* Allocate space for both the pJournal and pMaster file descriptors.\n  ** If successful, open the master journal file for reading.\n  */\n  pMaster = (sqlite3_file *)sqlite3MallocZero(pVfs->szOsFile * 2);\n  pJournal = (sqlite3_file *)(((u8 *)pMaster) + pVfs->szOsFile);\n  if( !pMaster ){\n    rc = SQLITE_NOMEM_BKPT;\n  }else{\n    const int flags = (SQLITE_OPEN_READONLY|SQLITE_OPEN_MASTER_JOURNAL);\n    rc = sqlite3OsOpen(pVfs, zMaster, pMaster, flags, 0);\n  }\n  if( rc!=SQLITE_OK ) goto delmaster_out;\n\n  /* Load the entire master journal file into space obtained from\n  ** sqlite3_malloc() and pointed to by zMasterJournal.   Also obtain\n  ** sufficient space (in zMasterPtr) to hold the names of master\n  ** journal files extracted from regular rollback-journals.\n  */\n  rc = sqlite3OsFileSize(pMaster, &nMasterJournal);\n  if( rc!=SQLITE_OK ) goto delmaster_out;\n  nMasterPtr = pVfs->mxPathname+1;\n  zMasterJournal = sqlite3Malloc(nMasterJournal + nMasterPtr + 1);\n  if( !zMasterJournal ){\n    rc = SQLITE_NOMEM_BKPT;\n    goto delmaster_out;\n  }\n  zMasterPtr = &zMasterJournal[nMasterJournal+1];\n  rc = sqlite3OsRead(pMaster, zMasterJournal, (int)nMasterJournal, 0);\n  if( rc!=SQLITE_OK ) goto delmaster_out;\n  zMasterJournal[nMasterJournal] = 0;\n\n  zJournal = zMasterJournal;\n  while( (zJournal-zMasterJournal)<nMasterJournal ){\n    int exists;\n    rc = sqlite3OsAccess(pVfs, zJournal, SQLITE_ACCESS_EXISTS, &exists);\n    if( rc!=SQLITE_OK ){\n      goto delmaster_out;\n    }\n    if( exists ){\n      /* One of the journals pointed to by the master journal exists.\n      ** Open it and check if it points at the master journal. If\n      ** so, return without deleting the master journal file.\n      */\n      int c;\n      int flags = (SQLITE_OPEN_READONLY|SQLITE_OPEN_MAIN_JOURNAL);\n      rc = sqlite3OsOpen(pVfs, zJournal, pJournal, flags, 0);\n      if( rc!=SQLITE_OK ){\n        goto delmaster_out;\n      }\n\n      rc = readMasterJournal(pJournal, zMasterPtr, nMasterPtr);\n      sqlite3OsClose(pJournal);\n      if( rc!=SQLITE_OK ){\n        goto delmaster_out;\n      }\n\n      c = zMasterPtr[0]!=0 && strcmp(zMasterPtr, zMaster)==0;\n      if( c ){\n        /* We have a match. Do not delete the master journal file. */\n        goto delmaster_out;\n      }\n    }\n    zJournal += (sqlite3Strlen30(zJournal)+1);\n  }\n \n  sqlite3OsClose(pMaster);\n  rc = sqlite3OsDelete(pVfs, zMaster, 0);\n\ndelmaster_out:\n  sqlite3_free(zMasterJournal);\n  if( pMaster ){\n    sqlite3OsClose(pMaster);\n    assert( !isOpen(pJournal) );\n    sqlite3_free(pMaster);\n  }\n  return rc;\n}\n\n\n/*\n** This function is used to change the actual size of the database \n** file in the file-system. This only happens when committing a transaction,\n** or rolling back a transaction (including rolling back a hot-journal).\n**\n** If the main database file is not open, or the pager is not in either\n** DBMOD or OPEN state, this function is a no-op. Otherwise, the size \n** of the file is changed to nPage pages (nPage*pPager->pageSize bytes). \n** If the file on disk is currently larger than nPage pages, then use the VFS\n** xTruncate() method to truncate it.\n**\n** Or, it might be the case that the file on disk is smaller than \n** nPage pages. Some operating system implementations can get confused if \n** you try to truncate a file to some size that is larger than it \n** currently is, so detect this case and write a single zero byte to \n** the end of the new file instead.\n**\n** If successful, return SQLITE_OK. If an IO error occurs while modifying\n** the database file, return the error code to the caller.\n*/\nstatic int pager_truncate(Pager *pPager, Pgno nPage){\n  int rc = SQLITE_OK;\n  assert( pPager->eState!=PAGER_ERROR );\n  assert( pPager->eState!=PAGER_READER );\n  \n  if( isOpen(pPager->fd) \n   && (pPager->eState>=PAGER_WRITER_DBMOD || pPager->eState==PAGER_OPEN) \n  ){\n    i64 currentSize, newSize;\n    int szPage = pPager->pageSize;\n    assert( pPager->eLock==EXCLUSIVE_LOCK );\n    /* TODO: Is it safe to use Pager.dbFileSize here? */\n    rc = sqlite3OsFileSize(pPager->fd, &currentSize);\n    newSize = szPage*(i64)nPage;\n    if( rc==SQLITE_OK && currentSize!=newSize ){\n      if( currentSize>newSize ){\n        rc = sqlite3OsTruncate(pPager->fd, newSize);\n      }else if( (currentSize+szPage)<=newSize ){\n        char *pTmp = pPager->pTmpSpace;\n        memset(pTmp, 0, szPage);\n        testcase( (newSize-szPage) == currentSize );\n        testcase( (newSize-szPage) >  currentSize );\n        rc = sqlite3OsWrite(pPager->fd, pTmp, szPage, newSize-szPage);\n      }\n      if( rc==SQLITE_OK ){\n        pPager->dbFileSize = nPage;\n      }\n    }\n  }\n  return rc;\n}\n\n/*\n** Return a sanitized version of the sector-size of OS file pFile. The\n** return value is guaranteed to lie between 32 and MAX_SECTOR_SIZE.\n*/\nSQLITE_PRIVATE int sqlite3SectorSize(sqlite3_file *pFile){\n  int iRet = sqlite3OsSectorSize(pFile);\n  if( iRet<32 ){\n    iRet = 512;\n  }else if( iRet>MAX_SECTOR_SIZE ){\n    assert( MAX_SECTOR_SIZE>=512 );\n    iRet = MAX_SECTOR_SIZE;\n  }\n  return iRet;\n}\n\n/*\n** Set the value of the Pager.sectorSize variable for the given\n** pager based on the value returned by the xSectorSize method\n** of the open database file. The sector size will be used \n** to determine the size and alignment of journal header and \n** master journal pointers within created journal files.\n**\n** For temporary files the effective sector size is always 512 bytes.\n**\n** Otherwise, for non-temporary files, the effective sector size is\n** the value returned by the xSectorSize() method rounded up to 32 if\n** it is less than 32, or rounded down to MAX_SECTOR_SIZE if it\n** is greater than MAX_SECTOR_SIZE.\n**\n** If the file has the SQLITE_IOCAP_POWERSAFE_OVERWRITE property, then set\n** the effective sector size to its minimum value (512).  The purpose of\n** pPager->sectorSize is to define the \"blast radius\" of bytes that\n** might change if a crash occurs while writing to a single byte in\n** that range.  But with POWERSAFE_OVERWRITE, the blast radius is zero\n** (that is what POWERSAFE_OVERWRITE means), so we minimize the sector\n** size.  For backwards compatibility of the rollback journal file format,\n** we cannot reduce the effective sector size below 512.\n*/\nstatic void setSectorSize(Pager *pPager){\n  assert( isOpen(pPager->fd) || pPager->tempFile );\n\n  if( pPager->tempFile\n   || (sqlite3OsDeviceCharacteristics(pPager->fd) & \n              SQLITE_IOCAP_POWERSAFE_OVERWRITE)!=0\n  ){\n    /* Sector size doesn't matter for temporary files. Also, the file\n    ** may not have been opened yet, in which case the OsSectorSize()\n    ** call will segfault. */\n    pPager->sectorSize = 512;\n  }else{\n    pPager->sectorSize = sqlite3SectorSize(pPager->fd);\n  }\n}\n\n/*\n** Playback the journal and thus restore the database file to\n** the state it was in before we started making changes.  \n**\n** The journal file format is as follows: \n**\n**  (1)  8 byte prefix.  A copy of aJournalMagic[].\n**  (2)  4 byte big-endian integer which is the number of valid page records\n**       in the journal.  If this value is 0xffffffff, then compute the\n**       number of page records from the journal size.\n**  (3)  4 byte big-endian integer which is the initial value for the \n**       sanity checksum.\n**  (4)  4 byte integer which is the number of pages to truncate the\n**       database to during a rollback.\n**  (5)  4 byte big-endian integer which is the sector size.  The header\n**       is this many bytes in size.\n**  (6)  4 byte big-endian integer which is the page size.\n**  (7)  zero padding out to the next sector size.\n**  (8)  Zero or more pages instances, each as follows:\n**        +  4 byte page number.\n**        +  pPager->pageSize bytes of data.\n**        +  4 byte checksum\n**\n** When we speak of the journal header, we mean the first 7 items above.\n** Each entry in the journal is an instance of the 8th item.\n**\n** Call the value from the second bullet \"nRec\".  nRec is the number of\n** valid page entries in the journal.  In most cases, you can compute the\n** value of nRec from the size of the journal file.  But if a power\n** failure occurred while the journal was being written, it could be the\n** case that the size of the journal file had already been increased but\n** the extra entries had not yet made it safely to disk.  In such a case,\n** the value of nRec computed from the file size would be too large.  For\n** that reason, we always use the nRec value in the header.\n**\n** If the nRec value is 0xffffffff it means that nRec should be computed\n** from the file size.  This value is used when the user selects the\n** no-sync option for the journal.  A power failure could lead to corruption\n** in this case.  But for things like temporary table (which will be\n** deleted when the power is restored) we don't care.  \n**\n** If the file opened as the journal file is not a well-formed\n** journal file then all pages up to the first corrupted page are rolled\n** back (or no pages if the journal header is corrupted). The journal file\n** is then deleted and SQLITE_OK returned, just as if no corruption had\n** been encountered.\n**\n** If an I/O or malloc() error occurs, the journal-file is not deleted\n** and an error code is returned.\n**\n** The isHot parameter indicates that we are trying to rollback a journal\n** that might be a hot journal.  Or, it could be that the journal is \n** preserved because of JOURNALMODE_PERSIST or JOURNALMODE_TRUNCATE.\n** If the journal really is hot, reset the pager cache prior rolling\n** back any content.  If the journal is merely persistent, no reset is\n** needed.\n*/\nstatic int pager_playback(Pager *pPager, int isHot){\n  sqlite3_vfs *pVfs = pPager->pVfs;\n  i64 szJ;                 /* Size of the journal file in bytes */\n  u32 nRec;                /* Number of Records in the journal */\n  u32 u;                   /* Unsigned loop counter */\n  Pgno mxPg = 0;           /* Size of the original file in pages */\n  int rc;                  /* Result code of a subroutine */\n  int res = 1;             /* Value returned by sqlite3OsAccess() */\n  char *zMaster = 0;       /* Name of master journal file if any */\n  int needPagerReset;      /* True to reset page prior to first page rollback */\n  int nPlayback = 0;       /* Total number of pages restored from journal */\n  u32 savedPageSize = pPager->pageSize;\n\n  /* Figure out how many records are in the journal.  Abort early if\n  ** the journal is empty.\n  */\n  assert( isOpen(pPager->jfd) );\n  rc = sqlite3OsFileSize(pPager->jfd, &szJ);\n  if( rc!=SQLITE_OK ){\n    goto end_playback;\n  }\n\n  /* Read the master journal name from the journal, if it is present.\n  ** If a master journal file name is specified, but the file is not\n  ** present on disk, then the journal is not hot and does not need to be\n  ** played back.\n  **\n  ** TODO: Technically the following is an error because it assumes that\n  ** buffer Pager.pTmpSpace is (mxPathname+1) bytes or larger. i.e. that\n  ** (pPager->pageSize >= pPager->pVfs->mxPathname+1). Using os_unix.c,\n  ** mxPathname is 512, which is the same as the minimum allowable value\n  ** for pageSize.\n  */\n  zMaster = pPager->pTmpSpace;\n  rc = readMasterJournal(pPager->jfd, zMaster, pPager->pVfs->mxPathname+1);\n  if( rc==SQLITE_OK && zMaster[0] ){\n    rc = sqlite3OsAccess(pVfs, zMaster, SQLITE_ACCESS_EXISTS, &res);\n  }\n  zMaster = 0;\n  if( rc!=SQLITE_OK || !res ){\n    goto end_playback;\n  }\n  pPager->journalOff = 0;\n  needPagerReset = isHot;\n\n  /* This loop terminates either when a readJournalHdr() or \n  ** pager_playback_one_page() call returns SQLITE_DONE or an IO error \n  ** occurs. \n  */\n  while( 1 ){\n    /* Read the next journal header from the journal file.  If there are\n    ** not enough bytes left in the journal file for a complete header, or\n    ** it is corrupted, then a process must have failed while writing it.\n    ** This indicates nothing more needs to be rolled back.\n    */\n    rc = readJournalHdr(pPager, isHot, szJ, &nRec, &mxPg);\n    if( rc!=SQLITE_OK ){ \n      if( rc==SQLITE_DONE ){\n        rc = SQLITE_OK;\n      }\n      goto end_playback;\n    }\n\n    /* If nRec is 0xffffffff, then this journal was created by a process\n    ** working in no-sync mode. This means that the rest of the journal\n    ** file consists of pages, there are no more journal headers. Compute\n    ** the value of nRec based on this assumption.\n    */\n    if( nRec==0xffffffff ){\n      assert( pPager->journalOff==JOURNAL_HDR_SZ(pPager) );\n      nRec = (int)((szJ - JOURNAL_HDR_SZ(pPager))/JOURNAL_PG_SZ(pPager));\n    }\n\n    /* If nRec is 0 and this rollback is of a transaction created by this\n    ** process and if this is the final header in the journal, then it means\n    ** that this part of the journal was being filled but has not yet been\n    ** synced to disk.  Compute the number of pages based on the remaining\n    ** size of the file.\n    **\n    ** The third term of the test was added to fix ticket #2565.\n    ** When rolling back a hot journal, nRec==0 always means that the next\n    ** chunk of the journal contains zero pages to be rolled back.  But\n    ** when doing a ROLLBACK and the nRec==0 chunk is the last chunk in\n    ** the journal, it means that the journal might contain additional\n    ** pages that need to be rolled back and that the number of pages \n    ** should be computed based on the journal file size.\n    */\n    if( nRec==0 && !isHot &&\n        pPager->journalHdr+JOURNAL_HDR_SZ(pPager)==pPager->journalOff ){\n      nRec = (int)((szJ - pPager->journalOff) / JOURNAL_PG_SZ(pPager));\n    }\n\n    /* If this is the first header read from the journal, truncate the\n    ** database file back to its original size.\n    */\n    if( pPager->journalOff==JOURNAL_HDR_SZ(pPager) ){\n      rc = pager_truncate(pPager, mxPg);\n      if( rc!=SQLITE_OK ){\n        goto end_playback;\n      }\n      pPager->dbSize = mxPg;\n    }\n\n    /* Copy original pages out of the journal and back into the \n    ** database file and/or page cache.\n    */\n    for(u=0; u<nRec; u++){\n      if( needPagerReset ){\n        pager_reset(pPager);\n        needPagerReset = 0;\n      }\n      rc = pager_playback_one_page(pPager,&pPager->journalOff,0,1,0);\n      if( rc==SQLITE_OK ){\n        nPlayback++;\n      }else{\n        if( rc==SQLITE_DONE ){\n          pPager->journalOff = szJ;\n          break;\n        }else if( rc==SQLITE_IOERR_SHORT_READ ){\n          /* If the journal has been truncated, simply stop reading and\n          ** processing the journal. This might happen if the journal was\n          ** not completely written and synced prior to a crash.  In that\n          ** case, the database should have never been written in the\n          ** first place so it is OK to simply abandon the rollback. */\n          rc = SQLITE_OK;\n          goto end_playback;\n        }else{\n          /* If we are unable to rollback, quit and return the error\n          ** code.  This will cause the pager to enter the error state\n          ** so that no further harm will be done.  Perhaps the next\n          ** process to come along will be able to rollback the database.\n          */\n          goto end_playback;\n        }\n      }\n    }\n  }\n  /*NOTREACHED*/\n  assert( 0 );\n\nend_playback:\n  if( rc==SQLITE_OK ){\n    rc = sqlite3PagerSetPagesize(pPager, &savedPageSize, -1);\n  }\n  /* Following a rollback, the database file should be back in its original\n  ** state prior to the start of the transaction, so invoke the\n  ** SQLITE_FCNTL_DB_UNCHANGED file-control method to disable the\n  ** assertion that the transaction counter was modified.\n  */\n#ifdef SQLITE_DEBUG\n  if( pPager->fd->pMethods ){\n    sqlite3OsFileControlHint(pPager->fd,SQLITE_FCNTL_DB_UNCHANGED,0);\n  }\n#endif\n\n  /* If this playback is happening automatically as a result of an IO or \n  ** malloc error that occurred after the change-counter was updated but \n  ** before the transaction was committed, then the change-counter \n  ** modification may just have been reverted. If this happens in exclusive \n  ** mode, then subsequent transactions performed by the connection will not\n  ** update the change-counter at all. This may lead to cache inconsistency\n  ** problems for other processes at some point in the future. So, just\n  ** in case this has happened, clear the changeCountDone flag now.\n  */\n  pPager->changeCountDone = pPager->tempFile;\n\n  if( rc==SQLITE_OK ){\n    zMaster = pPager->pTmpSpace;\n    rc = readMasterJournal(pPager->jfd, zMaster, pPager->pVfs->mxPathname+1);\n    testcase( rc!=SQLITE_OK );\n  }\n  if( rc==SQLITE_OK\n   && (pPager->eState>=PAGER_WRITER_DBMOD || pPager->eState==PAGER_OPEN)\n  ){\n    rc = sqlite3PagerSync(pPager, 0);\n  }\n  if( rc==SQLITE_OK ){\n    rc = pager_end_transaction(pPager, zMaster[0]!='\\0', 0);\n    testcase( rc!=SQLITE_OK );\n  }\n  if( rc==SQLITE_OK && zMaster[0] && res ){\n    /* If there was a master journal and this routine will return success,\n    ** see if it is possible to delete the master journal.\n    */\n    rc = pager_delmaster(pPager, zMaster);\n    testcase( rc!=SQLITE_OK );\n  }\n  if( isHot && nPlayback ){\n    sqlite3_log(SQLITE_NOTICE_RECOVER_ROLLBACK, \"recovered %d pages from %s\",\n                nPlayback, pPager->zJournal);\n  }\n\n  /* The Pager.sectorSize variable may have been updated while rolling\n  ** back a journal created by a process with a different sector size\n  ** value. Reset it to the correct value for this process.\n  */\n  setSectorSize(pPager);\n  return rc;\n}\n\n\n/*\n** Read the content for page pPg out of the database file (or out of\n** the WAL if that is where the most recent copy if found) into \n** pPg->pData. A shared lock or greater must be held on the database\n** file before this function is called.\n**\n** If page 1 is read, then the value of Pager.dbFileVers[] is set to\n** the value read from the database file.\n**\n** If an IO error occurs, then the IO error is returned to the caller.\n** Otherwise, SQLITE_OK is returned.\n*/\nstatic int readDbPage(PgHdr *pPg){\n  Pager *pPager = pPg->pPager; /* Pager object associated with page pPg */\n  int rc = SQLITE_OK;          /* Return code */\n\n#ifndef SQLITE_OMIT_WAL\n  u32 iFrame = 0;              /* Frame of WAL containing pgno */\n\n  assert( pPager->eState>=PAGER_READER && !MEMDB );\n  assert( isOpen(pPager->fd) );\n\n  if( pagerUseWal(pPager) ){\n    rc = sqlite3WalFindFrame(pPager->pWal, pPg->pgno, &iFrame);\n    if( rc ) return rc;\n  }\n  if( iFrame ){\n    rc = sqlite3WalReadFrame(pPager->pWal, iFrame,pPager->pageSize,pPg->pData);\n  }else\n#endif\n  {\n    i64 iOffset = (pPg->pgno-1)*(i64)pPager->pageSize;\n    rc = sqlite3OsRead(pPager->fd, pPg->pData, pPager->pageSize, iOffset);\n    if( rc==SQLITE_IOERR_SHORT_READ ){\n      rc = SQLITE_OK;\n    }\n  }\n\n  if( pPg->pgno==1 ){\n    if( rc ){\n      /* If the read is unsuccessful, set the dbFileVers[] to something\n      ** that will never be a valid file version.  dbFileVers[] is a copy\n      ** of bytes 24..39 of the database.  Bytes 28..31 should always be\n      ** zero or the size of the database in page. Bytes 32..35 and 35..39\n      ** should be page numbers which are never 0xffffffff.  So filling\n      ** pPager->dbFileVers[] with all 0xff bytes should suffice.\n      **\n      ** For an encrypted database, the situation is more complex:  bytes\n      ** 24..39 of the database are white noise.  But the probability of\n      ** white noise equaling 16 bytes of 0xff is vanishingly small so\n      ** we should still be ok.\n      */\n      memset(pPager->dbFileVers, 0xff, sizeof(pPager->dbFileVers));\n    }else{\n      u8 *dbFileVers = &((u8*)pPg->pData)[24];\n      memcpy(&pPager->dbFileVers, dbFileVers, sizeof(pPager->dbFileVers));\n    }\n  }\n  CODEC1(pPager, pPg->pData, pPg->pgno, 3, rc = SQLITE_NOMEM_BKPT);\n\n  PAGER_INCR(sqlite3_pager_readdb_count);\n  PAGER_INCR(pPager->nRead);\n  IOTRACE((\"PGIN %p %d\\n\", pPager, pPg->pgno));\n  PAGERTRACE((\"FETCH %d page %d hash(%08x)\\n\",\n               PAGERID(pPager), pPg->pgno, pager_pagehash(pPg)));\n\n  return rc;\n}\n\n/*\n** Update the value of the change-counter at offsets 24 and 92 in\n** the header and the sqlite version number at offset 96.\n**\n** This is an unconditional update.  See also the pager_incr_changecounter()\n** routine which only updates the change-counter if the update is actually\n** needed, as determined by the pPager->changeCountDone state variable.\n*/\nstatic void pager_write_changecounter(PgHdr *pPg){\n  u32 change_counter;\n\n  /* Increment the value just read and write it back to byte 24. */\n  change_counter = sqlite3Get4byte((u8*)pPg->pPager->dbFileVers)+1;\n  put32bits(((char*)pPg->pData)+24, change_counter);\n\n  /* Also store the SQLite version number in bytes 96..99 and in\n  ** bytes 92..95 store the change counter for which the version number\n  ** is valid. */\n  put32bits(((char*)pPg->pData)+92, change_counter);\n  put32bits(((char*)pPg->pData)+96, SQLITE_VERSION_NUMBER);\n}\n\n#ifndef SQLITE_OMIT_WAL\n/*\n** This function is invoked once for each page that has already been \n** written into the log file when a WAL transaction is rolled back.\n** Parameter iPg is the page number of said page. The pCtx argument \n** is actually a pointer to the Pager structure.\n**\n** If page iPg is present in the cache, and has no outstanding references,\n** it is discarded. Otherwise, if there are one or more outstanding\n** references, the page content is reloaded from the database. If the\n** attempt to reload content from the database is required and fails, \n** return an SQLite error code. Otherwise, SQLITE_OK.\n*/\nstatic int pagerUndoCallback(void *pCtx, Pgno iPg){\n  int rc = SQLITE_OK;\n  Pager *pPager = (Pager *)pCtx;\n  PgHdr *pPg;\n\n  assert( pagerUseWal(pPager) );\n  pPg = sqlite3PagerLookup(pPager, iPg);\n  if( pPg ){\n    if( sqlite3PcachePageRefcount(pPg)==1 ){\n      sqlite3PcacheDrop(pPg);\n    }else{\n      rc = readDbPage(pPg);\n      if( rc==SQLITE_OK ){\n        pPager->xReiniter(pPg);\n      }\n      sqlite3PagerUnrefNotNull(pPg);\n    }\n  }\n\n  /* Normally, if a transaction is rolled back, any backup processes are\n  ** updated as data is copied out of the rollback journal and into the\n  ** database. This is not generally possible with a WAL database, as\n  ** rollback involves simply truncating the log file. Therefore, if one\n  ** or more frames have already been written to the log (and therefore \n  ** also copied into the backup databases) as part of this transaction,\n  ** the backups must be restarted.\n  */\n  sqlite3BackupRestart(pPager->pBackup);\n\n  return rc;\n}\n\n/*\n** This function is called to rollback a transaction on a WAL database.\n*/\nstatic int pagerRollbackWal(Pager *pPager){\n  int rc;                         /* Return Code */\n  PgHdr *pList;                   /* List of dirty pages to revert */\n\n  /* For all pages in the cache that are currently dirty or have already\n  ** been written (but not committed) to the log file, do one of the \n  ** following:\n  **\n  **   + Discard the cached page (if refcount==0), or\n  **   + Reload page content from the database (if refcount>0).\n  */\n  pPager->dbSize = pPager->dbOrigSize;\n  rc = sqlite3WalUndo(pPager->pWal, pagerUndoCallback, (void *)pPager);\n  pList = sqlite3PcacheDirtyList(pPager->pPCache);\n  while( pList && rc==SQLITE_OK ){\n    PgHdr *pNext = pList->pDirty;\n    rc = pagerUndoCallback((void *)pPager, pList->pgno);\n    pList = pNext;\n  }\n\n  return rc;\n}\n\n/*\n** This function is a wrapper around sqlite3WalFrames(). As well as logging\n** the contents of the list of pages headed by pList (connected by pDirty),\n** this function notifies any active backup processes that the pages have\n** changed. \n**\n** The list of pages passed into this routine is always sorted by page number.\n** Hence, if page 1 appears anywhere on the list, it will be the first page.\n*/ \nstatic int pagerWalFrames(\n  Pager *pPager,                  /* Pager object */\n  PgHdr *pList,                   /* List of frames to log */\n  Pgno nTruncate,                 /* Database size after this commit */\n  int isCommit                    /* True if this is a commit */\n){\n  int rc;                         /* Return code */\n  int nList;                      /* Number of pages in pList */\n  PgHdr *p;                       /* For looping over pages */\n\n  assert( pPager->pWal );\n  assert( pList );\n#ifdef SQLITE_DEBUG\n  /* Verify that the page list is in accending order */\n  for(p=pList; p && p->pDirty; p=p->pDirty){\n    assert( p->pgno < p->pDirty->pgno );\n  }\n#endif\n\n  assert( pList->pDirty==0 || isCommit );\n  if( isCommit ){\n    /* If a WAL transaction is being committed, there is no point in writing\n    ** any pages with page numbers greater than nTruncate into the WAL file.\n    ** They will never be read by any client. So remove them from the pDirty\n    ** list here. */\n    PgHdr **ppNext = &pList;\n    nList = 0;\n    for(p=pList; (*ppNext = p)!=0; p=p->pDirty){\n      if( p->pgno<=nTruncate ){\n        ppNext = &p->pDirty;\n        nList++;\n      }\n    }\n    assert( pList );\n  }else{\n    nList = 1;\n  }\n  pPager->aStat[PAGER_STAT_WRITE] += nList;\n\n  if( pList->pgno==1 ) pager_write_changecounter(pList);\n  rc = sqlite3WalFrames(pPager->pWal, \n      pPager->pageSize, pList, nTruncate, isCommit, pPager->walSyncFlags\n  );\n  if( rc==SQLITE_OK && pPager->pBackup ){\n    for(p=pList; p; p=p->pDirty){\n      sqlite3BackupUpdate(pPager->pBackup, p->pgno, (u8 *)p->pData);\n    }\n  }\n\n#ifdef SQLITE_CHECK_PAGES\n  pList = sqlite3PcacheDirtyList(pPager->pPCache);\n  for(p=pList; p; p=p->pDirty){\n    pager_set_pagehash(p);\n  }\n#endif\n\n  return rc;\n}\n\n/*\n** Begin a read transaction on the WAL.\n**\n** This routine used to be called \"pagerOpenSnapshot()\" because it essentially\n** makes a snapshot of the database at the current point in time and preserves\n** that snapshot for use by the reader in spite of concurrently changes by\n** other writers or checkpointers.\n*/\nstatic int pagerBeginReadTransaction(Pager *pPager){\n  int rc;                         /* Return code */\n  int changed = 0;                /* True if cache must be reset */\n\n  assert( pagerUseWal(pPager) );\n  assert( pPager->eState==PAGER_OPEN || pPager->eState==PAGER_READER );\n\n  /* sqlite3WalEndReadTransaction() was not called for the previous\n  ** transaction in locking_mode=EXCLUSIVE.  So call it now.  If we\n  ** are in locking_mode=NORMAL and EndRead() was previously called,\n  ** the duplicate call is harmless.\n  */\n  sqlite3WalEndReadTransaction(pPager->pWal);\n\n  rc = sqlite3WalBeginReadTransaction(pPager->pWal, &changed);\n  if( rc!=SQLITE_OK || changed ){\n    pager_reset(pPager);\n    if( USEFETCH(pPager) ) sqlite3OsUnfetch(pPager->fd, 0, 0);\n  }\n\n  return rc;\n}\n#endif\n\n/*\n** This function is called as part of the transition from PAGER_OPEN\n** to PAGER_READER state to determine the size of the database file\n** in pages (assuming the page size currently stored in Pager.pageSize).\n**\n** If no error occurs, SQLITE_OK is returned and the size of the database\n** in pages is stored in *pnPage. Otherwise, an error code (perhaps\n** SQLITE_IOERR_FSTAT) is returned and *pnPage is left unmodified.\n*/\nstatic int pagerPagecount(Pager *pPager, Pgno *pnPage){\n  Pgno nPage;                     /* Value to return via *pnPage */\n\n  /* Query the WAL sub-system for the database size. The WalDbsize()\n  ** function returns zero if the WAL is not open (i.e. Pager.pWal==0), or\n  ** if the database size is not available. The database size is not\n  ** available from the WAL sub-system if the log file is empty or\n  ** contains no valid committed transactions.\n  */\n  assert( pPager->eState==PAGER_OPEN );\n  assert( pPager->eLock>=SHARED_LOCK );\n  assert( isOpen(pPager->fd) );\n  assert( pPager->tempFile==0 );\n  nPage = sqlite3WalDbsize(pPager->pWal);\n\n  /* If the number of pages in the database is not available from the\n  ** WAL sub-system, determine the page count based on the size of\n  ** the database file.  If the size of the database file is not an\n  ** integer multiple of the page-size, round up the result.\n  */\n  if( nPage==0 && ALWAYS(isOpen(pPager->fd)) ){\n    i64 n = 0;                    /* Size of db file in bytes */\n    int rc = sqlite3OsFileSize(pPager->fd, &n);\n    if( rc!=SQLITE_OK ){\n      return rc;\n    }\n    nPage = (Pgno)((n+pPager->pageSize-1) / pPager->pageSize);\n  }\n\n  /* If the current number of pages in the file is greater than the\n  ** configured maximum pager number, increase the allowed limit so\n  ** that the file can be read.\n  */\n  if( nPage>pPager->mxPgno ){\n    pPager->mxPgno = (Pgno)nPage;\n  }\n\n  *pnPage = nPage;\n  return SQLITE_OK;\n}\n\n#ifndef SQLITE_OMIT_WAL\n/*\n** Check if the *-wal file that corresponds to the database opened by pPager\n** exists if the database is not empy, or verify that the *-wal file does\n** not exist (by deleting it) if the database file is empty.\n**\n** If the database is not empty and the *-wal file exists, open the pager\n** in WAL mode.  If the database is empty or if no *-wal file exists and\n** if no error occurs, make sure Pager.journalMode is not set to\n** PAGER_JOURNALMODE_WAL.\n**\n** Return SQLITE_OK or an error code.\n**\n** The caller must hold a SHARED lock on the database file to call this\n** function. Because an EXCLUSIVE lock on the db file is required to delete \n** a WAL on a none-empty database, this ensures there is no race condition \n** between the xAccess() below and an xDelete() being executed by some \n** other connection.\n*/\nstatic int pagerOpenWalIfPresent(Pager *pPager){\n  int rc = SQLITE_OK;\n  assert( pPager->eState==PAGER_OPEN );\n  assert( pPager->eLock>=SHARED_LOCK );\n\n  if( !pPager->tempFile ){\n    int isWal;                    /* True if WAL file exists */\n    rc = sqlite3OsAccess(\n        pPager->pVfs, pPager->zWal, SQLITE_ACCESS_EXISTS, &isWal\n    );\n    if( rc==SQLITE_OK ){\n      if( isWal ){\n        Pgno nPage;                   /* Size of the database file */\n\n        rc = pagerPagecount(pPager, &nPage);\n        if( rc ) return rc;\n        if( nPage==0 ){\n          rc = sqlite3OsDelete(pPager->pVfs, pPager->zWal, 0);\n        }else{\n          testcase( sqlite3PcachePagecount(pPager->pPCache)==0 );\n          rc = sqlite3PagerOpenWal(pPager, 0);\n        }\n      }else if( pPager->journalMode==PAGER_JOURNALMODE_WAL ){\n        pPager->journalMode = PAGER_JOURNALMODE_DELETE;\n      }\n    }\n  }\n  return rc;\n}\n#endif\n\n/*\n** Playback savepoint pSavepoint. Or, if pSavepoint==NULL, then playback\n** the entire master journal file. The case pSavepoint==NULL occurs when \n** a ROLLBACK TO command is invoked on a SAVEPOINT that is a transaction \n** savepoint.\n**\n** When pSavepoint is not NULL (meaning a non-transaction savepoint is \n** being rolled back), then the rollback consists of up to three stages,\n** performed in the order specified:\n**\n**   * Pages are played back from the main journal starting at byte\n**     offset PagerSavepoint.iOffset and continuing to \n**     PagerSavepoint.iHdrOffset, or to the end of the main journal\n**     file if PagerSavepoint.iHdrOffset is zero.\n**\n**   * If PagerSavepoint.iHdrOffset is not zero, then pages are played\n**     back starting from the journal header immediately following \n**     PagerSavepoint.iHdrOffset to the end of the main journal file.\n**\n**   * Pages are then played back from the sub-journal file, starting\n**     with the PagerSavepoint.iSubRec and continuing to the end of\n**     the journal file.\n**\n** Throughout the rollback process, each time a page is rolled back, the\n** corresponding bit is set in a bitvec structure (variable pDone in the\n** implementation below). This is used to ensure that a page is only\n** rolled back the first time it is encountered in either journal.\n**\n** If pSavepoint is NULL, then pages are only played back from the main\n** journal file. There is no need for a bitvec in this case.\n**\n** In either case, before playback commences the Pager.dbSize variable\n** is reset to the value that it held at the start of the savepoint \n** (or transaction). No page with a page-number greater than this value\n** is played back. If one is encountered it is simply skipped.\n*/\nstatic int pagerPlaybackSavepoint(Pager *pPager, PagerSavepoint *pSavepoint){\n  i64 szJ;                 /* Effective size of the main journal */\n  i64 iHdrOff;             /* End of first segment of main-journal records */\n  int rc = SQLITE_OK;      /* Return code */\n  Bitvec *pDone = 0;       /* Bitvec to ensure pages played back only once */\n\n  assert( pPager->eState!=PAGER_ERROR );\n  assert( pPager->eState>=PAGER_WRITER_LOCKED );\n\n  /* Allocate a bitvec to use to store the set of pages rolled back */\n  if( pSavepoint ){\n    pDone = sqlite3BitvecCreate(pSavepoint->nOrig);\n    if( !pDone ){\n      return SQLITE_NOMEM_BKPT;\n    }\n  }\n\n  /* Set the database size back to the value it was before the savepoint \n  ** being reverted was opened.\n  */\n  pPager->dbSize = pSavepoint ? pSavepoint->nOrig : pPager->dbOrigSize;\n  pPager->changeCountDone = pPager->tempFile;\n\n  if( !pSavepoint && pagerUseWal(pPager) ){\n    return pagerRollbackWal(pPager);\n  }\n\n  /* Use pPager->journalOff as the effective size of the main rollback\n  ** journal.  The actual file might be larger than this in\n  ** PAGER_JOURNALMODE_TRUNCATE or PAGER_JOURNALMODE_PERSIST.  But anything\n  ** past pPager->journalOff is off-limits to us.\n  */\n  szJ = pPager->journalOff;\n  assert( pagerUseWal(pPager)==0 || szJ==0 );\n\n  /* Begin by rolling back records from the main journal starting at\n  ** PagerSavepoint.iOffset and continuing to the next journal header.\n  ** There might be records in the main journal that have a page number\n  ** greater than the current database size (pPager->dbSize) but those\n  ** will be skipped automatically.  Pages are added to pDone as they\n  ** are played back.\n  */\n  if( pSavepoint && !pagerUseWal(pPager) ){\n    iHdrOff = pSavepoint->iHdrOffset ? pSavepoint->iHdrOffset : szJ;\n    pPager->journalOff = pSavepoint->iOffset;\n    while( rc==SQLITE_OK && pPager->journalOff<iHdrOff ){\n      rc = pager_playback_one_page(pPager, &pPager->journalOff, pDone, 1, 1);\n    }\n    assert( rc!=SQLITE_DONE );\n  }else{\n    pPager->journalOff = 0;\n  }\n\n  /* Continue rolling back records out of the main journal starting at\n  ** the first journal header seen and continuing until the effective end\n  ** of the main journal file.  Continue to skip out-of-range pages and\n  ** continue adding pages rolled back to pDone.\n  */\n  while( rc==SQLITE_OK && pPager->journalOff<szJ ){\n    u32 ii;            /* Loop counter */\n    u32 nJRec = 0;     /* Number of Journal Records */\n    u32 dummy;\n    rc = readJournalHdr(pPager, 0, szJ, &nJRec, &dummy);\n    assert( rc!=SQLITE_DONE );\n\n    /*\n    ** The \"pPager->journalHdr+JOURNAL_HDR_SZ(pPager)==pPager->journalOff\"\n    ** test is related to ticket #2565.  See the discussion in the\n    ** pager_playback() function for additional information.\n    */\n    if( nJRec==0 \n     && pPager->journalHdr+JOURNAL_HDR_SZ(pPager)==pPager->journalOff\n    ){\n      nJRec = (u32)((szJ - pPager->journalOff)/JOURNAL_PG_SZ(pPager));\n    }\n    for(ii=0; rc==SQLITE_OK && ii<nJRec && pPager->journalOff<szJ; ii++){\n      rc = pager_playback_one_page(pPager, &pPager->journalOff, pDone, 1, 1);\n    }\n    assert( rc!=SQLITE_DONE );\n  }\n  assert( rc!=SQLITE_OK || pPager->journalOff>=szJ );\n\n  /* Finally,  rollback pages from the sub-journal.  Page that were\n  ** previously rolled back out of the main journal (and are hence in pDone)\n  ** will be skipped.  Out-of-range pages are also skipped.\n  */\n  if( pSavepoint ){\n    u32 ii;            /* Loop counter */\n    i64 offset = (i64)pSavepoint->iSubRec*(4+pPager->pageSize);\n\n    if( pagerUseWal(pPager) ){\n      rc = sqlite3WalSavepointUndo(pPager->pWal, pSavepoint->aWalData);\n    }\n    for(ii=pSavepoint->iSubRec; rc==SQLITE_OK && ii<pPager->nSubRec; ii++){\n      assert( offset==(i64)ii*(4+pPager->pageSize) );\n      rc = pager_playback_one_page(pPager, &offset, pDone, 0, 1);\n    }\n    assert( rc!=SQLITE_DONE );\n  }\n\n  sqlite3BitvecDestroy(pDone);\n  if( rc==SQLITE_OK ){\n    pPager->journalOff = szJ;\n  }\n\n  return rc;\n}\n\n/*\n** Change the maximum number of in-memory pages that are allowed\n** before attempting to recycle clean and unused pages.\n*/\nSQLITE_PRIVATE void sqlite3PagerSetCachesize(Pager *pPager, int mxPage){\n  sqlite3PcacheSetCachesize(pPager->pPCache, mxPage);\n}\n\n/*\n** Change the maximum number of in-memory pages that are allowed\n** before attempting to spill pages to journal.\n*/\nSQLITE_PRIVATE int sqlite3PagerSetSpillsize(Pager *pPager, int mxPage){\n  return sqlite3PcacheSetSpillsize(pPager->pPCache, mxPage);\n}\n\n/*\n** Invoke SQLITE_FCNTL_MMAP_SIZE based on the current value of szMmap.\n*/\nstatic void pagerFixMaplimit(Pager *pPager){\n#if SQLITE_MAX_MMAP_SIZE>0\n  sqlite3_file *fd = pPager->fd;\n  if( isOpen(fd) && fd->pMethods->iVersion>=3 ){\n    sqlite3_int64 sz;\n    sz = pPager->szMmap;\n    pPager->bUseFetch = (sz>0);\n    setGetterMethod(pPager);\n    sqlite3OsFileControlHint(pPager->fd, SQLITE_FCNTL_MMAP_SIZE, &sz);\n  }\n#endif\n}\n\n/*\n** Change the maximum size of any memory mapping made of the database file.\n*/\nSQLITE_PRIVATE void sqlite3PagerSetMmapLimit(Pager *pPager, sqlite3_int64 szMmap){\n  pPager->szMmap = szMmap;\n  pagerFixMaplimit(pPager);\n}\n\n/*\n** Free as much memory as possible from the pager.\n*/\nSQLITE_PRIVATE void sqlite3PagerShrink(Pager *pPager){\n  sqlite3PcacheShrink(pPager->pPCache);\n}\n\n/*\n** Adjust settings of the pager to those specified in the pgFlags parameter.\n**\n** The \"level\" in pgFlags & PAGER_SYNCHRONOUS_MASK sets the robustness\n** of the database to damage due to OS crashes or power failures by\n** changing the number of syncs()s when writing the journals.\n** There are four levels:\n**\n**    OFF       sqlite3OsSync() is never called.  This is the default\n**              for temporary and transient files.\n**\n**    NORMAL    The journal is synced once before writes begin on the\n**              database.  This is normally adequate protection, but\n**              it is theoretically possible, though very unlikely,\n**              that an inopertune power failure could leave the journal\n**              in a state which would cause damage to the database\n**              when it is rolled back.\n**\n**    FULL      The journal is synced twice before writes begin on the\n**              database (with some additional information - the nRec field\n**              of the journal header - being written in between the two\n**              syncs).  If we assume that writing a\n**              single disk sector is atomic, then this mode provides\n**              assurance that the journal will not be corrupted to the\n**              point of causing damage to the database during rollback.\n**\n**    EXTRA     This is like FULL except that is also syncs the directory\n**              that contains the rollback journal after the rollback\n**              journal is unlinked.\n**\n** The above is for a rollback-journal mode.  For WAL mode, OFF continues\n** to mean that no syncs ever occur.  NORMAL means that the WAL is synced\n** prior to the start of checkpoint and that the database file is synced\n** at the conclusion of the checkpoint if the entire content of the WAL\n** was written back into the database.  But no sync operations occur for\n** an ordinary commit in NORMAL mode with WAL.  FULL means that the WAL\n** file is synced following each commit operation, in addition to the\n** syncs associated with NORMAL.  There is no difference between FULL\n** and EXTRA for WAL mode.\n**\n** Do not confuse synchronous=FULL with SQLITE_SYNC_FULL.  The\n** SQLITE_SYNC_FULL macro means to use the MacOSX-style full-fsync\n** using fcntl(F_FULLFSYNC).  SQLITE_SYNC_NORMAL means to do an\n** ordinary fsync() call.  There is no difference between SQLITE_SYNC_FULL\n** and SQLITE_SYNC_NORMAL on platforms other than MacOSX.  But the\n** synchronous=FULL versus synchronous=NORMAL setting determines when\n** the xSync primitive is called and is relevant to all platforms.\n**\n** Numeric values associated with these states are OFF==1, NORMAL=2,\n** and FULL=3.\n*/\n#ifndef SQLITE_OMIT_PAGER_PRAGMAS\nSQLITE_PRIVATE void sqlite3PagerSetFlags(\n  Pager *pPager,        /* The pager to set safety level for */\n  unsigned pgFlags      /* Various flags */\n){\n  unsigned level = pgFlags & PAGER_SYNCHRONOUS_MASK;\n  if( pPager->tempFile ){\n    pPager->noSync = 1;\n    pPager->fullSync = 0;\n    pPager->extraSync = 0;\n  }else{\n    pPager->noSync =  level==PAGER_SYNCHRONOUS_OFF ?1:0;\n    pPager->fullSync = level>=PAGER_SYNCHRONOUS_FULL ?1:0;\n    pPager->extraSync = level==PAGER_SYNCHRONOUS_EXTRA ?1:0;\n  }\n  if( pPager->noSync ){\n    pPager->syncFlags = 0;\n  }else if( pgFlags & PAGER_FULLFSYNC ){\n    pPager->syncFlags = SQLITE_SYNC_FULL;\n  }else{\n    pPager->syncFlags = SQLITE_SYNC_NORMAL;\n  }\n  pPager->walSyncFlags = (pPager->syncFlags<<2);\n  if( pPager->fullSync ){\n    pPager->walSyncFlags |= pPager->syncFlags;\n  }\n  if( (pgFlags & PAGER_CKPT_FULLFSYNC) && !pPager->noSync ){\n    pPager->walSyncFlags |= (SQLITE_SYNC_FULL<<2);\n  }\n  if( pgFlags & PAGER_CACHESPILL ){\n    pPager->doNotSpill &= ~SPILLFLAG_OFF;\n  }else{\n    pPager->doNotSpill |= SPILLFLAG_OFF;\n  }\n}\n#endif\n\n/*\n** The following global variable is incremented whenever the library\n** attempts to open a temporary file.  This information is used for\n** testing and analysis only.  \n*/\n#ifdef SQLITE_TEST\nSQLITE_API int sqlite3_opentemp_count = 0;\n#endif\n\n/*\n** Open a temporary file.\n**\n** Write the file descriptor into *pFile. Return SQLITE_OK on success \n** or some other error code if we fail. The OS will automatically \n** delete the temporary file when it is closed.\n**\n** The flags passed to the VFS layer xOpen() call are those specified\n** by parameter vfsFlags ORed with the following:\n**\n**     SQLITE_OPEN_READWRITE\n**     SQLITE_OPEN_CREATE\n**     SQLITE_OPEN_EXCLUSIVE\n**     SQLITE_OPEN_DELETEONCLOSE\n*/\nstatic int pagerOpentemp(\n  Pager *pPager,        /* The pager object */\n  sqlite3_file *pFile,  /* Write the file descriptor here */\n  int vfsFlags          /* Flags passed through to the VFS */\n){\n  int rc;               /* Return code */\n\n#ifdef SQLITE_TEST\n  sqlite3_opentemp_count++;  /* Used for testing and analysis only */\n#endif\n\n  vfsFlags |=  SQLITE_OPEN_READWRITE | SQLITE_OPEN_CREATE |\n            SQLITE_OPEN_EXCLUSIVE | SQLITE_OPEN_DELETEONCLOSE;\n  rc = sqlite3OsOpen(pPager->pVfs, 0, pFile, vfsFlags, 0);\n  assert( rc!=SQLITE_OK || isOpen(pFile) );\n  return rc;\n}\n\n/*\n** Set the busy handler function.\n**\n** The pager invokes the busy-handler if sqlite3OsLock() returns \n** SQLITE_BUSY when trying to upgrade from no-lock to a SHARED lock,\n** or when trying to upgrade from a RESERVED lock to an EXCLUSIVE \n** lock. It does *not* invoke the busy handler when upgrading from\n** SHARED to RESERVED, or when upgrading from SHARED to EXCLUSIVE\n** (which occurs during hot-journal rollback). Summary:\n**\n**   Transition                        | Invokes xBusyHandler\n**   --------------------------------------------------------\n**   NO_LOCK       -> SHARED_LOCK      | Yes\n**   SHARED_LOCK   -> RESERVED_LOCK    | No\n**   SHARED_LOCK   -> EXCLUSIVE_LOCK   | No\n**   RESERVED_LOCK -> EXCLUSIVE_LOCK   | Yes\n**\n** If the busy-handler callback returns non-zero, the lock is \n** retried. If it returns zero, then the SQLITE_BUSY error is\n** returned to the caller of the pager API function.\n*/\nSQLITE_PRIVATE void sqlite3PagerSetBusyhandler(\n  Pager *pPager,                       /* Pager object */\n  int (*xBusyHandler)(void *),         /* Pointer to busy-handler function */\n  void *pBusyHandlerArg                /* Argument to pass to xBusyHandler */\n){\n  pPager->xBusyHandler = xBusyHandler;\n  pPager->pBusyHandlerArg = pBusyHandlerArg;\n\n  if( isOpen(pPager->fd) ){\n    void **ap = (void **)&pPager->xBusyHandler;\n    assert( ((int(*)(void *))(ap[0]))==xBusyHandler );\n    assert( ap[1]==pBusyHandlerArg );\n    sqlite3OsFileControlHint(pPager->fd, SQLITE_FCNTL_BUSYHANDLER, (void *)ap);\n  }\n}\n\n/*\n** Change the page size used by the Pager object. The new page size \n** is passed in *pPageSize.\n**\n** If the pager is in the error state when this function is called, it\n** is a no-op. The value returned is the error state error code (i.e. \n** one of SQLITE_IOERR, an SQLITE_IOERR_xxx sub-code or SQLITE_FULL).\n**\n** Otherwise, if all of the following are true:\n**\n**   * the new page size (value of *pPageSize) is valid (a power \n**     of two between 512 and SQLITE_MAX_PAGE_SIZE, inclusive), and\n**\n**   * there are no outstanding page references, and\n**\n**   * the database is either not an in-memory database or it is\n**     an in-memory database that currently consists of zero pages.\n**\n** then the pager object page size is set to *pPageSize.\n**\n** If the page size is changed, then this function uses sqlite3PagerMalloc() \n** to obtain a new Pager.pTmpSpace buffer. If this allocation attempt \n** fails, SQLITE_NOMEM is returned and the page size remains unchanged. \n** In all other cases, SQLITE_OK is returned.\n**\n** If the page size is not changed, either because one of the enumerated\n** conditions above is not true, the pager was in error state when this\n** function was called, or because the memory allocation attempt failed, \n** then *pPageSize is set to the old, retained page size before returning.\n*/\nSQLITE_PRIVATE int sqlite3PagerSetPagesize(Pager *pPager, u32 *pPageSize, int nReserve){\n  int rc = SQLITE_OK;\n\n  /* It is not possible to do a full assert_pager_state() here, as this\n  ** function may be called from within PagerOpen(), before the state\n  ** of the Pager object is internally consistent.\n  **\n  ** At one point this function returned an error if the pager was in \n  ** PAGER_ERROR state. But since PAGER_ERROR state guarantees that\n  ** there is at least one outstanding page reference, this function\n  ** is a no-op for that case anyhow.\n  */\n\n  u32 pageSize = *pPageSize;\n  assert( pageSize==0 || (pageSize>=512 && pageSize<=SQLITE_MAX_PAGE_SIZE) );\n  if( (pPager->memDb==0 || pPager->dbSize==0)\n   && sqlite3PcacheRefCount(pPager->pPCache)==0 \n   && pageSize && pageSize!=(u32)pPager->pageSize \n  ){\n    char *pNew = NULL;             /* New temp space */\n    i64 nByte = 0;\n\n    if( pPager->eState>PAGER_OPEN && isOpen(pPager->fd) ){\n      rc = sqlite3OsFileSize(pPager->fd, &nByte);\n    }\n    if( rc==SQLITE_OK ){\n      pNew = (char *)sqlite3PageMalloc(pageSize);\n      if( !pNew ) rc = SQLITE_NOMEM_BKPT;\n    }\n\n    if( rc==SQLITE_OK ){\n      pager_reset(pPager);\n      rc = sqlite3PcacheSetPageSize(pPager->pPCache, pageSize);\n    }\n    if( rc==SQLITE_OK ){\n      sqlite3PageFree(pPager->pTmpSpace);\n      pPager->pTmpSpace = pNew;\n      pPager->dbSize = (Pgno)((nByte+pageSize-1)/pageSize);\n      pPager->pageSize = pageSize;\n    }else{\n      sqlite3PageFree(pNew);\n    }\n  }\n\n  *pPageSize = pPager->pageSize;\n  if( rc==SQLITE_OK ){\n    if( nReserve<0 ) nReserve = pPager->nReserve;\n    assert( nReserve>=0 && nReserve<1000 );\n    pPager->nReserve = (i16)nReserve;\n    pagerReportSize(pPager);\n    pagerFixMaplimit(pPager);\n  }\n  return rc;\n}\n\n/*\n** Return a pointer to the \"temporary page\" buffer held internally\n** by the pager.  This is a buffer that is big enough to hold the\n** entire content of a database page.  This buffer is used internally\n** during rollback and will be overwritten whenever a rollback\n** occurs.  But other modules are free to use it too, as long as\n** no rollbacks are happening.\n*/\nSQLITE_PRIVATE void *sqlite3PagerTempSpace(Pager *pPager){\n  return pPager->pTmpSpace;\n}\n\n/*\n** Attempt to set the maximum database page count if mxPage is positive. \n** Make no changes if mxPage is zero or negative.  And never reduce the\n** maximum page count below the current size of the database.\n**\n** Regardless of mxPage, return the current maximum page count.\n*/\nSQLITE_PRIVATE int sqlite3PagerMaxPageCount(Pager *pPager, int mxPage){\n  if( mxPage>0 ){\n    pPager->mxPgno = mxPage;\n  }\n  assert( pPager->eState!=PAGER_OPEN );      /* Called only by OP_MaxPgcnt */\n  assert( pPager->mxPgno>=pPager->dbSize );  /* OP_MaxPgcnt enforces this */\n  return pPager->mxPgno;\n}\n\n/*\n** The following set of routines are used to disable the simulated\n** I/O error mechanism.  These routines are used to avoid simulated\n** errors in places where we do not care about errors.\n**\n** Unless -DSQLITE_TEST=1 is used, these routines are all no-ops\n** and generate no code.\n*/\n#ifdef SQLITE_TEST\nSQLITE_API extern int sqlite3_io_error_pending;\nSQLITE_API extern int sqlite3_io_error_hit;\nstatic int saved_cnt;\nvoid disable_simulated_io_errors(void){\n  saved_cnt = sqlite3_io_error_pending;\n  sqlite3_io_error_pending = -1;\n}\nvoid enable_simulated_io_errors(void){\n  sqlite3_io_error_pending = saved_cnt;\n}\n#else\n# define disable_simulated_io_errors()\n# define enable_simulated_io_errors()\n#endif\n\n/*\n** Read the first N bytes from the beginning of the file into memory\n** that pDest points to. \n**\n** If the pager was opened on a transient file (zFilename==\"\"), or\n** opened on a file less than N bytes in size, the output buffer is\n** zeroed and SQLITE_OK returned. The rationale for this is that this \n** function is used to read database headers, and a new transient or\n** zero sized database has a header than consists entirely of zeroes.\n**\n** If any IO error apart from SQLITE_IOERR_SHORT_READ is encountered,\n** the error code is returned to the caller and the contents of the\n** output buffer undefined.\n*/\nSQLITE_PRIVATE int sqlite3PagerReadFileheader(Pager *pPager, int N, unsigned char *pDest){\n  int rc = SQLITE_OK;\n  memset(pDest, 0, N);\n  assert( isOpen(pPager->fd) || pPager->tempFile );\n\n  /* This routine is only called by btree immediately after creating\n  ** the Pager object.  There has not been an opportunity to transition\n  ** to WAL mode yet.\n  */\n  assert( !pagerUseWal(pPager) );\n\n  if( isOpen(pPager->fd) ){\n    IOTRACE((\"DBHDR %p 0 %d\\n\", pPager, N))\n    rc = sqlite3OsRead(pPager->fd, pDest, N, 0);\n    if( rc==SQLITE_IOERR_SHORT_READ ){\n      rc = SQLITE_OK;\n    }\n  }\n  return rc;\n}\n\n/*\n** This function may only be called when a read-transaction is open on\n** the pager. It returns the total number of pages in the database.\n**\n** However, if the file is between 1 and <page-size> bytes in size, then \n** this is considered a 1 page file.\n*/\nSQLITE_PRIVATE void sqlite3PagerPagecount(Pager *pPager, int *pnPage){\n  assert( pPager->eState>=PAGER_READER );\n  assert( pPager->eState!=PAGER_WRITER_FINISHED );\n  *pnPage = (int)pPager->dbSize;\n}\n\n\n/*\n** Try to obtain a lock of type locktype on the database file. If\n** a similar or greater lock is already held, this function is a no-op\n** (returning SQLITE_OK immediately).\n**\n** Otherwise, attempt to obtain the lock using sqlite3OsLock(). Invoke \n** the busy callback if the lock is currently not available. Repeat \n** until the busy callback returns false or until the attempt to \n** obtain the lock succeeds.\n**\n** Return SQLITE_OK on success and an error code if we cannot obtain\n** the lock. If the lock is obtained successfully, set the Pager.state \n** variable to locktype before returning.\n*/\nstatic int pager_wait_on_lock(Pager *pPager, int locktype){\n  int rc;                              /* Return code */\n\n  /* Check that this is either a no-op (because the requested lock is \n  ** already held), or one of the transitions that the busy-handler\n  ** may be invoked during, according to the comment above\n  ** sqlite3PagerSetBusyhandler().\n  */\n  assert( (pPager->eLock>=locktype)\n       || (pPager->eLock==NO_LOCK && locktype==SHARED_LOCK)\n       || (pPager->eLock==RESERVED_LOCK && locktype==EXCLUSIVE_LOCK)\n  );\n\n  do {\n    rc = pagerLockDb(pPager, locktype);\n  }while( rc==SQLITE_BUSY && pPager->xBusyHandler(pPager->pBusyHandlerArg) );\n  return rc;\n}\n\n/*\n** Function assertTruncateConstraint(pPager) checks that one of the \n** following is true for all dirty pages currently in the page-cache:\n**\n**   a) The page number is less than or equal to the size of the \n**      current database image, in pages, OR\n**\n**   b) if the page content were written at this time, it would not\n**      be necessary to write the current content out to the sub-journal\n**      (as determined by function subjRequiresPage()).\n**\n** If the condition asserted by this function were not true, and the\n** dirty page were to be discarded from the cache via the pagerStress()\n** routine, pagerStress() would not write the current page content to\n** the database file. If a savepoint transaction were rolled back after\n** this happened, the correct behavior would be to restore the current\n** content of the page. However, since this content is not present in either\n** the database file or the portion of the rollback journal and \n** sub-journal rolled back the content could not be restored and the\n** database image would become corrupt. It is therefore fortunate that \n** this circumstance cannot arise.\n*/\n#if defined(SQLITE_DEBUG)\nstatic void assertTruncateConstraintCb(PgHdr *pPg){\n  assert( pPg->flags&PGHDR_DIRTY );\n  assert( !subjRequiresPage(pPg) || pPg->pgno<=pPg->pPager->dbSize );\n}\nstatic void assertTruncateConstraint(Pager *pPager){\n  sqlite3PcacheIterateDirty(pPager->pPCache, assertTruncateConstraintCb);\n}\n#else\n# define assertTruncateConstraint(pPager)\n#endif\n\n/*\n** Truncate the in-memory database file image to nPage pages. This \n** function does not actually modify the database file on disk. It \n** just sets the internal state of the pager object so that the \n** truncation will be done when the current transaction is committed.\n**\n** This function is only called right before committing a transaction.\n** Once this function has been called, the transaction must either be\n** rolled back or committed. It is not safe to call this function and\n** then continue writing to the database.\n*/\nSQLITE_PRIVATE void sqlite3PagerTruncateImage(Pager *pPager, Pgno nPage){\n  assert( pPager->dbSize>=nPage );\n  assert( pPager->eState>=PAGER_WRITER_CACHEMOD );\n  pPager->dbSize = nPage;\n\n  /* At one point the code here called assertTruncateConstraint() to\n  ** ensure that all pages being truncated away by this operation are,\n  ** if one or more savepoints are open, present in the savepoint \n  ** journal so that they can be restored if the savepoint is rolled\n  ** back. This is no longer necessary as this function is now only\n  ** called right before committing a transaction. So although the \n  ** Pager object may still have open savepoints (Pager.nSavepoint!=0), \n  ** they cannot be rolled back. So the assertTruncateConstraint() call\n  ** is no longer correct. */\n}\n\n\n/*\n** This function is called before attempting a hot-journal rollback. It\n** syncs the journal file to disk, then sets pPager->journalHdr to the\n** size of the journal file so that the pager_playback() routine knows\n** that the entire journal file has been synced.\n**\n** Syncing a hot-journal to disk before attempting to roll it back ensures \n** that if a power-failure occurs during the rollback, the process that\n** attempts rollback following system recovery sees the same journal\n** content as this process.\n**\n** If everything goes as planned, SQLITE_OK is returned. Otherwise, \n** an SQLite error code.\n*/\nstatic int pagerSyncHotJournal(Pager *pPager){\n  int rc = SQLITE_OK;\n  if( !pPager->noSync ){\n    rc = sqlite3OsSync(pPager->jfd, SQLITE_SYNC_NORMAL);\n  }\n  if( rc==SQLITE_OK ){\n    rc = sqlite3OsFileSize(pPager->jfd, &pPager->journalHdr);\n  }\n  return rc;\n}\n\n#if SQLITE_MAX_MMAP_SIZE>0\n/*\n** Obtain a reference to a memory mapped page object for page number pgno. \n** The new object will use the pointer pData, obtained from xFetch().\n** If successful, set *ppPage to point to the new page reference\n** and return SQLITE_OK. Otherwise, return an SQLite error code and set\n** *ppPage to zero.\n**\n** Page references obtained by calling this function should be released\n** by calling pagerReleaseMapPage().\n*/\nstatic int pagerAcquireMapPage(\n  Pager *pPager,                  /* Pager object */\n  Pgno pgno,                      /* Page number */\n  void *pData,                    /* xFetch()'d data for this page */\n  PgHdr **ppPage                  /* OUT: Acquired page object */\n){\n  PgHdr *p;                       /* Memory mapped page to return */\n  \n  if( pPager->pMmapFreelist ){\n    *ppPage = p = pPager->pMmapFreelist;\n    pPager->pMmapFreelist = p->pDirty;\n    p->pDirty = 0;\n    assert( pPager->nExtra>=8 );\n    memset(p->pExtra, 0, 8);\n  }else{\n    *ppPage = p = (PgHdr *)sqlite3MallocZero(sizeof(PgHdr) + pPager->nExtra);\n    if( p==0 ){\n      sqlite3OsUnfetch(pPager->fd, (i64)(pgno-1) * pPager->pageSize, pData);\n      return SQLITE_NOMEM_BKPT;\n    }\n    p->pExtra = (void *)&p[1];\n    p->flags = PGHDR_MMAP;\n    p->nRef = 1;\n    p->pPager = pPager;\n  }\n\n  assert( p->pExtra==(void *)&p[1] );\n  assert( p->pPage==0 );\n  assert( p->flags==PGHDR_MMAP );\n  assert( p->pPager==pPager );\n  assert( p->nRef==1 );\n\n  p->pgno = pgno;\n  p->pData = pData;\n  pPager->nMmapOut++;\n\n  return SQLITE_OK;\n}\n#endif\n\n/*\n** Release a reference to page pPg. pPg must have been returned by an \n** earlier call to pagerAcquireMapPage().\n*/\nstatic void pagerReleaseMapPage(PgHdr *pPg){\n  Pager *pPager = pPg->pPager;\n  pPager->nMmapOut--;\n  pPg->pDirty = pPager->pMmapFreelist;\n  pPager->pMmapFreelist = pPg;\n\n  assert( pPager->fd->pMethods->iVersion>=3 );\n  sqlite3OsUnfetch(pPager->fd, (i64)(pPg->pgno-1)*pPager->pageSize, pPg->pData);\n}\n\n/*\n** Free all PgHdr objects stored in the Pager.pMmapFreelist list.\n*/\nstatic void pagerFreeMapHdrs(Pager *pPager){\n  PgHdr *p;\n  PgHdr *pNext;\n  for(p=pPager->pMmapFreelist; p; p=pNext){\n    pNext = p->pDirty;\n    sqlite3_free(p);\n  }\n}\n\n/* Verify that the database file has not be deleted or renamed out from\n** under the pager.  Return SQLITE_OK if the database is still where it ought\n** to be on disk.  Return non-zero (SQLITE_READONLY_DBMOVED or some other error\n** code from sqlite3OsAccess()) if the database has gone missing.\n*/\nstatic int databaseIsUnmoved(Pager *pPager){\n  int bHasMoved = 0;\n  int rc;\n\n  if( pPager->tempFile ) return SQLITE_OK;\n  if( pPager->dbSize==0 ) return SQLITE_OK;\n  assert( pPager->zFilename && pPager->zFilename[0] );\n  rc = sqlite3OsFileControl(pPager->fd, SQLITE_FCNTL_HAS_MOVED, &bHasMoved);\n  if( rc==SQLITE_NOTFOUND ){\n    /* If the HAS_MOVED file-control is unimplemented, assume that the file\n    ** has not been moved.  That is the historical behavior of SQLite: prior to\n    ** version 3.8.3, it never checked */\n    rc = SQLITE_OK;\n  }else if( rc==SQLITE_OK && bHasMoved ){\n    rc = SQLITE_READONLY_DBMOVED;\n  }\n  return rc;\n}\n\n\n/*\n** Shutdown the page cache.  Free all memory and close all files.\n**\n** If a transaction was in progress when this routine is called, that\n** transaction is rolled back.  All outstanding pages are invalidated\n** and their memory is freed.  Any attempt to use a page associated\n** with this page cache after this function returns will likely\n** result in a coredump.\n**\n** This function always succeeds. If a transaction is active an attempt\n** is made to roll it back. If an error occurs during the rollback \n** a hot journal may be left in the filesystem but no error is returned\n** to the caller.\n*/\nSQLITE_PRIVATE int sqlite3PagerClose(Pager *pPager, sqlite3 *db){\n  u8 *pTmp = (u8*)pPager->pTmpSpace;\n  assert( db || pagerUseWal(pPager)==0 );\n  assert( assert_pager_state(pPager) );\n  disable_simulated_io_errors();\n  sqlite3BeginBenignMalloc();\n  pagerFreeMapHdrs(pPager);\n  /* pPager->errCode = 0; */\n  pPager->exclusiveMode = 0;\n#ifndef SQLITE_OMIT_WAL\n  {\n    u8 *a = 0;\n    assert( db || pPager->pWal==0 );\n    if( db && 0==(db->flags & SQLITE_NoCkptOnClose) \n     && SQLITE_OK==databaseIsUnmoved(pPager)\n    ){\n      a = pTmp;\n    }\n    sqlite3WalClose(pPager->pWal, db, pPager->walSyncFlags, pPager->pageSize,a);\n    pPager->pWal = 0;\n  }\n#endif\n  pager_reset(pPager);\n  if( MEMDB ){\n    pager_unlock(pPager);\n  }else{\n    /* If it is open, sync the journal file before calling UnlockAndRollback.\n    ** If this is not done, then an unsynced portion of the open journal \n    ** file may be played back into the database. If a power failure occurs \n    ** while this is happening, the database could become corrupt.\n    **\n    ** If an error occurs while trying to sync the journal, shift the pager\n    ** into the ERROR state. This causes UnlockAndRollback to unlock the\n    ** database and close the journal file without attempting to roll it\n    ** back or finalize it. The next database user will have to do hot-journal\n    ** rollback before accessing the database file.\n    */\n    if( isOpen(pPager->jfd) ){\n      pager_error(pPager, pagerSyncHotJournal(pPager));\n    }\n    pagerUnlockAndRollback(pPager);\n  }\n  sqlite3EndBenignMalloc();\n  enable_simulated_io_errors();\n  PAGERTRACE((\"CLOSE %d\\n\", PAGERID(pPager)));\n  IOTRACE((\"CLOSE %p\\n\", pPager))\n  sqlite3OsClose(pPager->jfd);\n  sqlite3OsClose(pPager->fd);\n  sqlite3PageFree(pTmp);\n  sqlite3PcacheClose(pPager->pPCache);\n\n#ifdef SQLITE_HAS_CODEC\n  if( pPager->xCodecFree ) pPager->xCodecFree(pPager->pCodec);\n#endif\n\n  assert( !pPager->aSavepoint && !pPager->pInJournal );\n  assert( !isOpen(pPager->jfd) && !isOpen(pPager->sjfd) );\n\n  sqlite3_free(pPager);\n  return SQLITE_OK;\n}\n\n#if !defined(NDEBUG) || defined(SQLITE_TEST)\n/*\n** Return the page number for page pPg.\n*/\nSQLITE_PRIVATE Pgno sqlite3PagerPagenumber(DbPage *pPg){\n  return pPg->pgno;\n}\n#endif\n\n/*\n** Increment the reference count for page pPg.\n*/\nSQLITE_PRIVATE void sqlite3PagerRef(DbPage *pPg){\n  sqlite3PcacheRef(pPg);\n}\n\n/*\n** Sync the journal. In other words, make sure all the pages that have\n** been written to the journal have actually reached the surface of the\n** disk and can be restored in the event of a hot-journal rollback.\n**\n** If the Pager.noSync flag is set, then this function is a no-op.\n** Otherwise, the actions required depend on the journal-mode and the \n** device characteristics of the file-system, as follows:\n**\n**   * If the journal file is an in-memory journal file, no action need\n**     be taken.\n**\n**   * Otherwise, if the device does not support the SAFE_APPEND property,\n**     then the nRec field of the most recently written journal header\n**     is updated to contain the number of journal records that have\n**     been written following it. If the pager is operating in full-sync\n**     mode, then the journal file is synced before this field is updated.\n**\n**   * If the device does not support the SEQUENTIAL property, then \n**     journal file is synced.\n**\n** Or, in pseudo-code:\n**\n**   if( NOT <in-memory journal> ){\n**     if( NOT SAFE_APPEND ){\n**       if( <full-sync mode> ) xSync(<journal file>);\n**       <update nRec field>\n**     } \n**     if( NOT SEQUENTIAL ) xSync(<journal file>);\n**   }\n**\n** If successful, this routine clears the PGHDR_NEED_SYNC flag of every \n** page currently held in memory before returning SQLITE_OK. If an IO\n** error is encountered, then the IO error code is returned to the caller.\n*/\nstatic int syncJournal(Pager *pPager, int newHdr){\n  int rc;                         /* Return code */\n\n  assert( pPager->eState==PAGER_WRITER_CACHEMOD\n       || pPager->eState==PAGER_WRITER_DBMOD\n  );\n  assert( assert_pager_state(pPager) );\n  assert( !pagerUseWal(pPager) );\n\n  rc = sqlite3PagerExclusiveLock(pPager);\n  if( rc!=SQLITE_OK ) return rc;\n\n  if( !pPager->noSync ){\n    assert( !pPager->tempFile );\n    if( isOpen(pPager->jfd) && pPager->journalMode!=PAGER_JOURNALMODE_MEMORY ){\n      const int iDc = sqlite3OsDeviceCharacteristics(pPager->fd);\n      assert( isOpen(pPager->jfd) );\n\n      if( 0==(iDc&SQLITE_IOCAP_SAFE_APPEND) ){\n        /* This block deals with an obscure problem. If the last connection\n        ** that wrote to this database was operating in persistent-journal\n        ** mode, then the journal file may at this point actually be larger\n        ** than Pager.journalOff bytes. If the next thing in the journal\n        ** file happens to be a journal-header (written as part of the\n        ** previous connection's transaction), and a crash or power-failure \n        ** occurs after nRec is updated but before this connection writes \n        ** anything else to the journal file (or commits/rolls back its \n        ** transaction), then SQLite may become confused when doing the \n        ** hot-journal rollback following recovery. It may roll back all\n        ** of this connections data, then proceed to rolling back the old,\n        ** out-of-date data that follows it. Database corruption.\n        **\n        ** To work around this, if the journal file does appear to contain\n        ** a valid header following Pager.journalOff, then write a 0x00\n        ** byte to the start of it to prevent it from being recognized.\n        **\n        ** Variable iNextHdrOffset is set to the offset at which this\n        ** problematic header will occur, if it exists. aMagic is used \n        ** as a temporary buffer to inspect the first couple of bytes of\n        ** the potential journal header.\n        */\n        i64 iNextHdrOffset;\n        u8 aMagic[8];\n        u8 zHeader[sizeof(aJournalMagic)+4];\n\n        memcpy(zHeader, aJournalMagic, sizeof(aJournalMagic));\n        put32bits(&zHeader[sizeof(aJournalMagic)], pPager->nRec);\n\n        iNextHdrOffset = journalHdrOffset(pPager);\n        rc = sqlite3OsRead(pPager->jfd, aMagic, 8, iNextHdrOffset);\n        if( rc==SQLITE_OK && 0==memcmp(aMagic, aJournalMagic, 8) ){\n          static const u8 zerobyte = 0;\n          rc = sqlite3OsWrite(pPager->jfd, &zerobyte, 1, iNextHdrOffset);\n        }\n        if( rc!=SQLITE_OK && rc!=SQLITE_IOERR_SHORT_READ ){\n          return rc;\n        }\n\n        /* Write the nRec value into the journal file header. If in\n        ** full-synchronous mode, sync the journal first. This ensures that\n        ** all data has really hit the disk before nRec is updated to mark\n        ** it as a candidate for rollback.\n        **\n        ** This is not required if the persistent media supports the\n        ** SAFE_APPEND property. Because in this case it is not possible \n        ** for garbage data to be appended to the file, the nRec field\n        ** is populated with 0xFFFFFFFF when the journal header is written\n        ** and never needs to be updated.\n        */\n        if( pPager->fullSync && 0==(iDc&SQLITE_IOCAP_SEQUENTIAL) ){\n          PAGERTRACE((\"SYNC journal of %d\\n\", PAGERID(pPager)));\n          IOTRACE((\"JSYNC %p\\n\", pPager))\n          rc = sqlite3OsSync(pPager->jfd, pPager->syncFlags);\n          if( rc!=SQLITE_OK ) return rc;\n        }\n        IOTRACE((\"JHDR %p %lld\\n\", pPager, pPager->journalHdr));\n        rc = sqlite3OsWrite(\n            pPager->jfd, zHeader, sizeof(zHeader), pPager->journalHdr\n        );\n        if( rc!=SQLITE_OK ) return rc;\n      }\n      if( 0==(iDc&SQLITE_IOCAP_SEQUENTIAL) ){\n        PAGERTRACE((\"SYNC journal of %d\\n\", PAGERID(pPager)));\n        IOTRACE((\"JSYNC %p\\n\", pPager))\n        rc = sqlite3OsSync(pPager->jfd, pPager->syncFlags| \n          (pPager->syncFlags==SQLITE_SYNC_FULL?SQLITE_SYNC_DATAONLY:0)\n        );\n        if( rc!=SQLITE_OK ) return rc;\n      }\n\n      pPager->journalHdr = pPager->journalOff;\n      if( newHdr && 0==(iDc&SQLITE_IOCAP_SAFE_APPEND) ){\n        pPager->nRec = 0;\n        rc = writeJournalHdr(pPager);\n        if( rc!=SQLITE_OK ) return rc;\n      }\n    }else{\n      pPager->journalHdr = pPager->journalOff;\n    }\n  }\n\n  /* Unless the pager is in noSync mode, the journal file was just \n  ** successfully synced. Either way, clear the PGHDR_NEED_SYNC flag on \n  ** all pages.\n  */\n  sqlite3PcacheClearSyncFlags(pPager->pPCache);\n  pPager->eState = PAGER_WRITER_DBMOD;\n  assert( assert_pager_state(pPager) );\n  return SQLITE_OK;\n}\n\n/*\n** The argument is the first in a linked list of dirty pages connected\n** by the PgHdr.pDirty pointer. This function writes each one of the\n** in-memory pages in the list to the database file. The argument may\n** be NULL, representing an empty list. In this case this function is\n** a no-op.\n**\n** The pager must hold at least a RESERVED lock when this function\n** is called. Before writing anything to the database file, this lock\n** is upgraded to an EXCLUSIVE lock. If the lock cannot be obtained,\n** SQLITE_BUSY is returned and no data is written to the database file.\n** \n** If the pager is a temp-file pager and the actual file-system file\n** is not yet open, it is created and opened before any data is \n** written out.\n**\n** Once the lock has been upgraded and, if necessary, the file opened,\n** the pages are written out to the database file in list order. Writing\n** a page is skipped if it meets either of the following criteria:\n**\n**   * The page number is greater than Pager.dbSize, or\n**   * The PGHDR_DONT_WRITE flag is set on the page.\n**\n** If writing out a page causes the database file to grow, Pager.dbFileSize\n** is updated accordingly. If page 1 is written out, then the value cached\n** in Pager.dbFileVers[] is updated to match the new value stored in\n** the database file.\n**\n** If everything is successful, SQLITE_OK is returned. If an IO error \n** occurs, an IO error code is returned. Or, if the EXCLUSIVE lock cannot\n** be obtained, SQLITE_BUSY is returned.\n*/\nstatic int pager_write_pagelist(Pager *pPager, PgHdr *pList){\n  int rc = SQLITE_OK;                  /* Return code */\n\n  /* This function is only called for rollback pagers in WRITER_DBMOD state. */\n  assert( !pagerUseWal(pPager) );\n  assert( pPager->tempFile || pPager->eState==PAGER_WRITER_DBMOD );\n  assert( pPager->eLock==EXCLUSIVE_LOCK );\n  assert( isOpen(pPager->fd) || pList->pDirty==0 );\n\n  /* If the file is a temp-file has not yet been opened, open it now. It\n  ** is not possible for rc to be other than SQLITE_OK if this branch\n  ** is taken, as pager_wait_on_lock() is a no-op for temp-files.\n  */\n  if( !isOpen(pPager->fd) ){\n    assert( pPager->tempFile && rc==SQLITE_OK );\n    rc = pagerOpentemp(pPager, pPager->fd, pPager->vfsFlags);\n  }\n\n  /* Before the first write, give the VFS a hint of what the final\n  ** file size will be.\n  */\n  assert( rc!=SQLITE_OK || isOpen(pPager->fd) );\n  if( rc==SQLITE_OK \n   && pPager->dbHintSize<pPager->dbSize\n   && (pList->pDirty || pList->pgno>pPager->dbHintSize)\n  ){\n    sqlite3_int64 szFile = pPager->pageSize * (sqlite3_int64)pPager->dbSize;\n    sqlite3OsFileControlHint(pPager->fd, SQLITE_FCNTL_SIZE_HINT, &szFile);\n    pPager->dbHintSize = pPager->dbSize;\n  }\n\n  while( rc==SQLITE_OK && pList ){\n    Pgno pgno = pList->pgno;\n\n    /* If there are dirty pages in the page cache with page numbers greater\n    ** than Pager.dbSize, this means sqlite3PagerTruncateImage() was called to\n    ** make the file smaller (presumably by auto-vacuum code). Do not write\n    ** any such pages to the file.\n    **\n    ** Also, do not write out any page that has the PGHDR_DONT_WRITE flag\n    ** set (set by sqlite3PagerDontWrite()).\n    */\n    if( pgno<=pPager->dbSize && 0==(pList->flags&PGHDR_DONT_WRITE) ){\n      i64 offset = (pgno-1)*(i64)pPager->pageSize;   /* Offset to write */\n      char *pData;                                   /* Data to write */    \n\n      assert( (pList->flags&PGHDR_NEED_SYNC)==0 );\n      if( pList->pgno==1 ) pager_write_changecounter(pList);\n\n      /* Encode the database */\n      CODEC2(pPager, pList->pData, pgno, 6, return SQLITE_NOMEM_BKPT, pData);\n\n      /* Write out the page data. */\n      rc = sqlite3OsWrite(pPager->fd, pData, pPager->pageSize, offset);\n\n      /* If page 1 was just written, update Pager.dbFileVers to match\n      ** the value now stored in the database file. If writing this \n      ** page caused the database file to grow, update dbFileSize. \n      */\n      if( pgno==1 ){\n        memcpy(&pPager->dbFileVers, &pData[24], sizeof(pPager->dbFileVers));\n      }\n      if( pgno>pPager->dbFileSize ){\n        pPager->dbFileSize = pgno;\n      }\n      pPager->aStat[PAGER_STAT_WRITE]++;\n\n      /* Update any backup objects copying the contents of this pager. */\n      sqlite3BackupUpdate(pPager->pBackup, pgno, (u8*)pList->pData);\n\n      PAGERTRACE((\"STORE %d page %d hash(%08x)\\n\",\n                   PAGERID(pPager), pgno, pager_pagehash(pList)));\n      IOTRACE((\"PGOUT %p %d\\n\", pPager, pgno));\n      PAGER_INCR(sqlite3_pager_writedb_count);\n    }else{\n      PAGERTRACE((\"NOSTORE %d page %d\\n\", PAGERID(pPager), pgno));\n    }\n    pager_set_pagehash(pList);\n    pList = pList->pDirty;\n  }\n\n  return rc;\n}\n\n/*\n** Ensure that the sub-journal file is open. If it is already open, this \n** function is a no-op.\n**\n** SQLITE_OK is returned if everything goes according to plan. An \n** SQLITE_IOERR_XXX error code is returned if a call to sqlite3OsOpen() \n** fails.\n*/\nstatic int openSubJournal(Pager *pPager){\n  int rc = SQLITE_OK;\n  if( !isOpen(pPager->sjfd) ){\n    const int flags =  SQLITE_OPEN_SUBJOURNAL | SQLITE_OPEN_READWRITE \n      | SQLITE_OPEN_CREATE | SQLITE_OPEN_EXCLUSIVE \n      | SQLITE_OPEN_DELETEONCLOSE;\n    int nStmtSpill = sqlite3Config.nStmtSpill;\n    if( pPager->journalMode==PAGER_JOURNALMODE_MEMORY || pPager->subjInMemory ){\n      nStmtSpill = -1;\n    }\n    rc = sqlite3JournalOpen(pPager->pVfs, 0, pPager->sjfd, flags, nStmtSpill);\n  }\n  return rc;\n}\n\n/*\n** Append a record of the current state of page pPg to the sub-journal. \n**\n** If successful, set the bit corresponding to pPg->pgno in the bitvecs\n** for all open savepoints before returning.\n**\n** This function returns SQLITE_OK if everything is successful, an IO\n** error code if the attempt to write to the sub-journal fails, or \n** SQLITE_NOMEM if a malloc fails while setting a bit in a savepoint\n** bitvec.\n*/\nstatic int subjournalPage(PgHdr *pPg){\n  int rc = SQLITE_OK;\n  Pager *pPager = pPg->pPager;\n  if( pPager->journalMode!=PAGER_JOURNALMODE_OFF ){\n\n    /* Open the sub-journal, if it has not already been opened */\n    assert( pPager->useJournal );\n    assert( isOpen(pPager->jfd) || pagerUseWal(pPager) );\n    assert( isOpen(pPager->sjfd) || pPager->nSubRec==0 );\n    assert( pagerUseWal(pPager) \n         || pageInJournal(pPager, pPg) \n         || pPg->pgno>pPager->dbOrigSize \n    );\n    rc = openSubJournal(pPager);\n\n    /* If the sub-journal was opened successfully (or was already open),\n    ** write the journal record into the file.  */\n    if( rc==SQLITE_OK ){\n      void *pData = pPg->pData;\n      i64 offset = (i64)pPager->nSubRec*(4+pPager->pageSize);\n      char *pData2;\n\n#if SQLITE_HAS_CODEC   \n      if( !pPager->subjInMemory ){\n        CODEC2(pPager, pData, pPg->pgno, 7, return SQLITE_NOMEM_BKPT, pData2);\n      }else\n#endif\n      pData2 = pData;\n      PAGERTRACE((\"STMT-JOURNAL %d page %d\\n\", PAGERID(pPager), pPg->pgno));\n      rc = write32bits(pPager->sjfd, offset, pPg->pgno);\n      if( rc==SQLITE_OK ){\n        rc = sqlite3OsWrite(pPager->sjfd, pData2, pPager->pageSize, offset+4);\n      }\n    }\n  }\n  if( rc==SQLITE_OK ){\n    pPager->nSubRec++;\n    assert( pPager->nSavepoint>0 );\n    rc = addToSavepointBitvecs(pPager, pPg->pgno);\n  }\n  return rc;\n}\nstatic int subjournalPageIfRequired(PgHdr *pPg){\n  if( subjRequiresPage(pPg) ){\n    return subjournalPage(pPg);\n  }else{\n    return SQLITE_OK;\n  }\n}\n\n/*\n** This function is called by the pcache layer when it has reached some\n** soft memory limit. The first argument is a pointer to a Pager object\n** (cast as a void*). The pager is always 'purgeable' (not an in-memory\n** database). The second argument is a reference to a page that is \n** currently dirty but has no outstanding references. The page\n** is always associated with the Pager object passed as the first \n** argument.\n**\n** The job of this function is to make pPg clean by writing its contents\n** out to the database file, if possible. This may involve syncing the\n** journal file. \n**\n** If successful, sqlite3PcacheMakeClean() is called on the page and\n** SQLITE_OK returned. If an IO error occurs while trying to make the\n** page clean, the IO error code is returned. If the page cannot be\n** made clean for some other reason, but no error occurs, then SQLITE_OK\n** is returned by sqlite3PcacheMakeClean() is not called.\n*/\nstatic int pagerStress(void *p, PgHdr *pPg){\n  Pager *pPager = (Pager *)p;\n  int rc = SQLITE_OK;\n\n  assert( pPg->pPager==pPager );\n  assert( pPg->flags&PGHDR_DIRTY );\n\n  /* The doNotSpill NOSYNC bit is set during times when doing a sync of\n  ** journal (and adding a new header) is not allowed.  This occurs\n  ** during calls to sqlite3PagerWrite() while trying to journal multiple\n  ** pages belonging to the same sector.\n  **\n  ** The doNotSpill ROLLBACK and OFF bits inhibits all cache spilling\n  ** regardless of whether or not a sync is required.  This is set during\n  ** a rollback or by user request, respectively.\n  **\n  ** Spilling is also prohibited when in an error state since that could\n  ** lead to database corruption.   In the current implementation it \n  ** is impossible for sqlite3PcacheFetch() to be called with createFlag==3\n  ** while in the error state, hence it is impossible for this routine to\n  ** be called in the error state.  Nevertheless, we include a NEVER()\n  ** test for the error state as a safeguard against future changes.\n  */\n  if( NEVER(pPager->errCode) ) return SQLITE_OK;\n  testcase( pPager->doNotSpill & SPILLFLAG_ROLLBACK );\n  testcase( pPager->doNotSpill & SPILLFLAG_OFF );\n  testcase( pPager->doNotSpill & SPILLFLAG_NOSYNC );\n  if( pPager->doNotSpill\n   && ((pPager->doNotSpill & (SPILLFLAG_ROLLBACK|SPILLFLAG_OFF))!=0\n      || (pPg->flags & PGHDR_NEED_SYNC)!=0)\n  ){\n    return SQLITE_OK;\n  }\n\n  pPg->pDirty = 0;\n  if( pagerUseWal(pPager) ){\n    /* Write a single frame for this page to the log. */\n    rc = subjournalPageIfRequired(pPg); \n    if( rc==SQLITE_OK ){\n      rc = pagerWalFrames(pPager, pPg, 0, 0);\n    }\n  }else{\n    \n#ifdef SQLITE_ENABLE_BATCH_ATOMIC_WRITE\n    if( pPager->tempFile==0 ){\n      rc = sqlite3JournalCreate(pPager->jfd);\n      if( rc!=SQLITE_OK ) return pager_error(pPager, rc);\n    }\n#endif\n  \n    /* Sync the journal file if required. */\n    if( pPg->flags&PGHDR_NEED_SYNC \n     || pPager->eState==PAGER_WRITER_CACHEMOD\n    ){\n      rc = syncJournal(pPager, 1);\n    }\n  \n    /* Write the contents of the page out to the database file. */\n    if( rc==SQLITE_OK ){\n      assert( (pPg->flags&PGHDR_NEED_SYNC)==0 );\n      rc = pager_write_pagelist(pPager, pPg);\n    }\n  }\n\n  /* Mark the page as clean. */\n  if( rc==SQLITE_OK ){\n    PAGERTRACE((\"STRESS %d page %d\\n\", PAGERID(pPager), pPg->pgno));\n    sqlite3PcacheMakeClean(pPg);\n  }\n\n  return pager_error(pPager, rc); \n}\n\n/*\n** Flush all unreferenced dirty pages to disk.\n*/\nSQLITE_PRIVATE int sqlite3PagerFlush(Pager *pPager){\n  int rc = pPager->errCode;\n  if( !MEMDB ){\n    PgHdr *pList = sqlite3PcacheDirtyList(pPager->pPCache);\n    assert( assert_pager_state(pPager) );\n    while( rc==SQLITE_OK && pList ){\n      PgHdr *pNext = pList->pDirty;\n      if( pList->nRef==0 ){\n        rc = pagerStress((void*)pPager, pList);\n      }\n      pList = pNext;\n    }\n  }\n\n  return rc;\n}\n\n/*\n** Allocate and initialize a new Pager object and put a pointer to it\n** in *ppPager. The pager should eventually be freed by passing it\n** to sqlite3PagerClose().\n**\n** The zFilename argument is the path to the database file to open.\n** If zFilename is NULL then a randomly-named temporary file is created\n** and used as the file to be cached. Temporary files are be deleted\n** automatically when they are closed. If zFilename is \":memory:\" then \n** all information is held in cache. It is never written to disk. \n** This can be used to implement an in-memory database.\n**\n** The nExtra parameter specifies the number of bytes of space allocated\n** along with each page reference. This space is available to the user\n** via the sqlite3PagerGetExtra() API.  When a new page is allocated, the\n** first 8 bytes of this space are zeroed but the remainder is uninitialized.\n** (The extra space is used by btree as the MemPage object.)\n**\n** The flags argument is used to specify properties that affect the\n** operation of the pager. It should be passed some bitwise combination\n** of the PAGER_* flags.\n**\n** The vfsFlags parameter is a bitmask to pass to the flags parameter\n** of the xOpen() method of the supplied VFS when opening files. \n**\n** If the pager object is allocated and the specified file opened \n** successfully, SQLITE_OK is returned and *ppPager set to point to\n** the new pager object. If an error occurs, *ppPager is set to NULL\n** and error code returned. This function may return SQLITE_NOMEM\n** (sqlite3Malloc() is used to allocate memory), SQLITE_CANTOPEN or \n** various SQLITE_IO_XXX errors.\n*/\nSQLITE_PRIVATE int sqlite3PagerOpen(\n  sqlite3_vfs *pVfs,       /* The virtual file system to use */\n  Pager **ppPager,         /* OUT: Return the Pager structure here */\n  const char *zFilename,   /* Name of the database file to open */\n  int nExtra,              /* Extra bytes append to each in-memory page */\n  int flags,               /* flags controlling this file */\n  int vfsFlags,            /* flags passed through to sqlite3_vfs.xOpen() */\n  void (*xReinit)(DbPage*) /* Function to reinitialize pages */\n){\n  u8 *pPtr;\n  Pager *pPager = 0;       /* Pager object to allocate and return */\n  int rc = SQLITE_OK;      /* Return code */\n  int tempFile = 0;        /* True for temp files (incl. in-memory files) */\n  int memDb = 0;           /* True if this is an in-memory file */\n  int readOnly = 0;        /* True if this is a read-only file */\n  int journalFileSize;     /* Bytes to allocate for each journal fd */\n  char *zPathname = 0;     /* Full path to database file */\n  int nPathname = 0;       /* Number of bytes in zPathname */\n  int useJournal = (flags & PAGER_OMIT_JOURNAL)==0; /* False to omit journal */\n  int pcacheSize = sqlite3PcacheSize();       /* Bytes to allocate for PCache */\n  u32 szPageDflt = SQLITE_DEFAULT_PAGE_SIZE;  /* Default page size */\n  const char *zUri = 0;    /* URI args to copy */\n  int nUri = 0;            /* Number of bytes of URI args at *zUri */\n\n  /* Figure out how much space is required for each journal file-handle\n  ** (there are two of them, the main journal and the sub-journal).  */\n  journalFileSize = ROUND8(sqlite3JournalSize(pVfs));\n\n  /* Set the output variable to NULL in case an error occurs. */\n  *ppPager = 0;\n\n#ifndef SQLITE_OMIT_MEMORYDB\n  if( flags & PAGER_MEMORY ){\n    memDb = 1;\n    if( zFilename && zFilename[0] ){\n      zPathname = sqlite3DbStrDup(0, zFilename);\n      if( zPathname==0  ) return SQLITE_NOMEM_BKPT;\n      nPathname = sqlite3Strlen30(zPathname);\n      zFilename = 0;\n    }\n  }\n#endif\n\n  /* Compute and store the full pathname in an allocated buffer pointed\n  ** to by zPathname, length nPathname. Or, if this is a temporary file,\n  ** leave both nPathname and zPathname set to 0.\n  */\n  if( zFilename && zFilename[0] ){\n    const char *z;\n    nPathname = pVfs->mxPathname+1;\n    zPathname = sqlite3DbMallocRaw(0, nPathname*2);\n    if( zPathname==0 ){\n      return SQLITE_NOMEM_BKPT;\n    }\n    zPathname[0] = 0; /* Make sure initialized even if FullPathname() fails */\n    rc = sqlite3OsFullPathname(pVfs, zFilename, nPathname, zPathname);\n    nPathname = sqlite3Strlen30(zPathname);\n    z = zUri = &zFilename[sqlite3Strlen30(zFilename)+1];\n    while( *z ){\n      z += sqlite3Strlen30(z)+1;\n      z += sqlite3Strlen30(z)+1;\n    }\n    nUri = (int)(&z[1] - zUri);\n    assert( nUri>=0 );\n    if( rc==SQLITE_OK && nPathname+8>pVfs->mxPathname ){\n      /* This branch is taken when the journal path required by\n      ** the database being opened will be more than pVfs->mxPathname\n      ** bytes in length. This means the database cannot be opened,\n      ** as it will not be possible to open the journal file or even\n      ** check for a hot-journal before reading.\n      */\n      rc = SQLITE_CANTOPEN_BKPT;\n    }\n    if( rc!=SQLITE_OK ){\n      sqlite3DbFree(0, zPathname);\n      return rc;\n    }\n  }\n\n  /* Allocate memory for the Pager structure, PCache object, the\n  ** three file descriptors, the database file name and the journal \n  ** file name. The layout in memory is as follows:\n  **\n  **     Pager object                    (sizeof(Pager) bytes)\n  **     PCache object                   (sqlite3PcacheSize() bytes)\n  **     Database file handle            (pVfs->szOsFile bytes)\n  **     Sub-journal file handle         (journalFileSize bytes)\n  **     Main journal file handle        (journalFileSize bytes)\n  **     Database file name              (nPathname+1 bytes)\n  **     Journal file name               (nPathname+8+1 bytes)\n  */\n  pPtr = (u8 *)sqlite3MallocZero(\n    ROUND8(sizeof(*pPager)) +      /* Pager structure */\n    ROUND8(pcacheSize) +           /* PCache object */\n    ROUND8(pVfs->szOsFile) +       /* The main db file */\n    journalFileSize * 2 +          /* The two journal files */ \n    nPathname + 1 + nUri +         /* zFilename */\n    nPathname + 8 + 2              /* zJournal */\n#ifndef SQLITE_OMIT_WAL\n    + nPathname + 4 + 2            /* zWal */\n#endif\n  );\n  assert( EIGHT_BYTE_ALIGNMENT(SQLITE_INT_TO_PTR(journalFileSize)) );\n  if( !pPtr ){\n    sqlite3DbFree(0, zPathname);\n    return SQLITE_NOMEM_BKPT;\n  }\n  pPager =              (Pager*)(pPtr);\n  pPager->pPCache =    (PCache*)(pPtr += ROUND8(sizeof(*pPager)));\n  pPager->fd =   (sqlite3_file*)(pPtr += ROUND8(pcacheSize));\n  pPager->sjfd = (sqlite3_file*)(pPtr += ROUND8(pVfs->szOsFile));\n  pPager->jfd =  (sqlite3_file*)(pPtr += journalFileSize);\n  pPager->zFilename =    (char*)(pPtr += journalFileSize);\n  assert( EIGHT_BYTE_ALIGNMENT(pPager->jfd) );\n\n  /* Fill in the Pager.zFilename and Pager.zJournal buffers, if required. */\n  if( zPathname ){\n    assert( nPathname>0 );\n    pPager->zJournal =   (char*)(pPtr += nPathname + 1 + nUri);\n    memcpy(pPager->zFilename, zPathname, nPathname);\n    if( nUri ) memcpy(&pPager->zFilename[nPathname+1], zUri, nUri);\n    memcpy(pPager->zJournal, zPathname, nPathname);\n    memcpy(&pPager->zJournal[nPathname], \"-journal\\000\", 8+2);\n    sqlite3FileSuffix3(pPager->zFilename, pPager->zJournal);\n#ifndef SQLITE_OMIT_WAL\n    pPager->zWal = &pPager->zJournal[nPathname+8+1];\n    memcpy(pPager->zWal, zPathname, nPathname);\n    memcpy(&pPager->zWal[nPathname], \"-wal\\000\", 4+1);\n    sqlite3FileSuffix3(pPager->zFilename, pPager->zWal);\n#endif\n    sqlite3DbFree(0, zPathname);\n  }\n  pPager->pVfs = pVfs;\n  pPager->vfsFlags = vfsFlags;\n\n  /* Open the pager file.\n  */\n  if( zFilename && zFilename[0] ){\n    int fout = 0;                    /* VFS flags returned by xOpen() */\n    rc = sqlite3OsOpen(pVfs, pPager->zFilename, pPager->fd, vfsFlags, &fout);\n    assert( !memDb );\n    readOnly = (fout&SQLITE_OPEN_READONLY);\n\n    /* If the file was successfully opened for read/write access,\n    ** choose a default page size in case we have to create the\n    ** database file. The default page size is the maximum of:\n    **\n    **    + SQLITE_DEFAULT_PAGE_SIZE,\n    **    + The value returned by sqlite3OsSectorSize()\n    **    + The largest page size that can be written atomically.\n    */\n    if( rc==SQLITE_OK ){\n      int iDc = sqlite3OsDeviceCharacteristics(pPager->fd);\n      if( !readOnly ){\n        setSectorSize(pPager);\n        assert(SQLITE_DEFAULT_PAGE_SIZE<=SQLITE_MAX_DEFAULT_PAGE_SIZE);\n        if( szPageDflt<pPager->sectorSize ){\n          if( pPager->sectorSize>SQLITE_MAX_DEFAULT_PAGE_SIZE ){\n            szPageDflt = SQLITE_MAX_DEFAULT_PAGE_SIZE;\n          }else{\n            szPageDflt = (u32)pPager->sectorSize;\n          }\n        }\n#ifdef SQLITE_ENABLE_ATOMIC_WRITE\n        {\n          int ii;\n          assert(SQLITE_IOCAP_ATOMIC512==(512>>8));\n          assert(SQLITE_IOCAP_ATOMIC64K==(65536>>8));\n          assert(SQLITE_MAX_DEFAULT_PAGE_SIZE<=65536);\n          for(ii=szPageDflt; ii<=SQLITE_MAX_DEFAULT_PAGE_SIZE; ii=ii*2){\n            if( iDc&(SQLITE_IOCAP_ATOMIC|(ii>>8)) ){\n              szPageDflt = ii;\n            }\n          }\n        }\n#endif\n      }\n      pPager->noLock = sqlite3_uri_boolean(zFilename, \"nolock\", 0);\n      if( (iDc & SQLITE_IOCAP_IMMUTABLE)!=0\n       || sqlite3_uri_boolean(zFilename, \"immutable\", 0) ){\n          vfsFlags |= SQLITE_OPEN_READONLY;\n          goto act_like_temp_file;\n      }\n    }\n  }else{\n    /* If a temporary file is requested, it is not opened immediately.\n    ** In this case we accept the default page size and delay actually\n    ** opening the file until the first call to OsWrite().\n    **\n    ** This branch is also run for an in-memory database. An in-memory\n    ** database is the same as a temp-file that is never written out to\n    ** disk and uses an in-memory rollback journal.\n    **\n    ** This branch also runs for files marked as immutable.\n    */ \nact_like_temp_file:\n    tempFile = 1;\n    pPager->eState = PAGER_READER;     /* Pretend we already have a lock */\n    pPager->eLock = EXCLUSIVE_LOCK;    /* Pretend we are in EXCLUSIVE mode */\n    pPager->noLock = 1;                /* Do no locking */\n    readOnly = (vfsFlags&SQLITE_OPEN_READONLY);\n  }\n\n  /* The following call to PagerSetPagesize() serves to set the value of \n  ** Pager.pageSize and to allocate the Pager.pTmpSpace buffer.\n  */\n  if( rc==SQLITE_OK ){\n    assert( pPager->memDb==0 );\n    rc = sqlite3PagerSetPagesize(pPager, &szPageDflt, -1);\n    testcase( rc!=SQLITE_OK );\n  }\n\n  /* Initialize the PCache object. */\n  if( rc==SQLITE_OK ){\n    nExtra = ROUND8(nExtra);\n    assert( nExtra>=8 && nExtra<1000 );\n    rc = sqlite3PcacheOpen(szPageDflt, nExtra, !memDb,\n                       !memDb?pagerStress:0, (void *)pPager, pPager->pPCache);\n  }\n\n  /* If an error occurred above, free the  Pager structure and close the file.\n  */\n  if( rc!=SQLITE_OK ){\n    sqlite3OsClose(pPager->fd);\n    sqlite3PageFree(pPager->pTmpSpace);\n    sqlite3_free(pPager);\n    return rc;\n  }\n\n  PAGERTRACE((\"OPEN %d %s\\n\", FILEHANDLEID(pPager->fd), pPager->zFilename));\n  IOTRACE((\"OPEN %p %s\\n\", pPager, pPager->zFilename))\n\n  pPager->useJournal = (u8)useJournal;\n  /* pPager->stmtOpen = 0; */\n  /* pPager->stmtInUse = 0; */\n  /* pPager->nRef = 0; */\n  /* pPager->stmtSize = 0; */\n  /* pPager->stmtJSize = 0; */\n  /* pPager->nPage = 0; */\n  pPager->mxPgno = SQLITE_MAX_PAGE_COUNT;\n  /* pPager->state = PAGER_UNLOCK; */\n  /* pPager->errMask = 0; */\n  pPager->tempFile = (u8)tempFile;\n  assert( tempFile==PAGER_LOCKINGMODE_NORMAL \n          || tempFile==PAGER_LOCKINGMODE_EXCLUSIVE );\n  assert( PAGER_LOCKINGMODE_EXCLUSIVE==1 );\n  pPager->exclusiveMode = (u8)tempFile; \n  pPager->changeCountDone = pPager->tempFile;\n  pPager->memDb = (u8)memDb;\n  pPager->readOnly = (u8)readOnly;\n  assert( useJournal || pPager->tempFile );\n  pPager->noSync = pPager->tempFile;\n  if( pPager->noSync ){\n    assert( pPager->fullSync==0 );\n    assert( pPager->extraSync==0 );\n    assert( pPager->syncFlags==0 );\n    assert( pPager->walSyncFlags==0 );\n  }else{\n    pPager->fullSync = 1;\n    pPager->extraSync = 0;\n    pPager->syncFlags = SQLITE_SYNC_NORMAL;\n    pPager->walSyncFlags = SQLITE_SYNC_NORMAL | (SQLITE_SYNC_NORMAL<<2);\n  }\n  /* pPager->pFirst = 0; */\n  /* pPager->pFirstSynced = 0; */\n  /* pPager->pLast = 0; */\n  pPager->nExtra = (u16)nExtra;\n  pPager->journalSizeLimit = SQLITE_DEFAULT_JOURNAL_SIZE_LIMIT;\n  assert( isOpen(pPager->fd) || tempFile );\n  setSectorSize(pPager);\n  if( !useJournal ){\n    pPager->journalMode = PAGER_JOURNALMODE_OFF;\n  }else if( memDb ){\n    pPager->journalMode = PAGER_JOURNALMODE_MEMORY;\n  }\n  /* pPager->xBusyHandler = 0; */\n  /* pPager->pBusyHandlerArg = 0; */\n  pPager->xReiniter = xReinit;\n  setGetterMethod(pPager);\n  /* memset(pPager->aHash, 0, sizeof(pPager->aHash)); */\n  /* pPager->szMmap = SQLITE_DEFAULT_MMAP_SIZE // will be set by btree.c */\n\n  *ppPager = pPager;\n  return SQLITE_OK;\n}\n\n\n\n/*\n** This function is called after transitioning from PAGER_UNLOCK to\n** PAGER_SHARED state. It tests if there is a hot journal present in\n** the file-system for the given pager. A hot journal is one that \n** needs to be played back. According to this function, a hot-journal\n** file exists if the following criteria are met:\n**\n**   * The journal file exists in the file system, and\n**   * No process holds a RESERVED or greater lock on the database file, and\n**   * The database file itself is greater than 0 bytes in size, and\n**   * The first byte of the journal file exists and is not 0x00.\n**\n** If the current size of the database file is 0 but a journal file\n** exists, that is probably an old journal left over from a prior\n** database with the same name. In this case the journal file is\n** just deleted using OsDelete, *pExists is set to 0 and SQLITE_OK\n** is returned.\n**\n** This routine does not check if there is a master journal filename\n** at the end of the file. If there is, and that master journal file\n** does not exist, then the journal file is not really hot. In this\n** case this routine will return a false-positive. The pager_playback()\n** routine will discover that the journal file is not really hot and \n** will not roll it back. \n**\n** If a hot-journal file is found to exist, *pExists is set to 1 and \n** SQLITE_OK returned. If no hot-journal file is present, *pExists is\n** set to 0 and SQLITE_OK returned. If an IO error occurs while trying\n** to determine whether or not a hot-journal file exists, the IO error\n** code is returned and the value of *pExists is undefined.\n*/\nstatic int hasHotJournal(Pager *pPager, int *pExists){\n  sqlite3_vfs * const pVfs = pPager->pVfs;\n  int rc = SQLITE_OK;           /* Return code */\n  int exists = 1;               /* True if a journal file is present */\n  int jrnlOpen = !!isOpen(pPager->jfd);\n\n  assert( pPager->useJournal );\n  assert( isOpen(pPager->fd) );\n  assert( pPager->eState==PAGER_OPEN );\n\n  assert( jrnlOpen==0 || ( sqlite3OsDeviceCharacteristics(pPager->jfd) &\n    SQLITE_IOCAP_UNDELETABLE_WHEN_OPEN\n  ));\n\n  *pExists = 0;\n  if( !jrnlOpen ){\n    rc = sqlite3OsAccess(pVfs, pPager->zJournal, SQLITE_ACCESS_EXISTS, &exists);\n  }\n  if( rc==SQLITE_OK && exists ){\n    int locked = 0;             /* True if some process holds a RESERVED lock */\n\n    /* Race condition here:  Another process might have been holding the\n    ** the RESERVED lock and have a journal open at the sqlite3OsAccess() \n    ** call above, but then delete the journal and drop the lock before\n    ** we get to the following sqlite3OsCheckReservedLock() call.  If that\n    ** is the case, this routine might think there is a hot journal when\n    ** in fact there is none.  This results in a false-positive which will\n    ** be dealt with by the playback routine.  Ticket #3883.\n    */\n    rc = sqlite3OsCheckReservedLock(pPager->fd, &locked);\n    if( rc==SQLITE_OK && !locked ){\n      Pgno nPage;                 /* Number of pages in database file */\n\n      assert( pPager->tempFile==0 );\n      rc = pagerPagecount(pPager, &nPage);\n      if( rc==SQLITE_OK ){\n        /* If the database is zero pages in size, that means that either (1) the\n        ** journal is a remnant from a prior database with the same name where\n        ** the database file but not the journal was deleted, or (2) the initial\n        ** transaction that populates a new database is being rolled back.\n        ** In either case, the journal file can be deleted.  However, take care\n        ** not to delete the journal file if it is already open due to\n        ** journal_mode=PERSIST.\n        */\n        if( nPage==0 && !jrnlOpen ){\n          sqlite3BeginBenignMalloc();\n          if( pagerLockDb(pPager, RESERVED_LOCK)==SQLITE_OK ){\n            sqlite3OsDelete(pVfs, pPager->zJournal, 0);\n            if( !pPager->exclusiveMode ) pagerUnlockDb(pPager, SHARED_LOCK);\n          }\n          sqlite3EndBenignMalloc();\n        }else{\n          /* The journal file exists and no other connection has a reserved\n          ** or greater lock on the database file. Now check that there is\n          ** at least one non-zero bytes at the start of the journal file.\n          ** If there is, then we consider this journal to be hot. If not, \n          ** it can be ignored.\n          */\n          if( !jrnlOpen ){\n            int f = SQLITE_OPEN_READONLY|SQLITE_OPEN_MAIN_JOURNAL;\n            rc = sqlite3OsOpen(pVfs, pPager->zJournal, pPager->jfd, f, &f);\n          }\n          if( rc==SQLITE_OK ){\n            u8 first = 0;\n            rc = sqlite3OsRead(pPager->jfd, (void *)&first, 1, 0);\n            if( rc==SQLITE_IOERR_SHORT_READ ){\n              rc = SQLITE_OK;\n            }\n            if( !jrnlOpen ){\n              sqlite3OsClose(pPager->jfd);\n            }\n            *pExists = (first!=0);\n          }else if( rc==SQLITE_CANTOPEN ){\n            /* If we cannot open the rollback journal file in order to see if\n            ** it has a zero header, that might be due to an I/O error, or\n            ** it might be due to the race condition described above and in\n            ** ticket #3883.  Either way, assume that the journal is hot.\n            ** This might be a false positive.  But if it is, then the\n            ** automatic journal playback and recovery mechanism will deal\n            ** with it under an EXCLUSIVE lock where we do not need to\n            ** worry so much with race conditions.\n            */\n            *pExists = 1;\n            rc = SQLITE_OK;\n          }\n        }\n      }\n    }\n  }\n\n  return rc;\n}\n\n/*\n** This function is called to obtain a shared lock on the database file.\n** It is illegal to call sqlite3PagerGet() until after this function\n** has been successfully called. If a shared-lock is already held when\n** this function is called, it is a no-op.\n**\n** The following operations are also performed by this function.\n**\n**   1) If the pager is currently in PAGER_OPEN state (no lock held\n**      on the database file), then an attempt is made to obtain a\n**      SHARED lock on the database file. Immediately after obtaining\n**      the SHARED lock, the file-system is checked for a hot-journal,\n**      which is played back if present. Following any hot-journal \n**      rollback, the contents of the cache are validated by checking\n**      the 'change-counter' field of the database file header and\n**      discarded if they are found to be invalid.\n**\n**   2) If the pager is running in exclusive-mode, and there are currently\n**      no outstanding references to any pages, and is in the error state,\n**      then an attempt is made to clear the error state by discarding\n**      the contents of the page cache and rolling back any open journal\n**      file.\n**\n** If everything is successful, SQLITE_OK is returned. If an IO error \n** occurs while locking the database, checking for a hot-journal file or \n** rolling back a journal file, the IO error code is returned.\n*/\nSQLITE_PRIVATE int sqlite3PagerSharedLock(Pager *pPager){\n  int rc = SQLITE_OK;                /* Return code */\n\n  /* This routine is only called from b-tree and only when there are no\n  ** outstanding pages. This implies that the pager state should either\n  ** be OPEN or READER. READER is only possible if the pager is or was in \n  ** exclusive access mode.  */\n  assert( sqlite3PcacheRefCount(pPager->pPCache)==0 );\n  assert( assert_pager_state(pPager) );\n  assert( pPager->eState==PAGER_OPEN || pPager->eState==PAGER_READER );\n  assert( pPager->errCode==SQLITE_OK );\n\n  if( !pagerUseWal(pPager) && pPager->eState==PAGER_OPEN ){\n    int bHotJournal = 1;          /* True if there exists a hot journal-file */\n\n    assert( !MEMDB );\n    assert( pPager->tempFile==0 || pPager->eLock==EXCLUSIVE_LOCK );\n\n    rc = pager_wait_on_lock(pPager, SHARED_LOCK);\n    if( rc!=SQLITE_OK ){\n      assert( pPager->eLock==NO_LOCK || pPager->eLock==UNKNOWN_LOCK );\n      goto failed;\n    }\n\n    /* If a journal file exists, and there is no RESERVED lock on the\n    ** database file, then it either needs to be played back or deleted.\n    */\n    if( pPager->eLock<=SHARED_LOCK ){\n      rc = hasHotJournal(pPager, &bHotJournal);\n    }\n    if( rc!=SQLITE_OK ){\n      goto failed;\n    }\n    if( bHotJournal ){\n      if( pPager->readOnly ){\n        rc = SQLITE_READONLY_ROLLBACK;\n        goto failed;\n      }\n\n      /* Get an EXCLUSIVE lock on the database file. At this point it is\n      ** important that a RESERVED lock is not obtained on the way to the\n      ** EXCLUSIVE lock. If it were, another process might open the\n      ** database file, detect the RESERVED lock, and conclude that the\n      ** database is safe to read while this process is still rolling the \n      ** hot-journal back.\n      ** \n      ** Because the intermediate RESERVED lock is not requested, any\n      ** other process attempting to access the database file will get to \n      ** this point in the code and fail to obtain its own EXCLUSIVE lock \n      ** on the database file.\n      **\n      ** Unless the pager is in locking_mode=exclusive mode, the lock is\n      ** downgraded to SHARED_LOCK before this function returns.\n      */\n      rc = pagerLockDb(pPager, EXCLUSIVE_LOCK);\n      if( rc!=SQLITE_OK ){\n        goto failed;\n      }\n \n      /* If it is not already open and the file exists on disk, open the \n      ** journal for read/write access. Write access is required because \n      ** in exclusive-access mode the file descriptor will be kept open \n      ** and possibly used for a transaction later on. Also, write-access \n      ** is usually required to finalize the journal in journal_mode=persist \n      ** mode (and also for journal_mode=truncate on some systems).\n      **\n      ** If the journal does not exist, it usually means that some \n      ** other connection managed to get in and roll it back before \n      ** this connection obtained the exclusive lock above. Or, it \n      ** may mean that the pager was in the error-state when this\n      ** function was called and the journal file does not exist.\n      */\n      if( !isOpen(pPager->jfd) ){\n        sqlite3_vfs * const pVfs = pPager->pVfs;\n        int bExists;              /* True if journal file exists */\n        rc = sqlite3OsAccess(\n            pVfs, pPager->zJournal, SQLITE_ACCESS_EXISTS, &bExists);\n        if( rc==SQLITE_OK && bExists ){\n          int fout = 0;\n          int f = SQLITE_OPEN_READWRITE|SQLITE_OPEN_MAIN_JOURNAL;\n          assert( !pPager->tempFile );\n          rc = sqlite3OsOpen(pVfs, pPager->zJournal, pPager->jfd, f, &fout);\n          assert( rc!=SQLITE_OK || isOpen(pPager->jfd) );\n          if( rc==SQLITE_OK && fout&SQLITE_OPEN_READONLY ){\n            rc = SQLITE_CANTOPEN_BKPT;\n            sqlite3OsClose(pPager->jfd);\n          }\n        }\n      }\n \n      /* Playback and delete the journal.  Drop the database write\n      ** lock and reacquire the read lock. Purge the cache before\n      ** playing back the hot-journal so that we don't end up with\n      ** an inconsistent cache.  Sync the hot journal before playing\n      ** it back since the process that crashed and left the hot journal\n      ** probably did not sync it and we are required to always sync\n      ** the journal before playing it back.\n      */\n      if( isOpen(pPager->jfd) ){\n        assert( rc==SQLITE_OK );\n        rc = pagerSyncHotJournal(pPager);\n        if( rc==SQLITE_OK ){\n          rc = pager_playback(pPager, !pPager->tempFile);\n          pPager->eState = PAGER_OPEN;\n        }\n      }else if( !pPager->exclusiveMode ){\n        pagerUnlockDb(pPager, SHARED_LOCK);\n      }\n\n      if( rc!=SQLITE_OK ){\n        /* This branch is taken if an error occurs while trying to open\n        ** or roll back a hot-journal while holding an EXCLUSIVE lock. The\n        ** pager_unlock() routine will be called before returning to unlock\n        ** the file. If the unlock attempt fails, then Pager.eLock must be\n        ** set to UNKNOWN_LOCK (see the comment above the #define for \n        ** UNKNOWN_LOCK above for an explanation). \n        **\n        ** In order to get pager_unlock() to do this, set Pager.eState to\n        ** PAGER_ERROR now. This is not actually counted as a transition\n        ** to ERROR state in the state diagram at the top of this file,\n        ** since we know that the same call to pager_unlock() will very\n        ** shortly transition the pager object to the OPEN state. Calling\n        ** assert_pager_state() would fail now, as it should not be possible\n        ** to be in ERROR state when there are zero outstanding page \n        ** references.\n        */\n        pager_error(pPager, rc);\n        goto failed;\n      }\n\n      assert( pPager->eState==PAGER_OPEN );\n      assert( (pPager->eLock==SHARED_LOCK)\n           || (pPager->exclusiveMode && pPager->eLock>SHARED_LOCK)\n      );\n    }\n\n    if( !pPager->tempFile && pPager->hasHeldSharedLock ){\n      /* The shared-lock has just been acquired then check to\n      ** see if the database has been modified.  If the database has changed,\n      ** flush the cache.  The hasHeldSharedLock flag prevents this from\n      ** occurring on the very first access to a file, in order to save a\n      ** single unnecessary sqlite3OsRead() call at the start-up.\n      **\n      ** Database changes are detected by looking at 15 bytes beginning\n      ** at offset 24 into the file.  The first 4 of these 16 bytes are\n      ** a 32-bit counter that is incremented with each change.  The\n      ** other bytes change randomly with each file change when\n      ** a codec is in use.\n      ** \n      ** There is a vanishingly small chance that a change will not be \n      ** detected.  The chance of an undetected change is so small that\n      ** it can be neglected.\n      */\n      char dbFileVers[sizeof(pPager->dbFileVers)];\n\n      IOTRACE((\"CKVERS %p %d\\n\", pPager, sizeof(dbFileVers)));\n      rc = sqlite3OsRead(pPager->fd, &dbFileVers, sizeof(dbFileVers), 24);\n      if( rc!=SQLITE_OK ){\n        if( rc!=SQLITE_IOERR_SHORT_READ ){\n          goto failed;\n        }\n        memset(dbFileVers, 0, sizeof(dbFileVers));\n      }\n\n      if( memcmp(pPager->dbFileVers, dbFileVers, sizeof(dbFileVers))!=0 ){\n        pager_reset(pPager);\n\n        /* Unmap the database file. It is possible that external processes\n        ** may have truncated the database file and then extended it back\n        ** to its original size while this process was not holding a lock.\n        ** In this case there may exist a Pager.pMap mapping that appears\n        ** to be the right size but is not actually valid. Avoid this\n        ** possibility by unmapping the db here. */\n        if( USEFETCH(pPager) ){\n          sqlite3OsUnfetch(pPager->fd, 0, 0);\n        }\n      }\n    }\n\n    /* If there is a WAL file in the file-system, open this database in WAL\n    ** mode. Otherwise, the following function call is a no-op.\n    */\n    rc = pagerOpenWalIfPresent(pPager);\n#ifndef SQLITE_OMIT_WAL\n    assert( pPager->pWal==0 || rc==SQLITE_OK );\n#endif\n  }\n\n  if( pagerUseWal(pPager) ){\n    assert( rc==SQLITE_OK );\n    rc = pagerBeginReadTransaction(pPager);\n  }\n\n  if( pPager->tempFile==0 && pPager->eState==PAGER_OPEN && rc==SQLITE_OK ){\n    rc = pagerPagecount(pPager, &pPager->dbSize);\n  }\n\n failed:\n  if( rc!=SQLITE_OK ){\n    assert( !MEMDB );\n    pager_unlock(pPager);\n    assert( pPager->eState==PAGER_OPEN );\n  }else{\n    pPager->eState = PAGER_READER;\n    pPager->hasHeldSharedLock = 1;\n  }\n  return rc;\n}\n\n/*\n** If the reference count has reached zero, rollback any active\n** transaction and unlock the pager.\n**\n** Except, in locking_mode=EXCLUSIVE when there is nothing to in\n** the rollback journal, the unlock is not performed and there is\n** nothing to rollback, so this routine is a no-op.\n*/ \nstatic void pagerUnlockIfUnused(Pager *pPager){\n  if( sqlite3PcacheRefCount(pPager->pPCache)==0 ){\n    assert( pPager->nMmapOut==0 ); /* because page1 is never memory mapped */\n    pagerUnlockAndRollback(pPager);\n  }\n}\n\n/*\n** The page getter methods each try to acquire a reference to a\n** page with page number pgno. If the requested reference is \n** successfully obtained, it is copied to *ppPage and SQLITE_OK returned.\n**\n** There are different implementations of the getter method depending\n** on the current state of the pager.\n**\n**     getPageNormal()         --  The normal getter\n**     getPageError()          --  Used if the pager is in an error state\n**     getPageMmap()           --  Used if memory-mapped I/O is enabled\n**\n** If the requested page is already in the cache, it is returned. \n** Otherwise, a new page object is allocated and populated with data\n** read from the database file. In some cases, the pcache module may\n** choose not to allocate a new page object and may reuse an existing\n** object with no outstanding references.\n**\n** The extra data appended to a page is always initialized to zeros the \n** first time a page is loaded into memory. If the page requested is \n** already in the cache when this function is called, then the extra\n** data is left as it was when the page object was last used.\n**\n** If the database image is smaller than the requested page or if \n** the flags parameter contains the PAGER_GET_NOCONTENT bit and the \n** requested page is not already stored in the cache, then no \n** actual disk read occurs. In this case the memory image of the \n** page is initialized to all zeros. \n**\n** If PAGER_GET_NOCONTENT is true, it means that we do not care about\n** the contents of the page. This occurs in two scenarios:\n**\n**   a) When reading a free-list leaf page from the database, and\n**\n**   b) When a savepoint is being rolled back and we need to load\n**      a new page into the cache to be filled with the data read\n**      from the savepoint journal.\n**\n** If PAGER_GET_NOCONTENT is true, then the data returned is zeroed instead\n** of being read from the database. Additionally, the bits corresponding\n** to pgno in Pager.pInJournal (bitvec of pages already written to the\n** journal file) and the PagerSavepoint.pInSavepoint bitvecs of any open\n** savepoints are set. This means if the page is made writable at any\n** point in the future, using a call to sqlite3PagerWrite(), its contents\n** will not be journaled. This saves IO.\n**\n** The acquisition might fail for several reasons.  In all cases,\n** an appropriate error code is returned and *ppPage is set to NULL.\n**\n** See also sqlite3PagerLookup().  Both this routine and Lookup() attempt\n** to find a page in the in-memory cache first.  If the page is not already\n** in memory, this routine goes to disk to read it in whereas Lookup()\n** just returns 0.  This routine acquires a read-lock the first time it\n** has to go to disk, and could also playback an old journal if necessary.\n** Since Lookup() never goes to disk, it never has to deal with locks\n** or journal files.\n*/\nstatic int getPageNormal(\n  Pager *pPager,      /* The pager open on the database file */\n  Pgno pgno,          /* Page number to fetch */\n  DbPage **ppPage,    /* Write a pointer to the page here */\n  int flags           /* PAGER_GET_XXX flags */\n){\n  int rc = SQLITE_OK;\n  PgHdr *pPg;\n  u8 noContent;                   /* True if PAGER_GET_NOCONTENT is set */\n  sqlite3_pcache_page *pBase;\n\n  assert( pPager->errCode==SQLITE_OK );\n  assert( pPager->eState>=PAGER_READER );\n  assert( assert_pager_state(pPager) );\n  assert( pPager->hasHeldSharedLock==1 );\n\n  if( pgno==0 ) return SQLITE_CORRUPT_BKPT;\n  pBase = sqlite3PcacheFetch(pPager->pPCache, pgno, 3);\n  if( pBase==0 ){\n    pPg = 0;\n    rc = sqlite3PcacheFetchStress(pPager->pPCache, pgno, &pBase);\n    if( rc!=SQLITE_OK ) goto pager_acquire_err;\n    if( pBase==0 ){\n      rc = SQLITE_NOMEM_BKPT;\n      goto pager_acquire_err;\n    }\n  }\n  pPg = *ppPage = sqlite3PcacheFetchFinish(pPager->pPCache, pgno, pBase);\n  assert( pPg==(*ppPage) );\n  assert( pPg->pgno==pgno );\n  assert( pPg->pPager==pPager || pPg->pPager==0 );\n\n  noContent = (flags & PAGER_GET_NOCONTENT)!=0;\n  if( pPg->pPager && !noContent ){\n    /* In this case the pcache already contains an initialized copy of\n    ** the page. Return without further ado.  */\n    assert( pgno<=PAGER_MAX_PGNO && pgno!=PAGER_MJ_PGNO(pPager) );\n    pPager->aStat[PAGER_STAT_HIT]++;\n    return SQLITE_OK;\n\n  }else{\n    /* The pager cache has created a new page. Its content needs to \n    ** be initialized. But first some error checks:\n    **\n    ** (1) The maximum page number is 2^31\n    ** (2) Never try to fetch the locking page\n    */\n    if( pgno>PAGER_MAX_PGNO || pgno==PAGER_MJ_PGNO(pPager) ){\n      rc = SQLITE_CORRUPT_BKPT;\n      goto pager_acquire_err;\n    }\n\n    pPg->pPager = pPager;\n\n    assert( !isOpen(pPager->fd) || !MEMDB );\n    if( !isOpen(pPager->fd) || pPager->dbSize<pgno || noContent ){\n      if( pgno>pPager->mxPgno ){\n        rc = SQLITE_FULL;\n        goto pager_acquire_err;\n      }\n      if( noContent ){\n        /* Failure to set the bits in the InJournal bit-vectors is benign.\n        ** It merely means that we might do some extra work to journal a \n        ** page that does not need to be journaled.  Nevertheless, be sure \n        ** to test the case where a malloc error occurs while trying to set \n        ** a bit in a bit vector.\n        */\n        sqlite3BeginBenignMalloc();\n        if( pgno<=pPager->dbOrigSize ){\n          TESTONLY( rc = ) sqlite3BitvecSet(pPager->pInJournal, pgno);\n          testcase( rc==SQLITE_NOMEM );\n        }\n        TESTONLY( rc = ) addToSavepointBitvecs(pPager, pgno);\n        testcase( rc==SQLITE_NOMEM );\n        sqlite3EndBenignMalloc();\n      }\n      memset(pPg->pData, 0, pPager->pageSize);\n      IOTRACE((\"ZERO %p %d\\n\", pPager, pgno));\n    }else{\n      assert( pPg->pPager==pPager );\n      pPager->aStat[PAGER_STAT_MISS]++;\n      rc = readDbPage(pPg);\n      if( rc!=SQLITE_OK ){\n        goto pager_acquire_err;\n      }\n    }\n    pager_set_pagehash(pPg);\n  }\n  return SQLITE_OK;\n\npager_acquire_err:\n  assert( rc!=SQLITE_OK );\n  if( pPg ){\n    sqlite3PcacheDrop(pPg);\n  }\n  pagerUnlockIfUnused(pPager);\n  *ppPage = 0;\n  return rc;\n}\n\n#if SQLITE_MAX_MMAP_SIZE>0\n/* The page getter for when memory-mapped I/O is enabled */\nstatic int getPageMMap(\n  Pager *pPager,      /* The pager open on the database file */\n  Pgno pgno,          /* Page number to fetch */\n  DbPage **ppPage,    /* Write a pointer to the page here */\n  int flags           /* PAGER_GET_XXX flags */\n){\n  int rc = SQLITE_OK;\n  PgHdr *pPg = 0;\n  u32 iFrame = 0;                 /* Frame to read from WAL file */\n\n  /* It is acceptable to use a read-only (mmap) page for any page except\n  ** page 1 if there is no write-transaction open or the ACQUIRE_READONLY\n  ** flag was specified by the caller. And so long as the db is not a \n  ** temporary or in-memory database.  */\n  const int bMmapOk = (pgno>1\n   && (pPager->eState==PAGER_READER || (flags & PAGER_GET_READONLY))\n  );\n\n  assert( USEFETCH(pPager) );\n#ifdef SQLITE_HAS_CODEC\n  assert( pPager->xCodec==0 );\n#endif\n\n  /* Optimization note:  Adding the \"pgno<=1\" term before \"pgno==0\" here\n  ** allows the compiler optimizer to reuse the results of the \"pgno>1\"\n  ** test in the previous statement, and avoid testing pgno==0 in the\n  ** common case where pgno is large. */\n  if( pgno<=1 && pgno==0 ){\n    return SQLITE_CORRUPT_BKPT;\n  }\n  assert( pPager->eState>=PAGER_READER );\n  assert( assert_pager_state(pPager) );\n  assert( pPager->hasHeldSharedLock==1 );\n  assert( pPager->errCode==SQLITE_OK );\n\n  if( bMmapOk && pagerUseWal(pPager) ){\n    rc = sqlite3WalFindFrame(pPager->pWal, pgno, &iFrame);\n    if( rc!=SQLITE_OK ){\n      *ppPage = 0;\n      return rc;\n    }\n  }\n  if( bMmapOk && iFrame==0 ){\n    void *pData = 0;\n    rc = sqlite3OsFetch(pPager->fd, \n        (i64)(pgno-1) * pPager->pageSize, pPager->pageSize, &pData\n    );\n    if( rc==SQLITE_OK && pData ){\n      if( pPager->eState>PAGER_READER || pPager->tempFile ){\n        pPg = sqlite3PagerLookup(pPager, pgno);\n      }\n      if( pPg==0 ){\n        rc = pagerAcquireMapPage(pPager, pgno, pData, &pPg);\n      }else{\n        sqlite3OsUnfetch(pPager->fd, (i64)(pgno-1)*pPager->pageSize, pData);\n      }\n      if( pPg ){\n        assert( rc==SQLITE_OK );\n        *ppPage = pPg;\n        return SQLITE_OK;\n      }\n    }\n    if( rc!=SQLITE_OK ){\n      *ppPage = 0;\n      return rc;\n    }\n  }\n  return getPageNormal(pPager, pgno, ppPage, flags);\n}\n#endif /* SQLITE_MAX_MMAP_SIZE>0 */\n\n/* The page getter method for when the pager is an error state */\nstatic int getPageError(\n  Pager *pPager,      /* The pager open on the database file */\n  Pgno pgno,          /* Page number to fetch */\n  DbPage **ppPage,    /* Write a pointer to the page here */\n  int flags           /* PAGER_GET_XXX flags */\n){\n  UNUSED_PARAMETER(pgno);\n  UNUSED_PARAMETER(flags);\n  assert( pPager->errCode!=SQLITE_OK );\n  *ppPage = 0;\n  return pPager->errCode;\n}\n\n\n/* Dispatch all page fetch requests to the appropriate getter method.\n*/\nSQLITE_PRIVATE int sqlite3PagerGet(\n  Pager *pPager,      /* The pager open on the database file */\n  Pgno pgno,          /* Page number to fetch */\n  DbPage **ppPage,    /* Write a pointer to the page here */\n  int flags           /* PAGER_GET_XXX flags */\n){\n  return pPager->xGet(pPager, pgno, ppPage, flags);\n}\n\n/*\n** Acquire a page if it is already in the in-memory cache.  Do\n** not read the page from disk.  Return a pointer to the page,\n** or 0 if the page is not in cache. \n**\n** See also sqlite3PagerGet().  The difference between this routine\n** and sqlite3PagerGet() is that _get() will go to the disk and read\n** in the page if the page is not already in cache.  This routine\n** returns NULL if the page is not in cache or if a disk I/O error \n** has ever happened.\n*/\nSQLITE_PRIVATE DbPage *sqlite3PagerLookup(Pager *pPager, Pgno pgno){\n  sqlite3_pcache_page *pPage;\n  assert( pPager!=0 );\n  assert( pgno!=0 );\n  assert( pPager->pPCache!=0 );\n  pPage = sqlite3PcacheFetch(pPager->pPCache, pgno, 0);\n  assert( pPage==0 || pPager->hasHeldSharedLock );\n  if( pPage==0 ) return 0;\n  return sqlite3PcacheFetchFinish(pPager->pPCache, pgno, pPage);\n}\n\n/*\n** Release a page reference.\n**\n** The sqlite3PagerUnref() and sqlite3PagerUnrefNotNull() may only be\n** used if we know that the page being released is not the last page.\n** The btree layer always holds page1 open until the end, so these first\n** to routines can be used to release any page other than BtShared.pPage1.\n**\n** Use sqlite3PagerUnrefPageOne() to release page1.  This latter routine\n** checks the total number of outstanding pages and if the number of\n** pages reaches zero it drops the database lock.\n*/\nSQLITE_PRIVATE void sqlite3PagerUnrefNotNull(DbPage *pPg){\n  TESTONLY( Pager *pPager = pPg->pPager; )\n  assert( pPg!=0 );\n  if( pPg->flags & PGHDR_MMAP ){\n    assert( pPg->pgno!=1 );  /* Page1 is never memory mapped */\n    pagerReleaseMapPage(pPg);\n  }else{\n    sqlite3PcacheRelease(pPg);\n  }\n  /* Do not use this routine to release the last reference to page1 */\n  assert( sqlite3PcacheRefCount(pPager->pPCache)>0 );\n}\nSQLITE_PRIVATE void sqlite3PagerUnref(DbPage *pPg){\n  if( pPg ) sqlite3PagerUnrefNotNull(pPg);\n}\nSQLITE_PRIVATE void sqlite3PagerUnrefPageOne(DbPage *pPg){\n  Pager *pPager;\n  assert( pPg!=0 );\n  assert( pPg->pgno==1 );\n  assert( (pPg->flags & PGHDR_MMAP)==0 ); /* Page1 is never memory mapped */\n  pPager = pPg->pPager;\n  sqlite3PcacheRelease(pPg);\n  pagerUnlockIfUnused(pPager);\n}\n\n/*\n** This function is called at the start of every write transaction.\n** There must already be a RESERVED or EXCLUSIVE lock on the database \n** file when this routine is called.\n**\n** Open the journal file for pager pPager and write a journal header\n** to the start of it. If there are active savepoints, open the sub-journal\n** as well. This function is only used when the journal file is being \n** opened to write a rollback log for a transaction. It is not used \n** when opening a hot journal file to roll it back.\n**\n** If the journal file is already open (as it may be in exclusive mode),\n** then this function just writes a journal header to the start of the\n** already open file. \n**\n** Whether or not the journal file is opened by this function, the\n** Pager.pInJournal bitvec structure is allocated.\n**\n** Return SQLITE_OK if everything is successful. Otherwise, return \n** SQLITE_NOMEM if the attempt to allocate Pager.pInJournal fails, or \n** an IO error code if opening or writing the journal file fails.\n*/\nstatic int pager_open_journal(Pager *pPager){\n  int rc = SQLITE_OK;                        /* Return code */\n  sqlite3_vfs * const pVfs = pPager->pVfs;   /* Local cache of vfs pointer */\n\n  assert( pPager->eState==PAGER_WRITER_LOCKED );\n  assert( assert_pager_state(pPager) );\n  assert( pPager->pInJournal==0 );\n  \n  /* If already in the error state, this function is a no-op.  But on\n  ** the other hand, this routine is never called if we are already in\n  ** an error state. */\n  if( NEVER(pPager->errCode) ) return pPager->errCode;\n\n  if( !pagerUseWal(pPager) && pPager->journalMode!=PAGER_JOURNALMODE_OFF ){\n    pPager->pInJournal = sqlite3BitvecCreate(pPager->dbSize);\n    if( pPager->pInJournal==0 ){\n      return SQLITE_NOMEM_BKPT;\n    }\n  \n    /* Open the journal file if it is not already open. */\n    if( !isOpen(pPager->jfd) ){\n      if( pPager->journalMode==PAGER_JOURNALMODE_MEMORY ){\n        sqlite3MemJournalOpen(pPager->jfd);\n      }else{\n        int flags = SQLITE_OPEN_READWRITE|SQLITE_OPEN_CREATE;\n        int nSpill;\n\n        if( pPager->tempFile ){\n          flags |= (SQLITE_OPEN_DELETEONCLOSE|SQLITE_OPEN_TEMP_JOURNAL);\n          nSpill = sqlite3Config.nStmtSpill;\n        }else{\n          flags |= SQLITE_OPEN_MAIN_JOURNAL;\n          nSpill = jrnlBufferSize(pPager);\n        }\n          \n        /* Verify that the database still has the same name as it did when\n        ** it was originally opened. */\n        rc = databaseIsUnmoved(pPager);\n        if( rc==SQLITE_OK ){\n          rc = sqlite3JournalOpen (\n              pVfs, pPager->zJournal, pPager->jfd, flags, nSpill\n          );\n        }\n      }\n      assert( rc!=SQLITE_OK || isOpen(pPager->jfd) );\n    }\n  \n  \n    /* Write the first journal header to the journal file and open \n    ** the sub-journal if necessary.\n    */\n    if( rc==SQLITE_OK ){\n      /* TODO: Check if all of these are really required. */\n      pPager->nRec = 0;\n      pPager->journalOff = 0;\n      pPager->setMaster = 0;\n      pPager->journalHdr = 0;\n      rc = writeJournalHdr(pPager);\n    }\n  }\n\n  if( rc!=SQLITE_OK ){\n    sqlite3BitvecDestroy(pPager->pInJournal);\n    pPager->pInJournal = 0;\n  }else{\n    assert( pPager->eState==PAGER_WRITER_LOCKED );\n    pPager->eState = PAGER_WRITER_CACHEMOD;\n  }\n\n  return rc;\n}\n\n/*\n** Begin a write-transaction on the specified pager object. If a \n** write-transaction has already been opened, this function is a no-op.\n**\n** If the exFlag argument is false, then acquire at least a RESERVED\n** lock on the database file. If exFlag is true, then acquire at least\n** an EXCLUSIVE lock. If such a lock is already held, no locking \n** functions need be called.\n**\n** If the subjInMemory argument is non-zero, then any sub-journal opened\n** within this transaction will be opened as an in-memory file. This\n** has no effect if the sub-journal is already opened (as it may be when\n** running in exclusive mode) or if the transaction does not require a\n** sub-journal. If the subjInMemory argument is zero, then any required\n** sub-journal is implemented in-memory if pPager is an in-memory database, \n** or using a temporary file otherwise.\n*/\nSQLITE_PRIVATE int sqlite3PagerBegin(Pager *pPager, int exFlag, int subjInMemory){\n  int rc = SQLITE_OK;\n\n  if( pPager->errCode ) return pPager->errCode;\n  assert( pPager->eState>=PAGER_READER && pPager->eState<PAGER_ERROR );\n  pPager->subjInMemory = (u8)subjInMemory;\n\n  if( ALWAYS(pPager->eState==PAGER_READER) ){\n    assert( pPager->pInJournal==0 );\n\n    if( pagerUseWal(pPager) ){\n      /* If the pager is configured to use locking_mode=exclusive, and an\n      ** exclusive lock on the database is not already held, obtain it now.\n      */\n      if( pPager->exclusiveMode && sqlite3WalExclusiveMode(pPager->pWal, -1) ){\n        rc = pagerLockDb(pPager, EXCLUSIVE_LOCK);\n        if( rc!=SQLITE_OK ){\n          return rc;\n        }\n        (void)sqlite3WalExclusiveMode(pPager->pWal, 1);\n      }\n\n      /* Grab the write lock on the log file. If successful, upgrade to\n      ** PAGER_RESERVED state. Otherwise, return an error code to the caller.\n      ** The busy-handler is not invoked if another connection already\n      ** holds the write-lock. If possible, the upper layer will call it.\n      */\n      rc = sqlite3WalBeginWriteTransaction(pPager->pWal);\n    }else{\n      /* Obtain a RESERVED lock on the database file. If the exFlag parameter\n      ** is true, then immediately upgrade this to an EXCLUSIVE lock. The\n      ** busy-handler callback can be used when upgrading to the EXCLUSIVE\n      ** lock, but not when obtaining the RESERVED lock.\n      */\n      rc = pagerLockDb(pPager, RESERVED_LOCK);\n      if( rc==SQLITE_OK && exFlag ){\n        rc = pager_wait_on_lock(pPager, EXCLUSIVE_LOCK);\n      }\n    }\n\n    if( rc==SQLITE_OK ){\n      /* Change to WRITER_LOCKED state.\n      **\n      ** WAL mode sets Pager.eState to PAGER_WRITER_LOCKED or CACHEMOD\n      ** when it has an open transaction, but never to DBMOD or FINISHED.\n      ** This is because in those states the code to roll back savepoint \n      ** transactions may copy data from the sub-journal into the database \n      ** file as well as into the page cache. Which would be incorrect in \n      ** WAL mode.\n      */\n      pPager->eState = PAGER_WRITER_LOCKED;\n      pPager->dbHintSize = pPager->dbSize;\n      pPager->dbFileSize = pPager->dbSize;\n      pPager->dbOrigSize = pPager->dbSize;\n      pPager->journalOff = 0;\n    }\n\n    assert( rc==SQLITE_OK || pPager->eState==PAGER_READER );\n    assert( rc!=SQLITE_OK || pPager->eState==PAGER_WRITER_LOCKED );\n    assert( assert_pager_state(pPager) );\n  }\n\n  PAGERTRACE((\"TRANSACTION %d\\n\", PAGERID(pPager)));\n  return rc;\n}\n\n/*\n** Write page pPg onto the end of the rollback journal.\n*/\nstatic SQLITE_NOINLINE int pagerAddPageToRollbackJournal(PgHdr *pPg){\n  Pager *pPager = pPg->pPager;\n  int rc;\n  u32 cksum;\n  char *pData2;\n  i64 iOff = pPager->journalOff;\n\n  /* We should never write to the journal file the page that\n  ** contains the database locks.  The following assert verifies\n  ** that we do not. */\n  assert( pPg->pgno!=PAGER_MJ_PGNO(pPager) );\n\n  assert( pPager->journalHdr<=pPager->journalOff );\n  CODEC2(pPager, pPg->pData, pPg->pgno, 7, return SQLITE_NOMEM_BKPT, pData2);\n  cksum = pager_cksum(pPager, (u8*)pData2);\n\n  /* Even if an IO or diskfull error occurs while journalling the\n  ** page in the block above, set the need-sync flag for the page.\n  ** Otherwise, when the transaction is rolled back, the logic in\n  ** playback_one_page() will think that the page needs to be restored\n  ** in the database file. And if an IO error occurs while doing so,\n  ** then corruption may follow.\n  */\n  pPg->flags |= PGHDR_NEED_SYNC;\n\n  rc = write32bits(pPager->jfd, iOff, pPg->pgno);\n  if( rc!=SQLITE_OK ) return rc;\n  rc = sqlite3OsWrite(pPager->jfd, pData2, pPager->pageSize, iOff+4);\n  if( rc!=SQLITE_OK ) return rc;\n  rc = write32bits(pPager->jfd, iOff+pPager->pageSize+4, cksum);\n  if( rc!=SQLITE_OK ) return rc;\n\n  IOTRACE((\"JOUT %p %d %lld %d\\n\", pPager, pPg->pgno, \n           pPager->journalOff, pPager->pageSize));\n  PAGER_INCR(sqlite3_pager_writej_count);\n  PAGERTRACE((\"JOURNAL %d page %d needSync=%d hash(%08x)\\n\",\n       PAGERID(pPager), pPg->pgno, \n       ((pPg->flags&PGHDR_NEED_SYNC)?1:0), pager_pagehash(pPg)));\n\n  pPager->journalOff += 8 + pPager->pageSize;\n  pPager->nRec++;\n  assert( pPager->pInJournal!=0 );\n  rc = sqlite3BitvecSet(pPager->pInJournal, pPg->pgno);\n  testcase( rc==SQLITE_NOMEM );\n  assert( rc==SQLITE_OK || rc==SQLITE_NOMEM );\n  rc |= addToSavepointBitvecs(pPager, pPg->pgno);\n  assert( rc==SQLITE_OK || rc==SQLITE_NOMEM );\n  return rc;\n}\n\n/*\n** Mark a single data page as writeable. The page is written into the \n** main journal or sub-journal as required. If the page is written into\n** one of the journals, the corresponding bit is set in the \n** Pager.pInJournal bitvec and the PagerSavepoint.pInSavepoint bitvecs\n** of any open savepoints as appropriate.\n*/\nstatic int pager_write(PgHdr *pPg){\n  Pager *pPager = pPg->pPager;\n  int rc = SQLITE_OK;\n\n  /* This routine is not called unless a write-transaction has already \n  ** been started. The journal file may or may not be open at this point.\n  ** It is never called in the ERROR state.\n  */\n  assert( pPager->eState==PAGER_WRITER_LOCKED\n       || pPager->eState==PAGER_WRITER_CACHEMOD\n       || pPager->eState==PAGER_WRITER_DBMOD\n  );\n  assert( assert_pager_state(pPager) );\n  assert( pPager->errCode==0 );\n  assert( pPager->readOnly==0 );\n  CHECK_PAGE(pPg);\n\n  /* The journal file needs to be opened. Higher level routines have already\n  ** obtained the necessary locks to begin the write-transaction, but the\n  ** rollback journal might not yet be open. Open it now if this is the case.\n  **\n  ** This is done before calling sqlite3PcacheMakeDirty() on the page. \n  ** Otherwise, if it were done after calling sqlite3PcacheMakeDirty(), then\n  ** an error might occur and the pager would end up in WRITER_LOCKED state\n  ** with pages marked as dirty in the cache.\n  */\n  if( pPager->eState==PAGER_WRITER_LOCKED ){\n    rc = pager_open_journal(pPager);\n    if( rc!=SQLITE_OK ) return rc;\n  }\n  assert( pPager->eState>=PAGER_WRITER_CACHEMOD );\n  assert( assert_pager_state(pPager) );\n\n  /* Mark the page that is about to be modified as dirty. */\n  sqlite3PcacheMakeDirty(pPg);\n\n  /* If a rollback journal is in use, them make sure the page that is about\n  ** to change is in the rollback journal, or if the page is a new page off\n  ** then end of the file, make sure it is marked as PGHDR_NEED_SYNC.\n  */\n  assert( (pPager->pInJournal!=0) == isOpen(pPager->jfd) );\n  if( pPager->pInJournal!=0\n   && sqlite3BitvecTestNotNull(pPager->pInJournal, pPg->pgno)==0\n  ){\n    assert( pagerUseWal(pPager)==0 );\n    if( pPg->pgno<=pPager->dbOrigSize ){\n      rc = pagerAddPageToRollbackJournal(pPg);\n      if( rc!=SQLITE_OK ){\n        return rc;\n      }\n    }else{\n      if( pPager->eState!=PAGER_WRITER_DBMOD ){\n        pPg->flags |= PGHDR_NEED_SYNC;\n      }\n      PAGERTRACE((\"APPEND %d page %d needSync=%d\\n\",\n              PAGERID(pPager), pPg->pgno,\n             ((pPg->flags&PGHDR_NEED_SYNC)?1:0)));\n    }\n  }\n\n  /* The PGHDR_DIRTY bit is set above when the page was added to the dirty-list\n  ** and before writing the page into the rollback journal.  Wait until now,\n  ** after the page has been successfully journalled, before setting the\n  ** PGHDR_WRITEABLE bit that indicates that the page can be safely modified.\n  */\n  pPg->flags |= PGHDR_WRITEABLE;\n  \n  /* If the statement journal is open and the page is not in it,\n  ** then write the page into the statement journal.\n  */\n  if( pPager->nSavepoint>0 ){\n    rc = subjournalPageIfRequired(pPg);\n  }\n\n  /* Update the database size and return. */\n  if( pPager->dbSize<pPg->pgno ){\n    pPager->dbSize = pPg->pgno;\n  }\n  return rc;\n}\n\n/*\n** This is a variant of sqlite3PagerWrite() that runs when the sector size\n** is larger than the page size.  SQLite makes the (reasonable) assumption that\n** all bytes of a sector are written together by hardware.  Hence, all bytes of\n** a sector need to be journalled in case of a power loss in the middle of\n** a write.\n**\n** Usually, the sector size is less than or equal to the page size, in which\n** case pages can be individually written.  This routine only runs in the\n** exceptional case where the page size is smaller than the sector size.\n*/\nstatic SQLITE_NOINLINE int pagerWriteLargeSector(PgHdr *pPg){\n  int rc = SQLITE_OK;          /* Return code */\n  Pgno nPageCount;             /* Total number of pages in database file */\n  Pgno pg1;                    /* First page of the sector pPg is located on. */\n  int nPage = 0;               /* Number of pages starting at pg1 to journal */\n  int ii;                      /* Loop counter */\n  int needSync = 0;            /* True if any page has PGHDR_NEED_SYNC */\n  Pager *pPager = pPg->pPager; /* The pager that owns pPg */\n  Pgno nPagePerSector = (pPager->sectorSize/pPager->pageSize);\n\n  /* Set the doNotSpill NOSYNC bit to 1. This is because we cannot allow\n  ** a journal header to be written between the pages journaled by\n  ** this function.\n  */\n  assert( !MEMDB );\n  assert( (pPager->doNotSpill & SPILLFLAG_NOSYNC)==0 );\n  pPager->doNotSpill |= SPILLFLAG_NOSYNC;\n\n  /* This trick assumes that both the page-size and sector-size are\n  ** an integer power of 2. It sets variable pg1 to the identifier\n  ** of the first page of the sector pPg is located on.\n  */\n  pg1 = ((pPg->pgno-1) & ~(nPagePerSector-1)) + 1;\n\n  nPageCount = pPager->dbSize;\n  if( pPg->pgno>nPageCount ){\n    nPage = (pPg->pgno - pg1)+1;\n  }else if( (pg1+nPagePerSector-1)>nPageCount ){\n    nPage = nPageCount+1-pg1;\n  }else{\n    nPage = nPagePerSector;\n  }\n  assert(nPage>0);\n  assert(pg1<=pPg->pgno);\n  assert((pg1+nPage)>pPg->pgno);\n\n  for(ii=0; ii<nPage && rc==SQLITE_OK; ii++){\n    Pgno pg = pg1+ii;\n    PgHdr *pPage;\n    if( pg==pPg->pgno || !sqlite3BitvecTest(pPager->pInJournal, pg) ){\n      if( pg!=PAGER_MJ_PGNO(pPager) ){\n        rc = sqlite3PagerGet(pPager, pg, &pPage, 0);\n        if( rc==SQLITE_OK ){\n          rc = pager_write(pPage);\n          if( pPage->flags&PGHDR_NEED_SYNC ){\n            needSync = 1;\n          }\n          sqlite3PagerUnrefNotNull(pPage);\n        }\n      }\n    }else if( (pPage = sqlite3PagerLookup(pPager, pg))!=0 ){\n      if( pPage->flags&PGHDR_NEED_SYNC ){\n        needSync = 1;\n      }\n      sqlite3PagerUnrefNotNull(pPage);\n    }\n  }\n\n  /* If the PGHDR_NEED_SYNC flag is set for any of the nPage pages \n  ** starting at pg1, then it needs to be set for all of them. Because\n  ** writing to any of these nPage pages may damage the others, the\n  ** journal file must contain sync()ed copies of all of them\n  ** before any of them can be written out to the database file.\n  */\n  if( rc==SQLITE_OK && needSync ){\n    assert( !MEMDB );\n    for(ii=0; ii<nPage; ii++){\n      PgHdr *pPage = sqlite3PagerLookup(pPager, pg1+ii);\n      if( pPage ){\n        pPage->flags |= PGHDR_NEED_SYNC;\n        sqlite3PagerUnrefNotNull(pPage);\n      }\n    }\n  }\n\n  assert( (pPager->doNotSpill & SPILLFLAG_NOSYNC)!=0 );\n  pPager->doNotSpill &= ~SPILLFLAG_NOSYNC;\n  return rc;\n}\n\n/*\n** Mark a data page as writeable. This routine must be called before \n** making changes to a page. The caller must check the return value \n** of this function and be careful not to change any page data unless \n** this routine returns SQLITE_OK.\n**\n** The difference between this function and pager_write() is that this\n** function also deals with the special case where 2 or more pages\n** fit on a single disk sector. In this case all co-resident pages\n** must have been written to the journal file before returning.\n**\n** If an error occurs, SQLITE_NOMEM or an IO error code is returned\n** as appropriate. Otherwise, SQLITE_OK.\n*/\nSQLITE_PRIVATE int sqlite3PagerWrite(PgHdr *pPg){\n  Pager *pPager = pPg->pPager;\n  assert( (pPg->flags & PGHDR_MMAP)==0 );\n  assert( pPager->eState>=PAGER_WRITER_LOCKED );\n  assert( assert_pager_state(pPager) );\n  if( (pPg->flags & PGHDR_WRITEABLE)!=0 && pPager->dbSize>=pPg->pgno ){\n    if( pPager->nSavepoint ) return subjournalPageIfRequired(pPg);\n    return SQLITE_OK;\n  }else if( pPager->errCode ){\n    return pPager->errCode;\n  }else if( pPager->sectorSize > (u32)pPager->pageSize ){\n    assert( pPager->tempFile==0 );\n    return pagerWriteLargeSector(pPg);\n  }else{\n    return pager_write(pPg);\n  }\n}\n\n/*\n** Return TRUE if the page given in the argument was previously passed\n** to sqlite3PagerWrite().  In other words, return TRUE if it is ok\n** to change the content of the page.\n*/\n#ifndef NDEBUG\nSQLITE_PRIVATE int sqlite3PagerIswriteable(DbPage *pPg){\n  return pPg->flags & PGHDR_WRITEABLE;\n}\n#endif\n\n/*\n** A call to this routine tells the pager that it is not necessary to\n** write the information on page pPg back to the disk, even though\n** that page might be marked as dirty.  This happens, for example, when\n** the page has been added as a leaf of the freelist and so its\n** content no longer matters.\n**\n** The overlying software layer calls this routine when all of the data\n** on the given page is unused. The pager marks the page as clean so\n** that it does not get written to disk.\n**\n** Tests show that this optimization can quadruple the speed of large \n** DELETE operations.\n**\n** This optimization cannot be used with a temp-file, as the page may\n** have been dirty at the start of the transaction. In that case, if\n** memory pressure forces page pPg out of the cache, the data does need \n** to be written out to disk so that it may be read back in if the \n** current transaction is rolled back.\n*/\nSQLITE_PRIVATE void sqlite3PagerDontWrite(PgHdr *pPg){\n  Pager *pPager = pPg->pPager;\n  if( !pPager->tempFile && (pPg->flags&PGHDR_DIRTY) && pPager->nSavepoint==0 ){\n    PAGERTRACE((\"DONT_WRITE page %d of %d\\n\", pPg->pgno, PAGERID(pPager)));\n    IOTRACE((\"CLEAN %p %d\\n\", pPager, pPg->pgno))\n    pPg->flags |= PGHDR_DONT_WRITE;\n    pPg->flags &= ~PGHDR_WRITEABLE;\n    testcase( pPg->flags & PGHDR_NEED_SYNC );\n    pager_set_pagehash(pPg);\n  }\n}\n\n/*\n** This routine is called to increment the value of the database file \n** change-counter, stored as a 4-byte big-endian integer starting at \n** byte offset 24 of the pager file.  The secondary change counter at\n** 92 is also updated, as is the SQLite version number at offset 96.\n**\n** But this only happens if the pPager->changeCountDone flag is false.\n** To avoid excess churning of page 1, the update only happens once.\n** See also the pager_write_changecounter() routine that does an \n** unconditional update of the change counters.\n**\n** If the isDirectMode flag is zero, then this is done by calling \n** sqlite3PagerWrite() on page 1, then modifying the contents of the\n** page data. In this case the file will be updated when the current\n** transaction is committed.\n**\n** The isDirectMode flag may only be non-zero if the library was compiled\n** with the SQLITE_ENABLE_ATOMIC_WRITE macro defined. In this case,\n** if isDirect is non-zero, then the database file is updated directly\n** by writing an updated version of page 1 using a call to the \n** sqlite3OsWrite() function.\n*/\nstatic int pager_incr_changecounter(Pager *pPager, int isDirectMode){\n  int rc = SQLITE_OK;\n\n  assert( pPager->eState==PAGER_WRITER_CACHEMOD\n       || pPager->eState==PAGER_WRITER_DBMOD\n  );\n  assert( assert_pager_state(pPager) );\n\n  /* Declare and initialize constant integer 'isDirect'. If the\n  ** atomic-write optimization is enabled in this build, then isDirect\n  ** is initialized to the value passed as the isDirectMode parameter\n  ** to this function. Otherwise, it is always set to zero.\n  **\n  ** The idea is that if the atomic-write optimization is not\n  ** enabled at compile time, the compiler can omit the tests of\n  ** 'isDirect' below, as well as the block enclosed in the\n  ** \"if( isDirect )\" condition.\n  */\n#ifndef SQLITE_ENABLE_ATOMIC_WRITE\n# define DIRECT_MODE 0\n  assert( isDirectMode==0 );\n  UNUSED_PARAMETER(isDirectMode);\n#else\n# define DIRECT_MODE isDirectMode\n#endif\n\n  if( !pPager->changeCountDone && ALWAYS(pPager->dbSize>0) ){\n    PgHdr *pPgHdr;                /* Reference to page 1 */\n\n    assert( !pPager->tempFile && isOpen(pPager->fd) );\n\n    /* Open page 1 of the file for writing. */\n    rc = sqlite3PagerGet(pPager, 1, &pPgHdr, 0);\n    assert( pPgHdr==0 || rc==SQLITE_OK );\n\n    /* If page one was fetched successfully, and this function is not\n    ** operating in direct-mode, make page 1 writable.  When not in \n    ** direct mode, page 1 is always held in cache and hence the PagerGet()\n    ** above is always successful - hence the ALWAYS on rc==SQLITE_OK.\n    */\n    if( !DIRECT_MODE && ALWAYS(rc==SQLITE_OK) ){\n      rc = sqlite3PagerWrite(pPgHdr);\n    }\n\n    if( rc==SQLITE_OK ){\n      /* Actually do the update of the change counter */\n      pager_write_changecounter(pPgHdr);\n\n      /* If running in direct mode, write the contents of page 1 to the file. */\n      if( DIRECT_MODE ){\n        const void *zBuf;\n        assert( pPager->dbFileSize>0 );\n        CODEC2(pPager, pPgHdr->pData, 1, 6, rc=SQLITE_NOMEM_BKPT, zBuf);\n        if( rc==SQLITE_OK ){\n          rc = sqlite3OsWrite(pPager->fd, zBuf, pPager->pageSize, 0);\n          pPager->aStat[PAGER_STAT_WRITE]++;\n        }\n        if( rc==SQLITE_OK ){\n          /* Update the pager's copy of the change-counter. Otherwise, the\n          ** next time a read transaction is opened the cache will be\n          ** flushed (as the change-counter values will not match).  */\n          const void *pCopy = (const void *)&((const char *)zBuf)[24];\n          memcpy(&pPager->dbFileVers, pCopy, sizeof(pPager->dbFileVers));\n          pPager->changeCountDone = 1;\n        }\n      }else{\n        pPager->changeCountDone = 1;\n      }\n    }\n\n    /* Release the page reference. */\n    sqlite3PagerUnref(pPgHdr);\n  }\n  return rc;\n}\n\n/*\n** Sync the database file to disk. This is a no-op for in-memory databases\n** or pages with the Pager.noSync flag set.\n**\n** If successful, or if called on a pager for which it is a no-op, this\n** function returns SQLITE_OK. Otherwise, an IO error code is returned.\n*/\nSQLITE_PRIVATE int sqlite3PagerSync(Pager *pPager, const char *zMaster){\n  int rc = SQLITE_OK;\n\n  if( isOpen(pPager->fd) ){\n    void *pArg = (void*)zMaster;\n    rc = sqlite3OsFileControl(pPager->fd, SQLITE_FCNTL_SYNC, pArg);\n    if( rc==SQLITE_NOTFOUND ) rc = SQLITE_OK;\n  }\n  if( rc==SQLITE_OK && !pPager->noSync ){\n    assert( !MEMDB );\n    rc = sqlite3OsSync(pPager->fd, pPager->syncFlags);\n  }\n  return rc;\n}\n\n/*\n** This function may only be called while a write-transaction is active in\n** rollback. If the connection is in WAL mode, this call is a no-op. \n** Otherwise, if the connection does not already have an EXCLUSIVE lock on \n** the database file, an attempt is made to obtain one.\n**\n** If the EXCLUSIVE lock is already held or the attempt to obtain it is\n** successful, or the connection is in WAL mode, SQLITE_OK is returned.\n** Otherwise, either SQLITE_BUSY or an SQLITE_IOERR_XXX error code is \n** returned.\n*/\nSQLITE_PRIVATE int sqlite3PagerExclusiveLock(Pager *pPager){\n  int rc = pPager->errCode;\n  assert( assert_pager_state(pPager) );\n  if( rc==SQLITE_OK ){\n    assert( pPager->eState==PAGER_WRITER_CACHEMOD \n         || pPager->eState==PAGER_WRITER_DBMOD \n         || pPager->eState==PAGER_WRITER_LOCKED \n    );\n    assert( assert_pager_state(pPager) );\n    if( 0==pagerUseWal(pPager) ){\n      rc = pager_wait_on_lock(pPager, EXCLUSIVE_LOCK);\n    }\n  }\n  return rc;\n}\n\n/*\n** Sync the database file for the pager pPager. zMaster points to the name\n** of a master journal file that should be written into the individual\n** journal file. zMaster may be NULL, which is interpreted as no master\n** journal (a single database transaction).\n**\n** This routine ensures that:\n**\n**   * The database file change-counter is updated,\n**   * the journal is synced (unless the atomic-write optimization is used),\n**   * all dirty pages are written to the database file, \n**   * the database file is truncated (if required), and\n**   * the database file synced. \n**\n** The only thing that remains to commit the transaction is to finalize \n** (delete, truncate or zero the first part of) the journal file (or \n** delete the master journal file if specified).\n**\n** Note that if zMaster==NULL, this does not overwrite a previous value\n** passed to an sqlite3PagerCommitPhaseOne() call.\n**\n** If the final parameter - noSync - is true, then the database file itself\n** is not synced. The caller must call sqlite3PagerSync() directly to\n** sync the database file before calling CommitPhaseTwo() to delete the\n** journal file in this case.\n*/\nSQLITE_PRIVATE int sqlite3PagerCommitPhaseOne(\n  Pager *pPager,                  /* Pager object */\n  const char *zMaster,            /* If not NULL, the master journal name */\n  int noSync                      /* True to omit the xSync on the db file */\n){\n  int rc = SQLITE_OK;             /* Return code */\n\n  assert( pPager->eState==PAGER_WRITER_LOCKED\n       || pPager->eState==PAGER_WRITER_CACHEMOD\n       || pPager->eState==PAGER_WRITER_DBMOD\n       || pPager->eState==PAGER_ERROR\n  );\n  assert( assert_pager_state(pPager) );\n\n  /* If a prior error occurred, report that error again. */\n  if( NEVER(pPager->errCode) ) return pPager->errCode;\n\n  /* Provide the ability to easily simulate an I/O error during testing */\n  if( sqlite3FaultSim(400) ) return SQLITE_IOERR;\n\n  PAGERTRACE((\"DATABASE SYNC: File=%s zMaster=%s nSize=%d\\n\", \n      pPager->zFilename, zMaster, pPager->dbSize));\n\n  /* If no database changes have been made, return early. */\n  if( pPager->eState<PAGER_WRITER_CACHEMOD ) return SQLITE_OK;\n\n  assert( MEMDB==0 || pPager->tempFile );\n  assert( isOpen(pPager->fd) || pPager->tempFile );\n  if( 0==pagerFlushOnCommit(pPager, 1) ){\n    /* If this is an in-memory db, or no pages have been written to, or this\n    ** function has already been called, it is mostly a no-op.  However, any\n    ** backup in progress needs to be restarted.  */\n    sqlite3BackupRestart(pPager->pBackup);\n  }else{\n    if( pagerUseWal(pPager) ){\n      PgHdr *pList = sqlite3PcacheDirtyList(pPager->pPCache);\n      PgHdr *pPageOne = 0;\n      if( pList==0 ){\n        /* Must have at least one page for the WAL commit flag.\n        ** Ticket [2d1a5c67dfc2363e44f29d9bbd57f] 2011-05-18 */\n        rc = sqlite3PagerGet(pPager, 1, &pPageOne, 0);\n        pList = pPageOne;\n        pList->pDirty = 0;\n      }\n      assert( rc==SQLITE_OK );\n      if( ALWAYS(pList) ){\n        rc = pagerWalFrames(pPager, pList, pPager->dbSize, 1);\n      }\n      sqlite3PagerUnref(pPageOne);\n      if( rc==SQLITE_OK ){\n        sqlite3PcacheCleanAll(pPager->pPCache);\n      }\n    }else{\n      /* The bBatch boolean is true if the batch-atomic-write commit method\n      ** should be used.  No rollback journal is created if batch-atomic-write\n      ** is enabled.\n      */\n      sqlite3_file *fd = pPager->fd;\n#ifdef SQLITE_ENABLE_BATCH_ATOMIC_WRITE\n      const int bBatch = zMaster==0    /* An SQLITE_IOCAP_BATCH_ATOMIC commit */\n        && (sqlite3OsDeviceCharacteristics(fd) & SQLITE_IOCAP_BATCH_ATOMIC)\n        && !pPager->noSync\n        && sqlite3JournalIsInMemory(pPager->jfd);\n#else\n# define bBatch 0\n#endif\n\n#ifdef SQLITE_ENABLE_ATOMIC_WRITE\n      /* The following block updates the change-counter. Exactly how it\n      ** does this depends on whether or not the atomic-update optimization\n      ** was enabled at compile time, and if this transaction meets the \n      ** runtime criteria to use the operation: \n      **\n      **    * The file-system supports the atomic-write property for\n      **      blocks of size page-size, and \n      **    * This commit is not part of a multi-file transaction, and\n      **    * Exactly one page has been modified and store in the journal file.\n      **\n      ** If the optimization was not enabled at compile time, then the\n      ** pager_incr_changecounter() function is called to update the change\n      ** counter in 'indirect-mode'. If the optimization is compiled in but\n      ** is not applicable to this transaction, call sqlite3JournalCreate()\n      ** to make sure the journal file has actually been created, then call\n      ** pager_incr_changecounter() to update the change-counter in indirect\n      ** mode. \n      **\n      ** Otherwise, if the optimization is both enabled and applicable,\n      ** then call pager_incr_changecounter() to update the change-counter\n      ** in 'direct' mode. In this case the journal file will never be\n      ** created for this transaction.\n      */\n      if( bBatch==0 ){\n        PgHdr *pPg;\n        assert( isOpen(pPager->jfd) \n            || pPager->journalMode==PAGER_JOURNALMODE_OFF \n            || pPager->journalMode==PAGER_JOURNALMODE_WAL \n            );\n        if( !zMaster && isOpen(pPager->jfd) \n         && pPager->journalOff==jrnlBufferSize(pPager) \n         && pPager->dbSize>=pPager->dbOrigSize\n         && (!(pPg = sqlite3PcacheDirtyList(pPager->pPCache)) || 0==pPg->pDirty)\n        ){\n          /* Update the db file change counter via the direct-write method. The \n          ** following call will modify the in-memory representation of page 1 \n          ** to include the updated change counter and then write page 1 \n          ** directly to the database file. Because of the atomic-write \n          ** property of the host file-system, this is safe.\n          */\n          rc = pager_incr_changecounter(pPager, 1);\n        }else{\n          rc = sqlite3JournalCreate(pPager->jfd);\n          if( rc==SQLITE_OK ){\n            rc = pager_incr_changecounter(pPager, 0);\n          }\n        }\n      }\n#else \n#ifdef SQLITE_ENABLE_BATCH_ATOMIC_WRITE\n      if( zMaster ){\n        rc = sqlite3JournalCreate(pPager->jfd);\n        if( rc!=SQLITE_OK ) goto commit_phase_one_exit;\n      }\n#endif\n      rc = pager_incr_changecounter(pPager, 0);\n#endif\n      if( rc!=SQLITE_OK ) goto commit_phase_one_exit;\n  \n      /* Write the master journal name into the journal file. If a master \n      ** journal file name has already been written to the journal file, \n      ** or if zMaster is NULL (no master journal), then this call is a no-op.\n      */\n      rc = writeMasterJournal(pPager, zMaster);\n      if( rc!=SQLITE_OK ) goto commit_phase_one_exit;\n  \n      /* Sync the journal file and write all dirty pages to the database.\n      ** If the atomic-update optimization is being used, this sync will not \n      ** create the journal file or perform any real IO.\n      **\n      ** Because the change-counter page was just modified, unless the\n      ** atomic-update optimization is used it is almost certain that the\n      ** journal requires a sync here. However, in locking_mode=exclusive\n      ** on a system under memory pressure it is just possible that this is \n      ** not the case. In this case it is likely enough that the redundant\n      ** xSync() call will be changed to a no-op by the OS anyhow. \n      */\n      rc = syncJournal(pPager, 0);\n      if( rc!=SQLITE_OK ) goto commit_phase_one_exit;\n\n      if( bBatch ){\n        /* The pager is now in DBMOD state. But regardless of what happens\n        ** next, attempting to play the journal back into the database would\n        ** be unsafe. Close it now to make sure that does not happen.  */\n        sqlite3OsClose(pPager->jfd);\n        rc = sqlite3OsFileControl(fd, SQLITE_FCNTL_BEGIN_ATOMIC_WRITE, 0);\n        if( rc!=SQLITE_OK ) goto commit_phase_one_exit;\n      }\n      rc = pager_write_pagelist(pPager,sqlite3PcacheDirtyList(pPager->pPCache));\n      if( bBatch ){\n        if( rc==SQLITE_OK ){\n          rc = sqlite3OsFileControl(fd, SQLITE_FCNTL_COMMIT_ATOMIC_WRITE, 0);\n        }\n        if( rc!=SQLITE_OK ){\n          sqlite3OsFileControlHint(fd, SQLITE_FCNTL_ROLLBACK_ATOMIC_WRITE, 0);\n        }\n      }\n\n      if( rc!=SQLITE_OK ){\n        assert( rc!=SQLITE_IOERR_BLOCKED );\n        goto commit_phase_one_exit;\n      }\n      sqlite3PcacheCleanAll(pPager->pPCache);\n\n      /* If the file on disk is smaller than the database image, use \n      ** pager_truncate to grow the file here. This can happen if the database\n      ** image was extended as part of the current transaction and then the\n      ** last page in the db image moved to the free-list. In this case the\n      ** last page is never written out to disk, leaving the database file\n      ** undersized. Fix this now if it is the case.  */\n      if( pPager->dbSize>pPager->dbFileSize ){\n        Pgno nNew = pPager->dbSize - (pPager->dbSize==PAGER_MJ_PGNO(pPager));\n        assert( pPager->eState==PAGER_WRITER_DBMOD );\n        rc = pager_truncate(pPager, nNew);\n        if( rc!=SQLITE_OK ) goto commit_phase_one_exit;\n      }\n  \n      /* Finally, sync the database file. */\n      if( !noSync ){\n        rc = sqlite3PagerSync(pPager, zMaster);\n      }\n      IOTRACE((\"DBSYNC %p\\n\", pPager))\n    }\n  }\n\ncommit_phase_one_exit:\n  if( rc==SQLITE_OK && !pagerUseWal(pPager) ){\n    pPager->eState = PAGER_WRITER_FINISHED;\n  }\n  return rc;\n}\n\n\n/*\n** When this function is called, the database file has been completely\n** updated to reflect the changes made by the current transaction and\n** synced to disk. The journal file still exists in the file-system \n** though, and if a failure occurs at this point it will eventually\n** be used as a hot-journal and the current transaction rolled back.\n**\n** This function finalizes the journal file, either by deleting, \n** truncating or partially zeroing it, so that it cannot be used \n** for hot-journal rollback. Once this is done the transaction is\n** irrevocably committed.\n**\n** If an error occurs, an IO error code is returned and the pager\n** moves into the error state. Otherwise, SQLITE_OK is returned.\n*/\nSQLITE_PRIVATE int sqlite3PagerCommitPhaseTwo(Pager *pPager){\n  int rc = SQLITE_OK;                  /* Return code */\n\n  /* This routine should not be called if a prior error has occurred.\n  ** But if (due to a coding error elsewhere in the system) it does get\n  ** called, just return the same error code without doing anything. */\n  if( NEVER(pPager->errCode) ) return pPager->errCode;\n\n  assert( pPager->eState==PAGER_WRITER_LOCKED\n       || pPager->eState==PAGER_WRITER_FINISHED\n       || (pagerUseWal(pPager) && pPager->eState==PAGER_WRITER_CACHEMOD)\n  );\n  assert( assert_pager_state(pPager) );\n\n  /* An optimization. If the database was not actually modified during\n  ** this transaction, the pager is running in exclusive-mode and is\n  ** using persistent journals, then this function is a no-op.\n  **\n  ** The start of the journal file currently contains a single journal \n  ** header with the nRec field set to 0. If such a journal is used as\n  ** a hot-journal during hot-journal rollback, 0 changes will be made\n  ** to the database file. So there is no need to zero the journal \n  ** header. Since the pager is in exclusive mode, there is no need\n  ** to drop any locks either.\n  */\n  if( pPager->eState==PAGER_WRITER_LOCKED \n   && pPager->exclusiveMode \n   && pPager->journalMode==PAGER_JOURNALMODE_PERSIST\n  ){\n    assert( pPager->journalOff==JOURNAL_HDR_SZ(pPager) || !pPager->journalOff );\n    pPager->eState = PAGER_READER;\n    return SQLITE_OK;\n  }\n\n  PAGERTRACE((\"COMMIT %d\\n\", PAGERID(pPager)));\n  pPager->iDataVersion++;\n  rc = pager_end_transaction(pPager, pPager->setMaster, 1);\n  return pager_error(pPager, rc);\n}\n\n/*\n** If a write transaction is open, then all changes made within the \n** transaction are reverted and the current write-transaction is closed.\n** The pager falls back to PAGER_READER state if successful, or PAGER_ERROR\n** state if an error occurs.\n**\n** If the pager is already in PAGER_ERROR state when this function is called,\n** it returns Pager.errCode immediately. No work is performed in this case.\n**\n** Otherwise, in rollback mode, this function performs two functions:\n**\n**   1) It rolls back the journal file, restoring all database file and \n**      in-memory cache pages to the state they were in when the transaction\n**      was opened, and\n**\n**   2) It finalizes the journal file, so that it is not used for hot\n**      rollback at any point in the future.\n**\n** Finalization of the journal file (task 2) is only performed if the \n** rollback is successful.\n**\n** In WAL mode, all cache-entries containing data modified within the\n** current transaction are either expelled from the cache or reverted to\n** their pre-transaction state by re-reading data from the database or\n** WAL files. The WAL transaction is then closed.\n*/\nSQLITE_PRIVATE int sqlite3PagerRollback(Pager *pPager){\n  int rc = SQLITE_OK;                  /* Return code */\n  PAGERTRACE((\"ROLLBACK %d\\n\", PAGERID(pPager)));\n\n  /* PagerRollback() is a no-op if called in READER or OPEN state. If\n  ** the pager is already in the ERROR state, the rollback is not \n  ** attempted here. Instead, the error code is returned to the caller.\n  */\n  assert( assert_pager_state(pPager) );\n  if( pPager->eState==PAGER_ERROR ) return pPager->errCode;\n  if( pPager->eState<=PAGER_READER ) return SQLITE_OK;\n\n  if( pagerUseWal(pPager) ){\n    int rc2;\n    rc = sqlite3PagerSavepoint(pPager, SAVEPOINT_ROLLBACK, -1);\n    rc2 = pager_end_transaction(pPager, pPager->setMaster, 0);\n    if( rc==SQLITE_OK ) rc = rc2;\n  }else if( !isOpen(pPager->jfd) || pPager->eState==PAGER_WRITER_LOCKED ){\n    int eState = pPager->eState;\n    rc = pager_end_transaction(pPager, 0, 0);\n    if( !MEMDB && eState>PAGER_WRITER_LOCKED ){\n      /* This can happen using journal_mode=off. Move the pager to the error \n      ** state to indicate that the contents of the cache may not be trusted.\n      ** Any active readers will get SQLITE_ABORT.\n      */\n      pPager->errCode = SQLITE_ABORT;\n      pPager->eState = PAGER_ERROR;\n      setGetterMethod(pPager);\n      return rc;\n    }\n  }else{\n    rc = pager_playback(pPager, 0);\n  }\n\n  assert( pPager->eState==PAGER_READER || rc!=SQLITE_OK );\n  assert( rc==SQLITE_OK || rc==SQLITE_FULL || rc==SQLITE_CORRUPT\n          || rc==SQLITE_NOMEM || (rc&0xFF)==SQLITE_IOERR \n          || rc==SQLITE_CANTOPEN\n  );\n\n  /* If an error occurs during a ROLLBACK, we can no longer trust the pager\n  ** cache. So call pager_error() on the way out to make any error persistent.\n  */\n  return pager_error(pPager, rc);\n}\n\n/*\n** Return TRUE if the database file is opened read-only.  Return FALSE\n** if the database is (in theory) writable.\n*/\nSQLITE_PRIVATE u8 sqlite3PagerIsreadonly(Pager *pPager){\n  return pPager->readOnly;\n}\n\n#ifdef SQLITE_DEBUG\n/*\n** Return the sum of the reference counts for all pages held by pPager.\n*/\nSQLITE_PRIVATE int sqlite3PagerRefcount(Pager *pPager){\n  return sqlite3PcacheRefCount(pPager->pPCache);\n}\n#endif\n\n/*\n** Return the approximate number of bytes of memory currently\n** used by the pager and its associated cache.\n*/\nSQLITE_PRIVATE int sqlite3PagerMemUsed(Pager *pPager){\n  int perPageSize = pPager->pageSize + pPager->nExtra + sizeof(PgHdr)\n                                     + 5*sizeof(void*);\n  return perPageSize*sqlite3PcachePagecount(pPager->pPCache)\n           + sqlite3MallocSize(pPager)\n           + pPager->pageSize;\n}\n\n/*\n** Return the number of references to the specified page.\n*/\nSQLITE_PRIVATE int sqlite3PagerPageRefcount(DbPage *pPage){\n  return sqlite3PcachePageRefcount(pPage);\n}\n\n#ifdef SQLITE_TEST\n/*\n** This routine is used for testing and analysis only.\n*/\nSQLITE_PRIVATE int *sqlite3PagerStats(Pager *pPager){\n  static int a[11];\n  a[0] = sqlite3PcacheRefCount(pPager->pPCache);\n  a[1] = sqlite3PcachePagecount(pPager->pPCache);\n  a[2] = sqlite3PcacheGetCachesize(pPager->pPCache);\n  a[3] = pPager->eState==PAGER_OPEN ? -1 : (int) pPager->dbSize;\n  a[4] = pPager->eState;\n  a[5] = pPager->errCode;\n  a[6] = pPager->aStat[PAGER_STAT_HIT];\n  a[7] = pPager->aStat[PAGER_STAT_MISS];\n  a[8] = 0;  /* Used to be pPager->nOvfl */\n  a[9] = pPager->nRead;\n  a[10] = pPager->aStat[PAGER_STAT_WRITE];\n  return a;\n}\n#endif\n\n/*\n** Parameter eStat must be either SQLITE_DBSTATUS_CACHE_HIT or\n** SQLITE_DBSTATUS_CACHE_MISS. Before returning, *pnVal is incremented by the\n** current cache hit or miss count, according to the value of eStat. If the \n** reset parameter is non-zero, the cache hit or miss count is zeroed before \n** returning.\n*/\nSQLITE_PRIVATE void sqlite3PagerCacheStat(Pager *pPager, int eStat, int reset, int *pnVal){\n\n  assert( eStat==SQLITE_DBSTATUS_CACHE_HIT\n       || eStat==SQLITE_DBSTATUS_CACHE_MISS\n       || eStat==SQLITE_DBSTATUS_CACHE_WRITE\n  );\n\n  assert( SQLITE_DBSTATUS_CACHE_HIT+1==SQLITE_DBSTATUS_CACHE_MISS );\n  assert( SQLITE_DBSTATUS_CACHE_HIT+2==SQLITE_DBSTATUS_CACHE_WRITE );\n  assert( PAGER_STAT_HIT==0 && PAGER_STAT_MISS==1 && PAGER_STAT_WRITE==2 );\n\n  *pnVal += pPager->aStat[eStat - SQLITE_DBSTATUS_CACHE_HIT];\n  if( reset ){\n    pPager->aStat[eStat - SQLITE_DBSTATUS_CACHE_HIT] = 0;\n  }\n}\n\n/*\n** Return true if this is an in-memory or temp-file backed pager.\n*/\nSQLITE_PRIVATE int sqlite3PagerIsMemdb(Pager *pPager){\n  return pPager->tempFile;\n}\n\n/*\n** Check that there are at least nSavepoint savepoints open. If there are\n** currently less than nSavepoints open, then open one or more savepoints\n** to make up the difference. If the number of savepoints is already\n** equal to nSavepoint, then this function is a no-op.\n**\n** If a memory allocation fails, SQLITE_NOMEM is returned. If an error \n** occurs while opening the sub-journal file, then an IO error code is\n** returned. Otherwise, SQLITE_OK.\n*/\nstatic SQLITE_NOINLINE int pagerOpenSavepoint(Pager *pPager, int nSavepoint){\n  int rc = SQLITE_OK;                       /* Return code */\n  int nCurrent = pPager->nSavepoint;        /* Current number of savepoints */\n  int ii;                                   /* Iterator variable */\n  PagerSavepoint *aNew;                     /* New Pager.aSavepoint array */\n\n  assert( pPager->eState>=PAGER_WRITER_LOCKED );\n  assert( assert_pager_state(pPager) );\n  assert( nSavepoint>nCurrent && pPager->useJournal );\n\n  /* Grow the Pager.aSavepoint array using realloc(). Return SQLITE_NOMEM\n  ** if the allocation fails. Otherwise, zero the new portion in case a \n  ** malloc failure occurs while populating it in the for(...) loop below.\n  */\n  aNew = (PagerSavepoint *)sqlite3Realloc(\n      pPager->aSavepoint, sizeof(PagerSavepoint)*nSavepoint\n  );\n  if( !aNew ){\n    return SQLITE_NOMEM_BKPT;\n  }\n  memset(&aNew[nCurrent], 0, (nSavepoint-nCurrent) * sizeof(PagerSavepoint));\n  pPager->aSavepoint = aNew;\n\n  /* Populate the PagerSavepoint structures just allocated. */\n  for(ii=nCurrent; ii<nSavepoint; ii++){\n    aNew[ii].nOrig = pPager->dbSize;\n    if( isOpen(pPager->jfd) && pPager->journalOff>0 ){\n      aNew[ii].iOffset = pPager->journalOff;\n    }else{\n      aNew[ii].iOffset = JOURNAL_HDR_SZ(pPager);\n    }\n    aNew[ii].iSubRec = pPager->nSubRec;\n    aNew[ii].pInSavepoint = sqlite3BitvecCreate(pPager->dbSize);\n    if( !aNew[ii].pInSavepoint ){\n      return SQLITE_NOMEM_BKPT;\n    }\n    if( pagerUseWal(pPager) ){\n      sqlite3WalSavepoint(pPager->pWal, aNew[ii].aWalData);\n    }\n    pPager->nSavepoint = ii+1;\n  }\n  assert( pPager->nSavepoint==nSavepoint );\n  assertTruncateConstraint(pPager);\n  return rc;\n}\nSQLITE_PRIVATE int sqlite3PagerOpenSavepoint(Pager *pPager, int nSavepoint){\n  assert( pPager->eState>=PAGER_WRITER_LOCKED );\n  assert( assert_pager_state(pPager) );\n\n  if( nSavepoint>pPager->nSavepoint && pPager->useJournal ){\n    return pagerOpenSavepoint(pPager, nSavepoint);\n  }else{\n    return SQLITE_OK;\n  }\n}\n\n\n/*\n** This function is called to rollback or release (commit) a savepoint.\n** The savepoint to release or rollback need not be the most recently \n** created savepoint.\n**\n** Parameter op is always either SAVEPOINT_ROLLBACK or SAVEPOINT_RELEASE.\n** If it is SAVEPOINT_RELEASE, then release and destroy the savepoint with\n** index iSavepoint. If it is SAVEPOINT_ROLLBACK, then rollback all changes\n** that have occurred since the specified savepoint was created.\n**\n** The savepoint to rollback or release is identified by parameter \n** iSavepoint. A value of 0 means to operate on the outermost savepoint\n** (the first created). A value of (Pager.nSavepoint-1) means operate\n** on the most recently created savepoint. If iSavepoint is greater than\n** (Pager.nSavepoint-1), then this function is a no-op.\n**\n** If a negative value is passed to this function, then the current\n** transaction is rolled back. This is different to calling \n** sqlite3PagerRollback() because this function does not terminate\n** the transaction or unlock the database, it just restores the \n** contents of the database to its original state. \n**\n** In any case, all savepoints with an index greater than iSavepoint \n** are destroyed. If this is a release operation (op==SAVEPOINT_RELEASE),\n** then savepoint iSavepoint is also destroyed.\n**\n** This function may return SQLITE_NOMEM if a memory allocation fails,\n** or an IO error code if an IO error occurs while rolling back a \n** savepoint. If no errors occur, SQLITE_OK is returned.\n*/ \nSQLITE_PRIVATE int sqlite3PagerSavepoint(Pager *pPager, int op, int iSavepoint){\n  int rc = pPager->errCode;\n  \n#ifdef SQLITE_ENABLE_ZIPVFS\n  if( op==SAVEPOINT_RELEASE ) rc = SQLITE_OK;\n#endif\n\n  assert( op==SAVEPOINT_RELEASE || op==SAVEPOINT_ROLLBACK );\n  assert( iSavepoint>=0 || op==SAVEPOINT_ROLLBACK );\n\n  if( rc==SQLITE_OK && iSavepoint<pPager->nSavepoint ){\n    int ii;            /* Iterator variable */\n    int nNew;          /* Number of remaining savepoints after this op. */\n\n    /* Figure out how many savepoints will still be active after this\n    ** operation. Store this value in nNew. Then free resources associated \n    ** with any savepoints that are destroyed by this operation.\n    */\n    nNew = iSavepoint + (( op==SAVEPOINT_RELEASE ) ? 0 : 1);\n    for(ii=nNew; ii<pPager->nSavepoint; ii++){\n      sqlite3BitvecDestroy(pPager->aSavepoint[ii].pInSavepoint);\n    }\n    pPager->nSavepoint = nNew;\n\n    /* If this is a release of the outermost savepoint, truncate \n    ** the sub-journal to zero bytes in size. */\n    if( op==SAVEPOINT_RELEASE ){\n      if( nNew==0 && isOpen(pPager->sjfd) ){\n        /* Only truncate if it is an in-memory sub-journal. */\n        if( sqlite3JournalIsInMemory(pPager->sjfd) ){\n          rc = sqlite3OsTruncate(pPager->sjfd, 0);\n          assert( rc==SQLITE_OK );\n        }\n        pPager->nSubRec = 0;\n      }\n    }\n    /* Else this is a rollback operation, playback the specified savepoint.\n    ** If this is a temp-file, it is possible that the journal file has\n    ** not yet been opened. In this case there have been no changes to\n    ** the database file, so the playback operation can be skipped.\n    */\n    else if( pagerUseWal(pPager) || isOpen(pPager->jfd) ){\n      PagerSavepoint *pSavepoint = (nNew==0)?0:&pPager->aSavepoint[nNew-1];\n      rc = pagerPlaybackSavepoint(pPager, pSavepoint);\n      assert(rc!=SQLITE_DONE);\n    }\n    \n#ifdef SQLITE_ENABLE_ZIPVFS\n    /* If the cache has been modified but the savepoint cannot be rolled \n    ** back journal_mode=off, put the pager in the error state. This way,\n    ** if the VFS used by this pager includes ZipVFS, the entire transaction\n    ** can be rolled back at the ZipVFS level.  */\n    else if( \n        pPager->journalMode==PAGER_JOURNALMODE_OFF \n     && pPager->eState>=PAGER_WRITER_CACHEMOD\n    ){\n      pPager->errCode = SQLITE_ABORT;\n      pPager->eState = PAGER_ERROR;\n      setGetterMethod(pPager);\n    }\n#endif\n  }\n\n  return rc;\n}\n\n/*\n** Return the full pathname of the database file.\n**\n** Except, if the pager is in-memory only, then return an empty string if\n** nullIfMemDb is true.  This routine is called with nullIfMemDb==1 when\n** used to report the filename to the user, for compatibility with legacy\n** behavior.  But when the Btree needs to know the filename for matching to\n** shared cache, it uses nullIfMemDb==0 so that in-memory databases can\n** participate in shared-cache.\n*/\nSQLITE_PRIVATE const char *sqlite3PagerFilename(Pager *pPager, int nullIfMemDb){\n  return (nullIfMemDb && pPager->memDb) ? \"\" : pPager->zFilename;\n}\n\n/*\n** Return the VFS structure for the pager.\n*/\nSQLITE_PRIVATE sqlite3_vfs *sqlite3PagerVfs(Pager *pPager){\n  return pPager->pVfs;\n}\n\n/*\n** Return the file handle for the database file associated\n** with the pager.  This might return NULL if the file has\n** not yet been opened.\n*/\nSQLITE_PRIVATE sqlite3_file *sqlite3PagerFile(Pager *pPager){\n  return pPager->fd;\n}\n\n/*\n** Return the file handle for the journal file (if it exists).\n** This will be either the rollback journal or the WAL file.\n*/\nSQLITE_PRIVATE sqlite3_file *sqlite3PagerJrnlFile(Pager *pPager){\n#if SQLITE_OMIT_WAL\n  return pPager->jfd;\n#else\n  return pPager->pWal ? sqlite3WalFile(pPager->pWal) : pPager->jfd;\n#endif\n}\n\n/*\n** Return the full pathname of the journal file.\n*/\nSQLITE_PRIVATE const char *sqlite3PagerJournalname(Pager *pPager){\n  return pPager->zJournal;\n}\n\n#ifdef SQLITE_HAS_CODEC\n/*\n** Set or retrieve the codec for this pager\n*/\nSQLITE_PRIVATE void sqlite3PagerSetCodec(\n  Pager *pPager,\n  void *(*xCodec)(void*,void*,Pgno,int),\n  void (*xCodecSizeChng)(void*,int,int),\n  void (*xCodecFree)(void*),\n  void *pCodec\n){\n  if( pPager->xCodecFree ) pPager->xCodecFree(pPager->pCodec);\n  pPager->xCodec = pPager->memDb ? 0 : xCodec;\n  pPager->xCodecSizeChng = xCodecSizeChng;\n  pPager->xCodecFree = xCodecFree;\n  pPager->pCodec = pCodec;\n  setGetterMethod(pPager);\n  pagerReportSize(pPager);\n}\nSQLITE_PRIVATE void *sqlite3PagerGetCodec(Pager *pPager){\n  return pPager->pCodec;\n}\n\n/*\n** This function is called by the wal module when writing page content\n** into the log file.\n**\n** This function returns a pointer to a buffer containing the encrypted\n** page content. If a malloc fails, this function may return NULL.\n*/\nSQLITE_PRIVATE void *sqlite3PagerCodec(PgHdr *pPg){\n  void *aData = 0;\n  CODEC2(pPg->pPager, pPg->pData, pPg->pgno, 6, return 0, aData);\n  return aData;\n}\n\n/*\n** Return the current pager state\n*/\nSQLITE_PRIVATE int sqlite3PagerState(Pager *pPager){\n  return pPager->eState;\n}\n#endif /* SQLITE_HAS_CODEC */\n\n#ifndef SQLITE_OMIT_AUTOVACUUM\n/*\n** Move the page pPg to location pgno in the file.\n**\n** There must be no references to the page previously located at\n** pgno (which we call pPgOld) though that page is allowed to be\n** in cache.  If the page previously located at pgno is not already\n** in the rollback journal, it is not put there by by this routine.\n**\n** References to the page pPg remain valid. Updating any\n** meta-data associated with pPg (i.e. data stored in the nExtra bytes\n** allocated along with the page) is the responsibility of the caller.\n**\n** A transaction must be active when this routine is called. It used to be\n** required that a statement transaction was not active, but this restriction\n** has been removed (CREATE INDEX needs to move a page when a statement\n** transaction is active).\n**\n** If the fourth argument, isCommit, is non-zero, then this page is being\n** moved as part of a database reorganization just before the transaction \n** is being committed. In this case, it is guaranteed that the database page \n** pPg refers to will not be written to again within this transaction.\n**\n** This function may return SQLITE_NOMEM or an IO error code if an error\n** occurs. Otherwise, it returns SQLITE_OK.\n*/\nSQLITE_PRIVATE int sqlite3PagerMovepage(Pager *pPager, DbPage *pPg, Pgno pgno, int isCommit){\n  PgHdr *pPgOld;               /* The page being overwritten. */\n  Pgno needSyncPgno = 0;       /* Old value of pPg->pgno, if sync is required */\n  int rc;                      /* Return code */\n  Pgno origPgno;               /* The original page number */\n\n  assert( pPg->nRef>0 );\n  assert( pPager->eState==PAGER_WRITER_CACHEMOD\n       || pPager->eState==PAGER_WRITER_DBMOD\n  );\n  assert( assert_pager_state(pPager) );\n\n  /* In order to be able to rollback, an in-memory database must journal\n  ** the page we are moving from.\n  */\n  assert( pPager->tempFile || !MEMDB );\n  if( pPager->tempFile ){\n    rc = sqlite3PagerWrite(pPg);\n    if( rc ) return rc;\n  }\n\n  /* If the page being moved is dirty and has not been saved by the latest\n  ** savepoint, then save the current contents of the page into the \n  ** sub-journal now. This is required to handle the following scenario:\n  **\n  **   BEGIN;\n  **     <journal page X, then modify it in memory>\n  **     SAVEPOINT one;\n  **       <Move page X to location Y>\n  **     ROLLBACK TO one;\n  **\n  ** If page X were not written to the sub-journal here, it would not\n  ** be possible to restore its contents when the \"ROLLBACK TO one\"\n  ** statement were is processed.\n  **\n  ** subjournalPage() may need to allocate space to store pPg->pgno into\n  ** one or more savepoint bitvecs. This is the reason this function\n  ** may return SQLITE_NOMEM.\n  */\n  if( (pPg->flags & PGHDR_DIRTY)!=0\n   && SQLITE_OK!=(rc = subjournalPageIfRequired(pPg))\n  ){\n    return rc;\n  }\n\n  PAGERTRACE((\"MOVE %d page %d (needSync=%d) moves to %d\\n\", \n      PAGERID(pPager), pPg->pgno, (pPg->flags&PGHDR_NEED_SYNC)?1:0, pgno));\n  IOTRACE((\"MOVE %p %d %d\\n\", pPager, pPg->pgno, pgno))\n\n  /* If the journal needs to be sync()ed before page pPg->pgno can\n  ** be written to, store pPg->pgno in local variable needSyncPgno.\n  **\n  ** If the isCommit flag is set, there is no need to remember that\n  ** the journal needs to be sync()ed before database page pPg->pgno \n  ** can be written to. The caller has already promised not to write to it.\n  */\n  if( (pPg->flags&PGHDR_NEED_SYNC) && !isCommit ){\n    needSyncPgno = pPg->pgno;\n    assert( pPager->journalMode==PAGER_JOURNALMODE_OFF ||\n            pageInJournal(pPager, pPg) || pPg->pgno>pPager->dbOrigSize );\n    assert( pPg->flags&PGHDR_DIRTY );\n  }\n\n  /* If the cache contains a page with page-number pgno, remove it\n  ** from its hash chain. Also, if the PGHDR_NEED_SYNC flag was set for \n  ** page pgno before the 'move' operation, it needs to be retained \n  ** for the page moved there.\n  */\n  pPg->flags &= ~PGHDR_NEED_SYNC;\n  pPgOld = sqlite3PagerLookup(pPager, pgno);\n  assert( !pPgOld || pPgOld->nRef==1 );\n  if( pPgOld ){\n    pPg->flags |= (pPgOld->flags&PGHDR_NEED_SYNC);\n    if( pPager->tempFile ){\n      /* Do not discard pages from an in-memory database since we might\n      ** need to rollback later.  Just move the page out of the way. */\n      sqlite3PcacheMove(pPgOld, pPager->dbSize+1);\n    }else{\n      sqlite3PcacheDrop(pPgOld);\n    }\n  }\n\n  origPgno = pPg->pgno;\n  sqlite3PcacheMove(pPg, pgno);\n  sqlite3PcacheMakeDirty(pPg);\n\n  /* For an in-memory database, make sure the original page continues\n  ** to exist, in case the transaction needs to roll back.  Use pPgOld\n  ** as the original page since it has already been allocated.\n  */\n  if( pPager->tempFile && pPgOld ){\n    sqlite3PcacheMove(pPgOld, origPgno);\n    sqlite3PagerUnrefNotNull(pPgOld);\n  }\n\n  if( needSyncPgno ){\n    /* If needSyncPgno is non-zero, then the journal file needs to be \n    ** sync()ed before any data is written to database file page needSyncPgno.\n    ** Currently, no such page exists in the page-cache and the \n    ** \"is journaled\" bitvec flag has been set. This needs to be remedied by\n    ** loading the page into the pager-cache and setting the PGHDR_NEED_SYNC\n    ** flag.\n    **\n    ** If the attempt to load the page into the page-cache fails, (due\n    ** to a malloc() or IO failure), clear the bit in the pInJournal[]\n    ** array. Otherwise, if the page is loaded and written again in\n    ** this transaction, it may be written to the database file before\n    ** it is synced into the journal file. This way, it may end up in\n    ** the journal file twice, but that is not a problem.\n    */\n    PgHdr *pPgHdr;\n    rc = sqlite3PagerGet(pPager, needSyncPgno, &pPgHdr, 0);\n    if( rc!=SQLITE_OK ){\n      if( needSyncPgno<=pPager->dbOrigSize ){\n        assert( pPager->pTmpSpace!=0 );\n        sqlite3BitvecClear(pPager->pInJournal, needSyncPgno, pPager->pTmpSpace);\n      }\n      return rc;\n    }\n    pPgHdr->flags |= PGHDR_NEED_SYNC;\n    sqlite3PcacheMakeDirty(pPgHdr);\n    sqlite3PagerUnrefNotNull(pPgHdr);\n  }\n\n  return SQLITE_OK;\n}\n#endif\n\n/*\n** The page handle passed as the first argument refers to a dirty page \n** with a page number other than iNew. This function changes the page's \n** page number to iNew and sets the value of the PgHdr.flags field to \n** the value passed as the third parameter.\n*/\nSQLITE_PRIVATE void sqlite3PagerRekey(DbPage *pPg, Pgno iNew, u16 flags){\n  assert( pPg->pgno!=iNew );\n  pPg->flags = flags;\n  sqlite3PcacheMove(pPg, iNew);\n}\n\n/*\n** Return a pointer to the data for the specified page.\n*/\nSQLITE_PRIVATE void *sqlite3PagerGetData(DbPage *pPg){\n  assert( pPg->nRef>0 || pPg->pPager->memDb );\n  return pPg->pData;\n}\n\n/*\n** Return a pointer to the Pager.nExtra bytes of \"extra\" space \n** allocated along with the specified page.\n*/\nSQLITE_PRIVATE void *sqlite3PagerGetExtra(DbPage *pPg){\n  return pPg->pExtra;\n}\n\n/*\n** Get/set the locking-mode for this pager. Parameter eMode must be one\n** of PAGER_LOCKINGMODE_QUERY, PAGER_LOCKINGMODE_NORMAL or \n** PAGER_LOCKINGMODE_EXCLUSIVE. If the parameter is not _QUERY, then\n** the locking-mode is set to the value specified.\n**\n** The returned value is either PAGER_LOCKINGMODE_NORMAL or\n** PAGER_LOCKINGMODE_EXCLUSIVE, indicating the current (possibly updated)\n** locking-mode.\n*/\nSQLITE_PRIVATE int sqlite3PagerLockingMode(Pager *pPager, int eMode){\n  assert( eMode==PAGER_LOCKINGMODE_QUERY\n            || eMode==PAGER_LOCKINGMODE_NORMAL\n            || eMode==PAGER_LOCKINGMODE_EXCLUSIVE );\n  assert( PAGER_LOCKINGMODE_QUERY<0 );\n  assert( PAGER_LOCKINGMODE_NORMAL>=0 && PAGER_LOCKINGMODE_EXCLUSIVE>=0 );\n  assert( pPager->exclusiveMode || 0==sqlite3WalHeapMemory(pPager->pWal) );\n  if( eMode>=0 && !pPager->tempFile && !sqlite3WalHeapMemory(pPager->pWal) ){\n    pPager->exclusiveMode = (u8)eMode;\n  }\n  return (int)pPager->exclusiveMode;\n}\n\n/*\n** Set the journal-mode for this pager. Parameter eMode must be one of:\n**\n**    PAGER_JOURNALMODE_DELETE\n**    PAGER_JOURNALMODE_TRUNCATE\n**    PAGER_JOURNALMODE_PERSIST\n**    PAGER_JOURNALMODE_OFF\n**    PAGER_JOURNALMODE_MEMORY\n**    PAGER_JOURNALMODE_WAL\n**\n** The journalmode is set to the value specified if the change is allowed.\n** The change may be disallowed for the following reasons:\n**\n**   *  An in-memory database can only have its journal_mode set to _OFF\n**      or _MEMORY.\n**\n**   *  Temporary databases cannot have _WAL journalmode.\n**\n** The returned indicate the current (possibly updated) journal-mode.\n*/\nSQLITE_PRIVATE int sqlite3PagerSetJournalMode(Pager *pPager, int eMode){\n  u8 eOld = pPager->journalMode;    /* Prior journalmode */\n\n#ifdef SQLITE_DEBUG\n  /* The print_pager_state() routine is intended to be used by the debugger\n  ** only.  We invoke it once here to suppress a compiler warning. */\n  print_pager_state(pPager);\n#endif\n\n\n  /* The eMode parameter is always valid */\n  assert(      eMode==PAGER_JOURNALMODE_DELETE\n            || eMode==PAGER_JOURNALMODE_TRUNCATE\n            || eMode==PAGER_JOURNALMODE_PERSIST\n            || eMode==PAGER_JOURNALMODE_OFF \n            || eMode==PAGER_JOURNALMODE_WAL \n            || eMode==PAGER_JOURNALMODE_MEMORY );\n\n  /* This routine is only called from the OP_JournalMode opcode, and\n  ** the logic there will never allow a temporary file to be changed\n  ** to WAL mode.\n  */\n  assert( pPager->tempFile==0 || eMode!=PAGER_JOURNALMODE_WAL );\n\n  /* Do allow the journalmode of an in-memory database to be set to\n  ** anything other than MEMORY or OFF\n  */\n  if( MEMDB ){\n    assert( eOld==PAGER_JOURNALMODE_MEMORY || eOld==PAGER_JOURNALMODE_OFF );\n    if( eMode!=PAGER_JOURNALMODE_MEMORY && eMode!=PAGER_JOURNALMODE_OFF ){\n      eMode = eOld;\n    }\n  }\n\n  if( eMode!=eOld ){\n\n    /* Change the journal mode. */\n    assert( pPager->eState!=PAGER_ERROR );\n    pPager->journalMode = (u8)eMode;\n\n    /* When transistioning from TRUNCATE or PERSIST to any other journal\n    ** mode except WAL, unless the pager is in locking_mode=exclusive mode,\n    ** delete the journal file.\n    */\n    assert( (PAGER_JOURNALMODE_TRUNCATE & 5)==1 );\n    assert( (PAGER_JOURNALMODE_PERSIST & 5)==1 );\n    assert( (PAGER_JOURNALMODE_DELETE & 5)==0 );\n    assert( (PAGER_JOURNALMODE_MEMORY & 5)==4 );\n    assert( (PAGER_JOURNALMODE_OFF & 5)==0 );\n    assert( (PAGER_JOURNALMODE_WAL & 5)==5 );\n\n    assert( isOpen(pPager->fd) || pPager->exclusiveMode );\n    if( !pPager->exclusiveMode && (eOld & 5)==1 && (eMode & 1)==0 ){\n\n      /* In this case we would like to delete the journal file. If it is\n      ** not possible, then that is not a problem. Deleting the journal file\n      ** here is an optimization only.\n      **\n      ** Before deleting the journal file, obtain a RESERVED lock on the\n      ** database file. This ensures that the journal file is not deleted\n      ** while it is in use by some other client.\n      */\n      sqlite3OsClose(pPager->jfd);\n      if( pPager->eLock>=RESERVED_LOCK ){\n        sqlite3OsDelete(pPager->pVfs, pPager->zJournal, 0);\n      }else{\n        int rc = SQLITE_OK;\n        int state = pPager->eState;\n        assert( state==PAGER_OPEN || state==PAGER_READER );\n        if( state==PAGER_OPEN ){\n          rc = sqlite3PagerSharedLock(pPager);\n        }\n        if( pPager->eState==PAGER_READER ){\n          assert( rc==SQLITE_OK );\n          rc = pagerLockDb(pPager, RESERVED_LOCK);\n        }\n        if( rc==SQLITE_OK ){\n          sqlite3OsDelete(pPager->pVfs, pPager->zJournal, 0);\n        }\n        if( rc==SQLITE_OK && state==PAGER_READER ){\n          pagerUnlockDb(pPager, SHARED_LOCK);\n        }else if( state==PAGER_OPEN ){\n          pager_unlock(pPager);\n        }\n        assert( state==pPager->eState );\n      }\n    }else if( eMode==PAGER_JOURNALMODE_OFF ){\n      sqlite3OsClose(pPager->jfd);\n    }\n  }\n\n  /* Return the new journal mode */\n  return (int)pPager->journalMode;\n}\n\n/*\n** Return the current journal mode.\n*/\nSQLITE_PRIVATE int sqlite3PagerGetJournalMode(Pager *pPager){\n  return (int)pPager->journalMode;\n}\n\n/*\n** Return TRUE if the pager is in a state where it is OK to change the\n** journalmode.  Journalmode changes can only happen when the database\n** is unmodified.\n*/\nSQLITE_PRIVATE int sqlite3PagerOkToChangeJournalMode(Pager *pPager){\n  assert( assert_pager_state(pPager) );\n  if( pPager->eState>=PAGER_WRITER_CACHEMOD ) return 0;\n  if( NEVER(isOpen(pPager->jfd) && pPager->journalOff>0) ) return 0;\n  return 1;\n}\n\n/*\n** Get/set the size-limit used for persistent journal files.\n**\n** Setting the size limit to -1 means no limit is enforced.\n** An attempt to set a limit smaller than -1 is a no-op.\n*/\nSQLITE_PRIVATE i64 sqlite3PagerJournalSizeLimit(Pager *pPager, i64 iLimit){\n  if( iLimit>=-1 ){\n    pPager->journalSizeLimit = iLimit;\n    sqlite3WalLimit(pPager->pWal, iLimit);\n  }\n  return pPager->journalSizeLimit;\n}\n\n/*\n** Return a pointer to the pPager->pBackup variable. The backup module\n** in backup.c maintains the content of this variable. This module\n** uses it opaquely as an argument to sqlite3BackupRestart() and\n** sqlite3BackupUpdate() only.\n*/\nSQLITE_PRIVATE sqlite3_backup **sqlite3PagerBackupPtr(Pager *pPager){\n  return &pPager->pBackup;\n}\n\n#ifndef SQLITE_OMIT_VACUUM\n/*\n** Unless this is an in-memory or temporary database, clear the pager cache.\n*/\nSQLITE_PRIVATE void sqlite3PagerClearCache(Pager *pPager){\n  assert( MEMDB==0 || pPager->tempFile );\n  if( pPager->tempFile==0 ) pager_reset(pPager);\n}\n#endif\n\n\n#ifndef SQLITE_OMIT_WAL\n/*\n** This function is called when the user invokes \"PRAGMA wal_checkpoint\",\n** \"PRAGMA wal_blocking_checkpoint\" or calls the sqlite3_wal_checkpoint()\n** or wal_blocking_checkpoint() API functions.\n**\n** Parameter eMode is one of SQLITE_CHECKPOINT_PASSIVE, FULL or RESTART.\n*/\nSQLITE_PRIVATE int sqlite3PagerCheckpoint(\n  Pager *pPager,                  /* Checkpoint on this pager */\n  sqlite3 *db,                    /* Db handle used to check for interrupts */\n  int eMode,                      /* Type of checkpoint */\n  int *pnLog,                     /* OUT: Final number of frames in log */\n  int *pnCkpt                     /* OUT: Final number of checkpointed frames */\n){\n  int rc = SQLITE_OK;\n  if( pPager->pWal ){\n    rc = sqlite3WalCheckpoint(pPager->pWal, db, eMode,\n        (eMode==SQLITE_CHECKPOINT_PASSIVE ? 0 : pPager->xBusyHandler),\n        pPager->pBusyHandlerArg,\n        pPager->walSyncFlags, pPager->pageSize, (u8 *)pPager->pTmpSpace,\n        pnLog, pnCkpt\n    );\n  }\n  return rc;\n}\n\nSQLITE_PRIVATE int sqlite3PagerWalCallback(Pager *pPager){\n  return sqlite3WalCallback(pPager->pWal);\n}\n\n/*\n** Return true if the underlying VFS for the given pager supports the\n** primitives necessary for write-ahead logging.\n*/\nSQLITE_PRIVATE int sqlite3PagerWalSupported(Pager *pPager){\n  const sqlite3_io_methods *pMethods = pPager->fd->pMethods;\n  if( pPager->noLock ) return 0;\n  return pPager->exclusiveMode || (pMethods->iVersion>=2 && pMethods->xShmMap);\n}\n\n/*\n** Attempt to take an exclusive lock on the database file. If a PENDING lock\n** is obtained instead, immediately release it.\n*/\nstatic int pagerExclusiveLock(Pager *pPager){\n  int rc;                         /* Return code */\n\n  assert( pPager->eLock==SHARED_LOCK || pPager->eLock==EXCLUSIVE_LOCK );\n  rc = pagerLockDb(pPager, EXCLUSIVE_LOCK);\n  if( rc!=SQLITE_OK ){\n    /* If the attempt to grab the exclusive lock failed, release the \n    ** pending lock that may have been obtained instead.  */\n    pagerUnlockDb(pPager, SHARED_LOCK);\n  }\n\n  return rc;\n}\n\n/*\n** Call sqlite3WalOpen() to open the WAL handle. If the pager is in \n** exclusive-locking mode when this function is called, take an EXCLUSIVE\n** lock on the database file and use heap-memory to store the wal-index\n** in. Otherwise, use the normal shared-memory.\n*/\nstatic int pagerOpenWal(Pager *pPager){\n  int rc = SQLITE_OK;\n\n  assert( pPager->pWal==0 && pPager->tempFile==0 );\n  assert( pPager->eLock==SHARED_LOCK || pPager->eLock==EXCLUSIVE_LOCK );\n\n  /* If the pager is already in exclusive-mode, the WAL module will use \n  ** heap-memory for the wal-index instead of the VFS shared-memory \n  ** implementation. Take the exclusive lock now, before opening the WAL\n  ** file, to make sure this is safe.\n  */\n  if( pPager->exclusiveMode ){\n    rc = pagerExclusiveLock(pPager);\n  }\n\n  /* Open the connection to the log file. If this operation fails, \n  ** (e.g. due to malloc() failure), return an error code.\n  */\n  if( rc==SQLITE_OK ){\n    rc = sqlite3WalOpen(pPager->pVfs,\n        pPager->fd, pPager->zWal, pPager->exclusiveMode,\n        pPager->journalSizeLimit, &pPager->pWal\n    );\n  }\n  pagerFixMaplimit(pPager);\n\n  return rc;\n}\n\n\n/*\n** The caller must be holding a SHARED lock on the database file to call\n** this function.\n**\n** If the pager passed as the first argument is open on a real database\n** file (not a temp file or an in-memory database), and the WAL file\n** is not already open, make an attempt to open it now. If successful,\n** return SQLITE_OK. If an error occurs or the VFS used by the pager does \n** not support the xShmXXX() methods, return an error code. *pbOpen is\n** not modified in either case.\n**\n** If the pager is open on a temp-file (or in-memory database), or if\n** the WAL file is already open, set *pbOpen to 1 and return SQLITE_OK\n** without doing anything.\n*/\nSQLITE_PRIVATE int sqlite3PagerOpenWal(\n  Pager *pPager,                  /* Pager object */\n  int *pbOpen                     /* OUT: Set to true if call is a no-op */\n){\n  int rc = SQLITE_OK;             /* Return code */\n\n  assert( assert_pager_state(pPager) );\n  assert( pPager->eState==PAGER_OPEN   || pbOpen );\n  assert( pPager->eState==PAGER_READER || !pbOpen );\n  assert( pbOpen==0 || *pbOpen==0 );\n  assert( pbOpen!=0 || (!pPager->tempFile && !pPager->pWal) );\n\n  if( !pPager->tempFile && !pPager->pWal ){\n    if( !sqlite3PagerWalSupported(pPager) ) return SQLITE_CANTOPEN;\n\n    /* Close any rollback journal previously open */\n    sqlite3OsClose(pPager->jfd);\n\n    rc = pagerOpenWal(pPager);\n    if( rc==SQLITE_OK ){\n      pPager->journalMode = PAGER_JOURNALMODE_WAL;\n      pPager->eState = PAGER_OPEN;\n    }\n  }else{\n    *pbOpen = 1;\n  }\n\n  return rc;\n}\n\n/*\n** This function is called to close the connection to the log file prior\n** to switching from WAL to rollback mode.\n**\n** Before closing the log file, this function attempts to take an \n** EXCLUSIVE lock on the database file. If this cannot be obtained, an\n** error (SQLITE_BUSY) is returned and the log connection is not closed.\n** If successful, the EXCLUSIVE lock is not released before returning.\n*/\nSQLITE_PRIVATE int sqlite3PagerCloseWal(Pager *pPager, sqlite3 *db){\n  int rc = SQLITE_OK;\n\n  assert( pPager->journalMode==PAGER_JOURNALMODE_WAL );\n\n  /* If the log file is not already open, but does exist in the file-system,\n  ** it may need to be checkpointed before the connection can switch to\n  ** rollback mode. Open it now so this can happen.\n  */\n  if( !pPager->pWal ){\n    int logexists = 0;\n    rc = pagerLockDb(pPager, SHARED_LOCK);\n    if( rc==SQLITE_OK ){\n      rc = sqlite3OsAccess(\n          pPager->pVfs, pPager->zWal, SQLITE_ACCESS_EXISTS, &logexists\n      );\n    }\n    if( rc==SQLITE_OK && logexists ){\n      rc = pagerOpenWal(pPager);\n    }\n  }\n    \n  /* Checkpoint and close the log. Because an EXCLUSIVE lock is held on\n  ** the database file, the log and log-summary files will be deleted.\n  */\n  if( rc==SQLITE_OK && pPager->pWal ){\n    rc = pagerExclusiveLock(pPager);\n    if( rc==SQLITE_OK ){\n      rc = sqlite3WalClose(pPager->pWal, db, pPager->walSyncFlags,\n                           pPager->pageSize, (u8*)pPager->pTmpSpace);\n      pPager->pWal = 0;\n      pagerFixMaplimit(pPager);\n      if( rc && !pPager->exclusiveMode ) pagerUnlockDb(pPager, SHARED_LOCK);\n    }\n  }\n  return rc;\n}\n\n#ifdef SQLITE_ENABLE_SNAPSHOT\n/*\n** If this is a WAL database, obtain a snapshot handle for the snapshot\n** currently open. Otherwise, return an error.\n*/\nSQLITE_PRIVATE int sqlite3PagerSnapshotGet(Pager *pPager, sqlite3_snapshot **ppSnapshot){\n  int rc = SQLITE_ERROR;\n  if( pPager->pWal ){\n    rc = sqlite3WalSnapshotGet(pPager->pWal, ppSnapshot);\n  }\n  return rc;\n}\n\n/*\n** If this is a WAL database, store a pointer to pSnapshot. Next time a\n** read transaction is opened, attempt to read from the snapshot it \n** identifies. If this is not a WAL database, return an error.\n*/\nSQLITE_PRIVATE int sqlite3PagerSnapshotOpen(Pager *pPager, sqlite3_snapshot *pSnapshot){\n  int rc = SQLITE_OK;\n  if( pPager->pWal ){\n    sqlite3WalSnapshotOpen(pPager->pWal, pSnapshot);\n  }else{\n    rc = SQLITE_ERROR;\n  }\n  return rc;\n}\n\n/*\n** If this is a WAL database, call sqlite3WalSnapshotRecover(). If this \n** is not a WAL database, return an error.\n*/\nSQLITE_PRIVATE int sqlite3PagerSnapshotRecover(Pager *pPager){\n  int rc;\n  if( pPager->pWal ){\n    rc = sqlite3WalSnapshotRecover(pPager->pWal);\n  }else{\n    rc = SQLITE_ERROR;\n  }\n  return rc;\n}\n#endif /* SQLITE_ENABLE_SNAPSHOT */\n#endif /* !SQLITE_OMIT_WAL */\n\n#ifdef SQLITE_ENABLE_ZIPVFS\n/*\n** A read-lock must be held on the pager when this function is called. If\n** the pager is in WAL mode and the WAL file currently contains one or more\n** frames, return the size in bytes of the page images stored within the\n** WAL frames. Otherwise, if this is not a WAL database or the WAL file\n** is empty, return 0.\n*/\nSQLITE_PRIVATE int sqlite3PagerWalFramesize(Pager *pPager){\n  assert( pPager->eState>=PAGER_READER );\n  return sqlite3WalFramesize(pPager->pWal);\n}\n#endif\n\n#endif /* SQLITE_OMIT_DISKIO */\n\n/************** End of pager.c ***********************************************/\n/************** Begin file wal.c *********************************************/\n/*\n** 2010 February 1\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n*************************************************************************\n**\n** This file contains the implementation of a write-ahead log (WAL) used in \n** \"journal_mode=WAL\" mode.\n**\n** WRITE-AHEAD LOG (WAL) FILE FORMAT\n**\n** A WAL file consists of a header followed by zero or more \"frames\".\n** Each frame records the revised content of a single page from the\n** database file.  All changes to the database are recorded by writing\n** frames into the WAL.  Transactions commit when a frame is written that\n** contains a commit marker.  A single WAL can and usually does record \n** multiple transactions.  Periodically, the content of the WAL is\n** transferred back into the database file in an operation called a\n** \"checkpoint\".\n**\n** A single WAL file can be used multiple times.  In other words, the\n** WAL can fill up with frames and then be checkpointed and then new\n** frames can overwrite the old ones.  A WAL always grows from beginning\n** toward the end.  Checksums and counters attached to each frame are\n** used to determine which frames within the WAL are valid and which\n** are leftovers from prior checkpoints.\n**\n** The WAL header is 32 bytes in size and consists of the following eight\n** big-endian 32-bit unsigned integer values:\n**\n**     0: Magic number.  0x377f0682 or 0x377f0683\n**     4: File format version.  Currently 3007000\n**     8: Database page size.  Example: 1024\n**    12: Checkpoint sequence number\n**    16: Salt-1, random integer incremented with each checkpoint\n**    20: Salt-2, a different random integer changing with each ckpt\n**    24: Checksum-1 (first part of checksum for first 24 bytes of header).\n**    28: Checksum-2 (second part of checksum for first 24 bytes of header).\n**\n** Immediately following the wal-header are zero or more frames. Each\n** frame consists of a 24-byte frame-header followed by a <page-size> bytes\n** of page data. The frame-header is six big-endian 32-bit unsigned \n** integer values, as follows:\n**\n**     0: Page number.\n**     4: For commit records, the size of the database image in pages \n**        after the commit. For all other records, zero.\n**     8: Salt-1 (copied from the header)\n**    12: Salt-2 (copied from the header)\n**    16: Checksum-1.\n**    20: Checksum-2.\n**\n** A frame is considered valid if and only if the following conditions are\n** true:\n**\n**    (1) The salt-1 and salt-2 values in the frame-header match\n**        salt values in the wal-header\n**\n**    (2) The checksum values in the final 8 bytes of the frame-header\n**        exactly match the checksum computed consecutively on the\n**        WAL header and the first 8 bytes and the content of all frames\n**        up to and including the current frame.\n**\n** The checksum is computed using 32-bit big-endian integers if the\n** magic number in the first 4 bytes of the WAL is 0x377f0683 and it\n** is computed using little-endian if the magic number is 0x377f0682.\n** The checksum values are always stored in the frame header in a\n** big-endian format regardless of which byte order is used to compute\n** the checksum.  The checksum is computed by interpreting the input as\n** an even number of unsigned 32-bit integers: x[0] through x[N].  The\n** algorithm used for the checksum is as follows:\n** \n**   for i from 0 to n-1 step 2:\n**     s0 += x[i] + s1;\n**     s1 += x[i+1] + s0;\n**   endfor\n**\n** Note that s0 and s1 are both weighted checksums using fibonacci weights\n** in reverse order (the largest fibonacci weight occurs on the first element\n** of the sequence being summed.)  The s1 value spans all 32-bit \n** terms of the sequence whereas s0 omits the final term.\n**\n** On a checkpoint, the WAL is first VFS.xSync-ed, then valid content of the\n** WAL is transferred into the database, then the database is VFS.xSync-ed.\n** The VFS.xSync operations serve as write barriers - all writes launched\n** before the xSync must complete before any write that launches after the\n** xSync begins.\n**\n** After each checkpoint, the salt-1 value is incremented and the salt-2\n** value is randomized.  This prevents old and new frames in the WAL from\n** being considered valid at the same time and being checkpointing together\n** following a crash.\n**\n** READER ALGORITHM\n**\n** To read a page from the database (call it page number P), a reader\n** first checks the WAL to see if it contains page P.  If so, then the\n** last valid instance of page P that is a followed by a commit frame\n** or is a commit frame itself becomes the value read.  If the WAL\n** contains no copies of page P that are valid and which are a commit\n** frame or are followed by a commit frame, then page P is read from\n** the database file.\n**\n** To start a read transaction, the reader records the index of the last\n** valid frame in the WAL.  The reader uses this recorded \"mxFrame\" value\n** for all subsequent read operations.  New transactions can be appended\n** to the WAL, but as long as the reader uses its original mxFrame value\n** and ignores the newly appended content, it will see a consistent snapshot\n** of the database from a single point in time.  This technique allows\n** multiple concurrent readers to view different versions of the database\n** content simultaneously.\n**\n** The reader algorithm in the previous paragraphs works correctly, but \n** because frames for page P can appear anywhere within the WAL, the\n** reader has to scan the entire WAL looking for page P frames.  If the\n** WAL is large (multiple megabytes is typical) that scan can be slow,\n** and read performance suffers.  To overcome this problem, a separate\n** data structure called the wal-index is maintained to expedite the\n** search for frames of a particular page.\n** \n** WAL-INDEX FORMAT\n**\n** Conceptually, the wal-index is shared memory, though VFS implementations\n** might choose to implement the wal-index using a mmapped file.  Because\n** the wal-index is shared memory, SQLite does not support journal_mode=WAL \n** on a network filesystem.  All users of the database must be able to\n** share memory.\n**\n** In the default unix and windows implementation, the wal-index is a mmapped\n** file whose name is the database name with a \"-shm\" suffix added.  For that\n** reason, the wal-index is sometimes called the \"shm\" file.\n**\n** The wal-index is transient.  After a crash, the wal-index can (and should\n** be) reconstructed from the original WAL file.  In fact, the VFS is required\n** to either truncate or zero the header of the wal-index when the last\n** connection to it closes.  Because the wal-index is transient, it can\n** use an architecture-specific format; it does not have to be cross-platform.\n** Hence, unlike the database and WAL file formats which store all values\n** as big endian, the wal-index can store multi-byte values in the native\n** byte order of the host computer.\n**\n** The purpose of the wal-index is to answer this question quickly:  Given\n** a page number P and a maximum frame index M, return the index of the \n** last frame in the wal before frame M for page P in the WAL, or return\n** NULL if there are no frames for page P in the WAL prior to M.\n**\n** The wal-index consists of a header region, followed by an one or\n** more index blocks.  \n**\n** The wal-index header contains the total number of frames within the WAL\n** in the mxFrame field.\n**\n** Each index block except for the first contains information on \n** HASHTABLE_NPAGE frames. The first index block contains information on\n** HASHTABLE_NPAGE_ONE frames. The values of HASHTABLE_NPAGE_ONE and \n** HASHTABLE_NPAGE are selected so that together the wal-index header and\n** first index block are the same size as all other index blocks in the\n** wal-index.\n**\n** Each index block contains two sections, a page-mapping that contains the\n** database page number associated with each wal frame, and a hash-table \n** that allows readers to query an index block for a specific page number.\n** The page-mapping is an array of HASHTABLE_NPAGE (or HASHTABLE_NPAGE_ONE\n** for the first index block) 32-bit page numbers. The first entry in the \n** first index-block contains the database page number corresponding to the\n** first frame in the WAL file. The first entry in the second index block\n** in the WAL file corresponds to the (HASHTABLE_NPAGE_ONE+1)th frame in\n** the log, and so on.\n**\n** The last index block in a wal-index usually contains less than the full\n** complement of HASHTABLE_NPAGE (or HASHTABLE_NPAGE_ONE) page-numbers,\n** depending on the contents of the WAL file. This does not change the\n** allocated size of the page-mapping array - the page-mapping array merely\n** contains unused entries.\n**\n** Even without using the hash table, the last frame for page P\n** can be found by scanning the page-mapping sections of each index block\n** starting with the last index block and moving toward the first, and\n** within each index block, starting at the end and moving toward the\n** beginning.  The first entry that equals P corresponds to the frame\n** holding the content for that page.\n**\n** The hash table consists of HASHTABLE_NSLOT 16-bit unsigned integers.\n** HASHTABLE_NSLOT = 2*HASHTABLE_NPAGE, and there is one entry in the\n** hash table for each page number in the mapping section, so the hash \n** table is never more than half full.  The expected number of collisions \n** prior to finding a match is 1.  Each entry of the hash table is an\n** 1-based index of an entry in the mapping section of the same\n** index block.   Let K be the 1-based index of the largest entry in\n** the mapping section.  (For index blocks other than the last, K will\n** always be exactly HASHTABLE_NPAGE (4096) and for the last index block\n** K will be (mxFrame%HASHTABLE_NPAGE).)  Unused slots of the hash table\n** contain a value of 0.\n**\n** To look for page P in the hash table, first compute a hash iKey on\n** P as follows:\n**\n**      iKey = (P * 383) % HASHTABLE_NSLOT\n**\n** Then start scanning entries of the hash table, starting with iKey\n** (wrapping around to the beginning when the end of the hash table is\n** reached) until an unused hash slot is found. Let the first unused slot\n** be at index iUnused.  (iUnused might be less than iKey if there was\n** wrap-around.) Because the hash table is never more than half full,\n** the search is guaranteed to eventually hit an unused entry.  Let \n** iMax be the value between iKey and iUnused, closest to iUnused,\n** where aHash[iMax]==P.  If there is no iMax entry (if there exists\n** no hash slot such that aHash[i]==p) then page P is not in the\n** current index block.  Otherwise the iMax-th mapping entry of the\n** current index block corresponds to the last entry that references \n** page P.\n**\n** A hash search begins with the last index block and moves toward the\n** first index block, looking for entries corresponding to page P.  On\n** average, only two or three slots in each index block need to be\n** examined in order to either find the last entry for page P, or to\n** establish that no such entry exists in the block.  Each index block\n** holds over 4000 entries.  So two or three index blocks are sufficient\n** to cover a typical 10 megabyte WAL file, assuming 1K pages.  8 or 10\n** comparisons (on average) suffice to either locate a frame in the\n** WAL or to establish that the frame does not exist in the WAL.  This\n** is much faster than scanning the entire 10MB WAL.\n**\n** Note that entries are added in order of increasing K.  Hence, one\n** reader might be using some value K0 and a second reader that started\n** at a later time (after additional transactions were added to the WAL\n** and to the wal-index) might be using a different value K1, where K1>K0.\n** Both readers can use the same hash table and mapping section to get\n** the correct result.  There may be entries in the hash table with\n** K>K0 but to the first reader, those entries will appear to be unused\n** slots in the hash table and so the first reader will get an answer as\n** if no values greater than K0 had ever been inserted into the hash table\n** in the first place - which is what reader one wants.  Meanwhile, the\n** second reader using K1 will see additional values that were inserted\n** later, which is exactly what reader two wants.  \n**\n** When a rollback occurs, the value of K is decreased. Hash table entries\n** that correspond to frames greater than the new K value are removed\n** from the hash table at this point.\n*/\n#ifndef SQLITE_OMIT_WAL\n\n/* #include \"wal.h\" */\n\n/*\n** Trace output macros\n*/\n#if defined(SQLITE_TEST) && defined(SQLITE_DEBUG)\nSQLITE_PRIVATE int sqlite3WalTrace = 0;\n# define WALTRACE(X)  if(sqlite3WalTrace) sqlite3DebugPrintf X\n#else\n# define WALTRACE(X)\n#endif\n\n/*\n** The maximum (and only) versions of the wal and wal-index formats\n** that may be interpreted by this version of SQLite.\n**\n** If a client begins recovering a WAL file and finds that (a) the checksum\n** values in the wal-header are correct and (b) the version field is not\n** WAL_MAX_VERSION, recovery fails and SQLite returns SQLITE_CANTOPEN.\n**\n** Similarly, if a client successfully reads a wal-index header (i.e. the \n** checksum test is successful) and finds that the version field is not\n** WALINDEX_MAX_VERSION, then no read-transaction is opened and SQLite\n** returns SQLITE_CANTOPEN.\n*/\n#define WAL_MAX_VERSION      3007000\n#define WALINDEX_MAX_VERSION 3007000\n\n/*\n** Index numbers for various locking bytes.   WAL_NREADER is the number\n** of available reader locks and should be at least 3.  The default\n** is SQLITE_SHM_NLOCK==8 and  WAL_NREADER==5.\n**\n** Technically, the various VFSes are free to implement these locks however\n** they see fit.  However, compatibility is encouraged so that VFSes can\n** interoperate.  The standard implemention used on both unix and windows\n** is for the index number to indicate a byte offset into the\n** WalCkptInfo.aLock[] array in the wal-index header.  In other words, all\n** locks are on the shm file.  The WALINDEX_LOCK_OFFSET constant (which\n** should be 120) is the location in the shm file for the first locking\n** byte.\n*/\n#define WAL_WRITE_LOCK         0\n#define WAL_ALL_BUT_WRITE      1\n#define WAL_CKPT_LOCK          1\n#define WAL_RECOVER_LOCK       2\n#define WAL_READ_LOCK(I)       (3+(I))\n#define WAL_NREADER            (SQLITE_SHM_NLOCK-3)\n\n\n/* Object declarations */\ntypedef struct WalIndexHdr WalIndexHdr;\ntypedef struct WalIterator WalIterator;\ntypedef struct WalCkptInfo WalCkptInfo;\n\n\n/*\n** The following object holds a copy of the wal-index header content.\n**\n** The actual header in the wal-index consists of two copies of this\n** object followed by one instance of the WalCkptInfo object.\n** For all versions of SQLite through 3.10.0 and probably beyond,\n** the locking bytes (WalCkptInfo.aLock) start at offset 120 and\n** the total header size is 136 bytes.\n**\n** The szPage value can be any power of 2 between 512 and 32768, inclusive.\n** Or it can be 1 to represent a 65536-byte page.  The latter case was\n** added in 3.7.1 when support for 64K pages was added.  \n*/\nstruct WalIndexHdr {\n  u32 iVersion;                   /* Wal-index version */\n  u32 unused;                     /* Unused (padding) field */\n  u32 iChange;                    /* Counter incremented each transaction */\n  u8 isInit;                      /* 1 when initialized */\n  u8 bigEndCksum;                 /* True if checksums in WAL are big-endian */\n  u16 szPage;                     /* Database page size in bytes. 1==64K */\n  u32 mxFrame;                    /* Index of last valid frame in the WAL */\n  u32 nPage;                      /* Size of database in pages */\n  u32 aFrameCksum[2];             /* Checksum of last frame in log */\n  u32 aSalt[2];                   /* Two salt values copied from WAL header */\n  u32 aCksum[2];                  /* Checksum over all prior fields */\n};\n\n/*\n** A copy of the following object occurs in the wal-index immediately\n** following the second copy of the WalIndexHdr.  This object stores\n** information used by checkpoint.\n**\n** nBackfill is the number of frames in the WAL that have been written\n** back into the database. (We call the act of moving content from WAL to\n** database \"backfilling\".)  The nBackfill number is never greater than\n** WalIndexHdr.mxFrame.  nBackfill can only be increased by threads\n** holding the WAL_CKPT_LOCK lock (which includes a recovery thread).\n** However, a WAL_WRITE_LOCK thread can move the value of nBackfill from\n** mxFrame back to zero when the WAL is reset.\n**\n** nBackfillAttempted is the largest value of nBackfill that a checkpoint\n** has attempted to achieve.  Normally nBackfill==nBackfillAtempted, however\n** the nBackfillAttempted is set before any backfilling is done and the\n** nBackfill is only set after all backfilling completes.  So if a checkpoint\n** crashes, nBackfillAttempted might be larger than nBackfill.  The\n** WalIndexHdr.mxFrame must never be less than nBackfillAttempted.\n**\n** The aLock[] field is a set of bytes used for locking.  These bytes should\n** never be read or written.\n**\n** There is one entry in aReadMark[] for each reader lock.  If a reader\n** holds read-lock K, then the value in aReadMark[K] is no greater than\n** the mxFrame for that reader.  The value READMARK_NOT_USED (0xffffffff)\n** for any aReadMark[] means that entry is unused.  aReadMark[0] is \n** a special case; its value is never used and it exists as a place-holder\n** to avoid having to offset aReadMark[] indexs by one.  Readers holding\n** WAL_READ_LOCK(0) always ignore the entire WAL and read all content\n** directly from the database.\n**\n** The value of aReadMark[K] may only be changed by a thread that\n** is holding an exclusive lock on WAL_READ_LOCK(K).  Thus, the value of\n** aReadMark[K] cannot changed while there is a reader is using that mark\n** since the reader will be holding a shared lock on WAL_READ_LOCK(K).\n**\n** The checkpointer may only transfer frames from WAL to database where\n** the frame numbers are less than or equal to every aReadMark[] that is\n** in use (that is, every aReadMark[j] for which there is a corresponding\n** WAL_READ_LOCK(j)).  New readers (usually) pick the aReadMark[] with the\n** largest value and will increase an unused aReadMark[] to mxFrame if there\n** is not already an aReadMark[] equal to mxFrame.  The exception to the\n** previous sentence is when nBackfill equals mxFrame (meaning that everything\n** in the WAL has been backfilled into the database) then new readers\n** will choose aReadMark[0] which has value 0 and hence such reader will\n** get all their all content directly from the database file and ignore \n** the WAL.\n**\n** Writers normally append new frames to the end of the WAL.  However,\n** if nBackfill equals mxFrame (meaning that all WAL content has been\n** written back into the database) and if no readers are using the WAL\n** (in other words, if there are no WAL_READ_LOCK(i) where i>0) then\n** the writer will first \"reset\" the WAL back to the beginning and start\n** writing new content beginning at frame 1.\n**\n** We assume that 32-bit loads are atomic and so no locks are needed in\n** order to read from any aReadMark[] entries.\n*/\nstruct WalCkptInfo {\n  u32 nBackfill;                  /* Number of WAL frames backfilled into DB */\n  u32 aReadMark[WAL_NREADER];     /* Reader marks */\n  u8 aLock[SQLITE_SHM_NLOCK];     /* Reserved space for locks */\n  u32 nBackfillAttempted;         /* WAL frames perhaps written, or maybe not */\n  u32 notUsed0;                   /* Available for future enhancements */\n};\n#define READMARK_NOT_USED  0xffffffff\n\n\n/* A block of WALINDEX_LOCK_RESERVED bytes beginning at\n** WALINDEX_LOCK_OFFSET is reserved for locks. Since some systems\n** only support mandatory file-locks, we do not read or write data\n** from the region of the file on which locks are applied.\n*/\n#define WALINDEX_LOCK_OFFSET (sizeof(WalIndexHdr)*2+offsetof(WalCkptInfo,aLock))\n#define WALINDEX_HDR_SIZE    (sizeof(WalIndexHdr)*2+sizeof(WalCkptInfo))\n\n/* Size of header before each frame in wal */\n#define WAL_FRAME_HDRSIZE 24\n\n/* Size of write ahead log header, including checksum. */\n#define WAL_HDRSIZE 32\n\n/* WAL magic value. Either this value, or the same value with the least\n** significant bit also set (WAL_MAGIC | 0x00000001) is stored in 32-bit\n** big-endian format in the first 4 bytes of a WAL file.\n**\n** If the LSB is set, then the checksums for each frame within the WAL\n** file are calculated by treating all data as an array of 32-bit \n** big-endian words. Otherwise, they are calculated by interpreting \n** all data as 32-bit little-endian words.\n*/\n#define WAL_MAGIC 0x377f0682\n\n/*\n** Return the offset of frame iFrame in the write-ahead log file, \n** assuming a database page size of szPage bytes. The offset returned\n** is to the start of the write-ahead log frame-header.\n*/\n#define walFrameOffset(iFrame, szPage) (                               \\\n  WAL_HDRSIZE + ((iFrame)-1)*(i64)((szPage)+WAL_FRAME_HDRSIZE)         \\\n)\n\n/*\n** An open write-ahead log file is represented by an instance of the\n** following object.\n*/\nstruct Wal {\n  sqlite3_vfs *pVfs;         /* The VFS used to create pDbFd */\n  sqlite3_file *pDbFd;       /* File handle for the database file */\n  sqlite3_file *pWalFd;      /* File handle for WAL file */\n  u32 iCallback;             /* Value to pass to log callback (or 0) */\n  i64 mxWalSize;             /* Truncate WAL to this size upon reset */\n  int nWiData;               /* Size of array apWiData */\n  int szFirstBlock;          /* Size of first block written to WAL file */\n  volatile u32 **apWiData;   /* Pointer to wal-index content in memory */\n  u32 szPage;                /* Database page size */\n  i16 readLock;              /* Which read lock is being held.  -1 for none */\n  u8 syncFlags;              /* Flags to use to sync header writes */\n  u8 exclusiveMode;          /* Non-zero if connection is in exclusive mode */\n  u8 writeLock;              /* True if in a write transaction */\n  u8 ckptLock;               /* True if holding a checkpoint lock */\n  u8 readOnly;               /* WAL_RDWR, WAL_RDONLY, or WAL_SHM_RDONLY */\n  u8 truncateOnCommit;       /* True to truncate WAL file on commit */\n  u8 syncHeader;             /* Fsync the WAL header if true */\n  u8 padToSectorBoundary;    /* Pad transactions out to the next sector */\n  u8 bShmUnreliable;         /* SHM content is read-only and unreliable */\n  WalIndexHdr hdr;           /* Wal-index header for current transaction */\n  u32 minFrame;              /* Ignore wal frames before this one */\n  u32 iReCksum;              /* On commit, recalculate checksums from here */\n  const char *zWalName;      /* Name of WAL file */\n  u32 nCkpt;                 /* Checkpoint sequence counter in the wal-header */\n#ifdef SQLITE_DEBUG\n  u8 lockError;              /* True if a locking error has occurred */\n#endif\n#ifdef SQLITE_ENABLE_SNAPSHOT\n  WalIndexHdr *pSnapshot;    /* Start transaction here if not NULL */\n#endif\n};\n\n/*\n** Candidate values for Wal.exclusiveMode.\n*/\n#define WAL_NORMAL_MODE     0\n#define WAL_EXCLUSIVE_MODE  1     \n#define WAL_HEAPMEMORY_MODE 2\n\n/*\n** Possible values for WAL.readOnly\n*/\n#define WAL_RDWR        0    /* Normal read/write connection */\n#define WAL_RDONLY      1    /* The WAL file is readonly */\n#define WAL_SHM_RDONLY  2    /* The SHM file is readonly */\n\n/*\n** Each page of the wal-index mapping contains a hash-table made up of\n** an array of HASHTABLE_NSLOT elements of the following type.\n*/\ntypedef u16 ht_slot;\n\n/*\n** This structure is used to implement an iterator that loops through\n** all frames in the WAL in database page order. Where two or more frames\n** correspond to the same database page, the iterator visits only the \n** frame most recently written to the WAL (in other words, the frame with\n** the largest index).\n**\n** The internals of this structure are only accessed by:\n**\n**   walIteratorInit() - Create a new iterator,\n**   walIteratorNext() - Step an iterator,\n**   walIteratorFree() - Free an iterator.\n**\n** This functionality is used by the checkpoint code (see walCheckpoint()).\n*/\nstruct WalIterator {\n  int iPrior;                     /* Last result returned from the iterator */\n  int nSegment;                   /* Number of entries in aSegment[] */\n  struct WalSegment {\n    int iNext;                    /* Next slot in aIndex[] not yet returned */\n    ht_slot *aIndex;              /* i0, i1, i2... such that aPgno[iN] ascend */\n    u32 *aPgno;                   /* Array of page numbers. */\n    int nEntry;                   /* Nr. of entries in aPgno[] and aIndex[] */\n    int iZero;                    /* Frame number associated with aPgno[0] */\n  } aSegment[1];                  /* One for every 32KB page in the wal-index */\n};\n\n/*\n** Define the parameters of the hash tables in the wal-index file. There\n** is a hash-table following every HASHTABLE_NPAGE page numbers in the\n** wal-index.\n**\n** Changing any of these constants will alter the wal-index format and\n** create incompatibilities.\n*/\n#define HASHTABLE_NPAGE      4096                 /* Must be power of 2 */\n#define HASHTABLE_HASH_1     383                  /* Should be prime */\n#define HASHTABLE_NSLOT      (HASHTABLE_NPAGE*2)  /* Must be a power of 2 */\n\n/* \n** The block of page numbers associated with the first hash-table in a\n** wal-index is smaller than usual. This is so that there is a complete\n** hash-table on each aligned 32KB page of the wal-index.\n*/\n#define HASHTABLE_NPAGE_ONE  (HASHTABLE_NPAGE - (WALINDEX_HDR_SIZE/sizeof(u32)))\n\n/* The wal-index is divided into pages of WALINDEX_PGSZ bytes each. */\n#define WALINDEX_PGSZ   (                                         \\\n    sizeof(ht_slot)*HASHTABLE_NSLOT + HASHTABLE_NPAGE*sizeof(u32) \\\n)\n\n/*\n** Obtain a pointer to the iPage'th page of the wal-index. The wal-index\n** is broken into pages of WALINDEX_PGSZ bytes. Wal-index pages are\n** numbered from zero.\n**\n** If the wal-index is currently smaller the iPage pages then the size\n** of the wal-index might be increased, but only if it is safe to do\n** so.  It is safe to enlarge the wal-index if pWal->writeLock is true\n** or pWal->exclusiveMode==WAL_HEAPMEMORY_MODE.\n**\n** If this call is successful, *ppPage is set to point to the wal-index\n** page and SQLITE_OK is returned. If an error (an OOM or VFS error) occurs,\n** then an SQLite error code is returned and *ppPage is set to 0.\n*/\nstatic SQLITE_NOINLINE int walIndexPageRealloc(\n  Wal *pWal,               /* The WAL context */\n  int iPage,               /* The page we seek */\n  volatile u32 **ppPage    /* Write the page pointer here */\n){\n  int rc = SQLITE_OK;\n\n  /* Enlarge the pWal->apWiData[] array if required */\n  if( pWal->nWiData<=iPage ){\n    int nByte = sizeof(u32*)*(iPage+1);\n    volatile u32 **apNew;\n    apNew = (volatile u32 **)sqlite3_realloc64((void *)pWal->apWiData, nByte);\n    if( !apNew ){\n      *ppPage = 0;\n      return SQLITE_NOMEM_BKPT;\n    }\n    memset((void*)&apNew[pWal->nWiData], 0,\n           sizeof(u32*)*(iPage+1-pWal->nWiData));\n    pWal->apWiData = apNew;\n    pWal->nWiData = iPage+1;\n  }\n\n  /* Request a pointer to the required page from the VFS */\n  assert( pWal->apWiData[iPage]==0 );\n  if( pWal->exclusiveMode==WAL_HEAPMEMORY_MODE ){\n    pWal->apWiData[iPage] = (u32 volatile *)sqlite3MallocZero(WALINDEX_PGSZ);\n    if( !pWal->apWiData[iPage] ) rc = SQLITE_NOMEM_BKPT;\n  }else{\n    rc = sqlite3OsShmMap(pWal->pDbFd, iPage, WALINDEX_PGSZ, \n        pWal->writeLock, (void volatile **)&pWal->apWiData[iPage]\n    );\n    assert( pWal->apWiData[iPage]!=0 || rc!=SQLITE_OK || pWal->writeLock==0 );\n    testcase( pWal->apWiData[iPage]==0 && rc==SQLITE_OK );\n    if( (rc&0xff)==SQLITE_READONLY ){\n      pWal->readOnly |= WAL_SHM_RDONLY;\n      if( rc==SQLITE_READONLY ){\n        rc = SQLITE_OK;\n      }\n    }\n  }\n\n  *ppPage = pWal->apWiData[iPage];\n  assert( iPage==0 || *ppPage || rc!=SQLITE_OK );\n  return rc;\n}\nstatic int walIndexPage(\n  Wal *pWal,               /* The WAL context */\n  int iPage,               /* The page we seek */\n  volatile u32 **ppPage    /* Write the page pointer here */\n){\n  if( pWal->nWiData<=iPage || (*ppPage = pWal->apWiData[iPage])==0 ){\n    return walIndexPageRealloc(pWal, iPage, ppPage);\n  }\n  return SQLITE_OK;\n}\n\n/*\n** Return a pointer to the WalCkptInfo structure in the wal-index.\n*/\nstatic volatile WalCkptInfo *walCkptInfo(Wal *pWal){\n  assert( pWal->nWiData>0 && pWal->apWiData[0] );\n  return (volatile WalCkptInfo*)&(pWal->apWiData[0][sizeof(WalIndexHdr)/2]);\n}\n\n/*\n** Return a pointer to the WalIndexHdr structure in the wal-index.\n*/\nstatic volatile WalIndexHdr *walIndexHdr(Wal *pWal){\n  assert( pWal->nWiData>0 && pWal->apWiData[0] );\n  return (volatile WalIndexHdr*)pWal->apWiData[0];\n}\n\n/*\n** The argument to this macro must be of type u32. On a little-endian\n** architecture, it returns the u32 value that results from interpreting\n** the 4 bytes as a big-endian value. On a big-endian architecture, it\n** returns the value that would be produced by interpreting the 4 bytes\n** of the input value as a little-endian integer.\n*/\n#define BYTESWAP32(x) ( \\\n    (((x)&0x000000FF)<<24) + (((x)&0x0000FF00)<<8)  \\\n  + (((x)&0x00FF0000)>>8)  + (((x)&0xFF000000)>>24) \\\n)\n\n/*\n** Generate or extend an 8 byte checksum based on the data in \n** array aByte[] and the initial values of aIn[0] and aIn[1] (or\n** initial values of 0 and 0 if aIn==NULL).\n**\n** The checksum is written back into aOut[] before returning.\n**\n** nByte must be a positive multiple of 8.\n*/\nstatic void walChecksumBytes(\n  int nativeCksum, /* True for native byte-order, false for non-native */\n  u8 *a,           /* Content to be checksummed */\n  int nByte,       /* Bytes of content in a[].  Must be a multiple of 8. */\n  const u32 *aIn,  /* Initial checksum value input */\n  u32 *aOut        /* OUT: Final checksum value output */\n){\n  u32 s1, s2;\n  u32 *aData = (u32 *)a;\n  u32 *aEnd = (u32 *)&a[nByte];\n\n  if( aIn ){\n    s1 = aIn[0];\n    s2 = aIn[1];\n  }else{\n    s1 = s2 = 0;\n  }\n\n  assert( nByte>=8 );\n  assert( (nByte&0x00000007)==0 );\n\n  if( nativeCksum ){\n    do {\n      s1 += *aData++ + s2;\n      s2 += *aData++ + s1;\n    }while( aData<aEnd );\n  }else{\n    do {\n      s1 += BYTESWAP32(aData[0]) + s2;\n      s2 += BYTESWAP32(aData[1]) + s1;\n      aData += 2;\n    }while( aData<aEnd );\n  }\n\n  aOut[0] = s1;\n  aOut[1] = s2;\n}\n\nstatic void walShmBarrier(Wal *pWal){\n  if( pWal->exclusiveMode!=WAL_HEAPMEMORY_MODE ){\n    sqlite3OsShmBarrier(pWal->pDbFd);\n  }\n}\n\n/*\n** Write the header information in pWal->hdr into the wal-index.\n**\n** The checksum on pWal->hdr is updated before it is written.\n*/\nstatic void walIndexWriteHdr(Wal *pWal){\n  volatile WalIndexHdr *aHdr = walIndexHdr(pWal);\n  const int nCksum = offsetof(WalIndexHdr, aCksum);\n\n  assert( pWal->writeLock );\n  pWal->hdr.isInit = 1;\n  pWal->hdr.iVersion = WALINDEX_MAX_VERSION;\n  walChecksumBytes(1, (u8*)&pWal->hdr, nCksum, 0, pWal->hdr.aCksum);\n  memcpy((void*)&aHdr[1], (const void*)&pWal->hdr, sizeof(WalIndexHdr));\n  walShmBarrier(pWal);\n  memcpy((void*)&aHdr[0], (const void*)&pWal->hdr, sizeof(WalIndexHdr));\n}\n\n/*\n** This function encodes a single frame header and writes it to a buffer\n** supplied by the caller. A frame-header is made up of a series of \n** 4-byte big-endian integers, as follows:\n**\n**     0: Page number.\n**     4: For commit records, the size of the database image in pages \n**        after the commit. For all other records, zero.\n**     8: Salt-1 (copied from the wal-header)\n**    12: Salt-2 (copied from the wal-header)\n**    16: Checksum-1.\n**    20: Checksum-2.\n*/\nstatic void walEncodeFrame(\n  Wal *pWal,                      /* The write-ahead log */\n  u32 iPage,                      /* Database page number for frame */\n  u32 nTruncate,                  /* New db size (or 0 for non-commit frames) */\n  u8 *aData,                      /* Pointer to page data */\n  u8 *aFrame                      /* OUT: Write encoded frame here */\n){\n  int nativeCksum;                /* True for native byte-order checksums */\n  u32 *aCksum = pWal->hdr.aFrameCksum;\n  assert( WAL_FRAME_HDRSIZE==24 );\n  sqlite3Put4byte(&aFrame[0], iPage);\n  sqlite3Put4byte(&aFrame[4], nTruncate);\n  if( pWal->iReCksum==0 ){\n    memcpy(&aFrame[8], pWal->hdr.aSalt, 8);\n\n    nativeCksum = (pWal->hdr.bigEndCksum==SQLITE_BIGENDIAN);\n    walChecksumBytes(nativeCksum, aFrame, 8, aCksum, aCksum);\n    walChecksumBytes(nativeCksum, aData, pWal->szPage, aCksum, aCksum);\n\n    sqlite3Put4byte(&aFrame[16], aCksum[0]);\n    sqlite3Put4byte(&aFrame[20], aCksum[1]);\n  }else{\n    memset(&aFrame[8], 0, 16);\n  }\n}\n\n/*\n** Check to see if the frame with header in aFrame[] and content\n** in aData[] is valid.  If it is a valid frame, fill *piPage and\n** *pnTruncate and return true.  Return if the frame is not valid.\n*/\nstatic int walDecodeFrame(\n  Wal *pWal,                      /* The write-ahead log */\n  u32 *piPage,                    /* OUT: Database page number for frame */\n  u32 *pnTruncate,                /* OUT: New db size (or 0 if not commit) */\n  u8 *aData,                      /* Pointer to page data (for checksum) */\n  u8 *aFrame                      /* Frame data */\n){\n  int nativeCksum;                /* True for native byte-order checksums */\n  u32 *aCksum = pWal->hdr.aFrameCksum;\n  u32 pgno;                       /* Page number of the frame */\n  assert( WAL_FRAME_HDRSIZE==24 );\n\n  /* A frame is only valid if the salt values in the frame-header\n  ** match the salt values in the wal-header. \n  */\n  if( memcmp(&pWal->hdr.aSalt, &aFrame[8], 8)!=0 ){\n    return 0;\n  }\n\n  /* A frame is only valid if the page number is creater than zero.\n  */\n  pgno = sqlite3Get4byte(&aFrame[0]);\n  if( pgno==0 ){\n    return 0;\n  }\n\n  /* A frame is only valid if a checksum of the WAL header,\n  ** all prior frams, the first 16 bytes of this frame-header, \n  ** and the frame-data matches the checksum in the last 8 \n  ** bytes of this frame-header.\n  */\n  nativeCksum = (pWal->hdr.bigEndCksum==SQLITE_BIGENDIAN);\n  walChecksumBytes(nativeCksum, aFrame, 8, aCksum, aCksum);\n  walChecksumBytes(nativeCksum, aData, pWal->szPage, aCksum, aCksum);\n  if( aCksum[0]!=sqlite3Get4byte(&aFrame[16]) \n   || aCksum[1]!=sqlite3Get4byte(&aFrame[20]) \n  ){\n    /* Checksum failed. */\n    return 0;\n  }\n\n  /* If we reach this point, the frame is valid.  Return the page number\n  ** and the new database size.\n  */\n  *piPage = pgno;\n  *pnTruncate = sqlite3Get4byte(&aFrame[4]);\n  return 1;\n}\n\n\n#if defined(SQLITE_TEST) && defined(SQLITE_DEBUG)\n/*\n** Names of locks.  This routine is used to provide debugging output and is not\n** a part of an ordinary build.\n*/\nstatic const char *walLockName(int lockIdx){\n  if( lockIdx==WAL_WRITE_LOCK ){\n    return \"WRITE-LOCK\";\n  }else if( lockIdx==WAL_CKPT_LOCK ){\n    return \"CKPT-LOCK\";\n  }else if( lockIdx==WAL_RECOVER_LOCK ){\n    return \"RECOVER-LOCK\";\n  }else{\n    static char zName[15];\n    sqlite3_snprintf(sizeof(zName), zName, \"READ-LOCK[%d]\",\n                     lockIdx-WAL_READ_LOCK(0));\n    return zName;\n  }\n}\n#endif /*defined(SQLITE_TEST) || defined(SQLITE_DEBUG) */\n    \n\n/*\n** Set or release locks on the WAL.  Locks are either shared or exclusive.\n** A lock cannot be moved directly between shared and exclusive - it must go\n** through the unlocked state first.\n**\n** In locking_mode=EXCLUSIVE, all of these routines become no-ops.\n*/\nstatic int walLockShared(Wal *pWal, int lockIdx){\n  int rc;\n  if( pWal->exclusiveMode ) return SQLITE_OK;\n  rc = sqlite3OsShmLock(pWal->pDbFd, lockIdx, 1,\n                        SQLITE_SHM_LOCK | SQLITE_SHM_SHARED);\n  WALTRACE((\"WAL%p: acquire SHARED-%s %s\\n\", pWal,\n            walLockName(lockIdx), rc ? \"failed\" : \"ok\"));\n  VVA_ONLY( pWal->lockError = (u8)(rc!=SQLITE_OK && rc!=SQLITE_BUSY); )\n  return rc;\n}\nstatic void walUnlockShared(Wal *pWal, int lockIdx){\n  if( pWal->exclusiveMode ) return;\n  (void)sqlite3OsShmLock(pWal->pDbFd, lockIdx, 1,\n                         SQLITE_SHM_UNLOCK | SQLITE_SHM_SHARED);\n  WALTRACE((\"WAL%p: release SHARED-%s\\n\", pWal, walLockName(lockIdx)));\n}\nstatic int walLockExclusive(Wal *pWal, int lockIdx, int n){\n  int rc;\n  if( pWal->exclusiveMode ) return SQLITE_OK;\n  rc = sqlite3OsShmLock(pWal->pDbFd, lockIdx, n,\n                        SQLITE_SHM_LOCK | SQLITE_SHM_EXCLUSIVE);\n  WALTRACE((\"WAL%p: acquire EXCLUSIVE-%s cnt=%d %s\\n\", pWal,\n            walLockName(lockIdx), n, rc ? \"failed\" : \"ok\"));\n  VVA_ONLY( pWal->lockError = (u8)(rc!=SQLITE_OK && rc!=SQLITE_BUSY); )\n  return rc;\n}\nstatic void walUnlockExclusive(Wal *pWal, int lockIdx, int n){\n  if( pWal->exclusiveMode ) return;\n  (void)sqlite3OsShmLock(pWal->pDbFd, lockIdx, n,\n                         SQLITE_SHM_UNLOCK | SQLITE_SHM_EXCLUSIVE);\n  WALTRACE((\"WAL%p: release EXCLUSIVE-%s cnt=%d\\n\", pWal,\n             walLockName(lockIdx), n));\n}\n\n/*\n** Compute a hash on a page number.  The resulting hash value must land\n** between 0 and (HASHTABLE_NSLOT-1).  The walHashNext() function advances\n** the hash to the next value in the event of a collision.\n*/\nstatic int walHash(u32 iPage){\n  assert( iPage>0 );\n  assert( (HASHTABLE_NSLOT & (HASHTABLE_NSLOT-1))==0 );\n  return (iPage*HASHTABLE_HASH_1) & (HASHTABLE_NSLOT-1);\n}\nstatic int walNextHash(int iPriorHash){\n  return (iPriorHash+1)&(HASHTABLE_NSLOT-1);\n}\n\n/* \n** Return pointers to the hash table and page number array stored on\n** page iHash of the wal-index. The wal-index is broken into 32KB pages\n** numbered starting from 0.\n**\n** Set output variable *paHash to point to the start of the hash table\n** in the wal-index file. Set *piZero to one less than the frame \n** number of the first frame indexed by this hash table. If a\n** slot in the hash table is set to N, it refers to frame number \n** (*piZero+N) in the log.\n**\n** Finally, set *paPgno so that *paPgno[1] is the page number of the\n** first frame indexed by the hash table, frame (*piZero+1).\n*/\nstatic int walHashGet(\n  Wal *pWal,                      /* WAL handle */\n  int iHash,                      /* Find the iHash'th table */\n  volatile ht_slot **paHash,      /* OUT: Pointer to hash index */\n  volatile u32 **paPgno,          /* OUT: Pointer to page number array */\n  u32 *piZero                     /* OUT: Frame associated with *paPgno[0] */\n){\n  int rc;                         /* Return code */\n  volatile u32 *aPgno;\n\n  rc = walIndexPage(pWal, iHash, &aPgno);\n  assert( rc==SQLITE_OK || iHash>0 );\n\n  if( rc==SQLITE_OK ){\n    u32 iZero;\n    volatile ht_slot *aHash;\n\n    aHash = (volatile ht_slot *)&aPgno[HASHTABLE_NPAGE];\n    if( iHash==0 ){\n      aPgno = &aPgno[WALINDEX_HDR_SIZE/sizeof(u32)];\n      iZero = 0;\n    }else{\n      iZero = HASHTABLE_NPAGE_ONE + (iHash-1)*HASHTABLE_NPAGE;\n    }\n  \n    *paPgno = &aPgno[-1];\n    *paHash = aHash;\n    *piZero = iZero;\n  }\n  return rc;\n}\n\n/*\n** Return the number of the wal-index page that contains the hash-table\n** and page-number array that contain entries corresponding to WAL frame\n** iFrame. The wal-index is broken up into 32KB pages. Wal-index pages \n** are numbered starting from 0.\n*/\nstatic int walFramePage(u32 iFrame){\n  int iHash = (iFrame+HASHTABLE_NPAGE-HASHTABLE_NPAGE_ONE-1) / HASHTABLE_NPAGE;\n  assert( (iHash==0 || iFrame>HASHTABLE_NPAGE_ONE)\n       && (iHash>=1 || iFrame<=HASHTABLE_NPAGE_ONE)\n       && (iHash<=1 || iFrame>(HASHTABLE_NPAGE_ONE+HASHTABLE_NPAGE))\n       && (iHash>=2 || iFrame<=HASHTABLE_NPAGE_ONE+HASHTABLE_NPAGE)\n       && (iHash<=2 || iFrame>(HASHTABLE_NPAGE_ONE+2*HASHTABLE_NPAGE))\n  );\n  return iHash;\n}\n\n/*\n** Return the page number associated with frame iFrame in this WAL.\n*/\nstatic u32 walFramePgno(Wal *pWal, u32 iFrame){\n  int iHash = walFramePage(iFrame);\n  if( iHash==0 ){\n    return pWal->apWiData[0][WALINDEX_HDR_SIZE/sizeof(u32) + iFrame - 1];\n  }\n  return pWal->apWiData[iHash][(iFrame-1-HASHTABLE_NPAGE_ONE)%HASHTABLE_NPAGE];\n}\n\n/*\n** Remove entries from the hash table that point to WAL slots greater\n** than pWal->hdr.mxFrame.\n**\n** This function is called whenever pWal->hdr.mxFrame is decreased due\n** to a rollback or savepoint.\n**\n** At most only the hash table containing pWal->hdr.mxFrame needs to be\n** updated.  Any later hash tables will be automatically cleared when\n** pWal->hdr.mxFrame advances to the point where those hash tables are\n** actually needed.\n*/\nstatic void walCleanupHash(Wal *pWal){\n  volatile ht_slot *aHash = 0;    /* Pointer to hash table to clear */\n  volatile u32 *aPgno = 0;        /* Page number array for hash table */\n  u32 iZero = 0;                  /* frame == (aHash[x]+iZero) */\n  int iLimit = 0;                 /* Zero values greater than this */\n  int nByte;                      /* Number of bytes to zero in aPgno[] */\n  int i;                          /* Used to iterate through aHash[] */\n\n  assert( pWal->writeLock );\n  testcase( pWal->hdr.mxFrame==HASHTABLE_NPAGE_ONE-1 );\n  testcase( pWal->hdr.mxFrame==HASHTABLE_NPAGE_ONE );\n  testcase( pWal->hdr.mxFrame==HASHTABLE_NPAGE_ONE+1 );\n\n  if( pWal->hdr.mxFrame==0 ) return;\n\n  /* Obtain pointers to the hash-table and page-number array containing \n  ** the entry that corresponds to frame pWal->hdr.mxFrame. It is guaranteed\n  ** that the page said hash-table and array reside on is already mapped.\n  */\n  assert( pWal->nWiData>walFramePage(pWal->hdr.mxFrame) );\n  assert( pWal->apWiData[walFramePage(pWal->hdr.mxFrame)] );\n  walHashGet(pWal, walFramePage(pWal->hdr.mxFrame), &aHash, &aPgno, &iZero);\n\n  /* Zero all hash-table entries that correspond to frame numbers greater\n  ** than pWal->hdr.mxFrame.\n  */\n  iLimit = pWal->hdr.mxFrame - iZero;\n  assert( iLimit>0 );\n  for(i=0; i<HASHTABLE_NSLOT; i++){\n    if( aHash[i]>iLimit ){\n      aHash[i] = 0;\n    }\n  }\n  \n  /* Zero the entries in the aPgno array that correspond to frames with\n  ** frame numbers greater than pWal->hdr.mxFrame. \n  */\n  nByte = (int)((char *)aHash - (char *)&aPgno[iLimit+1]);\n  memset((void *)&aPgno[iLimit+1], 0, nByte);\n\n#ifdef SQLITE_ENABLE_EXPENSIVE_ASSERT\n  /* Verify that the every entry in the mapping region is still reachable\n  ** via the hash table even after the cleanup.\n  */\n  if( iLimit ){\n    int j;           /* Loop counter */\n    int iKey;        /* Hash key */\n    for(j=1; j<=iLimit; j++){\n      for(iKey=walHash(aPgno[j]); aHash[iKey]; iKey=walNextHash(iKey)){\n        if( aHash[iKey]==j ) break;\n      }\n      assert( aHash[iKey]==j );\n    }\n  }\n#endif /* SQLITE_ENABLE_EXPENSIVE_ASSERT */\n}\n\n\n/*\n** Set an entry in the wal-index that will map database page number\n** pPage into WAL frame iFrame.\n*/\nstatic int walIndexAppend(Wal *pWal, u32 iFrame, u32 iPage){\n  int rc;                         /* Return code */\n  u32 iZero = 0;                  /* One less than frame number of aPgno[1] */\n  volatile u32 *aPgno = 0;        /* Page number array */\n  volatile ht_slot *aHash = 0;    /* Hash table */\n\n  rc = walHashGet(pWal, walFramePage(iFrame), &aHash, &aPgno, &iZero);\n\n  /* Assuming the wal-index file was successfully mapped, populate the\n  ** page number array and hash table entry.\n  */\n  if( rc==SQLITE_OK ){\n    int iKey;                     /* Hash table key */\n    int idx;                      /* Value to write to hash-table slot */\n    int nCollide;                 /* Number of hash collisions */\n\n    idx = iFrame - iZero;\n    assert( idx <= HASHTABLE_NSLOT/2 + 1 );\n    \n    /* If this is the first entry to be added to this hash-table, zero the\n    ** entire hash table and aPgno[] array before proceeding. \n    */\n    if( idx==1 ){\n      int nByte = (int)((u8 *)&aHash[HASHTABLE_NSLOT] - (u8 *)&aPgno[1]);\n      memset((void*)&aPgno[1], 0, nByte);\n    }\n\n    /* If the entry in aPgno[] is already set, then the previous writer\n    ** must have exited unexpectedly in the middle of a transaction (after\n    ** writing one or more dirty pages to the WAL to free up memory). \n    ** Remove the remnants of that writers uncommitted transaction from \n    ** the hash-table before writing any new entries.\n    */\n    if( aPgno[idx] ){\n      walCleanupHash(pWal);\n      assert( !aPgno[idx] );\n    }\n\n    /* Write the aPgno[] array entry and the hash-table slot. */\n    nCollide = idx;\n    for(iKey=walHash(iPage); aHash[iKey]; iKey=walNextHash(iKey)){\n      if( (nCollide--)==0 ) return SQLITE_CORRUPT_BKPT;\n    }\n    aPgno[idx] = iPage;\n    aHash[iKey] = (ht_slot)idx;\n\n#ifdef SQLITE_ENABLE_EXPENSIVE_ASSERT\n    /* Verify that the number of entries in the hash table exactly equals\n    ** the number of entries in the mapping region.\n    */\n    {\n      int i;           /* Loop counter */\n      int nEntry = 0;  /* Number of entries in the hash table */\n      for(i=0; i<HASHTABLE_NSLOT; i++){ if( aHash[i] ) nEntry++; }\n      assert( nEntry==idx );\n    }\n\n    /* Verify that the every entry in the mapping region is reachable\n    ** via the hash table.  This turns out to be a really, really expensive\n    ** thing to check, so only do this occasionally - not on every\n    ** iteration.\n    */\n    if( (idx&0x3ff)==0 ){\n      int i;           /* Loop counter */\n      for(i=1; i<=idx; i++){\n        for(iKey=walHash(aPgno[i]); aHash[iKey]; iKey=walNextHash(iKey)){\n          if( aHash[iKey]==i ) break;\n        }\n        assert( aHash[iKey]==i );\n      }\n    }\n#endif /* SQLITE_ENABLE_EXPENSIVE_ASSERT */\n  }\n\n\n  return rc;\n}\n\n\n/*\n** Recover the wal-index by reading the write-ahead log file. \n**\n** This routine first tries to establish an exclusive lock on the\n** wal-index to prevent other threads/processes from doing anything\n** with the WAL or wal-index while recovery is running.  The\n** WAL_RECOVER_LOCK is also held so that other threads will know\n** that this thread is running recovery.  If unable to establish\n** the necessary locks, this routine returns SQLITE_BUSY.\n*/\nstatic int walIndexRecover(Wal *pWal){\n  int rc;                         /* Return Code */\n  i64 nSize;                      /* Size of log file */\n  u32 aFrameCksum[2] = {0, 0};\n  int iLock;                      /* Lock offset to lock for checkpoint */\n\n  /* Obtain an exclusive lock on all byte in the locking range not already\n  ** locked by the caller. The caller is guaranteed to have locked the\n  ** WAL_WRITE_LOCK byte, and may have also locked the WAL_CKPT_LOCK byte.\n  ** If successful, the same bytes that are locked here are unlocked before\n  ** this function returns.\n  */\n  assert( pWal->ckptLock==1 || pWal->ckptLock==0 );\n  assert( WAL_ALL_BUT_WRITE==WAL_WRITE_LOCK+1 );\n  assert( WAL_CKPT_LOCK==WAL_ALL_BUT_WRITE );\n  assert( pWal->writeLock );\n  iLock = WAL_ALL_BUT_WRITE + pWal->ckptLock;\n  rc = walLockExclusive(pWal, iLock, WAL_READ_LOCK(0)-iLock);\n  if( rc==SQLITE_OK ){\n    rc = walLockExclusive(pWal, WAL_READ_LOCK(1), WAL_NREADER-1);\n    if( rc!=SQLITE_OK ){\n      walUnlockExclusive(pWal, iLock, WAL_READ_LOCK(0)-iLock);\n    }\n  }\n  if( rc ){\n    return rc;\n  }\n\n  WALTRACE((\"WAL%p: recovery begin...\\n\", pWal));\n\n  memset(&pWal->hdr, 0, sizeof(WalIndexHdr));\n\n  rc = sqlite3OsFileSize(pWal->pWalFd, &nSize);\n  if( rc!=SQLITE_OK ){\n    goto recovery_error;\n  }\n\n  if( nSize>WAL_HDRSIZE ){\n    u8 aBuf[WAL_HDRSIZE];         /* Buffer to load WAL header into */\n    u8 *aFrame = 0;               /* Malloc'd buffer to load entire frame */\n    int szFrame;                  /* Number of bytes in buffer aFrame[] */\n    u8 *aData;                    /* Pointer to data part of aFrame buffer */\n    int iFrame;                   /* Index of last frame read */\n    i64 iOffset;                  /* Next offset to read from log file */\n    int szPage;                   /* Page size according to the log */\n    u32 magic;                    /* Magic value read from WAL header */\n    u32 version;                  /* Magic value read from WAL header */\n    int isValid;                  /* True if this frame is valid */\n\n    /* Read in the WAL header. */\n    rc = sqlite3OsRead(pWal->pWalFd, aBuf, WAL_HDRSIZE, 0);\n    if( rc!=SQLITE_OK ){\n      goto recovery_error;\n    }\n\n    /* If the database page size is not a power of two, or is greater than\n    ** SQLITE_MAX_PAGE_SIZE, conclude that the WAL file contains no valid \n    ** data. Similarly, if the 'magic' value is invalid, ignore the whole\n    ** WAL file.\n    */\n    magic = sqlite3Get4byte(&aBuf[0]);\n    szPage = sqlite3Get4byte(&aBuf[8]);\n    if( (magic&0xFFFFFFFE)!=WAL_MAGIC \n     || szPage&(szPage-1) \n     || szPage>SQLITE_MAX_PAGE_SIZE \n     || szPage<512 \n    ){\n      goto finished;\n    }\n    pWal->hdr.bigEndCksum = (u8)(magic&0x00000001);\n    pWal->szPage = szPage;\n    pWal->nCkpt = sqlite3Get4byte(&aBuf[12]);\n    memcpy(&pWal->hdr.aSalt, &aBuf[16], 8);\n\n    /* Verify that the WAL header checksum is correct */\n    walChecksumBytes(pWal->hdr.bigEndCksum==SQLITE_BIGENDIAN, \n        aBuf, WAL_HDRSIZE-2*4, 0, pWal->hdr.aFrameCksum\n    );\n    if( pWal->hdr.aFrameCksum[0]!=sqlite3Get4byte(&aBuf[24])\n     || pWal->hdr.aFrameCksum[1]!=sqlite3Get4byte(&aBuf[28])\n    ){\n      goto finished;\n    }\n\n    /* Verify that the version number on the WAL format is one that\n    ** are able to understand */\n    version = sqlite3Get4byte(&aBuf[4]);\n    if( version!=WAL_MAX_VERSION ){\n      rc = SQLITE_CANTOPEN_BKPT;\n      goto finished;\n    }\n\n    /* Malloc a buffer to read frames into. */\n    szFrame = szPage + WAL_FRAME_HDRSIZE;\n    aFrame = (u8 *)sqlite3_malloc64(szFrame);\n    if( !aFrame ){\n      rc = SQLITE_NOMEM_BKPT;\n      goto recovery_error;\n    }\n    aData = &aFrame[WAL_FRAME_HDRSIZE];\n\n    /* Read all frames from the log file. */\n    iFrame = 0;\n    for(iOffset=WAL_HDRSIZE; (iOffset+szFrame)<=nSize; iOffset+=szFrame){\n      u32 pgno;                   /* Database page number for frame */\n      u32 nTruncate;              /* dbsize field from frame header */\n\n      /* Read and decode the next log frame. */\n      iFrame++;\n      rc = sqlite3OsRead(pWal->pWalFd, aFrame, szFrame, iOffset);\n      if( rc!=SQLITE_OK ) break;\n      isValid = walDecodeFrame(pWal, &pgno, &nTruncate, aData, aFrame);\n      if( !isValid ) break;\n      rc = walIndexAppend(pWal, iFrame, pgno);\n      if( rc!=SQLITE_OK ) break;\n\n      /* If nTruncate is non-zero, this is a commit record. */\n      if( nTruncate ){\n        pWal->hdr.mxFrame = iFrame;\n        pWal->hdr.nPage = nTruncate;\n        pWal->hdr.szPage = (u16)((szPage&0xff00) | (szPage>>16));\n        testcase( szPage<=32768 );\n        testcase( szPage>=65536 );\n        aFrameCksum[0] = pWal->hdr.aFrameCksum[0];\n        aFrameCksum[1] = pWal->hdr.aFrameCksum[1];\n      }\n    }\n\n    sqlite3_free(aFrame);\n  }\n\nfinished:\n  if( rc==SQLITE_OK ){\n    volatile WalCkptInfo *pInfo;\n    int i;\n    pWal->hdr.aFrameCksum[0] = aFrameCksum[0];\n    pWal->hdr.aFrameCksum[1] = aFrameCksum[1];\n    walIndexWriteHdr(pWal);\n\n    /* Reset the checkpoint-header. This is safe because this thread is \n    ** currently holding locks that exclude all other readers, writers and\n    ** checkpointers.\n    */\n    pInfo = walCkptInfo(pWal);\n    pInfo->nBackfill = 0;\n    pInfo->nBackfillAttempted = pWal->hdr.mxFrame;\n    pInfo->aReadMark[0] = 0;\n    for(i=1; i<WAL_NREADER; i++) pInfo->aReadMark[i] = READMARK_NOT_USED;\n    if( pWal->hdr.mxFrame ) pInfo->aReadMark[1] = pWal->hdr.mxFrame;\n\n    /* If more than one frame was recovered from the log file, report an\n    ** event via sqlite3_log(). This is to help with identifying performance\n    ** problems caused by applications routinely shutting down without\n    ** checkpointing the log file.\n    */\n    if( pWal->hdr.nPage ){\n      sqlite3_log(SQLITE_NOTICE_RECOVER_WAL,\n          \"recovered %d frames from WAL file %s\",\n          pWal->hdr.mxFrame, pWal->zWalName\n      );\n    }\n  }\n\nrecovery_error:\n  WALTRACE((\"WAL%p: recovery %s\\n\", pWal, rc ? \"failed\" : \"ok\"));\n  walUnlockExclusive(pWal, iLock, WAL_READ_LOCK(0)-iLock);\n  walUnlockExclusive(pWal, WAL_READ_LOCK(1), WAL_NREADER-1);\n  return rc;\n}\n\n/*\n** Close an open wal-index.\n*/\nstatic void walIndexClose(Wal *pWal, int isDelete){\n  if( pWal->exclusiveMode==WAL_HEAPMEMORY_MODE || pWal->bShmUnreliable ){\n    int i;\n    for(i=0; i<pWal->nWiData; i++){\n      sqlite3_free((void *)pWal->apWiData[i]);\n      pWal->apWiData[i] = 0;\n    }\n  }\n  if( pWal->exclusiveMode!=WAL_HEAPMEMORY_MODE ){\n    sqlite3OsShmUnmap(pWal->pDbFd, isDelete);\n  }\n}\n\n/* \n** Open a connection to the WAL file zWalName. The database file must \n** already be opened on connection pDbFd. The buffer that zWalName points\n** to must remain valid for the lifetime of the returned Wal* handle.\n**\n** A SHARED lock should be held on the database file when this function\n** is called. The purpose of this SHARED lock is to prevent any other\n** client from unlinking the WAL or wal-index file. If another process\n** were to do this just after this client opened one of these files, the\n** system would be badly broken.\n**\n** If the log file is successfully opened, SQLITE_OK is returned and \n** *ppWal is set to point to a new WAL handle. If an error occurs,\n** an SQLite error code is returned and *ppWal is left unmodified.\n*/\nSQLITE_PRIVATE int sqlite3WalOpen(\n  sqlite3_vfs *pVfs,              /* vfs module to open wal and wal-index */\n  sqlite3_file *pDbFd,            /* The open database file */\n  const char *zWalName,           /* Name of the WAL file */\n  int bNoShm,                     /* True to run in heap-memory mode */\n  i64 mxWalSize,                  /* Truncate WAL to this size on reset */\n  Wal **ppWal                     /* OUT: Allocated Wal handle */\n){\n  int rc;                         /* Return Code */\n  Wal *pRet;                      /* Object to allocate and return */\n  int flags;                      /* Flags passed to OsOpen() */\n\n  assert( zWalName && zWalName[0] );\n  assert( pDbFd );\n\n  /* In the amalgamation, the os_unix.c and os_win.c source files come before\n  ** this source file.  Verify that the #defines of the locking byte offsets\n  ** in os_unix.c and os_win.c agree with the WALINDEX_LOCK_OFFSET value.\n  ** For that matter, if the lock offset ever changes from its initial design\n  ** value of 120, we need to know that so there is an assert() to check it.\n  */\n  assert( 120==WALINDEX_LOCK_OFFSET );\n  assert( 136==WALINDEX_HDR_SIZE );\n#ifdef WIN_SHM_BASE\n  assert( WIN_SHM_BASE==WALINDEX_LOCK_OFFSET );\n#endif\n#ifdef UNIX_SHM_BASE\n  assert( UNIX_SHM_BASE==WALINDEX_LOCK_OFFSET );\n#endif\n\n\n  /* Allocate an instance of struct Wal to return. */\n  *ppWal = 0;\n  pRet = (Wal*)sqlite3MallocZero(sizeof(Wal) + pVfs->szOsFile);\n  if( !pRet ){\n    return SQLITE_NOMEM_BKPT;\n  }\n\n  pRet->pVfs = pVfs;\n  pRet->pWalFd = (sqlite3_file *)&pRet[1];\n  pRet->pDbFd = pDbFd;\n  pRet->readLock = -1;\n  pRet->mxWalSize = mxWalSize;\n  pRet->zWalName = zWalName;\n  pRet->syncHeader = 1;\n  pRet->padToSectorBoundary = 1;\n  pRet->exclusiveMode = (bNoShm ? WAL_HEAPMEMORY_MODE: WAL_NORMAL_MODE);\n\n  /* Open file handle on the write-ahead log file. */\n  flags = (SQLITE_OPEN_READWRITE|SQLITE_OPEN_CREATE|SQLITE_OPEN_WAL);\n  rc = sqlite3OsOpen(pVfs, zWalName, pRet->pWalFd, flags, &flags);\n  if( rc==SQLITE_OK && flags&SQLITE_OPEN_READONLY ){\n    pRet->readOnly = WAL_RDONLY;\n  }\n\n  if( rc!=SQLITE_OK ){\n    walIndexClose(pRet, 0);\n    sqlite3OsClose(pRet->pWalFd);\n    sqlite3_free(pRet);\n  }else{\n    int iDC = sqlite3OsDeviceCharacteristics(pDbFd);\n    if( iDC & SQLITE_IOCAP_SEQUENTIAL ){ pRet->syncHeader = 0; }\n    if( iDC & SQLITE_IOCAP_POWERSAFE_OVERWRITE ){\n      pRet->padToSectorBoundary = 0;\n    }\n    *ppWal = pRet;\n    WALTRACE((\"WAL%d: opened\\n\", pRet));\n  }\n  return rc;\n}\n\n/*\n** Change the size to which the WAL file is trucated on each reset.\n*/\nSQLITE_PRIVATE void sqlite3WalLimit(Wal *pWal, i64 iLimit){\n  if( pWal ) pWal->mxWalSize = iLimit;\n}\n\n/*\n** Find the smallest page number out of all pages held in the WAL that\n** has not been returned by any prior invocation of this method on the\n** same WalIterator object.   Write into *piFrame the frame index where\n** that page was last written into the WAL.  Write into *piPage the page\n** number.\n**\n** Return 0 on success.  If there are no pages in the WAL with a page\n** number larger than *piPage, then return 1.\n*/\nstatic int walIteratorNext(\n  WalIterator *p,               /* Iterator */\n  u32 *piPage,                  /* OUT: The page number of the next page */\n  u32 *piFrame                  /* OUT: Wal frame index of next page */\n){\n  u32 iMin;                     /* Result pgno must be greater than iMin */\n  u32 iRet = 0xFFFFFFFF;        /* 0xffffffff is never a valid page number */\n  int i;                        /* For looping through segments */\n\n  iMin = p->iPrior;\n  assert( iMin<0xffffffff );\n  for(i=p->nSegment-1; i>=0; i--){\n    struct WalSegment *pSegment = &p->aSegment[i];\n    while( pSegment->iNext<pSegment->nEntry ){\n      u32 iPg = pSegment->aPgno[pSegment->aIndex[pSegment->iNext]];\n      if( iPg>iMin ){\n        if( iPg<iRet ){\n          iRet = iPg;\n          *piFrame = pSegment->iZero + pSegment->aIndex[pSegment->iNext];\n        }\n        break;\n      }\n      pSegment->iNext++;\n    }\n  }\n\n  *piPage = p->iPrior = iRet;\n  return (iRet==0xFFFFFFFF);\n}\n\n/*\n** This function merges two sorted lists into a single sorted list.\n**\n** aLeft[] and aRight[] are arrays of indices.  The sort key is\n** aContent[aLeft[]] and aContent[aRight[]].  Upon entry, the following\n** is guaranteed for all J<K:\n**\n**        aContent[aLeft[J]] < aContent[aLeft[K]]\n**        aContent[aRight[J]] < aContent[aRight[K]]\n**\n** This routine overwrites aRight[] with a new (probably longer) sequence\n** of indices such that the aRight[] contains every index that appears in\n** either aLeft[] or the old aRight[] and such that the second condition\n** above is still met.\n**\n** The aContent[aLeft[X]] values will be unique for all X.  And the\n** aContent[aRight[X]] values will be unique too.  But there might be\n** one or more combinations of X and Y such that\n**\n**      aLeft[X]!=aRight[Y]  &&  aContent[aLeft[X]] == aContent[aRight[Y]]\n**\n** When that happens, omit the aLeft[X] and use the aRight[Y] index.\n*/\nstatic void walMerge(\n  const u32 *aContent,            /* Pages in wal - keys for the sort */\n  ht_slot *aLeft,                 /* IN: Left hand input list */\n  int nLeft,                      /* IN: Elements in array *paLeft */\n  ht_slot **paRight,              /* IN/OUT: Right hand input list */\n  int *pnRight,                   /* IN/OUT: Elements in *paRight */\n  ht_slot *aTmp                   /* Temporary buffer */\n){\n  int iLeft = 0;                  /* Current index in aLeft */\n  int iRight = 0;                 /* Current index in aRight */\n  int iOut = 0;                   /* Current index in output buffer */\n  int nRight = *pnRight;\n  ht_slot *aRight = *paRight;\n\n  assert( nLeft>0 && nRight>0 );\n  while( iRight<nRight || iLeft<nLeft ){\n    ht_slot logpage;\n    Pgno dbpage;\n\n    if( (iLeft<nLeft) \n     && (iRight>=nRight || aContent[aLeft[iLeft]]<aContent[aRight[iRight]])\n    ){\n      logpage = aLeft[iLeft++];\n    }else{\n      logpage = aRight[iRight++];\n    }\n    dbpage = aContent[logpage];\n\n    aTmp[iOut++] = logpage;\n    if( iLeft<nLeft && aContent[aLeft[iLeft]]==dbpage ) iLeft++;\n\n    assert( iLeft>=nLeft || aContent[aLeft[iLeft]]>dbpage );\n    assert( iRight>=nRight || aContent[aRight[iRight]]>dbpage );\n  }\n\n  *paRight = aLeft;\n  *pnRight = iOut;\n  memcpy(aLeft, aTmp, sizeof(aTmp[0])*iOut);\n}\n\n/*\n** Sort the elements in list aList using aContent[] as the sort key.\n** Remove elements with duplicate keys, preferring to keep the\n** larger aList[] values.\n**\n** The aList[] entries are indices into aContent[].  The values in\n** aList[] are to be sorted so that for all J<K:\n**\n**      aContent[aList[J]] < aContent[aList[K]]\n**\n** For any X and Y such that\n**\n**      aContent[aList[X]] == aContent[aList[Y]]\n**\n** Keep the larger of the two values aList[X] and aList[Y] and discard\n** the smaller.\n*/\nstatic void walMergesort(\n  const u32 *aContent,            /* Pages in wal */\n  ht_slot *aBuffer,               /* Buffer of at least *pnList items to use */\n  ht_slot *aList,                 /* IN/OUT: List to sort */\n  int *pnList                     /* IN/OUT: Number of elements in aList[] */\n){\n  struct Sublist {\n    int nList;                    /* Number of elements in aList */\n    ht_slot *aList;               /* Pointer to sub-list content */\n  };\n\n  const int nList = *pnList;      /* Size of input list */\n  int nMerge = 0;                 /* Number of elements in list aMerge */\n  ht_slot *aMerge = 0;            /* List to be merged */\n  int iList;                      /* Index into input list */\n  u32 iSub = 0;                   /* Index into aSub array */\n  struct Sublist aSub[13];        /* Array of sub-lists */\n\n  memset(aSub, 0, sizeof(aSub));\n  assert( nList<=HASHTABLE_NPAGE && nList>0 );\n  assert( HASHTABLE_NPAGE==(1<<(ArraySize(aSub)-1)) );\n\n  for(iList=0; iList<nList; iList++){\n    nMerge = 1;\n    aMerge = &aList[iList];\n    for(iSub=0; iList & (1<<iSub); iSub++){\n      struct Sublist *p;\n      assert( iSub<ArraySize(aSub) );\n      p = &aSub[iSub];\n      assert( p->aList && p->nList<=(1<<iSub) );\n      assert( p->aList==&aList[iList&~((2<<iSub)-1)] );\n      walMerge(aContent, p->aList, p->nList, &aMerge, &nMerge, aBuffer);\n    }\n    aSub[iSub].aList = aMerge;\n    aSub[iSub].nList = nMerge;\n  }\n\n  for(iSub++; iSub<ArraySize(aSub); iSub++){\n    if( nList & (1<<iSub) ){\n      struct Sublist *p;\n      assert( iSub<ArraySize(aSub) );\n      p = &aSub[iSub];\n      assert( p->nList<=(1<<iSub) );\n      assert( p->aList==&aList[nList&~((2<<iSub)-1)] );\n      walMerge(aContent, p->aList, p->nList, &aMerge, &nMerge, aBuffer);\n    }\n  }\n  assert( aMerge==aList );\n  *pnList = nMerge;\n\n#ifdef SQLITE_DEBUG\n  {\n    int i;\n    for(i=1; i<*pnList; i++){\n      assert( aContent[aList[i]] > aContent[aList[i-1]] );\n    }\n  }\n#endif\n}\n\n/* \n** Free an iterator allocated by walIteratorInit().\n*/\nstatic void walIteratorFree(WalIterator *p){\n  sqlite3_free(p);\n}\n\n/*\n** Construct a WalInterator object that can be used to loop over all \n** pages in the WAL in ascending order. The caller must hold the checkpoint\n** lock.\n**\n** On success, make *pp point to the newly allocated WalInterator object\n** return SQLITE_OK. Otherwise, return an error code. If this routine\n** returns an error, the value of *pp is undefined.\n**\n** The calling routine should invoke walIteratorFree() to destroy the\n** WalIterator object when it has finished with it.\n*/\nstatic int walIteratorInit(Wal *pWal, WalIterator **pp){\n  WalIterator *p;                 /* Return value */\n  int nSegment;                   /* Number of segments to merge */\n  u32 iLast;                      /* Last frame in log */\n  int nByte;                      /* Number of bytes to allocate */\n  int i;                          /* Iterator variable */\n  ht_slot *aTmp;                  /* Temp space used by merge-sort */\n  int rc = SQLITE_OK;             /* Return Code */\n\n  /* This routine only runs while holding the checkpoint lock. And\n  ** it only runs if there is actually content in the log (mxFrame>0).\n  */\n  assert( pWal->ckptLock && pWal->hdr.mxFrame>0 );\n  iLast = pWal->hdr.mxFrame;\n\n  /* Allocate space for the WalIterator object. */\n  nSegment = walFramePage(iLast) + 1;\n  nByte = sizeof(WalIterator) \n        + (nSegment-1)*sizeof(struct WalSegment)\n        + iLast*sizeof(ht_slot);\n  p = (WalIterator *)sqlite3_malloc64(nByte);\n  if( !p ){\n    return SQLITE_NOMEM_BKPT;\n  }\n  memset(p, 0, nByte);\n  p->nSegment = nSegment;\n\n  /* Allocate temporary space used by the merge-sort routine. This block\n  ** of memory will be freed before this function returns.\n  */\n  aTmp = (ht_slot *)sqlite3_malloc64(\n      sizeof(ht_slot) * (iLast>HASHTABLE_NPAGE?HASHTABLE_NPAGE:iLast)\n  );\n  if( !aTmp ){\n    rc = SQLITE_NOMEM_BKPT;\n  }\n\n  for(i=0; rc==SQLITE_OK && i<nSegment; i++){\n    volatile ht_slot *aHash;\n    u32 iZero;\n    volatile u32 *aPgno;\n\n    rc = walHashGet(pWal, i, &aHash, &aPgno, &iZero);\n    if( rc==SQLITE_OK ){\n      int j;                      /* Counter variable */\n      int nEntry;                 /* Number of entries in this segment */\n      ht_slot *aIndex;            /* Sorted index for this segment */\n\n      aPgno++;\n      if( (i+1)==nSegment ){\n        nEntry = (int)(iLast - iZero);\n      }else{\n        nEntry = (int)((u32*)aHash - (u32*)aPgno);\n      }\n      aIndex = &((ht_slot *)&p->aSegment[p->nSegment])[iZero];\n      iZero++;\n  \n      for(j=0; j<nEntry; j++){\n        aIndex[j] = (ht_slot)j;\n      }\n      walMergesort((u32 *)aPgno, aTmp, aIndex, &nEntry);\n      p->aSegment[i].iZero = iZero;\n      p->aSegment[i].nEntry = nEntry;\n      p->aSegment[i].aIndex = aIndex;\n      p->aSegment[i].aPgno = (u32 *)aPgno;\n    }\n  }\n  sqlite3_free(aTmp);\n\n  if( rc!=SQLITE_OK ){\n    walIteratorFree(p);\n  }\n  *pp = p;\n  return rc;\n}\n\n/*\n** Attempt to obtain the exclusive WAL lock defined by parameters lockIdx and\n** n. If the attempt fails and parameter xBusy is not NULL, then it is a\n** busy-handler function. Invoke it and retry the lock until either the\n** lock is successfully obtained or the busy-handler returns 0.\n*/\nstatic int walBusyLock(\n  Wal *pWal,                      /* WAL connection */\n  int (*xBusy)(void*),            /* Function to call when busy */\n  void *pBusyArg,                 /* Context argument for xBusyHandler */\n  int lockIdx,                    /* Offset of first byte to lock */\n  int n                           /* Number of bytes to lock */\n){\n  int rc;\n  do {\n    rc = walLockExclusive(pWal, lockIdx, n);\n  }while( xBusy && rc==SQLITE_BUSY && xBusy(pBusyArg) );\n  return rc;\n}\n\n/*\n** The cache of the wal-index header must be valid to call this function.\n** Return the page-size in bytes used by the database.\n*/\nstatic int walPagesize(Wal *pWal){\n  return (pWal->hdr.szPage&0xfe00) + ((pWal->hdr.szPage&0x0001)<<16);\n}\n\n/*\n** The following is guaranteed when this function is called:\n**\n**   a) the WRITER lock is held,\n**   b) the entire log file has been checkpointed, and\n**   c) any existing readers are reading exclusively from the database\n**      file - there are no readers that may attempt to read a frame from\n**      the log file.\n**\n** This function updates the shared-memory structures so that the next\n** client to write to the database (which may be this one) does so by\n** writing frames into the start of the log file.\n**\n** The value of parameter salt1 is used as the aSalt[1] value in the \n** new wal-index header. It should be passed a pseudo-random value (i.e. \n** one obtained from sqlite3_randomness()).\n*/\nstatic void walRestartHdr(Wal *pWal, u32 salt1){\n  volatile WalCkptInfo *pInfo = walCkptInfo(pWal);\n  int i;                          /* Loop counter */\n  u32 *aSalt = pWal->hdr.aSalt;   /* Big-endian salt values */\n  pWal->nCkpt++;\n  pWal->hdr.mxFrame = 0;\n  sqlite3Put4byte((u8*)&aSalt[0], 1 + sqlite3Get4byte((u8*)&aSalt[0]));\n  memcpy(&pWal->hdr.aSalt[1], &salt1, 4);\n  walIndexWriteHdr(pWal);\n  pInfo->nBackfill = 0;\n  pInfo->nBackfillAttempted = 0;\n  pInfo->aReadMark[1] = 0;\n  for(i=2; i<WAL_NREADER; i++) pInfo->aReadMark[i] = READMARK_NOT_USED;\n  assert( pInfo->aReadMark[0]==0 );\n}\n\n/*\n** Copy as much content as we can from the WAL back into the database file\n** in response to an sqlite3_wal_checkpoint() request or the equivalent.\n**\n** The amount of information copies from WAL to database might be limited\n** by active readers.  This routine will never overwrite a database page\n** that a concurrent reader might be using.\n**\n** All I/O barrier operations (a.k.a fsyncs) occur in this routine when\n** SQLite is in WAL-mode in synchronous=NORMAL.  That means that if \n** checkpoints are always run by a background thread or background \n** process, foreground threads will never block on a lengthy fsync call.\n**\n** Fsync is called on the WAL before writing content out of the WAL and\n** into the database.  This ensures that if the new content is persistent\n** in the WAL and can be recovered following a power-loss or hard reset.\n**\n** Fsync is also called on the database file if (and only if) the entire\n** WAL content is copied into the database file.  This second fsync makes\n** it safe to delete the WAL since the new content will persist in the\n** database file.\n**\n** This routine uses and updates the nBackfill field of the wal-index header.\n** This is the only routine that will increase the value of nBackfill.  \n** (A WAL reset or recovery will revert nBackfill to zero, but not increase\n** its value.)\n**\n** The caller must be holding sufficient locks to ensure that no other\n** checkpoint is running (in any other thread or process) at the same\n** time.\n*/\nstatic int walCheckpoint(\n  Wal *pWal,                      /* Wal connection */\n  sqlite3 *db,                    /* Check for interrupts on this handle */\n  int eMode,                      /* One of PASSIVE, FULL or RESTART */\n  int (*xBusy)(void*),            /* Function to call when busy */\n  void *pBusyArg,                 /* Context argument for xBusyHandler */\n  int sync_flags,                 /* Flags for OsSync() (or 0) */\n  u8 *zBuf                        /* Temporary buffer to use */\n){\n  int rc = SQLITE_OK;             /* Return code */\n  int szPage;                     /* Database page-size */\n  WalIterator *pIter = 0;         /* Wal iterator context */\n  u32 iDbpage = 0;                /* Next database page to write */\n  u32 iFrame = 0;                 /* Wal frame containing data for iDbpage */\n  u32 mxSafeFrame;                /* Max frame that can be backfilled */\n  u32 mxPage;                     /* Max database page to write */\n  int i;                          /* Loop counter */\n  volatile WalCkptInfo *pInfo;    /* The checkpoint status information */\n\n  szPage = walPagesize(pWal);\n  testcase( szPage<=32768 );\n  testcase( szPage>=65536 );\n  pInfo = walCkptInfo(pWal);\n  if( pInfo->nBackfill<pWal->hdr.mxFrame ){\n\n    /* Allocate the iterator */\n    rc = walIteratorInit(pWal, &pIter);\n    if( rc!=SQLITE_OK ){\n      return rc;\n    }\n    assert( pIter );\n\n    /* EVIDENCE-OF: R-62920-47450 The busy-handler callback is never invoked\n    ** in the SQLITE_CHECKPOINT_PASSIVE mode. */\n    assert( eMode!=SQLITE_CHECKPOINT_PASSIVE || xBusy==0 );\n\n    /* Compute in mxSafeFrame the index of the last frame of the WAL that is\n    ** safe to write into the database.  Frames beyond mxSafeFrame might\n    ** overwrite database pages that are in use by active readers and thus\n    ** cannot be backfilled from the WAL.\n    */\n    mxSafeFrame = pWal->hdr.mxFrame;\n    mxPage = pWal->hdr.nPage;\n    for(i=1; i<WAL_NREADER; i++){\n      /* Thread-sanitizer reports that the following is an unsafe read,\n      ** as some other thread may be in the process of updating the value\n      ** of the aReadMark[] slot. The assumption here is that if that is\n      ** happening, the other client may only be increasing the value,\n      ** not decreasing it. So assuming either that either the \"old\" or\n      ** \"new\" version of the value is read, and not some arbitrary value\n      ** that would never be written by a real client, things are still \n      ** safe.  */\n      u32 y = pInfo->aReadMark[i];\n      if( mxSafeFrame>y ){\n        assert( y<=pWal->hdr.mxFrame );\n        rc = walBusyLock(pWal, xBusy, pBusyArg, WAL_READ_LOCK(i), 1);\n        if( rc==SQLITE_OK ){\n          pInfo->aReadMark[i] = (i==1 ? mxSafeFrame : READMARK_NOT_USED);\n          walUnlockExclusive(pWal, WAL_READ_LOCK(i), 1);\n        }else if( rc==SQLITE_BUSY ){\n          mxSafeFrame = y;\n          xBusy = 0;\n        }else{\n          goto walcheckpoint_out;\n        }\n      }\n    }\n\n    if( pInfo->nBackfill<mxSafeFrame\n     && (rc = walBusyLock(pWal, xBusy, pBusyArg, WAL_READ_LOCK(0),1))==SQLITE_OK\n    ){\n      i64 nSize;                    /* Current size of database file */\n      u32 nBackfill = pInfo->nBackfill;\n\n      pInfo->nBackfillAttempted = mxSafeFrame;\n\n      /* Sync the WAL to disk */\n      rc = sqlite3OsSync(pWal->pWalFd, CKPT_SYNC_FLAGS(sync_flags));\n\n      /* If the database may grow as a result of this checkpoint, hint\n      ** about the eventual size of the db file to the VFS layer.\n      */\n      if( rc==SQLITE_OK ){\n        i64 nReq = ((i64)mxPage * szPage);\n        rc = sqlite3OsFileSize(pWal->pDbFd, &nSize);\n        if( rc==SQLITE_OK && nSize<nReq ){\n          sqlite3OsFileControlHint(pWal->pDbFd, SQLITE_FCNTL_SIZE_HINT, &nReq);\n        }\n      }\n\n\n      /* Iterate through the contents of the WAL, copying data to the db file */\n      while( rc==SQLITE_OK && 0==walIteratorNext(pIter, &iDbpage, &iFrame) ){\n        i64 iOffset;\n        assert( walFramePgno(pWal, iFrame)==iDbpage );\n        if( db->u1.isInterrupted ){\n          rc = db->mallocFailed ? SQLITE_NOMEM_BKPT : SQLITE_INTERRUPT;\n          break;\n        }\n        if( iFrame<=nBackfill || iFrame>mxSafeFrame || iDbpage>mxPage ){\n          continue;\n        }\n        iOffset = walFrameOffset(iFrame, szPage) + WAL_FRAME_HDRSIZE;\n        /* testcase( IS_BIG_INT(iOffset) ); // requires a 4GiB WAL file */\n        rc = sqlite3OsRead(pWal->pWalFd, zBuf, szPage, iOffset);\n        if( rc!=SQLITE_OK ) break;\n        iOffset = (iDbpage-1)*(i64)szPage;\n        testcase( IS_BIG_INT(iOffset) );\n        rc = sqlite3OsWrite(pWal->pDbFd, zBuf, szPage, iOffset);\n        if( rc!=SQLITE_OK ) break;\n      }\n\n      /* If work was actually accomplished... */\n      if( rc==SQLITE_OK ){\n        if( mxSafeFrame==walIndexHdr(pWal)->mxFrame ){\n          i64 szDb = pWal->hdr.nPage*(i64)szPage;\n          testcase( IS_BIG_INT(szDb) );\n          rc = sqlite3OsTruncate(pWal->pDbFd, szDb);\n          if( rc==SQLITE_OK ){\n            rc = sqlite3OsSync(pWal->pDbFd, CKPT_SYNC_FLAGS(sync_flags));\n          }\n        }\n        if( rc==SQLITE_OK ){\n          pInfo->nBackfill = mxSafeFrame;\n        }\n      }\n\n      /* Release the reader lock held while backfilling */\n      walUnlockExclusive(pWal, WAL_READ_LOCK(0), 1);\n    }\n\n    if( rc==SQLITE_BUSY ){\n      /* Reset the return code so as not to report a checkpoint failure\n      ** just because there are active readers.  */\n      rc = SQLITE_OK;\n    }\n  }\n\n  /* If this is an SQLITE_CHECKPOINT_RESTART or TRUNCATE operation, and the\n  ** entire wal file has been copied into the database file, then block \n  ** until all readers have finished using the wal file. This ensures that \n  ** the next process to write to the database restarts the wal file.\n  */\n  if( rc==SQLITE_OK && eMode!=SQLITE_CHECKPOINT_PASSIVE ){\n    assert( pWal->writeLock );\n    if( pInfo->nBackfill<pWal->hdr.mxFrame ){\n      rc = SQLITE_BUSY;\n    }else if( eMode>=SQLITE_CHECKPOINT_RESTART ){\n      u32 salt1;\n      sqlite3_randomness(4, &salt1);\n      assert( pInfo->nBackfill==pWal->hdr.mxFrame );\n      rc = walBusyLock(pWal, xBusy, pBusyArg, WAL_READ_LOCK(1), WAL_NREADER-1);\n      if( rc==SQLITE_OK ){\n        if( eMode==SQLITE_CHECKPOINT_TRUNCATE ){\n          /* IMPLEMENTATION-OF: R-44699-57140 This mode works the same way as\n          ** SQLITE_CHECKPOINT_RESTART with the addition that it also\n          ** truncates the log file to zero bytes just prior to a\n          ** successful return.\n          **\n          ** In theory, it might be safe to do this without updating the\n          ** wal-index header in shared memory, as all subsequent reader or\n          ** writer clients should see that the entire log file has been\n          ** checkpointed and behave accordingly. This seems unsafe though,\n          ** as it would leave the system in a state where the contents of\n          ** the wal-index header do not match the contents of the \n          ** file-system. To avoid this, update the wal-index header to\n          ** indicate that the log file contains zero valid frames.  */\n          walRestartHdr(pWal, salt1);\n          rc = sqlite3OsTruncate(pWal->pWalFd, 0);\n        }\n        walUnlockExclusive(pWal, WAL_READ_LOCK(1), WAL_NREADER-1);\n      }\n    }\n  }\n\n walcheckpoint_out:\n  walIteratorFree(pIter);\n  return rc;\n}\n\n/*\n** If the WAL file is currently larger than nMax bytes in size, truncate\n** it to exactly nMax bytes. If an error occurs while doing so, ignore it.\n*/\nstatic void walLimitSize(Wal *pWal, i64 nMax){\n  i64 sz;\n  int rx;\n  sqlite3BeginBenignMalloc();\n  rx = sqlite3OsFileSize(pWal->pWalFd, &sz);\n  if( rx==SQLITE_OK && (sz > nMax ) ){\n    rx = sqlite3OsTruncate(pWal->pWalFd, nMax);\n  }\n  sqlite3EndBenignMalloc();\n  if( rx ){\n    sqlite3_log(rx, \"cannot limit WAL size: %s\", pWal->zWalName);\n  }\n}\n\n/*\n** Close a connection to a log file.\n*/\nSQLITE_PRIVATE int sqlite3WalClose(\n  Wal *pWal,                      /* Wal to close */\n  sqlite3 *db,                    /* For interrupt flag */\n  int sync_flags,                 /* Flags to pass to OsSync() (or 0) */\n  int nBuf,\n  u8 *zBuf                        /* Buffer of at least nBuf bytes */\n){\n  int rc = SQLITE_OK;\n  if( pWal ){\n    int isDelete = 0;             /* True to unlink wal and wal-index files */\n\n    /* If an EXCLUSIVE lock can be obtained on the database file (using the\n    ** ordinary, rollback-mode locking methods, this guarantees that the\n    ** connection associated with this log file is the only connection to\n    ** the database. In this case checkpoint the database and unlink both\n    ** the wal and wal-index files.\n    **\n    ** The EXCLUSIVE lock is not released before returning.\n    */\n    if( zBuf!=0\n     && SQLITE_OK==(rc = sqlite3OsLock(pWal->pDbFd, SQLITE_LOCK_EXCLUSIVE))\n    ){\n      if( pWal->exclusiveMode==WAL_NORMAL_MODE ){\n        pWal->exclusiveMode = WAL_EXCLUSIVE_MODE;\n      }\n      rc = sqlite3WalCheckpoint(pWal, db, \n          SQLITE_CHECKPOINT_PASSIVE, 0, 0, sync_flags, nBuf, zBuf, 0, 0\n      );\n      if( rc==SQLITE_OK ){\n        int bPersist = -1;\n        sqlite3OsFileControlHint(\n            pWal->pDbFd, SQLITE_FCNTL_PERSIST_WAL, &bPersist\n        );\n        if( bPersist!=1 ){\n          /* Try to delete the WAL file if the checkpoint completed and\n          ** fsyned (rc==SQLITE_OK) and if we are not in persistent-wal\n          ** mode (!bPersist) */\n          isDelete = 1;\n        }else if( pWal->mxWalSize>=0 ){\n          /* Try to truncate the WAL file to zero bytes if the checkpoint\n          ** completed and fsynced (rc==SQLITE_OK) and we are in persistent\n          ** WAL mode (bPersist) and if the PRAGMA journal_size_limit is a\n          ** non-negative value (pWal->mxWalSize>=0).  Note that we truncate\n          ** to zero bytes as truncating to the journal_size_limit might\n          ** leave a corrupt WAL file on disk. */\n          walLimitSize(pWal, 0);\n        }\n      }\n    }\n\n    walIndexClose(pWal, isDelete);\n    sqlite3OsClose(pWal->pWalFd);\n    if( isDelete ){\n      sqlite3BeginBenignMalloc();\n      sqlite3OsDelete(pWal->pVfs, pWal->zWalName, 0);\n      sqlite3EndBenignMalloc();\n    }\n    WALTRACE((\"WAL%p: closed\\n\", pWal));\n    sqlite3_free((void *)pWal->apWiData);\n    sqlite3_free(pWal);\n  }\n  return rc;\n}\n\n/*\n** Try to read the wal-index header.  Return 0 on success and 1 if\n** there is a problem.\n**\n** The wal-index is in shared memory.  Another thread or process might\n** be writing the header at the same time this procedure is trying to\n** read it, which might result in inconsistency.  A dirty read is detected\n** by verifying that both copies of the header are the same and also by\n** a checksum on the header.\n**\n** If and only if the read is consistent and the header is different from\n** pWal->hdr, then pWal->hdr is updated to the content of the new header\n** and *pChanged is set to 1.\n**\n** If the checksum cannot be verified return non-zero. If the header\n** is read successfully and the checksum verified, return zero.\n*/\nstatic int walIndexTryHdr(Wal *pWal, int *pChanged){\n  u32 aCksum[2];                  /* Checksum on the header content */\n  WalIndexHdr h1, h2;             /* Two copies of the header content */\n  WalIndexHdr volatile *aHdr;     /* Header in shared memory */\n\n  /* The first page of the wal-index must be mapped at this point. */\n  assert( pWal->nWiData>0 && pWal->apWiData[0] );\n\n  /* Read the header. This might happen concurrently with a write to the\n  ** same area of shared memory on a different CPU in a SMP,\n  ** meaning it is possible that an inconsistent snapshot is read\n  ** from the file. If this happens, return non-zero.\n  **\n  ** There are two copies of the header at the beginning of the wal-index.\n  ** When reading, read [0] first then [1].  Writes are in the reverse order.\n  ** Memory barriers are used to prevent the compiler or the hardware from\n  ** reordering the reads and writes.\n  */\n  aHdr = walIndexHdr(pWal);\n  memcpy(&h1, (void *)&aHdr[0], sizeof(h1));\n  walShmBarrier(pWal);\n  memcpy(&h2, (void *)&aHdr[1], sizeof(h2));\n\n  if( memcmp(&h1, &h2, sizeof(h1))!=0 ){\n    return 1;   /* Dirty read */\n  }  \n  if( h1.isInit==0 ){\n    return 1;   /* Malformed header - probably all zeros */\n  }\n  walChecksumBytes(1, (u8*)&h1, sizeof(h1)-sizeof(h1.aCksum), 0, aCksum);\n  if( aCksum[0]!=h1.aCksum[0] || aCksum[1]!=h1.aCksum[1] ){\n    return 1;   /* Checksum does not match */\n  }\n\n  if( memcmp(&pWal->hdr, &h1, sizeof(WalIndexHdr)) ){\n    *pChanged = 1;\n    memcpy(&pWal->hdr, &h1, sizeof(WalIndexHdr));\n    pWal->szPage = (pWal->hdr.szPage&0xfe00) + ((pWal->hdr.szPage&0x0001)<<16);\n    testcase( pWal->szPage<=32768 );\n    testcase( pWal->szPage>=65536 );\n  }\n\n  /* The header was successfully read. Return zero. */\n  return 0;\n}\n\n/*\n** This is the value that walTryBeginRead returns when it needs to\n** be retried.\n*/\n#define WAL_RETRY  (-1)\n\n/*\n** Read the wal-index header from the wal-index and into pWal->hdr.\n** If the wal-header appears to be corrupt, try to reconstruct the\n** wal-index from the WAL before returning.\n**\n** Set *pChanged to 1 if the wal-index header value in pWal->hdr is\n** changed by this operation.  If pWal->hdr is unchanged, set *pChanged\n** to 0.\n**\n** If the wal-index header is successfully read, return SQLITE_OK. \n** Otherwise an SQLite error code.\n*/\nstatic int walIndexReadHdr(Wal *pWal, int *pChanged){\n  int rc;                         /* Return code */\n  int badHdr;                     /* True if a header read failed */\n  volatile u32 *page0;            /* Chunk of wal-index containing header */\n\n  /* Ensure that page 0 of the wal-index (the page that contains the \n  ** wal-index header) is mapped. Return early if an error occurs here.\n  */\n  assert( pChanged );\n  rc = walIndexPage(pWal, 0, &page0);\n  if( rc!=SQLITE_OK ){\n    assert( rc!=SQLITE_READONLY ); /* READONLY changed to OK in walIndexPage */\n    if( rc==SQLITE_READONLY_CANTINIT ){\n      /* The SQLITE_READONLY_CANTINIT return means that the shared-memory\n      ** was openable but is not writable, and this thread is unable to\n      ** confirm that another write-capable connection has the shared-memory\n      ** open, and hence the content of the shared-memory is unreliable,\n      ** since the shared-memory might be inconsistent with the WAL file\n      ** and there is no writer on hand to fix it. */\n      assert( page0==0 );\n      assert( pWal->writeLock==0 );\n      assert( pWal->readOnly & WAL_SHM_RDONLY );\n      pWal->bShmUnreliable = 1;\n      pWal->exclusiveMode = WAL_HEAPMEMORY_MODE;\n      *pChanged = 1;\n    }else{\n      return rc; /* Any other non-OK return is just an error */\n    }\n  }else{\n    /* page0 can be NULL if the SHM is zero bytes in size and pWal->writeLock\n    ** is zero, which prevents the SHM from growing */\n    testcase( page0!=0 );\n  }\n  assert( page0!=0 || pWal->writeLock==0 );\n\n  /* If the first page of the wal-index has been mapped, try to read the\n  ** wal-index header immediately, without holding any lock. This usually\n  ** works, but may fail if the wal-index header is corrupt or currently \n  ** being modified by another thread or process.\n  */\n  badHdr = (page0 ? walIndexTryHdr(pWal, pChanged) : 1);\n\n  /* If the first attempt failed, it might have been due to a race\n  ** with a writer.  So get a WRITE lock and try again.\n  */\n  assert( badHdr==0 || pWal->writeLock==0 );\n  if( badHdr ){\n    if( pWal->bShmUnreliable==0 && (pWal->readOnly & WAL_SHM_RDONLY) ){\n      if( SQLITE_OK==(rc = walLockShared(pWal, WAL_WRITE_LOCK)) ){\n        walUnlockShared(pWal, WAL_WRITE_LOCK);\n        rc = SQLITE_READONLY_RECOVERY;\n      }\n    }else if( SQLITE_OK==(rc = walLockExclusive(pWal, WAL_WRITE_LOCK, 1)) ){\n      pWal->writeLock = 1;\n      if( SQLITE_OK==(rc = walIndexPage(pWal, 0, &page0)) ){\n        badHdr = walIndexTryHdr(pWal, pChanged);\n        if( badHdr ){\n          /* If the wal-index header is still malformed even while holding\n          ** a WRITE lock, it can only mean that the header is corrupted and\n          ** needs to be reconstructed.  So run recovery to do exactly that.\n          */\n          rc = walIndexRecover(pWal);\n          *pChanged = 1;\n        }\n      }\n      pWal->writeLock = 0;\n      walUnlockExclusive(pWal, WAL_WRITE_LOCK, 1);\n    }\n  }\n\n  /* If the header is read successfully, check the version number to make\n  ** sure the wal-index was not constructed with some future format that\n  ** this version of SQLite cannot understand.\n  */\n  if( badHdr==0 && pWal->hdr.iVersion!=WALINDEX_MAX_VERSION ){\n    rc = SQLITE_CANTOPEN_BKPT;\n  }\n  if( pWal->bShmUnreliable ){\n    if( rc!=SQLITE_OK ){\n      walIndexClose(pWal, 0);\n      pWal->bShmUnreliable = 0;\n      assert( pWal->nWiData>0 && pWal->apWiData[0]==0 );\n      /* walIndexRecover() might have returned SHORT_READ if a concurrent\n      ** writer truncated the WAL out from under it.  If that happens, it\n      ** indicates that a writer has fixed the SHM file for us, so retry */\n      if( rc==SQLITE_IOERR_SHORT_READ ) rc = WAL_RETRY;\n    }\n    pWal->exclusiveMode = WAL_NORMAL_MODE;\n  }\n\n  return rc;\n}\n\n/*\n** Open a transaction in a connection where the shared-memory is read-only\n** and where we cannot verify that there is a separate write-capable connection\n** on hand to keep the shared-memory up-to-date with the WAL file.\n**\n** This can happen, for example, when the shared-memory is implemented by\n** memory-mapping a *-shm file, where a prior writer has shut down and\n** left the *-shm file on disk, and now the present connection is trying\n** to use that database but lacks write permission on the *-shm file.\n** Other scenarios are also possible, depending on the VFS implementation.\n**\n** Precondition:\n**\n**    The *-wal file has been read and an appropriate wal-index has been\n**    constructed in pWal->apWiData[] using heap memory instead of shared\n**    memory. \n**\n** If this function returns SQLITE_OK, then the read transaction has\n** been successfully opened. In this case output variable (*pChanged) \n** is set to true before returning if the caller should discard the\n** contents of the page cache before proceeding. Or, if it returns \n** WAL_RETRY, then the heap memory wal-index has been discarded and \n** the caller should retry opening the read transaction from the \n** beginning (including attempting to map the *-shm file). \n**\n** If an error occurs, an SQLite error code is returned.\n*/\nstatic int walBeginShmUnreliable(Wal *pWal, int *pChanged){\n  i64 szWal;                      /* Size of wal file on disk in bytes */\n  i64 iOffset;                    /* Current offset when reading wal file */\n  u8 aBuf[WAL_HDRSIZE];           /* Buffer to load WAL header into */\n  u8 *aFrame = 0;                 /* Malloc'd buffer to load entire frame */\n  int szFrame;                    /* Number of bytes in buffer aFrame[] */\n  u8 *aData;                      /* Pointer to data part of aFrame buffer */\n  volatile void *pDummy;          /* Dummy argument for xShmMap */\n  int rc;                         /* Return code */\n  u32 aSaveCksum[2];              /* Saved copy of pWal->hdr.aFrameCksum */\n\n  assert( pWal->bShmUnreliable );\n  assert( pWal->readOnly & WAL_SHM_RDONLY );\n  assert( pWal->nWiData>0 && pWal->apWiData[0] );\n\n  /* Take WAL_READ_LOCK(0). This has the effect of preventing any\n  ** writers from running a checkpoint, but does not stop them\n  ** from running recovery.  */\n  rc = walLockShared(pWal, WAL_READ_LOCK(0));\n  if( rc!=SQLITE_OK ){\n    if( rc==SQLITE_BUSY ) rc = WAL_RETRY;\n    goto begin_unreliable_shm_out;\n  }\n  pWal->readLock = 0;\n\n  /* Check to see if a separate writer has attached to the shared-memory area,\n  ** thus making the shared-memory \"reliable\" again.  Do this by invoking\n  ** the xShmMap() routine of the VFS and looking to see if the return\n  ** is SQLITE_READONLY instead of SQLITE_READONLY_CANTINIT.\n  **\n  ** If the shared-memory is now \"reliable\" return WAL_RETRY, which will\n  ** cause the heap-memory WAL-index to be discarded and the actual\n  ** shared memory to be used in its place.\n  **\n  ** This step is important because, even though this connection is holding\n  ** the WAL_READ_LOCK(0) which prevents a checkpoint, a writer might\n  ** have already checkpointed the WAL file and, while the current\n  ** is active, wrap the WAL and start overwriting frames that this\n  ** process wants to use.\n  **\n  ** Once sqlite3OsShmMap() has been called for an sqlite3_file and has\n  ** returned any SQLITE_READONLY value, it must return only SQLITE_READONLY\n  ** or SQLITE_READONLY_CANTINIT or some error for all subsequent invocations,\n  ** even if some external agent does a \"chmod\" to make the shared-memory\n  ** writable by us, until sqlite3OsShmUnmap() has been called.\n  ** This is a requirement on the VFS implementation.\n   */\n  rc = sqlite3OsShmMap(pWal->pDbFd, 0, WALINDEX_PGSZ, 0, &pDummy);\n  assert( rc!=SQLITE_OK ); /* SQLITE_OK not possible for read-only connection */\n  if( rc!=SQLITE_READONLY_CANTINIT ){\n    rc = (rc==SQLITE_READONLY ? WAL_RETRY : rc);\n    goto begin_unreliable_shm_out;\n  }\n\n  /* We reach this point only if the real shared-memory is still unreliable.\n  ** Assume the in-memory WAL-index substitute is correct and load it\n  ** into pWal->hdr.\n  */\n  memcpy(&pWal->hdr, (void*)walIndexHdr(pWal), sizeof(WalIndexHdr));\n\n  /* Make sure some writer hasn't come in and changed the WAL file out\n  ** from under us, then disconnected, while we were not looking.\n  */\n  rc = sqlite3OsFileSize(pWal->pWalFd, &szWal);\n  if( rc!=SQLITE_OK ){\n    goto begin_unreliable_shm_out;\n  }\n  if( szWal<WAL_HDRSIZE ){\n    /* If the wal file is too small to contain a wal-header and the\n    ** wal-index header has mxFrame==0, then it must be safe to proceed\n    ** reading the database file only. However, the page cache cannot\n    ** be trusted, as a read/write connection may have connected, written\n    ** the db, run a checkpoint, truncated the wal file and disconnected\n    ** since this client's last read transaction.  */\n    *pChanged = 1;\n    rc = (pWal->hdr.mxFrame==0 ? SQLITE_OK : WAL_RETRY);\n    goto begin_unreliable_shm_out;\n  }\n\n  /* Check the salt keys at the start of the wal file still match. */\n  rc = sqlite3OsRead(pWal->pWalFd, aBuf, WAL_HDRSIZE, 0);\n  if( rc!=SQLITE_OK ){\n    goto begin_unreliable_shm_out;\n  }\n  if( memcmp(&pWal->hdr.aSalt, &aBuf[16], 8) ){\n    /* Some writer has wrapped the WAL file while we were not looking.\n    ** Return WAL_RETRY which will cause the in-memory WAL-index to be\n    ** rebuilt. */\n    rc = WAL_RETRY;\n    goto begin_unreliable_shm_out;\n  }\n\n  /* Allocate a buffer to read frames into */\n  szFrame = pWal->hdr.szPage + WAL_FRAME_HDRSIZE;\n  aFrame = (u8 *)sqlite3_malloc64(szFrame);\n  if( aFrame==0 ){\n    rc = SQLITE_NOMEM_BKPT;\n    goto begin_unreliable_shm_out;\n  }\n  aData = &aFrame[WAL_FRAME_HDRSIZE];\n\n  /* Check to see if a complete transaction has been appended to the\n  ** wal file since the heap-memory wal-index was created. If so, the\n  ** heap-memory wal-index is discarded and WAL_RETRY returned to\n  ** the caller.  */\n  aSaveCksum[0] = pWal->hdr.aFrameCksum[0];\n  aSaveCksum[1] = pWal->hdr.aFrameCksum[1];\n  for(iOffset=walFrameOffset(pWal->hdr.mxFrame+1, pWal->hdr.szPage); \n      iOffset+szFrame<=szWal; \n      iOffset+=szFrame\n  ){\n    u32 pgno;                   /* Database page number for frame */\n    u32 nTruncate;              /* dbsize field from frame header */\n\n    /* Read and decode the next log frame. */\n    rc = sqlite3OsRead(pWal->pWalFd, aFrame, szFrame, iOffset);\n    if( rc!=SQLITE_OK ) break;\n    if( !walDecodeFrame(pWal, &pgno, &nTruncate, aData, aFrame) ) break;\n\n    /* If nTruncate is non-zero, then a complete transaction has been\n    ** appended to this wal file. Set rc to WAL_RETRY and break out of\n    ** the loop.  */\n    if( nTruncate ){\n      rc = WAL_RETRY;\n      break;\n    }\n  }\n  pWal->hdr.aFrameCksum[0] = aSaveCksum[0];\n  pWal->hdr.aFrameCksum[1] = aSaveCksum[1];\n\n begin_unreliable_shm_out:\n  sqlite3_free(aFrame);\n  if( rc!=SQLITE_OK ){\n    int i;\n    for(i=0; i<pWal->nWiData; i++){\n      sqlite3_free((void*)pWal->apWiData[i]);\n      pWal->apWiData[i] = 0;\n    }\n    pWal->bShmUnreliable = 0;\n    sqlite3WalEndReadTransaction(pWal);\n    *pChanged = 1;\n  }\n  return rc;\n}\n\n/*\n** Attempt to start a read transaction.  This might fail due to a race or\n** other transient condition.  When that happens, it returns WAL_RETRY to\n** indicate to the caller that it is safe to retry immediately.\n**\n** On success return SQLITE_OK.  On a permanent failure (such an\n** I/O error or an SQLITE_BUSY because another process is running\n** recovery) return a positive error code.\n**\n** The useWal parameter is true to force the use of the WAL and disable\n** the case where the WAL is bypassed because it has been completely\n** checkpointed.  If useWal==0 then this routine calls walIndexReadHdr() \n** to make a copy of the wal-index header into pWal->hdr.  If the \n** wal-index header has changed, *pChanged is set to 1 (as an indication \n** to the caller that the local page cache is obsolete and needs to be \n** flushed.)  When useWal==1, the wal-index header is assumed to already\n** be loaded and the pChanged parameter is unused.\n**\n** The caller must set the cnt parameter to the number of prior calls to\n** this routine during the current read attempt that returned WAL_RETRY.\n** This routine will start taking more aggressive measures to clear the\n** race conditions after multiple WAL_RETRY returns, and after an excessive\n** number of errors will ultimately return SQLITE_PROTOCOL.  The\n** SQLITE_PROTOCOL return indicates that some other process has gone rogue\n** and is not honoring the locking protocol.  There is a vanishingly small\n** chance that SQLITE_PROTOCOL could be returned because of a run of really\n** bad luck when there is lots of contention for the wal-index, but that\n** possibility is so small that it can be safely neglected, we believe.\n**\n** On success, this routine obtains a read lock on \n** WAL_READ_LOCK(pWal->readLock).  The pWal->readLock integer is\n** in the range 0 <= pWal->readLock < WAL_NREADER.  If pWal->readLock==(-1)\n** that means the Wal does not hold any read lock.  The reader must not\n** access any database page that is modified by a WAL frame up to and\n** including frame number aReadMark[pWal->readLock].  The reader will\n** use WAL frames up to and including pWal->hdr.mxFrame if pWal->readLock>0\n** Or if pWal->readLock==0, then the reader will ignore the WAL\n** completely and get all content directly from the database file.\n** If the useWal parameter is 1 then the WAL will never be ignored and\n** this routine will always set pWal->readLock>0 on success.\n** When the read transaction is completed, the caller must release the\n** lock on WAL_READ_LOCK(pWal->readLock) and set pWal->readLock to -1.\n**\n** This routine uses the nBackfill and aReadMark[] fields of the header\n** to select a particular WAL_READ_LOCK() that strives to let the\n** checkpoint process do as much work as possible.  This routine might\n** update values of the aReadMark[] array in the header, but if it does\n** so it takes care to hold an exclusive lock on the corresponding\n** WAL_READ_LOCK() while changing values.\n*/\nstatic int walTryBeginRead(Wal *pWal, int *pChanged, int useWal, int cnt){\n  volatile WalCkptInfo *pInfo;    /* Checkpoint information in wal-index */\n  u32 mxReadMark;                 /* Largest aReadMark[] value */\n  int mxI;                        /* Index of largest aReadMark[] value */\n  int i;                          /* Loop counter */\n  int rc = SQLITE_OK;             /* Return code  */\n  u32 mxFrame;                    /* Wal frame to lock to */\n\n  assert( pWal->readLock<0 );     /* Not currently locked */\n\n  /* useWal may only be set for read/write connections */\n  assert( (pWal->readOnly & WAL_SHM_RDONLY)==0 || useWal==0 );\n\n  /* Take steps to avoid spinning forever if there is a protocol error.\n  **\n  ** Circumstances that cause a RETRY should only last for the briefest\n  ** instances of time.  No I/O or other system calls are done while the\n  ** locks are held, so the locks should not be held for very long. But \n  ** if we are unlucky, another process that is holding a lock might get\n  ** paged out or take a page-fault that is time-consuming to resolve, \n  ** during the few nanoseconds that it is holding the lock.  In that case,\n  ** it might take longer than normal for the lock to free.\n  **\n  ** After 5 RETRYs, we begin calling sqlite3OsSleep().  The first few\n  ** calls to sqlite3OsSleep() have a delay of 1 microsecond.  Really this\n  ** is more of a scheduler yield than an actual delay.  But on the 10th\n  ** an subsequent retries, the delays start becoming longer and longer, \n  ** so that on the 100th (and last) RETRY we delay for 323 milliseconds.\n  ** The total delay time before giving up is less than 10 seconds.\n  */\n  if( cnt>5 ){\n    int nDelay = 1;                      /* Pause time in microseconds */\n    if( cnt>100 ){\n      VVA_ONLY( pWal->lockError = 1; )\n      return SQLITE_PROTOCOL;\n    }\n    if( cnt>=10 ) nDelay = (cnt-9)*(cnt-9)*39;\n    sqlite3OsSleep(pWal->pVfs, nDelay);\n  }\n\n  if( !useWal ){\n    assert( rc==SQLITE_OK );\n    if( pWal->bShmUnreliable==0 ){\n      rc = walIndexReadHdr(pWal, pChanged);\n    }\n    if( rc==SQLITE_BUSY ){\n      /* If there is not a recovery running in another thread or process\n      ** then convert BUSY errors to WAL_RETRY.  If recovery is known to\n      ** be running, convert BUSY to BUSY_RECOVERY.  There is a race here\n      ** which might cause WAL_RETRY to be returned even if BUSY_RECOVERY\n      ** would be technically correct.  But the race is benign since with\n      ** WAL_RETRY this routine will be called again and will probably be\n      ** right on the second iteration.\n      */\n      if( pWal->apWiData[0]==0 ){\n        /* This branch is taken when the xShmMap() method returns SQLITE_BUSY.\n        ** We assume this is a transient condition, so return WAL_RETRY. The\n        ** xShmMap() implementation used by the default unix and win32 VFS \n        ** modules may return SQLITE_BUSY due to a race condition in the \n        ** code that determines whether or not the shared-memory region \n        ** must be zeroed before the requested page is returned.\n        */\n        rc = WAL_RETRY;\n      }else if( SQLITE_OK==(rc = walLockShared(pWal, WAL_RECOVER_LOCK)) ){\n        walUnlockShared(pWal, WAL_RECOVER_LOCK);\n        rc = WAL_RETRY;\n      }else if( rc==SQLITE_BUSY ){\n        rc = SQLITE_BUSY_RECOVERY;\n      }\n    }\n    if( rc!=SQLITE_OK ){\n      return rc;\n    }\n    else if( pWal->bShmUnreliable ){\n      return walBeginShmUnreliable(pWal, pChanged);\n    }\n  }\n\n  assert( pWal->nWiData>0 );\n  assert( pWal->apWiData[0]!=0 );\n  pInfo = walCkptInfo(pWal);\n  if( !useWal && pInfo->nBackfill==pWal->hdr.mxFrame\n#ifdef SQLITE_ENABLE_SNAPSHOT\n   && (pWal->pSnapshot==0 || pWal->hdr.mxFrame==0)\n#endif\n  ){\n    /* The WAL has been completely backfilled (or it is empty).\n    ** and can be safely ignored.\n    */\n    rc = walLockShared(pWal, WAL_READ_LOCK(0));\n    walShmBarrier(pWal);\n    if( rc==SQLITE_OK ){\n      if( memcmp((void *)walIndexHdr(pWal), &pWal->hdr, sizeof(WalIndexHdr)) ){\n        /* It is not safe to allow the reader to continue here if frames\n        ** may have been appended to the log before READ_LOCK(0) was obtained.\n        ** When holding READ_LOCK(0), the reader ignores the entire log file,\n        ** which implies that the database file contains a trustworthy\n        ** snapshot. Since holding READ_LOCK(0) prevents a checkpoint from\n        ** happening, this is usually correct.\n        **\n        ** However, if frames have been appended to the log (or if the log \n        ** is wrapped and written for that matter) before the READ_LOCK(0)\n        ** is obtained, that is not necessarily true. A checkpointer may\n        ** have started to backfill the appended frames but crashed before\n        ** it finished. Leaving a corrupt image in the database file.\n        */\n        walUnlockShared(pWal, WAL_READ_LOCK(0));\n        return WAL_RETRY;\n      }\n      pWal->readLock = 0;\n      return SQLITE_OK;\n    }else if( rc!=SQLITE_BUSY ){\n      return rc;\n    }\n  }\n\n  /* If we get this far, it means that the reader will want to use\n  ** the WAL to get at content from recent commits.  The job now is\n  ** to select one of the aReadMark[] entries that is closest to\n  ** but not exceeding pWal->hdr.mxFrame and lock that entry.\n  */\n  mxReadMark = 0;\n  mxI = 0;\n  mxFrame = pWal->hdr.mxFrame;\n#ifdef SQLITE_ENABLE_SNAPSHOT\n  if( pWal->pSnapshot && pWal->pSnapshot->mxFrame<mxFrame ){\n    mxFrame = pWal->pSnapshot->mxFrame;\n  }\n#endif\n  for(i=1; i<WAL_NREADER; i++){\n    u32 thisMark = pInfo->aReadMark[i];\n    if( mxReadMark<=thisMark && thisMark<=mxFrame ){\n      assert( thisMark!=READMARK_NOT_USED );\n      mxReadMark = thisMark;\n      mxI = i;\n    }\n  }\n  if( (pWal->readOnly & WAL_SHM_RDONLY)==0\n   && (mxReadMark<mxFrame || mxI==0)\n  ){\n    for(i=1; i<WAL_NREADER; i++){\n      rc = walLockExclusive(pWal, WAL_READ_LOCK(i), 1);\n      if( rc==SQLITE_OK ){\n        mxReadMark = pInfo->aReadMark[i] = mxFrame;\n        mxI = i;\n        walUnlockExclusive(pWal, WAL_READ_LOCK(i), 1);\n        break;\n      }else if( rc!=SQLITE_BUSY ){\n        return rc;\n      }\n    }\n  }\n  if( mxI==0 ){\n    assert( rc==SQLITE_BUSY || (pWal->readOnly & WAL_SHM_RDONLY)!=0 );\n    return rc==SQLITE_BUSY ? WAL_RETRY : SQLITE_READONLY_CANTINIT;\n  }\n\n  rc = walLockShared(pWal, WAL_READ_LOCK(mxI));\n  if( rc ){\n    return rc==SQLITE_BUSY ? WAL_RETRY : rc;\n  }\n  /* Now that the read-lock has been obtained, check that neither the\n  ** value in the aReadMark[] array or the contents of the wal-index\n  ** header have changed.\n  **\n  ** It is necessary to check that the wal-index header did not change\n  ** between the time it was read and when the shared-lock was obtained\n  ** on WAL_READ_LOCK(mxI) was obtained to account for the possibility\n  ** that the log file may have been wrapped by a writer, or that frames\n  ** that occur later in the log than pWal->hdr.mxFrame may have been\n  ** copied into the database by a checkpointer. If either of these things\n  ** happened, then reading the database with the current value of\n  ** pWal->hdr.mxFrame risks reading a corrupted snapshot. So, retry\n  ** instead.\n  **\n  ** Before checking that the live wal-index header has not changed\n  ** since it was read, set Wal.minFrame to the first frame in the wal\n  ** file that has not yet been checkpointed. This client will not need\n  ** to read any frames earlier than minFrame from the wal file - they\n  ** can be safely read directly from the database file.\n  **\n  ** Because a ShmBarrier() call is made between taking the copy of \n  ** nBackfill and checking that the wal-header in shared-memory still\n  ** matches the one cached in pWal->hdr, it is guaranteed that the \n  ** checkpointer that set nBackfill was not working with a wal-index\n  ** header newer than that cached in pWal->hdr. If it were, that could\n  ** cause a problem. The checkpointer could omit to checkpoint\n  ** a version of page X that lies before pWal->minFrame (call that version\n  ** A) on the basis that there is a newer version (version B) of the same\n  ** page later in the wal file. But if version B happens to like past\n  ** frame pWal->hdr.mxFrame - then the client would incorrectly assume\n  ** that it can read version A from the database file. However, since\n  ** we can guarantee that the checkpointer that set nBackfill could not\n  ** see any pages past pWal->hdr.mxFrame, this problem does not come up.\n  */\n  pWal->minFrame = pInfo->nBackfill+1;\n  walShmBarrier(pWal);\n  if( pInfo->aReadMark[mxI]!=mxReadMark\n   || memcmp((void *)walIndexHdr(pWal), &pWal->hdr, sizeof(WalIndexHdr))\n  ){\n    walUnlockShared(pWal, WAL_READ_LOCK(mxI));\n    return WAL_RETRY;\n  }else{\n    assert( mxReadMark<=pWal->hdr.mxFrame );\n    pWal->readLock = (i16)mxI;\n  }\n  return rc;\n}\n\n#ifdef SQLITE_ENABLE_SNAPSHOT\n/*\n** Attempt to reduce the value of the WalCkptInfo.nBackfillAttempted \n** variable so that older snapshots can be accessed. To do this, loop\n** through all wal frames from nBackfillAttempted to (nBackfill+1), \n** comparing their content to the corresponding page with the database\n** file, if any. Set nBackfillAttempted to the frame number of the\n** first frame for which the wal file content matches the db file.\n**\n** This is only really safe if the file-system is such that any page \n** writes made by earlier checkpointers were atomic operations, which \n** is not always true. It is also possible that nBackfillAttempted\n** may be left set to a value larger than expected, if a wal frame\n** contains content that duplicate of an earlier version of the same\n** page.\n**\n** SQLITE_OK is returned if successful, or an SQLite error code if an\n** error occurs. It is not an error if nBackfillAttempted cannot be\n** decreased at all.\n*/\nSQLITE_PRIVATE int sqlite3WalSnapshotRecover(Wal *pWal){\n  int rc;\n\n  assert( pWal->readLock>=0 );\n  rc = walLockExclusive(pWal, WAL_CKPT_LOCK, 1);\n  if( rc==SQLITE_OK ){\n    volatile WalCkptInfo *pInfo = walCkptInfo(pWal);\n    int szPage = (int)pWal->szPage;\n    i64 szDb;                   /* Size of db file in bytes */\n\n    rc = sqlite3OsFileSize(pWal->pDbFd, &szDb);\n    if( rc==SQLITE_OK ){\n      void *pBuf1 = sqlite3_malloc(szPage);\n      void *pBuf2 = sqlite3_malloc(szPage);\n      if( pBuf1==0 || pBuf2==0 ){\n        rc = SQLITE_NOMEM;\n      }else{\n        u32 i = pInfo->nBackfillAttempted;\n        for(i=pInfo->nBackfillAttempted; i>pInfo->nBackfill; i--){\n          volatile ht_slot *dummy;\n          volatile u32 *aPgno;      /* Array of page numbers */\n          u32 iZero;                /* Frame corresponding to aPgno[0] */\n          u32 pgno;                 /* Page number in db file */\n          i64 iDbOff;               /* Offset of db file entry */\n          i64 iWalOff;              /* Offset of wal file entry */\n\n          rc = walHashGet(pWal, walFramePage(i), &dummy, &aPgno, &iZero);\n          if( rc!=SQLITE_OK ) break;\n          pgno = aPgno[i-iZero];\n          iDbOff = (i64)(pgno-1) * szPage;\n\n          if( iDbOff+szPage<=szDb ){\n            iWalOff = walFrameOffset(i, szPage) + WAL_FRAME_HDRSIZE;\n            rc = sqlite3OsRead(pWal->pWalFd, pBuf1, szPage, iWalOff);\n\n            if( rc==SQLITE_OK ){\n              rc = sqlite3OsRead(pWal->pDbFd, pBuf2, szPage, iDbOff);\n            }\n\n            if( rc!=SQLITE_OK || 0==memcmp(pBuf1, pBuf2, szPage) ){\n              break;\n            }\n          }\n\n          pInfo->nBackfillAttempted = i-1;\n        }\n      }\n\n      sqlite3_free(pBuf1);\n      sqlite3_free(pBuf2);\n    }\n    walUnlockExclusive(pWal, WAL_CKPT_LOCK, 1);\n  }\n\n  return rc;\n}\n#endif /* SQLITE_ENABLE_SNAPSHOT */\n\n/*\n** Begin a read transaction on the database.\n**\n** This routine used to be called sqlite3OpenSnapshot() and with good reason:\n** it takes a snapshot of the state of the WAL and wal-index for the current\n** instant in time.  The current thread will continue to use this snapshot.\n** Other threads might append new content to the WAL and wal-index but\n** that extra content is ignored by the current thread.\n**\n** If the database contents have changes since the previous read\n** transaction, then *pChanged is set to 1 before returning.  The\n** Pager layer will use this to know that is cache is stale and\n** needs to be flushed.\n*/\nSQLITE_PRIVATE int sqlite3WalBeginReadTransaction(Wal *pWal, int *pChanged){\n  int rc;                         /* Return code */\n  int cnt = 0;                    /* Number of TryBeginRead attempts */\n\n#ifdef SQLITE_ENABLE_SNAPSHOT\n  int bChanged = 0;\n  WalIndexHdr *pSnapshot = pWal->pSnapshot;\n  if( pSnapshot && memcmp(pSnapshot, &pWal->hdr, sizeof(WalIndexHdr))!=0 ){\n    bChanged = 1;\n  }\n#endif\n\n  do{\n    rc = walTryBeginRead(pWal, pChanged, 0, ++cnt);\n  }while( rc==WAL_RETRY );\n  testcase( (rc&0xff)==SQLITE_BUSY );\n  testcase( (rc&0xff)==SQLITE_IOERR );\n  testcase( rc==SQLITE_PROTOCOL );\n  testcase( rc==SQLITE_OK );\n\n#ifdef SQLITE_ENABLE_SNAPSHOT\n  if( rc==SQLITE_OK ){\n    if( pSnapshot && memcmp(pSnapshot, &pWal->hdr, sizeof(WalIndexHdr))!=0 ){\n      /* At this point the client has a lock on an aReadMark[] slot holding\n      ** a value equal to or smaller than pSnapshot->mxFrame, but pWal->hdr\n      ** is populated with the wal-index header corresponding to the head\n      ** of the wal file. Verify that pSnapshot is still valid before\n      ** continuing.  Reasons why pSnapshot might no longer be valid:\n      **\n      **    (1)  The WAL file has been reset since the snapshot was taken.\n      **         In this case, the salt will have changed.\n      **\n      **    (2)  A checkpoint as been attempted that wrote frames past\n      **         pSnapshot->mxFrame into the database file.  Note that the\n      **         checkpoint need not have completed for this to cause problems.\n      */\n      volatile WalCkptInfo *pInfo = walCkptInfo(pWal);\n\n      assert( pWal->readLock>0 || pWal->hdr.mxFrame==0 );\n      assert( pInfo->aReadMark[pWal->readLock]<=pSnapshot->mxFrame );\n\n      /* It is possible that there is a checkpointer thread running \n      ** concurrent with this code. If this is the case, it may be that the\n      ** checkpointer has already determined that it will checkpoint \n      ** snapshot X, where X is later in the wal file than pSnapshot, but \n      ** has not yet set the pInfo->nBackfillAttempted variable to indicate \n      ** its intent. To avoid the race condition this leads to, ensure that\n      ** there is no checkpointer process by taking a shared CKPT lock \n      ** before checking pInfo->nBackfillAttempted.  \n      **\n      ** TODO: Does the aReadMark[] lock prevent a checkpointer from doing\n      **       this already?\n      */\n      rc = walLockShared(pWal, WAL_CKPT_LOCK);\n\n      if( rc==SQLITE_OK ){\n        /* Check that the wal file has not been wrapped. Assuming that it has\n        ** not, also check that no checkpointer has attempted to checkpoint any\n        ** frames beyond pSnapshot->mxFrame. If either of these conditions are\n        ** true, return SQLITE_BUSY_SNAPSHOT. Otherwise, overwrite pWal->hdr\n        ** with *pSnapshot and set *pChanged as appropriate for opening the\n        ** snapshot.  */\n        if( !memcmp(pSnapshot->aSalt, pWal->hdr.aSalt, sizeof(pWal->hdr.aSalt))\n         && pSnapshot->mxFrame>=pInfo->nBackfillAttempted\n        ){\n          assert( pWal->readLock>0 );\n          memcpy(&pWal->hdr, pSnapshot, sizeof(WalIndexHdr));\n          *pChanged = bChanged;\n        }else{\n          rc = SQLITE_BUSY_SNAPSHOT;\n        }\n\n        /* Release the shared CKPT lock obtained above. */\n        walUnlockShared(pWal, WAL_CKPT_LOCK);\n      }\n\n\n      if( rc!=SQLITE_OK ){\n        sqlite3WalEndReadTransaction(pWal);\n      }\n    }\n  }\n#endif\n  return rc;\n}\n\n/*\n** Finish with a read transaction.  All this does is release the\n** read-lock.\n*/\nSQLITE_PRIVATE void sqlite3WalEndReadTransaction(Wal *pWal){\n  sqlite3WalEndWriteTransaction(pWal);\n  if( pWal->readLock>=0 ){\n    walUnlockShared(pWal, WAL_READ_LOCK(pWal->readLock));\n    pWal->readLock = -1;\n  }\n}\n\n/*\n** Search the wal file for page pgno. If found, set *piRead to the frame that\n** contains the page. Otherwise, if pgno is not in the wal file, set *piRead\n** to zero.\n**\n** Return SQLITE_OK if successful, or an error code if an error occurs. If an\n** error does occur, the final value of *piRead is undefined.\n*/\nSQLITE_PRIVATE int sqlite3WalFindFrame(\n  Wal *pWal,                      /* WAL handle */\n  Pgno pgno,                      /* Database page number to read data for */\n  u32 *piRead                     /* OUT: Frame number (or zero) */\n){\n  u32 iRead = 0;                  /* If !=0, WAL frame to return data from */\n  u32 iLast = pWal->hdr.mxFrame;  /* Last page in WAL for this reader */\n  int iHash;                      /* Used to loop through N hash tables */\n  int iMinHash;\n\n  /* This routine is only be called from within a read transaction. */\n  assert( pWal->readLock>=0 || pWal->lockError );\n\n  /* If the \"last page\" field of the wal-index header snapshot is 0, then\n  ** no data will be read from the wal under any circumstances. Return early\n  ** in this case as an optimization.  Likewise, if pWal->readLock==0, \n  ** then the WAL is ignored by the reader so return early, as if the \n  ** WAL were empty.\n  */\n  if( iLast==0 || (pWal->readLock==0 && pWal->bShmUnreliable==0) ){\n    *piRead = 0;\n    return SQLITE_OK;\n  }\n\n  /* Search the hash table or tables for an entry matching page number\n  ** pgno. Each iteration of the following for() loop searches one\n  ** hash table (each hash table indexes up to HASHTABLE_NPAGE frames).\n  **\n  ** This code might run concurrently to the code in walIndexAppend()\n  ** that adds entries to the wal-index (and possibly to this hash \n  ** table). This means the value just read from the hash \n  ** slot (aHash[iKey]) may have been added before or after the \n  ** current read transaction was opened. Values added after the\n  ** read transaction was opened may have been written incorrectly -\n  ** i.e. these slots may contain garbage data. However, we assume\n  ** that any slots written before the current read transaction was\n  ** opened remain unmodified.\n  **\n  ** For the reasons above, the if(...) condition featured in the inner\n  ** loop of the following block is more stringent that would be required \n  ** if we had exclusive access to the hash-table:\n  **\n  **   (aPgno[iFrame]==pgno): \n  **     This condition filters out normal hash-table collisions.\n  **\n  **   (iFrame<=iLast): \n  **     This condition filters out entries that were added to the hash\n  **     table after the current read-transaction had started.\n  */\n  iMinHash = walFramePage(pWal->minFrame);\n  for(iHash=walFramePage(iLast); iHash>=iMinHash; iHash--){\n    volatile ht_slot *aHash;      /* Pointer to hash table */\n    volatile u32 *aPgno;          /* Pointer to array of page numbers */\n    u32 iZero;                    /* Frame number corresponding to aPgno[0] */\n    int iKey;                     /* Hash slot index */\n    int nCollide;                 /* Number of hash collisions remaining */\n    int rc;                       /* Error code */\n\n    rc = walHashGet(pWal, iHash, &aHash, &aPgno, &iZero);\n    if( rc!=SQLITE_OK ){\n      return rc;\n    }\n    nCollide = HASHTABLE_NSLOT;\n    for(iKey=walHash(pgno); aHash[iKey]; iKey=walNextHash(iKey)){\n      u32 iFrame = aHash[iKey] + iZero;\n      if( iFrame<=iLast && iFrame>=pWal->minFrame && aPgno[aHash[iKey]]==pgno ){\n        assert( iFrame>iRead || CORRUPT_DB );\n        iRead = iFrame;\n      }\n      if( (nCollide--)==0 ){\n        return SQLITE_CORRUPT_BKPT;\n      }\n    }\n    if( iRead ) break;\n  }\n\n#ifdef SQLITE_ENABLE_EXPENSIVE_ASSERT\n  /* If expensive assert() statements are available, do a linear search\n  ** of the wal-index file content. Make sure the results agree with the\n  ** result obtained using the hash indexes above.  */\n  {\n    u32 iRead2 = 0;\n    u32 iTest;\n    assert( pWal->bShmUnreliable || pWal->minFrame>0 );\n    for(iTest=iLast; iTest>=pWal->minFrame && iTest>0; iTest--){\n      if( walFramePgno(pWal, iTest)==pgno ){\n        iRead2 = iTest;\n        break;\n      }\n    }\n    assert( iRead==iRead2 );\n  }\n#endif\n\n  *piRead = iRead;\n  return SQLITE_OK;\n}\n\n/*\n** Read the contents of frame iRead from the wal file into buffer pOut\n** (which is nOut bytes in size). Return SQLITE_OK if successful, or an\n** error code otherwise.\n*/\nSQLITE_PRIVATE int sqlite3WalReadFrame(\n  Wal *pWal,                      /* WAL handle */\n  u32 iRead,                      /* Frame to read */\n  int nOut,                       /* Size of buffer pOut in bytes */\n  u8 *pOut                        /* Buffer to write page data to */\n){\n  int sz;\n  i64 iOffset;\n  sz = pWal->hdr.szPage;\n  sz = (sz&0xfe00) + ((sz&0x0001)<<16);\n  testcase( sz<=32768 );\n  testcase( sz>=65536 );\n  iOffset = walFrameOffset(iRead, sz) + WAL_FRAME_HDRSIZE;\n  /* testcase( IS_BIG_INT(iOffset) ); // requires a 4GiB WAL */\n  return sqlite3OsRead(pWal->pWalFd, pOut, (nOut>sz ? sz : nOut), iOffset);\n}\n\n/* \n** Return the size of the database in pages (or zero, if unknown).\n*/\nSQLITE_PRIVATE Pgno sqlite3WalDbsize(Wal *pWal){\n  if( pWal && ALWAYS(pWal->readLock>=0) ){\n    return pWal->hdr.nPage;\n  }\n  return 0;\n}\n\n\n/* \n** This function starts a write transaction on the WAL.\n**\n** A read transaction must have already been started by a prior call\n** to sqlite3WalBeginReadTransaction().\n**\n** If another thread or process has written into the database since\n** the read transaction was started, then it is not possible for this\n** thread to write as doing so would cause a fork.  So this routine\n** returns SQLITE_BUSY in that case and no write transaction is started.\n**\n** There can only be a single writer active at a time.\n*/\nSQLITE_PRIVATE int sqlite3WalBeginWriteTransaction(Wal *pWal){\n  int rc;\n\n  /* Cannot start a write transaction without first holding a read\n  ** transaction. */\n  assert( pWal->readLock>=0 );\n  assert( pWal->writeLock==0 && pWal->iReCksum==0 );\n\n  if( pWal->readOnly ){\n    return SQLITE_READONLY;\n  }\n\n  /* Only one writer allowed at a time.  Get the write lock.  Return\n  ** SQLITE_BUSY if unable.\n  */\n  rc = walLockExclusive(pWal, WAL_WRITE_LOCK, 1);\n  if( rc ){\n    return rc;\n  }\n  pWal->writeLock = 1;\n\n  /* If another connection has written to the database file since the\n  ** time the read transaction on this connection was started, then\n  ** the write is disallowed.\n  */\n  if( memcmp(&pWal->hdr, (void *)walIndexHdr(pWal), sizeof(WalIndexHdr))!=0 ){\n    walUnlockExclusive(pWal, WAL_WRITE_LOCK, 1);\n    pWal->writeLock = 0;\n    rc = SQLITE_BUSY_SNAPSHOT;\n  }\n\n  return rc;\n}\n\n/*\n** End a write transaction.  The commit has already been done.  This\n** routine merely releases the lock.\n*/\nSQLITE_PRIVATE int sqlite3WalEndWriteTransaction(Wal *pWal){\n  if( pWal->writeLock ){\n    walUnlockExclusive(pWal, WAL_WRITE_LOCK, 1);\n    pWal->writeLock = 0;\n    pWal->iReCksum = 0;\n    pWal->truncateOnCommit = 0;\n  }\n  return SQLITE_OK;\n}\n\n/*\n** If any data has been written (but not committed) to the log file, this\n** function moves the write-pointer back to the start of the transaction.\n**\n** Additionally, the callback function is invoked for each frame written\n** to the WAL since the start of the transaction. If the callback returns\n** other than SQLITE_OK, it is not invoked again and the error code is\n** returned to the caller.\n**\n** Otherwise, if the callback function does not return an error, this\n** function returns SQLITE_OK.\n*/\nSQLITE_PRIVATE int sqlite3WalUndo(Wal *pWal, int (*xUndo)(void *, Pgno), void *pUndoCtx){\n  int rc = SQLITE_OK;\n  if( ALWAYS(pWal->writeLock) ){\n    Pgno iMax = pWal->hdr.mxFrame;\n    Pgno iFrame;\n  \n    /* Restore the clients cache of the wal-index header to the state it\n    ** was in before the client began writing to the database. \n    */\n    memcpy(&pWal->hdr, (void *)walIndexHdr(pWal), sizeof(WalIndexHdr));\n\n    for(iFrame=pWal->hdr.mxFrame+1; \n        ALWAYS(rc==SQLITE_OK) && iFrame<=iMax; \n        iFrame++\n    ){\n      /* This call cannot fail. Unless the page for which the page number\n      ** is passed as the second argument is (a) in the cache and \n      ** (b) has an outstanding reference, then xUndo is either a no-op\n      ** (if (a) is false) or simply expels the page from the cache (if (b)\n      ** is false).\n      **\n      ** If the upper layer is doing a rollback, it is guaranteed that there\n      ** are no outstanding references to any page other than page 1. And\n      ** page 1 is never written to the log until the transaction is\n      ** committed. As a result, the call to xUndo may not fail.\n      */\n      assert( walFramePgno(pWal, iFrame)!=1 );\n      rc = xUndo(pUndoCtx, walFramePgno(pWal, iFrame));\n    }\n    if( iMax!=pWal->hdr.mxFrame ) walCleanupHash(pWal);\n  }\n  return rc;\n}\n\n/* \n** Argument aWalData must point to an array of WAL_SAVEPOINT_NDATA u32 \n** values. This function populates the array with values required to \n** \"rollback\" the write position of the WAL handle back to the current \n** point in the event of a savepoint rollback (via WalSavepointUndo()).\n*/\nSQLITE_PRIVATE void sqlite3WalSavepoint(Wal *pWal, u32 *aWalData){\n  assert( pWal->writeLock );\n  aWalData[0] = pWal->hdr.mxFrame;\n  aWalData[1] = pWal->hdr.aFrameCksum[0];\n  aWalData[2] = pWal->hdr.aFrameCksum[1];\n  aWalData[3] = pWal->nCkpt;\n}\n\n/* \n** Move the write position of the WAL back to the point identified by\n** the values in the aWalData[] array. aWalData must point to an array\n** of WAL_SAVEPOINT_NDATA u32 values that has been previously populated\n** by a call to WalSavepoint().\n*/\nSQLITE_PRIVATE int sqlite3WalSavepointUndo(Wal *pWal, u32 *aWalData){\n  int rc = SQLITE_OK;\n\n  assert( pWal->writeLock );\n  assert( aWalData[3]!=pWal->nCkpt || aWalData[0]<=pWal->hdr.mxFrame );\n\n  if( aWalData[3]!=pWal->nCkpt ){\n    /* This savepoint was opened immediately after the write-transaction\n    ** was started. Right after that, the writer decided to wrap around\n    ** to the start of the log. Update the savepoint values to match.\n    */\n    aWalData[0] = 0;\n    aWalData[3] = pWal->nCkpt;\n  }\n\n  if( aWalData[0]<pWal->hdr.mxFrame ){\n    pWal->hdr.mxFrame = aWalData[0];\n    pWal->hdr.aFrameCksum[0] = aWalData[1];\n    pWal->hdr.aFrameCksum[1] = aWalData[2];\n    walCleanupHash(pWal);\n  }\n\n  return rc;\n}\n\n/*\n** This function is called just before writing a set of frames to the log\n** file (see sqlite3WalFrames()). It checks to see if, instead of appending\n** to the current log file, it is possible to overwrite the start of the\n** existing log file with the new frames (i.e. \"reset\" the log). If so,\n** it sets pWal->hdr.mxFrame to 0. Otherwise, pWal->hdr.mxFrame is left\n** unchanged.\n**\n** SQLITE_OK is returned if no error is encountered (regardless of whether\n** or not pWal->hdr.mxFrame is modified). An SQLite error code is returned\n** if an error occurs.\n*/\nstatic int walRestartLog(Wal *pWal){\n  int rc = SQLITE_OK;\n  int cnt;\n\n  if( pWal->readLock==0 ){\n    volatile WalCkptInfo *pInfo = walCkptInfo(pWal);\n    assert( pInfo->nBackfill==pWal->hdr.mxFrame );\n    if( pInfo->nBackfill>0 ){\n      u32 salt1;\n      sqlite3_randomness(4, &salt1);\n      rc = walLockExclusive(pWal, WAL_READ_LOCK(1), WAL_NREADER-1);\n      if( rc==SQLITE_OK ){\n        /* If all readers are using WAL_READ_LOCK(0) (in other words if no\n        ** readers are currently using the WAL), then the transactions\n        ** frames will overwrite the start of the existing log. Update the\n        ** wal-index header to reflect this.\n        **\n        ** In theory it would be Ok to update the cache of the header only\n        ** at this point. But updating the actual wal-index header is also\n        ** safe and means there is no special case for sqlite3WalUndo()\n        ** to handle if this transaction is rolled back.  */\n        walRestartHdr(pWal, salt1);\n        walUnlockExclusive(pWal, WAL_READ_LOCK(1), WAL_NREADER-1);\n      }else if( rc!=SQLITE_BUSY ){\n        return rc;\n      }\n    }\n    walUnlockShared(pWal, WAL_READ_LOCK(0));\n    pWal->readLock = -1;\n    cnt = 0;\n    do{\n      int notUsed;\n      rc = walTryBeginRead(pWal, &notUsed, 1, ++cnt);\n    }while( rc==WAL_RETRY );\n    assert( (rc&0xff)!=SQLITE_BUSY ); /* BUSY not possible when useWal==1 */\n    testcase( (rc&0xff)==SQLITE_IOERR );\n    testcase( rc==SQLITE_PROTOCOL );\n    testcase( rc==SQLITE_OK );\n  }\n  return rc;\n}\n\n/*\n** Information about the current state of the WAL file and where\n** the next fsync should occur - passed from sqlite3WalFrames() into\n** walWriteToLog().\n*/\ntypedef struct WalWriter {\n  Wal *pWal;                   /* The complete WAL information */\n  sqlite3_file *pFd;           /* The WAL file to which we write */\n  sqlite3_int64 iSyncPoint;    /* Fsync at this offset */\n  int syncFlags;               /* Flags for the fsync */\n  int szPage;                  /* Size of one page */\n} WalWriter;\n\n/*\n** Write iAmt bytes of content into the WAL file beginning at iOffset.\n** Do a sync when crossing the p->iSyncPoint boundary.\n**\n** In other words, if iSyncPoint is in between iOffset and iOffset+iAmt,\n** first write the part before iSyncPoint, then sync, then write the\n** rest.\n*/\nstatic int walWriteToLog(\n  WalWriter *p,              /* WAL to write to */\n  void *pContent,            /* Content to be written */\n  int iAmt,                  /* Number of bytes to write */\n  sqlite3_int64 iOffset      /* Start writing at this offset */\n){\n  int rc;\n  if( iOffset<p->iSyncPoint && iOffset+iAmt>=p->iSyncPoint ){\n    int iFirstAmt = (int)(p->iSyncPoint - iOffset);\n    rc = sqlite3OsWrite(p->pFd, pContent, iFirstAmt, iOffset);\n    if( rc ) return rc;\n    iOffset += iFirstAmt;\n    iAmt -= iFirstAmt;\n    pContent = (void*)(iFirstAmt + (char*)pContent);\n    assert( WAL_SYNC_FLAGS(p->syncFlags)!=0 );\n    rc = sqlite3OsSync(p->pFd, WAL_SYNC_FLAGS(p->syncFlags));\n    if( iAmt==0 || rc ) return rc;\n  }\n  rc = sqlite3OsWrite(p->pFd, pContent, iAmt, iOffset);\n  return rc;\n}\n\n/*\n** Write out a single frame of the WAL\n*/\nstatic int walWriteOneFrame(\n  WalWriter *p,               /* Where to write the frame */\n  PgHdr *pPage,               /* The page of the frame to be written */\n  int nTruncate,              /* The commit flag.  Usually 0.  >0 for commit */\n  sqlite3_int64 iOffset       /* Byte offset at which to write */\n){\n  int rc;                         /* Result code from subfunctions */\n  void *pData;                    /* Data actually written */\n  u8 aFrame[WAL_FRAME_HDRSIZE];   /* Buffer to assemble frame-header in */\n#if defined(SQLITE_HAS_CODEC)\n  if( (pData = sqlite3PagerCodec(pPage))==0 ) return SQLITE_NOMEM_BKPT;\n#else\n  pData = pPage->pData;\n#endif\n  walEncodeFrame(p->pWal, pPage->pgno, nTruncate, pData, aFrame);\n  rc = walWriteToLog(p, aFrame, sizeof(aFrame), iOffset);\n  if( rc ) return rc;\n  /* Write the page data */\n  rc = walWriteToLog(p, pData, p->szPage, iOffset+sizeof(aFrame));\n  return rc;\n}\n\n/*\n** This function is called as part of committing a transaction within which\n** one or more frames have been overwritten. It updates the checksums for\n** all frames written to the wal file by the current transaction starting\n** with the earliest to have been overwritten.\n**\n** SQLITE_OK is returned if successful, or an SQLite error code otherwise.\n*/\nstatic int walRewriteChecksums(Wal *pWal, u32 iLast){\n  const int szPage = pWal->szPage;/* Database page size */\n  int rc = SQLITE_OK;             /* Return code */\n  u8 *aBuf;                       /* Buffer to load data from wal file into */\n  u8 aFrame[WAL_FRAME_HDRSIZE];   /* Buffer to assemble frame-headers in */\n  u32 iRead;                      /* Next frame to read from wal file */\n  i64 iCksumOff;\n\n  aBuf = sqlite3_malloc(szPage + WAL_FRAME_HDRSIZE);\n  if( aBuf==0 ) return SQLITE_NOMEM_BKPT;\n\n  /* Find the checksum values to use as input for the recalculating the\n  ** first checksum. If the first frame is frame 1 (implying that the current\n  ** transaction restarted the wal file), these values must be read from the\n  ** wal-file header. Otherwise, read them from the frame header of the\n  ** previous frame.  */\n  assert( pWal->iReCksum>0 );\n  if( pWal->iReCksum==1 ){\n    iCksumOff = 24;\n  }else{\n    iCksumOff = walFrameOffset(pWal->iReCksum-1, szPage) + 16;\n  }\n  rc = sqlite3OsRead(pWal->pWalFd, aBuf, sizeof(u32)*2, iCksumOff);\n  pWal->hdr.aFrameCksum[0] = sqlite3Get4byte(aBuf);\n  pWal->hdr.aFrameCksum[1] = sqlite3Get4byte(&aBuf[sizeof(u32)]);\n\n  iRead = pWal->iReCksum;\n  pWal->iReCksum = 0;\n  for(; rc==SQLITE_OK && iRead<=iLast; iRead++){\n    i64 iOff = walFrameOffset(iRead, szPage);\n    rc = sqlite3OsRead(pWal->pWalFd, aBuf, szPage+WAL_FRAME_HDRSIZE, iOff);\n    if( rc==SQLITE_OK ){\n      u32 iPgno, nDbSize;\n      iPgno = sqlite3Get4byte(aBuf);\n      nDbSize = sqlite3Get4byte(&aBuf[4]);\n\n      walEncodeFrame(pWal, iPgno, nDbSize, &aBuf[WAL_FRAME_HDRSIZE], aFrame);\n      rc = sqlite3OsWrite(pWal->pWalFd, aFrame, sizeof(aFrame), iOff);\n    }\n  }\n\n  sqlite3_free(aBuf);\n  return rc;\n}\n\n/* \n** Write a set of frames to the log. The caller must hold the write-lock\n** on the log file (obtained using sqlite3WalBeginWriteTransaction()).\n*/\nSQLITE_PRIVATE int sqlite3WalFrames(\n  Wal *pWal,                      /* Wal handle to write to */\n  int szPage,                     /* Database page-size in bytes */\n  PgHdr *pList,                   /* List of dirty pages to write */\n  Pgno nTruncate,                 /* Database size after this commit */\n  int isCommit,                   /* True if this is a commit */\n  int sync_flags                  /* Flags to pass to OsSync() (or 0) */\n){\n  int rc;                         /* Used to catch return codes */\n  u32 iFrame;                     /* Next frame address */\n  PgHdr *p;                       /* Iterator to run through pList with. */\n  PgHdr *pLast = 0;               /* Last frame in list */\n  int nExtra = 0;                 /* Number of extra copies of last page */\n  int szFrame;                    /* The size of a single frame */\n  i64 iOffset;                    /* Next byte to write in WAL file */\n  WalWriter w;                    /* The writer */\n  u32 iFirst = 0;                 /* First frame that may be overwritten */\n  WalIndexHdr *pLive;             /* Pointer to shared header */\n\n  assert( pList );\n  assert( pWal->writeLock );\n\n  /* If this frame set completes a transaction, then nTruncate>0.  If\n  ** nTruncate==0 then this frame set does not complete the transaction. */\n  assert( (isCommit!=0)==(nTruncate!=0) );\n\n#if defined(SQLITE_TEST) && defined(SQLITE_DEBUG)\n  { int cnt; for(cnt=0, p=pList; p; p=p->pDirty, cnt++){}\n    WALTRACE((\"WAL%p: frame write begin. %d frames. mxFrame=%d. %s\\n\",\n              pWal, cnt, pWal->hdr.mxFrame, isCommit ? \"Commit\" : \"Spill\"));\n  }\n#endif\n\n  pLive = (WalIndexHdr*)walIndexHdr(pWal);\n  if( memcmp(&pWal->hdr, (void *)pLive, sizeof(WalIndexHdr))!=0 ){\n    iFirst = pLive->mxFrame+1;\n  }\n\n  /* See if it is possible to write these frames into the start of the\n  ** log file, instead of appending to it at pWal->hdr.mxFrame.\n  */\n  if( SQLITE_OK!=(rc = walRestartLog(pWal)) ){\n    return rc;\n  }\n\n  /* If this is the first frame written into the log, write the WAL\n  ** header to the start of the WAL file. See comments at the top of\n  ** this source file for a description of the WAL header format.\n  */\n  iFrame = pWal->hdr.mxFrame;\n  if( iFrame==0 ){\n    u8 aWalHdr[WAL_HDRSIZE];      /* Buffer to assemble wal-header in */\n    u32 aCksum[2];                /* Checksum for wal-header */\n\n    sqlite3Put4byte(&aWalHdr[0], (WAL_MAGIC | SQLITE_BIGENDIAN));\n    sqlite3Put4byte(&aWalHdr[4], WAL_MAX_VERSION);\n    sqlite3Put4byte(&aWalHdr[8], szPage);\n    sqlite3Put4byte(&aWalHdr[12], pWal->nCkpt);\n    if( pWal->nCkpt==0 ) sqlite3_randomness(8, pWal->hdr.aSalt);\n    memcpy(&aWalHdr[16], pWal->hdr.aSalt, 8);\n    walChecksumBytes(1, aWalHdr, WAL_HDRSIZE-2*4, 0, aCksum);\n    sqlite3Put4byte(&aWalHdr[24], aCksum[0]);\n    sqlite3Put4byte(&aWalHdr[28], aCksum[1]);\n    \n    pWal->szPage = szPage;\n    pWal->hdr.bigEndCksum = SQLITE_BIGENDIAN;\n    pWal->hdr.aFrameCksum[0] = aCksum[0];\n    pWal->hdr.aFrameCksum[1] = aCksum[1];\n    pWal->truncateOnCommit = 1;\n\n    rc = sqlite3OsWrite(pWal->pWalFd, aWalHdr, sizeof(aWalHdr), 0);\n    WALTRACE((\"WAL%p: wal-header write %s\\n\", pWal, rc ? \"failed\" : \"ok\"));\n    if( rc!=SQLITE_OK ){\n      return rc;\n    }\n\n    /* Sync the header (unless SQLITE_IOCAP_SEQUENTIAL is true or unless\n    ** all syncing is turned off by PRAGMA synchronous=OFF).  Otherwise\n    ** an out-of-order write following a WAL restart could result in\n    ** database corruption.  See the ticket:\n    **\n    **     https://sqlite.org/src/info/ff5be73dee\n    */\n    if( pWal->syncHeader ){\n      rc = sqlite3OsSync(pWal->pWalFd, CKPT_SYNC_FLAGS(sync_flags));\n      if( rc ) return rc;\n    }\n  }\n  assert( (int)pWal->szPage==szPage );\n\n  /* Setup information needed to write frames into the WAL */\n  w.pWal = pWal;\n  w.pFd = pWal->pWalFd;\n  w.iSyncPoint = 0;\n  w.syncFlags = sync_flags;\n  w.szPage = szPage;\n  iOffset = walFrameOffset(iFrame+1, szPage);\n  szFrame = szPage + WAL_FRAME_HDRSIZE;\n\n  /* Write all frames into the log file exactly once */\n  for(p=pList; p; p=p->pDirty){\n    int nDbSize;   /* 0 normally.  Positive == commit flag */\n\n    /* Check if this page has already been written into the wal file by\n    ** the current transaction. If so, overwrite the existing frame and\n    ** set Wal.writeLock to WAL_WRITELOCK_RECKSUM - indicating that \n    ** checksums must be recomputed when the transaction is committed.  */\n    if( iFirst && (p->pDirty || isCommit==0) ){\n      u32 iWrite = 0;\n      VVA_ONLY(rc =) sqlite3WalFindFrame(pWal, p->pgno, &iWrite);\n      assert( rc==SQLITE_OK || iWrite==0 );\n      if( iWrite>=iFirst ){\n        i64 iOff = walFrameOffset(iWrite, szPage) + WAL_FRAME_HDRSIZE;\n        void *pData;\n        if( pWal->iReCksum==0 || iWrite<pWal->iReCksum ){\n          pWal->iReCksum = iWrite;\n        }\n#if defined(SQLITE_HAS_CODEC)\n        if( (pData = sqlite3PagerCodec(p))==0 ) return SQLITE_NOMEM;\n#else\n        pData = p->pData;\n#endif\n        rc = sqlite3OsWrite(pWal->pWalFd, pData, szPage, iOff);\n        if( rc ) return rc;\n        p->flags &= ~PGHDR_WAL_APPEND;\n        continue;\n      }\n    }\n\n    iFrame++;\n    assert( iOffset==walFrameOffset(iFrame, szPage) );\n    nDbSize = (isCommit && p->pDirty==0) ? nTruncate : 0;\n    rc = walWriteOneFrame(&w, p, nDbSize, iOffset);\n    if( rc ) return rc;\n    pLast = p;\n    iOffset += szFrame;\n    p->flags |= PGHDR_WAL_APPEND;\n  }\n\n  /* Recalculate checksums within the wal file if required. */\n  if( isCommit && pWal->iReCksum ){\n    rc = walRewriteChecksums(pWal, iFrame);\n    if( rc ) return rc;\n  }\n\n  /* If this is the end of a transaction, then we might need to pad\n  ** the transaction and/or sync the WAL file.\n  **\n  ** Padding and syncing only occur if this set of frames complete a\n  ** transaction and if PRAGMA synchronous=FULL.  If synchronous==NORMAL\n  ** or synchronous==OFF, then no padding or syncing are needed.\n  **\n  ** If SQLITE_IOCAP_POWERSAFE_OVERWRITE is defined, then padding is not\n  ** needed and only the sync is done.  If padding is needed, then the\n  ** final frame is repeated (with its commit mark) until the next sector\n  ** boundary is crossed.  Only the part of the WAL prior to the last\n  ** sector boundary is synced; the part of the last frame that extends\n  ** past the sector boundary is written after the sync.\n  */\n  if( isCommit && WAL_SYNC_FLAGS(sync_flags)!=0 ){\n    int bSync = 1;\n    if( pWal->padToSectorBoundary ){\n      int sectorSize = sqlite3SectorSize(pWal->pWalFd);\n      w.iSyncPoint = ((iOffset+sectorSize-1)/sectorSize)*sectorSize;\n      bSync = (w.iSyncPoint==iOffset);\n      testcase( bSync );\n      while( iOffset<w.iSyncPoint ){\n        rc = walWriteOneFrame(&w, pLast, nTruncate, iOffset);\n        if( rc ) return rc;\n        iOffset += szFrame;\n        nExtra++;\n      }\n    }\n    if( bSync ){\n      assert( rc==SQLITE_OK );\n      rc = sqlite3OsSync(w.pFd, WAL_SYNC_FLAGS(sync_flags));\n    }\n  }\n\n  /* If this frame set completes the first transaction in the WAL and\n  ** if PRAGMA journal_size_limit is set, then truncate the WAL to the\n  ** journal size limit, if possible.\n  */\n  if( isCommit && pWal->truncateOnCommit && pWal->mxWalSize>=0 ){\n    i64 sz = pWal->mxWalSize;\n    if( walFrameOffset(iFrame+nExtra+1, szPage)>pWal->mxWalSize ){\n      sz = walFrameOffset(iFrame+nExtra+1, szPage);\n    }\n    walLimitSize(pWal, sz);\n    pWal->truncateOnCommit = 0;\n  }\n\n  /* Append data to the wal-index. It is not necessary to lock the \n  ** wal-index to do this as the SQLITE_SHM_WRITE lock held on the wal-index\n  ** guarantees that there are no other writers, and no data that may\n  ** be in use by existing readers is being overwritten.\n  */\n  iFrame = pWal->hdr.mxFrame;\n  for(p=pList; p && rc==SQLITE_OK; p=p->pDirty){\n    if( (p->flags & PGHDR_WAL_APPEND)==0 ) continue;\n    iFrame++;\n    rc = walIndexAppend(pWal, iFrame, p->pgno);\n  }\n  while( rc==SQLITE_OK && nExtra>0 ){\n    iFrame++;\n    nExtra--;\n    rc = walIndexAppend(pWal, iFrame, pLast->pgno);\n  }\n\n  if( rc==SQLITE_OK ){\n    /* Update the private copy of the header. */\n    pWal->hdr.szPage = (u16)((szPage&0xff00) | (szPage>>16));\n    testcase( szPage<=32768 );\n    testcase( szPage>=65536 );\n    pWal->hdr.mxFrame = iFrame;\n    if( isCommit ){\n      pWal->hdr.iChange++;\n      pWal->hdr.nPage = nTruncate;\n    }\n    /* If this is a commit, update the wal-index header too. */\n    if( isCommit ){\n      walIndexWriteHdr(pWal);\n      pWal->iCallback = iFrame;\n    }\n  }\n\n  WALTRACE((\"WAL%p: frame write %s\\n\", pWal, rc ? \"failed\" : \"ok\"));\n  return rc;\n}\n\n/* \n** This routine is called to implement sqlite3_wal_checkpoint() and\n** related interfaces.\n**\n** Obtain a CHECKPOINT lock and then backfill as much information as\n** we can from WAL into the database.\n**\n** If parameter xBusy is not NULL, it is a pointer to a busy-handler\n** callback. In this case this function runs a blocking checkpoint.\n*/\nSQLITE_PRIVATE int sqlite3WalCheckpoint(\n  Wal *pWal,                      /* Wal connection */\n  sqlite3 *db,                    /* Check this handle's interrupt flag */\n  int eMode,                      /* PASSIVE, FULL, RESTART, or TRUNCATE */\n  int (*xBusy)(void*),            /* Function to call when busy */\n  void *pBusyArg,                 /* Context argument for xBusyHandler */\n  int sync_flags,                 /* Flags to sync db file with (or 0) */\n  int nBuf,                       /* Size of temporary buffer */\n  u8 *zBuf,                       /* Temporary buffer to use */\n  int *pnLog,                     /* OUT: Number of frames in WAL */\n  int *pnCkpt                     /* OUT: Number of backfilled frames in WAL */\n){\n  int rc;                         /* Return code */\n  int isChanged = 0;              /* True if a new wal-index header is loaded */\n  int eMode2 = eMode;             /* Mode to pass to walCheckpoint() */\n  int (*xBusy2)(void*) = xBusy;   /* Busy handler for eMode2 */\n\n  assert( pWal->ckptLock==0 );\n  assert( pWal->writeLock==0 );\n\n  /* EVIDENCE-OF: R-62920-47450 The busy-handler callback is never invoked\n  ** in the SQLITE_CHECKPOINT_PASSIVE mode. */\n  assert( eMode!=SQLITE_CHECKPOINT_PASSIVE || xBusy==0 );\n\n  if( pWal->readOnly ) return SQLITE_READONLY;\n  WALTRACE((\"WAL%p: checkpoint begins\\n\", pWal));\n\n  /* IMPLEMENTATION-OF: R-62028-47212 All calls obtain an exclusive \n  ** \"checkpoint\" lock on the database file. */\n  rc = walLockExclusive(pWal, WAL_CKPT_LOCK, 1);\n  if( rc ){\n    /* EVIDENCE-OF: R-10421-19736 If any other process is running a\n    ** checkpoint operation at the same time, the lock cannot be obtained and\n    ** SQLITE_BUSY is returned.\n    ** EVIDENCE-OF: R-53820-33897 Even if there is a busy-handler configured,\n    ** it will not be invoked in this case.\n    */\n    testcase( rc==SQLITE_BUSY );\n    testcase( xBusy!=0 );\n    return rc;\n  }\n  pWal->ckptLock = 1;\n\n  /* IMPLEMENTATION-OF: R-59782-36818 The SQLITE_CHECKPOINT_FULL, RESTART and\n  ** TRUNCATE modes also obtain the exclusive \"writer\" lock on the database\n  ** file.\n  **\n  ** EVIDENCE-OF: R-60642-04082 If the writer lock cannot be obtained\n  ** immediately, and a busy-handler is configured, it is invoked and the\n  ** writer lock retried until either the busy-handler returns 0 or the\n  ** lock is successfully obtained.\n  */\n  if( eMode!=SQLITE_CHECKPOINT_PASSIVE ){\n    rc = walBusyLock(pWal, xBusy, pBusyArg, WAL_WRITE_LOCK, 1);\n    if( rc==SQLITE_OK ){\n      pWal->writeLock = 1;\n    }else if( rc==SQLITE_BUSY ){\n      eMode2 = SQLITE_CHECKPOINT_PASSIVE;\n      xBusy2 = 0;\n      rc = SQLITE_OK;\n    }\n  }\n\n  /* Read the wal-index header. */\n  if( rc==SQLITE_OK ){\n    rc = walIndexReadHdr(pWal, &isChanged);\n    if( isChanged && pWal->pDbFd->pMethods->iVersion>=3 ){\n      sqlite3OsUnfetch(pWal->pDbFd, 0, 0);\n    }\n  }\n\n  /* Copy data from the log to the database file. */\n  if( rc==SQLITE_OK ){\n\n    if( pWal->hdr.mxFrame && walPagesize(pWal)!=nBuf ){\n      rc = SQLITE_CORRUPT_BKPT;\n    }else{\n      rc = walCheckpoint(pWal, db, eMode2, xBusy2, pBusyArg, sync_flags, zBuf);\n    }\n\n    /* If no error occurred, set the output variables. */\n    if( rc==SQLITE_OK || rc==SQLITE_BUSY ){\n      if( pnLog ) *pnLog = (int)pWal->hdr.mxFrame;\n      if( pnCkpt ) *pnCkpt = (int)(walCkptInfo(pWal)->nBackfill);\n    }\n  }\n\n  if( isChanged ){\n    /* If a new wal-index header was loaded before the checkpoint was \n    ** performed, then the pager-cache associated with pWal is now\n    ** out of date. So zero the cached wal-index header to ensure that\n    ** next time the pager opens a snapshot on this database it knows that\n    ** the cache needs to be reset.\n    */\n    memset(&pWal->hdr, 0, sizeof(WalIndexHdr));\n  }\n\n  /* Release the locks. */\n  sqlite3WalEndWriteTransaction(pWal);\n  walUnlockExclusive(pWal, WAL_CKPT_LOCK, 1);\n  pWal->ckptLock = 0;\n  WALTRACE((\"WAL%p: checkpoint %s\\n\", pWal, rc ? \"failed\" : \"ok\"));\n  return (rc==SQLITE_OK && eMode!=eMode2 ? SQLITE_BUSY : rc);\n}\n\n/* Return the value to pass to a sqlite3_wal_hook callback, the\n** number of frames in the WAL at the point of the last commit since\n** sqlite3WalCallback() was called.  If no commits have occurred since\n** the last call, then return 0.\n*/\nSQLITE_PRIVATE int sqlite3WalCallback(Wal *pWal){\n  u32 ret = 0;\n  if( pWal ){\n    ret = pWal->iCallback;\n    pWal->iCallback = 0;\n  }\n  return (int)ret;\n}\n\n/*\n** This function is called to change the WAL subsystem into or out\n** of locking_mode=EXCLUSIVE.\n**\n** If op is zero, then attempt to change from locking_mode=EXCLUSIVE\n** into locking_mode=NORMAL.  This means that we must acquire a lock\n** on the pWal->readLock byte.  If the WAL is already in locking_mode=NORMAL\n** or if the acquisition of the lock fails, then return 0.  If the\n** transition out of exclusive-mode is successful, return 1.  This\n** operation must occur while the pager is still holding the exclusive\n** lock on the main database file.\n**\n** If op is one, then change from locking_mode=NORMAL into \n** locking_mode=EXCLUSIVE.  This means that the pWal->readLock must\n** be released.  Return 1 if the transition is made and 0 if the\n** WAL is already in exclusive-locking mode - meaning that this\n** routine is a no-op.  The pager must already hold the exclusive lock\n** on the main database file before invoking this operation.\n**\n** If op is negative, then do a dry-run of the op==1 case but do\n** not actually change anything. The pager uses this to see if it\n** should acquire the database exclusive lock prior to invoking\n** the op==1 case.\n*/\nSQLITE_PRIVATE int sqlite3WalExclusiveMode(Wal *pWal, int op){\n  int rc;\n  assert( pWal->writeLock==0 );\n  assert( pWal->exclusiveMode!=WAL_HEAPMEMORY_MODE || op==-1 );\n\n  /* pWal->readLock is usually set, but might be -1 if there was a \n  ** prior error while attempting to acquire are read-lock. This cannot \n  ** happen if the connection is actually in exclusive mode (as no xShmLock\n  ** locks are taken in this case). Nor should the pager attempt to\n  ** upgrade to exclusive-mode following such an error.\n  */\n  assert( pWal->readLock>=0 || pWal->lockError );\n  assert( pWal->readLock>=0 || (op<=0 && pWal->exclusiveMode==0) );\n\n  if( op==0 ){\n    if( pWal->exclusiveMode!=WAL_NORMAL_MODE ){\n      pWal->exclusiveMode = WAL_NORMAL_MODE;\n      if( walLockShared(pWal, WAL_READ_LOCK(pWal->readLock))!=SQLITE_OK ){\n        pWal->exclusiveMode = WAL_EXCLUSIVE_MODE;\n      }\n      rc = pWal->exclusiveMode==WAL_NORMAL_MODE;\n    }else{\n      /* Already in locking_mode=NORMAL */\n      rc = 0;\n    }\n  }else if( op>0 ){\n    assert( pWal->exclusiveMode==WAL_NORMAL_MODE );\n    assert( pWal->readLock>=0 );\n    walUnlockShared(pWal, WAL_READ_LOCK(pWal->readLock));\n    pWal->exclusiveMode = WAL_EXCLUSIVE_MODE;\n    rc = 1;\n  }else{\n    rc = pWal->exclusiveMode==WAL_NORMAL_MODE;\n  }\n  return rc;\n}\n\n/* \n** Return true if the argument is non-NULL and the WAL module is using\n** heap-memory for the wal-index. Otherwise, if the argument is NULL or the\n** WAL module is using shared-memory, return false. \n*/\nSQLITE_PRIVATE int sqlite3WalHeapMemory(Wal *pWal){\n  return (pWal && pWal->exclusiveMode==WAL_HEAPMEMORY_MODE );\n}\n\n#ifdef SQLITE_ENABLE_SNAPSHOT\n/* Create a snapshot object.  The content of a snapshot is opaque to\n** every other subsystem, so the WAL module can put whatever it needs\n** in the object.\n*/\nSQLITE_PRIVATE int sqlite3WalSnapshotGet(Wal *pWal, sqlite3_snapshot **ppSnapshot){\n  int rc = SQLITE_OK;\n  WalIndexHdr *pRet;\n  static const u32 aZero[4] = { 0, 0, 0, 0 };\n\n  assert( pWal->readLock>=0 && pWal->writeLock==0 );\n\n  if( memcmp(&pWal->hdr.aFrameCksum[0],aZero,16)==0 ){\n    *ppSnapshot = 0;\n    return SQLITE_ERROR;\n  }\n  pRet = (WalIndexHdr*)sqlite3_malloc(sizeof(WalIndexHdr));\n  if( pRet==0 ){\n    rc = SQLITE_NOMEM_BKPT;\n  }else{\n    memcpy(pRet, &pWal->hdr, sizeof(WalIndexHdr));\n    *ppSnapshot = (sqlite3_snapshot*)pRet;\n  }\n\n  return rc;\n}\n\n/* Try to open on pSnapshot when the next read-transaction starts\n*/\nSQLITE_PRIVATE void sqlite3WalSnapshotOpen(Wal *pWal, sqlite3_snapshot *pSnapshot){\n  pWal->pSnapshot = (WalIndexHdr*)pSnapshot;\n}\n\n/* \n** Return a +ve value if snapshot p1 is newer than p2. A -ve value if\n** p1 is older than p2 and zero if p1 and p2 are the same snapshot.\n*/\nSQLITE_API int sqlite3_snapshot_cmp(sqlite3_snapshot *p1, sqlite3_snapshot *p2){\n  WalIndexHdr *pHdr1 = (WalIndexHdr*)p1;\n  WalIndexHdr *pHdr2 = (WalIndexHdr*)p2;\n\n  /* aSalt[0] is a copy of the value stored in the wal file header. It\n  ** is incremented each time the wal file is restarted.  */\n  if( pHdr1->aSalt[0]<pHdr2->aSalt[0] ) return -1;\n  if( pHdr1->aSalt[0]>pHdr2->aSalt[0] ) return +1;\n  if( pHdr1->mxFrame<pHdr2->mxFrame ) return -1;\n  if( pHdr1->mxFrame>pHdr2->mxFrame ) return +1;\n  return 0;\n}\n#endif /* SQLITE_ENABLE_SNAPSHOT */\n\n#ifdef SQLITE_ENABLE_ZIPVFS\n/*\n** If the argument is not NULL, it points to a Wal object that holds a\n** read-lock. This function returns the database page-size if it is known,\n** or zero if it is not (or if pWal is NULL).\n*/\nSQLITE_PRIVATE int sqlite3WalFramesize(Wal *pWal){\n  assert( pWal==0 || pWal->readLock>=0 );\n  return (pWal ? pWal->szPage : 0);\n}\n#endif\n\n/* Return the sqlite3_file object for the WAL file\n*/\nSQLITE_PRIVATE sqlite3_file *sqlite3WalFile(Wal *pWal){\n  return pWal->pWalFd;\n}\n\n#endif /* #ifndef SQLITE_OMIT_WAL */\n\n/************** End of wal.c *************************************************/\n/************** Begin file btmutex.c *****************************************/\n/*\n** 2007 August 27\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n*************************************************************************\n**\n** This file contains code used to implement mutexes on Btree objects.\n** This code really belongs in btree.c.  But btree.c is getting too\n** big and we want to break it down some.  This packaged seemed like\n** a good breakout.\n*/\n/************** Include btreeInt.h in the middle of btmutex.c ****************/\n/************** Begin file btreeInt.h ****************************************/\n/*\n** 2004 April 6\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n*************************************************************************\n** This file implements an external (disk-based) database using BTrees.\n** For a detailed discussion of BTrees, refer to\n**\n**     Donald E. Knuth, THE ART OF COMPUTER PROGRAMMING, Volume 3:\n**     \"Sorting And Searching\", pages 473-480. Addison-Wesley\n**     Publishing Company, Reading, Massachusetts.\n**\n** The basic idea is that each page of the file contains N database\n** entries and N+1 pointers to subpages.\n**\n**   ----------------------------------------------------------------\n**   |  Ptr(0) | Key(0) | Ptr(1) | Key(1) | ... | Key(N-1) | Ptr(N) |\n**   ----------------------------------------------------------------\n**\n** All of the keys on the page that Ptr(0) points to have values less\n** than Key(0).  All of the keys on page Ptr(1) and its subpages have\n** values greater than Key(0) and less than Key(1).  All of the keys\n** on Ptr(N) and its subpages have values greater than Key(N-1).  And\n** so forth.\n**\n** Finding a particular key requires reading O(log(M)) pages from the \n** disk where M is the number of entries in the tree.\n**\n** In this implementation, a single file can hold one or more separate \n** BTrees.  Each BTree is identified by the index of its root page.  The\n** key and data for any entry are combined to form the \"payload\".  A\n** fixed amount of payload can be carried directly on the database\n** page.  If the payload is larger than the preset amount then surplus\n** bytes are stored on overflow pages.  The payload for an entry\n** and the preceding pointer are combined to form a \"Cell\".  Each \n** page has a small header which contains the Ptr(N) pointer and other\n** information such as the size of key and data.\n**\n** FORMAT DETAILS\n**\n** The file is divided into pages.  The first page is called page 1,\n** the second is page 2, and so forth.  A page number of zero indicates\n** \"no such page\".  The page size can be any power of 2 between 512 and 65536.\n** Each page can be either a btree page, a freelist page, an overflow\n** page, or a pointer-map page.\n**\n** The first page is always a btree page.  The first 100 bytes of the first\n** page contain a special header (the \"file header\") that describes the file.\n** The format of the file header is as follows:\n**\n**   OFFSET   SIZE    DESCRIPTION\n**      0      16     Header string: \"SQLite format 3\\000\"\n**     16       2     Page size in bytes.  (1 means 65536)\n**     18       1     File format write version\n**     19       1     File format read version\n**     20       1     Bytes of unused space at the end of each page\n**     21       1     Max embedded payload fraction (must be 64)\n**     22       1     Min embedded payload fraction (must be 32)\n**     23       1     Min leaf payload fraction (must be 32)\n**     24       4     File change counter\n**     28       4     Reserved for future use\n**     32       4     First freelist page\n**     36       4     Number of freelist pages in the file\n**     40      60     15 4-byte meta values passed to higher layers\n**\n**     40       4     Schema cookie\n**     44       4     File format of schema layer\n**     48       4     Size of page cache\n**     52       4     Largest root-page (auto/incr_vacuum)\n**     56       4     1=UTF-8 2=UTF16le 3=UTF16be\n**     60       4     User version\n**     64       4     Incremental vacuum mode\n**     68       4     Application-ID\n**     72      20     unused\n**     92       4     The version-valid-for number\n**     96       4     SQLITE_VERSION_NUMBER\n**\n** All of the integer values are big-endian (most significant byte first).\n**\n** The file change counter is incremented when the database is changed\n** This counter allows other processes to know when the file has changed\n** and thus when they need to flush their cache.\n**\n** The max embedded payload fraction is the amount of the total usable\n** space in a page that can be consumed by a single cell for standard\n** B-tree (non-LEAFDATA) tables.  A value of 255 means 100%.  The default\n** is to limit the maximum cell size so that at least 4 cells will fit\n** on one page.  Thus the default max embedded payload fraction is 64.\n**\n** If the payload for a cell is larger than the max payload, then extra\n** payload is spilled to overflow pages.  Once an overflow page is allocated,\n** as many bytes as possible are moved into the overflow pages without letting\n** the cell size drop below the min embedded payload fraction.\n**\n** The min leaf payload fraction is like the min embedded payload fraction\n** except that it applies to leaf nodes in a LEAFDATA tree.  The maximum\n** payload fraction for a LEAFDATA tree is always 100% (or 255) and it\n** not specified in the header.\n**\n** Each btree pages is divided into three sections:  The header, the\n** cell pointer array, and the cell content area.  Page 1 also has a 100-byte\n** file header that occurs before the page header.\n**\n**      |----------------|\n**      | file header    |   100 bytes.  Page 1 only.\n**      |----------------|\n**      | page header    |   8 bytes for leaves.  12 bytes for interior nodes\n**      |----------------|\n**      | cell pointer   |   |  2 bytes per cell.  Sorted order.\n**      | array          |   |  Grows downward\n**      |                |   v\n**      |----------------|\n**      | unallocated    |\n**      | space          |\n**      |----------------|   ^  Grows upwards\n**      | cell content   |   |  Arbitrary order interspersed with freeblocks.\n**      | area           |   |  and free space fragments.\n**      |----------------|\n**\n** The page headers looks like this:\n**\n**   OFFSET   SIZE     DESCRIPTION\n**      0       1      Flags. 1: intkey, 2: zerodata, 4: leafdata, 8: leaf\n**      1       2      byte offset to the first freeblock\n**      3       2      number of cells on this page\n**      5       2      first byte of the cell content area\n**      7       1      number of fragmented free bytes\n**      8       4      Right child (the Ptr(N) value).  Omitted on leaves.\n**\n** The flags define the format of this btree page.  The leaf flag means that\n** this page has no children.  The zerodata flag means that this page carries\n** only keys and no data.  The intkey flag means that the key is an integer\n** which is stored in the key size entry of the cell header rather than in\n** the payload area.\n**\n** The cell pointer array begins on the first byte after the page header.\n** The cell pointer array contains zero or more 2-byte numbers which are\n** offsets from the beginning of the page to the cell content in the cell\n** content area.  The cell pointers occur in sorted order.  The system strives\n** to keep free space after the last cell pointer so that new cells can\n** be easily added without having to defragment the page.\n**\n** Cell content is stored at the very end of the page and grows toward the\n** beginning of the page.\n**\n** Unused space within the cell content area is collected into a linked list of\n** freeblocks.  Each freeblock is at least 4 bytes in size.  The byte offset\n** to the first freeblock is given in the header.  Freeblocks occur in\n** increasing order.  Because a freeblock must be at least 4 bytes in size,\n** any group of 3 or fewer unused bytes in the cell content area cannot\n** exist on the freeblock chain.  A group of 3 or fewer free bytes is called\n** a fragment.  The total number of bytes in all fragments is recorded.\n** in the page header at offset 7.\n**\n**    SIZE    DESCRIPTION\n**      2     Byte offset of the next freeblock\n**      2     Bytes in this freeblock\n**\n** Cells are of variable length.  Cells are stored in the cell content area at\n** the end of the page.  Pointers to the cells are in the cell pointer array\n** that immediately follows the page header.  Cells is not necessarily\n** contiguous or in order, but cell pointers are contiguous and in order.\n**\n** Cell content makes use of variable length integers.  A variable\n** length integer is 1 to 9 bytes where the lower 7 bits of each \n** byte are used.  The integer consists of all bytes that have bit 8 set and\n** the first byte with bit 8 clear.  The most significant byte of the integer\n** appears first.  A variable-length integer may not be more than 9 bytes long.\n** As a special case, all 8 bytes of the 9th byte are used as data.  This\n** allows a 64-bit integer to be encoded in 9 bytes.\n**\n**    0x00                      becomes  0x00000000\n**    0x7f                      becomes  0x0000007f\n**    0x81 0x00                 becomes  0x00000080\n**    0x82 0x00                 becomes  0x00000100\n**    0x80 0x7f                 becomes  0x0000007f\n**    0x8a 0x91 0xd1 0xac 0x78  becomes  0x12345678\n**    0x81 0x81 0x81 0x81 0x01  becomes  0x10204081\n**\n** Variable length integers are used for rowids and to hold the number of\n** bytes of key and data in a btree cell.\n**\n** The content of a cell looks like this:\n**\n**    SIZE    DESCRIPTION\n**      4     Page number of the left child. Omitted if leaf flag is set.\n**     var    Number of bytes of data. Omitted if the zerodata flag is set.\n**     var    Number of bytes of key. Or the key itself if intkey flag is set.\n**      *     Payload\n**      4     First page of the overflow chain.  Omitted if no overflow\n**\n** Overflow pages form a linked list.  Each page except the last is completely\n** filled with data (pagesize - 4 bytes).  The last page can have as little\n** as 1 byte of data.\n**\n**    SIZE    DESCRIPTION\n**      4     Page number of next overflow page\n**      *     Data\n**\n** Freelist pages come in two subtypes: trunk pages and leaf pages.  The\n** file header points to the first in a linked list of trunk page.  Each trunk\n** page points to multiple leaf pages.  The content of a leaf page is\n** unspecified.  A trunk page looks like this:\n**\n**    SIZE    DESCRIPTION\n**      4     Page number of next trunk page\n**      4     Number of leaf pointers on this page\n**      *     zero or more pages numbers of leaves\n*/\n/* #include \"sqliteInt.h\" */\n\n\n/* The following value is the maximum cell size assuming a maximum page\n** size give above.\n*/\n#define MX_CELL_SIZE(pBt)  ((int)(pBt->pageSize-8))\n\n/* The maximum number of cells on a single page of the database.  This\n** assumes a minimum cell size of 6 bytes  (4 bytes for the cell itself\n** plus 2 bytes for the index to the cell in the page header).  Such\n** small cells will be rare, but they are possible.\n*/\n#define MX_CELL(pBt) ((pBt->pageSize-8)/6)\n\n/* Forward declarations */\ntypedef struct MemPage MemPage;\ntypedef struct BtLock BtLock;\ntypedef struct CellInfo CellInfo;\n\n/*\n** This is a magic string that appears at the beginning of every\n** SQLite database in order to identify the file as a real database.\n**\n** You can change this value at compile-time by specifying a\n** -DSQLITE_FILE_HEADER=\"...\" on the compiler command-line.  The\n** header must be exactly 16 bytes including the zero-terminator so\n** the string itself should be 15 characters long.  If you change\n** the header, then your custom library will not be able to read \n** databases generated by the standard tools and the standard tools\n** will not be able to read databases created by your custom library.\n*/\n#ifndef SQLITE_FILE_HEADER /* 123456789 123456 */\n#  define SQLITE_FILE_HEADER \"SQLite format 3\"\n#endif\n\n/*\n** Page type flags.  An ORed combination of these flags appear as the\n** first byte of on-disk image of every BTree page.\n*/\n#define PTF_INTKEY    0x01\n#define PTF_ZERODATA  0x02\n#define PTF_LEAFDATA  0x04\n#define PTF_LEAF      0x08\n\n/*\n** An instance of this object stores information about each a single database\n** page that has been loaded into memory.  The information in this object\n** is derived from the raw on-disk page content.\n**\n** As each database page is loaded into memory, the pager allocats an\n** instance of this object and zeros the first 8 bytes.  (This is the\n** \"extra\" information associated with each page of the pager.)\n**\n** Access to all fields of this structure is controlled by the mutex\n** stored in MemPage.pBt->mutex.\n*/\nstruct MemPage {\n  u8 isInit;           /* True if previously initialized. MUST BE FIRST! */\n  u8 bBusy;            /* Prevent endless loops on corrupt database files */\n  u8 intKey;           /* True if table b-trees.  False for index b-trees */\n  u8 intKeyLeaf;       /* True if the leaf of an intKey table */\n  Pgno pgno;           /* Page number for this page */\n  /* Only the first 8 bytes (above) are zeroed by pager.c when a new page\n  ** is allocated. All fields that follow must be initialized before use */\n  u8 leaf;             /* True if a leaf page */\n  u8 hdrOffset;        /* 100 for page 1.  0 otherwise */\n  u8 childPtrSize;     /* 0 if leaf==1.  4 if leaf==0 */\n  u8 max1bytePayload;  /* min(maxLocal,127) */\n  u8 nOverflow;        /* Number of overflow cell bodies in aCell[] */\n  u16 maxLocal;        /* Copy of BtShared.maxLocal or BtShared.maxLeaf */\n  u16 minLocal;        /* Copy of BtShared.minLocal or BtShared.minLeaf */\n  u16 cellOffset;      /* Index in aData of first cell pointer */\n  u16 nFree;           /* Number of free bytes on the page */\n  u16 nCell;           /* Number of cells on this page, local and ovfl */\n  u16 maskPage;        /* Mask for page offset */\n  u16 aiOvfl[4];       /* Insert the i-th overflow cell before the aiOvfl-th\n                       ** non-overflow cell */\n  u8 *apOvfl[4];       /* Pointers to the body of overflow cells */\n  BtShared *pBt;       /* Pointer to BtShared that this page is part of */\n  u8 *aData;           /* Pointer to disk image of the page data */\n  u8 *aDataEnd;        /* One byte past the end of usable data */\n  u8 *aCellIdx;        /* The cell index area */\n  u8 *aDataOfst;       /* Same as aData for leaves.  aData+4 for interior */\n  DbPage *pDbPage;     /* Pager page handle */\n  u16 (*xCellSize)(MemPage*,u8*);             /* cellSizePtr method */\n  void (*xParseCell)(MemPage*,u8*,CellInfo*); /* btreeParseCell method */\n};\n\n/*\n** A linked list of the following structures is stored at BtShared.pLock.\n** Locks are added (or upgraded from READ_LOCK to WRITE_LOCK) when a cursor \n** is opened on the table with root page BtShared.iTable. Locks are removed\n** from this list when a transaction is committed or rolled back, or when\n** a btree handle is closed.\n*/\nstruct BtLock {\n  Btree *pBtree;        /* Btree handle holding this lock */\n  Pgno iTable;          /* Root page of table */\n  u8 eLock;             /* READ_LOCK or WRITE_LOCK */\n  BtLock *pNext;        /* Next in BtShared.pLock list */\n};\n\n/* Candidate values for BtLock.eLock */\n#define READ_LOCK     1\n#define WRITE_LOCK    2\n\n/* A Btree handle\n**\n** A database connection contains a pointer to an instance of\n** this object for every database file that it has open.  This structure\n** is opaque to the database connection.  The database connection cannot\n** see the internals of this structure and only deals with pointers to\n** this structure.\n**\n** For some database files, the same underlying database cache might be \n** shared between multiple connections.  In that case, each connection\n** has it own instance of this object.  But each instance of this object\n** points to the same BtShared object.  The database cache and the\n** schema associated with the database file are all contained within\n** the BtShared object.\n**\n** All fields in this structure are accessed under sqlite3.mutex.\n** The pBt pointer itself may not be changed while there exists cursors \n** in the referenced BtShared that point back to this Btree since those\n** cursors have to go through this Btree to find their BtShared and\n** they often do so without holding sqlite3.mutex.\n*/\nstruct Btree {\n  sqlite3 *db;       /* The database connection holding this btree */\n  BtShared *pBt;     /* Sharable content of this btree */\n  u8 inTrans;        /* TRANS_NONE, TRANS_READ or TRANS_WRITE */\n  u8 sharable;       /* True if we can share pBt with another db */\n  u8 locked;         /* True if db currently has pBt locked */\n  u8 hasIncrblobCur; /* True if there are one or more Incrblob cursors */\n  int wantToLock;    /* Number of nested calls to sqlite3BtreeEnter() */\n  int nBackup;       /* Number of backup operations reading this btree */\n  u32 iDataVersion;  /* Combines with pBt->pPager->iDataVersion */\n  Btree *pNext;      /* List of other sharable Btrees from the same db */\n  Btree *pPrev;      /* Back pointer of the same list */\n#ifndef SQLITE_OMIT_SHARED_CACHE\n  BtLock lock;       /* Object used to lock page 1 */\n#endif\n};\n\n/*\n** Btree.inTrans may take one of the following values.\n**\n** If the shared-data extension is enabled, there may be multiple users\n** of the Btree structure. At most one of these may open a write transaction,\n** but any number may have active read transactions.\n*/\n#define TRANS_NONE  0\n#define TRANS_READ  1\n#define TRANS_WRITE 2\n\n/*\n** An instance of this object represents a single database file.\n** \n** A single database file can be in use at the same time by two\n** or more database connections.  When two or more connections are\n** sharing the same database file, each connection has it own\n** private Btree object for the file and each of those Btrees points\n** to this one BtShared object.  BtShared.nRef is the number of\n** connections currently sharing this database file.\n**\n** Fields in this structure are accessed under the BtShared.mutex\n** mutex, except for nRef and pNext which are accessed under the\n** global SQLITE_MUTEX_STATIC_MASTER mutex.  The pPager field\n** may not be modified once it is initially set as long as nRef>0.\n** The pSchema field may be set once under BtShared.mutex and\n** thereafter is unchanged as long as nRef>0.\n**\n** isPending:\n**\n**   If a BtShared client fails to obtain a write-lock on a database\n**   table (because there exists one or more read-locks on the table),\n**   the shared-cache enters 'pending-lock' state and isPending is\n**   set to true.\n**\n**   The shared-cache leaves the 'pending lock' state when either of\n**   the following occur:\n**\n**     1) The current writer (BtShared.pWriter) concludes its transaction, OR\n**     2) The number of locks held by other connections drops to zero.\n**\n**   while in the 'pending-lock' state, no connection may start a new\n**   transaction.\n**\n**   This feature is included to help prevent writer-starvation.\n*/\nstruct BtShared {\n  Pager *pPager;        /* The page cache */\n  sqlite3 *db;          /* Database connection currently using this Btree */\n  BtCursor *pCursor;    /* A list of all open cursors */\n  MemPage *pPage1;      /* First page of the database */\n  u8 openFlags;         /* Flags to sqlite3BtreeOpen() */\n#ifndef SQLITE_OMIT_AUTOVACUUM\n  u8 autoVacuum;        /* True if auto-vacuum is enabled */\n  u8 incrVacuum;        /* True if incr-vacuum is enabled */\n  u8 bDoTruncate;       /* True to truncate db on commit */\n#endif\n  u8 inTransaction;     /* Transaction state */\n  u8 max1bytePayload;   /* Maximum first byte of cell for a 1-byte payload */\n#ifdef SQLITE_HAS_CODEC\n  u8 optimalReserve;    /* Desired amount of reserved space per page */\n#endif\n  u16 btsFlags;         /* Boolean parameters.  See BTS_* macros below */\n  u16 maxLocal;         /* Maximum local payload in non-LEAFDATA tables */\n  u16 minLocal;         /* Minimum local payload in non-LEAFDATA tables */\n  u16 maxLeaf;          /* Maximum local payload in a LEAFDATA table */\n  u16 minLeaf;          /* Minimum local payload in a LEAFDATA table */\n  u32 pageSize;         /* Total number of bytes on a page */\n  u32 usableSize;       /* Number of usable bytes on each page */\n  int nTransaction;     /* Number of open transactions (read + write) */\n  u32 nPage;            /* Number of pages in the database */\n  void *pSchema;        /* Pointer to space allocated by sqlite3BtreeSchema() */\n  void (*xFreeSchema)(void*);  /* Destructor for BtShared.pSchema */\n  sqlite3_mutex *mutex; /* Non-recursive mutex required to access this object */\n  Bitvec *pHasContent;  /* Set of pages moved to free-list this transaction */\n#ifndef SQLITE_OMIT_SHARED_CACHE\n  int nRef;             /* Number of references to this structure */\n  BtShared *pNext;      /* Next on a list of sharable BtShared structs */\n  BtLock *pLock;        /* List of locks held on this shared-btree struct */\n  Btree *pWriter;       /* Btree with currently open write transaction */\n#endif\n  u8 *pTmpSpace;        /* Temp space sufficient to hold a single cell */\n};\n\n/*\n** Allowed values for BtShared.btsFlags\n*/\n#define BTS_READ_ONLY        0x0001   /* Underlying file is readonly */\n#define BTS_PAGESIZE_FIXED   0x0002   /* Page size can no longer be changed */\n#define BTS_SECURE_DELETE    0x0004   /* PRAGMA secure_delete is enabled */\n#define BTS_OVERWRITE        0x0008   /* Overwrite deleted content with zeros */\n#define BTS_FAST_SECURE      0x000c   /* Combination of the previous two */\n#define BTS_INITIALLY_EMPTY  0x0010   /* Database was empty at trans start */\n#define BTS_NO_WAL           0x0020   /* Do not open write-ahead-log files */\n#define BTS_EXCLUSIVE        0x0040   /* pWriter has an exclusive lock */\n#define BTS_PENDING          0x0080   /* Waiting for read-locks to clear */\n\n/*\n** An instance of the following structure is used to hold information\n** about a cell.  The parseCellPtr() function fills in this structure\n** based on information extract from the raw disk page.\n*/\nstruct CellInfo {\n  i64 nKey;      /* The key for INTKEY tables, or nPayload otherwise */\n  u8 *pPayload;  /* Pointer to the start of payload */\n  u32 nPayload;  /* Bytes of payload */\n  u16 nLocal;    /* Amount of payload held locally, not on overflow */\n  u16 nSize;     /* Size of the cell content on the main b-tree page */\n};\n\n/*\n** Maximum depth of an SQLite B-Tree structure. Any B-Tree deeper than\n** this will be declared corrupt. This value is calculated based on a\n** maximum database size of 2^31 pages a minimum fanout of 2 for a\n** root-node and 3 for all other internal nodes.\n**\n** If a tree that appears to be taller than this is encountered, it is\n** assumed that the database is corrupt.\n*/\n#define BTCURSOR_MAX_DEPTH 20\n\n/*\n** A cursor is a pointer to a particular entry within a particular\n** b-tree within a database file.\n**\n** The entry is identified by its MemPage and the index in\n** MemPage.aCell[] of the entry.\n**\n** A single database file can be shared by two more database connections,\n** but cursors cannot be shared.  Each cursor is associated with a\n** particular database connection identified BtCursor.pBtree.db.\n**\n** Fields in this structure are accessed under the BtShared.mutex\n** found at self->pBt->mutex. \n**\n** skipNext meaning:\n**    eState==SKIPNEXT && skipNext>0:  Next sqlite3BtreeNext() is no-op.\n**    eState==SKIPNEXT && skipNext<0:  Next sqlite3BtreePrevious() is no-op.\n**    eState==FAULT:                   Cursor fault with skipNext as error code.\n*/\nstruct BtCursor {\n  u8 eState;                /* One of the CURSOR_XXX constants (see below) */\n  u8 curFlags;              /* zero or more BTCF_* flags defined below */\n  u8 curPagerFlags;         /* Flags to send to sqlite3PagerGet() */\n  u8 hints;                 /* As configured by CursorSetHints() */\n  int skipNext;    /* Prev() is noop if negative. Next() is noop if positive.\n                   ** Error code if eState==CURSOR_FAULT */\n  Btree *pBtree;            /* The Btree to which this cursor belongs */\n  Pgno *aOverflow;          /* Cache of overflow page locations */\n  void *pKey;               /* Saved key that was cursor last known position */\n  /* All fields above are zeroed when the cursor is allocated.  See\n  ** sqlite3BtreeCursorZero().  Fields that follow must be manually\n  ** initialized. */\n#define BTCURSOR_FIRST_UNINIT pBt   /* Name of first uninitialized field */\n  BtShared *pBt;            /* The BtShared this cursor points to */\n  BtCursor *pNext;          /* Forms a linked list of all cursors */\n  CellInfo info;            /* A parse of the cell we are pointing at */\n  i64 nKey;                 /* Size of pKey, or last integer key */\n  Pgno pgnoRoot;            /* The root page of this tree */\n  i8 iPage;                 /* Index of current page in apPage */\n  u8 curIntKey;             /* Value of apPage[0]->intKey */\n  u16 ix;                   /* Current index for apPage[iPage] */\n  u16 aiIdx[BTCURSOR_MAX_DEPTH-1];     /* Current index in apPage[i] */\n  struct KeyInfo *pKeyInfo;            /* Arg passed to comparison function */\n  MemPage *pPage;                        /* Current page */\n  MemPage *apPage[BTCURSOR_MAX_DEPTH-1]; /* Stack of parents of current page */\n};\n\n/*\n** Legal values for BtCursor.curFlags\n*/\n#define BTCF_WriteFlag    0x01   /* True if a write cursor */\n#define BTCF_ValidNKey    0x02   /* True if info.nKey is valid */\n#define BTCF_ValidOvfl    0x04   /* True if aOverflow is valid */\n#define BTCF_AtLast       0x08   /* Cursor is pointing ot the last entry */\n#define BTCF_Incrblob     0x10   /* True if an incremental I/O handle */\n#define BTCF_Multiple     0x20   /* Maybe another cursor on the same btree */\n\n/*\n** Potential values for BtCursor.eState.\n**\n** CURSOR_INVALID:\n**   Cursor does not point to a valid entry. This can happen (for example) \n**   because the table is empty or because BtreeCursorFirst() has not been\n**   called.\n**\n** CURSOR_VALID:\n**   Cursor points to a valid entry. getPayload() etc. may be called.\n**\n** CURSOR_SKIPNEXT:\n**   Cursor is valid except that the Cursor.skipNext field is non-zero\n**   indicating that the next sqlite3BtreeNext() or sqlite3BtreePrevious()\n**   operation should be a no-op.\n**\n** CURSOR_REQUIRESEEK:\n**   The table that this cursor was opened on still exists, but has been \n**   modified since the cursor was last used. The cursor position is saved\n**   in variables BtCursor.pKey and BtCursor.nKey. When a cursor is in \n**   this state, restoreCursorPosition() can be called to attempt to\n**   seek the cursor to the saved position.\n**\n** CURSOR_FAULT:\n**   An unrecoverable error (an I/O error or a malloc failure) has occurred\n**   on a different connection that shares the BtShared cache with this\n**   cursor.  The error has left the cache in an inconsistent state.\n**   Do nothing else with this cursor.  Any attempt to use the cursor\n**   should return the error code stored in BtCursor.skipNext\n*/\n#define CURSOR_VALID             0\n#define CURSOR_INVALID           1\n#define CURSOR_SKIPNEXT          2\n#define CURSOR_REQUIRESEEK       3\n#define CURSOR_FAULT             4\n\n/* \n** The database page the PENDING_BYTE occupies. This page is never used.\n*/\n# define PENDING_BYTE_PAGE(pBt) PAGER_MJ_PGNO(pBt)\n\n/*\n** These macros define the location of the pointer-map entry for a \n** database page. The first argument to each is the number of usable\n** bytes on each page of the database (often 1024). The second is the\n** page number to look up in the pointer map.\n**\n** PTRMAP_PAGENO returns the database page number of the pointer-map\n** page that stores the required pointer. PTRMAP_PTROFFSET returns\n** the offset of the requested map entry.\n**\n** If the pgno argument passed to PTRMAP_PAGENO is a pointer-map page,\n** then pgno is returned. So (pgno==PTRMAP_PAGENO(pgsz, pgno)) can be\n** used to test if pgno is a pointer-map page. PTRMAP_ISPAGE implements\n** this test.\n*/\n#define PTRMAP_PAGENO(pBt, pgno) ptrmapPageno(pBt, pgno)\n#define PTRMAP_PTROFFSET(pgptrmap, pgno) (5*(pgno-pgptrmap-1))\n#define PTRMAP_ISPAGE(pBt, pgno) (PTRMAP_PAGENO((pBt),(pgno))==(pgno))\n\n/*\n** The pointer map is a lookup table that identifies the parent page for\n** each child page in the database file.  The parent page is the page that\n** contains a pointer to the child.  Every page in the database contains\n** 0 or 1 parent pages.  (In this context 'database page' refers\n** to any page that is not part of the pointer map itself.)  Each pointer map\n** entry consists of a single byte 'type' and a 4 byte parent page number.\n** The PTRMAP_XXX identifiers below are the valid types.\n**\n** The purpose of the pointer map is to facility moving pages from one\n** position in the file to another as part of autovacuum.  When a page\n** is moved, the pointer in its parent must be updated to point to the\n** new location.  The pointer map is used to locate the parent page quickly.\n**\n** PTRMAP_ROOTPAGE: The database page is a root-page. The page-number is not\n**                  used in this case.\n**\n** PTRMAP_FREEPAGE: The database page is an unused (free) page. The page-number \n**                  is not used in this case.\n**\n** PTRMAP_OVERFLOW1: The database page is the first page in a list of \n**                   overflow pages. The page number identifies the page that\n**                   contains the cell with a pointer to this overflow page.\n**\n** PTRMAP_OVERFLOW2: The database page is the second or later page in a list of\n**                   overflow pages. The page-number identifies the previous\n**                   page in the overflow page list.\n**\n** PTRMAP_BTREE: The database page is a non-root btree page. The page number\n**               identifies the parent page in the btree.\n*/\n#define PTRMAP_ROOTPAGE 1\n#define PTRMAP_FREEPAGE 2\n#define PTRMAP_OVERFLOW1 3\n#define PTRMAP_OVERFLOW2 4\n#define PTRMAP_BTREE 5\n\n/* A bunch of assert() statements to check the transaction state variables\n** of handle p (type Btree*) are internally consistent.\n*/\n#define btreeIntegrity(p) \\\n  assert( p->pBt->inTransaction!=TRANS_NONE || p->pBt->nTransaction==0 ); \\\n  assert( p->pBt->inTransaction>=p->inTrans ); \n\n\n/*\n** The ISAUTOVACUUM macro is used within balance_nonroot() to determine\n** if the database supports auto-vacuum or not. Because it is used\n** within an expression that is an argument to another macro \n** (sqliteMallocRaw), it is not possible to use conditional compilation.\n** So, this macro is defined instead.\n*/\n#ifndef SQLITE_OMIT_AUTOVACUUM\n#define ISAUTOVACUUM (pBt->autoVacuum)\n#else\n#define ISAUTOVACUUM 0\n#endif\n\n\n/*\n** This structure is passed around through all the sanity checking routines\n** in order to keep track of some global state information.\n**\n** The aRef[] array is allocated so that there is 1 bit for each page in\n** the database. As the integrity-check proceeds, for each page used in\n** the database the corresponding bit is set. This allows integrity-check to \n** detect pages that are used twice and orphaned pages (both of which \n** indicate corruption).\n*/\ntypedef struct IntegrityCk IntegrityCk;\nstruct IntegrityCk {\n  BtShared *pBt;    /* The tree being checked out */\n  Pager *pPager;    /* The associated pager.  Also accessible by pBt->pPager */\n  u8 *aPgRef;       /* 1 bit per page in the db (see above) */\n  Pgno nPage;       /* Number of pages in the database */\n  int mxErr;        /* Stop accumulating errors when this reaches zero */\n  int nErr;         /* Number of messages written to zErrMsg so far */\n  int mallocFailed; /* A memory allocation error has occurred */\n  const char *zPfx; /* Error message prefix */\n  int v1, v2;       /* Values for up to two %d fields in zPfx */\n  StrAccum errMsg;  /* Accumulate the error message text here */\n  u32 *heap;        /* Min-heap used for analyzing cell coverage */\n};\n\n/*\n** Routines to read or write a two- and four-byte big-endian integer values.\n*/\n#define get2byte(x)   ((x)[0]<<8 | (x)[1])\n#define put2byte(p,v) ((p)[0] = (u8)((v)>>8), (p)[1] = (u8)(v))\n#define get4byte sqlite3Get4byte\n#define put4byte sqlite3Put4byte\n\n/*\n** get2byteAligned(), unlike get2byte(), requires that its argument point to a\n** two-byte aligned address.  get2bytea() is only used for accessing the\n** cell addresses in a btree header.\n*/\n#if SQLITE_BYTEORDER==4321\n# define get2byteAligned(x)  (*(u16*)(x))\n#elif SQLITE_BYTEORDER==1234 && GCC_VERSION>=4008000\n# define get2byteAligned(x)  __builtin_bswap16(*(u16*)(x))\n#elif SQLITE_BYTEORDER==1234 && MSVC_VERSION>=1300\n# define get2byteAligned(x)  _byteswap_ushort(*(u16*)(x))\n#else\n# define get2byteAligned(x)  ((x)[0]<<8 | (x)[1])\n#endif\n\n/************** End of btreeInt.h ********************************************/\n/************** Continuing where we left off in btmutex.c ********************/\n#ifndef SQLITE_OMIT_SHARED_CACHE\n#if SQLITE_THREADSAFE\n\n/*\n** Obtain the BtShared mutex associated with B-Tree handle p. Also,\n** set BtShared.db to the database handle associated with p and the\n** p->locked boolean to true.\n*/\nstatic void lockBtreeMutex(Btree *p){\n  assert( p->locked==0 );\n  assert( sqlite3_mutex_notheld(p->pBt->mutex) );\n  assert( sqlite3_mutex_held(p->db->mutex) );\n\n  sqlite3_mutex_enter(p->pBt->mutex);\n  p->pBt->db = p->db;\n  p->locked = 1;\n}\n\n/*\n** Release the BtShared mutex associated with B-Tree handle p and\n** clear the p->locked boolean.\n*/\nstatic void SQLITE_NOINLINE unlockBtreeMutex(Btree *p){\n  BtShared *pBt = p->pBt;\n  assert( p->locked==1 );\n  assert( sqlite3_mutex_held(pBt->mutex) );\n  assert( sqlite3_mutex_held(p->db->mutex) );\n  assert( p->db==pBt->db );\n\n  sqlite3_mutex_leave(pBt->mutex);\n  p->locked = 0;\n}\n\n/* Forward reference */\nstatic void SQLITE_NOINLINE btreeLockCarefully(Btree *p);\n\n/*\n** Enter a mutex on the given BTree object.\n**\n** If the object is not sharable, then no mutex is ever required\n** and this routine is a no-op.  The underlying mutex is non-recursive.\n** But we keep a reference count in Btree.wantToLock so the behavior\n** of this interface is recursive.\n**\n** To avoid deadlocks, multiple Btrees are locked in the same order\n** by all database connections.  The p->pNext is a list of other\n** Btrees belonging to the same database connection as the p Btree\n** which need to be locked after p.  If we cannot get a lock on\n** p, then first unlock all of the others on p->pNext, then wait\n** for the lock to become available on p, then relock all of the\n** subsequent Btrees that desire a lock.\n*/\nSQLITE_PRIVATE void sqlite3BtreeEnter(Btree *p){\n  /* Some basic sanity checking on the Btree.  The list of Btrees\n  ** connected by pNext and pPrev should be in sorted order by\n  ** Btree.pBt value. All elements of the list should belong to\n  ** the same connection. Only shared Btrees are on the list. */\n  assert( p->pNext==0 || p->pNext->pBt>p->pBt );\n  assert( p->pPrev==0 || p->pPrev->pBt<p->pBt );\n  assert( p->pNext==0 || p->pNext->db==p->db );\n  assert( p->pPrev==0 || p->pPrev->db==p->db );\n  assert( p->sharable || (p->pNext==0 && p->pPrev==0) );\n\n  /* Check for locking consistency */\n  assert( !p->locked || p->wantToLock>0 );\n  assert( p->sharable || p->wantToLock==0 );\n\n  /* We should already hold a lock on the database connection */\n  assert( sqlite3_mutex_held(p->db->mutex) );\n\n  /* Unless the database is sharable and unlocked, then BtShared.db\n  ** should already be set correctly. */\n  assert( (p->locked==0 && p->sharable) || p->pBt->db==p->db );\n\n  if( !p->sharable ) return;\n  p->wantToLock++;\n  if( p->locked ) return;\n  btreeLockCarefully(p);\n}\n\n/* This is a helper function for sqlite3BtreeLock(). By moving\n** complex, but seldom used logic, out of sqlite3BtreeLock() and\n** into this routine, we avoid unnecessary stack pointer changes\n** and thus help the sqlite3BtreeLock() routine to run much faster\n** in the common case.\n*/\nstatic void SQLITE_NOINLINE btreeLockCarefully(Btree *p){\n  Btree *pLater;\n\n  /* In most cases, we should be able to acquire the lock we\n  ** want without having to go through the ascending lock\n  ** procedure that follows.  Just be sure not to block.\n  */\n  if( sqlite3_mutex_try(p->pBt->mutex)==SQLITE_OK ){\n    p->pBt->db = p->db;\n    p->locked = 1;\n    return;\n  }\n\n  /* To avoid deadlock, first release all locks with a larger\n  ** BtShared address.  Then acquire our lock.  Then reacquire\n  ** the other BtShared locks that we used to hold in ascending\n  ** order.\n  */\n  for(pLater=p->pNext; pLater; pLater=pLater->pNext){\n    assert( pLater->sharable );\n    assert( pLater->pNext==0 || pLater->pNext->pBt>pLater->pBt );\n    assert( !pLater->locked || pLater->wantToLock>0 );\n    if( pLater->locked ){\n      unlockBtreeMutex(pLater);\n    }\n  }\n  lockBtreeMutex(p);\n  for(pLater=p->pNext; pLater; pLater=pLater->pNext){\n    if( pLater->wantToLock ){\n      lockBtreeMutex(pLater);\n    }\n  }\n}\n\n\n/*\n** Exit the recursive mutex on a Btree.\n*/\nSQLITE_PRIVATE void sqlite3BtreeLeave(Btree *p){\n  assert( sqlite3_mutex_held(p->db->mutex) );\n  if( p->sharable ){\n    assert( p->wantToLock>0 );\n    p->wantToLock--;\n    if( p->wantToLock==0 ){\n      unlockBtreeMutex(p);\n    }\n  }\n}\n\n#ifndef NDEBUG\n/*\n** Return true if the BtShared mutex is held on the btree, or if the\n** B-Tree is not marked as sharable.\n**\n** This routine is used only from within assert() statements.\n*/\nSQLITE_PRIVATE int sqlite3BtreeHoldsMutex(Btree *p){\n  assert( p->sharable==0 || p->locked==0 || p->wantToLock>0 );\n  assert( p->sharable==0 || p->locked==0 || p->db==p->pBt->db );\n  assert( p->sharable==0 || p->locked==0 || sqlite3_mutex_held(p->pBt->mutex) );\n  assert( p->sharable==0 || p->locked==0 || sqlite3_mutex_held(p->db->mutex) );\n\n  return (p->sharable==0 || p->locked);\n}\n#endif\n\n\n/*\n** Enter the mutex on every Btree associated with a database\n** connection.  This is needed (for example) prior to parsing\n** a statement since we will be comparing table and column names\n** against all schemas and we do not want those schemas being\n** reset out from under us.\n**\n** There is a corresponding leave-all procedures.\n**\n** Enter the mutexes in accending order by BtShared pointer address\n** to avoid the possibility of deadlock when two threads with\n** two or more btrees in common both try to lock all their btrees\n** at the same instant.\n*/\nstatic void SQLITE_NOINLINE btreeEnterAll(sqlite3 *db){\n  int i;\n  int skipOk = 1;\n  Btree *p;\n  assert( sqlite3_mutex_held(db->mutex) );\n  for(i=0; i<db->nDb; i++){\n    p = db->aDb[i].pBt;\n    if( p && p->sharable ){\n      sqlite3BtreeEnter(p);\n      skipOk = 0;\n    }\n  }\n  db->skipBtreeMutex = skipOk;\n}\nSQLITE_PRIVATE void sqlite3BtreeEnterAll(sqlite3 *db){\n  if( db->skipBtreeMutex==0 ) btreeEnterAll(db);\n}\nstatic void SQLITE_NOINLINE btreeLeaveAll(sqlite3 *db){\n  int i;\n  Btree *p;\n  assert( sqlite3_mutex_held(db->mutex) );\n  for(i=0; i<db->nDb; i++){\n    p = db->aDb[i].pBt;\n    if( p ) sqlite3BtreeLeave(p);\n  }\n}\nSQLITE_PRIVATE void sqlite3BtreeLeaveAll(sqlite3 *db){\n  if( db->skipBtreeMutex==0 ) btreeLeaveAll(db);\n}\n\n#ifndef NDEBUG\n/*\n** Return true if the current thread holds the database connection\n** mutex and all required BtShared mutexes.\n**\n** This routine is used inside assert() statements only.\n*/\nSQLITE_PRIVATE int sqlite3BtreeHoldsAllMutexes(sqlite3 *db){\n  int i;\n  if( !sqlite3_mutex_held(db->mutex) ){\n    return 0;\n  }\n  for(i=0; i<db->nDb; i++){\n    Btree *p;\n    p = db->aDb[i].pBt;\n    if( p && p->sharable &&\n         (p->wantToLock==0 || !sqlite3_mutex_held(p->pBt->mutex)) ){\n      return 0;\n    }\n  }\n  return 1;\n}\n#endif /* NDEBUG */\n\n#ifndef NDEBUG\n/*\n** Return true if the correct mutexes are held for accessing the\n** db->aDb[iDb].pSchema structure.  The mutexes required for schema\n** access are:\n**\n**   (1) The mutex on db\n**   (2) if iDb!=1, then the mutex on db->aDb[iDb].pBt.\n**\n** If pSchema is not NULL, then iDb is computed from pSchema and\n** db using sqlite3SchemaToIndex().\n*/\nSQLITE_PRIVATE int sqlite3SchemaMutexHeld(sqlite3 *db, int iDb, Schema *pSchema){\n  Btree *p;\n  assert( db!=0 );\n  if( pSchema ) iDb = sqlite3SchemaToIndex(db, pSchema);\n  assert( iDb>=0 && iDb<db->nDb );\n  if( !sqlite3_mutex_held(db->mutex) ) return 0;\n  if( iDb==1 ) return 1;\n  p = db->aDb[iDb].pBt;\n  assert( p!=0 );\n  return p->sharable==0 || p->locked==1;\n}\n#endif /* NDEBUG */\n\n#else /* SQLITE_THREADSAFE>0 above.  SQLITE_THREADSAFE==0 below */\n/*\n** The following are special cases for mutex enter routines for use\n** in single threaded applications that use shared cache.  Except for\n** these two routines, all mutex operations are no-ops in that case and\n** are null #defines in btree.h.\n**\n** If shared cache is disabled, then all btree mutex routines, including\n** the ones below, are no-ops and are null #defines in btree.h.\n*/\n\nSQLITE_PRIVATE void sqlite3BtreeEnter(Btree *p){\n  p->pBt->db = p->db;\n}\nSQLITE_PRIVATE void sqlite3BtreeEnterAll(sqlite3 *db){\n  int i;\n  for(i=0; i<db->nDb; i++){\n    Btree *p = db->aDb[i].pBt;\n    if( p ){\n      p->pBt->db = p->db;\n    }\n  }\n}\n#endif /* if SQLITE_THREADSAFE */\n\n#ifndef SQLITE_OMIT_INCRBLOB\n/*\n** Enter a mutex on a Btree given a cursor owned by that Btree. \n**\n** These entry points are used by incremental I/O only. Enter() is required \n** any time OMIT_SHARED_CACHE is not defined, regardless of whether or not \n** the build is threadsafe. Leave() is only required by threadsafe builds.\n*/\nSQLITE_PRIVATE void sqlite3BtreeEnterCursor(BtCursor *pCur){\n  sqlite3BtreeEnter(pCur->pBtree);\n}\n# if SQLITE_THREADSAFE\nSQLITE_PRIVATE void sqlite3BtreeLeaveCursor(BtCursor *pCur){\n  sqlite3BtreeLeave(pCur->pBtree);\n}\n# endif\n#endif /* ifndef SQLITE_OMIT_INCRBLOB */\n\n#endif /* ifndef SQLITE_OMIT_SHARED_CACHE */\n\n/************** End of btmutex.c *********************************************/\n/************** Begin file btree.c *******************************************/\n/*\n** 2004 April 6\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n*************************************************************************\n** This file implements an external (disk-based) database using BTrees.\n** See the header comment on \"btreeInt.h\" for additional information.\n** Including a description of file format and an overview of operation.\n*/\n/* #include \"btreeInt.h\" */\n\n/*\n** The header string that appears at the beginning of every\n** SQLite database.\n*/\nstatic const char zMagicHeader[] = SQLITE_FILE_HEADER;\n\n/*\n** Set this global variable to 1 to enable tracing using the TRACE\n** macro.\n*/\n#if 0\nint sqlite3BtreeTrace=1;  /* True to enable tracing */\n# define TRACE(X)  if(sqlite3BtreeTrace){printf X;fflush(stdout);}\n#else\n# define TRACE(X)\n#endif\n\n/*\n** Extract a 2-byte big-endian integer from an array of unsigned bytes.\n** But if the value is zero, make it 65536.\n**\n** This routine is used to extract the \"offset to cell content area\" value\n** from the header of a btree page.  If the page size is 65536 and the page\n** is empty, the offset should be 65536, but the 2-byte value stores zero.\n** This routine makes the necessary adjustment to 65536.\n*/\n#define get2byteNotZero(X)  (((((int)get2byte(X))-1)&0xffff)+1)\n\n/*\n** Values passed as the 5th argument to allocateBtreePage()\n*/\n#define BTALLOC_ANY   0           /* Allocate any page */\n#define BTALLOC_EXACT 1           /* Allocate exact page if possible */\n#define BTALLOC_LE    2           /* Allocate any page <= the parameter */\n\n/*\n** Macro IfNotOmitAV(x) returns (x) if SQLITE_OMIT_AUTOVACUUM is not \n** defined, or 0 if it is. For example:\n**\n**   bIncrVacuum = IfNotOmitAV(pBtShared->incrVacuum);\n*/\n#ifndef SQLITE_OMIT_AUTOVACUUM\n#define IfNotOmitAV(expr) (expr)\n#else\n#define IfNotOmitAV(expr) 0\n#endif\n\n#ifndef SQLITE_OMIT_SHARED_CACHE\n/*\n** A list of BtShared objects that are eligible for participation\n** in shared cache.  This variable has file scope during normal builds,\n** but the test harness needs to access it so we make it global for \n** test builds.\n**\n** Access to this variable is protected by SQLITE_MUTEX_STATIC_MASTER.\n*/\n#ifdef SQLITE_TEST\nSQLITE_PRIVATE BtShared *SQLITE_WSD sqlite3SharedCacheList = 0;\n#else\nstatic BtShared *SQLITE_WSD sqlite3SharedCacheList = 0;\n#endif\n#endif /* SQLITE_OMIT_SHARED_CACHE */\n\n#ifndef SQLITE_OMIT_SHARED_CACHE\n/*\n** Enable or disable the shared pager and schema features.\n**\n** This routine has no effect on existing database connections.\n** The shared cache setting effects only future calls to\n** sqlite3_open(), sqlite3_open16(), or sqlite3_open_v2().\n*/\nSQLITE_API int sqlite3_enable_shared_cache(int enable){\n  sqlite3GlobalConfig.sharedCacheEnabled = enable;\n  return SQLITE_OK;\n}\n#endif\n\n\n\n#ifdef SQLITE_OMIT_SHARED_CACHE\n  /*\n  ** The functions querySharedCacheTableLock(), setSharedCacheTableLock(),\n  ** and clearAllSharedCacheTableLocks()\n  ** manipulate entries in the BtShared.pLock linked list used to store\n  ** shared-cache table level locks. If the library is compiled with the\n  ** shared-cache feature disabled, then there is only ever one user\n  ** of each BtShared structure and so this locking is not necessary. \n  ** So define the lock related functions as no-ops.\n  */\n  #define querySharedCacheTableLock(a,b,c) SQLITE_OK\n  #define setSharedCacheTableLock(a,b,c) SQLITE_OK\n  #define clearAllSharedCacheTableLocks(a)\n  #define downgradeAllSharedCacheTableLocks(a)\n  #define hasSharedCacheTableLock(a,b,c,d) 1\n  #define hasReadConflicts(a, b) 0\n#endif\n\n/*\n** Implementation of the SQLITE_CORRUPT_PAGE() macro. Takes a single\n** (MemPage*) as an argument. The (MemPage*) must not be NULL.\n**\n** If SQLITE_DEBUG is not defined, then this macro is equivalent to\n** SQLITE_CORRUPT_BKPT. Or, if SQLITE_DEBUG is set, then the log message\n** normally produced as a side-effect of SQLITE_CORRUPT_BKPT is augmented\n** with the page number and filename associated with the (MemPage*).\n*/\n#ifdef SQLITE_DEBUG\nint corruptPageError(int lineno, MemPage *p){\n  char *zMsg;\n  sqlite3BeginBenignMalloc();\n  zMsg = sqlite3_mprintf(\"database corruption page %d of %s\",\n      (int)p->pgno, sqlite3PagerFilename(p->pBt->pPager, 0)\n  );\n  sqlite3EndBenignMalloc();\n  if( zMsg ){\n    sqlite3ReportError(SQLITE_CORRUPT, lineno, zMsg);\n  }\n  sqlite3_free(zMsg);\n  return SQLITE_CORRUPT_BKPT;\n}\n# define SQLITE_CORRUPT_PAGE(pMemPage) corruptPageError(__LINE__, pMemPage)\n#else\n# define SQLITE_CORRUPT_PAGE(pMemPage) SQLITE_CORRUPT_PGNO(pMemPage->pgno)\n#endif\n\n#ifndef SQLITE_OMIT_SHARED_CACHE\n\n#ifdef SQLITE_DEBUG\n/*\n**** This function is only used as part of an assert() statement. ***\n**\n** Check to see if pBtree holds the required locks to read or write to the \n** table with root page iRoot.   Return 1 if it does and 0 if not.\n**\n** For example, when writing to a table with root-page iRoot via \n** Btree connection pBtree:\n**\n**    assert( hasSharedCacheTableLock(pBtree, iRoot, 0, WRITE_LOCK) );\n**\n** When writing to an index that resides in a sharable database, the \n** caller should have first obtained a lock specifying the root page of\n** the corresponding table. This makes things a bit more complicated,\n** as this module treats each table as a separate structure. To determine\n** the table corresponding to the index being written, this\n** function has to search through the database schema.\n**\n** Instead of a lock on the table/index rooted at page iRoot, the caller may\n** hold a write-lock on the schema table (root page 1). This is also\n** acceptable.\n*/\nstatic int hasSharedCacheTableLock(\n  Btree *pBtree,         /* Handle that must hold lock */\n  Pgno iRoot,            /* Root page of b-tree */\n  int isIndex,           /* True if iRoot is the root of an index b-tree */\n  int eLockType          /* Required lock type (READ_LOCK or WRITE_LOCK) */\n){\n  Schema *pSchema = (Schema *)pBtree->pBt->pSchema;\n  Pgno iTab = 0;\n  BtLock *pLock;\n\n  /* If this database is not shareable, or if the client is reading\n  ** and has the read-uncommitted flag set, then no lock is required. \n  ** Return true immediately.\n  */\n  if( (pBtree->sharable==0)\n   || (eLockType==READ_LOCK && (pBtree->db->flags & SQLITE_ReadUncommit))\n  ){\n    return 1;\n  }\n\n  /* If the client is reading  or writing an index and the schema is\n  ** not loaded, then it is too difficult to actually check to see if\n  ** the correct locks are held.  So do not bother - just return true.\n  ** This case does not come up very often anyhow.\n  */\n  if( isIndex && (!pSchema || (pSchema->schemaFlags&DB_SchemaLoaded)==0) ){\n    return 1;\n  }\n\n  /* Figure out the root-page that the lock should be held on. For table\n  ** b-trees, this is just the root page of the b-tree being read or\n  ** written. For index b-trees, it is the root page of the associated\n  ** table.  */\n  if( isIndex ){\n    HashElem *p;\n    for(p=sqliteHashFirst(&pSchema->idxHash); p; p=sqliteHashNext(p)){\n      Index *pIdx = (Index *)sqliteHashData(p);\n      if( pIdx->tnum==(int)iRoot ){\n        if( iTab ){\n          /* Two or more indexes share the same root page.  There must\n          ** be imposter tables.  So just return true.  The assert is not\n          ** useful in that case. */\n          return 1;\n        }\n        iTab = pIdx->pTable->tnum;\n      }\n    }\n  }else{\n    iTab = iRoot;\n  }\n\n  /* Search for the required lock. Either a write-lock on root-page iTab, a \n  ** write-lock on the schema table, or (if the client is reading) a\n  ** read-lock on iTab will suffice. Return 1 if any of these are found.  */\n  for(pLock=pBtree->pBt->pLock; pLock; pLock=pLock->pNext){\n    if( pLock->pBtree==pBtree \n     && (pLock->iTable==iTab || (pLock->eLock==WRITE_LOCK && pLock->iTable==1))\n     && pLock->eLock>=eLockType \n    ){\n      return 1;\n    }\n  }\n\n  /* Failed to find the required lock. */\n  return 0;\n}\n#endif /* SQLITE_DEBUG */\n\n#ifdef SQLITE_DEBUG\n/*\n**** This function may be used as part of assert() statements only. ****\n**\n** Return true if it would be illegal for pBtree to write into the\n** table or index rooted at iRoot because other shared connections are\n** simultaneously reading that same table or index.\n**\n** It is illegal for pBtree to write if some other Btree object that\n** shares the same BtShared object is currently reading or writing\n** the iRoot table.  Except, if the other Btree object has the\n** read-uncommitted flag set, then it is OK for the other object to\n** have a read cursor.\n**\n** For example, before writing to any part of the table or index\n** rooted at page iRoot, one should call:\n**\n**    assert( !hasReadConflicts(pBtree, iRoot) );\n*/\nstatic int hasReadConflicts(Btree *pBtree, Pgno iRoot){\n  BtCursor *p;\n  for(p=pBtree->pBt->pCursor; p; p=p->pNext){\n    if( p->pgnoRoot==iRoot \n     && p->pBtree!=pBtree\n     && 0==(p->pBtree->db->flags & SQLITE_ReadUncommit)\n    ){\n      return 1;\n    }\n  }\n  return 0;\n}\n#endif    /* #ifdef SQLITE_DEBUG */\n\n/*\n** Query to see if Btree handle p may obtain a lock of type eLock \n** (READ_LOCK or WRITE_LOCK) on the table with root-page iTab. Return\n** SQLITE_OK if the lock may be obtained (by calling\n** setSharedCacheTableLock()), or SQLITE_LOCKED if not.\n*/\nstatic int querySharedCacheTableLock(Btree *p, Pgno iTab, u8 eLock){\n  BtShared *pBt = p->pBt;\n  BtLock *pIter;\n\n  assert( sqlite3BtreeHoldsMutex(p) );\n  assert( eLock==READ_LOCK || eLock==WRITE_LOCK );\n  assert( p->db!=0 );\n  assert( !(p->db->flags&SQLITE_ReadUncommit)||eLock==WRITE_LOCK||iTab==1 );\n  \n  /* If requesting a write-lock, then the Btree must have an open write\n  ** transaction on this file. And, obviously, for this to be so there \n  ** must be an open write transaction on the file itself.\n  */\n  assert( eLock==READ_LOCK || (p==pBt->pWriter && p->inTrans==TRANS_WRITE) );\n  assert( eLock==READ_LOCK || pBt->inTransaction==TRANS_WRITE );\n  \n  /* This routine is a no-op if the shared-cache is not enabled */\n  if( !p->sharable ){\n    return SQLITE_OK;\n  }\n\n  /* If some other connection is holding an exclusive lock, the\n  ** requested lock may not be obtained.\n  */\n  if( pBt->pWriter!=p && (pBt->btsFlags & BTS_EXCLUSIVE)!=0 ){\n    sqlite3ConnectionBlocked(p->db, pBt->pWriter->db);\n    return SQLITE_LOCKED_SHAREDCACHE;\n  }\n\n  for(pIter=pBt->pLock; pIter; pIter=pIter->pNext){\n    /* The condition (pIter->eLock!=eLock) in the following if(...) \n    ** statement is a simplification of:\n    **\n    **   (eLock==WRITE_LOCK || pIter->eLock==WRITE_LOCK)\n    **\n    ** since we know that if eLock==WRITE_LOCK, then no other connection\n    ** may hold a WRITE_LOCK on any table in this file (since there can\n    ** only be a single writer).\n    */\n    assert( pIter->eLock==READ_LOCK || pIter->eLock==WRITE_LOCK );\n    assert( eLock==READ_LOCK || pIter->pBtree==p || pIter->eLock==READ_LOCK);\n    if( pIter->pBtree!=p && pIter->iTable==iTab && pIter->eLock!=eLock ){\n      sqlite3ConnectionBlocked(p->db, pIter->pBtree->db);\n      if( eLock==WRITE_LOCK ){\n        assert( p==pBt->pWriter );\n        pBt->btsFlags |= BTS_PENDING;\n      }\n      return SQLITE_LOCKED_SHAREDCACHE;\n    }\n  }\n  return SQLITE_OK;\n}\n#endif /* !SQLITE_OMIT_SHARED_CACHE */\n\n#ifndef SQLITE_OMIT_SHARED_CACHE\n/*\n** Add a lock on the table with root-page iTable to the shared-btree used\n** by Btree handle p. Parameter eLock must be either READ_LOCK or \n** WRITE_LOCK.\n**\n** This function assumes the following:\n**\n**   (a) The specified Btree object p is connected to a sharable\n**       database (one with the BtShared.sharable flag set), and\n**\n**   (b) No other Btree objects hold a lock that conflicts\n**       with the requested lock (i.e. querySharedCacheTableLock() has\n**       already been called and returned SQLITE_OK).\n**\n** SQLITE_OK is returned if the lock is added successfully. SQLITE_NOMEM \n** is returned if a malloc attempt fails.\n*/\nstatic int setSharedCacheTableLock(Btree *p, Pgno iTable, u8 eLock){\n  BtShared *pBt = p->pBt;\n  BtLock *pLock = 0;\n  BtLock *pIter;\n\n  assert( sqlite3BtreeHoldsMutex(p) );\n  assert( eLock==READ_LOCK || eLock==WRITE_LOCK );\n  assert( p->db!=0 );\n\n  /* A connection with the read-uncommitted flag set will never try to\n  ** obtain a read-lock using this function. The only read-lock obtained\n  ** by a connection in read-uncommitted mode is on the sqlite_master \n  ** table, and that lock is obtained in BtreeBeginTrans().  */\n  assert( 0==(p->db->flags&SQLITE_ReadUncommit) || eLock==WRITE_LOCK );\n\n  /* This function should only be called on a sharable b-tree after it \n  ** has been determined that no other b-tree holds a conflicting lock.  */\n  assert( p->sharable );\n  assert( SQLITE_OK==querySharedCacheTableLock(p, iTable, eLock) );\n\n  /* First search the list for an existing lock on this table. */\n  for(pIter=pBt->pLock; pIter; pIter=pIter->pNext){\n    if( pIter->iTable==iTable && pIter->pBtree==p ){\n      pLock = pIter;\n      break;\n    }\n  }\n\n  /* If the above search did not find a BtLock struct associating Btree p\n  ** with table iTable, allocate one and link it into the list.\n  */\n  if( !pLock ){\n    pLock = (BtLock *)sqlite3MallocZero(sizeof(BtLock));\n    if( !pLock ){\n      return SQLITE_NOMEM_BKPT;\n    }\n    pLock->iTable = iTable;\n    pLock->pBtree = p;\n    pLock->pNext = pBt->pLock;\n    pBt->pLock = pLock;\n  }\n\n  /* Set the BtLock.eLock variable to the maximum of the current lock\n  ** and the requested lock. This means if a write-lock was already held\n  ** and a read-lock requested, we don't incorrectly downgrade the lock.\n  */\n  assert( WRITE_LOCK>READ_LOCK );\n  if( eLock>pLock->eLock ){\n    pLock->eLock = eLock;\n  }\n\n  return SQLITE_OK;\n}\n#endif /* !SQLITE_OMIT_SHARED_CACHE */\n\n#ifndef SQLITE_OMIT_SHARED_CACHE\n/*\n** Release all the table locks (locks obtained via calls to\n** the setSharedCacheTableLock() procedure) held by Btree object p.\n**\n** This function assumes that Btree p has an open read or write \n** transaction. If it does not, then the BTS_PENDING flag\n** may be incorrectly cleared.\n*/\nstatic void clearAllSharedCacheTableLocks(Btree *p){\n  BtShared *pBt = p->pBt;\n  BtLock **ppIter = &pBt->pLock;\n\n  assert( sqlite3BtreeHoldsMutex(p) );\n  assert( p->sharable || 0==*ppIter );\n  assert( p->inTrans>0 );\n\n  while( *ppIter ){\n    BtLock *pLock = *ppIter;\n    assert( (pBt->btsFlags & BTS_EXCLUSIVE)==0 || pBt->pWriter==pLock->pBtree );\n    assert( pLock->pBtree->inTrans>=pLock->eLock );\n    if( pLock->pBtree==p ){\n      *ppIter = pLock->pNext;\n      assert( pLock->iTable!=1 || pLock==&p->lock );\n      if( pLock->iTable!=1 ){\n        sqlite3_free(pLock);\n      }\n    }else{\n      ppIter = &pLock->pNext;\n    }\n  }\n\n  assert( (pBt->btsFlags & BTS_PENDING)==0 || pBt->pWriter );\n  if( pBt->pWriter==p ){\n    pBt->pWriter = 0;\n    pBt->btsFlags &= ~(BTS_EXCLUSIVE|BTS_PENDING);\n  }else if( pBt->nTransaction==2 ){\n    /* This function is called when Btree p is concluding its \n    ** transaction. If there currently exists a writer, and p is not\n    ** that writer, then the number of locks held by connections other\n    ** than the writer must be about to drop to zero. In this case\n    ** set the BTS_PENDING flag to 0.\n    **\n    ** If there is not currently a writer, then BTS_PENDING must\n    ** be zero already. So this next line is harmless in that case.\n    */\n    pBt->btsFlags &= ~BTS_PENDING;\n  }\n}\n\n/*\n** This function changes all write-locks held by Btree p into read-locks.\n*/\nstatic void downgradeAllSharedCacheTableLocks(Btree *p){\n  BtShared *pBt = p->pBt;\n  if( pBt->pWriter==p ){\n    BtLock *pLock;\n    pBt->pWriter = 0;\n    pBt->btsFlags &= ~(BTS_EXCLUSIVE|BTS_PENDING);\n    for(pLock=pBt->pLock; pLock; pLock=pLock->pNext){\n      assert( pLock->eLock==READ_LOCK || pLock->pBtree==p );\n      pLock->eLock = READ_LOCK;\n    }\n  }\n}\n\n#endif /* SQLITE_OMIT_SHARED_CACHE */\n\nstatic void releasePage(MemPage *pPage);         /* Forward reference */\nstatic void releasePageOne(MemPage *pPage);      /* Forward reference */\nstatic void releasePageNotNull(MemPage *pPage);  /* Forward reference */\n\n/*\n***** This routine is used inside of assert() only ****\n**\n** Verify that the cursor holds the mutex on its BtShared\n*/\n#ifdef SQLITE_DEBUG\nstatic int cursorHoldsMutex(BtCursor *p){\n  return sqlite3_mutex_held(p->pBt->mutex);\n}\n\n/* Verify that the cursor and the BtShared agree about what is the current\n** database connetion. This is important in shared-cache mode. If the database \n** connection pointers get out-of-sync, it is possible for routines like\n** btreeInitPage() to reference an stale connection pointer that references a\n** a connection that has already closed.  This routine is used inside assert()\n** statements only and for the purpose of double-checking that the btree code\n** does keep the database connection pointers up-to-date.\n*/\nstatic int cursorOwnsBtShared(BtCursor *p){\n  assert( cursorHoldsMutex(p) );\n  return (p->pBtree->db==p->pBt->db);\n}\n#endif\n\n/*\n** Invalidate the overflow cache of the cursor passed as the first argument.\n** on the shared btree structure pBt.\n*/\n#define invalidateOverflowCache(pCur) (pCur->curFlags &= ~BTCF_ValidOvfl)\n\n/*\n** Invalidate the overflow page-list cache for all cursors opened\n** on the shared btree structure pBt.\n*/\nstatic void invalidateAllOverflowCache(BtShared *pBt){\n  BtCursor *p;\n  assert( sqlite3_mutex_held(pBt->mutex) );\n  for(p=pBt->pCursor; p; p=p->pNext){\n    invalidateOverflowCache(p);\n  }\n}\n\n#ifndef SQLITE_OMIT_INCRBLOB\n/*\n** This function is called before modifying the contents of a table\n** to invalidate any incrblob cursors that are open on the\n** row or one of the rows being modified.\n**\n** If argument isClearTable is true, then the entire contents of the\n** table is about to be deleted. In this case invalidate all incrblob\n** cursors open on any row within the table with root-page pgnoRoot.\n**\n** Otherwise, if argument isClearTable is false, then the row with\n** rowid iRow is being replaced or deleted. In this case invalidate\n** only those incrblob cursors open on that specific row.\n*/\nstatic void invalidateIncrblobCursors(\n  Btree *pBtree,          /* The database file to check */\n  Pgno pgnoRoot,          /* The table that might be changing */\n  i64 iRow,               /* The rowid that might be changing */\n  int isClearTable        /* True if all rows are being deleted */\n){\n  BtCursor *p;\n  if( pBtree->hasIncrblobCur==0 ) return;\n  assert( sqlite3BtreeHoldsMutex(pBtree) );\n  pBtree->hasIncrblobCur = 0;\n  for(p=pBtree->pBt->pCursor; p; p=p->pNext){\n    if( (p->curFlags & BTCF_Incrblob)!=0 ){\n      pBtree->hasIncrblobCur = 1;\n      if( p->pgnoRoot==pgnoRoot && (isClearTable || p->info.nKey==iRow) ){\n        p->eState = CURSOR_INVALID;\n      }\n    }\n  }\n}\n\n#else\n  /* Stub function when INCRBLOB is omitted */\n  #define invalidateIncrblobCursors(w,x,y,z)\n#endif /* SQLITE_OMIT_INCRBLOB */\n\n/*\n** Set bit pgno of the BtShared.pHasContent bitvec. This is called \n** when a page that previously contained data becomes a free-list leaf \n** page.\n**\n** The BtShared.pHasContent bitvec exists to work around an obscure\n** bug caused by the interaction of two useful IO optimizations surrounding\n** free-list leaf pages:\n**\n**   1) When all data is deleted from a page and the page becomes\n**      a free-list leaf page, the page is not written to the database\n**      (as free-list leaf pages contain no meaningful data). Sometimes\n**      such a page is not even journalled (as it will not be modified,\n**      why bother journalling it?).\n**\n**   2) When a free-list leaf page is reused, its content is not read\n**      from the database or written to the journal file (why should it\n**      be, if it is not at all meaningful?).\n**\n** By themselves, these optimizations work fine and provide a handy\n** performance boost to bulk delete or insert operations. However, if\n** a page is moved to the free-list and then reused within the same\n** transaction, a problem comes up. If the page is not journalled when\n** it is moved to the free-list and it is also not journalled when it\n** is extracted from the free-list and reused, then the original data\n** may be lost. In the event of a rollback, it may not be possible\n** to restore the database to its original configuration.\n**\n** The solution is the BtShared.pHasContent bitvec. Whenever a page is \n** moved to become a free-list leaf page, the corresponding bit is\n** set in the bitvec. Whenever a leaf page is extracted from the free-list,\n** optimization 2 above is omitted if the corresponding bit is already\n** set in BtShared.pHasContent. The contents of the bitvec are cleared\n** at the end of every transaction.\n*/\nstatic int btreeSetHasContent(BtShared *pBt, Pgno pgno){\n  int rc = SQLITE_OK;\n  if( !pBt->pHasContent ){\n    assert( pgno<=pBt->nPage );\n    pBt->pHasContent = sqlite3BitvecCreate(pBt->nPage);\n    if( !pBt->pHasContent ){\n      rc = SQLITE_NOMEM_BKPT;\n    }\n  }\n  if( rc==SQLITE_OK && pgno<=sqlite3BitvecSize(pBt->pHasContent) ){\n    rc = sqlite3BitvecSet(pBt->pHasContent, pgno);\n  }\n  return rc;\n}\n\n/*\n** Query the BtShared.pHasContent vector.\n**\n** This function is called when a free-list leaf page is removed from the\n** free-list for reuse. It returns false if it is safe to retrieve the\n** page from the pager layer with the 'no-content' flag set. True otherwise.\n*/\nstatic int btreeGetHasContent(BtShared *pBt, Pgno pgno){\n  Bitvec *p = pBt->pHasContent;\n  return (p && (pgno>sqlite3BitvecSize(p) || sqlite3BitvecTest(p, pgno)));\n}\n\n/*\n** Clear (destroy) the BtShared.pHasContent bitvec. This should be\n** invoked at the conclusion of each write-transaction.\n*/\nstatic void btreeClearHasContent(BtShared *pBt){\n  sqlite3BitvecDestroy(pBt->pHasContent);\n  pBt->pHasContent = 0;\n}\n\n/*\n** Release all of the apPage[] pages for a cursor.\n*/\nstatic void btreeReleaseAllCursorPages(BtCursor *pCur){\n  int i;\n  if( pCur->iPage>=0 ){\n    for(i=0; i<pCur->iPage; i++){\n      releasePageNotNull(pCur->apPage[i]);\n    }\n    releasePageNotNull(pCur->pPage);\n    pCur->iPage = -1;\n  }\n}\n\n/*\n** The cursor passed as the only argument must point to a valid entry\n** when this function is called (i.e. have eState==CURSOR_VALID). This\n** function saves the current cursor key in variables pCur->nKey and\n** pCur->pKey. SQLITE_OK is returned if successful or an SQLite error \n** code otherwise.\n**\n** If the cursor is open on an intkey table, then the integer key\n** (the rowid) is stored in pCur->nKey and pCur->pKey is left set to\n** NULL. If the cursor is open on a non-intkey table, then pCur->pKey is \n** set to point to a malloced buffer pCur->nKey bytes in size containing \n** the key.\n*/\nstatic int saveCursorKey(BtCursor *pCur){\n  int rc = SQLITE_OK;\n  assert( CURSOR_VALID==pCur->eState );\n  assert( 0==pCur->pKey );\n  assert( cursorHoldsMutex(pCur) );\n\n  if( pCur->curIntKey ){\n    /* Only the rowid is required for a table btree */\n    pCur->nKey = sqlite3BtreeIntegerKey(pCur);\n  }else{\n    /* For an index btree, save the complete key content */\n    void *pKey;\n    pCur->nKey = sqlite3BtreePayloadSize(pCur);\n    pKey = sqlite3Malloc( pCur->nKey );\n    if( pKey ){\n      rc = sqlite3BtreePayload(pCur, 0, (int)pCur->nKey, pKey);\n      if( rc==SQLITE_OK ){\n        pCur->pKey = pKey;\n      }else{\n        sqlite3_free(pKey);\n      }\n    }else{\n      rc = SQLITE_NOMEM_BKPT;\n    }\n  }\n  assert( !pCur->curIntKey || !pCur->pKey );\n  return rc;\n}\n\n/*\n** Save the current cursor position in the variables BtCursor.nKey \n** and BtCursor.pKey. The cursor's state is set to CURSOR_REQUIRESEEK.\n**\n** The caller must ensure that the cursor is valid (has eState==CURSOR_VALID)\n** prior to calling this routine.  \n*/\nstatic int saveCursorPosition(BtCursor *pCur){\n  int rc;\n\n  assert( CURSOR_VALID==pCur->eState || CURSOR_SKIPNEXT==pCur->eState );\n  assert( 0==pCur->pKey );\n  assert( cursorHoldsMutex(pCur) );\n\n  if( pCur->eState==CURSOR_SKIPNEXT ){\n    pCur->eState = CURSOR_VALID;\n  }else{\n    pCur->skipNext = 0;\n  }\n\n  rc = saveCursorKey(pCur);\n  if( rc==SQLITE_OK ){\n    btreeReleaseAllCursorPages(pCur);\n    pCur->eState = CURSOR_REQUIRESEEK;\n  }\n\n  pCur->curFlags &= ~(BTCF_ValidNKey|BTCF_ValidOvfl|BTCF_AtLast);\n  return rc;\n}\n\n/* Forward reference */\nstatic int SQLITE_NOINLINE saveCursorsOnList(BtCursor*,Pgno,BtCursor*);\n\n/*\n** Save the positions of all cursors (except pExcept) that are open on\n** the table with root-page iRoot.  \"Saving the cursor position\" means that\n** the location in the btree is remembered in such a way that it can be\n** moved back to the same spot after the btree has been modified.  This\n** routine is called just before cursor pExcept is used to modify the\n** table, for example in BtreeDelete() or BtreeInsert().\n**\n** If there are two or more cursors on the same btree, then all such \n** cursors should have their BTCF_Multiple flag set.  The btreeCursor()\n** routine enforces that rule.  This routine only needs to be called in\n** the uncommon case when pExpect has the BTCF_Multiple flag set.\n**\n** If pExpect!=NULL and if no other cursors are found on the same root-page,\n** then the BTCF_Multiple flag on pExpect is cleared, to avoid another\n** pointless call to this routine.\n**\n** Implementation note:  This routine merely checks to see if any cursors\n** need to be saved.  It calls out to saveCursorsOnList() in the (unusual)\n** event that cursors are in need to being saved.\n*/\nstatic int saveAllCursors(BtShared *pBt, Pgno iRoot, BtCursor *pExcept){\n  BtCursor *p;\n  assert( sqlite3_mutex_held(pBt->mutex) );\n  assert( pExcept==0 || pExcept->pBt==pBt );\n  for(p=pBt->pCursor; p; p=p->pNext){\n    if( p!=pExcept && (0==iRoot || p->pgnoRoot==iRoot) ) break;\n  }\n  if( p ) return saveCursorsOnList(p, iRoot, pExcept);\n  if( pExcept ) pExcept->curFlags &= ~BTCF_Multiple;\n  return SQLITE_OK;\n}\n\n/* This helper routine to saveAllCursors does the actual work of saving\n** the cursors if and when a cursor is found that actually requires saving.\n** The common case is that no cursors need to be saved, so this routine is\n** broken out from its caller to avoid unnecessary stack pointer movement.\n*/\nstatic int SQLITE_NOINLINE saveCursorsOnList(\n  BtCursor *p,         /* The first cursor that needs saving */\n  Pgno iRoot,          /* Only save cursor with this iRoot. Save all if zero */\n  BtCursor *pExcept    /* Do not save this cursor */\n){\n  do{\n    if( p!=pExcept && (0==iRoot || p->pgnoRoot==iRoot) ){\n      if( p->eState==CURSOR_VALID || p->eState==CURSOR_SKIPNEXT ){\n        int rc = saveCursorPosition(p);\n        if( SQLITE_OK!=rc ){\n          return rc;\n        }\n      }else{\n        testcase( p->iPage>=0 );\n        btreeReleaseAllCursorPages(p);\n      }\n    }\n    p = p->pNext;\n  }while( p );\n  return SQLITE_OK;\n}\n\n/*\n** Clear the current cursor position.\n*/\nSQLITE_PRIVATE void sqlite3BtreeClearCursor(BtCursor *pCur){\n  assert( cursorHoldsMutex(pCur) );\n  sqlite3_free(pCur->pKey);\n  pCur->pKey = 0;\n  pCur->eState = CURSOR_INVALID;\n}\n\n/*\n** In this version of BtreeMoveto, pKey is a packed index record\n** such as is generated by the OP_MakeRecord opcode.  Unpack the\n** record and then call BtreeMovetoUnpacked() to do the work.\n*/\nstatic int btreeMoveto(\n  BtCursor *pCur,     /* Cursor open on the btree to be searched */\n  const void *pKey,   /* Packed key if the btree is an index */\n  i64 nKey,           /* Integer key for tables.  Size of pKey for indices */\n  int bias,           /* Bias search to the high end */\n  int *pRes           /* Write search results here */\n){\n  int rc;                    /* Status code */\n  UnpackedRecord *pIdxKey;   /* Unpacked index key */\n\n  if( pKey ){\n    assert( nKey==(i64)(int)nKey );\n    pIdxKey = sqlite3VdbeAllocUnpackedRecord(pCur->pKeyInfo);\n    if( pIdxKey==0 ) return SQLITE_NOMEM_BKPT;\n    sqlite3VdbeRecordUnpack(pCur->pKeyInfo, (int)nKey, pKey, pIdxKey);\n    if( pIdxKey->nField==0 ){\n      rc = SQLITE_CORRUPT_BKPT;\n      goto moveto_done;\n    }\n  }else{\n    pIdxKey = 0;\n  }\n  rc = sqlite3BtreeMovetoUnpacked(pCur, pIdxKey, nKey, bias, pRes);\nmoveto_done:\n  if( pIdxKey ){\n    sqlite3DbFree(pCur->pKeyInfo->db, pIdxKey);\n  }\n  return rc;\n}\n\n/*\n** Restore the cursor to the position it was in (or as close to as possible)\n** when saveCursorPosition() was called. Note that this call deletes the \n** saved position info stored by saveCursorPosition(), so there can be\n** at most one effective restoreCursorPosition() call after each \n** saveCursorPosition().\n*/\nstatic int btreeRestoreCursorPosition(BtCursor *pCur){\n  int rc;\n  int skipNext;\n  assert( cursorOwnsBtShared(pCur) );\n  assert( pCur->eState>=CURSOR_REQUIRESEEK );\n  if( pCur->eState==CURSOR_FAULT ){\n    return pCur->skipNext;\n  }\n  pCur->eState = CURSOR_INVALID;\n  rc = btreeMoveto(pCur, pCur->pKey, pCur->nKey, 0, &skipNext);\n  if( rc==SQLITE_OK ){\n    sqlite3_free(pCur->pKey);\n    pCur->pKey = 0;\n    assert( pCur->eState==CURSOR_VALID || pCur->eState==CURSOR_INVALID );\n    pCur->skipNext |= skipNext;\n    if( pCur->skipNext && pCur->eState==CURSOR_VALID ){\n      pCur->eState = CURSOR_SKIPNEXT;\n    }\n  }\n  return rc;\n}\n\n#define restoreCursorPosition(p) \\\n  (p->eState>=CURSOR_REQUIRESEEK ? \\\n         btreeRestoreCursorPosition(p) : \\\n         SQLITE_OK)\n\n/*\n** Determine whether or not a cursor has moved from the position where\n** it was last placed, or has been invalidated for any other reason.\n** Cursors can move when the row they are pointing at is deleted out\n** from under them, for example.  Cursor might also move if a btree\n** is rebalanced.\n**\n** Calling this routine with a NULL cursor pointer returns false.\n**\n** Use the separate sqlite3BtreeCursorRestore() routine to restore a cursor\n** back to where it ought to be if this routine returns true.\n*/\nSQLITE_PRIVATE int sqlite3BtreeCursorHasMoved(BtCursor *pCur){\n  return pCur->eState!=CURSOR_VALID;\n}\n\n/*\n** Return a pointer to a fake BtCursor object that will always answer\n** false to the sqlite3BtreeCursorHasMoved() routine above.  The fake\n** cursor returned must not be used with any other Btree interface.\n*/\nSQLITE_PRIVATE BtCursor *sqlite3BtreeFakeValidCursor(void){\n  static u8 fakeCursor = CURSOR_VALID;\n  assert( offsetof(BtCursor, eState)==0 );\n  return (BtCursor*)&fakeCursor;\n}\n\n/*\n** This routine restores a cursor back to its original position after it\n** has been moved by some outside activity (such as a btree rebalance or\n** a row having been deleted out from under the cursor).  \n**\n** On success, the *pDifferentRow parameter is false if the cursor is left\n** pointing at exactly the same row.  *pDifferntRow is the row the cursor\n** was pointing to has been deleted, forcing the cursor to point to some\n** nearby row.\n**\n** This routine should only be called for a cursor that just returned\n** TRUE from sqlite3BtreeCursorHasMoved().\n*/\nSQLITE_PRIVATE int sqlite3BtreeCursorRestore(BtCursor *pCur, int *pDifferentRow){\n  int rc;\n\n  assert( pCur!=0 );\n  assert( pCur->eState!=CURSOR_VALID );\n  rc = restoreCursorPosition(pCur);\n  if( rc ){\n    *pDifferentRow = 1;\n    return rc;\n  }\n  if( pCur->eState!=CURSOR_VALID ){\n    *pDifferentRow = 1;\n  }else{\n    assert( pCur->skipNext==0 );\n    *pDifferentRow = 0;\n  }\n  return SQLITE_OK;\n}\n\n#ifdef SQLITE_ENABLE_CURSOR_HINTS\n/*\n** Provide hints to the cursor.  The particular hint given (and the type\n** and number of the varargs parameters) is determined by the eHintType\n** parameter.  See the definitions of the BTREE_HINT_* macros for details.\n*/\nSQLITE_PRIVATE void sqlite3BtreeCursorHint(BtCursor *pCur, int eHintType, ...){\n  /* Used only by system that substitute their own storage engine */\n}\n#endif\n\n/*\n** Provide flag hints to the cursor.\n*/\nSQLITE_PRIVATE void sqlite3BtreeCursorHintFlags(BtCursor *pCur, unsigned x){\n  assert( x==BTREE_SEEK_EQ || x==BTREE_BULKLOAD || x==0 );\n  pCur->hints = x;\n}\n\n\n#ifndef SQLITE_OMIT_AUTOVACUUM\n/*\n** Given a page number of a regular database page, return the page\n** number for the pointer-map page that contains the entry for the\n** input page number.\n**\n** Return 0 (not a valid page) for pgno==1 since there is\n** no pointer map associated with page 1.  The integrity_check logic\n** requires that ptrmapPageno(*,1)!=1.\n*/\nstatic Pgno ptrmapPageno(BtShared *pBt, Pgno pgno){\n  int nPagesPerMapPage;\n  Pgno iPtrMap, ret;\n  assert( sqlite3_mutex_held(pBt->mutex) );\n  if( pgno<2 ) return 0;\n  nPagesPerMapPage = (pBt->usableSize/5)+1;\n  iPtrMap = (pgno-2)/nPagesPerMapPage;\n  ret = (iPtrMap*nPagesPerMapPage) + 2; \n  if( ret==PENDING_BYTE_PAGE(pBt) ){\n    ret++;\n  }\n  return ret;\n}\n\n/*\n** Write an entry into the pointer map.\n**\n** This routine updates the pointer map entry for page number 'key'\n** so that it maps to type 'eType' and parent page number 'pgno'.\n**\n** If *pRC is initially non-zero (non-SQLITE_OK) then this routine is\n** a no-op.  If an error occurs, the appropriate error code is written\n** into *pRC.\n*/\nstatic void ptrmapPut(BtShared *pBt, Pgno key, u8 eType, Pgno parent, int *pRC){\n  DbPage *pDbPage;  /* The pointer map page */\n  u8 *pPtrmap;      /* The pointer map data */\n  Pgno iPtrmap;     /* The pointer map page number */\n  int offset;       /* Offset in pointer map page */\n  int rc;           /* Return code from subfunctions */\n\n  if( *pRC ) return;\n\n  assert( sqlite3_mutex_held(pBt->mutex) );\n  /* The master-journal page number must never be used as a pointer map page */\n  assert( 0==PTRMAP_ISPAGE(pBt, PENDING_BYTE_PAGE(pBt)) );\n\n  assert( pBt->autoVacuum );\n  if( key==0 ){\n    *pRC = SQLITE_CORRUPT_BKPT;\n    return;\n  }\n  iPtrmap = PTRMAP_PAGENO(pBt, key);\n  rc = sqlite3PagerGet(pBt->pPager, iPtrmap, &pDbPage, 0);\n  if( rc!=SQLITE_OK ){\n    *pRC = rc;\n    return;\n  }\n  offset = PTRMAP_PTROFFSET(iPtrmap, key);\n  if( offset<0 ){\n    *pRC = SQLITE_CORRUPT_BKPT;\n    goto ptrmap_exit;\n  }\n  assert( offset <= (int)pBt->usableSize-5 );\n  pPtrmap = (u8 *)sqlite3PagerGetData(pDbPage);\n\n  if( eType!=pPtrmap[offset] || get4byte(&pPtrmap[offset+1])!=parent ){\n    TRACE((\"PTRMAP_UPDATE: %d->(%d,%d)\\n\", key, eType, parent));\n    *pRC= rc = sqlite3PagerWrite(pDbPage);\n    if( rc==SQLITE_OK ){\n      pPtrmap[offset] = eType;\n      put4byte(&pPtrmap[offset+1], parent);\n    }\n  }\n\nptrmap_exit:\n  sqlite3PagerUnref(pDbPage);\n}\n\n/*\n** Read an entry from the pointer map.\n**\n** This routine retrieves the pointer map entry for page 'key', writing\n** the type and parent page number to *pEType and *pPgno respectively.\n** An error code is returned if something goes wrong, otherwise SQLITE_OK.\n*/\nstatic int ptrmapGet(BtShared *pBt, Pgno key, u8 *pEType, Pgno *pPgno){\n  DbPage *pDbPage;   /* The pointer map page */\n  int iPtrmap;       /* Pointer map page index */\n  u8 *pPtrmap;       /* Pointer map page data */\n  int offset;        /* Offset of entry in pointer map */\n  int rc;\n\n  assert( sqlite3_mutex_held(pBt->mutex) );\n\n  iPtrmap = PTRMAP_PAGENO(pBt, key);\n  rc = sqlite3PagerGet(pBt->pPager, iPtrmap, &pDbPage, 0);\n  if( rc!=0 ){\n    return rc;\n  }\n  pPtrmap = (u8 *)sqlite3PagerGetData(pDbPage);\n\n  offset = PTRMAP_PTROFFSET(iPtrmap, key);\n  if( offset<0 ){\n    sqlite3PagerUnref(pDbPage);\n    return SQLITE_CORRUPT_BKPT;\n  }\n  assert( offset <= (int)pBt->usableSize-5 );\n  assert( pEType!=0 );\n  *pEType = pPtrmap[offset];\n  if( pPgno ) *pPgno = get4byte(&pPtrmap[offset+1]);\n\n  sqlite3PagerUnref(pDbPage);\n  if( *pEType<1 || *pEType>5 ) return SQLITE_CORRUPT_PGNO(iPtrmap);\n  return SQLITE_OK;\n}\n\n#else /* if defined SQLITE_OMIT_AUTOVACUUM */\n  #define ptrmapPut(w,x,y,z,rc)\n  #define ptrmapGet(w,x,y,z) SQLITE_OK\n  #define ptrmapPutOvflPtr(x, y, rc)\n#endif\n\n/*\n** Given a btree page and a cell index (0 means the first cell on\n** the page, 1 means the second cell, and so forth) return a pointer\n** to the cell content.\n**\n** findCellPastPtr() does the same except it skips past the initial\n** 4-byte child pointer found on interior pages, if there is one.\n**\n** This routine works only for pages that do not contain overflow cells.\n*/\n#define findCell(P,I) \\\n  ((P)->aData + ((P)->maskPage & get2byteAligned(&(P)->aCellIdx[2*(I)])))\n#define findCellPastPtr(P,I) \\\n  ((P)->aDataOfst + ((P)->maskPage & get2byteAligned(&(P)->aCellIdx[2*(I)])))\n\n\n/*\n** This is common tail processing for btreeParseCellPtr() and\n** btreeParseCellPtrIndex() for the case when the cell does not fit entirely\n** on a single B-tree page.  Make necessary adjustments to the CellInfo\n** structure.\n*/\nstatic SQLITE_NOINLINE void btreeParseCellAdjustSizeForOverflow(\n  MemPage *pPage,         /* Page containing the cell */\n  u8 *pCell,              /* Pointer to the cell text. */\n  CellInfo *pInfo         /* Fill in this structure */\n){\n  /* If the payload will not fit completely on the local page, we have\n  ** to decide how much to store locally and how much to spill onto\n  ** overflow pages.  The strategy is to minimize the amount of unused\n  ** space on overflow pages while keeping the amount of local storage\n  ** in between minLocal and maxLocal.\n  **\n  ** Warning:  changing the way overflow payload is distributed in any\n  ** way will result in an incompatible file format.\n  */\n  int minLocal;  /* Minimum amount of payload held locally */\n  int maxLocal;  /* Maximum amount of payload held locally */\n  int surplus;   /* Overflow payload available for local storage */\n\n  minLocal = pPage->minLocal;\n  maxLocal = pPage->maxLocal;\n  surplus = minLocal + (pInfo->nPayload - minLocal)%(pPage->pBt->usableSize-4);\n  testcase( surplus==maxLocal );\n  testcase( surplus==maxLocal+1 );\n  if( surplus <= maxLocal ){\n    pInfo->nLocal = (u16)surplus;\n  }else{\n    pInfo->nLocal = (u16)minLocal;\n  }\n  pInfo->nSize = (u16)(&pInfo->pPayload[pInfo->nLocal] - pCell) + 4;\n}\n\n/*\n** The following routines are implementations of the MemPage.xParseCell()\n** method.\n**\n** Parse a cell content block and fill in the CellInfo structure.\n**\n** btreeParseCellPtr()        =>   table btree leaf nodes\n** btreeParseCellNoPayload()  =>   table btree internal nodes\n** btreeParseCellPtrIndex()   =>   index btree nodes\n**\n** There is also a wrapper function btreeParseCell() that works for\n** all MemPage types and that references the cell by index rather than\n** by pointer.\n*/\nstatic void btreeParseCellPtrNoPayload(\n  MemPage *pPage,         /* Page containing the cell */\n  u8 *pCell,              /* Pointer to the cell text. */\n  CellInfo *pInfo         /* Fill in this structure */\n){\n  assert( sqlite3_mutex_held(pPage->pBt->mutex) );\n  assert( pPage->leaf==0 );\n  assert( pPage->childPtrSize==4 );\n#ifndef SQLITE_DEBUG\n  UNUSED_PARAMETER(pPage);\n#endif\n  pInfo->nSize = 4 + getVarint(&pCell[4], (u64*)&pInfo->nKey);\n  pInfo->nPayload = 0;\n  pInfo->nLocal = 0;\n  pInfo->pPayload = 0;\n  return;\n}\nstatic void btreeParseCellPtr(\n  MemPage *pPage,         /* Page containing the cell */\n  u8 *pCell,              /* Pointer to the cell text. */\n  CellInfo *pInfo         /* Fill in this structure */\n){\n  u8 *pIter;              /* For scanning through pCell */\n  u32 nPayload;           /* Number of bytes of cell payload */\n  u64 iKey;               /* Extracted Key value */\n\n  assert( sqlite3_mutex_held(pPage->pBt->mutex) );\n  assert( pPage->leaf==0 || pPage->leaf==1 );\n  assert( pPage->intKeyLeaf );\n  assert( pPage->childPtrSize==0 );\n  pIter = pCell;\n\n  /* The next block of code is equivalent to:\n  **\n  **     pIter += getVarint32(pIter, nPayload);\n  **\n  ** The code is inlined to avoid a function call.\n  */\n  nPayload = *pIter;\n  if( nPayload>=0x80 ){\n    u8 *pEnd = &pIter[8];\n    nPayload &= 0x7f;\n    do{\n      nPayload = (nPayload<<7) | (*++pIter & 0x7f);\n    }while( (*pIter)>=0x80 && pIter<pEnd );\n  }\n  pIter++;\n\n  /* The next block of code is equivalent to:\n  **\n  **     pIter += getVarint(pIter, (u64*)&pInfo->nKey);\n  **\n  ** The code is inlined to avoid a function call.\n  */\n  iKey = *pIter;\n  if( iKey>=0x80 ){\n    u8 *pEnd = &pIter[7];\n    iKey &= 0x7f;\n    while(1){\n      iKey = (iKey<<7) | (*++pIter & 0x7f);\n      if( (*pIter)<0x80 ) break;\n      if( pIter>=pEnd ){\n        iKey = (iKey<<8) | *++pIter;\n        break;\n      }\n    }\n  }\n  pIter++;\n\n  pInfo->nKey = *(i64*)&iKey;\n  pInfo->nPayload = nPayload;\n  pInfo->pPayload = pIter;\n  testcase( nPayload==pPage->maxLocal );\n  testcase( nPayload==pPage->maxLocal+1 );\n  if( nPayload<=pPage->maxLocal ){\n    /* This is the (easy) common case where the entire payload fits\n    ** on the local page.  No overflow is required.\n    */\n    pInfo->nSize = nPayload + (u16)(pIter - pCell);\n    if( pInfo->nSize<4 ) pInfo->nSize = 4;\n    pInfo->nLocal = (u16)nPayload;\n  }else{\n    btreeParseCellAdjustSizeForOverflow(pPage, pCell, pInfo);\n  }\n}\nstatic void btreeParseCellPtrIndex(\n  MemPage *pPage,         /* Page containing the cell */\n  u8 *pCell,              /* Pointer to the cell text. */\n  CellInfo *pInfo         /* Fill in this structure */\n){\n  u8 *pIter;              /* For scanning through pCell */\n  u32 nPayload;           /* Number of bytes of cell payload */\n\n  assert( sqlite3_mutex_held(pPage->pBt->mutex) );\n  assert( pPage->leaf==0 || pPage->leaf==1 );\n  assert( pPage->intKeyLeaf==0 );\n  pIter = pCell + pPage->childPtrSize;\n  nPayload = *pIter;\n  if( nPayload>=0x80 ){\n    u8 *pEnd = &pIter[8];\n    nPayload &= 0x7f;\n    do{\n      nPayload = (nPayload<<7) | (*++pIter & 0x7f);\n    }while( *(pIter)>=0x80 && pIter<pEnd );\n  }\n  pIter++;\n  pInfo->nKey = nPayload;\n  pInfo->nPayload = nPayload;\n  pInfo->pPayload = pIter;\n  testcase( nPayload==pPage->maxLocal );\n  testcase( nPayload==pPage->maxLocal+1 );\n  if( nPayload<=pPage->maxLocal ){\n    /* This is the (easy) common case where the entire payload fits\n    ** on the local page.  No overflow is required.\n    */\n    pInfo->nSize = nPayload + (u16)(pIter - pCell);\n    if( pInfo->nSize<4 ) pInfo->nSize = 4;\n    pInfo->nLocal = (u16)nPayload;\n  }else{\n    btreeParseCellAdjustSizeForOverflow(pPage, pCell, pInfo);\n  }\n}\nstatic void btreeParseCell(\n  MemPage *pPage,         /* Page containing the cell */\n  int iCell,              /* The cell index.  First cell is 0 */\n  CellInfo *pInfo         /* Fill in this structure */\n){\n  pPage->xParseCell(pPage, findCell(pPage, iCell), pInfo);\n}\n\n/*\n** The following routines are implementations of the MemPage.xCellSize\n** method.\n**\n** Compute the total number of bytes that a Cell needs in the cell\n** data area of the btree-page.  The return number includes the cell\n** data header and the local payload, but not any overflow page or\n** the space used by the cell pointer.\n**\n** cellSizePtrNoPayload()    =>   table internal nodes\n** cellSizePtr()             =>   all index nodes & table leaf nodes\n*/\nstatic u16 cellSizePtr(MemPage *pPage, u8 *pCell){\n  u8 *pIter = pCell + pPage->childPtrSize; /* For looping over bytes of pCell */\n  u8 *pEnd;                                /* End mark for a varint */\n  u32 nSize;                               /* Size value to return */\n\n#ifdef SQLITE_DEBUG\n  /* The value returned by this function should always be the same as\n  ** the (CellInfo.nSize) value found by doing a full parse of the\n  ** cell. If SQLITE_DEBUG is defined, an assert() at the bottom of\n  ** this function verifies that this invariant is not violated. */\n  CellInfo debuginfo;\n  pPage->xParseCell(pPage, pCell, &debuginfo);\n#endif\n\n  nSize = *pIter;\n  if( nSize>=0x80 ){\n    pEnd = &pIter[8];\n    nSize &= 0x7f;\n    do{\n      nSize = (nSize<<7) | (*++pIter & 0x7f);\n    }while( *(pIter)>=0x80 && pIter<pEnd );\n  }\n  pIter++;\n  if( pPage->intKey ){\n    /* pIter now points at the 64-bit integer key value, a variable length \n    ** integer. The following block moves pIter to point at the first byte\n    ** past the end of the key value. */\n    pEnd = &pIter[9];\n    while( (*pIter++)&0x80 && pIter<pEnd );\n  }\n  testcase( nSize==pPage->maxLocal );\n  testcase( nSize==pPage->maxLocal+1 );\n  if( nSize<=pPage->maxLocal ){\n    nSize += (u32)(pIter - pCell);\n    if( nSize<4 ) nSize = 4;\n  }else{\n    int minLocal = pPage->minLocal;\n    nSize = minLocal + (nSize - minLocal) % (pPage->pBt->usableSize - 4);\n    testcase( nSize==pPage->maxLocal );\n    testcase( nSize==pPage->maxLocal+1 );\n    if( nSize>pPage->maxLocal ){\n      nSize = minLocal;\n    }\n    nSize += 4 + (u16)(pIter - pCell);\n  }\n  assert( nSize==debuginfo.nSize || CORRUPT_DB );\n  return (u16)nSize;\n}\nstatic u16 cellSizePtrNoPayload(MemPage *pPage, u8 *pCell){\n  u8 *pIter = pCell + 4; /* For looping over bytes of pCell */\n  u8 *pEnd;              /* End mark for a varint */\n\n#ifdef SQLITE_DEBUG\n  /* The value returned by this function should always be the same as\n  ** the (CellInfo.nSize) value found by doing a full parse of the\n  ** cell. If SQLITE_DEBUG is defined, an assert() at the bottom of\n  ** this function verifies that this invariant is not violated. */\n  CellInfo debuginfo;\n  pPage->xParseCell(pPage, pCell, &debuginfo);\n#else\n  UNUSED_PARAMETER(pPage);\n#endif\n\n  assert( pPage->childPtrSize==4 );\n  pEnd = pIter + 9;\n  while( (*pIter++)&0x80 && pIter<pEnd );\n  assert( debuginfo.nSize==(u16)(pIter - pCell) || CORRUPT_DB );\n  return (u16)(pIter - pCell);\n}\n\n\n#ifdef SQLITE_DEBUG\n/* This variation on cellSizePtr() is used inside of assert() statements\n** only. */\nstatic u16 cellSize(MemPage *pPage, int iCell){\n  return pPage->xCellSize(pPage, findCell(pPage, iCell));\n}\n#endif\n\n#ifndef SQLITE_OMIT_AUTOVACUUM\n/*\n** If the cell pCell, part of page pPage contains a pointer\n** to an overflow page, insert an entry into the pointer-map\n** for the overflow page.\n*/\nstatic void ptrmapPutOvflPtr(MemPage *pPage, u8 *pCell, int *pRC){\n  CellInfo info;\n  if( *pRC ) return;\n  assert( pCell!=0 );\n  pPage->xParseCell(pPage, pCell, &info);\n  if( info.nLocal<info.nPayload ){\n    Pgno ovfl = get4byte(&pCell[info.nSize-4]);\n    ptrmapPut(pPage->pBt, ovfl, PTRMAP_OVERFLOW1, pPage->pgno, pRC);\n  }\n}\n#endif\n\n\n/*\n** Defragment the page given. This routine reorganizes cells within the\n** page so that there are no free-blocks on the free-block list.\n**\n** Parameter nMaxFrag is the maximum amount of fragmented space that may be\n** present in the page after this routine returns.\n**\n** EVIDENCE-OF: R-44582-60138 SQLite may from time to time reorganize a\n** b-tree page so that there are no freeblocks or fragment bytes, all\n** unused bytes are contained in the unallocated space region, and all\n** cells are packed tightly at the end of the page.\n*/\nstatic int defragmentPage(MemPage *pPage, int nMaxFrag){\n  int i;                     /* Loop counter */\n  int pc;                    /* Address of the i-th cell */\n  int hdr;                   /* Offset to the page header */\n  int size;                  /* Size of a cell */\n  int usableSize;            /* Number of usable bytes on a page */\n  int cellOffset;            /* Offset to the cell pointer array */\n  int cbrk;                  /* Offset to the cell content area */\n  int nCell;                 /* Number of cells on the page */\n  unsigned char *data;       /* The page data */\n  unsigned char *temp;       /* Temp area for cell content */\n  unsigned char *src;        /* Source of content */\n  int iCellFirst;            /* First allowable cell index */\n  int iCellLast;             /* Last possible cell index */\n\n  assert( sqlite3PagerIswriteable(pPage->pDbPage) );\n  assert( pPage->pBt!=0 );\n  assert( pPage->pBt->usableSize <= SQLITE_MAX_PAGE_SIZE );\n  assert( pPage->nOverflow==0 );\n  assert( sqlite3_mutex_held(pPage->pBt->mutex) );\n  temp = 0;\n  src = data = pPage->aData;\n  hdr = pPage->hdrOffset;\n  cellOffset = pPage->cellOffset;\n  nCell = pPage->nCell;\n  assert( nCell==get2byte(&data[hdr+3]) );\n  iCellFirst = cellOffset + 2*nCell;\n  usableSize = pPage->pBt->usableSize;\n\n  /* This block handles pages with two or fewer free blocks and nMaxFrag\n  ** or fewer fragmented bytes. In this case it is faster to move the\n  ** two (or one) blocks of cells using memmove() and add the required\n  ** offsets to each pointer in the cell-pointer array than it is to \n  ** reconstruct the entire page.  */\n  if( (int)data[hdr+7]<=nMaxFrag ){\n    int iFree = get2byte(&data[hdr+1]);\n    if( iFree ){\n      int iFree2 = get2byte(&data[iFree]);\n\n      /* pageFindSlot() has already verified that free blocks are sorted\n      ** in order of offset within the page, and that no block extends\n      ** past the end of the page. Provided the two free slots do not \n      ** overlap, this guarantees that the memmove() calls below will not\n      ** overwrite the usableSize byte buffer, even if the database page\n      ** is corrupt.  */\n      assert( iFree2==0 || iFree2>iFree );\n      assert( iFree+get2byte(&data[iFree+2]) <= usableSize );\n      assert( iFree2==0 || iFree2+get2byte(&data[iFree2+2]) <= usableSize );\n\n      if( 0==iFree2 || (data[iFree2]==0 && data[iFree2+1]==0) ){\n        u8 *pEnd = &data[cellOffset + nCell*2];\n        u8 *pAddr;\n        int sz2 = 0;\n        int sz = get2byte(&data[iFree+2]);\n        int top = get2byte(&data[hdr+5]);\n        if( top>=iFree ){\n          return SQLITE_CORRUPT_PAGE(pPage);\n        }\n        if( iFree2 ){\n          assert( iFree+sz<=iFree2 ); /* Verified by pageFindSlot() */\n          sz2 = get2byte(&data[iFree2+2]);\n          assert( iFree+sz+sz2+iFree2-(iFree+sz) <= usableSize );\n          memmove(&data[iFree+sz+sz2], &data[iFree+sz], iFree2-(iFree+sz));\n          sz += sz2;\n        }\n        cbrk = top+sz;\n        assert( cbrk+(iFree-top) <= usableSize );\n        memmove(&data[cbrk], &data[top], iFree-top);\n        for(pAddr=&data[cellOffset]; pAddr<pEnd; pAddr+=2){\n          pc = get2byte(pAddr);\n          if( pc<iFree ){ put2byte(pAddr, pc+sz); }\n          else if( pc<iFree2 ){ put2byte(pAddr, pc+sz2); }\n        }\n        goto defragment_out;\n      }\n    }\n  }\n\n  cbrk = usableSize;\n  iCellLast = usableSize - 4;\n  for(i=0; i<nCell; i++){\n    u8 *pAddr;     /* The i-th cell pointer */\n    pAddr = &data[cellOffset + i*2];\n    pc = get2byte(pAddr);\n    testcase( pc==iCellFirst );\n    testcase( pc==iCellLast );\n    /* These conditions have already been verified in btreeInitPage()\n    ** if PRAGMA cell_size_check=ON.\n    */\n    if( pc<iCellFirst || pc>iCellLast ){\n      return SQLITE_CORRUPT_PAGE(pPage);\n    }\n    assert( pc>=iCellFirst && pc<=iCellLast );\n    size = pPage->xCellSize(pPage, &src[pc]);\n    cbrk -= size;\n    if( cbrk<iCellFirst || pc+size>usableSize ){\n      return SQLITE_CORRUPT_PAGE(pPage);\n    }\n    assert( cbrk+size<=usableSize && cbrk>=iCellFirst );\n    testcase( cbrk+size==usableSize );\n    testcase( pc+size==usableSize );\n    put2byte(pAddr, cbrk);\n    if( temp==0 ){\n      int x;\n      if( cbrk==pc ) continue;\n      temp = sqlite3PagerTempSpace(pPage->pBt->pPager);\n      x = get2byte(&data[hdr+5]);\n      memcpy(&temp[x], &data[x], (cbrk+size) - x);\n      src = temp;\n    }\n    memcpy(&data[cbrk], &src[pc], size);\n  }\n  data[hdr+7] = 0;\n\n defragment_out:\n  if( data[hdr+7]+cbrk-iCellFirst!=pPage->nFree ){\n    return SQLITE_CORRUPT_PAGE(pPage);\n  }\n  assert( cbrk>=iCellFirst );\n  put2byte(&data[hdr+5], cbrk);\n  data[hdr+1] = 0;\n  data[hdr+2] = 0;\n  memset(&data[iCellFirst], 0, cbrk-iCellFirst);\n  assert( sqlite3PagerIswriteable(pPage->pDbPage) );\n  return SQLITE_OK;\n}\n\n/*\n** Search the free-list on page pPg for space to store a cell nByte bytes in\n** size. If one can be found, return a pointer to the space and remove it\n** from the free-list.\n**\n** If no suitable space can be found on the free-list, return NULL.\n**\n** This function may detect corruption within pPg.  If corruption is\n** detected then *pRc is set to SQLITE_CORRUPT and NULL is returned.\n**\n** Slots on the free list that are between 1 and 3 bytes larger than nByte\n** will be ignored if adding the extra space to the fragmentation count\n** causes the fragmentation count to exceed 60.\n*/\nstatic u8 *pageFindSlot(MemPage *pPg, int nByte, int *pRc){\n  const int hdr = pPg->hdrOffset;\n  u8 * const aData = pPg->aData;\n  int iAddr = hdr + 1;\n  int pc = get2byte(&aData[iAddr]);\n  int x;\n  int usableSize = pPg->pBt->usableSize;\n  int size;            /* Size of the free slot */\n\n  assert( pc>0 );\n  while( pc<=usableSize-4 ){\n    /* EVIDENCE-OF: R-22710-53328 The third and fourth bytes of each\n    ** freeblock form a big-endian integer which is the size of the freeblock\n    ** in bytes, including the 4-byte header. */\n    size = get2byte(&aData[pc+2]);\n    if( (x = size - nByte)>=0 ){\n      testcase( x==4 );\n      testcase( x==3 );\n      if( size+pc > usableSize ){\n        *pRc = SQLITE_CORRUPT_PAGE(pPg);\n        return 0;\n      }else if( x<4 ){\n        /* EVIDENCE-OF: R-11498-58022 In a well-formed b-tree page, the total\n        ** number of bytes in fragments may not exceed 60. */\n        if( aData[hdr+7]>57 ) return 0;\n\n        /* Remove the slot from the free-list. Update the number of\n        ** fragmented bytes within the page. */\n        memcpy(&aData[iAddr], &aData[pc], 2);\n        aData[hdr+7] += (u8)x;\n      }else{\n        /* The slot remains on the free-list. Reduce its size to account\n         ** for the portion used by the new allocation. */\n        put2byte(&aData[pc+2], x);\n      }\n      return &aData[pc + x];\n    }\n    iAddr = pc;\n    pc = get2byte(&aData[pc]);\n    if( pc<iAddr+size ) break;\n  }\n  if( pc ){\n    *pRc = SQLITE_CORRUPT_PAGE(pPg);\n  }\n\n  return 0;\n}\n\n/*\n** Allocate nByte bytes of space from within the B-Tree page passed\n** as the first argument. Write into *pIdx the index into pPage->aData[]\n** of the first byte of allocated space. Return either SQLITE_OK or\n** an error code (usually SQLITE_CORRUPT).\n**\n** The caller guarantees that there is sufficient space to make the\n** allocation.  This routine might need to defragment in order to bring\n** all the space together, however.  This routine will avoid using\n** the first two bytes past the cell pointer area since presumably this\n** allocation is being made in order to insert a new cell, so we will\n** also end up needing a new cell pointer.\n*/\nstatic int allocateSpace(MemPage *pPage, int nByte, int *pIdx){\n  const int hdr = pPage->hdrOffset;    /* Local cache of pPage->hdrOffset */\n  u8 * const data = pPage->aData;      /* Local cache of pPage->aData */\n  int top;                             /* First byte of cell content area */\n  int rc = SQLITE_OK;                  /* Integer return code */\n  int gap;        /* First byte of gap between cell pointers and cell content */\n  \n  assert( sqlite3PagerIswriteable(pPage->pDbPage) );\n  assert( pPage->pBt );\n  assert( sqlite3_mutex_held(pPage->pBt->mutex) );\n  assert( nByte>=0 );  /* Minimum cell size is 4 */\n  assert( pPage->nFree>=nByte );\n  assert( pPage->nOverflow==0 );\n  assert( nByte < (int)(pPage->pBt->usableSize-8) );\n\n  assert( pPage->cellOffset == hdr + 12 - 4*pPage->leaf );\n  gap = pPage->cellOffset + 2*pPage->nCell;\n  assert( gap<=65536 );\n  /* EVIDENCE-OF: R-29356-02391 If the database uses a 65536-byte page size\n  ** and the reserved space is zero (the usual value for reserved space)\n  ** then the cell content offset of an empty page wants to be 65536.\n  ** However, that integer is too large to be stored in a 2-byte unsigned\n  ** integer, so a value of 0 is used in its place. */\n  top = get2byte(&data[hdr+5]);\n  assert( top<=(int)pPage->pBt->usableSize ); /* Prevent by getAndInitPage() */\n  if( gap>top ){\n    if( top==0 && pPage->pBt->usableSize==65536 ){\n      top = 65536;\n    }else{\n      return SQLITE_CORRUPT_PAGE(pPage);\n    }\n  }\n\n  /* If there is enough space between gap and top for one more cell pointer\n  ** array entry offset, and if the freelist is not empty, then search the\n  ** freelist looking for a free slot big enough to satisfy the request.\n  */\n  testcase( gap+2==top );\n  testcase( gap+1==top );\n  testcase( gap==top );\n  if( (data[hdr+2] || data[hdr+1]) && gap+2<=top ){\n    u8 *pSpace = pageFindSlot(pPage, nByte, &rc);\n    if( pSpace ){\n      assert( pSpace>=data && (pSpace - data)<65536 );\n      *pIdx = (int)(pSpace - data);\n      return SQLITE_OK;\n    }else if( rc ){\n      return rc;\n    }\n  }\n\n  /* The request could not be fulfilled using a freelist slot.  Check\n  ** to see if defragmentation is necessary.\n  */\n  testcase( gap+2+nByte==top );\n  if( gap+2+nByte>top ){\n    assert( pPage->nCell>0 || CORRUPT_DB );\n    rc = defragmentPage(pPage, MIN(4, pPage->nFree - (2+nByte)));\n    if( rc ) return rc;\n    top = get2byteNotZero(&data[hdr+5]);\n    assert( gap+2+nByte<=top );\n  }\n\n\n  /* Allocate memory from the gap in between the cell pointer array\n  ** and the cell content area.  The btreeInitPage() call has already\n  ** validated the freelist.  Given that the freelist is valid, there\n  ** is no way that the allocation can extend off the end of the page.\n  ** The assert() below verifies the previous sentence.\n  */\n  top -= nByte;\n  put2byte(&data[hdr+5], top);\n  assert( top+nByte <= (int)pPage->pBt->usableSize );\n  *pIdx = top;\n  return SQLITE_OK;\n}\n\n/*\n** Return a section of the pPage->aData to the freelist.\n** The first byte of the new free block is pPage->aData[iStart]\n** and the size of the block is iSize bytes.\n**\n** Adjacent freeblocks are coalesced.\n**\n** Note that even though the freeblock list was checked by btreeInitPage(),\n** that routine will not detect overlap between cells or freeblocks.  Nor\n** does it detect cells or freeblocks that encrouch into the reserved bytes\n** at the end of the page.  So do additional corruption checks inside this\n** routine and return SQLITE_CORRUPT if any problems are found.\n*/\nstatic int freeSpace(MemPage *pPage, u16 iStart, u16 iSize){\n  u16 iPtr;                             /* Address of ptr to next freeblock */\n  u16 iFreeBlk;                         /* Address of the next freeblock */\n  u8 hdr;                               /* Page header size.  0 or 100 */\n  u8 nFrag = 0;                         /* Reduction in fragmentation */\n  u16 iOrigSize = iSize;                /* Original value of iSize */\n  u16 x;                                /* Offset to cell content area */\n  u32 iEnd = iStart + iSize;            /* First byte past the iStart buffer */\n  unsigned char *data = pPage->aData;   /* Page content */\n\n  assert( pPage->pBt!=0 );\n  assert( sqlite3PagerIswriteable(pPage->pDbPage) );\n  assert( CORRUPT_DB || iStart>=pPage->hdrOffset+6+pPage->childPtrSize );\n  assert( CORRUPT_DB || iEnd <= pPage->pBt->usableSize );\n  assert( sqlite3_mutex_held(pPage->pBt->mutex) );\n  assert( iSize>=4 );   /* Minimum cell size is 4 */\n  assert( iStart<=pPage->pBt->usableSize-4 );\n\n  /* The list of freeblocks must be in ascending order.  Find the \n  ** spot on the list where iStart should be inserted.\n  */\n  hdr = pPage->hdrOffset;\n  iPtr = hdr + 1;\n  if( data[iPtr+1]==0 && data[iPtr]==0 ){\n    iFreeBlk = 0;  /* Shortcut for the case when the freelist is empty */\n  }else{\n    while( (iFreeBlk = get2byte(&data[iPtr]))<iStart ){\n      if( iFreeBlk<iPtr+4 ){\n        if( iFreeBlk==0 ) break;\n        return SQLITE_CORRUPT_PAGE(pPage);\n      }\n      iPtr = iFreeBlk;\n    }\n    if( iFreeBlk>pPage->pBt->usableSize-4 ){\n      return SQLITE_CORRUPT_PAGE(pPage);\n    }\n    assert( iFreeBlk>iPtr || iFreeBlk==0 );\n  \n    /* At this point:\n    **    iFreeBlk:   First freeblock after iStart, or zero if none\n    **    iPtr:       The address of a pointer to iFreeBlk\n    **\n    ** Check to see if iFreeBlk should be coalesced onto the end of iStart.\n    */\n    if( iFreeBlk && iEnd+3>=iFreeBlk ){\n      nFrag = iFreeBlk - iEnd;\n      if( iEnd>iFreeBlk ) return SQLITE_CORRUPT_PAGE(pPage);\n      iEnd = iFreeBlk + get2byte(&data[iFreeBlk+2]);\n      if( iEnd > pPage->pBt->usableSize ){\n        return SQLITE_CORRUPT_PAGE(pPage);\n      }\n      iSize = iEnd - iStart;\n      iFreeBlk = get2byte(&data[iFreeBlk]);\n    }\n  \n    /* If iPtr is another freeblock (that is, if iPtr is not the freelist\n    ** pointer in the page header) then check to see if iStart should be\n    ** coalesced onto the end of iPtr.\n    */\n    if( iPtr>hdr+1 ){\n      int iPtrEnd = iPtr + get2byte(&data[iPtr+2]);\n      if( iPtrEnd+3>=iStart ){\n        if( iPtrEnd>iStart ) return SQLITE_CORRUPT_PAGE(pPage);\n        nFrag += iStart - iPtrEnd;\n        iSize = iEnd - iPtr;\n        iStart = iPtr;\n      }\n    }\n    if( nFrag>data[hdr+7] ) return SQLITE_CORRUPT_PAGE(pPage);\n    data[hdr+7] -= nFrag;\n  }\n  x = get2byte(&data[hdr+5]);\n  if( iStart<=x ){\n    /* The new freeblock is at the beginning of the cell content area,\n    ** so just extend the cell content area rather than create another\n    ** freelist entry */\n    if( iStart<x || iPtr!=hdr+1 ) return SQLITE_CORRUPT_PAGE(pPage);\n    put2byte(&data[hdr+1], iFreeBlk);\n    put2byte(&data[hdr+5], iEnd);\n  }else{\n    /* Insert the new freeblock into the freelist */\n    put2byte(&data[iPtr], iStart);\n  }\n  if( pPage->pBt->btsFlags & BTS_FAST_SECURE ){\n    /* Overwrite deleted information with zeros when the secure_delete\n    ** option is enabled */\n    memset(&data[iStart], 0, iSize);\n  }\n  put2byte(&data[iStart], iFreeBlk);\n  put2byte(&data[iStart+2], iSize);\n  pPage->nFree += iOrigSize;\n  return SQLITE_OK;\n}\n\n/*\n** Decode the flags byte (the first byte of the header) for a page\n** and initialize fields of the MemPage structure accordingly.\n**\n** Only the following combinations are supported.  Anything different\n** indicates a corrupt database files:\n**\n**         PTF_ZERODATA\n**         PTF_ZERODATA | PTF_LEAF\n**         PTF_LEAFDATA | PTF_INTKEY\n**         PTF_LEAFDATA | PTF_INTKEY | PTF_LEAF\n*/\nstatic int decodeFlags(MemPage *pPage, int flagByte){\n  BtShared *pBt;     /* A copy of pPage->pBt */\n\n  assert( pPage->hdrOffset==(pPage->pgno==1 ? 100 : 0) );\n  assert( sqlite3_mutex_held(pPage->pBt->mutex) );\n  pPage->leaf = (u8)(flagByte>>3);  assert( PTF_LEAF == 1<<3 );\n  flagByte &= ~PTF_LEAF;\n  pPage->childPtrSize = 4-4*pPage->leaf;\n  pPage->xCellSize = cellSizePtr;\n  pBt = pPage->pBt;\n  if( flagByte==(PTF_LEAFDATA | PTF_INTKEY) ){\n    /* EVIDENCE-OF: R-07291-35328 A value of 5 (0x05) means the page is an\n    ** interior table b-tree page. */\n    assert( (PTF_LEAFDATA|PTF_INTKEY)==5 );\n    /* EVIDENCE-OF: R-26900-09176 A value of 13 (0x0d) means the page is a\n    ** leaf table b-tree page. */\n    assert( (PTF_LEAFDATA|PTF_INTKEY|PTF_LEAF)==13 );\n    pPage->intKey = 1;\n    if( pPage->leaf ){\n      pPage->intKeyLeaf = 1;\n      pPage->xParseCell = btreeParseCellPtr;\n    }else{\n      pPage->intKeyLeaf = 0;\n      pPage->xCellSize = cellSizePtrNoPayload;\n      pPage->xParseCell = btreeParseCellPtrNoPayload;\n    }\n    pPage->maxLocal = pBt->maxLeaf;\n    pPage->minLocal = pBt->minLeaf;\n  }else if( flagByte==PTF_ZERODATA ){\n    /* EVIDENCE-OF: R-43316-37308 A value of 2 (0x02) means the page is an\n    ** interior index b-tree page. */\n    assert( (PTF_ZERODATA)==2 );\n    /* EVIDENCE-OF: R-59615-42828 A value of 10 (0x0a) means the page is a\n    ** leaf index b-tree page. */\n    assert( (PTF_ZERODATA|PTF_LEAF)==10 );\n    pPage->intKey = 0;\n    pPage->intKeyLeaf = 0;\n    pPage->xParseCell = btreeParseCellPtrIndex;\n    pPage->maxLocal = pBt->maxLocal;\n    pPage->minLocal = pBt->minLocal;\n  }else{\n    /* EVIDENCE-OF: R-47608-56469 Any other value for the b-tree page type is\n    ** an error. */\n    return SQLITE_CORRUPT_PAGE(pPage);\n  }\n  pPage->max1bytePayload = pBt->max1bytePayload;\n  return SQLITE_OK;\n}\n\n/*\n** Initialize the auxiliary information for a disk block.\n**\n** Return SQLITE_OK on success.  If we see that the page does\n** not contain a well-formed database page, then return \n** SQLITE_CORRUPT.  Note that a return of SQLITE_OK does not\n** guarantee that the page is well-formed.  It only shows that\n** we failed to detect any corruption.\n*/\nstatic int btreeInitPage(MemPage *pPage){\n  int pc;            /* Address of a freeblock within pPage->aData[] */\n  u8 hdr;            /* Offset to beginning of page header */\n  u8 *data;          /* Equal to pPage->aData */\n  BtShared *pBt;        /* The main btree structure */\n  int usableSize;    /* Amount of usable space on each page */\n  u16 cellOffset;    /* Offset from start of page to first cell pointer */\n  int nFree;         /* Number of unused bytes on the page */\n  int top;           /* First byte of the cell content area */\n  int iCellFirst;    /* First allowable cell or freeblock offset */\n  int iCellLast;     /* Last possible cell or freeblock offset */\n\n  assert( pPage->pBt!=0 );\n  assert( pPage->pBt->db!=0 );\n  assert( sqlite3_mutex_held(pPage->pBt->mutex) );\n  assert( pPage->pgno==sqlite3PagerPagenumber(pPage->pDbPage) );\n  assert( pPage == sqlite3PagerGetExtra(pPage->pDbPage) );\n  assert( pPage->aData == sqlite3PagerGetData(pPage->pDbPage) );\n  assert( pPage->isInit==0 );\n\n  pBt = pPage->pBt;\n  hdr = pPage->hdrOffset;\n  data = pPage->aData;\n  /* EVIDENCE-OF: R-28594-02890 The one-byte flag at offset 0 indicating\n  ** the b-tree page type. */\n  if( decodeFlags(pPage, data[hdr]) ){\n    return SQLITE_CORRUPT_PAGE(pPage);\n  }\n  assert( pBt->pageSize>=512 && pBt->pageSize<=65536 );\n  pPage->maskPage = (u16)(pBt->pageSize - 1);\n  pPage->nOverflow = 0;\n  usableSize = pBt->usableSize;\n  pPage->cellOffset = cellOffset = hdr + 8 + pPage->childPtrSize;\n  pPage->aDataEnd = &data[usableSize];\n  pPage->aCellIdx = &data[cellOffset];\n  pPage->aDataOfst = &data[pPage->childPtrSize];\n  /* EVIDENCE-OF: R-58015-48175 The two-byte integer at offset 5 designates\n  ** the start of the cell content area. A zero value for this integer is\n  ** interpreted as 65536. */\n  top = get2byteNotZero(&data[hdr+5]);\n  /* EVIDENCE-OF: R-37002-32774 The two-byte integer at offset 3 gives the\n  ** number of cells on the page. */\n  pPage->nCell = get2byte(&data[hdr+3]);\n  if( pPage->nCell>MX_CELL(pBt) ){\n    /* To many cells for a single page.  The page must be corrupt */\n    return SQLITE_CORRUPT_PAGE(pPage);\n  }\n  testcase( pPage->nCell==MX_CELL(pBt) );\n  /* EVIDENCE-OF: R-24089-57979 If a page contains no cells (which is only\n  ** possible for a root page of a table that contains no rows) then the\n  ** offset to the cell content area will equal the page size minus the\n  ** bytes of reserved space. */\n  assert( pPage->nCell>0 || top==usableSize || CORRUPT_DB );\n\n  /* A malformed database page might cause us to read past the end\n  ** of page when parsing a cell.  \n  **\n  ** The following block of code checks early to see if a cell extends\n  ** past the end of a page boundary and causes SQLITE_CORRUPT to be \n  ** returned if it does.\n  */\n  iCellFirst = cellOffset + 2*pPage->nCell;\n  iCellLast = usableSize - 4;\n  if( pBt->db->flags & SQLITE_CellSizeCk ){\n    int i;            /* Index into the cell pointer array */\n    int sz;           /* Size of a cell */\n\n    if( !pPage->leaf ) iCellLast--;\n    for(i=0; i<pPage->nCell; i++){\n      pc = get2byteAligned(&data[cellOffset+i*2]);\n      testcase( pc==iCellFirst );\n      testcase( pc==iCellLast );\n      if( pc<iCellFirst || pc>iCellLast ){\n        return SQLITE_CORRUPT_PAGE(pPage);\n      }\n      sz = pPage->xCellSize(pPage, &data[pc]);\n      testcase( pc+sz==usableSize );\n      if( pc+sz>usableSize ){\n        return SQLITE_CORRUPT_PAGE(pPage);\n      }\n    }\n    if( !pPage->leaf ) iCellLast++;\n  }  \n\n  /* Compute the total free space on the page\n  ** EVIDENCE-OF: R-23588-34450 The two-byte integer at offset 1 gives the\n  ** start of the first freeblock on the page, or is zero if there are no\n  ** freeblocks. */\n  pc = get2byte(&data[hdr+1]);\n  nFree = data[hdr+7] + top;  /* Init nFree to non-freeblock free space */\n  if( pc>0 ){\n    u32 next, size;\n    if( pc<iCellFirst ){\n      /* EVIDENCE-OF: R-55530-52930 In a well-formed b-tree page, there will\n      ** always be at least one cell before the first freeblock.\n      */\n      return SQLITE_CORRUPT_PAGE(pPage); \n    }\n    while( 1 ){\n      if( pc>iCellLast ){\n        /* Freeblock off the end of the page */\n        return SQLITE_CORRUPT_PAGE(pPage);\n      }\n      next = get2byte(&data[pc]);\n      size = get2byte(&data[pc+2]);\n      nFree = nFree + size;\n      if( next<=pc+size+3 ) break;\n      pc = next;\n    }\n    if( next>0 ){\n      /* Freeblock not in ascending order */\n      return SQLITE_CORRUPT_PAGE(pPage);\n    }\n    if( pc+size>(unsigned int)usableSize ){\n      /* Last freeblock extends past page end */\n      return SQLITE_CORRUPT_PAGE(pPage);\n    }\n  }\n\n  /* At this point, nFree contains the sum of the offset to the start\n  ** of the cell-content area plus the number of free bytes within\n  ** the cell-content area. If this is greater than the usable-size\n  ** of the page, then the page must be corrupted. This check also\n  ** serves to verify that the offset to the start of the cell-content\n  ** area, according to the page header, lies within the page.\n  */\n  if( nFree>usableSize ){\n    return SQLITE_CORRUPT_PAGE(pPage);\n  }\n  pPage->nFree = (u16)(nFree - iCellFirst);\n  pPage->isInit = 1;\n  return SQLITE_OK;\n}\n\n/*\n** Set up a raw page so that it looks like a database page holding\n** no entries.\n*/\nstatic void zeroPage(MemPage *pPage, int flags){\n  unsigned char *data = pPage->aData;\n  BtShared *pBt = pPage->pBt;\n  u8 hdr = pPage->hdrOffset;\n  u16 first;\n\n  assert( sqlite3PagerPagenumber(pPage->pDbPage)==pPage->pgno );\n  assert( sqlite3PagerGetExtra(pPage->pDbPage) == (void*)pPage );\n  assert( sqlite3PagerGetData(pPage->pDbPage) == data );\n  assert( sqlite3PagerIswriteable(pPage->pDbPage) );\n  assert( sqlite3_mutex_held(pBt->mutex) );\n  if( pBt->btsFlags & BTS_FAST_SECURE ){\n    memset(&data[hdr], 0, pBt->usableSize - hdr);\n  }\n  data[hdr] = (char)flags;\n  first = hdr + ((flags&PTF_LEAF)==0 ? 12 : 8);\n  memset(&data[hdr+1], 0, 4);\n  data[hdr+7] = 0;\n  put2byte(&data[hdr+5], pBt->usableSize);\n  pPage->nFree = (u16)(pBt->usableSize - first);\n  decodeFlags(pPage, flags);\n  pPage->cellOffset = first;\n  pPage->aDataEnd = &data[pBt->usableSize];\n  pPage->aCellIdx = &data[first];\n  pPage->aDataOfst = &data[pPage->childPtrSize];\n  pPage->nOverflow = 0;\n  assert( pBt->pageSize>=512 && pBt->pageSize<=65536 );\n  pPage->maskPage = (u16)(pBt->pageSize - 1);\n  pPage->nCell = 0;\n  pPage->isInit = 1;\n}\n\n\n/*\n** Convert a DbPage obtained from the pager into a MemPage used by\n** the btree layer.\n*/\nstatic MemPage *btreePageFromDbPage(DbPage *pDbPage, Pgno pgno, BtShared *pBt){\n  MemPage *pPage = (MemPage*)sqlite3PagerGetExtra(pDbPage);\n  if( pgno!=pPage->pgno ){\n    pPage->aData = sqlite3PagerGetData(pDbPage);\n    pPage->pDbPage = pDbPage;\n    pPage->pBt = pBt;\n    pPage->pgno = pgno;\n    pPage->hdrOffset = pgno==1 ? 100 : 0;\n  }\n  assert( pPage->aData==sqlite3PagerGetData(pDbPage) );\n  return pPage; \n}\n\n/*\n** Get a page from the pager.  Initialize the MemPage.pBt and\n** MemPage.aData elements if needed.  See also: btreeGetUnusedPage().\n**\n** If the PAGER_GET_NOCONTENT flag is set, it means that we do not care\n** about the content of the page at this time.  So do not go to the disk\n** to fetch the content.  Just fill in the content with zeros for now.\n** If in the future we call sqlite3PagerWrite() on this page, that\n** means we have started to be concerned about content and the disk\n** read should occur at that point.\n*/\nstatic int btreeGetPage(\n  BtShared *pBt,       /* The btree */\n  Pgno pgno,           /* Number of the page to fetch */\n  MemPage **ppPage,    /* Return the page in this parameter */\n  int flags            /* PAGER_GET_NOCONTENT or PAGER_GET_READONLY */\n){\n  int rc;\n  DbPage *pDbPage;\n\n  assert( flags==0 || flags==PAGER_GET_NOCONTENT || flags==PAGER_GET_READONLY );\n  assert( sqlite3_mutex_held(pBt->mutex) );\n  rc = sqlite3PagerGet(pBt->pPager, pgno, (DbPage**)&pDbPage, flags);\n  if( rc ) return rc;\n  *ppPage = btreePageFromDbPage(pDbPage, pgno, pBt);\n  return SQLITE_OK;\n}\n\n/*\n** Retrieve a page from the pager cache. If the requested page is not\n** already in the pager cache return NULL. Initialize the MemPage.pBt and\n** MemPage.aData elements if needed.\n*/\nstatic MemPage *btreePageLookup(BtShared *pBt, Pgno pgno){\n  DbPage *pDbPage;\n  assert( sqlite3_mutex_held(pBt->mutex) );\n  pDbPage = sqlite3PagerLookup(pBt->pPager, pgno);\n  if( pDbPage ){\n    return btreePageFromDbPage(pDbPage, pgno, pBt);\n  }\n  return 0;\n}\n\n/*\n** Return the size of the database file in pages. If there is any kind of\n** error, return ((unsigned int)-1).\n*/\nstatic Pgno btreePagecount(BtShared *pBt){\n  return pBt->nPage;\n}\nSQLITE_PRIVATE u32 sqlite3BtreeLastPage(Btree *p){\n  assert( sqlite3BtreeHoldsMutex(p) );\n  assert( ((p->pBt->nPage)&0x80000000)==0 );\n  return btreePagecount(p->pBt);\n}\n\n/*\n** Get a page from the pager and initialize it.\n**\n** If pCur!=0 then the page is being fetched as part of a moveToChild()\n** call.  Do additional sanity checking on the page in this case.\n** And if the fetch fails, this routine must decrement pCur->iPage.\n**\n** The page is fetched as read-write unless pCur is not NULL and is\n** a read-only cursor.\n**\n** If an error occurs, then *ppPage is undefined. It\n** may remain unchanged, or it may be set to an invalid value.\n*/\nstatic int getAndInitPage(\n  BtShared *pBt,                  /* The database file */\n  Pgno pgno,                      /* Number of the page to get */\n  MemPage **ppPage,               /* Write the page pointer here */\n  BtCursor *pCur,                 /* Cursor to receive the page, or NULL */\n  int bReadOnly                   /* True for a read-only page */\n){\n  int rc;\n  DbPage *pDbPage;\n  assert( sqlite3_mutex_held(pBt->mutex) );\n  assert( pCur==0 || ppPage==&pCur->pPage );\n  assert( pCur==0 || bReadOnly==pCur->curPagerFlags );\n  assert( pCur==0 || pCur->iPage>0 );\n\n  if( pgno>btreePagecount(pBt) ){\n    rc = SQLITE_CORRUPT_BKPT;\n    goto getAndInitPage_error;\n  }\n  rc = sqlite3PagerGet(pBt->pPager, pgno, (DbPage**)&pDbPage, bReadOnly);\n  if( rc ){\n    goto getAndInitPage_error;\n  }\n  *ppPage = (MemPage*)sqlite3PagerGetExtra(pDbPage);\n  if( (*ppPage)->isInit==0 ){\n    btreePageFromDbPage(pDbPage, pgno, pBt);\n    rc = btreeInitPage(*ppPage);\n    if( rc!=SQLITE_OK ){\n      releasePage(*ppPage);\n      goto getAndInitPage_error;\n    }\n  }\n  assert( (*ppPage)->pgno==pgno );\n  assert( (*ppPage)->aData==sqlite3PagerGetData(pDbPage) );\n\n  /* If obtaining a child page for a cursor, we must verify that the page is\n  ** compatible with the root page. */\n  if( pCur && ((*ppPage)->nCell<1 || (*ppPage)->intKey!=pCur->curIntKey) ){\n    rc = SQLITE_CORRUPT_PGNO(pgno);\n    releasePage(*ppPage);\n    goto getAndInitPage_error;\n  }\n  return SQLITE_OK;\n\ngetAndInitPage_error:\n  if( pCur ){\n    pCur->iPage--;\n    pCur->pPage = pCur->apPage[pCur->iPage];\n  }\n  testcase( pgno==0 );\n  assert( pgno!=0 || rc==SQLITE_CORRUPT );\n  return rc;\n}\n\n/*\n** Release a MemPage.  This should be called once for each prior\n** call to btreeGetPage.\n**\n** Page1 is a special case and must be released using releasePageOne().\n*/\nstatic void releasePageNotNull(MemPage *pPage){\n  assert( pPage->aData );\n  assert( pPage->pBt );\n  assert( pPage->pDbPage!=0 );\n  assert( sqlite3PagerGetExtra(pPage->pDbPage) == (void*)pPage );\n  assert( sqlite3PagerGetData(pPage->pDbPage)==pPage->aData );\n  assert( sqlite3_mutex_held(pPage->pBt->mutex) );\n  sqlite3PagerUnrefNotNull(pPage->pDbPage);\n}\nstatic void releasePage(MemPage *pPage){\n  if( pPage ) releasePageNotNull(pPage);\n}\nstatic void releasePageOne(MemPage *pPage){\n  assert( pPage!=0 );\n  assert( pPage->aData );\n  assert( pPage->pBt );\n  assert( pPage->pDbPage!=0 );\n  assert( sqlite3PagerGetExtra(pPage->pDbPage) == (void*)pPage );\n  assert( sqlite3PagerGetData(pPage->pDbPage)==pPage->aData );\n  assert( sqlite3_mutex_held(pPage->pBt->mutex) );\n  sqlite3PagerUnrefPageOne(pPage->pDbPage);\n}\n\n/*\n** Get an unused page.\n**\n** This works just like btreeGetPage() with the addition:\n**\n**   *  If the page is already in use for some other purpose, immediately\n**      release it and return an SQLITE_CURRUPT error.\n**   *  Make sure the isInit flag is clear\n*/\nstatic int btreeGetUnusedPage(\n  BtShared *pBt,       /* The btree */\n  Pgno pgno,           /* Number of the page to fetch */\n  MemPage **ppPage,    /* Return the page in this parameter */\n  int flags            /* PAGER_GET_NOCONTENT or PAGER_GET_READONLY */\n){\n  int rc = btreeGetPage(pBt, pgno, ppPage, flags);\n  if( rc==SQLITE_OK ){\n    if( sqlite3PagerPageRefcount((*ppPage)->pDbPage)>1 ){\n      releasePage(*ppPage);\n      *ppPage = 0;\n      return SQLITE_CORRUPT_BKPT;\n    }\n    (*ppPage)->isInit = 0;\n  }else{\n    *ppPage = 0;\n  }\n  return rc;\n}\n\n\n/*\n** During a rollback, when the pager reloads information into the cache\n** so that the cache is restored to its original state at the start of\n** the transaction, for each page restored this routine is called.\n**\n** This routine needs to reset the extra data section at the end of the\n** page to agree with the restored data.\n*/\nstatic void pageReinit(DbPage *pData){\n  MemPage *pPage;\n  pPage = (MemPage *)sqlite3PagerGetExtra(pData);\n  assert( sqlite3PagerPageRefcount(pData)>0 );\n  if( pPage->isInit ){\n    assert( sqlite3_mutex_held(pPage->pBt->mutex) );\n    pPage->isInit = 0;\n    if( sqlite3PagerPageRefcount(pData)>1 ){\n      /* pPage might not be a btree page;  it might be an overflow page\n      ** or ptrmap page or a free page.  In those cases, the following\n      ** call to btreeInitPage() will likely return SQLITE_CORRUPT.\n      ** But no harm is done by this.  And it is very important that\n      ** btreeInitPage() be called on every btree page so we make\n      ** the call for every page that comes in for re-initing. */\n      btreeInitPage(pPage);\n    }\n  }\n}\n\n/*\n** Invoke the busy handler for a btree.\n*/\nstatic int btreeInvokeBusyHandler(void *pArg){\n  BtShared *pBt = (BtShared*)pArg;\n  assert( pBt->db );\n  assert( sqlite3_mutex_held(pBt->db->mutex) );\n  return sqlite3InvokeBusyHandler(&pBt->db->busyHandler);\n}\n\n/*\n** Open a database file.\n** \n** zFilename is the name of the database file.  If zFilename is NULL\n** then an ephemeral database is created.  The ephemeral database might\n** be exclusively in memory, or it might use a disk-based memory cache.\n** Either way, the ephemeral database will be automatically deleted \n** when sqlite3BtreeClose() is called.\n**\n** If zFilename is \":memory:\" then an in-memory database is created\n** that is automatically destroyed when it is closed.\n**\n** The \"flags\" parameter is a bitmask that might contain bits like\n** BTREE_OMIT_JOURNAL and/or BTREE_MEMORY.\n**\n** If the database is already opened in the same database connection\n** and we are in shared cache mode, then the open will fail with an\n** SQLITE_CONSTRAINT error.  We cannot allow two or more BtShared\n** objects in the same database connection since doing so will lead\n** to problems with locking.\n*/\nSQLITE_PRIVATE int sqlite3BtreeOpen(\n  sqlite3_vfs *pVfs,      /* VFS to use for this b-tree */\n  const char *zFilename,  /* Name of the file containing the BTree database */\n  sqlite3 *db,            /* Associated database handle */\n  Btree **ppBtree,        /* Pointer to new Btree object written here */\n  int flags,              /* Options */\n  int vfsFlags            /* Flags passed through to sqlite3_vfs.xOpen() */\n){\n  BtShared *pBt = 0;             /* Shared part of btree structure */\n  Btree *p;                      /* Handle to return */\n  sqlite3_mutex *mutexOpen = 0;  /* Prevents a race condition. Ticket #3537 */\n  int rc = SQLITE_OK;            /* Result code from this function */\n  u8 nReserve;                   /* Byte of unused space on each page */\n  unsigned char zDbHeader[100];  /* Database header content */\n\n  /* True if opening an ephemeral, temporary database */\n  const int isTempDb = zFilename==0 || zFilename[0]==0;\n\n  /* Set the variable isMemdb to true for an in-memory database, or \n  ** false for a file-based database.\n  */\n#ifdef SQLITE_OMIT_MEMORYDB\n  const int isMemdb = 0;\n#else\n  const int isMemdb = (zFilename && strcmp(zFilename, \":memory:\")==0)\n                       || (isTempDb && sqlite3TempInMemory(db))\n                       || (vfsFlags & SQLITE_OPEN_MEMORY)!=0;\n#endif\n\n  assert( db!=0 );\n  assert( pVfs!=0 );\n  assert( sqlite3_mutex_held(db->mutex) );\n  assert( (flags&0xff)==flags );   /* flags fit in 8 bits */\n\n  /* Only a BTREE_SINGLE database can be BTREE_UNORDERED */\n  assert( (flags & BTREE_UNORDERED)==0 || (flags & BTREE_SINGLE)!=0 );\n\n  /* A BTREE_SINGLE database is always a temporary and/or ephemeral */\n  assert( (flags & BTREE_SINGLE)==0 || isTempDb );\n\n  if( isMemdb ){\n    flags |= BTREE_MEMORY;\n  }\n  if( (vfsFlags & SQLITE_OPEN_MAIN_DB)!=0 && (isMemdb || isTempDb) ){\n    vfsFlags = (vfsFlags & ~SQLITE_OPEN_MAIN_DB) | SQLITE_OPEN_TEMP_DB;\n  }\n  p = sqlite3MallocZero(sizeof(Btree));\n  if( !p ){\n    return SQLITE_NOMEM_BKPT;\n  }\n  p->inTrans = TRANS_NONE;\n  p->db = db;\n#ifndef SQLITE_OMIT_SHARED_CACHE\n  p->lock.pBtree = p;\n  p->lock.iTable = 1;\n#endif\n\n#if !defined(SQLITE_OMIT_SHARED_CACHE) && !defined(SQLITE_OMIT_DISKIO)\n  /*\n  ** If this Btree is a candidate for shared cache, try to find an\n  ** existing BtShared object that we can share with\n  */\n  if( isTempDb==0 && (isMemdb==0 || (vfsFlags&SQLITE_OPEN_URI)!=0) ){\n    if( vfsFlags & SQLITE_OPEN_SHAREDCACHE ){\n      int nFilename = sqlite3Strlen30(zFilename)+1;\n      int nFullPathname = pVfs->mxPathname+1;\n      char *zFullPathname = sqlite3Malloc(MAX(nFullPathname,nFilename));\n      MUTEX_LOGIC( sqlite3_mutex *mutexShared; )\n\n      p->sharable = 1;\n      if( !zFullPathname ){\n        sqlite3_free(p);\n        return SQLITE_NOMEM_BKPT;\n      }\n      if( isMemdb ){\n        memcpy(zFullPathname, zFilename, nFilename);\n      }else{\n        rc = sqlite3OsFullPathname(pVfs, zFilename,\n                                   nFullPathname, zFullPathname);\n        if( rc ){\n          sqlite3_free(zFullPathname);\n          sqlite3_free(p);\n          return rc;\n        }\n      }\n#if SQLITE_THREADSAFE\n      mutexOpen = sqlite3MutexAlloc(SQLITE_MUTEX_STATIC_OPEN);\n      sqlite3_mutex_enter(mutexOpen);\n      mutexShared = sqlite3MutexAlloc(SQLITE_MUTEX_STATIC_MASTER);\n      sqlite3_mutex_enter(mutexShared);\n#endif\n      for(pBt=GLOBAL(BtShared*,sqlite3SharedCacheList); pBt; pBt=pBt->pNext){\n        assert( pBt->nRef>0 );\n        if( 0==strcmp(zFullPathname, sqlite3PagerFilename(pBt->pPager, 0))\n                 && sqlite3PagerVfs(pBt->pPager)==pVfs ){\n          int iDb;\n          for(iDb=db->nDb-1; iDb>=0; iDb--){\n            Btree *pExisting = db->aDb[iDb].pBt;\n            if( pExisting && pExisting->pBt==pBt ){\n              sqlite3_mutex_leave(mutexShared);\n              sqlite3_mutex_leave(mutexOpen);\n              sqlite3_free(zFullPathname);\n              sqlite3_free(p);\n              return SQLITE_CONSTRAINT;\n            }\n          }\n          p->pBt = pBt;\n          pBt->nRef++;\n          break;\n        }\n      }\n      sqlite3_mutex_leave(mutexShared);\n      sqlite3_free(zFullPathname);\n    }\n#ifdef SQLITE_DEBUG\n    else{\n      /* In debug mode, we mark all persistent databases as sharable\n      ** even when they are not.  This exercises the locking code and\n      ** gives more opportunity for asserts(sqlite3_mutex_held())\n      ** statements to find locking problems.\n      */\n      p->sharable = 1;\n    }\n#endif\n  }\n#endif\n  if( pBt==0 ){\n    /*\n    ** The following asserts make sure that structures used by the btree are\n    ** the right size.  This is to guard against size changes that result\n    ** when compiling on a different architecture.\n    */\n    assert( sizeof(i64)==8 );\n    assert( sizeof(u64)==8 );\n    assert( sizeof(u32)==4 );\n    assert( sizeof(u16)==2 );\n    assert( sizeof(Pgno)==4 );\n  \n    pBt = sqlite3MallocZero( sizeof(*pBt) );\n    if( pBt==0 ){\n      rc = SQLITE_NOMEM_BKPT;\n      goto btree_open_out;\n    }\n    rc = sqlite3PagerOpen(pVfs, &pBt->pPager, zFilename,\n                          sizeof(MemPage), flags, vfsFlags, pageReinit);\n    if( rc==SQLITE_OK ){\n      sqlite3PagerSetMmapLimit(pBt->pPager, db->szMmap);\n      rc = sqlite3PagerReadFileheader(pBt->pPager,sizeof(zDbHeader),zDbHeader);\n    }\n    if( rc!=SQLITE_OK ){\n      goto btree_open_out;\n    }\n    pBt->openFlags = (u8)flags;\n    pBt->db = db;\n    sqlite3PagerSetBusyhandler(pBt->pPager, btreeInvokeBusyHandler, pBt);\n    p->pBt = pBt;\n  \n    pBt->pCursor = 0;\n    pBt->pPage1 = 0;\n    if( sqlite3PagerIsreadonly(pBt->pPager) ) pBt->btsFlags |= BTS_READ_ONLY;\n#if defined(SQLITE_SECURE_DELETE)\n    pBt->btsFlags |= BTS_SECURE_DELETE;\n#elif defined(SQLITE_FAST_SECURE_DELETE)\n    pBt->btsFlags |= BTS_OVERWRITE;\n#endif\n    /* EVIDENCE-OF: R-51873-39618 The page size for a database file is\n    ** determined by the 2-byte integer located at an offset of 16 bytes from\n    ** the beginning of the database file. */\n    pBt->pageSize = (zDbHeader[16]<<8) | (zDbHeader[17]<<16);\n    if( pBt->pageSize<512 || pBt->pageSize>SQLITE_MAX_PAGE_SIZE\n         || ((pBt->pageSize-1)&pBt->pageSize)!=0 ){\n      pBt->pageSize = 0;\n#ifndef SQLITE_OMIT_AUTOVACUUM\n      /* If the magic name \":memory:\" will create an in-memory database, then\n      ** leave the autoVacuum mode at 0 (do not auto-vacuum), even if\n      ** SQLITE_DEFAULT_AUTOVACUUM is true. On the other hand, if\n      ** SQLITE_OMIT_MEMORYDB has been defined, then \":memory:\" is just a\n      ** regular file-name. In this case the auto-vacuum applies as per normal.\n      */\n      if( zFilename && !isMemdb ){\n        pBt->autoVacuum = (SQLITE_DEFAULT_AUTOVACUUM ? 1 : 0);\n        pBt->incrVacuum = (SQLITE_DEFAULT_AUTOVACUUM==2 ? 1 : 0);\n      }\n#endif\n      nReserve = 0;\n    }else{\n      /* EVIDENCE-OF: R-37497-42412 The size of the reserved region is\n      ** determined by the one-byte unsigned integer found at an offset of 20\n      ** into the database file header. */\n      nReserve = zDbHeader[20];\n      pBt->btsFlags |= BTS_PAGESIZE_FIXED;\n#ifndef SQLITE_OMIT_AUTOVACUUM\n      pBt->autoVacuum = (get4byte(&zDbHeader[36 + 4*4])?1:0);\n      pBt->incrVacuum = (get4byte(&zDbHeader[36 + 7*4])?1:0);\n#endif\n    }\n    rc = sqlite3PagerSetPagesize(pBt->pPager, &pBt->pageSize, nReserve);\n    if( rc ) goto btree_open_out;\n    pBt->usableSize = pBt->pageSize - nReserve;\n    assert( (pBt->pageSize & 7)==0 );  /* 8-byte alignment of pageSize */\n   \n#if !defined(SQLITE_OMIT_SHARED_CACHE) && !defined(SQLITE_OMIT_DISKIO)\n    /* Add the new BtShared object to the linked list sharable BtShareds.\n    */\n    pBt->nRef = 1;\n    if( p->sharable ){\n      MUTEX_LOGIC( sqlite3_mutex *mutexShared; )\n      MUTEX_LOGIC( mutexShared = sqlite3MutexAlloc(SQLITE_MUTEX_STATIC_MASTER);)\n      if( SQLITE_THREADSAFE && sqlite3GlobalConfig.bCoreMutex ){\n        pBt->mutex = sqlite3MutexAlloc(SQLITE_MUTEX_FAST);\n        if( pBt->mutex==0 ){\n          rc = SQLITE_NOMEM_BKPT;\n          goto btree_open_out;\n        }\n      }\n      sqlite3_mutex_enter(mutexShared);\n      pBt->pNext = GLOBAL(BtShared*,sqlite3SharedCacheList);\n      GLOBAL(BtShared*,sqlite3SharedCacheList) = pBt;\n      sqlite3_mutex_leave(mutexShared);\n    }\n#endif\n  }\n\n#if !defined(SQLITE_OMIT_SHARED_CACHE) && !defined(SQLITE_OMIT_DISKIO)\n  /* If the new Btree uses a sharable pBtShared, then link the new\n  ** Btree into the list of all sharable Btrees for the same connection.\n  ** The list is kept in ascending order by pBt address.\n  */\n  if( p->sharable ){\n    int i;\n    Btree *pSib;\n    for(i=0; i<db->nDb; i++){\n      if( (pSib = db->aDb[i].pBt)!=0 && pSib->sharable ){\n        while( pSib->pPrev ){ pSib = pSib->pPrev; }\n        if( (uptr)p->pBt<(uptr)pSib->pBt ){\n          p->pNext = pSib;\n          p->pPrev = 0;\n          pSib->pPrev = p;\n        }else{\n          while( pSib->pNext && (uptr)pSib->pNext->pBt<(uptr)p->pBt ){\n            pSib = pSib->pNext;\n          }\n          p->pNext = pSib->pNext;\n          p->pPrev = pSib;\n          if( p->pNext ){\n            p->pNext->pPrev = p;\n          }\n          pSib->pNext = p;\n        }\n        break;\n      }\n    }\n  }\n#endif\n  *ppBtree = p;\n\nbtree_open_out:\n  if( rc!=SQLITE_OK ){\n    if( pBt && pBt->pPager ){\n      sqlite3PagerClose(pBt->pPager, 0);\n    }\n    sqlite3_free(pBt);\n    sqlite3_free(p);\n    *ppBtree = 0;\n  }else{\n    sqlite3_file *pFile;\n\n    /* If the B-Tree was successfully opened, set the pager-cache size to the\n    ** default value. Except, when opening on an existing shared pager-cache,\n    ** do not change the pager-cache size.\n    */\n    if( sqlite3BtreeSchema(p, 0, 0)==0 ){\n      sqlite3PagerSetCachesize(p->pBt->pPager, SQLITE_DEFAULT_CACHE_SIZE);\n    }\n\n    pFile = sqlite3PagerFile(pBt->pPager);\n    if( pFile->pMethods ){\n      sqlite3OsFileControlHint(pFile, SQLITE_FCNTL_PDB, (void*)&pBt->db);\n    }\n  }\n  if( mutexOpen ){\n    assert( sqlite3_mutex_held(mutexOpen) );\n    sqlite3_mutex_leave(mutexOpen);\n  }\n  assert( rc!=SQLITE_OK || sqlite3BtreeConnectionCount(*ppBtree)>0 );\n  return rc;\n}\n\n/*\n** Decrement the BtShared.nRef counter.  When it reaches zero,\n** remove the BtShared structure from the sharing list.  Return\n** true if the BtShared.nRef counter reaches zero and return\n** false if it is still positive.\n*/\nstatic int removeFromSharingList(BtShared *pBt){\n#ifndef SQLITE_OMIT_SHARED_CACHE\n  MUTEX_LOGIC( sqlite3_mutex *pMaster; )\n  BtShared *pList;\n  int removed = 0;\n\n  assert( sqlite3_mutex_notheld(pBt->mutex) );\n  MUTEX_LOGIC( pMaster = sqlite3MutexAlloc(SQLITE_MUTEX_STATIC_MASTER); )\n  sqlite3_mutex_enter(pMaster);\n  pBt->nRef--;\n  if( pBt->nRef<=0 ){\n    if( GLOBAL(BtShared*,sqlite3SharedCacheList)==pBt ){\n      GLOBAL(BtShared*,sqlite3SharedCacheList) = pBt->pNext;\n    }else{\n      pList = GLOBAL(BtShared*,sqlite3SharedCacheList);\n      while( ALWAYS(pList) && pList->pNext!=pBt ){\n        pList=pList->pNext;\n      }\n      if( ALWAYS(pList) ){\n        pList->pNext = pBt->pNext;\n      }\n    }\n    if( SQLITE_THREADSAFE ){\n      sqlite3_mutex_free(pBt->mutex);\n    }\n    removed = 1;\n  }\n  sqlite3_mutex_leave(pMaster);\n  return removed;\n#else\n  return 1;\n#endif\n}\n\n/*\n** Make sure pBt->pTmpSpace points to an allocation of \n** MX_CELL_SIZE(pBt) bytes with a 4-byte prefix for a left-child\n** pointer.\n*/\nstatic void allocateTempSpace(BtShared *pBt){\n  if( !pBt->pTmpSpace ){\n    pBt->pTmpSpace = sqlite3PageMalloc( pBt->pageSize );\n\n    /* One of the uses of pBt->pTmpSpace is to format cells before\n    ** inserting them into a leaf page (function fillInCell()). If\n    ** a cell is less than 4 bytes in size, it is rounded up to 4 bytes\n    ** by the various routines that manipulate binary cells. Which\n    ** can mean that fillInCell() only initializes the first 2 or 3\n    ** bytes of pTmpSpace, but that the first 4 bytes are copied from\n    ** it into a database page. This is not actually a problem, but it\n    ** does cause a valgrind error when the 1 or 2 bytes of unitialized \n    ** data is passed to system call write(). So to avoid this error,\n    ** zero the first 4 bytes of temp space here.\n    **\n    ** Also:  Provide four bytes of initialized space before the\n    ** beginning of pTmpSpace as an area available to prepend the\n    ** left-child pointer to the beginning of a cell.\n    */\n    if( pBt->pTmpSpace ){\n      memset(pBt->pTmpSpace, 0, 8);\n      pBt->pTmpSpace += 4;\n    }\n  }\n}\n\n/*\n** Free the pBt->pTmpSpace allocation\n*/\nstatic void freeTempSpace(BtShared *pBt){\n  if( pBt->pTmpSpace ){\n    pBt->pTmpSpace -= 4;\n    sqlite3PageFree(pBt->pTmpSpace);\n    pBt->pTmpSpace = 0;\n  }\n}\n\n/*\n** Close an open database and invalidate all cursors.\n*/\nSQLITE_PRIVATE int sqlite3BtreeClose(Btree *p){\n  BtShared *pBt = p->pBt;\n  BtCursor *pCur;\n\n  /* Close all cursors opened via this handle.  */\n  assert( sqlite3_mutex_held(p->db->mutex) );\n  sqlite3BtreeEnter(p);\n  pCur = pBt->pCursor;\n  while( pCur ){\n    BtCursor *pTmp = pCur;\n    pCur = pCur->pNext;\n    if( pTmp->pBtree==p ){\n      sqlite3BtreeCloseCursor(pTmp);\n    }\n  }\n\n  /* Rollback any active transaction and free the handle structure.\n  ** The call to sqlite3BtreeRollback() drops any table-locks held by\n  ** this handle.\n  */\n  sqlite3BtreeRollback(p, SQLITE_OK, 0);\n  sqlite3BtreeLeave(p);\n\n  /* If there are still other outstanding references to the shared-btree\n  ** structure, return now. The remainder of this procedure cleans \n  ** up the shared-btree.\n  */\n  assert( p->wantToLock==0 && p->locked==0 );\n  if( !p->sharable || removeFromSharingList(pBt) ){\n    /* The pBt is no longer on the sharing list, so we can access\n    ** it without having to hold the mutex.\n    **\n    ** Clean out and delete the BtShared object.\n    */\n    assert( !pBt->pCursor );\n    sqlite3PagerClose(pBt->pPager, p->db);\n    if( pBt->xFreeSchema && pBt->pSchema ){\n      pBt->xFreeSchema(pBt->pSchema);\n    }\n    sqlite3DbFree(0, pBt->pSchema);\n    freeTempSpace(pBt);\n    sqlite3_free(pBt);\n  }\n\n#ifndef SQLITE_OMIT_SHARED_CACHE\n  assert( p->wantToLock==0 );\n  assert( p->locked==0 );\n  if( p->pPrev ) p->pPrev->pNext = p->pNext;\n  if( p->pNext ) p->pNext->pPrev = p->pPrev;\n#endif\n\n  sqlite3_free(p);\n  return SQLITE_OK;\n}\n\n/*\n** Change the \"soft\" limit on the number of pages in the cache.\n** Unused and unmodified pages will be recycled when the number of\n** pages in the cache exceeds this soft limit.  But the size of the\n** cache is allowed to grow larger than this limit if it contains\n** dirty pages or pages still in active use.\n*/\nSQLITE_PRIVATE int sqlite3BtreeSetCacheSize(Btree *p, int mxPage){\n  BtShared *pBt = p->pBt;\n  assert( sqlite3_mutex_held(p->db->mutex) );\n  sqlite3BtreeEnter(p);\n  sqlite3PagerSetCachesize(pBt->pPager, mxPage);\n  sqlite3BtreeLeave(p);\n  return SQLITE_OK;\n}\n\n/*\n** Change the \"spill\" limit on the number of pages in the cache.\n** If the number of pages exceeds this limit during a write transaction,\n** the pager might attempt to \"spill\" pages to the journal early in\n** order to free up memory.\n**\n** The value returned is the current spill size.  If zero is passed\n** as an argument, no changes are made to the spill size setting, so\n** using mxPage of 0 is a way to query the current spill size.\n*/\nSQLITE_PRIVATE int sqlite3BtreeSetSpillSize(Btree *p, int mxPage){\n  BtShared *pBt = p->pBt;\n  int res;\n  assert( sqlite3_mutex_held(p->db->mutex) );\n  sqlite3BtreeEnter(p);\n  res = sqlite3PagerSetSpillsize(pBt->pPager, mxPage);\n  sqlite3BtreeLeave(p);\n  return res;\n}\n\n#if SQLITE_MAX_MMAP_SIZE>0\n/*\n** Change the limit on the amount of the database file that may be\n** memory mapped.\n*/\nSQLITE_PRIVATE int sqlite3BtreeSetMmapLimit(Btree *p, sqlite3_int64 szMmap){\n  BtShared *pBt = p->pBt;\n  assert( sqlite3_mutex_held(p->db->mutex) );\n  sqlite3BtreeEnter(p);\n  sqlite3PagerSetMmapLimit(pBt->pPager, szMmap);\n  sqlite3BtreeLeave(p);\n  return SQLITE_OK;\n}\n#endif /* SQLITE_MAX_MMAP_SIZE>0 */\n\n/*\n** Change the way data is synced to disk in order to increase or decrease\n** how well the database resists damage due to OS crashes and power\n** failures.  Level 1 is the same as asynchronous (no syncs() occur and\n** there is a high probability of damage)  Level 2 is the default.  There\n** is a very low but non-zero probability of damage.  Level 3 reduces the\n** probability of damage to near zero but with a write performance reduction.\n*/\n#ifndef SQLITE_OMIT_PAGER_PRAGMAS\nSQLITE_PRIVATE int sqlite3BtreeSetPagerFlags(\n  Btree *p,              /* The btree to set the safety level on */\n  unsigned pgFlags       /* Various PAGER_* flags */\n){\n  BtShared *pBt = p->pBt;\n  assert( sqlite3_mutex_held(p->db->mutex) );\n  sqlite3BtreeEnter(p);\n  sqlite3PagerSetFlags(pBt->pPager, pgFlags);\n  sqlite3BtreeLeave(p);\n  return SQLITE_OK;\n}\n#endif\n\n/*\n** Change the default pages size and the number of reserved bytes per page.\n** Or, if the page size has already been fixed, return SQLITE_READONLY \n** without changing anything.\n**\n** The page size must be a power of 2 between 512 and 65536.  If the page\n** size supplied does not meet this constraint then the page size is not\n** changed.\n**\n** Page sizes are constrained to be a power of two so that the region\n** of the database file used for locking (beginning at PENDING_BYTE,\n** the first byte past the 1GB boundary, 0x40000000) needs to occur\n** at the beginning of a page.\n**\n** If parameter nReserve is less than zero, then the number of reserved\n** bytes per page is left unchanged.\n**\n** If the iFix!=0 then the BTS_PAGESIZE_FIXED flag is set so that the page size\n** and autovacuum mode can no longer be changed.\n*/\nSQLITE_PRIVATE int sqlite3BtreeSetPageSize(Btree *p, int pageSize, int nReserve, int iFix){\n  int rc = SQLITE_OK;\n  BtShared *pBt = p->pBt;\n  assert( nReserve>=-1 && nReserve<=255 );\n  sqlite3BtreeEnter(p);\n#if SQLITE_HAS_CODEC\n  if( nReserve>pBt->optimalReserve ) pBt->optimalReserve = (u8)nReserve;\n#endif\n  if( pBt->btsFlags & BTS_PAGESIZE_FIXED ){\n    sqlite3BtreeLeave(p);\n    return SQLITE_READONLY;\n  }\n  if( nReserve<0 ){\n    nReserve = pBt->pageSize - pBt->usableSize;\n  }\n  assert( nReserve>=0 && nReserve<=255 );\n  if( pageSize>=512 && pageSize<=SQLITE_MAX_PAGE_SIZE &&\n        ((pageSize-1)&pageSize)==0 ){\n    assert( (pageSize & 7)==0 );\n    assert( !pBt->pCursor );\n    pBt->pageSize = (u32)pageSize;\n    freeTempSpace(pBt);\n  }\n  rc = sqlite3PagerSetPagesize(pBt->pPager, &pBt->pageSize, nReserve);\n  pBt->usableSize = pBt->pageSize - (u16)nReserve;\n  if( iFix ) pBt->btsFlags |= BTS_PAGESIZE_FIXED;\n  sqlite3BtreeLeave(p);\n  return rc;\n}\n\n/*\n** Return the currently defined page size\n*/\nSQLITE_PRIVATE int sqlite3BtreeGetPageSize(Btree *p){\n  return p->pBt->pageSize;\n}\n\n/*\n** This function is similar to sqlite3BtreeGetReserve(), except that it\n** may only be called if it is guaranteed that the b-tree mutex is already\n** held.\n**\n** This is useful in one special case in the backup API code where it is\n** known that the shared b-tree mutex is held, but the mutex on the \n** database handle that owns *p is not. In this case if sqlite3BtreeEnter()\n** were to be called, it might collide with some other operation on the\n** database handle that owns *p, causing undefined behavior.\n*/\nSQLITE_PRIVATE int sqlite3BtreeGetReserveNoMutex(Btree *p){\n  int n;\n  assert( sqlite3_mutex_held(p->pBt->mutex) );\n  n = p->pBt->pageSize - p->pBt->usableSize;\n  return n;\n}\n\n/*\n** Return the number of bytes of space at the end of every page that\n** are intentually left unused.  This is the \"reserved\" space that is\n** sometimes used by extensions.\n**\n** If SQLITE_HAS_MUTEX is defined then the number returned is the\n** greater of the current reserved space and the maximum requested\n** reserve space.\n*/\nSQLITE_PRIVATE int sqlite3BtreeGetOptimalReserve(Btree *p){\n  int n;\n  sqlite3BtreeEnter(p);\n  n = sqlite3BtreeGetReserveNoMutex(p);\n#ifdef SQLITE_HAS_CODEC\n  if( n<p->pBt->optimalReserve ) n = p->pBt->optimalReserve;\n#endif\n  sqlite3BtreeLeave(p);\n  return n;\n}\n\n\n/*\n** Set the maximum page count for a database if mxPage is positive.\n** No changes are made if mxPage is 0 or negative.\n** Regardless of the value of mxPage, return the maximum page count.\n*/\nSQLITE_PRIVATE int sqlite3BtreeMaxPageCount(Btree *p, int mxPage){\n  int n;\n  sqlite3BtreeEnter(p);\n  n = sqlite3PagerMaxPageCount(p->pBt->pPager, mxPage);\n  sqlite3BtreeLeave(p);\n  return n;\n}\n\n/*\n** Change the values for the BTS_SECURE_DELETE and BTS_OVERWRITE flags:\n**\n**    newFlag==0       Both BTS_SECURE_DELETE and BTS_OVERWRITE are cleared\n**    newFlag==1       BTS_SECURE_DELETE set and BTS_OVERWRITE is cleared\n**    newFlag==2       BTS_SECURE_DELETE cleared and BTS_OVERWRITE is set\n**    newFlag==(-1)    No changes\n**\n** This routine acts as a query if newFlag is less than zero\n**\n** With BTS_OVERWRITE set, deleted content is overwritten by zeros, but\n** freelist leaf pages are not written back to the database.  Thus in-page\n** deleted content is cleared, but freelist deleted content is not.\n**\n** With BTS_SECURE_DELETE, operation is like BTS_OVERWRITE with the addition\n** that freelist leaf pages are written back into the database, increasing\n** the amount of disk I/O.\n*/\nSQLITE_PRIVATE int sqlite3BtreeSecureDelete(Btree *p, int newFlag){\n  int b;\n  if( p==0 ) return 0;\n  sqlite3BtreeEnter(p);\n  assert( BTS_OVERWRITE==BTS_SECURE_DELETE*2 );\n  assert( BTS_FAST_SECURE==(BTS_OVERWRITE|BTS_SECURE_DELETE) );\n  if( newFlag>=0 ){\n    p->pBt->btsFlags &= ~BTS_FAST_SECURE;\n    p->pBt->btsFlags |= BTS_SECURE_DELETE*newFlag;\n  }\n  b = (p->pBt->btsFlags & BTS_FAST_SECURE)/BTS_SECURE_DELETE;\n  sqlite3BtreeLeave(p);\n  return b;\n}\n\n/*\n** Change the 'auto-vacuum' property of the database. If the 'autoVacuum'\n** parameter is non-zero, then auto-vacuum mode is enabled. If zero, it\n** is disabled. The default value for the auto-vacuum property is \n** determined by the SQLITE_DEFAULT_AUTOVACUUM macro.\n*/\nSQLITE_PRIVATE int sqlite3BtreeSetAutoVacuum(Btree *p, int autoVacuum){\n#ifdef SQLITE_OMIT_AUTOVACUUM\n  return SQLITE_READONLY;\n#else\n  BtShared *pBt = p->pBt;\n  int rc = SQLITE_OK;\n  u8 av = (u8)autoVacuum;\n\n  sqlite3BtreeEnter(p);\n  if( (pBt->btsFlags & BTS_PAGESIZE_FIXED)!=0 && (av ?1:0)!=pBt->autoVacuum ){\n    rc = SQLITE_READONLY;\n  }else{\n    pBt->autoVacuum = av ?1:0;\n    pBt->incrVacuum = av==2 ?1:0;\n  }\n  sqlite3BtreeLeave(p);\n  return rc;\n#endif\n}\n\n/*\n** Return the value of the 'auto-vacuum' property. If auto-vacuum is \n** enabled 1 is returned. Otherwise 0.\n*/\nSQLITE_PRIVATE int sqlite3BtreeGetAutoVacuum(Btree *p){\n#ifdef SQLITE_OMIT_AUTOVACUUM\n  return BTREE_AUTOVACUUM_NONE;\n#else\n  int rc;\n  sqlite3BtreeEnter(p);\n  rc = (\n    (!p->pBt->autoVacuum)?BTREE_AUTOVACUUM_NONE:\n    (!p->pBt->incrVacuum)?BTREE_AUTOVACUUM_FULL:\n    BTREE_AUTOVACUUM_INCR\n  );\n  sqlite3BtreeLeave(p);\n  return rc;\n#endif\n}\n\n/*\n** If the user has not set the safety-level for this database connection\n** using \"PRAGMA synchronous\", and if the safety-level is not already\n** set to the value passed to this function as the second parameter,\n** set it so.\n*/\n#if SQLITE_DEFAULT_SYNCHRONOUS!=SQLITE_DEFAULT_WAL_SYNCHRONOUS \\\n    && !defined(SQLITE_OMIT_WAL)\nstatic void setDefaultSyncFlag(BtShared *pBt, u8 safety_level){\n  sqlite3 *db;\n  Db *pDb;\n  if( (db=pBt->db)!=0 && (pDb=db->aDb)!=0 ){\n    while( pDb->pBt==0 || pDb->pBt->pBt!=pBt ){ pDb++; }\n    if( pDb->bSyncSet==0 \n     && pDb->safety_level!=safety_level \n     && pDb!=&db->aDb[1] \n    ){\n      pDb->safety_level = safety_level;\n      sqlite3PagerSetFlags(pBt->pPager,\n          pDb->safety_level | (db->flags & PAGER_FLAGS_MASK));\n    }\n  }\n}\n#else\n# define setDefaultSyncFlag(pBt,safety_level)\n#endif\n\n/*\n** Get a reference to pPage1 of the database file.  This will\n** also acquire a readlock on that file.\n**\n** SQLITE_OK is returned on success.  If the file is not a\n** well-formed database file, then SQLITE_CORRUPT is returned.\n** SQLITE_BUSY is returned if the database is locked.  SQLITE_NOMEM\n** is returned if we run out of memory. \n*/\nstatic int lockBtree(BtShared *pBt){\n  int rc;              /* Result code from subfunctions */\n  MemPage *pPage1;     /* Page 1 of the database file */\n  int nPage;           /* Number of pages in the database */\n  int nPageFile = 0;   /* Number of pages in the database file */\n  int nPageHeader;     /* Number of pages in the database according to hdr */\n\n  assert( sqlite3_mutex_held(pBt->mutex) );\n  assert( pBt->pPage1==0 );\n  rc = sqlite3PagerSharedLock(pBt->pPager);\n  if( rc!=SQLITE_OK ) return rc;\n  rc = btreeGetPage(pBt, 1, &pPage1, 0);\n  if( rc!=SQLITE_OK ) return rc;\n\n  /* Do some checking to help insure the file we opened really is\n  ** a valid database file. \n  */\n  nPage = nPageHeader = get4byte(28+(u8*)pPage1->aData);\n  sqlite3PagerPagecount(pBt->pPager, &nPageFile);\n  if( nPage==0 || memcmp(24+(u8*)pPage1->aData, 92+(u8*)pPage1->aData,4)!=0 ){\n    nPage = nPageFile;\n  }\n  if( nPage>0 ){\n    u32 pageSize;\n    u32 usableSize;\n    u8 *page1 = pPage1->aData;\n    rc = SQLITE_NOTADB;\n    /* EVIDENCE-OF: R-43737-39999 Every valid SQLite database file begins\n    ** with the following 16 bytes (in hex): 53 51 4c 69 74 65 20 66 6f 72 6d\n    ** 61 74 20 33 00. */\n    if( memcmp(page1, zMagicHeader, 16)!=0 ){\n      goto page1_init_failed;\n    }\n\n#ifdef SQLITE_OMIT_WAL\n    if( page1[18]>1 ){\n      pBt->btsFlags |= BTS_READ_ONLY;\n    }\n    if( page1[19]>1 ){\n      goto page1_init_failed;\n    }\n#else\n    if( page1[18]>2 ){\n      pBt->btsFlags |= BTS_READ_ONLY;\n    }\n    if( page1[19]>2 ){\n      goto page1_init_failed;\n    }\n\n    /* If the write version is set to 2, this database should be accessed\n    ** in WAL mode. If the log is not already open, open it now. Then \n    ** return SQLITE_OK and return without populating BtShared.pPage1.\n    ** The caller detects this and calls this function again. This is\n    ** required as the version of page 1 currently in the page1 buffer\n    ** may not be the latest version - there may be a newer one in the log\n    ** file.\n    */\n    if( page1[19]==2 && (pBt->btsFlags & BTS_NO_WAL)==0 ){\n      int isOpen = 0;\n      rc = sqlite3PagerOpenWal(pBt->pPager, &isOpen);\n      if( rc!=SQLITE_OK ){\n        goto page1_init_failed;\n      }else{\n        setDefaultSyncFlag(pBt, SQLITE_DEFAULT_WAL_SYNCHRONOUS+1);\n        if( isOpen==0 ){\n          releasePageOne(pPage1);\n          return SQLITE_OK;\n        }\n      }\n      rc = SQLITE_NOTADB;\n    }else{\n      setDefaultSyncFlag(pBt, SQLITE_DEFAULT_SYNCHRONOUS+1);\n    }\n#endif\n\n    /* EVIDENCE-OF: R-15465-20813 The maximum and minimum embedded payload\n    ** fractions and the leaf payload fraction values must be 64, 32, and 32.\n    **\n    ** The original design allowed these amounts to vary, but as of\n    ** version 3.6.0, we require them to be fixed.\n    */\n    if( memcmp(&page1[21], \"\\100\\040\\040\",3)!=0 ){\n      goto page1_init_failed;\n    }\n    /* EVIDENCE-OF: R-51873-39618 The page size for a database file is\n    ** determined by the 2-byte integer located at an offset of 16 bytes from\n    ** the beginning of the database file. */\n    pageSize = (page1[16]<<8) | (page1[17]<<16);\n    /* EVIDENCE-OF: R-25008-21688 The size of a page is a power of two\n    ** between 512 and 65536 inclusive. */\n    if( ((pageSize-1)&pageSize)!=0\n     || pageSize>SQLITE_MAX_PAGE_SIZE \n     || pageSize<=256 \n    ){\n      goto page1_init_failed;\n    }\n    assert( (pageSize & 7)==0 );\n    /* EVIDENCE-OF: R-59310-51205 The \"reserved space\" size in the 1-byte\n    ** integer at offset 20 is the number of bytes of space at the end of\n    ** each page to reserve for extensions. \n    **\n    ** EVIDENCE-OF: R-37497-42412 The size of the reserved region is\n    ** determined by the one-byte unsigned integer found at an offset of 20\n    ** into the database file header. */\n    usableSize = pageSize - page1[20];\n    if( (u32)pageSize!=pBt->pageSize ){\n      /* After reading the first page of the database assuming a page size\n      ** of BtShared.pageSize, we have discovered that the page-size is\n      ** actually pageSize. Unlock the database, leave pBt->pPage1 at\n      ** zero and return SQLITE_OK. The caller will call this function\n      ** again with the correct page-size.\n      */\n      releasePageOne(pPage1);\n      pBt->usableSize = usableSize;\n      pBt->pageSize = pageSize;\n      freeTempSpace(pBt);\n      rc = sqlite3PagerSetPagesize(pBt->pPager, &pBt->pageSize,\n                                   pageSize-usableSize);\n      return rc;\n    }\n    if( (pBt->db->flags & SQLITE_WriteSchema)==0 && nPage>nPageFile ){\n      rc = SQLITE_CORRUPT_BKPT;\n      goto page1_init_failed;\n    }\n    /* EVIDENCE-OF: R-28312-64704 However, the usable size is not allowed to\n    ** be less than 480. In other words, if the page size is 512, then the\n    ** reserved space size cannot exceed 32. */\n    if( usableSize<480 ){\n      goto page1_init_failed;\n    }\n    pBt->pageSize = pageSize;\n    pBt->usableSize = usableSize;\n#ifndef SQLITE_OMIT_AUTOVACUUM\n    pBt->autoVacuum = (get4byte(&page1[36 + 4*4])?1:0);\n    pBt->incrVacuum = (get4byte(&page1[36 + 7*4])?1:0);\n#endif\n  }\n\n  /* maxLocal is the maximum amount of payload to store locally for\n  ** a cell.  Make sure it is small enough so that at least minFanout\n  ** cells can will fit on one page.  We assume a 10-byte page header.\n  ** Besides the payload, the cell must store:\n  **     2-byte pointer to the cell\n  **     4-byte child pointer\n  **     9-byte nKey value\n  **     4-byte nData value\n  **     4-byte overflow page pointer\n  ** So a cell consists of a 2-byte pointer, a header which is as much as\n  ** 17 bytes long, 0 to N bytes of payload, and an optional 4 byte overflow\n  ** page pointer.\n  */\n  pBt->maxLocal = (u16)((pBt->usableSize-12)*64/255 - 23);\n  pBt->minLocal = (u16)((pBt->usableSize-12)*32/255 - 23);\n  pBt->maxLeaf = (u16)(pBt->usableSize - 35);\n  pBt->minLeaf = (u16)((pBt->usableSize-12)*32/255 - 23);\n  if( pBt->maxLocal>127 ){\n    pBt->max1bytePayload = 127;\n  }else{\n    pBt->max1bytePayload = (u8)pBt->maxLocal;\n  }\n  assert( pBt->maxLeaf + 23 <= MX_CELL_SIZE(pBt) );\n  pBt->pPage1 = pPage1;\n  pBt->nPage = nPage;\n  return SQLITE_OK;\n\npage1_init_failed:\n  releasePageOne(pPage1);\n  pBt->pPage1 = 0;\n  return rc;\n}\n\n#ifndef NDEBUG\n/*\n** Return the number of cursors open on pBt. This is for use\n** in assert() expressions, so it is only compiled if NDEBUG is not\n** defined.\n**\n** Only write cursors are counted if wrOnly is true.  If wrOnly is\n** false then all cursors are counted.\n**\n** For the purposes of this routine, a cursor is any cursor that\n** is capable of reading or writing to the database.  Cursors that\n** have been tripped into the CURSOR_FAULT state are not counted.\n*/\nstatic int countValidCursors(BtShared *pBt, int wrOnly){\n  BtCursor *pCur;\n  int r = 0;\n  for(pCur=pBt->pCursor; pCur; pCur=pCur->pNext){\n    if( (wrOnly==0 || (pCur->curFlags & BTCF_WriteFlag)!=0)\n     && pCur->eState!=CURSOR_FAULT ) r++; \n  }\n  return r;\n}\n#endif\n\n/*\n** If there are no outstanding cursors and we are not in the middle\n** of a transaction but there is a read lock on the database, then\n** this routine unrefs the first page of the database file which \n** has the effect of releasing the read lock.\n**\n** If there is a transaction in progress, this routine is a no-op.\n*/\nstatic void unlockBtreeIfUnused(BtShared *pBt){\n  assert( sqlite3_mutex_held(pBt->mutex) );\n  assert( countValidCursors(pBt,0)==0 || pBt->inTransaction>TRANS_NONE );\n  if( pBt->inTransaction==TRANS_NONE && pBt->pPage1!=0 ){\n    MemPage *pPage1 = pBt->pPage1;\n    assert( pPage1->aData );\n    assert( sqlite3PagerRefcount(pBt->pPager)==1 );\n    pBt->pPage1 = 0;\n    releasePageOne(pPage1);\n  }\n}\n\n/*\n** If pBt points to an empty file then convert that empty file\n** into a new empty database by initializing the first page of\n** the database.\n*/\nstatic int newDatabase(BtShared *pBt){\n  MemPage *pP1;\n  unsigned char *data;\n  int rc;\n\n  assert( sqlite3_mutex_held(pBt->mutex) );\n  if( pBt->nPage>0 ){\n    return SQLITE_OK;\n  }\n  pP1 = pBt->pPage1;\n  assert( pP1!=0 );\n  data = pP1->aData;\n  rc = sqlite3PagerWrite(pP1->pDbPage);\n  if( rc ) return rc;\n  memcpy(data, zMagicHeader, sizeof(zMagicHeader));\n  assert( sizeof(zMagicHeader)==16 );\n  data[16] = (u8)((pBt->pageSize>>8)&0xff);\n  data[17] = (u8)((pBt->pageSize>>16)&0xff);\n  data[18] = 1;\n  data[19] = 1;\n  assert( pBt->usableSize<=pBt->pageSize && pBt->usableSize+255>=pBt->pageSize);\n  data[20] = (u8)(pBt->pageSize - pBt->usableSize);\n  data[21] = 64;\n  data[22] = 32;\n  data[23] = 32;\n  memset(&data[24], 0, 100-24);\n  zeroPage(pP1, PTF_INTKEY|PTF_LEAF|PTF_LEAFDATA );\n  pBt->btsFlags |= BTS_PAGESIZE_FIXED;\n#ifndef SQLITE_OMIT_AUTOVACUUM\n  assert( pBt->autoVacuum==1 || pBt->autoVacuum==0 );\n  assert( pBt->incrVacuum==1 || pBt->incrVacuum==0 );\n  put4byte(&data[36 + 4*4], pBt->autoVacuum);\n  put4byte(&data[36 + 7*4], pBt->incrVacuum);\n#endif\n  pBt->nPage = 1;\n  data[31] = 1;\n  return SQLITE_OK;\n}\n\n/*\n** Initialize the first page of the database file (creating a database\n** consisting of a single page and no schema objects). Return SQLITE_OK\n** if successful, or an SQLite error code otherwise.\n*/\nSQLITE_PRIVATE int sqlite3BtreeNewDb(Btree *p){\n  int rc;\n  sqlite3BtreeEnter(p);\n  p->pBt->nPage = 0;\n  rc = newDatabase(p->pBt);\n  sqlite3BtreeLeave(p);\n  return rc;\n}\n\n/*\n** Attempt to start a new transaction. A write-transaction\n** is started if the second argument is nonzero, otherwise a read-\n** transaction.  If the second argument is 2 or more and exclusive\n** transaction is started, meaning that no other process is allowed\n** to access the database.  A preexisting transaction may not be\n** upgraded to exclusive by calling this routine a second time - the\n** exclusivity flag only works for a new transaction.\n**\n** A write-transaction must be started before attempting any \n** changes to the database.  None of the following routines \n** will work unless a transaction is started first:\n**\n**      sqlite3BtreeCreateTable()\n**      sqlite3BtreeCreateIndex()\n**      sqlite3BtreeClearTable()\n**      sqlite3BtreeDropTable()\n**      sqlite3BtreeInsert()\n**      sqlite3BtreeDelete()\n**      sqlite3BtreeUpdateMeta()\n**\n** If an initial attempt to acquire the lock fails because of lock contention\n** and the database was previously unlocked, then invoke the busy handler\n** if there is one.  But if there was previously a read-lock, do not\n** invoke the busy handler - just return SQLITE_BUSY.  SQLITE_BUSY is \n** returned when there is already a read-lock in order to avoid a deadlock.\n**\n** Suppose there are two processes A and B.  A has a read lock and B has\n** a reserved lock.  B tries to promote to exclusive but is blocked because\n** of A's read lock.  A tries to promote to reserved but is blocked by B.\n** One or the other of the two processes must give way or there can be\n** no progress.  By returning SQLITE_BUSY and not invoking the busy callback\n** when A already has a read lock, we encourage A to give up and let B\n** proceed.\n*/\nSQLITE_PRIVATE int sqlite3BtreeBeginTrans(Btree *p, int wrflag){\n  BtShared *pBt = p->pBt;\n  int rc = SQLITE_OK;\n\n  sqlite3BtreeEnter(p);\n  btreeIntegrity(p);\n\n  /* If the btree is already in a write-transaction, or it\n  ** is already in a read-transaction and a read-transaction\n  ** is requested, this is a no-op.\n  */\n  if( p->inTrans==TRANS_WRITE || (p->inTrans==TRANS_READ && !wrflag) ){\n    goto trans_begun;\n  }\n  assert( pBt->inTransaction==TRANS_WRITE || IfNotOmitAV(pBt->bDoTruncate)==0 );\n\n  /* Write transactions are not possible on a read-only database */\n  if( (pBt->btsFlags & BTS_READ_ONLY)!=0 && wrflag ){\n    rc = SQLITE_READONLY;\n    goto trans_begun;\n  }\n\n#ifndef SQLITE_OMIT_SHARED_CACHE\n  {\n    sqlite3 *pBlock = 0;\n    /* If another database handle has already opened a write transaction \n    ** on this shared-btree structure and a second write transaction is\n    ** requested, return SQLITE_LOCKED.\n    */\n    if( (wrflag && pBt->inTransaction==TRANS_WRITE)\n     || (pBt->btsFlags & BTS_PENDING)!=0\n    ){\n      pBlock = pBt->pWriter->db;\n    }else if( wrflag>1 ){\n      BtLock *pIter;\n      for(pIter=pBt->pLock; pIter; pIter=pIter->pNext){\n        if( pIter->pBtree!=p ){\n          pBlock = pIter->pBtree->db;\n          break;\n        }\n      }\n    }\n    if( pBlock ){\n      sqlite3ConnectionBlocked(p->db, pBlock);\n      rc = SQLITE_LOCKED_SHAREDCACHE;\n      goto trans_begun;\n    }\n  }\n#endif\n\n  /* Any read-only or read-write transaction implies a read-lock on \n  ** page 1. So if some other shared-cache client already has a write-lock \n  ** on page 1, the transaction cannot be opened. */\n  rc = querySharedCacheTableLock(p, MASTER_ROOT, READ_LOCK);\n  if( SQLITE_OK!=rc ) goto trans_begun;\n\n  pBt->btsFlags &= ~BTS_INITIALLY_EMPTY;\n  if( pBt->nPage==0 ) pBt->btsFlags |= BTS_INITIALLY_EMPTY;\n  do {\n    /* Call lockBtree() until either pBt->pPage1 is populated or\n    ** lockBtree() returns something other than SQLITE_OK. lockBtree()\n    ** may return SQLITE_OK but leave pBt->pPage1 set to 0 if after\n    ** reading page 1 it discovers that the page-size of the database \n    ** file is not pBt->pageSize. In this case lockBtree() will update\n    ** pBt->pageSize to the page-size of the file on disk.\n    */\n    while( pBt->pPage1==0 && SQLITE_OK==(rc = lockBtree(pBt)) );\n\n    if( rc==SQLITE_OK && wrflag ){\n      if( (pBt->btsFlags & BTS_READ_ONLY)!=0 ){\n        rc = SQLITE_READONLY;\n      }else{\n        rc = sqlite3PagerBegin(pBt->pPager,wrflag>1,sqlite3TempInMemory(p->db));\n        if( rc==SQLITE_OK ){\n          rc = newDatabase(pBt);\n        }\n      }\n    }\n  \n    if( rc!=SQLITE_OK ){\n      unlockBtreeIfUnused(pBt);\n    }\n  }while( (rc&0xFF)==SQLITE_BUSY && pBt->inTransaction==TRANS_NONE &&\n          btreeInvokeBusyHandler(pBt) );\n\n  if( rc==SQLITE_OK ){\n    if( p->inTrans==TRANS_NONE ){\n      pBt->nTransaction++;\n#ifndef SQLITE_OMIT_SHARED_CACHE\n      if( p->sharable ){\n        assert( p->lock.pBtree==p && p->lock.iTable==1 );\n        p->lock.eLock = READ_LOCK;\n        p->lock.pNext = pBt->pLock;\n        pBt->pLock = &p->lock;\n      }\n#endif\n    }\n    p->inTrans = (wrflag?TRANS_WRITE:TRANS_READ);\n    if( p->inTrans>pBt->inTransaction ){\n      pBt->inTransaction = p->inTrans;\n    }\n    if( wrflag ){\n      MemPage *pPage1 = pBt->pPage1;\n#ifndef SQLITE_OMIT_SHARED_CACHE\n      assert( !pBt->pWriter );\n      pBt->pWriter = p;\n      pBt->btsFlags &= ~BTS_EXCLUSIVE;\n      if( wrflag>1 ) pBt->btsFlags |= BTS_EXCLUSIVE;\n#endif\n\n      /* If the db-size header field is incorrect (as it may be if an old\n      ** client has been writing the database file), update it now. Doing\n      ** this sooner rather than later means the database size can safely \n      ** re-read the database size from page 1 if a savepoint or transaction\n      ** rollback occurs within the transaction.\n      */\n      if( pBt->nPage!=get4byte(&pPage1->aData[28]) ){\n        rc = sqlite3PagerWrite(pPage1->pDbPage);\n        if( rc==SQLITE_OK ){\n          put4byte(&pPage1->aData[28], pBt->nPage);\n        }\n      }\n    }\n  }\n\n\ntrans_begun:\n  if( rc==SQLITE_OK && wrflag ){\n    /* This call makes sure that the pager has the correct number of\n    ** open savepoints. If the second parameter is greater than 0 and\n    ** the sub-journal is not already open, then it will be opened here.\n    */\n    rc = sqlite3PagerOpenSavepoint(pBt->pPager, p->db->nSavepoint);\n  }\n\n  btreeIntegrity(p);\n  sqlite3BtreeLeave(p);\n  return rc;\n}\n\n#ifndef SQLITE_OMIT_AUTOVACUUM\n\n/*\n** Set the pointer-map entries for all children of page pPage. Also, if\n** pPage contains cells that point to overflow pages, set the pointer\n** map entries for the overflow pages as well.\n*/\nstatic int setChildPtrmaps(MemPage *pPage){\n  int i;                             /* Counter variable */\n  int nCell;                         /* Number of cells in page pPage */\n  int rc;                            /* Return code */\n  BtShared *pBt = pPage->pBt;\n  Pgno pgno = pPage->pgno;\n\n  assert( sqlite3_mutex_held(pPage->pBt->mutex) );\n  rc = pPage->isInit ? SQLITE_OK : btreeInitPage(pPage);\n  if( rc!=SQLITE_OK ) return rc;\n  nCell = pPage->nCell;\n\n  for(i=0; i<nCell; i++){\n    u8 *pCell = findCell(pPage, i);\n\n    ptrmapPutOvflPtr(pPage, pCell, &rc);\n\n    if( !pPage->leaf ){\n      Pgno childPgno = get4byte(pCell);\n      ptrmapPut(pBt, childPgno, PTRMAP_BTREE, pgno, &rc);\n    }\n  }\n\n  if( !pPage->leaf ){\n    Pgno childPgno = get4byte(&pPage->aData[pPage->hdrOffset+8]);\n    ptrmapPut(pBt, childPgno, PTRMAP_BTREE, pgno, &rc);\n  }\n\n  return rc;\n}\n\n/*\n** Somewhere on pPage is a pointer to page iFrom.  Modify this pointer so\n** that it points to iTo. Parameter eType describes the type of pointer to\n** be modified, as  follows:\n**\n** PTRMAP_BTREE:     pPage is a btree-page. The pointer points at a child \n**                   page of pPage.\n**\n** PTRMAP_OVERFLOW1: pPage is a btree-page. The pointer points at an overflow\n**                   page pointed to by one of the cells on pPage.\n**\n** PTRMAP_OVERFLOW2: pPage is an overflow-page. The pointer points at the next\n**                   overflow page in the list.\n*/\nstatic int modifyPagePointer(MemPage *pPage, Pgno iFrom, Pgno iTo, u8 eType){\n  assert( sqlite3_mutex_held(pPage->pBt->mutex) );\n  assert( sqlite3PagerIswriteable(pPage->pDbPage) );\n  if( eType==PTRMAP_OVERFLOW2 ){\n    /* The pointer is always the first 4 bytes of the page in this case.  */\n    if( get4byte(pPage->aData)!=iFrom ){\n      return SQLITE_CORRUPT_PAGE(pPage);\n    }\n    put4byte(pPage->aData, iTo);\n  }else{\n    int i;\n    int nCell;\n    int rc;\n\n    rc = pPage->isInit ? SQLITE_OK : btreeInitPage(pPage);\n    if( rc ) return rc;\n    nCell = pPage->nCell;\n\n    for(i=0; i<nCell; i++){\n      u8 *pCell = findCell(pPage, i);\n      if( eType==PTRMAP_OVERFLOW1 ){\n        CellInfo info;\n        pPage->xParseCell(pPage, pCell, &info);\n        if( info.nLocal<info.nPayload ){\n          if( pCell+info.nSize > pPage->aData+pPage->pBt->usableSize ){\n            return SQLITE_CORRUPT_PAGE(pPage);\n          }\n          if( iFrom==get4byte(pCell+info.nSize-4) ){\n            put4byte(pCell+info.nSize-4, iTo);\n            break;\n          }\n        }\n      }else{\n        if( get4byte(pCell)==iFrom ){\n          put4byte(pCell, iTo);\n          break;\n        }\n      }\n    }\n  \n    if( i==nCell ){\n      if( eType!=PTRMAP_BTREE || \n          get4byte(&pPage->aData[pPage->hdrOffset+8])!=iFrom ){\n        return SQLITE_CORRUPT_PAGE(pPage);\n      }\n      put4byte(&pPage->aData[pPage->hdrOffset+8], iTo);\n    }\n  }\n  return SQLITE_OK;\n}\n\n\n/*\n** Move the open database page pDbPage to location iFreePage in the \n** database. The pDbPage reference remains valid.\n**\n** The isCommit flag indicates that there is no need to remember that\n** the journal needs to be sync()ed before database page pDbPage->pgno \n** can be written to. The caller has already promised not to write to that\n** page.\n*/\nstatic int relocatePage(\n  BtShared *pBt,           /* Btree */\n  MemPage *pDbPage,        /* Open page to move */\n  u8 eType,                /* Pointer map 'type' entry for pDbPage */\n  Pgno iPtrPage,           /* Pointer map 'page-no' entry for pDbPage */\n  Pgno iFreePage,          /* The location to move pDbPage to */\n  int isCommit             /* isCommit flag passed to sqlite3PagerMovepage */\n){\n  MemPage *pPtrPage;   /* The page that contains a pointer to pDbPage */\n  Pgno iDbPage = pDbPage->pgno;\n  Pager *pPager = pBt->pPager;\n  int rc;\n\n  assert( eType==PTRMAP_OVERFLOW2 || eType==PTRMAP_OVERFLOW1 || \n      eType==PTRMAP_BTREE || eType==PTRMAP_ROOTPAGE );\n  assert( sqlite3_mutex_held(pBt->mutex) );\n  assert( pDbPage->pBt==pBt );\n\n  /* Move page iDbPage from its current location to page number iFreePage */\n  TRACE((\"AUTOVACUUM: Moving %d to free page %d (ptr page %d type %d)\\n\", \n      iDbPage, iFreePage, iPtrPage, eType));\n  rc = sqlite3PagerMovepage(pPager, pDbPage->pDbPage, iFreePage, isCommit);\n  if( rc!=SQLITE_OK ){\n    return rc;\n  }\n  pDbPage->pgno = iFreePage;\n\n  /* If pDbPage was a btree-page, then it may have child pages and/or cells\n  ** that point to overflow pages. The pointer map entries for all these\n  ** pages need to be changed.\n  **\n  ** If pDbPage is an overflow page, then the first 4 bytes may store a\n  ** pointer to a subsequent overflow page. If this is the case, then\n  ** the pointer map needs to be updated for the subsequent overflow page.\n  */\n  if( eType==PTRMAP_BTREE || eType==PTRMAP_ROOTPAGE ){\n    rc = setChildPtrmaps(pDbPage);\n    if( rc!=SQLITE_OK ){\n      return rc;\n    }\n  }else{\n    Pgno nextOvfl = get4byte(pDbPage->aData);\n    if( nextOvfl!=0 ){\n      ptrmapPut(pBt, nextOvfl, PTRMAP_OVERFLOW2, iFreePage, &rc);\n      if( rc!=SQLITE_OK ){\n        return rc;\n      }\n    }\n  }\n\n  /* Fix the database pointer on page iPtrPage that pointed at iDbPage so\n  ** that it points at iFreePage. Also fix the pointer map entry for\n  ** iPtrPage.\n  */\n  if( eType!=PTRMAP_ROOTPAGE ){\n    rc = btreeGetPage(pBt, iPtrPage, &pPtrPage, 0);\n    if( rc!=SQLITE_OK ){\n      return rc;\n    }\n    rc = sqlite3PagerWrite(pPtrPage->pDbPage);\n    if( rc!=SQLITE_OK ){\n      releasePage(pPtrPage);\n      return rc;\n    }\n    rc = modifyPagePointer(pPtrPage, iDbPage, iFreePage, eType);\n    releasePage(pPtrPage);\n    if( rc==SQLITE_OK ){\n      ptrmapPut(pBt, iFreePage, eType, iPtrPage, &rc);\n    }\n  }\n  return rc;\n}\n\n/* Forward declaration required by incrVacuumStep(). */\nstatic int allocateBtreePage(BtShared *, MemPage **, Pgno *, Pgno, u8);\n\n/*\n** Perform a single step of an incremental-vacuum. If successful, return\n** SQLITE_OK. If there is no work to do (and therefore no point in \n** calling this function again), return SQLITE_DONE. Or, if an error \n** occurs, return some other error code.\n**\n** More specifically, this function attempts to re-organize the database so \n** that the last page of the file currently in use is no longer in use.\n**\n** Parameter nFin is the number of pages that this database would contain\n** were this function called until it returns SQLITE_DONE.\n**\n** If the bCommit parameter is non-zero, this function assumes that the \n** caller will keep calling incrVacuumStep() until it returns SQLITE_DONE \n** or an error. bCommit is passed true for an auto-vacuum-on-commit \n** operation, or false for an incremental vacuum.\n*/\nstatic int incrVacuumStep(BtShared *pBt, Pgno nFin, Pgno iLastPg, int bCommit){\n  Pgno nFreeList;           /* Number of pages still on the free-list */\n  int rc;\n\n  assert( sqlite3_mutex_held(pBt->mutex) );\n  assert( iLastPg>nFin );\n\n  if( !PTRMAP_ISPAGE(pBt, iLastPg) && iLastPg!=PENDING_BYTE_PAGE(pBt) ){\n    u8 eType;\n    Pgno iPtrPage;\n\n    nFreeList = get4byte(&pBt->pPage1->aData[36]);\n    if( nFreeList==0 ){\n      return SQLITE_DONE;\n    }\n\n    rc = ptrmapGet(pBt, iLastPg, &eType, &iPtrPage);\n    if( rc!=SQLITE_OK ){\n      return rc;\n    }\n    if( eType==PTRMAP_ROOTPAGE ){\n      return SQLITE_CORRUPT_BKPT;\n    }\n\n    if( eType==PTRMAP_FREEPAGE ){\n      if( bCommit==0 ){\n        /* Remove the page from the files free-list. This is not required\n        ** if bCommit is non-zero. In that case, the free-list will be\n        ** truncated to zero after this function returns, so it doesn't \n        ** matter if it still contains some garbage entries.\n        */\n        Pgno iFreePg;\n        MemPage *pFreePg;\n        rc = allocateBtreePage(pBt, &pFreePg, &iFreePg, iLastPg, BTALLOC_EXACT);\n        if( rc!=SQLITE_OK ){\n          return rc;\n        }\n        assert( iFreePg==iLastPg );\n        releasePage(pFreePg);\n      }\n    } else {\n      Pgno iFreePg;             /* Index of free page to move pLastPg to */\n      MemPage *pLastPg;\n      u8 eMode = BTALLOC_ANY;   /* Mode parameter for allocateBtreePage() */\n      Pgno iNear = 0;           /* nearby parameter for allocateBtreePage() */\n\n      rc = btreeGetPage(pBt, iLastPg, &pLastPg, 0);\n      if( rc!=SQLITE_OK ){\n        return rc;\n      }\n\n      /* If bCommit is zero, this loop runs exactly once and page pLastPg\n      ** is swapped with the first free page pulled off the free list.\n      **\n      ** On the other hand, if bCommit is greater than zero, then keep\n      ** looping until a free-page located within the first nFin pages\n      ** of the file is found.\n      */\n      if( bCommit==0 ){\n        eMode = BTALLOC_LE;\n        iNear = nFin;\n      }\n      do {\n        MemPage *pFreePg;\n        rc = allocateBtreePage(pBt, &pFreePg, &iFreePg, iNear, eMode);\n        if( rc!=SQLITE_OK ){\n          releasePage(pLastPg);\n          return rc;\n        }\n        releasePage(pFreePg);\n      }while( bCommit && iFreePg>nFin );\n      assert( iFreePg<iLastPg );\n      \n      rc = relocatePage(pBt, pLastPg, eType, iPtrPage, iFreePg, bCommit);\n      releasePage(pLastPg);\n      if( rc!=SQLITE_OK ){\n        return rc;\n      }\n    }\n  }\n\n  if( bCommit==0 ){\n    do {\n      iLastPg--;\n    }while( iLastPg==PENDING_BYTE_PAGE(pBt) || PTRMAP_ISPAGE(pBt, iLastPg) );\n    pBt->bDoTruncate = 1;\n    pBt->nPage = iLastPg;\n  }\n  return SQLITE_OK;\n}\n\n/*\n** The database opened by the first argument is an auto-vacuum database\n** nOrig pages in size containing nFree free pages. Return the expected \n** size of the database in pages following an auto-vacuum operation.\n*/\nstatic Pgno finalDbSize(BtShared *pBt, Pgno nOrig, Pgno nFree){\n  int nEntry;                     /* Number of entries on one ptrmap page */\n  Pgno nPtrmap;                   /* Number of PtrMap pages to be freed */\n  Pgno nFin;                      /* Return value */\n\n  nEntry = pBt->usableSize/5;\n  nPtrmap = (nFree-nOrig+PTRMAP_PAGENO(pBt, nOrig)+nEntry)/nEntry;\n  nFin = nOrig - nFree - nPtrmap;\n  if( nOrig>PENDING_BYTE_PAGE(pBt) && nFin<PENDING_BYTE_PAGE(pBt) ){\n    nFin--;\n  }\n  while( PTRMAP_ISPAGE(pBt, nFin) || nFin==PENDING_BYTE_PAGE(pBt) ){\n    nFin--;\n  }\n\n  return nFin;\n}\n\n/*\n** A write-transaction must be opened before calling this function.\n** It performs a single unit of work towards an incremental vacuum.\n**\n** If the incremental vacuum is finished after this function has run,\n** SQLITE_DONE is returned. If it is not finished, but no error occurred,\n** SQLITE_OK is returned. Otherwise an SQLite error code. \n*/\nSQLITE_PRIVATE int sqlite3BtreeIncrVacuum(Btree *p){\n  int rc;\n  BtShared *pBt = p->pBt;\n\n  sqlite3BtreeEnter(p);\n  assert( pBt->inTransaction==TRANS_WRITE && p->inTrans==TRANS_WRITE );\n  if( !pBt->autoVacuum ){\n    rc = SQLITE_DONE;\n  }else{\n    Pgno nOrig = btreePagecount(pBt);\n    Pgno nFree = get4byte(&pBt->pPage1->aData[36]);\n    Pgno nFin = finalDbSize(pBt, nOrig, nFree);\n\n    if( nOrig<nFin ){\n      rc = SQLITE_CORRUPT_BKPT;\n    }else if( nFree>0 ){\n      rc = saveAllCursors(pBt, 0, 0);\n      if( rc==SQLITE_OK ){\n        invalidateAllOverflowCache(pBt);\n        rc = incrVacuumStep(pBt, nFin, nOrig, 0);\n      }\n      if( rc==SQLITE_OK ){\n        rc = sqlite3PagerWrite(pBt->pPage1->pDbPage);\n        put4byte(&pBt->pPage1->aData[28], pBt->nPage);\n      }\n    }else{\n      rc = SQLITE_DONE;\n    }\n  }\n  sqlite3BtreeLeave(p);\n  return rc;\n}\n\n/*\n** This routine is called prior to sqlite3PagerCommit when a transaction\n** is committed for an auto-vacuum database.\n**\n** If SQLITE_OK is returned, then *pnTrunc is set to the number of pages\n** the database file should be truncated to during the commit process. \n** i.e. the database has been reorganized so that only the first *pnTrunc\n** pages are in use.\n*/\nstatic int autoVacuumCommit(BtShared *pBt){\n  int rc = SQLITE_OK;\n  Pager *pPager = pBt->pPager;\n  VVA_ONLY( int nRef = sqlite3PagerRefcount(pPager); )\n\n  assert( sqlite3_mutex_held(pBt->mutex) );\n  invalidateAllOverflowCache(pBt);\n  assert(pBt->autoVacuum);\n  if( !pBt->incrVacuum ){\n    Pgno nFin;         /* Number of pages in database after autovacuuming */\n    Pgno nFree;        /* Number of pages on the freelist initially */\n    Pgno iFree;        /* The next page to be freed */\n    Pgno nOrig;        /* Database size before freeing */\n\n    nOrig = btreePagecount(pBt);\n    if( PTRMAP_ISPAGE(pBt, nOrig) || nOrig==PENDING_BYTE_PAGE(pBt) ){\n      /* It is not possible to create a database for which the final page\n      ** is either a pointer-map page or the pending-byte page. If one\n      ** is encountered, this indicates corruption.\n      */\n      return SQLITE_CORRUPT_BKPT;\n    }\n\n    nFree = get4byte(&pBt->pPage1->aData[36]);\n    nFin = finalDbSize(pBt, nOrig, nFree);\n    if( nFin>nOrig ) return SQLITE_CORRUPT_BKPT;\n    if( nFin<nOrig ){\n      rc = saveAllCursors(pBt, 0, 0);\n    }\n    for(iFree=nOrig; iFree>nFin && rc==SQLITE_OK; iFree--){\n      rc = incrVacuumStep(pBt, nFin, iFree, 1);\n    }\n    if( (rc==SQLITE_DONE || rc==SQLITE_OK) && nFree>0 ){\n      rc = sqlite3PagerWrite(pBt->pPage1->pDbPage);\n      put4byte(&pBt->pPage1->aData[32], 0);\n      put4byte(&pBt->pPage1->aData[36], 0);\n      put4byte(&pBt->pPage1->aData[28], nFin);\n      pBt->bDoTruncate = 1;\n      pBt->nPage = nFin;\n    }\n    if( rc!=SQLITE_OK ){\n      sqlite3PagerRollback(pPager);\n    }\n  }\n\n  assert( nRef>=sqlite3PagerRefcount(pPager) );\n  return rc;\n}\n\n#else /* ifndef SQLITE_OMIT_AUTOVACUUM */\n# define setChildPtrmaps(x) SQLITE_OK\n#endif\n\n/*\n** This routine does the first phase of a two-phase commit.  This routine\n** causes a rollback journal to be created (if it does not already exist)\n** and populated with enough information so that if a power loss occurs\n** the database can be restored to its original state by playing back\n** the journal.  Then the contents of the journal are flushed out to\n** the disk.  After the journal is safely on oxide, the changes to the\n** database are written into the database file and flushed to oxide.\n** At the end of this call, the rollback journal still exists on the\n** disk and we are still holding all locks, so the transaction has not\n** committed.  See sqlite3BtreeCommitPhaseTwo() for the second phase of the\n** commit process.\n**\n** This call is a no-op if no write-transaction is currently active on pBt.\n**\n** Otherwise, sync the database file for the btree pBt. zMaster points to\n** the name of a master journal file that should be written into the\n** individual journal file, or is NULL, indicating no master journal file \n** (single database transaction).\n**\n** When this is called, the master journal should already have been\n** created, populated with this journal pointer and synced to disk.\n**\n** Once this is routine has returned, the only thing required to commit\n** the write-transaction for this database file is to delete the journal.\n*/\nSQLITE_PRIVATE int sqlite3BtreeCommitPhaseOne(Btree *p, const char *zMaster){\n  int rc = SQLITE_OK;\n  if( p->inTrans==TRANS_WRITE ){\n    BtShared *pBt = p->pBt;\n    sqlite3BtreeEnter(p);\n#ifndef SQLITE_OMIT_AUTOVACUUM\n    if( pBt->autoVacuum ){\n      rc = autoVacuumCommit(pBt);\n      if( rc!=SQLITE_OK ){\n        sqlite3BtreeLeave(p);\n        return rc;\n      }\n    }\n    if( pBt->bDoTruncate ){\n      sqlite3PagerTruncateImage(pBt->pPager, pBt->nPage);\n    }\n#endif\n    rc = sqlite3PagerCommitPhaseOne(pBt->pPager, zMaster, 0);\n    sqlite3BtreeLeave(p);\n  }\n  return rc;\n}\n\n/*\n** This function is called from both BtreeCommitPhaseTwo() and BtreeRollback()\n** at the conclusion of a transaction.\n*/\nstatic void btreeEndTransaction(Btree *p){\n  BtShared *pBt = p->pBt;\n  sqlite3 *db = p->db;\n  assert( sqlite3BtreeHoldsMutex(p) );\n\n#ifndef SQLITE_OMIT_AUTOVACUUM\n  pBt->bDoTruncate = 0;\n#endif\n  if( p->inTrans>TRANS_NONE && db->nVdbeRead>1 ){\n    /* If there are other active statements that belong to this database\n    ** handle, downgrade to a read-only transaction. The other statements\n    ** may still be reading from the database.  */\n    downgradeAllSharedCacheTableLocks(p);\n    p->inTrans = TRANS_READ;\n  }else{\n    /* If the handle had any kind of transaction open, decrement the \n    ** transaction count of the shared btree. If the transaction count \n    ** reaches 0, set the shared state to TRANS_NONE. The unlockBtreeIfUnused()\n    ** call below will unlock the pager.  */\n    if( p->inTrans!=TRANS_NONE ){\n      clearAllSharedCacheTableLocks(p);\n      pBt->nTransaction--;\n      if( 0==pBt->nTransaction ){\n        pBt->inTransaction = TRANS_NONE;\n      }\n    }\n\n    /* Set the current transaction state to TRANS_NONE and unlock the \n    ** pager if this call closed the only read or write transaction.  */\n    p->inTrans = TRANS_NONE;\n    unlockBtreeIfUnused(pBt);\n  }\n\n  btreeIntegrity(p);\n}\n\n/*\n** Commit the transaction currently in progress.\n**\n** This routine implements the second phase of a 2-phase commit.  The\n** sqlite3BtreeCommitPhaseOne() routine does the first phase and should\n** be invoked prior to calling this routine.  The sqlite3BtreeCommitPhaseOne()\n** routine did all the work of writing information out to disk and flushing the\n** contents so that they are written onto the disk platter.  All this\n** routine has to do is delete or truncate or zero the header in the\n** the rollback journal (which causes the transaction to commit) and\n** drop locks.\n**\n** Normally, if an error occurs while the pager layer is attempting to \n** finalize the underlying journal file, this function returns an error and\n** the upper layer will attempt a rollback. However, if the second argument\n** is non-zero then this b-tree transaction is part of a multi-file \n** transaction. In this case, the transaction has already been committed \n** (by deleting a master journal file) and the caller will ignore this \n** functions return code. So, even if an error occurs in the pager layer,\n** reset the b-tree objects internal state to indicate that the write\n** transaction has been closed. This is quite safe, as the pager will have\n** transitioned to the error state.\n**\n** This will release the write lock on the database file.  If there\n** are no active cursors, it also releases the read lock.\n*/\nSQLITE_PRIVATE int sqlite3BtreeCommitPhaseTwo(Btree *p, int bCleanup){\n\n  if( p->inTrans==TRANS_NONE ) return SQLITE_OK;\n  sqlite3BtreeEnter(p);\n  btreeIntegrity(p);\n\n  /* If the handle has a write-transaction open, commit the shared-btrees \n  ** transaction and set the shared state to TRANS_READ.\n  */\n  if( p->inTrans==TRANS_WRITE ){\n    int rc;\n    BtShared *pBt = p->pBt;\n    assert( pBt->inTransaction==TRANS_WRITE );\n    assert( pBt->nTransaction>0 );\n    rc = sqlite3PagerCommitPhaseTwo(pBt->pPager);\n    if( rc!=SQLITE_OK && bCleanup==0 ){\n      sqlite3BtreeLeave(p);\n      return rc;\n    }\n    p->iDataVersion--;  /* Compensate for pPager->iDataVersion++; */\n    pBt->inTransaction = TRANS_READ;\n    btreeClearHasContent(pBt);\n  }\n\n  btreeEndTransaction(p);\n  sqlite3BtreeLeave(p);\n  return SQLITE_OK;\n}\n\n/*\n** Do both phases of a commit.\n*/\nSQLITE_PRIVATE int sqlite3BtreeCommit(Btree *p){\n  int rc;\n  sqlite3BtreeEnter(p);\n  rc = sqlite3BtreeCommitPhaseOne(p, 0);\n  if( rc==SQLITE_OK ){\n    rc = sqlite3BtreeCommitPhaseTwo(p, 0);\n  }\n  sqlite3BtreeLeave(p);\n  return rc;\n}\n\n/*\n** This routine sets the state to CURSOR_FAULT and the error\n** code to errCode for every cursor on any BtShared that pBtree\n** references.  Or if the writeOnly flag is set to 1, then only\n** trip write cursors and leave read cursors unchanged.\n**\n** Every cursor is a candidate to be tripped, including cursors\n** that belong to other database connections that happen to be\n** sharing the cache with pBtree.\n**\n** This routine gets called when a rollback occurs. If the writeOnly\n** flag is true, then only write-cursors need be tripped - read-only\n** cursors save their current positions so that they may continue \n** following the rollback. Or, if writeOnly is false, all cursors are \n** tripped. In general, writeOnly is false if the transaction being\n** rolled back modified the database schema. In this case b-tree root\n** pages may be moved or deleted from the database altogether, making\n** it unsafe for read cursors to continue.\n**\n** If the writeOnly flag is true and an error is encountered while \n** saving the current position of a read-only cursor, all cursors, \n** including all read-cursors are tripped.\n**\n** SQLITE_OK is returned if successful, or if an error occurs while\n** saving a cursor position, an SQLite error code.\n*/\nSQLITE_PRIVATE int sqlite3BtreeTripAllCursors(Btree *pBtree, int errCode, int writeOnly){\n  BtCursor *p;\n  int rc = SQLITE_OK;\n\n  assert( (writeOnly==0 || writeOnly==1) && BTCF_WriteFlag==1 );\n  if( pBtree ){\n    sqlite3BtreeEnter(pBtree);\n    for(p=pBtree->pBt->pCursor; p; p=p->pNext){\n      if( writeOnly && (p->curFlags & BTCF_WriteFlag)==0 ){\n        if( p->eState==CURSOR_VALID || p->eState==CURSOR_SKIPNEXT ){\n          rc = saveCursorPosition(p);\n          if( rc!=SQLITE_OK ){\n            (void)sqlite3BtreeTripAllCursors(pBtree, rc, 0);\n            break;\n          }\n        }\n      }else{\n        sqlite3BtreeClearCursor(p);\n        p->eState = CURSOR_FAULT;\n        p->skipNext = errCode;\n      }\n      btreeReleaseAllCursorPages(p);\n    }\n    sqlite3BtreeLeave(pBtree);\n  }\n  return rc;\n}\n\n/*\n** Rollback the transaction in progress.\n**\n** If tripCode is not SQLITE_OK then cursors will be invalidated (tripped).\n** Only write cursors are tripped if writeOnly is true but all cursors are\n** tripped if writeOnly is false.  Any attempt to use\n** a tripped cursor will result in an error.\n**\n** This will release the write lock on the database file.  If there\n** are no active cursors, it also releases the read lock.\n*/\nSQLITE_PRIVATE int sqlite3BtreeRollback(Btree *p, int tripCode, int writeOnly){\n  int rc;\n  BtShared *pBt = p->pBt;\n  MemPage *pPage1;\n\n  assert( writeOnly==1 || writeOnly==0 );\n  assert( tripCode==SQLITE_ABORT_ROLLBACK || tripCode==SQLITE_OK );\n  sqlite3BtreeEnter(p);\n  if( tripCode==SQLITE_OK ){\n    rc = tripCode = saveAllCursors(pBt, 0, 0);\n    if( rc ) writeOnly = 0;\n  }else{\n    rc = SQLITE_OK;\n  }\n  if( tripCode ){\n    int rc2 = sqlite3BtreeTripAllCursors(p, tripCode, writeOnly);\n    assert( rc==SQLITE_OK || (writeOnly==0 && rc2==SQLITE_OK) );\n    if( rc2!=SQLITE_OK ) rc = rc2;\n  }\n  btreeIntegrity(p);\n\n  if( p->inTrans==TRANS_WRITE ){\n    int rc2;\n\n    assert( TRANS_WRITE==pBt->inTransaction );\n    rc2 = sqlite3PagerRollback(pBt->pPager);\n    if( rc2!=SQLITE_OK ){\n      rc = rc2;\n    }\n\n    /* The rollback may have destroyed the pPage1->aData value.  So\n    ** call btreeGetPage() on page 1 again to make\n    ** sure pPage1->aData is set correctly. */\n    if( btreeGetPage(pBt, 1, &pPage1, 0)==SQLITE_OK ){\n      int nPage = get4byte(28+(u8*)pPage1->aData);\n      testcase( nPage==0 );\n      if( nPage==0 ) sqlite3PagerPagecount(pBt->pPager, &nPage);\n      testcase( pBt->nPage!=nPage );\n      pBt->nPage = nPage;\n      releasePageOne(pPage1);\n    }\n    assert( countValidCursors(pBt, 1)==0 );\n    pBt->inTransaction = TRANS_READ;\n    btreeClearHasContent(pBt);\n  }\n\n  btreeEndTransaction(p);\n  sqlite3BtreeLeave(p);\n  return rc;\n}\n\n/*\n** Start a statement subtransaction. The subtransaction can be rolled\n** back independently of the main transaction. You must start a transaction \n** before starting a subtransaction. The subtransaction is ended automatically \n** if the main transaction commits or rolls back.\n**\n** Statement subtransactions are used around individual SQL statements\n** that are contained within a BEGIN...COMMIT block.  If a constraint\n** error occurs within the statement, the effect of that one statement\n** can be rolled back without having to rollback the entire transaction.\n**\n** A statement sub-transaction is implemented as an anonymous savepoint. The\n** value passed as the second parameter is the total number of savepoints,\n** including the new anonymous savepoint, open on the B-Tree. i.e. if there\n** are no active savepoints and no other statement-transactions open,\n** iStatement is 1. This anonymous savepoint can be released or rolled back\n** using the sqlite3BtreeSavepoint() function.\n*/\nSQLITE_PRIVATE int sqlite3BtreeBeginStmt(Btree *p, int iStatement){\n  int rc;\n  BtShared *pBt = p->pBt;\n  sqlite3BtreeEnter(p);\n  assert( p->inTrans==TRANS_WRITE );\n  assert( (pBt->btsFlags & BTS_READ_ONLY)==0 );\n  assert( iStatement>0 );\n  assert( iStatement>p->db->nSavepoint );\n  assert( pBt->inTransaction==TRANS_WRITE );\n  /* At the pager level, a statement transaction is a savepoint with\n  ** an index greater than all savepoints created explicitly using\n  ** SQL statements. It is illegal to open, release or rollback any\n  ** such savepoints while the statement transaction savepoint is active.\n  */\n  rc = sqlite3PagerOpenSavepoint(pBt->pPager, iStatement);\n  sqlite3BtreeLeave(p);\n  return rc;\n}\n\n/*\n** The second argument to this function, op, is always SAVEPOINT_ROLLBACK\n** or SAVEPOINT_RELEASE. This function either releases or rolls back the\n** savepoint identified by parameter iSavepoint, depending on the value \n** of op.\n**\n** Normally, iSavepoint is greater than or equal to zero. However, if op is\n** SAVEPOINT_ROLLBACK, then iSavepoint may also be -1. In this case the \n** contents of the entire transaction are rolled back. This is different\n** from a normal transaction rollback, as no locks are released and the\n** transaction remains open.\n*/\nSQLITE_PRIVATE int sqlite3BtreeSavepoint(Btree *p, int op, int iSavepoint){\n  int rc = SQLITE_OK;\n  if( p && p->inTrans==TRANS_WRITE ){\n    BtShared *pBt = p->pBt;\n    assert( op==SAVEPOINT_RELEASE || op==SAVEPOINT_ROLLBACK );\n    assert( iSavepoint>=0 || (iSavepoint==-1 && op==SAVEPOINT_ROLLBACK) );\n    sqlite3BtreeEnter(p);\n    if( op==SAVEPOINT_ROLLBACK ){\n      rc = saveAllCursors(pBt, 0, 0);\n    }\n    if( rc==SQLITE_OK ){\n      rc = sqlite3PagerSavepoint(pBt->pPager, op, iSavepoint);\n    }\n    if( rc==SQLITE_OK ){\n      if( iSavepoint<0 && (pBt->btsFlags & BTS_INITIALLY_EMPTY)!=0 ){\n        pBt->nPage = 0;\n      }\n      rc = newDatabase(pBt);\n      pBt->nPage = get4byte(28 + pBt->pPage1->aData);\n\n      /* The database size was written into the offset 28 of the header\n      ** when the transaction started, so we know that the value at offset\n      ** 28 is nonzero. */\n      assert( pBt->nPage>0 );\n    }\n    sqlite3BtreeLeave(p);\n  }\n  return rc;\n}\n\n/*\n** Create a new cursor for the BTree whose root is on the page\n** iTable. If a read-only cursor is requested, it is assumed that\n** the caller already has at least a read-only transaction open\n** on the database already. If a write-cursor is requested, then\n** the caller is assumed to have an open write transaction.\n**\n** If the BTREE_WRCSR bit of wrFlag is clear, then the cursor can only\n** be used for reading.  If the BTREE_WRCSR bit is set, then the cursor\n** can be used for reading or for writing if other conditions for writing\n** are also met.  These are the conditions that must be met in order\n** for writing to be allowed:\n**\n** 1:  The cursor must have been opened with wrFlag containing BTREE_WRCSR\n**\n** 2:  Other database connections that share the same pager cache\n**     but which are not in the READ_UNCOMMITTED state may not have\n**     cursors open with wrFlag==0 on the same table.  Otherwise\n**     the changes made by this write cursor would be visible to\n**     the read cursors in the other database connection.\n**\n** 3:  The database must be writable (not on read-only media)\n**\n** 4:  There must be an active transaction.\n**\n** The BTREE_FORDELETE bit of wrFlag may optionally be set if BTREE_WRCSR\n** is set.  If FORDELETE is set, that is a hint to the implementation that\n** this cursor will only be used to seek to and delete entries of an index\n** as part of a larger DELETE statement.  The FORDELETE hint is not used by\n** this implementation.  But in a hypothetical alternative storage engine \n** in which index entries are automatically deleted when corresponding table\n** rows are deleted, the FORDELETE flag is a hint that all SEEK and DELETE\n** operations on this cursor can be no-ops and all READ operations can \n** return a null row (2-bytes: 0x01 0x00).\n**\n** No checking is done to make sure that page iTable really is the\n** root page of a b-tree.  If it is not, then the cursor acquired\n** will not work correctly.\n**\n** It is assumed that the sqlite3BtreeCursorZero() has been called\n** on pCur to initialize the memory space prior to invoking this routine.\n*/\nstatic int btreeCursor(\n  Btree *p,                              /* The btree */\n  int iTable,                            /* Root page of table to open */\n  int wrFlag,                            /* 1 to write. 0 read-only */\n  struct KeyInfo *pKeyInfo,              /* First arg to comparison function */\n  BtCursor *pCur                         /* Space for new cursor */\n){\n  BtShared *pBt = p->pBt;                /* Shared b-tree handle */\n  BtCursor *pX;                          /* Looping over other all cursors */\n\n  assert( sqlite3BtreeHoldsMutex(p) );\n  assert( wrFlag==0 \n       || wrFlag==BTREE_WRCSR \n       || wrFlag==(BTREE_WRCSR|BTREE_FORDELETE) \n  );\n\n  /* The following assert statements verify that if this is a sharable \n  ** b-tree database, the connection is holding the required table locks, \n  ** and that no other connection has any open cursor that conflicts with \n  ** this lock.  */\n  assert( hasSharedCacheTableLock(p, iTable, pKeyInfo!=0, (wrFlag?2:1)) );\n  assert( wrFlag==0 || !hasReadConflicts(p, iTable) );\n\n  /* Assert that the caller has opened the required transaction. */\n  assert( p->inTrans>TRANS_NONE );\n  assert( wrFlag==0 || p->inTrans==TRANS_WRITE );\n  assert( pBt->pPage1 && pBt->pPage1->aData );\n  assert( wrFlag==0 || (pBt->btsFlags & BTS_READ_ONLY)==0 );\n\n  if( wrFlag ){\n    allocateTempSpace(pBt);\n    if( pBt->pTmpSpace==0 ) return SQLITE_NOMEM_BKPT;\n  }\n  if( iTable==1 && btreePagecount(pBt)==0 ){\n    assert( wrFlag==0 );\n    iTable = 0;\n  }\n\n  /* Now that no other errors can occur, finish filling in the BtCursor\n  ** variables and link the cursor into the BtShared list.  */\n  pCur->pgnoRoot = (Pgno)iTable;\n  pCur->iPage = -1;\n  pCur->pKeyInfo = pKeyInfo;\n  pCur->pBtree = p;\n  pCur->pBt = pBt;\n  pCur->curFlags = wrFlag ? BTCF_WriteFlag : 0;\n  pCur->curPagerFlags = wrFlag ? 0 : PAGER_GET_READONLY;\n  /* If there are two or more cursors on the same btree, then all such\n  ** cursors *must* have the BTCF_Multiple flag set. */\n  for(pX=pBt->pCursor; pX; pX=pX->pNext){\n    if( pX->pgnoRoot==(Pgno)iTable ){\n      pX->curFlags |= BTCF_Multiple;\n      pCur->curFlags |= BTCF_Multiple;\n    }\n  }\n  pCur->pNext = pBt->pCursor;\n  pBt->pCursor = pCur;\n  pCur->eState = CURSOR_INVALID;\n  return SQLITE_OK;\n}\nSQLITE_PRIVATE int sqlite3BtreeCursor(\n  Btree *p,                                   /* The btree */\n  int iTable,                                 /* Root page of table to open */\n  int wrFlag,                                 /* 1 to write. 0 read-only */\n  struct KeyInfo *pKeyInfo,                   /* First arg to xCompare() */\n  BtCursor *pCur                              /* Write new cursor here */\n){\n  int rc;\n  if( iTable<1 ){\n    rc = SQLITE_CORRUPT_BKPT;\n  }else{\n    sqlite3BtreeEnter(p);\n    rc = btreeCursor(p, iTable, wrFlag, pKeyInfo, pCur);\n    sqlite3BtreeLeave(p);\n  }\n  return rc;\n}\n\n/*\n** Return the size of a BtCursor object in bytes.\n**\n** This interfaces is needed so that users of cursors can preallocate\n** sufficient storage to hold a cursor.  The BtCursor object is opaque\n** to users so they cannot do the sizeof() themselves - they must call\n** this routine.\n*/\nSQLITE_PRIVATE int sqlite3BtreeCursorSize(void){\n  return ROUND8(sizeof(BtCursor));\n}\n\n/*\n** Initialize memory that will be converted into a BtCursor object.\n**\n** The simple approach here would be to memset() the entire object\n** to zero.  But it turns out that the apPage[] and aiIdx[] arrays\n** do not need to be zeroed and they are large, so we can save a lot\n** of run-time by skipping the initialization of those elements.\n*/\nSQLITE_PRIVATE void sqlite3BtreeCursorZero(BtCursor *p){\n  memset(p, 0, offsetof(BtCursor, BTCURSOR_FIRST_UNINIT));\n}\n\n/*\n** Close a cursor.  The read lock on the database file is released\n** when the last cursor is closed.\n*/\nSQLITE_PRIVATE int sqlite3BtreeCloseCursor(BtCursor *pCur){\n  Btree *pBtree = pCur->pBtree;\n  if( pBtree ){\n    BtShared *pBt = pCur->pBt;\n    sqlite3BtreeEnter(pBtree);\n    assert( pBt->pCursor!=0 );\n    if( pBt->pCursor==pCur ){\n      pBt->pCursor = pCur->pNext;\n    }else{\n      BtCursor *pPrev = pBt->pCursor;\n      do{\n        if( pPrev->pNext==pCur ){\n          pPrev->pNext = pCur->pNext;\n          break;\n        }\n        pPrev = pPrev->pNext;\n      }while( ALWAYS(pPrev) );\n    }\n    btreeReleaseAllCursorPages(pCur);\n    unlockBtreeIfUnused(pBt);\n    sqlite3_free(pCur->aOverflow);\n    sqlite3_free(pCur->pKey);\n    sqlite3BtreeLeave(pBtree);\n  }\n  return SQLITE_OK;\n}\n\n/*\n** Make sure the BtCursor* given in the argument has a valid\n** BtCursor.info structure.  If it is not already valid, call\n** btreeParseCell() to fill it in.\n**\n** BtCursor.info is a cache of the information in the current cell.\n** Using this cache reduces the number of calls to btreeParseCell().\n*/\n#ifndef NDEBUG\n  static int cellInfoEqual(CellInfo *a, CellInfo *b){\n    if( a->nKey!=b->nKey ) return 0;\n    if( a->pPayload!=b->pPayload ) return 0;\n    if( a->nPayload!=b->nPayload ) return 0;\n    if( a->nLocal!=b->nLocal ) return 0;\n    if( a->nSize!=b->nSize ) return 0;\n    return 1;\n  }\n  static void assertCellInfo(BtCursor *pCur){\n    CellInfo info;\n    memset(&info, 0, sizeof(info));\n    btreeParseCell(pCur->pPage, pCur->ix, &info);\n    assert( CORRUPT_DB || cellInfoEqual(&info, &pCur->info) );\n  }\n#else\n  #define assertCellInfo(x)\n#endif\nstatic SQLITE_NOINLINE void getCellInfo(BtCursor *pCur){\n  if( pCur->info.nSize==0 ){\n    pCur->curFlags |= BTCF_ValidNKey;\n    btreeParseCell(pCur->pPage,pCur->ix,&pCur->info);\n  }else{\n    assertCellInfo(pCur);\n  }\n}\n\n#ifndef NDEBUG  /* The next routine used only within assert() statements */\n/*\n** Return true if the given BtCursor is valid.  A valid cursor is one\n** that is currently pointing to a row in a (non-empty) table.\n** This is a verification routine is used only within assert() statements.\n*/\nSQLITE_PRIVATE int sqlite3BtreeCursorIsValid(BtCursor *pCur){\n  return pCur && pCur->eState==CURSOR_VALID;\n}\n#endif /* NDEBUG */\nSQLITE_PRIVATE int sqlite3BtreeCursorIsValidNN(BtCursor *pCur){\n  assert( pCur!=0 );\n  return pCur->eState==CURSOR_VALID;\n}\n\n/*\n** Return the value of the integer key or \"rowid\" for a table btree.\n** This routine is only valid for a cursor that is pointing into a\n** ordinary table btree.  If the cursor points to an index btree or\n** is invalid, the result of this routine is undefined.\n*/\nSQLITE_PRIVATE i64 sqlite3BtreeIntegerKey(BtCursor *pCur){\n  assert( cursorHoldsMutex(pCur) );\n  assert( pCur->eState==CURSOR_VALID );\n  assert( pCur->curIntKey );\n  getCellInfo(pCur);\n  return pCur->info.nKey;\n}\n\n#ifdef SQLITE_ENABLE_OFFSET_SQL_FUNC\n/*\n** Return the offset into the database file for the start of the\n** payload to which the cursor is pointing.\n*/\nSQLITE_PRIVATE i64 sqlite3BtreeOffset(BtCursor *pCur){\n  assert( cursorHoldsMutex(pCur) );\n  assert( pCur->eState==CURSOR_VALID );\n  getCellInfo(pCur);\n  return (i64)pCur->pBt->pageSize*((i64)pCur->pPage->pgno - 1) +\n         (i64)(pCur->info.pPayload - pCur->pPage->aData);\n}\n#endif /* SQLITE_ENABLE_OFFSET_SQL_FUNC */\n\n/*\n** Return the number of bytes of payload for the entry that pCur is\n** currently pointing to.  For table btrees, this will be the amount\n** of data.  For index btrees, this will be the size of the key.\n**\n** The caller must guarantee that the cursor is pointing to a non-NULL\n** valid entry.  In other words, the calling procedure must guarantee\n** that the cursor has Cursor.eState==CURSOR_VALID.\n*/\nSQLITE_PRIVATE u32 sqlite3BtreePayloadSize(BtCursor *pCur){\n  assert( cursorHoldsMutex(pCur) );\n  assert( pCur->eState==CURSOR_VALID );\n  getCellInfo(pCur);\n  return pCur->info.nPayload;\n}\n\n/*\n** Given the page number of an overflow page in the database (parameter\n** ovfl), this function finds the page number of the next page in the \n** linked list of overflow pages. If possible, it uses the auto-vacuum\n** pointer-map data instead of reading the content of page ovfl to do so. \n**\n** If an error occurs an SQLite error code is returned. Otherwise:\n**\n** The page number of the next overflow page in the linked list is \n** written to *pPgnoNext. If page ovfl is the last page in its linked \n** list, *pPgnoNext is set to zero. \n**\n** If ppPage is not NULL, and a reference to the MemPage object corresponding\n** to page number pOvfl was obtained, then *ppPage is set to point to that\n** reference. It is the responsibility of the caller to call releasePage()\n** on *ppPage to free the reference. In no reference was obtained (because\n** the pointer-map was used to obtain the value for *pPgnoNext), then\n** *ppPage is set to zero.\n*/\nstatic int getOverflowPage(\n  BtShared *pBt,               /* The database file */\n  Pgno ovfl,                   /* Current overflow page number */\n  MemPage **ppPage,            /* OUT: MemPage handle (may be NULL) */\n  Pgno *pPgnoNext              /* OUT: Next overflow page number */\n){\n  Pgno next = 0;\n  MemPage *pPage = 0;\n  int rc = SQLITE_OK;\n\n  assert( sqlite3_mutex_held(pBt->mutex) );\n  assert(pPgnoNext);\n\n#ifndef SQLITE_OMIT_AUTOVACUUM\n  /* Try to find the next page in the overflow list using the\n  ** autovacuum pointer-map pages. Guess that the next page in \n  ** the overflow list is page number (ovfl+1). If that guess turns \n  ** out to be wrong, fall back to loading the data of page \n  ** number ovfl to determine the next page number.\n  */\n  if( pBt->autoVacuum ){\n    Pgno pgno;\n    Pgno iGuess = ovfl+1;\n    u8 eType;\n\n    while( PTRMAP_ISPAGE(pBt, iGuess) || iGuess==PENDING_BYTE_PAGE(pBt) ){\n      iGuess++;\n    }\n\n    if( iGuess<=btreePagecount(pBt) ){\n      rc = ptrmapGet(pBt, iGuess, &eType, &pgno);\n      if( rc==SQLITE_OK && eType==PTRMAP_OVERFLOW2 && pgno==ovfl ){\n        next = iGuess;\n        rc = SQLITE_DONE;\n      }\n    }\n  }\n#endif\n\n  assert( next==0 || rc==SQLITE_DONE );\n  if( rc==SQLITE_OK ){\n    rc = btreeGetPage(pBt, ovfl, &pPage, (ppPage==0) ? PAGER_GET_READONLY : 0);\n    assert( rc==SQLITE_OK || pPage==0 );\n    if( rc==SQLITE_OK ){\n      next = get4byte(pPage->aData);\n    }\n  }\n\n  *pPgnoNext = next;\n  if( ppPage ){\n    *ppPage = pPage;\n  }else{\n    releasePage(pPage);\n  }\n  return (rc==SQLITE_DONE ? SQLITE_OK : rc);\n}\n\n/*\n** Copy data from a buffer to a page, or from a page to a buffer.\n**\n** pPayload is a pointer to data stored on database page pDbPage.\n** If argument eOp is false, then nByte bytes of data are copied\n** from pPayload to the buffer pointed at by pBuf. If eOp is true,\n** then sqlite3PagerWrite() is called on pDbPage and nByte bytes\n** of data are copied from the buffer pBuf to pPayload.\n**\n** SQLITE_OK is returned on success, otherwise an error code.\n*/\nstatic int copyPayload(\n  void *pPayload,           /* Pointer to page data */\n  void *pBuf,               /* Pointer to buffer */\n  int nByte,                /* Number of bytes to copy */\n  int eOp,                  /* 0 -> copy from page, 1 -> copy to page */\n  DbPage *pDbPage           /* Page containing pPayload */\n){\n  if( eOp ){\n    /* Copy data from buffer to page (a write operation) */\n    int rc = sqlite3PagerWrite(pDbPage);\n    if( rc!=SQLITE_OK ){\n      return rc;\n    }\n    memcpy(pPayload, pBuf, nByte);\n  }else{\n    /* Copy data from page to buffer (a read operation) */\n    memcpy(pBuf, pPayload, nByte);\n  }\n  return SQLITE_OK;\n}\n\n/*\n** This function is used to read or overwrite payload information\n** for the entry that the pCur cursor is pointing to. The eOp\n** argument is interpreted as follows:\n**\n**   0: The operation is a read. Populate the overflow cache.\n**   1: The operation is a write. Populate the overflow cache.\n**\n** A total of \"amt\" bytes are read or written beginning at \"offset\".\n** Data is read to or from the buffer pBuf.\n**\n** The content being read or written might appear on the main page\n** or be scattered out on multiple overflow pages.\n**\n** If the current cursor entry uses one or more overflow pages\n** this function may allocate space for and lazily populate\n** the overflow page-list cache array (BtCursor.aOverflow). \n** Subsequent calls use this cache to make seeking to the supplied offset \n** more efficient.\n**\n** Once an overflow page-list cache has been allocated, it must be\n** invalidated if some other cursor writes to the same table, or if\n** the cursor is moved to a different row. Additionally, in auto-vacuum\n** mode, the following events may invalidate an overflow page-list cache.\n**\n**   * An incremental vacuum,\n**   * A commit in auto_vacuum=\"full\" mode,\n**   * Creating a table (may require moving an overflow page).\n*/\nstatic int accessPayload(\n  BtCursor *pCur,      /* Cursor pointing to entry to read from */\n  u32 offset,          /* Begin reading this far into payload */\n  u32 amt,             /* Read this many bytes */\n  unsigned char *pBuf, /* Write the bytes into this buffer */ \n  int eOp              /* zero to read. non-zero to write. */\n){\n  unsigned char *aPayload;\n  int rc = SQLITE_OK;\n  int iIdx = 0;\n  MemPage *pPage = pCur->pPage;               /* Btree page of current entry */\n  BtShared *pBt = pCur->pBt;                  /* Btree this cursor belongs to */\n#ifdef SQLITE_DIRECT_OVERFLOW_READ\n  unsigned char * const pBufStart = pBuf;     /* Start of original out buffer */\n#endif\n\n  assert( pPage );\n  assert( eOp==0 || eOp==1 );\n  assert( pCur->eState==CURSOR_VALID );\n  assert( pCur->ix<pPage->nCell );\n  assert( cursorHoldsMutex(pCur) );\n\n  getCellInfo(pCur);\n  aPayload = pCur->info.pPayload;\n  assert( offset+amt <= pCur->info.nPayload );\n\n  assert( aPayload > pPage->aData );\n  if( (uptr)(aPayload - pPage->aData) > (pBt->usableSize - pCur->info.nLocal) ){\n    /* Trying to read or write past the end of the data is an error.  The\n    ** conditional above is really:\n    **    &aPayload[pCur->info.nLocal] > &pPage->aData[pBt->usableSize]\n    ** but is recast into its current form to avoid integer overflow problems\n    */\n    return SQLITE_CORRUPT_PAGE(pPage);\n  }\n\n  /* Check if data must be read/written to/from the btree page itself. */\n  if( offset<pCur->info.nLocal ){\n    int a = amt;\n    if( a+offset>pCur->info.nLocal ){\n      a = pCur->info.nLocal - offset;\n    }\n    rc = copyPayload(&aPayload[offset], pBuf, a, eOp, pPage->pDbPage);\n    offset = 0;\n    pBuf += a;\n    amt -= a;\n  }else{\n    offset -= pCur->info.nLocal;\n  }\n\n\n  if( rc==SQLITE_OK && amt>0 ){\n    const u32 ovflSize = pBt->usableSize - 4;  /* Bytes content per ovfl page */\n    Pgno nextPage;\n\n    nextPage = get4byte(&aPayload[pCur->info.nLocal]);\n\n    /* If the BtCursor.aOverflow[] has not been allocated, allocate it now.\n    **\n    ** The aOverflow[] array is sized at one entry for each overflow page\n    ** in the overflow chain. The page number of the first overflow page is\n    ** stored in aOverflow[0], etc. A value of 0 in the aOverflow[] array\n    ** means \"not yet known\" (the cache is lazily populated).\n    */\n    if( (pCur->curFlags & BTCF_ValidOvfl)==0 ){\n      int nOvfl = (pCur->info.nPayload-pCur->info.nLocal+ovflSize-1)/ovflSize;\n      if( pCur->aOverflow==0\n       || nOvfl*(int)sizeof(Pgno) > sqlite3MallocSize(pCur->aOverflow)\n      ){\n        Pgno *aNew = (Pgno*)sqlite3Realloc(\n            pCur->aOverflow, nOvfl*2*sizeof(Pgno)\n        );\n        if( aNew==0 ){\n          return SQLITE_NOMEM_BKPT;\n        }else{\n          pCur->aOverflow = aNew;\n        }\n      }\n      memset(pCur->aOverflow, 0, nOvfl*sizeof(Pgno));\n      pCur->curFlags |= BTCF_ValidOvfl;\n    }else{\n      /* If the overflow page-list cache has been allocated and the\n      ** entry for the first required overflow page is valid, skip\n      ** directly to it.\n      */\n      if( pCur->aOverflow[offset/ovflSize] ){\n        iIdx = (offset/ovflSize);\n        nextPage = pCur->aOverflow[iIdx];\n        offset = (offset%ovflSize);\n      }\n    }\n\n    assert( rc==SQLITE_OK && amt>0 );\n    while( nextPage ){\n      /* If required, populate the overflow page-list cache. */\n      assert( pCur->aOverflow[iIdx]==0\n              || pCur->aOverflow[iIdx]==nextPage\n              || CORRUPT_DB );\n      pCur->aOverflow[iIdx] = nextPage;\n\n      if( offset>=ovflSize ){\n        /* The only reason to read this page is to obtain the page\n        ** number for the next page in the overflow chain. The page\n        ** data is not required. So first try to lookup the overflow\n        ** page-list cache, if any, then fall back to the getOverflowPage()\n        ** function.\n        */\n        assert( pCur->curFlags & BTCF_ValidOvfl );\n        assert( pCur->pBtree->db==pBt->db );\n        if( pCur->aOverflow[iIdx+1] ){\n          nextPage = pCur->aOverflow[iIdx+1];\n        }else{\n          rc = getOverflowPage(pBt, nextPage, 0, &nextPage);\n        }\n        offset -= ovflSize;\n      }else{\n        /* Need to read this page properly. It contains some of the\n        ** range of data that is being read (eOp==0) or written (eOp!=0).\n        */\n#ifdef SQLITE_DIRECT_OVERFLOW_READ\n        sqlite3_file *fd;      /* File from which to do direct overflow read */\n#endif\n        int a = amt;\n        if( a + offset > ovflSize ){\n          a = ovflSize - offset;\n        }\n\n#ifdef SQLITE_DIRECT_OVERFLOW_READ\n        /* If all the following are true:\n        **\n        **   1) this is a read operation, and \n        **   2) data is required from the start of this overflow page, and\n        **   3) there is no open write-transaction, and\n        **   4) the database is file-backed, and\n        **   5) the page is not in the WAL file\n        **   6) at least 4 bytes have already been read into the output buffer \n        **\n        ** then data can be read directly from the database file into the\n        ** output buffer, bypassing the page-cache altogether. This speeds\n        ** up loading large records that span many overflow pages.\n        */\n        if( eOp==0                                             /* (1) */\n         && offset==0                                          /* (2) */\n         && pBt->inTransaction==TRANS_READ                     /* (3) */\n         && (fd = sqlite3PagerFile(pBt->pPager))->pMethods     /* (4) */\n         && 0==sqlite3PagerUseWal(pBt->pPager, nextPage)       /* (5) */\n         && &pBuf[-4]>=pBufStart                               /* (6) */\n        ){\n          u8 aSave[4];\n          u8 *aWrite = &pBuf[-4];\n          assert( aWrite>=pBufStart );                         /* due to (6) */\n          memcpy(aSave, aWrite, 4);\n          rc = sqlite3OsRead(fd, aWrite, a+4, (i64)pBt->pageSize*(nextPage-1));\n          nextPage = get4byte(aWrite);\n          memcpy(aWrite, aSave, 4);\n        }else\n#endif\n\n        {\n          DbPage *pDbPage;\n          rc = sqlite3PagerGet(pBt->pPager, nextPage, &pDbPage,\n              (eOp==0 ? PAGER_GET_READONLY : 0)\n          );\n          if( rc==SQLITE_OK ){\n            aPayload = sqlite3PagerGetData(pDbPage);\n            nextPage = get4byte(aPayload);\n            rc = copyPayload(&aPayload[offset+4], pBuf, a, eOp, pDbPage);\n            sqlite3PagerUnref(pDbPage);\n            offset = 0;\n          }\n        }\n        amt -= a;\n        if( amt==0 ) return rc;\n        pBuf += a;\n      }\n      if( rc ) break;\n      iIdx++;\n    }\n  }\n\n  if( rc==SQLITE_OK && amt>0 ){\n    /* Overflow chain ends prematurely */\n    return SQLITE_CORRUPT_PAGE(pPage);\n  }\n  return rc;\n}\n\n/*\n** Read part of the payload for the row at which that cursor pCur is currently\n** pointing.  \"amt\" bytes will be transferred into pBuf[].  The transfer\n** begins at \"offset\".\n**\n** pCur can be pointing to either a table or an index b-tree.\n** If pointing to a table btree, then the content section is read.  If\n** pCur is pointing to an index b-tree then the key section is read.\n**\n** For sqlite3BtreePayload(), the caller must ensure that pCur is pointing\n** to a valid row in the table.  For sqlite3BtreePayloadChecked(), the\n** cursor might be invalid or might need to be restored before being read.\n**\n** Return SQLITE_OK on success or an error code if anything goes\n** wrong.  An error is returned if \"offset+amt\" is larger than\n** the available payload.\n*/\nSQLITE_PRIVATE int sqlite3BtreePayload(BtCursor *pCur, u32 offset, u32 amt, void *pBuf){\n  assert( cursorHoldsMutex(pCur) );\n  assert( pCur->eState==CURSOR_VALID );\n  assert( pCur->iPage>=0 && pCur->pPage );\n  assert( pCur->ix<pCur->pPage->nCell );\n  return accessPayload(pCur, offset, amt, (unsigned char*)pBuf, 0);\n}\n\n/*\n** This variant of sqlite3BtreePayload() works even if the cursor has not\n** in the CURSOR_VALID state.  It is only used by the sqlite3_blob_read()\n** interface.\n*/\n#ifndef SQLITE_OMIT_INCRBLOB\nstatic SQLITE_NOINLINE int accessPayloadChecked(\n  BtCursor *pCur,\n  u32 offset,\n  u32 amt,\n  void *pBuf\n){\n  int rc;\n  if ( pCur->eState==CURSOR_INVALID ){\n    return SQLITE_ABORT;\n  }\n  assert( cursorOwnsBtShared(pCur) );\n  rc = btreeRestoreCursorPosition(pCur);\n  return rc ? rc : accessPayload(pCur, offset, amt, pBuf, 0);\n}\nSQLITE_PRIVATE int sqlite3BtreePayloadChecked(BtCursor *pCur, u32 offset, u32 amt, void *pBuf){\n  if( pCur->eState==CURSOR_VALID ){\n    assert( cursorOwnsBtShared(pCur) );\n    return accessPayload(pCur, offset, amt, pBuf, 0);\n  }else{\n    return accessPayloadChecked(pCur, offset, amt, pBuf);\n  }\n}\n#endif /* SQLITE_OMIT_INCRBLOB */\n\n/*\n** Return a pointer to payload information from the entry that the \n** pCur cursor is pointing to.  The pointer is to the beginning of\n** the key if index btrees (pPage->intKey==0) and is the data for\n** table btrees (pPage->intKey==1). The number of bytes of available\n** key/data is written into *pAmt.  If *pAmt==0, then the value\n** returned will not be a valid pointer.\n**\n** This routine is an optimization.  It is common for the entire key\n** and data to fit on the local page and for there to be no overflow\n** pages.  When that is so, this routine can be used to access the\n** key and data without making a copy.  If the key and/or data spills\n** onto overflow pages, then accessPayload() must be used to reassemble\n** the key/data and copy it into a preallocated buffer.\n**\n** The pointer returned by this routine looks directly into the cached\n** page of the database.  The data might change or move the next time\n** any btree routine is called.\n*/\nstatic const void *fetchPayload(\n  BtCursor *pCur,      /* Cursor pointing to entry to read from */\n  u32 *pAmt            /* Write the number of available bytes here */\n){\n  int amt;\n  assert( pCur!=0 && pCur->iPage>=0 && pCur->pPage);\n  assert( pCur->eState==CURSOR_VALID );\n  assert( sqlite3_mutex_held(pCur->pBtree->db->mutex) );\n  assert( cursorOwnsBtShared(pCur) );\n  assert( pCur->ix<pCur->pPage->nCell );\n  assert( pCur->info.nSize>0 );\n  assert( pCur->info.pPayload>pCur->pPage->aData || CORRUPT_DB );\n  assert( pCur->info.pPayload<pCur->pPage->aDataEnd ||CORRUPT_DB);\n  amt = pCur->info.nLocal;\n  if( amt>(int)(pCur->pPage->aDataEnd - pCur->info.pPayload) ){\n    /* There is too little space on the page for the expected amount\n    ** of local content. Database must be corrupt. */\n    assert( CORRUPT_DB );\n    amt = MAX(0, (int)(pCur->pPage->aDataEnd - pCur->info.pPayload));\n  }\n  *pAmt = (u32)amt;\n  return (void*)pCur->info.pPayload;\n}\n\n\n/*\n** For the entry that cursor pCur is point to, return as\n** many bytes of the key or data as are available on the local\n** b-tree page.  Write the number of available bytes into *pAmt.\n**\n** The pointer returned is ephemeral.  The key/data may move\n** or be destroyed on the next call to any Btree routine,\n** including calls from other threads against the same cache.\n** Hence, a mutex on the BtShared should be held prior to calling\n** this routine.\n**\n** These routines is used to get quick access to key and data\n** in the common case where no overflow pages are used.\n*/\nSQLITE_PRIVATE const void *sqlite3BtreePayloadFetch(BtCursor *pCur, u32 *pAmt){\n  return fetchPayload(pCur, pAmt);\n}\n\n\n/*\n** Move the cursor down to a new child page.  The newPgno argument is the\n** page number of the child page to move to.\n**\n** This function returns SQLITE_CORRUPT if the page-header flags field of\n** the new child page does not match the flags field of the parent (i.e.\n** if an intkey page appears to be the parent of a non-intkey page, or\n** vice-versa).\n*/\nstatic int moveToChild(BtCursor *pCur, u32 newPgno){\n  BtShared *pBt = pCur->pBt;\n\n  assert( cursorOwnsBtShared(pCur) );\n  assert( pCur->eState==CURSOR_VALID );\n  assert( pCur->iPage<BTCURSOR_MAX_DEPTH );\n  assert( pCur->iPage>=0 );\n  if( pCur->iPage>=(BTCURSOR_MAX_DEPTH-1) ){\n    return SQLITE_CORRUPT_BKPT;\n  }\n  pCur->info.nSize = 0;\n  pCur->curFlags &= ~(BTCF_ValidNKey|BTCF_ValidOvfl);\n  pCur->aiIdx[pCur->iPage] = pCur->ix;\n  pCur->apPage[pCur->iPage] = pCur->pPage;\n  pCur->ix = 0;\n  pCur->iPage++;\n  return getAndInitPage(pBt, newPgno, &pCur->pPage, pCur, pCur->curPagerFlags);\n}\n\n#ifdef SQLITE_DEBUG\n/*\n** Page pParent is an internal (non-leaf) tree page. This function \n** asserts that page number iChild is the left-child if the iIdx'th\n** cell in page pParent. Or, if iIdx is equal to the total number of\n** cells in pParent, that page number iChild is the right-child of\n** the page.\n*/\nstatic void assertParentIndex(MemPage *pParent, int iIdx, Pgno iChild){\n  if( CORRUPT_DB ) return;  /* The conditions tested below might not be true\n                            ** in a corrupt database */\n  assert( iIdx<=pParent->nCell );\n  if( iIdx==pParent->nCell ){\n    assert( get4byte(&pParent->aData[pParent->hdrOffset+8])==iChild );\n  }else{\n    assert( get4byte(findCell(pParent, iIdx))==iChild );\n  }\n}\n#else\n#  define assertParentIndex(x,y,z) \n#endif\n\n/*\n** Move the cursor up to the parent page.\n**\n** pCur->idx is set to the cell index that contains the pointer\n** to the page we are coming from.  If we are coming from the\n** right-most child page then pCur->idx is set to one more than\n** the largest cell index.\n*/\nstatic void moveToParent(BtCursor *pCur){\n  MemPage *pLeaf;\n  assert( cursorOwnsBtShared(pCur) );\n  assert( pCur->eState==CURSOR_VALID );\n  assert( pCur->iPage>0 );\n  assert( pCur->pPage );\n  assertParentIndex(\n    pCur->apPage[pCur->iPage-1], \n    pCur->aiIdx[pCur->iPage-1], \n    pCur->pPage->pgno\n  );\n  testcase( pCur->aiIdx[pCur->iPage-1] > pCur->apPage[pCur->iPage-1]->nCell );\n  pCur->info.nSize = 0;\n  pCur->curFlags &= ~(BTCF_ValidNKey|BTCF_ValidOvfl);\n  pCur->ix = pCur->aiIdx[pCur->iPage-1];\n  pLeaf = pCur->pPage;\n  pCur->pPage = pCur->apPage[--pCur->iPage];\n  releasePageNotNull(pLeaf);\n}\n\n/*\n** Move the cursor to point to the root page of its b-tree structure.\n**\n** If the table has a virtual root page, then the cursor is moved to point\n** to the virtual root page instead of the actual root page. A table has a\n** virtual root page when the actual root page contains no cells and a \n** single child page. This can only happen with the table rooted at page 1.\n**\n** If the b-tree structure is empty, the cursor state is set to \n** CURSOR_INVALID and this routine returns SQLITE_EMPTY. Otherwise,\n** the cursor is set to point to the first cell located on the root\n** (or virtual root) page and the cursor state is set to CURSOR_VALID.\n**\n** If this function returns successfully, it may be assumed that the\n** page-header flags indicate that the [virtual] root-page is the expected \n** kind of b-tree page (i.e. if when opening the cursor the caller did not\n** specify a KeyInfo structure the flags byte is set to 0x05 or 0x0D,\n** indicating a table b-tree, or if the caller did specify a KeyInfo \n** structure the flags byte is set to 0x02 or 0x0A, indicating an index\n** b-tree).\n*/\nstatic int moveToRoot(BtCursor *pCur){\n  MemPage *pRoot;\n  int rc = SQLITE_OK;\n\n  assert( cursorOwnsBtShared(pCur) );\n  assert( CURSOR_INVALID < CURSOR_REQUIRESEEK );\n  assert( CURSOR_VALID   < CURSOR_REQUIRESEEK );\n  assert( CURSOR_FAULT   > CURSOR_REQUIRESEEK );\n  assert( pCur->eState < CURSOR_REQUIRESEEK || pCur->iPage<0 );\n  assert( pCur->pgnoRoot>0 || pCur->iPage<0 );\n\n  if( pCur->iPage>=0 ){\n    if( pCur->iPage ){\n      releasePageNotNull(pCur->pPage);\n      while( --pCur->iPage ){\n        releasePageNotNull(pCur->apPage[pCur->iPage]);\n      }\n      pCur->pPage = pCur->apPage[0];\n      goto skip_init;\n    }\n  }else if( pCur->pgnoRoot==0 ){\n    pCur->eState = CURSOR_INVALID;\n    return SQLITE_EMPTY;\n  }else{\n    assert( pCur->iPage==(-1) );\n    if( pCur->eState>=CURSOR_REQUIRESEEK ){\n      if( pCur->eState==CURSOR_FAULT ){\n        assert( pCur->skipNext!=SQLITE_OK );\n        return pCur->skipNext;\n      }\n      sqlite3BtreeClearCursor(pCur);\n    }\n    rc = getAndInitPage(pCur->pBtree->pBt, pCur->pgnoRoot, &pCur->pPage,\n                        0, pCur->curPagerFlags);\n    if( rc!=SQLITE_OK ){\n      pCur->eState = CURSOR_INVALID;\n      return rc;\n    }\n    pCur->iPage = 0;\n    pCur->curIntKey = pCur->pPage->intKey;\n  }\n  pRoot = pCur->pPage;\n  assert( pRoot->pgno==pCur->pgnoRoot );\n\n  /* If pCur->pKeyInfo is not NULL, then the caller that opened this cursor\n  ** expected to open it on an index b-tree. Otherwise, if pKeyInfo is\n  ** NULL, the caller expects a table b-tree. If this is not the case,\n  ** return an SQLITE_CORRUPT error. \n  **\n  ** Earlier versions of SQLite assumed that this test could not fail\n  ** if the root page was already loaded when this function was called (i.e.\n  ** if pCur->iPage>=0). But this is not so if the database is corrupted \n  ** in such a way that page pRoot is linked into a second b-tree table \n  ** (or the freelist).  */\n  assert( pRoot->intKey==1 || pRoot->intKey==0 );\n  if( pRoot->isInit==0 || (pCur->pKeyInfo==0)!=pRoot->intKey ){\n    return SQLITE_CORRUPT_PAGE(pCur->pPage);\n  }\n\nskip_init:  \n  pCur->ix = 0;\n  pCur->info.nSize = 0;\n  pCur->curFlags &= ~(BTCF_AtLast|BTCF_ValidNKey|BTCF_ValidOvfl);\n\n  pRoot = pCur->pPage;\n  if( pRoot->nCell>0 ){\n    pCur->eState = CURSOR_VALID;\n  }else if( !pRoot->leaf ){\n    Pgno subpage;\n    if( pRoot->pgno!=1 ) return SQLITE_CORRUPT_BKPT;\n    subpage = get4byte(&pRoot->aData[pRoot->hdrOffset+8]);\n    pCur->eState = CURSOR_VALID;\n    rc = moveToChild(pCur, subpage);\n  }else{\n    pCur->eState = CURSOR_INVALID;\n    rc = SQLITE_EMPTY;\n  }\n  return rc;\n}\n\n/*\n** Move the cursor down to the left-most leaf entry beneath the\n** entry to which it is currently pointing.\n**\n** The left-most leaf is the one with the smallest key - the first\n** in ascending order.\n*/\nstatic int moveToLeftmost(BtCursor *pCur){\n  Pgno pgno;\n  int rc = SQLITE_OK;\n  MemPage *pPage;\n\n  assert( cursorOwnsBtShared(pCur) );\n  assert( pCur->eState==CURSOR_VALID );\n  while( rc==SQLITE_OK && !(pPage = pCur->pPage)->leaf ){\n    assert( pCur->ix<pPage->nCell );\n    pgno = get4byte(findCell(pPage, pCur->ix));\n    rc = moveToChild(pCur, pgno);\n  }\n  return rc;\n}\n\n/*\n** Move the cursor down to the right-most leaf entry beneath the\n** page to which it is currently pointing.  Notice the difference\n** between moveToLeftmost() and moveToRightmost().  moveToLeftmost()\n** finds the left-most entry beneath the *entry* whereas moveToRightmost()\n** finds the right-most entry beneath the *page*.\n**\n** The right-most entry is the one with the largest key - the last\n** key in ascending order.\n*/\nstatic int moveToRightmost(BtCursor *pCur){\n  Pgno pgno;\n  int rc = SQLITE_OK;\n  MemPage *pPage = 0;\n\n  assert( cursorOwnsBtShared(pCur) );\n  assert( pCur->eState==CURSOR_VALID );\n  while( !(pPage = pCur->pPage)->leaf ){\n    pgno = get4byte(&pPage->aData[pPage->hdrOffset+8]);\n    pCur->ix = pPage->nCell;\n    rc = moveToChild(pCur, pgno);\n    if( rc ) return rc;\n  }\n  pCur->ix = pPage->nCell-1;\n  assert( pCur->info.nSize==0 );\n  assert( (pCur->curFlags & BTCF_ValidNKey)==0 );\n  return SQLITE_OK;\n}\n\n/* Move the cursor to the first entry in the table.  Return SQLITE_OK\n** on success.  Set *pRes to 0 if the cursor actually points to something\n** or set *pRes to 1 if the table is empty.\n*/\nSQLITE_PRIVATE int sqlite3BtreeFirst(BtCursor *pCur, int *pRes){\n  int rc;\n\n  assert( cursorOwnsBtShared(pCur) );\n  assert( sqlite3_mutex_held(pCur->pBtree->db->mutex) );\n  rc = moveToRoot(pCur);\n  if( rc==SQLITE_OK ){\n    assert( pCur->pPage->nCell>0 );\n    *pRes = 0;\n    rc = moveToLeftmost(pCur);\n  }else if( rc==SQLITE_EMPTY ){\n    assert( pCur->pgnoRoot==0 || pCur->pPage->nCell==0 );\n    *pRes = 1;\n    rc = SQLITE_OK;\n  }\n  return rc;\n}\n\n/* Move the cursor to the last entry in the table.  Return SQLITE_OK\n** on success.  Set *pRes to 0 if the cursor actually points to something\n** or set *pRes to 1 if the table is empty.\n*/\nSQLITE_PRIVATE int sqlite3BtreeLast(BtCursor *pCur, int *pRes){\n  int rc;\n \n  assert( cursorOwnsBtShared(pCur) );\n  assert( sqlite3_mutex_held(pCur->pBtree->db->mutex) );\n\n  /* If the cursor already points to the last entry, this is a no-op. */\n  if( CURSOR_VALID==pCur->eState && (pCur->curFlags & BTCF_AtLast)!=0 ){\n#ifdef SQLITE_DEBUG\n    /* This block serves to assert() that the cursor really does point \n    ** to the last entry in the b-tree. */\n    int ii;\n    for(ii=0; ii<pCur->iPage; ii++){\n      assert( pCur->aiIdx[ii]==pCur->apPage[ii]->nCell );\n    }\n    assert( pCur->ix==pCur->pPage->nCell-1 );\n    assert( pCur->pPage->leaf );\n#endif\n    return SQLITE_OK;\n  }\n\n  rc = moveToRoot(pCur);\n  if( rc==SQLITE_OK ){\n    assert( pCur->eState==CURSOR_VALID );\n    *pRes = 0;\n    rc = moveToRightmost(pCur);\n    if( rc==SQLITE_OK ){\n      pCur->curFlags |= BTCF_AtLast;\n    }else{\n      pCur->curFlags &= ~BTCF_AtLast;\n    }\n  }else if( rc==SQLITE_EMPTY ){\n    assert( pCur->pgnoRoot==0 || pCur->pPage->nCell==0 );\n    *pRes = 1;\n    rc = SQLITE_OK;\n  }\n  return rc;\n}\n\n/* Move the cursor so that it points to an entry near the key \n** specified by pIdxKey or intKey.   Return a success code.\n**\n** For INTKEY tables, the intKey parameter is used.  pIdxKey \n** must be NULL.  For index tables, pIdxKey is used and intKey\n** is ignored.\n**\n** If an exact match is not found, then the cursor is always\n** left pointing at a leaf page which would hold the entry if it\n** were present.  The cursor might point to an entry that comes\n** before or after the key.\n**\n** An integer is written into *pRes which is the result of\n** comparing the key with the entry to which the cursor is \n** pointing.  The meaning of the integer written into\n** *pRes is as follows:\n**\n**     *pRes<0      The cursor is left pointing at an entry that\n**                  is smaller than intKey/pIdxKey or if the table is empty\n**                  and the cursor is therefore left point to nothing.\n**\n**     *pRes==0     The cursor is left pointing at an entry that\n**                  exactly matches intKey/pIdxKey.\n**\n**     *pRes>0      The cursor is left pointing at an entry that\n**                  is larger than intKey/pIdxKey.\n**\n** For index tables, the pIdxKey->eqSeen field is set to 1 if there\n** exists an entry in the table that exactly matches pIdxKey.  \n*/\nSQLITE_PRIVATE int sqlite3BtreeMovetoUnpacked(\n  BtCursor *pCur,          /* The cursor to be moved */\n  UnpackedRecord *pIdxKey, /* Unpacked index key */\n  i64 intKey,              /* The table key */\n  int biasRight,           /* If true, bias the search to the high end */\n  int *pRes                /* Write search results here */\n){\n  int rc;\n  RecordCompare xRecordCompare;\n\n  assert( cursorOwnsBtShared(pCur) );\n  assert( sqlite3_mutex_held(pCur->pBtree->db->mutex) );\n  assert( pRes );\n  assert( (pIdxKey==0)==(pCur->pKeyInfo==0) );\n  assert( pCur->eState!=CURSOR_VALID || (pIdxKey==0)==(pCur->curIntKey!=0) );\n\n  /* If the cursor is already positioned at the point we are trying\n  ** to move to, then just return without doing any work */\n  if( pIdxKey==0\n   && pCur->eState==CURSOR_VALID && (pCur->curFlags & BTCF_ValidNKey)!=0\n  ){\n    if( pCur->info.nKey==intKey ){\n      *pRes = 0;\n      return SQLITE_OK;\n    }\n    if( pCur->info.nKey<intKey ){\n      if( (pCur->curFlags & BTCF_AtLast)!=0 ){\n        *pRes = -1;\n        return SQLITE_OK;\n      }\n      /* If the requested key is one more than the previous key, then\n      ** try to get there using sqlite3BtreeNext() rather than a full\n      ** binary search.  This is an optimization only.  The correct answer\n      ** is still obtained without this case, only a little more slowely */\n      if( pCur->info.nKey+1==intKey && !pCur->skipNext ){\n        *pRes = 0;\n        rc = sqlite3BtreeNext(pCur, 0);\n        if( rc==SQLITE_OK ){\n          getCellInfo(pCur);\n          if( pCur->info.nKey==intKey ){\n            return SQLITE_OK;\n          }\n        }else if( rc==SQLITE_DONE ){\n          rc = SQLITE_OK;\n        }else{\n          return rc;\n        }\n      }\n    }\n  }\n\n  if( pIdxKey ){\n    xRecordCompare = sqlite3VdbeFindCompare(pIdxKey);\n    pIdxKey->errCode = 0;\n    assert( pIdxKey->default_rc==1 \n         || pIdxKey->default_rc==0 \n         || pIdxKey->default_rc==-1\n    );\n  }else{\n    xRecordCompare = 0; /* All keys are integers */\n  }\n\n  rc = moveToRoot(pCur);\n  if( rc ){\n    if( rc==SQLITE_EMPTY ){\n      assert( pCur->pgnoRoot==0 || pCur->pPage->nCell==0 );\n      *pRes = -1;\n      return SQLITE_OK;\n    }\n    return rc;\n  }\n  assert( pCur->pPage );\n  assert( pCur->pPage->isInit );\n  assert( pCur->eState==CURSOR_VALID );\n  assert( pCur->pPage->nCell > 0 );\n  assert( pCur->iPage==0 || pCur->apPage[0]->intKey==pCur->curIntKey );\n  assert( pCur->curIntKey || pIdxKey );\n  for(;;){\n    int lwr, upr, idx, c;\n    Pgno chldPg;\n    MemPage *pPage = pCur->pPage;\n    u8 *pCell;                          /* Pointer to current cell in pPage */\n\n    /* pPage->nCell must be greater than zero. If this is the root-page\n    ** the cursor would have been INVALID above and this for(;;) loop\n    ** not run. If this is not the root-page, then the moveToChild() routine\n    ** would have already detected db corruption. Similarly, pPage must\n    ** be the right kind (index or table) of b-tree page. Otherwise\n    ** a moveToChild() or moveToRoot() call would have detected corruption.  */\n    assert( pPage->nCell>0 );\n    assert( pPage->intKey==(pIdxKey==0) );\n    lwr = 0;\n    upr = pPage->nCell-1;\n    assert( biasRight==0 || biasRight==1 );\n    idx = upr>>(1-biasRight); /* idx = biasRight ? upr : (lwr+upr)/2; */\n    pCur->ix = (u16)idx;\n    if( xRecordCompare==0 ){\n      for(;;){\n        i64 nCellKey;\n        pCell = findCellPastPtr(pPage, idx);\n        if( pPage->intKeyLeaf ){\n          while( 0x80 <= *(pCell++) ){\n            if( pCell>=pPage->aDataEnd ){\n              return SQLITE_CORRUPT_PAGE(pPage);\n            }\n          }\n        }\n        getVarint(pCell, (u64*)&nCellKey);\n        if( nCellKey<intKey ){\n          lwr = idx+1;\n          if( lwr>upr ){ c = -1; break; }\n        }else if( nCellKey>intKey ){\n          upr = idx-1;\n          if( lwr>upr ){ c = +1; break; }\n        }else{\n          assert( nCellKey==intKey );\n          pCur->ix = (u16)idx;\n          if( !pPage->leaf ){\n            lwr = idx;\n            goto moveto_next_layer;\n          }else{\n            pCur->curFlags |= BTCF_ValidNKey;\n            pCur->info.nKey = nCellKey;\n            pCur->info.nSize = 0;\n            *pRes = 0;\n            return SQLITE_OK;\n          }\n        }\n        assert( lwr+upr>=0 );\n        idx = (lwr+upr)>>1;  /* idx = (lwr+upr)/2; */\n      }\n    }else{\n      for(;;){\n        int nCell;  /* Size of the pCell cell in bytes */\n        pCell = findCellPastPtr(pPage, idx);\n\n        /* The maximum supported page-size is 65536 bytes. This means that\n        ** the maximum number of record bytes stored on an index B-Tree\n        ** page is less than 16384 bytes and may be stored as a 2-byte\n        ** varint. This information is used to attempt to avoid parsing \n        ** the entire cell by checking for the cases where the record is \n        ** stored entirely within the b-tree page by inspecting the first \n        ** 2 bytes of the cell.\n        */\n        nCell = pCell[0];\n        if( nCell<=pPage->max1bytePayload ){\n          /* This branch runs if the record-size field of the cell is a\n          ** single byte varint and the record fits entirely on the main\n          ** b-tree page.  */\n          testcase( pCell+nCell+1==pPage->aDataEnd );\n          c = xRecordCompare(nCell, (void*)&pCell[1], pIdxKey);\n        }else if( !(pCell[1] & 0x80) \n          && (nCell = ((nCell&0x7f)<<7) + pCell[1])<=pPage->maxLocal\n        ){\n          /* The record-size field is a 2 byte varint and the record \n          ** fits entirely on the main b-tree page.  */\n          testcase( pCell+nCell+2==pPage->aDataEnd );\n          c = xRecordCompare(nCell, (void*)&pCell[2], pIdxKey);\n        }else{\n          /* The record flows over onto one or more overflow pages. In\n          ** this case the whole cell needs to be parsed, a buffer allocated\n          ** and accessPayload() used to retrieve the record into the\n          ** buffer before VdbeRecordCompare() can be called. \n          **\n          ** If the record is corrupt, the xRecordCompare routine may read\n          ** up to two varints past the end of the buffer. An extra 18 \n          ** bytes of padding is allocated at the end of the buffer in\n          ** case this happens.  */\n          void *pCellKey;\n          u8 * const pCellBody = pCell - pPage->childPtrSize;\n          pPage->xParseCell(pPage, pCellBody, &pCur->info);\n          nCell = (int)pCur->info.nKey;\n          testcase( nCell<0 );   /* True if key size is 2^32 or more */\n          testcase( nCell==0 );  /* Invalid key size:  0x80 0x80 0x00 */\n          testcase( nCell==1 );  /* Invalid key size:  0x80 0x80 0x01 */\n          testcase( nCell==2 );  /* Minimum legal index key size */\n          if( nCell<2 ){\n            rc = SQLITE_CORRUPT_PAGE(pPage);\n            goto moveto_finish;\n          }\n          pCellKey = sqlite3Malloc( nCell+18 );\n          if( pCellKey==0 ){\n            rc = SQLITE_NOMEM_BKPT;\n            goto moveto_finish;\n          }\n          pCur->ix = (u16)idx;\n          rc = accessPayload(pCur, 0, nCell, (unsigned char*)pCellKey, 0);\n          pCur->curFlags &= ~BTCF_ValidOvfl;\n          if( rc ){\n            sqlite3_free(pCellKey);\n            goto moveto_finish;\n          }\n          c = xRecordCompare(nCell, pCellKey, pIdxKey);\n          sqlite3_free(pCellKey);\n        }\n        assert( \n            (pIdxKey->errCode!=SQLITE_CORRUPT || c==0)\n         && (pIdxKey->errCode!=SQLITE_NOMEM || pCur->pBtree->db->mallocFailed)\n        );\n        if( c<0 ){\n          lwr = idx+1;\n        }else if( c>0 ){\n          upr = idx-1;\n        }else{\n          assert( c==0 );\n          *pRes = 0;\n          rc = SQLITE_OK;\n          pCur->ix = (u16)idx;\n          if( pIdxKey->errCode ) rc = SQLITE_CORRUPT_BKPT;\n          goto moveto_finish;\n        }\n        if( lwr>upr ) break;\n        assert( lwr+upr>=0 );\n        idx = (lwr+upr)>>1;  /* idx = (lwr+upr)/2 */\n      }\n    }\n    assert( lwr==upr+1 || (pPage->intKey && !pPage->leaf) );\n    assert( pPage->isInit );\n    if( pPage->leaf ){\n      assert( pCur->ix<pCur->pPage->nCell );\n      pCur->ix = (u16)idx;\n      *pRes = c;\n      rc = SQLITE_OK;\n      goto moveto_finish;\n    }\nmoveto_next_layer:\n    if( lwr>=pPage->nCell ){\n      chldPg = get4byte(&pPage->aData[pPage->hdrOffset+8]);\n    }else{\n      chldPg = get4byte(findCell(pPage, lwr));\n    }\n    pCur->ix = (u16)lwr;\n    rc = moveToChild(pCur, chldPg);\n    if( rc ) break;\n  }\nmoveto_finish:\n  pCur->info.nSize = 0;\n  assert( (pCur->curFlags & BTCF_ValidOvfl)==0 );\n  return rc;\n}\n\n\n/*\n** Return TRUE if the cursor is not pointing at an entry of the table.\n**\n** TRUE will be returned after a call to sqlite3BtreeNext() moves\n** past the last entry in the table or sqlite3BtreePrev() moves past\n** the first entry.  TRUE is also returned if the table is empty.\n*/\nSQLITE_PRIVATE int sqlite3BtreeEof(BtCursor *pCur){\n  /* TODO: What if the cursor is in CURSOR_REQUIRESEEK but all table entries\n  ** have been deleted? This API will need to change to return an error code\n  ** as well as the boolean result value.\n  */\n  return (CURSOR_VALID!=pCur->eState);\n}\n\n/*\n** Return an estimate for the number of rows in the table that pCur is\n** pointing to.  Return a negative number if no estimate is currently \n** available.\n*/\nSQLITE_PRIVATE i64 sqlite3BtreeRowCountEst(BtCursor *pCur){\n  i64 n;\n  u8 i;\n\n  assert( cursorOwnsBtShared(pCur) );\n  assert( sqlite3_mutex_held(pCur->pBtree->db->mutex) );\n\n  /* Currently this interface is only called by the OP_IfSmaller\n  ** opcode, and it that case the cursor will always be valid and\n  ** will always point to a leaf node. */\n  if( NEVER(pCur->eState!=CURSOR_VALID) ) return -1;\n  if( NEVER(pCur->pPage->leaf==0) ) return -1;\n\n  n = pCur->pPage->nCell;\n  for(i=0; i<pCur->iPage; i++){\n    n *= pCur->apPage[i]->nCell;\n  }\n  return n;\n}\n\n/*\n** Advance the cursor to the next entry in the database. \n** Return value:\n**\n**    SQLITE_OK        success\n**    SQLITE_DONE      cursor is already pointing at the last element\n**    otherwise        some kind of error occurred\n**\n** The main entry point is sqlite3BtreeNext().  That routine is optimized\n** for the common case of merely incrementing the cell counter BtCursor.aiIdx\n** to the next cell on the current page.  The (slower) btreeNext() helper\n** routine is called when it is necessary to move to a different page or\n** to restore the cursor.\n**\n** If bit 0x01 of the F argument in sqlite3BtreeNext(C,F) is 1, then the\n** cursor corresponds to an SQL index and this routine could have been\n** skipped if the SQL index had been a unique index.  The F argument\n** is a hint to the implement.  SQLite btree implementation does not use\n** this hint, but COMDB2 does.\n*/\nstatic SQLITE_NOINLINE int btreeNext(BtCursor *pCur){\n  int rc;\n  int idx;\n  MemPage *pPage;\n\n  assert( cursorOwnsBtShared(pCur) );\n  assert( pCur->skipNext==0 || pCur->eState!=CURSOR_VALID );\n  if( pCur->eState!=CURSOR_VALID ){\n    assert( (pCur->curFlags & BTCF_ValidOvfl)==0 );\n    rc = restoreCursorPosition(pCur);\n    if( rc!=SQLITE_OK ){\n      return rc;\n    }\n    if( CURSOR_INVALID==pCur->eState ){\n      return SQLITE_DONE;\n    }\n    if( pCur->skipNext ){\n      assert( pCur->eState==CURSOR_VALID || pCur->eState==CURSOR_SKIPNEXT );\n      pCur->eState = CURSOR_VALID;\n      if( pCur->skipNext>0 ){\n        pCur->skipNext = 0;\n        return SQLITE_OK;\n      }\n      pCur->skipNext = 0;\n    }\n  }\n\n  pPage = pCur->pPage;\n  idx = ++pCur->ix;\n  assert( pPage->isInit );\n\n  /* If the database file is corrupt, it is possible for the value of idx \n  ** to be invalid here. This can only occur if a second cursor modifies\n  ** the page while cursor pCur is holding a reference to it. Which can\n  ** only happen if the database is corrupt in such a way as to link the\n  ** page into more than one b-tree structure. */\n  testcase( idx>pPage->nCell );\n\n  if( idx>=pPage->nCell ){\n    if( !pPage->leaf ){\n      rc = moveToChild(pCur, get4byte(&pPage->aData[pPage->hdrOffset+8]));\n      if( rc ) return rc;\n      return moveToLeftmost(pCur);\n    }\n    do{\n      if( pCur->iPage==0 ){\n        pCur->eState = CURSOR_INVALID;\n        return SQLITE_DONE;\n      }\n      moveToParent(pCur);\n      pPage = pCur->pPage;\n    }while( pCur->ix>=pPage->nCell );\n    if( pPage->intKey ){\n      return sqlite3BtreeNext(pCur, 0);\n    }else{\n      return SQLITE_OK;\n    }\n  }\n  if( pPage->leaf ){\n    return SQLITE_OK;\n  }else{\n    return moveToLeftmost(pCur);\n  }\n}\nSQLITE_PRIVATE int sqlite3BtreeNext(BtCursor *pCur, int flags){\n  MemPage *pPage;\n  UNUSED_PARAMETER( flags );  /* Used in COMDB2 but not native SQLite */\n  assert( cursorOwnsBtShared(pCur) );\n  assert( flags==0 || flags==1 );\n  assert( pCur->skipNext==0 || pCur->eState!=CURSOR_VALID );\n  pCur->info.nSize = 0;\n  pCur->curFlags &= ~(BTCF_ValidNKey|BTCF_ValidOvfl);\n  if( pCur->eState!=CURSOR_VALID ) return btreeNext(pCur);\n  pPage = pCur->pPage;\n  if( (++pCur->ix)>=pPage->nCell ){\n    pCur->ix--;\n    return btreeNext(pCur);\n  }\n  if( pPage->leaf ){\n    return SQLITE_OK;\n  }else{\n    return moveToLeftmost(pCur);\n  }\n}\n\n/*\n** Step the cursor to the back to the previous entry in the database.\n** Return values:\n**\n**     SQLITE_OK     success\n**     SQLITE_DONE   the cursor is already on the first element of the table\n**     otherwise     some kind of error occurred\n**\n** The main entry point is sqlite3BtreePrevious().  That routine is optimized\n** for the common case of merely decrementing the cell counter BtCursor.aiIdx\n** to the previous cell on the current page.  The (slower) btreePrevious()\n** helper routine is called when it is necessary to move to a different page\n** or to restore the cursor.\n**\n** If bit 0x01 of the F argument to sqlite3BtreePrevious(C,F) is 1, then\n** the cursor corresponds to an SQL index and this routine could have been\n** skipped if the SQL index had been a unique index.  The F argument is a\n** hint to the implement.  The native SQLite btree implementation does not\n** use this hint, but COMDB2 does.\n*/\nstatic SQLITE_NOINLINE int btreePrevious(BtCursor *pCur){\n  int rc;\n  MemPage *pPage;\n\n  assert( cursorOwnsBtShared(pCur) );\n  assert( pCur->skipNext==0 || pCur->eState!=CURSOR_VALID );\n  assert( (pCur->curFlags & (BTCF_AtLast|BTCF_ValidOvfl|BTCF_ValidNKey))==0 );\n  assert( pCur->info.nSize==0 );\n  if( pCur->eState!=CURSOR_VALID ){\n    rc = restoreCursorPosition(pCur);\n    if( rc!=SQLITE_OK ){\n      return rc;\n    }\n    if( CURSOR_INVALID==pCur->eState ){\n      return SQLITE_DONE;\n    }\n    if( pCur->skipNext ){\n      assert( pCur->eState==CURSOR_VALID || pCur->eState==CURSOR_SKIPNEXT );\n      pCur->eState = CURSOR_VALID;\n      if( pCur->skipNext<0 ){\n        pCur->skipNext = 0;\n        return SQLITE_OK;\n      }\n      pCur->skipNext = 0;\n    }\n  }\n\n  pPage = pCur->pPage;\n  assert( pPage->isInit );\n  if( !pPage->leaf ){\n    int idx = pCur->ix;\n    rc = moveToChild(pCur, get4byte(findCell(pPage, idx)));\n    if( rc ) return rc;\n    rc = moveToRightmost(pCur);\n  }else{\n    while( pCur->ix==0 ){\n      if( pCur->iPage==0 ){\n        pCur->eState = CURSOR_INVALID;\n        return SQLITE_DONE;\n      }\n      moveToParent(pCur);\n    }\n    assert( pCur->info.nSize==0 );\n    assert( (pCur->curFlags & (BTCF_ValidOvfl))==0 );\n\n    pCur->ix--;\n    pPage = pCur->pPage;\n    if( pPage->intKey && !pPage->leaf ){\n      rc = sqlite3BtreePrevious(pCur, 0);\n    }else{\n      rc = SQLITE_OK;\n    }\n  }\n  return rc;\n}\nSQLITE_PRIVATE int sqlite3BtreePrevious(BtCursor *pCur, int flags){\n  assert( cursorOwnsBtShared(pCur) );\n  assert( flags==0 || flags==1 );\n  assert( pCur->skipNext==0 || pCur->eState!=CURSOR_VALID );\n  UNUSED_PARAMETER( flags );  /* Used in COMDB2 but not native SQLite */\n  pCur->curFlags &= ~(BTCF_AtLast|BTCF_ValidOvfl|BTCF_ValidNKey);\n  pCur->info.nSize = 0;\n  if( pCur->eState!=CURSOR_VALID\n   || pCur->ix==0\n   || pCur->pPage->leaf==0\n  ){\n    return btreePrevious(pCur);\n  }\n  pCur->ix--;\n  return SQLITE_OK;\n}\n\n/*\n** Allocate a new page from the database file.\n**\n** The new page is marked as dirty.  (In other words, sqlite3PagerWrite()\n** has already been called on the new page.)  The new page has also\n** been referenced and the calling routine is responsible for calling\n** sqlite3PagerUnref() on the new page when it is done.\n**\n** SQLITE_OK is returned on success.  Any other return value indicates\n** an error.  *ppPage is set to NULL in the event of an error.\n**\n** If the \"nearby\" parameter is not 0, then an effort is made to \n** locate a page close to the page number \"nearby\".  This can be used in an\n** attempt to keep related pages close to each other in the database file,\n** which in turn can make database access faster.\n**\n** If the eMode parameter is BTALLOC_EXACT and the nearby page exists\n** anywhere on the free-list, then it is guaranteed to be returned.  If\n** eMode is BTALLOC_LT then the page returned will be less than or equal\n** to nearby if any such page exists.  If eMode is BTALLOC_ANY then there\n** are no restrictions on which page is returned.\n*/\nstatic int allocateBtreePage(\n  BtShared *pBt,         /* The btree */\n  MemPage **ppPage,      /* Store pointer to the allocated page here */\n  Pgno *pPgno,           /* Store the page number here */\n  Pgno nearby,           /* Search for a page near this one */\n  u8 eMode               /* BTALLOC_EXACT, BTALLOC_LT, or BTALLOC_ANY */\n){\n  MemPage *pPage1;\n  int rc;\n  u32 n;     /* Number of pages on the freelist */\n  u32 k;     /* Number of leaves on the trunk of the freelist */\n  MemPage *pTrunk = 0;\n  MemPage *pPrevTrunk = 0;\n  Pgno mxPage;     /* Total size of the database file */\n\n  assert( sqlite3_mutex_held(pBt->mutex) );\n  assert( eMode==BTALLOC_ANY || (nearby>0 && IfNotOmitAV(pBt->autoVacuum)) );\n  pPage1 = pBt->pPage1;\n  mxPage = btreePagecount(pBt);\n  /* EVIDENCE-OF: R-05119-02637 The 4-byte big-endian integer at offset 36\n  ** stores stores the total number of pages on the freelist. */\n  n = get4byte(&pPage1->aData[36]);\n  testcase( n==mxPage-1 );\n  if( n>=mxPage ){\n    return SQLITE_CORRUPT_BKPT;\n  }\n  if( n>0 ){\n    /* There are pages on the freelist.  Reuse one of those pages. */\n    Pgno iTrunk;\n    u8 searchList = 0; /* If the free-list must be searched for 'nearby' */\n    u32 nSearch = 0;   /* Count of the number of search attempts */\n    \n    /* If eMode==BTALLOC_EXACT and a query of the pointer-map\n    ** shows that the page 'nearby' is somewhere on the free-list, then\n    ** the entire-list will be searched for that page.\n    */\n#ifndef SQLITE_OMIT_AUTOVACUUM\n    if( eMode==BTALLOC_EXACT ){\n      if( nearby<=mxPage ){\n        u8 eType;\n        assert( nearby>0 );\n        assert( pBt->autoVacuum );\n        rc = ptrmapGet(pBt, nearby, &eType, 0);\n        if( rc ) return rc;\n        if( eType==PTRMAP_FREEPAGE ){\n          searchList = 1;\n        }\n      }\n    }else if( eMode==BTALLOC_LE ){\n      searchList = 1;\n    }\n#endif\n\n    /* Decrement the free-list count by 1. Set iTrunk to the index of the\n    ** first free-list trunk page. iPrevTrunk is initially 1.\n    */\n    rc = sqlite3PagerWrite(pPage1->pDbPage);\n    if( rc ) return rc;\n    put4byte(&pPage1->aData[36], n-1);\n\n    /* The code within this loop is run only once if the 'searchList' variable\n    ** is not true. Otherwise, it runs once for each trunk-page on the\n    ** free-list until the page 'nearby' is located (eMode==BTALLOC_EXACT)\n    ** or until a page less than 'nearby' is located (eMode==BTALLOC_LT)\n    */\n    do {\n      pPrevTrunk = pTrunk;\n      if( pPrevTrunk ){\n        /* EVIDENCE-OF: R-01506-11053 The first integer on a freelist trunk page\n        ** is the page number of the next freelist trunk page in the list or\n        ** zero if this is the last freelist trunk page. */\n        iTrunk = get4byte(&pPrevTrunk->aData[0]);\n      }else{\n        /* EVIDENCE-OF: R-59841-13798 The 4-byte big-endian integer at offset 32\n        ** stores the page number of the first page of the freelist, or zero if\n        ** the freelist is empty. */\n        iTrunk = get4byte(&pPage1->aData[32]);\n      }\n      testcase( iTrunk==mxPage );\n      if( iTrunk>mxPage || nSearch++ > n ){\n        rc = SQLITE_CORRUPT_PGNO(pPrevTrunk ? pPrevTrunk->pgno : 1);\n      }else{\n        rc = btreeGetUnusedPage(pBt, iTrunk, &pTrunk, 0);\n      }\n      if( rc ){\n        pTrunk = 0;\n        goto end_allocate_page;\n      }\n      assert( pTrunk!=0 );\n      assert( pTrunk->aData!=0 );\n      /* EVIDENCE-OF: R-13523-04394 The second integer on a freelist trunk page\n      ** is the number of leaf page pointers to follow. */\n      k = get4byte(&pTrunk->aData[4]);\n      if( k==0 && !searchList ){\n        /* The trunk has no leaves and the list is not being searched. \n        ** So extract the trunk page itself and use it as the newly \n        ** allocated page */\n        assert( pPrevTrunk==0 );\n        rc = sqlite3PagerWrite(pTrunk->pDbPage);\n        if( rc ){\n          goto end_allocate_page;\n        }\n        *pPgno = iTrunk;\n        memcpy(&pPage1->aData[32], &pTrunk->aData[0], 4);\n        *ppPage = pTrunk;\n        pTrunk = 0;\n        TRACE((\"ALLOCATE: %d trunk - %d free pages left\\n\", *pPgno, n-1));\n      }else if( k>(u32)(pBt->usableSize/4 - 2) ){\n        /* Value of k is out of range.  Database corruption */\n        rc = SQLITE_CORRUPT_PGNO(iTrunk);\n        goto end_allocate_page;\n#ifndef SQLITE_OMIT_AUTOVACUUM\n      }else if( searchList \n            && (nearby==iTrunk || (iTrunk<nearby && eMode==BTALLOC_LE)) \n      ){\n        /* The list is being searched and this trunk page is the page\n        ** to allocate, regardless of whether it has leaves.\n        */\n        *pPgno = iTrunk;\n        *ppPage = pTrunk;\n        searchList = 0;\n        rc = sqlite3PagerWrite(pTrunk->pDbPage);\n        if( rc ){\n          goto end_allocate_page;\n        }\n        if( k==0 ){\n          if( !pPrevTrunk ){\n            memcpy(&pPage1->aData[32], &pTrunk->aData[0], 4);\n          }else{\n            rc = sqlite3PagerWrite(pPrevTrunk->pDbPage);\n            if( rc!=SQLITE_OK ){\n              goto end_allocate_page;\n            }\n            memcpy(&pPrevTrunk->aData[0], &pTrunk->aData[0], 4);\n          }\n        }else{\n          /* The trunk page is required by the caller but it contains \n          ** pointers to free-list leaves. The first leaf becomes a trunk\n          ** page in this case.\n          */\n          MemPage *pNewTrunk;\n          Pgno iNewTrunk = get4byte(&pTrunk->aData[8]);\n          if( iNewTrunk>mxPage ){ \n            rc = SQLITE_CORRUPT_PGNO(iTrunk);\n            goto end_allocate_page;\n          }\n          testcase( iNewTrunk==mxPage );\n          rc = btreeGetUnusedPage(pBt, iNewTrunk, &pNewTrunk, 0);\n          if( rc!=SQLITE_OK ){\n            goto end_allocate_page;\n          }\n          rc = sqlite3PagerWrite(pNewTrunk->pDbPage);\n          if( rc!=SQLITE_OK ){\n            releasePage(pNewTrunk);\n            goto end_allocate_page;\n          }\n          memcpy(&pNewTrunk->aData[0], &pTrunk->aData[0], 4);\n          put4byte(&pNewTrunk->aData[4], k-1);\n          memcpy(&pNewTrunk->aData[8], &pTrunk->aData[12], (k-1)*4);\n          releasePage(pNewTrunk);\n          if( !pPrevTrunk ){\n            assert( sqlite3PagerIswriteable(pPage1->pDbPage) );\n            put4byte(&pPage1->aData[32], iNewTrunk);\n          }else{\n            rc = sqlite3PagerWrite(pPrevTrunk->pDbPage);\n            if( rc ){\n              goto end_allocate_page;\n            }\n            put4byte(&pPrevTrunk->aData[0], iNewTrunk);\n          }\n        }\n        pTrunk = 0;\n        TRACE((\"ALLOCATE: %d trunk - %d free pages left\\n\", *pPgno, n-1));\n#endif\n      }else if( k>0 ){\n        /* Extract a leaf from the trunk */\n        u32 closest;\n        Pgno iPage;\n        unsigned char *aData = pTrunk->aData;\n        if( nearby>0 ){\n          u32 i;\n          closest = 0;\n          if( eMode==BTALLOC_LE ){\n            for(i=0; i<k; i++){\n              iPage = get4byte(&aData[8+i*4]);\n              if( iPage<=nearby ){\n                closest = i;\n                break;\n              }\n            }\n          }else{\n            int dist;\n            dist = sqlite3AbsInt32(get4byte(&aData[8]) - nearby);\n            for(i=1; i<k; i++){\n              int d2 = sqlite3AbsInt32(get4byte(&aData[8+i*4]) - nearby);\n              if( d2<dist ){\n                closest = i;\n                dist = d2;\n              }\n            }\n          }\n        }else{\n          closest = 0;\n        }\n\n        iPage = get4byte(&aData[8+closest*4]);\n        testcase( iPage==mxPage );\n        if( iPage>mxPage ){\n          rc = SQLITE_CORRUPT_PGNO(iTrunk);\n          goto end_allocate_page;\n        }\n        testcase( iPage==mxPage );\n        if( !searchList \n         || (iPage==nearby || (iPage<nearby && eMode==BTALLOC_LE)) \n        ){\n          int noContent;\n          *pPgno = iPage;\n          TRACE((\"ALLOCATE: %d was leaf %d of %d on trunk %d\"\n                 \": %d more free pages\\n\",\n                 *pPgno, closest+1, k, pTrunk->pgno, n-1));\n          rc = sqlite3PagerWrite(pTrunk->pDbPage);\n          if( rc ) goto end_allocate_page;\n          if( closest<k-1 ){\n            memcpy(&aData[8+closest*4], &aData[4+k*4], 4);\n          }\n          put4byte(&aData[4], k-1);\n          noContent = !btreeGetHasContent(pBt, *pPgno)? PAGER_GET_NOCONTENT : 0;\n          rc = btreeGetUnusedPage(pBt, *pPgno, ppPage, noContent);\n          if( rc==SQLITE_OK ){\n            rc = sqlite3PagerWrite((*ppPage)->pDbPage);\n            if( rc!=SQLITE_OK ){\n              releasePage(*ppPage);\n              *ppPage = 0;\n            }\n          }\n          searchList = 0;\n        }\n      }\n      releasePage(pPrevTrunk);\n      pPrevTrunk = 0;\n    }while( searchList );\n  }else{\n    /* There are no pages on the freelist, so append a new page to the\n    ** database image.\n    **\n    ** Normally, new pages allocated by this block can be requested from the\n    ** pager layer with the 'no-content' flag set. This prevents the pager\n    ** from trying to read the pages content from disk. However, if the\n    ** current transaction has already run one or more incremental-vacuum\n    ** steps, then the page we are about to allocate may contain content\n    ** that is required in the event of a rollback. In this case, do\n    ** not set the no-content flag. This causes the pager to load and journal\n    ** the current page content before overwriting it.\n    **\n    ** Note that the pager will not actually attempt to load or journal \n    ** content for any page that really does lie past the end of the database\n    ** file on disk. So the effects of disabling the no-content optimization\n    ** here are confined to those pages that lie between the end of the\n    ** database image and the end of the database file.\n    */\n    int bNoContent = (0==IfNotOmitAV(pBt->bDoTruncate))? PAGER_GET_NOCONTENT:0;\n\n    rc = sqlite3PagerWrite(pBt->pPage1->pDbPage);\n    if( rc ) return rc;\n    pBt->nPage++;\n    if( pBt->nPage==PENDING_BYTE_PAGE(pBt) ) pBt->nPage++;\n\n#ifndef SQLITE_OMIT_AUTOVACUUM\n    if( pBt->autoVacuum && PTRMAP_ISPAGE(pBt, pBt->nPage) ){\n      /* If *pPgno refers to a pointer-map page, allocate two new pages\n      ** at the end of the file instead of one. The first allocated page\n      ** becomes a new pointer-map page, the second is used by the caller.\n      */\n      MemPage *pPg = 0;\n      TRACE((\"ALLOCATE: %d from end of file (pointer-map page)\\n\", pBt->nPage));\n      assert( pBt->nPage!=PENDING_BYTE_PAGE(pBt) );\n      rc = btreeGetUnusedPage(pBt, pBt->nPage, &pPg, bNoContent);\n      if( rc==SQLITE_OK ){\n        rc = sqlite3PagerWrite(pPg->pDbPage);\n        releasePage(pPg);\n      }\n      if( rc ) return rc;\n      pBt->nPage++;\n      if( pBt->nPage==PENDING_BYTE_PAGE(pBt) ){ pBt->nPage++; }\n    }\n#endif\n    put4byte(28 + (u8*)pBt->pPage1->aData, pBt->nPage);\n    *pPgno = pBt->nPage;\n\n    assert( *pPgno!=PENDING_BYTE_PAGE(pBt) );\n    rc = btreeGetUnusedPage(pBt, *pPgno, ppPage, bNoContent);\n    if( rc ) return rc;\n    rc = sqlite3PagerWrite((*ppPage)->pDbPage);\n    if( rc!=SQLITE_OK ){\n      releasePage(*ppPage);\n      *ppPage = 0;\n    }\n    TRACE((\"ALLOCATE: %d from end of file\\n\", *pPgno));\n  }\n\n  assert( *pPgno!=PENDING_BYTE_PAGE(pBt) );\n\nend_allocate_page:\n  releasePage(pTrunk);\n  releasePage(pPrevTrunk);\n  assert( rc!=SQLITE_OK || sqlite3PagerPageRefcount((*ppPage)->pDbPage)<=1 );\n  assert( rc!=SQLITE_OK || (*ppPage)->isInit==0 );\n  return rc;\n}\n\n/*\n** This function is used to add page iPage to the database file free-list. \n** It is assumed that the page is not already a part of the free-list.\n**\n** The value passed as the second argument to this function is optional.\n** If the caller happens to have a pointer to the MemPage object \n** corresponding to page iPage handy, it may pass it as the second value. \n** Otherwise, it may pass NULL.\n**\n** If a pointer to a MemPage object is passed as the second argument,\n** its reference count is not altered by this function.\n*/\nstatic int freePage2(BtShared *pBt, MemPage *pMemPage, Pgno iPage){\n  MemPage *pTrunk = 0;                /* Free-list trunk page */\n  Pgno iTrunk = 0;                    /* Page number of free-list trunk page */ \n  MemPage *pPage1 = pBt->pPage1;      /* Local reference to page 1 */\n  MemPage *pPage;                     /* Page being freed. May be NULL. */\n  int rc;                             /* Return Code */\n  int nFree;                          /* Initial number of pages on free-list */\n\n  assert( sqlite3_mutex_held(pBt->mutex) );\n  assert( CORRUPT_DB || iPage>1 );\n  assert( !pMemPage || pMemPage->pgno==iPage );\n\n  if( iPage<2 ) return SQLITE_CORRUPT_BKPT;\n  if( pMemPage ){\n    pPage = pMemPage;\n    sqlite3PagerRef(pPage->pDbPage);\n  }else{\n    pPage = btreePageLookup(pBt, iPage);\n  }\n\n  /* Increment the free page count on pPage1 */\n  rc = sqlite3PagerWrite(pPage1->pDbPage);\n  if( rc ) goto freepage_out;\n  nFree = get4byte(&pPage1->aData[36]);\n  put4byte(&pPage1->aData[36], nFree+1);\n\n  if( pBt->btsFlags & BTS_SECURE_DELETE ){\n    /* If the secure_delete option is enabled, then\n    ** always fully overwrite deleted information with zeros.\n    */\n    if( (!pPage && ((rc = btreeGetPage(pBt, iPage, &pPage, 0))!=0) )\n     ||            ((rc = sqlite3PagerWrite(pPage->pDbPage))!=0)\n    ){\n      goto freepage_out;\n    }\n    memset(pPage->aData, 0, pPage->pBt->pageSize);\n  }\n\n  /* If the database supports auto-vacuum, write an entry in the pointer-map\n  ** to indicate that the page is free.\n  */\n  if( ISAUTOVACUUM ){\n    ptrmapPut(pBt, iPage, PTRMAP_FREEPAGE, 0, &rc);\n    if( rc ) goto freepage_out;\n  }\n\n  /* Now manipulate the actual database free-list structure. There are two\n  ** possibilities. If the free-list is currently empty, or if the first\n  ** trunk page in the free-list is full, then this page will become a\n  ** new free-list trunk page. Otherwise, it will become a leaf of the\n  ** first trunk page in the current free-list. This block tests if it\n  ** is possible to add the page as a new free-list leaf.\n  */\n  if( nFree!=0 ){\n    u32 nLeaf;                /* Initial number of leaf cells on trunk page */\n\n    iTrunk = get4byte(&pPage1->aData[32]);\n    rc = btreeGetPage(pBt, iTrunk, &pTrunk, 0);\n    if( rc!=SQLITE_OK ){\n      goto freepage_out;\n    }\n\n    nLeaf = get4byte(&pTrunk->aData[4]);\n    assert( pBt->usableSize>32 );\n    if( nLeaf > (u32)pBt->usableSize/4 - 2 ){\n      rc = SQLITE_CORRUPT_BKPT;\n      goto freepage_out;\n    }\n    if( nLeaf < (u32)pBt->usableSize/4 - 8 ){\n      /* In this case there is room on the trunk page to insert the page\n      ** being freed as a new leaf.\n      **\n      ** Note that the trunk page is not really full until it contains\n      ** usableSize/4 - 2 entries, not usableSize/4 - 8 entries as we have\n      ** coded.  But due to a coding error in versions of SQLite prior to\n      ** 3.6.0, databases with freelist trunk pages holding more than\n      ** usableSize/4 - 8 entries will be reported as corrupt.  In order\n      ** to maintain backwards compatibility with older versions of SQLite,\n      ** we will continue to restrict the number of entries to usableSize/4 - 8\n      ** for now.  At some point in the future (once everyone has upgraded\n      ** to 3.6.0 or later) we should consider fixing the conditional above\n      ** to read \"usableSize/4-2\" instead of \"usableSize/4-8\".\n      **\n      ** EVIDENCE-OF: R-19920-11576 However, newer versions of SQLite still\n      ** avoid using the last six entries in the freelist trunk page array in\n      ** order that database files created by newer versions of SQLite can be\n      ** read by older versions of SQLite.\n      */\n      rc = sqlite3PagerWrite(pTrunk->pDbPage);\n      if( rc==SQLITE_OK ){\n        put4byte(&pTrunk->aData[4], nLeaf+1);\n        put4byte(&pTrunk->aData[8+nLeaf*4], iPage);\n        if( pPage && (pBt->btsFlags & BTS_SECURE_DELETE)==0 ){\n          sqlite3PagerDontWrite(pPage->pDbPage);\n        }\n        rc = btreeSetHasContent(pBt, iPage);\n      }\n      TRACE((\"FREE-PAGE: %d leaf on trunk page %d\\n\",pPage->pgno,pTrunk->pgno));\n      goto freepage_out;\n    }\n  }\n\n  /* If control flows to this point, then it was not possible to add the\n  ** the page being freed as a leaf page of the first trunk in the free-list.\n  ** Possibly because the free-list is empty, or possibly because the \n  ** first trunk in the free-list is full. Either way, the page being freed\n  ** will become the new first trunk page in the free-list.\n  */\n  if( pPage==0 && SQLITE_OK!=(rc = btreeGetPage(pBt, iPage, &pPage, 0)) ){\n    goto freepage_out;\n  }\n  rc = sqlite3PagerWrite(pPage->pDbPage);\n  if( rc!=SQLITE_OK ){\n    goto freepage_out;\n  }\n  put4byte(pPage->aData, iTrunk);\n  put4byte(&pPage->aData[4], 0);\n  put4byte(&pPage1->aData[32], iPage);\n  TRACE((\"FREE-PAGE: %d new trunk page replacing %d\\n\", pPage->pgno, iTrunk));\n\nfreepage_out:\n  if( pPage ){\n    pPage->isInit = 0;\n  }\n  releasePage(pPage);\n  releasePage(pTrunk);\n  return rc;\n}\nstatic void freePage(MemPage *pPage, int *pRC){\n  if( (*pRC)==SQLITE_OK ){\n    *pRC = freePage2(pPage->pBt, pPage, pPage->pgno);\n  }\n}\n\n/*\n** Free any overflow pages associated with the given Cell.  Store\n** size information about the cell in pInfo.\n*/\nstatic int clearCell(\n  MemPage *pPage,          /* The page that contains the Cell */\n  unsigned char *pCell,    /* First byte of the Cell */\n  CellInfo *pInfo          /* Size information about the cell */\n){\n  BtShared *pBt;\n  Pgno ovflPgno;\n  int rc;\n  int nOvfl;\n  u32 ovflPageSize;\n\n  assert( sqlite3_mutex_held(pPage->pBt->mutex) );\n  pPage->xParseCell(pPage, pCell, pInfo);\n  if( pInfo->nLocal==pInfo->nPayload ){\n    return SQLITE_OK;  /* No overflow pages. Return without doing anything */\n  }\n  if( pCell+pInfo->nSize-1 > pPage->aData+pPage->maskPage ){\n    /* Cell extends past end of page */\n    return SQLITE_CORRUPT_PAGE(pPage);\n  }\n  ovflPgno = get4byte(pCell + pInfo->nSize - 4);\n  pBt = pPage->pBt;\n  assert( pBt->usableSize > 4 );\n  ovflPageSize = pBt->usableSize - 4;\n  nOvfl = (pInfo->nPayload - pInfo->nLocal + ovflPageSize - 1)/ovflPageSize;\n  assert( nOvfl>0 || \n    (CORRUPT_DB && (pInfo->nPayload + ovflPageSize)<ovflPageSize)\n  );\n  while( nOvfl-- ){\n    Pgno iNext = 0;\n    MemPage *pOvfl = 0;\n    if( ovflPgno<2 || ovflPgno>btreePagecount(pBt) ){\n      /* 0 is not a legal page number and page 1 cannot be an \n      ** overflow page. Therefore if ovflPgno<2 or past the end of the \n      ** file the database must be corrupt. */\n      return SQLITE_CORRUPT_BKPT;\n    }\n    if( nOvfl ){\n      rc = getOverflowPage(pBt, ovflPgno, &pOvfl, &iNext);\n      if( rc ) return rc;\n    }\n\n    if( ( pOvfl || ((pOvfl = btreePageLookup(pBt, ovflPgno))!=0) )\n     && sqlite3PagerPageRefcount(pOvfl->pDbPage)!=1\n    ){\n      /* There is no reason any cursor should have an outstanding reference \n      ** to an overflow page belonging to a cell that is being deleted/updated.\n      ** So if there exists more than one reference to this page, then it \n      ** must not really be an overflow page and the database must be corrupt. \n      ** It is helpful to detect this before calling freePage2(), as \n      ** freePage2() may zero the page contents if secure-delete mode is\n      ** enabled. If this 'overflow' page happens to be a page that the\n      ** caller is iterating through or using in some other way, this\n      ** can be problematic.\n      */\n      rc = SQLITE_CORRUPT_BKPT;\n    }else{\n      rc = freePage2(pBt, pOvfl, ovflPgno);\n    }\n\n    if( pOvfl ){\n      sqlite3PagerUnref(pOvfl->pDbPage);\n    }\n    if( rc ) return rc;\n    ovflPgno = iNext;\n  }\n  return SQLITE_OK;\n}\n\n/*\n** Create the byte sequence used to represent a cell on page pPage\n** and write that byte sequence into pCell[].  Overflow pages are\n** allocated and filled in as necessary.  The calling procedure\n** is responsible for making sure sufficient space has been allocated\n** for pCell[].\n**\n** Note that pCell does not necessary need to point to the pPage->aData\n** area.  pCell might point to some temporary storage.  The cell will\n** be constructed in this temporary area then copied into pPage->aData\n** later.\n*/\nstatic int fillInCell(\n  MemPage *pPage,                /* The page that contains the cell */\n  unsigned char *pCell,          /* Complete text of the cell */\n  const BtreePayload *pX,        /* Payload with which to construct the cell */\n  int *pnSize                    /* Write cell size here */\n){\n  int nPayload;\n  const u8 *pSrc;\n  int nSrc, n, rc, mn;\n  int spaceLeft;\n  MemPage *pToRelease;\n  unsigned char *pPrior;\n  unsigned char *pPayload;\n  BtShared *pBt;\n  Pgno pgnoOvfl;\n  int nHeader;\n\n  assert( sqlite3_mutex_held(pPage->pBt->mutex) );\n\n  /* pPage is not necessarily writeable since pCell might be auxiliary\n  ** buffer space that is separate from the pPage buffer area */\n  assert( pCell<pPage->aData || pCell>=&pPage->aData[pPage->pBt->pageSize]\n            || sqlite3PagerIswriteable(pPage->pDbPage) );\n\n  /* Fill in the header. */\n  nHeader = pPage->childPtrSize;\n  if( pPage->intKey ){\n    nPayload = pX->nData + pX->nZero;\n    pSrc = pX->pData;\n    nSrc = pX->nData;\n    assert( pPage->intKeyLeaf ); /* fillInCell() only called for leaves */\n    nHeader += putVarint32(&pCell[nHeader], nPayload);\n    nHeader += putVarint(&pCell[nHeader], *(u64*)&pX->nKey);\n  }else{\n    assert( pX->nKey<=0x7fffffff && pX->pKey!=0 );\n    nSrc = nPayload = (int)pX->nKey;\n    pSrc = pX->pKey;\n    nHeader += putVarint32(&pCell[nHeader], nPayload);\n  }\n  \n  /* Fill in the payload */\n  pPayload = &pCell[nHeader];\n  if( nPayload<=pPage->maxLocal ){\n    /* This is the common case where everything fits on the btree page\n    ** and no overflow pages are required. */\n    n = nHeader + nPayload;\n    testcase( n==3 );\n    testcase( n==4 );\n    if( n<4 ) n = 4;\n    *pnSize = n;\n    assert( nSrc<=nPayload );\n    testcase( nSrc<nPayload );\n    memcpy(pPayload, pSrc, nSrc);\n    memset(pPayload+nSrc, 0, nPayload-nSrc);\n    return SQLITE_OK;\n  }\n\n  /* If we reach this point, it means that some of the content will need\n  ** to spill onto overflow pages.\n  */\n  mn = pPage->minLocal;\n  n = mn + (nPayload - mn) % (pPage->pBt->usableSize - 4);\n  testcase( n==pPage->maxLocal );\n  testcase( n==pPage->maxLocal+1 );\n  if( n > pPage->maxLocal ) n = mn;\n  spaceLeft = n;\n  *pnSize = n + nHeader + 4;\n  pPrior = &pCell[nHeader+n];\n  pToRelease = 0;\n  pgnoOvfl = 0;\n  pBt = pPage->pBt;\n\n  /* At this point variables should be set as follows:\n  **\n  **   nPayload           Total payload size in bytes\n  **   pPayload           Begin writing payload here\n  **   spaceLeft          Space available at pPayload.  If nPayload>spaceLeft,\n  **                      that means content must spill into overflow pages.\n  **   *pnSize            Size of the local cell (not counting overflow pages)\n  **   pPrior             Where to write the pgno of the first overflow page\n  **\n  ** Use a call to btreeParseCellPtr() to verify that the values above\n  ** were computed correctly.\n  */\n#ifdef SQLITE_DEBUG\n  {\n    CellInfo info;\n    pPage->xParseCell(pPage, pCell, &info);\n    assert( nHeader==(int)(info.pPayload - pCell) );\n    assert( info.nKey==pX->nKey );\n    assert( *pnSize == info.nSize );\n    assert( spaceLeft == info.nLocal );\n  }\n#endif\n\n  /* Write the payload into the local Cell and any extra into overflow pages */\n  while( 1 ){\n    n = nPayload;\n    if( n>spaceLeft ) n = spaceLeft;\n\n    /* If pToRelease is not zero than pPayload points into the data area\n    ** of pToRelease.  Make sure pToRelease is still writeable. */\n    assert( pToRelease==0 || sqlite3PagerIswriteable(pToRelease->pDbPage) );\n\n    /* If pPayload is part of the data area of pPage, then make sure pPage\n    ** is still writeable */\n    assert( pPayload<pPage->aData || pPayload>=&pPage->aData[pBt->pageSize]\n            || sqlite3PagerIswriteable(pPage->pDbPage) );\n\n    if( nSrc>=n ){\n      memcpy(pPayload, pSrc, n);\n    }else if( nSrc>0 ){\n      n = nSrc;\n      memcpy(pPayload, pSrc, n);\n    }else{\n      memset(pPayload, 0, n);\n    }\n    nPayload -= n;\n    if( nPayload<=0 ) break;\n    pPayload += n;\n    pSrc += n;\n    nSrc -= n;\n    spaceLeft -= n;\n    if( spaceLeft==0 ){\n      MemPage *pOvfl = 0;\n#ifndef SQLITE_OMIT_AUTOVACUUM\n      Pgno pgnoPtrmap = pgnoOvfl; /* Overflow page pointer-map entry page */\n      if( pBt->autoVacuum ){\n        do{\n          pgnoOvfl++;\n        } while( \n          PTRMAP_ISPAGE(pBt, pgnoOvfl) || pgnoOvfl==PENDING_BYTE_PAGE(pBt) \n        );\n      }\n#endif\n      rc = allocateBtreePage(pBt, &pOvfl, &pgnoOvfl, pgnoOvfl, 0);\n#ifndef SQLITE_OMIT_AUTOVACUUM\n      /* If the database supports auto-vacuum, and the second or subsequent\n      ** overflow page is being allocated, add an entry to the pointer-map\n      ** for that page now. \n      **\n      ** If this is the first overflow page, then write a partial entry \n      ** to the pointer-map. If we write nothing to this pointer-map slot,\n      ** then the optimistic overflow chain processing in clearCell()\n      ** may misinterpret the uninitialized values and delete the\n      ** wrong pages from the database.\n      */\n      if( pBt->autoVacuum && rc==SQLITE_OK ){\n        u8 eType = (pgnoPtrmap?PTRMAP_OVERFLOW2:PTRMAP_OVERFLOW1);\n        ptrmapPut(pBt, pgnoOvfl, eType, pgnoPtrmap, &rc);\n        if( rc ){\n          releasePage(pOvfl);\n        }\n      }\n#endif\n      if( rc ){\n        releasePage(pToRelease);\n        return rc;\n      }\n\n      /* If pToRelease is not zero than pPrior points into the data area\n      ** of pToRelease.  Make sure pToRelease is still writeable. */\n      assert( pToRelease==0 || sqlite3PagerIswriteable(pToRelease->pDbPage) );\n\n      /* If pPrior is part of the data area of pPage, then make sure pPage\n      ** is still writeable */\n      assert( pPrior<pPage->aData || pPrior>=&pPage->aData[pBt->pageSize]\n            || sqlite3PagerIswriteable(pPage->pDbPage) );\n\n      put4byte(pPrior, pgnoOvfl);\n      releasePage(pToRelease);\n      pToRelease = pOvfl;\n      pPrior = pOvfl->aData;\n      put4byte(pPrior, 0);\n      pPayload = &pOvfl->aData[4];\n      spaceLeft = pBt->usableSize - 4;\n    }\n  }\n  releasePage(pToRelease);\n  return SQLITE_OK;\n}\n\n/*\n** Remove the i-th cell from pPage.  This routine effects pPage only.\n** The cell content is not freed or deallocated.  It is assumed that\n** the cell content has been copied someplace else.  This routine just\n** removes the reference to the cell from pPage.\n**\n** \"sz\" must be the number of bytes in the cell.\n*/\nstatic void dropCell(MemPage *pPage, int idx, int sz, int *pRC){\n  u32 pc;         /* Offset to cell content of cell being deleted */\n  u8 *data;       /* pPage->aData */\n  u8 *ptr;        /* Used to move bytes around within data[] */\n  int rc;         /* The return code */\n  int hdr;        /* Beginning of the header.  0 most pages.  100 page 1 */\n\n  if( *pRC ) return;\n  assert( idx>=0 && idx<pPage->nCell );\n  assert( CORRUPT_DB || sz==cellSize(pPage, idx) );\n  assert( sqlite3PagerIswriteable(pPage->pDbPage) );\n  assert( sqlite3_mutex_held(pPage->pBt->mutex) );\n  data = pPage->aData;\n  ptr = &pPage->aCellIdx[2*idx];\n  pc = get2byte(ptr);\n  hdr = pPage->hdrOffset;\n  testcase( pc==get2byte(&data[hdr+5]) );\n  testcase( pc+sz==pPage->pBt->usableSize );\n  if( pc+sz > pPage->pBt->usableSize ){\n    *pRC = SQLITE_CORRUPT_BKPT;\n    return;\n  }\n  rc = freeSpace(pPage, pc, sz);\n  if( rc ){\n    *pRC = rc;\n    return;\n  }\n  pPage->nCell--;\n  if( pPage->nCell==0 ){\n    memset(&data[hdr+1], 0, 4);\n    data[hdr+7] = 0;\n    put2byte(&data[hdr+5], pPage->pBt->usableSize);\n    pPage->nFree = pPage->pBt->usableSize - pPage->hdrOffset\n                       - pPage->childPtrSize - 8;\n  }else{\n    memmove(ptr, ptr+2, 2*(pPage->nCell - idx));\n    put2byte(&data[hdr+3], pPage->nCell);\n    pPage->nFree += 2;\n  }\n}\n\n/*\n** Insert a new cell on pPage at cell index \"i\".  pCell points to the\n** content of the cell.\n**\n** If the cell content will fit on the page, then put it there.  If it\n** will not fit, then make a copy of the cell content into pTemp if\n** pTemp is not null.  Regardless of pTemp, allocate a new entry\n** in pPage->apOvfl[] and make it point to the cell content (either\n** in pTemp or the original pCell) and also record its index. \n** Allocating a new entry in pPage->aCell[] implies that \n** pPage->nOverflow is incremented.\n**\n** *pRC must be SQLITE_OK when this routine is called.\n*/\nstatic void insertCell(\n  MemPage *pPage,   /* Page into which we are copying */\n  int i,            /* New cell becomes the i-th cell of the page */\n  u8 *pCell,        /* Content of the new cell */\n  int sz,           /* Bytes of content in pCell */\n  u8 *pTemp,        /* Temp storage space for pCell, if needed */\n  Pgno iChild,      /* If non-zero, replace first 4 bytes with this value */\n  int *pRC          /* Read and write return code from here */\n){\n  int idx = 0;      /* Where to write new cell content in data[] */\n  int j;            /* Loop counter */\n  u8 *data;         /* The content of the whole page */\n  u8 *pIns;         /* The point in pPage->aCellIdx[] where no cell inserted */\n\n  assert( *pRC==SQLITE_OK );\n  assert( i>=0 && i<=pPage->nCell+pPage->nOverflow );\n  assert( MX_CELL(pPage->pBt)<=10921 );\n  assert( pPage->nCell<=MX_CELL(pPage->pBt) || CORRUPT_DB );\n  assert( pPage->nOverflow<=ArraySize(pPage->apOvfl) );\n  assert( ArraySize(pPage->apOvfl)==ArraySize(pPage->aiOvfl) );\n  assert( sqlite3_mutex_held(pPage->pBt->mutex) );\n  /* The cell should normally be sized correctly.  However, when moving a\n  ** malformed cell from a leaf page to an interior page, if the cell size\n  ** wanted to be less than 4 but got rounded up to 4 on the leaf, then size\n  ** might be less than 8 (leaf-size + pointer) on the interior node.  Hence\n  ** the term after the || in the following assert(). */\n  assert( sz==pPage->xCellSize(pPage, pCell) || (sz==8 && iChild>0) );\n  if( pPage->nOverflow || sz+2>pPage->nFree ){\n    if( pTemp ){\n      memcpy(pTemp, pCell, sz);\n      pCell = pTemp;\n    }\n    if( iChild ){\n      put4byte(pCell, iChild);\n    }\n    j = pPage->nOverflow++;\n    /* Comparison against ArraySize-1 since we hold back one extra slot\n    ** as a contingency.  In other words, never need more than 3 overflow\n    ** slots but 4 are allocated, just to be safe. */\n    assert( j < ArraySize(pPage->apOvfl)-1 );\n    pPage->apOvfl[j] = pCell;\n    pPage->aiOvfl[j] = (u16)i;\n\n    /* When multiple overflows occur, they are always sequential and in\n    ** sorted order.  This invariants arise because multiple overflows can\n    ** only occur when inserting divider cells into the parent page during\n    ** balancing, and the dividers are adjacent and sorted.\n    */\n    assert( j==0 || pPage->aiOvfl[j-1]<(u16)i ); /* Overflows in sorted order */\n    assert( j==0 || i==pPage->aiOvfl[j-1]+1 );   /* Overflows are sequential */\n  }else{\n    int rc = sqlite3PagerWrite(pPage->pDbPage);\n    if( rc!=SQLITE_OK ){\n      *pRC = rc;\n      return;\n    }\n    assert( sqlite3PagerIswriteable(pPage->pDbPage) );\n    data = pPage->aData;\n    assert( &data[pPage->cellOffset]==pPage->aCellIdx );\n    rc = allocateSpace(pPage, sz, &idx);\n    if( rc ){ *pRC = rc; return; }\n    /* The allocateSpace() routine guarantees the following properties\n    ** if it returns successfully */\n    assert( idx >= 0 );\n    assert( idx >= pPage->cellOffset+2*pPage->nCell+2 || CORRUPT_DB );\n    assert( idx+sz <= (int)pPage->pBt->usableSize );\n    pPage->nFree -= (u16)(2 + sz);\n    memcpy(&data[idx], pCell, sz);\n    if( iChild ){\n      put4byte(&data[idx], iChild);\n    }\n    pIns = pPage->aCellIdx + i*2;\n    memmove(pIns+2, pIns, 2*(pPage->nCell - i));\n    put2byte(pIns, idx);\n    pPage->nCell++;\n    /* increment the cell count */\n    if( (++data[pPage->hdrOffset+4])==0 ) data[pPage->hdrOffset+3]++;\n    assert( get2byte(&data[pPage->hdrOffset+3])==pPage->nCell );\n#ifndef SQLITE_OMIT_AUTOVACUUM\n    if( pPage->pBt->autoVacuum ){\n      /* The cell may contain a pointer to an overflow page. If so, write\n      ** the entry for the overflow page into the pointer map.\n      */\n      ptrmapPutOvflPtr(pPage, pCell, pRC);\n    }\n#endif\n  }\n}\n\n/*\n** A CellArray object contains a cache of pointers and sizes for a\n** consecutive sequence of cells that might be held on multiple pages.\n*/\ntypedef struct CellArray CellArray;\nstruct CellArray {\n  int nCell;              /* Number of cells in apCell[] */\n  MemPage *pRef;          /* Reference page */\n  u8 **apCell;            /* All cells begin balanced */\n  u16 *szCell;            /* Local size of all cells in apCell[] */\n};\n\n/*\n** Make sure the cell sizes at idx, idx+1, ..., idx+N-1 have been\n** computed.\n*/\nstatic void populateCellCache(CellArray *p, int idx, int N){\n  assert( idx>=0 && idx+N<=p->nCell );\n  while( N>0 ){\n    assert( p->apCell[idx]!=0 );\n    if( p->szCell[idx]==0 ){\n      p->szCell[idx] = p->pRef->xCellSize(p->pRef, p->apCell[idx]);\n    }else{\n      assert( CORRUPT_DB ||\n              p->szCell[idx]==p->pRef->xCellSize(p->pRef, p->apCell[idx]) );\n    }\n    idx++;\n    N--;\n  }\n}\n\n/*\n** Return the size of the Nth element of the cell array\n*/\nstatic SQLITE_NOINLINE u16 computeCellSize(CellArray *p, int N){\n  assert( N>=0 && N<p->nCell );\n  assert( p->szCell[N]==0 );\n  p->szCell[N] = p->pRef->xCellSize(p->pRef, p->apCell[N]);\n  return p->szCell[N];\n}\nstatic u16 cachedCellSize(CellArray *p, int N){\n  assert( N>=0 && N<p->nCell );\n  if( p->szCell[N] ) return p->szCell[N];\n  return computeCellSize(p, N);\n}\n\n/*\n** Array apCell[] contains pointers to nCell b-tree page cells. The \n** szCell[] array contains the size in bytes of each cell. This function\n** replaces the current contents of page pPg with the contents of the cell\n** array.\n**\n** Some of the cells in apCell[] may currently be stored in pPg. This\n** function works around problems caused by this by making a copy of any \n** such cells before overwriting the page data.\n**\n** The MemPage.nFree field is invalidated by this function. It is the \n** responsibility of the caller to set it correctly.\n*/\nstatic int rebuildPage(\n  MemPage *pPg,                   /* Edit this page */\n  int nCell,                      /* Final number of cells on page */\n  u8 **apCell,                    /* Array of cells */\n  u16 *szCell                     /* Array of cell sizes */\n){\n  const int hdr = pPg->hdrOffset;          /* Offset of header on pPg */\n  u8 * const aData = pPg->aData;           /* Pointer to data for pPg */\n  const int usableSize = pPg->pBt->usableSize;\n  u8 * const pEnd = &aData[usableSize];\n  int i;\n  u8 *pCellptr = pPg->aCellIdx;\n  u8 *pTmp = sqlite3PagerTempSpace(pPg->pBt->pPager);\n  u8 *pData;\n\n  i = get2byte(&aData[hdr+5]);\n  memcpy(&pTmp[i], &aData[i], usableSize - i);\n\n  pData = pEnd;\n  for(i=0; i<nCell; i++){\n    u8 *pCell = apCell[i];\n    if( SQLITE_WITHIN(pCell,aData,pEnd) ){\n      pCell = &pTmp[pCell - aData];\n    }\n    pData -= szCell[i];\n    put2byte(pCellptr, (pData - aData));\n    pCellptr += 2;\n    if( pData < pCellptr ) return SQLITE_CORRUPT_BKPT;\n    memcpy(pData, pCell, szCell[i]);\n    assert( szCell[i]==pPg->xCellSize(pPg, pCell) || CORRUPT_DB );\n    testcase( szCell[i]!=pPg->xCellSize(pPg,pCell) );\n  }\n\n  /* The pPg->nFree field is now set incorrectly. The caller will fix it. */\n  pPg->nCell = nCell;\n  pPg->nOverflow = 0;\n\n  put2byte(&aData[hdr+1], 0);\n  put2byte(&aData[hdr+3], pPg->nCell);\n  put2byte(&aData[hdr+5], pData - aData);\n  aData[hdr+7] = 0x00;\n  return SQLITE_OK;\n}\n\n/*\n** Array apCell[] contains nCell pointers to b-tree cells. Array szCell\n** contains the size in bytes of each such cell. This function attempts to \n** add the cells stored in the array to page pPg. If it cannot (because \n** the page needs to be defragmented before the cells will fit), non-zero\n** is returned. Otherwise, if the cells are added successfully, zero is\n** returned.\n**\n** Argument pCellptr points to the first entry in the cell-pointer array\n** (part of page pPg) to populate. After cell apCell[0] is written to the\n** page body, a 16-bit offset is written to pCellptr. And so on, for each\n** cell in the array. It is the responsibility of the caller to ensure\n** that it is safe to overwrite this part of the cell-pointer array.\n**\n** When this function is called, *ppData points to the start of the \n** content area on page pPg. If the size of the content area is extended,\n** *ppData is updated to point to the new start of the content area\n** before returning.\n**\n** Finally, argument pBegin points to the byte immediately following the\n** end of the space required by this page for the cell-pointer area (for\n** all cells - not just those inserted by the current call). If the content\n** area must be extended to before this point in order to accomodate all\n** cells in apCell[], then the cells do not fit and non-zero is returned.\n*/\nstatic int pageInsertArray(\n  MemPage *pPg,                   /* Page to add cells to */\n  u8 *pBegin,                     /* End of cell-pointer array */\n  u8 **ppData,                    /* IN/OUT: Page content -area pointer */\n  u8 *pCellptr,                   /* Pointer to cell-pointer area */\n  int iFirst,                     /* Index of first cell to add */\n  int nCell,                      /* Number of cells to add to pPg */\n  CellArray *pCArray              /* Array of cells */\n){\n  int i;\n  u8 *aData = pPg->aData;\n  u8 *pData = *ppData;\n  int iEnd = iFirst + nCell;\n  assert( CORRUPT_DB || pPg->hdrOffset==0 );    /* Never called on page 1 */\n  for(i=iFirst; i<iEnd; i++){\n    int sz, rc;\n    u8 *pSlot;\n    sz = cachedCellSize(pCArray, i);\n    if( (aData[1]==0 && aData[2]==0) || (pSlot = pageFindSlot(pPg,sz,&rc))==0 ){\n      if( (pData - pBegin)<sz ) return 1;\n      pData -= sz;\n      pSlot = pData;\n    }\n    /* pSlot and pCArray->apCell[i] will never overlap on a well-formed\n    ** database.  But they might for a corrupt database.  Hence use memmove()\n    ** since memcpy() sends SIGABORT with overlapping buffers on OpenBSD */\n    assert( (pSlot+sz)<=pCArray->apCell[i]\n         || pSlot>=(pCArray->apCell[i]+sz)\n         || CORRUPT_DB );\n    memmove(pSlot, pCArray->apCell[i], sz);\n    put2byte(pCellptr, (pSlot - aData));\n    pCellptr += 2;\n  }\n  *ppData = pData;\n  return 0;\n}\n\n/*\n** Array apCell[] contains nCell pointers to b-tree cells. Array szCell \n** contains the size in bytes of each such cell. This function adds the\n** space associated with each cell in the array that is currently stored \n** within the body of pPg to the pPg free-list. The cell-pointers and other\n** fields of the page are not updated.\n**\n** This function returns the total number of cells added to the free-list.\n*/\nstatic int pageFreeArray(\n  MemPage *pPg,                   /* Page to edit */\n  int iFirst,                     /* First cell to delete */\n  int nCell,                      /* Cells to delete */\n  CellArray *pCArray              /* Array of cells */\n){\n  u8 * const aData = pPg->aData;\n  u8 * const pEnd = &aData[pPg->pBt->usableSize];\n  u8 * const pStart = &aData[pPg->hdrOffset + 8 + pPg->childPtrSize];\n  int nRet = 0;\n  int i;\n  int iEnd = iFirst + nCell;\n  u8 *pFree = 0;\n  int szFree = 0;\n\n  for(i=iFirst; i<iEnd; i++){\n    u8 *pCell = pCArray->apCell[i];\n    if( SQLITE_WITHIN(pCell, pStart, pEnd) ){\n      int sz;\n      /* No need to use cachedCellSize() here.  The sizes of all cells that\n      ** are to be freed have already been computing while deciding which\n      ** cells need freeing */\n      sz = pCArray->szCell[i];  assert( sz>0 );\n      if( pFree!=(pCell + sz) ){\n        if( pFree ){\n          assert( pFree>aData && (pFree - aData)<65536 );\n          freeSpace(pPg, (u16)(pFree - aData), szFree);\n        }\n        pFree = pCell;\n        szFree = sz;\n        if( pFree+sz>pEnd ) return 0;\n      }else{\n        pFree = pCell;\n        szFree += sz;\n      }\n      nRet++;\n    }\n  }\n  if( pFree ){\n    assert( pFree>aData && (pFree - aData)<65536 );\n    freeSpace(pPg, (u16)(pFree - aData), szFree);\n  }\n  return nRet;\n}\n\n/*\n** apCell[] and szCell[] contains pointers to and sizes of all cells in the\n** pages being balanced.  The current page, pPg, has pPg->nCell cells starting\n** with apCell[iOld].  After balancing, this page should hold nNew cells\n** starting at apCell[iNew].\n**\n** This routine makes the necessary adjustments to pPg so that it contains\n** the correct cells after being balanced.\n**\n** The pPg->nFree field is invalid when this function returns. It is the\n** responsibility of the caller to set it correctly.\n*/\nstatic int editPage(\n  MemPage *pPg,                   /* Edit this page */\n  int iOld,                       /* Index of first cell currently on page */\n  int iNew,                       /* Index of new first cell on page */\n  int nNew,                       /* Final number of cells on page */\n  CellArray *pCArray              /* Array of cells and sizes */\n){\n  u8 * const aData = pPg->aData;\n  const int hdr = pPg->hdrOffset;\n  u8 *pBegin = &pPg->aCellIdx[nNew * 2];\n  int nCell = pPg->nCell;       /* Cells stored on pPg */\n  u8 *pData;\n  u8 *pCellptr;\n  int i;\n  int iOldEnd = iOld + pPg->nCell + pPg->nOverflow;\n  int iNewEnd = iNew + nNew;\n\n#ifdef SQLITE_DEBUG\n  u8 *pTmp = sqlite3PagerTempSpace(pPg->pBt->pPager);\n  memcpy(pTmp, aData, pPg->pBt->usableSize);\n#endif\n\n  /* Remove cells from the start and end of the page */\n  if( iOld<iNew ){\n    int nShift = pageFreeArray(pPg, iOld, iNew-iOld, pCArray);\n    memmove(pPg->aCellIdx, &pPg->aCellIdx[nShift*2], nCell*2);\n    nCell -= nShift;\n  }\n  if( iNewEnd < iOldEnd ){\n    nCell -= pageFreeArray(pPg, iNewEnd, iOldEnd - iNewEnd, pCArray);\n  }\n\n  pData = &aData[get2byteNotZero(&aData[hdr+5])];\n  if( pData<pBegin ) goto editpage_fail;\n\n  /* Add cells to the start of the page */\n  if( iNew<iOld ){\n    int nAdd = MIN(nNew,iOld-iNew);\n    assert( (iOld-iNew)<nNew || nCell==0 || CORRUPT_DB );\n    pCellptr = pPg->aCellIdx;\n    memmove(&pCellptr[nAdd*2], pCellptr, nCell*2);\n    if( pageInsertArray(\n          pPg, pBegin, &pData, pCellptr,\n          iNew, nAdd, pCArray\n    ) ) goto editpage_fail;\n    nCell += nAdd;\n  }\n\n  /* Add any overflow cells */\n  for(i=0; i<pPg->nOverflow; i++){\n    int iCell = (iOld + pPg->aiOvfl[i]) - iNew;\n    if( iCell>=0 && iCell<nNew ){\n      pCellptr = &pPg->aCellIdx[iCell * 2];\n      memmove(&pCellptr[2], pCellptr, (nCell - iCell) * 2);\n      nCell++;\n      if( pageInsertArray(\n            pPg, pBegin, &pData, pCellptr,\n            iCell+iNew, 1, pCArray\n      ) ) goto editpage_fail;\n    }\n  }\n\n  /* Append cells to the end of the page */\n  pCellptr = &pPg->aCellIdx[nCell*2];\n  if( pageInsertArray(\n        pPg, pBegin, &pData, pCellptr,\n        iNew+nCell, nNew-nCell, pCArray\n  ) ) goto editpage_fail;\n\n  pPg->nCell = nNew;\n  pPg->nOverflow = 0;\n\n  put2byte(&aData[hdr+3], pPg->nCell);\n  put2byte(&aData[hdr+5], pData - aData);\n\n#ifdef SQLITE_DEBUG\n  for(i=0; i<nNew && !CORRUPT_DB; i++){\n    u8 *pCell = pCArray->apCell[i+iNew];\n    int iOff = get2byteAligned(&pPg->aCellIdx[i*2]);\n    if( SQLITE_WITHIN(pCell, aData, &aData[pPg->pBt->usableSize]) ){\n      pCell = &pTmp[pCell - aData];\n    }\n    assert( 0==memcmp(pCell, &aData[iOff],\n            pCArray->pRef->xCellSize(pCArray->pRef, pCArray->apCell[i+iNew])) );\n  }\n#endif\n\n  return SQLITE_OK;\n editpage_fail:\n  /* Unable to edit this page. Rebuild it from scratch instead. */\n  populateCellCache(pCArray, iNew, nNew);\n  return rebuildPage(pPg, nNew, &pCArray->apCell[iNew], &pCArray->szCell[iNew]);\n}\n\n/*\n** The following parameters determine how many adjacent pages get involved\n** in a balancing operation.  NN is the number of neighbors on either side\n** of the page that participate in the balancing operation.  NB is the\n** total number of pages that participate, including the target page and\n** NN neighbors on either side.\n**\n** The minimum value of NN is 1 (of course).  Increasing NN above 1\n** (to 2 or 3) gives a modest improvement in SELECT and DELETE performance\n** in exchange for a larger degradation in INSERT and UPDATE performance.\n** The value of NN appears to give the best results overall.\n*/\n#define NN 1             /* Number of neighbors on either side of pPage */\n#define NB (NN*2+1)      /* Total pages involved in the balance */\n\n\n#ifndef SQLITE_OMIT_QUICKBALANCE\n/*\n** This version of balance() handles the common special case where\n** a new entry is being inserted on the extreme right-end of the\n** tree, in other words, when the new entry will become the largest\n** entry in the tree.\n**\n** Instead of trying to balance the 3 right-most leaf pages, just add\n** a new page to the right-hand side and put the one new entry in\n** that page.  This leaves the right side of the tree somewhat\n** unbalanced.  But odds are that we will be inserting new entries\n** at the end soon afterwards so the nearly empty page will quickly\n** fill up.  On average.\n**\n** pPage is the leaf page which is the right-most page in the tree.\n** pParent is its parent.  pPage must have a single overflow entry\n** which is also the right-most entry on the page.\n**\n** The pSpace buffer is used to store a temporary copy of the divider\n** cell that will be inserted into pParent. Such a cell consists of a 4\n** byte page number followed by a variable length integer. In other\n** words, at most 13 bytes. Hence the pSpace buffer must be at\n** least 13 bytes in size.\n*/\nstatic int balance_quick(MemPage *pParent, MemPage *pPage, u8 *pSpace){\n  BtShared *const pBt = pPage->pBt;    /* B-Tree Database */\n  MemPage *pNew;                       /* Newly allocated page */\n  int rc;                              /* Return Code */\n  Pgno pgnoNew;                        /* Page number of pNew */\n\n  assert( sqlite3_mutex_held(pPage->pBt->mutex) );\n  assert( sqlite3PagerIswriteable(pParent->pDbPage) );\n  assert( pPage->nOverflow==1 );\n\n  /* This error condition is now caught prior to reaching this function */\n  if( NEVER(pPage->nCell==0) ) return SQLITE_CORRUPT_BKPT;\n\n  /* Allocate a new page. This page will become the right-sibling of \n  ** pPage. Make the parent page writable, so that the new divider cell\n  ** may be inserted. If both these operations are successful, proceed.\n  */\n  rc = allocateBtreePage(pBt, &pNew, &pgnoNew, 0, 0);\n\n  if( rc==SQLITE_OK ){\n\n    u8 *pOut = &pSpace[4];\n    u8 *pCell = pPage->apOvfl[0];\n    u16 szCell = pPage->xCellSize(pPage, pCell);\n    u8 *pStop;\n\n    assert( sqlite3PagerIswriteable(pNew->pDbPage) );\n    assert( pPage->aData[0]==(PTF_INTKEY|PTF_LEAFDATA|PTF_LEAF) );\n    zeroPage(pNew, PTF_INTKEY|PTF_LEAFDATA|PTF_LEAF);\n    rc = rebuildPage(pNew, 1, &pCell, &szCell);\n    if( NEVER(rc) ) return rc;\n    pNew->nFree = pBt->usableSize - pNew->cellOffset - 2 - szCell;\n\n    /* If this is an auto-vacuum database, update the pointer map\n    ** with entries for the new page, and any pointer from the \n    ** cell on the page to an overflow page. If either of these\n    ** operations fails, the return code is set, but the contents\n    ** of the parent page are still manipulated by thh code below.\n    ** That is Ok, at this point the parent page is guaranteed to\n    ** be marked as dirty. Returning an error code will cause a\n    ** rollback, undoing any changes made to the parent page.\n    */\n    if( ISAUTOVACUUM ){\n      ptrmapPut(pBt, pgnoNew, PTRMAP_BTREE, pParent->pgno, &rc);\n      if( szCell>pNew->minLocal ){\n        ptrmapPutOvflPtr(pNew, pCell, &rc);\n      }\n    }\n  \n    /* Create a divider cell to insert into pParent. The divider cell\n    ** consists of a 4-byte page number (the page number of pPage) and\n    ** a variable length key value (which must be the same value as the\n    ** largest key on pPage).\n    **\n    ** To find the largest key value on pPage, first find the right-most \n    ** cell on pPage. The first two fields of this cell are the \n    ** record-length (a variable length integer at most 32-bits in size)\n    ** and the key value (a variable length integer, may have any value).\n    ** The first of the while(...) loops below skips over the record-length\n    ** field. The second while(...) loop copies the key value from the\n    ** cell on pPage into the pSpace buffer.\n    */\n    pCell = findCell(pPage, pPage->nCell-1);\n    pStop = &pCell[9];\n    while( (*(pCell++)&0x80) && pCell<pStop );\n    pStop = &pCell[9];\n    while( ((*(pOut++) = *(pCell++))&0x80) && pCell<pStop );\n\n    /* Insert the new divider cell into pParent. */\n    if( rc==SQLITE_OK ){\n      insertCell(pParent, pParent->nCell, pSpace, (int)(pOut-pSpace),\n                   0, pPage->pgno, &rc);\n    }\n\n    /* Set the right-child pointer of pParent to point to the new page. */\n    put4byte(&pParent->aData[pParent->hdrOffset+8], pgnoNew);\n  \n    /* Release the reference to the new page. */\n    releasePage(pNew);\n  }\n\n  return rc;\n}\n#endif /* SQLITE_OMIT_QUICKBALANCE */\n\n#if 0\n/*\n** This function does not contribute anything to the operation of SQLite.\n** it is sometimes activated temporarily while debugging code responsible \n** for setting pointer-map entries.\n*/\nstatic int ptrmapCheckPages(MemPage **apPage, int nPage){\n  int i, j;\n  for(i=0; i<nPage; i++){\n    Pgno n;\n    u8 e;\n    MemPage *pPage = apPage[i];\n    BtShared *pBt = pPage->pBt;\n    assert( pPage->isInit );\n\n    for(j=0; j<pPage->nCell; j++){\n      CellInfo info;\n      u8 *z;\n     \n      z = findCell(pPage, j);\n      pPage->xParseCell(pPage, z, &info);\n      if( info.nLocal<info.nPayload ){\n        Pgno ovfl = get4byte(&z[info.nSize-4]);\n        ptrmapGet(pBt, ovfl, &e, &n);\n        assert( n==pPage->pgno && e==PTRMAP_OVERFLOW1 );\n      }\n      if( !pPage->leaf ){\n        Pgno child = get4byte(z);\n        ptrmapGet(pBt, child, &e, &n);\n        assert( n==pPage->pgno && e==PTRMAP_BTREE );\n      }\n    }\n    if( !pPage->leaf ){\n      Pgno child = get4byte(&pPage->aData[pPage->hdrOffset+8]);\n      ptrmapGet(pBt, child, &e, &n);\n      assert( n==pPage->pgno && e==PTRMAP_BTREE );\n    }\n  }\n  return 1;\n}\n#endif\n\n/*\n** This function is used to copy the contents of the b-tree node stored \n** on page pFrom to page pTo. If page pFrom was not a leaf page, then\n** the pointer-map entries for each child page are updated so that the\n** parent page stored in the pointer map is page pTo. If pFrom contained\n** any cells with overflow page pointers, then the corresponding pointer\n** map entries are also updated so that the parent page is page pTo.\n**\n** If pFrom is currently carrying any overflow cells (entries in the\n** MemPage.apOvfl[] array), they are not copied to pTo. \n**\n** Before returning, page pTo is reinitialized using btreeInitPage().\n**\n** The performance of this function is not critical. It is only used by \n** the balance_shallower() and balance_deeper() procedures, neither of\n** which are called often under normal circumstances.\n*/\nstatic void copyNodeContent(MemPage *pFrom, MemPage *pTo, int *pRC){\n  if( (*pRC)==SQLITE_OK ){\n    BtShared * const pBt = pFrom->pBt;\n    u8 * const aFrom = pFrom->aData;\n    u8 * const aTo = pTo->aData;\n    int const iFromHdr = pFrom->hdrOffset;\n    int const iToHdr = ((pTo->pgno==1) ? 100 : 0);\n    int rc;\n    int iData;\n  \n  \n    assert( pFrom->isInit );\n    assert( pFrom->nFree>=iToHdr );\n    assert( get2byte(&aFrom[iFromHdr+5]) <= (int)pBt->usableSize );\n  \n    /* Copy the b-tree node content from page pFrom to page pTo. */\n    iData = get2byte(&aFrom[iFromHdr+5]);\n    memcpy(&aTo[iData], &aFrom[iData], pBt->usableSize-iData);\n    memcpy(&aTo[iToHdr], &aFrom[iFromHdr], pFrom->cellOffset + 2*pFrom->nCell);\n  \n    /* Reinitialize page pTo so that the contents of the MemPage structure\n    ** match the new data. The initialization of pTo can actually fail under\n    ** fairly obscure circumstances, even though it is a copy of initialized \n    ** page pFrom.\n    */\n    pTo->isInit = 0;\n    rc = btreeInitPage(pTo);\n    if( rc!=SQLITE_OK ){\n      *pRC = rc;\n      return;\n    }\n  \n    /* If this is an auto-vacuum database, update the pointer-map entries\n    ** for any b-tree or overflow pages that pTo now contains the pointers to.\n    */\n    if( ISAUTOVACUUM ){\n      *pRC = setChildPtrmaps(pTo);\n    }\n  }\n}\n\n/*\n** This routine redistributes cells on the iParentIdx'th child of pParent\n** (hereafter \"the page\") and up to 2 siblings so that all pages have about the\n** same amount of free space. Usually a single sibling on either side of the\n** page are used in the balancing, though both siblings might come from one\n** side if the page is the first or last child of its parent. If the page \n** has fewer than 2 siblings (something which can only happen if the page\n** is a root page or a child of a root page) then all available siblings\n** participate in the balancing.\n**\n** The number of siblings of the page might be increased or decreased by \n** one or two in an effort to keep pages nearly full but not over full. \n**\n** Note that when this routine is called, some of the cells on the page\n** might not actually be stored in MemPage.aData[]. This can happen\n** if the page is overfull. This routine ensures that all cells allocated\n** to the page and its siblings fit into MemPage.aData[] before returning.\n**\n** In the course of balancing the page and its siblings, cells may be\n** inserted into or removed from the parent page (pParent). Doing so\n** may cause the parent page to become overfull or underfull. If this\n** happens, it is the responsibility of the caller to invoke the correct\n** balancing routine to fix this problem (see the balance() routine). \n**\n** If this routine fails for any reason, it might leave the database\n** in a corrupted state. So if this routine fails, the database should\n** be rolled back.\n**\n** The third argument to this function, aOvflSpace, is a pointer to a\n** buffer big enough to hold one page. If while inserting cells into the parent\n** page (pParent) the parent page becomes overfull, this buffer is\n** used to store the parent's overflow cells. Because this function inserts\n** a maximum of four divider cells into the parent page, and the maximum\n** size of a cell stored within an internal node is always less than 1/4\n** of the page-size, the aOvflSpace[] buffer is guaranteed to be large\n** enough for all overflow cells.\n**\n** If aOvflSpace is set to a null pointer, this function returns \n** SQLITE_NOMEM.\n*/\nstatic int balance_nonroot(\n  MemPage *pParent,               /* Parent page of siblings being balanced */\n  int iParentIdx,                 /* Index of \"the page\" in pParent */\n  u8 *aOvflSpace,                 /* page-size bytes of space for parent ovfl */\n  int isRoot,                     /* True if pParent is a root-page */\n  int bBulk                       /* True if this call is part of a bulk load */\n){\n  BtShared *pBt;               /* The whole database */\n  int nMaxCells = 0;           /* Allocated size of apCell, szCell, aFrom. */\n  int nNew = 0;                /* Number of pages in apNew[] */\n  int nOld;                    /* Number of pages in apOld[] */\n  int i, j, k;                 /* Loop counters */\n  int nxDiv;                   /* Next divider slot in pParent->aCell[] */\n  int rc = SQLITE_OK;          /* The return code */\n  u16 leafCorrection;          /* 4 if pPage is a leaf.  0 if not */\n  int leafData;                /* True if pPage is a leaf of a LEAFDATA tree */\n  int usableSpace;             /* Bytes in pPage beyond the header */\n  int pageFlags;               /* Value of pPage->aData[0] */\n  int iSpace1 = 0;             /* First unused byte of aSpace1[] */\n  int iOvflSpace = 0;          /* First unused byte of aOvflSpace[] */\n  int szScratch;               /* Size of scratch memory requested */\n  MemPage *apOld[NB];          /* pPage and up to two siblings */\n  MemPage *apNew[NB+2];        /* pPage and up to NB siblings after balancing */\n  u8 *pRight;                  /* Location in parent of right-sibling pointer */\n  u8 *apDiv[NB-1];             /* Divider cells in pParent */\n  int cntNew[NB+2];            /* Index in b.paCell[] of cell after i-th page */\n  int cntOld[NB+2];            /* Old index in b.apCell[] */\n  int szNew[NB+2];             /* Combined size of cells placed on i-th page */\n  u8 *aSpace1;                 /* Space for copies of dividers cells */\n  Pgno pgno;                   /* Temp var to store a page number in */\n  u8 abDone[NB+2];             /* True after i'th new page is populated */\n  Pgno aPgno[NB+2];            /* Page numbers of new pages before shuffling */\n  Pgno aPgOrder[NB+2];         /* Copy of aPgno[] used for sorting pages */\n  u16 aPgFlags[NB+2];          /* flags field of new pages before shuffling */\n  CellArray b;                  /* Parsed information on cells being balanced */\n\n  memset(abDone, 0, sizeof(abDone));\n  b.nCell = 0;\n  b.apCell = 0;\n  pBt = pParent->pBt;\n  assert( sqlite3_mutex_held(pBt->mutex) );\n  assert( sqlite3PagerIswriteable(pParent->pDbPage) );\n\n#if 0\n  TRACE((\"BALANCE: begin page %d child of %d\\n\", pPage->pgno, pParent->pgno));\n#endif\n\n  /* At this point pParent may have at most one overflow cell. And if\n  ** this overflow cell is present, it must be the cell with \n  ** index iParentIdx. This scenario comes about when this function\n  ** is called (indirectly) from sqlite3BtreeDelete().\n  */\n  assert( pParent->nOverflow==0 || pParent->nOverflow==1 );\n  assert( pParent->nOverflow==0 || pParent->aiOvfl[0]==iParentIdx );\n\n  if( !aOvflSpace ){\n    return SQLITE_NOMEM_BKPT;\n  }\n\n  /* Find the sibling pages to balance. Also locate the cells in pParent \n  ** that divide the siblings. An attempt is made to find NN siblings on \n  ** either side of pPage. More siblings are taken from one side, however, \n  ** if there are fewer than NN siblings on the other side. If pParent\n  ** has NB or fewer children then all children of pParent are taken.  \n  **\n  ** This loop also drops the divider cells from the parent page. This\n  ** way, the remainder of the function does not have to deal with any\n  ** overflow cells in the parent page, since if any existed they will\n  ** have already been removed.\n  */\n  i = pParent->nOverflow + pParent->nCell;\n  if( i<2 ){\n    nxDiv = 0;\n  }else{\n    assert( bBulk==0 || bBulk==1 );\n    if( iParentIdx==0 ){                 \n      nxDiv = 0;\n    }else if( iParentIdx==i ){\n      nxDiv = i-2+bBulk;\n    }else{\n      nxDiv = iParentIdx-1;\n    }\n    i = 2-bBulk;\n  }\n  nOld = i+1;\n  if( (i+nxDiv-pParent->nOverflow)==pParent->nCell ){\n    pRight = &pParent->aData[pParent->hdrOffset+8];\n  }else{\n    pRight = findCell(pParent, i+nxDiv-pParent->nOverflow);\n  }\n  pgno = get4byte(pRight);\n  while( 1 ){\n    rc = getAndInitPage(pBt, pgno, &apOld[i], 0, 0);\n    if( rc ){\n      memset(apOld, 0, (i+1)*sizeof(MemPage*));\n      goto balance_cleanup;\n    }\n    nMaxCells += 1+apOld[i]->nCell+apOld[i]->nOverflow;\n    if( (i--)==0 ) break;\n\n    if( pParent->nOverflow && i+nxDiv==pParent->aiOvfl[0] ){\n      apDiv[i] = pParent->apOvfl[0];\n      pgno = get4byte(apDiv[i]);\n      szNew[i] = pParent->xCellSize(pParent, apDiv[i]);\n      pParent->nOverflow = 0;\n    }else{\n      apDiv[i] = findCell(pParent, i+nxDiv-pParent->nOverflow);\n      pgno = get4byte(apDiv[i]);\n      szNew[i] = pParent->xCellSize(pParent, apDiv[i]);\n\n      /* Drop the cell from the parent page. apDiv[i] still points to\n      ** the cell within the parent, even though it has been dropped.\n      ** This is safe because dropping a cell only overwrites the first\n      ** four bytes of it, and this function does not need the first\n      ** four bytes of the divider cell. So the pointer is safe to use\n      ** later on.  \n      **\n      ** But not if we are in secure-delete mode. In secure-delete mode,\n      ** the dropCell() routine will overwrite the entire cell with zeroes.\n      ** In this case, temporarily copy the cell into the aOvflSpace[]\n      ** buffer. It will be copied out again as soon as the aSpace[] buffer\n      ** is allocated.  */\n      if( pBt->btsFlags & BTS_FAST_SECURE ){\n        int iOff;\n\n        iOff = SQLITE_PTR_TO_INT(apDiv[i]) - SQLITE_PTR_TO_INT(pParent->aData);\n        if( (iOff+szNew[i])>(int)pBt->usableSize ){\n          rc = SQLITE_CORRUPT_BKPT;\n          memset(apOld, 0, (i+1)*sizeof(MemPage*));\n          goto balance_cleanup;\n        }else{\n          memcpy(&aOvflSpace[iOff], apDiv[i], szNew[i]);\n          apDiv[i] = &aOvflSpace[apDiv[i]-pParent->aData];\n        }\n      }\n      dropCell(pParent, i+nxDiv-pParent->nOverflow, szNew[i], &rc);\n    }\n  }\n\n  /* Make nMaxCells a multiple of 4 in order to preserve 8-byte\n  ** alignment */\n  nMaxCells = (nMaxCells + 3)&~3;\n\n  /*\n  ** Allocate space for memory structures\n  */\n  szScratch =\n       nMaxCells*sizeof(u8*)                       /* b.apCell */\n     + nMaxCells*sizeof(u16)                       /* b.szCell */\n     + pBt->pageSize;                              /* aSpace1 */\n\n  assert( szScratch<=6*(int)pBt->pageSize );\n  b.apCell = sqlite3StackAllocRaw(0, szScratch );\n  if( b.apCell==0 ){\n    rc = SQLITE_NOMEM_BKPT;\n    goto balance_cleanup;\n  }\n  b.szCell = (u16*)&b.apCell[nMaxCells];\n  aSpace1 = (u8*)&b.szCell[nMaxCells];\n  assert( EIGHT_BYTE_ALIGNMENT(aSpace1) );\n\n  /*\n  ** Load pointers to all cells on sibling pages and the divider cells\n  ** into the local b.apCell[] array.  Make copies of the divider cells\n  ** into space obtained from aSpace1[]. The divider cells have already\n  ** been removed from pParent.\n  **\n  ** If the siblings are on leaf pages, then the child pointers of the\n  ** divider cells are stripped from the cells before they are copied\n  ** into aSpace1[].  In this way, all cells in b.apCell[] are without\n  ** child pointers.  If siblings are not leaves, then all cell in\n  ** b.apCell[] include child pointers.  Either way, all cells in b.apCell[]\n  ** are alike.\n  **\n  ** leafCorrection:  4 if pPage is a leaf.  0 if pPage is not a leaf.\n  **       leafData:  1 if pPage holds key+data and pParent holds only keys.\n  */\n  b.pRef = apOld[0];\n  leafCorrection = b.pRef->leaf*4;\n  leafData = b.pRef->intKeyLeaf;\n  for(i=0; i<nOld; i++){\n    MemPage *pOld = apOld[i];\n    int limit = pOld->nCell;\n    u8 *aData = pOld->aData;\n    u16 maskPage = pOld->maskPage;\n    u8 *piCell = aData + pOld->cellOffset;\n    u8 *piEnd;\n\n    /* Verify that all sibling pages are of the same \"type\" (table-leaf,\n    ** table-interior, index-leaf, or index-interior).\n    */\n    if( pOld->aData[0]!=apOld[0]->aData[0] ){\n      rc = SQLITE_CORRUPT_BKPT;\n      goto balance_cleanup;\n    }\n\n    /* Load b.apCell[] with pointers to all cells in pOld.  If pOld\n    ** contains overflow cells, include them in the b.apCell[] array\n    ** in the correct spot.\n    **\n    ** Note that when there are multiple overflow cells, it is always the\n    ** case that they are sequential and adjacent.  This invariant arises\n    ** because multiple overflows can only occurs when inserting divider\n    ** cells into a parent on a prior balance, and divider cells are always\n    ** adjacent and are inserted in order.  There is an assert() tagged\n    ** with \"NOTE 1\" in the overflow cell insertion loop to prove this\n    ** invariant.\n    **\n    ** This must be done in advance.  Once the balance starts, the cell\n    ** offset section of the btree page will be overwritten and we will no\n    ** long be able to find the cells if a pointer to each cell is not saved\n    ** first.\n    */\n    memset(&b.szCell[b.nCell], 0, sizeof(b.szCell[0])*(limit+pOld->nOverflow));\n    if( pOld->nOverflow>0 ){\n      limit = pOld->aiOvfl[0];\n      for(j=0; j<limit; j++){\n        b.apCell[b.nCell] = aData + (maskPage & get2byteAligned(piCell));\n        piCell += 2;\n        b.nCell++;\n      }\n      for(k=0; k<pOld->nOverflow; k++){\n        assert( k==0 || pOld->aiOvfl[k-1]+1==pOld->aiOvfl[k] );/* NOTE 1 */\n        b.apCell[b.nCell] = pOld->apOvfl[k];\n        b.nCell++;\n      }\n    }\n    piEnd = aData + pOld->cellOffset + 2*pOld->nCell;\n    while( piCell<piEnd ){\n      assert( b.nCell<nMaxCells );\n      b.apCell[b.nCell] = aData + (maskPage & get2byteAligned(piCell));\n      piCell += 2;\n      b.nCell++;\n    }\n\n    cntOld[i] = b.nCell;\n    if( i<nOld-1 && !leafData){\n      u16 sz = (u16)szNew[i];\n      u8 *pTemp;\n      assert( b.nCell<nMaxCells );\n      b.szCell[b.nCell] = sz;\n      pTemp = &aSpace1[iSpace1];\n      iSpace1 += sz;\n      assert( sz<=pBt->maxLocal+23 );\n      assert( iSpace1 <= (int)pBt->pageSize );\n      memcpy(pTemp, apDiv[i], sz);\n      b.apCell[b.nCell] = pTemp+leafCorrection;\n      assert( leafCorrection==0 || leafCorrection==4 );\n      b.szCell[b.nCell] = b.szCell[b.nCell] - leafCorrection;\n      if( !pOld->leaf ){\n        assert( leafCorrection==0 );\n        assert( pOld->hdrOffset==0 );\n        /* The right pointer of the child page pOld becomes the left\n        ** pointer of the divider cell */\n        memcpy(b.apCell[b.nCell], &pOld->aData[8], 4);\n      }else{\n        assert( leafCorrection==4 );\n        while( b.szCell[b.nCell]<4 ){\n          /* Do not allow any cells smaller than 4 bytes. If a smaller cell\n          ** does exist, pad it with 0x00 bytes. */\n          assert( b.szCell[b.nCell]==3 || CORRUPT_DB );\n          assert( b.apCell[b.nCell]==&aSpace1[iSpace1-3] || CORRUPT_DB );\n          aSpace1[iSpace1++] = 0x00;\n          b.szCell[b.nCell]++;\n        }\n      }\n      b.nCell++;\n    }\n  }\n\n  /*\n  ** Figure out the number of pages needed to hold all b.nCell cells.\n  ** Store this number in \"k\".  Also compute szNew[] which is the total\n  ** size of all cells on the i-th page and cntNew[] which is the index\n  ** in b.apCell[] of the cell that divides page i from page i+1.  \n  ** cntNew[k] should equal b.nCell.\n  **\n  ** Values computed by this block:\n  **\n  **           k: The total number of sibling pages\n  **    szNew[i]: Spaced used on the i-th sibling page.\n  **   cntNew[i]: Index in b.apCell[] and b.szCell[] for the first cell to\n  **              the right of the i-th sibling page.\n  ** usableSpace: Number of bytes of space available on each sibling.\n  ** \n  */\n  usableSpace = pBt->usableSize - 12 + leafCorrection;\n  for(i=0; i<nOld; i++){\n    MemPage *p = apOld[i];\n    szNew[i] = usableSpace - p->nFree;\n    for(j=0; j<p->nOverflow; j++){\n      szNew[i] += 2 + p->xCellSize(p, p->apOvfl[j]);\n    }\n    cntNew[i] = cntOld[i];\n  }\n  k = nOld;\n  for(i=0; i<k; i++){\n    int sz;\n    while( szNew[i]>usableSpace ){\n      if( i+1>=k ){\n        k = i+2;\n        if( k>NB+2 ){ rc = SQLITE_CORRUPT_BKPT; goto balance_cleanup; }\n        szNew[k-1] = 0;\n        cntNew[k-1] = b.nCell;\n      }\n      sz = 2 + cachedCellSize(&b, cntNew[i]-1);\n      szNew[i] -= sz;\n      if( !leafData ){\n        if( cntNew[i]<b.nCell ){\n          sz = 2 + cachedCellSize(&b, cntNew[i]);\n        }else{\n          sz = 0;\n        }\n      }\n      szNew[i+1] += sz;\n      cntNew[i]--;\n    }\n    while( cntNew[i]<b.nCell ){\n      sz = 2 + cachedCellSize(&b, cntNew[i]);\n      if( szNew[i]+sz>usableSpace ) break;\n      szNew[i] += sz;\n      cntNew[i]++;\n      if( !leafData ){\n        if( cntNew[i]<b.nCell ){\n          sz = 2 + cachedCellSize(&b, cntNew[i]);\n        }else{\n          sz = 0;\n        }\n      }\n      szNew[i+1] -= sz;\n    }\n    if( cntNew[i]>=b.nCell ){\n      k = i+1;\n    }else if( cntNew[i] <= (i>0 ? cntNew[i-1] : 0) ){\n      rc = SQLITE_CORRUPT_BKPT;\n      goto balance_cleanup;\n    }\n  }\n\n  /*\n  ** The packing computed by the previous block is biased toward the siblings\n  ** on the left side (siblings with smaller keys). The left siblings are\n  ** always nearly full, while the right-most sibling might be nearly empty.\n  ** The next block of code attempts to adjust the packing of siblings to\n  ** get a better balance.\n  **\n  ** This adjustment is more than an optimization.  The packing above might\n  ** be so out of balance as to be illegal.  For example, the right-most\n  ** sibling might be completely empty.  This adjustment is not optional.\n  */\n  for(i=k-1; i>0; i--){\n    int szRight = szNew[i];  /* Size of sibling on the right */\n    int szLeft = szNew[i-1]; /* Size of sibling on the left */\n    int r;              /* Index of right-most cell in left sibling */\n    int d;              /* Index of first cell to the left of right sibling */\n\n    r = cntNew[i-1] - 1;\n    d = r + 1 - leafData;\n    (void)cachedCellSize(&b, d);\n    do{\n      assert( d<nMaxCells );\n      assert( r<nMaxCells );\n      (void)cachedCellSize(&b, r);\n      if( szRight!=0\n       && (bBulk || szRight+b.szCell[d]+2 > szLeft-(b.szCell[r]+(i==k-1?0:2)))){\n        break;\n      }\n      szRight += b.szCell[d] + 2;\n      szLeft -= b.szCell[r] + 2;\n      cntNew[i-1] = r;\n      r--;\n      d--;\n    }while( r>=0 );\n    szNew[i] = szRight;\n    szNew[i-1] = szLeft;\n    if( cntNew[i-1] <= (i>1 ? cntNew[i-2] : 0) ){\n      rc = SQLITE_CORRUPT_BKPT;\n      goto balance_cleanup;\n    }\n  }\n\n  /* Sanity check:  For a non-corrupt database file one of the follwing\n  ** must be true:\n  **    (1) We found one or more cells (cntNew[0])>0), or\n  **    (2) pPage is a virtual root page.  A virtual root page is when\n  **        the real root page is page 1 and we are the only child of\n  **        that page.\n  */\n  assert( cntNew[0]>0 || (pParent->pgno==1 && pParent->nCell==0) || CORRUPT_DB);\n  TRACE((\"BALANCE: old: %d(nc=%d) %d(nc=%d) %d(nc=%d)\\n\",\n    apOld[0]->pgno, apOld[0]->nCell,\n    nOld>=2 ? apOld[1]->pgno : 0, nOld>=2 ? apOld[1]->nCell : 0,\n    nOld>=3 ? apOld[2]->pgno : 0, nOld>=3 ? apOld[2]->nCell : 0\n  ));\n\n  /*\n  ** Allocate k new pages.  Reuse old pages where possible.\n  */\n  pageFlags = apOld[0]->aData[0];\n  for(i=0; i<k; i++){\n    MemPage *pNew;\n    if( i<nOld ){\n      pNew = apNew[i] = apOld[i];\n      apOld[i] = 0;\n      rc = sqlite3PagerWrite(pNew->pDbPage);\n      nNew++;\n      if( rc ) goto balance_cleanup;\n    }else{\n      assert( i>0 );\n      rc = allocateBtreePage(pBt, &pNew, &pgno, (bBulk ? 1 : pgno), 0);\n      if( rc ) goto balance_cleanup;\n      zeroPage(pNew, pageFlags);\n      apNew[i] = pNew;\n      nNew++;\n      cntOld[i] = b.nCell;\n\n      /* Set the pointer-map entry for the new sibling page. */\n      if( ISAUTOVACUUM ){\n        ptrmapPut(pBt, pNew->pgno, PTRMAP_BTREE, pParent->pgno, &rc);\n        if( rc!=SQLITE_OK ){\n          goto balance_cleanup;\n        }\n      }\n    }\n  }\n\n  /*\n  ** Reassign page numbers so that the new pages are in ascending order. \n  ** This helps to keep entries in the disk file in order so that a scan\n  ** of the table is closer to a linear scan through the file. That in turn \n  ** helps the operating system to deliver pages from the disk more rapidly.\n  **\n  ** An O(n^2) insertion sort algorithm is used, but since n is never more \n  ** than (NB+2) (a small constant), that should not be a problem.\n  **\n  ** When NB==3, this one optimization makes the database about 25% faster \n  ** for large insertions and deletions.\n  */\n  for(i=0; i<nNew; i++){\n    aPgOrder[i] = aPgno[i] = apNew[i]->pgno;\n    aPgFlags[i] = apNew[i]->pDbPage->flags;\n    for(j=0; j<i; j++){\n      if( aPgno[j]==aPgno[i] ){\n        /* This branch is taken if the set of sibling pages somehow contains\n        ** duplicate entries. This can happen if the database is corrupt. \n        ** It would be simpler to detect this as part of the loop below, but\n        ** we do the detection here in order to avoid populating the pager\n        ** cache with two separate objects associated with the same\n        ** page number.  */\n        assert( CORRUPT_DB );\n        rc = SQLITE_CORRUPT_BKPT;\n        goto balance_cleanup;\n      }\n    }\n  }\n  for(i=0; i<nNew; i++){\n    int iBest = 0;                /* aPgno[] index of page number to use */\n    for(j=1; j<nNew; j++){\n      if( aPgOrder[j]<aPgOrder[iBest] ) iBest = j;\n    }\n    pgno = aPgOrder[iBest];\n    aPgOrder[iBest] = 0xffffffff;\n    if( iBest!=i ){\n      if( iBest>i ){\n        sqlite3PagerRekey(apNew[iBest]->pDbPage, pBt->nPage+iBest+1, 0);\n      }\n      sqlite3PagerRekey(apNew[i]->pDbPage, pgno, aPgFlags[iBest]);\n      apNew[i]->pgno = pgno;\n    }\n  }\n\n  TRACE((\"BALANCE: new: %d(%d nc=%d) %d(%d nc=%d) %d(%d nc=%d) \"\n         \"%d(%d nc=%d) %d(%d nc=%d)\\n\",\n    apNew[0]->pgno, szNew[0], cntNew[0],\n    nNew>=2 ? apNew[1]->pgno : 0, nNew>=2 ? szNew[1] : 0,\n    nNew>=2 ? cntNew[1] - cntNew[0] - !leafData : 0,\n    nNew>=3 ? apNew[2]->pgno : 0, nNew>=3 ? szNew[2] : 0,\n    nNew>=3 ? cntNew[2] - cntNew[1] - !leafData : 0,\n    nNew>=4 ? apNew[3]->pgno : 0, nNew>=4 ? szNew[3] : 0,\n    nNew>=4 ? cntNew[3] - cntNew[2] - !leafData : 0,\n    nNew>=5 ? apNew[4]->pgno : 0, nNew>=5 ? szNew[4] : 0,\n    nNew>=5 ? cntNew[4] - cntNew[3] - !leafData : 0\n  ));\n\n  assert( sqlite3PagerIswriteable(pParent->pDbPage) );\n  put4byte(pRight, apNew[nNew-1]->pgno);\n\n  /* If the sibling pages are not leaves, ensure that the right-child pointer\n  ** of the right-most new sibling page is set to the value that was \n  ** originally in the same field of the right-most old sibling page. */\n  if( (pageFlags & PTF_LEAF)==0 && nOld!=nNew ){\n    MemPage *pOld = (nNew>nOld ? apNew : apOld)[nOld-1];\n    memcpy(&apNew[nNew-1]->aData[8], &pOld->aData[8], 4);\n  }\n\n  /* Make any required updates to pointer map entries associated with \n  ** cells stored on sibling pages following the balance operation. Pointer\n  ** map entries associated with divider cells are set by the insertCell()\n  ** routine. The associated pointer map entries are:\n  **\n  **   a) if the cell contains a reference to an overflow chain, the\n  **      entry associated with the first page in the overflow chain, and\n  **\n  **   b) if the sibling pages are not leaves, the child page associated\n  **      with the cell.\n  **\n  ** If the sibling pages are not leaves, then the pointer map entry \n  ** associated with the right-child of each sibling may also need to be \n  ** updated. This happens below, after the sibling pages have been \n  ** populated, not here.\n  */\n  if( ISAUTOVACUUM ){\n    MemPage *pNew = apNew[0];\n    u8 *aOld = pNew->aData;\n    int cntOldNext = pNew->nCell + pNew->nOverflow;\n    int usableSize = pBt->usableSize;\n    int iNew = 0;\n    int iOld = 0;\n\n    for(i=0; i<b.nCell; i++){\n      u8 *pCell = b.apCell[i];\n      if( i==cntOldNext ){\n        MemPage *pOld = (++iOld)<nNew ? apNew[iOld] : apOld[iOld];\n        cntOldNext += pOld->nCell + pOld->nOverflow + !leafData;\n        aOld = pOld->aData;\n      }\n      if( i==cntNew[iNew] ){\n        pNew = apNew[++iNew];\n        if( !leafData ) continue;\n      }\n\n      /* Cell pCell is destined for new sibling page pNew. Originally, it\n      ** was either part of sibling page iOld (possibly an overflow cell), \n      ** or else the divider cell to the left of sibling page iOld. So,\n      ** if sibling page iOld had the same page number as pNew, and if\n      ** pCell really was a part of sibling page iOld (not a divider or\n      ** overflow cell), we can skip updating the pointer map entries.  */\n      if( iOld>=nNew\n       || pNew->pgno!=aPgno[iOld]\n       || !SQLITE_WITHIN(pCell,aOld,&aOld[usableSize])\n      ){\n        if( !leafCorrection ){\n          ptrmapPut(pBt, get4byte(pCell), PTRMAP_BTREE, pNew->pgno, &rc);\n        }\n        if( cachedCellSize(&b,i)>pNew->minLocal ){\n          ptrmapPutOvflPtr(pNew, pCell, &rc);\n        }\n        if( rc ) goto balance_cleanup;\n      }\n    }\n  }\n\n  /* Insert new divider cells into pParent. */\n  for(i=0; i<nNew-1; i++){\n    u8 *pCell;\n    u8 *pTemp;\n    int sz;\n    MemPage *pNew = apNew[i];\n    j = cntNew[i];\n\n    assert( j<nMaxCells );\n    assert( b.apCell[j]!=0 );\n    pCell = b.apCell[j];\n    sz = b.szCell[j] + leafCorrection;\n    pTemp = &aOvflSpace[iOvflSpace];\n    if( !pNew->leaf ){\n      memcpy(&pNew->aData[8], pCell, 4);\n    }else if( leafData ){\n      /* If the tree is a leaf-data tree, and the siblings are leaves, \n      ** then there is no divider cell in b.apCell[]. Instead, the divider \n      ** cell consists of the integer key for the right-most cell of \n      ** the sibling-page assembled above only.\n      */\n      CellInfo info;\n      j--;\n      pNew->xParseCell(pNew, b.apCell[j], &info);\n      pCell = pTemp;\n      sz = 4 + putVarint(&pCell[4], info.nKey);\n      pTemp = 0;\n    }else{\n      pCell -= 4;\n      /* Obscure case for non-leaf-data trees: If the cell at pCell was\n      ** previously stored on a leaf node, and its reported size was 4\n      ** bytes, then it may actually be smaller than this \n      ** (see btreeParseCellPtr(), 4 bytes is the minimum size of\n      ** any cell). But it is important to pass the correct size to \n      ** insertCell(), so reparse the cell now.\n      **\n      ** This can only happen for b-trees used to evaluate \"IN (SELECT ...)\"\n      ** and WITHOUT ROWID tables with exactly one column which is the\n      ** primary key.\n      */\n      if( b.szCell[j]==4 ){\n        assert(leafCorrection==4);\n        sz = pParent->xCellSize(pParent, pCell);\n      }\n    }\n    iOvflSpace += sz;\n    assert( sz<=pBt->maxLocal+23 );\n    assert( iOvflSpace <= (int)pBt->pageSize );\n    insertCell(pParent, nxDiv+i, pCell, sz, pTemp, pNew->pgno, &rc);\n    if( rc!=SQLITE_OK ) goto balance_cleanup;\n    assert( sqlite3PagerIswriteable(pParent->pDbPage) );\n  }\n\n  /* Now update the actual sibling pages. The order in which they are updated\n  ** is important, as this code needs to avoid disrupting any page from which\n  ** cells may still to be read. In practice, this means:\n  **\n  **  (1) If cells are moving left (from apNew[iPg] to apNew[iPg-1])\n  **      then it is not safe to update page apNew[iPg] until after\n  **      the left-hand sibling apNew[iPg-1] has been updated.\n  **\n  **  (2) If cells are moving right (from apNew[iPg] to apNew[iPg+1])\n  **      then it is not safe to update page apNew[iPg] until after\n  **      the right-hand sibling apNew[iPg+1] has been updated.\n  **\n  ** If neither of the above apply, the page is safe to update.\n  **\n  ** The iPg value in the following loop starts at nNew-1 goes down\n  ** to 0, then back up to nNew-1 again, thus making two passes over\n  ** the pages.  On the initial downward pass, only condition (1) above\n  ** needs to be tested because (2) will always be true from the previous\n  ** step.  On the upward pass, both conditions are always true, so the\n  ** upwards pass simply processes pages that were missed on the downward\n  ** pass.\n  */\n  for(i=1-nNew; i<nNew; i++){\n    int iPg = i<0 ? -i : i;\n    assert( iPg>=0 && iPg<nNew );\n    if( abDone[iPg] ) continue;         /* Skip pages already processed */\n    if( i>=0                            /* On the upwards pass, or... */\n     || cntOld[iPg-1]>=cntNew[iPg-1]    /* Condition (1) is true */\n    ){\n      int iNew;\n      int iOld;\n      int nNewCell;\n\n      /* Verify condition (1):  If cells are moving left, update iPg\n      ** only after iPg-1 has already been updated. */\n      assert( iPg==0 || cntOld[iPg-1]>=cntNew[iPg-1] || abDone[iPg-1] );\n\n      /* Verify condition (2):  If cells are moving right, update iPg\n      ** only after iPg+1 has already been updated. */\n      assert( cntNew[iPg]>=cntOld[iPg] || abDone[iPg+1] );\n\n      if( iPg==0 ){\n        iNew = iOld = 0;\n        nNewCell = cntNew[0];\n      }else{\n        iOld = iPg<nOld ? (cntOld[iPg-1] + !leafData) : b.nCell;\n        iNew = cntNew[iPg-1] + !leafData;\n        nNewCell = cntNew[iPg] - iNew;\n      }\n\n      rc = editPage(apNew[iPg], iOld, iNew, nNewCell, &b);\n      if( rc ) goto balance_cleanup;\n      abDone[iPg]++;\n      apNew[iPg]->nFree = usableSpace-szNew[iPg];\n      assert( apNew[iPg]->nOverflow==0 );\n      assert( apNew[iPg]->nCell==nNewCell );\n    }\n  }\n\n  /* All pages have been processed exactly once */\n  assert( memcmp(abDone, \"\\01\\01\\01\\01\\01\", nNew)==0 );\n\n  assert( nOld>0 );\n  assert( nNew>0 );\n\n  if( isRoot && pParent->nCell==0 && pParent->hdrOffset<=apNew[0]->nFree ){\n    /* The root page of the b-tree now contains no cells. The only sibling\n    ** page is the right-child of the parent. Copy the contents of the\n    ** child page into the parent, decreasing the overall height of the\n    ** b-tree structure by one. This is described as the \"balance-shallower\"\n    ** sub-algorithm in some documentation.\n    **\n    ** If this is an auto-vacuum database, the call to copyNodeContent() \n    ** sets all pointer-map entries corresponding to database image pages \n    ** for which the pointer is stored within the content being copied.\n    **\n    ** It is critical that the child page be defragmented before being\n    ** copied into the parent, because if the parent is page 1 then it will\n    ** by smaller than the child due to the database header, and so all the\n    ** free space needs to be up front.\n    */\n    assert( nNew==1 || CORRUPT_DB );\n    rc = defragmentPage(apNew[0], -1);\n    testcase( rc!=SQLITE_OK );\n    assert( apNew[0]->nFree == \n        (get2byte(&apNew[0]->aData[5])-apNew[0]->cellOffset-apNew[0]->nCell*2)\n      || rc!=SQLITE_OK\n    );\n    copyNodeContent(apNew[0], pParent, &rc);\n    freePage(apNew[0], &rc);\n  }else if( ISAUTOVACUUM && !leafCorrection ){\n    /* Fix the pointer map entries associated with the right-child of each\n    ** sibling page. All other pointer map entries have already been taken\n    ** care of.  */\n    for(i=0; i<nNew; i++){\n      u32 key = get4byte(&apNew[i]->aData[8]);\n      ptrmapPut(pBt, key, PTRMAP_BTREE, apNew[i]->pgno, &rc);\n    }\n  }\n\n  assert( pParent->isInit );\n  TRACE((\"BALANCE: finished: old=%d new=%d cells=%d\\n\",\n          nOld, nNew, b.nCell));\n\n  /* Free any old pages that were not reused as new pages.\n  */\n  for(i=nNew; i<nOld; i++){\n    freePage(apOld[i], &rc);\n  }\n\n#if 0\n  if( ISAUTOVACUUM && rc==SQLITE_OK && apNew[0]->isInit ){\n    /* The ptrmapCheckPages() contains assert() statements that verify that\n    ** all pointer map pages are set correctly. This is helpful while \n    ** debugging. This is usually disabled because a corrupt database may\n    ** cause an assert() statement to fail.  */\n    ptrmapCheckPages(apNew, nNew);\n    ptrmapCheckPages(&pParent, 1);\n  }\n#endif\n\n  /*\n  ** Cleanup before returning.\n  */\nbalance_cleanup:\n  sqlite3StackFree(0, b.apCell);\n  for(i=0; i<nOld; i++){\n    releasePage(apOld[i]);\n  }\n  for(i=0; i<nNew; i++){\n    releasePage(apNew[i]);\n  }\n\n  return rc;\n}\n\n\n/*\n** This function is called when the root page of a b-tree structure is\n** overfull (has one or more overflow pages).\n**\n** A new child page is allocated and the contents of the current root\n** page, including overflow cells, are copied into the child. The root\n** page is then overwritten to make it an empty page with the right-child \n** pointer pointing to the new page.\n**\n** Before returning, all pointer-map entries corresponding to pages \n** that the new child-page now contains pointers to are updated. The\n** entry corresponding to the new right-child pointer of the root\n** page is also updated.\n**\n** If successful, *ppChild is set to contain a reference to the child \n** page and SQLITE_OK is returned. In this case the caller is required\n** to call releasePage() on *ppChild exactly once. If an error occurs,\n** an error code is returned and *ppChild is set to 0.\n*/\nstatic int balance_deeper(MemPage *pRoot, MemPage **ppChild){\n  int rc;                        /* Return value from subprocedures */\n  MemPage *pChild = 0;           /* Pointer to a new child page */\n  Pgno pgnoChild = 0;            /* Page number of the new child page */\n  BtShared *pBt = pRoot->pBt;    /* The BTree */\n\n  assert( pRoot->nOverflow>0 );\n  assert( sqlite3_mutex_held(pBt->mutex) );\n\n  /* Make pRoot, the root page of the b-tree, writable. Allocate a new \n  ** page that will become the new right-child of pPage. Copy the contents\n  ** of the node stored on pRoot into the new child page.\n  */\n  rc = sqlite3PagerWrite(pRoot->pDbPage);\n  if( rc==SQLITE_OK ){\n    rc = allocateBtreePage(pBt,&pChild,&pgnoChild,pRoot->pgno,0);\n    copyNodeContent(pRoot, pChild, &rc);\n    if( ISAUTOVACUUM ){\n      ptrmapPut(pBt, pgnoChild, PTRMAP_BTREE, pRoot->pgno, &rc);\n    }\n  }\n  if( rc ){\n    *ppChild = 0;\n    releasePage(pChild);\n    return rc;\n  }\n  assert( sqlite3PagerIswriteable(pChild->pDbPage) );\n  assert( sqlite3PagerIswriteable(pRoot->pDbPage) );\n  assert( pChild->nCell==pRoot->nCell );\n\n  TRACE((\"BALANCE: copy root %d into %d\\n\", pRoot->pgno, pChild->pgno));\n\n  /* Copy the overflow cells from pRoot to pChild */\n  memcpy(pChild->aiOvfl, pRoot->aiOvfl,\n         pRoot->nOverflow*sizeof(pRoot->aiOvfl[0]));\n  memcpy(pChild->apOvfl, pRoot->apOvfl,\n         pRoot->nOverflow*sizeof(pRoot->apOvfl[0]));\n  pChild->nOverflow = pRoot->nOverflow;\n\n  /* Zero the contents of pRoot. Then install pChild as the right-child. */\n  zeroPage(pRoot, pChild->aData[0] & ~PTF_LEAF);\n  put4byte(&pRoot->aData[pRoot->hdrOffset+8], pgnoChild);\n\n  *ppChild = pChild;\n  return SQLITE_OK;\n}\n\n/*\n** The page that pCur currently points to has just been modified in\n** some way. This function figures out if this modification means the\n** tree needs to be balanced, and if so calls the appropriate balancing \n** routine. Balancing routines are:\n**\n**   balance_quick()\n**   balance_deeper()\n**   balance_nonroot()\n*/\nstatic int balance(BtCursor *pCur){\n  int rc = SQLITE_OK;\n  const int nMin = pCur->pBt->usableSize * 2 / 3;\n  u8 aBalanceQuickSpace[13];\n  u8 *pFree = 0;\n\n  VVA_ONLY( int balance_quick_called = 0 );\n  VVA_ONLY( int balance_deeper_called = 0 );\n\n  do {\n    int iPage = pCur->iPage;\n    MemPage *pPage = pCur->pPage;\n\n    if( iPage==0 ){\n      if( pPage->nOverflow ){\n        /* The root page of the b-tree is overfull. In this case call the\n        ** balance_deeper() function to create a new child for the root-page\n        ** and copy the current contents of the root-page to it. The\n        ** next iteration of the do-loop will balance the child page.\n        */ \n        assert( balance_deeper_called==0 );\n        VVA_ONLY( balance_deeper_called++ );\n        rc = balance_deeper(pPage, &pCur->apPage[1]);\n        if( rc==SQLITE_OK ){\n          pCur->iPage = 1;\n          pCur->ix = 0;\n          pCur->aiIdx[0] = 0;\n          pCur->apPage[0] = pPage;\n          pCur->pPage = pCur->apPage[1];\n          assert( pCur->pPage->nOverflow );\n        }\n      }else{\n        break;\n      }\n    }else if( pPage->nOverflow==0 && pPage->nFree<=nMin ){\n      break;\n    }else{\n      MemPage * const pParent = pCur->apPage[iPage-1];\n      int const iIdx = pCur->aiIdx[iPage-1];\n\n      rc = sqlite3PagerWrite(pParent->pDbPage);\n      if( rc==SQLITE_OK ){\n#ifndef SQLITE_OMIT_QUICKBALANCE\n        if( pPage->intKeyLeaf\n         && pPage->nOverflow==1\n         && pPage->aiOvfl[0]==pPage->nCell\n         && pParent->pgno!=1\n         && pParent->nCell==iIdx\n        ){\n          /* Call balance_quick() to create a new sibling of pPage on which\n          ** to store the overflow cell. balance_quick() inserts a new cell\n          ** into pParent, which may cause pParent overflow. If this\n          ** happens, the next iteration of the do-loop will balance pParent \n          ** use either balance_nonroot() or balance_deeper(). Until this\n          ** happens, the overflow cell is stored in the aBalanceQuickSpace[]\n          ** buffer. \n          **\n          ** The purpose of the following assert() is to check that only a\n          ** single call to balance_quick() is made for each call to this\n          ** function. If this were not verified, a subtle bug involving reuse\n          ** of the aBalanceQuickSpace[] might sneak in.\n          */\n          assert( balance_quick_called==0 ); \n          VVA_ONLY( balance_quick_called++ );\n          rc = balance_quick(pParent, pPage, aBalanceQuickSpace);\n        }else\n#endif\n        {\n          /* In this case, call balance_nonroot() to redistribute cells\n          ** between pPage and up to 2 of its sibling pages. This involves\n          ** modifying the contents of pParent, which may cause pParent to\n          ** become overfull or underfull. The next iteration of the do-loop\n          ** will balance the parent page to correct this.\n          ** \n          ** If the parent page becomes overfull, the overflow cell or cells\n          ** are stored in the pSpace buffer allocated immediately below. \n          ** A subsequent iteration of the do-loop will deal with this by\n          ** calling balance_nonroot() (balance_deeper() may be called first,\n          ** but it doesn't deal with overflow cells - just moves them to a\n          ** different page). Once this subsequent call to balance_nonroot() \n          ** has completed, it is safe to release the pSpace buffer used by\n          ** the previous call, as the overflow cell data will have been \n          ** copied either into the body of a database page or into the new\n          ** pSpace buffer passed to the latter call to balance_nonroot().\n          */\n          u8 *pSpace = sqlite3PageMalloc(pCur->pBt->pageSize);\n          rc = balance_nonroot(pParent, iIdx, pSpace, iPage==1,\n                               pCur->hints&BTREE_BULKLOAD);\n          if( pFree ){\n            /* If pFree is not NULL, it points to the pSpace buffer used \n            ** by a previous call to balance_nonroot(). Its contents are\n            ** now stored either on real database pages or within the \n            ** new pSpace buffer, so it may be safely freed here. */\n            sqlite3PageFree(pFree);\n          }\n\n          /* The pSpace buffer will be freed after the next call to\n          ** balance_nonroot(), or just before this function returns, whichever\n          ** comes first. */\n          pFree = pSpace;\n        }\n      }\n\n      pPage->nOverflow = 0;\n\n      /* The next iteration of the do-loop balances the parent page. */\n      releasePage(pPage);\n      pCur->iPage--;\n      assert( pCur->iPage>=0 );\n      pCur->pPage = pCur->apPage[pCur->iPage];\n    }\n  }while( rc==SQLITE_OK );\n\n  if( pFree ){\n    sqlite3PageFree(pFree);\n  }\n  return rc;\n}\n\n\n/*\n** Insert a new record into the BTree.  The content of the new record\n** is described by the pX object.  The pCur cursor is used only to\n** define what table the record should be inserted into, and is left\n** pointing at a random location.\n**\n** For a table btree (used for rowid tables), only the pX.nKey value of\n** the key is used. The pX.pKey value must be NULL.  The pX.nKey is the\n** rowid or INTEGER PRIMARY KEY of the row.  The pX.nData,pData,nZero fields\n** hold the content of the row.\n**\n** For an index btree (used for indexes and WITHOUT ROWID tables), the\n** key is an arbitrary byte sequence stored in pX.pKey,nKey.  The \n** pX.pData,nData,nZero fields must be zero.\n**\n** If the seekResult parameter is non-zero, then a successful call to\n** MovetoUnpacked() to seek cursor pCur to (pKey,nKey) has already\n** been performed.  In other words, if seekResult!=0 then the cursor\n** is currently pointing to a cell that will be adjacent to the cell\n** to be inserted.  If seekResult<0 then pCur points to a cell that is\n** smaller then (pKey,nKey).  If seekResult>0 then pCur points to a cell\n** that is larger than (pKey,nKey).\n**\n** If seekResult==0, that means pCur is pointing at some unknown location.\n** In that case, this routine must seek the cursor to the correct insertion\n** point for (pKey,nKey) before doing the insertion.  For index btrees,\n** if pX->nMem is non-zero, then pX->aMem contains pointers to the unpacked\n** key values and pX->aMem can be used instead of pX->pKey to avoid having\n** to decode the key.\n*/\nSQLITE_PRIVATE int sqlite3BtreeInsert(\n  BtCursor *pCur,                /* Insert data into the table of this cursor */\n  const BtreePayload *pX,        /* Content of the row to be inserted */\n  int flags,                     /* True if this is likely an append */\n  int seekResult                 /* Result of prior MovetoUnpacked() call */\n){\n  int rc;\n  int loc = seekResult;          /* -1: before desired location  +1: after */\n  int szNew = 0;\n  int idx;\n  MemPage *pPage;\n  Btree *p = pCur->pBtree;\n  BtShared *pBt = p->pBt;\n  unsigned char *oldCell;\n  unsigned char *newCell = 0;\n\n  assert( (flags & (BTREE_SAVEPOSITION|BTREE_APPEND))==flags );\n\n  if( pCur->eState==CURSOR_FAULT ){\n    assert( pCur->skipNext!=SQLITE_OK );\n    return pCur->skipNext;\n  }\n\n  assert( cursorOwnsBtShared(pCur) );\n  assert( (pCur->curFlags & BTCF_WriteFlag)!=0\n              && pBt->inTransaction==TRANS_WRITE\n              && (pBt->btsFlags & BTS_READ_ONLY)==0 );\n  assert( hasSharedCacheTableLock(p, pCur->pgnoRoot, pCur->pKeyInfo!=0, 2) );\n\n  /* Assert that the caller has been consistent. If this cursor was opened\n  ** expecting an index b-tree, then the caller should be inserting blob\n  ** keys with no associated data. If the cursor was opened expecting an\n  ** intkey table, the caller should be inserting integer keys with a\n  ** blob of associated data.  */\n  assert( (pX->pKey==0)==(pCur->pKeyInfo==0) );\n\n  /* Save the positions of any other cursors open on this table.\n  **\n  ** In some cases, the call to btreeMoveto() below is a no-op. For\n  ** example, when inserting data into a table with auto-generated integer\n  ** keys, the VDBE layer invokes sqlite3BtreeLast() to figure out the \n  ** integer key to use. It then calls this function to actually insert the \n  ** data into the intkey B-Tree. In this case btreeMoveto() recognizes\n  ** that the cursor is already where it needs to be and returns without\n  ** doing any work. To avoid thwarting these optimizations, it is important\n  ** not to clear the cursor here.\n  */\n  if( pCur->curFlags & BTCF_Multiple ){\n    rc = saveAllCursors(pBt, pCur->pgnoRoot, pCur);\n    if( rc ) return rc;\n  }\n\n  if( pCur->pKeyInfo==0 ){\n    assert( pX->pKey==0 );\n    /* If this is an insert into a table b-tree, invalidate any incrblob \n    ** cursors open on the row being replaced */\n    invalidateIncrblobCursors(p, pCur->pgnoRoot, pX->nKey, 0);\n\n    /* If BTREE_SAVEPOSITION is set, the cursor must already be pointing \n    ** to a row with the same key as the new entry being inserted.  */\n    assert( (flags & BTREE_SAVEPOSITION)==0 || \n            ((pCur->curFlags&BTCF_ValidNKey)!=0 && pX->nKey==pCur->info.nKey) );\n\n    /* If the cursor is currently on the last row and we are appending a\n    ** new row onto the end, set the \"loc\" to avoid an unnecessary\n    ** btreeMoveto() call */\n    if( (pCur->curFlags&BTCF_ValidNKey)!=0 && pX->nKey==pCur->info.nKey ){\n      loc = 0;\n    }else if( loc==0 ){\n      rc = sqlite3BtreeMovetoUnpacked(pCur, 0, pX->nKey, flags!=0, &loc);\n      if( rc ) return rc;\n    }\n  }else if( loc==0 && (flags & BTREE_SAVEPOSITION)==0 ){\n    if( pX->nMem ){\n      UnpackedRecord r;\n      r.pKeyInfo = pCur->pKeyInfo;\n      r.aMem = pX->aMem;\n      r.nField = pX->nMem;\n      r.default_rc = 0;\n      r.errCode = 0;\n      r.r1 = 0;\n      r.r2 = 0;\n      r.eqSeen = 0;\n      rc = sqlite3BtreeMovetoUnpacked(pCur, &r, 0, flags!=0, &loc);\n    }else{\n      rc = btreeMoveto(pCur, pX->pKey, pX->nKey, flags!=0, &loc);\n    }\n    if( rc ) return rc;\n  }\n  assert( pCur->eState==CURSOR_VALID || (pCur->eState==CURSOR_INVALID && loc) );\n\n  pPage = pCur->pPage;\n  assert( pPage->intKey || pX->nKey>=0 );\n  assert( pPage->leaf || !pPage->intKey );\n\n  TRACE((\"INSERT: table=%d nkey=%lld ndata=%d page=%d %s\\n\",\n          pCur->pgnoRoot, pX->nKey, pX->nData, pPage->pgno,\n          loc==0 ? \"overwrite\" : \"new entry\"));\n  assert( pPage->isInit );\n  newCell = pBt->pTmpSpace;\n  assert( newCell!=0 );\n  rc = fillInCell(pPage, newCell, pX, &szNew);\n  if( rc ) goto end_insert;\n  assert( szNew==pPage->xCellSize(pPage, newCell) );\n  assert( szNew <= MX_CELL_SIZE(pBt) );\n  idx = pCur->ix;\n  if( loc==0 ){\n    CellInfo info;\n    assert( idx<pPage->nCell );\n    rc = sqlite3PagerWrite(pPage->pDbPage);\n    if( rc ){\n      goto end_insert;\n    }\n    oldCell = findCell(pPage, idx);\n    if( !pPage->leaf ){\n      memcpy(newCell, oldCell, 4);\n    }\n    rc = clearCell(pPage, oldCell, &info);\n    if( info.nSize==szNew && info.nLocal==info.nPayload \n     && (!ISAUTOVACUUM || szNew<pPage->minLocal)\n    ){\n      /* Overwrite the old cell with the new if they are the same size.\n      ** We could also try to do this if the old cell is smaller, then add\n      ** the leftover space to the free list.  But experiments show that\n      ** doing that is no faster then skipping this optimization and just\n      ** calling dropCell() and insertCell(). \n      **\n      ** This optimization cannot be used on an autovacuum database if the\n      ** new entry uses overflow pages, as the insertCell() call below is\n      ** necessary to add the PTRMAP_OVERFLOW1 pointer-map entry.  */\n      assert( rc==SQLITE_OK ); /* clearCell never fails when nLocal==nPayload */\n      if( oldCell+szNew > pPage->aDataEnd ) return SQLITE_CORRUPT_BKPT;\n      memcpy(oldCell, newCell, szNew);\n      return SQLITE_OK;\n    }\n    dropCell(pPage, idx, info.nSize, &rc);\n    if( rc ) goto end_insert;\n  }else if( loc<0 && pPage->nCell>0 ){\n    assert( pPage->leaf );\n    idx = ++pCur->ix;\n    pCur->curFlags &= ~BTCF_ValidNKey;\n  }else{\n    assert( pPage->leaf );\n  }\n  insertCell(pPage, idx, newCell, szNew, 0, 0, &rc);\n  assert( pPage->nOverflow==0 || rc==SQLITE_OK );\n  assert( rc!=SQLITE_OK || pPage->nCell>0 || pPage->nOverflow>0 );\n\n  /* If no error has occurred and pPage has an overflow cell, call balance() \n  ** to redistribute the cells within the tree. Since balance() may move\n  ** the cursor, zero the BtCursor.info.nSize and BTCF_ValidNKey\n  ** variables.\n  **\n  ** Previous versions of SQLite called moveToRoot() to move the cursor\n  ** back to the root page as balance() used to invalidate the contents\n  ** of BtCursor.apPage[] and BtCursor.aiIdx[]. Instead of doing that,\n  ** set the cursor state to \"invalid\". This makes common insert operations\n  ** slightly faster.\n  **\n  ** There is a subtle but important optimization here too. When inserting\n  ** multiple records into an intkey b-tree using a single cursor (as can\n  ** happen while processing an \"INSERT INTO ... SELECT\" statement), it\n  ** is advantageous to leave the cursor pointing to the last entry in\n  ** the b-tree if possible. If the cursor is left pointing to the last\n  ** entry in the table, and the next row inserted has an integer key\n  ** larger than the largest existing key, it is possible to insert the\n  ** row without seeking the cursor. This can be a big performance boost.\n  */\n  pCur->info.nSize = 0;\n  if( pPage->nOverflow ){\n    assert( rc==SQLITE_OK );\n    pCur->curFlags &= ~(BTCF_ValidNKey);\n    rc = balance(pCur);\n\n    /* Must make sure nOverflow is reset to zero even if the balance()\n    ** fails. Internal data structure corruption will result otherwise. \n    ** Also, set the cursor state to invalid. This stops saveCursorPosition()\n    ** from trying to save the current position of the cursor.  */\n    pCur->pPage->nOverflow = 0;\n    pCur->eState = CURSOR_INVALID;\n    if( (flags & BTREE_SAVEPOSITION) && rc==SQLITE_OK ){\n      btreeReleaseAllCursorPages(pCur);\n      if( pCur->pKeyInfo ){\n        assert( pCur->pKey==0 );\n        pCur->pKey = sqlite3Malloc( pX->nKey );\n        if( pCur->pKey==0 ){\n          rc = SQLITE_NOMEM;\n        }else{\n          memcpy(pCur->pKey, pX->pKey, pX->nKey);\n        }\n      }\n      pCur->eState = CURSOR_REQUIRESEEK;\n      pCur->nKey = pX->nKey;\n    }\n  }\n  assert( pCur->iPage<0 || pCur->pPage->nOverflow==0 );\n\nend_insert:\n  return rc;\n}\n\n/*\n** Delete the entry that the cursor is pointing to. \n**\n** If the BTREE_SAVEPOSITION bit of the flags parameter is zero, then\n** the cursor is left pointing at an arbitrary location after the delete.\n** But if that bit is set, then the cursor is left in a state such that\n** the next call to BtreeNext() or BtreePrev() moves it to the same row\n** as it would have been on if the call to BtreeDelete() had been omitted.\n**\n** The BTREE_AUXDELETE bit of flags indicates that is one of several deletes\n** associated with a single table entry and its indexes.  Only one of those\n** deletes is considered the \"primary\" delete.  The primary delete occurs\n** on a cursor that is not a BTREE_FORDELETE cursor.  All but one delete\n** operation on non-FORDELETE cursors is tagged with the AUXDELETE flag.\n** The BTREE_AUXDELETE bit is a hint that is not used by this implementation,\n** but which might be used by alternative storage engines.\n*/\nSQLITE_PRIVATE int sqlite3BtreeDelete(BtCursor *pCur, u8 flags){\n  Btree *p = pCur->pBtree;\n  BtShared *pBt = p->pBt;              \n  int rc;                              /* Return code */\n  MemPage *pPage;                      /* Page to delete cell from */\n  unsigned char *pCell;                /* Pointer to cell to delete */\n  int iCellIdx;                        /* Index of cell to delete */\n  int iCellDepth;                      /* Depth of node containing pCell */ \n  CellInfo info;                       /* Size of the cell being deleted */\n  int bSkipnext = 0;                   /* Leaf cursor in SKIPNEXT state */\n  u8 bPreserve = flags & BTREE_SAVEPOSITION;  /* Keep cursor valid */\n\n  assert( cursorOwnsBtShared(pCur) );\n  assert( pBt->inTransaction==TRANS_WRITE );\n  assert( (pBt->btsFlags & BTS_READ_ONLY)==0 );\n  assert( pCur->curFlags & BTCF_WriteFlag );\n  assert( hasSharedCacheTableLock(p, pCur->pgnoRoot, pCur->pKeyInfo!=0, 2) );\n  assert( !hasReadConflicts(p, pCur->pgnoRoot) );\n  assert( pCur->ix<pCur->pPage->nCell );\n  assert( pCur->eState==CURSOR_VALID );\n  assert( (flags & ~(BTREE_SAVEPOSITION | BTREE_AUXDELETE))==0 );\n\n  iCellDepth = pCur->iPage;\n  iCellIdx = pCur->ix;\n  pPage = pCur->pPage;\n  pCell = findCell(pPage, iCellIdx);\n\n  /* If the bPreserve flag is set to true, then the cursor position must\n  ** be preserved following this delete operation. If the current delete\n  ** will cause a b-tree rebalance, then this is done by saving the cursor\n  ** key and leaving the cursor in CURSOR_REQUIRESEEK state before \n  ** returning. \n  **\n  ** Or, if the current delete will not cause a rebalance, then the cursor\n  ** will be left in CURSOR_SKIPNEXT state pointing to the entry immediately\n  ** before or after the deleted entry. In this case set bSkipnext to true.  */\n  if( bPreserve ){\n    if( !pPage->leaf \n     || (pPage->nFree+cellSizePtr(pPage,pCell)+2)>(int)(pBt->usableSize*2/3)\n    ){\n      /* A b-tree rebalance will be required after deleting this entry.\n      ** Save the cursor key.  */\n      rc = saveCursorKey(pCur);\n      if( rc ) return rc;\n    }else{\n      bSkipnext = 1;\n    }\n  }\n\n  /* If the page containing the entry to delete is not a leaf page, move\n  ** the cursor to the largest entry in the tree that is smaller than\n  ** the entry being deleted. This cell will replace the cell being deleted\n  ** from the internal node. The 'previous' entry is used for this instead\n  ** of the 'next' entry, as the previous entry is always a part of the\n  ** sub-tree headed by the child page of the cell being deleted. This makes\n  ** balancing the tree following the delete operation easier.  */\n  if( !pPage->leaf ){\n    rc = sqlite3BtreePrevious(pCur, 0);\n    assert( rc!=SQLITE_DONE );\n    if( rc ) return rc;\n  }\n\n  /* Save the positions of any other cursors open on this table before\n  ** making any modifications.  */\n  if( pCur->curFlags & BTCF_Multiple ){\n    rc = saveAllCursors(pBt, pCur->pgnoRoot, pCur);\n    if( rc ) return rc;\n  }\n\n  /* If this is a delete operation to remove a row from a table b-tree,\n  ** invalidate any incrblob cursors open on the row being deleted.  */\n  if( pCur->pKeyInfo==0 ){\n    invalidateIncrblobCursors(p, pCur->pgnoRoot, pCur->info.nKey, 0);\n  }\n\n  /* Make the page containing the entry to be deleted writable. Then free any\n  ** overflow pages associated with the entry and finally remove the cell\n  ** itself from within the page.  */\n  rc = sqlite3PagerWrite(pPage->pDbPage);\n  if( rc ) return rc;\n  rc = clearCell(pPage, pCell, &info);\n  dropCell(pPage, iCellIdx, info.nSize, &rc);\n  if( rc ) return rc;\n\n  /* If the cell deleted was not located on a leaf page, then the cursor\n  ** is currently pointing to the largest entry in the sub-tree headed\n  ** by the child-page of the cell that was just deleted from an internal\n  ** node. The cell from the leaf node needs to be moved to the internal\n  ** node to replace the deleted cell.  */\n  if( !pPage->leaf ){\n    MemPage *pLeaf = pCur->pPage;\n    int nCell;\n    Pgno n;\n    unsigned char *pTmp;\n\n    if( iCellDepth<pCur->iPage-1 ){\n      n = pCur->apPage[iCellDepth+1]->pgno;\n    }else{\n      n = pCur->pPage->pgno;\n    }\n    pCell = findCell(pLeaf, pLeaf->nCell-1);\n    if( pCell<&pLeaf->aData[4] ) return SQLITE_CORRUPT_BKPT;\n    nCell = pLeaf->xCellSize(pLeaf, pCell);\n    assert( MX_CELL_SIZE(pBt) >= nCell );\n    pTmp = pBt->pTmpSpace;\n    assert( pTmp!=0 );\n    rc = sqlite3PagerWrite(pLeaf->pDbPage);\n    if( rc==SQLITE_OK ){\n      insertCell(pPage, iCellIdx, pCell-4, nCell+4, pTmp, n, &rc);\n    }\n    dropCell(pLeaf, pLeaf->nCell-1, nCell, &rc);\n    if( rc ) return rc;\n  }\n\n  /* Balance the tree. If the entry deleted was located on a leaf page,\n  ** then the cursor still points to that page. In this case the first\n  ** call to balance() repairs the tree, and the if(...) condition is\n  ** never true.\n  **\n  ** Otherwise, if the entry deleted was on an internal node page, then\n  ** pCur is pointing to the leaf page from which a cell was removed to\n  ** replace the cell deleted from the internal node. This is slightly\n  ** tricky as the leaf node may be underfull, and the internal node may\n  ** be either under or overfull. In this case run the balancing algorithm\n  ** on the leaf node first. If the balance proceeds far enough up the\n  ** tree that we can be sure that any problem in the internal node has\n  ** been corrected, so be it. Otherwise, after balancing the leaf node,\n  ** walk the cursor up the tree to the internal node and balance it as \n  ** well.  */\n  rc = balance(pCur);\n  if( rc==SQLITE_OK && pCur->iPage>iCellDepth ){\n    releasePageNotNull(pCur->pPage);\n    pCur->iPage--;\n    while( pCur->iPage>iCellDepth ){\n      releasePage(pCur->apPage[pCur->iPage--]);\n    }\n    pCur->pPage = pCur->apPage[pCur->iPage];\n    rc = balance(pCur);\n  }\n\n  if( rc==SQLITE_OK ){\n    if( bSkipnext ){\n      assert( bPreserve && (pCur->iPage==iCellDepth || CORRUPT_DB) );\n      assert( pPage==pCur->pPage || CORRUPT_DB );\n      assert( (pPage->nCell>0 || CORRUPT_DB) && iCellIdx<=pPage->nCell );\n      pCur->eState = CURSOR_SKIPNEXT;\n      if( iCellIdx>=pPage->nCell ){\n        pCur->skipNext = -1;\n        pCur->ix = pPage->nCell-1;\n      }else{\n        pCur->skipNext = 1;\n      }\n    }else{\n      rc = moveToRoot(pCur);\n      if( bPreserve ){\n        btreeReleaseAllCursorPages(pCur);\n        pCur->eState = CURSOR_REQUIRESEEK;\n      }\n      if( rc==SQLITE_EMPTY ) rc = SQLITE_OK;\n    }\n  }\n  return rc;\n}\n\n/*\n** Create a new BTree table.  Write into *piTable the page\n** number for the root page of the new table.\n**\n** The type of type is determined by the flags parameter.  Only the\n** following values of flags are currently in use.  Other values for\n** flags might not work:\n**\n**     BTREE_INTKEY|BTREE_LEAFDATA     Used for SQL tables with rowid keys\n**     BTREE_ZERODATA                  Used for SQL indices\n*/\nstatic int btreeCreateTable(Btree *p, int *piTable, int createTabFlags){\n  BtShared *pBt = p->pBt;\n  MemPage *pRoot;\n  Pgno pgnoRoot;\n  int rc;\n  int ptfFlags;          /* Page-type flage for the root page of new table */\n\n  assert( sqlite3BtreeHoldsMutex(p) );\n  assert( pBt->inTransaction==TRANS_WRITE );\n  assert( (pBt->btsFlags & BTS_READ_ONLY)==0 );\n\n#ifdef SQLITE_OMIT_AUTOVACUUM\n  rc = allocateBtreePage(pBt, &pRoot, &pgnoRoot, 1, 0);\n  if( rc ){\n    return rc;\n  }\n#else\n  if( pBt->autoVacuum ){\n    Pgno pgnoMove;      /* Move a page here to make room for the root-page */\n    MemPage *pPageMove; /* The page to move to. */\n\n    /* Creating a new table may probably require moving an existing database\n    ** to make room for the new tables root page. In case this page turns\n    ** out to be an overflow page, delete all overflow page-map caches\n    ** held by open cursors.\n    */\n    invalidateAllOverflowCache(pBt);\n\n    /* Read the value of meta[3] from the database to determine where the\n    ** root page of the new table should go. meta[3] is the largest root-page\n    ** created so far, so the new root-page is (meta[3]+1).\n    */\n    sqlite3BtreeGetMeta(p, BTREE_LARGEST_ROOT_PAGE, &pgnoRoot);\n    pgnoRoot++;\n\n    /* The new root-page may not be allocated on a pointer-map page, or the\n    ** PENDING_BYTE page.\n    */\n    while( pgnoRoot==PTRMAP_PAGENO(pBt, pgnoRoot) ||\n        pgnoRoot==PENDING_BYTE_PAGE(pBt) ){\n      pgnoRoot++;\n    }\n    assert( pgnoRoot>=3 || CORRUPT_DB );\n    testcase( pgnoRoot<3 );\n\n    /* Allocate a page. The page that currently resides at pgnoRoot will\n    ** be moved to the allocated page (unless the allocated page happens\n    ** to reside at pgnoRoot).\n    */\n    rc = allocateBtreePage(pBt, &pPageMove, &pgnoMove, pgnoRoot, BTALLOC_EXACT);\n    if( rc!=SQLITE_OK ){\n      return rc;\n    }\n\n    if( pgnoMove!=pgnoRoot ){\n      /* pgnoRoot is the page that will be used for the root-page of\n      ** the new table (assuming an error did not occur). But we were\n      ** allocated pgnoMove. If required (i.e. if it was not allocated\n      ** by extending the file), the current page at position pgnoMove\n      ** is already journaled.\n      */\n      u8 eType = 0;\n      Pgno iPtrPage = 0;\n\n      /* Save the positions of any open cursors. This is required in\n      ** case they are holding a reference to an xFetch reference\n      ** corresponding to page pgnoRoot.  */\n      rc = saveAllCursors(pBt, 0, 0);\n      releasePage(pPageMove);\n      if( rc!=SQLITE_OK ){\n        return rc;\n      }\n\n      /* Move the page currently at pgnoRoot to pgnoMove. */\n      rc = btreeGetPage(pBt, pgnoRoot, &pRoot, 0);\n      if( rc!=SQLITE_OK ){\n        return rc;\n      }\n      rc = ptrmapGet(pBt, pgnoRoot, &eType, &iPtrPage);\n      if( eType==PTRMAP_ROOTPAGE || eType==PTRMAP_FREEPAGE ){\n        rc = SQLITE_CORRUPT_BKPT;\n      }\n      if( rc!=SQLITE_OK ){\n        releasePage(pRoot);\n        return rc;\n      }\n      assert( eType!=PTRMAP_ROOTPAGE );\n      assert( eType!=PTRMAP_FREEPAGE );\n      rc = relocatePage(pBt, pRoot, eType, iPtrPage, pgnoMove, 0);\n      releasePage(pRoot);\n\n      /* Obtain the page at pgnoRoot */\n      if( rc!=SQLITE_OK ){\n        return rc;\n      }\n      rc = btreeGetPage(pBt, pgnoRoot, &pRoot, 0);\n      if( rc!=SQLITE_OK ){\n        return rc;\n      }\n      rc = sqlite3PagerWrite(pRoot->pDbPage);\n      if( rc!=SQLITE_OK ){\n        releasePage(pRoot);\n        return rc;\n      }\n    }else{\n      pRoot = pPageMove;\n    } \n\n    /* Update the pointer-map and meta-data with the new root-page number. */\n    ptrmapPut(pBt, pgnoRoot, PTRMAP_ROOTPAGE, 0, &rc);\n    if( rc ){\n      releasePage(pRoot);\n      return rc;\n    }\n\n    /* When the new root page was allocated, page 1 was made writable in\n    ** order either to increase the database filesize, or to decrement the\n    ** freelist count.  Hence, the sqlite3BtreeUpdateMeta() call cannot fail.\n    */\n    assert( sqlite3PagerIswriteable(pBt->pPage1->pDbPage) );\n    rc = sqlite3BtreeUpdateMeta(p, 4, pgnoRoot);\n    if( NEVER(rc) ){\n      releasePage(pRoot);\n      return rc;\n    }\n\n  }else{\n    rc = allocateBtreePage(pBt, &pRoot, &pgnoRoot, 1, 0);\n    if( rc ) return rc;\n  }\n#endif\n  assert( sqlite3PagerIswriteable(pRoot->pDbPage) );\n  if( createTabFlags & BTREE_INTKEY ){\n    ptfFlags = PTF_INTKEY | PTF_LEAFDATA | PTF_LEAF;\n  }else{\n    ptfFlags = PTF_ZERODATA | PTF_LEAF;\n  }\n  zeroPage(pRoot, ptfFlags);\n  sqlite3PagerUnref(pRoot->pDbPage);\n  assert( (pBt->openFlags & BTREE_SINGLE)==0 || pgnoRoot==2 );\n  *piTable = (int)pgnoRoot;\n  return SQLITE_OK;\n}\nSQLITE_PRIVATE int sqlite3BtreeCreateTable(Btree *p, int *piTable, int flags){\n  int rc;\n  sqlite3BtreeEnter(p);\n  rc = btreeCreateTable(p, piTable, flags);\n  sqlite3BtreeLeave(p);\n  return rc;\n}\n\n/*\n** Erase the given database page and all its children.  Return\n** the page to the freelist.\n*/\nstatic int clearDatabasePage(\n  BtShared *pBt,           /* The BTree that contains the table */\n  Pgno pgno,               /* Page number to clear */\n  int freePageFlag,        /* Deallocate page if true */\n  int *pnChange            /* Add number of Cells freed to this counter */\n){\n  MemPage *pPage;\n  int rc;\n  unsigned char *pCell;\n  int i;\n  int hdr;\n  CellInfo info;\n\n  assert( sqlite3_mutex_held(pBt->mutex) );\n  if( pgno>btreePagecount(pBt) ){\n    return SQLITE_CORRUPT_BKPT;\n  }\n  rc = getAndInitPage(pBt, pgno, &pPage, 0, 0);\n  if( rc ) return rc;\n  if( pPage->bBusy ){\n    rc = SQLITE_CORRUPT_BKPT;\n    goto cleardatabasepage_out;\n  }\n  pPage->bBusy = 1;\n  hdr = pPage->hdrOffset;\n  for(i=0; i<pPage->nCell; i++){\n    pCell = findCell(pPage, i);\n    if( !pPage->leaf ){\n      rc = clearDatabasePage(pBt, get4byte(pCell), 1, pnChange);\n      if( rc ) goto cleardatabasepage_out;\n    }\n    rc = clearCell(pPage, pCell, &info);\n    if( rc ) goto cleardatabasepage_out;\n  }\n  if( !pPage->leaf ){\n    rc = clearDatabasePage(pBt, get4byte(&pPage->aData[hdr+8]), 1, pnChange);\n    if( rc ) goto cleardatabasepage_out;\n  }else if( pnChange ){\n    assert( pPage->intKey || CORRUPT_DB );\n    testcase( !pPage->intKey );\n    *pnChange += pPage->nCell;\n  }\n  if( freePageFlag ){\n    freePage(pPage, &rc);\n  }else if( (rc = sqlite3PagerWrite(pPage->pDbPage))==0 ){\n    zeroPage(pPage, pPage->aData[hdr] | PTF_LEAF);\n  }\n\ncleardatabasepage_out:\n  pPage->bBusy = 0;\n  releasePage(pPage);\n  return rc;\n}\n\n/*\n** Delete all information from a single table in the database.  iTable is\n** the page number of the root of the table.  After this routine returns,\n** the root page is empty, but still exists.\n**\n** This routine will fail with SQLITE_LOCKED if there are any open\n** read cursors on the table.  Open write cursors are moved to the\n** root of the table.\n**\n** If pnChange is not NULL, then table iTable must be an intkey table. The\n** integer value pointed to by pnChange is incremented by the number of\n** entries in the table.\n*/\nSQLITE_PRIVATE int sqlite3BtreeClearTable(Btree *p, int iTable, int *pnChange){\n  int rc;\n  BtShared *pBt = p->pBt;\n  sqlite3BtreeEnter(p);\n  assert( p->inTrans==TRANS_WRITE );\n\n  rc = saveAllCursors(pBt, (Pgno)iTable, 0);\n\n  if( SQLITE_OK==rc ){\n    /* Invalidate all incrblob cursors open on table iTable (assuming iTable\n    ** is the root of a table b-tree - if it is not, the following call is\n    ** a no-op).  */\n    invalidateIncrblobCursors(p, (Pgno)iTable, 0, 1);\n    rc = clearDatabasePage(pBt, (Pgno)iTable, 0, pnChange);\n  }\n  sqlite3BtreeLeave(p);\n  return rc;\n}\n\n/*\n** Delete all information from the single table that pCur is open on.\n**\n** This routine only work for pCur on an ephemeral table.\n*/\nSQLITE_PRIVATE int sqlite3BtreeClearTableOfCursor(BtCursor *pCur){\n  return sqlite3BtreeClearTable(pCur->pBtree, pCur->pgnoRoot, 0);\n}\n\n/*\n** Erase all information in a table and add the root of the table to\n** the freelist.  Except, the root of the principle table (the one on\n** page 1) is never added to the freelist.\n**\n** This routine will fail with SQLITE_LOCKED if there are any open\n** cursors on the table.\n**\n** If AUTOVACUUM is enabled and the page at iTable is not the last\n** root page in the database file, then the last root page \n** in the database file is moved into the slot formerly occupied by\n** iTable and that last slot formerly occupied by the last root page\n** is added to the freelist instead of iTable.  In this say, all\n** root pages are kept at the beginning of the database file, which\n** is necessary for AUTOVACUUM to work right.  *piMoved is set to the \n** page number that used to be the last root page in the file before\n** the move.  If no page gets moved, *piMoved is set to 0.\n** The last root page is recorded in meta[3] and the value of\n** meta[3] is updated by this procedure.\n*/\nstatic int btreeDropTable(Btree *p, Pgno iTable, int *piMoved){\n  int rc;\n  MemPage *pPage = 0;\n  BtShared *pBt = p->pBt;\n\n  assert( sqlite3BtreeHoldsMutex(p) );\n  assert( p->inTrans==TRANS_WRITE );\n  assert( iTable>=2 );\n\n  rc = btreeGetPage(pBt, (Pgno)iTable, &pPage, 0);\n  if( rc ) return rc;\n  rc = sqlite3BtreeClearTable(p, iTable, 0);\n  if( rc ){\n    releasePage(pPage);\n    return rc;\n  }\n\n  *piMoved = 0;\n\n#ifdef SQLITE_OMIT_AUTOVACUUM\n  freePage(pPage, &rc);\n  releasePage(pPage);\n#else\n  if( pBt->autoVacuum ){\n    Pgno maxRootPgno;\n    sqlite3BtreeGetMeta(p, BTREE_LARGEST_ROOT_PAGE, &maxRootPgno);\n\n    if( iTable==maxRootPgno ){\n      /* If the table being dropped is the table with the largest root-page\n      ** number in the database, put the root page on the free list. \n      */\n      freePage(pPage, &rc);\n      releasePage(pPage);\n      if( rc!=SQLITE_OK ){\n        return rc;\n      }\n    }else{\n      /* The table being dropped does not have the largest root-page\n      ** number in the database. So move the page that does into the \n      ** gap left by the deleted root-page.\n      */\n      MemPage *pMove;\n      releasePage(pPage);\n      rc = btreeGetPage(pBt, maxRootPgno, &pMove, 0);\n      if( rc!=SQLITE_OK ){\n        return rc;\n      }\n      rc = relocatePage(pBt, pMove, PTRMAP_ROOTPAGE, 0, iTable, 0);\n      releasePage(pMove);\n      if( rc!=SQLITE_OK ){\n        return rc;\n      }\n      pMove = 0;\n      rc = btreeGetPage(pBt, maxRootPgno, &pMove, 0);\n      freePage(pMove, &rc);\n      releasePage(pMove);\n      if( rc!=SQLITE_OK ){\n        return rc;\n      }\n      *piMoved = maxRootPgno;\n    }\n\n    /* Set the new 'max-root-page' value in the database header. This\n    ** is the old value less one, less one more if that happens to\n    ** be a root-page number, less one again if that is the\n    ** PENDING_BYTE_PAGE.\n    */\n    maxRootPgno--;\n    while( maxRootPgno==PENDING_BYTE_PAGE(pBt)\n           || PTRMAP_ISPAGE(pBt, maxRootPgno) ){\n      maxRootPgno--;\n    }\n    assert( maxRootPgno!=PENDING_BYTE_PAGE(pBt) );\n\n    rc = sqlite3BtreeUpdateMeta(p, 4, maxRootPgno);\n  }else{\n    freePage(pPage, &rc);\n    releasePage(pPage);\n  }\n#endif\n  return rc;  \n}\nSQLITE_PRIVATE int sqlite3BtreeDropTable(Btree *p, int iTable, int *piMoved){\n  int rc;\n  sqlite3BtreeEnter(p);\n  rc = btreeDropTable(p, iTable, piMoved);\n  sqlite3BtreeLeave(p);\n  return rc;\n}\n\n\n/*\n** This function may only be called if the b-tree connection already\n** has a read or write transaction open on the database.\n**\n** Read the meta-information out of a database file.  Meta[0]\n** is the number of free pages currently in the database.  Meta[1]\n** through meta[15] are available for use by higher layers.  Meta[0]\n** is read-only, the others are read/write.\n** \n** The schema layer numbers meta values differently.  At the schema\n** layer (and the SetCookie and ReadCookie opcodes) the number of\n** free pages is not visible.  So Cookie[0] is the same as Meta[1].\n**\n** This routine treats Meta[BTREE_DATA_VERSION] as a special case.  Instead\n** of reading the value out of the header, it instead loads the \"DataVersion\"\n** from the pager.  The BTREE_DATA_VERSION value is not actually stored in the\n** database file.  It is a number computed by the pager.  But its access\n** pattern is the same as header meta values, and so it is convenient to\n** read it from this routine.\n*/\nSQLITE_PRIVATE void sqlite3BtreeGetMeta(Btree *p, int idx, u32 *pMeta){\n  BtShared *pBt = p->pBt;\n\n  sqlite3BtreeEnter(p);\n  assert( p->inTrans>TRANS_NONE );\n  assert( SQLITE_OK==querySharedCacheTableLock(p, MASTER_ROOT, READ_LOCK) );\n  assert( pBt->pPage1 );\n  assert( idx>=0 && idx<=15 );\n\n  if( idx==BTREE_DATA_VERSION ){\n    *pMeta = sqlite3PagerDataVersion(pBt->pPager) + p->iDataVersion;\n  }else{\n    *pMeta = get4byte(&pBt->pPage1->aData[36 + idx*4]);\n  }\n\n  /* If auto-vacuum is disabled in this build and this is an auto-vacuum\n  ** database, mark the database as read-only.  */\n#ifdef SQLITE_OMIT_AUTOVACUUM\n  if( idx==BTREE_LARGEST_ROOT_PAGE && *pMeta>0 ){\n    pBt->btsFlags |= BTS_READ_ONLY;\n  }\n#endif\n\n  sqlite3BtreeLeave(p);\n}\n\n/*\n** Write meta-information back into the database.  Meta[0] is\n** read-only and may not be written.\n*/\nSQLITE_PRIVATE int sqlite3BtreeUpdateMeta(Btree *p, int idx, u32 iMeta){\n  BtShared *pBt = p->pBt;\n  unsigned char *pP1;\n  int rc;\n  assert( idx>=1 && idx<=15 );\n  sqlite3BtreeEnter(p);\n  assert( p->inTrans==TRANS_WRITE );\n  assert( pBt->pPage1!=0 );\n  pP1 = pBt->pPage1->aData;\n  rc = sqlite3PagerWrite(pBt->pPage1->pDbPage);\n  if( rc==SQLITE_OK ){\n    put4byte(&pP1[36 + idx*4], iMeta);\n#ifndef SQLITE_OMIT_AUTOVACUUM\n    if( idx==BTREE_INCR_VACUUM ){\n      assert( pBt->autoVacuum || iMeta==0 );\n      assert( iMeta==0 || iMeta==1 );\n      pBt->incrVacuum = (u8)iMeta;\n    }\n#endif\n  }\n  sqlite3BtreeLeave(p);\n  return rc;\n}\n\n#ifndef SQLITE_OMIT_BTREECOUNT\n/*\n** The first argument, pCur, is a cursor opened on some b-tree. Count the\n** number of entries in the b-tree and write the result to *pnEntry.\n**\n** SQLITE_OK is returned if the operation is successfully executed. \n** Otherwise, if an error is encountered (i.e. an IO error or database\n** corruption) an SQLite error code is returned.\n*/\nSQLITE_PRIVATE int sqlite3BtreeCount(BtCursor *pCur, i64 *pnEntry){\n  i64 nEntry = 0;                      /* Value to return in *pnEntry */\n  int rc;                              /* Return code */\n\n  rc = moveToRoot(pCur);\n  if( rc==SQLITE_EMPTY ){\n    *pnEntry = 0;\n    return SQLITE_OK;\n  }\n\n  /* Unless an error occurs, the following loop runs one iteration for each\n  ** page in the B-Tree structure (not including overflow pages). \n  */\n  while( rc==SQLITE_OK ){\n    int iIdx;                          /* Index of child node in parent */\n    MemPage *pPage;                    /* Current page of the b-tree */\n\n    /* If this is a leaf page or the tree is not an int-key tree, then \n    ** this page contains countable entries. Increment the entry counter\n    ** accordingly.\n    */\n    pPage = pCur->pPage;\n    if( pPage->leaf || !pPage->intKey ){\n      nEntry += pPage->nCell;\n    }\n\n    /* pPage is a leaf node. This loop navigates the cursor so that it \n    ** points to the first interior cell that it points to the parent of\n    ** the next page in the tree that has not yet been visited. The\n    ** pCur->aiIdx[pCur->iPage] value is set to the index of the parent cell\n    ** of the page, or to the number of cells in the page if the next page\n    ** to visit is the right-child of its parent.\n    **\n    ** If all pages in the tree have been visited, return SQLITE_OK to the\n    ** caller.\n    */\n    if( pPage->leaf ){\n      do {\n        if( pCur->iPage==0 ){\n          /* All pages of the b-tree have been visited. Return successfully. */\n          *pnEntry = nEntry;\n          return moveToRoot(pCur);\n        }\n        moveToParent(pCur);\n      }while ( pCur->ix>=pCur->pPage->nCell );\n\n      pCur->ix++;\n      pPage = pCur->pPage;\n    }\n\n    /* Descend to the child node of the cell that the cursor currently \n    ** points at. This is the right-child if (iIdx==pPage->nCell).\n    */\n    iIdx = pCur->ix;\n    if( iIdx==pPage->nCell ){\n      rc = moveToChild(pCur, get4byte(&pPage->aData[pPage->hdrOffset+8]));\n    }else{\n      rc = moveToChild(pCur, get4byte(findCell(pPage, iIdx)));\n    }\n  }\n\n  /* An error has occurred. Return an error code. */\n  return rc;\n}\n#endif\n\n/*\n** Return the pager associated with a BTree.  This routine is used for\n** testing and debugging only.\n*/\nSQLITE_PRIVATE Pager *sqlite3BtreePager(Btree *p){\n  return p->pBt->pPager;\n}\n\n#ifndef SQLITE_OMIT_INTEGRITY_CHECK\n/*\n** Append a message to the error message string.\n*/\nstatic void checkAppendMsg(\n  IntegrityCk *pCheck,\n  const char *zFormat,\n  ...\n){\n  va_list ap;\n  if( !pCheck->mxErr ) return;\n  pCheck->mxErr--;\n  pCheck->nErr++;\n  va_start(ap, zFormat);\n  if( pCheck->errMsg.nChar ){\n    sqlite3StrAccumAppend(&pCheck->errMsg, \"\\n\", 1);\n  }\n  if( pCheck->zPfx ){\n    sqlite3XPrintf(&pCheck->errMsg, pCheck->zPfx, pCheck->v1, pCheck->v2);\n  }\n  sqlite3VXPrintf(&pCheck->errMsg, zFormat, ap);\n  va_end(ap);\n  if( pCheck->errMsg.accError==STRACCUM_NOMEM ){\n    pCheck->mallocFailed = 1;\n  }\n}\n#endif /* SQLITE_OMIT_INTEGRITY_CHECK */\n\n#ifndef SQLITE_OMIT_INTEGRITY_CHECK\n\n/*\n** Return non-zero if the bit in the IntegrityCk.aPgRef[] array that\n** corresponds to page iPg is already set.\n*/\nstatic int getPageReferenced(IntegrityCk *pCheck, Pgno iPg){\n  assert( iPg<=pCheck->nPage && sizeof(pCheck->aPgRef[0])==1 );\n  return (pCheck->aPgRef[iPg/8] & (1 << (iPg & 0x07)));\n}\n\n/*\n** Set the bit in the IntegrityCk.aPgRef[] array that corresponds to page iPg.\n*/\nstatic void setPageReferenced(IntegrityCk *pCheck, Pgno iPg){\n  assert( iPg<=pCheck->nPage && sizeof(pCheck->aPgRef[0])==1 );\n  pCheck->aPgRef[iPg/8] |= (1 << (iPg & 0x07));\n}\n\n\n/*\n** Add 1 to the reference count for page iPage.  If this is the second\n** reference to the page, add an error message to pCheck->zErrMsg.\n** Return 1 if there are 2 or more references to the page and 0 if\n** if this is the first reference to the page.\n**\n** Also check that the page number is in bounds.\n*/\nstatic int checkRef(IntegrityCk *pCheck, Pgno iPage){\n  if( iPage==0 ) return 1;\n  if( iPage>pCheck->nPage ){\n    checkAppendMsg(pCheck, \"invalid page number %d\", iPage);\n    return 1;\n  }\n  if( getPageReferenced(pCheck, iPage) ){\n    checkAppendMsg(pCheck, \"2nd reference to page %d\", iPage);\n    return 1;\n  }\n  setPageReferenced(pCheck, iPage);\n  return 0;\n}\n\n#ifndef SQLITE_OMIT_AUTOVACUUM\n/*\n** Check that the entry in the pointer-map for page iChild maps to \n** page iParent, pointer type ptrType. If not, append an error message\n** to pCheck.\n*/\nstatic void checkPtrmap(\n  IntegrityCk *pCheck,   /* Integrity check context */\n  Pgno iChild,           /* Child page number */\n  u8 eType,              /* Expected pointer map type */\n  Pgno iParent           /* Expected pointer map parent page number */\n){\n  int rc;\n  u8 ePtrmapType;\n  Pgno iPtrmapParent;\n\n  rc = ptrmapGet(pCheck->pBt, iChild, &ePtrmapType, &iPtrmapParent);\n  if( rc!=SQLITE_OK ){\n    if( rc==SQLITE_NOMEM || rc==SQLITE_IOERR_NOMEM ) pCheck->mallocFailed = 1;\n    checkAppendMsg(pCheck, \"Failed to read ptrmap key=%d\", iChild);\n    return;\n  }\n\n  if( ePtrmapType!=eType || iPtrmapParent!=iParent ){\n    checkAppendMsg(pCheck,\n      \"Bad ptr map entry key=%d expected=(%d,%d) got=(%d,%d)\", \n      iChild, eType, iParent, ePtrmapType, iPtrmapParent);\n  }\n}\n#endif\n\n/*\n** Check the integrity of the freelist or of an overflow page list.\n** Verify that the number of pages on the list is N.\n*/\nstatic void checkList(\n  IntegrityCk *pCheck,  /* Integrity checking context */\n  int isFreeList,       /* True for a freelist.  False for overflow page list */\n  int iPage,            /* Page number for first page in the list */\n  int N                 /* Expected number of pages in the list */\n){\n  int i;\n  int expected = N;\n  int iFirst = iPage;\n  while( N-- > 0 && pCheck->mxErr ){\n    DbPage *pOvflPage;\n    unsigned char *pOvflData;\n    if( iPage<1 ){\n      checkAppendMsg(pCheck,\n         \"%d of %d pages missing from overflow list starting at %d\",\n          N+1, expected, iFirst);\n      break;\n    }\n    if( checkRef(pCheck, iPage) ) break;\n    if( sqlite3PagerGet(pCheck->pPager, (Pgno)iPage, &pOvflPage, 0) ){\n      checkAppendMsg(pCheck, \"failed to get page %d\", iPage);\n      break;\n    }\n    pOvflData = (unsigned char *)sqlite3PagerGetData(pOvflPage);\n    if( isFreeList ){\n      int n = get4byte(&pOvflData[4]);\n#ifndef SQLITE_OMIT_AUTOVACUUM\n      if( pCheck->pBt->autoVacuum ){\n        checkPtrmap(pCheck, iPage, PTRMAP_FREEPAGE, 0);\n      }\n#endif\n      if( n>(int)pCheck->pBt->usableSize/4-2 ){\n        checkAppendMsg(pCheck,\n           \"freelist leaf count too big on page %d\", iPage);\n        N--;\n      }else{\n        for(i=0; i<n; i++){\n          Pgno iFreePage = get4byte(&pOvflData[8+i*4]);\n#ifndef SQLITE_OMIT_AUTOVACUUM\n          if( pCheck->pBt->autoVacuum ){\n            checkPtrmap(pCheck, iFreePage, PTRMAP_FREEPAGE, 0);\n          }\n#endif\n          checkRef(pCheck, iFreePage);\n        }\n        N -= n;\n      }\n    }\n#ifndef SQLITE_OMIT_AUTOVACUUM\n    else{\n      /* If this database supports auto-vacuum and iPage is not the last\n      ** page in this overflow list, check that the pointer-map entry for\n      ** the following page matches iPage.\n      */\n      if( pCheck->pBt->autoVacuum && N>0 ){\n        i = get4byte(pOvflData);\n        checkPtrmap(pCheck, i, PTRMAP_OVERFLOW2, iPage);\n      }\n    }\n#endif\n    iPage = get4byte(pOvflData);\n    sqlite3PagerUnref(pOvflPage);\n\n    if( isFreeList && N<(iPage!=0) ){\n      checkAppendMsg(pCheck, \"free-page count in header is too small\");\n    }\n  }\n}\n#endif /* SQLITE_OMIT_INTEGRITY_CHECK */\n\n/*\n** An implementation of a min-heap.\n**\n** aHeap[0] is the number of elements on the heap.  aHeap[1] is the\n** root element.  The daughter nodes of aHeap[N] are aHeap[N*2]\n** and aHeap[N*2+1].\n**\n** The heap property is this:  Every node is less than or equal to both\n** of its daughter nodes.  A consequence of the heap property is that the\n** root node aHeap[1] is always the minimum value currently in the heap.\n**\n** The btreeHeapInsert() routine inserts an unsigned 32-bit number onto\n** the heap, preserving the heap property.  The btreeHeapPull() routine\n** removes the root element from the heap (the minimum value in the heap)\n** and then moves other nodes around as necessary to preserve the heap\n** property.\n**\n** This heap is used for cell overlap and coverage testing.  Each u32\n** entry represents the span of a cell or freeblock on a btree page.  \n** The upper 16 bits are the index of the first byte of a range and the\n** lower 16 bits are the index of the last byte of that range.\n*/\nstatic void btreeHeapInsert(u32 *aHeap, u32 x){\n  u32 j, i = ++aHeap[0];\n  aHeap[i] = x;\n  while( (j = i/2)>0 && aHeap[j]>aHeap[i] ){\n    x = aHeap[j];\n    aHeap[j] = aHeap[i];\n    aHeap[i] = x;\n    i = j;\n  }\n}\nstatic int btreeHeapPull(u32 *aHeap, u32 *pOut){\n  u32 j, i, x;\n  if( (x = aHeap[0])==0 ) return 0;\n  *pOut = aHeap[1];\n  aHeap[1] = aHeap[x];\n  aHeap[x] = 0xffffffff;\n  aHeap[0]--;\n  i = 1;\n  while( (j = i*2)<=aHeap[0] ){\n    if( aHeap[j]>aHeap[j+1] ) j++;\n    if( aHeap[i]<aHeap[j] ) break;\n    x = aHeap[i];\n    aHeap[i] = aHeap[j];\n    aHeap[j] = x;\n    i = j;\n  }\n  return 1;  \n}\n\n#ifndef SQLITE_OMIT_INTEGRITY_CHECK\n/*\n** Do various sanity checks on a single page of a tree.  Return\n** the tree depth.  Root pages return 0.  Parents of root pages\n** return 1, and so forth.\n** \n** These checks are done:\n**\n**      1.  Make sure that cells and freeblocks do not overlap\n**          but combine to completely cover the page.\n**      2.  Make sure integer cell keys are in order.\n**      3.  Check the integrity of overflow pages.\n**      4.  Recursively call checkTreePage on all children.\n**      5.  Verify that the depth of all children is the same.\n*/\nstatic int checkTreePage(\n  IntegrityCk *pCheck,  /* Context for the sanity check */\n  int iPage,            /* Page number of the page to check */\n  i64 *piMinKey,        /* Write minimum integer primary key here */\n  i64 maxKey            /* Error if integer primary key greater than this */\n){\n  MemPage *pPage = 0;      /* The page being analyzed */\n  int i;                   /* Loop counter */\n  int rc;                  /* Result code from subroutine call */\n  int depth = -1, d2;      /* Depth of a subtree */\n  int pgno;                /* Page number */\n  int nFrag;               /* Number of fragmented bytes on the page */\n  int hdr;                 /* Offset to the page header */\n  int cellStart;           /* Offset to the start of the cell pointer array */\n  int nCell;               /* Number of cells */\n  int doCoverageCheck = 1; /* True if cell coverage checking should be done */\n  int keyCanBeEqual = 1;   /* True if IPK can be equal to maxKey\n                           ** False if IPK must be strictly less than maxKey */\n  u8 *data;                /* Page content */\n  u8 *pCell;               /* Cell content */\n  u8 *pCellIdx;            /* Next element of the cell pointer array */\n  BtShared *pBt;           /* The BtShared object that owns pPage */\n  u32 pc;                  /* Address of a cell */\n  u32 usableSize;          /* Usable size of the page */\n  u32 contentOffset;       /* Offset to the start of the cell content area */\n  u32 *heap = 0;           /* Min-heap used for checking cell coverage */\n  u32 x, prev = 0;         /* Next and previous entry on the min-heap */\n  const char *saved_zPfx = pCheck->zPfx;\n  int saved_v1 = pCheck->v1;\n  int saved_v2 = pCheck->v2;\n  u8 savedIsInit = 0;\n\n  /* Check that the page exists\n  */\n  pBt = pCheck->pBt;\n  usableSize = pBt->usableSize;\n  if( iPage==0 ) return 0;\n  if( checkRef(pCheck, iPage) ) return 0;\n  pCheck->zPfx = \"Page %d: \";\n  pCheck->v1 = iPage;\n  if( (rc = btreeGetPage(pBt, (Pgno)iPage, &pPage, 0))!=0 ){\n    checkAppendMsg(pCheck,\n       \"unable to get the page. error code=%d\", rc);\n    goto end_of_check;\n  }\n\n  /* Clear MemPage.isInit to make sure the corruption detection code in\n  ** btreeInitPage() is executed.  */\n  savedIsInit = pPage->isInit;\n  pPage->isInit = 0;\n  if( (rc = btreeInitPage(pPage))!=0 ){\n    assert( rc==SQLITE_CORRUPT );  /* The only possible error from InitPage */\n    checkAppendMsg(pCheck,\n                   \"btreeInitPage() returns error code %d\", rc);\n    goto end_of_check;\n  }\n  data = pPage->aData;\n  hdr = pPage->hdrOffset;\n\n  /* Set up for cell analysis */\n  pCheck->zPfx = \"On tree page %d cell %d: \";\n  contentOffset = get2byteNotZero(&data[hdr+5]);\n  assert( contentOffset<=usableSize );  /* Enforced by btreeInitPage() */\n\n  /* EVIDENCE-OF: R-37002-32774 The two-byte integer at offset 3 gives the\n  ** number of cells on the page. */\n  nCell = get2byte(&data[hdr+3]);\n  assert( pPage->nCell==nCell );\n\n  /* EVIDENCE-OF: R-23882-45353 The cell pointer array of a b-tree page\n  ** immediately follows the b-tree page header. */\n  cellStart = hdr + 12 - 4*pPage->leaf;\n  assert( pPage->aCellIdx==&data[cellStart] );\n  pCellIdx = &data[cellStart + 2*(nCell-1)];\n\n  if( !pPage->leaf ){\n    /* Analyze the right-child page of internal pages */\n    pgno = get4byte(&data[hdr+8]);\n#ifndef SQLITE_OMIT_AUTOVACUUM\n    if( pBt->autoVacuum ){\n      pCheck->zPfx = \"On page %d at right child: \";\n      checkPtrmap(pCheck, pgno, PTRMAP_BTREE, iPage);\n    }\n#endif\n    depth = checkTreePage(pCheck, pgno, &maxKey, maxKey);\n    keyCanBeEqual = 0;\n  }else{\n    /* For leaf pages, the coverage check will occur in the same loop\n    ** as the other cell checks, so initialize the heap.  */\n    heap = pCheck->heap;\n    heap[0] = 0;\n  }\n\n  /* EVIDENCE-OF: R-02776-14802 The cell pointer array consists of K 2-byte\n  ** integer offsets to the cell contents. */\n  for(i=nCell-1; i>=0 && pCheck->mxErr; i--){\n    CellInfo info;\n\n    /* Check cell size */\n    pCheck->v2 = i;\n    assert( pCellIdx==&data[cellStart + i*2] );\n    pc = get2byteAligned(pCellIdx);\n    pCellIdx -= 2;\n    if( pc<contentOffset || pc>usableSize-4 ){\n      checkAppendMsg(pCheck, \"Offset %d out of range %d..%d\",\n                             pc, contentOffset, usableSize-4);\n      doCoverageCheck = 0;\n      continue;\n    }\n    pCell = &data[pc];\n    pPage->xParseCell(pPage, pCell, &info);\n    if( pc+info.nSize>usableSize ){\n      checkAppendMsg(pCheck, \"Extends off end of page\");\n      doCoverageCheck = 0;\n      continue;\n    }\n\n    /* Check for integer primary key out of range */\n    if( pPage->intKey ){\n      if( keyCanBeEqual ? (info.nKey > maxKey) : (info.nKey >= maxKey) ){\n        checkAppendMsg(pCheck, \"Rowid %lld out of order\", info.nKey);\n      }\n      maxKey = info.nKey;\n      keyCanBeEqual = 0;     /* Only the first key on the page may ==maxKey */\n    }\n\n    /* Check the content overflow list */\n    if( info.nPayload>info.nLocal ){\n      int nPage;       /* Number of pages on the overflow chain */\n      Pgno pgnoOvfl;   /* First page of the overflow chain */\n      assert( pc + info.nSize - 4 <= usableSize );\n      nPage = (info.nPayload - info.nLocal + usableSize - 5)/(usableSize - 4);\n      pgnoOvfl = get4byte(&pCell[info.nSize - 4]);\n#ifndef SQLITE_OMIT_AUTOVACUUM\n      if( pBt->autoVacuum ){\n        checkPtrmap(pCheck, pgnoOvfl, PTRMAP_OVERFLOW1, iPage);\n      }\n#endif\n      checkList(pCheck, 0, pgnoOvfl, nPage);\n    }\n\n    if( !pPage->leaf ){\n      /* Check sanity of left child page for internal pages */\n      pgno = get4byte(pCell);\n#ifndef SQLITE_OMIT_AUTOVACUUM\n      if( pBt->autoVacuum ){\n        checkPtrmap(pCheck, pgno, PTRMAP_BTREE, iPage);\n      }\n#endif\n      d2 = checkTreePage(pCheck, pgno, &maxKey, maxKey);\n      keyCanBeEqual = 0;\n      if( d2!=depth ){\n        checkAppendMsg(pCheck, \"Child page depth differs\");\n        depth = d2;\n      }\n    }else{\n      /* Populate the coverage-checking heap for leaf pages */\n      btreeHeapInsert(heap, (pc<<16)|(pc+info.nSize-1));\n    }\n  }\n  *piMinKey = maxKey;\n\n  /* Check for complete coverage of the page\n  */\n  pCheck->zPfx = 0;\n  if( doCoverageCheck && pCheck->mxErr>0 ){\n    /* For leaf pages, the min-heap has already been initialized and the\n    ** cells have already been inserted.  But for internal pages, that has\n    ** not yet been done, so do it now */\n    if( !pPage->leaf ){\n      heap = pCheck->heap;\n      heap[0] = 0;\n      for(i=nCell-1; i>=0; i--){\n        u32 size;\n        pc = get2byteAligned(&data[cellStart+i*2]);\n        size = pPage->xCellSize(pPage, &data[pc]);\n        btreeHeapInsert(heap, (pc<<16)|(pc+size-1));\n      }\n    }\n    /* Add the freeblocks to the min-heap\n    **\n    ** EVIDENCE-OF: R-20690-50594 The second field of the b-tree page header\n    ** is the offset of the first freeblock, or zero if there are no\n    ** freeblocks on the page. \n    */\n    i = get2byte(&data[hdr+1]);\n    while( i>0 ){\n      int size, j;\n      assert( (u32)i<=usableSize-4 );     /* Enforced by btreeInitPage() */\n      size = get2byte(&data[i+2]);\n      assert( (u32)(i+size)<=usableSize );  /* Enforced by btreeInitPage() */\n      btreeHeapInsert(heap, (((u32)i)<<16)|(i+size-1));\n      /* EVIDENCE-OF: R-58208-19414 The first 2 bytes of a freeblock are a\n      ** big-endian integer which is the offset in the b-tree page of the next\n      ** freeblock in the chain, or zero if the freeblock is the last on the\n      ** chain. */\n      j = get2byte(&data[i]);\n      /* EVIDENCE-OF: R-06866-39125 Freeblocks are always connected in order of\n      ** increasing offset. */\n      assert( j==0 || j>i+size );  /* Enforced by btreeInitPage() */\n      assert( (u32)j<=usableSize-4 );   /* Enforced by btreeInitPage() */\n      i = j;\n    }\n    /* Analyze the min-heap looking for overlap between cells and/or \n    ** freeblocks, and counting the number of untracked bytes in nFrag.\n    ** \n    ** Each min-heap entry is of the form:    (start_address<<16)|end_address.\n    ** There is an implied first entry the covers the page header, the cell\n    ** pointer index, and the gap between the cell pointer index and the start\n    ** of cell content.  \n    **\n    ** The loop below pulls entries from the min-heap in order and compares\n    ** the start_address against the previous end_address.  If there is an\n    ** overlap, that means bytes are used multiple times.  If there is a gap,\n    ** that gap is added to the fragmentation count.\n    */\n    nFrag = 0;\n    prev = contentOffset - 1;   /* Implied first min-heap entry */\n    while( btreeHeapPull(heap,&x) ){\n      if( (prev&0xffff)>=(x>>16) ){\n        checkAppendMsg(pCheck,\n          \"Multiple uses for byte %u of page %d\", x>>16, iPage);\n        break;\n      }else{\n        nFrag += (x>>16) - (prev&0xffff) - 1;\n        prev = x;\n      }\n    }\n    nFrag += usableSize - (prev&0xffff) - 1;\n    /* EVIDENCE-OF: R-43263-13491 The total number of bytes in all fragments\n    ** is stored in the fifth field of the b-tree page header.\n    ** EVIDENCE-OF: R-07161-27322 The one-byte integer at offset 7 gives the\n    ** number of fragmented free bytes within the cell content area.\n    */\n    if( heap[0]==0 && nFrag!=data[hdr+7] ){\n      checkAppendMsg(pCheck,\n          \"Fragmentation of %d bytes reported as %d on page %d\",\n          nFrag, data[hdr+7], iPage);\n    }\n  }\n\nend_of_check:\n  if( !doCoverageCheck ) pPage->isInit = savedIsInit;\n  releasePage(pPage);\n  pCheck->zPfx = saved_zPfx;\n  pCheck->v1 = saved_v1;\n  pCheck->v2 = saved_v2;\n  return depth+1;\n}\n#endif /* SQLITE_OMIT_INTEGRITY_CHECK */\n\n#ifndef SQLITE_OMIT_INTEGRITY_CHECK\n/*\n** This routine does a complete check of the given BTree file.  aRoot[] is\n** an array of pages numbers were each page number is the root page of\n** a table.  nRoot is the number of entries in aRoot.\n**\n** A read-only or read-write transaction must be opened before calling\n** this function.\n**\n** Write the number of error seen in *pnErr.  Except for some memory\n** allocation errors,  an error message held in memory obtained from\n** malloc is returned if *pnErr is non-zero.  If *pnErr==0 then NULL is\n** returned.  If a memory allocation error occurs, NULL is returned.\n*/\nSQLITE_PRIVATE char *sqlite3BtreeIntegrityCheck(\n  Btree *p,     /* The btree to be checked */\n  int *aRoot,   /* An array of root pages numbers for individual trees */\n  int nRoot,    /* Number of entries in aRoot[] */\n  int mxErr,    /* Stop reporting errors after this many */\n  int *pnErr    /* Write number of errors seen to this variable */\n){\n  Pgno i;\n  IntegrityCk sCheck;\n  BtShared *pBt = p->pBt;\n  int savedDbFlags = pBt->db->flags;\n  char zErr[100];\n  VVA_ONLY( int nRef );\n\n  sqlite3BtreeEnter(p);\n  assert( p->inTrans>TRANS_NONE && pBt->inTransaction>TRANS_NONE );\n  VVA_ONLY( nRef = sqlite3PagerRefcount(pBt->pPager) );\n  assert( nRef>=0 );\n  sCheck.pBt = pBt;\n  sCheck.pPager = pBt->pPager;\n  sCheck.nPage = btreePagecount(sCheck.pBt);\n  sCheck.mxErr = mxErr;\n  sCheck.nErr = 0;\n  sCheck.mallocFailed = 0;\n  sCheck.zPfx = 0;\n  sCheck.v1 = 0;\n  sCheck.v2 = 0;\n  sCheck.aPgRef = 0;\n  sCheck.heap = 0;\n  sqlite3StrAccumInit(&sCheck.errMsg, 0, zErr, sizeof(zErr), SQLITE_MAX_LENGTH);\n  sCheck.errMsg.printfFlags = SQLITE_PRINTF_INTERNAL;\n  if( sCheck.nPage==0 ){\n    goto integrity_ck_cleanup;\n  }\n\n  sCheck.aPgRef = sqlite3MallocZero((sCheck.nPage / 8)+ 1);\n  if( !sCheck.aPgRef ){\n    sCheck.mallocFailed = 1;\n    goto integrity_ck_cleanup;\n  }\n  sCheck.heap = (u32*)sqlite3PageMalloc( pBt->pageSize );\n  if( sCheck.heap==0 ){\n    sCheck.mallocFailed = 1;\n    goto integrity_ck_cleanup;\n  }\n\n  i = PENDING_BYTE_PAGE(pBt);\n  if( i<=sCheck.nPage ) setPageReferenced(&sCheck, i);\n\n  /* Check the integrity of the freelist\n  */\n  sCheck.zPfx = \"Main freelist: \";\n  checkList(&sCheck, 1, get4byte(&pBt->pPage1->aData[32]),\n            get4byte(&pBt->pPage1->aData[36]));\n  sCheck.zPfx = 0;\n\n  /* Check all the tables.\n  */\n  testcase( pBt->db->flags & SQLITE_CellSizeCk );\n  pBt->db->flags &= ~SQLITE_CellSizeCk;\n  for(i=0; (int)i<nRoot && sCheck.mxErr; i++){\n    i64 notUsed;\n    if( aRoot[i]==0 ) continue;\n#ifndef SQLITE_OMIT_AUTOVACUUM\n    if( pBt->autoVacuum && aRoot[i]>1 ){\n      checkPtrmap(&sCheck, aRoot[i], PTRMAP_ROOTPAGE, 0);\n    }\n#endif\n    checkTreePage(&sCheck, aRoot[i], &notUsed, LARGEST_INT64);\n  }\n  pBt->db->flags = savedDbFlags;\n\n  /* Make sure every page in the file is referenced\n  */\n  for(i=1; i<=sCheck.nPage && sCheck.mxErr; i++){\n#ifdef SQLITE_OMIT_AUTOVACUUM\n    if( getPageReferenced(&sCheck, i)==0 ){\n      checkAppendMsg(&sCheck, \"Page %d is never used\", i);\n    }\n#else\n    /* If the database supports auto-vacuum, make sure no tables contain\n    ** references to pointer-map pages.\n    */\n    if( getPageReferenced(&sCheck, i)==0 && \n       (PTRMAP_PAGENO(pBt, i)!=i || !pBt->autoVacuum) ){\n      checkAppendMsg(&sCheck, \"Page %d is never used\", i);\n    }\n    if( getPageReferenced(&sCheck, i)!=0 && \n       (PTRMAP_PAGENO(pBt, i)==i && pBt->autoVacuum) ){\n      checkAppendMsg(&sCheck, \"Pointer map page %d is referenced\", i);\n    }\n#endif\n  }\n\n  /* Clean  up and report errors.\n  */\nintegrity_ck_cleanup:\n  sqlite3PageFree(sCheck.heap);\n  sqlite3_free(sCheck.aPgRef);\n  if( sCheck.mallocFailed ){\n    sqlite3StrAccumReset(&sCheck.errMsg);\n    sCheck.nErr++;\n  }\n  *pnErr = sCheck.nErr;\n  if( sCheck.nErr==0 ) sqlite3StrAccumReset(&sCheck.errMsg);\n  /* Make sure this analysis did not leave any unref() pages. */\n  assert( nRef==sqlite3PagerRefcount(pBt->pPager) );\n  sqlite3BtreeLeave(p);\n  return sqlite3StrAccumFinish(&sCheck.errMsg);\n}\n#endif /* SQLITE_OMIT_INTEGRITY_CHECK */\n\n/*\n** Return the full pathname of the underlying database file.  Return\n** an empty string if the database is in-memory or a TEMP database.\n**\n** The pager filename is invariant as long as the pager is\n** open so it is safe to access without the BtShared mutex.\n*/\nSQLITE_PRIVATE const char *sqlite3BtreeGetFilename(Btree *p){\n  assert( p->pBt->pPager!=0 );\n  return sqlite3PagerFilename(p->pBt->pPager, 1);\n}\n\n/*\n** Return the pathname of the journal file for this database. The return\n** value of this routine is the same regardless of whether the journal file\n** has been created or not.\n**\n** The pager journal filename is invariant as long as the pager is\n** open so it is safe to access without the BtShared mutex.\n*/\nSQLITE_PRIVATE const char *sqlite3BtreeGetJournalname(Btree *p){\n  assert( p->pBt->pPager!=0 );\n  return sqlite3PagerJournalname(p->pBt->pPager);\n}\n\n/*\n** Return non-zero if a transaction is active.\n*/\nSQLITE_PRIVATE int sqlite3BtreeIsInTrans(Btree *p){\n  assert( p==0 || sqlite3_mutex_held(p->db->mutex) );\n  return (p && (p->inTrans==TRANS_WRITE));\n}\n\n#ifndef SQLITE_OMIT_WAL\n/*\n** Run a checkpoint on the Btree passed as the first argument.\n**\n** Return SQLITE_LOCKED if this or any other connection has an open \n** transaction on the shared-cache the argument Btree is connected to.\n**\n** Parameter eMode is one of SQLITE_CHECKPOINT_PASSIVE, FULL or RESTART.\n*/\nSQLITE_PRIVATE int sqlite3BtreeCheckpoint(Btree *p, int eMode, int *pnLog, int *pnCkpt){\n  int rc = SQLITE_OK;\n  if( p ){\n    BtShared *pBt = p->pBt;\n    sqlite3BtreeEnter(p);\n    if( pBt->inTransaction!=TRANS_NONE ){\n      rc = SQLITE_LOCKED;\n    }else{\n      rc = sqlite3PagerCheckpoint(pBt->pPager, p->db, eMode, pnLog, pnCkpt);\n    }\n    sqlite3BtreeLeave(p);\n  }\n  return rc;\n}\n#endif\n\n/*\n** Return non-zero if a read (or write) transaction is active.\n*/\nSQLITE_PRIVATE int sqlite3BtreeIsInReadTrans(Btree *p){\n  assert( p );\n  assert( sqlite3_mutex_held(p->db->mutex) );\n  return p->inTrans!=TRANS_NONE;\n}\n\nSQLITE_PRIVATE int sqlite3BtreeIsInBackup(Btree *p){\n  assert( p );\n  assert( sqlite3_mutex_held(p->db->mutex) );\n  return p->nBackup!=0;\n}\n\n/*\n** This function returns a pointer to a blob of memory associated with\n** a single shared-btree. The memory is used by client code for its own\n** purposes (for example, to store a high-level schema associated with \n** the shared-btree). The btree layer manages reference counting issues.\n**\n** The first time this is called on a shared-btree, nBytes bytes of memory\n** are allocated, zeroed, and returned to the caller. For each subsequent \n** call the nBytes parameter is ignored and a pointer to the same blob\n** of memory returned. \n**\n** If the nBytes parameter is 0 and the blob of memory has not yet been\n** allocated, a null pointer is returned. If the blob has already been\n** allocated, it is returned as normal.\n**\n** Just before the shared-btree is closed, the function passed as the \n** xFree argument when the memory allocation was made is invoked on the \n** blob of allocated memory. The xFree function should not call sqlite3_free()\n** on the memory, the btree layer does that.\n*/\nSQLITE_PRIVATE void *sqlite3BtreeSchema(Btree *p, int nBytes, void(*xFree)(void *)){\n  BtShared *pBt = p->pBt;\n  sqlite3BtreeEnter(p);\n  if( !pBt->pSchema && nBytes ){\n    pBt->pSchema = sqlite3DbMallocZero(0, nBytes);\n    pBt->xFreeSchema = xFree;\n  }\n  sqlite3BtreeLeave(p);\n  return pBt->pSchema;\n}\n\n/*\n** Return SQLITE_LOCKED_SHAREDCACHE if another user of the same shared \n** btree as the argument handle holds an exclusive lock on the \n** sqlite_master table. Otherwise SQLITE_OK.\n*/\nSQLITE_PRIVATE int sqlite3BtreeSchemaLocked(Btree *p){\n  int rc;\n  assert( sqlite3_mutex_held(p->db->mutex) );\n  sqlite3BtreeEnter(p);\n  rc = querySharedCacheTableLock(p, MASTER_ROOT, READ_LOCK);\n  assert( rc==SQLITE_OK || rc==SQLITE_LOCKED_SHAREDCACHE );\n  sqlite3BtreeLeave(p);\n  return rc;\n}\n\n\n#ifndef SQLITE_OMIT_SHARED_CACHE\n/*\n** Obtain a lock on the table whose root page is iTab.  The\n** lock is a write lock if isWritelock is true or a read lock\n** if it is false.\n*/\nSQLITE_PRIVATE int sqlite3BtreeLockTable(Btree *p, int iTab, u8 isWriteLock){\n  int rc = SQLITE_OK;\n  assert( p->inTrans!=TRANS_NONE );\n  if( p->sharable ){\n    u8 lockType = READ_LOCK + isWriteLock;\n    assert( READ_LOCK+1==WRITE_LOCK );\n    assert( isWriteLock==0 || isWriteLock==1 );\n\n    sqlite3BtreeEnter(p);\n    rc = querySharedCacheTableLock(p, iTab, lockType);\n    if( rc==SQLITE_OK ){\n      rc = setSharedCacheTableLock(p, iTab, lockType);\n    }\n    sqlite3BtreeLeave(p);\n  }\n  return rc;\n}\n#endif\n\n#ifndef SQLITE_OMIT_INCRBLOB\n/*\n** Argument pCsr must be a cursor opened for writing on an \n** INTKEY table currently pointing at a valid table entry. \n** This function modifies the data stored as part of that entry.\n**\n** Only the data content may only be modified, it is not possible to \n** change the length of the data stored. If this function is called with\n** parameters that attempt to write past the end of the existing data,\n** no modifications are made and SQLITE_CORRUPT is returned.\n*/\nSQLITE_PRIVATE int sqlite3BtreePutData(BtCursor *pCsr, u32 offset, u32 amt, void *z){\n  int rc;\n  assert( cursorOwnsBtShared(pCsr) );\n  assert( sqlite3_mutex_held(pCsr->pBtree->db->mutex) );\n  assert( pCsr->curFlags & BTCF_Incrblob );\n\n  rc = restoreCursorPosition(pCsr);\n  if( rc!=SQLITE_OK ){\n    return rc;\n  }\n  assert( pCsr->eState!=CURSOR_REQUIRESEEK );\n  if( pCsr->eState!=CURSOR_VALID ){\n    return SQLITE_ABORT;\n  }\n\n  /* Save the positions of all other cursors open on this table. This is\n  ** required in case any of them are holding references to an xFetch\n  ** version of the b-tree page modified by the accessPayload call below.\n  **\n  ** Note that pCsr must be open on a INTKEY table and saveCursorPosition()\n  ** and hence saveAllCursors() cannot fail on a BTREE_INTKEY table, hence\n  ** saveAllCursors can only return SQLITE_OK.\n  */\n  VVA_ONLY(rc =) saveAllCursors(pCsr->pBt, pCsr->pgnoRoot, pCsr);\n  assert( rc==SQLITE_OK );\n\n  /* Check some assumptions: \n  **   (a) the cursor is open for writing,\n  **   (b) there is a read/write transaction open,\n  **   (c) the connection holds a write-lock on the table (if required),\n  **   (d) there are no conflicting read-locks, and\n  **   (e) the cursor points at a valid row of an intKey table.\n  */\n  if( (pCsr->curFlags & BTCF_WriteFlag)==0 ){\n    return SQLITE_READONLY;\n  }\n  assert( (pCsr->pBt->btsFlags & BTS_READ_ONLY)==0\n              && pCsr->pBt->inTransaction==TRANS_WRITE );\n  assert( hasSharedCacheTableLock(pCsr->pBtree, pCsr->pgnoRoot, 0, 2) );\n  assert( !hasReadConflicts(pCsr->pBtree, pCsr->pgnoRoot) );\n  assert( pCsr->pPage->intKey );\n\n  return accessPayload(pCsr, offset, amt, (unsigned char *)z, 1);\n}\n\n/* \n** Mark this cursor as an incremental blob cursor.\n*/\nSQLITE_PRIVATE void sqlite3BtreeIncrblobCursor(BtCursor *pCur){\n  pCur->curFlags |= BTCF_Incrblob;\n  pCur->pBtree->hasIncrblobCur = 1;\n}\n#endif\n\n/*\n** Set both the \"read version\" (single byte at byte offset 18) and \n** \"write version\" (single byte at byte offset 19) fields in the database\n** header to iVersion.\n*/\nSQLITE_PRIVATE int sqlite3BtreeSetVersion(Btree *pBtree, int iVersion){\n  BtShared *pBt = pBtree->pBt;\n  int rc;                         /* Return code */\n \n  assert( iVersion==1 || iVersion==2 );\n\n  /* If setting the version fields to 1, do not automatically open the\n  ** WAL connection, even if the version fields are currently set to 2.\n  */\n  pBt->btsFlags &= ~BTS_NO_WAL;\n  if( iVersion==1 ) pBt->btsFlags |= BTS_NO_WAL;\n\n  rc = sqlite3BtreeBeginTrans(pBtree, 0);\n  if( rc==SQLITE_OK ){\n    u8 *aData = pBt->pPage1->aData;\n    if( aData[18]!=(u8)iVersion || aData[19]!=(u8)iVersion ){\n      rc = sqlite3BtreeBeginTrans(pBtree, 2);\n      if( rc==SQLITE_OK ){\n        rc = sqlite3PagerWrite(pBt->pPage1->pDbPage);\n        if( rc==SQLITE_OK ){\n          aData[18] = (u8)iVersion;\n          aData[19] = (u8)iVersion;\n        }\n      }\n    }\n  }\n\n  pBt->btsFlags &= ~BTS_NO_WAL;\n  return rc;\n}\n\n/*\n** Return true if the cursor has a hint specified.  This routine is\n** only used from within assert() statements\n*/\nSQLITE_PRIVATE int sqlite3BtreeCursorHasHint(BtCursor *pCsr, unsigned int mask){\n  return (pCsr->hints & mask)!=0;\n}\n\n/*\n** Return true if the given Btree is read-only.\n*/\nSQLITE_PRIVATE int sqlite3BtreeIsReadonly(Btree *p){\n  return (p->pBt->btsFlags & BTS_READ_ONLY)!=0;\n}\n\n/*\n** Return the size of the header added to each page by this module.\n*/\nSQLITE_PRIVATE int sqlite3HeaderSizeBtree(void){ return ROUND8(sizeof(MemPage)); }\n\n#if !defined(SQLITE_OMIT_SHARED_CACHE)\n/*\n** Return true if the Btree passed as the only argument is sharable.\n*/\nSQLITE_PRIVATE int sqlite3BtreeSharable(Btree *p){\n  return p->sharable;\n}\n\n/*\n** Return the number of connections to the BtShared object accessed by\n** the Btree handle passed as the only argument. For private caches \n** this is always 1. For shared caches it may be 1 or greater.\n*/\nSQLITE_PRIVATE int sqlite3BtreeConnectionCount(Btree *p){\n  testcase( p->sharable );\n  return p->pBt->nRef;\n}\n#endif\n\n/************** End of btree.c ***********************************************/\n/************** Begin file backup.c ******************************************/\n/*\n** 2009 January 28\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n*************************************************************************\n** This file contains the implementation of the sqlite3_backup_XXX() \n** API functions and the related features.\n*/\n/* #include \"sqliteInt.h\" */\n/* #include \"btreeInt.h\" */\n\n/*\n** Structure allocated for each backup operation.\n*/\nstruct sqlite3_backup {\n  sqlite3* pDestDb;        /* Destination database handle */\n  Btree *pDest;            /* Destination b-tree file */\n  u32 iDestSchema;         /* Original schema cookie in destination */\n  int bDestLocked;         /* True once a write-transaction is open on pDest */\n\n  Pgno iNext;              /* Page number of the next source page to copy */\n  sqlite3* pSrcDb;         /* Source database handle */\n  Btree *pSrc;             /* Source b-tree file */\n\n  int rc;                  /* Backup process error code */\n\n  /* These two variables are set by every call to backup_step(). They are\n  ** read by calls to backup_remaining() and backup_pagecount().\n  */\n  Pgno nRemaining;         /* Number of pages left to copy */\n  Pgno nPagecount;         /* Total number of pages to copy */\n\n  int isAttached;          /* True once backup has been registered with pager */\n  sqlite3_backup *pNext;   /* Next backup associated with source pager */\n};\n\n/*\n** THREAD SAFETY NOTES:\n**\n**   Once it has been created using backup_init(), a single sqlite3_backup\n**   structure may be accessed via two groups of thread-safe entry points:\n**\n**     * Via the sqlite3_backup_XXX() API function backup_step() and \n**       backup_finish(). Both these functions obtain the source database\n**       handle mutex and the mutex associated with the source BtShared \n**       structure, in that order.\n**\n**     * Via the BackupUpdate() and BackupRestart() functions, which are\n**       invoked by the pager layer to report various state changes in\n**       the page cache associated with the source database. The mutex\n**       associated with the source database BtShared structure will always \n**       be held when either of these functions are invoked.\n**\n**   The other sqlite3_backup_XXX() API functions, backup_remaining() and\n**   backup_pagecount() are not thread-safe functions. If they are called\n**   while some other thread is calling backup_step() or backup_finish(),\n**   the values returned may be invalid. There is no way for a call to\n**   BackupUpdate() or BackupRestart() to interfere with backup_remaining()\n**   or backup_pagecount().\n**\n**   Depending on the SQLite configuration, the database handles and/or\n**   the Btree objects may have their own mutexes that require locking.\n**   Non-sharable Btrees (in-memory databases for example), do not have\n**   associated mutexes.\n*/\n\n/*\n** Return a pointer corresponding to database zDb (i.e. \"main\", \"temp\")\n** in connection handle pDb. If such a database cannot be found, return\n** a NULL pointer and write an error message to pErrorDb.\n**\n** If the \"temp\" database is requested, it may need to be opened by this \n** function. If an error occurs while doing so, return 0 and write an \n** error message to pErrorDb.\n*/\nstatic Btree *findBtree(sqlite3 *pErrorDb, sqlite3 *pDb, const char *zDb){\n  int i = sqlite3FindDbName(pDb, zDb);\n\n  if( i==1 ){\n    Parse sParse;\n    int rc = 0;\n    memset(&sParse, 0, sizeof(sParse));\n    sParse.db = pDb;\n    if( sqlite3OpenTempDatabase(&sParse) ){\n      sqlite3ErrorWithMsg(pErrorDb, sParse.rc, \"%s\", sParse.zErrMsg);\n      rc = SQLITE_ERROR;\n    }\n    sqlite3DbFree(pErrorDb, sParse.zErrMsg);\n    sqlite3ParserReset(&sParse);\n    if( rc ){\n      return 0;\n    }\n  }\n\n  if( i<0 ){\n    sqlite3ErrorWithMsg(pErrorDb, SQLITE_ERROR, \"unknown database %s\", zDb);\n    return 0;\n  }\n\n  return pDb->aDb[i].pBt;\n}\n\n/*\n** Attempt to set the page size of the destination to match the page size\n** of the source.\n*/\nstatic int setDestPgsz(sqlite3_backup *p){\n  int rc;\n  rc = sqlite3BtreeSetPageSize(p->pDest,sqlite3BtreeGetPageSize(p->pSrc),-1,0);\n  return rc;\n}\n\n/*\n** Check that there is no open read-transaction on the b-tree passed as the\n** second argument. If there is not, return SQLITE_OK. Otherwise, if there\n** is an open read-transaction, return SQLITE_ERROR and leave an error \n** message in database handle db.\n*/\nstatic int checkReadTransaction(sqlite3 *db, Btree *p){\n  if( sqlite3BtreeIsInReadTrans(p) ){\n    sqlite3ErrorWithMsg(db, SQLITE_ERROR, \"destination database is in use\");\n    return SQLITE_ERROR;\n  }\n  return SQLITE_OK;\n}\n\n/*\n** Create an sqlite3_backup process to copy the contents of zSrcDb from\n** connection handle pSrcDb to zDestDb in pDestDb. If successful, return\n** a pointer to the new sqlite3_backup object.\n**\n** If an error occurs, NULL is returned and an error code and error message\n** stored in database handle pDestDb.\n*/\nSQLITE_API sqlite3_backup *sqlite3_backup_init(\n  sqlite3* pDestDb,                     /* Database to write to */\n  const char *zDestDb,                  /* Name of database within pDestDb */\n  sqlite3* pSrcDb,                      /* Database connection to read from */\n  const char *zSrcDb                    /* Name of database within pSrcDb */\n){\n  sqlite3_backup *p;                    /* Value to return */\n\n#ifdef SQLITE_ENABLE_API_ARMOR\n  if( !sqlite3SafetyCheckOk(pSrcDb)||!sqlite3SafetyCheckOk(pDestDb) ){\n    (void)SQLITE_MISUSE_BKPT;\n    return 0;\n  }\n#endif\n\n  /* Lock the source database handle. The destination database\n  ** handle is not locked in this routine, but it is locked in\n  ** sqlite3_backup_step(). The user is required to ensure that no\n  ** other thread accesses the destination handle for the duration\n  ** of the backup operation.  Any attempt to use the destination\n  ** database connection while a backup is in progress may cause\n  ** a malfunction or a deadlock.\n  */\n  sqlite3_mutex_enter(pSrcDb->mutex);\n  sqlite3_mutex_enter(pDestDb->mutex);\n\n  if( pSrcDb==pDestDb ){\n    sqlite3ErrorWithMsg(\n        pDestDb, SQLITE_ERROR, \"source and destination must be distinct\"\n    );\n    p = 0;\n  }else {\n    /* Allocate space for a new sqlite3_backup object...\n    ** EVIDENCE-OF: R-64852-21591 The sqlite3_backup object is created by a\n    ** call to sqlite3_backup_init() and is destroyed by a call to\n    ** sqlite3_backup_finish(). */\n    p = (sqlite3_backup *)sqlite3MallocZero(sizeof(sqlite3_backup));\n    if( !p ){\n      sqlite3Error(pDestDb, SQLITE_NOMEM_BKPT);\n    }\n  }\n\n  /* If the allocation succeeded, populate the new object. */\n  if( p ){\n    p->pSrc = findBtree(pDestDb, pSrcDb, zSrcDb);\n    p->pDest = findBtree(pDestDb, pDestDb, zDestDb);\n    p->pDestDb = pDestDb;\n    p->pSrcDb = pSrcDb;\n    p->iNext = 1;\n    p->isAttached = 0;\n\n    if( 0==p->pSrc || 0==p->pDest \n     || checkReadTransaction(pDestDb, p->pDest)!=SQLITE_OK \n     ){\n      /* One (or both) of the named databases did not exist or an OOM\n      ** error was hit. Or there is a transaction open on the destination\n      ** database. The error has already been written into the pDestDb \n      ** handle. All that is left to do here is free the sqlite3_backup \n      ** structure.  */\n      sqlite3_free(p);\n      p = 0;\n    }\n  }\n  if( p ){\n    p->pSrc->nBackup++;\n  }\n\n  sqlite3_mutex_leave(pDestDb->mutex);\n  sqlite3_mutex_leave(pSrcDb->mutex);\n  return p;\n}\n\n/*\n** Argument rc is an SQLite error code. Return true if this error is \n** considered fatal if encountered during a backup operation. All errors\n** are considered fatal except for SQLITE_BUSY and SQLITE_LOCKED.\n*/\nstatic int isFatalError(int rc){\n  return (rc!=SQLITE_OK && rc!=SQLITE_BUSY && ALWAYS(rc!=SQLITE_LOCKED));\n}\n\n/*\n** Parameter zSrcData points to a buffer containing the data for \n** page iSrcPg from the source database. Copy this data into the \n** destination database.\n*/\nstatic int backupOnePage(\n  sqlite3_backup *p,              /* Backup handle */\n  Pgno iSrcPg,                    /* Source database page to backup */\n  const u8 *zSrcData,             /* Source database page data */\n  int bUpdate                     /* True for an update, false otherwise */\n){\n  Pager * const pDestPager = sqlite3BtreePager(p->pDest);\n  const int nSrcPgsz = sqlite3BtreeGetPageSize(p->pSrc);\n  int nDestPgsz = sqlite3BtreeGetPageSize(p->pDest);\n  const int nCopy = MIN(nSrcPgsz, nDestPgsz);\n  const i64 iEnd = (i64)iSrcPg*(i64)nSrcPgsz;\n#ifdef SQLITE_HAS_CODEC\n  /* Use BtreeGetReserveNoMutex() for the source b-tree, as although it is\n  ** guaranteed that the shared-mutex is held by this thread, handle\n  ** p->pSrc may not actually be the owner.  */\n  int nSrcReserve = sqlite3BtreeGetReserveNoMutex(p->pSrc);\n  int nDestReserve = sqlite3BtreeGetOptimalReserve(p->pDest);\n#endif\n  int rc = SQLITE_OK;\n  i64 iOff;\n\n  assert( sqlite3BtreeGetReserveNoMutex(p->pSrc)>=0 );\n  assert( p->bDestLocked );\n  assert( !isFatalError(p->rc) );\n  assert( iSrcPg!=PENDING_BYTE_PAGE(p->pSrc->pBt) );\n  assert( zSrcData );\n\n  /* Catch the case where the destination is an in-memory database and the\n  ** page sizes of the source and destination differ. \n  */\n  if( nSrcPgsz!=nDestPgsz && sqlite3PagerIsMemdb(pDestPager) ){\n    rc = SQLITE_READONLY;\n  }\n\n#ifdef SQLITE_HAS_CODEC\n  /* Backup is not possible if the page size of the destination is changing\n  ** and a codec is in use.\n  */\n  if( nSrcPgsz!=nDestPgsz && sqlite3PagerGetCodec(pDestPager)!=0 ){\n    rc = SQLITE_READONLY;\n  }\n\n  /* Backup is not possible if the number of bytes of reserve space differ\n  ** between source and destination.  If there is a difference, try to\n  ** fix the destination to agree with the source.  If that is not possible,\n  ** then the backup cannot proceed.\n  */\n  if( nSrcReserve!=nDestReserve ){\n    u32 newPgsz = nSrcPgsz;\n    rc = sqlite3PagerSetPagesize(pDestPager, &newPgsz, nSrcReserve);\n    if( rc==SQLITE_OK && newPgsz!=nSrcPgsz ) rc = SQLITE_READONLY;\n  }\n#endif\n\n  /* This loop runs once for each destination page spanned by the source \n  ** page. For each iteration, variable iOff is set to the byte offset\n  ** of the destination page.\n  */\n  for(iOff=iEnd-(i64)nSrcPgsz; rc==SQLITE_OK && iOff<iEnd; iOff+=nDestPgsz){\n    DbPage *pDestPg = 0;\n    Pgno iDest = (Pgno)(iOff/nDestPgsz)+1;\n    if( iDest==PENDING_BYTE_PAGE(p->pDest->pBt) ) continue;\n    if( SQLITE_OK==(rc = sqlite3PagerGet(pDestPager, iDest, &pDestPg, 0))\n     && SQLITE_OK==(rc = sqlite3PagerWrite(pDestPg))\n    ){\n      const u8 *zIn = &zSrcData[iOff%nSrcPgsz];\n      u8 *zDestData = sqlite3PagerGetData(pDestPg);\n      u8 *zOut = &zDestData[iOff%nDestPgsz];\n\n      /* Copy the data from the source page into the destination page.\n      ** Then clear the Btree layer MemPage.isInit flag. Both this module\n      ** and the pager code use this trick (clearing the first byte\n      ** of the page 'extra' space to invalidate the Btree layers\n      ** cached parse of the page). MemPage.isInit is marked \n      ** \"MUST BE FIRST\" for this purpose.\n      */\n      memcpy(zOut, zIn, nCopy);\n      ((u8 *)sqlite3PagerGetExtra(pDestPg))[0] = 0;\n      if( iOff==0 && bUpdate==0 ){\n        sqlite3Put4byte(&zOut[28], sqlite3BtreeLastPage(p->pSrc));\n      }\n    }\n    sqlite3PagerUnref(pDestPg);\n  }\n\n  return rc;\n}\n\n/*\n** If pFile is currently larger than iSize bytes, then truncate it to\n** exactly iSize bytes. If pFile is not larger than iSize bytes, then\n** this function is a no-op.\n**\n** Return SQLITE_OK if everything is successful, or an SQLite error \n** code if an error occurs.\n*/\nstatic int backupTruncateFile(sqlite3_file *pFile, i64 iSize){\n  i64 iCurrent;\n  int rc = sqlite3OsFileSize(pFile, &iCurrent);\n  if( rc==SQLITE_OK && iCurrent>iSize ){\n    rc = sqlite3OsTruncate(pFile, iSize);\n  }\n  return rc;\n}\n\n/*\n** Register this backup object with the associated source pager for\n** callbacks when pages are changed or the cache invalidated.\n*/\nstatic void attachBackupObject(sqlite3_backup *p){\n  sqlite3_backup **pp;\n  assert( sqlite3BtreeHoldsMutex(p->pSrc) );\n  pp = sqlite3PagerBackupPtr(sqlite3BtreePager(p->pSrc));\n  p->pNext = *pp;\n  *pp = p;\n  p->isAttached = 1;\n}\n\n/*\n** Copy nPage pages from the source b-tree to the destination.\n*/\nSQLITE_API int sqlite3_backup_step(sqlite3_backup *p, int nPage){\n  int rc;\n  int destMode;       /* Destination journal mode */\n  int pgszSrc = 0;    /* Source page size */\n  int pgszDest = 0;   /* Destination page size */\n\n#ifdef SQLITE_ENABLE_API_ARMOR\n  if( p==0 ) return SQLITE_MISUSE_BKPT;\n#endif\n  sqlite3_mutex_enter(p->pSrcDb->mutex);\n  sqlite3BtreeEnter(p->pSrc);\n  if( p->pDestDb ){\n    sqlite3_mutex_enter(p->pDestDb->mutex);\n  }\n\n  rc = p->rc;\n  if( !isFatalError(rc) ){\n    Pager * const pSrcPager = sqlite3BtreePager(p->pSrc);     /* Source pager */\n    Pager * const pDestPager = sqlite3BtreePager(p->pDest);   /* Dest pager */\n    int ii;                            /* Iterator variable */\n    int nSrcPage = -1;                 /* Size of source db in pages */\n    int bCloseTrans = 0;               /* True if src db requires unlocking */\n\n    /* If the source pager is currently in a write-transaction, return\n    ** SQLITE_BUSY immediately.\n    */\n    if( p->pDestDb && p->pSrc->pBt->inTransaction==TRANS_WRITE ){\n      rc = SQLITE_BUSY;\n    }else{\n      rc = SQLITE_OK;\n    }\n\n    /* If there is no open read-transaction on the source database, open\n    ** one now. If a transaction is opened here, then it will be closed\n    ** before this function exits.\n    */\n    if( rc==SQLITE_OK && 0==sqlite3BtreeIsInReadTrans(p->pSrc) ){\n      rc = sqlite3BtreeBeginTrans(p->pSrc, 0);\n      bCloseTrans = 1;\n    }\n\n    /* If the destination database has not yet been locked (i.e. if this\n    ** is the first call to backup_step() for the current backup operation),\n    ** try to set its page size to the same as the source database. This\n    ** is especially important on ZipVFS systems, as in that case it is\n    ** not possible to create a database file that uses one page size by\n    ** writing to it with another.  */\n    if( p->bDestLocked==0 && rc==SQLITE_OK && setDestPgsz(p)==SQLITE_NOMEM ){\n      rc = SQLITE_NOMEM;\n    }\n\n    /* Lock the destination database, if it is not locked already. */\n    if( SQLITE_OK==rc && p->bDestLocked==0\n     && SQLITE_OK==(rc = sqlite3BtreeBeginTrans(p->pDest, 2)) \n    ){\n      p->bDestLocked = 1;\n      sqlite3BtreeGetMeta(p->pDest, BTREE_SCHEMA_VERSION, &p->iDestSchema);\n    }\n\n    /* Do not allow backup if the destination database is in WAL mode\n    ** and the page sizes are different between source and destination */\n    pgszSrc = sqlite3BtreeGetPageSize(p->pSrc);\n    pgszDest = sqlite3BtreeGetPageSize(p->pDest);\n    destMode = sqlite3PagerGetJournalMode(sqlite3BtreePager(p->pDest));\n    if( SQLITE_OK==rc && destMode==PAGER_JOURNALMODE_WAL && pgszSrc!=pgszDest ){\n      rc = SQLITE_READONLY;\n    }\n  \n    /* Now that there is a read-lock on the source database, query the\n    ** source pager for the number of pages in the database.\n    */\n    nSrcPage = (int)sqlite3BtreeLastPage(p->pSrc);\n    assert( nSrcPage>=0 );\n    for(ii=0; (nPage<0 || ii<nPage) && p->iNext<=(Pgno)nSrcPage && !rc; ii++){\n      const Pgno iSrcPg = p->iNext;                 /* Source page number */\n      if( iSrcPg!=PENDING_BYTE_PAGE(p->pSrc->pBt) ){\n        DbPage *pSrcPg;                             /* Source page object */\n        rc = sqlite3PagerGet(pSrcPager, iSrcPg, &pSrcPg,PAGER_GET_READONLY);\n        if( rc==SQLITE_OK ){\n          rc = backupOnePage(p, iSrcPg, sqlite3PagerGetData(pSrcPg), 0);\n          sqlite3PagerUnref(pSrcPg);\n        }\n      }\n      p->iNext++;\n    }\n    if( rc==SQLITE_OK ){\n      p->nPagecount = nSrcPage;\n      p->nRemaining = nSrcPage+1-p->iNext;\n      if( p->iNext>(Pgno)nSrcPage ){\n        rc = SQLITE_DONE;\n      }else if( !p->isAttached ){\n        attachBackupObject(p);\n      }\n    }\n  \n    /* Update the schema version field in the destination database. This\n    ** is to make sure that the schema-version really does change in\n    ** the case where the source and destination databases have the\n    ** same schema version.\n    */\n    if( rc==SQLITE_DONE ){\n      if( nSrcPage==0 ){\n        rc = sqlite3BtreeNewDb(p->pDest);\n        nSrcPage = 1;\n      }\n      if( rc==SQLITE_OK || rc==SQLITE_DONE ){\n        rc = sqlite3BtreeUpdateMeta(p->pDest,1,p->iDestSchema+1);\n      }\n      if( rc==SQLITE_OK ){\n        if( p->pDestDb ){\n          sqlite3ResetAllSchemasOfConnection(p->pDestDb);\n        }\n        if( destMode==PAGER_JOURNALMODE_WAL ){\n          rc = sqlite3BtreeSetVersion(p->pDest, 2);\n        }\n      }\n      if( rc==SQLITE_OK ){\n        int nDestTruncate;\n        /* Set nDestTruncate to the final number of pages in the destination\n        ** database. The complication here is that the destination page\n        ** size may be different to the source page size. \n        **\n        ** If the source page size is smaller than the destination page size, \n        ** round up. In this case the call to sqlite3OsTruncate() below will\n        ** fix the size of the file. However it is important to call\n        ** sqlite3PagerTruncateImage() here so that any pages in the \n        ** destination file that lie beyond the nDestTruncate page mark are\n        ** journalled by PagerCommitPhaseOne() before they are destroyed\n        ** by the file truncation.\n        */\n        assert( pgszSrc==sqlite3BtreeGetPageSize(p->pSrc) );\n        assert( pgszDest==sqlite3BtreeGetPageSize(p->pDest) );\n        if( pgszSrc<pgszDest ){\n          int ratio = pgszDest/pgszSrc;\n          nDestTruncate = (nSrcPage+ratio-1)/ratio;\n          if( nDestTruncate==(int)PENDING_BYTE_PAGE(p->pDest->pBt) ){\n            nDestTruncate--;\n          }\n        }else{\n          nDestTruncate = nSrcPage * (pgszSrc/pgszDest);\n        }\n        assert( nDestTruncate>0 );\n\n        if( pgszSrc<pgszDest ){\n          /* If the source page-size is smaller than the destination page-size,\n          ** two extra things may need to happen:\n          **\n          **   * The destination may need to be truncated, and\n          **\n          **   * Data stored on the pages immediately following the \n          **     pending-byte page in the source database may need to be\n          **     copied into the destination database.\n          */\n          const i64 iSize = (i64)pgszSrc * (i64)nSrcPage;\n          sqlite3_file * const pFile = sqlite3PagerFile(pDestPager);\n          Pgno iPg;\n          int nDstPage;\n          i64 iOff;\n          i64 iEnd;\n\n          assert( pFile );\n          assert( nDestTruncate==0 \n              || (i64)nDestTruncate*(i64)pgszDest >= iSize || (\n                nDestTruncate==(int)(PENDING_BYTE_PAGE(p->pDest->pBt)-1)\n             && iSize>=PENDING_BYTE && iSize<=PENDING_BYTE+pgszDest\n          ));\n\n          /* This block ensures that all data required to recreate the original\n          ** database has been stored in the journal for pDestPager and the\n          ** journal synced to disk. So at this point we may safely modify\n          ** the database file in any way, knowing that if a power failure\n          ** occurs, the original database will be reconstructed from the \n          ** journal file.  */\n          sqlite3PagerPagecount(pDestPager, &nDstPage);\n          for(iPg=nDestTruncate; rc==SQLITE_OK && iPg<=(Pgno)nDstPage; iPg++){\n            if( iPg!=PENDING_BYTE_PAGE(p->pDest->pBt) ){\n              DbPage *pPg;\n              rc = sqlite3PagerGet(pDestPager, iPg, &pPg, 0);\n              if( rc==SQLITE_OK ){\n                rc = sqlite3PagerWrite(pPg);\n                sqlite3PagerUnref(pPg);\n              }\n            }\n          }\n          if( rc==SQLITE_OK ){\n            rc = sqlite3PagerCommitPhaseOne(pDestPager, 0, 1);\n          }\n\n          /* Write the extra pages and truncate the database file as required */\n          iEnd = MIN(PENDING_BYTE + pgszDest, iSize);\n          for(\n            iOff=PENDING_BYTE+pgszSrc; \n            rc==SQLITE_OK && iOff<iEnd; \n            iOff+=pgszSrc\n          ){\n            PgHdr *pSrcPg = 0;\n            const Pgno iSrcPg = (Pgno)((iOff/pgszSrc)+1);\n            rc = sqlite3PagerGet(pSrcPager, iSrcPg, &pSrcPg, 0);\n            if( rc==SQLITE_OK ){\n              u8 *zData = sqlite3PagerGetData(pSrcPg);\n              rc = sqlite3OsWrite(pFile, zData, pgszSrc, iOff);\n            }\n            sqlite3PagerUnref(pSrcPg);\n          }\n          if( rc==SQLITE_OK ){\n            rc = backupTruncateFile(pFile, iSize);\n          }\n\n          /* Sync the database file to disk. */\n          if( rc==SQLITE_OK ){\n            rc = sqlite3PagerSync(pDestPager, 0);\n          }\n        }else{\n          sqlite3PagerTruncateImage(pDestPager, nDestTruncate);\n          rc = sqlite3PagerCommitPhaseOne(pDestPager, 0, 0);\n        }\n    \n        /* Finish committing the transaction to the destination database. */\n        if( SQLITE_OK==rc\n         && SQLITE_OK==(rc = sqlite3BtreeCommitPhaseTwo(p->pDest, 0))\n        ){\n          rc = SQLITE_DONE;\n        }\n      }\n    }\n  \n    /* If bCloseTrans is true, then this function opened a read transaction\n    ** on the source database. Close the read transaction here. There is\n    ** no need to check the return values of the btree methods here, as\n    ** \"committing\" a read-only transaction cannot fail.\n    */\n    if( bCloseTrans ){\n      TESTONLY( int rc2 );\n      TESTONLY( rc2  = ) sqlite3BtreeCommitPhaseOne(p->pSrc, 0);\n      TESTONLY( rc2 |= ) sqlite3BtreeCommitPhaseTwo(p->pSrc, 0);\n      assert( rc2==SQLITE_OK );\n    }\n  \n    if( rc==SQLITE_IOERR_NOMEM ){\n      rc = SQLITE_NOMEM_BKPT;\n    }\n    p->rc = rc;\n  }\n  if( p->pDestDb ){\n    sqlite3_mutex_leave(p->pDestDb->mutex);\n  }\n  sqlite3BtreeLeave(p->pSrc);\n  sqlite3_mutex_leave(p->pSrcDb->mutex);\n  return rc;\n}\n\n/*\n** Release all resources associated with an sqlite3_backup* handle.\n*/\nSQLITE_API int sqlite3_backup_finish(sqlite3_backup *p){\n  sqlite3_backup **pp;                 /* Ptr to head of pagers backup list */\n  sqlite3 *pSrcDb;                     /* Source database connection */\n  int rc;                              /* Value to return */\n\n  /* Enter the mutexes */\n  if( p==0 ) return SQLITE_OK;\n  pSrcDb = p->pSrcDb;\n  sqlite3_mutex_enter(pSrcDb->mutex);\n  sqlite3BtreeEnter(p->pSrc);\n  if( p->pDestDb ){\n    sqlite3_mutex_enter(p->pDestDb->mutex);\n  }\n\n  /* Detach this backup from the source pager. */\n  if( p->pDestDb ){\n    p->pSrc->nBackup--;\n  }\n  if( p->isAttached ){\n    pp = sqlite3PagerBackupPtr(sqlite3BtreePager(p->pSrc));\n    while( *pp!=p ){\n      pp = &(*pp)->pNext;\n    }\n    *pp = p->pNext;\n  }\n\n  /* If a transaction is still open on the Btree, roll it back. */\n  sqlite3BtreeRollback(p->pDest, SQLITE_OK, 0);\n\n  /* Set the error code of the destination database handle. */\n  rc = (p->rc==SQLITE_DONE) ? SQLITE_OK : p->rc;\n  if( p->pDestDb ){\n    sqlite3Error(p->pDestDb, rc);\n\n    /* Exit the mutexes and free the backup context structure. */\n    sqlite3LeaveMutexAndCloseZombie(p->pDestDb);\n  }\n  sqlite3BtreeLeave(p->pSrc);\n  if( p->pDestDb ){\n    /* EVIDENCE-OF: R-64852-21591 The sqlite3_backup object is created by a\n    ** call to sqlite3_backup_init() and is destroyed by a call to\n    ** sqlite3_backup_finish(). */\n    sqlite3_free(p);\n  }\n  sqlite3LeaveMutexAndCloseZombie(pSrcDb);\n  return rc;\n}\n\n/*\n** Return the number of pages still to be backed up as of the most recent\n** call to sqlite3_backup_step().\n*/\nSQLITE_API int sqlite3_backup_remaining(sqlite3_backup *p){\n#ifdef SQLITE_ENABLE_API_ARMOR\n  if( p==0 ){\n    (void)SQLITE_MISUSE_BKPT;\n    return 0;\n  }\n#endif\n  return p->nRemaining;\n}\n\n/*\n** Return the total number of pages in the source database as of the most \n** recent call to sqlite3_backup_step().\n*/\nSQLITE_API int sqlite3_backup_pagecount(sqlite3_backup *p){\n#ifdef SQLITE_ENABLE_API_ARMOR\n  if( p==0 ){\n    (void)SQLITE_MISUSE_BKPT;\n    return 0;\n  }\n#endif\n  return p->nPagecount;\n}\n\n/*\n** This function is called after the contents of page iPage of the\n** source database have been modified. If page iPage has already been \n** copied into the destination database, then the data written to the\n** destination is now invalidated. The destination copy of iPage needs\n** to be updated with the new data before the backup operation is\n** complete.\n**\n** It is assumed that the mutex associated with the BtShared object\n** corresponding to the source database is held when this function is\n** called.\n*/\nstatic SQLITE_NOINLINE void backupUpdate(\n  sqlite3_backup *p,\n  Pgno iPage,\n  const u8 *aData\n){\n  assert( p!=0 );\n  do{\n    assert( sqlite3_mutex_held(p->pSrc->pBt->mutex) );\n    if( !isFatalError(p->rc) && iPage<p->iNext ){\n      /* The backup process p has already copied page iPage. But now it\n      ** has been modified by a transaction on the source pager. Copy\n      ** the new data into the backup.\n      */\n      int rc;\n      assert( p->pDestDb );\n      sqlite3_mutex_enter(p->pDestDb->mutex);\n      rc = backupOnePage(p, iPage, aData, 1);\n      sqlite3_mutex_leave(p->pDestDb->mutex);\n      assert( rc!=SQLITE_BUSY && rc!=SQLITE_LOCKED );\n      if( rc!=SQLITE_OK ){\n        p->rc = rc;\n      }\n    }\n  }while( (p = p->pNext)!=0 );\n}\nSQLITE_PRIVATE void sqlite3BackupUpdate(sqlite3_backup *pBackup, Pgno iPage, const u8 *aData){\n  if( pBackup ) backupUpdate(pBackup, iPage, aData);\n}\n\n/*\n** Restart the backup process. This is called when the pager layer\n** detects that the database has been modified by an external database\n** connection. In this case there is no way of knowing which of the\n** pages that have been copied into the destination database are still \n** valid and which are not, so the entire process needs to be restarted.\n**\n** It is assumed that the mutex associated with the BtShared object\n** corresponding to the source database is held when this function is\n** called.\n*/\nSQLITE_PRIVATE void sqlite3BackupRestart(sqlite3_backup *pBackup){\n  sqlite3_backup *p;                   /* Iterator variable */\n  for(p=pBackup; p; p=p->pNext){\n    assert( sqlite3_mutex_held(p->pSrc->pBt->mutex) );\n    p->iNext = 1;\n  }\n}\n\n#ifndef SQLITE_OMIT_VACUUM\n/*\n** Copy the complete content of pBtFrom into pBtTo.  A transaction\n** must be active for both files.\n**\n** The size of file pTo may be reduced by this operation. If anything \n** goes wrong, the transaction on pTo is rolled back. If successful, the \n** transaction is committed before returning.\n*/\nSQLITE_PRIVATE int sqlite3BtreeCopyFile(Btree *pTo, Btree *pFrom){\n  int rc;\n  sqlite3_file *pFd;              /* File descriptor for database pTo */\n  sqlite3_backup b;\n  sqlite3BtreeEnter(pTo);\n  sqlite3BtreeEnter(pFrom);\n\n  assert( sqlite3BtreeIsInTrans(pTo) );\n  pFd = sqlite3PagerFile(sqlite3BtreePager(pTo));\n  if( pFd->pMethods ){\n    i64 nByte = sqlite3BtreeGetPageSize(pFrom)*(i64)sqlite3BtreeLastPage(pFrom);\n    rc = sqlite3OsFileControl(pFd, SQLITE_FCNTL_OVERWRITE, &nByte);\n    if( rc==SQLITE_NOTFOUND ) rc = SQLITE_OK;\n    if( rc ) goto copy_finished;\n  }\n\n  /* Set up an sqlite3_backup object. sqlite3_backup.pDestDb must be set\n  ** to 0. This is used by the implementations of sqlite3_backup_step()\n  ** and sqlite3_backup_finish() to detect that they are being called\n  ** from this function, not directly by the user.\n  */\n  memset(&b, 0, sizeof(b));\n  b.pSrcDb = pFrom->db;\n  b.pSrc = pFrom;\n  b.pDest = pTo;\n  b.iNext = 1;\n\n#ifdef SQLITE_HAS_CODEC\n  sqlite3PagerAlignReserve(sqlite3BtreePager(pTo), sqlite3BtreePager(pFrom));\n#endif\n\n  /* 0x7FFFFFFF is the hard limit for the number of pages in a database\n  ** file. By passing this as the number of pages to copy to\n  ** sqlite3_backup_step(), we can guarantee that the copy finishes \n  ** within a single call (unless an error occurs). The assert() statement\n  ** checks this assumption - (p->rc) should be set to either SQLITE_DONE \n  ** or an error code.  */\n  sqlite3_backup_step(&b, 0x7FFFFFFF);\n  assert( b.rc!=SQLITE_OK );\n\n  rc = sqlite3_backup_finish(&b);\n  if( rc==SQLITE_OK ){\n    pTo->pBt->btsFlags &= ~BTS_PAGESIZE_FIXED;\n  }else{\n    sqlite3PagerClearCache(sqlite3BtreePager(b.pDest));\n  }\n\n  assert( sqlite3BtreeIsInTrans(pTo)==0 );\ncopy_finished:\n  sqlite3BtreeLeave(pFrom);\n  sqlite3BtreeLeave(pTo);\n  return rc;\n}\n#endif /* SQLITE_OMIT_VACUUM */\n\n/************** End of backup.c **********************************************/\n/************** Begin file vdbemem.c *****************************************/\n/*\n** 2004 May 26\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n*************************************************************************\n**\n** This file contains code use to manipulate \"Mem\" structure.  A \"Mem\"\n** stores a single value in the VDBE.  Mem is an opaque structure visible\n** only within the VDBE.  Interface routines refer to a Mem using the\n** name sqlite_value\n*/\n/* #include \"sqliteInt.h\" */\n/* #include \"vdbeInt.h\" */\n\n#ifdef SQLITE_DEBUG\n/*\n** Check invariants on a Mem object.\n**\n** This routine is intended for use inside of assert() statements, like\n** this:    assert( sqlite3VdbeCheckMemInvariants(pMem) );\n*/\nSQLITE_PRIVATE int sqlite3VdbeCheckMemInvariants(Mem *p){\n  /* If MEM_Dyn is set then Mem.xDel!=0.  \n  ** Mem.xDel might not be initialized if MEM_Dyn is clear.\n  */\n  assert( (p->flags & MEM_Dyn)==0 || p->xDel!=0 );\n\n  /* MEM_Dyn may only be set if Mem.szMalloc==0.  In this way we\n  ** ensure that if Mem.szMalloc>0 then it is safe to do\n  ** Mem.z = Mem.zMalloc without having to check Mem.flags&MEM_Dyn.\n  ** That saves a few cycles in inner loops. */\n  assert( (p->flags & MEM_Dyn)==0 || p->szMalloc==0 );\n\n  /* Cannot be both MEM_Int and MEM_Real at the same time */\n  assert( (p->flags & (MEM_Int|MEM_Real))!=(MEM_Int|MEM_Real) );\n\n  if( p->flags & MEM_Null ){\n    /* Cannot be both MEM_Null and some other type */\n    assert( (p->flags & (MEM_Int|MEM_Real|MEM_Str|MEM_Blob\n                         |MEM_RowSet|MEM_Frame|MEM_Agg))==0 );\n\n    /* If MEM_Null is set, then either the value is a pure NULL (the usual\n    ** case) or it is a pointer set using sqlite3_bind_pointer() or\n    ** sqlite3_result_pointer().  If a pointer, then MEM_Term must also be\n    ** set.\n    */\n    if( (p->flags & (MEM_Term|MEM_Subtype))==(MEM_Term|MEM_Subtype) ){\n      /* This is a pointer type.  There may be a flag to indicate what to\n      ** do with the pointer. */\n      assert( ((p->flags&MEM_Dyn)!=0 ? 1 : 0) +\n              ((p->flags&MEM_Ephem)!=0 ? 1 : 0) +\n              ((p->flags&MEM_Static)!=0 ? 1 : 0) <= 1 );\n\n      /* No other bits set */\n      assert( (p->flags & ~(MEM_Null|MEM_Term|MEM_Subtype\n                           |MEM_Dyn|MEM_Ephem|MEM_Static))==0 );\n    }else{\n      /* A pure NULL might have other flags, such as MEM_Static, MEM_Dyn,\n      ** MEM_Ephem, MEM_Cleared, or MEM_Subtype */\n    }\n  }else{\n    /* The MEM_Cleared bit is only allowed on NULLs */\n    assert( (p->flags & MEM_Cleared)==0 );\n  }\n\n  /* The szMalloc field holds the correct memory allocation size */\n  assert( p->szMalloc==0\n       || p->szMalloc==sqlite3DbMallocSize(p->db,p->zMalloc) );\n\n  /* If p holds a string or blob, the Mem.z must point to exactly\n  ** one of the following:\n  **\n  **   (1) Memory in Mem.zMalloc and managed by the Mem object\n  **   (2) Memory to be freed using Mem.xDel\n  **   (3) An ephemeral string or blob\n  **   (4) A static string or blob\n  */\n  if( (p->flags & (MEM_Str|MEM_Blob)) && p->n>0 ){\n    assert( \n      ((p->szMalloc>0 && p->z==p->zMalloc)? 1 : 0) +\n      ((p->flags&MEM_Dyn)!=0 ? 1 : 0) +\n      ((p->flags&MEM_Ephem)!=0 ? 1 : 0) +\n      ((p->flags&MEM_Static)!=0 ? 1 : 0) == 1\n    );\n  }\n  return 1;\n}\n#endif\n\n#ifdef SQLITE_DEBUG\n/*\n** Check that string value of pMem agrees with its integer or real value.\n**\n** A single int or real value always converts to the same strings.  But\n** many different strings can be converted into the same int or real.\n** If a table contains a numeric value and an index is based on the\n** corresponding string value, then it is important that the string be\n** derived from the numeric value, not the other way around, to ensure\n** that the index and table are consistent.  See ticket\n** https://www.sqlite.org/src/info/343634942dd54ab (2018-01-31) for\n** an example.\n**\n** This routine looks at pMem to verify that if it has both a numeric\n** representation and a string representation then the string rep has\n** been derived from the numeric and not the other way around.  It returns\n** true if everything is ok and false if there is a problem.\n**\n** This routine is for use inside of assert() statements only.\n*/\nSQLITE_PRIVATE int sqlite3VdbeMemConsistentDualRep(Mem *p){\n  char zBuf[100];\n  char *z;\n  int i, j, incr;\n  if( (p->flags & MEM_Str)==0 ) return 1;\n  if( (p->flags & (MEM_Int|MEM_Real))==0 ) return 1;\n  if( p->flags & MEM_Int ){\n    sqlite3_snprintf(sizeof(zBuf),zBuf,\"%lld\",p->u.i);\n  }else{\n    sqlite3_snprintf(sizeof(zBuf),zBuf,\"%!.15g\",p->u.r);\n  }\n  z = p->z;\n  i = j = 0;\n  incr = 1;\n  if( p->enc!=SQLITE_UTF8 ){\n    incr = 2;\n    if( p->enc==SQLITE_UTF16BE ) z++;\n  }\n  while( zBuf[j] ){\n    if( zBuf[j++]!=z[i] ) return 0;\n    i += incr;\n  }\n  return 1;\n}\n#endif /* SQLITE_DEBUG */\n\n/*\n** If pMem is an object with a valid string representation, this routine\n** ensures the internal encoding for the string representation is\n** 'desiredEnc', one of SQLITE_UTF8, SQLITE_UTF16LE or SQLITE_UTF16BE.\n**\n** If pMem is not a string object, or the encoding of the string\n** representation is already stored using the requested encoding, then this\n** routine is a no-op.\n**\n** SQLITE_OK is returned if the conversion is successful (or not required).\n** SQLITE_NOMEM may be returned if a malloc() fails during conversion\n** between formats.\n*/\nSQLITE_PRIVATE int sqlite3VdbeChangeEncoding(Mem *pMem, int desiredEnc){\n#ifndef SQLITE_OMIT_UTF16\n  int rc;\n#endif\n  assert( (pMem->flags&MEM_RowSet)==0 );\n  assert( desiredEnc==SQLITE_UTF8 || desiredEnc==SQLITE_UTF16LE\n           || desiredEnc==SQLITE_UTF16BE );\n  if( !(pMem->flags&MEM_Str) || pMem->enc==desiredEnc ){\n    return SQLITE_OK;\n  }\n  assert( pMem->db==0 || sqlite3_mutex_held(pMem->db->mutex) );\n#ifdef SQLITE_OMIT_UTF16\n  return SQLITE_ERROR;\n#else\n\n  /* MemTranslate() may return SQLITE_OK or SQLITE_NOMEM. If NOMEM is returned,\n  ** then the encoding of the value may not have changed.\n  */\n  rc = sqlite3VdbeMemTranslate(pMem, (u8)desiredEnc);\n  assert(rc==SQLITE_OK    || rc==SQLITE_NOMEM);\n  assert(rc==SQLITE_OK    || pMem->enc!=desiredEnc);\n  assert(rc==SQLITE_NOMEM || pMem->enc==desiredEnc);\n  return rc;\n#endif\n}\n\n/*\n** Make sure pMem->z points to a writable allocation of at least \n** min(n,32) bytes.\n**\n** If the bPreserve argument is true, then copy of the content of\n** pMem->z into the new allocation.  pMem must be either a string or\n** blob if bPreserve is true.  If bPreserve is false, any prior content\n** in pMem->z is discarded.\n*/\nSQLITE_PRIVATE SQLITE_NOINLINE int sqlite3VdbeMemGrow(Mem *pMem, int n, int bPreserve){\n  assert( sqlite3VdbeCheckMemInvariants(pMem) );\n  assert( (pMem->flags&MEM_RowSet)==0 );\n  testcase( pMem->db==0 );\n\n  /* If the bPreserve flag is set to true, then the memory cell must already\n  ** contain a valid string or blob value.  */\n  assert( bPreserve==0 || pMem->flags&(MEM_Blob|MEM_Str) );\n  testcase( bPreserve && pMem->z==0 );\n\n  assert( pMem->szMalloc==0\n       || pMem->szMalloc==sqlite3DbMallocSize(pMem->db, pMem->zMalloc) );\n  if( n<32 ) n = 32;\n  if( pMem->szMalloc>0 && bPreserve && pMem->z==pMem->zMalloc ){\n    pMem->z = pMem->zMalloc = sqlite3DbReallocOrFree(pMem->db, pMem->z, n);\n    bPreserve = 0;\n  }else{\n    if( pMem->szMalloc>0 ) sqlite3DbFreeNN(pMem->db, pMem->zMalloc);\n    pMem->zMalloc = sqlite3DbMallocRaw(pMem->db, n);\n  }\n  if( pMem->zMalloc==0 ){\n    sqlite3VdbeMemSetNull(pMem);\n    pMem->z = 0;\n    pMem->szMalloc = 0;\n    return SQLITE_NOMEM_BKPT;\n  }else{\n    pMem->szMalloc = sqlite3DbMallocSize(pMem->db, pMem->zMalloc);\n  }\n\n  if( bPreserve && pMem->z ){\n    assert( pMem->z!=pMem->zMalloc );\n    memcpy(pMem->zMalloc, pMem->z, pMem->n);\n  }\n  if( (pMem->flags&MEM_Dyn)!=0 ){\n    assert( pMem->xDel!=0 && pMem->xDel!=SQLITE_DYNAMIC );\n    pMem->xDel((void *)(pMem->z));\n  }\n\n  pMem->z = pMem->zMalloc;\n  pMem->flags &= ~(MEM_Dyn|MEM_Ephem|MEM_Static);\n  return SQLITE_OK;\n}\n\n/*\n** Change the pMem->zMalloc allocation to be at least szNew bytes.\n** If pMem->zMalloc already meets or exceeds the requested size, this\n** routine is a no-op.\n**\n** Any prior string or blob content in the pMem object may be discarded.\n** The pMem->xDel destructor is called, if it exists.  Though MEM_Str\n** and MEM_Blob values may be discarded, MEM_Int, MEM_Real, and MEM_Null\n** values are preserved.\n**\n** Return SQLITE_OK on success or an error code (probably SQLITE_NOMEM)\n** if unable to complete the resizing.\n*/\nSQLITE_PRIVATE int sqlite3VdbeMemClearAndResize(Mem *pMem, int szNew){\n  assert( szNew>0 );\n  assert( (pMem->flags & MEM_Dyn)==0 || pMem->szMalloc==0 );\n  if( pMem->szMalloc<szNew ){\n    return sqlite3VdbeMemGrow(pMem, szNew, 0);\n  }\n  assert( (pMem->flags & MEM_Dyn)==0 );\n  pMem->z = pMem->zMalloc;\n  pMem->flags &= (MEM_Null|MEM_Int|MEM_Real);\n  return SQLITE_OK;\n}\n\n/*\n** It is already known that pMem contains an unterminated string.\n** Add the zero terminator.\n*/\nstatic SQLITE_NOINLINE int vdbeMemAddTerminator(Mem *pMem){\n  if( sqlite3VdbeMemGrow(pMem, pMem->n+2, 1) ){\n    return SQLITE_NOMEM_BKPT;\n  }\n  pMem->z[pMem->n] = 0;\n  pMem->z[pMem->n+1] = 0;\n  pMem->flags |= MEM_Term;\n  return SQLITE_OK;\n}\n\n/*\n** Change pMem so that its MEM_Str or MEM_Blob value is stored in\n** MEM.zMalloc, where it can be safely written.\n**\n** Return SQLITE_OK on success or SQLITE_NOMEM if malloc fails.\n*/\nSQLITE_PRIVATE int sqlite3VdbeMemMakeWriteable(Mem *pMem){\n  assert( pMem->db==0 || sqlite3_mutex_held(pMem->db->mutex) );\n  assert( (pMem->flags&MEM_RowSet)==0 );\n  if( (pMem->flags & (MEM_Str|MEM_Blob))!=0 ){\n    if( ExpandBlob(pMem) ) return SQLITE_NOMEM;\n    if( pMem->szMalloc==0 || pMem->z!=pMem->zMalloc ){\n      int rc = vdbeMemAddTerminator(pMem);\n      if( rc ) return rc;\n    }\n  }\n  pMem->flags &= ~MEM_Ephem;\n#ifdef SQLITE_DEBUG\n  pMem->pScopyFrom = 0;\n#endif\n\n  return SQLITE_OK;\n}\n\n/*\n** If the given Mem* has a zero-filled tail, turn it into an ordinary\n** blob stored in dynamically allocated space.\n*/\n#ifndef SQLITE_OMIT_INCRBLOB\nSQLITE_PRIVATE int sqlite3VdbeMemExpandBlob(Mem *pMem){\n  int nByte;\n  assert( pMem->flags & MEM_Zero );\n  assert( pMem->flags&MEM_Blob );\n  assert( (pMem->flags&MEM_RowSet)==0 );\n  assert( pMem->db==0 || sqlite3_mutex_held(pMem->db->mutex) );\n\n  /* Set nByte to the number of bytes required to store the expanded blob. */\n  nByte = pMem->n + pMem->u.nZero;\n  if( nByte<=0 ){\n    nByte = 1;\n  }\n  if( sqlite3VdbeMemGrow(pMem, nByte, 1) ){\n    return SQLITE_NOMEM_BKPT;\n  }\n\n  memset(&pMem->z[pMem->n], 0, pMem->u.nZero);\n  pMem->n += pMem->u.nZero;\n  pMem->flags &= ~(MEM_Zero|MEM_Term);\n  return SQLITE_OK;\n}\n#endif\n\n/*\n** Make sure the given Mem is \\u0000 terminated.\n*/\nSQLITE_PRIVATE int sqlite3VdbeMemNulTerminate(Mem *pMem){\n  assert( pMem->db==0 || sqlite3_mutex_held(pMem->db->mutex) );\n  testcase( (pMem->flags & (MEM_Term|MEM_Str))==(MEM_Term|MEM_Str) );\n  testcase( (pMem->flags & (MEM_Term|MEM_Str))==0 );\n  if( (pMem->flags & (MEM_Term|MEM_Str))!=MEM_Str ){\n    return SQLITE_OK;   /* Nothing to do */\n  }else{\n    return vdbeMemAddTerminator(pMem);\n  }\n}\n\n/*\n** Add MEM_Str to the set of representations for the given Mem.  Numbers\n** are converted using sqlite3_snprintf().  Converting a BLOB to a string\n** is a no-op.\n**\n** Existing representations MEM_Int and MEM_Real are invalidated if\n** bForce is true but are retained if bForce is false.\n**\n** A MEM_Null value will never be passed to this function. This function is\n** used for converting values to text for returning to the user (i.e. via\n** sqlite3_value_text()), or for ensuring that values to be used as btree\n** keys are strings. In the former case a NULL pointer is returned the\n** user and the latter is an internal programming error.\n*/\nSQLITE_PRIVATE int sqlite3VdbeMemStringify(Mem *pMem, u8 enc, u8 bForce){\n  int fg = pMem->flags;\n  const int nByte = 32;\n\n  assert( pMem->db==0 || sqlite3_mutex_held(pMem->db->mutex) );\n  assert( !(fg&MEM_Zero) );\n  assert( !(fg&(MEM_Str|MEM_Blob)) );\n  assert( fg&(MEM_Int|MEM_Real) );\n  assert( (pMem->flags&MEM_RowSet)==0 );\n  assert( EIGHT_BYTE_ALIGNMENT(pMem) );\n\n\n  if( sqlite3VdbeMemClearAndResize(pMem, nByte) ){\n    pMem->enc = 0;\n    return SQLITE_NOMEM_BKPT;\n  }\n\n  /* For a Real or Integer, use sqlite3_snprintf() to produce the UTF-8\n  ** string representation of the value. Then, if the required encoding\n  ** is UTF-16le or UTF-16be do a translation.\n  ** \n  ** FIX ME: It would be better if sqlite3_snprintf() could do UTF-16.\n  */\n  if( fg & MEM_Int ){\n    sqlite3_snprintf(nByte, pMem->z, \"%lld\", pMem->u.i);\n  }else{\n    assert( fg & MEM_Real );\n    sqlite3_snprintf(nByte, pMem->z, \"%!.15g\", pMem->u.r);\n  }\n  pMem->n = sqlite3Strlen30(pMem->z);\n  pMem->enc = SQLITE_UTF8;\n  pMem->flags |= MEM_Str|MEM_Term;\n  if( bForce ) pMem->flags &= ~(MEM_Int|MEM_Real);\n  sqlite3VdbeChangeEncoding(pMem, enc);\n  return SQLITE_OK;\n}\n\n/*\n** Memory cell pMem contains the context of an aggregate function.\n** This routine calls the finalize method for that function.  The\n** result of the aggregate is stored back into pMem.\n**\n** Return SQLITE_ERROR if the finalizer reports an error.  SQLITE_OK\n** otherwise.\n*/\nSQLITE_PRIVATE int sqlite3VdbeMemFinalize(Mem *pMem, FuncDef *pFunc){\n  sqlite3_context ctx;\n  Mem t;\n  assert( pFunc!=0 );\n  assert( pFunc->xFinalize!=0 );\n  assert( (pMem->flags & MEM_Null)!=0 || pFunc==pMem->u.pDef );\n  assert( pMem->db==0 || sqlite3_mutex_held(pMem->db->mutex) );\n  memset(&ctx, 0, sizeof(ctx));\n  memset(&t, 0, sizeof(t));\n  t.flags = MEM_Null;\n  t.db = pMem->db;\n  ctx.pOut = &t;\n  ctx.pMem = pMem;\n  ctx.pFunc = pFunc;\n  pFunc->xFinalize(&ctx); /* IMP: R-24505-23230 */\n  assert( (pMem->flags & MEM_Dyn)==0 );\n  if( pMem->szMalloc>0 ) sqlite3DbFreeNN(pMem->db, pMem->zMalloc);\n  memcpy(pMem, &t, sizeof(t));\n  return ctx.isError;\n}\n\n/*\n** If the memory cell contains a value that must be freed by\n** invoking the external callback in Mem.xDel, then this routine\n** will free that value.  It also sets Mem.flags to MEM_Null.\n**\n** This is a helper routine for sqlite3VdbeMemSetNull() and\n** for sqlite3VdbeMemRelease().  Use those other routines as the\n** entry point for releasing Mem resources.\n*/\nstatic SQLITE_NOINLINE void vdbeMemClearExternAndSetNull(Mem *p){\n  assert( p->db==0 || sqlite3_mutex_held(p->db->mutex) );\n  assert( VdbeMemDynamic(p) );\n  if( p->flags&MEM_Agg ){\n    sqlite3VdbeMemFinalize(p, p->u.pDef);\n    assert( (p->flags & MEM_Agg)==0 );\n    testcase( p->flags & MEM_Dyn );\n  }\n  if( p->flags&MEM_Dyn ){\n    assert( (p->flags&MEM_RowSet)==0 );\n    assert( p->xDel!=SQLITE_DYNAMIC && p->xDel!=0 );\n    p->xDel((void *)p->z);\n  }else if( p->flags&MEM_RowSet ){\n    sqlite3RowSetClear(p->u.pRowSet);\n  }else if( p->flags&MEM_Frame ){\n    VdbeFrame *pFrame = p->u.pFrame;\n    pFrame->pParent = pFrame->v->pDelFrame;\n    pFrame->v->pDelFrame = pFrame;\n  }\n  p->flags = MEM_Null;\n}\n\n/*\n** Release memory held by the Mem p, both external memory cleared\n** by p->xDel and memory in p->zMalloc.\n**\n** This is a helper routine invoked by sqlite3VdbeMemRelease() in\n** the unusual case where there really is memory in p that needs\n** to be freed.\n*/\nstatic SQLITE_NOINLINE void vdbeMemClear(Mem *p){\n  if( VdbeMemDynamic(p) ){\n    vdbeMemClearExternAndSetNull(p);\n  }\n  if( p->szMalloc ){\n    sqlite3DbFreeNN(p->db, p->zMalloc);\n    p->szMalloc = 0;\n  }\n  p->z = 0;\n}\n\n/*\n** Release any memory resources held by the Mem.  Both the memory that is\n** free by Mem.xDel and the Mem.zMalloc allocation are freed.\n**\n** Use this routine prior to clean up prior to abandoning a Mem, or to\n** reset a Mem back to its minimum memory utilization.\n**\n** Use sqlite3VdbeMemSetNull() to release just the Mem.xDel space\n** prior to inserting new content into the Mem.\n*/\nSQLITE_PRIVATE void sqlite3VdbeMemRelease(Mem *p){\n  assert( sqlite3VdbeCheckMemInvariants(p) );\n  if( VdbeMemDynamic(p) || p->szMalloc ){\n    vdbeMemClear(p);\n  }\n}\n\n/*\n** Convert a 64-bit IEEE double into a 64-bit signed integer.\n** If the double is out of range of a 64-bit signed integer then\n** return the closest available 64-bit signed integer.\n*/\nstatic SQLITE_NOINLINE i64 doubleToInt64(double r){\n#ifdef SQLITE_OMIT_FLOATING_POINT\n  /* When floating-point is omitted, double and int64 are the same thing */\n  return r;\n#else\n  /*\n  ** Many compilers we encounter do not define constants for the\n  ** minimum and maximum 64-bit integers, or they define them\n  ** inconsistently.  And many do not understand the \"LL\" notation.\n  ** So we define our own static constants here using nothing\n  ** larger than a 32-bit integer constant.\n  */\n  static const i64 maxInt = LARGEST_INT64;\n  static const i64 minInt = SMALLEST_INT64;\n\n  if( r<=(double)minInt ){\n    return minInt;\n  }else if( r>=(double)maxInt ){\n    return maxInt;\n  }else{\n    return (i64)r;\n  }\n#endif\n}\n\n/*\n** Return some kind of integer value which is the best we can do\n** at representing the value that *pMem describes as an integer.\n** If pMem is an integer, then the value is exact.  If pMem is\n** a floating-point then the value returned is the integer part.\n** If pMem is a string or blob, then we make an attempt to convert\n** it into an integer and return that.  If pMem represents an\n** an SQL-NULL value, return 0.\n**\n** If pMem represents a string value, its encoding might be changed.\n*/\nstatic SQLITE_NOINLINE i64 memIntValue(Mem *pMem){\n  i64 value = 0;\n  sqlite3Atoi64(pMem->z, &value, pMem->n, pMem->enc);\n  return value;\n}\nSQLITE_PRIVATE i64 sqlite3VdbeIntValue(Mem *pMem){\n  int flags;\n  assert( pMem->db==0 || sqlite3_mutex_held(pMem->db->mutex) );\n  assert( EIGHT_BYTE_ALIGNMENT(pMem) );\n  flags = pMem->flags;\n  if( flags & MEM_Int ){\n    return pMem->u.i;\n  }else if( flags & MEM_Real ){\n    return doubleToInt64(pMem->u.r);\n  }else if( flags & (MEM_Str|MEM_Blob) ){\n    assert( pMem->z || pMem->n==0 );\n    return memIntValue(pMem);\n  }else{\n    return 0;\n  }\n}\n\n/*\n** Return the best representation of pMem that we can get into a\n** double.  If pMem is already a double or an integer, return its\n** value.  If it is a string or blob, try to convert it to a double.\n** If it is a NULL, return 0.0.\n*/\nstatic SQLITE_NOINLINE double memRealValue(Mem *pMem){\n  /* (double)0 In case of SQLITE_OMIT_FLOATING_POINT... */\n  double val = (double)0;\n  sqlite3AtoF(pMem->z, &val, pMem->n, pMem->enc);\n  return val;\n}\nSQLITE_PRIVATE double sqlite3VdbeRealValue(Mem *pMem){\n  assert( pMem->db==0 || sqlite3_mutex_held(pMem->db->mutex) );\n  assert( EIGHT_BYTE_ALIGNMENT(pMem) );\n  if( pMem->flags & MEM_Real ){\n    return pMem->u.r;\n  }else if( pMem->flags & MEM_Int ){\n    return (double)pMem->u.i;\n  }else if( pMem->flags & (MEM_Str|MEM_Blob) ){\n    return memRealValue(pMem);\n  }else{\n    /* (double)0 In case of SQLITE_OMIT_FLOATING_POINT... */\n    return (double)0;\n  }\n}\n\n/*\n** Return 1 if pMem represents true, and return 0 if pMem represents false.\n** Return the value ifNull if pMem is NULL.  \n*/\nSQLITE_PRIVATE int sqlite3VdbeBooleanValue(Mem *pMem, int ifNull){\n  if( pMem->flags & MEM_Int ) return pMem->u.i!=0;\n  if( pMem->flags & MEM_Null ) return ifNull;\n  return sqlite3VdbeRealValue(pMem)!=0.0;\n}\n\n/*\n** The MEM structure is already a MEM_Real.  Try to also make it a\n** MEM_Int if we can.\n*/\nSQLITE_PRIVATE void sqlite3VdbeIntegerAffinity(Mem *pMem){\n  i64 ix;\n  assert( pMem->flags & MEM_Real );\n  assert( (pMem->flags & MEM_RowSet)==0 );\n  assert( pMem->db==0 || sqlite3_mutex_held(pMem->db->mutex) );\n  assert( EIGHT_BYTE_ALIGNMENT(pMem) );\n\n  ix = doubleToInt64(pMem->u.r);\n\n  /* Only mark the value as an integer if\n  **\n  **    (1) the round-trip conversion real->int->real is a no-op, and\n  **    (2) The integer is neither the largest nor the smallest\n  **        possible integer (ticket #3922)\n  **\n  ** The second and third terms in the following conditional enforces\n  ** the second condition under the assumption that addition overflow causes\n  ** values to wrap around.\n  */\n  if( pMem->u.r==ix && ix>SMALLEST_INT64 && ix<LARGEST_INT64 ){\n    pMem->u.i = ix;\n    MemSetTypeFlag(pMem, MEM_Int);\n  }\n}\n\n/*\n** Convert pMem to type integer.  Invalidate any prior representations.\n*/\nSQLITE_PRIVATE int sqlite3VdbeMemIntegerify(Mem *pMem){\n  assert( pMem->db==0 || sqlite3_mutex_held(pMem->db->mutex) );\n  assert( (pMem->flags & MEM_RowSet)==0 );\n  assert( EIGHT_BYTE_ALIGNMENT(pMem) );\n\n  pMem->u.i = sqlite3VdbeIntValue(pMem);\n  MemSetTypeFlag(pMem, MEM_Int);\n  return SQLITE_OK;\n}\n\n/*\n** Convert pMem so that it is of type MEM_Real.\n** Invalidate any prior representations.\n*/\nSQLITE_PRIVATE int sqlite3VdbeMemRealify(Mem *pMem){\n  assert( pMem->db==0 || sqlite3_mutex_held(pMem->db->mutex) );\n  assert( EIGHT_BYTE_ALIGNMENT(pMem) );\n\n  pMem->u.r = sqlite3VdbeRealValue(pMem);\n  MemSetTypeFlag(pMem, MEM_Real);\n  return SQLITE_OK;\n}\n\n/* Compare a floating point value to an integer.  Return true if the two\n** values are the same within the precision of the floating point value.\n**\n** For some versions of GCC on 32-bit machines, if you do the more obvious\n** comparison of \"r1==(double)i\" you sometimes get an answer of false even\n** though the r1 and (double)i values are bit-for-bit the same.\n*/\nstatic int sqlite3RealSameAsInt(double r1, sqlite3_int64 i){\n  double r2 = (double)i;\n  return memcmp(&r1, &r2, sizeof(r1))==0;\n}\n\n/*\n** Convert pMem so that it has types MEM_Real or MEM_Int or both.\n** Invalidate any prior representations.\n**\n** Every effort is made to force the conversion, even if the input\n** is a string that does not look completely like a number.  Convert\n** as much of the string as we can and ignore the rest.\n*/\nSQLITE_PRIVATE int sqlite3VdbeMemNumerify(Mem *pMem){\n  if( (pMem->flags & (MEM_Int|MEM_Real|MEM_Null))==0 ){\n    int rc;\n    assert( (pMem->flags & (MEM_Blob|MEM_Str))!=0 );\n    assert( pMem->db==0 || sqlite3_mutex_held(pMem->db->mutex) );\n    rc = sqlite3Atoi64(pMem->z, &pMem->u.i, pMem->n, pMem->enc);\n    if( rc==0 ){\n      MemSetTypeFlag(pMem, MEM_Int);\n    }else{\n      i64 i = pMem->u.i;\n      sqlite3AtoF(pMem->z, &pMem->u.r, pMem->n, pMem->enc);\n      if( rc==1 && sqlite3RealSameAsInt(pMem->u.r, i) ){\n        pMem->u.i = i;\n        MemSetTypeFlag(pMem, MEM_Int);\n      }else{\n        MemSetTypeFlag(pMem, MEM_Real);\n      }\n    }\n  }\n  assert( (pMem->flags & (MEM_Int|MEM_Real|MEM_Null))!=0 );\n  pMem->flags &= ~(MEM_Str|MEM_Blob|MEM_Zero);\n  return SQLITE_OK;\n}\n\n/*\n** Cast the datatype of the value in pMem according to the affinity\n** \"aff\".  Casting is different from applying affinity in that a cast\n** is forced.  In other words, the value is converted into the desired\n** affinity even if that results in loss of data.  This routine is\n** used (for example) to implement the SQL \"cast()\" operator.\n*/\nSQLITE_PRIVATE void sqlite3VdbeMemCast(Mem *pMem, u8 aff, u8 encoding){\n  if( pMem->flags & MEM_Null ) return;\n  switch( aff ){\n    case SQLITE_AFF_BLOB: {   /* Really a cast to BLOB */\n      if( (pMem->flags & MEM_Blob)==0 ){\n        sqlite3ValueApplyAffinity(pMem, SQLITE_AFF_TEXT, encoding);\n        assert( pMem->flags & MEM_Str || pMem->db->mallocFailed );\n        if( pMem->flags & MEM_Str ) MemSetTypeFlag(pMem, MEM_Blob);\n      }else{\n        pMem->flags &= ~(MEM_TypeMask&~MEM_Blob);\n      }\n      break;\n    }\n    case SQLITE_AFF_NUMERIC: {\n      sqlite3VdbeMemNumerify(pMem);\n      break;\n    }\n    case SQLITE_AFF_INTEGER: {\n      sqlite3VdbeMemIntegerify(pMem);\n      break;\n    }\n    case SQLITE_AFF_REAL: {\n      sqlite3VdbeMemRealify(pMem);\n      break;\n    }\n    default: {\n      assert( aff==SQLITE_AFF_TEXT );\n      assert( MEM_Str==(MEM_Blob>>3) );\n      pMem->flags |= (pMem->flags&MEM_Blob)>>3;\n      sqlite3ValueApplyAffinity(pMem, SQLITE_AFF_TEXT, encoding);\n      assert( pMem->flags & MEM_Str || pMem->db->mallocFailed );\n      pMem->flags &= ~(MEM_Int|MEM_Real|MEM_Blob|MEM_Zero);\n      break;\n    }\n  }\n}\n\n/*\n** Initialize bulk memory to be a consistent Mem object.\n**\n** The minimum amount of initialization feasible is performed.\n*/\nSQLITE_PRIVATE void sqlite3VdbeMemInit(Mem *pMem, sqlite3 *db, u16 flags){\n  assert( (flags & ~MEM_TypeMask)==0 );\n  pMem->flags = flags;\n  pMem->db = db;\n  pMem->szMalloc = 0;\n}\n\n\n/*\n** Delete any previous value and set the value stored in *pMem to NULL.\n**\n** This routine calls the Mem.xDel destructor to dispose of values that\n** require the destructor.  But it preserves the Mem.zMalloc memory allocation.\n** To free all resources, use sqlite3VdbeMemRelease(), which both calls this\n** routine to invoke the destructor and deallocates Mem.zMalloc.\n**\n** Use this routine to reset the Mem prior to insert a new value.\n**\n** Use sqlite3VdbeMemRelease() to complete erase the Mem prior to abandoning it.\n*/\nSQLITE_PRIVATE void sqlite3VdbeMemSetNull(Mem *pMem){\n  if( VdbeMemDynamic(pMem) ){\n    vdbeMemClearExternAndSetNull(pMem);\n  }else{\n    pMem->flags = MEM_Null;\n  }\n}\nSQLITE_PRIVATE void sqlite3ValueSetNull(sqlite3_value *p){\n  sqlite3VdbeMemSetNull((Mem*)p); \n}\n\n/*\n** Delete any previous value and set the value to be a BLOB of length\n** n containing all zeros.\n*/\nSQLITE_PRIVATE void sqlite3VdbeMemSetZeroBlob(Mem *pMem, int n){\n  sqlite3VdbeMemRelease(pMem);\n  pMem->flags = MEM_Blob|MEM_Zero;\n  pMem->n = 0;\n  if( n<0 ) n = 0;\n  pMem->u.nZero = n;\n  pMem->enc = SQLITE_UTF8;\n  pMem->z = 0;\n}\n\n/*\n** The pMem is known to contain content that needs to be destroyed prior\n** to a value change.  So invoke the destructor, then set the value to\n** a 64-bit integer.\n*/\nstatic SQLITE_NOINLINE void vdbeReleaseAndSetInt64(Mem *pMem, i64 val){\n  sqlite3VdbeMemSetNull(pMem);\n  pMem->u.i = val;\n  pMem->flags = MEM_Int;\n}\n\n/*\n** Delete any previous value and set the value stored in *pMem to val,\n** manifest type INTEGER.\n*/\nSQLITE_PRIVATE void sqlite3VdbeMemSetInt64(Mem *pMem, i64 val){\n  if( VdbeMemDynamic(pMem) ){\n    vdbeReleaseAndSetInt64(pMem, val);\n  }else{\n    pMem->u.i = val;\n    pMem->flags = MEM_Int;\n  }\n}\n\n/* A no-op destructor */\nstatic void sqlite3NoopDestructor(void *p){ UNUSED_PARAMETER(p); }\n\n/*\n** Set the value stored in *pMem should already be a NULL.\n** Also store a pointer to go with it.\n*/\nSQLITE_PRIVATE void sqlite3VdbeMemSetPointer(\n  Mem *pMem,\n  void *pPtr,\n  const char *zPType,\n  void (*xDestructor)(void*)\n){\n  assert( pMem->flags==MEM_Null );\n  pMem->u.zPType = zPType ? zPType : \"\";\n  pMem->z = pPtr;\n  pMem->flags = MEM_Null|MEM_Dyn|MEM_Subtype|MEM_Term;\n  pMem->eSubtype = 'p';\n  pMem->xDel = xDestructor ? xDestructor : sqlite3NoopDestructor;\n}\n\n#ifndef SQLITE_OMIT_FLOATING_POINT\n/*\n** Delete any previous value and set the value stored in *pMem to val,\n** manifest type REAL.\n*/\nSQLITE_PRIVATE void sqlite3VdbeMemSetDouble(Mem *pMem, double val){\n  sqlite3VdbeMemSetNull(pMem);\n  if( !sqlite3IsNaN(val) ){\n    pMem->u.r = val;\n    pMem->flags = MEM_Real;\n  }\n}\n#endif\n\n/*\n** Delete any previous value and set the value of pMem to be an\n** empty boolean index.\n*/\nSQLITE_PRIVATE void sqlite3VdbeMemSetRowSet(Mem *pMem){\n  sqlite3 *db = pMem->db;\n  assert( db!=0 );\n  assert( (pMem->flags & MEM_RowSet)==0 );\n  sqlite3VdbeMemRelease(pMem);\n  pMem->zMalloc = sqlite3DbMallocRawNN(db, 64);\n  if( db->mallocFailed ){\n    pMem->flags = MEM_Null;\n    pMem->szMalloc = 0;\n  }else{\n    assert( pMem->zMalloc );\n    pMem->szMalloc = sqlite3DbMallocSize(db, pMem->zMalloc);\n    pMem->u.pRowSet = sqlite3RowSetInit(db, pMem->zMalloc, pMem->szMalloc);\n    assert( pMem->u.pRowSet!=0 );\n    pMem->flags = MEM_RowSet;\n  }\n}\n\n/*\n** Return true if the Mem object contains a TEXT or BLOB that is\n** too large - whose size exceeds SQLITE_MAX_LENGTH.\n*/\nSQLITE_PRIVATE int sqlite3VdbeMemTooBig(Mem *p){\n  assert( p->db!=0 );\n  if( p->flags & (MEM_Str|MEM_Blob) ){\n    int n = p->n;\n    if( p->flags & MEM_Zero ){\n      n += p->u.nZero;\n    }\n    return n>p->db->aLimit[SQLITE_LIMIT_LENGTH];\n  }\n  return 0; \n}\n\n#ifdef SQLITE_DEBUG\n/*\n** This routine prepares a memory cell for modification by breaking\n** its link to a shallow copy and by marking any current shallow\n** copies of this cell as invalid.\n**\n** This is used for testing and debugging only - to make sure shallow\n** copies are not misused.\n*/\nSQLITE_PRIVATE void sqlite3VdbeMemAboutToChange(Vdbe *pVdbe, Mem *pMem){\n  int i;\n  Mem *pX;\n  for(i=0, pX=pVdbe->aMem; i<pVdbe->nMem; i++, pX++){\n    if( pX->pScopyFrom==pMem ){\n      pX->flags |= MEM_Undefined;\n      pX->pScopyFrom = 0;\n    }\n  }\n  pMem->pScopyFrom = 0;\n}\n#endif /* SQLITE_DEBUG */\n\n\n/*\n** Make an shallow copy of pFrom into pTo.  Prior contents of\n** pTo are freed.  The pFrom->z field is not duplicated.  If\n** pFrom->z is used, then pTo->z points to the same thing as pFrom->z\n** and flags gets srcType (either MEM_Ephem or MEM_Static).\n*/\nstatic SQLITE_NOINLINE void vdbeClrCopy(Mem *pTo, const Mem *pFrom, int eType){\n  vdbeMemClearExternAndSetNull(pTo);\n  assert( !VdbeMemDynamic(pTo) );\n  sqlite3VdbeMemShallowCopy(pTo, pFrom, eType);\n}\nSQLITE_PRIVATE void sqlite3VdbeMemShallowCopy(Mem *pTo, const Mem *pFrom, int srcType){\n  assert( (pFrom->flags & MEM_RowSet)==0 );\n  assert( pTo->db==pFrom->db );\n  if( VdbeMemDynamic(pTo) ){ vdbeClrCopy(pTo,pFrom,srcType); return; }\n  memcpy(pTo, pFrom, MEMCELLSIZE);\n  if( (pFrom->flags&MEM_Static)==0 ){\n    pTo->flags &= ~(MEM_Dyn|MEM_Static|MEM_Ephem);\n    assert( srcType==MEM_Ephem || srcType==MEM_Static );\n    pTo->flags |= srcType;\n  }\n}\n\n/*\n** Make a full copy of pFrom into pTo.  Prior contents of pTo are\n** freed before the copy is made.\n*/\nSQLITE_PRIVATE int sqlite3VdbeMemCopy(Mem *pTo, const Mem *pFrom){\n  int rc = SQLITE_OK;\n\n  assert( (pFrom->flags & MEM_RowSet)==0 );\n  if( VdbeMemDynamic(pTo) ) vdbeMemClearExternAndSetNull(pTo);\n  memcpy(pTo, pFrom, MEMCELLSIZE);\n  pTo->flags &= ~MEM_Dyn;\n  if( pTo->flags&(MEM_Str|MEM_Blob) ){\n    if( 0==(pFrom->flags&MEM_Static) ){\n      pTo->flags |= MEM_Ephem;\n      rc = sqlite3VdbeMemMakeWriteable(pTo);\n    }\n  }\n\n  return rc;\n}\n\n/*\n** Transfer the contents of pFrom to pTo. Any existing value in pTo is\n** freed. If pFrom contains ephemeral data, a copy is made.\n**\n** pFrom contains an SQL NULL when this routine returns.\n*/\nSQLITE_PRIVATE void sqlite3VdbeMemMove(Mem *pTo, Mem *pFrom){\n  assert( pFrom->db==0 || sqlite3_mutex_held(pFrom->db->mutex) );\n  assert( pTo->db==0 || sqlite3_mutex_held(pTo->db->mutex) );\n  assert( pFrom->db==0 || pTo->db==0 || pFrom->db==pTo->db );\n\n  sqlite3VdbeMemRelease(pTo);\n  memcpy(pTo, pFrom, sizeof(Mem));\n  pFrom->flags = MEM_Null;\n  pFrom->szMalloc = 0;\n}\n\n/*\n** Change the value of a Mem to be a string or a BLOB.\n**\n** The memory management strategy depends on the value of the xDel\n** parameter. If the value passed is SQLITE_TRANSIENT, then the \n** string is copied into a (possibly existing) buffer managed by the \n** Mem structure. Otherwise, any existing buffer is freed and the\n** pointer copied.\n**\n** If the string is too large (if it exceeds the SQLITE_LIMIT_LENGTH\n** size limit) then no memory allocation occurs.  If the string can be\n** stored without allocating memory, then it is.  If a memory allocation\n** is required to store the string, then value of pMem is unchanged.  In\n** either case, SQLITE_TOOBIG is returned.\n*/\nSQLITE_PRIVATE int sqlite3VdbeMemSetStr(\n  Mem *pMem,          /* Memory cell to set to string value */\n  const char *z,      /* String pointer */\n  int n,              /* Bytes in string, or negative */\n  u8 enc,             /* Encoding of z.  0 for BLOBs */\n  void (*xDel)(void*) /* Destructor function */\n){\n  int nByte = n;      /* New value for pMem->n */\n  int iLimit;         /* Maximum allowed string or blob size */\n  u16 flags = 0;      /* New value for pMem->flags */\n\n  assert( pMem->db==0 || sqlite3_mutex_held(pMem->db->mutex) );\n  assert( (pMem->flags & MEM_RowSet)==0 );\n\n  /* If z is a NULL pointer, set pMem to contain an SQL NULL. */\n  if( !z ){\n    sqlite3VdbeMemSetNull(pMem);\n    return SQLITE_OK;\n  }\n\n  if( pMem->db ){\n    iLimit = pMem->db->aLimit[SQLITE_LIMIT_LENGTH];\n  }else{\n    iLimit = SQLITE_MAX_LENGTH;\n  }\n  flags = (enc==0?MEM_Blob:MEM_Str);\n  if( nByte<0 ){\n    assert( enc!=0 );\n    if( enc==SQLITE_UTF8 ){\n      nByte = 0x7fffffff & (int)strlen(z);\n      if( nByte>iLimit ) nByte = iLimit+1;\n    }else{\n      for(nByte=0; nByte<=iLimit && (z[nByte] | z[nByte+1]); nByte+=2){}\n    }\n    flags |= MEM_Term;\n  }\n\n  /* The following block sets the new values of Mem.z and Mem.xDel. It\n  ** also sets a flag in local variable \"flags\" to indicate the memory\n  ** management (one of MEM_Dyn or MEM_Static).\n  */\n  if( xDel==SQLITE_TRANSIENT ){\n    int nAlloc = nByte;\n    if( flags&MEM_Term ){\n      nAlloc += (enc==SQLITE_UTF8?1:2);\n    }\n    if( nByte>iLimit ){\n      return SQLITE_TOOBIG;\n    }\n    testcase( nAlloc==0 );\n    testcase( nAlloc==31 );\n    testcase( nAlloc==32 );\n    if( sqlite3VdbeMemClearAndResize(pMem, MAX(nAlloc,32)) ){\n      return SQLITE_NOMEM_BKPT;\n    }\n    memcpy(pMem->z, z, nAlloc);\n  }else if( xDel==SQLITE_DYNAMIC ){\n    sqlite3VdbeMemRelease(pMem);\n    pMem->zMalloc = pMem->z = (char *)z;\n    pMem->szMalloc = sqlite3DbMallocSize(pMem->db, pMem->zMalloc);\n  }else{\n    sqlite3VdbeMemRelease(pMem);\n    pMem->z = (char *)z;\n    pMem->xDel = xDel;\n    flags |= ((xDel==SQLITE_STATIC)?MEM_Static:MEM_Dyn);\n  }\n\n  pMem->n = nByte;\n  pMem->flags = flags;\n  pMem->enc = (enc==0 ? SQLITE_UTF8 : enc);\n\n#ifndef SQLITE_OMIT_UTF16\n  if( pMem->enc!=SQLITE_UTF8 && sqlite3VdbeMemHandleBom(pMem) ){\n    return SQLITE_NOMEM_BKPT;\n  }\n#endif\n\n  if( nByte>iLimit ){\n    return SQLITE_TOOBIG;\n  }\n\n  return SQLITE_OK;\n}\n\n/*\n** Move data out of a btree key or data field and into a Mem structure.\n** The data is payload from the entry that pCur is currently pointing\n** to.  offset and amt determine what portion of the data or key to retrieve.\n** The result is written into the pMem element.\n**\n** The pMem object must have been initialized.  This routine will use\n** pMem->zMalloc to hold the content from the btree, if possible.  New\n** pMem->zMalloc space will be allocated if necessary.  The calling routine\n** is responsible for making sure that the pMem object is eventually\n** destroyed.\n**\n** If this routine fails for any reason (malloc returns NULL or unable\n** to read from the disk) then the pMem is left in an inconsistent state.\n*/\nstatic SQLITE_NOINLINE int vdbeMemFromBtreeResize(\n  BtCursor *pCur,   /* Cursor pointing at record to retrieve. */\n  u32 offset,       /* Offset from the start of data to return bytes from. */\n  u32 amt,          /* Number of bytes to return. */\n  Mem *pMem         /* OUT: Return data in this Mem structure. */\n){\n  int rc;\n  pMem->flags = MEM_Null;\n  if( SQLITE_OK==(rc = sqlite3VdbeMemClearAndResize(pMem, amt+1)) ){\n    rc = sqlite3BtreePayload(pCur, offset, amt, pMem->z);\n    if( rc==SQLITE_OK ){\n      pMem->z[amt] = 0;   /* Overrun area used when reading malformed records */\n      pMem->flags = MEM_Blob;\n      pMem->n = (int)amt;\n    }else{\n      sqlite3VdbeMemRelease(pMem);\n    }\n  }\n  return rc;\n}\nSQLITE_PRIVATE int sqlite3VdbeMemFromBtree(\n  BtCursor *pCur,   /* Cursor pointing at record to retrieve. */\n  u32 offset,       /* Offset from the start of data to return bytes from. */\n  u32 amt,          /* Number of bytes to return. */\n  Mem *pMem         /* OUT: Return data in this Mem structure. */\n){\n  char *zData;        /* Data from the btree layer */\n  u32 available = 0;  /* Number of bytes available on the local btree page */\n  int rc = SQLITE_OK; /* Return code */\n\n  assert( sqlite3BtreeCursorIsValid(pCur) );\n  assert( !VdbeMemDynamic(pMem) );\n\n  /* Note: the calls to BtreeKeyFetch() and DataFetch() below assert() \n  ** that both the BtShared and database handle mutexes are held. */\n  assert( (pMem->flags & MEM_RowSet)==0 );\n  zData = (char *)sqlite3BtreePayloadFetch(pCur, &available);\n  assert( zData!=0 );\n\n  if( offset+amt<=available ){\n    pMem->z = &zData[offset];\n    pMem->flags = MEM_Blob|MEM_Ephem;\n    pMem->n = (int)amt;\n  }else{\n    rc = vdbeMemFromBtreeResize(pCur, offset, amt, pMem);\n  }\n\n  return rc;\n}\n\n/*\n** The pVal argument is known to be a value other than NULL.\n** Convert it into a string with encoding enc and return a pointer\n** to a zero-terminated version of that string.\n*/\nstatic SQLITE_NOINLINE const void *valueToText(sqlite3_value* pVal, u8 enc){\n  assert( pVal!=0 );\n  assert( pVal->db==0 || sqlite3_mutex_held(pVal->db->mutex) );\n  assert( (enc&3)==(enc&~SQLITE_UTF16_ALIGNED) );\n  assert( (pVal->flags & MEM_RowSet)==0 );\n  assert( (pVal->flags & (MEM_Null))==0 );\n  if( pVal->flags & (MEM_Blob|MEM_Str) ){\n    if( ExpandBlob(pVal) ) return 0;\n    pVal->flags |= MEM_Str;\n    if( pVal->enc != (enc & ~SQLITE_UTF16_ALIGNED) ){\n      sqlite3VdbeChangeEncoding(pVal, enc & ~SQLITE_UTF16_ALIGNED);\n    }\n    if( (enc & SQLITE_UTF16_ALIGNED)!=0 && 1==(1&SQLITE_PTR_TO_INT(pVal->z)) ){\n      assert( (pVal->flags & (MEM_Ephem|MEM_Static))!=0 );\n      if( sqlite3VdbeMemMakeWriteable(pVal)!=SQLITE_OK ){\n        return 0;\n      }\n    }\n    sqlite3VdbeMemNulTerminate(pVal); /* IMP: R-31275-44060 */\n  }else{\n    sqlite3VdbeMemStringify(pVal, enc, 0);\n    assert( 0==(1&SQLITE_PTR_TO_INT(pVal->z)) );\n  }\n  assert(pVal->enc==(enc & ~SQLITE_UTF16_ALIGNED) || pVal->db==0\n              || pVal->db->mallocFailed );\n  if( pVal->enc==(enc & ~SQLITE_UTF16_ALIGNED) ){\n    assert( sqlite3VdbeMemConsistentDualRep(pVal) );\n    return pVal->z;\n  }else{\n    return 0;\n  }\n}\n\n/* This function is only available internally, it is not part of the\n** external API. It works in a similar way to sqlite3_value_text(),\n** except the data returned is in the encoding specified by the second\n** parameter, which must be one of SQLITE_UTF16BE, SQLITE_UTF16LE or\n** SQLITE_UTF8.\n**\n** (2006-02-16:)  The enc value can be or-ed with SQLITE_UTF16_ALIGNED.\n** If that is the case, then the result must be aligned on an even byte\n** boundary.\n*/\nSQLITE_PRIVATE const void *sqlite3ValueText(sqlite3_value* pVal, u8 enc){\n  if( !pVal ) return 0;\n  assert( pVal->db==0 || sqlite3_mutex_held(pVal->db->mutex) );\n  assert( (enc&3)==(enc&~SQLITE_UTF16_ALIGNED) );\n  assert( (pVal->flags & MEM_RowSet)==0 );\n  if( (pVal->flags&(MEM_Str|MEM_Term))==(MEM_Str|MEM_Term) && pVal->enc==enc ){\n    assert( sqlite3VdbeMemConsistentDualRep(pVal) );\n    return pVal->z;\n  }\n  if( pVal->flags&MEM_Null ){\n    return 0;\n  }\n  return valueToText(pVal, enc);\n}\n\n/*\n** Create a new sqlite3_value object.\n*/\nSQLITE_PRIVATE sqlite3_value *sqlite3ValueNew(sqlite3 *db){\n  Mem *p = sqlite3DbMallocZero(db, sizeof(*p));\n  if( p ){\n    p->flags = MEM_Null;\n    p->db = db;\n  }\n  return p;\n}\n\n/*\n** Context object passed by sqlite3Stat4ProbeSetValue() through to \n** valueNew(). See comments above valueNew() for details.\n*/\nstruct ValueNewStat4Ctx {\n  Parse *pParse;\n  Index *pIdx;\n  UnpackedRecord **ppRec;\n  int iVal;\n};\n\n/*\n** Allocate and return a pointer to a new sqlite3_value object. If\n** the second argument to this function is NULL, the object is allocated\n** by calling sqlite3ValueNew().\n**\n** Otherwise, if the second argument is non-zero, then this function is \n** being called indirectly by sqlite3Stat4ProbeSetValue(). If it has not\n** already been allocated, allocate the UnpackedRecord structure that \n** that function will return to its caller here. Then return a pointer to\n** an sqlite3_value within the UnpackedRecord.a[] array.\n*/\nstatic sqlite3_value *valueNew(sqlite3 *db, struct ValueNewStat4Ctx *p){\n#ifdef SQLITE_ENABLE_STAT3_OR_STAT4\n  if( p ){\n    UnpackedRecord *pRec = p->ppRec[0];\n\n    if( pRec==0 ){\n      Index *pIdx = p->pIdx;      /* Index being probed */\n      int nByte;                  /* Bytes of space to allocate */\n      int i;                      /* Counter variable */\n      int nCol = pIdx->nColumn;   /* Number of index columns including rowid */\n  \n      nByte = sizeof(Mem) * nCol + ROUND8(sizeof(UnpackedRecord));\n      pRec = (UnpackedRecord*)sqlite3DbMallocZero(db, nByte);\n      if( pRec ){\n        pRec->pKeyInfo = sqlite3KeyInfoOfIndex(p->pParse, pIdx);\n        if( pRec->pKeyInfo ){\n          assert( pRec->pKeyInfo->nAllField==nCol );\n          assert( pRec->pKeyInfo->enc==ENC(db) );\n          pRec->aMem = (Mem *)((u8*)pRec + ROUND8(sizeof(UnpackedRecord)));\n          for(i=0; i<nCol; i++){\n            pRec->aMem[i].flags = MEM_Null;\n            pRec->aMem[i].db = db;\n          }\n        }else{\n          sqlite3DbFreeNN(db, pRec);\n          pRec = 0;\n        }\n      }\n      if( pRec==0 ) return 0;\n      p->ppRec[0] = pRec;\n    }\n  \n    pRec->nField = p->iVal+1;\n    return &pRec->aMem[p->iVal];\n  }\n#else\n  UNUSED_PARAMETER(p);\n#endif /* defined(SQLITE_ENABLE_STAT3_OR_STAT4) */\n  return sqlite3ValueNew(db);\n}\n\n/*\n** The expression object indicated by the second argument is guaranteed\n** to be a scalar SQL function. If\n**\n**   * all function arguments are SQL literals,\n**   * one of the SQLITE_FUNC_CONSTANT or _SLOCHNG function flags is set, and\n**   * the SQLITE_FUNC_NEEDCOLL function flag is not set,\n**\n** then this routine attempts to invoke the SQL function. Assuming no\n** error occurs, output parameter (*ppVal) is set to point to a value \n** object containing the result before returning SQLITE_OK.\n**\n** Affinity aff is applied to the result of the function before returning.\n** If the result is a text value, the sqlite3_value object uses encoding \n** enc.\n**\n** If the conditions above are not met, this function returns SQLITE_OK\n** and sets (*ppVal) to NULL. Or, if an error occurs, (*ppVal) is set to\n** NULL and an SQLite error code returned.\n*/\n#ifdef SQLITE_ENABLE_STAT3_OR_STAT4\nstatic int valueFromFunction(\n  sqlite3 *db,                    /* The database connection */\n  Expr *p,                        /* The expression to evaluate */\n  u8 enc,                         /* Encoding to use */\n  u8 aff,                         /* Affinity to use */\n  sqlite3_value **ppVal,          /* Write the new value here */\n  struct ValueNewStat4Ctx *pCtx   /* Second argument for valueNew() */\n){\n  sqlite3_context ctx;            /* Context object for function invocation */\n  sqlite3_value **apVal = 0;      /* Function arguments */\n  int nVal = 0;                   /* Size of apVal[] array */\n  FuncDef *pFunc = 0;             /* Function definition */\n  sqlite3_value *pVal = 0;        /* New value */\n  int rc = SQLITE_OK;             /* Return code */\n  ExprList *pList = 0;            /* Function arguments */\n  int i;                          /* Iterator variable */\n\n  assert( pCtx!=0 );\n  assert( (p->flags & EP_TokenOnly)==0 );\n  pList = p->x.pList;\n  if( pList ) nVal = pList->nExpr;\n  pFunc = sqlite3FindFunction(db, p->u.zToken, nVal, enc, 0);\n  assert( pFunc );\n  if( (pFunc->funcFlags & (SQLITE_FUNC_CONSTANT|SQLITE_FUNC_SLOCHNG))==0 \n   || (pFunc->funcFlags & SQLITE_FUNC_NEEDCOLL)\n  ){\n    return SQLITE_OK;\n  }\n\n  if( pList ){\n    apVal = (sqlite3_value**)sqlite3DbMallocZero(db, sizeof(apVal[0]) * nVal);\n    if( apVal==0 ){\n      rc = SQLITE_NOMEM_BKPT;\n      goto value_from_function_out;\n    }\n    for(i=0; i<nVal; i++){\n      rc = sqlite3ValueFromExpr(db, pList->a[i].pExpr, enc, aff, &apVal[i]);\n      if( apVal[i]==0 || rc!=SQLITE_OK ) goto value_from_function_out;\n    }\n  }\n\n  pVal = valueNew(db, pCtx);\n  if( pVal==0 ){\n    rc = SQLITE_NOMEM_BKPT;\n    goto value_from_function_out;\n  }\n\n  assert( pCtx->pParse->rc==SQLITE_OK );\n  memset(&ctx, 0, sizeof(ctx));\n  ctx.pOut = pVal;\n  ctx.pFunc = pFunc;\n  pFunc->xSFunc(&ctx, nVal, apVal);\n  if( ctx.isError ){\n    rc = ctx.isError;\n    sqlite3ErrorMsg(pCtx->pParse, \"%s\", sqlite3_value_text(pVal));\n  }else{\n    sqlite3ValueApplyAffinity(pVal, aff, SQLITE_UTF8);\n    assert( rc==SQLITE_OK );\n    rc = sqlite3VdbeChangeEncoding(pVal, enc);\n    if( rc==SQLITE_OK && sqlite3VdbeMemTooBig(pVal) ){\n      rc = SQLITE_TOOBIG;\n      pCtx->pParse->nErr++;\n    }\n  }\n  pCtx->pParse->rc = rc;\n\n value_from_function_out:\n  if( rc!=SQLITE_OK ){\n    pVal = 0;\n  }\n  if( apVal ){\n    for(i=0; i<nVal; i++){\n      sqlite3ValueFree(apVal[i]);\n    }\n    sqlite3DbFreeNN(db, apVal);\n  }\n\n  *ppVal = pVal;\n  return rc;\n}\n#else\n# define valueFromFunction(a,b,c,d,e,f) SQLITE_OK\n#endif /* defined(SQLITE_ENABLE_STAT3_OR_STAT4) */\n\n/*\n** Extract a value from the supplied expression in the manner described\n** above sqlite3ValueFromExpr(). Allocate the sqlite3_value object\n** using valueNew().\n**\n** If pCtx is NULL and an error occurs after the sqlite3_value object\n** has been allocated, it is freed before returning. Or, if pCtx is not\n** NULL, it is assumed that the caller will free any allocated object\n** in all cases.\n*/\nstatic int valueFromExpr(\n  sqlite3 *db,                    /* The database connection */\n  Expr *pExpr,                    /* The expression to evaluate */\n  u8 enc,                         /* Encoding to use */\n  u8 affinity,                    /* Affinity to use */\n  sqlite3_value **ppVal,          /* Write the new value here */\n  struct ValueNewStat4Ctx *pCtx   /* Second argument for valueNew() */\n){\n  int op;\n  char *zVal = 0;\n  sqlite3_value *pVal = 0;\n  int negInt = 1;\n  const char *zNeg = \"\";\n  int rc = SQLITE_OK;\n\n  assert( pExpr!=0 );\n  while( (op = pExpr->op)==TK_UPLUS || op==TK_SPAN ) pExpr = pExpr->pLeft;\n#if defined(SQLITE_ENABLE_STAT3_OR_STAT4)\n  if( op==TK_REGISTER ) op = pExpr->op2;\n#else\n  if( NEVER(op==TK_REGISTER) ) op = pExpr->op2;\n#endif\n\n  /* Compressed expressions only appear when parsing the DEFAULT clause\n  ** on a table column definition, and hence only when pCtx==0.  This\n  ** check ensures that an EP_TokenOnly expression is never passed down\n  ** into valueFromFunction(). */\n  assert( (pExpr->flags & EP_TokenOnly)==0 || pCtx==0 );\n\n  if( op==TK_CAST ){\n    u8 aff = sqlite3AffinityType(pExpr->u.zToken,0);\n    rc = valueFromExpr(db, pExpr->pLeft, enc, aff, ppVal, pCtx);\n    testcase( rc!=SQLITE_OK );\n    if( *ppVal ){\n      sqlite3VdbeMemCast(*ppVal, aff, SQLITE_UTF8);\n      sqlite3ValueApplyAffinity(*ppVal, affinity, SQLITE_UTF8);\n    }\n    return rc;\n  }\n\n  /* Handle negative integers in a single step.  This is needed in the\n  ** case when the value is -9223372036854775808.\n  */\n  if( op==TK_UMINUS\n   && (pExpr->pLeft->op==TK_INTEGER || pExpr->pLeft->op==TK_FLOAT) ){\n    pExpr = pExpr->pLeft;\n    op = pExpr->op;\n    negInt = -1;\n    zNeg = \"-\";\n  }\n\n  if( op==TK_STRING || op==TK_FLOAT || op==TK_INTEGER ){\n    pVal = valueNew(db, pCtx);\n    if( pVal==0 ) goto no_mem;\n    if( ExprHasProperty(pExpr, EP_IntValue) ){\n      sqlite3VdbeMemSetInt64(pVal, (i64)pExpr->u.iValue*negInt);\n    }else{\n      zVal = sqlite3MPrintf(db, \"%s%s\", zNeg, pExpr->u.zToken);\n      if( zVal==0 ) goto no_mem;\n      sqlite3ValueSetStr(pVal, -1, zVal, SQLITE_UTF8, SQLITE_DYNAMIC);\n    }\n    if( (op==TK_INTEGER || op==TK_FLOAT ) && affinity==SQLITE_AFF_BLOB ){\n      sqlite3ValueApplyAffinity(pVal, SQLITE_AFF_NUMERIC, SQLITE_UTF8);\n    }else{\n      sqlite3ValueApplyAffinity(pVal, affinity, SQLITE_UTF8);\n    }\n    if( pVal->flags & (MEM_Int|MEM_Real) ) pVal->flags &= ~MEM_Str;\n    if( enc!=SQLITE_UTF8 ){\n      rc = sqlite3VdbeChangeEncoding(pVal, enc);\n    }\n  }else if( op==TK_UMINUS ) {\n    /* This branch happens for multiple negative signs.  Ex: -(-5) */\n    if( SQLITE_OK==valueFromExpr(db,pExpr->pLeft,enc,affinity,&pVal,pCtx) \n     && pVal!=0\n    ){\n      sqlite3VdbeMemNumerify(pVal);\n      if( pVal->flags & MEM_Real ){\n        pVal->u.r = -pVal->u.r;\n      }else if( pVal->u.i==SMALLEST_INT64 ){\n        pVal->u.r = -(double)SMALLEST_INT64;\n        MemSetTypeFlag(pVal, MEM_Real);\n      }else{\n        pVal->u.i = -pVal->u.i;\n      }\n      sqlite3ValueApplyAffinity(pVal, affinity, enc);\n    }\n  }else if( op==TK_NULL ){\n    pVal = valueNew(db, pCtx);\n    if( pVal==0 ) goto no_mem;\n    sqlite3VdbeMemNumerify(pVal);\n  }\n#ifndef SQLITE_OMIT_BLOB_LITERAL\n  else if( op==TK_BLOB ){\n    int nVal;\n    assert( pExpr->u.zToken[0]=='x' || pExpr->u.zToken[0]=='X' );\n    assert( pExpr->u.zToken[1]=='\\'' );\n    pVal = valueNew(db, pCtx);\n    if( !pVal ) goto no_mem;\n    zVal = &pExpr->u.zToken[2];\n    nVal = sqlite3Strlen30(zVal)-1;\n    assert( zVal[nVal]=='\\'' );\n    sqlite3VdbeMemSetStr(pVal, sqlite3HexToBlob(db, zVal, nVal), nVal/2,\n                         0, SQLITE_DYNAMIC);\n  }\n#endif\n\n#ifdef SQLITE_ENABLE_STAT3_OR_STAT4\n  else if( op==TK_FUNCTION && pCtx!=0 ){\n    rc = valueFromFunction(db, pExpr, enc, affinity, &pVal, pCtx);\n  }\n#endif\n\n  *ppVal = pVal;\n  return rc;\n\nno_mem:\n#ifdef SQLITE_ENABLE_STAT3_OR_STAT4\n  if( pCtx==0 || pCtx->pParse->nErr==0 )\n#endif\n    sqlite3OomFault(db);\n  sqlite3DbFree(db, zVal);\n  assert( *ppVal==0 );\n#ifdef SQLITE_ENABLE_STAT3_OR_STAT4\n  if( pCtx==0 ) sqlite3ValueFree(pVal);\n#else\n  assert( pCtx==0 ); sqlite3ValueFree(pVal);\n#endif\n  return SQLITE_NOMEM_BKPT;\n}\n\n/*\n** Create a new sqlite3_value object, containing the value of pExpr.\n**\n** This only works for very simple expressions that consist of one constant\n** token (i.e. \"5\", \"5.1\", \"'a string'\"). If the expression can\n** be converted directly into a value, then the value is allocated and\n** a pointer written to *ppVal. The caller is responsible for deallocating\n** the value by passing it to sqlite3ValueFree() later on. If the expression\n** cannot be converted to a value, then *ppVal is set to NULL.\n*/\nSQLITE_PRIVATE int sqlite3ValueFromExpr(\n  sqlite3 *db,              /* The database connection */\n  Expr *pExpr,              /* The expression to evaluate */\n  u8 enc,                   /* Encoding to use */\n  u8 affinity,              /* Affinity to use */\n  sqlite3_value **ppVal     /* Write the new value here */\n){\n  return pExpr ? valueFromExpr(db, pExpr, enc, affinity, ppVal, 0) : 0;\n}\n\n#ifdef SQLITE_ENABLE_STAT3_OR_STAT4\n/*\n** The implementation of the sqlite_record() function. This function accepts\n** a single argument of any type. The return value is a formatted database \n** record (a blob) containing the argument value.\n**\n** This is used to convert the value stored in the 'sample' column of the\n** sqlite_stat3 table to the record format SQLite uses internally.\n*/\nstatic void recordFunc(\n  sqlite3_context *context,\n  int argc,\n  sqlite3_value **argv\n){\n  const int file_format = 1;\n  u32 iSerial;                    /* Serial type */\n  int nSerial;                    /* Bytes of space for iSerial as varint */\n  u32 nVal;                       /* Bytes of space required for argv[0] */\n  int nRet;\n  sqlite3 *db;\n  u8 *aRet;\n\n  UNUSED_PARAMETER( argc );\n  iSerial = sqlite3VdbeSerialType(argv[0], file_format, &nVal);\n  nSerial = sqlite3VarintLen(iSerial);\n  db = sqlite3_context_db_handle(context);\n\n  nRet = 1 + nSerial + nVal;\n  aRet = sqlite3DbMallocRawNN(db, nRet);\n  if( aRet==0 ){\n    sqlite3_result_error_nomem(context);\n  }else{\n    aRet[0] = nSerial+1;\n    putVarint32(&aRet[1], iSerial);\n    sqlite3VdbeSerialPut(&aRet[1+nSerial], argv[0], iSerial);\n    sqlite3_result_blob(context, aRet, nRet, SQLITE_TRANSIENT);\n    sqlite3DbFreeNN(db, aRet);\n  }\n}\n\n/*\n** Register built-in functions used to help read ANALYZE data.\n*/\nSQLITE_PRIVATE void sqlite3AnalyzeFunctions(void){\n  static FuncDef aAnalyzeTableFuncs[] = {\n    FUNCTION(sqlite_record,   1, 0, 0, recordFunc),\n  };\n  sqlite3InsertBuiltinFuncs(aAnalyzeTableFuncs, ArraySize(aAnalyzeTableFuncs));\n}\n\n/*\n** Attempt to extract a value from pExpr and use it to construct *ppVal.\n**\n** If pAlloc is not NULL, then an UnpackedRecord object is created for\n** pAlloc if one does not exist and the new value is added to the\n** UnpackedRecord object.\n**\n** A value is extracted in the following cases:\n**\n**  * (pExpr==0). In this case the value is assumed to be an SQL NULL,\n**\n**  * The expression is a bound variable, and this is a reprepare, or\n**\n**  * The expression is a literal value.\n**\n** On success, *ppVal is made to point to the extracted value.  The caller\n** is responsible for ensuring that the value is eventually freed.\n*/\nstatic int stat4ValueFromExpr(\n  Parse *pParse,                  /* Parse context */\n  Expr *pExpr,                    /* The expression to extract a value from */\n  u8 affinity,                    /* Affinity to use */\n  struct ValueNewStat4Ctx *pAlloc,/* How to allocate space.  Or NULL */\n  sqlite3_value **ppVal           /* OUT: New value object (or NULL) */\n){\n  int rc = SQLITE_OK;\n  sqlite3_value *pVal = 0;\n  sqlite3 *db = pParse->db;\n\n  /* Skip over any TK_COLLATE nodes */\n  pExpr = sqlite3ExprSkipCollate(pExpr);\n\n  assert( pExpr==0 || pExpr->op!=TK_REGISTER || pExpr->op2!=TK_VARIABLE );\n  if( !pExpr ){\n    pVal = valueNew(db, pAlloc);\n    if( pVal ){\n      sqlite3VdbeMemSetNull((Mem*)pVal);\n    }\n  }else if( pExpr->op==TK_VARIABLE && (db->flags & SQLITE_EnableQPSG)==0 ){\n    Vdbe *v;\n    int iBindVar = pExpr->iColumn;\n    sqlite3VdbeSetVarmask(pParse->pVdbe, iBindVar);\n    if( (v = pParse->pReprepare)!=0 ){\n      pVal = valueNew(db, pAlloc);\n      if( pVal ){\n        rc = sqlite3VdbeMemCopy((Mem*)pVal, &v->aVar[iBindVar-1]);\n        sqlite3ValueApplyAffinity(pVal, affinity, ENC(db));\n        pVal->db = pParse->db;\n      }\n    }\n  }else{\n    rc = valueFromExpr(db, pExpr, ENC(db), affinity, &pVal, pAlloc);\n  }\n\n  assert( pVal==0 || pVal->db==db );\n  *ppVal = pVal;\n  return rc;\n}\n\n/*\n** This function is used to allocate and populate UnpackedRecord \n** structures intended to be compared against sample index keys stored \n** in the sqlite_stat4 table.\n**\n** A single call to this function populates zero or more fields of the\n** record starting with field iVal (fields are numbered from left to\n** right starting with 0). A single field is populated if:\n**\n**  * (pExpr==0). In this case the value is assumed to be an SQL NULL,\n**\n**  * The expression is a bound variable, and this is a reprepare, or\n**\n**  * The sqlite3ValueFromExpr() function is able to extract a value \n**    from the expression (i.e. the expression is a literal value).\n**\n** Or, if pExpr is a TK_VECTOR, one field is populated for each of the\n** vector components that match either of the two latter criteria listed\n** above.\n**\n** Before any value is appended to the record, the affinity of the \n** corresponding column within index pIdx is applied to it. Before\n** this function returns, output parameter *pnExtract is set to the\n** number of values appended to the record.\n**\n** When this function is called, *ppRec must either point to an object\n** allocated by an earlier call to this function, or must be NULL. If it\n** is NULL and a value can be successfully extracted, a new UnpackedRecord\n** is allocated (and *ppRec set to point to it) before returning.\n**\n** Unless an error is encountered, SQLITE_OK is returned. It is not an\n** error if a value cannot be extracted from pExpr. If an error does\n** occur, an SQLite error code is returned.\n*/\nSQLITE_PRIVATE int sqlite3Stat4ProbeSetValue(\n  Parse *pParse,                  /* Parse context */\n  Index *pIdx,                    /* Index being probed */\n  UnpackedRecord **ppRec,         /* IN/OUT: Probe record */\n  Expr *pExpr,                    /* The expression to extract a value from */\n  int nElem,                      /* Maximum number of values to append */\n  int iVal,                       /* Array element to populate */\n  int *pnExtract                  /* OUT: Values appended to the record */\n){\n  int rc = SQLITE_OK;\n  int nExtract = 0;\n\n  if( pExpr==0 || pExpr->op!=TK_SELECT ){\n    int i;\n    struct ValueNewStat4Ctx alloc;\n\n    alloc.pParse = pParse;\n    alloc.pIdx = pIdx;\n    alloc.ppRec = ppRec;\n\n    for(i=0; i<nElem; i++){\n      sqlite3_value *pVal = 0;\n      Expr *pElem = (pExpr ? sqlite3VectorFieldSubexpr(pExpr, i) : 0);\n      u8 aff = sqlite3IndexColumnAffinity(pParse->db, pIdx, iVal+i);\n      alloc.iVal = iVal+i;\n      rc = stat4ValueFromExpr(pParse, pElem, aff, &alloc, &pVal);\n      if( !pVal ) break;\n      nExtract++;\n    }\n  }\n\n  *pnExtract = nExtract;\n  return rc;\n}\n\n/*\n** Attempt to extract a value from expression pExpr using the methods\n** as described for sqlite3Stat4ProbeSetValue() above. \n**\n** If successful, set *ppVal to point to a new value object and return \n** SQLITE_OK. If no value can be extracted, but no other error occurs\n** (e.g. OOM), return SQLITE_OK and set *ppVal to NULL. Or, if an error\n** does occur, return an SQLite error code. The final value of *ppVal\n** is undefined in this case.\n*/\nSQLITE_PRIVATE int sqlite3Stat4ValueFromExpr(\n  Parse *pParse,                  /* Parse context */\n  Expr *pExpr,                    /* The expression to extract a value from */\n  u8 affinity,                    /* Affinity to use */\n  sqlite3_value **ppVal           /* OUT: New value object (or NULL) */\n){\n  return stat4ValueFromExpr(pParse, pExpr, affinity, 0, ppVal);\n}\n\n/*\n** Extract the iCol-th column from the nRec-byte record in pRec.  Write\n** the column value into *ppVal.  If *ppVal is initially NULL then a new\n** sqlite3_value object is allocated.\n**\n** If *ppVal is initially NULL then the caller is responsible for \n** ensuring that the value written into *ppVal is eventually freed.\n*/\nSQLITE_PRIVATE int sqlite3Stat4Column(\n  sqlite3 *db,                    /* Database handle */\n  const void *pRec,               /* Pointer to buffer containing record */\n  int nRec,                       /* Size of buffer pRec in bytes */\n  int iCol,                       /* Column to extract */\n  sqlite3_value **ppVal           /* OUT: Extracted value */\n){\n  u32 t;                          /* a column type code */\n  int nHdr;                       /* Size of the header in the record */\n  int iHdr;                       /* Next unread header byte */\n  int iField;                     /* Next unread data byte */\n  int szField;                    /* Size of the current data field */\n  int i;                          /* Column index */\n  u8 *a = (u8*)pRec;              /* Typecast byte array */\n  Mem *pMem = *ppVal;             /* Write result into this Mem object */\n\n  assert( iCol>0 );\n  iHdr = getVarint32(a, nHdr);\n  if( nHdr>nRec || iHdr>=nHdr ) return SQLITE_CORRUPT_BKPT;\n  iField = nHdr;\n  for(i=0; i<=iCol; i++){\n    iHdr += getVarint32(&a[iHdr], t);\n    testcase( iHdr==nHdr );\n    testcase( iHdr==nHdr+1 );\n    if( iHdr>nHdr ) return SQLITE_CORRUPT_BKPT;\n    szField = sqlite3VdbeSerialTypeLen(t);\n    iField += szField;\n  }\n  testcase( iField==nRec );\n  testcase( iField==nRec+1 );\n  if( iField>nRec ) return SQLITE_CORRUPT_BKPT;\n  if( pMem==0 ){\n    pMem = *ppVal = sqlite3ValueNew(db);\n    if( pMem==0 ) return SQLITE_NOMEM_BKPT;\n  }\n  sqlite3VdbeSerialGet(&a[iField-szField], t, pMem);\n  pMem->enc = ENC(db);\n  return SQLITE_OK;\n}\n\n/*\n** Unless it is NULL, the argument must be an UnpackedRecord object returned\n** by an earlier call to sqlite3Stat4ProbeSetValue(). This call deletes\n** the object.\n*/\nSQLITE_PRIVATE void sqlite3Stat4ProbeFree(UnpackedRecord *pRec){\n  if( pRec ){\n    int i;\n    int nCol = pRec->pKeyInfo->nAllField;\n    Mem *aMem = pRec->aMem;\n    sqlite3 *db = aMem[0].db;\n    for(i=0; i<nCol; i++){\n      sqlite3VdbeMemRelease(&aMem[i]);\n    }\n    sqlite3KeyInfoUnref(pRec->pKeyInfo);\n    sqlite3DbFreeNN(db, pRec);\n  }\n}\n#endif /* ifdef SQLITE_ENABLE_STAT4 */\n\n/*\n** Change the string value of an sqlite3_value object\n*/\nSQLITE_PRIVATE void sqlite3ValueSetStr(\n  sqlite3_value *v,     /* Value to be set */\n  int n,                /* Length of string z */\n  const void *z,        /* Text of the new string */\n  u8 enc,               /* Encoding to use */\n  void (*xDel)(void*)   /* Destructor for the string */\n){\n  if( v ) sqlite3VdbeMemSetStr((Mem *)v, z, n, enc, xDel);\n}\n\n/*\n** Free an sqlite3_value object\n*/\nSQLITE_PRIVATE void sqlite3ValueFree(sqlite3_value *v){\n  if( !v ) return;\n  sqlite3VdbeMemRelease((Mem *)v);\n  sqlite3DbFreeNN(((Mem*)v)->db, v);\n}\n\n/*\n** The sqlite3ValueBytes() routine returns the number of bytes in the\n** sqlite3_value object assuming that it uses the encoding \"enc\".\n** The valueBytes() routine is a helper function.\n*/\nstatic SQLITE_NOINLINE int valueBytes(sqlite3_value *pVal, u8 enc){\n  return valueToText(pVal, enc)!=0 ? pVal->n : 0;\n}\nSQLITE_PRIVATE int sqlite3ValueBytes(sqlite3_value *pVal, u8 enc){\n  Mem *p = (Mem*)pVal;\n  assert( (p->flags & MEM_Null)==0 || (p->flags & (MEM_Str|MEM_Blob))==0 );\n  if( (p->flags & MEM_Str)!=0 && pVal->enc==enc ){\n    return p->n;\n  }\n  if( (p->flags & MEM_Blob)!=0 ){\n    if( p->flags & MEM_Zero ){\n      return p->n + p->u.nZero;\n    }else{\n      return p->n;\n    }\n  }\n  if( p->flags & MEM_Null ) return 0;\n  return valueBytes(pVal, enc);\n}\n\n/************** End of vdbemem.c *********************************************/\n/************** Begin file vdbeaux.c *****************************************/\n/*\n** 2003 September 6\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n*************************************************************************\n** This file contains code used for creating, destroying, and populating\n** a VDBE (or an \"sqlite3_stmt\" as it is known to the outside world.) \n*/\n/* #include \"sqliteInt.h\" */\n/* #include \"vdbeInt.h\" */\n\n/*\n** Create a new virtual database engine.\n*/\nSQLITE_PRIVATE Vdbe *sqlite3VdbeCreate(Parse *pParse){\n  sqlite3 *db = pParse->db;\n  Vdbe *p;\n  p = sqlite3DbMallocRawNN(db, sizeof(Vdbe) );\n  if( p==0 ) return 0;\n  memset(&p->aOp, 0, sizeof(Vdbe)-offsetof(Vdbe,aOp));\n  p->db = db;\n  if( db->pVdbe ){\n    db->pVdbe->pPrev = p;\n  }\n  p->pNext = db->pVdbe;\n  p->pPrev = 0;\n  db->pVdbe = p;\n  p->magic = VDBE_MAGIC_INIT;\n  p->pParse = pParse;\n  pParse->pVdbe = p;\n  assert( pParse->aLabel==0 );\n  assert( pParse->nLabel==0 );\n  assert( pParse->nOpAlloc==0 );\n  assert( pParse->szOpAlloc==0 );\n  sqlite3VdbeAddOp2(p, OP_Init, 0, 1);\n  return p;\n}\n\n/*\n** Change the error string stored in Vdbe.zErrMsg\n*/\nSQLITE_PRIVATE void sqlite3VdbeError(Vdbe *p, const char *zFormat, ...){\n  va_list ap;\n  sqlite3DbFree(p->db, p->zErrMsg);\n  va_start(ap, zFormat);\n  p->zErrMsg = sqlite3VMPrintf(p->db, zFormat, ap);\n  va_end(ap);\n}\n\n/*\n** Remember the SQL string for a prepared statement.\n*/\nSQLITE_PRIVATE void sqlite3VdbeSetSql(Vdbe *p, const char *z, int n, u8 prepFlags){\n  if( p==0 ) return;\n  p->prepFlags = prepFlags;\n  if( (prepFlags & SQLITE_PREPARE_SAVESQL)==0 ){\n    p->expmask = 0;\n  }\n  assert( p->zSql==0 );\n  p->zSql = sqlite3DbStrNDup(p->db, z, n);\n}\n\n/*\n** Swap all content between two VDBE structures.\n*/\nSQLITE_PRIVATE void sqlite3VdbeSwap(Vdbe *pA, Vdbe *pB){\n  Vdbe tmp, *pTmp;\n  char *zTmp;\n  assert( pA->db==pB->db );\n  tmp = *pA;\n  *pA = *pB;\n  *pB = tmp;\n  pTmp = pA->pNext;\n  pA->pNext = pB->pNext;\n  pB->pNext = pTmp;\n  pTmp = pA->pPrev;\n  pA->pPrev = pB->pPrev;\n  pB->pPrev = pTmp;\n  zTmp = pA->zSql;\n  pA->zSql = pB->zSql;\n  pB->zSql = zTmp;\n  pB->expmask = pA->expmask;\n  pB->prepFlags = pA->prepFlags;\n  memcpy(pB->aCounter, pA->aCounter, sizeof(pB->aCounter));\n  pB->aCounter[SQLITE_STMTSTATUS_REPREPARE]++;\n}\n\n/*\n** Resize the Vdbe.aOp array so that it is at least nOp elements larger \n** than its current size. nOp is guaranteed to be less than or equal\n** to 1024/sizeof(Op).\n**\n** If an out-of-memory error occurs while resizing the array, return\n** SQLITE_NOMEM. In this case Vdbe.aOp and Parse.nOpAlloc remain \n** unchanged (this is so that any opcodes already allocated can be \n** correctly deallocated along with the rest of the Vdbe).\n*/\nstatic int growOpArray(Vdbe *v, int nOp){\n  VdbeOp *pNew;\n  Parse *p = v->pParse;\n\n  /* The SQLITE_TEST_REALLOC_STRESS compile-time option is designed to force\n  ** more frequent reallocs and hence provide more opportunities for \n  ** simulated OOM faults.  SQLITE_TEST_REALLOC_STRESS is generally used\n  ** during testing only.  With SQLITE_TEST_REALLOC_STRESS grow the op array\n  ** by the minimum* amount required until the size reaches 512.  Normal\n  ** operation (without SQLITE_TEST_REALLOC_STRESS) is to double the current\n  ** size of the op array or add 1KB of space, whichever is smaller. */\n#ifdef SQLITE_TEST_REALLOC_STRESS\n  int nNew = (p->nOpAlloc>=512 ? p->nOpAlloc*2 : p->nOpAlloc+nOp);\n#else\n  int nNew = (p->nOpAlloc ? p->nOpAlloc*2 : (int)(1024/sizeof(Op)));\n  UNUSED_PARAMETER(nOp);\n#endif\n\n  /* Ensure that the size of a VDBE does not grow too large */\n  if( nNew > p->db->aLimit[SQLITE_LIMIT_VDBE_OP] ){\n    sqlite3OomFault(p->db);\n    return SQLITE_NOMEM;\n  }\n\n  assert( nOp<=(1024/sizeof(Op)) );\n  assert( nNew>=(p->nOpAlloc+nOp) );\n  pNew = sqlite3DbRealloc(p->db, v->aOp, nNew*sizeof(Op));\n  if( pNew ){\n    p->szOpAlloc = sqlite3DbMallocSize(p->db, pNew);\n    p->nOpAlloc = p->szOpAlloc/sizeof(Op);\n    v->aOp = pNew;\n  }\n  return (pNew ? SQLITE_OK : SQLITE_NOMEM_BKPT);\n}\n\n#ifdef SQLITE_DEBUG\n/* This routine is just a convenient place to set a breakpoint that will\n** fire after each opcode is inserted and displayed using\n** \"PRAGMA vdbe_addoptrace=on\".\n*/\nstatic void test_addop_breakpoint(void){\n  static int n = 0;\n  n++;\n}\n#endif\n\n/*\n** Add a new instruction to the list of instructions current in the\n** VDBE.  Return the address of the new instruction.\n**\n** Parameters:\n**\n**    p               Pointer to the VDBE\n**\n**    op              The opcode for this instruction\n**\n**    p1, p2, p3      Operands\n**\n** Use the sqlite3VdbeResolveLabel() function to fix an address and\n** the sqlite3VdbeChangeP4() function to change the value of the P4\n** operand.\n*/\nstatic SQLITE_NOINLINE int growOp3(Vdbe *p, int op, int p1, int p2, int p3){\n  assert( p->pParse->nOpAlloc<=p->nOp );\n  if( growOpArray(p, 1) ) return 1;\n  assert( p->pParse->nOpAlloc>p->nOp );\n  return sqlite3VdbeAddOp3(p, op, p1, p2, p3);\n}\nSQLITE_PRIVATE int sqlite3VdbeAddOp3(Vdbe *p, int op, int p1, int p2, int p3){\n  int i;\n  VdbeOp *pOp;\n\n  i = p->nOp;\n  assert( p->magic==VDBE_MAGIC_INIT );\n  assert( op>=0 && op<0xff );\n  if( p->pParse->nOpAlloc<=i ){\n    return growOp3(p, op, p1, p2, p3);\n  }\n  p->nOp++;\n  pOp = &p->aOp[i];\n  pOp->opcode = (u8)op;\n  pOp->p5 = 0;\n  pOp->p1 = p1;\n  pOp->p2 = p2;\n  pOp->p3 = p3;\n  pOp->p4.p = 0;\n  pOp->p4type = P4_NOTUSED;\n#ifdef SQLITE_ENABLE_EXPLAIN_COMMENTS\n  pOp->zComment = 0;\n#endif\n#ifdef SQLITE_DEBUG\n  if( p->db->flags & SQLITE_VdbeAddopTrace ){\n    int jj, kk;\n    Parse *pParse = p->pParse;\n    for(jj=kk=0; jj<pParse->nColCache; jj++){\n      struct yColCache *x = pParse->aColCache + jj;\n      printf(\" r[%d]={%d:%d}\", x->iReg, x->iTable, x->iColumn);\n      kk++;\n    }\n    if( kk ) printf(\"\\n\");\n    sqlite3VdbePrintOp(0, i, &p->aOp[i]);\n    test_addop_breakpoint();\n  }\n#endif\n#ifdef VDBE_PROFILE\n  pOp->cycles = 0;\n  pOp->cnt = 0;\n#endif\n#ifdef SQLITE_VDBE_COVERAGE\n  pOp->iSrcLine = 0;\n#endif\n  return i;\n}\nSQLITE_PRIVATE int sqlite3VdbeAddOp0(Vdbe *p, int op){\n  return sqlite3VdbeAddOp3(p, op, 0, 0, 0);\n}\nSQLITE_PRIVATE int sqlite3VdbeAddOp1(Vdbe *p, int op, int p1){\n  return sqlite3VdbeAddOp3(p, op, p1, 0, 0);\n}\nSQLITE_PRIVATE int sqlite3VdbeAddOp2(Vdbe *p, int op, int p1, int p2){\n  return sqlite3VdbeAddOp3(p, op, p1, p2, 0);\n}\n\n/* Generate code for an unconditional jump to instruction iDest\n*/\nSQLITE_PRIVATE int sqlite3VdbeGoto(Vdbe *p, int iDest){\n  return sqlite3VdbeAddOp3(p, OP_Goto, 0, iDest, 0);\n}\n\n/* Generate code to cause the string zStr to be loaded into\n** register iDest\n*/\nSQLITE_PRIVATE int sqlite3VdbeLoadString(Vdbe *p, int iDest, const char *zStr){\n  return sqlite3VdbeAddOp4(p, OP_String8, 0, iDest, 0, zStr, 0);\n}\n\n/*\n** Generate code that initializes multiple registers to string or integer\n** constants.  The registers begin with iDest and increase consecutively.\n** One register is initialized for each characgter in zTypes[].  For each\n** \"s\" character in zTypes[], the register is a string if the argument is\n** not NULL, or OP_Null if the value is a null pointer.  For each \"i\" character\n** in zTypes[], the register is initialized to an integer.\n**\n** If the input string does not end with \"X\" then an OP_ResultRow instruction\n** is generated for the values inserted.\n*/\nSQLITE_PRIVATE void sqlite3VdbeMultiLoad(Vdbe *p, int iDest, const char *zTypes, ...){\n  va_list ap;\n  int i;\n  char c;\n  va_start(ap, zTypes);\n  for(i=0; (c = zTypes[i])!=0; i++){\n    if( c=='s' ){\n      const char *z = va_arg(ap, const char*);\n      sqlite3VdbeAddOp4(p, z==0 ? OP_Null : OP_String8, 0, iDest+i, 0, z, 0);\n    }else if( c=='i' ){\n      sqlite3VdbeAddOp2(p, OP_Integer, va_arg(ap, int), iDest+i);\n    }else{\n      goto skip_op_resultrow;\n    }\n  }\n  sqlite3VdbeAddOp2(p, OP_ResultRow, iDest, i);\nskip_op_resultrow:\n  va_end(ap);\n}\n\n/*\n** Add an opcode that includes the p4 value as a pointer.\n*/\nSQLITE_PRIVATE int sqlite3VdbeAddOp4(\n  Vdbe *p,            /* Add the opcode to this VM */\n  int op,             /* The new opcode */\n  int p1,             /* The P1 operand */\n  int p2,             /* The P2 operand */\n  int p3,             /* The P3 operand */\n  const char *zP4,    /* The P4 operand */\n  int p4type          /* P4 operand type */\n){\n  int addr = sqlite3VdbeAddOp3(p, op, p1, p2, p3);\n  sqlite3VdbeChangeP4(p, addr, zP4, p4type);\n  return addr;\n}\n\n/*\n** Add an opcode that includes the p4 value with a P4_INT64 or\n** P4_REAL type.\n*/\nSQLITE_PRIVATE int sqlite3VdbeAddOp4Dup8(\n  Vdbe *p,            /* Add the opcode to this VM */\n  int op,             /* The new opcode */\n  int p1,             /* The P1 operand */\n  int p2,             /* The P2 operand */\n  int p3,             /* The P3 operand */\n  const u8 *zP4,      /* The P4 operand */\n  int p4type          /* P4 operand type */\n){\n  char *p4copy = sqlite3DbMallocRawNN(sqlite3VdbeDb(p), 8);\n  if( p4copy ) memcpy(p4copy, zP4, 8);\n  return sqlite3VdbeAddOp4(p, op, p1, p2, p3, p4copy, p4type);\n}\n\n/*\n** Add an OP_ParseSchema opcode.  This routine is broken out from\n** sqlite3VdbeAddOp4() since it needs to also needs to mark all btrees\n** as having been used.\n**\n** The zWhere string must have been obtained from sqlite3_malloc().\n** This routine will take ownership of the allocated memory.\n*/\nSQLITE_PRIVATE void sqlite3VdbeAddParseSchemaOp(Vdbe *p, int iDb, char *zWhere){\n  int j;\n  sqlite3VdbeAddOp4(p, OP_ParseSchema, iDb, 0, 0, zWhere, P4_DYNAMIC);\n  for(j=0; j<p->db->nDb; j++) sqlite3VdbeUsesBtree(p, j);\n}\n\n/*\n** Add an opcode that includes the p4 value as an integer.\n*/\nSQLITE_PRIVATE int sqlite3VdbeAddOp4Int(\n  Vdbe *p,            /* Add the opcode to this VM */\n  int op,             /* The new opcode */\n  int p1,             /* The P1 operand */\n  int p2,             /* The P2 operand */\n  int p3,             /* The P3 operand */\n  int p4              /* The P4 operand as an integer */\n){\n  int addr = sqlite3VdbeAddOp3(p, op, p1, p2, p3);\n  if( p->db->mallocFailed==0 ){\n    VdbeOp *pOp = &p->aOp[addr];\n    pOp->p4type = P4_INT32;\n    pOp->p4.i = p4;\n  }\n  return addr;\n}\n\n/* Insert the end of a co-routine\n*/\nSQLITE_PRIVATE void sqlite3VdbeEndCoroutine(Vdbe *v, int regYield){\n  sqlite3VdbeAddOp1(v, OP_EndCoroutine, regYield);\n\n  /* Clear the temporary register cache, thereby ensuring that each\n  ** co-routine has its own independent set of registers, because co-routines\n  ** might expect their registers to be preserved across an OP_Yield, and\n  ** that could cause problems if two or more co-routines are using the same\n  ** temporary register.\n  */\n  v->pParse->nTempReg = 0;\n  v->pParse->nRangeReg = 0;\n}\n\n/*\n** Create a new symbolic label for an instruction that has yet to be\n** coded.  The symbolic label is really just a negative number.  The\n** label can be used as the P2 value of an operation.  Later, when\n** the label is resolved to a specific address, the VDBE will scan\n** through its operation list and change all values of P2 which match\n** the label into the resolved address.\n**\n** The VDBE knows that a P2 value is a label because labels are\n** always negative and P2 values are suppose to be non-negative.\n** Hence, a negative P2 value is a label that has yet to be resolved.\n**\n** Zero is returned if a malloc() fails.\n*/\nSQLITE_PRIVATE int sqlite3VdbeMakeLabel(Vdbe *v){\n  Parse *p = v->pParse;\n  int i = p->nLabel++;\n  assert( v->magic==VDBE_MAGIC_INIT );\n  if( (i & (i-1))==0 ){\n    p->aLabel = sqlite3DbReallocOrFree(p->db, p->aLabel, \n                                       (i*2+1)*sizeof(p->aLabel[0]));\n  }\n  if( p->aLabel ){\n    p->aLabel[i] = -1;\n  }\n  return ADDR(i);\n}\n\n/*\n** Resolve label \"x\" to be the address of the next instruction to\n** be inserted.  The parameter \"x\" must have been obtained from\n** a prior call to sqlite3VdbeMakeLabel().\n*/\nSQLITE_PRIVATE void sqlite3VdbeResolveLabel(Vdbe *v, int x){\n  Parse *p = v->pParse;\n  int j = ADDR(x);\n  assert( v->magic==VDBE_MAGIC_INIT );\n  assert( j<p->nLabel );\n  assert( j>=0 );\n  if( p->aLabel ){\n    p->aLabel[j] = v->nOp;\n  }\n}\n\n/*\n** Mark the VDBE as one that can only be run one time.\n*/\nSQLITE_PRIVATE void sqlite3VdbeRunOnlyOnce(Vdbe *p){\n  p->runOnlyOnce = 1;\n}\n\n/*\n** Mark the VDBE as one that can only be run multiple times.\n*/\nSQLITE_PRIVATE void sqlite3VdbeReusable(Vdbe *p){\n  p->runOnlyOnce = 0;\n}\n\n#ifdef SQLITE_DEBUG /* sqlite3AssertMayAbort() logic */\n\n/*\n** The following type and function are used to iterate through all opcodes\n** in a Vdbe main program and each of the sub-programs (triggers) it may \n** invoke directly or indirectly. It should be used as follows:\n**\n**   Op *pOp;\n**   VdbeOpIter sIter;\n**\n**   memset(&sIter, 0, sizeof(sIter));\n**   sIter.v = v;                            // v is of type Vdbe* \n**   while( (pOp = opIterNext(&sIter)) ){\n**     // Do something with pOp\n**   }\n**   sqlite3DbFree(v->db, sIter.apSub);\n** \n*/\ntypedef struct VdbeOpIter VdbeOpIter;\nstruct VdbeOpIter {\n  Vdbe *v;                   /* Vdbe to iterate through the opcodes of */\n  SubProgram **apSub;        /* Array of subprograms */\n  int nSub;                  /* Number of entries in apSub */\n  int iAddr;                 /* Address of next instruction to return */\n  int iSub;                  /* 0 = main program, 1 = first sub-program etc. */\n};\nstatic Op *opIterNext(VdbeOpIter *p){\n  Vdbe *v = p->v;\n  Op *pRet = 0;\n  Op *aOp;\n  int nOp;\n\n  if( p->iSub<=p->nSub ){\n\n    if( p->iSub==0 ){\n      aOp = v->aOp;\n      nOp = v->nOp;\n    }else{\n      aOp = p->apSub[p->iSub-1]->aOp;\n      nOp = p->apSub[p->iSub-1]->nOp;\n    }\n    assert( p->iAddr<nOp );\n\n    pRet = &aOp[p->iAddr];\n    p->iAddr++;\n    if( p->iAddr==nOp ){\n      p->iSub++;\n      p->iAddr = 0;\n    }\n  \n    if( pRet->p4type==P4_SUBPROGRAM ){\n      int nByte = (p->nSub+1)*sizeof(SubProgram*);\n      int j;\n      for(j=0; j<p->nSub; j++){\n        if( p->apSub[j]==pRet->p4.pProgram ) break;\n      }\n      if( j==p->nSub ){\n        p->apSub = sqlite3DbReallocOrFree(v->db, p->apSub, nByte);\n        if( !p->apSub ){\n          pRet = 0;\n        }else{\n          p->apSub[p->nSub++] = pRet->p4.pProgram;\n        }\n      }\n    }\n  }\n\n  return pRet;\n}\n\n/*\n** Check if the program stored in the VM associated with pParse may\n** throw an ABORT exception (causing the statement, but not entire transaction\n** to be rolled back). This condition is true if the main program or any\n** sub-programs contains any of the following:\n**\n**   *  OP_Halt with P1=SQLITE_CONSTRAINT and P2=OE_Abort.\n**   *  OP_HaltIfNull with P1=SQLITE_CONSTRAINT and P2=OE_Abort.\n**   *  OP_Destroy\n**   *  OP_VUpdate\n**   *  OP_VRename\n**   *  OP_FkCounter with P2==0 (immediate foreign key constraint)\n**   *  OP_CreateBtree/BTREE_INTKEY and OP_InitCoroutine \n**      (for CREATE TABLE AS SELECT ...)\n**\n** Then check that the value of Parse.mayAbort is true if an\n** ABORT may be thrown, or false otherwise. Return true if it does\n** match, or false otherwise. This function is intended to be used as\n** part of an assert statement in the compiler. Similar to:\n**\n**   assert( sqlite3VdbeAssertMayAbort(pParse->pVdbe, pParse->mayAbort) );\n*/\nSQLITE_PRIVATE int sqlite3VdbeAssertMayAbort(Vdbe *v, int mayAbort){\n  int hasAbort = 0;\n  int hasFkCounter = 0;\n  int hasCreateTable = 0;\n  int hasInitCoroutine = 0;\n  Op *pOp;\n  VdbeOpIter sIter;\n  memset(&sIter, 0, sizeof(sIter));\n  sIter.v = v;\n\n  while( (pOp = opIterNext(&sIter))!=0 ){\n    int opcode = pOp->opcode;\n    if( opcode==OP_Destroy || opcode==OP_VUpdate || opcode==OP_VRename \n     || ((opcode==OP_Halt || opcode==OP_HaltIfNull) \n      && ((pOp->p1&0xff)==SQLITE_CONSTRAINT && pOp->p2==OE_Abort))\n    ){\n      hasAbort = 1;\n      break;\n    }\n    if( opcode==OP_CreateBtree && pOp->p3==BTREE_INTKEY ) hasCreateTable = 1;\n    if( opcode==OP_InitCoroutine ) hasInitCoroutine = 1;\n#ifndef SQLITE_OMIT_FOREIGN_KEY\n    if( opcode==OP_FkCounter && pOp->p1==0 && pOp->p2==1 ){\n      hasFkCounter = 1;\n    }\n#endif\n  }\n  sqlite3DbFree(v->db, sIter.apSub);\n\n  /* Return true if hasAbort==mayAbort. Or if a malloc failure occurred.\n  ** If malloc failed, then the while() loop above may not have iterated\n  ** through all opcodes and hasAbort may be set incorrectly. Return\n  ** true for this case to prevent the assert() in the callers frame\n  ** from failing.  */\n  return ( v->db->mallocFailed || hasAbort==mayAbort || hasFkCounter\n              || (hasCreateTable && hasInitCoroutine) );\n}\n#endif /* SQLITE_DEBUG - the sqlite3AssertMayAbort() function */\n\n/*\n** This routine is called after all opcodes have been inserted.  It loops\n** through all the opcodes and fixes up some details.\n**\n** (1) For each jump instruction with a negative P2 value (a label)\n**     resolve the P2 value to an actual address.\n**\n** (2) Compute the maximum number of arguments used by any SQL function\n**     and store that value in *pMaxFuncArgs.\n**\n** (3) Update the Vdbe.readOnly and Vdbe.bIsReader flags to accurately\n**     indicate what the prepared statement actually does.\n**\n** (4) Initialize the p4.xAdvance pointer on opcodes that use it.\n**\n** (5) Reclaim the memory allocated for storing labels.\n**\n** This routine will only function correctly if the mkopcodeh.tcl generator\n** script numbers the opcodes correctly.  Changes to this routine must be\n** coordinated with changes to mkopcodeh.tcl.\n*/\nstatic void resolveP2Values(Vdbe *p, int *pMaxFuncArgs){\n  int nMaxArgs = *pMaxFuncArgs;\n  Op *pOp;\n  Parse *pParse = p->pParse;\n  int *aLabel = pParse->aLabel;\n  p->readOnly = 1;\n  p->bIsReader = 0;\n  pOp = &p->aOp[p->nOp-1];\n  while(1){\n\n    /* Only JUMP opcodes and the short list of special opcodes in the switch\n    ** below need to be considered.  The mkopcodeh.tcl generator script groups\n    ** all these opcodes together near the front of the opcode list.  Skip\n    ** any opcode that does not need processing by virtual of the fact that\n    ** it is larger than SQLITE_MX_JUMP_OPCODE, as a performance optimization.\n    */\n    if( pOp->opcode<=SQLITE_MX_JUMP_OPCODE ){\n      /* NOTE: Be sure to update mkopcodeh.tcl when adding or removing\n      ** cases from this switch! */\n      switch( pOp->opcode ){\n        case OP_Transaction: {\n          if( pOp->p2!=0 ) p->readOnly = 0;\n          /* fall thru */\n        }\n        case OP_AutoCommit:\n        case OP_Savepoint: {\n          p->bIsReader = 1;\n          break;\n        }\n#ifndef SQLITE_OMIT_WAL\n        case OP_Checkpoint:\n#endif\n        case OP_Vacuum:\n        case OP_JournalMode: {\n          p->readOnly = 0;\n          p->bIsReader = 1;\n          break;\n        }\n        case OP_Next:\n        case OP_NextIfOpen:\n        case OP_SorterNext: {\n          pOp->p4.xAdvance = sqlite3BtreeNext;\n          pOp->p4type = P4_ADVANCE;\n          /* The code generator never codes any of these opcodes as a jump\n          ** to a label.  They are always coded as a jump backwards to a \n          ** known address */\n          assert( pOp->p2>=0 );\n          break;\n        }\n        case OP_Prev:\n        case OP_PrevIfOpen: {\n          pOp->p4.xAdvance = sqlite3BtreePrevious;\n          pOp->p4type = P4_ADVANCE;\n          /* The code generator never codes any of these opcodes as a jump\n          ** to a label.  They are always coded as a jump backwards to a \n          ** known address */\n          assert( pOp->p2>=0 );\n          break;\n        }\n#ifndef SQLITE_OMIT_VIRTUALTABLE\n        case OP_VUpdate: {\n          if( pOp->p2>nMaxArgs ) nMaxArgs = pOp->p2;\n          break;\n        }\n        case OP_VFilter: {\n          int n;\n          assert( (pOp - p->aOp) >= 3 );\n          assert( pOp[-1].opcode==OP_Integer );\n          n = pOp[-1].p1;\n          if( n>nMaxArgs ) nMaxArgs = n;\n          /* Fall through into the default case */\n        }\n#endif\n        default: {\n          if( pOp->p2<0 ){\n            /* The mkopcodeh.tcl script has so arranged things that the only\n            ** non-jump opcodes less than SQLITE_MX_JUMP_CODE are guaranteed to\n            ** have non-negative values for P2. */\n            assert( (sqlite3OpcodeProperty[pOp->opcode] & OPFLG_JUMP)!=0 );\n            assert( ADDR(pOp->p2)<pParse->nLabel );\n            pOp->p2 = aLabel[ADDR(pOp->p2)];\n          }\n          break;\n        }\n      }\n      /* The mkopcodeh.tcl script has so arranged things that the only\n      ** non-jump opcodes less than SQLITE_MX_JUMP_CODE are guaranteed to\n      ** have non-negative values for P2. */\n      assert( (sqlite3OpcodeProperty[pOp->opcode]&OPFLG_JUMP)==0 || pOp->p2>=0);\n    }\n    if( pOp==p->aOp ) break;\n    pOp--;\n  }\n  sqlite3DbFree(p->db, pParse->aLabel);\n  pParse->aLabel = 0;\n  pParse->nLabel = 0;\n  *pMaxFuncArgs = nMaxArgs;\n  assert( p->bIsReader!=0 || DbMaskAllZero(p->btreeMask) );\n}\n\n/*\n** Return the address of the next instruction to be inserted.\n*/\nSQLITE_PRIVATE int sqlite3VdbeCurrentAddr(Vdbe *p){\n  assert( p->magic==VDBE_MAGIC_INIT );\n  return p->nOp;\n}\n\n/*\n** Verify that at least N opcode slots are available in p without\n** having to malloc for more space (except when compiled using\n** SQLITE_TEST_REALLOC_STRESS).  This interface is used during testing\n** to verify that certain calls to sqlite3VdbeAddOpList() can never\n** fail due to a OOM fault and hence that the return value from\n** sqlite3VdbeAddOpList() will always be non-NULL.\n*/\n#if defined(SQLITE_DEBUG) && !defined(SQLITE_TEST_REALLOC_STRESS)\nSQLITE_PRIVATE void sqlite3VdbeVerifyNoMallocRequired(Vdbe *p, int N){\n  assert( p->nOp + N <= p->pParse->nOpAlloc );\n}\n#endif\n\n/*\n** Verify that the VM passed as the only argument does not contain\n** an OP_ResultRow opcode. Fail an assert() if it does. This is used\n** by code in pragma.c to ensure that the implementation of certain\n** pragmas comports with the flags specified in the mkpragmatab.tcl\n** script.\n*/\n#if defined(SQLITE_DEBUG) && !defined(SQLITE_TEST_REALLOC_STRESS)\nSQLITE_PRIVATE void sqlite3VdbeVerifyNoResultRow(Vdbe *p){\n  int i;\n  for(i=0; i<p->nOp; i++){\n    assert( p->aOp[i].opcode!=OP_ResultRow );\n  }\n}\n#endif\n\n/*\n** This function returns a pointer to the array of opcodes associated with\n** the Vdbe passed as the first argument. It is the callers responsibility\n** to arrange for the returned array to be eventually freed using the \n** vdbeFreeOpArray() function.\n**\n** Before returning, *pnOp is set to the number of entries in the returned\n** array. Also, *pnMaxArg is set to the larger of its current value and \n** the number of entries in the Vdbe.apArg[] array required to execute the \n** returned program.\n*/\nSQLITE_PRIVATE VdbeOp *sqlite3VdbeTakeOpArray(Vdbe *p, int *pnOp, int *pnMaxArg){\n  VdbeOp *aOp = p->aOp;\n  assert( aOp && !p->db->mallocFailed );\n\n  /* Check that sqlite3VdbeUsesBtree() was not called on this VM */\n  assert( DbMaskAllZero(p->btreeMask) );\n\n  resolveP2Values(p, pnMaxArg);\n  *pnOp = p->nOp;\n  p->aOp = 0;\n  return aOp;\n}\n\n/*\n** Add a whole list of operations to the operation stack.  Return a\n** pointer to the first operation inserted.\n**\n** Non-zero P2 arguments to jump instructions are automatically adjusted\n** so that the jump target is relative to the first operation inserted.\n*/\nSQLITE_PRIVATE VdbeOp *sqlite3VdbeAddOpList(\n  Vdbe *p,                     /* Add opcodes to the prepared statement */\n  int nOp,                     /* Number of opcodes to add */\n  VdbeOpList const *aOp,       /* The opcodes to be added */\n  int iLineno                  /* Source-file line number of first opcode */\n){\n  int i;\n  VdbeOp *pOut, *pFirst;\n  assert( nOp>0 );\n  assert( p->magic==VDBE_MAGIC_INIT );\n  if( p->nOp + nOp > p->pParse->nOpAlloc && growOpArray(p, nOp) ){\n    return 0;\n  }\n  pFirst = pOut = &p->aOp[p->nOp];\n  for(i=0; i<nOp; i++, aOp++, pOut++){\n    pOut->opcode = aOp->opcode;\n    pOut->p1 = aOp->p1;\n    pOut->p2 = aOp->p2;\n    assert( aOp->p2>=0 );\n    if( (sqlite3OpcodeProperty[aOp->opcode] & OPFLG_JUMP)!=0 && aOp->p2>0 ){\n      pOut->p2 += p->nOp;\n    }\n    pOut->p3 = aOp->p3;\n    pOut->p4type = P4_NOTUSED;\n    pOut->p4.p = 0;\n    pOut->p5 = 0;\n#ifdef SQLITE_ENABLE_EXPLAIN_COMMENTS\n    pOut->zComment = 0;\n#endif\n#ifdef SQLITE_VDBE_COVERAGE\n    pOut->iSrcLine = iLineno+i;\n#else\n    (void)iLineno;\n#endif\n#ifdef SQLITE_DEBUG\n    if( p->db->flags & SQLITE_VdbeAddopTrace ){\n      sqlite3VdbePrintOp(0, i+p->nOp, &p->aOp[i+p->nOp]);\n    }\n#endif\n  }\n  p->nOp += nOp;\n  return pFirst;\n}\n\n#if defined(SQLITE_ENABLE_STMT_SCANSTATUS)\n/*\n** Add an entry to the array of counters managed by sqlite3_stmt_scanstatus().\n*/\nSQLITE_PRIVATE void sqlite3VdbeScanStatus(\n  Vdbe *p,                        /* VM to add scanstatus() to */\n  int addrExplain,                /* Address of OP_Explain (or 0) */\n  int addrLoop,                   /* Address of loop counter */ \n  int addrVisit,                  /* Address of rows visited counter */\n  LogEst nEst,                    /* Estimated number of output rows */\n  const char *zName               /* Name of table or index being scanned */\n){\n  int nByte = (p->nScan+1) * sizeof(ScanStatus);\n  ScanStatus *aNew;\n  aNew = (ScanStatus*)sqlite3DbRealloc(p->db, p->aScan, nByte);\n  if( aNew ){\n    ScanStatus *pNew = &aNew[p->nScan++];\n    pNew->addrExplain = addrExplain;\n    pNew->addrLoop = addrLoop;\n    pNew->addrVisit = addrVisit;\n    pNew->nEst = nEst;\n    pNew->zName = sqlite3DbStrDup(p->db, zName);\n    p->aScan = aNew;\n  }\n}\n#endif\n\n\n/*\n** Change the value of the opcode, or P1, P2, P3, or P5 operands\n** for a specific instruction.\n*/\nSQLITE_PRIVATE void sqlite3VdbeChangeOpcode(Vdbe *p, u32 addr, u8 iNewOpcode){\n  sqlite3VdbeGetOp(p,addr)->opcode = iNewOpcode;\n}\nSQLITE_PRIVATE void sqlite3VdbeChangeP1(Vdbe *p, u32 addr, int val){\n  sqlite3VdbeGetOp(p,addr)->p1 = val;\n}\nSQLITE_PRIVATE void sqlite3VdbeChangeP2(Vdbe *p, u32 addr, int val){\n  sqlite3VdbeGetOp(p,addr)->p2 = val;\n}\nSQLITE_PRIVATE void sqlite3VdbeChangeP3(Vdbe *p, u32 addr, int val){\n  sqlite3VdbeGetOp(p,addr)->p3 = val;\n}\nSQLITE_PRIVATE void sqlite3VdbeChangeP5(Vdbe *p, u16 p5){\n  assert( p->nOp>0 || p->db->mallocFailed );\n  if( p->nOp>0 ) p->aOp[p->nOp-1].p5 = p5;\n}\n\n/*\n** Change the P2 operand of instruction addr so that it points to\n** the address of the next instruction to be coded.\n*/\nSQLITE_PRIVATE void sqlite3VdbeJumpHere(Vdbe *p, int addr){\n  sqlite3VdbeChangeP2(p, addr, p->nOp);\n}\n\n\n/*\n** If the input FuncDef structure is ephemeral, then free it.  If\n** the FuncDef is not ephermal, then do nothing.\n*/\nstatic void freeEphemeralFunction(sqlite3 *db, FuncDef *pDef){\n  if( (pDef->funcFlags & SQLITE_FUNC_EPHEM)!=0 ){\n    sqlite3DbFreeNN(db, pDef);\n  }\n}\n\nstatic void vdbeFreeOpArray(sqlite3 *, Op *, int);\n\n/*\n** Delete a P4 value if necessary.\n*/\nstatic SQLITE_NOINLINE void freeP4Mem(sqlite3 *db, Mem *p){\n  if( p->szMalloc ) sqlite3DbFree(db, p->zMalloc);\n  sqlite3DbFreeNN(db, p);\n}\nstatic SQLITE_NOINLINE void freeP4FuncCtx(sqlite3 *db, sqlite3_context *p){\n  freeEphemeralFunction(db, p->pFunc);\n sqlite3DbFreeNN(db, p);\n}\nstatic void freeP4(sqlite3 *db, int p4type, void *p4){\n  assert( db );\n  switch( p4type ){\n    case P4_FUNCCTX: {\n      freeP4FuncCtx(db, (sqlite3_context*)p4);\n      break;\n    }\n    case P4_REAL:\n    case P4_INT64:\n    case P4_DYNAMIC:\n    case P4_DYNBLOB:\n    case P4_INTARRAY: {\n      sqlite3DbFree(db, p4);\n      break;\n    }\n    case P4_KEYINFO: {\n      if( db->pnBytesFreed==0 ) sqlite3KeyInfoUnref((KeyInfo*)p4);\n      break;\n    }\n#ifdef SQLITE_ENABLE_CURSOR_HINTS\n    case P4_EXPR: {\n      sqlite3ExprDelete(db, (Expr*)p4);\n      break;\n    }\n#endif\n    case P4_FUNCDEF: {\n      freeEphemeralFunction(db, (FuncDef*)p4);\n      break;\n    }\n    case P4_MEM: {\n      if( db->pnBytesFreed==0 ){\n        sqlite3ValueFree((sqlite3_value*)p4);\n      }else{\n        freeP4Mem(db, (Mem*)p4);\n      }\n      break;\n    }\n    case P4_VTAB : {\n      if( db->pnBytesFreed==0 ) sqlite3VtabUnlock((VTable *)p4);\n      break;\n    }\n  }\n}\n\n/*\n** Free the space allocated for aOp and any p4 values allocated for the\n** opcodes contained within. If aOp is not NULL it is assumed to contain \n** nOp entries. \n*/\nstatic void vdbeFreeOpArray(sqlite3 *db, Op *aOp, int nOp){\n  if( aOp ){\n    Op *pOp;\n    for(pOp=&aOp[nOp-1]; pOp>=aOp; pOp--){\n      if( pOp->p4type <= P4_FREE_IF_LE ) freeP4(db, pOp->p4type, pOp->p4.p);\n#ifdef SQLITE_ENABLE_EXPLAIN_COMMENTS\n      sqlite3DbFree(db, pOp->zComment);\n#endif     \n    }\n    sqlite3DbFreeNN(db, aOp);\n  }\n}\n\n/*\n** Link the SubProgram object passed as the second argument into the linked\n** list at Vdbe.pSubProgram. This list is used to delete all sub-program\n** objects when the VM is no longer required.\n*/\nSQLITE_PRIVATE void sqlite3VdbeLinkSubProgram(Vdbe *pVdbe, SubProgram *p){\n  p->pNext = pVdbe->pProgram;\n  pVdbe->pProgram = p;\n}\n\n/*\n** Change the opcode at addr into OP_Noop\n*/\nSQLITE_PRIVATE int sqlite3VdbeChangeToNoop(Vdbe *p, int addr){\n  VdbeOp *pOp;\n  if( p->db->mallocFailed ) return 0;\n  assert( addr>=0 && addr<p->nOp );\n  pOp = &p->aOp[addr];\n  freeP4(p->db, pOp->p4type, pOp->p4.p);\n  pOp->p4type = P4_NOTUSED;\n  pOp->p4.z = 0;\n  pOp->opcode = OP_Noop;\n  return 1;\n}\n\n/*\n** If the last opcode is \"op\" and it is not a jump destination,\n** then remove it.  Return true if and only if an opcode was removed.\n*/\nSQLITE_PRIVATE int sqlite3VdbeDeletePriorOpcode(Vdbe *p, u8 op){\n  if( p->nOp>0 && p->aOp[p->nOp-1].opcode==op ){\n    return sqlite3VdbeChangeToNoop(p, p->nOp-1);\n  }else{\n    return 0;\n  }\n}\n\n/*\n** Change the value of the P4 operand for a specific instruction.\n** This routine is useful when a large program is loaded from a\n** static array using sqlite3VdbeAddOpList but we want to make a\n** few minor changes to the program.\n**\n** If n>=0 then the P4 operand is dynamic, meaning that a copy of\n** the string is made into memory obtained from sqlite3_malloc().\n** A value of n==0 means copy bytes of zP4 up to and including the\n** first null byte.  If n>0 then copy n+1 bytes of zP4.\n** \n** Other values of n (P4_STATIC, P4_COLLSEQ etc.) indicate that zP4 points\n** to a string or structure that is guaranteed to exist for the lifetime of\n** the Vdbe. In these cases we can just copy the pointer.\n**\n** If addr<0 then change P4 on the most recently inserted instruction.\n*/\nstatic void SQLITE_NOINLINE vdbeChangeP4Full(\n  Vdbe *p,\n  Op *pOp,\n  const char *zP4,\n  int n\n){\n  if( pOp->p4type ){\n    freeP4(p->db, pOp->p4type, pOp->p4.p);\n    pOp->p4type = 0;\n    pOp->p4.p = 0;\n  }\n  if( n<0 ){\n    sqlite3VdbeChangeP4(p, (int)(pOp - p->aOp), zP4, n);\n  }else{\n    if( n==0 ) n = sqlite3Strlen30(zP4);\n    pOp->p4.z = sqlite3DbStrNDup(p->db, zP4, n);\n    pOp->p4type = P4_DYNAMIC;\n  }\n}\nSQLITE_PRIVATE void sqlite3VdbeChangeP4(Vdbe *p, int addr, const char *zP4, int n){\n  Op *pOp;\n  sqlite3 *db;\n  assert( p!=0 );\n  db = p->db;\n  assert( p->magic==VDBE_MAGIC_INIT );\n  assert( p->aOp!=0 || db->mallocFailed );\n  if( db->mallocFailed ){\n    if( n!=P4_VTAB ) freeP4(db, n, (void*)*(char**)&zP4);\n    return;\n  }\n  assert( p->nOp>0 );\n  assert( addr<p->nOp );\n  if( addr<0 ){\n    addr = p->nOp - 1;\n  }\n  pOp = &p->aOp[addr];\n  if( n>=0 || pOp->p4type ){\n    vdbeChangeP4Full(p, pOp, zP4, n);\n    return;\n  }\n  if( n==P4_INT32 ){\n    /* Note: this cast is safe, because the origin data point was an int\n    ** that was cast to a (const char *). */\n    pOp->p4.i = SQLITE_PTR_TO_INT(zP4);\n    pOp->p4type = P4_INT32;\n  }else if( zP4!=0 ){\n    assert( n<0 );\n    pOp->p4.p = (void*)zP4;\n    pOp->p4type = (signed char)n;\n    if( n==P4_VTAB ) sqlite3VtabLock((VTable*)zP4);\n  }\n}\n\n/*\n** Change the P4 operand of the most recently coded instruction \n** to the value defined by the arguments.  This is a high-speed\n** version of sqlite3VdbeChangeP4().\n**\n** The P4 operand must not have been previously defined.  And the new\n** P4 must not be P4_INT32.  Use sqlite3VdbeChangeP4() in either of\n** those cases.\n*/\nSQLITE_PRIVATE void sqlite3VdbeAppendP4(Vdbe *p, void *pP4, int n){\n  VdbeOp *pOp;\n  assert( n!=P4_INT32 && n!=P4_VTAB );\n  assert( n<=0 );\n  if( p->db->mallocFailed ){\n    freeP4(p->db, n, pP4);\n  }else{\n    assert( pP4!=0 );\n    assert( p->nOp>0 );\n    pOp = &p->aOp[p->nOp-1];\n    assert( pOp->p4type==P4_NOTUSED );\n    pOp->p4type = n;\n    pOp->p4.p = pP4;\n  }\n}\n\n/*\n** Set the P4 on the most recently added opcode to the KeyInfo for the\n** index given.\n*/\nSQLITE_PRIVATE void sqlite3VdbeSetP4KeyInfo(Parse *pParse, Index *pIdx){\n  Vdbe *v = pParse->pVdbe;\n  KeyInfo *pKeyInfo;\n  assert( v!=0 );\n  assert( pIdx!=0 );\n  pKeyInfo = sqlite3KeyInfoOfIndex(pParse, pIdx);\n  if( pKeyInfo ) sqlite3VdbeAppendP4(v, pKeyInfo, P4_KEYINFO);\n}\n\n#ifdef SQLITE_ENABLE_EXPLAIN_COMMENTS\n/*\n** Change the comment on the most recently coded instruction.  Or\n** insert a No-op and add the comment to that new instruction.  This\n** makes the code easier to read during debugging.  None of this happens\n** in a production build.\n*/\nstatic void vdbeVComment(Vdbe *p, const char *zFormat, va_list ap){\n  assert( p->nOp>0 || p->aOp==0 );\n  assert( p->aOp==0 || p->aOp[p->nOp-1].zComment==0 || p->db->mallocFailed );\n  if( p->nOp ){\n    assert( p->aOp );\n    sqlite3DbFree(p->db, p->aOp[p->nOp-1].zComment);\n    p->aOp[p->nOp-1].zComment = sqlite3VMPrintf(p->db, zFormat, ap);\n  }\n}\nSQLITE_PRIVATE void sqlite3VdbeComment(Vdbe *p, const char *zFormat, ...){\n  va_list ap;\n  if( p ){\n    va_start(ap, zFormat);\n    vdbeVComment(p, zFormat, ap);\n    va_end(ap);\n  }\n}\nSQLITE_PRIVATE void sqlite3VdbeNoopComment(Vdbe *p, const char *zFormat, ...){\n  va_list ap;\n  if( p ){\n    sqlite3VdbeAddOp0(p, OP_Noop);\n    va_start(ap, zFormat);\n    vdbeVComment(p, zFormat, ap);\n    va_end(ap);\n  }\n}\n#endif  /* NDEBUG */\n\n#ifdef SQLITE_VDBE_COVERAGE\n/*\n** Set the value if the iSrcLine field for the previously coded instruction.\n*/\nSQLITE_PRIVATE void sqlite3VdbeSetLineNumber(Vdbe *v, int iLine){\n  sqlite3VdbeGetOp(v,-1)->iSrcLine = iLine;\n}\n#endif /* SQLITE_VDBE_COVERAGE */\n\n/*\n** Return the opcode for a given address.  If the address is -1, then\n** return the most recently inserted opcode.\n**\n** If a memory allocation error has occurred prior to the calling of this\n** routine, then a pointer to a dummy VdbeOp will be returned.  That opcode\n** is readable but not writable, though it is cast to a writable value.\n** The return of a dummy opcode allows the call to continue functioning\n** after an OOM fault without having to check to see if the return from \n** this routine is a valid pointer.  But because the dummy.opcode is 0,\n** dummy will never be written to.  This is verified by code inspection and\n** by running with Valgrind.\n*/\nSQLITE_PRIVATE VdbeOp *sqlite3VdbeGetOp(Vdbe *p, int addr){\n  /* C89 specifies that the constant \"dummy\" will be initialized to all\n  ** zeros, which is correct.  MSVC generates a warning, nevertheless. */\n  static VdbeOp dummy;  /* Ignore the MSVC warning about no initializer */\n  assert( p->magic==VDBE_MAGIC_INIT );\n  if( addr<0 ){\n    addr = p->nOp - 1;\n  }\n  assert( (addr>=0 && addr<p->nOp) || p->db->mallocFailed );\n  if( p->db->mallocFailed ){\n    return (VdbeOp*)&dummy;\n  }else{\n    return &p->aOp[addr];\n  }\n}\n\n#if defined(SQLITE_ENABLE_EXPLAIN_COMMENTS)\n/*\n** Return an integer value for one of the parameters to the opcode pOp\n** determined by character c.\n*/\nstatic int translateP(char c, const Op *pOp){\n  if( c=='1' ) return pOp->p1;\n  if( c=='2' ) return pOp->p2;\n  if( c=='3' ) return pOp->p3;\n  if( c=='4' ) return pOp->p4.i;\n  return pOp->p5;\n}\n\n/*\n** Compute a string for the \"comment\" field of a VDBE opcode listing.\n**\n** The Synopsis: field in comments in the vdbe.c source file gets converted\n** to an extra string that is appended to the sqlite3OpcodeName().  In the\n** absence of other comments, this synopsis becomes the comment on the opcode.\n** Some translation occurs:\n**\n**       \"PX\"      ->  \"r[X]\"\n**       \"PX@PY\"   ->  \"r[X..X+Y-1]\"  or \"r[x]\" if y is 0 or 1\n**       \"PX@PY+1\" ->  \"r[X..X+Y]\"    or \"r[x]\" if y is 0\n**       \"PY..PY\"  ->  \"r[X..Y]\"      or \"r[x]\" if y<=x\n*/\nstatic int displayComment(\n  const Op *pOp,     /* The opcode to be commented */\n  const char *zP4,   /* Previously obtained value for P4 */\n  char *zTemp,       /* Write result here */\n  int nTemp          /* Space available in zTemp[] */\n){\n  const char *zOpName;\n  const char *zSynopsis;\n  int nOpName;\n  int ii, jj;\n  char zAlt[50];\n  zOpName = sqlite3OpcodeName(pOp->opcode);\n  nOpName = sqlite3Strlen30(zOpName);\n  if( zOpName[nOpName+1] ){\n    int seenCom = 0;\n    char c;\n    zSynopsis = zOpName += nOpName + 1;\n    if( strncmp(zSynopsis,\"IF \",3)==0 ){\n      if( pOp->p5 & SQLITE_STOREP2 ){\n        sqlite3_snprintf(sizeof(zAlt), zAlt, \"r[P2] = (%s)\", zSynopsis+3);\n      }else{\n        sqlite3_snprintf(sizeof(zAlt), zAlt, \"if %s goto P2\", zSynopsis+3);\n      }\n      zSynopsis = zAlt;\n    }\n    for(ii=jj=0; jj<nTemp-1 && (c = zSynopsis[ii])!=0; ii++){\n      if( c=='P' ){\n        c = zSynopsis[++ii];\n        if( c=='4' ){\n          sqlite3_snprintf(nTemp-jj, zTemp+jj, \"%s\", zP4);\n        }else if( c=='X' ){\n          sqlite3_snprintf(nTemp-jj, zTemp+jj, \"%s\", pOp->zComment);\n          seenCom = 1;\n        }else{\n          int v1 = translateP(c, pOp);\n          int v2;\n          sqlite3_snprintf(nTemp-jj, zTemp+jj, \"%d\", v1);\n          if( strncmp(zSynopsis+ii+1, \"@P\", 2)==0 ){\n            ii += 3;\n            jj += sqlite3Strlen30(zTemp+jj);\n            v2 = translateP(zSynopsis[ii], pOp);\n            if( strncmp(zSynopsis+ii+1,\"+1\",2)==0 ){\n              ii += 2;\n              v2++;\n            }\n            if( v2>1 ){\n              sqlite3_snprintf(nTemp-jj, zTemp+jj, \"..%d\", v1+v2-1);\n            }\n          }else if( strncmp(zSynopsis+ii+1, \"..P3\", 4)==0 && pOp->p3==0 ){\n            ii += 4;\n          }\n        }\n        jj += sqlite3Strlen30(zTemp+jj);\n      }else{\n        zTemp[jj++] = c;\n      }\n    }\n    if( !seenCom && jj<nTemp-5 && pOp->zComment ){\n      sqlite3_snprintf(nTemp-jj, zTemp+jj, \"; %s\", pOp->zComment);\n      jj += sqlite3Strlen30(zTemp+jj);\n    }\n    if( jj<nTemp ) zTemp[jj] = 0;\n  }else if( pOp->zComment ){\n    sqlite3_snprintf(nTemp, zTemp, \"%s\", pOp->zComment);\n    jj = sqlite3Strlen30(zTemp);\n  }else{\n    zTemp[0] = 0;\n    jj = 0;\n  }\n  return jj;\n}\n#endif /* SQLITE_DEBUG */\n\n#if VDBE_DISPLAY_P4 && defined(SQLITE_ENABLE_CURSOR_HINTS)\n/*\n** Translate the P4.pExpr value for an OP_CursorHint opcode into text\n** that can be displayed in the P4 column of EXPLAIN output.\n*/\nstatic void displayP4Expr(StrAccum *p, Expr *pExpr){\n  const char *zOp = 0;\n  switch( pExpr->op ){\n    case TK_STRING:\n      sqlite3XPrintf(p, \"%Q\", pExpr->u.zToken);\n      break;\n    case TK_INTEGER:\n      sqlite3XPrintf(p, \"%d\", pExpr->u.iValue);\n      break;\n    case TK_NULL:\n      sqlite3XPrintf(p, \"NULL\");\n      break;\n    case TK_REGISTER: {\n      sqlite3XPrintf(p, \"r[%d]\", pExpr->iTable);\n      break;\n    }\n    case TK_COLUMN: {\n      if( pExpr->iColumn<0 ){\n        sqlite3XPrintf(p, \"rowid\");\n      }else{\n        sqlite3XPrintf(p, \"c%d\", (int)pExpr->iColumn);\n      }\n      break;\n    }\n    case TK_LT:      zOp = \"LT\";      break;\n    case TK_LE:      zOp = \"LE\";      break;\n    case TK_GT:      zOp = \"GT\";      break;\n    case TK_GE:      zOp = \"GE\";      break;\n    case TK_NE:      zOp = \"NE\";      break;\n    case TK_EQ:      zOp = \"EQ\";      break;\n    case TK_IS:      zOp = \"IS\";      break;\n    case TK_ISNOT:   zOp = \"ISNOT\";   break;\n    case TK_AND:     zOp = \"AND\";     break;\n    case TK_OR:      zOp = \"OR\";      break;\n    case TK_PLUS:    zOp = \"ADD\";     break;\n    case TK_STAR:    zOp = \"MUL\";     break;\n    case TK_MINUS:   zOp = \"SUB\";     break;\n    case TK_REM:     zOp = \"REM\";     break;\n    case TK_BITAND:  zOp = \"BITAND\";  break;\n    case TK_BITOR:   zOp = \"BITOR\";   break;\n    case TK_SLASH:   zOp = \"DIV\";     break;\n    case TK_LSHIFT:  zOp = \"LSHIFT\";  break;\n    case TK_RSHIFT:  zOp = \"RSHIFT\";  break;\n    case TK_CONCAT:  zOp = \"CONCAT\";  break;\n    case TK_UMINUS:  zOp = \"MINUS\";   break;\n    case TK_UPLUS:   zOp = \"PLUS\";    break;\n    case TK_BITNOT:  zOp = \"BITNOT\";  break;\n    case TK_NOT:     zOp = \"NOT\";     break;\n    case TK_ISNULL:  zOp = \"ISNULL\";  break;\n    case TK_NOTNULL: zOp = \"NOTNULL\"; break;\n\n    default:\n      sqlite3XPrintf(p, \"%s\", \"expr\");\n      break;\n  }\n\n  if( zOp ){\n    sqlite3XPrintf(p, \"%s(\", zOp);\n    displayP4Expr(p, pExpr->pLeft);\n    if( pExpr->pRight ){\n      sqlite3StrAccumAppend(p, \",\", 1);\n      displayP4Expr(p, pExpr->pRight);\n    }\n    sqlite3StrAccumAppend(p, \")\", 1);\n  }\n}\n#endif /* VDBE_DISPLAY_P4 && defined(SQLITE_ENABLE_CURSOR_HINTS) */\n\n\n#if VDBE_DISPLAY_P4\n/*\n** Compute a string that describes the P4 parameter for an opcode.\n** Use zTemp for any required temporary buffer space.\n*/\nstatic char *displayP4(Op *pOp, char *zTemp, int nTemp){\n  char *zP4 = zTemp;\n  StrAccum x;\n  assert( nTemp>=20 );\n  sqlite3StrAccumInit(&x, 0, zTemp, nTemp, 0);\n  switch( pOp->p4type ){\n    case P4_KEYINFO: {\n      int j;\n      KeyInfo *pKeyInfo = pOp->p4.pKeyInfo;\n      assert( pKeyInfo->aSortOrder!=0 );\n      sqlite3XPrintf(&x, \"k(%d\", pKeyInfo->nKeyField);\n      for(j=0; j<pKeyInfo->nKeyField; j++){\n        CollSeq *pColl = pKeyInfo->aColl[j];\n        const char *zColl = pColl ? pColl->zName : \"\";\n        if( strcmp(zColl, \"BINARY\")==0 ) zColl = \"B\";\n        sqlite3XPrintf(&x, \",%s%s\", pKeyInfo->aSortOrder[j] ? \"-\" : \"\", zColl);\n      }\n      sqlite3StrAccumAppend(&x, \")\", 1);\n      break;\n    }\n#ifdef SQLITE_ENABLE_CURSOR_HINTS\n    case P4_EXPR: {\n      displayP4Expr(&x, pOp->p4.pExpr);\n      break;\n    }\n#endif\n    case P4_COLLSEQ: {\n      CollSeq *pColl = pOp->p4.pColl;\n      sqlite3XPrintf(&x, \"(%.20s)\", pColl->zName);\n      break;\n    }\n    case P4_FUNCDEF: {\n      FuncDef *pDef = pOp->p4.pFunc;\n      sqlite3XPrintf(&x, \"%s(%d)\", pDef->zName, pDef->nArg);\n      break;\n    }\n#if defined(SQLITE_DEBUG) || defined(VDBE_PROFILE)\n    case P4_FUNCCTX: {\n      FuncDef *pDef = pOp->p4.pCtx->pFunc;\n      sqlite3XPrintf(&x, \"%s(%d)\", pDef->zName, pDef->nArg);\n      break;\n    }\n#endif\n    case P4_INT64: {\n      sqlite3XPrintf(&x, \"%lld\", *pOp->p4.pI64);\n      break;\n    }\n    case P4_INT32: {\n      sqlite3XPrintf(&x, \"%d\", pOp->p4.i);\n      break;\n    }\n    case P4_REAL: {\n      sqlite3XPrintf(&x, \"%.16g\", *pOp->p4.pReal);\n      break;\n    }\n    case P4_MEM: {\n      Mem *pMem = pOp->p4.pMem;\n      if( pMem->flags & MEM_Str ){\n        zP4 = pMem->z;\n      }else if( pMem->flags & MEM_Int ){\n        sqlite3XPrintf(&x, \"%lld\", pMem->u.i);\n      }else if( pMem->flags & MEM_Real ){\n        sqlite3XPrintf(&x, \"%.16g\", pMem->u.r);\n      }else if( pMem->flags & MEM_Null ){\n        zP4 = \"NULL\";\n      }else{\n        assert( pMem->flags & MEM_Blob );\n        zP4 = \"(blob)\";\n      }\n      break;\n    }\n#ifndef SQLITE_OMIT_VIRTUALTABLE\n    case P4_VTAB: {\n      sqlite3_vtab *pVtab = pOp->p4.pVtab->pVtab;\n      sqlite3XPrintf(&x, \"vtab:%p\", pVtab);\n      break;\n    }\n#endif\n    case P4_INTARRAY: {\n      int i;\n      int *ai = pOp->p4.ai;\n      int n = ai[0];   /* The first element of an INTARRAY is always the\n                       ** count of the number of elements to follow */\n      for(i=1; i<=n; i++){\n        sqlite3XPrintf(&x, \",%d\", ai[i]);\n      }\n      zTemp[0] = '[';\n      sqlite3StrAccumAppend(&x, \"]\", 1);\n      break;\n    }\n    case P4_SUBPROGRAM: {\n      sqlite3XPrintf(&x, \"program\");\n      break;\n    }\n    case P4_DYNBLOB:\n    case P4_ADVANCE: {\n      zTemp[0] = 0;\n      break;\n    }\n    case P4_TABLE: {\n      sqlite3XPrintf(&x, \"%s\", pOp->p4.pTab->zName);\n      break;\n    }\n    default: {\n      zP4 = pOp->p4.z;\n      if( zP4==0 ){\n        zP4 = zTemp;\n        zTemp[0] = 0;\n      }\n    }\n  }\n  sqlite3StrAccumFinish(&x);\n  assert( zP4!=0 );\n  return zP4;\n}\n#endif /* VDBE_DISPLAY_P4 */\n\n/*\n** Declare to the Vdbe that the BTree object at db->aDb[i] is used.\n**\n** The prepared statements need to know in advance the complete set of\n** attached databases that will be use.  A mask of these databases\n** is maintained in p->btreeMask.  The p->lockMask value is the subset of\n** p->btreeMask of databases that will require a lock.\n*/\nSQLITE_PRIVATE void sqlite3VdbeUsesBtree(Vdbe *p, int i){\n  assert( i>=0 && i<p->db->nDb && i<(int)sizeof(yDbMask)*8 );\n  assert( i<(int)sizeof(p->btreeMask)*8 );\n  DbMaskSet(p->btreeMask, i);\n  if( i!=1 && sqlite3BtreeSharable(p->db->aDb[i].pBt) ){\n    DbMaskSet(p->lockMask, i);\n  }\n}\n\n#if !defined(SQLITE_OMIT_SHARED_CACHE)\n/*\n** If SQLite is compiled to support shared-cache mode and to be threadsafe,\n** this routine obtains the mutex associated with each BtShared structure\n** that may be accessed by the VM passed as an argument. In doing so it also\n** sets the BtShared.db member of each of the BtShared structures, ensuring\n** that the correct busy-handler callback is invoked if required.\n**\n** If SQLite is not threadsafe but does support shared-cache mode, then\n** sqlite3BtreeEnter() is invoked to set the BtShared.db variables\n** of all of BtShared structures accessible via the database handle \n** associated with the VM.\n**\n** If SQLite is not threadsafe and does not support shared-cache mode, this\n** function is a no-op.\n**\n** The p->btreeMask field is a bitmask of all btrees that the prepared \n** statement p will ever use.  Let N be the number of bits in p->btreeMask\n** corresponding to btrees that use shared cache.  Then the runtime of\n** this routine is N*N.  But as N is rarely more than 1, this should not\n** be a problem.\n*/\nSQLITE_PRIVATE void sqlite3VdbeEnter(Vdbe *p){\n  int i;\n  sqlite3 *db;\n  Db *aDb;\n  int nDb;\n  if( DbMaskAllZero(p->lockMask) ) return;  /* The common case */\n  db = p->db;\n  aDb = db->aDb;\n  nDb = db->nDb;\n  for(i=0; i<nDb; i++){\n    if( i!=1 && DbMaskTest(p->lockMask,i) && ALWAYS(aDb[i].pBt!=0) ){\n      sqlite3BtreeEnter(aDb[i].pBt);\n    }\n  }\n}\n#endif\n\n#if !defined(SQLITE_OMIT_SHARED_CACHE) && SQLITE_THREADSAFE>0\n/*\n** Unlock all of the btrees previously locked by a call to sqlite3VdbeEnter().\n*/\nstatic SQLITE_NOINLINE void vdbeLeave(Vdbe *p){\n  int i;\n  sqlite3 *db;\n  Db *aDb;\n  int nDb;\n  db = p->db;\n  aDb = db->aDb;\n  nDb = db->nDb;\n  for(i=0; i<nDb; i++){\n    if( i!=1 && DbMaskTest(p->lockMask,i) && ALWAYS(aDb[i].pBt!=0) ){\n      sqlite3BtreeLeave(aDb[i].pBt);\n    }\n  }\n}\nSQLITE_PRIVATE void sqlite3VdbeLeave(Vdbe *p){\n  if( DbMaskAllZero(p->lockMask) ) return;  /* The common case */\n  vdbeLeave(p);\n}\n#endif\n\n#if defined(VDBE_PROFILE) || defined(SQLITE_DEBUG)\n/*\n** Print a single opcode.  This routine is used for debugging only.\n*/\nSQLITE_PRIVATE void sqlite3VdbePrintOp(FILE *pOut, int pc, Op *pOp){\n  char *zP4;\n  char zPtr[50];\n  char zCom[100];\n  static const char *zFormat1 = \"%4d %-13s %4d %4d %4d %-13s %.2X %s\\n\";\n  if( pOut==0 ) pOut = stdout;\n  zP4 = displayP4(pOp, zPtr, sizeof(zPtr));\n#ifdef SQLITE_ENABLE_EXPLAIN_COMMENTS\n  displayComment(pOp, zP4, zCom, sizeof(zCom));\n#else\n  zCom[0] = 0;\n#endif\n  /* NB:  The sqlite3OpcodeName() function is implemented by code created\n  ** by the mkopcodeh.awk and mkopcodec.awk scripts which extract the\n  ** information from the vdbe.c source text */\n  fprintf(pOut, zFormat1, pc, \n      sqlite3OpcodeName(pOp->opcode), pOp->p1, pOp->p2, pOp->p3, zP4, pOp->p5,\n      zCom\n  );\n  fflush(pOut);\n}\n#endif\n\n/*\n** Initialize an array of N Mem element.\n*/\nstatic void initMemArray(Mem *p, int N, sqlite3 *db, u16 flags){\n  while( (N--)>0 ){\n    p->db = db;\n    p->flags = flags;\n    p->szMalloc = 0;\n#ifdef SQLITE_DEBUG\n    p->pScopyFrom = 0;\n#endif\n    p++;\n  }\n}\n\n/*\n** Release an array of N Mem elements\n*/\nstatic void releaseMemArray(Mem *p, int N){\n  if( p && N ){\n    Mem *pEnd = &p[N];\n    sqlite3 *db = p->db;\n    if( db->pnBytesFreed ){\n      do{\n        if( p->szMalloc ) sqlite3DbFree(db, p->zMalloc);\n      }while( (++p)<pEnd );\n      return;\n    }\n    do{\n      assert( (&p[1])==pEnd || p[0].db==p[1].db );\n      assert( sqlite3VdbeCheckMemInvariants(p) );\n\n      /* This block is really an inlined version of sqlite3VdbeMemRelease()\n      ** that takes advantage of the fact that the memory cell value is \n      ** being set to NULL after releasing any dynamic resources.\n      **\n      ** The justification for duplicating code is that according to \n      ** callgrind, this causes a certain test case to hit the CPU 4.7 \n      ** percent less (x86 linux, gcc version 4.1.2, -O6) than if \n      ** sqlite3MemRelease() were called from here. With -O2, this jumps\n      ** to 6.6 percent. The test case is inserting 1000 rows into a table \n      ** with no indexes using a single prepared INSERT statement, bind() \n      ** and reset(). Inserts are grouped into a transaction.\n      */\n      testcase( p->flags & MEM_Agg );\n      testcase( p->flags & MEM_Dyn );\n      testcase( p->flags & MEM_Frame );\n      testcase( p->flags & MEM_RowSet );\n      if( p->flags&(MEM_Agg|MEM_Dyn|MEM_Frame|MEM_RowSet) ){\n        sqlite3VdbeMemRelease(p);\n      }else if( p->szMalloc ){\n        sqlite3DbFreeNN(db, p->zMalloc);\n        p->szMalloc = 0;\n      }\n\n      p->flags = MEM_Undefined;\n    }while( (++p)<pEnd );\n  }\n}\n\n/*\n** Delete a VdbeFrame object and its contents. VdbeFrame objects are\n** allocated by the OP_Program opcode in sqlite3VdbeExec().\n*/\nSQLITE_PRIVATE void sqlite3VdbeFrameDelete(VdbeFrame *p){\n  int i;\n  Mem *aMem = VdbeFrameMem(p);\n  VdbeCursor **apCsr = (VdbeCursor **)&aMem[p->nChildMem];\n  for(i=0; i<p->nChildCsr; i++){\n    sqlite3VdbeFreeCursor(p->v, apCsr[i]);\n  }\n  releaseMemArray(aMem, p->nChildMem);\n  sqlite3VdbeDeleteAuxData(p->v->db, &p->pAuxData, -1, 0);\n  sqlite3DbFree(p->v->db, p);\n}\n\n#ifndef SQLITE_OMIT_EXPLAIN\n/*\n** Give a listing of the program in the virtual machine.\n**\n** The interface is the same as sqlite3VdbeExec().  But instead of\n** running the code, it invokes the callback once for each instruction.\n** This feature is used to implement \"EXPLAIN\".\n**\n** When p->explain==1, each instruction is listed.  When\n** p->explain==2, only OP_Explain instructions are listed and these\n** are shown in a different format.  p->explain==2 is used to implement\n** EXPLAIN QUERY PLAN.\n**\n** When p->explain==1, first the main program is listed, then each of\n** the trigger subprograms are listed one by one.\n*/\nSQLITE_PRIVATE int sqlite3VdbeList(\n  Vdbe *p                   /* The VDBE */\n){\n  int nRow;                            /* Stop when row count reaches this */\n  int nSub = 0;                        /* Number of sub-vdbes seen so far */\n  SubProgram **apSub = 0;              /* Array of sub-vdbes */\n  Mem *pSub = 0;                       /* Memory cell hold array of subprogs */\n  sqlite3 *db = p->db;                 /* The database connection */\n  int i;                               /* Loop counter */\n  int rc = SQLITE_OK;                  /* Return code */\n  Mem *pMem = &p->aMem[1];             /* First Mem of result set */\n  int bListSubprogs = (p->explain==1 || (db->flags & SQLITE_TriggerEQP)!=0);\n  Op *pOp = 0;\n\n  assert( p->explain );\n  assert( p->magic==VDBE_MAGIC_RUN );\n  assert( p->rc==SQLITE_OK || p->rc==SQLITE_BUSY || p->rc==SQLITE_NOMEM );\n\n  /* Even though this opcode does not use dynamic strings for\n  ** the result, result columns may become dynamic if the user calls\n  ** sqlite3_column_text16(), causing a translation to UTF-16 encoding.\n  */\n  releaseMemArray(pMem, 8);\n  p->pResultSet = 0;\n\n  if( p->rc==SQLITE_NOMEM ){\n    /* This happens if a malloc() inside a call to sqlite3_column_text() or\n    ** sqlite3_column_text16() failed.  */\n    sqlite3OomFault(db);\n    return SQLITE_ERROR;\n  }\n\n  /* When the number of output rows reaches nRow, that means the\n  ** listing has finished and sqlite3_step() should return SQLITE_DONE.\n  ** nRow is the sum of the number of rows in the main program, plus\n  ** the sum of the number of rows in all trigger subprograms encountered\n  ** so far.  The nRow value will increase as new trigger subprograms are\n  ** encountered, but p->pc will eventually catch up to nRow.\n  */\n  nRow = p->nOp;\n  if( bListSubprogs ){\n    /* The first 8 memory cells are used for the result set.  So we will\n    ** commandeer the 9th cell to use as storage for an array of pointers\n    ** to trigger subprograms.  The VDBE is guaranteed to have at least 9\n    ** cells.  */\n    assert( p->nMem>9 );\n    pSub = &p->aMem[9];\n    if( pSub->flags&MEM_Blob ){\n      /* On the first call to sqlite3_step(), pSub will hold a NULL.  It is\n      ** initialized to a BLOB by the P4_SUBPROGRAM processing logic below */\n      nSub = pSub->n/sizeof(Vdbe*);\n      apSub = (SubProgram **)pSub->z;\n    }\n    for(i=0; i<nSub; i++){\n      nRow += apSub[i]->nOp;\n    }\n  }\n\n  do{\n    i = p->pc++;\n    if( i>=nRow ){\n      p->rc = SQLITE_OK;\n      rc = SQLITE_DONE;\n      break;\n    }\n    if( i<p->nOp ){\n      /* The output line number is small enough that we are still in the\n      ** main program. */\n      pOp = &p->aOp[i];\n    }else{\n      /* We are currently listing subprograms.  Figure out which one and\n      ** pick up the appropriate opcode. */\n      int j;\n      i -= p->nOp;\n      for(j=0; i>=apSub[j]->nOp; j++){\n        i -= apSub[j]->nOp;\n      }\n      pOp = &apSub[j]->aOp[i];\n    }\n\n    /* When an OP_Program opcode is encounter (the only opcode that has\n    ** a P4_SUBPROGRAM argument), expand the size of the array of subprograms\n    ** kept in p->aMem[9].z to hold the new program - assuming this subprogram\n    ** has not already been seen.\n    */\n    if( bListSubprogs && pOp->p4type==P4_SUBPROGRAM ){\n      int nByte = (nSub+1)*sizeof(SubProgram*);\n      int j;\n      for(j=0; j<nSub; j++){\n        if( apSub[j]==pOp->p4.pProgram ) break;\n      }\n      if( j==nSub ){\n        p->rc = sqlite3VdbeMemGrow(pSub, nByte, nSub!=0);\n        if( p->rc!=SQLITE_OK ){\n          rc = SQLITE_ERROR;\n          break;\n        }\n        apSub = (SubProgram **)pSub->z;\n        apSub[nSub++] = pOp->p4.pProgram;\n        pSub->flags |= MEM_Blob;\n        pSub->n = nSub*sizeof(SubProgram*);\n        nRow += pOp->p4.pProgram->nOp;\n      }\n    }\n  }while( p->explain==2 && pOp->opcode!=OP_Explain );\n\n  if( rc==SQLITE_OK ){\n    if( db->u1.isInterrupted ){\n      p->rc = SQLITE_INTERRUPT;\n      rc = SQLITE_ERROR;\n      sqlite3VdbeError(p, sqlite3ErrStr(p->rc));\n    }else{\n      char *zP4;\n      if( p->explain==1 ){\n        pMem->flags = MEM_Int;\n        pMem->u.i = i;                                /* Program counter */\n        pMem++;\n    \n        pMem->flags = MEM_Static|MEM_Str|MEM_Term;\n        pMem->z = (char*)sqlite3OpcodeName(pOp->opcode); /* Opcode */\n        assert( pMem->z!=0 );\n        pMem->n = sqlite3Strlen30(pMem->z);\n        pMem->enc = SQLITE_UTF8;\n        pMem++;\n      }\n\n      pMem->flags = MEM_Int;\n      pMem->u.i = pOp->p1;                          /* P1 */\n      pMem++;\n\n      pMem->flags = MEM_Int;\n      pMem->u.i = pOp->p2;                          /* P2 */\n      pMem++;\n\n      pMem->flags = MEM_Int;\n      pMem->u.i = pOp->p3;                          /* P3 */\n      pMem++;\n\n      if( sqlite3VdbeMemClearAndResize(pMem, 100) ){ /* P4 */\n        assert( p->db->mallocFailed );\n        return SQLITE_ERROR;\n      }\n      pMem->flags = MEM_Str|MEM_Term;\n      zP4 = displayP4(pOp, pMem->z, pMem->szMalloc);\n      if( zP4!=pMem->z ){\n        pMem->n = 0;\n        sqlite3VdbeMemSetStr(pMem, zP4, -1, SQLITE_UTF8, 0);\n      }else{\n        assert( pMem->z!=0 );\n        pMem->n = sqlite3Strlen30(pMem->z);\n        pMem->enc = SQLITE_UTF8;\n      }\n      pMem++;\n\n      if( p->explain==1 ){\n        if( sqlite3VdbeMemClearAndResize(pMem, 4) ){\n          assert( p->db->mallocFailed );\n          return SQLITE_ERROR;\n        }\n        pMem->flags = MEM_Str|MEM_Term;\n        pMem->n = 2;\n        sqlite3_snprintf(3, pMem->z, \"%.2x\", pOp->p5);   /* P5 */\n        pMem->enc = SQLITE_UTF8;\n        pMem++;\n    \n#ifdef SQLITE_ENABLE_EXPLAIN_COMMENTS\n        if( sqlite3VdbeMemClearAndResize(pMem, 500) ){\n          assert( p->db->mallocFailed );\n          return SQLITE_ERROR;\n        }\n        pMem->flags = MEM_Str|MEM_Term;\n        pMem->n = displayComment(pOp, zP4, pMem->z, 500);\n        pMem->enc = SQLITE_UTF8;\n#else\n        pMem->flags = MEM_Null;                       /* Comment */\n#endif\n      }\n\n      p->nResColumn = 8 - 4*(p->explain-1);\n      p->pResultSet = &p->aMem[1];\n      p->rc = SQLITE_OK;\n      rc = SQLITE_ROW;\n    }\n  }\n  return rc;\n}\n#endif /* SQLITE_OMIT_EXPLAIN */\n\n#ifdef SQLITE_DEBUG\n/*\n** Print the SQL that was used to generate a VDBE program.\n*/\nSQLITE_PRIVATE void sqlite3VdbePrintSql(Vdbe *p){\n  const char *z = 0;\n  if( p->zSql ){\n    z = p->zSql;\n  }else if( p->nOp>=1 ){\n    const VdbeOp *pOp = &p->aOp[0];\n    if( pOp->opcode==OP_Init && pOp->p4.z!=0 ){\n      z = pOp->p4.z;\n      while( sqlite3Isspace(*z) ) z++;\n    }\n  }\n  if( z ) printf(\"SQL: [%s]\\n\", z);\n}\n#endif\n\n#if !defined(SQLITE_OMIT_TRACE) && defined(SQLITE_ENABLE_IOTRACE)\n/*\n** Print an IOTRACE message showing SQL content.\n*/\nSQLITE_PRIVATE void sqlite3VdbeIOTraceSql(Vdbe *p){\n  int nOp = p->nOp;\n  VdbeOp *pOp;\n  if( sqlite3IoTrace==0 ) return;\n  if( nOp<1 ) return;\n  pOp = &p->aOp[0];\n  if( pOp->opcode==OP_Init && pOp->p4.z!=0 ){\n    int i, j;\n    char z[1000];\n    sqlite3_snprintf(sizeof(z), z, \"%s\", pOp->p4.z);\n    for(i=0; sqlite3Isspace(z[i]); i++){}\n    for(j=0; z[i]; i++){\n      if( sqlite3Isspace(z[i]) ){\n        if( z[i-1]!=' ' ){\n          z[j++] = ' ';\n        }\n      }else{\n        z[j++] = z[i];\n      }\n    }\n    z[j] = 0;\n    sqlite3IoTrace(\"SQL %s\\n\", z);\n  }\n}\n#endif /* !SQLITE_OMIT_TRACE && SQLITE_ENABLE_IOTRACE */\n\n/* An instance of this object describes bulk memory available for use\n** by subcomponents of a prepared statement.  Space is allocated out\n** of a ReusableSpace object by the allocSpace() routine below.\n*/\nstruct ReusableSpace {\n  u8 *pSpace;          /* Available memory */\n  int nFree;           /* Bytes of available memory */\n  int nNeeded;         /* Total bytes that could not be allocated */\n};\n\n/* Try to allocate nByte bytes of 8-byte aligned bulk memory for pBuf\n** from the ReusableSpace object.  Return a pointer to the allocated\n** memory on success.  If insufficient memory is available in the\n** ReusableSpace object, increase the ReusableSpace.nNeeded\n** value by the amount needed and return NULL.\n**\n** If pBuf is not initially NULL, that means that the memory has already\n** been allocated by a prior call to this routine, so just return a copy\n** of pBuf and leave ReusableSpace unchanged.\n**\n** This allocator is employed to repurpose unused slots at the end of the\n** opcode array of prepared state for other memory needs of the prepared\n** statement.\n*/\nstatic void *allocSpace(\n  struct ReusableSpace *p,  /* Bulk memory available for allocation */\n  void *pBuf,               /* Pointer to a prior allocation */\n  int nByte                 /* Bytes of memory needed */\n){\n  assert( EIGHT_BYTE_ALIGNMENT(p->pSpace) );\n  if( pBuf==0 ){\n    nByte = ROUND8(nByte);\n    if( nByte <= p->nFree ){\n      p->nFree -= nByte;\n      pBuf = &p->pSpace[p->nFree];\n    }else{\n      p->nNeeded += nByte;\n    }\n  }\n  assert( EIGHT_BYTE_ALIGNMENT(pBuf) );\n  return pBuf;\n}\n\n/*\n** Rewind the VDBE back to the beginning in preparation for\n** running it.\n*/\nSQLITE_PRIVATE void sqlite3VdbeRewind(Vdbe *p){\n#if defined(SQLITE_DEBUG) || defined(VDBE_PROFILE)\n  int i;\n#endif\n  assert( p!=0 );\n  assert( p->magic==VDBE_MAGIC_INIT || p->magic==VDBE_MAGIC_RESET );\n\n  /* There should be at least one opcode.\n  */\n  assert( p->nOp>0 );\n\n  /* Set the magic to VDBE_MAGIC_RUN sooner rather than later. */\n  p->magic = VDBE_MAGIC_RUN;\n\n#ifdef SQLITE_DEBUG\n  for(i=0; i<p->nMem; i++){\n    assert( p->aMem[i].db==p->db );\n  }\n#endif\n  p->pc = -1;\n  p->rc = SQLITE_OK;\n  p->errorAction = OE_Abort;\n  p->nChange = 0;\n  p->cacheCtr = 1;\n  p->minWriteFileFormat = 255;\n  p->iStatement = 0;\n  p->nFkConstraint = 0;\n#ifdef VDBE_PROFILE\n  for(i=0; i<p->nOp; i++){\n    p->aOp[i].cnt = 0;\n    p->aOp[i].cycles = 0;\n  }\n#endif\n}\n\n/*\n** Prepare a virtual machine for execution for the first time after\n** creating the virtual machine.  This involves things such\n** as allocating registers and initializing the program counter.\n** After the VDBE has be prepped, it can be executed by one or more\n** calls to sqlite3VdbeExec().  \n**\n** This function may be called exactly once on each virtual machine.\n** After this routine is called the VM has been \"packaged\" and is ready\n** to run.  After this routine is called, further calls to \n** sqlite3VdbeAddOp() functions are prohibited.  This routine disconnects\n** the Vdbe from the Parse object that helped generate it so that the\n** the Vdbe becomes an independent entity and the Parse object can be\n** destroyed.\n**\n** Use the sqlite3VdbeRewind() procedure to restore a virtual machine back\n** to its initial state after it has been run.\n*/\nSQLITE_PRIVATE void sqlite3VdbeMakeReady(\n  Vdbe *p,                       /* The VDBE */\n  Parse *pParse                  /* Parsing context */\n){\n  sqlite3 *db;                   /* The database connection */\n  int nVar;                      /* Number of parameters */\n  int nMem;                      /* Number of VM memory registers */\n  int nCursor;                   /* Number of cursors required */\n  int nArg;                      /* Number of arguments in subprograms */\n  int n;                         /* Loop counter */\n  struct ReusableSpace x;        /* Reusable bulk memory */\n\n  assert( p!=0 );\n  assert( p->nOp>0 );\n  assert( pParse!=0 );\n  assert( p->magic==VDBE_MAGIC_INIT );\n  assert( pParse==p->pParse );\n  db = p->db;\n  assert( db->mallocFailed==0 );\n  nVar = pParse->nVar;\n  nMem = pParse->nMem;\n  nCursor = pParse->nTab;\n  nArg = pParse->nMaxArg;\n  \n  /* Each cursor uses a memory cell.  The first cursor (cursor 0) can\n  ** use aMem[0] which is not otherwise used by the VDBE program.  Allocate\n  ** space at the end of aMem[] for cursors 1 and greater.\n  ** See also: allocateCursor().\n  */\n  nMem += nCursor;\n  if( nCursor==0 && nMem>0 ) nMem++;  /* Space for aMem[0] even if not used */\n\n  /* Figure out how much reusable memory is available at the end of the\n  ** opcode array.  This extra memory will be reallocated for other elements\n  ** of the prepared statement.\n  */\n  n = ROUND8(sizeof(Op)*p->nOp);              /* Bytes of opcode memory used */\n  x.pSpace = &((u8*)p->aOp)[n];               /* Unused opcode memory */\n  assert( EIGHT_BYTE_ALIGNMENT(x.pSpace) );\n  x.nFree = ROUNDDOWN8(pParse->szOpAlloc - n);  /* Bytes of unused memory */\n  assert( x.nFree>=0 );\n  assert( EIGHT_BYTE_ALIGNMENT(&x.pSpace[x.nFree]) );\n\n  resolveP2Values(p, &nArg);\n  p->usesStmtJournal = (u8)(pParse->isMultiWrite && pParse->mayAbort);\n  if( pParse->explain && nMem<10 ){\n    nMem = 10;\n  }\n  p->expired = 0;\n\n  /* Memory for registers, parameters, cursor, etc, is allocated in one or two\n  ** passes.  On the first pass, we try to reuse unused memory at the \n  ** end of the opcode array.  If we are unable to satisfy all memory\n  ** requirements by reusing the opcode array tail, then the second\n  ** pass will fill in the remainder using a fresh memory allocation.  \n  **\n  ** This two-pass approach that reuses as much memory as possible from\n  ** the leftover memory at the end of the opcode array.  This can significantly\n  ** reduce the amount of memory held by a prepared statement.\n  */\n  do {\n    x.nNeeded = 0;\n    p->aMem = allocSpace(&x, p->aMem, nMem*sizeof(Mem));\n    p->aVar = allocSpace(&x, p->aVar, nVar*sizeof(Mem));\n    p->apArg = allocSpace(&x, p->apArg, nArg*sizeof(Mem*));\n    p->apCsr = allocSpace(&x, p->apCsr, nCursor*sizeof(VdbeCursor*));\n#ifdef SQLITE_ENABLE_STMT_SCANSTATUS\n    p->anExec = allocSpace(&x, p->anExec, p->nOp*sizeof(i64));\n#endif\n    if( x.nNeeded==0 ) break;\n    x.pSpace = p->pFree = sqlite3DbMallocRawNN(db, x.nNeeded);\n    x.nFree = x.nNeeded;\n  }while( !db->mallocFailed );\n\n  p->pVList = pParse->pVList;\n  pParse->pVList =  0;\n  p->explain = pParse->explain;\n  if( db->mallocFailed ){\n    p->nVar = 0;\n    p->nCursor = 0;\n    p->nMem = 0;\n  }else{\n    p->nCursor = nCursor;\n    p->nVar = (ynVar)nVar;\n    initMemArray(p->aVar, nVar, db, MEM_Null);\n    p->nMem = nMem;\n    initMemArray(p->aMem, nMem, db, MEM_Undefined);\n    memset(p->apCsr, 0, nCursor*sizeof(VdbeCursor*));\n#ifdef SQLITE_ENABLE_STMT_SCANSTATUS\n    memset(p->anExec, 0, p->nOp*sizeof(i64));\n#endif\n  }\n  sqlite3VdbeRewind(p);\n}\n\n/*\n** Close a VDBE cursor and release all the resources that cursor \n** happens to hold.\n*/\nSQLITE_PRIVATE void sqlite3VdbeFreeCursor(Vdbe *p, VdbeCursor *pCx){\n  if( pCx==0 ){\n    return;\n  }\n  assert( pCx->pBtx==0 || pCx->eCurType==CURTYPE_BTREE );\n  switch( pCx->eCurType ){\n    case CURTYPE_SORTER: {\n      sqlite3VdbeSorterClose(p->db, pCx);\n      break;\n    }\n    case CURTYPE_BTREE: {\n      if( pCx->isEphemeral ){\n        if( pCx->pBtx ) sqlite3BtreeClose(pCx->pBtx);\n        /* The pCx->pCursor will be close automatically, if it exists, by\n        ** the call above. */\n      }else{\n        assert( pCx->uc.pCursor!=0 );\n        sqlite3BtreeCloseCursor(pCx->uc.pCursor);\n      }\n      break;\n    }\n#ifndef SQLITE_OMIT_VIRTUALTABLE\n    case CURTYPE_VTAB: {\n      sqlite3_vtab_cursor *pVCur = pCx->uc.pVCur;\n      const sqlite3_module *pModule = pVCur->pVtab->pModule;\n      assert( pVCur->pVtab->nRef>0 );\n      pVCur->pVtab->nRef--;\n      pModule->xClose(pVCur);\n      break;\n    }\n#endif\n  }\n}\n\n/*\n** Close all cursors in the current frame.\n*/\nstatic void closeCursorsInFrame(Vdbe *p){\n  if( p->apCsr ){\n    int i;\n    for(i=0; i<p->nCursor; i++){\n      VdbeCursor *pC = p->apCsr[i];\n      if( pC ){\n        sqlite3VdbeFreeCursor(p, pC);\n        p->apCsr[i] = 0;\n      }\n    }\n  }\n}\n\n/*\n** Copy the values stored in the VdbeFrame structure to its Vdbe. This\n** is used, for example, when a trigger sub-program is halted to restore\n** control to the main program.\n*/\nSQLITE_PRIVATE int sqlite3VdbeFrameRestore(VdbeFrame *pFrame){\n  Vdbe *v = pFrame->v;\n  closeCursorsInFrame(v);\n#ifdef SQLITE_ENABLE_STMT_SCANSTATUS\n  v->anExec = pFrame->anExec;\n#endif\n  v->aOp = pFrame->aOp;\n  v->nOp = pFrame->nOp;\n  v->aMem = pFrame->aMem;\n  v->nMem = pFrame->nMem;\n  v->apCsr = pFrame->apCsr;\n  v->nCursor = pFrame->nCursor;\n  v->db->lastRowid = pFrame->lastRowid;\n  v->nChange = pFrame->nChange;\n  v->db->nChange = pFrame->nDbChange;\n  sqlite3VdbeDeleteAuxData(v->db, &v->pAuxData, -1, 0);\n  v->pAuxData = pFrame->pAuxData;\n  pFrame->pAuxData = 0;\n  return pFrame->pc;\n}\n\n/*\n** Close all cursors.\n**\n** Also release any dynamic memory held by the VM in the Vdbe.aMem memory \n** cell array. This is necessary as the memory cell array may contain\n** pointers to VdbeFrame objects, which may in turn contain pointers to\n** open cursors.\n*/\nstatic void closeAllCursors(Vdbe *p){\n  if( p->pFrame ){\n    VdbeFrame *pFrame;\n    for(pFrame=p->pFrame; pFrame->pParent; pFrame=pFrame->pParent);\n    sqlite3VdbeFrameRestore(pFrame);\n    p->pFrame = 0;\n    p->nFrame = 0;\n  }\n  assert( p->nFrame==0 );\n  closeCursorsInFrame(p);\n  if( p->aMem ){\n    releaseMemArray(p->aMem, p->nMem);\n  }\n  while( p->pDelFrame ){\n    VdbeFrame *pDel = p->pDelFrame;\n    p->pDelFrame = pDel->pParent;\n    sqlite3VdbeFrameDelete(pDel);\n  }\n\n  /* Delete any auxdata allocations made by the VM */\n  if( p->pAuxData ) sqlite3VdbeDeleteAuxData(p->db, &p->pAuxData, -1, 0);\n  assert( p->pAuxData==0 );\n}\n\n/*\n** Set the number of result columns that will be returned by this SQL\n** statement. This is now set at compile time, rather than during\n** execution of the vdbe program so that sqlite3_column_count() can\n** be called on an SQL statement before sqlite3_step().\n*/\nSQLITE_PRIVATE void sqlite3VdbeSetNumCols(Vdbe *p, int nResColumn){\n  int n;\n  sqlite3 *db = p->db;\n\n  if( p->nResColumn ){\n    releaseMemArray(p->aColName, p->nResColumn*COLNAME_N);\n    sqlite3DbFree(db, p->aColName);\n  }\n  n = nResColumn*COLNAME_N;\n  p->nResColumn = (u16)nResColumn;\n  p->aColName = (Mem*)sqlite3DbMallocRawNN(db, sizeof(Mem)*n );\n  if( p->aColName==0 ) return;\n  initMemArray(p->aColName, n, db, MEM_Null);\n}\n\n/*\n** Set the name of the idx'th column to be returned by the SQL statement.\n** zName must be a pointer to a nul terminated string.\n**\n** This call must be made after a call to sqlite3VdbeSetNumCols().\n**\n** The final parameter, xDel, must be one of SQLITE_DYNAMIC, SQLITE_STATIC\n** or SQLITE_TRANSIENT. If it is SQLITE_DYNAMIC, then the buffer pointed\n** to by zName will be freed by sqlite3DbFree() when the vdbe is destroyed.\n*/\nSQLITE_PRIVATE int sqlite3VdbeSetColName(\n  Vdbe *p,                         /* Vdbe being configured */\n  int idx,                         /* Index of column zName applies to */\n  int var,                         /* One of the COLNAME_* constants */\n  const char *zName,               /* Pointer to buffer containing name */\n  void (*xDel)(void*)              /* Memory management strategy for zName */\n){\n  int rc;\n  Mem *pColName;\n  assert( idx<p->nResColumn );\n  assert( var<COLNAME_N );\n  if( p->db->mallocFailed ){\n    assert( !zName || xDel!=SQLITE_DYNAMIC );\n    return SQLITE_NOMEM_BKPT;\n  }\n  assert( p->aColName!=0 );\n  pColName = &(p->aColName[idx+var*p->nResColumn]);\n  rc = sqlite3VdbeMemSetStr(pColName, zName, -1, SQLITE_UTF8, xDel);\n  assert( rc!=0 || !zName || (pColName->flags&MEM_Term)!=0 );\n  return rc;\n}\n\n/*\n** A read or write transaction may or may not be active on database handle\n** db. If a transaction is active, commit it. If there is a\n** write-transaction spanning more than one database file, this routine\n** takes care of the master journal trickery.\n*/\nstatic int vdbeCommit(sqlite3 *db, Vdbe *p){\n  int i;\n  int nTrans = 0;  /* Number of databases with an active write-transaction\n                   ** that are candidates for a two-phase commit using a\n                   ** master-journal */\n  int rc = SQLITE_OK;\n  int needXcommit = 0;\n\n#ifdef SQLITE_OMIT_VIRTUALTABLE\n  /* With this option, sqlite3VtabSync() is defined to be simply \n  ** SQLITE_OK so p is not used. \n  */\n  UNUSED_PARAMETER(p);\n#endif\n\n  /* Before doing anything else, call the xSync() callback for any\n  ** virtual module tables written in this transaction. This has to\n  ** be done before determining whether a master journal file is \n  ** required, as an xSync() callback may add an attached database\n  ** to the transaction.\n  */\n  rc = sqlite3VtabSync(db, p);\n\n  /* This loop determines (a) if the commit hook should be invoked and\n  ** (b) how many database files have open write transactions, not \n  ** including the temp database. (b) is important because if more than \n  ** one database file has an open write transaction, a master journal\n  ** file is required for an atomic commit.\n  */ \n  for(i=0; rc==SQLITE_OK && i<db->nDb; i++){ \n    Btree *pBt = db->aDb[i].pBt;\n    if( sqlite3BtreeIsInTrans(pBt) ){\n      /* Whether or not a database might need a master journal depends upon\n      ** its journal mode (among other things).  This matrix determines which\n      ** journal modes use a master journal and which do not */\n      static const u8 aMJNeeded[] = {\n        /* DELETE   */  1,\n        /* PERSIST   */ 1,\n        /* OFF       */ 0,\n        /* TRUNCATE  */ 1,\n        /* MEMORY    */ 0,\n        /* WAL       */ 0\n      };\n      Pager *pPager;   /* Pager associated with pBt */\n      needXcommit = 1;\n      sqlite3BtreeEnter(pBt);\n      pPager = sqlite3BtreePager(pBt);\n      if( db->aDb[i].safety_level!=PAGER_SYNCHRONOUS_OFF\n       && aMJNeeded[sqlite3PagerGetJournalMode(pPager)]\n       && sqlite3PagerIsMemdb(pPager)==0\n      ){ \n        assert( i!=1 );\n        nTrans++;\n      }\n      rc = sqlite3PagerExclusiveLock(pPager);\n      sqlite3BtreeLeave(pBt);\n    }\n  }\n  if( rc!=SQLITE_OK ){\n    return rc;\n  }\n\n  /* If there are any write-transactions at all, invoke the commit hook */\n  if( needXcommit && db->xCommitCallback ){\n    rc = db->xCommitCallback(db->pCommitArg);\n    if( rc ){\n      return SQLITE_CONSTRAINT_COMMITHOOK;\n    }\n  }\n\n  /* The simple case - no more than one database file (not counting the\n  ** TEMP database) has a transaction active.   There is no need for the\n  ** master-journal.\n  **\n  ** If the return value of sqlite3BtreeGetFilename() is a zero length\n  ** string, it means the main database is :memory: or a temp file.  In \n  ** that case we do not support atomic multi-file commits, so use the \n  ** simple case then too.\n  */\n  if( 0==sqlite3Strlen30(sqlite3BtreeGetFilename(db->aDb[0].pBt))\n   || nTrans<=1\n  ){\n    for(i=0; rc==SQLITE_OK && i<db->nDb; i++){\n      Btree *pBt = db->aDb[i].pBt;\n      if( pBt ){\n        rc = sqlite3BtreeCommitPhaseOne(pBt, 0);\n      }\n    }\n\n    /* Do the commit only if all databases successfully complete phase 1. \n    ** If one of the BtreeCommitPhaseOne() calls fails, this indicates an\n    ** IO error while deleting or truncating a journal file. It is unlikely,\n    ** but could happen. In this case abandon processing and return the error.\n    */\n    for(i=0; rc==SQLITE_OK && i<db->nDb; i++){\n      Btree *pBt = db->aDb[i].pBt;\n      if( pBt ){\n        rc = sqlite3BtreeCommitPhaseTwo(pBt, 0);\n      }\n    }\n    if( rc==SQLITE_OK ){\n      sqlite3VtabCommit(db);\n    }\n  }\n\n  /* The complex case - There is a multi-file write-transaction active.\n  ** This requires a master journal file to ensure the transaction is\n  ** committed atomically.\n  */\n#ifndef SQLITE_OMIT_DISKIO\n  else{\n    sqlite3_vfs *pVfs = db->pVfs;\n    char *zMaster = 0;   /* File-name for the master journal */\n    char const *zMainFile = sqlite3BtreeGetFilename(db->aDb[0].pBt);\n    sqlite3_file *pMaster = 0;\n    i64 offset = 0;\n    int res;\n    int retryCount = 0;\n    int nMainFile;\n\n    /* Select a master journal file name */\n    nMainFile = sqlite3Strlen30(zMainFile);\n    zMaster = sqlite3MPrintf(db, \"%s-mjXXXXXX9XXz\", zMainFile);\n    if( zMaster==0 ) return SQLITE_NOMEM_BKPT;\n    do {\n      u32 iRandom;\n      if( retryCount ){\n        if( retryCount>100 ){\n          sqlite3_log(SQLITE_FULL, \"MJ delete: %s\", zMaster);\n          sqlite3OsDelete(pVfs, zMaster, 0);\n          break;\n        }else if( retryCount==1 ){\n          sqlite3_log(SQLITE_FULL, \"MJ collide: %s\", zMaster);\n        }\n      }\n      retryCount++;\n      sqlite3_randomness(sizeof(iRandom), &iRandom);\n      sqlite3_snprintf(13, &zMaster[nMainFile], \"-mj%06X9%02X\",\n                               (iRandom>>8)&0xffffff, iRandom&0xff);\n      /* The antipenultimate character of the master journal name must\n      ** be \"9\" to avoid name collisions when using 8+3 filenames. */\n      assert( zMaster[sqlite3Strlen30(zMaster)-3]=='9' );\n      sqlite3FileSuffix3(zMainFile, zMaster);\n      rc = sqlite3OsAccess(pVfs, zMaster, SQLITE_ACCESS_EXISTS, &res);\n    }while( rc==SQLITE_OK && res );\n    if( rc==SQLITE_OK ){\n      /* Open the master journal. */\n      rc = sqlite3OsOpenMalloc(pVfs, zMaster, &pMaster, \n          SQLITE_OPEN_READWRITE|SQLITE_OPEN_CREATE|\n          SQLITE_OPEN_EXCLUSIVE|SQLITE_OPEN_MASTER_JOURNAL, 0\n      );\n    }\n    if( rc!=SQLITE_OK ){\n      sqlite3DbFree(db, zMaster);\n      return rc;\n    }\n \n    /* Write the name of each database file in the transaction into the new\n    ** master journal file. If an error occurs at this point close\n    ** and delete the master journal file. All the individual journal files\n    ** still have 'null' as the master journal pointer, so they will roll\n    ** back independently if a failure occurs.\n    */\n    for(i=0; i<db->nDb; i++){\n      Btree *pBt = db->aDb[i].pBt;\n      if( sqlite3BtreeIsInTrans(pBt) ){\n        char const *zFile = sqlite3BtreeGetJournalname(pBt);\n        if( zFile==0 ){\n          continue;  /* Ignore TEMP and :memory: databases */\n        }\n        assert( zFile[0]!=0 );\n        rc = sqlite3OsWrite(pMaster, zFile, sqlite3Strlen30(zFile)+1, offset);\n        offset += sqlite3Strlen30(zFile)+1;\n        if( rc!=SQLITE_OK ){\n          sqlite3OsCloseFree(pMaster);\n          sqlite3OsDelete(pVfs, zMaster, 0);\n          sqlite3DbFree(db, zMaster);\n          return rc;\n        }\n      }\n    }\n\n    /* Sync the master journal file. If the IOCAP_SEQUENTIAL device\n    ** flag is set this is not required.\n    */\n    if( 0==(sqlite3OsDeviceCharacteristics(pMaster)&SQLITE_IOCAP_SEQUENTIAL)\n     && SQLITE_OK!=(rc = sqlite3OsSync(pMaster, SQLITE_SYNC_NORMAL))\n    ){\n      sqlite3OsCloseFree(pMaster);\n      sqlite3OsDelete(pVfs, zMaster, 0);\n      sqlite3DbFree(db, zMaster);\n      return rc;\n    }\n\n    /* Sync all the db files involved in the transaction. The same call\n    ** sets the master journal pointer in each individual journal. If\n    ** an error occurs here, do not delete the master journal file.\n    **\n    ** If the error occurs during the first call to\n    ** sqlite3BtreeCommitPhaseOne(), then there is a chance that the\n    ** master journal file will be orphaned. But we cannot delete it,\n    ** in case the master journal file name was written into the journal\n    ** file before the failure occurred.\n    */\n    for(i=0; rc==SQLITE_OK && i<db->nDb; i++){ \n      Btree *pBt = db->aDb[i].pBt;\n      if( pBt ){\n        rc = sqlite3BtreeCommitPhaseOne(pBt, zMaster);\n      }\n    }\n    sqlite3OsCloseFree(pMaster);\n    assert( rc!=SQLITE_BUSY );\n    if( rc!=SQLITE_OK ){\n      sqlite3DbFree(db, zMaster);\n      return rc;\n    }\n\n    /* Delete the master journal file. This commits the transaction. After\n    ** doing this the directory is synced again before any individual\n    ** transaction files are deleted.\n    */\n    rc = sqlite3OsDelete(pVfs, zMaster, 1);\n    sqlite3DbFree(db, zMaster);\n    zMaster = 0;\n    if( rc ){\n      return rc;\n    }\n\n    /* All files and directories have already been synced, so the following\n    ** calls to sqlite3BtreeCommitPhaseTwo() are only closing files and\n    ** deleting or truncating journals. If something goes wrong while\n    ** this is happening we don't really care. The integrity of the\n    ** transaction is already guaranteed, but some stray 'cold' journals\n    ** may be lying around. Returning an error code won't help matters.\n    */\n    disable_simulated_io_errors();\n    sqlite3BeginBenignMalloc();\n    for(i=0; i<db->nDb; i++){ \n      Btree *pBt = db->aDb[i].pBt;\n      if( pBt ){\n        sqlite3BtreeCommitPhaseTwo(pBt, 1);\n      }\n    }\n    sqlite3EndBenignMalloc();\n    enable_simulated_io_errors();\n\n    sqlite3VtabCommit(db);\n  }\n#endif\n\n  return rc;\n}\n\n/* \n** This routine checks that the sqlite3.nVdbeActive count variable\n** matches the number of vdbe's in the list sqlite3.pVdbe that are\n** currently active. An assertion fails if the two counts do not match.\n** This is an internal self-check only - it is not an essential processing\n** step.\n**\n** This is a no-op if NDEBUG is defined.\n*/\n#ifndef NDEBUG\nstatic void checkActiveVdbeCnt(sqlite3 *db){\n  Vdbe *p;\n  int cnt = 0;\n  int nWrite = 0;\n  int nRead = 0;\n  p = db->pVdbe;\n  while( p ){\n    if( sqlite3_stmt_busy((sqlite3_stmt*)p) ){\n      cnt++;\n      if( p->readOnly==0 ) nWrite++;\n      if( p->bIsReader ) nRead++;\n    }\n    p = p->pNext;\n  }\n  assert( cnt==db->nVdbeActive );\n  assert( nWrite==db->nVdbeWrite );\n  assert( nRead==db->nVdbeRead );\n}\n#else\n#define checkActiveVdbeCnt(x)\n#endif\n\n/*\n** If the Vdbe passed as the first argument opened a statement-transaction,\n** close it now. Argument eOp must be either SAVEPOINT_ROLLBACK or\n** SAVEPOINT_RELEASE. If it is SAVEPOINT_ROLLBACK, then the statement\n** transaction is rolled back. If eOp is SAVEPOINT_RELEASE, then the \n** statement transaction is committed.\n**\n** If an IO error occurs, an SQLITE_IOERR_XXX error code is returned. \n** Otherwise SQLITE_OK.\n*/\nstatic SQLITE_NOINLINE int vdbeCloseStatement(Vdbe *p, int eOp){\n  sqlite3 *const db = p->db;\n  int rc = SQLITE_OK;\n  int i;\n  const int iSavepoint = p->iStatement-1;\n\n  assert( eOp==SAVEPOINT_ROLLBACK || eOp==SAVEPOINT_RELEASE);\n  assert( db->nStatement>0 );\n  assert( p->iStatement==(db->nStatement+db->nSavepoint) );\n\n  for(i=0; i<db->nDb; i++){ \n    int rc2 = SQLITE_OK;\n    Btree *pBt = db->aDb[i].pBt;\n    if( pBt ){\n      if( eOp==SAVEPOINT_ROLLBACK ){\n        rc2 = sqlite3BtreeSavepoint(pBt, SAVEPOINT_ROLLBACK, iSavepoint);\n      }\n      if( rc2==SQLITE_OK ){\n        rc2 = sqlite3BtreeSavepoint(pBt, SAVEPOINT_RELEASE, iSavepoint);\n      }\n      if( rc==SQLITE_OK ){\n        rc = rc2;\n      }\n    }\n  }\n  db->nStatement--;\n  p->iStatement = 0;\n\n  if( rc==SQLITE_OK ){\n    if( eOp==SAVEPOINT_ROLLBACK ){\n      rc = sqlite3VtabSavepoint(db, SAVEPOINT_ROLLBACK, iSavepoint);\n    }\n    if( rc==SQLITE_OK ){\n      rc = sqlite3VtabSavepoint(db, SAVEPOINT_RELEASE, iSavepoint);\n    }\n  }\n\n  /* If the statement transaction is being rolled back, also restore the \n  ** database handles deferred constraint counter to the value it had when \n  ** the statement transaction was opened.  */\n  if( eOp==SAVEPOINT_ROLLBACK ){\n    db->nDeferredCons = p->nStmtDefCons;\n    db->nDeferredImmCons = p->nStmtDefImmCons;\n  }\n  return rc;\n}\nSQLITE_PRIVATE int sqlite3VdbeCloseStatement(Vdbe *p, int eOp){\n  if( p->db->nStatement && p->iStatement ){\n    return vdbeCloseStatement(p, eOp);\n  }\n  return SQLITE_OK;\n}\n\n\n/*\n** This function is called when a transaction opened by the database \n** handle associated with the VM passed as an argument is about to be \n** committed. If there are outstanding deferred foreign key constraint\n** violations, return SQLITE_ERROR. Otherwise, SQLITE_OK.\n**\n** If there are outstanding FK violations and this function returns \n** SQLITE_ERROR, set the result of the VM to SQLITE_CONSTRAINT_FOREIGNKEY\n** and write an error message to it. Then return SQLITE_ERROR.\n*/\n#ifndef SQLITE_OMIT_FOREIGN_KEY\nSQLITE_PRIVATE int sqlite3VdbeCheckFk(Vdbe *p, int deferred){\n  sqlite3 *db = p->db;\n  if( (deferred && (db->nDeferredCons+db->nDeferredImmCons)>0) \n   || (!deferred && p->nFkConstraint>0) \n  ){\n    p->rc = SQLITE_CONSTRAINT_FOREIGNKEY;\n    p->errorAction = OE_Abort;\n    sqlite3VdbeError(p, \"FOREIGN KEY constraint failed\");\n    return SQLITE_ERROR;\n  }\n  return SQLITE_OK;\n}\n#endif\n\n/*\n** This routine is called the when a VDBE tries to halt.  If the VDBE\n** has made changes and is in autocommit mode, then commit those\n** changes.  If a rollback is needed, then do the rollback.\n**\n** This routine is the only way to move the state of a VM from\n** SQLITE_MAGIC_RUN to SQLITE_MAGIC_HALT.  It is harmless to\n** call this on a VM that is in the SQLITE_MAGIC_HALT state.\n**\n** Return an error code.  If the commit could not complete because of\n** lock contention, return SQLITE_BUSY.  If SQLITE_BUSY is returned, it\n** means the close did not happen and needs to be repeated.\n*/\nSQLITE_PRIVATE int sqlite3VdbeHalt(Vdbe *p){\n  int rc;                         /* Used to store transient return codes */\n  sqlite3 *db = p->db;\n\n  /* This function contains the logic that determines if a statement or\n  ** transaction will be committed or rolled back as a result of the\n  ** execution of this virtual machine. \n  **\n  ** If any of the following errors occur:\n  **\n  **     SQLITE_NOMEM\n  **     SQLITE_IOERR\n  **     SQLITE_FULL\n  **     SQLITE_INTERRUPT\n  **\n  ** Then the internal cache might have been left in an inconsistent\n  ** state.  We need to rollback the statement transaction, if there is\n  ** one, or the complete transaction if there is no statement transaction.\n  */\n\n  if( p->magic!=VDBE_MAGIC_RUN ){\n    return SQLITE_OK;\n  }\n  if( db->mallocFailed ){\n    p->rc = SQLITE_NOMEM_BKPT;\n  }\n  closeAllCursors(p);\n  checkActiveVdbeCnt(db);\n\n  /* No commit or rollback needed if the program never started or if the\n  ** SQL statement does not read or write a database file.  */\n  if( p->pc>=0 && p->bIsReader ){\n    int mrc;   /* Primary error code from p->rc */\n    int eStatementOp = 0;\n    int isSpecialError;            /* Set to true if a 'special' error */\n\n    /* Lock all btrees used by the statement */\n    sqlite3VdbeEnter(p);\n\n    /* Check for one of the special errors */\n    mrc = p->rc & 0xff;\n    isSpecialError = mrc==SQLITE_NOMEM || mrc==SQLITE_IOERR\n                     || mrc==SQLITE_INTERRUPT || mrc==SQLITE_FULL;\n    if( isSpecialError ){\n      /* If the query was read-only and the error code is SQLITE_INTERRUPT, \n      ** no rollback is necessary. Otherwise, at least a savepoint \n      ** transaction must be rolled back to restore the database to a \n      ** consistent state.\n      **\n      ** Even if the statement is read-only, it is important to perform\n      ** a statement or transaction rollback operation. If the error \n      ** occurred while writing to the journal, sub-journal or database\n      ** file as part of an effort to free up cache space (see function\n      ** pagerStress() in pager.c), the rollback is required to restore \n      ** the pager to a consistent state.\n      */\n      if( !p->readOnly || mrc!=SQLITE_INTERRUPT ){\n        if( (mrc==SQLITE_NOMEM || mrc==SQLITE_FULL) && p->usesStmtJournal ){\n          eStatementOp = SAVEPOINT_ROLLBACK;\n        }else{\n          /* We are forced to roll back the active transaction. Before doing\n          ** so, abort any other statements this handle currently has active.\n          */\n          sqlite3RollbackAll(db, SQLITE_ABORT_ROLLBACK);\n          sqlite3CloseSavepoints(db);\n          db->autoCommit = 1;\n          p->nChange = 0;\n        }\n      }\n    }\n\n    /* Check for immediate foreign key violations. */\n    if( p->rc==SQLITE_OK ){\n      sqlite3VdbeCheckFk(p, 0);\n    }\n  \n    /* If the auto-commit flag is set and this is the only active writer \n    ** VM, then we do either a commit or rollback of the current transaction. \n    **\n    ** Note: This block also runs if one of the special errors handled \n    ** above has occurred. \n    */\n    if( !sqlite3VtabInSync(db) \n     && db->autoCommit \n     && db->nVdbeWrite==(p->readOnly==0) \n    ){\n      if( p->rc==SQLITE_OK || (p->errorAction==OE_Fail && !isSpecialError) ){\n        rc = sqlite3VdbeCheckFk(p, 1);\n        if( rc!=SQLITE_OK ){\n          if( NEVER(p->readOnly) ){\n            sqlite3VdbeLeave(p);\n            return SQLITE_ERROR;\n          }\n          rc = SQLITE_CONSTRAINT_FOREIGNKEY;\n        }else{ \n          /* The auto-commit flag is true, the vdbe program was successful \n          ** or hit an 'OR FAIL' constraint and there are no deferred foreign\n          ** key constraints to hold up the transaction. This means a commit \n          ** is required. */\n          rc = vdbeCommit(db, p);\n        }\n        if( rc==SQLITE_BUSY && p->readOnly ){\n          sqlite3VdbeLeave(p);\n          return SQLITE_BUSY;\n        }else if( rc!=SQLITE_OK ){\n          p->rc = rc;\n          sqlite3RollbackAll(db, SQLITE_OK);\n          p->nChange = 0;\n        }else{\n          db->nDeferredCons = 0;\n          db->nDeferredImmCons = 0;\n          db->flags &= ~SQLITE_DeferFKs;\n          sqlite3CommitInternalChanges(db);\n        }\n      }else{\n        sqlite3RollbackAll(db, SQLITE_OK);\n        p->nChange = 0;\n      }\n      db->nStatement = 0;\n    }else if( eStatementOp==0 ){\n      if( p->rc==SQLITE_OK || p->errorAction==OE_Fail ){\n        eStatementOp = SAVEPOINT_RELEASE;\n      }else if( p->errorAction==OE_Abort ){\n        eStatementOp = SAVEPOINT_ROLLBACK;\n      }else{\n        sqlite3RollbackAll(db, SQLITE_ABORT_ROLLBACK);\n        sqlite3CloseSavepoints(db);\n        db->autoCommit = 1;\n        p->nChange = 0;\n      }\n    }\n  \n    /* If eStatementOp is non-zero, then a statement transaction needs to\n    ** be committed or rolled back. Call sqlite3VdbeCloseStatement() to\n    ** do so. If this operation returns an error, and the current statement\n    ** error code is SQLITE_OK or SQLITE_CONSTRAINT, then promote the\n    ** current statement error code.\n    */\n    if( eStatementOp ){\n      rc = sqlite3VdbeCloseStatement(p, eStatementOp);\n      if( rc ){\n        if( p->rc==SQLITE_OK || (p->rc&0xff)==SQLITE_CONSTRAINT ){\n          p->rc = rc;\n          sqlite3DbFree(db, p->zErrMsg);\n          p->zErrMsg = 0;\n        }\n        sqlite3RollbackAll(db, SQLITE_ABORT_ROLLBACK);\n        sqlite3CloseSavepoints(db);\n        db->autoCommit = 1;\n        p->nChange = 0;\n      }\n    }\n  \n    /* If this was an INSERT, UPDATE or DELETE and no statement transaction\n    ** has been rolled back, update the database connection change-counter. \n    */\n    if( p->changeCntOn ){\n      if( eStatementOp!=SAVEPOINT_ROLLBACK ){\n        sqlite3VdbeSetChanges(db, p->nChange);\n      }else{\n        sqlite3VdbeSetChanges(db, 0);\n      }\n      p->nChange = 0;\n    }\n\n    /* Release the locks */\n    sqlite3VdbeLeave(p);\n  }\n\n  /* We have successfully halted and closed the VM.  Record this fact. */\n  if( p->pc>=0 ){\n    db->nVdbeActive--;\n    if( !p->readOnly ) db->nVdbeWrite--;\n    if( p->bIsReader ) db->nVdbeRead--;\n    assert( db->nVdbeActive>=db->nVdbeRead );\n    assert( db->nVdbeRead>=db->nVdbeWrite );\n    assert( db->nVdbeWrite>=0 );\n  }\n  p->magic = VDBE_MAGIC_HALT;\n  checkActiveVdbeCnt(db);\n  if( db->mallocFailed ){\n    p->rc = SQLITE_NOMEM_BKPT;\n  }\n\n  /* If the auto-commit flag is set to true, then any locks that were held\n  ** by connection db have now been released. Call sqlite3ConnectionUnlocked() \n  ** to invoke any required unlock-notify callbacks.\n  */\n  if( db->autoCommit ){\n    sqlite3ConnectionUnlocked(db);\n  }\n\n  assert( db->nVdbeActive>0 || db->autoCommit==0 || db->nStatement==0 );\n  return (p->rc==SQLITE_BUSY ? SQLITE_BUSY : SQLITE_OK);\n}\n\n\n/*\n** Each VDBE holds the result of the most recent sqlite3_step() call\n** in p->rc.  This routine sets that result back to SQLITE_OK.\n*/\nSQLITE_PRIVATE void sqlite3VdbeResetStepResult(Vdbe *p){\n  p->rc = SQLITE_OK;\n}\n\n/*\n** Copy the error code and error message belonging to the VDBE passed\n** as the first argument to its database handle (so that they will be \n** returned by calls to sqlite3_errcode() and sqlite3_errmsg()).\n**\n** This function does not clear the VDBE error code or message, just\n** copies them to the database handle.\n*/\nSQLITE_PRIVATE int sqlite3VdbeTransferError(Vdbe *p){\n  sqlite3 *db = p->db;\n  int rc = p->rc;\n  if( p->zErrMsg ){\n    db->bBenignMalloc++;\n    sqlite3BeginBenignMalloc();\n    if( db->pErr==0 ) db->pErr = sqlite3ValueNew(db);\n    sqlite3ValueSetStr(db->pErr, -1, p->zErrMsg, SQLITE_UTF8, SQLITE_TRANSIENT);\n    sqlite3EndBenignMalloc();\n    db->bBenignMalloc--;\n  }else if( db->pErr ){\n    sqlite3ValueSetNull(db->pErr);\n  }\n  db->errCode = rc;\n  return rc;\n}\n\n#ifdef SQLITE_ENABLE_SQLLOG\n/*\n** If an SQLITE_CONFIG_SQLLOG hook is registered and the VM has been run, \n** invoke it.\n*/\nstatic void vdbeInvokeSqllog(Vdbe *v){\n  if( sqlite3GlobalConfig.xSqllog && v->rc==SQLITE_OK && v->zSql && v->pc>=0 ){\n    char *zExpanded = sqlite3VdbeExpandSql(v, v->zSql);\n    assert( v->db->init.busy==0 );\n    if( zExpanded ){\n      sqlite3GlobalConfig.xSqllog(\n          sqlite3GlobalConfig.pSqllogArg, v->db, zExpanded, 1\n      );\n      sqlite3DbFree(v->db, zExpanded);\n    }\n  }\n}\n#else\n# define vdbeInvokeSqllog(x)\n#endif\n\n/*\n** Clean up a VDBE after execution but do not delete the VDBE just yet.\n** Write any error messages into *pzErrMsg.  Return the result code.\n**\n** After this routine is run, the VDBE should be ready to be executed\n** again.\n**\n** To look at it another way, this routine resets the state of the\n** virtual machine from VDBE_MAGIC_RUN or VDBE_MAGIC_HALT back to\n** VDBE_MAGIC_INIT.\n*/\nSQLITE_PRIVATE int sqlite3VdbeReset(Vdbe *p){\n#if defined(SQLITE_DEBUG) || defined(VDBE_PROFILE)\n  int i;\n#endif\n\n  sqlite3 *db;\n  db = p->db;\n\n  /* If the VM did not run to completion or if it encountered an\n  ** error, then it might not have been halted properly.  So halt\n  ** it now.\n  */\n  sqlite3VdbeHalt(p);\n\n  /* If the VDBE has be run even partially, then transfer the error code\n  ** and error message from the VDBE into the main database structure.  But\n  ** if the VDBE has just been set to run but has not actually executed any\n  ** instructions yet, leave the main database error information unchanged.\n  */\n  if( p->pc>=0 ){\n    vdbeInvokeSqllog(p);\n    sqlite3VdbeTransferError(p);\n    if( p->runOnlyOnce ) p->expired = 1;\n  }else if( p->rc && p->expired ){\n    /* The expired flag was set on the VDBE before the first call\n    ** to sqlite3_step(). For consistency (since sqlite3_step() was\n    ** called), set the database error in this case as well.\n    */\n    sqlite3ErrorWithMsg(db, p->rc, p->zErrMsg ? \"%s\" : 0, p->zErrMsg);\n  }\n\n  /* Reset register contents and reclaim error message memory.\n  */\n#ifdef SQLITE_DEBUG\n  /* Execute assert() statements to ensure that the Vdbe.apCsr[] and \n  ** Vdbe.aMem[] arrays have already been cleaned up.  */\n  if( p->apCsr ) for(i=0; i<p->nCursor; i++) assert( p->apCsr[i]==0 );\n  if( p->aMem ){\n    for(i=0; i<p->nMem; i++) assert( p->aMem[i].flags==MEM_Undefined );\n  }\n#endif\n  sqlite3DbFree(db, p->zErrMsg);\n  p->zErrMsg = 0;\n  p->pResultSet = 0;\n\n  /* Save profiling information from this VDBE run.\n  */\n#ifdef VDBE_PROFILE\n  {\n    FILE *out = fopen(\"vdbe_profile.out\", \"a\");\n    if( out ){\n      fprintf(out, \"---- \");\n      for(i=0; i<p->nOp; i++){\n        fprintf(out, \"%02x\", p->aOp[i].opcode);\n      }\n      fprintf(out, \"\\n\");\n      if( p->zSql ){\n        char c, pc = 0;\n        fprintf(out, \"-- \");\n        for(i=0; (c = p->zSql[i])!=0; i++){\n          if( pc=='\\n' ) fprintf(out, \"-- \");\n          putc(c, out);\n          pc = c;\n        }\n        if( pc!='\\n' ) fprintf(out, \"\\n\");\n      }\n      for(i=0; i<p->nOp; i++){\n        char zHdr[100];\n        sqlite3_snprintf(sizeof(zHdr), zHdr, \"%6u %12llu %8llu \",\n           p->aOp[i].cnt,\n           p->aOp[i].cycles,\n           p->aOp[i].cnt>0 ? p->aOp[i].cycles/p->aOp[i].cnt : 0\n        );\n        fprintf(out, \"%s\", zHdr);\n        sqlite3VdbePrintOp(out, i, &p->aOp[i]);\n      }\n      fclose(out);\n    }\n  }\n#endif\n  p->magic = VDBE_MAGIC_RESET;\n  return p->rc & db->errMask;\n}\n \n/*\n** Clean up and delete a VDBE after execution.  Return an integer which is\n** the result code.  Write any error message text into *pzErrMsg.\n*/\nSQLITE_PRIVATE int sqlite3VdbeFinalize(Vdbe *p){\n  int rc = SQLITE_OK;\n  if( p->magic==VDBE_MAGIC_RUN || p->magic==VDBE_MAGIC_HALT ){\n    rc = sqlite3VdbeReset(p);\n    assert( (rc & p->db->errMask)==rc );\n  }\n  sqlite3VdbeDelete(p);\n  return rc;\n}\n\n/*\n** If parameter iOp is less than zero, then invoke the destructor for\n** all auxiliary data pointers currently cached by the VM passed as\n** the first argument.\n**\n** Or, if iOp is greater than or equal to zero, then the destructor is\n** only invoked for those auxiliary data pointers created by the user \n** function invoked by the OP_Function opcode at instruction iOp of \n** VM pVdbe, and only then if:\n**\n**    * the associated function parameter is the 32nd or later (counting\n**      from left to right), or\n**\n**    * the corresponding bit in argument mask is clear (where the first\n**      function parameter corresponds to bit 0 etc.).\n*/\nSQLITE_PRIVATE void sqlite3VdbeDeleteAuxData(sqlite3 *db, AuxData **pp, int iOp, int mask){\n  while( *pp ){\n    AuxData *pAux = *pp;\n    if( (iOp<0)\n     || (pAux->iAuxOp==iOp\n          && pAux->iAuxArg>=0\n          && (pAux->iAuxArg>31 || !(mask & MASKBIT32(pAux->iAuxArg))))\n    ){\n      testcase( pAux->iAuxArg==31 );\n      if( pAux->xDeleteAux ){\n        pAux->xDeleteAux(pAux->pAux);\n      }\n      *pp = pAux->pNextAux;\n      sqlite3DbFree(db, pAux);\n    }else{\n      pp= &pAux->pNextAux;\n    }\n  }\n}\n\n/*\n** Free all memory associated with the Vdbe passed as the second argument,\n** except for object itself, which is preserved.\n**\n** The difference between this function and sqlite3VdbeDelete() is that\n** VdbeDelete() also unlinks the Vdbe from the list of VMs associated with\n** the database connection and frees the object itself.\n*/\nSQLITE_PRIVATE void sqlite3VdbeClearObject(sqlite3 *db, Vdbe *p){\n  SubProgram *pSub, *pNext;\n  assert( p->db==0 || p->db==db );\n  releaseMemArray(p->aColName, p->nResColumn*COLNAME_N);\n  for(pSub=p->pProgram; pSub; pSub=pNext){\n    pNext = pSub->pNext;\n    vdbeFreeOpArray(db, pSub->aOp, pSub->nOp);\n    sqlite3DbFree(db, pSub);\n  }\n  if( p->magic!=VDBE_MAGIC_INIT ){\n    releaseMemArray(p->aVar, p->nVar);\n    sqlite3DbFree(db, p->pVList);\n    sqlite3DbFree(db, p->pFree);\n  }\n  vdbeFreeOpArray(db, p->aOp, p->nOp);\n  sqlite3DbFree(db, p->aColName);\n  sqlite3DbFree(db, p->zSql);\n#ifdef SQLITE_ENABLE_STMT_SCANSTATUS\n  {\n    int i;\n    for(i=0; i<p->nScan; i++){\n      sqlite3DbFree(db, p->aScan[i].zName);\n    }\n    sqlite3DbFree(db, p->aScan);\n  }\n#endif\n}\n\n/*\n** Delete an entire VDBE.\n*/\nSQLITE_PRIVATE void sqlite3VdbeDelete(Vdbe *p){\n  sqlite3 *db;\n\n  assert( p!=0 );\n  db = p->db;\n  assert( sqlite3_mutex_held(db->mutex) );\n  sqlite3VdbeClearObject(db, p);\n  if( p->pPrev ){\n    p->pPrev->pNext = p->pNext;\n  }else{\n    assert( db->pVdbe==p );\n    db->pVdbe = p->pNext;\n  }\n  if( p->pNext ){\n    p->pNext->pPrev = p->pPrev;\n  }\n  p->magic = VDBE_MAGIC_DEAD;\n  p->db = 0;\n  sqlite3DbFreeNN(db, p);\n}\n\n/*\n** The cursor \"p\" has a pending seek operation that has not yet been\n** carried out.  Seek the cursor now.  If an error occurs, return\n** the appropriate error code.\n*/\nstatic int SQLITE_NOINLINE handleDeferredMoveto(VdbeCursor *p){\n  int res, rc;\n#ifdef SQLITE_TEST\n  extern int sqlite3_search_count;\n#endif\n  assert( p->deferredMoveto );\n  assert( p->isTable );\n  assert( p->eCurType==CURTYPE_BTREE );\n  rc = sqlite3BtreeMovetoUnpacked(p->uc.pCursor, 0, p->movetoTarget, 0, &res);\n  if( rc ) return rc;\n  if( res!=0 ) return SQLITE_CORRUPT_BKPT;\n#ifdef SQLITE_TEST\n  sqlite3_search_count++;\n#endif\n  p->deferredMoveto = 0;\n  p->cacheStatus = CACHE_STALE;\n  return SQLITE_OK;\n}\n\n/*\n** Something has moved cursor \"p\" out of place.  Maybe the row it was\n** pointed to was deleted out from under it.  Or maybe the btree was\n** rebalanced.  Whatever the cause, try to restore \"p\" to the place it\n** is supposed to be pointing.  If the row was deleted out from under the\n** cursor, set the cursor to point to a NULL row.\n*/\nstatic int SQLITE_NOINLINE handleMovedCursor(VdbeCursor *p){\n  int isDifferentRow, rc;\n  assert( p->eCurType==CURTYPE_BTREE );\n  assert( p->uc.pCursor!=0 );\n  assert( sqlite3BtreeCursorHasMoved(p->uc.pCursor) );\n  rc = sqlite3BtreeCursorRestore(p->uc.pCursor, &isDifferentRow);\n  p->cacheStatus = CACHE_STALE;\n  if( isDifferentRow ) p->nullRow = 1;\n  return rc;\n}\n\n/*\n** Check to ensure that the cursor is valid.  Restore the cursor\n** if need be.  Return any I/O error from the restore operation.\n*/\nSQLITE_PRIVATE int sqlite3VdbeCursorRestore(VdbeCursor *p){\n  assert( p->eCurType==CURTYPE_BTREE );\n  if( sqlite3BtreeCursorHasMoved(p->uc.pCursor) ){\n    return handleMovedCursor(p);\n  }\n  return SQLITE_OK;\n}\n\n/*\n** Make sure the cursor p is ready to read or write the row to which it\n** was last positioned.  Return an error code if an OOM fault or I/O error\n** prevents us from positioning the cursor to its correct position.\n**\n** If a MoveTo operation is pending on the given cursor, then do that\n** MoveTo now.  If no move is pending, check to see if the row has been\n** deleted out from under the cursor and if it has, mark the row as\n** a NULL row.\n**\n** If the cursor is already pointing to the correct row and that row has\n** not been deleted out from under the cursor, then this routine is a no-op.\n*/\nSQLITE_PRIVATE int sqlite3VdbeCursorMoveto(VdbeCursor **pp, int *piCol){\n  VdbeCursor *p = *pp;\n  assert( p->eCurType==CURTYPE_BTREE || p->eCurType==CURTYPE_PSEUDO );\n  if( p->deferredMoveto ){\n    int iMap;\n    if( p->aAltMap && (iMap = p->aAltMap[1+*piCol])>0 ){\n      *pp = p->pAltCursor;\n      *piCol = iMap - 1;\n      return SQLITE_OK;\n    }\n    return handleDeferredMoveto(p);\n  }\n  if( sqlite3BtreeCursorHasMoved(p->uc.pCursor) ){\n    return handleMovedCursor(p);\n  }\n  return SQLITE_OK;\n}\n\n/*\n** The following functions:\n**\n** sqlite3VdbeSerialType()\n** sqlite3VdbeSerialTypeLen()\n** sqlite3VdbeSerialLen()\n** sqlite3VdbeSerialPut()\n** sqlite3VdbeSerialGet()\n**\n** encapsulate the code that serializes values for storage in SQLite\n** data and index records. Each serialized value consists of a\n** 'serial-type' and a blob of data. The serial type is an 8-byte unsigned\n** integer, stored as a varint.\n**\n** In an SQLite index record, the serial type is stored directly before\n** the blob of data that it corresponds to. In a table record, all serial\n** types are stored at the start of the record, and the blobs of data at\n** the end. Hence these functions allow the caller to handle the\n** serial-type and data blob separately.\n**\n** The following table describes the various storage classes for data:\n**\n**   serial type        bytes of data      type\n**   --------------     ---------------    ---------------\n**      0                     0            NULL\n**      1                     1            signed integer\n**      2                     2            signed integer\n**      3                     3            signed integer\n**      4                     4            signed integer\n**      5                     6            signed integer\n**      6                     8            signed integer\n**      7                     8            IEEE float\n**      8                     0            Integer constant 0\n**      9                     0            Integer constant 1\n**     10,11                               reserved for expansion\n**    N>=12 and even       (N-12)/2        BLOB\n**    N>=13 and odd        (N-13)/2        text\n**\n** The 8 and 9 types were added in 3.3.0, file format 4.  Prior versions\n** of SQLite will not understand those serial types.\n*/\n\n/*\n** Return the serial-type for the value stored in pMem.\n*/\nSQLITE_PRIVATE u32 sqlite3VdbeSerialType(Mem *pMem, int file_format, u32 *pLen){\n  int flags = pMem->flags;\n  u32 n;\n\n  assert( pLen!=0 );\n  if( flags&MEM_Null ){\n    *pLen = 0;\n    return 0;\n  }\n  if( flags&MEM_Int ){\n    /* Figure out whether to use 1, 2, 4, 6 or 8 bytes. */\n#   define MAX_6BYTE ((((i64)0x00008000)<<32)-1)\n    i64 i = pMem->u.i;\n    u64 u;\n    if( i<0 ){\n      u = ~i;\n    }else{\n      u = i;\n    }\n    if( u<=127 ){\n      if( (i&1)==i && file_format>=4 ){\n        *pLen = 0;\n        return 8+(u32)u;\n      }else{\n        *pLen = 1;\n        return 1;\n      }\n    }\n    if( u<=32767 ){ *pLen = 2; return 2; }\n    if( u<=8388607 ){ *pLen = 3; return 3; }\n    if( u<=2147483647 ){ *pLen = 4; return 4; }\n    if( u<=MAX_6BYTE ){ *pLen = 6; return 5; }\n    *pLen = 8;\n    return 6;\n  }\n  if( flags&MEM_Real ){\n    *pLen = 8;\n    return 7;\n  }\n  assert( pMem->db->mallocFailed || flags&(MEM_Str|MEM_Blob) );\n  assert( pMem->n>=0 );\n  n = (u32)pMem->n;\n  if( flags & MEM_Zero ){\n    n += pMem->u.nZero;\n  }\n  *pLen = n;\n  return ((n*2) + 12 + ((flags&MEM_Str)!=0));\n}\n\n/*\n** The sizes for serial types less than 128\n*/\nstatic const u8 sqlite3SmallTypeSizes[] = {\n        /*  0   1   2   3   4   5   6   7   8   9 */   \n/*   0 */   0,  1,  2,  3,  4,  6,  8,  8,  0,  0,\n/*  10 */   0,  0,  0,  0,  1,  1,  2,  2,  3,  3,\n/*  20 */   4,  4,  5,  5,  6,  6,  7,  7,  8,  8,\n/*  30 */   9,  9, 10, 10, 11, 11, 12, 12, 13, 13,\n/*  40 */  14, 14, 15, 15, 16, 16, 17, 17, 18, 18,\n/*  50 */  19, 19, 20, 20, 21, 21, 22, 22, 23, 23,\n/*  60 */  24, 24, 25, 25, 26, 26, 27, 27, 28, 28,\n/*  70 */  29, 29, 30, 30, 31, 31, 32, 32, 33, 33,\n/*  80 */  34, 34, 35, 35, 36, 36, 37, 37, 38, 38,\n/*  90 */  39, 39, 40, 40, 41, 41, 42, 42, 43, 43,\n/* 100 */  44, 44, 45, 45, 46, 46, 47, 47, 48, 48,\n/* 110 */  49, 49, 50, 50, 51, 51, 52, 52, 53, 53,\n/* 120 */  54, 54, 55, 55, 56, 56, 57, 57\n};\n\n/*\n** Return the length of the data corresponding to the supplied serial-type.\n*/\nSQLITE_PRIVATE u32 sqlite3VdbeSerialTypeLen(u32 serial_type){\n  if( serial_type>=128 ){\n    return (serial_type-12)/2;\n  }else{\n    assert( serial_type<12 \n            || sqlite3SmallTypeSizes[serial_type]==(serial_type - 12)/2 );\n    return sqlite3SmallTypeSizes[serial_type];\n  }\n}\nSQLITE_PRIVATE u8 sqlite3VdbeOneByteSerialTypeLen(u8 serial_type){\n  assert( serial_type<128 );\n  return sqlite3SmallTypeSizes[serial_type];  \n}\n\n/*\n** If we are on an architecture with mixed-endian floating \n** points (ex: ARM7) then swap the lower 4 bytes with the \n** upper 4 bytes.  Return the result.\n**\n** For most architectures, this is a no-op.\n**\n** (later):  It is reported to me that the mixed-endian problem\n** on ARM7 is an issue with GCC, not with the ARM7 chip.  It seems\n** that early versions of GCC stored the two words of a 64-bit\n** float in the wrong order.  And that error has been propagated\n** ever since.  The blame is not necessarily with GCC, though.\n** GCC might have just copying the problem from a prior compiler.\n** I am also told that newer versions of GCC that follow a different\n** ABI get the byte order right.\n**\n** Developers using SQLite on an ARM7 should compile and run their\n** application using -DSQLITE_DEBUG=1 at least once.  With DEBUG\n** enabled, some asserts below will ensure that the byte order of\n** floating point values is correct.\n**\n** (2007-08-30)  Frank van Vugt has studied this problem closely\n** and has send his findings to the SQLite developers.  Frank\n** writes that some Linux kernels offer floating point hardware\n** emulation that uses only 32-bit mantissas instead of a full \n** 48-bits as required by the IEEE standard.  (This is the\n** CONFIG_FPE_FASTFPE option.)  On such systems, floating point\n** byte swapping becomes very complicated.  To avoid problems,\n** the necessary byte swapping is carried out using a 64-bit integer\n** rather than a 64-bit float.  Frank assures us that the code here\n** works for him.  We, the developers, have no way to independently\n** verify this, but Frank seems to know what he is talking about\n** so we trust him.\n*/\n#ifdef SQLITE_MIXED_ENDIAN_64BIT_FLOAT\nstatic u64 floatSwap(u64 in){\n  union {\n    u64 r;\n    u32 i[2];\n  } u;\n  u32 t;\n\n  u.r = in;\n  t = u.i[0];\n  u.i[0] = u.i[1];\n  u.i[1] = t;\n  return u.r;\n}\n# define swapMixedEndianFloat(X)  X = floatSwap(X)\n#else\n# define swapMixedEndianFloat(X)\n#endif\n\n/*\n** Write the serialized data blob for the value stored in pMem into \n** buf. It is assumed that the caller has allocated sufficient space.\n** Return the number of bytes written.\n**\n** nBuf is the amount of space left in buf[].  The caller is responsible\n** for allocating enough space to buf[] to hold the entire field, exclusive\n** of the pMem->u.nZero bytes for a MEM_Zero value.\n**\n** Return the number of bytes actually written into buf[].  The number\n** of bytes in the zero-filled tail is included in the return value only\n** if those bytes were zeroed in buf[].\n*/ \nSQLITE_PRIVATE u32 sqlite3VdbeSerialPut(u8 *buf, Mem *pMem, u32 serial_type){\n  u32 len;\n\n  /* Integer and Real */\n  if( serial_type<=7 && serial_type>0 ){\n    u64 v;\n    u32 i;\n    if( serial_type==7 ){\n      assert( sizeof(v)==sizeof(pMem->u.r) );\n      memcpy(&v, &pMem->u.r, sizeof(v));\n      swapMixedEndianFloat(v);\n    }else{\n      v = pMem->u.i;\n    }\n    len = i = sqlite3SmallTypeSizes[serial_type];\n    assert( i>0 );\n    do{\n      buf[--i] = (u8)(v&0xFF);\n      v >>= 8;\n    }while( i );\n    return len;\n  }\n\n  /* String or blob */\n  if( serial_type>=12 ){\n    assert( pMem->n + ((pMem->flags & MEM_Zero)?pMem->u.nZero:0)\n             == (int)sqlite3VdbeSerialTypeLen(serial_type) );\n    len = pMem->n;\n    if( len>0 ) memcpy(buf, pMem->z, len);\n    return len;\n  }\n\n  /* NULL or constants 0 or 1 */\n  return 0;\n}\n\n/* Input \"x\" is a sequence of unsigned characters that represent a\n** big-endian integer.  Return the equivalent native integer\n*/\n#define ONE_BYTE_INT(x)    ((i8)(x)[0])\n#define TWO_BYTE_INT(x)    (256*(i8)((x)[0])|(x)[1])\n#define THREE_BYTE_INT(x)  (65536*(i8)((x)[0])|((x)[1]<<8)|(x)[2])\n#define FOUR_BYTE_UINT(x)  (((u32)(x)[0]<<24)|((x)[1]<<16)|((x)[2]<<8)|(x)[3])\n#define FOUR_BYTE_INT(x) (16777216*(i8)((x)[0])|((x)[1]<<16)|((x)[2]<<8)|(x)[3])\n\n/*\n** Deserialize the data blob pointed to by buf as serial type serial_type\n** and store the result in pMem.  Return the number of bytes read.\n**\n** This function is implemented as two separate routines for performance.\n** The few cases that require local variables are broken out into a separate\n** routine so that in most cases the overhead of moving the stack pointer\n** is avoided.\n*/ \nstatic u32 SQLITE_NOINLINE serialGet(\n  const unsigned char *buf,     /* Buffer to deserialize from */\n  u32 serial_type,              /* Serial type to deserialize */\n  Mem *pMem                     /* Memory cell to write value into */\n){\n  u64 x = FOUR_BYTE_UINT(buf);\n  u32 y = FOUR_BYTE_UINT(buf+4);\n  x = (x<<32) + y;\n  if( serial_type==6 ){\n    /* EVIDENCE-OF: R-29851-52272 Value is a big-endian 64-bit\n    ** twos-complement integer. */\n    pMem->u.i = *(i64*)&x;\n    pMem->flags = MEM_Int;\n    testcase( pMem->u.i<0 );\n  }else{\n    /* EVIDENCE-OF: R-57343-49114 Value is a big-endian IEEE 754-2008 64-bit\n    ** floating point number. */\n#if !defined(NDEBUG) && !defined(SQLITE_OMIT_FLOATING_POINT)\n    /* Verify that integers and floating point values use the same\n    ** byte order.  Or, that if SQLITE_MIXED_ENDIAN_64BIT_FLOAT is\n    ** defined that 64-bit floating point values really are mixed\n    ** endian.\n    */\n    static const u64 t1 = ((u64)0x3ff00000)<<32;\n    static const double r1 = 1.0;\n    u64 t2 = t1;\n    swapMixedEndianFloat(t2);\n    assert( sizeof(r1)==sizeof(t2) && memcmp(&r1, &t2, sizeof(r1))==0 );\n#endif\n    assert( sizeof(x)==8 && sizeof(pMem->u.r)==8 );\n    swapMixedEndianFloat(x);\n    memcpy(&pMem->u.r, &x, sizeof(x));\n    pMem->flags = sqlite3IsNaN(pMem->u.r) ? MEM_Null : MEM_Real;\n  }\n  return 8;\n}\nSQLITE_PRIVATE u32 sqlite3VdbeSerialGet(\n  const unsigned char *buf,     /* Buffer to deserialize from */\n  u32 serial_type,              /* Serial type to deserialize */\n  Mem *pMem                     /* Memory cell to write value into */\n){\n  switch( serial_type ){\n    case 10: { /* Internal use only: NULL with virtual table\n               ** UPDATE no-change flag set */\n      pMem->flags = MEM_Null|MEM_Zero;\n      pMem->n = 0;\n      pMem->u.nZero = 0;\n      break;\n    }\n    case 11:   /* Reserved for future use */\n    case 0: {  /* Null */\n      /* EVIDENCE-OF: R-24078-09375 Value is a NULL. */\n      pMem->flags = MEM_Null;\n      break;\n    }\n    case 1: {\n      /* EVIDENCE-OF: R-44885-25196 Value is an 8-bit twos-complement\n      ** integer. */\n      pMem->u.i = ONE_BYTE_INT(buf);\n      pMem->flags = MEM_Int;\n      testcase( pMem->u.i<0 );\n      return 1;\n    }\n    case 2: { /* 2-byte signed integer */\n      /* EVIDENCE-OF: R-49794-35026 Value is a big-endian 16-bit\n      ** twos-complement integer. */\n      pMem->u.i = TWO_BYTE_INT(buf);\n      pMem->flags = MEM_Int;\n      testcase( pMem->u.i<0 );\n      return 2;\n    }\n    case 3: { /* 3-byte signed integer */\n      /* EVIDENCE-OF: R-37839-54301 Value is a big-endian 24-bit\n      ** twos-complement integer. */\n      pMem->u.i = THREE_BYTE_INT(buf);\n      pMem->flags = MEM_Int;\n      testcase( pMem->u.i<0 );\n      return 3;\n    }\n    case 4: { /* 4-byte signed integer */\n      /* EVIDENCE-OF: R-01849-26079 Value is a big-endian 32-bit\n      ** twos-complement integer. */\n      pMem->u.i = FOUR_BYTE_INT(buf);\n#ifdef __HP_cc \n      /* Work around a sign-extension bug in the HP compiler for HP/UX */\n      if( buf[0]&0x80 ) pMem->u.i |= 0xffffffff80000000LL;\n#endif\n      pMem->flags = MEM_Int;\n      testcase( pMem->u.i<0 );\n      return 4;\n    }\n    case 5: { /* 6-byte signed integer */\n      /* EVIDENCE-OF: R-50385-09674 Value is a big-endian 48-bit\n      ** twos-complement integer. */\n      pMem->u.i = FOUR_BYTE_UINT(buf+2) + (((i64)1)<<32)*TWO_BYTE_INT(buf);\n      pMem->flags = MEM_Int;\n      testcase( pMem->u.i<0 );\n      return 6;\n    }\n    case 6:   /* 8-byte signed integer */\n    case 7: { /* IEEE floating point */\n      /* These use local variables, so do them in a separate routine\n      ** to avoid having to move the frame pointer in the common case */\n      return serialGet(buf,serial_type,pMem);\n    }\n    case 8:    /* Integer 0 */\n    case 9: {  /* Integer 1 */\n      /* EVIDENCE-OF: R-12976-22893 Value is the integer 0. */\n      /* EVIDENCE-OF: R-18143-12121 Value is the integer 1. */\n      pMem->u.i = serial_type-8;\n      pMem->flags = MEM_Int;\n      return 0;\n    }\n    default: {\n      /* EVIDENCE-OF: R-14606-31564 Value is a BLOB that is (N-12)/2 bytes in\n      ** length.\n      ** EVIDENCE-OF: R-28401-00140 Value is a string in the text encoding and\n      ** (N-13)/2 bytes in length. */\n      static const u16 aFlag[] = { MEM_Blob|MEM_Ephem, MEM_Str|MEM_Ephem };\n      pMem->z = (char *)buf;\n      pMem->n = (serial_type-12)/2;\n      pMem->flags = aFlag[serial_type&1];\n      return pMem->n;\n    }\n  }\n  return 0;\n}\n/*\n** This routine is used to allocate sufficient space for an UnpackedRecord\n** structure large enough to be used with sqlite3VdbeRecordUnpack() if\n** the first argument is a pointer to KeyInfo structure pKeyInfo.\n**\n** The space is either allocated using sqlite3DbMallocRaw() or from within\n** the unaligned buffer passed via the second and third arguments (presumably\n** stack space). If the former, then *ppFree is set to a pointer that should\n** be eventually freed by the caller using sqlite3DbFree(). Or, if the \n** allocation comes from the pSpace/szSpace buffer, *ppFree is set to NULL\n** before returning.\n**\n** If an OOM error occurs, NULL is returned.\n*/\nSQLITE_PRIVATE UnpackedRecord *sqlite3VdbeAllocUnpackedRecord(\n  KeyInfo *pKeyInfo               /* Description of the record */\n){\n  UnpackedRecord *p;              /* Unpacked record to return */\n  int nByte;                      /* Number of bytes required for *p */\n  nByte = ROUND8(sizeof(UnpackedRecord)) + sizeof(Mem)*(pKeyInfo->nKeyField+1);\n  p = (UnpackedRecord *)sqlite3DbMallocRaw(pKeyInfo->db, nByte);\n  if( !p ) return 0;\n  p->aMem = (Mem*)&((char*)p)[ROUND8(sizeof(UnpackedRecord))];\n  assert( pKeyInfo->aSortOrder!=0 );\n  p->pKeyInfo = pKeyInfo;\n  p->nField = pKeyInfo->nKeyField + 1;\n  return p;\n}\n\n/*\n** Given the nKey-byte encoding of a record in pKey[], populate the \n** UnpackedRecord structure indicated by the fourth argument with the\n** contents of the decoded record.\n*/ \nSQLITE_PRIVATE void sqlite3VdbeRecordUnpack(\n  KeyInfo *pKeyInfo,     /* Information about the record format */\n  int nKey,              /* Size of the binary record */\n  const void *pKey,      /* The binary record */\n  UnpackedRecord *p      /* Populate this structure before returning. */\n){\n  const unsigned char *aKey = (const unsigned char *)pKey;\n  int d; \n  u32 idx;                        /* Offset in aKey[] to read from */\n  u16 u;                          /* Unsigned loop counter */\n  u32 szHdr;\n  Mem *pMem = p->aMem;\n\n  p->default_rc = 0;\n  assert( EIGHT_BYTE_ALIGNMENT(pMem) );\n  idx = getVarint32(aKey, szHdr);\n  d = szHdr;\n  u = 0;\n  while( idx<szHdr && d<=nKey ){\n    u32 serial_type;\n\n    idx += getVarint32(&aKey[idx], serial_type);\n    pMem->enc = pKeyInfo->enc;\n    pMem->db = pKeyInfo->db;\n    /* pMem->flags = 0; // sqlite3VdbeSerialGet() will set this for us */\n    pMem->szMalloc = 0;\n    pMem->z = 0;\n    d += sqlite3VdbeSerialGet(&aKey[d], serial_type, pMem);\n    pMem++;\n    if( (++u)>=p->nField ) break;\n  }\n  assert( u<=pKeyInfo->nKeyField + 1 );\n  p->nField = u;\n}\n\n#ifdef SQLITE_DEBUG\n/*\n** This function compares two index or table record keys in the same way\n** as the sqlite3VdbeRecordCompare() routine. Unlike VdbeRecordCompare(),\n** this function deserializes and compares values using the\n** sqlite3VdbeSerialGet() and sqlite3MemCompare() functions. It is used\n** in assert() statements to ensure that the optimized code in\n** sqlite3VdbeRecordCompare() returns results with these two primitives.\n**\n** Return true if the result of comparison is equivalent to desiredResult.\n** Return false if there is a disagreement.\n*/\nstatic int vdbeRecordCompareDebug(\n  int nKey1, const void *pKey1, /* Left key */\n  const UnpackedRecord *pPKey2, /* Right key */\n  int desiredResult             /* Correct answer */\n){\n  u32 d1;            /* Offset into aKey[] of next data element */\n  u32 idx1;          /* Offset into aKey[] of next header element */\n  u32 szHdr1;        /* Number of bytes in header */\n  int i = 0;\n  int rc = 0;\n  const unsigned char *aKey1 = (const unsigned char *)pKey1;\n  KeyInfo *pKeyInfo;\n  Mem mem1;\n\n  pKeyInfo = pPKey2->pKeyInfo;\n  if( pKeyInfo->db==0 ) return 1;\n  mem1.enc = pKeyInfo->enc;\n  mem1.db = pKeyInfo->db;\n  /* mem1.flags = 0;  // Will be initialized by sqlite3VdbeSerialGet() */\n  VVA_ONLY( mem1.szMalloc = 0; ) /* Only needed by assert() statements */\n\n  /* Compilers may complain that mem1.u.i is potentially uninitialized.\n  ** We could initialize it, as shown here, to silence those complaints.\n  ** But in fact, mem1.u.i will never actually be used uninitialized, and doing \n  ** the unnecessary initialization has a measurable negative performance\n  ** impact, since this routine is a very high runner.  And so, we choose\n  ** to ignore the compiler warnings and leave this variable uninitialized.\n  */\n  /*  mem1.u.i = 0;  // not needed, here to silence compiler warning */\n  \n  idx1 = getVarint32(aKey1, szHdr1);\n  if( szHdr1>98307 ) return SQLITE_CORRUPT;\n  d1 = szHdr1;\n  assert( pKeyInfo->nAllField>=pPKey2->nField || CORRUPT_DB );\n  assert( pKeyInfo->aSortOrder!=0 );\n  assert( pKeyInfo->nKeyField>0 );\n  assert( idx1<=szHdr1 || CORRUPT_DB );\n  do{\n    u32 serial_type1;\n\n    /* Read the serial types for the next element in each key. */\n    idx1 += getVarint32( aKey1+idx1, serial_type1 );\n\n    /* Verify that there is enough key space remaining to avoid\n    ** a buffer overread.  The \"d1+serial_type1+2\" subexpression will\n    ** always be greater than or equal to the amount of required key space.\n    ** Use that approximation to avoid the more expensive call to\n    ** sqlite3VdbeSerialTypeLen() in the common case.\n    */\n    if( d1+serial_type1+2>(u32)nKey1\n     && d1+sqlite3VdbeSerialTypeLen(serial_type1)>(u32)nKey1 \n    ){\n      break;\n    }\n\n    /* Extract the values to be compared.\n    */\n    d1 += sqlite3VdbeSerialGet(&aKey1[d1], serial_type1, &mem1);\n\n    /* Do the comparison\n    */\n    rc = sqlite3MemCompare(&mem1, &pPKey2->aMem[i], pKeyInfo->aColl[i]);\n    if( rc!=0 ){\n      assert( mem1.szMalloc==0 );  /* See comment below */\n      if( pKeyInfo->aSortOrder[i] ){\n        rc = -rc;  /* Invert the result for DESC sort order. */\n      }\n      goto debugCompareEnd;\n    }\n    i++;\n  }while( idx1<szHdr1 && i<pPKey2->nField );\n\n  /* No memory allocation is ever used on mem1.  Prove this using\n  ** the following assert().  If the assert() fails, it indicates a\n  ** memory leak and a need to call sqlite3VdbeMemRelease(&mem1).\n  */\n  assert( mem1.szMalloc==0 );\n\n  /* rc==0 here means that one of the keys ran out of fields and\n  ** all the fields up to that point were equal. Return the default_rc\n  ** value.  */\n  rc = pPKey2->default_rc;\n\ndebugCompareEnd:\n  if( desiredResult==0 && rc==0 ) return 1;\n  if( desiredResult<0 && rc<0 ) return 1;\n  if( desiredResult>0 && rc>0 ) return 1;\n  if( CORRUPT_DB ) return 1;\n  if( pKeyInfo->db->mallocFailed ) return 1;\n  return 0;\n}\n#endif\n\n#ifdef SQLITE_DEBUG\n/*\n** Count the number of fields (a.k.a. columns) in the record given by\n** pKey,nKey.  The verify that this count is less than or equal to the\n** limit given by pKeyInfo->nAllField.\n**\n** If this constraint is not satisfied, it means that the high-speed\n** vdbeRecordCompareInt() and vdbeRecordCompareString() routines will\n** not work correctly.  If this assert() ever fires, it probably means\n** that the KeyInfo.nKeyField or KeyInfo.nAllField values were computed\n** incorrectly.\n*/\nstatic void vdbeAssertFieldCountWithinLimits(\n  int nKey, const void *pKey,   /* The record to verify */ \n  const KeyInfo *pKeyInfo       /* Compare size with this KeyInfo */\n){\n  int nField = 0;\n  u32 szHdr;\n  u32 idx;\n  u32 notUsed;\n  const unsigned char *aKey = (const unsigned char*)pKey;\n\n  if( CORRUPT_DB ) return;\n  idx = getVarint32(aKey, szHdr);\n  assert( nKey>=0 );\n  assert( szHdr<=(u32)nKey );\n  while( idx<szHdr ){\n    idx += getVarint32(aKey+idx, notUsed);\n    nField++;\n  }\n  assert( nField <= pKeyInfo->nAllField );\n}\n#else\n# define vdbeAssertFieldCountWithinLimits(A,B,C)\n#endif\n\n/*\n** Both *pMem1 and *pMem2 contain string values. Compare the two values\n** using the collation sequence pColl. As usual, return a negative , zero\n** or positive value if *pMem1 is less than, equal to or greater than \n** *pMem2, respectively. Similar in spirit to \"rc = (*pMem1) - (*pMem2);\".\n*/\nstatic int vdbeCompareMemString(\n  const Mem *pMem1,\n  const Mem *pMem2,\n  const CollSeq *pColl,\n  u8 *prcErr                      /* If an OOM occurs, set to SQLITE_NOMEM */\n){\n  if( pMem1->enc==pColl->enc ){\n    /* The strings are already in the correct encoding.  Call the\n     ** comparison function directly */\n    return pColl->xCmp(pColl->pUser,pMem1->n,pMem1->z,pMem2->n,pMem2->z);\n  }else{\n    int rc;\n    const void *v1, *v2;\n    Mem c1;\n    Mem c2;\n    sqlite3VdbeMemInit(&c1, pMem1->db, MEM_Null);\n    sqlite3VdbeMemInit(&c2, pMem1->db, MEM_Null);\n    sqlite3VdbeMemShallowCopy(&c1, pMem1, MEM_Ephem);\n    sqlite3VdbeMemShallowCopy(&c2, pMem2, MEM_Ephem);\n    v1 = sqlite3ValueText((sqlite3_value*)&c1, pColl->enc);\n    v2 = sqlite3ValueText((sqlite3_value*)&c2, pColl->enc);\n    if( (v1==0 || v2==0) ){\n      if( prcErr ) *prcErr = SQLITE_NOMEM_BKPT;\n      rc = 0;\n    }else{\n      rc = pColl->xCmp(pColl->pUser, c1.n, v1, c2.n, v2);\n    }\n    sqlite3VdbeMemRelease(&c1);\n    sqlite3VdbeMemRelease(&c2);\n    return rc;\n  }\n}\n\n/*\n** The input pBlob is guaranteed to be a Blob that is not marked\n** with MEM_Zero.  Return true if it could be a zero-blob.\n*/\nstatic int isAllZero(const char *z, int n){\n  int i;\n  for(i=0; i<n; i++){\n    if( z[i] ) return 0;\n  }\n  return 1;\n}\n\n/*\n** Compare two blobs.  Return negative, zero, or positive if the first\n** is less than, equal to, or greater than the second, respectively.\n** If one blob is a prefix of the other, then the shorter is the lessor.\n*/\nstatic SQLITE_NOINLINE int sqlite3BlobCompare(const Mem *pB1, const Mem *pB2){\n  int c;\n  int n1 = pB1->n;\n  int n2 = pB2->n;\n\n  /* It is possible to have a Blob value that has some non-zero content\n  ** followed by zero content.  But that only comes up for Blobs formed\n  ** by the OP_MakeRecord opcode, and such Blobs never get passed into\n  ** sqlite3MemCompare(). */\n  assert( (pB1->flags & MEM_Zero)==0 || n1==0 );\n  assert( (pB2->flags & MEM_Zero)==0 || n2==0 );\n\n  if( (pB1->flags|pB2->flags) & MEM_Zero ){\n    if( pB1->flags & pB2->flags & MEM_Zero ){\n      return pB1->u.nZero - pB2->u.nZero;\n    }else if( pB1->flags & MEM_Zero ){\n      if( !isAllZero(pB2->z, pB2->n) ) return -1;\n      return pB1->u.nZero - n2;\n    }else{\n      if( !isAllZero(pB1->z, pB1->n) ) return +1;\n      return n1 - pB2->u.nZero;\n    }\n  }\n  c = memcmp(pB1->z, pB2->z, n1>n2 ? n2 : n1);\n  if( c ) return c;\n  return n1 - n2;\n}\n\n/*\n** Do a comparison between a 64-bit signed integer and a 64-bit floating-point\n** number.  Return negative, zero, or positive if the first (i64) is less than,\n** equal to, or greater than the second (double).\n*/\nstatic int sqlite3IntFloatCompare(i64 i, double r){\n  if( sizeof(LONGDOUBLE_TYPE)>8 ){\n    LONGDOUBLE_TYPE x = (LONGDOUBLE_TYPE)i;\n    if( x<r ) return -1;\n    if( x>r ) return +1;\n    return 0;\n  }else{\n    i64 y;\n    double s;\n    if( r<-9223372036854775808.0 ) return +1;\n    if( r>9223372036854775807.0 ) return -1;\n    y = (i64)r;\n    if( i<y ) return -1;\n    if( i>y ){\n      if( y==SMALLEST_INT64 && r>0.0 ) return -1;\n      return +1;\n    }\n    s = (double)i;\n    if( s<r ) return -1;\n    if( s>r ) return +1;\n    return 0;\n  }\n}\n\n/*\n** Compare the values contained by the two memory cells, returning\n** negative, zero or positive if pMem1 is less than, equal to, or greater\n** than pMem2. Sorting order is NULL's first, followed by numbers (integers\n** and reals) sorted numerically, followed by text ordered by the collating\n** sequence pColl and finally blob's ordered by memcmp().\n**\n** Two NULL values are considered equal by this function.\n*/\nSQLITE_PRIVATE int sqlite3MemCompare(const Mem *pMem1, const Mem *pMem2, const CollSeq *pColl){\n  int f1, f2;\n  int combined_flags;\n\n  f1 = pMem1->flags;\n  f2 = pMem2->flags;\n  combined_flags = f1|f2;\n  assert( (combined_flags & MEM_RowSet)==0 );\n \n  /* If one value is NULL, it is less than the other. If both values\n  ** are NULL, return 0.\n  */\n  if( combined_flags&MEM_Null ){\n    return (f2&MEM_Null) - (f1&MEM_Null);\n  }\n\n  /* At least one of the two values is a number\n  */\n  if( combined_flags&(MEM_Int|MEM_Real) ){\n    if( (f1 & f2 & MEM_Int)!=0 ){\n      if( pMem1->u.i < pMem2->u.i ) return -1;\n      if( pMem1->u.i > pMem2->u.i ) return +1;\n      return 0;\n    }\n    if( (f1 & f2 & MEM_Real)!=0 ){\n      if( pMem1->u.r < pMem2->u.r ) return -1;\n      if( pMem1->u.r > pMem2->u.r ) return +1;\n      return 0;\n    }\n    if( (f1&MEM_Int)!=0 ){\n      if( (f2&MEM_Real)!=0 ){\n        return sqlite3IntFloatCompare(pMem1->u.i, pMem2->u.r);\n      }else{\n        return -1;\n      }\n    }\n    if( (f1&MEM_Real)!=0 ){\n      if( (f2&MEM_Int)!=0 ){\n        return -sqlite3IntFloatCompare(pMem2->u.i, pMem1->u.r);\n      }else{\n        return -1;\n      }\n    }\n    return +1;\n  }\n\n  /* If one value is a string and the other is a blob, the string is less.\n  ** If both are strings, compare using the collating functions.\n  */\n  if( combined_flags&MEM_Str ){\n    if( (f1 & MEM_Str)==0 ){\n      return 1;\n    }\n    if( (f2 & MEM_Str)==0 ){\n      return -1;\n    }\n\n    assert( pMem1->enc==pMem2->enc || pMem1->db->mallocFailed );\n    assert( pMem1->enc==SQLITE_UTF8 || \n            pMem1->enc==SQLITE_UTF16LE || pMem1->enc==SQLITE_UTF16BE );\n\n    /* The collation sequence must be defined at this point, even if\n    ** the user deletes the collation sequence after the vdbe program is\n    ** compiled (this was not always the case).\n    */\n    assert( !pColl || pColl->xCmp );\n\n    if( pColl ){\n      return vdbeCompareMemString(pMem1, pMem2, pColl, 0);\n    }\n    /* If a NULL pointer was passed as the collate function, fall through\n    ** to the blob case and use memcmp().  */\n  }\n \n  /* Both values must be blobs.  Compare using memcmp().  */\n  return sqlite3BlobCompare(pMem1, pMem2);\n}\n\n\n/*\n** The first argument passed to this function is a serial-type that\n** corresponds to an integer - all values between 1 and 9 inclusive \n** except 7. The second points to a buffer containing an integer value\n** serialized according to serial_type. This function deserializes\n** and returns the value.\n*/\nstatic i64 vdbeRecordDecodeInt(u32 serial_type, const u8 *aKey){\n  u32 y;\n  assert( CORRUPT_DB || (serial_type>=1 && serial_type<=9 && serial_type!=7) );\n  switch( serial_type ){\n    case 0:\n    case 1:\n      testcase( aKey[0]&0x80 );\n      return ONE_BYTE_INT(aKey);\n    case 2:\n      testcase( aKey[0]&0x80 );\n      return TWO_BYTE_INT(aKey);\n    case 3:\n      testcase( aKey[0]&0x80 );\n      return THREE_BYTE_INT(aKey);\n    case 4: {\n      testcase( aKey[0]&0x80 );\n      y = FOUR_BYTE_UINT(aKey);\n      return (i64)*(int*)&y;\n    }\n    case 5: {\n      testcase( aKey[0]&0x80 );\n      return FOUR_BYTE_UINT(aKey+2) + (((i64)1)<<32)*TWO_BYTE_INT(aKey);\n    }\n    case 6: {\n      u64 x = FOUR_BYTE_UINT(aKey);\n      testcase( aKey[0]&0x80 );\n      x = (x<<32) | FOUR_BYTE_UINT(aKey+4);\n      return (i64)*(i64*)&x;\n    }\n  }\n\n  return (serial_type - 8);\n}\n\n/*\n** This function compares the two table rows or index records\n** specified by {nKey1, pKey1} and pPKey2.  It returns a negative, zero\n** or positive integer if key1 is less than, equal to or \n** greater than key2.  The {nKey1, pKey1} key must be a blob\n** created by the OP_MakeRecord opcode of the VDBE.  The pPKey2\n** key must be a parsed key such as obtained from\n** sqlite3VdbeParseRecord.\n**\n** If argument bSkip is non-zero, it is assumed that the caller has already\n** determined that the first fields of the keys are equal.\n**\n** Key1 and Key2 do not have to contain the same number of fields. If all \n** fields that appear in both keys are equal, then pPKey2->default_rc is \n** returned.\n**\n** If database corruption is discovered, set pPKey2->errCode to \n** SQLITE_CORRUPT and return 0. If an OOM error is encountered, \n** pPKey2->errCode is set to SQLITE_NOMEM and, if it is not NULL, the\n** malloc-failed flag set on database handle (pPKey2->pKeyInfo->db).\n*/\nSQLITE_PRIVATE int sqlite3VdbeRecordCompareWithSkip(\n  int nKey1, const void *pKey1,   /* Left key */\n  UnpackedRecord *pPKey2,         /* Right key */\n  int bSkip                       /* If true, skip the first field */\n){\n  u32 d1;                         /* Offset into aKey[] of next data element */\n  int i;                          /* Index of next field to compare */\n  u32 szHdr1;                     /* Size of record header in bytes */\n  u32 idx1;                       /* Offset of first type in header */\n  int rc = 0;                     /* Return value */\n  Mem *pRhs = pPKey2->aMem;       /* Next field of pPKey2 to compare */\n  KeyInfo *pKeyInfo = pPKey2->pKeyInfo;\n  const unsigned char *aKey1 = (const unsigned char *)pKey1;\n  Mem mem1;\n\n  /* If bSkip is true, then the caller has already determined that the first\n  ** two elements in the keys are equal. Fix the various stack variables so\n  ** that this routine begins comparing at the second field. */\n  if( bSkip ){\n    u32 s1;\n    idx1 = 1 + getVarint32(&aKey1[1], s1);\n    szHdr1 = aKey1[0];\n    d1 = szHdr1 + sqlite3VdbeSerialTypeLen(s1);\n    i = 1;\n    pRhs++;\n  }else{\n    idx1 = getVarint32(aKey1, szHdr1);\n    d1 = szHdr1;\n    if( d1>(unsigned)nKey1 ){ \n      pPKey2->errCode = (u8)SQLITE_CORRUPT_BKPT;\n      return 0;  /* Corruption */\n    }\n    i = 0;\n  }\n\n  VVA_ONLY( mem1.szMalloc = 0; ) /* Only needed by assert() statements */\n  assert( pPKey2->pKeyInfo->nAllField>=pPKey2->nField \n       || CORRUPT_DB );\n  assert( pPKey2->pKeyInfo->aSortOrder!=0 );\n  assert( pPKey2->pKeyInfo->nKeyField>0 );\n  assert( idx1<=szHdr1 || CORRUPT_DB );\n  do{\n    u32 serial_type;\n\n    /* RHS is an integer */\n    if( pRhs->flags & MEM_Int ){\n      serial_type = aKey1[idx1];\n      testcase( serial_type==12 );\n      if( serial_type>=10 ){\n        rc = +1;\n      }else if( serial_type==0 ){\n        rc = -1;\n      }else if( serial_type==7 ){\n        sqlite3VdbeSerialGet(&aKey1[d1], serial_type, &mem1);\n        rc = -sqlite3IntFloatCompare(pRhs->u.i, mem1.u.r);\n      }else{\n        i64 lhs = vdbeRecordDecodeInt(serial_type, &aKey1[d1]);\n        i64 rhs = pRhs->u.i;\n        if( lhs<rhs ){\n          rc = -1;\n        }else if( lhs>rhs ){\n          rc = +1;\n        }\n      }\n    }\n\n    /* RHS is real */\n    else if( pRhs->flags & MEM_Real ){\n      serial_type = aKey1[idx1];\n      if( serial_type>=10 ){\n        /* Serial types 12 or greater are strings and blobs (greater than\n        ** numbers). Types 10 and 11 are currently \"reserved for future \n        ** use\", so it doesn't really matter what the results of comparing\n        ** them to numberic values are.  */\n        rc = +1;\n      }else if( serial_type==0 ){\n        rc = -1;\n      }else{\n        sqlite3VdbeSerialGet(&aKey1[d1], serial_type, &mem1);\n        if( serial_type==7 ){\n          if( mem1.u.r<pRhs->u.r ){\n            rc = -1;\n          }else if( mem1.u.r>pRhs->u.r ){\n            rc = +1;\n          }\n        }else{\n          rc = sqlite3IntFloatCompare(mem1.u.i, pRhs->u.r);\n        }\n      }\n    }\n\n    /* RHS is a string */\n    else if( pRhs->flags & MEM_Str ){\n      getVarint32(&aKey1[idx1], serial_type);\n      testcase( serial_type==12 );\n      if( serial_type<12 ){\n        rc = -1;\n      }else if( !(serial_type & 0x01) ){\n        rc = +1;\n      }else{\n        mem1.n = (serial_type - 12) / 2;\n        testcase( (d1+mem1.n)==(unsigned)nKey1 );\n        testcase( (d1+mem1.n+1)==(unsigned)nKey1 );\n        if( (d1+mem1.n) > (unsigned)nKey1 ){\n          pPKey2->errCode = (u8)SQLITE_CORRUPT_BKPT;\n          return 0;                /* Corruption */\n        }else if( pKeyInfo->aColl[i] ){\n          mem1.enc = pKeyInfo->enc;\n          mem1.db = pKeyInfo->db;\n          mem1.flags = MEM_Str;\n          mem1.z = (char*)&aKey1[d1];\n          rc = vdbeCompareMemString(\n              &mem1, pRhs, pKeyInfo->aColl[i], &pPKey2->errCode\n          );\n        }else{\n          int nCmp = MIN(mem1.n, pRhs->n);\n          rc = memcmp(&aKey1[d1], pRhs->z, nCmp);\n          if( rc==0 ) rc = mem1.n - pRhs->n; \n        }\n      }\n    }\n\n    /* RHS is a blob */\n    else if( pRhs->flags & MEM_Blob ){\n      assert( (pRhs->flags & MEM_Zero)==0 || pRhs->n==0 );\n      getVarint32(&aKey1[idx1], serial_type);\n      testcase( serial_type==12 );\n      if( serial_type<12 || (serial_type & 0x01) ){\n        rc = -1;\n      }else{\n        int nStr = (serial_type - 12) / 2;\n        testcase( (d1+nStr)==(unsigned)nKey1 );\n        testcase( (d1+nStr+1)==(unsigned)nKey1 );\n        if( (d1+nStr) > (unsigned)nKey1 ){\n          pPKey2->errCode = (u8)SQLITE_CORRUPT_BKPT;\n          return 0;                /* Corruption */\n        }else if( pRhs->flags & MEM_Zero ){\n          if( !isAllZero((const char*)&aKey1[d1],nStr) ){\n            rc = 1;\n          }else{\n            rc = nStr - pRhs->u.nZero;\n          }\n        }else{\n          int nCmp = MIN(nStr, pRhs->n);\n          rc = memcmp(&aKey1[d1], pRhs->z, nCmp);\n          if( rc==0 ) rc = nStr - pRhs->n;\n        }\n      }\n    }\n\n    /* RHS is null */\n    else{\n      serial_type = aKey1[idx1];\n      rc = (serial_type!=0);\n    }\n\n    if( rc!=0 ){\n      if( pKeyInfo->aSortOrder[i] ){\n        rc = -rc;\n      }\n      assert( vdbeRecordCompareDebug(nKey1, pKey1, pPKey2, rc) );\n      assert( mem1.szMalloc==0 );  /* See comment below */\n      return rc;\n    }\n\n    i++;\n    pRhs++;\n    d1 += sqlite3VdbeSerialTypeLen(serial_type);\n    idx1 += sqlite3VarintLen(serial_type);\n  }while( idx1<(unsigned)szHdr1 && i<pPKey2->nField && d1<=(unsigned)nKey1 );\n\n  /* No memory allocation is ever used on mem1.  Prove this using\n  ** the following assert().  If the assert() fails, it indicates a\n  ** memory leak and a need to call sqlite3VdbeMemRelease(&mem1).  */\n  assert( mem1.szMalloc==0 );\n\n  /* rc==0 here means that one or both of the keys ran out of fields and\n  ** all the fields up to that point were equal. Return the default_rc\n  ** value.  */\n  assert( CORRUPT_DB \n       || vdbeRecordCompareDebug(nKey1, pKey1, pPKey2, pPKey2->default_rc) \n       || pKeyInfo->db->mallocFailed\n  );\n  pPKey2->eqSeen = 1;\n  return pPKey2->default_rc;\n}\nSQLITE_PRIVATE int sqlite3VdbeRecordCompare(\n  int nKey1, const void *pKey1,   /* Left key */\n  UnpackedRecord *pPKey2          /* Right key */\n){\n  return sqlite3VdbeRecordCompareWithSkip(nKey1, pKey1, pPKey2, 0);\n}\n\n\n/*\n** This function is an optimized version of sqlite3VdbeRecordCompare() \n** that (a) the first field of pPKey2 is an integer, and (b) the \n** size-of-header varint at the start of (pKey1/nKey1) fits in a single\n** byte (i.e. is less than 128).\n**\n** To avoid concerns about buffer overreads, this routine is only used\n** on schemas where the maximum valid header size is 63 bytes or less.\n*/\nstatic int vdbeRecordCompareInt(\n  int nKey1, const void *pKey1, /* Left key */\n  UnpackedRecord *pPKey2        /* Right key */\n){\n  const u8 *aKey = &((const u8*)pKey1)[*(const u8*)pKey1 & 0x3F];\n  int serial_type = ((const u8*)pKey1)[1];\n  int res;\n  u32 y;\n  u64 x;\n  i64 v;\n  i64 lhs;\n\n  vdbeAssertFieldCountWithinLimits(nKey1, pKey1, pPKey2->pKeyInfo);\n  assert( (*(u8*)pKey1)<=0x3F || CORRUPT_DB );\n  switch( serial_type ){\n    case 1: { /* 1-byte signed integer */\n      lhs = ONE_BYTE_INT(aKey);\n      testcase( lhs<0 );\n      break;\n    }\n    case 2: { /* 2-byte signed integer */\n      lhs = TWO_BYTE_INT(aKey);\n      testcase( lhs<0 );\n      break;\n    }\n    case 3: { /* 3-byte signed integer */\n      lhs = THREE_BYTE_INT(aKey);\n      testcase( lhs<0 );\n      break;\n    }\n    case 4: { /* 4-byte signed integer */\n      y = FOUR_BYTE_UINT(aKey);\n      lhs = (i64)*(int*)&y;\n      testcase( lhs<0 );\n      break;\n    }\n    case 5: { /* 6-byte signed integer */\n      lhs = FOUR_BYTE_UINT(aKey+2) + (((i64)1)<<32)*TWO_BYTE_INT(aKey);\n      testcase( lhs<0 );\n      break;\n    }\n    case 6: { /* 8-byte signed integer */\n      x = FOUR_BYTE_UINT(aKey);\n      x = (x<<32) | FOUR_BYTE_UINT(aKey+4);\n      lhs = *(i64*)&x;\n      testcase( lhs<0 );\n      break;\n    }\n    case 8: \n      lhs = 0;\n      break;\n    case 9:\n      lhs = 1;\n      break;\n\n    /* This case could be removed without changing the results of running\n    ** this code. Including it causes gcc to generate a faster switch \n    ** statement (since the range of switch targets now starts at zero and\n    ** is contiguous) but does not cause any duplicate code to be generated\n    ** (as gcc is clever enough to combine the two like cases). Other \n    ** compilers might be similar.  */ \n    case 0: case 7:\n      return sqlite3VdbeRecordCompare(nKey1, pKey1, pPKey2);\n\n    default:\n      return sqlite3VdbeRecordCompare(nKey1, pKey1, pPKey2);\n  }\n\n  v = pPKey2->aMem[0].u.i;\n  if( v>lhs ){\n    res = pPKey2->r1;\n  }else if( v<lhs ){\n    res = pPKey2->r2;\n  }else if( pPKey2->nField>1 ){\n    /* The first fields of the two keys are equal. Compare the trailing \n    ** fields.  */\n    res = sqlite3VdbeRecordCompareWithSkip(nKey1, pKey1, pPKey2, 1);\n  }else{\n    /* The first fields of the two keys are equal and there are no trailing\n    ** fields. Return pPKey2->default_rc in this case. */\n    res = pPKey2->default_rc;\n    pPKey2->eqSeen = 1;\n  }\n\n  assert( vdbeRecordCompareDebug(nKey1, pKey1, pPKey2, res) );\n  return res;\n}\n\n/*\n** This function is an optimized version of sqlite3VdbeRecordCompare() \n** that (a) the first field of pPKey2 is a string, that (b) the first field\n** uses the collation sequence BINARY and (c) that the size-of-header varint \n** at the start of (pKey1/nKey1) fits in a single byte.\n*/\nstatic int vdbeRecordCompareString(\n  int nKey1, const void *pKey1, /* Left key */\n  UnpackedRecord *pPKey2        /* Right key */\n){\n  const u8 *aKey1 = (const u8*)pKey1;\n  int serial_type;\n  int res;\n\n  assert( pPKey2->aMem[0].flags & MEM_Str );\n  vdbeAssertFieldCountWithinLimits(nKey1, pKey1, pPKey2->pKeyInfo);\n  getVarint32(&aKey1[1], serial_type);\n  if( serial_type<12 ){\n    res = pPKey2->r1;      /* (pKey1/nKey1) is a number or a null */\n  }else if( !(serial_type & 0x01) ){ \n    res = pPKey2->r2;      /* (pKey1/nKey1) is a blob */\n  }else{\n    int nCmp;\n    int nStr;\n    int szHdr = aKey1[0];\n\n    nStr = (serial_type-12) / 2;\n    if( (szHdr + nStr) > nKey1 ){\n      pPKey2->errCode = (u8)SQLITE_CORRUPT_BKPT;\n      return 0;    /* Corruption */\n    }\n    nCmp = MIN( pPKey2->aMem[0].n, nStr );\n    res = memcmp(&aKey1[szHdr], pPKey2->aMem[0].z, nCmp);\n\n    if( res==0 ){\n      res = nStr - pPKey2->aMem[0].n;\n      if( res==0 ){\n        if( pPKey2->nField>1 ){\n          res = sqlite3VdbeRecordCompareWithSkip(nKey1, pKey1, pPKey2, 1);\n        }else{\n          res = pPKey2->default_rc;\n          pPKey2->eqSeen = 1;\n        }\n      }else if( res>0 ){\n        res = pPKey2->r2;\n      }else{\n        res = pPKey2->r1;\n      }\n    }else if( res>0 ){\n      res = pPKey2->r2;\n    }else{\n      res = pPKey2->r1;\n    }\n  }\n\n  assert( vdbeRecordCompareDebug(nKey1, pKey1, pPKey2, res)\n       || CORRUPT_DB\n       || pPKey2->pKeyInfo->db->mallocFailed\n  );\n  return res;\n}\n\n/*\n** Return a pointer to an sqlite3VdbeRecordCompare() compatible function\n** suitable for comparing serialized records to the unpacked record passed\n** as the only argument.\n*/\nSQLITE_PRIVATE RecordCompare sqlite3VdbeFindCompare(UnpackedRecord *p){\n  /* varintRecordCompareInt() and varintRecordCompareString() both assume\n  ** that the size-of-header varint that occurs at the start of each record\n  ** fits in a single byte (i.e. is 127 or less). varintRecordCompareInt()\n  ** also assumes that it is safe to overread a buffer by at least the \n  ** maximum possible legal header size plus 8 bytes. Because there is\n  ** guaranteed to be at least 74 (but not 136) bytes of padding following each\n  ** buffer passed to varintRecordCompareInt() this makes it convenient to\n  ** limit the size of the header to 64 bytes in cases where the first field\n  ** is an integer.\n  **\n  ** The easiest way to enforce this limit is to consider only records with\n  ** 13 fields or less. If the first field is an integer, the maximum legal\n  ** header size is (12*5 + 1 + 1) bytes.  */\n  if( p->pKeyInfo->nAllField<=13 ){\n    int flags = p->aMem[0].flags;\n    if( p->pKeyInfo->aSortOrder[0] ){\n      p->r1 = 1;\n      p->r2 = -1;\n    }else{\n      p->r1 = -1;\n      p->r2 = 1;\n    }\n    if( (flags & MEM_Int) ){\n      return vdbeRecordCompareInt;\n    }\n    testcase( flags & MEM_Real );\n    testcase( flags & MEM_Null );\n    testcase( flags & MEM_Blob );\n    if( (flags & (MEM_Real|MEM_Null|MEM_Blob))==0 && p->pKeyInfo->aColl[0]==0 ){\n      assert( flags & MEM_Str );\n      return vdbeRecordCompareString;\n    }\n  }\n\n  return sqlite3VdbeRecordCompare;\n}\n\n/*\n** pCur points at an index entry created using the OP_MakeRecord opcode.\n** Read the rowid (the last field in the record) and store it in *rowid.\n** Return SQLITE_OK if everything works, or an error code otherwise.\n**\n** pCur might be pointing to text obtained from a corrupt database file.\n** So the content cannot be trusted.  Do appropriate checks on the content.\n*/\nSQLITE_PRIVATE int sqlite3VdbeIdxRowid(sqlite3 *db, BtCursor *pCur, i64 *rowid){\n  i64 nCellKey = 0;\n  int rc;\n  u32 szHdr;        /* Size of the header */\n  u32 typeRowid;    /* Serial type of the rowid */\n  u32 lenRowid;     /* Size of the rowid */\n  Mem m, v;\n\n  /* Get the size of the index entry.  Only indices entries of less\n  ** than 2GiB are support - anything large must be database corruption.\n  ** Any corruption is detected in sqlite3BtreeParseCellPtr(), though, so\n  ** this code can safely assume that nCellKey is 32-bits  \n  */\n  assert( sqlite3BtreeCursorIsValid(pCur) );\n  nCellKey = sqlite3BtreePayloadSize(pCur);\n  assert( (nCellKey & SQLITE_MAX_U32)==(u64)nCellKey );\n\n  /* Read in the complete content of the index entry */\n  sqlite3VdbeMemInit(&m, db, 0);\n  rc = sqlite3VdbeMemFromBtree(pCur, 0, (u32)nCellKey, &m);\n  if( rc ){\n    return rc;\n  }\n\n  /* The index entry must begin with a header size */\n  (void)getVarint32((u8*)m.z, szHdr);\n  testcase( szHdr==3 );\n  testcase( szHdr==m.n );\n  if( unlikely(szHdr<3 || (int)szHdr>m.n) ){\n    goto idx_rowid_corruption;\n  }\n\n  /* The last field of the index should be an integer - the ROWID.\n  ** Verify that the last entry really is an integer. */\n  (void)getVarint32((u8*)&m.z[szHdr-1], typeRowid);\n  testcase( typeRowid==1 );\n  testcase( typeRowid==2 );\n  testcase( typeRowid==3 );\n  testcase( typeRowid==4 );\n  testcase( typeRowid==5 );\n  testcase( typeRowid==6 );\n  testcase( typeRowid==8 );\n  testcase( typeRowid==9 );\n  if( unlikely(typeRowid<1 || typeRowid>9 || typeRowid==7) ){\n    goto idx_rowid_corruption;\n  }\n  lenRowid = sqlite3SmallTypeSizes[typeRowid];\n  testcase( (u32)m.n==szHdr+lenRowid );\n  if( unlikely((u32)m.n<szHdr+lenRowid) ){\n    goto idx_rowid_corruption;\n  }\n\n  /* Fetch the integer off the end of the index record */\n  sqlite3VdbeSerialGet((u8*)&m.z[m.n-lenRowid], typeRowid, &v);\n  *rowid = v.u.i;\n  sqlite3VdbeMemRelease(&m);\n  return SQLITE_OK;\n\n  /* Jump here if database corruption is detected after m has been\n  ** allocated.  Free the m object and return SQLITE_CORRUPT. */\nidx_rowid_corruption:\n  testcase( m.szMalloc!=0 );\n  sqlite3VdbeMemRelease(&m);\n  return SQLITE_CORRUPT_BKPT;\n}\n\n/*\n** Compare the key of the index entry that cursor pC is pointing to against\n** the key string in pUnpacked.  Write into *pRes a number\n** that is negative, zero, or positive if pC is less than, equal to,\n** or greater than pUnpacked.  Return SQLITE_OK on success.\n**\n** pUnpacked is either created without a rowid or is truncated so that it\n** omits the rowid at the end.  The rowid at the end of the index entry\n** is ignored as well.  Hence, this routine only compares the prefixes \n** of the keys prior to the final rowid, not the entire key.\n*/\nSQLITE_PRIVATE int sqlite3VdbeIdxKeyCompare(\n  sqlite3 *db,                     /* Database connection */\n  VdbeCursor *pC,                  /* The cursor to compare against */\n  UnpackedRecord *pUnpacked,       /* Unpacked version of key */\n  int *res                         /* Write the comparison result here */\n){\n  i64 nCellKey = 0;\n  int rc;\n  BtCursor *pCur;\n  Mem m;\n\n  assert( pC->eCurType==CURTYPE_BTREE );\n  pCur = pC->uc.pCursor;\n  assert( sqlite3BtreeCursorIsValid(pCur) );\n  nCellKey = sqlite3BtreePayloadSize(pCur);\n  /* nCellKey will always be between 0 and 0xffffffff because of the way\n  ** that btreeParseCellPtr() and sqlite3GetVarint32() are implemented */\n  if( nCellKey<=0 || nCellKey>0x7fffffff ){\n    *res = 0;\n    return SQLITE_CORRUPT_BKPT;\n  }\n  sqlite3VdbeMemInit(&m, db, 0);\n  rc = sqlite3VdbeMemFromBtree(pCur, 0, (u32)nCellKey, &m);\n  if( rc ){\n    return rc;\n  }\n  *res = sqlite3VdbeRecordCompare(m.n, m.z, pUnpacked);\n  sqlite3VdbeMemRelease(&m);\n  return SQLITE_OK;\n}\n\n/*\n** This routine sets the value to be returned by subsequent calls to\n** sqlite3_changes() on the database handle 'db'. \n*/\nSQLITE_PRIVATE void sqlite3VdbeSetChanges(sqlite3 *db, int nChange){\n  assert( sqlite3_mutex_held(db->mutex) );\n  db->nChange = nChange;\n  db->nTotalChange += nChange;\n}\n\n/*\n** Set a flag in the vdbe to update the change counter when it is finalised\n** or reset.\n*/\nSQLITE_PRIVATE void sqlite3VdbeCountChanges(Vdbe *v){\n  v->changeCntOn = 1;\n}\n\n/*\n** Mark every prepared statement associated with a database connection\n** as expired.\n**\n** An expired statement means that recompilation of the statement is\n** recommend.  Statements expire when things happen that make their\n** programs obsolete.  Removing user-defined functions or collating\n** sequences, or changing an authorization function are the types of\n** things that make prepared statements obsolete.\n*/\nSQLITE_PRIVATE void sqlite3ExpirePreparedStatements(sqlite3 *db){\n  Vdbe *p;\n  for(p = db->pVdbe; p; p=p->pNext){\n    p->expired = 1;\n  }\n}\n\n/*\n** Return the database associated with the Vdbe.\n*/\nSQLITE_PRIVATE sqlite3 *sqlite3VdbeDb(Vdbe *v){\n  return v->db;\n}\n\n/*\n** Return the SQLITE_PREPARE flags for a Vdbe.\n*/\nSQLITE_PRIVATE u8 sqlite3VdbePrepareFlags(Vdbe *v){\n  return v->prepFlags;\n}\n\n/*\n** Return a pointer to an sqlite3_value structure containing the value bound\n** parameter iVar of VM v. Except, if the value is an SQL NULL, return \n** 0 instead. Unless it is NULL, apply affinity aff (one of the SQLITE_AFF_*\n** constants) to the value before returning it.\n**\n** The returned value must be freed by the caller using sqlite3ValueFree().\n*/\nSQLITE_PRIVATE sqlite3_value *sqlite3VdbeGetBoundValue(Vdbe *v, int iVar, u8 aff){\n  assert( iVar>0 );\n  if( v ){\n    Mem *pMem = &v->aVar[iVar-1];\n    assert( (v->db->flags & SQLITE_EnableQPSG)==0 );\n    if( 0==(pMem->flags & MEM_Null) ){\n      sqlite3_value *pRet = sqlite3ValueNew(v->db);\n      if( pRet ){\n        sqlite3VdbeMemCopy((Mem *)pRet, pMem);\n        sqlite3ValueApplyAffinity(pRet, aff, SQLITE_UTF8);\n      }\n      return pRet;\n    }\n  }\n  return 0;\n}\n\n/*\n** Configure SQL variable iVar so that binding a new value to it signals\n** to sqlite3_reoptimize() that re-preparing the statement may result\n** in a better query plan.\n*/\nSQLITE_PRIVATE void sqlite3VdbeSetVarmask(Vdbe *v, int iVar){\n  assert( iVar>0 );\n  assert( (v->db->flags & SQLITE_EnableQPSG)==0 );\n  if( iVar>=32 ){\n    v->expmask |= 0x80000000;\n  }else{\n    v->expmask |= ((u32)1 << (iVar-1));\n  }\n}\n\n/*\n** Cause a function to throw an error if it was call from OP_PureFunc\n** rather than OP_Function.\n**\n** OP_PureFunc means that the function must be deterministic, and should\n** throw an error if it is given inputs that would make it non-deterministic.\n** This routine is invoked by date/time functions that use non-deterministic\n** features such as 'now'.\n*/\nSQLITE_PRIVATE int sqlite3NotPureFunc(sqlite3_context *pCtx){\n#ifdef SQLITE_ENABLE_STAT3_OR_STAT4\n  if( pCtx->pVdbe==0 ) return 1;\n#endif\n  if( pCtx->pVdbe->aOp[pCtx->iOp].opcode==OP_PureFunc ){\n    sqlite3_result_error(pCtx, \n       \"non-deterministic function in index expression or CHECK constraint\",\n       -1);\n    return 0;\n  }\n  return 1;\n}\n\n#ifndef SQLITE_OMIT_VIRTUALTABLE\n/*\n** Transfer error message text from an sqlite3_vtab.zErrMsg (text stored\n** in memory obtained from sqlite3_malloc) into a Vdbe.zErrMsg (text stored\n** in memory obtained from sqlite3DbMalloc).\n*/\nSQLITE_PRIVATE void sqlite3VtabImportErrmsg(Vdbe *p, sqlite3_vtab *pVtab){\n  if( pVtab->zErrMsg ){\n    sqlite3 *db = p->db;\n    sqlite3DbFree(db, p->zErrMsg);\n    p->zErrMsg = sqlite3DbStrDup(db, pVtab->zErrMsg);\n    sqlite3_free(pVtab->zErrMsg);\n    pVtab->zErrMsg = 0;\n  }\n}\n#endif /* SQLITE_OMIT_VIRTUALTABLE */\n\n#ifdef SQLITE_ENABLE_PREUPDATE_HOOK\n\n/*\n** If the second argument is not NULL, release any allocations associated \n** with the memory cells in the p->aMem[] array. Also free the UnpackedRecord\n** structure itself, using sqlite3DbFree().\n**\n** This function is used to free UnpackedRecord structures allocated by\n** the vdbeUnpackRecord() function found in vdbeapi.c.\n*/\nstatic void vdbeFreeUnpacked(sqlite3 *db, int nField, UnpackedRecord *p){\n  if( p ){\n    int i;\n    for(i=0; i<nField; i++){\n      Mem *pMem = &p->aMem[i];\n      if( pMem->zMalloc ) sqlite3VdbeMemRelease(pMem);\n    }\n    sqlite3DbFreeNN(db, p);\n  }\n}\n#endif /* SQLITE_ENABLE_PREUPDATE_HOOK */\n\n#ifdef SQLITE_ENABLE_PREUPDATE_HOOK\n/*\n** Invoke the pre-update hook. If this is an UPDATE or DELETE pre-update call,\n** then cursor passed as the second argument should point to the row about\n** to be update or deleted. If the application calls sqlite3_preupdate_old(),\n** the required value will be read from the row the cursor points to.\n*/\nSQLITE_PRIVATE void sqlite3VdbePreUpdateHook(\n  Vdbe *v,                        /* Vdbe pre-update hook is invoked by */\n  VdbeCursor *pCsr,               /* Cursor to grab old.* values from */\n  int op,                         /* SQLITE_INSERT, UPDATE or DELETE */\n  const char *zDb,                /* Database name */\n  Table *pTab,                    /* Modified table */\n  i64 iKey1,                      /* Initial key value */\n  int iReg                        /* Register for new.* record */\n){\n  sqlite3 *db = v->db;\n  i64 iKey2;\n  PreUpdate preupdate;\n  const char *zTbl = pTab->zName;\n  static const u8 fakeSortOrder = 0;\n\n  assert( db->pPreUpdate==0 );\n  memset(&preupdate, 0, sizeof(PreUpdate));\n  if( HasRowid(pTab)==0 ){\n    iKey1 = iKey2 = 0;\n    preupdate.pPk = sqlite3PrimaryKeyIndex(pTab);\n  }else{\n    if( op==SQLITE_UPDATE ){\n      iKey2 = v->aMem[iReg].u.i;\n    }else{\n      iKey2 = iKey1;\n    }\n  }\n\n  assert( pCsr->nField==pTab->nCol \n       || (pCsr->nField==pTab->nCol+1 && op==SQLITE_DELETE && iReg==-1)\n  );\n\n  preupdate.v = v;\n  preupdate.pCsr = pCsr;\n  preupdate.op = op;\n  preupdate.iNewReg = iReg;\n  preupdate.keyinfo.db = db;\n  preupdate.keyinfo.enc = ENC(db);\n  preupdate.keyinfo.nKeyField = pTab->nCol;\n  preupdate.keyinfo.aSortOrder = (u8*)&fakeSortOrder;\n  preupdate.iKey1 = iKey1;\n  preupdate.iKey2 = iKey2;\n  preupdate.pTab = pTab;\n\n  db->pPreUpdate = &preupdate;\n  db->xPreUpdateCallback(db->pPreUpdateArg, db, op, zDb, zTbl, iKey1, iKey2);\n  db->pPreUpdate = 0;\n  sqlite3DbFree(db, preupdate.aRecord);\n  vdbeFreeUnpacked(db, preupdate.keyinfo.nKeyField+1, preupdate.pUnpacked);\n  vdbeFreeUnpacked(db, preupdate.keyinfo.nKeyField+1, preupdate.pNewUnpacked);\n  if( preupdate.aNew ){\n    int i;\n    for(i=0; i<pCsr->nField; i++){\n      sqlite3VdbeMemRelease(&preupdate.aNew[i]);\n    }\n    sqlite3DbFreeNN(db, preupdate.aNew);\n  }\n}\n#endif /* SQLITE_ENABLE_PREUPDATE_HOOK */\n\n/************** End of vdbeaux.c *********************************************/\n/************** Begin file vdbeapi.c *****************************************/\n/*\n** 2004 May 26\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n*************************************************************************\n**\n** This file contains code use to implement APIs that are part of the\n** VDBE.\n*/\n/* #include \"sqliteInt.h\" */\n/* #include \"vdbeInt.h\" */\n\n#ifndef SQLITE_OMIT_DEPRECATED\n/*\n** Return TRUE (non-zero) of the statement supplied as an argument needs\n** to be recompiled.  A statement needs to be recompiled whenever the\n** execution environment changes in a way that would alter the program\n** that sqlite3_prepare() generates.  For example, if new functions or\n** collating sequences are registered or if an authorizer function is\n** added or changed.\n*/\nSQLITE_API int sqlite3_expired(sqlite3_stmt *pStmt){\n  Vdbe *p = (Vdbe*)pStmt;\n  return p==0 || p->expired;\n}\n#endif\n\n/*\n** Check on a Vdbe to make sure it has not been finalized.  Log\n** an error and return true if it has been finalized (or is otherwise\n** invalid).  Return false if it is ok.\n*/\nstatic int vdbeSafety(Vdbe *p){\n  if( p->db==0 ){\n    sqlite3_log(SQLITE_MISUSE, \"API called with finalized prepared statement\");\n    return 1;\n  }else{\n    return 0;\n  }\n}\nstatic int vdbeSafetyNotNull(Vdbe *p){\n  if( p==0 ){\n    sqlite3_log(SQLITE_MISUSE, \"API called with NULL prepared statement\");\n    return 1;\n  }else{\n    return vdbeSafety(p);\n  }\n}\n\n#ifndef SQLITE_OMIT_TRACE\n/*\n** Invoke the profile callback.  This routine is only called if we already\n** know that the profile callback is defined and needs to be invoked.\n*/\nstatic SQLITE_NOINLINE void invokeProfileCallback(sqlite3 *db, Vdbe *p){\n  sqlite3_int64 iNow;\n  sqlite3_int64 iElapse;\n  assert( p->startTime>0 );\n  assert( db->xProfile!=0 || (db->mTrace & SQLITE_TRACE_PROFILE)!=0 );\n  assert( db->init.busy==0 );\n  assert( p->zSql!=0 );\n  sqlite3OsCurrentTimeInt64(db->pVfs, &iNow);\n  iElapse = (iNow - p->startTime)*1000000;\n  if( db->xProfile ){\n    db->xProfile(db->pProfileArg, p->zSql, iElapse);\n  }\n  if( db->mTrace & SQLITE_TRACE_PROFILE ){\n    db->xTrace(SQLITE_TRACE_PROFILE, db->pTraceArg, p, (void*)&iElapse);\n  }\n  p->startTime = 0;\n}\n/*\n** The checkProfileCallback(DB,P) macro checks to see if a profile callback\n** is needed, and it invokes the callback if it is needed.\n*/\n# define checkProfileCallback(DB,P) \\\n   if( ((P)->startTime)>0 ){ invokeProfileCallback(DB,P); }\n#else\n# define checkProfileCallback(DB,P)  /*no-op*/\n#endif\n\n/*\n** The following routine destroys a virtual machine that is created by\n** the sqlite3_compile() routine. The integer returned is an SQLITE_\n** success/failure code that describes the result of executing the virtual\n** machine.\n**\n** This routine sets the error code and string returned by\n** sqlite3_errcode(), sqlite3_errmsg() and sqlite3_errmsg16().\n*/\nSQLITE_API int sqlite3_finalize(sqlite3_stmt *pStmt){\n  int rc;\n  if( pStmt==0 ){\n    /* IMPLEMENTATION-OF: R-57228-12904 Invoking sqlite3_finalize() on a NULL\n    ** pointer is a harmless no-op. */\n    rc = SQLITE_OK;\n  }else{\n    Vdbe *v = (Vdbe*)pStmt;\n    sqlite3 *db = v->db;\n    if( vdbeSafety(v) ) return SQLITE_MISUSE_BKPT;\n    sqlite3_mutex_enter(db->mutex);\n    checkProfileCallback(db, v);\n    rc = sqlite3VdbeFinalize(v);\n    rc = sqlite3ApiExit(db, rc);\n    sqlite3LeaveMutexAndCloseZombie(db);\n  }\n  return rc;\n}\n\n/*\n** Terminate the current execution of an SQL statement and reset it\n** back to its starting state so that it can be reused. A success code from\n** the prior execution is returned.\n**\n** This routine sets the error code and string returned by\n** sqlite3_errcode(), sqlite3_errmsg() and sqlite3_errmsg16().\n*/\nSQLITE_API int sqlite3_reset(sqlite3_stmt *pStmt){\n  int rc;\n  if( pStmt==0 ){\n    rc = SQLITE_OK;\n  }else{\n    Vdbe *v = (Vdbe*)pStmt;\n    sqlite3 *db = v->db;\n    sqlite3_mutex_enter(db->mutex);\n    checkProfileCallback(db, v);\n    rc = sqlite3VdbeReset(v);\n    sqlite3VdbeRewind(v);\n    assert( (rc & (db->errMask))==rc );\n    rc = sqlite3ApiExit(db, rc);\n    sqlite3_mutex_leave(db->mutex);\n  }\n  return rc;\n}\n\n/*\n** Set all the parameters in the compiled SQL statement to NULL.\n*/\nSQLITE_API int sqlite3_clear_bindings(sqlite3_stmt *pStmt){\n  int i;\n  int rc = SQLITE_OK;\n  Vdbe *p = (Vdbe*)pStmt;\n#if SQLITE_THREADSAFE\n  sqlite3_mutex *mutex = ((Vdbe*)pStmt)->db->mutex;\n#endif\n  sqlite3_mutex_enter(mutex);\n  for(i=0; i<p->nVar; i++){\n    sqlite3VdbeMemRelease(&p->aVar[i]);\n    p->aVar[i].flags = MEM_Null;\n  }\n  assert( (p->prepFlags & SQLITE_PREPARE_SAVESQL)!=0 || p->expmask==0 );\n  if( p->expmask ){\n    p->expired = 1;\n  }\n  sqlite3_mutex_leave(mutex);\n  return rc;\n}\n\n\n/**************************** sqlite3_value_  *******************************\n** The following routines extract information from a Mem or sqlite3_value\n** structure.\n*/\nSQLITE_API const void *sqlite3_value_blob(sqlite3_value *pVal){\n  Mem *p = (Mem*)pVal;\n  if( p->flags & (MEM_Blob|MEM_Str) ){\n    if( ExpandBlob(p)!=SQLITE_OK ){\n      assert( p->flags==MEM_Null && p->z==0 );\n      return 0;\n    }\n    p->flags |= MEM_Blob;\n    return p->n ? p->z : 0;\n  }else{\n    return sqlite3_value_text(pVal);\n  }\n}\nSQLITE_API int sqlite3_value_bytes(sqlite3_value *pVal){\n  return sqlite3ValueBytes(pVal, SQLITE_UTF8);\n}\nSQLITE_API int sqlite3_value_bytes16(sqlite3_value *pVal){\n  return sqlite3ValueBytes(pVal, SQLITE_UTF16NATIVE);\n}\nSQLITE_API double sqlite3_value_double(sqlite3_value *pVal){\n  return sqlite3VdbeRealValue((Mem*)pVal);\n}\nSQLITE_API int sqlite3_value_int(sqlite3_value *pVal){\n  return (int)sqlite3VdbeIntValue((Mem*)pVal);\n}\nSQLITE_API sqlite_int64 sqlite3_value_int64(sqlite3_value *pVal){\n  return sqlite3VdbeIntValue((Mem*)pVal);\n}\nSQLITE_API unsigned int sqlite3_value_subtype(sqlite3_value *pVal){\n  Mem *pMem = (Mem*)pVal;\n  return ((pMem->flags & MEM_Subtype) ? pMem->eSubtype : 0);\n}\nSQLITE_API void *sqlite3_value_pointer(sqlite3_value *pVal, const char *zPType){\n  Mem *p = (Mem*)pVal;\n  if( (p->flags&(MEM_TypeMask|MEM_Term|MEM_Subtype)) ==\n                 (MEM_Null|MEM_Term|MEM_Subtype)\n   && zPType!=0\n   && p->eSubtype=='p'\n   && strcmp(p->u.zPType, zPType)==0\n  ){\n    return (void*)p->z;\n  }else{\n    return 0;\n  }\n}\nSQLITE_API const unsigned char *sqlite3_value_text(sqlite3_value *pVal){\n  return (const unsigned char *)sqlite3ValueText(pVal, SQLITE_UTF8);\n}\n#ifndef SQLITE_OMIT_UTF16\nSQLITE_API const void *sqlite3_value_text16(sqlite3_value* pVal){\n  return sqlite3ValueText(pVal, SQLITE_UTF16NATIVE);\n}\nSQLITE_API const void *sqlite3_value_text16be(sqlite3_value *pVal){\n  return sqlite3ValueText(pVal, SQLITE_UTF16BE);\n}\nSQLITE_API const void *sqlite3_value_text16le(sqlite3_value *pVal){\n  return sqlite3ValueText(pVal, SQLITE_UTF16LE);\n}\n#endif /* SQLITE_OMIT_UTF16 */\n/* EVIDENCE-OF: R-12793-43283 Every value in SQLite has one of five\n** fundamental datatypes: 64-bit signed integer 64-bit IEEE floating\n** point number string BLOB NULL\n*/\nSQLITE_API int sqlite3_value_type(sqlite3_value* pVal){\n  static const u8 aType[] = {\n     SQLITE_BLOB,     /* 0x00 */\n     SQLITE_NULL,     /* 0x01 */\n     SQLITE_TEXT,     /* 0x02 */\n     SQLITE_NULL,     /* 0x03 */\n     SQLITE_INTEGER,  /* 0x04 */\n     SQLITE_NULL,     /* 0x05 */\n     SQLITE_INTEGER,  /* 0x06 */\n     SQLITE_NULL,     /* 0x07 */\n     SQLITE_FLOAT,    /* 0x08 */\n     SQLITE_NULL,     /* 0x09 */\n     SQLITE_FLOAT,    /* 0x0a */\n     SQLITE_NULL,     /* 0x0b */\n     SQLITE_INTEGER,  /* 0x0c */\n     SQLITE_NULL,     /* 0x0d */\n     SQLITE_INTEGER,  /* 0x0e */\n     SQLITE_NULL,     /* 0x0f */\n     SQLITE_BLOB,     /* 0x10 */\n     SQLITE_NULL,     /* 0x11 */\n     SQLITE_TEXT,     /* 0x12 */\n     SQLITE_NULL,     /* 0x13 */\n     SQLITE_INTEGER,  /* 0x14 */\n     SQLITE_NULL,     /* 0x15 */\n     SQLITE_INTEGER,  /* 0x16 */\n     SQLITE_NULL,     /* 0x17 */\n     SQLITE_FLOAT,    /* 0x18 */\n     SQLITE_NULL,     /* 0x19 */\n     SQLITE_FLOAT,    /* 0x1a */\n     SQLITE_NULL,     /* 0x1b */\n     SQLITE_INTEGER,  /* 0x1c */\n     SQLITE_NULL,     /* 0x1d */\n     SQLITE_INTEGER,  /* 0x1e */\n     SQLITE_NULL,     /* 0x1f */\n  };\n  return aType[pVal->flags&MEM_AffMask];\n}\n\n/* Return true if a parameter to xUpdate represents an unchanged column */\nSQLITE_API int sqlite3_value_nochange(sqlite3_value *pVal){\n  return (pVal->flags&(MEM_Null|MEM_Zero))==(MEM_Null|MEM_Zero);\n}\n\n/* Make a copy of an sqlite3_value object\n*/\nSQLITE_API sqlite3_value *sqlite3_value_dup(const sqlite3_value *pOrig){\n  sqlite3_value *pNew;\n  if( pOrig==0 ) return 0;\n  pNew = sqlite3_malloc( sizeof(*pNew) );\n  if( pNew==0 ) return 0;\n  memset(pNew, 0, sizeof(*pNew));\n  memcpy(pNew, pOrig, MEMCELLSIZE);\n  pNew->flags &= ~MEM_Dyn;\n  pNew->db = 0;\n  if( pNew->flags&(MEM_Str|MEM_Blob) ){\n    pNew->flags &= ~(MEM_Static|MEM_Dyn);\n    pNew->flags |= MEM_Ephem;\n    if( sqlite3VdbeMemMakeWriteable(pNew)!=SQLITE_OK ){\n      sqlite3ValueFree(pNew);\n      pNew = 0;\n    }\n  }\n  return pNew;\n}\n\n/* Destroy an sqlite3_value object previously obtained from\n** sqlite3_value_dup().\n*/\nSQLITE_API void sqlite3_value_free(sqlite3_value *pOld){\n  sqlite3ValueFree(pOld);\n}\n  \n\n/**************************** sqlite3_result_  *******************************\n** The following routines are used by user-defined functions to specify\n** the function result.\n**\n** The setStrOrError() function calls sqlite3VdbeMemSetStr() to store the\n** result as a string or blob but if the string or blob is too large, it\n** then sets the error code to SQLITE_TOOBIG\n**\n** The invokeValueDestructor(P,X) routine invokes destructor function X()\n** on value P is not going to be used and need to be destroyed.\n*/\nstatic void setResultStrOrError(\n  sqlite3_context *pCtx,  /* Function context */\n  const char *z,          /* String pointer */\n  int n,                  /* Bytes in string, or negative */\n  u8 enc,                 /* Encoding of z.  0 for BLOBs */\n  void (*xDel)(void*)     /* Destructor function */\n){\n  if( sqlite3VdbeMemSetStr(pCtx->pOut, z, n, enc, xDel)==SQLITE_TOOBIG ){\n    sqlite3_result_error_toobig(pCtx);\n  }\n}\nstatic int invokeValueDestructor(\n  const void *p,             /* Value to destroy */\n  void (*xDel)(void*),       /* The destructor */\n  sqlite3_context *pCtx      /* Set a SQLITE_TOOBIG error if no NULL */\n){\n  assert( xDel!=SQLITE_DYNAMIC );\n  if( xDel==0 ){\n    /* noop */\n  }else if( xDel==SQLITE_TRANSIENT ){\n    /* noop */\n  }else{\n    xDel((void*)p);\n  }\n  if( pCtx ) sqlite3_result_error_toobig(pCtx);\n  return SQLITE_TOOBIG;\n}\nSQLITE_API void sqlite3_result_blob(\n  sqlite3_context *pCtx, \n  const void *z, \n  int n, \n  void (*xDel)(void *)\n){\n  assert( n>=0 );\n  assert( sqlite3_mutex_held(pCtx->pOut->db->mutex) );\n  setResultStrOrError(pCtx, z, n, 0, xDel);\n}\nSQLITE_API void sqlite3_result_blob64(\n  sqlite3_context *pCtx, \n  const void *z, \n  sqlite3_uint64 n,\n  void (*xDel)(void *)\n){\n  assert( sqlite3_mutex_held(pCtx->pOut->db->mutex) );\n  assert( xDel!=SQLITE_DYNAMIC );\n  if( n>0x7fffffff ){\n    (void)invokeValueDestructor(z, xDel, pCtx);\n  }else{\n    setResultStrOrError(pCtx, z, (int)n, 0, xDel);\n  }\n}\nSQLITE_API void sqlite3_result_double(sqlite3_context *pCtx, double rVal){\n  assert( sqlite3_mutex_held(pCtx->pOut->db->mutex) );\n  sqlite3VdbeMemSetDouble(pCtx->pOut, rVal);\n}\nSQLITE_API void sqlite3_result_error(sqlite3_context *pCtx, const char *z, int n){\n  assert( sqlite3_mutex_held(pCtx->pOut->db->mutex) );\n  pCtx->isError = SQLITE_ERROR;\n  sqlite3VdbeMemSetStr(pCtx->pOut, z, n, SQLITE_UTF8, SQLITE_TRANSIENT);\n}\n#ifndef SQLITE_OMIT_UTF16\nSQLITE_API void sqlite3_result_error16(sqlite3_context *pCtx, const void *z, int n){\n  assert( sqlite3_mutex_held(pCtx->pOut->db->mutex) );\n  pCtx->isError = SQLITE_ERROR;\n  sqlite3VdbeMemSetStr(pCtx->pOut, z, n, SQLITE_UTF16NATIVE, SQLITE_TRANSIENT);\n}\n#endif\nSQLITE_API void sqlite3_result_int(sqlite3_context *pCtx, int iVal){\n  assert( sqlite3_mutex_held(pCtx->pOut->db->mutex) );\n  sqlite3VdbeMemSetInt64(pCtx->pOut, (i64)iVal);\n}\nSQLITE_API void sqlite3_result_int64(sqlite3_context *pCtx, i64 iVal){\n  assert( sqlite3_mutex_held(pCtx->pOut->db->mutex) );\n  sqlite3VdbeMemSetInt64(pCtx->pOut, iVal);\n}\nSQLITE_API void sqlite3_result_null(sqlite3_context *pCtx){\n  assert( sqlite3_mutex_held(pCtx->pOut->db->mutex) );\n  sqlite3VdbeMemSetNull(pCtx->pOut);\n}\nSQLITE_API void sqlite3_result_pointer(\n  sqlite3_context *pCtx,\n  void *pPtr,\n  const char *zPType,\n  void (*xDestructor)(void*)\n){\n  Mem *pOut = pCtx->pOut;\n  assert( sqlite3_mutex_held(pOut->db->mutex) );\n  sqlite3VdbeMemRelease(pOut);\n  pOut->flags = MEM_Null;\n  sqlite3VdbeMemSetPointer(pOut, pPtr, zPType, xDestructor);\n}\nSQLITE_API void sqlite3_result_subtype(sqlite3_context *pCtx, unsigned int eSubtype){\n  Mem *pOut = pCtx->pOut;\n  assert( sqlite3_mutex_held(pOut->db->mutex) );\n  pOut->eSubtype = eSubtype & 0xff;\n  pOut->flags |= MEM_Subtype;\n}\nSQLITE_API void sqlite3_result_text(\n  sqlite3_context *pCtx, \n  const char *z, \n  int n,\n  void (*xDel)(void *)\n){\n  assert( sqlite3_mutex_held(pCtx->pOut->db->mutex) );\n  setResultStrOrError(pCtx, z, n, SQLITE_UTF8, xDel);\n}\nSQLITE_API void sqlite3_result_text64(\n  sqlite3_context *pCtx, \n  const char *z, \n  sqlite3_uint64 n,\n  void (*xDel)(void *),\n  unsigned char enc\n){\n  assert( sqlite3_mutex_held(pCtx->pOut->db->mutex) );\n  assert( xDel!=SQLITE_DYNAMIC );\n  if( enc==SQLITE_UTF16 ) enc = SQLITE_UTF16NATIVE;\n  if( n>0x7fffffff ){\n    (void)invokeValueDestructor(z, xDel, pCtx);\n  }else{\n    setResultStrOrError(pCtx, z, (int)n, enc, xDel);\n  }\n}\n#ifndef SQLITE_OMIT_UTF16\nSQLITE_API void sqlite3_result_text16(\n  sqlite3_context *pCtx, \n  const void *z, \n  int n, \n  void (*xDel)(void *)\n){\n  assert( sqlite3_mutex_held(pCtx->pOut->db->mutex) );\n  setResultStrOrError(pCtx, z, n, SQLITE_UTF16NATIVE, xDel);\n}\nSQLITE_API void sqlite3_result_text16be(\n  sqlite3_context *pCtx, \n  const void *z, \n  int n, \n  void (*xDel)(void *)\n){\n  assert( sqlite3_mutex_held(pCtx->pOut->db->mutex) );\n  setResultStrOrError(pCtx, z, n, SQLITE_UTF16BE, xDel);\n}\nSQLITE_API void sqlite3_result_text16le(\n  sqlite3_context *pCtx, \n  const void *z, \n  int n, \n  void (*xDel)(void *)\n){\n  assert( sqlite3_mutex_held(pCtx->pOut->db->mutex) );\n  setResultStrOrError(pCtx, z, n, SQLITE_UTF16LE, xDel);\n}\n#endif /* SQLITE_OMIT_UTF16 */\nSQLITE_API void sqlite3_result_value(sqlite3_context *pCtx, sqlite3_value *pValue){\n  assert( sqlite3_mutex_held(pCtx->pOut->db->mutex) );\n  sqlite3VdbeMemCopy(pCtx->pOut, pValue);\n}\nSQLITE_API void sqlite3_result_zeroblob(sqlite3_context *pCtx, int n){\n  assert( sqlite3_mutex_held(pCtx->pOut->db->mutex) );\n  sqlite3VdbeMemSetZeroBlob(pCtx->pOut, n);\n}\nSQLITE_API int sqlite3_result_zeroblob64(sqlite3_context *pCtx, u64 n){\n  Mem *pOut = pCtx->pOut;\n  assert( sqlite3_mutex_held(pOut->db->mutex) );\n  if( n>(u64)pOut->db->aLimit[SQLITE_LIMIT_LENGTH] ){\n    return SQLITE_TOOBIG;\n  }\n  sqlite3VdbeMemSetZeroBlob(pCtx->pOut, (int)n);\n  return SQLITE_OK;\n}\nSQLITE_API void sqlite3_result_error_code(sqlite3_context *pCtx, int errCode){\n  pCtx->isError = errCode ? errCode : -1;\n#ifdef SQLITE_DEBUG\n  if( pCtx->pVdbe ) pCtx->pVdbe->rcApp = errCode;\n#endif\n  if( pCtx->pOut->flags & MEM_Null ){\n    sqlite3VdbeMemSetStr(pCtx->pOut, sqlite3ErrStr(errCode), -1, \n                         SQLITE_UTF8, SQLITE_STATIC);\n  }\n}\n\n/* Force an SQLITE_TOOBIG error. */\nSQLITE_API void sqlite3_result_error_toobig(sqlite3_context *pCtx){\n  assert( sqlite3_mutex_held(pCtx->pOut->db->mutex) );\n  pCtx->isError = SQLITE_TOOBIG;\n  sqlite3VdbeMemSetStr(pCtx->pOut, \"string or blob too big\", -1, \n                       SQLITE_UTF8, SQLITE_STATIC);\n}\n\n/* An SQLITE_NOMEM error. */\nSQLITE_API void sqlite3_result_error_nomem(sqlite3_context *pCtx){\n  assert( sqlite3_mutex_held(pCtx->pOut->db->mutex) );\n  sqlite3VdbeMemSetNull(pCtx->pOut);\n  pCtx->isError = SQLITE_NOMEM_BKPT;\n  sqlite3OomFault(pCtx->pOut->db);\n}\n\n/*\n** This function is called after a transaction has been committed. It \n** invokes callbacks registered with sqlite3_wal_hook() as required.\n*/\nstatic int doWalCallbacks(sqlite3 *db){\n  int rc = SQLITE_OK;\n#ifndef SQLITE_OMIT_WAL\n  int i;\n  for(i=0; i<db->nDb; i++){\n    Btree *pBt = db->aDb[i].pBt;\n    if( pBt ){\n      int nEntry;\n      sqlite3BtreeEnter(pBt);\n      nEntry = sqlite3PagerWalCallback(sqlite3BtreePager(pBt));\n      sqlite3BtreeLeave(pBt);\n      if( nEntry>0 && db->xWalCallback && rc==SQLITE_OK ){\n        rc = db->xWalCallback(db->pWalArg, db, db->aDb[i].zDbSName, nEntry);\n      }\n    }\n  }\n#endif\n  return rc;\n}\n\n\n/*\n** Execute the statement pStmt, either until a row of data is ready, the\n** statement is completely executed or an error occurs.\n**\n** This routine implements the bulk of the logic behind the sqlite_step()\n** API.  The only thing omitted is the automatic recompile if a \n** schema change has occurred.  That detail is handled by the\n** outer sqlite3_step() wrapper procedure.\n*/\nstatic int sqlite3Step(Vdbe *p){\n  sqlite3 *db;\n  int rc;\n\n  assert(p);\n  if( p->magic!=VDBE_MAGIC_RUN ){\n    /* We used to require that sqlite3_reset() be called before retrying\n    ** sqlite3_step() after any error or after SQLITE_DONE.  But beginning\n    ** with version 3.7.0, we changed this so that sqlite3_reset() would\n    ** be called automatically instead of throwing the SQLITE_MISUSE error.\n    ** This \"automatic-reset\" change is not technically an incompatibility, \n    ** since any application that receives an SQLITE_MISUSE is broken by\n    ** definition.\n    **\n    ** Nevertheless, some published applications that were originally written\n    ** for version 3.6.23 or earlier do in fact depend on SQLITE_MISUSE \n    ** returns, and those were broken by the automatic-reset change.  As a\n    ** a work-around, the SQLITE_OMIT_AUTORESET compile-time restores the\n    ** legacy behavior of returning SQLITE_MISUSE for cases where the \n    ** previous sqlite3_step() returned something other than a SQLITE_LOCKED\n    ** or SQLITE_BUSY error.\n    */\n#ifdef SQLITE_OMIT_AUTORESET\n    if( (rc = p->rc&0xff)==SQLITE_BUSY || rc==SQLITE_LOCKED ){\n      sqlite3_reset((sqlite3_stmt*)p);\n    }else{\n      return SQLITE_MISUSE_BKPT;\n    }\n#else\n    sqlite3_reset((sqlite3_stmt*)p);\n#endif\n  }\n\n  /* Check that malloc() has not failed. If it has, return early. */\n  db = p->db;\n  if( db->mallocFailed ){\n    p->rc = SQLITE_NOMEM;\n    return SQLITE_NOMEM_BKPT;\n  }\n\n  if( p->pc<=0 && p->expired ){\n    p->rc = SQLITE_SCHEMA;\n    rc = SQLITE_ERROR;\n    goto end_of_step;\n  }\n  if( p->pc<0 ){\n    /* If there are no other statements currently running, then\n    ** reset the interrupt flag.  This prevents a call to sqlite3_interrupt\n    ** from interrupting a statement that has not yet started.\n    */\n    if( db->nVdbeActive==0 ){\n      db->u1.isInterrupted = 0;\n    }\n\n    assert( db->nVdbeWrite>0 || db->autoCommit==0 \n        || (db->nDeferredCons==0 && db->nDeferredImmCons==0)\n    );\n\n#ifndef SQLITE_OMIT_TRACE\n    if( (db->xProfile || (db->mTrace & SQLITE_TRACE_PROFILE)!=0)\n        && !db->init.busy && p->zSql ){\n      sqlite3OsCurrentTimeInt64(db->pVfs, &p->startTime);\n    }else{\n      assert( p->startTime==0 );\n    }\n#endif\n\n    db->nVdbeActive++;\n    if( p->readOnly==0 ) db->nVdbeWrite++;\n    if( p->bIsReader ) db->nVdbeRead++;\n    p->pc = 0;\n  }\n#ifdef SQLITE_DEBUG\n  p->rcApp = SQLITE_OK;\n#endif\n#ifndef SQLITE_OMIT_EXPLAIN\n  if( p->explain ){\n    rc = sqlite3VdbeList(p);\n  }else\n#endif /* SQLITE_OMIT_EXPLAIN */\n  {\n    db->nVdbeExec++;\n    rc = sqlite3VdbeExec(p);\n    db->nVdbeExec--;\n  }\n\n#ifndef SQLITE_OMIT_TRACE\n  /* If the statement completed successfully, invoke the profile callback */\n  if( rc!=SQLITE_ROW ) checkProfileCallback(db, p);\n#endif\n\n  if( rc==SQLITE_DONE && db->autoCommit ){\n    assert( p->rc==SQLITE_OK );\n    p->rc = doWalCallbacks(db);\n    if( p->rc!=SQLITE_OK ){\n      rc = SQLITE_ERROR;\n    }\n  }\n\n  db->errCode = rc;\n  if( SQLITE_NOMEM==sqlite3ApiExit(p->db, p->rc) ){\n    p->rc = SQLITE_NOMEM_BKPT;\n  }\nend_of_step:\n  /* At this point local variable rc holds the value that should be \n  ** returned if this statement was compiled using the legacy \n  ** sqlite3_prepare() interface. According to the docs, this can only\n  ** be one of the values in the first assert() below. Variable p->rc \n  ** contains the value that would be returned if sqlite3_finalize() \n  ** were called on statement p.\n  */\n  assert( rc==SQLITE_ROW  || rc==SQLITE_DONE   || rc==SQLITE_ERROR \n       || (rc&0xff)==SQLITE_BUSY || rc==SQLITE_MISUSE\n  );\n  assert( (p->rc!=SQLITE_ROW && p->rc!=SQLITE_DONE) || p->rc==p->rcApp );\n  if( (p->prepFlags & SQLITE_PREPARE_SAVESQL)!=0 \n   && rc!=SQLITE_ROW \n   && rc!=SQLITE_DONE \n  ){\n    /* If this statement was prepared using saved SQL and an \n    ** error has occurred, then return the error code in p->rc to the\n    ** caller. Set the error code in the database handle to the same value.\n    */ \n    rc = sqlite3VdbeTransferError(p);\n  }\n  return (rc&db->errMask);\n}\n\n/*\n** This is the top-level implementation of sqlite3_step().  Call\n** sqlite3Step() to do most of the work.  If a schema error occurs,\n** call sqlite3Reprepare() and try again.\n*/\nSQLITE_API int sqlite3_step(sqlite3_stmt *pStmt){\n  int rc = SQLITE_OK;      /* Result from sqlite3Step() */\n  Vdbe *v = (Vdbe*)pStmt;  /* the prepared statement */\n  int cnt = 0;             /* Counter to prevent infinite loop of reprepares */\n  sqlite3 *db;             /* The database connection */\n\n  if( vdbeSafetyNotNull(v) ){\n    return SQLITE_MISUSE_BKPT;\n  }\n  db = v->db;\n  sqlite3_mutex_enter(db->mutex);\n  v->doingRerun = 0;\n  while( (rc = sqlite3Step(v))==SQLITE_SCHEMA\n         && cnt++ < SQLITE_MAX_SCHEMA_RETRY ){\n    int savedPc = v->pc;\n    rc = sqlite3Reprepare(v);\n    if( rc!=SQLITE_OK ){\n      /* This case occurs after failing to recompile an sql statement. \n      ** The error message from the SQL compiler has already been loaded \n      ** into the database handle. This block copies the error message \n      ** from the database handle into the statement and sets the statement\n      ** program counter to 0 to ensure that when the statement is \n      ** finalized or reset the parser error message is available via\n      ** sqlite3_errmsg() and sqlite3_errcode().\n      */\n      const char *zErr = (const char *)sqlite3_value_text(db->pErr); \n      sqlite3DbFree(db, v->zErrMsg);\n      if( !db->mallocFailed ){\n        v->zErrMsg = sqlite3DbStrDup(db, zErr);\n        v->rc = rc = sqlite3ApiExit(db, rc);\n      } else {\n        v->zErrMsg = 0;\n        v->rc = rc = SQLITE_NOMEM_BKPT;\n      }\n      break;\n    }\n    sqlite3_reset(pStmt);\n    if( savedPc>=0 ) v->doingRerun = 1;\n    assert( v->expired==0 );\n  }\n  sqlite3_mutex_leave(db->mutex);\n  return rc;\n}\n\n\n/*\n** Extract the user data from a sqlite3_context structure and return a\n** pointer to it.\n*/\nSQLITE_API void *sqlite3_user_data(sqlite3_context *p){\n  assert( p && p->pFunc );\n  return p->pFunc->pUserData;\n}\n\n/*\n** Extract the user data from a sqlite3_context structure and return a\n** pointer to it.\n**\n** IMPLEMENTATION-OF: R-46798-50301 The sqlite3_context_db_handle() interface\n** returns a copy of the pointer to the database connection (the 1st\n** parameter) of the sqlite3_create_function() and\n** sqlite3_create_function16() routines that originally registered the\n** application defined function.\n*/\nSQLITE_API sqlite3 *sqlite3_context_db_handle(sqlite3_context *p){\n  assert( p && p->pOut );\n  return p->pOut->db;\n}\n\n/*\n** If this routine is invoked from within an xColumn method of a virtual\n** table, then it returns true if and only if the the call is during an\n** UPDATE operation and the value of the column will not be modified\n** by the UPDATE.\n**\n** If this routine is called from any context other than within the\n** xColumn method of a virtual table, then the return value is meaningless\n** and arbitrary.\n**\n** Virtual table implements might use this routine to optimize their\n** performance by substituting a NULL result, or some other light-weight\n** value, as a signal to the xUpdate routine that the column is unchanged.\n*/\nSQLITE_API int sqlite3_vtab_nochange(sqlite3_context *p){\n  assert( p );\n  return sqlite3_value_nochange(p->pOut);\n}\n\n/*\n** Return the current time for a statement.  If the current time\n** is requested more than once within the same run of a single prepared\n** statement, the exact same time is returned for each invocation regardless\n** of the amount of time that elapses between invocations.  In other words,\n** the time returned is always the time of the first call.\n*/\nSQLITE_PRIVATE sqlite3_int64 sqlite3StmtCurrentTime(sqlite3_context *p){\n  int rc;\n#ifndef SQLITE_ENABLE_STAT3_OR_STAT4\n  sqlite3_int64 *piTime = &p->pVdbe->iCurrentTime;\n  assert( p->pVdbe!=0 );\n#else\n  sqlite3_int64 iTime = 0;\n  sqlite3_int64 *piTime = p->pVdbe!=0 ? &p->pVdbe->iCurrentTime : &iTime;\n#endif\n  if( *piTime==0 ){\n    rc = sqlite3OsCurrentTimeInt64(p->pOut->db->pVfs, piTime);\n    if( rc ) *piTime = 0;\n  }\n  return *piTime;\n}\n\n/*\n** The following is the implementation of an SQL function that always\n** fails with an error message stating that the function is used in the\n** wrong context.  The sqlite3_overload_function() API might construct\n** SQL function that use this routine so that the functions will exist\n** for name resolution but are actually overloaded by the xFindFunction\n** method of virtual tables.\n*/\nSQLITE_PRIVATE void sqlite3InvalidFunction(\n  sqlite3_context *context,  /* The function calling context */\n  int NotUsed,               /* Number of arguments to the function */\n  sqlite3_value **NotUsed2   /* Value of each argument */\n){\n  const char *zName = context->pFunc->zName;\n  char *zErr;\n  UNUSED_PARAMETER2(NotUsed, NotUsed2);\n  zErr = sqlite3_mprintf(\n      \"unable to use function %s in the requested context\", zName);\n  sqlite3_result_error(context, zErr, -1);\n  sqlite3_free(zErr);\n}\n\n/*\n** Create a new aggregate context for p and return a pointer to\n** its pMem->z element.\n*/\nstatic SQLITE_NOINLINE void *createAggContext(sqlite3_context *p, int nByte){\n  Mem *pMem = p->pMem;\n  assert( (pMem->flags & MEM_Agg)==0 );\n  if( nByte<=0 ){\n    sqlite3VdbeMemSetNull(pMem);\n    pMem->z = 0;\n  }else{\n    sqlite3VdbeMemClearAndResize(pMem, nByte);\n    pMem->flags = MEM_Agg;\n    pMem->u.pDef = p->pFunc;\n    if( pMem->z ){\n      memset(pMem->z, 0, nByte);\n    }\n  }\n  return (void*)pMem->z;\n}\n\n/*\n** Allocate or return the aggregate context for a user function.  A new\n** context is allocated on the first call.  Subsequent calls return the\n** same context that was returned on prior calls.\n*/\nSQLITE_API void *sqlite3_aggregate_context(sqlite3_context *p, int nByte){\n  assert( p && p->pFunc && p->pFunc->xFinalize );\n  assert( sqlite3_mutex_held(p->pOut->db->mutex) );\n  testcase( nByte<0 );\n  if( (p->pMem->flags & MEM_Agg)==0 ){\n    return createAggContext(p, nByte);\n  }else{\n    return (void*)p->pMem->z;\n  }\n}\n\n/*\n** Return the auxiliary data pointer, if any, for the iArg'th argument to\n** the user-function defined by pCtx.\n**\n** The left-most argument is 0.\n**\n** Undocumented behavior:  If iArg is negative then access a cache of\n** auxiliary data pointers that is available to all functions within a\n** single prepared statement.  The iArg values must match.\n*/\nSQLITE_API void *sqlite3_get_auxdata(sqlite3_context *pCtx, int iArg){\n  AuxData *pAuxData;\n\n  assert( sqlite3_mutex_held(pCtx->pOut->db->mutex) );\n#if SQLITE_ENABLE_STAT3_OR_STAT4\n  if( pCtx->pVdbe==0 ) return 0;\n#else\n  assert( pCtx->pVdbe!=0 );\n#endif\n  for(pAuxData=pCtx->pVdbe->pAuxData; pAuxData; pAuxData=pAuxData->pNextAux){\n    if(  pAuxData->iAuxArg==iArg && (pAuxData->iAuxOp==pCtx->iOp || iArg<0) ){\n      return pAuxData->pAux;\n    }\n  }\n  return 0;\n}\n\n/*\n** Set the auxiliary data pointer and delete function, for the iArg'th\n** argument to the user-function defined by pCtx. Any previous value is\n** deleted by calling the delete function specified when it was set.\n**\n** The left-most argument is 0.\n**\n** Undocumented behavior:  If iArg is negative then make the data available\n** to all functions within the current prepared statement using iArg as an\n** access code.\n*/\nSQLITE_API void sqlite3_set_auxdata(\n  sqlite3_context *pCtx, \n  int iArg, \n  void *pAux, \n  void (*xDelete)(void*)\n){\n  AuxData *pAuxData;\n  Vdbe *pVdbe = pCtx->pVdbe;\n\n  assert( sqlite3_mutex_held(pCtx->pOut->db->mutex) );\n#ifdef SQLITE_ENABLE_STAT3_OR_STAT4\n  if( pVdbe==0 ) goto failed;\n#else\n  assert( pVdbe!=0 );\n#endif\n\n  for(pAuxData=pVdbe->pAuxData; pAuxData; pAuxData=pAuxData->pNextAux){\n    if( pAuxData->iAuxArg==iArg && (pAuxData->iAuxOp==pCtx->iOp || iArg<0) ){\n      break;\n    }\n  }\n  if( pAuxData==0 ){\n    pAuxData = sqlite3DbMallocZero(pVdbe->db, sizeof(AuxData));\n    if( !pAuxData ) goto failed;\n    pAuxData->iAuxOp = pCtx->iOp;\n    pAuxData->iAuxArg = iArg;\n    pAuxData->pNextAux = pVdbe->pAuxData;\n    pVdbe->pAuxData = pAuxData;\n    if( pCtx->isError==0 ) pCtx->isError = -1;\n  }else if( pAuxData->xDeleteAux ){\n    pAuxData->xDeleteAux(pAuxData->pAux);\n  }\n\n  pAuxData->pAux = pAux;\n  pAuxData->xDeleteAux = xDelete;\n  return;\n\nfailed:\n  if( xDelete ){\n    xDelete(pAux);\n  }\n}\n\n#ifndef SQLITE_OMIT_DEPRECATED\n/*\n** Return the number of times the Step function of an aggregate has been \n** called.\n**\n** This function is deprecated.  Do not use it for new code.  It is\n** provide only to avoid breaking legacy code.  New aggregate function\n** implementations should keep their own counts within their aggregate\n** context.\n*/\nSQLITE_API int sqlite3_aggregate_count(sqlite3_context *p){\n  assert( p && p->pMem && p->pFunc && p->pFunc->xFinalize );\n  return p->pMem->n;\n}\n#endif\n\n/*\n** Return the number of columns in the result set for the statement pStmt.\n*/\nSQLITE_API int sqlite3_column_count(sqlite3_stmt *pStmt){\n  Vdbe *pVm = (Vdbe *)pStmt;\n  return pVm ? pVm->nResColumn : 0;\n}\n\n/*\n** Return the number of values available from the current row of the\n** currently executing statement pStmt.\n*/\nSQLITE_API int sqlite3_data_count(sqlite3_stmt *pStmt){\n  Vdbe *pVm = (Vdbe *)pStmt;\n  if( pVm==0 || pVm->pResultSet==0 ) return 0;\n  return pVm->nResColumn;\n}\n\n/*\n** Return a pointer to static memory containing an SQL NULL value.\n*/\nstatic const Mem *columnNullValue(void){\n  /* Even though the Mem structure contains an element\n  ** of type i64, on certain architectures (x86) with certain compiler\n  ** switches (-Os), gcc may align this Mem object on a 4-byte boundary\n  ** instead of an 8-byte one. This all works fine, except that when\n  ** running with SQLITE_DEBUG defined the SQLite code sometimes assert()s\n  ** that a Mem structure is located on an 8-byte boundary. To prevent\n  ** these assert()s from failing, when building with SQLITE_DEBUG defined\n  ** using gcc, we force nullMem to be 8-byte aligned using the magical\n  ** __attribute__((aligned(8))) macro.  */\n  static const Mem nullMem \n#if defined(SQLITE_DEBUG) && defined(__GNUC__)\n    __attribute__((aligned(8))) \n#endif\n    = {\n        /* .u          = */ {0},\n        /* .flags      = */ (u16)MEM_Null,\n        /* .enc        = */ (u8)0,\n        /* .eSubtype   = */ (u8)0,\n        /* .n          = */ (int)0,\n        /* .z          = */ (char*)0,\n        /* .zMalloc    = */ (char*)0,\n        /* .szMalloc   = */ (int)0,\n        /* .uTemp      = */ (u32)0,\n        /* .db         = */ (sqlite3*)0,\n        /* .xDel       = */ (void(*)(void*))0,\n#ifdef SQLITE_DEBUG\n        /* .pScopyFrom = */ (Mem*)0,\n        /* .pFiller    = */ (void*)0,\n#endif\n      };\n  return &nullMem;\n}\n\n/*\n** Check to see if column iCol of the given statement is valid.  If\n** it is, return a pointer to the Mem for the value of that column.\n** If iCol is not valid, return a pointer to a Mem which has a value\n** of NULL.\n*/\nstatic Mem *columnMem(sqlite3_stmt *pStmt, int i){\n  Vdbe *pVm;\n  Mem *pOut;\n\n  pVm = (Vdbe *)pStmt;\n  if( pVm==0 ) return (Mem*)columnNullValue();\n  assert( pVm->db );\n  sqlite3_mutex_enter(pVm->db->mutex);\n  if( pVm->pResultSet!=0 && i<pVm->nResColumn && i>=0 ){\n    pOut = &pVm->pResultSet[i];\n  }else{\n    sqlite3Error(pVm->db, SQLITE_RANGE);\n    pOut = (Mem*)columnNullValue();\n  }\n  return pOut;\n}\n\n/*\n** This function is called after invoking an sqlite3_value_XXX function on a \n** column value (i.e. a value returned by evaluating an SQL expression in the\n** select list of a SELECT statement) that may cause a malloc() failure. If \n** malloc() has failed, the threads mallocFailed flag is cleared and the result\n** code of statement pStmt set to SQLITE_NOMEM.\n**\n** Specifically, this is called from within:\n**\n**     sqlite3_column_int()\n**     sqlite3_column_int64()\n**     sqlite3_column_text()\n**     sqlite3_column_text16()\n**     sqlite3_column_real()\n**     sqlite3_column_bytes()\n**     sqlite3_column_bytes16()\n**     sqiite3_column_blob()\n*/\nstatic void columnMallocFailure(sqlite3_stmt *pStmt)\n{\n  /* If malloc() failed during an encoding conversion within an\n  ** sqlite3_column_XXX API, then set the return code of the statement to\n  ** SQLITE_NOMEM. The next call to _step() (if any) will return SQLITE_ERROR\n  ** and _finalize() will return NOMEM.\n  */\n  Vdbe *p = (Vdbe *)pStmt;\n  if( p ){\n    assert( p->db!=0 );\n    assert( sqlite3_mutex_held(p->db->mutex) );\n    p->rc = sqlite3ApiExit(p->db, p->rc);\n    sqlite3_mutex_leave(p->db->mutex);\n  }\n}\n\n/**************************** sqlite3_column_  *******************************\n** The following routines are used to access elements of the current row\n** in the result set.\n*/\nSQLITE_API const void *sqlite3_column_blob(sqlite3_stmt *pStmt, int i){\n  const void *val;\n  val = sqlite3_value_blob( columnMem(pStmt,i) );\n  /* Even though there is no encoding conversion, value_blob() might\n  ** need to call malloc() to expand the result of a zeroblob() \n  ** expression. \n  */\n  columnMallocFailure(pStmt);\n  return val;\n}\nSQLITE_API int sqlite3_column_bytes(sqlite3_stmt *pStmt, int i){\n  int val = sqlite3_value_bytes( columnMem(pStmt,i) );\n  columnMallocFailure(pStmt);\n  return val;\n}\nSQLITE_API int sqlite3_column_bytes16(sqlite3_stmt *pStmt, int i){\n  int val = sqlite3_value_bytes16( columnMem(pStmt,i) );\n  columnMallocFailure(pStmt);\n  return val;\n}\nSQLITE_API double sqlite3_column_double(sqlite3_stmt *pStmt, int i){\n  double val = sqlite3_value_double( columnMem(pStmt,i) );\n  columnMallocFailure(pStmt);\n  return val;\n}\nSQLITE_API int sqlite3_column_int(sqlite3_stmt *pStmt, int i){\n  int val = sqlite3_value_int( columnMem(pStmt,i) );\n  columnMallocFailure(pStmt);\n  return val;\n}\nSQLITE_API sqlite_int64 sqlite3_column_int64(sqlite3_stmt *pStmt, int i){\n  sqlite_int64 val = sqlite3_value_int64( columnMem(pStmt,i) );\n  columnMallocFailure(pStmt);\n  return val;\n}\nSQLITE_API const unsigned char *sqlite3_column_text(sqlite3_stmt *pStmt, int i){\n  const unsigned char *val = sqlite3_value_text( columnMem(pStmt,i) );\n  columnMallocFailure(pStmt);\n  return val;\n}\nSQLITE_API sqlite3_value *sqlite3_column_value(sqlite3_stmt *pStmt, int i){\n  Mem *pOut = columnMem(pStmt, i);\n  if( pOut->flags&MEM_Static ){\n    pOut->flags &= ~MEM_Static;\n    pOut->flags |= MEM_Ephem;\n  }\n  columnMallocFailure(pStmt);\n  return (sqlite3_value *)pOut;\n}\n#ifndef SQLITE_OMIT_UTF16\nSQLITE_API const void *sqlite3_column_text16(sqlite3_stmt *pStmt, int i){\n  const void *val = sqlite3_value_text16( columnMem(pStmt,i) );\n  columnMallocFailure(pStmt);\n  return val;\n}\n#endif /* SQLITE_OMIT_UTF16 */\nSQLITE_API int sqlite3_column_type(sqlite3_stmt *pStmt, int i){\n  int iType = sqlite3_value_type( columnMem(pStmt,i) );\n  columnMallocFailure(pStmt);\n  return iType;\n}\n\n/*\n** Convert the N-th element of pStmt->pColName[] into a string using\n** xFunc() then return that string.  If N is out of range, return 0.\n**\n** There are up to 5 names for each column.  useType determines which\n** name is returned.  Here are the names:\n**\n**    0      The column name as it should be displayed for output\n**    1      The datatype name for the column\n**    2      The name of the database that the column derives from\n**    3      The name of the table that the column derives from\n**    4      The name of the table column that the result column derives from\n**\n** If the result is not a simple column reference (if it is an expression\n** or a constant) then useTypes 2, 3, and 4 return NULL.\n*/\nstatic const void *columnName(\n  sqlite3_stmt *pStmt,\n  int N,\n  const void *(*xFunc)(Mem*),\n  int useType\n){\n  const void *ret;\n  Vdbe *p;\n  int n;\n  sqlite3 *db;\n#ifdef SQLITE_ENABLE_API_ARMOR\n  if( pStmt==0 ){\n    (void)SQLITE_MISUSE_BKPT;\n    return 0;\n  }\n#endif\n  ret = 0;\n  p = (Vdbe *)pStmt;\n  db = p->db;\n  assert( db!=0 );\n  n = sqlite3_column_count(pStmt);\n  if( N<n && N>=0 ){\n    N += useType*n;\n    sqlite3_mutex_enter(db->mutex);\n    assert( db->mallocFailed==0 );\n    ret = xFunc(&p->aColName[N]);\n     /* A malloc may have failed inside of the xFunc() call. If this\n    ** is the case, clear the mallocFailed flag and return NULL.\n    */\n    if( db->mallocFailed ){\n      sqlite3OomClear(db);\n      ret = 0;\n    }\n    sqlite3_mutex_leave(db->mutex);\n  }\n  return ret;\n}\n\n/*\n** Return the name of the Nth column of the result set returned by SQL\n** statement pStmt.\n*/\nSQLITE_API const char *sqlite3_column_name(sqlite3_stmt *pStmt, int N){\n  return columnName(\n      pStmt, N, (const void*(*)(Mem*))sqlite3_value_text, COLNAME_NAME);\n}\n#ifndef SQLITE_OMIT_UTF16\nSQLITE_API const void *sqlite3_column_name16(sqlite3_stmt *pStmt, int N){\n  return columnName(\n      pStmt, N, (const void*(*)(Mem*))sqlite3_value_text16, COLNAME_NAME);\n}\n#endif\n\n/*\n** Constraint:  If you have ENABLE_COLUMN_METADATA then you must\n** not define OMIT_DECLTYPE.\n*/\n#if defined(SQLITE_OMIT_DECLTYPE) && defined(SQLITE_ENABLE_COLUMN_METADATA)\n# error \"Must not define both SQLITE_OMIT_DECLTYPE \\\n         and SQLITE_ENABLE_COLUMN_METADATA\"\n#endif\n\n#ifndef SQLITE_OMIT_DECLTYPE\n/*\n** Return the column declaration type (if applicable) of the 'i'th column\n** of the result set of SQL statement pStmt.\n*/\nSQLITE_API const char *sqlite3_column_decltype(sqlite3_stmt *pStmt, int N){\n  return columnName(\n      pStmt, N, (const void*(*)(Mem*))sqlite3_value_text, COLNAME_DECLTYPE);\n}\n#ifndef SQLITE_OMIT_UTF16\nSQLITE_API const void *sqlite3_column_decltype16(sqlite3_stmt *pStmt, int N){\n  return columnName(\n      pStmt, N, (const void*(*)(Mem*))sqlite3_value_text16, COLNAME_DECLTYPE);\n}\n#endif /* SQLITE_OMIT_UTF16 */\n#endif /* SQLITE_OMIT_DECLTYPE */\n\n#ifdef SQLITE_ENABLE_COLUMN_METADATA\n/*\n** Return the name of the database from which a result column derives.\n** NULL is returned if the result column is an expression or constant or\n** anything else which is not an unambiguous reference to a database column.\n*/\nSQLITE_API const char *sqlite3_column_database_name(sqlite3_stmt *pStmt, int N){\n  return columnName(\n      pStmt, N, (const void*(*)(Mem*))sqlite3_value_text, COLNAME_DATABASE);\n}\n#ifndef SQLITE_OMIT_UTF16\nSQLITE_API const void *sqlite3_column_database_name16(sqlite3_stmt *pStmt, int N){\n  return columnName(\n      pStmt, N, (const void*(*)(Mem*))sqlite3_value_text16, COLNAME_DATABASE);\n}\n#endif /* SQLITE_OMIT_UTF16 */\n\n/*\n** Return the name of the table from which a result column derives.\n** NULL is returned if the result column is an expression or constant or\n** anything else which is not an unambiguous reference to a database column.\n*/\nSQLITE_API const char *sqlite3_column_table_name(sqlite3_stmt *pStmt, int N){\n  return columnName(\n      pStmt, N, (const void*(*)(Mem*))sqlite3_value_text, COLNAME_TABLE);\n}\n#ifndef SQLITE_OMIT_UTF16\nSQLITE_API const void *sqlite3_column_table_name16(sqlite3_stmt *pStmt, int N){\n  return columnName(\n      pStmt, N, (const void*(*)(Mem*))sqlite3_value_text16, COLNAME_TABLE);\n}\n#endif /* SQLITE_OMIT_UTF16 */\n\n/*\n** Return the name of the table column from which a result column derives.\n** NULL is returned if the result column is an expression or constant or\n** anything else which is not an unambiguous reference to a database column.\n*/\nSQLITE_API const char *sqlite3_column_origin_name(sqlite3_stmt *pStmt, int N){\n  return columnName(\n      pStmt, N, (const void*(*)(Mem*))sqlite3_value_text, COLNAME_COLUMN);\n}\n#ifndef SQLITE_OMIT_UTF16\nSQLITE_API const void *sqlite3_column_origin_name16(sqlite3_stmt *pStmt, int N){\n  return columnName(\n      pStmt, N, (const void*(*)(Mem*))sqlite3_value_text16, COLNAME_COLUMN);\n}\n#endif /* SQLITE_OMIT_UTF16 */\n#endif /* SQLITE_ENABLE_COLUMN_METADATA */\n\n\n/******************************* sqlite3_bind_  ***************************\n** \n** Routines used to attach values to wildcards in a compiled SQL statement.\n*/\n/*\n** Unbind the value bound to variable i in virtual machine p. This is the \n** the same as binding a NULL value to the column. If the \"i\" parameter is\n** out of range, then SQLITE_RANGE is returned. Othewise SQLITE_OK.\n**\n** A successful evaluation of this routine acquires the mutex on p.\n** the mutex is released if any kind of error occurs.\n**\n** The error code stored in database p->db is overwritten with the return\n** value in any case.\n*/\nstatic int vdbeUnbind(Vdbe *p, int i){\n  Mem *pVar;\n  if( vdbeSafetyNotNull(p) ){\n    return SQLITE_MISUSE_BKPT;\n  }\n  sqlite3_mutex_enter(p->db->mutex);\n  if( p->magic!=VDBE_MAGIC_RUN || p->pc>=0 ){\n    sqlite3Error(p->db, SQLITE_MISUSE);\n    sqlite3_mutex_leave(p->db->mutex);\n    sqlite3_log(SQLITE_MISUSE, \n        \"bind on a busy prepared statement: [%s]\", p->zSql);\n    return SQLITE_MISUSE_BKPT;\n  }\n  if( i<1 || i>p->nVar ){\n    sqlite3Error(p->db, SQLITE_RANGE);\n    sqlite3_mutex_leave(p->db->mutex);\n    return SQLITE_RANGE;\n  }\n  i--;\n  pVar = &p->aVar[i];\n  sqlite3VdbeMemRelease(pVar);\n  pVar->flags = MEM_Null;\n  sqlite3Error(p->db, SQLITE_OK);\n\n  /* If the bit corresponding to this variable in Vdbe.expmask is set, then \n  ** binding a new value to this variable invalidates the current query plan.\n  **\n  ** IMPLEMENTATION-OF: R-48440-37595 If the specific value bound to host\n  ** parameter in the WHERE clause might influence the choice of query plan\n  ** for a statement, then the statement will be automatically recompiled,\n  ** as if there had been a schema change, on the first sqlite3_step() call\n  ** following any change to the bindings of that parameter.\n  */\n  assert( (p->prepFlags & SQLITE_PREPARE_SAVESQL)!=0 || p->expmask==0 );\n  if( p->expmask!=0 && (p->expmask & (i>=31 ? 0x80000000 : (u32)1<<i))!=0 ){\n    p->expired = 1;\n  }\n  return SQLITE_OK;\n}\n\n/*\n** Bind a text or BLOB value.\n*/\nstatic int bindText(\n  sqlite3_stmt *pStmt,   /* The statement to bind against */\n  int i,                 /* Index of the parameter to bind */\n  const void *zData,     /* Pointer to the data to be bound */\n  int nData,             /* Number of bytes of data to be bound */\n  void (*xDel)(void*),   /* Destructor for the data */\n  u8 encoding            /* Encoding for the data */\n){\n  Vdbe *p = (Vdbe *)pStmt;\n  Mem *pVar;\n  int rc;\n\n  rc = vdbeUnbind(p, i);\n  if( rc==SQLITE_OK ){\n    if( zData!=0 ){\n      pVar = &p->aVar[i-1];\n      rc = sqlite3VdbeMemSetStr(pVar, zData, nData, encoding, xDel);\n      if( rc==SQLITE_OK && encoding!=0 ){\n        rc = sqlite3VdbeChangeEncoding(pVar, ENC(p->db));\n      }\n      if( rc ){\n        sqlite3Error(p->db, rc);\n        rc = sqlite3ApiExit(p->db, rc);\n      }\n    }\n    sqlite3_mutex_leave(p->db->mutex);\n  }else if( xDel!=SQLITE_STATIC && xDel!=SQLITE_TRANSIENT ){\n    xDel((void*)zData);\n  }\n  return rc;\n}\n\n\n/*\n** Bind a blob value to an SQL statement variable.\n*/\nSQLITE_API int sqlite3_bind_blob(\n  sqlite3_stmt *pStmt, \n  int i, \n  const void *zData, \n  int nData, \n  void (*xDel)(void*)\n){\n#ifdef SQLITE_ENABLE_API_ARMOR\n  if( nData<0 ) return SQLITE_MISUSE_BKPT;\n#endif\n  return bindText(pStmt, i, zData, nData, xDel, 0);\n}\nSQLITE_API int sqlite3_bind_blob64(\n  sqlite3_stmt *pStmt, \n  int i, \n  const void *zData, \n  sqlite3_uint64 nData, \n  void (*xDel)(void*)\n){\n  assert( xDel!=SQLITE_DYNAMIC );\n  if( nData>0x7fffffff ){\n    return invokeValueDestructor(zData, xDel, 0);\n  }else{\n    return bindText(pStmt, i, zData, (int)nData, xDel, 0);\n  }\n}\nSQLITE_API int sqlite3_bind_double(sqlite3_stmt *pStmt, int i, double rValue){\n  int rc;\n  Vdbe *p = (Vdbe *)pStmt;\n  rc = vdbeUnbind(p, i);\n  if( rc==SQLITE_OK ){\n    sqlite3VdbeMemSetDouble(&p->aVar[i-1], rValue);\n    sqlite3_mutex_leave(p->db->mutex);\n  }\n  return rc;\n}\nSQLITE_API int sqlite3_bind_int(sqlite3_stmt *p, int i, int iValue){\n  return sqlite3_bind_int64(p, i, (i64)iValue);\n}\nSQLITE_API int sqlite3_bind_int64(sqlite3_stmt *pStmt, int i, sqlite_int64 iValue){\n  int rc;\n  Vdbe *p = (Vdbe *)pStmt;\n  rc = vdbeUnbind(p, i);\n  if( rc==SQLITE_OK ){\n    sqlite3VdbeMemSetInt64(&p->aVar[i-1], iValue);\n    sqlite3_mutex_leave(p->db->mutex);\n  }\n  return rc;\n}\nSQLITE_API int sqlite3_bind_null(sqlite3_stmt *pStmt, int i){\n  int rc;\n  Vdbe *p = (Vdbe*)pStmt;\n  rc = vdbeUnbind(p, i);\n  if( rc==SQLITE_OK ){\n    sqlite3_mutex_leave(p->db->mutex);\n  }\n  return rc;\n}\nSQLITE_API int sqlite3_bind_pointer(\n  sqlite3_stmt *pStmt,\n  int i,\n  void *pPtr,\n  const char *zPTtype,\n  void (*xDestructor)(void*)\n){\n  int rc;\n  Vdbe *p = (Vdbe*)pStmt;\n  rc = vdbeUnbind(p, i);\n  if( rc==SQLITE_OK ){\n    sqlite3VdbeMemSetPointer(&p->aVar[i-1], pPtr, zPTtype, xDestructor);\n    sqlite3_mutex_leave(p->db->mutex);\n  }else if( xDestructor ){\n    xDestructor(pPtr);\n  }\n  return rc;\n}\nSQLITE_API int sqlite3_bind_text( \n  sqlite3_stmt *pStmt, \n  int i, \n  const char *zData, \n  int nData, \n  void (*xDel)(void*)\n){\n  return bindText(pStmt, i, zData, nData, xDel, SQLITE_UTF8);\n}\nSQLITE_API int sqlite3_bind_text64( \n  sqlite3_stmt *pStmt, \n  int i, \n  const char *zData, \n  sqlite3_uint64 nData, \n  void (*xDel)(void*),\n  unsigned char enc\n){\n  assert( xDel!=SQLITE_DYNAMIC );\n  if( nData>0x7fffffff ){\n    return invokeValueDestructor(zData, xDel, 0);\n  }else{\n    if( enc==SQLITE_UTF16 ) enc = SQLITE_UTF16NATIVE;\n    return bindText(pStmt, i, zData, (int)nData, xDel, enc);\n  }\n}\n#ifndef SQLITE_OMIT_UTF16\nSQLITE_API int sqlite3_bind_text16(\n  sqlite3_stmt *pStmt, \n  int i, \n  const void *zData, \n  int nData, \n  void (*xDel)(void*)\n){\n  return bindText(pStmt, i, zData, nData, xDel, SQLITE_UTF16NATIVE);\n}\n#endif /* SQLITE_OMIT_UTF16 */\nSQLITE_API int sqlite3_bind_value(sqlite3_stmt *pStmt, int i, const sqlite3_value *pValue){\n  int rc;\n  switch( sqlite3_value_type((sqlite3_value*)pValue) ){\n    case SQLITE_INTEGER: {\n      rc = sqlite3_bind_int64(pStmt, i, pValue->u.i);\n      break;\n    }\n    case SQLITE_FLOAT: {\n      rc = sqlite3_bind_double(pStmt, i, pValue->u.r);\n      break;\n    }\n    case SQLITE_BLOB: {\n      if( pValue->flags & MEM_Zero ){\n        rc = sqlite3_bind_zeroblob(pStmt, i, pValue->u.nZero);\n      }else{\n        rc = sqlite3_bind_blob(pStmt, i, pValue->z, pValue->n,SQLITE_TRANSIENT);\n      }\n      break;\n    }\n    case SQLITE_TEXT: {\n      rc = bindText(pStmt,i,  pValue->z, pValue->n, SQLITE_TRANSIENT,\n                              pValue->enc);\n      break;\n    }\n    default: {\n      rc = sqlite3_bind_null(pStmt, i);\n      break;\n    }\n  }\n  return rc;\n}\nSQLITE_API int sqlite3_bind_zeroblob(sqlite3_stmt *pStmt, int i, int n){\n  int rc;\n  Vdbe *p = (Vdbe *)pStmt;\n  rc = vdbeUnbind(p, i);\n  if( rc==SQLITE_OK ){\n    sqlite3VdbeMemSetZeroBlob(&p->aVar[i-1], n);\n    sqlite3_mutex_leave(p->db->mutex);\n  }\n  return rc;\n}\nSQLITE_API int sqlite3_bind_zeroblob64(sqlite3_stmt *pStmt, int i, sqlite3_uint64 n){\n  int rc;\n  Vdbe *p = (Vdbe *)pStmt;\n  sqlite3_mutex_enter(p->db->mutex);\n  if( n>(u64)p->db->aLimit[SQLITE_LIMIT_LENGTH] ){\n    rc = SQLITE_TOOBIG;\n  }else{\n    assert( (n & 0x7FFFFFFF)==n );\n    rc = sqlite3_bind_zeroblob(pStmt, i, n);\n  }\n  rc = sqlite3ApiExit(p->db, rc);\n  sqlite3_mutex_leave(p->db->mutex);\n  return rc;\n}\n\n/*\n** Return the number of wildcards that can be potentially bound to.\n** This routine is added to support DBD::SQLite.  \n*/\nSQLITE_API int sqlite3_bind_parameter_count(sqlite3_stmt *pStmt){\n  Vdbe *p = (Vdbe*)pStmt;\n  return p ? p->nVar : 0;\n}\n\n/*\n** Return the name of a wildcard parameter.  Return NULL if the index\n** is out of range or if the wildcard is unnamed.\n**\n** The result is always UTF-8.\n*/\nSQLITE_API const char *sqlite3_bind_parameter_name(sqlite3_stmt *pStmt, int i){\n  Vdbe *p = (Vdbe*)pStmt;\n  if( p==0 ) return 0;\n  return sqlite3VListNumToName(p->pVList, i);\n}\n\n/*\n** Given a wildcard parameter name, return the index of the variable\n** with that name.  If there is no variable with the given name,\n** return 0.\n*/\nSQLITE_PRIVATE int sqlite3VdbeParameterIndex(Vdbe *p, const char *zName, int nName){\n  if( p==0 || zName==0 ) return 0;\n  return sqlite3VListNameToNum(p->pVList, zName, nName);\n}\nSQLITE_API int sqlite3_bind_parameter_index(sqlite3_stmt *pStmt, const char *zName){\n  return sqlite3VdbeParameterIndex((Vdbe*)pStmt, zName, sqlite3Strlen30(zName));\n}\n\n/*\n** Transfer all bindings from the first statement over to the second.\n*/\nSQLITE_PRIVATE int sqlite3TransferBindings(sqlite3_stmt *pFromStmt, sqlite3_stmt *pToStmt){\n  Vdbe *pFrom = (Vdbe*)pFromStmt;\n  Vdbe *pTo = (Vdbe*)pToStmt;\n  int i;\n  assert( pTo->db==pFrom->db );\n  assert( pTo->nVar==pFrom->nVar );\n  sqlite3_mutex_enter(pTo->db->mutex);\n  for(i=0; i<pFrom->nVar; i++){\n    sqlite3VdbeMemMove(&pTo->aVar[i], &pFrom->aVar[i]);\n  }\n  sqlite3_mutex_leave(pTo->db->mutex);\n  return SQLITE_OK;\n}\n\n#ifndef SQLITE_OMIT_DEPRECATED\n/*\n** Deprecated external interface.  Internal/core SQLite code\n** should call sqlite3TransferBindings.\n**\n** It is misuse to call this routine with statements from different\n** database connections.  But as this is a deprecated interface, we\n** will not bother to check for that condition.\n**\n** If the two statements contain a different number of bindings, then\n** an SQLITE_ERROR is returned.  Nothing else can go wrong, so otherwise\n** SQLITE_OK is returned.\n*/\nSQLITE_API int sqlite3_transfer_bindings(sqlite3_stmt *pFromStmt, sqlite3_stmt *pToStmt){\n  Vdbe *pFrom = (Vdbe*)pFromStmt;\n  Vdbe *pTo = (Vdbe*)pToStmt;\n  if( pFrom->nVar!=pTo->nVar ){\n    return SQLITE_ERROR;\n  }\n  assert( (pTo->prepFlags & SQLITE_PREPARE_SAVESQL)!=0 || pTo->expmask==0 );\n  if( pTo->expmask ){\n    pTo->expired = 1;\n  }\n  assert( (pFrom->prepFlags & SQLITE_PREPARE_SAVESQL)!=0 || pFrom->expmask==0 );\n  if( pFrom->expmask ){\n    pFrom->expired = 1;\n  }\n  return sqlite3TransferBindings(pFromStmt, pToStmt);\n}\n#endif\n\n/*\n** Return the sqlite3* database handle to which the prepared statement given\n** in the argument belongs.  This is the same database handle that was\n** the first argument to the sqlite3_prepare() that was used to create\n** the statement in the first place.\n*/\nSQLITE_API sqlite3 *sqlite3_db_handle(sqlite3_stmt *pStmt){\n  return pStmt ? ((Vdbe*)pStmt)->db : 0;\n}\n\n/*\n** Return true if the prepared statement is guaranteed to not modify the\n** database.\n*/\nSQLITE_API int sqlite3_stmt_readonly(sqlite3_stmt *pStmt){\n  return pStmt ? ((Vdbe*)pStmt)->readOnly : 1;\n}\n\n/*\n** Return true if the prepared statement is in need of being reset.\n*/\nSQLITE_API int sqlite3_stmt_busy(sqlite3_stmt *pStmt){\n  Vdbe *v = (Vdbe*)pStmt;\n  return v!=0 && v->magic==VDBE_MAGIC_RUN && v->pc>=0;\n}\n\n/*\n** Return a pointer to the next prepared statement after pStmt associated\n** with database connection pDb.  If pStmt is NULL, return the first\n** prepared statement for the database connection.  Return NULL if there\n** are no more.\n*/\nSQLITE_API sqlite3_stmt *sqlite3_next_stmt(sqlite3 *pDb, sqlite3_stmt *pStmt){\n  sqlite3_stmt *pNext;\n#ifdef SQLITE_ENABLE_API_ARMOR\n  if( !sqlite3SafetyCheckOk(pDb) ){\n    (void)SQLITE_MISUSE_BKPT;\n    return 0;\n  }\n#endif\n  sqlite3_mutex_enter(pDb->mutex);\n  if( pStmt==0 ){\n    pNext = (sqlite3_stmt*)pDb->pVdbe;\n  }else{\n    pNext = (sqlite3_stmt*)((Vdbe*)pStmt)->pNext;\n  }\n  sqlite3_mutex_leave(pDb->mutex);\n  return pNext;\n}\n\n/*\n** Return the value of a status counter for a prepared statement\n*/\nSQLITE_API int sqlite3_stmt_status(sqlite3_stmt *pStmt, int op, int resetFlag){\n  Vdbe *pVdbe = (Vdbe*)pStmt;\n  u32 v;\n#ifdef SQLITE_ENABLE_API_ARMOR\n  if( !pStmt ){\n    (void)SQLITE_MISUSE_BKPT;\n    return 0;\n  }\n#endif\n  if( op==SQLITE_STMTSTATUS_MEMUSED ){\n    sqlite3 *db = pVdbe->db;\n    sqlite3_mutex_enter(db->mutex);\n    v = 0;\n    db->pnBytesFreed = (int*)&v;\n    sqlite3VdbeClearObject(db, pVdbe);\n    sqlite3DbFree(db, pVdbe);\n    db->pnBytesFreed = 0;\n    sqlite3_mutex_leave(db->mutex);\n  }else{\n    v = pVdbe->aCounter[op];\n    if( resetFlag ) pVdbe->aCounter[op] = 0;\n  }\n  return (int)v;\n}\n\n/*\n** Return the SQL associated with a prepared statement\n*/\nSQLITE_API const char *sqlite3_sql(sqlite3_stmt *pStmt){\n  Vdbe *p = (Vdbe *)pStmt;\n  return p ? p->zSql : 0;\n}\n\n/*\n** Return the SQL associated with a prepared statement with\n** bound parameters expanded.  Space to hold the returned string is\n** obtained from sqlite3_malloc().  The caller is responsible for\n** freeing the returned string by passing it to sqlite3_free().\n**\n** The SQLITE_TRACE_SIZE_LIMIT puts an upper bound on the size of\n** expanded bound parameters.\n*/\nSQLITE_API char *sqlite3_expanded_sql(sqlite3_stmt *pStmt){\n#ifdef SQLITE_OMIT_TRACE\n  return 0;\n#else\n  char *z = 0;\n  const char *zSql = sqlite3_sql(pStmt);\n  if( zSql ){\n    Vdbe *p = (Vdbe *)pStmt;\n    sqlite3_mutex_enter(p->db->mutex);\n    z = sqlite3VdbeExpandSql(p, zSql);\n    sqlite3_mutex_leave(p->db->mutex);\n  }\n  return z;\n#endif\n}\n\n#ifdef SQLITE_ENABLE_PREUPDATE_HOOK\n/*\n** Allocate and populate an UnpackedRecord structure based on the serialized\n** record in nKey/pKey. Return a pointer to the new UnpackedRecord structure\n** if successful, or a NULL pointer if an OOM error is encountered.\n*/\nstatic UnpackedRecord *vdbeUnpackRecord(\n  KeyInfo *pKeyInfo, \n  int nKey, \n  const void *pKey\n){\n  UnpackedRecord *pRet;           /* Return value */\n\n  pRet = sqlite3VdbeAllocUnpackedRecord(pKeyInfo);\n  if( pRet ){\n    memset(pRet->aMem, 0, sizeof(Mem)*(pKeyInfo->nKeyField+1));\n    sqlite3VdbeRecordUnpack(pKeyInfo, nKey, pKey, pRet);\n  }\n  return pRet;\n}\n\n/*\n** This function is called from within a pre-update callback to retrieve\n** a field of the row currently being updated or deleted.\n*/\nSQLITE_API int sqlite3_preupdate_old(sqlite3 *db, int iIdx, sqlite3_value **ppValue){\n  PreUpdate *p = db->pPreUpdate;\n  Mem *pMem;\n  int rc = SQLITE_OK;\n\n  /* Test that this call is being made from within an SQLITE_DELETE or\n  ** SQLITE_UPDATE pre-update callback, and that iIdx is within range. */\n  if( !p || p->op==SQLITE_INSERT ){\n    rc = SQLITE_MISUSE_BKPT;\n    goto preupdate_old_out;\n  }\n  if( p->pPk ){\n    iIdx = sqlite3ColumnOfIndex(p->pPk, iIdx);\n  }\n  if( iIdx>=p->pCsr->nField || iIdx<0 ){\n    rc = SQLITE_RANGE;\n    goto preupdate_old_out;\n  }\n\n  /* If the old.* record has not yet been loaded into memory, do so now. */\n  if( p->pUnpacked==0 ){\n    u32 nRec;\n    u8 *aRec;\n\n    nRec = sqlite3BtreePayloadSize(p->pCsr->uc.pCursor);\n    aRec = sqlite3DbMallocRaw(db, nRec);\n    if( !aRec ) goto preupdate_old_out;\n    rc = sqlite3BtreePayload(p->pCsr->uc.pCursor, 0, nRec, aRec);\n    if( rc==SQLITE_OK ){\n      p->pUnpacked = vdbeUnpackRecord(&p->keyinfo, nRec, aRec);\n      if( !p->pUnpacked ) rc = SQLITE_NOMEM;\n    }\n    if( rc!=SQLITE_OK ){\n      sqlite3DbFree(db, aRec);\n      goto preupdate_old_out;\n    }\n    p->aRecord = aRec;\n  }\n\n  pMem = *ppValue = &p->pUnpacked->aMem[iIdx];\n  if( iIdx==p->pTab->iPKey ){\n    sqlite3VdbeMemSetInt64(pMem, p->iKey1);\n  }else if( iIdx>=p->pUnpacked->nField ){\n    *ppValue = (sqlite3_value *)columnNullValue();\n  }else if( p->pTab->aCol[iIdx].affinity==SQLITE_AFF_REAL ){\n    if( pMem->flags & MEM_Int ){\n      sqlite3VdbeMemRealify(pMem);\n    }\n  }\n\n preupdate_old_out:\n  sqlite3Error(db, rc);\n  return sqlite3ApiExit(db, rc);\n}\n#endif /* SQLITE_ENABLE_PREUPDATE_HOOK */\n\n#ifdef SQLITE_ENABLE_PREUPDATE_HOOK\n/*\n** This function is called from within a pre-update callback to retrieve\n** the number of columns in the row being updated, deleted or inserted.\n*/\nSQLITE_API int sqlite3_preupdate_count(sqlite3 *db){\n  PreUpdate *p = db->pPreUpdate;\n  return (p ? p->keyinfo.nKeyField : 0);\n}\n#endif /* SQLITE_ENABLE_PREUPDATE_HOOK */\n\n#ifdef SQLITE_ENABLE_PREUPDATE_HOOK\n/*\n** This function is designed to be called from within a pre-update callback\n** only. It returns zero if the change that caused the callback was made\n** immediately by a user SQL statement. Or, if the change was made by a\n** trigger program, it returns the number of trigger programs currently\n** on the stack (1 for a top-level trigger, 2 for a trigger fired by a \n** top-level trigger etc.).\n**\n** For the purposes of the previous paragraph, a foreign key CASCADE, SET NULL\n** or SET DEFAULT action is considered a trigger.\n*/\nSQLITE_API int sqlite3_preupdate_depth(sqlite3 *db){\n  PreUpdate *p = db->pPreUpdate;\n  return (p ? p->v->nFrame : 0);\n}\n#endif /* SQLITE_ENABLE_PREUPDATE_HOOK */\n\n#ifdef SQLITE_ENABLE_PREUPDATE_HOOK\n/*\n** This function is called from within a pre-update callback to retrieve\n** a field of the row currently being updated or inserted.\n*/\nSQLITE_API int sqlite3_preupdate_new(sqlite3 *db, int iIdx, sqlite3_value **ppValue){\n  PreUpdate *p = db->pPreUpdate;\n  int rc = SQLITE_OK;\n  Mem *pMem;\n\n  if( !p || p->op==SQLITE_DELETE ){\n    rc = SQLITE_MISUSE_BKPT;\n    goto preupdate_new_out;\n  }\n  if( p->pPk && p->op!=SQLITE_UPDATE ){\n    iIdx = sqlite3ColumnOfIndex(p->pPk, iIdx);\n  }\n  if( iIdx>=p->pCsr->nField || iIdx<0 ){\n    rc = SQLITE_RANGE;\n    goto preupdate_new_out;\n  }\n\n  if( p->op==SQLITE_INSERT ){\n    /* For an INSERT, memory cell p->iNewReg contains the serialized record\n    ** that is being inserted. Deserialize it. */\n    UnpackedRecord *pUnpack = p->pNewUnpacked;\n    if( !pUnpack ){\n      Mem *pData = &p->v->aMem[p->iNewReg];\n      rc = ExpandBlob(pData);\n      if( rc!=SQLITE_OK ) goto preupdate_new_out;\n      pUnpack = vdbeUnpackRecord(&p->keyinfo, pData->n, pData->z);\n      if( !pUnpack ){\n        rc = SQLITE_NOMEM;\n        goto preupdate_new_out;\n      }\n      p->pNewUnpacked = pUnpack;\n    }\n    pMem = &pUnpack->aMem[iIdx];\n    if( iIdx==p->pTab->iPKey ){\n      sqlite3VdbeMemSetInt64(pMem, p->iKey2);\n    }else if( iIdx>=pUnpack->nField ){\n      pMem = (sqlite3_value *)columnNullValue();\n    }\n  }else{\n    /* For an UPDATE, memory cell (p->iNewReg+1+iIdx) contains the required\n    ** value. Make a copy of the cell contents and return a pointer to it.\n    ** It is not safe to return a pointer to the memory cell itself as the\n    ** caller may modify the value text encoding.\n    */\n    assert( p->op==SQLITE_UPDATE );\n    if( !p->aNew ){\n      p->aNew = (Mem *)sqlite3DbMallocZero(db, sizeof(Mem) * p->pCsr->nField);\n      if( !p->aNew ){\n        rc = SQLITE_NOMEM;\n        goto preupdate_new_out;\n      }\n    }\n    assert( iIdx>=0 && iIdx<p->pCsr->nField );\n    pMem = &p->aNew[iIdx];\n    if( pMem->flags==0 ){\n      if( iIdx==p->pTab->iPKey ){\n        sqlite3VdbeMemSetInt64(pMem, p->iKey2);\n      }else{\n        rc = sqlite3VdbeMemCopy(pMem, &p->v->aMem[p->iNewReg+1+iIdx]);\n        if( rc!=SQLITE_OK ) goto preupdate_new_out;\n      }\n    }\n  }\n  *ppValue = pMem;\n\n preupdate_new_out:\n  sqlite3Error(db, rc);\n  return sqlite3ApiExit(db, rc);\n}\n#endif /* SQLITE_ENABLE_PREUPDATE_HOOK */\n\n#ifdef SQLITE_ENABLE_STMT_SCANSTATUS\n/*\n** Return status data for a single loop within query pStmt.\n*/\nSQLITE_API int sqlite3_stmt_scanstatus(\n  sqlite3_stmt *pStmt,            /* Prepared statement being queried */\n  int idx,                        /* Index of loop to report on */\n  int iScanStatusOp,              /* Which metric to return */\n  void *pOut                      /* OUT: Write the answer here */\n){\n  Vdbe *p = (Vdbe*)pStmt;\n  ScanStatus *pScan;\n  if( idx<0 || idx>=p->nScan ) return 1;\n  pScan = &p->aScan[idx];\n  switch( iScanStatusOp ){\n    case SQLITE_SCANSTAT_NLOOP: {\n      *(sqlite3_int64*)pOut = p->anExec[pScan->addrLoop];\n      break;\n    }\n    case SQLITE_SCANSTAT_NVISIT: {\n      *(sqlite3_int64*)pOut = p->anExec[pScan->addrVisit];\n      break;\n    }\n    case SQLITE_SCANSTAT_EST: {\n      double r = 1.0;\n      LogEst x = pScan->nEst;\n      while( x<100 ){\n        x += 10;\n        r *= 0.5;\n      }\n      *(double*)pOut = r*sqlite3LogEstToInt(x);\n      break;\n    }\n    case SQLITE_SCANSTAT_NAME: {\n      *(const char**)pOut = pScan->zName;\n      break;\n    }\n    case SQLITE_SCANSTAT_EXPLAIN: {\n      if( pScan->addrExplain ){\n        *(const char**)pOut = p->aOp[ pScan->addrExplain ].p4.z;\n      }else{\n        *(const char**)pOut = 0;\n      }\n      break;\n    }\n    case SQLITE_SCANSTAT_SELECTID: {\n      if( pScan->addrExplain ){\n        *(int*)pOut = p->aOp[ pScan->addrExplain ].p1;\n      }else{\n        *(int*)pOut = -1;\n      }\n      break;\n    }\n    default: {\n      return 1;\n    }\n  }\n  return 0;\n}\n\n/*\n** Zero all counters associated with the sqlite3_stmt_scanstatus() data.\n*/\nSQLITE_API void sqlite3_stmt_scanstatus_reset(sqlite3_stmt *pStmt){\n  Vdbe *p = (Vdbe*)pStmt;\n  memset(p->anExec, 0, p->nOp * sizeof(i64));\n}\n#endif /* SQLITE_ENABLE_STMT_SCANSTATUS */\n\n/************** End of vdbeapi.c *********************************************/\n/************** Begin file vdbetrace.c ***************************************/\n/*\n** 2009 November 25\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n*************************************************************************\n**\n** This file contains code used to insert the values of host parameters\n** (aka \"wildcards\") into the SQL text output by sqlite3_trace().\n**\n** The Vdbe parse-tree explainer is also found here.\n*/\n/* #include \"sqliteInt.h\" */\n/* #include \"vdbeInt.h\" */\n\n#ifndef SQLITE_OMIT_TRACE\n\n/*\n** zSql is a zero-terminated string of UTF-8 SQL text.  Return the number of\n** bytes in this text up to but excluding the first character in\n** a host parameter.  If the text contains no host parameters, return\n** the total number of bytes in the text.\n*/\nstatic int findNextHostParameter(const char *zSql, int *pnToken){\n  int tokenType;\n  int nTotal = 0;\n  int n;\n\n  *pnToken = 0;\n  while( zSql[0] ){\n    n = sqlite3GetToken((u8*)zSql, &tokenType);\n    assert( n>0 && tokenType!=TK_ILLEGAL );\n    if( tokenType==TK_VARIABLE ){\n      *pnToken = n;\n      break;\n    }\n    nTotal += n;\n    zSql += n;\n  }\n  return nTotal;\n}\n\n/*\n** This function returns a pointer to a nul-terminated string in memory\n** obtained from sqlite3DbMalloc(). If sqlite3.nVdbeExec is 1, then the\n** string contains a copy of zRawSql but with host parameters expanded to \n** their current bindings. Or, if sqlite3.nVdbeExec is greater than 1, \n** then the returned string holds a copy of zRawSql with \"-- \" prepended\n** to each line of text.\n**\n** If the SQLITE_TRACE_SIZE_LIMIT macro is defined to an integer, then\n** then long strings and blobs are truncated to that many bytes.  This\n** can be used to prevent unreasonably large trace strings when dealing\n** with large (multi-megabyte) strings and blobs.\n**\n** The calling function is responsible for making sure the memory returned\n** is eventually freed.\n**\n** ALGORITHM:  Scan the input string looking for host parameters in any of\n** these forms:  ?, ?N, $A, @A, :A.  Take care to avoid text within\n** string literals, quoted identifier names, and comments.  For text forms,\n** the host parameter index is found by scanning the prepared\n** statement for the corresponding OP_Variable opcode.  Once the host\n** parameter index is known, locate the value in p->aVar[].  Then render\n** the value as a literal in place of the host parameter name.\n*/\nSQLITE_PRIVATE char *sqlite3VdbeExpandSql(\n  Vdbe *p,                 /* The prepared statement being evaluated */\n  const char *zRawSql      /* Raw text of the SQL statement */\n){\n  sqlite3 *db;             /* The database connection */\n  int idx = 0;             /* Index of a host parameter */\n  int nextIndex = 1;       /* Index of next ? host parameter */\n  int n;                   /* Length of a token prefix */\n  int nToken;              /* Length of the parameter token */\n  int i;                   /* Loop counter */\n  Mem *pVar;               /* Value of a host parameter */\n  StrAccum out;            /* Accumulate the output here */\n#ifndef SQLITE_OMIT_UTF16\n  Mem utf8;                /* Used to convert UTF16 into UTF8 for display */\n#endif\n  char zBase[100];         /* Initial working space */\n\n  db = p->db;\n  sqlite3StrAccumInit(&out, 0, zBase, sizeof(zBase), \n                      db->aLimit[SQLITE_LIMIT_LENGTH]);\n  if( db->nVdbeExec>1 ){\n    while( *zRawSql ){\n      const char *zStart = zRawSql;\n      while( *(zRawSql++)!='\\n' && *zRawSql );\n      sqlite3StrAccumAppend(&out, \"-- \", 3);\n      assert( (zRawSql - zStart) > 0 );\n      sqlite3StrAccumAppend(&out, zStart, (int)(zRawSql-zStart));\n    }\n  }else if( p->nVar==0 ){\n    sqlite3StrAccumAppend(&out, zRawSql, sqlite3Strlen30(zRawSql));\n  }else{\n    while( zRawSql[0] ){\n      n = findNextHostParameter(zRawSql, &nToken);\n      assert( n>0 );\n      sqlite3StrAccumAppend(&out, zRawSql, n);\n      zRawSql += n;\n      assert( zRawSql[0] || nToken==0 );\n      if( nToken==0 ) break;\n      if( zRawSql[0]=='?' ){\n        if( nToken>1 ){\n          assert( sqlite3Isdigit(zRawSql[1]) );\n          sqlite3GetInt32(&zRawSql[1], &idx);\n        }else{\n          idx = nextIndex;\n        }\n      }else{\n        assert( zRawSql[0]==':' || zRawSql[0]=='$' ||\n                zRawSql[0]=='@' || zRawSql[0]=='#' );\n        testcase( zRawSql[0]==':' );\n        testcase( zRawSql[0]=='$' );\n        testcase( zRawSql[0]=='@' );\n        testcase( zRawSql[0]=='#' );\n        idx = sqlite3VdbeParameterIndex(p, zRawSql, nToken);\n        assert( idx>0 );\n      }\n      zRawSql += nToken;\n      nextIndex = idx + 1;\n      assert( idx>0 && idx<=p->nVar );\n      pVar = &p->aVar[idx-1];\n      if( pVar->flags & MEM_Null ){\n        sqlite3StrAccumAppend(&out, \"NULL\", 4);\n      }else if( pVar->flags & MEM_Int ){\n        sqlite3XPrintf(&out, \"%lld\", pVar->u.i);\n      }else if( pVar->flags & MEM_Real ){\n        sqlite3XPrintf(&out, \"%!.15g\", pVar->u.r);\n      }else if( pVar->flags & MEM_Str ){\n        int nOut;  /* Number of bytes of the string text to include in output */\n#ifndef SQLITE_OMIT_UTF16\n        u8 enc = ENC(db);\n        if( enc!=SQLITE_UTF8 ){\n          memset(&utf8, 0, sizeof(utf8));\n          utf8.db = db;\n          sqlite3VdbeMemSetStr(&utf8, pVar->z, pVar->n, enc, SQLITE_STATIC);\n          if( SQLITE_NOMEM==sqlite3VdbeChangeEncoding(&utf8, SQLITE_UTF8) ){\n            out.accError = STRACCUM_NOMEM;\n            out.nAlloc = 0;\n          }\n          pVar = &utf8;\n        }\n#endif\n        nOut = pVar->n;\n#ifdef SQLITE_TRACE_SIZE_LIMIT\n        if( nOut>SQLITE_TRACE_SIZE_LIMIT ){\n          nOut = SQLITE_TRACE_SIZE_LIMIT;\n          while( nOut<pVar->n && (pVar->z[nOut]&0xc0)==0x80 ){ nOut++; }\n        }\n#endif    \n        sqlite3XPrintf(&out, \"'%.*q'\", nOut, pVar->z);\n#ifdef SQLITE_TRACE_SIZE_LIMIT\n        if( nOut<pVar->n ){\n          sqlite3XPrintf(&out, \"/*+%d bytes*/\", pVar->n-nOut);\n        }\n#endif\n#ifndef SQLITE_OMIT_UTF16\n        if( enc!=SQLITE_UTF8 ) sqlite3VdbeMemRelease(&utf8);\n#endif\n      }else if( pVar->flags & MEM_Zero ){\n        sqlite3XPrintf(&out, \"zeroblob(%d)\", pVar->u.nZero);\n      }else{\n        int nOut;  /* Number of bytes of the blob to include in output */\n        assert( pVar->flags & MEM_Blob );\n        sqlite3StrAccumAppend(&out, \"x'\", 2);\n        nOut = pVar->n;\n#ifdef SQLITE_TRACE_SIZE_LIMIT\n        if( nOut>SQLITE_TRACE_SIZE_LIMIT ) nOut = SQLITE_TRACE_SIZE_LIMIT;\n#endif\n        for(i=0; i<nOut; i++){\n          sqlite3XPrintf(&out, \"%02x\", pVar->z[i]&0xff);\n        }\n        sqlite3StrAccumAppend(&out, \"'\", 1);\n#ifdef SQLITE_TRACE_SIZE_LIMIT\n        if( nOut<pVar->n ){\n          sqlite3XPrintf(&out, \"/*+%d bytes*/\", pVar->n-nOut);\n        }\n#endif\n      }\n    }\n  }\n  if( out.accError ) sqlite3StrAccumReset(&out);\n  return sqlite3StrAccumFinish(&out);\n}\n\n#endif /* #ifndef SQLITE_OMIT_TRACE */\n\n/************** End of vdbetrace.c *******************************************/\n/************** Begin file vdbe.c ********************************************/\n/*\n** 2001 September 15\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n*************************************************************************\n** The code in this file implements the function that runs the\n** bytecode of a prepared statement.\n**\n** Various scripts scan this source file in order to generate HTML\n** documentation, headers files, or other derived files.  The formatting\n** of the code in this file is, therefore, important.  See other comments\n** in this file for details.  If in doubt, do not deviate from existing\n** commenting and indentation practices when changing or adding code.\n*/\n/* #include \"sqliteInt.h\" */\n/* #include \"vdbeInt.h\" */\n\n/*\n** Invoke this macro on memory cells just prior to changing the\n** value of the cell.  This macro verifies that shallow copies are\n** not misused.  A shallow copy of a string or blob just copies a\n** pointer to the string or blob, not the content.  If the original\n** is changed while the copy is still in use, the string or blob might\n** be changed out from under the copy.  This macro verifies that nothing\n** like that ever happens.\n*/\n#ifdef SQLITE_DEBUG\n# define memAboutToChange(P,M) sqlite3VdbeMemAboutToChange(P,M)\n#else\n# define memAboutToChange(P,M)\n#endif\n\n/*\n** The following global variable is incremented every time a cursor\n** moves, either by the OP_SeekXX, OP_Next, or OP_Prev opcodes.  The test\n** procedures use this information to make sure that indices are\n** working correctly.  This variable has no function other than to\n** help verify the correct operation of the library.\n*/\n#ifdef SQLITE_TEST\nSQLITE_API int sqlite3_search_count = 0;\n#endif\n\n/*\n** When this global variable is positive, it gets decremented once before\n** each instruction in the VDBE.  When it reaches zero, the u1.isInterrupted\n** field of the sqlite3 structure is set in order to simulate an interrupt.\n**\n** This facility is used for testing purposes only.  It does not function\n** in an ordinary build.\n*/\n#ifdef SQLITE_TEST\nSQLITE_API int sqlite3_interrupt_count = 0;\n#endif\n\n/*\n** The next global variable is incremented each type the OP_Sort opcode\n** is executed.  The test procedures use this information to make sure that\n** sorting is occurring or not occurring at appropriate times.   This variable\n** has no function other than to help verify the correct operation of the\n** library.\n*/\n#ifdef SQLITE_TEST\nSQLITE_API int sqlite3_sort_count = 0;\n#endif\n\n/*\n** The next global variable records the size of the largest MEM_Blob\n** or MEM_Str that has been used by a VDBE opcode.  The test procedures\n** use this information to make sure that the zero-blob functionality\n** is working correctly.   This variable has no function other than to\n** help verify the correct operation of the library.\n*/\n#ifdef SQLITE_TEST\nSQLITE_API int sqlite3_max_blobsize = 0;\nstatic void updateMaxBlobsize(Mem *p){\n  if( (p->flags & (MEM_Str|MEM_Blob))!=0 && p->n>sqlite3_max_blobsize ){\n    sqlite3_max_blobsize = p->n;\n  }\n}\n#endif\n\n/*\n** This macro evaluates to true if either the update hook or the preupdate\n** hook are enabled for database connect DB.\n*/\n#ifdef SQLITE_ENABLE_PREUPDATE_HOOK\n# define HAS_UPDATE_HOOK(DB) ((DB)->xPreUpdateCallback||(DB)->xUpdateCallback)\n#else\n# define HAS_UPDATE_HOOK(DB) ((DB)->xUpdateCallback)\n#endif\n\n/*\n** The next global variable is incremented each time the OP_Found opcode\n** is executed. This is used to test whether or not the foreign key\n** operation implemented using OP_FkIsZero is working. This variable\n** has no function other than to help verify the correct operation of the\n** library.\n*/\n#ifdef SQLITE_TEST\nSQLITE_API int sqlite3_found_count = 0;\n#endif\n\n/*\n** Test a register to see if it exceeds the current maximum blob size.\n** If it does, record the new maximum blob size.\n*/\n#if defined(SQLITE_TEST) && !defined(SQLITE_UNTESTABLE)\n# define UPDATE_MAX_BLOBSIZE(P)  updateMaxBlobsize(P)\n#else\n# define UPDATE_MAX_BLOBSIZE(P)\n#endif\n\n/*\n** Invoke the VDBE coverage callback, if that callback is defined.  This\n** feature is used for test suite validation only and does not appear an\n** production builds.\n**\n** M is an integer, 2 or 3, that indices how many different ways the\n** branch can go.  It is usually 2.  \"I\" is the direction the branch\n** goes.  0 means falls through.  1 means branch is taken.  2 means the\n** second alternative branch is taken.\n**\n** iSrcLine is the source code line (from the __LINE__ macro) that\n** generated the VDBE instruction.  This instrumentation assumes that all\n** source code is in a single file (the amalgamation).  Special values 1\n** and 2 for the iSrcLine parameter mean that this particular branch is\n** always taken or never taken, respectively.\n*/\n#if !defined(SQLITE_VDBE_COVERAGE)\n# define VdbeBranchTaken(I,M)\n#else\n# define VdbeBranchTaken(I,M) vdbeTakeBranch(pOp->iSrcLine,I,M)\n  static void vdbeTakeBranch(int iSrcLine, u8 I, u8 M){\n    if( iSrcLine<=2 && ALWAYS(iSrcLine>0) ){\n      M = iSrcLine;\n      /* Assert the truth of VdbeCoverageAlwaysTaken() and \n      ** VdbeCoverageNeverTaken() */\n      assert( (M & I)==I );\n    }else{\n      if( sqlite3GlobalConfig.xVdbeBranch==0 ) return;  /*NO_TEST*/\n      sqlite3GlobalConfig.xVdbeBranch(sqlite3GlobalConfig.pVdbeBranchArg,\n                                      iSrcLine,I,M);\n    }\n  }\n#endif\n\n/*\n** Convert the given register into a string if it isn't one\n** already. Return non-zero if a malloc() fails.\n*/\n#define Stringify(P, enc) \\\n   if(((P)->flags&(MEM_Str|MEM_Blob))==0 && sqlite3VdbeMemStringify(P,enc,0)) \\\n     { goto no_mem; }\n\n/*\n** An ephemeral string value (signified by the MEM_Ephem flag) contains\n** a pointer to a dynamically allocated string where some other entity\n** is responsible for deallocating that string.  Because the register\n** does not control the string, it might be deleted without the register\n** knowing it.\n**\n** This routine converts an ephemeral string into a dynamically allocated\n** string that the register itself controls.  In other words, it\n** converts an MEM_Ephem string into a string with P.z==P.zMalloc.\n*/\n#define Deephemeralize(P) \\\n   if( ((P)->flags&MEM_Ephem)!=0 \\\n       && sqlite3VdbeMemMakeWriteable(P) ){ goto no_mem;}\n\n/* Return true if the cursor was opened using the OP_OpenSorter opcode. */\n#define isSorter(x) ((x)->eCurType==CURTYPE_SORTER)\n\n/*\n** Allocate VdbeCursor number iCur.  Return a pointer to it.  Return NULL\n** if we run out of memory.\n*/\nstatic VdbeCursor *allocateCursor(\n  Vdbe *p,              /* The virtual machine */\n  int iCur,             /* Index of the new VdbeCursor */\n  int nField,           /* Number of fields in the table or index */\n  int iDb,              /* Database the cursor belongs to, or -1 */\n  u8 eCurType           /* Type of the new cursor */\n){\n  /* Find the memory cell that will be used to store the blob of memory\n  ** required for this VdbeCursor structure. It is convenient to use a \n  ** vdbe memory cell to manage the memory allocation required for a\n  ** VdbeCursor structure for the following reasons:\n  **\n  **   * Sometimes cursor numbers are used for a couple of different\n  **     purposes in a vdbe program. The different uses might require\n  **     different sized allocations. Memory cells provide growable\n  **     allocations.\n  **\n  **   * When using ENABLE_MEMORY_MANAGEMENT, memory cell buffers can\n  **     be freed lazily via the sqlite3_release_memory() API. This\n  **     minimizes the number of malloc calls made by the system.\n  **\n  ** The memory cell for cursor 0 is aMem[0]. The rest are allocated from\n  ** the top of the register space.  Cursor 1 is at Mem[p->nMem-1].\n  ** Cursor 2 is at Mem[p->nMem-2]. And so forth.\n  */\n  Mem *pMem = iCur>0 ? &p->aMem[p->nMem-iCur] : p->aMem;\n\n  int nByte;\n  VdbeCursor *pCx = 0;\n  nByte = \n      ROUND8(sizeof(VdbeCursor)) + 2*sizeof(u32)*nField + \n      (eCurType==CURTYPE_BTREE?sqlite3BtreeCursorSize():0);\n\n  assert( iCur>=0 && iCur<p->nCursor );\n  if( p->apCsr[iCur] ){ /*OPTIMIZATION-IF-FALSE*/\n    sqlite3VdbeFreeCursor(p, p->apCsr[iCur]);\n    p->apCsr[iCur] = 0;\n  }\n  if( SQLITE_OK==sqlite3VdbeMemClearAndResize(pMem, nByte) ){\n    p->apCsr[iCur] = pCx = (VdbeCursor*)pMem->z;\n    memset(pCx, 0, offsetof(VdbeCursor,pAltCursor));\n    pCx->eCurType = eCurType;\n    pCx->iDb = iDb;\n    pCx->nField = nField;\n    pCx->aOffset = &pCx->aType[nField];\n    if( eCurType==CURTYPE_BTREE ){\n      pCx->uc.pCursor = (BtCursor*)\n          &pMem->z[ROUND8(sizeof(VdbeCursor))+2*sizeof(u32)*nField];\n      sqlite3BtreeCursorZero(pCx->uc.pCursor);\n    }\n  }\n  return pCx;\n}\n\n/*\n** Try to convert a value into a numeric representation if we can\n** do so without loss of information.  In other words, if the string\n** looks like a number, convert it into a number.  If it does not\n** look like a number, leave it alone.\n**\n** If the bTryForInt flag is true, then extra effort is made to give\n** an integer representation.  Strings that look like floating point\n** values but which have no fractional component (example: '48.00')\n** will have a MEM_Int representation when bTryForInt is true.\n**\n** If bTryForInt is false, then if the input string contains a decimal\n** point or exponential notation, the result is only MEM_Real, even\n** if there is an exact integer representation of the quantity.\n*/\nstatic void applyNumericAffinity(Mem *pRec, int bTryForInt){\n  double rValue;\n  i64 iValue;\n  u8 enc = pRec->enc;\n  assert( (pRec->flags & (MEM_Str|MEM_Int|MEM_Real))==MEM_Str );\n  if( sqlite3AtoF(pRec->z, &rValue, pRec->n, enc)==0 ) return;\n  if( 0==sqlite3Atoi64(pRec->z, &iValue, pRec->n, enc) ){\n    pRec->u.i = iValue;\n    pRec->flags |= MEM_Int;\n  }else{\n    pRec->u.r = rValue;\n    pRec->flags |= MEM_Real;\n    if( bTryForInt ) sqlite3VdbeIntegerAffinity(pRec);\n  }\n  /* TEXT->NUMERIC is many->one.  Hence, it is important to invalidate the\n  ** string representation after computing a numeric equivalent, because the\n  ** string representation might not be the canonical representation for the\n  ** numeric value.  Ticket [343634942dd54ab57b7024] 2018-01-31. */\n  pRec->flags &= ~MEM_Str;\n}\n\n/*\n** Processing is determine by the affinity parameter:\n**\n** SQLITE_AFF_INTEGER:\n** SQLITE_AFF_REAL:\n** SQLITE_AFF_NUMERIC:\n**    Try to convert pRec to an integer representation or a \n**    floating-point representation if an integer representation\n**    is not possible.  Note that the integer representation is\n**    always preferred, even if the affinity is REAL, because\n**    an integer representation is more space efficient on disk.\n**\n** SQLITE_AFF_TEXT:\n**    Convert pRec to a text representation.\n**\n** SQLITE_AFF_BLOB:\n**    No-op.  pRec is unchanged.\n*/\nstatic void applyAffinity(\n  Mem *pRec,          /* The value to apply affinity to */\n  char affinity,      /* The affinity to be applied */\n  u8 enc              /* Use this text encoding */\n){\n  if( affinity>=SQLITE_AFF_NUMERIC ){\n    assert( affinity==SQLITE_AFF_INTEGER || affinity==SQLITE_AFF_REAL\n             || affinity==SQLITE_AFF_NUMERIC );\n    if( (pRec->flags & MEM_Int)==0 ){ /*OPTIMIZATION-IF-FALSE*/\n      if( (pRec->flags & MEM_Real)==0 ){\n        if( pRec->flags & MEM_Str ) applyNumericAffinity(pRec,1);\n      }else{\n        sqlite3VdbeIntegerAffinity(pRec);\n      }\n    }\n  }else if( affinity==SQLITE_AFF_TEXT ){\n    /* Only attempt the conversion to TEXT if there is an integer or real\n    ** representation (blob and NULL do not get converted) but no string\n    ** representation.  It would be harmless to repeat the conversion if \n    ** there is already a string rep, but it is pointless to waste those\n    ** CPU cycles. */\n    if( 0==(pRec->flags&MEM_Str) ){ /*OPTIMIZATION-IF-FALSE*/\n      if( (pRec->flags&(MEM_Real|MEM_Int)) ){\n        sqlite3VdbeMemStringify(pRec, enc, 1);\n      }\n    }\n    pRec->flags &= ~(MEM_Real|MEM_Int);\n  }\n}\n\n/*\n** Try to convert the type of a function argument or a result column\n** into a numeric representation.  Use either INTEGER or REAL whichever\n** is appropriate.  But only do the conversion if it is possible without\n** loss of information and return the revised type of the argument.\n*/\nSQLITE_API int sqlite3_value_numeric_type(sqlite3_value *pVal){\n  int eType = sqlite3_value_type(pVal);\n  if( eType==SQLITE_TEXT ){\n    Mem *pMem = (Mem*)pVal;\n    applyNumericAffinity(pMem, 0);\n    eType = sqlite3_value_type(pVal);\n  }\n  return eType;\n}\n\n/*\n** Exported version of applyAffinity(). This one works on sqlite3_value*, \n** not the internal Mem* type.\n*/\nSQLITE_PRIVATE void sqlite3ValueApplyAffinity(\n  sqlite3_value *pVal, \n  u8 affinity, \n  u8 enc\n){\n  applyAffinity((Mem *)pVal, affinity, enc);\n}\n\n/*\n** pMem currently only holds a string type (or maybe a BLOB that we can\n** interpret as a string if we want to).  Compute its corresponding\n** numeric type, if has one.  Set the pMem->u.r and pMem->u.i fields\n** accordingly.\n*/\nstatic u16 SQLITE_NOINLINE computeNumericType(Mem *pMem){\n  assert( (pMem->flags & (MEM_Int|MEM_Real))==0 );\n  assert( (pMem->flags & (MEM_Str|MEM_Blob))!=0 );\n  if( sqlite3AtoF(pMem->z, &pMem->u.r, pMem->n, pMem->enc)==0 ){\n    return 0;\n  }\n  if( sqlite3Atoi64(pMem->z, &pMem->u.i, pMem->n, pMem->enc)==0 ){\n    return MEM_Int;\n  }\n  return MEM_Real;\n}\n\n/*\n** Return the numeric type for pMem, either MEM_Int or MEM_Real or both or\n** none.  \n**\n** Unlike applyNumericAffinity(), this routine does not modify pMem->flags.\n** But it does set pMem->u.r and pMem->u.i appropriately.\n*/\nstatic u16 numericType(Mem *pMem){\n  if( pMem->flags & (MEM_Int|MEM_Real) ){\n    return pMem->flags & (MEM_Int|MEM_Real);\n  }\n  if( pMem->flags & (MEM_Str|MEM_Blob) ){\n    return computeNumericType(pMem);\n  }\n  return 0;\n}\n\n#ifdef SQLITE_DEBUG\n/*\n** Write a nice string representation of the contents of cell pMem\n** into buffer zBuf, length nBuf.\n*/\nSQLITE_PRIVATE void sqlite3VdbeMemPrettyPrint(Mem *pMem, char *zBuf){\n  char *zCsr = zBuf;\n  int f = pMem->flags;\n\n  static const char *const encnames[] = {\"(X)\", \"(8)\", \"(16LE)\", \"(16BE)\"};\n\n  if( f&MEM_Blob ){\n    int i;\n    char c;\n    if( f & MEM_Dyn ){\n      c = 'z';\n      assert( (f & (MEM_Static|MEM_Ephem))==0 );\n    }else if( f & MEM_Static ){\n      c = 't';\n      assert( (f & (MEM_Dyn|MEM_Ephem))==0 );\n    }else if( f & MEM_Ephem ){\n      c = 'e';\n      assert( (f & (MEM_Static|MEM_Dyn))==0 );\n    }else{\n      c = 's';\n    }\n    *(zCsr++) = c;\n    sqlite3_snprintf(100, zCsr, \"%d[\", pMem->n);\n    zCsr += sqlite3Strlen30(zCsr);\n    for(i=0; i<16 && i<pMem->n; i++){\n      sqlite3_snprintf(100, zCsr, \"%02X\", ((int)pMem->z[i] & 0xFF));\n      zCsr += sqlite3Strlen30(zCsr);\n    }\n    for(i=0; i<16 && i<pMem->n; i++){\n      char z = pMem->z[i];\n      if( z<32 || z>126 ) *zCsr++ = '.';\n      else *zCsr++ = z;\n    }\n    *(zCsr++) = ']';\n    if( f & MEM_Zero ){\n      sqlite3_snprintf(100, zCsr,\"+%dz\",pMem->u.nZero);\n      zCsr += sqlite3Strlen30(zCsr);\n    }\n    *zCsr = '\\0';\n  }else if( f & MEM_Str ){\n    int j, k;\n    zBuf[0] = ' ';\n    if( f & MEM_Dyn ){\n      zBuf[1] = 'z';\n      assert( (f & (MEM_Static|MEM_Ephem))==0 );\n    }else if( f & MEM_Static ){\n      zBuf[1] = 't';\n      assert( (f & (MEM_Dyn|MEM_Ephem))==0 );\n    }else if( f & MEM_Ephem ){\n      zBuf[1] = 'e';\n      assert( (f & (MEM_Static|MEM_Dyn))==0 );\n    }else{\n      zBuf[1] = 's';\n    }\n    k = 2;\n    sqlite3_snprintf(100, &zBuf[k], \"%d\", pMem->n);\n    k += sqlite3Strlen30(&zBuf[k]);\n    zBuf[k++] = '[';\n    for(j=0; j<15 && j<pMem->n; j++){\n      u8 c = pMem->z[j];\n      if( c>=0x20 && c<0x7f ){\n        zBuf[k++] = c;\n      }else{\n        zBuf[k++] = '.';\n      }\n    }\n    zBuf[k++] = ']';\n    sqlite3_snprintf(100,&zBuf[k], encnames[pMem->enc]);\n    k += sqlite3Strlen30(&zBuf[k]);\n    zBuf[k++] = 0;\n  }\n}\n#endif\n\n#ifdef SQLITE_DEBUG\n/*\n** Print the value of a register for tracing purposes:\n*/\nstatic void memTracePrint(Mem *p){\n  if( p->flags & MEM_Undefined ){\n    printf(\" undefined\");\n  }else if( p->flags & MEM_Null ){\n    printf(p->flags & MEM_Zero ? \" NULL-nochng\" : \" NULL\");\n  }else if( (p->flags & (MEM_Int|MEM_Str))==(MEM_Int|MEM_Str) ){\n    printf(\" si:%lld\", p->u.i);\n  }else if( p->flags & MEM_Int ){\n    printf(\" i:%lld\", p->u.i);\n#ifndef SQLITE_OMIT_FLOATING_POINT\n  }else if( p->flags & MEM_Real ){\n    printf(\" r:%g\", p->u.r);\n#endif\n  }else if( p->flags & MEM_RowSet ){\n    printf(\" (rowset)\");\n  }else{\n    char zBuf[200];\n    sqlite3VdbeMemPrettyPrint(p, zBuf);\n    printf(\" %s\", zBuf);\n  }\n  if( p->flags & MEM_Subtype ) printf(\" subtype=0x%02x\", p->eSubtype);\n}\nstatic void registerTrace(int iReg, Mem *p){\n  printf(\"REG[%d] = \", iReg);\n  memTracePrint(p);\n  printf(\"\\n\");\n  sqlite3VdbeCheckMemInvariants(p);\n}\n#endif\n\n#ifdef SQLITE_DEBUG\n#  define REGISTER_TRACE(R,M) if(db->flags&SQLITE_VdbeTrace)registerTrace(R,M)\n#else\n#  define REGISTER_TRACE(R,M)\n#endif\n\n\n#ifdef VDBE_PROFILE\n\n/* \n** hwtime.h contains inline assembler code for implementing \n** high-performance timing routines.\n*/\n/************** Include hwtime.h in the middle of vdbe.c *********************/\n/************** Begin file hwtime.h ******************************************/\n/*\n** 2008 May 27\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n******************************************************************************\n**\n** This file contains inline asm code for retrieving \"high-performance\"\n** counters for x86 class CPUs.\n*/\n#ifndef SQLITE_HWTIME_H\n#define SQLITE_HWTIME_H\n\n/*\n** The following routine only works on pentium-class (or newer) processors.\n** It uses the RDTSC opcode to read the cycle count value out of the\n** processor and returns that value.  This can be used for high-res\n** profiling.\n*/\n#if (defined(__GNUC__) || defined(_MSC_VER)) && \\\n      (defined(i386) || defined(__i386__) || defined(_M_IX86))\n\n  #if defined(__GNUC__)\n\n  __inline__ sqlite_uint64 sqlite3Hwtime(void){\n     unsigned int lo, hi;\n     __asm__ __volatile__ (\"rdtsc\" : \"=a\" (lo), \"=d\" (hi));\n     return (sqlite_uint64)hi << 32 | lo;\n  }\n\n  #elif defined(_MSC_VER)\n\n  __declspec(naked) __inline sqlite_uint64 __cdecl sqlite3Hwtime(void){\n     __asm {\n        rdtsc\n        ret       ; return value at EDX:EAX\n     }\n  }\n\n  #endif\n\n#elif (defined(__GNUC__) && defined(__x86_64__))\n\n  __inline__ sqlite_uint64 sqlite3Hwtime(void){\n      unsigned long val;\n      __asm__ __volatile__ (\"rdtsc\" : \"=A\" (val));\n      return val;\n  }\n \n#elif (defined(__GNUC__) && defined(__ppc__))\n\n  __inline__ sqlite_uint64 sqlite3Hwtime(void){\n      unsigned long long retval;\n      unsigned long junk;\n      __asm__ __volatile__ (\"\\n\\\n          1:      mftbu   %1\\n\\\n                  mftb    %L0\\n\\\n                  mftbu   %0\\n\\\n                  cmpw    %0,%1\\n\\\n                  bne     1b\"\n                  : \"=r\" (retval), \"=r\" (junk));\n      return retval;\n  }\n\n#else\n\n  #error Need implementation of sqlite3Hwtime() for your platform.\n\n  /*\n  ** To compile without implementing sqlite3Hwtime() for your platform,\n  ** you can remove the above #error and use the following\n  ** stub function.  You will lose timing support for many\n  ** of the debugging and testing utilities, but it should at\n  ** least compile and run.\n  */\nSQLITE_PRIVATE   sqlite_uint64 sqlite3Hwtime(void){ return ((sqlite_uint64)0); }\n\n#endif\n\n#endif /* !defined(SQLITE_HWTIME_H) */\n\n/************** End of hwtime.h **********************************************/\n/************** Continuing where we left off in vdbe.c ***********************/\n\n#endif\n\n#ifndef NDEBUG\n/*\n** This function is only called from within an assert() expression. It\n** checks that the sqlite3.nTransaction variable is correctly set to\n** the number of non-transaction savepoints currently in the \n** linked list starting at sqlite3.pSavepoint.\n** \n** Usage:\n**\n**     assert( checkSavepointCount(db) );\n*/\nstatic int checkSavepointCount(sqlite3 *db){\n  int n = 0;\n  Savepoint *p;\n  for(p=db->pSavepoint; p; p=p->pNext) n++;\n  assert( n==(db->nSavepoint + db->isTransactionSavepoint) );\n  return 1;\n}\n#endif\n\n/*\n** Return the register of pOp->p2 after first preparing it to be\n** overwritten with an integer value.\n*/\nstatic SQLITE_NOINLINE Mem *out2PrereleaseWithClear(Mem *pOut){\n  sqlite3VdbeMemSetNull(pOut);\n  pOut->flags = MEM_Int;\n  return pOut;\n}\nstatic Mem *out2Prerelease(Vdbe *p, VdbeOp *pOp){\n  Mem *pOut;\n  assert( pOp->p2>0 );\n  assert( pOp->p2<=(p->nMem+1 - p->nCursor) );\n  pOut = &p->aMem[pOp->p2];\n  memAboutToChange(p, pOut);\n  if( VdbeMemDynamic(pOut) ){ /*OPTIMIZATION-IF-FALSE*/\n    return out2PrereleaseWithClear(pOut);\n  }else{\n    pOut->flags = MEM_Int;\n    return pOut;\n  }\n}\n\n\n/*\n** Execute as much of a VDBE program as we can.\n** This is the core of sqlite3_step().  \n*/\nSQLITE_PRIVATE int sqlite3VdbeExec(\n  Vdbe *p                    /* The VDBE */\n){\n  Op *aOp = p->aOp;          /* Copy of p->aOp */\n  Op *pOp = aOp;             /* Current operation */\n#if defined(SQLITE_DEBUG) || defined(VDBE_PROFILE)\n  Op *pOrigOp;               /* Value of pOp at the top of the loop */\n#endif\n#ifdef SQLITE_DEBUG\n  int nExtraDelete = 0;      /* Verifies FORDELETE and AUXDELETE flags */\n#endif\n  int rc = SQLITE_OK;        /* Value to return */\n  sqlite3 *db = p->db;       /* The database */\n  u8 resetSchemaOnFault = 0; /* Reset schema after an error if positive */\n  u8 encoding = ENC(db);     /* The database encoding */\n  int iCompare = 0;          /* Result of last comparison */\n  unsigned nVmStep = 0;      /* Number of virtual machine steps */\n#ifndef SQLITE_OMIT_PROGRESS_CALLBACK\n  unsigned nProgressLimit;   /* Invoke xProgress() when nVmStep reaches this */\n#endif\n  Mem *aMem = p->aMem;       /* Copy of p->aMem */\n  Mem *pIn1 = 0;             /* 1st input operand */\n  Mem *pIn2 = 0;             /* 2nd input operand */\n  Mem *pIn3 = 0;             /* 3rd input operand */\n  Mem *pOut = 0;             /* Output operand */\n#ifdef VDBE_PROFILE\n  u64 start;                 /* CPU clock count at start of opcode */\n#endif\n  /*** INSERT STACK UNION HERE ***/\n\n  assert( p->magic==VDBE_MAGIC_RUN );  /* sqlite3_step() verifies this */\n  sqlite3VdbeEnter(p);\n  if( p->rc==SQLITE_NOMEM ){\n    /* This happens if a malloc() inside a call to sqlite3_column_text() or\n    ** sqlite3_column_text16() failed.  */\n    goto no_mem;\n  }\n  assert( p->rc==SQLITE_OK || (p->rc&0xff)==SQLITE_BUSY );\n  assert( p->bIsReader || p->readOnly!=0 );\n  p->iCurrentTime = 0;\n  assert( p->explain==0 );\n  p->pResultSet = 0;\n  db->busyHandler.nBusy = 0;\n  if( db->u1.isInterrupted ) goto abort_due_to_interrupt;\n  sqlite3VdbeIOTraceSql(p);\n#ifndef SQLITE_OMIT_PROGRESS_CALLBACK\n  if( db->xProgress ){\n    u32 iPrior = p->aCounter[SQLITE_STMTSTATUS_VM_STEP];\n    assert( 0 < db->nProgressOps );\n    nProgressLimit = db->nProgressOps - (iPrior % db->nProgressOps);\n  }else{\n    nProgressLimit = 0xffffffff;\n  }\n#endif\n#ifdef SQLITE_DEBUG\n  sqlite3BeginBenignMalloc();\n  if( p->pc==0\n   && (p->db->flags & (SQLITE_VdbeListing|SQLITE_VdbeEQP|SQLITE_VdbeTrace))!=0\n  ){\n    int i;\n    int once = 1;\n    sqlite3VdbePrintSql(p);\n    if( p->db->flags & SQLITE_VdbeListing ){\n      printf(\"VDBE Program Listing:\\n\");\n      for(i=0; i<p->nOp; i++){\n        sqlite3VdbePrintOp(stdout, i, &aOp[i]);\n      }\n    }\n    if( p->db->flags & SQLITE_VdbeEQP ){\n      for(i=0; i<p->nOp; i++){\n        if( aOp[i].opcode==OP_Explain ){\n          if( once ) printf(\"VDBE Query Plan:\\n\");\n          printf(\"%s\\n\", aOp[i].p4.z);\n          once = 0;\n        }\n      }\n    }\n    if( p->db->flags & SQLITE_VdbeTrace )  printf(\"VDBE Trace:\\n\");\n  }\n  sqlite3EndBenignMalloc();\n#endif\n  for(pOp=&aOp[p->pc]; 1; pOp++){\n    /* Errors are detected by individual opcodes, with an immediate\n    ** jumps to abort_due_to_error. */\n    assert( rc==SQLITE_OK );\n\n    assert( pOp>=aOp && pOp<&aOp[p->nOp]);\n#ifdef VDBE_PROFILE\n    start = sqlite3NProfileCnt ? sqlite3NProfileCnt : sqlite3Hwtime();\n#endif\n    nVmStep++;\n#ifdef SQLITE_ENABLE_STMT_SCANSTATUS\n    if( p->anExec ) p->anExec[(int)(pOp-aOp)]++;\n#endif\n\n    /* Only allow tracing if SQLITE_DEBUG is defined.\n    */\n#ifdef SQLITE_DEBUG\n    if( db->flags & SQLITE_VdbeTrace ){\n      sqlite3VdbePrintOp(stdout, (int)(pOp - aOp), pOp);\n    }\n#endif\n      \n\n    /* Check to see if we need to simulate an interrupt.  This only happens\n    ** if we have a special test build.\n    */\n#ifdef SQLITE_TEST\n    if( sqlite3_interrupt_count>0 ){\n      sqlite3_interrupt_count--;\n      if( sqlite3_interrupt_count==0 ){\n        sqlite3_interrupt(db);\n      }\n    }\n#endif\n\n    /* Sanity checking on other operands */\n#ifdef SQLITE_DEBUG\n    {\n      u8 opProperty = sqlite3OpcodeProperty[pOp->opcode];\n      if( (opProperty & OPFLG_IN1)!=0 ){\n        assert( pOp->p1>0 );\n        assert( pOp->p1<=(p->nMem+1 - p->nCursor) );\n        assert( memIsValid(&aMem[pOp->p1]) );\n        assert( sqlite3VdbeCheckMemInvariants(&aMem[pOp->p1]) );\n        REGISTER_TRACE(pOp->p1, &aMem[pOp->p1]);\n      }\n      if( (opProperty & OPFLG_IN2)!=0 ){\n        assert( pOp->p2>0 );\n        assert( pOp->p2<=(p->nMem+1 - p->nCursor) );\n        assert( memIsValid(&aMem[pOp->p2]) );\n        assert( sqlite3VdbeCheckMemInvariants(&aMem[pOp->p2]) );\n        REGISTER_TRACE(pOp->p2, &aMem[pOp->p2]);\n      }\n      if( (opProperty & OPFLG_IN3)!=0 ){\n        assert( pOp->p3>0 );\n        assert( pOp->p3<=(p->nMem+1 - p->nCursor) );\n        assert( memIsValid(&aMem[pOp->p3]) );\n        assert( sqlite3VdbeCheckMemInvariants(&aMem[pOp->p3]) );\n        REGISTER_TRACE(pOp->p3, &aMem[pOp->p3]);\n      }\n      if( (opProperty & OPFLG_OUT2)!=0 ){\n        assert( pOp->p2>0 );\n        assert( pOp->p2<=(p->nMem+1 - p->nCursor) );\n        memAboutToChange(p, &aMem[pOp->p2]);\n      }\n      if( (opProperty & OPFLG_OUT3)!=0 ){\n        assert( pOp->p3>0 );\n        assert( pOp->p3<=(p->nMem+1 - p->nCursor) );\n        memAboutToChange(p, &aMem[pOp->p3]);\n      }\n    }\n#endif\n#if defined(SQLITE_DEBUG) || defined(VDBE_PROFILE)\n    pOrigOp = pOp;\n#endif\n  \n    switch( pOp->opcode ){\n\n/*****************************************************************************\n** What follows is a massive switch statement where each case implements a\n** separate instruction in the virtual machine.  If we follow the usual\n** indentation conventions, each case should be indented by 6 spaces.  But\n** that is a lot of wasted space on the left margin.  So the code within\n** the switch statement will break with convention and be flush-left. Another\n** big comment (similar to this one) will mark the point in the code where\n** we transition back to normal indentation.\n**\n** The formatting of each case is important.  The makefile for SQLite\n** generates two C files \"opcodes.h\" and \"opcodes.c\" by scanning this\n** file looking for lines that begin with \"case OP_\".  The opcodes.h files\n** will be filled with #defines that give unique integer values to each\n** opcode and the opcodes.c file is filled with an array of strings where\n** each string is the symbolic name for the corresponding opcode.  If the\n** case statement is followed by a comment of the form \"/# same as ... #/\"\n** that comment is used to determine the particular value of the opcode.\n**\n** Other keywords in the comment that follows each case are used to\n** construct the OPFLG_INITIALIZER value that initializes opcodeProperty[].\n** Keywords include: in1, in2, in3, out2, out3.  See\n** the mkopcodeh.awk script for additional information.\n**\n** Documentation about VDBE opcodes is generated by scanning this file\n** for lines of that contain \"Opcode:\".  That line and all subsequent\n** comment lines are used in the generation of the opcode.html documentation\n** file.\n**\n** SUMMARY:\n**\n**     Formatting is important to scripts that scan this file.\n**     Do not deviate from the formatting style currently in use.\n**\n*****************************************************************************/\n\n/* Opcode:  Goto * P2 * * *\n**\n** An unconditional jump to address P2.\n** The next instruction executed will be \n** the one at index P2 from the beginning of\n** the program.\n**\n** The P1 parameter is not actually used by this opcode.  However, it\n** is sometimes set to 1 instead of 0 as a hint to the command-line shell\n** that this Goto is the bottom of a loop and that the lines from P2 down\n** to the current line should be indented for EXPLAIN output.\n*/\ncase OP_Goto: {             /* jump */\njump_to_p2_and_check_for_interrupt:\n  pOp = &aOp[pOp->p2 - 1];\n\n  /* Opcodes that are used as the bottom of a loop (OP_Next, OP_Prev,\n  ** OP_VNext, or OP_SorterNext) all jump here upon\n  ** completion.  Check to see if sqlite3_interrupt() has been called\n  ** or if the progress callback needs to be invoked. \n  **\n  ** This code uses unstructured \"goto\" statements and does not look clean.\n  ** But that is not due to sloppy coding habits. The code is written this\n  ** way for performance, to avoid having to run the interrupt and progress\n  ** checks on every opcode.  This helps sqlite3_step() to run about 1.5%\n  ** faster according to \"valgrind --tool=cachegrind\" */\ncheck_for_interrupt:\n  if( db->u1.isInterrupted ) goto abort_due_to_interrupt;\n#ifndef SQLITE_OMIT_PROGRESS_CALLBACK\n  /* Call the progress callback if it is configured and the required number\n  ** of VDBE ops have been executed (either since this invocation of\n  ** sqlite3VdbeExec() or since last time the progress callback was called).\n  ** If the progress callback returns non-zero, exit the virtual machine with\n  ** a return code SQLITE_ABORT.\n  */\n  if( nVmStep>=nProgressLimit && db->xProgress!=0 ){\n    assert( db->nProgressOps!=0 );\n    nProgressLimit = nVmStep + db->nProgressOps - (nVmStep%db->nProgressOps);\n    if( db->xProgress(db->pProgressArg) ){\n      rc = SQLITE_INTERRUPT;\n      goto abort_due_to_error;\n    }\n  }\n#endif\n  \n  break;\n}\n\n/* Opcode:  Gosub P1 P2 * * *\n**\n** Write the current address onto register P1\n** and then jump to address P2.\n*/\ncase OP_Gosub: {            /* jump */\n  assert( pOp->p1>0 && pOp->p1<=(p->nMem+1 - p->nCursor) );\n  pIn1 = &aMem[pOp->p1];\n  assert( VdbeMemDynamic(pIn1)==0 );\n  memAboutToChange(p, pIn1);\n  pIn1->flags = MEM_Int;\n  pIn1->u.i = (int)(pOp-aOp);\n  REGISTER_TRACE(pOp->p1, pIn1);\n\n  /* Most jump operations do a goto to this spot in order to update\n  ** the pOp pointer. */\njump_to_p2:\n  pOp = &aOp[pOp->p2 - 1];\n  break;\n}\n\n/* Opcode:  Return P1 * * * *\n**\n** Jump to the next instruction after the address in register P1.  After\n** the jump, register P1 becomes undefined.\n*/\ncase OP_Return: {           /* in1 */\n  pIn1 = &aMem[pOp->p1];\n  assert( pIn1->flags==MEM_Int );\n  pOp = &aOp[pIn1->u.i];\n  pIn1->flags = MEM_Undefined;\n  break;\n}\n\n/* Opcode: InitCoroutine P1 P2 P3 * *\n**\n** Set up register P1 so that it will Yield to the coroutine\n** located at address P3.\n**\n** If P2!=0 then the coroutine implementation immediately follows\n** this opcode.  So jump over the coroutine implementation to\n** address P2.\n**\n** See also: EndCoroutine\n*/\ncase OP_InitCoroutine: {     /* jump */\n  assert( pOp->p1>0 &&  pOp->p1<=(p->nMem+1 - p->nCursor) );\n  assert( pOp->p2>=0 && pOp->p2<p->nOp );\n  assert( pOp->p3>=0 && pOp->p3<p->nOp );\n  pOut = &aMem[pOp->p1];\n  assert( !VdbeMemDynamic(pOut) );\n  pOut->u.i = pOp->p3 - 1;\n  pOut->flags = MEM_Int;\n  if( pOp->p2 ) goto jump_to_p2;\n  break;\n}\n\n/* Opcode:  EndCoroutine P1 * * * *\n**\n** The instruction at the address in register P1 is a Yield.\n** Jump to the P2 parameter of that Yield.\n** After the jump, register P1 becomes undefined.\n**\n** See also: InitCoroutine\n*/\ncase OP_EndCoroutine: {           /* in1 */\n  VdbeOp *pCaller;\n  pIn1 = &aMem[pOp->p1];\n  assert( pIn1->flags==MEM_Int );\n  assert( pIn1->u.i>=0 && pIn1->u.i<p->nOp );\n  pCaller = &aOp[pIn1->u.i];\n  assert( pCaller->opcode==OP_Yield );\n  assert( pCaller->p2>=0 && pCaller->p2<p->nOp );\n  pOp = &aOp[pCaller->p2 - 1];\n  pIn1->flags = MEM_Undefined;\n  break;\n}\n\n/* Opcode:  Yield P1 P2 * * *\n**\n** Swap the program counter with the value in register P1.  This\n** has the effect of yielding to a coroutine.\n**\n** If the coroutine that is launched by this instruction ends with\n** Yield or Return then continue to the next instruction.  But if\n** the coroutine launched by this instruction ends with\n** EndCoroutine, then jump to P2 rather than continuing with the\n** next instruction.\n**\n** See also: InitCoroutine\n*/\ncase OP_Yield: {            /* in1, jump */\n  int pcDest;\n  pIn1 = &aMem[pOp->p1];\n  assert( VdbeMemDynamic(pIn1)==0 );\n  pIn1->flags = MEM_Int;\n  pcDest = (int)pIn1->u.i;\n  pIn1->u.i = (int)(pOp - aOp);\n  REGISTER_TRACE(pOp->p1, pIn1);\n  pOp = &aOp[pcDest];\n  break;\n}\n\n/* Opcode:  HaltIfNull  P1 P2 P3 P4 P5\n** Synopsis: if r[P3]=null halt\n**\n** Check the value in register P3.  If it is NULL then Halt using\n** parameter P1, P2, and P4 as if this were a Halt instruction.  If the\n** value in register P3 is not NULL, then this routine is a no-op.\n** The P5 parameter should be 1.\n*/\ncase OP_HaltIfNull: {      /* in3 */\n  pIn3 = &aMem[pOp->p3];\n  if( (pIn3->flags & MEM_Null)==0 ) break;\n  /* Fall through into OP_Halt */\n}\n\n/* Opcode:  Halt P1 P2 * P4 P5\n**\n** Exit immediately.  All open cursors, etc are closed\n** automatically.\n**\n** P1 is the result code returned by sqlite3_exec(), sqlite3_reset(),\n** or sqlite3_finalize().  For a normal halt, this should be SQLITE_OK (0).\n** For errors, it can be some other value.  If P1!=0 then P2 will determine\n** whether or not to rollback the current transaction.  Do not rollback\n** if P2==OE_Fail. Do the rollback if P2==OE_Rollback.  If P2==OE_Abort,\n** then back out all changes that have occurred during this execution of the\n** VDBE, but do not rollback the transaction. \n**\n** If P4 is not null then it is an error message string.\n**\n** P5 is a value between 0 and 4, inclusive, that modifies the P4 string.\n**\n**    0:  (no change)\n**    1:  NOT NULL contraint failed: P4\n**    2:  UNIQUE constraint failed: P4\n**    3:  CHECK constraint failed: P4\n**    4:  FOREIGN KEY constraint failed: P4\n**\n** If P5 is not zero and P4 is NULL, then everything after the \":\" is\n** omitted.\n**\n** There is an implied \"Halt 0 0 0\" instruction inserted at the very end of\n** every program.  So a jump past the last instruction of the program\n** is the same as executing Halt.\n*/\ncase OP_Halt: {\n  VdbeFrame *pFrame;\n  int pcx;\n\n  pcx = (int)(pOp - aOp);\n  if( pOp->p1==SQLITE_OK && p->pFrame ){\n    /* Halt the sub-program. Return control to the parent frame. */\n    pFrame = p->pFrame;\n    p->pFrame = pFrame->pParent;\n    p->nFrame--;\n    sqlite3VdbeSetChanges(db, p->nChange);\n    pcx = sqlite3VdbeFrameRestore(pFrame);\n    if( pOp->p2==OE_Ignore ){\n      /* Instruction pcx is the OP_Program that invoked the sub-program \n      ** currently being halted. If the p2 instruction of this OP_Halt\n      ** instruction is set to OE_Ignore, then the sub-program is throwing\n      ** an IGNORE exception. In this case jump to the address specified\n      ** as the p2 of the calling OP_Program.  */\n      pcx = p->aOp[pcx].p2-1;\n    }\n    aOp = p->aOp;\n    aMem = p->aMem;\n    pOp = &aOp[pcx];\n    break;\n  }\n  p->rc = pOp->p1;\n  p->errorAction = (u8)pOp->p2;\n  p->pc = pcx;\n  assert( pOp->p5<=4 );\n  if( p->rc ){\n    if( pOp->p5 ){\n      static const char * const azType[] = { \"NOT NULL\", \"UNIQUE\", \"CHECK\",\n                                             \"FOREIGN KEY\" };\n      testcase( pOp->p5==1 );\n      testcase( pOp->p5==2 );\n      testcase( pOp->p5==3 );\n      testcase( pOp->p5==4 );\n      sqlite3VdbeError(p, \"%s constraint failed\", azType[pOp->p5-1]);\n      if( pOp->p4.z ){\n        p->zErrMsg = sqlite3MPrintf(db, \"%z: %s\", p->zErrMsg, pOp->p4.z);\n      }\n    }else{\n      sqlite3VdbeError(p, \"%s\", pOp->p4.z);\n    }\n    sqlite3_log(pOp->p1, \"abort at %d in [%s]: %s\", pcx, p->zSql, p->zErrMsg);\n  }\n  rc = sqlite3VdbeHalt(p);\n  assert( rc==SQLITE_BUSY || rc==SQLITE_OK || rc==SQLITE_ERROR );\n  if( rc==SQLITE_BUSY ){\n    p->rc = SQLITE_BUSY;\n  }else{\n    assert( rc==SQLITE_OK || (p->rc&0xff)==SQLITE_CONSTRAINT );\n    assert( rc==SQLITE_OK || db->nDeferredCons>0 || db->nDeferredImmCons>0 );\n    rc = p->rc ? SQLITE_ERROR : SQLITE_DONE;\n  }\n  goto vdbe_return;\n}\n\n/* Opcode: Integer P1 P2 * * *\n** Synopsis: r[P2]=P1\n**\n** The 32-bit integer value P1 is written into register P2.\n*/\ncase OP_Integer: {         /* out2 */\n  pOut = out2Prerelease(p, pOp);\n  pOut->u.i = pOp->p1;\n  break;\n}\n\n/* Opcode: Int64 * P2 * P4 *\n** Synopsis: r[P2]=P4\n**\n** P4 is a pointer to a 64-bit integer value.\n** Write that value into register P2.\n*/\ncase OP_Int64: {           /* out2 */\n  pOut = out2Prerelease(p, pOp);\n  assert( pOp->p4.pI64!=0 );\n  pOut->u.i = *pOp->p4.pI64;\n  break;\n}\n\n#ifndef SQLITE_OMIT_FLOATING_POINT\n/* Opcode: Real * P2 * P4 *\n** Synopsis: r[P2]=P4\n**\n** P4 is a pointer to a 64-bit floating point value.\n** Write that value into register P2.\n*/\ncase OP_Real: {            /* same as TK_FLOAT, out2 */\n  pOut = out2Prerelease(p, pOp);\n  pOut->flags = MEM_Real;\n  assert( !sqlite3IsNaN(*pOp->p4.pReal) );\n  pOut->u.r = *pOp->p4.pReal;\n  break;\n}\n#endif\n\n/* Opcode: String8 * P2 * P4 *\n** Synopsis: r[P2]='P4'\n**\n** P4 points to a nul terminated UTF-8 string. This opcode is transformed \n** into a String opcode before it is executed for the first time.  During\n** this transformation, the length of string P4 is computed and stored\n** as the P1 parameter.\n*/\ncase OP_String8: {         /* same as TK_STRING, out2 */\n  assert( pOp->p4.z!=0 );\n  pOut = out2Prerelease(p, pOp);\n  pOp->opcode = OP_String;\n  pOp->p1 = sqlite3Strlen30(pOp->p4.z);\n\n#ifndef SQLITE_OMIT_UTF16\n  if( encoding!=SQLITE_UTF8 ){\n    rc = sqlite3VdbeMemSetStr(pOut, pOp->p4.z, -1, SQLITE_UTF8, SQLITE_STATIC);\n    assert( rc==SQLITE_OK || rc==SQLITE_TOOBIG );\n    if( SQLITE_OK!=sqlite3VdbeChangeEncoding(pOut, encoding) ) goto no_mem;\n    assert( pOut->szMalloc>0 && pOut->zMalloc==pOut->z );\n    assert( VdbeMemDynamic(pOut)==0 );\n    pOut->szMalloc = 0;\n    pOut->flags |= MEM_Static;\n    if( pOp->p4type==P4_DYNAMIC ){\n      sqlite3DbFree(db, pOp->p4.z);\n    }\n    pOp->p4type = P4_DYNAMIC;\n    pOp->p4.z = pOut->z;\n    pOp->p1 = pOut->n;\n  }\n  testcase( rc==SQLITE_TOOBIG );\n#endif\n  if( pOp->p1>db->aLimit[SQLITE_LIMIT_LENGTH] ){\n    goto too_big;\n  }\n  assert( rc==SQLITE_OK );\n  /* Fall through to the next case, OP_String */\n}\n  \n/* Opcode: String P1 P2 P3 P4 P5\n** Synopsis: r[P2]='P4' (len=P1)\n**\n** The string value P4 of length P1 (bytes) is stored in register P2.\n**\n** If P3 is not zero and the content of register P3 is equal to P5, then\n** the datatype of the register P2 is converted to BLOB.  The content is\n** the same sequence of bytes, it is merely interpreted as a BLOB instead\n** of a string, as if it had been CAST.  In other words:\n**\n** if( P3!=0 and reg[P3]==P5 ) reg[P2] := CAST(reg[P2] as BLOB)\n*/\ncase OP_String: {          /* out2 */\n  assert( pOp->p4.z!=0 );\n  pOut = out2Prerelease(p, pOp);\n  pOut->flags = MEM_Str|MEM_Static|MEM_Term;\n  pOut->z = pOp->p4.z;\n  pOut->n = pOp->p1;\n  pOut->enc = encoding;\n  UPDATE_MAX_BLOBSIZE(pOut);\n#ifndef SQLITE_LIKE_DOESNT_MATCH_BLOBS\n  if( pOp->p3>0 ){\n    assert( pOp->p3<=(p->nMem+1 - p->nCursor) );\n    pIn3 = &aMem[pOp->p3];\n    assert( pIn3->flags & MEM_Int );\n    if( pIn3->u.i==pOp->p5 ) pOut->flags = MEM_Blob|MEM_Static|MEM_Term;\n  }\n#endif\n  break;\n}\n\n/* Opcode: Null P1 P2 P3 * *\n** Synopsis: r[P2..P3]=NULL\n**\n** Write a NULL into registers P2.  If P3 greater than P2, then also write\n** NULL into register P3 and every register in between P2 and P3.  If P3\n** is less than P2 (typically P3 is zero) then only register P2 is\n** set to NULL.\n**\n** If the P1 value is non-zero, then also set the MEM_Cleared flag so that\n** NULL values will not compare equal even if SQLITE_NULLEQ is set on\n** OP_Ne or OP_Eq.\n*/\ncase OP_Null: {           /* out2 */\n  int cnt;\n  u16 nullFlag;\n  pOut = out2Prerelease(p, pOp);\n  cnt = pOp->p3-pOp->p2;\n  assert( pOp->p3<=(p->nMem+1 - p->nCursor) );\n  pOut->flags = nullFlag = pOp->p1 ? (MEM_Null|MEM_Cleared) : MEM_Null;\n  pOut->n = 0;\n  while( cnt>0 ){\n    pOut++;\n    memAboutToChange(p, pOut);\n    sqlite3VdbeMemSetNull(pOut);\n    pOut->flags = nullFlag;\n    pOut->n = 0;\n    cnt--;\n  }\n  break;\n}\n\n/* Opcode: SoftNull P1 * * * *\n** Synopsis: r[P1]=NULL\n**\n** Set register P1 to have the value NULL as seen by the OP_MakeRecord\n** instruction, but do not free any string or blob memory associated with\n** the register, so that if the value was a string or blob that was\n** previously copied using OP_SCopy, the copies will continue to be valid.\n*/\ncase OP_SoftNull: {\n  assert( pOp->p1>0 && pOp->p1<=(p->nMem+1 - p->nCursor) );\n  pOut = &aMem[pOp->p1];\n  pOut->flags = (pOut->flags&~(MEM_Undefined|MEM_AffMask))|MEM_Null;\n  break;\n}\n\n/* Opcode: Blob P1 P2 * P4 *\n** Synopsis: r[P2]=P4 (len=P1)\n**\n** P4 points to a blob of data P1 bytes long.  Store this\n** blob in register P2.\n*/\ncase OP_Blob: {                /* out2 */\n  assert( pOp->p1 <= SQLITE_MAX_LENGTH );\n  pOut = out2Prerelease(p, pOp);\n  sqlite3VdbeMemSetStr(pOut, pOp->p4.z, pOp->p1, 0, 0);\n  pOut->enc = encoding;\n  UPDATE_MAX_BLOBSIZE(pOut);\n  break;\n}\n\n/* Opcode: Variable P1 P2 * P4 *\n** Synopsis: r[P2]=parameter(P1,P4)\n**\n** Transfer the values of bound parameter P1 into register P2\n**\n** If the parameter is named, then its name appears in P4.\n** The P4 value is used by sqlite3_bind_parameter_name().\n*/\ncase OP_Variable: {            /* out2 */\n  Mem *pVar;       /* Value being transferred */\n\n  assert( pOp->p1>0 && pOp->p1<=p->nVar );\n  assert( pOp->p4.z==0 || pOp->p4.z==sqlite3VListNumToName(p->pVList,pOp->p1) );\n  pVar = &p->aVar[pOp->p1 - 1];\n  if( sqlite3VdbeMemTooBig(pVar) ){\n    goto too_big;\n  }\n  pOut = &aMem[pOp->p2];\n  sqlite3VdbeMemShallowCopy(pOut, pVar, MEM_Static);\n  UPDATE_MAX_BLOBSIZE(pOut);\n  break;\n}\n\n/* Opcode: Move P1 P2 P3 * *\n** Synopsis: r[P2@P3]=r[P1@P3]\n**\n** Move the P3 values in register P1..P1+P3-1 over into\n** registers P2..P2+P3-1.  Registers P1..P1+P3-1 are\n** left holding a NULL.  It is an error for register ranges\n** P1..P1+P3-1 and P2..P2+P3-1 to overlap.  It is an error\n** for P3 to be less than 1.\n*/\ncase OP_Move: {\n  int n;           /* Number of registers left to copy */\n  int p1;          /* Register to copy from */\n  int p2;          /* Register to copy to */\n\n  n = pOp->p3;\n  p1 = pOp->p1;\n  p2 = pOp->p2;\n  assert( n>0 && p1>0 && p2>0 );\n  assert( p1+n<=p2 || p2+n<=p1 );\n\n  pIn1 = &aMem[p1];\n  pOut = &aMem[p2];\n  do{\n    assert( pOut<=&aMem[(p->nMem+1 - p->nCursor)] );\n    assert( pIn1<=&aMem[(p->nMem+1 - p->nCursor)] );\n    assert( memIsValid(pIn1) );\n    memAboutToChange(p, pOut);\n    sqlite3VdbeMemMove(pOut, pIn1);\n#ifdef SQLITE_DEBUG\n    if( pOut->pScopyFrom>=&aMem[p1] && pOut->pScopyFrom<pOut ){\n      pOut->pScopyFrom += pOp->p2 - p1;\n    }\n#endif\n    Deephemeralize(pOut);\n    REGISTER_TRACE(p2++, pOut);\n    pIn1++;\n    pOut++;\n  }while( --n );\n  break;\n}\n\n/* Opcode: Copy P1 P2 P3 * *\n** Synopsis: r[P2@P3+1]=r[P1@P3+1]\n**\n** Make a copy of registers P1..P1+P3 into registers P2..P2+P3.\n**\n** This instruction makes a deep copy of the value.  A duplicate\n** is made of any string or blob constant.  See also OP_SCopy.\n*/\ncase OP_Copy: {\n  int n;\n\n  n = pOp->p3;\n  pIn1 = &aMem[pOp->p1];\n  pOut = &aMem[pOp->p2];\n  assert( pOut!=pIn1 );\n  while( 1 ){\n    sqlite3VdbeMemShallowCopy(pOut, pIn1, MEM_Ephem);\n    Deephemeralize(pOut);\n#ifdef SQLITE_DEBUG\n    pOut->pScopyFrom = 0;\n#endif\n    REGISTER_TRACE(pOp->p2+pOp->p3-n, pOut);\n    if( (n--)==0 ) break;\n    pOut++;\n    pIn1++;\n  }\n  break;\n}\n\n/* Opcode: SCopy P1 P2 * * *\n** Synopsis: r[P2]=r[P1]\n**\n** Make a shallow copy of register P1 into register P2.\n**\n** This instruction makes a shallow copy of the value.  If the value\n** is a string or blob, then the copy is only a pointer to the\n** original and hence if the original changes so will the copy.\n** Worse, if the original is deallocated, the copy becomes invalid.\n** Thus the program must guarantee that the original will not change\n** during the lifetime of the copy.  Use OP_Copy to make a complete\n** copy.\n*/\ncase OP_SCopy: {            /* out2 */\n  pIn1 = &aMem[pOp->p1];\n  pOut = &aMem[pOp->p2];\n  assert( pOut!=pIn1 );\n  sqlite3VdbeMemShallowCopy(pOut, pIn1, MEM_Ephem);\n#ifdef SQLITE_DEBUG\n  if( pOut->pScopyFrom==0 ) pOut->pScopyFrom = pIn1;\n#endif\n  break;\n}\n\n/* Opcode: IntCopy P1 P2 * * *\n** Synopsis: r[P2]=r[P1]\n**\n** Transfer the integer value held in register P1 into register P2.\n**\n** This is an optimized version of SCopy that works only for integer\n** values.\n*/\ncase OP_IntCopy: {            /* out2 */\n  pIn1 = &aMem[pOp->p1];\n  assert( (pIn1->flags & MEM_Int)!=0 );\n  pOut = &aMem[pOp->p2];\n  sqlite3VdbeMemSetInt64(pOut, pIn1->u.i);\n  break;\n}\n\n/* Opcode: ResultRow P1 P2 * * *\n** Synopsis: output=r[P1@P2]\n**\n** The registers P1 through P1+P2-1 contain a single row of\n** results. This opcode causes the sqlite3_step() call to terminate\n** with an SQLITE_ROW return code and it sets up the sqlite3_stmt\n** structure to provide access to the r(P1)..r(P1+P2-1) values as\n** the result row.\n*/\ncase OP_ResultRow: {\n  Mem *pMem;\n  int i;\n  assert( p->nResColumn==pOp->p2 );\n  assert( pOp->p1>0 );\n  assert( pOp->p1+pOp->p2<=(p->nMem+1 - p->nCursor)+1 );\n\n#ifndef SQLITE_OMIT_PROGRESS_CALLBACK\n  /* Run the progress counter just before returning.\n  */\n  if( db->xProgress!=0\n   && nVmStep>=nProgressLimit \n   && db->xProgress(db->pProgressArg)!=0\n  ){\n    rc = SQLITE_INTERRUPT;\n    goto abort_due_to_error;\n  }\n#endif\n\n  /* If this statement has violated immediate foreign key constraints, do\n  ** not return the number of rows modified. And do not RELEASE the statement\n  ** transaction. It needs to be rolled back.  */\n  if( SQLITE_OK!=(rc = sqlite3VdbeCheckFk(p, 0)) ){\n    assert( db->flags&SQLITE_CountRows );\n    assert( p->usesStmtJournal );\n    goto abort_due_to_error;\n  }\n\n  /* If the SQLITE_CountRows flag is set in sqlite3.flags mask, then \n  ** DML statements invoke this opcode to return the number of rows \n  ** modified to the user. This is the only way that a VM that\n  ** opens a statement transaction may invoke this opcode.\n  **\n  ** In case this is such a statement, close any statement transaction\n  ** opened by this VM before returning control to the user. This is to\n  ** ensure that statement-transactions are always nested, not overlapping.\n  ** If the open statement-transaction is not closed here, then the user\n  ** may step another VM that opens its own statement transaction. This\n  ** may lead to overlapping statement transactions.\n  **\n  ** The statement transaction is never a top-level transaction.  Hence\n  ** the RELEASE call below can never fail.\n  */\n  assert( p->iStatement==0 || db->flags&SQLITE_CountRows );\n  rc = sqlite3VdbeCloseStatement(p, SAVEPOINT_RELEASE);\n  assert( rc==SQLITE_OK );\n\n  /* Invalidate all ephemeral cursor row caches */\n  p->cacheCtr = (p->cacheCtr + 2)|1;\n\n  /* Make sure the results of the current row are \\000 terminated\n  ** and have an assigned type.  The results are de-ephemeralized as\n  ** a side effect.\n  */\n  pMem = p->pResultSet = &aMem[pOp->p1];\n  for(i=0; i<pOp->p2; i++){\n    assert( memIsValid(&pMem[i]) );\n    Deephemeralize(&pMem[i]);\n    assert( (pMem[i].flags & MEM_Ephem)==0\n            || (pMem[i].flags & (MEM_Str|MEM_Blob))==0 );\n    sqlite3VdbeMemNulTerminate(&pMem[i]);\n    REGISTER_TRACE(pOp->p1+i, &pMem[i]);\n  }\n  if( db->mallocFailed ) goto no_mem;\n\n  if( db->mTrace & SQLITE_TRACE_ROW ){\n    db->xTrace(SQLITE_TRACE_ROW, db->pTraceArg, p, 0);\n  }\n\n  /* Return SQLITE_ROW\n  */\n  p->pc = (int)(pOp - aOp) + 1;\n  rc = SQLITE_ROW;\n  goto vdbe_return;\n}\n\n/* Opcode: Concat P1 P2 P3 * *\n** Synopsis: r[P3]=r[P2]+r[P1]\n**\n** Add the text in register P1 onto the end of the text in\n** register P2 and store the result in register P3.\n** If either the P1 or P2 text are NULL then store NULL in P3.\n**\n**   P3 = P2 || P1\n**\n** It is illegal for P1 and P3 to be the same register. Sometimes,\n** if P3 is the same register as P2, the implementation is able\n** to avoid a memcpy().\n*/\ncase OP_Concat: {           /* same as TK_CONCAT, in1, in2, out3 */\n  i64 nByte;\n\n  pIn1 = &aMem[pOp->p1];\n  pIn2 = &aMem[pOp->p2];\n  pOut = &aMem[pOp->p3];\n  assert( pIn1!=pOut );\n  if( (pIn1->flags | pIn2->flags) & MEM_Null ){\n    sqlite3VdbeMemSetNull(pOut);\n    break;\n  }\n  if( ExpandBlob(pIn1) || ExpandBlob(pIn2) ) goto no_mem;\n  Stringify(pIn1, encoding);\n  Stringify(pIn2, encoding);\n  nByte = pIn1->n + pIn2->n;\n  if( nByte>db->aLimit[SQLITE_LIMIT_LENGTH] ){\n    goto too_big;\n  }\n  if( sqlite3VdbeMemGrow(pOut, (int)nByte+2, pOut==pIn2) ){\n    goto no_mem;\n  }\n  MemSetTypeFlag(pOut, MEM_Str);\n  if( pOut!=pIn2 ){\n    memcpy(pOut->z, pIn2->z, pIn2->n);\n  }\n  memcpy(&pOut->z[pIn2->n], pIn1->z, pIn1->n);\n  pOut->z[nByte]=0;\n  pOut->z[nByte+1] = 0;\n  pOut->flags |= MEM_Term;\n  pOut->n = (int)nByte;\n  pOut->enc = encoding;\n  UPDATE_MAX_BLOBSIZE(pOut);\n  break;\n}\n\n/* Opcode: Add P1 P2 P3 * *\n** Synopsis: r[P3]=r[P1]+r[P2]\n**\n** Add the value in register P1 to the value in register P2\n** and store the result in register P3.\n** If either input is NULL, the result is NULL.\n*/\n/* Opcode: Multiply P1 P2 P3 * *\n** Synopsis: r[P3]=r[P1]*r[P2]\n**\n**\n** Multiply the value in register P1 by the value in register P2\n** and store the result in register P3.\n** If either input is NULL, the result is NULL.\n*/\n/* Opcode: Subtract P1 P2 P3 * *\n** Synopsis: r[P3]=r[P2]-r[P1]\n**\n** Subtract the value in register P1 from the value in register P2\n** and store the result in register P3.\n** If either input is NULL, the result is NULL.\n*/\n/* Opcode: Divide P1 P2 P3 * *\n** Synopsis: r[P3]=r[P2]/r[P1]\n**\n** Divide the value in register P1 by the value in register P2\n** and store the result in register P3 (P3=P2/P1). If the value in \n** register P1 is zero, then the result is NULL. If either input is \n** NULL, the result is NULL.\n*/\n/* Opcode: Remainder P1 P2 P3 * *\n** Synopsis: r[P3]=r[P2]%r[P1]\n**\n** Compute the remainder after integer register P2 is divided by \n** register P1 and store the result in register P3. \n** If the value in register P1 is zero the result is NULL.\n** If either operand is NULL, the result is NULL.\n*/\ncase OP_Add:                   /* same as TK_PLUS, in1, in2, out3 */\ncase OP_Subtract:              /* same as TK_MINUS, in1, in2, out3 */\ncase OP_Multiply:              /* same as TK_STAR, in1, in2, out3 */\ncase OP_Divide:                /* same as TK_SLASH, in1, in2, out3 */\ncase OP_Remainder: {           /* same as TK_REM, in1, in2, out3 */\n  char bIntint;   /* Started out as two integer operands */\n  u16 flags;      /* Combined MEM_* flags from both inputs */\n  u16 type1;      /* Numeric type of left operand */\n  u16 type2;      /* Numeric type of right operand */\n  i64 iA;         /* Integer value of left operand */\n  i64 iB;         /* Integer value of right operand */\n  double rA;      /* Real value of left operand */\n  double rB;      /* Real value of right operand */\n\n  pIn1 = &aMem[pOp->p1];\n  type1 = numericType(pIn1);\n  pIn2 = &aMem[pOp->p2];\n  type2 = numericType(pIn2);\n  pOut = &aMem[pOp->p3];\n  flags = pIn1->flags | pIn2->flags;\n  if( (type1 & type2 & MEM_Int)!=0 ){\n    iA = pIn1->u.i;\n    iB = pIn2->u.i;\n    bIntint = 1;\n    switch( pOp->opcode ){\n      case OP_Add:       if( sqlite3AddInt64(&iB,iA) ) goto fp_math;  break;\n      case OP_Subtract:  if( sqlite3SubInt64(&iB,iA) ) goto fp_math;  break;\n      case OP_Multiply:  if( sqlite3MulInt64(&iB,iA) ) goto fp_math;  break;\n      case OP_Divide: {\n        if( iA==0 ) goto arithmetic_result_is_null;\n        if( iA==-1 && iB==SMALLEST_INT64 ) goto fp_math;\n        iB /= iA;\n        break;\n      }\n      default: {\n        if( iA==0 ) goto arithmetic_result_is_null;\n        if( iA==-1 ) iA = 1;\n        iB %= iA;\n        break;\n      }\n    }\n    pOut->u.i = iB;\n    MemSetTypeFlag(pOut, MEM_Int);\n  }else if( (flags & MEM_Null)!=0 ){\n    goto arithmetic_result_is_null;\n  }else{\n    bIntint = 0;\nfp_math:\n    rA = sqlite3VdbeRealValue(pIn1);\n    rB = sqlite3VdbeRealValue(pIn2);\n    switch( pOp->opcode ){\n      case OP_Add:         rB += rA;       break;\n      case OP_Subtract:    rB -= rA;       break;\n      case OP_Multiply:    rB *= rA;       break;\n      case OP_Divide: {\n        /* (double)0 In case of SQLITE_OMIT_FLOATING_POINT... */\n        if( rA==(double)0 ) goto arithmetic_result_is_null;\n        rB /= rA;\n        break;\n      }\n      default: {\n        iA = (i64)rA;\n        iB = (i64)rB;\n        if( iA==0 ) goto arithmetic_result_is_null;\n        if( iA==-1 ) iA = 1;\n        rB = (double)(iB % iA);\n        break;\n      }\n    }\n#ifdef SQLITE_OMIT_FLOATING_POINT\n    pOut->u.i = rB;\n    MemSetTypeFlag(pOut, MEM_Int);\n#else\n    if( sqlite3IsNaN(rB) ){\n      goto arithmetic_result_is_null;\n    }\n    pOut->u.r = rB;\n    MemSetTypeFlag(pOut, MEM_Real);\n    if( ((type1|type2)&MEM_Real)==0 && !bIntint ){\n      sqlite3VdbeIntegerAffinity(pOut);\n    }\n#endif\n  }\n  break;\n\narithmetic_result_is_null:\n  sqlite3VdbeMemSetNull(pOut);\n  break;\n}\n\n/* Opcode: CollSeq P1 * * P4\n**\n** P4 is a pointer to a CollSeq object. If the next call to a user function\n** or aggregate calls sqlite3GetFuncCollSeq(), this collation sequence will\n** be returned. This is used by the built-in min(), max() and nullif()\n** functions.\n**\n** If P1 is not zero, then it is a register that a subsequent min() or\n** max() aggregate will set to 1 if the current row is not the minimum or\n** maximum.  The P1 register is initialized to 0 by this instruction.\n**\n** The interface used by the implementation of the aforementioned functions\n** to retrieve the collation sequence set by this opcode is not available\n** publicly.  Only built-in functions have access to this feature.\n*/\ncase OP_CollSeq: {\n  assert( pOp->p4type==P4_COLLSEQ );\n  if( pOp->p1 ){\n    sqlite3VdbeMemSetInt64(&aMem[pOp->p1], 0);\n  }\n  break;\n}\n\n/* Opcode: BitAnd P1 P2 P3 * *\n** Synopsis: r[P3]=r[P1]&r[P2]\n**\n** Take the bit-wise AND of the values in register P1 and P2 and\n** store the result in register P3.\n** If either input is NULL, the result is NULL.\n*/\n/* Opcode: BitOr P1 P2 P3 * *\n** Synopsis: r[P3]=r[P1]|r[P2]\n**\n** Take the bit-wise OR of the values in register P1 and P2 and\n** store the result in register P3.\n** If either input is NULL, the result is NULL.\n*/\n/* Opcode: ShiftLeft P1 P2 P3 * *\n** Synopsis: r[P3]=r[P2]<<r[P1]\n**\n** Shift the integer value in register P2 to the left by the\n** number of bits specified by the integer in register P1.\n** Store the result in register P3.\n** If either input is NULL, the result is NULL.\n*/\n/* Opcode: ShiftRight P1 P2 P3 * *\n** Synopsis: r[P3]=r[P2]>>r[P1]\n**\n** Shift the integer value in register P2 to the right by the\n** number of bits specified by the integer in register P1.\n** Store the result in register P3.\n** If either input is NULL, the result is NULL.\n*/\ncase OP_BitAnd:                 /* same as TK_BITAND, in1, in2, out3 */\ncase OP_BitOr:                  /* same as TK_BITOR, in1, in2, out3 */\ncase OP_ShiftLeft:              /* same as TK_LSHIFT, in1, in2, out3 */\ncase OP_ShiftRight: {           /* same as TK_RSHIFT, in1, in2, out3 */\n  i64 iA;\n  u64 uA;\n  i64 iB;\n  u8 op;\n\n  pIn1 = &aMem[pOp->p1];\n  pIn2 = &aMem[pOp->p2];\n  pOut = &aMem[pOp->p3];\n  if( (pIn1->flags | pIn2->flags) & MEM_Null ){\n    sqlite3VdbeMemSetNull(pOut);\n    break;\n  }\n  iA = sqlite3VdbeIntValue(pIn2);\n  iB = sqlite3VdbeIntValue(pIn1);\n  op = pOp->opcode;\n  if( op==OP_BitAnd ){\n    iA &= iB;\n  }else if( op==OP_BitOr ){\n    iA |= iB;\n  }else if( iB!=0 ){\n    assert( op==OP_ShiftRight || op==OP_ShiftLeft );\n\n    /* If shifting by a negative amount, shift in the other direction */\n    if( iB<0 ){\n      assert( OP_ShiftRight==OP_ShiftLeft+1 );\n      op = 2*OP_ShiftLeft + 1 - op;\n      iB = iB>(-64) ? -iB : 64;\n    }\n\n    if( iB>=64 ){\n      iA = (iA>=0 || op==OP_ShiftLeft) ? 0 : -1;\n    }else{\n      memcpy(&uA, &iA, sizeof(uA));\n      if( op==OP_ShiftLeft ){\n        uA <<= iB;\n      }else{\n        uA >>= iB;\n        /* Sign-extend on a right shift of a negative number */\n        if( iA<0 ) uA |= ((((u64)0xffffffff)<<32)|0xffffffff) << (64-iB);\n      }\n      memcpy(&iA, &uA, sizeof(iA));\n    }\n  }\n  pOut->u.i = iA;\n  MemSetTypeFlag(pOut, MEM_Int);\n  break;\n}\n\n/* Opcode: AddImm  P1 P2 * * *\n** Synopsis: r[P1]=r[P1]+P2\n** \n** Add the constant P2 to the value in register P1.\n** The result is always an integer.\n**\n** To force any register to be an integer, just add 0.\n*/\ncase OP_AddImm: {            /* in1 */\n  pIn1 = &aMem[pOp->p1];\n  memAboutToChange(p, pIn1);\n  sqlite3VdbeMemIntegerify(pIn1);\n  pIn1->u.i += pOp->p2;\n  break;\n}\n\n/* Opcode: MustBeInt P1 P2 * * *\n** \n** Force the value in register P1 to be an integer.  If the value\n** in P1 is not an integer and cannot be converted into an integer\n** without data loss, then jump immediately to P2, or if P2==0\n** raise an SQLITE_MISMATCH exception.\n*/\ncase OP_MustBeInt: {            /* jump, in1 */\n  pIn1 = &aMem[pOp->p1];\n  if( (pIn1->flags & MEM_Int)==0 ){\n    applyAffinity(pIn1, SQLITE_AFF_NUMERIC, encoding);\n    VdbeBranchTaken((pIn1->flags&MEM_Int)==0, 2);\n    if( (pIn1->flags & MEM_Int)==0 ){\n      if( pOp->p2==0 ){\n        rc = SQLITE_MISMATCH;\n        goto abort_due_to_error;\n      }else{\n        goto jump_to_p2;\n      }\n    }\n  }\n  MemSetTypeFlag(pIn1, MEM_Int);\n  break;\n}\n\n#ifndef SQLITE_OMIT_FLOATING_POINT\n/* Opcode: RealAffinity P1 * * * *\n**\n** If register P1 holds an integer convert it to a real value.\n**\n** This opcode is used when extracting information from a column that\n** has REAL affinity.  Such column values may still be stored as\n** integers, for space efficiency, but after extraction we want them\n** to have only a real value.\n*/\ncase OP_RealAffinity: {                  /* in1 */\n  pIn1 = &aMem[pOp->p1];\n  if( pIn1->flags & MEM_Int ){\n    sqlite3VdbeMemRealify(pIn1);\n  }\n  break;\n}\n#endif\n\n#ifndef SQLITE_OMIT_CAST\n/* Opcode: Cast P1 P2 * * *\n** Synopsis: affinity(r[P1])\n**\n** Force the value in register P1 to be the type defined by P2.\n** \n** <ul>\n** <li> P2=='A' &rarr; BLOB\n** <li> P2=='B' &rarr; TEXT\n** <li> P2=='C' &rarr; NUMERIC\n** <li> P2=='D' &rarr; INTEGER\n** <li> P2=='E' &rarr; REAL\n** </ul>\n**\n** A NULL value is not changed by this routine.  It remains NULL.\n*/\ncase OP_Cast: {                  /* in1 */\n  assert( pOp->p2>=SQLITE_AFF_BLOB && pOp->p2<=SQLITE_AFF_REAL );\n  testcase( pOp->p2==SQLITE_AFF_TEXT );\n  testcase( pOp->p2==SQLITE_AFF_BLOB );\n  testcase( pOp->p2==SQLITE_AFF_NUMERIC );\n  testcase( pOp->p2==SQLITE_AFF_INTEGER );\n  testcase( pOp->p2==SQLITE_AFF_REAL );\n  pIn1 = &aMem[pOp->p1];\n  memAboutToChange(p, pIn1);\n  rc = ExpandBlob(pIn1);\n  sqlite3VdbeMemCast(pIn1, pOp->p2, encoding);\n  UPDATE_MAX_BLOBSIZE(pIn1);\n  if( rc ) goto abort_due_to_error;\n  break;\n}\n#endif /* SQLITE_OMIT_CAST */\n\n/* Opcode: Eq P1 P2 P3 P4 P5\n** Synopsis: IF r[P3]==r[P1]\n**\n** Compare the values in register P1 and P3.  If reg(P3)==reg(P1) then\n** jump to address P2.  Or if the SQLITE_STOREP2 flag is set in P5, then\n** store the result of comparison in register P2.\n**\n** The SQLITE_AFF_MASK portion of P5 must be an affinity character -\n** SQLITE_AFF_TEXT, SQLITE_AFF_INTEGER, and so forth. An attempt is made \n** to coerce both inputs according to this affinity before the\n** comparison is made. If the SQLITE_AFF_MASK is 0x00, then numeric\n** affinity is used. Note that the affinity conversions are stored\n** back into the input registers P1 and P3.  So this opcode can cause\n** persistent changes to registers P1 and P3.\n**\n** Once any conversions have taken place, and neither value is NULL, \n** the values are compared. If both values are blobs then memcmp() is\n** used to determine the results of the comparison.  If both values\n** are text, then the appropriate collating function specified in\n** P4 is used to do the comparison.  If P4 is not specified then\n** memcmp() is used to compare text string.  If both values are\n** numeric, then a numeric comparison is used. If the two values\n** are of different types, then numbers are considered less than\n** strings and strings are considered less than blobs.\n**\n** If SQLITE_NULLEQ is set in P5 then the result of comparison is always either\n** true or false and is never NULL.  If both operands are NULL then the result\n** of comparison is true.  If either operand is NULL then the result is false.\n** If neither operand is NULL the result is the same as it would be if\n** the SQLITE_NULLEQ flag were omitted from P5.\n**\n** If both SQLITE_STOREP2 and SQLITE_KEEPNULL flags are set then the\n** content of r[P2] is only changed if the new value is NULL or 0 (false).\n** In other words, a prior r[P2] value will not be overwritten by 1 (true).\n*/\n/* Opcode: Ne P1 P2 P3 P4 P5\n** Synopsis: IF r[P3]!=r[P1]\n**\n** This works just like the Eq opcode except that the jump is taken if\n** the operands in registers P1 and P3 are not equal.  See the Eq opcode for\n** additional information.\n**\n** If both SQLITE_STOREP2 and SQLITE_KEEPNULL flags are set then the\n** content of r[P2] is only changed if the new value is NULL or 1 (true).\n** In other words, a prior r[P2] value will not be overwritten by 0 (false).\n*/\n/* Opcode: Lt P1 P2 P3 P4 P5\n** Synopsis: IF r[P3]<r[P1]\n**\n** Compare the values in register P1 and P3.  If reg(P3)<reg(P1) then\n** jump to address P2.  Or if the SQLITE_STOREP2 flag is set in P5 store\n** the result of comparison (0 or 1 or NULL) into register P2.\n**\n** If the SQLITE_JUMPIFNULL bit of P5 is set and either reg(P1) or\n** reg(P3) is NULL then the take the jump.  If the SQLITE_JUMPIFNULL \n** bit is clear then fall through if either operand is NULL.\n**\n** The SQLITE_AFF_MASK portion of P5 must be an affinity character -\n** SQLITE_AFF_TEXT, SQLITE_AFF_INTEGER, and so forth. An attempt is made \n** to coerce both inputs according to this affinity before the\n** comparison is made. If the SQLITE_AFF_MASK is 0x00, then numeric\n** affinity is used. Note that the affinity conversions are stored\n** back into the input registers P1 and P3.  So this opcode can cause\n** persistent changes to registers P1 and P3.\n**\n** Once any conversions have taken place, and neither value is NULL, \n** the values are compared. If both values are blobs then memcmp() is\n** used to determine the results of the comparison.  If both values\n** are text, then the appropriate collating function specified in\n** P4 is  used to do the comparison.  If P4 is not specified then\n** memcmp() is used to compare text string.  If both values are\n** numeric, then a numeric comparison is used. If the two values\n** are of different types, then numbers are considered less than\n** strings and strings are considered less than blobs.\n*/\n/* Opcode: Le P1 P2 P3 P4 P5\n** Synopsis: IF r[P3]<=r[P1]\n**\n** This works just like the Lt opcode except that the jump is taken if\n** the content of register P3 is less than or equal to the content of\n** register P1.  See the Lt opcode for additional information.\n*/\n/* Opcode: Gt P1 P2 P3 P4 P5\n** Synopsis: IF r[P3]>r[P1]\n**\n** This works just like the Lt opcode except that the jump is taken if\n** the content of register P3 is greater than the content of\n** register P1.  See the Lt opcode for additional information.\n*/\n/* Opcode: Ge P1 P2 P3 P4 P5\n** Synopsis: IF r[P3]>=r[P1]\n**\n** This works just like the Lt opcode except that the jump is taken if\n** the content of register P3 is greater than or equal to the content of\n** register P1.  See the Lt opcode for additional information.\n*/\ncase OP_Eq:               /* same as TK_EQ, jump, in1, in3 */\ncase OP_Ne:               /* same as TK_NE, jump, in1, in3 */\ncase OP_Lt:               /* same as TK_LT, jump, in1, in3 */\ncase OP_Le:               /* same as TK_LE, jump, in1, in3 */\ncase OP_Gt:               /* same as TK_GT, jump, in1, in3 */\ncase OP_Ge: {             /* same as TK_GE, jump, in1, in3 */\n  int res, res2;      /* Result of the comparison of pIn1 against pIn3 */\n  char affinity;      /* Affinity to use for comparison */\n  u16 flags1;         /* Copy of initial value of pIn1->flags */\n  u16 flags3;         /* Copy of initial value of pIn3->flags */\n\n  pIn1 = &aMem[pOp->p1];\n  pIn3 = &aMem[pOp->p3];\n  flags1 = pIn1->flags;\n  flags3 = pIn3->flags;\n  if( (flags1 | flags3)&MEM_Null ){\n    /* One or both operands are NULL */\n    if( pOp->p5 & SQLITE_NULLEQ ){\n      /* If SQLITE_NULLEQ is set (which will only happen if the operator is\n      ** OP_Eq or OP_Ne) then take the jump or not depending on whether\n      ** or not both operands are null.\n      */\n      assert( pOp->opcode==OP_Eq || pOp->opcode==OP_Ne );\n      assert( (flags1 & MEM_Cleared)==0 );\n      assert( (pOp->p5 & SQLITE_JUMPIFNULL)==0 );\n      if( (flags1&flags3&MEM_Null)!=0\n       && (flags3&MEM_Cleared)==0\n      ){\n        res = 0;  /* Operands are equal */\n      }else{\n        res = 1;  /* Operands are not equal */\n      }\n    }else{\n      /* SQLITE_NULLEQ is clear and at least one operand is NULL,\n      ** then the result is always NULL.\n      ** The jump is taken if the SQLITE_JUMPIFNULL bit is set.\n      */\n      if( pOp->p5 & SQLITE_STOREP2 ){\n        pOut = &aMem[pOp->p2];\n        iCompare = 1;    /* Operands are not equal */\n        memAboutToChange(p, pOut);\n        MemSetTypeFlag(pOut, MEM_Null);\n        REGISTER_TRACE(pOp->p2, pOut);\n      }else{\n        VdbeBranchTaken(2,3);\n        if( pOp->p5 & SQLITE_JUMPIFNULL ){\n          goto jump_to_p2;\n        }\n      }\n      break;\n    }\n  }else{\n    /* Neither operand is NULL.  Do a comparison. */\n    affinity = pOp->p5 & SQLITE_AFF_MASK;\n    if( affinity>=SQLITE_AFF_NUMERIC ){\n      if( (flags1 | flags3)&MEM_Str ){\n        if( (flags1 & (MEM_Int|MEM_Real|MEM_Str))==MEM_Str ){\n          applyNumericAffinity(pIn1,0);\n          testcase( flags3!=pIn3->flags ); /* Possible if pIn1==pIn3 */\n          flags3 = pIn3->flags;\n        }\n        if( (flags3 & (MEM_Int|MEM_Real|MEM_Str))==MEM_Str ){\n          applyNumericAffinity(pIn3,0);\n        }\n      }\n      /* Handle the common case of integer comparison here, as an\n      ** optimization, to avoid a call to sqlite3MemCompare() */\n      if( (pIn1->flags & pIn3->flags & MEM_Int)!=0 ){\n        if( pIn3->u.i > pIn1->u.i ){ res = +1; goto compare_op; }\n        if( pIn3->u.i < pIn1->u.i ){ res = -1; goto compare_op; }\n        res = 0;\n        goto compare_op;\n      }\n    }else if( affinity==SQLITE_AFF_TEXT ){\n      if( (flags1 & MEM_Str)==0 && (flags1 & (MEM_Int|MEM_Real))!=0 ){\n        testcase( pIn1->flags & MEM_Int );\n        testcase( pIn1->flags & MEM_Real );\n        sqlite3VdbeMemStringify(pIn1, encoding, 1);\n        testcase( (flags1&MEM_Dyn) != (pIn1->flags&MEM_Dyn) );\n        flags1 = (pIn1->flags & ~MEM_TypeMask) | (flags1 & MEM_TypeMask);\n        assert( pIn1!=pIn3 );\n      }\n      if( (flags3 & MEM_Str)==0 && (flags3 & (MEM_Int|MEM_Real))!=0 ){\n        testcase( pIn3->flags & MEM_Int );\n        testcase( pIn3->flags & MEM_Real );\n        sqlite3VdbeMemStringify(pIn3, encoding, 1);\n        testcase( (flags3&MEM_Dyn) != (pIn3->flags&MEM_Dyn) );\n        flags3 = (pIn3->flags & ~MEM_TypeMask) | (flags3 & MEM_TypeMask);\n      }\n    }\n    assert( pOp->p4type==P4_COLLSEQ || pOp->p4.pColl==0 );\n    res = sqlite3MemCompare(pIn3, pIn1, pOp->p4.pColl);\n  }\ncompare_op:\n  /* At this point, res is negative, zero, or positive if reg[P1] is\n  ** less than, equal to, or greater than reg[P3], respectively.  Compute\n  ** the answer to this operator in res2, depending on what the comparison\n  ** operator actually is.  The next block of code depends on the fact\n  ** that the 6 comparison operators are consecutive integers in this\n  ** order:  NE, EQ, GT, LE, LT, GE */\n  assert( OP_Eq==OP_Ne+1 ); assert( OP_Gt==OP_Ne+2 ); assert( OP_Le==OP_Ne+3 );\n  assert( OP_Lt==OP_Ne+4 ); assert( OP_Ge==OP_Ne+5 );\n  if( res<0 ){                        /* ne, eq, gt, le, lt, ge */\n    static const unsigned char aLTb[] = { 1,  0,  0,  1,  1,  0 };\n    res2 = aLTb[pOp->opcode - OP_Ne];\n  }else if( res==0 ){\n    static const unsigned char aEQb[] = { 0,  1,  0,  1,  0,  1 };\n    res2 = aEQb[pOp->opcode - OP_Ne];\n  }else{\n    static const unsigned char aGTb[] = { 1,  0,  1,  0,  0,  1 };\n    res2 = aGTb[pOp->opcode - OP_Ne];\n  }\n\n  /* Undo any changes made by applyAffinity() to the input registers. */\n  assert( (pIn1->flags & MEM_Dyn) == (flags1 & MEM_Dyn) );\n  pIn1->flags = flags1;\n  assert( (pIn3->flags & MEM_Dyn) == (flags3 & MEM_Dyn) );\n  pIn3->flags = flags3;\n\n  if( pOp->p5 & SQLITE_STOREP2 ){\n    pOut = &aMem[pOp->p2];\n    iCompare = res;\n    if( (pOp->p5 & SQLITE_KEEPNULL)!=0 ){\n      /* The KEEPNULL flag prevents OP_Eq from overwriting a NULL with 1\n      ** and prevents OP_Ne from overwriting NULL with 0.  This flag\n      ** is only used in contexts where either:\n      **   (1) op==OP_Eq && (r[P2]==NULL || r[P2]==0)\n      **   (2) op==OP_Ne && (r[P2]==NULL || r[P2]==1)\n      ** Therefore it is not necessary to check the content of r[P2] for\n      ** NULL. */\n      assert( pOp->opcode==OP_Ne || pOp->opcode==OP_Eq );\n      assert( res2==0 || res2==1 );\n      testcase( res2==0 && pOp->opcode==OP_Eq );\n      testcase( res2==1 && pOp->opcode==OP_Eq );\n      testcase( res2==0 && pOp->opcode==OP_Ne );\n      testcase( res2==1 && pOp->opcode==OP_Ne );\n      if( (pOp->opcode==OP_Eq)==res2 ) break;\n    }\n    memAboutToChange(p, pOut);\n    MemSetTypeFlag(pOut, MEM_Int);\n    pOut->u.i = res2;\n    REGISTER_TRACE(pOp->p2, pOut);\n  }else{\n    VdbeBranchTaken(res!=0, (pOp->p5 & SQLITE_NULLEQ)?2:3);\n    if( res2 ){\n      goto jump_to_p2;\n    }\n  }\n  break;\n}\n\n/* Opcode: ElseNotEq * P2 * * *\n**\n** This opcode must immediately follow an OP_Lt or OP_Gt comparison operator.\n** If result of an OP_Eq comparison on the same two operands\n** would have be NULL or false (0), then then jump to P2. \n** If the result of an OP_Eq comparison on the two previous operands\n** would have been true (1), then fall through.\n*/\ncase OP_ElseNotEq: {       /* same as TK_ESCAPE, jump */\n  assert( pOp>aOp );\n  assert( pOp[-1].opcode==OP_Lt || pOp[-1].opcode==OP_Gt );\n  assert( pOp[-1].p5 & SQLITE_STOREP2 );\n  VdbeBranchTaken(iCompare!=0, 2);\n  if( iCompare!=0 ) goto jump_to_p2;\n  break;\n}\n\n\n/* Opcode: Permutation * * * P4 *\n**\n** Set the permutation used by the OP_Compare operator in the next\n** instruction.  The permutation is stored in the P4 operand.\n**\n** The permutation is only valid until the next OP_Compare that has\n** the OPFLAG_PERMUTE bit set in P5. Typically the OP_Permutation should \n** occur immediately prior to the OP_Compare.\n**\n** The first integer in the P4 integer array is the length of the array\n** and does not become part of the permutation.\n*/\ncase OP_Permutation: {\n  assert( pOp->p4type==P4_INTARRAY );\n  assert( pOp->p4.ai );\n  assert( pOp[1].opcode==OP_Compare );\n  assert( pOp[1].p5 & OPFLAG_PERMUTE );\n  break;\n}\n\n/* Opcode: Compare P1 P2 P3 P4 P5\n** Synopsis: r[P1@P3] <-> r[P2@P3]\n**\n** Compare two vectors of registers in reg(P1)..reg(P1+P3-1) (call this\n** vector \"A\") and in reg(P2)..reg(P2+P3-1) (\"B\").  Save the result of\n** the comparison for use by the next OP_Jump instruct.\n**\n** If P5 has the OPFLAG_PERMUTE bit set, then the order of comparison is\n** determined by the most recent OP_Permutation operator.  If the\n** OPFLAG_PERMUTE bit is clear, then register are compared in sequential\n** order.\n**\n** P4 is a KeyInfo structure that defines collating sequences and sort\n** orders for the comparison.  The permutation applies to registers\n** only.  The KeyInfo elements are used sequentially.\n**\n** The comparison is a sort comparison, so NULLs compare equal,\n** NULLs are less than numbers, numbers are less than strings,\n** and strings are less than blobs.\n*/\ncase OP_Compare: {\n  int n;\n  int i;\n  int p1;\n  int p2;\n  const KeyInfo *pKeyInfo;\n  int idx;\n  CollSeq *pColl;    /* Collating sequence to use on this term */\n  int bRev;          /* True for DESCENDING sort order */\n  int *aPermute;     /* The permutation */\n\n  if( (pOp->p5 & OPFLAG_PERMUTE)==0 ){\n    aPermute = 0;\n  }else{\n    assert( pOp>aOp );\n    assert( pOp[-1].opcode==OP_Permutation );\n    assert( pOp[-1].p4type==P4_INTARRAY );\n    aPermute = pOp[-1].p4.ai + 1;\n    assert( aPermute!=0 );\n  }\n  n = pOp->p3;\n  pKeyInfo = pOp->p4.pKeyInfo;\n  assert( n>0 );\n  assert( pKeyInfo!=0 );\n  p1 = pOp->p1;\n  p2 = pOp->p2;\n#ifdef SQLITE_DEBUG\n  if( aPermute ){\n    int k, mx = 0;\n    for(k=0; k<n; k++) if( aPermute[k]>mx ) mx = aPermute[k];\n    assert( p1>0 && p1+mx<=(p->nMem+1 - p->nCursor)+1 );\n    assert( p2>0 && p2+mx<=(p->nMem+1 - p->nCursor)+1 );\n  }else{\n    assert( p1>0 && p1+n<=(p->nMem+1 - p->nCursor)+1 );\n    assert( p2>0 && p2+n<=(p->nMem+1 - p->nCursor)+1 );\n  }\n#endif /* SQLITE_DEBUG */\n  for(i=0; i<n; i++){\n    idx = aPermute ? aPermute[i] : i;\n    assert( memIsValid(&aMem[p1+idx]) );\n    assert( memIsValid(&aMem[p2+idx]) );\n    REGISTER_TRACE(p1+idx, &aMem[p1+idx]);\n    REGISTER_TRACE(p2+idx, &aMem[p2+idx]);\n    assert( i<pKeyInfo->nKeyField );\n    pColl = pKeyInfo->aColl[i];\n    bRev = pKeyInfo->aSortOrder[i];\n    iCompare = sqlite3MemCompare(&aMem[p1+idx], &aMem[p2+idx], pColl);\n    if( iCompare ){\n      if( bRev ) iCompare = -iCompare;\n      break;\n    }\n  }\n  break;\n}\n\n/* Opcode: Jump P1 P2 P3 * *\n**\n** Jump to the instruction at address P1, P2, or P3 depending on whether\n** in the most recent OP_Compare instruction the P1 vector was less than\n** equal to, or greater than the P2 vector, respectively.\n*/\ncase OP_Jump: {             /* jump */\n  if( iCompare<0 ){\n    VdbeBranchTaken(0,3); pOp = &aOp[pOp->p1 - 1];\n  }else if( iCompare==0 ){\n    VdbeBranchTaken(1,3); pOp = &aOp[pOp->p2 - 1];\n  }else{\n    VdbeBranchTaken(2,3); pOp = &aOp[pOp->p3 - 1];\n  }\n  break;\n}\n\n/* Opcode: And P1 P2 P3 * *\n** Synopsis: r[P3]=(r[P1] && r[P2])\n**\n** Take the logical AND of the values in registers P1 and P2 and\n** write the result into register P3.\n**\n** If either P1 or P2 is 0 (false) then the result is 0 even if\n** the other input is NULL.  A NULL and true or two NULLs give\n** a NULL output.\n*/\n/* Opcode: Or P1 P2 P3 * *\n** Synopsis: r[P3]=(r[P1] || r[P2])\n**\n** Take the logical OR of the values in register P1 and P2 and\n** store the answer in register P3.\n**\n** If either P1 or P2 is nonzero (true) then the result is 1 (true)\n** even if the other input is NULL.  A NULL and false or two NULLs\n** give a NULL output.\n*/\ncase OP_And:              /* same as TK_AND, in1, in2, out3 */\ncase OP_Or: {             /* same as TK_OR, in1, in2, out3 */\n  int v1;    /* Left operand:  0==FALSE, 1==TRUE, 2==UNKNOWN or NULL */\n  int v2;    /* Right operand: 0==FALSE, 1==TRUE, 2==UNKNOWN or NULL */\n\n  v1 = sqlite3VdbeBooleanValue(&aMem[pOp->p1], 2);\n  v2 = sqlite3VdbeBooleanValue(&aMem[pOp->p2], 2);\n  if( pOp->opcode==OP_And ){\n    static const unsigned char and_logic[] = { 0, 0, 0, 0, 1, 2, 0, 2, 2 };\n    v1 = and_logic[v1*3+v2];\n  }else{\n    static const unsigned char or_logic[] = { 0, 1, 2, 1, 1, 1, 2, 1, 2 };\n    v1 = or_logic[v1*3+v2];\n  }\n  pOut = &aMem[pOp->p3];\n  if( v1==2 ){\n    MemSetTypeFlag(pOut, MEM_Null);\n  }else{\n    pOut->u.i = v1;\n    MemSetTypeFlag(pOut, MEM_Int);\n  }\n  break;\n}\n\n/* Opcode: IsTrue P1 P2 P3 P4 *\n** Synopsis: r[P2] = coalesce(r[P1]==TRUE,P3) ^ P4\n**\n** This opcode implements the IS TRUE, IS FALSE, IS NOT TRUE, and\n** IS NOT FALSE operators.\n**\n** Interpret the value in register P1 as a boolean value.  Store that\n** boolean (a 0 or 1) in register P2.  Or if the value in register P1 is \n** NULL, then the P3 is stored in register P2.  Invert the answer if P4\n** is 1.\n**\n** The logic is summarized like this:\n**\n** <ul> \n** <li> If P3==0 and P4==0  then  r[P2] := r[P1] IS TRUE\n** <li> If P3==1 and P4==1  then  r[P2] := r[P1] IS FALSE\n** <li> If P3==0 and P4==1  then  r[P2] := r[P1] IS NOT TRUE\n** <li> If P3==1 and P4==0  then  r[P2] := r[P1] IS NOT FALSE\n** </ul>\n*/\ncase OP_IsTrue: {               /* in1, out2 */\n  assert( pOp->p4type==P4_INT32 );\n  assert( pOp->p4.i==0 || pOp->p4.i==1 );\n  assert( pOp->p3==0 || pOp->p3==1 );\n  sqlite3VdbeMemSetInt64(&aMem[pOp->p2],\n      sqlite3VdbeBooleanValue(&aMem[pOp->p1], pOp->p3) ^ pOp->p4.i);\n  break;\n}\n\n/* Opcode: Not P1 P2 * * *\n** Synopsis: r[P2]= !r[P1]\n**\n** Interpret the value in register P1 as a boolean value.  Store the\n** boolean complement in register P2.  If the value in register P1 is \n** NULL, then a NULL is stored in P2.\n*/\ncase OP_Not: {                /* same as TK_NOT, in1, out2 */\n  pIn1 = &aMem[pOp->p1];\n  pOut = &aMem[pOp->p2];\n  if( (pIn1->flags & MEM_Null)==0 ){\n    sqlite3VdbeMemSetInt64(pOut, !sqlite3VdbeBooleanValue(pIn1,0));\n  }else{\n    sqlite3VdbeMemSetNull(pOut);\n  }\n  break;\n}\n\n/* Opcode: BitNot P1 P2 * * *\n** Synopsis: r[P1]= ~r[P1]\n**\n** Interpret the content of register P1 as an integer.  Store the\n** ones-complement of the P1 value into register P2.  If P1 holds\n** a NULL then store a NULL in P2.\n*/\ncase OP_BitNot: {             /* same as TK_BITNOT, in1, out2 */\n  pIn1 = &aMem[pOp->p1];\n  pOut = &aMem[pOp->p2];\n  sqlite3VdbeMemSetNull(pOut);\n  if( (pIn1->flags & MEM_Null)==0 ){\n    pOut->flags = MEM_Int;\n    pOut->u.i = ~sqlite3VdbeIntValue(pIn1);\n  }\n  break;\n}\n\n/* Opcode: Once P1 P2 * * *\n**\n** Fall through to the next instruction the first time this opcode is\n** encountered on each invocation of the byte-code program.  Jump to P2\n** on the second and all subsequent encounters during the same invocation.\n**\n** Top-level programs determine first invocation by comparing the P1\n** operand against the P1 operand on the OP_Init opcode at the beginning\n** of the program.  If the P1 values differ, then fall through and make\n** the P1 of this opcode equal to the P1 of OP_Init.  If P1 values are\n** the same then take the jump.\n**\n** For subprograms, there is a bitmask in the VdbeFrame that determines\n** whether or not the jump should be taken.  The bitmask is necessary\n** because the self-altering code trick does not work for recursive\n** triggers.\n*/\ncase OP_Once: {             /* jump */\n  u32 iAddr;                /* Address of this instruction */\n  assert( p->aOp[0].opcode==OP_Init );\n  if( p->pFrame ){\n    iAddr = (int)(pOp - p->aOp);\n    if( (p->pFrame->aOnce[iAddr/8] & (1<<(iAddr & 7)))!=0 ){\n      VdbeBranchTaken(1, 2);\n      goto jump_to_p2;\n    }\n    p->pFrame->aOnce[iAddr/8] |= 1<<(iAddr & 7);\n  }else{\n    if( p->aOp[0].p1==pOp->p1 ){\n      VdbeBranchTaken(1, 2);\n      goto jump_to_p2;\n    }\n  }\n  VdbeBranchTaken(0, 2);\n  pOp->p1 = p->aOp[0].p1;\n  break;\n}\n\n/* Opcode: If P1 P2 P3 * *\n**\n** Jump to P2 if the value in register P1 is true.  The value\n** is considered true if it is numeric and non-zero.  If the value\n** in P1 is NULL then take the jump if and only if P3 is non-zero.\n*/\ncase OP_If:  {               /* jump, in1 */\n  int c;\n  c = sqlite3VdbeBooleanValue(&aMem[pOp->p1], pOp->p3);\n  VdbeBranchTaken(c!=0, 2);\n  if( c ) goto jump_to_p2;\n  break;\n}\n\n/* Opcode: IfNot P1 P2 P3 * *\n**\n** Jump to P2 if the value in register P1 is False.  The value\n** is considered false if it has a numeric value of zero.  If the value\n** in P1 is NULL then take the jump if and only if P3 is non-zero.\n*/\ncase OP_IfNot: {            /* jump, in1 */\n  int c;\n  c = !sqlite3VdbeBooleanValue(&aMem[pOp->p1], !pOp->p3);\n  VdbeBranchTaken(c!=0, 2);\n  if( c ) goto jump_to_p2;\n  break;\n}\n\n/* Opcode: IsNull P1 P2 * * *\n** Synopsis: if r[P1]==NULL goto P2\n**\n** Jump to P2 if the value in register P1 is NULL.\n*/\ncase OP_IsNull: {            /* same as TK_ISNULL, jump, in1 */\n  pIn1 = &aMem[pOp->p1];\n  VdbeBranchTaken( (pIn1->flags & MEM_Null)!=0, 2);\n  if( (pIn1->flags & MEM_Null)!=0 ){\n    goto jump_to_p2;\n  }\n  break;\n}\n\n/* Opcode: NotNull P1 P2 * * *\n** Synopsis: if r[P1]!=NULL goto P2\n**\n** Jump to P2 if the value in register P1 is not NULL.  \n*/\ncase OP_NotNull: {            /* same as TK_NOTNULL, jump, in1 */\n  pIn1 = &aMem[pOp->p1];\n  VdbeBranchTaken( (pIn1->flags & MEM_Null)==0, 2);\n  if( (pIn1->flags & MEM_Null)==0 ){\n    goto jump_to_p2;\n  }\n  break;\n}\n\n/* Opcode: IfNullRow P1 P2 P3 * *\n** Synopsis: if P1.nullRow then r[P3]=NULL, goto P2\n**\n** Check the cursor P1 to see if it is currently pointing at a NULL row.\n** If it is, then set register P3 to NULL and jump immediately to P2.\n** If P1 is not on a NULL row, then fall through without making any\n** changes.\n*/\ncase OP_IfNullRow: {         /* jump */\n  assert( pOp->p1>=0 && pOp->p1<p->nCursor );\n  assert( p->apCsr[pOp->p1]!=0 );\n  if( p->apCsr[pOp->p1]->nullRow ){\n    sqlite3VdbeMemSetNull(aMem + pOp->p3);\n    goto jump_to_p2;\n  }\n  break;\n}\n\n#ifdef SQLITE_ENABLE_OFFSET_SQL_FUNC\n/* Opcode: Offset P1 P2 P3 * *\n** Synopsis: r[P3] = sqlite_offset(P1)\n**\n** Store in register r[P3] the byte offset into the database file that is the\n** start of the payload for the record at which that cursor P1 is currently\n** pointing.\n**\n** P2 is the column number for the argument to the sqlite_offset() function.\n** This opcode does not use P2 itself, but the P2 value is used by the\n** code generator.  The P1, P2, and P3 operands to this opcode are the\n** as as for OP_Column.\n**\n** This opcode is only available if SQLite is compiled with the\n** -DSQLITE_ENABLE_OFFSET_SQL_FUNC option.\n*/\ncase OP_Offset: {          /* out3 */\n  VdbeCursor *pC;    /* The VDBE cursor */\n  assert( pOp->p1>=0 && pOp->p1<p->nCursor );\n  pC = p->apCsr[pOp->p1];\n  pOut = &p->aMem[pOp->p3];\n  if( NEVER(pC==0) || pC->eCurType!=CURTYPE_BTREE ){\n    sqlite3VdbeMemSetNull(pOut);\n  }else{\n    sqlite3VdbeMemSetInt64(pOut, sqlite3BtreeOffset(pC->uc.pCursor));\n  }\n  break;\n}\n#endif /* SQLITE_ENABLE_OFFSET_SQL_FUNC */\n\n/* Opcode: Column P1 P2 P3 P4 P5\n** Synopsis: r[P3]=PX\n**\n** Interpret the data that cursor P1 points to as a structure built using\n** the MakeRecord instruction.  (See the MakeRecord opcode for additional\n** information about the format of the data.)  Extract the P2-th column\n** from this record.  If there are less that (P2+1) \n** values in the record, extract a NULL.\n**\n** The value extracted is stored in register P3.\n**\n** If the record contains fewer than P2 fields, then extract a NULL.  Or,\n** if the P4 argument is a P4_MEM use the value of the P4 argument as\n** the result.\n**\n** If the OPFLAG_CLEARCACHE bit is set on P5 and P1 is a pseudo-table cursor,\n** then the cache of the cursor is reset prior to extracting the column.\n** The first OP_Column against a pseudo-table after the value of the content\n** register has changed should have this bit set.\n**\n** If the OPFLAG_LENGTHARG and OPFLAG_TYPEOFARG bits are set on P5 then\n** the result is guaranteed to only be used as the argument of a length()\n** or typeof() function, respectively.  The loading of large blobs can be\n** skipped for length() and all content loading can be skipped for typeof().\n*/\ncase OP_Column: {\n  int p2;            /* column number to retrieve */\n  VdbeCursor *pC;    /* The VDBE cursor */\n  BtCursor *pCrsr;   /* The BTree cursor */\n  u32 *aOffset;      /* aOffset[i] is offset to start of data for i-th column */\n  int len;           /* The length of the serialized data for the column */\n  int i;             /* Loop counter */\n  Mem *pDest;        /* Where to write the extracted value */\n  Mem sMem;          /* For storing the record being decoded */\n  const u8 *zData;   /* Part of the record being decoded */\n  const u8 *zHdr;    /* Next unparsed byte of the header */\n  const u8 *zEndHdr; /* Pointer to first byte after the header */\n  u64 offset64;      /* 64-bit offset */\n  u32 t;             /* A type code from the record header */\n  Mem *pReg;         /* PseudoTable input register */\n\n  pC = p->apCsr[pOp->p1];\n  p2 = pOp->p2;\n\n  /* If the cursor cache is stale (meaning it is not currently point at\n  ** the correct row) then bring it up-to-date by doing the necessary \n  ** B-Tree seek. */\n  rc = sqlite3VdbeCursorMoveto(&pC, &p2);\n  if( rc ) goto abort_due_to_error;\n\n  assert( pOp->p3>0 && pOp->p3<=(p->nMem+1 - p->nCursor) );\n  pDest = &aMem[pOp->p3];\n  memAboutToChange(p, pDest);\n  assert( pOp->p1>=0 && pOp->p1<p->nCursor );\n  assert( pC!=0 );\n  assert( p2<pC->nField );\n  aOffset = pC->aOffset;\n  assert( pC->eCurType!=CURTYPE_VTAB );\n  assert( pC->eCurType!=CURTYPE_PSEUDO || pC->nullRow );\n  assert( pC->eCurType!=CURTYPE_SORTER );\n\n  if( pC->cacheStatus!=p->cacheCtr ){                /*OPTIMIZATION-IF-FALSE*/\n    if( pC->nullRow ){\n      if( pC->eCurType==CURTYPE_PSEUDO ){\n        /* For the special case of as pseudo-cursor, the seekResult field\n        ** identifies the register that holds the record */\n        assert( pC->seekResult>0 );\n        pReg = &aMem[pC->seekResult];\n        assert( pReg->flags & MEM_Blob );\n        assert( memIsValid(pReg) );\n        pC->payloadSize = pC->szRow = pReg->n;\n        pC->aRow = (u8*)pReg->z;\n      }else{\n        sqlite3VdbeMemSetNull(pDest);\n        goto op_column_out;\n      }\n    }else{\n      pCrsr = pC->uc.pCursor;\n      assert( pC->eCurType==CURTYPE_BTREE );\n      assert( pCrsr );\n      assert( sqlite3BtreeCursorIsValid(pCrsr) );\n      pC->payloadSize = sqlite3BtreePayloadSize(pCrsr);\n      pC->aRow = sqlite3BtreePayloadFetch(pCrsr, &pC->szRow);\n      assert( pC->szRow<=pC->payloadSize );\n      assert( pC->szRow<=65536 );  /* Maximum page size is 64KiB */\n      if( pC->payloadSize > (u32)db->aLimit[SQLITE_LIMIT_LENGTH] ){\n        goto too_big;\n      }\n    }\n    pC->cacheStatus = p->cacheCtr;\n    pC->iHdrOffset = getVarint32(pC->aRow, aOffset[0]);\n    pC->nHdrParsed = 0;\n\n\n    if( pC->szRow<aOffset[0] ){      /*OPTIMIZATION-IF-FALSE*/\n      /* pC->aRow does not have to hold the entire row, but it does at least\n      ** need to cover the header of the record.  If pC->aRow does not contain\n      ** the complete header, then set it to zero, forcing the header to be\n      ** dynamically allocated. */\n      pC->aRow = 0;\n      pC->szRow = 0;\n\n      /* Make sure a corrupt database has not given us an oversize header.\n      ** Do this now to avoid an oversize memory allocation.\n      **\n      ** Type entries can be between 1 and 5 bytes each.  But 4 and 5 byte\n      ** types use so much data space that there can only be 4096 and 32 of\n      ** them, respectively.  So the maximum header length results from a\n      ** 3-byte type for each of the maximum of 32768 columns plus three\n      ** extra bytes for the header length itself.  32768*3 + 3 = 98307.\n      */\n      if( aOffset[0] > 98307 || aOffset[0] > pC->payloadSize ){\n        goto op_column_corrupt;\n      }\n    }else{\n      /* This is an optimization.  By skipping over the first few tests\n      ** (ex: pC->nHdrParsed<=p2) in the next section, we achieve a\n      ** measurable performance gain.\n      **\n      ** This branch is taken even if aOffset[0]==0.  Such a record is never\n      ** generated by SQLite, and could be considered corruption, but we\n      ** accept it for historical reasons.  When aOffset[0]==0, the code this\n      ** branch jumps to reads past the end of the record, but never more\n      ** than a few bytes.  Even if the record occurs at the end of the page\n      ** content area, the \"page header\" comes after the page content and so\n      ** this overread is harmless.  Similar overreads can occur for a corrupt\n      ** database file.\n      */\n      zData = pC->aRow;\n      assert( pC->nHdrParsed<=p2 );         /* Conditional skipped */\n      testcase( aOffset[0]==0 );\n      goto op_column_read_header;\n    }\n  }\n\n  /* Make sure at least the first p2+1 entries of the header have been\n  ** parsed and valid information is in aOffset[] and pC->aType[].\n  */\n  if( pC->nHdrParsed<=p2 ){\n    /* If there is more header available for parsing in the record, try\n    ** to extract additional fields up through the p2+1-th field \n    */\n    if( pC->iHdrOffset<aOffset[0] ){\n      /* Make sure zData points to enough of the record to cover the header. */\n      if( pC->aRow==0 ){\n        memset(&sMem, 0, sizeof(sMem));\n        rc = sqlite3VdbeMemFromBtree(pC->uc.pCursor, 0, aOffset[0], &sMem);\n        if( rc!=SQLITE_OK ) goto abort_due_to_error;\n        zData = (u8*)sMem.z;\n      }else{\n        zData = pC->aRow;\n      }\n  \n      /* Fill in pC->aType[i] and aOffset[i] values through the p2-th field. */\n    op_column_read_header:\n      i = pC->nHdrParsed;\n      offset64 = aOffset[i];\n      zHdr = zData + pC->iHdrOffset;\n      zEndHdr = zData + aOffset[0];\n      testcase( zHdr>=zEndHdr );\n      do{\n        if( (t = zHdr[0])<0x80 ){\n          zHdr++;\n          offset64 += sqlite3VdbeOneByteSerialTypeLen(t);\n        }else{\n          zHdr += sqlite3GetVarint32(zHdr, &t);\n          offset64 += sqlite3VdbeSerialTypeLen(t);\n        }\n        pC->aType[i++] = t;\n        aOffset[i] = (u32)(offset64 & 0xffffffff);\n      }while( i<=p2 && zHdr<zEndHdr );\n\n      /* The record is corrupt if any of the following are true:\n      ** (1) the bytes of the header extend past the declared header size\n      ** (2) the entire header was used but not all data was used\n      ** (3) the end of the data extends beyond the end of the record.\n      */\n      if( (zHdr>=zEndHdr && (zHdr>zEndHdr || offset64!=pC->payloadSize))\n       || (offset64 > pC->payloadSize)\n      ){\n        if( aOffset[0]==0 ){\n          i = 0;\n          zHdr = zEndHdr;\n        }else{\n          if( pC->aRow==0 ) sqlite3VdbeMemRelease(&sMem);\n          goto op_column_corrupt;\n        }\n      }\n\n      pC->nHdrParsed = i;\n      pC->iHdrOffset = (u32)(zHdr - zData);\n      if( pC->aRow==0 ) sqlite3VdbeMemRelease(&sMem);\n    }else{\n      t = 0;\n    }\n\n    /* If after trying to extract new entries from the header, nHdrParsed is\n    ** still not up to p2, that means that the record has fewer than p2\n    ** columns.  So the result will be either the default value or a NULL.\n    */\n    if( pC->nHdrParsed<=p2 ){\n      if( pOp->p4type==P4_MEM ){\n        sqlite3VdbeMemShallowCopy(pDest, pOp->p4.pMem, MEM_Static);\n      }else{\n        sqlite3VdbeMemSetNull(pDest);\n      }\n      goto op_column_out;\n    }\n  }else{\n    t = pC->aType[p2];\n  }\n\n  /* Extract the content for the p2+1-th column.  Control can only\n  ** reach this point if aOffset[p2], aOffset[p2+1], and pC->aType[p2] are\n  ** all valid.\n  */\n  assert( p2<pC->nHdrParsed );\n  assert( rc==SQLITE_OK );\n  assert( sqlite3VdbeCheckMemInvariants(pDest) );\n  if( VdbeMemDynamic(pDest) ){\n    sqlite3VdbeMemSetNull(pDest);\n  }\n  assert( t==pC->aType[p2] );\n  if( pC->szRow>=aOffset[p2+1] ){\n    /* This is the common case where the desired content fits on the original\n    ** page - where the content is not on an overflow page */\n    zData = pC->aRow + aOffset[p2];\n    if( t<12 ){\n      sqlite3VdbeSerialGet(zData, t, pDest);\n    }else{\n      /* If the column value is a string, we need a persistent value, not\n      ** a MEM_Ephem value.  This branch is a fast short-cut that is equivalent\n      ** to calling sqlite3VdbeSerialGet() and sqlite3VdbeDeephemeralize().\n      */\n      static const u16 aFlag[] = { MEM_Blob, MEM_Str|MEM_Term };\n      pDest->n = len = (t-12)/2;\n      pDest->enc = encoding;\n      if( pDest->szMalloc < len+2 ){\n        pDest->flags = MEM_Null;\n        if( sqlite3VdbeMemGrow(pDest, len+2, 0) ) goto no_mem;\n      }else{\n        pDest->z = pDest->zMalloc;\n      }\n      memcpy(pDest->z, zData, len);\n      pDest->z[len] = 0;\n      pDest->z[len+1] = 0;\n      pDest->flags = aFlag[t&1];\n    }\n  }else{\n    pDest->enc = encoding;\n    /* This branch happens only when content is on overflow pages */\n    if( ((pOp->p5 & (OPFLAG_LENGTHARG|OPFLAG_TYPEOFARG))!=0\n          && ((t>=12 && (t&1)==0) || (pOp->p5 & OPFLAG_TYPEOFARG)!=0))\n     || (len = sqlite3VdbeSerialTypeLen(t))==0\n    ){\n      /* Content is irrelevant for\n      **    1. the typeof() function,\n      **    2. the length(X) function if X is a blob, and\n      **    3. if the content length is zero.\n      ** So we might as well use bogus content rather than reading\n      ** content from disk. \n      **\n      ** Although sqlite3VdbeSerialGet() may read at most 8 bytes from the\n      ** buffer passed to it, debugging function VdbeMemPrettyPrint() may\n      ** read up to 16. So 16 bytes of bogus content is supplied.\n      */\n      static u8 aZero[16];  /* This is the bogus content */\n      sqlite3VdbeSerialGet(aZero, t, pDest);\n    }else{\n      rc = sqlite3VdbeMemFromBtree(pC->uc.pCursor, aOffset[p2], len, pDest);\n      if( rc!=SQLITE_OK ) goto abort_due_to_error;\n      sqlite3VdbeSerialGet((const u8*)pDest->z, t, pDest);\n      pDest->flags &= ~MEM_Ephem;\n    }\n  }\n\nop_column_out:\n  UPDATE_MAX_BLOBSIZE(pDest);\n  REGISTER_TRACE(pOp->p3, pDest);\n  break;\n\nop_column_corrupt:\n  if( aOp[0].p3>0 ){\n    pOp = &aOp[aOp[0].p3-1];\n    break;\n  }else{\n    rc = SQLITE_CORRUPT_BKPT;\n    goto abort_due_to_error;\n  }\n}\n\n/* Opcode: Affinity P1 P2 * P4 *\n** Synopsis: affinity(r[P1@P2])\n**\n** Apply affinities to a range of P2 registers starting with P1.\n**\n** P4 is a string that is P2 characters long. The N-th character of the\n** string indicates the column affinity that should be used for the N-th\n** memory cell in the range.\n*/\ncase OP_Affinity: {\n  const char *zAffinity;   /* The affinity to be applied */\n\n  zAffinity = pOp->p4.z;\n  assert( zAffinity!=0 );\n  assert( pOp->p2>0 );\n  assert( zAffinity[pOp->p2]==0 );\n  pIn1 = &aMem[pOp->p1];\n  do{\n    assert( pIn1 <= &p->aMem[(p->nMem+1 - p->nCursor)] );\n    assert( memIsValid(pIn1) );\n    applyAffinity(pIn1, *(zAffinity++), encoding);\n    pIn1++;\n  }while( zAffinity[0] );\n  break;\n}\n\n/* Opcode: MakeRecord P1 P2 P3 P4 *\n** Synopsis: r[P3]=mkrec(r[P1@P2])\n**\n** Convert P2 registers beginning with P1 into the [record format]\n** use as a data record in a database table or as a key\n** in an index.  The OP_Column opcode can decode the record later.\n**\n** P4 may be a string that is P2 characters long.  The N-th character of the\n** string indicates the column affinity that should be used for the N-th\n** field of the index key.\n**\n** The mapping from character to affinity is given by the SQLITE_AFF_\n** macros defined in sqliteInt.h.\n**\n** If P4 is NULL then all index fields have the affinity BLOB.\n*/\ncase OP_MakeRecord: {\n  u8 *zNewRecord;        /* A buffer to hold the data for the new record */\n  Mem *pRec;             /* The new record */\n  u64 nData;             /* Number of bytes of data space */\n  int nHdr;              /* Number of bytes of header space */\n  i64 nByte;             /* Data space required for this record */\n  i64 nZero;             /* Number of zero bytes at the end of the record */\n  int nVarint;           /* Number of bytes in a varint */\n  u32 serial_type;       /* Type field */\n  Mem *pData0;           /* First field to be combined into the record */\n  Mem *pLast;            /* Last field of the record */\n  int nField;            /* Number of fields in the record */\n  char *zAffinity;       /* The affinity string for the record */\n  int file_format;       /* File format to use for encoding */\n  int i;                 /* Space used in zNewRecord[] header */\n  int j;                 /* Space used in zNewRecord[] content */\n  u32 len;               /* Length of a field */\n\n  /* Assuming the record contains N fields, the record format looks\n  ** like this:\n  **\n  ** ------------------------------------------------------------------------\n  ** | hdr-size | type 0 | type 1 | ... | type N-1 | data0 | ... | data N-1 | \n  ** ------------------------------------------------------------------------\n  **\n  ** Data(0) is taken from register P1.  Data(1) comes from register P1+1\n  ** and so forth.\n  **\n  ** Each type field is a varint representing the serial type of the \n  ** corresponding data element (see sqlite3VdbeSerialType()). The\n  ** hdr-size field is also a varint which is the offset from the beginning\n  ** of the record to data0.\n  */\n  nData = 0;         /* Number of bytes of data space */\n  nHdr = 0;          /* Number of bytes of header space */\n  nZero = 0;         /* Number of zero bytes at the end of the record */\n  nField = pOp->p1;\n  zAffinity = pOp->p4.z;\n  assert( nField>0 && pOp->p2>0 && pOp->p2+nField<=(p->nMem+1 - p->nCursor)+1 );\n  pData0 = &aMem[nField];\n  nField = pOp->p2;\n  pLast = &pData0[nField-1];\n  file_format = p->minWriteFileFormat;\n\n  /* Identify the output register */\n  assert( pOp->p3<pOp->p1 || pOp->p3>=pOp->p1+pOp->p2 );\n  pOut = &aMem[pOp->p3];\n  memAboutToChange(p, pOut);\n\n  /* Apply the requested affinity to all inputs\n  */\n  assert( pData0<=pLast );\n  if( zAffinity ){\n    pRec = pData0;\n    do{\n      applyAffinity(pRec++, *(zAffinity++), encoding);\n      assert( zAffinity[0]==0 || pRec<=pLast );\n    }while( zAffinity[0] );\n  }\n\n#ifdef SQLITE_ENABLE_NULL_TRIM\n  /* NULLs can be safely trimmed from the end of the record, as long as\n  ** as the schema format is 2 or more and none of the omitted columns\n  ** have a non-NULL default value.  Also, the record must be left with\n  ** at least one field.  If P5>0 then it will be one more than the\n  ** index of the right-most column with a non-NULL default value */\n  if( pOp->p5 ){\n    while( (pLast->flags & MEM_Null)!=0 && nField>pOp->p5 ){\n      pLast--;\n      nField--;\n    }\n  }\n#endif\n\n  /* Loop through the elements that will make up the record to figure\n  ** out how much space is required for the new record.\n  */\n  pRec = pLast;\n  do{\n    assert( memIsValid(pRec) );\n    serial_type = sqlite3VdbeSerialType(pRec, file_format, &len);\n    if( pRec->flags & MEM_Zero ){\n      if( serial_type==0 ){\n        /* Values with MEM_Null and MEM_Zero are created by xColumn virtual\n        ** table methods that never invoke sqlite3_result_xxxxx() while\n        ** computing an unchanging column value in an UPDATE statement.\n        ** Give such values a special internal-use-only serial-type of 10\n        ** so that they can be passed through to xUpdate and have\n        ** a true sqlite3_value_nochange(). */\n        assert( pOp->p5==OPFLAG_NOCHNG_MAGIC || CORRUPT_DB );\n        serial_type = 10;\n      }else if( nData ){\n        if( sqlite3VdbeMemExpandBlob(pRec) ) goto no_mem;\n      }else{\n        nZero += pRec->u.nZero;\n        len -= pRec->u.nZero;\n      }\n    }\n    nData += len;\n    testcase( serial_type==127 );\n    testcase( serial_type==128 );\n    nHdr += serial_type<=127 ? 1 : sqlite3VarintLen(serial_type);\n    pRec->uTemp = serial_type;\n    if( pRec==pData0 ) break;\n    pRec--;\n  }while(1);\n\n  /* EVIDENCE-OF: R-22564-11647 The header begins with a single varint\n  ** which determines the total number of bytes in the header. The varint\n  ** value is the size of the header in bytes including the size varint\n  ** itself. */\n  testcase( nHdr==126 );\n  testcase( nHdr==127 );\n  if( nHdr<=126 ){\n    /* The common case */\n    nHdr += 1;\n  }else{\n    /* Rare case of a really large header */\n    nVarint = sqlite3VarintLen(nHdr);\n    nHdr += nVarint;\n    if( nVarint<sqlite3VarintLen(nHdr) ) nHdr++;\n  }\n  nByte = nHdr+nData;\n  if( nByte+nZero>db->aLimit[SQLITE_LIMIT_LENGTH] ){\n    goto too_big;\n  }\n\n  /* Make sure the output register has a buffer large enough to store \n  ** the new record. The output register (pOp->p3) is not allowed to\n  ** be one of the input registers (because the following call to\n  ** sqlite3VdbeMemClearAndResize() could clobber the value before it is used).\n  */\n  if( sqlite3VdbeMemClearAndResize(pOut, (int)nByte) ){\n    goto no_mem;\n  }\n  zNewRecord = (u8 *)pOut->z;\n\n  /* Write the record */\n  i = putVarint32(zNewRecord, nHdr);\n  j = nHdr;\n  assert( pData0<=pLast );\n  pRec = pData0;\n  do{\n    serial_type = pRec->uTemp;\n    /* EVIDENCE-OF: R-06529-47362 Following the size varint are one or more\n    ** additional varints, one per column. */\n    i += putVarint32(&zNewRecord[i], serial_type);            /* serial type */\n    /* EVIDENCE-OF: R-64536-51728 The values for each column in the record\n    ** immediately follow the header. */\n    j += sqlite3VdbeSerialPut(&zNewRecord[j], pRec, serial_type); /* content */\n  }while( (++pRec)<=pLast );\n  assert( i==nHdr );\n  assert( j==nByte );\n\n  assert( pOp->p3>0 && pOp->p3<=(p->nMem+1 - p->nCursor) );\n  pOut->n = (int)nByte;\n  pOut->flags = MEM_Blob;\n  if( nZero ){\n    pOut->u.nZero = nZero;\n    pOut->flags |= MEM_Zero;\n  }\n  REGISTER_TRACE(pOp->p3, pOut);\n  UPDATE_MAX_BLOBSIZE(pOut);\n  break;\n}\n\n/* Opcode: Count P1 P2 * * *\n** Synopsis: r[P2]=count()\n**\n** Store the number of entries (an integer value) in the table or index \n** opened by cursor P1 in register P2\n*/\n#ifndef SQLITE_OMIT_BTREECOUNT\ncase OP_Count: {         /* out2 */\n  i64 nEntry;\n  BtCursor *pCrsr;\n\n  assert( p->apCsr[pOp->p1]->eCurType==CURTYPE_BTREE );\n  pCrsr = p->apCsr[pOp->p1]->uc.pCursor;\n  assert( pCrsr );\n  nEntry = 0;  /* Not needed.  Only used to silence a warning. */\n  rc = sqlite3BtreeCount(pCrsr, &nEntry);\n  if( rc ) goto abort_due_to_error;\n  pOut = out2Prerelease(p, pOp);\n  pOut->u.i = nEntry;\n  break;\n}\n#endif\n\n/* Opcode: Savepoint P1 * * P4 *\n**\n** Open, release or rollback the savepoint named by parameter P4, depending\n** on the value of P1. To open a new savepoint, P1==0. To release (commit) an\n** existing savepoint, P1==1, or to rollback an existing savepoint P1==2.\n*/\ncase OP_Savepoint: {\n  int p1;                         /* Value of P1 operand */\n  char *zName;                    /* Name of savepoint */\n  int nName;\n  Savepoint *pNew;\n  Savepoint *pSavepoint;\n  Savepoint *pTmp;\n  int iSavepoint;\n  int ii;\n\n  p1 = pOp->p1;\n  zName = pOp->p4.z;\n\n  /* Assert that the p1 parameter is valid. Also that if there is no open\n  ** transaction, then there cannot be any savepoints. \n  */\n  assert( db->pSavepoint==0 || db->autoCommit==0 );\n  assert( p1==SAVEPOINT_BEGIN||p1==SAVEPOINT_RELEASE||p1==SAVEPOINT_ROLLBACK );\n  assert( db->pSavepoint || db->isTransactionSavepoint==0 );\n  assert( checkSavepointCount(db) );\n  assert( p->bIsReader );\n\n  if( p1==SAVEPOINT_BEGIN ){\n    if( db->nVdbeWrite>0 ){\n      /* A new savepoint cannot be created if there are active write \n      ** statements (i.e. open read/write incremental blob handles).\n      */\n      sqlite3VdbeError(p, \"cannot open savepoint - SQL statements in progress\");\n      rc = SQLITE_BUSY;\n    }else{\n      nName = sqlite3Strlen30(zName);\n\n#ifndef SQLITE_OMIT_VIRTUALTABLE\n      /* This call is Ok even if this savepoint is actually a transaction\n      ** savepoint (and therefore should not prompt xSavepoint()) callbacks.\n      ** If this is a transaction savepoint being opened, it is guaranteed\n      ** that the db->aVTrans[] array is empty.  */\n      assert( db->autoCommit==0 || db->nVTrans==0 );\n      rc = sqlite3VtabSavepoint(db, SAVEPOINT_BEGIN,\n                                db->nStatement+db->nSavepoint);\n      if( rc!=SQLITE_OK ) goto abort_due_to_error;\n#endif\n\n      /* Create a new savepoint structure. */\n      pNew = sqlite3DbMallocRawNN(db, sizeof(Savepoint)+nName+1);\n      if( pNew ){\n        pNew->zName = (char *)&pNew[1];\n        memcpy(pNew->zName, zName, nName+1);\n    \n        /* If there is no open transaction, then mark this as a special\n        ** \"transaction savepoint\". */\n        if( db->autoCommit ){\n          db->autoCommit = 0;\n          db->isTransactionSavepoint = 1;\n        }else{\n          db->nSavepoint++;\n        }\n\n        /* Link the new savepoint into the database handle's list. */\n        pNew->pNext = db->pSavepoint;\n        db->pSavepoint = pNew;\n        pNew->nDeferredCons = db->nDeferredCons;\n        pNew->nDeferredImmCons = db->nDeferredImmCons;\n      }\n    }\n  }else{\n    iSavepoint = 0;\n\n    /* Find the named savepoint. If there is no such savepoint, then an\n    ** an error is returned to the user.  */\n    for(\n      pSavepoint = db->pSavepoint; \n      pSavepoint && sqlite3StrICmp(pSavepoint->zName, zName);\n      pSavepoint = pSavepoint->pNext\n    ){\n      iSavepoint++;\n    }\n    if( !pSavepoint ){\n      sqlite3VdbeError(p, \"no such savepoint: %s\", zName);\n      rc = SQLITE_ERROR;\n    }else if( db->nVdbeWrite>0 && p1==SAVEPOINT_RELEASE ){\n      /* It is not possible to release (commit) a savepoint if there are \n      ** active write statements.\n      */\n      sqlite3VdbeError(p, \"cannot release savepoint - \"\n                          \"SQL statements in progress\");\n      rc = SQLITE_BUSY;\n    }else{\n\n      /* Determine whether or not this is a transaction savepoint. If so,\n      ** and this is a RELEASE command, then the current transaction \n      ** is committed. \n      */\n      int isTransaction = pSavepoint->pNext==0 && db->isTransactionSavepoint;\n      if( isTransaction && p1==SAVEPOINT_RELEASE ){\n        if( (rc = sqlite3VdbeCheckFk(p, 1))!=SQLITE_OK ){\n          goto vdbe_return;\n        }\n        db->autoCommit = 1;\n        if( sqlite3VdbeHalt(p)==SQLITE_BUSY ){\n          p->pc = (int)(pOp - aOp);\n          db->autoCommit = 0;\n          p->rc = rc = SQLITE_BUSY;\n          goto vdbe_return;\n        }\n        db->isTransactionSavepoint = 0;\n        rc = p->rc;\n      }else{\n        int isSchemaChange;\n        iSavepoint = db->nSavepoint - iSavepoint - 1;\n        if( p1==SAVEPOINT_ROLLBACK ){\n          isSchemaChange = (db->mDbFlags & DBFLAG_SchemaChange)!=0;\n          for(ii=0; ii<db->nDb; ii++){\n            rc = sqlite3BtreeTripAllCursors(db->aDb[ii].pBt,\n                                       SQLITE_ABORT_ROLLBACK,\n                                       isSchemaChange==0);\n            if( rc!=SQLITE_OK ) goto abort_due_to_error;\n          }\n        }else{\n          isSchemaChange = 0;\n        }\n        for(ii=0; ii<db->nDb; ii++){\n          rc = sqlite3BtreeSavepoint(db->aDb[ii].pBt, p1, iSavepoint);\n          if( rc!=SQLITE_OK ){\n            goto abort_due_to_error;\n          }\n        }\n        if( isSchemaChange ){\n          sqlite3ExpirePreparedStatements(db);\n          sqlite3ResetAllSchemasOfConnection(db);\n          db->mDbFlags |= DBFLAG_SchemaChange;\n        }\n      }\n  \n      /* Regardless of whether this is a RELEASE or ROLLBACK, destroy all \n      ** savepoints nested inside of the savepoint being operated on. */\n      while( db->pSavepoint!=pSavepoint ){\n        pTmp = db->pSavepoint;\n        db->pSavepoint = pTmp->pNext;\n        sqlite3DbFree(db, pTmp);\n        db->nSavepoint--;\n      }\n\n      /* If it is a RELEASE, then destroy the savepoint being operated on \n      ** too. If it is a ROLLBACK TO, then set the number of deferred \n      ** constraint violations present in the database to the value stored\n      ** when the savepoint was created.  */\n      if( p1==SAVEPOINT_RELEASE ){\n        assert( pSavepoint==db->pSavepoint );\n        db->pSavepoint = pSavepoint->pNext;\n        sqlite3DbFree(db, pSavepoint);\n        if( !isTransaction ){\n          db->nSavepoint--;\n        }\n      }else{\n        db->nDeferredCons = pSavepoint->nDeferredCons;\n        db->nDeferredImmCons = pSavepoint->nDeferredImmCons;\n      }\n\n      if( !isTransaction || p1==SAVEPOINT_ROLLBACK ){\n        rc = sqlite3VtabSavepoint(db, p1, iSavepoint);\n        if( rc!=SQLITE_OK ) goto abort_due_to_error;\n      }\n    }\n  }\n  if( rc ) goto abort_due_to_error;\n\n  break;\n}\n\n/* Opcode: AutoCommit P1 P2 * * *\n**\n** Set the database auto-commit flag to P1 (1 or 0). If P2 is true, roll\n** back any currently active btree transactions. If there are any active\n** VMs (apart from this one), then a ROLLBACK fails.  A COMMIT fails if\n** there are active writing VMs or active VMs that use shared cache.\n**\n** This instruction causes the VM to halt.\n*/\ncase OP_AutoCommit: {\n  int desiredAutoCommit;\n  int iRollback;\n\n  desiredAutoCommit = pOp->p1;\n  iRollback = pOp->p2;\n  assert( desiredAutoCommit==1 || desiredAutoCommit==0 );\n  assert( desiredAutoCommit==1 || iRollback==0 );\n  assert( db->nVdbeActive>0 );  /* At least this one VM is active */\n  assert( p->bIsReader );\n\n  if( desiredAutoCommit!=db->autoCommit ){\n    if( iRollback ){\n      assert( desiredAutoCommit==1 );\n      sqlite3RollbackAll(db, SQLITE_ABORT_ROLLBACK);\n      db->autoCommit = 1;\n    }else if( desiredAutoCommit && db->nVdbeWrite>0 ){\n      /* If this instruction implements a COMMIT and other VMs are writing\n      ** return an error indicating that the other VMs must complete first. \n      */\n      sqlite3VdbeError(p, \"cannot commit transaction - \"\n                          \"SQL statements in progress\");\n      rc = SQLITE_BUSY;\n      goto abort_due_to_error;\n    }else if( (rc = sqlite3VdbeCheckFk(p, 1))!=SQLITE_OK ){\n      goto vdbe_return;\n    }else{\n      db->autoCommit = (u8)desiredAutoCommit;\n    }\n    if( sqlite3VdbeHalt(p)==SQLITE_BUSY ){\n      p->pc = (int)(pOp - aOp);\n      db->autoCommit = (u8)(1-desiredAutoCommit);\n      p->rc = rc = SQLITE_BUSY;\n      goto vdbe_return;\n    }\n    assert( db->nStatement==0 );\n    sqlite3CloseSavepoints(db);\n    if( p->rc==SQLITE_OK ){\n      rc = SQLITE_DONE;\n    }else{\n      rc = SQLITE_ERROR;\n    }\n    goto vdbe_return;\n  }else{\n    sqlite3VdbeError(p,\n        (!desiredAutoCommit)?\"cannot start a transaction within a transaction\":(\n        (iRollback)?\"cannot rollback - no transaction is active\":\n                   \"cannot commit - no transaction is active\"));\n         \n    rc = SQLITE_ERROR;\n    goto abort_due_to_error;\n  }\n  break;\n}\n\n/* Opcode: Transaction P1 P2 P3 P4 P5\n**\n** Begin a transaction on database P1 if a transaction is not already\n** active.\n** If P2 is non-zero, then a write-transaction is started, or if a \n** read-transaction is already active, it is upgraded to a write-transaction.\n** If P2 is zero, then a read-transaction is started.\n**\n** P1 is the index of the database file on which the transaction is\n** started.  Index 0 is the main database file and index 1 is the\n** file used for temporary tables.  Indices of 2 or more are used for\n** attached databases.\n**\n** If a write-transaction is started and the Vdbe.usesStmtJournal flag is\n** true (this flag is set if the Vdbe may modify more than one row and may\n** throw an ABORT exception), a statement transaction may also be opened.\n** More specifically, a statement transaction is opened iff the database\n** connection is currently not in autocommit mode, or if there are other\n** active statements. A statement transaction allows the changes made by this\n** VDBE to be rolled back after an error without having to roll back the\n** entire transaction. If no error is encountered, the statement transaction\n** will automatically commit when the VDBE halts.\n**\n** If P5!=0 then this opcode also checks the schema cookie against P3\n** and the schema generation counter against P4.\n** The cookie changes its value whenever the database schema changes.\n** This operation is used to detect when that the cookie has changed\n** and that the current process needs to reread the schema.  If the schema\n** cookie in P3 differs from the schema cookie in the database header or\n** if the schema generation counter in P4 differs from the current\n** generation counter, then an SQLITE_SCHEMA error is raised and execution\n** halts.  The sqlite3_step() wrapper function might then reprepare the\n** statement and rerun it from the beginning.\n*/\ncase OP_Transaction: {\n  Btree *pBt;\n  int iMeta;\n  int iGen;\n\n  assert( p->bIsReader );\n  assert( p->readOnly==0 || pOp->p2==0 );\n  assert( pOp->p1>=0 && pOp->p1<db->nDb );\n  assert( DbMaskTest(p->btreeMask, pOp->p1) );\n  if( pOp->p2 && (db->flags & SQLITE_QueryOnly)!=0 ){\n    rc = SQLITE_READONLY;\n    goto abort_due_to_error;\n  }\n  pBt = db->aDb[pOp->p1].pBt;\n\n  if( pBt ){\n    rc = sqlite3BtreeBeginTrans(pBt, pOp->p2);\n    testcase( rc==SQLITE_BUSY_SNAPSHOT );\n    testcase( rc==SQLITE_BUSY_RECOVERY );\n    if( rc!=SQLITE_OK ){\n      if( (rc&0xff)==SQLITE_BUSY ){\n        p->pc = (int)(pOp - aOp);\n        p->rc = rc;\n        goto vdbe_return;\n      }\n      goto abort_due_to_error;\n    }\n\n    if( pOp->p2 && p->usesStmtJournal \n     && (db->autoCommit==0 || db->nVdbeRead>1) \n    ){\n      assert( sqlite3BtreeIsInTrans(pBt) );\n      if( p->iStatement==0 ){\n        assert( db->nStatement>=0 && db->nSavepoint>=0 );\n        db->nStatement++; \n        p->iStatement = db->nSavepoint + db->nStatement;\n      }\n\n      rc = sqlite3VtabSavepoint(db, SAVEPOINT_BEGIN, p->iStatement-1);\n      if( rc==SQLITE_OK ){\n        rc = sqlite3BtreeBeginStmt(pBt, p->iStatement);\n      }\n\n      /* Store the current value of the database handles deferred constraint\n      ** counter. If the statement transaction needs to be rolled back,\n      ** the value of this counter needs to be restored too.  */\n      p->nStmtDefCons = db->nDeferredCons;\n      p->nStmtDefImmCons = db->nDeferredImmCons;\n    }\n\n    /* Gather the schema version number for checking:\n    ** IMPLEMENTATION-OF: R-03189-51135 As each SQL statement runs, the schema\n    ** version is checked to ensure that the schema has not changed since the\n    ** SQL statement was prepared.\n    */\n    sqlite3BtreeGetMeta(pBt, BTREE_SCHEMA_VERSION, (u32 *)&iMeta);\n    iGen = db->aDb[pOp->p1].pSchema->iGeneration;\n  }else{\n    iGen = iMeta = 0;\n  }\n  assert( pOp->p5==0 || pOp->p4type==P4_INT32 );\n  if( pOp->p5 && (iMeta!=pOp->p3 || iGen!=pOp->p4.i) ){\n    sqlite3DbFree(db, p->zErrMsg);\n    p->zErrMsg = sqlite3DbStrDup(db, \"database schema has changed\");\n    /* If the schema-cookie from the database file matches the cookie \n    ** stored with the in-memory representation of the schema, do\n    ** not reload the schema from the database file.\n    **\n    ** If virtual-tables are in use, this is not just an optimization.\n    ** Often, v-tables store their data in other SQLite tables, which\n    ** are queried from within xNext() and other v-table methods using\n    ** prepared queries. If such a query is out-of-date, we do not want to\n    ** discard the database schema, as the user code implementing the\n    ** v-table would have to be ready for the sqlite3_vtab structure itself\n    ** to be invalidated whenever sqlite3_step() is called from within \n    ** a v-table method.\n    */\n    if( db->aDb[pOp->p1].pSchema->schema_cookie!=iMeta ){\n      sqlite3ResetOneSchema(db, pOp->p1);\n    }\n    p->expired = 1;\n    rc = SQLITE_SCHEMA;\n  }\n  if( rc ) goto abort_due_to_error;\n  break;\n}\n\n/* Opcode: ReadCookie P1 P2 P3 * *\n**\n** Read cookie number P3 from database P1 and write it into register P2.\n** P3==1 is the schema version.  P3==2 is the database format.\n** P3==3 is the recommended pager cache size, and so forth.  P1==0 is\n** the main database file and P1==1 is the database file used to store\n** temporary tables.\n**\n** There must be a read-lock on the database (either a transaction\n** must be started or there must be an open cursor) before\n** executing this instruction.\n*/\ncase OP_ReadCookie: {               /* out2 */\n  int iMeta;\n  int iDb;\n  int iCookie;\n\n  assert( p->bIsReader );\n  iDb = pOp->p1;\n  iCookie = pOp->p3;\n  assert( pOp->p3<SQLITE_N_BTREE_META );\n  assert( iDb>=0 && iDb<db->nDb );\n  assert( db->aDb[iDb].pBt!=0 );\n  assert( DbMaskTest(p->btreeMask, iDb) );\n\n  sqlite3BtreeGetMeta(db->aDb[iDb].pBt, iCookie, (u32 *)&iMeta);\n  pOut = out2Prerelease(p, pOp);\n  pOut->u.i = iMeta;\n  break;\n}\n\n/* Opcode: SetCookie P1 P2 P3 * *\n**\n** Write the integer value P3 into cookie number P2 of database P1.\n** P2==1 is the schema version.  P2==2 is the database format.\n** P2==3 is the recommended pager cache \n** size, and so forth.  P1==0 is the main database file and P1==1 is the \n** database file used to store temporary tables.\n**\n** A transaction must be started before executing this opcode.\n*/\ncase OP_SetCookie: {\n  Db *pDb;\n  assert( pOp->p2<SQLITE_N_BTREE_META );\n  assert( pOp->p1>=0 && pOp->p1<db->nDb );\n  assert( DbMaskTest(p->btreeMask, pOp->p1) );\n  assert( p->readOnly==0 );\n  pDb = &db->aDb[pOp->p1];\n  assert( pDb->pBt!=0 );\n  assert( sqlite3SchemaMutexHeld(db, pOp->p1, 0) );\n  /* See note about index shifting on OP_ReadCookie */\n  rc = sqlite3BtreeUpdateMeta(pDb->pBt, pOp->p2, pOp->p3);\n  if( pOp->p2==BTREE_SCHEMA_VERSION ){\n    /* When the schema cookie changes, record the new cookie internally */\n    pDb->pSchema->schema_cookie = pOp->p3;\n    db->mDbFlags |= DBFLAG_SchemaChange;\n  }else if( pOp->p2==BTREE_FILE_FORMAT ){\n    /* Record changes in the file format */\n    pDb->pSchema->file_format = pOp->p3;\n  }\n  if( pOp->p1==1 ){\n    /* Invalidate all prepared statements whenever the TEMP database\n    ** schema is changed.  Ticket #1644 */\n    sqlite3ExpirePreparedStatements(db);\n    p->expired = 0;\n  }\n  if( rc ) goto abort_due_to_error;\n  break;\n}\n\n/* Opcode: OpenRead P1 P2 P3 P4 P5\n** Synopsis: root=P2 iDb=P3\n**\n** Open a read-only cursor for the database table whose root page is\n** P2 in a database file.  The database file is determined by P3. \n** P3==0 means the main database, P3==1 means the database used for \n** temporary tables, and P3>1 means used the corresponding attached\n** database.  Give the new cursor an identifier of P1.  The P1\n** values need not be contiguous but all P1 values should be small integers.\n** It is an error for P1 to be negative.\n**\n** If P5!=0 then use the content of register P2 as the root page, not\n** the value of P2 itself.\n**\n** There will be a read lock on the database whenever there is an\n** open cursor.  If the database was unlocked prior to this instruction\n** then a read lock is acquired as part of this instruction.  A read\n** lock allows other processes to read the database but prohibits\n** any other process from modifying the database.  The read lock is\n** released when all cursors are closed.  If this instruction attempts\n** to get a read lock but fails, the script terminates with an\n** SQLITE_BUSY error code.\n**\n** The P4 value may be either an integer (P4_INT32) or a pointer to\n** a KeyInfo structure (P4_KEYINFO). If it is a pointer to a KeyInfo \n** structure, then said structure defines the content and collating \n** sequence of the index being opened. Otherwise, if P4 is an integer \n** value, it is set to the number of columns in the table.\n**\n** See also: OpenWrite, ReopenIdx\n*/\n/* Opcode: ReopenIdx P1 P2 P3 P4 P5\n** Synopsis: root=P2 iDb=P3\n**\n** The ReopenIdx opcode works exactly like ReadOpen except that it first\n** checks to see if the cursor on P1 is already open with a root page\n** number of P2 and if it is this opcode becomes a no-op.  In other words,\n** if the cursor is already open, do not reopen it.\n**\n** The ReopenIdx opcode may only be used with P5==0 and with P4 being\n** a P4_KEYINFO object.  Furthermore, the P3 value must be the same as\n** every other ReopenIdx or OpenRead for the same cursor number.\n**\n** See the OpenRead opcode documentation for additional information.\n*/\n/* Opcode: OpenWrite P1 P2 P3 P4 P5\n** Synopsis: root=P2 iDb=P3\n**\n** Open a read/write cursor named P1 on the table or index whose root\n** page is P2.  Or if P5!=0 use the content of register P2 to find the\n** root page.\n**\n** The P4 value may be either an integer (P4_INT32) or a pointer to\n** a KeyInfo structure (P4_KEYINFO). If it is a pointer to a KeyInfo \n** structure, then said structure defines the content and collating \n** sequence of the index being opened. Otherwise, if P4 is an integer \n** value, it is set to the number of columns in the table, or to the\n** largest index of any column of the table that is actually used.\n**\n** This instruction works just like OpenRead except that it opens the cursor\n** in read/write mode.  For a given table, there can be one or more read-only\n** cursors or a single read/write cursor but not both.\n**\n** See also OpenRead.\n*/\ncase OP_ReopenIdx: {\n  int nField;\n  KeyInfo *pKeyInfo;\n  int p2;\n  int iDb;\n  int wrFlag;\n  Btree *pX;\n  VdbeCursor *pCur;\n  Db *pDb;\n\n  assert( pOp->p5==0 || pOp->p5==OPFLAG_SEEKEQ );\n  assert( pOp->p4type==P4_KEYINFO );\n  pCur = p->apCsr[pOp->p1];\n  if( pCur && pCur->pgnoRoot==(u32)pOp->p2 ){\n    assert( pCur->iDb==pOp->p3 );      /* Guaranteed by the code generator */\n    goto open_cursor_set_hints;\n  }\n  /* If the cursor is not currently open or is open on a different\n  ** index, then fall through into OP_OpenRead to force a reopen */\ncase OP_OpenRead:\ncase OP_OpenWrite:\n\n  assert( pOp->opcode==OP_OpenWrite || pOp->p5==0 || pOp->p5==OPFLAG_SEEKEQ );\n  assert( p->bIsReader );\n  assert( pOp->opcode==OP_OpenRead || pOp->opcode==OP_ReopenIdx\n          || p->readOnly==0 );\n\n  if( p->expired ){\n    rc = SQLITE_ABORT_ROLLBACK;\n    goto abort_due_to_error;\n  }\n\n  nField = 0;\n  pKeyInfo = 0;\n  p2 = pOp->p2;\n  iDb = pOp->p3;\n  assert( iDb>=0 && iDb<db->nDb );\n  assert( DbMaskTest(p->btreeMask, iDb) );\n  pDb = &db->aDb[iDb];\n  pX = pDb->pBt;\n  assert( pX!=0 );\n  if( pOp->opcode==OP_OpenWrite ){\n    assert( OPFLAG_FORDELETE==BTREE_FORDELETE );\n    wrFlag = BTREE_WRCSR | (pOp->p5 & OPFLAG_FORDELETE);\n    assert( sqlite3SchemaMutexHeld(db, iDb, 0) );\n    if( pDb->pSchema->file_format < p->minWriteFileFormat ){\n      p->minWriteFileFormat = pDb->pSchema->file_format;\n    }\n  }else{\n    wrFlag = 0;\n  }\n  if( pOp->p5 & OPFLAG_P2ISREG ){\n    assert( p2>0 );\n    assert( p2<=(p->nMem+1 - p->nCursor) );\n    pIn2 = &aMem[p2];\n    assert( memIsValid(pIn2) );\n    assert( (pIn2->flags & MEM_Int)!=0 );\n    sqlite3VdbeMemIntegerify(pIn2);\n    p2 = (int)pIn2->u.i;\n    /* The p2 value always comes from a prior OP_CreateBtree opcode and\n    ** that opcode will always set the p2 value to 2 or more or else fail.\n    ** If there were a failure, the prepared statement would have halted\n    ** before reaching this instruction. */\n    assert( p2>=2 );\n  }\n  if( pOp->p4type==P4_KEYINFO ){\n    pKeyInfo = pOp->p4.pKeyInfo;\n    assert( pKeyInfo->enc==ENC(db) );\n    assert( pKeyInfo->db==db );\n    nField = pKeyInfo->nAllField;\n  }else if( pOp->p4type==P4_INT32 ){\n    nField = pOp->p4.i;\n  }\n  assert( pOp->p1>=0 );\n  assert( nField>=0 );\n  testcase( nField==0 );  /* Table with INTEGER PRIMARY KEY and nothing else */\n  pCur = allocateCursor(p, pOp->p1, nField, iDb, CURTYPE_BTREE);\n  if( pCur==0 ) goto no_mem;\n  pCur->nullRow = 1;\n  pCur->isOrdered = 1;\n  pCur->pgnoRoot = p2;\n#ifdef SQLITE_DEBUG\n  pCur->wrFlag = wrFlag;\n#endif\n  rc = sqlite3BtreeCursor(pX, p2, wrFlag, pKeyInfo, pCur->uc.pCursor);\n  pCur->pKeyInfo = pKeyInfo;\n  /* Set the VdbeCursor.isTable variable. Previous versions of\n  ** SQLite used to check if the root-page flags were sane at this point\n  ** and report database corruption if they were not, but this check has\n  ** since moved into the btree layer.  */  \n  pCur->isTable = pOp->p4type!=P4_KEYINFO;\n\nopen_cursor_set_hints:\n  assert( OPFLAG_BULKCSR==BTREE_BULKLOAD );\n  assert( OPFLAG_SEEKEQ==BTREE_SEEK_EQ );\n  testcase( pOp->p5 & OPFLAG_BULKCSR );\n#ifdef SQLITE_ENABLE_CURSOR_HINTS\n  testcase( pOp->p2 & OPFLAG_SEEKEQ );\n#endif\n  sqlite3BtreeCursorHintFlags(pCur->uc.pCursor,\n                               (pOp->p5 & (OPFLAG_BULKCSR|OPFLAG_SEEKEQ)));\n  if( rc ) goto abort_due_to_error;\n  break;\n}\n\n/* Opcode: OpenDup P1 P2 * * *\n**\n** Open a new cursor P1 that points to the same ephemeral table as\n** cursor P2.  The P2 cursor must have been opened by a prior OP_OpenEphemeral\n** opcode.  Only ephemeral cursors may be duplicated.\n**\n** Duplicate ephemeral cursors are used for self-joins of materialized views.\n*/\ncase OP_OpenDup: {\n  VdbeCursor *pOrig;    /* The original cursor to be duplicated */\n  VdbeCursor *pCx;      /* The new cursor */\n\n  pOrig = p->apCsr[pOp->p2];\n  assert( pOrig->pBtx!=0 );  /* Only ephemeral cursors can be duplicated */\n\n  pCx = allocateCursor(p, pOp->p1, pOrig->nField, -1, CURTYPE_BTREE);\n  if( pCx==0 ) goto no_mem;\n  pCx->nullRow = 1;\n  pCx->isEphemeral = 1;\n  pCx->pKeyInfo = pOrig->pKeyInfo;\n  pCx->isTable = pOrig->isTable;\n  rc = sqlite3BtreeCursor(pOrig->pBtx, MASTER_ROOT, BTREE_WRCSR,\n                          pCx->pKeyInfo, pCx->uc.pCursor);\n  /* The sqlite3BtreeCursor() routine can only fail for the first cursor\n  ** opened for a database.  Since there is already an open cursor when this\n  ** opcode is run, the sqlite3BtreeCursor() cannot fail */\n  assert( rc==SQLITE_OK );\n  break;\n}\n\n\n/* Opcode: OpenEphemeral P1 P2 * P4 P5\n** Synopsis: nColumn=P2\n**\n** Open a new cursor P1 to a transient table.\n** The cursor is always opened read/write even if \n** the main database is read-only.  The ephemeral\n** table is deleted automatically when the cursor is closed.\n**\n** P2 is the number of columns in the ephemeral table.\n** The cursor points to a BTree table if P4==0 and to a BTree index\n** if P4 is not 0.  If P4 is not NULL, it points to a KeyInfo structure\n** that defines the format of keys in the index.\n**\n** The P5 parameter can be a mask of the BTREE_* flags defined\n** in btree.h.  These flags control aspects of the operation of\n** the btree.  The BTREE_OMIT_JOURNAL and BTREE_SINGLE flags are\n** added automatically.\n*/\n/* Opcode: OpenAutoindex P1 P2 * P4 *\n** Synopsis: nColumn=P2\n**\n** This opcode works the same as OP_OpenEphemeral.  It has a\n** different name to distinguish its use.  Tables created using\n** by this opcode will be used for automatically created transient\n** indices in joins.\n*/\ncase OP_OpenAutoindex: \ncase OP_OpenEphemeral: {\n  VdbeCursor *pCx;\n  KeyInfo *pKeyInfo;\n\n  static const int vfsFlags = \n      SQLITE_OPEN_READWRITE |\n      SQLITE_OPEN_CREATE |\n      SQLITE_OPEN_EXCLUSIVE |\n      SQLITE_OPEN_DELETEONCLOSE |\n      SQLITE_OPEN_TRANSIENT_DB;\n  assert( pOp->p1>=0 );\n  assert( pOp->p2>=0 );\n  pCx = allocateCursor(p, pOp->p1, pOp->p2, -1, CURTYPE_BTREE);\n  if( pCx==0 ) goto no_mem;\n  pCx->nullRow = 1;\n  pCx->isEphemeral = 1;\n  rc = sqlite3BtreeOpen(db->pVfs, 0, db, &pCx->pBtx, \n                        BTREE_OMIT_JOURNAL | BTREE_SINGLE | pOp->p5, vfsFlags);\n  if( rc==SQLITE_OK ){\n    rc = sqlite3BtreeBeginTrans(pCx->pBtx, 1);\n  }\n  if( rc==SQLITE_OK ){\n    /* If a transient index is required, create it by calling\n    ** sqlite3BtreeCreateTable() with the BTREE_BLOBKEY flag before\n    ** opening it. If a transient table is required, just use the\n    ** automatically created table with root-page 1 (an BLOB_INTKEY table).\n    */\n    if( (pCx->pKeyInfo = pKeyInfo = pOp->p4.pKeyInfo)!=0 ){\n      int pgno;\n      assert( pOp->p4type==P4_KEYINFO );\n      rc = sqlite3BtreeCreateTable(pCx->pBtx, &pgno, BTREE_BLOBKEY | pOp->p5); \n      if( rc==SQLITE_OK ){\n        assert( pgno==MASTER_ROOT+1 );\n        assert( pKeyInfo->db==db );\n        assert( pKeyInfo->enc==ENC(db) );\n        rc = sqlite3BtreeCursor(pCx->pBtx, pgno, BTREE_WRCSR,\n                                pKeyInfo, pCx->uc.pCursor);\n      }\n      pCx->isTable = 0;\n    }else{\n      rc = sqlite3BtreeCursor(pCx->pBtx, MASTER_ROOT, BTREE_WRCSR,\n                              0, pCx->uc.pCursor);\n      pCx->isTable = 1;\n    }\n  }\n  if( rc ) goto abort_due_to_error;\n  pCx->isOrdered = (pOp->p5!=BTREE_UNORDERED);\n  break;\n}\n\n/* Opcode: SorterOpen P1 P2 P3 P4 *\n**\n** This opcode works like OP_OpenEphemeral except that it opens\n** a transient index that is specifically designed to sort large\n** tables using an external merge-sort algorithm.\n**\n** If argument P3 is non-zero, then it indicates that the sorter may\n** assume that a stable sort considering the first P3 fields of each\n** key is sufficient to produce the required results.\n*/\ncase OP_SorterOpen: {\n  VdbeCursor *pCx;\n\n  assert( pOp->p1>=0 );\n  assert( pOp->p2>=0 );\n  pCx = allocateCursor(p, pOp->p1, pOp->p2, -1, CURTYPE_SORTER);\n  if( pCx==0 ) goto no_mem;\n  pCx->pKeyInfo = pOp->p4.pKeyInfo;\n  assert( pCx->pKeyInfo->db==db );\n  assert( pCx->pKeyInfo->enc==ENC(db) );\n  rc = sqlite3VdbeSorterInit(db, pOp->p3, pCx);\n  if( rc ) goto abort_due_to_error;\n  break;\n}\n\n/* Opcode: SequenceTest P1 P2 * * *\n** Synopsis: if( cursor[P1].ctr++ ) pc = P2\n**\n** P1 is a sorter cursor. If the sequence counter is currently zero, jump\n** to P2. Regardless of whether or not the jump is taken, increment the\n** the sequence value.\n*/\ncase OP_SequenceTest: {\n  VdbeCursor *pC;\n  assert( pOp->p1>=0 && pOp->p1<p->nCursor );\n  pC = p->apCsr[pOp->p1];\n  assert( isSorter(pC) );\n  if( (pC->seqCount++)==0 ){\n    goto jump_to_p2;\n  }\n  break;\n}\n\n/* Opcode: OpenPseudo P1 P2 P3 * *\n** Synopsis: P3 columns in r[P2]\n**\n** Open a new cursor that points to a fake table that contains a single\n** row of data.  The content of that one row is the content of memory\n** register P2.  In other words, cursor P1 becomes an alias for the \n** MEM_Blob content contained in register P2.\n**\n** A pseudo-table created by this opcode is used to hold a single\n** row output from the sorter so that the row can be decomposed into\n** individual columns using the OP_Column opcode.  The OP_Column opcode\n** is the only cursor opcode that works with a pseudo-table.\n**\n** P3 is the number of fields in the records that will be stored by\n** the pseudo-table.\n*/\ncase OP_OpenPseudo: {\n  VdbeCursor *pCx;\n\n  assert( pOp->p1>=0 );\n  assert( pOp->p3>=0 );\n  pCx = allocateCursor(p, pOp->p1, pOp->p3, -1, CURTYPE_PSEUDO);\n  if( pCx==0 ) goto no_mem;\n  pCx->nullRow = 1;\n  pCx->seekResult = pOp->p2;\n  pCx->isTable = 1;\n  /* Give this pseudo-cursor a fake BtCursor pointer so that pCx\n  ** can be safely passed to sqlite3VdbeCursorMoveto().  This avoids a test\n  ** for pCx->eCurType==CURTYPE_BTREE inside of sqlite3VdbeCursorMoveto()\n  ** which is a performance optimization */\n  pCx->uc.pCursor = sqlite3BtreeFakeValidCursor();\n  assert( pOp->p5==0 );\n  break;\n}\n\n/* Opcode: Close P1 * * * *\n**\n** Close a cursor previously opened as P1.  If P1 is not\n** currently open, this instruction is a no-op.\n*/\ncase OP_Close: {\n  assert( pOp->p1>=0 && pOp->p1<p->nCursor );\n  sqlite3VdbeFreeCursor(p, p->apCsr[pOp->p1]);\n  p->apCsr[pOp->p1] = 0;\n  break;\n}\n\n#ifdef SQLITE_ENABLE_COLUMN_USED_MASK\n/* Opcode: ColumnsUsed P1 * * P4 *\n**\n** This opcode (which only exists if SQLite was compiled with\n** SQLITE_ENABLE_COLUMN_USED_MASK) identifies which columns of the\n** table or index for cursor P1 are used.  P4 is a 64-bit integer\n** (P4_INT64) in which the first 63 bits are one for each of the\n** first 63 columns of the table or index that are actually used\n** by the cursor.  The high-order bit is set if any column after\n** the 64th is used.\n*/\ncase OP_ColumnsUsed: {\n  VdbeCursor *pC;\n  pC = p->apCsr[pOp->p1];\n  assert( pC->eCurType==CURTYPE_BTREE );\n  pC->maskUsed = *(u64*)pOp->p4.pI64;\n  break;\n}\n#endif\n\n/* Opcode: SeekGE P1 P2 P3 P4 *\n** Synopsis: key=r[P3@P4]\n**\n** If cursor P1 refers to an SQL table (B-Tree that uses integer keys), \n** use the value in register P3 as the key.  If cursor P1 refers \n** to an SQL index, then P3 is the first in an array of P4 registers \n** that are used as an unpacked index key. \n**\n** Reposition cursor P1 so that  it points to the smallest entry that \n** is greater than or equal to the key value. If there are no records \n** greater than or equal to the key and P2 is not zero, then jump to P2.\n**\n** If the cursor P1 was opened using the OPFLAG_SEEKEQ flag, then this\n** opcode will always land on a record that equally equals the key, or\n** else jump immediately to P2.  When the cursor is OPFLAG_SEEKEQ, this\n** opcode must be followed by an IdxLE opcode with the same arguments.\n** The IdxLE opcode will be skipped if this opcode succeeds, but the\n** IdxLE opcode will be used on subsequent loop iterations.\n**\n** This opcode leaves the cursor configured to move in forward order,\n** from the beginning toward the end.  In other words, the cursor is\n** configured to use Next, not Prev.\n**\n** See also: Found, NotFound, SeekLt, SeekGt, SeekLe\n*/\n/* Opcode: SeekGT P1 P2 P3 P4 *\n** Synopsis: key=r[P3@P4]\n**\n** If cursor P1 refers to an SQL table (B-Tree that uses integer keys), \n** use the value in register P3 as a key. If cursor P1 refers \n** to an SQL index, then P3 is the first in an array of P4 registers \n** that are used as an unpacked index key. \n**\n** Reposition cursor P1 so that  it points to the smallest entry that \n** is greater than the key value. If there are no records greater than \n** the key and P2 is not zero, then jump to P2.\n**\n** This opcode leaves the cursor configured to move in forward order,\n** from the beginning toward the end.  In other words, the cursor is\n** configured to use Next, not Prev.\n**\n** See also: Found, NotFound, SeekLt, SeekGe, SeekLe\n*/\n/* Opcode: SeekLT P1 P2 P3 P4 * \n** Synopsis: key=r[P3@P4]\n**\n** If cursor P1 refers to an SQL table (B-Tree that uses integer keys), \n** use the value in register P3 as a key. If cursor P1 refers \n** to an SQL index, then P3 is the first in an array of P4 registers \n** that are used as an unpacked index key. \n**\n** Reposition cursor P1 so that  it points to the largest entry that \n** is less than the key value. If there are no records less than \n** the key and P2 is not zero, then jump to P2.\n**\n** This opcode leaves the cursor configured to move in reverse order,\n** from the end toward the beginning.  In other words, the cursor is\n** configured to use Prev, not Next.\n**\n** See also: Found, NotFound, SeekGt, SeekGe, SeekLe\n*/\n/* Opcode: SeekLE P1 P2 P3 P4 *\n** Synopsis: key=r[P3@P4]\n**\n** If cursor P1 refers to an SQL table (B-Tree that uses integer keys), \n** use the value in register P3 as a key. If cursor P1 refers \n** to an SQL index, then P3 is the first in an array of P4 registers \n** that are used as an unpacked index key. \n**\n** Reposition cursor P1 so that it points to the largest entry that \n** is less than or equal to the key value. If there are no records \n** less than or equal to the key and P2 is not zero, then jump to P2.\n**\n** This opcode leaves the cursor configured to move in reverse order,\n** from the end toward the beginning.  In other words, the cursor is\n** configured to use Prev, not Next.\n**\n** If the cursor P1 was opened using the OPFLAG_SEEKEQ flag, then this\n** opcode will always land on a record that equally equals the key, or\n** else jump immediately to P2.  When the cursor is OPFLAG_SEEKEQ, this\n** opcode must be followed by an IdxGE opcode with the same arguments.\n** The IdxGE opcode will be skipped if this opcode succeeds, but the\n** IdxGE opcode will be used on subsequent loop iterations.\n**\n** See also: Found, NotFound, SeekGt, SeekGe, SeekLt\n*/\ncase OP_SeekLT:         /* jump, in3 */\ncase OP_SeekLE:         /* jump, in3 */\ncase OP_SeekGE:         /* jump, in3 */\ncase OP_SeekGT: {       /* jump, in3 */\n  int res;           /* Comparison result */\n  int oc;            /* Opcode */\n  VdbeCursor *pC;    /* The cursor to seek */\n  UnpackedRecord r;  /* The key to seek for */\n  int nField;        /* Number of columns or fields in the key */\n  i64 iKey;          /* The rowid we are to seek to */\n  int eqOnly;        /* Only interested in == results */\n\n  assert( pOp->p1>=0 && pOp->p1<p->nCursor );\n  assert( pOp->p2!=0 );\n  pC = p->apCsr[pOp->p1];\n  assert( pC!=0 );\n  assert( pC->eCurType==CURTYPE_BTREE );\n  assert( OP_SeekLE == OP_SeekLT+1 );\n  assert( OP_SeekGE == OP_SeekLT+2 );\n  assert( OP_SeekGT == OP_SeekLT+3 );\n  assert( pC->isOrdered );\n  assert( pC->uc.pCursor!=0 );\n  oc = pOp->opcode;\n  eqOnly = 0;\n  pC->nullRow = 0;\n#ifdef SQLITE_DEBUG\n  pC->seekOp = pOp->opcode;\n#endif\n\n  if( pC->isTable ){\n    /* The BTREE_SEEK_EQ flag is only set on index cursors */\n    assert( sqlite3BtreeCursorHasHint(pC->uc.pCursor, BTREE_SEEK_EQ)==0\n              || CORRUPT_DB );\n\n    /* The input value in P3 might be of any type: integer, real, string,\n    ** blob, or NULL.  But it needs to be an integer before we can do\n    ** the seek, so convert it. */\n    pIn3 = &aMem[pOp->p3];\n    if( (pIn3->flags & (MEM_Int|MEM_Real|MEM_Str))==MEM_Str ){\n      applyNumericAffinity(pIn3, 0);\n    }\n    iKey = sqlite3VdbeIntValue(pIn3);\n\n    /* If the P3 value could not be converted into an integer without\n    ** loss of information, then special processing is required... */\n    if( (pIn3->flags & MEM_Int)==0 ){\n      if( (pIn3->flags & MEM_Real)==0 ){\n        /* If the P3 value cannot be converted into any kind of a number,\n        ** then the seek is not possible, so jump to P2 */\n        VdbeBranchTaken(1,2); goto jump_to_p2;\n        break;\n      }\n\n      /* If the approximation iKey is larger than the actual real search\n      ** term, substitute >= for > and < for <=. e.g. if the search term\n      ** is 4.9 and the integer approximation 5:\n      **\n      **        (x >  4.9)    ->     (x >= 5)\n      **        (x <= 4.9)    ->     (x <  5)\n      */\n      if( pIn3->u.r<(double)iKey ){\n        assert( OP_SeekGE==(OP_SeekGT-1) );\n        assert( OP_SeekLT==(OP_SeekLE-1) );\n        assert( (OP_SeekLE & 0x0001)==(OP_SeekGT & 0x0001) );\n        if( (oc & 0x0001)==(OP_SeekGT & 0x0001) ) oc--;\n      }\n\n      /* If the approximation iKey is smaller than the actual real search\n      ** term, substitute <= for < and > for >=.  */\n      else if( pIn3->u.r>(double)iKey ){\n        assert( OP_SeekLE==(OP_SeekLT+1) );\n        assert( OP_SeekGT==(OP_SeekGE+1) );\n        assert( (OP_SeekLT & 0x0001)==(OP_SeekGE & 0x0001) );\n        if( (oc & 0x0001)==(OP_SeekLT & 0x0001) ) oc++;\n      }\n    } \n    rc = sqlite3BtreeMovetoUnpacked(pC->uc.pCursor, 0, (u64)iKey, 0, &res);\n    pC->movetoTarget = iKey;  /* Used by OP_Delete */\n    if( rc!=SQLITE_OK ){\n      goto abort_due_to_error;\n    }\n  }else{\n    /* For a cursor with the BTREE_SEEK_EQ hint, only the OP_SeekGE and\n    ** OP_SeekLE opcodes are allowed, and these must be immediately followed\n    ** by an OP_IdxGT or OP_IdxLT opcode, respectively, with the same key.\n    */\n    if( sqlite3BtreeCursorHasHint(pC->uc.pCursor, BTREE_SEEK_EQ) ){\n      eqOnly = 1;\n      assert( pOp->opcode==OP_SeekGE || pOp->opcode==OP_SeekLE );\n      assert( pOp[1].opcode==OP_IdxLT || pOp[1].opcode==OP_IdxGT );\n      assert( pOp[1].p1==pOp[0].p1 );\n      assert( pOp[1].p2==pOp[0].p2 );\n      assert( pOp[1].p3==pOp[0].p3 );\n      assert( pOp[1].p4.i==pOp[0].p4.i );\n    }\n\n    nField = pOp->p4.i;\n    assert( pOp->p4type==P4_INT32 );\n    assert( nField>0 );\n    r.pKeyInfo = pC->pKeyInfo;\n    r.nField = (u16)nField;\n\n    /* The next line of code computes as follows, only faster:\n    **   if( oc==OP_SeekGT || oc==OP_SeekLE ){\n    **     r.default_rc = -1;\n    **   }else{\n    **     r.default_rc = +1;\n    **   }\n    */\n    r.default_rc = ((1 & (oc - OP_SeekLT)) ? -1 : +1);\n    assert( oc!=OP_SeekGT || r.default_rc==-1 );\n    assert( oc!=OP_SeekLE || r.default_rc==-1 );\n    assert( oc!=OP_SeekGE || r.default_rc==+1 );\n    assert( oc!=OP_SeekLT || r.default_rc==+1 );\n\n    r.aMem = &aMem[pOp->p3];\n#ifdef SQLITE_DEBUG\n    { int i; for(i=0; i<r.nField; i++) assert( memIsValid(&r.aMem[i]) ); }\n#endif\n    r.eqSeen = 0;\n    rc = sqlite3BtreeMovetoUnpacked(pC->uc.pCursor, &r, 0, 0, &res);\n    if( rc!=SQLITE_OK ){\n      goto abort_due_to_error;\n    }\n    if( eqOnly && r.eqSeen==0 ){\n      assert( res!=0 );\n      goto seek_not_found;\n    }\n  }\n  pC->deferredMoveto = 0;\n  pC->cacheStatus = CACHE_STALE;\n#ifdef SQLITE_TEST\n  sqlite3_search_count++;\n#endif\n  if( oc>=OP_SeekGE ){  assert( oc==OP_SeekGE || oc==OP_SeekGT );\n    if( res<0 || (res==0 && oc==OP_SeekGT) ){\n      res = 0;\n      rc = sqlite3BtreeNext(pC->uc.pCursor, 0);\n      if( rc!=SQLITE_OK ){\n        if( rc==SQLITE_DONE ){\n          rc = SQLITE_OK;\n          res = 1;\n        }else{\n          goto abort_due_to_error;\n        }\n      }\n    }else{\n      res = 0;\n    }\n  }else{\n    assert( oc==OP_SeekLT || oc==OP_SeekLE );\n    if( res>0 || (res==0 && oc==OP_SeekLT) ){\n      res = 0;\n      rc = sqlite3BtreePrevious(pC->uc.pCursor, 0);\n      if( rc!=SQLITE_OK ){\n        if( rc==SQLITE_DONE ){\n          rc = SQLITE_OK;\n          res = 1;\n        }else{\n          goto abort_due_to_error;\n        }\n      }\n    }else{\n      /* res might be negative because the table is empty.  Check to\n      ** see if this is the case.\n      */\n      res = sqlite3BtreeEof(pC->uc.pCursor);\n    }\n  }\nseek_not_found:\n  assert( pOp->p2>0 );\n  VdbeBranchTaken(res!=0,2);\n  if( res ){\n    goto jump_to_p2;\n  }else if( eqOnly ){\n    assert( pOp[1].opcode==OP_IdxLT || pOp[1].opcode==OP_IdxGT );\n    pOp++; /* Skip the OP_IdxLt or OP_IdxGT that follows */\n  }\n  break;\n}\n\n/* Opcode: Found P1 P2 P3 P4 *\n** Synopsis: key=r[P3@P4]\n**\n** If P4==0 then register P3 holds a blob constructed by MakeRecord.  If\n** P4>0 then register P3 is the first of P4 registers that form an unpacked\n** record.\n**\n** Cursor P1 is on an index btree.  If the record identified by P3 and P4\n** is a prefix of any entry in P1 then a jump is made to P2 and\n** P1 is left pointing at the matching entry.\n**\n** This operation leaves the cursor in a state where it can be\n** advanced in the forward direction.  The Next instruction will work,\n** but not the Prev instruction.\n**\n** See also: NotFound, NoConflict, NotExists. SeekGe\n*/\n/* Opcode: NotFound P1 P2 P3 P4 *\n** Synopsis: key=r[P3@P4]\n**\n** If P4==0 then register P3 holds a blob constructed by MakeRecord.  If\n** P4>0 then register P3 is the first of P4 registers that form an unpacked\n** record.\n** \n** Cursor P1 is on an index btree.  If the record identified by P3 and P4\n** is not the prefix of any entry in P1 then a jump is made to P2.  If P1 \n** does contain an entry whose prefix matches the P3/P4 record then control\n** falls through to the next instruction and P1 is left pointing at the\n** matching entry.\n**\n** This operation leaves the cursor in a state where it cannot be\n** advanced in either direction.  In other words, the Next and Prev\n** opcodes do not work after this operation.\n**\n** See also: Found, NotExists, NoConflict\n*/\n/* Opcode: NoConflict P1 P2 P3 P4 *\n** Synopsis: key=r[P3@P4]\n**\n** If P4==0 then register P3 holds a blob constructed by MakeRecord.  If\n** P4>0 then register P3 is the first of P4 registers that form an unpacked\n** record.\n** \n** Cursor P1 is on an index btree.  If the record identified by P3 and P4\n** contains any NULL value, jump immediately to P2.  If all terms of the\n** record are not-NULL then a check is done to determine if any row in the\n** P1 index btree has a matching key prefix.  If there are no matches, jump\n** immediately to P2.  If there is a match, fall through and leave the P1\n** cursor pointing to the matching row.\n**\n** This opcode is similar to OP_NotFound with the exceptions that the\n** branch is always taken if any part of the search key input is NULL.\n**\n** This operation leaves the cursor in a state where it cannot be\n** advanced in either direction.  In other words, the Next and Prev\n** opcodes do not work after this operation.\n**\n** See also: NotFound, Found, NotExists\n*/\ncase OP_NoConflict:     /* jump, in3 */\ncase OP_NotFound:       /* jump, in3 */\ncase OP_Found: {        /* jump, in3 */\n  int alreadyExists;\n  int takeJump;\n  int ii;\n  VdbeCursor *pC;\n  int res;\n  UnpackedRecord *pFree;\n  UnpackedRecord *pIdxKey;\n  UnpackedRecord r;\n\n#ifdef SQLITE_TEST\n  if( pOp->opcode!=OP_NoConflict ) sqlite3_found_count++;\n#endif\n\n  assert( pOp->p1>=0 && pOp->p1<p->nCursor );\n  assert( pOp->p4type==P4_INT32 );\n  pC = p->apCsr[pOp->p1];\n  assert( pC!=0 );\n#ifdef SQLITE_DEBUG\n  pC->seekOp = pOp->opcode;\n#endif\n  pIn3 = &aMem[pOp->p3];\n  assert( pC->eCurType==CURTYPE_BTREE );\n  assert( pC->uc.pCursor!=0 );\n  assert( pC->isTable==0 );\n  if( pOp->p4.i>0 ){\n    r.pKeyInfo = pC->pKeyInfo;\n    r.nField = (u16)pOp->p4.i;\n    r.aMem = pIn3;\n#ifdef SQLITE_DEBUG\n    for(ii=0; ii<r.nField; ii++){\n      assert( memIsValid(&r.aMem[ii]) );\n      assert( (r.aMem[ii].flags & MEM_Zero)==0 || r.aMem[ii].n==0 );\n      if( ii ) REGISTER_TRACE(pOp->p3+ii, &r.aMem[ii]);\n    }\n#endif\n    pIdxKey = &r;\n    pFree = 0;\n  }else{\n    assert( pIn3->flags & MEM_Blob );\n    rc = ExpandBlob(pIn3);\n    assert( rc==SQLITE_OK || rc==SQLITE_NOMEM );\n    if( rc ) goto no_mem;\n    pFree = pIdxKey = sqlite3VdbeAllocUnpackedRecord(pC->pKeyInfo);\n    if( pIdxKey==0 ) goto no_mem;\n    sqlite3VdbeRecordUnpack(pC->pKeyInfo, pIn3->n, pIn3->z, pIdxKey);\n  }\n  pIdxKey->default_rc = 0;\n  takeJump = 0;\n  if( pOp->opcode==OP_NoConflict ){\n    /* For the OP_NoConflict opcode, take the jump if any of the\n    ** input fields are NULL, since any key with a NULL will not\n    ** conflict */\n    for(ii=0; ii<pIdxKey->nField; ii++){\n      if( pIdxKey->aMem[ii].flags & MEM_Null ){\n        takeJump = 1;\n        break;\n      }\n    }\n  }\n  rc = sqlite3BtreeMovetoUnpacked(pC->uc.pCursor, pIdxKey, 0, 0, &res);\n  if( pFree ) sqlite3DbFreeNN(db, pFree);\n  if( rc!=SQLITE_OK ){\n    goto abort_due_to_error;\n  }\n  pC->seekResult = res;\n  alreadyExists = (res==0);\n  pC->nullRow = 1-alreadyExists;\n  pC->deferredMoveto = 0;\n  pC->cacheStatus = CACHE_STALE;\n  if( pOp->opcode==OP_Found ){\n    VdbeBranchTaken(alreadyExists!=0,2);\n    if( alreadyExists ) goto jump_to_p2;\n  }else{\n    VdbeBranchTaken(takeJump||alreadyExists==0,2);\n    if( takeJump || !alreadyExists ) goto jump_to_p2;\n  }\n  break;\n}\n\n/* Opcode: SeekRowid P1 P2 P3 * *\n** Synopsis: intkey=r[P3]\n**\n** P1 is the index of a cursor open on an SQL table btree (with integer\n** keys).  If register P3 does not contain an integer or if P1 does not\n** contain a record with rowid P3 then jump immediately to P2.  \n** Or, if P2 is 0, raise an SQLITE_CORRUPT error. If P1 does contain\n** a record with rowid P3 then \n** leave the cursor pointing at that record and fall through to the next\n** instruction.\n**\n** The OP_NotExists opcode performs the same operation, but with OP_NotExists\n** the P3 register must be guaranteed to contain an integer value.  With this\n** opcode, register P3 might not contain an integer.\n**\n** The OP_NotFound opcode performs the same operation on index btrees\n** (with arbitrary multi-value keys).\n**\n** This opcode leaves the cursor in a state where it cannot be advanced\n** in either direction.  In other words, the Next and Prev opcodes will\n** not work following this opcode.\n**\n** See also: Found, NotFound, NoConflict, SeekRowid\n*/\n/* Opcode: NotExists P1 P2 P3 * *\n** Synopsis: intkey=r[P3]\n**\n** P1 is the index of a cursor open on an SQL table btree (with integer\n** keys).  P3 is an integer rowid.  If P1 does not contain a record with\n** rowid P3 then jump immediately to P2.  Or, if P2 is 0, raise an\n** SQLITE_CORRUPT error. If P1 does contain a record with rowid P3 then \n** leave the cursor pointing at that record and fall through to the next\n** instruction.\n**\n** The OP_SeekRowid opcode performs the same operation but also allows the\n** P3 register to contain a non-integer value, in which case the jump is\n** always taken.  This opcode requires that P3 always contain an integer.\n**\n** The OP_NotFound opcode performs the same operation on index btrees\n** (with arbitrary multi-value keys).\n**\n** This opcode leaves the cursor in a state where it cannot be advanced\n** in either direction.  In other words, the Next and Prev opcodes will\n** not work following this opcode.\n**\n** See also: Found, NotFound, NoConflict, SeekRowid\n*/\ncase OP_SeekRowid: {        /* jump, in3 */\n  VdbeCursor *pC;\n  BtCursor *pCrsr;\n  int res;\n  u64 iKey;\n\n  pIn3 = &aMem[pOp->p3];\n  if( (pIn3->flags & MEM_Int)==0 ){\n    applyAffinity(pIn3, SQLITE_AFF_NUMERIC, encoding);\n    if( (pIn3->flags & MEM_Int)==0 ) goto jump_to_p2;\n  }\n  /* Fall through into OP_NotExists */\ncase OP_NotExists:          /* jump, in3 */\n  pIn3 = &aMem[pOp->p3];\n  assert( pIn3->flags & MEM_Int );\n  assert( pOp->p1>=0 && pOp->p1<p->nCursor );\n  pC = p->apCsr[pOp->p1];\n  assert( pC!=0 );\n#ifdef SQLITE_DEBUG\n  pC->seekOp = 0;\n#endif\n  assert( pC->isTable );\n  assert( pC->eCurType==CURTYPE_BTREE );\n  pCrsr = pC->uc.pCursor;\n  assert( pCrsr!=0 );\n  res = 0;\n  iKey = pIn3->u.i;\n  rc = sqlite3BtreeMovetoUnpacked(pCrsr, 0, iKey, 0, &res);\n  assert( rc==SQLITE_OK || res==0 );\n  pC->movetoTarget = iKey;  /* Used by OP_Delete */\n  pC->nullRow = 0;\n  pC->cacheStatus = CACHE_STALE;\n  pC->deferredMoveto = 0;\n  VdbeBranchTaken(res!=0,2);\n  pC->seekResult = res;\n  if( res!=0 ){\n    assert( rc==SQLITE_OK );\n    if( pOp->p2==0 ){\n      rc = SQLITE_CORRUPT_BKPT;\n    }else{\n      goto jump_to_p2;\n    }\n  }\n  if( rc ) goto abort_due_to_error;\n  break;\n}\n\n/* Opcode: Sequence P1 P2 * * *\n** Synopsis: r[P2]=cursor[P1].ctr++\n**\n** Find the next available sequence number for cursor P1.\n** Write the sequence number into register P2.\n** The sequence number on the cursor is incremented after this\n** instruction.  \n*/\ncase OP_Sequence: {           /* out2 */\n  assert( pOp->p1>=0 && pOp->p1<p->nCursor );\n  assert( p->apCsr[pOp->p1]!=0 );\n  assert( p->apCsr[pOp->p1]->eCurType!=CURTYPE_VTAB );\n  pOut = out2Prerelease(p, pOp);\n  pOut->u.i = p->apCsr[pOp->p1]->seqCount++;\n  break;\n}\n\n\n/* Opcode: NewRowid P1 P2 P3 * *\n** Synopsis: r[P2]=rowid\n**\n** Get a new integer record number (a.k.a \"rowid\") used as the key to a table.\n** The record number is not previously used as a key in the database\n** table that cursor P1 points to.  The new record number is written\n** written to register P2.\n**\n** If P3>0 then P3 is a register in the root frame of this VDBE that holds \n** the largest previously generated record number. No new record numbers are\n** allowed to be less than this value. When this value reaches its maximum, \n** an SQLITE_FULL error is generated. The P3 register is updated with the '\n** generated record number. This P3 mechanism is used to help implement the\n** AUTOINCREMENT feature.\n*/\ncase OP_NewRowid: {           /* out2 */\n  i64 v;                 /* The new rowid */\n  VdbeCursor *pC;        /* Cursor of table to get the new rowid */\n  int res;               /* Result of an sqlite3BtreeLast() */\n  int cnt;               /* Counter to limit the number of searches */\n  Mem *pMem;             /* Register holding largest rowid for AUTOINCREMENT */\n  VdbeFrame *pFrame;     /* Root frame of VDBE */\n\n  v = 0;\n  res = 0;\n  pOut = out2Prerelease(p, pOp);\n  assert( pOp->p1>=0 && pOp->p1<p->nCursor );\n  pC = p->apCsr[pOp->p1];\n  assert( pC!=0 );\n  assert( pC->eCurType==CURTYPE_BTREE );\n  assert( pC->uc.pCursor!=0 );\n  {\n    /* The next rowid or record number (different terms for the same\n    ** thing) is obtained in a two-step algorithm.\n    **\n    ** First we attempt to find the largest existing rowid and add one\n    ** to that.  But if the largest existing rowid is already the maximum\n    ** positive integer, we have to fall through to the second\n    ** probabilistic algorithm\n    **\n    ** The second algorithm is to select a rowid at random and see if\n    ** it already exists in the table.  If it does not exist, we have\n    ** succeeded.  If the random rowid does exist, we select a new one\n    ** and try again, up to 100 times.\n    */\n    assert( pC->isTable );\n\n#ifdef SQLITE_32BIT_ROWID\n#   define MAX_ROWID 0x7fffffff\n#else\n    /* Some compilers complain about constants of the form 0x7fffffffffffffff.\n    ** Others complain about 0x7ffffffffffffffffLL.  The following macro seems\n    ** to provide the constant while making all compilers happy.\n    */\n#   define MAX_ROWID  (i64)( (((u64)0x7fffffff)<<32) | (u64)0xffffffff )\n#endif\n\n    if( !pC->useRandomRowid ){\n      rc = sqlite3BtreeLast(pC->uc.pCursor, &res);\n      if( rc!=SQLITE_OK ){\n        goto abort_due_to_error;\n      }\n      if( res ){\n        v = 1;   /* IMP: R-61914-48074 */\n      }else{\n        assert( sqlite3BtreeCursorIsValid(pC->uc.pCursor) );\n        v = sqlite3BtreeIntegerKey(pC->uc.pCursor);\n        if( v>=MAX_ROWID ){\n          pC->useRandomRowid = 1;\n        }else{\n          v++;   /* IMP: R-29538-34987 */\n        }\n      }\n    }\n\n#ifndef SQLITE_OMIT_AUTOINCREMENT\n    if( pOp->p3 ){\n      /* Assert that P3 is a valid memory cell. */\n      assert( pOp->p3>0 );\n      if( p->pFrame ){\n        for(pFrame=p->pFrame; pFrame->pParent; pFrame=pFrame->pParent);\n        /* Assert that P3 is a valid memory cell. */\n        assert( pOp->p3<=pFrame->nMem );\n        pMem = &pFrame->aMem[pOp->p3];\n      }else{\n        /* Assert that P3 is a valid memory cell. */\n        assert( pOp->p3<=(p->nMem+1 - p->nCursor) );\n        pMem = &aMem[pOp->p3];\n        memAboutToChange(p, pMem);\n      }\n      assert( memIsValid(pMem) );\n\n      REGISTER_TRACE(pOp->p3, pMem);\n      sqlite3VdbeMemIntegerify(pMem);\n      assert( (pMem->flags & MEM_Int)!=0 );  /* mem(P3) holds an integer */\n      if( pMem->u.i==MAX_ROWID || pC->useRandomRowid ){\n        rc = SQLITE_FULL;   /* IMP: R-17817-00630 */\n        goto abort_due_to_error;\n      }\n      if( v<pMem->u.i+1 ){\n        v = pMem->u.i + 1;\n      }\n      pMem->u.i = v;\n    }\n#endif\n    if( pC->useRandomRowid ){\n      /* IMPLEMENTATION-OF: R-07677-41881 If the largest ROWID is equal to the\n      ** largest possible integer (9223372036854775807) then the database\n      ** engine starts picking positive candidate ROWIDs at random until\n      ** it finds one that is not previously used. */\n      assert( pOp->p3==0 );  /* We cannot be in random rowid mode if this is\n                             ** an AUTOINCREMENT table. */\n      cnt = 0;\n      do{\n        sqlite3_randomness(sizeof(v), &v);\n        v &= (MAX_ROWID>>1); v++;  /* Ensure that v is greater than zero */\n      }while(  ((rc = sqlite3BtreeMovetoUnpacked(pC->uc.pCursor, 0, (u64)v,\n                                                 0, &res))==SQLITE_OK)\n            && (res==0)\n            && (++cnt<100));\n      if( rc ) goto abort_due_to_error;\n      if( res==0 ){\n        rc = SQLITE_FULL;   /* IMP: R-38219-53002 */\n        goto abort_due_to_error;\n      }\n      assert( v>0 );  /* EV: R-40812-03570 */\n    }\n    pC->deferredMoveto = 0;\n    pC->cacheStatus = CACHE_STALE;\n  }\n  pOut->u.i = v;\n  break;\n}\n\n/* Opcode: Insert P1 P2 P3 P4 P5\n** Synopsis: intkey=r[P3] data=r[P2]\n**\n** Write an entry into the table of cursor P1.  A new entry is\n** created if it doesn't already exist or the data for an existing\n** entry is overwritten.  The data is the value MEM_Blob stored in register\n** number P2. The key is stored in register P3. The key must\n** be a MEM_Int.\n**\n** If the OPFLAG_NCHANGE flag of P5 is set, then the row change count is\n** incremented (otherwise not).  If the OPFLAG_LASTROWID flag of P5 is set,\n** then rowid is stored for subsequent return by the\n** sqlite3_last_insert_rowid() function (otherwise it is unmodified).\n**\n** If the OPFLAG_USESEEKRESULT flag of P5 is set, the implementation might\n** run faster by avoiding an unnecessary seek on cursor P1.  However,\n** the OPFLAG_USESEEKRESULT flag must only be set if there have been no prior\n** seeks on the cursor or if the most recent seek used a key equal to P3.\n**\n** If the OPFLAG_ISUPDATE flag is set, then this opcode is part of an\n** UPDATE operation.  Otherwise (if the flag is clear) then this opcode\n** is part of an INSERT operation.  The difference is only important to\n** the update hook.\n**\n** Parameter P4 may point to a Table structure, or may be NULL. If it is \n** not NULL, then the update-hook (sqlite3.xUpdateCallback) is invoked \n** following a successful insert.\n**\n** (WARNING/TODO: If P1 is a pseudo-cursor and P2 is dynamically\n** allocated, then ownership of P2 is transferred to the pseudo-cursor\n** and register P2 becomes ephemeral.  If the cursor is changed, the\n** value of register P2 will then change.  Make sure this does not\n** cause any problems.)\n**\n** This instruction only works on tables.  The equivalent instruction\n** for indices is OP_IdxInsert.\n*/\n/* Opcode: InsertInt P1 P2 P3 P4 P5\n** Synopsis: intkey=P3 data=r[P2]\n**\n** This works exactly like OP_Insert except that the key is the\n** integer value P3, not the value of the integer stored in register P3.\n*/\ncase OP_Insert: \ncase OP_InsertInt: {\n  Mem *pData;       /* MEM cell holding data for the record to be inserted */\n  Mem *pKey;        /* MEM cell holding key  for the record */\n  VdbeCursor *pC;   /* Cursor to table into which insert is written */\n  int seekResult;   /* Result of prior seek or 0 if no USESEEKRESULT flag */\n  const char *zDb;  /* database name - used by the update hook */\n  Table *pTab;      /* Table structure - used by update and pre-update hooks */\n  BtreePayload x;   /* Payload to be inserted */\n\n  pData = &aMem[pOp->p2];\n  assert( pOp->p1>=0 && pOp->p1<p->nCursor );\n  assert( memIsValid(pData) );\n  pC = p->apCsr[pOp->p1];\n  assert( pC!=0 );\n  assert( pC->eCurType==CURTYPE_BTREE );\n  assert( pC->uc.pCursor!=0 );\n  assert( (pOp->p5 & OPFLAG_ISNOOP) || pC->isTable );\n  assert( pOp->p4type==P4_TABLE || pOp->p4type>=P4_STATIC );\n  REGISTER_TRACE(pOp->p2, pData);\n\n  if( pOp->opcode==OP_Insert ){\n    pKey = &aMem[pOp->p3];\n    assert( pKey->flags & MEM_Int );\n    assert( memIsValid(pKey) );\n    REGISTER_TRACE(pOp->p3, pKey);\n    x.nKey = pKey->u.i;\n  }else{\n    assert( pOp->opcode==OP_InsertInt );\n    x.nKey = pOp->p3;\n  }\n\n  if( pOp->p4type==P4_TABLE && HAS_UPDATE_HOOK(db) ){\n    assert( pC->iDb>=0 );\n    zDb = db->aDb[pC->iDb].zDbSName;\n    pTab = pOp->p4.pTab;\n    assert( (pOp->p5 & OPFLAG_ISNOOP) || HasRowid(pTab) );\n  }else{\n    pTab = 0;\n    zDb = 0;  /* Not needed.  Silence a compiler warning. */\n  }\n\n#ifdef SQLITE_ENABLE_PREUPDATE_HOOK\n  /* Invoke the pre-update hook, if any */\n  if( pTab ){\n    if( db->xPreUpdateCallback && !(pOp->p5 & OPFLAG_ISUPDATE) ){\n      sqlite3VdbePreUpdateHook(p, pC, SQLITE_INSERT, zDb, pTab, x.nKey,pOp->p2);\n    }\n    if( db->xUpdateCallback==0 || pTab->aCol==0 ){\n      /* Prevent post-update hook from running in cases when it should not */\n      pTab = 0;\n    }\n  }\n  if( pOp->p5 & OPFLAG_ISNOOP ) break;\n#endif\n\n  if( pOp->p5 & OPFLAG_NCHANGE ) p->nChange++;\n  if( pOp->p5 & OPFLAG_LASTROWID ) db->lastRowid = x.nKey;\n  assert( pData->flags & (MEM_Blob|MEM_Str) );\n  x.pData = pData->z;\n  x.nData = pData->n;\n  seekResult = ((pOp->p5 & OPFLAG_USESEEKRESULT) ? pC->seekResult : 0);\n  if( pData->flags & MEM_Zero ){\n    x.nZero = pData->u.nZero;\n  }else{\n    x.nZero = 0;\n  }\n  x.pKey = 0;\n  rc = sqlite3BtreeInsert(pC->uc.pCursor, &x,\n      (pOp->p5 & (OPFLAG_APPEND|OPFLAG_SAVEPOSITION)), seekResult\n  );\n  pC->deferredMoveto = 0;\n  pC->cacheStatus = CACHE_STALE;\n\n  /* Invoke the update-hook if required. */\n  if( rc ) goto abort_due_to_error;\n  if( pTab ){\n    assert( db->xUpdateCallback!=0 );\n    assert( pTab->aCol!=0 );\n    db->xUpdateCallback(db->pUpdateArg,\n           (pOp->p5 & OPFLAG_ISUPDATE) ? SQLITE_UPDATE : SQLITE_INSERT,\n           zDb, pTab->zName, x.nKey);\n  }\n  break;\n}\n\n/* Opcode: Delete P1 P2 P3 P4 P5\n**\n** Delete the record at which the P1 cursor is currently pointing.\n**\n** If the OPFLAG_SAVEPOSITION bit of the P5 parameter is set, then\n** the cursor will be left pointing at  either the next or the previous\n** record in the table. If it is left pointing at the next record, then\n** the next Next instruction will be a no-op. As a result, in this case\n** it is ok to delete a record from within a Next loop. If \n** OPFLAG_SAVEPOSITION bit of P5 is clear, then the cursor will be\n** left in an undefined state.\n**\n** If the OPFLAG_AUXDELETE bit is set on P5, that indicates that this\n** delete one of several associated with deleting a table row and all its\n** associated index entries.  Exactly one of those deletes is the \"primary\"\n** delete.  The others are all on OPFLAG_FORDELETE cursors or else are\n** marked with the AUXDELETE flag.\n**\n** If the OPFLAG_NCHANGE flag of P2 (NB: P2 not P5) is set, then the row\n** change count is incremented (otherwise not).\n**\n** P1 must not be pseudo-table.  It has to be a real table with\n** multiple rows.\n**\n** If P4 is not NULL then it points to a Table object. In this case either \n** the update or pre-update hook, or both, may be invoked. The P1 cursor must\n** have been positioned using OP_NotFound prior to invoking this opcode in \n** this case. Specifically, if one is configured, the pre-update hook is \n** invoked if P4 is not NULL. The update-hook is invoked if one is configured, \n** P4 is not NULL, and the OPFLAG_NCHANGE flag is set in P2.\n**\n** If the OPFLAG_ISUPDATE flag is set in P2, then P3 contains the address\n** of the memory cell that contains the value that the rowid of the row will\n** be set to by the update.\n*/\ncase OP_Delete: {\n  VdbeCursor *pC;\n  const char *zDb;\n  Table *pTab;\n  int opflags;\n\n  opflags = pOp->p2;\n  assert( pOp->p1>=0 && pOp->p1<p->nCursor );\n  pC = p->apCsr[pOp->p1];\n  assert( pC!=0 );\n  assert( pC->eCurType==CURTYPE_BTREE );\n  assert( pC->uc.pCursor!=0 );\n  assert( pC->deferredMoveto==0 );\n\n#ifdef SQLITE_DEBUG\n  if( pOp->p4type==P4_TABLE && HasRowid(pOp->p4.pTab) && pOp->p5==0 ){\n    /* If p5 is zero, the seek operation that positioned the cursor prior to\n    ** OP_Delete will have also set the pC->movetoTarget field to the rowid of\n    ** the row that is being deleted */\n    i64 iKey = sqlite3BtreeIntegerKey(pC->uc.pCursor);\n    assert( pC->movetoTarget==iKey );\n  }\n#endif\n\n  /* If the update-hook or pre-update-hook will be invoked, set zDb to\n  ** the name of the db to pass as to it. Also set local pTab to a copy\n  ** of p4.pTab. Finally, if p5 is true, indicating that this cursor was\n  ** last moved with OP_Next or OP_Prev, not Seek or NotFound, set \n  ** VdbeCursor.movetoTarget to the current rowid.  */\n  if( pOp->p4type==P4_TABLE && HAS_UPDATE_HOOK(db) ){\n    assert( pC->iDb>=0 );\n    assert( pOp->p4.pTab!=0 );\n    zDb = db->aDb[pC->iDb].zDbSName;\n    pTab = pOp->p4.pTab;\n    if( (pOp->p5 & OPFLAG_SAVEPOSITION)!=0 && pC->isTable ){\n      pC->movetoTarget = sqlite3BtreeIntegerKey(pC->uc.pCursor);\n    }\n  }else{\n    zDb = 0;   /* Not needed.  Silence a compiler warning. */\n    pTab = 0;  /* Not needed.  Silence a compiler warning. */\n  }\n\n#ifdef SQLITE_ENABLE_PREUPDATE_HOOK\n  /* Invoke the pre-update-hook if required. */\n  if( db->xPreUpdateCallback && pOp->p4.pTab ){\n    assert( !(opflags & OPFLAG_ISUPDATE) \n         || HasRowid(pTab)==0 \n         || (aMem[pOp->p3].flags & MEM_Int) \n    );\n    sqlite3VdbePreUpdateHook(p, pC,\n        (opflags & OPFLAG_ISUPDATE) ? SQLITE_UPDATE : SQLITE_DELETE, \n        zDb, pTab, pC->movetoTarget,\n        pOp->p3\n    );\n  }\n  if( opflags & OPFLAG_ISNOOP ) break;\n#endif\n \n  /* Only flags that can be set are SAVEPOISTION and AUXDELETE */ \n  assert( (pOp->p5 & ~(OPFLAG_SAVEPOSITION|OPFLAG_AUXDELETE))==0 );\n  assert( OPFLAG_SAVEPOSITION==BTREE_SAVEPOSITION );\n  assert( OPFLAG_AUXDELETE==BTREE_AUXDELETE );\n\n#ifdef SQLITE_DEBUG\n  if( p->pFrame==0 ){\n    if( pC->isEphemeral==0\n        && (pOp->p5 & OPFLAG_AUXDELETE)==0\n        && (pC->wrFlag & OPFLAG_FORDELETE)==0\n      ){\n      nExtraDelete++;\n    }\n    if( pOp->p2 & OPFLAG_NCHANGE ){\n      nExtraDelete--;\n    }\n  }\n#endif\n\n  rc = sqlite3BtreeDelete(pC->uc.pCursor, pOp->p5);\n  pC->cacheStatus = CACHE_STALE;\n  pC->seekResult = 0;\n  if( rc ) goto abort_due_to_error;\n\n  /* Invoke the update-hook if required. */\n  if( opflags & OPFLAG_NCHANGE ){\n    p->nChange++;\n    if( db->xUpdateCallback && HasRowid(pTab) ){\n      db->xUpdateCallback(db->pUpdateArg, SQLITE_DELETE, zDb, pTab->zName,\n          pC->movetoTarget);\n      assert( pC->iDb>=0 );\n    }\n  }\n\n  break;\n}\n/* Opcode: ResetCount * * * * *\n**\n** The value of the change counter is copied to the database handle\n** change counter (returned by subsequent calls to sqlite3_changes()).\n** Then the VMs internal change counter resets to 0.\n** This is used by trigger programs.\n*/\ncase OP_ResetCount: {\n  sqlite3VdbeSetChanges(db, p->nChange);\n  p->nChange = 0;\n  break;\n}\n\n/* Opcode: SorterCompare P1 P2 P3 P4\n** Synopsis: if key(P1)!=trim(r[P3],P4) goto P2\n**\n** P1 is a sorter cursor. This instruction compares a prefix of the\n** record blob in register P3 against a prefix of the entry that \n** the sorter cursor currently points to.  Only the first P4 fields\n** of r[P3] and the sorter record are compared.\n**\n** If either P3 or the sorter contains a NULL in one of their significant\n** fields (not counting the P4 fields at the end which are ignored) then\n** the comparison is assumed to be equal.\n**\n** Fall through to next instruction if the two records compare equal to\n** each other.  Jump to P2 if they are different.\n*/\ncase OP_SorterCompare: {\n  VdbeCursor *pC;\n  int res;\n  int nKeyCol;\n\n  pC = p->apCsr[pOp->p1];\n  assert( isSorter(pC) );\n  assert( pOp->p4type==P4_INT32 );\n  pIn3 = &aMem[pOp->p3];\n  nKeyCol = pOp->p4.i;\n  res = 0;\n  rc = sqlite3VdbeSorterCompare(pC, pIn3, nKeyCol, &res);\n  VdbeBranchTaken(res!=0,2);\n  if( rc ) goto abort_due_to_error;\n  if( res ) goto jump_to_p2;\n  break;\n};\n\n/* Opcode: SorterData P1 P2 P3 * *\n** Synopsis: r[P2]=data\n**\n** Write into register P2 the current sorter data for sorter cursor P1.\n** Then clear the column header cache on cursor P3.\n**\n** This opcode is normally use to move a record out of the sorter and into\n** a register that is the source for a pseudo-table cursor created using\n** OpenPseudo.  That pseudo-table cursor is the one that is identified by\n** parameter P3.  Clearing the P3 column cache as part of this opcode saves\n** us from having to issue a separate NullRow instruction to clear that cache.\n*/\ncase OP_SorterData: {\n  VdbeCursor *pC;\n\n  pOut = &aMem[pOp->p2];\n  pC = p->apCsr[pOp->p1];\n  assert( isSorter(pC) );\n  rc = sqlite3VdbeSorterRowkey(pC, pOut);\n  assert( rc!=SQLITE_OK || (pOut->flags & MEM_Blob) );\n  assert( pOp->p1>=0 && pOp->p1<p->nCursor );\n  if( rc ) goto abort_due_to_error;\n  p->apCsr[pOp->p3]->cacheStatus = CACHE_STALE;\n  break;\n}\n\n/* Opcode: RowData P1 P2 P3 * *\n** Synopsis: r[P2]=data\n**\n** Write into register P2 the complete row content for the row at \n** which cursor P1 is currently pointing.\n** There is no interpretation of the data.  \n** It is just copied onto the P2 register exactly as \n** it is found in the database file.\n**\n** If cursor P1 is an index, then the content is the key of the row.\n** If cursor P2 is a table, then the content extracted is the data.\n**\n** If the P1 cursor must be pointing to a valid row (not a NULL row)\n** of a real table, not a pseudo-table.\n**\n** If P3!=0 then this opcode is allowed to make an ephermeral pointer\n** into the database page.  That means that the content of the output\n** register will be invalidated as soon as the cursor moves - including\n** moves caused by other cursors that \"save\" the the current cursors\n** position in order that they can write to the same table.  If P3==0\n** then a copy of the data is made into memory.  P3!=0 is faster, but\n** P3==0 is safer.\n**\n** If P3!=0 then the content of the P2 register is unsuitable for use\n** in OP_Result and any OP_Result will invalidate the P2 register content.\n** The P2 register content is invalidated by opcodes like OP_Function or\n** by any use of another cursor pointing to the same table.\n*/\ncase OP_RowData: {\n  VdbeCursor *pC;\n  BtCursor *pCrsr;\n  u32 n;\n\n  pOut = out2Prerelease(p, pOp);\n\n  assert( pOp->p1>=0 && pOp->p1<p->nCursor );\n  pC = p->apCsr[pOp->p1];\n  assert( pC!=0 );\n  assert( pC->eCurType==CURTYPE_BTREE );\n  assert( isSorter(pC)==0 );\n  assert( pC->nullRow==0 );\n  assert( pC->uc.pCursor!=0 );\n  pCrsr = pC->uc.pCursor;\n\n  /* The OP_RowData opcodes always follow OP_NotExists or\n  ** OP_SeekRowid or OP_Rewind/Op_Next with no intervening instructions\n  ** that might invalidate the cursor.\n  ** If this where not the case, on of the following assert()s\n  ** would fail.  Should this ever change (because of changes in the code\n  ** generator) then the fix would be to insert a call to\n  ** sqlite3VdbeCursorMoveto().\n  */\n  assert( pC->deferredMoveto==0 );\n  assert( sqlite3BtreeCursorIsValid(pCrsr) );\n#if 0  /* Not required due to the previous to assert() statements */\n  rc = sqlite3VdbeCursorMoveto(pC);\n  if( rc!=SQLITE_OK ) goto abort_due_to_error;\n#endif\n\n  n = sqlite3BtreePayloadSize(pCrsr);\n  if( n>(u32)db->aLimit[SQLITE_LIMIT_LENGTH] ){\n    goto too_big;\n  }\n  testcase( n==0 );\n  rc = sqlite3VdbeMemFromBtree(pCrsr, 0, n, pOut);\n  if( rc ) goto abort_due_to_error;\n  if( !pOp->p3 ) Deephemeralize(pOut);\n  UPDATE_MAX_BLOBSIZE(pOut);\n  REGISTER_TRACE(pOp->p2, pOut);\n  break;\n}\n\n/* Opcode: Rowid P1 P2 * * *\n** Synopsis: r[P2]=rowid\n**\n** Store in register P2 an integer which is the key of the table entry that\n** P1 is currently point to.\n**\n** P1 can be either an ordinary table or a virtual table.  There used to\n** be a separate OP_VRowid opcode for use with virtual tables, but this\n** one opcode now works for both table types.\n*/\ncase OP_Rowid: {                 /* out2 */\n  VdbeCursor *pC;\n  i64 v;\n  sqlite3_vtab *pVtab;\n  const sqlite3_module *pModule;\n\n  pOut = out2Prerelease(p, pOp);\n  assert( pOp->p1>=0 && pOp->p1<p->nCursor );\n  pC = p->apCsr[pOp->p1];\n  assert( pC!=0 );\n  assert( pC->eCurType!=CURTYPE_PSEUDO || pC->nullRow );\n  if( pC->nullRow ){\n    pOut->flags = MEM_Null;\n    break;\n  }else if( pC->deferredMoveto ){\n    v = pC->movetoTarget;\n#ifndef SQLITE_OMIT_VIRTUALTABLE\n  }else if( pC->eCurType==CURTYPE_VTAB ){\n    assert( pC->uc.pVCur!=0 );\n    pVtab = pC->uc.pVCur->pVtab;\n    pModule = pVtab->pModule;\n    assert( pModule->xRowid );\n    rc = pModule->xRowid(pC->uc.pVCur, &v);\n    sqlite3VtabImportErrmsg(p, pVtab);\n    if( rc ) goto abort_due_to_error;\n#endif /* SQLITE_OMIT_VIRTUALTABLE */\n  }else{\n    assert( pC->eCurType==CURTYPE_BTREE );\n    assert( pC->uc.pCursor!=0 );\n    rc = sqlite3VdbeCursorRestore(pC);\n    if( rc ) goto abort_due_to_error;\n    if( pC->nullRow ){\n      pOut->flags = MEM_Null;\n      break;\n    }\n    v = sqlite3BtreeIntegerKey(pC->uc.pCursor);\n  }\n  pOut->u.i = v;\n  break;\n}\n\n/* Opcode: NullRow P1 * * * *\n**\n** Move the cursor P1 to a null row.  Any OP_Column operations\n** that occur while the cursor is on the null row will always\n** write a NULL.\n*/\ncase OP_NullRow: {\n  VdbeCursor *pC;\n\n  assert( pOp->p1>=0 && pOp->p1<p->nCursor );\n  pC = p->apCsr[pOp->p1];\n  assert( pC!=0 );\n  pC->nullRow = 1;\n  pC->cacheStatus = CACHE_STALE;\n  if( pC->eCurType==CURTYPE_BTREE ){\n    assert( pC->uc.pCursor!=0 );\n    sqlite3BtreeClearCursor(pC->uc.pCursor);\n  }\n  break;\n}\n\n/* Opcode: SeekEnd P1 * * * *\n**\n** Position cursor P1 at the end of the btree for the purpose of\n** appending a new entry onto the btree.\n**\n** It is assumed that the cursor is used only for appending and so\n** if the cursor is valid, then the cursor must already be pointing\n** at the end of the btree and so no changes are made to\n** the cursor.\n*/\n/* Opcode: Last P1 P2 * * *\n**\n** The next use of the Rowid or Column or Prev instruction for P1 \n** will refer to the last entry in the database table or index.\n** If the table or index is empty and P2>0, then jump immediately to P2.\n** If P2 is 0 or if the table or index is not empty, fall through\n** to the following instruction.\n**\n** This opcode leaves the cursor configured to move in reverse order,\n** from the end toward the beginning.  In other words, the cursor is\n** configured to use Prev, not Next.\n*/\ncase OP_SeekEnd:\ncase OP_Last: {        /* jump */\n  VdbeCursor *pC;\n  BtCursor *pCrsr;\n  int res;\n\n  assert( pOp->p1>=0 && pOp->p1<p->nCursor );\n  pC = p->apCsr[pOp->p1];\n  assert( pC!=0 );\n  assert( pC->eCurType==CURTYPE_BTREE );\n  pCrsr = pC->uc.pCursor;\n  res = 0;\n  assert( pCrsr!=0 );\n#ifdef SQLITE_DEBUG\n  pC->seekOp = pOp->opcode;\n#endif\n  if( pOp->opcode==OP_SeekEnd ){\n    assert( pOp->p2==0 );\n    pC->seekResult = -1;\n    if( sqlite3BtreeCursorIsValidNN(pCrsr) ){\n      break;\n    }\n  }\n  rc = sqlite3BtreeLast(pCrsr, &res);\n  pC->nullRow = (u8)res;\n  pC->deferredMoveto = 0;\n  pC->cacheStatus = CACHE_STALE;\n  if( rc ) goto abort_due_to_error;\n  if( pOp->p2>0 ){\n    VdbeBranchTaken(res!=0,2);\n    if( res ) goto jump_to_p2;\n  }\n  break;\n}\n\n/* Opcode: IfSmaller P1 P2 P3 * *\n**\n** Estimate the number of rows in the table P1.  Jump to P2 if that\n** estimate is less than approximately 2**(0.1*P3).\n*/\ncase OP_IfSmaller: {        /* jump */\n  VdbeCursor *pC;\n  BtCursor *pCrsr;\n  int res;\n  i64 sz;\n\n  assert( pOp->p1>=0 && pOp->p1<p->nCursor );\n  pC = p->apCsr[pOp->p1];\n  assert( pC!=0 );\n  pCrsr = pC->uc.pCursor;\n  assert( pCrsr );\n  rc = sqlite3BtreeFirst(pCrsr, &res);\n  if( rc ) goto abort_due_to_error;\n  if( res==0 ){\n    sz = sqlite3BtreeRowCountEst(pCrsr);\n    if( ALWAYS(sz>=0) && sqlite3LogEst((u64)sz)<pOp->p3 ) res = 1;\n  }\n  VdbeBranchTaken(res!=0,2);\n  if( res ) goto jump_to_p2;\n  break;\n}\n\n\n/* Opcode: SorterSort P1 P2 * * *\n**\n** After all records have been inserted into the Sorter object\n** identified by P1, invoke this opcode to actually do the sorting.\n** Jump to P2 if there are no records to be sorted.\n**\n** This opcode is an alias for OP_Sort and OP_Rewind that is used\n** for Sorter objects.\n*/\n/* Opcode: Sort P1 P2 * * *\n**\n** This opcode does exactly the same thing as OP_Rewind except that\n** it increments an undocumented global variable used for testing.\n**\n** Sorting is accomplished by writing records into a sorting index,\n** then rewinding that index and playing it back from beginning to\n** end.  We use the OP_Sort opcode instead of OP_Rewind to do the\n** rewinding so that the global variable will be incremented and\n** regression tests can determine whether or not the optimizer is\n** correctly optimizing out sorts.\n*/\ncase OP_SorterSort:    /* jump */\ncase OP_Sort: {        /* jump */\n#ifdef SQLITE_TEST\n  sqlite3_sort_count++;\n  sqlite3_search_count--;\n#endif\n  p->aCounter[SQLITE_STMTSTATUS_SORT]++;\n  /* Fall through into OP_Rewind */\n}\n/* Opcode: Rewind P1 P2 * * *\n**\n** The next use of the Rowid or Column or Next instruction for P1 \n** will refer to the first entry in the database table or index.\n** If the table or index is empty, jump immediately to P2.\n** If the table or index is not empty, fall through to the following \n** instruction.\n**\n** This opcode leaves the cursor configured to move in forward order,\n** from the beginning toward the end.  In other words, the cursor is\n** configured to use Next, not Prev.\n*/\ncase OP_Rewind: {        /* jump */\n  VdbeCursor *pC;\n  BtCursor *pCrsr;\n  int res;\n\n  assert( pOp->p1>=0 && pOp->p1<p->nCursor );\n  pC = p->apCsr[pOp->p1];\n  assert( pC!=0 );\n  assert( isSorter(pC)==(pOp->opcode==OP_SorterSort) );\n  res = 1;\n#ifdef SQLITE_DEBUG\n  pC->seekOp = OP_Rewind;\n#endif\n  if( isSorter(pC) ){\n    rc = sqlite3VdbeSorterRewind(pC, &res);\n  }else{\n    assert( pC->eCurType==CURTYPE_BTREE );\n    pCrsr = pC->uc.pCursor;\n    assert( pCrsr );\n    rc = sqlite3BtreeFirst(pCrsr, &res);\n    pC->deferredMoveto = 0;\n    pC->cacheStatus = CACHE_STALE;\n  }\n  if( rc ) goto abort_due_to_error;\n  pC->nullRow = (u8)res;\n  assert( pOp->p2>0 && pOp->p2<p->nOp );\n  VdbeBranchTaken(res!=0,2);\n  if( res ) goto jump_to_p2;\n  break;\n}\n\n/* Opcode: Next P1 P2 P3 P4 P5\n**\n** Advance cursor P1 so that it points to the next key/data pair in its\n** table or index.  If there are no more key/value pairs then fall through\n** to the following instruction.  But if the cursor advance was successful,\n** jump immediately to P2.\n**\n** The Next opcode is only valid following an SeekGT, SeekGE, or\n** OP_Rewind opcode used to position the cursor.  Next is not allowed\n** to follow SeekLT, SeekLE, or OP_Last.\n**\n** The P1 cursor must be for a real table, not a pseudo-table.  P1 must have\n** been opened prior to this opcode or the program will segfault.\n**\n** The P3 value is a hint to the btree implementation. If P3==1, that\n** means P1 is an SQL index and that this instruction could have been\n** omitted if that index had been unique.  P3 is usually 0.  P3 is\n** always either 0 or 1.\n**\n** P4 is always of type P4_ADVANCE. The function pointer points to\n** sqlite3BtreeNext().\n**\n** If P5 is positive and the jump is taken, then event counter\n** number P5-1 in the prepared statement is incremented.\n**\n** See also: Prev, NextIfOpen\n*/\n/* Opcode: NextIfOpen P1 P2 P3 P4 P5\n**\n** This opcode works just like Next except that if cursor P1 is not\n** open it behaves a no-op.\n*/\n/* Opcode: Prev P1 P2 P3 P4 P5\n**\n** Back up cursor P1 so that it points to the previous key/data pair in its\n** table or index.  If there is no previous key/value pairs then fall through\n** to the following instruction.  But if the cursor backup was successful,\n** jump immediately to P2.\n**\n**\n** The Prev opcode is only valid following an SeekLT, SeekLE, or\n** OP_Last opcode used to position the cursor.  Prev is not allowed\n** to follow SeekGT, SeekGE, or OP_Rewind.\n**\n** The P1 cursor must be for a real table, not a pseudo-table.  If P1 is\n** not open then the behavior is undefined.\n**\n** The P3 value is a hint to the btree implementation. If P3==1, that\n** means P1 is an SQL index and that this instruction could have been\n** omitted if that index had been unique.  P3 is usually 0.  P3 is\n** always either 0 or 1.\n**\n** P4 is always of type P4_ADVANCE. The function pointer points to\n** sqlite3BtreePrevious().\n**\n** If P5 is positive and the jump is taken, then event counter\n** number P5-1 in the prepared statement is incremented.\n*/\n/* Opcode: PrevIfOpen P1 P2 P3 P4 P5\n**\n** This opcode works just like Prev except that if cursor P1 is not\n** open it behaves a no-op.\n*/\n/* Opcode: SorterNext P1 P2 * * P5\n**\n** This opcode works just like OP_Next except that P1 must be a\n** sorter object for which the OP_SorterSort opcode has been\n** invoked.  This opcode advances the cursor to the next sorted\n** record, or jumps to P2 if there are no more sorted records.\n*/\ncase OP_SorterNext: {  /* jump */\n  VdbeCursor *pC;\n\n  pC = p->apCsr[pOp->p1];\n  assert( isSorter(pC) );\n  rc = sqlite3VdbeSorterNext(db, pC);\n  goto next_tail;\ncase OP_PrevIfOpen:    /* jump */\ncase OP_NextIfOpen:    /* jump */\n  if( p->apCsr[pOp->p1]==0 ) break;\n  /* Fall through */\ncase OP_Prev:          /* jump */\ncase OP_Next:          /* jump */\n  assert( pOp->p1>=0 && pOp->p1<p->nCursor );\n  assert( pOp->p5<ArraySize(p->aCounter) );\n  pC = p->apCsr[pOp->p1];\n  assert( pC!=0 );\n  assert( pC->deferredMoveto==0 );\n  assert( pC->eCurType==CURTYPE_BTREE );\n  assert( pOp->opcode!=OP_Next || pOp->p4.xAdvance==sqlite3BtreeNext );\n  assert( pOp->opcode!=OP_Prev || pOp->p4.xAdvance==sqlite3BtreePrevious );\n  assert( pOp->opcode!=OP_NextIfOpen || pOp->p4.xAdvance==sqlite3BtreeNext );\n  assert( pOp->opcode!=OP_PrevIfOpen || pOp->p4.xAdvance==sqlite3BtreePrevious);\n\n  /* The Next opcode is only used after SeekGT, SeekGE, and Rewind.\n  ** The Prev opcode is only used after SeekLT, SeekLE, and Last. */\n  assert( pOp->opcode!=OP_Next || pOp->opcode!=OP_NextIfOpen\n       || pC->seekOp==OP_SeekGT || pC->seekOp==OP_SeekGE\n       || pC->seekOp==OP_Rewind || pC->seekOp==OP_Found);\n  assert( pOp->opcode!=OP_Prev || pOp->opcode!=OP_PrevIfOpen\n       || pC->seekOp==OP_SeekLT || pC->seekOp==OP_SeekLE\n       || pC->seekOp==OP_Last );\n\n  rc = pOp->p4.xAdvance(pC->uc.pCursor, pOp->p3);\nnext_tail:\n  pC->cacheStatus = CACHE_STALE;\n  VdbeBranchTaken(rc==SQLITE_OK,2);\n  if( rc==SQLITE_OK ){\n    pC->nullRow = 0;\n    p->aCounter[pOp->p5]++;\n#ifdef SQLITE_TEST\n    sqlite3_search_count++;\n#endif\n    goto jump_to_p2_and_check_for_interrupt;\n  }\n  if( rc!=SQLITE_DONE ) goto abort_due_to_error;\n  rc = SQLITE_OK;\n  pC->nullRow = 1;\n  goto check_for_interrupt;\n}\n\n/* Opcode: IdxInsert P1 P2 P3 P4 P5\n** Synopsis: key=r[P2]\n**\n** Register P2 holds an SQL index key made using the\n** MakeRecord instructions.  This opcode writes that key\n** into the index P1.  Data for the entry is nil.\n**\n** If P4 is not zero, then it is the number of values in the unpacked\n** key of reg(P2).  In that case, P3 is the index of the first register\n** for the unpacked key.  The availability of the unpacked key can sometimes\n** be an optimization.\n**\n** If P5 has the OPFLAG_APPEND bit set, that is a hint to the b-tree layer\n** that this insert is likely to be an append.\n**\n** If P5 has the OPFLAG_NCHANGE bit set, then the change counter is\n** incremented by this instruction.  If the OPFLAG_NCHANGE bit is clear,\n** then the change counter is unchanged.\n**\n** If the OPFLAG_USESEEKRESULT flag of P5 is set, the implementation might\n** run faster by avoiding an unnecessary seek on cursor P1.  However,\n** the OPFLAG_USESEEKRESULT flag must only be set if there have been no prior\n** seeks on the cursor or if the most recent seek used a key equivalent\n** to P2. \n**\n** This instruction only works for indices.  The equivalent instruction\n** for tables is OP_Insert.\n*/\n/* Opcode: SorterInsert P1 P2 * * *\n** Synopsis: key=r[P2]\n**\n** Register P2 holds an SQL index key made using the\n** MakeRecord instructions.  This opcode writes that key\n** into the sorter P1.  Data for the entry is nil.\n*/\ncase OP_SorterInsert:       /* in2 */\ncase OP_IdxInsert: {        /* in2 */\n  VdbeCursor *pC;\n  BtreePayload x;\n\n  assert( pOp->p1>=0 && pOp->p1<p->nCursor );\n  pC = p->apCsr[pOp->p1];\n  assert( pC!=0 );\n  assert( isSorter(pC)==(pOp->opcode==OP_SorterInsert) );\n  pIn2 = &aMem[pOp->p2];\n  assert( pIn2->flags & MEM_Blob );\n  if( pOp->p5 & OPFLAG_NCHANGE ) p->nChange++;\n  assert( pC->eCurType==CURTYPE_BTREE || pOp->opcode==OP_SorterInsert );\n  assert( pC->isTable==0 );\n  rc = ExpandBlob(pIn2);\n  if( rc ) goto abort_due_to_error;\n  if( pOp->opcode==OP_SorterInsert ){\n    rc = sqlite3VdbeSorterWrite(pC, pIn2);\n  }else{\n    x.nKey = pIn2->n;\n    x.pKey = pIn2->z;\n    x.aMem = aMem + pOp->p3;\n    x.nMem = (u16)pOp->p4.i;\n    rc = sqlite3BtreeInsert(pC->uc.pCursor, &x,\n         (pOp->p5 & (OPFLAG_APPEND|OPFLAG_SAVEPOSITION)), \n        ((pOp->p5 & OPFLAG_USESEEKRESULT) ? pC->seekResult : 0)\n        );\n    assert( pC->deferredMoveto==0 );\n    pC->cacheStatus = CACHE_STALE;\n  }\n  if( rc) goto abort_due_to_error;\n  break;\n}\n\n/* Opcode: IdxDelete P1 P2 P3 * *\n** Synopsis: key=r[P2@P3]\n**\n** The content of P3 registers starting at register P2 form\n** an unpacked index key. This opcode removes that entry from the \n** index opened by cursor P1.\n*/\ncase OP_IdxDelete: {\n  VdbeCursor *pC;\n  BtCursor *pCrsr;\n  int res;\n  UnpackedRecord r;\n\n  assert( pOp->p3>0 );\n  assert( pOp->p2>0 && pOp->p2+pOp->p3<=(p->nMem+1 - p->nCursor)+1 );\n  assert( pOp->p1>=0 && pOp->p1<p->nCursor );\n  pC = p->apCsr[pOp->p1];\n  assert( pC!=0 );\n  assert( pC->eCurType==CURTYPE_BTREE );\n  pCrsr = pC->uc.pCursor;\n  assert( pCrsr!=0 );\n  assert( pOp->p5==0 );\n  r.pKeyInfo = pC->pKeyInfo;\n  r.nField = (u16)pOp->p3;\n  r.default_rc = 0;\n  r.aMem = &aMem[pOp->p2];\n  rc = sqlite3BtreeMovetoUnpacked(pCrsr, &r, 0, 0, &res);\n  if( rc ) goto abort_due_to_error;\n  if( res==0 ){\n    rc = sqlite3BtreeDelete(pCrsr, BTREE_AUXDELETE);\n    if( rc ) goto abort_due_to_error;\n  }\n  assert( pC->deferredMoveto==0 );\n  pC->cacheStatus = CACHE_STALE;\n  pC->seekResult = 0;\n  break;\n}\n\n/* Opcode: DeferredSeek P1 * P3 P4 *\n** Synopsis: Move P3 to P1.rowid if needed\n**\n** P1 is an open index cursor and P3 is a cursor on the corresponding\n** table.  This opcode does a deferred seek of the P3 table cursor\n** to the row that corresponds to the current row of P1.\n**\n** This is a deferred seek.  Nothing actually happens until\n** the cursor is used to read a record.  That way, if no reads\n** occur, no unnecessary I/O happens.\n**\n** P4 may be an array of integers (type P4_INTARRAY) containing\n** one entry for each column in the P3 table.  If array entry a(i)\n** is non-zero, then reading column a(i)-1 from cursor P3 is \n** equivalent to performing the deferred seek and then reading column i \n** from P1.  This information is stored in P3 and used to redirect\n** reads against P3 over to P1, thus possibly avoiding the need to\n** seek and read cursor P3.\n*/\n/* Opcode: IdxRowid P1 P2 * * *\n** Synopsis: r[P2]=rowid\n**\n** Write into register P2 an integer which is the last entry in the record at\n** the end of the index key pointed to by cursor P1.  This integer should be\n** the rowid of the table entry to which this index entry points.\n**\n** See also: Rowid, MakeRecord.\n*/\ncase OP_DeferredSeek:\ncase OP_IdxRowid: {           /* out2 */\n  VdbeCursor *pC;             /* The P1 index cursor */\n  VdbeCursor *pTabCur;        /* The P2 table cursor (OP_DeferredSeek only) */\n  i64 rowid;                  /* Rowid that P1 current points to */\n\n  assert( pOp->p1>=0 && pOp->p1<p->nCursor );\n  pC = p->apCsr[pOp->p1];\n  assert( pC!=0 );\n  assert( pC->eCurType==CURTYPE_BTREE );\n  assert( pC->uc.pCursor!=0 );\n  assert( pC->isTable==0 );\n  assert( pC->deferredMoveto==0 );\n  assert( !pC->nullRow || pOp->opcode==OP_IdxRowid );\n\n  /* The IdxRowid and Seek opcodes are combined because of the commonality\n  ** of sqlite3VdbeCursorRestore() and sqlite3VdbeIdxRowid(). */\n  rc = sqlite3VdbeCursorRestore(pC);\n\n  /* sqlite3VbeCursorRestore() can only fail if the record has been deleted\n  ** out from under the cursor.  That will never happens for an IdxRowid\n  ** or Seek opcode */\n  if( NEVER(rc!=SQLITE_OK) ) goto abort_due_to_error;\n\n  if( !pC->nullRow ){\n    rowid = 0;  /* Not needed.  Only used to silence a warning. */\n    rc = sqlite3VdbeIdxRowid(db, pC->uc.pCursor, &rowid);\n    if( rc!=SQLITE_OK ){\n      goto abort_due_to_error;\n    }\n    if( pOp->opcode==OP_DeferredSeek ){\n      assert( pOp->p3>=0 && pOp->p3<p->nCursor );\n      pTabCur = p->apCsr[pOp->p3];\n      assert( pTabCur!=0 );\n      assert( pTabCur->eCurType==CURTYPE_BTREE );\n      assert( pTabCur->uc.pCursor!=0 );\n      assert( pTabCur->isTable );\n      pTabCur->nullRow = 0;\n      pTabCur->movetoTarget = rowid;\n      pTabCur->deferredMoveto = 1;\n      assert( pOp->p4type==P4_INTARRAY || pOp->p4.ai==0 );\n      pTabCur->aAltMap = pOp->p4.ai;\n      pTabCur->pAltCursor = pC;\n    }else{\n      pOut = out2Prerelease(p, pOp);\n      pOut->u.i = rowid;\n    }\n  }else{\n    assert( pOp->opcode==OP_IdxRowid );\n    sqlite3VdbeMemSetNull(&aMem[pOp->p2]);\n  }\n  break;\n}\n\n/* Opcode: IdxGE P1 P2 P3 P4 P5\n** Synopsis: key=r[P3@P4]\n**\n** The P4 register values beginning with P3 form an unpacked index \n** key that omits the PRIMARY KEY.  Compare this key value against the index \n** that P1 is currently pointing to, ignoring the PRIMARY KEY or ROWID \n** fields at the end.\n**\n** If the P1 index entry is greater than or equal to the key value\n** then jump to P2.  Otherwise fall through to the next instruction.\n*/\n/* Opcode: IdxGT P1 P2 P3 P4 P5\n** Synopsis: key=r[P3@P4]\n**\n** The P4 register values beginning with P3 form an unpacked index \n** key that omits the PRIMARY KEY.  Compare this key value against the index \n** that P1 is currently pointing to, ignoring the PRIMARY KEY or ROWID \n** fields at the end.\n**\n** If the P1 index entry is greater than the key value\n** then jump to P2.  Otherwise fall through to the next instruction.\n*/\n/* Opcode: IdxLT P1 P2 P3 P4 P5\n** Synopsis: key=r[P3@P4]\n**\n** The P4 register values beginning with P3 form an unpacked index \n** key that omits the PRIMARY KEY or ROWID.  Compare this key value against\n** the index that P1 is currently pointing to, ignoring the PRIMARY KEY or\n** ROWID on the P1 index.\n**\n** If the P1 index entry is less than the key value then jump to P2.\n** Otherwise fall through to the next instruction.\n*/\n/* Opcode: IdxLE P1 P2 P3 P4 P5\n** Synopsis: key=r[P3@P4]\n**\n** The P4 register values beginning with P3 form an unpacked index \n** key that omits the PRIMARY KEY or ROWID.  Compare this key value against\n** the index that P1 is currently pointing to, ignoring the PRIMARY KEY or\n** ROWID on the P1 index.\n**\n** If the P1 index entry is less than or equal to the key value then jump\n** to P2. Otherwise fall through to the next instruction.\n*/\ncase OP_IdxLE:          /* jump */\ncase OP_IdxGT:          /* jump */\ncase OP_IdxLT:          /* jump */\ncase OP_IdxGE:  {       /* jump */\n  VdbeCursor *pC;\n  int res;\n  UnpackedRecord r;\n\n  assert( pOp->p1>=0 && pOp->p1<p->nCursor );\n  pC = p->apCsr[pOp->p1];\n  assert( pC!=0 );\n  assert( pC->isOrdered );\n  assert( pC->eCurType==CURTYPE_BTREE );\n  assert( pC->uc.pCursor!=0);\n  assert( pC->deferredMoveto==0 );\n  assert( pOp->p5==0 || pOp->p5==1 );\n  assert( pOp->p4type==P4_INT32 );\n  r.pKeyInfo = pC->pKeyInfo;\n  r.nField = (u16)pOp->p4.i;\n  if( pOp->opcode<OP_IdxLT ){\n    assert( pOp->opcode==OP_IdxLE || pOp->opcode==OP_IdxGT );\n    r.default_rc = -1;\n  }else{\n    assert( pOp->opcode==OP_IdxGE || pOp->opcode==OP_IdxLT );\n    r.default_rc = 0;\n  }\n  r.aMem = &aMem[pOp->p3];\n#ifdef SQLITE_DEBUG\n  { int i; for(i=0; i<r.nField; i++) assert( memIsValid(&r.aMem[i]) ); }\n#endif\n  res = 0;  /* Not needed.  Only used to silence a warning. */\n  rc = sqlite3VdbeIdxKeyCompare(db, pC, &r, &res);\n  assert( (OP_IdxLE&1)==(OP_IdxLT&1) && (OP_IdxGE&1)==(OP_IdxGT&1) );\n  if( (pOp->opcode&1)==(OP_IdxLT&1) ){\n    assert( pOp->opcode==OP_IdxLE || pOp->opcode==OP_IdxLT );\n    res = -res;\n  }else{\n    assert( pOp->opcode==OP_IdxGE || pOp->opcode==OP_IdxGT );\n    res++;\n  }\n  VdbeBranchTaken(res>0,2);\n  if( rc ) goto abort_due_to_error;\n  if( res>0 ) goto jump_to_p2;\n  break;\n}\n\n/* Opcode: Destroy P1 P2 P3 * *\n**\n** Delete an entire database table or index whose root page in the database\n** file is given by P1.\n**\n** The table being destroyed is in the main database file if P3==0.  If\n** P3==1 then the table to be clear is in the auxiliary database file\n** that is used to store tables create using CREATE TEMPORARY TABLE.\n**\n** If AUTOVACUUM is enabled then it is possible that another root page\n** might be moved into the newly deleted root page in order to keep all\n** root pages contiguous at the beginning of the database.  The former\n** value of the root page that moved - its value before the move occurred -\n** is stored in register P2. If no page movement was required (because the\n** table being dropped was already the last one in the database) then a \n** zero is stored in register P2.  If AUTOVACUUM is disabled then a zero \n** is stored in register P2.\n**\n** This opcode throws an error if there are any active reader VMs when\n** it is invoked. This is done to avoid the difficulty associated with \n** updating existing cursors when a root page is moved in an AUTOVACUUM \n** database. This error is thrown even if the database is not an AUTOVACUUM \n** db in order to avoid introducing an incompatibility between autovacuum \n** and non-autovacuum modes.\n**\n** See also: Clear\n*/\ncase OP_Destroy: {     /* out2 */\n  int iMoved;\n  int iDb;\n\n  assert( p->readOnly==0 );\n  assert( pOp->p1>1 );\n  pOut = out2Prerelease(p, pOp);\n  pOut->flags = MEM_Null;\n  if( db->nVdbeRead > db->nVDestroy+1 ){\n    rc = SQLITE_LOCKED;\n    p->errorAction = OE_Abort;\n    goto abort_due_to_error;\n  }else{\n    iDb = pOp->p3;\n    assert( DbMaskTest(p->btreeMask, iDb) );\n    iMoved = 0;  /* Not needed.  Only to silence a warning. */\n    rc = sqlite3BtreeDropTable(db->aDb[iDb].pBt, pOp->p1, &iMoved);\n    pOut->flags = MEM_Int;\n    pOut->u.i = iMoved;\n    if( rc ) goto abort_due_to_error;\n#ifndef SQLITE_OMIT_AUTOVACUUM\n    if( iMoved!=0 ){\n      sqlite3RootPageMoved(db, iDb, iMoved, pOp->p1);\n      /* All OP_Destroy operations occur on the same btree */\n      assert( resetSchemaOnFault==0 || resetSchemaOnFault==iDb+1 );\n      resetSchemaOnFault = iDb+1;\n    }\n#endif\n  }\n  break;\n}\n\n/* Opcode: Clear P1 P2 P3\n**\n** Delete all contents of the database table or index whose root page\n** in the database file is given by P1.  But, unlike Destroy, do not\n** remove the table or index from the database file.\n**\n** The table being clear is in the main database file if P2==0.  If\n** P2==1 then the table to be clear is in the auxiliary database file\n** that is used to store tables create using CREATE TEMPORARY TABLE.\n**\n** If the P3 value is non-zero, then the table referred to must be an\n** intkey table (an SQL table, not an index). In this case the row change \n** count is incremented by the number of rows in the table being cleared. \n** If P3 is greater than zero, then the value stored in register P3 is\n** also incremented by the number of rows in the table being cleared.\n**\n** See also: Destroy\n*/\ncase OP_Clear: {\n  int nChange;\n \n  nChange = 0;\n  assert( p->readOnly==0 );\n  assert( DbMaskTest(p->btreeMask, pOp->p2) );\n  rc = sqlite3BtreeClearTable(\n      db->aDb[pOp->p2].pBt, pOp->p1, (pOp->p3 ? &nChange : 0)\n  );\n  if( pOp->p3 ){\n    p->nChange += nChange;\n    if( pOp->p3>0 ){\n      assert( memIsValid(&aMem[pOp->p3]) );\n      memAboutToChange(p, &aMem[pOp->p3]);\n      aMem[pOp->p3].u.i += nChange;\n    }\n  }\n  if( rc ) goto abort_due_to_error;\n  break;\n}\n\n/* Opcode: ResetSorter P1 * * * *\n**\n** Delete all contents from the ephemeral table or sorter\n** that is open on cursor P1.\n**\n** This opcode only works for cursors used for sorting and\n** opened with OP_OpenEphemeral or OP_SorterOpen.\n*/\ncase OP_ResetSorter: {\n  VdbeCursor *pC;\n \n  assert( pOp->p1>=0 && pOp->p1<p->nCursor );\n  pC = p->apCsr[pOp->p1];\n  assert( pC!=0 );\n  if( isSorter(pC) ){\n    sqlite3VdbeSorterReset(db, pC->uc.pSorter);\n  }else{\n    assert( pC->eCurType==CURTYPE_BTREE );\n    assert( pC->isEphemeral );\n    rc = sqlite3BtreeClearTableOfCursor(pC->uc.pCursor);\n    if( rc ) goto abort_due_to_error;\n  }\n  break;\n}\n\n/* Opcode: CreateBtree P1 P2 P3 * *\n** Synopsis: r[P2]=root iDb=P1 flags=P3\n**\n** Allocate a new b-tree in the main database file if P1==0 or in the\n** TEMP database file if P1==1 or in an attached database if\n** P1>1.  The P3 argument must be 1 (BTREE_INTKEY) for a rowid table\n** it must be 2 (BTREE_BLOBKEY) for a index or WITHOUT ROWID table.\n** The root page number of the new b-tree is stored in register P2.\n*/\ncase OP_CreateBtree: {          /* out2 */\n  int pgno;\n  Db *pDb;\n\n  pOut = out2Prerelease(p, pOp);\n  pgno = 0;\n  assert( pOp->p3==BTREE_INTKEY || pOp->p3==BTREE_BLOBKEY );\n  assert( pOp->p1>=0 && pOp->p1<db->nDb );\n  assert( DbMaskTest(p->btreeMask, pOp->p1) );\n  assert( p->readOnly==0 );\n  pDb = &db->aDb[pOp->p1];\n  assert( pDb->pBt!=0 );\n  rc = sqlite3BtreeCreateTable(pDb->pBt, &pgno, pOp->p3);\n  if( rc ) goto abort_due_to_error;\n  pOut->u.i = pgno;\n  break;\n}\n\n/* Opcode: SqlExec * * * P4 *\n**\n** Run the SQL statement or statements specified in the P4 string.\n*/\ncase OP_SqlExec: {\n  db->nSqlExec++;\n  rc = sqlite3_exec(db, pOp->p4.z, 0, 0, 0);\n  db->nSqlExec--;\n  if( rc ) goto abort_due_to_error;\n  break;\n}\n\n/* Opcode: ParseSchema P1 * * P4 *\n**\n** Read and parse all entries from the SQLITE_MASTER table of database P1\n** that match the WHERE clause P4. \n**\n** This opcode invokes the parser to create a new virtual machine,\n** then runs the new virtual machine.  It is thus a re-entrant opcode.\n*/\ncase OP_ParseSchema: {\n  int iDb;\n  const char *zMaster;\n  char *zSql;\n  InitData initData;\n\n  /* Any prepared statement that invokes this opcode will hold mutexes\n  ** on every btree.  This is a prerequisite for invoking \n  ** sqlite3InitCallback().\n  */\n#ifdef SQLITE_DEBUG\n  for(iDb=0; iDb<db->nDb; iDb++){\n    assert( iDb==1 || sqlite3BtreeHoldsMutex(db->aDb[iDb].pBt) );\n  }\n#endif\n\n  iDb = pOp->p1;\n  assert( iDb>=0 && iDb<db->nDb );\n  assert( DbHasProperty(db, iDb, DB_SchemaLoaded) );\n  /* Used to be a conditional */ {\n    zMaster = MASTER_NAME;\n    initData.db = db;\n    initData.iDb = pOp->p1;\n    initData.pzErrMsg = &p->zErrMsg;\n    zSql = sqlite3MPrintf(db,\n       \"SELECT name, rootpage, sql FROM '%q'.%s WHERE %s ORDER BY rowid\",\n       db->aDb[iDb].zDbSName, zMaster, pOp->p4.z);\n    if( zSql==0 ){\n      rc = SQLITE_NOMEM_BKPT;\n    }else{\n      assert( db->init.busy==0 );\n      db->init.busy = 1;\n      initData.rc = SQLITE_OK;\n      assert( !db->mallocFailed );\n      rc = sqlite3_exec(db, zSql, sqlite3InitCallback, &initData, 0);\n      if( rc==SQLITE_OK ) rc = initData.rc;\n      sqlite3DbFreeNN(db, zSql);\n      db->init.busy = 0;\n    }\n  }\n  if( rc ){\n    sqlite3ResetAllSchemasOfConnection(db);\n    if( rc==SQLITE_NOMEM ){\n      goto no_mem;\n    }\n    goto abort_due_to_error;\n  }\n  break;  \n}\n\n#if !defined(SQLITE_OMIT_ANALYZE)\n/* Opcode: LoadAnalysis P1 * * * *\n**\n** Read the sqlite_stat1 table for database P1 and load the content\n** of that table into the internal index hash table.  This will cause\n** the analysis to be used when preparing all subsequent queries.\n*/\ncase OP_LoadAnalysis: {\n  assert( pOp->p1>=0 && pOp->p1<db->nDb );\n  rc = sqlite3AnalysisLoad(db, pOp->p1);\n  if( rc ) goto abort_due_to_error;\n  break;  \n}\n#endif /* !defined(SQLITE_OMIT_ANALYZE) */\n\n/* Opcode: DropTable P1 * * P4 *\n**\n** Remove the internal (in-memory) data structures that describe\n** the table named P4 in database P1.  This is called after a table\n** is dropped from disk (using the Destroy opcode) in order to keep \n** the internal representation of the\n** schema consistent with what is on disk.\n*/\ncase OP_DropTable: {\n  sqlite3UnlinkAndDeleteTable(db, pOp->p1, pOp->p4.z);\n  break;\n}\n\n/* Opcode: DropIndex P1 * * P4 *\n**\n** Remove the internal (in-memory) data structures that describe\n** the index named P4 in database P1.  This is called after an index\n** is dropped from disk (using the Destroy opcode)\n** in order to keep the internal representation of the\n** schema consistent with what is on disk.\n*/\ncase OP_DropIndex: {\n  sqlite3UnlinkAndDeleteIndex(db, pOp->p1, pOp->p4.z);\n  break;\n}\n\n/* Opcode: DropTrigger P1 * * P4 *\n**\n** Remove the internal (in-memory) data structures that describe\n** the trigger named P4 in database P1.  This is called after a trigger\n** is dropped from disk (using the Destroy opcode) in order to keep \n** the internal representation of the\n** schema consistent with what is on disk.\n*/\ncase OP_DropTrigger: {\n  sqlite3UnlinkAndDeleteTrigger(db, pOp->p1, pOp->p4.z);\n  break;\n}\n\n\n#ifndef SQLITE_OMIT_INTEGRITY_CHECK\n/* Opcode: IntegrityCk P1 P2 P3 P4 P5\n**\n** Do an analysis of the currently open database.  Store in\n** register P1 the text of an error message describing any problems.\n** If no problems are found, store a NULL in register P1.\n**\n** The register P3 contains one less than the maximum number of allowed errors.\n** At most reg(P3) errors will be reported.\n** In other words, the analysis stops as soon as reg(P1) errors are \n** seen.  Reg(P1) is updated with the number of errors remaining.\n**\n** The root page numbers of all tables in the database are integers\n** stored in P4_INTARRAY argument.\n**\n** If P5 is not zero, the check is done on the auxiliary database\n** file, not the main database file.\n**\n** This opcode is used to implement the integrity_check pragma.\n*/\ncase OP_IntegrityCk: {\n  int nRoot;      /* Number of tables to check.  (Number of root pages.) */\n  int *aRoot;     /* Array of rootpage numbers for tables to be checked */\n  int nErr;       /* Number of errors reported */\n  char *z;        /* Text of the error report */\n  Mem *pnErr;     /* Register keeping track of errors remaining */\n\n  assert( p->bIsReader );\n  nRoot = pOp->p2;\n  aRoot = pOp->p4.ai;\n  assert( nRoot>0 );\n  assert( aRoot[0]==nRoot );\n  assert( pOp->p3>0 && pOp->p3<=(p->nMem+1 - p->nCursor) );\n  pnErr = &aMem[pOp->p3];\n  assert( (pnErr->flags & MEM_Int)!=0 );\n  assert( (pnErr->flags & (MEM_Str|MEM_Blob))==0 );\n  pIn1 = &aMem[pOp->p1];\n  assert( pOp->p5<db->nDb );\n  assert( DbMaskTest(p->btreeMask, pOp->p5) );\n  z = sqlite3BtreeIntegrityCheck(db->aDb[pOp->p5].pBt, &aRoot[1], nRoot,\n                                 (int)pnErr->u.i+1, &nErr);\n  sqlite3VdbeMemSetNull(pIn1);\n  if( nErr==0 ){\n    assert( z==0 );\n  }else if( z==0 ){\n    goto no_mem;\n  }else{\n    pnErr->u.i -= nErr-1;\n    sqlite3VdbeMemSetStr(pIn1, z, -1, SQLITE_UTF8, sqlite3_free);\n  }\n  UPDATE_MAX_BLOBSIZE(pIn1);\n  sqlite3VdbeChangeEncoding(pIn1, encoding);\n  break;\n}\n#endif /* SQLITE_OMIT_INTEGRITY_CHECK */\n\n/* Opcode: RowSetAdd P1 P2 * * *\n** Synopsis: rowset(P1)=r[P2]\n**\n** Insert the integer value held by register P2 into a RowSet object\n** held in register P1.\n**\n** An assertion fails if P2 is not an integer.\n*/\ncase OP_RowSetAdd: {       /* in1, in2 */\n  pIn1 = &aMem[pOp->p1];\n  pIn2 = &aMem[pOp->p2];\n  assert( (pIn2->flags & MEM_Int)!=0 );\n  if( (pIn1->flags & MEM_RowSet)==0 ){\n    sqlite3VdbeMemSetRowSet(pIn1);\n    if( (pIn1->flags & MEM_RowSet)==0 ) goto no_mem;\n  }\n  sqlite3RowSetInsert(pIn1->u.pRowSet, pIn2->u.i);\n  break;\n}\n\n/* Opcode: RowSetRead P1 P2 P3 * *\n** Synopsis: r[P3]=rowset(P1)\n**\n** Extract the smallest value from the RowSet object in P1\n** and put that value into register P3.\n** Or, if RowSet object P1 is initially empty, leave P3\n** unchanged and jump to instruction P2.\n*/\ncase OP_RowSetRead: {       /* jump, in1, out3 */\n  i64 val;\n\n  pIn1 = &aMem[pOp->p1];\n  if( (pIn1->flags & MEM_RowSet)==0 \n   || sqlite3RowSetNext(pIn1->u.pRowSet, &val)==0\n  ){\n    /* The boolean index is empty */\n    sqlite3VdbeMemSetNull(pIn1);\n    VdbeBranchTaken(1,2);\n    goto jump_to_p2_and_check_for_interrupt;\n  }else{\n    /* A value was pulled from the index */\n    VdbeBranchTaken(0,2);\n    sqlite3VdbeMemSetInt64(&aMem[pOp->p3], val);\n  }\n  goto check_for_interrupt;\n}\n\n/* Opcode: RowSetTest P1 P2 P3 P4\n** Synopsis: if r[P3] in rowset(P1) goto P2\n**\n** Register P3 is assumed to hold a 64-bit integer value. If register P1\n** contains a RowSet object and that RowSet object contains\n** the value held in P3, jump to register P2. Otherwise, insert the\n** integer in P3 into the RowSet and continue on to the\n** next opcode.\n**\n** The RowSet object is optimized for the case where sets of integers\n** are inserted in distinct phases, which each set contains no duplicates.\n** Each set is identified by a unique P4 value. The first set\n** must have P4==0, the final set must have P4==-1, and for all other sets\n** must have P4>0.\n**\n** This allows optimizations: (a) when P4==0 there is no need to test\n** the RowSet object for P3, as it is guaranteed not to contain it,\n** (b) when P4==-1 there is no need to insert the value, as it will\n** never be tested for, and (c) when a value that is part of set X is\n** inserted, there is no need to search to see if the same value was\n** previously inserted as part of set X (only if it was previously\n** inserted as part of some other set).\n*/\ncase OP_RowSetTest: {                     /* jump, in1, in3 */\n  int iSet;\n  int exists;\n\n  pIn1 = &aMem[pOp->p1];\n  pIn3 = &aMem[pOp->p3];\n  iSet = pOp->p4.i;\n  assert( pIn3->flags&MEM_Int );\n\n  /* If there is anything other than a rowset object in memory cell P1,\n  ** delete it now and initialize P1 with an empty rowset\n  */\n  if( (pIn1->flags & MEM_RowSet)==0 ){\n    sqlite3VdbeMemSetRowSet(pIn1);\n    if( (pIn1->flags & MEM_RowSet)==0 ) goto no_mem;\n  }\n\n  assert( pOp->p4type==P4_INT32 );\n  assert( iSet==-1 || iSet>=0 );\n  if( iSet ){\n    exists = sqlite3RowSetTest(pIn1->u.pRowSet, iSet, pIn3->u.i);\n    VdbeBranchTaken(exists!=0,2);\n    if( exists ) goto jump_to_p2;\n  }\n  if( iSet>=0 ){\n    sqlite3RowSetInsert(pIn1->u.pRowSet, pIn3->u.i);\n  }\n  break;\n}\n\n\n#ifndef SQLITE_OMIT_TRIGGER\n\n/* Opcode: Program P1 P2 P3 P4 P5\n**\n** Execute the trigger program passed as P4 (type P4_SUBPROGRAM). \n**\n** P1 contains the address of the memory cell that contains the first memory \n** cell in an array of values used as arguments to the sub-program. P2 \n** contains the address to jump to if the sub-program throws an IGNORE \n** exception using the RAISE() function. Register P3 contains the address \n** of a memory cell in this (the parent) VM that is used to allocate the \n** memory required by the sub-vdbe at runtime.\n**\n** P4 is a pointer to the VM containing the trigger program.\n**\n** If P5 is non-zero, then recursive program invocation is enabled.\n*/\ncase OP_Program: {        /* jump */\n  int nMem;               /* Number of memory registers for sub-program */\n  int nByte;              /* Bytes of runtime space required for sub-program */\n  Mem *pRt;               /* Register to allocate runtime space */\n  Mem *pMem;              /* Used to iterate through memory cells */\n  Mem *pEnd;              /* Last memory cell in new array */\n  VdbeFrame *pFrame;      /* New vdbe frame to execute in */\n  SubProgram *pProgram;   /* Sub-program to execute */\n  void *t;                /* Token identifying trigger */\n\n  pProgram = pOp->p4.pProgram;\n  pRt = &aMem[pOp->p3];\n  assert( pProgram->nOp>0 );\n  \n  /* If the p5 flag is clear, then recursive invocation of triggers is \n  ** disabled for backwards compatibility (p5 is set if this sub-program\n  ** is really a trigger, not a foreign key action, and the flag set\n  ** and cleared by the \"PRAGMA recursive_triggers\" command is clear).\n  ** \n  ** It is recursive invocation of triggers, at the SQL level, that is \n  ** disabled. In some cases a single trigger may generate more than one \n  ** SubProgram (if the trigger may be executed with more than one different \n  ** ON CONFLICT algorithm). SubProgram structures associated with a\n  ** single trigger all have the same value for the SubProgram.token \n  ** variable.  */\n  if( pOp->p5 ){\n    t = pProgram->token;\n    for(pFrame=p->pFrame; pFrame && pFrame->token!=t; pFrame=pFrame->pParent);\n    if( pFrame ) break;\n  }\n\n  if( p->nFrame>=db->aLimit[SQLITE_LIMIT_TRIGGER_DEPTH] ){\n    rc = SQLITE_ERROR;\n    sqlite3VdbeError(p, \"too many levels of trigger recursion\");\n    goto abort_due_to_error;\n  }\n\n  /* Register pRt is used to store the memory required to save the state\n  ** of the current program, and the memory required at runtime to execute\n  ** the trigger program. If this trigger has been fired before, then pRt \n  ** is already allocated. Otherwise, it must be initialized.  */\n  if( (pRt->flags&MEM_Frame)==0 ){\n    /* SubProgram.nMem is set to the number of memory cells used by the \n    ** program stored in SubProgram.aOp. As well as these, one memory\n    ** cell is required for each cursor used by the program. Set local\n    ** variable nMem (and later, VdbeFrame.nChildMem) to this value.\n    */\n    nMem = pProgram->nMem + pProgram->nCsr;\n    assert( nMem>0 );\n    if( pProgram->nCsr==0 ) nMem++;\n    nByte = ROUND8(sizeof(VdbeFrame))\n              + nMem * sizeof(Mem)\n              + pProgram->nCsr * sizeof(VdbeCursor*)\n              + (pProgram->nOp + 7)/8;\n    pFrame = sqlite3DbMallocZero(db, nByte);\n    if( !pFrame ){\n      goto no_mem;\n    }\n    sqlite3VdbeMemRelease(pRt);\n    pRt->flags = MEM_Frame;\n    pRt->u.pFrame = pFrame;\n\n    pFrame->v = p;\n    pFrame->nChildMem = nMem;\n    pFrame->nChildCsr = pProgram->nCsr;\n    pFrame->pc = (int)(pOp - aOp);\n    pFrame->aMem = p->aMem;\n    pFrame->nMem = p->nMem;\n    pFrame->apCsr = p->apCsr;\n    pFrame->nCursor = p->nCursor;\n    pFrame->aOp = p->aOp;\n    pFrame->nOp = p->nOp;\n    pFrame->token = pProgram->token;\n#ifdef SQLITE_ENABLE_STMT_SCANSTATUS\n    pFrame->anExec = p->anExec;\n#endif\n\n    pEnd = &VdbeFrameMem(pFrame)[pFrame->nChildMem];\n    for(pMem=VdbeFrameMem(pFrame); pMem!=pEnd; pMem++){\n      pMem->flags = MEM_Undefined;\n      pMem->db = db;\n    }\n  }else{\n    pFrame = pRt->u.pFrame;\n    assert( pProgram->nMem+pProgram->nCsr==pFrame->nChildMem \n        || (pProgram->nCsr==0 && pProgram->nMem+1==pFrame->nChildMem) );\n    assert( pProgram->nCsr==pFrame->nChildCsr );\n    assert( (int)(pOp - aOp)==pFrame->pc );\n  }\n\n  p->nFrame++;\n  pFrame->pParent = p->pFrame;\n  pFrame->lastRowid = db->lastRowid;\n  pFrame->nChange = p->nChange;\n  pFrame->nDbChange = p->db->nChange;\n  assert( pFrame->pAuxData==0 );\n  pFrame->pAuxData = p->pAuxData;\n  p->pAuxData = 0;\n  p->nChange = 0;\n  p->pFrame = pFrame;\n  p->aMem = aMem = VdbeFrameMem(pFrame);\n  p->nMem = pFrame->nChildMem;\n  p->nCursor = (u16)pFrame->nChildCsr;\n  p->apCsr = (VdbeCursor **)&aMem[p->nMem];\n  pFrame->aOnce = (u8*)&p->apCsr[pProgram->nCsr];\n  memset(pFrame->aOnce, 0, (pProgram->nOp + 7)/8);\n  p->aOp = aOp = pProgram->aOp;\n  p->nOp = pProgram->nOp;\n#ifdef SQLITE_ENABLE_STMT_SCANSTATUS\n  p->anExec = 0;\n#endif\n  pOp = &aOp[-1];\n\n  break;\n}\n\n/* Opcode: Param P1 P2 * * *\n**\n** This opcode is only ever present in sub-programs called via the \n** OP_Program instruction. Copy a value currently stored in a memory \n** cell of the calling (parent) frame to cell P2 in the current frames \n** address space. This is used by trigger programs to access the new.* \n** and old.* values.\n**\n** The address of the cell in the parent frame is determined by adding\n** the value of the P1 argument to the value of the P1 argument to the\n** calling OP_Program instruction.\n*/\ncase OP_Param: {           /* out2 */\n  VdbeFrame *pFrame;\n  Mem *pIn;\n  pOut = out2Prerelease(p, pOp);\n  pFrame = p->pFrame;\n  pIn = &pFrame->aMem[pOp->p1 + pFrame->aOp[pFrame->pc].p1];   \n  sqlite3VdbeMemShallowCopy(pOut, pIn, MEM_Ephem);\n  break;\n}\n\n#endif /* #ifndef SQLITE_OMIT_TRIGGER */\n\n#ifndef SQLITE_OMIT_FOREIGN_KEY\n/* Opcode: FkCounter P1 P2 * * *\n** Synopsis: fkctr[P1]+=P2\n**\n** Increment a \"constraint counter\" by P2 (P2 may be negative or positive).\n** If P1 is non-zero, the database constraint counter is incremented \n** (deferred foreign key constraints). Otherwise, if P1 is zero, the \n** statement counter is incremented (immediate foreign key constraints).\n*/\ncase OP_FkCounter: {\n  if( db->flags & SQLITE_DeferFKs ){\n    db->nDeferredImmCons += pOp->p2;\n  }else if( pOp->p1 ){\n    db->nDeferredCons += pOp->p2;\n  }else{\n    p->nFkConstraint += pOp->p2;\n  }\n  break;\n}\n\n/* Opcode: FkIfZero P1 P2 * * *\n** Synopsis: if fkctr[P1]==0 goto P2\n**\n** This opcode tests if a foreign key constraint-counter is currently zero.\n** If so, jump to instruction P2. Otherwise, fall through to the next \n** instruction.\n**\n** If P1 is non-zero, then the jump is taken if the database constraint-counter\n** is zero (the one that counts deferred constraint violations). If P1 is\n** zero, the jump is taken if the statement constraint-counter is zero\n** (immediate foreign key constraint violations).\n*/\ncase OP_FkIfZero: {         /* jump */\n  if( pOp->p1 ){\n    VdbeBranchTaken(db->nDeferredCons==0 && db->nDeferredImmCons==0, 2);\n    if( db->nDeferredCons==0 && db->nDeferredImmCons==0 ) goto jump_to_p2;\n  }else{\n    VdbeBranchTaken(p->nFkConstraint==0 && db->nDeferredImmCons==0, 2);\n    if( p->nFkConstraint==0 && db->nDeferredImmCons==0 ) goto jump_to_p2;\n  }\n  break;\n}\n#endif /* #ifndef SQLITE_OMIT_FOREIGN_KEY */\n\n#ifndef SQLITE_OMIT_AUTOINCREMENT\n/* Opcode: MemMax P1 P2 * * *\n** Synopsis: r[P1]=max(r[P1],r[P2])\n**\n** P1 is a register in the root frame of this VM (the root frame is\n** different from the current frame if this instruction is being executed\n** within a sub-program). Set the value of register P1 to the maximum of \n** its current value and the value in register P2.\n**\n** This instruction throws an error if the memory cell is not initially\n** an integer.\n*/\ncase OP_MemMax: {        /* in2 */\n  VdbeFrame *pFrame;\n  if( p->pFrame ){\n    for(pFrame=p->pFrame; pFrame->pParent; pFrame=pFrame->pParent);\n    pIn1 = &pFrame->aMem[pOp->p1];\n  }else{\n    pIn1 = &aMem[pOp->p1];\n  }\n  assert( memIsValid(pIn1) );\n  sqlite3VdbeMemIntegerify(pIn1);\n  pIn2 = &aMem[pOp->p2];\n  sqlite3VdbeMemIntegerify(pIn2);\n  if( pIn1->u.i<pIn2->u.i){\n    pIn1->u.i = pIn2->u.i;\n  }\n  break;\n}\n#endif /* SQLITE_OMIT_AUTOINCREMENT */\n\n/* Opcode: IfPos P1 P2 P3 * *\n** Synopsis: if r[P1]>0 then r[P1]-=P3, goto P2\n**\n** Register P1 must contain an integer.\n** If the value of register P1 is 1 or greater, subtract P3 from the\n** value in P1 and jump to P2.\n**\n** If the initial value of register P1 is less than 1, then the\n** value is unchanged and control passes through to the next instruction.\n*/\ncase OP_IfPos: {        /* jump, in1 */\n  pIn1 = &aMem[pOp->p1];\n  assert( pIn1->flags&MEM_Int );\n  VdbeBranchTaken( pIn1->u.i>0, 2);\n  if( pIn1->u.i>0 ){\n    pIn1->u.i -= pOp->p3;\n    goto jump_to_p2;\n  }\n  break;\n}\n\n/* Opcode: OffsetLimit P1 P2 P3 * *\n** Synopsis: if r[P1]>0 then r[P2]=r[P1]+max(0,r[P3]) else r[P2]=(-1)\n**\n** This opcode performs a commonly used computation associated with\n** LIMIT and OFFSET process.  r[P1] holds the limit counter.  r[P3]\n** holds the offset counter.  The opcode computes the combined value\n** of the LIMIT and OFFSET and stores that value in r[P2].  The r[P2]\n** value computed is the total number of rows that will need to be\n** visited in order to complete the query.\n**\n** If r[P3] is zero or negative, that means there is no OFFSET\n** and r[P2] is set to be the value of the LIMIT, r[P1].\n**\n** if r[P1] is zero or negative, that means there is no LIMIT\n** and r[P2] is set to -1. \n**\n** Otherwise, r[P2] is set to the sum of r[P1] and r[P3].\n*/\ncase OP_OffsetLimit: {    /* in1, out2, in3 */\n  i64 x;\n  pIn1 = &aMem[pOp->p1];\n  pIn3 = &aMem[pOp->p3];\n  pOut = out2Prerelease(p, pOp);\n  assert( pIn1->flags & MEM_Int );\n  assert( pIn3->flags & MEM_Int );\n  x = pIn1->u.i;\n  if( x<=0 || sqlite3AddInt64(&x, pIn3->u.i>0?pIn3->u.i:0) ){\n    /* If the LIMIT is less than or equal to zero, loop forever.  This\n    ** is documented.  But also, if the LIMIT+OFFSET exceeds 2^63 then\n    ** also loop forever.  This is undocumented.  In fact, one could argue\n    ** that the loop should terminate.  But assuming 1 billion iterations\n    ** per second (far exceeding the capabilities of any current hardware)\n    ** it would take nearly 300 years to actually reach the limit.  So\n    ** looping forever is a reasonable approximation. */\n    pOut->u.i = -1;\n  }else{\n    pOut->u.i = x;\n  }\n  break;\n}\n\n/* Opcode: IfNotZero P1 P2 * * *\n** Synopsis: if r[P1]!=0 then r[P1]--, goto P2\n**\n** Register P1 must contain an integer.  If the content of register P1 is\n** initially greater than zero, then decrement the value in register P1.\n** If it is non-zero (negative or positive) and then also jump to P2.  \n** If register P1 is initially zero, leave it unchanged and fall through.\n*/\ncase OP_IfNotZero: {        /* jump, in1 */\n  pIn1 = &aMem[pOp->p1];\n  assert( pIn1->flags&MEM_Int );\n  VdbeBranchTaken(pIn1->u.i<0, 2);\n  if( pIn1->u.i ){\n     if( pIn1->u.i>0 ) pIn1->u.i--;\n     goto jump_to_p2;\n  }\n  break;\n}\n\n/* Opcode: DecrJumpZero P1 P2 * * *\n** Synopsis: if (--r[P1])==0 goto P2\n**\n** Register P1 must hold an integer.  Decrement the value in P1\n** and jump to P2 if the new value is exactly zero.\n*/\ncase OP_DecrJumpZero: {      /* jump, in1 */\n  pIn1 = &aMem[pOp->p1];\n  assert( pIn1->flags&MEM_Int );\n  if( pIn1->u.i>SMALLEST_INT64 ) pIn1->u.i--;\n  VdbeBranchTaken(pIn1->u.i==0, 2);\n  if( pIn1->u.i==0 ) goto jump_to_p2;\n  break;\n}\n\n\n/* Opcode: AggStep0 * P2 P3 P4 P5\n** Synopsis: accum=r[P3] step(r[P2@P5])\n**\n** Execute the step function for an aggregate.  The\n** function has P5 arguments.   P4 is a pointer to the FuncDef\n** structure that specifies the function.  Register P3 is the\n** accumulator.\n**\n** The P5 arguments are taken from register P2 and its\n** successors.\n*/\n/* Opcode: AggStep * P2 P3 P4 P5\n** Synopsis: accum=r[P3] step(r[P2@P5])\n**\n** Execute the step function for an aggregate.  The\n** function has P5 arguments.   P4 is a pointer to an sqlite3_context\n** object that is used to run the function.  Register P3 is\n** as the accumulator.\n**\n** The P5 arguments are taken from register P2 and its\n** successors.\n**\n** This opcode is initially coded as OP_AggStep0.  On first evaluation,\n** the FuncDef stored in P4 is converted into an sqlite3_context and\n** the opcode is changed.  In this way, the initialization of the\n** sqlite3_context only happens once, instead of on each call to the\n** step function.\n*/\ncase OP_AggStep0: {\n  int n;\n  sqlite3_context *pCtx;\n\n  assert( pOp->p4type==P4_FUNCDEF );\n  n = pOp->p5;\n  assert( pOp->p3>0 && pOp->p3<=(p->nMem+1 - p->nCursor) );\n  assert( n==0 || (pOp->p2>0 && pOp->p2+n<=(p->nMem+1 - p->nCursor)+1) );\n  assert( pOp->p3<pOp->p2 || pOp->p3>=pOp->p2+n );\n  pCtx = sqlite3DbMallocRawNN(db, n*sizeof(sqlite3_value*) +\n               (sizeof(pCtx[0]) + sizeof(Mem) - sizeof(sqlite3_value*)));\n  if( pCtx==0 ) goto no_mem;\n  pCtx->pMem = 0;\n  pCtx->pOut = (Mem*)&(pCtx->argv[n]);\n  sqlite3VdbeMemInit(pCtx->pOut, db, MEM_Null);\n  pCtx->pFunc = pOp->p4.pFunc;\n  pCtx->iOp = (int)(pOp - aOp);\n  pCtx->pVdbe = p;\n  pCtx->skipFlag = 0;\n  pCtx->isError = 0;\n  pCtx->argc = n;\n  pOp->p4type = P4_FUNCCTX;\n  pOp->p4.pCtx = pCtx;\n  pOp->opcode = OP_AggStep;\n  /* Fall through into OP_AggStep */\n}\ncase OP_AggStep: {\n  int i;\n  sqlite3_context *pCtx;\n  Mem *pMem;\n\n  assert( pOp->p4type==P4_FUNCCTX );\n  pCtx = pOp->p4.pCtx;\n  pMem = &aMem[pOp->p3];\n\n  /* If this function is inside of a trigger, the register array in aMem[]\n  ** might change from one evaluation to the next.  The next block of code\n  ** checks to see if the register array has changed, and if so it\n  ** reinitializes the relavant parts of the sqlite3_context object */\n  if( pCtx->pMem != pMem ){\n    pCtx->pMem = pMem;\n    for(i=pCtx->argc-1; i>=0; i--) pCtx->argv[i] = &aMem[pOp->p2+i];\n  }\n\n#ifdef SQLITE_DEBUG\n  for(i=0; i<pCtx->argc; i++){\n    assert( memIsValid(pCtx->argv[i]) );\n    REGISTER_TRACE(pOp->p2+i, pCtx->argv[i]);\n  }\n#endif\n\n  pMem->n++;\n  assert( pCtx->pOut->flags==MEM_Null );\n  assert( pCtx->isError==0 );\n  assert( pCtx->skipFlag==0 );\n  (pCtx->pFunc->xSFunc)(pCtx,pCtx->argc,pCtx->argv); /* IMP: R-24505-23230 */\n  if( pCtx->isError ){\n    if( pCtx->isError>0 ){\n      sqlite3VdbeError(p, \"%s\", sqlite3_value_text(pCtx->pOut));\n      rc = pCtx->isError;\n    }\n    if( pCtx->skipFlag ){\n      assert( pOp[-1].opcode==OP_CollSeq );\n      i = pOp[-1].p1;\n      if( i ) sqlite3VdbeMemSetInt64(&aMem[i], 1);\n      pCtx->skipFlag = 0;\n    }\n    sqlite3VdbeMemRelease(pCtx->pOut);\n    pCtx->pOut->flags = MEM_Null;\n    pCtx->isError = 0;\n    if( rc ) goto abort_due_to_error;\n  }\n  assert( pCtx->pOut->flags==MEM_Null );\n  assert( pCtx->skipFlag==0 );\n  break;\n}\n\n/* Opcode: AggFinal P1 P2 * P4 *\n** Synopsis: accum=r[P1] N=P2\n**\n** Execute the finalizer function for an aggregate.  P1 is\n** the memory location that is the accumulator for the aggregate.\n**\n** P2 is the number of arguments that the step function takes and\n** P4 is a pointer to the FuncDef for this function.  The P2\n** argument is not used by this opcode.  It is only there to disambiguate\n** functions that can take varying numbers of arguments.  The\n** P4 argument is only needed for the degenerate case where\n** the step function was not previously called.\n*/\ncase OP_AggFinal: {\n  Mem *pMem;\n  assert( pOp->p1>0 && pOp->p1<=(p->nMem+1 - p->nCursor) );\n  pMem = &aMem[pOp->p1];\n  assert( (pMem->flags & ~(MEM_Null|MEM_Agg))==0 );\n  rc = sqlite3VdbeMemFinalize(pMem, pOp->p4.pFunc);\n  if( rc ){\n    sqlite3VdbeError(p, \"%s\", sqlite3_value_text(pMem));\n    goto abort_due_to_error;\n  }\n  sqlite3VdbeChangeEncoding(pMem, encoding);\n  UPDATE_MAX_BLOBSIZE(pMem);\n  if( sqlite3VdbeMemTooBig(pMem) ){\n    goto too_big;\n  }\n  break;\n}\n\n#ifndef SQLITE_OMIT_WAL\n/* Opcode: Checkpoint P1 P2 P3 * *\n**\n** Checkpoint database P1. This is a no-op if P1 is not currently in\n** WAL mode. Parameter P2 is one of SQLITE_CHECKPOINT_PASSIVE, FULL,\n** RESTART, or TRUNCATE.  Write 1 or 0 into mem[P3] if the checkpoint returns\n** SQLITE_BUSY or not, respectively.  Write the number of pages in the\n** WAL after the checkpoint into mem[P3+1] and the number of pages\n** in the WAL that have been checkpointed after the checkpoint\n** completes into mem[P3+2].  However on an error, mem[P3+1] and\n** mem[P3+2] are initialized to -1.\n*/\ncase OP_Checkpoint: {\n  int i;                          /* Loop counter */\n  int aRes[3];                    /* Results */\n  Mem *pMem;                      /* Write results here */\n\n  assert( p->readOnly==0 );\n  aRes[0] = 0;\n  aRes[1] = aRes[2] = -1;\n  assert( pOp->p2==SQLITE_CHECKPOINT_PASSIVE\n       || pOp->p2==SQLITE_CHECKPOINT_FULL\n       || pOp->p2==SQLITE_CHECKPOINT_RESTART\n       || pOp->p2==SQLITE_CHECKPOINT_TRUNCATE\n  );\n  rc = sqlite3Checkpoint(db, pOp->p1, pOp->p2, &aRes[1], &aRes[2]);\n  if( rc ){\n    if( rc!=SQLITE_BUSY ) goto abort_due_to_error;\n    rc = SQLITE_OK;\n    aRes[0] = 1;\n  }\n  for(i=0, pMem = &aMem[pOp->p3]; i<3; i++, pMem++){\n    sqlite3VdbeMemSetInt64(pMem, (i64)aRes[i]);\n  }    \n  break;\n};  \n#endif\n\n#ifndef SQLITE_OMIT_PRAGMA\n/* Opcode: JournalMode P1 P2 P3 * *\n**\n** Change the journal mode of database P1 to P3. P3 must be one of the\n** PAGER_JOURNALMODE_XXX values. If changing between the various rollback\n** modes (delete, truncate, persist, off and memory), this is a simple\n** operation. No IO is required.\n**\n** If changing into or out of WAL mode the procedure is more complicated.\n**\n** Write a string containing the final journal-mode to register P2.\n*/\ncase OP_JournalMode: {    /* out2 */\n  Btree *pBt;                     /* Btree to change journal mode of */\n  Pager *pPager;                  /* Pager associated with pBt */\n  int eNew;                       /* New journal mode */\n  int eOld;                       /* The old journal mode */\n#ifndef SQLITE_OMIT_WAL\n  const char *zFilename;          /* Name of database file for pPager */\n#endif\n\n  pOut = out2Prerelease(p, pOp);\n  eNew = pOp->p3;\n  assert( eNew==PAGER_JOURNALMODE_DELETE \n       || eNew==PAGER_JOURNALMODE_TRUNCATE \n       || eNew==PAGER_JOURNALMODE_PERSIST \n       || eNew==PAGER_JOURNALMODE_OFF\n       || eNew==PAGER_JOURNALMODE_MEMORY\n       || eNew==PAGER_JOURNALMODE_WAL\n       || eNew==PAGER_JOURNALMODE_QUERY\n  );\n  assert( pOp->p1>=0 && pOp->p1<db->nDb );\n  assert( p->readOnly==0 );\n\n  pBt = db->aDb[pOp->p1].pBt;\n  pPager = sqlite3BtreePager(pBt);\n  eOld = sqlite3PagerGetJournalMode(pPager);\n  if( eNew==PAGER_JOURNALMODE_QUERY ) eNew = eOld;\n  if( !sqlite3PagerOkToChangeJournalMode(pPager) ) eNew = eOld;\n\n#ifndef SQLITE_OMIT_WAL\n  zFilename = sqlite3PagerFilename(pPager, 1);\n\n  /* Do not allow a transition to journal_mode=WAL for a database\n  ** in temporary storage or if the VFS does not support shared memory \n  */\n  if( eNew==PAGER_JOURNALMODE_WAL\n   && (sqlite3Strlen30(zFilename)==0           /* Temp file */\n       || !sqlite3PagerWalSupported(pPager))   /* No shared-memory support */\n  ){\n    eNew = eOld;\n  }\n\n  if( (eNew!=eOld)\n   && (eOld==PAGER_JOURNALMODE_WAL || eNew==PAGER_JOURNALMODE_WAL)\n  ){\n    if( !db->autoCommit || db->nVdbeRead>1 ){\n      rc = SQLITE_ERROR;\n      sqlite3VdbeError(p,\n          \"cannot change %s wal mode from within a transaction\",\n          (eNew==PAGER_JOURNALMODE_WAL ? \"into\" : \"out of\")\n      );\n      goto abort_due_to_error;\n    }else{\n \n      if( eOld==PAGER_JOURNALMODE_WAL ){\n        /* If leaving WAL mode, close the log file. If successful, the call\n        ** to PagerCloseWal() checkpoints and deletes the write-ahead-log \n        ** file. An EXCLUSIVE lock may still be held on the database file \n        ** after a successful return. \n        */\n        rc = sqlite3PagerCloseWal(pPager, db);\n        if( rc==SQLITE_OK ){\n          sqlite3PagerSetJournalMode(pPager, eNew);\n        }\n      }else if( eOld==PAGER_JOURNALMODE_MEMORY ){\n        /* Cannot transition directly from MEMORY to WAL.  Use mode OFF\n        ** as an intermediate */\n        sqlite3PagerSetJournalMode(pPager, PAGER_JOURNALMODE_OFF);\n      }\n  \n      /* Open a transaction on the database file. Regardless of the journal\n      ** mode, this transaction always uses a rollback journal.\n      */\n      assert( sqlite3BtreeIsInTrans(pBt)==0 );\n      if( rc==SQLITE_OK ){\n        rc = sqlite3BtreeSetVersion(pBt, (eNew==PAGER_JOURNALMODE_WAL ? 2 : 1));\n      }\n    }\n  }\n#endif /* ifndef SQLITE_OMIT_WAL */\n\n  if( rc ) eNew = eOld;\n  eNew = sqlite3PagerSetJournalMode(pPager, eNew);\n\n  pOut->flags = MEM_Str|MEM_Static|MEM_Term;\n  pOut->z = (char *)sqlite3JournalModename(eNew);\n  pOut->n = sqlite3Strlen30(pOut->z);\n  pOut->enc = SQLITE_UTF8;\n  sqlite3VdbeChangeEncoding(pOut, encoding);\n  if( rc ) goto abort_due_to_error;\n  break;\n};\n#endif /* SQLITE_OMIT_PRAGMA */\n\n#if !defined(SQLITE_OMIT_VACUUM) && !defined(SQLITE_OMIT_ATTACH)\n/* Opcode: Vacuum P1 * * * *\n**\n** Vacuum the entire database P1.  P1 is 0 for \"main\", and 2 or more\n** for an attached database.  The \"temp\" database may not be vacuumed.\n*/\ncase OP_Vacuum: {\n  assert( p->readOnly==0 );\n  rc = sqlite3RunVacuum(&p->zErrMsg, db, pOp->p1);\n  if( rc ) goto abort_due_to_error;\n  break;\n}\n#endif\n\n#if !defined(SQLITE_OMIT_AUTOVACUUM)\n/* Opcode: IncrVacuum P1 P2 * * *\n**\n** Perform a single step of the incremental vacuum procedure on\n** the P1 database. If the vacuum has finished, jump to instruction\n** P2. Otherwise, fall through to the next instruction.\n*/\ncase OP_IncrVacuum: {        /* jump */\n  Btree *pBt;\n\n  assert( pOp->p1>=0 && pOp->p1<db->nDb );\n  assert( DbMaskTest(p->btreeMask, pOp->p1) );\n  assert( p->readOnly==0 );\n  pBt = db->aDb[pOp->p1].pBt;\n  rc = sqlite3BtreeIncrVacuum(pBt);\n  VdbeBranchTaken(rc==SQLITE_DONE,2);\n  if( rc ){\n    if( rc!=SQLITE_DONE ) goto abort_due_to_error;\n    rc = SQLITE_OK;\n    goto jump_to_p2;\n  }\n  break;\n}\n#endif\n\n/* Opcode: Expire P1 * * * *\n**\n** Cause precompiled statements to expire.  When an expired statement\n** is executed using sqlite3_step() it will either automatically\n** reprepare itself (if it was originally created using sqlite3_prepare_v2())\n** or it will fail with SQLITE_SCHEMA.\n** \n** If P1 is 0, then all SQL statements become expired. If P1 is non-zero,\n** then only the currently executing statement is expired.\n*/\ncase OP_Expire: {\n  if( !pOp->p1 ){\n    sqlite3ExpirePreparedStatements(db);\n  }else{\n    p->expired = 1;\n  }\n  break;\n}\n\n#ifndef SQLITE_OMIT_SHARED_CACHE\n/* Opcode: TableLock P1 P2 P3 P4 *\n** Synopsis: iDb=P1 root=P2 write=P3\n**\n** Obtain a lock on a particular table. This instruction is only used when\n** the shared-cache feature is enabled. \n**\n** P1 is the index of the database in sqlite3.aDb[] of the database\n** on which the lock is acquired.  A readlock is obtained if P3==0 or\n** a write lock if P3==1.\n**\n** P2 contains the root-page of the table to lock.\n**\n** P4 contains a pointer to the name of the table being locked. This is only\n** used to generate an error message if the lock cannot be obtained.\n*/\ncase OP_TableLock: {\n  u8 isWriteLock = (u8)pOp->p3;\n  if( isWriteLock || 0==(db->flags&SQLITE_ReadUncommit) ){\n    int p1 = pOp->p1; \n    assert( p1>=0 && p1<db->nDb );\n    assert( DbMaskTest(p->btreeMask, p1) );\n    assert( isWriteLock==0 || isWriteLock==1 );\n    rc = sqlite3BtreeLockTable(db->aDb[p1].pBt, pOp->p2, isWriteLock);\n    if( rc ){\n      if( (rc&0xFF)==SQLITE_LOCKED ){\n        const char *z = pOp->p4.z;\n        sqlite3VdbeError(p, \"database table is locked: %s\", z);\n      }\n      goto abort_due_to_error;\n    }\n  }\n  break;\n}\n#endif /* SQLITE_OMIT_SHARED_CACHE */\n\n#ifndef SQLITE_OMIT_VIRTUALTABLE\n/* Opcode: VBegin * * * P4 *\n**\n** P4 may be a pointer to an sqlite3_vtab structure. If so, call the \n** xBegin method for that table.\n**\n** Also, whether or not P4 is set, check that this is not being called from\n** within a callback to a virtual table xSync() method. If it is, the error\n** code will be set to SQLITE_LOCKED.\n*/\ncase OP_VBegin: {\n  VTable *pVTab;\n  pVTab = pOp->p4.pVtab;\n  rc = sqlite3VtabBegin(db, pVTab);\n  if( pVTab ) sqlite3VtabImportErrmsg(p, pVTab->pVtab);\n  if( rc ) goto abort_due_to_error;\n  break;\n}\n#endif /* SQLITE_OMIT_VIRTUALTABLE */\n\n#ifndef SQLITE_OMIT_VIRTUALTABLE\n/* Opcode: VCreate P1 P2 * * *\n**\n** P2 is a register that holds the name of a virtual table in database \n** P1. Call the xCreate method for that table.\n*/\ncase OP_VCreate: {\n  Mem sMem;          /* For storing the record being decoded */\n  const char *zTab;  /* Name of the virtual table */\n\n  memset(&sMem, 0, sizeof(sMem));\n  sMem.db = db;\n  /* Because P2 is always a static string, it is impossible for the\n  ** sqlite3VdbeMemCopy() to fail */\n  assert( (aMem[pOp->p2].flags & MEM_Str)!=0 );\n  assert( (aMem[pOp->p2].flags & MEM_Static)!=0 );\n  rc = sqlite3VdbeMemCopy(&sMem, &aMem[pOp->p2]);\n  assert( rc==SQLITE_OK );\n  zTab = (const char*)sqlite3_value_text(&sMem);\n  assert( zTab || db->mallocFailed );\n  if( zTab ){\n    rc = sqlite3VtabCallCreate(db, pOp->p1, zTab, &p->zErrMsg);\n  }\n  sqlite3VdbeMemRelease(&sMem);\n  if( rc ) goto abort_due_to_error;\n  break;\n}\n#endif /* SQLITE_OMIT_VIRTUALTABLE */\n\n#ifndef SQLITE_OMIT_VIRTUALTABLE\n/* Opcode: VDestroy P1 * * P4 *\n**\n** P4 is the name of a virtual table in database P1.  Call the xDestroy method\n** of that table.\n*/\ncase OP_VDestroy: {\n  db->nVDestroy++;\n  rc = sqlite3VtabCallDestroy(db, pOp->p1, pOp->p4.z);\n  db->nVDestroy--;\n  if( rc ) goto abort_due_to_error;\n  break;\n}\n#endif /* SQLITE_OMIT_VIRTUALTABLE */\n\n#ifndef SQLITE_OMIT_VIRTUALTABLE\n/* Opcode: VOpen P1 * * P4 *\n**\n** P4 is a pointer to a virtual table object, an sqlite3_vtab structure.\n** P1 is a cursor number.  This opcode opens a cursor to the virtual\n** table and stores that cursor in P1.\n*/\ncase OP_VOpen: {\n  VdbeCursor *pCur;\n  sqlite3_vtab_cursor *pVCur;\n  sqlite3_vtab *pVtab;\n  const sqlite3_module *pModule;\n\n  assert( p->bIsReader );\n  pCur = 0;\n  pVCur = 0;\n  pVtab = pOp->p4.pVtab->pVtab;\n  if( pVtab==0 || NEVER(pVtab->pModule==0) ){\n    rc = SQLITE_LOCKED;\n    goto abort_due_to_error;\n  }\n  pModule = pVtab->pModule;\n  rc = pModule->xOpen(pVtab, &pVCur);\n  sqlite3VtabImportErrmsg(p, pVtab);\n  if( rc ) goto abort_due_to_error;\n\n  /* Initialize sqlite3_vtab_cursor base class */\n  pVCur->pVtab = pVtab;\n\n  /* Initialize vdbe cursor object */\n  pCur = allocateCursor(p, pOp->p1, 0, -1, CURTYPE_VTAB);\n  if( pCur ){\n    pCur->uc.pVCur = pVCur;\n    pVtab->nRef++;\n  }else{\n    assert( db->mallocFailed );\n    pModule->xClose(pVCur);\n    goto no_mem;\n  }\n  break;\n}\n#endif /* SQLITE_OMIT_VIRTUALTABLE */\n\n#ifndef SQLITE_OMIT_VIRTUALTABLE\n/* Opcode: VFilter P1 P2 P3 P4 *\n** Synopsis: iplan=r[P3] zplan='P4'\n**\n** P1 is a cursor opened using VOpen.  P2 is an address to jump to if\n** the filtered result set is empty.\n**\n** P4 is either NULL or a string that was generated by the xBestIndex\n** method of the module.  The interpretation of the P4 string is left\n** to the module implementation.\n**\n** This opcode invokes the xFilter method on the virtual table specified\n** by P1.  The integer query plan parameter to xFilter is stored in register\n** P3. Register P3+1 stores the argc parameter to be passed to the\n** xFilter method. Registers P3+2..P3+1+argc are the argc\n** additional parameters which are passed to\n** xFilter as argv. Register P3+2 becomes argv[0] when passed to xFilter.\n**\n** A jump is made to P2 if the result set after filtering would be empty.\n*/\ncase OP_VFilter: {   /* jump */\n  int nArg;\n  int iQuery;\n  const sqlite3_module *pModule;\n  Mem *pQuery;\n  Mem *pArgc;\n  sqlite3_vtab_cursor *pVCur;\n  sqlite3_vtab *pVtab;\n  VdbeCursor *pCur;\n  int res;\n  int i;\n  Mem **apArg;\n\n  pQuery = &aMem[pOp->p3];\n  pArgc = &pQuery[1];\n  pCur = p->apCsr[pOp->p1];\n  assert( memIsValid(pQuery) );\n  REGISTER_TRACE(pOp->p3, pQuery);\n  assert( pCur->eCurType==CURTYPE_VTAB );\n  pVCur = pCur->uc.pVCur;\n  pVtab = pVCur->pVtab;\n  pModule = pVtab->pModule;\n\n  /* Grab the index number and argc parameters */\n  assert( (pQuery->flags&MEM_Int)!=0 && pArgc->flags==MEM_Int );\n  nArg = (int)pArgc->u.i;\n  iQuery = (int)pQuery->u.i;\n\n  /* Invoke the xFilter method */\n  res = 0;\n  apArg = p->apArg;\n  for(i = 0; i<nArg; i++){\n    apArg[i] = &pArgc[i+1];\n  }\n  rc = pModule->xFilter(pVCur, iQuery, pOp->p4.z, nArg, apArg);\n  sqlite3VtabImportErrmsg(p, pVtab);\n  if( rc ) goto abort_due_to_error;\n  res = pModule->xEof(pVCur);\n  pCur->nullRow = 0;\n  VdbeBranchTaken(res!=0,2);\n  if( res ) goto jump_to_p2;\n  break;\n}\n#endif /* SQLITE_OMIT_VIRTUALTABLE */\n\n#ifndef SQLITE_OMIT_VIRTUALTABLE\n/* Opcode: VColumn P1 P2 P3 * P5\n** Synopsis: r[P3]=vcolumn(P2)\n**\n** Store in register P3 the value of the P2-th column of\n** the current row of the virtual-table of cursor P1.\n**\n** If the VColumn opcode is being used to fetch the value of\n** an unchanging column during an UPDATE operation, then the P5\n** value is 1.  Otherwise, P5 is 0.  The P5 value is returned\n** by sqlite3_vtab_nochange() routine can can be used\n** by virtual table implementations to return special \"no-change\"\n** marks which can be more efficient, depending on the virtual table.\n*/\ncase OP_VColumn: {\n  sqlite3_vtab *pVtab;\n  const sqlite3_module *pModule;\n  Mem *pDest;\n  sqlite3_context sContext;\n\n  VdbeCursor *pCur = p->apCsr[pOp->p1];\n  assert( pCur->eCurType==CURTYPE_VTAB );\n  assert( pOp->p3>0 && pOp->p3<=(p->nMem+1 - p->nCursor) );\n  pDest = &aMem[pOp->p3];\n  memAboutToChange(p, pDest);\n  if( pCur->nullRow ){\n    sqlite3VdbeMemSetNull(pDest);\n    break;\n  }\n  pVtab = pCur->uc.pVCur->pVtab;\n  pModule = pVtab->pModule;\n  assert( pModule->xColumn );\n  memset(&sContext, 0, sizeof(sContext));\n  sContext.pOut = pDest;\n  if( pOp->p5 ){\n    sqlite3VdbeMemSetNull(pDest);\n    pDest->flags = MEM_Null|MEM_Zero;\n    pDest->u.nZero = 0;\n  }else{\n    MemSetTypeFlag(pDest, MEM_Null);\n  }\n  rc = pModule->xColumn(pCur->uc.pVCur, &sContext, pOp->p2);\n  sqlite3VtabImportErrmsg(p, pVtab);\n  if( sContext.isError>0 ){\n    sqlite3VdbeError(p, \"%s\", sqlite3_value_text(pDest));\n    rc = sContext.isError;\n  }\n  sqlite3VdbeChangeEncoding(pDest, encoding);\n  REGISTER_TRACE(pOp->p3, pDest);\n  UPDATE_MAX_BLOBSIZE(pDest);\n\n  if( sqlite3VdbeMemTooBig(pDest) ){\n    goto too_big;\n  }\n  if( rc ) goto abort_due_to_error;\n  break;\n}\n#endif /* SQLITE_OMIT_VIRTUALTABLE */\n\n#ifndef SQLITE_OMIT_VIRTUALTABLE\n/* Opcode: VNext P1 P2 * * *\n**\n** Advance virtual table P1 to the next row in its result set and\n** jump to instruction P2.  Or, if the virtual table has reached\n** the end of its result set, then fall through to the next instruction.\n*/\ncase OP_VNext: {   /* jump */\n  sqlite3_vtab *pVtab;\n  const sqlite3_module *pModule;\n  int res;\n  VdbeCursor *pCur;\n\n  res = 0;\n  pCur = p->apCsr[pOp->p1];\n  assert( pCur->eCurType==CURTYPE_VTAB );\n  if( pCur->nullRow ){\n    break;\n  }\n  pVtab = pCur->uc.pVCur->pVtab;\n  pModule = pVtab->pModule;\n  assert( pModule->xNext );\n\n  /* Invoke the xNext() method of the module. There is no way for the\n  ** underlying implementation to return an error if one occurs during\n  ** xNext(). Instead, if an error occurs, true is returned (indicating that \n  ** data is available) and the error code returned when xColumn or\n  ** some other method is next invoked on the save virtual table cursor.\n  */\n  rc = pModule->xNext(pCur->uc.pVCur);\n  sqlite3VtabImportErrmsg(p, pVtab);\n  if( rc ) goto abort_due_to_error;\n  res = pModule->xEof(pCur->uc.pVCur);\n  VdbeBranchTaken(!res,2);\n  if( !res ){\n    /* If there is data, jump to P2 */\n    goto jump_to_p2_and_check_for_interrupt;\n  }\n  goto check_for_interrupt;\n}\n#endif /* SQLITE_OMIT_VIRTUALTABLE */\n\n#ifndef SQLITE_OMIT_VIRTUALTABLE\n/* Opcode: VRename P1 * * P4 *\n**\n** P4 is a pointer to a virtual table object, an sqlite3_vtab structure.\n** This opcode invokes the corresponding xRename method. The value\n** in register P1 is passed as the zName argument to the xRename method.\n*/\ncase OP_VRename: {\n  sqlite3_vtab *pVtab;\n  Mem *pName;\n\n  pVtab = pOp->p4.pVtab->pVtab;\n  pName = &aMem[pOp->p1];\n  assert( pVtab->pModule->xRename );\n  assert( memIsValid(pName) );\n  assert( p->readOnly==0 );\n  REGISTER_TRACE(pOp->p1, pName);\n  assert( pName->flags & MEM_Str );\n  testcase( pName->enc==SQLITE_UTF8 );\n  testcase( pName->enc==SQLITE_UTF16BE );\n  testcase( pName->enc==SQLITE_UTF16LE );\n  rc = sqlite3VdbeChangeEncoding(pName, SQLITE_UTF8);\n  if( rc ) goto abort_due_to_error;\n  rc = pVtab->pModule->xRename(pVtab, pName->z);\n  sqlite3VtabImportErrmsg(p, pVtab);\n  p->expired = 0;\n  if( rc ) goto abort_due_to_error;\n  break;\n}\n#endif\n\n#ifndef SQLITE_OMIT_VIRTUALTABLE\n/* Opcode: VUpdate P1 P2 P3 P4 P5\n** Synopsis: data=r[P3@P2]\n**\n** P4 is a pointer to a virtual table object, an sqlite3_vtab structure.\n** This opcode invokes the corresponding xUpdate method. P2 values\n** are contiguous memory cells starting at P3 to pass to the xUpdate \n** invocation. The value in register (P3+P2-1) corresponds to the \n** p2th element of the argv array passed to xUpdate.\n**\n** The xUpdate method will do a DELETE or an INSERT or both.\n** The argv[0] element (which corresponds to memory cell P3)\n** is the rowid of a row to delete.  If argv[0] is NULL then no \n** deletion occurs.  The argv[1] element is the rowid of the new \n** row.  This can be NULL to have the virtual table select the new \n** rowid for itself.  The subsequent elements in the array are \n** the values of columns in the new row.\n**\n** If P2==1 then no insert is performed.  argv[0] is the rowid of\n** a row to delete.\n**\n** P1 is a boolean flag. If it is set to true and the xUpdate call\n** is successful, then the value returned by sqlite3_last_insert_rowid() \n** is set to the value of the rowid for the row just inserted.\n**\n** P5 is the error actions (OE_Replace, OE_Fail, OE_Ignore, etc) to\n** apply in the case of a constraint failure on an insert or update.\n*/\ncase OP_VUpdate: {\n  sqlite3_vtab *pVtab;\n  const sqlite3_module *pModule;\n  int nArg;\n  int i;\n  sqlite_int64 rowid;\n  Mem **apArg;\n  Mem *pX;\n\n  assert( pOp->p2==1        || pOp->p5==OE_Fail   || pOp->p5==OE_Rollback \n       || pOp->p5==OE_Abort || pOp->p5==OE_Ignore || pOp->p5==OE_Replace\n  );\n  assert( p->readOnly==0 );\n  pVtab = pOp->p4.pVtab->pVtab;\n  if( pVtab==0 || NEVER(pVtab->pModule==0) ){\n    rc = SQLITE_LOCKED;\n    goto abort_due_to_error;\n  }\n  pModule = pVtab->pModule;\n  nArg = pOp->p2;\n  assert( pOp->p4type==P4_VTAB );\n  if( ALWAYS(pModule->xUpdate) ){\n    u8 vtabOnConflict = db->vtabOnConflict;\n    apArg = p->apArg;\n    pX = &aMem[pOp->p3];\n    for(i=0; i<nArg; i++){\n      assert( memIsValid(pX) );\n      memAboutToChange(p, pX);\n      apArg[i] = pX;\n      pX++;\n    }\n    db->vtabOnConflict = pOp->p5;\n    rc = pModule->xUpdate(pVtab, nArg, apArg, &rowid);\n    db->vtabOnConflict = vtabOnConflict;\n    sqlite3VtabImportErrmsg(p, pVtab);\n    if( rc==SQLITE_OK && pOp->p1 ){\n      assert( nArg>1 && apArg[0] && (apArg[0]->flags&MEM_Null) );\n      db->lastRowid = rowid;\n    }\n    if( (rc&0xff)==SQLITE_CONSTRAINT && pOp->p4.pVtab->bConstraint ){\n      if( pOp->p5==OE_Ignore ){\n        rc = SQLITE_OK;\n      }else{\n        p->errorAction = ((pOp->p5==OE_Replace) ? OE_Abort : pOp->p5);\n      }\n    }else{\n      p->nChange++;\n    }\n    if( rc ) goto abort_due_to_error;\n  }\n  break;\n}\n#endif /* SQLITE_OMIT_VIRTUALTABLE */\n\n#ifndef  SQLITE_OMIT_PAGER_PRAGMAS\n/* Opcode: Pagecount P1 P2 * * *\n**\n** Write the current number of pages in database P1 to memory cell P2.\n*/\ncase OP_Pagecount: {            /* out2 */\n  pOut = out2Prerelease(p, pOp);\n  pOut->u.i = sqlite3BtreeLastPage(db->aDb[pOp->p1].pBt);\n  break;\n}\n#endif\n\n\n#ifndef  SQLITE_OMIT_PAGER_PRAGMAS\n/* Opcode: MaxPgcnt P1 P2 P3 * *\n**\n** Try to set the maximum page count for database P1 to the value in P3.\n** Do not let the maximum page count fall below the current page count and\n** do not change the maximum page count value if P3==0.\n**\n** Store the maximum page count after the change in register P2.\n*/\ncase OP_MaxPgcnt: {            /* out2 */\n  unsigned int newMax;\n  Btree *pBt;\n\n  pOut = out2Prerelease(p, pOp);\n  pBt = db->aDb[pOp->p1].pBt;\n  newMax = 0;\n  if( pOp->p3 ){\n    newMax = sqlite3BtreeLastPage(pBt);\n    if( newMax < (unsigned)pOp->p3 ) newMax = (unsigned)pOp->p3;\n  }\n  pOut->u.i = sqlite3BtreeMaxPageCount(pBt, newMax);\n  break;\n}\n#endif\n\n/* Opcode: Function0 P1 P2 P3 P4 P5\n** Synopsis: r[P3]=func(r[P2@P5])\n**\n** Invoke a user function (P4 is a pointer to a FuncDef object that\n** defines the function) with P5 arguments taken from register P2 and\n** successors.  The result of the function is stored in register P3.\n** Register P3 must not be one of the function inputs.\n**\n** P1 is a 32-bit bitmask indicating whether or not each argument to the \n** function was determined to be constant at compile time. If the first\n** argument was constant then bit 0 of P1 is set. This is used to determine\n** whether meta data associated with a user function argument using the\n** sqlite3_set_auxdata() API may be safely retained until the next\n** invocation of this opcode.\n**\n** See also: Function, AggStep, AggFinal\n*/\n/* Opcode: Function P1 P2 P3 P4 P5\n** Synopsis: r[P3]=func(r[P2@P5])\n**\n** Invoke a user function (P4 is a pointer to an sqlite3_context object that\n** contains a pointer to the function to be run) with P5 arguments taken\n** from register P2 and successors.  The result of the function is stored\n** in register P3.  Register P3 must not be one of the function inputs.\n**\n** P1 is a 32-bit bitmask indicating whether or not each argument to the \n** function was determined to be constant at compile time. If the first\n** argument was constant then bit 0 of P1 is set. This is used to determine\n** whether meta data associated with a user function argument using the\n** sqlite3_set_auxdata() API may be safely retained until the next\n** invocation of this opcode.\n**\n** SQL functions are initially coded as OP_Function0 with P4 pointing\n** to a FuncDef object.  But on first evaluation, the P4 operand is\n** automatically converted into an sqlite3_context object and the operation\n** changed to this OP_Function opcode.  In this way, the initialization of\n** the sqlite3_context object occurs only once, rather than once for each\n** evaluation of the function.\n**\n** See also: Function0, AggStep, AggFinal\n*/\ncase OP_PureFunc0:\ncase OP_Function0: {\n  int n;\n  sqlite3_context *pCtx;\n\n  assert( pOp->p4type==P4_FUNCDEF );\n  n = pOp->p5;\n  assert( pOp->p3>0 && pOp->p3<=(p->nMem+1 - p->nCursor) );\n  assert( n==0 || (pOp->p2>0 && pOp->p2+n<=(p->nMem+1 - p->nCursor)+1) );\n  assert( pOp->p3<pOp->p2 || pOp->p3>=pOp->p2+n );\n  pCtx = sqlite3DbMallocRawNN(db, sizeof(*pCtx) + (n-1)*sizeof(sqlite3_value*));\n  if( pCtx==0 ) goto no_mem;\n  pCtx->pOut = 0;\n  pCtx->pFunc = pOp->p4.pFunc;\n  pCtx->iOp = (int)(pOp - aOp);\n  pCtx->pVdbe = p;\n  pCtx->isError = 0;\n  pCtx->argc = n;\n  pOp->p4type = P4_FUNCCTX;\n  pOp->p4.pCtx = pCtx;\n  assert( OP_PureFunc == OP_PureFunc0+2 );\n  assert( OP_Function == OP_Function0+2 );\n  pOp->opcode += 2;\n  /* Fall through into OP_Function */\n}\ncase OP_PureFunc:\ncase OP_Function: {\n  int i;\n  sqlite3_context *pCtx;\n\n  assert( pOp->p4type==P4_FUNCCTX );\n  pCtx = pOp->p4.pCtx;\n\n  /* If this function is inside of a trigger, the register array in aMem[]\n  ** might change from one evaluation to the next.  The next block of code\n  ** checks to see if the register array has changed, and if so it\n  ** reinitializes the relavant parts of the sqlite3_context object */\n  pOut = &aMem[pOp->p3];\n  if( pCtx->pOut != pOut ){\n    pCtx->pOut = pOut;\n    for(i=pCtx->argc-1; i>=0; i--) pCtx->argv[i] = &aMem[pOp->p2+i];\n  }\n\n  memAboutToChange(p, pOut);\n#ifdef SQLITE_DEBUG\n  for(i=0; i<pCtx->argc; i++){\n    assert( memIsValid(pCtx->argv[i]) );\n    REGISTER_TRACE(pOp->p2+i, pCtx->argv[i]);\n  }\n#endif\n  MemSetTypeFlag(pOut, MEM_Null);\n  assert( pCtx->isError==0 );\n  (*pCtx->pFunc->xSFunc)(pCtx, pCtx->argc, pCtx->argv);/* IMP: R-24505-23230 */\n\n  /* If the function returned an error, throw an exception */\n  if( pCtx->isError ){\n    if( pCtx->isError>0 ){\n      sqlite3VdbeError(p, \"%s\", sqlite3_value_text(pOut));\n      rc = pCtx->isError;\n    }\n    sqlite3VdbeDeleteAuxData(db, &p->pAuxData, pCtx->iOp, pOp->p1);\n    pCtx->isError = 0;\n    if( rc ) goto abort_due_to_error;\n  }\n\n  /* Copy the result of the function into register P3 */\n  if( pOut->flags & (MEM_Str|MEM_Blob) ){\n    sqlite3VdbeChangeEncoding(pOut, encoding);\n    if( sqlite3VdbeMemTooBig(pOut) ) goto too_big;\n  }\n\n  REGISTER_TRACE(pOp->p3, pOut);\n  UPDATE_MAX_BLOBSIZE(pOut);\n  break;\n}\n\n/* Opcode: Trace P1 P2 * P4 *\n**\n** Write P4 on the statement trace output if statement tracing is\n** enabled.\n**\n** Operand P1 must be 0x7fffffff and P2 must positive.\n*/\n/* Opcode: Init P1 P2 P3 P4 *\n** Synopsis: Start at P2\n**\n** Programs contain a single instance of this opcode as the very first\n** opcode.\n**\n** If tracing is enabled (by the sqlite3_trace()) interface, then\n** the UTF-8 string contained in P4 is emitted on the trace callback.\n** Or if P4 is blank, use the string returned by sqlite3_sql().\n**\n** If P2 is not zero, jump to instruction P2.\n**\n** Increment the value of P1 so that OP_Once opcodes will jump the\n** first time they are evaluated for this run.\n**\n** If P3 is not zero, then it is an address to jump to if an SQLITE_CORRUPT\n** error is encountered.\n*/\ncase OP_Trace:\ncase OP_Init: {          /* jump */\n  int i;\n#ifndef SQLITE_OMIT_TRACE\n  char *zTrace;\n#endif\n\n  /* If the P4 argument is not NULL, then it must be an SQL comment string.\n  ** The \"--\" string is broken up to prevent false-positives with srcck1.c.\n  **\n  ** This assert() provides evidence for:\n  ** EVIDENCE-OF: R-50676-09860 The callback can compute the same text that\n  ** would have been returned by the legacy sqlite3_trace() interface by\n  ** using the X argument when X begins with \"--\" and invoking\n  ** sqlite3_expanded_sql(P) otherwise.\n  */\n  assert( pOp->p4.z==0 || strncmp(pOp->p4.z, \"-\" \"- \", 3)==0 );\n\n  /* OP_Init is always instruction 0 */\n  assert( pOp==p->aOp || pOp->opcode==OP_Trace );\n\n#ifndef SQLITE_OMIT_TRACE\n  if( (db->mTrace & (SQLITE_TRACE_STMT|SQLITE_TRACE_LEGACY))!=0\n   && !p->doingRerun\n   && (zTrace = (pOp->p4.z ? pOp->p4.z : p->zSql))!=0\n  ){\n#ifndef SQLITE_OMIT_DEPRECATED\n    if( db->mTrace & SQLITE_TRACE_LEGACY ){\n      void (*x)(void*,const char*) = (void(*)(void*,const char*))db->xTrace;\n      char *z = sqlite3VdbeExpandSql(p, zTrace);\n      x(db->pTraceArg, z);\n      sqlite3_free(z);\n    }else\n#endif\n    if( db->nVdbeExec>1 ){\n      char *z = sqlite3MPrintf(db, \"-- %s\", zTrace);\n      (void)db->xTrace(SQLITE_TRACE_STMT, db->pTraceArg, p, z);\n      sqlite3DbFree(db, z);\n    }else{\n      (void)db->xTrace(SQLITE_TRACE_STMT, db->pTraceArg, p, zTrace);\n    }\n  }\n#ifdef SQLITE_USE_FCNTL_TRACE\n  zTrace = (pOp->p4.z ? pOp->p4.z : p->zSql);\n  if( zTrace ){\n    int j;\n    for(j=0; j<db->nDb; j++){\n      if( DbMaskTest(p->btreeMask, j)==0 ) continue;\n      sqlite3_file_control(db, db->aDb[j].zDbSName, SQLITE_FCNTL_TRACE, zTrace);\n    }\n  }\n#endif /* SQLITE_USE_FCNTL_TRACE */\n#ifdef SQLITE_DEBUG\n  if( (db->flags & SQLITE_SqlTrace)!=0\n   && (zTrace = (pOp->p4.z ? pOp->p4.z : p->zSql))!=0\n  ){\n    sqlite3DebugPrintf(\"SQL-trace: %s\\n\", zTrace);\n  }\n#endif /* SQLITE_DEBUG */\n#endif /* SQLITE_OMIT_TRACE */\n  assert( pOp->p2>0 );\n  if( pOp->p1>=sqlite3GlobalConfig.iOnceResetThreshold ){\n    if( pOp->opcode==OP_Trace ) break;\n    for(i=1; i<p->nOp; i++){\n      if( p->aOp[i].opcode==OP_Once ) p->aOp[i].p1 = 0;\n    }\n    pOp->p1 = 0;\n  }\n  pOp->p1++;\n  p->aCounter[SQLITE_STMTSTATUS_RUN]++;\n  goto jump_to_p2;\n}\n\n#ifdef SQLITE_ENABLE_CURSOR_HINTS\n/* Opcode: CursorHint P1 * * P4 *\n**\n** Provide a hint to cursor P1 that it only needs to return rows that\n** satisfy the Expr in P4.  TK_REGISTER terms in the P4 expression refer\n** to values currently held in registers.  TK_COLUMN terms in the P4\n** expression refer to columns in the b-tree to which cursor P1 is pointing.\n*/\ncase OP_CursorHint: {\n  VdbeCursor *pC;\n\n  assert( pOp->p1>=0 && pOp->p1<p->nCursor );\n  assert( pOp->p4type==P4_EXPR );\n  pC = p->apCsr[pOp->p1];\n  if( pC ){\n    assert( pC->eCurType==CURTYPE_BTREE );\n    sqlite3BtreeCursorHint(pC->uc.pCursor, BTREE_HINT_RANGE,\n                           pOp->p4.pExpr, aMem);\n  }\n  break;\n}\n#endif /* SQLITE_ENABLE_CURSOR_HINTS */\n\n/* Opcode: Noop * * * * *\n**\n** Do nothing.  This instruction is often useful as a jump\n** destination.\n*/\n/*\n** The magic Explain opcode are only inserted when explain==2 (which\n** is to say when the EXPLAIN QUERY PLAN syntax is used.)\n** This opcode records information from the optimizer.  It is the\n** the same as a no-op.  This opcodesnever appears in a real VM program.\n*/\ndefault: {          /* This is really OP_Noop and OP_Explain */\n  assert( pOp->opcode==OP_Noop || pOp->opcode==OP_Explain );\n  break;\n}\n\n/*****************************************************************************\n** The cases of the switch statement above this line should all be indented\n** by 6 spaces.  But the left-most 6 spaces have been removed to improve the\n** readability.  From this point on down, the normal indentation rules are\n** restored.\n*****************************************************************************/\n    }\n\n#ifdef VDBE_PROFILE\n    {\n      u64 endTime = sqlite3NProfileCnt ? sqlite3NProfileCnt : sqlite3Hwtime();\n      if( endTime>start ) pOrigOp->cycles += endTime - start;\n      pOrigOp->cnt++;\n    }\n#endif\n\n    /* The following code adds nothing to the actual functionality\n    ** of the program.  It is only here for testing and debugging.\n    ** On the other hand, it does burn CPU cycles every time through\n    ** the evaluator loop.  So we can leave it out when NDEBUG is defined.\n    */\n#ifndef NDEBUG\n    assert( pOp>=&aOp[-1] && pOp<&aOp[p->nOp-1] );\n\n#ifdef SQLITE_DEBUG\n    if( db->flags & SQLITE_VdbeTrace ){\n      u8 opProperty = sqlite3OpcodeProperty[pOrigOp->opcode];\n      if( rc!=0 ) printf(\"rc=%d\\n\",rc);\n      if( opProperty & (OPFLG_OUT2) ){\n        registerTrace(pOrigOp->p2, &aMem[pOrigOp->p2]);\n      }\n      if( opProperty & OPFLG_OUT3 ){\n        registerTrace(pOrigOp->p3, &aMem[pOrigOp->p3]);\n      }\n    }\n#endif  /* SQLITE_DEBUG */\n#endif  /* NDEBUG */\n  }  /* The end of the for(;;) loop the loops through opcodes */\n\n  /* If we reach this point, it means that execution is finished with\n  ** an error of some kind.\n  */\nabort_due_to_error:\n  if( db->mallocFailed ) rc = SQLITE_NOMEM_BKPT;\n  assert( rc );\n  if( p->zErrMsg==0 && rc!=SQLITE_IOERR_NOMEM ){\n    sqlite3VdbeError(p, \"%s\", sqlite3ErrStr(rc));\n  }\n  p->rc = rc;\n  sqlite3SystemError(db, rc);\n  testcase( sqlite3GlobalConfig.xLog!=0 );\n  sqlite3_log(rc, \"statement aborts at %d: [%s] %s\", \n                   (int)(pOp - aOp), p->zSql, p->zErrMsg);\n  sqlite3VdbeHalt(p);\n  if( rc==SQLITE_IOERR_NOMEM ) sqlite3OomFault(db);\n  rc = SQLITE_ERROR;\n  if( resetSchemaOnFault>0 ){\n    sqlite3ResetOneSchema(db, resetSchemaOnFault-1);\n  }\n\n  /* This is the only way out of this procedure.  We have to\n  ** release the mutexes on btrees that were acquired at the\n  ** top. */\nvdbe_return:\n  testcase( nVmStep>0 );\n  p->aCounter[SQLITE_STMTSTATUS_VM_STEP] += (int)nVmStep;\n  sqlite3VdbeLeave(p);\n  assert( rc!=SQLITE_OK || nExtraDelete==0 \n       || sqlite3_strlike(\"DELETE%\",p->zSql,0)!=0 \n  );\n  return rc;\n\n  /* Jump to here if a string or blob larger than SQLITE_MAX_LENGTH\n  ** is encountered.\n  */\ntoo_big:\n  sqlite3VdbeError(p, \"string or blob too big\");\n  rc = SQLITE_TOOBIG;\n  goto abort_due_to_error;\n\n  /* Jump to here if a malloc() fails.\n  */\nno_mem:\n  sqlite3OomFault(db);\n  sqlite3VdbeError(p, \"out of memory\");\n  rc = SQLITE_NOMEM_BKPT;\n  goto abort_due_to_error;\n\n  /* Jump to here if the sqlite3_interrupt() API sets the interrupt\n  ** flag.\n  */\nabort_due_to_interrupt:\n  assert( db->u1.isInterrupted );\n  rc = db->mallocFailed ? SQLITE_NOMEM_BKPT : SQLITE_INTERRUPT;\n  p->rc = rc;\n  sqlite3VdbeError(p, \"%s\", sqlite3ErrStr(rc));\n  goto abort_due_to_error;\n}\n\n\n/************** End of vdbe.c ************************************************/\n/************** Begin file vdbeblob.c ****************************************/\n/*\n** 2007 May 1\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n*************************************************************************\n**\n** This file contains code used to implement incremental BLOB I/O.\n*/\n\n/* #include \"sqliteInt.h\" */\n/* #include \"vdbeInt.h\" */\n\n#ifndef SQLITE_OMIT_INCRBLOB\n\n/*\n** Valid sqlite3_blob* handles point to Incrblob structures.\n*/\ntypedef struct Incrblob Incrblob;\nstruct Incrblob {\n  int nByte;              /* Size of open blob, in bytes */\n  int iOffset;            /* Byte offset of blob in cursor data */\n  u16 iCol;               /* Table column this handle is open on */\n  BtCursor *pCsr;         /* Cursor pointing at blob row */\n  sqlite3_stmt *pStmt;    /* Statement holding cursor open */\n  sqlite3 *db;            /* The associated database */\n  char *zDb;              /* Database name */\n  Table *pTab;            /* Table object */\n};\n\n\n/*\n** This function is used by both blob_open() and blob_reopen(). It seeks\n** the b-tree cursor associated with blob handle p to point to row iRow.\n** If successful, SQLITE_OK is returned and subsequent calls to\n** sqlite3_blob_read() or sqlite3_blob_write() access the specified row.\n**\n** If an error occurs, or if the specified row does not exist or does not\n** contain a value of type TEXT or BLOB in the column nominated when the\n** blob handle was opened, then an error code is returned and *pzErr may\n** be set to point to a buffer containing an error message. It is the\n** responsibility of the caller to free the error message buffer using\n** sqlite3DbFree().\n**\n** If an error does occur, then the b-tree cursor is closed. All subsequent\n** calls to sqlite3_blob_read(), blob_write() or blob_reopen() will \n** immediately return SQLITE_ABORT.\n*/\nstatic int blobSeekToRow(Incrblob *p, sqlite3_int64 iRow, char **pzErr){\n  int rc;                         /* Error code */\n  char *zErr = 0;                 /* Error message */\n  Vdbe *v = (Vdbe *)p->pStmt;\n\n  /* Set the value of register r[1] in the SQL statement to integer iRow. \n  ** This is done directly as a performance optimization\n  */\n  v->aMem[1].flags = MEM_Int;\n  v->aMem[1].u.i = iRow;\n\n  /* If the statement has been run before (and is paused at the OP_ResultRow)\n  ** then back it up to the point where it does the OP_NotExists.  This could\n  ** have been down with an extra OP_Goto, but simply setting the program\n  ** counter is faster. */\n  if( v->pc>4 ){\n    v->pc = 4;\n    assert( v->aOp[v->pc].opcode==OP_NotExists );\n    rc = sqlite3VdbeExec(v);\n  }else{\n    rc = sqlite3_step(p->pStmt);\n  }\n  if( rc==SQLITE_ROW ){\n    VdbeCursor *pC = v->apCsr[0];\n    u32 type = pC->nHdrParsed>p->iCol ? pC->aType[p->iCol] : 0;\n    testcase( pC->nHdrParsed==p->iCol );\n    testcase( pC->nHdrParsed==p->iCol+1 );\n    if( type<12 ){\n      zErr = sqlite3MPrintf(p->db, \"cannot open value of type %s\",\n          type==0?\"null\": type==7?\"real\": \"integer\"\n      );\n      rc = SQLITE_ERROR;\n      sqlite3_finalize(p->pStmt);\n      p->pStmt = 0;\n    }else{\n      p->iOffset = pC->aType[p->iCol + pC->nField];\n      p->nByte = sqlite3VdbeSerialTypeLen(type);\n      p->pCsr =  pC->uc.pCursor;\n      sqlite3BtreeIncrblobCursor(p->pCsr);\n    }\n  }\n\n  if( rc==SQLITE_ROW ){\n    rc = SQLITE_OK;\n  }else if( p->pStmt ){\n    rc = sqlite3_finalize(p->pStmt);\n    p->pStmt = 0;\n    if( rc==SQLITE_OK ){\n      zErr = sqlite3MPrintf(p->db, \"no such rowid: %lld\", iRow);\n      rc = SQLITE_ERROR;\n    }else{\n      zErr = sqlite3MPrintf(p->db, \"%s\", sqlite3_errmsg(p->db));\n    }\n  }\n\n  assert( rc!=SQLITE_OK || zErr==0 );\n  assert( rc!=SQLITE_ROW && rc!=SQLITE_DONE );\n\n  *pzErr = zErr;\n  return rc;\n}\n\n/*\n** Open a blob handle.\n*/\nSQLITE_API int sqlite3_blob_open(\n  sqlite3* db,            /* The database connection */\n  const char *zDb,        /* The attached database containing the blob */\n  const char *zTable,     /* The table containing the blob */\n  const char *zColumn,    /* The column containing the blob */\n  sqlite_int64 iRow,      /* The row containing the glob */\n  int wrFlag,             /* True -> read/write access, false -> read-only */\n  sqlite3_blob **ppBlob   /* Handle for accessing the blob returned here */\n){\n  int nAttempt = 0;\n  int iCol;               /* Index of zColumn in row-record */\n  int rc = SQLITE_OK;\n  char *zErr = 0;\n  Table *pTab;\n  Incrblob *pBlob = 0;\n  Parse sParse;\n\n#ifdef SQLITE_ENABLE_API_ARMOR\n  if( ppBlob==0 ){\n    return SQLITE_MISUSE_BKPT;\n  }\n#endif\n  *ppBlob = 0;\n#ifdef SQLITE_ENABLE_API_ARMOR\n  if( !sqlite3SafetyCheckOk(db) || zTable==0 ){\n    return SQLITE_MISUSE_BKPT;\n  }\n#endif\n  wrFlag = !!wrFlag;                /* wrFlag = (wrFlag ? 1 : 0); */\n\n  sqlite3_mutex_enter(db->mutex);\n\n  pBlob = (Incrblob *)sqlite3DbMallocZero(db, sizeof(Incrblob));\n  do {\n    memset(&sParse, 0, sizeof(Parse));\n    if( !pBlob ) goto blob_open_out;\n    sParse.db = db;\n    sqlite3DbFree(db, zErr);\n    zErr = 0;\n\n    sqlite3BtreeEnterAll(db);\n    pTab = sqlite3LocateTable(&sParse, 0, zTable, zDb);\n    if( pTab && IsVirtual(pTab) ){\n      pTab = 0;\n      sqlite3ErrorMsg(&sParse, \"cannot open virtual table: %s\", zTable);\n    }\n    if( pTab && !HasRowid(pTab) ){\n      pTab = 0;\n      sqlite3ErrorMsg(&sParse, \"cannot open table without rowid: %s\", zTable);\n    }\n#ifndef SQLITE_OMIT_VIEW\n    if( pTab && pTab->pSelect ){\n      pTab = 0;\n      sqlite3ErrorMsg(&sParse, \"cannot open view: %s\", zTable);\n    }\n#endif\n    if( !pTab ){\n      if( sParse.zErrMsg ){\n        sqlite3DbFree(db, zErr);\n        zErr = sParse.zErrMsg;\n        sParse.zErrMsg = 0;\n      }\n      rc = SQLITE_ERROR;\n      sqlite3BtreeLeaveAll(db);\n      goto blob_open_out;\n    }\n    pBlob->pTab = pTab;\n    pBlob->zDb = db->aDb[sqlite3SchemaToIndex(db, pTab->pSchema)].zDbSName;\n\n    /* Now search pTab for the exact column. */\n    for(iCol=0; iCol<pTab->nCol; iCol++) {\n      if( sqlite3StrICmp(pTab->aCol[iCol].zName, zColumn)==0 ){\n        break;\n      }\n    }\n    if( iCol==pTab->nCol ){\n      sqlite3DbFree(db, zErr);\n      zErr = sqlite3MPrintf(db, \"no such column: \\\"%s\\\"\", zColumn);\n      rc = SQLITE_ERROR;\n      sqlite3BtreeLeaveAll(db);\n      goto blob_open_out;\n    }\n\n    /* If the value is being opened for writing, check that the\n    ** column is not indexed, and that it is not part of a foreign key. \n    */\n    if( wrFlag ){\n      const char *zFault = 0;\n      Index *pIdx;\n#ifndef SQLITE_OMIT_FOREIGN_KEY\n      if( db->flags&SQLITE_ForeignKeys ){\n        /* Check that the column is not part of an FK child key definition. It\n        ** is not necessary to check if it is part of a parent key, as parent\n        ** key columns must be indexed. The check below will pick up this \n        ** case.  */\n        FKey *pFKey;\n        for(pFKey=pTab->pFKey; pFKey; pFKey=pFKey->pNextFrom){\n          int j;\n          for(j=0; j<pFKey->nCol; j++){\n            if( pFKey->aCol[j].iFrom==iCol ){\n              zFault = \"foreign key\";\n            }\n          }\n        }\n      }\n#endif\n      for(pIdx=pTab->pIndex; pIdx; pIdx=pIdx->pNext){\n        int j;\n        for(j=0; j<pIdx->nKeyCol; j++){\n          /* FIXME: Be smarter about indexes that use expressions */\n          if( pIdx->aiColumn[j]==iCol || pIdx->aiColumn[j]==XN_EXPR ){\n            zFault = \"indexed\";\n          }\n        }\n      }\n      if( zFault ){\n        sqlite3DbFree(db, zErr);\n        zErr = sqlite3MPrintf(db, \"cannot open %s column for writing\", zFault);\n        rc = SQLITE_ERROR;\n        sqlite3BtreeLeaveAll(db);\n        goto blob_open_out;\n      }\n    }\n\n    pBlob->pStmt = (sqlite3_stmt *)sqlite3VdbeCreate(&sParse);\n    assert( pBlob->pStmt || db->mallocFailed );\n    if( pBlob->pStmt ){\n      \n      /* This VDBE program seeks a btree cursor to the identified \n      ** db/table/row entry. The reason for using a vdbe program instead\n      ** of writing code to use the b-tree layer directly is that the\n      ** vdbe program will take advantage of the various transaction,\n      ** locking and error handling infrastructure built into the vdbe.\n      **\n      ** After seeking the cursor, the vdbe executes an OP_ResultRow.\n      ** Code external to the Vdbe then \"borrows\" the b-tree cursor and\n      ** uses it to implement the blob_read(), blob_write() and \n      ** blob_bytes() functions.\n      **\n      ** The sqlite3_blob_close() function finalizes the vdbe program,\n      ** which closes the b-tree cursor and (possibly) commits the \n      ** transaction.\n      */\n      static const int iLn = VDBE_OFFSET_LINENO(2);\n      static const VdbeOpList openBlob[] = {\n        {OP_TableLock,      0, 0, 0},  /* 0: Acquire a read or write lock */\n        {OP_OpenRead,       0, 0, 0},  /* 1: Open a cursor */\n        /* blobSeekToRow() will initialize r[1] to the desired rowid */\n        {OP_NotExists,      0, 5, 1},  /* 2: Seek the cursor to rowid=r[1] */\n        {OP_Column,         0, 0, 1},  /* 3  */\n        {OP_ResultRow,      1, 0, 0},  /* 4  */\n        {OP_Halt,           0, 0, 0},  /* 5  */\n      };\n      Vdbe *v = (Vdbe *)pBlob->pStmt;\n      int iDb = sqlite3SchemaToIndex(db, pTab->pSchema);\n      VdbeOp *aOp;\n\n      sqlite3VdbeAddOp4Int(v, OP_Transaction, iDb, wrFlag, \n                           pTab->pSchema->schema_cookie,\n                           pTab->pSchema->iGeneration);\n      sqlite3VdbeChangeP5(v, 1);\n      assert( sqlite3VdbeCurrentAddr(v)==2 || db->mallocFailed );\n      aOp = sqlite3VdbeAddOpList(v, ArraySize(openBlob), openBlob, iLn);\n\n      /* Make sure a mutex is held on the table to be accessed */\n      sqlite3VdbeUsesBtree(v, iDb); \n\n      if( db->mallocFailed==0 ){\n        assert( aOp!=0 );\n        /* Configure the OP_TableLock instruction */\n#ifdef SQLITE_OMIT_SHARED_CACHE\n        aOp[0].opcode = OP_Noop;\n#else\n        aOp[0].p1 = iDb;\n        aOp[0].p2 = pTab->tnum;\n        aOp[0].p3 = wrFlag;\n        sqlite3VdbeChangeP4(v, 2, pTab->zName, P4_TRANSIENT);\n      }\n      if( db->mallocFailed==0 ){\n#endif\n\n        /* Remove either the OP_OpenWrite or OpenRead. Set the P2 \n        ** parameter of the other to pTab->tnum.  */\n        if( wrFlag ) aOp[1].opcode = OP_OpenWrite;\n        aOp[1].p2 = pTab->tnum;\n        aOp[1].p3 = iDb;   \n\n        /* Configure the number of columns. Configure the cursor to\n        ** think that the table has one more column than it really\n        ** does. An OP_Column to retrieve this imaginary column will\n        ** always return an SQL NULL. This is useful because it means\n        ** we can invoke OP_Column to fill in the vdbe cursors type \n        ** and offset cache without causing any IO.\n        */\n        aOp[1].p4type = P4_INT32;\n        aOp[1].p4.i = pTab->nCol+1;\n        aOp[3].p2 = pTab->nCol;\n\n        sParse.nVar = 0;\n        sParse.nMem = 1;\n        sParse.nTab = 1;\n        sqlite3VdbeMakeReady(v, &sParse);\n      }\n    }\n   \n    pBlob->iCol = iCol;\n    pBlob->db = db;\n    sqlite3BtreeLeaveAll(db);\n    if( db->mallocFailed ){\n      goto blob_open_out;\n    }\n    rc = blobSeekToRow(pBlob, iRow, &zErr);\n  } while( (++nAttempt)<SQLITE_MAX_SCHEMA_RETRY && rc==SQLITE_SCHEMA );\n\nblob_open_out:\n  if( rc==SQLITE_OK && db->mallocFailed==0 ){\n    *ppBlob = (sqlite3_blob *)pBlob;\n  }else{\n    if( pBlob && pBlob->pStmt ) sqlite3VdbeFinalize((Vdbe *)pBlob->pStmt);\n    sqlite3DbFree(db, pBlob);\n  }\n  sqlite3ErrorWithMsg(db, rc, (zErr ? \"%s\" : 0), zErr);\n  sqlite3DbFree(db, zErr);\n  sqlite3ParserReset(&sParse);\n  rc = sqlite3ApiExit(db, rc);\n  sqlite3_mutex_leave(db->mutex);\n  return rc;\n}\n\n/*\n** Close a blob handle that was previously created using\n** sqlite3_blob_open().\n*/\nSQLITE_API int sqlite3_blob_close(sqlite3_blob *pBlob){\n  Incrblob *p = (Incrblob *)pBlob;\n  int rc;\n  sqlite3 *db;\n\n  if( p ){\n    db = p->db;\n    sqlite3_mutex_enter(db->mutex);\n    rc = sqlite3_finalize(p->pStmt);\n    sqlite3DbFree(db, p);\n    sqlite3_mutex_leave(db->mutex);\n  }else{\n    rc = SQLITE_OK;\n  }\n  return rc;\n}\n\n/*\n** Perform a read or write operation on a blob\n*/\nstatic int blobReadWrite(\n  sqlite3_blob *pBlob, \n  void *z, \n  int n, \n  int iOffset, \n  int (*xCall)(BtCursor*, u32, u32, void*)\n){\n  int rc;\n  Incrblob *p = (Incrblob *)pBlob;\n  Vdbe *v;\n  sqlite3 *db;\n\n  if( p==0 ) return SQLITE_MISUSE_BKPT;\n  db = p->db;\n  sqlite3_mutex_enter(db->mutex);\n  v = (Vdbe*)p->pStmt;\n\n  if( n<0 || iOffset<0 || ((sqlite3_int64)iOffset+n)>p->nByte ){\n    /* Request is out of range. Return a transient error. */\n    rc = SQLITE_ERROR;\n  }else if( v==0 ){\n    /* If there is no statement handle, then the blob-handle has\n    ** already been invalidated. Return SQLITE_ABORT in this case.\n    */\n    rc = SQLITE_ABORT;\n  }else{\n    /* Call either BtreeData() or BtreePutData(). If SQLITE_ABORT is\n    ** returned, clean-up the statement handle.\n    */\n    assert( db == v->db );\n    sqlite3BtreeEnterCursor(p->pCsr);\n\n#ifdef SQLITE_ENABLE_PREUPDATE_HOOK\n    if( xCall==sqlite3BtreePutData && db->xPreUpdateCallback ){\n      /* If a pre-update hook is registered and this is a write cursor, \n      ** invoke it here. \n      ** \n      ** TODO: The preupdate-hook is passed SQLITE_DELETE, even though this\n      ** operation should really be an SQLITE_UPDATE. This is probably\n      ** incorrect, but is convenient because at this point the new.* values \n      ** are not easily obtainable. And for the sessions module, an \n      ** SQLITE_UPDATE where the PK columns do not change is handled in the \n      ** same way as an SQLITE_DELETE (the SQLITE_DELETE code is actually\n      ** slightly more efficient). Since you cannot write to a PK column\n      ** using the incremental-blob API, this works. For the sessions module\n      ** anyhow.\n      */\n      sqlite3_int64 iKey;\n      iKey = sqlite3BtreeIntegerKey(p->pCsr);\n      sqlite3VdbePreUpdateHook(\n          v, v->apCsr[0], SQLITE_DELETE, p->zDb, p->pTab, iKey, -1\n      );\n    }\n#endif\n\n    rc = xCall(p->pCsr, iOffset+p->iOffset, n, z);\n    sqlite3BtreeLeaveCursor(p->pCsr);\n    if( rc==SQLITE_ABORT ){\n      sqlite3VdbeFinalize(v);\n      p->pStmt = 0;\n    }else{\n      v->rc = rc;\n    }\n  }\n  sqlite3Error(db, rc);\n  rc = sqlite3ApiExit(db, rc);\n  sqlite3_mutex_leave(db->mutex);\n  return rc;\n}\n\n/*\n** Read data from a blob handle.\n*/\nSQLITE_API int sqlite3_blob_read(sqlite3_blob *pBlob, void *z, int n, int iOffset){\n  return blobReadWrite(pBlob, z, n, iOffset, sqlite3BtreePayloadChecked);\n}\n\n/*\n** Write data to a blob handle.\n*/\nSQLITE_API int sqlite3_blob_write(sqlite3_blob *pBlob, const void *z, int n, int iOffset){\n  return blobReadWrite(pBlob, (void *)z, n, iOffset, sqlite3BtreePutData);\n}\n\n/*\n** Query a blob handle for the size of the data.\n**\n** The Incrblob.nByte field is fixed for the lifetime of the Incrblob\n** so no mutex is required for access.\n*/\nSQLITE_API int sqlite3_blob_bytes(sqlite3_blob *pBlob){\n  Incrblob *p = (Incrblob *)pBlob;\n  return (p && p->pStmt) ? p->nByte : 0;\n}\n\n/*\n** Move an existing blob handle to point to a different row of the same\n** database table.\n**\n** If an error occurs, or if the specified row does not exist or does not\n** contain a blob or text value, then an error code is returned and the\n** database handle error code and message set. If this happens, then all \n** subsequent calls to sqlite3_blob_xxx() functions (except blob_close()) \n** immediately return SQLITE_ABORT.\n*/\nSQLITE_API int sqlite3_blob_reopen(sqlite3_blob *pBlob, sqlite3_int64 iRow){\n  int rc;\n  Incrblob *p = (Incrblob *)pBlob;\n  sqlite3 *db;\n\n  if( p==0 ) return SQLITE_MISUSE_BKPT;\n  db = p->db;\n  sqlite3_mutex_enter(db->mutex);\n\n  if( p->pStmt==0 ){\n    /* If there is no statement handle, then the blob-handle has\n    ** already been invalidated. Return SQLITE_ABORT in this case.\n    */\n    rc = SQLITE_ABORT;\n  }else{\n    char *zErr;\n    rc = blobSeekToRow(p, iRow, &zErr);\n    if( rc!=SQLITE_OK ){\n      sqlite3ErrorWithMsg(db, rc, (zErr ? \"%s\" : 0), zErr);\n      sqlite3DbFree(db, zErr);\n    }\n    assert( rc!=SQLITE_SCHEMA );\n  }\n\n  rc = sqlite3ApiExit(db, rc);\n  assert( rc==SQLITE_OK || p->pStmt==0 );\n  sqlite3_mutex_leave(db->mutex);\n  return rc;\n}\n\n#endif /* #ifndef SQLITE_OMIT_INCRBLOB */\n\n/************** End of vdbeblob.c ********************************************/\n/************** Begin file vdbesort.c ****************************************/\n/*\n** 2011-07-09\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n*************************************************************************\n** This file contains code for the VdbeSorter object, used in concert with\n** a VdbeCursor to sort large numbers of keys for CREATE INDEX statements\n** or by SELECT statements with ORDER BY clauses that cannot be satisfied\n** using indexes and without LIMIT clauses.\n**\n** The VdbeSorter object implements a multi-threaded external merge sort\n** algorithm that is efficient even if the number of elements being sorted\n** exceeds the available memory.\n**\n** Here is the (internal, non-API) interface between this module and the\n** rest of the SQLite system:\n**\n**    sqlite3VdbeSorterInit()       Create a new VdbeSorter object.\n**\n**    sqlite3VdbeSorterWrite()      Add a single new row to the VdbeSorter\n**                                  object.  The row is a binary blob in the\n**                                  OP_MakeRecord format that contains both\n**                                  the ORDER BY key columns and result columns\n**                                  in the case of a SELECT w/ ORDER BY, or\n**                                  the complete record for an index entry\n**                                  in the case of a CREATE INDEX.\n**\n**    sqlite3VdbeSorterRewind()     Sort all content previously added.\n**                                  Position the read cursor on the\n**                                  first sorted element.\n**\n**    sqlite3VdbeSorterNext()       Advance the read cursor to the next sorted\n**                                  element.\n**\n**    sqlite3VdbeSorterRowkey()     Return the complete binary blob for the\n**                                  row currently under the read cursor.\n**\n**    sqlite3VdbeSorterCompare()    Compare the binary blob for the row\n**                                  currently under the read cursor against\n**                                  another binary blob X and report if\n**                                  X is strictly less than the read cursor.\n**                                  Used to enforce uniqueness in a\n**                                  CREATE UNIQUE INDEX statement.\n**\n**    sqlite3VdbeSorterClose()      Close the VdbeSorter object and reclaim\n**                                  all resources.\n**\n**    sqlite3VdbeSorterReset()      Refurbish the VdbeSorter for reuse.  This\n**                                  is like Close() followed by Init() only\n**                                  much faster.\n**\n** The interfaces above must be called in a particular order.  Write() can \n** only occur in between Init()/Reset() and Rewind().  Next(), Rowkey(), and\n** Compare() can only occur in between Rewind() and Close()/Reset(). i.e.\n**\n**   Init()\n**   for each record: Write()\n**   Rewind()\n**     Rowkey()/Compare()\n**   Next() \n**   Close()\n**\n** Algorithm:\n**\n** Records passed to the sorter via calls to Write() are initially held \n** unsorted in main memory. Assuming the amount of memory used never exceeds\n** a threshold, when Rewind() is called the set of records is sorted using\n** an in-memory merge sort. In this case, no temporary files are required\n** and subsequent calls to Rowkey(), Next() and Compare() read records \n** directly from main memory.\n**\n** If the amount of space used to store records in main memory exceeds the\n** threshold, then the set of records currently in memory are sorted and\n** written to a temporary file in \"Packed Memory Array\" (PMA) format.\n** A PMA created at this point is known as a \"level-0 PMA\". Higher levels\n** of PMAs may be created by merging existing PMAs together - for example\n** merging two or more level-0 PMAs together creates a level-1 PMA.\n**\n** The threshold for the amount of main memory to use before flushing \n** records to a PMA is roughly the same as the limit configured for the\n** page-cache of the main database. Specifically, the threshold is set to \n** the value returned by \"PRAGMA main.page_size\" multipled by \n** that returned by \"PRAGMA main.cache_size\", in bytes.\n**\n** If the sorter is running in single-threaded mode, then all PMAs generated\n** are appended to a single temporary file. Or, if the sorter is running in\n** multi-threaded mode then up to (N+1) temporary files may be opened, where\n** N is the configured number of worker threads. In this case, instead of\n** sorting the records and writing the PMA to a temporary file itself, the\n** calling thread usually launches a worker thread to do so. Except, if\n** there are already N worker threads running, the main thread does the work\n** itself.\n**\n** The sorter is running in multi-threaded mode if (a) the library was built\n** with pre-processor symbol SQLITE_MAX_WORKER_THREADS set to a value greater\n** than zero, and (b) worker threads have been enabled at runtime by calling\n** \"PRAGMA threads=N\" with some value of N greater than 0.\n**\n** When Rewind() is called, any data remaining in memory is flushed to a \n** final PMA. So at this point the data is stored in some number of sorted\n** PMAs within temporary files on disk.\n**\n** If there are fewer than SORTER_MAX_MERGE_COUNT PMAs in total and the\n** sorter is running in single-threaded mode, then these PMAs are merged\n** incrementally as keys are retreived from the sorter by the VDBE.  The\n** MergeEngine object, described in further detail below, performs this\n** merge.\n**\n** Or, if running in multi-threaded mode, then a background thread is\n** launched to merge the existing PMAs. Once the background thread has\n** merged T bytes of data into a single sorted PMA, the main thread \n** begins reading keys from that PMA while the background thread proceeds\n** with merging the next T bytes of data. And so on.\n**\n** Parameter T is set to half the value of the memory threshold used \n** by Write() above to determine when to create a new PMA.\n**\n** If there are more than SORTER_MAX_MERGE_COUNT PMAs in total when \n** Rewind() is called, then a hierarchy of incremental-merges is used. \n** First, T bytes of data from the first SORTER_MAX_MERGE_COUNT PMAs on \n** disk are merged together. Then T bytes of data from the second set, and\n** so on, such that no operation ever merges more than SORTER_MAX_MERGE_COUNT\n** PMAs at a time. This done is to improve locality.\n**\n** If running in multi-threaded mode and there are more than\n** SORTER_MAX_MERGE_COUNT PMAs on disk when Rewind() is called, then more\n** than one background thread may be created. Specifically, there may be\n** one background thread for each temporary file on disk, and one background\n** thread to merge the output of each of the others to a single PMA for\n** the main thread to read from.\n*/\n/* #include \"sqliteInt.h\" */\n/* #include \"vdbeInt.h\" */\n\n/* \n** If SQLITE_DEBUG_SORTER_THREADS is defined, this module outputs various\n** messages to stderr that may be helpful in understanding the performance\n** characteristics of the sorter in multi-threaded mode.\n*/\n#if 0\n# define SQLITE_DEBUG_SORTER_THREADS 1\n#endif\n\n/*\n** Hard-coded maximum amount of data to accumulate in memory before flushing\n** to a level 0 PMA. The purpose of this limit is to prevent various integer\n** overflows. 512MiB.\n*/\n#define SQLITE_MAX_PMASZ    (1<<29)\n\n/*\n** Private objects used by the sorter\n*/\ntypedef struct MergeEngine MergeEngine;     /* Merge PMAs together */\ntypedef struct PmaReader PmaReader;         /* Incrementally read one PMA */\ntypedef struct PmaWriter PmaWriter;         /* Incrementally write one PMA */\ntypedef struct SorterRecord SorterRecord;   /* A record being sorted */\ntypedef struct SortSubtask SortSubtask;     /* A sub-task in the sort process */\ntypedef struct SorterFile SorterFile;       /* Temporary file object wrapper */\ntypedef struct SorterList SorterList;       /* In-memory list of records */\ntypedef struct IncrMerger IncrMerger;       /* Read & merge multiple PMAs */\n\n/*\n** A container for a temp file handle and the current amount of data \n** stored in the file.\n*/\nstruct SorterFile {\n  sqlite3_file *pFd;              /* File handle */\n  i64 iEof;                       /* Bytes of data stored in pFd */\n};\n\n/*\n** An in-memory list of objects to be sorted.\n**\n** If aMemory==0 then each object is allocated separately and the objects\n** are connected using SorterRecord.u.pNext.  If aMemory!=0 then all objects\n** are stored in the aMemory[] bulk memory, one right after the other, and\n** are connected using SorterRecord.u.iNext.\n*/\nstruct SorterList {\n  SorterRecord *pList;            /* Linked list of records */\n  u8 *aMemory;                    /* If non-NULL, bulk memory to hold pList */\n  int szPMA;                      /* Size of pList as PMA in bytes */\n};\n\n/*\n** The MergeEngine object is used to combine two or more smaller PMAs into\n** one big PMA using a merge operation.  Separate PMAs all need to be\n** combined into one big PMA in order to be able to step through the sorted\n** records in order.\n**\n** The aReadr[] array contains a PmaReader object for each of the PMAs being\n** merged.  An aReadr[] object either points to a valid key or else is at EOF.\n** (\"EOF\" means \"End Of File\".  When aReadr[] is at EOF there is no more data.)\n** For the purposes of the paragraphs below, we assume that the array is\n** actually N elements in size, where N is the smallest power of 2 greater\n** to or equal to the number of PMAs being merged. The extra aReadr[] elements\n** are treated as if they are empty (always at EOF).\n**\n** The aTree[] array is also N elements in size. The value of N is stored in\n** the MergeEngine.nTree variable.\n**\n** The final (N/2) elements of aTree[] contain the results of comparing\n** pairs of PMA keys together. Element i contains the result of \n** comparing aReadr[2*i-N] and aReadr[2*i-N+1]. Whichever key is smaller, the\n** aTree element is set to the index of it. \n**\n** For the purposes of this comparison, EOF is considered greater than any\n** other key value. If the keys are equal (only possible with two EOF\n** values), it doesn't matter which index is stored.\n**\n** The (N/4) elements of aTree[] that precede the final (N/2) described \n** above contains the index of the smallest of each block of 4 PmaReaders\n** And so on. So that aTree[1] contains the index of the PmaReader that \n** currently points to the smallest key value. aTree[0] is unused.\n**\n** Example:\n**\n**     aReadr[0] -> Banana\n**     aReadr[1] -> Feijoa\n**     aReadr[2] -> Elderberry\n**     aReadr[3] -> Currant\n**     aReadr[4] -> Grapefruit\n**     aReadr[5] -> Apple\n**     aReadr[6] -> Durian\n**     aReadr[7] -> EOF\n**\n**     aTree[] = { X, 5   0, 5    0, 3, 5, 6 }\n**\n** The current element is \"Apple\" (the value of the key indicated by \n** PmaReader 5). When the Next() operation is invoked, PmaReader 5 will\n** be advanced to the next key in its segment. Say the next key is\n** \"Eggplant\":\n**\n**     aReadr[5] -> Eggplant\n**\n** The contents of aTree[] are updated first by comparing the new PmaReader\n** 5 key to the current key of PmaReader 4 (still \"Grapefruit\"). The PmaReader\n** 5 value is still smaller, so aTree[6] is set to 5. And so on up the tree.\n** The value of PmaReader 6 - \"Durian\" - is now smaller than that of PmaReader\n** 5, so aTree[3] is set to 6. Key 0 is smaller than key 6 (Banana<Durian),\n** so the value written into element 1 of the array is 0. As follows:\n**\n**     aTree[] = { X, 0   0, 6    0, 3, 5, 6 }\n**\n** In other words, each time we advance to the next sorter element, log2(N)\n** key comparison operations are required, where N is the number of segments\n** being merged (rounded up to the next power of 2).\n*/\nstruct MergeEngine {\n  int nTree;                 /* Used size of aTree/aReadr (power of 2) */\n  SortSubtask *pTask;        /* Used by this thread only */\n  int *aTree;                /* Current state of incremental merge */\n  PmaReader *aReadr;         /* Array of PmaReaders to merge data from */\n};\n\n/*\n** This object represents a single thread of control in a sort operation.\n** Exactly VdbeSorter.nTask instances of this object are allocated\n** as part of each VdbeSorter object. Instances are never allocated any\n** other way. VdbeSorter.nTask is set to the number of worker threads allowed\n** (see SQLITE_CONFIG_WORKER_THREADS) plus one (the main thread).  Thus for\n** single-threaded operation, there is exactly one instance of this object\n** and for multi-threaded operation there are two or more instances.\n**\n** Essentially, this structure contains all those fields of the VdbeSorter\n** structure for which each thread requires a separate instance. For example,\n** each thread requries its own UnpackedRecord object to unpack records in\n** as part of comparison operations.\n**\n** Before a background thread is launched, variable bDone is set to 0. Then, \n** right before it exits, the thread itself sets bDone to 1. This is used for \n** two purposes:\n**\n**   1. When flushing the contents of memory to a level-0 PMA on disk, to\n**      attempt to select a SortSubtask for which there is not already an\n**      active background thread (since doing so causes the main thread\n**      to block until it finishes).\n**\n**   2. If SQLITE_DEBUG_SORTER_THREADS is defined, to determine if a call\n**      to sqlite3ThreadJoin() is likely to block. Cases that are likely to\n**      block provoke debugging output.\n**\n** In both cases, the effects of the main thread seeing (bDone==0) even\n** after the thread has finished are not dire. So we don't worry about\n** memory barriers and such here.\n*/\ntypedef int (*SorterCompare)(SortSubtask*,int*,const void*,int,const void*,int);\nstruct SortSubtask {\n  SQLiteThread *pThread;          /* Background thread, if any */\n  int bDone;                      /* Set if thread is finished but not joined */\n  VdbeSorter *pSorter;            /* Sorter that owns this sub-task */\n  UnpackedRecord *pUnpacked;      /* Space to unpack a record */\n  SorterList list;                /* List for thread to write to a PMA */\n  int nPMA;                       /* Number of PMAs currently in file */\n  SorterCompare xCompare;         /* Compare function to use */\n  SorterFile file;                /* Temp file for level-0 PMAs */\n  SorterFile file2;               /* Space for other PMAs */\n};\n\n\n/*\n** Main sorter structure. A single instance of this is allocated for each \n** sorter cursor created by the VDBE.\n**\n** mxKeysize:\n**   As records are added to the sorter by calls to sqlite3VdbeSorterWrite(),\n**   this variable is updated so as to be set to the size on disk of the\n**   largest record in the sorter.\n*/\nstruct VdbeSorter {\n  int mnPmaSize;                  /* Minimum PMA size, in bytes */\n  int mxPmaSize;                  /* Maximum PMA size, in bytes.  0==no limit */\n  int mxKeysize;                  /* Largest serialized key seen so far */\n  int pgsz;                       /* Main database page size */\n  PmaReader *pReader;             /* Readr data from here after Rewind() */\n  MergeEngine *pMerger;           /* Or here, if bUseThreads==0 */\n  sqlite3 *db;                    /* Database connection */\n  KeyInfo *pKeyInfo;              /* How to compare records */\n  UnpackedRecord *pUnpacked;      /* Used by VdbeSorterCompare() */\n  SorterList list;                /* List of in-memory records */\n  int iMemory;                    /* Offset of free space in list.aMemory */\n  int nMemory;                    /* Size of list.aMemory allocation in bytes */\n  u8 bUsePMA;                     /* True if one or more PMAs created */\n  u8 bUseThreads;                 /* True to use background threads */\n  u8 iPrev;                       /* Previous thread used to flush PMA */\n  u8 nTask;                       /* Size of aTask[] array */\n  u8 typeMask;\n  SortSubtask aTask[1];           /* One or more subtasks */\n};\n\n#define SORTER_TYPE_INTEGER 0x01\n#define SORTER_TYPE_TEXT    0x02\n\n/*\n** An instance of the following object is used to read records out of a\n** PMA, in sorted order.  The next key to be read is cached in nKey/aKey.\n** aKey might point into aMap or into aBuffer.  If neither of those locations\n** contain a contiguous representation of the key, then aAlloc is allocated\n** and the key is copied into aAlloc and aKey is made to poitn to aAlloc.\n**\n** pFd==0 at EOF.\n*/\nstruct PmaReader {\n  i64 iReadOff;               /* Current read offset */\n  i64 iEof;                   /* 1 byte past EOF for this PmaReader */\n  int nAlloc;                 /* Bytes of space at aAlloc */\n  int nKey;                   /* Number of bytes in key */\n  sqlite3_file *pFd;          /* File handle we are reading from */\n  u8 *aAlloc;                 /* Space for aKey if aBuffer and pMap wont work */\n  u8 *aKey;                   /* Pointer to current key */\n  u8 *aBuffer;                /* Current read buffer */\n  int nBuffer;                /* Size of read buffer in bytes */\n  u8 *aMap;                   /* Pointer to mapping of entire file */\n  IncrMerger *pIncr;          /* Incremental merger */\n};\n\n/*\n** Normally, a PmaReader object iterates through an existing PMA stored \n** within a temp file. However, if the PmaReader.pIncr variable points to\n** an object of the following type, it may be used to iterate/merge through\n** multiple PMAs simultaneously.\n**\n** There are two types of IncrMerger object - single (bUseThread==0) and \n** multi-threaded (bUseThread==1). \n**\n** A multi-threaded IncrMerger object uses two temporary files - aFile[0] \n** and aFile[1]. Neither file is allowed to grow to more than mxSz bytes in \n** size. When the IncrMerger is initialized, it reads enough data from \n** pMerger to populate aFile[0]. It then sets variables within the \n** corresponding PmaReader object to read from that file and kicks off \n** a background thread to populate aFile[1] with the next mxSz bytes of \n** sorted record data from pMerger. \n**\n** When the PmaReader reaches the end of aFile[0], it blocks until the\n** background thread has finished populating aFile[1]. It then exchanges\n** the contents of the aFile[0] and aFile[1] variables within this structure,\n** sets the PmaReader fields to read from the new aFile[0] and kicks off\n** another background thread to populate the new aFile[1]. And so on, until\n** the contents of pMerger are exhausted.\n**\n** A single-threaded IncrMerger does not open any temporary files of its\n** own. Instead, it has exclusive access to mxSz bytes of space beginning\n** at offset iStartOff of file pTask->file2. And instead of using a \n** background thread to prepare data for the PmaReader, with a single\n** threaded IncrMerger the allocate part of pTask->file2 is \"refilled\" with\n** keys from pMerger by the calling thread whenever the PmaReader runs out\n** of data.\n*/\nstruct IncrMerger {\n  SortSubtask *pTask;             /* Task that owns this merger */\n  MergeEngine *pMerger;           /* Merge engine thread reads data from */\n  i64 iStartOff;                  /* Offset to start writing file at */\n  int mxSz;                       /* Maximum bytes of data to store */\n  int bEof;                       /* Set to true when merge is finished */\n  int bUseThread;                 /* True to use a bg thread for this object */\n  SorterFile aFile[2];            /* aFile[0] for reading, [1] for writing */\n};\n\n/*\n** An instance of this object is used for writing a PMA.\n**\n** The PMA is written one record at a time.  Each record is of an arbitrary\n** size.  But I/O is more efficient if it occurs in page-sized blocks where\n** each block is aligned on a page boundary.  This object caches writes to\n** the PMA so that aligned, page-size blocks are written.\n*/\nstruct PmaWriter {\n  int eFWErr;                     /* Non-zero if in an error state */\n  u8 *aBuffer;                    /* Pointer to write buffer */\n  int nBuffer;                    /* Size of write buffer in bytes */\n  int iBufStart;                  /* First byte of buffer to write */\n  int iBufEnd;                    /* Last byte of buffer to write */\n  i64 iWriteOff;                  /* Offset of start of buffer in file */\n  sqlite3_file *pFd;              /* File handle to write to */\n};\n\n/*\n** This object is the header on a single record while that record is being\n** held in memory and prior to being written out as part of a PMA.\n**\n** How the linked list is connected depends on how memory is being managed\n** by this module. If using a separate allocation for each in-memory record\n** (VdbeSorter.list.aMemory==0), then the list is always connected using the\n** SorterRecord.u.pNext pointers.\n**\n** Or, if using the single large allocation method (VdbeSorter.list.aMemory!=0),\n** then while records are being accumulated the list is linked using the\n** SorterRecord.u.iNext offset. This is because the aMemory[] array may\n** be sqlite3Realloc()ed while records are being accumulated. Once the VM\n** has finished passing records to the sorter, or when the in-memory buffer\n** is full, the list is sorted. As part of the sorting process, it is\n** converted to use the SorterRecord.u.pNext pointers. See function\n** vdbeSorterSort() for details.\n*/\nstruct SorterRecord {\n  int nVal;                       /* Size of the record in bytes */\n  union {\n    SorterRecord *pNext;          /* Pointer to next record in list */\n    int iNext;                    /* Offset within aMemory of next record */\n  } u;\n  /* The data for the record immediately follows this header */\n};\n\n/* Return a pointer to the buffer containing the record data for SorterRecord\n** object p. Should be used as if:\n**\n**   void *SRVAL(SorterRecord *p) { return (void*)&p[1]; }\n*/\n#define SRVAL(p) ((void*)((SorterRecord*)(p) + 1))\n\n\n/* Maximum number of PMAs that a single MergeEngine can merge */\n#define SORTER_MAX_MERGE_COUNT 16\n\nstatic int vdbeIncrSwap(IncrMerger*);\nstatic void vdbeIncrFree(IncrMerger *);\n\n/*\n** Free all memory belonging to the PmaReader object passed as the\n** argument. All structure fields are set to zero before returning.\n*/\nstatic void vdbePmaReaderClear(PmaReader *pReadr){\n  sqlite3_free(pReadr->aAlloc);\n  sqlite3_free(pReadr->aBuffer);\n  if( pReadr->aMap ) sqlite3OsUnfetch(pReadr->pFd, 0, pReadr->aMap);\n  vdbeIncrFree(pReadr->pIncr);\n  memset(pReadr, 0, sizeof(PmaReader));\n}\n\n/*\n** Read the next nByte bytes of data from the PMA p.\n** If successful, set *ppOut to point to a buffer containing the data\n** and return SQLITE_OK. Otherwise, if an error occurs, return an SQLite\n** error code.\n**\n** The buffer returned in *ppOut is only valid until the\n** next call to this function.\n*/\nstatic int vdbePmaReadBlob(\n  PmaReader *p,                   /* PmaReader from which to take the blob */\n  int nByte,                      /* Bytes of data to read */\n  u8 **ppOut                      /* OUT: Pointer to buffer containing data */\n){\n  int iBuf;                       /* Offset within buffer to read from */\n  int nAvail;                     /* Bytes of data available in buffer */\n\n  if( p->aMap ){\n    *ppOut = &p->aMap[p->iReadOff];\n    p->iReadOff += nByte;\n    return SQLITE_OK;\n  }\n\n  assert( p->aBuffer );\n\n  /* If there is no more data to be read from the buffer, read the next \n  ** p->nBuffer bytes of data from the file into it. Or, if there are less\n  ** than p->nBuffer bytes remaining in the PMA, read all remaining data.  */\n  iBuf = p->iReadOff % p->nBuffer;\n  if( iBuf==0 ){\n    int nRead;                    /* Bytes to read from disk */\n    int rc;                       /* sqlite3OsRead() return code */\n\n    /* Determine how many bytes of data to read. */\n    if( (p->iEof - p->iReadOff) > (i64)p->nBuffer ){\n      nRead = p->nBuffer;\n    }else{\n      nRead = (int)(p->iEof - p->iReadOff);\n    }\n    assert( nRead>0 );\n\n    /* Readr data from the file. Return early if an error occurs. */\n    rc = sqlite3OsRead(p->pFd, p->aBuffer, nRead, p->iReadOff);\n    assert( rc!=SQLITE_IOERR_SHORT_READ );\n    if( rc!=SQLITE_OK ) return rc;\n  }\n  nAvail = p->nBuffer - iBuf; \n\n  if( nByte<=nAvail ){\n    /* The requested data is available in the in-memory buffer. In this\n    ** case there is no need to make a copy of the data, just return a \n    ** pointer into the buffer to the caller.  */\n    *ppOut = &p->aBuffer[iBuf];\n    p->iReadOff += nByte;\n  }else{\n    /* The requested data is not all available in the in-memory buffer.\n    ** In this case, allocate space at p->aAlloc[] to copy the requested\n    ** range into. Then return a copy of pointer p->aAlloc to the caller.  */\n    int nRem;                     /* Bytes remaining to copy */\n\n    /* Extend the p->aAlloc[] allocation if required. */\n    if( p->nAlloc<nByte ){\n      u8 *aNew;\n      int nNew = MAX(128, p->nAlloc*2);\n      while( nByte>nNew ) nNew = nNew*2;\n      aNew = sqlite3Realloc(p->aAlloc, nNew);\n      if( !aNew ) return SQLITE_NOMEM_BKPT;\n      p->nAlloc = nNew;\n      p->aAlloc = aNew;\n    }\n\n    /* Copy as much data as is available in the buffer into the start of\n    ** p->aAlloc[].  */\n    memcpy(p->aAlloc, &p->aBuffer[iBuf], nAvail);\n    p->iReadOff += nAvail;\n    nRem = nByte - nAvail;\n\n    /* The following loop copies up to p->nBuffer bytes per iteration into\n    ** the p->aAlloc[] buffer.  */\n    while( nRem>0 ){\n      int rc;                     /* vdbePmaReadBlob() return code */\n      int nCopy;                  /* Number of bytes to copy */\n      u8 *aNext;                  /* Pointer to buffer to copy data from */\n\n      nCopy = nRem;\n      if( nRem>p->nBuffer ) nCopy = p->nBuffer;\n      rc = vdbePmaReadBlob(p, nCopy, &aNext);\n      if( rc!=SQLITE_OK ) return rc;\n      assert( aNext!=p->aAlloc );\n      memcpy(&p->aAlloc[nByte - nRem], aNext, nCopy);\n      nRem -= nCopy;\n    }\n\n    *ppOut = p->aAlloc;\n  }\n\n  return SQLITE_OK;\n}\n\n/*\n** Read a varint from the stream of data accessed by p. Set *pnOut to\n** the value read.\n*/\nstatic int vdbePmaReadVarint(PmaReader *p, u64 *pnOut){\n  int iBuf;\n\n  if( p->aMap ){\n    p->iReadOff += sqlite3GetVarint(&p->aMap[p->iReadOff], pnOut);\n  }else{\n    iBuf = p->iReadOff % p->nBuffer;\n    if( iBuf && (p->nBuffer-iBuf)>=9 ){\n      p->iReadOff += sqlite3GetVarint(&p->aBuffer[iBuf], pnOut);\n    }else{\n      u8 aVarint[16], *a;\n      int i = 0, rc;\n      do{\n        rc = vdbePmaReadBlob(p, 1, &a);\n        if( rc ) return rc;\n        aVarint[(i++)&0xf] = a[0];\n      }while( (a[0]&0x80)!=0 );\n      sqlite3GetVarint(aVarint, pnOut);\n    }\n  }\n\n  return SQLITE_OK;\n}\n\n/*\n** Attempt to memory map file pFile. If successful, set *pp to point to the\n** new mapping and return SQLITE_OK. If the mapping is not attempted \n** (because the file is too large or the VFS layer is configured not to use\n** mmap), return SQLITE_OK and set *pp to NULL.\n**\n** Or, if an error occurs, return an SQLite error code. The final value of\n** *pp is undefined in this case.\n*/\nstatic int vdbeSorterMapFile(SortSubtask *pTask, SorterFile *pFile, u8 **pp){\n  int rc = SQLITE_OK;\n  if( pFile->iEof<=(i64)(pTask->pSorter->db->nMaxSorterMmap) ){\n    sqlite3_file *pFd = pFile->pFd;\n    if( pFd->pMethods->iVersion>=3 ){\n      rc = sqlite3OsFetch(pFd, 0, (int)pFile->iEof, (void**)pp);\n      testcase( rc!=SQLITE_OK );\n    }\n  }\n  return rc;\n}\n\n/*\n** Attach PmaReader pReadr to file pFile (if it is not already attached to\n** that file) and seek it to offset iOff within the file.  Return SQLITE_OK \n** if successful, or an SQLite error code if an error occurs.\n*/\nstatic int vdbePmaReaderSeek(\n  SortSubtask *pTask,             /* Task context */\n  PmaReader *pReadr,              /* Reader whose cursor is to be moved */\n  SorterFile *pFile,              /* Sorter file to read from */\n  i64 iOff                        /* Offset in pFile */\n){\n  int rc = SQLITE_OK;\n\n  assert( pReadr->pIncr==0 || pReadr->pIncr->bEof==0 );\n\n  if( sqlite3FaultSim(201) ) return SQLITE_IOERR_READ;\n  if( pReadr->aMap ){\n    sqlite3OsUnfetch(pReadr->pFd, 0, pReadr->aMap);\n    pReadr->aMap = 0;\n  }\n  pReadr->iReadOff = iOff;\n  pReadr->iEof = pFile->iEof;\n  pReadr->pFd = pFile->pFd;\n\n  rc = vdbeSorterMapFile(pTask, pFile, &pReadr->aMap);\n  if( rc==SQLITE_OK && pReadr->aMap==0 ){\n    int pgsz = pTask->pSorter->pgsz;\n    int iBuf = pReadr->iReadOff % pgsz;\n    if( pReadr->aBuffer==0 ){\n      pReadr->aBuffer = (u8*)sqlite3Malloc(pgsz);\n      if( pReadr->aBuffer==0 ) rc = SQLITE_NOMEM_BKPT;\n      pReadr->nBuffer = pgsz;\n    }\n    if( rc==SQLITE_OK && iBuf ){\n      int nRead = pgsz - iBuf;\n      if( (pReadr->iReadOff + nRead) > pReadr->iEof ){\n        nRead = (int)(pReadr->iEof - pReadr->iReadOff);\n      }\n      rc = sqlite3OsRead(\n          pReadr->pFd, &pReadr->aBuffer[iBuf], nRead, pReadr->iReadOff\n      );\n      testcase( rc!=SQLITE_OK );\n    }\n  }\n\n  return rc;\n}\n\n/*\n** Advance PmaReader pReadr to the next key in its PMA. Return SQLITE_OK if\n** no error occurs, or an SQLite error code if one does.\n*/\nstatic int vdbePmaReaderNext(PmaReader *pReadr){\n  int rc = SQLITE_OK;             /* Return Code */\n  u64 nRec = 0;                   /* Size of record in bytes */\n\n\n  if( pReadr->iReadOff>=pReadr->iEof ){\n    IncrMerger *pIncr = pReadr->pIncr;\n    int bEof = 1;\n    if( pIncr ){\n      rc = vdbeIncrSwap(pIncr);\n      if( rc==SQLITE_OK && pIncr->bEof==0 ){\n        rc = vdbePmaReaderSeek(\n            pIncr->pTask, pReadr, &pIncr->aFile[0], pIncr->iStartOff\n        );\n        bEof = 0;\n      }\n    }\n\n    if( bEof ){\n      /* This is an EOF condition */\n      vdbePmaReaderClear(pReadr);\n      testcase( rc!=SQLITE_OK );\n      return rc;\n    }\n  }\n\n  if( rc==SQLITE_OK ){\n    rc = vdbePmaReadVarint(pReadr, &nRec);\n  }\n  if( rc==SQLITE_OK ){\n    pReadr->nKey = (int)nRec;\n    rc = vdbePmaReadBlob(pReadr, (int)nRec, &pReadr->aKey);\n    testcase( rc!=SQLITE_OK );\n  }\n\n  return rc;\n}\n\n/*\n** Initialize PmaReader pReadr to scan through the PMA stored in file pFile\n** starting at offset iStart and ending at offset iEof-1. This function \n** leaves the PmaReader pointing to the first key in the PMA (or EOF if the \n** PMA is empty).\n**\n** If the pnByte parameter is NULL, then it is assumed that the file \n** contains a single PMA, and that that PMA omits the initial length varint.\n*/\nstatic int vdbePmaReaderInit(\n  SortSubtask *pTask,             /* Task context */\n  SorterFile *pFile,              /* Sorter file to read from */\n  i64 iStart,                     /* Start offset in pFile */\n  PmaReader *pReadr,              /* PmaReader to populate */\n  i64 *pnByte                     /* IN/OUT: Increment this value by PMA size */\n){\n  int rc;\n\n  assert( pFile->iEof>iStart );\n  assert( pReadr->aAlloc==0 && pReadr->nAlloc==0 );\n  assert( pReadr->aBuffer==0 );\n  assert( pReadr->aMap==0 );\n\n  rc = vdbePmaReaderSeek(pTask, pReadr, pFile, iStart);\n  if( rc==SQLITE_OK ){\n    u64 nByte = 0;                 /* Size of PMA in bytes */\n    rc = vdbePmaReadVarint(pReadr, &nByte);\n    pReadr->iEof = pReadr->iReadOff + nByte;\n    *pnByte += nByte;\n  }\n\n  if( rc==SQLITE_OK ){\n    rc = vdbePmaReaderNext(pReadr);\n  }\n  return rc;\n}\n\n/*\n** A version of vdbeSorterCompare() that assumes that it has already been\n** determined that the first field of key1 is equal to the first field of \n** key2.\n*/\nstatic int vdbeSorterCompareTail(\n  SortSubtask *pTask,             /* Subtask context (for pKeyInfo) */\n  int *pbKey2Cached,              /* True if pTask->pUnpacked is pKey2 */\n  const void *pKey1, int nKey1,   /* Left side of comparison */\n  const void *pKey2, int nKey2    /* Right side of comparison */\n){\n  UnpackedRecord *r2 = pTask->pUnpacked;\n  if( *pbKey2Cached==0 ){\n    sqlite3VdbeRecordUnpack(pTask->pSorter->pKeyInfo, nKey2, pKey2, r2);\n    *pbKey2Cached = 1;\n  }\n  return sqlite3VdbeRecordCompareWithSkip(nKey1, pKey1, r2, 1);\n}\n\n/*\n** Compare key1 (buffer pKey1, size nKey1 bytes) with key2 (buffer pKey2, \n** size nKey2 bytes). Use (pTask->pKeyInfo) for the collation sequences\n** used by the comparison. Return the result of the comparison.\n**\n** If IN/OUT parameter *pbKey2Cached is true when this function is called,\n** it is assumed that (pTask->pUnpacked) contains the unpacked version\n** of key2. If it is false, (pTask->pUnpacked) is populated with the unpacked\n** version of key2 and *pbKey2Cached set to true before returning.\n**\n** If an OOM error is encountered, (pTask->pUnpacked->error_rc) is set\n** to SQLITE_NOMEM.\n*/\nstatic int vdbeSorterCompare(\n  SortSubtask *pTask,             /* Subtask context (for pKeyInfo) */\n  int *pbKey2Cached,              /* True if pTask->pUnpacked is pKey2 */\n  const void *pKey1, int nKey1,   /* Left side of comparison */\n  const void *pKey2, int nKey2    /* Right side of comparison */\n){\n  UnpackedRecord *r2 = pTask->pUnpacked;\n  if( !*pbKey2Cached ){\n    sqlite3VdbeRecordUnpack(pTask->pSorter->pKeyInfo, nKey2, pKey2, r2);\n    *pbKey2Cached = 1;\n  }\n  return sqlite3VdbeRecordCompare(nKey1, pKey1, r2);\n}\n\n/*\n** A specially optimized version of vdbeSorterCompare() that assumes that\n** the first field of each key is a TEXT value and that the collation\n** sequence to compare them with is BINARY.\n*/\nstatic int vdbeSorterCompareText(\n  SortSubtask *pTask,             /* Subtask context (for pKeyInfo) */\n  int *pbKey2Cached,              /* True if pTask->pUnpacked is pKey2 */\n  const void *pKey1, int nKey1,   /* Left side of comparison */\n  const void *pKey2, int nKey2    /* Right side of comparison */\n){\n  const u8 * const p1 = (const u8 * const)pKey1;\n  const u8 * const p2 = (const u8 * const)pKey2;\n  const u8 * const v1 = &p1[ p1[0] ];   /* Pointer to value 1 */\n  const u8 * const v2 = &p2[ p2[0] ];   /* Pointer to value 2 */\n\n  int n1;\n  int n2;\n  int res;\n\n  getVarint32(&p1[1], n1);\n  getVarint32(&p2[1], n2);\n  res = memcmp(v1, v2, (MIN(n1, n2) - 13)/2);\n  if( res==0 ){\n    res = n1 - n2;\n  }\n\n  if( res==0 ){\n    if( pTask->pSorter->pKeyInfo->nKeyField>1 ){\n      res = vdbeSorterCompareTail(\n          pTask, pbKey2Cached, pKey1, nKey1, pKey2, nKey2\n      );\n    }\n  }else{\n    if( pTask->pSorter->pKeyInfo->aSortOrder[0] ){\n      res = res * -1;\n    }\n  }\n\n  return res;\n}\n\n/*\n** A specially optimized version of vdbeSorterCompare() that assumes that\n** the first field of each key is an INTEGER value.\n*/\nstatic int vdbeSorterCompareInt(\n  SortSubtask *pTask,             /* Subtask context (for pKeyInfo) */\n  int *pbKey2Cached,              /* True if pTask->pUnpacked is pKey2 */\n  const void *pKey1, int nKey1,   /* Left side of comparison */\n  const void *pKey2, int nKey2    /* Right side of comparison */\n){\n  const u8 * const p1 = (const u8 * const)pKey1;\n  const u8 * const p2 = (const u8 * const)pKey2;\n  const int s1 = p1[1];                 /* Left hand serial type */\n  const int s2 = p2[1];                 /* Right hand serial type */\n  const u8 * const v1 = &p1[ p1[0] ];   /* Pointer to value 1 */\n  const u8 * const v2 = &p2[ p2[0] ];   /* Pointer to value 2 */\n  int res;                              /* Return value */\n\n  assert( (s1>0 && s1<7) || s1==8 || s1==9 );\n  assert( (s2>0 && s2<7) || s2==8 || s2==9 );\n\n  if( s1==s2 ){\n    /* The two values have the same sign. Compare using memcmp(). */\n    static const u8 aLen[] = {0, 1, 2, 3, 4, 6, 8, 0, 0, 0 };\n    const u8 n = aLen[s1];\n    int i;\n    res = 0;\n    for(i=0; i<n; i++){\n      if( (res = v1[i] - v2[i])!=0 ){\n        if( ((v1[0] ^ v2[0]) & 0x80)!=0 ){\n          res = v1[0] & 0x80 ? -1 : +1;\n        }\n        break;\n      }\n    }\n  }else if( s1>7 && s2>7 ){\n    res = s1 - s2;\n  }else{\n    if( s2>7 ){\n      res = +1;\n    }else if( s1>7 ){\n      res = -1;\n    }else{\n      res = s1 - s2;\n    }\n    assert( res!=0 );\n\n    if( res>0 ){\n      if( *v1 & 0x80 ) res = -1;\n    }else{\n      if( *v2 & 0x80 ) res = +1;\n    }\n  }\n\n  if( res==0 ){\n    if( pTask->pSorter->pKeyInfo->nKeyField>1 ){\n      res = vdbeSorterCompareTail(\n          pTask, pbKey2Cached, pKey1, nKey1, pKey2, nKey2\n      );\n    }\n  }else if( pTask->pSorter->pKeyInfo->aSortOrder[0] ){\n    res = res * -1;\n  }\n\n  return res;\n}\n\n/*\n** Initialize the temporary index cursor just opened as a sorter cursor.\n**\n** Usually, the sorter module uses the value of (pCsr->pKeyInfo->nKeyField)\n** to determine the number of fields that should be compared from the\n** records being sorted. However, if the value passed as argument nField\n** is non-zero and the sorter is able to guarantee a stable sort, nField\n** is used instead. This is used when sorting records for a CREATE INDEX\n** statement. In this case, keys are always delivered to the sorter in\n** order of the primary key, which happens to be make up the final part \n** of the records being sorted. So if the sort is stable, there is never\n** any reason to compare PK fields and they can be ignored for a small\n** performance boost.\n**\n** The sorter can guarantee a stable sort when running in single-threaded\n** mode, but not in multi-threaded mode.\n**\n** SQLITE_OK is returned if successful, or an SQLite error code otherwise.\n*/\nSQLITE_PRIVATE int sqlite3VdbeSorterInit(\n  sqlite3 *db,                    /* Database connection (for malloc()) */\n  int nField,                     /* Number of key fields in each record */\n  VdbeCursor *pCsr                /* Cursor that holds the new sorter */\n){\n  int pgsz;                       /* Page size of main database */\n  int i;                          /* Used to iterate through aTask[] */\n  VdbeSorter *pSorter;            /* The new sorter */\n  KeyInfo *pKeyInfo;              /* Copy of pCsr->pKeyInfo with db==0 */\n  int szKeyInfo;                  /* Size of pCsr->pKeyInfo in bytes */\n  int sz;                         /* Size of pSorter in bytes */\n  int rc = SQLITE_OK;\n#if SQLITE_MAX_WORKER_THREADS==0\n# define nWorker 0\n#else\n  int nWorker;\n#endif\n\n  /* Initialize the upper limit on the number of worker threads */\n#if SQLITE_MAX_WORKER_THREADS>0\n  if( sqlite3TempInMemory(db) || sqlite3GlobalConfig.bCoreMutex==0 ){\n    nWorker = 0;\n  }else{\n    nWorker = db->aLimit[SQLITE_LIMIT_WORKER_THREADS];\n  }\n#endif\n\n  /* Do not allow the total number of threads (main thread + all workers)\n  ** to exceed the maximum merge count */\n#if SQLITE_MAX_WORKER_THREADS>=SORTER_MAX_MERGE_COUNT\n  if( nWorker>=SORTER_MAX_MERGE_COUNT ){\n    nWorker = SORTER_MAX_MERGE_COUNT-1;\n  }\n#endif\n\n  assert( pCsr->pKeyInfo && pCsr->pBtx==0 );\n  assert( pCsr->eCurType==CURTYPE_SORTER );\n  szKeyInfo = sizeof(KeyInfo) + (pCsr->pKeyInfo->nKeyField-1)*sizeof(CollSeq*);\n  sz = sizeof(VdbeSorter) + nWorker * sizeof(SortSubtask);\n\n  pSorter = (VdbeSorter*)sqlite3DbMallocZero(db, sz + szKeyInfo);\n  pCsr->uc.pSorter = pSorter;\n  if( pSorter==0 ){\n    rc = SQLITE_NOMEM_BKPT;\n  }else{\n    pSorter->pKeyInfo = pKeyInfo = (KeyInfo*)((u8*)pSorter + sz);\n    memcpy(pKeyInfo, pCsr->pKeyInfo, szKeyInfo);\n    pKeyInfo->db = 0;\n    if( nField && nWorker==0 ){\n      pKeyInfo->nKeyField = nField;\n    }\n    pSorter->pgsz = pgsz = sqlite3BtreeGetPageSize(db->aDb[0].pBt);\n    pSorter->nTask = nWorker + 1;\n    pSorter->iPrev = (u8)(nWorker - 1);\n    pSorter->bUseThreads = (pSorter->nTask>1);\n    pSorter->db = db;\n    for(i=0; i<pSorter->nTask; i++){\n      SortSubtask *pTask = &pSorter->aTask[i];\n      pTask->pSorter = pSorter;\n    }\n\n    if( !sqlite3TempInMemory(db) ){\n      i64 mxCache;                /* Cache size in bytes*/\n      u32 szPma = sqlite3GlobalConfig.szPma;\n      pSorter->mnPmaSize = szPma * pgsz;\n\n      mxCache = db->aDb[0].pSchema->cache_size;\n      if( mxCache<0 ){\n        /* A negative cache-size value C indicates that the cache is abs(C)\n        ** KiB in size.  */\n        mxCache = mxCache * -1024;\n      }else{\n        mxCache = mxCache * pgsz;\n      }\n      mxCache = MIN(mxCache, SQLITE_MAX_PMASZ);\n      pSorter->mxPmaSize = MAX(pSorter->mnPmaSize, (int)mxCache);\n\n      /* Avoid large memory allocations if the application has requested\n      ** SQLITE_CONFIG_SMALL_MALLOC. */\n      if( sqlite3GlobalConfig.bSmallMalloc==0 ){\n        assert( pSorter->iMemory==0 );\n        pSorter->nMemory = pgsz;\n        pSorter->list.aMemory = (u8*)sqlite3Malloc(pgsz);\n        if( !pSorter->list.aMemory ) rc = SQLITE_NOMEM_BKPT;\n      }\n    }\n\n    if( pKeyInfo->nAllField<13 \n     && (pKeyInfo->aColl[0]==0 || pKeyInfo->aColl[0]==db->pDfltColl)\n    ){\n      pSorter->typeMask = SORTER_TYPE_INTEGER | SORTER_TYPE_TEXT;\n    }\n  }\n\n  return rc;\n}\n#undef nWorker   /* Defined at the top of this function */\n\n/*\n** Free the list of sorted records starting at pRecord.\n*/\nstatic void vdbeSorterRecordFree(sqlite3 *db, SorterRecord *pRecord){\n  SorterRecord *p;\n  SorterRecord *pNext;\n  for(p=pRecord; p; p=pNext){\n    pNext = p->u.pNext;\n    sqlite3DbFree(db, p);\n  }\n}\n\n/*\n** Free all resources owned by the object indicated by argument pTask. All \n** fields of *pTask are zeroed before returning.\n*/\nstatic void vdbeSortSubtaskCleanup(sqlite3 *db, SortSubtask *pTask){\n  sqlite3DbFree(db, pTask->pUnpacked);\n#if SQLITE_MAX_WORKER_THREADS>0\n  /* pTask->list.aMemory can only be non-zero if it was handed memory\n  ** from the main thread.  That only occurs SQLITE_MAX_WORKER_THREADS>0 */\n  if( pTask->list.aMemory ){\n    sqlite3_free(pTask->list.aMemory);\n  }else\n#endif\n  {\n    assert( pTask->list.aMemory==0 );\n    vdbeSorterRecordFree(0, pTask->list.pList);\n  }\n  if( pTask->file.pFd ){\n    sqlite3OsCloseFree(pTask->file.pFd);\n  }\n  if( pTask->file2.pFd ){\n    sqlite3OsCloseFree(pTask->file2.pFd);\n  }\n  memset(pTask, 0, sizeof(SortSubtask));\n}\n\n#ifdef SQLITE_DEBUG_SORTER_THREADS\nstatic void vdbeSorterWorkDebug(SortSubtask *pTask, const char *zEvent){\n  i64 t;\n  int iTask = (pTask - pTask->pSorter->aTask);\n  sqlite3OsCurrentTimeInt64(pTask->pSorter->db->pVfs, &t);\n  fprintf(stderr, \"%lld:%d %s\\n\", t, iTask, zEvent);\n}\nstatic void vdbeSorterRewindDebug(const char *zEvent){\n  i64 t;\n  sqlite3OsCurrentTimeInt64(sqlite3_vfs_find(0), &t);\n  fprintf(stderr, \"%lld:X %s\\n\", t, zEvent);\n}\nstatic void vdbeSorterPopulateDebug(\n  SortSubtask *pTask,\n  const char *zEvent\n){\n  i64 t;\n  int iTask = (pTask - pTask->pSorter->aTask);\n  sqlite3OsCurrentTimeInt64(pTask->pSorter->db->pVfs, &t);\n  fprintf(stderr, \"%lld:bg%d %s\\n\", t, iTask, zEvent);\n}\nstatic void vdbeSorterBlockDebug(\n  SortSubtask *pTask,\n  int bBlocked,\n  const char *zEvent\n){\n  if( bBlocked ){\n    i64 t;\n    sqlite3OsCurrentTimeInt64(pTask->pSorter->db->pVfs, &t);\n    fprintf(stderr, \"%lld:main %s\\n\", t, zEvent);\n  }\n}\n#else\n# define vdbeSorterWorkDebug(x,y)\n# define vdbeSorterRewindDebug(y)\n# define vdbeSorterPopulateDebug(x,y)\n# define vdbeSorterBlockDebug(x,y,z)\n#endif\n\n#if SQLITE_MAX_WORKER_THREADS>0\n/*\n** Join thread pTask->thread.\n*/\nstatic int vdbeSorterJoinThread(SortSubtask *pTask){\n  int rc = SQLITE_OK;\n  if( pTask->pThread ){\n#ifdef SQLITE_DEBUG_SORTER_THREADS\n    int bDone = pTask->bDone;\n#endif\n    void *pRet = SQLITE_INT_TO_PTR(SQLITE_ERROR);\n    vdbeSorterBlockDebug(pTask, !bDone, \"enter\");\n    (void)sqlite3ThreadJoin(pTask->pThread, &pRet);\n    vdbeSorterBlockDebug(pTask, !bDone, \"exit\");\n    rc = SQLITE_PTR_TO_INT(pRet);\n    assert( pTask->bDone==1 );\n    pTask->bDone = 0;\n    pTask->pThread = 0;\n  }\n  return rc;\n}\n\n/*\n** Launch a background thread to run xTask(pIn).\n*/\nstatic int vdbeSorterCreateThread(\n  SortSubtask *pTask,             /* Thread will use this task object */\n  void *(*xTask)(void*),          /* Routine to run in a separate thread */\n  void *pIn                       /* Argument passed into xTask() */\n){\n  assert( pTask->pThread==0 && pTask->bDone==0 );\n  return sqlite3ThreadCreate(&pTask->pThread, xTask, pIn);\n}\n\n/*\n** Join all outstanding threads launched by SorterWrite() to create \n** level-0 PMAs.\n*/\nstatic int vdbeSorterJoinAll(VdbeSorter *pSorter, int rcin){\n  int rc = rcin;\n  int i;\n\n  /* This function is always called by the main user thread.\n  **\n  ** If this function is being called after SorterRewind() has been called, \n  ** it is possible that thread pSorter->aTask[pSorter->nTask-1].pThread\n  ** is currently attempt to join one of the other threads. To avoid a race\n  ** condition where this thread also attempts to join the same object, join \n  ** thread pSorter->aTask[pSorter->nTask-1].pThread first. */\n  for(i=pSorter->nTask-1; i>=0; i--){\n    SortSubtask *pTask = &pSorter->aTask[i];\n    int rc2 = vdbeSorterJoinThread(pTask);\n    if( rc==SQLITE_OK ) rc = rc2;\n  }\n  return rc;\n}\n#else\n# define vdbeSorterJoinAll(x,rcin) (rcin)\n# define vdbeSorterJoinThread(pTask) SQLITE_OK\n#endif\n\n/*\n** Allocate a new MergeEngine object capable of handling up to\n** nReader PmaReader inputs.\n**\n** nReader is automatically rounded up to the next power of two.\n** nReader may not exceed SORTER_MAX_MERGE_COUNT even after rounding up.\n*/\nstatic MergeEngine *vdbeMergeEngineNew(int nReader){\n  int N = 2;                      /* Smallest power of two >= nReader */\n  int nByte;                      /* Total bytes of space to allocate */\n  MergeEngine *pNew;              /* Pointer to allocated object to return */\n\n  assert( nReader<=SORTER_MAX_MERGE_COUNT );\n\n  while( N<nReader ) N += N;\n  nByte = sizeof(MergeEngine) + N * (sizeof(int) + sizeof(PmaReader));\n\n  pNew = sqlite3FaultSim(100) ? 0 : (MergeEngine*)sqlite3MallocZero(nByte);\n  if( pNew ){\n    pNew->nTree = N;\n    pNew->pTask = 0;\n    pNew->aReadr = (PmaReader*)&pNew[1];\n    pNew->aTree = (int*)&pNew->aReadr[N];\n  }\n  return pNew;\n}\n\n/*\n** Free the MergeEngine object passed as the only argument.\n*/\nstatic void vdbeMergeEngineFree(MergeEngine *pMerger){\n  int i;\n  if( pMerger ){\n    for(i=0; i<pMerger->nTree; i++){\n      vdbePmaReaderClear(&pMerger->aReadr[i]);\n    }\n  }\n  sqlite3_free(pMerger);\n}\n\n/*\n** Free all resources associated with the IncrMerger object indicated by\n** the first argument.\n*/\nstatic void vdbeIncrFree(IncrMerger *pIncr){\n  if( pIncr ){\n#if SQLITE_MAX_WORKER_THREADS>0\n    if( pIncr->bUseThread ){\n      vdbeSorterJoinThread(pIncr->pTask);\n      if( pIncr->aFile[0].pFd ) sqlite3OsCloseFree(pIncr->aFile[0].pFd);\n      if( pIncr->aFile[1].pFd ) sqlite3OsCloseFree(pIncr->aFile[1].pFd);\n    }\n#endif\n    vdbeMergeEngineFree(pIncr->pMerger);\n    sqlite3_free(pIncr);\n  }\n}\n\n/*\n** Reset a sorting cursor back to its original empty state.\n*/\nSQLITE_PRIVATE void sqlite3VdbeSorterReset(sqlite3 *db, VdbeSorter *pSorter){\n  int i;\n  (void)vdbeSorterJoinAll(pSorter, SQLITE_OK);\n  assert( pSorter->bUseThreads || pSorter->pReader==0 );\n#if SQLITE_MAX_WORKER_THREADS>0\n  if( pSorter->pReader ){\n    vdbePmaReaderClear(pSorter->pReader);\n    sqlite3DbFree(db, pSorter->pReader);\n    pSorter->pReader = 0;\n  }\n#endif\n  vdbeMergeEngineFree(pSorter->pMerger);\n  pSorter->pMerger = 0;\n  for(i=0; i<pSorter->nTask; i++){\n    SortSubtask *pTask = &pSorter->aTask[i];\n    vdbeSortSubtaskCleanup(db, pTask);\n    pTask->pSorter = pSorter;\n  }\n  if( pSorter->list.aMemory==0 ){\n    vdbeSorterRecordFree(0, pSorter->list.pList);\n  }\n  pSorter->list.pList = 0;\n  pSorter->list.szPMA = 0;\n  pSorter->bUsePMA = 0;\n  pSorter->iMemory = 0;\n  pSorter->mxKeysize = 0;\n  sqlite3DbFree(db, pSorter->pUnpacked);\n  pSorter->pUnpacked = 0;\n}\n\n/*\n** Free any cursor components allocated by sqlite3VdbeSorterXXX routines.\n*/\nSQLITE_PRIVATE void sqlite3VdbeSorterClose(sqlite3 *db, VdbeCursor *pCsr){\n  VdbeSorter *pSorter;\n  assert( pCsr->eCurType==CURTYPE_SORTER );\n  pSorter = pCsr->uc.pSorter;\n  if( pSorter ){\n    sqlite3VdbeSorterReset(db, pSorter);\n    sqlite3_free(pSorter->list.aMemory);\n    sqlite3DbFree(db, pSorter);\n    pCsr->uc.pSorter = 0;\n  }\n}\n\n#if SQLITE_MAX_MMAP_SIZE>0\n/*\n** The first argument is a file-handle open on a temporary file. The file\n** is guaranteed to be nByte bytes or smaller in size. This function\n** attempts to extend the file to nByte bytes in size and to ensure that\n** the VFS has memory mapped it.\n**\n** Whether or not the file does end up memory mapped of course depends on\n** the specific VFS implementation.\n*/\nstatic void vdbeSorterExtendFile(sqlite3 *db, sqlite3_file *pFd, i64 nByte){\n  if( nByte<=(i64)(db->nMaxSorterMmap) && pFd->pMethods->iVersion>=3 ){\n    void *p = 0;\n    int chunksize = 4*1024;\n    sqlite3OsFileControlHint(pFd, SQLITE_FCNTL_CHUNK_SIZE, &chunksize);\n    sqlite3OsFileControlHint(pFd, SQLITE_FCNTL_SIZE_HINT, &nByte);\n    sqlite3OsFetch(pFd, 0, (int)nByte, &p);\n    sqlite3OsUnfetch(pFd, 0, p);\n  }\n}\n#else\n# define vdbeSorterExtendFile(x,y,z)\n#endif\n\n/*\n** Allocate space for a file-handle and open a temporary file. If successful,\n** set *ppFd to point to the malloc'd file-handle and return SQLITE_OK.\n** Otherwise, set *ppFd to 0 and return an SQLite error code.\n*/\nstatic int vdbeSorterOpenTempFile(\n  sqlite3 *db,                    /* Database handle doing sort */\n  i64 nExtend,                    /* Attempt to extend file to this size */\n  sqlite3_file **ppFd\n){\n  int rc;\n  if( sqlite3FaultSim(202) ) return SQLITE_IOERR_ACCESS;\n  rc = sqlite3OsOpenMalloc(db->pVfs, 0, ppFd,\n      SQLITE_OPEN_TEMP_JOURNAL |\n      SQLITE_OPEN_READWRITE    | SQLITE_OPEN_CREATE |\n      SQLITE_OPEN_EXCLUSIVE    | SQLITE_OPEN_DELETEONCLOSE, &rc\n  );\n  if( rc==SQLITE_OK ){\n    i64 max = SQLITE_MAX_MMAP_SIZE;\n    sqlite3OsFileControlHint(*ppFd, SQLITE_FCNTL_MMAP_SIZE, (void*)&max);\n    if( nExtend>0 ){\n      vdbeSorterExtendFile(db, *ppFd, nExtend);\n    }\n  }\n  return rc;\n}\n\n/*\n** If it has not already been allocated, allocate the UnpackedRecord \n** structure at pTask->pUnpacked. Return SQLITE_OK if successful (or \n** if no allocation was required), or SQLITE_NOMEM otherwise.\n*/\nstatic int vdbeSortAllocUnpacked(SortSubtask *pTask){\n  if( pTask->pUnpacked==0 ){\n    pTask->pUnpacked = sqlite3VdbeAllocUnpackedRecord(pTask->pSorter->pKeyInfo);\n    if( pTask->pUnpacked==0 ) return SQLITE_NOMEM_BKPT;\n    pTask->pUnpacked->nField = pTask->pSorter->pKeyInfo->nKeyField;\n    pTask->pUnpacked->errCode = 0;\n  }\n  return SQLITE_OK;\n}\n\n\n/*\n** Merge the two sorted lists p1 and p2 into a single list.\n*/\nstatic SorterRecord *vdbeSorterMerge(\n  SortSubtask *pTask,             /* Calling thread context */\n  SorterRecord *p1,               /* First list to merge */\n  SorterRecord *p2                /* Second list to merge */\n){\n  SorterRecord *pFinal = 0;\n  SorterRecord **pp = &pFinal;\n  int bCached = 0;\n\n  assert( p1!=0 && p2!=0 );\n  for(;;){\n    int res;\n    res = pTask->xCompare(\n        pTask, &bCached, SRVAL(p1), p1->nVal, SRVAL(p2), p2->nVal\n    );\n\n    if( res<=0 ){\n      *pp = p1;\n      pp = &p1->u.pNext;\n      p1 = p1->u.pNext;\n      if( p1==0 ){\n        *pp = p2;\n        break;\n      }\n    }else{\n      *pp = p2;\n      pp = &p2->u.pNext;\n      p2 = p2->u.pNext;\n      bCached = 0;\n      if( p2==0 ){\n        *pp = p1;\n        break;\n      }\n    }\n  }\n  return pFinal;\n}\n\n/*\n** Return the SorterCompare function to compare values collected by the\n** sorter object passed as the only argument.\n*/\nstatic SorterCompare vdbeSorterGetCompare(VdbeSorter *p){\n  if( p->typeMask==SORTER_TYPE_INTEGER ){\n    return vdbeSorterCompareInt;\n  }else if( p->typeMask==SORTER_TYPE_TEXT ){\n    return vdbeSorterCompareText; \n  }\n  return vdbeSorterCompare;\n}\n\n/*\n** Sort the linked list of records headed at pTask->pList. Return \n** SQLITE_OK if successful, or an SQLite error code (i.e. SQLITE_NOMEM) if \n** an error occurs.\n*/\nstatic int vdbeSorterSort(SortSubtask *pTask, SorterList *pList){\n  int i;\n  SorterRecord **aSlot;\n  SorterRecord *p;\n  int rc;\n\n  rc = vdbeSortAllocUnpacked(pTask);\n  if( rc!=SQLITE_OK ) return rc;\n\n  p = pList->pList;\n  pTask->xCompare = vdbeSorterGetCompare(pTask->pSorter);\n\n  aSlot = (SorterRecord **)sqlite3MallocZero(64 * sizeof(SorterRecord *));\n  if( !aSlot ){\n    return SQLITE_NOMEM_BKPT;\n  }\n\n  while( p ){\n    SorterRecord *pNext;\n    if( pList->aMemory ){\n      if( (u8*)p==pList->aMemory ){\n        pNext = 0;\n      }else{\n        assert( p->u.iNext<sqlite3MallocSize(pList->aMemory) );\n        pNext = (SorterRecord*)&pList->aMemory[p->u.iNext];\n      }\n    }else{\n      pNext = p->u.pNext;\n    }\n\n    p->u.pNext = 0;\n    for(i=0; aSlot[i]; i++){\n      p = vdbeSorterMerge(pTask, p, aSlot[i]);\n      aSlot[i] = 0;\n    }\n    aSlot[i] = p;\n    p = pNext;\n  }\n\n  p = 0;\n  for(i=0; i<64; i++){\n    if( aSlot[i]==0 ) continue;\n    p = p ? vdbeSorterMerge(pTask, p, aSlot[i]) : aSlot[i];\n  }\n  pList->pList = p;\n\n  sqlite3_free(aSlot);\n  assert( pTask->pUnpacked->errCode==SQLITE_OK \n       || pTask->pUnpacked->errCode==SQLITE_NOMEM \n  );\n  return pTask->pUnpacked->errCode;\n}\n\n/*\n** Initialize a PMA-writer object.\n*/\nstatic void vdbePmaWriterInit(\n  sqlite3_file *pFd,              /* File handle to write to */\n  PmaWriter *p,                   /* Object to populate */\n  int nBuf,                       /* Buffer size */\n  i64 iStart                      /* Offset of pFd to begin writing at */\n){\n  memset(p, 0, sizeof(PmaWriter));\n  p->aBuffer = (u8*)sqlite3Malloc(nBuf);\n  if( !p->aBuffer ){\n    p->eFWErr = SQLITE_NOMEM_BKPT;\n  }else{\n    p->iBufEnd = p->iBufStart = (iStart % nBuf);\n    p->iWriteOff = iStart - p->iBufStart;\n    p->nBuffer = nBuf;\n    p->pFd = pFd;\n  }\n}\n\n/*\n** Write nData bytes of data to the PMA. Return SQLITE_OK\n** if successful, or an SQLite error code if an error occurs.\n*/\nstatic void vdbePmaWriteBlob(PmaWriter *p, u8 *pData, int nData){\n  int nRem = nData;\n  while( nRem>0 && p->eFWErr==0 ){\n    int nCopy = nRem;\n    if( nCopy>(p->nBuffer - p->iBufEnd) ){\n      nCopy = p->nBuffer - p->iBufEnd;\n    }\n\n    memcpy(&p->aBuffer[p->iBufEnd], &pData[nData-nRem], nCopy);\n    p->iBufEnd += nCopy;\n    if( p->iBufEnd==p->nBuffer ){\n      p->eFWErr = sqlite3OsWrite(p->pFd, \n          &p->aBuffer[p->iBufStart], p->iBufEnd - p->iBufStart, \n          p->iWriteOff + p->iBufStart\n      );\n      p->iBufStart = p->iBufEnd = 0;\n      p->iWriteOff += p->nBuffer;\n    }\n    assert( p->iBufEnd<p->nBuffer );\n\n    nRem -= nCopy;\n  }\n}\n\n/*\n** Flush any buffered data to disk and clean up the PMA-writer object.\n** The results of using the PMA-writer after this call are undefined.\n** Return SQLITE_OK if flushing the buffered data succeeds or is not \n** required. Otherwise, return an SQLite error code.\n**\n** Before returning, set *piEof to the offset immediately following the\n** last byte written to the file.\n*/\nstatic int vdbePmaWriterFinish(PmaWriter *p, i64 *piEof){\n  int rc;\n  if( p->eFWErr==0 && ALWAYS(p->aBuffer) && p->iBufEnd>p->iBufStart ){\n    p->eFWErr = sqlite3OsWrite(p->pFd, \n        &p->aBuffer[p->iBufStart], p->iBufEnd - p->iBufStart, \n        p->iWriteOff + p->iBufStart\n    );\n  }\n  *piEof = (p->iWriteOff + p->iBufEnd);\n  sqlite3_free(p->aBuffer);\n  rc = p->eFWErr;\n  memset(p, 0, sizeof(PmaWriter));\n  return rc;\n}\n\n/*\n** Write value iVal encoded as a varint to the PMA. Return \n** SQLITE_OK if successful, or an SQLite error code if an error occurs.\n*/\nstatic void vdbePmaWriteVarint(PmaWriter *p, u64 iVal){\n  int nByte; \n  u8 aByte[10];\n  nByte = sqlite3PutVarint(aByte, iVal);\n  vdbePmaWriteBlob(p, aByte, nByte);\n}\n\n/*\n** Write the current contents of in-memory linked-list pList to a level-0\n** PMA in the temp file belonging to sub-task pTask. Return SQLITE_OK if \n** successful, or an SQLite error code otherwise.\n**\n** The format of a PMA is:\n**\n**     * A varint. This varint contains the total number of bytes of content\n**       in the PMA (not including the varint itself).\n**\n**     * One or more records packed end-to-end in order of ascending keys. \n**       Each record consists of a varint followed by a blob of data (the \n**       key). The varint is the number of bytes in the blob of data.\n*/\nstatic int vdbeSorterListToPMA(SortSubtask *pTask, SorterList *pList){\n  sqlite3 *db = pTask->pSorter->db;\n  int rc = SQLITE_OK;             /* Return code */\n  PmaWriter writer;               /* Object used to write to the file */\n\n#ifdef SQLITE_DEBUG\n  /* Set iSz to the expected size of file pTask->file after writing the PMA. \n  ** This is used by an assert() statement at the end of this function.  */\n  i64 iSz = pList->szPMA + sqlite3VarintLen(pList->szPMA) + pTask->file.iEof;\n#endif\n\n  vdbeSorterWorkDebug(pTask, \"enter\");\n  memset(&writer, 0, sizeof(PmaWriter));\n  assert( pList->szPMA>0 );\n\n  /* If the first temporary PMA file has not been opened, open it now. */\n  if( pTask->file.pFd==0 ){\n    rc = vdbeSorterOpenTempFile(db, 0, &pTask->file.pFd);\n    assert( rc!=SQLITE_OK || pTask->file.pFd );\n    assert( pTask->file.iEof==0 );\n    assert( pTask->nPMA==0 );\n  }\n\n  /* Try to get the file to memory map */\n  if( rc==SQLITE_OK ){\n    vdbeSorterExtendFile(db, pTask->file.pFd, pTask->file.iEof+pList->szPMA+9);\n  }\n\n  /* Sort the list */\n  if( rc==SQLITE_OK ){\n    rc = vdbeSorterSort(pTask, pList);\n  }\n\n  if( rc==SQLITE_OK ){\n    SorterRecord *p;\n    SorterRecord *pNext = 0;\n\n    vdbePmaWriterInit(pTask->file.pFd, &writer, pTask->pSorter->pgsz,\n                      pTask->file.iEof);\n    pTask->nPMA++;\n    vdbePmaWriteVarint(&writer, pList->szPMA);\n    for(p=pList->pList; p; p=pNext){\n      pNext = p->u.pNext;\n      vdbePmaWriteVarint(&writer, p->nVal);\n      vdbePmaWriteBlob(&writer, SRVAL(p), p->nVal);\n      if( pList->aMemory==0 ) sqlite3_free(p);\n    }\n    pList->pList = p;\n    rc = vdbePmaWriterFinish(&writer, &pTask->file.iEof);\n  }\n\n  vdbeSorterWorkDebug(pTask, \"exit\");\n  assert( rc!=SQLITE_OK || pList->pList==0 );\n  assert( rc!=SQLITE_OK || pTask->file.iEof==iSz );\n  return rc;\n}\n\n/*\n** Advance the MergeEngine to its next entry.\n** Set *pbEof to true there is no next entry because\n** the MergeEngine has reached the end of all its inputs.\n**\n** Return SQLITE_OK if successful or an error code if an error occurs.\n*/\nstatic int vdbeMergeEngineStep(\n  MergeEngine *pMerger,      /* The merge engine to advance to the next row */\n  int *pbEof                 /* Set TRUE at EOF.  Set false for more content */\n){\n  int rc;\n  int iPrev = pMerger->aTree[1];/* Index of PmaReader to advance */\n  SortSubtask *pTask = pMerger->pTask;\n\n  /* Advance the current PmaReader */\n  rc = vdbePmaReaderNext(&pMerger->aReadr[iPrev]);\n\n  /* Update contents of aTree[] */\n  if( rc==SQLITE_OK ){\n    int i;                      /* Index of aTree[] to recalculate */\n    PmaReader *pReadr1;         /* First PmaReader to compare */\n    PmaReader *pReadr2;         /* Second PmaReader to compare */\n    int bCached = 0;\n\n    /* Find the first two PmaReaders to compare. The one that was just\n    ** advanced (iPrev) and the one next to it in the array.  */\n    pReadr1 = &pMerger->aReadr[(iPrev & 0xFFFE)];\n    pReadr2 = &pMerger->aReadr[(iPrev | 0x0001)];\n\n    for(i=(pMerger->nTree+iPrev)/2; i>0; i=i/2){\n      /* Compare pReadr1 and pReadr2. Store the result in variable iRes. */\n      int iRes;\n      if( pReadr1->pFd==0 ){\n        iRes = +1;\n      }else if( pReadr2->pFd==0 ){\n        iRes = -1;\n      }else{\n        iRes = pTask->xCompare(pTask, &bCached,\n            pReadr1->aKey, pReadr1->nKey, pReadr2->aKey, pReadr2->nKey\n        );\n      }\n\n      /* If pReadr1 contained the smaller value, set aTree[i] to its index.\n      ** Then set pReadr2 to the next PmaReader to compare to pReadr1. In this\n      ** case there is no cache of pReadr2 in pTask->pUnpacked, so set\n      ** pKey2 to point to the record belonging to pReadr2.\n      **\n      ** Alternatively, if pReadr2 contains the smaller of the two values,\n      ** set aTree[i] to its index and update pReadr1. If vdbeSorterCompare()\n      ** was actually called above, then pTask->pUnpacked now contains\n      ** a value equivalent to pReadr2. So set pKey2 to NULL to prevent\n      ** vdbeSorterCompare() from decoding pReadr2 again.\n      **\n      ** If the two values were equal, then the value from the oldest\n      ** PMA should be considered smaller. The VdbeSorter.aReadr[] array\n      ** is sorted from oldest to newest, so pReadr1 contains older values\n      ** than pReadr2 iff (pReadr1<pReadr2).  */\n      if( iRes<0 || (iRes==0 && pReadr1<pReadr2) ){\n        pMerger->aTree[i] = (int)(pReadr1 - pMerger->aReadr);\n        pReadr2 = &pMerger->aReadr[ pMerger->aTree[i ^ 0x0001] ];\n        bCached = 0;\n      }else{\n        if( pReadr1->pFd ) bCached = 0;\n        pMerger->aTree[i] = (int)(pReadr2 - pMerger->aReadr);\n        pReadr1 = &pMerger->aReadr[ pMerger->aTree[i ^ 0x0001] ];\n      }\n    }\n    *pbEof = (pMerger->aReadr[pMerger->aTree[1]].pFd==0);\n  }\n\n  return (rc==SQLITE_OK ? pTask->pUnpacked->errCode : rc);\n}\n\n#if SQLITE_MAX_WORKER_THREADS>0\n/*\n** The main routine for background threads that write level-0 PMAs.\n*/\nstatic void *vdbeSorterFlushThread(void *pCtx){\n  SortSubtask *pTask = (SortSubtask*)pCtx;\n  int rc;                         /* Return code */\n  assert( pTask->bDone==0 );\n  rc = vdbeSorterListToPMA(pTask, &pTask->list);\n  pTask->bDone = 1;\n  return SQLITE_INT_TO_PTR(rc);\n}\n#endif /* SQLITE_MAX_WORKER_THREADS>0 */\n\n/*\n** Flush the current contents of VdbeSorter.list to a new PMA, possibly\n** using a background thread.\n*/\nstatic int vdbeSorterFlushPMA(VdbeSorter *pSorter){\n#if SQLITE_MAX_WORKER_THREADS==0\n  pSorter->bUsePMA = 1;\n  return vdbeSorterListToPMA(&pSorter->aTask[0], &pSorter->list);\n#else\n  int rc = SQLITE_OK;\n  int i;\n  SortSubtask *pTask = 0;    /* Thread context used to create new PMA */\n  int nWorker = (pSorter->nTask-1);\n\n  /* Set the flag to indicate that at least one PMA has been written. \n  ** Or will be, anyhow.  */\n  pSorter->bUsePMA = 1;\n\n  /* Select a sub-task to sort and flush the current list of in-memory\n  ** records to disk. If the sorter is running in multi-threaded mode,\n  ** round-robin between the first (pSorter->nTask-1) tasks. Except, if\n  ** the background thread from a sub-tasks previous turn is still running,\n  ** skip it. If the first (pSorter->nTask-1) sub-tasks are all still busy,\n  ** fall back to using the final sub-task. The first (pSorter->nTask-1)\n  ** sub-tasks are prefered as they use background threads - the final \n  ** sub-task uses the main thread. */\n  for(i=0; i<nWorker; i++){\n    int iTest = (pSorter->iPrev + i + 1) % nWorker;\n    pTask = &pSorter->aTask[iTest];\n    if( pTask->bDone ){\n      rc = vdbeSorterJoinThread(pTask);\n    }\n    if( rc!=SQLITE_OK || pTask->pThread==0 ) break;\n  }\n\n  if( rc==SQLITE_OK ){\n    if( i==nWorker ){\n      /* Use the foreground thread for this operation */\n      rc = vdbeSorterListToPMA(&pSorter->aTask[nWorker], &pSorter->list);\n    }else{\n      /* Launch a background thread for this operation */\n      u8 *aMem = pTask->list.aMemory;\n      void *pCtx = (void*)pTask;\n\n      assert( pTask->pThread==0 && pTask->bDone==0 );\n      assert( pTask->list.pList==0 );\n      assert( pTask->list.aMemory==0 || pSorter->list.aMemory!=0 );\n\n      pSorter->iPrev = (u8)(pTask - pSorter->aTask);\n      pTask->list = pSorter->list;\n      pSorter->list.pList = 0;\n      pSorter->list.szPMA = 0;\n      if( aMem ){\n        pSorter->list.aMemory = aMem;\n        pSorter->nMemory = sqlite3MallocSize(aMem);\n      }else if( pSorter->list.aMemory ){\n        pSorter->list.aMemory = sqlite3Malloc(pSorter->nMemory);\n        if( !pSorter->list.aMemory ) return SQLITE_NOMEM_BKPT;\n      }\n\n      rc = vdbeSorterCreateThread(pTask, vdbeSorterFlushThread, pCtx);\n    }\n  }\n\n  return rc;\n#endif /* SQLITE_MAX_WORKER_THREADS!=0 */\n}\n\n/*\n** Add a record to the sorter.\n*/\nSQLITE_PRIVATE int sqlite3VdbeSorterWrite(\n  const VdbeCursor *pCsr,         /* Sorter cursor */\n  Mem *pVal                       /* Memory cell containing record */\n){\n  VdbeSorter *pSorter;\n  int rc = SQLITE_OK;             /* Return Code */\n  SorterRecord *pNew;             /* New list element */\n  int bFlush;                     /* True to flush contents of memory to PMA */\n  int nReq;                       /* Bytes of memory required */\n  int nPMA;                       /* Bytes of PMA space required */\n  int t;                          /* serial type of first record field */\n\n  assert( pCsr->eCurType==CURTYPE_SORTER );\n  pSorter = pCsr->uc.pSorter;\n  getVarint32((const u8*)&pVal->z[1], t);\n  if( t>0 && t<10 && t!=7 ){\n    pSorter->typeMask &= SORTER_TYPE_INTEGER;\n  }else if( t>10 && (t & 0x01) ){\n    pSorter->typeMask &= SORTER_TYPE_TEXT;\n  }else{\n    pSorter->typeMask = 0;\n  }\n\n  assert( pSorter );\n\n  /* Figure out whether or not the current contents of memory should be\n  ** flushed to a PMA before continuing. If so, do so.\n  **\n  ** If using the single large allocation mode (pSorter->aMemory!=0), then\n  ** flush the contents of memory to a new PMA if (a) at least one value is\n  ** already in memory and (b) the new value will not fit in memory.\n  ** \n  ** Or, if using separate allocations for each record, flush the contents\n  ** of memory to a PMA if either of the following are true:\n  **\n  **   * The total memory allocated for the in-memory list is greater \n  **     than (page-size * cache-size), or\n  **\n  **   * The total memory allocated for the in-memory list is greater \n  **     than (page-size * 10) and sqlite3HeapNearlyFull() returns true.\n  */\n  nReq = pVal->n + sizeof(SorterRecord);\n  nPMA = pVal->n + sqlite3VarintLen(pVal->n);\n  if( pSorter->mxPmaSize ){\n    if( pSorter->list.aMemory ){\n      bFlush = pSorter->iMemory && (pSorter->iMemory+nReq) > pSorter->mxPmaSize;\n    }else{\n      bFlush = (\n          (pSorter->list.szPMA > pSorter->mxPmaSize)\n       || (pSorter->list.szPMA > pSorter->mnPmaSize && sqlite3HeapNearlyFull())\n      );\n    }\n    if( bFlush ){\n      rc = vdbeSorterFlushPMA(pSorter);\n      pSorter->list.szPMA = 0;\n      pSorter->iMemory = 0;\n      assert( rc!=SQLITE_OK || pSorter->list.pList==0 );\n    }\n  }\n\n  pSorter->list.szPMA += nPMA;\n  if( nPMA>pSorter->mxKeysize ){\n    pSorter->mxKeysize = nPMA;\n  }\n\n  if( pSorter->list.aMemory ){\n    int nMin = pSorter->iMemory + nReq;\n\n    if( nMin>pSorter->nMemory ){\n      u8 *aNew;\n      int iListOff = (u8*)pSorter->list.pList - pSorter->list.aMemory;\n      int nNew = pSorter->nMemory * 2;\n      while( nNew < nMin ) nNew = nNew*2;\n      if( nNew > pSorter->mxPmaSize ) nNew = pSorter->mxPmaSize;\n      if( nNew < nMin ) nNew = nMin;\n\n      aNew = sqlite3Realloc(pSorter->list.aMemory, nNew);\n      if( !aNew ) return SQLITE_NOMEM_BKPT;\n      pSorter->list.pList = (SorterRecord*)&aNew[iListOff];\n      pSorter->list.aMemory = aNew;\n      pSorter->nMemory = nNew;\n    }\n\n    pNew = (SorterRecord*)&pSorter->list.aMemory[pSorter->iMemory];\n    pSorter->iMemory += ROUND8(nReq);\n    if( pSorter->list.pList ){\n      pNew->u.iNext = (int)((u8*)(pSorter->list.pList) - pSorter->list.aMemory);\n    }\n  }else{\n    pNew = (SorterRecord *)sqlite3Malloc(nReq);\n    if( pNew==0 ){\n      return SQLITE_NOMEM_BKPT;\n    }\n    pNew->u.pNext = pSorter->list.pList;\n  }\n\n  memcpy(SRVAL(pNew), pVal->z, pVal->n);\n  pNew->nVal = pVal->n;\n  pSorter->list.pList = pNew;\n\n  return rc;\n}\n\n/*\n** Read keys from pIncr->pMerger and populate pIncr->aFile[1]. The format\n** of the data stored in aFile[1] is the same as that used by regular PMAs,\n** except that the number-of-bytes varint is omitted from the start.\n*/\nstatic int vdbeIncrPopulate(IncrMerger *pIncr){\n  int rc = SQLITE_OK;\n  int rc2;\n  i64 iStart = pIncr->iStartOff;\n  SorterFile *pOut = &pIncr->aFile[1];\n  SortSubtask *pTask = pIncr->pTask;\n  MergeEngine *pMerger = pIncr->pMerger;\n  PmaWriter writer;\n  assert( pIncr->bEof==0 );\n\n  vdbeSorterPopulateDebug(pTask, \"enter\");\n\n  vdbePmaWriterInit(pOut->pFd, &writer, pTask->pSorter->pgsz, iStart);\n  while( rc==SQLITE_OK ){\n    int dummy;\n    PmaReader *pReader = &pMerger->aReadr[ pMerger->aTree[1] ];\n    int nKey = pReader->nKey;\n    i64 iEof = writer.iWriteOff + writer.iBufEnd;\n\n    /* Check if the output file is full or if the input has been exhausted.\n    ** In either case exit the loop. */\n    if( pReader->pFd==0 ) break;\n    if( (iEof + nKey + sqlite3VarintLen(nKey))>(iStart + pIncr->mxSz) ) break;\n\n    /* Write the next key to the output. */\n    vdbePmaWriteVarint(&writer, nKey);\n    vdbePmaWriteBlob(&writer, pReader->aKey, nKey);\n    assert( pIncr->pMerger->pTask==pTask );\n    rc = vdbeMergeEngineStep(pIncr->pMerger, &dummy);\n  }\n\n  rc2 = vdbePmaWriterFinish(&writer, &pOut->iEof);\n  if( rc==SQLITE_OK ) rc = rc2;\n  vdbeSorterPopulateDebug(pTask, \"exit\");\n  return rc;\n}\n\n#if SQLITE_MAX_WORKER_THREADS>0\n/*\n** The main routine for background threads that populate aFile[1] of\n** multi-threaded IncrMerger objects.\n*/\nstatic void *vdbeIncrPopulateThread(void *pCtx){\n  IncrMerger *pIncr = (IncrMerger*)pCtx;\n  void *pRet = SQLITE_INT_TO_PTR( vdbeIncrPopulate(pIncr) );\n  pIncr->pTask->bDone = 1;\n  return pRet;\n}\n\n/*\n** Launch a background thread to populate aFile[1] of pIncr.\n*/\nstatic int vdbeIncrBgPopulate(IncrMerger *pIncr){\n  void *p = (void*)pIncr;\n  assert( pIncr->bUseThread );\n  return vdbeSorterCreateThread(pIncr->pTask, vdbeIncrPopulateThread, p);\n}\n#endif\n\n/*\n** This function is called when the PmaReader corresponding to pIncr has\n** finished reading the contents of aFile[0]. Its purpose is to \"refill\"\n** aFile[0] such that the PmaReader should start rereading it from the\n** beginning.\n**\n** For single-threaded objects, this is accomplished by literally reading \n** keys from pIncr->pMerger and repopulating aFile[0]. \n**\n** For multi-threaded objects, all that is required is to wait until the \n** background thread is finished (if it is not already) and then swap \n** aFile[0] and aFile[1] in place. If the contents of pMerger have not\n** been exhausted, this function also launches a new background thread\n** to populate the new aFile[1].\n**\n** SQLITE_OK is returned on success, or an SQLite error code otherwise.\n*/\nstatic int vdbeIncrSwap(IncrMerger *pIncr){\n  int rc = SQLITE_OK;\n\n#if SQLITE_MAX_WORKER_THREADS>0\n  if( pIncr->bUseThread ){\n    rc = vdbeSorterJoinThread(pIncr->pTask);\n\n    if( rc==SQLITE_OK ){\n      SorterFile f0 = pIncr->aFile[0];\n      pIncr->aFile[0] = pIncr->aFile[1];\n      pIncr->aFile[1] = f0;\n    }\n\n    if( rc==SQLITE_OK ){\n      if( pIncr->aFile[0].iEof==pIncr->iStartOff ){\n        pIncr->bEof = 1;\n      }else{\n        rc = vdbeIncrBgPopulate(pIncr);\n      }\n    }\n  }else\n#endif\n  {\n    rc = vdbeIncrPopulate(pIncr);\n    pIncr->aFile[0] = pIncr->aFile[1];\n    if( pIncr->aFile[0].iEof==pIncr->iStartOff ){\n      pIncr->bEof = 1;\n    }\n  }\n\n  return rc;\n}\n\n/*\n** Allocate and return a new IncrMerger object to read data from pMerger.\n**\n** If an OOM condition is encountered, return NULL. In this case free the\n** pMerger argument before returning.\n*/\nstatic int vdbeIncrMergerNew(\n  SortSubtask *pTask,     /* The thread that will be using the new IncrMerger */\n  MergeEngine *pMerger,   /* The MergeEngine that the IncrMerger will control */\n  IncrMerger **ppOut      /* Write the new IncrMerger here */\n){\n  int rc = SQLITE_OK;\n  IncrMerger *pIncr = *ppOut = (IncrMerger*)\n       (sqlite3FaultSim(100) ? 0 : sqlite3MallocZero(sizeof(*pIncr)));\n  if( pIncr ){\n    pIncr->pMerger = pMerger;\n    pIncr->pTask = pTask;\n    pIncr->mxSz = MAX(pTask->pSorter->mxKeysize+9,pTask->pSorter->mxPmaSize/2);\n    pTask->file2.iEof += pIncr->mxSz;\n  }else{\n    vdbeMergeEngineFree(pMerger);\n    rc = SQLITE_NOMEM_BKPT;\n  }\n  return rc;\n}\n\n#if SQLITE_MAX_WORKER_THREADS>0\n/*\n** Set the \"use-threads\" flag on object pIncr.\n*/\nstatic void vdbeIncrMergerSetThreads(IncrMerger *pIncr){\n  pIncr->bUseThread = 1;\n  pIncr->pTask->file2.iEof -= pIncr->mxSz;\n}\n#endif /* SQLITE_MAX_WORKER_THREADS>0 */\n\n\n\n/*\n** Recompute pMerger->aTree[iOut] by comparing the next keys on the\n** two PmaReaders that feed that entry.  Neither of the PmaReaders\n** are advanced.  This routine merely does the comparison.\n*/\nstatic void vdbeMergeEngineCompare(\n  MergeEngine *pMerger,  /* Merge engine containing PmaReaders to compare */\n  int iOut               /* Store the result in pMerger->aTree[iOut] */\n){\n  int i1;\n  int i2;\n  int iRes;\n  PmaReader *p1;\n  PmaReader *p2;\n\n  assert( iOut<pMerger->nTree && iOut>0 );\n\n  if( iOut>=(pMerger->nTree/2) ){\n    i1 = (iOut - pMerger->nTree/2) * 2;\n    i2 = i1 + 1;\n  }else{\n    i1 = pMerger->aTree[iOut*2];\n    i2 = pMerger->aTree[iOut*2+1];\n  }\n\n  p1 = &pMerger->aReadr[i1];\n  p2 = &pMerger->aReadr[i2];\n\n  if( p1->pFd==0 ){\n    iRes = i2;\n  }else if( p2->pFd==0 ){\n    iRes = i1;\n  }else{\n    SortSubtask *pTask = pMerger->pTask;\n    int bCached = 0;\n    int res;\n    assert( pTask->pUnpacked!=0 );  /* from vdbeSortSubtaskMain() */\n    res = pTask->xCompare(\n        pTask, &bCached, p1->aKey, p1->nKey, p2->aKey, p2->nKey\n    );\n    if( res<=0 ){\n      iRes = i1;\n    }else{\n      iRes = i2;\n    }\n  }\n\n  pMerger->aTree[iOut] = iRes;\n}\n\n/*\n** Allowed values for the eMode parameter to vdbeMergeEngineInit()\n** and vdbePmaReaderIncrMergeInit().\n**\n** Only INCRINIT_NORMAL is valid in single-threaded builds (when\n** SQLITE_MAX_WORKER_THREADS==0).  The other values are only used\n** when there exists one or more separate worker threads.\n*/\n#define INCRINIT_NORMAL 0\n#define INCRINIT_TASK   1\n#define INCRINIT_ROOT   2\n\n/* \n** Forward reference required as the vdbeIncrMergeInit() and\n** vdbePmaReaderIncrInit() routines are called mutually recursively when\n** building a merge tree.\n*/\nstatic int vdbePmaReaderIncrInit(PmaReader *pReadr, int eMode);\n\n/*\n** Initialize the MergeEngine object passed as the second argument. Once this\n** function returns, the first key of merged data may be read from the \n** MergeEngine object in the usual fashion.\n**\n** If argument eMode is INCRINIT_ROOT, then it is assumed that any IncrMerge\n** objects attached to the PmaReader objects that the merger reads from have\n** already been populated, but that they have not yet populated aFile[0] and\n** set the PmaReader objects up to read from it. In this case all that is\n** required is to call vdbePmaReaderNext() on each PmaReader to point it at\n** its first key.\n**\n** Otherwise, if eMode is any value other than INCRINIT_ROOT, then use \n** vdbePmaReaderIncrMergeInit() to initialize each PmaReader that feeds data \n** to pMerger.\n**\n** SQLITE_OK is returned if successful, or an SQLite error code otherwise.\n*/\nstatic int vdbeMergeEngineInit(\n  SortSubtask *pTask,             /* Thread that will run pMerger */\n  MergeEngine *pMerger,           /* MergeEngine to initialize */\n  int eMode                       /* One of the INCRINIT_XXX constants */\n){\n  int rc = SQLITE_OK;             /* Return code */\n  int i;                          /* For looping over PmaReader objects */\n  int nTree = pMerger->nTree;\n\n  /* eMode is always INCRINIT_NORMAL in single-threaded mode */\n  assert( SQLITE_MAX_WORKER_THREADS>0 || eMode==INCRINIT_NORMAL );\n\n  /* Verify that the MergeEngine is assigned to a single thread */\n  assert( pMerger->pTask==0 );\n  pMerger->pTask = pTask;\n\n  for(i=0; i<nTree; i++){\n    if( SQLITE_MAX_WORKER_THREADS>0 && eMode==INCRINIT_ROOT ){\n      /* PmaReaders should be normally initialized in order, as if they are\n      ** reading from the same temp file this makes for more linear file IO.\n      ** However, in the INCRINIT_ROOT case, if PmaReader aReadr[nTask-1] is\n      ** in use it will block the vdbePmaReaderNext() call while it uses\n      ** the main thread to fill its buffer. So calling PmaReaderNext()\n      ** on this PmaReader before any of the multi-threaded PmaReaders takes\n      ** better advantage of multi-processor hardware. */\n      rc = vdbePmaReaderNext(&pMerger->aReadr[nTree-i-1]);\n    }else{\n      rc = vdbePmaReaderIncrInit(&pMerger->aReadr[i], INCRINIT_NORMAL);\n    }\n    if( rc!=SQLITE_OK ) return rc;\n  }\n\n  for(i=pMerger->nTree-1; i>0; i--){\n    vdbeMergeEngineCompare(pMerger, i);\n  }\n  return pTask->pUnpacked->errCode;\n}\n\n/*\n** The PmaReader passed as the first argument is guaranteed to be an\n** incremental-reader (pReadr->pIncr!=0). This function serves to open\n** and/or initialize the temp file related fields of the IncrMerge\n** object at (pReadr->pIncr).\n**\n** If argument eMode is set to INCRINIT_NORMAL, then all PmaReaders\n** in the sub-tree headed by pReadr are also initialized. Data is then \n** loaded into the buffers belonging to pReadr and it is set to point to \n** the first key in its range.\n**\n** If argument eMode is set to INCRINIT_TASK, then pReadr is guaranteed\n** to be a multi-threaded PmaReader and this function is being called in a\n** background thread. In this case all PmaReaders in the sub-tree are \n** initialized as for INCRINIT_NORMAL and the aFile[1] buffer belonging to\n** pReadr is populated. However, pReadr itself is not set up to point\n** to its first key. A call to vdbePmaReaderNext() is still required to do\n** that. \n**\n** The reason this function does not call vdbePmaReaderNext() immediately \n** in the INCRINIT_TASK case is that vdbePmaReaderNext() assumes that it has\n** to block on thread (pTask->thread) before accessing aFile[1]. But, since\n** this entire function is being run by thread (pTask->thread), that will\n** lead to the current background thread attempting to join itself.\n**\n** Finally, if argument eMode is set to INCRINIT_ROOT, it may be assumed\n** that pReadr->pIncr is a multi-threaded IncrMerge objects, and that all\n** child-trees have already been initialized using IncrInit(INCRINIT_TASK).\n** In this case vdbePmaReaderNext() is called on all child PmaReaders and\n** the current PmaReader set to point to the first key in its range.\n**\n** SQLITE_OK is returned if successful, or an SQLite error code otherwise.\n*/\nstatic int vdbePmaReaderIncrMergeInit(PmaReader *pReadr, int eMode){\n  int rc = SQLITE_OK;\n  IncrMerger *pIncr = pReadr->pIncr;\n  SortSubtask *pTask = pIncr->pTask;\n  sqlite3 *db = pTask->pSorter->db;\n\n  /* eMode is always INCRINIT_NORMAL in single-threaded mode */\n  assert( SQLITE_MAX_WORKER_THREADS>0 || eMode==INCRINIT_NORMAL );\n\n  rc = vdbeMergeEngineInit(pTask, pIncr->pMerger, eMode);\n\n  /* Set up the required files for pIncr. A multi-theaded IncrMerge object\n  ** requires two temp files to itself, whereas a single-threaded object\n  ** only requires a region of pTask->file2. */\n  if( rc==SQLITE_OK ){\n    int mxSz = pIncr->mxSz;\n#if SQLITE_MAX_WORKER_THREADS>0\n    if( pIncr->bUseThread ){\n      rc = vdbeSorterOpenTempFile(db, mxSz, &pIncr->aFile[0].pFd);\n      if( rc==SQLITE_OK ){\n        rc = vdbeSorterOpenTempFile(db, mxSz, &pIncr->aFile[1].pFd);\n      }\n    }else\n#endif\n    /*if( !pIncr->bUseThread )*/{\n      if( pTask->file2.pFd==0 ){\n        assert( pTask->file2.iEof>0 );\n        rc = vdbeSorterOpenTempFile(db, pTask->file2.iEof, &pTask->file2.pFd);\n        pTask->file2.iEof = 0;\n      }\n      if( rc==SQLITE_OK ){\n        pIncr->aFile[1].pFd = pTask->file2.pFd;\n        pIncr->iStartOff = pTask->file2.iEof;\n        pTask->file2.iEof += mxSz;\n      }\n    }\n  }\n\n#if SQLITE_MAX_WORKER_THREADS>0\n  if( rc==SQLITE_OK && pIncr->bUseThread ){\n    /* Use the current thread to populate aFile[1], even though this\n    ** PmaReader is multi-threaded. If this is an INCRINIT_TASK object,\n    ** then this function is already running in background thread \n    ** pIncr->pTask->thread. \n    **\n    ** If this is the INCRINIT_ROOT object, then it is running in the \n    ** main VDBE thread. But that is Ok, as that thread cannot return\n    ** control to the VDBE or proceed with anything useful until the \n    ** first results are ready from this merger object anyway.\n    */\n    assert( eMode==INCRINIT_ROOT || eMode==INCRINIT_TASK );\n    rc = vdbeIncrPopulate(pIncr);\n  }\n#endif\n\n  if( rc==SQLITE_OK && (SQLITE_MAX_WORKER_THREADS==0 || eMode!=INCRINIT_TASK) ){\n    rc = vdbePmaReaderNext(pReadr);\n  }\n\n  return rc;\n}\n\n#if SQLITE_MAX_WORKER_THREADS>0\n/*\n** The main routine for vdbePmaReaderIncrMergeInit() operations run in \n** background threads.\n*/\nstatic void *vdbePmaReaderBgIncrInit(void *pCtx){\n  PmaReader *pReader = (PmaReader*)pCtx;\n  void *pRet = SQLITE_INT_TO_PTR(\n                  vdbePmaReaderIncrMergeInit(pReader,INCRINIT_TASK)\n               );\n  pReader->pIncr->pTask->bDone = 1;\n  return pRet;\n}\n#endif\n\n/*\n** If the PmaReader passed as the first argument is not an incremental-reader\n** (if pReadr->pIncr==0), then this function is a no-op. Otherwise, it invokes\n** the vdbePmaReaderIncrMergeInit() function with the parameters passed to\n** this routine to initialize the incremental merge.\n** \n** If the IncrMerger object is multi-threaded (IncrMerger.bUseThread==1), \n** then a background thread is launched to call vdbePmaReaderIncrMergeInit().\n** Or, if the IncrMerger is single threaded, the same function is called\n** using the current thread.\n*/\nstatic int vdbePmaReaderIncrInit(PmaReader *pReadr, int eMode){\n  IncrMerger *pIncr = pReadr->pIncr;   /* Incremental merger */\n  int rc = SQLITE_OK;                  /* Return code */\n  if( pIncr ){\n#if SQLITE_MAX_WORKER_THREADS>0\n    assert( pIncr->bUseThread==0 || eMode==INCRINIT_TASK );\n    if( pIncr->bUseThread ){\n      void *pCtx = (void*)pReadr;\n      rc = vdbeSorterCreateThread(pIncr->pTask, vdbePmaReaderBgIncrInit, pCtx);\n    }else\n#endif\n    {\n      rc = vdbePmaReaderIncrMergeInit(pReadr, eMode);\n    }\n  }\n  return rc;\n}\n\n/*\n** Allocate a new MergeEngine object to merge the contents of nPMA level-0\n** PMAs from pTask->file. If no error occurs, set *ppOut to point to\n** the new object and return SQLITE_OK. Or, if an error does occur, set *ppOut\n** to NULL and return an SQLite error code.\n**\n** When this function is called, *piOffset is set to the offset of the\n** first PMA to read from pTask->file. Assuming no error occurs, it is \n** set to the offset immediately following the last byte of the last\n** PMA before returning. If an error does occur, then the final value of\n** *piOffset is undefined.\n*/\nstatic int vdbeMergeEngineLevel0(\n  SortSubtask *pTask,             /* Sorter task to read from */\n  int nPMA,                       /* Number of PMAs to read */\n  i64 *piOffset,                  /* IN/OUT: Readr offset in pTask->file */\n  MergeEngine **ppOut             /* OUT: New merge-engine */\n){\n  MergeEngine *pNew;              /* Merge engine to return */\n  i64 iOff = *piOffset;\n  int i;\n  int rc = SQLITE_OK;\n\n  *ppOut = pNew = vdbeMergeEngineNew(nPMA);\n  if( pNew==0 ) rc = SQLITE_NOMEM_BKPT;\n\n  for(i=0; i<nPMA && rc==SQLITE_OK; i++){\n    i64 nDummy = 0;\n    PmaReader *pReadr = &pNew->aReadr[i];\n    rc = vdbePmaReaderInit(pTask, &pTask->file, iOff, pReadr, &nDummy);\n    iOff = pReadr->iEof;\n  }\n\n  if( rc!=SQLITE_OK ){\n    vdbeMergeEngineFree(pNew);\n    *ppOut = 0;\n  }\n  *piOffset = iOff;\n  return rc;\n}\n\n/*\n** Return the depth of a tree comprising nPMA PMAs, assuming a fanout of\n** SORTER_MAX_MERGE_COUNT. The returned value does not include leaf nodes.\n**\n** i.e.\n**\n**   nPMA<=16    -> TreeDepth() == 0\n**   nPMA<=256   -> TreeDepth() == 1\n**   nPMA<=65536 -> TreeDepth() == 2\n*/\nstatic int vdbeSorterTreeDepth(int nPMA){\n  int nDepth = 0;\n  i64 nDiv = SORTER_MAX_MERGE_COUNT;\n  while( nDiv < (i64)nPMA ){\n    nDiv = nDiv * SORTER_MAX_MERGE_COUNT;\n    nDepth++;\n  }\n  return nDepth;\n}\n\n/*\n** pRoot is the root of an incremental merge-tree with depth nDepth (according\n** to vdbeSorterTreeDepth()). pLeaf is the iSeq'th leaf to be added to the\n** tree, counting from zero. This function adds pLeaf to the tree.\n**\n** If successful, SQLITE_OK is returned. If an error occurs, an SQLite error\n** code is returned and pLeaf is freed.\n*/\nstatic int vdbeSorterAddToTree(\n  SortSubtask *pTask,             /* Task context */\n  int nDepth,                     /* Depth of tree according to TreeDepth() */\n  int iSeq,                       /* Sequence number of leaf within tree */\n  MergeEngine *pRoot,             /* Root of tree */\n  MergeEngine *pLeaf              /* Leaf to add to tree */\n){\n  int rc = SQLITE_OK;\n  int nDiv = 1;\n  int i;\n  MergeEngine *p = pRoot;\n  IncrMerger *pIncr;\n\n  rc = vdbeIncrMergerNew(pTask, pLeaf, &pIncr);\n\n  for(i=1; i<nDepth; i++){\n    nDiv = nDiv * SORTER_MAX_MERGE_COUNT;\n  }\n\n  for(i=1; i<nDepth && rc==SQLITE_OK; i++){\n    int iIter = (iSeq / nDiv) % SORTER_MAX_MERGE_COUNT;\n    PmaReader *pReadr = &p->aReadr[iIter];\n\n    if( pReadr->pIncr==0 ){\n      MergeEngine *pNew = vdbeMergeEngineNew(SORTER_MAX_MERGE_COUNT);\n      if( pNew==0 ){\n        rc = SQLITE_NOMEM_BKPT;\n      }else{\n        rc = vdbeIncrMergerNew(pTask, pNew, &pReadr->pIncr);\n      }\n    }\n    if( rc==SQLITE_OK ){\n      p = pReadr->pIncr->pMerger;\n      nDiv = nDiv / SORTER_MAX_MERGE_COUNT;\n    }\n  }\n\n  if( rc==SQLITE_OK ){\n    p->aReadr[iSeq % SORTER_MAX_MERGE_COUNT].pIncr = pIncr;\n  }else{\n    vdbeIncrFree(pIncr);\n  }\n  return rc;\n}\n\n/*\n** This function is called as part of a SorterRewind() operation on a sorter\n** that has already written two or more level-0 PMAs to one or more temp\n** files. It builds a tree of MergeEngine/IncrMerger/PmaReader objects that \n** can be used to incrementally merge all PMAs on disk.\n**\n** If successful, SQLITE_OK is returned and *ppOut set to point to the\n** MergeEngine object at the root of the tree before returning. Or, if an\n** error occurs, an SQLite error code is returned and the final value \n** of *ppOut is undefined.\n*/\nstatic int vdbeSorterMergeTreeBuild(\n  VdbeSorter *pSorter,       /* The VDBE cursor that implements the sort */\n  MergeEngine **ppOut        /* Write the MergeEngine here */\n){\n  MergeEngine *pMain = 0;\n  int rc = SQLITE_OK;\n  int iTask;\n\n#if SQLITE_MAX_WORKER_THREADS>0\n  /* If the sorter uses more than one task, then create the top-level \n  ** MergeEngine here. This MergeEngine will read data from exactly \n  ** one PmaReader per sub-task.  */\n  assert( pSorter->bUseThreads || pSorter->nTask==1 );\n  if( pSorter->nTask>1 ){\n    pMain = vdbeMergeEngineNew(pSorter->nTask);\n    if( pMain==0 ) rc = SQLITE_NOMEM_BKPT;\n  }\n#endif\n\n  for(iTask=0; rc==SQLITE_OK && iTask<pSorter->nTask; iTask++){\n    SortSubtask *pTask = &pSorter->aTask[iTask];\n    assert( pTask->nPMA>0 || SQLITE_MAX_WORKER_THREADS>0 );\n    if( SQLITE_MAX_WORKER_THREADS==0 || pTask->nPMA ){\n      MergeEngine *pRoot = 0;     /* Root node of tree for this task */\n      int nDepth = vdbeSorterTreeDepth(pTask->nPMA);\n      i64 iReadOff = 0;\n\n      if( pTask->nPMA<=SORTER_MAX_MERGE_COUNT ){\n        rc = vdbeMergeEngineLevel0(pTask, pTask->nPMA, &iReadOff, &pRoot);\n      }else{\n        int i;\n        int iSeq = 0;\n        pRoot = vdbeMergeEngineNew(SORTER_MAX_MERGE_COUNT);\n        if( pRoot==0 ) rc = SQLITE_NOMEM_BKPT;\n        for(i=0; i<pTask->nPMA && rc==SQLITE_OK; i += SORTER_MAX_MERGE_COUNT){\n          MergeEngine *pMerger = 0; /* New level-0 PMA merger */\n          int nReader;              /* Number of level-0 PMAs to merge */\n\n          nReader = MIN(pTask->nPMA - i, SORTER_MAX_MERGE_COUNT);\n          rc = vdbeMergeEngineLevel0(pTask, nReader, &iReadOff, &pMerger);\n          if( rc==SQLITE_OK ){\n            rc = vdbeSorterAddToTree(pTask, nDepth, iSeq++, pRoot, pMerger);\n          }\n        }\n      }\n\n      if( rc==SQLITE_OK ){\n#if SQLITE_MAX_WORKER_THREADS>0\n        if( pMain!=0 ){\n          rc = vdbeIncrMergerNew(pTask, pRoot, &pMain->aReadr[iTask].pIncr);\n        }else\n#endif\n        {\n          assert( pMain==0 );\n          pMain = pRoot;\n        }\n      }else{\n        vdbeMergeEngineFree(pRoot);\n      }\n    }\n  }\n\n  if( rc!=SQLITE_OK ){\n    vdbeMergeEngineFree(pMain);\n    pMain = 0;\n  }\n  *ppOut = pMain;\n  return rc;\n}\n\n/*\n** This function is called as part of an sqlite3VdbeSorterRewind() operation\n** on a sorter that has written two or more PMAs to temporary files. It sets\n** up either VdbeSorter.pMerger (for single threaded sorters) or pReader\n** (for multi-threaded sorters) so that it can be used to iterate through\n** all records stored in the sorter.\n**\n** SQLITE_OK is returned if successful, or an SQLite error code otherwise.\n*/\nstatic int vdbeSorterSetupMerge(VdbeSorter *pSorter){\n  int rc;                         /* Return code */\n  SortSubtask *pTask0 = &pSorter->aTask[0];\n  MergeEngine *pMain = 0;\n#if SQLITE_MAX_WORKER_THREADS\n  sqlite3 *db = pTask0->pSorter->db;\n  int i;\n  SorterCompare xCompare = vdbeSorterGetCompare(pSorter);\n  for(i=0; i<pSorter->nTask; i++){\n    pSorter->aTask[i].xCompare = xCompare;\n  }\n#endif\n\n  rc = vdbeSorterMergeTreeBuild(pSorter, &pMain);\n  if( rc==SQLITE_OK ){\n#if SQLITE_MAX_WORKER_THREADS\n    assert( pSorter->bUseThreads==0 || pSorter->nTask>1 );\n    if( pSorter->bUseThreads ){\n      int iTask;\n      PmaReader *pReadr = 0;\n      SortSubtask *pLast = &pSorter->aTask[pSorter->nTask-1];\n      rc = vdbeSortAllocUnpacked(pLast);\n      if( rc==SQLITE_OK ){\n        pReadr = (PmaReader*)sqlite3DbMallocZero(db, sizeof(PmaReader));\n        pSorter->pReader = pReadr;\n        if( pReadr==0 ) rc = SQLITE_NOMEM_BKPT;\n      }\n      if( rc==SQLITE_OK ){\n        rc = vdbeIncrMergerNew(pLast, pMain, &pReadr->pIncr);\n        if( rc==SQLITE_OK ){\n          vdbeIncrMergerSetThreads(pReadr->pIncr);\n          for(iTask=0; iTask<(pSorter->nTask-1); iTask++){\n            IncrMerger *pIncr;\n            if( (pIncr = pMain->aReadr[iTask].pIncr) ){\n              vdbeIncrMergerSetThreads(pIncr);\n              assert( pIncr->pTask!=pLast );\n            }\n          }\n          for(iTask=0; rc==SQLITE_OK && iTask<pSorter->nTask; iTask++){\n            /* Check that:\n            **   \n            **   a) The incremental merge object is configured to use the\n            **      right task, and\n            **   b) If it is using task (nTask-1), it is configured to run\n            **      in single-threaded mode. This is important, as the\n            **      root merge (INCRINIT_ROOT) will be using the same task\n            **      object.\n            */\n            PmaReader *p = &pMain->aReadr[iTask];\n            assert( p->pIncr==0 || (\n                (p->pIncr->pTask==&pSorter->aTask[iTask])             /* a */\n             && (iTask!=pSorter->nTask-1 || p->pIncr->bUseThread==0)  /* b */\n            ));\n            rc = vdbePmaReaderIncrInit(p, INCRINIT_TASK);\n          }\n        }\n        pMain = 0;\n      }\n      if( rc==SQLITE_OK ){\n        rc = vdbePmaReaderIncrMergeInit(pReadr, INCRINIT_ROOT);\n      }\n    }else\n#endif\n    {\n      rc = vdbeMergeEngineInit(pTask0, pMain, INCRINIT_NORMAL);\n      pSorter->pMerger = pMain;\n      pMain = 0;\n    }\n  }\n\n  if( rc!=SQLITE_OK ){\n    vdbeMergeEngineFree(pMain);\n  }\n  return rc;\n}\n\n\n/*\n** Once the sorter has been populated by calls to sqlite3VdbeSorterWrite,\n** this function is called to prepare for iterating through the records\n** in sorted order.\n*/\nSQLITE_PRIVATE int sqlite3VdbeSorterRewind(const VdbeCursor *pCsr, int *pbEof){\n  VdbeSorter *pSorter;\n  int rc = SQLITE_OK;             /* Return code */\n\n  assert( pCsr->eCurType==CURTYPE_SORTER );\n  pSorter = pCsr->uc.pSorter;\n  assert( pSorter );\n\n  /* If no data has been written to disk, then do not do so now. Instead,\n  ** sort the VdbeSorter.pRecord list. The vdbe layer will read data directly\n  ** from the in-memory list.  */\n  if( pSorter->bUsePMA==0 ){\n    if( pSorter->list.pList ){\n      *pbEof = 0;\n      rc = vdbeSorterSort(&pSorter->aTask[0], &pSorter->list);\n    }else{\n      *pbEof = 1;\n    }\n    return rc;\n  }\n\n  /* Write the current in-memory list to a PMA. When the VdbeSorterWrite() \n  ** function flushes the contents of memory to disk, it immediately always\n  ** creates a new list consisting of a single key immediately afterwards.\n  ** So the list is never empty at this point.  */\n  assert( pSorter->list.pList );\n  rc = vdbeSorterFlushPMA(pSorter);\n\n  /* Join all threads */\n  rc = vdbeSorterJoinAll(pSorter, rc);\n\n  vdbeSorterRewindDebug(\"rewind\");\n\n  /* Assuming no errors have occurred, set up a merger structure to \n  ** incrementally read and merge all remaining PMAs.  */\n  assert( pSorter->pReader==0 );\n  if( rc==SQLITE_OK ){\n    rc = vdbeSorterSetupMerge(pSorter);\n    *pbEof = 0;\n  }\n\n  vdbeSorterRewindDebug(\"rewinddone\");\n  return rc;\n}\n\n/*\n** Advance to the next element in the sorter.  Return value:\n**\n**    SQLITE_OK     success\n**    SQLITE_DONE   end of data\n**    otherwise     some kind of error.\n*/\nSQLITE_PRIVATE int sqlite3VdbeSorterNext(sqlite3 *db, const VdbeCursor *pCsr){\n  VdbeSorter *pSorter;\n  int rc;                         /* Return code */\n\n  assert( pCsr->eCurType==CURTYPE_SORTER );\n  pSorter = pCsr->uc.pSorter;\n  assert( pSorter->bUsePMA || (pSorter->pReader==0 && pSorter->pMerger==0) );\n  if( pSorter->bUsePMA ){\n    assert( pSorter->pReader==0 || pSorter->pMerger==0 );\n    assert( pSorter->bUseThreads==0 || pSorter->pReader );\n    assert( pSorter->bUseThreads==1 || pSorter->pMerger );\n#if SQLITE_MAX_WORKER_THREADS>0\n    if( pSorter->bUseThreads ){\n      rc = vdbePmaReaderNext(pSorter->pReader);\n      if( rc==SQLITE_OK && pSorter->pReader->pFd==0 ) rc = SQLITE_DONE;\n    }else\n#endif\n    /*if( !pSorter->bUseThreads )*/ {\n      int res = 0;\n      assert( pSorter->pMerger!=0 );\n      assert( pSorter->pMerger->pTask==(&pSorter->aTask[0]) );\n      rc = vdbeMergeEngineStep(pSorter->pMerger, &res);\n      if( rc==SQLITE_OK && res ) rc = SQLITE_DONE;\n    }\n  }else{\n    SorterRecord *pFree = pSorter->list.pList;\n    pSorter->list.pList = pFree->u.pNext;\n    pFree->u.pNext = 0;\n    if( pSorter->list.aMemory==0 ) vdbeSorterRecordFree(db, pFree);\n    rc = pSorter->list.pList ? SQLITE_OK : SQLITE_DONE;\n  }\n  return rc;\n}\n\n/*\n** Return a pointer to a buffer owned by the sorter that contains the \n** current key.\n*/\nstatic void *vdbeSorterRowkey(\n  const VdbeSorter *pSorter,      /* Sorter object */\n  int *pnKey                      /* OUT: Size of current key in bytes */\n){\n  void *pKey;\n  if( pSorter->bUsePMA ){\n    PmaReader *pReader;\n#if SQLITE_MAX_WORKER_THREADS>0\n    if( pSorter->bUseThreads ){\n      pReader = pSorter->pReader;\n    }else\n#endif\n    /*if( !pSorter->bUseThreads )*/{\n      pReader = &pSorter->pMerger->aReadr[pSorter->pMerger->aTree[1]];\n    }\n    *pnKey = pReader->nKey;\n    pKey = pReader->aKey;\n  }else{\n    *pnKey = pSorter->list.pList->nVal;\n    pKey = SRVAL(pSorter->list.pList);\n  }\n  return pKey;\n}\n\n/*\n** Copy the current sorter key into the memory cell pOut.\n*/\nSQLITE_PRIVATE int sqlite3VdbeSorterRowkey(const VdbeCursor *pCsr, Mem *pOut){\n  VdbeSorter *pSorter;\n  void *pKey; int nKey;           /* Sorter key to copy into pOut */\n\n  assert( pCsr->eCurType==CURTYPE_SORTER );\n  pSorter = pCsr->uc.pSorter;\n  pKey = vdbeSorterRowkey(pSorter, &nKey);\n  if( sqlite3VdbeMemClearAndResize(pOut, nKey) ){\n    return SQLITE_NOMEM_BKPT;\n  }\n  pOut->n = nKey;\n  MemSetTypeFlag(pOut, MEM_Blob);\n  memcpy(pOut->z, pKey, nKey);\n\n  return SQLITE_OK;\n}\n\n/*\n** Compare the key in memory cell pVal with the key that the sorter cursor\n** passed as the first argument currently points to. For the purposes of\n** the comparison, ignore the rowid field at the end of each record.\n**\n** If the sorter cursor key contains any NULL values, consider it to be\n** less than pVal. Even if pVal also contains NULL values.\n**\n** If an error occurs, return an SQLite error code (i.e. SQLITE_NOMEM).\n** Otherwise, set *pRes to a negative, zero or positive value if the\n** key in pVal is smaller than, equal to or larger than the current sorter\n** key.\n**\n** This routine forms the core of the OP_SorterCompare opcode, which in\n** turn is used to verify uniqueness when constructing a UNIQUE INDEX.\n*/\nSQLITE_PRIVATE int sqlite3VdbeSorterCompare(\n  const VdbeCursor *pCsr,         /* Sorter cursor */\n  Mem *pVal,                      /* Value to compare to current sorter key */\n  int nKeyCol,                    /* Compare this many columns */\n  int *pRes                       /* OUT: Result of comparison */\n){\n  VdbeSorter *pSorter;\n  UnpackedRecord *r2;\n  KeyInfo *pKeyInfo;\n  int i;\n  void *pKey; int nKey;           /* Sorter key to compare pVal with */\n\n  assert( pCsr->eCurType==CURTYPE_SORTER );\n  pSorter = pCsr->uc.pSorter;\n  r2 = pSorter->pUnpacked;\n  pKeyInfo = pCsr->pKeyInfo;\n  if( r2==0 ){\n    r2 = pSorter->pUnpacked = sqlite3VdbeAllocUnpackedRecord(pKeyInfo);\n    if( r2==0 ) return SQLITE_NOMEM_BKPT;\n    r2->nField = nKeyCol;\n  }\n  assert( r2->nField==nKeyCol );\n\n  pKey = vdbeSorterRowkey(pSorter, &nKey);\n  sqlite3VdbeRecordUnpack(pKeyInfo, nKey, pKey, r2);\n  for(i=0; i<nKeyCol; i++){\n    if( r2->aMem[i].flags & MEM_Null ){\n      *pRes = -1;\n      return SQLITE_OK;\n    }\n  }\n\n  *pRes = sqlite3VdbeRecordCompare(pVal->n, pVal->z, r2);\n  return SQLITE_OK;\n}\n\n/************** End of vdbesort.c ********************************************/\n/************** Begin file memjournal.c **************************************/\n/*\n** 2008 October 7\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n*************************************************************************\n**\n** This file contains code use to implement an in-memory rollback journal.\n** The in-memory rollback journal is used to journal transactions for\n** \":memory:\" databases and when the journal_mode=MEMORY pragma is used.\n**\n** Update:  The in-memory journal is also used to temporarily cache\n** smaller journals that are not critical for power-loss recovery.\n** For example, statement journals that are not too big will be held\n** entirely in memory, thus reducing the number of file I/O calls, and\n** more importantly, reducing temporary file creation events.  If these\n** journals become too large for memory, they are spilled to disk.  But\n** in the common case, they are usually small and no file I/O needs to\n** occur.\n*/\n/* #include \"sqliteInt.h\" */\n\n/* Forward references to internal structures */\ntypedef struct MemJournal MemJournal;\ntypedef struct FilePoint FilePoint;\ntypedef struct FileChunk FileChunk;\n\n/*\n** The rollback journal is composed of a linked list of these structures.\n**\n** The zChunk array is always at least 8 bytes in size - usually much more.\n** Its actual size is stored in the MemJournal.nChunkSize variable.\n*/\nstruct FileChunk {\n  FileChunk *pNext;               /* Next chunk in the journal */\n  u8 zChunk[8];                   /* Content of this chunk */\n};\n\n/*\n** By default, allocate this many bytes of memory for each FileChunk object.\n*/\n#define MEMJOURNAL_DFLT_FILECHUNKSIZE 1024\n\n/*\n** For chunk size nChunkSize, return the number of bytes that should\n** be allocated for each FileChunk structure.\n*/\n#define fileChunkSize(nChunkSize) (sizeof(FileChunk) + ((nChunkSize)-8))\n\n/*\n** An instance of this object serves as a cursor into the rollback journal.\n** The cursor can be either for reading or writing.\n*/\nstruct FilePoint {\n  sqlite3_int64 iOffset;          /* Offset from the beginning of the file */\n  FileChunk *pChunk;              /* Specific chunk into which cursor points */\n};\n\n/*\n** This structure is a subclass of sqlite3_file. Each open memory-journal\n** is an instance of this class.\n*/\nstruct MemJournal {\n  const sqlite3_io_methods *pMethod; /* Parent class. MUST BE FIRST */\n  int nChunkSize;                 /* In-memory chunk-size */\n\n  int nSpill;                     /* Bytes of data before flushing */\n  int nSize;                      /* Bytes of data currently in memory */\n  FileChunk *pFirst;              /* Head of in-memory chunk-list */\n  FilePoint endpoint;             /* Pointer to the end of the file */\n  FilePoint readpoint;            /* Pointer to the end of the last xRead() */\n\n  int flags;                      /* xOpen flags */\n  sqlite3_vfs *pVfs;              /* The \"real\" underlying VFS */\n  const char *zJournal;           /* Name of the journal file */\n};\n\n/*\n** Read data from the in-memory journal file.  This is the implementation\n** of the sqlite3_vfs.xRead method.\n*/\nstatic int memjrnlRead(\n  sqlite3_file *pJfd,    /* The journal file from which to read */\n  void *zBuf,            /* Put the results here */\n  int iAmt,              /* Number of bytes to read */\n  sqlite_int64 iOfst     /* Begin reading at this offset */\n){\n  MemJournal *p = (MemJournal *)pJfd;\n  u8 *zOut = zBuf;\n  int nRead = iAmt;\n  int iChunkOffset;\n  FileChunk *pChunk;\n\n#if defined(SQLITE_ENABLE_ATOMIC_WRITE) \\\n || defined(SQLITE_ENABLE_BATCH_ATOMIC_WRITE)\n  if( (iAmt+iOfst)>p->endpoint.iOffset ){\n    return SQLITE_IOERR_SHORT_READ;\n  }\n#endif\n\n  assert( (iAmt+iOfst)<=p->endpoint.iOffset );\n  assert( p->readpoint.iOffset==0 || p->readpoint.pChunk!=0 );\n  if( p->readpoint.iOffset!=iOfst || iOfst==0 ){\n    sqlite3_int64 iOff = 0;\n    for(pChunk=p->pFirst; \n        ALWAYS(pChunk) && (iOff+p->nChunkSize)<=iOfst;\n        pChunk=pChunk->pNext\n    ){\n      iOff += p->nChunkSize;\n    }\n  }else{\n    pChunk = p->readpoint.pChunk;\n    assert( pChunk!=0 );\n  }\n\n  iChunkOffset = (int)(iOfst%p->nChunkSize);\n  do {\n    int iSpace = p->nChunkSize - iChunkOffset;\n    int nCopy = MIN(nRead, (p->nChunkSize - iChunkOffset));\n    memcpy(zOut, (u8*)pChunk->zChunk + iChunkOffset, nCopy);\n    zOut += nCopy;\n    nRead -= iSpace;\n    iChunkOffset = 0;\n  } while( nRead>=0 && (pChunk=pChunk->pNext)!=0 && nRead>0 );\n  p->readpoint.iOffset = pChunk ? iOfst+iAmt : 0;\n  p->readpoint.pChunk = pChunk;\n\n  return SQLITE_OK;\n}\n\n/*\n** Free the list of FileChunk structures headed at MemJournal.pFirst.\n*/\nstatic void memjrnlFreeChunks(MemJournal *p){\n  FileChunk *pIter;\n  FileChunk *pNext;\n  for(pIter=p->pFirst; pIter; pIter=pNext){\n    pNext = pIter->pNext;\n    sqlite3_free(pIter);\n  } \n  p->pFirst = 0;\n}\n\n/*\n** Flush the contents of memory to a real file on disk.\n*/\nstatic int memjrnlCreateFile(MemJournal *p){\n  int rc;\n  sqlite3_file *pReal = (sqlite3_file*)p;\n  MemJournal copy = *p;\n\n  memset(p, 0, sizeof(MemJournal));\n  rc = sqlite3OsOpen(copy.pVfs, copy.zJournal, pReal, copy.flags, 0);\n  if( rc==SQLITE_OK ){\n    int nChunk = copy.nChunkSize;\n    i64 iOff = 0;\n    FileChunk *pIter;\n    for(pIter=copy.pFirst; pIter; pIter=pIter->pNext){\n      if( iOff + nChunk > copy.endpoint.iOffset ){\n        nChunk = copy.endpoint.iOffset - iOff;\n      }\n      rc = sqlite3OsWrite(pReal, (u8*)pIter->zChunk, nChunk, iOff);\n      if( rc ) break;\n      iOff += nChunk;\n    }\n    if( rc==SQLITE_OK ){\n      /* No error has occurred. Free the in-memory buffers. */\n      memjrnlFreeChunks(&copy);\n    }\n  }\n  if( rc!=SQLITE_OK ){\n    /* If an error occurred while creating or writing to the file, restore\n    ** the original before returning. This way, SQLite uses the in-memory\n    ** journal data to roll back changes made to the internal page-cache\n    ** before this function was called.  */\n    sqlite3OsClose(pReal);\n    *p = copy;\n  }\n  return rc;\n}\n\n\n/*\n** Write data to the file.\n*/\nstatic int memjrnlWrite(\n  sqlite3_file *pJfd,    /* The journal file into which to write */\n  const void *zBuf,      /* Take data to be written from here */\n  int iAmt,              /* Number of bytes to write */\n  sqlite_int64 iOfst     /* Begin writing at this offset into the file */\n){\n  MemJournal *p = (MemJournal *)pJfd;\n  int nWrite = iAmt;\n  u8 *zWrite = (u8 *)zBuf;\n\n  /* If the file should be created now, create it and write the new data\n  ** into the file on disk. */\n  if( p->nSpill>0 && (iAmt+iOfst)>p->nSpill ){\n    int rc = memjrnlCreateFile(p);\n    if( rc==SQLITE_OK ){\n      rc = sqlite3OsWrite(pJfd, zBuf, iAmt, iOfst);\n    }\n    return rc;\n  }\n\n  /* If the contents of this write should be stored in memory */\n  else{\n    /* An in-memory journal file should only ever be appended to. Random\n    ** access writes are not required. The only exception to this is when\n    ** the in-memory journal is being used by a connection using the\n    ** atomic-write optimization. In this case the first 28 bytes of the\n    ** journal file may be written as part of committing the transaction. */ \n    assert( iOfst==p->endpoint.iOffset || iOfst==0 );\n#if defined(SQLITE_ENABLE_ATOMIC_WRITE) \\\n || defined(SQLITE_ENABLE_BATCH_ATOMIC_WRITE)\n    if( iOfst==0 && p->pFirst ){\n      assert( p->nChunkSize>iAmt );\n      memcpy((u8*)p->pFirst->zChunk, zBuf, iAmt);\n    }else\n#else\n    assert( iOfst>0 || p->pFirst==0 );\n#endif\n    {\n      while( nWrite>0 ){\n        FileChunk *pChunk = p->endpoint.pChunk;\n        int iChunkOffset = (int)(p->endpoint.iOffset%p->nChunkSize);\n        int iSpace = MIN(nWrite, p->nChunkSize - iChunkOffset);\n\n        if( iChunkOffset==0 ){\n          /* New chunk is required to extend the file. */\n          FileChunk *pNew = sqlite3_malloc(fileChunkSize(p->nChunkSize));\n          if( !pNew ){\n            return SQLITE_IOERR_NOMEM_BKPT;\n          }\n          pNew->pNext = 0;\n          if( pChunk ){\n            assert( p->pFirst );\n            pChunk->pNext = pNew;\n          }else{\n            assert( !p->pFirst );\n            p->pFirst = pNew;\n          }\n          p->endpoint.pChunk = pNew;\n        }\n\n        memcpy((u8*)p->endpoint.pChunk->zChunk + iChunkOffset, zWrite, iSpace);\n        zWrite += iSpace;\n        nWrite -= iSpace;\n        p->endpoint.iOffset += iSpace;\n      }\n      p->nSize = iAmt + iOfst;\n    }\n  }\n\n  return SQLITE_OK;\n}\n\n/*\n** Truncate the file.\n**\n** If the journal file is already on disk, truncate it there. Or, if it\n** is still in main memory but is being truncated to zero bytes in size,\n** ignore \n*/\nstatic int memjrnlTruncate(sqlite3_file *pJfd, sqlite_int64 size){\n  MemJournal *p = (MemJournal *)pJfd;\n  if( ALWAYS(size==0) ){\n    memjrnlFreeChunks(p);\n    p->nSize = 0;\n    p->endpoint.pChunk = 0;\n    p->endpoint.iOffset = 0;\n    p->readpoint.pChunk = 0;\n    p->readpoint.iOffset = 0;\n  }\n  return SQLITE_OK;\n}\n\n/*\n** Close the file.\n*/\nstatic int memjrnlClose(sqlite3_file *pJfd){\n  MemJournal *p = (MemJournal *)pJfd;\n  memjrnlFreeChunks(p);\n  return SQLITE_OK;\n}\n\n/*\n** Sync the file.\n**\n** If the real file has been created, call its xSync method. Otherwise, \n** syncing an in-memory journal is a no-op. \n*/\nstatic int memjrnlSync(sqlite3_file *pJfd, int flags){\n  UNUSED_PARAMETER2(pJfd, flags);\n  return SQLITE_OK;\n}\n\n/*\n** Query the size of the file in bytes.\n*/\nstatic int memjrnlFileSize(sqlite3_file *pJfd, sqlite_int64 *pSize){\n  MemJournal *p = (MemJournal *)pJfd;\n  *pSize = (sqlite_int64) p->endpoint.iOffset;\n  return SQLITE_OK;\n}\n\n/*\n** Table of methods for MemJournal sqlite3_file object.\n*/\nstatic const struct sqlite3_io_methods MemJournalMethods = {\n  1,                /* iVersion */\n  memjrnlClose,     /* xClose */\n  memjrnlRead,      /* xRead */\n  memjrnlWrite,     /* xWrite */\n  memjrnlTruncate,  /* xTruncate */\n  memjrnlSync,      /* xSync */\n  memjrnlFileSize,  /* xFileSize */\n  0,                /* xLock */\n  0,                /* xUnlock */\n  0,                /* xCheckReservedLock */\n  0,                /* xFileControl */\n  0,                /* xSectorSize */\n  0,                /* xDeviceCharacteristics */\n  0,                /* xShmMap */\n  0,                /* xShmLock */\n  0,                /* xShmBarrier */\n  0,                /* xShmUnmap */\n  0,                /* xFetch */\n  0                 /* xUnfetch */\n};\n\n/* \n** Open a journal file. \n**\n** The behaviour of the journal file depends on the value of parameter \n** nSpill. If nSpill is 0, then the journal file is always create and \n** accessed using the underlying VFS. If nSpill is less than zero, then\n** all content is always stored in main-memory. Finally, if nSpill is a\n** positive value, then the journal file is initially created in-memory\n** but may be flushed to disk later on. In this case the journal file is\n** flushed to disk either when it grows larger than nSpill bytes in size,\n** or when sqlite3JournalCreate() is called.\n*/\nSQLITE_PRIVATE int sqlite3JournalOpen(\n  sqlite3_vfs *pVfs,         /* The VFS to use for actual file I/O */\n  const char *zName,         /* Name of the journal file */\n  sqlite3_file *pJfd,        /* Preallocated, blank file handle */\n  int flags,                 /* Opening flags */\n  int nSpill                 /* Bytes buffered before opening the file */\n){\n  MemJournal *p = (MemJournal*)pJfd;\n\n  /* Zero the file-handle object. If nSpill was passed zero, initialize\n  ** it using the sqlite3OsOpen() function of the underlying VFS. In this\n  ** case none of the code in this module is executed as a result of calls\n  ** made on the journal file-handle.  */\n  memset(p, 0, sizeof(MemJournal));\n  if( nSpill==0 ){\n    return sqlite3OsOpen(pVfs, zName, pJfd, flags, 0);\n  }\n\n  if( nSpill>0 ){\n    p->nChunkSize = nSpill;\n  }else{\n    p->nChunkSize = 8 + MEMJOURNAL_DFLT_FILECHUNKSIZE - sizeof(FileChunk);\n    assert( MEMJOURNAL_DFLT_FILECHUNKSIZE==fileChunkSize(p->nChunkSize) );\n  }\n\n  p->pMethod = (const sqlite3_io_methods*)&MemJournalMethods;\n  p->nSpill = nSpill;\n  p->flags = flags;\n  p->zJournal = zName;\n  p->pVfs = pVfs;\n  return SQLITE_OK;\n}\n\n/*\n** Open an in-memory journal file.\n*/\nSQLITE_PRIVATE void sqlite3MemJournalOpen(sqlite3_file *pJfd){\n  sqlite3JournalOpen(0, 0, pJfd, 0, -1);\n}\n\n#if defined(SQLITE_ENABLE_ATOMIC_WRITE) \\\n || defined(SQLITE_ENABLE_BATCH_ATOMIC_WRITE)\n/*\n** If the argument p points to a MemJournal structure that is not an \n** in-memory-only journal file (i.e. is one that was opened with a +ve\n** nSpill parameter or as SQLITE_OPEN_MAIN_JOURNAL), and the underlying \n** file has not yet been created, create it now.\n*/\nSQLITE_PRIVATE int sqlite3JournalCreate(sqlite3_file *pJfd){\n  int rc = SQLITE_OK;\n  MemJournal *p = (MemJournal*)pJfd;\n  if( p->pMethod==&MemJournalMethods && (\n#ifdef SQLITE_ENABLE_ATOMIC_WRITE\n     p->nSpill>0\n#else\n     /* While this appears to not be possible without ATOMIC_WRITE, the\n     ** paths are complex, so it seems prudent to leave the test in as\n     ** a NEVER(), in case our analysis is subtly flawed. */\n     NEVER(p->nSpill>0)\n#endif\n#ifdef SQLITE_ENABLE_BATCH_ATOMIC_WRITE\n     || (p->flags & SQLITE_OPEN_MAIN_JOURNAL)\n#endif\n  )){\n    rc = memjrnlCreateFile(p);\n  }\n  return rc;\n}\n#endif\n\n/*\n** The file-handle passed as the only argument is open on a journal file.\n** Return true if this \"journal file\" is currently stored in heap memory,\n** or false otherwise.\n*/\nSQLITE_PRIVATE int sqlite3JournalIsInMemory(sqlite3_file *p){\n  return p->pMethods==&MemJournalMethods;\n}\n\n/* \n** Return the number of bytes required to store a JournalFile that uses vfs\n** pVfs to create the underlying on-disk files.\n*/\nSQLITE_PRIVATE int sqlite3JournalSize(sqlite3_vfs *pVfs){\n  return MAX(pVfs->szOsFile, (int)sizeof(MemJournal));\n}\n\n/************** End of memjournal.c ******************************************/\n/************** Begin file walker.c ******************************************/\n/*\n** 2008 August 16\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n*************************************************************************\n** This file contains routines used for walking the parser tree for\n** an SQL statement.\n*/\n/* #include \"sqliteInt.h\" */\n/* #include <stdlib.h> */\n/* #include <string.h> */\n\n\n/*\n** Walk an expression tree.  Invoke the callback once for each node\n** of the expression, while descending.  (In other words, the callback\n** is invoked before visiting children.)\n**\n** The return value from the callback should be one of the WRC_*\n** constants to specify how to proceed with the walk.\n**\n**    WRC_Continue      Continue descending down the tree.\n**\n**    WRC_Prune         Do not descend into child nodes, but allow\n**                      the walk to continue with sibling nodes.\n**\n**    WRC_Abort         Do no more callbacks.  Unwind the stack and\n**                      return from the top-level walk call.\n**\n** The return value from this routine is WRC_Abort to abandon the tree walk\n** and WRC_Continue to continue.\n*/\nstatic SQLITE_NOINLINE int walkExpr(Walker *pWalker, Expr *pExpr){\n  int rc;\n  testcase( ExprHasProperty(pExpr, EP_TokenOnly) );\n  testcase( ExprHasProperty(pExpr, EP_Reduced) );\n  while(1){\n    rc = pWalker->xExprCallback(pWalker, pExpr);\n    if( rc ) return rc & WRC_Abort;\n    if( !ExprHasProperty(pExpr,(EP_TokenOnly|EP_Leaf)) ){\n      if( pExpr->pLeft && walkExpr(pWalker, pExpr->pLeft) ) return WRC_Abort;\n       assert( pExpr->x.pList==0 || pExpr->pRight==0 );\n      if( pExpr->pRight ){\n        pExpr = pExpr->pRight;\n        continue;\n      }else if( ExprHasProperty(pExpr, EP_xIsSelect) ){\n        if( sqlite3WalkSelect(pWalker, pExpr->x.pSelect) ) return WRC_Abort;\n      }else if( pExpr->x.pList ){\n        if( sqlite3WalkExprList(pWalker, pExpr->x.pList) ) return WRC_Abort;\n      }\n    }\n    break;\n  }\n  return WRC_Continue;\n}\nSQLITE_PRIVATE int sqlite3WalkExpr(Walker *pWalker, Expr *pExpr){\n  return pExpr ? walkExpr(pWalker,pExpr) : WRC_Continue;\n}\n\n/*\n** Call sqlite3WalkExpr() for every expression in list p or until\n** an abort request is seen.\n*/\nSQLITE_PRIVATE int sqlite3WalkExprList(Walker *pWalker, ExprList *p){\n  int i;\n  struct ExprList_item *pItem;\n  if( p ){\n    for(i=p->nExpr, pItem=p->a; i>0; i--, pItem++){\n      if( sqlite3WalkExpr(pWalker, pItem->pExpr) ) return WRC_Abort;\n    }\n  }\n  return WRC_Continue;\n}\n\n/*\n** Walk all expressions associated with SELECT statement p.  Do\n** not invoke the SELECT callback on p, but do (of course) invoke\n** any expr callbacks and SELECT callbacks that come from subqueries.\n** Return WRC_Abort or WRC_Continue.\n*/\nSQLITE_PRIVATE int sqlite3WalkSelectExpr(Walker *pWalker, Select *p){\n  if( sqlite3WalkExprList(pWalker, p->pEList) ) return WRC_Abort;\n  if( sqlite3WalkExpr(pWalker, p->pWhere) ) return WRC_Abort;\n  if( sqlite3WalkExprList(pWalker, p->pGroupBy) ) return WRC_Abort;\n  if( sqlite3WalkExpr(pWalker, p->pHaving) ) return WRC_Abort;\n  if( sqlite3WalkExprList(pWalker, p->pOrderBy) ) return WRC_Abort;\n  if( sqlite3WalkExpr(pWalker, p->pLimit) ) return WRC_Abort;\n  return WRC_Continue;\n}\n\n/*\n** Walk the parse trees associated with all subqueries in the\n** FROM clause of SELECT statement p.  Do not invoke the select\n** callback on p, but do invoke it on each FROM clause subquery\n** and on any subqueries further down in the tree.  Return \n** WRC_Abort or WRC_Continue;\n*/\nSQLITE_PRIVATE int sqlite3WalkSelectFrom(Walker *pWalker, Select *p){\n  SrcList *pSrc;\n  int i;\n  struct SrcList_item *pItem;\n\n  pSrc = p->pSrc;\n  assert( pSrc!=0 );\n  for(i=pSrc->nSrc, pItem=pSrc->a; i>0; i--, pItem++){\n    if( pItem->pSelect && sqlite3WalkSelect(pWalker, pItem->pSelect) ){\n      return WRC_Abort;\n    }\n    if( pItem->fg.isTabFunc\n     && sqlite3WalkExprList(pWalker, pItem->u1.pFuncArg)\n    ){\n      return WRC_Abort;\n    }\n  }\n  return WRC_Continue;\n} \n\n/*\n** Call sqlite3WalkExpr() for every expression in Select statement p.\n** Invoke sqlite3WalkSelect() for subqueries in the FROM clause and\n** on the compound select chain, p->pPrior. \n**\n** If it is not NULL, the xSelectCallback() callback is invoked before\n** the walk of the expressions and FROM clause. The xSelectCallback2()\n** method is invoked following the walk of the expressions and FROM clause,\n** but only if both xSelectCallback and xSelectCallback2 are both non-NULL\n** and if the expressions and FROM clause both return WRC_Continue;\n**\n** Return WRC_Continue under normal conditions.  Return WRC_Abort if\n** there is an abort request.\n**\n** If the Walker does not have an xSelectCallback() then this routine\n** is a no-op returning WRC_Continue.\n*/\nSQLITE_PRIVATE int sqlite3WalkSelect(Walker *pWalker, Select *p){\n  int rc;\n  if( p==0 ) return WRC_Continue;\n  if( pWalker->xSelectCallback==0 ) return WRC_Continue;\n  do{\n    rc = pWalker->xSelectCallback(pWalker, p);\n    if( rc ) return rc & WRC_Abort;\n    if( sqlite3WalkSelectExpr(pWalker, p)\n     || sqlite3WalkSelectFrom(pWalker, p)\n    ){\n      return WRC_Abort;\n    }\n    if( pWalker->xSelectCallback2 ){\n      pWalker->xSelectCallback2(pWalker, p);\n    }\n    p = p->pPrior;\n  }while( p!=0 );\n  return WRC_Continue;\n}\n\n/************** End of walker.c **********************************************/\n/************** Begin file resolve.c *****************************************/\n/*\n** 2008 August 18\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n*************************************************************************\n**\n** This file contains routines used for walking the parser tree and\n** resolve all identifiers by associating them with a particular\n** table and column.\n*/\n/* #include \"sqliteInt.h\" */\n\n/*\n** Walk the expression tree pExpr and increase the aggregate function\n** depth (the Expr.op2 field) by N on every TK_AGG_FUNCTION node.\n** This needs to occur when copying a TK_AGG_FUNCTION node from an\n** outer query into an inner subquery.\n**\n** incrAggFunctionDepth(pExpr,n) is the main routine.  incrAggDepth(..)\n** is a helper function - a callback for the tree walker.\n*/\nstatic int incrAggDepth(Walker *pWalker, Expr *pExpr){\n  if( pExpr->op==TK_AGG_FUNCTION ) pExpr->op2 += pWalker->u.n;\n  return WRC_Continue;\n}\nstatic void incrAggFunctionDepth(Expr *pExpr, int N){\n  if( N>0 ){\n    Walker w;\n    memset(&w, 0, sizeof(w));\n    w.xExprCallback = incrAggDepth;\n    w.u.n = N;\n    sqlite3WalkExpr(&w, pExpr);\n  }\n}\n\n/*\n** Turn the pExpr expression into an alias for the iCol-th column of the\n** result set in pEList.\n**\n** If the reference is followed by a COLLATE operator, then make sure\n** the COLLATE operator is preserved.  For example:\n**\n**     SELECT a+b, c+d FROM t1 ORDER BY 1 COLLATE nocase;\n**\n** Should be transformed into:\n**\n**     SELECT a+b, c+d FROM t1 ORDER BY (a+b) COLLATE nocase;\n**\n** The nSubquery parameter specifies how many levels of subquery the\n** alias is removed from the original expression.  The usual value is\n** zero but it might be more if the alias is contained within a subquery\n** of the original expression.  The Expr.op2 field of TK_AGG_FUNCTION\n** structures must be increased by the nSubquery amount.\n*/\nstatic void resolveAlias(\n  Parse *pParse,         /* Parsing context */\n  ExprList *pEList,      /* A result set */\n  int iCol,              /* A column in the result set.  0..pEList->nExpr-1 */\n  Expr *pExpr,           /* Transform this into an alias to the result set */\n  const char *zType,     /* \"GROUP\" or \"ORDER\" or \"\" */\n  int nSubquery          /* Number of subqueries that the label is moving */\n){\n  Expr *pOrig;           /* The iCol-th column of the result set */\n  Expr *pDup;            /* Copy of pOrig */\n  sqlite3 *db;           /* The database connection */\n\n  assert( iCol>=0 && iCol<pEList->nExpr );\n  pOrig = pEList->a[iCol].pExpr;\n  assert( pOrig!=0 );\n  db = pParse->db;\n  pDup = sqlite3ExprDup(db, pOrig, 0);\n  if( pDup==0 ) return;\n  if( zType[0]!='G' ) incrAggFunctionDepth(pDup, nSubquery);\n  if( pExpr->op==TK_COLLATE ){\n    pDup = sqlite3ExprAddCollateString(pParse, pDup, pExpr->u.zToken);\n  }\n  ExprSetProperty(pDup, EP_Alias);\n\n  /* Before calling sqlite3ExprDelete(), set the EP_Static flag. This \n  ** prevents ExprDelete() from deleting the Expr structure itself,\n  ** allowing it to be repopulated by the memcpy() on the following line.\n  ** The pExpr->u.zToken might point into memory that will be freed by the\n  ** sqlite3DbFree(db, pDup) on the last line of this block, so be sure to\n  ** make a copy of the token before doing the sqlite3DbFree().\n  */\n  ExprSetProperty(pExpr, EP_Static);\n  sqlite3ExprDelete(db, pExpr);\n  memcpy(pExpr, pDup, sizeof(*pExpr));\n  if( !ExprHasProperty(pExpr, EP_IntValue) && pExpr->u.zToken!=0 ){\n    assert( (pExpr->flags & (EP_Reduced|EP_TokenOnly))==0 );\n    pExpr->u.zToken = sqlite3DbStrDup(db, pExpr->u.zToken);\n    pExpr->flags |= EP_MemToken;\n  }\n  sqlite3DbFree(db, pDup);\n}\n\n\n/*\n** Return TRUE if the name zCol occurs anywhere in the USING clause.\n**\n** Return FALSE if the USING clause is NULL or if it does not contain\n** zCol.\n*/\nstatic int nameInUsingClause(IdList *pUsing, const char *zCol){\n  if( pUsing ){\n    int k;\n    for(k=0; k<pUsing->nId; k++){\n      if( sqlite3StrICmp(pUsing->a[k].zName, zCol)==0 ) return 1;\n    }\n  }\n  return 0;\n}\n\n/*\n** Subqueries stores the original database, table and column names for their\n** result sets in ExprList.a[].zSpan, in the form \"DATABASE.TABLE.COLUMN\".\n** Check to see if the zSpan given to this routine matches the zDb, zTab,\n** and zCol.  If any of zDb, zTab, and zCol are NULL then those fields will\n** match anything.\n*/\nSQLITE_PRIVATE int sqlite3MatchSpanName(\n  const char *zSpan,\n  const char *zCol,\n  const char *zTab,\n  const char *zDb\n){\n  int n;\n  for(n=0; ALWAYS(zSpan[n]) && zSpan[n]!='.'; n++){}\n  if( zDb && (sqlite3StrNICmp(zSpan, zDb, n)!=0 || zDb[n]!=0) ){\n    return 0;\n  }\n  zSpan += n+1;\n  for(n=0; ALWAYS(zSpan[n]) && zSpan[n]!='.'; n++){}\n  if( zTab && (sqlite3StrNICmp(zSpan, zTab, n)!=0 || zTab[n]!=0) ){\n    return 0;\n  }\n  zSpan += n+1;\n  if( zCol && sqlite3StrICmp(zSpan, zCol)!=0 ){\n    return 0;\n  }\n  return 1;\n}\n\n/*\n** Given the name of a column of the form X.Y.Z or Y.Z or just Z, look up\n** that name in the set of source tables in pSrcList and make the pExpr \n** expression node refer back to that source column.  The following changes\n** are made to pExpr:\n**\n**    pExpr->iDb           Set the index in db->aDb[] of the database X\n**                         (even if X is implied).\n**    pExpr->iTable        Set to the cursor number for the table obtained\n**                         from pSrcList.\n**    pExpr->pTab          Points to the Table structure of X.Y (even if\n**                         X and/or Y are implied.)\n**    pExpr->iColumn       Set to the column number within the table.\n**    pExpr->op            Set to TK_COLUMN.\n**    pExpr->pLeft         Any expression this points to is deleted\n**    pExpr->pRight        Any expression this points to is deleted.\n**\n** The zDb variable is the name of the database (the \"X\").  This value may be\n** NULL meaning that name is of the form Y.Z or Z.  Any available database\n** can be used.  The zTable variable is the name of the table (the \"Y\").  This\n** value can be NULL if zDb is also NULL.  If zTable is NULL it\n** means that the form of the name is Z and that columns from any table\n** can be used.\n**\n** If the name cannot be resolved unambiguously, leave an error message\n** in pParse and return WRC_Abort.  Return WRC_Prune on success.\n*/\nstatic int lookupName(\n  Parse *pParse,       /* The parsing context */\n  const char *zDb,     /* Name of the database containing table, or NULL */\n  const char *zTab,    /* Name of table containing column, or NULL */\n  const char *zCol,    /* Name of the column. */\n  NameContext *pNC,    /* The name context used to resolve the name */\n  Expr *pExpr          /* Make this EXPR node point to the selected column */\n){\n  int i, j;                         /* Loop counters */\n  int cnt = 0;                      /* Number of matching column names */\n  int cntTab = 0;                   /* Number of matching table names */\n  int nSubquery = 0;                /* How many levels of subquery */\n  sqlite3 *db = pParse->db;         /* The database connection */\n  struct SrcList_item *pItem;       /* Use for looping over pSrcList items */\n  struct SrcList_item *pMatch = 0;  /* The matching pSrcList item */\n  NameContext *pTopNC = pNC;        /* First namecontext in the list */\n  Schema *pSchema = 0;              /* Schema of the expression */\n  int isTrigger = 0;                /* True if resolved to a trigger column */\n  Table *pTab = 0;                  /* Table hold the row */\n  Column *pCol;                     /* A column of pTab */\n\n  assert( pNC );     /* the name context cannot be NULL. */\n  assert( zCol );    /* The Z in X.Y.Z cannot be NULL */\n  assert( !ExprHasProperty(pExpr, EP_TokenOnly|EP_Reduced) );\n\n  /* Initialize the node to no-match */\n  pExpr->iTable = -1;\n  pExpr->pTab = 0;\n  ExprSetVVAProperty(pExpr, EP_NoReduce);\n\n  /* Translate the schema name in zDb into a pointer to the corresponding\n  ** schema.  If not found, pSchema will remain NULL and nothing will match\n  ** resulting in an appropriate error message toward the end of this routine\n  */\n  if( zDb ){\n    testcase( pNC->ncFlags & NC_PartIdx );\n    testcase( pNC->ncFlags & NC_IsCheck );\n    if( (pNC->ncFlags & (NC_PartIdx|NC_IsCheck))!=0 ){\n      /* Silently ignore database qualifiers inside CHECK constraints and\n      ** partial indices.  Do not raise errors because that might break\n      ** legacy and because it does not hurt anything to just ignore the\n      ** database name. */\n      zDb = 0;\n    }else{\n      for(i=0; i<db->nDb; i++){\n        assert( db->aDb[i].zDbSName );\n        if( sqlite3StrICmp(db->aDb[i].zDbSName,zDb)==0 ){\n          pSchema = db->aDb[i].pSchema;\n          break;\n        }\n      }\n    }\n  }\n\n  /* Start at the inner-most context and move outward until a match is found */\n  assert( pNC && cnt==0 );\n  do{\n    ExprList *pEList;\n    SrcList *pSrcList = pNC->pSrcList;\n\n    if( pSrcList ){\n      for(i=0, pItem=pSrcList->a; i<pSrcList->nSrc; i++, pItem++){\n        pTab = pItem->pTab;\n        assert( pTab!=0 && pTab->zName!=0 );\n        assert( pTab->nCol>0 );\n        if( pItem->pSelect && (pItem->pSelect->selFlags & SF_NestedFrom)!=0 ){\n          int hit = 0;\n          pEList = pItem->pSelect->pEList;\n          for(j=0; j<pEList->nExpr; j++){\n            if( sqlite3MatchSpanName(pEList->a[j].zSpan, zCol, zTab, zDb) ){\n              cnt++;\n              cntTab = 2;\n              pMatch = pItem;\n              pExpr->iColumn = j;\n              hit = 1;\n            }\n          }\n          if( hit || zTab==0 ) continue;\n        }\n        if( zDb && pTab->pSchema!=pSchema ){\n          continue;\n        }\n        if( zTab ){\n          const char *zTabName = pItem->zAlias ? pItem->zAlias : pTab->zName;\n          assert( zTabName!=0 );\n          if( sqlite3StrICmp(zTabName, zTab)!=0 ){\n            continue;\n          }\n        }\n        if( 0==(cntTab++) ){\n          pMatch = pItem;\n        }\n        for(j=0, pCol=pTab->aCol; j<pTab->nCol; j++, pCol++){\n          if( sqlite3StrICmp(pCol->zName, zCol)==0 ){\n            /* If there has been exactly one prior match and this match\n            ** is for the right-hand table of a NATURAL JOIN or is in a \n            ** USING clause, then skip this match.\n            */\n            if( cnt==1 ){\n              if( pItem->fg.jointype & JT_NATURAL ) continue;\n              if( nameInUsingClause(pItem->pUsing, zCol) ) continue;\n            }\n            cnt++;\n            pMatch = pItem;\n            /* Substitute the rowid (column -1) for the INTEGER PRIMARY KEY */\n            pExpr->iColumn = j==pTab->iPKey ? -1 : (i16)j;\n            break;\n          }\n        }\n      }\n      if( pMatch ){\n        pExpr->iTable = pMatch->iCursor;\n        pExpr->pTab = pMatch->pTab;\n        /* RIGHT JOIN not (yet) supported */\n        assert( (pMatch->fg.jointype & JT_RIGHT)==0 );\n        if( (pMatch->fg.jointype & JT_LEFT)!=0 ){\n          ExprSetProperty(pExpr, EP_CanBeNull);\n        }\n        pSchema = pExpr->pTab->pSchema;\n      }\n    } /* if( pSrcList ) */\n\n#ifndef SQLITE_OMIT_TRIGGER\n    /* If we have not already resolved the name, then maybe \n    ** it is a new.* or old.* trigger argument reference\n    */\n    if( zDb==0 && zTab!=0 && cntTab==0 && pParse->pTriggerTab!=0 ){\n      int op = pParse->eTriggerOp;\n      assert( op==TK_DELETE || op==TK_UPDATE || op==TK_INSERT );\n      if( op!=TK_DELETE && sqlite3StrICmp(\"new\",zTab) == 0 ){\n        pExpr->iTable = 1;\n        pTab = pParse->pTriggerTab;\n      }else if( op!=TK_INSERT && sqlite3StrICmp(\"old\",zTab)==0 ){\n        pExpr->iTable = 0;\n        pTab = pParse->pTriggerTab;\n      }else{\n        pTab = 0;\n      }\n\n      if( pTab ){ \n        int iCol;\n        pSchema = pTab->pSchema;\n        cntTab++;\n        for(iCol=0, pCol=pTab->aCol; iCol<pTab->nCol; iCol++, pCol++){\n          if( sqlite3StrICmp(pCol->zName, zCol)==0 ){\n            if( iCol==pTab->iPKey ){\n              iCol = -1;\n            }\n            break;\n          }\n        }\n        if( iCol>=pTab->nCol && sqlite3IsRowid(zCol) && VisibleRowid(pTab) ){\n          /* IMP: R-51414-32910 */\n          iCol = -1;\n        }\n        if( iCol<pTab->nCol ){\n          cnt++;\n          if( iCol<0 ){\n            pExpr->affinity = SQLITE_AFF_INTEGER;\n          }else if( pExpr->iTable==0 ){\n            testcase( iCol==31 );\n            testcase( iCol==32 );\n            pParse->oldmask |= (iCol>=32 ? 0xffffffff : (((u32)1)<<iCol));\n          }else{\n            testcase( iCol==31 );\n            testcase( iCol==32 );\n            pParse->newmask |= (iCol>=32 ? 0xffffffff : (((u32)1)<<iCol));\n          }\n          pExpr->iColumn = (i16)iCol;\n          pExpr->pTab = pTab;\n          isTrigger = 1;\n        }\n      }\n    }\n#endif /* !defined(SQLITE_OMIT_TRIGGER) */\n\n    /*\n    ** Perhaps the name is a reference to the ROWID\n    */\n    if( cnt==0\n     && cntTab==1\n     && pMatch\n     && (pNC->ncFlags & NC_IdxExpr)==0\n     && sqlite3IsRowid(zCol)\n     && VisibleRowid(pMatch->pTab)\n    ){\n      cnt = 1;\n      pExpr->iColumn = -1;\n      pExpr->affinity = SQLITE_AFF_INTEGER;\n    }\n\n    /*\n    ** If the input is of the form Z (not Y.Z or X.Y.Z) then the name Z\n    ** might refer to an result-set alias.  This happens, for example, when\n    ** we are resolving names in the WHERE clause of the following command:\n    **\n    **     SELECT a+b AS x FROM table WHERE x<10;\n    **\n    ** In cases like this, replace pExpr with a copy of the expression that\n    ** forms the result set entry (\"a+b\" in the example) and return immediately.\n    ** Note that the expression in the result set should have already been\n    ** resolved by the time the WHERE clause is resolved.\n    **\n    ** The ability to use an output result-set column in the WHERE, GROUP BY,\n    ** or HAVING clauses, or as part of a larger expression in the ORDER BY\n    ** clause is not standard SQL.  This is a (goofy) SQLite extension, that\n    ** is supported for backwards compatibility only. Hence, we issue a warning\n    ** on sqlite3_log() whenever the capability is used.\n    */\n    if( (pEList = pNC->pEList)!=0\n     && zTab==0\n     && cnt==0\n    ){\n      for(j=0; j<pEList->nExpr; j++){\n        char *zAs = pEList->a[j].zName;\n        if( zAs!=0 && sqlite3StrICmp(zAs, zCol)==0 ){\n          Expr *pOrig;\n          assert( pExpr->pLeft==0 && pExpr->pRight==0 );\n          assert( pExpr->x.pList==0 );\n          assert( pExpr->x.pSelect==0 );\n          pOrig = pEList->a[j].pExpr;\n          if( (pNC->ncFlags&NC_AllowAgg)==0 && ExprHasProperty(pOrig, EP_Agg) ){\n            sqlite3ErrorMsg(pParse, \"misuse of aliased aggregate %s\", zAs);\n            return WRC_Abort;\n          }\n          if( sqlite3ExprVectorSize(pOrig)!=1 ){\n            sqlite3ErrorMsg(pParse, \"row value misused\");\n            return WRC_Abort;\n          }\n          resolveAlias(pParse, pEList, j, pExpr, \"\", nSubquery);\n          cnt = 1;\n          pMatch = 0;\n          assert( zTab==0 && zDb==0 );\n          goto lookupname_end;\n        }\n      } \n    }\n\n    /* Advance to the next name context.  The loop will exit when either\n    ** we have a match (cnt>0) or when we run out of name contexts.\n    */\n    if( cnt ) break;\n    pNC = pNC->pNext;\n    nSubquery++;\n  }while( pNC );\n\n\n  /*\n  ** If X and Y are NULL (in other words if only the column name Z is\n  ** supplied) and the value of Z is enclosed in double-quotes, then\n  ** Z is a string literal if it doesn't match any column names.  In that\n  ** case, we need to return right away and not make any changes to\n  ** pExpr.\n  **\n  ** Because no reference was made to outer contexts, the pNC->nRef\n  ** fields are not changed in any context.\n  */\n  if( cnt==0 && zTab==0 ){\n    assert( pExpr->op==TK_ID );\n    if( ExprHasProperty(pExpr,EP_DblQuoted) ){\n      pExpr->op = TK_STRING;\n      pExpr->pTab = 0;\n      return WRC_Prune;\n    }\n    if( sqlite3ExprIdToTrueFalse(pExpr) ){\n      return WRC_Prune;\n    }\n  }\n\n  /*\n  ** cnt==0 means there was not match.  cnt>1 means there were two or\n  ** more matches.  Either way, we have an error.\n  */\n  if( cnt!=1 ){\n    const char *zErr;\n    zErr = cnt==0 ? \"no such column\" : \"ambiguous column name\";\n    if( zDb ){\n      sqlite3ErrorMsg(pParse, \"%s: %s.%s.%s\", zErr, zDb, zTab, zCol);\n    }else if( zTab ){\n      sqlite3ErrorMsg(pParse, \"%s: %s.%s\", zErr, zTab, zCol);\n    }else{\n      sqlite3ErrorMsg(pParse, \"%s: %s\", zErr, zCol);\n    }\n    pParse->checkSchema = 1;\n    pTopNC->nErr++;\n  }\n\n  /* If a column from a table in pSrcList is referenced, then record\n  ** this fact in the pSrcList.a[].colUsed bitmask.  Column 0 causes\n  ** bit 0 to be set.  Column 1 sets bit 1.  And so forth.  If the\n  ** column number is greater than the number of bits in the bitmask\n  ** then set the high-order bit of the bitmask.\n  */\n  if( pExpr->iColumn>=0 && pMatch!=0 ){\n    int n = pExpr->iColumn;\n    testcase( n==BMS-1 );\n    if( n>=BMS ){\n      n = BMS-1;\n    }\n    assert( pMatch->iCursor==pExpr->iTable );\n    pMatch->colUsed |= ((Bitmask)1)<<n;\n  }\n\n  /* Clean up and return\n  */\n  sqlite3ExprDelete(db, pExpr->pLeft);\n  pExpr->pLeft = 0;\n  sqlite3ExprDelete(db, pExpr->pRight);\n  pExpr->pRight = 0;\n  pExpr->op = (isTrigger ? TK_TRIGGER : TK_COLUMN);\n  ExprSetProperty(pExpr, EP_Leaf);\nlookupname_end:\n  if( cnt==1 ){\n    assert( pNC!=0 );\n    if( !ExprHasProperty(pExpr, EP_Alias) ){\n      sqlite3AuthRead(pParse, pExpr, pSchema, pNC->pSrcList);\n    }\n    /* Increment the nRef value on all name contexts from TopNC up to\n    ** the point where the name matched. */\n    for(;;){\n      assert( pTopNC!=0 );\n      pTopNC->nRef++;\n      if( pTopNC==pNC ) break;\n      pTopNC = pTopNC->pNext;\n    }\n    return WRC_Prune;\n  } else {\n    return WRC_Abort;\n  }\n}\n\n/*\n** Allocate and return a pointer to an expression to load the column iCol\n** from datasource iSrc in SrcList pSrc.\n*/\nSQLITE_PRIVATE Expr *sqlite3CreateColumnExpr(sqlite3 *db, SrcList *pSrc, int iSrc, int iCol){\n  Expr *p = sqlite3ExprAlloc(db, TK_COLUMN, 0, 0);\n  if( p ){\n    struct SrcList_item *pItem = &pSrc->a[iSrc];\n    p->pTab = pItem->pTab;\n    p->iTable = pItem->iCursor;\n    if( p->pTab->iPKey==iCol ){\n      p->iColumn = -1;\n    }else{\n      p->iColumn = (ynVar)iCol;\n      testcase( iCol==BMS );\n      testcase( iCol==BMS-1 );\n      pItem->colUsed |= ((Bitmask)1)<<(iCol>=BMS ? BMS-1 : iCol);\n    }\n  }\n  return p;\n}\n\n/*\n** Report an error that an expression is not valid for some set of\n** pNC->ncFlags values determined by validMask.\n*/\nstatic void notValid(\n  Parse *pParse,       /* Leave error message here */\n  NameContext *pNC,    /* The name context */\n  const char *zMsg,    /* Type of error */\n  int validMask        /* Set of contexts for which prohibited */\n){\n  assert( (validMask&~(NC_IsCheck|NC_PartIdx|NC_IdxExpr))==0 );\n  if( (pNC->ncFlags & validMask)!=0 ){\n    const char *zIn = \"partial index WHERE clauses\";\n    if( pNC->ncFlags & NC_IdxExpr )      zIn = \"index expressions\";\n#ifndef SQLITE_OMIT_CHECK\n    else if( pNC->ncFlags & NC_IsCheck ) zIn = \"CHECK constraints\";\n#endif\n    sqlite3ErrorMsg(pParse, \"%s prohibited in %s\", zMsg, zIn);\n  }\n}\n\n/*\n** Expression p should encode a floating point value between 1.0 and 0.0.\n** Return 1024 times this value.  Or return -1 if p is not a floating point\n** value between 1.0 and 0.0.\n*/\nstatic int exprProbability(Expr *p){\n  double r = -1.0;\n  if( p->op!=TK_FLOAT ) return -1;\n  sqlite3AtoF(p->u.zToken, &r, sqlite3Strlen30(p->u.zToken), SQLITE_UTF8);\n  assert( r>=0.0 );\n  if( r>1.0 ) return -1;\n  return (int)(r*134217728.0);\n}\n\n/*\n** This routine is callback for sqlite3WalkExpr().\n**\n** Resolve symbolic names into TK_COLUMN operators for the current\n** node in the expression tree.  Return 0 to continue the search down\n** the tree or 2 to abort the tree walk.\n**\n** This routine also does error checking and name resolution for\n** function names.  The operator for aggregate functions is changed\n** to TK_AGG_FUNCTION.\n*/\nstatic int resolveExprStep(Walker *pWalker, Expr *pExpr){\n  NameContext *pNC;\n  Parse *pParse;\n\n  pNC = pWalker->u.pNC;\n  assert( pNC!=0 );\n  pParse = pNC->pParse;\n  assert( pParse==pWalker->pParse );\n\n#ifndef NDEBUG\n  if( pNC->pSrcList && pNC->pSrcList->nAlloc>0 ){\n    SrcList *pSrcList = pNC->pSrcList;\n    int i;\n    for(i=0; i<pNC->pSrcList->nSrc; i++){\n      assert( pSrcList->a[i].iCursor>=0 && pSrcList->a[i].iCursor<pParse->nTab);\n    }\n  }\n#endif\n  switch( pExpr->op ){\n\n#if defined(SQLITE_ENABLE_UPDATE_DELETE_LIMIT) && !defined(SQLITE_OMIT_SUBQUERY)\n    /* The special operator TK_ROW means use the rowid for the first\n    ** column in the FROM clause.  This is used by the LIMIT and ORDER BY\n    ** clause processing on UPDATE and DELETE statements.\n    */\n    case TK_ROW: {\n      SrcList *pSrcList = pNC->pSrcList;\n      struct SrcList_item *pItem;\n      assert( pSrcList && pSrcList->nSrc==1 );\n      pItem = pSrcList->a;\n      assert( HasRowid(pItem->pTab) && pItem->pTab->pSelect==0 );\n      pExpr->op = TK_COLUMN;\n      pExpr->pTab = pItem->pTab;\n      pExpr->iTable = pItem->iCursor;\n      pExpr->iColumn = -1;\n      pExpr->affinity = SQLITE_AFF_INTEGER;\n      break;\n    }\n#endif /* defined(SQLITE_ENABLE_UPDATE_DELETE_LIMIT)\n          && !defined(SQLITE_OMIT_SUBQUERY) */\n\n    /* A column name:                    ID\n    ** Or table name and column name:    ID.ID\n    ** Or a database, table and column:  ID.ID.ID\n    **\n    ** The TK_ID and TK_OUT cases are combined so that there will only\n    ** be one call to lookupName().  Then the compiler will in-line \n    ** lookupName() for a size reduction and performance increase.\n    */\n    case TK_ID:\n    case TK_DOT: {\n      const char *zColumn;\n      const char *zTable;\n      const char *zDb;\n      Expr *pRight;\n\n      if( pExpr->op==TK_ID ){\n        zDb = 0;\n        zTable = 0;\n        zColumn = pExpr->u.zToken;\n      }else{\n        notValid(pParse, pNC, \"the \\\".\\\" operator\", NC_IdxExpr);\n        pRight = pExpr->pRight;\n        if( pRight->op==TK_ID ){\n          zDb = 0;\n          zTable = pExpr->pLeft->u.zToken;\n          zColumn = pRight->u.zToken;\n        }else{\n          assert( pRight->op==TK_DOT );\n          zDb = pExpr->pLeft->u.zToken;\n          zTable = pRight->pLeft->u.zToken;\n          zColumn = pRight->pRight->u.zToken;\n        }\n      }\n      return lookupName(pParse, zDb, zTable, zColumn, pNC, pExpr);\n    }\n\n    /* Resolve function names\n    */\n    case TK_FUNCTION: {\n      ExprList *pList = pExpr->x.pList;    /* The argument list */\n      int n = pList ? pList->nExpr : 0;    /* Number of arguments */\n      int no_such_func = 0;       /* True if no such function exists */\n      int wrong_num_args = 0;     /* True if wrong number of arguments */\n      int is_agg = 0;             /* True if is an aggregate function */\n      int nId;                    /* Number of characters in function name */\n      const char *zId;            /* The function name. */\n      FuncDef *pDef;              /* Information about the function */\n      u8 enc = ENC(pParse->db);   /* The database encoding */\n\n      assert( !ExprHasProperty(pExpr, EP_xIsSelect) );\n      zId = pExpr->u.zToken;\n      nId = sqlite3Strlen30(zId);\n      pDef = sqlite3FindFunction(pParse->db, zId, n, enc, 0);\n      if( pDef==0 ){\n        pDef = sqlite3FindFunction(pParse->db, zId, -2, enc, 0);\n        if( pDef==0 ){\n          no_such_func = 1;\n        }else{\n          wrong_num_args = 1;\n        }\n      }else{\n        is_agg = pDef->xFinalize!=0;\n        if( pDef->funcFlags & SQLITE_FUNC_UNLIKELY ){\n          ExprSetProperty(pExpr, EP_Unlikely|EP_Skip);\n          if( n==2 ){\n            pExpr->iTable = exprProbability(pList->a[1].pExpr);\n            if( pExpr->iTable<0 ){\n              sqlite3ErrorMsg(pParse,\n                \"second argument to likelihood() must be a \"\n                \"constant between 0.0 and 1.0\");\n              pNC->nErr++;\n            }\n          }else{\n            /* EVIDENCE-OF: R-61304-29449 The unlikely(X) function is\n            ** equivalent to likelihood(X, 0.0625).\n            ** EVIDENCE-OF: R-01283-11636 The unlikely(X) function is\n            ** short-hand for likelihood(X,0.0625).\n            ** EVIDENCE-OF: R-36850-34127 The likely(X) function is short-hand\n            ** for likelihood(X,0.9375).\n            ** EVIDENCE-OF: R-53436-40973 The likely(X) function is equivalent\n            ** to likelihood(X,0.9375). */\n            /* TUNING: unlikely() probability is 0.0625.  likely() is 0.9375 */\n            pExpr->iTable = pDef->zName[0]=='u' ? 8388608 : 125829120;\n          }             \n        }\n#ifndef SQLITE_OMIT_AUTHORIZATION\n        {\n          int auth = sqlite3AuthCheck(pParse, SQLITE_FUNCTION, 0,pDef->zName,0);\n          if( auth!=SQLITE_OK ){\n            if( auth==SQLITE_DENY ){\n              sqlite3ErrorMsg(pParse, \"not authorized to use function: %s\",\n                                      pDef->zName);\n              pNC->nErr++;\n            }\n            pExpr->op = TK_NULL;\n            return WRC_Prune;\n          }\n        }\n#endif\n        if( pDef->funcFlags & (SQLITE_FUNC_CONSTANT|SQLITE_FUNC_SLOCHNG) ){\n          /* For the purposes of the EP_ConstFunc flag, date and time\n          ** functions and other functions that change slowly are considered\n          ** constant because they are constant for the duration of one query */\n          ExprSetProperty(pExpr,EP_ConstFunc);\n        }\n        if( (pDef->funcFlags & SQLITE_FUNC_CONSTANT)==0 ){\n          /* Date/time functions that use 'now', and other functions like\n          ** sqlite_version() that might change over time cannot be used\n          ** in an index. */\n          notValid(pParse, pNC, \"non-deterministic functions\",\n                   NC_IdxExpr|NC_PartIdx);\n        }\n      }\n      if( is_agg && (pNC->ncFlags & NC_AllowAgg)==0 ){\n        sqlite3ErrorMsg(pParse, \"misuse of aggregate function %.*s()\", nId,zId);\n        pNC->nErr++;\n        is_agg = 0;\n      }else if( no_such_func && pParse->db->init.busy==0\n#ifdef SQLITE_ENABLE_UNKNOWN_SQL_FUNCTION\n                && pParse->explain==0\n#endif\n      ){\n        sqlite3ErrorMsg(pParse, \"no such function: %.*s\", nId, zId);\n        pNC->nErr++;\n      }else if( wrong_num_args ){\n        sqlite3ErrorMsg(pParse,\"wrong number of arguments to function %.*s()\",\n             nId, zId);\n        pNC->nErr++;\n      }\n      if( is_agg ) pNC->ncFlags &= ~NC_AllowAgg;\n      sqlite3WalkExprList(pWalker, pList);\n      if( is_agg ){\n        NameContext *pNC2 = pNC;\n        pExpr->op = TK_AGG_FUNCTION;\n        pExpr->op2 = 0;\n        while( pNC2 && !sqlite3FunctionUsesThisSrc(pExpr, pNC2->pSrcList) ){\n          pExpr->op2++;\n          pNC2 = pNC2->pNext;\n        }\n        assert( pDef!=0 );\n        if( pNC2 ){\n          assert( SQLITE_FUNC_MINMAX==NC_MinMaxAgg );\n          testcase( (pDef->funcFlags & SQLITE_FUNC_MINMAX)!=0 );\n          pNC2->ncFlags |= NC_HasAgg | (pDef->funcFlags & SQLITE_FUNC_MINMAX);\n\n        }\n        pNC->ncFlags |= NC_AllowAgg;\n      }\n      /* FIX ME:  Compute pExpr->affinity based on the expected return\n      ** type of the function \n      */\n      return WRC_Prune;\n    }\n#ifndef SQLITE_OMIT_SUBQUERY\n    case TK_SELECT:\n    case TK_EXISTS:  testcase( pExpr->op==TK_EXISTS );\n#endif\n    case TK_IN: {\n      testcase( pExpr->op==TK_IN );\n      if( ExprHasProperty(pExpr, EP_xIsSelect) ){\n        int nRef = pNC->nRef;\n        notValid(pParse, pNC, \"subqueries\", NC_IsCheck|NC_PartIdx|NC_IdxExpr);\n        sqlite3WalkSelect(pWalker, pExpr->x.pSelect);\n        assert( pNC->nRef>=nRef );\n        if( nRef!=pNC->nRef ){\n          ExprSetProperty(pExpr, EP_VarSelect);\n          pNC->ncFlags |= NC_VarSelect;\n        }\n      }\n      break;\n    }\n    case TK_VARIABLE: {\n      notValid(pParse, pNC, \"parameters\", NC_IsCheck|NC_PartIdx|NC_IdxExpr);\n      break;\n    }\n    case TK_IS:\n    case TK_ISNOT: {\n      Expr *pRight;\n      assert( !ExprHasProperty(pExpr, EP_Reduced) );\n      /* Handle special cases of \"x IS TRUE\", \"x IS FALSE\", \"x IS NOT TRUE\",\n      ** and \"x IS NOT FALSE\". */\n      if( (pRight = pExpr->pRight)->op==TK_ID ){\n        int rc = resolveExprStep(pWalker, pRight);\n        if( rc==WRC_Abort ) return WRC_Abort;\n        if( pRight->op==TK_TRUEFALSE ){\n          pExpr->op2 = pExpr->op;\n          pExpr->op = TK_TRUTH;\n          return WRC_Continue;\n        }\n      }\n      /* Fall thru */\n    }\n    case TK_BETWEEN:\n    case TK_EQ:\n    case TK_NE:\n    case TK_LT:\n    case TK_LE:\n    case TK_GT:\n    case TK_GE: {\n      int nLeft, nRight;\n      if( pParse->db->mallocFailed ) break;\n      assert( pExpr->pLeft!=0 );\n      nLeft = sqlite3ExprVectorSize(pExpr->pLeft);\n      if( pExpr->op==TK_BETWEEN ){\n        nRight = sqlite3ExprVectorSize(pExpr->x.pList->a[0].pExpr);\n        if( nRight==nLeft ){\n          nRight = sqlite3ExprVectorSize(pExpr->x.pList->a[1].pExpr);\n        }\n      }else{\n        assert( pExpr->pRight!=0 );\n        nRight = sqlite3ExprVectorSize(pExpr->pRight);\n      }\n      if( nLeft!=nRight ){\n        testcase( pExpr->op==TK_EQ );\n        testcase( pExpr->op==TK_NE );\n        testcase( pExpr->op==TK_LT );\n        testcase( pExpr->op==TK_LE );\n        testcase( pExpr->op==TK_GT );\n        testcase( pExpr->op==TK_GE );\n        testcase( pExpr->op==TK_IS );\n        testcase( pExpr->op==TK_ISNOT );\n        testcase( pExpr->op==TK_BETWEEN );\n        sqlite3ErrorMsg(pParse, \"row value misused\");\n      }\n      break; \n    }\n  }\n  return (pParse->nErr || pParse->db->mallocFailed) ? WRC_Abort : WRC_Continue;\n}\n\n/*\n** pEList is a list of expressions which are really the result set of the\n** a SELECT statement.  pE is a term in an ORDER BY or GROUP BY clause.\n** This routine checks to see if pE is a simple identifier which corresponds\n** to the AS-name of one of the terms of the expression list.  If it is,\n** this routine return an integer between 1 and N where N is the number of\n** elements in pEList, corresponding to the matching entry.  If there is\n** no match, or if pE is not a simple identifier, then this routine\n** return 0.\n**\n** pEList has been resolved.  pE has not.\n*/\nstatic int resolveAsName(\n  Parse *pParse,     /* Parsing context for error messages */\n  ExprList *pEList,  /* List of expressions to scan */\n  Expr *pE           /* Expression we are trying to match */\n){\n  int i;             /* Loop counter */\n\n  UNUSED_PARAMETER(pParse);\n\n  if( pE->op==TK_ID ){\n    char *zCol = pE->u.zToken;\n    for(i=0; i<pEList->nExpr; i++){\n      char *zAs = pEList->a[i].zName;\n      if( zAs!=0 && sqlite3StrICmp(zAs, zCol)==0 ){\n        return i+1;\n      }\n    }\n  }\n  return 0;\n}\n\n/*\n** pE is a pointer to an expression which is a single term in the\n** ORDER BY of a compound SELECT.  The expression has not been\n** name resolved.\n**\n** At the point this routine is called, we already know that the\n** ORDER BY term is not an integer index into the result set.  That\n** case is handled by the calling routine.\n**\n** Attempt to match pE against result set columns in the left-most\n** SELECT statement.  Return the index i of the matching column,\n** as an indication to the caller that it should sort by the i-th column.\n** The left-most column is 1.  In other words, the value returned is the\n** same integer value that would be used in the SQL statement to indicate\n** the column.\n**\n** If there is no match, return 0.  Return -1 if an error occurs.\n*/\nstatic int resolveOrderByTermToExprList(\n  Parse *pParse,     /* Parsing context for error messages */\n  Select *pSelect,   /* The SELECT statement with the ORDER BY clause */\n  Expr *pE           /* The specific ORDER BY term */\n){\n  int i;             /* Loop counter */\n  ExprList *pEList;  /* The columns of the result set */\n  NameContext nc;    /* Name context for resolving pE */\n  sqlite3 *db;       /* Database connection */\n  int rc;            /* Return code from subprocedures */\n  u8 savedSuppErr;   /* Saved value of db->suppressErr */\n\n  assert( sqlite3ExprIsInteger(pE, &i)==0 );\n  pEList = pSelect->pEList;\n\n  /* Resolve all names in the ORDER BY term expression\n  */\n  memset(&nc, 0, sizeof(nc));\n  nc.pParse = pParse;\n  nc.pSrcList = pSelect->pSrc;\n  nc.pEList = pEList;\n  nc.ncFlags = NC_AllowAgg;\n  nc.nErr = 0;\n  db = pParse->db;\n  savedSuppErr = db->suppressErr;\n  db->suppressErr = 1;\n  rc = sqlite3ResolveExprNames(&nc, pE);\n  db->suppressErr = savedSuppErr;\n  if( rc ) return 0;\n\n  /* Try to match the ORDER BY expression against an expression\n  ** in the result set.  Return an 1-based index of the matching\n  ** result-set entry.\n  */\n  for(i=0; i<pEList->nExpr; i++){\n    if( sqlite3ExprCompare(0, pEList->a[i].pExpr, pE, -1)<2 ){\n      return i+1;\n    }\n  }\n\n  /* If no match, return 0. */\n  return 0;\n}\n\n/*\n** Generate an ORDER BY or GROUP BY term out-of-range error.\n*/\nstatic void resolveOutOfRangeError(\n  Parse *pParse,         /* The error context into which to write the error */\n  const char *zType,     /* \"ORDER\" or \"GROUP\" */\n  int i,                 /* The index (1-based) of the term out of range */\n  int mx                 /* Largest permissible value of i */\n){\n  sqlite3ErrorMsg(pParse, \n    \"%r %s BY term out of range - should be \"\n    \"between 1 and %d\", i, zType, mx);\n}\n\n/*\n** Analyze the ORDER BY clause in a compound SELECT statement.   Modify\n** each term of the ORDER BY clause is a constant integer between 1\n** and N where N is the number of columns in the compound SELECT.\n**\n** ORDER BY terms that are already an integer between 1 and N are\n** unmodified.  ORDER BY terms that are integers outside the range of\n** 1 through N generate an error.  ORDER BY terms that are expressions\n** are matched against result set expressions of compound SELECT\n** beginning with the left-most SELECT and working toward the right.\n** At the first match, the ORDER BY expression is transformed into\n** the integer column number.\n**\n** Return the number of errors seen.\n*/\nstatic int resolveCompoundOrderBy(\n  Parse *pParse,        /* Parsing context.  Leave error messages here */\n  Select *pSelect       /* The SELECT statement containing the ORDER BY */\n){\n  int i;\n  ExprList *pOrderBy;\n  ExprList *pEList;\n  sqlite3 *db;\n  int moreToDo = 1;\n\n  pOrderBy = pSelect->pOrderBy;\n  if( pOrderBy==0 ) return 0;\n  db = pParse->db;\n  if( pOrderBy->nExpr>db->aLimit[SQLITE_LIMIT_COLUMN] ){\n    sqlite3ErrorMsg(pParse, \"too many terms in ORDER BY clause\");\n    return 1;\n  }\n  for(i=0; i<pOrderBy->nExpr; i++){\n    pOrderBy->a[i].done = 0;\n  }\n  pSelect->pNext = 0;\n  while( pSelect->pPrior ){\n    pSelect->pPrior->pNext = pSelect;\n    pSelect = pSelect->pPrior;\n  }\n  while( pSelect && moreToDo ){\n    struct ExprList_item *pItem;\n    moreToDo = 0;\n    pEList = pSelect->pEList;\n    assert( pEList!=0 );\n    for(i=0, pItem=pOrderBy->a; i<pOrderBy->nExpr; i++, pItem++){\n      int iCol = -1;\n      Expr *pE, *pDup;\n      if( pItem->done ) continue;\n      pE = sqlite3ExprSkipCollate(pItem->pExpr);\n      if( sqlite3ExprIsInteger(pE, &iCol) ){\n        if( iCol<=0 || iCol>pEList->nExpr ){\n          resolveOutOfRangeError(pParse, \"ORDER\", i+1, pEList->nExpr);\n          return 1;\n        }\n      }else{\n        iCol = resolveAsName(pParse, pEList, pE);\n        if( iCol==0 ){\n          pDup = sqlite3ExprDup(db, pE, 0);\n          if( !db->mallocFailed ){\n            assert(pDup);\n            iCol = resolveOrderByTermToExprList(pParse, pSelect, pDup);\n          }\n          sqlite3ExprDelete(db, pDup);\n        }\n      }\n      if( iCol>0 ){\n        /* Convert the ORDER BY term into an integer column number iCol,\n        ** taking care to preserve the COLLATE clause if it exists */\n        Expr *pNew = sqlite3Expr(db, TK_INTEGER, 0);\n        if( pNew==0 ) return 1;\n        pNew->flags |= EP_IntValue;\n        pNew->u.iValue = iCol;\n        if( pItem->pExpr==pE ){\n          pItem->pExpr = pNew;\n        }else{\n          Expr *pParent = pItem->pExpr;\n          assert( pParent->op==TK_COLLATE );\n          while( pParent->pLeft->op==TK_COLLATE ) pParent = pParent->pLeft;\n          assert( pParent->pLeft==pE );\n          pParent->pLeft = pNew;\n        }\n        sqlite3ExprDelete(db, pE);\n        pItem->u.x.iOrderByCol = (u16)iCol;\n        pItem->done = 1;\n      }else{\n        moreToDo = 1;\n      }\n    }\n    pSelect = pSelect->pNext;\n  }\n  for(i=0; i<pOrderBy->nExpr; i++){\n    if( pOrderBy->a[i].done==0 ){\n      sqlite3ErrorMsg(pParse, \"%r ORDER BY term does not match any \"\n            \"column in the result set\", i+1);\n      return 1;\n    }\n  }\n  return 0;\n}\n\n/*\n** Check every term in the ORDER BY or GROUP BY clause pOrderBy of\n** the SELECT statement pSelect.  If any term is reference to a\n** result set expression (as determined by the ExprList.a.u.x.iOrderByCol\n** field) then convert that term into a copy of the corresponding result set\n** column.\n**\n** If any errors are detected, add an error message to pParse and\n** return non-zero.  Return zero if no errors are seen.\n*/\nSQLITE_PRIVATE int sqlite3ResolveOrderGroupBy(\n  Parse *pParse,        /* Parsing context.  Leave error messages here */\n  Select *pSelect,      /* The SELECT statement containing the clause */\n  ExprList *pOrderBy,   /* The ORDER BY or GROUP BY clause to be processed */\n  const char *zType     /* \"ORDER\" or \"GROUP\" */\n){\n  int i;\n  sqlite3 *db = pParse->db;\n  ExprList *pEList;\n  struct ExprList_item *pItem;\n\n  if( pOrderBy==0 || pParse->db->mallocFailed ) return 0;\n  if( pOrderBy->nExpr>db->aLimit[SQLITE_LIMIT_COLUMN] ){\n    sqlite3ErrorMsg(pParse, \"too many terms in %s BY clause\", zType);\n    return 1;\n  }\n  pEList = pSelect->pEList;\n  assert( pEList!=0 );  /* sqlite3SelectNew() guarantees this */\n  for(i=0, pItem=pOrderBy->a; i<pOrderBy->nExpr; i++, pItem++){\n    if( pItem->u.x.iOrderByCol ){\n      if( pItem->u.x.iOrderByCol>pEList->nExpr ){\n        resolveOutOfRangeError(pParse, zType, i+1, pEList->nExpr);\n        return 1;\n      }\n      resolveAlias(pParse, pEList, pItem->u.x.iOrderByCol-1, pItem->pExpr,\n                   zType,0);\n    }\n  }\n  return 0;\n}\n\n/*\n** pOrderBy is an ORDER BY or GROUP BY clause in SELECT statement pSelect.\n** The Name context of the SELECT statement is pNC.  zType is either\n** \"ORDER\" or \"GROUP\" depending on which type of clause pOrderBy is.\n**\n** This routine resolves each term of the clause into an expression.\n** If the order-by term is an integer I between 1 and N (where N is the\n** number of columns in the result set of the SELECT) then the expression\n** in the resolution is a copy of the I-th result-set expression.  If\n** the order-by term is an identifier that corresponds to the AS-name of\n** a result-set expression, then the term resolves to a copy of the\n** result-set expression.  Otherwise, the expression is resolved in\n** the usual way - using sqlite3ResolveExprNames().\n**\n** This routine returns the number of errors.  If errors occur, then\n** an appropriate error message might be left in pParse.  (OOM errors\n** excepted.)\n*/\nstatic int resolveOrderGroupBy(\n  NameContext *pNC,     /* The name context of the SELECT statement */\n  Select *pSelect,      /* The SELECT statement holding pOrderBy */\n  ExprList *pOrderBy,   /* An ORDER BY or GROUP BY clause to resolve */\n  const char *zType     /* Either \"ORDER\" or \"GROUP\", as appropriate */\n){\n  int i, j;                      /* Loop counters */\n  int iCol;                      /* Column number */\n  struct ExprList_item *pItem;   /* A term of the ORDER BY clause */\n  Parse *pParse;                 /* Parsing context */\n  int nResult;                   /* Number of terms in the result set */\n\n  if( pOrderBy==0 ) return 0;\n  nResult = pSelect->pEList->nExpr;\n  pParse = pNC->pParse;\n  for(i=0, pItem=pOrderBy->a; i<pOrderBy->nExpr; i++, pItem++){\n    Expr *pE = pItem->pExpr;\n    Expr *pE2 = sqlite3ExprSkipCollate(pE);\n    if( zType[0]!='G' ){\n      iCol = resolveAsName(pParse, pSelect->pEList, pE2);\n      if( iCol>0 ){\n        /* If an AS-name match is found, mark this ORDER BY column as being\n        ** a copy of the iCol-th result-set column.  The subsequent call to\n        ** sqlite3ResolveOrderGroupBy() will convert the expression to a\n        ** copy of the iCol-th result-set expression. */\n        pItem->u.x.iOrderByCol = (u16)iCol;\n        continue;\n      }\n    }\n    if( sqlite3ExprIsInteger(pE2, &iCol) ){\n      /* The ORDER BY term is an integer constant.  Again, set the column\n      ** number so that sqlite3ResolveOrderGroupBy() will convert the\n      ** order-by term to a copy of the result-set expression */\n      if( iCol<1 || iCol>0xffff ){\n        resolveOutOfRangeError(pParse, zType, i+1, nResult);\n        return 1;\n      }\n      pItem->u.x.iOrderByCol = (u16)iCol;\n      continue;\n    }\n\n    /* Otherwise, treat the ORDER BY term as an ordinary expression */\n    pItem->u.x.iOrderByCol = 0;\n    if( sqlite3ResolveExprNames(pNC, pE) ){\n      return 1;\n    }\n    for(j=0; j<pSelect->pEList->nExpr; j++){\n      if( sqlite3ExprCompare(0, pE, pSelect->pEList->a[j].pExpr, -1)==0 ){\n        pItem->u.x.iOrderByCol = j+1;\n      }\n    }\n  }\n  return sqlite3ResolveOrderGroupBy(pParse, pSelect, pOrderBy, zType);\n}\n\n/*\n** Resolve names in the SELECT statement p and all of its descendants.\n*/\nstatic int resolveSelectStep(Walker *pWalker, Select *p){\n  NameContext *pOuterNC;  /* Context that contains this SELECT */\n  NameContext sNC;        /* Name context of this SELECT */\n  int isCompound;         /* True if p is a compound select */\n  int nCompound;          /* Number of compound terms processed so far */\n  Parse *pParse;          /* Parsing context */\n  int i;                  /* Loop counter */\n  ExprList *pGroupBy;     /* The GROUP BY clause */\n  Select *pLeftmost;      /* Left-most of SELECT of a compound */\n  sqlite3 *db;            /* Database connection */\n  \n\n  assert( p!=0 );\n  if( p->selFlags & SF_Resolved ){\n    return WRC_Prune;\n  }\n  pOuterNC = pWalker->u.pNC;\n  pParse = pWalker->pParse;\n  db = pParse->db;\n\n  /* Normally sqlite3SelectExpand() will be called first and will have\n  ** already expanded this SELECT.  However, if this is a subquery within\n  ** an expression, sqlite3ResolveExprNames() will be called without a\n  ** prior call to sqlite3SelectExpand().  When that happens, let\n  ** sqlite3SelectPrep() do all of the processing for this SELECT.\n  ** sqlite3SelectPrep() will invoke both sqlite3SelectExpand() and\n  ** this routine in the correct order.\n  */\n  if( (p->selFlags & SF_Expanded)==0 ){\n    sqlite3SelectPrep(pParse, p, pOuterNC);\n    return (pParse->nErr || db->mallocFailed) ? WRC_Abort : WRC_Prune;\n  }\n\n  isCompound = p->pPrior!=0;\n  nCompound = 0;\n  pLeftmost = p;\n  while( p ){\n    assert( (p->selFlags & SF_Expanded)!=0 );\n    assert( (p->selFlags & SF_Resolved)==0 );\n    p->selFlags |= SF_Resolved;\n\n    /* Resolve the expressions in the LIMIT and OFFSET clauses. These\n    ** are not allowed to refer to any names, so pass an empty NameContext.\n    */\n    memset(&sNC, 0, sizeof(sNC));\n    sNC.pParse = pParse;\n    if( sqlite3ResolveExprNames(&sNC, p->pLimit) ){\n      return WRC_Abort;\n    }\n\n    /* If the SF_Converted flags is set, then this Select object was\n    ** was created by the convertCompoundSelectToSubquery() function.\n    ** In this case the ORDER BY clause (p->pOrderBy) should be resolved\n    ** as if it were part of the sub-query, not the parent. This block\n    ** moves the pOrderBy down to the sub-query. It will be moved back\n    ** after the names have been resolved.  */\n    if( p->selFlags & SF_Converted ){\n      Select *pSub = p->pSrc->a[0].pSelect;\n      assert( p->pSrc->nSrc==1 && p->pOrderBy );\n      assert( pSub->pPrior && pSub->pOrderBy==0 );\n      pSub->pOrderBy = p->pOrderBy;\n      p->pOrderBy = 0;\n    }\n  \n    /* Recursively resolve names in all subqueries\n    */\n    for(i=0; i<p->pSrc->nSrc; i++){\n      struct SrcList_item *pItem = &p->pSrc->a[i];\n      if( pItem->pSelect ){\n        NameContext *pNC;         /* Used to iterate name contexts */\n        int nRef = 0;             /* Refcount for pOuterNC and outer contexts */\n        const char *zSavedContext = pParse->zAuthContext;\n\n        /* Count the total number of references to pOuterNC and all of its\n        ** parent contexts. After resolving references to expressions in\n        ** pItem->pSelect, check if this value has changed. If so, then\n        ** SELECT statement pItem->pSelect must be correlated. Set the\n        ** pItem->fg.isCorrelated flag if this is the case. */\n        for(pNC=pOuterNC; pNC; pNC=pNC->pNext) nRef += pNC->nRef;\n\n        if( pItem->zName ) pParse->zAuthContext = pItem->zName;\n        sqlite3ResolveSelectNames(pParse, pItem->pSelect, pOuterNC);\n        pParse->zAuthContext = zSavedContext;\n        if( pParse->nErr || db->mallocFailed ) return WRC_Abort;\n\n        for(pNC=pOuterNC; pNC; pNC=pNC->pNext) nRef -= pNC->nRef;\n        assert( pItem->fg.isCorrelated==0 && nRef<=0 );\n        pItem->fg.isCorrelated = (nRef!=0);\n      }\n    }\n  \n    /* Set up the local name-context to pass to sqlite3ResolveExprNames() to\n    ** resolve the result-set expression list.\n    */\n    sNC.ncFlags = NC_AllowAgg;\n    sNC.pSrcList = p->pSrc;\n    sNC.pNext = pOuterNC;\n  \n    /* Resolve names in the result set. */\n    if( sqlite3ResolveExprListNames(&sNC, p->pEList) ) return WRC_Abort;\n  \n    /* If there are no aggregate functions in the result-set, and no GROUP BY \n    ** expression, do not allow aggregates in any of the other expressions.\n    */\n    assert( (p->selFlags & SF_Aggregate)==0 );\n    pGroupBy = p->pGroupBy;\n    if( pGroupBy || (sNC.ncFlags & NC_HasAgg)!=0 ){\n      assert( NC_MinMaxAgg==SF_MinMaxAgg );\n      p->selFlags |= SF_Aggregate | (sNC.ncFlags&NC_MinMaxAgg);\n    }else{\n      sNC.ncFlags &= ~NC_AllowAgg;\n    }\n  \n    /* If a HAVING clause is present, then there must be a GROUP BY clause.\n    */\n    if( p->pHaving && !pGroupBy ){\n      sqlite3ErrorMsg(pParse, \"a GROUP BY clause is required before HAVING\");\n      return WRC_Abort;\n    }\n  \n    /* Add the output column list to the name-context before parsing the\n    ** other expressions in the SELECT statement. This is so that\n    ** expressions in the WHERE clause (etc.) can refer to expressions by\n    ** aliases in the result set.\n    **\n    ** Minor point: If this is the case, then the expression will be\n    ** re-evaluated for each reference to it.\n    */\n    sNC.pEList = p->pEList;\n    if( sqlite3ResolveExprNames(&sNC, p->pHaving) ) return WRC_Abort;\n    if( sqlite3ResolveExprNames(&sNC, p->pWhere) ) return WRC_Abort;\n\n    /* Resolve names in table-valued-function arguments */\n    for(i=0; i<p->pSrc->nSrc; i++){\n      struct SrcList_item *pItem = &p->pSrc->a[i];\n      if( pItem->fg.isTabFunc\n       && sqlite3ResolveExprListNames(&sNC, pItem->u1.pFuncArg) \n      ){\n        return WRC_Abort;\n      }\n    }\n\n    /* The ORDER BY and GROUP BY clauses may not refer to terms in\n    ** outer queries \n    */\n    sNC.pNext = 0;\n    sNC.ncFlags |= NC_AllowAgg;\n\n    /* If this is a converted compound query, move the ORDER BY clause from \n    ** the sub-query back to the parent query. At this point each term\n    ** within the ORDER BY clause has been transformed to an integer value.\n    ** These integers will be replaced by copies of the corresponding result\n    ** set expressions by the call to resolveOrderGroupBy() below.  */\n    if( p->selFlags & SF_Converted ){\n      Select *pSub = p->pSrc->a[0].pSelect;\n      p->pOrderBy = pSub->pOrderBy;\n      pSub->pOrderBy = 0;\n    }\n\n    /* Process the ORDER BY clause for singleton SELECT statements.\n    ** The ORDER BY clause for compounds SELECT statements is handled\n    ** below, after all of the result-sets for all of the elements of\n    ** the compound have been resolved.\n    **\n    ** If there is an ORDER BY clause on a term of a compound-select other\n    ** than the right-most term, then that is a syntax error.  But the error\n    ** is not detected until much later, and so we need to go ahead and\n    ** resolve those symbols on the incorrect ORDER BY for consistency.\n    */\n    if( isCompound<=nCompound  /* Defer right-most ORDER BY of a compound */\n     && resolveOrderGroupBy(&sNC, p, p->pOrderBy, \"ORDER\")\n    ){\n      return WRC_Abort;\n    }\n    if( db->mallocFailed ){\n      return WRC_Abort;\n    }\n  \n    /* Resolve the GROUP BY clause.  At the same time, make sure \n    ** the GROUP BY clause does not contain aggregate functions.\n    */\n    if( pGroupBy ){\n      struct ExprList_item *pItem;\n    \n      if( resolveOrderGroupBy(&sNC, p, pGroupBy, \"GROUP\") || db->mallocFailed ){\n        return WRC_Abort;\n      }\n      for(i=0, pItem=pGroupBy->a; i<pGroupBy->nExpr; i++, pItem++){\n        if( ExprHasProperty(pItem->pExpr, EP_Agg) ){\n          sqlite3ErrorMsg(pParse, \"aggregate functions are not allowed in \"\n              \"the GROUP BY clause\");\n          return WRC_Abort;\n        }\n      }\n    }\n\n    /* If this is part of a compound SELECT, check that it has the right\n    ** number of expressions in the select list. */\n    if( p->pNext && p->pEList->nExpr!=p->pNext->pEList->nExpr ){\n      sqlite3SelectWrongNumTermsError(pParse, p->pNext);\n      return WRC_Abort;\n    }\n\n    /* Advance to the next term of the compound\n    */\n    p = p->pPrior;\n    nCompound++;\n  }\n\n  /* Resolve the ORDER BY on a compound SELECT after all terms of\n  ** the compound have been resolved.\n  */\n  if( isCompound && resolveCompoundOrderBy(pParse, pLeftmost) ){\n    return WRC_Abort;\n  }\n\n  return WRC_Prune;\n}\n\n/*\n** This routine walks an expression tree and resolves references to\n** table columns and result-set columns.  At the same time, do error\n** checking on function usage and set a flag if any aggregate functions\n** are seen.\n**\n** To resolve table columns references we look for nodes (or subtrees) of the \n** form X.Y.Z or Y.Z or just Z where\n**\n**      X:   The name of a database.  Ex:  \"main\" or \"temp\" or\n**           the symbolic name assigned to an ATTACH-ed database.\n**\n**      Y:   The name of a table in a FROM clause.  Or in a trigger\n**           one of the special names \"old\" or \"new\".\n**\n**      Z:   The name of a column in table Y.\n**\n** The node at the root of the subtree is modified as follows:\n**\n**    Expr.op        Changed to TK_COLUMN\n**    Expr.pTab      Points to the Table object for X.Y\n**    Expr.iColumn   The column index in X.Y.  -1 for the rowid.\n**    Expr.iTable    The VDBE cursor number for X.Y\n**\n**\n** To resolve result-set references, look for expression nodes of the\n** form Z (with no X and Y prefix) where the Z matches the right-hand\n** size of an AS clause in the result-set of a SELECT.  The Z expression\n** is replaced by a copy of the left-hand side of the result-set expression.\n** Table-name and function resolution occurs on the substituted expression\n** tree.  For example, in:\n**\n**      SELECT a+b AS x, c+d AS y FROM t1 ORDER BY x;\n**\n** The \"x\" term of the order by is replaced by \"a+b\" to render:\n**\n**      SELECT a+b AS x, c+d AS y FROM t1 ORDER BY a+b;\n**\n** Function calls are checked to make sure that the function is \n** defined and that the correct number of arguments are specified.\n** If the function is an aggregate function, then the NC_HasAgg flag is\n** set and the opcode is changed from TK_FUNCTION to TK_AGG_FUNCTION.\n** If an expression contains aggregate functions then the EP_Agg\n** property on the expression is set.\n**\n** An error message is left in pParse if anything is amiss.  The number\n** if errors is returned.\n*/\nSQLITE_PRIVATE int sqlite3ResolveExprNames( \n  NameContext *pNC,       /* Namespace to resolve expressions in. */\n  Expr *pExpr             /* The expression to be analyzed. */\n){\n  u16 savedHasAgg;\n  Walker w;\n\n  if( pExpr==0 ) return SQLITE_OK;\n  savedHasAgg = pNC->ncFlags & (NC_HasAgg|NC_MinMaxAgg);\n  pNC->ncFlags &= ~(NC_HasAgg|NC_MinMaxAgg);\n  w.pParse = pNC->pParse;\n  w.xExprCallback = resolveExprStep;\n  w.xSelectCallback = resolveSelectStep;\n  w.xSelectCallback2 = 0;\n  w.u.pNC = pNC;\n#if SQLITE_MAX_EXPR_DEPTH>0\n  w.pParse->nHeight += pExpr->nHeight;\n  if( sqlite3ExprCheckHeight(w.pParse, w.pParse->nHeight) ){\n    return SQLITE_ERROR;\n  }\n#endif\n  sqlite3WalkExpr(&w, pExpr);\n#if SQLITE_MAX_EXPR_DEPTH>0\n  w.pParse->nHeight -= pExpr->nHeight;\n#endif\n  if( pNC->ncFlags & NC_HasAgg ){\n    ExprSetProperty(pExpr, EP_Agg);\n  }\n  pNC->ncFlags |= savedHasAgg;\n  return pNC->nErr>0 || w.pParse->nErr>0;\n}\n\n/*\n** Resolve all names for all expression in an expression list.  This is\n** just like sqlite3ResolveExprNames() except that it works for an expression\n** list rather than a single expression.\n*/\nSQLITE_PRIVATE int sqlite3ResolveExprListNames( \n  NameContext *pNC,       /* Namespace to resolve expressions in. */\n  ExprList *pList         /* The expression list to be analyzed. */\n){\n  int i;\n  if( pList ){\n    for(i=0; i<pList->nExpr; i++){\n      if( sqlite3ResolveExprNames(pNC, pList->a[i].pExpr) ) return WRC_Abort;\n    }\n  }\n  return WRC_Continue;\n}\n\n/*\n** Resolve all names in all expressions of a SELECT and in all\n** decendents of the SELECT, including compounds off of p->pPrior,\n** subqueries in expressions, and subqueries used as FROM clause\n** terms.\n**\n** See sqlite3ResolveExprNames() for a description of the kinds of\n** transformations that occur.\n**\n** All SELECT statements should have been expanded using\n** sqlite3SelectExpand() prior to invoking this routine.\n*/\nSQLITE_PRIVATE void sqlite3ResolveSelectNames(\n  Parse *pParse,         /* The parser context */\n  Select *p,             /* The SELECT statement being coded. */\n  NameContext *pOuterNC  /* Name context for parent SELECT statement */\n){\n  Walker w;\n\n  assert( p!=0 );\n  w.xExprCallback = resolveExprStep;\n  w.xSelectCallback = resolveSelectStep;\n  w.xSelectCallback2 = 0;\n  w.pParse = pParse;\n  w.u.pNC = pOuterNC;\n  sqlite3WalkSelect(&w, p);\n}\n\n/*\n** Resolve names in expressions that can only reference a single table:\n**\n**    *   CHECK constraints\n**    *   WHERE clauses on partial indices\n**\n** The Expr.iTable value for Expr.op==TK_COLUMN nodes of the expression\n** is set to -1 and the Expr.iColumn value is set to the column number.\n**\n** Any errors cause an error message to be set in pParse.\n*/\nSQLITE_PRIVATE void sqlite3ResolveSelfReference(\n  Parse *pParse,      /* Parsing context */\n  Table *pTab,        /* The table being referenced */\n  int type,           /* NC_IsCheck or NC_PartIdx or NC_IdxExpr */\n  Expr *pExpr,        /* Expression to resolve.  May be NULL. */\n  ExprList *pList     /* Expression list to resolve.  May be NUL. */\n){\n  SrcList sSrc;                   /* Fake SrcList for pParse->pNewTable */\n  NameContext sNC;                /* Name context for pParse->pNewTable */\n\n  assert( type==NC_IsCheck || type==NC_PartIdx || type==NC_IdxExpr );\n  memset(&sNC, 0, sizeof(sNC));\n  memset(&sSrc, 0, sizeof(sSrc));\n  sSrc.nSrc = 1;\n  sSrc.a[0].zName = pTab->zName;\n  sSrc.a[0].pTab = pTab;\n  sSrc.a[0].iCursor = -1;\n  sNC.pParse = pParse;\n  sNC.pSrcList = &sSrc;\n  sNC.ncFlags = type;\n  if( sqlite3ResolveExprNames(&sNC, pExpr) ) return;\n  if( pList ) sqlite3ResolveExprListNames(&sNC, pList);\n}\n\n/************** End of resolve.c *********************************************/\n/************** Begin file expr.c ********************************************/\n/*\n** 2001 September 15\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n*************************************************************************\n** This file contains routines used for analyzing expressions and\n** for generating VDBE code that evaluates expressions in SQLite.\n*/\n/* #include \"sqliteInt.h\" */\n\n/* Forward declarations */\nstatic void exprCodeBetween(Parse*,Expr*,int,void(*)(Parse*,Expr*,int,int),int);\nstatic int exprCodeVector(Parse *pParse, Expr *p, int *piToFree);\n\n/*\n** Return the affinity character for a single column of a table.\n*/\nSQLITE_PRIVATE char sqlite3TableColumnAffinity(Table *pTab, int iCol){\n  assert( iCol<pTab->nCol );\n  return iCol>=0 ? pTab->aCol[iCol].affinity : SQLITE_AFF_INTEGER;\n}\n\n/*\n** Return the 'affinity' of the expression pExpr if any.\n**\n** If pExpr is a column, a reference to a column via an 'AS' alias,\n** or a sub-select with a column as the return value, then the \n** affinity of that column is returned. Otherwise, 0x00 is returned,\n** indicating no affinity for the expression.\n**\n** i.e. the WHERE clause expressions in the following statements all\n** have an affinity:\n**\n** CREATE TABLE t1(a);\n** SELECT * FROM t1 WHERE a;\n** SELECT a AS b FROM t1 WHERE b;\n** SELECT * FROM t1 WHERE (select a from t1);\n*/\nSQLITE_PRIVATE char sqlite3ExprAffinity(Expr *pExpr){\n  int op;\n  pExpr = sqlite3ExprSkipCollate(pExpr);\n  if( pExpr->flags & EP_Generic ) return 0;\n  op = pExpr->op;\n  if( op==TK_SELECT ){\n    assert( pExpr->flags&EP_xIsSelect );\n    return sqlite3ExprAffinity(pExpr->x.pSelect->pEList->a[0].pExpr);\n  }\n  if( op==TK_REGISTER ) op = pExpr->op2;\n#ifndef SQLITE_OMIT_CAST\n  if( op==TK_CAST ){\n    assert( !ExprHasProperty(pExpr, EP_IntValue) );\n    return sqlite3AffinityType(pExpr->u.zToken, 0);\n  }\n#endif\n  if( (op==TK_AGG_COLUMN || op==TK_COLUMN) && pExpr->pTab ){\n    return sqlite3TableColumnAffinity(pExpr->pTab, pExpr->iColumn);\n  }\n  if( op==TK_SELECT_COLUMN ){\n    assert( pExpr->pLeft->flags&EP_xIsSelect );\n    return sqlite3ExprAffinity(\n        pExpr->pLeft->x.pSelect->pEList->a[pExpr->iColumn].pExpr\n    );\n  }\n  return pExpr->affinity;\n}\n\n/*\n** Set the collating sequence for expression pExpr to be the collating\n** sequence named by pToken.   Return a pointer to a new Expr node that\n** implements the COLLATE operator.\n**\n** If a memory allocation error occurs, that fact is recorded in pParse->db\n** and the pExpr parameter is returned unchanged.\n*/\nSQLITE_PRIVATE Expr *sqlite3ExprAddCollateToken(\n  Parse *pParse,           /* Parsing context */\n  Expr *pExpr,             /* Add the \"COLLATE\" clause to this expression */\n  const Token *pCollName,  /* Name of collating sequence */\n  int dequote              /* True to dequote pCollName */\n){\n  if( pCollName->n>0 ){\n    Expr *pNew = sqlite3ExprAlloc(pParse->db, TK_COLLATE, pCollName, dequote);\n    if( pNew ){\n      pNew->pLeft = pExpr;\n      pNew->flags |= EP_Collate|EP_Skip;\n      pExpr = pNew;\n    }\n  }\n  return pExpr;\n}\nSQLITE_PRIVATE Expr *sqlite3ExprAddCollateString(Parse *pParse, Expr *pExpr, const char *zC){\n  Token s;\n  assert( zC!=0 );\n  sqlite3TokenInit(&s, (char*)zC);\n  return sqlite3ExprAddCollateToken(pParse, pExpr, &s, 0);\n}\n\n/*\n** Skip over any TK_COLLATE operators and any unlikely()\n** or likelihood() function at the root of an expression.\n*/\nSQLITE_PRIVATE Expr *sqlite3ExprSkipCollate(Expr *pExpr){\n  while( pExpr && ExprHasProperty(pExpr, EP_Skip) ){\n    if( ExprHasProperty(pExpr, EP_Unlikely) ){\n      assert( !ExprHasProperty(pExpr, EP_xIsSelect) );\n      assert( pExpr->x.pList->nExpr>0 );\n      assert( pExpr->op==TK_FUNCTION );\n      pExpr = pExpr->x.pList->a[0].pExpr;\n    }else{\n      assert( pExpr->op==TK_COLLATE );\n      pExpr = pExpr->pLeft;\n    }\n  }   \n  return pExpr;\n}\n\n/*\n** Return the collation sequence for the expression pExpr. If\n** there is no defined collating sequence, return NULL.\n**\n** See also: sqlite3ExprNNCollSeq()\n**\n** The sqlite3ExprNNCollSeq() works the same exact that it returns the\n** default collation if pExpr has no defined collation.\n**\n** The collating sequence might be determined by a COLLATE operator\n** or by the presence of a column with a defined collating sequence.\n** COLLATE operators take first precedence.  Left operands take\n** precedence over right operands.\n*/\nSQLITE_PRIVATE CollSeq *sqlite3ExprCollSeq(Parse *pParse, Expr *pExpr){\n  sqlite3 *db = pParse->db;\n  CollSeq *pColl = 0;\n  Expr *p = pExpr;\n  while( p ){\n    int op = p->op;\n    if( p->flags & EP_Generic ) break;\n    if( op==TK_CAST || op==TK_UPLUS ){\n      p = p->pLeft;\n      continue;\n    }\n    if( op==TK_COLLATE || (op==TK_REGISTER && p->op2==TK_COLLATE) ){\n      pColl = sqlite3GetCollSeq(pParse, ENC(db), 0, p->u.zToken);\n      break;\n    }\n    if( (op==TK_AGG_COLUMN || op==TK_COLUMN\n          || op==TK_REGISTER || op==TK_TRIGGER)\n     && p->pTab!=0\n    ){\n      /* op==TK_REGISTER && p->pTab!=0 happens when pExpr was originally\n      ** a TK_COLUMN but was previously evaluated and cached in a register */\n      int j = p->iColumn;\n      if( j>=0 ){\n        const char *zColl = p->pTab->aCol[j].zColl;\n        pColl = sqlite3FindCollSeq(db, ENC(db), zColl, 0);\n      }\n      break;\n    }\n    if( p->flags & EP_Collate ){\n      if( p->pLeft && (p->pLeft->flags & EP_Collate)!=0 ){\n        p = p->pLeft;\n      }else{\n        Expr *pNext  = p->pRight;\n        /* The Expr.x union is never used at the same time as Expr.pRight */\n        assert( p->x.pList==0 || p->pRight==0 );\n        /* p->flags holds EP_Collate and p->pLeft->flags does not.  And\n        ** p->x.pSelect cannot.  So if p->x.pLeft exists, it must hold at\n        ** least one EP_Collate. Thus the following two ALWAYS. */\n        if( p->x.pList!=0 && ALWAYS(!ExprHasProperty(p, EP_xIsSelect)) ){\n          int i;\n          for(i=0; ALWAYS(i<p->x.pList->nExpr); i++){\n            if( ExprHasProperty(p->x.pList->a[i].pExpr, EP_Collate) ){\n              pNext = p->x.pList->a[i].pExpr;\n              break;\n            }\n          }\n        }\n        p = pNext;\n      }\n    }else{\n      break;\n    }\n  }\n  if( sqlite3CheckCollSeq(pParse, pColl) ){ \n    pColl = 0;\n  }\n  return pColl;\n}\n\n/*\n** Return the collation sequence for the expression pExpr. If\n** there is no defined collating sequence, return a pointer to the\n** defautl collation sequence.\n**\n** See also: sqlite3ExprCollSeq()\n**\n** The sqlite3ExprCollSeq() routine works the same except that it\n** returns NULL if there is no defined collation.\n*/\nSQLITE_PRIVATE CollSeq *sqlite3ExprNNCollSeq(Parse *pParse, Expr *pExpr){\n  CollSeq *p = sqlite3ExprCollSeq(pParse, pExpr);\n  if( p==0 ) p = pParse->db->pDfltColl;\n  assert( p!=0 );\n  return p;\n}\n\n/*\n** Return TRUE if the two expressions have equivalent collating sequences.\n*/\nSQLITE_PRIVATE int sqlite3ExprCollSeqMatch(Parse *pParse, Expr *pE1, Expr *pE2){\n  CollSeq *pColl1 = sqlite3ExprNNCollSeq(pParse, pE1);\n  CollSeq *pColl2 = sqlite3ExprNNCollSeq(pParse, pE2);\n  return sqlite3StrICmp(pColl1->zName, pColl2->zName)==0;\n}\n\n/*\n** pExpr is an operand of a comparison operator.  aff2 is the\n** type affinity of the other operand.  This routine returns the\n** type affinity that should be used for the comparison operator.\n*/\nSQLITE_PRIVATE char sqlite3CompareAffinity(Expr *pExpr, char aff2){\n  char aff1 = sqlite3ExprAffinity(pExpr);\n  if( aff1 && aff2 ){\n    /* Both sides of the comparison are columns. If one has numeric\n    ** affinity, use that. Otherwise use no affinity.\n    */\n    if( sqlite3IsNumericAffinity(aff1) || sqlite3IsNumericAffinity(aff2) ){\n      return SQLITE_AFF_NUMERIC;\n    }else{\n      return SQLITE_AFF_BLOB;\n    }\n  }else if( !aff1 && !aff2 ){\n    /* Neither side of the comparison is a column.  Compare the\n    ** results directly.\n    */\n    return SQLITE_AFF_BLOB;\n  }else{\n    /* One side is a column, the other is not. Use the columns affinity. */\n    assert( aff1==0 || aff2==0 );\n    return (aff1 + aff2);\n  }\n}\n\n/*\n** pExpr is a comparison operator.  Return the type affinity that should\n** be applied to both operands prior to doing the comparison.\n*/\nstatic char comparisonAffinity(Expr *pExpr){\n  char aff;\n  assert( pExpr->op==TK_EQ || pExpr->op==TK_IN || pExpr->op==TK_LT ||\n          pExpr->op==TK_GT || pExpr->op==TK_GE || pExpr->op==TK_LE ||\n          pExpr->op==TK_NE || pExpr->op==TK_IS || pExpr->op==TK_ISNOT );\n  assert( pExpr->pLeft );\n  aff = sqlite3ExprAffinity(pExpr->pLeft);\n  if( pExpr->pRight ){\n    aff = sqlite3CompareAffinity(pExpr->pRight, aff);\n  }else if( ExprHasProperty(pExpr, EP_xIsSelect) ){\n    aff = sqlite3CompareAffinity(pExpr->x.pSelect->pEList->a[0].pExpr, aff);\n  }else if( aff==0 ){\n    aff = SQLITE_AFF_BLOB;\n  }\n  return aff;\n}\n\n/*\n** pExpr is a comparison expression, eg. '=', '<', IN(...) etc.\n** idx_affinity is the affinity of an indexed column. Return true\n** if the index with affinity idx_affinity may be used to implement\n** the comparison in pExpr.\n*/\nSQLITE_PRIVATE int sqlite3IndexAffinityOk(Expr *pExpr, char idx_affinity){\n  char aff = comparisonAffinity(pExpr);\n  switch( aff ){\n    case SQLITE_AFF_BLOB:\n      return 1;\n    case SQLITE_AFF_TEXT:\n      return idx_affinity==SQLITE_AFF_TEXT;\n    default:\n      return sqlite3IsNumericAffinity(idx_affinity);\n  }\n}\n\n/*\n** Return the P5 value that should be used for a binary comparison\n** opcode (OP_Eq, OP_Ge etc.) used to compare pExpr1 and pExpr2.\n*/\nstatic u8 binaryCompareP5(Expr *pExpr1, Expr *pExpr2, int jumpIfNull){\n  u8 aff = (char)sqlite3ExprAffinity(pExpr2);\n  aff = (u8)sqlite3CompareAffinity(pExpr1, aff) | (u8)jumpIfNull;\n  return aff;\n}\n\n/*\n** Return a pointer to the collation sequence that should be used by\n** a binary comparison operator comparing pLeft and pRight.\n**\n** If the left hand expression has a collating sequence type, then it is\n** used. Otherwise the collation sequence for the right hand expression\n** is used, or the default (BINARY) if neither expression has a collating\n** type.\n**\n** Argument pRight (but not pLeft) may be a null pointer. In this case,\n** it is not considered.\n*/\nSQLITE_PRIVATE CollSeq *sqlite3BinaryCompareCollSeq(\n  Parse *pParse, \n  Expr *pLeft, \n  Expr *pRight\n){\n  CollSeq *pColl;\n  assert( pLeft );\n  if( pLeft->flags & EP_Collate ){\n    pColl = sqlite3ExprCollSeq(pParse, pLeft);\n  }else if( pRight && (pRight->flags & EP_Collate)!=0 ){\n    pColl = sqlite3ExprCollSeq(pParse, pRight);\n  }else{\n    pColl = sqlite3ExprCollSeq(pParse, pLeft);\n    if( !pColl ){\n      pColl = sqlite3ExprCollSeq(pParse, pRight);\n    }\n  }\n  return pColl;\n}\n\n/*\n** Generate code for a comparison operator.\n*/\nstatic int codeCompare(\n  Parse *pParse,    /* The parsing (and code generating) context */\n  Expr *pLeft,      /* The left operand */\n  Expr *pRight,     /* The right operand */\n  int opcode,       /* The comparison opcode */\n  int in1, int in2, /* Register holding operands */\n  int dest,         /* Jump here if true.  */\n  int jumpIfNull    /* If true, jump if either operand is NULL */\n){\n  int p5;\n  int addr;\n  CollSeq *p4;\n\n  p4 = sqlite3BinaryCompareCollSeq(pParse, pLeft, pRight);\n  p5 = binaryCompareP5(pLeft, pRight, jumpIfNull);\n  addr = sqlite3VdbeAddOp4(pParse->pVdbe, opcode, in2, dest, in1,\n                           (void*)p4, P4_COLLSEQ);\n  sqlite3VdbeChangeP5(pParse->pVdbe, (u8)p5);\n  return addr;\n}\n\n/*\n** Return true if expression pExpr is a vector, or false otherwise.\n**\n** A vector is defined as any expression that results in two or more\n** columns of result.  Every TK_VECTOR node is an vector because the\n** parser will not generate a TK_VECTOR with fewer than two entries.\n** But a TK_SELECT might be either a vector or a scalar. It is only\n** considered a vector if it has two or more result columns.\n*/\nSQLITE_PRIVATE int sqlite3ExprIsVector(Expr *pExpr){\n  return sqlite3ExprVectorSize(pExpr)>1;\n}\n\n/*\n** If the expression passed as the only argument is of type TK_VECTOR \n** return the number of expressions in the vector. Or, if the expression\n** is a sub-select, return the number of columns in the sub-select. For\n** any other type of expression, return 1.\n*/\nSQLITE_PRIVATE int sqlite3ExprVectorSize(Expr *pExpr){\n  u8 op = pExpr->op;\n  if( op==TK_REGISTER ) op = pExpr->op2;\n  if( op==TK_VECTOR ){\n    return pExpr->x.pList->nExpr;\n  }else if( op==TK_SELECT ){\n    return pExpr->x.pSelect->pEList->nExpr;\n  }else{\n    return 1;\n  }\n}\n\n/*\n** Return a pointer to a subexpression of pVector that is the i-th\n** column of the vector (numbered starting with 0).  The caller must\n** ensure that i is within range.\n**\n** If pVector is really a scalar (and \"scalar\" here includes subqueries\n** that return a single column!) then return pVector unmodified.\n**\n** pVector retains ownership of the returned subexpression.\n**\n** If the vector is a (SELECT ...) then the expression returned is\n** just the expression for the i-th term of the result set, and may\n** not be ready for evaluation because the table cursor has not yet\n** been positioned.\n*/\nSQLITE_PRIVATE Expr *sqlite3VectorFieldSubexpr(Expr *pVector, int i){\n  assert( i<sqlite3ExprVectorSize(pVector) );\n  if( sqlite3ExprIsVector(pVector) ){\n    assert( pVector->op2==0 || pVector->op==TK_REGISTER );\n    if( pVector->op==TK_SELECT || pVector->op2==TK_SELECT ){\n      return pVector->x.pSelect->pEList->a[i].pExpr;\n    }else{\n      return pVector->x.pList->a[i].pExpr;\n    }\n  }\n  return pVector;\n}\n\n/*\n** Compute and return a new Expr object which when passed to\n** sqlite3ExprCode() will generate all necessary code to compute\n** the iField-th column of the vector expression pVector.\n**\n** It is ok for pVector to be a scalar (as long as iField==0).  \n** In that case, this routine works like sqlite3ExprDup().\n**\n** The caller owns the returned Expr object and is responsible for\n** ensuring that the returned value eventually gets freed.\n**\n** The caller retains ownership of pVector.  If pVector is a TK_SELECT,\n** then the returned object will reference pVector and so pVector must remain\n** valid for the life of the returned object.  If pVector is a TK_VECTOR\n** or a scalar expression, then it can be deleted as soon as this routine\n** returns.\n**\n** A trick to cause a TK_SELECT pVector to be deleted together with\n** the returned Expr object is to attach the pVector to the pRight field\n** of the returned TK_SELECT_COLUMN Expr object.\n*/\nSQLITE_PRIVATE Expr *sqlite3ExprForVectorField(\n  Parse *pParse,       /* Parsing context */\n  Expr *pVector,       /* The vector.  List of expressions or a sub-SELECT */\n  int iField           /* Which column of the vector to return */\n){\n  Expr *pRet;\n  if( pVector->op==TK_SELECT ){\n    assert( pVector->flags & EP_xIsSelect );\n    /* The TK_SELECT_COLUMN Expr node:\n    **\n    ** pLeft:           pVector containing TK_SELECT.  Not deleted.\n    ** pRight:          not used.  But recursively deleted.\n    ** iColumn:         Index of a column in pVector\n    ** iTable:          0 or the number of columns on the LHS of an assignment\n    ** pLeft->iTable:   First in an array of register holding result, or 0\n    **                  if the result is not yet computed.\n    **\n    ** sqlite3ExprDelete() specifically skips the recursive delete of\n    ** pLeft on TK_SELECT_COLUMN nodes.  But pRight is followed, so pVector\n    ** can be attached to pRight to cause this node to take ownership of\n    ** pVector.  Typically there will be multiple TK_SELECT_COLUMN nodes\n    ** with the same pLeft pointer to the pVector, but only one of them\n    ** will own the pVector.\n    */\n    pRet = sqlite3PExpr(pParse, TK_SELECT_COLUMN, 0, 0);\n    if( pRet ){\n      pRet->iColumn = iField;\n      pRet->pLeft = pVector;\n    }\n    assert( pRet==0 || pRet->iTable==0 );\n  }else{\n    if( pVector->op==TK_VECTOR ) pVector = pVector->x.pList->a[iField].pExpr;\n    pRet = sqlite3ExprDup(pParse->db, pVector, 0);\n  }\n  return pRet;\n}\n\n/*\n** If expression pExpr is of type TK_SELECT, generate code to evaluate\n** it. Return the register in which the result is stored (or, if the \n** sub-select returns more than one column, the first in an array\n** of registers in which the result is stored).\n**\n** If pExpr is not a TK_SELECT expression, return 0.\n*/\nstatic int exprCodeSubselect(Parse *pParse, Expr *pExpr){\n  int reg = 0;\n#ifndef SQLITE_OMIT_SUBQUERY\n  if( pExpr->op==TK_SELECT ){\n    reg = sqlite3CodeSubselect(pParse, pExpr, 0, 0);\n  }\n#endif\n  return reg;\n}\n\n/*\n** Argument pVector points to a vector expression - either a TK_VECTOR\n** or TK_SELECT that returns more than one column. This function returns\n** the register number of a register that contains the value of\n** element iField of the vector.\n**\n** If pVector is a TK_SELECT expression, then code for it must have \n** already been generated using the exprCodeSubselect() routine. In this\n** case parameter regSelect should be the first in an array of registers\n** containing the results of the sub-select. \n**\n** If pVector is of type TK_VECTOR, then code for the requested field\n** is generated. In this case (*pRegFree) may be set to the number of\n** a temporary register to be freed by the caller before returning.\n**\n** Before returning, output parameter (*ppExpr) is set to point to the\n** Expr object corresponding to element iElem of the vector.\n*/\nstatic int exprVectorRegister(\n  Parse *pParse,                  /* Parse context */\n  Expr *pVector,                  /* Vector to extract element from */\n  int iField,                     /* Field to extract from pVector */\n  int regSelect,                  /* First in array of registers */\n  Expr **ppExpr,                  /* OUT: Expression element */\n  int *pRegFree                   /* OUT: Temp register to free */\n){\n  u8 op = pVector->op;\n  assert( op==TK_VECTOR || op==TK_REGISTER || op==TK_SELECT );\n  if( op==TK_REGISTER ){\n    *ppExpr = sqlite3VectorFieldSubexpr(pVector, iField);\n    return pVector->iTable+iField;\n  }\n  if( op==TK_SELECT ){\n    *ppExpr = pVector->x.pSelect->pEList->a[iField].pExpr;\n     return regSelect+iField;\n  }\n  *ppExpr = pVector->x.pList->a[iField].pExpr;\n  return sqlite3ExprCodeTemp(pParse, *ppExpr, pRegFree);\n}\n\n/*\n** Expression pExpr is a comparison between two vector values. Compute\n** the result of the comparison (1, 0, or NULL) and write that\n** result into register dest.\n**\n** The caller must satisfy the following preconditions:\n**\n**    if pExpr->op==TK_IS:      op==TK_EQ and p5==SQLITE_NULLEQ\n**    if pExpr->op==TK_ISNOT:   op==TK_NE and p5==SQLITE_NULLEQ\n**    otherwise:                op==pExpr->op and p5==0\n*/\nstatic void codeVectorCompare(\n  Parse *pParse,        /* Code generator context */\n  Expr *pExpr,          /* The comparison operation */\n  int dest,             /* Write results into this register */\n  u8 op,                /* Comparison operator */\n  u8 p5                 /* SQLITE_NULLEQ or zero */\n){\n  Vdbe *v = pParse->pVdbe;\n  Expr *pLeft = pExpr->pLeft;\n  Expr *pRight = pExpr->pRight;\n  int nLeft = sqlite3ExprVectorSize(pLeft);\n  int i;\n  int regLeft = 0;\n  int regRight = 0;\n  u8 opx = op;\n  int addrDone = sqlite3VdbeMakeLabel(v);\n\n  if( nLeft!=sqlite3ExprVectorSize(pRight) ){\n    sqlite3ErrorMsg(pParse, \"row value misused\");\n    return;\n  }\n  assert( pExpr->op==TK_EQ || pExpr->op==TK_NE \n       || pExpr->op==TK_IS || pExpr->op==TK_ISNOT \n       || pExpr->op==TK_LT || pExpr->op==TK_GT \n       || pExpr->op==TK_LE || pExpr->op==TK_GE \n  );\n  assert( pExpr->op==op || (pExpr->op==TK_IS && op==TK_EQ)\n            || (pExpr->op==TK_ISNOT && op==TK_NE) );\n  assert( p5==0 || pExpr->op!=op );\n  assert( p5==SQLITE_NULLEQ || pExpr->op==op );\n\n  p5 |= SQLITE_STOREP2;\n  if( opx==TK_LE ) opx = TK_LT;\n  if( opx==TK_GE ) opx = TK_GT;\n\n  regLeft = exprCodeSubselect(pParse, pLeft);\n  regRight = exprCodeSubselect(pParse, pRight);\n\n  for(i=0; 1 /*Loop exits by \"break\"*/; i++){\n    int regFree1 = 0, regFree2 = 0;\n    Expr *pL, *pR; \n    int r1, r2;\n    assert( i>=0 && i<nLeft );\n    if( i>0 ) sqlite3ExprCachePush(pParse);\n    r1 = exprVectorRegister(pParse, pLeft, i, regLeft, &pL, &regFree1);\n    r2 = exprVectorRegister(pParse, pRight, i, regRight, &pR, &regFree2);\n    codeCompare(pParse, pL, pR, opx, r1, r2, dest, p5);\n    testcase(op==OP_Lt); VdbeCoverageIf(v,op==OP_Lt);\n    testcase(op==OP_Le); VdbeCoverageIf(v,op==OP_Le);\n    testcase(op==OP_Gt); VdbeCoverageIf(v,op==OP_Gt);\n    testcase(op==OP_Ge); VdbeCoverageIf(v,op==OP_Ge);\n    testcase(op==OP_Eq); VdbeCoverageIf(v,op==OP_Eq);\n    testcase(op==OP_Ne); VdbeCoverageIf(v,op==OP_Ne);\n    sqlite3ReleaseTempReg(pParse, regFree1);\n    sqlite3ReleaseTempReg(pParse, regFree2);\n    if( i>0 ) sqlite3ExprCachePop(pParse);\n    if( i==nLeft-1 ){\n      break;\n    }\n    if( opx==TK_EQ ){\n      sqlite3VdbeAddOp2(v, OP_IfNot, dest, addrDone); VdbeCoverage(v);\n      p5 |= SQLITE_KEEPNULL;\n    }else if( opx==TK_NE ){\n      sqlite3VdbeAddOp2(v, OP_If, dest, addrDone); VdbeCoverage(v);\n      p5 |= SQLITE_KEEPNULL;\n    }else{\n      assert( op==TK_LT || op==TK_GT || op==TK_LE || op==TK_GE );\n      sqlite3VdbeAddOp2(v, OP_ElseNotEq, 0, addrDone);\n      VdbeCoverageIf(v, op==TK_LT);\n      VdbeCoverageIf(v, op==TK_GT);\n      VdbeCoverageIf(v, op==TK_LE);\n      VdbeCoverageIf(v, op==TK_GE);\n      if( i==nLeft-2 ) opx = op;\n    }\n  }\n  sqlite3VdbeResolveLabel(v, addrDone);\n}\n\n#if SQLITE_MAX_EXPR_DEPTH>0\n/*\n** Check that argument nHeight is less than or equal to the maximum\n** expression depth allowed. If it is not, leave an error message in\n** pParse.\n*/\nSQLITE_PRIVATE int sqlite3ExprCheckHeight(Parse *pParse, int nHeight){\n  int rc = SQLITE_OK;\n  int mxHeight = pParse->db->aLimit[SQLITE_LIMIT_EXPR_DEPTH];\n  if( nHeight>mxHeight ){\n    sqlite3ErrorMsg(pParse, \n       \"Expression tree is too large (maximum depth %d)\", mxHeight\n    );\n    rc = SQLITE_ERROR;\n  }\n  return rc;\n}\n\n/* The following three functions, heightOfExpr(), heightOfExprList()\n** and heightOfSelect(), are used to determine the maximum height\n** of any expression tree referenced by the structure passed as the\n** first argument.\n**\n** If this maximum height is greater than the current value pointed\n** to by pnHeight, the second parameter, then set *pnHeight to that\n** value.\n*/\nstatic void heightOfExpr(Expr *p, int *pnHeight){\n  if( p ){\n    if( p->nHeight>*pnHeight ){\n      *pnHeight = p->nHeight;\n    }\n  }\n}\nstatic void heightOfExprList(ExprList *p, int *pnHeight){\n  if( p ){\n    int i;\n    for(i=0; i<p->nExpr; i++){\n      heightOfExpr(p->a[i].pExpr, pnHeight);\n    }\n  }\n}\nstatic void heightOfSelect(Select *pSelect, int *pnHeight){\n  Select *p;\n  for(p=pSelect; p; p=p->pPrior){\n    heightOfExpr(p->pWhere, pnHeight);\n    heightOfExpr(p->pHaving, pnHeight);\n    heightOfExpr(p->pLimit, pnHeight);\n    heightOfExprList(p->pEList, pnHeight);\n    heightOfExprList(p->pGroupBy, pnHeight);\n    heightOfExprList(p->pOrderBy, pnHeight);\n  }\n}\n\n/*\n** Set the Expr.nHeight variable in the structure passed as an \n** argument. An expression with no children, Expr.pList or \n** Expr.pSelect member has a height of 1. Any other expression\n** has a height equal to the maximum height of any other \n** referenced Expr plus one.\n**\n** Also propagate EP_Propagate flags up from Expr.x.pList to Expr.flags,\n** if appropriate.\n*/\nstatic void exprSetHeight(Expr *p){\n  int nHeight = 0;\n  heightOfExpr(p->pLeft, &nHeight);\n  heightOfExpr(p->pRight, &nHeight);\n  if( ExprHasProperty(p, EP_xIsSelect) ){\n    heightOfSelect(p->x.pSelect, &nHeight);\n  }else if( p->x.pList ){\n    heightOfExprList(p->x.pList, &nHeight);\n    p->flags |= EP_Propagate & sqlite3ExprListFlags(p->x.pList);\n  }\n  p->nHeight = nHeight + 1;\n}\n\n/*\n** Set the Expr.nHeight variable using the exprSetHeight() function. If\n** the height is greater than the maximum allowed expression depth,\n** leave an error in pParse.\n**\n** Also propagate all EP_Propagate flags from the Expr.x.pList into\n** Expr.flags. \n*/\nSQLITE_PRIVATE void sqlite3ExprSetHeightAndFlags(Parse *pParse, Expr *p){\n  if( pParse->nErr ) return;\n  exprSetHeight(p);\n  sqlite3ExprCheckHeight(pParse, p->nHeight);\n}\n\n/*\n** Return the maximum height of any expression tree referenced\n** by the select statement passed as an argument.\n*/\nSQLITE_PRIVATE int sqlite3SelectExprHeight(Select *p){\n  int nHeight = 0;\n  heightOfSelect(p, &nHeight);\n  return nHeight;\n}\n#else /* ABOVE:  Height enforcement enabled.  BELOW: Height enforcement off */\n/*\n** Propagate all EP_Propagate flags from the Expr.x.pList into\n** Expr.flags. \n*/\nSQLITE_PRIVATE void sqlite3ExprSetHeightAndFlags(Parse *pParse, Expr *p){\n  if( p && p->x.pList && !ExprHasProperty(p, EP_xIsSelect) ){\n    p->flags |= EP_Propagate & sqlite3ExprListFlags(p->x.pList);\n  }\n}\n#define exprSetHeight(y)\n#endif /* SQLITE_MAX_EXPR_DEPTH>0 */\n\n/*\n** This routine is the core allocator for Expr nodes.\n**\n** Construct a new expression node and return a pointer to it.  Memory\n** for this node and for the pToken argument is a single allocation\n** obtained from sqlite3DbMalloc().  The calling function\n** is responsible for making sure the node eventually gets freed.\n**\n** If dequote is true, then the token (if it exists) is dequoted.\n** If dequote is false, no dequoting is performed.  The deQuote\n** parameter is ignored if pToken is NULL or if the token does not\n** appear to be quoted.  If the quotes were of the form \"...\" (double-quotes)\n** then the EP_DblQuoted flag is set on the expression node.\n**\n** Special case:  If op==TK_INTEGER and pToken points to a string that\n** can be translated into a 32-bit integer, then the token is not\n** stored in u.zToken.  Instead, the integer values is written\n** into u.iValue and the EP_IntValue flag is set.  No extra storage\n** is allocated to hold the integer text and the dequote flag is ignored.\n*/\nSQLITE_PRIVATE Expr *sqlite3ExprAlloc(\n  sqlite3 *db,            /* Handle for sqlite3DbMallocRawNN() */\n  int op,                 /* Expression opcode */\n  const Token *pToken,    /* Token argument.  Might be NULL */\n  int dequote             /* True to dequote */\n){\n  Expr *pNew;\n  int nExtra = 0;\n  int iValue = 0;\n\n  assert( db!=0 );\n  if( pToken ){\n    if( op!=TK_INTEGER || pToken->z==0\n          || sqlite3GetInt32(pToken->z, &iValue)==0 ){\n      nExtra = pToken->n+1;\n      assert( iValue>=0 );\n    }\n  }\n  pNew = sqlite3DbMallocRawNN(db, sizeof(Expr)+nExtra);\n  if( pNew ){\n    memset(pNew, 0, sizeof(Expr));\n    pNew->op = (u8)op;\n    pNew->iAgg = -1;\n    if( pToken ){\n      if( nExtra==0 ){\n        pNew->flags |= EP_IntValue|EP_Leaf;\n        pNew->u.iValue = iValue;\n      }else{\n        pNew->u.zToken = (char*)&pNew[1];\n        assert( pToken->z!=0 || pToken->n==0 );\n        if( pToken->n ) memcpy(pNew->u.zToken, pToken->z, pToken->n);\n        pNew->u.zToken[pToken->n] = 0;\n        if( dequote && sqlite3Isquote(pNew->u.zToken[0]) ){\n          if( pNew->u.zToken[0]=='\"' ) pNew->flags |= EP_DblQuoted;\n          sqlite3Dequote(pNew->u.zToken);\n        }\n      }\n    }\n#if SQLITE_MAX_EXPR_DEPTH>0\n    pNew->nHeight = 1;\n#endif  \n  }\n  return pNew;\n}\n\n/*\n** Allocate a new expression node from a zero-terminated token that has\n** already been dequoted.\n*/\nSQLITE_PRIVATE Expr *sqlite3Expr(\n  sqlite3 *db,            /* Handle for sqlite3DbMallocZero() (may be null) */\n  int op,                 /* Expression opcode */\n  const char *zToken      /* Token argument.  Might be NULL */\n){\n  Token x;\n  x.z = zToken;\n  x.n = sqlite3Strlen30(zToken);\n  return sqlite3ExprAlloc(db, op, &x, 0);\n}\n\n/*\n** Attach subtrees pLeft and pRight to the Expr node pRoot.\n**\n** If pRoot==NULL that means that a memory allocation error has occurred.\n** In that case, delete the subtrees pLeft and pRight.\n*/\nSQLITE_PRIVATE void sqlite3ExprAttachSubtrees(\n  sqlite3 *db,\n  Expr *pRoot,\n  Expr *pLeft,\n  Expr *pRight\n){\n  if( pRoot==0 ){\n    assert( db->mallocFailed );\n    sqlite3ExprDelete(db, pLeft);\n    sqlite3ExprDelete(db, pRight);\n  }else{\n    if( pRight ){\n      pRoot->pRight = pRight;\n      pRoot->flags |= EP_Propagate & pRight->flags;\n    }\n    if( pLeft ){\n      pRoot->pLeft = pLeft;\n      pRoot->flags |= EP_Propagate & pLeft->flags;\n    }\n    exprSetHeight(pRoot);\n  }\n}\n\n/*\n** Allocate an Expr node which joins as many as two subtrees.\n**\n** One or both of the subtrees can be NULL.  Return a pointer to the new\n** Expr node.  Or, if an OOM error occurs, set pParse->db->mallocFailed,\n** free the subtrees and return NULL.\n*/\nSQLITE_PRIVATE Expr *sqlite3PExpr(\n  Parse *pParse,          /* Parsing context */\n  int op,                 /* Expression opcode */\n  Expr *pLeft,            /* Left operand */\n  Expr *pRight            /* Right operand */\n){\n  Expr *p;\n  if( op==TK_AND && pParse->nErr==0 ){\n    /* Take advantage of short-circuit false optimization for AND */\n    p = sqlite3ExprAnd(pParse->db, pLeft, pRight);\n  }else{\n    p = sqlite3DbMallocRawNN(pParse->db, sizeof(Expr));\n    if( p ){\n      memset(p, 0, sizeof(Expr));\n      p->op = op & TKFLG_MASK;\n      p->iAgg = -1;\n    }\n    sqlite3ExprAttachSubtrees(pParse->db, p, pLeft, pRight);\n  }\n  if( p ) {\n    sqlite3ExprCheckHeight(pParse, p->nHeight);\n  }\n  return p;\n}\n\n/*\n** Add pSelect to the Expr.x.pSelect field.  Or, if pExpr is NULL (due\n** do a memory allocation failure) then delete the pSelect object.\n*/\nSQLITE_PRIVATE void sqlite3PExprAddSelect(Parse *pParse, Expr *pExpr, Select *pSelect){\n  if( pExpr ){\n    pExpr->x.pSelect = pSelect;\n    ExprSetProperty(pExpr, EP_xIsSelect|EP_Subquery);\n    sqlite3ExprSetHeightAndFlags(pParse, pExpr);\n  }else{\n    assert( pParse->db->mallocFailed );\n    sqlite3SelectDelete(pParse->db, pSelect);\n  }\n}\n\n\n/*\n** If the expression is always either TRUE or FALSE (respectively),\n** then return 1.  If one cannot determine the truth value of the\n** expression at compile-time return 0.\n**\n** This is an optimization.  If is OK to return 0 here even if\n** the expression really is always false or false (a false negative).\n** But it is a bug to return 1 if the expression might have different\n** boolean values in different circumstances (a false positive.)\n**\n** Note that if the expression is part of conditional for a\n** LEFT JOIN, then we cannot determine at compile-time whether or not\n** is it true or false, so always return 0.\n*/\nstatic int exprAlwaysTrue(Expr *p){\n  int v = 0;\n  if( ExprHasProperty(p, EP_FromJoin) ) return 0;\n  if( !sqlite3ExprIsInteger(p, &v) ) return 0;\n  return v!=0;\n}\nstatic int exprAlwaysFalse(Expr *p){\n  int v = 0;\n  if( ExprHasProperty(p, EP_FromJoin) ) return 0;\n  if( !sqlite3ExprIsInteger(p, &v) ) return 0;\n  return v==0;\n}\n\n/*\n** Join two expressions using an AND operator.  If either expression is\n** NULL, then just return the other expression.\n**\n** If one side or the other of the AND is known to be false, then instead\n** of returning an AND expression, just return a constant expression with\n** a value of false.\n*/\nSQLITE_PRIVATE Expr *sqlite3ExprAnd(sqlite3 *db, Expr *pLeft, Expr *pRight){\n  if( pLeft==0 ){\n    return pRight;\n  }else if( pRight==0 ){\n    return pLeft;\n  }else if( exprAlwaysFalse(pLeft) || exprAlwaysFalse(pRight) ){\n    sqlite3ExprDelete(db, pLeft);\n    sqlite3ExprDelete(db, pRight);\n    return sqlite3ExprAlloc(db, TK_INTEGER, &sqlite3IntTokens[0], 0);\n  }else{\n    Expr *pNew = sqlite3ExprAlloc(db, TK_AND, 0, 0);\n    sqlite3ExprAttachSubtrees(db, pNew, pLeft, pRight);\n    return pNew;\n  }\n}\n\n/*\n** Construct a new expression node for a function with multiple\n** arguments.\n*/\nSQLITE_PRIVATE Expr *sqlite3ExprFunction(Parse *pParse, ExprList *pList, Token *pToken){\n  Expr *pNew;\n  sqlite3 *db = pParse->db;\n  assert( pToken );\n  pNew = sqlite3ExprAlloc(db, TK_FUNCTION, pToken, 1);\n  if( pNew==0 ){\n    sqlite3ExprListDelete(db, pList); /* Avoid memory leak when malloc fails */\n    return 0;\n  }\n  pNew->x.pList = pList;\n  ExprSetProperty(pNew, EP_HasFunc);\n  assert( !ExprHasProperty(pNew, EP_xIsSelect) );\n  sqlite3ExprSetHeightAndFlags(pParse, pNew);\n  return pNew;\n}\n\n/*\n** Assign a variable number to an expression that encodes a wildcard\n** in the original SQL statement.  \n**\n** Wildcards consisting of a single \"?\" are assigned the next sequential\n** variable number.\n**\n** Wildcards of the form \"?nnn\" are assigned the number \"nnn\".  We make\n** sure \"nnn\" is not too big to avoid a denial of service attack when\n** the SQL statement comes from an external source.\n**\n** Wildcards of the form \":aaa\", \"@aaa\", or \"$aaa\" are assigned the same number\n** as the previous instance of the same wildcard.  Or if this is the first\n** instance of the wildcard, the next sequential variable number is\n** assigned.\n*/\nSQLITE_PRIVATE void sqlite3ExprAssignVarNumber(Parse *pParse, Expr *pExpr, u32 n){\n  sqlite3 *db = pParse->db;\n  const char *z;\n  ynVar x;\n\n  if( pExpr==0 ) return;\n  assert( !ExprHasProperty(pExpr, EP_IntValue|EP_Reduced|EP_TokenOnly) );\n  z = pExpr->u.zToken;\n  assert( z!=0 );\n  assert( z[0]!=0 );\n  assert( n==(u32)sqlite3Strlen30(z) );\n  if( z[1]==0 ){\n    /* Wildcard of the form \"?\".  Assign the next variable number */\n    assert( z[0]=='?' );\n    x = (ynVar)(++pParse->nVar);\n  }else{\n    int doAdd = 0;\n    if( z[0]=='?' ){\n      /* Wildcard of the form \"?nnn\".  Convert \"nnn\" to an integer and\n      ** use it as the variable number */\n      i64 i;\n      int bOk;\n      if( n==2 ){ /*OPTIMIZATION-IF-TRUE*/\n        i = z[1]-'0';  /* The common case of ?N for a single digit N */\n        bOk = 1;\n      }else{\n        bOk = 0==sqlite3Atoi64(&z[1], &i, n-1, SQLITE_UTF8);\n      }\n      testcase( i==0 );\n      testcase( i==1 );\n      testcase( i==db->aLimit[SQLITE_LIMIT_VARIABLE_NUMBER]-1 );\n      testcase( i==db->aLimit[SQLITE_LIMIT_VARIABLE_NUMBER] );\n      if( bOk==0 || i<1 || i>db->aLimit[SQLITE_LIMIT_VARIABLE_NUMBER] ){\n        sqlite3ErrorMsg(pParse, \"variable number must be between ?1 and ?%d\",\n            db->aLimit[SQLITE_LIMIT_VARIABLE_NUMBER]);\n        return;\n      }\n      x = (ynVar)i;\n      if( x>pParse->nVar ){\n        pParse->nVar = (int)x;\n        doAdd = 1;\n      }else if( sqlite3VListNumToName(pParse->pVList, x)==0 ){\n        doAdd = 1;\n      }\n    }else{\n      /* Wildcards like \":aaa\", \"$aaa\" or \"@aaa\".  Reuse the same variable\n      ** number as the prior appearance of the same name, or if the name\n      ** has never appeared before, reuse the same variable number\n      */\n      x = (ynVar)sqlite3VListNameToNum(pParse->pVList, z, n);\n      if( x==0 ){\n        x = (ynVar)(++pParse->nVar);\n        doAdd = 1;\n      }\n    }\n    if( doAdd ){\n      pParse->pVList = sqlite3VListAdd(db, pParse->pVList, z, n, x);\n    }\n  }\n  pExpr->iColumn = x;\n  if( x>db->aLimit[SQLITE_LIMIT_VARIABLE_NUMBER] ){\n    sqlite3ErrorMsg(pParse, \"too many SQL variables\");\n  }\n}\n\n/*\n** Recursively delete an expression tree.\n*/\nstatic SQLITE_NOINLINE void sqlite3ExprDeleteNN(sqlite3 *db, Expr *p){\n  assert( p!=0 );\n  /* Sanity check: Assert that the IntValue is non-negative if it exists */\n  assert( !ExprHasProperty(p, EP_IntValue) || p->u.iValue>=0 );\n#ifdef SQLITE_DEBUG\n  if( ExprHasProperty(p, EP_Leaf) && !ExprHasProperty(p, EP_TokenOnly) ){\n    assert( p->pLeft==0 );\n    assert( p->pRight==0 );\n    assert( p->x.pSelect==0 );\n  }\n#endif\n  if( !ExprHasProperty(p, (EP_TokenOnly|EP_Leaf)) ){\n    /* The Expr.x union is never used at the same time as Expr.pRight */\n    assert( p->x.pList==0 || p->pRight==0 );\n    if( p->pLeft && p->op!=TK_SELECT_COLUMN ) sqlite3ExprDeleteNN(db, p->pLeft);\n    if( p->pRight ){\n      sqlite3ExprDeleteNN(db, p->pRight);\n    }else if( ExprHasProperty(p, EP_xIsSelect) ){\n      sqlite3SelectDelete(db, p->x.pSelect);\n    }else{\n      sqlite3ExprListDelete(db, p->x.pList);\n    }\n  }\n  if( ExprHasProperty(p, EP_MemToken) ) sqlite3DbFree(db, p->u.zToken);\n  if( !ExprHasProperty(p, EP_Static) ){\n    sqlite3DbFreeNN(db, p);\n  }\n}\nSQLITE_PRIVATE void sqlite3ExprDelete(sqlite3 *db, Expr *p){\n  if( p ) sqlite3ExprDeleteNN(db, p);\n}\n\n/*\n** Return the number of bytes allocated for the expression structure \n** passed as the first argument. This is always one of EXPR_FULLSIZE,\n** EXPR_REDUCEDSIZE or EXPR_TOKENONLYSIZE.\n*/\nstatic int exprStructSize(Expr *p){\n  if( ExprHasProperty(p, EP_TokenOnly) ) return EXPR_TOKENONLYSIZE;\n  if( ExprHasProperty(p, EP_Reduced) ) return EXPR_REDUCEDSIZE;\n  return EXPR_FULLSIZE;\n}\n\n/*\n** The dupedExpr*Size() routines each return the number of bytes required\n** to store a copy of an expression or expression tree.  They differ in\n** how much of the tree is measured.\n**\n**     dupedExprStructSize()     Size of only the Expr structure \n**     dupedExprNodeSize()       Size of Expr + space for token\n**     dupedExprSize()           Expr + token + subtree components\n**\n***************************************************************************\n**\n** The dupedExprStructSize() function returns two values OR-ed together:  \n** (1) the space required for a copy of the Expr structure only and \n** (2) the EP_xxx flags that indicate what the structure size should be.\n** The return values is always one of:\n**\n**      EXPR_FULLSIZE\n**      EXPR_REDUCEDSIZE   | EP_Reduced\n**      EXPR_TOKENONLYSIZE | EP_TokenOnly\n**\n** The size of the structure can be found by masking the return value\n** of this routine with 0xfff.  The flags can be found by masking the\n** return value with EP_Reduced|EP_TokenOnly.\n**\n** Note that with flags==EXPRDUP_REDUCE, this routines works on full-size\n** (unreduced) Expr objects as they or originally constructed by the parser.\n** During expression analysis, extra information is computed and moved into\n** later parts of teh Expr object and that extra information might get chopped\n** off if the expression is reduced.  Note also that it does not work to\n** make an EXPRDUP_REDUCE copy of a reduced expression.  It is only legal\n** to reduce a pristine expression tree from the parser.  The implementation\n** of dupedExprStructSize() contain multiple assert() statements that attempt\n** to enforce this constraint.\n*/\nstatic int dupedExprStructSize(Expr *p, int flags){\n  int nSize;\n  assert( flags==EXPRDUP_REDUCE || flags==0 ); /* Only one flag value allowed */\n  assert( EXPR_FULLSIZE<=0xfff );\n  assert( (0xfff & (EP_Reduced|EP_TokenOnly))==0 );\n  if( 0==flags || p->op==TK_SELECT_COLUMN ){\n    nSize = EXPR_FULLSIZE;\n  }else{\n    assert( !ExprHasProperty(p, EP_TokenOnly|EP_Reduced) );\n    assert( !ExprHasProperty(p, EP_FromJoin) ); \n    assert( !ExprHasProperty(p, EP_MemToken) );\n    assert( !ExprHasProperty(p, EP_NoReduce) );\n    if( p->pLeft || p->x.pList ){\n      nSize = EXPR_REDUCEDSIZE | EP_Reduced;\n    }else{\n      assert( p->pRight==0 );\n      nSize = EXPR_TOKENONLYSIZE | EP_TokenOnly;\n    }\n  }\n  return nSize;\n}\n\n/*\n** This function returns the space in bytes required to store the copy \n** of the Expr structure and a copy of the Expr.u.zToken string (if that\n** string is defined.)\n*/\nstatic int dupedExprNodeSize(Expr *p, int flags){\n  int nByte = dupedExprStructSize(p, flags) & 0xfff;\n  if( !ExprHasProperty(p, EP_IntValue) && p->u.zToken ){\n    nByte += sqlite3Strlen30(p->u.zToken)+1;\n  }\n  return ROUND8(nByte);\n}\n\n/*\n** Return the number of bytes required to create a duplicate of the \n** expression passed as the first argument. The second argument is a\n** mask containing EXPRDUP_XXX flags.\n**\n** The value returned includes space to create a copy of the Expr struct\n** itself and the buffer referred to by Expr.u.zToken, if any.\n**\n** If the EXPRDUP_REDUCE flag is set, then the return value includes \n** space to duplicate all Expr nodes in the tree formed by Expr.pLeft \n** and Expr.pRight variables (but not for any structures pointed to or \n** descended from the Expr.x.pList or Expr.x.pSelect variables).\n*/\nstatic int dupedExprSize(Expr *p, int flags){\n  int nByte = 0;\n  if( p ){\n    nByte = dupedExprNodeSize(p, flags);\n    if( flags&EXPRDUP_REDUCE ){\n      nByte += dupedExprSize(p->pLeft, flags) + dupedExprSize(p->pRight, flags);\n    }\n  }\n  return nByte;\n}\n\n/*\n** This function is similar to sqlite3ExprDup(), except that if pzBuffer \n** is not NULL then *pzBuffer is assumed to point to a buffer large enough \n** to store the copy of expression p, the copies of p->u.zToken\n** (if applicable), and the copies of the p->pLeft and p->pRight expressions,\n** if any. Before returning, *pzBuffer is set to the first byte past the\n** portion of the buffer copied into by this function.\n*/\nstatic Expr *exprDup(sqlite3 *db, Expr *p, int dupFlags, u8 **pzBuffer){\n  Expr *pNew;           /* Value to return */\n  u8 *zAlloc;           /* Memory space from which to build Expr object */\n  u32 staticFlag;       /* EP_Static if space not obtained from malloc */\n\n  assert( db!=0 );\n  assert( p );\n  assert( dupFlags==0 || dupFlags==EXPRDUP_REDUCE );\n  assert( pzBuffer==0 || dupFlags==EXPRDUP_REDUCE );\n\n  /* Figure out where to write the new Expr structure. */\n  if( pzBuffer ){\n    zAlloc = *pzBuffer;\n    staticFlag = EP_Static;\n  }else{\n    zAlloc = sqlite3DbMallocRawNN(db, dupedExprSize(p, dupFlags));\n    staticFlag = 0;\n  }\n  pNew = (Expr *)zAlloc;\n\n  if( pNew ){\n    /* Set nNewSize to the size allocated for the structure pointed to\n    ** by pNew. This is either EXPR_FULLSIZE, EXPR_REDUCEDSIZE or\n    ** EXPR_TOKENONLYSIZE. nToken is set to the number of bytes consumed\n    ** by the copy of the p->u.zToken string (if any).\n    */\n    const unsigned nStructSize = dupedExprStructSize(p, dupFlags);\n    const int nNewSize = nStructSize & 0xfff;\n    int nToken;\n    if( !ExprHasProperty(p, EP_IntValue) && p->u.zToken ){\n      nToken = sqlite3Strlen30(p->u.zToken) + 1;\n    }else{\n      nToken = 0;\n    }\n    if( dupFlags ){\n      assert( ExprHasProperty(p, EP_Reduced)==0 );\n      memcpy(zAlloc, p, nNewSize);\n    }else{\n      u32 nSize = (u32)exprStructSize(p);\n      memcpy(zAlloc, p, nSize);\n      if( nSize<EXPR_FULLSIZE ){ \n        memset(&zAlloc[nSize], 0, EXPR_FULLSIZE-nSize);\n      }\n    }\n\n    /* Set the EP_Reduced, EP_TokenOnly, and EP_Static flags appropriately. */\n    pNew->flags &= ~(EP_Reduced|EP_TokenOnly|EP_Static|EP_MemToken);\n    pNew->flags |= nStructSize & (EP_Reduced|EP_TokenOnly);\n    pNew->flags |= staticFlag;\n\n    /* Copy the p->u.zToken string, if any. */\n    if( nToken ){\n      char *zToken = pNew->u.zToken = (char*)&zAlloc[nNewSize];\n      memcpy(zToken, p->u.zToken, nToken);\n    }\n\n    if( 0==((p->flags|pNew->flags) & (EP_TokenOnly|EP_Leaf)) ){\n      /* Fill in the pNew->x.pSelect or pNew->x.pList member. */\n      if( ExprHasProperty(p, EP_xIsSelect) ){\n        pNew->x.pSelect = sqlite3SelectDup(db, p->x.pSelect, dupFlags);\n      }else{\n        pNew->x.pList = sqlite3ExprListDup(db, p->x.pList, dupFlags);\n      }\n    }\n\n    /* Fill in pNew->pLeft and pNew->pRight. */\n    if( ExprHasProperty(pNew, EP_Reduced|EP_TokenOnly) ){\n      zAlloc += dupedExprNodeSize(p, dupFlags);\n      if( !ExprHasProperty(pNew, EP_TokenOnly|EP_Leaf) ){\n        pNew->pLeft = p->pLeft ?\n                      exprDup(db, p->pLeft, EXPRDUP_REDUCE, &zAlloc) : 0;\n        pNew->pRight = p->pRight ?\n                       exprDup(db, p->pRight, EXPRDUP_REDUCE, &zAlloc) : 0;\n      }\n      if( pzBuffer ){\n        *pzBuffer = zAlloc;\n      }\n    }else{\n      if( !ExprHasProperty(p, EP_TokenOnly|EP_Leaf) ){\n        if( pNew->op==TK_SELECT_COLUMN ){\n          pNew->pLeft = p->pLeft;\n          assert( p->iColumn==0 || p->pRight==0 );\n          assert( p->pRight==0  || p->pRight==p->pLeft );\n        }else{\n          pNew->pLeft = sqlite3ExprDup(db, p->pLeft, 0);\n        }\n        pNew->pRight = sqlite3ExprDup(db, p->pRight, 0);\n      }\n    }\n  }\n  return pNew;\n}\n\n/*\n** Create and return a deep copy of the object passed as the second \n** argument. If an OOM condition is encountered, NULL is returned\n** and the db->mallocFailed flag set.\n*/\n#ifndef SQLITE_OMIT_CTE\nstatic With *withDup(sqlite3 *db, With *p){\n  With *pRet = 0;\n  if( p ){\n    int nByte = sizeof(*p) + sizeof(p->a[0]) * (p->nCte-1);\n    pRet = sqlite3DbMallocZero(db, nByte);\n    if( pRet ){\n      int i;\n      pRet->nCte = p->nCte;\n      for(i=0; i<p->nCte; i++){\n        pRet->a[i].pSelect = sqlite3SelectDup(db, p->a[i].pSelect, 0);\n        pRet->a[i].pCols = sqlite3ExprListDup(db, p->a[i].pCols, 0);\n        pRet->a[i].zName = sqlite3DbStrDup(db, p->a[i].zName);\n      }\n    }\n  }\n  return pRet;\n}\n#else\n# define withDup(x,y) 0\n#endif\n\n/*\n** The following group of routines make deep copies of expressions,\n** expression lists, ID lists, and select statements.  The copies can\n** be deleted (by being passed to their respective ...Delete() routines)\n** without effecting the originals.\n**\n** The expression list, ID, and source lists return by sqlite3ExprListDup(),\n** sqlite3IdListDup(), and sqlite3SrcListDup() can not be further expanded \n** by subsequent calls to sqlite*ListAppend() routines.\n**\n** Any tables that the SrcList might point to are not duplicated.\n**\n** The flags parameter contains a combination of the EXPRDUP_XXX flags.\n** If the EXPRDUP_REDUCE flag is set, then the structure returned is a\n** truncated version of the usual Expr structure that will be stored as\n** part of the in-memory representation of the database schema.\n*/\nSQLITE_PRIVATE Expr *sqlite3ExprDup(sqlite3 *db, Expr *p, int flags){\n  assert( flags==0 || flags==EXPRDUP_REDUCE );\n  return p ? exprDup(db, p, flags, 0) : 0;\n}\nSQLITE_PRIVATE ExprList *sqlite3ExprListDup(sqlite3 *db, ExprList *p, int flags){\n  ExprList *pNew;\n  struct ExprList_item *pItem, *pOldItem;\n  int i;\n  Expr *pPriorSelectCol = 0;\n  assert( db!=0 );\n  if( p==0 ) return 0;\n  pNew = sqlite3DbMallocRawNN(db, sqlite3DbMallocSize(db, p));\n  if( pNew==0 ) return 0;\n  pNew->nExpr = p->nExpr;\n  pItem = pNew->a;\n  pOldItem = p->a;\n  for(i=0; i<p->nExpr; i++, pItem++, pOldItem++){\n    Expr *pOldExpr = pOldItem->pExpr;\n    Expr *pNewExpr;\n    pItem->pExpr = sqlite3ExprDup(db, pOldExpr, flags);\n    if( pOldExpr \n     && pOldExpr->op==TK_SELECT_COLUMN\n     && (pNewExpr = pItem->pExpr)!=0 \n    ){\n      assert( pNewExpr->iColumn==0 || i>0 );\n      if( pNewExpr->iColumn==0 ){\n        assert( pOldExpr->pLeft==pOldExpr->pRight );\n        pPriorSelectCol = pNewExpr->pLeft = pNewExpr->pRight;\n      }else{\n        assert( i>0 );\n        assert( pItem[-1].pExpr!=0 );\n        assert( pNewExpr->iColumn==pItem[-1].pExpr->iColumn+1 );\n        assert( pPriorSelectCol==pItem[-1].pExpr->pLeft );\n        pNewExpr->pLeft = pPriorSelectCol;\n      }\n    }\n    pItem->zName = sqlite3DbStrDup(db, pOldItem->zName);\n    pItem->zSpan = sqlite3DbStrDup(db, pOldItem->zSpan);\n    pItem->sortOrder = pOldItem->sortOrder;\n    pItem->done = 0;\n    pItem->bSpanIsTab = pOldItem->bSpanIsTab;\n    pItem->u = pOldItem->u;\n  }\n  return pNew;\n}\n\n/*\n** If cursors, triggers, views and subqueries are all omitted from\n** the build, then none of the following routines, except for \n** sqlite3SelectDup(), can be called. sqlite3SelectDup() is sometimes\n** called with a NULL argument.\n*/\n#if !defined(SQLITE_OMIT_VIEW) || !defined(SQLITE_OMIT_TRIGGER) \\\n || !defined(SQLITE_OMIT_SUBQUERY)\nSQLITE_PRIVATE SrcList *sqlite3SrcListDup(sqlite3 *db, SrcList *p, int flags){\n  SrcList *pNew;\n  int i;\n  int nByte;\n  assert( db!=0 );\n  if( p==0 ) return 0;\n  nByte = sizeof(*p) + (p->nSrc>0 ? sizeof(p->a[0]) * (p->nSrc-1) : 0);\n  pNew = sqlite3DbMallocRawNN(db, nByte );\n  if( pNew==0 ) return 0;\n  pNew->nSrc = pNew->nAlloc = p->nSrc;\n  for(i=0; i<p->nSrc; i++){\n    struct SrcList_item *pNewItem = &pNew->a[i];\n    struct SrcList_item *pOldItem = &p->a[i];\n    Table *pTab;\n    pNewItem->pSchema = pOldItem->pSchema;\n    pNewItem->zDatabase = sqlite3DbStrDup(db, pOldItem->zDatabase);\n    pNewItem->zName = sqlite3DbStrDup(db, pOldItem->zName);\n    pNewItem->zAlias = sqlite3DbStrDup(db, pOldItem->zAlias);\n    pNewItem->fg = pOldItem->fg;\n    pNewItem->iCursor = pOldItem->iCursor;\n    pNewItem->addrFillSub = pOldItem->addrFillSub;\n    pNewItem->regReturn = pOldItem->regReturn;\n    if( pNewItem->fg.isIndexedBy ){\n      pNewItem->u1.zIndexedBy = sqlite3DbStrDup(db, pOldItem->u1.zIndexedBy);\n    }\n    pNewItem->pIBIndex = pOldItem->pIBIndex;\n    if( pNewItem->fg.isTabFunc ){\n      pNewItem->u1.pFuncArg = \n          sqlite3ExprListDup(db, pOldItem->u1.pFuncArg, flags);\n    }\n    pTab = pNewItem->pTab = pOldItem->pTab;\n    if( pTab ){\n      pTab->nTabRef++;\n    }\n    pNewItem->pSelect = sqlite3SelectDup(db, pOldItem->pSelect, flags);\n    pNewItem->pOn = sqlite3ExprDup(db, pOldItem->pOn, flags);\n    pNewItem->pUsing = sqlite3IdListDup(db, pOldItem->pUsing);\n    pNewItem->colUsed = pOldItem->colUsed;\n  }\n  return pNew;\n}\nSQLITE_PRIVATE IdList *sqlite3IdListDup(sqlite3 *db, IdList *p){\n  IdList *pNew;\n  int i;\n  assert( db!=0 );\n  if( p==0 ) return 0;\n  pNew = sqlite3DbMallocRawNN(db, sizeof(*pNew) );\n  if( pNew==0 ) return 0;\n  pNew->nId = p->nId;\n  pNew->a = sqlite3DbMallocRawNN(db, p->nId*sizeof(p->a[0]) );\n  if( pNew->a==0 ){\n    sqlite3DbFreeNN(db, pNew);\n    return 0;\n  }\n  /* Note that because the size of the allocation for p->a[] is not\n  ** necessarily a power of two, sqlite3IdListAppend() may not be called\n  ** on the duplicate created by this function. */\n  for(i=0; i<p->nId; i++){\n    struct IdList_item *pNewItem = &pNew->a[i];\n    struct IdList_item *pOldItem = &p->a[i];\n    pNewItem->zName = sqlite3DbStrDup(db, pOldItem->zName);\n    pNewItem->idx = pOldItem->idx;\n  }\n  return pNew;\n}\nSQLITE_PRIVATE Select *sqlite3SelectDup(sqlite3 *db, Select *pDup, int flags){\n  Select *pRet = 0;\n  Select *pNext = 0;\n  Select **pp = &pRet;\n  Select *p;\n\n  assert( db!=0 );\n  for(p=pDup; p; p=p->pPrior){\n    Select *pNew = sqlite3DbMallocRawNN(db, sizeof(*p) );\n    if( pNew==0 ) break;\n    pNew->pEList = sqlite3ExprListDup(db, p->pEList, flags);\n    pNew->pSrc = sqlite3SrcListDup(db, p->pSrc, flags);\n    pNew->pWhere = sqlite3ExprDup(db, p->pWhere, flags);\n    pNew->pGroupBy = sqlite3ExprListDup(db, p->pGroupBy, flags);\n    pNew->pHaving = sqlite3ExprDup(db, p->pHaving, flags);\n    pNew->pOrderBy = sqlite3ExprListDup(db, p->pOrderBy, flags);\n    pNew->op = p->op;\n    pNew->pNext = pNext;\n    pNew->pPrior = 0;\n    pNew->pLimit = sqlite3ExprDup(db, p->pLimit, flags);\n    pNew->iLimit = 0;\n    pNew->iOffset = 0;\n    pNew->selFlags = p->selFlags & ~SF_UsesEphemeral;\n    pNew->addrOpenEphm[0] = -1;\n    pNew->addrOpenEphm[1] = -1;\n    pNew->nSelectRow = p->nSelectRow;\n    pNew->pWith = withDup(db, p->pWith);\n    sqlite3SelectSetName(pNew, p->zSelName);\n    *pp = pNew;\n    pp = &pNew->pPrior;\n    pNext = pNew;\n  }\n\n  return pRet;\n}\n#else\nSQLITE_PRIVATE Select *sqlite3SelectDup(sqlite3 *db, Select *p, int flags){\n  assert( p==0 );\n  return 0;\n}\n#endif\n\n\n/*\n** Add a new element to the end of an expression list.  If pList is\n** initially NULL, then create a new expression list.\n**\n** The pList argument must be either NULL or a pointer to an ExprList\n** obtained from a prior call to sqlite3ExprListAppend().  This routine\n** may not be used with an ExprList obtained from sqlite3ExprListDup().\n** Reason:  This routine assumes that the number of slots in pList->a[]\n** is a power of two.  That is true for sqlite3ExprListAppend() returns\n** but is not necessarily true from the return value of sqlite3ExprListDup().\n**\n** If a memory allocation error occurs, the entire list is freed and\n** NULL is returned.  If non-NULL is returned, then it is guaranteed\n** that the new entry was successfully appended.\n*/\nSQLITE_PRIVATE ExprList *sqlite3ExprListAppend(\n  Parse *pParse,          /* Parsing context */\n  ExprList *pList,        /* List to which to append. Might be NULL */\n  Expr *pExpr             /* Expression to be appended. Might be NULL */\n){\n  struct ExprList_item *pItem;\n  sqlite3 *db = pParse->db;\n  assert( db!=0 );\n  if( pList==0 ){\n    pList = sqlite3DbMallocRawNN(db, sizeof(ExprList) );\n    if( pList==0 ){\n      goto no_mem;\n    }\n    pList->nExpr = 0;\n  }else if( (pList->nExpr & (pList->nExpr-1))==0 ){\n    ExprList *pNew;\n    pNew = sqlite3DbRealloc(db, pList, \n             sizeof(*pList)+(2*pList->nExpr - 1)*sizeof(pList->a[0]));\n    if( pNew==0 ){\n      goto no_mem;\n    }\n    pList = pNew;\n  }\n  pItem = &pList->a[pList->nExpr++];\n  assert( offsetof(struct ExprList_item,zName)==sizeof(pItem->pExpr) );\n  assert( offsetof(struct ExprList_item,pExpr)==0 );\n  memset(&pItem->zName,0,sizeof(*pItem)-offsetof(struct ExprList_item,zName));\n  pItem->pExpr = pExpr;\n  return pList;\n\nno_mem:     \n  /* Avoid leaking memory if malloc has failed. */\n  sqlite3ExprDelete(db, pExpr);\n  sqlite3ExprListDelete(db, pList);\n  return 0;\n}\n\n/*\n** pColumns and pExpr form a vector assignment which is part of the SET\n** clause of an UPDATE statement.  Like this:\n**\n**        (a,b,c) = (expr1,expr2,expr3)\n** Or:    (a,b,c) = (SELECT x,y,z FROM ....)\n**\n** For each term of the vector assignment, append new entries to the\n** expression list pList.  In the case of a subquery on the RHS, append\n** TK_SELECT_COLUMN expressions.\n*/\nSQLITE_PRIVATE ExprList *sqlite3ExprListAppendVector(\n  Parse *pParse,         /* Parsing context */\n  ExprList *pList,       /* List to which to append. Might be NULL */\n  IdList *pColumns,      /* List of names of LHS of the assignment */\n  Expr *pExpr            /* Vector expression to be appended. Might be NULL */\n){\n  sqlite3 *db = pParse->db;\n  int n;\n  int i;\n  int iFirst = pList ? pList->nExpr : 0;\n  /* pColumns can only be NULL due to an OOM but an OOM will cause an\n  ** exit prior to this routine being invoked */\n  if( NEVER(pColumns==0) ) goto vector_append_error;\n  if( pExpr==0 ) goto vector_append_error;\n\n  /* If the RHS is a vector, then we can immediately check to see that \n  ** the size of the RHS and LHS match.  But if the RHS is a SELECT, \n  ** wildcards (\"*\") in the result set of the SELECT must be expanded before\n  ** we can do the size check, so defer the size check until code generation.\n  */\n  if( pExpr->op!=TK_SELECT && pColumns->nId!=(n=sqlite3ExprVectorSize(pExpr)) ){\n    sqlite3ErrorMsg(pParse, \"%d columns assigned %d values\",\n                    pColumns->nId, n);\n    goto vector_append_error;\n  }\n\n  for(i=0; i<pColumns->nId; i++){\n    Expr *pSubExpr = sqlite3ExprForVectorField(pParse, pExpr, i);\n    pList = sqlite3ExprListAppend(pParse, pList, pSubExpr);\n    if( pList ){\n      assert( pList->nExpr==iFirst+i+1 );\n      pList->a[pList->nExpr-1].zName = pColumns->a[i].zName;\n      pColumns->a[i].zName = 0;\n    }\n  }\n\n  if( !db->mallocFailed && pExpr->op==TK_SELECT && ALWAYS(pList!=0) ){\n    Expr *pFirst = pList->a[iFirst].pExpr;\n    assert( pFirst!=0 );\n    assert( pFirst->op==TK_SELECT_COLUMN );\n     \n    /* Store the SELECT statement in pRight so it will be deleted when\n    ** sqlite3ExprListDelete() is called */\n    pFirst->pRight = pExpr;\n    pExpr = 0;\n\n    /* Remember the size of the LHS in iTable so that we can check that\n    ** the RHS and LHS sizes match during code generation. */\n    pFirst->iTable = pColumns->nId;\n  }\n\nvector_append_error:\n  sqlite3ExprDelete(db, pExpr);\n  sqlite3IdListDelete(db, pColumns);\n  return pList;\n}\n\n/*\n** Set the sort order for the last element on the given ExprList.\n*/\nSQLITE_PRIVATE void sqlite3ExprListSetSortOrder(ExprList *p, int iSortOrder){\n  if( p==0 ) return;\n  assert( SQLITE_SO_UNDEFINED<0 && SQLITE_SO_ASC>=0 && SQLITE_SO_DESC>0 );\n  assert( p->nExpr>0 );\n  if( iSortOrder<0 ){\n    assert( p->a[p->nExpr-1].sortOrder==SQLITE_SO_ASC );\n    return;\n  }\n  p->a[p->nExpr-1].sortOrder = (u8)iSortOrder;\n}\n\n/*\n** Set the ExprList.a[].zName element of the most recently added item\n** on the expression list.\n**\n** pList might be NULL following an OOM error.  But pName should never be\n** NULL.  If a memory allocation fails, the pParse->db->mallocFailed flag\n** is set.\n*/\nSQLITE_PRIVATE void sqlite3ExprListSetName(\n  Parse *pParse,          /* Parsing context */\n  ExprList *pList,        /* List to which to add the span. */\n  Token *pName,           /* Name to be added */\n  int dequote             /* True to cause the name to be dequoted */\n){\n  assert( pList!=0 || pParse->db->mallocFailed!=0 );\n  if( pList ){\n    struct ExprList_item *pItem;\n    assert( pList->nExpr>0 );\n    pItem = &pList->a[pList->nExpr-1];\n    assert( pItem->zName==0 );\n    pItem->zName = sqlite3DbStrNDup(pParse->db, pName->z, pName->n);\n    if( dequote ) sqlite3Dequote(pItem->zName);\n  }\n}\n\n/*\n** Set the ExprList.a[].zSpan element of the most recently added item\n** on the expression list.\n**\n** pList might be NULL following an OOM error.  But pSpan should never be\n** NULL.  If a memory allocation fails, the pParse->db->mallocFailed flag\n** is set.\n*/\nSQLITE_PRIVATE void sqlite3ExprListSetSpan(\n  Parse *pParse,          /* Parsing context */\n  ExprList *pList,        /* List to which to add the span. */\n  const char *zStart,     /* Start of the span */\n  const char *zEnd        /* End of the span */\n){\n  sqlite3 *db = pParse->db;\n  assert( pList!=0 || db->mallocFailed!=0 );\n  if( pList ){\n    struct ExprList_item *pItem = &pList->a[pList->nExpr-1];\n    assert( pList->nExpr>0 );\n    sqlite3DbFree(db, pItem->zSpan);\n    pItem->zSpan = sqlite3DbSpanDup(db, zStart, zEnd);\n  }\n}\n\n/*\n** If the expression list pEList contains more than iLimit elements,\n** leave an error message in pParse.\n*/\nSQLITE_PRIVATE void sqlite3ExprListCheckLength(\n  Parse *pParse,\n  ExprList *pEList,\n  const char *zObject\n){\n  int mx = pParse->db->aLimit[SQLITE_LIMIT_COLUMN];\n  testcase( pEList && pEList->nExpr==mx );\n  testcase( pEList && pEList->nExpr==mx+1 );\n  if( pEList && pEList->nExpr>mx ){\n    sqlite3ErrorMsg(pParse, \"too many columns in %s\", zObject);\n  }\n}\n\n/*\n** Delete an entire expression list.\n*/\nstatic SQLITE_NOINLINE void exprListDeleteNN(sqlite3 *db, ExprList *pList){\n  int i = pList->nExpr;\n  struct ExprList_item *pItem =  pList->a;\n  assert( pList->nExpr>0 );\n  do{\n    sqlite3ExprDelete(db, pItem->pExpr);\n    sqlite3DbFree(db, pItem->zName);\n    sqlite3DbFree(db, pItem->zSpan);\n    pItem++;\n  }while( --i>0 );\n  sqlite3DbFreeNN(db, pList);\n}\nSQLITE_PRIVATE void sqlite3ExprListDelete(sqlite3 *db, ExprList *pList){\n  if( pList ) exprListDeleteNN(db, pList);\n}\n\n/*\n** Return the bitwise-OR of all Expr.flags fields in the given\n** ExprList.\n*/\nSQLITE_PRIVATE u32 sqlite3ExprListFlags(const ExprList *pList){\n  int i;\n  u32 m = 0;\n  assert( pList!=0 );\n  for(i=0; i<pList->nExpr; i++){\n     Expr *pExpr = pList->a[i].pExpr;\n     assert( pExpr!=0 );\n     m |= pExpr->flags;\n  }\n  return m;\n}\n\n/*\n** This is a SELECT-node callback for the expression walker that\n** always \"fails\".  By \"fail\" in this case, we mean set\n** pWalker->eCode to zero and abort.\n**\n** This callback is used by multiple expression walkers.\n*/\nSQLITE_PRIVATE int sqlite3SelectWalkFail(Walker *pWalker, Select *NotUsed){\n  UNUSED_PARAMETER(NotUsed);\n  pWalker->eCode = 0;\n  return WRC_Abort;\n}\n\n/*\n** If the input expression is an ID with the name \"true\" or \"false\"\n** then convert it into an TK_TRUEFALSE term.  Return non-zero if\n** the conversion happened, and zero if the expression is unaltered.\n*/\nSQLITE_PRIVATE int sqlite3ExprIdToTrueFalse(Expr *pExpr){\n  assert( pExpr->op==TK_ID || pExpr->op==TK_STRING );\n  if( sqlite3StrICmp(pExpr->u.zToken, \"true\")==0\n   || sqlite3StrICmp(pExpr->u.zToken, \"false\")==0\n  ){\n    pExpr->op = TK_TRUEFALSE;\n    return 1;\n  }\n  return 0;\n}\n\n/*\n** The argument must be a TK_TRUEFALSE Expr node.  Return 1 if it is TRUE\n** and 0 if it is FALSE.\n*/\nSQLITE_PRIVATE int sqlite3ExprTruthValue(const Expr *pExpr){\n  assert( pExpr->op==TK_TRUEFALSE );\n  assert( sqlite3StrICmp(pExpr->u.zToken,\"true\")==0\n       || sqlite3StrICmp(pExpr->u.zToken,\"false\")==0 );\n  return pExpr->u.zToken[4]==0;\n}\n\n\n/*\n** These routines are Walker callbacks used to check expressions to\n** see if they are \"constant\" for some definition of constant.  The\n** Walker.eCode value determines the type of \"constant\" we are looking\n** for.\n**\n** These callback routines are used to implement the following:\n**\n**     sqlite3ExprIsConstant()                  pWalker->eCode==1\n**     sqlite3ExprIsConstantNotJoin()           pWalker->eCode==2\n**     sqlite3ExprIsTableConstant()             pWalker->eCode==3\n**     sqlite3ExprIsConstantOrFunction()        pWalker->eCode==4 or 5\n**\n** In all cases, the callbacks set Walker.eCode=0 and abort if the expression\n** is found to not be a constant.\n**\n** The sqlite3ExprIsConstantOrFunction() is used for evaluating expressions\n** in a CREATE TABLE statement.  The Walker.eCode value is 5 when parsing\n** an existing schema and 4 when processing a new statement.  A bound\n** parameter raises an error for new statements, but is silently converted\n** to NULL for existing schemas.  This allows sqlite_master tables that \n** contain a bound parameter because they were generated by older versions\n** of SQLite to be parsed by newer versions of SQLite without raising a\n** malformed schema error.\n*/\nstatic int exprNodeIsConstant(Walker *pWalker, Expr *pExpr){\n\n  /* If pWalker->eCode is 2 then any term of the expression that comes from\n  ** the ON or USING clauses of a left join disqualifies the expression\n  ** from being considered constant. */\n  if( pWalker->eCode==2 && ExprHasProperty(pExpr, EP_FromJoin) ){\n    pWalker->eCode = 0;\n    return WRC_Abort;\n  }\n\n  switch( pExpr->op ){\n    /* Consider functions to be constant if all their arguments are constant\n    ** and either pWalker->eCode==4 or 5 or the function has the\n    ** SQLITE_FUNC_CONST flag. */\n    case TK_FUNCTION:\n      if( pWalker->eCode>=4 || ExprHasProperty(pExpr,EP_ConstFunc) ){\n        return WRC_Continue;\n      }else{\n        pWalker->eCode = 0;\n        return WRC_Abort;\n      }\n    case TK_ID:\n      /* Convert \"true\" or \"false\" in a DEFAULT clause into the\n      ** appropriate TK_TRUEFALSE operator */\n      if( sqlite3ExprIdToTrueFalse(pExpr) ){\n        return WRC_Prune;\n      }\n      /* Fall thru */\n    case TK_COLUMN:\n    case TK_AGG_FUNCTION:\n    case TK_AGG_COLUMN:\n      testcase( pExpr->op==TK_ID );\n      testcase( pExpr->op==TK_COLUMN );\n      testcase( pExpr->op==TK_AGG_FUNCTION );\n      testcase( pExpr->op==TK_AGG_COLUMN );\n      if( pWalker->eCode==3 && pExpr->iTable==pWalker->u.iCur ){\n        return WRC_Continue;\n      }\n      /* Fall through */\n    case TK_IF_NULL_ROW:\n      testcase( pExpr->op==TK_IF_NULL_ROW );\n      pWalker->eCode = 0;\n      return WRC_Abort;\n    case TK_VARIABLE:\n      if( pWalker->eCode==5 ){\n        /* Silently convert bound parameters that appear inside of CREATE\n        ** statements into a NULL when parsing the CREATE statement text out\n        ** of the sqlite_master table */\n        pExpr->op = TK_NULL;\n      }else if( pWalker->eCode==4 ){\n        /* A bound parameter in a CREATE statement that originates from\n        ** sqlite3_prepare() causes an error */\n        pWalker->eCode = 0;\n        return WRC_Abort;\n      }\n      /* Fall through */\n    default:\n      testcase( pExpr->op==TK_SELECT ); /* sqlite3SelectWalkFail will disallow */\n      testcase( pExpr->op==TK_EXISTS ); /* sqlite3SelectWalkFail will disallow */\n      return WRC_Continue;\n  }\n}\nstatic int exprIsConst(Expr *p, int initFlag, int iCur){\n  Walker w;\n  w.eCode = initFlag;\n  w.xExprCallback = exprNodeIsConstant;\n  w.xSelectCallback = sqlite3SelectWalkFail;\n#ifdef SQLITE_DEBUG\n  w.xSelectCallback2 = sqlite3SelectWalkAssert2;\n#endif\n  w.u.iCur = iCur;\n  sqlite3WalkExpr(&w, p);\n  return w.eCode;\n}\n\n/*\n** Walk an expression tree.  Return non-zero if the expression is constant\n** and 0 if it involves variables or function calls.\n**\n** For the purposes of this function, a double-quoted string (ex: \"abc\")\n** is considered a variable but a single-quoted string (ex: 'abc') is\n** a constant.\n*/\nSQLITE_PRIVATE int sqlite3ExprIsConstant(Expr *p){\n  return exprIsConst(p, 1, 0);\n}\n\n/*\n** Walk an expression tree.  Return non-zero if the expression is constant\n** that does no originate from the ON or USING clauses of a join.\n** Return 0 if it involves variables or function calls or terms from\n** an ON or USING clause.\n*/\nSQLITE_PRIVATE int sqlite3ExprIsConstantNotJoin(Expr *p){\n  return exprIsConst(p, 2, 0);\n}\n\n/*\n** Walk an expression tree.  Return non-zero if the expression is constant\n** for any single row of the table with cursor iCur.  In other words, the\n** expression must not refer to any non-deterministic function nor any\n** table other than iCur.\n*/\nSQLITE_PRIVATE int sqlite3ExprIsTableConstant(Expr *p, int iCur){\n  return exprIsConst(p, 3, iCur);\n}\n\n\n/*\n** sqlite3WalkExpr() callback used by sqlite3ExprIsConstantOrGroupBy().\n*/\nstatic int exprNodeIsConstantOrGroupBy(Walker *pWalker, Expr *pExpr){\n  ExprList *pGroupBy = pWalker->u.pGroupBy;\n  int i;\n\n  /* Check if pExpr is identical to any GROUP BY term. If so, consider\n  ** it constant.  */\n  for(i=0; i<pGroupBy->nExpr; i++){\n    Expr *p = pGroupBy->a[i].pExpr;\n    if( sqlite3ExprCompare(0, pExpr, p, -1)<2 ){\n      CollSeq *pColl = sqlite3ExprNNCollSeq(pWalker->pParse, p);\n      if( sqlite3_stricmp(\"BINARY\", pColl->zName)==0 ){\n        return WRC_Prune;\n      }\n    }\n  }\n\n  /* Check if pExpr is a sub-select. If so, consider it variable. */\n  if( ExprHasProperty(pExpr, EP_xIsSelect) ){\n    pWalker->eCode = 0;\n    return WRC_Abort;\n  }\n\n  return exprNodeIsConstant(pWalker, pExpr);\n}\n\n/*\n** Walk the expression tree passed as the first argument. Return non-zero\n** if the expression consists entirely of constants or copies of terms \n** in pGroupBy that sort with the BINARY collation sequence.\n**\n** This routine is used to determine if a term of the HAVING clause can\n** be promoted into the WHERE clause.  In order for such a promotion to work,\n** the value of the HAVING clause term must be the same for all members of\n** a \"group\".  The requirement that the GROUP BY term must be BINARY\n** assumes that no other collating sequence will have a finer-grained\n** grouping than binary.  In other words (A=B COLLATE binary) implies\n** A=B in every other collating sequence.  The requirement that the\n** GROUP BY be BINARY is stricter than necessary.  It would also work\n** to promote HAVING clauses that use the same alternative collating\n** sequence as the GROUP BY term, but that is much harder to check,\n** alternative collating sequences are uncommon, and this is only an\n** optimization, so we take the easy way out and simply require the\n** GROUP BY to use the BINARY collating sequence.\n*/\nSQLITE_PRIVATE int sqlite3ExprIsConstantOrGroupBy(Parse *pParse, Expr *p, ExprList *pGroupBy){\n  Walker w;\n  w.eCode = 1;\n  w.xExprCallback = exprNodeIsConstantOrGroupBy;\n  w.xSelectCallback = 0;\n  w.u.pGroupBy = pGroupBy;\n  w.pParse = pParse;\n  sqlite3WalkExpr(&w, p);\n  return w.eCode;\n}\n\n/*\n** Walk an expression tree.  Return non-zero if the expression is constant\n** or a function call with constant arguments.  Return and 0 if there\n** are any variables.\n**\n** For the purposes of this function, a double-quoted string (ex: \"abc\")\n** is considered a variable but a single-quoted string (ex: 'abc') is\n** a constant.\n*/\nSQLITE_PRIVATE int sqlite3ExprIsConstantOrFunction(Expr *p, u8 isInit){\n  assert( isInit==0 || isInit==1 );\n  return exprIsConst(p, 4+isInit, 0);\n}\n\n#ifdef SQLITE_ENABLE_CURSOR_HINTS\n/*\n** Walk an expression tree.  Return 1 if the expression contains a\n** subquery of some kind.  Return 0 if there are no subqueries.\n*/\nSQLITE_PRIVATE int sqlite3ExprContainsSubquery(Expr *p){\n  Walker w;\n  w.eCode = 1;\n  w.xExprCallback = sqlite3ExprWalkNoop;\n  w.xSelectCallback = sqlite3SelectWalkFail;\n#ifdef SQLITE_DEBUG\n  w.xSelectCallback2 = sqlite3SelectWalkAssert2;\n#endif\n  sqlite3WalkExpr(&w, p);\n  return w.eCode==0;\n}\n#endif\n\n/*\n** If the expression p codes a constant integer that is small enough\n** to fit in a 32-bit integer, return 1 and put the value of the integer\n** in *pValue.  If the expression is not an integer or if it is too big\n** to fit in a signed 32-bit integer, return 0 and leave *pValue unchanged.\n*/\nSQLITE_PRIVATE int sqlite3ExprIsInteger(Expr *p, int *pValue){\n  int rc = 0;\n  if( p==0 ) return 0;  /* Can only happen following on OOM */\n\n  /* If an expression is an integer literal that fits in a signed 32-bit\n  ** integer, then the EP_IntValue flag will have already been set */\n  assert( p->op!=TK_INTEGER || (p->flags & EP_IntValue)!=0\n           || sqlite3GetInt32(p->u.zToken, &rc)==0 );\n\n  if( p->flags & EP_IntValue ){\n    *pValue = p->u.iValue;\n    return 1;\n  }\n  switch( p->op ){\n    case TK_UPLUS: {\n      rc = sqlite3ExprIsInteger(p->pLeft, pValue);\n      break;\n    }\n    case TK_UMINUS: {\n      int v;\n      if( sqlite3ExprIsInteger(p->pLeft, &v) ){\n        assert( v!=(-2147483647-1) );\n        *pValue = -v;\n        rc = 1;\n      }\n      break;\n    }\n    default: break;\n  }\n  return rc;\n}\n\n/*\n** Return FALSE if there is no chance that the expression can be NULL.\n**\n** If the expression might be NULL or if the expression is too complex\n** to tell return TRUE.  \n**\n** This routine is used as an optimization, to skip OP_IsNull opcodes\n** when we know that a value cannot be NULL.  Hence, a false positive\n** (returning TRUE when in fact the expression can never be NULL) might\n** be a small performance hit but is otherwise harmless.  On the other\n** hand, a false negative (returning FALSE when the result could be NULL)\n** will likely result in an incorrect answer.  So when in doubt, return\n** TRUE.\n*/\nSQLITE_PRIVATE int sqlite3ExprCanBeNull(const Expr *p){\n  u8 op;\n  while( p->op==TK_UPLUS || p->op==TK_UMINUS ){ p = p->pLeft; }\n  op = p->op;\n  if( op==TK_REGISTER ) op = p->op2;\n  switch( op ){\n    case TK_INTEGER:\n    case TK_STRING:\n    case TK_FLOAT:\n    case TK_BLOB:\n      return 0;\n    case TK_COLUMN:\n      return ExprHasProperty(p, EP_CanBeNull) ||\n             p->pTab==0 ||  /* Reference to column of index on expression */\n             (p->iColumn>=0 && p->pTab->aCol[p->iColumn].notNull==0);\n    default:\n      return 1;\n  }\n}\n\n/*\n** Return TRUE if the given expression is a constant which would be\n** unchanged by OP_Affinity with the affinity given in the second\n** argument.\n**\n** This routine is used to determine if the OP_Affinity operation\n** can be omitted.  When in doubt return FALSE.  A false negative\n** is harmless.  A false positive, however, can result in the wrong\n** answer.\n*/\nSQLITE_PRIVATE int sqlite3ExprNeedsNoAffinityChange(const Expr *p, char aff){\n  u8 op;\n  if( aff==SQLITE_AFF_BLOB ) return 1;\n  while( p->op==TK_UPLUS || p->op==TK_UMINUS ){ p = p->pLeft; }\n  op = p->op;\n  if( op==TK_REGISTER ) op = p->op2;\n  switch( op ){\n    case TK_INTEGER: {\n      return aff==SQLITE_AFF_INTEGER || aff==SQLITE_AFF_NUMERIC;\n    }\n    case TK_FLOAT: {\n      return aff==SQLITE_AFF_REAL || aff==SQLITE_AFF_NUMERIC;\n    }\n    case TK_STRING: {\n      return aff==SQLITE_AFF_TEXT;\n    }\n    case TK_BLOB: {\n      return 1;\n    }\n    case TK_COLUMN: {\n      assert( p->iTable>=0 );  /* p cannot be part of a CHECK constraint */\n      return p->iColumn<0\n          && (aff==SQLITE_AFF_INTEGER || aff==SQLITE_AFF_NUMERIC);\n    }\n    default: {\n      return 0;\n    }\n  }\n}\n\n/*\n** Return TRUE if the given string is a row-id column name.\n*/\nSQLITE_PRIVATE int sqlite3IsRowid(const char *z){\n  if( sqlite3StrICmp(z, \"_ROWID_\")==0 ) return 1;\n  if( sqlite3StrICmp(z, \"ROWID\")==0 ) return 1;\n  if( sqlite3StrICmp(z, \"OID\")==0 ) return 1;\n  return 0;\n}\n\n/*\n** pX is the RHS of an IN operator.  If pX is a SELECT statement \n** that can be simplified to a direct table access, then return\n** a pointer to the SELECT statement.  If pX is not a SELECT statement,\n** or if the SELECT statement needs to be manifested into a transient\n** table, then return NULL.\n*/\n#ifndef SQLITE_OMIT_SUBQUERY\nstatic Select *isCandidateForInOpt(Expr *pX){\n  Select *p;\n  SrcList *pSrc;\n  ExprList *pEList;\n  Table *pTab;\n  int i;\n  if( !ExprHasProperty(pX, EP_xIsSelect) ) return 0;  /* Not a subquery */\n  if( ExprHasProperty(pX, EP_VarSelect)  ) return 0;  /* Correlated subq */\n  p = pX->x.pSelect;\n  if( p->pPrior ) return 0;              /* Not a compound SELECT */\n  if( p->selFlags & (SF_Distinct|SF_Aggregate) ){\n    testcase( (p->selFlags & (SF_Distinct|SF_Aggregate))==SF_Distinct );\n    testcase( (p->selFlags & (SF_Distinct|SF_Aggregate))==SF_Aggregate );\n    return 0; /* No DISTINCT keyword and no aggregate functions */\n  }\n  assert( p->pGroupBy==0 );              /* Has no GROUP BY clause */\n  if( p->pLimit ) return 0;              /* Has no LIMIT clause */\n  if( p->pWhere ) return 0;              /* Has no WHERE clause */\n  pSrc = p->pSrc;\n  assert( pSrc!=0 );\n  if( pSrc->nSrc!=1 ) return 0;          /* Single term in FROM clause */\n  if( pSrc->a[0].pSelect ) return 0;     /* FROM is not a subquery or view */\n  pTab = pSrc->a[0].pTab;\n  assert( pTab!=0 );\n  assert( pTab->pSelect==0 );            /* FROM clause is not a view */\n  if( IsVirtual(pTab) ) return 0;        /* FROM clause not a virtual table */\n  pEList = p->pEList;\n  assert( pEList!=0 );\n  /* All SELECT results must be columns. */\n  for(i=0; i<pEList->nExpr; i++){\n    Expr *pRes = pEList->a[i].pExpr;\n    if( pRes->op!=TK_COLUMN ) return 0;\n    assert( pRes->iTable==pSrc->a[0].iCursor );  /* Not a correlated subquery */\n  }\n  return p;\n}\n#endif /* SQLITE_OMIT_SUBQUERY */\n\n#ifndef SQLITE_OMIT_SUBQUERY\n/*\n** Generate code that checks the left-most column of index table iCur to see if\n** it contains any NULL entries.  Cause the register at regHasNull to be set\n** to a non-NULL value if iCur contains no NULLs.  Cause register regHasNull\n** to be set to NULL if iCur contains one or more NULL values.\n*/\nstatic void sqlite3SetHasNullFlag(Vdbe *v, int iCur, int regHasNull){\n  int addr1;\n  sqlite3VdbeAddOp2(v, OP_Integer, 0, regHasNull);\n  addr1 = sqlite3VdbeAddOp1(v, OP_Rewind, iCur); VdbeCoverage(v);\n  sqlite3VdbeAddOp3(v, OP_Column, iCur, 0, regHasNull);\n  sqlite3VdbeChangeP5(v, OPFLAG_TYPEOFARG);\n  VdbeComment((v, \"first_entry_in(%d)\", iCur));\n  sqlite3VdbeJumpHere(v, addr1);\n}\n#endif\n\n\n#ifndef SQLITE_OMIT_SUBQUERY\n/*\n** The argument is an IN operator with a list (not a subquery) on the \n** right-hand side.  Return TRUE if that list is constant.\n*/\nstatic int sqlite3InRhsIsConstant(Expr *pIn){\n  Expr *pLHS;\n  int res;\n  assert( !ExprHasProperty(pIn, EP_xIsSelect) );\n  pLHS = pIn->pLeft;\n  pIn->pLeft = 0;\n  res = sqlite3ExprIsConstant(pIn);\n  pIn->pLeft = pLHS;\n  return res;\n}\n#endif\n\n/*\n** This function is used by the implementation of the IN (...) operator.\n** The pX parameter is the expression on the RHS of the IN operator, which\n** might be either a list of expressions or a subquery.\n**\n** The job of this routine is to find or create a b-tree object that can\n** be used either to test for membership in the RHS set or to iterate through\n** all members of the RHS set, skipping duplicates.\n**\n** A cursor is opened on the b-tree object that is the RHS of the IN operator\n** and pX->iTable is set to the index of that cursor.\n**\n** The returned value of this function indicates the b-tree type, as follows:\n**\n**   IN_INDEX_ROWID      - The cursor was opened on a database table.\n**   IN_INDEX_INDEX_ASC  - The cursor was opened on an ascending index.\n**   IN_INDEX_INDEX_DESC - The cursor was opened on a descending index.\n**   IN_INDEX_EPH        - The cursor was opened on a specially created and\n**                         populated epheremal table.\n**   IN_INDEX_NOOP       - No cursor was allocated.  The IN operator must be\n**                         implemented as a sequence of comparisons.\n**\n** An existing b-tree might be used if the RHS expression pX is a simple\n** subquery such as:\n**\n**     SELECT <column1>, <column2>... FROM <table>\n**\n** If the RHS of the IN operator is a list or a more complex subquery, then\n** an ephemeral table might need to be generated from the RHS and then\n** pX->iTable made to point to the ephemeral table instead of an\n** existing table.\n**\n** The inFlags parameter must contain, at a minimum, one of the bits\n** IN_INDEX_MEMBERSHIP or IN_INDEX_LOOP but not both.  If inFlags contains\n** IN_INDEX_MEMBERSHIP, then the generated table will be used for a fast\n** membership test.  When the IN_INDEX_LOOP bit is set, the IN index will\n** be used to loop over all values of the RHS of the IN operator.\n**\n** When IN_INDEX_LOOP is used (and the b-tree will be used to iterate\n** through the set members) then the b-tree must not contain duplicates.\n** An epheremal table will be created unless the selected columns are guaranteed\n** to be unique - either because it is an INTEGER PRIMARY KEY or due to\n** a UNIQUE constraint or index.\n**\n** When IN_INDEX_MEMBERSHIP is used (and the b-tree will be used \n** for fast set membership tests) then an epheremal table must \n** be used unless <columns> is a single INTEGER PRIMARY KEY column or an \n** index can be found with the specified <columns> as its left-most.\n**\n** If the IN_INDEX_NOOP_OK and IN_INDEX_MEMBERSHIP are both set and\n** if the RHS of the IN operator is a list (not a subquery) then this\n** routine might decide that creating an ephemeral b-tree for membership\n** testing is too expensive and return IN_INDEX_NOOP.  In that case, the\n** calling routine should implement the IN operator using a sequence\n** of Eq or Ne comparison operations.\n**\n** When the b-tree is being used for membership tests, the calling function\n** might need to know whether or not the RHS side of the IN operator\n** contains a NULL.  If prRhsHasNull is not a NULL pointer and \n** if there is any chance that the (...) might contain a NULL value at\n** runtime, then a register is allocated and the register number written\n** to *prRhsHasNull. If there is no chance that the (...) contains a\n** NULL value, then *prRhsHasNull is left unchanged.\n**\n** If a register is allocated and its location stored in *prRhsHasNull, then\n** the value in that register will be NULL if the b-tree contains one or more\n** NULL values, and it will be some non-NULL value if the b-tree contains no\n** NULL values.\n**\n** If the aiMap parameter is not NULL, it must point to an array containing\n** one element for each column returned by the SELECT statement on the RHS\n** of the IN(...) operator. The i'th entry of the array is populated with the\n** offset of the index column that matches the i'th column returned by the\n** SELECT. For example, if the expression and selected index are:\n**\n**   (?,?,?) IN (SELECT a, b, c FROM t1)\n**   CREATE INDEX i1 ON t1(b, c, a);\n**\n** then aiMap[] is populated with {2, 0, 1}.\n*/\n#ifndef SQLITE_OMIT_SUBQUERY\nSQLITE_PRIVATE int sqlite3FindInIndex(\n  Parse *pParse,             /* Parsing context */\n  Expr *pX,                  /* The right-hand side (RHS) of the IN operator */\n  u32 inFlags,               /* IN_INDEX_LOOP, _MEMBERSHIP, and/or _NOOP_OK */\n  int *prRhsHasNull,         /* Register holding NULL status.  See notes */\n  int *aiMap                 /* Mapping from Index fields to RHS fields */\n){\n  Select *p;                            /* SELECT to the right of IN operator */\n  int eType = 0;                        /* Type of RHS table. IN_INDEX_* */\n  int iTab = pParse->nTab++;            /* Cursor of the RHS table */\n  int mustBeUnique;                     /* True if RHS must be unique */\n  Vdbe *v = sqlite3GetVdbe(pParse);     /* Virtual machine being coded */\n\n  assert( pX->op==TK_IN );\n  mustBeUnique = (inFlags & IN_INDEX_LOOP)!=0;\n\n  /* If the RHS of this IN(...) operator is a SELECT, and if it matters \n  ** whether or not the SELECT result contains NULL values, check whether\n  ** or not NULL is actually possible (it may not be, for example, due \n  ** to NOT NULL constraints in the schema). If no NULL values are possible,\n  ** set prRhsHasNull to 0 before continuing.  */\n  if( prRhsHasNull && (pX->flags & EP_xIsSelect) ){\n    int i;\n    ExprList *pEList = pX->x.pSelect->pEList;\n    for(i=0; i<pEList->nExpr; i++){\n      if( sqlite3ExprCanBeNull(pEList->a[i].pExpr) ) break;\n    }\n    if( i==pEList->nExpr ){\n      prRhsHasNull = 0;\n    }\n  }\n\n  /* Check to see if an existing table or index can be used to\n  ** satisfy the query.  This is preferable to generating a new \n  ** ephemeral table.  */\n  if( pParse->nErr==0 && (p = isCandidateForInOpt(pX))!=0 ){\n    sqlite3 *db = pParse->db;              /* Database connection */\n    Table *pTab;                           /* Table <table>. */\n    i16 iDb;                               /* Database idx for pTab */\n    ExprList *pEList = p->pEList;\n    int nExpr = pEList->nExpr;\n\n    assert( p->pEList!=0 );             /* Because of isCandidateForInOpt(p) */\n    assert( p->pEList->a[0].pExpr!=0 ); /* Because of isCandidateForInOpt(p) */\n    assert( p->pSrc!=0 );               /* Because of isCandidateForInOpt(p) */\n    pTab = p->pSrc->a[0].pTab;\n\n    /* Code an OP_Transaction and OP_TableLock for <table>. */\n    iDb = sqlite3SchemaToIndex(db, pTab->pSchema);\n    sqlite3CodeVerifySchema(pParse, iDb);\n    sqlite3TableLock(pParse, iDb, pTab->tnum, 0, pTab->zName);\n\n    assert(v);  /* sqlite3GetVdbe() has always been previously called */\n    if( nExpr==1 && pEList->a[0].pExpr->iColumn<0 ){\n      /* The \"x IN (SELECT rowid FROM table)\" case */\n      int iAddr = sqlite3VdbeAddOp0(v, OP_Once);\n      VdbeCoverage(v);\n\n      sqlite3OpenTable(pParse, iTab, iDb, pTab, OP_OpenRead);\n      eType = IN_INDEX_ROWID;\n\n      sqlite3VdbeJumpHere(v, iAddr);\n    }else{\n      Index *pIdx;                         /* Iterator variable */\n      int affinity_ok = 1;\n      int i;\n\n      /* Check that the affinity that will be used to perform each \n      ** comparison is the same as the affinity of each column in table\n      ** on the RHS of the IN operator.  If it not, it is not possible to\n      ** use any index of the RHS table.  */\n      for(i=0; i<nExpr && affinity_ok; i++){\n        Expr *pLhs = sqlite3VectorFieldSubexpr(pX->pLeft, i);\n        int iCol = pEList->a[i].pExpr->iColumn;\n        char idxaff = sqlite3TableColumnAffinity(pTab,iCol); /* RHS table */\n        char cmpaff = sqlite3CompareAffinity(pLhs, idxaff);\n        testcase( cmpaff==SQLITE_AFF_BLOB );\n        testcase( cmpaff==SQLITE_AFF_TEXT );\n        switch( cmpaff ){\n          case SQLITE_AFF_BLOB:\n            break;\n          case SQLITE_AFF_TEXT:\n            /* sqlite3CompareAffinity() only returns TEXT if one side or the\n            ** other has no affinity and the other side is TEXT.  Hence,\n            ** the only way for cmpaff to be TEXT is for idxaff to be TEXT\n            ** and for the term on the LHS of the IN to have no affinity. */\n            assert( idxaff==SQLITE_AFF_TEXT );\n            break;\n          default:\n            affinity_ok = sqlite3IsNumericAffinity(idxaff);\n        }\n      }\n\n      if( affinity_ok ){\n        /* Search for an existing index that will work for this IN operator */\n        for(pIdx=pTab->pIndex; pIdx && eType==0; pIdx=pIdx->pNext){\n          Bitmask colUsed;      /* Columns of the index used */\n          Bitmask mCol;         /* Mask for the current column */\n          if( pIdx->nColumn<nExpr ) continue;\n          /* Maximum nColumn is BMS-2, not BMS-1, so that we can compute\n          ** BITMASK(nExpr) without overflowing */\n          testcase( pIdx->nColumn==BMS-2 );\n          testcase( pIdx->nColumn==BMS-1 );\n          if( pIdx->nColumn>=BMS-1 ) continue;\n          if( mustBeUnique ){\n            if( pIdx->nKeyCol>nExpr\n             ||(pIdx->nColumn>nExpr && !IsUniqueIndex(pIdx))\n            ){\n              continue;  /* This index is not unique over the IN RHS columns */\n            }\n          }\n  \n          colUsed = 0;   /* Columns of index used so far */\n          for(i=0; i<nExpr; i++){\n            Expr *pLhs = sqlite3VectorFieldSubexpr(pX->pLeft, i);\n            Expr *pRhs = pEList->a[i].pExpr;\n            CollSeq *pReq = sqlite3BinaryCompareCollSeq(pParse, pLhs, pRhs);\n            int j;\n  \n            assert( pReq!=0 || pRhs->iColumn==XN_ROWID || pParse->nErr );\n            for(j=0; j<nExpr; j++){\n              if( pIdx->aiColumn[j]!=pRhs->iColumn ) continue;\n              assert( pIdx->azColl[j] );\n              if( pReq!=0 && sqlite3StrICmp(pReq->zName, pIdx->azColl[j])!=0 ){\n                continue;\n              }\n              break;\n            }\n            if( j==nExpr ) break;\n            mCol = MASKBIT(j);\n            if( mCol & colUsed ) break; /* Each column used only once */\n            colUsed |= mCol;\n            if( aiMap ) aiMap[i] = j;\n          }\n  \n          assert( i==nExpr || colUsed!=(MASKBIT(nExpr)-1) );\n          if( colUsed==(MASKBIT(nExpr)-1) ){\n            /* If we reach this point, that means the index pIdx is usable */\n            int iAddr = sqlite3VdbeAddOp0(v, OP_Once); VdbeCoverage(v);\n#ifndef SQLITE_OMIT_EXPLAIN\n            sqlite3VdbeAddOp4(v, OP_Explain, 0, 0, 0,\n              sqlite3MPrintf(db, \"USING INDEX %s FOR IN-OPERATOR\",pIdx->zName),\n              P4_DYNAMIC);\n#endif\n            sqlite3VdbeAddOp3(v, OP_OpenRead, iTab, pIdx->tnum, iDb);\n            sqlite3VdbeSetP4KeyInfo(pParse, pIdx);\n            VdbeComment((v, \"%s\", pIdx->zName));\n            assert( IN_INDEX_INDEX_DESC == IN_INDEX_INDEX_ASC+1 );\n            eType = IN_INDEX_INDEX_ASC + pIdx->aSortOrder[0];\n  \n            if( prRhsHasNull ){\n#ifdef SQLITE_ENABLE_COLUMN_USED_MASK\n              i64 mask = (1<<nExpr)-1;\n              sqlite3VdbeAddOp4Dup8(v, OP_ColumnsUsed, \n                  iTab, 0, 0, (u8*)&mask, P4_INT64);\n#endif\n              *prRhsHasNull = ++pParse->nMem;\n              if( nExpr==1 ){\n                sqlite3SetHasNullFlag(v, iTab, *prRhsHasNull);\n              }\n            }\n            sqlite3VdbeJumpHere(v, iAddr);\n          }\n        } /* End loop over indexes */\n      } /* End if( affinity_ok ) */\n    } /* End if not an rowid index */\n  } /* End attempt to optimize using an index */\n\n  /* If no preexisting index is available for the IN clause\n  ** and IN_INDEX_NOOP is an allowed reply\n  ** and the RHS of the IN operator is a list, not a subquery\n  ** and the RHS is not constant or has two or fewer terms,\n  ** then it is not worth creating an ephemeral table to evaluate\n  ** the IN operator so return IN_INDEX_NOOP.\n  */\n  if( eType==0\n   && (inFlags & IN_INDEX_NOOP_OK)\n   && !ExprHasProperty(pX, EP_xIsSelect)\n   && (!sqlite3InRhsIsConstant(pX) || pX->x.pList->nExpr<=2)\n  ){\n    eType = IN_INDEX_NOOP;\n  }\n\n  if( eType==0 ){\n    /* Could not find an existing table or index to use as the RHS b-tree.\n    ** We will have to generate an ephemeral table to do the job.\n    */\n    u32 savedNQueryLoop = pParse->nQueryLoop;\n    int rMayHaveNull = 0;\n    eType = IN_INDEX_EPH;\n    if( inFlags & IN_INDEX_LOOP ){\n      pParse->nQueryLoop = 0;\n      if( pX->pLeft->iColumn<0 && !ExprHasProperty(pX, EP_xIsSelect) ){\n        eType = IN_INDEX_ROWID;\n      }\n    }else if( prRhsHasNull ){\n      *prRhsHasNull = rMayHaveNull = ++pParse->nMem;\n    }\n    sqlite3CodeSubselect(pParse, pX, rMayHaveNull, eType==IN_INDEX_ROWID);\n    pParse->nQueryLoop = savedNQueryLoop;\n  }else{\n    pX->iTable = iTab;\n  }\n\n  if( aiMap && eType!=IN_INDEX_INDEX_ASC && eType!=IN_INDEX_INDEX_DESC ){\n    int i, n;\n    n = sqlite3ExprVectorSize(pX->pLeft);\n    for(i=0; i<n; i++) aiMap[i] = i;\n  }\n  return eType;\n}\n#endif\n\n#ifndef SQLITE_OMIT_SUBQUERY\n/*\n** Argument pExpr is an (?, ?...) IN(...) expression. This \n** function allocates and returns a nul-terminated string containing \n** the affinities to be used for each column of the comparison.\n**\n** It is the responsibility of the caller to ensure that the returned\n** string is eventually freed using sqlite3DbFree().\n*/\nstatic char *exprINAffinity(Parse *pParse, Expr *pExpr){\n  Expr *pLeft = pExpr->pLeft;\n  int nVal = sqlite3ExprVectorSize(pLeft);\n  Select *pSelect = (pExpr->flags & EP_xIsSelect) ? pExpr->x.pSelect : 0;\n  char *zRet;\n\n  assert( pExpr->op==TK_IN );\n  zRet = sqlite3DbMallocRaw(pParse->db, nVal+1);\n  if( zRet ){\n    int i;\n    for(i=0; i<nVal; i++){\n      Expr *pA = sqlite3VectorFieldSubexpr(pLeft, i);\n      char a = sqlite3ExprAffinity(pA);\n      if( pSelect ){\n        zRet[i] = sqlite3CompareAffinity(pSelect->pEList->a[i].pExpr, a);\n      }else{\n        zRet[i] = a;\n      }\n    }\n    zRet[nVal] = '\\0';\n  }\n  return zRet;\n}\n#endif\n\n#ifndef SQLITE_OMIT_SUBQUERY\n/*\n** Load the Parse object passed as the first argument with an error \n** message of the form:\n**\n**   \"sub-select returns N columns - expected M\"\n*/   \nSQLITE_PRIVATE void sqlite3SubselectError(Parse *pParse, int nActual, int nExpect){\n  const char *zFmt = \"sub-select returns %d columns - expected %d\";\n  sqlite3ErrorMsg(pParse, zFmt, nActual, nExpect);\n}\n#endif\n\n/*\n** Expression pExpr is a vector that has been used in a context where\n** it is not permitted. If pExpr is a sub-select vector, this routine \n** loads the Parse object with a message of the form:\n**\n**   \"sub-select returns N columns - expected 1\"\n**\n** Or, if it is a regular scalar vector:\n**\n**   \"row value misused\"\n*/   \nSQLITE_PRIVATE void sqlite3VectorErrorMsg(Parse *pParse, Expr *pExpr){\n#ifndef SQLITE_OMIT_SUBQUERY\n  if( pExpr->flags & EP_xIsSelect ){\n    sqlite3SubselectError(pParse, pExpr->x.pSelect->pEList->nExpr, 1);\n  }else\n#endif\n  {\n    sqlite3ErrorMsg(pParse, \"row value misused\");\n  }\n}\n\n/*\n** Generate code for scalar subqueries used as a subquery expression, EXISTS,\n** or IN operators.  Examples:\n**\n**     (SELECT a FROM b)          -- subquery\n**     EXISTS (SELECT a FROM b)   -- EXISTS subquery\n**     x IN (4,5,11)              -- IN operator with list on right-hand side\n**     x IN (SELECT a FROM b)     -- IN operator with subquery on the right\n**\n** The pExpr parameter describes the expression that contains the IN\n** operator or subquery.\n**\n** If parameter isRowid is non-zero, then expression pExpr is guaranteed\n** to be of the form \"<rowid> IN (?, ?, ?)\", where <rowid> is a reference\n** to some integer key column of a table B-Tree. In this case, use an\n** intkey B-Tree to store the set of IN(...) values instead of the usual\n** (slower) variable length keys B-Tree.\n**\n** If rMayHaveNull is non-zero, that means that the operation is an IN\n** (not a SELECT or EXISTS) and that the RHS might contains NULLs.\n** All this routine does is initialize the register given by rMayHaveNull\n** to NULL.  Calling routines will take care of changing this register\n** value to non-NULL if the RHS is NULL-free.\n**\n** For a SELECT or EXISTS operator, return the register that holds the\n** result.  For a multi-column SELECT, the result is stored in a contiguous\n** array of registers and the return value is the register of the left-most\n** result column.  Return 0 for IN operators or if an error occurs.\n*/\n#ifndef SQLITE_OMIT_SUBQUERY\nSQLITE_PRIVATE int sqlite3CodeSubselect(\n  Parse *pParse,          /* Parsing context */\n  Expr *pExpr,            /* The IN, SELECT, or EXISTS operator */\n  int rHasNullFlag,       /* Register that records whether NULLs exist in RHS */\n  int isRowid             /* If true, LHS of IN operator is a rowid */\n){\n  int jmpIfDynamic = -1;                      /* One-time test address */\n  int rReg = 0;                           /* Register storing resulting */\n  Vdbe *v = sqlite3GetVdbe(pParse);\n  if( NEVER(v==0) ) return 0;\n  sqlite3ExprCachePush(pParse);\n\n  /* The evaluation of the IN/EXISTS/SELECT must be repeated every time it\n  ** is encountered if any of the following is true:\n  **\n  **    *  The right-hand side is a correlated subquery\n  **    *  The right-hand side is an expression list containing variables\n  **    *  We are inside a trigger\n  **\n  ** If all of the above are false, then we can run this code just once\n  ** save the results, and reuse the same result on subsequent invocations.\n  */\n  if( !ExprHasProperty(pExpr, EP_VarSelect) ){\n    jmpIfDynamic = sqlite3VdbeAddOp0(v, OP_Once); VdbeCoverage(v);\n  }\n\n#ifndef SQLITE_OMIT_EXPLAIN\n  if( pParse->explain==2 ){\n    char *zMsg = sqlite3MPrintf(pParse->db, \"EXECUTE %s%s SUBQUERY %d\",\n        jmpIfDynamic>=0?\"\":\"CORRELATED \",\n        pExpr->op==TK_IN?\"LIST\":\"SCALAR\",\n        pParse->iNextSelectId\n    );\n    sqlite3VdbeAddOp4(v, OP_Explain, pParse->iSelectId, 0, 0, zMsg, P4_DYNAMIC);\n  }\n#endif\n\n  switch( pExpr->op ){\n    case TK_IN: {\n      int addr;                   /* Address of OP_OpenEphemeral instruction */\n      Expr *pLeft = pExpr->pLeft; /* the LHS of the IN operator */\n      KeyInfo *pKeyInfo = 0;      /* Key information */\n      int nVal;                   /* Size of vector pLeft */\n      \n      nVal = sqlite3ExprVectorSize(pLeft);\n      assert( !isRowid || nVal==1 );\n\n      /* Whether this is an 'x IN(SELECT...)' or an 'x IN(<exprlist>)'\n      ** expression it is handled the same way.  An ephemeral table is \n      ** filled with index keys representing the results from the \n      ** SELECT or the <exprlist>.\n      **\n      ** If the 'x' expression is a column value, or the SELECT...\n      ** statement returns a column value, then the affinity of that\n      ** column is used to build the index keys. If both 'x' and the\n      ** SELECT... statement are columns, then numeric affinity is used\n      ** if either column has NUMERIC or INTEGER affinity. If neither\n      ** 'x' nor the SELECT... statement are columns, then numeric affinity\n      ** is used.\n      */\n      pExpr->iTable = pParse->nTab++;\n      addr = sqlite3VdbeAddOp2(v, OP_OpenEphemeral, \n          pExpr->iTable, (isRowid?0:nVal));\n      pKeyInfo = isRowid ? 0 : sqlite3KeyInfoAlloc(pParse->db, nVal, 1);\n\n      if( ExprHasProperty(pExpr, EP_xIsSelect) ){\n        /* Case 1:     expr IN (SELECT ...)\n        **\n        ** Generate code to write the results of the select into the temporary\n        ** table allocated and opened above.\n        */\n        Select *pSelect = pExpr->x.pSelect;\n        ExprList *pEList = pSelect->pEList;\n\n        assert( !isRowid );\n        /* If the LHS and RHS of the IN operator do not match, that\n        ** error will have been caught long before we reach this point. */\n        if( ALWAYS(pEList->nExpr==nVal) ){\n          SelectDest dest;\n          int i;\n          sqlite3SelectDestInit(&dest, SRT_Set, pExpr->iTable);\n          dest.zAffSdst = exprINAffinity(pParse, pExpr);\n          pSelect->iLimit = 0;\n          testcase( pSelect->selFlags & SF_Distinct );\n          testcase( pKeyInfo==0 ); /* Caused by OOM in sqlite3KeyInfoAlloc() */\n          if( sqlite3Select(pParse, pSelect, &dest) ){\n            sqlite3DbFree(pParse->db, dest.zAffSdst);\n            sqlite3KeyInfoUnref(pKeyInfo);\n            return 0;\n          }\n          sqlite3DbFree(pParse->db, dest.zAffSdst);\n          assert( pKeyInfo!=0 ); /* OOM will cause exit after sqlite3Select() */\n          assert( pEList!=0 );\n          assert( pEList->nExpr>0 );\n          assert( sqlite3KeyInfoIsWriteable(pKeyInfo) );\n          for(i=0; i<nVal; i++){\n            Expr *p = sqlite3VectorFieldSubexpr(pLeft, i);\n            pKeyInfo->aColl[i] = sqlite3BinaryCompareCollSeq(\n                pParse, p, pEList->a[i].pExpr\n            );\n          }\n        }\n      }else if( ALWAYS(pExpr->x.pList!=0) ){\n        /* Case 2:     expr IN (exprlist)\n        **\n        ** For each expression, build an index key from the evaluation and\n        ** store it in the temporary table. If <expr> is a column, then use\n        ** that columns affinity when building index keys. If <expr> is not\n        ** a column, use numeric affinity.\n        */\n        char affinity;            /* Affinity of the LHS of the IN */\n        int i;\n        ExprList *pList = pExpr->x.pList;\n        struct ExprList_item *pItem;\n        int r1, r2, r3;\n\n        affinity = sqlite3ExprAffinity(pLeft);\n        if( !affinity ){\n          affinity = SQLITE_AFF_BLOB;\n        }\n        if( pKeyInfo ){\n          assert( sqlite3KeyInfoIsWriteable(pKeyInfo) );\n          pKeyInfo->aColl[0] = sqlite3ExprCollSeq(pParse, pExpr->pLeft);\n        }\n\n        /* Loop through each expression in <exprlist>. */\n        r1 = sqlite3GetTempReg(pParse);\n        r2 = sqlite3GetTempReg(pParse);\n        if( isRowid ) sqlite3VdbeAddOp4(v, OP_Blob, 0, r2, 0, \"\", P4_STATIC);\n        for(i=pList->nExpr, pItem=pList->a; i>0; i--, pItem++){\n          Expr *pE2 = pItem->pExpr;\n          int iValToIns;\n\n          /* If the expression is not constant then we will need to\n          ** disable the test that was generated above that makes sure\n          ** this code only executes once.  Because for a non-constant\n          ** expression we need to rerun this code each time.\n          */\n          if( jmpIfDynamic>=0 && !sqlite3ExprIsConstant(pE2) ){\n            sqlite3VdbeChangeToNoop(v, jmpIfDynamic);\n            jmpIfDynamic = -1;\n          }\n\n          /* Evaluate the expression and insert it into the temp table */\n          if( isRowid && sqlite3ExprIsInteger(pE2, &iValToIns) ){\n            sqlite3VdbeAddOp3(v, OP_InsertInt, pExpr->iTable, r2, iValToIns);\n          }else{\n            r3 = sqlite3ExprCodeTarget(pParse, pE2, r1);\n            if( isRowid ){\n              sqlite3VdbeAddOp2(v, OP_MustBeInt, r3,\n                                sqlite3VdbeCurrentAddr(v)+2);\n              VdbeCoverage(v);\n              sqlite3VdbeAddOp3(v, OP_Insert, pExpr->iTable, r2, r3);\n            }else{\n              sqlite3VdbeAddOp4(v, OP_MakeRecord, r3, 1, r2, &affinity, 1);\n              sqlite3ExprCacheAffinityChange(pParse, r3, 1);\n              sqlite3VdbeAddOp4Int(v, OP_IdxInsert, pExpr->iTable, r2, r3, 1);\n            }\n          }\n        }\n        sqlite3ReleaseTempReg(pParse, r1);\n        sqlite3ReleaseTempReg(pParse, r2);\n      }\n      if( pKeyInfo ){\n        sqlite3VdbeChangeP4(v, addr, (void *)pKeyInfo, P4_KEYINFO);\n      }\n      break;\n    }\n\n    case TK_EXISTS:\n    case TK_SELECT:\n    default: {\n      /* Case 3:    (SELECT ... FROM ...)\n      **     or:    EXISTS(SELECT ... FROM ...)\n      **\n      ** For a SELECT, generate code to put the values for all columns of\n      ** the first row into an array of registers and return the index of\n      ** the first register.\n      **\n      ** If this is an EXISTS, write an integer 0 (not exists) or 1 (exists)\n      ** into a register and return that register number.\n      **\n      ** In both cases, the query is augmented with \"LIMIT 1\".  Any \n      ** preexisting limit is discarded in place of the new LIMIT 1.\n      */\n      Select *pSel;                         /* SELECT statement to encode */\n      SelectDest dest;                      /* How to deal with SELECT result */\n      int nReg;                             /* Registers to allocate */\n      Expr *pLimit;                         /* New limit expression */\n\n      testcase( pExpr->op==TK_EXISTS );\n      testcase( pExpr->op==TK_SELECT );\n      assert( pExpr->op==TK_EXISTS || pExpr->op==TK_SELECT );\n      assert( ExprHasProperty(pExpr, EP_xIsSelect) );\n\n      pSel = pExpr->x.pSelect;\n      nReg = pExpr->op==TK_SELECT ? pSel->pEList->nExpr : 1;\n      sqlite3SelectDestInit(&dest, 0, pParse->nMem+1);\n      pParse->nMem += nReg;\n      if( pExpr->op==TK_SELECT ){\n        dest.eDest = SRT_Mem;\n        dest.iSdst = dest.iSDParm;\n        dest.nSdst = nReg;\n        sqlite3VdbeAddOp3(v, OP_Null, 0, dest.iSDParm, dest.iSDParm+nReg-1);\n        VdbeComment((v, \"Init subquery result\"));\n      }else{\n        dest.eDest = SRT_Exists;\n        sqlite3VdbeAddOp2(v, OP_Integer, 0, dest.iSDParm);\n        VdbeComment((v, \"Init EXISTS result\"));\n      }\n      pLimit = sqlite3ExprAlloc(pParse->db, TK_INTEGER,&sqlite3IntTokens[1], 0);\n      if( pSel->pLimit ){\n        sqlite3ExprDelete(pParse->db, pSel->pLimit->pLeft);\n        pSel->pLimit->pLeft = pLimit;\n      }else{\n        pSel->pLimit = sqlite3PExpr(pParse, TK_LIMIT, pLimit, 0);\n      }\n      pSel->iLimit = 0;\n      if( sqlite3Select(pParse, pSel, &dest) ){\n        return 0;\n      }\n      rReg = dest.iSDParm;\n      ExprSetVVAProperty(pExpr, EP_NoReduce);\n      break;\n    }\n  }\n\n  if( rHasNullFlag ){\n    sqlite3SetHasNullFlag(v, pExpr->iTable, rHasNullFlag);\n  }\n\n  if( jmpIfDynamic>=0 ){\n    sqlite3VdbeJumpHere(v, jmpIfDynamic);\n  }\n  sqlite3ExprCachePop(pParse);\n\n  return rReg;\n}\n#endif /* SQLITE_OMIT_SUBQUERY */\n\n#ifndef SQLITE_OMIT_SUBQUERY\n/*\n** Expr pIn is an IN(...) expression. This function checks that the \n** sub-select on the RHS of the IN() operator has the same number of \n** columns as the vector on the LHS. Or, if the RHS of the IN() is not \n** a sub-query, that the LHS is a vector of size 1.\n*/\nSQLITE_PRIVATE int sqlite3ExprCheckIN(Parse *pParse, Expr *pIn){\n  int nVector = sqlite3ExprVectorSize(pIn->pLeft);\n  if( (pIn->flags & EP_xIsSelect) ){\n    if( nVector!=pIn->x.pSelect->pEList->nExpr ){\n      sqlite3SubselectError(pParse, pIn->x.pSelect->pEList->nExpr, nVector);\n      return 1;\n    }\n  }else if( nVector!=1 ){\n    sqlite3VectorErrorMsg(pParse, pIn->pLeft);\n    return 1;\n  }\n  return 0;\n}\n#endif\n\n#ifndef SQLITE_OMIT_SUBQUERY\n/*\n** Generate code for an IN expression.\n**\n**      x IN (SELECT ...)\n**      x IN (value, value, ...)\n**\n** The left-hand side (LHS) is a scalar or vector expression.  The \n** right-hand side (RHS) is an array of zero or more scalar values, or a\n** subquery.  If the RHS is a subquery, the number of result columns must\n** match the number of columns in the vector on the LHS.  If the RHS is\n** a list of values, the LHS must be a scalar. \n**\n** The IN operator is true if the LHS value is contained within the RHS.\n** The result is false if the LHS is definitely not in the RHS.  The \n** result is NULL if the presence of the LHS in the RHS cannot be \n** determined due to NULLs.\n**\n** This routine generates code that jumps to destIfFalse if the LHS is not \n** contained within the RHS.  If due to NULLs we cannot determine if the LHS\n** is contained in the RHS then jump to destIfNull.  If the LHS is contained\n** within the RHS then fall through.\n**\n** See the separate in-operator.md documentation file in the canonical\n** SQLite source tree for additional information.\n*/\nstatic void sqlite3ExprCodeIN(\n  Parse *pParse,        /* Parsing and code generating context */\n  Expr *pExpr,          /* The IN expression */\n  int destIfFalse,      /* Jump here if LHS is not contained in the RHS */\n  int destIfNull        /* Jump here if the results are unknown due to NULLs */\n){\n  int rRhsHasNull = 0;  /* Register that is true if RHS contains NULL values */\n  int eType;            /* Type of the RHS */\n  int rLhs;             /* Register(s) holding the LHS values */\n  int rLhsOrig;         /* LHS values prior to reordering by aiMap[] */\n  Vdbe *v;              /* Statement under construction */\n  int *aiMap = 0;       /* Map from vector field to index column */\n  char *zAff = 0;       /* Affinity string for comparisons */\n  int nVector;          /* Size of vectors for this IN operator */\n  int iDummy;           /* Dummy parameter to exprCodeVector() */\n  Expr *pLeft;          /* The LHS of the IN operator */\n  int i;                /* loop counter */\n  int destStep2;        /* Where to jump when NULLs seen in step 2 */\n  int destStep6 = 0;    /* Start of code for Step 6 */\n  int addrTruthOp;      /* Address of opcode that determines the IN is true */\n  int destNotNull;      /* Jump here if a comparison is not true in step 6 */\n  int addrTop;          /* Top of the step-6 loop */ \n\n  pLeft = pExpr->pLeft;\n  if( sqlite3ExprCheckIN(pParse, pExpr) ) return;\n  zAff = exprINAffinity(pParse, pExpr);\n  nVector = sqlite3ExprVectorSize(pExpr->pLeft);\n  aiMap = (int*)sqlite3DbMallocZero(\n      pParse->db, nVector*(sizeof(int) + sizeof(char)) + 1\n  );\n  if( pParse->db->mallocFailed ) goto sqlite3ExprCodeIN_oom_error;\n\n  /* Attempt to compute the RHS. After this step, if anything other than\n  ** IN_INDEX_NOOP is returned, the table opened ith cursor pExpr->iTable \n  ** contains the values that make up the RHS. If IN_INDEX_NOOP is returned,\n  ** the RHS has not yet been coded.  */\n  v = pParse->pVdbe;\n  assert( v!=0 );       /* OOM detected prior to this routine */\n  VdbeNoopComment((v, \"begin IN expr\"));\n  eType = sqlite3FindInIndex(pParse, pExpr,\n                             IN_INDEX_MEMBERSHIP | IN_INDEX_NOOP_OK,\n                             destIfFalse==destIfNull ? 0 : &rRhsHasNull, aiMap);\n\n  assert( pParse->nErr || nVector==1 || eType==IN_INDEX_EPH\n       || eType==IN_INDEX_INDEX_ASC || eType==IN_INDEX_INDEX_DESC \n  );\n#ifdef SQLITE_DEBUG\n  /* Confirm that aiMap[] contains nVector integer values between 0 and\n  ** nVector-1. */\n  for(i=0; i<nVector; i++){\n    int j, cnt;\n    for(cnt=j=0; j<nVector; j++) if( aiMap[j]==i ) cnt++;\n    assert( cnt==1 );\n  }\n#endif\n\n  /* Code the LHS, the <expr> from \"<expr> IN (...)\". If the LHS is a \n  ** vector, then it is stored in an array of nVector registers starting \n  ** at r1.\n  **\n  ** sqlite3FindInIndex() might have reordered the fields of the LHS vector\n  ** so that the fields are in the same order as an existing index.   The\n  ** aiMap[] array contains a mapping from the original LHS field order to\n  ** the field order that matches the RHS index.\n  */\n  sqlite3ExprCachePush(pParse);\n  rLhsOrig = exprCodeVector(pParse, pLeft, &iDummy);\n  for(i=0; i<nVector && aiMap[i]==i; i++){} /* Are LHS fields reordered? */\n  if( i==nVector ){\n    /* LHS fields are not reordered */\n    rLhs = rLhsOrig;\n  }else{\n    /* Need to reorder the LHS fields according to aiMap */\n    rLhs = sqlite3GetTempRange(pParse, nVector);\n    for(i=0; i<nVector; i++){\n      sqlite3VdbeAddOp3(v, OP_Copy, rLhsOrig+i, rLhs+aiMap[i], 0);\n    }\n  }\n\n  /* If sqlite3FindInIndex() did not find or create an index that is\n  ** suitable for evaluating the IN operator, then evaluate using a\n  ** sequence of comparisons.\n  **\n  ** This is step (1) in the in-operator.md optimized algorithm.\n  */\n  if( eType==IN_INDEX_NOOP ){\n    ExprList *pList = pExpr->x.pList;\n    CollSeq *pColl = sqlite3ExprCollSeq(pParse, pExpr->pLeft);\n    int labelOk = sqlite3VdbeMakeLabel(v);\n    int r2, regToFree;\n    int regCkNull = 0;\n    int ii;\n    assert( !ExprHasProperty(pExpr, EP_xIsSelect) );\n    if( destIfNull!=destIfFalse ){\n      regCkNull = sqlite3GetTempReg(pParse);\n      sqlite3VdbeAddOp3(v, OP_BitAnd, rLhs, rLhs, regCkNull);\n    }\n    for(ii=0; ii<pList->nExpr; ii++){\n      r2 = sqlite3ExprCodeTemp(pParse, pList->a[ii].pExpr, &regToFree);\n      if( regCkNull && sqlite3ExprCanBeNull(pList->a[ii].pExpr) ){\n        sqlite3VdbeAddOp3(v, OP_BitAnd, regCkNull, r2, regCkNull);\n      }\n      if( ii<pList->nExpr-1 || destIfNull!=destIfFalse ){\n        sqlite3VdbeAddOp4(v, OP_Eq, rLhs, labelOk, r2,\n                          (void*)pColl, P4_COLLSEQ);\n        VdbeCoverageIf(v, ii<pList->nExpr-1);\n        VdbeCoverageIf(v, ii==pList->nExpr-1);\n        sqlite3VdbeChangeP5(v, zAff[0]);\n      }else{\n        assert( destIfNull==destIfFalse );\n        sqlite3VdbeAddOp4(v, OP_Ne, rLhs, destIfFalse, r2,\n                          (void*)pColl, P4_COLLSEQ); VdbeCoverage(v);\n        sqlite3VdbeChangeP5(v, zAff[0] | SQLITE_JUMPIFNULL);\n      }\n      sqlite3ReleaseTempReg(pParse, regToFree);\n    }\n    if( regCkNull ){\n      sqlite3VdbeAddOp2(v, OP_IsNull, regCkNull, destIfNull); VdbeCoverage(v);\n      sqlite3VdbeGoto(v, destIfFalse);\n    }\n    sqlite3VdbeResolveLabel(v, labelOk);\n    sqlite3ReleaseTempReg(pParse, regCkNull);\n    goto sqlite3ExprCodeIN_finished;\n  }\n\n  /* Step 2: Check to see if the LHS contains any NULL columns.  If the\n  ** LHS does contain NULLs then the result must be either FALSE or NULL.\n  ** We will then skip the binary search of the RHS.\n  */\n  if( destIfNull==destIfFalse ){\n    destStep2 = destIfFalse;\n  }else{\n    destStep2 = destStep6 = sqlite3VdbeMakeLabel(v);\n  }\n  for(i=0; i<nVector; i++){\n    Expr *p = sqlite3VectorFieldSubexpr(pExpr->pLeft, i);\n    if( sqlite3ExprCanBeNull(p) ){\n      sqlite3VdbeAddOp2(v, OP_IsNull, rLhs+i, destStep2);\n      VdbeCoverage(v);\n    }\n  }\n\n  /* Step 3.  The LHS is now known to be non-NULL.  Do the binary search\n  ** of the RHS using the LHS as a probe.  If found, the result is\n  ** true.\n  */\n  if( eType==IN_INDEX_ROWID ){\n    /* In this case, the RHS is the ROWID of table b-tree and so we also\n    ** know that the RHS is non-NULL.  Hence, we combine steps 3 and 4\n    ** into a single opcode. */\n    sqlite3VdbeAddOp3(v, OP_SeekRowid, pExpr->iTable, destIfFalse, rLhs);\n    VdbeCoverage(v);\n    addrTruthOp = sqlite3VdbeAddOp0(v, OP_Goto);  /* Return True */\n  }else{\n    sqlite3VdbeAddOp4(v, OP_Affinity, rLhs, nVector, 0, zAff, nVector);\n    if( destIfFalse==destIfNull ){\n      /* Combine Step 3 and Step 5 into a single opcode */\n      sqlite3VdbeAddOp4Int(v, OP_NotFound, pExpr->iTable, destIfFalse,\n                           rLhs, nVector); VdbeCoverage(v);\n      goto sqlite3ExprCodeIN_finished;\n    }\n    /* Ordinary Step 3, for the case where FALSE and NULL are distinct */\n    addrTruthOp = sqlite3VdbeAddOp4Int(v, OP_Found, pExpr->iTable, 0,\n                                      rLhs, nVector); VdbeCoverage(v);\n  }\n\n  /* Step 4.  If the RHS is known to be non-NULL and we did not find\n  ** an match on the search above, then the result must be FALSE.\n  */\n  if( rRhsHasNull && nVector==1 ){\n    sqlite3VdbeAddOp2(v, OP_NotNull, rRhsHasNull, destIfFalse);\n    VdbeCoverage(v);\n  }\n\n  /* Step 5.  If we do not care about the difference between NULL and\n  ** FALSE, then just return false. \n  */\n  if( destIfFalse==destIfNull ) sqlite3VdbeGoto(v, destIfFalse);\n\n  /* Step 6: Loop through rows of the RHS.  Compare each row to the LHS.\n  ** If any comparison is NULL, then the result is NULL.  If all\n  ** comparisons are FALSE then the final result is FALSE.\n  **\n  ** For a scalar LHS, it is sufficient to check just the first row\n  ** of the RHS.\n  */\n  if( destStep6 ) sqlite3VdbeResolveLabel(v, destStep6);\n  addrTop = sqlite3VdbeAddOp2(v, OP_Rewind, pExpr->iTable, destIfFalse);\n  VdbeCoverage(v);\n  if( nVector>1 ){\n    destNotNull = sqlite3VdbeMakeLabel(v);\n  }else{\n    /* For nVector==1, combine steps 6 and 7 by immediately returning\n    ** FALSE if the first comparison is not NULL */\n    destNotNull = destIfFalse;\n  }\n  for(i=0; i<nVector; i++){\n    Expr *p;\n    CollSeq *pColl;\n    int r3 = sqlite3GetTempReg(pParse);\n    p = sqlite3VectorFieldSubexpr(pLeft, i);\n    pColl = sqlite3ExprCollSeq(pParse, p);\n    sqlite3VdbeAddOp3(v, OP_Column, pExpr->iTable, i, r3);\n    sqlite3VdbeAddOp4(v, OP_Ne, rLhs+i, destNotNull, r3,\n                      (void*)pColl, P4_COLLSEQ);\n    VdbeCoverage(v);\n    sqlite3ReleaseTempReg(pParse, r3);\n  }\n  sqlite3VdbeAddOp2(v, OP_Goto, 0, destIfNull);\n  if( nVector>1 ){\n    sqlite3VdbeResolveLabel(v, destNotNull);\n    sqlite3VdbeAddOp2(v, OP_Next, pExpr->iTable, addrTop+1);\n    VdbeCoverage(v);\n\n    /* Step 7:  If we reach this point, we know that the result must\n    ** be false. */\n    sqlite3VdbeAddOp2(v, OP_Goto, 0, destIfFalse);\n  }\n\n  /* Jumps here in order to return true. */\n  sqlite3VdbeJumpHere(v, addrTruthOp);\n\nsqlite3ExprCodeIN_finished:\n  if( rLhs!=rLhsOrig ) sqlite3ReleaseTempReg(pParse, rLhs);\n  sqlite3ExprCachePop(pParse);\n  VdbeComment((v, \"end IN expr\"));\nsqlite3ExprCodeIN_oom_error:\n  sqlite3DbFree(pParse->db, aiMap);\n  sqlite3DbFree(pParse->db, zAff);\n}\n#endif /* SQLITE_OMIT_SUBQUERY */\n\n#ifndef SQLITE_OMIT_FLOATING_POINT\n/*\n** Generate an instruction that will put the floating point\n** value described by z[0..n-1] into register iMem.\n**\n** The z[] string will probably not be zero-terminated.  But the \n** z[n] character is guaranteed to be something that does not look\n** like the continuation of the number.\n*/\nstatic void codeReal(Vdbe *v, const char *z, int negateFlag, int iMem){\n  if( ALWAYS(z!=0) ){\n    double value;\n    sqlite3AtoF(z, &value, sqlite3Strlen30(z), SQLITE_UTF8);\n    assert( !sqlite3IsNaN(value) ); /* The new AtoF never returns NaN */\n    if( negateFlag ) value = -value;\n    sqlite3VdbeAddOp4Dup8(v, OP_Real, 0, iMem, 0, (u8*)&value, P4_REAL);\n  }\n}\n#endif\n\n\n/*\n** Generate an instruction that will put the integer describe by\n** text z[0..n-1] into register iMem.\n**\n** Expr.u.zToken is always UTF8 and zero-terminated.\n*/\nstatic void codeInteger(Parse *pParse, Expr *pExpr, int negFlag, int iMem){\n  Vdbe *v = pParse->pVdbe;\n  if( pExpr->flags & EP_IntValue ){\n    int i = pExpr->u.iValue;\n    assert( i>=0 );\n    if( negFlag ) i = -i;\n    sqlite3VdbeAddOp2(v, OP_Integer, i, iMem);\n  }else{\n    int c;\n    i64 value;\n    const char *z = pExpr->u.zToken;\n    assert( z!=0 );\n    c = sqlite3DecOrHexToI64(z, &value);\n    if( (c==3 && !negFlag) || (c==2) || (negFlag && value==SMALLEST_INT64)){\n#ifdef SQLITE_OMIT_FLOATING_POINT\n      sqlite3ErrorMsg(pParse, \"oversized integer: %s%s\", negFlag ? \"-\" : \"\", z);\n#else\n#ifndef SQLITE_OMIT_HEX_INTEGER\n      if( sqlite3_strnicmp(z,\"0x\",2)==0 ){\n        sqlite3ErrorMsg(pParse, \"hex literal too big: %s%s\", negFlag?\"-\":\"\",z);\n      }else\n#endif\n      {\n        codeReal(v, z, negFlag, iMem);\n      }\n#endif\n    }else{\n      if( negFlag ){ value = c==3 ? SMALLEST_INT64 : -value; }\n      sqlite3VdbeAddOp4Dup8(v, OP_Int64, 0, iMem, 0, (u8*)&value, P4_INT64);\n    }\n  }\n}\n\n/*\n** Erase column-cache entry number i\n*/\nstatic void cacheEntryClear(Parse *pParse, int i){\n  if( pParse->aColCache[i].tempReg ){\n    if( pParse->nTempReg<ArraySize(pParse->aTempReg) ){\n      pParse->aTempReg[pParse->nTempReg++] = pParse->aColCache[i].iReg;\n    }\n  }\n  pParse->nColCache--;\n  if( i<pParse->nColCache ){\n    pParse->aColCache[i] = pParse->aColCache[pParse->nColCache];\n  }\n}\n\n\n/*\n** Record in the column cache that a particular column from a\n** particular table is stored in a particular register.\n*/\nSQLITE_PRIVATE void sqlite3ExprCacheStore(Parse *pParse, int iTab, int iCol, int iReg){\n  int i;\n  int minLru;\n  int idxLru;\n  struct yColCache *p;\n\n  /* Unless an error has occurred, register numbers are always positive. */\n  assert( iReg>0 || pParse->nErr || pParse->db->mallocFailed );\n  assert( iCol>=-1 && iCol<32768 );  /* Finite column numbers */\n\n  /* The SQLITE_ColumnCache flag disables the column cache.  This is used\n  ** for testing only - to verify that SQLite always gets the same answer\n  ** with and without the column cache.\n  */\n  if( OptimizationDisabled(pParse->db, SQLITE_ColumnCache) ) return;\n\n  /* First replace any existing entry.\n  **\n  ** Actually, the way the column cache is currently used, we are guaranteed\n  ** that the object will never already be in cache.  Verify this guarantee.\n  */\n#ifndef NDEBUG\n  for(i=0, p=pParse->aColCache; i<pParse->nColCache; i++, p++){\n    assert( p->iTable!=iTab || p->iColumn!=iCol );\n  }\n#endif\n\n  /* If the cache is already full, delete the least recently used entry */\n  if( pParse->nColCache>=SQLITE_N_COLCACHE ){\n    minLru = 0x7fffffff;\n    idxLru = -1;\n    for(i=0, p=pParse->aColCache; i<SQLITE_N_COLCACHE; i++, p++){\n      if( p->lru<minLru ){\n        idxLru = i;\n        minLru = p->lru;\n      }\n    }\n    p = &pParse->aColCache[idxLru];\n  }else{\n    p = &pParse->aColCache[pParse->nColCache++];\n  }\n\n  /* Add the new entry to the end of the cache */\n  p->iLevel = pParse->iCacheLevel;\n  p->iTable = iTab;\n  p->iColumn = iCol;\n  p->iReg = iReg;\n  p->tempReg = 0;\n  p->lru = pParse->iCacheCnt++;\n}\n\n/*\n** Indicate that registers between iReg..iReg+nReg-1 are being overwritten.\n** Purge the range of registers from the column cache.\n*/\nSQLITE_PRIVATE void sqlite3ExprCacheRemove(Parse *pParse, int iReg, int nReg){\n  int i = 0;\n  while( i<pParse->nColCache ){\n    struct yColCache *p = &pParse->aColCache[i];\n    if( p->iReg >= iReg && p->iReg < iReg+nReg ){\n      cacheEntryClear(pParse, i);\n    }else{\n      i++;\n    }\n  }\n}\n\n/*\n** Remember the current column cache context.  Any new entries added\n** added to the column cache after this call are removed when the\n** corresponding pop occurs.\n*/\nSQLITE_PRIVATE void sqlite3ExprCachePush(Parse *pParse){\n  pParse->iCacheLevel++;\n#ifdef SQLITE_DEBUG\n  if( pParse->db->flags & SQLITE_VdbeAddopTrace ){\n    printf(\"PUSH to %d\\n\", pParse->iCacheLevel);\n  }\n#endif\n}\n\n/*\n** Remove from the column cache any entries that were added since the\n** the previous sqlite3ExprCachePush operation.  In other words, restore\n** the cache to the state it was in prior the most recent Push.\n*/\nSQLITE_PRIVATE void sqlite3ExprCachePop(Parse *pParse){\n  int i = 0;\n  assert( pParse->iCacheLevel>=1 );\n  pParse->iCacheLevel--;\n#ifdef SQLITE_DEBUG\n  if( pParse->db->flags & SQLITE_VdbeAddopTrace ){\n    printf(\"POP  to %d\\n\", pParse->iCacheLevel);\n  }\n#endif\n  while( i<pParse->nColCache ){\n    if( pParse->aColCache[i].iLevel>pParse->iCacheLevel ){\n      cacheEntryClear(pParse, i);\n    }else{\n      i++;\n    }\n  }\n}\n\n/*\n** When a cached column is reused, make sure that its register is\n** no longer available as a temp register.  ticket #3879:  that same\n** register might be in the cache in multiple places, so be sure to\n** get them all.\n*/\nstatic void sqlite3ExprCachePinRegister(Parse *pParse, int iReg){\n  int i;\n  struct yColCache *p;\n  for(i=0, p=pParse->aColCache; i<pParse->nColCache; i++, p++){\n    if( p->iReg==iReg ){\n      p->tempReg = 0;\n    }\n  }\n}\n\n/* Generate code that will load into register regOut a value that is\n** appropriate for the iIdxCol-th column of index pIdx.\n*/\nSQLITE_PRIVATE void sqlite3ExprCodeLoadIndexColumn(\n  Parse *pParse,  /* The parsing context */\n  Index *pIdx,    /* The index whose column is to be loaded */\n  int iTabCur,    /* Cursor pointing to a table row */\n  int iIdxCol,    /* The column of the index to be loaded */\n  int regOut      /* Store the index column value in this register */\n){\n  i16 iTabCol = pIdx->aiColumn[iIdxCol];\n  if( iTabCol==XN_EXPR ){\n    assert( pIdx->aColExpr );\n    assert( pIdx->aColExpr->nExpr>iIdxCol );\n    pParse->iSelfTab = iTabCur + 1;\n    sqlite3ExprCodeCopy(pParse, pIdx->aColExpr->a[iIdxCol].pExpr, regOut);\n    pParse->iSelfTab = 0;\n  }else{\n    sqlite3ExprCodeGetColumnOfTable(pParse->pVdbe, pIdx->pTable, iTabCur,\n                                    iTabCol, regOut);\n  }\n}\n\n/*\n** Generate code to extract the value of the iCol-th column of a table.\n*/\nSQLITE_PRIVATE void sqlite3ExprCodeGetColumnOfTable(\n  Vdbe *v,        /* The VDBE under construction */\n  Table *pTab,    /* The table containing the value */\n  int iTabCur,    /* The table cursor.  Or the PK cursor for WITHOUT ROWID */\n  int iCol,       /* Index of the column to extract */\n  int regOut      /* Extract the value into this register */\n){\n  if( pTab==0 ){\n    sqlite3VdbeAddOp3(v, OP_Column, iTabCur, iCol, regOut);\n    return;\n  }\n  if( iCol<0 || iCol==pTab->iPKey ){\n    sqlite3VdbeAddOp2(v, OP_Rowid, iTabCur, regOut);\n  }else{\n    int op = IsVirtual(pTab) ? OP_VColumn : OP_Column;\n    int x = iCol;\n    if( !HasRowid(pTab) && !IsVirtual(pTab) ){\n      x = sqlite3ColumnOfIndex(sqlite3PrimaryKeyIndex(pTab), iCol);\n    }\n    sqlite3VdbeAddOp3(v, op, iTabCur, x, regOut);\n  }\n  if( iCol>=0 ){\n    sqlite3ColumnDefault(v, pTab, iCol, regOut);\n  }\n}\n\n/*\n** Generate code that will extract the iColumn-th column from\n** table pTab and store the column value in a register. \n**\n** An effort is made to store the column value in register iReg.  This\n** is not garanteeed for GetColumn() - the result can be stored in\n** any register.  But the result is guaranteed to land in register iReg\n** for GetColumnToReg().\n**\n** There must be an open cursor to pTab in iTable when this routine\n** is called.  If iColumn<0 then code is generated that extracts the rowid.\n*/\nSQLITE_PRIVATE int sqlite3ExprCodeGetColumn(\n  Parse *pParse,   /* Parsing and code generating context */\n  Table *pTab,     /* Description of the table we are reading from */\n  int iColumn,     /* Index of the table column */\n  int iTable,      /* The cursor pointing to the table */\n  int iReg,        /* Store results here */\n  u8 p5            /* P5 value for OP_Column + FLAGS */\n){\n  Vdbe *v = pParse->pVdbe;\n  int i;\n  struct yColCache *p;\n\n  for(i=0, p=pParse->aColCache; i<pParse->nColCache; i++, p++){\n    if( p->iTable==iTable && p->iColumn==iColumn ){\n      p->lru = pParse->iCacheCnt++;\n      sqlite3ExprCachePinRegister(pParse, p->iReg);\n      return p->iReg;\n    }\n  }  \n  assert( v!=0 );\n  sqlite3ExprCodeGetColumnOfTable(v, pTab, iTable, iColumn, iReg);\n  if( p5 ){\n    sqlite3VdbeChangeP5(v, p5);\n  }else{   \n    sqlite3ExprCacheStore(pParse, iTable, iColumn, iReg);\n  }\n  return iReg;\n}\nSQLITE_PRIVATE void sqlite3ExprCodeGetColumnToReg(\n  Parse *pParse,   /* Parsing and code generating context */\n  Table *pTab,     /* Description of the table we are reading from */\n  int iColumn,     /* Index of the table column */\n  int iTable,      /* The cursor pointing to the table */\n  int iReg         /* Store results here */\n){\n  int r1 = sqlite3ExprCodeGetColumn(pParse, pTab, iColumn, iTable, iReg, 0);\n  if( r1!=iReg ) sqlite3VdbeAddOp2(pParse->pVdbe, OP_SCopy, r1, iReg);\n}\n\n\n/*\n** Clear all column cache entries.\n*/\nSQLITE_PRIVATE void sqlite3ExprCacheClear(Parse *pParse){\n  int i;\n\n#ifdef SQLITE_DEBUG\n  if( pParse->db->flags & SQLITE_VdbeAddopTrace ){\n    printf(\"CLEAR\\n\");\n  }\n#endif\n  for(i=0; i<pParse->nColCache; i++){\n    if( pParse->aColCache[i].tempReg\n     && pParse->nTempReg<ArraySize(pParse->aTempReg)\n    ){\n       pParse->aTempReg[pParse->nTempReg++] = pParse->aColCache[i].iReg;\n    }\n  }\n  pParse->nColCache = 0;\n}\n\n/*\n** Record the fact that an affinity change has occurred on iCount\n** registers starting with iStart.\n*/\nSQLITE_PRIVATE void sqlite3ExprCacheAffinityChange(Parse *pParse, int iStart, int iCount){\n  sqlite3ExprCacheRemove(pParse, iStart, iCount);\n}\n\n/*\n** Generate code to move content from registers iFrom...iFrom+nReg-1\n** over to iTo..iTo+nReg-1. Keep the column cache up-to-date.\n*/\nSQLITE_PRIVATE void sqlite3ExprCodeMove(Parse *pParse, int iFrom, int iTo, int nReg){\n  assert( iFrom>=iTo+nReg || iFrom+nReg<=iTo );\n  sqlite3VdbeAddOp3(pParse->pVdbe, OP_Move, iFrom, iTo, nReg);\n  sqlite3ExprCacheRemove(pParse, iFrom, nReg);\n}\n\n#if defined(SQLITE_DEBUG) || defined(SQLITE_COVERAGE_TEST)\n/*\n** Return true if any register in the range iFrom..iTo (inclusive)\n** is used as part of the column cache.\n**\n** This routine is used within assert() and testcase() macros only\n** and does not appear in a normal build.\n*/\nstatic int usedAsColumnCache(Parse *pParse, int iFrom, int iTo){\n  int i;\n  struct yColCache *p;\n  for(i=0, p=pParse->aColCache; i<pParse->nColCache; i++, p++){\n    int r = p->iReg;\n    if( r>=iFrom && r<=iTo ) return 1;    /*NO_TEST*/\n  }\n  return 0;\n}\n#endif /* SQLITE_DEBUG || SQLITE_COVERAGE_TEST */\n\n\n/*\n** Convert a scalar expression node to a TK_REGISTER referencing\n** register iReg.  The caller must ensure that iReg already contains\n** the correct value for the expression.\n*/\nstatic void exprToRegister(Expr *p, int iReg){\n  p->op2 = p->op;\n  p->op = TK_REGISTER;\n  p->iTable = iReg;\n  ExprClearProperty(p, EP_Skip);\n}\n\n/*\n** Evaluate an expression (either a vector or a scalar expression) and store\n** the result in continguous temporary registers.  Return the index of\n** the first register used to store the result.\n**\n** If the returned result register is a temporary scalar, then also write\n** that register number into *piFreeable.  If the returned result register\n** is not a temporary or if the expression is a vector set *piFreeable\n** to 0.\n*/\nstatic int exprCodeVector(Parse *pParse, Expr *p, int *piFreeable){\n  int iResult;\n  int nResult = sqlite3ExprVectorSize(p);\n  if( nResult==1 ){\n    iResult = sqlite3ExprCodeTemp(pParse, p, piFreeable);\n  }else{\n    *piFreeable = 0;\n    if( p->op==TK_SELECT ){\n#if SQLITE_OMIT_SUBQUERY\n      iResult = 0;\n#else\n      iResult = sqlite3CodeSubselect(pParse, p, 0, 0);\n#endif\n    }else{\n      int i;\n      iResult = pParse->nMem+1;\n      pParse->nMem += nResult;\n      for(i=0; i<nResult; i++){\n        sqlite3ExprCodeFactorable(pParse, p->x.pList->a[i].pExpr, i+iResult);\n      }\n    }\n  }\n  return iResult;\n}\n\n\n/*\n** Generate code into the current Vdbe to evaluate the given\n** expression.  Attempt to store the results in register \"target\".\n** Return the register where results are stored.\n**\n** With this routine, there is no guarantee that results will\n** be stored in target.  The result might be stored in some other\n** register if it is convenient to do so.  The calling function\n** must check the return code and move the results to the desired\n** register.\n*/\nSQLITE_PRIVATE int sqlite3ExprCodeTarget(Parse *pParse, Expr *pExpr, int target){\n  Vdbe *v = pParse->pVdbe;  /* The VM under construction */\n  int op;                   /* The opcode being coded */\n  int inReg = target;       /* Results stored in register inReg */\n  int regFree1 = 0;         /* If non-zero free this temporary register */\n  int regFree2 = 0;         /* If non-zero free this temporary register */\n  int r1, r2;               /* Various register numbers */\n  Expr tempX;               /* Temporary expression node */\n  int p5 = 0;\n\n  assert( target>0 && target<=pParse->nMem );\n  if( v==0 ){\n    assert( pParse->db->mallocFailed );\n    return 0;\n  }\n\n  if( pExpr==0 ){\n    op = TK_NULL;\n  }else{\n    op = pExpr->op;\n  }\n  switch( op ){\n    case TK_AGG_COLUMN: {\n      AggInfo *pAggInfo = pExpr->pAggInfo;\n      struct AggInfo_col *pCol = &pAggInfo->aCol[pExpr->iAgg];\n      if( !pAggInfo->directMode ){\n        assert( pCol->iMem>0 );\n        return pCol->iMem;\n      }else if( pAggInfo->useSortingIdx ){\n        sqlite3VdbeAddOp3(v, OP_Column, pAggInfo->sortingIdxPTab,\n                              pCol->iSorterColumn, target);\n        return target;\n      }\n      /* Otherwise, fall thru into the TK_COLUMN case */\n    }\n    case TK_COLUMN: {\n      int iTab = pExpr->iTable;\n      if( iTab<0 ){\n        if( pParse->iSelfTab<0 ){\n          /* Generating CHECK constraints or inserting into partial index */\n          return pExpr->iColumn - pParse->iSelfTab;\n        }else{\n          /* Coding an expression that is part of an index where column names\n          ** in the index refer to the table to which the index belongs */\n          iTab = pParse->iSelfTab - 1;\n        }\n      }\n      return sqlite3ExprCodeGetColumn(pParse, pExpr->pTab,\n                               pExpr->iColumn, iTab, target,\n                               pExpr->op2);\n    }\n    case TK_INTEGER: {\n      codeInteger(pParse, pExpr, 0, target);\n      return target;\n    }\n    case TK_TRUEFALSE: {\n      sqlite3VdbeAddOp2(v, OP_Integer, sqlite3ExprTruthValue(pExpr), target);\n      return target;\n    }\n#ifndef SQLITE_OMIT_FLOATING_POINT\n    case TK_FLOAT: {\n      assert( !ExprHasProperty(pExpr, EP_IntValue) );\n      codeReal(v, pExpr->u.zToken, 0, target);\n      return target;\n    }\n#endif\n    case TK_STRING: {\n      assert( !ExprHasProperty(pExpr, EP_IntValue) );\n      sqlite3VdbeLoadString(v, target, pExpr->u.zToken);\n      return target;\n    }\n    case TK_NULL: {\n      sqlite3VdbeAddOp2(v, OP_Null, 0, target);\n      return target;\n    }\n#ifndef SQLITE_OMIT_BLOB_LITERAL\n    case TK_BLOB: {\n      int n;\n      const char *z;\n      char *zBlob;\n      assert( !ExprHasProperty(pExpr, EP_IntValue) );\n      assert( pExpr->u.zToken[0]=='x' || pExpr->u.zToken[0]=='X' );\n      assert( pExpr->u.zToken[1]=='\\'' );\n      z = &pExpr->u.zToken[2];\n      n = sqlite3Strlen30(z) - 1;\n      assert( z[n]=='\\'' );\n      zBlob = sqlite3HexToBlob(sqlite3VdbeDb(v), z, n);\n      sqlite3VdbeAddOp4(v, OP_Blob, n/2, target, 0, zBlob, P4_DYNAMIC);\n      return target;\n    }\n#endif\n    case TK_VARIABLE: {\n      assert( !ExprHasProperty(pExpr, EP_IntValue) );\n      assert( pExpr->u.zToken!=0 );\n      assert( pExpr->u.zToken[0]!=0 );\n      sqlite3VdbeAddOp2(v, OP_Variable, pExpr->iColumn, target);\n      if( pExpr->u.zToken[1]!=0 ){\n        const char *z = sqlite3VListNumToName(pParse->pVList, pExpr->iColumn);\n        assert( pExpr->u.zToken[0]=='?' || strcmp(pExpr->u.zToken, z)==0 );\n        pParse->pVList[0] = 0; /* Indicate VList may no longer be enlarged */\n        sqlite3VdbeAppendP4(v, (char*)z, P4_STATIC);\n      }\n      return target;\n    }\n    case TK_REGISTER: {\n      return pExpr->iTable;\n    }\n#ifndef SQLITE_OMIT_CAST\n    case TK_CAST: {\n      /* Expressions of the form:   CAST(pLeft AS token) */\n      inReg = sqlite3ExprCodeTarget(pParse, pExpr->pLeft, target);\n      if( inReg!=target ){\n        sqlite3VdbeAddOp2(v, OP_SCopy, inReg, target);\n        inReg = target;\n      }\n      sqlite3VdbeAddOp2(v, OP_Cast, target,\n                        sqlite3AffinityType(pExpr->u.zToken, 0));\n      testcase( usedAsColumnCache(pParse, inReg, inReg) );\n      sqlite3ExprCacheAffinityChange(pParse, inReg, 1);\n      return inReg;\n    }\n#endif /* SQLITE_OMIT_CAST */\n    case TK_IS:\n    case TK_ISNOT:\n      op = (op==TK_IS) ? TK_EQ : TK_NE;\n      p5 = SQLITE_NULLEQ;\n      /* fall-through */\n    case TK_LT:\n    case TK_LE:\n    case TK_GT:\n    case TK_GE:\n    case TK_NE:\n    case TK_EQ: {\n      Expr *pLeft = pExpr->pLeft;\n      if( sqlite3ExprIsVector(pLeft) ){\n        codeVectorCompare(pParse, pExpr, target, op, p5);\n      }else{\n        r1 = sqlite3ExprCodeTemp(pParse, pLeft, &regFree1);\n        r2 = sqlite3ExprCodeTemp(pParse, pExpr->pRight, &regFree2);\n        codeCompare(pParse, pLeft, pExpr->pRight, op,\n            r1, r2, inReg, SQLITE_STOREP2 | p5);\n        assert(TK_LT==OP_Lt); testcase(op==OP_Lt); VdbeCoverageIf(v,op==OP_Lt);\n        assert(TK_LE==OP_Le); testcase(op==OP_Le); VdbeCoverageIf(v,op==OP_Le);\n        assert(TK_GT==OP_Gt); testcase(op==OP_Gt); VdbeCoverageIf(v,op==OP_Gt);\n        assert(TK_GE==OP_Ge); testcase(op==OP_Ge); VdbeCoverageIf(v,op==OP_Ge);\n        assert(TK_EQ==OP_Eq); testcase(op==OP_Eq); VdbeCoverageIf(v,op==OP_Eq);\n        assert(TK_NE==OP_Ne); testcase(op==OP_Ne); VdbeCoverageIf(v,op==OP_Ne);\n        testcase( regFree1==0 );\n        testcase( regFree2==0 );\n      }\n      break;\n    }\n    case TK_AND:\n    case TK_OR:\n    case TK_PLUS:\n    case TK_STAR:\n    case TK_MINUS:\n    case TK_REM:\n    case TK_BITAND:\n    case TK_BITOR:\n    case TK_SLASH:\n    case TK_LSHIFT:\n    case TK_RSHIFT: \n    case TK_CONCAT: {\n      assert( TK_AND==OP_And );            testcase( op==TK_AND );\n      assert( TK_OR==OP_Or );              testcase( op==TK_OR );\n      assert( TK_PLUS==OP_Add );           testcase( op==TK_PLUS );\n      assert( TK_MINUS==OP_Subtract );     testcase( op==TK_MINUS );\n      assert( TK_REM==OP_Remainder );      testcase( op==TK_REM );\n      assert( TK_BITAND==OP_BitAnd );      testcase( op==TK_BITAND );\n      assert( TK_BITOR==OP_BitOr );        testcase( op==TK_BITOR );\n      assert( TK_SLASH==OP_Divide );       testcase( op==TK_SLASH );\n      assert( TK_LSHIFT==OP_ShiftLeft );   testcase( op==TK_LSHIFT );\n      assert( TK_RSHIFT==OP_ShiftRight );  testcase( op==TK_RSHIFT );\n      assert( TK_CONCAT==OP_Concat );      testcase( op==TK_CONCAT );\n      r1 = sqlite3ExprCodeTemp(pParse, pExpr->pLeft, &regFree1);\n      r2 = sqlite3ExprCodeTemp(pParse, pExpr->pRight, &regFree2);\n      sqlite3VdbeAddOp3(v, op, r2, r1, target);\n      testcase( regFree1==0 );\n      testcase( regFree2==0 );\n      break;\n    }\n    case TK_UMINUS: {\n      Expr *pLeft = pExpr->pLeft;\n      assert( pLeft );\n      if( pLeft->op==TK_INTEGER ){\n        codeInteger(pParse, pLeft, 1, target);\n        return target;\n#ifndef SQLITE_OMIT_FLOATING_POINT\n      }else if( pLeft->op==TK_FLOAT ){\n        assert( !ExprHasProperty(pExpr, EP_IntValue) );\n        codeReal(v, pLeft->u.zToken, 1, target);\n        return target;\n#endif\n      }else{\n        tempX.op = TK_INTEGER;\n        tempX.flags = EP_IntValue|EP_TokenOnly;\n        tempX.u.iValue = 0;\n        r1 = sqlite3ExprCodeTemp(pParse, &tempX, &regFree1);\n        r2 = sqlite3ExprCodeTemp(pParse, pExpr->pLeft, &regFree2);\n        sqlite3VdbeAddOp3(v, OP_Subtract, r2, r1, target);\n        testcase( regFree2==0 );\n      }\n      break;\n    }\n    case TK_BITNOT:\n    case TK_NOT: {\n      assert( TK_BITNOT==OP_BitNot );   testcase( op==TK_BITNOT );\n      assert( TK_NOT==OP_Not );         testcase( op==TK_NOT );\n      r1 = sqlite3ExprCodeTemp(pParse, pExpr->pLeft, &regFree1);\n      testcase( regFree1==0 );\n      sqlite3VdbeAddOp2(v, op, r1, inReg);\n      break;\n    }\n    case TK_TRUTH: {\n      int isTrue;    /* IS TRUE or IS NOT TRUE */\n      int bNormal;   /* IS TRUE or IS FALSE */\n      r1 = sqlite3ExprCodeTemp(pParse, pExpr->pLeft, &regFree1);\n      testcase( regFree1==0 );\n      isTrue = sqlite3ExprTruthValue(pExpr->pRight);\n      bNormal = pExpr->op2==TK_IS;\n      testcase( isTrue && bNormal);\n      testcase( !isTrue && bNormal);\n      sqlite3VdbeAddOp4Int(v, OP_IsTrue, r1, inReg, !isTrue, isTrue ^ bNormal);\n      break;\n    }\n    case TK_ISNULL:\n    case TK_NOTNULL: {\n      int addr;\n      assert( TK_ISNULL==OP_IsNull );   testcase( op==TK_ISNULL );\n      assert( TK_NOTNULL==OP_NotNull ); testcase( op==TK_NOTNULL );\n      sqlite3VdbeAddOp2(v, OP_Integer, 1, target);\n      r1 = sqlite3ExprCodeTemp(pParse, pExpr->pLeft, &regFree1);\n      testcase( regFree1==0 );\n      addr = sqlite3VdbeAddOp1(v, op, r1);\n      VdbeCoverageIf(v, op==TK_ISNULL);\n      VdbeCoverageIf(v, op==TK_NOTNULL);\n      sqlite3VdbeAddOp2(v, OP_Integer, 0, target);\n      sqlite3VdbeJumpHere(v, addr);\n      break;\n    }\n    case TK_AGG_FUNCTION: {\n      AggInfo *pInfo = pExpr->pAggInfo;\n      if( pInfo==0 ){\n        assert( !ExprHasProperty(pExpr, EP_IntValue) );\n        sqlite3ErrorMsg(pParse, \"misuse of aggregate: %s()\", pExpr->u.zToken);\n      }else{\n        return pInfo->aFunc[pExpr->iAgg].iMem;\n      }\n      break;\n    }\n    case TK_FUNCTION: {\n      ExprList *pFarg;       /* List of function arguments */\n      int nFarg;             /* Number of function arguments */\n      FuncDef *pDef;         /* The function definition object */\n      const char *zId;       /* The function name */\n      u32 constMask = 0;     /* Mask of function arguments that are constant */\n      int i;                 /* Loop counter */\n      sqlite3 *db = pParse->db;  /* The database connection */\n      u8 enc = ENC(db);      /* The text encoding used by this database */\n      CollSeq *pColl = 0;    /* A collating sequence */\n\n      if( ConstFactorOk(pParse) && sqlite3ExprIsConstantNotJoin(pExpr) ){\n        /* SQL functions can be expensive. So try to move constant functions\n        ** out of the inner loop, even if that means an extra OP_Copy. */\n        return sqlite3ExprCodeAtInit(pParse, pExpr, -1);\n      }\n      assert( !ExprHasProperty(pExpr, EP_xIsSelect) );\n      if( ExprHasProperty(pExpr, EP_TokenOnly) ){\n        pFarg = 0;\n      }else{\n        pFarg = pExpr->x.pList;\n      }\n      nFarg = pFarg ? pFarg->nExpr : 0;\n      assert( !ExprHasProperty(pExpr, EP_IntValue) );\n      zId = pExpr->u.zToken;\n      pDef = sqlite3FindFunction(db, zId, nFarg, enc, 0);\n#ifdef SQLITE_ENABLE_UNKNOWN_SQL_FUNCTION\n      if( pDef==0 && pParse->explain ){\n        pDef = sqlite3FindFunction(db, \"unknown\", nFarg, enc, 0);\n      }\n#endif\n      if( pDef==0 || pDef->xFinalize!=0 ){\n        sqlite3ErrorMsg(pParse, \"unknown function: %s()\", zId);\n        break;\n      }\n\n      /* Attempt a direct implementation of the built-in COALESCE() and\n      ** IFNULL() functions.  This avoids unnecessary evaluation of\n      ** arguments past the first non-NULL argument.\n      */\n      if( pDef->funcFlags & SQLITE_FUNC_COALESCE ){\n        int endCoalesce = sqlite3VdbeMakeLabel(v);\n        assert( nFarg>=2 );\n        sqlite3ExprCode(pParse, pFarg->a[0].pExpr, target);\n        for(i=1; i<nFarg; i++){\n          sqlite3VdbeAddOp2(v, OP_NotNull, target, endCoalesce);\n          VdbeCoverage(v);\n          sqlite3ExprCacheRemove(pParse, target, 1);\n          sqlite3ExprCachePush(pParse);\n          sqlite3ExprCode(pParse, pFarg->a[i].pExpr, target);\n          sqlite3ExprCachePop(pParse);\n        }\n        sqlite3VdbeResolveLabel(v, endCoalesce);\n        break;\n      }\n\n      /* The UNLIKELY() function is a no-op.  The result is the value\n      ** of the first argument.\n      */\n      if( pDef->funcFlags & SQLITE_FUNC_UNLIKELY ){\n        assert( nFarg>=1 );\n        return sqlite3ExprCodeTarget(pParse, pFarg->a[0].pExpr, target);\n      }\n\n#ifdef SQLITE_DEBUG\n      /* The AFFINITY() function evaluates to a string that describes\n      ** the type affinity of the argument.  This is used for testing of\n      ** the SQLite type logic.\n      */\n      if( pDef->funcFlags & SQLITE_FUNC_AFFINITY ){\n        const char *azAff[] = { \"blob\", \"text\", \"numeric\", \"integer\", \"real\" };\n        char aff;\n        assert( nFarg==1 );\n        aff = sqlite3ExprAffinity(pFarg->a[0].pExpr);\n        sqlite3VdbeLoadString(v, target, \n                              aff ? azAff[aff-SQLITE_AFF_BLOB] : \"none\");\n        return target;\n      }\n#endif\n\n      for(i=0; i<nFarg; i++){\n        if( i<32 && sqlite3ExprIsConstant(pFarg->a[i].pExpr) ){\n          testcase( i==31 );\n          constMask |= MASKBIT32(i);\n        }\n        if( (pDef->funcFlags & SQLITE_FUNC_NEEDCOLL)!=0 && !pColl ){\n          pColl = sqlite3ExprCollSeq(pParse, pFarg->a[i].pExpr);\n        }\n      }\n      if( pFarg ){\n        if( constMask ){\n          r1 = pParse->nMem+1;\n          pParse->nMem += nFarg;\n        }else{\n          r1 = sqlite3GetTempRange(pParse, nFarg);\n        }\n\n        /* For length() and typeof() functions with a column argument,\n        ** set the P5 parameter to the OP_Column opcode to OPFLAG_LENGTHARG\n        ** or OPFLAG_TYPEOFARG respectively, to avoid unnecessary data\n        ** loading.\n        */\n        if( (pDef->funcFlags & (SQLITE_FUNC_LENGTH|SQLITE_FUNC_TYPEOF))!=0 ){\n          u8 exprOp;\n          assert( nFarg==1 );\n          assert( pFarg->a[0].pExpr!=0 );\n          exprOp = pFarg->a[0].pExpr->op;\n          if( exprOp==TK_COLUMN || exprOp==TK_AGG_COLUMN ){\n            assert( SQLITE_FUNC_LENGTH==OPFLAG_LENGTHARG );\n            assert( SQLITE_FUNC_TYPEOF==OPFLAG_TYPEOFARG );\n            testcase( pDef->funcFlags & OPFLAG_LENGTHARG );\n            pFarg->a[0].pExpr->op2 = \n                  pDef->funcFlags & (OPFLAG_LENGTHARG|OPFLAG_TYPEOFARG);\n          }\n        }\n\n        sqlite3ExprCachePush(pParse);     /* Ticket 2ea2425d34be */\n        sqlite3ExprCodeExprList(pParse, pFarg, r1, 0,\n                                SQLITE_ECEL_DUP|SQLITE_ECEL_FACTOR);\n        sqlite3ExprCachePop(pParse);      /* Ticket 2ea2425d34be */\n      }else{\n        r1 = 0;\n      }\n#ifndef SQLITE_OMIT_VIRTUALTABLE\n      /* Possibly overload the function if the first argument is\n      ** a virtual table column.\n      **\n      ** For infix functions (LIKE, GLOB, REGEXP, and MATCH) use the\n      ** second argument, not the first, as the argument to test to\n      ** see if it is a column in a virtual table.  This is done because\n      ** the left operand of infix functions (the operand we want to\n      ** control overloading) ends up as the second argument to the\n      ** function.  The expression \"A glob B\" is equivalent to \n      ** \"glob(B,A).  We want to use the A in \"A glob B\" to test\n      ** for function overloading.  But we use the B term in \"glob(B,A)\".\n      */\n      if( nFarg>=2 && (pExpr->flags & EP_InfixFunc) ){\n        pDef = sqlite3VtabOverloadFunction(db, pDef, nFarg, pFarg->a[1].pExpr);\n      }else if( nFarg>0 ){\n        pDef = sqlite3VtabOverloadFunction(db, pDef, nFarg, pFarg->a[0].pExpr);\n      }\n#endif\n      if( pDef->funcFlags & SQLITE_FUNC_NEEDCOLL ){\n        if( !pColl ) pColl = db->pDfltColl; \n        sqlite3VdbeAddOp4(v, OP_CollSeq, 0, 0, 0, (char *)pColl, P4_COLLSEQ);\n      }\n#ifdef SQLITE_ENABLE_OFFSET_SQL_FUNC\n      if( pDef->funcFlags & SQLITE_FUNC_OFFSET ){\n        Expr *pArg = pFarg->a[0].pExpr;\n        if( pArg->op==TK_COLUMN ){\n          sqlite3VdbeAddOp3(v, OP_Offset, pArg->iTable, pArg->iColumn, target);\n        }else{\n          sqlite3VdbeAddOp2(v, OP_Null, 0, target);\n        }\n      }else\n#endif\n      {\n        sqlite3VdbeAddOp4(v, pParse->iSelfTab ? OP_PureFunc0 : OP_Function0,\n                          constMask, r1, target, (char*)pDef, P4_FUNCDEF);\n        sqlite3VdbeChangeP5(v, (u8)nFarg);\n      }\n      if( nFarg && constMask==0 ){\n        sqlite3ReleaseTempRange(pParse, r1, nFarg);\n      }\n      return target;\n    }\n#ifndef SQLITE_OMIT_SUBQUERY\n    case TK_EXISTS:\n    case TK_SELECT: {\n      int nCol;\n      testcase( op==TK_EXISTS );\n      testcase( op==TK_SELECT );\n      if( op==TK_SELECT && (nCol = pExpr->x.pSelect->pEList->nExpr)!=1 ){\n        sqlite3SubselectError(pParse, nCol, 1);\n      }else{\n        return sqlite3CodeSubselect(pParse, pExpr, 0, 0);\n      }\n      break;\n    }\n    case TK_SELECT_COLUMN: {\n      int n;\n      if( pExpr->pLeft->iTable==0 ){\n        pExpr->pLeft->iTable = sqlite3CodeSubselect(pParse, pExpr->pLeft, 0, 0);\n      }\n      assert( pExpr->iTable==0 || pExpr->pLeft->op==TK_SELECT );\n      if( pExpr->iTable\n       && pExpr->iTable!=(n = sqlite3ExprVectorSize(pExpr->pLeft)) \n      ){\n        sqlite3ErrorMsg(pParse, \"%d columns assigned %d values\",\n                                pExpr->iTable, n);\n      }\n      return pExpr->pLeft->iTable + pExpr->iColumn;\n    }\n    case TK_IN: {\n      int destIfFalse = sqlite3VdbeMakeLabel(v);\n      int destIfNull = sqlite3VdbeMakeLabel(v);\n      sqlite3VdbeAddOp2(v, OP_Null, 0, target);\n      sqlite3ExprCodeIN(pParse, pExpr, destIfFalse, destIfNull);\n      sqlite3VdbeAddOp2(v, OP_Integer, 1, target);\n      sqlite3VdbeResolveLabel(v, destIfFalse);\n      sqlite3VdbeAddOp2(v, OP_AddImm, target, 0);\n      sqlite3VdbeResolveLabel(v, destIfNull);\n      return target;\n    }\n#endif /* SQLITE_OMIT_SUBQUERY */\n\n\n    /*\n    **    x BETWEEN y AND z\n    **\n    ** This is equivalent to\n    **\n    **    x>=y AND x<=z\n    **\n    ** X is stored in pExpr->pLeft.\n    ** Y is stored in pExpr->pList->a[0].pExpr.\n    ** Z is stored in pExpr->pList->a[1].pExpr.\n    */\n    case TK_BETWEEN: {\n      exprCodeBetween(pParse, pExpr, target, 0, 0);\n      return target;\n    }\n    case TK_SPAN:\n    case TK_COLLATE: \n    case TK_UPLUS: {\n      return sqlite3ExprCodeTarget(pParse, pExpr->pLeft, target);\n    }\n\n    case TK_TRIGGER: {\n      /* If the opcode is TK_TRIGGER, then the expression is a reference\n      ** to a column in the new.* or old.* pseudo-tables available to\n      ** trigger programs. In this case Expr.iTable is set to 1 for the\n      ** new.* pseudo-table, or 0 for the old.* pseudo-table. Expr.iColumn\n      ** is set to the column of the pseudo-table to read, or to -1 to\n      ** read the rowid field.\n      **\n      ** The expression is implemented using an OP_Param opcode. The p1\n      ** parameter is set to 0 for an old.rowid reference, or to (i+1)\n      ** to reference another column of the old.* pseudo-table, where \n      ** i is the index of the column. For a new.rowid reference, p1 is\n      ** set to (n+1), where n is the number of columns in each pseudo-table.\n      ** For a reference to any other column in the new.* pseudo-table, p1\n      ** is set to (n+2+i), where n and i are as defined previously. For\n      ** example, if the table on which triggers are being fired is\n      ** declared as:\n      **\n      **   CREATE TABLE t1(a, b);\n      **\n      ** Then p1 is interpreted as follows:\n      **\n      **   p1==0   ->    old.rowid     p1==3   ->    new.rowid\n      **   p1==1   ->    old.a         p1==4   ->    new.a\n      **   p1==2   ->    old.b         p1==5   ->    new.b       \n      */\n      Table *pTab = pExpr->pTab;\n      int p1 = pExpr->iTable * (pTab->nCol+1) + 1 + pExpr->iColumn;\n\n      assert( pExpr->iTable==0 || pExpr->iTable==1 );\n      assert( pExpr->iColumn>=-1 && pExpr->iColumn<pTab->nCol );\n      assert( pTab->iPKey<0 || pExpr->iColumn!=pTab->iPKey );\n      assert( p1>=0 && p1<(pTab->nCol*2+2) );\n\n      sqlite3VdbeAddOp2(v, OP_Param, p1, target);\n      VdbeComment((v, \"%s.%s -> $%d\",\n        (pExpr->iTable ? \"new\" : \"old\"),\n        (pExpr->iColumn<0 ? \"rowid\" : pExpr->pTab->aCol[pExpr->iColumn].zName),\n        target\n      ));\n\n#ifndef SQLITE_OMIT_FLOATING_POINT\n      /* If the column has REAL affinity, it may currently be stored as an\n      ** integer. Use OP_RealAffinity to make sure it is really real.\n      **\n      ** EVIDENCE-OF: R-60985-57662 SQLite will convert the value back to\n      ** floating point when extracting it from the record.  */\n      if( pExpr->iColumn>=0 \n       && pTab->aCol[pExpr->iColumn].affinity==SQLITE_AFF_REAL\n      ){\n        sqlite3VdbeAddOp1(v, OP_RealAffinity, target);\n      }\n#endif\n      break;\n    }\n\n    case TK_VECTOR: {\n      sqlite3ErrorMsg(pParse, \"row value misused\");\n      break;\n    }\n\n    case TK_IF_NULL_ROW: {\n      int addrINR;\n      addrINR = sqlite3VdbeAddOp1(v, OP_IfNullRow, pExpr->iTable);\n      sqlite3ExprCachePush(pParse);\n      inReg = sqlite3ExprCodeTarget(pParse, pExpr->pLeft, target);\n      sqlite3ExprCachePop(pParse);\n      sqlite3VdbeJumpHere(v, addrINR);\n      sqlite3VdbeChangeP3(v, addrINR, inReg);\n      break;\n    }\n\n    /*\n    ** Form A:\n    **   CASE x WHEN e1 THEN r1 WHEN e2 THEN r2 ... WHEN eN THEN rN ELSE y END\n    **\n    ** Form B:\n    **   CASE WHEN e1 THEN r1 WHEN e2 THEN r2 ... WHEN eN THEN rN ELSE y END\n    **\n    ** Form A is can be transformed into the equivalent form B as follows:\n    **   CASE WHEN x=e1 THEN r1 WHEN x=e2 THEN r2 ...\n    **        WHEN x=eN THEN rN ELSE y END\n    **\n    ** X (if it exists) is in pExpr->pLeft.\n    ** Y is in the last element of pExpr->x.pList if pExpr->x.pList->nExpr is\n    ** odd.  The Y is also optional.  If the number of elements in x.pList\n    ** is even, then Y is omitted and the \"otherwise\" result is NULL.\n    ** Ei is in pExpr->pList->a[i*2] and Ri is pExpr->pList->a[i*2+1].\n    **\n    ** The result of the expression is the Ri for the first matching Ei,\n    ** or if there is no matching Ei, the ELSE term Y, or if there is\n    ** no ELSE term, NULL.\n    */\n    default: assert( op==TK_CASE ); {\n      int endLabel;                     /* GOTO label for end of CASE stmt */\n      int nextCase;                     /* GOTO label for next WHEN clause */\n      int nExpr;                        /* 2x number of WHEN terms */\n      int i;                            /* Loop counter */\n      ExprList *pEList;                 /* List of WHEN terms */\n      struct ExprList_item *aListelem;  /* Array of WHEN terms */\n      Expr opCompare;                   /* The X==Ei expression */\n      Expr *pX;                         /* The X expression */\n      Expr *pTest = 0;                  /* X==Ei (form A) or just Ei (form B) */\n      VVA_ONLY( int iCacheLevel = pParse->iCacheLevel; )\n\n      assert( !ExprHasProperty(pExpr, EP_xIsSelect) && pExpr->x.pList );\n      assert(pExpr->x.pList->nExpr > 0);\n      pEList = pExpr->x.pList;\n      aListelem = pEList->a;\n      nExpr = pEList->nExpr;\n      endLabel = sqlite3VdbeMakeLabel(v);\n      if( (pX = pExpr->pLeft)!=0 ){\n        tempX = *pX;\n        testcase( pX->op==TK_COLUMN );\n        exprToRegister(&tempX, exprCodeVector(pParse, &tempX, &regFree1));\n        testcase( regFree1==0 );\n        memset(&opCompare, 0, sizeof(opCompare));\n        opCompare.op = TK_EQ;\n        opCompare.pLeft = &tempX;\n        pTest = &opCompare;\n        /* Ticket b351d95f9cd5ef17e9d9dbae18f5ca8611190001:\n        ** The value in regFree1 might get SCopy-ed into the file result.\n        ** So make sure that the regFree1 register is not reused for other\n        ** purposes and possibly overwritten.  */\n        regFree1 = 0;\n      }\n      for(i=0; i<nExpr-1; i=i+2){\n        sqlite3ExprCachePush(pParse);\n        if( pX ){\n          assert( pTest!=0 );\n          opCompare.pRight = aListelem[i].pExpr;\n        }else{\n          pTest = aListelem[i].pExpr;\n        }\n        nextCase = sqlite3VdbeMakeLabel(v);\n        testcase( pTest->op==TK_COLUMN );\n        sqlite3ExprIfFalse(pParse, pTest, nextCase, SQLITE_JUMPIFNULL);\n        testcase( aListelem[i+1].pExpr->op==TK_COLUMN );\n        sqlite3ExprCode(pParse, aListelem[i+1].pExpr, target);\n        sqlite3VdbeGoto(v, endLabel);\n        sqlite3ExprCachePop(pParse);\n        sqlite3VdbeResolveLabel(v, nextCase);\n      }\n      if( (nExpr&1)!=0 ){\n        sqlite3ExprCachePush(pParse);\n        sqlite3ExprCode(pParse, pEList->a[nExpr-1].pExpr, target);\n        sqlite3ExprCachePop(pParse);\n      }else{\n        sqlite3VdbeAddOp2(v, OP_Null, 0, target);\n      }\n      assert( pParse->db->mallocFailed || pParse->nErr>0 \n           || pParse->iCacheLevel==iCacheLevel );\n      sqlite3VdbeResolveLabel(v, endLabel);\n      break;\n    }\n#ifndef SQLITE_OMIT_TRIGGER\n    case TK_RAISE: {\n      assert( pExpr->affinity==OE_Rollback \n           || pExpr->affinity==OE_Abort\n           || pExpr->affinity==OE_Fail\n           || pExpr->affinity==OE_Ignore\n      );\n      if( !pParse->pTriggerTab ){\n        sqlite3ErrorMsg(pParse,\n                       \"RAISE() may only be used within a trigger-program\");\n        return 0;\n      }\n      if( pExpr->affinity==OE_Abort ){\n        sqlite3MayAbort(pParse);\n      }\n      assert( !ExprHasProperty(pExpr, EP_IntValue) );\n      if( pExpr->affinity==OE_Ignore ){\n        sqlite3VdbeAddOp4(\n            v, OP_Halt, SQLITE_OK, OE_Ignore, 0, pExpr->u.zToken,0);\n        VdbeCoverage(v);\n      }else{\n        sqlite3HaltConstraint(pParse, SQLITE_CONSTRAINT_TRIGGER,\n                              pExpr->affinity, pExpr->u.zToken, 0, 0);\n      }\n\n      break;\n    }\n#endif\n  }\n  sqlite3ReleaseTempReg(pParse, regFree1);\n  sqlite3ReleaseTempReg(pParse, regFree2);\n  return inReg;\n}\n\n/*\n** Factor out the code of the given expression to initialization time.\n**\n** If regDest>=0 then the result is always stored in that register and the\n** result is not reusable.  If regDest<0 then this routine is free to \n** store the value whereever it wants.  The register where the expression \n** is stored is returned.  When regDest<0, two identical expressions will\n** code to the same register.\n*/\nSQLITE_PRIVATE int sqlite3ExprCodeAtInit(\n  Parse *pParse,    /* Parsing context */\n  Expr *pExpr,      /* The expression to code when the VDBE initializes */\n  int regDest       /* Store the value in this register */\n){\n  ExprList *p;\n  assert( ConstFactorOk(pParse) );\n  p = pParse->pConstExpr;\n  if( regDest<0 && p ){\n    struct ExprList_item *pItem;\n    int i;\n    for(pItem=p->a, i=p->nExpr; i>0; pItem++, i--){\n      if( pItem->reusable && sqlite3ExprCompare(0,pItem->pExpr,pExpr,-1)==0 ){\n        return pItem->u.iConstExprReg;\n      }\n    }\n  }\n  pExpr = sqlite3ExprDup(pParse->db, pExpr, 0);\n  p = sqlite3ExprListAppend(pParse, p, pExpr);\n  if( p ){\n     struct ExprList_item *pItem = &p->a[p->nExpr-1];\n     pItem->reusable = regDest<0;\n     if( regDest<0 ) regDest = ++pParse->nMem;\n     pItem->u.iConstExprReg = regDest;\n  }\n  pParse->pConstExpr = p;\n  return regDest;\n}\n\n/*\n** Generate code to evaluate an expression and store the results\n** into a register.  Return the register number where the results\n** are stored.\n**\n** If the register is a temporary register that can be deallocated,\n** then write its number into *pReg.  If the result register is not\n** a temporary, then set *pReg to zero.\n**\n** If pExpr is a constant, then this routine might generate this\n** code to fill the register in the initialization section of the\n** VDBE program, in order to factor it out of the evaluation loop.\n*/\nSQLITE_PRIVATE int sqlite3ExprCodeTemp(Parse *pParse, Expr *pExpr, int *pReg){\n  int r2;\n  pExpr = sqlite3ExprSkipCollate(pExpr);\n  if( ConstFactorOk(pParse)\n   && pExpr->op!=TK_REGISTER\n   && sqlite3ExprIsConstantNotJoin(pExpr)\n  ){\n    *pReg  = 0;\n    r2 = sqlite3ExprCodeAtInit(pParse, pExpr, -1);\n  }else{\n    int r1 = sqlite3GetTempReg(pParse);\n    r2 = sqlite3ExprCodeTarget(pParse, pExpr, r1);\n    if( r2==r1 ){\n      *pReg = r1;\n    }else{\n      sqlite3ReleaseTempReg(pParse, r1);\n      *pReg = 0;\n    }\n  }\n  return r2;\n}\n\n/*\n** Generate code that will evaluate expression pExpr and store the\n** results in register target.  The results are guaranteed to appear\n** in register target.\n*/\nSQLITE_PRIVATE void sqlite3ExprCode(Parse *pParse, Expr *pExpr, int target){\n  int inReg;\n\n  assert( target>0 && target<=pParse->nMem );\n  if( pExpr && pExpr->op==TK_REGISTER ){\n    sqlite3VdbeAddOp2(pParse->pVdbe, OP_Copy, pExpr->iTable, target);\n  }else{\n    inReg = sqlite3ExprCodeTarget(pParse, pExpr, target);\n    assert( pParse->pVdbe!=0 || pParse->db->mallocFailed );\n    if( inReg!=target && pParse->pVdbe ){\n      sqlite3VdbeAddOp2(pParse->pVdbe, OP_SCopy, inReg, target);\n    }\n  }\n}\n\n/*\n** Make a transient copy of expression pExpr and then code it using\n** sqlite3ExprCode().  This routine works just like sqlite3ExprCode()\n** except that the input expression is guaranteed to be unchanged.\n*/\nSQLITE_PRIVATE void sqlite3ExprCodeCopy(Parse *pParse, Expr *pExpr, int target){\n  sqlite3 *db = pParse->db;\n  pExpr = sqlite3ExprDup(db, pExpr, 0);\n  if( !db->mallocFailed ) sqlite3ExprCode(pParse, pExpr, target);\n  sqlite3ExprDelete(db, pExpr);\n}\n\n/*\n** Generate code that will evaluate expression pExpr and store the\n** results in register target.  The results are guaranteed to appear\n** in register target.  If the expression is constant, then this routine\n** might choose to code the expression at initialization time.\n*/\nSQLITE_PRIVATE void sqlite3ExprCodeFactorable(Parse *pParse, Expr *pExpr, int target){\n  if( pParse->okConstFactor && sqlite3ExprIsConstant(pExpr) ){\n    sqlite3ExprCodeAtInit(pParse, pExpr, target);\n  }else{\n    sqlite3ExprCode(pParse, pExpr, target);\n  }\n}\n\n/*\n** Generate code that evaluates the given expression and puts the result\n** in register target.\n**\n** Also make a copy of the expression results into another \"cache\" register\n** and modify the expression so that the next time it is evaluated,\n** the result is a copy of the cache register.\n**\n** This routine is used for expressions that are used multiple \n** times.  They are evaluated once and the results of the expression\n** are reused.\n*/\nSQLITE_PRIVATE void sqlite3ExprCodeAndCache(Parse *pParse, Expr *pExpr, int target){\n  Vdbe *v = pParse->pVdbe;\n  int iMem;\n\n  assert( target>0 );\n  assert( pExpr->op!=TK_REGISTER );\n  sqlite3ExprCode(pParse, pExpr, target);\n  iMem = ++pParse->nMem;\n  sqlite3VdbeAddOp2(v, OP_Copy, target, iMem);\n  exprToRegister(pExpr, iMem);\n}\n\n/*\n** Generate code that pushes the value of every element of the given\n** expression list into a sequence of registers beginning at target.\n**\n** Return the number of elements evaluated.  The number returned will\n** usually be pList->nExpr but might be reduced if SQLITE_ECEL_OMITREF\n** is defined.\n**\n** The SQLITE_ECEL_DUP flag prevents the arguments from being\n** filled using OP_SCopy.  OP_Copy must be used instead.\n**\n** The SQLITE_ECEL_FACTOR argument allows constant arguments to be\n** factored out into initialization code.\n**\n** The SQLITE_ECEL_REF flag means that expressions in the list with\n** ExprList.a[].u.x.iOrderByCol>0 have already been evaluated and stored\n** in registers at srcReg, and so the value can be copied from there.\n** If SQLITE_ECEL_OMITREF is also set, then the values with u.x.iOrderByCol>0\n** are simply omitted rather than being copied from srcReg.\n*/\nSQLITE_PRIVATE int sqlite3ExprCodeExprList(\n  Parse *pParse,     /* Parsing context */\n  ExprList *pList,   /* The expression list to be coded */\n  int target,        /* Where to write results */\n  int srcReg,        /* Source registers if SQLITE_ECEL_REF */\n  u8 flags           /* SQLITE_ECEL_* flags */\n){\n  struct ExprList_item *pItem;\n  int i, j, n;\n  u8 copyOp = (flags & SQLITE_ECEL_DUP) ? OP_Copy : OP_SCopy;\n  Vdbe *v = pParse->pVdbe;\n  assert( pList!=0 );\n  assert( target>0 );\n  assert( pParse->pVdbe!=0 );  /* Never gets this far otherwise */\n  n = pList->nExpr;\n  if( !ConstFactorOk(pParse) ) flags &= ~SQLITE_ECEL_FACTOR;\n  for(pItem=pList->a, i=0; i<n; i++, pItem++){\n    Expr *pExpr = pItem->pExpr;\n    if( (flags & SQLITE_ECEL_REF)!=0 && (j = pItem->u.x.iOrderByCol)>0 ){\n      if( flags & SQLITE_ECEL_OMITREF ){\n        i--;\n        n--;\n      }else{\n        sqlite3VdbeAddOp2(v, copyOp, j+srcReg-1, target+i);\n      }\n    }else if( (flags & SQLITE_ECEL_FACTOR)!=0 && sqlite3ExprIsConstant(pExpr) ){\n      sqlite3ExprCodeAtInit(pParse, pExpr, target+i);\n    }else{\n      int inReg = sqlite3ExprCodeTarget(pParse, pExpr, target+i);\n      if( inReg!=target+i ){\n        VdbeOp *pOp;\n        if( copyOp==OP_Copy\n         && (pOp=sqlite3VdbeGetOp(v, -1))->opcode==OP_Copy\n         && pOp->p1+pOp->p3+1==inReg\n         && pOp->p2+pOp->p3+1==target+i\n        ){\n          pOp->p3++;\n        }else{\n          sqlite3VdbeAddOp2(v, copyOp, inReg, target+i);\n        }\n      }\n    }\n  }\n  return n;\n}\n\n/*\n** Generate code for a BETWEEN operator.\n**\n**    x BETWEEN y AND z\n**\n** The above is equivalent to \n**\n**    x>=y AND x<=z\n**\n** Code it as such, taking care to do the common subexpression\n** elimination of x.\n**\n** The xJumpIf parameter determines details:\n**\n**    NULL:                   Store the boolean result in reg[dest]\n**    sqlite3ExprIfTrue:      Jump to dest if true\n**    sqlite3ExprIfFalse:     Jump to dest if false\n**\n** The jumpIfNull parameter is ignored if xJumpIf is NULL.\n*/\nstatic void exprCodeBetween(\n  Parse *pParse,    /* Parsing and code generating context */\n  Expr *pExpr,      /* The BETWEEN expression */\n  int dest,         /* Jump destination or storage location */\n  void (*xJump)(Parse*,Expr*,int,int), /* Action to take */\n  int jumpIfNull    /* Take the jump if the BETWEEN is NULL */\n){\n Expr exprAnd;     /* The AND operator in  x>=y AND x<=z  */\n  Expr compLeft;    /* The  x>=y  term */\n  Expr compRight;   /* The  x<=z  term */\n  Expr exprX;       /* The  x  subexpression */\n  int regFree1 = 0; /* Temporary use register */\n\n\n  memset(&compLeft, 0, sizeof(Expr));\n  memset(&compRight, 0, sizeof(Expr));\n  memset(&exprAnd, 0, sizeof(Expr));\n\n  assert( !ExprHasProperty(pExpr, EP_xIsSelect) );\n  exprX = *pExpr->pLeft;\n  exprAnd.op = TK_AND;\n  exprAnd.pLeft = &compLeft;\n  exprAnd.pRight = &compRight;\n  compLeft.op = TK_GE;\n  compLeft.pLeft = &exprX;\n  compLeft.pRight = pExpr->x.pList->a[0].pExpr;\n  compRight.op = TK_LE;\n  compRight.pLeft = &exprX;\n  compRight.pRight = pExpr->x.pList->a[1].pExpr;\n  exprToRegister(&exprX, exprCodeVector(pParse, &exprX, &regFree1));\n  if( xJump ){\n    xJump(pParse, &exprAnd, dest, jumpIfNull);\n  }else{\n    /* Mark the expression is being from the ON or USING clause of a join\n    ** so that the sqlite3ExprCodeTarget() routine will not attempt to move\n    ** it into the Parse.pConstExpr list.  We should use a new bit for this,\n    ** for clarity, but we are out of bits in the Expr.flags field so we\n    ** have to reuse the EP_FromJoin bit.  Bummer. */\n    exprX.flags |= EP_FromJoin;\n    sqlite3ExprCodeTarget(pParse, &exprAnd, dest);\n  }\n  sqlite3ReleaseTempReg(pParse, regFree1);\n\n  /* Ensure adequate test coverage */\n  testcase( xJump==sqlite3ExprIfTrue  && jumpIfNull==0 && regFree1==0 );\n  testcase( xJump==sqlite3ExprIfTrue  && jumpIfNull==0 && regFree1!=0 );\n  testcase( xJump==sqlite3ExprIfTrue  && jumpIfNull!=0 && regFree1==0 );\n  testcase( xJump==sqlite3ExprIfTrue  && jumpIfNull!=0 && regFree1!=0 );\n  testcase( xJump==sqlite3ExprIfFalse && jumpIfNull==0 && regFree1==0 );\n  testcase( xJump==sqlite3ExprIfFalse && jumpIfNull==0 && regFree1!=0 );\n  testcase( xJump==sqlite3ExprIfFalse && jumpIfNull!=0 && regFree1==0 );\n  testcase( xJump==sqlite3ExprIfFalse && jumpIfNull!=0 && regFree1!=0 );\n  testcase( xJump==0 );\n}\n\n/*\n** Generate code for a boolean expression such that a jump is made\n** to the label \"dest\" if the expression is true but execution\n** continues straight thru if the expression is false.\n**\n** If the expression evaluates to NULL (neither true nor false), then\n** take the jump if the jumpIfNull flag is SQLITE_JUMPIFNULL.\n**\n** This code depends on the fact that certain token values (ex: TK_EQ)\n** are the same as opcode values (ex: OP_Eq) that implement the corresponding\n** operation.  Special comments in vdbe.c and the mkopcodeh.awk script in\n** the make process cause these values to align.  Assert()s in the code\n** below verify that the numbers are aligned correctly.\n*/\nSQLITE_PRIVATE void sqlite3ExprIfTrue(Parse *pParse, Expr *pExpr, int dest, int jumpIfNull){\n  Vdbe *v = pParse->pVdbe;\n  int op = 0;\n  int regFree1 = 0;\n  int regFree2 = 0;\n  int r1, r2;\n\n  assert( jumpIfNull==SQLITE_JUMPIFNULL || jumpIfNull==0 );\n  if( NEVER(v==0) )     return;  /* Existence of VDBE checked by caller */\n  if( NEVER(pExpr==0) ) return;  /* No way this can happen */\n  op = pExpr->op;\n  switch( op ){\n    case TK_AND: {\n      int d2 = sqlite3VdbeMakeLabel(v);\n      testcase( jumpIfNull==0 );\n      sqlite3ExprIfFalse(pParse, pExpr->pLeft, d2,jumpIfNull^SQLITE_JUMPIFNULL);\n      sqlite3ExprCachePush(pParse);\n      sqlite3ExprIfTrue(pParse, pExpr->pRight, dest, jumpIfNull);\n      sqlite3VdbeResolveLabel(v, d2);\n      sqlite3ExprCachePop(pParse);\n      break;\n    }\n    case TK_OR: {\n      testcase( jumpIfNull==0 );\n      sqlite3ExprIfTrue(pParse, pExpr->pLeft, dest, jumpIfNull);\n      sqlite3ExprCachePush(pParse);\n      sqlite3ExprIfTrue(pParse, pExpr->pRight, dest, jumpIfNull);\n      sqlite3ExprCachePop(pParse);\n      break;\n    }\n    case TK_NOT: {\n      testcase( jumpIfNull==0 );\n      sqlite3ExprIfFalse(pParse, pExpr->pLeft, dest, jumpIfNull);\n      break;\n    }\n    case TK_TRUTH: {\n      int isNot;      /* IS NOT TRUE or IS NOT FALSE */\n      int isTrue;     /* IS TRUE or IS NOT TRUE */\n      testcase( jumpIfNull==0 );\n      isNot = pExpr->op2==TK_ISNOT;\n      isTrue = sqlite3ExprTruthValue(pExpr->pRight);\n      testcase( isTrue && isNot );\n      testcase( !isTrue && isNot );\n      if( isTrue ^ isNot ){\n        sqlite3ExprIfTrue(pParse, pExpr->pLeft, dest,\n                          isNot ? SQLITE_JUMPIFNULL : 0);\n      }else{\n        sqlite3ExprIfFalse(pParse, pExpr->pLeft, dest,\n                           isNot ? SQLITE_JUMPIFNULL : 0);\n      }\n      break;\n    }\n    case TK_IS:\n    case TK_ISNOT:\n      testcase( op==TK_IS );\n      testcase( op==TK_ISNOT );\n      op = (op==TK_IS) ? TK_EQ : TK_NE;\n      jumpIfNull = SQLITE_NULLEQ;\n      /* Fall thru */\n    case TK_LT:\n    case TK_LE:\n    case TK_GT:\n    case TK_GE:\n    case TK_NE:\n    case TK_EQ: {\n      if( sqlite3ExprIsVector(pExpr->pLeft) ) goto default_expr;\n      testcase( jumpIfNull==0 );\n      r1 = sqlite3ExprCodeTemp(pParse, pExpr->pLeft, &regFree1);\n      r2 = sqlite3ExprCodeTemp(pParse, pExpr->pRight, &regFree2);\n      codeCompare(pParse, pExpr->pLeft, pExpr->pRight, op,\n                  r1, r2, dest, jumpIfNull);\n      assert(TK_LT==OP_Lt); testcase(op==OP_Lt); VdbeCoverageIf(v,op==OP_Lt);\n      assert(TK_LE==OP_Le); testcase(op==OP_Le); VdbeCoverageIf(v,op==OP_Le);\n      assert(TK_GT==OP_Gt); testcase(op==OP_Gt); VdbeCoverageIf(v,op==OP_Gt);\n      assert(TK_GE==OP_Ge); testcase(op==OP_Ge); VdbeCoverageIf(v,op==OP_Ge);\n      assert(TK_EQ==OP_Eq); testcase(op==OP_Eq);\n      VdbeCoverageIf(v, op==OP_Eq && jumpIfNull==SQLITE_NULLEQ);\n      VdbeCoverageIf(v, op==OP_Eq && jumpIfNull!=SQLITE_NULLEQ);\n      assert(TK_NE==OP_Ne); testcase(op==OP_Ne);\n      VdbeCoverageIf(v, op==OP_Ne && jumpIfNull==SQLITE_NULLEQ);\n      VdbeCoverageIf(v, op==OP_Ne && jumpIfNull!=SQLITE_NULLEQ);\n      testcase( regFree1==0 );\n      testcase( regFree2==0 );\n      break;\n    }\n    case TK_ISNULL:\n    case TK_NOTNULL: {\n      assert( TK_ISNULL==OP_IsNull );   testcase( op==TK_ISNULL );\n      assert( TK_NOTNULL==OP_NotNull ); testcase( op==TK_NOTNULL );\n      r1 = sqlite3ExprCodeTemp(pParse, pExpr->pLeft, &regFree1);\n      sqlite3VdbeAddOp2(v, op, r1, dest);\n      VdbeCoverageIf(v, op==TK_ISNULL);\n      VdbeCoverageIf(v, op==TK_NOTNULL);\n      testcase( regFree1==0 );\n      break;\n    }\n    case TK_BETWEEN: {\n      testcase( jumpIfNull==0 );\n      exprCodeBetween(pParse, pExpr, dest, sqlite3ExprIfTrue, jumpIfNull);\n      break;\n    }\n#ifndef SQLITE_OMIT_SUBQUERY\n    case TK_IN: {\n      int destIfFalse = sqlite3VdbeMakeLabel(v);\n      int destIfNull = jumpIfNull ? dest : destIfFalse;\n      sqlite3ExprCodeIN(pParse, pExpr, destIfFalse, destIfNull);\n      sqlite3VdbeGoto(v, dest);\n      sqlite3VdbeResolveLabel(v, destIfFalse);\n      break;\n    }\n#endif\n    default: {\n    default_expr:\n      if( exprAlwaysTrue(pExpr) ){\n        sqlite3VdbeGoto(v, dest);\n      }else if( exprAlwaysFalse(pExpr) ){\n        /* No-op */\n      }else{\n        r1 = sqlite3ExprCodeTemp(pParse, pExpr, &regFree1);\n        sqlite3VdbeAddOp3(v, OP_If, r1, dest, jumpIfNull!=0);\n        VdbeCoverage(v);\n        testcase( regFree1==0 );\n        testcase( jumpIfNull==0 );\n      }\n      break;\n    }\n  }\n  sqlite3ReleaseTempReg(pParse, regFree1);\n  sqlite3ReleaseTempReg(pParse, regFree2);  \n}\n\n/*\n** Generate code for a boolean expression such that a jump is made\n** to the label \"dest\" if the expression is false but execution\n** continues straight thru if the expression is true.\n**\n** If the expression evaluates to NULL (neither true nor false) then\n** jump if jumpIfNull is SQLITE_JUMPIFNULL or fall through if jumpIfNull\n** is 0.\n*/\nSQLITE_PRIVATE void sqlite3ExprIfFalse(Parse *pParse, Expr *pExpr, int dest, int jumpIfNull){\n  Vdbe *v = pParse->pVdbe;\n  int op = 0;\n  int regFree1 = 0;\n  int regFree2 = 0;\n  int r1, r2;\n\n  assert( jumpIfNull==SQLITE_JUMPIFNULL || jumpIfNull==0 );\n  if( NEVER(v==0) ) return; /* Existence of VDBE checked by caller */\n  if( pExpr==0 )    return;\n\n  /* The value of pExpr->op and op are related as follows:\n  **\n  **       pExpr->op            op\n  **       ---------          ----------\n  **       TK_ISNULL          OP_NotNull\n  **       TK_NOTNULL         OP_IsNull\n  **       TK_NE              OP_Eq\n  **       TK_EQ              OP_Ne\n  **       TK_GT              OP_Le\n  **       TK_LE              OP_Gt\n  **       TK_GE              OP_Lt\n  **       TK_LT              OP_Ge\n  **\n  ** For other values of pExpr->op, op is undefined and unused.\n  ** The value of TK_ and OP_ constants are arranged such that we\n  ** can compute the mapping above using the following expression.\n  ** Assert()s verify that the computation is correct.\n  */\n  op = ((pExpr->op+(TK_ISNULL&1))^1)-(TK_ISNULL&1);\n\n  /* Verify correct alignment of TK_ and OP_ constants\n  */\n  assert( pExpr->op!=TK_ISNULL || op==OP_NotNull );\n  assert( pExpr->op!=TK_NOTNULL || op==OP_IsNull );\n  assert( pExpr->op!=TK_NE || op==OP_Eq );\n  assert( pExpr->op!=TK_EQ || op==OP_Ne );\n  assert( pExpr->op!=TK_LT || op==OP_Ge );\n  assert( pExpr->op!=TK_LE || op==OP_Gt );\n  assert( pExpr->op!=TK_GT || op==OP_Le );\n  assert( pExpr->op!=TK_GE || op==OP_Lt );\n\n  switch( pExpr->op ){\n    case TK_AND: {\n      testcase( jumpIfNull==0 );\n      sqlite3ExprIfFalse(pParse, pExpr->pLeft, dest, jumpIfNull);\n      sqlite3ExprCachePush(pParse);\n      sqlite3ExprIfFalse(pParse, pExpr->pRight, dest, jumpIfNull);\n      sqlite3ExprCachePop(pParse);\n      break;\n    }\n    case TK_OR: {\n      int d2 = sqlite3VdbeMakeLabel(v);\n      testcase( jumpIfNull==0 );\n      sqlite3ExprIfTrue(pParse, pExpr->pLeft, d2, jumpIfNull^SQLITE_JUMPIFNULL);\n      sqlite3ExprCachePush(pParse);\n      sqlite3ExprIfFalse(pParse, pExpr->pRight, dest, jumpIfNull);\n      sqlite3VdbeResolveLabel(v, d2);\n      sqlite3ExprCachePop(pParse);\n      break;\n    }\n    case TK_NOT: {\n      testcase( jumpIfNull==0 );\n      sqlite3ExprIfTrue(pParse, pExpr->pLeft, dest, jumpIfNull);\n      break;\n    }\n    case TK_TRUTH: {\n      int isNot;   /* IS NOT TRUE or IS NOT FALSE */\n      int isTrue;  /* IS TRUE or IS NOT TRUE */\n      testcase( jumpIfNull==0 );\n      isNot = pExpr->op2==TK_ISNOT;\n      isTrue = sqlite3ExprTruthValue(pExpr->pRight);\n      testcase( isTrue && isNot );\n      testcase( !isTrue && isNot );\n      if( isTrue ^ isNot ){\n        /* IS TRUE and IS NOT FALSE */\n        sqlite3ExprIfFalse(pParse, pExpr->pLeft, dest,\n                           isNot ? 0 : SQLITE_JUMPIFNULL);\n\n      }else{\n        /* IS FALSE and IS NOT TRUE */\n        sqlite3ExprIfTrue(pParse, pExpr->pLeft, dest,\n                          isNot ? 0 : SQLITE_JUMPIFNULL);\n      }\n      break;\n    }\n    case TK_IS:\n    case TK_ISNOT:\n      testcase( pExpr->op==TK_IS );\n      testcase( pExpr->op==TK_ISNOT );\n      op = (pExpr->op==TK_IS) ? TK_NE : TK_EQ;\n      jumpIfNull = SQLITE_NULLEQ;\n      /* Fall thru */\n    case TK_LT:\n    case TK_LE:\n    case TK_GT:\n    case TK_GE:\n    case TK_NE:\n    case TK_EQ: {\n      if( sqlite3ExprIsVector(pExpr->pLeft) ) goto default_expr;\n      testcase( jumpIfNull==0 );\n      r1 = sqlite3ExprCodeTemp(pParse, pExpr->pLeft, &regFree1);\n      r2 = sqlite3ExprCodeTemp(pParse, pExpr->pRight, &regFree2);\n      codeCompare(pParse, pExpr->pLeft, pExpr->pRight, op,\n                  r1, r2, dest, jumpIfNull);\n      assert(TK_LT==OP_Lt); testcase(op==OP_Lt); VdbeCoverageIf(v,op==OP_Lt);\n      assert(TK_LE==OP_Le); testcase(op==OP_Le); VdbeCoverageIf(v,op==OP_Le);\n      assert(TK_GT==OP_Gt); testcase(op==OP_Gt); VdbeCoverageIf(v,op==OP_Gt);\n      assert(TK_GE==OP_Ge); testcase(op==OP_Ge); VdbeCoverageIf(v,op==OP_Ge);\n      assert(TK_EQ==OP_Eq); testcase(op==OP_Eq);\n      VdbeCoverageIf(v, op==OP_Eq && jumpIfNull!=SQLITE_NULLEQ);\n      VdbeCoverageIf(v, op==OP_Eq && jumpIfNull==SQLITE_NULLEQ);\n      assert(TK_NE==OP_Ne); testcase(op==OP_Ne);\n      VdbeCoverageIf(v, op==OP_Ne && jumpIfNull!=SQLITE_NULLEQ);\n      VdbeCoverageIf(v, op==OP_Ne && jumpIfNull==SQLITE_NULLEQ);\n      testcase( regFree1==0 );\n      testcase( regFree2==0 );\n      break;\n    }\n    case TK_ISNULL:\n    case TK_NOTNULL: {\n      r1 = sqlite3ExprCodeTemp(pParse, pExpr->pLeft, &regFree1);\n      sqlite3VdbeAddOp2(v, op, r1, dest);\n      testcase( op==TK_ISNULL );   VdbeCoverageIf(v, op==TK_ISNULL);\n      testcase( op==TK_NOTNULL );  VdbeCoverageIf(v, op==TK_NOTNULL);\n      testcase( regFree1==0 );\n      break;\n    }\n    case TK_BETWEEN: {\n      testcase( jumpIfNull==0 );\n      exprCodeBetween(pParse, pExpr, dest, sqlite3ExprIfFalse, jumpIfNull);\n      break;\n    }\n#ifndef SQLITE_OMIT_SUBQUERY\n    case TK_IN: {\n      if( jumpIfNull ){\n        sqlite3ExprCodeIN(pParse, pExpr, dest, dest);\n      }else{\n        int destIfNull = sqlite3VdbeMakeLabel(v);\n        sqlite3ExprCodeIN(pParse, pExpr, dest, destIfNull);\n        sqlite3VdbeResolveLabel(v, destIfNull);\n      }\n      break;\n    }\n#endif\n    default: {\n    default_expr: \n      if( exprAlwaysFalse(pExpr) ){\n        sqlite3VdbeGoto(v, dest);\n      }else if( exprAlwaysTrue(pExpr) ){\n        /* no-op */\n      }else{\n        r1 = sqlite3ExprCodeTemp(pParse, pExpr, &regFree1);\n        sqlite3VdbeAddOp3(v, OP_IfNot, r1, dest, jumpIfNull!=0);\n        VdbeCoverage(v);\n        testcase( regFree1==0 );\n        testcase( jumpIfNull==0 );\n      }\n      break;\n    }\n  }\n  sqlite3ReleaseTempReg(pParse, regFree1);\n  sqlite3ReleaseTempReg(pParse, regFree2);\n}\n\n/*\n** Like sqlite3ExprIfFalse() except that a copy is made of pExpr before\n** code generation, and that copy is deleted after code generation. This\n** ensures that the original pExpr is unchanged.\n*/\nSQLITE_PRIVATE void sqlite3ExprIfFalseDup(Parse *pParse, Expr *pExpr, int dest,int jumpIfNull){\n  sqlite3 *db = pParse->db;\n  Expr *pCopy = sqlite3ExprDup(db, pExpr, 0);\n  if( db->mallocFailed==0 ){\n    sqlite3ExprIfFalse(pParse, pCopy, dest, jumpIfNull);\n  }\n  sqlite3ExprDelete(db, pCopy);\n}\n\n/*\n** Expression pVar is guaranteed to be an SQL variable. pExpr may be any\n** type of expression.\n**\n** If pExpr is a simple SQL value - an integer, real, string, blob\n** or NULL value - then the VDBE currently being prepared is configured\n** to re-prepare each time a new value is bound to variable pVar.\n**\n** Additionally, if pExpr is a simple SQL value and the value is the\n** same as that currently bound to variable pVar, non-zero is returned.\n** Otherwise, if the values are not the same or if pExpr is not a simple\n** SQL value, zero is returned.\n*/\nstatic int exprCompareVariable(Parse *pParse, Expr *pVar, Expr *pExpr){\n  int res = 0;\n  int iVar;\n  sqlite3_value *pL, *pR = 0;\n  \n  sqlite3ValueFromExpr(pParse->db, pExpr, SQLITE_UTF8, SQLITE_AFF_BLOB, &pR);\n  if( pR ){\n    iVar = pVar->iColumn;\n    sqlite3VdbeSetVarmask(pParse->pVdbe, iVar);\n    pL = sqlite3VdbeGetBoundValue(pParse->pReprepare, iVar, SQLITE_AFF_BLOB);\n    if( pL ){\n      if( sqlite3_value_type(pL)==SQLITE_TEXT ){\n        sqlite3_value_text(pL); /* Make sure the encoding is UTF-8 */\n      }\n      res =  0==sqlite3MemCompare(pL, pR, 0);\n    }\n    sqlite3ValueFree(pR);\n    sqlite3ValueFree(pL);\n  }\n\n  return res;\n}\n\n/*\n** Do a deep comparison of two expression trees.  Return 0 if the two\n** expressions are completely identical.  Return 1 if they differ only\n** by a COLLATE operator at the top level.  Return 2 if there are differences\n** other than the top-level COLLATE operator.\n**\n** If any subelement of pB has Expr.iTable==(-1) then it is allowed\n** to compare equal to an equivalent element in pA with Expr.iTable==iTab.\n**\n** The pA side might be using TK_REGISTER.  If that is the case and pB is\n** not using TK_REGISTER but is otherwise equivalent, then still return 0.\n**\n** Sometimes this routine will return 2 even if the two expressions\n** really are equivalent.  If we cannot prove that the expressions are\n** identical, we return 2 just to be safe.  So if this routine\n** returns 2, then you do not really know for certain if the two\n** expressions are the same.  But if you get a 0 or 1 return, then you\n** can be sure the expressions are the same.  In the places where\n** this routine is used, it does not hurt to get an extra 2 - that\n** just might result in some slightly slower code.  But returning\n** an incorrect 0 or 1 could lead to a malfunction.\n**\n** If pParse is not NULL then TK_VARIABLE terms in pA with bindings in\n** pParse->pReprepare can be matched against literals in pB.  The \n** pParse->pVdbe->expmask bitmask is updated for each variable referenced.\n** If pParse is NULL (the normal case) then any TK_VARIABLE term in \n** Argument pParse should normally be NULL. If it is not NULL and pA or\n** pB causes a return value of 2.\n*/\nSQLITE_PRIVATE int sqlite3ExprCompare(Parse *pParse, Expr *pA, Expr *pB, int iTab){\n  u32 combinedFlags;\n  if( pA==0 || pB==0 ){\n    return pB==pA ? 0 : 2;\n  }\n  if( pParse && pA->op==TK_VARIABLE && exprCompareVariable(pParse, pA, pB) ){\n    return 0;\n  }\n  combinedFlags = pA->flags | pB->flags;\n  if( combinedFlags & EP_IntValue ){\n    if( (pA->flags&pB->flags&EP_IntValue)!=0 && pA->u.iValue==pB->u.iValue ){\n      return 0;\n    }\n    return 2;\n  }\n  if( pA->op!=pB->op ){\n    if( pA->op==TK_COLLATE && sqlite3ExprCompare(pParse, pA->pLeft,pB,iTab)<2 ){\n      return 1;\n    }\n    if( pB->op==TK_COLLATE && sqlite3ExprCompare(pParse, pA,pB->pLeft,iTab)<2 ){\n      return 1;\n    }\n    return 2;\n  }\n  if( pA->op!=TK_COLUMN && pA->op!=TK_AGG_COLUMN && pA->u.zToken ){\n    if( pA->op==TK_FUNCTION ){\n      if( sqlite3StrICmp(pA->u.zToken,pB->u.zToken)!=0 ) return 2;\n    }else if( strcmp(pA->u.zToken,pB->u.zToken)!=0 ){\n      return pA->op==TK_COLLATE ? 1 : 2;\n    }\n  }\n  if( (pA->flags & EP_Distinct)!=(pB->flags & EP_Distinct) ) return 2;\n  if( ALWAYS((combinedFlags & EP_TokenOnly)==0) ){\n    if( combinedFlags & EP_xIsSelect ) return 2;\n    if( sqlite3ExprCompare(pParse, pA->pLeft, pB->pLeft, iTab) ) return 2;\n    if( sqlite3ExprCompare(pParse, pA->pRight, pB->pRight, iTab) ) return 2;\n    if( sqlite3ExprListCompare(pA->x.pList, pB->x.pList, iTab) ) return 2;\n    if( ALWAYS((combinedFlags & EP_Reduced)==0) && pA->op!=TK_STRING ){\n      if( pA->iColumn!=pB->iColumn ) return 2;\n      if( pA->iTable!=pB->iTable \n       && (pA->iTable!=iTab || NEVER(pB->iTable>=0)) ) return 2;\n    }\n  }\n  return 0;\n}\n\n/*\n** Compare two ExprList objects.  Return 0 if they are identical and \n** non-zero if they differ in any way.\n**\n** If any subelement of pB has Expr.iTable==(-1) then it is allowed\n** to compare equal to an equivalent element in pA with Expr.iTable==iTab.\n**\n** This routine might return non-zero for equivalent ExprLists.  The\n** only consequence will be disabled optimizations.  But this routine\n** must never return 0 if the two ExprList objects are different, or\n** a malfunction will result.\n**\n** Two NULL pointers are considered to be the same.  But a NULL pointer\n** always differs from a non-NULL pointer.\n*/\nSQLITE_PRIVATE int sqlite3ExprListCompare(ExprList *pA, ExprList *pB, int iTab){\n  int i;\n  if( pA==0 && pB==0 ) return 0;\n  if( pA==0 || pB==0 ) return 1;\n  if( pA->nExpr!=pB->nExpr ) return 1;\n  for(i=0; i<pA->nExpr; i++){\n    Expr *pExprA = pA->a[i].pExpr;\n    Expr *pExprB = pB->a[i].pExpr;\n    if( pA->a[i].sortOrder!=pB->a[i].sortOrder ) return 1;\n    if( sqlite3ExprCompare(0, pExprA, pExprB, iTab) ) return 1;\n  }\n  return 0;\n}\n\n/*\n** Like sqlite3ExprCompare() except COLLATE operators at the top-level\n** are ignored.\n*/\nSQLITE_PRIVATE int sqlite3ExprCompareSkip(Expr *pA, Expr *pB, int iTab){\n  return sqlite3ExprCompare(0,\n             sqlite3ExprSkipCollate(pA),\n             sqlite3ExprSkipCollate(pB),\n             iTab);\n}\n\n/*\n** Return true if we can prove the pE2 will always be true if pE1 is\n** true.  Return false if we cannot complete the proof or if pE2 might\n** be false.  Examples:\n**\n**     pE1: x==5       pE2: x==5             Result: true\n**     pE1: x>0        pE2: x==5             Result: false\n**     pE1: x=21       pE2: x=21 OR y=43     Result: true\n**     pE1: x!=123     pE2: x IS NOT NULL    Result: true\n**     pE1: x!=?1      pE2: x IS NOT NULL    Result: true\n**     pE1: x IS NULL  pE2: x IS NOT NULL    Result: false\n**     pE1: x IS ?2    pE2: x IS NOT NULL    Reuslt: false\n**\n** When comparing TK_COLUMN nodes between pE1 and pE2, if pE2 has\n** Expr.iTable<0 then assume a table number given by iTab.\n**\n** If pParse is not NULL, then the values of bound variables in pE1 are \n** compared against literal values in pE2 and pParse->pVdbe->expmask is\n** modified to record which bound variables are referenced.  If pParse \n** is NULL, then false will be returned if pE1 contains any bound variables.\n**\n** When in doubt, return false.  Returning true might give a performance\n** improvement.  Returning false might cause a performance reduction, but\n** it will always give the correct answer and is hence always safe.\n*/\nSQLITE_PRIVATE int sqlite3ExprImpliesExpr(Parse *pParse, Expr *pE1, Expr *pE2, int iTab){\n  if( sqlite3ExprCompare(pParse, pE1, pE2, iTab)==0 ){\n    return 1;\n  }\n  if( pE2->op==TK_OR\n   && (sqlite3ExprImpliesExpr(pParse, pE1, pE2->pLeft, iTab)\n             || sqlite3ExprImpliesExpr(pParse, pE1, pE2->pRight, iTab) )\n  ){\n    return 1;\n  }\n  if( pE2->op==TK_NOTNULL && pE1->op!=TK_ISNULL && pE1->op!=TK_IS ){\n    Expr *pX = sqlite3ExprSkipCollate(pE1->pLeft);\n    testcase( pX!=pE1->pLeft );\n    if( sqlite3ExprCompare(pParse, pX, pE2->pLeft, iTab)==0 ) return 1;\n  }\n  return 0;\n}\n\n/*\n** An instance of the following structure is used by the tree walker\n** to determine if an expression can be evaluated by reference to the\n** index only, without having to do a search for the corresponding\n** table entry.  The IdxCover.pIdx field is the index.  IdxCover.iCur\n** is the cursor for the table.\n*/\nstruct IdxCover {\n  Index *pIdx;     /* The index to be tested for coverage */\n  int iCur;        /* Cursor number for the table corresponding to the index */\n};\n\n/*\n** Check to see if there are references to columns in table \n** pWalker->u.pIdxCover->iCur can be satisfied using the index\n** pWalker->u.pIdxCover->pIdx.\n*/\nstatic int exprIdxCover(Walker *pWalker, Expr *pExpr){\n  if( pExpr->op==TK_COLUMN\n   && pExpr->iTable==pWalker->u.pIdxCover->iCur\n   && sqlite3ColumnOfIndex(pWalker->u.pIdxCover->pIdx, pExpr->iColumn)<0\n  ){\n    pWalker->eCode = 1;\n    return WRC_Abort;\n  }\n  return WRC_Continue;\n}\n\n/*\n** Determine if an index pIdx on table with cursor iCur contains will\n** the expression pExpr.  Return true if the index does cover the\n** expression and false if the pExpr expression references table columns\n** that are not found in the index pIdx.\n**\n** An index covering an expression means that the expression can be\n** evaluated using only the index and without having to lookup the\n** corresponding table entry.\n*/\nSQLITE_PRIVATE int sqlite3ExprCoveredByIndex(\n  Expr *pExpr,        /* The index to be tested */\n  int iCur,           /* The cursor number for the corresponding table */\n  Index *pIdx         /* The index that might be used for coverage */\n){\n  Walker w;\n  struct IdxCover xcov;\n  memset(&w, 0, sizeof(w));\n  xcov.iCur = iCur;\n  xcov.pIdx = pIdx;\n  w.xExprCallback = exprIdxCover;\n  w.u.pIdxCover = &xcov;\n  sqlite3WalkExpr(&w, pExpr);\n  return !w.eCode;\n}\n\n\n/*\n** An instance of the following structure is used by the tree walker\n** to count references to table columns in the arguments of an \n** aggregate function, in order to implement the\n** sqlite3FunctionThisSrc() routine.\n*/\nstruct SrcCount {\n  SrcList *pSrc;   /* One particular FROM clause in a nested query */\n  int nThis;       /* Number of references to columns in pSrcList */\n  int nOther;      /* Number of references to columns in other FROM clauses */\n};\n\n/*\n** Count the number of references to columns.\n*/\nstatic int exprSrcCount(Walker *pWalker, Expr *pExpr){\n  /* The NEVER() on the second term is because sqlite3FunctionUsesThisSrc()\n  ** is always called before sqlite3ExprAnalyzeAggregates() and so the\n  ** TK_COLUMNs have not yet been converted into TK_AGG_COLUMN.  If\n  ** sqlite3FunctionUsesThisSrc() is used differently in the future, the\n  ** NEVER() will need to be removed. */\n  if( pExpr->op==TK_COLUMN || NEVER(pExpr->op==TK_AGG_COLUMN) ){\n    int i;\n    struct SrcCount *p = pWalker->u.pSrcCount;\n    SrcList *pSrc = p->pSrc;\n    int nSrc = pSrc ? pSrc->nSrc : 0;\n    for(i=0; i<nSrc; i++){\n      if( pExpr->iTable==pSrc->a[i].iCursor ) break;\n    }\n    if( i<nSrc ){\n      p->nThis++;\n    }else{\n      p->nOther++;\n    }\n  }\n  return WRC_Continue;\n}\n\n/*\n** Determine if any of the arguments to the pExpr Function reference\n** pSrcList.  Return true if they do.  Also return true if the function\n** has no arguments or has only constant arguments.  Return false if pExpr\n** references columns but not columns of tables found in pSrcList.\n*/\nSQLITE_PRIVATE int sqlite3FunctionUsesThisSrc(Expr *pExpr, SrcList *pSrcList){\n  Walker w;\n  struct SrcCount cnt;\n  assert( pExpr->op==TK_AGG_FUNCTION );\n  w.xExprCallback = exprSrcCount;\n  w.xSelectCallback = 0;\n  w.u.pSrcCount = &cnt;\n  cnt.pSrc = pSrcList;\n  cnt.nThis = 0;\n  cnt.nOther = 0;\n  sqlite3WalkExprList(&w, pExpr->x.pList);\n  return cnt.nThis>0 || cnt.nOther==0;\n}\n\n/*\n** Add a new element to the pAggInfo->aCol[] array.  Return the index of\n** the new element.  Return a negative number if malloc fails.\n*/\nstatic int addAggInfoColumn(sqlite3 *db, AggInfo *pInfo){\n  int i;\n  pInfo->aCol = sqlite3ArrayAllocate(\n       db,\n       pInfo->aCol,\n       sizeof(pInfo->aCol[0]),\n       &pInfo->nColumn,\n       &i\n  );\n  return i;\n}    \n\n/*\n** Add a new element to the pAggInfo->aFunc[] array.  Return the index of\n** the new element.  Return a negative number if malloc fails.\n*/\nstatic int addAggInfoFunc(sqlite3 *db, AggInfo *pInfo){\n  int i;\n  pInfo->aFunc = sqlite3ArrayAllocate(\n       db, \n       pInfo->aFunc,\n       sizeof(pInfo->aFunc[0]),\n       &pInfo->nFunc,\n       &i\n  );\n  return i;\n}    \n\n/*\n** This is the xExprCallback for a tree walker.  It is used to\n** implement sqlite3ExprAnalyzeAggregates().  See sqlite3ExprAnalyzeAggregates\n** for additional information.\n*/\nstatic int analyzeAggregate(Walker *pWalker, Expr *pExpr){\n  int i;\n  NameContext *pNC = pWalker->u.pNC;\n  Parse *pParse = pNC->pParse;\n  SrcList *pSrcList = pNC->pSrcList;\n  AggInfo *pAggInfo = pNC->pAggInfo;\n\n  switch( pExpr->op ){\n    case TK_AGG_COLUMN:\n    case TK_COLUMN: {\n      testcase( pExpr->op==TK_AGG_COLUMN );\n      testcase( pExpr->op==TK_COLUMN );\n      /* Check to see if the column is in one of the tables in the FROM\n      ** clause of the aggregate query */\n      if( ALWAYS(pSrcList!=0) ){\n        struct SrcList_item *pItem = pSrcList->a;\n        for(i=0; i<pSrcList->nSrc; i++, pItem++){\n          struct AggInfo_col *pCol;\n          assert( !ExprHasProperty(pExpr, EP_TokenOnly|EP_Reduced) );\n          if( pExpr->iTable==pItem->iCursor ){\n            /* If we reach this point, it means that pExpr refers to a table\n            ** that is in the FROM clause of the aggregate query.  \n            **\n            ** Make an entry for the column in pAggInfo->aCol[] if there\n            ** is not an entry there already.\n            */\n            int k;\n            pCol = pAggInfo->aCol;\n            for(k=0; k<pAggInfo->nColumn; k++, pCol++){\n              if( pCol->iTable==pExpr->iTable &&\n                  pCol->iColumn==pExpr->iColumn ){\n                break;\n              }\n            }\n            if( (k>=pAggInfo->nColumn)\n             && (k = addAggInfoColumn(pParse->db, pAggInfo))>=0 \n            ){\n              pCol = &pAggInfo->aCol[k];\n              pCol->pTab = pExpr->pTab;\n              pCol->iTable = pExpr->iTable;\n              pCol->iColumn = pExpr->iColumn;\n              pCol->iMem = ++pParse->nMem;\n              pCol->iSorterColumn = -1;\n              pCol->pExpr = pExpr;\n              if( pAggInfo->pGroupBy ){\n                int j, n;\n                ExprList *pGB = pAggInfo->pGroupBy;\n                struct ExprList_item *pTerm = pGB->a;\n                n = pGB->nExpr;\n                for(j=0; j<n; j++, pTerm++){\n                  Expr *pE = pTerm->pExpr;\n                  if( pE->op==TK_COLUMN && pE->iTable==pExpr->iTable &&\n                      pE->iColumn==pExpr->iColumn ){\n                    pCol->iSorterColumn = j;\n                    break;\n                  }\n                }\n              }\n              if( pCol->iSorterColumn<0 ){\n                pCol->iSorterColumn = pAggInfo->nSortingColumn++;\n              }\n            }\n            /* There is now an entry for pExpr in pAggInfo->aCol[] (either\n            ** because it was there before or because we just created it).\n            ** Convert the pExpr to be a TK_AGG_COLUMN referring to that\n            ** pAggInfo->aCol[] entry.\n            */\n            ExprSetVVAProperty(pExpr, EP_NoReduce);\n            pExpr->pAggInfo = pAggInfo;\n            pExpr->op = TK_AGG_COLUMN;\n            pExpr->iAgg = (i16)k;\n            break;\n          } /* endif pExpr->iTable==pItem->iCursor */\n        } /* end loop over pSrcList */\n      }\n      return WRC_Prune;\n    }\n    case TK_AGG_FUNCTION: {\n      if( (pNC->ncFlags & NC_InAggFunc)==0\n       && pWalker->walkerDepth==pExpr->op2\n      ){\n        /* Check to see if pExpr is a duplicate of another aggregate \n        ** function that is already in the pAggInfo structure\n        */\n        struct AggInfo_func *pItem = pAggInfo->aFunc;\n        for(i=0; i<pAggInfo->nFunc; i++, pItem++){\n          if( sqlite3ExprCompare(0, pItem->pExpr, pExpr, -1)==0 ){\n            break;\n          }\n        }\n        if( i>=pAggInfo->nFunc ){\n          /* pExpr is original.  Make a new entry in pAggInfo->aFunc[]\n          */\n          u8 enc = ENC(pParse->db);\n          i = addAggInfoFunc(pParse->db, pAggInfo);\n          if( i>=0 ){\n            assert( !ExprHasProperty(pExpr, EP_xIsSelect) );\n            pItem = &pAggInfo->aFunc[i];\n            pItem->pExpr = pExpr;\n            pItem->iMem = ++pParse->nMem;\n            assert( !ExprHasProperty(pExpr, EP_IntValue) );\n            pItem->pFunc = sqlite3FindFunction(pParse->db,\n                   pExpr->u.zToken, \n                   pExpr->x.pList ? pExpr->x.pList->nExpr : 0, enc, 0);\n            if( pExpr->flags & EP_Distinct ){\n              pItem->iDistinct = pParse->nTab++;\n            }else{\n              pItem->iDistinct = -1;\n            }\n          }\n        }\n        /* Make pExpr point to the appropriate pAggInfo->aFunc[] entry\n        */\n        assert( !ExprHasProperty(pExpr, EP_TokenOnly|EP_Reduced) );\n        ExprSetVVAProperty(pExpr, EP_NoReduce);\n        pExpr->iAgg = (i16)i;\n        pExpr->pAggInfo = pAggInfo;\n        return WRC_Prune;\n      }else{\n        return WRC_Continue;\n      }\n    }\n  }\n  return WRC_Continue;\n}\nstatic int analyzeAggregatesInSelect(Walker *pWalker, Select *pSelect){\n  UNUSED_PARAMETER(pSelect);\n  pWalker->walkerDepth++;\n  return WRC_Continue;\n}\nstatic void analyzeAggregatesInSelectEnd(Walker *pWalker, Select *pSelect){\n  UNUSED_PARAMETER(pSelect);\n  pWalker->walkerDepth--;\n}\n\n/*\n** Analyze the pExpr expression looking for aggregate functions and\n** for variables that need to be added to AggInfo object that pNC->pAggInfo\n** points to.  Additional entries are made on the AggInfo object as\n** necessary.\n**\n** This routine should only be called after the expression has been\n** analyzed by sqlite3ResolveExprNames().\n*/\nSQLITE_PRIVATE void sqlite3ExprAnalyzeAggregates(NameContext *pNC, Expr *pExpr){\n  Walker w;\n  w.xExprCallback = analyzeAggregate;\n  w.xSelectCallback = analyzeAggregatesInSelect;\n  w.xSelectCallback2 = analyzeAggregatesInSelectEnd;\n  w.walkerDepth = 0;\n  w.u.pNC = pNC;\n  assert( pNC->pSrcList!=0 );\n  sqlite3WalkExpr(&w, pExpr);\n}\n\n/*\n** Call sqlite3ExprAnalyzeAggregates() for every expression in an\n** expression list.  Return the number of errors.\n**\n** If an error is found, the analysis is cut short.\n*/\nSQLITE_PRIVATE void sqlite3ExprAnalyzeAggList(NameContext *pNC, ExprList *pList){\n  struct ExprList_item *pItem;\n  int i;\n  if( pList ){\n    for(pItem=pList->a, i=0; i<pList->nExpr; i++, pItem++){\n      sqlite3ExprAnalyzeAggregates(pNC, pItem->pExpr);\n    }\n  }\n}\n\n/*\n** Allocate a single new register for use to hold some intermediate result.\n*/\nSQLITE_PRIVATE int sqlite3GetTempReg(Parse *pParse){\n  if( pParse->nTempReg==0 ){\n    return ++pParse->nMem;\n  }\n  return pParse->aTempReg[--pParse->nTempReg];\n}\n\n/*\n** Deallocate a register, making available for reuse for some other\n** purpose.\n**\n** If a register is currently being used by the column cache, then\n** the deallocation is deferred until the column cache line that uses\n** the register becomes stale.\n*/\nSQLITE_PRIVATE void sqlite3ReleaseTempReg(Parse *pParse, int iReg){\n  if( iReg && pParse->nTempReg<ArraySize(pParse->aTempReg) ){\n    int i;\n    struct yColCache *p;\n    for(i=0, p=pParse->aColCache; i<pParse->nColCache; i++, p++){\n      if( p->iReg==iReg ){\n        p->tempReg = 1;\n        return;\n      }\n    }\n    pParse->aTempReg[pParse->nTempReg++] = iReg;\n  }\n}\n\n/*\n** Allocate or deallocate a block of nReg consecutive registers.\n*/\nSQLITE_PRIVATE int sqlite3GetTempRange(Parse *pParse, int nReg){\n  int i, n;\n  if( nReg==1 ) return sqlite3GetTempReg(pParse);\n  i = pParse->iRangeReg;\n  n = pParse->nRangeReg;\n  if( nReg<=n ){\n    assert( !usedAsColumnCache(pParse, i, i+n-1) );\n    pParse->iRangeReg += nReg;\n    pParse->nRangeReg -= nReg;\n  }else{\n    i = pParse->nMem+1;\n    pParse->nMem += nReg;\n  }\n  return i;\n}\nSQLITE_PRIVATE void sqlite3ReleaseTempRange(Parse *pParse, int iReg, int nReg){\n  if( nReg==1 ){\n    sqlite3ReleaseTempReg(pParse, iReg);\n    return;\n  }\n  sqlite3ExprCacheRemove(pParse, iReg, nReg);\n  if( nReg>pParse->nRangeReg ){\n    pParse->nRangeReg = nReg;\n    pParse->iRangeReg = iReg;\n  }\n}\n\n/*\n** Mark all temporary registers as being unavailable for reuse.\n*/\nSQLITE_PRIVATE void sqlite3ClearTempRegCache(Parse *pParse){\n  pParse->nTempReg = 0;\n  pParse->nRangeReg = 0;\n}\n\n/*\n** Validate that no temporary register falls within the range of\n** iFirst..iLast, inclusive.  This routine is only call from within assert()\n** statements.\n*/\n#ifdef SQLITE_DEBUG\nSQLITE_PRIVATE int sqlite3NoTempsInRange(Parse *pParse, int iFirst, int iLast){\n  int i;\n  if( pParse->nRangeReg>0\n   && pParse->iRangeReg+pParse->nRangeReg > iFirst\n   && pParse->iRangeReg <= iLast\n  ){\n     return 0;\n  }\n  for(i=0; i<pParse->nTempReg; i++){\n    if( pParse->aTempReg[i]>=iFirst && pParse->aTempReg[i]<=iLast ){\n      return 0;\n    }\n  }\n  return 1;\n}\n#endif /* SQLITE_DEBUG */\n\n/************** End of expr.c ************************************************/\n/************** Begin file alter.c *******************************************/\n/*\n** 2005 February 15\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n*************************************************************************\n** This file contains C code routines that used to generate VDBE code\n** that implements the ALTER TABLE command.\n*/\n/* #include \"sqliteInt.h\" */\n\n/*\n** The code in this file only exists if we are not omitting the\n** ALTER TABLE logic from the build.\n*/\n#ifndef SQLITE_OMIT_ALTERTABLE\n\n\n/*\n** This function is used by SQL generated to implement the \n** ALTER TABLE command. The first argument is the text of a CREATE TABLE or\n** CREATE INDEX command. The second is a table name. The table name in \n** the CREATE TABLE or CREATE INDEX statement is replaced with the third\n** argument and the result returned. Examples:\n**\n** sqlite_rename_table('CREATE TABLE abc(a, b, c)', 'def')\n**     -> 'CREATE TABLE def(a, b, c)'\n**\n** sqlite_rename_table('CREATE INDEX i ON abc(a)', 'def')\n**     -> 'CREATE INDEX i ON def(a, b, c)'\n*/\nstatic void renameTableFunc(\n  sqlite3_context *context,\n  int NotUsed,\n  sqlite3_value **argv\n){\n  unsigned char const *zSql = sqlite3_value_text(argv[0]);\n  unsigned char const *zTableName = sqlite3_value_text(argv[1]);\n\n  int token;\n  Token tname;\n  unsigned char const *zCsr = zSql;\n  int len = 0;\n  char *zRet;\n\n  sqlite3 *db = sqlite3_context_db_handle(context);\n\n  UNUSED_PARAMETER(NotUsed);\n\n  /* The principle used to locate the table name in the CREATE TABLE \n  ** statement is that the table name is the first non-space token that\n  ** is immediately followed by a TK_LP or TK_USING token.\n  */\n  if( zSql ){\n    do {\n      if( !*zCsr ){\n        /* Ran out of input before finding an opening bracket. Return NULL. */\n        return;\n      }\n\n      /* Store the token that zCsr points to in tname. */\n      tname.z = (char*)zCsr;\n      tname.n = len;\n\n      /* Advance zCsr to the next token. Store that token type in 'token',\n      ** and its length in 'len' (to be used next iteration of this loop).\n      */\n      do {\n        zCsr += len;\n        len = sqlite3GetToken(zCsr, &token);\n      } while( token==TK_SPACE );\n      assert( len>0 );\n    } while( token!=TK_LP && token!=TK_USING );\n\n    zRet = sqlite3MPrintf(db, \"%.*s\\\"%w\\\"%s\", (int)(((u8*)tname.z) - zSql),\n       zSql, zTableName, tname.z+tname.n);\n    sqlite3_result_text(context, zRet, -1, SQLITE_DYNAMIC);\n  }\n}\n\n/*\n** This C function implements an SQL user function that is used by SQL code\n** generated by the ALTER TABLE ... RENAME command to modify the definition\n** of any foreign key constraints that use the table being renamed as the \n** parent table. It is passed three arguments:\n**\n**   1) The complete text of the CREATE TABLE statement being modified,\n**   2) The old name of the table being renamed, and\n**   3) The new name of the table being renamed.\n**\n** It returns the new CREATE TABLE statement. For example:\n**\n**   sqlite_rename_parent('CREATE TABLE t1(a REFERENCES t2)', 't2', 't3')\n**       -> 'CREATE TABLE t1(a REFERENCES t3)'\n*/\n#ifndef SQLITE_OMIT_FOREIGN_KEY\nstatic void renameParentFunc(\n  sqlite3_context *context,\n  int NotUsed,\n  sqlite3_value **argv\n){\n  sqlite3 *db = sqlite3_context_db_handle(context);\n  char *zOutput = 0;\n  char *zResult;\n  unsigned char const *zInput = sqlite3_value_text(argv[0]);\n  unsigned char const *zOld = sqlite3_value_text(argv[1]);\n  unsigned char const *zNew = sqlite3_value_text(argv[2]);\n\n  unsigned const char *z;         /* Pointer to token */\n  int n;                          /* Length of token z */\n  int token;                      /* Type of token */\n\n  UNUSED_PARAMETER(NotUsed);\n  if( zInput==0 || zOld==0 ) return;\n  for(z=zInput; *z; z=z+n){\n    n = sqlite3GetToken(z, &token);\n    if( token==TK_REFERENCES ){\n      char *zParent;\n      do {\n        z += n;\n        n = sqlite3GetToken(z, &token);\n      }while( token==TK_SPACE );\n\n      if( token==TK_ILLEGAL ) break;\n      zParent = sqlite3DbStrNDup(db, (const char *)z, n);\n      if( zParent==0 ) break;\n      sqlite3Dequote(zParent);\n      if( 0==sqlite3StrICmp((const char *)zOld, zParent) ){\n        char *zOut = sqlite3MPrintf(db, \"%s%.*s\\\"%w\\\"\", \n            (zOutput?zOutput:\"\"), (int)(z-zInput), zInput, (const char *)zNew\n        );\n        sqlite3DbFree(db, zOutput);\n        zOutput = zOut;\n        zInput = &z[n];\n      }\n      sqlite3DbFree(db, zParent);\n    }\n  }\n\n  zResult = sqlite3MPrintf(db, \"%s%s\", (zOutput?zOutput:\"\"), zInput), \n  sqlite3_result_text(context, zResult, -1, SQLITE_DYNAMIC);\n  sqlite3DbFree(db, zOutput);\n}\n#endif\n\n#ifndef SQLITE_OMIT_TRIGGER\n/* This function is used by SQL generated to implement the\n** ALTER TABLE command. The first argument is the text of a CREATE TRIGGER \n** statement. The second is a table name. The table name in the CREATE \n** TRIGGER statement is replaced with the third argument and the result \n** returned. This is analagous to renameTableFunc() above, except for CREATE\n** TRIGGER, not CREATE INDEX and CREATE TABLE.\n*/\nstatic void renameTriggerFunc(\n  sqlite3_context *context,\n  int NotUsed,\n  sqlite3_value **argv\n){\n  unsigned char const *zSql = sqlite3_value_text(argv[0]);\n  unsigned char const *zTableName = sqlite3_value_text(argv[1]);\n\n  int token;\n  Token tname;\n  int dist = 3;\n  unsigned char const *zCsr = zSql;\n  int len = 0;\n  char *zRet;\n  sqlite3 *db = sqlite3_context_db_handle(context);\n\n  UNUSED_PARAMETER(NotUsed);\n\n  /* The principle used to locate the table name in the CREATE TRIGGER \n  ** statement is that the table name is the first token that is immediately\n  ** preceded by either TK_ON or TK_DOT and immediately followed by one\n  ** of TK_WHEN, TK_BEGIN or TK_FOR.\n  */\n  if( zSql ){\n    do {\n\n      if( !*zCsr ){\n        /* Ran out of input before finding the table name. Return NULL. */\n        return;\n      }\n\n      /* Store the token that zCsr points to in tname. */\n      tname.z = (char*)zCsr;\n      tname.n = len;\n\n      /* Advance zCsr to the next token. Store that token type in 'token',\n      ** and its length in 'len' (to be used next iteration of this loop).\n      */\n      do {\n        zCsr += len;\n        len = sqlite3GetToken(zCsr, &token);\n      }while( token==TK_SPACE );\n      assert( len>0 );\n\n      /* Variable 'dist' stores the number of tokens read since the most\n      ** recent TK_DOT or TK_ON. This means that when a WHEN, FOR or BEGIN \n      ** token is read and 'dist' equals 2, the condition stated above\n      ** to be met.\n      **\n      ** Note that ON cannot be a database, table or column name, so\n      ** there is no need to worry about syntax like \n      ** \"CREATE TRIGGER ... ON ON.ON BEGIN ...\" etc.\n      */\n      dist++;\n      if( token==TK_DOT || token==TK_ON ){\n        dist = 0;\n      }\n    } while( dist!=2 || (token!=TK_WHEN && token!=TK_FOR && token!=TK_BEGIN) );\n\n    /* Variable tname now contains the token that is the old table-name\n    ** in the CREATE TRIGGER statement.\n    */\n    zRet = sqlite3MPrintf(db, \"%.*s\\\"%w\\\"%s\", (int)(((u8*)tname.z) - zSql),\n       zSql, zTableName, tname.z+tname.n);\n    sqlite3_result_text(context, zRet, -1, SQLITE_DYNAMIC);\n  }\n}\n#endif   /* !SQLITE_OMIT_TRIGGER */\n\n/*\n** Register built-in functions used to help implement ALTER TABLE\n*/\nSQLITE_PRIVATE void sqlite3AlterFunctions(void){\n  static FuncDef aAlterTableFuncs[] = {\n    FUNCTION(sqlite_rename_table,   2, 0, 0, renameTableFunc),\n#ifndef SQLITE_OMIT_TRIGGER\n    FUNCTION(sqlite_rename_trigger, 2, 0, 0, renameTriggerFunc),\n#endif\n#ifndef SQLITE_OMIT_FOREIGN_KEY\n    FUNCTION(sqlite_rename_parent,  3, 0, 0, renameParentFunc),\n#endif\n  };\n  sqlite3InsertBuiltinFuncs(aAlterTableFuncs, ArraySize(aAlterTableFuncs));\n}\n\n/*\n** This function is used to create the text of expressions of the form:\n**\n**   name=<constant1> OR name=<constant2> OR ...\n**\n** If argument zWhere is NULL, then a pointer string containing the text \n** \"name=<constant>\" is returned, where <constant> is the quoted version\n** of the string passed as argument zConstant. The returned buffer is\n** allocated using sqlite3DbMalloc(). It is the responsibility of the\n** caller to ensure that it is eventually freed.\n**\n** If argument zWhere is not NULL, then the string returned is \n** \"<where> OR name=<constant>\", where <where> is the contents of zWhere.\n** In this case zWhere is passed to sqlite3DbFree() before returning.\n** \n*/\nstatic char *whereOrName(sqlite3 *db, char *zWhere, char *zConstant){\n  char *zNew;\n  if( !zWhere ){\n    zNew = sqlite3MPrintf(db, \"name=%Q\", zConstant);\n  }else{\n    zNew = sqlite3MPrintf(db, \"%s OR name=%Q\", zWhere, zConstant);\n    sqlite3DbFree(db, zWhere);\n  }\n  return zNew;\n}\n\n#if !defined(SQLITE_OMIT_FOREIGN_KEY) && !defined(SQLITE_OMIT_TRIGGER)\n/*\n** Generate the text of a WHERE expression which can be used to select all\n** tables that have foreign key constraints that refer to table pTab (i.e.\n** constraints for which pTab is the parent table) from the sqlite_master\n** table.\n*/\nstatic char *whereForeignKeys(Parse *pParse, Table *pTab){\n  FKey *p;\n  char *zWhere = 0;\n  for(p=sqlite3FkReferences(pTab); p; p=p->pNextTo){\n    zWhere = whereOrName(pParse->db, zWhere, p->pFrom->zName);\n  }\n  return zWhere;\n}\n#endif\n\n/*\n** Generate the text of a WHERE expression which can be used to select all\n** temporary triggers on table pTab from the sqlite_temp_master table. If\n** table pTab has no temporary triggers, or is itself stored in the \n** temporary database, NULL is returned.\n*/\nstatic char *whereTempTriggers(Parse *pParse, Table *pTab){\n  Trigger *pTrig;\n  char *zWhere = 0;\n  const Schema *pTempSchema = pParse->db->aDb[1].pSchema; /* Temp db schema */\n\n  /* If the table is not located in the temp-db (in which case NULL is \n  ** returned, loop through the tables list of triggers. For each trigger\n  ** that is not part of the temp-db schema, add a clause to the WHERE \n  ** expression being built up in zWhere.\n  */\n  if( pTab->pSchema!=pTempSchema ){\n    sqlite3 *db = pParse->db;\n    for(pTrig=sqlite3TriggerList(pParse, pTab); pTrig; pTrig=pTrig->pNext){\n      if( pTrig->pSchema==pTempSchema ){\n        zWhere = whereOrName(db, zWhere, pTrig->zName);\n      }\n    }\n  }\n  if( zWhere ){\n    char *zNew = sqlite3MPrintf(pParse->db, \"type='trigger' AND (%s)\", zWhere);\n    sqlite3DbFree(pParse->db, zWhere);\n    zWhere = zNew;\n  }\n  return zWhere;\n}\n\n/*\n** Generate code to drop and reload the internal representation of table\n** pTab from the database, including triggers and temporary triggers.\n** Argument zName is the name of the table in the database schema at\n** the time the generated code is executed. This can be different from\n** pTab->zName if this function is being called to code part of an \n** \"ALTER TABLE RENAME TO\" statement.\n*/\nstatic void reloadTableSchema(Parse *pParse, Table *pTab, const char *zName){\n  Vdbe *v;\n  char *zWhere;\n  int iDb;                   /* Index of database containing pTab */\n#ifndef SQLITE_OMIT_TRIGGER\n  Trigger *pTrig;\n#endif\n\n  v = sqlite3GetVdbe(pParse);\n  if( NEVER(v==0) ) return;\n  assert( sqlite3BtreeHoldsAllMutexes(pParse->db) );\n  iDb = sqlite3SchemaToIndex(pParse->db, pTab->pSchema);\n  assert( iDb>=0 );\n\n#ifndef SQLITE_OMIT_TRIGGER\n  /* Drop any table triggers from the internal schema. */\n  for(pTrig=sqlite3TriggerList(pParse, pTab); pTrig; pTrig=pTrig->pNext){\n    int iTrigDb = sqlite3SchemaToIndex(pParse->db, pTrig->pSchema);\n    assert( iTrigDb==iDb || iTrigDb==1 );\n    sqlite3VdbeAddOp4(v, OP_DropTrigger, iTrigDb, 0, 0, pTrig->zName, 0);\n  }\n#endif\n\n  /* Drop the table and index from the internal schema.  */\n  sqlite3VdbeAddOp4(v, OP_DropTable, iDb, 0, 0, pTab->zName, 0);\n\n  /* Reload the table, index and permanent trigger schemas. */\n  zWhere = sqlite3MPrintf(pParse->db, \"tbl_name=%Q\", zName);\n  if( !zWhere ) return;\n  sqlite3VdbeAddParseSchemaOp(v, iDb, zWhere);\n\n#ifndef SQLITE_OMIT_TRIGGER\n  /* Now, if the table is not stored in the temp database, reload any temp \n  ** triggers. Don't use IN(...) in case SQLITE_OMIT_SUBQUERY is defined. \n  */\n  if( (zWhere=whereTempTriggers(pParse, pTab))!=0 ){\n    sqlite3VdbeAddParseSchemaOp(v, 1, zWhere);\n  }\n#endif\n}\n\n/*\n** Parameter zName is the name of a table that is about to be altered\n** (either with ALTER TABLE ... RENAME TO or ALTER TABLE ... ADD COLUMN).\n** If the table is a system table, this function leaves an error message\n** in pParse->zErr (system tables may not be altered) and returns non-zero.\n**\n** Or, if zName is not a system table, zero is returned.\n*/\nstatic int isSystemTable(Parse *pParse, const char *zName){\n  if( 0==sqlite3StrNICmp(zName, \"sqlite_\", 7) ){\n    sqlite3ErrorMsg(pParse, \"table %s may not be altered\", zName);\n    return 1;\n  }\n  return 0;\n}\n\n/*\n** Generate code to implement the \"ALTER TABLE xxx RENAME TO yyy\" \n** command. \n*/\nSQLITE_PRIVATE void sqlite3AlterRenameTable(\n  Parse *pParse,            /* Parser context. */\n  SrcList *pSrc,            /* The table to rename. */\n  Token *pName              /* The new table name. */\n){\n  int iDb;                  /* Database that contains the table */\n  char *zDb;                /* Name of database iDb */\n  Table *pTab;              /* Table being renamed */\n  char *zName = 0;          /* NULL-terminated version of pName */ \n  sqlite3 *db = pParse->db; /* Database connection */\n  int nTabName;             /* Number of UTF-8 characters in zTabName */\n  const char *zTabName;     /* Original name of the table */\n  Vdbe *v;\n#ifndef SQLITE_OMIT_TRIGGER\n  char *zWhere = 0;         /* Where clause to locate temp triggers */\n#endif\n  VTable *pVTab = 0;        /* Non-zero if this is a v-tab with an xRename() */\n  u32 savedDbFlags;         /* Saved value of db->mDbFlags */\n\n  savedDbFlags = db->mDbFlags;  \n  if( NEVER(db->mallocFailed) ) goto exit_rename_table;\n  assert( pSrc->nSrc==1 );\n  assert( sqlite3BtreeHoldsAllMutexes(pParse->db) );\n\n  pTab = sqlite3LocateTableItem(pParse, 0, &pSrc->a[0]);\n  if( !pTab ) goto exit_rename_table;\n  iDb = sqlite3SchemaToIndex(pParse->db, pTab->pSchema);\n  zDb = db->aDb[iDb].zDbSName;\n  db->mDbFlags |= DBFLAG_PreferBuiltin;\n\n  /* Get a NULL terminated version of the new table name. */\n  zName = sqlite3NameFromToken(db, pName);\n  if( !zName ) goto exit_rename_table;\n\n  /* Check that a table or index named 'zName' does not already exist\n  ** in database iDb. If so, this is an error.\n  */\n  if( sqlite3FindTable(db, zName, zDb) || sqlite3FindIndex(db, zName, zDb) ){\n    sqlite3ErrorMsg(pParse, \n        \"there is already another table or index with this name: %s\", zName);\n    goto exit_rename_table;\n  }\n\n  /* Make sure it is not a system table being altered, or a reserved name\n  ** that the table is being renamed to.\n  */\n  if( SQLITE_OK!=isSystemTable(pParse, pTab->zName) ){\n    goto exit_rename_table;\n  }\n  if( SQLITE_OK!=sqlite3CheckObjectName(pParse, zName) ){ goto\n    exit_rename_table;\n  }\n\n#ifndef SQLITE_OMIT_VIEW\n  if( pTab->pSelect ){\n    sqlite3ErrorMsg(pParse, \"view %s may not be altered\", pTab->zName);\n    goto exit_rename_table;\n  }\n#endif\n\n#ifndef SQLITE_OMIT_AUTHORIZATION\n  /* Invoke the authorization callback. */\n  if( sqlite3AuthCheck(pParse, SQLITE_ALTER_TABLE, zDb, pTab->zName, 0) ){\n    goto exit_rename_table;\n  }\n#endif\n\n#ifndef SQLITE_OMIT_VIRTUALTABLE\n  if( sqlite3ViewGetColumnNames(pParse, pTab) ){\n    goto exit_rename_table;\n  }\n  if( IsVirtual(pTab) ){\n    pVTab = sqlite3GetVTable(db, pTab);\n    if( pVTab->pVtab->pModule->xRename==0 ){\n      pVTab = 0;\n    }\n  }\n#endif\n\n  /* Begin a transaction for database iDb. \n  ** Then modify the schema cookie (since the ALTER TABLE modifies the\n  ** schema). Open a statement transaction if the table is a virtual\n  ** table.\n  */\n  v = sqlite3GetVdbe(pParse);\n  if( v==0 ){\n    goto exit_rename_table;\n  }\n  sqlite3BeginWriteOperation(pParse, pVTab!=0, iDb);\n  sqlite3ChangeCookie(pParse, iDb);\n\n  /* If this is a virtual table, invoke the xRename() function if\n  ** one is defined. The xRename() callback will modify the names\n  ** of any resources used by the v-table implementation (including other\n  ** SQLite tables) that are identified by the name of the virtual table.\n  */\n#ifndef SQLITE_OMIT_VIRTUALTABLE\n  if( pVTab ){\n    int i = ++pParse->nMem;\n    sqlite3VdbeLoadString(v, i, zName);\n    sqlite3VdbeAddOp4(v, OP_VRename, i, 0, 0,(const char*)pVTab, P4_VTAB);\n    sqlite3MayAbort(pParse);\n  }\n#endif\n\n  /* figure out how many UTF-8 characters are in zName */\n  zTabName = pTab->zName;\n  nTabName = sqlite3Utf8CharLen(zTabName, -1);\n\n#if !defined(SQLITE_OMIT_FOREIGN_KEY) && !defined(SQLITE_OMIT_TRIGGER)\n  if( db->flags&SQLITE_ForeignKeys ){\n    /* If foreign-key support is enabled, rewrite the CREATE TABLE \n    ** statements corresponding to all child tables of foreign key constraints\n    ** for which the renamed table is the parent table.  */\n    if( (zWhere=whereForeignKeys(pParse, pTab))!=0 ){\n      sqlite3NestedParse(pParse, \n          \"UPDATE \\\"%w\\\".%s SET \"\n              \"sql = sqlite_rename_parent(sql, %Q, %Q) \"\n              \"WHERE %s;\", zDb, MASTER_NAME, zTabName, zName, zWhere);\n      sqlite3DbFree(db, zWhere);\n    }\n  }\n#endif\n\n  /* Modify the sqlite_master table to use the new table name. */\n  sqlite3NestedParse(pParse,\n      \"UPDATE %Q.%s SET \"\n#ifdef SQLITE_OMIT_TRIGGER\n          \"sql = sqlite_rename_table(sql, %Q), \"\n#else\n          \"sql = CASE \"\n            \"WHEN type = 'trigger' THEN sqlite_rename_trigger(sql, %Q)\"\n            \"ELSE sqlite_rename_table(sql, %Q) END, \"\n#endif\n          \"tbl_name = %Q, \"\n          \"name = CASE \"\n            \"WHEN type='table' THEN %Q \"\n            \"WHEN name LIKE 'sqlite_autoindex%%' AND type='index' THEN \"\n             \"'sqlite_autoindex_' || %Q || substr(name,%d+18) \"\n            \"ELSE name END \"\n      \"WHERE tbl_name=%Q COLLATE nocase AND \"\n          \"(type='table' OR type='index' OR type='trigger');\", \n      zDb, MASTER_NAME, zName, zName, zName, \n#ifndef SQLITE_OMIT_TRIGGER\n      zName,\n#endif\n      zName, nTabName, zTabName\n  );\n\n#ifndef SQLITE_OMIT_AUTOINCREMENT\n  /* If the sqlite_sequence table exists in this database, then update \n  ** it with the new table name.\n  */\n  if( sqlite3FindTable(db, \"sqlite_sequence\", zDb) ){\n    sqlite3NestedParse(pParse,\n        \"UPDATE \\\"%w\\\".sqlite_sequence set name = %Q WHERE name = %Q\",\n        zDb, zName, pTab->zName);\n  }\n#endif\n\n#ifndef SQLITE_OMIT_TRIGGER\n  /* If there are TEMP triggers on this table, modify the sqlite_temp_master\n  ** table. Don't do this if the table being ALTERed is itself located in\n  ** the temp database.\n  */\n  if( (zWhere=whereTempTriggers(pParse, pTab))!=0 ){\n    sqlite3NestedParse(pParse, \n        \"UPDATE sqlite_temp_master SET \"\n            \"sql = sqlite_rename_trigger(sql, %Q), \"\n            \"tbl_name = %Q \"\n            \"WHERE %s;\", zName, zName, zWhere);\n    sqlite3DbFree(db, zWhere);\n  }\n#endif\n\n#if !defined(SQLITE_OMIT_FOREIGN_KEY) && !defined(SQLITE_OMIT_TRIGGER)\n  if( db->flags&SQLITE_ForeignKeys ){\n    FKey *p;\n    for(p=sqlite3FkReferences(pTab); p; p=p->pNextTo){\n      Table *pFrom = p->pFrom;\n      if( pFrom!=pTab ){\n        reloadTableSchema(pParse, p->pFrom, pFrom->zName);\n      }\n    }\n  }\n#endif\n\n  /* Drop and reload the internal table schema. */\n  reloadTableSchema(pParse, pTab, zName);\n\nexit_rename_table:\n  sqlite3SrcListDelete(db, pSrc);\n  sqlite3DbFree(db, zName);\n  db->mDbFlags = savedDbFlags;\n}\n\n/*\n** This function is called after an \"ALTER TABLE ... ADD\" statement\n** has been parsed. Argument pColDef contains the text of the new\n** column definition.\n**\n** The Table structure pParse->pNewTable was extended to include\n** the new column during parsing.\n*/\nSQLITE_PRIVATE void sqlite3AlterFinishAddColumn(Parse *pParse, Token *pColDef){\n  Table *pNew;              /* Copy of pParse->pNewTable */\n  Table *pTab;              /* Table being altered */\n  int iDb;                  /* Database number */\n  const char *zDb;          /* Database name */\n  const char *zTab;         /* Table name */\n  char *zCol;               /* Null-terminated column definition */\n  Column *pCol;             /* The new column */\n  Expr *pDflt;              /* Default value for the new column */\n  sqlite3 *db;              /* The database connection; */\n  Vdbe *v = pParse->pVdbe;  /* The prepared statement under construction */\n  int r1;                   /* Temporary registers */\n\n  db = pParse->db;\n  if( pParse->nErr || db->mallocFailed ) return;\n  assert( v!=0 );\n  pNew = pParse->pNewTable;\n  assert( pNew );\n\n  assert( sqlite3BtreeHoldsAllMutexes(db) );\n  iDb = sqlite3SchemaToIndex(db, pNew->pSchema);\n  zDb = db->aDb[iDb].zDbSName;\n  zTab = &pNew->zName[16];  /* Skip the \"sqlite_altertab_\" prefix on the name */\n  pCol = &pNew->aCol[pNew->nCol-1];\n  pDflt = pCol->pDflt;\n  pTab = sqlite3FindTable(db, zTab, zDb);\n  assert( pTab );\n\n#ifndef SQLITE_OMIT_AUTHORIZATION\n  /* Invoke the authorization callback. */\n  if( sqlite3AuthCheck(pParse, SQLITE_ALTER_TABLE, zDb, pTab->zName, 0) ){\n    return;\n  }\n#endif\n\n  /* If the default value for the new column was specified with a \n  ** literal NULL, then set pDflt to 0. This simplifies checking\n  ** for an SQL NULL default below.\n  */\n  assert( pDflt==0 || pDflt->op==TK_SPAN );\n  if( pDflt && pDflt->pLeft->op==TK_NULL ){\n    pDflt = 0;\n  }\n\n  /* Check that the new column is not specified as PRIMARY KEY or UNIQUE.\n  ** If there is a NOT NULL constraint, then the default value for the\n  ** column must not be NULL.\n  */\n  if( pCol->colFlags & COLFLAG_PRIMKEY ){\n    sqlite3ErrorMsg(pParse, \"Cannot add a PRIMARY KEY column\");\n    return;\n  }\n  if( pNew->pIndex ){\n    sqlite3ErrorMsg(pParse, \"Cannot add a UNIQUE column\");\n    return;\n  }\n  if( (db->flags&SQLITE_ForeignKeys) && pNew->pFKey && pDflt ){\n    sqlite3ErrorMsg(pParse, \n        \"Cannot add a REFERENCES column with non-NULL default value\");\n    return;\n  }\n  if( pCol->notNull && !pDflt ){\n    sqlite3ErrorMsg(pParse, \n        \"Cannot add a NOT NULL column with default value NULL\");\n    return;\n  }\n\n  /* Ensure the default expression is something that sqlite3ValueFromExpr()\n  ** can handle (i.e. not CURRENT_TIME etc.)\n  */\n  if( pDflt ){\n    sqlite3_value *pVal = 0;\n    int rc;\n    rc = sqlite3ValueFromExpr(db, pDflt, SQLITE_UTF8, SQLITE_AFF_BLOB, &pVal);\n    assert( rc==SQLITE_OK || rc==SQLITE_NOMEM );\n    if( rc!=SQLITE_OK ){\n      assert( db->mallocFailed == 1 );\n      return;\n    }\n    if( !pVal ){\n      sqlite3ErrorMsg(pParse, \"Cannot add a column with non-constant default\");\n      return;\n    }\n    sqlite3ValueFree(pVal);\n  }\n\n  /* Modify the CREATE TABLE statement. */\n  zCol = sqlite3DbStrNDup(db, (char*)pColDef->z, pColDef->n);\n  if( zCol ){\n    char *zEnd = &zCol[pColDef->n-1];\n    u32 savedDbFlags = db->mDbFlags;\n    while( zEnd>zCol && (*zEnd==';' || sqlite3Isspace(*zEnd)) ){\n      *zEnd-- = '\\0';\n    }\n    db->mDbFlags |= DBFLAG_PreferBuiltin;\n    sqlite3NestedParse(pParse, \n        \"UPDATE \\\"%w\\\".%s SET \"\n          \"sql = substr(sql,1,%d) || ', ' || %Q || substr(sql,%d) \"\n        \"WHERE type = 'table' AND name = %Q\", \n      zDb, MASTER_NAME, pNew->addColOffset, zCol, pNew->addColOffset+1,\n      zTab\n    );\n    sqlite3DbFree(db, zCol);\n    db->mDbFlags = savedDbFlags;\n  }\n\n  /* Make sure the schema version is at least 3.  But do not upgrade\n  ** from less than 3 to 4, as that will corrupt any preexisting DESC\n  ** index.\n  */\n  r1 = sqlite3GetTempReg(pParse);\n  sqlite3VdbeAddOp3(v, OP_ReadCookie, iDb, r1, BTREE_FILE_FORMAT);\n  sqlite3VdbeUsesBtree(v, iDb);\n  sqlite3VdbeAddOp2(v, OP_AddImm, r1, -2);\n  sqlite3VdbeAddOp2(v, OP_IfPos, r1, sqlite3VdbeCurrentAddr(v)+2);\n  VdbeCoverage(v);\n  sqlite3VdbeAddOp3(v, OP_SetCookie, iDb, BTREE_FILE_FORMAT, 3);\n  sqlite3ReleaseTempReg(pParse, r1);\n\n  /* Reload the schema of the modified table. */\n  reloadTableSchema(pParse, pTab, pTab->zName);\n}\n\n/*\n** This function is called by the parser after the table-name in\n** an \"ALTER TABLE <table-name> ADD\" statement is parsed. Argument \n** pSrc is the full-name of the table being altered.\n**\n** This routine makes a (partial) copy of the Table structure\n** for the table being altered and sets Parse.pNewTable to point\n** to it. Routines called by the parser as the column definition\n** is parsed (i.e. sqlite3AddColumn()) add the new Column data to \n** the copy. The copy of the Table structure is deleted by tokenize.c \n** after parsing is finished.\n**\n** Routine sqlite3AlterFinishAddColumn() will be called to complete\n** coding the \"ALTER TABLE ... ADD\" statement.\n*/\nSQLITE_PRIVATE void sqlite3AlterBeginAddColumn(Parse *pParse, SrcList *pSrc){\n  Table *pNew;\n  Table *pTab;\n  Vdbe *v;\n  int iDb;\n  int i;\n  int nAlloc;\n  sqlite3 *db = pParse->db;\n\n  /* Look up the table being altered. */\n  assert( pParse->pNewTable==0 );\n  assert( sqlite3BtreeHoldsAllMutexes(db) );\n  if( db->mallocFailed ) goto exit_begin_add_column;\n  pTab = sqlite3LocateTableItem(pParse, 0, &pSrc->a[0]);\n  if( !pTab ) goto exit_begin_add_column;\n\n#ifndef SQLITE_OMIT_VIRTUALTABLE\n  if( IsVirtual(pTab) ){\n    sqlite3ErrorMsg(pParse, \"virtual tables may not be altered\");\n    goto exit_begin_add_column;\n  }\n#endif\n\n  /* Make sure this is not an attempt to ALTER a view. */\n  if( pTab->pSelect ){\n    sqlite3ErrorMsg(pParse, \"Cannot add a column to a view\");\n    goto exit_begin_add_column;\n  }\n  if( SQLITE_OK!=isSystemTable(pParse, pTab->zName) ){\n    goto exit_begin_add_column;\n  }\n\n  assert( pTab->addColOffset>0 );\n  iDb = sqlite3SchemaToIndex(db, pTab->pSchema);\n\n  /* Put a copy of the Table struct in Parse.pNewTable for the\n  ** sqlite3AddColumn() function and friends to modify.  But modify\n  ** the name by adding an \"sqlite_altertab_\" prefix.  By adding this\n  ** prefix, we insure that the name will not collide with an existing\n  ** table because user table are not allowed to have the \"sqlite_\"\n  ** prefix on their name.\n  */\n  pNew = (Table*)sqlite3DbMallocZero(db, sizeof(Table));\n  if( !pNew ) goto exit_begin_add_column;\n  pParse->pNewTable = pNew;\n  pNew->nTabRef = 1;\n  pNew->nCol = pTab->nCol;\n  assert( pNew->nCol>0 );\n  nAlloc = (((pNew->nCol-1)/8)*8)+8;\n  assert( nAlloc>=pNew->nCol && nAlloc%8==0 && nAlloc-pNew->nCol<8 );\n  pNew->aCol = (Column*)sqlite3DbMallocZero(db, sizeof(Column)*nAlloc);\n  pNew->zName = sqlite3MPrintf(db, \"sqlite_altertab_%s\", pTab->zName);\n  if( !pNew->aCol || !pNew->zName ){\n    assert( db->mallocFailed );\n    goto exit_begin_add_column;\n  }\n  memcpy(pNew->aCol, pTab->aCol, sizeof(Column)*pNew->nCol);\n  for(i=0; i<pNew->nCol; i++){\n    Column *pCol = &pNew->aCol[i];\n    pCol->zName = sqlite3DbStrDup(db, pCol->zName);\n    pCol->zColl = 0;\n    pCol->pDflt = 0;\n  }\n  pNew->pSchema = db->aDb[iDb].pSchema;\n  pNew->addColOffset = pTab->addColOffset;\n  pNew->nTabRef = 1;\n\n  /* Begin a transaction and increment the schema cookie.  */\n  sqlite3BeginWriteOperation(pParse, 0, iDb);\n  v = sqlite3GetVdbe(pParse);\n  if( !v ) goto exit_begin_add_column;\n  sqlite3ChangeCookie(pParse, iDb);\n\nexit_begin_add_column:\n  sqlite3SrcListDelete(db, pSrc);\n  return;\n}\n#endif  /* SQLITE_ALTER_TABLE */\n\n/************** End of alter.c ***********************************************/\n/************** Begin file analyze.c *****************************************/\n/*\n** 2005-07-08\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n*************************************************************************\n** This file contains code associated with the ANALYZE command.\n**\n** The ANALYZE command gather statistics about the content of tables\n** and indices.  These statistics are made available to the query planner\n** to help it make better decisions about how to perform queries.\n**\n** The following system tables are or have been supported:\n**\n**    CREATE TABLE sqlite_stat1(tbl, idx, stat);\n**    CREATE TABLE sqlite_stat2(tbl, idx, sampleno, sample);\n**    CREATE TABLE sqlite_stat3(tbl, idx, nEq, nLt, nDLt, sample);\n**    CREATE TABLE sqlite_stat4(tbl, idx, nEq, nLt, nDLt, sample);\n**\n** Additional tables might be added in future releases of SQLite.\n** The sqlite_stat2 table is not created or used unless the SQLite version\n** is between 3.6.18 and 3.7.8, inclusive, and unless SQLite is compiled\n** with SQLITE_ENABLE_STAT2.  The sqlite_stat2 table is deprecated.\n** The sqlite_stat2 table is superseded by sqlite_stat3, which is only\n** created and used by SQLite versions 3.7.9 and later and with\n** SQLITE_ENABLE_STAT3 defined.  The functionality of sqlite_stat3\n** is a superset of sqlite_stat2.  The sqlite_stat4 is an enhanced\n** version of sqlite_stat3 and is only available when compiled with\n** SQLITE_ENABLE_STAT4 and in SQLite versions 3.8.1 and later.  It is\n** not possible to enable both STAT3 and STAT4 at the same time.  If they\n** are both enabled, then STAT4 takes precedence.\n**\n** For most applications, sqlite_stat1 provides all the statistics required\n** for the query planner to make good choices.\n**\n** Format of sqlite_stat1:\n**\n** There is normally one row per index, with the index identified by the\n** name in the idx column.  The tbl column is the name of the table to\n** which the index belongs.  In each such row, the stat column will be\n** a string consisting of a list of integers.  The first integer in this\n** list is the number of rows in the index.  (This is the same as the\n** number of rows in the table, except for partial indices.)  The second\n** integer is the average number of rows in the index that have the same\n** value in the first column of the index.  The third integer is the average\n** number of rows in the index that have the same value for the first two\n** columns.  The N-th integer (for N>1) is the average number of rows in \n** the index which have the same value for the first N-1 columns.  For\n** a K-column index, there will be K+1 integers in the stat column.  If\n** the index is unique, then the last integer will be 1.\n**\n** The list of integers in the stat column can optionally be followed\n** by the keyword \"unordered\".  The \"unordered\" keyword, if it is present,\n** must be separated from the last integer by a single space.  If the\n** \"unordered\" keyword is present, then the query planner assumes that\n** the index is unordered and will not use the index for a range query.\n** \n** If the sqlite_stat1.idx column is NULL, then the sqlite_stat1.stat\n** column contains a single integer which is the (estimated) number of\n** rows in the table identified by sqlite_stat1.tbl.\n**\n** Format of sqlite_stat2:\n**\n** The sqlite_stat2 is only created and is only used if SQLite is compiled\n** with SQLITE_ENABLE_STAT2 and if the SQLite version number is between\n** 3.6.18 and 3.7.8.  The \"stat2\" table contains additional information\n** about the distribution of keys within an index.  The index is identified by\n** the \"idx\" column and the \"tbl\" column is the name of the table to which\n** the index belongs.  There are usually 10 rows in the sqlite_stat2\n** table for each index.\n**\n** The sqlite_stat2 entries for an index that have sampleno between 0 and 9\n** inclusive are samples of the left-most key value in the index taken at\n** evenly spaced points along the index.  Let the number of samples be S\n** (10 in the standard build) and let C be the number of rows in the index.\n** Then the sampled rows are given by:\n**\n**     rownumber = (i*C*2 + C)/(S*2)\n**\n** For i between 0 and S-1.  Conceptually, the index space is divided into\n** S uniform buckets and the samples are the middle row from each bucket.\n**\n** The format for sqlite_stat2 is recorded here for legacy reference.  This\n** version of SQLite does not support sqlite_stat2.  It neither reads nor\n** writes the sqlite_stat2 table.  This version of SQLite only supports\n** sqlite_stat3.\n**\n** Format for sqlite_stat3:\n**\n** The sqlite_stat3 format is a subset of sqlite_stat4.  Hence, the\n** sqlite_stat4 format will be described first.  Further information\n** about sqlite_stat3 follows the sqlite_stat4 description.\n**\n** Format for sqlite_stat4:\n**\n** As with sqlite_stat2, the sqlite_stat4 table contains histogram data\n** to aid the query planner in choosing good indices based on the values\n** that indexed columns are compared against in the WHERE clauses of\n** queries.\n**\n** The sqlite_stat4 table contains multiple entries for each index.\n** The idx column names the index and the tbl column is the table of the\n** index.  If the idx and tbl columns are the same, then the sample is\n** of the INTEGER PRIMARY KEY.  The sample column is a blob which is the\n** binary encoding of a key from the index.  The nEq column is a\n** list of integers.  The first integer is the approximate number\n** of entries in the index whose left-most column exactly matches\n** the left-most column of the sample.  The second integer in nEq\n** is the approximate number of entries in the index where the\n** first two columns match the first two columns of the sample.\n** And so forth.  nLt is another list of integers that show the approximate\n** number of entries that are strictly less than the sample.  The first\n** integer in nLt contains the number of entries in the index where the\n** left-most column is less than the left-most column of the sample.\n** The K-th integer in the nLt entry is the number of index entries \n** where the first K columns are less than the first K columns of the\n** sample.  The nDLt column is like nLt except that it contains the \n** number of distinct entries in the index that are less than the\n** sample.\n**\n** There can be an arbitrary number of sqlite_stat4 entries per index.\n** The ANALYZE command will typically generate sqlite_stat4 tables\n** that contain between 10 and 40 samples which are distributed across\n** the key space, though not uniformly, and which include samples with\n** large nEq values.\n**\n** Format for sqlite_stat3 redux:\n**\n** The sqlite_stat3 table is like sqlite_stat4 except that it only\n** looks at the left-most column of the index.  The sqlite_stat3.sample\n** column contains the actual value of the left-most column instead\n** of a blob encoding of the complete index key as is found in\n** sqlite_stat4.sample.  The nEq, nLt, and nDLt entries of sqlite_stat3\n** all contain just a single integer which is the same as the first\n** integer in the equivalent columns in sqlite_stat4.\n*/\n#ifndef SQLITE_OMIT_ANALYZE\n/* #include \"sqliteInt.h\" */\n\n#if defined(SQLITE_ENABLE_STAT4)\n# define IsStat4     1\n# define IsStat3     0\n#elif defined(SQLITE_ENABLE_STAT3)\n# define IsStat4     0\n# define IsStat3     1\n#else\n# define IsStat4     0\n# define IsStat3     0\n# undef SQLITE_STAT4_SAMPLES\n# define SQLITE_STAT4_SAMPLES 1\n#endif\n#define IsStat34    (IsStat3+IsStat4)  /* 1 for STAT3 or STAT4. 0 otherwise */\n\n/*\n** This routine generates code that opens the sqlite_statN tables.\n** The sqlite_stat1 table is always relevant.  sqlite_stat2 is now\n** obsolete.  sqlite_stat3 and sqlite_stat4 are only opened when\n** appropriate compile-time options are provided.\n**\n** If the sqlite_statN tables do not previously exist, it is created.\n**\n** Argument zWhere may be a pointer to a buffer containing a table name,\n** or it may be a NULL pointer. If it is not NULL, then all entries in\n** the sqlite_statN tables associated with the named table are deleted.\n** If zWhere==0, then code is generated to delete all stat table entries.\n*/\nstatic void openStatTable(\n  Parse *pParse,          /* Parsing context */\n  int iDb,                /* The database we are looking in */\n  int iStatCur,           /* Open the sqlite_stat1 table on this cursor */\n  const char *zWhere,     /* Delete entries for this table or index */\n  const char *zWhereType  /* Either \"tbl\" or \"idx\" */\n){\n  static const struct {\n    const char *zName;\n    const char *zCols;\n  } aTable[] = {\n    { \"sqlite_stat1\", \"tbl,idx,stat\" },\n#if defined(SQLITE_ENABLE_STAT4)\n    { \"sqlite_stat4\", \"tbl,idx,neq,nlt,ndlt,sample\" },\n    { \"sqlite_stat3\", 0 },\n#elif defined(SQLITE_ENABLE_STAT3)\n    { \"sqlite_stat3\", \"tbl,idx,neq,nlt,ndlt,sample\" },\n    { \"sqlite_stat4\", 0 },\n#else\n    { \"sqlite_stat3\", 0 },\n    { \"sqlite_stat4\", 0 },\n#endif\n  };\n  int i;\n  sqlite3 *db = pParse->db;\n  Db *pDb;\n  Vdbe *v = sqlite3GetVdbe(pParse);\n  int aRoot[ArraySize(aTable)];\n  u8 aCreateTbl[ArraySize(aTable)];\n\n  if( v==0 ) return;\n  assert( sqlite3BtreeHoldsAllMutexes(db) );\n  assert( sqlite3VdbeDb(v)==db );\n  pDb = &db->aDb[iDb];\n\n  /* Create new statistic tables if they do not exist, or clear them\n  ** if they do already exist.\n  */\n  for(i=0; i<ArraySize(aTable); i++){\n    const char *zTab = aTable[i].zName;\n    Table *pStat;\n    if( (pStat = sqlite3FindTable(db, zTab, pDb->zDbSName))==0 ){\n      if( aTable[i].zCols ){\n        /* The sqlite_statN table does not exist. Create it. Note that a \n        ** side-effect of the CREATE TABLE statement is to leave the rootpage \n        ** of the new table in register pParse->regRoot. This is important \n        ** because the OpenWrite opcode below will be needing it. */\n        sqlite3NestedParse(pParse,\n            \"CREATE TABLE %Q.%s(%s)\", pDb->zDbSName, zTab, aTable[i].zCols\n        );\n        aRoot[i] = pParse->regRoot;\n        aCreateTbl[i] = OPFLAG_P2ISREG;\n      }\n    }else{\n      /* The table already exists. If zWhere is not NULL, delete all entries \n      ** associated with the table zWhere. If zWhere is NULL, delete the\n      ** entire contents of the table. */\n      aRoot[i] = pStat->tnum;\n      aCreateTbl[i] = 0;\n      sqlite3TableLock(pParse, iDb, aRoot[i], 1, zTab);\n      if( zWhere ){\n        sqlite3NestedParse(pParse,\n           \"DELETE FROM %Q.%s WHERE %s=%Q\",\n           pDb->zDbSName, zTab, zWhereType, zWhere\n        );\n#ifdef SQLITE_ENABLE_PREUPDATE_HOOK\n      }else if( db->xPreUpdateCallback ){\n        sqlite3NestedParse(pParse, \"DELETE FROM %Q.%s\", pDb->zDbSName, zTab);\n#endif\n      }else{\n        /* The sqlite_stat[134] table already exists.  Delete all rows. */\n        sqlite3VdbeAddOp2(v, OP_Clear, aRoot[i], iDb);\n      }\n    }\n  }\n\n  /* Open the sqlite_stat[134] tables for writing. */\n  for(i=0; aTable[i].zCols; i++){\n    assert( i<ArraySize(aTable) );\n    sqlite3VdbeAddOp4Int(v, OP_OpenWrite, iStatCur+i, aRoot[i], iDb, 3);\n    sqlite3VdbeChangeP5(v, aCreateTbl[i]);\n    VdbeComment((v, aTable[i].zName));\n  }\n}\n\n/*\n** Recommended number of samples for sqlite_stat4\n*/\n#ifndef SQLITE_STAT4_SAMPLES\n# define SQLITE_STAT4_SAMPLES 24\n#endif\n\n/*\n** Three SQL functions - stat_init(), stat_push(), and stat_get() -\n** share an instance of the following structure to hold their state\n** information.\n*/\ntypedef struct Stat4Accum Stat4Accum;\ntypedef struct Stat4Sample Stat4Sample;\nstruct Stat4Sample {\n  tRowcnt *anEq;                  /* sqlite_stat4.nEq */\n  tRowcnt *anDLt;                 /* sqlite_stat4.nDLt */\n#ifdef SQLITE_ENABLE_STAT3_OR_STAT4\n  tRowcnt *anLt;                  /* sqlite_stat4.nLt */\n  union {\n    i64 iRowid;                     /* Rowid in main table of the key */\n    u8 *aRowid;                     /* Key for WITHOUT ROWID tables */\n  } u;\n  u32 nRowid;                     /* Sizeof aRowid[] */\n  u8 isPSample;                   /* True if a periodic sample */\n  int iCol;                       /* If !isPSample, the reason for inclusion */\n  u32 iHash;                      /* Tiebreaker hash */\n#endif\n};                                                    \nstruct Stat4Accum {\n  tRowcnt nRow;             /* Number of rows in the entire table */\n  tRowcnt nPSample;         /* How often to do a periodic sample */\n  int nCol;                 /* Number of columns in index + pk/rowid */\n  int nKeyCol;              /* Number of index columns w/o the pk/rowid */\n  int mxSample;             /* Maximum number of samples to accumulate */\n  Stat4Sample current;      /* Current row as a Stat4Sample */\n  u32 iPrn;                 /* Pseudo-random number used for sampling */\n  Stat4Sample *aBest;       /* Array of nCol best samples */\n  int iMin;                 /* Index in a[] of entry with minimum score */\n  int nSample;              /* Current number of samples */\n  int nMaxEqZero;           /* Max leading 0 in anEq[] for any a[] entry */\n  int iGet;                 /* Index of current sample accessed by stat_get() */\n  Stat4Sample *a;           /* Array of mxSample Stat4Sample objects */\n  sqlite3 *db;              /* Database connection, for malloc() */\n};\n\n/* Reclaim memory used by a Stat4Sample\n*/\n#ifdef SQLITE_ENABLE_STAT3_OR_STAT4\nstatic void sampleClear(sqlite3 *db, Stat4Sample *p){\n  assert( db!=0 );\n  if( p->nRowid ){\n    sqlite3DbFree(db, p->u.aRowid);\n    p->nRowid = 0;\n  }\n}\n#endif\n\n/* Initialize the BLOB value of a ROWID\n*/\n#ifdef SQLITE_ENABLE_STAT3_OR_STAT4\nstatic void sampleSetRowid(sqlite3 *db, Stat4Sample *p, int n, const u8 *pData){\n  assert( db!=0 );\n  if( p->nRowid ) sqlite3DbFree(db, p->u.aRowid);\n  p->u.aRowid = sqlite3DbMallocRawNN(db, n);\n  if( p->u.aRowid ){\n    p->nRowid = n;\n    memcpy(p->u.aRowid, pData, n);\n  }else{\n    p->nRowid = 0;\n  }\n}\n#endif\n\n/* Initialize the INTEGER value of a ROWID.\n*/\n#ifdef SQLITE_ENABLE_STAT3_OR_STAT4\nstatic void sampleSetRowidInt64(sqlite3 *db, Stat4Sample *p, i64 iRowid){\n  assert( db!=0 );\n  if( p->nRowid ) sqlite3DbFree(db, p->u.aRowid);\n  p->nRowid = 0;\n  p->u.iRowid = iRowid;\n}\n#endif\n\n\n/*\n** Copy the contents of object (*pFrom) into (*pTo).\n*/\n#ifdef SQLITE_ENABLE_STAT3_OR_STAT4\nstatic void sampleCopy(Stat4Accum *p, Stat4Sample *pTo, Stat4Sample *pFrom){\n  pTo->isPSample = pFrom->isPSample;\n  pTo->iCol = pFrom->iCol;\n  pTo->iHash = pFrom->iHash;\n  memcpy(pTo->anEq, pFrom->anEq, sizeof(tRowcnt)*p->nCol);\n  memcpy(pTo->anLt, pFrom->anLt, sizeof(tRowcnt)*p->nCol);\n  memcpy(pTo->anDLt, pFrom->anDLt, sizeof(tRowcnt)*p->nCol);\n  if( pFrom->nRowid ){\n    sampleSetRowid(p->db, pTo, pFrom->nRowid, pFrom->u.aRowid);\n  }else{\n    sampleSetRowidInt64(p->db, pTo, pFrom->u.iRowid);\n  }\n}\n#endif\n\n/*\n** Reclaim all memory of a Stat4Accum structure.\n*/\nstatic void stat4Destructor(void *pOld){\n  Stat4Accum *p = (Stat4Accum*)pOld;\n#ifdef SQLITE_ENABLE_STAT3_OR_STAT4\n  int i;\n  for(i=0; i<p->nCol; i++) sampleClear(p->db, p->aBest+i);\n  for(i=0; i<p->mxSample; i++) sampleClear(p->db, p->a+i);\n  sampleClear(p->db, &p->current);\n#endif\n  sqlite3DbFree(p->db, p);\n}\n\n/*\n** Implementation of the stat_init(N,K,C) SQL function. The three parameters\n** are:\n**     N:    The number of columns in the index including the rowid/pk (note 1)\n**     K:    The number of columns in the index excluding the rowid/pk.\n**     C:    The number of rows in the index (note 2)\n**\n** Note 1:  In the special case of the covering index that implements a\n** WITHOUT ROWID table, N is the number of PRIMARY KEY columns, not the\n** total number of columns in the table.\n**\n** Note 2:  C is only used for STAT3 and STAT4.\n**\n** For indexes on ordinary rowid tables, N==K+1.  But for indexes on\n** WITHOUT ROWID tables, N=K+P where P is the number of columns in the\n** PRIMARY KEY of the table.  The covering index that implements the\n** original WITHOUT ROWID table as N==K as a special case.\n**\n** This routine allocates the Stat4Accum object in heap memory. The return \n** value is a pointer to the Stat4Accum object.  The datatype of the\n** return value is BLOB, but it is really just a pointer to the Stat4Accum\n** object.\n*/\nstatic void statInit(\n  sqlite3_context *context,\n  int argc,\n  sqlite3_value **argv\n){\n  Stat4Accum *p;\n  int nCol;                       /* Number of columns in index being sampled */\n  int nKeyCol;                    /* Number of key columns */\n  int nColUp;                     /* nCol rounded up for alignment */\n  int n;                          /* Bytes of space to allocate */\n  sqlite3 *db;                    /* Database connection */\n#ifdef SQLITE_ENABLE_STAT3_OR_STAT4\n  int mxSample = SQLITE_STAT4_SAMPLES;\n#endif\n\n  /* Decode the three function arguments */\n  UNUSED_PARAMETER(argc);\n  nCol = sqlite3_value_int(argv[0]);\n  assert( nCol>0 );\n  nColUp = sizeof(tRowcnt)<8 ? (nCol+1)&~1 : nCol;\n  nKeyCol = sqlite3_value_int(argv[1]);\n  assert( nKeyCol<=nCol );\n  assert( nKeyCol>0 );\n\n  /* Allocate the space required for the Stat4Accum object */\n  n = sizeof(*p) \n    + sizeof(tRowcnt)*nColUp                  /* Stat4Accum.anEq */\n    + sizeof(tRowcnt)*nColUp                  /* Stat4Accum.anDLt */\n#ifdef SQLITE_ENABLE_STAT3_OR_STAT4\n    + sizeof(tRowcnt)*nColUp                  /* Stat4Accum.anLt */\n    + sizeof(Stat4Sample)*(nCol+mxSample)     /* Stat4Accum.aBest[], a[] */\n    + sizeof(tRowcnt)*3*nColUp*(nCol+mxSample)\n#endif\n  ;\n  db = sqlite3_context_db_handle(context);\n  p = sqlite3DbMallocZero(db, n);\n  if( p==0 ){\n    sqlite3_result_error_nomem(context);\n    return;\n  }\n\n  p->db = db;\n  p->nRow = 0;\n  p->nCol = nCol;\n  p->nKeyCol = nKeyCol;\n  p->current.anDLt = (tRowcnt*)&p[1];\n  p->current.anEq = &p->current.anDLt[nColUp];\n\n#ifdef SQLITE_ENABLE_STAT3_OR_STAT4\n  {\n    u8 *pSpace;                     /* Allocated space not yet assigned */\n    int i;                          /* Used to iterate through p->aSample[] */\n\n    p->iGet = -1;\n    p->mxSample = mxSample;\n    p->nPSample = (tRowcnt)(sqlite3_value_int64(argv[2])/(mxSample/3+1) + 1);\n    p->current.anLt = &p->current.anEq[nColUp];\n    p->iPrn = 0x689e962d*(u32)nCol ^ 0xd0944565*(u32)sqlite3_value_int(argv[2]);\n  \n    /* Set up the Stat4Accum.a[] and aBest[] arrays */\n    p->a = (struct Stat4Sample*)&p->current.anLt[nColUp];\n    p->aBest = &p->a[mxSample];\n    pSpace = (u8*)(&p->a[mxSample+nCol]);\n    for(i=0; i<(mxSample+nCol); i++){\n      p->a[i].anEq = (tRowcnt *)pSpace; pSpace += (sizeof(tRowcnt) * nColUp);\n      p->a[i].anLt = (tRowcnt *)pSpace; pSpace += (sizeof(tRowcnt) * nColUp);\n      p->a[i].anDLt = (tRowcnt *)pSpace; pSpace += (sizeof(tRowcnt) * nColUp);\n    }\n    assert( (pSpace - (u8*)p)==n );\n  \n    for(i=0; i<nCol; i++){\n      p->aBest[i].iCol = i;\n    }\n  }\n#endif\n\n  /* Return a pointer to the allocated object to the caller.  Note that\n  ** only the pointer (the 2nd parameter) matters.  The size of the object\n  ** (given by the 3rd parameter) is never used and can be any positive\n  ** value. */\n  sqlite3_result_blob(context, p, sizeof(*p), stat4Destructor);\n}\nstatic const FuncDef statInitFuncdef = {\n  2+IsStat34,      /* nArg */\n  SQLITE_UTF8,     /* funcFlags */\n  0,               /* pUserData */\n  0,               /* pNext */\n  statInit,        /* xSFunc */\n  0,               /* xFinalize */\n  \"stat_init\",     /* zName */\n  {0}\n};\n\n#ifdef SQLITE_ENABLE_STAT4\n/*\n** pNew and pOld are both candidate non-periodic samples selected for \n** the same column (pNew->iCol==pOld->iCol). Ignoring this column and \n** considering only any trailing columns and the sample hash value, this\n** function returns true if sample pNew is to be preferred over pOld.\n** In other words, if we assume that the cardinalities of the selected\n** column for pNew and pOld are equal, is pNew to be preferred over pOld.\n**\n** This function assumes that for each argument sample, the contents of\n** the anEq[] array from pSample->anEq[pSample->iCol+1] onwards are valid. \n*/\nstatic int sampleIsBetterPost(\n  Stat4Accum *pAccum, \n  Stat4Sample *pNew, \n  Stat4Sample *pOld\n){\n  int nCol = pAccum->nCol;\n  int i;\n  assert( pNew->iCol==pOld->iCol );\n  for(i=pNew->iCol+1; i<nCol; i++){\n    if( pNew->anEq[i]>pOld->anEq[i] ) return 1;\n    if( pNew->anEq[i]<pOld->anEq[i] ) return 0;\n  }\n  if( pNew->iHash>pOld->iHash ) return 1;\n  return 0;\n}\n#endif\n\n#ifdef SQLITE_ENABLE_STAT3_OR_STAT4\n/*\n** Return true if pNew is to be preferred over pOld.\n**\n** This function assumes that for each argument sample, the contents of\n** the anEq[] array from pSample->anEq[pSample->iCol] onwards are valid. \n*/\nstatic int sampleIsBetter(\n  Stat4Accum *pAccum, \n  Stat4Sample *pNew, \n  Stat4Sample *pOld\n){\n  tRowcnt nEqNew = pNew->anEq[pNew->iCol];\n  tRowcnt nEqOld = pOld->anEq[pOld->iCol];\n\n  assert( pOld->isPSample==0 && pNew->isPSample==0 );\n  assert( IsStat4 || (pNew->iCol==0 && pOld->iCol==0) );\n\n  if( (nEqNew>nEqOld) ) return 1;\n#ifdef SQLITE_ENABLE_STAT4\n  if( nEqNew==nEqOld ){\n    if( pNew->iCol<pOld->iCol ) return 1;\n    return (pNew->iCol==pOld->iCol && sampleIsBetterPost(pAccum, pNew, pOld));\n  }\n  return 0;\n#else\n  return (nEqNew==nEqOld && pNew->iHash>pOld->iHash);\n#endif\n}\n\n/*\n** Copy the contents of sample *pNew into the p->a[] array. If necessary,\n** remove the least desirable sample from p->a[] to make room.\n*/\nstatic void sampleInsert(Stat4Accum *p, Stat4Sample *pNew, int nEqZero){\n  Stat4Sample *pSample = 0;\n  int i;\n\n  assert( IsStat4 || nEqZero==0 );\n\n#ifdef SQLITE_ENABLE_STAT4\n  /* Stat4Accum.nMaxEqZero is set to the maximum number of leading 0\n  ** values in the anEq[] array of any sample in Stat4Accum.a[]. In\n  ** other words, if nMaxEqZero is n, then it is guaranteed that there\n  ** are no samples with Stat4Sample.anEq[m]==0 for (m>=n). */\n  if( nEqZero>p->nMaxEqZero ){\n    p->nMaxEqZero = nEqZero;\n  }\n  if( pNew->isPSample==0 ){\n    Stat4Sample *pUpgrade = 0;\n    assert( pNew->anEq[pNew->iCol]>0 );\n\n    /* This sample is being added because the prefix that ends in column \n    ** iCol occurs many times in the table. However, if we have already\n    ** added a sample that shares this prefix, there is no need to add\n    ** this one. Instead, upgrade the priority of the highest priority\n    ** existing sample that shares this prefix.  */\n    for(i=p->nSample-1; i>=0; i--){\n      Stat4Sample *pOld = &p->a[i];\n      if( pOld->anEq[pNew->iCol]==0 ){\n        if( pOld->isPSample ) return;\n        assert( pOld->iCol>pNew->iCol );\n        assert( sampleIsBetter(p, pNew, pOld) );\n        if( pUpgrade==0 || sampleIsBetter(p, pOld, pUpgrade) ){\n          pUpgrade = pOld;\n        }\n      }\n    }\n    if( pUpgrade ){\n      pUpgrade->iCol = pNew->iCol;\n      pUpgrade->anEq[pUpgrade->iCol] = pNew->anEq[pUpgrade->iCol];\n      goto find_new_min;\n    }\n  }\n#endif\n\n  /* If necessary, remove sample iMin to make room for the new sample. */\n  if( p->nSample>=p->mxSample ){\n    Stat4Sample *pMin = &p->a[p->iMin];\n    tRowcnt *anEq = pMin->anEq;\n    tRowcnt *anLt = pMin->anLt;\n    tRowcnt *anDLt = pMin->anDLt;\n    sampleClear(p->db, pMin);\n    memmove(pMin, &pMin[1], sizeof(p->a[0])*(p->nSample-p->iMin-1));\n    pSample = &p->a[p->nSample-1];\n    pSample->nRowid = 0;\n    pSample->anEq = anEq;\n    pSample->anDLt = anDLt;\n    pSample->anLt = anLt;\n    p->nSample = p->mxSample-1;\n  }\n\n  /* The \"rows less-than\" for the rowid column must be greater than that\n  ** for the last sample in the p->a[] array. Otherwise, the samples would\n  ** be out of order. */\n#ifdef SQLITE_ENABLE_STAT4\n  assert( p->nSample==0 \n       || pNew->anLt[p->nCol-1] > p->a[p->nSample-1].anLt[p->nCol-1] );\n#endif\n\n  /* Insert the new sample */\n  pSample = &p->a[p->nSample];\n  sampleCopy(p, pSample, pNew);\n  p->nSample++;\n\n  /* Zero the first nEqZero entries in the anEq[] array. */\n  memset(pSample->anEq, 0, sizeof(tRowcnt)*nEqZero);\n\n#ifdef SQLITE_ENABLE_STAT4\n find_new_min:\n#endif\n  if( p->nSample>=p->mxSample ){\n    int iMin = -1;\n    for(i=0; i<p->mxSample; i++){\n      if( p->a[i].isPSample ) continue;\n      if( iMin<0 || sampleIsBetter(p, &p->a[iMin], &p->a[i]) ){\n        iMin = i;\n      }\n    }\n    assert( iMin>=0 );\n    p->iMin = iMin;\n  }\n}\n#endif /* SQLITE_ENABLE_STAT3_OR_STAT4 */\n\n/*\n** Field iChng of the index being scanned has changed. So at this point\n** p->current contains a sample that reflects the previous row of the\n** index. The value of anEq[iChng] and subsequent anEq[] elements are\n** correct at this point.\n*/\nstatic void samplePushPrevious(Stat4Accum *p, int iChng){\n#ifdef SQLITE_ENABLE_STAT4\n  int i;\n\n  /* Check if any samples from the aBest[] array should be pushed\n  ** into IndexSample.a[] at this point.  */\n  for(i=(p->nCol-2); i>=iChng; i--){\n    Stat4Sample *pBest = &p->aBest[i];\n    pBest->anEq[i] = p->current.anEq[i];\n    if( p->nSample<p->mxSample || sampleIsBetter(p, pBest, &p->a[p->iMin]) ){\n      sampleInsert(p, pBest, i);\n    }\n  }\n\n  /* Check that no sample contains an anEq[] entry with an index of\n  ** p->nMaxEqZero or greater set to zero. */\n  for(i=p->nSample-1; i>=0; i--){\n    int j;\n    for(j=p->nMaxEqZero; j<p->nCol; j++) assert( p->a[i].anEq[j]>0 );\n  }\n\n  /* Update the anEq[] fields of any samples already collected. */\n  if( iChng<p->nMaxEqZero ){\n    for(i=p->nSample-1; i>=0; i--){\n      int j;\n      for(j=iChng; j<p->nCol; j++){\n        if( p->a[i].anEq[j]==0 ) p->a[i].anEq[j] = p->current.anEq[j];\n      }\n    }\n    p->nMaxEqZero = iChng;\n  }\n#endif\n\n#if defined(SQLITE_ENABLE_STAT3) && !defined(SQLITE_ENABLE_STAT4)\n  if( iChng==0 ){\n    tRowcnt nLt = p->current.anLt[0];\n    tRowcnt nEq = p->current.anEq[0];\n\n    /* Check if this is to be a periodic sample. If so, add it. */\n    if( (nLt/p->nPSample)!=(nLt+nEq)/p->nPSample ){\n      p->current.isPSample = 1;\n      sampleInsert(p, &p->current, 0);\n      p->current.isPSample = 0;\n    }else \n\n    /* Or if it is a non-periodic sample. Add it in this case too. */\n    if( p->nSample<p->mxSample \n     || sampleIsBetter(p, &p->current, &p->a[p->iMin]) \n    ){\n      sampleInsert(p, &p->current, 0);\n    }\n  }\n#endif\n\n#ifndef SQLITE_ENABLE_STAT3_OR_STAT4\n  UNUSED_PARAMETER( p );\n  UNUSED_PARAMETER( iChng );\n#endif\n}\n\n/*\n** Implementation of the stat_push SQL function:  stat_push(P,C,R)\n** Arguments:\n**\n**    P     Pointer to the Stat4Accum object created by stat_init()\n**    C     Index of left-most column to differ from previous row\n**    R     Rowid for the current row.  Might be a key record for\n**          WITHOUT ROWID tables.\n**\n** This SQL function always returns NULL.  It's purpose it to accumulate\n** statistical data and/or samples in the Stat4Accum object about the\n** index being analyzed.  The stat_get() SQL function will later be used to\n** extract relevant information for constructing the sqlite_statN tables.\n**\n** The R parameter is only used for STAT3 and STAT4\n*/\nstatic void statPush(\n  sqlite3_context *context,\n  int argc,\n  sqlite3_value **argv\n){\n  int i;\n\n  /* The three function arguments */\n  Stat4Accum *p = (Stat4Accum*)sqlite3_value_blob(argv[0]);\n  int iChng = sqlite3_value_int(argv[1]);\n\n  UNUSED_PARAMETER( argc );\n  UNUSED_PARAMETER( context );\n  assert( p->nCol>0 );\n  assert( iChng<p->nCol );\n\n  if( p->nRow==0 ){\n    /* This is the first call to this function. Do initialization. */\n    for(i=0; i<p->nCol; i++) p->current.anEq[i] = 1;\n  }else{\n    /* Second and subsequent calls get processed here */\n    samplePushPrevious(p, iChng);\n\n    /* Update anDLt[], anLt[] and anEq[] to reflect the values that apply\n    ** to the current row of the index. */\n    for(i=0; i<iChng; i++){\n      p->current.anEq[i]++;\n    }\n    for(i=iChng; i<p->nCol; i++){\n      p->current.anDLt[i]++;\n#ifdef SQLITE_ENABLE_STAT3_OR_STAT4\n      p->current.anLt[i] += p->current.anEq[i];\n#endif\n      p->current.anEq[i] = 1;\n    }\n  }\n  p->nRow++;\n#ifdef SQLITE_ENABLE_STAT3_OR_STAT4\n  if( sqlite3_value_type(argv[2])==SQLITE_INTEGER ){\n    sampleSetRowidInt64(p->db, &p->current, sqlite3_value_int64(argv[2]));\n  }else{\n    sampleSetRowid(p->db, &p->current, sqlite3_value_bytes(argv[2]),\n                                       sqlite3_value_blob(argv[2]));\n  }\n  p->current.iHash = p->iPrn = p->iPrn*1103515245 + 12345;\n#endif\n\n#ifdef SQLITE_ENABLE_STAT4\n  {\n    tRowcnt nLt = p->current.anLt[p->nCol-1];\n\n    /* Check if this is to be a periodic sample. If so, add it. */\n    if( (nLt/p->nPSample)!=(nLt+1)/p->nPSample ){\n      p->current.isPSample = 1;\n      p->current.iCol = 0;\n      sampleInsert(p, &p->current, p->nCol-1);\n      p->current.isPSample = 0;\n    }\n\n    /* Update the aBest[] array. */\n    for(i=0; i<(p->nCol-1); i++){\n      p->current.iCol = i;\n      if( i>=iChng || sampleIsBetterPost(p, &p->current, &p->aBest[i]) ){\n        sampleCopy(p, &p->aBest[i], &p->current);\n      }\n    }\n  }\n#endif\n}\nstatic const FuncDef statPushFuncdef = {\n  2+IsStat34,      /* nArg */\n  SQLITE_UTF8,     /* funcFlags */\n  0,               /* pUserData */\n  0,               /* pNext */\n  statPush,        /* xSFunc */\n  0,               /* xFinalize */\n  \"stat_push\",     /* zName */\n  {0}\n};\n\n#define STAT_GET_STAT1 0          /* \"stat\" column of stat1 table */\n#define STAT_GET_ROWID 1          /* \"rowid\" column of stat[34] entry */\n#define STAT_GET_NEQ   2          /* \"neq\" column of stat[34] entry */\n#define STAT_GET_NLT   3          /* \"nlt\" column of stat[34] entry */\n#define STAT_GET_NDLT  4          /* \"ndlt\" column of stat[34] entry */\n\n/*\n** Implementation of the stat_get(P,J) SQL function.  This routine is\n** used to query statistical information that has been gathered into\n** the Stat4Accum object by prior calls to stat_push().  The P parameter\n** has type BLOB but it is really just a pointer to the Stat4Accum object.\n** The content to returned is determined by the parameter J\n** which is one of the STAT_GET_xxxx values defined above.\n**\n** The stat_get(P,J) function is not available to generic SQL.  It is\n** inserted as part of a manually constructed bytecode program.  (See\n** the callStatGet() routine below.)  It is guaranteed that the P\n** parameter will always be a poiner to a Stat4Accum object, never a\n** NULL.\n**\n** If neither STAT3 nor STAT4 are enabled, then J is always\n** STAT_GET_STAT1 and is hence omitted and this routine becomes\n** a one-parameter function, stat_get(P), that always returns the\n** stat1 table entry information.\n*/\nstatic void statGet(\n  sqlite3_context *context,\n  int argc,\n  sqlite3_value **argv\n){\n  Stat4Accum *p = (Stat4Accum*)sqlite3_value_blob(argv[0]);\n#ifdef SQLITE_ENABLE_STAT3_OR_STAT4\n  /* STAT3 and STAT4 have a parameter on this routine. */\n  int eCall = sqlite3_value_int(argv[1]);\n  assert( argc==2 );\n  assert( eCall==STAT_GET_STAT1 || eCall==STAT_GET_NEQ \n       || eCall==STAT_GET_ROWID || eCall==STAT_GET_NLT\n       || eCall==STAT_GET_NDLT \n  );\n  if( eCall==STAT_GET_STAT1 )\n#else\n  assert( argc==1 );\n#endif\n  {\n    /* Return the value to store in the \"stat\" column of the sqlite_stat1\n    ** table for this index.\n    **\n    ** The value is a string composed of a list of integers describing \n    ** the index. The first integer in the list is the total number of \n    ** entries in the index. There is one additional integer in the list \n    ** for each indexed column. This additional integer is an estimate of\n    ** the number of rows matched by a stabbing query on the index using\n    ** a key with the corresponding number of fields. In other words,\n    ** if the index is on columns (a,b) and the sqlite_stat1 value is \n    ** \"100 10 2\", then SQLite estimates that:\n    **\n    **   * the index contains 100 rows,\n    **   * \"WHERE a=?\" matches 10 rows, and\n    **   * \"WHERE a=? AND b=?\" matches 2 rows.\n    **\n    ** If D is the count of distinct values and K is the total number of \n    ** rows, then each estimate is computed as:\n    **\n    **        I = (K+D-1)/D\n    */\n    char *z;\n    int i;\n\n    char *zRet = sqlite3MallocZero( (p->nKeyCol+1)*25 );\n    if( zRet==0 ){\n      sqlite3_result_error_nomem(context);\n      return;\n    }\n\n    sqlite3_snprintf(24, zRet, \"%llu\", (u64)p->nRow);\n    z = zRet + sqlite3Strlen30(zRet);\n    for(i=0; i<p->nKeyCol; i++){\n      u64 nDistinct = p->current.anDLt[i] + 1;\n      u64 iVal = (p->nRow + nDistinct - 1) / nDistinct;\n      sqlite3_snprintf(24, z, \" %llu\", iVal);\n      z += sqlite3Strlen30(z);\n      assert( p->current.anEq[i] );\n    }\n    assert( z[0]=='\\0' && z>zRet );\n\n    sqlite3_result_text(context, zRet, -1, sqlite3_free);\n  }\n#ifdef SQLITE_ENABLE_STAT3_OR_STAT4\n  else if( eCall==STAT_GET_ROWID ){\n    if( p->iGet<0 ){\n      samplePushPrevious(p, 0);\n      p->iGet = 0;\n    }\n    if( p->iGet<p->nSample ){\n      Stat4Sample *pS = p->a + p->iGet;\n      if( pS->nRowid==0 ){\n        sqlite3_result_int64(context, pS->u.iRowid);\n      }else{\n        sqlite3_result_blob(context, pS->u.aRowid, pS->nRowid,\n                            SQLITE_TRANSIENT);\n      }\n    }\n  }else{\n    tRowcnt *aCnt = 0;\n\n    assert( p->iGet<p->nSample );\n    switch( eCall ){\n      case STAT_GET_NEQ:  aCnt = p->a[p->iGet].anEq; break;\n      case STAT_GET_NLT:  aCnt = p->a[p->iGet].anLt; break;\n      default: {\n        aCnt = p->a[p->iGet].anDLt; \n        p->iGet++;\n        break;\n      }\n    }\n\n    if( IsStat3 ){\n      sqlite3_result_int64(context, (i64)aCnt[0]);\n    }else{\n      char *zRet = sqlite3MallocZero(p->nCol * 25);\n      if( zRet==0 ){\n        sqlite3_result_error_nomem(context);\n      }else{\n        int i;\n        char *z = zRet;\n        for(i=0; i<p->nCol; i++){\n          sqlite3_snprintf(24, z, \"%llu \", (u64)aCnt[i]);\n          z += sqlite3Strlen30(z);\n        }\n        assert( z[0]=='\\0' && z>zRet );\n        z[-1] = '\\0';\n        sqlite3_result_text(context, zRet, -1, sqlite3_free);\n      }\n    }\n  }\n#endif /* SQLITE_ENABLE_STAT3_OR_STAT4 */\n#ifndef SQLITE_DEBUG\n  UNUSED_PARAMETER( argc );\n#endif\n}\nstatic const FuncDef statGetFuncdef = {\n  1+IsStat34,      /* nArg */\n  SQLITE_UTF8,     /* funcFlags */\n  0,               /* pUserData */\n  0,               /* pNext */\n  statGet,         /* xSFunc */\n  0,               /* xFinalize */\n  \"stat_get\",      /* zName */\n  {0}\n};\n\nstatic void callStatGet(Vdbe *v, int regStat4, int iParam, int regOut){\n  assert( regOut!=regStat4 && regOut!=regStat4+1 );\n#ifdef SQLITE_ENABLE_STAT3_OR_STAT4\n  sqlite3VdbeAddOp2(v, OP_Integer, iParam, regStat4+1);\n#elif SQLITE_DEBUG\n  assert( iParam==STAT_GET_STAT1 );\n#else\n  UNUSED_PARAMETER( iParam );\n#endif\n  sqlite3VdbeAddOp4(v, OP_Function0, 0, regStat4, regOut,\n                    (char*)&statGetFuncdef, P4_FUNCDEF);\n  sqlite3VdbeChangeP5(v, 1 + IsStat34);\n}\n\n/*\n** Generate code to do an analysis of all indices associated with\n** a single table.\n*/\nstatic void analyzeOneTable(\n  Parse *pParse,   /* Parser context */\n  Table *pTab,     /* Table whose indices are to be analyzed */\n  Index *pOnlyIdx, /* If not NULL, only analyze this one index */\n  int iStatCur,    /* Index of VdbeCursor that writes the sqlite_stat1 table */\n  int iMem,        /* Available memory locations begin here */\n  int iTab         /* Next available cursor */\n){\n  sqlite3 *db = pParse->db;    /* Database handle */\n  Index *pIdx;                 /* An index to being analyzed */\n  int iIdxCur;                 /* Cursor open on index being analyzed */\n  int iTabCur;                 /* Table cursor */\n  Vdbe *v;                     /* The virtual machine being built up */\n  int i;                       /* Loop counter */\n  int jZeroRows = -1;          /* Jump from here if number of rows is zero */\n  int iDb;                     /* Index of database containing pTab */\n  u8 needTableCnt = 1;         /* True to count the table */\n  int regNewRowid = iMem++;    /* Rowid for the inserted record */\n  int regStat4 = iMem++;       /* Register to hold Stat4Accum object */\n  int regChng = iMem++;        /* Index of changed index field */\n#ifdef SQLITE_ENABLE_STAT3_OR_STAT4\n  int regRowid = iMem++;       /* Rowid argument passed to stat_push() */\n#endif\n  int regTemp = iMem++;        /* Temporary use register */\n  int regTabname = iMem++;     /* Register containing table name */\n  int regIdxname = iMem++;     /* Register containing index name */\n  int regStat1 = iMem++;       /* Value for the stat column of sqlite_stat1 */\n  int regPrev = iMem;          /* MUST BE LAST (see below) */\n#ifdef SQLITE_ENABLE_PREUPDATE_HOOK\n  Table *pStat1 = 0; \n#endif\n\n  pParse->nMem = MAX(pParse->nMem, iMem);\n  v = sqlite3GetVdbe(pParse);\n  if( v==0 || NEVER(pTab==0) ){\n    return;\n  }\n  if( pTab->tnum==0 ){\n    /* Do not gather statistics on views or virtual tables */\n    return;\n  }\n  if( sqlite3_strlike(\"sqlite_%\", pTab->zName, 0)==0 ){\n    /* Do not gather statistics on system tables */\n    return;\n  }\n  assert( sqlite3BtreeHoldsAllMutexes(db) );\n  iDb = sqlite3SchemaToIndex(db, pTab->pSchema);\n  assert( iDb>=0 );\n  assert( sqlite3SchemaMutexHeld(db, iDb, 0) );\n#ifndef SQLITE_OMIT_AUTHORIZATION\n  if( sqlite3AuthCheck(pParse, SQLITE_ANALYZE, pTab->zName, 0,\n      db->aDb[iDb].zDbSName ) ){\n    return;\n  }\n#endif\n\n#ifdef SQLITE_ENABLE_PREUPDATE_HOOK\n  if( db->xPreUpdateCallback ){\n    pStat1 = (Table*)sqlite3DbMallocZero(db, sizeof(Table) + 13);\n    if( pStat1==0 ) return;\n    pStat1->zName = (char*)&pStat1[1];\n    memcpy(pStat1->zName, \"sqlite_stat1\", 13);\n    pStat1->nCol = 3;\n    pStat1->iPKey = -1;\n    sqlite3VdbeAddOp4(pParse->pVdbe, OP_Noop, 0, 0, 0,(char*)pStat1,P4_DYNBLOB);\n  }\n#endif\n\n  /* Establish a read-lock on the table at the shared-cache level. \n  ** Open a read-only cursor on the table. Also allocate a cursor number\n  ** to use for scanning indexes (iIdxCur). No index cursor is opened at\n  ** this time though.  */\n  sqlite3TableLock(pParse, iDb, pTab->tnum, 0, pTab->zName);\n  iTabCur = iTab++;\n  iIdxCur = iTab++;\n  pParse->nTab = MAX(pParse->nTab, iTab);\n  sqlite3OpenTable(pParse, iTabCur, iDb, pTab, OP_OpenRead);\n  sqlite3VdbeLoadString(v, regTabname, pTab->zName);\n\n  for(pIdx=pTab->pIndex; pIdx; pIdx=pIdx->pNext){\n    int nCol;                     /* Number of columns in pIdx. \"N\" */\n    int addrRewind;               /* Address of \"OP_Rewind iIdxCur\" */\n    int addrNextRow;              /* Address of \"next_row:\" */\n    const char *zIdxName;         /* Name of the index */\n    int nColTest;                 /* Number of columns to test for changes */\n\n    if( pOnlyIdx && pOnlyIdx!=pIdx ) continue;\n    if( pIdx->pPartIdxWhere==0 ) needTableCnt = 0;\n    if( !HasRowid(pTab) && IsPrimaryKeyIndex(pIdx) ){\n      nCol = pIdx->nKeyCol;\n      zIdxName = pTab->zName;\n      nColTest = nCol - 1;\n    }else{\n      nCol = pIdx->nColumn;\n      zIdxName = pIdx->zName;\n      nColTest = pIdx->uniqNotNull ? pIdx->nKeyCol-1 : nCol-1;\n    }\n\n    /* Populate the register containing the index name. */\n    sqlite3VdbeLoadString(v, regIdxname, zIdxName);\n    VdbeComment((v, \"Analysis for %s.%s\", pTab->zName, zIdxName));\n\n    /*\n    ** Pseudo-code for loop that calls stat_push():\n    **\n    **   Rewind csr\n    **   if eof(csr) goto end_of_scan;\n    **   regChng = 0\n    **   goto chng_addr_0;\n    **\n    **  next_row:\n    **   regChng = 0\n    **   if( idx(0) != regPrev(0) ) goto chng_addr_0\n    **   regChng = 1\n    **   if( idx(1) != regPrev(1) ) goto chng_addr_1\n    **   ...\n    **   regChng = N\n    **   goto chng_addr_N\n    **\n    **  chng_addr_0:\n    **   regPrev(0) = idx(0)\n    **  chng_addr_1:\n    **   regPrev(1) = idx(1)\n    **  ...\n    **\n    **  endDistinctTest:\n    **   regRowid = idx(rowid)\n    **   stat_push(P, regChng, regRowid)\n    **   Next csr\n    **   if !eof(csr) goto next_row;\n    **\n    **  end_of_scan:\n    */\n\n    /* Make sure there are enough memory cells allocated to accommodate \n    ** the regPrev array and a trailing rowid (the rowid slot is required\n    ** when building a record to insert into the sample column of \n    ** the sqlite_stat4 table.  */\n    pParse->nMem = MAX(pParse->nMem, regPrev+nColTest);\n\n    /* Open a read-only cursor on the index being analyzed. */\n    assert( iDb==sqlite3SchemaToIndex(db, pIdx->pSchema) );\n    sqlite3VdbeAddOp3(v, OP_OpenRead, iIdxCur, pIdx->tnum, iDb);\n    sqlite3VdbeSetP4KeyInfo(pParse, pIdx);\n    VdbeComment((v, \"%s\", pIdx->zName));\n\n    /* Invoke the stat_init() function. The arguments are:\n    ** \n    **    (1) the number of columns in the index including the rowid\n    **        (or for a WITHOUT ROWID table, the number of PK columns),\n    **    (2) the number of columns in the key without the rowid/pk\n    **    (3) the number of rows in the index,\n    **\n    **\n    ** The third argument is only used for STAT3 and STAT4\n    */\n#ifdef SQLITE_ENABLE_STAT3_OR_STAT4\n    sqlite3VdbeAddOp2(v, OP_Count, iIdxCur, regStat4+3);\n#endif\n    sqlite3VdbeAddOp2(v, OP_Integer, nCol, regStat4+1);\n    sqlite3VdbeAddOp2(v, OP_Integer, pIdx->nKeyCol, regStat4+2);\n    sqlite3VdbeAddOp4(v, OP_Function0, 0, regStat4+1, regStat4,\n                     (char*)&statInitFuncdef, P4_FUNCDEF);\n    sqlite3VdbeChangeP5(v, 2+IsStat34);\n\n    /* Implementation of the following:\n    **\n    **   Rewind csr\n    **   if eof(csr) goto end_of_scan;\n    **   regChng = 0\n    **   goto next_push_0;\n    **\n    */\n    addrRewind = sqlite3VdbeAddOp1(v, OP_Rewind, iIdxCur);\n    VdbeCoverage(v);\n    sqlite3VdbeAddOp2(v, OP_Integer, 0, regChng);\n    addrNextRow = sqlite3VdbeCurrentAddr(v);\n\n    if( nColTest>0 ){\n      int endDistinctTest = sqlite3VdbeMakeLabel(v);\n      int *aGotoChng;               /* Array of jump instruction addresses */\n      aGotoChng = sqlite3DbMallocRawNN(db, sizeof(int)*nColTest);\n      if( aGotoChng==0 ) continue;\n\n      /*\n      **  next_row:\n      **   regChng = 0\n      **   if( idx(0) != regPrev(0) ) goto chng_addr_0\n      **   regChng = 1\n      **   if( idx(1) != regPrev(1) ) goto chng_addr_1\n      **   ...\n      **   regChng = N\n      **   goto endDistinctTest\n      */\n      sqlite3VdbeAddOp0(v, OP_Goto);\n      addrNextRow = sqlite3VdbeCurrentAddr(v);\n      if( nColTest==1 && pIdx->nKeyCol==1 && IsUniqueIndex(pIdx) ){\n        /* For a single-column UNIQUE index, once we have found a non-NULL\n        ** row, we know that all the rest will be distinct, so skip \n        ** subsequent distinctness tests. */\n        sqlite3VdbeAddOp2(v, OP_NotNull, regPrev, endDistinctTest);\n        VdbeCoverage(v);\n      }\n      for(i=0; i<nColTest; i++){\n        char *pColl = (char*)sqlite3LocateCollSeq(pParse, pIdx->azColl[i]);\n        sqlite3VdbeAddOp2(v, OP_Integer, i, regChng);\n        sqlite3VdbeAddOp3(v, OP_Column, iIdxCur, i, regTemp);\n        aGotoChng[i] = \n        sqlite3VdbeAddOp4(v, OP_Ne, regTemp, 0, regPrev+i, pColl, P4_COLLSEQ);\n        sqlite3VdbeChangeP5(v, SQLITE_NULLEQ);\n        VdbeCoverage(v);\n      }\n      sqlite3VdbeAddOp2(v, OP_Integer, nColTest, regChng);\n      sqlite3VdbeGoto(v, endDistinctTest);\n  \n  \n      /*\n      **  chng_addr_0:\n      **   regPrev(0) = idx(0)\n      **  chng_addr_1:\n      **   regPrev(1) = idx(1)\n      **  ...\n      */\n      sqlite3VdbeJumpHere(v, addrNextRow-1);\n      for(i=0; i<nColTest; i++){\n        sqlite3VdbeJumpHere(v, aGotoChng[i]);\n        sqlite3VdbeAddOp3(v, OP_Column, iIdxCur, i, regPrev+i);\n      }\n      sqlite3VdbeResolveLabel(v, endDistinctTest);\n      sqlite3DbFree(db, aGotoChng);\n    }\n  \n    /*\n    **  chng_addr_N:\n    **   regRowid = idx(rowid)            // STAT34 only\n    **   stat_push(P, regChng, regRowid)  // 3rd parameter STAT34 only\n    **   Next csr\n    **   if !eof(csr) goto next_row;\n    */\n#ifdef SQLITE_ENABLE_STAT3_OR_STAT4\n    assert( regRowid==(regStat4+2) );\n    if( HasRowid(pTab) ){\n      sqlite3VdbeAddOp2(v, OP_IdxRowid, iIdxCur, regRowid);\n    }else{\n      Index *pPk = sqlite3PrimaryKeyIndex(pIdx->pTable);\n      int j, k, regKey;\n      regKey = sqlite3GetTempRange(pParse, pPk->nKeyCol);\n      for(j=0; j<pPk->nKeyCol; j++){\n        k = sqlite3ColumnOfIndex(pIdx, pPk->aiColumn[j]);\n        assert( k>=0 && k<pIdx->nColumn );\n        sqlite3VdbeAddOp3(v, OP_Column, iIdxCur, k, regKey+j);\n        VdbeComment((v, \"%s\", pTab->aCol[pPk->aiColumn[j]].zName));\n      }\n      sqlite3VdbeAddOp3(v, OP_MakeRecord, regKey, pPk->nKeyCol, regRowid);\n      sqlite3ReleaseTempRange(pParse, regKey, pPk->nKeyCol);\n    }\n#endif\n    assert( regChng==(regStat4+1) );\n    sqlite3VdbeAddOp4(v, OP_Function0, 1, regStat4, regTemp,\n                     (char*)&statPushFuncdef, P4_FUNCDEF);\n    sqlite3VdbeChangeP5(v, 2+IsStat34);\n    sqlite3VdbeAddOp2(v, OP_Next, iIdxCur, addrNextRow); VdbeCoverage(v);\n\n    /* Add the entry to the stat1 table. */\n    callStatGet(v, regStat4, STAT_GET_STAT1, regStat1);\n    assert( \"BBB\"[0]==SQLITE_AFF_TEXT );\n    sqlite3VdbeAddOp4(v, OP_MakeRecord, regTabname, 3, regTemp, \"BBB\", 0);\n    sqlite3VdbeAddOp2(v, OP_NewRowid, iStatCur, regNewRowid);\n    sqlite3VdbeAddOp3(v, OP_Insert, iStatCur, regTemp, regNewRowid);\n#ifdef SQLITE_ENABLE_PREUPDATE_HOOK\n    sqlite3VdbeChangeP4(v, -1, (char*)pStat1, P4_TABLE);\n#endif\n    sqlite3VdbeChangeP5(v, OPFLAG_APPEND);\n\n    /* Add the entries to the stat3 or stat4 table. */\n#ifdef SQLITE_ENABLE_STAT3_OR_STAT4\n    {\n      int regEq = regStat1;\n      int regLt = regStat1+1;\n      int regDLt = regStat1+2;\n      int regSample = regStat1+3;\n      int regCol = regStat1+4;\n      int regSampleRowid = regCol + nCol;\n      int addrNext;\n      int addrIsNull;\n      u8 seekOp = HasRowid(pTab) ? OP_NotExists : OP_NotFound;\n\n      pParse->nMem = MAX(pParse->nMem, regCol+nCol);\n\n      addrNext = sqlite3VdbeCurrentAddr(v);\n      callStatGet(v, regStat4, STAT_GET_ROWID, regSampleRowid);\n      addrIsNull = sqlite3VdbeAddOp1(v, OP_IsNull, regSampleRowid);\n      VdbeCoverage(v);\n      callStatGet(v, regStat4, STAT_GET_NEQ, regEq);\n      callStatGet(v, regStat4, STAT_GET_NLT, regLt);\n      callStatGet(v, regStat4, STAT_GET_NDLT, regDLt);\n      sqlite3VdbeAddOp4Int(v, seekOp, iTabCur, addrNext, regSampleRowid, 0);\n      /* We know that the regSampleRowid row exists because it was read by\n      ** the previous loop.  Thus the not-found jump of seekOp will never\n      ** be taken */\n      VdbeCoverageNeverTaken(v);\n#ifdef SQLITE_ENABLE_STAT3\n      sqlite3ExprCodeLoadIndexColumn(pParse, pIdx, iTabCur, 0, regSample);\n#else\n      for(i=0; i<nCol; i++){\n        sqlite3ExprCodeLoadIndexColumn(pParse, pIdx, iTabCur, i, regCol+i);\n      }\n      sqlite3VdbeAddOp3(v, OP_MakeRecord, regCol, nCol, regSample);\n#endif\n      sqlite3VdbeAddOp3(v, OP_MakeRecord, regTabname, 6, regTemp);\n      sqlite3VdbeAddOp2(v, OP_NewRowid, iStatCur+1, regNewRowid);\n      sqlite3VdbeAddOp3(v, OP_Insert, iStatCur+1, regTemp, regNewRowid);\n      sqlite3VdbeAddOp2(v, OP_Goto, 1, addrNext); /* P1==1 for end-of-loop */\n      sqlite3VdbeJumpHere(v, addrIsNull);\n    }\n#endif /* SQLITE_ENABLE_STAT3_OR_STAT4 */\n\n    /* End of analysis */\n    sqlite3VdbeJumpHere(v, addrRewind);\n  }\n\n\n  /* Create a single sqlite_stat1 entry containing NULL as the index\n  ** name and the row count as the content.\n  */\n  if( pOnlyIdx==0 && needTableCnt ){\n    VdbeComment((v, \"%s\", pTab->zName));\n    sqlite3VdbeAddOp2(v, OP_Count, iTabCur, regStat1);\n    jZeroRows = sqlite3VdbeAddOp1(v, OP_IfNot, regStat1); VdbeCoverage(v);\n    sqlite3VdbeAddOp2(v, OP_Null, 0, regIdxname);\n    assert( \"BBB\"[0]==SQLITE_AFF_TEXT );\n    sqlite3VdbeAddOp4(v, OP_MakeRecord, regTabname, 3, regTemp, \"BBB\", 0);\n    sqlite3VdbeAddOp2(v, OP_NewRowid, iStatCur, regNewRowid);\n    sqlite3VdbeAddOp3(v, OP_Insert, iStatCur, regTemp, regNewRowid);\n    sqlite3VdbeChangeP5(v, OPFLAG_APPEND);\n#ifdef SQLITE_ENABLE_PREUPDATE_HOOK\n    sqlite3VdbeChangeP4(v, -1, (char*)pStat1, P4_TABLE);\n#endif\n    sqlite3VdbeJumpHere(v, jZeroRows);\n  }\n}\n\n\n/*\n** Generate code that will cause the most recent index analysis to\n** be loaded into internal hash tables where is can be used.\n*/\nstatic void loadAnalysis(Parse *pParse, int iDb){\n  Vdbe *v = sqlite3GetVdbe(pParse);\n  if( v ){\n    sqlite3VdbeAddOp1(v, OP_LoadAnalysis, iDb);\n  }\n}\n\n/*\n** Generate code that will do an analysis of an entire database\n*/\nstatic void analyzeDatabase(Parse *pParse, int iDb){\n  sqlite3 *db = pParse->db;\n  Schema *pSchema = db->aDb[iDb].pSchema;    /* Schema of database iDb */\n  HashElem *k;\n  int iStatCur;\n  int iMem;\n  int iTab;\n\n  sqlite3BeginWriteOperation(pParse, 0, iDb);\n  iStatCur = pParse->nTab;\n  pParse->nTab += 3;\n  openStatTable(pParse, iDb, iStatCur, 0, 0);\n  iMem = pParse->nMem+1;\n  iTab = pParse->nTab;\n  assert( sqlite3SchemaMutexHeld(db, iDb, 0) );\n  for(k=sqliteHashFirst(&pSchema->tblHash); k; k=sqliteHashNext(k)){\n    Table *pTab = (Table*)sqliteHashData(k);\n    analyzeOneTable(pParse, pTab, 0, iStatCur, iMem, iTab);\n  }\n  loadAnalysis(pParse, iDb);\n}\n\n/*\n** Generate code that will do an analysis of a single table in\n** a database.  If pOnlyIdx is not NULL then it is a single index\n** in pTab that should be analyzed.\n*/\nstatic void analyzeTable(Parse *pParse, Table *pTab, Index *pOnlyIdx){\n  int iDb;\n  int iStatCur;\n\n  assert( pTab!=0 );\n  assert( sqlite3BtreeHoldsAllMutexes(pParse->db) );\n  iDb = sqlite3SchemaToIndex(pParse->db, pTab->pSchema);\n  sqlite3BeginWriteOperation(pParse, 0, iDb);\n  iStatCur = pParse->nTab;\n  pParse->nTab += 3;\n  if( pOnlyIdx ){\n    openStatTable(pParse, iDb, iStatCur, pOnlyIdx->zName, \"idx\");\n  }else{\n    openStatTable(pParse, iDb, iStatCur, pTab->zName, \"tbl\");\n  }\n  analyzeOneTable(pParse, pTab, pOnlyIdx, iStatCur,pParse->nMem+1,pParse->nTab);\n  loadAnalysis(pParse, iDb);\n}\n\n/*\n** Generate code for the ANALYZE command.  The parser calls this routine\n** when it recognizes an ANALYZE command.\n**\n**        ANALYZE                            -- 1\n**        ANALYZE  <database>                -- 2\n**        ANALYZE  ?<database>.?<tablename>  -- 3\n**\n** Form 1 causes all indices in all attached databases to be analyzed.\n** Form 2 analyzes all indices the single database named.\n** Form 3 analyzes all indices associated with the named table.\n*/\nSQLITE_PRIVATE void sqlite3Analyze(Parse *pParse, Token *pName1, Token *pName2){\n  sqlite3 *db = pParse->db;\n  int iDb;\n  int i;\n  char *z, *zDb;\n  Table *pTab;\n  Index *pIdx;\n  Token *pTableName;\n  Vdbe *v;\n\n  /* Read the database schema. If an error occurs, leave an error message\n  ** and code in pParse and return NULL. */\n  assert( sqlite3BtreeHoldsAllMutexes(pParse->db) );\n  if( SQLITE_OK!=sqlite3ReadSchema(pParse) ){\n    return;\n  }\n\n  assert( pName2!=0 || pName1==0 );\n  if( pName1==0 ){\n    /* Form 1:  Analyze everything */\n    for(i=0; i<db->nDb; i++){\n      if( i==1 ) continue;  /* Do not analyze the TEMP database */\n      analyzeDatabase(pParse, i);\n    }\n  }else if( pName2->n==0 && (iDb = sqlite3FindDb(db, pName1))>=0 ){\n    /* Analyze the schema named as the argument */\n    analyzeDatabase(pParse, iDb);\n  }else{\n    /* Form 3: Analyze the table or index named as an argument */\n    iDb = sqlite3TwoPartName(pParse, pName1, pName2, &pTableName);\n    if( iDb>=0 ){\n      zDb = pName2->n ? db->aDb[iDb].zDbSName : 0;\n      z = sqlite3NameFromToken(db, pTableName);\n      if( z ){\n        if( (pIdx = sqlite3FindIndex(db, z, zDb))!=0 ){\n          analyzeTable(pParse, pIdx->pTable, pIdx);\n        }else if( (pTab = sqlite3LocateTable(pParse, 0, z, zDb))!=0 ){\n          analyzeTable(pParse, pTab, 0);\n        }\n        sqlite3DbFree(db, z);\n      }\n    }\n  }\n  if( db->nSqlExec==0 && (v = sqlite3GetVdbe(pParse))!=0 ){\n    sqlite3VdbeAddOp0(v, OP_Expire);\n  }\n}\n\n/*\n** Used to pass information from the analyzer reader through to the\n** callback routine.\n*/\ntypedef struct analysisInfo analysisInfo;\nstruct analysisInfo {\n  sqlite3 *db;\n  const char *zDatabase;\n};\n\n/*\n** The first argument points to a nul-terminated string containing a\n** list of space separated integers. Read the first nOut of these into\n** the array aOut[].\n*/\nstatic void decodeIntArray(\n  char *zIntArray,       /* String containing int array to decode */\n  int nOut,              /* Number of slots in aOut[] */\n  tRowcnt *aOut,         /* Store integers here */\n  LogEst *aLog,          /* Or, if aOut==0, here */\n  Index *pIndex          /* Handle extra flags for this index, if not NULL */\n){\n  char *z = zIntArray;\n  int c;\n  int i;\n  tRowcnt v;\n\n#ifdef SQLITE_ENABLE_STAT3_OR_STAT4\n  if( z==0 ) z = \"\";\n#else\n  assert( z!=0 );\n#endif\n  for(i=0; *z && i<nOut; i++){\n    v = 0;\n    while( (c=z[0])>='0' && c<='9' ){\n      v = v*10 + c - '0';\n      z++;\n    }\n#ifdef SQLITE_ENABLE_STAT3_OR_STAT4\n    if( aOut ) aOut[i] = v;\n    if( aLog ) aLog[i] = sqlite3LogEst(v);\n#else\n    assert( aOut==0 );\n    UNUSED_PARAMETER(aOut);\n    assert( aLog!=0 );\n    aLog[i] = sqlite3LogEst(v);\n#endif\n    if( *z==' ' ) z++;\n  }\n#ifndef SQLITE_ENABLE_STAT3_OR_STAT4\n  assert( pIndex!=0 ); {\n#else\n  if( pIndex ){\n#endif\n    pIndex->bUnordered = 0;\n    pIndex->noSkipScan = 0;\n    while( z[0] ){\n      if( sqlite3_strglob(\"unordered*\", z)==0 ){\n        pIndex->bUnordered = 1;\n      }else if( sqlite3_strglob(\"sz=[0-9]*\", z)==0 ){\n        pIndex->szIdxRow = sqlite3LogEst(sqlite3Atoi(z+3));\n      }else if( sqlite3_strglob(\"noskipscan*\", z)==0 ){\n        pIndex->noSkipScan = 1;\n      }\n#ifdef SQLITE_ENABLE_COSTMULT\n      else if( sqlite3_strglob(\"costmult=[0-9]*\",z)==0 ){\n        pIndex->pTable->costMult = sqlite3LogEst(sqlite3Atoi(z+9));\n      }\n#endif\n      while( z[0]!=0 && z[0]!=' ' ) z++;\n      while( z[0]==' ' ) z++;\n    }\n  }\n}\n\n/*\n** This callback is invoked once for each index when reading the\n** sqlite_stat1 table.  \n**\n**     argv[0] = name of the table\n**     argv[1] = name of the index (might be NULL)\n**     argv[2] = results of analysis - on integer for each column\n**\n** Entries for which argv[1]==NULL simply record the number of rows in\n** the table.\n*/\nstatic int analysisLoader(void *pData, int argc, char **argv, char **NotUsed){\n  analysisInfo *pInfo = (analysisInfo*)pData;\n  Index *pIndex;\n  Table *pTable;\n  const char *z;\n\n  assert( argc==3 );\n  UNUSED_PARAMETER2(NotUsed, argc);\n\n  if( argv==0 || argv[0]==0 || argv[2]==0 ){\n    return 0;\n  }\n  pTable = sqlite3FindTable(pInfo->db, argv[0], pInfo->zDatabase);\n  if( pTable==0 ){\n    return 0;\n  }\n  if( argv[1]==0 ){\n    pIndex = 0;\n  }else if( sqlite3_stricmp(argv[0],argv[1])==0 ){\n    pIndex = sqlite3PrimaryKeyIndex(pTable);\n  }else{\n    pIndex = sqlite3FindIndex(pInfo->db, argv[1], pInfo->zDatabase);\n  }\n  z = argv[2];\n\n  if( pIndex ){\n    tRowcnt *aiRowEst = 0;\n    int nCol = pIndex->nKeyCol+1;\n#ifdef SQLITE_ENABLE_STAT3_OR_STAT4\n    /* Index.aiRowEst may already be set here if there are duplicate \n    ** sqlite_stat1 entries for this index. In that case just clobber\n    ** the old data with the new instead of allocating a new array.  */\n    if( pIndex->aiRowEst==0 ){\n      pIndex->aiRowEst = (tRowcnt*)sqlite3MallocZero(sizeof(tRowcnt) * nCol);\n      if( pIndex->aiRowEst==0 ) sqlite3OomFault(pInfo->db);\n    }\n    aiRowEst = pIndex->aiRowEst;\n#endif\n    pIndex->bUnordered = 0;\n    decodeIntArray((char*)z, nCol, aiRowEst, pIndex->aiRowLogEst, pIndex);\n    pIndex->hasStat1 = 1;\n    if( pIndex->pPartIdxWhere==0 ){\n      pTable->nRowLogEst = pIndex->aiRowLogEst[0];\n      pTable->tabFlags |= TF_HasStat1;\n    }\n  }else{\n    Index fakeIdx;\n    fakeIdx.szIdxRow = pTable->szTabRow;\n#ifdef SQLITE_ENABLE_COSTMULT\n    fakeIdx.pTable = pTable;\n#endif\n    decodeIntArray((char*)z, 1, 0, &pTable->nRowLogEst, &fakeIdx);\n    pTable->szTabRow = fakeIdx.szIdxRow;\n    pTable->tabFlags |= TF_HasStat1;\n  }\n\n  return 0;\n}\n\n/*\n** If the Index.aSample variable is not NULL, delete the aSample[] array\n** and its contents.\n*/\nSQLITE_PRIVATE void sqlite3DeleteIndexSamples(sqlite3 *db, Index *pIdx){\n#ifdef SQLITE_ENABLE_STAT3_OR_STAT4\n  if( pIdx->aSample ){\n    int j;\n    for(j=0; j<pIdx->nSample; j++){\n      IndexSample *p = &pIdx->aSample[j];\n      sqlite3DbFree(db, p->p);\n    }\n    sqlite3DbFree(db, pIdx->aSample);\n  }\n  if( db && db->pnBytesFreed==0 ){\n    pIdx->nSample = 0;\n    pIdx->aSample = 0;\n  }\n#else\n  UNUSED_PARAMETER(db);\n  UNUSED_PARAMETER(pIdx);\n#endif /* SQLITE_ENABLE_STAT3_OR_STAT4 */\n}\n\n#ifdef SQLITE_ENABLE_STAT3_OR_STAT4\n/*\n** Populate the pIdx->aAvgEq[] array based on the samples currently\n** stored in pIdx->aSample[]. \n*/\nstatic void initAvgEq(Index *pIdx){\n  if( pIdx ){\n    IndexSample *aSample = pIdx->aSample;\n    IndexSample *pFinal = &aSample[pIdx->nSample-1];\n    int iCol;\n    int nCol = 1;\n    if( pIdx->nSampleCol>1 ){\n      /* If this is stat4 data, then calculate aAvgEq[] values for all\n      ** sample columns except the last. The last is always set to 1, as\n      ** once the trailing PK fields are considered all index keys are\n      ** unique.  */\n      nCol = pIdx->nSampleCol-1;\n      pIdx->aAvgEq[nCol] = 1;\n    }\n    for(iCol=0; iCol<nCol; iCol++){\n      int nSample = pIdx->nSample;\n      int i;                    /* Used to iterate through samples */\n      tRowcnt sumEq = 0;        /* Sum of the nEq values */\n      tRowcnt avgEq = 0;\n      tRowcnt nRow;             /* Number of rows in index */\n      i64 nSum100 = 0;          /* Number of terms contributing to sumEq */\n      i64 nDist100;             /* Number of distinct values in index */\n\n      if( !pIdx->aiRowEst || iCol>=pIdx->nKeyCol || pIdx->aiRowEst[iCol+1]==0 ){\n        nRow = pFinal->anLt[iCol];\n        nDist100 = (i64)100 * pFinal->anDLt[iCol];\n        nSample--;\n      }else{\n        nRow = pIdx->aiRowEst[0];\n        nDist100 = ((i64)100 * pIdx->aiRowEst[0]) / pIdx->aiRowEst[iCol+1];\n      }\n      pIdx->nRowEst0 = nRow;\n\n      /* Set nSum to the number of distinct (iCol+1) field prefixes that\n      ** occur in the stat4 table for this index. Set sumEq to the sum of \n      ** the nEq values for column iCol for the same set (adding the value \n      ** only once where there exist duplicate prefixes).  */\n      for(i=0; i<nSample; i++){\n        if( i==(pIdx->nSample-1)\n         || aSample[i].anDLt[iCol]!=aSample[i+1].anDLt[iCol] \n        ){\n          sumEq += aSample[i].anEq[iCol];\n          nSum100 += 100;\n        }\n      }\n\n      if( nDist100>nSum100 && sumEq<nRow ){\n        avgEq = ((i64)100 * (nRow - sumEq))/(nDist100 - nSum100);\n      }\n      if( avgEq==0 ) avgEq = 1;\n      pIdx->aAvgEq[iCol] = avgEq;\n    }\n  }\n}\n\n/*\n** Look up an index by name.  Or, if the name of a WITHOUT ROWID table\n** is supplied instead, find the PRIMARY KEY index for that table.\n*/\nstatic Index *findIndexOrPrimaryKey(\n  sqlite3 *db,\n  const char *zName,\n  const char *zDb\n){\n  Index *pIdx = sqlite3FindIndex(db, zName, zDb);\n  if( pIdx==0 ){\n    Table *pTab = sqlite3FindTable(db, zName, zDb);\n    if( pTab && !HasRowid(pTab) ) pIdx = sqlite3PrimaryKeyIndex(pTab);\n  }\n  return pIdx;\n}\n\n/*\n** Load the content from either the sqlite_stat4 or sqlite_stat3 table \n** into the relevant Index.aSample[] arrays.\n**\n** Arguments zSql1 and zSql2 must point to SQL statements that return\n** data equivalent to the following (statements are different for stat3,\n** see the caller of this function for details):\n**\n**    zSql1: SELECT idx,count(*) FROM %Q.sqlite_stat4 GROUP BY idx\n**    zSql2: SELECT idx,neq,nlt,ndlt,sample FROM %Q.sqlite_stat4\n**\n** where %Q is replaced with the database name before the SQL is executed.\n*/\nstatic int loadStatTbl(\n  sqlite3 *db,                  /* Database handle */\n  int bStat3,                   /* Assume single column records only */\n  const char *zSql1,            /* SQL statement 1 (see above) */\n  const char *zSql2,            /* SQL statement 2 (see above) */\n  const char *zDb               /* Database name (e.g. \"main\") */\n){\n  int rc;                       /* Result codes from subroutines */\n  sqlite3_stmt *pStmt = 0;      /* An SQL statement being run */\n  char *zSql;                   /* Text of the SQL statement */\n  Index *pPrevIdx = 0;          /* Previous index in the loop */\n  IndexSample *pSample;         /* A slot in pIdx->aSample[] */\n\n  assert( db->lookaside.bDisable );\n  zSql = sqlite3MPrintf(db, zSql1, zDb);\n  if( !zSql ){\n    return SQLITE_NOMEM_BKPT;\n  }\n  rc = sqlite3_prepare(db, zSql, -1, &pStmt, 0);\n  sqlite3DbFree(db, zSql);\n  if( rc ) return rc;\n\n  while( sqlite3_step(pStmt)==SQLITE_ROW ){\n    int nIdxCol = 1;              /* Number of columns in stat4 records */\n\n    char *zIndex;   /* Index name */\n    Index *pIdx;    /* Pointer to the index object */\n    int nSample;    /* Number of samples */\n    int nByte;      /* Bytes of space required */\n    int i;          /* Bytes of space required */\n    tRowcnt *pSpace;\n\n    zIndex = (char *)sqlite3_column_text(pStmt, 0);\n    if( zIndex==0 ) continue;\n    nSample = sqlite3_column_int(pStmt, 1);\n    pIdx = findIndexOrPrimaryKey(db, zIndex, zDb);\n    assert( pIdx==0 || bStat3 || pIdx->nSample==0 );\n    /* Index.nSample is non-zero at this point if data has already been\n    ** loaded from the stat4 table. In this case ignore stat3 data.  */\n    if( pIdx==0 || pIdx->nSample ) continue;\n    if( bStat3==0 ){\n      assert( !HasRowid(pIdx->pTable) || pIdx->nColumn==pIdx->nKeyCol+1 );\n      if( !HasRowid(pIdx->pTable) && IsPrimaryKeyIndex(pIdx) ){\n        nIdxCol = pIdx->nKeyCol;\n      }else{\n        nIdxCol = pIdx->nColumn;\n      }\n    }\n    pIdx->nSampleCol = nIdxCol;\n    nByte = sizeof(IndexSample) * nSample;\n    nByte += sizeof(tRowcnt) * nIdxCol * 3 * nSample;\n    nByte += nIdxCol * sizeof(tRowcnt);     /* Space for Index.aAvgEq[] */\n\n    pIdx->aSample = sqlite3DbMallocZero(db, nByte);\n    if( pIdx->aSample==0 ){\n      sqlite3_finalize(pStmt);\n      return SQLITE_NOMEM_BKPT;\n    }\n    pSpace = (tRowcnt*)&pIdx->aSample[nSample];\n    pIdx->aAvgEq = pSpace; pSpace += nIdxCol;\n    for(i=0; i<nSample; i++){\n      pIdx->aSample[i].anEq = pSpace; pSpace += nIdxCol;\n      pIdx->aSample[i].anLt = pSpace; pSpace += nIdxCol;\n      pIdx->aSample[i].anDLt = pSpace; pSpace += nIdxCol;\n    }\n    assert( ((u8*)pSpace)-nByte==(u8*)(pIdx->aSample) );\n  }\n  rc = sqlite3_finalize(pStmt);\n  if( rc ) return rc;\n\n  zSql = sqlite3MPrintf(db, zSql2, zDb);\n  if( !zSql ){\n    return SQLITE_NOMEM_BKPT;\n  }\n  rc = sqlite3_prepare(db, zSql, -1, &pStmt, 0);\n  sqlite3DbFree(db, zSql);\n  if( rc ) return rc;\n\n  while( sqlite3_step(pStmt)==SQLITE_ROW ){\n    char *zIndex;                 /* Index name */\n    Index *pIdx;                  /* Pointer to the index object */\n    int nCol = 1;                 /* Number of columns in index */\n\n    zIndex = (char *)sqlite3_column_text(pStmt, 0);\n    if( zIndex==0 ) continue;\n    pIdx = findIndexOrPrimaryKey(db, zIndex, zDb);\n    if( pIdx==0 ) continue;\n    /* This next condition is true if data has already been loaded from \n    ** the sqlite_stat4 table. In this case ignore stat3 data.  */\n    nCol = pIdx->nSampleCol;\n    if( bStat3 && nCol>1 ) continue;\n    if( pIdx!=pPrevIdx ){\n      initAvgEq(pPrevIdx);\n      pPrevIdx = pIdx;\n    }\n    pSample = &pIdx->aSample[pIdx->nSample];\n    decodeIntArray((char*)sqlite3_column_text(pStmt,1),nCol,pSample->anEq,0,0);\n    decodeIntArray((char*)sqlite3_column_text(pStmt,2),nCol,pSample->anLt,0,0);\n    decodeIntArray((char*)sqlite3_column_text(pStmt,3),nCol,pSample->anDLt,0,0);\n\n    /* Take a copy of the sample. Add two 0x00 bytes the end of the buffer.\n    ** This is in case the sample record is corrupted. In that case, the\n    ** sqlite3VdbeRecordCompare() may read up to two varints past the\n    ** end of the allocated buffer before it realizes it is dealing with\n    ** a corrupt record. Adding the two 0x00 bytes prevents this from causing\n    ** a buffer overread.  */\n    pSample->n = sqlite3_column_bytes(pStmt, 4);\n    pSample->p = sqlite3DbMallocZero(db, pSample->n + 2);\n    if( pSample->p==0 ){\n      sqlite3_finalize(pStmt);\n      return SQLITE_NOMEM_BKPT;\n    }\n    if( pSample->n ){\n      memcpy(pSample->p, sqlite3_column_blob(pStmt, 4), pSample->n);\n    }\n    pIdx->nSample++;\n  }\n  rc = sqlite3_finalize(pStmt);\n  if( rc==SQLITE_OK ) initAvgEq(pPrevIdx);\n  return rc;\n}\n\n/*\n** Load content from the sqlite_stat4 and sqlite_stat3 tables into \n** the Index.aSample[] arrays of all indices.\n*/\nstatic int loadStat4(sqlite3 *db, const char *zDb){\n  int rc = SQLITE_OK;             /* Result codes from subroutines */\n\n  assert( db->lookaside.bDisable );\n  if( sqlite3FindTable(db, \"sqlite_stat4\", zDb) ){\n    rc = loadStatTbl(db, 0,\n      \"SELECT idx,count(*) FROM %Q.sqlite_stat4 GROUP BY idx\", \n      \"SELECT idx,neq,nlt,ndlt,sample FROM %Q.sqlite_stat4\",\n      zDb\n    );\n  }\n\n  if( rc==SQLITE_OK && sqlite3FindTable(db, \"sqlite_stat3\", zDb) ){\n    rc = loadStatTbl(db, 1,\n      \"SELECT idx,count(*) FROM %Q.sqlite_stat3 GROUP BY idx\", \n      \"SELECT idx,neq,nlt,ndlt,sqlite_record(sample) FROM %Q.sqlite_stat3\",\n      zDb\n    );\n  }\n\n  return rc;\n}\n#endif /* SQLITE_ENABLE_STAT3_OR_STAT4 */\n\n/*\n** Load the content of the sqlite_stat1 and sqlite_stat3/4 tables. The\n** contents of sqlite_stat1 are used to populate the Index.aiRowEst[]\n** arrays. The contents of sqlite_stat3/4 are used to populate the\n** Index.aSample[] arrays.\n**\n** If the sqlite_stat1 table is not present in the database, SQLITE_ERROR\n** is returned. In this case, even if SQLITE_ENABLE_STAT3/4 was defined \n** during compilation and the sqlite_stat3/4 table is present, no data is \n** read from it.\n**\n** If SQLITE_ENABLE_STAT3/4 was defined during compilation and the \n** sqlite_stat4 table is not present in the database, SQLITE_ERROR is\n** returned. However, in this case, data is read from the sqlite_stat1\n** table (if it is present) before returning.\n**\n** If an OOM error occurs, this function always sets db->mallocFailed.\n** This means if the caller does not care about other errors, the return\n** code may be ignored.\n*/\nSQLITE_PRIVATE int sqlite3AnalysisLoad(sqlite3 *db, int iDb){\n  analysisInfo sInfo;\n  HashElem *i;\n  char *zSql;\n  int rc = SQLITE_OK;\n  Schema *pSchema = db->aDb[iDb].pSchema;\n\n  assert( iDb>=0 && iDb<db->nDb );\n  assert( db->aDb[iDb].pBt!=0 );\n\n  /* Clear any prior statistics */\n  assert( sqlite3SchemaMutexHeld(db, iDb, 0) );\n  for(i=sqliteHashFirst(&pSchema->tblHash); i; i=sqliteHashNext(i)){\n    Table *pTab = sqliteHashData(i);\n    pTab->tabFlags &= ~TF_HasStat1;\n  }\n  for(i=sqliteHashFirst(&pSchema->idxHash); i; i=sqliteHashNext(i)){\n    Index *pIdx = sqliteHashData(i);\n    pIdx->hasStat1 = 0;\n#ifdef SQLITE_ENABLE_STAT3_OR_STAT4\n    sqlite3DeleteIndexSamples(db, pIdx);\n    pIdx->aSample = 0;\n#endif\n  }\n\n  /* Load new statistics out of the sqlite_stat1 table */\n  sInfo.db = db;\n  sInfo.zDatabase = db->aDb[iDb].zDbSName;\n  if( sqlite3FindTable(db, \"sqlite_stat1\", sInfo.zDatabase)!=0 ){\n    zSql = sqlite3MPrintf(db, \n        \"SELECT tbl,idx,stat FROM %Q.sqlite_stat1\", sInfo.zDatabase);\n    if( zSql==0 ){\n      rc = SQLITE_NOMEM_BKPT;\n    }else{\n      rc = sqlite3_exec(db, zSql, analysisLoader, &sInfo, 0);\n      sqlite3DbFree(db, zSql);\n    }\n  }\n\n  /* Set appropriate defaults on all indexes not in the sqlite_stat1 table */\n  assert( sqlite3SchemaMutexHeld(db, iDb, 0) );\n  for(i=sqliteHashFirst(&pSchema->idxHash); i; i=sqliteHashNext(i)){\n    Index *pIdx = sqliteHashData(i);\n    if( !pIdx->hasStat1 ) sqlite3DefaultRowEst(pIdx);\n  }\n\n  /* Load the statistics from the sqlite_stat4 table. */\n#ifdef SQLITE_ENABLE_STAT3_OR_STAT4\n  if( rc==SQLITE_OK && OptimizationEnabled(db, SQLITE_Stat34) ){\n    db->lookaside.bDisable++;\n    rc = loadStat4(db, sInfo.zDatabase);\n    db->lookaside.bDisable--;\n  }\n  for(i=sqliteHashFirst(&pSchema->idxHash); i; i=sqliteHashNext(i)){\n    Index *pIdx = sqliteHashData(i);\n    sqlite3_free(pIdx->aiRowEst);\n    pIdx->aiRowEst = 0;\n  }\n#endif\n\n  if( rc==SQLITE_NOMEM ){\n    sqlite3OomFault(db);\n  }\n  return rc;\n}\n\n\n#endif /* SQLITE_OMIT_ANALYZE */\n\n/************** End of analyze.c *********************************************/\n/************** Begin file attach.c ******************************************/\n/*\n** 2003 April 6\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n*************************************************************************\n** This file contains code used to implement the ATTACH and DETACH commands.\n*/\n/* #include \"sqliteInt.h\" */\n\n#ifndef SQLITE_OMIT_ATTACH\n/*\n** Resolve an expression that was part of an ATTACH or DETACH statement. This\n** is slightly different from resolving a normal SQL expression, because simple\n** identifiers are treated as strings, not possible column names or aliases.\n**\n** i.e. if the parser sees:\n**\n**     ATTACH DATABASE abc AS def\n**\n** it treats the two expressions as literal strings 'abc' and 'def' instead of\n** looking for columns of the same name.\n**\n** This only applies to the root node of pExpr, so the statement:\n**\n**     ATTACH DATABASE abc||def AS 'db2'\n**\n** will fail because neither abc or def can be resolved.\n*/\nstatic int resolveAttachExpr(NameContext *pName, Expr *pExpr)\n{\n  int rc = SQLITE_OK;\n  if( pExpr ){\n    if( pExpr->op!=TK_ID ){\n      rc = sqlite3ResolveExprNames(pName, pExpr);\n    }else{\n      pExpr->op = TK_STRING;\n    }\n  }\n  return rc;\n}\n\n/*\n** An SQL user-function registered to do the work of an ATTACH statement. The\n** three arguments to the function come directly from an attach statement:\n**\n**     ATTACH DATABASE x AS y KEY z\n**\n**     SELECT sqlite_attach(x, y, z)\n**\n** If the optional \"KEY z\" syntax is omitted, an SQL NULL is passed as the\n** third argument.\n*/\nstatic void attachFunc(\n  sqlite3_context *context,\n  int NotUsed,\n  sqlite3_value **argv\n){\n  int i;\n  int rc = 0;\n  sqlite3 *db = sqlite3_context_db_handle(context);\n  const char *zName;\n  const char *zFile;\n  char *zPath = 0;\n  char *zErr = 0;\n  unsigned int flags;\n  Db *aNew;                 /* New array of Db pointers */\n  Db *pNew;                 /* Db object for the newly attached database */\n  char *zErrDyn = 0;\n  sqlite3_vfs *pVfs;\n\n  UNUSED_PARAMETER(NotUsed);\n\n  zFile = (const char *)sqlite3_value_text(argv[0]);\n  zName = (const char *)sqlite3_value_text(argv[1]);\n  if( zFile==0 ) zFile = \"\";\n  if( zName==0 ) zName = \"\";\n\n  /* Check for the following errors:\n  **\n  **     * Too many attached databases,\n  **     * Transaction currently open\n  **     * Specified database name already being used.\n  */\n  if( db->nDb>=db->aLimit[SQLITE_LIMIT_ATTACHED]+2 ){\n    zErrDyn = sqlite3MPrintf(db, \"too many attached databases - max %d\", \n      db->aLimit[SQLITE_LIMIT_ATTACHED]\n    );\n    goto attach_error;\n  }\n  for(i=0; i<db->nDb; i++){\n    char *z = db->aDb[i].zDbSName;\n    assert( z && zName );\n    if( sqlite3StrICmp(z, zName)==0 ){\n      zErrDyn = sqlite3MPrintf(db, \"database %s is already in use\", zName);\n      goto attach_error;\n    }\n  }\n\n  /* Allocate the new entry in the db->aDb[] array and initialize the schema\n  ** hash tables.\n  */\n  if( db->aDb==db->aDbStatic ){\n    aNew = sqlite3DbMallocRawNN(db, sizeof(db->aDb[0])*3 );\n    if( aNew==0 ) return;\n    memcpy(aNew, db->aDb, sizeof(db->aDb[0])*2);\n  }else{\n    aNew = sqlite3DbRealloc(db, db->aDb, sizeof(db->aDb[0])*(db->nDb+1) );\n    if( aNew==0 ) return;\n  }\n  db->aDb = aNew;\n  pNew = &db->aDb[db->nDb];\n  memset(pNew, 0, sizeof(*pNew));\n\n  /* Open the database file. If the btree is successfully opened, use\n  ** it to obtain the database schema. At this point the schema may\n  ** or may not be initialized.\n  */\n  flags = db->openFlags;\n  rc = sqlite3ParseUri(db->pVfs->zName, zFile, &flags, &pVfs, &zPath, &zErr);\n  if( rc!=SQLITE_OK ){\n    if( rc==SQLITE_NOMEM ) sqlite3OomFault(db);\n    sqlite3_result_error(context, zErr, -1);\n    sqlite3_free(zErr);\n    return;\n  }\n  assert( pVfs );\n  flags |= SQLITE_OPEN_MAIN_DB;\n  rc = sqlite3BtreeOpen(pVfs, zPath, db, &pNew->pBt, 0, flags);\n  sqlite3_free( zPath );\n  db->nDb++;\n  db->skipBtreeMutex = 0;\n  if( rc==SQLITE_CONSTRAINT ){\n    rc = SQLITE_ERROR;\n    zErrDyn = sqlite3MPrintf(db, \"database is already attached\");\n  }else if( rc==SQLITE_OK ){\n    Pager *pPager;\n    pNew->pSchema = sqlite3SchemaGet(db, pNew->pBt);\n    if( !pNew->pSchema ){\n      rc = SQLITE_NOMEM_BKPT;\n    }else if( pNew->pSchema->file_format && pNew->pSchema->enc!=ENC(db) ){\n      zErrDyn = sqlite3MPrintf(db, \n        \"attached databases must use the same text encoding as main database\");\n      rc = SQLITE_ERROR;\n    }\n    sqlite3BtreeEnter(pNew->pBt);\n    pPager = sqlite3BtreePager(pNew->pBt);\n    sqlite3PagerLockingMode(pPager, db->dfltLockMode);\n    sqlite3BtreeSecureDelete(pNew->pBt,\n                             sqlite3BtreeSecureDelete(db->aDb[0].pBt,-1) );\n#ifndef SQLITE_OMIT_PAGER_PRAGMAS\n    sqlite3BtreeSetPagerFlags(pNew->pBt,\n                      PAGER_SYNCHRONOUS_FULL | (db->flags & PAGER_FLAGS_MASK));\n#endif\n    sqlite3BtreeLeave(pNew->pBt);\n  }\n  pNew->safety_level = SQLITE_DEFAULT_SYNCHRONOUS+1;\n  pNew->zDbSName = sqlite3DbStrDup(db, zName);\n  if( rc==SQLITE_OK && pNew->zDbSName==0 ){\n    rc = SQLITE_NOMEM_BKPT;\n  }\n\n\n#ifdef SQLITE_HAS_CODEC\n  if( rc==SQLITE_OK ){\n    extern int sqlite3CodecAttach(sqlite3*, int, const void*, int);\n    extern void sqlite3CodecGetKey(sqlite3*, int, void**, int*);\n    int nKey;\n    char *zKey;\n    int t = sqlite3_value_type(argv[2]);\n    switch( t ){\n      case SQLITE_INTEGER:\n      case SQLITE_FLOAT:\n        zErrDyn = sqlite3DbStrDup(db, \"Invalid key value\");\n        rc = SQLITE_ERROR;\n        break;\n        \n      case SQLITE_TEXT:\n      case SQLITE_BLOB:\n        nKey = sqlite3_value_bytes(argv[2]);\n        zKey = (char *)sqlite3_value_blob(argv[2]);\n        rc = sqlite3CodecAttach(db, db->nDb-1, zKey, nKey);\n        break;\n\n      case SQLITE_NULL:\n        /* No key specified.  Use the key from the main database */\n        sqlite3CodecGetKey(db, 0, (void**)&zKey, &nKey);\n        if( nKey || sqlite3BtreeGetOptimalReserve(db->aDb[0].pBt)>0 ){\n          rc = sqlite3CodecAttach(db, db->nDb-1, zKey, nKey);\n        }\n        break;\n    }\n  }\n#endif\n\n  /* If the file was opened successfully, read the schema for the new database.\n  ** If this fails, or if opening the file failed, then close the file and \n  ** remove the entry from the db->aDb[] array. i.e. put everything back the way\n  ** we found it.\n  */\n  if( rc==SQLITE_OK ){\n    sqlite3BtreeEnterAll(db);\n    rc = sqlite3Init(db, &zErrDyn);\n    sqlite3BtreeLeaveAll(db);\n  }\n#ifdef SQLITE_USER_AUTHENTICATION\n  if( rc==SQLITE_OK ){\n    u8 newAuth = 0;\n    rc = sqlite3UserAuthCheckLogin(db, zName, &newAuth);\n    if( newAuth<db->auth.authLevel ){\n      rc = SQLITE_AUTH_USER;\n    }\n  }\n#endif\n  if( rc ){\n    int iDb = db->nDb - 1;\n    assert( iDb>=2 );\n    if( db->aDb[iDb].pBt ){\n      sqlite3BtreeClose(db->aDb[iDb].pBt);\n      db->aDb[iDb].pBt = 0;\n      db->aDb[iDb].pSchema = 0;\n    }\n    sqlite3ResetAllSchemasOfConnection(db);\n    db->nDb = iDb;\n    if( rc==SQLITE_NOMEM || rc==SQLITE_IOERR_NOMEM ){\n      sqlite3OomFault(db);\n      sqlite3DbFree(db, zErrDyn);\n      zErrDyn = sqlite3MPrintf(db, \"out of memory\");\n    }else if( zErrDyn==0 ){\n      zErrDyn = sqlite3MPrintf(db, \"unable to open database: %s\", zFile);\n    }\n    goto attach_error;\n  }\n  \n  return;\n\nattach_error:\n  /* Return an error if we get here */\n  if( zErrDyn ){\n    sqlite3_result_error(context, zErrDyn, -1);\n    sqlite3DbFree(db, zErrDyn);\n  }\n  if( rc ) sqlite3_result_error_code(context, rc);\n}\n\n/*\n** An SQL user-function registered to do the work of an DETACH statement. The\n** three arguments to the function come directly from a detach statement:\n**\n**     DETACH DATABASE x\n**\n**     SELECT sqlite_detach(x)\n*/\nstatic void detachFunc(\n  sqlite3_context *context,\n  int NotUsed,\n  sqlite3_value **argv\n){\n  const char *zName = (const char *)sqlite3_value_text(argv[0]);\n  sqlite3 *db = sqlite3_context_db_handle(context);\n  int i;\n  Db *pDb = 0;\n  char zErr[128];\n\n  UNUSED_PARAMETER(NotUsed);\n\n  if( zName==0 ) zName = \"\";\n  for(i=0; i<db->nDb; i++){\n    pDb = &db->aDb[i];\n    if( pDb->pBt==0 ) continue;\n    if( sqlite3StrICmp(pDb->zDbSName, zName)==0 ) break;\n  }\n\n  if( i>=db->nDb ){\n    sqlite3_snprintf(sizeof(zErr),zErr, \"no such database: %s\", zName);\n    goto detach_error;\n  }\n  if( i<2 ){\n    sqlite3_snprintf(sizeof(zErr),zErr, \"cannot detach database %s\", zName);\n    goto detach_error;\n  }\n  if( sqlite3BtreeIsInReadTrans(pDb->pBt) || sqlite3BtreeIsInBackup(pDb->pBt) ){\n    sqlite3_snprintf(sizeof(zErr),zErr, \"database %s is locked\", zName);\n    goto detach_error;\n  }\n\n  sqlite3BtreeClose(pDb->pBt);\n  pDb->pBt = 0;\n  pDb->pSchema = 0;\n  sqlite3CollapseDatabaseArray(db);\n  return;\n\ndetach_error:\n  sqlite3_result_error(context, zErr, -1);\n}\n\n/*\n** This procedure generates VDBE code for a single invocation of either the\n** sqlite_detach() or sqlite_attach() SQL user functions.\n*/\nstatic void codeAttach(\n  Parse *pParse,       /* The parser context */\n  int type,            /* Either SQLITE_ATTACH or SQLITE_DETACH */\n  FuncDef const *pFunc,/* FuncDef wrapper for detachFunc() or attachFunc() */\n  Expr *pAuthArg,      /* Expression to pass to authorization callback */\n  Expr *pFilename,     /* Name of database file */\n  Expr *pDbname,       /* Name of the database to use internally */\n  Expr *pKey           /* Database key for encryption extension */\n){\n  int rc;\n  NameContext sName;\n  Vdbe *v;\n  sqlite3* db = pParse->db;\n  int regArgs;\n\n  if( pParse->nErr ) goto attach_end;\n  memset(&sName, 0, sizeof(NameContext));\n  sName.pParse = pParse;\n\n  if( \n      SQLITE_OK!=(rc = resolveAttachExpr(&sName, pFilename)) ||\n      SQLITE_OK!=(rc = resolveAttachExpr(&sName, pDbname)) ||\n      SQLITE_OK!=(rc = resolveAttachExpr(&sName, pKey))\n  ){\n    goto attach_end;\n  }\n\n#ifndef SQLITE_OMIT_AUTHORIZATION\n  if( pAuthArg ){\n    char *zAuthArg;\n    if( pAuthArg->op==TK_STRING ){\n      zAuthArg = pAuthArg->u.zToken;\n    }else{\n      zAuthArg = 0;\n    }\n    rc = sqlite3AuthCheck(pParse, type, zAuthArg, 0, 0);\n    if(rc!=SQLITE_OK ){\n      goto attach_end;\n    }\n  }\n#endif /* SQLITE_OMIT_AUTHORIZATION */\n\n\n  v = sqlite3GetVdbe(pParse);\n  regArgs = sqlite3GetTempRange(pParse, 4);\n  sqlite3ExprCode(pParse, pFilename, regArgs);\n  sqlite3ExprCode(pParse, pDbname, regArgs+1);\n  sqlite3ExprCode(pParse, pKey, regArgs+2);\n\n  assert( v || db->mallocFailed );\n  if( v ){\n    sqlite3VdbeAddOp4(v, OP_Function0, 0, regArgs+3-pFunc->nArg, regArgs+3,\n                      (char *)pFunc, P4_FUNCDEF);\n    assert( pFunc->nArg==-1 || (pFunc->nArg&0xff)==pFunc->nArg );\n    sqlite3VdbeChangeP5(v, (u8)(pFunc->nArg));\n \n    /* Code an OP_Expire. For an ATTACH statement, set P1 to true (expire this\n    ** statement only). For DETACH, set it to false (expire all existing\n    ** statements).\n    */\n    sqlite3VdbeAddOp1(v, OP_Expire, (type==SQLITE_ATTACH));\n  }\n  \nattach_end:\n  sqlite3ExprDelete(db, pFilename);\n  sqlite3ExprDelete(db, pDbname);\n  sqlite3ExprDelete(db, pKey);\n}\n\n/*\n** Called by the parser to compile a DETACH statement.\n**\n**     DETACH pDbname\n*/\nSQLITE_PRIVATE void sqlite3Detach(Parse *pParse, Expr *pDbname){\n  static const FuncDef detach_func = {\n    1,                /* nArg */\n    SQLITE_UTF8,      /* funcFlags */\n    0,                /* pUserData */\n    0,                /* pNext */\n    detachFunc,       /* xSFunc */\n    0,                /* xFinalize */\n    \"sqlite_detach\",  /* zName */\n    {0}\n  };\n  codeAttach(pParse, SQLITE_DETACH, &detach_func, pDbname, 0, 0, pDbname);\n}\n\n/*\n** Called by the parser to compile an ATTACH statement.\n**\n**     ATTACH p AS pDbname KEY pKey\n*/\nSQLITE_PRIVATE void sqlite3Attach(Parse *pParse, Expr *p, Expr *pDbname, Expr *pKey){\n  static const FuncDef attach_func = {\n    3,                /* nArg */\n    SQLITE_UTF8,      /* funcFlags */\n    0,                /* pUserData */\n    0,                /* pNext */\n    attachFunc,       /* xSFunc */\n    0,                /* xFinalize */\n    \"sqlite_attach\",  /* zName */\n    {0}\n  };\n  codeAttach(pParse, SQLITE_ATTACH, &attach_func, p, p, pDbname, pKey);\n}\n#endif /* SQLITE_OMIT_ATTACH */\n\n/*\n** Initialize a DbFixer structure.  This routine must be called prior\n** to passing the structure to one of the sqliteFixAAAA() routines below.\n*/\nSQLITE_PRIVATE void sqlite3FixInit(\n  DbFixer *pFix,      /* The fixer to be initialized */\n  Parse *pParse,      /* Error messages will be written here */\n  int iDb,            /* This is the database that must be used */\n  const char *zType,  /* \"view\", \"trigger\", or \"index\" */\n  const Token *pName  /* Name of the view, trigger, or index */\n){\n  sqlite3 *db;\n\n  db = pParse->db;\n  assert( db->nDb>iDb );\n  pFix->pParse = pParse;\n  pFix->zDb = db->aDb[iDb].zDbSName;\n  pFix->pSchema = db->aDb[iDb].pSchema;\n  pFix->zType = zType;\n  pFix->pName = pName;\n  pFix->bVarOnly = (iDb==1);\n}\n\n/*\n** The following set of routines walk through the parse tree and assign\n** a specific database to all table references where the database name\n** was left unspecified in the original SQL statement.  The pFix structure\n** must have been initialized by a prior call to sqlite3FixInit().\n**\n** These routines are used to make sure that an index, trigger, or\n** view in one database does not refer to objects in a different database.\n** (Exception: indices, triggers, and views in the TEMP database are\n** allowed to refer to anything.)  If a reference is explicitly made\n** to an object in a different database, an error message is added to\n** pParse->zErrMsg and these routines return non-zero.  If everything\n** checks out, these routines return 0.\n*/\nSQLITE_PRIVATE int sqlite3FixSrcList(\n  DbFixer *pFix,       /* Context of the fixation */\n  SrcList *pList       /* The Source list to check and modify */\n){\n  int i;\n  const char *zDb;\n  struct SrcList_item *pItem;\n\n  if( NEVER(pList==0) ) return 0;\n  zDb = pFix->zDb;\n  for(i=0, pItem=pList->a; i<pList->nSrc; i++, pItem++){\n    if( pFix->bVarOnly==0 ){\n      if( pItem->zDatabase && sqlite3StrICmp(pItem->zDatabase, zDb) ){\n        sqlite3ErrorMsg(pFix->pParse,\n            \"%s %T cannot reference objects in database %s\",\n            pFix->zType, pFix->pName, pItem->zDatabase);\n        return 1;\n      }\n      sqlite3DbFree(pFix->pParse->db, pItem->zDatabase);\n      pItem->zDatabase = 0;\n      pItem->pSchema = pFix->pSchema;\n    }\n#if !defined(SQLITE_OMIT_VIEW) || !defined(SQLITE_OMIT_TRIGGER)\n    if( sqlite3FixSelect(pFix, pItem->pSelect) ) return 1;\n    if( sqlite3FixExpr(pFix, pItem->pOn) ) return 1;\n#endif\n  }\n  return 0;\n}\n#if !defined(SQLITE_OMIT_VIEW) || !defined(SQLITE_OMIT_TRIGGER)\nSQLITE_PRIVATE int sqlite3FixSelect(\n  DbFixer *pFix,       /* Context of the fixation */\n  Select *pSelect      /* The SELECT statement to be fixed to one database */\n){\n  while( pSelect ){\n    if( sqlite3FixExprList(pFix, pSelect->pEList) ){\n      return 1;\n    }\n    if( sqlite3FixSrcList(pFix, pSelect->pSrc) ){\n      return 1;\n    }\n    if( sqlite3FixExpr(pFix, pSelect->pWhere) ){\n      return 1;\n    }\n    if( sqlite3FixExprList(pFix, pSelect->pGroupBy) ){\n      return 1;\n    }\n    if( sqlite3FixExpr(pFix, pSelect->pHaving) ){\n      return 1;\n    }\n    if( sqlite3FixExprList(pFix, pSelect->pOrderBy) ){\n      return 1;\n    }\n    if( sqlite3FixExpr(pFix, pSelect->pLimit) ){\n      return 1;\n    }\n    if( pSelect->pWith ){\n      int i;\n      for(i=0; i<pSelect->pWith->nCte; i++){\n        if( sqlite3FixSelect(pFix, pSelect->pWith->a[i].pSelect) ){\n          return 1;\n        }\n      }\n    }\n    pSelect = pSelect->pPrior;\n  }\n  return 0;\n}\nSQLITE_PRIVATE int sqlite3FixExpr(\n  DbFixer *pFix,     /* Context of the fixation */\n  Expr *pExpr        /* The expression to be fixed to one database */\n){\n  while( pExpr ){\n    if( pExpr->op==TK_VARIABLE ){\n      if( pFix->pParse->db->init.busy ){\n        pExpr->op = TK_NULL;\n      }else{\n        sqlite3ErrorMsg(pFix->pParse, \"%s cannot use variables\", pFix->zType);\n        return 1;\n      }\n    }\n    if( ExprHasProperty(pExpr, EP_TokenOnly|EP_Leaf) ) break;\n    if( ExprHasProperty(pExpr, EP_xIsSelect) ){\n      if( sqlite3FixSelect(pFix, pExpr->x.pSelect) ) return 1;\n    }else{\n      if( sqlite3FixExprList(pFix, pExpr->x.pList) ) return 1;\n    }\n    if( sqlite3FixExpr(pFix, pExpr->pRight) ){\n      return 1;\n    }\n    pExpr = pExpr->pLeft;\n  }\n  return 0;\n}\nSQLITE_PRIVATE int sqlite3FixExprList(\n  DbFixer *pFix,     /* Context of the fixation */\n  ExprList *pList    /* The expression to be fixed to one database */\n){\n  int i;\n  struct ExprList_item *pItem;\n  if( pList==0 ) return 0;\n  for(i=0, pItem=pList->a; i<pList->nExpr; i++, pItem++){\n    if( sqlite3FixExpr(pFix, pItem->pExpr) ){\n      return 1;\n    }\n  }\n  return 0;\n}\n#endif\n\n#ifndef SQLITE_OMIT_TRIGGER\nSQLITE_PRIVATE int sqlite3FixTriggerStep(\n  DbFixer *pFix,     /* Context of the fixation */\n  TriggerStep *pStep /* The trigger step be fixed to one database */\n){\n  while( pStep ){\n    if( sqlite3FixSelect(pFix, pStep->pSelect) ){\n      return 1;\n    }\n    if( sqlite3FixExpr(pFix, pStep->pWhere) ){\n      return 1;\n    }\n    if( sqlite3FixExprList(pFix, pStep->pExprList) ){\n      return 1;\n    }\n    pStep = pStep->pNext;\n  }\n  return 0;\n}\n#endif\n\n/************** End of attach.c **********************************************/\n/************** Begin file auth.c ********************************************/\n/*\n** 2003 January 11\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n*************************************************************************\n** This file contains code used to implement the sqlite3_set_authorizer()\n** API.  This facility is an optional feature of the library.  Embedded\n** systems that do not need this facility may omit it by recompiling\n** the library with -DSQLITE_OMIT_AUTHORIZATION=1\n*/\n/* #include \"sqliteInt.h\" */\n\n/*\n** All of the code in this file may be omitted by defining a single\n** macro.\n*/\n#ifndef SQLITE_OMIT_AUTHORIZATION\n\n/*\n** Set or clear the access authorization function.\n**\n** The access authorization function is be called during the compilation\n** phase to verify that the user has read and/or write access permission on\n** various fields of the database.  The first argument to the auth function\n** is a copy of the 3rd argument to this routine.  The second argument\n** to the auth function is one of these constants:\n**\n**       SQLITE_CREATE_INDEX\n**       SQLITE_CREATE_TABLE\n**       SQLITE_CREATE_TEMP_INDEX\n**       SQLITE_CREATE_TEMP_TABLE\n**       SQLITE_CREATE_TEMP_TRIGGER\n**       SQLITE_CREATE_TEMP_VIEW\n**       SQLITE_CREATE_TRIGGER\n**       SQLITE_CREATE_VIEW\n**       SQLITE_DELETE\n**       SQLITE_DROP_INDEX\n**       SQLITE_DROP_TABLE\n**       SQLITE_DROP_TEMP_INDEX\n**       SQLITE_DROP_TEMP_TABLE\n**       SQLITE_DROP_TEMP_TRIGGER\n**       SQLITE_DROP_TEMP_VIEW\n**       SQLITE_DROP_TRIGGER\n**       SQLITE_DROP_VIEW\n**       SQLITE_INSERT\n**       SQLITE_PRAGMA\n**       SQLITE_READ\n**       SQLITE_SELECT\n**       SQLITE_TRANSACTION\n**       SQLITE_UPDATE\n**\n** The third and fourth arguments to the auth function are the name of\n** the table and the column that are being accessed.  The auth function\n** should return either SQLITE_OK, SQLITE_DENY, or SQLITE_IGNORE.  If\n** SQLITE_OK is returned, it means that access is allowed.  SQLITE_DENY\n** means that the SQL statement will never-run - the sqlite3_exec() call\n** will return with an error.  SQLITE_IGNORE means that the SQL statement\n** should run but attempts to read the specified column will return NULL\n** and attempts to write the column will be ignored.\n**\n** Setting the auth function to NULL disables this hook.  The default\n** setting of the auth function is NULL.\n*/\nSQLITE_API int sqlite3_set_authorizer(\n  sqlite3 *db,\n  int (*xAuth)(void*,int,const char*,const char*,const char*,const char*),\n  void *pArg\n){\n#ifdef SQLITE_ENABLE_API_ARMOR\n  if( !sqlite3SafetyCheckOk(db) ) return SQLITE_MISUSE_BKPT;\n#endif\n  sqlite3_mutex_enter(db->mutex);\n  db->xAuth = (sqlite3_xauth)xAuth;\n  db->pAuthArg = pArg;\n  sqlite3ExpirePreparedStatements(db);\n  sqlite3_mutex_leave(db->mutex);\n  return SQLITE_OK;\n}\n\n/*\n** Write an error message into pParse->zErrMsg that explains that the\n** user-supplied authorization function returned an illegal value.\n*/\nstatic void sqliteAuthBadReturnCode(Parse *pParse){\n  sqlite3ErrorMsg(pParse, \"authorizer malfunction\");\n  pParse->rc = SQLITE_ERROR;\n}\n\n/*\n** Invoke the authorization callback for permission to read column zCol from\n** table zTab in database zDb. This function assumes that an authorization\n** callback has been registered (i.e. that sqlite3.xAuth is not NULL).\n**\n** If SQLITE_IGNORE is returned and pExpr is not NULL, then pExpr is changed\n** to an SQL NULL expression. Otherwise, if pExpr is NULL, then SQLITE_IGNORE\n** is treated as SQLITE_DENY. In this case an error is left in pParse.\n*/\nSQLITE_PRIVATE int sqlite3AuthReadCol(\n  Parse *pParse,                  /* The parser context */\n  const char *zTab,               /* Table name */\n  const char *zCol,               /* Column name */\n  int iDb                         /* Index of containing database. */\n){\n  sqlite3 *db = pParse->db;          /* Database handle */\n  char *zDb = db->aDb[iDb].zDbSName; /* Schema name of attached database */\n  int rc;                            /* Auth callback return code */\n\n  if( db->init.busy ) return SQLITE_OK;\n  rc = db->xAuth(db->pAuthArg, SQLITE_READ, zTab,zCol,zDb,pParse->zAuthContext\n#ifdef SQLITE_USER_AUTHENTICATION\n                 ,db->auth.zAuthUser\n#endif\n                );\n  if( rc==SQLITE_DENY ){\n    char *z = sqlite3_mprintf(\"%s.%s\", zTab, zCol);\n    if( db->nDb>2 || iDb!=0 ) z = sqlite3_mprintf(\"%s.%z\", zDb, z);\n    sqlite3ErrorMsg(pParse, \"access to %z is prohibited\", z);\n    pParse->rc = SQLITE_AUTH;\n  }else if( rc!=SQLITE_IGNORE && rc!=SQLITE_OK ){\n    sqliteAuthBadReturnCode(pParse);\n  }\n  return rc;\n}\n\n/*\n** The pExpr should be a TK_COLUMN expression.  The table referred to\n** is in pTabList or else it is the NEW or OLD table of a trigger.  \n** Check to see if it is OK to read this particular column.\n**\n** If the auth function returns SQLITE_IGNORE, change the TK_COLUMN \n** instruction into a TK_NULL.  If the auth function returns SQLITE_DENY,\n** then generate an error.\n*/\nSQLITE_PRIVATE void sqlite3AuthRead(\n  Parse *pParse,        /* The parser context */\n  Expr *pExpr,          /* The expression to check authorization on */\n  Schema *pSchema,      /* The schema of the expression */\n  SrcList *pTabList     /* All table that pExpr might refer to */\n){\n  sqlite3 *db = pParse->db;\n  Table *pTab = 0;      /* The table being read */\n  const char *zCol;     /* Name of the column of the table */\n  int iSrc;             /* Index in pTabList->a[] of table being read */\n  int iDb;              /* The index of the database the expression refers to */\n  int iCol;             /* Index of column in table */\n\n  if( db->xAuth==0 ) return;\n  iDb = sqlite3SchemaToIndex(pParse->db, pSchema);\n  if( iDb<0 ){\n    /* An attempt to read a column out of a subquery or other\n    ** temporary table. */\n    return;\n  }\n\n  assert( pExpr->op==TK_COLUMN || pExpr->op==TK_TRIGGER );\n  if( pExpr->op==TK_TRIGGER ){\n    pTab = pParse->pTriggerTab;\n  }else{\n    assert( pTabList );\n    for(iSrc=0; ALWAYS(iSrc<pTabList->nSrc); iSrc++){\n      if( pExpr->iTable==pTabList->a[iSrc].iCursor ){\n        pTab = pTabList->a[iSrc].pTab;\n        break;\n      }\n    }\n  }\n  iCol = pExpr->iColumn;\n  if( NEVER(pTab==0) ) return;\n\n  if( iCol>=0 ){\n    assert( iCol<pTab->nCol );\n    zCol = pTab->aCol[iCol].zName;\n  }else if( pTab->iPKey>=0 ){\n    assert( pTab->iPKey<pTab->nCol );\n    zCol = pTab->aCol[pTab->iPKey].zName;\n  }else{\n    zCol = \"ROWID\";\n  }\n  assert( iDb>=0 && iDb<db->nDb );\n  if( SQLITE_IGNORE==sqlite3AuthReadCol(pParse, pTab->zName, zCol, iDb) ){\n    pExpr->op = TK_NULL;\n  }\n}\n\n/*\n** Do an authorization check using the code and arguments given.  Return\n** either SQLITE_OK (zero) or SQLITE_IGNORE or SQLITE_DENY.  If SQLITE_DENY\n** is returned, then the error count and error message in pParse are\n** modified appropriately.\n*/\nSQLITE_PRIVATE int sqlite3AuthCheck(\n  Parse *pParse,\n  int code,\n  const char *zArg1,\n  const char *zArg2,\n  const char *zArg3\n){\n  sqlite3 *db = pParse->db;\n  int rc;\n\n  /* Don't do any authorization checks if the database is initialising\n  ** or if the parser is being invoked from within sqlite3_declare_vtab.\n  */\n  if( db->init.busy || IN_DECLARE_VTAB ){\n    return SQLITE_OK;\n  }\n\n  if( db->xAuth==0 ){\n    return SQLITE_OK;\n  }\n\n  /* EVIDENCE-OF: R-43249-19882 The third through sixth parameters to the\n  ** callback are either NULL pointers or zero-terminated strings that\n  ** contain additional details about the action to be authorized.\n  **\n  ** The following testcase() macros show that any of the 3rd through 6th\n  ** parameters can be either NULL or a string. */\n  testcase( zArg1==0 );\n  testcase( zArg2==0 );\n  testcase( zArg3==0 );\n  testcase( pParse->zAuthContext==0 );\n\n  rc = db->xAuth(db->pAuthArg, code, zArg1, zArg2, zArg3, pParse->zAuthContext\n#ifdef SQLITE_USER_AUTHENTICATION\n                 ,db->auth.zAuthUser\n#endif\n                );\n  if( rc==SQLITE_DENY ){\n    sqlite3ErrorMsg(pParse, \"not authorized\");\n    pParse->rc = SQLITE_AUTH;\n  }else if( rc!=SQLITE_OK && rc!=SQLITE_IGNORE ){\n    rc = SQLITE_DENY;\n    sqliteAuthBadReturnCode(pParse);\n  }\n  return rc;\n}\n\n/*\n** Push an authorization context.  After this routine is called, the\n** zArg3 argument to authorization callbacks will be zContext until\n** popped.  Or if pParse==0, this routine is a no-op.\n*/\nSQLITE_PRIVATE void sqlite3AuthContextPush(\n  Parse *pParse,\n  AuthContext *pContext, \n  const char *zContext\n){\n  assert( pParse );\n  pContext->pParse = pParse;\n  pContext->zAuthContext = pParse->zAuthContext;\n  pParse->zAuthContext = zContext;\n}\n\n/*\n** Pop an authorization context that was previously pushed\n** by sqlite3AuthContextPush\n*/\nSQLITE_PRIVATE void sqlite3AuthContextPop(AuthContext *pContext){\n  if( pContext->pParse ){\n    pContext->pParse->zAuthContext = pContext->zAuthContext;\n    pContext->pParse = 0;\n  }\n}\n\n#endif /* SQLITE_OMIT_AUTHORIZATION */\n\n/************** End of auth.c ************************************************/\n/************** Begin file build.c *******************************************/\n/*\n** 2001 September 15\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n*************************************************************************\n** This file contains C code routines that are called by the SQLite parser\n** when syntax rules are reduced.  The routines in this file handle the\n** following kinds of SQL syntax:\n**\n**     CREATE TABLE\n**     DROP TABLE\n**     CREATE INDEX\n**     DROP INDEX\n**     creating ID lists\n**     BEGIN TRANSACTION\n**     COMMIT\n**     ROLLBACK\n*/\n/* #include \"sqliteInt.h\" */\n\n#ifndef SQLITE_OMIT_SHARED_CACHE\n/*\n** The TableLock structure is only used by the sqlite3TableLock() and\n** codeTableLocks() functions.\n*/\nstruct TableLock {\n  int iDb;               /* The database containing the table to be locked */\n  int iTab;              /* The root page of the table to be locked */\n  u8 isWriteLock;        /* True for write lock.  False for a read lock */\n  const char *zLockName; /* Name of the table */\n};\n\n/*\n** Record the fact that we want to lock a table at run-time.  \n**\n** The table to be locked has root page iTab and is found in database iDb.\n** A read or a write lock can be taken depending on isWritelock.\n**\n** This routine just records the fact that the lock is desired.  The\n** code to make the lock occur is generated by a later call to\n** codeTableLocks() which occurs during sqlite3FinishCoding().\n*/\nSQLITE_PRIVATE void sqlite3TableLock(\n  Parse *pParse,     /* Parsing context */\n  int iDb,           /* Index of the database containing the table to lock */\n  int iTab,          /* Root page number of the table to be locked */\n  u8 isWriteLock,    /* True for a write lock */\n  const char *zName  /* Name of the table to be locked */\n){\n  Parse *pToplevel = sqlite3ParseToplevel(pParse);\n  int i;\n  int nBytes;\n  TableLock *p;\n  assert( iDb>=0 );\n\n  if( iDb==1 ) return;\n  if( !sqlite3BtreeSharable(pParse->db->aDb[iDb].pBt) ) return;\n  for(i=0; i<pToplevel->nTableLock; i++){\n    p = &pToplevel->aTableLock[i];\n    if( p->iDb==iDb && p->iTab==iTab ){\n      p->isWriteLock = (p->isWriteLock || isWriteLock);\n      return;\n    }\n  }\n\n  nBytes = sizeof(TableLock) * (pToplevel->nTableLock+1);\n  pToplevel->aTableLock =\n      sqlite3DbReallocOrFree(pToplevel->db, pToplevel->aTableLock, nBytes);\n  if( pToplevel->aTableLock ){\n    p = &pToplevel->aTableLock[pToplevel->nTableLock++];\n    p->iDb = iDb;\n    p->iTab = iTab;\n    p->isWriteLock = isWriteLock;\n    p->zLockName = zName;\n  }else{\n    pToplevel->nTableLock = 0;\n    sqlite3OomFault(pToplevel->db);\n  }\n}\n\n/*\n** Code an OP_TableLock instruction for each table locked by the\n** statement (configured by calls to sqlite3TableLock()).\n*/\nstatic void codeTableLocks(Parse *pParse){\n  int i;\n  Vdbe *pVdbe; \n\n  pVdbe = sqlite3GetVdbe(pParse);\n  assert( pVdbe!=0 ); /* sqlite3GetVdbe cannot fail: VDBE already allocated */\n\n  for(i=0; i<pParse->nTableLock; i++){\n    TableLock *p = &pParse->aTableLock[i];\n    int p1 = p->iDb;\n    sqlite3VdbeAddOp4(pVdbe, OP_TableLock, p1, p->iTab, p->isWriteLock,\n                      p->zLockName, P4_STATIC);\n  }\n}\n#else\n  #define codeTableLocks(x)\n#endif\n\n/*\n** Return TRUE if the given yDbMask object is empty - if it contains no\n** 1 bits.  This routine is used by the DbMaskAllZero() and DbMaskNotZero()\n** macros when SQLITE_MAX_ATTACHED is greater than 30.\n*/\n#if SQLITE_MAX_ATTACHED>30\nSQLITE_PRIVATE int sqlite3DbMaskAllZero(yDbMask m){\n  int i;\n  for(i=0; i<sizeof(yDbMask); i++) if( m[i] ) return 0;\n  return 1;\n}\n#endif\n\n/*\n** This routine is called after a single SQL statement has been\n** parsed and a VDBE program to execute that statement has been\n** prepared.  This routine puts the finishing touches on the\n** VDBE program and resets the pParse structure for the next\n** parse.\n**\n** Note that if an error occurred, it might be the case that\n** no VDBE code was generated.\n*/\nSQLITE_PRIVATE void sqlite3FinishCoding(Parse *pParse){\n  sqlite3 *db;\n  Vdbe *v;\n\n  assert( pParse->pToplevel==0 );\n  db = pParse->db;\n  if( pParse->nested ) return;\n  if( db->mallocFailed || pParse->nErr ){\n    if( pParse->rc==SQLITE_OK ) pParse->rc = SQLITE_ERROR;\n    return;\n  }\n\n  /* Begin by generating some termination code at the end of the\n  ** vdbe program\n  */\n  v = sqlite3GetVdbe(pParse);\n  assert( !pParse->isMultiWrite \n       || sqlite3VdbeAssertMayAbort(v, pParse->mayAbort));\n  if( v ){\n    sqlite3VdbeAddOp0(v, OP_Halt);\n\n#if SQLITE_USER_AUTHENTICATION\n    if( pParse->nTableLock>0 && db->init.busy==0 ){\n      sqlite3UserAuthInit(db);\n      if( db->auth.authLevel<UAUTH_User ){\n        sqlite3ErrorMsg(pParse, \"user not authenticated\");\n        pParse->rc = SQLITE_AUTH_USER;\n        return;\n      }\n    }\n#endif\n\n    /* The cookie mask contains one bit for each database file open.\n    ** (Bit 0 is for main, bit 1 is for temp, and so forth.)  Bits are\n    ** set for each database that is used.  Generate code to start a\n    ** transaction on each used database and to verify the schema cookie\n    ** on each used database.\n    */\n    if( db->mallocFailed==0 \n     && (DbMaskNonZero(pParse->cookieMask) || pParse->pConstExpr)\n    ){\n      int iDb, i;\n      assert( sqlite3VdbeGetOp(v, 0)->opcode==OP_Init );\n      sqlite3VdbeJumpHere(v, 0);\n      for(iDb=0; iDb<db->nDb; iDb++){\n        Schema *pSchema;\n        if( DbMaskTest(pParse->cookieMask, iDb)==0 ) continue;\n        sqlite3VdbeUsesBtree(v, iDb);\n        pSchema = db->aDb[iDb].pSchema;\n        sqlite3VdbeAddOp4Int(v,\n          OP_Transaction,                    /* Opcode */\n          iDb,                               /* P1 */\n          DbMaskTest(pParse->writeMask,iDb), /* P2 */\n          pSchema->schema_cookie,            /* P3 */\n          pSchema->iGeneration               /* P4 */\n        );\n        if( db->init.busy==0 ) sqlite3VdbeChangeP5(v, 1);\n        VdbeComment((v,\n              \"usesStmtJournal=%d\", pParse->mayAbort && pParse->isMultiWrite));\n      }\n#ifndef SQLITE_OMIT_VIRTUALTABLE\n      for(i=0; i<pParse->nVtabLock; i++){\n        char *vtab = (char *)sqlite3GetVTable(db, pParse->apVtabLock[i]);\n        sqlite3VdbeAddOp4(v, OP_VBegin, 0, 0, 0, vtab, P4_VTAB);\n      }\n      pParse->nVtabLock = 0;\n#endif\n\n      /* Once all the cookies have been verified and transactions opened, \n      ** obtain the required table-locks. This is a no-op unless the \n      ** shared-cache feature is enabled.\n      */\n      codeTableLocks(pParse);\n\n      /* Initialize any AUTOINCREMENT data structures required.\n      */\n      sqlite3AutoincrementBegin(pParse);\n\n      /* Code constant expressions that where factored out of inner loops */\n      if( pParse->pConstExpr ){\n        ExprList *pEL = pParse->pConstExpr;\n        pParse->okConstFactor = 0;\n        for(i=0; i<pEL->nExpr; i++){\n          sqlite3ExprCode(pParse, pEL->a[i].pExpr, pEL->a[i].u.iConstExprReg);\n        }\n      }\n\n      /* Finally, jump back to the beginning of the executable code. */\n      sqlite3VdbeGoto(v, 1);\n    }\n  }\n\n\n  /* Get the VDBE program ready for execution\n  */\n  if( v && pParse->nErr==0 && !db->mallocFailed ){\n    assert( pParse->iCacheLevel==0 );  /* Disables and re-enables match */\n    /* A minimum of one cursor is required if autoincrement is used\n    *  See ticket [a696379c1f08866] */\n    if( pParse->pAinc!=0 && pParse->nTab==0 ) pParse->nTab = 1;\n    sqlite3VdbeMakeReady(v, pParse);\n    pParse->rc = SQLITE_DONE;\n  }else{\n    pParse->rc = SQLITE_ERROR;\n  }\n}\n\n/*\n** Run the parser and code generator recursively in order to generate\n** code for the SQL statement given onto the end of the pParse context\n** currently under construction.  When the parser is run recursively\n** this way, the final OP_Halt is not appended and other initialization\n** and finalization steps are omitted because those are handling by the\n** outermost parser.\n**\n** Not everything is nestable.  This facility is designed to permit\n** INSERT, UPDATE, and DELETE operations against SQLITE_MASTER.  Use\n** care if you decide to try to use this routine for some other purposes.\n*/\nSQLITE_PRIVATE void sqlite3NestedParse(Parse *pParse, const char *zFormat, ...){\n  va_list ap;\n  char *zSql;\n  char *zErrMsg = 0;\n  sqlite3 *db = pParse->db;\n  char saveBuf[PARSE_TAIL_SZ];\n\n  if( pParse->nErr ) return;\n  assert( pParse->nested<10 );  /* Nesting should only be of limited depth */\n  va_start(ap, zFormat);\n  zSql = sqlite3VMPrintf(db, zFormat, ap);\n  va_end(ap);\n  if( zSql==0 ){\n    return;   /* A malloc must have failed */\n  }\n  pParse->nested++;\n  memcpy(saveBuf, PARSE_TAIL(pParse), PARSE_TAIL_SZ);\n  memset(PARSE_TAIL(pParse), 0, PARSE_TAIL_SZ);\n  sqlite3RunParser(pParse, zSql, &zErrMsg);\n  sqlite3DbFree(db, zErrMsg);\n  sqlite3DbFree(db, zSql);\n  memcpy(PARSE_TAIL(pParse), saveBuf, PARSE_TAIL_SZ);\n  pParse->nested--;\n}\n\n#if SQLITE_USER_AUTHENTICATION\n/*\n** Return TRUE if zTable is the name of the system table that stores the\n** list of users and their access credentials.\n*/\nSQLITE_PRIVATE int sqlite3UserAuthTable(const char *zTable){\n  return sqlite3_stricmp(zTable, \"sqlite_user\")==0;\n}\n#endif\n\n/*\n** Locate the in-memory structure that describes a particular database\n** table given the name of that table and (optionally) the name of the\n** database containing the table.  Return NULL if not found.\n**\n** If zDatabase is 0, all databases are searched for the table and the\n** first matching table is returned.  (No checking for duplicate table\n** names is done.)  The search order is TEMP first, then MAIN, then any\n** auxiliary databases added using the ATTACH command.\n**\n** See also sqlite3LocateTable().\n*/\nSQLITE_PRIVATE Table *sqlite3FindTable(sqlite3 *db, const char *zName, const char *zDatabase){\n  Table *p = 0;\n  int i;\n\n  /* All mutexes are required for schema access.  Make sure we hold them. */\n  assert( zDatabase!=0 || sqlite3BtreeHoldsAllMutexes(db) );\n#if SQLITE_USER_AUTHENTICATION\n  /* Only the admin user is allowed to know that the sqlite_user table\n  ** exists */\n  if( db->auth.authLevel<UAUTH_Admin && sqlite3UserAuthTable(zName)!=0 ){\n    return 0;\n  }\n#endif\n  while(1){\n    for(i=OMIT_TEMPDB; i<db->nDb; i++){\n      int j = (i<2) ? i^1 : i;   /* Search TEMP before MAIN */\n      if( zDatabase==0 || sqlite3StrICmp(zDatabase, db->aDb[j].zDbSName)==0 ){\n        assert( sqlite3SchemaMutexHeld(db, j, 0) );\n        p = sqlite3HashFind(&db->aDb[j].pSchema->tblHash, zName);\n        if( p ) return p;\n      }\n    }\n    /* Not found.  If the name we were looking for was temp.sqlite_master\n    ** then change the name to sqlite_temp_master and try again. */\n    if( sqlite3StrICmp(zName, MASTER_NAME)!=0 ) break;\n    if( sqlite3_stricmp(zDatabase, db->aDb[1].zDbSName)!=0 ) break;\n    zName = TEMP_MASTER_NAME;\n  }\n  return 0;\n}\n\n/*\n** Locate the in-memory structure that describes a particular database\n** table given the name of that table and (optionally) the name of the\n** database containing the table.  Return NULL if not found.  Also leave an\n** error message in pParse->zErrMsg.\n**\n** The difference between this routine and sqlite3FindTable() is that this\n** routine leaves an error message in pParse->zErrMsg where\n** sqlite3FindTable() does not.\n*/\nSQLITE_PRIVATE Table *sqlite3LocateTable(\n  Parse *pParse,         /* context in which to report errors */\n  u32 flags,             /* LOCATE_VIEW or LOCATE_NOERR */\n  const char *zName,     /* Name of the table we are looking for */\n  const char *zDbase     /* Name of the database.  Might be NULL */\n){\n  Table *p;\n\n  /* Read the database schema. If an error occurs, leave an error message\n  ** and code in pParse and return NULL. */\n  if( SQLITE_OK!=sqlite3ReadSchema(pParse) ){\n    return 0;\n  }\n\n  p = sqlite3FindTable(pParse->db, zName, zDbase);\n  if( p==0 ){\n    const char *zMsg = flags & LOCATE_VIEW ? \"no such view\" : \"no such table\";\n#ifndef SQLITE_OMIT_VIRTUALTABLE\n    if( sqlite3FindDbName(pParse->db, zDbase)<1 ){\n      /* If zName is the not the name of a table in the schema created using\n      ** CREATE, then check to see if it is the name of an virtual table that\n      ** can be an eponymous virtual table. */\n      Module *pMod = (Module*)sqlite3HashFind(&pParse->db->aModule, zName);\n      if( pMod==0 && sqlite3_strnicmp(zName, \"pragma_\", 7)==0 ){\n        pMod = sqlite3PragmaVtabRegister(pParse->db, zName);\n      }\n      if( pMod && sqlite3VtabEponymousTableInit(pParse, pMod) ){\n        return pMod->pEpoTab;\n      }\n    }\n#endif\n    if( (flags & LOCATE_NOERR)==0 ){\n      if( zDbase ){\n        sqlite3ErrorMsg(pParse, \"%s: %s.%s\", zMsg, zDbase, zName);\n      }else{\n        sqlite3ErrorMsg(pParse, \"%s: %s\", zMsg, zName);\n      }\n      pParse->checkSchema = 1;\n    }\n  }\n\n  return p;\n}\n\n/*\n** Locate the table identified by *p.\n**\n** This is a wrapper around sqlite3LocateTable(). The difference between\n** sqlite3LocateTable() and this function is that this function restricts\n** the search to schema (p->pSchema) if it is not NULL. p->pSchema may be\n** non-NULL if it is part of a view or trigger program definition. See\n** sqlite3FixSrcList() for details.\n*/\nSQLITE_PRIVATE Table *sqlite3LocateTableItem(\n  Parse *pParse, \n  u32 flags,\n  struct SrcList_item *p\n){\n  const char *zDb;\n  assert( p->pSchema==0 || p->zDatabase==0 );\n  if( p->pSchema ){\n    int iDb = sqlite3SchemaToIndex(pParse->db, p->pSchema);\n    zDb = pParse->db->aDb[iDb].zDbSName;\n  }else{\n    zDb = p->zDatabase;\n  }\n  return sqlite3LocateTable(pParse, flags, p->zName, zDb);\n}\n\n/*\n** Locate the in-memory structure that describes \n** a particular index given the name of that index\n** and the name of the database that contains the index.\n** Return NULL if not found.\n**\n** If zDatabase is 0, all databases are searched for the\n** table and the first matching index is returned.  (No checking\n** for duplicate index names is done.)  The search order is\n** TEMP first, then MAIN, then any auxiliary databases added\n** using the ATTACH command.\n*/\nSQLITE_PRIVATE Index *sqlite3FindIndex(sqlite3 *db, const char *zName, const char *zDb){\n  Index *p = 0;\n  int i;\n  /* All mutexes are required for schema access.  Make sure we hold them. */\n  assert( zDb!=0 || sqlite3BtreeHoldsAllMutexes(db) );\n  for(i=OMIT_TEMPDB; i<db->nDb; i++){\n    int j = (i<2) ? i^1 : i;  /* Search TEMP before MAIN */\n    Schema *pSchema = db->aDb[j].pSchema;\n    assert( pSchema );\n    if( zDb && sqlite3StrICmp(zDb, db->aDb[j].zDbSName) ) continue;\n    assert( sqlite3SchemaMutexHeld(db, j, 0) );\n    p = sqlite3HashFind(&pSchema->idxHash, zName);\n    if( p ) break;\n  }\n  return p;\n}\n\n/*\n** Reclaim the memory used by an index\n*/\nstatic void freeIndex(sqlite3 *db, Index *p){\n#ifndef SQLITE_OMIT_ANALYZE\n  sqlite3DeleteIndexSamples(db, p);\n#endif\n  sqlite3ExprDelete(db, p->pPartIdxWhere);\n  sqlite3ExprListDelete(db, p->aColExpr);\n  sqlite3DbFree(db, p->zColAff);\n  if( p->isResized ) sqlite3DbFree(db, (void *)p->azColl);\n#ifdef SQLITE_ENABLE_STAT3_OR_STAT4\n  sqlite3_free(p->aiRowEst);\n#endif\n  sqlite3DbFree(db, p);\n}\n\n/*\n** For the index called zIdxName which is found in the database iDb,\n** unlike that index from its Table then remove the index from\n** the index hash table and free all memory structures associated\n** with the index.\n*/\nSQLITE_PRIVATE void sqlite3UnlinkAndDeleteIndex(sqlite3 *db, int iDb, const char *zIdxName){\n  Index *pIndex;\n  Hash *pHash;\n\n  assert( sqlite3SchemaMutexHeld(db, iDb, 0) );\n  pHash = &db->aDb[iDb].pSchema->idxHash;\n  pIndex = sqlite3HashInsert(pHash, zIdxName, 0);\n  if( ALWAYS(pIndex) ){\n    if( pIndex->pTable->pIndex==pIndex ){\n      pIndex->pTable->pIndex = pIndex->pNext;\n    }else{\n      Index *p;\n      /* Justification of ALWAYS();  The index must be on the list of\n      ** indices. */\n      p = pIndex->pTable->pIndex;\n      while( ALWAYS(p) && p->pNext!=pIndex ){ p = p->pNext; }\n      if( ALWAYS(p && p->pNext==pIndex) ){\n        p->pNext = pIndex->pNext;\n      }\n    }\n    freeIndex(db, pIndex);\n  }\n  db->mDbFlags |= DBFLAG_SchemaChange;\n}\n\n/*\n** Look through the list of open database files in db->aDb[] and if\n** any have been closed, remove them from the list.  Reallocate the\n** db->aDb[] structure to a smaller size, if possible.\n**\n** Entry 0 (the \"main\" database) and entry 1 (the \"temp\" database)\n** are never candidates for being collapsed.\n*/\nSQLITE_PRIVATE void sqlite3CollapseDatabaseArray(sqlite3 *db){\n  int i, j;\n  for(i=j=2; i<db->nDb; i++){\n    struct Db *pDb = &db->aDb[i];\n    if( pDb->pBt==0 ){\n      sqlite3DbFree(db, pDb->zDbSName);\n      pDb->zDbSName = 0;\n      continue;\n    }\n    if( j<i ){\n      db->aDb[j] = db->aDb[i];\n    }\n    j++;\n  }\n  db->nDb = j;\n  if( db->nDb<=2 && db->aDb!=db->aDbStatic ){\n    memcpy(db->aDbStatic, db->aDb, 2*sizeof(db->aDb[0]));\n    sqlite3DbFree(db, db->aDb);\n    db->aDb = db->aDbStatic;\n  }\n}\n\n/*\n** Reset the schema for the database at index iDb.  Also reset the\n** TEMP schema.  The reset is deferred if db->nSchemaLock is not zero.\n** Deferred resets may be run by calling with iDb<0.\n*/\nSQLITE_PRIVATE void sqlite3ResetOneSchema(sqlite3 *db, int iDb){\n  int i;\n  assert( iDb<db->nDb );\n\n  if( iDb>=0 ){\n    assert( sqlite3SchemaMutexHeld(db, iDb, 0) );\n    DbSetProperty(db, iDb, DB_ResetWanted);\n    DbSetProperty(db, 1, DB_ResetWanted);\n  }\n\n  if( db->nSchemaLock==0 ){\n    for(i=0; i<db->nDb; i++){\n      if( DbHasProperty(db, i, DB_ResetWanted) ){\n        sqlite3SchemaClear(db->aDb[i].pSchema);\n      }\n    }\n  }\n}\n\n/*\n** Erase all schema information from all attached databases (including\n** \"main\" and \"temp\") for a single database connection.\n*/\nSQLITE_PRIVATE void sqlite3ResetAllSchemasOfConnection(sqlite3 *db){\n  int i;\n  sqlite3BtreeEnterAll(db);\n  assert( db->nSchemaLock==0 );\n  for(i=0; i<db->nDb; i++){\n    Db *pDb = &db->aDb[i];\n    if( pDb->pSchema ){\n      sqlite3SchemaClear(pDb->pSchema);\n    }\n  }\n  db->mDbFlags &= ~DBFLAG_SchemaChange;\n  sqlite3VtabUnlockList(db);\n  sqlite3BtreeLeaveAll(db);\n  sqlite3CollapseDatabaseArray(db);\n}\n\n/*\n** This routine is called when a commit occurs.\n*/\nSQLITE_PRIVATE void sqlite3CommitInternalChanges(sqlite3 *db){\n  db->mDbFlags &= ~DBFLAG_SchemaChange;\n}\n\n/*\n** Delete memory allocated for the column names of a table or view (the\n** Table.aCol[] array).\n*/\nSQLITE_PRIVATE void sqlite3DeleteColumnNames(sqlite3 *db, Table *pTable){\n  int i;\n  Column *pCol;\n  assert( pTable!=0 );\n  if( (pCol = pTable->aCol)!=0 ){\n    for(i=0; i<pTable->nCol; i++, pCol++){\n      sqlite3DbFree(db, pCol->zName);\n      sqlite3ExprDelete(db, pCol->pDflt);\n      sqlite3DbFree(db, pCol->zColl);\n    }\n    sqlite3DbFree(db, pTable->aCol);\n  }\n}\n\n/*\n** Remove the memory data structures associated with the given\n** Table.  No changes are made to disk by this routine.\n**\n** This routine just deletes the data structure.  It does not unlink\n** the table data structure from the hash table.  But it does destroy\n** memory structures of the indices and foreign keys associated with \n** the table.\n**\n** The db parameter is optional.  It is needed if the Table object \n** contains lookaside memory.  (Table objects in the schema do not use\n** lookaside memory, but some ephemeral Table objects do.)  Or the\n** db parameter can be used with db->pnBytesFreed to measure the memory\n** used by the Table object.\n*/\nstatic void SQLITE_NOINLINE deleteTable(sqlite3 *db, Table *pTable){\n  Index *pIndex, *pNext;\n\n#ifdef SQLITE_DEBUG\n  /* Record the number of outstanding lookaside allocations in schema Tables\n  ** prior to doing any free() operations.  Since schema Tables do not use\n  ** lookaside, this number should not change. */\n  int nLookaside = 0;\n  if( db && (pTable->tabFlags & TF_Ephemeral)==0 ){\n    nLookaside = sqlite3LookasideUsed(db, 0);\n  }\n#endif\n\n  /* Delete all indices associated with this table. */\n  for(pIndex = pTable->pIndex; pIndex; pIndex=pNext){\n    pNext = pIndex->pNext;\n    assert( pIndex->pSchema==pTable->pSchema\n         || (IsVirtual(pTable) && pIndex->idxType!=SQLITE_IDXTYPE_APPDEF) );\n    if( (db==0 || db->pnBytesFreed==0) && !IsVirtual(pTable) ){\n      char *zName = pIndex->zName; \n      TESTONLY ( Index *pOld = ) sqlite3HashInsert(\n         &pIndex->pSchema->idxHash, zName, 0\n      );\n      assert( db==0 || sqlite3SchemaMutexHeld(db, 0, pIndex->pSchema) );\n      assert( pOld==pIndex || pOld==0 );\n    }\n    freeIndex(db, pIndex);\n  }\n\n  /* Delete any foreign keys attached to this table. */\n  sqlite3FkDelete(db, pTable);\n\n  /* Delete the Table structure itself.\n  */\n  sqlite3DeleteColumnNames(db, pTable);\n  sqlite3DbFree(db, pTable->zName);\n  sqlite3DbFree(db, pTable->zColAff);\n  sqlite3SelectDelete(db, pTable->pSelect);\n  sqlite3ExprListDelete(db, pTable->pCheck);\n#ifndef SQLITE_OMIT_VIRTUALTABLE\n  sqlite3VtabClear(db, pTable);\n#endif\n  sqlite3DbFree(db, pTable);\n\n  /* Verify that no lookaside memory was used by schema tables */\n  assert( nLookaside==0 || nLookaside==sqlite3LookasideUsed(db,0) );\n}\nSQLITE_PRIVATE void sqlite3DeleteTable(sqlite3 *db, Table *pTable){\n  /* Do not delete the table until the reference count reaches zero. */\n  if( !pTable ) return;\n  if( ((!db || db->pnBytesFreed==0) && (--pTable->nTabRef)>0) ) return;\n  deleteTable(db, pTable);\n}\n\n\n/*\n** Unlink the given table from the hash tables and the delete the\n** table structure with all its indices and foreign keys.\n*/\nSQLITE_PRIVATE void sqlite3UnlinkAndDeleteTable(sqlite3 *db, int iDb, const char *zTabName){\n  Table *p;\n  Db *pDb;\n\n  assert( db!=0 );\n  assert( iDb>=0 && iDb<db->nDb );\n  assert( zTabName );\n  assert( sqlite3SchemaMutexHeld(db, iDb, 0) );\n  testcase( zTabName[0]==0 );  /* Zero-length table names are allowed */\n  pDb = &db->aDb[iDb];\n  p = sqlite3HashInsert(&pDb->pSchema->tblHash, zTabName, 0);\n  sqlite3DeleteTable(db, p);\n  db->mDbFlags |= DBFLAG_SchemaChange;\n}\n\n/*\n** Given a token, return a string that consists of the text of that\n** token.  Space to hold the returned string\n** is obtained from sqliteMalloc() and must be freed by the calling\n** function.\n**\n** Any quotation marks (ex:  \"name\", 'name', [name], or `name`) that\n** surround the body of the token are removed.\n**\n** Tokens are often just pointers into the original SQL text and so\n** are not \\000 terminated and are not persistent.  The returned string\n** is \\000 terminated and is persistent.\n*/\nSQLITE_PRIVATE char *sqlite3NameFromToken(sqlite3 *db, Token *pName){\n  char *zName;\n  if( pName ){\n    zName = sqlite3DbStrNDup(db, (char*)pName->z, pName->n);\n    sqlite3Dequote(zName);\n  }else{\n    zName = 0;\n  }\n  return zName;\n}\n\n/*\n** Open the sqlite_master table stored in database number iDb for\n** writing. The table is opened using cursor 0.\n*/\nSQLITE_PRIVATE void sqlite3OpenMasterTable(Parse *p, int iDb){\n  Vdbe *v = sqlite3GetVdbe(p);\n  sqlite3TableLock(p, iDb, MASTER_ROOT, 1, MASTER_NAME);\n  sqlite3VdbeAddOp4Int(v, OP_OpenWrite, 0, MASTER_ROOT, iDb, 5);\n  if( p->nTab==0 ){\n    p->nTab = 1;\n  }\n}\n\n/*\n** Parameter zName points to a nul-terminated buffer containing the name\n** of a database (\"main\", \"temp\" or the name of an attached db). This\n** function returns the index of the named database in db->aDb[], or\n** -1 if the named db cannot be found.\n*/\nSQLITE_PRIVATE int sqlite3FindDbName(sqlite3 *db, const char *zName){\n  int i = -1;         /* Database number */\n  if( zName ){\n    Db *pDb;\n    for(i=(db->nDb-1), pDb=&db->aDb[i]; i>=0; i--, pDb--){\n      if( 0==sqlite3_stricmp(pDb->zDbSName, zName) ) break;\n      /* \"main\" is always an acceptable alias for the primary database\n      ** even if it has been renamed using SQLITE_DBCONFIG_MAINDBNAME. */\n      if( i==0 && 0==sqlite3_stricmp(\"main\", zName) ) break;\n    }\n  }\n  return i;\n}\n\n/*\n** The token *pName contains the name of a database (either \"main\" or\n** \"temp\" or the name of an attached db). This routine returns the\n** index of the named database in db->aDb[], or -1 if the named db \n** does not exist.\n*/\nSQLITE_PRIVATE int sqlite3FindDb(sqlite3 *db, Token *pName){\n  int i;                               /* Database number */\n  char *zName;                         /* Name we are searching for */\n  zName = sqlite3NameFromToken(db, pName);\n  i = sqlite3FindDbName(db, zName);\n  sqlite3DbFree(db, zName);\n  return i;\n}\n\n/* The table or view or trigger name is passed to this routine via tokens\n** pName1 and pName2. If the table name was fully qualified, for example:\n**\n** CREATE TABLE xxx.yyy (...);\n** \n** Then pName1 is set to \"xxx\" and pName2 \"yyy\". On the other hand if\n** the table name is not fully qualified, i.e.:\n**\n** CREATE TABLE yyy(...);\n**\n** Then pName1 is set to \"yyy\" and pName2 is \"\".\n**\n** This routine sets the *ppUnqual pointer to point at the token (pName1 or\n** pName2) that stores the unqualified table name.  The index of the\n** database \"xxx\" is returned.\n*/\nSQLITE_PRIVATE int sqlite3TwoPartName(\n  Parse *pParse,      /* Parsing and code generating context */\n  Token *pName1,      /* The \"xxx\" in the name \"xxx.yyy\" or \"xxx\" */\n  Token *pName2,      /* The \"yyy\" in the name \"xxx.yyy\" */\n  Token **pUnqual     /* Write the unqualified object name here */\n){\n  int iDb;                    /* Database holding the object */\n  sqlite3 *db = pParse->db;\n\n  assert( pName2!=0 );\n  if( pName2->n>0 ){\n    if( db->init.busy ) {\n      sqlite3ErrorMsg(pParse, \"corrupt database\");\n      return -1;\n    }\n    *pUnqual = pName2;\n    iDb = sqlite3FindDb(db, pName1);\n    if( iDb<0 ){\n      sqlite3ErrorMsg(pParse, \"unknown database %T\", pName1);\n      return -1;\n    }\n  }else{\n    assert( db->init.iDb==0 || db->init.busy\n             || (db->mDbFlags & DBFLAG_Vacuum)!=0);\n    iDb = db->init.iDb;\n    *pUnqual = pName1;\n  }\n  return iDb;\n}\n\n/*\n** This routine is used to check if the UTF-8 string zName is a legal\n** unqualified name for a new schema object (table, index, view or\n** trigger). All names are legal except those that begin with the string\n** \"sqlite_\" (in upper, lower or mixed case). This portion of the namespace\n** is reserved for internal use.\n*/\nSQLITE_PRIVATE int sqlite3CheckObjectName(Parse *pParse, const char *zName){\n  if( !pParse->db->init.busy && pParse->nested==0 \n          && (pParse->db->flags & SQLITE_WriteSchema)==0\n          && 0==sqlite3StrNICmp(zName, \"sqlite_\", 7) ){\n    sqlite3ErrorMsg(pParse, \"object name reserved for internal use: %s\", zName);\n    return SQLITE_ERROR;\n  }\n  return SQLITE_OK;\n}\n\n/*\n** Return the PRIMARY KEY index of a table\n*/\nSQLITE_PRIVATE Index *sqlite3PrimaryKeyIndex(Table *pTab){\n  Index *p;\n  for(p=pTab->pIndex; p && !IsPrimaryKeyIndex(p); p=p->pNext){}\n  return p;\n}\n\n/*\n** Return the column of index pIdx that corresponds to table\n** column iCol.  Return -1 if not found.\n*/\nSQLITE_PRIVATE i16 sqlite3ColumnOfIndex(Index *pIdx, i16 iCol){\n  int i;\n  for(i=0; i<pIdx->nColumn; i++){\n    if( iCol==pIdx->aiColumn[i] ) return i;\n  }\n  return -1;\n}\n\n/*\n** Begin constructing a new table representation in memory.  This is\n** the first of several action routines that get called in response\n** to a CREATE TABLE statement.  In particular, this routine is called\n** after seeing tokens \"CREATE\" and \"TABLE\" and the table name. The isTemp\n** flag is true if the table should be stored in the auxiliary database\n** file instead of in the main database file.  This is normally the case\n** when the \"TEMP\" or \"TEMPORARY\" keyword occurs in between\n** CREATE and TABLE.\n**\n** The new table record is initialized and put in pParse->pNewTable.\n** As more of the CREATE TABLE statement is parsed, additional action\n** routines will be called to add more information to this record.\n** At the end of the CREATE TABLE statement, the sqlite3EndTable() routine\n** is called to complete the construction of the new table record.\n*/\nSQLITE_PRIVATE void sqlite3StartTable(\n  Parse *pParse,   /* Parser context */\n  Token *pName1,   /* First part of the name of the table or view */\n  Token *pName2,   /* Second part of the name of the table or view */\n  int isTemp,      /* True if this is a TEMP table */\n  int isView,      /* True if this is a VIEW */\n  int isVirtual,   /* True if this is a VIRTUAL table */\n  int noErr        /* Do nothing if table already exists */\n){\n  Table *pTable;\n  char *zName = 0; /* The name of the new table */\n  sqlite3 *db = pParse->db;\n  Vdbe *v;\n  int iDb;         /* Database number to create the table in */\n  Token *pName;    /* Unqualified name of the table to create */\n\n  if( db->init.busy && db->init.newTnum==1 ){\n    /* Special case:  Parsing the sqlite_master or sqlite_temp_master schema */\n    iDb = db->init.iDb;\n    zName = sqlite3DbStrDup(db, SCHEMA_TABLE(iDb));\n    pName = pName1;\n  }else{\n    /* The common case */\n    iDb = sqlite3TwoPartName(pParse, pName1, pName2, &pName);\n    if( iDb<0 ) return;\n    if( !OMIT_TEMPDB && isTemp && pName2->n>0 && iDb!=1 ){\n      /* If creating a temp table, the name may not be qualified. Unless \n      ** the database name is \"temp\" anyway.  */\n      sqlite3ErrorMsg(pParse, \"temporary table name must be unqualified\");\n      return;\n    }\n    if( !OMIT_TEMPDB && isTemp ) iDb = 1;\n    zName = sqlite3NameFromToken(db, pName);\n  }\n  pParse->sNameToken = *pName;\n  if( zName==0 ) return;\n  if( SQLITE_OK!=sqlite3CheckObjectName(pParse, zName) ){\n    goto begin_table_error;\n  }\n  if( db->init.iDb==1 ) isTemp = 1;\n#ifndef SQLITE_OMIT_AUTHORIZATION\n  assert( isTemp==0 || isTemp==1 );\n  assert( isView==0 || isView==1 );\n  {\n    static const u8 aCode[] = {\n       SQLITE_CREATE_TABLE,\n       SQLITE_CREATE_TEMP_TABLE,\n       SQLITE_CREATE_VIEW,\n       SQLITE_CREATE_TEMP_VIEW\n    };\n    char *zDb = db->aDb[iDb].zDbSName;\n    if( sqlite3AuthCheck(pParse, SQLITE_INSERT, SCHEMA_TABLE(isTemp), 0, zDb) ){\n      goto begin_table_error;\n    }\n    if( !isVirtual && sqlite3AuthCheck(pParse, (int)aCode[isTemp+2*isView],\n                                       zName, 0, zDb) ){\n      goto begin_table_error;\n    }\n  }\n#endif\n\n  /* Make sure the new table name does not collide with an existing\n  ** index or table name in the same database.  Issue an error message if\n  ** it does. The exception is if the statement being parsed was passed\n  ** to an sqlite3_declare_vtab() call. In that case only the column names\n  ** and types will be used, so there is no need to test for namespace\n  ** collisions.\n  */\n  if( !IN_DECLARE_VTAB ){\n    char *zDb = db->aDb[iDb].zDbSName;\n    if( SQLITE_OK!=sqlite3ReadSchema(pParse) ){\n      goto begin_table_error;\n    }\n    pTable = sqlite3FindTable(db, zName, zDb);\n    if( pTable ){\n      if( !noErr ){\n        sqlite3ErrorMsg(pParse, \"table %T already exists\", pName);\n      }else{\n        assert( !db->init.busy || CORRUPT_DB );\n        sqlite3CodeVerifySchema(pParse, iDb);\n      }\n      goto begin_table_error;\n    }\n    if( sqlite3FindIndex(db, zName, zDb)!=0 ){\n      sqlite3ErrorMsg(pParse, \"there is already an index named %s\", zName);\n      goto begin_table_error;\n    }\n  }\n\n  pTable = sqlite3DbMallocZero(db, sizeof(Table));\n  if( pTable==0 ){\n    assert( db->mallocFailed );\n    pParse->rc = SQLITE_NOMEM_BKPT;\n    pParse->nErr++;\n    goto begin_table_error;\n  }\n  pTable->zName = zName;\n  pTable->iPKey = -1;\n  pTable->pSchema = db->aDb[iDb].pSchema;\n  pTable->nTabRef = 1;\n#ifdef SQLITE_DEFAULT_ROWEST\n  pTable->nRowLogEst = sqlite3LogEst(SQLITE_DEFAULT_ROWEST);\n#else\n  pTable->nRowLogEst = 200; assert( 200==sqlite3LogEst(1048576) );\n#endif\n  assert( pParse->pNewTable==0 );\n  pParse->pNewTable = pTable;\n\n  /* If this is the magic sqlite_sequence table used by autoincrement,\n  ** then record a pointer to this table in the main database structure\n  ** so that INSERT can find the table easily.\n  */\n#ifndef SQLITE_OMIT_AUTOINCREMENT\n  if( !pParse->nested && strcmp(zName, \"sqlite_sequence\")==0 ){\n    assert( sqlite3SchemaMutexHeld(db, iDb, 0) );\n    pTable->pSchema->pSeqTab = pTable;\n  }\n#endif\n\n  /* Begin generating the code that will insert the table record into\n  ** the SQLITE_MASTER table.  Note in particular that we must go ahead\n  ** and allocate the record number for the table entry now.  Before any\n  ** PRIMARY KEY or UNIQUE keywords are parsed.  Those keywords will cause\n  ** indices to be created and the table record must come before the \n  ** indices.  Hence, the record number for the table must be allocated\n  ** now.\n  */\n  if( !db->init.busy && (v = sqlite3GetVdbe(pParse))!=0 ){\n    int addr1;\n    int fileFormat;\n    int reg1, reg2, reg3;\n    /* nullRow[] is an OP_Record encoding of a row containing 5 NULLs */\n    static const char nullRow[] = { 6, 0, 0, 0, 0, 0 };\n    sqlite3BeginWriteOperation(pParse, 1, iDb);\n\n#ifndef SQLITE_OMIT_VIRTUALTABLE\n    if( isVirtual ){\n      sqlite3VdbeAddOp0(v, OP_VBegin);\n    }\n#endif\n\n    /* If the file format and encoding in the database have not been set, \n    ** set them now.\n    */\n    reg1 = pParse->regRowid = ++pParse->nMem;\n    reg2 = pParse->regRoot = ++pParse->nMem;\n    reg3 = ++pParse->nMem;\n    sqlite3VdbeAddOp3(v, OP_ReadCookie, iDb, reg3, BTREE_FILE_FORMAT);\n    sqlite3VdbeUsesBtree(v, iDb);\n    addr1 = sqlite3VdbeAddOp1(v, OP_If, reg3); VdbeCoverage(v);\n    fileFormat = (db->flags & SQLITE_LegacyFileFmt)!=0 ?\n                  1 : SQLITE_MAX_FILE_FORMAT;\n    sqlite3VdbeAddOp3(v, OP_SetCookie, iDb, BTREE_FILE_FORMAT, fileFormat);\n    sqlite3VdbeAddOp3(v, OP_SetCookie, iDb, BTREE_TEXT_ENCODING, ENC(db));\n    sqlite3VdbeJumpHere(v, addr1);\n\n    /* This just creates a place-holder record in the sqlite_master table.\n    ** The record created does not contain anything yet.  It will be replaced\n    ** by the real entry in code generated at sqlite3EndTable().\n    **\n    ** The rowid for the new entry is left in register pParse->regRowid.\n    ** The root page number of the new table is left in reg pParse->regRoot.\n    ** The rowid and root page number values are needed by the code that\n    ** sqlite3EndTable will generate.\n    */\n#if !defined(SQLITE_OMIT_VIEW) || !defined(SQLITE_OMIT_VIRTUALTABLE)\n    if( isView || isVirtual ){\n      sqlite3VdbeAddOp2(v, OP_Integer, 0, reg2);\n    }else\n#endif\n    {\n      pParse->addrCrTab =\n         sqlite3VdbeAddOp3(v, OP_CreateBtree, iDb, reg2, BTREE_INTKEY);\n    }\n    sqlite3OpenMasterTable(pParse, iDb);\n    sqlite3VdbeAddOp2(v, OP_NewRowid, 0, reg1);\n    sqlite3VdbeAddOp4(v, OP_Blob, 6, reg3, 0, nullRow, P4_STATIC);\n    sqlite3VdbeAddOp3(v, OP_Insert, 0, reg3, reg1);\n    sqlite3VdbeChangeP5(v, OPFLAG_APPEND);\n    sqlite3VdbeAddOp0(v, OP_Close);\n  }\n\n  /* Normal (non-error) return. */\n  return;\n\n  /* If an error occurs, we jump here */\nbegin_table_error:\n  sqlite3DbFree(db, zName);\n  return;\n}\n\n/* Set properties of a table column based on the (magical)\n** name of the column.\n*/\n#if SQLITE_ENABLE_HIDDEN_COLUMNS\nSQLITE_PRIVATE void sqlite3ColumnPropertiesFromName(Table *pTab, Column *pCol){\n  if( sqlite3_strnicmp(pCol->zName, \"__hidden__\", 10)==0 ){\n    pCol->colFlags |= COLFLAG_HIDDEN;\n  }else if( pTab && pCol!=pTab->aCol && (pCol[-1].colFlags & COLFLAG_HIDDEN) ){\n    pTab->tabFlags |= TF_OOOHidden;\n  }\n}\n#endif\n\n\n/*\n** Add a new column to the table currently being constructed.\n**\n** The parser calls this routine once for each column declaration\n** in a CREATE TABLE statement.  sqlite3StartTable() gets called\n** first to get things going.  Then this routine is called for each\n** column.\n*/\nSQLITE_PRIVATE void sqlite3AddColumn(Parse *pParse, Token *pName, Token *pType){\n  Table *p;\n  int i;\n  char *z;\n  char *zType;\n  Column *pCol;\n  sqlite3 *db = pParse->db;\n  if( (p = pParse->pNewTable)==0 ) return;\n  if( p->nCol+1>db->aLimit[SQLITE_LIMIT_COLUMN] ){\n    sqlite3ErrorMsg(pParse, \"too many columns on %s\", p->zName);\n    return;\n  }\n  z = sqlite3DbMallocRaw(db, pName->n + pType->n + 2);\n  if( z==0 ) return;\n  memcpy(z, pName->z, pName->n);\n  z[pName->n] = 0;\n  sqlite3Dequote(z);\n  for(i=0; i<p->nCol; i++){\n    if( sqlite3_stricmp(z, p->aCol[i].zName)==0 ){\n      sqlite3ErrorMsg(pParse, \"duplicate column name: %s\", z);\n      sqlite3DbFree(db, z);\n      return;\n    }\n  }\n  if( (p->nCol & 0x7)==0 ){\n    Column *aNew;\n    aNew = sqlite3DbRealloc(db,p->aCol,(p->nCol+8)*sizeof(p->aCol[0]));\n    if( aNew==0 ){\n      sqlite3DbFree(db, z);\n      return;\n    }\n    p->aCol = aNew;\n  }\n  pCol = &p->aCol[p->nCol];\n  memset(pCol, 0, sizeof(p->aCol[0]));\n  pCol->zName = z;\n  sqlite3ColumnPropertiesFromName(p, pCol);\n \n  if( pType->n==0 ){\n    /* If there is no type specified, columns have the default affinity\n    ** 'BLOB'. */\n    pCol->affinity = SQLITE_AFF_BLOB;\n    pCol->szEst = 1;\n  }else{\n    zType = z + sqlite3Strlen30(z) + 1;\n    memcpy(zType, pType->z, pType->n);\n    zType[pType->n] = 0;\n    sqlite3Dequote(zType);\n    pCol->affinity = sqlite3AffinityType(zType, &pCol->szEst);\n    pCol->colFlags |= COLFLAG_HASTYPE;\n  }\n  p->nCol++;\n  pParse->constraintName.n = 0;\n}\n\n/*\n** This routine is called by the parser while in the middle of\n** parsing a CREATE TABLE statement.  A \"NOT NULL\" constraint has\n** been seen on a column.  This routine sets the notNull flag on\n** the column currently under construction.\n*/\nSQLITE_PRIVATE void sqlite3AddNotNull(Parse *pParse, int onError){\n  Table *p;\n  Column *pCol;\n  p = pParse->pNewTable;\n  if( p==0 || NEVER(p->nCol<1) ) return;\n  pCol = &p->aCol[p->nCol-1];\n  pCol->notNull = (u8)onError;\n  p->tabFlags |= TF_HasNotNull;\n\n  /* Set the uniqNotNull flag on any UNIQUE or PK indexes already created\n  ** on this column.  */\n  if( pCol->colFlags & COLFLAG_UNIQUE ){\n    Index *pIdx;\n    for(pIdx=p->pIndex; pIdx; pIdx=pIdx->pNext){\n      assert( pIdx->nKeyCol==1 && pIdx->onError!=OE_None );\n      if( pIdx->aiColumn[0]==p->nCol-1 ){\n        pIdx->uniqNotNull = 1;\n      }\n    }\n  }\n}\n\n/*\n** Scan the column type name zType (length nType) and return the\n** associated affinity type.\n**\n** This routine does a case-independent search of zType for the \n** substrings in the following table. If one of the substrings is\n** found, the corresponding affinity is returned. If zType contains\n** more than one of the substrings, entries toward the top of \n** the table take priority. For example, if zType is 'BLOBINT', \n** SQLITE_AFF_INTEGER is returned.\n**\n** Substring     | Affinity\n** --------------------------------\n** 'INT'         | SQLITE_AFF_INTEGER\n** 'CHAR'        | SQLITE_AFF_TEXT\n** 'CLOB'        | SQLITE_AFF_TEXT\n** 'TEXT'        | SQLITE_AFF_TEXT\n** 'BLOB'        | SQLITE_AFF_BLOB\n** 'REAL'        | SQLITE_AFF_REAL\n** 'FLOA'        | SQLITE_AFF_REAL\n** 'DOUB'        | SQLITE_AFF_REAL\n**\n** If none of the substrings in the above table are found,\n** SQLITE_AFF_NUMERIC is returned.\n*/\nSQLITE_PRIVATE char sqlite3AffinityType(const char *zIn, u8 *pszEst){\n  u32 h = 0;\n  char aff = SQLITE_AFF_NUMERIC;\n  const char *zChar = 0;\n\n  assert( zIn!=0 );\n  while( zIn[0] ){\n    h = (h<<8) + sqlite3UpperToLower[(*zIn)&0xff];\n    zIn++;\n    if( h==(('c'<<24)+('h'<<16)+('a'<<8)+'r') ){             /* CHAR */\n      aff = SQLITE_AFF_TEXT;\n      zChar = zIn;\n    }else if( h==(('c'<<24)+('l'<<16)+('o'<<8)+'b') ){       /* CLOB */\n      aff = SQLITE_AFF_TEXT;\n    }else if( h==(('t'<<24)+('e'<<16)+('x'<<8)+'t') ){       /* TEXT */\n      aff = SQLITE_AFF_TEXT;\n    }else if( h==(('b'<<24)+('l'<<16)+('o'<<8)+'b')          /* BLOB */\n        && (aff==SQLITE_AFF_NUMERIC || aff==SQLITE_AFF_REAL) ){\n      aff = SQLITE_AFF_BLOB;\n      if( zIn[0]=='(' ) zChar = zIn;\n#ifndef SQLITE_OMIT_FLOATING_POINT\n    }else if( h==(('r'<<24)+('e'<<16)+('a'<<8)+'l')          /* REAL */\n        && aff==SQLITE_AFF_NUMERIC ){\n      aff = SQLITE_AFF_REAL;\n    }else if( h==(('f'<<24)+('l'<<16)+('o'<<8)+'a')          /* FLOA */\n        && aff==SQLITE_AFF_NUMERIC ){\n      aff = SQLITE_AFF_REAL;\n    }else if( h==(('d'<<24)+('o'<<16)+('u'<<8)+'b')          /* DOUB */\n        && aff==SQLITE_AFF_NUMERIC ){\n      aff = SQLITE_AFF_REAL;\n#endif\n    }else if( (h&0x00FFFFFF)==(('i'<<16)+('n'<<8)+'t') ){    /* INT */\n      aff = SQLITE_AFF_INTEGER;\n      break;\n    }\n  }\n\n  /* If pszEst is not NULL, store an estimate of the field size.  The\n  ** estimate is scaled so that the size of an integer is 1.  */\n  if( pszEst ){\n    *pszEst = 1;   /* default size is approx 4 bytes */\n    if( aff<SQLITE_AFF_NUMERIC ){\n      if( zChar ){\n        while( zChar[0] ){\n          if( sqlite3Isdigit(zChar[0]) ){\n            int v = 0;\n            sqlite3GetInt32(zChar, &v);\n            v = v/4 + 1;\n            if( v>255 ) v = 255;\n            *pszEst = v; /* BLOB(k), VARCHAR(k), CHAR(k) -> r=(k/4+1) */\n            break;\n          }\n          zChar++;\n        }\n      }else{\n        *pszEst = 5;   /* BLOB, TEXT, CLOB -> r=5  (approx 20 bytes)*/\n      }\n    }\n  }\n  return aff;\n}\n\n/*\n** The expression is the default value for the most recently added column\n** of the table currently under construction.\n**\n** Default value expressions must be constant.  Raise an exception if this\n** is not the case.\n**\n** This routine is called by the parser while in the middle of\n** parsing a CREATE TABLE statement.\n*/\nSQLITE_PRIVATE void sqlite3AddDefaultValue(\n  Parse *pParse,           /* Parsing context */\n  Expr *pExpr,             /* The parsed expression of the default value */\n  const char *zStart,      /* Start of the default value text */\n  const char *zEnd         /* First character past end of defaut value text */\n){\n  Table *p;\n  Column *pCol;\n  sqlite3 *db = pParse->db;\n  p = pParse->pNewTable;\n  if( p!=0 ){\n    pCol = &(p->aCol[p->nCol-1]);\n    if( !sqlite3ExprIsConstantOrFunction(pExpr, db->init.busy) ){\n      sqlite3ErrorMsg(pParse, \"default value of column [%s] is not constant\",\n          pCol->zName);\n    }else{\n      /* A copy of pExpr is used instead of the original, as pExpr contains\n      ** tokens that point to volatile memory.\t\n      */\n      Expr x;\n      sqlite3ExprDelete(db, pCol->pDflt);\n      memset(&x, 0, sizeof(x));\n      x.op = TK_SPAN;\n      x.u.zToken = sqlite3DbSpanDup(db, zStart, zEnd);\n      x.pLeft = pExpr;\n      x.flags = EP_Skip;\n      pCol->pDflt = sqlite3ExprDup(db, &x, EXPRDUP_REDUCE);\n      sqlite3DbFree(db, x.u.zToken);\n    }\n  }\n  sqlite3ExprDelete(db, pExpr);\n}\n\n/*\n** Backwards Compatibility Hack:\n** \n** Historical versions of SQLite accepted strings as column names in\n** indexes and PRIMARY KEY constraints and in UNIQUE constraints.  Example:\n**\n**     CREATE TABLE xyz(a,b,c,d,e,PRIMARY KEY('a'),UNIQUE('b','c' COLLATE trim)\n**     CREATE INDEX abc ON xyz('c','d' DESC,'e' COLLATE nocase DESC);\n**\n** This is goofy.  But to preserve backwards compatibility we continue to\n** accept it.  This routine does the necessary conversion.  It converts\n** the expression given in its argument from a TK_STRING into a TK_ID\n** if the expression is just a TK_STRING with an optional COLLATE clause.\n** If the epxression is anything other than TK_STRING, the expression is\n** unchanged.\n*/\nstatic void sqlite3StringToId(Expr *p){\n  if( p->op==TK_STRING ){\n    p->op = TK_ID;\n  }else if( p->op==TK_COLLATE && p->pLeft->op==TK_STRING ){\n    p->pLeft->op = TK_ID;\n  }\n}\n\n/*\n** Designate the PRIMARY KEY for the table.  pList is a list of names \n** of columns that form the primary key.  If pList is NULL, then the\n** most recently added column of the table is the primary key.\n**\n** A table can have at most one primary key.  If the table already has\n** a primary key (and this is the second primary key) then create an\n** error.\n**\n** If the PRIMARY KEY is on a single column whose datatype is INTEGER,\n** then we will try to use that column as the rowid.  Set the Table.iPKey\n** field of the table under construction to be the index of the\n** INTEGER PRIMARY KEY column.  Table.iPKey is set to -1 if there is\n** no INTEGER PRIMARY KEY.\n**\n** If the key is not an INTEGER PRIMARY KEY, then create a unique\n** index for the key.  No index is created for INTEGER PRIMARY KEYs.\n*/\nSQLITE_PRIVATE void sqlite3AddPrimaryKey(\n  Parse *pParse,    /* Parsing context */\n  ExprList *pList,  /* List of field names to be indexed */\n  int onError,      /* What to do with a uniqueness conflict */\n  int autoInc,      /* True if the AUTOINCREMENT keyword is present */\n  int sortOrder     /* SQLITE_SO_ASC or SQLITE_SO_DESC */\n){\n  Table *pTab = pParse->pNewTable;\n  Column *pCol = 0;\n  int iCol = -1, i;\n  int nTerm;\n  if( pTab==0 ) goto primary_key_exit;\n  if( pTab->tabFlags & TF_HasPrimaryKey ){\n    sqlite3ErrorMsg(pParse, \n      \"table \\\"%s\\\" has more than one primary key\", pTab->zName);\n    goto primary_key_exit;\n  }\n  pTab->tabFlags |= TF_HasPrimaryKey;\n  if( pList==0 ){\n    iCol = pTab->nCol - 1;\n    pCol = &pTab->aCol[iCol];\n    pCol->colFlags |= COLFLAG_PRIMKEY;\n    nTerm = 1;\n  }else{\n    nTerm = pList->nExpr;\n    for(i=0; i<nTerm; i++){\n      Expr *pCExpr = sqlite3ExprSkipCollate(pList->a[i].pExpr);\n      assert( pCExpr!=0 );\n      sqlite3StringToId(pCExpr);\n      if( pCExpr->op==TK_ID ){\n        const char *zCName = pCExpr->u.zToken;\n        for(iCol=0; iCol<pTab->nCol; iCol++){\n          if( sqlite3StrICmp(zCName, pTab->aCol[iCol].zName)==0 ){\n            pCol = &pTab->aCol[iCol];\n            pCol->colFlags |= COLFLAG_PRIMKEY;\n            break;\n          }\n        }\n      }\n    }\n  }\n  if( nTerm==1\n   && pCol\n   && sqlite3StrICmp(sqlite3ColumnType(pCol,\"\"), \"INTEGER\")==0\n   && sortOrder!=SQLITE_SO_DESC\n  ){\n    pTab->iPKey = iCol;\n    pTab->keyConf = (u8)onError;\n    assert( autoInc==0 || autoInc==1 );\n    pTab->tabFlags |= autoInc*TF_Autoincrement;\n    if( pList ) pParse->iPkSortOrder = pList->a[0].sortOrder;\n  }else if( autoInc ){\n#ifndef SQLITE_OMIT_AUTOINCREMENT\n    sqlite3ErrorMsg(pParse, \"AUTOINCREMENT is only allowed on an \"\n       \"INTEGER PRIMARY KEY\");\n#endif\n  }else{\n    sqlite3CreateIndex(pParse, 0, 0, 0, pList, onError, 0,\n                           0, sortOrder, 0, SQLITE_IDXTYPE_PRIMARYKEY);\n    pList = 0;\n  }\n\nprimary_key_exit:\n  sqlite3ExprListDelete(pParse->db, pList);\n  return;\n}\n\n/*\n** Add a new CHECK constraint to the table currently under construction.\n*/\nSQLITE_PRIVATE void sqlite3AddCheckConstraint(\n  Parse *pParse,    /* Parsing context */\n  Expr *pCheckExpr  /* The check expression */\n){\n#ifndef SQLITE_OMIT_CHECK\n  Table *pTab = pParse->pNewTable;\n  sqlite3 *db = pParse->db;\n  if( pTab && !IN_DECLARE_VTAB\n   && !sqlite3BtreeIsReadonly(db->aDb[db->init.iDb].pBt)\n  ){\n    pTab->pCheck = sqlite3ExprListAppend(pParse, pTab->pCheck, pCheckExpr);\n    if( pParse->constraintName.n ){\n      sqlite3ExprListSetName(pParse, pTab->pCheck, &pParse->constraintName, 1);\n    }\n  }else\n#endif\n  {\n    sqlite3ExprDelete(pParse->db, pCheckExpr);\n  }\n}\n\n/*\n** Set the collation function of the most recently parsed table column\n** to the CollSeq given.\n*/\nSQLITE_PRIVATE void sqlite3AddCollateType(Parse *pParse, Token *pToken){\n  Table *p;\n  int i;\n  char *zColl;              /* Dequoted name of collation sequence */\n  sqlite3 *db;\n\n  if( (p = pParse->pNewTable)==0 ) return;\n  i = p->nCol-1;\n  db = pParse->db;\n  zColl = sqlite3NameFromToken(db, pToken);\n  if( !zColl ) return;\n\n  if( sqlite3LocateCollSeq(pParse, zColl) ){\n    Index *pIdx;\n    sqlite3DbFree(db, p->aCol[i].zColl);\n    p->aCol[i].zColl = zColl;\n  \n    /* If the column is declared as \"<name> PRIMARY KEY COLLATE <type>\",\n    ** then an index may have been created on this column before the\n    ** collation type was added. Correct this if it is the case.\n    */\n    for(pIdx=p->pIndex; pIdx; pIdx=pIdx->pNext){\n      assert( pIdx->nKeyCol==1 );\n      if( pIdx->aiColumn[0]==i ){\n        pIdx->azColl[0] = p->aCol[i].zColl;\n      }\n    }\n  }else{\n    sqlite3DbFree(db, zColl);\n  }\n}\n\n/*\n** This function returns the collation sequence for database native text\n** encoding identified by the string zName, length nName.\n**\n** If the requested collation sequence is not available, or not available\n** in the database native encoding, the collation factory is invoked to\n** request it. If the collation factory does not supply such a sequence,\n** and the sequence is available in another text encoding, then that is\n** returned instead.\n**\n** If no versions of the requested collations sequence are available, or\n** another error occurs, NULL is returned and an error message written into\n** pParse.\n**\n** This routine is a wrapper around sqlite3FindCollSeq().  This routine\n** invokes the collation factory if the named collation cannot be found\n** and generates an error message.\n**\n** See also: sqlite3FindCollSeq(), sqlite3GetCollSeq()\n*/\nSQLITE_PRIVATE CollSeq *sqlite3LocateCollSeq(Parse *pParse, const char *zName){\n  sqlite3 *db = pParse->db;\n  u8 enc = ENC(db);\n  u8 initbusy = db->init.busy;\n  CollSeq *pColl;\n\n  pColl = sqlite3FindCollSeq(db, enc, zName, initbusy);\n  if( !initbusy && (!pColl || !pColl->xCmp) ){\n    pColl = sqlite3GetCollSeq(pParse, enc, pColl, zName);\n  }\n\n  return pColl;\n}\n\n\n/*\n** Generate code that will increment the schema cookie.\n**\n** The schema cookie is used to determine when the schema for the\n** database changes.  After each schema change, the cookie value\n** changes.  When a process first reads the schema it records the\n** cookie.  Thereafter, whenever it goes to access the database,\n** it checks the cookie to make sure the schema has not changed\n** since it was last read.\n**\n** This plan is not completely bullet-proof.  It is possible for\n** the schema to change multiple times and for the cookie to be\n** set back to prior value.  But schema changes are infrequent\n** and the probability of hitting the same cookie value is only\n** 1 chance in 2^32.  So we're safe enough.\n**\n** IMPLEMENTATION-OF: R-34230-56049 SQLite automatically increments\n** the schema-version whenever the schema changes.\n*/\nSQLITE_PRIVATE void sqlite3ChangeCookie(Parse *pParse, int iDb){\n  sqlite3 *db = pParse->db;\n  Vdbe *v = pParse->pVdbe;\n  assert( sqlite3SchemaMutexHeld(db, iDb, 0) );\n  sqlite3VdbeAddOp3(v, OP_SetCookie, iDb, BTREE_SCHEMA_VERSION, \n                    db->aDb[iDb].pSchema->schema_cookie+1);\n}\n\n/*\n** Measure the number of characters needed to output the given\n** identifier.  The number returned includes any quotes used\n** but does not include the null terminator.\n**\n** The estimate is conservative.  It might be larger that what is\n** really needed.\n*/\nstatic int identLength(const char *z){\n  int n;\n  for(n=0; *z; n++, z++){\n    if( *z=='\"' ){ n++; }\n  }\n  return n + 2;\n}\n\n/*\n** The first parameter is a pointer to an output buffer. The second \n** parameter is a pointer to an integer that contains the offset at\n** which to write into the output buffer. This function copies the\n** nul-terminated string pointed to by the third parameter, zSignedIdent,\n** to the specified offset in the buffer and updates *pIdx to refer\n** to the first byte after the last byte written before returning.\n** \n** If the string zSignedIdent consists entirely of alpha-numeric\n** characters, does not begin with a digit and is not an SQL keyword,\n** then it is copied to the output buffer exactly as it is. Otherwise,\n** it is quoted using double-quotes.\n*/\nstatic void identPut(char *z, int *pIdx, char *zSignedIdent){\n  unsigned char *zIdent = (unsigned char*)zSignedIdent;\n  int i, j, needQuote;\n  i = *pIdx;\n\n  for(j=0; zIdent[j]; j++){\n    if( !sqlite3Isalnum(zIdent[j]) && zIdent[j]!='_' ) break;\n  }\n  needQuote = sqlite3Isdigit(zIdent[0])\n            || sqlite3KeywordCode(zIdent, j)!=TK_ID\n            || zIdent[j]!=0\n            || j==0;\n\n  if( needQuote ) z[i++] = '\"';\n  for(j=0; zIdent[j]; j++){\n    z[i++] = zIdent[j];\n    if( zIdent[j]=='\"' ) z[i++] = '\"';\n  }\n  if( needQuote ) z[i++] = '\"';\n  z[i] = 0;\n  *pIdx = i;\n}\n\n/*\n** Generate a CREATE TABLE statement appropriate for the given\n** table.  Memory to hold the text of the statement is obtained\n** from sqliteMalloc() and must be freed by the calling function.\n*/\nstatic char *createTableStmt(sqlite3 *db, Table *p){\n  int i, k, n;\n  char *zStmt;\n  char *zSep, *zSep2, *zEnd;\n  Column *pCol;\n  n = 0;\n  for(pCol = p->aCol, i=0; i<p->nCol; i++, pCol++){\n    n += identLength(pCol->zName) + 5;\n  }\n  n += identLength(p->zName);\n  if( n<50 ){ \n    zSep = \"\";\n    zSep2 = \",\";\n    zEnd = \")\";\n  }else{\n    zSep = \"\\n  \";\n    zSep2 = \",\\n  \";\n    zEnd = \"\\n)\";\n  }\n  n += 35 + 6*p->nCol;\n  zStmt = sqlite3DbMallocRaw(0, n);\n  if( zStmt==0 ){\n    sqlite3OomFault(db);\n    return 0;\n  }\n  sqlite3_snprintf(n, zStmt, \"CREATE TABLE \");\n  k = sqlite3Strlen30(zStmt);\n  identPut(zStmt, &k, p->zName);\n  zStmt[k++] = '(';\n  for(pCol=p->aCol, i=0; i<p->nCol; i++, pCol++){\n    static const char * const azType[] = {\n        /* SQLITE_AFF_BLOB    */ \"\",\n        /* SQLITE_AFF_TEXT    */ \" TEXT\",\n        /* SQLITE_AFF_NUMERIC */ \" NUM\",\n        /* SQLITE_AFF_INTEGER */ \" INT\",\n        /* SQLITE_AFF_REAL    */ \" REAL\"\n    };\n    int len;\n    const char *zType;\n\n    sqlite3_snprintf(n-k, &zStmt[k], zSep);\n    k += sqlite3Strlen30(&zStmt[k]);\n    zSep = zSep2;\n    identPut(zStmt, &k, pCol->zName);\n    assert( pCol->affinity-SQLITE_AFF_BLOB >= 0 );\n    assert( pCol->affinity-SQLITE_AFF_BLOB < ArraySize(azType) );\n    testcase( pCol->affinity==SQLITE_AFF_BLOB );\n    testcase( pCol->affinity==SQLITE_AFF_TEXT );\n    testcase( pCol->affinity==SQLITE_AFF_NUMERIC );\n    testcase( pCol->affinity==SQLITE_AFF_INTEGER );\n    testcase( pCol->affinity==SQLITE_AFF_REAL );\n    \n    zType = azType[pCol->affinity - SQLITE_AFF_BLOB];\n    len = sqlite3Strlen30(zType);\n    assert( pCol->affinity==SQLITE_AFF_BLOB \n            || pCol->affinity==sqlite3AffinityType(zType, 0) );\n    memcpy(&zStmt[k], zType, len);\n    k += len;\n    assert( k<=n );\n  }\n  sqlite3_snprintf(n-k, &zStmt[k], \"%s\", zEnd);\n  return zStmt;\n}\n\n/*\n** Resize an Index object to hold N columns total.  Return SQLITE_OK\n** on success and SQLITE_NOMEM on an OOM error.\n*/\nstatic int resizeIndexObject(sqlite3 *db, Index *pIdx, int N){\n  char *zExtra;\n  int nByte;\n  if( pIdx->nColumn>=N ) return SQLITE_OK;\n  assert( pIdx->isResized==0 );\n  nByte = (sizeof(char*) + sizeof(i16) + 1)*N;\n  zExtra = sqlite3DbMallocZero(db, nByte);\n  if( zExtra==0 ) return SQLITE_NOMEM_BKPT;\n  memcpy(zExtra, pIdx->azColl, sizeof(char*)*pIdx->nColumn);\n  pIdx->azColl = (const char**)zExtra;\n  zExtra += sizeof(char*)*N;\n  memcpy(zExtra, pIdx->aiColumn, sizeof(i16)*pIdx->nColumn);\n  pIdx->aiColumn = (i16*)zExtra;\n  zExtra += sizeof(i16)*N;\n  memcpy(zExtra, pIdx->aSortOrder, pIdx->nColumn);\n  pIdx->aSortOrder = (u8*)zExtra;\n  pIdx->nColumn = N;\n  pIdx->isResized = 1;\n  return SQLITE_OK;\n}\n\n/*\n** Estimate the total row width for a table.\n*/\nstatic void estimateTableWidth(Table *pTab){\n  unsigned wTable = 0;\n  const Column *pTabCol;\n  int i;\n  for(i=pTab->nCol, pTabCol=pTab->aCol; i>0; i--, pTabCol++){\n    wTable += pTabCol->szEst;\n  }\n  if( pTab->iPKey<0 ) wTable++;\n  pTab->szTabRow = sqlite3LogEst(wTable*4);\n}\n\n/*\n** Estimate the average size of a row for an index.\n*/\nstatic void estimateIndexWidth(Index *pIdx){\n  unsigned wIndex = 0;\n  int i;\n  const Column *aCol = pIdx->pTable->aCol;\n  for(i=0; i<pIdx->nColumn; i++){\n    i16 x = pIdx->aiColumn[i];\n    assert( x<pIdx->pTable->nCol );\n    wIndex += x<0 ? 1 : aCol[pIdx->aiColumn[i]].szEst;\n  }\n  pIdx->szIdxRow = sqlite3LogEst(wIndex*4);\n}\n\n/* Return true if value x is found any of the first nCol entries of aiCol[]\n*/\nstatic int hasColumn(const i16 *aiCol, int nCol, int x){\n  while( nCol-- > 0 ) if( x==*(aiCol++) ) return 1;\n  return 0;\n}\n\n/*\n** This routine runs at the end of parsing a CREATE TABLE statement that\n** has a WITHOUT ROWID clause.  The job of this routine is to convert both\n** internal schema data structures and the generated VDBE code so that they\n** are appropriate for a WITHOUT ROWID table instead of a rowid table.\n** Changes include:\n**\n**     (1)  Set all columns of the PRIMARY KEY schema object to be NOT NULL.\n**     (2)  Convert P3 parameter of the OP_CreateBtree from BTREE_INTKEY \n**          into BTREE_BLOBKEY.\n**     (3)  Bypass the creation of the sqlite_master table entry\n**          for the PRIMARY KEY as the primary key index is now\n**          identified by the sqlite_master table entry of the table itself.\n**     (4)  Set the Index.tnum of the PRIMARY KEY Index object in the\n**          schema to the rootpage from the main table.\n**     (5)  Add all table columns to the PRIMARY KEY Index object\n**          so that the PRIMARY KEY is a covering index.  The surplus\n**          columns are part of KeyInfo.nAllField and are not used for\n**          sorting or lookup or uniqueness checks.\n**     (6)  Replace the rowid tail on all automatically generated UNIQUE\n**          indices with the PRIMARY KEY columns.\n**\n** For virtual tables, only (1) is performed.\n*/\nstatic void convertToWithoutRowidTable(Parse *pParse, Table *pTab){\n  Index *pIdx;\n  Index *pPk;\n  int nPk;\n  int i, j;\n  sqlite3 *db = pParse->db;\n  Vdbe *v = pParse->pVdbe;\n\n  /* Mark every PRIMARY KEY column as NOT NULL (except for imposter tables)\n  */\n  if( !db->init.imposterTable ){\n    for(i=0; i<pTab->nCol; i++){\n      if( (pTab->aCol[i].colFlags & COLFLAG_PRIMKEY)!=0 ){\n        pTab->aCol[i].notNull = OE_Abort;\n      }\n    }\n  }\n\n  /* The remaining transformations only apply to b-tree tables, not to\n  ** virtual tables */\n  if( IN_DECLARE_VTAB ) return;\n\n  /* Convert the P3 operand of the OP_CreateBtree opcode from BTREE_INTKEY\n  ** into BTREE_BLOBKEY.\n  */\n  if( pParse->addrCrTab ){\n    assert( v );\n    sqlite3VdbeChangeP3(v, pParse->addrCrTab, BTREE_BLOBKEY);\n  }\n\n  /* Locate the PRIMARY KEY index.  Or, if this table was originally\n  ** an INTEGER PRIMARY KEY table, create a new PRIMARY KEY index. \n  */\n  if( pTab->iPKey>=0 ){\n    ExprList *pList;\n    Token ipkToken;\n    sqlite3TokenInit(&ipkToken, pTab->aCol[pTab->iPKey].zName);\n    pList = sqlite3ExprListAppend(pParse, 0, \n                  sqlite3ExprAlloc(db, TK_ID, &ipkToken, 0));\n    if( pList==0 ) return;\n    pList->a[0].sortOrder = pParse->iPkSortOrder;\n    assert( pParse->pNewTable==pTab );\n    sqlite3CreateIndex(pParse, 0, 0, 0, pList, pTab->keyConf, 0, 0, 0, 0,\n                       SQLITE_IDXTYPE_PRIMARYKEY);\n    if( db->mallocFailed ) return;\n    pPk = sqlite3PrimaryKeyIndex(pTab);\n    pTab->iPKey = -1;\n  }else{\n    pPk = sqlite3PrimaryKeyIndex(pTab);\n\n    /*\n    ** Remove all redundant columns from the PRIMARY KEY.  For example, change\n    ** \"PRIMARY KEY(a,b,a,b,c,b,c,d)\" into just \"PRIMARY KEY(a,b,c,d)\".  Later\n    ** code assumes the PRIMARY KEY contains no repeated columns.\n    */\n    for(i=j=1; i<pPk->nKeyCol; i++){\n      if( hasColumn(pPk->aiColumn, j, pPk->aiColumn[i]) ){\n        pPk->nColumn--;\n      }else{\n        pPk->aiColumn[j++] = pPk->aiColumn[i];\n      }\n    }\n    pPk->nKeyCol = j;\n  }\n  assert( pPk!=0 );\n  pPk->isCovering = 1;\n  if( !db->init.imposterTable ) pPk->uniqNotNull = 1;\n  nPk = pPk->nKeyCol;\n\n  /* Bypass the creation of the PRIMARY KEY btree and the sqlite_master\n  ** table entry. This is only required if currently generating VDBE\n  ** code for a CREATE TABLE (not when parsing one as part of reading\n  ** a database schema).  */\n  if( v && pPk->tnum>0 ){\n    assert( db->init.busy==0 );\n    sqlite3VdbeChangeOpcode(v, pPk->tnum, OP_Goto);\n  }\n\n  /* The root page of the PRIMARY KEY is the table root page */\n  pPk->tnum = pTab->tnum;\n\n  /* Update the in-memory representation of all UNIQUE indices by converting\n  ** the final rowid column into one or more columns of the PRIMARY KEY.\n  */\n  for(pIdx=pTab->pIndex; pIdx; pIdx=pIdx->pNext){\n    int n;\n    if( IsPrimaryKeyIndex(pIdx) ) continue;\n    for(i=n=0; i<nPk; i++){\n      if( !hasColumn(pIdx->aiColumn, pIdx->nKeyCol, pPk->aiColumn[i]) ) n++;\n    }\n    if( n==0 ){\n      /* This index is a superset of the primary key */\n      pIdx->nColumn = pIdx->nKeyCol;\n      continue;\n    }\n    if( resizeIndexObject(db, pIdx, pIdx->nKeyCol+n) ) return;\n    for(i=0, j=pIdx->nKeyCol; i<nPk; i++){\n      if( !hasColumn(pIdx->aiColumn, pIdx->nKeyCol, pPk->aiColumn[i]) ){\n        pIdx->aiColumn[j] = pPk->aiColumn[i];\n        pIdx->azColl[j] = pPk->azColl[i];\n        j++;\n      }\n    }\n    assert( pIdx->nColumn>=pIdx->nKeyCol+n );\n    assert( pIdx->nColumn>=j );\n  }\n\n  /* Add all table columns to the PRIMARY KEY index\n  */\n  if( nPk<pTab->nCol ){\n    if( resizeIndexObject(db, pPk, pTab->nCol) ) return;\n    for(i=0, j=nPk; i<pTab->nCol; i++){\n      if( !hasColumn(pPk->aiColumn, j, i) ){\n        assert( j<pPk->nColumn );\n        pPk->aiColumn[j] = i;\n        pPk->azColl[j] = sqlite3StrBINARY;\n        j++;\n      }\n    }\n    assert( pPk->nColumn==j );\n    assert( pTab->nCol==j );\n  }else{\n    pPk->nColumn = pTab->nCol;\n  }\n}\n\n/*\n** This routine is called to report the final \")\" that terminates\n** a CREATE TABLE statement.\n**\n** The table structure that other action routines have been building\n** is added to the internal hash tables, assuming no errors have\n** occurred.\n**\n** An entry for the table is made in the master table on disk, unless\n** this is a temporary table or db->init.busy==1.  When db->init.busy==1\n** it means we are reading the sqlite_master table because we just\n** connected to the database or because the sqlite_master table has\n** recently changed, so the entry for this table already exists in\n** the sqlite_master table.  We do not want to create it again.\n**\n** If the pSelect argument is not NULL, it means that this routine\n** was called to create a table generated from a \n** \"CREATE TABLE ... AS SELECT ...\" statement.  The column names of\n** the new table will match the result set of the SELECT.\n*/\nSQLITE_PRIVATE void sqlite3EndTable(\n  Parse *pParse,          /* Parse context */\n  Token *pCons,           /* The ',' token after the last column defn. */\n  Token *pEnd,            /* The ')' before options in the CREATE TABLE */\n  u8 tabOpts,             /* Extra table options. Usually 0. */\n  Select *pSelect         /* Select from a \"CREATE ... AS SELECT\" */\n){\n  Table *p;                 /* The new table */\n  sqlite3 *db = pParse->db; /* The database connection */\n  int iDb;                  /* Database in which the table lives */\n  Index *pIdx;              /* An implied index of the table */\n\n  if( pEnd==0 && pSelect==0 ){\n    return;\n  }\n  assert( !db->mallocFailed );\n  p = pParse->pNewTable;\n  if( p==0 ) return;\n\n  assert( !db->init.busy || !pSelect );\n\n  /* If the db->init.busy is 1 it means we are reading the SQL off the\n  ** \"sqlite_master\" or \"sqlite_temp_master\" table on the disk.\n  ** So do not write to the disk again.  Extract the root page number\n  ** for the table from the db->init.newTnum field.  (The page number\n  ** should have been put there by the sqliteOpenCb routine.)\n  **\n  ** If the root page number is 1, that means this is the sqlite_master\n  ** table itself.  So mark it read-only.\n  */\n  if( db->init.busy ){\n    p->tnum = db->init.newTnum;\n    if( p->tnum==1 ) p->tabFlags |= TF_Readonly;\n  }\n\n  /* Special processing for WITHOUT ROWID Tables */\n  if( tabOpts & TF_WithoutRowid ){\n    if( (p->tabFlags & TF_Autoincrement) ){\n      sqlite3ErrorMsg(pParse,\n          \"AUTOINCREMENT not allowed on WITHOUT ROWID tables\");\n      return;\n    }\n    if( (p->tabFlags & TF_HasPrimaryKey)==0 ){\n      sqlite3ErrorMsg(pParse, \"PRIMARY KEY missing on table %s\", p->zName);\n    }else{\n      p->tabFlags |= TF_WithoutRowid | TF_NoVisibleRowid;\n      convertToWithoutRowidTable(pParse, p);\n    }\n  }\n\n  iDb = sqlite3SchemaToIndex(db, p->pSchema);\n\n#ifndef SQLITE_OMIT_CHECK\n  /* Resolve names in all CHECK constraint expressions.\n  */\n  if( p->pCheck ){\n    sqlite3ResolveSelfReference(pParse, p, NC_IsCheck, 0, p->pCheck);\n  }\n#endif /* !defined(SQLITE_OMIT_CHECK) */\n\n  /* Estimate the average row size for the table and for all implied indices */\n  estimateTableWidth(p);\n  for(pIdx=p->pIndex; pIdx; pIdx=pIdx->pNext){\n    estimateIndexWidth(pIdx);\n  }\n\n  /* If not initializing, then create a record for the new table\n  ** in the SQLITE_MASTER table of the database.\n  **\n  ** If this is a TEMPORARY table, write the entry into the auxiliary\n  ** file instead of into the main database file.\n  */\n  if( !db->init.busy ){\n    int n;\n    Vdbe *v;\n    char *zType;    /* \"view\" or \"table\" */\n    char *zType2;   /* \"VIEW\" or \"TABLE\" */\n    char *zStmt;    /* Text of the CREATE TABLE or CREATE VIEW statement */\n\n    v = sqlite3GetVdbe(pParse);\n    if( NEVER(v==0) ) return;\n\n    sqlite3VdbeAddOp1(v, OP_Close, 0);\n\n    /* \n    ** Initialize zType for the new view or table.\n    */\n    if( p->pSelect==0 ){\n      /* A regular table */\n      zType = \"table\";\n      zType2 = \"TABLE\";\n#ifndef SQLITE_OMIT_VIEW\n    }else{\n      /* A view */\n      zType = \"view\";\n      zType2 = \"VIEW\";\n#endif\n    }\n\n    /* If this is a CREATE TABLE xx AS SELECT ..., execute the SELECT\n    ** statement to populate the new table. The root-page number for the\n    ** new table is in register pParse->regRoot.\n    **\n    ** Once the SELECT has been coded by sqlite3Select(), it is in a\n    ** suitable state to query for the column names and types to be used\n    ** by the new table.\n    **\n    ** A shared-cache write-lock is not required to write to the new table,\n    ** as a schema-lock must have already been obtained to create it. Since\n    ** a schema-lock excludes all other database users, the write-lock would\n    ** be redundant.\n    */\n    if( pSelect ){\n      SelectDest dest;    /* Where the SELECT should store results */\n      int regYield;       /* Register holding co-routine entry-point */\n      int addrTop;        /* Top of the co-routine */\n      int regRec;         /* A record to be insert into the new table */\n      int regRowid;       /* Rowid of the next row to insert */\n      int addrInsLoop;    /* Top of the loop for inserting rows */\n      Table *pSelTab;     /* A table that describes the SELECT results */\n\n      regYield = ++pParse->nMem;\n      regRec = ++pParse->nMem;\n      regRowid = ++pParse->nMem;\n      assert(pParse->nTab==1);\n      sqlite3MayAbort(pParse);\n      sqlite3VdbeAddOp3(v, OP_OpenWrite, 1, pParse->regRoot, iDb);\n      sqlite3VdbeChangeP5(v, OPFLAG_P2ISREG);\n      pParse->nTab = 2;\n      addrTop = sqlite3VdbeCurrentAddr(v) + 1;\n      sqlite3VdbeAddOp3(v, OP_InitCoroutine, regYield, 0, addrTop);\n      if( pParse->nErr ) return;\n      pSelTab = sqlite3ResultSetOfSelect(pParse, pSelect);\n      if( pSelTab==0 ) return;\n      assert( p->aCol==0 );\n      p->nCol = pSelTab->nCol;\n      p->aCol = pSelTab->aCol;\n      pSelTab->nCol = 0;\n      pSelTab->aCol = 0;\n      sqlite3DeleteTable(db, pSelTab);\n      sqlite3SelectDestInit(&dest, SRT_Coroutine, regYield);\n      sqlite3Select(pParse, pSelect, &dest);\n      if( pParse->nErr ) return;\n      sqlite3VdbeEndCoroutine(v, regYield);\n      sqlite3VdbeJumpHere(v, addrTop - 1);\n      addrInsLoop = sqlite3VdbeAddOp1(v, OP_Yield, dest.iSDParm);\n      VdbeCoverage(v);\n      sqlite3VdbeAddOp3(v, OP_MakeRecord, dest.iSdst, dest.nSdst, regRec);\n      sqlite3TableAffinity(v, p, 0);\n      sqlite3VdbeAddOp2(v, OP_NewRowid, 1, regRowid);\n      sqlite3VdbeAddOp3(v, OP_Insert, 1, regRec, regRowid);\n      sqlite3VdbeGoto(v, addrInsLoop);\n      sqlite3VdbeJumpHere(v, addrInsLoop);\n      sqlite3VdbeAddOp1(v, OP_Close, 1);\n    }\n\n    /* Compute the complete text of the CREATE statement */\n    if( pSelect ){\n      zStmt = createTableStmt(db, p);\n    }else{\n      Token *pEnd2 = tabOpts ? &pParse->sLastToken : pEnd;\n      n = (int)(pEnd2->z - pParse->sNameToken.z);\n      if( pEnd2->z[0]!=';' ) n += pEnd2->n;\n      zStmt = sqlite3MPrintf(db, \n          \"CREATE %s %.*s\", zType2, n, pParse->sNameToken.z\n      );\n    }\n\n    /* A slot for the record has already been allocated in the \n    ** SQLITE_MASTER table.  We just need to update that slot with all\n    ** the information we've collected.\n    */\n    sqlite3NestedParse(pParse,\n      \"UPDATE %Q.%s \"\n         \"SET type='%s', name=%Q, tbl_name=%Q, rootpage=#%d, sql=%Q \"\n       \"WHERE rowid=#%d\",\n      db->aDb[iDb].zDbSName, MASTER_NAME,\n      zType,\n      p->zName,\n      p->zName,\n      pParse->regRoot,\n      zStmt,\n      pParse->regRowid\n    );\n    sqlite3DbFree(db, zStmt);\n    sqlite3ChangeCookie(pParse, iDb);\n\n#ifndef SQLITE_OMIT_AUTOINCREMENT\n    /* Check to see if we need to create an sqlite_sequence table for\n    ** keeping track of autoincrement keys.\n    */\n    if( (p->tabFlags & TF_Autoincrement)!=0 ){\n      Db *pDb = &db->aDb[iDb];\n      assert( sqlite3SchemaMutexHeld(db, iDb, 0) );\n      if( pDb->pSchema->pSeqTab==0 ){\n        sqlite3NestedParse(pParse,\n          \"CREATE TABLE %Q.sqlite_sequence(name,seq)\",\n          pDb->zDbSName\n        );\n      }\n    }\n#endif\n\n    /* Reparse everything to update our internal data structures */\n    sqlite3VdbeAddParseSchemaOp(v, iDb,\n           sqlite3MPrintf(db, \"tbl_name='%q' AND type!='trigger'\", p->zName));\n  }\n\n\n  /* Add the table to the in-memory representation of the database.\n  */\n  if( db->init.busy ){\n    Table *pOld;\n    Schema *pSchema = p->pSchema;\n    assert( sqlite3SchemaMutexHeld(db, iDb, 0) );\n    pOld = sqlite3HashInsert(&pSchema->tblHash, p->zName, p);\n    if( pOld ){\n      assert( p==pOld );  /* Malloc must have failed inside HashInsert() */\n      sqlite3OomFault(db);\n      return;\n    }\n    pParse->pNewTable = 0;\n    db->mDbFlags |= DBFLAG_SchemaChange;\n\n#ifndef SQLITE_OMIT_ALTERTABLE\n    if( !p->pSelect ){\n      const char *zName = (const char *)pParse->sNameToken.z;\n      int nName;\n      assert( !pSelect && pCons && pEnd );\n      if( pCons->z==0 ){\n        pCons = pEnd;\n      }\n      nName = (int)((const char *)pCons->z - zName);\n      p->addColOffset = 13 + sqlite3Utf8CharLen(zName, nName);\n    }\n#endif\n  }\n}\n\n#ifndef SQLITE_OMIT_VIEW\n/*\n** The parser calls this routine in order to create a new VIEW\n*/\nSQLITE_PRIVATE void sqlite3CreateView(\n  Parse *pParse,     /* The parsing context */\n  Token *pBegin,     /* The CREATE token that begins the statement */\n  Token *pName1,     /* The token that holds the name of the view */\n  Token *pName2,     /* The token that holds the name of the view */\n  ExprList *pCNames, /* Optional list of view column names */\n  Select *pSelect,   /* A SELECT statement that will become the new view */\n  int isTemp,        /* TRUE for a TEMPORARY view */\n  int noErr          /* Suppress error messages if VIEW already exists */\n){\n  Table *p;\n  int n;\n  const char *z;\n  Token sEnd;\n  DbFixer sFix;\n  Token *pName = 0;\n  int iDb;\n  sqlite3 *db = pParse->db;\n\n  if( pParse->nVar>0 ){\n    sqlite3ErrorMsg(pParse, \"parameters are not allowed in views\");\n    goto create_view_fail;\n  }\n  sqlite3StartTable(pParse, pName1, pName2, isTemp, 1, 0, noErr);\n  p = pParse->pNewTable;\n  if( p==0 || pParse->nErr ) goto create_view_fail;\n  sqlite3TwoPartName(pParse, pName1, pName2, &pName);\n  iDb = sqlite3SchemaToIndex(db, p->pSchema);\n  sqlite3FixInit(&sFix, pParse, iDb, \"view\", pName);\n  if( sqlite3FixSelect(&sFix, pSelect) ) goto create_view_fail;\n\n  /* Make a copy of the entire SELECT statement that defines the view.\n  ** This will force all the Expr.token.z values to be dynamically\n  ** allocated rather than point to the input string - which means that\n  ** they will persist after the current sqlite3_exec() call returns.\n  */\n  p->pSelect = sqlite3SelectDup(db, pSelect, EXPRDUP_REDUCE);\n  p->pCheck = sqlite3ExprListDup(db, pCNames, EXPRDUP_REDUCE);\n  if( db->mallocFailed ) goto create_view_fail;\n\n  /* Locate the end of the CREATE VIEW statement.  Make sEnd point to\n  ** the end.\n  */\n  sEnd = pParse->sLastToken;\n  assert( sEnd.z[0]!=0 || sEnd.n==0 );\n  if( sEnd.z[0]!=';' ){\n    sEnd.z += sEnd.n;\n  }\n  sEnd.n = 0;\n  n = (int)(sEnd.z - pBegin->z);\n  assert( n>0 );\n  z = pBegin->z;\n  while( sqlite3Isspace(z[n-1]) ){ n--; }\n  sEnd.z = &z[n-1];\n  sEnd.n = 1;\n\n  /* Use sqlite3EndTable() to add the view to the SQLITE_MASTER table */\n  sqlite3EndTable(pParse, 0, &sEnd, 0, 0);\n\ncreate_view_fail:\n  sqlite3SelectDelete(db, pSelect);\n  sqlite3ExprListDelete(db, pCNames);\n  return;\n}\n#endif /* SQLITE_OMIT_VIEW */\n\n#if !defined(SQLITE_OMIT_VIEW) || !defined(SQLITE_OMIT_VIRTUALTABLE)\n/*\n** The Table structure pTable is really a VIEW.  Fill in the names of\n** the columns of the view in the pTable structure.  Return the number\n** of errors.  If an error is seen leave an error message in pParse->zErrMsg.\n*/\nSQLITE_PRIVATE int sqlite3ViewGetColumnNames(Parse *pParse, Table *pTable){\n  Table *pSelTab;   /* A fake table from which we get the result set */\n  Select *pSel;     /* Copy of the SELECT that implements the view */\n  int nErr = 0;     /* Number of errors encountered */\n  int n;            /* Temporarily holds the number of cursors assigned */\n  sqlite3 *db = pParse->db;  /* Database connection for malloc errors */\n#ifndef SQLITE_OMIT_VIRTUALTABLE\t\n  int rc;\n#endif\n#ifndef SQLITE_OMIT_AUTHORIZATION\n  sqlite3_xauth xAuth;       /* Saved xAuth pointer */\n#endif\n\n  assert( pTable );\n\n#ifndef SQLITE_OMIT_VIRTUALTABLE\n  db->nSchemaLock++;\n  rc = sqlite3VtabCallConnect(pParse, pTable);\n  db->nSchemaLock--;\n  if( rc ){\n    return 1;\n  }\n  if( IsVirtual(pTable) ) return 0;\n#endif\n\n#ifndef SQLITE_OMIT_VIEW\n  /* A positive nCol means the columns names for this view are\n  ** already known.\n  */\n  if( pTable->nCol>0 ) return 0;\n\n  /* A negative nCol is a special marker meaning that we are currently\n  ** trying to compute the column names.  If we enter this routine with\n  ** a negative nCol, it means two or more views form a loop, like this:\n  **\n  **     CREATE VIEW one AS SELECT * FROM two;\n  **     CREATE VIEW two AS SELECT * FROM one;\n  **\n  ** Actually, the error above is now caught prior to reaching this point.\n  ** But the following test is still important as it does come up\n  ** in the following:\n  ** \n  **     CREATE TABLE main.ex1(a);\n  **     CREATE TEMP VIEW ex1 AS SELECT a FROM ex1;\n  **     SELECT * FROM temp.ex1;\n  */\n  if( pTable->nCol<0 ){\n    sqlite3ErrorMsg(pParse, \"view %s is circularly defined\", pTable->zName);\n    return 1;\n  }\n  assert( pTable->nCol>=0 );\n\n  /* If we get this far, it means we need to compute the table names.\n  ** Note that the call to sqlite3ResultSetOfSelect() will expand any\n  ** \"*\" elements in the results set of the view and will assign cursors\n  ** to the elements of the FROM clause.  But we do not want these changes\n  ** to be permanent.  So the computation is done on a copy of the SELECT\n  ** statement that defines the view.\n  */\n  assert( pTable->pSelect );\n  pSel = sqlite3SelectDup(db, pTable->pSelect, 0);\n  if( pSel ){\n    n = pParse->nTab;\n    sqlite3SrcListAssignCursors(pParse, pSel->pSrc);\n    pTable->nCol = -1;\n    db->lookaside.bDisable++;\n#ifndef SQLITE_OMIT_AUTHORIZATION\n    xAuth = db->xAuth;\n    db->xAuth = 0;\n    pSelTab = sqlite3ResultSetOfSelect(pParse, pSel);\n    db->xAuth = xAuth;\n#else\n    pSelTab = sqlite3ResultSetOfSelect(pParse, pSel);\n#endif\n    pParse->nTab = n;\n    if( pTable->pCheck ){\n      /* CREATE VIEW name(arglist) AS ...\n      ** The names of the columns in the table are taken from\n      ** arglist which is stored in pTable->pCheck.  The pCheck field\n      ** normally holds CHECK constraints on an ordinary table, but for\n      ** a VIEW it holds the list of column names.\n      */\n      sqlite3ColumnsFromExprList(pParse, pTable->pCheck, \n                                 &pTable->nCol, &pTable->aCol);\n      if( db->mallocFailed==0 \n       && pParse->nErr==0\n       && pTable->nCol==pSel->pEList->nExpr\n      ){\n        sqlite3SelectAddColumnTypeAndCollation(pParse, pTable, pSel);\n      }\n    }else if( pSelTab ){\n      /* CREATE VIEW name AS...  without an argument list.  Construct\n      ** the column names from the SELECT statement that defines the view.\n      */\n      assert( pTable->aCol==0 );\n      pTable->nCol = pSelTab->nCol;\n      pTable->aCol = pSelTab->aCol;\n      pSelTab->nCol = 0;\n      pSelTab->aCol = 0;\n      assert( sqlite3SchemaMutexHeld(db, 0, pTable->pSchema) );\n    }else{\n      pTable->nCol = 0;\n      nErr++;\n    }\n    sqlite3DeleteTable(db, pSelTab);\n    sqlite3SelectDelete(db, pSel);\n    db->lookaside.bDisable--;\n  } else {\n    nErr++;\n  }\n  pTable->pSchema->schemaFlags |= DB_UnresetViews;\n#endif /* SQLITE_OMIT_VIEW */\n  return nErr;  \n}\n#endif /* !defined(SQLITE_OMIT_VIEW) || !defined(SQLITE_OMIT_VIRTUALTABLE) */\n\n#ifndef SQLITE_OMIT_VIEW\n/*\n** Clear the column names from every VIEW in database idx.\n*/\nstatic void sqliteViewResetAll(sqlite3 *db, int idx){\n  HashElem *i;\n  assert( sqlite3SchemaMutexHeld(db, idx, 0) );\n  if( !DbHasProperty(db, idx, DB_UnresetViews) ) return;\n  for(i=sqliteHashFirst(&db->aDb[idx].pSchema->tblHash); i;i=sqliteHashNext(i)){\n    Table *pTab = sqliteHashData(i);\n    if( pTab->pSelect ){\n      sqlite3DeleteColumnNames(db, pTab);\n      pTab->aCol = 0;\n      pTab->nCol = 0;\n    }\n  }\n  DbClearProperty(db, idx, DB_UnresetViews);\n}\n#else\n# define sqliteViewResetAll(A,B)\n#endif /* SQLITE_OMIT_VIEW */\n\n/*\n** This function is called by the VDBE to adjust the internal schema\n** used by SQLite when the btree layer moves a table root page. The\n** root-page of a table or index in database iDb has changed from iFrom\n** to iTo.\n**\n** Ticket #1728:  The symbol table might still contain information\n** on tables and/or indices that are the process of being deleted.\n** If you are unlucky, one of those deleted indices or tables might\n** have the same rootpage number as the real table or index that is\n** being moved.  So we cannot stop searching after the first match \n** because the first match might be for one of the deleted indices\n** or tables and not the table/index that is actually being moved.\n** We must continue looping until all tables and indices with\n** rootpage==iFrom have been converted to have a rootpage of iTo\n** in order to be certain that we got the right one.\n*/\n#ifndef SQLITE_OMIT_AUTOVACUUM\nSQLITE_PRIVATE void sqlite3RootPageMoved(sqlite3 *db, int iDb, int iFrom, int iTo){\n  HashElem *pElem;\n  Hash *pHash;\n  Db *pDb;\n\n  assert( sqlite3SchemaMutexHeld(db, iDb, 0) );\n  pDb = &db->aDb[iDb];\n  pHash = &pDb->pSchema->tblHash;\n  for(pElem=sqliteHashFirst(pHash); pElem; pElem=sqliteHashNext(pElem)){\n    Table *pTab = sqliteHashData(pElem);\n    if( pTab->tnum==iFrom ){\n      pTab->tnum = iTo;\n    }\n  }\n  pHash = &pDb->pSchema->idxHash;\n  for(pElem=sqliteHashFirst(pHash); pElem; pElem=sqliteHashNext(pElem)){\n    Index *pIdx = sqliteHashData(pElem);\n    if( pIdx->tnum==iFrom ){\n      pIdx->tnum = iTo;\n    }\n  }\n}\n#endif\n\n/*\n** Write code to erase the table with root-page iTable from database iDb.\n** Also write code to modify the sqlite_master table and internal schema\n** if a root-page of another table is moved by the btree-layer whilst\n** erasing iTable (this can happen with an auto-vacuum database).\n*/ \nstatic void destroyRootPage(Parse *pParse, int iTable, int iDb){\n  Vdbe *v = sqlite3GetVdbe(pParse);\n  int r1 = sqlite3GetTempReg(pParse);\n  assert( iTable>1 );\n  sqlite3VdbeAddOp3(v, OP_Destroy, iTable, r1, iDb);\n  sqlite3MayAbort(pParse);\n#ifndef SQLITE_OMIT_AUTOVACUUM\n  /* OP_Destroy stores an in integer r1. If this integer\n  ** is non-zero, then it is the root page number of a table moved to\n  ** location iTable. The following code modifies the sqlite_master table to\n  ** reflect this.\n  **\n  ** The \"#NNN\" in the SQL is a special constant that means whatever value\n  ** is in register NNN.  See grammar rules associated with the TK_REGISTER\n  ** token for additional information.\n  */\n  sqlite3NestedParse(pParse, \n     \"UPDATE %Q.%s SET rootpage=%d WHERE #%d AND rootpage=#%d\",\n     pParse->db->aDb[iDb].zDbSName, MASTER_NAME, iTable, r1, r1);\n#endif\n  sqlite3ReleaseTempReg(pParse, r1);\n}\n\n/*\n** Write VDBE code to erase table pTab and all associated indices on disk.\n** Code to update the sqlite_master tables and internal schema definitions\n** in case a root-page belonging to another table is moved by the btree layer\n** is also added (this can happen with an auto-vacuum database).\n*/\nstatic void destroyTable(Parse *pParse, Table *pTab){\n  /* If the database may be auto-vacuum capable (if SQLITE_OMIT_AUTOVACUUM\n  ** is not defined), then it is important to call OP_Destroy on the\n  ** table and index root-pages in order, starting with the numerically \n  ** largest root-page number. This guarantees that none of the root-pages\n  ** to be destroyed is relocated by an earlier OP_Destroy. i.e. if the\n  ** following were coded:\n  **\n  ** OP_Destroy 4 0\n  ** ...\n  ** OP_Destroy 5 0\n  **\n  ** and root page 5 happened to be the largest root-page number in the\n  ** database, then root page 5 would be moved to page 4 by the \n  ** \"OP_Destroy 4 0\" opcode. The subsequent \"OP_Destroy 5 0\" would hit\n  ** a free-list page.\n  */\n  int iTab = pTab->tnum;\n  int iDestroyed = 0;\n\n  while( 1 ){\n    Index *pIdx;\n    int iLargest = 0;\n\n    if( iDestroyed==0 || iTab<iDestroyed ){\n      iLargest = iTab;\n    }\n    for(pIdx=pTab->pIndex; pIdx; pIdx=pIdx->pNext){\n      int iIdx = pIdx->tnum;\n      assert( pIdx->pSchema==pTab->pSchema );\n      if( (iDestroyed==0 || (iIdx<iDestroyed)) && iIdx>iLargest ){\n        iLargest = iIdx;\n      }\n    }\n    if( iLargest==0 ){\n      return;\n    }else{\n      int iDb = sqlite3SchemaToIndex(pParse->db, pTab->pSchema);\n      assert( iDb>=0 && iDb<pParse->db->nDb );\n      destroyRootPage(pParse, iLargest, iDb);\n      iDestroyed = iLargest;\n    }\n  }\n}\n\n/*\n** Remove entries from the sqlite_statN tables (for N in (1,2,3))\n** after a DROP INDEX or DROP TABLE command.\n*/\nstatic void sqlite3ClearStatTables(\n  Parse *pParse,         /* The parsing context */\n  int iDb,               /* The database number */\n  const char *zType,     /* \"idx\" or \"tbl\" */\n  const char *zName      /* Name of index or table */\n){\n  int i;\n  const char *zDbName = pParse->db->aDb[iDb].zDbSName;\n  for(i=1; i<=4; i++){\n    char zTab[24];\n    sqlite3_snprintf(sizeof(zTab),zTab,\"sqlite_stat%d\",i);\n    if( sqlite3FindTable(pParse->db, zTab, zDbName) ){\n      sqlite3NestedParse(pParse,\n        \"DELETE FROM %Q.%s WHERE %s=%Q\",\n        zDbName, zTab, zType, zName\n      );\n    }\n  }\n}\n\n/*\n** Generate code to drop a table.\n*/\nSQLITE_PRIVATE void sqlite3CodeDropTable(Parse *pParse, Table *pTab, int iDb, int isView){\n  Vdbe *v;\n  sqlite3 *db = pParse->db;\n  Trigger *pTrigger;\n  Db *pDb = &db->aDb[iDb];\n\n  v = sqlite3GetVdbe(pParse);\n  assert( v!=0 );\n  sqlite3BeginWriteOperation(pParse, 1, iDb);\n\n#ifndef SQLITE_OMIT_VIRTUALTABLE\n  if( IsVirtual(pTab) ){\n    sqlite3VdbeAddOp0(v, OP_VBegin);\n  }\n#endif\n\n  /* Drop all triggers associated with the table being dropped. Code\n  ** is generated to remove entries from sqlite_master and/or\n  ** sqlite_temp_master if required.\n  */\n  pTrigger = sqlite3TriggerList(pParse, pTab);\n  while( pTrigger ){\n    assert( pTrigger->pSchema==pTab->pSchema || \n        pTrigger->pSchema==db->aDb[1].pSchema );\n    sqlite3DropTriggerPtr(pParse, pTrigger);\n    pTrigger = pTrigger->pNext;\n  }\n\n#ifndef SQLITE_OMIT_AUTOINCREMENT\n  /* Remove any entries of the sqlite_sequence table associated with\n  ** the table being dropped. This is done before the table is dropped\n  ** at the btree level, in case the sqlite_sequence table needs to\n  ** move as a result of the drop (can happen in auto-vacuum mode).\n  */\n  if( pTab->tabFlags & TF_Autoincrement ){\n    sqlite3NestedParse(pParse,\n      \"DELETE FROM %Q.sqlite_sequence WHERE name=%Q\",\n      pDb->zDbSName, pTab->zName\n    );\n  }\n#endif\n\n  /* Drop all SQLITE_MASTER table and index entries that refer to the\n  ** table. The program name loops through the master table and deletes\n  ** every row that refers to a table of the same name as the one being\n  ** dropped. Triggers are handled separately because a trigger can be\n  ** created in the temp database that refers to a table in another\n  ** database.\n  */\n  sqlite3NestedParse(pParse, \n      \"DELETE FROM %Q.%s WHERE tbl_name=%Q and type!='trigger'\",\n      pDb->zDbSName, MASTER_NAME, pTab->zName);\n  if( !isView && !IsVirtual(pTab) ){\n    destroyTable(pParse, pTab);\n  }\n\n  /* Remove the table entry from SQLite's internal schema and modify\n  ** the schema cookie.\n  */\n  if( IsVirtual(pTab) ){\n    sqlite3VdbeAddOp4(v, OP_VDestroy, iDb, 0, 0, pTab->zName, 0);\n  }\n  sqlite3VdbeAddOp4(v, OP_DropTable, iDb, 0, 0, pTab->zName, 0);\n  sqlite3ChangeCookie(pParse, iDb);\n  sqliteViewResetAll(db, iDb);\n}\n\n/*\n** This routine is called to do the work of a DROP TABLE statement.\n** pName is the name of the table to be dropped.\n*/\nSQLITE_PRIVATE void sqlite3DropTable(Parse *pParse, SrcList *pName, int isView, int noErr){\n  Table *pTab;\n  Vdbe *v;\n  sqlite3 *db = pParse->db;\n  int iDb;\n\n  if( db->mallocFailed ){\n    goto exit_drop_table;\n  }\n  assert( pParse->nErr==0 );\n  assert( pName->nSrc==1 );\n  if( sqlite3ReadSchema(pParse) ) goto exit_drop_table;\n  if( noErr ) db->suppressErr++;\n  assert( isView==0 || isView==LOCATE_VIEW );\n  pTab = sqlite3LocateTableItem(pParse, isView, &pName->a[0]);\n  if( noErr ) db->suppressErr--;\n\n  if( pTab==0 ){\n    if( noErr ) sqlite3CodeVerifyNamedSchema(pParse, pName->a[0].zDatabase);\n    goto exit_drop_table;\n  }\n  iDb = sqlite3SchemaToIndex(db, pTab->pSchema);\n  assert( iDb>=0 && iDb<db->nDb );\n\n  /* If pTab is a virtual table, call ViewGetColumnNames() to ensure\n  ** it is initialized.\n  */\n  if( IsVirtual(pTab) && sqlite3ViewGetColumnNames(pParse, pTab) ){\n    goto exit_drop_table;\n  }\n#ifndef SQLITE_OMIT_AUTHORIZATION\n  {\n    int code;\n    const char *zTab = SCHEMA_TABLE(iDb);\n    const char *zDb = db->aDb[iDb].zDbSName;\n    const char *zArg2 = 0;\n    if( sqlite3AuthCheck(pParse, SQLITE_DELETE, zTab, 0, zDb)){\n      goto exit_drop_table;\n    }\n    if( isView ){\n      if( !OMIT_TEMPDB && iDb==1 ){\n        code = SQLITE_DROP_TEMP_VIEW;\n      }else{\n        code = SQLITE_DROP_VIEW;\n      }\n#ifndef SQLITE_OMIT_VIRTUALTABLE\n    }else if( IsVirtual(pTab) ){\n      code = SQLITE_DROP_VTABLE;\n      zArg2 = sqlite3GetVTable(db, pTab)->pMod->zName;\n#endif\n    }else{\n      if( !OMIT_TEMPDB && iDb==1 ){\n        code = SQLITE_DROP_TEMP_TABLE;\n      }else{\n        code = SQLITE_DROP_TABLE;\n      }\n    }\n    if( sqlite3AuthCheck(pParse, code, pTab->zName, zArg2, zDb) ){\n      goto exit_drop_table;\n    }\n    if( sqlite3AuthCheck(pParse, SQLITE_DELETE, pTab->zName, 0, zDb) ){\n      goto exit_drop_table;\n    }\n  }\n#endif\n  if( sqlite3StrNICmp(pTab->zName, \"sqlite_\", 7)==0 \n    && sqlite3StrNICmp(pTab->zName, \"sqlite_stat\", 11)!=0 ){\n    sqlite3ErrorMsg(pParse, \"table %s may not be dropped\", pTab->zName);\n    goto exit_drop_table;\n  }\n\n#ifndef SQLITE_OMIT_VIEW\n  /* Ensure DROP TABLE is not used on a view, and DROP VIEW is not used\n  ** on a table.\n  */\n  if( isView && pTab->pSelect==0 ){\n    sqlite3ErrorMsg(pParse, \"use DROP TABLE to delete table %s\", pTab->zName);\n    goto exit_drop_table;\n  }\n  if( !isView && pTab->pSelect ){\n    sqlite3ErrorMsg(pParse, \"use DROP VIEW to delete view %s\", pTab->zName);\n    goto exit_drop_table;\n  }\n#endif\n\n  /* Generate code to remove the table from the master table\n  ** on disk.\n  */\n  v = sqlite3GetVdbe(pParse);\n  if( v ){\n    sqlite3BeginWriteOperation(pParse, 1, iDb);\n    sqlite3ClearStatTables(pParse, iDb, \"tbl\", pTab->zName);\n    sqlite3FkDropTable(pParse, pName, pTab);\n    sqlite3CodeDropTable(pParse, pTab, iDb, isView);\n  }\n\nexit_drop_table:\n  sqlite3SrcListDelete(db, pName);\n}\n\n/*\n** This routine is called to create a new foreign key on the table\n** currently under construction.  pFromCol determines which columns\n** in the current table point to the foreign key.  If pFromCol==0 then\n** connect the key to the last column inserted.  pTo is the name of\n** the table referred to (a.k.a the \"parent\" table).  pToCol is a list\n** of tables in the parent pTo table.  flags contains all\n** information about the conflict resolution algorithms specified\n** in the ON DELETE, ON UPDATE and ON INSERT clauses.\n**\n** An FKey structure is created and added to the table currently\n** under construction in the pParse->pNewTable field.\n**\n** The foreign key is set for IMMEDIATE processing.  A subsequent call\n** to sqlite3DeferForeignKey() might change this to DEFERRED.\n*/\nSQLITE_PRIVATE void sqlite3CreateForeignKey(\n  Parse *pParse,       /* Parsing context */\n  ExprList *pFromCol,  /* Columns in this table that point to other table */\n  Token *pTo,          /* Name of the other table */\n  ExprList *pToCol,    /* Columns in the other table */\n  int flags            /* Conflict resolution algorithms. */\n){\n  sqlite3 *db = pParse->db;\n#ifndef SQLITE_OMIT_FOREIGN_KEY\n  FKey *pFKey = 0;\n  FKey *pNextTo;\n  Table *p = pParse->pNewTable;\n  int nByte;\n  int i;\n  int nCol;\n  char *z;\n\n  assert( pTo!=0 );\n  if( p==0 || IN_DECLARE_VTAB ) goto fk_end;\n  if( pFromCol==0 ){\n    int iCol = p->nCol-1;\n    if( NEVER(iCol<0) ) goto fk_end;\n    if( pToCol && pToCol->nExpr!=1 ){\n      sqlite3ErrorMsg(pParse, \"foreign key on %s\"\n         \" should reference only one column of table %T\",\n         p->aCol[iCol].zName, pTo);\n      goto fk_end;\n    }\n    nCol = 1;\n  }else if( pToCol && pToCol->nExpr!=pFromCol->nExpr ){\n    sqlite3ErrorMsg(pParse,\n        \"number of columns in foreign key does not match the number of \"\n        \"columns in the referenced table\");\n    goto fk_end;\n  }else{\n    nCol = pFromCol->nExpr;\n  }\n  nByte = sizeof(*pFKey) + (nCol-1)*sizeof(pFKey->aCol[0]) + pTo->n + 1;\n  if( pToCol ){\n    for(i=0; i<pToCol->nExpr; i++){\n      nByte += sqlite3Strlen30(pToCol->a[i].zName) + 1;\n    }\n  }\n  pFKey = sqlite3DbMallocZero(db, nByte );\n  if( pFKey==0 ){\n    goto fk_end;\n  }\n  pFKey->pFrom = p;\n  pFKey->pNextFrom = p->pFKey;\n  z = (char*)&pFKey->aCol[nCol];\n  pFKey->zTo = z;\n  memcpy(z, pTo->z, pTo->n);\n  z[pTo->n] = 0;\n  sqlite3Dequote(z);\n  z += pTo->n+1;\n  pFKey->nCol = nCol;\n  if( pFromCol==0 ){\n    pFKey->aCol[0].iFrom = p->nCol-1;\n  }else{\n    for(i=0; i<nCol; i++){\n      int j;\n      for(j=0; j<p->nCol; j++){\n        if( sqlite3StrICmp(p->aCol[j].zName, pFromCol->a[i].zName)==0 ){\n          pFKey->aCol[i].iFrom = j;\n          break;\n        }\n      }\n      if( j>=p->nCol ){\n        sqlite3ErrorMsg(pParse, \n          \"unknown column \\\"%s\\\" in foreign key definition\", \n          pFromCol->a[i].zName);\n        goto fk_end;\n      }\n    }\n  }\n  if( pToCol ){\n    for(i=0; i<nCol; i++){\n      int n = sqlite3Strlen30(pToCol->a[i].zName);\n      pFKey->aCol[i].zCol = z;\n      memcpy(z, pToCol->a[i].zName, n);\n      z[n] = 0;\n      z += n+1;\n    }\n  }\n  pFKey->isDeferred = 0;\n  pFKey->aAction[0] = (u8)(flags & 0xff);            /* ON DELETE action */\n  pFKey->aAction[1] = (u8)((flags >> 8 ) & 0xff);    /* ON UPDATE action */\n\n  assert( sqlite3SchemaMutexHeld(db, 0, p->pSchema) );\n  pNextTo = (FKey *)sqlite3HashInsert(&p->pSchema->fkeyHash, \n      pFKey->zTo, (void *)pFKey\n  );\n  if( pNextTo==pFKey ){\n    sqlite3OomFault(db);\n    goto fk_end;\n  }\n  if( pNextTo ){\n    assert( pNextTo->pPrevTo==0 );\n    pFKey->pNextTo = pNextTo;\n    pNextTo->pPrevTo = pFKey;\n  }\n\n  /* Link the foreign key to the table as the last step.\n  */\n  p->pFKey = pFKey;\n  pFKey = 0;\n\nfk_end:\n  sqlite3DbFree(db, pFKey);\n#endif /* !defined(SQLITE_OMIT_FOREIGN_KEY) */\n  sqlite3ExprListDelete(db, pFromCol);\n  sqlite3ExprListDelete(db, pToCol);\n}\n\n/*\n** This routine is called when an INITIALLY IMMEDIATE or INITIALLY DEFERRED\n** clause is seen as part of a foreign key definition.  The isDeferred\n** parameter is 1 for INITIALLY DEFERRED and 0 for INITIALLY IMMEDIATE.\n** The behavior of the most recently created foreign key is adjusted\n** accordingly.\n*/\nSQLITE_PRIVATE void sqlite3DeferForeignKey(Parse *pParse, int isDeferred){\n#ifndef SQLITE_OMIT_FOREIGN_KEY\n  Table *pTab;\n  FKey *pFKey;\n  if( (pTab = pParse->pNewTable)==0 || (pFKey = pTab->pFKey)==0 ) return;\n  assert( isDeferred==0 || isDeferred==1 ); /* EV: R-30323-21917 */\n  pFKey->isDeferred = (u8)isDeferred;\n#endif\n}\n\n/*\n** Generate code that will erase and refill index *pIdx.  This is\n** used to initialize a newly created index or to recompute the\n** content of an index in response to a REINDEX command.\n**\n** if memRootPage is not negative, it means that the index is newly\n** created.  The register specified by memRootPage contains the\n** root page number of the index.  If memRootPage is negative, then\n** the index already exists and must be cleared before being refilled and\n** the root page number of the index is taken from pIndex->tnum.\n*/\nstatic void sqlite3RefillIndex(Parse *pParse, Index *pIndex, int memRootPage){\n  Table *pTab = pIndex->pTable;  /* The table that is indexed */\n  int iTab = pParse->nTab++;     /* Btree cursor used for pTab */\n  int iIdx = pParse->nTab++;     /* Btree cursor used for pIndex */\n  int iSorter;                   /* Cursor opened by OpenSorter (if in use) */\n  int addr1;                     /* Address of top of loop */\n  int addr2;                     /* Address to jump to for next iteration */\n  int tnum;                      /* Root page of index */\n  int iPartIdxLabel;             /* Jump to this label to skip a row */\n  Vdbe *v;                       /* Generate code into this virtual machine */\n  KeyInfo *pKey;                 /* KeyInfo for index */\n  int regRecord;                 /* Register holding assembled index record */\n  sqlite3 *db = pParse->db;      /* The database connection */\n  int iDb = sqlite3SchemaToIndex(db, pIndex->pSchema);\n\n#ifndef SQLITE_OMIT_AUTHORIZATION\n  if( sqlite3AuthCheck(pParse, SQLITE_REINDEX, pIndex->zName, 0,\n      db->aDb[iDb].zDbSName ) ){\n    return;\n  }\n#endif\n\n  /* Require a write-lock on the table to perform this operation */\n  sqlite3TableLock(pParse, iDb, pTab->tnum, 1, pTab->zName);\n\n  v = sqlite3GetVdbe(pParse);\n  if( v==0 ) return;\n  if( memRootPage>=0 ){\n    tnum = memRootPage;\n  }else{\n    tnum = pIndex->tnum;\n  }\n  pKey = sqlite3KeyInfoOfIndex(pParse, pIndex);\n  assert( pKey!=0 || db->mallocFailed || pParse->nErr );\n\n  /* Open the sorter cursor if we are to use one. */\n  iSorter = pParse->nTab++;\n  sqlite3VdbeAddOp4(v, OP_SorterOpen, iSorter, 0, pIndex->nKeyCol, (char*)\n                    sqlite3KeyInfoRef(pKey), P4_KEYINFO);\n\n  /* Open the table. Loop through all rows of the table, inserting index\n  ** records into the sorter. */\n  sqlite3OpenTable(pParse, iTab, iDb, pTab, OP_OpenRead);\n  addr1 = sqlite3VdbeAddOp2(v, OP_Rewind, iTab, 0); VdbeCoverage(v);\n  regRecord = sqlite3GetTempReg(pParse);\n\n  sqlite3GenerateIndexKey(pParse,pIndex,iTab,regRecord,0,&iPartIdxLabel,0,0);\n  sqlite3VdbeAddOp2(v, OP_SorterInsert, iSorter, regRecord);\n  sqlite3ResolvePartIdxLabel(pParse, iPartIdxLabel);\n  sqlite3VdbeAddOp2(v, OP_Next, iTab, addr1+1); VdbeCoverage(v);\n  sqlite3VdbeJumpHere(v, addr1);\n  if( memRootPage<0 ) sqlite3VdbeAddOp2(v, OP_Clear, tnum, iDb);\n  sqlite3VdbeAddOp4(v, OP_OpenWrite, iIdx, tnum, iDb, \n                    (char *)pKey, P4_KEYINFO);\n  sqlite3VdbeChangeP5(v, OPFLAG_BULKCSR|((memRootPage>=0)?OPFLAG_P2ISREG:0));\n\n  addr1 = sqlite3VdbeAddOp2(v, OP_SorterSort, iSorter, 0); VdbeCoverage(v);\n  if( IsUniqueIndex(pIndex) ){\n    int j2 = sqlite3VdbeCurrentAddr(v) + 3;\n    sqlite3VdbeGoto(v, j2);\n    addr2 = sqlite3VdbeCurrentAddr(v);\n    sqlite3VdbeAddOp4Int(v, OP_SorterCompare, iSorter, j2, regRecord,\n                         pIndex->nKeyCol); VdbeCoverage(v);\n    sqlite3UniqueConstraint(pParse, OE_Abort, pIndex);\n  }else{\n    addr2 = sqlite3VdbeCurrentAddr(v);\n  }\n  sqlite3VdbeAddOp3(v, OP_SorterData, iSorter, regRecord, iIdx);\n  sqlite3VdbeAddOp1(v, OP_SeekEnd, iIdx);\n  sqlite3VdbeAddOp2(v, OP_IdxInsert, iIdx, regRecord);\n  sqlite3VdbeChangeP5(v, OPFLAG_USESEEKRESULT);\n  sqlite3ReleaseTempReg(pParse, regRecord);\n  sqlite3VdbeAddOp2(v, OP_SorterNext, iSorter, addr2); VdbeCoverage(v);\n  sqlite3VdbeJumpHere(v, addr1);\n\n  sqlite3VdbeAddOp1(v, OP_Close, iTab);\n  sqlite3VdbeAddOp1(v, OP_Close, iIdx);\n  sqlite3VdbeAddOp1(v, OP_Close, iSorter);\n}\n\n/*\n** Allocate heap space to hold an Index object with nCol columns.\n**\n** Increase the allocation size to provide an extra nExtra bytes\n** of 8-byte aligned space after the Index object and return a\n** pointer to this extra space in *ppExtra.\n*/\nSQLITE_PRIVATE Index *sqlite3AllocateIndexObject(\n  sqlite3 *db,         /* Database connection */\n  i16 nCol,            /* Total number of columns in the index */\n  int nExtra,          /* Number of bytes of extra space to alloc */\n  char **ppExtra       /* Pointer to the \"extra\" space */\n){\n  Index *p;            /* Allocated index object */\n  int nByte;           /* Bytes of space for Index object + arrays */\n\n  nByte = ROUND8(sizeof(Index)) +              /* Index structure  */\n          ROUND8(sizeof(char*)*nCol) +         /* Index.azColl     */\n          ROUND8(sizeof(LogEst)*(nCol+1) +     /* Index.aiRowLogEst   */\n                 sizeof(i16)*nCol +            /* Index.aiColumn   */\n                 sizeof(u8)*nCol);             /* Index.aSortOrder */\n  p = sqlite3DbMallocZero(db, nByte + nExtra);\n  if( p ){\n    char *pExtra = ((char*)p)+ROUND8(sizeof(Index));\n    p->azColl = (const char**)pExtra; pExtra += ROUND8(sizeof(char*)*nCol);\n    p->aiRowLogEst = (LogEst*)pExtra; pExtra += sizeof(LogEst)*(nCol+1);\n    p->aiColumn = (i16*)pExtra;       pExtra += sizeof(i16)*nCol;\n    p->aSortOrder = (u8*)pExtra;\n    p->nColumn = nCol;\n    p->nKeyCol = nCol - 1;\n    *ppExtra = ((char*)p) + nByte;\n  }\n  return p;\n}\n\n/*\n** Create a new index for an SQL table.  pName1.pName2 is the name of the index \n** and pTblList is the name of the table that is to be indexed.  Both will \n** be NULL for a primary key or an index that is created to satisfy a\n** UNIQUE constraint.  If pTable and pIndex are NULL, use pParse->pNewTable\n** as the table to be indexed.  pParse->pNewTable is a table that is\n** currently being constructed by a CREATE TABLE statement.\n**\n** pList is a list of columns to be indexed.  pList will be NULL if this\n** is a primary key or unique-constraint on the most recent column added\n** to the table currently under construction.  \n*/\nSQLITE_PRIVATE void sqlite3CreateIndex(\n  Parse *pParse,     /* All information about this parse */\n  Token *pName1,     /* First part of index name. May be NULL */\n  Token *pName2,     /* Second part of index name. May be NULL */\n  SrcList *pTblName, /* Table to index. Use pParse->pNewTable if 0 */\n  ExprList *pList,   /* A list of columns to be indexed */\n  int onError,       /* OE_Abort, OE_Ignore, OE_Replace, or OE_None */\n  Token *pStart,     /* The CREATE token that begins this statement */\n  Expr *pPIWhere,    /* WHERE clause for partial indices */\n  int sortOrder,     /* Sort order of primary key when pList==NULL */\n  int ifNotExist,    /* Omit error if index already exists */\n  u8 idxType         /* The index type */\n){\n  Table *pTab = 0;     /* Table to be indexed */\n  Index *pIndex = 0;   /* The index to be created */\n  char *zName = 0;     /* Name of the index */\n  int nName;           /* Number of characters in zName */\n  int i, j;\n  DbFixer sFix;        /* For assigning database names to pTable */\n  int sortOrderMask;   /* 1 to honor DESC in index.  0 to ignore. */\n  sqlite3 *db = pParse->db;\n  Db *pDb;             /* The specific table containing the indexed database */\n  int iDb;             /* Index of the database that is being written */\n  Token *pName = 0;    /* Unqualified name of the index to create */\n  struct ExprList_item *pListItem; /* For looping over pList */\n  int nExtra = 0;                  /* Space allocated for zExtra[] */\n  int nExtraCol;                   /* Number of extra columns needed */\n  char *zExtra = 0;                /* Extra space after the Index object */\n  Index *pPk = 0;      /* PRIMARY KEY index for WITHOUT ROWID tables */\n\n  if( db->mallocFailed || pParse->nErr>0 ){\n    goto exit_create_index;\n  }\n  if( IN_DECLARE_VTAB && idxType!=SQLITE_IDXTYPE_PRIMARYKEY ){\n    goto exit_create_index;\n  }\n  if( SQLITE_OK!=sqlite3ReadSchema(pParse) ){\n    goto exit_create_index;\n  }\n\n  /*\n  ** Find the table that is to be indexed.  Return early if not found.\n  */\n  if( pTblName!=0 ){\n\n    /* Use the two-part index name to determine the database \n    ** to search for the table. 'Fix' the table name to this db\n    ** before looking up the table.\n    */\n    assert( pName1 && pName2 );\n    iDb = sqlite3TwoPartName(pParse, pName1, pName2, &pName);\n    if( iDb<0 ) goto exit_create_index;\n    assert( pName && pName->z );\n\n#ifndef SQLITE_OMIT_TEMPDB\n    /* If the index name was unqualified, check if the table\n    ** is a temp table. If so, set the database to 1. Do not do this\n    ** if initialising a database schema.\n    */\n    if( !db->init.busy ){\n      pTab = sqlite3SrcListLookup(pParse, pTblName);\n      if( pName2->n==0 && pTab && pTab->pSchema==db->aDb[1].pSchema ){\n        iDb = 1;\n      }\n    }\n#endif\n\n    sqlite3FixInit(&sFix, pParse, iDb, \"index\", pName);\n    if( sqlite3FixSrcList(&sFix, pTblName) ){\n      /* Because the parser constructs pTblName from a single identifier,\n      ** sqlite3FixSrcList can never fail. */\n      assert(0);\n    }\n    pTab = sqlite3LocateTableItem(pParse, 0, &pTblName->a[0]);\n    assert( db->mallocFailed==0 || pTab==0 );\n    if( pTab==0 ) goto exit_create_index;\n    if( iDb==1 && db->aDb[iDb].pSchema!=pTab->pSchema ){\n      sqlite3ErrorMsg(pParse, \n           \"cannot create a TEMP index on non-TEMP table \\\"%s\\\"\",\n           pTab->zName);\n      goto exit_create_index;\n    }\n    if( !HasRowid(pTab) ) pPk = sqlite3PrimaryKeyIndex(pTab);\n  }else{\n    assert( pName==0 );\n    assert( pStart==0 );\n    pTab = pParse->pNewTable;\n    if( !pTab ) goto exit_create_index;\n    iDb = sqlite3SchemaToIndex(db, pTab->pSchema);\n  }\n  pDb = &db->aDb[iDb];\n\n  assert( pTab!=0 );\n  assert( pParse->nErr==0 );\n  if( sqlite3StrNICmp(pTab->zName, \"sqlite_\", 7)==0 \n       && db->init.busy==0\n#if SQLITE_USER_AUTHENTICATION\n       && sqlite3UserAuthTable(pTab->zName)==0\n#endif\n       && sqlite3StrNICmp(&pTab->zName[7],\"altertab_\",9)!=0 ){\n    sqlite3ErrorMsg(pParse, \"table %s may not be indexed\", pTab->zName);\n    goto exit_create_index;\n  }\n#ifndef SQLITE_OMIT_VIEW\n  if( pTab->pSelect ){\n    sqlite3ErrorMsg(pParse, \"views may not be indexed\");\n    goto exit_create_index;\n  }\n#endif\n#ifndef SQLITE_OMIT_VIRTUALTABLE\n  if( IsVirtual(pTab) ){\n    sqlite3ErrorMsg(pParse, \"virtual tables may not be indexed\");\n    goto exit_create_index;\n  }\n#endif\n\n  /*\n  ** Find the name of the index.  Make sure there is not already another\n  ** index or table with the same name.  \n  **\n  ** Exception:  If we are reading the names of permanent indices from the\n  ** sqlite_master table (because some other process changed the schema) and\n  ** one of the index names collides with the name of a temporary table or\n  ** index, then we will continue to process this index.\n  **\n  ** If pName==0 it means that we are\n  ** dealing with a primary key or UNIQUE constraint.  We have to invent our\n  ** own name.\n  */\n  if( pName ){\n    zName = sqlite3NameFromToken(db, pName);\n    if( zName==0 ) goto exit_create_index;\n    assert( pName->z!=0 );\n    if( SQLITE_OK!=sqlite3CheckObjectName(pParse, zName) ){\n      goto exit_create_index;\n    }\n    if( !db->init.busy ){\n      if( sqlite3FindTable(db, zName, 0)!=0 ){\n        sqlite3ErrorMsg(pParse, \"there is already a table named %s\", zName);\n        goto exit_create_index;\n      }\n    }\n    if( sqlite3FindIndex(db, zName, pDb->zDbSName)!=0 ){\n      if( !ifNotExist ){\n        sqlite3ErrorMsg(pParse, \"index %s already exists\", zName);\n      }else{\n        assert( !db->init.busy );\n        sqlite3CodeVerifySchema(pParse, iDb);\n      }\n      goto exit_create_index;\n    }\n  }else{\n    int n;\n    Index *pLoop;\n    for(pLoop=pTab->pIndex, n=1; pLoop; pLoop=pLoop->pNext, n++){}\n    zName = sqlite3MPrintf(db, \"sqlite_autoindex_%s_%d\", pTab->zName, n);\n    if( zName==0 ){\n      goto exit_create_index;\n    }\n\n    /* Automatic index names generated from within sqlite3_declare_vtab()\n    ** must have names that are distinct from normal automatic index names.\n    ** The following statement converts \"sqlite3_autoindex...\" into\n    ** \"sqlite3_butoindex...\" in order to make the names distinct.\n    ** The \"vtab_err.test\" test demonstrates the need of this statement. */\n    if( IN_DECLARE_VTAB ) zName[7]++;\n  }\n\n  /* Check for authorization to create an index.\n  */\n#ifndef SQLITE_OMIT_AUTHORIZATION\n  {\n    const char *zDb = pDb->zDbSName;\n    if( sqlite3AuthCheck(pParse, SQLITE_INSERT, SCHEMA_TABLE(iDb), 0, zDb) ){\n      goto exit_create_index;\n    }\n    i = SQLITE_CREATE_INDEX;\n    if( !OMIT_TEMPDB && iDb==1 ) i = SQLITE_CREATE_TEMP_INDEX;\n    if( sqlite3AuthCheck(pParse, i, zName, pTab->zName, zDb) ){\n      goto exit_create_index;\n    }\n  }\n#endif\n\n  /* If pList==0, it means this routine was called to make a primary\n  ** key out of the last column added to the table under construction.\n  ** So create a fake list to simulate this.\n  */\n  if( pList==0 ){\n    Token prevCol;\n    Column *pCol = &pTab->aCol[pTab->nCol-1];\n    pCol->colFlags |= COLFLAG_UNIQUE;\n    sqlite3TokenInit(&prevCol, pCol->zName);\n    pList = sqlite3ExprListAppend(pParse, 0,\n              sqlite3ExprAlloc(db, TK_ID, &prevCol, 0));\n    if( pList==0 ) goto exit_create_index;\n    assert( pList->nExpr==1 );\n    sqlite3ExprListSetSortOrder(pList, sortOrder);\n  }else{\n    sqlite3ExprListCheckLength(pParse, pList, \"index\");\n  }\n\n  /* Figure out how many bytes of space are required to store explicitly\n  ** specified collation sequence names.\n  */\n  for(i=0; i<pList->nExpr; i++){\n    Expr *pExpr = pList->a[i].pExpr;\n    assert( pExpr!=0 );\n    if( pExpr->op==TK_COLLATE ){\n      nExtra += (1 + sqlite3Strlen30(pExpr->u.zToken));\n    }\n  }\n\n  /* \n  ** Allocate the index structure. \n  */\n  nName = sqlite3Strlen30(zName);\n  nExtraCol = pPk ? pPk->nKeyCol : 1;\n  pIndex = sqlite3AllocateIndexObject(db, pList->nExpr + nExtraCol,\n                                      nName + nExtra + 1, &zExtra);\n  if( db->mallocFailed ){\n    goto exit_create_index;\n  }\n  assert( EIGHT_BYTE_ALIGNMENT(pIndex->aiRowLogEst) );\n  assert( EIGHT_BYTE_ALIGNMENT(pIndex->azColl) );\n  pIndex->zName = zExtra;\n  zExtra += nName + 1;\n  memcpy(pIndex->zName, zName, nName+1);\n  pIndex->pTable = pTab;\n  pIndex->onError = (u8)onError;\n  pIndex->uniqNotNull = onError!=OE_None;\n  pIndex->idxType = idxType;\n  pIndex->pSchema = db->aDb[iDb].pSchema;\n  pIndex->nKeyCol = pList->nExpr;\n  if( pPIWhere ){\n    sqlite3ResolveSelfReference(pParse, pTab, NC_PartIdx, pPIWhere, 0);\n    pIndex->pPartIdxWhere = pPIWhere;\n    pPIWhere = 0;\n  }\n  assert( sqlite3SchemaMutexHeld(db, iDb, 0) );\n\n  /* Check to see if we should honor DESC requests on index columns\n  */\n  if( pDb->pSchema->file_format>=4 ){\n    sortOrderMask = -1;   /* Honor DESC */\n  }else{\n    sortOrderMask = 0;    /* Ignore DESC */\n  }\n\n  /* Analyze the list of expressions that form the terms of the index and\n  ** report any errors.  In the common case where the expression is exactly\n  ** a table column, store that column in aiColumn[].  For general expressions,\n  ** populate pIndex->aColExpr and store XN_EXPR (-2) in aiColumn[].\n  **\n  ** TODO: Issue a warning if two or more columns of the index are identical.\n  ** TODO: Issue a warning if the table primary key is used as part of the\n  ** index key.\n  */\n  for(i=0, pListItem=pList->a; i<pList->nExpr; i++, pListItem++){\n    Expr *pCExpr;                  /* The i-th index expression */\n    int requestedSortOrder;        /* ASC or DESC on the i-th expression */\n    const char *zColl;             /* Collation sequence name */\n\n    sqlite3StringToId(pListItem->pExpr);\n    sqlite3ResolveSelfReference(pParse, pTab, NC_IdxExpr, pListItem->pExpr, 0);\n    if( pParse->nErr ) goto exit_create_index;\n    pCExpr = sqlite3ExprSkipCollate(pListItem->pExpr);\n    if( pCExpr->op!=TK_COLUMN ){\n      if( pTab==pParse->pNewTable ){\n        sqlite3ErrorMsg(pParse, \"expressions prohibited in PRIMARY KEY and \"\n                                \"UNIQUE constraints\");\n        goto exit_create_index;\n      }\n      if( pIndex->aColExpr==0 ){\n        ExprList *pCopy = sqlite3ExprListDup(db, pList, 0);\n        pIndex->aColExpr = pCopy;\n        if( !db->mallocFailed ){\n          assert( pCopy!=0 );\n          pListItem = &pCopy->a[i];\n        }\n      }\n      j = XN_EXPR;\n      pIndex->aiColumn[i] = XN_EXPR;\n      pIndex->uniqNotNull = 0;\n    }else{\n      j = pCExpr->iColumn;\n      assert( j<=0x7fff );\n      if( j<0 ){\n        j = pTab->iPKey;\n      }else if( pTab->aCol[j].notNull==0 ){\n        pIndex->uniqNotNull = 0;\n      }\n      pIndex->aiColumn[i] = (i16)j;\n    }\n    zColl = 0;\n    if( pListItem->pExpr->op==TK_COLLATE ){\n      int nColl;\n      zColl = pListItem->pExpr->u.zToken;\n      nColl = sqlite3Strlen30(zColl) + 1;\n      assert( nExtra>=nColl );\n      memcpy(zExtra, zColl, nColl);\n      zColl = zExtra;\n      zExtra += nColl;\n      nExtra -= nColl;\n    }else if( j>=0 ){\n      zColl = pTab->aCol[j].zColl;\n    }\n    if( !zColl ) zColl = sqlite3StrBINARY;\n    if( !db->init.busy && !sqlite3LocateCollSeq(pParse, zColl) ){\n      goto exit_create_index;\n    }\n    pIndex->azColl[i] = zColl;\n    requestedSortOrder = pListItem->sortOrder & sortOrderMask;\n    pIndex->aSortOrder[i] = (u8)requestedSortOrder;\n  }\n\n  /* Append the table key to the end of the index.  For WITHOUT ROWID\n  ** tables (when pPk!=0) this will be the declared PRIMARY KEY.  For\n  ** normal tables (when pPk==0) this will be the rowid.\n  */\n  if( pPk ){\n    for(j=0; j<pPk->nKeyCol; j++){\n      int x = pPk->aiColumn[j];\n      assert( x>=0 );\n      if( hasColumn(pIndex->aiColumn, pIndex->nKeyCol, x) ){\n        pIndex->nColumn--; \n      }else{\n        pIndex->aiColumn[i] = x;\n        pIndex->azColl[i] = pPk->azColl[j];\n        pIndex->aSortOrder[i] = pPk->aSortOrder[j];\n        i++;\n      }\n    }\n    assert( i==pIndex->nColumn );\n  }else{\n    pIndex->aiColumn[i] = XN_ROWID;\n    pIndex->azColl[i] = sqlite3StrBINARY;\n  }\n  sqlite3DefaultRowEst(pIndex);\n  if( pParse->pNewTable==0 ) estimateIndexWidth(pIndex);\n\n  /* If this index contains every column of its table, then mark\n  ** it as a covering index */\n  assert( HasRowid(pTab) \n      || pTab->iPKey<0 || sqlite3ColumnOfIndex(pIndex, pTab->iPKey)>=0 );\n  if( pTblName!=0 && pIndex->nColumn>=pTab->nCol ){\n    pIndex->isCovering = 1;\n    for(j=0; j<pTab->nCol; j++){\n      if( j==pTab->iPKey ) continue;\n      if( sqlite3ColumnOfIndex(pIndex,j)>=0 ) continue;\n      pIndex->isCovering = 0;\n      break;\n    }\n  }\n\n  if( pTab==pParse->pNewTable ){\n    /* This routine has been called to create an automatic index as a\n    ** result of a PRIMARY KEY or UNIQUE clause on a column definition, or\n    ** a PRIMARY KEY or UNIQUE clause following the column definitions.\n    ** i.e. one of:\n    **\n    ** CREATE TABLE t(x PRIMARY KEY, y);\n    ** CREATE TABLE t(x, y, UNIQUE(x, y));\n    **\n    ** Either way, check to see if the table already has such an index. If\n    ** so, don't bother creating this one. This only applies to\n    ** automatically created indices. Users can do as they wish with\n    ** explicit indices.\n    **\n    ** Two UNIQUE or PRIMARY KEY constraints are considered equivalent\n    ** (and thus suppressing the second one) even if they have different\n    ** sort orders.\n    **\n    ** If there are different collating sequences or if the columns of\n    ** the constraint occur in different orders, then the constraints are\n    ** considered distinct and both result in separate indices.\n    */\n    Index *pIdx;\n    for(pIdx=pTab->pIndex; pIdx; pIdx=pIdx->pNext){\n      int k;\n      assert( IsUniqueIndex(pIdx) );\n      assert( pIdx->idxType!=SQLITE_IDXTYPE_APPDEF );\n      assert( IsUniqueIndex(pIndex) );\n\n      if( pIdx->nKeyCol!=pIndex->nKeyCol ) continue;\n      for(k=0; k<pIdx->nKeyCol; k++){\n        const char *z1;\n        const char *z2;\n        assert( pIdx->aiColumn[k]>=0 );\n        if( pIdx->aiColumn[k]!=pIndex->aiColumn[k] ) break;\n        z1 = pIdx->azColl[k];\n        z2 = pIndex->azColl[k];\n        if( sqlite3StrICmp(z1, z2) ) break;\n      }\n      if( k==pIdx->nKeyCol ){\n        if( pIdx->onError!=pIndex->onError ){\n          /* This constraint creates the same index as a previous\n          ** constraint specified somewhere in the CREATE TABLE statement.\n          ** However the ON CONFLICT clauses are different. If both this \n          ** constraint and the previous equivalent constraint have explicit\n          ** ON CONFLICT clauses this is an error. Otherwise, use the\n          ** explicitly specified behavior for the index.\n          */\n          if( !(pIdx->onError==OE_Default || pIndex->onError==OE_Default) ){\n            sqlite3ErrorMsg(pParse, \n                \"conflicting ON CONFLICT clauses specified\", 0);\n          }\n          if( pIdx->onError==OE_Default ){\n            pIdx->onError = pIndex->onError;\n          }\n        }\n        if( idxType==SQLITE_IDXTYPE_PRIMARYKEY ) pIdx->idxType = idxType;\n        goto exit_create_index;\n      }\n    }\n  }\n\n  /* Link the new Index structure to its table and to the other\n  ** in-memory database structures. \n  */\n  assert( pParse->nErr==0 );\n  if( db->init.busy ){\n    Index *p;\n    assert( !IN_DECLARE_VTAB );\n    assert( sqlite3SchemaMutexHeld(db, 0, pIndex->pSchema) );\n    p = sqlite3HashInsert(&pIndex->pSchema->idxHash, \n                          pIndex->zName, pIndex);\n    if( p ){\n      assert( p==pIndex );  /* Malloc must have failed */\n      sqlite3OomFault(db);\n      goto exit_create_index;\n    }\n    db->mDbFlags |= DBFLAG_SchemaChange;\n    if( pTblName!=0 ){\n      pIndex->tnum = db->init.newTnum;\n    }\n  }\n\n  /* If this is the initial CREATE INDEX statement (or CREATE TABLE if the\n  ** index is an implied index for a UNIQUE or PRIMARY KEY constraint) then\n  ** emit code to allocate the index rootpage on disk and make an entry for\n  ** the index in the sqlite_master table and populate the index with\n  ** content.  But, do not do this if we are simply reading the sqlite_master\n  ** table to parse the schema, or if this index is the PRIMARY KEY index\n  ** of a WITHOUT ROWID table.\n  **\n  ** If pTblName==0 it means this index is generated as an implied PRIMARY KEY\n  ** or UNIQUE index in a CREATE TABLE statement.  Since the table\n  ** has just been created, it contains no data and the index initialization\n  ** step can be skipped.\n  */\n  else if( HasRowid(pTab) || pTblName!=0 ){\n    Vdbe *v;\n    char *zStmt;\n    int iMem = ++pParse->nMem;\n\n    v = sqlite3GetVdbe(pParse);\n    if( v==0 ) goto exit_create_index;\n\n    sqlite3BeginWriteOperation(pParse, 1, iDb);\n\n    /* Create the rootpage for the index using CreateIndex. But before\n    ** doing so, code a Noop instruction and store its address in \n    ** Index.tnum. This is required in case this index is actually a \n    ** PRIMARY KEY and the table is actually a WITHOUT ROWID table. In \n    ** that case the convertToWithoutRowidTable() routine will replace\n    ** the Noop with a Goto to jump over the VDBE code generated below. */\n    pIndex->tnum = sqlite3VdbeAddOp0(v, OP_Noop);\n    sqlite3VdbeAddOp3(v, OP_CreateBtree, iDb, iMem, BTREE_BLOBKEY);\n\n    /* Gather the complete text of the CREATE INDEX statement into\n    ** the zStmt variable\n    */\n    if( pStart ){\n      int n = (int)(pParse->sLastToken.z - pName->z) + pParse->sLastToken.n;\n      if( pName->z[n-1]==';' ) n--;\n      /* A named index with an explicit CREATE INDEX statement */\n      zStmt = sqlite3MPrintf(db, \"CREATE%s INDEX %.*s\",\n        onError==OE_None ? \"\" : \" UNIQUE\", n, pName->z);\n    }else{\n      /* An automatic index created by a PRIMARY KEY or UNIQUE constraint */\n      /* zStmt = sqlite3MPrintf(\"\"); */\n      zStmt = 0;\n    }\n\n    /* Add an entry in sqlite_master for this index\n    */\n    sqlite3NestedParse(pParse, \n        \"INSERT INTO %Q.%s VALUES('index',%Q,%Q,#%d,%Q);\",\n        db->aDb[iDb].zDbSName, MASTER_NAME,\n        pIndex->zName,\n        pTab->zName,\n        iMem,\n        zStmt\n    );\n    sqlite3DbFree(db, zStmt);\n\n    /* Fill the index with data and reparse the schema. Code an OP_Expire\n    ** to invalidate all pre-compiled statements.\n    */\n    if( pTblName ){\n      sqlite3RefillIndex(pParse, pIndex, iMem);\n      sqlite3ChangeCookie(pParse, iDb);\n      sqlite3VdbeAddParseSchemaOp(v, iDb,\n         sqlite3MPrintf(db, \"name='%q' AND type='index'\", pIndex->zName));\n      sqlite3VdbeAddOp0(v, OP_Expire);\n    }\n\n    sqlite3VdbeJumpHere(v, pIndex->tnum);\n  }\n\n  /* When adding an index to the list of indices for a table, make\n  ** sure all indices labeled OE_Replace come after all those labeled\n  ** OE_Ignore.  This is necessary for the correct constraint check\n  ** processing (in sqlite3GenerateConstraintChecks()) as part of\n  ** UPDATE and INSERT statements.  \n  */\n  if( db->init.busy || pTblName==0 ){\n    if( onError!=OE_Replace || pTab->pIndex==0\n         || pTab->pIndex->onError==OE_Replace){\n      pIndex->pNext = pTab->pIndex;\n      pTab->pIndex = pIndex;\n    }else{\n      Index *pOther = pTab->pIndex;\n      while( pOther->pNext && pOther->pNext->onError!=OE_Replace ){\n        pOther = pOther->pNext;\n      }\n      pIndex->pNext = pOther->pNext;\n      pOther->pNext = pIndex;\n    }\n    pIndex = 0;\n  }\n\n  /* Clean up before exiting */\nexit_create_index:\n  if( pIndex ) freeIndex(db, pIndex);\n  sqlite3ExprDelete(db, pPIWhere);\n  sqlite3ExprListDelete(db, pList);\n  sqlite3SrcListDelete(db, pTblName);\n  sqlite3DbFree(db, zName);\n}\n\n/*\n** Fill the Index.aiRowEst[] array with default information - information\n** to be used when we have not run the ANALYZE command.\n**\n** aiRowEst[0] is supposed to contain the number of elements in the index.\n** Since we do not know, guess 1 million.  aiRowEst[1] is an estimate of the\n** number of rows in the table that match any particular value of the\n** first column of the index.  aiRowEst[2] is an estimate of the number\n** of rows that match any particular combination of the first 2 columns\n** of the index.  And so forth.  It must always be the case that\n*\n**           aiRowEst[N]<=aiRowEst[N-1]\n**           aiRowEst[N]>=1\n**\n** Apart from that, we have little to go on besides intuition as to\n** how aiRowEst[] should be initialized.  The numbers generated here\n** are based on typical values found in actual indices.\n*/\nSQLITE_PRIVATE void sqlite3DefaultRowEst(Index *pIdx){\n  /*                10,  9,  8,  7,  6 */\n  LogEst aVal[] = { 33, 32, 30, 28, 26 };\n  LogEst *a = pIdx->aiRowLogEst;\n  int nCopy = MIN(ArraySize(aVal), pIdx->nKeyCol);\n  int i;\n\n  /* Indexes with default row estimates should not have stat1 data */\n  assert( !pIdx->hasStat1 );\n\n  /* Set the first entry (number of rows in the index) to the estimated \n  ** number of rows in the table, or half the number of rows in the table\n  ** for a partial index.   But do not let the estimate drop below 10. */\n  a[0] = pIdx->pTable->nRowLogEst;\n  if( pIdx->pPartIdxWhere!=0 ) a[0] -= 10;  assert( 10==sqlite3LogEst(2) );\n  if( a[0]<33 ) a[0] = 33;                  assert( 33==sqlite3LogEst(10) );\n\n  /* Estimate that a[1] is 10, a[2] is 9, a[3] is 8, a[4] is 7, a[5] is\n  ** 6 and each subsequent value (if any) is 5.  */\n  memcpy(&a[1], aVal, nCopy*sizeof(LogEst));\n  for(i=nCopy+1; i<=pIdx->nKeyCol; i++){\n    a[i] = 23;                    assert( 23==sqlite3LogEst(5) );\n  }\n\n  assert( 0==sqlite3LogEst(1) );\n  if( IsUniqueIndex(pIdx) ) a[pIdx->nKeyCol] = 0;\n}\n\n/*\n** This routine will drop an existing named index.  This routine\n** implements the DROP INDEX statement.\n*/\nSQLITE_PRIVATE void sqlite3DropIndex(Parse *pParse, SrcList *pName, int ifExists){\n  Index *pIndex;\n  Vdbe *v;\n  sqlite3 *db = pParse->db;\n  int iDb;\n\n  assert( pParse->nErr==0 );   /* Never called with prior errors */\n  if( db->mallocFailed ){\n    goto exit_drop_index;\n  }\n  assert( pName->nSrc==1 );\n  if( SQLITE_OK!=sqlite3ReadSchema(pParse) ){\n    goto exit_drop_index;\n  }\n  pIndex = sqlite3FindIndex(db, pName->a[0].zName, pName->a[0].zDatabase);\n  if( pIndex==0 ){\n    if( !ifExists ){\n      sqlite3ErrorMsg(pParse, \"no such index: %S\", pName, 0);\n    }else{\n      sqlite3CodeVerifyNamedSchema(pParse, pName->a[0].zDatabase);\n    }\n    pParse->checkSchema = 1;\n    goto exit_drop_index;\n  }\n  if( pIndex->idxType!=SQLITE_IDXTYPE_APPDEF ){\n    sqlite3ErrorMsg(pParse, \"index associated with UNIQUE \"\n      \"or PRIMARY KEY constraint cannot be dropped\", 0);\n    goto exit_drop_index;\n  }\n  iDb = sqlite3SchemaToIndex(db, pIndex->pSchema);\n#ifndef SQLITE_OMIT_AUTHORIZATION\n  {\n    int code = SQLITE_DROP_INDEX;\n    Table *pTab = pIndex->pTable;\n    const char *zDb = db->aDb[iDb].zDbSName;\n    const char *zTab = SCHEMA_TABLE(iDb);\n    if( sqlite3AuthCheck(pParse, SQLITE_DELETE, zTab, 0, zDb) ){\n      goto exit_drop_index;\n    }\n    if( !OMIT_TEMPDB && iDb ) code = SQLITE_DROP_TEMP_INDEX;\n    if( sqlite3AuthCheck(pParse, code, pIndex->zName, pTab->zName, zDb) ){\n      goto exit_drop_index;\n    }\n  }\n#endif\n\n  /* Generate code to remove the index and from the master table */\n  v = sqlite3GetVdbe(pParse);\n  if( v ){\n    sqlite3BeginWriteOperation(pParse, 1, iDb);\n    sqlite3NestedParse(pParse,\n       \"DELETE FROM %Q.%s WHERE name=%Q AND type='index'\",\n       db->aDb[iDb].zDbSName, MASTER_NAME, pIndex->zName\n    );\n    sqlite3ClearStatTables(pParse, iDb, \"idx\", pIndex->zName);\n    sqlite3ChangeCookie(pParse, iDb);\n    destroyRootPage(pParse, pIndex->tnum, iDb);\n    sqlite3VdbeAddOp4(v, OP_DropIndex, iDb, 0, 0, pIndex->zName, 0);\n  }\n\nexit_drop_index:\n  sqlite3SrcListDelete(db, pName);\n}\n\n/*\n** pArray is a pointer to an array of objects. Each object in the\n** array is szEntry bytes in size. This routine uses sqlite3DbRealloc()\n** to extend the array so that there is space for a new object at the end.\n**\n** When this function is called, *pnEntry contains the current size of\n** the array (in entries - so the allocation is ((*pnEntry) * szEntry) bytes\n** in total).\n**\n** If the realloc() is successful (i.e. if no OOM condition occurs), the\n** space allocated for the new object is zeroed, *pnEntry updated to\n** reflect the new size of the array and a pointer to the new allocation\n** returned. *pIdx is set to the index of the new array entry in this case.\n**\n** Otherwise, if the realloc() fails, *pIdx is set to -1, *pnEntry remains\n** unchanged and a copy of pArray returned.\n*/\nSQLITE_PRIVATE void *sqlite3ArrayAllocate(\n  sqlite3 *db,      /* Connection to notify of malloc failures */\n  void *pArray,     /* Array of objects.  Might be reallocated */\n  int szEntry,      /* Size of each object in the array */\n  int *pnEntry,     /* Number of objects currently in use */\n  int *pIdx         /* Write the index of a new slot here */\n){\n  char *z;\n  int n = *pnEntry;\n  if( (n & (n-1))==0 ){\n    int sz = (n==0) ? 1 : 2*n;\n    void *pNew = sqlite3DbRealloc(db, pArray, sz*szEntry);\n    if( pNew==0 ){\n      *pIdx = -1;\n      return pArray;\n    }\n    pArray = pNew;\n  }\n  z = (char*)pArray;\n  memset(&z[n * szEntry], 0, szEntry);\n  *pIdx = n;\n  ++*pnEntry;\n  return pArray;\n}\n\n/*\n** Append a new element to the given IdList.  Create a new IdList if\n** need be.\n**\n** A new IdList is returned, or NULL if malloc() fails.\n*/\nSQLITE_PRIVATE IdList *sqlite3IdListAppend(sqlite3 *db, IdList *pList, Token *pToken){\n  int i;\n  if( pList==0 ){\n    pList = sqlite3DbMallocZero(db, sizeof(IdList) );\n    if( pList==0 ) return 0;\n  }\n  pList->a = sqlite3ArrayAllocate(\n      db,\n      pList->a,\n      sizeof(pList->a[0]),\n      &pList->nId,\n      &i\n  );\n  if( i<0 ){\n    sqlite3IdListDelete(db, pList);\n    return 0;\n  }\n  pList->a[i].zName = sqlite3NameFromToken(db, pToken);\n  return pList;\n}\n\n/*\n** Delete an IdList.\n*/\nSQLITE_PRIVATE void sqlite3IdListDelete(sqlite3 *db, IdList *pList){\n  int i;\n  if( pList==0 ) return;\n  for(i=0; i<pList->nId; i++){\n    sqlite3DbFree(db, pList->a[i].zName);\n  }\n  sqlite3DbFree(db, pList->a);\n  sqlite3DbFreeNN(db, pList);\n}\n\n/*\n** Return the index in pList of the identifier named zId.  Return -1\n** if not found.\n*/\nSQLITE_PRIVATE int sqlite3IdListIndex(IdList *pList, const char *zName){\n  int i;\n  if( pList==0 ) return -1;\n  for(i=0; i<pList->nId; i++){\n    if( sqlite3StrICmp(pList->a[i].zName, zName)==0 ) return i;\n  }\n  return -1;\n}\n\n/*\n** Expand the space allocated for the given SrcList object by\n** creating nExtra new slots beginning at iStart.  iStart is zero based.\n** New slots are zeroed.\n**\n** For example, suppose a SrcList initially contains two entries: A,B.\n** To append 3 new entries onto the end, do this:\n**\n**    sqlite3SrcListEnlarge(db, pSrclist, 3, 2);\n**\n** After the call above it would contain:  A, B, nil, nil, nil.\n** If the iStart argument had been 1 instead of 2, then the result\n** would have been:  A, nil, nil, nil, B.  To prepend the new slots,\n** the iStart value would be 0.  The result then would\n** be: nil, nil, nil, A, B.\n**\n** If a memory allocation fails the SrcList is unchanged.  The\n** db->mallocFailed flag will be set to true.\n*/\nSQLITE_PRIVATE SrcList *sqlite3SrcListEnlarge(\n  sqlite3 *db,       /* Database connection to notify of OOM errors */\n  SrcList *pSrc,     /* The SrcList to be enlarged */\n  int nExtra,        /* Number of new slots to add to pSrc->a[] */\n  int iStart         /* Index in pSrc->a[] of first new slot */\n){\n  int i;\n\n  /* Sanity checking on calling parameters */\n  assert( iStart>=0 );\n  assert( nExtra>=1 );\n  assert( pSrc!=0 );\n  assert( iStart<=pSrc->nSrc );\n\n  /* Allocate additional space if needed */\n  if( (u32)pSrc->nSrc+nExtra>pSrc->nAlloc ){\n    SrcList *pNew;\n    int nAlloc = pSrc->nSrc*2+nExtra;\n    int nGot;\n    pNew = sqlite3DbRealloc(db, pSrc,\n               sizeof(*pSrc) + (nAlloc-1)*sizeof(pSrc->a[0]) );\n    if( pNew==0 ){\n      assert( db->mallocFailed );\n      return pSrc;\n    }\n    pSrc = pNew;\n    nGot = (sqlite3DbMallocSize(db, pNew) - sizeof(*pSrc))/sizeof(pSrc->a[0])+1;\n    pSrc->nAlloc = nGot;\n  }\n\n  /* Move existing slots that come after the newly inserted slots\n  ** out of the way */\n  for(i=pSrc->nSrc-1; i>=iStart; i--){\n    pSrc->a[i+nExtra] = pSrc->a[i];\n  }\n  pSrc->nSrc += nExtra;\n\n  /* Zero the newly allocated slots */\n  memset(&pSrc->a[iStart], 0, sizeof(pSrc->a[0])*nExtra);\n  for(i=iStart; i<iStart+nExtra; i++){\n    pSrc->a[i].iCursor = -1;\n  }\n\n  /* Return a pointer to the enlarged SrcList */\n  return pSrc;\n}\n\n\n/*\n** Append a new table name to the given SrcList.  Create a new SrcList if\n** need be.  A new entry is created in the SrcList even if pTable is NULL.\n**\n** A SrcList is returned, or NULL if there is an OOM error.  The returned\n** SrcList might be the same as the SrcList that was input or it might be\n** a new one.  If an OOM error does occurs, then the prior value of pList\n** that is input to this routine is automatically freed.\n**\n** If pDatabase is not null, it means that the table has an optional\n** database name prefix.  Like this:  \"database.table\".  The pDatabase\n** points to the table name and the pTable points to the database name.\n** The SrcList.a[].zName field is filled with the table name which might\n** come from pTable (if pDatabase is NULL) or from pDatabase.  \n** SrcList.a[].zDatabase is filled with the database name from pTable,\n** or with NULL if no database is specified.\n**\n** In other words, if call like this:\n**\n**         sqlite3SrcListAppend(D,A,B,0);\n**\n** Then B is a table name and the database name is unspecified.  If called\n** like this:\n**\n**         sqlite3SrcListAppend(D,A,B,C);\n**\n** Then C is the table name and B is the database name.  If C is defined\n** then so is B.  In other words, we never have a case where:\n**\n**         sqlite3SrcListAppend(D,A,0,C);\n**\n** Both pTable and pDatabase are assumed to be quoted.  They are dequoted\n** before being added to the SrcList.\n*/\nSQLITE_PRIVATE SrcList *sqlite3SrcListAppend(\n  sqlite3 *db,        /* Connection to notify of malloc failures */\n  SrcList *pList,     /* Append to this SrcList. NULL creates a new SrcList */\n  Token *pTable,      /* Table to append */\n  Token *pDatabase    /* Database of the table */\n){\n  struct SrcList_item *pItem;\n  assert( pDatabase==0 || pTable!=0 );  /* Cannot have C without B */\n  assert( db!=0 );\n  if( pList==0 ){\n    pList = sqlite3DbMallocRawNN(db, sizeof(SrcList) );\n    if( pList==0 ) return 0;\n    pList->nAlloc = 1;\n    pList->nSrc = 1;\n    memset(&pList->a[0], 0, sizeof(pList->a[0]));\n    pList->a[0].iCursor = -1;\n  }else{\n    pList = sqlite3SrcListEnlarge(db, pList, 1, pList->nSrc);\n  }\n  if( db->mallocFailed ){\n    sqlite3SrcListDelete(db, pList);\n    return 0;\n  }\n  pItem = &pList->a[pList->nSrc-1];\n  if( pDatabase && pDatabase->z==0 ){\n    pDatabase = 0;\n  }\n  if( pDatabase ){\n    pItem->zName = sqlite3NameFromToken(db, pDatabase);\n    pItem->zDatabase = sqlite3NameFromToken(db, pTable);\n  }else{\n    pItem->zName = sqlite3NameFromToken(db, pTable);\n    pItem->zDatabase = 0;\n  }\n  return pList;\n}\n\n/*\n** Assign VdbeCursor index numbers to all tables in a SrcList\n*/\nSQLITE_PRIVATE void sqlite3SrcListAssignCursors(Parse *pParse, SrcList *pList){\n  int i;\n  struct SrcList_item *pItem;\n  assert(pList || pParse->db->mallocFailed );\n  if( pList ){\n    for(i=0, pItem=pList->a; i<pList->nSrc; i++, pItem++){\n      if( pItem->iCursor>=0 ) break;\n      pItem->iCursor = pParse->nTab++;\n      if( pItem->pSelect ){\n        sqlite3SrcListAssignCursors(pParse, pItem->pSelect->pSrc);\n      }\n    }\n  }\n}\n\n/*\n** Delete an entire SrcList including all its substructure.\n*/\nSQLITE_PRIVATE void sqlite3SrcListDelete(sqlite3 *db, SrcList *pList){\n  int i;\n  struct SrcList_item *pItem;\n  if( pList==0 ) return;\n  for(pItem=pList->a, i=0; i<pList->nSrc; i++, pItem++){\n    sqlite3DbFree(db, pItem->zDatabase);\n    sqlite3DbFree(db, pItem->zName);\n    sqlite3DbFree(db, pItem->zAlias);\n    if( pItem->fg.isIndexedBy ) sqlite3DbFree(db, pItem->u1.zIndexedBy);\n    if( pItem->fg.isTabFunc ) sqlite3ExprListDelete(db, pItem->u1.pFuncArg);\n    sqlite3DeleteTable(db, pItem->pTab);\n    sqlite3SelectDelete(db, pItem->pSelect);\n    sqlite3ExprDelete(db, pItem->pOn);\n    sqlite3IdListDelete(db, pItem->pUsing);\n  }\n  sqlite3DbFreeNN(db, pList);\n}\n\n/*\n** This routine is called by the parser to add a new term to the\n** end of a growing FROM clause.  The \"p\" parameter is the part of\n** the FROM clause that has already been constructed.  \"p\" is NULL\n** if this is the first term of the FROM clause.  pTable and pDatabase\n** are the name of the table and database named in the FROM clause term.\n** pDatabase is NULL if the database name qualifier is missing - the\n** usual case.  If the term has an alias, then pAlias points to the\n** alias token.  If the term is a subquery, then pSubquery is the\n** SELECT statement that the subquery encodes.  The pTable and\n** pDatabase parameters are NULL for subqueries.  The pOn and pUsing\n** parameters are the content of the ON and USING clauses.\n**\n** Return a new SrcList which encodes is the FROM with the new\n** term added.\n*/\nSQLITE_PRIVATE SrcList *sqlite3SrcListAppendFromTerm(\n  Parse *pParse,          /* Parsing context */\n  SrcList *p,             /* The left part of the FROM clause already seen */\n  Token *pTable,          /* Name of the table to add to the FROM clause */\n  Token *pDatabase,       /* Name of the database containing pTable */\n  Token *pAlias,          /* The right-hand side of the AS subexpression */\n  Select *pSubquery,      /* A subquery used in place of a table name */\n  Expr *pOn,              /* The ON clause of a join */\n  IdList *pUsing          /* The USING clause of a join */\n){\n  struct SrcList_item *pItem;\n  sqlite3 *db = pParse->db;\n  if( !p && (pOn || pUsing) ){\n    sqlite3ErrorMsg(pParse, \"a JOIN clause is required before %s\", \n      (pOn ? \"ON\" : \"USING\")\n    );\n    goto append_from_error;\n  }\n  p = sqlite3SrcListAppend(db, p, pTable, pDatabase);\n  if( p==0 ){\n    goto append_from_error;\n  }\n  assert( p->nSrc>0 );\n  pItem = &p->a[p->nSrc-1];\n  assert( pAlias!=0 );\n  if( pAlias->n ){\n    pItem->zAlias = sqlite3NameFromToken(db, pAlias);\n  }\n  pItem->pSelect = pSubquery;\n  pItem->pOn = pOn;\n  pItem->pUsing = pUsing;\n  return p;\n\n append_from_error:\n  assert( p==0 );\n  sqlite3ExprDelete(db, pOn);\n  sqlite3IdListDelete(db, pUsing);\n  sqlite3SelectDelete(db, pSubquery);\n  return 0;\n}\n\n/*\n** Add an INDEXED BY or NOT INDEXED clause to the most recently added \n** element of the source-list passed as the second argument.\n*/\nSQLITE_PRIVATE void sqlite3SrcListIndexedBy(Parse *pParse, SrcList *p, Token *pIndexedBy){\n  assert( pIndexedBy!=0 );\n  if( p && pIndexedBy->n>0 ){\n    struct SrcList_item *pItem;\n    assert( p->nSrc>0 );\n    pItem = &p->a[p->nSrc-1];\n    assert( pItem->fg.notIndexed==0 );\n    assert( pItem->fg.isIndexedBy==0 );\n    assert( pItem->fg.isTabFunc==0 );\n    if( pIndexedBy->n==1 && !pIndexedBy->z ){\n      /* A \"NOT INDEXED\" clause was supplied. See parse.y \n      ** construct \"indexed_opt\" for details. */\n      pItem->fg.notIndexed = 1;\n    }else{\n      pItem->u1.zIndexedBy = sqlite3NameFromToken(pParse->db, pIndexedBy);\n      pItem->fg.isIndexedBy = 1;\n    }\n  }\n}\n\n/*\n** Add the list of function arguments to the SrcList entry for a\n** table-valued-function.\n*/\nSQLITE_PRIVATE void sqlite3SrcListFuncArgs(Parse *pParse, SrcList *p, ExprList *pList){\n  if( p ){\n    struct SrcList_item *pItem = &p->a[p->nSrc-1];\n    assert( pItem->fg.notIndexed==0 );\n    assert( pItem->fg.isIndexedBy==0 );\n    assert( pItem->fg.isTabFunc==0 );\n    pItem->u1.pFuncArg = pList;\n    pItem->fg.isTabFunc = 1;\n  }else{\n    sqlite3ExprListDelete(pParse->db, pList);\n  }\n}\n\n/*\n** When building up a FROM clause in the parser, the join operator\n** is initially attached to the left operand.  But the code generator\n** expects the join operator to be on the right operand.  This routine\n** Shifts all join operators from left to right for an entire FROM\n** clause.\n**\n** Example: Suppose the join is like this:\n**\n**           A natural cross join B\n**\n** The operator is \"natural cross join\".  The A and B operands are stored\n** in p->a[0] and p->a[1], respectively.  The parser initially stores the\n** operator with A.  This routine shifts that operator over to B.\n*/\nSQLITE_PRIVATE void sqlite3SrcListShiftJoinType(SrcList *p){\n  if( p ){\n    int i;\n    for(i=p->nSrc-1; i>0; i--){\n      p->a[i].fg.jointype = p->a[i-1].fg.jointype;\n    }\n    p->a[0].fg.jointype = 0;\n  }\n}\n\n/*\n** Generate VDBE code for a BEGIN statement.\n*/\nSQLITE_PRIVATE void sqlite3BeginTransaction(Parse *pParse, int type){\n  sqlite3 *db;\n  Vdbe *v;\n  int i;\n\n  assert( pParse!=0 );\n  db = pParse->db;\n  assert( db!=0 );\n  if( sqlite3AuthCheck(pParse, SQLITE_TRANSACTION, \"BEGIN\", 0, 0) ){\n    return;\n  }\n  v = sqlite3GetVdbe(pParse);\n  if( !v ) return;\n  if( type!=TK_DEFERRED ){\n    for(i=0; i<db->nDb; i++){\n      sqlite3VdbeAddOp2(v, OP_Transaction, i, (type==TK_EXCLUSIVE)+1);\n      sqlite3VdbeUsesBtree(v, i);\n    }\n  }\n  sqlite3VdbeAddOp0(v, OP_AutoCommit);\n}\n\n/*\n** Generate VDBE code for a COMMIT or ROLLBACK statement.\n** Code for ROLLBACK is generated if eType==TK_ROLLBACK.  Otherwise\n** code is generated for a COMMIT.\n*/\nSQLITE_PRIVATE void sqlite3EndTransaction(Parse *pParse, int eType){\n  Vdbe *v;\n  int isRollback;\n\n  assert( pParse!=0 );\n  assert( pParse->db!=0 );\n  assert( eType==TK_COMMIT || eType==TK_END || eType==TK_ROLLBACK );\n  isRollback = eType==TK_ROLLBACK;\n  if( sqlite3AuthCheck(pParse, SQLITE_TRANSACTION, \n       isRollback ? \"ROLLBACK\" : \"COMMIT\", 0, 0) ){\n    return;\n  }\n  v = sqlite3GetVdbe(pParse);\n  if( v ){\n    sqlite3VdbeAddOp2(v, OP_AutoCommit, 1, isRollback);\n  }\n}\n\n/*\n** This function is called by the parser when it parses a command to create,\n** release or rollback an SQL savepoint. \n*/\nSQLITE_PRIVATE void sqlite3Savepoint(Parse *pParse, int op, Token *pName){\n  char *zName = sqlite3NameFromToken(pParse->db, pName);\n  if( zName ){\n    Vdbe *v = sqlite3GetVdbe(pParse);\n#ifndef SQLITE_OMIT_AUTHORIZATION\n    static const char * const az[] = { \"BEGIN\", \"RELEASE\", \"ROLLBACK\" };\n    assert( !SAVEPOINT_BEGIN && SAVEPOINT_RELEASE==1 && SAVEPOINT_ROLLBACK==2 );\n#endif\n    if( !v || sqlite3AuthCheck(pParse, SQLITE_SAVEPOINT, az[op], zName, 0) ){\n      sqlite3DbFree(pParse->db, zName);\n      return;\n    }\n    sqlite3VdbeAddOp4(v, OP_Savepoint, op, 0, 0, zName, P4_DYNAMIC);\n  }\n}\n\n/*\n** Make sure the TEMP database is open and available for use.  Return\n** the number of errors.  Leave any error messages in the pParse structure.\n*/\nSQLITE_PRIVATE int sqlite3OpenTempDatabase(Parse *pParse){\n  sqlite3 *db = pParse->db;\n  if( db->aDb[1].pBt==0 && !pParse->explain ){\n    int rc;\n    Btree *pBt;\n    static const int flags = \n          SQLITE_OPEN_READWRITE |\n          SQLITE_OPEN_CREATE |\n          SQLITE_OPEN_EXCLUSIVE |\n          SQLITE_OPEN_DELETEONCLOSE |\n          SQLITE_OPEN_TEMP_DB;\n\n    rc = sqlite3BtreeOpen(db->pVfs, 0, db, &pBt, 0, flags);\n    if( rc!=SQLITE_OK ){\n      sqlite3ErrorMsg(pParse, \"unable to open a temporary database \"\n        \"file for storing temporary tables\");\n      pParse->rc = rc;\n      return 1;\n    }\n    db->aDb[1].pBt = pBt;\n    assert( db->aDb[1].pSchema );\n    if( SQLITE_NOMEM==sqlite3BtreeSetPageSize(pBt, db->nextPagesize, -1, 0) ){\n      sqlite3OomFault(db);\n      return 1;\n    }\n  }\n  return 0;\n}\n\n/*\n** Record the fact that the schema cookie will need to be verified\n** for database iDb.  The code to actually verify the schema cookie\n** will occur at the end of the top-level VDBE and will be generated\n** later, by sqlite3FinishCoding().\n*/\nSQLITE_PRIVATE void sqlite3CodeVerifySchema(Parse *pParse, int iDb){\n  Parse *pToplevel = sqlite3ParseToplevel(pParse);\n\n  assert( iDb>=0 && iDb<pParse->db->nDb );\n  assert( pParse->db->aDb[iDb].pBt!=0 || iDb==1 );\n  assert( iDb<SQLITE_MAX_ATTACHED+2 );\n  assert( sqlite3SchemaMutexHeld(pParse->db, iDb, 0) );\n  if( DbMaskTest(pToplevel->cookieMask, iDb)==0 ){\n    DbMaskSet(pToplevel->cookieMask, iDb);\n    if( !OMIT_TEMPDB && iDb==1 ){\n      sqlite3OpenTempDatabase(pToplevel);\n    }\n  }\n}\n\n/*\n** If argument zDb is NULL, then call sqlite3CodeVerifySchema() for each \n** attached database. Otherwise, invoke it for the database named zDb only.\n*/\nSQLITE_PRIVATE void sqlite3CodeVerifyNamedSchema(Parse *pParse, const char *zDb){\n  sqlite3 *db = pParse->db;\n  int i;\n  for(i=0; i<db->nDb; i++){\n    Db *pDb = &db->aDb[i];\n    if( pDb->pBt && (!zDb || 0==sqlite3StrICmp(zDb, pDb->zDbSName)) ){\n      sqlite3CodeVerifySchema(pParse, i);\n    }\n  }\n}\n\n/*\n** Generate VDBE code that prepares for doing an operation that\n** might change the database.\n**\n** This routine starts a new transaction if we are not already within\n** a transaction.  If we are already within a transaction, then a checkpoint\n** is set if the setStatement parameter is true.  A checkpoint should\n** be set for operations that might fail (due to a constraint) part of\n** the way through and which will need to undo some writes without having to\n** rollback the whole transaction.  For operations where all constraints\n** can be checked before any changes are made to the database, it is never\n** necessary to undo a write and the checkpoint should not be set.\n*/\nSQLITE_PRIVATE void sqlite3BeginWriteOperation(Parse *pParse, int setStatement, int iDb){\n  Parse *pToplevel = sqlite3ParseToplevel(pParse);\n  sqlite3CodeVerifySchema(pParse, iDb);\n  DbMaskSet(pToplevel->writeMask, iDb);\n  pToplevel->isMultiWrite |= setStatement;\n}\n\n/*\n** Indicate that the statement currently under construction might write\n** more than one entry (example: deleting one row then inserting another,\n** inserting multiple rows in a table, or inserting a row and index entries.)\n** If an abort occurs after some of these writes have completed, then it will\n** be necessary to undo the completed writes.\n*/\nSQLITE_PRIVATE void sqlite3MultiWrite(Parse *pParse){\n  Parse *pToplevel = sqlite3ParseToplevel(pParse);\n  pToplevel->isMultiWrite = 1;\n}\n\n/* \n** The code generator calls this routine if is discovers that it is\n** possible to abort a statement prior to completion.  In order to \n** perform this abort without corrupting the database, we need to make\n** sure that the statement is protected by a statement transaction.\n**\n** Technically, we only need to set the mayAbort flag if the\n** isMultiWrite flag was previously set.  There is a time dependency\n** such that the abort must occur after the multiwrite.  This makes\n** some statements involving the REPLACE conflict resolution algorithm\n** go a little faster.  But taking advantage of this time dependency\n** makes it more difficult to prove that the code is correct (in \n** particular, it prevents us from writing an effective\n** implementation of sqlite3AssertMayAbort()) and so we have chosen\n** to take the safe route and skip the optimization.\n*/\nSQLITE_PRIVATE void sqlite3MayAbort(Parse *pParse){\n  Parse *pToplevel = sqlite3ParseToplevel(pParse);\n  pToplevel->mayAbort = 1;\n}\n\n/*\n** Code an OP_Halt that causes the vdbe to return an SQLITE_CONSTRAINT\n** error. The onError parameter determines which (if any) of the statement\n** and/or current transaction is rolled back.\n*/\nSQLITE_PRIVATE void sqlite3HaltConstraint(\n  Parse *pParse,    /* Parsing context */\n  int errCode,      /* extended error code */\n  int onError,      /* Constraint type */\n  char *p4,         /* Error message */\n  i8 p4type,        /* P4_STATIC or P4_TRANSIENT */\n  u8 p5Errmsg       /* P5_ErrMsg type */\n){\n  Vdbe *v = sqlite3GetVdbe(pParse);\n  assert( (errCode&0xff)==SQLITE_CONSTRAINT );\n  if( onError==OE_Abort ){\n    sqlite3MayAbort(pParse);\n  }\n  sqlite3VdbeAddOp4(v, OP_Halt, errCode, onError, 0, p4, p4type);\n  sqlite3VdbeChangeP5(v, p5Errmsg);\n}\n\n/*\n** Code an OP_Halt due to UNIQUE or PRIMARY KEY constraint violation.\n*/\nSQLITE_PRIVATE void sqlite3UniqueConstraint(\n  Parse *pParse,    /* Parsing context */\n  int onError,      /* Constraint type */\n  Index *pIdx       /* The index that triggers the constraint */\n){\n  char *zErr;\n  int j;\n  StrAccum errMsg;\n  Table *pTab = pIdx->pTable;\n\n  sqlite3StrAccumInit(&errMsg, pParse->db, 0, 0, 200);\n  if( pIdx->aColExpr ){\n    sqlite3XPrintf(&errMsg, \"index '%q'\", pIdx->zName);\n  }else{\n    for(j=0; j<pIdx->nKeyCol; j++){\n      char *zCol;\n      assert( pIdx->aiColumn[j]>=0 );\n      zCol = pTab->aCol[pIdx->aiColumn[j]].zName;\n      if( j ) sqlite3StrAccumAppend(&errMsg, \", \", 2);\n      sqlite3StrAccumAppendAll(&errMsg, pTab->zName);\n      sqlite3StrAccumAppend(&errMsg, \".\", 1);\n      sqlite3StrAccumAppendAll(&errMsg, zCol);\n    }\n  }\n  zErr = sqlite3StrAccumFinish(&errMsg);\n  sqlite3HaltConstraint(pParse, \n    IsPrimaryKeyIndex(pIdx) ? SQLITE_CONSTRAINT_PRIMARYKEY \n                            : SQLITE_CONSTRAINT_UNIQUE,\n    onError, zErr, P4_DYNAMIC, P5_ConstraintUnique);\n}\n\n\n/*\n** Code an OP_Halt due to non-unique rowid.\n*/\nSQLITE_PRIVATE void sqlite3RowidConstraint(\n  Parse *pParse,    /* Parsing context */\n  int onError,      /* Conflict resolution algorithm */\n  Table *pTab       /* The table with the non-unique rowid */ \n){\n  char *zMsg;\n  int rc;\n  if( pTab->iPKey>=0 ){\n    zMsg = sqlite3MPrintf(pParse->db, \"%s.%s\", pTab->zName,\n                          pTab->aCol[pTab->iPKey].zName);\n    rc = SQLITE_CONSTRAINT_PRIMARYKEY;\n  }else{\n    zMsg = sqlite3MPrintf(pParse->db, \"%s.rowid\", pTab->zName);\n    rc = SQLITE_CONSTRAINT_ROWID;\n  }\n  sqlite3HaltConstraint(pParse, rc, onError, zMsg, P4_DYNAMIC,\n                        P5_ConstraintUnique);\n}\n\n/*\n** Check to see if pIndex uses the collating sequence pColl.  Return\n** true if it does and false if it does not.\n*/\n#ifndef SQLITE_OMIT_REINDEX\nstatic int collationMatch(const char *zColl, Index *pIndex){\n  int i;\n  assert( zColl!=0 );\n  for(i=0; i<pIndex->nColumn; i++){\n    const char *z = pIndex->azColl[i];\n    assert( z!=0 || pIndex->aiColumn[i]<0 );\n    if( pIndex->aiColumn[i]>=0 && 0==sqlite3StrICmp(z, zColl) ){\n      return 1;\n    }\n  }\n  return 0;\n}\n#endif\n\n/*\n** Recompute all indices of pTab that use the collating sequence pColl.\n** If pColl==0 then recompute all indices of pTab.\n*/\n#ifndef SQLITE_OMIT_REINDEX\nstatic void reindexTable(Parse *pParse, Table *pTab, char const *zColl){\n  Index *pIndex;              /* An index associated with pTab */\n\n  for(pIndex=pTab->pIndex; pIndex; pIndex=pIndex->pNext){\n    if( zColl==0 || collationMatch(zColl, pIndex) ){\n      int iDb = sqlite3SchemaToIndex(pParse->db, pTab->pSchema);\n      sqlite3BeginWriteOperation(pParse, 0, iDb);\n      sqlite3RefillIndex(pParse, pIndex, -1);\n    }\n  }\n}\n#endif\n\n/*\n** Recompute all indices of all tables in all databases where the\n** indices use the collating sequence pColl.  If pColl==0 then recompute\n** all indices everywhere.\n*/\n#ifndef SQLITE_OMIT_REINDEX\nstatic void reindexDatabases(Parse *pParse, char const *zColl){\n  Db *pDb;                    /* A single database */\n  int iDb;                    /* The database index number */\n  sqlite3 *db = pParse->db;   /* The database connection */\n  HashElem *k;                /* For looping over tables in pDb */\n  Table *pTab;                /* A table in the database */\n\n  assert( sqlite3BtreeHoldsAllMutexes(db) );  /* Needed for schema access */\n  for(iDb=0, pDb=db->aDb; iDb<db->nDb; iDb++, pDb++){\n    assert( pDb!=0 );\n    for(k=sqliteHashFirst(&pDb->pSchema->tblHash);  k; k=sqliteHashNext(k)){\n      pTab = (Table*)sqliteHashData(k);\n      reindexTable(pParse, pTab, zColl);\n    }\n  }\n}\n#endif\n\n/*\n** Generate code for the REINDEX command.\n**\n**        REINDEX                            -- 1\n**        REINDEX  <collation>               -- 2\n**        REINDEX  ?<database>.?<tablename>  -- 3\n**        REINDEX  ?<database>.?<indexname>  -- 4\n**\n** Form 1 causes all indices in all attached databases to be rebuilt.\n** Form 2 rebuilds all indices in all databases that use the named\n** collating function.  Forms 3 and 4 rebuild the named index or all\n** indices associated with the named table.\n*/\n#ifndef SQLITE_OMIT_REINDEX\nSQLITE_PRIVATE void sqlite3Reindex(Parse *pParse, Token *pName1, Token *pName2){\n  CollSeq *pColl;             /* Collating sequence to be reindexed, or NULL */\n  char *z;                    /* Name of a table or index */\n  const char *zDb;            /* Name of the database */\n  Table *pTab;                /* A table in the database */\n  Index *pIndex;              /* An index associated with pTab */\n  int iDb;                    /* The database index number */\n  sqlite3 *db = pParse->db;   /* The database connection */\n  Token *pObjName;            /* Name of the table or index to be reindexed */\n\n  /* Read the database schema. If an error occurs, leave an error message\n  ** and code in pParse and return NULL. */\n  if( SQLITE_OK!=sqlite3ReadSchema(pParse) ){\n    return;\n  }\n\n  if( pName1==0 ){\n    reindexDatabases(pParse, 0);\n    return;\n  }else if( NEVER(pName2==0) || pName2->z==0 ){\n    char *zColl;\n    assert( pName1->z );\n    zColl = sqlite3NameFromToken(pParse->db, pName1);\n    if( !zColl ) return;\n    pColl = sqlite3FindCollSeq(db, ENC(db), zColl, 0);\n    if( pColl ){\n      reindexDatabases(pParse, zColl);\n      sqlite3DbFree(db, zColl);\n      return;\n    }\n    sqlite3DbFree(db, zColl);\n  }\n  iDb = sqlite3TwoPartName(pParse, pName1, pName2, &pObjName);\n  if( iDb<0 ) return;\n  z = sqlite3NameFromToken(db, pObjName);\n  if( z==0 ) return;\n  zDb = db->aDb[iDb].zDbSName;\n  pTab = sqlite3FindTable(db, z, zDb);\n  if( pTab ){\n    reindexTable(pParse, pTab, 0);\n    sqlite3DbFree(db, z);\n    return;\n  }\n  pIndex = sqlite3FindIndex(db, z, zDb);\n  sqlite3DbFree(db, z);\n  if( pIndex ){\n    sqlite3BeginWriteOperation(pParse, 0, iDb);\n    sqlite3RefillIndex(pParse, pIndex, -1);\n    return;\n  }\n  sqlite3ErrorMsg(pParse, \"unable to identify the object to be reindexed\");\n}\n#endif\n\n/*\n** Return a KeyInfo structure that is appropriate for the given Index.\n**\n** The caller should invoke sqlite3KeyInfoUnref() on the returned object\n** when it has finished using it.\n*/\nSQLITE_PRIVATE KeyInfo *sqlite3KeyInfoOfIndex(Parse *pParse, Index *pIdx){\n  int i;\n  int nCol = pIdx->nColumn;\n  int nKey = pIdx->nKeyCol;\n  KeyInfo *pKey;\n  if( pParse->nErr ) return 0;\n  if( pIdx->uniqNotNull ){\n    pKey = sqlite3KeyInfoAlloc(pParse->db, nKey, nCol-nKey);\n  }else{\n    pKey = sqlite3KeyInfoAlloc(pParse->db, nCol, 0);\n  }\n  if( pKey ){\n    assert( sqlite3KeyInfoIsWriteable(pKey) );\n    for(i=0; i<nCol; i++){\n      const char *zColl = pIdx->azColl[i];\n      pKey->aColl[i] = zColl==sqlite3StrBINARY ? 0 :\n                        sqlite3LocateCollSeq(pParse, zColl);\n      pKey->aSortOrder[i] = pIdx->aSortOrder[i];\n    }\n    if( pParse->nErr ){\n      assert( pParse->rc==SQLITE_ERROR_MISSING_COLLSEQ );\n      if( pIdx->bNoQuery==0 ){\n        /* Deactivate the index because it contains an unknown collating\n        ** sequence.  The only way to reactive the index is to reload the\n        ** schema.  Adding the missing collating sequence later does not\n        ** reactive the index.  The application had the chance to register\n        ** the missing index using the collation-needed callback.  For\n        ** simplicity, SQLite will not give the application a second chance.\n        */\n        pIdx->bNoQuery = 1;\n        pParse->rc = SQLITE_ERROR_RETRY;\n      }\n      sqlite3KeyInfoUnref(pKey);\n      pKey = 0;\n    }\n  }\n  return pKey;\n}\n\n#ifndef SQLITE_OMIT_CTE\n/* \n** This routine is invoked once per CTE by the parser while parsing a \n** WITH clause. \n*/\nSQLITE_PRIVATE With *sqlite3WithAdd(\n  Parse *pParse,          /* Parsing context */\n  With *pWith,            /* Existing WITH clause, or NULL */\n  Token *pName,           /* Name of the common-table */\n  ExprList *pArglist,     /* Optional column name list for the table */\n  Select *pQuery          /* Query used to initialize the table */\n){\n  sqlite3 *db = pParse->db;\n  With *pNew;\n  char *zName;\n\n  /* Check that the CTE name is unique within this WITH clause. If\n  ** not, store an error in the Parse structure. */\n  zName = sqlite3NameFromToken(pParse->db, pName);\n  if( zName && pWith ){\n    int i;\n    for(i=0; i<pWith->nCte; i++){\n      if( sqlite3StrICmp(zName, pWith->a[i].zName)==0 ){\n        sqlite3ErrorMsg(pParse, \"duplicate WITH table name: %s\", zName);\n      }\n    }\n  }\n\n  if( pWith ){\n    int nByte = sizeof(*pWith) + (sizeof(pWith->a[1]) * pWith->nCte);\n    pNew = sqlite3DbRealloc(db, pWith, nByte);\n  }else{\n    pNew = sqlite3DbMallocZero(db, sizeof(*pWith));\n  }\n  assert( (pNew!=0 && zName!=0) || db->mallocFailed );\n\n  if( db->mallocFailed ){\n    sqlite3ExprListDelete(db, pArglist);\n    sqlite3SelectDelete(db, pQuery);\n    sqlite3DbFree(db, zName);\n    pNew = pWith;\n  }else{\n    pNew->a[pNew->nCte].pSelect = pQuery;\n    pNew->a[pNew->nCte].pCols = pArglist;\n    pNew->a[pNew->nCte].zName = zName;\n    pNew->a[pNew->nCte].zCteErr = 0;\n    pNew->nCte++;\n  }\n\n  return pNew;\n}\n\n/*\n** Free the contents of the With object passed as the second argument.\n*/\nSQLITE_PRIVATE void sqlite3WithDelete(sqlite3 *db, With *pWith){\n  if( pWith ){\n    int i;\n    for(i=0; i<pWith->nCte; i++){\n      struct Cte *pCte = &pWith->a[i];\n      sqlite3ExprListDelete(db, pCte->pCols);\n      sqlite3SelectDelete(db, pCte->pSelect);\n      sqlite3DbFree(db, pCte->zName);\n    }\n    sqlite3DbFree(db, pWith);\n  }\n}\n#endif /* !defined(SQLITE_OMIT_CTE) */\n\n/************** End of build.c ***********************************************/\n/************** Begin file callback.c ****************************************/\n/*\n** 2005 May 23 \n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n*************************************************************************\n**\n** This file contains functions used to access the internal hash tables\n** of user defined functions and collation sequences.\n*/\n\n/* #include \"sqliteInt.h\" */\n\n/*\n** Invoke the 'collation needed' callback to request a collation sequence\n** in the encoding enc of name zName, length nName.\n*/\nstatic void callCollNeeded(sqlite3 *db, int enc, const char *zName){\n  assert( !db->xCollNeeded || !db->xCollNeeded16 );\n  if( db->xCollNeeded ){\n    char *zExternal = sqlite3DbStrDup(db, zName);\n    if( !zExternal ) return;\n    db->xCollNeeded(db->pCollNeededArg, db, enc, zExternal);\n    sqlite3DbFree(db, zExternal);\n  }\n#ifndef SQLITE_OMIT_UTF16\n  if( db->xCollNeeded16 ){\n    char const *zExternal;\n    sqlite3_value *pTmp = sqlite3ValueNew(db);\n    sqlite3ValueSetStr(pTmp, -1, zName, SQLITE_UTF8, SQLITE_STATIC);\n    zExternal = sqlite3ValueText(pTmp, SQLITE_UTF16NATIVE);\n    if( zExternal ){\n      db->xCollNeeded16(db->pCollNeededArg, db, (int)ENC(db), zExternal);\n    }\n    sqlite3ValueFree(pTmp);\n  }\n#endif\n}\n\n/*\n** This routine is called if the collation factory fails to deliver a\n** collation function in the best encoding but there may be other versions\n** of this collation function (for other text encodings) available. Use one\n** of these instead if they exist. Avoid a UTF-8 <-> UTF-16 conversion if\n** possible.\n*/\nstatic int synthCollSeq(sqlite3 *db, CollSeq *pColl){\n  CollSeq *pColl2;\n  char *z = pColl->zName;\n  int i;\n  static const u8 aEnc[] = { SQLITE_UTF16BE, SQLITE_UTF16LE, SQLITE_UTF8 };\n  for(i=0; i<3; i++){\n    pColl2 = sqlite3FindCollSeq(db, aEnc[i], z, 0);\n    if( pColl2->xCmp!=0 ){\n      memcpy(pColl, pColl2, sizeof(CollSeq));\n      pColl->xDel = 0;         /* Do not copy the destructor */\n      return SQLITE_OK;\n    }\n  }\n  return SQLITE_ERROR;\n}\n\n/*\n** This function is responsible for invoking the collation factory callback\n** or substituting a collation sequence of a different encoding when the\n** requested collation sequence is not available in the desired encoding.\n** \n** If it is not NULL, then pColl must point to the database native encoding \n** collation sequence with name zName, length nName.\n**\n** The return value is either the collation sequence to be used in database\n** db for collation type name zName, length nName, or NULL, if no collation\n** sequence can be found.  If no collation is found, leave an error message.\n**\n** See also: sqlite3LocateCollSeq(), sqlite3FindCollSeq()\n*/\nSQLITE_PRIVATE CollSeq *sqlite3GetCollSeq(\n  Parse *pParse,        /* Parsing context */\n  u8 enc,               /* The desired encoding for the collating sequence */\n  CollSeq *pColl,       /* Collating sequence with native encoding, or NULL */\n  const char *zName     /* Collating sequence name */\n){\n  CollSeq *p;\n  sqlite3 *db = pParse->db;\n\n  p = pColl;\n  if( !p ){\n    p = sqlite3FindCollSeq(db, enc, zName, 0);\n  }\n  if( !p || !p->xCmp ){\n    /* No collation sequence of this type for this encoding is registered.\n    ** Call the collation factory to see if it can supply us with one.\n    */\n    callCollNeeded(db, enc, zName);\n    p = sqlite3FindCollSeq(db, enc, zName, 0);\n  }\n  if( p && !p->xCmp && synthCollSeq(db, p) ){\n    p = 0;\n  }\n  assert( !p || p->xCmp );\n  if( p==0 ){\n    sqlite3ErrorMsg(pParse, \"no such collation sequence: %s\", zName);\n    pParse->rc = SQLITE_ERROR_MISSING_COLLSEQ;\n  }\n  return p;\n}\n\n/*\n** This routine is called on a collation sequence before it is used to\n** check that it is defined. An undefined collation sequence exists when\n** a database is loaded that contains references to collation sequences\n** that have not been defined by sqlite3_create_collation() etc.\n**\n** If required, this routine calls the 'collation needed' callback to\n** request a definition of the collating sequence. If this doesn't work, \n** an equivalent collating sequence that uses a text encoding different\n** from the main database is substituted, if one is available.\n*/\nSQLITE_PRIVATE int sqlite3CheckCollSeq(Parse *pParse, CollSeq *pColl){\n  if( pColl && pColl->xCmp==0 ){\n    const char *zName = pColl->zName;\n    sqlite3 *db = pParse->db;\n    CollSeq *p = sqlite3GetCollSeq(pParse, ENC(db), pColl, zName);\n    if( !p ){\n      return SQLITE_ERROR;\n    }\n    assert( p==pColl );\n  }\n  return SQLITE_OK;\n}\n\n\n\n/*\n** Locate and return an entry from the db.aCollSeq hash table. If the entry\n** specified by zName and nName is not found and parameter 'create' is\n** true, then create a new entry. Otherwise return NULL.\n**\n** Each pointer stored in the sqlite3.aCollSeq hash table contains an\n** array of three CollSeq structures. The first is the collation sequence\n** preferred for UTF-8, the second UTF-16le, and the third UTF-16be.\n**\n** Stored immediately after the three collation sequences is a copy of\n** the collation sequence name. A pointer to this string is stored in\n** each collation sequence structure.\n*/\nstatic CollSeq *findCollSeqEntry(\n  sqlite3 *db,          /* Database connection */\n  const char *zName,    /* Name of the collating sequence */\n  int create            /* Create a new entry if true */\n){\n  CollSeq *pColl;\n  pColl = sqlite3HashFind(&db->aCollSeq, zName);\n\n  if( 0==pColl && create ){\n    int nName = sqlite3Strlen30(zName) + 1;\n    pColl = sqlite3DbMallocZero(db, 3*sizeof(*pColl) + nName);\n    if( pColl ){\n      CollSeq *pDel = 0;\n      pColl[0].zName = (char*)&pColl[3];\n      pColl[0].enc = SQLITE_UTF8;\n      pColl[1].zName = (char*)&pColl[3];\n      pColl[1].enc = SQLITE_UTF16LE;\n      pColl[2].zName = (char*)&pColl[3];\n      pColl[2].enc = SQLITE_UTF16BE;\n      memcpy(pColl[0].zName, zName, nName);\n      pDel = sqlite3HashInsert(&db->aCollSeq, pColl[0].zName, pColl);\n\n      /* If a malloc() failure occurred in sqlite3HashInsert(), it will \n      ** return the pColl pointer to be deleted (because it wasn't added\n      ** to the hash table).\n      */\n      assert( pDel==0 || pDel==pColl );\n      if( pDel!=0 ){\n        sqlite3OomFault(db);\n        sqlite3DbFree(db, pDel);\n        pColl = 0;\n      }\n    }\n  }\n  return pColl;\n}\n\n/*\n** Parameter zName points to a UTF-8 encoded string nName bytes long.\n** Return the CollSeq* pointer for the collation sequence named zName\n** for the encoding 'enc' from the database 'db'.\n**\n** If the entry specified is not found and 'create' is true, then create a\n** new entry.  Otherwise return NULL.\n**\n** A separate function sqlite3LocateCollSeq() is a wrapper around\n** this routine.  sqlite3LocateCollSeq() invokes the collation factory\n** if necessary and generates an error message if the collating sequence\n** cannot be found.\n**\n** See also: sqlite3LocateCollSeq(), sqlite3GetCollSeq()\n*/\nSQLITE_PRIVATE CollSeq *sqlite3FindCollSeq(\n  sqlite3 *db,\n  u8 enc,\n  const char *zName,\n  int create\n){\n  CollSeq *pColl;\n  if( zName ){\n    pColl = findCollSeqEntry(db, zName, create);\n  }else{\n    pColl = db->pDfltColl;\n  }\n  assert( SQLITE_UTF8==1 && SQLITE_UTF16LE==2 && SQLITE_UTF16BE==3 );\n  assert( enc>=SQLITE_UTF8 && enc<=SQLITE_UTF16BE );\n  if( pColl ) pColl += enc-1;\n  return pColl;\n}\n\n/* During the search for the best function definition, this procedure\n** is called to test how well the function passed as the first argument\n** matches the request for a function with nArg arguments in a system\n** that uses encoding enc. The value returned indicates how well the\n** request is matched. A higher value indicates a better match.\n**\n** If nArg is -1 that means to only return a match (non-zero) if p->nArg\n** is also -1.  In other words, we are searching for a function that\n** takes a variable number of arguments.\n**\n** If nArg is -2 that means that we are searching for any function \n** regardless of the number of arguments it uses, so return a positive\n** match score for any\n**\n** The returned value is always between 0 and 6, as follows:\n**\n** 0: Not a match.\n** 1: UTF8/16 conversion required and function takes any number of arguments.\n** 2: UTF16 byte order change required and function takes any number of args.\n** 3: encoding matches and function takes any number of arguments\n** 4: UTF8/16 conversion required - argument count matches exactly\n** 5: UTF16 byte order conversion required - argument count matches exactly\n** 6: Perfect match:  encoding and argument count match exactly.\n**\n** If nArg==(-2) then any function with a non-null xSFunc is\n** a perfect match and any function with xSFunc NULL is\n** a non-match.\n*/\n#define FUNC_PERFECT_MATCH 6  /* The score for a perfect match */\nstatic int matchQuality(\n  FuncDef *p,     /* The function we are evaluating for match quality */\n  int nArg,       /* Desired number of arguments.  (-1)==any */\n  u8 enc          /* Desired text encoding */\n){\n  int match;\n\n  /* nArg of -2 is a special case */\n  if( nArg==(-2) ) return (p->xSFunc==0) ? 0 : FUNC_PERFECT_MATCH;\n\n  /* Wrong number of arguments means \"no match\" */\n  if( p->nArg!=nArg && p->nArg>=0 ) return 0;\n\n  /* Give a better score to a function with a specific number of arguments\n  ** than to function that accepts any number of arguments. */\n  if( p->nArg==nArg ){\n    match = 4;\n  }else{\n    match = 1;\n  }\n\n  /* Bonus points if the text encoding matches */\n  if( enc==(p->funcFlags & SQLITE_FUNC_ENCMASK) ){\n    match += 2;  /* Exact encoding match */\n  }else if( (enc & p->funcFlags & 2)!=0 ){\n    match += 1;  /* Both are UTF16, but with different byte orders */\n  }\n\n  return match;\n}\n\n/*\n** Search a FuncDefHash for a function with the given name.  Return\n** a pointer to the matching FuncDef if found, or 0 if there is no match.\n*/\nstatic FuncDef *functionSearch(\n  int h,               /* Hash of the name */\n  const char *zFunc    /* Name of function */\n){\n  FuncDef *p;\n  for(p=sqlite3BuiltinFunctions.a[h]; p; p=p->u.pHash){\n    if( sqlite3StrICmp(p->zName, zFunc)==0 ){\n      return p;\n    }\n  }\n  return 0;\n}\n\n/*\n** Insert a new FuncDef into a FuncDefHash hash table.\n*/\nSQLITE_PRIVATE void sqlite3InsertBuiltinFuncs(\n  FuncDef *aDef,      /* List of global functions to be inserted */\n  int nDef            /* Length of the apDef[] list */\n){\n  int i;\n  for(i=0; i<nDef; i++){\n    FuncDef *pOther;\n    const char *zName = aDef[i].zName;\n    int nName = sqlite3Strlen30(zName);\n    int h = (zName[0] + nName) % SQLITE_FUNC_HASH_SZ;\n    assert( zName[0]>='a' && zName[0]<='z' );\n    pOther = functionSearch(h, zName);\n    if( pOther ){\n      assert( pOther!=&aDef[i] && pOther->pNext!=&aDef[i] );\n      aDef[i].pNext = pOther->pNext;\n      pOther->pNext = &aDef[i];\n    }else{\n      aDef[i].pNext = 0;\n      aDef[i].u.pHash = sqlite3BuiltinFunctions.a[h];\n      sqlite3BuiltinFunctions.a[h] = &aDef[i];\n    }\n  }\n}\n  \n  \n\n/*\n** Locate a user function given a name, a number of arguments and a flag\n** indicating whether the function prefers UTF-16 over UTF-8.  Return a\n** pointer to the FuncDef structure that defines that function, or return\n** NULL if the function does not exist.\n**\n** If the createFlag argument is true, then a new (blank) FuncDef\n** structure is created and liked into the \"db\" structure if a\n** no matching function previously existed.\n**\n** If nArg is -2, then the first valid function found is returned.  A\n** function is valid if xSFunc is non-zero.  The nArg==(-2)\n** case is used to see if zName is a valid function name for some number\n** of arguments.  If nArg is -2, then createFlag must be 0.\n**\n** If createFlag is false, then a function with the required name and\n** number of arguments may be returned even if the eTextRep flag does not\n** match that requested.\n*/\nSQLITE_PRIVATE FuncDef *sqlite3FindFunction(\n  sqlite3 *db,       /* An open database */\n  const char *zName, /* Name of the function.  zero-terminated */\n  int nArg,          /* Number of arguments.  -1 means any number */\n  u8 enc,            /* Preferred text encoding */\n  u8 createFlag      /* Create new entry if true and does not otherwise exist */\n){\n  FuncDef *p;         /* Iterator variable */\n  FuncDef *pBest = 0; /* Best match found so far */\n  int bestScore = 0;  /* Score of best match */\n  int h;              /* Hash value */\n  int nName;          /* Length of the name */\n\n  assert( nArg>=(-2) );\n  assert( nArg>=(-1) || createFlag==0 );\n  nName = sqlite3Strlen30(zName);\n\n  /* First search for a match amongst the application-defined functions.\n  */\n  p = (FuncDef*)sqlite3HashFind(&db->aFunc, zName);\n  while( p ){\n    int score = matchQuality(p, nArg, enc);\n    if( score>bestScore ){\n      pBest = p;\n      bestScore = score;\n    }\n    p = p->pNext;\n  }\n\n  /* If no match is found, search the built-in functions.\n  **\n  ** If the DBFLAG_PreferBuiltin flag is set, then search the built-in\n  ** functions even if a prior app-defined function was found.  And give\n  ** priority to built-in functions.\n  **\n  ** Except, if createFlag is true, that means that we are trying to\n  ** install a new function.  Whatever FuncDef structure is returned it will\n  ** have fields overwritten with new information appropriate for the\n  ** new function.  But the FuncDefs for built-in functions are read-only.\n  ** So we must not search for built-ins when creating a new function.\n  */ \n  if( !createFlag && (pBest==0 || (db->mDbFlags & DBFLAG_PreferBuiltin)!=0) ){\n    bestScore = 0;\n    h = (sqlite3UpperToLower[(u8)zName[0]] + nName) % SQLITE_FUNC_HASH_SZ;\n    p = functionSearch(h, zName);\n    while( p ){\n      int score = matchQuality(p, nArg, enc);\n      if( score>bestScore ){\n        pBest = p;\n        bestScore = score;\n      }\n      p = p->pNext;\n    }\n  }\n\n  /* If the createFlag parameter is true and the search did not reveal an\n  ** exact match for the name, number of arguments and encoding, then add a\n  ** new entry to the hash table and return it.\n  */\n  if( createFlag && bestScore<FUNC_PERFECT_MATCH && \n      (pBest = sqlite3DbMallocZero(db, sizeof(*pBest)+nName+1))!=0 ){\n    FuncDef *pOther;\n    pBest->zName = (const char*)&pBest[1];\n    pBest->nArg = (u16)nArg;\n    pBest->funcFlags = enc;\n    memcpy((char*)&pBest[1], zName, nName+1);\n    pOther = (FuncDef*)sqlite3HashInsert(&db->aFunc, pBest->zName, pBest);\n    if( pOther==pBest ){\n      sqlite3DbFree(db, pBest);\n      sqlite3OomFault(db);\n      return 0;\n    }else{\n      pBest->pNext = pOther;\n    }\n  }\n\n  if( pBest && (pBest->xSFunc || createFlag) ){\n    return pBest;\n  }\n  return 0;\n}\n\n/*\n** Free all resources held by the schema structure. The void* argument points\n** at a Schema struct. This function does not call sqlite3DbFree(db, ) on the \n** pointer itself, it just cleans up subsidiary resources (i.e. the contents\n** of the schema hash tables).\n**\n** The Schema.cache_size variable is not cleared.\n*/\nSQLITE_PRIVATE void sqlite3SchemaClear(void *p){\n  Hash temp1;\n  Hash temp2;\n  HashElem *pElem;\n  Schema *pSchema = (Schema *)p;\n\n  temp1 = pSchema->tblHash;\n  temp2 = pSchema->trigHash;\n  sqlite3HashInit(&pSchema->trigHash);\n  sqlite3HashClear(&pSchema->idxHash);\n  for(pElem=sqliteHashFirst(&temp2); pElem; pElem=sqliteHashNext(pElem)){\n    sqlite3DeleteTrigger(0, (Trigger*)sqliteHashData(pElem));\n  }\n  sqlite3HashClear(&temp2);\n  sqlite3HashInit(&pSchema->tblHash);\n  for(pElem=sqliteHashFirst(&temp1); pElem; pElem=sqliteHashNext(pElem)){\n    Table *pTab = sqliteHashData(pElem);\n    sqlite3DeleteTable(0, pTab);\n  }\n  sqlite3HashClear(&temp1);\n  sqlite3HashClear(&pSchema->fkeyHash);\n  pSchema->pSeqTab = 0;\n  if( pSchema->schemaFlags & DB_SchemaLoaded ){\n    pSchema->iGeneration++;\n  }\n  pSchema->schemaFlags &= ~(DB_SchemaLoaded|DB_ResetWanted);\n}\n\n/*\n** Find and return the schema associated with a BTree.  Create\n** a new one if necessary.\n*/\nSQLITE_PRIVATE Schema *sqlite3SchemaGet(sqlite3 *db, Btree *pBt){\n  Schema * p;\n  if( pBt ){\n    p = (Schema *)sqlite3BtreeSchema(pBt, sizeof(Schema), sqlite3SchemaClear);\n  }else{\n    p = (Schema *)sqlite3DbMallocZero(0, sizeof(Schema));\n  }\n  if( !p ){\n    sqlite3OomFault(db);\n  }else if ( 0==p->file_format ){\n    sqlite3HashInit(&p->tblHash);\n    sqlite3HashInit(&p->idxHash);\n    sqlite3HashInit(&p->trigHash);\n    sqlite3HashInit(&p->fkeyHash);\n    p->enc = SQLITE_UTF8;\n  }\n  return p;\n}\n\n/************** End of callback.c ********************************************/\n/************** Begin file delete.c ******************************************/\n/*\n** 2001 September 15\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n*************************************************************************\n** This file contains C code routines that are called by the parser\n** in order to generate code for DELETE FROM statements.\n*/\n/* #include \"sqliteInt.h\" */\n\n/*\n** While a SrcList can in general represent multiple tables and subqueries\n** (as in the FROM clause of a SELECT statement) in this case it contains\n** the name of a single table, as one might find in an INSERT, DELETE,\n** or UPDATE statement.  Look up that table in the symbol table and\n** return a pointer.  Set an error message and return NULL if the table \n** name is not found or if any other error occurs.\n**\n** The following fields are initialized appropriate in pSrc:\n**\n**    pSrc->a[0].pTab       Pointer to the Table object\n**    pSrc->a[0].pIndex     Pointer to the INDEXED BY index, if there is one\n**\n*/\nSQLITE_PRIVATE Table *sqlite3SrcListLookup(Parse *pParse, SrcList *pSrc){\n  struct SrcList_item *pItem = pSrc->a;\n  Table *pTab;\n  assert( pItem && pSrc->nSrc==1 );\n  pTab = sqlite3LocateTableItem(pParse, 0, pItem);\n  sqlite3DeleteTable(pParse->db, pItem->pTab);\n  pItem->pTab = pTab;\n  if( pTab ){\n    pTab->nTabRef++;\n  }\n  if( sqlite3IndexedByLookup(pParse, pItem) ){\n    pTab = 0;\n  }\n  return pTab;\n}\n\n/*\n** Check to make sure the given table is writable.  If it is not\n** writable, generate an error message and return 1.  If it is\n** writable return 0;\n*/\nSQLITE_PRIVATE int sqlite3IsReadOnly(Parse *pParse, Table *pTab, int viewOk){\n  /* A table is not writable under the following circumstances:\n  **\n  **   1) It is a virtual table and no implementation of the xUpdate method\n  **      has been provided, or\n  **   2) It is a system table (i.e. sqlite_master), this call is not\n  **      part of a nested parse and writable_schema pragma has not \n  **      been specified.\n  **\n  ** In either case leave an error message in pParse and return non-zero.\n  */\n  if( ( IsVirtual(pTab) \n     && sqlite3GetVTable(pParse->db, pTab)->pMod->pModule->xUpdate==0 )\n   || ( (pTab->tabFlags & TF_Readonly)!=0\n     && (pParse->db->flags & SQLITE_WriteSchema)==0\n     && pParse->nested==0 )\n  ){\n    sqlite3ErrorMsg(pParse, \"table %s may not be modified\", pTab->zName);\n    return 1;\n  }\n\n#ifndef SQLITE_OMIT_VIEW\n  if( !viewOk && pTab->pSelect ){\n    sqlite3ErrorMsg(pParse,\"cannot modify %s because it is a view\",pTab->zName);\n    return 1;\n  }\n#endif\n  return 0;\n}\n\n\n#if !defined(SQLITE_OMIT_VIEW) && !defined(SQLITE_OMIT_TRIGGER)\n/*\n** Evaluate a view and store its result in an ephemeral table.  The\n** pWhere argument is an optional WHERE clause that restricts the\n** set of rows in the view that are to be added to the ephemeral table.\n*/\nSQLITE_PRIVATE void sqlite3MaterializeView(\n  Parse *pParse,       /* Parsing context */\n  Table *pView,        /* View definition */\n  Expr *pWhere,        /* Optional WHERE clause to be added */\n  ExprList *pOrderBy,  /* Optional ORDER BY clause */\n  Expr *pLimit,        /* Optional LIMIT clause */\n  int iCur             /* Cursor number for ephemeral table */\n){\n  SelectDest dest;\n  Select *pSel;\n  SrcList *pFrom;\n  sqlite3 *db = pParse->db;\n  int iDb = sqlite3SchemaToIndex(db, pView->pSchema);\n  pWhere = sqlite3ExprDup(db, pWhere, 0);\n  pFrom = sqlite3SrcListAppend(db, 0, 0, 0);\n  if( pFrom ){\n    assert( pFrom->nSrc==1 );\n    pFrom->a[0].zName = sqlite3DbStrDup(db, pView->zName);\n    pFrom->a[0].zDatabase = sqlite3DbStrDup(db, db->aDb[iDb].zDbSName);\n    assert( pFrom->a[0].pOn==0 );\n    assert( pFrom->a[0].pUsing==0 );\n  }\n  pSel = sqlite3SelectNew(pParse, 0, pFrom, pWhere, 0, 0, pOrderBy, \n                          SF_IncludeHidden, pLimit);\n  sqlite3SelectDestInit(&dest, SRT_EphemTab, iCur);\n  sqlite3Select(pParse, pSel, &dest);\n  sqlite3SelectDelete(db, pSel);\n}\n#endif /* !defined(SQLITE_OMIT_VIEW) && !defined(SQLITE_OMIT_TRIGGER) */\n\n#if defined(SQLITE_ENABLE_UPDATE_DELETE_LIMIT) && !defined(SQLITE_OMIT_SUBQUERY)\n/*\n** Generate an expression tree to implement the WHERE, ORDER BY,\n** and LIMIT/OFFSET portion of DELETE and UPDATE statements.\n**\n**     DELETE FROM table_wxyz WHERE a<5 ORDER BY a LIMIT 1;\n**                            \\__________________________/\n**                               pLimitWhere (pInClause)\n*/\nSQLITE_PRIVATE Expr *sqlite3LimitWhere(\n  Parse *pParse,               /* The parser context */\n  SrcList *pSrc,               /* the FROM clause -- which tables to scan */\n  Expr *pWhere,                /* The WHERE clause.  May be null */\n  ExprList *pOrderBy,          /* The ORDER BY clause.  May be null */\n  Expr *pLimit,                /* The LIMIT clause.  May be null */\n  char *zStmtType              /* Either DELETE or UPDATE.  For err msgs. */\n){\n  sqlite3 *db = pParse->db;\n  Expr *pLhs = NULL;           /* LHS of IN(SELECT...) operator */\n  Expr *pInClause = NULL;      /* WHERE rowid IN ( select ) */\n  ExprList *pEList = NULL;     /* Expression list contaning only pSelectRowid */\n  SrcList *pSelectSrc = NULL;  /* SELECT rowid FROM x ... (dup of pSrc) */\n  Select *pSelect = NULL;      /* Complete SELECT tree */\n  Table *pTab;\n\n  /* Check that there isn't an ORDER BY without a LIMIT clause.\n  */\n  if( pOrderBy && pLimit==0 ) {\n    sqlite3ErrorMsg(pParse, \"ORDER BY without LIMIT on %s\", zStmtType);\n    sqlite3ExprDelete(pParse->db, pWhere);\n    sqlite3ExprListDelete(pParse->db, pOrderBy);\n    return 0;\n  }\n\n  /* We only need to generate a select expression if there\n  ** is a limit/offset term to enforce.\n  */\n  if( pLimit == 0 ) {\n    return pWhere;\n  }\n\n  /* Generate a select expression tree to enforce the limit/offset \n  ** term for the DELETE or UPDATE statement.  For example:\n  **   DELETE FROM table_a WHERE col1=1 ORDER BY col2 LIMIT 1 OFFSET 1\n  ** becomes:\n  **   DELETE FROM table_a WHERE rowid IN ( \n  **     SELECT rowid FROM table_a WHERE col1=1 ORDER BY col2 LIMIT 1 OFFSET 1\n  **   );\n  */\n\n  pTab = pSrc->a[0].pTab;\n  if( HasRowid(pTab) ){\n    pLhs = sqlite3PExpr(pParse, TK_ROW, 0, 0);\n    pEList = sqlite3ExprListAppend(\n        pParse, 0, sqlite3PExpr(pParse, TK_ROW, 0, 0)\n    );\n  }else{\n    Index *pPk = sqlite3PrimaryKeyIndex(pTab);\n    if( pPk->nKeyCol==1 ){\n      const char *zName = pTab->aCol[pPk->aiColumn[0]].zName;\n      pLhs = sqlite3Expr(db, TK_ID, zName);\n      pEList = sqlite3ExprListAppend(pParse, 0, sqlite3Expr(db, TK_ID, zName));\n    }else{\n      int i;\n      for(i=0; i<pPk->nKeyCol; i++){\n        Expr *p = sqlite3Expr(db, TK_ID, pTab->aCol[pPk->aiColumn[i]].zName);\n        pEList = sqlite3ExprListAppend(pParse, pEList, p);\n      }\n      pLhs = sqlite3PExpr(pParse, TK_VECTOR, 0, 0);\n      if( pLhs ){\n        pLhs->x.pList = sqlite3ExprListDup(db, pEList, 0);\n      }\n    }\n  }\n\n  /* duplicate the FROM clause as it is needed by both the DELETE/UPDATE tree\n  ** and the SELECT subtree. */\n  pSrc->a[0].pTab = 0;\n  pSelectSrc = sqlite3SrcListDup(pParse->db, pSrc, 0);\n  pSrc->a[0].pTab = pTab;\n  pSrc->a[0].pIBIndex = 0;\n\n  /* generate the SELECT expression tree. */\n  pSelect = sqlite3SelectNew(pParse, pEList, pSelectSrc, pWhere, 0 ,0, \n      pOrderBy,0,pLimit\n  );\n\n  /* now generate the new WHERE rowid IN clause for the DELETE/UDPATE */\n  pInClause = sqlite3PExpr(pParse, TK_IN, pLhs, 0);\n  sqlite3PExprAddSelect(pParse, pInClause, pSelect);\n  return pInClause;\n}\n#endif /* defined(SQLITE_ENABLE_UPDATE_DELETE_LIMIT) */\n       /*      && !defined(SQLITE_OMIT_SUBQUERY) */\n\n/*\n** Generate code for a DELETE FROM statement.\n**\n**     DELETE FROM table_wxyz WHERE a<5 AND b NOT NULL;\n**                 \\________/       \\________________/\n**                  pTabList              pWhere\n*/\nSQLITE_PRIVATE void sqlite3DeleteFrom(\n  Parse *pParse,         /* The parser context */\n  SrcList *pTabList,     /* The table from which we should delete things */\n  Expr *pWhere,          /* The WHERE clause.  May be null */\n  ExprList *pOrderBy,    /* ORDER BY clause. May be null */\n  Expr *pLimit           /* LIMIT clause. May be null */\n){\n  Vdbe *v;               /* The virtual database engine */\n  Table *pTab;           /* The table from which records will be deleted */\n  int i;                 /* Loop counter */\n  WhereInfo *pWInfo;     /* Information about the WHERE clause */\n  Index *pIdx;           /* For looping over indices of the table */\n  int iTabCur;           /* Cursor number for the table */\n  int iDataCur = 0;      /* VDBE cursor for the canonical data source */\n  int iIdxCur = 0;       /* Cursor number of the first index */\n  int nIdx;              /* Number of indices */\n  sqlite3 *db;           /* Main database structure */\n  AuthContext sContext;  /* Authorization context */\n  NameContext sNC;       /* Name context to resolve expressions in */\n  int iDb;               /* Database number */\n  int memCnt = -1;       /* Memory cell used for change counting */\n  int rcauth;            /* Value returned by authorization callback */\n  int eOnePass;          /* ONEPASS_OFF or _SINGLE or _MULTI */\n  int aiCurOnePass[2];   /* The write cursors opened by WHERE_ONEPASS */\n  u8 *aToOpen = 0;       /* Open cursor iTabCur+j if aToOpen[j] is true */\n  Index *pPk;            /* The PRIMARY KEY index on the table */\n  int iPk = 0;           /* First of nPk registers holding PRIMARY KEY value */\n  i16 nPk = 1;           /* Number of columns in the PRIMARY KEY */\n  int iKey;              /* Memory cell holding key of row to be deleted */\n  i16 nKey;              /* Number of memory cells in the row key */\n  int iEphCur = 0;       /* Ephemeral table holding all primary key values */\n  int iRowSet = 0;       /* Register for rowset of rows to delete */\n  int addrBypass = 0;    /* Address of jump over the delete logic */\n  int addrLoop = 0;      /* Top of the delete loop */\n  int addrEphOpen = 0;   /* Instruction to open the Ephemeral table */\n  int bComplex;          /* True if there are triggers or FKs or\n                         ** subqueries in the WHERE clause */\n \n#ifndef SQLITE_OMIT_TRIGGER\n  int isView;                  /* True if attempting to delete from a view */\n  Trigger *pTrigger;           /* List of table triggers, if required */\n#endif\n\n  memset(&sContext, 0, sizeof(sContext));\n  db = pParse->db;\n  if( pParse->nErr || db->mallocFailed ){\n    goto delete_from_cleanup;\n  }\n  assert( pTabList->nSrc==1 );\n\n\n  /* Locate the table which we want to delete.  This table has to be\n  ** put in an SrcList structure because some of the subroutines we\n  ** will be calling are designed to work with multiple tables and expect\n  ** an SrcList* parameter instead of just a Table* parameter.\n  */\n  pTab = sqlite3SrcListLookup(pParse, pTabList);\n  if( pTab==0 )  goto delete_from_cleanup;\n\n  /* Figure out if we have any triggers and if the table being\n  ** deleted from is a view\n  */\n#ifndef SQLITE_OMIT_TRIGGER\n  pTrigger = sqlite3TriggersExist(pParse, pTab, TK_DELETE, 0, 0);\n  isView = pTab->pSelect!=0;\n#else\n# define pTrigger 0\n# define isView 0\n#endif\n  bComplex = pTrigger || sqlite3FkRequired(pParse, pTab, 0, 0);\n#ifdef SQLITE_OMIT_VIEW\n# undef isView\n# define isView 0\n#endif\n\n#ifdef SQLITE_ENABLE_UPDATE_DELETE_LIMIT\n  if( !isView ){\n    pWhere = sqlite3LimitWhere(\n        pParse, pTabList, pWhere, pOrderBy, pLimit, \"DELETE\"\n    );\n    pOrderBy = 0;\n    pLimit = 0;\n  }\n#endif\n\n  /* If pTab is really a view, make sure it has been initialized.\n  */\n  if( sqlite3ViewGetColumnNames(pParse, pTab) ){\n    goto delete_from_cleanup;\n  }\n\n  if( sqlite3IsReadOnly(pParse, pTab, (pTrigger?1:0)) ){\n    goto delete_from_cleanup;\n  }\n  iDb = sqlite3SchemaToIndex(db, pTab->pSchema);\n  assert( iDb<db->nDb );\n  rcauth = sqlite3AuthCheck(pParse, SQLITE_DELETE, pTab->zName, 0, \n                            db->aDb[iDb].zDbSName);\n  assert( rcauth==SQLITE_OK || rcauth==SQLITE_DENY || rcauth==SQLITE_IGNORE );\n  if( rcauth==SQLITE_DENY ){\n    goto delete_from_cleanup;\n  }\n  assert(!isView || pTrigger);\n\n  /* Assign cursor numbers to the table and all its indices.\n  */\n  assert( pTabList->nSrc==1 );\n  iTabCur = pTabList->a[0].iCursor = pParse->nTab++;\n  for(nIdx=0, pIdx=pTab->pIndex; pIdx; pIdx=pIdx->pNext, nIdx++){\n    pParse->nTab++;\n  }\n\n  /* Start the view context\n  */\n  if( isView ){\n    sqlite3AuthContextPush(pParse, &sContext, pTab->zName);\n  }\n\n  /* Begin generating code.\n  */\n  v = sqlite3GetVdbe(pParse);\n  if( v==0 ){\n    goto delete_from_cleanup;\n  }\n  if( pParse->nested==0 ) sqlite3VdbeCountChanges(v);\n  sqlite3BeginWriteOperation(pParse, 1, iDb);\n\n  /* If we are trying to delete from a view, realize that view into\n  ** an ephemeral table.\n  */\n#if !defined(SQLITE_OMIT_VIEW) && !defined(SQLITE_OMIT_TRIGGER)\n  if( isView ){\n    sqlite3MaterializeView(pParse, pTab, \n        pWhere, pOrderBy, pLimit, iTabCur\n    );\n    iDataCur = iIdxCur = iTabCur;\n    pOrderBy = 0;\n    pLimit = 0;\n  }\n#endif\n\n  /* Resolve the column names in the WHERE clause.\n  */\n  memset(&sNC, 0, sizeof(sNC));\n  sNC.pParse = pParse;\n  sNC.pSrcList = pTabList;\n  if( sqlite3ResolveExprNames(&sNC, pWhere) ){\n    goto delete_from_cleanup;\n  }\n\n  /* Initialize the counter of the number of rows deleted, if\n  ** we are counting rows.\n  */\n  if( db->flags & SQLITE_CountRows ){\n    memCnt = ++pParse->nMem;\n    sqlite3VdbeAddOp2(v, OP_Integer, 0, memCnt);\n  }\n\n#ifndef SQLITE_OMIT_TRUNCATE_OPTIMIZATION\n  /* Special case: A DELETE without a WHERE clause deletes everything.\n  ** It is easier just to erase the whole table. Prior to version 3.6.5,\n  ** this optimization caused the row change count (the value returned by \n  ** API function sqlite3_count_changes) to be set incorrectly.\n  **\n  ** The \"rcauth==SQLITE_OK\" terms is the\n  ** IMPLEMENTATION-OF: R-17228-37124 If the action code is SQLITE_DELETE and\n  ** the callback returns SQLITE_IGNORE then the DELETE operation proceeds but\n  ** the truncate optimization is disabled and all rows are deleted\n  ** individually.\n  */\n  if( rcauth==SQLITE_OK\n   && pWhere==0\n   && !bComplex\n   && !IsVirtual(pTab)\n#ifdef SQLITE_ENABLE_PREUPDATE_HOOK\n   && db->xPreUpdateCallback==0\n#endif\n  ){\n    assert( !isView );\n    sqlite3TableLock(pParse, iDb, pTab->tnum, 1, pTab->zName);\n    if( HasRowid(pTab) ){\n      sqlite3VdbeAddOp4(v, OP_Clear, pTab->tnum, iDb, memCnt,\n                        pTab->zName, P4_STATIC);\n    }\n    for(pIdx=pTab->pIndex; pIdx; pIdx=pIdx->pNext){\n      assert( pIdx->pSchema==pTab->pSchema );\n      sqlite3VdbeAddOp2(v, OP_Clear, pIdx->tnum, iDb);\n    }\n  }else\n#endif /* SQLITE_OMIT_TRUNCATE_OPTIMIZATION */\n  {\n    u16 wcf = WHERE_ONEPASS_DESIRED|WHERE_DUPLICATES_OK|WHERE_SEEK_TABLE;\n    if( sNC.ncFlags & NC_VarSelect ) bComplex = 1;\n    wcf |= (bComplex ? 0 : WHERE_ONEPASS_MULTIROW);\n    if( HasRowid(pTab) ){\n      /* For a rowid table, initialize the RowSet to an empty set */\n      pPk = 0;\n      nPk = 1;\n      iRowSet = ++pParse->nMem;\n      sqlite3VdbeAddOp2(v, OP_Null, 0, iRowSet);\n    }else{\n      /* For a WITHOUT ROWID table, create an ephemeral table used to\n      ** hold all primary keys for rows to be deleted. */\n      pPk = sqlite3PrimaryKeyIndex(pTab);\n      assert( pPk!=0 );\n      nPk = pPk->nKeyCol;\n      iPk = pParse->nMem+1;\n      pParse->nMem += nPk;\n      iEphCur = pParse->nTab++;\n      addrEphOpen = sqlite3VdbeAddOp2(v, OP_OpenEphemeral, iEphCur, nPk);\n      sqlite3VdbeSetP4KeyInfo(pParse, pPk);\n    }\n  \n    /* Construct a query to find the rowid or primary key for every row\n    ** to be deleted, based on the WHERE clause. Set variable eOnePass\n    ** to indicate the strategy used to implement this delete:\n    **\n    **  ONEPASS_OFF:    Two-pass approach - use a FIFO for rowids/PK values.\n    **  ONEPASS_SINGLE: One-pass approach - at most one row deleted.\n    **  ONEPASS_MULTI:  One-pass approach - any number of rows may be deleted.\n    */\n    pWInfo = sqlite3WhereBegin(pParse, pTabList, pWhere, 0, 0, wcf, iTabCur+1);\n    if( pWInfo==0 ) goto delete_from_cleanup;\n    eOnePass = sqlite3WhereOkOnePass(pWInfo, aiCurOnePass);\n    assert( IsVirtual(pTab)==0 || eOnePass!=ONEPASS_MULTI );\n    assert( IsVirtual(pTab) || bComplex || eOnePass!=ONEPASS_OFF );\n  \n    /* Keep track of the number of rows to be deleted */\n    if( db->flags & SQLITE_CountRows ){\n      sqlite3VdbeAddOp2(v, OP_AddImm, memCnt, 1);\n    }\n  \n    /* Extract the rowid or primary key for the current row */\n    if( pPk ){\n      for(i=0; i<nPk; i++){\n        assert( pPk->aiColumn[i]>=0 );\n        sqlite3ExprCodeGetColumnOfTable(v, pTab, iTabCur,\n                                        pPk->aiColumn[i], iPk+i);\n      }\n      iKey = iPk;\n    }else{\n      iKey = pParse->nMem + 1;\n      iKey = sqlite3ExprCodeGetColumn(pParse, pTab, -1, iTabCur, iKey, 0);\n      if( iKey>pParse->nMem ) pParse->nMem = iKey;\n    }\n  \n    if( eOnePass!=ONEPASS_OFF ){\n      /* For ONEPASS, no need to store the rowid/primary-key. There is only\n      ** one, so just keep it in its register(s) and fall through to the\n      ** delete code.  */\n      nKey = nPk; /* OP_Found will use an unpacked key */\n      aToOpen = sqlite3DbMallocRawNN(db, nIdx+2);\n      if( aToOpen==0 ){\n        sqlite3WhereEnd(pWInfo);\n        goto delete_from_cleanup;\n      }\n      memset(aToOpen, 1, nIdx+1);\n      aToOpen[nIdx+1] = 0;\n      if( aiCurOnePass[0]>=0 ) aToOpen[aiCurOnePass[0]-iTabCur] = 0;\n      if( aiCurOnePass[1]>=0 ) aToOpen[aiCurOnePass[1]-iTabCur] = 0;\n      if( addrEphOpen ) sqlite3VdbeChangeToNoop(v, addrEphOpen);\n    }else{\n      if( pPk ){\n        /* Add the PK key for this row to the temporary table */\n        iKey = ++pParse->nMem;\n        nKey = 0;   /* Zero tells OP_Found to use a composite key */\n        sqlite3VdbeAddOp4(v, OP_MakeRecord, iPk, nPk, iKey,\n            sqlite3IndexAffinityStr(pParse->db, pPk), nPk);\n        sqlite3VdbeAddOp4Int(v, OP_IdxInsert, iEphCur, iKey, iPk, nPk);\n      }else{\n        /* Add the rowid of the row to be deleted to the RowSet */\n        nKey = 1;  /* OP_DeferredSeek always uses a single rowid */\n        sqlite3VdbeAddOp2(v, OP_RowSetAdd, iRowSet, iKey);\n      }\n    }\n  \n    /* If this DELETE cannot use the ONEPASS strategy, this is the \n    ** end of the WHERE loop */\n    if( eOnePass!=ONEPASS_OFF ){\n      addrBypass = sqlite3VdbeMakeLabel(v);\n    }else{\n      sqlite3WhereEnd(pWInfo);\n    }\n  \n    /* Unless this is a view, open cursors for the table we are \n    ** deleting from and all its indices. If this is a view, then the\n    ** only effect this statement has is to fire the INSTEAD OF \n    ** triggers.\n    */\n    if( !isView ){\n      int iAddrOnce = 0;\n      if( eOnePass==ONEPASS_MULTI ){\n        iAddrOnce = sqlite3VdbeAddOp0(v, OP_Once); VdbeCoverage(v);\n      }\n      testcase( IsVirtual(pTab) );\n      sqlite3OpenTableAndIndices(pParse, pTab, OP_OpenWrite, OPFLAG_FORDELETE,\n                                 iTabCur, aToOpen, &iDataCur, &iIdxCur);\n      assert( pPk || IsVirtual(pTab) || iDataCur==iTabCur );\n      assert( pPk || IsVirtual(pTab) || iIdxCur==iDataCur+1 );\n      if( eOnePass==ONEPASS_MULTI ) sqlite3VdbeJumpHere(v, iAddrOnce);\n    }\n  \n    /* Set up a loop over the rowids/primary-keys that were found in the\n    ** where-clause loop above.\n    */\n    if( eOnePass!=ONEPASS_OFF ){\n      assert( nKey==nPk );  /* OP_Found will use an unpacked key */\n      if( !IsVirtual(pTab) && aToOpen[iDataCur-iTabCur] ){\n        assert( pPk!=0 || pTab->pSelect!=0 );\n        sqlite3VdbeAddOp4Int(v, OP_NotFound, iDataCur, addrBypass, iKey, nKey);\n        VdbeCoverage(v);\n      }\n    }else if( pPk ){\n      addrLoop = sqlite3VdbeAddOp1(v, OP_Rewind, iEphCur); VdbeCoverage(v);\n      if( IsVirtual(pTab) ){\n        sqlite3VdbeAddOp3(v, OP_Column, iEphCur, 0, iKey);\n      }else{\n        sqlite3VdbeAddOp2(v, OP_RowData, iEphCur, iKey);\n      }\n      assert( nKey==0 );  /* OP_Found will use a composite key */\n    }else{\n      addrLoop = sqlite3VdbeAddOp3(v, OP_RowSetRead, iRowSet, 0, iKey);\n      VdbeCoverage(v);\n      assert( nKey==1 );\n    }  \n  \n    /* Delete the row */\n#ifndef SQLITE_OMIT_VIRTUALTABLE\n    if( IsVirtual(pTab) ){\n      const char *pVTab = (const char *)sqlite3GetVTable(db, pTab);\n      sqlite3VtabMakeWritable(pParse, pTab);\n      sqlite3VdbeAddOp4(v, OP_VUpdate, 0, 1, iKey, pVTab, P4_VTAB);\n      sqlite3VdbeChangeP5(v, OE_Abort);\n      assert( eOnePass==ONEPASS_OFF || eOnePass==ONEPASS_SINGLE );\n      sqlite3MayAbort(pParse);\n      if( eOnePass==ONEPASS_SINGLE && sqlite3IsToplevel(pParse) ){\n        pParse->isMultiWrite = 0;\n      }\n    }else\n#endif\n    {\n      int count = (pParse->nested==0);    /* True to count changes */\n      sqlite3GenerateRowDelete(pParse, pTab, pTrigger, iDataCur, iIdxCur,\n          iKey, nKey, count, OE_Default, eOnePass, aiCurOnePass[1]);\n    }\n  \n    /* End of the loop over all rowids/primary-keys. */\n    if( eOnePass!=ONEPASS_OFF ){\n      sqlite3VdbeResolveLabel(v, addrBypass);\n      sqlite3WhereEnd(pWInfo);\n    }else if( pPk ){\n      sqlite3VdbeAddOp2(v, OP_Next, iEphCur, addrLoop+1); VdbeCoverage(v);\n      sqlite3VdbeJumpHere(v, addrLoop);\n    }else{\n      sqlite3VdbeGoto(v, addrLoop);\n      sqlite3VdbeJumpHere(v, addrLoop);\n    }     \n  } /* End non-truncate path */\n\n  /* Update the sqlite_sequence table by storing the content of the\n  ** maximum rowid counter values recorded while inserting into\n  ** autoincrement tables.\n  */\n  if( pParse->nested==0 && pParse->pTriggerTab==0 ){\n    sqlite3AutoincrementEnd(pParse);\n  }\n\n  /* Return the number of rows that were deleted. If this routine is \n  ** generating code because of a call to sqlite3NestedParse(), do not\n  ** invoke the callback function.\n  */\n  if( (db->flags&SQLITE_CountRows) && !pParse->nested && !pParse->pTriggerTab ){\n    sqlite3VdbeAddOp2(v, OP_ResultRow, memCnt, 1);\n    sqlite3VdbeSetNumCols(v, 1);\n    sqlite3VdbeSetColName(v, 0, COLNAME_NAME, \"rows deleted\", SQLITE_STATIC);\n  }\n\ndelete_from_cleanup:\n  sqlite3AuthContextPop(&sContext);\n  sqlite3SrcListDelete(db, pTabList);\n  sqlite3ExprDelete(db, pWhere);\n#if defined(SQLITE_ENABLE_UPDATE_DELETE_LIMIT) \n  sqlite3ExprListDelete(db, pOrderBy);\n  sqlite3ExprDelete(db, pLimit);\n#endif\n  sqlite3DbFree(db, aToOpen);\n  return;\n}\n/* Make sure \"isView\" and other macros defined above are undefined. Otherwise\n** they may interfere with compilation of other functions in this file\n** (or in another file, if this file becomes part of the amalgamation).  */\n#ifdef isView\n #undef isView\n#endif\n#ifdef pTrigger\n #undef pTrigger\n#endif\n\n/*\n** This routine generates VDBE code that causes a single row of a\n** single table to be deleted.  Both the original table entry and\n** all indices are removed.\n**\n** Preconditions:\n**\n**   1.  iDataCur is an open cursor on the btree that is the canonical data\n**       store for the table.  (This will be either the table itself,\n**       in the case of a rowid table, or the PRIMARY KEY index in the case\n**       of a WITHOUT ROWID table.)\n**\n**   2.  Read/write cursors for all indices of pTab must be open as\n**       cursor number iIdxCur+i for the i-th index.\n**\n**   3.  The primary key for the row to be deleted must be stored in a\n**       sequence of nPk memory cells starting at iPk.  If nPk==0 that means\n**       that a search record formed from OP_MakeRecord is contained in the\n**       single memory location iPk.\n**\n** eMode:\n**   Parameter eMode may be passed either ONEPASS_OFF (0), ONEPASS_SINGLE, or\n**   ONEPASS_MULTI.  If eMode is not ONEPASS_OFF, then the cursor\n**   iDataCur already points to the row to delete. If eMode is ONEPASS_OFF\n**   then this function must seek iDataCur to the entry identified by iPk\n**   and nPk before reading from it.\n**\n**   If eMode is ONEPASS_MULTI, then this call is being made as part\n**   of a ONEPASS delete that affects multiple rows. In this case, if \n**   iIdxNoSeek is a valid cursor number (>=0) and is not the same as\n**   iDataCur, then its position should be preserved following the delete\n**   operation. Or, if iIdxNoSeek is not a valid cursor number, the\n**   position of iDataCur should be preserved instead.\n**\n** iIdxNoSeek:\n**   If iIdxNoSeek is a valid cursor number (>=0) not equal to iDataCur,\n**   then it identifies an index cursor (from within array of cursors\n**   starting at iIdxCur) that already points to the index entry to be deleted.\n**   Except, this optimization is disabled if there are BEFORE triggers since\n**   the trigger body might have moved the cursor.\n*/\nSQLITE_PRIVATE void sqlite3GenerateRowDelete(\n  Parse *pParse,     /* Parsing context */\n  Table *pTab,       /* Table containing the row to be deleted */\n  Trigger *pTrigger, /* List of triggers to (potentially) fire */\n  int iDataCur,      /* Cursor from which column data is extracted */\n  int iIdxCur,       /* First index cursor */\n  int iPk,           /* First memory cell containing the PRIMARY KEY */\n  i16 nPk,           /* Number of PRIMARY KEY memory cells */\n  u8 count,          /* If non-zero, increment the row change counter */\n  u8 onconf,         /* Default ON CONFLICT policy for triggers */\n  u8 eMode,          /* ONEPASS_OFF, _SINGLE, or _MULTI.  See above */\n  int iIdxNoSeek     /* Cursor number of cursor that does not need seeking */\n){\n  Vdbe *v = pParse->pVdbe;        /* Vdbe */\n  int iOld = 0;                   /* First register in OLD.* array */\n  int iLabel;                     /* Label resolved to end of generated code */\n  u8 opSeek;                      /* Seek opcode */\n\n  /* Vdbe is guaranteed to have been allocated by this stage. */\n  assert( v );\n  VdbeModuleComment((v, \"BEGIN: GenRowDel(%d,%d,%d,%d)\",\n                         iDataCur, iIdxCur, iPk, (int)nPk));\n\n  /* Seek cursor iCur to the row to delete. If this row no longer exists \n  ** (this can happen if a trigger program has already deleted it), do\n  ** not attempt to delete it or fire any DELETE triggers.  */\n  iLabel = sqlite3VdbeMakeLabel(v);\n  opSeek = HasRowid(pTab) ? OP_NotExists : OP_NotFound;\n  if( eMode==ONEPASS_OFF ){\n    sqlite3VdbeAddOp4Int(v, opSeek, iDataCur, iLabel, iPk, nPk);\n    VdbeCoverageIf(v, opSeek==OP_NotExists);\n    VdbeCoverageIf(v, opSeek==OP_NotFound);\n  }\n \n  /* If there are any triggers to fire, allocate a range of registers to\n  ** use for the old.* references in the triggers.  */\n  if( sqlite3FkRequired(pParse, pTab, 0, 0) || pTrigger ){\n    u32 mask;                     /* Mask of OLD.* columns in use */\n    int iCol;                     /* Iterator used while populating OLD.* */\n    int addrStart;                /* Start of BEFORE trigger programs */\n\n    /* TODO: Could use temporary registers here. Also could attempt to\n    ** avoid copying the contents of the rowid register.  */\n    mask = sqlite3TriggerColmask(\n        pParse, pTrigger, 0, 0, TRIGGER_BEFORE|TRIGGER_AFTER, pTab, onconf\n    );\n    mask |= sqlite3FkOldmask(pParse, pTab);\n    iOld = pParse->nMem+1;\n    pParse->nMem += (1 + pTab->nCol);\n\n    /* Populate the OLD.* pseudo-table register array. These values will be \n    ** used by any BEFORE and AFTER triggers that exist.  */\n    sqlite3VdbeAddOp2(v, OP_Copy, iPk, iOld);\n    for(iCol=0; iCol<pTab->nCol; iCol++){\n      testcase( mask!=0xffffffff && iCol==31 );\n      testcase( mask!=0xffffffff && iCol==32 );\n      if( mask==0xffffffff || (iCol<=31 && (mask & MASKBIT32(iCol))!=0) ){\n        sqlite3ExprCodeGetColumnOfTable(v, pTab, iDataCur, iCol, iOld+iCol+1);\n      }\n    }\n\n    /* Invoke BEFORE DELETE trigger programs. */\n    addrStart = sqlite3VdbeCurrentAddr(v);\n    sqlite3CodeRowTrigger(pParse, pTrigger, \n        TK_DELETE, 0, TRIGGER_BEFORE, pTab, iOld, onconf, iLabel\n    );\n\n    /* If any BEFORE triggers were coded, then seek the cursor to the \n    ** row to be deleted again. It may be that the BEFORE triggers moved\n    ** the cursor or already deleted the row that the cursor was\n    ** pointing to.\n    **\n    ** Also disable the iIdxNoSeek optimization since the BEFORE trigger\n    ** may have moved that cursor.\n    */\n    if( addrStart<sqlite3VdbeCurrentAddr(v) ){\n      sqlite3VdbeAddOp4Int(v, opSeek, iDataCur, iLabel, iPk, nPk);\n      VdbeCoverageIf(v, opSeek==OP_NotExists);\n      VdbeCoverageIf(v, opSeek==OP_NotFound);\n      testcase( iIdxNoSeek>=0 );\n      iIdxNoSeek = -1;\n    }\n\n    /* Do FK processing. This call checks that any FK constraints that\n    ** refer to this table (i.e. constraints attached to other tables) \n    ** are not violated by deleting this row.  */\n    sqlite3FkCheck(pParse, pTab, iOld, 0, 0, 0);\n  }\n\n  /* Delete the index and table entries. Skip this step if pTab is really\n  ** a view (in which case the only effect of the DELETE statement is to\n  ** fire the INSTEAD OF triggers).  \n  **\n  ** If variable 'count' is non-zero, then this OP_Delete instruction should\n  ** invoke the update-hook. The pre-update-hook, on the other hand should\n  ** be invoked unless table pTab is a system table. The difference is that\n  ** the update-hook is not invoked for rows removed by REPLACE, but the \n  ** pre-update-hook is.\n  */ \n  if( pTab->pSelect==0 ){\n    u8 p5 = 0;\n    sqlite3GenerateRowIndexDelete(pParse, pTab, iDataCur, iIdxCur,0,iIdxNoSeek);\n    sqlite3VdbeAddOp2(v, OP_Delete, iDataCur, (count?OPFLAG_NCHANGE:0));\n    if( pParse->nested==0 || 0==sqlite3_stricmp(pTab->zName, \"sqlite_stat1\") ){\n      sqlite3VdbeAppendP4(v, (char*)pTab, P4_TABLE);\n    }\n    if( eMode!=ONEPASS_OFF ){\n      sqlite3VdbeChangeP5(v, OPFLAG_AUXDELETE);\n    }\n    if( iIdxNoSeek>=0 && iIdxNoSeek!=iDataCur ){\n      sqlite3VdbeAddOp1(v, OP_Delete, iIdxNoSeek);\n    }\n    if( eMode==ONEPASS_MULTI ) p5 |= OPFLAG_SAVEPOSITION;\n    sqlite3VdbeChangeP5(v, p5);\n  }\n\n  /* Do any ON CASCADE, SET NULL or SET DEFAULT operations required to\n  ** handle rows (possibly in other tables) that refer via a foreign key\n  ** to the row just deleted. */ \n  sqlite3FkActions(pParse, pTab, 0, iOld, 0, 0);\n\n  /* Invoke AFTER DELETE trigger programs. */\n  sqlite3CodeRowTrigger(pParse, pTrigger, \n      TK_DELETE, 0, TRIGGER_AFTER, pTab, iOld, onconf, iLabel\n  );\n\n  /* Jump here if the row had already been deleted before any BEFORE\n  ** trigger programs were invoked. Or if a trigger program throws a \n  ** RAISE(IGNORE) exception.  */\n  sqlite3VdbeResolveLabel(v, iLabel);\n  VdbeModuleComment((v, \"END: GenRowDel()\"));\n}\n\n/*\n** This routine generates VDBE code that causes the deletion of all\n** index entries associated with a single row of a single table, pTab\n**\n** Preconditions:\n**\n**   1.  A read/write cursor \"iDataCur\" must be open on the canonical storage\n**       btree for the table pTab.  (This will be either the table itself\n**       for rowid tables or to the primary key index for WITHOUT ROWID\n**       tables.)\n**\n**   2.  Read/write cursors for all indices of pTab must be open as\n**       cursor number iIdxCur+i for the i-th index.  (The pTab->pIndex\n**       index is the 0-th index.)\n**\n**   3.  The \"iDataCur\" cursor must be already be positioned on the row\n**       that is to be deleted.\n*/\nSQLITE_PRIVATE void sqlite3GenerateRowIndexDelete(\n  Parse *pParse,     /* Parsing and code generating context */\n  Table *pTab,       /* Table containing the row to be deleted */\n  int iDataCur,      /* Cursor of table holding data. */\n  int iIdxCur,       /* First index cursor */\n  int *aRegIdx,      /* Only delete if aRegIdx!=0 && aRegIdx[i]>0 */\n  int iIdxNoSeek     /* Do not delete from this cursor */\n){\n  int i;             /* Index loop counter */\n  int r1 = -1;       /* Register holding an index key */\n  int iPartIdxLabel; /* Jump destination for skipping partial index entries */\n  Index *pIdx;       /* Current index */\n  Index *pPrior = 0; /* Prior index */\n  Vdbe *v;           /* The prepared statement under construction */\n  Index *pPk;        /* PRIMARY KEY index, or NULL for rowid tables */\n\n  v = pParse->pVdbe;\n  pPk = HasRowid(pTab) ? 0 : sqlite3PrimaryKeyIndex(pTab);\n  for(i=0, pIdx=pTab->pIndex; pIdx; i++, pIdx=pIdx->pNext){\n    assert( iIdxCur+i!=iDataCur || pPk==pIdx );\n    if( aRegIdx!=0 && aRegIdx[i]==0 ) continue;\n    if( pIdx==pPk ) continue;\n    if( iIdxCur+i==iIdxNoSeek ) continue;\n    VdbeModuleComment((v, \"GenRowIdxDel for %s\", pIdx->zName));\n    r1 = sqlite3GenerateIndexKey(pParse, pIdx, iDataCur, 0, 1,\n        &iPartIdxLabel, pPrior, r1);\n    sqlite3VdbeAddOp3(v, OP_IdxDelete, iIdxCur+i, r1,\n        pIdx->uniqNotNull ? pIdx->nKeyCol : pIdx->nColumn);\n    sqlite3ResolvePartIdxLabel(pParse, iPartIdxLabel);\n    pPrior = pIdx;\n  }\n}\n\n/*\n** Generate code that will assemble an index key and stores it in register\n** regOut.  The key with be for index pIdx which is an index on pTab.\n** iCur is the index of a cursor open on the pTab table and pointing to\n** the entry that needs indexing.  If pTab is a WITHOUT ROWID table, then\n** iCur must be the cursor of the PRIMARY KEY index.\n**\n** Return a register number which is the first in a block of\n** registers that holds the elements of the index key.  The\n** block of registers has already been deallocated by the time\n** this routine returns.\n**\n** If *piPartIdxLabel is not NULL, fill it in with a label and jump\n** to that label if pIdx is a partial index that should be skipped.\n** The label should be resolved using sqlite3ResolvePartIdxLabel().\n** A partial index should be skipped if its WHERE clause evaluates\n** to false or null.  If pIdx is not a partial index, *piPartIdxLabel\n** will be set to zero which is an empty label that is ignored by\n** sqlite3ResolvePartIdxLabel().\n**\n** The pPrior and regPrior parameters are used to implement a cache to\n** avoid unnecessary register loads.  If pPrior is not NULL, then it is\n** a pointer to a different index for which an index key has just been\n** computed into register regPrior.  If the current pIdx index is generating\n** its key into the same sequence of registers and if pPrior and pIdx share\n** a column in common, then the register corresponding to that column already\n** holds the correct value and the loading of that register is skipped.\n** This optimization is helpful when doing a DELETE or an INTEGRITY_CHECK \n** on a table with multiple indices, and especially with the ROWID or\n** PRIMARY KEY columns of the index.\n*/\nSQLITE_PRIVATE int sqlite3GenerateIndexKey(\n  Parse *pParse,       /* Parsing context */\n  Index *pIdx,         /* The index for which to generate a key */\n  int iDataCur,        /* Cursor number from which to take column data */\n  int regOut,          /* Put the new key into this register if not 0 */\n  int prefixOnly,      /* Compute only a unique prefix of the key */\n  int *piPartIdxLabel, /* OUT: Jump to this label to skip partial index */\n  Index *pPrior,       /* Previously generated index key */\n  int regPrior         /* Register holding previous generated key */\n){\n  Vdbe *v = pParse->pVdbe;\n  int j;\n  int regBase;\n  int nCol;\n\n  if( piPartIdxLabel ){\n    if( pIdx->pPartIdxWhere ){\n      *piPartIdxLabel = sqlite3VdbeMakeLabel(v);\n      pParse->iSelfTab = iDataCur + 1;\n      sqlite3ExprCachePush(pParse);\n      sqlite3ExprIfFalseDup(pParse, pIdx->pPartIdxWhere, *piPartIdxLabel, \n                            SQLITE_JUMPIFNULL);\n      pParse->iSelfTab = 0;\n    }else{\n      *piPartIdxLabel = 0;\n    }\n  }\n  nCol = (prefixOnly && pIdx->uniqNotNull) ? pIdx->nKeyCol : pIdx->nColumn;\n  regBase = sqlite3GetTempRange(pParse, nCol);\n  if( pPrior && (regBase!=regPrior || pPrior->pPartIdxWhere) ) pPrior = 0;\n  for(j=0; j<nCol; j++){\n    if( pPrior\n     && pPrior->aiColumn[j]==pIdx->aiColumn[j]\n     && pPrior->aiColumn[j]!=XN_EXPR\n    ){\n      /* This column was already computed by the previous index */\n      continue;\n    }\n    sqlite3ExprCodeLoadIndexColumn(pParse, pIdx, iDataCur, j, regBase+j);\n    /* If the column affinity is REAL but the number is an integer, then it\n    ** might be stored in the table as an integer (using a compact\n    ** representation) then converted to REAL by an OP_RealAffinity opcode.\n    ** But we are getting ready to store this value back into an index, where\n    ** it should be converted by to INTEGER again.  So omit the OP_RealAffinity\n    ** opcode if it is present */\n    sqlite3VdbeDeletePriorOpcode(v, OP_RealAffinity);\n  }\n  if( regOut ){\n    sqlite3VdbeAddOp3(v, OP_MakeRecord, regBase, nCol, regOut);\n    if( pIdx->pTable->pSelect ){\n      const char *zAff = sqlite3IndexAffinityStr(pParse->db, pIdx);\n      sqlite3VdbeChangeP4(v, -1, zAff, P4_TRANSIENT);\n    }\n  }\n  sqlite3ReleaseTempRange(pParse, regBase, nCol);\n  return regBase;\n}\n\n/*\n** If a prior call to sqlite3GenerateIndexKey() generated a jump-over label\n** because it was a partial index, then this routine should be called to\n** resolve that label.\n*/\nSQLITE_PRIVATE void sqlite3ResolvePartIdxLabel(Parse *pParse, int iLabel){\n  if( iLabel ){\n    sqlite3VdbeResolveLabel(pParse->pVdbe, iLabel);\n    sqlite3ExprCachePop(pParse);\n  }\n}\n\n/************** End of delete.c **********************************************/\n/************** Begin file func.c ********************************************/\n/*\n** 2002 February 23\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n*************************************************************************\n** This file contains the C-language implementations for many of the SQL\n** functions of SQLite.  (Some function, and in particular the date and\n** time functions, are implemented separately.)\n*/\n/* #include \"sqliteInt.h\" */\n/* #include <stdlib.h> */\n/* #include <assert.h> */\n/* #include \"vdbeInt.h\" */\n\n/*\n** Return the collating function associated with a function.\n*/\nstatic CollSeq *sqlite3GetFuncCollSeq(sqlite3_context *context){\n  VdbeOp *pOp;\n  assert( context->pVdbe!=0 );\n  pOp = &context->pVdbe->aOp[context->iOp-1];\n  assert( pOp->opcode==OP_CollSeq );\n  assert( pOp->p4type==P4_COLLSEQ );\n  return pOp->p4.pColl;\n}\n\n/*\n** Indicate that the accumulator load should be skipped on this\n** iteration of the aggregate loop.\n*/\nstatic void sqlite3SkipAccumulatorLoad(sqlite3_context *context){\n  assert( context->isError<=0 );\n  context->isError = -1;\n  context->skipFlag = 1;\n}\n\n/*\n** Implementation of the non-aggregate min() and max() functions\n*/\nstatic void minmaxFunc(\n  sqlite3_context *context,\n  int argc,\n  sqlite3_value **argv\n){\n  int i;\n  int mask;    /* 0 for min() or 0xffffffff for max() */\n  int iBest;\n  CollSeq *pColl;\n\n  assert( argc>1 );\n  mask = sqlite3_user_data(context)==0 ? 0 : -1;\n  pColl = sqlite3GetFuncCollSeq(context);\n  assert( pColl );\n  assert( mask==-1 || mask==0 );\n  iBest = 0;\n  if( sqlite3_value_type(argv[0])==SQLITE_NULL ) return;\n  for(i=1; i<argc; i++){\n    if( sqlite3_value_type(argv[i])==SQLITE_NULL ) return;\n    if( (sqlite3MemCompare(argv[iBest], argv[i], pColl)^mask)>=0 ){\n      testcase( mask==0 );\n      iBest = i;\n    }\n  }\n  sqlite3_result_value(context, argv[iBest]);\n}\n\n/*\n** Return the type of the argument.\n*/\nstatic void typeofFunc(\n  sqlite3_context *context,\n  int NotUsed,\n  sqlite3_value **argv\n){\n  static const char *azType[] = { \"integer\", \"real\", \"text\", \"blob\", \"null\" };\n  int i = sqlite3_value_type(argv[0]) - 1;\n  UNUSED_PARAMETER(NotUsed);\n  assert( i>=0 && i<ArraySize(azType) );\n  assert( SQLITE_INTEGER==1 );\n  assert( SQLITE_FLOAT==2 );\n  assert( SQLITE_TEXT==3 );\n  assert( SQLITE_BLOB==4 );\n  assert( SQLITE_NULL==5 );\n  /* EVIDENCE-OF: R-01470-60482 The sqlite3_value_type(V) interface returns\n  ** the datatype code for the initial datatype of the sqlite3_value object\n  ** V. The returned value is one of SQLITE_INTEGER, SQLITE_FLOAT,\n  ** SQLITE_TEXT, SQLITE_BLOB, or SQLITE_NULL. */\n  sqlite3_result_text(context, azType[i], -1, SQLITE_STATIC);\n}\n\n\n/*\n** Implementation of the length() function\n*/\nstatic void lengthFunc(\n  sqlite3_context *context,\n  int argc,\n  sqlite3_value **argv\n){\n  assert( argc==1 );\n  UNUSED_PARAMETER(argc);\n  switch( sqlite3_value_type(argv[0]) ){\n    case SQLITE_BLOB:\n    case SQLITE_INTEGER:\n    case SQLITE_FLOAT: {\n      sqlite3_result_int(context, sqlite3_value_bytes(argv[0]));\n      break;\n    }\n    case SQLITE_TEXT: {\n      const unsigned char *z = sqlite3_value_text(argv[0]);\n      const unsigned char *z0;\n      unsigned char c;\n      if( z==0 ) return;\n      z0 = z;\n      while( (c = *z)!=0 ){\n        z++;\n        if( c>=0xc0 ){\n          while( (*z & 0xc0)==0x80 ){ z++; z0++; }\n        }\n      }\n      sqlite3_result_int(context, (int)(z-z0));\n      break;\n    }\n    default: {\n      sqlite3_result_null(context);\n      break;\n    }\n  }\n}\n\n/*\n** Implementation of the abs() function.\n**\n** IMP: R-23979-26855 The abs(X) function returns the absolute value of\n** the numeric argument X. \n*/\nstatic void absFunc(sqlite3_context *context, int argc, sqlite3_value **argv){\n  assert( argc==1 );\n  UNUSED_PARAMETER(argc);\n  switch( sqlite3_value_type(argv[0]) ){\n    case SQLITE_INTEGER: {\n      i64 iVal = sqlite3_value_int64(argv[0]);\n      if( iVal<0 ){\n        if( iVal==SMALLEST_INT64 ){\n          /* IMP: R-31676-45509 If X is the integer -9223372036854775808\n          ** then abs(X) throws an integer overflow error since there is no\n          ** equivalent positive 64-bit two complement value. */\n          sqlite3_result_error(context, \"integer overflow\", -1);\n          return;\n        }\n        iVal = -iVal;\n      } \n      sqlite3_result_int64(context, iVal);\n      break;\n    }\n    case SQLITE_NULL: {\n      /* IMP: R-37434-19929 Abs(X) returns NULL if X is NULL. */\n      sqlite3_result_null(context);\n      break;\n    }\n    default: {\n      /* Because sqlite3_value_double() returns 0.0 if the argument is not\n      ** something that can be converted into a number, we have:\n      ** IMP: R-01992-00519 Abs(X) returns 0.0 if X is a string or blob\n      ** that cannot be converted to a numeric value.\n      */\n      double rVal = sqlite3_value_double(argv[0]);\n      if( rVal<0 ) rVal = -rVal;\n      sqlite3_result_double(context, rVal);\n      break;\n    }\n  }\n}\n\n/*\n** Implementation of the instr() function.\n**\n** instr(haystack,needle) finds the first occurrence of needle\n** in haystack and returns the number of previous characters plus 1,\n** or 0 if needle does not occur within haystack.\n**\n** If both haystack and needle are BLOBs, then the result is one more than\n** the number of bytes in haystack prior to the first occurrence of needle,\n** or 0 if needle never occurs in haystack.\n*/\nstatic void instrFunc(\n  sqlite3_context *context,\n  int argc,\n  sqlite3_value **argv\n){\n  const unsigned char *zHaystack;\n  const unsigned char *zNeedle;\n  int nHaystack;\n  int nNeedle;\n  int typeHaystack, typeNeedle;\n  int N = 1;\n  int isText;\n\n  UNUSED_PARAMETER(argc);\n  typeHaystack = sqlite3_value_type(argv[0]);\n  typeNeedle = sqlite3_value_type(argv[1]);\n  if( typeHaystack==SQLITE_NULL || typeNeedle==SQLITE_NULL ) return;\n  nHaystack = sqlite3_value_bytes(argv[0]);\n  nNeedle = sqlite3_value_bytes(argv[1]);\n  if( nNeedle>0 ){\n    if( typeHaystack==SQLITE_BLOB && typeNeedle==SQLITE_BLOB ){\n      zHaystack = sqlite3_value_blob(argv[0]);\n      zNeedle = sqlite3_value_blob(argv[1]);\n      isText = 0;\n    }else{\n      zHaystack = sqlite3_value_text(argv[0]);\n      zNeedle = sqlite3_value_text(argv[1]);\n      isText = 1;\n    }\n    if( zNeedle==0 || (nHaystack && zHaystack==0) ) return;\n    while( nNeedle<=nHaystack && memcmp(zHaystack, zNeedle, nNeedle)!=0 ){\n      N++;\n      do{\n        nHaystack--;\n        zHaystack++;\n      }while( isText && (zHaystack[0]&0xc0)==0x80 );\n    }\n    if( nNeedle>nHaystack ) N = 0;\n  }\n  sqlite3_result_int(context, N);\n}\n\n/*\n** Implementation of the printf() function.\n*/\nstatic void printfFunc(\n  sqlite3_context *context,\n  int argc,\n  sqlite3_value **argv\n){\n  PrintfArguments x;\n  StrAccum str;\n  const char *zFormat;\n  int n;\n  sqlite3 *db = sqlite3_context_db_handle(context);\n\n  if( argc>=1 && (zFormat = (const char*)sqlite3_value_text(argv[0]))!=0 ){\n    x.nArg = argc-1;\n    x.nUsed = 0;\n    x.apArg = argv+1;\n    sqlite3StrAccumInit(&str, db, 0, 0, db->aLimit[SQLITE_LIMIT_LENGTH]);\n    str.printfFlags = SQLITE_PRINTF_SQLFUNC;\n    sqlite3XPrintf(&str, zFormat, &x);\n    n = str.nChar;\n    sqlite3_result_text(context, sqlite3StrAccumFinish(&str), n,\n                        SQLITE_DYNAMIC);\n  }\n}\n\n/*\n** Implementation of the substr() function.\n**\n** substr(x,p1,p2)  returns p2 characters of x[] beginning with p1.\n** p1 is 1-indexed.  So substr(x,1,1) returns the first character\n** of x.  If x is text, then we actually count UTF-8 characters.\n** If x is a blob, then we count bytes.\n**\n** If p1 is negative, then we begin abs(p1) from the end of x[].\n**\n** If p2 is negative, return the p2 characters preceding p1.\n*/\nstatic void substrFunc(\n  sqlite3_context *context,\n  int argc,\n  sqlite3_value **argv\n){\n  const unsigned char *z;\n  const unsigned char *z2;\n  int len;\n  int p0type;\n  i64 p1, p2;\n  int negP2 = 0;\n\n  assert( argc==3 || argc==2 );\n  if( sqlite3_value_type(argv[1])==SQLITE_NULL\n   || (argc==3 && sqlite3_value_type(argv[2])==SQLITE_NULL)\n  ){\n    return;\n  }\n  p0type = sqlite3_value_type(argv[0]);\n  p1 = sqlite3_value_int(argv[1]);\n  if( p0type==SQLITE_BLOB ){\n    len = sqlite3_value_bytes(argv[0]);\n    z = sqlite3_value_blob(argv[0]);\n    if( z==0 ) return;\n    assert( len==sqlite3_value_bytes(argv[0]) );\n  }else{\n    z = sqlite3_value_text(argv[0]);\n    if( z==0 ) return;\n    len = 0;\n    if( p1<0 ){\n      for(z2=z; *z2; len++){\n        SQLITE_SKIP_UTF8(z2);\n      }\n    }\n  }\n#ifdef SQLITE_SUBSTR_COMPATIBILITY\n  /* If SUBSTR_COMPATIBILITY is defined then substr(X,0,N) work the same as\n  ** as substr(X,1,N) - it returns the first N characters of X.  This\n  ** is essentially a back-out of the bug-fix in check-in [5fc125d362df4b8]\n  ** from 2009-02-02 for compatibility of applications that exploited the\n  ** old buggy behavior. */\n  if( p1==0 ) p1 = 1; /* <rdar://problem/6778339> */\n#endif\n  if( argc==3 ){\n    p2 = sqlite3_value_int(argv[2]);\n    if( p2<0 ){\n      p2 = -p2;\n      negP2 = 1;\n    }\n  }else{\n    p2 = sqlite3_context_db_handle(context)->aLimit[SQLITE_LIMIT_LENGTH];\n  }\n  if( p1<0 ){\n    p1 += len;\n    if( p1<0 ){\n      p2 += p1;\n      if( p2<0 ) p2 = 0;\n      p1 = 0;\n    }\n  }else if( p1>0 ){\n    p1--;\n  }else if( p2>0 ){\n    p2--;\n  }\n  if( negP2 ){\n    p1 -= p2;\n    if( p1<0 ){\n      p2 += p1;\n      p1 = 0;\n    }\n  }\n  assert( p1>=0 && p2>=0 );\n  if( p0type!=SQLITE_BLOB ){\n    while( *z && p1 ){\n      SQLITE_SKIP_UTF8(z);\n      p1--;\n    }\n    for(z2=z; *z2 && p2; p2--){\n      SQLITE_SKIP_UTF8(z2);\n    }\n    sqlite3_result_text64(context, (char*)z, z2-z, SQLITE_TRANSIENT,\n                          SQLITE_UTF8);\n  }else{\n    if( p1+p2>len ){\n      p2 = len-p1;\n      if( p2<0 ) p2 = 0;\n    }\n    sqlite3_result_blob64(context, (char*)&z[p1], (u64)p2, SQLITE_TRANSIENT);\n  }\n}\n\n/*\n** Implementation of the round() function\n*/\n#ifndef SQLITE_OMIT_FLOATING_POINT\nstatic void roundFunc(sqlite3_context *context, int argc, sqlite3_value **argv){\n  int n = 0;\n  double r;\n  char *zBuf;\n  assert( argc==1 || argc==2 );\n  if( argc==2 ){\n    if( SQLITE_NULL==sqlite3_value_type(argv[1]) ) return;\n    n = sqlite3_value_int(argv[1]);\n    if( n>30 ) n = 30;\n    if( n<0 ) n = 0;\n  }\n  if( sqlite3_value_type(argv[0])==SQLITE_NULL ) return;\n  r = sqlite3_value_double(argv[0]);\n  /* If Y==0 and X will fit in a 64-bit int,\n  ** handle the rounding directly,\n  ** otherwise use printf.\n  */\n  if( n==0 && r>=0 && r<LARGEST_INT64-1 ){\n    r = (double)((sqlite_int64)(r+0.5));\n  }else if( n==0 && r<0 && (-r)<LARGEST_INT64-1 ){\n    r = -(double)((sqlite_int64)((-r)+0.5));\n  }else{\n    zBuf = sqlite3_mprintf(\"%.*f\",n,r);\n    if( zBuf==0 ){\n      sqlite3_result_error_nomem(context);\n      return;\n    }\n    sqlite3AtoF(zBuf, &r, sqlite3Strlen30(zBuf), SQLITE_UTF8);\n    sqlite3_free(zBuf);\n  }\n  sqlite3_result_double(context, r);\n}\n#endif\n\n/*\n** Allocate nByte bytes of space using sqlite3Malloc(). If the\n** allocation fails, call sqlite3_result_error_nomem() to notify\n** the database handle that malloc() has failed and return NULL.\n** If nByte is larger than the maximum string or blob length, then\n** raise an SQLITE_TOOBIG exception and return NULL.\n*/\nstatic void *contextMalloc(sqlite3_context *context, i64 nByte){\n  char *z;\n  sqlite3 *db = sqlite3_context_db_handle(context);\n  assert( nByte>0 );\n  testcase( nByte==db->aLimit[SQLITE_LIMIT_LENGTH] );\n  testcase( nByte==db->aLimit[SQLITE_LIMIT_LENGTH]+1 );\n  if( nByte>db->aLimit[SQLITE_LIMIT_LENGTH] ){\n    sqlite3_result_error_toobig(context);\n    z = 0;\n  }else{\n    z = sqlite3Malloc(nByte);\n    if( !z ){\n      sqlite3_result_error_nomem(context);\n    }\n  }\n  return z;\n}\n\n/*\n** Implementation of the upper() and lower() SQL functions.\n*/\nstatic void upperFunc(sqlite3_context *context, int argc, sqlite3_value **argv){\n  char *z1;\n  const char *z2;\n  int i, n;\n  UNUSED_PARAMETER(argc);\n  z2 = (char*)sqlite3_value_text(argv[0]);\n  n = sqlite3_value_bytes(argv[0]);\n  /* Verify that the call to _bytes() does not invalidate the _text() pointer */\n  assert( z2==(char*)sqlite3_value_text(argv[0]) );\n  if( z2 ){\n    z1 = contextMalloc(context, ((i64)n)+1);\n    if( z1 ){\n      for(i=0; i<n; i++){\n        z1[i] = (char)sqlite3Toupper(z2[i]);\n      }\n      sqlite3_result_text(context, z1, n, sqlite3_free);\n    }\n  }\n}\nstatic void lowerFunc(sqlite3_context *context, int argc, sqlite3_value **argv){\n  char *z1;\n  const char *z2;\n  int i, n;\n  UNUSED_PARAMETER(argc);\n  z2 = (char*)sqlite3_value_text(argv[0]);\n  n = sqlite3_value_bytes(argv[0]);\n  /* Verify that the call to _bytes() does not invalidate the _text() pointer */\n  assert( z2==(char*)sqlite3_value_text(argv[0]) );\n  if( z2 ){\n    z1 = contextMalloc(context, ((i64)n)+1);\n    if( z1 ){\n      for(i=0; i<n; i++){\n        z1[i] = sqlite3Tolower(z2[i]);\n      }\n      sqlite3_result_text(context, z1, n, sqlite3_free);\n    }\n  }\n}\n\n/*\n** Some functions like COALESCE() and IFNULL() and UNLIKELY() are implemented\n** as VDBE code so that unused argument values do not have to be computed.\n** However, we still need some kind of function implementation for this\n** routines in the function table.  The noopFunc macro provides this.\n** noopFunc will never be called so it doesn't matter what the implementation\n** is.  We might as well use the \"version()\" function as a substitute.\n*/\n#define noopFunc versionFunc   /* Substitute function - never called */\n\n/*\n** Implementation of random().  Return a random integer.  \n*/\nstatic void randomFunc(\n  sqlite3_context *context,\n  int NotUsed,\n  sqlite3_value **NotUsed2\n){\n  sqlite_int64 r;\n  UNUSED_PARAMETER2(NotUsed, NotUsed2);\n  sqlite3_randomness(sizeof(r), &r);\n  if( r<0 ){\n    /* We need to prevent a random number of 0x8000000000000000 \n    ** (or -9223372036854775808) since when you do abs() of that\n    ** number of you get the same value back again.  To do this\n    ** in a way that is testable, mask the sign bit off of negative\n    ** values, resulting in a positive value.  Then take the \n    ** 2s complement of that positive value.  The end result can\n    ** therefore be no less than -9223372036854775807.\n    */\n    r = -(r & LARGEST_INT64);\n  }\n  sqlite3_result_int64(context, r);\n}\n\n/*\n** Implementation of randomblob(N).  Return a random blob\n** that is N bytes long.\n*/\nstatic void randomBlob(\n  sqlite3_context *context,\n  int argc,\n  sqlite3_value **argv\n){\n  int n;\n  unsigned char *p;\n  assert( argc==1 );\n  UNUSED_PARAMETER(argc);\n  n = sqlite3_value_int(argv[0]);\n  if( n<1 ){\n    n = 1;\n  }\n  p = contextMalloc(context, n);\n  if( p ){\n    sqlite3_randomness(n, p);\n    sqlite3_result_blob(context, (char*)p, n, sqlite3_free);\n  }\n}\n\n/*\n** Implementation of the last_insert_rowid() SQL function.  The return\n** value is the same as the sqlite3_last_insert_rowid() API function.\n*/\nstatic void last_insert_rowid(\n  sqlite3_context *context, \n  int NotUsed, \n  sqlite3_value **NotUsed2\n){\n  sqlite3 *db = sqlite3_context_db_handle(context);\n  UNUSED_PARAMETER2(NotUsed, NotUsed2);\n  /* IMP: R-51513-12026 The last_insert_rowid() SQL function is a\n  ** wrapper around the sqlite3_last_insert_rowid() C/C++ interface\n  ** function. */\n  sqlite3_result_int64(context, sqlite3_last_insert_rowid(db));\n}\n\n/*\n** Implementation of the changes() SQL function.\n**\n** IMP: R-62073-11209 The changes() SQL function is a wrapper\n** around the sqlite3_changes() C/C++ function and hence follows the same\n** rules for counting changes.\n*/\nstatic void changes(\n  sqlite3_context *context,\n  int NotUsed,\n  sqlite3_value **NotUsed2\n){\n  sqlite3 *db = sqlite3_context_db_handle(context);\n  UNUSED_PARAMETER2(NotUsed, NotUsed2);\n  sqlite3_result_int(context, sqlite3_changes(db));\n}\n\n/*\n** Implementation of the total_changes() SQL function.  The return value is\n** the same as the sqlite3_total_changes() API function.\n*/\nstatic void total_changes(\n  sqlite3_context *context,\n  int NotUsed,\n  sqlite3_value **NotUsed2\n){\n  sqlite3 *db = sqlite3_context_db_handle(context);\n  UNUSED_PARAMETER2(NotUsed, NotUsed2);\n  /* IMP: R-52756-41993 This function is a wrapper around the\n  ** sqlite3_total_changes() C/C++ interface. */\n  sqlite3_result_int(context, sqlite3_total_changes(db));\n}\n\n/*\n** A structure defining how to do GLOB-style comparisons.\n*/\nstruct compareInfo {\n  u8 matchAll;          /* \"*\" or \"%\" */\n  u8 matchOne;          /* \"?\" or \"_\" */\n  u8 matchSet;          /* \"[\" or 0 */\n  u8 noCase;            /* true to ignore case differences */\n};\n\n/*\n** For LIKE and GLOB matching on EBCDIC machines, assume that every\n** character is exactly one byte in size.  Also, provde the Utf8Read()\n** macro for fast reading of the next character in the common case where\n** the next character is ASCII.\n*/\n#if defined(SQLITE_EBCDIC)\n# define sqlite3Utf8Read(A)        (*((*A)++))\n# define Utf8Read(A)               (*(A++))\n#else\n# define Utf8Read(A)               (A[0]<0x80?*(A++):sqlite3Utf8Read(&A))\n#endif\n\nstatic const struct compareInfo globInfo = { '*', '?', '[', 0 };\n/* The correct SQL-92 behavior is for the LIKE operator to ignore\n** case.  Thus  'a' LIKE 'A' would be true. */\nstatic const struct compareInfo likeInfoNorm = { '%', '_',   0, 1 };\n/* If SQLITE_CASE_SENSITIVE_LIKE is defined, then the LIKE operator\n** is case sensitive causing 'a' LIKE 'A' to be false */\nstatic const struct compareInfo likeInfoAlt = { '%', '_',   0, 0 };\n\n/*\n** Possible error returns from patternMatch()\n*/\n#define SQLITE_MATCH             0\n#define SQLITE_NOMATCH           1\n#define SQLITE_NOWILDCARDMATCH   2\n\n/*\n** Compare two UTF-8 strings for equality where the first string is\n** a GLOB or LIKE expression.  Return values:\n**\n**    SQLITE_MATCH:            Match\n**    SQLITE_NOMATCH:          No match\n**    SQLITE_NOWILDCARDMATCH:  No match in spite of having * or % wildcards.\n**\n** Globbing rules:\n**\n**      '*'       Matches any sequence of zero or more characters.\n**\n**      '?'       Matches exactly one character.\n**\n**     [...]      Matches one character from the enclosed list of\n**                characters.\n**\n**     [^...]     Matches one character not in the enclosed list.\n**\n** With the [...] and [^...] matching, a ']' character can be included\n** in the list by making it the first character after '[' or '^'.  A\n** range of characters can be specified using '-'.  Example:\n** \"[a-z]\" matches any single lower-case letter.  To match a '-', make\n** it the last character in the list.\n**\n** Like matching rules:\n** \n**      '%'       Matches any sequence of zero or more characters\n**\n***     '_'       Matches any one character\n**\n**      Ec        Where E is the \"esc\" character and c is any other\n**                character, including '%', '_', and esc, match exactly c.\n**\n** The comments within this routine usually assume glob matching.\n**\n** This routine is usually quick, but can be N**2 in the worst case.\n*/\nstatic int patternCompare(\n  const u8 *zPattern,              /* The glob pattern */\n  const u8 *zString,               /* The string to compare against the glob */\n  const struct compareInfo *pInfo, /* Information about how to do the compare */\n  u32 matchOther                   /* The escape char (LIKE) or '[' (GLOB) */\n){\n  u32 c, c2;                       /* Next pattern and input string chars */\n  u32 matchOne = pInfo->matchOne;  /* \"?\" or \"_\" */\n  u32 matchAll = pInfo->matchAll;  /* \"*\" or \"%\" */\n  u8 noCase = pInfo->noCase;       /* True if uppercase==lowercase */\n  const u8 *zEscaped = 0;          /* One past the last escaped input char */\n  \n  while( (c = Utf8Read(zPattern))!=0 ){\n    if( c==matchAll ){  /* Match \"*\" */\n      /* Skip over multiple \"*\" characters in the pattern.  If there\n      ** are also \"?\" characters, skip those as well, but consume a\n      ** single character of the input string for each \"?\" skipped */\n      while( (c=Utf8Read(zPattern)) == matchAll || c == matchOne ){\n        if( c==matchOne && sqlite3Utf8Read(&zString)==0 ){\n          return SQLITE_NOWILDCARDMATCH;\n        }\n      }\n      if( c==0 ){\n        return SQLITE_MATCH;   /* \"*\" at the end of the pattern matches */\n      }else if( c==matchOther ){\n        if( pInfo->matchSet==0 ){\n          c = sqlite3Utf8Read(&zPattern);\n          if( c==0 ) return SQLITE_NOWILDCARDMATCH;\n        }else{\n          /* \"[...]\" immediately follows the \"*\".  We have to do a slow\n          ** recursive search in this case, but it is an unusual case. */\n          assert( matchOther<0x80 );  /* '[' is a single-byte character */\n          while( *zString ){\n            int bMatch = patternCompare(&zPattern[-1],zString,pInfo,matchOther);\n            if( bMatch!=SQLITE_NOMATCH ) return bMatch;\n            SQLITE_SKIP_UTF8(zString);\n          }\n          return SQLITE_NOWILDCARDMATCH;\n        }\n      }\n\n      /* At this point variable c contains the first character of the\n      ** pattern string past the \"*\".  Search in the input string for the\n      ** first matching character and recursively continue the match from\n      ** that point.\n      **\n      ** For a case-insensitive search, set variable cx to be the same as\n      ** c but in the other case and search the input string for either\n      ** c or cx.\n      */\n      if( c<=0x80 ){\n        char zStop[3];\n        int bMatch;\n        if( noCase ){\n          zStop[0] = sqlite3Toupper(c);\n          zStop[1] = sqlite3Tolower(c);\n          zStop[2] = 0;\n        }else{\n          zStop[0] = c;\n          zStop[1] = 0;\n        }\n        while(1){\n          zString += strcspn((const char*)zString, zStop);\n          if( zString[0]==0 ) break;\n          zString++;\n          bMatch = patternCompare(zPattern,zString,pInfo,matchOther);\n          if( bMatch!=SQLITE_NOMATCH ) return bMatch;\n        }\n      }else{\n        int bMatch;\n        while( (c2 = Utf8Read(zString))!=0 ){\n          if( c2!=c ) continue;\n          bMatch = patternCompare(zPattern,zString,pInfo,matchOther);\n          if( bMatch!=SQLITE_NOMATCH ) return bMatch;\n        }\n      }\n      return SQLITE_NOWILDCARDMATCH;\n    }\n    if( c==matchOther ){\n      if( pInfo->matchSet==0 ){\n        c = sqlite3Utf8Read(&zPattern);\n        if( c==0 ) return SQLITE_NOMATCH;\n        zEscaped = zPattern;\n      }else{\n        u32 prior_c = 0;\n        int seen = 0;\n        int invert = 0;\n        c = sqlite3Utf8Read(&zString);\n        if( c==0 ) return SQLITE_NOMATCH;\n        c2 = sqlite3Utf8Read(&zPattern);\n        if( c2=='^' ){\n          invert = 1;\n          c2 = sqlite3Utf8Read(&zPattern);\n        }\n        if( c2==']' ){\n          if( c==']' ) seen = 1;\n          c2 = sqlite3Utf8Read(&zPattern);\n        }\n        while( c2 && c2!=']' ){\n          if( c2=='-' && zPattern[0]!=']' && zPattern[0]!=0 && prior_c>0 ){\n            c2 = sqlite3Utf8Read(&zPattern);\n            if( c>=prior_c && c<=c2 ) seen = 1;\n            prior_c = 0;\n          }else{\n            if( c==c2 ){\n              seen = 1;\n            }\n            prior_c = c2;\n          }\n          c2 = sqlite3Utf8Read(&zPattern);\n        }\n        if( c2==0 || (seen ^ invert)==0 ){\n          return SQLITE_NOMATCH;\n        }\n        continue;\n      }\n    }\n    c2 = Utf8Read(zString);\n    if( c==c2 ) continue;\n    if( noCase  && sqlite3Tolower(c)==sqlite3Tolower(c2) && c<0x80 && c2<0x80 ){\n      continue;\n    }\n    if( c==matchOne && zPattern!=zEscaped && c2!=0 ) continue;\n    return SQLITE_NOMATCH;\n  }\n  return *zString==0 ? SQLITE_MATCH : SQLITE_NOMATCH;\n}\n\n/*\n** The sqlite3_strglob() interface.  Return 0 on a match (like strcmp()) and\n** non-zero if there is no match.\n*/\nSQLITE_API int sqlite3_strglob(const char *zGlobPattern, const char *zString){\n  return patternCompare((u8*)zGlobPattern, (u8*)zString, &globInfo, '[');\n}\n\n/*\n** The sqlite3_strlike() interface.  Return 0 on a match and non-zero for\n** a miss - like strcmp().\n*/\nSQLITE_API int sqlite3_strlike(const char *zPattern, const char *zStr, unsigned int esc){\n  return patternCompare((u8*)zPattern, (u8*)zStr, &likeInfoNorm, esc);\n}\n\n/*\n** Count the number of times that the LIKE operator (or GLOB which is\n** just a variation of LIKE) gets called.  This is used for testing\n** only.\n*/\n#ifdef SQLITE_TEST\nSQLITE_API int sqlite3_like_count = 0;\n#endif\n\n\n/*\n** Implementation of the like() SQL function.  This function implements\n** the build-in LIKE operator.  The first argument to the function is the\n** pattern and the second argument is the string.  So, the SQL statements:\n**\n**       A LIKE B\n**\n** is implemented as like(B,A).\n**\n** This same function (with a different compareInfo structure) computes\n** the GLOB operator.\n*/\nstatic void likeFunc(\n  sqlite3_context *context, \n  int argc, \n  sqlite3_value **argv\n){\n  const unsigned char *zA, *zB;\n  u32 escape;\n  int nPat;\n  sqlite3 *db = sqlite3_context_db_handle(context);\n  struct compareInfo *pInfo = sqlite3_user_data(context);\n\n#ifdef SQLITE_LIKE_DOESNT_MATCH_BLOBS\n  if( sqlite3_value_type(argv[0])==SQLITE_BLOB\n   || sqlite3_value_type(argv[1])==SQLITE_BLOB\n  ){\n#ifdef SQLITE_TEST\n    sqlite3_like_count++;\n#endif\n    sqlite3_result_int(context, 0);\n    return;\n  }\n#endif\n  zB = sqlite3_value_text(argv[0]);\n  zA = sqlite3_value_text(argv[1]);\n\n  /* Limit the length of the LIKE or GLOB pattern to avoid problems\n  ** of deep recursion and N*N behavior in patternCompare().\n  */\n  nPat = sqlite3_value_bytes(argv[0]);\n  testcase( nPat==db->aLimit[SQLITE_LIMIT_LIKE_PATTERN_LENGTH] );\n  testcase( nPat==db->aLimit[SQLITE_LIMIT_LIKE_PATTERN_LENGTH]+1 );\n  if( nPat > db->aLimit[SQLITE_LIMIT_LIKE_PATTERN_LENGTH] ){\n    sqlite3_result_error(context, \"LIKE or GLOB pattern too complex\", -1);\n    return;\n  }\n  assert( zB==sqlite3_value_text(argv[0]) );  /* Encoding did not change */\n\n  if( argc==3 ){\n    /* The escape character string must consist of a single UTF-8 character.\n    ** Otherwise, return an error.\n    */\n    const unsigned char *zEsc = sqlite3_value_text(argv[2]);\n    if( zEsc==0 ) return;\n    if( sqlite3Utf8CharLen((char*)zEsc, -1)!=1 ){\n      sqlite3_result_error(context, \n          \"ESCAPE expression must be a single character\", -1);\n      return;\n    }\n    escape = sqlite3Utf8Read(&zEsc);\n  }else{\n    escape = pInfo->matchSet;\n  }\n  if( zA && zB ){\n#ifdef SQLITE_TEST\n    sqlite3_like_count++;\n#endif\n    sqlite3_result_int(context,\n                      patternCompare(zB, zA, pInfo, escape)==SQLITE_MATCH);\n  }\n}\n\n/*\n** Implementation of the NULLIF(x,y) function.  The result is the first\n** argument if the arguments are different.  The result is NULL if the\n** arguments are equal to each other.\n*/\nstatic void nullifFunc(\n  sqlite3_context *context,\n  int NotUsed,\n  sqlite3_value **argv\n){\n  CollSeq *pColl = sqlite3GetFuncCollSeq(context);\n  UNUSED_PARAMETER(NotUsed);\n  if( sqlite3MemCompare(argv[0], argv[1], pColl)!=0 ){\n    sqlite3_result_value(context, argv[0]);\n  }\n}\n\n/*\n** Implementation of the sqlite_version() function.  The result is the version\n** of the SQLite library that is running.\n*/\nstatic void versionFunc(\n  sqlite3_context *context,\n  int NotUsed,\n  sqlite3_value **NotUsed2\n){\n  UNUSED_PARAMETER2(NotUsed, NotUsed2);\n  /* IMP: R-48699-48617 This function is an SQL wrapper around the\n  ** sqlite3_libversion() C-interface. */\n  sqlite3_result_text(context, sqlite3_libversion(), -1, SQLITE_STATIC);\n}\n\n/*\n** Implementation of the sqlite_source_id() function. The result is a string\n** that identifies the particular version of the source code used to build\n** SQLite.\n*/\nstatic void sourceidFunc(\n  sqlite3_context *context,\n  int NotUsed,\n  sqlite3_value **NotUsed2\n){\n  UNUSED_PARAMETER2(NotUsed, NotUsed2);\n  /* IMP: R-24470-31136 This function is an SQL wrapper around the\n  ** sqlite3_sourceid() C interface. */\n  sqlite3_result_text(context, sqlite3_sourceid(), -1, SQLITE_STATIC);\n}\n\n/*\n** Implementation of the sqlite_log() function.  This is a wrapper around\n** sqlite3_log().  The return value is NULL.  The function exists purely for\n** its side-effects.\n*/\nstatic void errlogFunc(\n  sqlite3_context *context,\n  int argc,\n  sqlite3_value **argv\n){\n  UNUSED_PARAMETER(argc);\n  UNUSED_PARAMETER(context);\n  sqlite3_log(sqlite3_value_int(argv[0]), \"%s\", sqlite3_value_text(argv[1]));\n}\n\n/*\n** Implementation of the sqlite_compileoption_used() function.\n** The result is an integer that identifies if the compiler option\n** was used to build SQLite.\n*/\n#ifndef SQLITE_OMIT_COMPILEOPTION_DIAGS\nstatic void compileoptionusedFunc(\n  sqlite3_context *context,\n  int argc,\n  sqlite3_value **argv\n){\n  const char *zOptName;\n  assert( argc==1 );\n  UNUSED_PARAMETER(argc);\n  /* IMP: R-39564-36305 The sqlite_compileoption_used() SQL\n  ** function is a wrapper around the sqlite3_compileoption_used() C/C++\n  ** function.\n  */\n  if( (zOptName = (const char*)sqlite3_value_text(argv[0]))!=0 ){\n    sqlite3_result_int(context, sqlite3_compileoption_used(zOptName));\n  }\n}\n#endif /* SQLITE_OMIT_COMPILEOPTION_DIAGS */\n\n/*\n** Implementation of the sqlite_compileoption_get() function. \n** The result is a string that identifies the compiler options \n** used to build SQLite.\n*/\n#ifndef SQLITE_OMIT_COMPILEOPTION_DIAGS\nstatic void compileoptiongetFunc(\n  sqlite3_context *context,\n  int argc,\n  sqlite3_value **argv\n){\n  int n;\n  assert( argc==1 );\n  UNUSED_PARAMETER(argc);\n  /* IMP: R-04922-24076 The sqlite_compileoption_get() SQL function\n  ** is a wrapper around the sqlite3_compileoption_get() C/C++ function.\n  */\n  n = sqlite3_value_int(argv[0]);\n  sqlite3_result_text(context, sqlite3_compileoption_get(n), -1, SQLITE_STATIC);\n}\n#endif /* SQLITE_OMIT_COMPILEOPTION_DIAGS */\n\n/* Array for converting from half-bytes (nybbles) into ASCII hex\n** digits. */\nstatic const char hexdigits[] = {\n  '0', '1', '2', '3', '4', '5', '6', '7',\n  '8', '9', 'A', 'B', 'C', 'D', 'E', 'F' \n};\n\n/*\n** Implementation of the QUOTE() function.  This function takes a single\n** argument.  If the argument is numeric, the return value is the same as\n** the argument.  If the argument is NULL, the return value is the string\n** \"NULL\".  Otherwise, the argument is enclosed in single quotes with\n** single-quote escapes.\n*/\nstatic void quoteFunc(sqlite3_context *context, int argc, sqlite3_value **argv){\n  assert( argc==1 );\n  UNUSED_PARAMETER(argc);\n  switch( sqlite3_value_type(argv[0]) ){\n    case SQLITE_FLOAT: {\n      double r1, r2;\n      char zBuf[50];\n      r1 = sqlite3_value_double(argv[0]);\n      sqlite3_snprintf(sizeof(zBuf), zBuf, \"%!.15g\", r1);\n      sqlite3AtoF(zBuf, &r2, 20, SQLITE_UTF8);\n      if( r1!=r2 ){\n        sqlite3_snprintf(sizeof(zBuf), zBuf, \"%!.20e\", r1);\n      }\n      sqlite3_result_text(context, zBuf, -1, SQLITE_TRANSIENT);\n      break;\n    }\n    case SQLITE_INTEGER: {\n      sqlite3_result_value(context, argv[0]);\n      break;\n    }\n    case SQLITE_BLOB: {\n      char *zText = 0;\n      char const *zBlob = sqlite3_value_blob(argv[0]);\n      int nBlob = sqlite3_value_bytes(argv[0]);\n      assert( zBlob==sqlite3_value_blob(argv[0]) ); /* No encoding change */\n      zText = (char *)contextMalloc(context, (2*(i64)nBlob)+4); \n      if( zText ){\n        int i;\n        for(i=0; i<nBlob; i++){\n          zText[(i*2)+2] = hexdigits[(zBlob[i]>>4)&0x0F];\n          zText[(i*2)+3] = hexdigits[(zBlob[i])&0x0F];\n        }\n        zText[(nBlob*2)+2] = '\\'';\n        zText[(nBlob*2)+3] = '\\0';\n        zText[0] = 'X';\n        zText[1] = '\\'';\n        sqlite3_result_text(context, zText, -1, SQLITE_TRANSIENT);\n        sqlite3_free(zText);\n      }\n      break;\n    }\n    case SQLITE_TEXT: {\n      int i,j;\n      u64 n;\n      const unsigned char *zArg = sqlite3_value_text(argv[0]);\n      char *z;\n\n      if( zArg==0 ) return;\n      for(i=0, n=0; zArg[i]; i++){ if( zArg[i]=='\\'' ) n++; }\n      z = contextMalloc(context, ((i64)i)+((i64)n)+3);\n      if( z ){\n        z[0] = '\\'';\n        for(i=0, j=1; zArg[i]; i++){\n          z[j++] = zArg[i];\n          if( zArg[i]=='\\'' ){\n            z[j++] = '\\'';\n          }\n        }\n        z[j++] = '\\'';\n        z[j] = 0;\n        sqlite3_result_text(context, z, j, sqlite3_free);\n      }\n      break;\n    }\n    default: {\n      assert( sqlite3_value_type(argv[0])==SQLITE_NULL );\n      sqlite3_result_text(context, \"NULL\", 4, SQLITE_STATIC);\n      break;\n    }\n  }\n}\n\n/*\n** The unicode() function.  Return the integer unicode code-point value\n** for the first character of the input string. \n*/\nstatic void unicodeFunc(\n  sqlite3_context *context,\n  int argc,\n  sqlite3_value **argv\n){\n  const unsigned char *z = sqlite3_value_text(argv[0]);\n  (void)argc;\n  if( z && z[0] ) sqlite3_result_int(context, sqlite3Utf8Read(&z));\n}\n\n/*\n** The char() function takes zero or more arguments, each of which is\n** an integer.  It constructs a string where each character of the string\n** is the unicode character for the corresponding integer argument.\n*/\nstatic void charFunc(\n  sqlite3_context *context,\n  int argc,\n  sqlite3_value **argv\n){\n  unsigned char *z, *zOut;\n  int i;\n  zOut = z = sqlite3_malloc64( argc*4+1 );\n  if( z==0 ){\n    sqlite3_result_error_nomem(context);\n    return;\n  }\n  for(i=0; i<argc; i++){\n    sqlite3_int64 x;\n    unsigned c;\n    x = sqlite3_value_int64(argv[i]);\n    if( x<0 || x>0x10ffff ) x = 0xfffd;\n    c = (unsigned)(x & 0x1fffff);\n    if( c<0x00080 ){\n      *zOut++ = (u8)(c&0xFF);\n    }else if( c<0x00800 ){\n      *zOut++ = 0xC0 + (u8)((c>>6)&0x1F);\n      *zOut++ = 0x80 + (u8)(c & 0x3F);\n    }else if( c<0x10000 ){\n      *zOut++ = 0xE0 + (u8)((c>>12)&0x0F);\n      *zOut++ = 0x80 + (u8)((c>>6) & 0x3F);\n      *zOut++ = 0x80 + (u8)(c & 0x3F);\n    }else{\n      *zOut++ = 0xF0 + (u8)((c>>18) & 0x07);\n      *zOut++ = 0x80 + (u8)((c>>12) & 0x3F);\n      *zOut++ = 0x80 + (u8)((c>>6) & 0x3F);\n      *zOut++ = 0x80 + (u8)(c & 0x3F);\n    }                                                    \\\n  }\n  sqlite3_result_text64(context, (char*)z, zOut-z, sqlite3_free, SQLITE_UTF8);\n}\n\n/*\n** The hex() function.  Interpret the argument as a blob.  Return\n** a hexadecimal rendering as text.\n*/\nstatic void hexFunc(\n  sqlite3_context *context,\n  int argc,\n  sqlite3_value **argv\n){\n  int i, n;\n  const unsigned char *pBlob;\n  char *zHex, *z;\n  assert( argc==1 );\n  UNUSED_PARAMETER(argc);\n  pBlob = sqlite3_value_blob(argv[0]);\n  n = sqlite3_value_bytes(argv[0]);\n  assert( pBlob==sqlite3_value_blob(argv[0]) );  /* No encoding change */\n  z = zHex = contextMalloc(context, ((i64)n)*2 + 1);\n  if( zHex ){\n    for(i=0; i<n; i++, pBlob++){\n      unsigned char c = *pBlob;\n      *(z++) = hexdigits[(c>>4)&0xf];\n      *(z++) = hexdigits[c&0xf];\n    }\n    *z = 0;\n    sqlite3_result_text(context, zHex, n*2, sqlite3_free);\n  }\n}\n\n/*\n** The zeroblob(N) function returns a zero-filled blob of size N bytes.\n*/\nstatic void zeroblobFunc(\n  sqlite3_context *context,\n  int argc,\n  sqlite3_value **argv\n){\n  i64 n;\n  int rc;\n  assert( argc==1 );\n  UNUSED_PARAMETER(argc);\n  n = sqlite3_value_int64(argv[0]);\n  if( n<0 ) n = 0;\n  rc = sqlite3_result_zeroblob64(context, n); /* IMP: R-00293-64994 */\n  if( rc ){\n    sqlite3_result_error_code(context, rc);\n  }\n}\n\n/*\n** The replace() function.  Three arguments are all strings: call\n** them A, B, and C. The result is also a string which is derived\n** from A by replacing every occurrence of B with C.  The match\n** must be exact.  Collating sequences are not used.\n*/\nstatic void replaceFunc(\n  sqlite3_context *context,\n  int argc,\n  sqlite3_value **argv\n){\n  const unsigned char *zStr;        /* The input string A */\n  const unsigned char *zPattern;    /* The pattern string B */\n  const unsigned char *zRep;        /* The replacement string C */\n  unsigned char *zOut;              /* The output */\n  int nStr;                /* Size of zStr */\n  int nPattern;            /* Size of zPattern */\n  int nRep;                /* Size of zRep */\n  i64 nOut;                /* Maximum size of zOut */\n  int loopLimit;           /* Last zStr[] that might match zPattern[] */\n  int i, j;                /* Loop counters */\n  unsigned cntExpand;      /* Number zOut expansions */\n  sqlite3 *db = sqlite3_context_db_handle(context);\n\n  assert( argc==3 );\n  UNUSED_PARAMETER(argc);\n  zStr = sqlite3_value_text(argv[0]);\n  if( zStr==0 ) return;\n  nStr = sqlite3_value_bytes(argv[0]);\n  assert( zStr==sqlite3_value_text(argv[0]) );  /* No encoding change */\n  zPattern = sqlite3_value_text(argv[1]);\n  if( zPattern==0 ){\n    assert( sqlite3_value_type(argv[1])==SQLITE_NULL\n            || sqlite3_context_db_handle(context)->mallocFailed );\n    return;\n  }\n  if( zPattern[0]==0 ){\n    assert( sqlite3_value_type(argv[1])!=SQLITE_NULL );\n    sqlite3_result_value(context, argv[0]);\n    return;\n  }\n  nPattern = sqlite3_value_bytes(argv[1]);\n  assert( zPattern==sqlite3_value_text(argv[1]) );  /* No encoding change */\n  zRep = sqlite3_value_text(argv[2]);\n  if( zRep==0 ) return;\n  nRep = sqlite3_value_bytes(argv[2]);\n  assert( zRep==sqlite3_value_text(argv[2]) );\n  nOut = nStr + 1;\n  assert( nOut<SQLITE_MAX_LENGTH );\n  zOut = contextMalloc(context, (i64)nOut);\n  if( zOut==0 ){\n    return;\n  }\n  loopLimit = nStr - nPattern;  \n  cntExpand = 0;\n  for(i=j=0; i<=loopLimit; i++){\n    if( zStr[i]!=zPattern[0] || memcmp(&zStr[i], zPattern, nPattern) ){\n      zOut[j++] = zStr[i];\n    }else{\n      if( nRep>nPattern ){\n        nOut += nRep - nPattern;\n        testcase( nOut-1==db->aLimit[SQLITE_LIMIT_LENGTH] );\n        testcase( nOut-2==db->aLimit[SQLITE_LIMIT_LENGTH] );\n        if( nOut-1>db->aLimit[SQLITE_LIMIT_LENGTH] ){\n          sqlite3_result_error_toobig(context);\n          sqlite3_free(zOut);\n          return;\n        }\n        cntExpand++;\n        if( (cntExpand&(cntExpand-1))==0 ){\n          /* Grow the size of the output buffer only on substitutions\n          ** whose index is a power of two: 1, 2, 4, 8, 16, 32, ... */\n          u8 *zOld;\n          zOld = zOut;\n          zOut = sqlite3_realloc64(zOut, (int)nOut + (nOut - nStr - 1));\n          if( zOut==0 ){\n            sqlite3_result_error_nomem(context);\n            sqlite3_free(zOld);\n            return;\n          }\n        }\n      }\n      memcpy(&zOut[j], zRep, nRep);\n      j += nRep;\n      i += nPattern-1;\n    }\n  }\n  assert( j+nStr-i+1<=nOut );\n  memcpy(&zOut[j], &zStr[i], nStr-i);\n  j += nStr - i;\n  assert( j<=nOut );\n  zOut[j] = 0;\n  sqlite3_result_text(context, (char*)zOut, j, sqlite3_free);\n}\n\n/*\n** Implementation of the TRIM(), LTRIM(), and RTRIM() functions.\n** The userdata is 0x1 for left trim, 0x2 for right trim, 0x3 for both.\n*/\nstatic void trimFunc(\n  sqlite3_context *context,\n  int argc,\n  sqlite3_value **argv\n){\n  const unsigned char *zIn;         /* Input string */\n  const unsigned char *zCharSet;    /* Set of characters to trim */\n  int nIn;                          /* Number of bytes in input */\n  int flags;                        /* 1: trimleft  2: trimright  3: trim */\n  int i;                            /* Loop counter */\n  unsigned char *aLen = 0;          /* Length of each character in zCharSet */\n  unsigned char **azChar = 0;       /* Individual characters in zCharSet */\n  int nChar;                        /* Number of characters in zCharSet */\n\n  if( sqlite3_value_type(argv[0])==SQLITE_NULL ){\n    return;\n  }\n  zIn = sqlite3_value_text(argv[0]);\n  if( zIn==0 ) return;\n  nIn = sqlite3_value_bytes(argv[0]);\n  assert( zIn==sqlite3_value_text(argv[0]) );\n  if( argc==1 ){\n    static const unsigned char lenOne[] = { 1 };\n    static unsigned char * const azOne[] = { (u8*)\" \" };\n    nChar = 1;\n    aLen = (u8*)lenOne;\n    azChar = (unsigned char **)azOne;\n    zCharSet = 0;\n  }else if( (zCharSet = sqlite3_value_text(argv[1]))==0 ){\n    return;\n  }else{\n    const unsigned char *z;\n    for(z=zCharSet, nChar=0; *z; nChar++){\n      SQLITE_SKIP_UTF8(z);\n    }\n    if( nChar>0 ){\n      azChar = contextMalloc(context, ((i64)nChar)*(sizeof(char*)+1));\n      if( azChar==0 ){\n        return;\n      }\n      aLen = (unsigned char*)&azChar[nChar];\n      for(z=zCharSet, nChar=0; *z; nChar++){\n        azChar[nChar] = (unsigned char *)z;\n        SQLITE_SKIP_UTF8(z);\n        aLen[nChar] = (u8)(z - azChar[nChar]);\n      }\n    }\n  }\n  if( nChar>0 ){\n    flags = SQLITE_PTR_TO_INT(sqlite3_user_data(context));\n    if( flags & 1 ){\n      while( nIn>0 ){\n        int len = 0;\n        for(i=0; i<nChar; i++){\n          len = aLen[i];\n          if( len<=nIn && memcmp(zIn, azChar[i], len)==0 ) break;\n        }\n        if( i>=nChar ) break;\n        zIn += len;\n        nIn -= len;\n      }\n    }\n    if( flags & 2 ){\n      while( nIn>0 ){\n        int len = 0;\n        for(i=0; i<nChar; i++){\n          len = aLen[i];\n          if( len<=nIn && memcmp(&zIn[nIn-len],azChar[i],len)==0 ) break;\n        }\n        if( i>=nChar ) break;\n        nIn -= len;\n      }\n    }\n    if( zCharSet ){\n      sqlite3_free(azChar);\n    }\n  }\n  sqlite3_result_text(context, (char*)zIn, nIn, SQLITE_TRANSIENT);\n}\n\n\n#ifdef SQLITE_ENABLE_UNKNOWN_SQL_FUNCTION\n/*\n** The \"unknown\" function is automatically substituted in place of\n** any unrecognized function name when doing an EXPLAIN or EXPLAIN QUERY PLAN\n** when the SQLITE_ENABLE_UNKNOWN_FUNCTION compile-time option is used.\n** When the \"sqlite3\" command-line shell is built using this functionality,\n** that allows an EXPLAIN or EXPLAIN QUERY PLAN for complex queries\n** involving application-defined functions to be examined in a generic\n** sqlite3 shell.\n*/\nstatic void unknownFunc(\n  sqlite3_context *context,\n  int argc,\n  sqlite3_value **argv\n){\n  /* no-op */\n}\n#endif /*SQLITE_ENABLE_UNKNOWN_SQL_FUNCTION*/\n\n\n/* IMP: R-25361-16150 This function is omitted from SQLite by default. It\n** is only available if the SQLITE_SOUNDEX compile-time option is used\n** when SQLite is built.\n*/\n#ifdef SQLITE_SOUNDEX\n/*\n** Compute the soundex encoding of a word.\n**\n** IMP: R-59782-00072 The soundex(X) function returns a string that is the\n** soundex encoding of the string X. \n*/\nstatic void soundexFunc(\n  sqlite3_context *context,\n  int argc,\n  sqlite3_value **argv\n){\n  char zResult[8];\n  const u8 *zIn;\n  int i, j;\n  static const unsigned char iCode[] = {\n    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n    0, 0, 1, 2, 3, 0, 1, 2, 0, 0, 2, 2, 4, 5, 5, 0,\n    1, 2, 6, 2, 3, 0, 1, 0, 2, 0, 2, 0, 0, 0, 0, 0,\n    0, 0, 1, 2, 3, 0, 1, 2, 0, 0, 2, 2, 4, 5, 5, 0,\n    1, 2, 6, 2, 3, 0, 1, 0, 2, 0, 2, 0, 0, 0, 0, 0,\n  };\n  assert( argc==1 );\n  zIn = (u8*)sqlite3_value_text(argv[0]);\n  if( zIn==0 ) zIn = (u8*)\"\";\n  for(i=0; zIn[i] && !sqlite3Isalpha(zIn[i]); i++){}\n  if( zIn[i] ){\n    u8 prevcode = iCode[zIn[i]&0x7f];\n    zResult[0] = sqlite3Toupper(zIn[i]);\n    for(j=1; j<4 && zIn[i]; i++){\n      int code = iCode[zIn[i]&0x7f];\n      if( code>0 ){\n        if( code!=prevcode ){\n          prevcode = code;\n          zResult[j++] = code + '0';\n        }\n      }else{\n        prevcode = 0;\n      }\n    }\n    while( j<4 ){\n      zResult[j++] = '0';\n    }\n    zResult[j] = 0;\n    sqlite3_result_text(context, zResult, 4, SQLITE_TRANSIENT);\n  }else{\n    /* IMP: R-64894-50321 The string \"?000\" is returned if the argument\n    ** is NULL or contains no ASCII alphabetic characters. */\n    sqlite3_result_text(context, \"?000\", 4, SQLITE_STATIC);\n  }\n}\n#endif /* SQLITE_SOUNDEX */\n\n#ifndef SQLITE_OMIT_LOAD_EXTENSION\n/*\n** A function that loads a shared-library extension then returns NULL.\n*/\nstatic void loadExt(sqlite3_context *context, int argc, sqlite3_value **argv){\n  const char *zFile = (const char *)sqlite3_value_text(argv[0]);\n  const char *zProc;\n  sqlite3 *db = sqlite3_context_db_handle(context);\n  char *zErrMsg = 0;\n\n  /* Disallow the load_extension() SQL function unless the SQLITE_LoadExtFunc\n  ** flag is set.  See the sqlite3_enable_load_extension() API.\n  */\n  if( (db->flags & SQLITE_LoadExtFunc)==0 ){\n    sqlite3_result_error(context, \"not authorized\", -1);\n    return;\n  }\n\n  if( argc==2 ){\n    zProc = (const char *)sqlite3_value_text(argv[1]);\n  }else{\n    zProc = 0;\n  }\n  if( zFile && sqlite3_load_extension(db, zFile, zProc, &zErrMsg) ){\n    sqlite3_result_error(context, zErrMsg, -1);\n    sqlite3_free(zErrMsg);\n  }\n}\n#endif\n\n\n/*\n** An instance of the following structure holds the context of a\n** sum() or avg() aggregate computation.\n*/\ntypedef struct SumCtx SumCtx;\nstruct SumCtx {\n  double rSum;      /* Floating point sum */\n  i64 iSum;         /* Integer sum */   \n  i64 cnt;          /* Number of elements summed */\n  u8 overflow;      /* True if integer overflow seen */\n  u8 approx;        /* True if non-integer value was input to the sum */\n};\n\n/*\n** Routines used to compute the sum, average, and total.\n**\n** The SUM() function follows the (broken) SQL standard which means\n** that it returns NULL if it sums over no inputs.  TOTAL returns\n** 0.0 in that case.  In addition, TOTAL always returns a float where\n** SUM might return an integer if it never encounters a floating point\n** value.  TOTAL never fails, but SUM might through an exception if\n** it overflows an integer.\n*/\nstatic void sumStep(sqlite3_context *context, int argc, sqlite3_value **argv){\n  SumCtx *p;\n  int type;\n  assert( argc==1 );\n  UNUSED_PARAMETER(argc);\n  p = sqlite3_aggregate_context(context, sizeof(*p));\n  type = sqlite3_value_numeric_type(argv[0]);\n  if( p && type!=SQLITE_NULL ){\n    p->cnt++;\n    if( type==SQLITE_INTEGER ){\n      i64 v = sqlite3_value_int64(argv[0]);\n      p->rSum += v;\n      if( (p->approx|p->overflow)==0 && sqlite3AddInt64(&p->iSum, v) ){\n        p->overflow = 1;\n      }\n    }else{\n      p->rSum += sqlite3_value_double(argv[0]);\n      p->approx = 1;\n    }\n  }\n}\nstatic void sumFinalize(sqlite3_context *context){\n  SumCtx *p;\n  p = sqlite3_aggregate_context(context, 0);\n  if( p && p->cnt>0 ){\n    if( p->overflow ){\n      sqlite3_result_error(context,\"integer overflow\",-1);\n    }else if( p->approx ){\n      sqlite3_result_double(context, p->rSum);\n    }else{\n      sqlite3_result_int64(context, p->iSum);\n    }\n  }\n}\nstatic void avgFinalize(sqlite3_context *context){\n  SumCtx *p;\n  p = sqlite3_aggregate_context(context, 0);\n  if( p && p->cnt>0 ){\n    sqlite3_result_double(context, p->rSum/(double)p->cnt);\n  }\n}\nstatic void totalFinalize(sqlite3_context *context){\n  SumCtx *p;\n  p = sqlite3_aggregate_context(context, 0);\n  /* (double)0 In case of SQLITE_OMIT_FLOATING_POINT... */\n  sqlite3_result_double(context, p ? p->rSum : (double)0);\n}\n\n/*\n** The following structure keeps track of state information for the\n** count() aggregate function.\n*/\ntypedef struct CountCtx CountCtx;\nstruct CountCtx {\n  i64 n;\n};\n\n/*\n** Routines to implement the count() aggregate function.\n*/\nstatic void countStep(sqlite3_context *context, int argc, sqlite3_value **argv){\n  CountCtx *p;\n  p = sqlite3_aggregate_context(context, sizeof(*p));\n  if( (argc==0 || SQLITE_NULL!=sqlite3_value_type(argv[0])) && p ){\n    p->n++;\n  }\n\n#ifndef SQLITE_OMIT_DEPRECATED\n  /* The sqlite3_aggregate_count() function is deprecated.  But just to make\n  ** sure it still operates correctly, verify that its count agrees with our \n  ** internal count when using count(*) and when the total count can be\n  ** expressed as a 32-bit integer. */\n  assert( argc==1 || p==0 || p->n>0x7fffffff\n          || p->n==sqlite3_aggregate_count(context) );\n#endif\n}   \nstatic void countFinalize(sqlite3_context *context){\n  CountCtx *p;\n  p = sqlite3_aggregate_context(context, 0);\n  sqlite3_result_int64(context, p ? p->n : 0);\n}\n\n/*\n** Routines to implement min() and max() aggregate functions.\n*/\nstatic void minmaxStep(\n  sqlite3_context *context, \n  int NotUsed, \n  sqlite3_value **argv\n){\n  Mem *pArg  = (Mem *)argv[0];\n  Mem *pBest;\n  UNUSED_PARAMETER(NotUsed);\n\n  pBest = (Mem *)sqlite3_aggregate_context(context, sizeof(*pBest));\n  if( !pBest ) return;\n\n  if( sqlite3_value_type(argv[0])==SQLITE_NULL ){\n    if( pBest->flags ) sqlite3SkipAccumulatorLoad(context);\n  }else if( pBest->flags ){\n    int max;\n    int cmp;\n    CollSeq *pColl = sqlite3GetFuncCollSeq(context);\n    /* This step function is used for both the min() and max() aggregates,\n    ** the only difference between the two being that the sense of the\n    ** comparison is inverted. For the max() aggregate, the\n    ** sqlite3_user_data() function returns (void *)-1. For min() it\n    ** returns (void *)db, where db is the sqlite3* database pointer.\n    ** Therefore the next statement sets variable 'max' to 1 for the max()\n    ** aggregate, or 0 for min().\n    */\n    max = sqlite3_user_data(context)!=0;\n    cmp = sqlite3MemCompare(pBest, pArg, pColl);\n    if( (max && cmp<0) || (!max && cmp>0) ){\n      sqlite3VdbeMemCopy(pBest, pArg);\n    }else{\n      sqlite3SkipAccumulatorLoad(context);\n    }\n  }else{\n    pBest->db = sqlite3_context_db_handle(context);\n    sqlite3VdbeMemCopy(pBest, pArg);\n  }\n}\nstatic void minMaxFinalize(sqlite3_context *context){\n  sqlite3_value *pRes;\n  pRes = (sqlite3_value *)sqlite3_aggregate_context(context, 0);\n  if( pRes ){\n    if( pRes->flags ){\n      sqlite3_result_value(context, pRes);\n    }\n    sqlite3VdbeMemRelease(pRes);\n  }\n}\n\n/*\n** group_concat(EXPR, ?SEPARATOR?)\n*/\nstatic void groupConcatStep(\n  sqlite3_context *context,\n  int argc,\n  sqlite3_value **argv\n){\n  const char *zVal;\n  StrAccum *pAccum;\n  const char *zSep;\n  int nVal, nSep;\n  assert( argc==1 || argc==2 );\n  if( sqlite3_value_type(argv[0])==SQLITE_NULL ) return;\n  pAccum = (StrAccum*)sqlite3_aggregate_context(context, sizeof(*pAccum));\n\n  if( pAccum ){\n    sqlite3 *db = sqlite3_context_db_handle(context);\n    int firstTerm = pAccum->mxAlloc==0;\n    pAccum->mxAlloc = db->aLimit[SQLITE_LIMIT_LENGTH];\n    if( !firstTerm ){\n      if( argc==2 ){\n        zSep = (char*)sqlite3_value_text(argv[1]);\n        nSep = sqlite3_value_bytes(argv[1]);\n      }else{\n        zSep = \",\";\n        nSep = 1;\n      }\n      if( zSep ) sqlite3StrAccumAppend(pAccum, zSep, nSep);\n    }\n    zVal = (char*)sqlite3_value_text(argv[0]);\n    nVal = sqlite3_value_bytes(argv[0]);\n    if( zVal ) sqlite3StrAccumAppend(pAccum, zVal, nVal);\n  }\n}\nstatic void groupConcatFinalize(sqlite3_context *context){\n  StrAccum *pAccum;\n  pAccum = sqlite3_aggregate_context(context, 0);\n  if( pAccum ){\n    if( pAccum->accError==STRACCUM_TOOBIG ){\n      sqlite3_result_error_toobig(context);\n    }else if( pAccum->accError==STRACCUM_NOMEM ){\n      sqlite3_result_error_nomem(context);\n    }else{    \n      sqlite3_result_text(context, sqlite3StrAccumFinish(pAccum), -1, \n                          sqlite3_free);\n    }\n  }\n}\n\n/*\n** This routine does per-connection function registration.  Most\n** of the built-in functions above are part of the global function set.\n** This routine only deals with those that are not global.\n*/\nSQLITE_PRIVATE void sqlite3RegisterPerConnectionBuiltinFunctions(sqlite3 *db){\n  int rc = sqlite3_overload_function(db, \"MATCH\", 2);\n  assert( rc==SQLITE_NOMEM || rc==SQLITE_OK );\n  if( rc==SQLITE_NOMEM ){\n    sqlite3OomFault(db);\n  }\n}\n\n/*\n** Set the LIKEOPT flag on the 2-argument function with the given name.\n*/\nstatic void setLikeOptFlag(sqlite3 *db, const char *zName, u8 flagVal){\n  FuncDef *pDef;\n  pDef = sqlite3FindFunction(db, zName, 2, SQLITE_UTF8, 0);\n  if( ALWAYS(pDef) ){\n    pDef->funcFlags |= flagVal;\n  }\n}\n\n/*\n** Register the built-in LIKE and GLOB functions.  The caseSensitive\n** parameter determines whether or not the LIKE operator is case\n** sensitive.  GLOB is always case sensitive.\n*/\nSQLITE_PRIVATE void sqlite3RegisterLikeFunctions(sqlite3 *db, int caseSensitive){\n  struct compareInfo *pInfo;\n  if( caseSensitive ){\n    pInfo = (struct compareInfo*)&likeInfoAlt;\n  }else{\n    pInfo = (struct compareInfo*)&likeInfoNorm;\n  }\n  sqlite3CreateFunc(db, \"like\", 2, SQLITE_UTF8, pInfo, likeFunc, 0, 0, 0);\n  sqlite3CreateFunc(db, \"like\", 3, SQLITE_UTF8, pInfo, likeFunc, 0, 0, 0);\n  sqlite3CreateFunc(db, \"glob\", 2, SQLITE_UTF8, \n      (struct compareInfo*)&globInfo, likeFunc, 0, 0, 0);\n  setLikeOptFlag(db, \"glob\", SQLITE_FUNC_LIKE | SQLITE_FUNC_CASE);\n  setLikeOptFlag(db, \"like\", \n      caseSensitive ? (SQLITE_FUNC_LIKE | SQLITE_FUNC_CASE) : SQLITE_FUNC_LIKE);\n}\n\n/*\n** pExpr points to an expression which implements a function.  If\n** it is appropriate to apply the LIKE optimization to that function\n** then set aWc[0] through aWc[2] to the wildcard characters and the\n** escape character and then return TRUE.  If the function is not a \n** LIKE-style function then return FALSE.\n**\n** The expression \"a LIKE b ESCAPE c\" is only considered a valid LIKE\n** operator if c is a string literal that is exactly one byte in length.\n** That one byte is stored in aWc[3].  aWc[3] is set to zero if there is\n** no ESCAPE clause.\n**\n** *pIsNocase is set to true if uppercase and lowercase are equivalent for\n** the function (default for LIKE).  If the function makes the distinction\n** between uppercase and lowercase (as does GLOB) then *pIsNocase is set to\n** false.\n*/\nSQLITE_PRIVATE int sqlite3IsLikeFunction(sqlite3 *db, Expr *pExpr, int *pIsNocase, char *aWc){\n  FuncDef *pDef;\n  int nExpr;\n  if( pExpr->op!=TK_FUNCTION || !pExpr->x.pList ){\n    return 0;\n  }\n  assert( !ExprHasProperty(pExpr, EP_xIsSelect) );\n  nExpr = pExpr->x.pList->nExpr;\n  pDef = sqlite3FindFunction(db, pExpr->u.zToken, nExpr, SQLITE_UTF8, 0);\n  if( NEVER(pDef==0) || (pDef->funcFlags & SQLITE_FUNC_LIKE)==0 ){\n    return 0;\n  }\n  if( nExpr<3 ){\n    aWc[3] = 0;\n  }else{\n    Expr *pEscape = pExpr->x.pList->a[2].pExpr;\n    char *zEscape;\n    if( pEscape->op!=TK_STRING ) return 0;\n    zEscape = pEscape->u.zToken;\n    if( zEscape[0]==0 || zEscape[1]!=0 ) return 0;\n    aWc[3] = zEscape[0];\n  }\n\n  /* The memcpy() statement assumes that the wildcard characters are\n  ** the first three statements in the compareInfo structure.  The\n  ** asserts() that follow verify that assumption\n  */\n  memcpy(aWc, pDef->pUserData, 3);\n  assert( (char*)&likeInfoAlt == (char*)&likeInfoAlt.matchAll );\n  assert( &((char*)&likeInfoAlt)[1] == (char*)&likeInfoAlt.matchOne );\n  assert( &((char*)&likeInfoAlt)[2] == (char*)&likeInfoAlt.matchSet );\n  *pIsNocase = (pDef->funcFlags & SQLITE_FUNC_CASE)==0;\n  return 1;\n}\n\n/*\n** All of the FuncDef structures in the aBuiltinFunc[] array above\n** to the global function hash table.  This occurs at start-time (as\n** a consequence of calling sqlite3_initialize()).\n**\n** After this routine runs\n*/\nSQLITE_PRIVATE void sqlite3RegisterBuiltinFunctions(void){\n  /*\n  ** The following array holds FuncDef structures for all of the functions\n  ** defined in this file.\n  **\n  ** The array cannot be constant since changes are made to the\n  ** FuncDef.pHash elements at start-time.  The elements of this array\n  ** are read-only after initialization is complete.\n  **\n  ** For peak efficiency, put the most frequently used function last.\n  */\n  static FuncDef aBuiltinFunc[] = {\n#ifdef SQLITE_SOUNDEX\n    FUNCTION(soundex,            1, 0, 0, soundexFunc      ),\n#endif\n#ifndef SQLITE_OMIT_LOAD_EXTENSION\n    VFUNCTION(load_extension,    1, 0, 0, loadExt          ),\n    VFUNCTION(load_extension,    2, 0, 0, loadExt          ),\n#endif\n#if SQLITE_USER_AUTHENTICATION\n    FUNCTION(sqlite_crypt,       2, 0, 0, sqlite3CryptFunc ),\n#endif\n#ifndef SQLITE_OMIT_COMPILEOPTION_DIAGS\n    DFUNCTION(sqlite_compileoption_used,1, 0, 0, compileoptionusedFunc  ),\n    DFUNCTION(sqlite_compileoption_get, 1, 0, 0, compileoptiongetFunc  ),\n#endif /* SQLITE_OMIT_COMPILEOPTION_DIAGS */\n    FUNCTION2(unlikely,          1, 0, 0, noopFunc,  SQLITE_FUNC_UNLIKELY),\n    FUNCTION2(likelihood,        2, 0, 0, noopFunc,  SQLITE_FUNC_UNLIKELY),\n    FUNCTION2(likely,            1, 0, 0, noopFunc,  SQLITE_FUNC_UNLIKELY),\n#ifdef SQLITE_DEBUG\n    FUNCTION2(affinity,          1, 0, 0, noopFunc,  SQLITE_FUNC_AFFINITY),\n#endif\n#ifdef SQLITE_ENABLE_OFFSET_SQL_FUNC\n    FUNCTION2(sqlite_offset,     1, 0, 0, noopFunc,  SQLITE_FUNC_OFFSET|\n                                                     SQLITE_FUNC_TYPEOF),\n#endif\n    FUNCTION(ltrim,              1, 1, 0, trimFunc         ),\n    FUNCTION(ltrim,              2, 1, 0, trimFunc         ),\n    FUNCTION(rtrim,              1, 2, 0, trimFunc         ),\n    FUNCTION(rtrim,              2, 2, 0, trimFunc         ),\n    FUNCTION(trim,               1, 3, 0, trimFunc         ),\n    FUNCTION(trim,               2, 3, 0, trimFunc         ),\n    FUNCTION(min,               -1, 0, 1, minmaxFunc       ),\n    FUNCTION(min,                0, 0, 1, 0                ),\n    AGGREGATE2(min,              1, 0, 1, minmaxStep,      minMaxFinalize,\n                                          SQLITE_FUNC_MINMAX ),\n    FUNCTION(max,               -1, 1, 1, minmaxFunc       ),\n    FUNCTION(max,                0, 1, 1, 0                ),\n    AGGREGATE2(max,              1, 1, 1, minmaxStep,      minMaxFinalize,\n                                          SQLITE_FUNC_MINMAX ),\n    FUNCTION2(typeof,            1, 0, 0, typeofFunc,  SQLITE_FUNC_TYPEOF),\n    FUNCTION2(length,            1, 0, 0, lengthFunc,  SQLITE_FUNC_LENGTH),\n    FUNCTION(instr,              2, 0, 0, instrFunc        ),\n    FUNCTION(printf,            -1, 0, 0, printfFunc       ),\n    FUNCTION(unicode,            1, 0, 0, unicodeFunc      ),\n    FUNCTION(char,              -1, 0, 0, charFunc         ),\n    FUNCTION(abs,                1, 0, 0, absFunc          ),\n#ifndef SQLITE_OMIT_FLOATING_POINT\n    FUNCTION(round,              1, 0, 0, roundFunc        ),\n    FUNCTION(round,              2, 0, 0, roundFunc        ),\n#endif\n    FUNCTION(upper,              1, 0, 0, upperFunc        ),\n    FUNCTION(lower,              1, 0, 0, lowerFunc        ),\n    FUNCTION(hex,                1, 0, 0, hexFunc          ),\n    FUNCTION2(ifnull,            2, 0, 0, noopFunc,  SQLITE_FUNC_COALESCE),\n    VFUNCTION(random,            0, 0, 0, randomFunc       ),\n    VFUNCTION(randomblob,        1, 0, 0, randomBlob       ),\n    FUNCTION(nullif,             2, 0, 1, nullifFunc       ),\n    DFUNCTION(sqlite_version,    0, 0, 0, versionFunc      ),\n    DFUNCTION(sqlite_source_id,  0, 0, 0, sourceidFunc     ),\n    FUNCTION(sqlite_log,         2, 0, 0, errlogFunc       ),\n    FUNCTION(quote,              1, 0, 0, quoteFunc        ),\n    VFUNCTION(last_insert_rowid, 0, 0, 0, last_insert_rowid),\n    VFUNCTION(changes,           0, 0, 0, changes          ),\n    VFUNCTION(total_changes,     0, 0, 0, total_changes    ),\n    FUNCTION(replace,            3, 0, 0, replaceFunc      ),\n    FUNCTION(zeroblob,           1, 0, 0, zeroblobFunc     ),\n    FUNCTION(substr,             2, 0, 0, substrFunc       ),\n    FUNCTION(substr,             3, 0, 0, substrFunc       ),\n    AGGREGATE(sum,               1, 0, 0, sumStep,         sumFinalize    ),\n    AGGREGATE(total,             1, 0, 0, sumStep,         totalFinalize    ),\n    AGGREGATE(avg,               1, 0, 0, sumStep,         avgFinalize    ),\n    AGGREGATE2(count,            0, 0, 0, countStep,       countFinalize,\n               SQLITE_FUNC_COUNT  ),\n    AGGREGATE(count,             1, 0, 0, countStep,       countFinalize  ),\n    AGGREGATE(group_concat,      1, 0, 0, groupConcatStep, groupConcatFinalize),\n    AGGREGATE(group_concat,      2, 0, 0, groupConcatStep, groupConcatFinalize),\n  \n    LIKEFUNC(glob, 2, &globInfo, SQLITE_FUNC_LIKE|SQLITE_FUNC_CASE),\n#ifdef SQLITE_CASE_SENSITIVE_LIKE\n    LIKEFUNC(like, 2, &likeInfoAlt, SQLITE_FUNC_LIKE|SQLITE_FUNC_CASE),\n    LIKEFUNC(like, 3, &likeInfoAlt, SQLITE_FUNC_LIKE|SQLITE_FUNC_CASE),\n#else\n    LIKEFUNC(like, 2, &likeInfoNorm, SQLITE_FUNC_LIKE),\n    LIKEFUNC(like, 3, &likeInfoNorm, SQLITE_FUNC_LIKE),\n#endif\n#ifdef SQLITE_ENABLE_UNKNOWN_SQL_FUNCTION\n    FUNCTION(unknown,           -1, 0, 0, unknownFunc      ),\n#endif\n    FUNCTION(coalesce,           1, 0, 0, 0                ),\n    FUNCTION(coalesce,           0, 0, 0, 0                ),\n    FUNCTION2(coalesce,         -1, 0, 0, noopFunc,  SQLITE_FUNC_COALESCE),\n  };\n#ifndef SQLITE_OMIT_ALTERTABLE\n  sqlite3AlterFunctions();\n#endif\n#if defined(SQLITE_ENABLE_STAT3) || defined(SQLITE_ENABLE_STAT4)\n  sqlite3AnalyzeFunctions();\n#endif\n  sqlite3RegisterDateTimeFunctions();\n  sqlite3InsertBuiltinFuncs(aBuiltinFunc, ArraySize(aBuiltinFunc));\n\n#if 0  /* Enable to print out how the built-in functions are hashed */\n  {\n    int i;\n    FuncDef *p;\n    for(i=0; i<SQLITE_FUNC_HASH_SZ; i++){\n      printf(\"FUNC-HASH %02d:\", i);\n      for(p=sqlite3BuiltinFunctions.a[i]; p; p=p->u.pHash){\n        int n = sqlite3Strlen30(p->zName);\n        int h = p->zName[0] + n;\n        printf(\" %s(%d)\", p->zName, h);\n      }\n      printf(\"\\n\");\n    }\n  }\n#endif\n}\n\n/************** End of func.c ************************************************/\n/************** Begin file fkey.c ********************************************/\n/*\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n*************************************************************************\n** This file contains code used by the compiler to add foreign key\n** support to compiled SQL statements.\n*/\n/* #include \"sqliteInt.h\" */\n\n#ifndef SQLITE_OMIT_FOREIGN_KEY\n#ifndef SQLITE_OMIT_TRIGGER\n\n/*\n** Deferred and Immediate FKs\n** --------------------------\n**\n** Foreign keys in SQLite come in two flavours: deferred and immediate.\n** If an immediate foreign key constraint is violated,\n** SQLITE_CONSTRAINT_FOREIGNKEY is returned and the current\n** statement transaction rolled back. If a \n** deferred foreign key constraint is violated, no action is taken \n** immediately. However if the application attempts to commit the \n** transaction before fixing the constraint violation, the attempt fails.\n**\n** Deferred constraints are implemented using a simple counter associated\n** with the database handle. The counter is set to zero each time a \n** database transaction is opened. Each time a statement is executed \n** that causes a foreign key violation, the counter is incremented. Each\n** time a statement is executed that removes an existing violation from\n** the database, the counter is decremented. When the transaction is\n** committed, the commit fails if the current value of the counter is\n** greater than zero. This scheme has two big drawbacks:\n**\n**   * When a commit fails due to a deferred foreign key constraint, \n**     there is no way to tell which foreign constraint is not satisfied,\n**     or which row it is not satisfied for.\n**\n**   * If the database contains foreign key violations when the \n**     transaction is opened, this may cause the mechanism to malfunction.\n**\n** Despite these problems, this approach is adopted as it seems simpler\n** than the alternatives.\n**\n** INSERT operations:\n**\n**   I.1) For each FK for which the table is the child table, search\n**        the parent table for a match. If none is found increment the\n**        constraint counter.\n**\n**   I.2) For each FK for which the table is the parent table, \n**        search the child table for rows that correspond to the new\n**        row in the parent table. Decrement the counter for each row\n**        found (as the constraint is now satisfied).\n**\n** DELETE operations:\n**\n**   D.1) For each FK for which the table is the child table, \n**        search the parent table for a row that corresponds to the \n**        deleted row in the child table. If such a row is not found, \n**        decrement the counter.\n**\n**   D.2) For each FK for which the table is the parent table, search \n**        the child table for rows that correspond to the deleted row \n**        in the parent table. For each found increment the counter.\n**\n** UPDATE operations:\n**\n**   An UPDATE command requires that all 4 steps above are taken, but only\n**   for FK constraints for which the affected columns are actually \n**   modified (values must be compared at runtime).\n**\n** Note that I.1 and D.1 are very similar operations, as are I.2 and D.2.\n** This simplifies the implementation a bit.\n**\n** For the purposes of immediate FK constraints, the OR REPLACE conflict\n** resolution is considered to delete rows before the new row is inserted.\n** If a delete caused by OR REPLACE violates an FK constraint, an exception\n** is thrown, even if the FK constraint would be satisfied after the new \n** row is inserted.\n**\n** Immediate constraints are usually handled similarly. The only difference \n** is that the counter used is stored as part of each individual statement\n** object (struct Vdbe). If, after the statement has run, its immediate\n** constraint counter is greater than zero,\n** it returns SQLITE_CONSTRAINT_FOREIGNKEY\n** and the statement transaction is rolled back. An exception is an INSERT\n** statement that inserts a single row only (no triggers). In this case,\n** instead of using a counter, an exception is thrown immediately if the\n** INSERT violates a foreign key constraint. This is necessary as such\n** an INSERT does not open a statement transaction.\n**\n** TODO: How should dropping a table be handled? How should renaming a \n** table be handled?\n**\n**\n** Query API Notes\n** ---------------\n**\n** Before coding an UPDATE or DELETE row operation, the code-generator\n** for those two operations needs to know whether or not the operation\n** requires any FK processing and, if so, which columns of the original\n** row are required by the FK processing VDBE code (i.e. if FKs were\n** implemented using triggers, which of the old.* columns would be \n** accessed). No information is required by the code-generator before\n** coding an INSERT operation. The functions used by the UPDATE/DELETE\n** generation code to query for this information are:\n**\n**   sqlite3FkRequired() - Test to see if FK processing is required.\n**   sqlite3FkOldmask()  - Query for the set of required old.* columns.\n**\n**\n** Externally accessible module functions\n** --------------------------------------\n**\n**   sqlite3FkCheck()    - Check for foreign key violations.\n**   sqlite3FkActions()  - Code triggers for ON UPDATE/ON DELETE actions.\n**   sqlite3FkDelete()   - Delete an FKey structure.\n*/\n\n/*\n** VDBE Calling Convention\n** -----------------------\n**\n** Example:\n**\n**   For the following INSERT statement:\n**\n**     CREATE TABLE t1(a, b INTEGER PRIMARY KEY, c);\n**     INSERT INTO t1 VALUES(1, 2, 3.1);\n**\n**   Register (x):        2    (type integer)\n**   Register (x+1):      1    (type integer)\n**   Register (x+2):      NULL (type NULL)\n**   Register (x+3):      3.1  (type real)\n*/\n\n/*\n** A foreign key constraint requires that the key columns in the parent\n** table are collectively subject to a UNIQUE or PRIMARY KEY constraint.\n** Given that pParent is the parent table for foreign key constraint pFKey, \n** search the schema for a unique index on the parent key columns. \n**\n** If successful, zero is returned. If the parent key is an INTEGER PRIMARY \n** KEY column, then output variable *ppIdx is set to NULL. Otherwise, *ppIdx \n** is set to point to the unique index. \n** \n** If the parent key consists of a single column (the foreign key constraint\n** is not a composite foreign key), output variable *paiCol is set to NULL.\n** Otherwise, it is set to point to an allocated array of size N, where\n** N is the number of columns in the parent key. The first element of the\n** array is the index of the child table column that is mapped by the FK\n** constraint to the parent table column stored in the left-most column\n** of index *ppIdx. The second element of the array is the index of the\n** child table column that corresponds to the second left-most column of\n** *ppIdx, and so on.\n**\n** If the required index cannot be found, either because:\n**\n**   1) The named parent key columns do not exist, or\n**\n**   2) The named parent key columns do exist, but are not subject to a\n**      UNIQUE or PRIMARY KEY constraint, or\n**\n**   3) No parent key columns were provided explicitly as part of the\n**      foreign key definition, and the parent table does not have a\n**      PRIMARY KEY, or\n**\n**   4) No parent key columns were provided explicitly as part of the\n**      foreign key definition, and the PRIMARY KEY of the parent table \n**      consists of a different number of columns to the child key in \n**      the child table.\n**\n** then non-zero is returned, and a \"foreign key mismatch\" error loaded\n** into pParse. If an OOM error occurs, non-zero is returned and the\n** pParse->db->mallocFailed flag is set.\n*/\nSQLITE_PRIVATE int sqlite3FkLocateIndex(\n  Parse *pParse,                  /* Parse context to store any error in */\n  Table *pParent,                 /* Parent table of FK constraint pFKey */\n  FKey *pFKey,                    /* Foreign key to find index for */\n  Index **ppIdx,                  /* OUT: Unique index on parent table */\n  int **paiCol                    /* OUT: Map of index columns in pFKey */\n){\n  Index *pIdx = 0;                    /* Value to return via *ppIdx */\n  int *aiCol = 0;                     /* Value to return via *paiCol */\n  int nCol = pFKey->nCol;             /* Number of columns in parent key */\n  char *zKey = pFKey->aCol[0].zCol;   /* Name of left-most parent key column */\n\n  /* The caller is responsible for zeroing output parameters. */\n  assert( ppIdx && *ppIdx==0 );\n  assert( !paiCol || *paiCol==0 );\n  assert( pParse );\n\n  /* If this is a non-composite (single column) foreign key, check if it \n  ** maps to the INTEGER PRIMARY KEY of table pParent. If so, leave *ppIdx \n  ** and *paiCol set to zero and return early. \n  **\n  ** Otherwise, for a composite foreign key (more than one column), allocate\n  ** space for the aiCol array (returned via output parameter *paiCol).\n  ** Non-composite foreign keys do not require the aiCol array.\n  */\n  if( nCol==1 ){\n    /* The FK maps to the IPK if any of the following are true:\n    **\n    **   1) There is an INTEGER PRIMARY KEY column and the FK is implicitly \n    **      mapped to the primary key of table pParent, or\n    **   2) The FK is explicitly mapped to a column declared as INTEGER\n    **      PRIMARY KEY.\n    */\n    if( pParent->iPKey>=0 ){\n      if( !zKey ) return 0;\n      if( !sqlite3StrICmp(pParent->aCol[pParent->iPKey].zName, zKey) ) return 0;\n    }\n  }else if( paiCol ){\n    assert( nCol>1 );\n    aiCol = (int *)sqlite3DbMallocRawNN(pParse->db, nCol*sizeof(int));\n    if( !aiCol ) return 1;\n    *paiCol = aiCol;\n  }\n\n  for(pIdx=pParent->pIndex; pIdx; pIdx=pIdx->pNext){\n    if( pIdx->nKeyCol==nCol && IsUniqueIndex(pIdx) && pIdx->pPartIdxWhere==0 ){ \n      /* pIdx is a UNIQUE index (or a PRIMARY KEY) and has the right number\n      ** of columns. If each indexed column corresponds to a foreign key\n      ** column of pFKey, then this index is a winner.  */\n\n      if( zKey==0 ){\n        /* If zKey is NULL, then this foreign key is implicitly mapped to \n        ** the PRIMARY KEY of table pParent. The PRIMARY KEY index may be \n        ** identified by the test.  */\n        if( IsPrimaryKeyIndex(pIdx) ){\n          if( aiCol ){\n            int i;\n            for(i=0; i<nCol; i++) aiCol[i] = pFKey->aCol[i].iFrom;\n          }\n          break;\n        }\n      }else{\n        /* If zKey is non-NULL, then this foreign key was declared to\n        ** map to an explicit list of columns in table pParent. Check if this\n        ** index matches those columns. Also, check that the index uses\n        ** the default collation sequences for each column. */\n        int i, j;\n        for(i=0; i<nCol; i++){\n          i16 iCol = pIdx->aiColumn[i];     /* Index of column in parent tbl */\n          const char *zDfltColl;            /* Def. collation for column */\n          char *zIdxCol;                    /* Name of indexed column */\n\n          if( iCol<0 ) break; /* No foreign keys against expression indexes */\n\n          /* If the index uses a collation sequence that is different from\n          ** the default collation sequence for the column, this index is\n          ** unusable. Bail out early in this case.  */\n          zDfltColl = pParent->aCol[iCol].zColl;\n          if( !zDfltColl ) zDfltColl = sqlite3StrBINARY;\n          if( sqlite3StrICmp(pIdx->azColl[i], zDfltColl) ) break;\n\n          zIdxCol = pParent->aCol[iCol].zName;\n          for(j=0; j<nCol; j++){\n            if( sqlite3StrICmp(pFKey->aCol[j].zCol, zIdxCol)==0 ){\n              if( aiCol ) aiCol[i] = pFKey->aCol[j].iFrom;\n              break;\n            }\n          }\n          if( j==nCol ) break;\n        }\n        if( i==nCol ) break;      /* pIdx is usable */\n      }\n    }\n  }\n\n  if( !pIdx ){\n    if( !pParse->disableTriggers ){\n      sqlite3ErrorMsg(pParse,\n           \"foreign key mismatch - \\\"%w\\\" referencing \\\"%w\\\"\",\n           pFKey->pFrom->zName, pFKey->zTo);\n    }\n    sqlite3DbFree(pParse->db, aiCol);\n    return 1;\n  }\n\n  *ppIdx = pIdx;\n  return 0;\n}\n\n/*\n** This function is called when a row is inserted into or deleted from the \n** child table of foreign key constraint pFKey. If an SQL UPDATE is executed \n** on the child table of pFKey, this function is invoked twice for each row\n** affected - once to \"delete\" the old row, and then again to \"insert\" the\n** new row.\n**\n** Each time it is called, this function generates VDBE code to locate the\n** row in the parent table that corresponds to the row being inserted into \n** or deleted from the child table. If the parent row can be found, no \n** special action is taken. Otherwise, if the parent row can *not* be\n** found in the parent table:\n**\n**   Operation | FK type   | Action taken\n**   --------------------------------------------------------------------------\n**   INSERT      immediate   Increment the \"immediate constraint counter\".\n**\n**   DELETE      immediate   Decrement the \"immediate constraint counter\".\n**\n**   INSERT      deferred    Increment the \"deferred constraint counter\".\n**\n**   DELETE      deferred    Decrement the \"deferred constraint counter\".\n**\n** These operations are identified in the comment at the top of this file \n** (fkey.c) as \"I.1\" and \"D.1\".\n*/\nstatic void fkLookupParent(\n  Parse *pParse,        /* Parse context */\n  int iDb,              /* Index of database housing pTab */\n  Table *pTab,          /* Parent table of FK pFKey */\n  Index *pIdx,          /* Unique index on parent key columns in pTab */\n  FKey *pFKey,          /* Foreign key constraint */\n  int *aiCol,           /* Map from parent key columns to child table columns */\n  int regData,          /* Address of array containing child table row */\n  int nIncr,            /* Increment constraint counter by this */\n  int isIgnore          /* If true, pretend pTab contains all NULL values */\n){\n  int i;                                    /* Iterator variable */\n  Vdbe *v = sqlite3GetVdbe(pParse);         /* Vdbe to add code to */\n  int iCur = pParse->nTab - 1;              /* Cursor number to use */\n  int iOk = sqlite3VdbeMakeLabel(v);        /* jump here if parent key found */\n\n  /* If nIncr is less than zero, then check at runtime if there are any\n  ** outstanding constraints to resolve. If there are not, there is no need\n  ** to check if deleting this row resolves any outstanding violations.\n  **\n  ** Check if any of the key columns in the child table row are NULL. If \n  ** any are, then the constraint is considered satisfied. No need to \n  ** search for a matching row in the parent table.  */\n  if( nIncr<0 ){\n    sqlite3VdbeAddOp2(v, OP_FkIfZero, pFKey->isDeferred, iOk);\n    VdbeCoverage(v);\n  }\n  for(i=0; i<pFKey->nCol; i++){\n    int iReg = aiCol[i] + regData + 1;\n    sqlite3VdbeAddOp2(v, OP_IsNull, iReg, iOk); VdbeCoverage(v);\n  }\n\n  if( isIgnore==0 ){\n    if( pIdx==0 ){\n      /* If pIdx is NULL, then the parent key is the INTEGER PRIMARY KEY\n      ** column of the parent table (table pTab).  */\n      int iMustBeInt;               /* Address of MustBeInt instruction */\n      int regTemp = sqlite3GetTempReg(pParse);\n  \n      /* Invoke MustBeInt to coerce the child key value to an integer (i.e. \n      ** apply the affinity of the parent key). If this fails, then there\n      ** is no matching parent key. Before using MustBeInt, make a copy of\n      ** the value. Otherwise, the value inserted into the child key column\n      ** will have INTEGER affinity applied to it, which may not be correct.  */\n      sqlite3VdbeAddOp2(v, OP_SCopy, aiCol[0]+1+regData, regTemp);\n      iMustBeInt = sqlite3VdbeAddOp2(v, OP_MustBeInt, regTemp, 0);\n      VdbeCoverage(v);\n  \n      /* If the parent table is the same as the child table, and we are about\n      ** to increment the constraint-counter (i.e. this is an INSERT operation),\n      ** then check if the row being inserted matches itself. If so, do not\n      ** increment the constraint-counter.  */\n      if( pTab==pFKey->pFrom && nIncr==1 ){\n        sqlite3VdbeAddOp3(v, OP_Eq, regData, iOk, regTemp); VdbeCoverage(v);\n        sqlite3VdbeChangeP5(v, SQLITE_NOTNULL);\n      }\n  \n      sqlite3OpenTable(pParse, iCur, iDb, pTab, OP_OpenRead);\n      sqlite3VdbeAddOp3(v, OP_NotExists, iCur, 0, regTemp); VdbeCoverage(v);\n      sqlite3VdbeGoto(v, iOk);\n      sqlite3VdbeJumpHere(v, sqlite3VdbeCurrentAddr(v)-2);\n      sqlite3VdbeJumpHere(v, iMustBeInt);\n      sqlite3ReleaseTempReg(pParse, regTemp);\n    }else{\n      int nCol = pFKey->nCol;\n      int regTemp = sqlite3GetTempRange(pParse, nCol);\n      int regRec = sqlite3GetTempReg(pParse);\n  \n      sqlite3VdbeAddOp3(v, OP_OpenRead, iCur, pIdx->tnum, iDb);\n      sqlite3VdbeSetP4KeyInfo(pParse, pIdx);\n      for(i=0; i<nCol; i++){\n        sqlite3VdbeAddOp2(v, OP_Copy, aiCol[i]+1+regData, regTemp+i);\n      }\n  \n      /* If the parent table is the same as the child table, and we are about\n      ** to increment the constraint-counter (i.e. this is an INSERT operation),\n      ** then check if the row being inserted matches itself. If so, do not\n      ** increment the constraint-counter. \n      **\n      ** If any of the parent-key values are NULL, then the row cannot match \n      ** itself. So set JUMPIFNULL to make sure we do the OP_Found if any\n      ** of the parent-key values are NULL (at this point it is known that\n      ** none of the child key values are).\n      */\n      if( pTab==pFKey->pFrom && nIncr==1 ){\n        int iJump = sqlite3VdbeCurrentAddr(v) + nCol + 1;\n        for(i=0; i<nCol; i++){\n          int iChild = aiCol[i]+1+regData;\n          int iParent = pIdx->aiColumn[i]+1+regData;\n          assert( pIdx->aiColumn[i]>=0 );\n          assert( aiCol[i]!=pTab->iPKey );\n          if( pIdx->aiColumn[i]==pTab->iPKey ){\n            /* The parent key is a composite key that includes the IPK column */\n            iParent = regData;\n          }\n          sqlite3VdbeAddOp3(v, OP_Ne, iChild, iJump, iParent); VdbeCoverage(v);\n          sqlite3VdbeChangeP5(v, SQLITE_JUMPIFNULL);\n        }\n        sqlite3VdbeGoto(v, iOk);\n      }\n  \n      sqlite3VdbeAddOp4(v, OP_MakeRecord, regTemp, nCol, regRec,\n                        sqlite3IndexAffinityStr(pParse->db,pIdx), nCol);\n      sqlite3VdbeAddOp4Int(v, OP_Found, iCur, iOk, regRec, 0); VdbeCoverage(v);\n  \n      sqlite3ReleaseTempReg(pParse, regRec);\n      sqlite3ReleaseTempRange(pParse, regTemp, nCol);\n    }\n  }\n\n  if( !pFKey->isDeferred && !(pParse->db->flags & SQLITE_DeferFKs)\n   && !pParse->pToplevel \n   && !pParse->isMultiWrite \n  ){\n    /* Special case: If this is an INSERT statement that will insert exactly\n    ** one row into the table, raise a constraint immediately instead of\n    ** incrementing a counter. This is necessary as the VM code is being\n    ** generated for will not open a statement transaction.  */\n    assert( nIncr==1 );\n    sqlite3HaltConstraint(pParse, SQLITE_CONSTRAINT_FOREIGNKEY,\n        OE_Abort, 0, P4_STATIC, P5_ConstraintFK);\n  }else{\n    if( nIncr>0 && pFKey->isDeferred==0 ){\n      sqlite3MayAbort(pParse);\n    }\n    sqlite3VdbeAddOp2(v, OP_FkCounter, pFKey->isDeferred, nIncr);\n  }\n\n  sqlite3VdbeResolveLabel(v, iOk);\n  sqlite3VdbeAddOp1(v, OP_Close, iCur);\n}\n\n\n/*\n** Return an Expr object that refers to a memory register corresponding\n** to column iCol of table pTab.\n**\n** regBase is the first of an array of register that contains the data\n** for pTab.  regBase itself holds the rowid.  regBase+1 holds the first\n** column.  regBase+2 holds the second column, and so forth.\n*/\nstatic Expr *exprTableRegister(\n  Parse *pParse,     /* Parsing and code generating context */\n  Table *pTab,       /* The table whose content is at r[regBase]... */\n  int regBase,       /* Contents of table pTab */\n  i16 iCol           /* Which column of pTab is desired */\n){\n  Expr *pExpr;\n  Column *pCol;\n  const char *zColl;\n  sqlite3 *db = pParse->db;\n\n  pExpr = sqlite3Expr(db, TK_REGISTER, 0);\n  if( pExpr ){\n    if( iCol>=0 && iCol!=pTab->iPKey ){\n      pCol = &pTab->aCol[iCol];\n      pExpr->iTable = regBase + iCol + 1;\n      pExpr->affinity = pCol->affinity;\n      zColl = pCol->zColl;\n      if( zColl==0 ) zColl = db->pDfltColl->zName;\n      pExpr = sqlite3ExprAddCollateString(pParse, pExpr, zColl);\n    }else{\n      pExpr->iTable = regBase;\n      pExpr->affinity = SQLITE_AFF_INTEGER;\n    }\n  }\n  return pExpr;\n}\n\n/*\n** Return an Expr object that refers to column iCol of table pTab which\n** has cursor iCur.\n*/\nstatic Expr *exprTableColumn(\n  sqlite3 *db,      /* The database connection */\n  Table *pTab,      /* The table whose column is desired */\n  int iCursor,      /* The open cursor on the table */\n  i16 iCol          /* The column that is wanted */\n){\n  Expr *pExpr = sqlite3Expr(db, TK_COLUMN, 0);\n  if( pExpr ){\n    pExpr->pTab = pTab;\n    pExpr->iTable = iCursor;\n    pExpr->iColumn = iCol;\n  }\n  return pExpr;\n}\n\n/*\n** This function is called to generate code executed when a row is deleted\n** from the parent table of foreign key constraint pFKey and, if pFKey is \n** deferred, when a row is inserted into the same table. When generating\n** code for an SQL UPDATE operation, this function may be called twice -\n** once to \"delete\" the old row and once to \"insert\" the new row.\n**\n** Parameter nIncr is passed -1 when inserting a row (as this may decrease\n** the number of FK violations in the db) or +1 when deleting one (as this\n** may increase the number of FK constraint problems).\n**\n** The code generated by this function scans through the rows in the child\n** table that correspond to the parent table row being deleted or inserted.\n** For each child row found, one of the following actions is taken:\n**\n**   Operation | FK type   | Action taken\n**   --------------------------------------------------------------------------\n**   DELETE      immediate   Increment the \"immediate constraint counter\".\n**                           Or, if the ON (UPDATE|DELETE) action is RESTRICT,\n**                           throw a \"FOREIGN KEY constraint failed\" exception.\n**\n**   INSERT      immediate   Decrement the \"immediate constraint counter\".\n**\n**   DELETE      deferred    Increment the \"deferred constraint counter\".\n**                           Or, if the ON (UPDATE|DELETE) action is RESTRICT,\n**                           throw a \"FOREIGN KEY constraint failed\" exception.\n**\n**   INSERT      deferred    Decrement the \"deferred constraint counter\".\n**\n** These operations are identified in the comment at the top of this file \n** (fkey.c) as \"I.2\" and \"D.2\".\n*/\nstatic void fkScanChildren(\n  Parse *pParse,                  /* Parse context */\n  SrcList *pSrc,                  /* The child table to be scanned */\n  Table *pTab,                    /* The parent table */\n  Index *pIdx,                    /* Index on parent covering the foreign key */\n  FKey *pFKey,                    /* The foreign key linking pSrc to pTab */\n  int *aiCol,                     /* Map from pIdx cols to child table cols */\n  int regData,                    /* Parent row data starts here */\n  int nIncr                       /* Amount to increment deferred counter by */\n){\n  sqlite3 *db = pParse->db;       /* Database handle */\n  int i;                          /* Iterator variable */\n  Expr *pWhere = 0;               /* WHERE clause to scan with */\n  NameContext sNameContext;       /* Context used to resolve WHERE clause */\n  WhereInfo *pWInfo;              /* Context used by sqlite3WhereXXX() */\n  int iFkIfZero = 0;              /* Address of OP_FkIfZero */\n  Vdbe *v = sqlite3GetVdbe(pParse);\n\n  assert( pIdx==0 || pIdx->pTable==pTab );\n  assert( pIdx==0 || pIdx->nKeyCol==pFKey->nCol );\n  assert( pIdx!=0 || pFKey->nCol==1 );\n  assert( pIdx!=0 || HasRowid(pTab) );\n\n  if( nIncr<0 ){\n    iFkIfZero = sqlite3VdbeAddOp2(v, OP_FkIfZero, pFKey->isDeferred, 0);\n    VdbeCoverage(v);\n  }\n\n  /* Create an Expr object representing an SQL expression like:\n  **\n  **   <parent-key1> = <child-key1> AND <parent-key2> = <child-key2> ...\n  **\n  ** The collation sequence used for the comparison should be that of\n  ** the parent key columns. The affinity of the parent key column should\n  ** be applied to each child key value before the comparison takes place.\n  */\n  for(i=0; i<pFKey->nCol; i++){\n    Expr *pLeft;                  /* Value from parent table row */\n    Expr *pRight;                 /* Column ref to child table */\n    Expr *pEq;                    /* Expression (pLeft = pRight) */\n    i16 iCol;                     /* Index of column in child table */ \n    const char *zCol;             /* Name of column in child table */\n\n    iCol = pIdx ? pIdx->aiColumn[i] : -1;\n    pLeft = exprTableRegister(pParse, pTab, regData, iCol);\n    iCol = aiCol ? aiCol[i] : pFKey->aCol[0].iFrom;\n    assert( iCol>=0 );\n    zCol = pFKey->pFrom->aCol[iCol].zName;\n    pRight = sqlite3Expr(db, TK_ID, zCol);\n    pEq = sqlite3PExpr(pParse, TK_EQ, pLeft, pRight);\n    pWhere = sqlite3ExprAnd(db, pWhere, pEq);\n  }\n\n  /* If the child table is the same as the parent table, then add terms\n  ** to the WHERE clause that prevent this entry from being scanned.\n  ** The added WHERE clause terms are like this:\n  **\n  **     $current_rowid!=rowid\n  **     NOT( $current_a==a AND $current_b==b AND ... )\n  **\n  ** The first form is used for rowid tables.  The second form is used\n  ** for WITHOUT ROWID tables.  In the second form, the primary key is\n  ** (a,b,...)\n  */\n  if( pTab==pFKey->pFrom && nIncr>0 ){\n    Expr *pNe;                    /* Expression (pLeft != pRight) */\n    Expr *pLeft;                  /* Value from parent table row */\n    Expr *pRight;                 /* Column ref to child table */\n    if( HasRowid(pTab) ){\n      pLeft = exprTableRegister(pParse, pTab, regData, -1);\n      pRight = exprTableColumn(db, pTab, pSrc->a[0].iCursor, -1);\n      pNe = sqlite3PExpr(pParse, TK_NE, pLeft, pRight);\n    }else{\n      Expr *pEq, *pAll = 0;\n      Index *pPk = sqlite3PrimaryKeyIndex(pTab);\n      assert( pIdx!=0 );\n      for(i=0; i<pPk->nKeyCol; i++){\n        i16 iCol = pIdx->aiColumn[i];\n        assert( iCol>=0 );\n        pLeft = exprTableRegister(pParse, pTab, regData, iCol);\n        pRight = exprTableColumn(db, pTab, pSrc->a[0].iCursor, iCol);\n        pEq = sqlite3PExpr(pParse, TK_EQ, pLeft, pRight);\n        pAll = sqlite3ExprAnd(db, pAll, pEq);\n      }\n      pNe = sqlite3PExpr(pParse, TK_NOT, pAll, 0);\n    }\n    pWhere = sqlite3ExprAnd(db, pWhere, pNe);\n  }\n\n  /* Resolve the references in the WHERE clause. */\n  memset(&sNameContext, 0, sizeof(NameContext));\n  sNameContext.pSrcList = pSrc;\n  sNameContext.pParse = pParse;\n  sqlite3ResolveExprNames(&sNameContext, pWhere);\n\n  /* Create VDBE to loop through the entries in pSrc that match the WHERE\n  ** clause. For each row found, increment either the deferred or immediate\n  ** foreign key constraint counter. */\n  if( pParse->nErr==0 ){\n    pWInfo = sqlite3WhereBegin(pParse, pSrc, pWhere, 0, 0, 0, 0);\n    sqlite3VdbeAddOp2(v, OP_FkCounter, pFKey->isDeferred, nIncr);\n    if( pWInfo ){\n      sqlite3WhereEnd(pWInfo);\n    }\n  }\n\n  /* Clean up the WHERE clause constructed above. */\n  sqlite3ExprDelete(db, pWhere);\n  if( iFkIfZero ){\n    sqlite3VdbeJumpHere(v, iFkIfZero);\n  }\n}\n\n/*\n** This function returns a linked list of FKey objects (connected by\n** FKey.pNextTo) holding all children of table pTab.  For example,\n** given the following schema:\n**\n**   CREATE TABLE t1(a PRIMARY KEY);\n**   CREATE TABLE t2(b REFERENCES t1(a);\n**\n** Calling this function with table \"t1\" as an argument returns a pointer\n** to the FKey structure representing the foreign key constraint on table\n** \"t2\". Calling this function with \"t2\" as the argument would return a\n** NULL pointer (as there are no FK constraints for which t2 is the parent\n** table).\n*/\nSQLITE_PRIVATE FKey *sqlite3FkReferences(Table *pTab){\n  return (FKey *)sqlite3HashFind(&pTab->pSchema->fkeyHash, pTab->zName);\n}\n\n/*\n** The second argument is a Trigger structure allocated by the \n** fkActionTrigger() routine. This function deletes the Trigger structure\n** and all of its sub-components.\n**\n** The Trigger structure or any of its sub-components may be allocated from\n** the lookaside buffer belonging to database handle dbMem.\n*/\nstatic void fkTriggerDelete(sqlite3 *dbMem, Trigger *p){\n  if( p ){\n    TriggerStep *pStep = p->step_list;\n    sqlite3ExprDelete(dbMem, pStep->pWhere);\n    sqlite3ExprListDelete(dbMem, pStep->pExprList);\n    sqlite3SelectDelete(dbMem, pStep->pSelect);\n    sqlite3ExprDelete(dbMem, p->pWhen);\n    sqlite3DbFree(dbMem, p);\n  }\n}\n\n/*\n** This function is called to generate code that runs when table pTab is\n** being dropped from the database. The SrcList passed as the second argument\n** to this function contains a single entry guaranteed to resolve to\n** table pTab.\n**\n** Normally, no code is required. However, if either\n**\n**   (a) The table is the parent table of a FK constraint, or\n**   (b) The table is the child table of a deferred FK constraint and it is\n**       determined at runtime that there are outstanding deferred FK \n**       constraint violations in the database,\n**\n** then the equivalent of \"DELETE FROM <tbl>\" is executed before dropping\n** the table from the database. Triggers are disabled while running this\n** DELETE, but foreign key actions are not.\n*/\nSQLITE_PRIVATE void sqlite3FkDropTable(Parse *pParse, SrcList *pName, Table *pTab){\n  sqlite3 *db = pParse->db;\n  if( (db->flags&SQLITE_ForeignKeys) && !IsVirtual(pTab) && !pTab->pSelect ){\n    int iSkip = 0;\n    Vdbe *v = sqlite3GetVdbe(pParse);\n\n    assert( v );                  /* VDBE has already been allocated */\n    if( sqlite3FkReferences(pTab)==0 ){\n      /* Search for a deferred foreign key constraint for which this table\n      ** is the child table. If one cannot be found, return without \n      ** generating any VDBE code. If one can be found, then jump over\n      ** the entire DELETE if there are no outstanding deferred constraints\n      ** when this statement is run.  */\n      FKey *p;\n      for(p=pTab->pFKey; p; p=p->pNextFrom){\n        if( p->isDeferred || (db->flags & SQLITE_DeferFKs) ) break;\n      }\n      if( !p ) return;\n      iSkip = sqlite3VdbeMakeLabel(v);\n      sqlite3VdbeAddOp2(v, OP_FkIfZero, 1, iSkip); VdbeCoverage(v);\n    }\n\n    pParse->disableTriggers = 1;\n    sqlite3DeleteFrom(pParse, sqlite3SrcListDup(db, pName, 0), 0, 0, 0);\n    pParse->disableTriggers = 0;\n\n    /* If the DELETE has generated immediate foreign key constraint \n    ** violations, halt the VDBE and return an error at this point, before\n    ** any modifications to the schema are made. This is because statement\n    ** transactions are not able to rollback schema changes.  \n    **\n    ** If the SQLITE_DeferFKs flag is set, then this is not required, as\n    ** the statement transaction will not be rolled back even if FK\n    ** constraints are violated.\n    */\n    if( (db->flags & SQLITE_DeferFKs)==0 ){\n      sqlite3VdbeAddOp2(v, OP_FkIfZero, 0, sqlite3VdbeCurrentAddr(v)+2);\n      VdbeCoverage(v);\n      sqlite3HaltConstraint(pParse, SQLITE_CONSTRAINT_FOREIGNKEY,\n          OE_Abort, 0, P4_STATIC, P5_ConstraintFK);\n    }\n\n    if( iSkip ){\n      sqlite3VdbeResolveLabel(v, iSkip);\n    }\n  }\n}\n\n\n/*\n** The second argument points to an FKey object representing a foreign key\n** for which pTab is the child table. An UPDATE statement against pTab\n** is currently being processed. For each column of the table that is \n** actually updated, the corresponding element in the aChange[] array\n** is zero or greater (if a column is unmodified the corresponding element\n** is set to -1). If the rowid column is modified by the UPDATE statement\n** the bChngRowid argument is non-zero.\n**\n** This function returns true if any of the columns that are part of the\n** child key for FK constraint *p are modified.\n*/\nstatic int fkChildIsModified(\n  Table *pTab,                    /* Table being updated */\n  FKey *p,                        /* Foreign key for which pTab is the child */\n  int *aChange,                   /* Array indicating modified columns */\n  int bChngRowid                  /* True if rowid is modified by this update */\n){\n  int i;\n  for(i=0; i<p->nCol; i++){\n    int iChildKey = p->aCol[i].iFrom;\n    if( aChange[iChildKey]>=0 ) return 1;\n    if( iChildKey==pTab->iPKey && bChngRowid ) return 1;\n  }\n  return 0;\n}\n\n/*\n** The second argument points to an FKey object representing a foreign key\n** for which pTab is the parent table. An UPDATE statement against pTab\n** is currently being processed. For each column of the table that is \n** actually updated, the corresponding element in the aChange[] array\n** is zero or greater (if a column is unmodified the corresponding element\n** is set to -1). If the rowid column is modified by the UPDATE statement\n** the bChngRowid argument is non-zero.\n**\n** This function returns true if any of the columns that are part of the\n** parent key for FK constraint *p are modified.\n*/\nstatic int fkParentIsModified(\n  Table *pTab, \n  FKey *p, \n  int *aChange, \n  int bChngRowid\n){\n  int i;\n  for(i=0; i<p->nCol; i++){\n    char *zKey = p->aCol[i].zCol;\n    int iKey;\n    for(iKey=0; iKey<pTab->nCol; iKey++){\n      if( aChange[iKey]>=0 || (iKey==pTab->iPKey && bChngRowid) ){\n        Column *pCol = &pTab->aCol[iKey];\n        if( zKey ){\n          if( 0==sqlite3StrICmp(pCol->zName, zKey) ) return 1;\n        }else if( pCol->colFlags & COLFLAG_PRIMKEY ){\n          return 1;\n        }\n      }\n    }\n  }\n  return 0;\n}\n\n/*\n** Return true if the parser passed as the first argument is being\n** used to code a trigger that is really a \"SET NULL\" action belonging\n** to trigger pFKey.\n*/\nstatic int isSetNullAction(Parse *pParse, FKey *pFKey){\n  Parse *pTop = sqlite3ParseToplevel(pParse);\n  if( pTop->pTriggerPrg ){\n    Trigger *p = pTop->pTriggerPrg->pTrigger;\n    if( (p==pFKey->apTrigger[0] && pFKey->aAction[0]==OE_SetNull)\n     || (p==pFKey->apTrigger[1] && pFKey->aAction[1]==OE_SetNull)\n    ){\n      return 1;\n    }\n  }\n  return 0;\n}\n\n/*\n** This function is called when inserting, deleting or updating a row of\n** table pTab to generate VDBE code to perform foreign key constraint \n** processing for the operation.\n**\n** For a DELETE operation, parameter regOld is passed the index of the\n** first register in an array of (pTab->nCol+1) registers containing the\n** rowid of the row being deleted, followed by each of the column values\n** of the row being deleted, from left to right. Parameter regNew is passed\n** zero in this case.\n**\n** For an INSERT operation, regOld is passed zero and regNew is passed the\n** first register of an array of (pTab->nCol+1) registers containing the new\n** row data.\n**\n** For an UPDATE operation, this function is called twice. Once before\n** the original record is deleted from the table using the calling convention\n** described for DELETE. Then again after the original record is deleted\n** but before the new record is inserted using the INSERT convention. \n*/\nSQLITE_PRIVATE void sqlite3FkCheck(\n  Parse *pParse,                  /* Parse context */\n  Table *pTab,                    /* Row is being deleted from this table */ \n  int regOld,                     /* Previous row data is stored here */\n  int regNew,                     /* New row data is stored here */\n  int *aChange,                   /* Array indicating UPDATEd columns (or 0) */\n  int bChngRowid                  /* True if rowid is UPDATEd */\n){\n  sqlite3 *db = pParse->db;       /* Database handle */\n  FKey *pFKey;                    /* Used to iterate through FKs */\n  int iDb;                        /* Index of database containing pTab */\n  const char *zDb;                /* Name of database containing pTab */\n  int isIgnoreErrors = pParse->disableTriggers;\n\n  /* Exactly one of regOld and regNew should be non-zero. */\n  assert( (regOld==0)!=(regNew==0) );\n\n  /* If foreign-keys are disabled, this function is a no-op. */\n  if( (db->flags&SQLITE_ForeignKeys)==0 ) return;\n\n  iDb = sqlite3SchemaToIndex(db, pTab->pSchema);\n  zDb = db->aDb[iDb].zDbSName;\n\n  /* Loop through all the foreign key constraints for which pTab is the\n  ** child table (the table that the foreign key definition is part of).  */\n  for(pFKey=pTab->pFKey; pFKey; pFKey=pFKey->pNextFrom){\n    Table *pTo;                   /* Parent table of foreign key pFKey */\n    Index *pIdx = 0;              /* Index on key columns in pTo */\n    int *aiFree = 0;\n    int *aiCol;\n    int iCol;\n    int i;\n    int bIgnore = 0;\n\n    if( aChange \n     && sqlite3_stricmp(pTab->zName, pFKey->zTo)!=0\n     && fkChildIsModified(pTab, pFKey, aChange, bChngRowid)==0 \n    ){\n      continue;\n    }\n\n    /* Find the parent table of this foreign key. Also find a unique index \n    ** on the parent key columns in the parent table. If either of these \n    ** schema items cannot be located, set an error in pParse and return \n    ** early.  */\n    if( pParse->disableTriggers ){\n      pTo = sqlite3FindTable(db, pFKey->zTo, zDb);\n    }else{\n      pTo = sqlite3LocateTable(pParse, 0, pFKey->zTo, zDb);\n    }\n    if( !pTo || sqlite3FkLocateIndex(pParse, pTo, pFKey, &pIdx, &aiFree) ){\n      assert( isIgnoreErrors==0 || (regOld!=0 && regNew==0) );\n      if( !isIgnoreErrors || db->mallocFailed ) return;\n      if( pTo==0 ){\n        /* If isIgnoreErrors is true, then a table is being dropped. In this\n        ** case SQLite runs a \"DELETE FROM xxx\" on the table being dropped\n        ** before actually dropping it in order to check FK constraints.\n        ** If the parent table of an FK constraint on the current table is\n        ** missing, behave as if it is empty. i.e. decrement the relevant\n        ** FK counter for each row of the current table with non-NULL keys.\n        */\n        Vdbe *v = sqlite3GetVdbe(pParse);\n        int iJump = sqlite3VdbeCurrentAddr(v) + pFKey->nCol + 1;\n        for(i=0; i<pFKey->nCol; i++){\n          int iReg = pFKey->aCol[i].iFrom + regOld + 1;\n          sqlite3VdbeAddOp2(v, OP_IsNull, iReg, iJump); VdbeCoverage(v);\n        }\n        sqlite3VdbeAddOp2(v, OP_FkCounter, pFKey->isDeferred, -1);\n      }\n      continue;\n    }\n    assert( pFKey->nCol==1 || (aiFree && pIdx) );\n\n    if( aiFree ){\n      aiCol = aiFree;\n    }else{\n      iCol = pFKey->aCol[0].iFrom;\n      aiCol = &iCol;\n    }\n    for(i=0; i<pFKey->nCol; i++){\n      if( aiCol[i]==pTab->iPKey ){\n        aiCol[i] = -1;\n      }\n      assert( pIdx==0 || pIdx->aiColumn[i]>=0 );\n#ifndef SQLITE_OMIT_AUTHORIZATION\n      /* Request permission to read the parent key columns. If the \n      ** authorization callback returns SQLITE_IGNORE, behave as if any\n      ** values read from the parent table are NULL. */\n      if( db->xAuth ){\n        int rcauth;\n        char *zCol = pTo->aCol[pIdx ? pIdx->aiColumn[i] : pTo->iPKey].zName;\n        rcauth = sqlite3AuthReadCol(pParse, pTo->zName, zCol, iDb);\n        bIgnore = (rcauth==SQLITE_IGNORE);\n      }\n#endif\n    }\n\n    /* Take a shared-cache advisory read-lock on the parent table. Allocate \n    ** a cursor to use to search the unique index on the parent key columns \n    ** in the parent table.  */\n    sqlite3TableLock(pParse, iDb, pTo->tnum, 0, pTo->zName);\n    pParse->nTab++;\n\n    if( regOld!=0 ){\n      /* A row is being removed from the child table. Search for the parent.\n      ** If the parent does not exist, removing the child row resolves an \n      ** outstanding foreign key constraint violation. */\n      fkLookupParent(pParse, iDb, pTo, pIdx, pFKey, aiCol, regOld, -1, bIgnore);\n    }\n    if( regNew!=0 && !isSetNullAction(pParse, pFKey) ){\n      /* A row is being added to the child table. If a parent row cannot\n      ** be found, adding the child row has violated the FK constraint. \n      **\n      ** If this operation is being performed as part of a trigger program\n      ** that is actually a \"SET NULL\" action belonging to this very \n      ** foreign key, then omit this scan altogether. As all child key\n      ** values are guaranteed to be NULL, it is not possible for adding\n      ** this row to cause an FK violation.  */\n      fkLookupParent(pParse, iDb, pTo, pIdx, pFKey, aiCol, regNew, +1, bIgnore);\n    }\n\n    sqlite3DbFree(db, aiFree);\n  }\n\n  /* Loop through all the foreign key constraints that refer to this table.\n  ** (the \"child\" constraints) */\n  for(pFKey = sqlite3FkReferences(pTab); pFKey; pFKey=pFKey->pNextTo){\n    Index *pIdx = 0;              /* Foreign key index for pFKey */\n    SrcList *pSrc;\n    int *aiCol = 0;\n\n    if( aChange && fkParentIsModified(pTab, pFKey, aChange, bChngRowid)==0 ){\n      continue;\n    }\n\n    if( !pFKey->isDeferred && !(db->flags & SQLITE_DeferFKs) \n     && !pParse->pToplevel && !pParse->isMultiWrite \n    ){\n      assert( regOld==0 && regNew!=0 );\n      /* Inserting a single row into a parent table cannot cause (or fix)\n      ** an immediate foreign key violation. So do nothing in this case.  */\n      continue;\n    }\n\n    if( sqlite3FkLocateIndex(pParse, pTab, pFKey, &pIdx, &aiCol) ){\n      if( !isIgnoreErrors || db->mallocFailed ) return;\n      continue;\n    }\n    assert( aiCol || pFKey->nCol==1 );\n\n    /* Create a SrcList structure containing the child table.  We need the\n    ** child table as a SrcList for sqlite3WhereBegin() */\n    pSrc = sqlite3SrcListAppend(db, 0, 0, 0);\n    if( pSrc ){\n      struct SrcList_item *pItem = pSrc->a;\n      pItem->pTab = pFKey->pFrom;\n      pItem->zName = pFKey->pFrom->zName;\n      pItem->pTab->nTabRef++;\n      pItem->iCursor = pParse->nTab++;\n  \n      if( regNew!=0 ){\n        fkScanChildren(pParse, pSrc, pTab, pIdx, pFKey, aiCol, regNew, -1);\n      }\n      if( regOld!=0 ){\n        int eAction = pFKey->aAction[aChange!=0];\n        fkScanChildren(pParse, pSrc, pTab, pIdx, pFKey, aiCol, regOld, 1);\n        /* If this is a deferred FK constraint, or a CASCADE or SET NULL\n        ** action applies, then any foreign key violations caused by\n        ** removing the parent key will be rectified by the action trigger.\n        ** So do not set the \"may-abort\" flag in this case.\n        **\n        ** Note 1: If the FK is declared \"ON UPDATE CASCADE\", then the\n        ** may-abort flag will eventually be set on this statement anyway\n        ** (when this function is called as part of processing the UPDATE\n        ** within the action trigger).\n        **\n        ** Note 2: At first glance it may seem like SQLite could simply omit\n        ** all OP_FkCounter related scans when either CASCADE or SET NULL\n        ** applies. The trouble starts if the CASCADE or SET NULL action \n        ** trigger causes other triggers or action rules attached to the \n        ** child table to fire. In these cases the fk constraint counters\n        ** might be set incorrectly if any OP_FkCounter related scans are \n        ** omitted.  */\n        if( !pFKey->isDeferred && eAction!=OE_Cascade && eAction!=OE_SetNull ){\n          sqlite3MayAbort(pParse);\n        }\n      }\n      pItem->zName = 0;\n      sqlite3SrcListDelete(db, pSrc);\n    }\n    sqlite3DbFree(db, aiCol);\n  }\n}\n\n#define COLUMN_MASK(x) (((x)>31) ? 0xffffffff : ((u32)1<<(x)))\n\n/*\n** This function is called before generating code to update or delete a \n** row contained in table pTab.\n*/\nSQLITE_PRIVATE u32 sqlite3FkOldmask(\n  Parse *pParse,                  /* Parse context */\n  Table *pTab                     /* Table being modified */\n){\n  u32 mask = 0;\n  if( pParse->db->flags&SQLITE_ForeignKeys ){\n    FKey *p;\n    int i;\n    for(p=pTab->pFKey; p; p=p->pNextFrom){\n      for(i=0; i<p->nCol; i++) mask |= COLUMN_MASK(p->aCol[i].iFrom);\n    }\n    for(p=sqlite3FkReferences(pTab); p; p=p->pNextTo){\n      Index *pIdx = 0;\n      sqlite3FkLocateIndex(pParse, pTab, p, &pIdx, 0);\n      if( pIdx ){\n        for(i=0; i<pIdx->nKeyCol; i++){\n          assert( pIdx->aiColumn[i]>=0 );\n          mask |= COLUMN_MASK(pIdx->aiColumn[i]);\n        }\n      }\n    }\n  }\n  return mask;\n}\n\n\n/*\n** This function is called before generating code to update or delete a \n** row contained in table pTab. If the operation is a DELETE, then\n** parameter aChange is passed a NULL value. For an UPDATE, aChange points\n** to an array of size N, where N is the number of columns in table pTab.\n** If the i'th column is not modified by the UPDATE, then the corresponding \n** entry in the aChange[] array is set to -1. If the column is modified,\n** the value is 0 or greater. Parameter chngRowid is set to true if the\n** UPDATE statement modifies the rowid fields of the table.\n**\n** If any foreign key processing will be required, this function returns\n** non-zero. If there is no foreign key related processing, this function \n** returns zero.\n**\n** For an UPDATE, this function returns 2 if:\n**\n**   * There are any FKs for which pTab is the child and the parent table, or\n**   * the UPDATE modifies one or more parent keys for which the action is\n**     not \"NO ACTION\" (i.e. is CASCADE, SET DEFAULT or SET NULL).\n**\n** Or, assuming some other foreign key processing is required, 1.\n*/\nSQLITE_PRIVATE int sqlite3FkRequired(\n  Parse *pParse,                  /* Parse context */\n  Table *pTab,                    /* Table being modified */\n  int *aChange,                   /* Non-NULL for UPDATE operations */\n  int chngRowid                   /* True for UPDATE that affects rowid */\n){\n  int eRet = 0;\n  if( pParse->db->flags&SQLITE_ForeignKeys ){\n    if( !aChange ){\n      /* A DELETE operation. Foreign key processing is required if the \n      ** table in question is either the child or parent table for any \n      ** foreign key constraint.  */\n      eRet = (sqlite3FkReferences(pTab) || pTab->pFKey);\n    }else{\n      /* This is an UPDATE. Foreign key processing is only required if the\n      ** operation modifies one or more child or parent key columns. */\n      FKey *p;\n\n      /* Check if any child key columns are being modified. */\n      for(p=pTab->pFKey; p; p=p->pNextFrom){\n        if( 0==sqlite3_stricmp(pTab->zName, p->zTo) ) return 2;\n        if( fkChildIsModified(pTab, p, aChange, chngRowid) ){\n          eRet = 1;\n        }\n      }\n\n      /* Check if any parent key columns are being modified. */\n      for(p=sqlite3FkReferences(pTab); p; p=p->pNextTo){\n        if( fkParentIsModified(pTab, p, aChange, chngRowid) ){\n          if( p->aAction[1]!=OE_None ) return 2;\n          eRet = 1;\n        }\n      }\n    }\n  }\n  return eRet;\n}\n\n/*\n** This function is called when an UPDATE or DELETE operation is being \n** compiled on table pTab, which is the parent table of foreign-key pFKey.\n** If the current operation is an UPDATE, then the pChanges parameter is\n** passed a pointer to the list of columns being modified. If it is a\n** DELETE, pChanges is passed a NULL pointer.\n**\n** It returns a pointer to a Trigger structure containing a trigger\n** equivalent to the ON UPDATE or ON DELETE action specified by pFKey.\n** If the action is \"NO ACTION\" or \"RESTRICT\", then a NULL pointer is\n** returned (these actions require no special handling by the triggers\n** sub-system, code for them is created by fkScanChildren()).\n**\n** For example, if pFKey is the foreign key and pTab is table \"p\" in \n** the following schema:\n**\n**   CREATE TABLE p(pk PRIMARY KEY);\n**   CREATE TABLE c(ck REFERENCES p ON DELETE CASCADE);\n**\n** then the returned trigger structure is equivalent to:\n**\n**   CREATE TRIGGER ... DELETE ON p BEGIN\n**     DELETE FROM c WHERE ck = old.pk;\n**   END;\n**\n** The returned pointer is cached as part of the foreign key object. It\n** is eventually freed along with the rest of the foreign key object by \n** sqlite3FkDelete().\n*/\nstatic Trigger *fkActionTrigger(\n  Parse *pParse,                  /* Parse context */\n  Table *pTab,                    /* Table being updated or deleted from */\n  FKey *pFKey,                    /* Foreign key to get action for */\n  ExprList *pChanges              /* Change-list for UPDATE, NULL for DELETE */\n){\n  sqlite3 *db = pParse->db;       /* Database handle */\n  int action;                     /* One of OE_None, OE_Cascade etc. */\n  Trigger *pTrigger;              /* Trigger definition to return */\n  int iAction = (pChanges!=0);    /* 1 for UPDATE, 0 for DELETE */\n\n  action = pFKey->aAction[iAction];\n  if( action==OE_Restrict && (db->flags & SQLITE_DeferFKs) ){\n    return 0;\n  }\n  pTrigger = pFKey->apTrigger[iAction];\n\n  if( action!=OE_None && !pTrigger ){\n    char const *zFrom;            /* Name of child table */\n    int nFrom;                    /* Length in bytes of zFrom */\n    Index *pIdx = 0;              /* Parent key index for this FK */\n    int *aiCol = 0;               /* child table cols -> parent key cols */\n    TriggerStep *pStep = 0;        /* First (only) step of trigger program */\n    Expr *pWhere = 0;             /* WHERE clause of trigger step */\n    ExprList *pList = 0;          /* Changes list if ON UPDATE CASCADE */\n    Select *pSelect = 0;          /* If RESTRICT, \"SELECT RAISE(...)\" */\n    int i;                        /* Iterator variable */\n    Expr *pWhen = 0;              /* WHEN clause for the trigger */\n\n    if( sqlite3FkLocateIndex(pParse, pTab, pFKey, &pIdx, &aiCol) ) return 0;\n    assert( aiCol || pFKey->nCol==1 );\n\n    for(i=0; i<pFKey->nCol; i++){\n      Token tOld = { \"old\", 3 };  /* Literal \"old\" token */\n      Token tNew = { \"new\", 3 };  /* Literal \"new\" token */\n      Token tFromCol;             /* Name of column in child table */\n      Token tToCol;               /* Name of column in parent table */\n      int iFromCol;               /* Idx of column in child table */\n      Expr *pEq;                  /* tFromCol = OLD.tToCol */\n\n      iFromCol = aiCol ? aiCol[i] : pFKey->aCol[0].iFrom;\n      assert( iFromCol>=0 );\n      assert( pIdx!=0 || (pTab->iPKey>=0 && pTab->iPKey<pTab->nCol) );\n      assert( pIdx==0 || pIdx->aiColumn[i]>=0 );\n      sqlite3TokenInit(&tToCol,\n                   pTab->aCol[pIdx ? pIdx->aiColumn[i] : pTab->iPKey].zName);\n      sqlite3TokenInit(&tFromCol, pFKey->pFrom->aCol[iFromCol].zName);\n\n      /* Create the expression \"OLD.zToCol = zFromCol\". It is important\n      ** that the \"OLD.zToCol\" term is on the LHS of the = operator, so\n      ** that the affinity and collation sequence associated with the\n      ** parent table are used for the comparison. */\n      pEq = sqlite3PExpr(pParse, TK_EQ,\n          sqlite3PExpr(pParse, TK_DOT, \n            sqlite3ExprAlloc(db, TK_ID, &tOld, 0),\n            sqlite3ExprAlloc(db, TK_ID, &tToCol, 0)),\n          sqlite3ExprAlloc(db, TK_ID, &tFromCol, 0)\n      );\n      pWhere = sqlite3ExprAnd(db, pWhere, pEq);\n\n      /* For ON UPDATE, construct the next term of the WHEN clause.\n      ** The final WHEN clause will be like this:\n      **\n      **    WHEN NOT(old.col1 IS new.col1 AND ... AND old.colN IS new.colN)\n      */\n      if( pChanges ){\n        pEq = sqlite3PExpr(pParse, TK_IS,\n            sqlite3PExpr(pParse, TK_DOT, \n              sqlite3ExprAlloc(db, TK_ID, &tOld, 0),\n              sqlite3ExprAlloc(db, TK_ID, &tToCol, 0)),\n            sqlite3PExpr(pParse, TK_DOT, \n              sqlite3ExprAlloc(db, TK_ID, &tNew, 0),\n              sqlite3ExprAlloc(db, TK_ID, &tToCol, 0))\n            );\n        pWhen = sqlite3ExprAnd(db, pWhen, pEq);\n      }\n  \n      if( action!=OE_Restrict && (action!=OE_Cascade || pChanges) ){\n        Expr *pNew;\n        if( action==OE_Cascade ){\n          pNew = sqlite3PExpr(pParse, TK_DOT, \n            sqlite3ExprAlloc(db, TK_ID, &tNew, 0),\n            sqlite3ExprAlloc(db, TK_ID, &tToCol, 0));\n        }else if( action==OE_SetDflt ){\n          Expr *pDflt = pFKey->pFrom->aCol[iFromCol].pDflt;\n          if( pDflt ){\n            pNew = sqlite3ExprDup(db, pDflt, 0);\n          }else{\n            pNew = sqlite3ExprAlloc(db, TK_NULL, 0, 0);\n          }\n        }else{\n          pNew = sqlite3ExprAlloc(db, TK_NULL, 0, 0);\n        }\n        pList = sqlite3ExprListAppend(pParse, pList, pNew);\n        sqlite3ExprListSetName(pParse, pList, &tFromCol, 0);\n      }\n    }\n    sqlite3DbFree(db, aiCol);\n\n    zFrom = pFKey->pFrom->zName;\n    nFrom = sqlite3Strlen30(zFrom);\n\n    if( action==OE_Restrict ){\n      Token tFrom;\n      Expr *pRaise; \n\n      tFrom.z = zFrom;\n      tFrom.n = nFrom;\n      pRaise = sqlite3Expr(db, TK_RAISE, \"FOREIGN KEY constraint failed\");\n      if( pRaise ){\n        pRaise->affinity = OE_Abort;\n      }\n      pSelect = sqlite3SelectNew(pParse, \n          sqlite3ExprListAppend(pParse, 0, pRaise),\n          sqlite3SrcListAppend(db, 0, &tFrom, 0),\n          pWhere,\n          0, 0, 0, 0, 0\n      );\n      pWhere = 0;\n    }\n\n    /* Disable lookaside memory allocation */\n    db->lookaside.bDisable++;\n\n    pTrigger = (Trigger *)sqlite3DbMallocZero(db, \n        sizeof(Trigger) +         /* struct Trigger */\n        sizeof(TriggerStep) +     /* Single step in trigger program */\n        nFrom + 1                 /* Space for pStep->zTarget */\n    );\n    if( pTrigger ){\n      pStep = pTrigger->step_list = (TriggerStep *)&pTrigger[1];\n      pStep->zTarget = (char *)&pStep[1];\n      memcpy((char *)pStep->zTarget, zFrom, nFrom);\n  \n      pStep->pWhere = sqlite3ExprDup(db, pWhere, EXPRDUP_REDUCE);\n      pStep->pExprList = sqlite3ExprListDup(db, pList, EXPRDUP_REDUCE);\n      pStep->pSelect = sqlite3SelectDup(db, pSelect, EXPRDUP_REDUCE);\n      if( pWhen ){\n        pWhen = sqlite3PExpr(pParse, TK_NOT, pWhen, 0);\n        pTrigger->pWhen = sqlite3ExprDup(db, pWhen, EXPRDUP_REDUCE);\n      }\n    }\n\n    /* Re-enable the lookaside buffer, if it was disabled earlier. */\n    db->lookaside.bDisable--;\n\n    sqlite3ExprDelete(db, pWhere);\n    sqlite3ExprDelete(db, pWhen);\n    sqlite3ExprListDelete(db, pList);\n    sqlite3SelectDelete(db, pSelect);\n    if( db->mallocFailed==1 ){\n      fkTriggerDelete(db, pTrigger);\n      return 0;\n    }\n    assert( pStep!=0 );\n\n    switch( action ){\n      case OE_Restrict:\n        pStep->op = TK_SELECT; \n        break;\n      case OE_Cascade: \n        if( !pChanges ){ \n          pStep->op = TK_DELETE; \n          break; \n        }\n      default:\n        pStep->op = TK_UPDATE;\n    }\n    pStep->pTrig = pTrigger;\n    pTrigger->pSchema = pTab->pSchema;\n    pTrigger->pTabSchema = pTab->pSchema;\n    pFKey->apTrigger[iAction] = pTrigger;\n    pTrigger->op = (pChanges ? TK_UPDATE : TK_DELETE);\n  }\n\n  return pTrigger;\n}\n\n/*\n** This function is called when deleting or updating a row to implement\n** any required CASCADE, SET NULL or SET DEFAULT actions.\n*/\nSQLITE_PRIVATE void sqlite3FkActions(\n  Parse *pParse,                  /* Parse context */\n  Table *pTab,                    /* Table being updated or deleted from */\n  ExprList *pChanges,             /* Change-list for UPDATE, NULL for DELETE */\n  int regOld,                     /* Address of array containing old row */\n  int *aChange,                   /* Array indicating UPDATEd columns (or 0) */\n  int bChngRowid                  /* True if rowid is UPDATEd */\n){\n  /* If foreign-key support is enabled, iterate through all FKs that \n  ** refer to table pTab. If there is an action associated with the FK \n  ** for this operation (either update or delete), invoke the associated \n  ** trigger sub-program.  */\n  if( pParse->db->flags&SQLITE_ForeignKeys ){\n    FKey *pFKey;                  /* Iterator variable */\n    for(pFKey = sqlite3FkReferences(pTab); pFKey; pFKey=pFKey->pNextTo){\n      if( aChange==0 || fkParentIsModified(pTab, pFKey, aChange, bChngRowid) ){\n        Trigger *pAct = fkActionTrigger(pParse, pTab, pFKey, pChanges);\n        if( pAct ){\n          sqlite3CodeRowTriggerDirect(pParse, pAct, pTab, regOld, OE_Abort, 0);\n        }\n      }\n    }\n  }\n}\n\n#endif /* ifndef SQLITE_OMIT_TRIGGER */\n\n/*\n** Free all memory associated with foreign key definitions attached to\n** table pTab. Remove the deleted foreign keys from the Schema.fkeyHash\n** hash table.\n*/\nSQLITE_PRIVATE void sqlite3FkDelete(sqlite3 *db, Table *pTab){\n  FKey *pFKey;                    /* Iterator variable */\n  FKey *pNext;                    /* Copy of pFKey->pNextFrom */\n\n  assert( db==0 || IsVirtual(pTab)\n         || sqlite3SchemaMutexHeld(db, 0, pTab->pSchema) );\n  for(pFKey=pTab->pFKey; pFKey; pFKey=pNext){\n\n    /* Remove the FK from the fkeyHash hash table. */\n    if( !db || db->pnBytesFreed==0 ){\n      if( pFKey->pPrevTo ){\n        pFKey->pPrevTo->pNextTo = pFKey->pNextTo;\n      }else{\n        void *p = (void *)pFKey->pNextTo;\n        const char *z = (p ? pFKey->pNextTo->zTo : pFKey->zTo);\n        sqlite3HashInsert(&pTab->pSchema->fkeyHash, z, p);\n      }\n      if( pFKey->pNextTo ){\n        pFKey->pNextTo->pPrevTo = pFKey->pPrevTo;\n      }\n    }\n\n    /* EV: R-30323-21917 Each foreign key constraint in SQLite is\n    ** classified as either immediate or deferred.\n    */\n    assert( pFKey->isDeferred==0 || pFKey->isDeferred==1 );\n\n    /* Delete any triggers created to implement actions for this FK. */\n#ifndef SQLITE_OMIT_TRIGGER\n    fkTriggerDelete(db, pFKey->apTrigger[0]);\n    fkTriggerDelete(db, pFKey->apTrigger[1]);\n#endif\n\n    pNext = pFKey->pNextFrom;\n    sqlite3DbFree(db, pFKey);\n  }\n}\n#endif /* ifndef SQLITE_OMIT_FOREIGN_KEY */\n\n/************** End of fkey.c ************************************************/\n/************** Begin file insert.c ******************************************/\n/*\n** 2001 September 15\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n*************************************************************************\n** This file contains C code routines that are called by the parser\n** to handle INSERT statements in SQLite.\n*/\n/* #include \"sqliteInt.h\" */\n\n/*\n** Generate code that will \n**\n**   (1) acquire a lock for table pTab then\n**   (2) open pTab as cursor iCur.\n**\n** If pTab is a WITHOUT ROWID table, then it is the PRIMARY KEY index\n** for that table that is actually opened.\n*/\nSQLITE_PRIVATE void sqlite3OpenTable(\n  Parse *pParse,  /* Generate code into this VDBE */\n  int iCur,       /* The cursor number of the table */\n  int iDb,        /* The database index in sqlite3.aDb[] */\n  Table *pTab,    /* The table to be opened */\n  int opcode      /* OP_OpenRead or OP_OpenWrite */\n){\n  Vdbe *v;\n  assert( !IsVirtual(pTab) );\n  v = sqlite3GetVdbe(pParse);\n  assert( opcode==OP_OpenWrite || opcode==OP_OpenRead );\n  sqlite3TableLock(pParse, iDb, pTab->tnum, \n                   (opcode==OP_OpenWrite)?1:0, pTab->zName);\n  if( HasRowid(pTab) ){\n    sqlite3VdbeAddOp4Int(v, opcode, iCur, pTab->tnum, iDb, pTab->nCol);\n    VdbeComment((v, \"%s\", pTab->zName));\n  }else{\n    Index *pPk = sqlite3PrimaryKeyIndex(pTab);\n    assert( pPk!=0 );\n    assert( pPk->tnum==pTab->tnum );\n    sqlite3VdbeAddOp3(v, opcode, iCur, pPk->tnum, iDb);\n    sqlite3VdbeSetP4KeyInfo(pParse, pPk);\n    VdbeComment((v, \"%s\", pTab->zName));\n  }\n}\n\n/*\n** Return a pointer to the column affinity string associated with index\n** pIdx. A column affinity string has one character for each column in \n** the table, according to the affinity of the column:\n**\n**  Character      Column affinity\n**  ------------------------------\n**  'A'            BLOB\n**  'B'            TEXT\n**  'C'            NUMERIC\n**  'D'            INTEGER\n**  'F'            REAL\n**\n** An extra 'D' is appended to the end of the string to cover the\n** rowid that appears as the last column in every index.\n**\n** Memory for the buffer containing the column index affinity string\n** is managed along with the rest of the Index structure. It will be\n** released when sqlite3DeleteIndex() is called.\n*/\nSQLITE_PRIVATE const char *sqlite3IndexAffinityStr(sqlite3 *db, Index *pIdx){\n  if( !pIdx->zColAff ){\n    /* The first time a column affinity string for a particular index is\n    ** required, it is allocated and populated here. It is then stored as\n    ** a member of the Index structure for subsequent use.\n    **\n    ** The column affinity string will eventually be deleted by\n    ** sqliteDeleteIndex() when the Index structure itself is cleaned\n    ** up.\n    */\n    int n;\n    Table *pTab = pIdx->pTable;\n    pIdx->zColAff = (char *)sqlite3DbMallocRaw(0, pIdx->nColumn+1);\n    if( !pIdx->zColAff ){\n      sqlite3OomFault(db);\n      return 0;\n    }\n    for(n=0; n<pIdx->nColumn; n++){\n      i16 x = pIdx->aiColumn[n];\n      if( x>=0 ){\n        pIdx->zColAff[n] = pTab->aCol[x].affinity;\n      }else if( x==XN_ROWID ){\n        pIdx->zColAff[n] = SQLITE_AFF_INTEGER;\n      }else{\n        char aff;\n        assert( x==XN_EXPR );\n        assert( pIdx->aColExpr!=0 );\n        aff = sqlite3ExprAffinity(pIdx->aColExpr->a[n].pExpr);\n        if( aff==0 ) aff = SQLITE_AFF_BLOB;\n        pIdx->zColAff[n] = aff;\n      }\n    }\n    pIdx->zColAff[n] = 0;\n  }\n \n  return pIdx->zColAff;\n}\n\n/*\n** Compute the affinity string for table pTab, if it has not already been\n** computed.  As an optimization, omit trailing SQLITE_AFF_BLOB affinities.\n**\n** If the affinity exists (if it is no entirely SQLITE_AFF_BLOB values) and\n** if iReg>0 then code an OP_Affinity opcode that will set the affinities\n** for register iReg and following.  Or if affinities exists and iReg==0,\n** then just set the P4 operand of the previous opcode (which should  be\n** an OP_MakeRecord) to the affinity string.\n**\n** A column affinity string has one character per column:\n**\n**  Character      Column affinity\n**  ------------------------------\n**  'A'            BLOB\n**  'B'            TEXT\n**  'C'            NUMERIC\n**  'D'            INTEGER\n**  'E'            REAL\n*/\nSQLITE_PRIVATE void sqlite3TableAffinity(Vdbe *v, Table *pTab, int iReg){\n  int i;\n  char *zColAff = pTab->zColAff;\n  if( zColAff==0 ){\n    sqlite3 *db = sqlite3VdbeDb(v);\n    zColAff = (char *)sqlite3DbMallocRaw(0, pTab->nCol+1);\n    if( !zColAff ){\n      sqlite3OomFault(db);\n      return;\n    }\n\n    for(i=0; i<pTab->nCol; i++){\n      zColAff[i] = pTab->aCol[i].affinity;\n    }\n    do{\n      zColAff[i--] = 0;\n    }while( i>=0 && zColAff[i]==SQLITE_AFF_BLOB );\n    pTab->zColAff = zColAff;\n  }\n  i = sqlite3Strlen30(zColAff);\n  if( i ){\n    if( iReg ){\n      sqlite3VdbeAddOp4(v, OP_Affinity, iReg, i, 0, zColAff, i);\n    }else{\n      sqlite3VdbeChangeP4(v, -1, zColAff, i);\n    }\n  }\n}\n\n/*\n** Return non-zero if the table pTab in database iDb or any of its indices\n** have been opened at any point in the VDBE program. This is used to see if \n** a statement of the form  \"INSERT INTO <iDb, pTab> SELECT ...\" can \n** run without using a temporary table for the results of the SELECT. \n*/\nstatic int readsTable(Parse *p, int iDb, Table *pTab){\n  Vdbe *v = sqlite3GetVdbe(p);\n  int i;\n  int iEnd = sqlite3VdbeCurrentAddr(v);\n#ifndef SQLITE_OMIT_VIRTUALTABLE\n  VTable *pVTab = IsVirtual(pTab) ? sqlite3GetVTable(p->db, pTab) : 0;\n#endif\n\n  for(i=1; i<iEnd; i++){\n    VdbeOp *pOp = sqlite3VdbeGetOp(v, i);\n    assert( pOp!=0 );\n    if( pOp->opcode==OP_OpenRead && pOp->p3==iDb ){\n      Index *pIndex;\n      int tnum = pOp->p2;\n      if( tnum==pTab->tnum ){\n        return 1;\n      }\n      for(pIndex=pTab->pIndex; pIndex; pIndex=pIndex->pNext){\n        if( tnum==pIndex->tnum ){\n          return 1;\n        }\n      }\n    }\n#ifndef SQLITE_OMIT_VIRTUALTABLE\n    if( pOp->opcode==OP_VOpen && pOp->p4.pVtab==pVTab ){\n      assert( pOp->p4.pVtab!=0 );\n      assert( pOp->p4type==P4_VTAB );\n      return 1;\n    }\n#endif\n  }\n  return 0;\n}\n\n#ifndef SQLITE_OMIT_AUTOINCREMENT\n/*\n** Locate or create an AutoincInfo structure associated with table pTab\n** which is in database iDb.  Return the register number for the register\n** that holds the maximum rowid.  Return zero if pTab is not an AUTOINCREMENT\n** table.  (Also return zero when doing a VACUUM since we do not want to\n** update the AUTOINCREMENT counters during a VACUUM.)\n**\n** There is at most one AutoincInfo structure per table even if the\n** same table is autoincremented multiple times due to inserts within\n** triggers.  A new AutoincInfo structure is created if this is the\n** first use of table pTab.  On 2nd and subsequent uses, the original\n** AutoincInfo structure is used.\n**\n** Three memory locations are allocated:\n**\n**   (1)  Register to hold the name of the pTab table.\n**   (2)  Register to hold the maximum ROWID of pTab.\n**   (3)  Register to hold the rowid in sqlite_sequence of pTab\n**\n** The 2nd register is the one that is returned.  That is all the\n** insert routine needs to know about.\n*/\nstatic int autoIncBegin(\n  Parse *pParse,      /* Parsing context */\n  int iDb,            /* Index of the database holding pTab */\n  Table *pTab         /* The table we are writing to */\n){\n  int memId = 0;      /* Register holding maximum rowid */\n  if( (pTab->tabFlags & TF_Autoincrement)!=0\n   && (pParse->db->mDbFlags & DBFLAG_Vacuum)==0\n  ){\n    Parse *pToplevel = sqlite3ParseToplevel(pParse);\n    AutoincInfo *pInfo;\n\n    pInfo = pToplevel->pAinc;\n    while( pInfo && pInfo->pTab!=pTab ){ pInfo = pInfo->pNext; }\n    if( pInfo==0 ){\n      pInfo = sqlite3DbMallocRawNN(pParse->db, sizeof(*pInfo));\n      if( pInfo==0 ) return 0;\n      pInfo->pNext = pToplevel->pAinc;\n      pToplevel->pAinc = pInfo;\n      pInfo->pTab = pTab;\n      pInfo->iDb = iDb;\n      pToplevel->nMem++;                  /* Register to hold name of table */\n      pInfo->regCtr = ++pToplevel->nMem;  /* Max rowid register */\n      pToplevel->nMem++;                  /* Rowid in sqlite_sequence */\n    }\n    memId = pInfo->regCtr;\n  }\n  return memId;\n}\n\n/*\n** This routine generates code that will initialize all of the\n** register used by the autoincrement tracker.  \n*/\nSQLITE_PRIVATE void sqlite3AutoincrementBegin(Parse *pParse){\n  AutoincInfo *p;            /* Information about an AUTOINCREMENT */\n  sqlite3 *db = pParse->db;  /* The database connection */\n  Db *pDb;                   /* Database only autoinc table */\n  int memId;                 /* Register holding max rowid */\n  Vdbe *v = pParse->pVdbe;   /* VDBE under construction */\n\n  /* This routine is never called during trigger-generation.  It is\n  ** only called from the top-level */\n  assert( pParse->pTriggerTab==0 );\n  assert( sqlite3IsToplevel(pParse) );\n\n  assert( v );   /* We failed long ago if this is not so */\n  for(p = pParse->pAinc; p; p = p->pNext){\n    static const int iLn = VDBE_OFFSET_LINENO(2);\n    static const VdbeOpList autoInc[] = {\n      /* 0  */ {OP_Null,    0,  0, 0},\n      /* 1  */ {OP_Rewind,  0,  9, 0},\n      /* 2  */ {OP_Column,  0,  0, 0},\n      /* 3  */ {OP_Ne,      0,  7, 0},\n      /* 4  */ {OP_Rowid,   0,  0, 0},\n      /* 5  */ {OP_Column,  0,  1, 0},\n      /* 6  */ {OP_Goto,    0,  9, 0},\n      /* 7  */ {OP_Next,    0,  2, 0},\n      /* 8  */ {OP_Integer, 0,  0, 0},\n      /* 9  */ {OP_Close,   0,  0, 0} \n    };\n    VdbeOp *aOp;\n    pDb = &db->aDb[p->iDb];\n    memId = p->regCtr;\n    assert( sqlite3SchemaMutexHeld(db, 0, pDb->pSchema) );\n    sqlite3OpenTable(pParse, 0, p->iDb, pDb->pSchema->pSeqTab, OP_OpenRead);\n    sqlite3VdbeLoadString(v, memId-1, p->pTab->zName);\n    aOp = sqlite3VdbeAddOpList(v, ArraySize(autoInc), autoInc, iLn);\n    if( aOp==0 ) break;\n    aOp[0].p2 = memId;\n    aOp[0].p3 = memId+1;\n    aOp[2].p3 = memId;\n    aOp[3].p1 = memId-1;\n    aOp[3].p3 = memId;\n    aOp[3].p5 = SQLITE_JUMPIFNULL;\n    aOp[4].p2 = memId+1;\n    aOp[5].p3 = memId;\n    aOp[8].p2 = memId;\n  }\n}\n\n/*\n** Update the maximum rowid for an autoincrement calculation.\n**\n** This routine should be called when the regRowid register holds a\n** new rowid that is about to be inserted.  If that new rowid is\n** larger than the maximum rowid in the memId memory cell, then the\n** memory cell is updated.\n*/\nstatic void autoIncStep(Parse *pParse, int memId, int regRowid){\n  if( memId>0 ){\n    sqlite3VdbeAddOp2(pParse->pVdbe, OP_MemMax, memId, regRowid);\n  }\n}\n\n/*\n** This routine generates the code needed to write autoincrement\n** maximum rowid values back into the sqlite_sequence register.\n** Every statement that might do an INSERT into an autoincrement\n** table (either directly or through triggers) needs to call this\n** routine just before the \"exit\" code.\n*/\nstatic SQLITE_NOINLINE void autoIncrementEnd(Parse *pParse){\n  AutoincInfo *p;\n  Vdbe *v = pParse->pVdbe;\n  sqlite3 *db = pParse->db;\n\n  assert( v );\n  for(p = pParse->pAinc; p; p = p->pNext){\n    static const int iLn = VDBE_OFFSET_LINENO(2);\n    static const VdbeOpList autoIncEnd[] = {\n      /* 0 */ {OP_NotNull,     0, 2, 0},\n      /* 1 */ {OP_NewRowid,    0, 0, 0},\n      /* 2 */ {OP_MakeRecord,  0, 2, 0},\n      /* 3 */ {OP_Insert,      0, 0, 0},\n      /* 4 */ {OP_Close,       0, 0, 0}\n    };\n    VdbeOp *aOp;\n    Db *pDb = &db->aDb[p->iDb];\n    int iRec;\n    int memId = p->regCtr;\n\n    iRec = sqlite3GetTempReg(pParse);\n    assert( sqlite3SchemaMutexHeld(db, 0, pDb->pSchema) );\n    sqlite3OpenTable(pParse, 0, p->iDb, pDb->pSchema->pSeqTab, OP_OpenWrite);\n    aOp = sqlite3VdbeAddOpList(v, ArraySize(autoIncEnd), autoIncEnd, iLn);\n    if( aOp==0 ) break;\n    aOp[0].p1 = memId+1;\n    aOp[1].p2 = memId+1;\n    aOp[2].p1 = memId-1;\n    aOp[2].p3 = iRec;\n    aOp[3].p2 = iRec;\n    aOp[3].p3 = memId+1;\n    aOp[3].p5 = OPFLAG_APPEND;\n    sqlite3ReleaseTempReg(pParse, iRec);\n  }\n}\nSQLITE_PRIVATE void sqlite3AutoincrementEnd(Parse *pParse){\n  if( pParse->pAinc ) autoIncrementEnd(pParse);\n}\n#else\n/*\n** If SQLITE_OMIT_AUTOINCREMENT is defined, then the three routines\n** above are all no-ops\n*/\n# define autoIncBegin(A,B,C) (0)\n# define autoIncStep(A,B,C)\n#endif /* SQLITE_OMIT_AUTOINCREMENT */\n\n\n/* Forward declaration */\nstatic int xferOptimization(\n  Parse *pParse,        /* Parser context */\n  Table *pDest,         /* The table we are inserting into */\n  Select *pSelect,      /* A SELECT statement to use as the data source */\n  int onError,          /* How to handle constraint errors */\n  int iDbDest           /* The database of pDest */\n);\n\n/*\n** This routine is called to handle SQL of the following forms:\n**\n**    insert into TABLE (IDLIST) values(EXPRLIST),(EXPRLIST),...\n**    insert into TABLE (IDLIST) select\n**    insert into TABLE (IDLIST) default values\n**\n** The IDLIST following the table name is always optional.  If omitted,\n** then a list of all (non-hidden) columns for the table is substituted.\n** The IDLIST appears in the pColumn parameter.  pColumn is NULL if IDLIST\n** is omitted.\n**\n** For the pSelect parameter holds the values to be inserted for the\n** first two forms shown above.  A VALUES clause is really just short-hand\n** for a SELECT statement that omits the FROM clause and everything else\n** that follows.  If the pSelect parameter is NULL, that means that the\n** DEFAULT VALUES form of the INSERT statement is intended.\n**\n** The code generated follows one of four templates.  For a simple\n** insert with data coming from a single-row VALUES clause, the code executes\n** once straight down through.  Pseudo-code follows (we call this\n** the \"1st template\"):\n**\n**         open write cursor to <table> and its indices\n**         put VALUES clause expressions into registers\n**         write the resulting record into <table>\n**         cleanup\n**\n** The three remaining templates assume the statement is of the form\n**\n**   INSERT INTO <table> SELECT ...\n**\n** If the SELECT clause is of the restricted form \"SELECT * FROM <table2>\" -\n** in other words if the SELECT pulls all columns from a single table\n** and there is no WHERE or LIMIT or GROUP BY or ORDER BY clauses, and\n** if <table2> and <table1> are distinct tables but have identical\n** schemas, including all the same indices, then a special optimization\n** is invoked that copies raw records from <table2> over to <table1>.\n** See the xferOptimization() function for the implementation of this\n** template.  This is the 2nd template.\n**\n**         open a write cursor to <table>\n**         open read cursor on <table2>\n**         transfer all records in <table2> over to <table>\n**         close cursors\n**         foreach index on <table>\n**           open a write cursor on the <table> index\n**           open a read cursor on the corresponding <table2> index\n**           transfer all records from the read to the write cursors\n**           close cursors\n**         end foreach\n**\n** The 3rd template is for when the second template does not apply\n** and the SELECT clause does not read from <table> at any time.\n** The generated code follows this template:\n**\n**         X <- A\n**         goto B\n**      A: setup for the SELECT\n**         loop over the rows in the SELECT\n**           load values into registers R..R+n\n**           yield X\n**         end loop\n**         cleanup after the SELECT\n**         end-coroutine X\n**      B: open write cursor to <table> and its indices\n**      C: yield X, at EOF goto D\n**         insert the select result into <table> from R..R+n\n**         goto C\n**      D: cleanup\n**\n** The 4th template is used if the insert statement takes its\n** values from a SELECT but the data is being inserted into a table\n** that is also read as part of the SELECT.  In the third form,\n** we have to use an intermediate table to store the results of\n** the select.  The template is like this:\n**\n**         X <- A\n**         goto B\n**      A: setup for the SELECT\n**         loop over the tables in the SELECT\n**           load value into register R..R+n\n**           yield X\n**         end loop\n**         cleanup after the SELECT\n**         end co-routine R\n**      B: open temp table\n**      L: yield X, at EOF goto M\n**         insert row from R..R+n into temp table\n**         goto L\n**      M: open write cursor to <table> and its indices\n**         rewind temp table\n**      C: loop over rows of intermediate table\n**           transfer values form intermediate table into <table>\n**         end loop\n**      D: cleanup\n*/\nSQLITE_PRIVATE void sqlite3Insert(\n  Parse *pParse,        /* Parser context */\n  SrcList *pTabList,    /* Name of table into which we are inserting */\n  Select *pSelect,      /* A SELECT statement to use as the data source */\n  IdList *pColumn,      /* Column names corresponding to IDLIST. */\n  int onError           /* How to handle constraint errors */\n){\n  sqlite3 *db;          /* The main database structure */\n  Table *pTab;          /* The table to insert into.  aka TABLE */\n  int i, j;             /* Loop counters */\n  Vdbe *v;              /* Generate code into this virtual machine */\n  Index *pIdx;          /* For looping over indices of the table */\n  int nColumn;          /* Number of columns in the data */\n  int nHidden = 0;      /* Number of hidden columns if TABLE is virtual */\n  int iDataCur = 0;     /* VDBE cursor that is the main data repository */\n  int iIdxCur = 0;      /* First index cursor */\n  int ipkColumn = -1;   /* Column that is the INTEGER PRIMARY KEY */\n  int endOfLoop;        /* Label for the end of the insertion loop */\n  int srcTab = 0;       /* Data comes from this temporary cursor if >=0 */\n  int addrInsTop = 0;   /* Jump to label \"D\" */\n  int addrCont = 0;     /* Top of insert loop. Label \"C\" in templates 3 and 4 */\n  SelectDest dest;      /* Destination for SELECT on rhs of INSERT */\n  int iDb;              /* Index of database holding TABLE */\n  u8 useTempTable = 0;  /* Store SELECT results in intermediate table */\n  u8 appendFlag = 0;    /* True if the insert is likely to be an append */\n  u8 withoutRowid;      /* 0 for normal table.  1 for WITHOUT ROWID table */\n  u8 bIdListInOrder;    /* True if IDLIST is in table order */\n  ExprList *pList = 0;  /* List of VALUES() to be inserted  */\n\n  /* Register allocations */\n  int regFromSelect = 0;/* Base register for data coming from SELECT */\n  int regAutoinc = 0;   /* Register holding the AUTOINCREMENT counter */\n  int regRowCount = 0;  /* Memory cell used for the row counter */\n  int regIns;           /* Block of regs holding rowid+data being inserted */\n  int regRowid;         /* registers holding insert rowid */\n  int regData;          /* register holding first column to insert */\n  int *aRegIdx = 0;     /* One register allocated to each index */\n\n#ifndef SQLITE_OMIT_TRIGGER\n  int isView;                 /* True if attempting to insert into a view */\n  Trigger *pTrigger;          /* List of triggers on pTab, if required */\n  int tmask;                  /* Mask of trigger times */\n#endif\n\n  db = pParse->db;\n  if( pParse->nErr || db->mallocFailed ){\n    goto insert_cleanup;\n  }\n  dest.iSDParm = 0;  /* Suppress a harmless compiler warning */\n\n  /* If the Select object is really just a simple VALUES() list with a\n  ** single row (the common case) then keep that one row of values\n  ** and discard the other (unused) parts of the pSelect object\n  */\n  if( pSelect && (pSelect->selFlags & SF_Values)!=0 && pSelect->pPrior==0 ){\n    pList = pSelect->pEList;\n    pSelect->pEList = 0;\n    sqlite3SelectDelete(db, pSelect);\n    pSelect = 0;\n  }\n\n  /* Locate the table into which we will be inserting new information.\n  */\n  assert( pTabList->nSrc==1 );\n  pTab = sqlite3SrcListLookup(pParse, pTabList);\n  if( pTab==0 ){\n    goto insert_cleanup;\n  }\n  iDb = sqlite3SchemaToIndex(db, pTab->pSchema);\n  assert( iDb<db->nDb );\n  if( sqlite3AuthCheck(pParse, SQLITE_INSERT, pTab->zName, 0,\n                       db->aDb[iDb].zDbSName) ){\n    goto insert_cleanup;\n  }\n  withoutRowid = !HasRowid(pTab);\n\n  /* Figure out if we have any triggers and if the table being\n  ** inserted into is a view\n  */\n#ifndef SQLITE_OMIT_TRIGGER\n  pTrigger = sqlite3TriggersExist(pParse, pTab, TK_INSERT, 0, &tmask);\n  isView = pTab->pSelect!=0;\n#else\n# define pTrigger 0\n# define tmask 0\n# define isView 0\n#endif\n#ifdef SQLITE_OMIT_VIEW\n# undef isView\n# define isView 0\n#endif\n  assert( (pTrigger && tmask) || (pTrigger==0 && tmask==0) );\n\n  /* If pTab is really a view, make sure it has been initialized.\n  ** ViewGetColumnNames() is a no-op if pTab is not a view.\n  */\n  if( sqlite3ViewGetColumnNames(pParse, pTab) ){\n    goto insert_cleanup;\n  }\n\n  /* Cannot insert into a read-only table.\n  */\n  if( sqlite3IsReadOnly(pParse, pTab, tmask) ){\n    goto insert_cleanup;\n  }\n\n  /* Allocate a VDBE\n  */\n  v = sqlite3GetVdbe(pParse);\n  if( v==0 ) goto insert_cleanup;\n  if( pParse->nested==0 ) sqlite3VdbeCountChanges(v);\n  sqlite3BeginWriteOperation(pParse, pSelect || pTrigger, iDb);\n\n#ifndef SQLITE_OMIT_XFER_OPT\n  /* If the statement is of the form\n  **\n  **       INSERT INTO <table1> SELECT * FROM <table2>;\n  **\n  ** Then special optimizations can be applied that make the transfer\n  ** very fast and which reduce fragmentation of indices.\n  **\n  ** This is the 2nd template.\n  */\n  if( pColumn==0 && xferOptimization(pParse, pTab, pSelect, onError, iDb) ){\n    assert( !pTrigger );\n    assert( pList==0 );\n    goto insert_end;\n  }\n#endif /* SQLITE_OMIT_XFER_OPT */\n\n  /* If this is an AUTOINCREMENT table, look up the sequence number in the\n  ** sqlite_sequence table and store it in memory cell regAutoinc.\n  */\n  regAutoinc = autoIncBegin(pParse, iDb, pTab);\n\n  /* Allocate registers for holding the rowid of the new row,\n  ** the content of the new row, and the assembled row record.\n  */\n  regRowid = regIns = pParse->nMem+1;\n  pParse->nMem += pTab->nCol + 1;\n  if( IsVirtual(pTab) ){\n    regRowid++;\n    pParse->nMem++;\n  }\n  regData = regRowid+1;\n\n  /* If the INSERT statement included an IDLIST term, then make sure\n  ** all elements of the IDLIST really are columns of the table and \n  ** remember the column indices.\n  **\n  ** If the table has an INTEGER PRIMARY KEY column and that column\n  ** is named in the IDLIST, then record in the ipkColumn variable\n  ** the index into IDLIST of the primary key column.  ipkColumn is\n  ** the index of the primary key as it appears in IDLIST, not as\n  ** is appears in the original table.  (The index of the INTEGER\n  ** PRIMARY KEY in the original table is pTab->iPKey.)\n  */\n  bIdListInOrder = (pTab->tabFlags & TF_OOOHidden)==0;\n  if( pColumn ){\n    for(i=0; i<pColumn->nId; i++){\n      pColumn->a[i].idx = -1;\n    }\n    for(i=0; i<pColumn->nId; i++){\n      for(j=0; j<pTab->nCol; j++){\n        if( sqlite3StrICmp(pColumn->a[i].zName, pTab->aCol[j].zName)==0 ){\n          pColumn->a[i].idx = j;\n          if( i!=j ) bIdListInOrder = 0;\n          if( j==pTab->iPKey ){\n            ipkColumn = i;  assert( !withoutRowid );\n          }\n          break;\n        }\n      }\n      if( j>=pTab->nCol ){\n        if( sqlite3IsRowid(pColumn->a[i].zName) && !withoutRowid ){\n          ipkColumn = i;\n          bIdListInOrder = 0;\n        }else{\n          sqlite3ErrorMsg(pParse, \"table %S has no column named %s\",\n              pTabList, 0, pColumn->a[i].zName);\n          pParse->checkSchema = 1;\n          goto insert_cleanup;\n        }\n      }\n    }\n  }\n\n  /* Figure out how many columns of data are supplied.  If the data\n  ** is coming from a SELECT statement, then generate a co-routine that\n  ** produces a single row of the SELECT on each invocation.  The\n  ** co-routine is the common header to the 3rd and 4th templates.\n  */\n  if( pSelect ){\n    /* Data is coming from a SELECT or from a multi-row VALUES clause.\n    ** Generate a co-routine to run the SELECT. */\n    int regYield;       /* Register holding co-routine entry-point */\n    int addrTop;        /* Top of the co-routine */\n    int rc;             /* Result code */\n\n    regYield = ++pParse->nMem;\n    addrTop = sqlite3VdbeCurrentAddr(v) + 1;\n    sqlite3VdbeAddOp3(v, OP_InitCoroutine, regYield, 0, addrTop);\n    sqlite3SelectDestInit(&dest, SRT_Coroutine, regYield);\n    dest.iSdst = bIdListInOrder ? regData : 0;\n    dest.nSdst = pTab->nCol;\n    rc = sqlite3Select(pParse, pSelect, &dest);\n    regFromSelect = dest.iSdst;\n    if( rc || db->mallocFailed || pParse->nErr ) goto insert_cleanup;\n    sqlite3VdbeEndCoroutine(v, regYield);\n    sqlite3VdbeJumpHere(v, addrTop - 1);                       /* label B: */\n    assert( pSelect->pEList );\n    nColumn = pSelect->pEList->nExpr;\n\n    /* Set useTempTable to TRUE if the result of the SELECT statement\n    ** should be written into a temporary table (template 4).  Set to\n    ** FALSE if each output row of the SELECT can be written directly into\n    ** the destination table (template 3).\n    **\n    ** A temp table must be used if the table being updated is also one\n    ** of the tables being read by the SELECT statement.  Also use a \n    ** temp table in the case of row triggers.\n    */\n    if( pTrigger || readsTable(pParse, iDb, pTab) ){\n      useTempTable = 1;\n    }\n\n    if( useTempTable ){\n      /* Invoke the coroutine to extract information from the SELECT\n      ** and add it to a transient table srcTab.  The code generated\n      ** here is from the 4th template:\n      **\n      **      B: open temp table\n      **      L: yield X, goto M at EOF\n      **         insert row from R..R+n into temp table\n      **         goto L\n      **      M: ...\n      */\n      int regRec;          /* Register to hold packed record */\n      int regTempRowid;    /* Register to hold temp table ROWID */\n      int addrL;           /* Label \"L\" */\n\n      srcTab = pParse->nTab++;\n      regRec = sqlite3GetTempReg(pParse);\n      regTempRowid = sqlite3GetTempReg(pParse);\n      sqlite3VdbeAddOp2(v, OP_OpenEphemeral, srcTab, nColumn);\n      addrL = sqlite3VdbeAddOp1(v, OP_Yield, dest.iSDParm); VdbeCoverage(v);\n      sqlite3VdbeAddOp3(v, OP_MakeRecord, regFromSelect, nColumn, regRec);\n      sqlite3VdbeAddOp2(v, OP_NewRowid, srcTab, regTempRowid);\n      sqlite3VdbeAddOp3(v, OP_Insert, srcTab, regRec, regTempRowid);\n      sqlite3VdbeGoto(v, addrL);\n      sqlite3VdbeJumpHere(v, addrL);\n      sqlite3ReleaseTempReg(pParse, regRec);\n      sqlite3ReleaseTempReg(pParse, regTempRowid);\n    }\n  }else{\n    /* This is the case if the data for the INSERT is coming from a \n    ** single-row VALUES clause\n    */\n    NameContext sNC;\n    memset(&sNC, 0, sizeof(sNC));\n    sNC.pParse = pParse;\n    srcTab = -1;\n    assert( useTempTable==0 );\n    if( pList ){\n      nColumn = pList->nExpr;\n      if( sqlite3ResolveExprListNames(&sNC, pList) ){\n        goto insert_cleanup;\n      }\n    }else{\n      nColumn = 0;\n    }\n  }\n\n  /* If there is no IDLIST term but the table has an integer primary\n  ** key, the set the ipkColumn variable to the integer primary key \n  ** column index in the original table definition.\n  */\n  if( pColumn==0 && nColumn>0 ){\n    ipkColumn = pTab->iPKey;\n  }\n\n  /* Make sure the number of columns in the source data matches the number\n  ** of columns to be inserted into the table.\n  */\n  for(i=0; i<pTab->nCol; i++){\n    nHidden += (IsHiddenColumn(&pTab->aCol[i]) ? 1 : 0);\n  }\n  if( pColumn==0 && nColumn && nColumn!=(pTab->nCol-nHidden) ){\n    sqlite3ErrorMsg(pParse, \n       \"table %S has %d columns but %d values were supplied\",\n       pTabList, 0, pTab->nCol-nHidden, nColumn);\n    goto insert_cleanup;\n  }\n  if( pColumn!=0 && nColumn!=pColumn->nId ){\n    sqlite3ErrorMsg(pParse, \"%d values for %d columns\", nColumn, pColumn->nId);\n    goto insert_cleanup;\n  }\n    \n  /* Initialize the count of rows to be inserted\n  */\n  if( db->flags & SQLITE_CountRows ){\n    regRowCount = ++pParse->nMem;\n    sqlite3VdbeAddOp2(v, OP_Integer, 0, regRowCount);\n  }\n\n  /* If this is not a view, open the table and and all indices */\n  if( !isView ){\n    int nIdx;\n    nIdx = sqlite3OpenTableAndIndices(pParse, pTab, OP_OpenWrite, 0, -1, 0,\n                                      &iDataCur, &iIdxCur);\n    aRegIdx = sqlite3DbMallocRawNN(db, sizeof(int)*(nIdx+1));\n    if( aRegIdx==0 ){\n      goto insert_cleanup;\n    }\n    for(i=0, pIdx=pTab->pIndex; i<nIdx; pIdx=pIdx->pNext, i++){\n      assert( pIdx );\n      aRegIdx[i] = ++pParse->nMem;\n      pParse->nMem += pIdx->nColumn;\n    }\n  }\n\n  /* This is the top of the main insertion loop */\n  if( useTempTable ){\n    /* This block codes the top of loop only.  The complete loop is the\n    ** following pseudocode (template 4):\n    **\n    **         rewind temp table, if empty goto D\n    **      C: loop over rows of intermediate table\n    **           transfer values form intermediate table into <table>\n    **         end loop\n    **      D: ...\n    */\n    addrInsTop = sqlite3VdbeAddOp1(v, OP_Rewind, srcTab); VdbeCoverage(v);\n    addrCont = sqlite3VdbeCurrentAddr(v);\n  }else if( pSelect ){\n    /* This block codes the top of loop only.  The complete loop is the\n    ** following pseudocode (template 3):\n    **\n    **      C: yield X, at EOF goto D\n    **         insert the select result into <table> from R..R+n\n    **         goto C\n    **      D: ...\n    */\n    addrInsTop = addrCont = sqlite3VdbeAddOp1(v, OP_Yield, dest.iSDParm);\n    VdbeCoverage(v);\n  }\n\n  /* Run the BEFORE and INSTEAD OF triggers, if there are any\n  */\n  endOfLoop = sqlite3VdbeMakeLabel(v);\n  if( tmask & TRIGGER_BEFORE ){\n    int regCols = sqlite3GetTempRange(pParse, pTab->nCol+1);\n\n    /* build the NEW.* reference row.  Note that if there is an INTEGER\n    ** PRIMARY KEY into which a NULL is being inserted, that NULL will be\n    ** translated into a unique ID for the row.  But on a BEFORE trigger,\n    ** we do not know what the unique ID will be (because the insert has\n    ** not happened yet) so we substitute a rowid of -1\n    */\n    if( ipkColumn<0 ){\n      sqlite3VdbeAddOp2(v, OP_Integer, -1, regCols);\n    }else{\n      int addr1;\n      assert( !withoutRowid );\n      if( useTempTable ){\n        sqlite3VdbeAddOp3(v, OP_Column, srcTab, ipkColumn, regCols);\n      }else{\n        assert( pSelect==0 );  /* Otherwise useTempTable is true */\n        sqlite3ExprCode(pParse, pList->a[ipkColumn].pExpr, regCols);\n      }\n      addr1 = sqlite3VdbeAddOp1(v, OP_NotNull, regCols); VdbeCoverage(v);\n      sqlite3VdbeAddOp2(v, OP_Integer, -1, regCols);\n      sqlite3VdbeJumpHere(v, addr1);\n      sqlite3VdbeAddOp1(v, OP_MustBeInt, regCols); VdbeCoverage(v);\n    }\n\n    /* Cannot have triggers on a virtual table. If it were possible,\n    ** this block would have to account for hidden column.\n    */\n    assert( !IsVirtual(pTab) );\n\n    /* Create the new column data\n    */\n    for(i=j=0; i<pTab->nCol; i++){\n      if( pColumn ){\n        for(j=0; j<pColumn->nId; j++){\n          if( pColumn->a[j].idx==i ) break;\n        }\n      }\n      if( (!useTempTable && !pList) || (pColumn && j>=pColumn->nId)\n            || (pColumn==0 && IsOrdinaryHiddenColumn(&pTab->aCol[i])) ){\n        sqlite3ExprCode(pParse, pTab->aCol[i].pDflt, regCols+i+1);\n      }else if( useTempTable ){\n        sqlite3VdbeAddOp3(v, OP_Column, srcTab, j, regCols+i+1); \n      }else{\n        assert( pSelect==0 ); /* Otherwise useTempTable is true */\n        sqlite3ExprCodeAndCache(pParse, pList->a[j].pExpr, regCols+i+1);\n      }\n      if( pColumn==0 && !IsOrdinaryHiddenColumn(&pTab->aCol[i]) ) j++;\n    }\n\n    /* If this is an INSERT on a view with an INSTEAD OF INSERT trigger,\n    ** do not attempt any conversions before assembling the record.\n    ** If this is a real table, attempt conversions as required by the\n    ** table column affinities.\n    */\n    if( !isView ){\n      sqlite3TableAffinity(v, pTab, regCols+1);\n    }\n\n    /* Fire BEFORE or INSTEAD OF triggers */\n    sqlite3CodeRowTrigger(pParse, pTrigger, TK_INSERT, 0, TRIGGER_BEFORE, \n        pTab, regCols-pTab->nCol-1, onError, endOfLoop);\n\n    sqlite3ReleaseTempRange(pParse, regCols, pTab->nCol+1);\n  }\n\n  /* Compute the content of the next row to insert into a range of\n  ** registers beginning at regIns.\n  */\n  if( !isView ){\n    if( IsVirtual(pTab) ){\n      /* The row that the VUpdate opcode will delete: none */\n      sqlite3VdbeAddOp2(v, OP_Null, 0, regIns);\n    }\n    if( ipkColumn>=0 ){\n      if( useTempTable ){\n        sqlite3VdbeAddOp3(v, OP_Column, srcTab, ipkColumn, regRowid);\n      }else if( pSelect ){\n        sqlite3VdbeAddOp2(v, OP_Copy, regFromSelect+ipkColumn, regRowid);\n      }else{\n        VdbeOp *pOp;\n        sqlite3ExprCode(pParse, pList->a[ipkColumn].pExpr, regRowid);\n        pOp = sqlite3VdbeGetOp(v, -1);\n        assert( pOp!=0 );\n        if( pOp->opcode==OP_Null && !IsVirtual(pTab) ){\n          appendFlag = 1;\n          pOp->opcode = OP_NewRowid;\n          pOp->p1 = iDataCur;\n          pOp->p2 = regRowid;\n          pOp->p3 = regAutoinc;\n        }\n      }\n      /* If the PRIMARY KEY expression is NULL, then use OP_NewRowid\n      ** to generate a unique primary key value.\n      */\n      if( !appendFlag ){\n        int addr1;\n        if( !IsVirtual(pTab) ){\n          addr1 = sqlite3VdbeAddOp1(v, OP_NotNull, regRowid); VdbeCoverage(v);\n          sqlite3VdbeAddOp3(v, OP_NewRowid, iDataCur, regRowid, regAutoinc);\n          sqlite3VdbeJumpHere(v, addr1);\n        }else{\n          addr1 = sqlite3VdbeCurrentAddr(v);\n          sqlite3VdbeAddOp2(v, OP_IsNull, regRowid, addr1+2); VdbeCoverage(v);\n        }\n        sqlite3VdbeAddOp1(v, OP_MustBeInt, regRowid); VdbeCoverage(v);\n      }\n    }else if( IsVirtual(pTab) || withoutRowid ){\n      sqlite3VdbeAddOp2(v, OP_Null, 0, regRowid);\n    }else{\n      sqlite3VdbeAddOp3(v, OP_NewRowid, iDataCur, regRowid, regAutoinc);\n      appendFlag = 1;\n    }\n    autoIncStep(pParse, regAutoinc, regRowid);\n\n    /* Compute data for all columns of the new entry, beginning\n    ** with the first column.\n    */\n    nHidden = 0;\n    for(i=0; i<pTab->nCol; i++){\n      int iRegStore = regRowid+1+i;\n      if( i==pTab->iPKey ){\n        /* The value of the INTEGER PRIMARY KEY column is always a NULL.\n        ** Whenever this column is read, the rowid will be substituted\n        ** in its place.  Hence, fill this column with a NULL to avoid\n        ** taking up data space with information that will never be used.\n        ** As there may be shallow copies of this value, make it a soft-NULL */\n        sqlite3VdbeAddOp1(v, OP_SoftNull, iRegStore);\n        continue;\n      }\n      if( pColumn==0 ){\n        if( IsHiddenColumn(&pTab->aCol[i]) ){\n          j = -1;\n          nHidden++;\n        }else{\n          j = i - nHidden;\n        }\n      }else{\n        for(j=0; j<pColumn->nId; j++){\n          if( pColumn->a[j].idx==i ) break;\n        }\n      }\n      if( j<0 || nColumn==0 || (pColumn && j>=pColumn->nId) ){\n        sqlite3ExprCodeFactorable(pParse, pTab->aCol[i].pDflt, iRegStore);\n      }else if( useTempTable ){\n        sqlite3VdbeAddOp3(v, OP_Column, srcTab, j, iRegStore); \n      }else if( pSelect ){\n        if( regFromSelect!=regData ){\n          sqlite3VdbeAddOp2(v, OP_SCopy, regFromSelect+j, iRegStore);\n        }\n      }else{\n        sqlite3ExprCode(pParse, pList->a[j].pExpr, iRegStore);\n      }\n    }\n\n    /* Generate code to check constraints and generate index keys and\n    ** do the insertion.\n    */\n#ifndef SQLITE_OMIT_VIRTUALTABLE\n    if( IsVirtual(pTab) ){\n      const char *pVTab = (const char *)sqlite3GetVTable(db, pTab);\n      sqlite3VtabMakeWritable(pParse, pTab);\n      sqlite3VdbeAddOp4(v, OP_VUpdate, 1, pTab->nCol+2, regIns, pVTab, P4_VTAB);\n      sqlite3VdbeChangeP5(v, onError==OE_Default ? OE_Abort : onError);\n      sqlite3MayAbort(pParse);\n    }else\n#endif\n    {\n      int isReplace;    /* Set to true if constraints may cause a replace */\n      int bUseSeek;     /* True to use OPFLAG_SEEKRESULT */\n      sqlite3GenerateConstraintChecks(pParse, pTab, aRegIdx, iDataCur, iIdxCur,\n          regIns, 0, ipkColumn>=0, onError, endOfLoop, &isReplace, 0\n      );\n      sqlite3FkCheck(pParse, pTab, 0, regIns, 0, 0);\n\n      /* Set the OPFLAG_USESEEKRESULT flag if either (a) there are no REPLACE\n      ** constraints or (b) there are no triggers and this table is not a\n      ** parent table in a foreign key constraint. It is safe to set the\n      ** flag in the second case as if any REPLACE constraint is hit, an\n      ** OP_Delete or OP_IdxDelete instruction will be executed on each \n      ** cursor that is disturbed. And these instructions both clear the\n      ** VdbeCursor.seekResult variable, disabling the OPFLAG_USESEEKRESULT\n      ** functionality.  */\n      bUseSeek = (isReplace==0 || (pTrigger==0 &&\n          ((db->flags & SQLITE_ForeignKeys)==0 || sqlite3FkReferences(pTab)==0)\n      ));\n      sqlite3CompleteInsertion(pParse, pTab, iDataCur, iIdxCur,\n          regIns, aRegIdx, 0, appendFlag, bUseSeek\n      );\n    }\n  }\n\n  /* Update the count of rows that are inserted\n  */\n  if( (db->flags & SQLITE_CountRows)!=0 ){\n    sqlite3VdbeAddOp2(v, OP_AddImm, regRowCount, 1);\n  }\n\n  if( pTrigger ){\n    /* Code AFTER triggers */\n    sqlite3CodeRowTrigger(pParse, pTrigger, TK_INSERT, 0, TRIGGER_AFTER, \n        pTab, regData-2-pTab->nCol, onError, endOfLoop);\n  }\n\n  /* The bottom of the main insertion loop, if the data source\n  ** is a SELECT statement.\n  */\n  sqlite3VdbeResolveLabel(v, endOfLoop);\n  if( useTempTable ){\n    sqlite3VdbeAddOp2(v, OP_Next, srcTab, addrCont); VdbeCoverage(v);\n    sqlite3VdbeJumpHere(v, addrInsTop);\n    sqlite3VdbeAddOp1(v, OP_Close, srcTab);\n  }else if( pSelect ){\n    sqlite3VdbeGoto(v, addrCont);\n    sqlite3VdbeJumpHere(v, addrInsTop);\n  }\n\ninsert_end:\n  /* Update the sqlite_sequence table by storing the content of the\n  ** maximum rowid counter values recorded while inserting into\n  ** autoincrement tables.\n  */\n  if( pParse->nested==0 && pParse->pTriggerTab==0 ){\n    sqlite3AutoincrementEnd(pParse);\n  }\n\n  /*\n  ** Return the number of rows inserted. If this routine is \n  ** generating code because of a call to sqlite3NestedParse(), do not\n  ** invoke the callback function.\n  */\n  if( (db->flags&SQLITE_CountRows) && !pParse->nested && !pParse->pTriggerTab ){\n    sqlite3VdbeAddOp2(v, OP_ResultRow, regRowCount, 1);\n    sqlite3VdbeSetNumCols(v, 1);\n    sqlite3VdbeSetColName(v, 0, COLNAME_NAME, \"rows inserted\", SQLITE_STATIC);\n  }\n\ninsert_cleanup:\n  sqlite3SrcListDelete(db, pTabList);\n  sqlite3ExprListDelete(db, pList);\n  sqlite3SelectDelete(db, pSelect);\n  sqlite3IdListDelete(db, pColumn);\n  sqlite3DbFree(db, aRegIdx);\n}\n\n/* Make sure \"isView\" and other macros defined above are undefined. Otherwise\n** they may interfere with compilation of other functions in this file\n** (or in another file, if this file becomes part of the amalgamation).  */\n#ifdef isView\n #undef isView\n#endif\n#ifdef pTrigger\n #undef pTrigger\n#endif\n#ifdef tmask\n #undef tmask\n#endif\n\n/*\n** Meanings of bits in of pWalker->eCode for checkConstraintUnchanged()\n*/\n#define CKCNSTRNT_COLUMN   0x01    /* CHECK constraint uses a changing column */\n#define CKCNSTRNT_ROWID    0x02    /* CHECK constraint references the ROWID */\n\n/* This is the Walker callback from checkConstraintUnchanged().  Set\n** bit 0x01 of pWalker->eCode if\n** pWalker->eCode to 0 if this expression node references any of the\n** columns that are being modifed by an UPDATE statement.\n*/\nstatic int checkConstraintExprNode(Walker *pWalker, Expr *pExpr){\n  if( pExpr->op==TK_COLUMN ){\n    assert( pExpr->iColumn>=0 || pExpr->iColumn==-1 );\n    if( pExpr->iColumn>=0 ){\n      if( pWalker->u.aiCol[pExpr->iColumn]>=0 ){\n        pWalker->eCode |= CKCNSTRNT_COLUMN;\n      }\n    }else{\n      pWalker->eCode |= CKCNSTRNT_ROWID;\n    }\n  }\n  return WRC_Continue;\n}\n\n/*\n** pExpr is a CHECK constraint on a row that is being UPDATE-ed.  The\n** only columns that are modified by the UPDATE are those for which\n** aiChng[i]>=0, and also the ROWID is modified if chngRowid is true.\n**\n** Return true if CHECK constraint pExpr does not use any of the\n** changing columns (or the rowid if it is changing).  In other words,\n** return true if this CHECK constraint can be skipped when validating\n** the new row in the UPDATE statement.\n*/\nstatic int checkConstraintUnchanged(Expr *pExpr, int *aiChng, int chngRowid){\n  Walker w;\n  memset(&w, 0, sizeof(w));\n  w.eCode = 0;\n  w.xExprCallback = checkConstraintExprNode;\n  w.u.aiCol = aiChng;\n  sqlite3WalkExpr(&w, pExpr);\n  if( !chngRowid ){\n    testcase( (w.eCode & CKCNSTRNT_ROWID)!=0 );\n    w.eCode &= ~CKCNSTRNT_ROWID;\n  }\n  testcase( w.eCode==0 );\n  testcase( w.eCode==CKCNSTRNT_COLUMN );\n  testcase( w.eCode==CKCNSTRNT_ROWID );\n  testcase( w.eCode==(CKCNSTRNT_ROWID|CKCNSTRNT_COLUMN) );\n  return !w.eCode;\n}\n\n/*\n** Generate code to do constraint checks prior to an INSERT or an UPDATE\n** on table pTab.\n**\n** The regNewData parameter is the first register in a range that contains\n** the data to be inserted or the data after the update.  There will be\n** pTab->nCol+1 registers in this range.  The first register (the one\n** that regNewData points to) will contain the new rowid, or NULL in the\n** case of a WITHOUT ROWID table.  The second register in the range will\n** contain the content of the first table column.  The third register will\n** contain the content of the second table column.  And so forth.\n**\n** The regOldData parameter is similar to regNewData except that it contains\n** the data prior to an UPDATE rather than afterwards.  regOldData is zero\n** for an INSERT.  This routine can distinguish between UPDATE and INSERT by\n** checking regOldData for zero.\n**\n** For an UPDATE, the pkChng boolean is true if the true primary key (the\n** rowid for a normal table or the PRIMARY KEY for a WITHOUT ROWID table)\n** might be modified by the UPDATE.  If pkChng is false, then the key of\n** the iDataCur content table is guaranteed to be unchanged by the UPDATE.\n**\n** For an INSERT, the pkChng boolean indicates whether or not the rowid\n** was explicitly specified as part of the INSERT statement.  If pkChng\n** is zero, it means that the either rowid is computed automatically or\n** that the table is a WITHOUT ROWID table and has no rowid.  On an INSERT,\n** pkChng will only be true if the INSERT statement provides an integer\n** value for either the rowid column or its INTEGER PRIMARY KEY alias.\n**\n** The code generated by this routine will store new index entries into\n** registers identified by aRegIdx[].  No index entry is created for\n** indices where aRegIdx[i]==0.  The order of indices in aRegIdx[] is\n** the same as the order of indices on the linked list of indices\n** at pTab->pIndex.\n**\n** The caller must have already opened writeable cursors on the main\n** table and all applicable indices (that is to say, all indices for which\n** aRegIdx[] is not zero).  iDataCur is the cursor for the main table when\n** inserting or updating a rowid table, or the cursor for the PRIMARY KEY\n** index when operating on a WITHOUT ROWID table.  iIdxCur is the cursor\n** for the first index in the pTab->pIndex list.  Cursors for other indices\n** are at iIdxCur+N for the N-th element of the pTab->pIndex list.\n**\n** This routine also generates code to check constraints.  NOT NULL,\n** CHECK, and UNIQUE constraints are all checked.  If a constraint fails,\n** then the appropriate action is performed.  There are five possible\n** actions: ROLLBACK, ABORT, FAIL, REPLACE, and IGNORE.\n**\n**  Constraint type  Action       What Happens\n**  ---------------  ----------   ----------------------------------------\n**  any              ROLLBACK     The current transaction is rolled back and\n**                                sqlite3_step() returns immediately with a\n**                                return code of SQLITE_CONSTRAINT.\n**\n**  any              ABORT        Back out changes from the current command\n**                                only (do not do a complete rollback) then\n**                                cause sqlite3_step() to return immediately\n**                                with SQLITE_CONSTRAINT.\n**\n**  any              FAIL         Sqlite3_step() returns immediately with a\n**                                return code of SQLITE_CONSTRAINT.  The\n**                                transaction is not rolled back and any\n**                                changes to prior rows are retained.\n**\n**  any              IGNORE       The attempt in insert or update the current\n**                                row is skipped, without throwing an error.\n**                                Processing continues with the next row.\n**                                (There is an immediate jump to ignoreDest.)\n**\n**  NOT NULL         REPLACE      The NULL value is replace by the default\n**                                value for that column.  If the default value\n**                                is NULL, the action is the same as ABORT.\n**\n**  UNIQUE           REPLACE      The other row that conflicts with the row\n**                                being inserted is removed.\n**\n**  CHECK            REPLACE      Illegal.  The results in an exception.\n**\n** Which action to take is determined by the overrideError parameter.\n** Or if overrideError==OE_Default, then the pParse->onError parameter\n** is used.  Or if pParse->onError==OE_Default then the onError value\n** for the constraint is used.\n*/\nSQLITE_PRIVATE void sqlite3GenerateConstraintChecks(\n  Parse *pParse,       /* The parser context */\n  Table *pTab,         /* The table being inserted or updated */\n  int *aRegIdx,        /* Use register aRegIdx[i] for index i.  0 for unused */\n  int iDataCur,        /* Canonical data cursor (main table or PK index) */\n  int iIdxCur,         /* First index cursor */\n  int regNewData,      /* First register in a range holding values to insert */\n  int regOldData,      /* Previous content.  0 for INSERTs */\n  u8 pkChng,           /* Non-zero if the rowid or PRIMARY KEY changed */\n  u8 overrideError,    /* Override onError to this if not OE_Default */\n  int ignoreDest,      /* Jump to this label on an OE_Ignore resolution */\n  int *pbMayReplace,   /* OUT: Set to true if constraint may cause a replace */\n  int *aiChng          /* column i is unchanged if aiChng[i]<0 */\n){\n  Vdbe *v;             /* VDBE under constrution */\n  Index *pIdx;         /* Pointer to one of the indices */\n  Index *pPk = 0;      /* The PRIMARY KEY index */\n  sqlite3 *db;         /* Database connection */\n  int i;               /* loop counter */\n  int ix;              /* Index loop counter */\n  int nCol;            /* Number of columns */\n  int onError;         /* Conflict resolution strategy */\n  int addr1;           /* Address of jump instruction */\n  int seenReplace = 0; /* True if REPLACE is used to resolve INT PK conflict */\n  int nPkField;        /* Number of fields in PRIMARY KEY. 1 for ROWID tables */\n  int ipkTop = 0;      /* Top of the rowid change constraint check */\n  int ipkBottom = 0;   /* Bottom of the rowid change constraint check */\n  u8 isUpdate;         /* True if this is an UPDATE operation */\n  u8 bAffinityDone = 0;  /* True if the OP_Affinity operation has been run */\n\n  isUpdate = regOldData!=0;\n  db = pParse->db;\n  v = sqlite3GetVdbe(pParse);\n  assert( v!=0 );\n  assert( pTab->pSelect==0 );  /* This table is not a VIEW */\n  nCol = pTab->nCol;\n  \n  /* pPk is the PRIMARY KEY index for WITHOUT ROWID tables and NULL for\n  ** normal rowid tables.  nPkField is the number of key fields in the \n  ** pPk index or 1 for a rowid table.  In other words, nPkField is the\n  ** number of fields in the true primary key of the table. */\n  if( HasRowid(pTab) ){\n    pPk = 0;\n    nPkField = 1;\n  }else{\n    pPk = sqlite3PrimaryKeyIndex(pTab);\n    nPkField = pPk->nKeyCol;\n  }\n\n  /* Record that this module has started */\n  VdbeModuleComment((v, \"BEGIN: GenCnstCks(%d,%d,%d,%d,%d)\",\n                     iDataCur, iIdxCur, regNewData, regOldData, pkChng));\n\n  /* Test all NOT NULL constraints.\n  */\n  for(i=0; i<nCol; i++){\n    if( i==pTab->iPKey ){\n      continue;        /* ROWID is never NULL */\n    }\n    if( aiChng && aiChng[i]<0 ){\n      /* Don't bother checking for NOT NULL on columns that do not change */\n      continue;\n    }\n    onError = pTab->aCol[i].notNull;\n    if( onError==OE_None ) continue;  /* This column is allowed to be NULL */\n    if( overrideError!=OE_Default ){\n      onError = overrideError;\n    }else if( onError==OE_Default ){\n      onError = OE_Abort;\n    }\n    if( onError==OE_Replace && pTab->aCol[i].pDflt==0 ){\n      onError = OE_Abort;\n    }\n    assert( onError==OE_Rollback || onError==OE_Abort || onError==OE_Fail\n        || onError==OE_Ignore || onError==OE_Replace );\n    switch( onError ){\n      case OE_Abort:\n        sqlite3MayAbort(pParse);\n        /* Fall through */\n      case OE_Rollback:\n      case OE_Fail: {\n        char *zMsg = sqlite3MPrintf(db, \"%s.%s\", pTab->zName,\n                                    pTab->aCol[i].zName);\n        sqlite3VdbeAddOp3(v, OP_HaltIfNull, SQLITE_CONSTRAINT_NOTNULL, onError,\n                          regNewData+1+i);\n        sqlite3VdbeAppendP4(v, zMsg, P4_DYNAMIC);\n        sqlite3VdbeChangeP5(v, P5_ConstraintNotNull);\n        VdbeCoverage(v);\n        break;\n      }\n      case OE_Ignore: {\n        sqlite3VdbeAddOp2(v, OP_IsNull, regNewData+1+i, ignoreDest);\n        VdbeCoverage(v);\n        break;\n      }\n      default: {\n        assert( onError==OE_Replace );\n        addr1 = sqlite3VdbeAddOp1(v, OP_NotNull, regNewData+1+i);\n           VdbeCoverage(v);\n        sqlite3ExprCode(pParse, pTab->aCol[i].pDflt, regNewData+1+i);\n        sqlite3VdbeJumpHere(v, addr1);\n        break;\n      }\n    }\n  }\n\n  /* Test all CHECK constraints\n  */\n#ifndef SQLITE_OMIT_CHECK\n  if( pTab->pCheck && (db->flags & SQLITE_IgnoreChecks)==0 ){\n    ExprList *pCheck = pTab->pCheck;\n    pParse->iSelfTab = -(regNewData+1);\n    onError = overrideError!=OE_Default ? overrideError : OE_Abort;\n    for(i=0; i<pCheck->nExpr; i++){\n      int allOk;\n      Expr *pExpr = pCheck->a[i].pExpr;\n      if( aiChng && checkConstraintUnchanged(pExpr, aiChng, pkChng) ) continue;\n      allOk = sqlite3VdbeMakeLabel(v);\n      sqlite3ExprIfTrue(pParse, pExpr, allOk, SQLITE_JUMPIFNULL);\n      if( onError==OE_Ignore ){\n        sqlite3VdbeGoto(v, ignoreDest);\n      }else{\n        char *zName = pCheck->a[i].zName;\n        if( zName==0 ) zName = pTab->zName;\n        if( onError==OE_Replace ) onError = OE_Abort; /* IMP: R-15569-63625 */\n        sqlite3HaltConstraint(pParse, SQLITE_CONSTRAINT_CHECK,\n                              onError, zName, P4_TRANSIENT,\n                              P5_ConstraintCheck);\n      }\n      sqlite3VdbeResolveLabel(v, allOk);\n    }\n    pParse->iSelfTab = 0;\n  }\n#endif /* !defined(SQLITE_OMIT_CHECK) */\n\n  /* If rowid is changing, make sure the new rowid does not previously\n  ** exist in the table.\n  */\n  if( pkChng && pPk==0 ){\n    int addrRowidOk = sqlite3VdbeMakeLabel(v);\n\n    /* Figure out what action to take in case of a rowid collision */\n    onError = pTab->keyConf;\n    if( overrideError!=OE_Default ){\n      onError = overrideError;\n    }else if( onError==OE_Default ){\n      onError = OE_Abort;\n    }\n\n    if( isUpdate ){\n      /* pkChng!=0 does not mean that the rowid has changed, only that\n      ** it might have changed.  Skip the conflict logic below if the rowid\n      ** is unchanged. */\n      sqlite3VdbeAddOp3(v, OP_Eq, regNewData, addrRowidOk, regOldData);\n      sqlite3VdbeChangeP5(v, SQLITE_NOTNULL);\n      VdbeCoverage(v);\n    }\n\n    /* If the response to a rowid conflict is REPLACE but the response\n    ** to some other UNIQUE constraint is FAIL or IGNORE, then we need\n    ** to defer the running of the rowid conflict checking until after\n    ** the UNIQUE constraints have run.\n    */\n    if( onError==OE_Replace && overrideError!=OE_Replace ){\n      for(pIdx=pTab->pIndex; pIdx; pIdx=pIdx->pNext){\n        if( pIdx->onError==OE_Ignore || pIdx->onError==OE_Fail ){\n          ipkTop = sqlite3VdbeAddOp0(v, OP_Goto);\n          break;\n        }\n      }\n    }\n\n    /* Check to see if the new rowid already exists in the table.  Skip\n    ** the following conflict logic if it does not. */\n    sqlite3VdbeAddOp3(v, OP_NotExists, iDataCur, addrRowidOk, regNewData);\n    VdbeCoverage(v);\n\n    /* Generate code that deals with a rowid collision */\n    switch( onError ){\n      default: {\n        onError = OE_Abort;\n        /* Fall thru into the next case */\n      }\n      case OE_Rollback:\n      case OE_Abort:\n      case OE_Fail: {\n        sqlite3RowidConstraint(pParse, onError, pTab);\n        break;\n      }\n      case OE_Replace: {\n        /* If there are DELETE triggers on this table and the\n        ** recursive-triggers flag is set, call GenerateRowDelete() to\n        ** remove the conflicting row from the table. This will fire\n        ** the triggers and remove both the table and index b-tree entries.\n        **\n        ** Otherwise, if there are no triggers or the recursive-triggers\n        ** flag is not set, but the table has one or more indexes, call \n        ** GenerateRowIndexDelete(). This removes the index b-tree entries \n        ** only. The table b-tree entry will be replaced by the new entry \n        ** when it is inserted.  \n        **\n        ** If either GenerateRowDelete() or GenerateRowIndexDelete() is called,\n        ** also invoke MultiWrite() to indicate that this VDBE may require\n        ** statement rollback (if the statement is aborted after the delete\n        ** takes place). Earlier versions called sqlite3MultiWrite() regardless,\n        ** but being more selective here allows statements like:\n        **\n        **   REPLACE INTO t(rowid) VALUES($newrowid)\n        **\n        ** to run without a statement journal if there are no indexes on the\n        ** table.\n        */\n        Trigger *pTrigger = 0;\n        if( db->flags&SQLITE_RecTriggers ){\n          pTrigger = sqlite3TriggersExist(pParse, pTab, TK_DELETE, 0, 0);\n        }\n        if( pTrigger || sqlite3FkRequired(pParse, pTab, 0, 0) ){\n          sqlite3MultiWrite(pParse);\n          sqlite3GenerateRowDelete(pParse, pTab, pTrigger, iDataCur, iIdxCur,\n                                   regNewData, 1, 0, OE_Replace, 1, -1);\n        }else{\n#ifdef SQLITE_ENABLE_PREUPDATE_HOOK\n          if( HasRowid(pTab) ){\n            /* This OP_Delete opcode fires the pre-update-hook only. It does\n            ** not modify the b-tree. It is more efficient to let the coming\n            ** OP_Insert replace the existing entry than it is to delete the\n            ** existing entry and then insert a new one. */\n            sqlite3VdbeAddOp2(v, OP_Delete, iDataCur, OPFLAG_ISNOOP);\n            sqlite3VdbeAppendP4(v, pTab, P4_TABLE);\n          }\n#endif /* SQLITE_ENABLE_PREUPDATE_HOOK */\n          if( pTab->pIndex ){\n            sqlite3MultiWrite(pParse);\n            sqlite3GenerateRowIndexDelete(pParse, pTab, iDataCur, iIdxCur,0,-1);\n          }\n        }\n        seenReplace = 1;\n        break;\n      }\n      case OE_Ignore: {\n        /*assert( seenReplace==0 );*/\n        sqlite3VdbeGoto(v, ignoreDest);\n        break;\n      }\n    }\n    sqlite3VdbeResolveLabel(v, addrRowidOk);\n    if( ipkTop ){\n      ipkBottom = sqlite3VdbeAddOp0(v, OP_Goto);\n      sqlite3VdbeJumpHere(v, ipkTop);\n    }\n  }\n\n  /* Test all UNIQUE constraints by creating entries for each UNIQUE\n  ** index and making sure that duplicate entries do not already exist.\n  ** Compute the revised record entries for indices as we go.\n  **\n  ** This loop also handles the case of the PRIMARY KEY index for a\n  ** WITHOUT ROWID table.\n  */\n  for(ix=0, pIdx=pTab->pIndex; pIdx; pIdx=pIdx->pNext, ix++){\n    int regIdx;          /* Range of registers hold conent for pIdx */\n    int regR;            /* Range of registers holding conflicting PK */\n    int iThisCur;        /* Cursor for this UNIQUE index */\n    int addrUniqueOk;    /* Jump here if the UNIQUE constraint is satisfied */\n\n    if( aRegIdx[ix]==0 ) continue;  /* Skip indices that do not change */\n    if( bAffinityDone==0 ){\n      sqlite3TableAffinity(v, pTab, regNewData+1);\n      bAffinityDone = 1;\n    }\n    iThisCur = iIdxCur+ix;\n    addrUniqueOk = sqlite3VdbeMakeLabel(v);\n\n    /* Skip partial indices for which the WHERE clause is not true */\n    if( pIdx->pPartIdxWhere ){\n      sqlite3VdbeAddOp2(v, OP_Null, 0, aRegIdx[ix]);\n      pParse->iSelfTab = -(regNewData+1);\n      sqlite3ExprIfFalseDup(pParse, pIdx->pPartIdxWhere, addrUniqueOk,\n                            SQLITE_JUMPIFNULL);\n      pParse->iSelfTab = 0;\n    }\n\n    /* Create a record for this index entry as it should appear after\n    ** the insert or update.  Store that record in the aRegIdx[ix] register\n    */\n    regIdx = aRegIdx[ix]+1;\n    for(i=0; i<pIdx->nColumn; i++){\n      int iField = pIdx->aiColumn[i];\n      int x;\n      if( iField==XN_EXPR ){\n        pParse->iSelfTab = -(regNewData+1);\n        sqlite3ExprCodeCopy(pParse, pIdx->aColExpr->a[i].pExpr, regIdx+i);\n        pParse->iSelfTab = 0;\n        VdbeComment((v, \"%s column %d\", pIdx->zName, i));\n      }else{\n        if( iField==XN_ROWID || iField==pTab->iPKey ){\n          x = regNewData;\n        }else{\n          x = iField + regNewData + 1;\n        }\n        sqlite3VdbeAddOp2(v, iField<0 ? OP_IntCopy : OP_SCopy, x, regIdx+i);\n        VdbeComment((v, \"%s\", iField<0 ? \"rowid\" : pTab->aCol[iField].zName));\n      }\n    }\n    sqlite3VdbeAddOp3(v, OP_MakeRecord, regIdx, pIdx->nColumn, aRegIdx[ix]);\n    VdbeComment((v, \"for %s\", pIdx->zName));\n#ifdef SQLITE_ENABLE_NULL_TRIM\n    if( pIdx->idxType==2 ) sqlite3SetMakeRecordP5(v, pIdx->pTable);\n#endif\n\n    /* In an UPDATE operation, if this index is the PRIMARY KEY index \n    ** of a WITHOUT ROWID table and there has been no change the\n    ** primary key, then no collision is possible.  The collision detection\n    ** logic below can all be skipped. */\n    if( isUpdate && pPk==pIdx && pkChng==0 ){\n      sqlite3VdbeResolveLabel(v, addrUniqueOk);\n      continue;\n    }\n\n    /* Find out what action to take in case there is a uniqueness conflict */\n    onError = pIdx->onError;\n    if( onError==OE_None ){ \n      sqlite3VdbeResolveLabel(v, addrUniqueOk);\n      continue;  /* pIdx is not a UNIQUE index */\n    }\n    if( overrideError!=OE_Default ){\n      onError = overrideError;\n    }else if( onError==OE_Default ){\n      onError = OE_Abort;\n    }\n\n    /* Collision detection may be omitted if all of the following are true:\n    **   (1) The conflict resolution algorithm is REPLACE\n    **   (2) The table is a WITHOUT ROWID table\n    **   (3) There are no secondary indexes on the table\n    **   (4) No delete triggers need to be fired if there is a conflict\n    **   (5) No FK constraint counters need to be updated if a conflict occurs.\n    */ \n    if( (ix==0 && pIdx->pNext==0)                   /* Condition 3 */\n     && pPk==pIdx                                   /* Condition 2 */\n     && onError==OE_Replace                         /* Condition 1 */\n     && ( 0==(db->flags&SQLITE_RecTriggers) ||      /* Condition 4 */\n          0==sqlite3TriggersExist(pParse, pTab, TK_DELETE, 0, 0))\n     && ( 0==(db->flags&SQLITE_ForeignKeys) ||      /* Condition 5 */\n         (0==pTab->pFKey && 0==sqlite3FkReferences(pTab)))\n    ){\n      sqlite3VdbeResolveLabel(v, addrUniqueOk);\n      continue;\n    }\n\n    /* Check to see if the new index entry will be unique */\n    sqlite3ExprCachePush(pParse);\n    sqlite3VdbeAddOp4Int(v, OP_NoConflict, iThisCur, addrUniqueOk,\n                         regIdx, pIdx->nKeyCol); VdbeCoverage(v);\n\n    /* Generate code to handle collisions */\n    regR = (pIdx==pPk) ? regIdx : sqlite3GetTempRange(pParse, nPkField);\n    if( isUpdate || onError==OE_Replace ){\n      if( HasRowid(pTab) ){\n        sqlite3VdbeAddOp2(v, OP_IdxRowid, iThisCur, regR);\n        /* Conflict only if the rowid of the existing index entry\n        ** is different from old-rowid */\n        if( isUpdate ){\n          sqlite3VdbeAddOp3(v, OP_Eq, regR, addrUniqueOk, regOldData);\n          sqlite3VdbeChangeP5(v, SQLITE_NOTNULL);\n          VdbeCoverage(v);\n        }\n      }else{\n        int x;\n        /* Extract the PRIMARY KEY from the end of the index entry and\n        ** store it in registers regR..regR+nPk-1 */\n        if( pIdx!=pPk ){\n          for(i=0; i<pPk->nKeyCol; i++){\n            assert( pPk->aiColumn[i]>=0 );\n            x = sqlite3ColumnOfIndex(pIdx, pPk->aiColumn[i]);\n            sqlite3VdbeAddOp3(v, OP_Column, iThisCur, x, regR+i);\n            VdbeComment((v, \"%s.%s\", pTab->zName,\n                         pTab->aCol[pPk->aiColumn[i]].zName));\n          }\n        }\n        if( isUpdate ){\n          /* If currently processing the PRIMARY KEY of a WITHOUT ROWID \n          ** table, only conflict if the new PRIMARY KEY values are actually\n          ** different from the old.\n          **\n          ** For a UNIQUE index, only conflict if the PRIMARY KEY values\n          ** of the matched index row are different from the original PRIMARY\n          ** KEY values of this row before the update.  */\n          int addrJump = sqlite3VdbeCurrentAddr(v)+pPk->nKeyCol;\n          int op = OP_Ne;\n          int regCmp = (IsPrimaryKeyIndex(pIdx) ? regIdx : regR);\n  \n          for(i=0; i<pPk->nKeyCol; i++){\n            char *p4 = (char*)sqlite3LocateCollSeq(pParse, pPk->azColl[i]);\n            x = pPk->aiColumn[i];\n            assert( x>=0 );\n            if( i==(pPk->nKeyCol-1) ){\n              addrJump = addrUniqueOk;\n              op = OP_Eq;\n            }\n            sqlite3VdbeAddOp4(v, op, \n                regOldData+1+x, addrJump, regCmp+i, p4, P4_COLLSEQ\n            );\n            sqlite3VdbeChangeP5(v, SQLITE_NOTNULL);\n            VdbeCoverageIf(v, op==OP_Eq);\n            VdbeCoverageIf(v, op==OP_Ne);\n          }\n        }\n      }\n    }\n\n    /* Generate code that executes if the new index entry is not unique */\n    assert( onError==OE_Rollback || onError==OE_Abort || onError==OE_Fail\n        || onError==OE_Ignore || onError==OE_Replace );\n    switch( onError ){\n      case OE_Rollback:\n      case OE_Abort:\n      case OE_Fail: {\n        sqlite3UniqueConstraint(pParse, onError, pIdx);\n        break;\n      }\n      case OE_Ignore: {\n        sqlite3VdbeGoto(v, ignoreDest);\n        break;\n      }\n      default: {\n        Trigger *pTrigger = 0;\n        assert( onError==OE_Replace );\n        sqlite3MultiWrite(pParse);\n        if( db->flags&SQLITE_RecTriggers ){\n          pTrigger = sqlite3TriggersExist(pParse, pTab, TK_DELETE, 0, 0);\n        }\n        sqlite3GenerateRowDelete(pParse, pTab, pTrigger, iDataCur, iIdxCur,\n            regR, nPkField, 0, OE_Replace,\n            (pIdx==pPk ? ONEPASS_SINGLE : ONEPASS_OFF), iThisCur);\n        seenReplace = 1;\n        break;\n      }\n    }\n    sqlite3VdbeResolveLabel(v, addrUniqueOk);\n    sqlite3ExprCachePop(pParse);\n    if( regR!=regIdx ) sqlite3ReleaseTempRange(pParse, regR, nPkField);\n  }\n  if( ipkTop ){\n    sqlite3VdbeGoto(v, ipkTop+1);\n    sqlite3VdbeJumpHere(v, ipkBottom);\n  }\n  \n  *pbMayReplace = seenReplace;\n  VdbeModuleComment((v, \"END: GenCnstCks(%d)\", seenReplace));\n}\n\n#ifdef SQLITE_ENABLE_NULL_TRIM\n/*\n** Change the P5 operand on the last opcode (which should be an OP_MakeRecord)\n** to be the number of columns in table pTab that must not be NULL-trimmed.\n**\n** Or if no columns of pTab may be NULL-trimmed, leave P5 at zero.\n*/\nSQLITE_PRIVATE void sqlite3SetMakeRecordP5(Vdbe *v, Table *pTab){\n  u16 i;\n\n  /* Records with omitted columns are only allowed for schema format\n  ** version 2 and later (SQLite version 3.1.4, 2005-02-20). */\n  if( pTab->pSchema->file_format<2 ) return;\n\n  for(i=pTab->nCol-1; i>0; i--){\n    if( pTab->aCol[i].pDflt!=0 ) break;\n    if( pTab->aCol[i].colFlags & COLFLAG_PRIMKEY ) break;\n  }\n  sqlite3VdbeChangeP5(v, i+1);\n}\n#endif\n\n/*\n** This routine generates code to finish the INSERT or UPDATE operation\n** that was started by a prior call to sqlite3GenerateConstraintChecks.\n** A consecutive range of registers starting at regNewData contains the\n** rowid and the content to be inserted.\n**\n** The arguments to this routine should be the same as the first six\n** arguments to sqlite3GenerateConstraintChecks.\n*/\nSQLITE_PRIVATE void sqlite3CompleteInsertion(\n  Parse *pParse,      /* The parser context */\n  Table *pTab,        /* the table into which we are inserting */\n  int iDataCur,       /* Cursor of the canonical data source */\n  int iIdxCur,        /* First index cursor */\n  int regNewData,     /* Range of content */\n  int *aRegIdx,       /* Register used by each index.  0 for unused indices */\n  int update_flags,   /* True for UPDATE, False for INSERT */\n  int appendBias,     /* True if this is likely to be an append */\n  int useSeekResult   /* True to set the USESEEKRESULT flag on OP_[Idx]Insert */\n){\n  Vdbe *v;            /* Prepared statements under construction */\n  Index *pIdx;        /* An index being inserted or updated */\n  u8 pik_flags;       /* flag values passed to the btree insert */\n  int regData;        /* Content registers (after the rowid) */\n  int regRec;         /* Register holding assembled record for the table */\n  int i;              /* Loop counter */\n  u8 bAffinityDone = 0; /* True if OP_Affinity has been run already */\n\n  assert( update_flags==0\n       || update_flags==OPFLAG_ISUPDATE\n       || update_flags==(OPFLAG_ISUPDATE|OPFLAG_SAVEPOSITION)\n  );\n\n  v = sqlite3GetVdbe(pParse);\n  assert( v!=0 );\n  assert( pTab->pSelect==0 );  /* This table is not a VIEW */\n  for(i=0, pIdx=pTab->pIndex; pIdx; pIdx=pIdx->pNext, i++){\n    if( aRegIdx[i]==0 ) continue;\n    bAffinityDone = 1;\n    if( pIdx->pPartIdxWhere ){\n      sqlite3VdbeAddOp2(v, OP_IsNull, aRegIdx[i], sqlite3VdbeCurrentAddr(v)+2);\n      VdbeCoverage(v);\n    }\n    pik_flags = (useSeekResult ? OPFLAG_USESEEKRESULT : 0);\n    if( IsPrimaryKeyIndex(pIdx) && !HasRowid(pTab) ){\n      assert( pParse->nested==0 );\n      pik_flags |= OPFLAG_NCHANGE;\n      pik_flags |= (update_flags & OPFLAG_SAVEPOSITION);\n#ifdef SQLITE_ENABLE_PREUPDATE_HOOK\n      if( update_flags==0 ){\n        sqlite3VdbeAddOp4(v, OP_InsertInt, \n            iIdxCur+i, aRegIdx[i], 0, (char*)pTab, P4_TABLE\n        );\n        sqlite3VdbeChangeP5(v, OPFLAG_ISNOOP);\n      }\n#endif\n    }\n    sqlite3VdbeAddOp4Int(v, OP_IdxInsert, iIdxCur+i, aRegIdx[i],\n                         aRegIdx[i]+1,\n                         pIdx->uniqNotNull ? pIdx->nKeyCol: pIdx->nColumn);\n    sqlite3VdbeChangeP5(v, pik_flags);\n  }\n  if( !HasRowid(pTab) ) return;\n  regData = regNewData + 1;\n  regRec = sqlite3GetTempReg(pParse);\n  sqlite3VdbeAddOp3(v, OP_MakeRecord, regData, pTab->nCol, regRec);\n  sqlite3SetMakeRecordP5(v, pTab);\n  if( !bAffinityDone ){\n    sqlite3TableAffinity(v, pTab, 0);\n    sqlite3ExprCacheAffinityChange(pParse, regData, pTab->nCol);\n  }\n  if( pParse->nested ){\n    pik_flags = 0;\n  }else{\n    pik_flags = OPFLAG_NCHANGE;\n    pik_flags |= (update_flags?update_flags:OPFLAG_LASTROWID);\n  }\n  if( appendBias ){\n    pik_flags |= OPFLAG_APPEND;\n  }\n  if( useSeekResult ){\n    pik_flags |= OPFLAG_USESEEKRESULT;\n  }\n  sqlite3VdbeAddOp3(v, OP_Insert, iDataCur, regRec, regNewData);\n  if( !pParse->nested ){\n    sqlite3VdbeAppendP4(v, pTab, P4_TABLE);\n  }\n  sqlite3VdbeChangeP5(v, pik_flags);\n}\n\n/*\n** Allocate cursors for the pTab table and all its indices and generate\n** code to open and initialized those cursors.\n**\n** The cursor for the object that contains the complete data (normally\n** the table itself, but the PRIMARY KEY index in the case of a WITHOUT\n** ROWID table) is returned in *piDataCur.  The first index cursor is\n** returned in *piIdxCur.  The number of indices is returned.\n**\n** Use iBase as the first cursor (either the *piDataCur for rowid tables\n** or the first index for WITHOUT ROWID tables) if it is non-negative.\n** If iBase is negative, then allocate the next available cursor.\n**\n** For a rowid table, *piDataCur will be exactly one less than *piIdxCur.\n** For a WITHOUT ROWID table, *piDataCur will be somewhere in the range\n** of *piIdxCurs, depending on where the PRIMARY KEY index appears on the\n** pTab->pIndex list.\n**\n** If pTab is a virtual table, then this routine is a no-op and the\n** *piDataCur and *piIdxCur values are left uninitialized.\n*/\nSQLITE_PRIVATE int sqlite3OpenTableAndIndices(\n  Parse *pParse,   /* Parsing context */\n  Table *pTab,     /* Table to be opened */\n  int op,          /* OP_OpenRead or OP_OpenWrite */\n  u8 p5,           /* P5 value for OP_Open* opcodes (except on WITHOUT ROWID) */\n  int iBase,       /* Use this for the table cursor, if there is one */\n  u8 *aToOpen,     /* If not NULL: boolean for each table and index */\n  int *piDataCur,  /* Write the database source cursor number here */\n  int *piIdxCur    /* Write the first index cursor number here */\n){\n  int i;\n  int iDb;\n  int iDataCur;\n  Index *pIdx;\n  Vdbe *v;\n\n  assert( op==OP_OpenRead || op==OP_OpenWrite );\n  assert( op==OP_OpenWrite || p5==0 );\n  if( IsVirtual(pTab) ){\n    /* This routine is a no-op for virtual tables. Leave the output\n    ** variables *piDataCur and *piIdxCur uninitialized so that valgrind\n    ** can detect if they are used by mistake in the caller. */\n    return 0;\n  }\n  iDb = sqlite3SchemaToIndex(pParse->db, pTab->pSchema);\n  v = sqlite3GetVdbe(pParse);\n  assert( v!=0 );\n  if( iBase<0 ) iBase = pParse->nTab;\n  iDataCur = iBase++;\n  if( piDataCur ) *piDataCur = iDataCur;\n  if( HasRowid(pTab) && (aToOpen==0 || aToOpen[0]) ){\n    sqlite3OpenTable(pParse, iDataCur, iDb, pTab, op);\n  }else{\n    sqlite3TableLock(pParse, iDb, pTab->tnum, op==OP_OpenWrite, pTab->zName);\n  }\n  if( piIdxCur ) *piIdxCur = iBase;\n  for(i=0, pIdx=pTab->pIndex; pIdx; pIdx=pIdx->pNext, i++){\n    int iIdxCur = iBase++;\n    assert( pIdx->pSchema==pTab->pSchema );\n    if( IsPrimaryKeyIndex(pIdx) && !HasRowid(pTab) ){\n      if( piDataCur ) *piDataCur = iIdxCur;\n      p5 = 0;\n    }\n    if( aToOpen==0 || aToOpen[i+1] ){\n      sqlite3VdbeAddOp3(v, op, iIdxCur, pIdx->tnum, iDb);\n      sqlite3VdbeSetP4KeyInfo(pParse, pIdx);\n      sqlite3VdbeChangeP5(v, p5);\n      VdbeComment((v, \"%s\", pIdx->zName));\n    }\n  }\n  if( iBase>pParse->nTab ) pParse->nTab = iBase;\n  return i;\n}\n\n\n#ifdef SQLITE_TEST\n/*\n** The following global variable is incremented whenever the\n** transfer optimization is used.  This is used for testing\n** purposes only - to make sure the transfer optimization really\n** is happening when it is supposed to.\n*/\nSQLITE_API int sqlite3_xferopt_count;\n#endif /* SQLITE_TEST */\n\n\n#ifndef SQLITE_OMIT_XFER_OPT\n/*\n** Check to see if index pSrc is compatible as a source of data\n** for index pDest in an insert transfer optimization.  The rules\n** for a compatible index:\n**\n**    *   The index is over the same set of columns\n**    *   The same DESC and ASC markings occurs on all columns\n**    *   The same onError processing (OE_Abort, OE_Ignore, etc)\n**    *   The same collating sequence on each column\n**    *   The index has the exact same WHERE clause\n*/\nstatic int xferCompatibleIndex(Index *pDest, Index *pSrc){\n  int i;\n  assert( pDest && pSrc );\n  assert( pDest->pTable!=pSrc->pTable );\n  if( pDest->nKeyCol!=pSrc->nKeyCol ){\n    return 0;   /* Different number of columns */\n  }\n  if( pDest->onError!=pSrc->onError ){\n    return 0;   /* Different conflict resolution strategies */\n  }\n  for(i=0; i<pSrc->nKeyCol; i++){\n    if( pSrc->aiColumn[i]!=pDest->aiColumn[i] ){\n      return 0;   /* Different columns indexed */\n    }\n    if( pSrc->aiColumn[i]==XN_EXPR ){\n      assert( pSrc->aColExpr!=0 && pDest->aColExpr!=0 );\n      if( sqlite3ExprCompare(0, pSrc->aColExpr->a[i].pExpr,\n                             pDest->aColExpr->a[i].pExpr, -1)!=0 ){\n        return 0;   /* Different expressions in the index */\n      }\n    }\n    if( pSrc->aSortOrder[i]!=pDest->aSortOrder[i] ){\n      return 0;   /* Different sort orders */\n    }\n    if( sqlite3_stricmp(pSrc->azColl[i],pDest->azColl[i])!=0 ){\n      return 0;   /* Different collating sequences */\n    }\n  }\n  if( sqlite3ExprCompare(0, pSrc->pPartIdxWhere, pDest->pPartIdxWhere, -1) ){\n    return 0;     /* Different WHERE clauses */\n  }\n\n  /* If no test above fails then the indices must be compatible */\n  return 1;\n}\n\n/*\n** Attempt the transfer optimization on INSERTs of the form\n**\n**     INSERT INTO tab1 SELECT * FROM tab2;\n**\n** The xfer optimization transfers raw records from tab2 over to tab1.  \n** Columns are not decoded and reassembled, which greatly improves\n** performance.  Raw index records are transferred in the same way.\n**\n** The xfer optimization is only attempted if tab1 and tab2 are compatible.\n** There are lots of rules for determining compatibility - see comments\n** embedded in the code for details.\n**\n** This routine returns TRUE if the optimization is guaranteed to be used.\n** Sometimes the xfer optimization will only work if the destination table\n** is empty - a factor that can only be determined at run-time.  In that\n** case, this routine generates code for the xfer optimization but also\n** does a test to see if the destination table is empty and jumps over the\n** xfer optimization code if the test fails.  In that case, this routine\n** returns FALSE so that the caller will know to go ahead and generate\n** an unoptimized transfer.  This routine also returns FALSE if there\n** is no chance that the xfer optimization can be applied.\n**\n** This optimization is particularly useful at making VACUUM run faster.\n*/\nstatic int xferOptimization(\n  Parse *pParse,        /* Parser context */\n  Table *pDest,         /* The table we are inserting into */\n  Select *pSelect,      /* A SELECT statement to use as the data source */\n  int onError,          /* How to handle constraint errors */\n  int iDbDest           /* The database of pDest */\n){\n  sqlite3 *db = pParse->db;\n  ExprList *pEList;                /* The result set of the SELECT */\n  Table *pSrc;                     /* The table in the FROM clause of SELECT */\n  Index *pSrcIdx, *pDestIdx;       /* Source and destination indices */\n  struct SrcList_item *pItem;      /* An element of pSelect->pSrc */\n  int i;                           /* Loop counter */\n  int iDbSrc;                      /* The database of pSrc */\n  int iSrc, iDest;                 /* Cursors from source and destination */\n  int addr1, addr2;                /* Loop addresses */\n  int emptyDestTest = 0;           /* Address of test for empty pDest */\n  int emptySrcTest = 0;            /* Address of test for empty pSrc */\n  Vdbe *v;                         /* The VDBE we are building */\n  int regAutoinc;                  /* Memory register used by AUTOINC */\n  int destHasUniqueIdx = 0;        /* True if pDest has a UNIQUE index */\n  int regData, regRowid;           /* Registers holding data and rowid */\n\n  if( pSelect==0 ){\n    return 0;   /* Must be of the form  INSERT INTO ... SELECT ... */\n  }\n  if( pParse->pWith || pSelect->pWith ){\n    /* Do not attempt to process this query if there are an WITH clauses\n    ** attached to it. Proceeding may generate a false \"no such table: xxx\"\n    ** error if pSelect reads from a CTE named \"xxx\".  */\n    return 0;\n  }\n  if( sqlite3TriggerList(pParse, pDest) ){\n    return 0;   /* tab1 must not have triggers */\n  }\n#ifndef SQLITE_OMIT_VIRTUALTABLE\n  if( IsVirtual(pDest) ){\n    return 0;   /* tab1 must not be a virtual table */\n  }\n#endif\n  if( onError==OE_Default ){\n    if( pDest->iPKey>=0 ) onError = pDest->keyConf;\n    if( onError==OE_Default ) onError = OE_Abort;\n  }\n  assert(pSelect->pSrc);   /* allocated even if there is no FROM clause */\n  if( pSelect->pSrc->nSrc!=1 ){\n    return 0;   /* FROM clause must have exactly one term */\n  }\n  if( pSelect->pSrc->a[0].pSelect ){\n    return 0;   /* FROM clause cannot contain a subquery */\n  }\n  if( pSelect->pWhere ){\n    return 0;   /* SELECT may not have a WHERE clause */\n  }\n  if( pSelect->pOrderBy ){\n    return 0;   /* SELECT may not have an ORDER BY clause */\n  }\n  /* Do not need to test for a HAVING clause.  If HAVING is present but\n  ** there is no ORDER BY, we will get an error. */\n  if( pSelect->pGroupBy ){\n    return 0;   /* SELECT may not have a GROUP BY clause */\n  }\n  if( pSelect->pLimit ){\n    return 0;   /* SELECT may not have a LIMIT clause */\n  }\n  if( pSelect->pPrior ){\n    return 0;   /* SELECT may not be a compound query */\n  }\n  if( pSelect->selFlags & SF_Distinct ){\n    return 0;   /* SELECT may not be DISTINCT */\n  }\n  pEList = pSelect->pEList;\n  assert( pEList!=0 );\n  if( pEList->nExpr!=1 ){\n    return 0;   /* The result set must have exactly one column */\n  }\n  assert( pEList->a[0].pExpr );\n  if( pEList->a[0].pExpr->op!=TK_ASTERISK ){\n    return 0;   /* The result set must be the special operator \"*\" */\n  }\n\n  /* At this point we have established that the statement is of the\n  ** correct syntactic form to participate in this optimization.  Now\n  ** we have to check the semantics.\n  */\n  pItem = pSelect->pSrc->a;\n  pSrc = sqlite3LocateTableItem(pParse, 0, pItem);\n  if( pSrc==0 ){\n    return 0;   /* FROM clause does not contain a real table */\n  }\n  if( pSrc==pDest ){\n    return 0;   /* tab1 and tab2 may not be the same table */\n  }\n  if( HasRowid(pDest)!=HasRowid(pSrc) ){\n    return 0;   /* source and destination must both be WITHOUT ROWID or not */\n  }\n#ifndef SQLITE_OMIT_VIRTUALTABLE\n  if( IsVirtual(pSrc) ){\n    return 0;   /* tab2 must not be a virtual table */\n  }\n#endif\n  if( pSrc->pSelect ){\n    return 0;   /* tab2 may not be a view */\n  }\n  if( pDest->nCol!=pSrc->nCol ){\n    return 0;   /* Number of columns must be the same in tab1 and tab2 */\n  }\n  if( pDest->iPKey!=pSrc->iPKey ){\n    return 0;   /* Both tables must have the same INTEGER PRIMARY KEY */\n  }\n  for(i=0; i<pDest->nCol; i++){\n    Column *pDestCol = &pDest->aCol[i];\n    Column *pSrcCol = &pSrc->aCol[i];\n#ifdef SQLITE_ENABLE_HIDDEN_COLUMNS\n    if( (db->mDbFlags & DBFLAG_Vacuum)==0 \n     && (pDestCol->colFlags | pSrcCol->colFlags) & COLFLAG_HIDDEN \n    ){\n      return 0;    /* Neither table may have __hidden__ columns */\n    }\n#endif\n    if( pDestCol->affinity!=pSrcCol->affinity ){\n      return 0;    /* Affinity must be the same on all columns */\n    }\n    if( sqlite3_stricmp(pDestCol->zColl, pSrcCol->zColl)!=0 ){\n      return 0;    /* Collating sequence must be the same on all columns */\n    }\n    if( pDestCol->notNull && !pSrcCol->notNull ){\n      return 0;    /* tab2 must be NOT NULL if tab1 is */\n    }\n    /* Default values for second and subsequent columns need to match. */\n    if( i>0 ){\n      assert( pDestCol->pDflt==0 || pDestCol->pDflt->op==TK_SPAN );\n      assert( pSrcCol->pDflt==0 || pSrcCol->pDflt->op==TK_SPAN );\n      if( (pDestCol->pDflt==0)!=(pSrcCol->pDflt==0) \n       || (pDestCol->pDflt && strcmp(pDestCol->pDflt->u.zToken,\n                                       pSrcCol->pDflt->u.zToken)!=0)\n      ){\n        return 0;    /* Default values must be the same for all columns */\n      }\n    }\n  }\n  for(pDestIdx=pDest->pIndex; pDestIdx; pDestIdx=pDestIdx->pNext){\n    if( IsUniqueIndex(pDestIdx) ){\n      destHasUniqueIdx = 1;\n    }\n    for(pSrcIdx=pSrc->pIndex; pSrcIdx; pSrcIdx=pSrcIdx->pNext){\n      if( xferCompatibleIndex(pDestIdx, pSrcIdx) ) break;\n    }\n    if( pSrcIdx==0 ){\n      return 0;    /* pDestIdx has no corresponding index in pSrc */\n    }\n  }\n#ifndef SQLITE_OMIT_CHECK\n  if( pDest->pCheck && sqlite3ExprListCompare(pSrc->pCheck,pDest->pCheck,-1) ){\n    return 0;   /* Tables have different CHECK constraints.  Ticket #2252 */\n  }\n#endif\n#ifndef SQLITE_OMIT_FOREIGN_KEY\n  /* Disallow the transfer optimization if the destination table constains\n  ** any foreign key constraints.  This is more restrictive than necessary.\n  ** But the main beneficiary of the transfer optimization is the VACUUM \n  ** command, and the VACUUM command disables foreign key constraints.  So\n  ** the extra complication to make this rule less restrictive is probably\n  ** not worth the effort.  Ticket [6284df89debdfa61db8073e062908af0c9b6118e]\n  */\n  if( (db->flags & SQLITE_ForeignKeys)!=0 && pDest->pFKey!=0 ){\n    return 0;\n  }\n#endif\n  if( (db->flags & SQLITE_CountRows)!=0 ){\n    return 0;  /* xfer opt does not play well with PRAGMA count_changes */\n  }\n\n  /* If we get this far, it means that the xfer optimization is at\n  ** least a possibility, though it might only work if the destination\n  ** table (tab1) is initially empty.\n  */\n#ifdef SQLITE_TEST\n  sqlite3_xferopt_count++;\n#endif\n  iDbSrc = sqlite3SchemaToIndex(db, pSrc->pSchema);\n  v = sqlite3GetVdbe(pParse);\n  sqlite3CodeVerifySchema(pParse, iDbSrc);\n  iSrc = pParse->nTab++;\n  iDest = pParse->nTab++;\n  regAutoinc = autoIncBegin(pParse, iDbDest, pDest);\n  regData = sqlite3GetTempReg(pParse);\n  regRowid = sqlite3GetTempReg(pParse);\n  sqlite3OpenTable(pParse, iDest, iDbDest, pDest, OP_OpenWrite);\n  assert( HasRowid(pDest) || destHasUniqueIdx );\n  if( (db->mDbFlags & DBFLAG_Vacuum)==0 && (\n      (pDest->iPKey<0 && pDest->pIndex!=0)          /* (1) */\n   || destHasUniqueIdx                              /* (2) */\n   || (onError!=OE_Abort && onError!=OE_Rollback)   /* (3) */\n  )){\n    /* In some circumstances, we are able to run the xfer optimization\n    ** only if the destination table is initially empty. Unless the\n    ** DBFLAG_Vacuum flag is set, this block generates code to make\n    ** that determination. If DBFLAG_Vacuum is set, then the destination\n    ** table is always empty.\n    **\n    ** Conditions under which the destination must be empty:\n    **\n    ** (1) There is no INTEGER PRIMARY KEY but there are indices.\n    **     (If the destination is not initially empty, the rowid fields\n    **     of index entries might need to change.)\n    **\n    ** (2) The destination has a unique index.  (The xfer optimization \n    **     is unable to test uniqueness.)\n    **\n    ** (3) onError is something other than OE_Abort and OE_Rollback.\n    */\n    addr1 = sqlite3VdbeAddOp2(v, OP_Rewind, iDest, 0); VdbeCoverage(v);\n    emptyDestTest = sqlite3VdbeAddOp0(v, OP_Goto);\n    sqlite3VdbeJumpHere(v, addr1);\n  }\n  if( HasRowid(pSrc) ){\n    u8 insFlags;\n    sqlite3OpenTable(pParse, iSrc, iDbSrc, pSrc, OP_OpenRead);\n    emptySrcTest = sqlite3VdbeAddOp2(v, OP_Rewind, iSrc, 0); VdbeCoverage(v);\n    if( pDest->iPKey>=0 ){\n      addr1 = sqlite3VdbeAddOp2(v, OP_Rowid, iSrc, regRowid);\n      addr2 = sqlite3VdbeAddOp3(v, OP_NotExists, iDest, 0, regRowid);\n      VdbeCoverage(v);\n      sqlite3RowidConstraint(pParse, onError, pDest);\n      sqlite3VdbeJumpHere(v, addr2);\n      autoIncStep(pParse, regAutoinc, regRowid);\n    }else if( pDest->pIndex==0 ){\n      addr1 = sqlite3VdbeAddOp2(v, OP_NewRowid, iDest, regRowid);\n    }else{\n      addr1 = sqlite3VdbeAddOp2(v, OP_Rowid, iSrc, regRowid);\n      assert( (pDest->tabFlags & TF_Autoincrement)==0 );\n    }\n    sqlite3VdbeAddOp3(v, OP_RowData, iSrc, regData, 1);\n    if( db->mDbFlags & DBFLAG_Vacuum ){\n      sqlite3VdbeAddOp1(v, OP_SeekEnd, iDest);\n      insFlags = OPFLAG_NCHANGE|OPFLAG_LASTROWID|\n                           OPFLAG_APPEND|OPFLAG_USESEEKRESULT;\n    }else{\n      insFlags = OPFLAG_NCHANGE|OPFLAG_LASTROWID|OPFLAG_APPEND;\n    }\n    sqlite3VdbeAddOp4(v, OP_Insert, iDest, regData, regRowid,\n                      (char*)pDest, P4_TABLE);\n    sqlite3VdbeChangeP5(v, insFlags);\n    sqlite3VdbeAddOp2(v, OP_Next, iSrc, addr1); VdbeCoverage(v);\n    sqlite3VdbeAddOp2(v, OP_Close, iSrc, 0);\n    sqlite3VdbeAddOp2(v, OP_Close, iDest, 0);\n  }else{\n    sqlite3TableLock(pParse, iDbDest, pDest->tnum, 1, pDest->zName);\n    sqlite3TableLock(pParse, iDbSrc, pSrc->tnum, 0, pSrc->zName);\n  }\n  for(pDestIdx=pDest->pIndex; pDestIdx; pDestIdx=pDestIdx->pNext){\n    u8 idxInsFlags = 0;\n    for(pSrcIdx=pSrc->pIndex; ALWAYS(pSrcIdx); pSrcIdx=pSrcIdx->pNext){\n      if( xferCompatibleIndex(pDestIdx, pSrcIdx) ) break;\n    }\n    assert( pSrcIdx );\n    sqlite3VdbeAddOp3(v, OP_OpenRead, iSrc, pSrcIdx->tnum, iDbSrc);\n    sqlite3VdbeSetP4KeyInfo(pParse, pSrcIdx);\n    VdbeComment((v, \"%s\", pSrcIdx->zName));\n    sqlite3VdbeAddOp3(v, OP_OpenWrite, iDest, pDestIdx->tnum, iDbDest);\n    sqlite3VdbeSetP4KeyInfo(pParse, pDestIdx);\n    sqlite3VdbeChangeP5(v, OPFLAG_BULKCSR);\n    VdbeComment((v, \"%s\", pDestIdx->zName));\n    addr1 = sqlite3VdbeAddOp2(v, OP_Rewind, iSrc, 0); VdbeCoverage(v);\n    sqlite3VdbeAddOp3(v, OP_RowData, iSrc, regData, 1);\n    if( db->mDbFlags & DBFLAG_Vacuum ){\n      /* This INSERT command is part of a VACUUM operation, which guarantees\n      ** that the destination table is empty. If all indexed columns use\n      ** collation sequence BINARY, then it can also be assumed that the\n      ** index will be populated by inserting keys in strictly sorted \n      ** order. In this case, instead of seeking within the b-tree as part\n      ** of every OP_IdxInsert opcode, an OP_SeekEnd is added before the\n      ** OP_IdxInsert to seek to the point within the b-tree where each key \n      ** should be inserted. This is faster.\n      **\n      ** If any of the indexed columns use a collation sequence other than\n      ** BINARY, this optimization is disabled. This is because the user \n      ** might change the definition of a collation sequence and then run\n      ** a VACUUM command. In that case keys may not be written in strictly\n      ** sorted order.  */\n      for(i=0; i<pSrcIdx->nColumn; i++){\n        const char *zColl = pSrcIdx->azColl[i];\n        if( sqlite3_stricmp(sqlite3StrBINARY, zColl) ) break;\n      }\n      if( i==pSrcIdx->nColumn ){\n        idxInsFlags = OPFLAG_USESEEKRESULT;\n        sqlite3VdbeAddOp1(v, OP_SeekEnd, iDest);\n      }\n    }\n    if( !HasRowid(pSrc) && pDestIdx->idxType==2 ){\n      idxInsFlags |= OPFLAG_NCHANGE;\n    }\n    sqlite3VdbeAddOp2(v, OP_IdxInsert, iDest, regData);\n    sqlite3VdbeChangeP5(v, idxInsFlags|OPFLAG_APPEND);\n    sqlite3VdbeAddOp2(v, OP_Next, iSrc, addr1+1); VdbeCoverage(v);\n    sqlite3VdbeJumpHere(v, addr1);\n    sqlite3VdbeAddOp2(v, OP_Close, iSrc, 0);\n    sqlite3VdbeAddOp2(v, OP_Close, iDest, 0);\n  }\n  if( emptySrcTest ) sqlite3VdbeJumpHere(v, emptySrcTest);\n  sqlite3ReleaseTempReg(pParse, regRowid);\n  sqlite3ReleaseTempReg(pParse, regData);\n  if( emptyDestTest ){\n    sqlite3AutoincrementEnd(pParse);\n    sqlite3VdbeAddOp2(v, OP_Halt, SQLITE_OK, 0);\n    sqlite3VdbeJumpHere(v, emptyDestTest);\n    sqlite3VdbeAddOp2(v, OP_Close, iDest, 0);\n    return 0;\n  }else{\n    return 1;\n  }\n}\n#endif /* SQLITE_OMIT_XFER_OPT */\n\n/************** End of insert.c **********************************************/\n/************** Begin file legacy.c ******************************************/\n/*\n** 2001 September 15\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n*************************************************************************\n** Main file for the SQLite library.  The routines in this file\n** implement the programmer interface to the library.  Routines in\n** other files are for internal use by SQLite and should not be\n** accessed by users of the library.\n*/\n\n/* #include \"sqliteInt.h\" */\n\n/*\n** Execute SQL code.  Return one of the SQLITE_ success/failure\n** codes.  Also write an error message into memory obtained from\n** malloc() and make *pzErrMsg point to that message.\n**\n** If the SQL is a query, then for each row in the query result\n** the xCallback() function is called.  pArg becomes the first\n** argument to xCallback().  If xCallback=NULL then no callback\n** is invoked, even for queries.\n*/\nSQLITE_API int sqlite3_exec(\n  sqlite3 *db,                /* The database on which the SQL executes */\n  const char *zSql,           /* The SQL to be executed */\n  sqlite3_callback xCallback, /* Invoke this callback routine */\n  void *pArg,                 /* First argument to xCallback() */\n  char **pzErrMsg             /* Write error messages here */\n){\n  int rc = SQLITE_OK;         /* Return code */\n  const char *zLeftover;      /* Tail of unprocessed SQL */\n  sqlite3_stmt *pStmt = 0;    /* The current SQL statement */\n  char **azCols = 0;          /* Names of result columns */\n  int callbackIsInit;         /* True if callback data is initialized */\n\n  if( !sqlite3SafetyCheckOk(db) ) return SQLITE_MISUSE_BKPT;\n  if( zSql==0 ) zSql = \"\";\n\n  sqlite3_mutex_enter(db->mutex);\n  sqlite3Error(db, SQLITE_OK);\n  while( rc==SQLITE_OK && zSql[0] ){\n    int nCol;\n    char **azVals = 0;\n\n    pStmt = 0;\n    rc = sqlite3_prepare_v2(db, zSql, -1, &pStmt, &zLeftover);\n    assert( rc==SQLITE_OK || pStmt==0 );\n    if( rc!=SQLITE_OK ){\n      continue;\n    }\n    if( !pStmt ){\n      /* this happens for a comment or white-space */\n      zSql = zLeftover;\n      continue;\n    }\n\n    callbackIsInit = 0;\n    nCol = sqlite3_column_count(pStmt);\n\n    while( 1 ){\n      int i;\n      rc = sqlite3_step(pStmt);\n\n      /* Invoke the callback function if required */\n      if( xCallback && (SQLITE_ROW==rc || \n          (SQLITE_DONE==rc && !callbackIsInit\n                           && db->flags&SQLITE_NullCallback)) ){\n        if( !callbackIsInit ){\n          azCols = sqlite3DbMallocRaw(db, (2*nCol+1)*sizeof(const char*));\n          if( azCols==0 ){\n            goto exec_out;\n          }\n          for(i=0; i<nCol; i++){\n            azCols[i] = (char *)sqlite3_column_name(pStmt, i);\n            /* sqlite3VdbeSetColName() installs column names as UTF8\n            ** strings so there is no way for sqlite3_column_name() to fail. */\n            assert( azCols[i]!=0 );\n          }\n          callbackIsInit = 1;\n        }\n        if( rc==SQLITE_ROW ){\n          azVals = &azCols[nCol];\n          for(i=0; i<nCol; i++){\n            azVals[i] = (char *)sqlite3_column_text(pStmt, i);\n            if( !azVals[i] && sqlite3_column_type(pStmt, i)!=SQLITE_NULL ){\n              sqlite3OomFault(db);\n              goto exec_out;\n            }\n          }\n          azVals[i] = 0;\n        }\n        if( xCallback(pArg, nCol, azVals, azCols) ){\n          /* EVIDENCE-OF: R-38229-40159 If the callback function to\n          ** sqlite3_exec() returns non-zero, then sqlite3_exec() will\n          ** return SQLITE_ABORT. */\n          rc = SQLITE_ABORT;\n          sqlite3VdbeFinalize((Vdbe *)pStmt);\n          pStmt = 0;\n          sqlite3Error(db, SQLITE_ABORT);\n          goto exec_out;\n        }\n      }\n\n      if( rc!=SQLITE_ROW ){\n        rc = sqlite3VdbeFinalize((Vdbe *)pStmt);\n        pStmt = 0;\n        zSql = zLeftover;\n        while( sqlite3Isspace(zSql[0]) ) zSql++;\n        break;\n      }\n    }\n\n    sqlite3DbFree(db, azCols);\n    azCols = 0;\n  }\n\nexec_out:\n  if( pStmt ) sqlite3VdbeFinalize((Vdbe *)pStmt);\n  sqlite3DbFree(db, azCols);\n\n  rc = sqlite3ApiExit(db, rc);\n  if( rc!=SQLITE_OK && pzErrMsg ){\n    *pzErrMsg = sqlite3DbStrDup(0, sqlite3_errmsg(db));\n    if( *pzErrMsg==0 ){\n      rc = SQLITE_NOMEM_BKPT;\n      sqlite3Error(db, SQLITE_NOMEM);\n    }\n  }else if( pzErrMsg ){\n    *pzErrMsg = 0;\n  }\n\n  assert( (rc&db->errMask)==rc );\n  sqlite3_mutex_leave(db->mutex);\n  return rc;\n}\n\n/************** End of legacy.c **********************************************/\n/************** Begin file loadext.c *****************************************/\n/*\n** 2006 June 7\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n*************************************************************************\n** This file contains code used to dynamically load extensions into\n** the SQLite library.\n*/\n\n#ifndef SQLITE_CORE\n  #define SQLITE_CORE 1  /* Disable the API redefinition in sqlite3ext.h */\n#endif\n/************** Include sqlite3ext.h in the middle of loadext.c **************/\n/************** Begin file sqlite3ext.h **************************************/\n/*\n** 2006 June 7\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n*************************************************************************\n** This header file defines the SQLite interface for use by\n** shared libraries that want to be imported as extensions into\n** an SQLite instance.  Shared libraries that intend to be loaded\n** as extensions by SQLite should #include this file instead of \n** sqlite3.h.\n*/\n#ifndef SQLITE3EXT_H\n#define SQLITE3EXT_H\n/* #include \"sqlite3.h\" */\n\n/*\n** The following structure holds pointers to all of the SQLite API\n** routines.\n**\n** WARNING:  In order to maintain backwards compatibility, add new\n** interfaces to the end of this structure only.  If you insert new\n** interfaces in the middle of this structure, then older different\n** versions of SQLite will not be able to load each other's shared\n** libraries!\n*/\nstruct sqlite3_api_routines {\n  void * (*aggregate_context)(sqlite3_context*,int nBytes);\n  int  (*aggregate_count)(sqlite3_context*);\n  int  (*bind_blob)(sqlite3_stmt*,int,const void*,int n,void(*)(void*));\n  int  (*bind_double)(sqlite3_stmt*,int,double);\n  int  (*bind_int)(sqlite3_stmt*,int,int);\n  int  (*bind_int64)(sqlite3_stmt*,int,sqlite_int64);\n  int  (*bind_null)(sqlite3_stmt*,int);\n  int  (*bind_parameter_count)(sqlite3_stmt*);\n  int  (*bind_parameter_index)(sqlite3_stmt*,const char*zName);\n  const char * (*bind_parameter_name)(sqlite3_stmt*,int);\n  int  (*bind_text)(sqlite3_stmt*,int,const char*,int n,void(*)(void*));\n  int  (*bind_text16)(sqlite3_stmt*,int,const void*,int,void(*)(void*));\n  int  (*bind_value)(sqlite3_stmt*,int,const sqlite3_value*);\n  int  (*busy_handler)(sqlite3*,int(*)(void*,int),void*);\n  int  (*busy_timeout)(sqlite3*,int ms);\n  int  (*changes)(sqlite3*);\n  int  (*close)(sqlite3*);\n  int  (*collation_needed)(sqlite3*,void*,void(*)(void*,sqlite3*,\n                           int eTextRep,const char*));\n  int  (*collation_needed16)(sqlite3*,void*,void(*)(void*,sqlite3*,\n                             int eTextRep,const void*));\n  const void * (*column_blob)(sqlite3_stmt*,int iCol);\n  int  (*column_bytes)(sqlite3_stmt*,int iCol);\n  int  (*column_bytes16)(sqlite3_stmt*,int iCol);\n  int  (*column_count)(sqlite3_stmt*pStmt);\n  const char * (*column_database_name)(sqlite3_stmt*,int);\n  const void * (*column_database_name16)(sqlite3_stmt*,int);\n  const char * (*column_decltype)(sqlite3_stmt*,int i);\n  const void * (*column_decltype16)(sqlite3_stmt*,int);\n  double  (*column_double)(sqlite3_stmt*,int iCol);\n  int  (*column_int)(sqlite3_stmt*,int iCol);\n  sqlite_int64  (*column_int64)(sqlite3_stmt*,int iCol);\n  const char * (*column_name)(sqlite3_stmt*,int);\n  const void * (*column_name16)(sqlite3_stmt*,int);\n  const char * (*column_origin_name)(sqlite3_stmt*,int);\n  const void * (*column_origin_name16)(sqlite3_stmt*,int);\n  const char * (*column_table_name)(sqlite3_stmt*,int);\n  const void * (*column_table_name16)(sqlite3_stmt*,int);\n  const unsigned char * (*column_text)(sqlite3_stmt*,int iCol);\n  const void * (*column_text16)(sqlite3_stmt*,int iCol);\n  int  (*column_type)(sqlite3_stmt*,int iCol);\n  sqlite3_value* (*column_value)(sqlite3_stmt*,int iCol);\n  void * (*commit_hook)(sqlite3*,int(*)(void*),void*);\n  int  (*complete)(const char*sql);\n  int  (*complete16)(const void*sql);\n  int  (*create_collation)(sqlite3*,const char*,int,void*,\n                           int(*)(void*,int,const void*,int,const void*));\n  int  (*create_collation16)(sqlite3*,const void*,int,void*,\n                             int(*)(void*,int,const void*,int,const void*));\n  int  (*create_function)(sqlite3*,const char*,int,int,void*,\n                          void (*xFunc)(sqlite3_context*,int,sqlite3_value**),\n                          void (*xStep)(sqlite3_context*,int,sqlite3_value**),\n                          void (*xFinal)(sqlite3_context*));\n  int  (*create_function16)(sqlite3*,const void*,int,int,void*,\n                            void (*xFunc)(sqlite3_context*,int,sqlite3_value**),\n                            void (*xStep)(sqlite3_context*,int,sqlite3_value**),\n                            void (*xFinal)(sqlite3_context*));\n  int (*create_module)(sqlite3*,const char*,const sqlite3_module*,void*);\n  int  (*data_count)(sqlite3_stmt*pStmt);\n  sqlite3 * (*db_handle)(sqlite3_stmt*);\n  int (*declare_vtab)(sqlite3*,const char*);\n  int  (*enable_shared_cache)(int);\n  int  (*errcode)(sqlite3*db);\n  const char * (*errmsg)(sqlite3*);\n  const void * (*errmsg16)(sqlite3*);\n  int  (*exec)(sqlite3*,const char*,sqlite3_callback,void*,char**);\n  int  (*expired)(sqlite3_stmt*);\n  int  (*finalize)(sqlite3_stmt*pStmt);\n  void  (*free)(void*);\n  void  (*free_table)(char**result);\n  int  (*get_autocommit)(sqlite3*);\n  void * (*get_auxdata)(sqlite3_context*,int);\n  int  (*get_table)(sqlite3*,const char*,char***,int*,int*,char**);\n  int  (*global_recover)(void);\n  void  (*interruptx)(sqlite3*);\n  sqlite_int64  (*last_insert_rowid)(sqlite3*);\n  const char * (*libversion)(void);\n  int  (*libversion_number)(void);\n  void *(*malloc)(int);\n  char * (*mprintf)(const char*,...);\n  int  (*open)(const char*,sqlite3**);\n  int  (*open16)(const void*,sqlite3**);\n  int  (*prepare)(sqlite3*,const char*,int,sqlite3_stmt**,const char**);\n  int  (*prepare16)(sqlite3*,const void*,int,sqlite3_stmt**,const void**);\n  void * (*profile)(sqlite3*,void(*)(void*,const char*,sqlite_uint64),void*);\n  void  (*progress_handler)(sqlite3*,int,int(*)(void*),void*);\n  void *(*realloc)(void*,int);\n  int  (*reset)(sqlite3_stmt*pStmt);\n  void  (*result_blob)(sqlite3_context*,const void*,int,void(*)(void*));\n  void  (*result_double)(sqlite3_context*,double);\n  void  (*result_error)(sqlite3_context*,const char*,int);\n  void  (*result_error16)(sqlite3_context*,const void*,int);\n  void  (*result_int)(sqlite3_context*,int);\n  void  (*result_int64)(sqlite3_context*,sqlite_int64);\n  void  (*result_null)(sqlite3_context*);\n  void  (*result_text)(sqlite3_context*,const char*,int,void(*)(void*));\n  void  (*result_text16)(sqlite3_context*,const void*,int,void(*)(void*));\n  void  (*result_text16be)(sqlite3_context*,const void*,int,void(*)(void*));\n  void  (*result_text16le)(sqlite3_context*,const void*,int,void(*)(void*));\n  void  (*result_value)(sqlite3_context*,sqlite3_value*);\n  void * (*rollback_hook)(sqlite3*,void(*)(void*),void*);\n  int  (*set_authorizer)(sqlite3*,int(*)(void*,int,const char*,const char*,\n                         const char*,const char*),void*);\n  void  (*set_auxdata)(sqlite3_context*,int,void*,void (*)(void*));\n  char * (*xsnprintf)(int,char*,const char*,...);\n  int  (*step)(sqlite3_stmt*);\n  int  (*table_column_metadata)(sqlite3*,const char*,const char*,const char*,\n                                char const**,char const**,int*,int*,int*);\n  void  (*thread_cleanup)(void);\n  int  (*total_changes)(sqlite3*);\n  void * (*trace)(sqlite3*,void(*xTrace)(void*,const char*),void*);\n  int  (*transfer_bindings)(sqlite3_stmt*,sqlite3_stmt*);\n  void * (*update_hook)(sqlite3*,void(*)(void*,int ,char const*,char const*,\n                                         sqlite_int64),void*);\n  void * (*user_data)(sqlite3_context*);\n  const void * (*value_blob)(sqlite3_value*);\n  int  (*value_bytes)(sqlite3_value*);\n  int  (*value_bytes16)(sqlite3_value*);\n  double  (*value_double)(sqlite3_value*);\n  int  (*value_int)(sqlite3_value*);\n  sqlite_int64  (*value_int64)(sqlite3_value*);\n  int  (*value_numeric_type)(sqlite3_value*);\n  const unsigned char * (*value_text)(sqlite3_value*);\n  const void * (*value_text16)(sqlite3_value*);\n  const void * (*value_text16be)(sqlite3_value*);\n  const void * (*value_text16le)(sqlite3_value*);\n  int  (*value_type)(sqlite3_value*);\n  char *(*vmprintf)(const char*,va_list);\n  /* Added ??? */\n  int (*overload_function)(sqlite3*, const char *zFuncName, int nArg);\n  /* Added by 3.3.13 */\n  int (*prepare_v2)(sqlite3*,const char*,int,sqlite3_stmt**,const char**);\n  int (*prepare16_v2)(sqlite3*,const void*,int,sqlite3_stmt**,const void**);\n  int (*clear_bindings)(sqlite3_stmt*);\n  /* Added by 3.4.1 */\n  int (*create_module_v2)(sqlite3*,const char*,const sqlite3_module*,void*,\n                          void (*xDestroy)(void *));\n  /* Added by 3.5.0 */\n  int (*bind_zeroblob)(sqlite3_stmt*,int,int);\n  int (*blob_bytes)(sqlite3_blob*);\n  int (*blob_close)(sqlite3_blob*);\n  int (*blob_open)(sqlite3*,const char*,const char*,const char*,sqlite3_int64,\n                   int,sqlite3_blob**);\n  int (*blob_read)(sqlite3_blob*,void*,int,int);\n  int (*blob_write)(sqlite3_blob*,const void*,int,int);\n  int (*create_collation_v2)(sqlite3*,const char*,int,void*,\n                             int(*)(void*,int,const void*,int,const void*),\n                             void(*)(void*));\n  int (*file_control)(sqlite3*,const char*,int,void*);\n  sqlite3_int64 (*memory_highwater)(int);\n  sqlite3_int64 (*memory_used)(void);\n  sqlite3_mutex *(*mutex_alloc)(int);\n  void (*mutex_enter)(sqlite3_mutex*);\n  void (*mutex_free)(sqlite3_mutex*);\n  void (*mutex_leave)(sqlite3_mutex*);\n  int (*mutex_try)(sqlite3_mutex*);\n  int (*open_v2)(const char*,sqlite3**,int,const char*);\n  int (*release_memory)(int);\n  void (*result_error_nomem)(sqlite3_context*);\n  void (*result_error_toobig)(sqlite3_context*);\n  int (*sleep)(int);\n  void (*soft_heap_limit)(int);\n  sqlite3_vfs *(*vfs_find)(const char*);\n  int (*vfs_register)(sqlite3_vfs*,int);\n  int (*vfs_unregister)(sqlite3_vfs*);\n  int (*xthreadsafe)(void);\n  void (*result_zeroblob)(sqlite3_context*,int);\n  void (*result_error_code)(sqlite3_context*,int);\n  int (*test_control)(int, ...);\n  void (*randomness)(int,void*);\n  sqlite3 *(*context_db_handle)(sqlite3_context*);\n  int (*extended_result_codes)(sqlite3*,int);\n  int (*limit)(sqlite3*,int,int);\n  sqlite3_stmt *(*next_stmt)(sqlite3*,sqlite3_stmt*);\n  const char *(*sql)(sqlite3_stmt*);\n  int (*status)(int,int*,int*,int);\n  int (*backup_finish)(sqlite3_backup*);\n  sqlite3_backup *(*backup_init)(sqlite3*,const char*,sqlite3*,const char*);\n  int (*backup_pagecount)(sqlite3_backup*);\n  int (*backup_remaining)(sqlite3_backup*);\n  int (*backup_step)(sqlite3_backup*,int);\n  const char *(*compileoption_get)(int);\n  int (*compileoption_used)(const char*);\n  int (*create_function_v2)(sqlite3*,const char*,int,int,void*,\n                            void (*xFunc)(sqlite3_context*,int,sqlite3_value**),\n                            void (*xStep)(sqlite3_context*,int,sqlite3_value**),\n                            void (*xFinal)(sqlite3_context*),\n                            void(*xDestroy)(void*));\n  int (*db_config)(sqlite3*,int,...);\n  sqlite3_mutex *(*db_mutex)(sqlite3*);\n  int (*db_status)(sqlite3*,int,int*,int*,int);\n  int (*extended_errcode)(sqlite3*);\n  void (*log)(int,const char*,...);\n  sqlite3_int64 (*soft_heap_limit64)(sqlite3_int64);\n  const char *(*sourceid)(void);\n  int (*stmt_status)(sqlite3_stmt*,int,int);\n  int (*strnicmp)(const char*,const char*,int);\n  int (*unlock_notify)(sqlite3*,void(*)(void**,int),void*);\n  int (*wal_autocheckpoint)(sqlite3*,int);\n  int (*wal_checkpoint)(sqlite3*,const char*);\n  void *(*wal_hook)(sqlite3*,int(*)(void*,sqlite3*,const char*,int),void*);\n  int (*blob_reopen)(sqlite3_blob*,sqlite3_int64);\n  int (*vtab_config)(sqlite3*,int op,...);\n  int (*vtab_on_conflict)(sqlite3*);\n  /* Version 3.7.16 and later */\n  int (*close_v2)(sqlite3*);\n  const char *(*db_filename)(sqlite3*,const char*);\n  int (*db_readonly)(sqlite3*,const char*);\n  int (*db_release_memory)(sqlite3*);\n  const char *(*errstr)(int);\n  int (*stmt_busy)(sqlite3_stmt*);\n  int (*stmt_readonly)(sqlite3_stmt*);\n  int (*stricmp)(const char*,const char*);\n  int (*uri_boolean)(const char*,const char*,int);\n  sqlite3_int64 (*uri_int64)(const char*,const char*,sqlite3_int64);\n  const char *(*uri_parameter)(const char*,const char*);\n  char *(*xvsnprintf)(int,char*,const char*,va_list);\n  int (*wal_checkpoint_v2)(sqlite3*,const char*,int,int*,int*);\n  /* Version 3.8.7 and later */\n  int (*auto_extension)(void(*)(void));\n  int (*bind_blob64)(sqlite3_stmt*,int,const void*,sqlite3_uint64,\n                     void(*)(void*));\n  int (*bind_text64)(sqlite3_stmt*,int,const char*,sqlite3_uint64,\n                      void(*)(void*),unsigned char);\n  int (*cancel_auto_extension)(void(*)(void));\n  int (*load_extension)(sqlite3*,const char*,const char*,char**);\n  void *(*malloc64)(sqlite3_uint64);\n  sqlite3_uint64 (*msize)(void*);\n  void *(*realloc64)(void*,sqlite3_uint64);\n  void (*reset_auto_extension)(void);\n  void (*result_blob64)(sqlite3_context*,const void*,sqlite3_uint64,\n                        void(*)(void*));\n  void (*result_text64)(sqlite3_context*,const char*,sqlite3_uint64,\n                         void(*)(void*), unsigned char);\n  int (*strglob)(const char*,const char*);\n  /* Version 3.8.11 and later */\n  sqlite3_value *(*value_dup)(const sqlite3_value*);\n  void (*value_free)(sqlite3_value*);\n  int (*result_zeroblob64)(sqlite3_context*,sqlite3_uint64);\n  int (*bind_zeroblob64)(sqlite3_stmt*, int, sqlite3_uint64);\n  /* Version 3.9.0 and later */\n  unsigned int (*value_subtype)(sqlite3_value*);\n  void (*result_subtype)(sqlite3_context*,unsigned int);\n  /* Version 3.10.0 and later */\n  int (*status64)(int,sqlite3_int64*,sqlite3_int64*,int);\n  int (*strlike)(const char*,const char*,unsigned int);\n  int (*db_cacheflush)(sqlite3*);\n  /* Version 3.12.0 and later */\n  int (*system_errno)(sqlite3*);\n  /* Version 3.14.0 and later */\n  int (*trace_v2)(sqlite3*,unsigned,int(*)(unsigned,void*,void*,void*),void*);\n  char *(*expanded_sql)(sqlite3_stmt*);\n  /* Version 3.18.0 and later */\n  void (*set_last_insert_rowid)(sqlite3*,sqlite3_int64);\n  /* Version 3.20.0 and later */\n  int (*prepare_v3)(sqlite3*,const char*,int,unsigned int,\n                    sqlite3_stmt**,const char**);\n  int (*prepare16_v3)(sqlite3*,const void*,int,unsigned int,\n                      sqlite3_stmt**,const void**);\n  int (*bind_pointer)(sqlite3_stmt*,int,void*,const char*,void(*)(void*));\n  void (*result_pointer)(sqlite3_context*,void*,const char*,void(*)(void*));\n  void *(*value_pointer)(sqlite3_value*,const char*);\n  int (*vtab_nochange)(sqlite3_context*);\n  int (*value_nochange)(sqlite3_value*);\n  const char *(*vtab_collation)(sqlite3_index_info*,int);\n};\n\n/*\n** This is the function signature used for all extension entry points.  It\n** is also defined in the file \"loadext.c\".\n*/\ntypedef int (*sqlite3_loadext_entry)(\n  sqlite3 *db,                       /* Handle to the database. */\n  char **pzErrMsg,                   /* Used to set error string on failure. */\n  const sqlite3_api_routines *pThunk /* Extension API function pointers. */\n);\n\n/*\n** The following macros redefine the API routines so that they are\n** redirected through the global sqlite3_api structure.\n**\n** This header file is also used by the loadext.c source file\n** (part of the main SQLite library - not an extension) so that\n** it can get access to the sqlite3_api_routines structure\n** definition.  But the main library does not want to redefine\n** the API.  So the redefinition macros are only valid if the\n** SQLITE_CORE macros is undefined.\n*/\n#if !defined(SQLITE_CORE) && !defined(SQLITE_OMIT_LOAD_EXTENSION)\n#define sqlite3_aggregate_context      sqlite3_api->aggregate_context\n#ifndef SQLITE_OMIT_DEPRECATED\n#define sqlite3_aggregate_count        sqlite3_api->aggregate_count\n#endif\n#define sqlite3_bind_blob              sqlite3_api->bind_blob\n#define sqlite3_bind_double            sqlite3_api->bind_double\n#define sqlite3_bind_int               sqlite3_api->bind_int\n#define sqlite3_bind_int64             sqlite3_api->bind_int64\n#define sqlite3_bind_null              sqlite3_api->bind_null\n#define sqlite3_bind_parameter_count   sqlite3_api->bind_parameter_count\n#define sqlite3_bind_parameter_index   sqlite3_api->bind_parameter_index\n#define sqlite3_bind_parameter_name    sqlite3_api->bind_parameter_name\n#define sqlite3_bind_text              sqlite3_api->bind_text\n#define sqlite3_bind_text16            sqlite3_api->bind_text16\n#define sqlite3_bind_value             sqlite3_api->bind_value\n#define sqlite3_busy_handler           sqlite3_api->busy_handler\n#define sqlite3_busy_timeout           sqlite3_api->busy_timeout\n#define sqlite3_changes                sqlite3_api->changes\n#define sqlite3_close                  sqlite3_api->close\n#define sqlite3_collation_needed       sqlite3_api->collation_needed\n#define sqlite3_collation_needed16     sqlite3_api->collation_needed16\n#define sqlite3_column_blob            sqlite3_api->column_blob\n#define sqlite3_column_bytes           sqlite3_api->column_bytes\n#define sqlite3_column_bytes16         sqlite3_api->column_bytes16\n#define sqlite3_column_count           sqlite3_api->column_count\n#define sqlite3_column_database_name   sqlite3_api->column_database_name\n#define sqlite3_column_database_name16 sqlite3_api->column_database_name16\n#define sqlite3_column_decltype        sqlite3_api->column_decltype\n#define sqlite3_column_decltype16      sqlite3_api->column_decltype16\n#define sqlite3_column_double          sqlite3_api->column_double\n#define sqlite3_column_int             sqlite3_api->column_int\n#define sqlite3_column_int64           sqlite3_api->column_int64\n#define sqlite3_column_name            sqlite3_api->column_name\n#define sqlite3_column_name16          sqlite3_api->column_name16\n#define sqlite3_column_origin_name     sqlite3_api->column_origin_name\n#define sqlite3_column_origin_name16   sqlite3_api->column_origin_name16\n#define sqlite3_column_table_name      sqlite3_api->column_table_name\n#define sqlite3_column_table_name16    sqlite3_api->column_table_name16\n#define sqlite3_column_text            sqlite3_api->column_text\n#define sqlite3_column_text16          sqlite3_api->column_text16\n#define sqlite3_column_type            sqlite3_api->column_type\n#define sqlite3_column_value           sqlite3_api->column_value\n#define sqlite3_commit_hook            sqlite3_api->commit_hook\n#define sqlite3_complete               sqlite3_api->complete\n#define sqlite3_complete16             sqlite3_api->complete16\n#define sqlite3_create_collation       sqlite3_api->create_collation\n#define sqlite3_create_collation16     sqlite3_api->create_collation16\n#define sqlite3_create_function        sqlite3_api->create_function\n#define sqlite3_create_function16      sqlite3_api->create_function16\n#define sqlite3_create_module          sqlite3_api->create_module\n#define sqlite3_create_module_v2       sqlite3_api->create_module_v2\n#define sqlite3_data_count             sqlite3_api->data_count\n#define sqlite3_db_handle              sqlite3_api->db_handle\n#define sqlite3_declare_vtab           sqlite3_api->declare_vtab\n#define sqlite3_enable_shared_cache    sqlite3_api->enable_shared_cache\n#define sqlite3_errcode                sqlite3_api->errcode\n#define sqlite3_errmsg                 sqlite3_api->errmsg\n#define sqlite3_errmsg16               sqlite3_api->errmsg16\n#define sqlite3_exec                   sqlite3_api->exec\n#ifndef SQLITE_OMIT_DEPRECATED\n#define sqlite3_expired                sqlite3_api->expired\n#endif\n#define sqlite3_finalize               sqlite3_api->finalize\n#define sqlite3_free                   sqlite3_api->free\n#define sqlite3_free_table             sqlite3_api->free_table\n#define sqlite3_get_autocommit         sqlite3_api->get_autocommit\n#define sqlite3_get_auxdata            sqlite3_api->get_auxdata\n#define sqlite3_get_table              sqlite3_api->get_table\n#ifndef SQLITE_OMIT_DEPRECATED\n#define sqlite3_global_recover         sqlite3_api->global_recover\n#endif\n#define sqlite3_interrupt              sqlite3_api->interruptx\n#define sqlite3_last_insert_rowid      sqlite3_api->last_insert_rowid\n#define sqlite3_libversion             sqlite3_api->libversion\n#define sqlite3_libversion_number      sqlite3_api->libversion_number\n#define sqlite3_malloc                 sqlite3_api->malloc\n#define sqlite3_mprintf                sqlite3_api->mprintf\n#define sqlite3_open                   sqlite3_api->open\n#define sqlite3_open16                 sqlite3_api->open16\n#define sqlite3_prepare                sqlite3_api->prepare\n#define sqlite3_prepare16              sqlite3_api->prepare16\n#define sqlite3_prepare_v2             sqlite3_api->prepare_v2\n#define sqlite3_prepare16_v2           sqlite3_api->prepare16_v2\n#define sqlite3_profile                sqlite3_api->profile\n#define sqlite3_progress_handler       sqlite3_api->progress_handler\n#define sqlite3_realloc                sqlite3_api->realloc\n#define sqlite3_reset                  sqlite3_api->reset\n#define sqlite3_result_blob            sqlite3_api->result_blob\n#define sqlite3_result_double          sqlite3_api->result_double\n#define sqlite3_result_error           sqlite3_api->result_error\n#define sqlite3_result_error16         sqlite3_api->result_error16\n#define sqlite3_result_int             sqlite3_api->result_int\n#define sqlite3_result_int64           sqlite3_api->result_int64\n#define sqlite3_result_null            sqlite3_api->result_null\n#define sqlite3_result_text            sqlite3_api->result_text\n#define sqlite3_result_text16          sqlite3_api->result_text16\n#define sqlite3_result_text16be        sqlite3_api->result_text16be\n#define sqlite3_result_text16le        sqlite3_api->result_text16le\n#define sqlite3_result_value           sqlite3_api->result_value\n#define sqlite3_rollback_hook          sqlite3_api->rollback_hook\n#define sqlite3_set_authorizer         sqlite3_api->set_authorizer\n#define sqlite3_set_auxdata            sqlite3_api->set_auxdata\n#define sqlite3_snprintf               sqlite3_api->xsnprintf\n#define sqlite3_step                   sqlite3_api->step\n#define sqlite3_table_column_metadata  sqlite3_api->table_column_metadata\n#define sqlite3_thread_cleanup         sqlite3_api->thread_cleanup\n#define sqlite3_total_changes          sqlite3_api->total_changes\n#define sqlite3_trace                  sqlite3_api->trace\n#ifndef SQLITE_OMIT_DEPRECATED\n#define sqlite3_transfer_bindings      sqlite3_api->transfer_bindings\n#endif\n#define sqlite3_update_hook            sqlite3_api->update_hook\n#define sqlite3_user_data              sqlite3_api->user_data\n#define sqlite3_value_blob             sqlite3_api->value_blob\n#define sqlite3_value_bytes            sqlite3_api->value_bytes\n#define sqlite3_value_bytes16          sqlite3_api->value_bytes16\n#define sqlite3_value_double           sqlite3_api->value_double\n#define sqlite3_value_int              sqlite3_api->value_int\n#define sqlite3_value_int64            sqlite3_api->value_int64\n#define sqlite3_value_numeric_type     sqlite3_api->value_numeric_type\n#define sqlite3_value_text             sqlite3_api->value_text\n#define sqlite3_value_text16           sqlite3_api->value_text16\n#define sqlite3_value_text16be         sqlite3_api->value_text16be\n#define sqlite3_value_text16le         sqlite3_api->value_text16le\n#define sqlite3_value_type             sqlite3_api->value_type\n#define sqlite3_vmprintf               sqlite3_api->vmprintf\n#define sqlite3_vsnprintf              sqlite3_api->xvsnprintf\n#define sqlite3_overload_function      sqlite3_api->overload_function\n#define sqlite3_prepare_v2             sqlite3_api->prepare_v2\n#define sqlite3_prepare16_v2           sqlite3_api->prepare16_v2\n#define sqlite3_clear_bindings         sqlite3_api->clear_bindings\n#define sqlite3_bind_zeroblob          sqlite3_api->bind_zeroblob\n#define sqlite3_blob_bytes             sqlite3_api->blob_bytes\n#define sqlite3_blob_close             sqlite3_api->blob_close\n#define sqlite3_blob_open              sqlite3_api->blob_open\n#define sqlite3_blob_read              sqlite3_api->blob_read\n#define sqlite3_blob_write             sqlite3_api->blob_write\n#define sqlite3_create_collation_v2    sqlite3_api->create_collation_v2\n#define sqlite3_file_control           sqlite3_api->file_control\n#define sqlite3_memory_highwater       sqlite3_api->memory_highwater\n#define sqlite3_memory_used            sqlite3_api->memory_used\n#define sqlite3_mutex_alloc            sqlite3_api->mutex_alloc\n#define sqlite3_mutex_enter            sqlite3_api->mutex_enter\n#define sqlite3_mutex_free             sqlite3_api->mutex_free\n#define sqlite3_mutex_leave            sqlite3_api->mutex_leave\n#define sqlite3_mutex_try              sqlite3_api->mutex_try\n#define sqlite3_open_v2                sqlite3_api->open_v2\n#define sqlite3_release_memory         sqlite3_api->release_memory\n#define sqlite3_result_error_nomem     sqlite3_api->result_error_nomem\n#define sqlite3_result_error_toobig    sqlite3_api->result_error_toobig\n#define sqlite3_sleep                  sqlite3_api->sleep\n#define sqlite3_soft_heap_limit        sqlite3_api->soft_heap_limit\n#define sqlite3_vfs_find               sqlite3_api->vfs_find\n#define sqlite3_vfs_register           sqlite3_api->vfs_register\n#define sqlite3_vfs_unregister         sqlite3_api->vfs_unregister\n#define sqlite3_threadsafe             sqlite3_api->xthreadsafe\n#define sqlite3_result_zeroblob        sqlite3_api->result_zeroblob\n#define sqlite3_result_error_code      sqlite3_api->result_error_code\n#define sqlite3_test_control           sqlite3_api->test_control\n#define sqlite3_randomness             sqlite3_api->randomness\n#define sqlite3_context_db_handle      sqlite3_api->context_db_handle\n#define sqlite3_extended_result_codes  sqlite3_api->extended_result_codes\n#define sqlite3_limit                  sqlite3_api->limit\n#define sqlite3_next_stmt              sqlite3_api->next_stmt\n#define sqlite3_sql                    sqlite3_api->sql\n#define sqlite3_status                 sqlite3_api->status\n#define sqlite3_backup_finish          sqlite3_api->backup_finish\n#define sqlite3_backup_init            sqlite3_api->backup_init\n#define sqlite3_backup_pagecount       sqlite3_api->backup_pagecount\n#define sqlite3_backup_remaining       sqlite3_api->backup_remaining\n#define sqlite3_backup_step            sqlite3_api->backup_step\n#define sqlite3_compileoption_get      sqlite3_api->compileoption_get\n#define sqlite3_compileoption_used     sqlite3_api->compileoption_used\n#define sqlite3_create_function_v2     sqlite3_api->create_function_v2\n#define sqlite3_db_config              sqlite3_api->db_config\n#define sqlite3_db_mutex               sqlite3_api->db_mutex\n#define sqlite3_db_status              sqlite3_api->db_status\n#define sqlite3_extended_errcode       sqlite3_api->extended_errcode\n#define sqlite3_log                    sqlite3_api->log\n#define sqlite3_soft_heap_limit64      sqlite3_api->soft_heap_limit64\n#define sqlite3_sourceid               sqlite3_api->sourceid\n#define sqlite3_stmt_status            sqlite3_api->stmt_status\n#define sqlite3_strnicmp               sqlite3_api->strnicmp\n#define sqlite3_unlock_notify          sqlite3_api->unlock_notify\n#define sqlite3_wal_autocheckpoint     sqlite3_api->wal_autocheckpoint\n#define sqlite3_wal_checkpoint         sqlite3_api->wal_checkpoint\n#define sqlite3_wal_hook               sqlite3_api->wal_hook\n#define sqlite3_blob_reopen            sqlite3_api->blob_reopen\n#define sqlite3_vtab_config            sqlite3_api->vtab_config\n#define sqlite3_vtab_on_conflict       sqlite3_api->vtab_on_conflict\n/* Version 3.7.16 and later */\n#define sqlite3_close_v2               sqlite3_api->close_v2\n#define sqlite3_db_filename            sqlite3_api->db_filename\n#define sqlite3_db_readonly            sqlite3_api->db_readonly\n#define sqlite3_db_release_memory      sqlite3_api->db_release_memory\n#define sqlite3_errstr                 sqlite3_api->errstr\n#define sqlite3_stmt_busy              sqlite3_api->stmt_busy\n#define sqlite3_stmt_readonly          sqlite3_api->stmt_readonly\n#define sqlite3_stricmp                sqlite3_api->stricmp\n#define sqlite3_uri_boolean            sqlite3_api->uri_boolean\n#define sqlite3_uri_int64              sqlite3_api->uri_int64\n#define sqlite3_uri_parameter          sqlite3_api->uri_parameter\n#define sqlite3_uri_vsnprintf          sqlite3_api->xvsnprintf\n#define sqlite3_wal_checkpoint_v2      sqlite3_api->wal_checkpoint_v2\n/* Version 3.8.7 and later */\n#define sqlite3_auto_extension         sqlite3_api->auto_extension\n#define sqlite3_bind_blob64            sqlite3_api->bind_blob64\n#define sqlite3_bind_text64            sqlite3_api->bind_text64\n#define sqlite3_cancel_auto_extension  sqlite3_api->cancel_auto_extension\n#define sqlite3_load_extension         sqlite3_api->load_extension\n#define sqlite3_malloc64               sqlite3_api->malloc64\n#define sqlite3_msize                  sqlite3_api->msize\n#define sqlite3_realloc64              sqlite3_api->realloc64\n#define sqlite3_reset_auto_extension   sqlite3_api->reset_auto_extension\n#define sqlite3_result_blob64          sqlite3_api->result_blob64\n#define sqlite3_result_text64          sqlite3_api->result_text64\n#define sqlite3_strglob                sqlite3_api->strglob\n/* Version 3.8.11 and later */\n#define sqlite3_value_dup              sqlite3_api->value_dup\n#define sqlite3_value_free             sqlite3_api->value_free\n#define sqlite3_result_zeroblob64      sqlite3_api->result_zeroblob64\n#define sqlite3_bind_zeroblob64        sqlite3_api->bind_zeroblob64\n/* Version 3.9.0 and later */\n#define sqlite3_value_subtype          sqlite3_api->value_subtype\n#define sqlite3_result_subtype         sqlite3_api->result_subtype\n/* Version 3.10.0 and later */\n#define sqlite3_status64               sqlite3_api->status64\n#define sqlite3_strlike                sqlite3_api->strlike\n#define sqlite3_db_cacheflush          sqlite3_api->db_cacheflush\n/* Version 3.12.0 and later */\n#define sqlite3_system_errno           sqlite3_api->system_errno\n/* Version 3.14.0 and later */\n#define sqlite3_trace_v2               sqlite3_api->trace_v2\n#define sqlite3_expanded_sql           sqlite3_api->expanded_sql\n/* Version 3.18.0 and later */\n#define sqlite3_set_last_insert_rowid  sqlite3_api->set_last_insert_rowid\n/* Version 3.20.0 and later */\n#define sqlite3_prepare_v3             sqlite3_api->prepare_v3\n#define sqlite3_prepare16_v3           sqlite3_api->prepare16_v3\n#define sqlite3_bind_pointer           sqlite3_api->bind_pointer\n#define sqlite3_result_pointer         sqlite3_api->result_pointer\n#define sqlite3_value_pointer          sqlite3_api->value_pointer\n/* Version 3.22.0 and later */\n#define sqlite3_vtab_nochange          sqlite3_api->vtab_nochange\n#define sqlite3_value_nochange         sqlite3_api->value_nochange\n#define sqlite3_vtab_collation         sqlite3_api->vtab_collation\n#endif /* !defined(SQLITE_CORE) && !defined(SQLITE_OMIT_LOAD_EXTENSION) */\n\n#if !defined(SQLITE_CORE) && !defined(SQLITE_OMIT_LOAD_EXTENSION)\n  /* This case when the file really is being compiled as a loadable \n  ** extension */\n# define SQLITE_EXTENSION_INIT1     const sqlite3_api_routines *sqlite3_api=0;\n# define SQLITE_EXTENSION_INIT2(v)  sqlite3_api=v;\n# define SQLITE_EXTENSION_INIT3     \\\n    extern const sqlite3_api_routines *sqlite3_api;\n#else\n  /* This case when the file is being statically linked into the \n  ** application */\n# define SQLITE_EXTENSION_INIT1     /*no-op*/\n# define SQLITE_EXTENSION_INIT2(v)  (void)v; /* unused parameter */\n# define SQLITE_EXTENSION_INIT3     /*no-op*/\n#endif\n\n#endif /* SQLITE3EXT_H */\n\n/************** End of sqlite3ext.h ******************************************/\n/************** Continuing where we left off in loadext.c ********************/\n/* #include \"sqliteInt.h\" */\n\n#ifndef SQLITE_OMIT_LOAD_EXTENSION\n/*\n** Some API routines are omitted when various features are\n** excluded from a build of SQLite.  Substitute a NULL pointer\n** for any missing APIs.\n*/\n#ifndef SQLITE_ENABLE_COLUMN_METADATA\n# define sqlite3_column_database_name   0\n# define sqlite3_column_database_name16 0\n# define sqlite3_column_table_name      0\n# define sqlite3_column_table_name16    0\n# define sqlite3_column_origin_name     0\n# define sqlite3_column_origin_name16   0\n#endif\n\n#ifdef SQLITE_OMIT_AUTHORIZATION\n# define sqlite3_set_authorizer         0\n#endif\n\n#ifdef SQLITE_OMIT_UTF16\n# define sqlite3_bind_text16            0\n# define sqlite3_collation_needed16     0\n# define sqlite3_column_decltype16      0\n# define sqlite3_column_name16          0\n# define sqlite3_column_text16          0\n# define sqlite3_complete16             0\n# define sqlite3_create_collation16     0\n# define sqlite3_create_function16      0\n# define sqlite3_errmsg16               0\n# define sqlite3_open16                 0\n# define sqlite3_prepare16              0\n# define sqlite3_prepare16_v2           0\n# define sqlite3_prepare16_v3           0\n# define sqlite3_result_error16         0\n# define sqlite3_result_text16          0\n# define sqlite3_result_text16be        0\n# define sqlite3_result_text16le        0\n# define sqlite3_value_text16           0\n# define sqlite3_value_text16be         0\n# define sqlite3_value_text16le         0\n# define sqlite3_column_database_name16 0\n# define sqlite3_column_table_name16    0\n# define sqlite3_column_origin_name16   0\n#endif\n\n#ifdef SQLITE_OMIT_COMPLETE\n# define sqlite3_complete 0\n# define sqlite3_complete16 0\n#endif\n\n#ifdef SQLITE_OMIT_DECLTYPE\n# define sqlite3_column_decltype16      0\n# define sqlite3_column_decltype        0\n#endif\n\n#ifdef SQLITE_OMIT_PROGRESS_CALLBACK\n# define sqlite3_progress_handler 0\n#endif\n\n#ifdef SQLITE_OMIT_VIRTUALTABLE\n# define sqlite3_create_module 0\n# define sqlite3_create_module_v2 0\n# define sqlite3_declare_vtab 0\n# define sqlite3_vtab_config 0\n# define sqlite3_vtab_on_conflict 0\n#endif\n\n#ifdef SQLITE_OMIT_SHARED_CACHE\n# define sqlite3_enable_shared_cache 0\n#endif\n\n#if defined(SQLITE_OMIT_TRACE) || defined(SQLITE_OMIT_DEPRECATED)\n# define sqlite3_profile       0\n# define sqlite3_trace         0\n#endif\n\n#ifdef SQLITE_OMIT_GET_TABLE\n# define sqlite3_free_table    0\n# define sqlite3_get_table     0\n#endif\n\n#ifdef SQLITE_OMIT_INCRBLOB\n#define sqlite3_bind_zeroblob  0\n#define sqlite3_blob_bytes     0\n#define sqlite3_blob_close     0\n#define sqlite3_blob_open      0\n#define sqlite3_blob_read      0\n#define sqlite3_blob_write     0\n#define sqlite3_blob_reopen    0\n#endif\n\n#if defined(SQLITE_OMIT_TRACE)\n# define sqlite3_trace_v2      0\n#endif\n\n/*\n** The following structure contains pointers to all SQLite API routines.\n** A pointer to this structure is passed into extensions when they are\n** loaded so that the extension can make calls back into the SQLite\n** library.\n**\n** When adding new APIs, add them to the bottom of this structure\n** in order to preserve backwards compatibility.\n**\n** Extensions that use newer APIs should first call the\n** sqlite3_libversion_number() to make sure that the API they\n** intend to use is supported by the library.  Extensions should\n** also check to make sure that the pointer to the function is\n** not NULL before calling it.\n*/\nstatic const sqlite3_api_routines sqlite3Apis = {\n  sqlite3_aggregate_context,\n#ifndef SQLITE_OMIT_DEPRECATED\n  sqlite3_aggregate_count,\n#else\n  0,\n#endif\n  sqlite3_bind_blob,\n  sqlite3_bind_double,\n  sqlite3_bind_int,\n  sqlite3_bind_int64,\n  sqlite3_bind_null,\n  sqlite3_bind_parameter_count,\n  sqlite3_bind_parameter_index,\n  sqlite3_bind_parameter_name,\n  sqlite3_bind_text,\n  sqlite3_bind_text16,\n  sqlite3_bind_value,\n  sqlite3_busy_handler,\n  sqlite3_busy_timeout,\n  sqlite3_changes,\n  sqlite3_close,\n  sqlite3_collation_needed,\n  sqlite3_collation_needed16,\n  sqlite3_column_blob,\n  sqlite3_column_bytes,\n  sqlite3_column_bytes16,\n  sqlite3_column_count,\n  sqlite3_column_database_name,\n  sqlite3_column_database_name16,\n  sqlite3_column_decltype,\n  sqlite3_column_decltype16,\n  sqlite3_column_double,\n  sqlite3_column_int,\n  sqlite3_column_int64,\n  sqlite3_column_name,\n  sqlite3_column_name16,\n  sqlite3_column_origin_name,\n  sqlite3_column_origin_name16,\n  sqlite3_column_table_name,\n  sqlite3_column_table_name16,\n  sqlite3_column_text,\n  sqlite3_column_text16,\n  sqlite3_column_type,\n  sqlite3_column_value,\n  sqlite3_commit_hook,\n  sqlite3_complete,\n  sqlite3_complete16,\n  sqlite3_create_collation,\n  sqlite3_create_collation16,\n  sqlite3_create_function,\n  sqlite3_create_function16,\n  sqlite3_create_module,\n  sqlite3_data_count,\n  sqlite3_db_handle,\n  sqlite3_declare_vtab,\n  sqlite3_enable_shared_cache,\n  sqlite3_errcode,\n  sqlite3_errmsg,\n  sqlite3_errmsg16,\n  sqlite3_exec,\n#ifndef SQLITE_OMIT_DEPRECATED\n  sqlite3_expired,\n#else\n  0,\n#endif\n  sqlite3_finalize,\n  sqlite3_free,\n  sqlite3_free_table,\n  sqlite3_get_autocommit,\n  sqlite3_get_auxdata,\n  sqlite3_get_table,\n  0,     /* Was sqlite3_global_recover(), but that function is deprecated */\n  sqlite3_interrupt,\n  sqlite3_last_insert_rowid,\n  sqlite3_libversion,\n  sqlite3_libversion_number,\n  sqlite3_malloc,\n  sqlite3_mprintf,\n  sqlite3_open,\n  sqlite3_open16,\n  sqlite3_prepare,\n  sqlite3_prepare16,\n  sqlite3_profile,\n  sqlite3_progress_handler,\n  sqlite3_realloc,\n  sqlite3_reset,\n  sqlite3_result_blob,\n  sqlite3_result_double,\n  sqlite3_result_error,\n  sqlite3_result_error16,\n  sqlite3_result_int,\n  sqlite3_result_int64,\n  sqlite3_result_null,\n  sqlite3_result_text,\n  sqlite3_result_text16,\n  sqlite3_result_text16be,\n  sqlite3_result_text16le,\n  sqlite3_result_value,\n  sqlite3_rollback_hook,\n  sqlite3_set_authorizer,\n  sqlite3_set_auxdata,\n  sqlite3_snprintf,\n  sqlite3_step,\n  sqlite3_table_column_metadata,\n#ifndef SQLITE_OMIT_DEPRECATED\n  sqlite3_thread_cleanup,\n#else\n  0,\n#endif\n  sqlite3_total_changes,\n  sqlite3_trace,\n#ifndef SQLITE_OMIT_DEPRECATED\n  sqlite3_transfer_bindings,\n#else\n  0,\n#endif\n  sqlite3_update_hook,\n  sqlite3_user_data,\n  sqlite3_value_blob,\n  sqlite3_value_bytes,\n  sqlite3_value_bytes16,\n  sqlite3_value_double,\n  sqlite3_value_int,\n  sqlite3_value_int64,\n  sqlite3_value_numeric_type,\n  sqlite3_value_text,\n  sqlite3_value_text16,\n  sqlite3_value_text16be,\n  sqlite3_value_text16le,\n  sqlite3_value_type,\n  sqlite3_vmprintf,\n  /*\n  ** The original API set ends here.  All extensions can call any\n  ** of the APIs above provided that the pointer is not NULL.  But\n  ** before calling APIs that follow, extension should check the\n  ** sqlite3_libversion_number() to make sure they are dealing with\n  ** a library that is new enough to support that API.\n  *************************************************************************\n  */\n  sqlite3_overload_function,\n\n  /*\n  ** Added after 3.3.13\n  */\n  sqlite3_prepare_v2,\n  sqlite3_prepare16_v2,\n  sqlite3_clear_bindings,\n\n  /*\n  ** Added for 3.4.1\n  */\n  sqlite3_create_module_v2,\n\n  /*\n  ** Added for 3.5.0\n  */\n  sqlite3_bind_zeroblob,\n  sqlite3_blob_bytes,\n  sqlite3_blob_close,\n  sqlite3_blob_open,\n  sqlite3_blob_read,\n  sqlite3_blob_write,\n  sqlite3_create_collation_v2,\n  sqlite3_file_control,\n  sqlite3_memory_highwater,\n  sqlite3_memory_used,\n#ifdef SQLITE_MUTEX_OMIT\n  0, \n  0, \n  0,\n  0,\n  0,\n#else\n  sqlite3_mutex_alloc,\n  sqlite3_mutex_enter,\n  sqlite3_mutex_free,\n  sqlite3_mutex_leave,\n  sqlite3_mutex_try,\n#endif\n  sqlite3_open_v2,\n  sqlite3_release_memory,\n  sqlite3_result_error_nomem,\n  sqlite3_result_error_toobig,\n  sqlite3_sleep,\n  sqlite3_soft_heap_limit,\n  sqlite3_vfs_find,\n  sqlite3_vfs_register,\n  sqlite3_vfs_unregister,\n\n  /*\n  ** Added for 3.5.8\n  */\n  sqlite3_threadsafe,\n  sqlite3_result_zeroblob,\n  sqlite3_result_error_code,\n  sqlite3_test_control,\n  sqlite3_randomness,\n  sqlite3_context_db_handle,\n\n  /*\n  ** Added for 3.6.0\n  */\n  sqlite3_extended_result_codes,\n  sqlite3_limit,\n  sqlite3_next_stmt,\n  sqlite3_sql,\n  sqlite3_status,\n\n  /*\n  ** Added for 3.7.4\n  */\n  sqlite3_backup_finish,\n  sqlite3_backup_init,\n  sqlite3_backup_pagecount,\n  sqlite3_backup_remaining,\n  sqlite3_backup_step,\n#ifndef SQLITE_OMIT_COMPILEOPTION_DIAGS\n  sqlite3_compileoption_get,\n  sqlite3_compileoption_used,\n#else\n  0,\n  0,\n#endif\n  sqlite3_create_function_v2,\n  sqlite3_db_config,\n  sqlite3_db_mutex,\n  sqlite3_db_status,\n  sqlite3_extended_errcode,\n  sqlite3_log,\n  sqlite3_soft_heap_limit64,\n  sqlite3_sourceid,\n  sqlite3_stmt_status,\n  sqlite3_strnicmp,\n#ifdef SQLITE_ENABLE_UNLOCK_NOTIFY\n  sqlite3_unlock_notify,\n#else\n  0,\n#endif\n#ifndef SQLITE_OMIT_WAL\n  sqlite3_wal_autocheckpoint,\n  sqlite3_wal_checkpoint,\n  sqlite3_wal_hook,\n#else\n  0,\n  0,\n  0,\n#endif\n  sqlite3_blob_reopen,\n  sqlite3_vtab_config,\n  sqlite3_vtab_on_conflict,\n  sqlite3_close_v2,\n  sqlite3_db_filename,\n  sqlite3_db_readonly,\n  sqlite3_db_release_memory,\n  sqlite3_errstr,\n  sqlite3_stmt_busy,\n  sqlite3_stmt_readonly,\n  sqlite3_stricmp,\n  sqlite3_uri_boolean,\n  sqlite3_uri_int64,\n  sqlite3_uri_parameter,\n  sqlite3_vsnprintf,\n  sqlite3_wal_checkpoint_v2,\n  /* Version 3.8.7 and later */\n  sqlite3_auto_extension,\n  sqlite3_bind_blob64,\n  sqlite3_bind_text64,\n  sqlite3_cancel_auto_extension,\n  sqlite3_load_extension,\n  sqlite3_malloc64,\n  sqlite3_msize,\n  sqlite3_realloc64,\n  sqlite3_reset_auto_extension,\n  sqlite3_result_blob64,\n  sqlite3_result_text64,\n  sqlite3_strglob,\n  /* Version 3.8.11 and later */\n  (sqlite3_value*(*)(const sqlite3_value*))sqlite3_value_dup,\n  sqlite3_value_free,\n  sqlite3_result_zeroblob64,\n  sqlite3_bind_zeroblob64,\n  /* Version 3.9.0 and later */\n  sqlite3_value_subtype,\n  sqlite3_result_subtype,\n  /* Version 3.10.0 and later */\n  sqlite3_status64,\n  sqlite3_strlike,\n  sqlite3_db_cacheflush,\n  /* Version 3.12.0 and later */\n  sqlite3_system_errno,\n  /* Version 3.14.0 and later */\n  sqlite3_trace_v2,\n  sqlite3_expanded_sql,\n  /* Version 3.18.0 and later */\n  sqlite3_set_last_insert_rowid,\n  /* Version 3.20.0 and later */\n  sqlite3_prepare_v3,\n  sqlite3_prepare16_v3,\n  sqlite3_bind_pointer,\n  sqlite3_result_pointer,\n  sqlite3_value_pointer,\n  /* Version 3.22.0 and later */\n  sqlite3_vtab_nochange,\n  sqlite3_value_nochange,\n  sqlite3_vtab_collation\n};\n\n/*\n** Attempt to load an SQLite extension library contained in the file\n** zFile.  The entry point is zProc.  zProc may be 0 in which case a\n** default entry point name (sqlite3_extension_init) is used.  Use\n** of the default name is recommended.\n**\n** Return SQLITE_OK on success and SQLITE_ERROR if something goes wrong.\n**\n** If an error occurs and pzErrMsg is not 0, then fill *pzErrMsg with \n** error message text.  The calling function should free this memory\n** by calling sqlite3DbFree(db, ).\n*/\nstatic int sqlite3LoadExtension(\n  sqlite3 *db,          /* Load the extension into this database connection */\n  const char *zFile,    /* Name of the shared library containing extension */\n  const char *zProc,    /* Entry point.  Use \"sqlite3_extension_init\" if 0 */\n  char **pzErrMsg       /* Put error message here if not 0 */\n){\n  sqlite3_vfs *pVfs = db->pVfs;\n  void *handle;\n  sqlite3_loadext_entry xInit;\n  char *zErrmsg = 0;\n  const char *zEntry;\n  char *zAltEntry = 0;\n  void **aHandle;\n  u64 nMsg = 300 + sqlite3Strlen30(zFile);\n  int ii;\n  int rc;\n\n  /* Shared library endings to try if zFile cannot be loaded as written */\n  static const char *azEndings[] = {\n#if SQLITE_OS_WIN\n     \"dll\"   \n#elif defined(__APPLE__)\n     \"dylib\"\n#else\n     \"so\"\n#endif\n  };\n\n\n  if( pzErrMsg ) *pzErrMsg = 0;\n\n  /* Ticket #1863.  To avoid a creating security problems for older\n  ** applications that relink against newer versions of SQLite, the\n  ** ability to run load_extension is turned off by default.  One\n  ** must call either sqlite3_enable_load_extension(db) or\n  ** sqlite3_db_config(db, SQLITE_DBCONFIG_ENABLE_LOAD_EXTENSION, 1, 0)\n  ** to turn on extension loading.\n  */\n  if( (db->flags & SQLITE_LoadExtension)==0 ){\n    if( pzErrMsg ){\n      *pzErrMsg = sqlite3_mprintf(\"not authorized\");\n    }\n    return SQLITE_ERROR;\n  }\n\n  zEntry = zProc ? zProc : \"sqlite3_extension_init\";\n\n  handle = sqlite3OsDlOpen(pVfs, zFile);\n#if SQLITE_OS_UNIX || SQLITE_OS_WIN\n  for(ii=0; ii<ArraySize(azEndings) && handle==0; ii++){\n    char *zAltFile = sqlite3_mprintf(\"%s.%s\", zFile, azEndings[ii]);\n    int bExists = 0;\n    if( zAltFile==0 ) return SQLITE_NOMEM_BKPT;\n    sqlite3OsAccess(pVfs, zAltFile, SQLITE_ACCESS_EXISTS, &bExists);\n    if( bExists )  handle = sqlite3OsDlOpen(pVfs, zAltFile);\n    sqlite3_free(zAltFile);\n  }\n#endif\n  if( handle==0 ){\n    if( pzErrMsg ){\n      *pzErrMsg = zErrmsg = sqlite3_malloc64(nMsg);\n      if( zErrmsg ){\n        sqlite3_snprintf(nMsg, zErrmsg, \n            \"unable to open shared library [%s]\", zFile);\n        sqlite3OsDlError(pVfs, nMsg-1, zErrmsg);\n      }\n    }\n    return SQLITE_ERROR;\n  }\n  xInit = (sqlite3_loadext_entry)sqlite3OsDlSym(pVfs, handle, zEntry);\n\n  /* If no entry point was specified and the default legacy\n  ** entry point name \"sqlite3_extension_init\" was not found, then\n  ** construct an entry point name \"sqlite3_X_init\" where the X is\n  ** replaced by the lowercase value of every ASCII alphabetic \n  ** character in the filename after the last \"/\" upto the first \".\",\n  ** and eliding the first three characters if they are \"lib\".  \n  ** Examples:\n  **\n  **    /usr/local/lib/libExample5.4.3.so ==>  sqlite3_example_init\n  **    C:/lib/mathfuncs.dll              ==>  sqlite3_mathfuncs_init\n  */\n  if( xInit==0 && zProc==0 ){\n    int iFile, iEntry, c;\n    int ncFile = sqlite3Strlen30(zFile);\n    zAltEntry = sqlite3_malloc64(ncFile+30);\n    if( zAltEntry==0 ){\n      sqlite3OsDlClose(pVfs, handle);\n      return SQLITE_NOMEM_BKPT;\n    }\n    memcpy(zAltEntry, \"sqlite3_\", 8);\n    for(iFile=ncFile-1; iFile>=0 && zFile[iFile]!='/'; iFile--){}\n    iFile++;\n    if( sqlite3_strnicmp(zFile+iFile, \"lib\", 3)==0 ) iFile += 3;\n    for(iEntry=8; (c = zFile[iFile])!=0 && c!='.'; iFile++){\n      if( sqlite3Isalpha(c) ){\n        zAltEntry[iEntry++] = (char)sqlite3UpperToLower[(unsigned)c];\n      }\n    }\n    memcpy(zAltEntry+iEntry, \"_init\", 6);\n    zEntry = zAltEntry;\n    xInit = (sqlite3_loadext_entry)sqlite3OsDlSym(pVfs, handle, zEntry);\n  }\n  if( xInit==0 ){\n    if( pzErrMsg ){\n      nMsg += sqlite3Strlen30(zEntry);\n      *pzErrMsg = zErrmsg = sqlite3_malloc64(nMsg);\n      if( zErrmsg ){\n        sqlite3_snprintf(nMsg, zErrmsg,\n            \"no entry point [%s] in shared library [%s]\", zEntry, zFile);\n        sqlite3OsDlError(pVfs, nMsg-1, zErrmsg);\n      }\n    }\n    sqlite3OsDlClose(pVfs, handle);\n    sqlite3_free(zAltEntry);\n    return SQLITE_ERROR;\n  }\n  sqlite3_free(zAltEntry);\n  rc = xInit(db, &zErrmsg, &sqlite3Apis);\n  if( rc ){\n    if( rc==SQLITE_OK_LOAD_PERMANENTLY ) return SQLITE_OK;\n    if( pzErrMsg ){\n      *pzErrMsg = sqlite3_mprintf(\"error during initialization: %s\", zErrmsg);\n    }\n    sqlite3_free(zErrmsg);\n    sqlite3OsDlClose(pVfs, handle);\n    return SQLITE_ERROR;\n  }\n\n  /* Append the new shared library handle to the db->aExtension array. */\n  aHandle = sqlite3DbMallocZero(db, sizeof(handle)*(db->nExtension+1));\n  if( aHandle==0 ){\n    return SQLITE_NOMEM_BKPT;\n  }\n  if( db->nExtension>0 ){\n    memcpy(aHandle, db->aExtension, sizeof(handle)*db->nExtension);\n  }\n  sqlite3DbFree(db, db->aExtension);\n  db->aExtension = aHandle;\n\n  db->aExtension[db->nExtension++] = handle;\n  return SQLITE_OK;\n}\nSQLITE_API int sqlite3_load_extension(\n  sqlite3 *db,          /* Load the extension into this database connection */\n  const char *zFile,    /* Name of the shared library containing extension */\n  const char *zProc,    /* Entry point.  Use \"sqlite3_extension_init\" if 0 */\n  char **pzErrMsg       /* Put error message here if not 0 */\n){\n  int rc;\n  sqlite3_mutex_enter(db->mutex);\n  rc = sqlite3LoadExtension(db, zFile, zProc, pzErrMsg);\n  rc = sqlite3ApiExit(db, rc);\n  sqlite3_mutex_leave(db->mutex);\n  return rc;\n}\n\n/*\n** Call this routine when the database connection is closing in order\n** to clean up loaded extensions\n*/\nSQLITE_PRIVATE void sqlite3CloseExtensions(sqlite3 *db){\n  int i;\n  assert( sqlite3_mutex_held(db->mutex) );\n  for(i=0; i<db->nExtension; i++){\n    sqlite3OsDlClose(db->pVfs, db->aExtension[i]);\n  }\n  sqlite3DbFree(db, db->aExtension);\n}\n\n/*\n** Enable or disable extension loading.  Extension loading is disabled by\n** default so as not to open security holes in older applications.\n*/\nSQLITE_API int sqlite3_enable_load_extension(sqlite3 *db, int onoff){\n  sqlite3_mutex_enter(db->mutex);\n  if( onoff ){\n    db->flags |= SQLITE_LoadExtension|SQLITE_LoadExtFunc;\n  }else{\n    db->flags &= ~(SQLITE_LoadExtension|SQLITE_LoadExtFunc);\n  }\n  sqlite3_mutex_leave(db->mutex);\n  return SQLITE_OK;\n}\n\n#endif /* !defined(SQLITE_OMIT_LOAD_EXTENSION) */\n\n/*\n** The following object holds the list of automatically loaded\n** extensions.\n**\n** This list is shared across threads.  The SQLITE_MUTEX_STATIC_MASTER\n** mutex must be held while accessing this list.\n*/\ntypedef struct sqlite3AutoExtList sqlite3AutoExtList;\nstatic SQLITE_WSD struct sqlite3AutoExtList {\n  u32 nExt;              /* Number of entries in aExt[] */          \n  void (**aExt)(void);   /* Pointers to the extension init functions */\n} sqlite3Autoext = { 0, 0 };\n\n/* The \"wsdAutoext\" macro will resolve to the autoextension\n** state vector.  If writable static data is unsupported on the target,\n** we have to locate the state vector at run-time.  In the more common\n** case where writable static data is supported, wsdStat can refer directly\n** to the \"sqlite3Autoext\" state vector declared above.\n*/\n#ifdef SQLITE_OMIT_WSD\n# define wsdAutoextInit \\\n  sqlite3AutoExtList *x = &GLOBAL(sqlite3AutoExtList,sqlite3Autoext)\n# define wsdAutoext x[0]\n#else\n# define wsdAutoextInit\n# define wsdAutoext sqlite3Autoext\n#endif\n\n\n/*\n** Register a statically linked extension that is automatically\n** loaded by every new database connection.\n*/\nSQLITE_API int sqlite3_auto_extension(\n  void (*xInit)(void)\n){\n  int rc = SQLITE_OK;\n#ifndef SQLITE_OMIT_AUTOINIT\n  rc = sqlite3_initialize();\n  if( rc ){\n    return rc;\n  }else\n#endif\n  {\n    u32 i;\n#if SQLITE_THREADSAFE\n    sqlite3_mutex *mutex = sqlite3MutexAlloc(SQLITE_MUTEX_STATIC_MASTER);\n#endif\n    wsdAutoextInit;\n    sqlite3_mutex_enter(mutex);\n    for(i=0; i<wsdAutoext.nExt; i++){\n      if( wsdAutoext.aExt[i]==xInit ) break;\n    }\n    if( i==wsdAutoext.nExt ){\n      u64 nByte = (wsdAutoext.nExt+1)*sizeof(wsdAutoext.aExt[0]);\n      void (**aNew)(void);\n      aNew = sqlite3_realloc64(wsdAutoext.aExt, nByte);\n      if( aNew==0 ){\n        rc = SQLITE_NOMEM_BKPT;\n      }else{\n        wsdAutoext.aExt = aNew;\n        wsdAutoext.aExt[wsdAutoext.nExt] = xInit;\n        wsdAutoext.nExt++;\n      }\n    }\n    sqlite3_mutex_leave(mutex);\n    assert( (rc&0xff)==rc );\n    return rc;\n  }\n}\n\n/*\n** Cancel a prior call to sqlite3_auto_extension.  Remove xInit from the\n** set of routines that is invoked for each new database connection, if it\n** is currently on the list.  If xInit is not on the list, then this\n** routine is a no-op.\n**\n** Return 1 if xInit was found on the list and removed.  Return 0 if xInit\n** was not on the list.\n*/\nSQLITE_API int sqlite3_cancel_auto_extension(\n  void (*xInit)(void)\n){\n#if SQLITE_THREADSAFE\n  sqlite3_mutex *mutex = sqlite3MutexAlloc(SQLITE_MUTEX_STATIC_MASTER);\n#endif\n  int i;\n  int n = 0;\n  wsdAutoextInit;\n  sqlite3_mutex_enter(mutex);\n  for(i=(int)wsdAutoext.nExt-1; i>=0; i--){\n    if( wsdAutoext.aExt[i]==xInit ){\n      wsdAutoext.nExt--;\n      wsdAutoext.aExt[i] = wsdAutoext.aExt[wsdAutoext.nExt];\n      n++;\n      break;\n    }\n  }\n  sqlite3_mutex_leave(mutex);\n  return n;\n}\n\n/*\n** Reset the automatic extension loading mechanism.\n*/\nSQLITE_API void sqlite3_reset_auto_extension(void){\n#ifndef SQLITE_OMIT_AUTOINIT\n  if( sqlite3_initialize()==SQLITE_OK )\n#endif\n  {\n#if SQLITE_THREADSAFE\n    sqlite3_mutex *mutex = sqlite3MutexAlloc(SQLITE_MUTEX_STATIC_MASTER);\n#endif\n    wsdAutoextInit;\n    sqlite3_mutex_enter(mutex);\n    sqlite3_free(wsdAutoext.aExt);\n    wsdAutoext.aExt = 0;\n    wsdAutoext.nExt = 0;\n    sqlite3_mutex_leave(mutex);\n  }\n}\n\n/*\n** Load all automatic extensions.\n**\n** If anything goes wrong, set an error in the database connection.\n*/\nSQLITE_PRIVATE void sqlite3AutoLoadExtensions(sqlite3 *db){\n  u32 i;\n  int go = 1;\n  int rc;\n  sqlite3_loadext_entry xInit;\n\n  wsdAutoextInit;\n  if( wsdAutoext.nExt==0 ){\n    /* Common case: early out without every having to acquire a mutex */\n    return;\n  }\n  for(i=0; go; i++){\n    char *zErrmsg;\n#if SQLITE_THREADSAFE\n    sqlite3_mutex *mutex = sqlite3MutexAlloc(SQLITE_MUTEX_STATIC_MASTER);\n#endif\n#ifdef SQLITE_OMIT_LOAD_EXTENSION\n    const sqlite3_api_routines *pThunk = 0;\n#else\n    const sqlite3_api_routines *pThunk = &sqlite3Apis;\n#endif\n    sqlite3_mutex_enter(mutex);\n    if( i>=wsdAutoext.nExt ){\n      xInit = 0;\n      go = 0;\n    }else{\n      xInit = (sqlite3_loadext_entry)wsdAutoext.aExt[i];\n    }\n    sqlite3_mutex_leave(mutex);\n    zErrmsg = 0;\n    if( xInit && (rc = xInit(db, &zErrmsg, pThunk))!=0 ){\n      sqlite3ErrorWithMsg(db, rc,\n            \"automatic extension loading failed: %s\", zErrmsg);\n      go = 0;\n    }\n    sqlite3_free(zErrmsg);\n  }\n}\n\n/************** End of loadext.c *********************************************/\n/************** Begin file pragma.c ******************************************/\n/*\n** 2003 April 6\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n*************************************************************************\n** This file contains code used to implement the PRAGMA command.\n*/\n/* #include \"sqliteInt.h\" */\n\n#if !defined(SQLITE_ENABLE_LOCKING_STYLE)\n#  if defined(__APPLE__)\n#    define SQLITE_ENABLE_LOCKING_STYLE 1\n#  else\n#    define SQLITE_ENABLE_LOCKING_STYLE 0\n#  endif\n#endif\n\n/***************************************************************************\n** The \"pragma.h\" include file is an automatically generated file that\n** that includes the PragType_XXXX macro definitions and the aPragmaName[]\n** object.  This ensures that the aPragmaName[] table is arranged in\n** lexicographical order to facility a binary search of the pragma name.\n** Do not edit pragma.h directly.  Edit and rerun the script in at \n** ../tool/mkpragmatab.tcl. */\n/************** Include pragma.h in the middle of pragma.c *******************/\n/************** Begin file pragma.h ******************************************/\n/* DO NOT EDIT!\n** This file is automatically generated by the script at\n** ../tool/mkpragmatab.tcl.  To update the set of pragmas, edit\n** that script and rerun it.\n*/\n\n/* The various pragma types */\n#define PragTyp_HEADER_VALUE                   0\n#define PragTyp_AUTO_VACUUM                    1\n#define PragTyp_FLAG                           2\n#define PragTyp_BUSY_TIMEOUT                   3\n#define PragTyp_CACHE_SIZE                     4\n#define PragTyp_CACHE_SPILL                    5\n#define PragTyp_CASE_SENSITIVE_LIKE            6\n#define PragTyp_COLLATION_LIST                 7\n#define PragTyp_COMPILE_OPTIONS                8\n#define PragTyp_DATA_STORE_DIRECTORY           9\n#define PragTyp_DATABASE_LIST                 10\n#define PragTyp_DEFAULT_CACHE_SIZE            11\n#define PragTyp_ENCODING                      12\n#define PragTyp_FOREIGN_KEY_CHECK             13\n#define PragTyp_FOREIGN_KEY_LIST              14\n#define PragTyp_FUNCTION_LIST                 15\n#define PragTyp_INCREMENTAL_VACUUM            16\n#define PragTyp_INDEX_INFO                    17\n#define PragTyp_INDEX_LIST                    18\n#define PragTyp_INTEGRITY_CHECK               19\n#define PragTyp_JOURNAL_MODE                  20\n#define PragTyp_JOURNAL_SIZE_LIMIT            21\n#define PragTyp_LOCK_PROXY_FILE               22\n#define PragTyp_LOCKING_MODE                  23\n#define PragTyp_PAGE_COUNT                    24\n#define PragTyp_MMAP_SIZE                     25\n#define PragTyp_MODULE_LIST                   26\n#define PragTyp_OPTIMIZE                      27\n#define PragTyp_PAGE_SIZE                     28\n#define PragTyp_PRAGMA_LIST                   29\n#define PragTyp_SECURE_DELETE                 30\n#define PragTyp_SHRINK_MEMORY                 31\n#define PragTyp_SOFT_HEAP_LIMIT               32\n#define PragTyp_SYNCHRONOUS                   33\n#define PragTyp_TABLE_INFO                    34\n#define PragTyp_TEMP_STORE                    35\n#define PragTyp_TEMP_STORE_DIRECTORY          36\n#define PragTyp_THREADS                       37\n#define PragTyp_WAL_AUTOCHECKPOINT            38\n#define PragTyp_WAL_CHECKPOINT                39\n#define PragTyp_ACTIVATE_EXTENSIONS           40\n#define PragTyp_HEXKEY                        41\n#define PragTyp_KEY                           42\n#define PragTyp_REKEY                         43\n#define PragTyp_LOCK_STATUS                   44\n#define PragTyp_PARSER_TRACE                  45\n#define PragTyp_STATS                         46\n\n/* Property flags associated with various pragma. */\n#define PragFlg_NeedSchema 0x01 /* Force schema load before running */\n#define PragFlg_NoColumns  0x02 /* OP_ResultRow called with zero columns */\n#define PragFlg_NoColumns1 0x04 /* zero columns if RHS argument is present */\n#define PragFlg_ReadOnly   0x08 /* Read-only HEADER_VALUE */\n#define PragFlg_Result0    0x10 /* Acts as query when no argument */\n#define PragFlg_Result1    0x20 /* Acts as query when has one argument */\n#define PragFlg_SchemaOpt  0x40 /* Schema restricts name search if present */\n#define PragFlg_SchemaReq  0x80 /* Schema required - \"main\" is default */\n\n/* Names of columns for pragmas that return multi-column result\n** or that return single-column results where the name of the\n** result column is different from the name of the pragma\n*/\nstatic const char *const pragCName[] = {\n  /*   0 */ \"cache_size\",  /* Used by: default_cache_size */\n  /*   1 */ \"cid\",         /* Used by: table_info */\n  /*   2 */ \"name\",       \n  /*   3 */ \"type\",       \n  /*   4 */ \"notnull\",    \n  /*   5 */ \"dflt_value\", \n  /*   6 */ \"pk\",         \n  /*   7 */ \"tbl\",         /* Used by: stats */\n  /*   8 */ \"idx\",        \n  /*   9 */ \"wdth\",       \n  /*  10 */ \"hght\",       \n  /*  11 */ \"flgs\",       \n  /*  12 */ \"seqno\",       /* Used by: index_info */\n  /*  13 */ \"cid\",        \n  /*  14 */ \"name\",       \n  /*  15 */ \"seqno\",       /* Used by: index_xinfo */\n  /*  16 */ \"cid\",        \n  /*  17 */ \"name\",       \n  /*  18 */ \"desc\",       \n  /*  19 */ \"coll\",       \n  /*  20 */ \"key\",        \n  /*  21 */ \"seq\",         /* Used by: index_list */\n  /*  22 */ \"name\",       \n  /*  23 */ \"unique\",     \n  /*  24 */ \"origin\",     \n  /*  25 */ \"partial\",    \n  /*  26 */ \"seq\",         /* Used by: database_list */\n  /*  27 */ \"name\",       \n  /*  28 */ \"file\",       \n  /*  29 */ \"name\",        /* Used by: function_list */\n  /*  30 */ \"builtin\",    \n  /*  31 */ \"name\",        /* Used by: module_list pragma_list */\n  /*  32 */ \"seq\",         /* Used by: collation_list */\n  /*  33 */ \"name\",       \n  /*  34 */ \"id\",          /* Used by: foreign_key_list */\n  /*  35 */ \"seq\",        \n  /*  36 */ \"table\",      \n  /*  37 */ \"from\",       \n  /*  38 */ \"to\",         \n  /*  39 */ \"on_update\",  \n  /*  40 */ \"on_delete\",  \n  /*  41 */ \"match\",      \n  /*  42 */ \"table\",       /* Used by: foreign_key_check */\n  /*  43 */ \"rowid\",      \n  /*  44 */ \"parent\",     \n  /*  45 */ \"fkid\",       \n  /*  46 */ \"busy\",        /* Used by: wal_checkpoint */\n  /*  47 */ \"log\",        \n  /*  48 */ \"checkpointed\",\n  /*  49 */ \"timeout\",     /* Used by: busy_timeout */\n  /*  50 */ \"database\",    /* Used by: lock_status */\n  /*  51 */ \"status\",     \n};\n\n/* Definitions of all built-in pragmas */\ntypedef struct PragmaName {\n  const char *const zName; /* Name of pragma */\n  u8 ePragTyp;             /* PragTyp_XXX value */\n  u8 mPragFlg;             /* Zero or more PragFlg_XXX values */\n  u8 iPragCName;           /* Start of column names in pragCName[] */\n  u8 nPragCName;           /* Num of col names. 0 means use pragma name */\n  u32 iArg;                /* Extra argument */\n} PragmaName;\nstatic const PragmaName aPragmaName[] = {\n#if defined(SQLITE_HAS_CODEC) || defined(SQLITE_ENABLE_CEROD)\n {/* zName:     */ \"activate_extensions\",\n  /* ePragTyp:  */ PragTyp_ACTIVATE_EXTENSIONS,\n  /* ePragFlg:  */ 0,\n  /* ColNames:  */ 0, 0,\n  /* iArg:      */ 0 },\n#endif\n#if !defined(SQLITE_OMIT_SCHEMA_VERSION_PRAGMAS)\n {/* zName:     */ \"application_id\",\n  /* ePragTyp:  */ PragTyp_HEADER_VALUE,\n  /* ePragFlg:  */ PragFlg_NoColumns1|PragFlg_Result0,\n  /* ColNames:  */ 0, 0,\n  /* iArg:      */ BTREE_APPLICATION_ID },\n#endif\n#if !defined(SQLITE_OMIT_AUTOVACUUM)\n {/* zName:     */ \"auto_vacuum\",\n  /* ePragTyp:  */ PragTyp_AUTO_VACUUM,\n  /* ePragFlg:  */ PragFlg_NeedSchema|PragFlg_Result0|PragFlg_SchemaReq|PragFlg_NoColumns1,\n  /* ColNames:  */ 0, 0,\n  /* iArg:      */ 0 },\n#endif\n#if !defined(SQLITE_OMIT_FLAG_PRAGMAS)\n#if !defined(SQLITE_OMIT_AUTOMATIC_INDEX)\n {/* zName:     */ \"automatic_index\",\n  /* ePragTyp:  */ PragTyp_FLAG,\n  /* ePragFlg:  */ PragFlg_Result0|PragFlg_NoColumns1,\n  /* ColNames:  */ 0, 0,\n  /* iArg:      */ SQLITE_AutoIndex },\n#endif\n#endif\n {/* zName:     */ \"busy_timeout\",\n  /* ePragTyp:  */ PragTyp_BUSY_TIMEOUT,\n  /* ePragFlg:  */ PragFlg_Result0,\n  /* ColNames:  */ 49, 1,\n  /* iArg:      */ 0 },\n#if !defined(SQLITE_OMIT_PAGER_PRAGMAS)\n {/* zName:     */ \"cache_size\",\n  /* ePragTyp:  */ PragTyp_CACHE_SIZE,\n  /* ePragFlg:  */ PragFlg_NeedSchema|PragFlg_Result0|PragFlg_SchemaReq|PragFlg_NoColumns1,\n  /* ColNames:  */ 0, 0,\n  /* iArg:      */ 0 },\n#endif\n#if !defined(SQLITE_OMIT_FLAG_PRAGMAS)\n {/* zName:     */ \"cache_spill\",\n  /* ePragTyp:  */ PragTyp_CACHE_SPILL,\n  /* ePragFlg:  */ PragFlg_Result0|PragFlg_SchemaReq|PragFlg_NoColumns1,\n  /* ColNames:  */ 0, 0,\n  /* iArg:      */ 0 },\n#endif\n {/* zName:     */ \"case_sensitive_like\",\n  /* ePragTyp:  */ PragTyp_CASE_SENSITIVE_LIKE,\n  /* ePragFlg:  */ PragFlg_NoColumns,\n  /* ColNames:  */ 0, 0,\n  /* iArg:      */ 0 },\n {/* zName:     */ \"cell_size_check\",\n  /* ePragTyp:  */ PragTyp_FLAG,\n  /* ePragFlg:  */ PragFlg_Result0|PragFlg_NoColumns1,\n  /* ColNames:  */ 0, 0,\n  /* iArg:      */ SQLITE_CellSizeCk },\n#if !defined(SQLITE_OMIT_FLAG_PRAGMAS)\n {/* zName:     */ \"checkpoint_fullfsync\",\n  /* ePragTyp:  */ PragTyp_FLAG,\n  /* ePragFlg:  */ PragFlg_Result0|PragFlg_NoColumns1,\n  /* ColNames:  */ 0, 0,\n  /* iArg:      */ SQLITE_CkptFullFSync },\n#endif\n#if !defined(SQLITE_OMIT_SCHEMA_PRAGMAS)\n {/* zName:     */ \"collation_list\",\n  /* ePragTyp:  */ PragTyp_COLLATION_LIST,\n  /* ePragFlg:  */ PragFlg_Result0,\n  /* ColNames:  */ 32, 2,\n  /* iArg:      */ 0 },\n#endif\n#if !defined(SQLITE_OMIT_COMPILEOPTION_DIAGS)\n {/* zName:     */ \"compile_options\",\n  /* ePragTyp:  */ PragTyp_COMPILE_OPTIONS,\n  /* ePragFlg:  */ PragFlg_Result0,\n  /* ColNames:  */ 0, 0,\n  /* iArg:      */ 0 },\n#endif\n#if !defined(SQLITE_OMIT_FLAG_PRAGMAS)\n {/* zName:     */ \"count_changes\",\n  /* ePragTyp:  */ PragTyp_FLAG,\n  /* ePragFlg:  */ PragFlg_Result0|PragFlg_NoColumns1,\n  /* ColNames:  */ 0, 0,\n  /* iArg:      */ SQLITE_CountRows },\n#endif\n#if !defined(SQLITE_OMIT_PAGER_PRAGMAS) && SQLITE_OS_WIN\n {/* zName:     */ \"data_store_directory\",\n  /* ePragTyp:  */ PragTyp_DATA_STORE_DIRECTORY,\n  /* ePragFlg:  */ PragFlg_NoColumns1,\n  /* ColNames:  */ 0, 0,\n  /* iArg:      */ 0 },\n#endif\n#if !defined(SQLITE_OMIT_SCHEMA_VERSION_PRAGMAS)\n {/* zName:     */ \"data_version\",\n  /* ePragTyp:  */ PragTyp_HEADER_VALUE,\n  /* ePragFlg:  */ PragFlg_ReadOnly|PragFlg_Result0,\n  /* ColNames:  */ 0, 0,\n  /* iArg:      */ BTREE_DATA_VERSION },\n#endif\n#if !defined(SQLITE_OMIT_SCHEMA_PRAGMAS)\n {/* zName:     */ \"database_list\",\n  /* ePragTyp:  */ PragTyp_DATABASE_LIST,\n  /* ePragFlg:  */ PragFlg_NeedSchema|PragFlg_Result0,\n  /* ColNames:  */ 26, 3,\n  /* iArg:      */ 0 },\n#endif\n#if !defined(SQLITE_OMIT_PAGER_PRAGMAS) && !defined(SQLITE_OMIT_DEPRECATED)\n {/* zName:     */ \"default_cache_size\",\n  /* ePragTyp:  */ PragTyp_DEFAULT_CACHE_SIZE,\n  /* ePragFlg:  */ PragFlg_NeedSchema|PragFlg_Result0|PragFlg_SchemaReq|PragFlg_NoColumns1,\n  /* ColNames:  */ 0, 1,\n  /* iArg:      */ 0 },\n#endif\n#if !defined(SQLITE_OMIT_FLAG_PRAGMAS)\n#if !defined(SQLITE_OMIT_FOREIGN_KEY) && !defined(SQLITE_OMIT_TRIGGER)\n {/* zName:     */ \"defer_foreign_keys\",\n  /* ePragTyp:  */ PragTyp_FLAG,\n  /* ePragFlg:  */ PragFlg_Result0|PragFlg_NoColumns1,\n  /* ColNames:  */ 0, 0,\n  /* iArg:      */ SQLITE_DeferFKs },\n#endif\n#endif\n#if !defined(SQLITE_OMIT_FLAG_PRAGMAS)\n {/* zName:     */ \"empty_result_callbacks\",\n  /* ePragTyp:  */ PragTyp_FLAG,\n  /* ePragFlg:  */ PragFlg_Result0|PragFlg_NoColumns1,\n  /* ColNames:  */ 0, 0,\n  /* iArg:      */ SQLITE_NullCallback },\n#endif\n#if !defined(SQLITE_OMIT_UTF16)\n {/* zName:     */ \"encoding\",\n  /* ePragTyp:  */ PragTyp_ENCODING,\n  /* ePragFlg:  */ PragFlg_Result0|PragFlg_NoColumns1,\n  /* ColNames:  */ 0, 0,\n  /* iArg:      */ 0 },\n#endif\n#if !defined(SQLITE_OMIT_FOREIGN_KEY) && !defined(SQLITE_OMIT_TRIGGER)\n {/* zName:     */ \"foreign_key_check\",\n  /* ePragTyp:  */ PragTyp_FOREIGN_KEY_CHECK,\n  /* ePragFlg:  */ PragFlg_NeedSchema|PragFlg_Result0,\n  /* ColNames:  */ 42, 4,\n  /* iArg:      */ 0 },\n#endif\n#if !defined(SQLITE_OMIT_FOREIGN_KEY)\n {/* zName:     */ \"foreign_key_list\",\n  /* ePragTyp:  */ PragTyp_FOREIGN_KEY_LIST,\n  /* ePragFlg:  */ PragFlg_NeedSchema|PragFlg_Result1|PragFlg_SchemaOpt,\n  /* ColNames:  */ 34, 8,\n  /* iArg:      */ 0 },\n#endif\n#if !defined(SQLITE_OMIT_FLAG_PRAGMAS)\n#if !defined(SQLITE_OMIT_FOREIGN_KEY) && !defined(SQLITE_OMIT_TRIGGER)\n {/* zName:     */ \"foreign_keys\",\n  /* ePragTyp:  */ PragTyp_FLAG,\n  /* ePragFlg:  */ PragFlg_Result0|PragFlg_NoColumns1,\n  /* ColNames:  */ 0, 0,\n  /* iArg:      */ SQLITE_ForeignKeys },\n#endif\n#endif\n#if !defined(SQLITE_OMIT_SCHEMA_VERSION_PRAGMAS)\n {/* zName:     */ \"freelist_count\",\n  /* ePragTyp:  */ PragTyp_HEADER_VALUE,\n  /* ePragFlg:  */ PragFlg_ReadOnly|PragFlg_Result0,\n  /* ColNames:  */ 0, 0,\n  /* iArg:      */ BTREE_FREE_PAGE_COUNT },\n#endif\n#if !defined(SQLITE_OMIT_FLAG_PRAGMAS)\n {/* zName:     */ \"full_column_names\",\n  /* ePragTyp:  */ PragTyp_FLAG,\n  /* ePragFlg:  */ PragFlg_Result0|PragFlg_NoColumns1,\n  /* ColNames:  */ 0, 0,\n  /* iArg:      */ SQLITE_FullColNames },\n {/* zName:     */ \"fullfsync\",\n  /* ePragTyp:  */ PragTyp_FLAG,\n  /* ePragFlg:  */ PragFlg_Result0|PragFlg_NoColumns1,\n  /* ColNames:  */ 0, 0,\n  /* iArg:      */ SQLITE_FullFSync },\n#endif\n#if !defined(SQLITE_OMIT_SCHEMA_PRAGMAS)\n#if defined(SQLITE_INTROSPECTION_PRAGMAS)\n {/* zName:     */ \"function_list\",\n  /* ePragTyp:  */ PragTyp_FUNCTION_LIST,\n  /* ePragFlg:  */ PragFlg_Result0,\n  /* ColNames:  */ 29, 2,\n  /* iArg:      */ 0 },\n#endif\n#endif\n#if defined(SQLITE_HAS_CODEC)\n {/* zName:     */ \"hexkey\",\n  /* ePragTyp:  */ PragTyp_HEXKEY,\n  /* ePragFlg:  */ 0,\n  /* ColNames:  */ 0, 0,\n  /* iArg:      */ 0 },\n {/* zName:     */ \"hexrekey\",\n  /* ePragTyp:  */ PragTyp_HEXKEY,\n  /* ePragFlg:  */ 0,\n  /* ColNames:  */ 0, 0,\n  /* iArg:      */ 0 },\n#endif\n#if !defined(SQLITE_OMIT_FLAG_PRAGMAS)\n#if !defined(SQLITE_OMIT_CHECK)\n {/* zName:     */ \"ignore_check_constraints\",\n  /* ePragTyp:  */ PragTyp_FLAG,\n  /* ePragFlg:  */ PragFlg_Result0|PragFlg_NoColumns1,\n  /* ColNames:  */ 0, 0,\n  /* iArg:      */ SQLITE_IgnoreChecks },\n#endif\n#endif\n#if !defined(SQLITE_OMIT_AUTOVACUUM)\n {/* zName:     */ \"incremental_vacuum\",\n  /* ePragTyp:  */ PragTyp_INCREMENTAL_VACUUM,\n  /* ePragFlg:  */ PragFlg_NeedSchema|PragFlg_NoColumns,\n  /* ColNames:  */ 0, 0,\n  /* iArg:      */ 0 },\n#endif\n#if !defined(SQLITE_OMIT_SCHEMA_PRAGMAS)\n {/* zName:     */ \"index_info\",\n  /* ePragTyp:  */ PragTyp_INDEX_INFO,\n  /* ePragFlg:  */ PragFlg_NeedSchema|PragFlg_Result1|PragFlg_SchemaOpt,\n  /* ColNames:  */ 12, 3,\n  /* iArg:      */ 0 },\n {/* zName:     */ \"index_list\",\n  /* ePragTyp:  */ PragTyp_INDEX_LIST,\n  /* ePragFlg:  */ PragFlg_NeedSchema|PragFlg_Result1|PragFlg_SchemaOpt,\n  /* ColNames:  */ 21, 5,\n  /* iArg:      */ 0 },\n {/* zName:     */ \"index_xinfo\",\n  /* ePragTyp:  */ PragTyp_INDEX_INFO,\n  /* ePragFlg:  */ PragFlg_NeedSchema|PragFlg_Result1|PragFlg_SchemaOpt,\n  /* ColNames:  */ 15, 6,\n  /* iArg:      */ 1 },\n#endif\n#if !defined(SQLITE_OMIT_INTEGRITY_CHECK)\n {/* zName:     */ \"integrity_check\",\n  /* ePragTyp:  */ PragTyp_INTEGRITY_CHECK,\n  /* ePragFlg:  */ PragFlg_NeedSchema|PragFlg_Result0|PragFlg_Result1,\n  /* ColNames:  */ 0, 0,\n  /* iArg:      */ 0 },\n#endif\n#if !defined(SQLITE_OMIT_PAGER_PRAGMAS)\n {/* zName:     */ \"journal_mode\",\n  /* ePragTyp:  */ PragTyp_JOURNAL_MODE,\n  /* ePragFlg:  */ PragFlg_NeedSchema|PragFlg_Result0|PragFlg_SchemaReq,\n  /* ColNames:  */ 0, 0,\n  /* iArg:      */ 0 },\n {/* zName:     */ \"journal_size_limit\",\n  /* ePragTyp:  */ PragTyp_JOURNAL_SIZE_LIMIT,\n  /* ePragFlg:  */ PragFlg_Result0|PragFlg_SchemaReq,\n  /* ColNames:  */ 0, 0,\n  /* iArg:      */ 0 },\n#endif\n#if defined(SQLITE_HAS_CODEC)\n {/* zName:     */ \"key\",\n  /* ePragTyp:  */ PragTyp_KEY,\n  /* ePragFlg:  */ 0,\n  /* ColNames:  */ 0, 0,\n  /* iArg:      */ 0 },\n#endif\n#if !defined(SQLITE_OMIT_FLAG_PRAGMAS)\n {/* zName:     */ \"legacy_file_format\",\n  /* ePragTyp:  */ PragTyp_FLAG,\n  /* ePragFlg:  */ PragFlg_Result0|PragFlg_NoColumns1,\n  /* ColNames:  */ 0, 0,\n  /* iArg:      */ SQLITE_LegacyFileFmt },\n#endif\n#if !defined(SQLITE_OMIT_PAGER_PRAGMAS) && SQLITE_ENABLE_LOCKING_STYLE\n {/* zName:     */ \"lock_proxy_file\",\n  /* ePragTyp:  */ PragTyp_LOCK_PROXY_FILE,\n  /* ePragFlg:  */ PragFlg_NoColumns1,\n  /* ColNames:  */ 0, 0,\n  /* iArg:      */ 0 },\n#endif\n#if defined(SQLITE_DEBUG) || defined(SQLITE_TEST)\n {/* zName:     */ \"lock_status\",\n  /* ePragTyp:  */ PragTyp_LOCK_STATUS,\n  /* ePragFlg:  */ PragFlg_Result0,\n  /* ColNames:  */ 50, 2,\n  /* iArg:      */ 0 },\n#endif\n#if !defined(SQLITE_OMIT_PAGER_PRAGMAS)\n {/* zName:     */ \"locking_mode\",\n  /* ePragTyp:  */ PragTyp_LOCKING_MODE,\n  /* ePragFlg:  */ PragFlg_Result0|PragFlg_SchemaReq,\n  /* ColNames:  */ 0, 0,\n  /* iArg:      */ 0 },\n {/* zName:     */ \"max_page_count\",\n  /* ePragTyp:  */ PragTyp_PAGE_COUNT,\n  /* ePragFlg:  */ PragFlg_NeedSchema|PragFlg_Result0|PragFlg_SchemaReq,\n  /* ColNames:  */ 0, 0,\n  /* iArg:      */ 0 },\n {/* zName:     */ \"mmap_size\",\n  /* ePragTyp:  */ PragTyp_MMAP_SIZE,\n  /* ePragFlg:  */ 0,\n  /* ColNames:  */ 0, 0,\n  /* iArg:      */ 0 },\n#endif\n#if !defined(SQLITE_OMIT_SCHEMA_PRAGMAS)\n#if !defined(SQLITE_OMIT_VIRTUALTABLE)\n#if defined(SQLITE_INTROSPECTION_PRAGMAS)\n {/* zName:     */ \"module_list\",\n  /* ePragTyp:  */ PragTyp_MODULE_LIST,\n  /* ePragFlg:  */ PragFlg_Result0,\n  /* ColNames:  */ 31, 1,\n  /* iArg:      */ 0 },\n#endif\n#endif\n#endif\n {/* zName:     */ \"optimize\",\n  /* ePragTyp:  */ PragTyp_OPTIMIZE,\n  /* ePragFlg:  */ PragFlg_Result1|PragFlg_NeedSchema,\n  /* ColNames:  */ 0, 0,\n  /* iArg:      */ 0 },\n#if !defined(SQLITE_OMIT_PAGER_PRAGMAS)\n {/* zName:     */ \"page_count\",\n  /* ePragTyp:  */ PragTyp_PAGE_COUNT,\n  /* ePragFlg:  */ PragFlg_NeedSchema|PragFlg_Result0|PragFlg_SchemaReq,\n  /* ColNames:  */ 0, 0,\n  /* iArg:      */ 0 },\n {/* zName:     */ \"page_size\",\n  /* ePragTyp:  */ PragTyp_PAGE_SIZE,\n  /* ePragFlg:  */ PragFlg_Result0|PragFlg_SchemaReq|PragFlg_NoColumns1,\n  /* ColNames:  */ 0, 0,\n  /* iArg:      */ 0 },\n#endif\n#if defined(SQLITE_DEBUG) && !defined(SQLITE_OMIT_PARSER_TRACE)\n {/* zName:     */ \"parser_trace\",\n  /* ePragTyp:  */ PragTyp_PARSER_TRACE,\n  /* ePragFlg:  */ 0,\n  /* ColNames:  */ 0, 0,\n  /* iArg:      */ 0 },\n#endif\n#if defined(SQLITE_INTROSPECTION_PRAGMAS)\n {/* zName:     */ \"pragma_list\",\n  /* ePragTyp:  */ PragTyp_PRAGMA_LIST,\n  /* ePragFlg:  */ PragFlg_Result0,\n  /* ColNames:  */ 31, 1,\n  /* iArg:      */ 0 },\n#endif\n#if !defined(SQLITE_OMIT_FLAG_PRAGMAS)\n {/* zName:     */ \"query_only\",\n  /* ePragTyp:  */ PragTyp_FLAG,\n  /* ePragFlg:  */ PragFlg_Result0|PragFlg_NoColumns1,\n  /* ColNames:  */ 0, 0,\n  /* iArg:      */ SQLITE_QueryOnly },\n#endif\n#if !defined(SQLITE_OMIT_INTEGRITY_CHECK)\n {/* zName:     */ \"quick_check\",\n  /* ePragTyp:  */ PragTyp_INTEGRITY_CHECK,\n  /* ePragFlg:  */ PragFlg_NeedSchema|PragFlg_Result0|PragFlg_Result1,\n  /* ColNames:  */ 0, 0,\n  /* iArg:      */ 0 },\n#endif\n#if !defined(SQLITE_OMIT_FLAG_PRAGMAS)\n {/* zName:     */ \"read_uncommitted\",\n  /* ePragTyp:  */ PragTyp_FLAG,\n  /* ePragFlg:  */ PragFlg_Result0|PragFlg_NoColumns1,\n  /* ColNames:  */ 0, 0,\n  /* iArg:      */ SQLITE_ReadUncommit },\n {/* zName:     */ \"recursive_triggers\",\n  /* ePragTyp:  */ PragTyp_FLAG,\n  /* ePragFlg:  */ PragFlg_Result0|PragFlg_NoColumns1,\n  /* ColNames:  */ 0, 0,\n  /* iArg:      */ SQLITE_RecTriggers },\n#endif\n#if defined(SQLITE_HAS_CODEC)\n {/* zName:     */ \"rekey\",\n  /* ePragTyp:  */ PragTyp_REKEY,\n  /* ePragFlg:  */ 0,\n  /* ColNames:  */ 0, 0,\n  /* iArg:      */ 0 },\n#endif\n#if !defined(SQLITE_OMIT_FLAG_PRAGMAS)\n {/* zName:     */ \"reverse_unordered_selects\",\n  /* ePragTyp:  */ PragTyp_FLAG,\n  /* ePragFlg:  */ PragFlg_Result0|PragFlg_NoColumns1,\n  /* ColNames:  */ 0, 0,\n  /* iArg:      */ SQLITE_ReverseOrder },\n#endif\n#if !defined(SQLITE_OMIT_SCHEMA_VERSION_PRAGMAS)\n {/* zName:     */ \"schema_version\",\n  /* ePragTyp:  */ PragTyp_HEADER_VALUE,\n  /* ePragFlg:  */ PragFlg_NoColumns1|PragFlg_Result0,\n  /* ColNames:  */ 0, 0,\n  /* iArg:      */ BTREE_SCHEMA_VERSION },\n#endif\n#if !defined(SQLITE_OMIT_PAGER_PRAGMAS)\n {/* zName:     */ \"secure_delete\",\n  /* ePragTyp:  */ PragTyp_SECURE_DELETE,\n  /* ePragFlg:  */ PragFlg_Result0,\n  /* ColNames:  */ 0, 0,\n  /* iArg:      */ 0 },\n#endif\n#if !defined(SQLITE_OMIT_FLAG_PRAGMAS)\n {/* zName:     */ \"short_column_names\",\n  /* ePragTyp:  */ PragTyp_FLAG,\n  /* ePragFlg:  */ PragFlg_Result0|PragFlg_NoColumns1,\n  /* ColNames:  */ 0, 0,\n  /* iArg:      */ SQLITE_ShortColNames },\n#endif\n {/* zName:     */ \"shrink_memory\",\n  /* ePragTyp:  */ PragTyp_SHRINK_MEMORY,\n  /* ePragFlg:  */ PragFlg_NoColumns,\n  /* ColNames:  */ 0, 0,\n  /* iArg:      */ 0 },\n {/* zName:     */ \"soft_heap_limit\",\n  /* ePragTyp:  */ PragTyp_SOFT_HEAP_LIMIT,\n  /* ePragFlg:  */ PragFlg_Result0,\n  /* ColNames:  */ 0, 0,\n  /* iArg:      */ 0 },\n#if !defined(SQLITE_OMIT_FLAG_PRAGMAS)\n#if defined(SQLITE_DEBUG)\n {/* zName:     */ \"sql_trace\",\n  /* ePragTyp:  */ PragTyp_FLAG,\n  /* ePragFlg:  */ PragFlg_Result0|PragFlg_NoColumns1,\n  /* ColNames:  */ 0, 0,\n  /* iArg:      */ SQLITE_SqlTrace },\n#endif\n#endif\n#if !defined(SQLITE_OMIT_SCHEMA_PRAGMAS) && defined(SQLITE_DEBUG)\n {/* zName:     */ \"stats\",\n  /* ePragTyp:  */ PragTyp_STATS,\n  /* ePragFlg:  */ PragFlg_NeedSchema|PragFlg_Result0|PragFlg_SchemaReq,\n  /* ColNames:  */ 7, 5,\n  /* iArg:      */ 0 },\n#endif\n#if !defined(SQLITE_OMIT_PAGER_PRAGMAS)\n {/* zName:     */ \"synchronous\",\n  /* ePragTyp:  */ PragTyp_SYNCHRONOUS,\n  /* ePragFlg:  */ PragFlg_NeedSchema|PragFlg_Result0|PragFlg_SchemaReq|PragFlg_NoColumns1,\n  /* ColNames:  */ 0, 0,\n  /* iArg:      */ 0 },\n#endif\n#if !defined(SQLITE_OMIT_SCHEMA_PRAGMAS)\n {/* zName:     */ \"table_info\",\n  /* ePragTyp:  */ PragTyp_TABLE_INFO,\n  /* ePragFlg:  */ PragFlg_NeedSchema|PragFlg_Result1|PragFlg_SchemaOpt,\n  /* ColNames:  */ 1, 6,\n  /* iArg:      */ 0 },\n#endif\n#if !defined(SQLITE_OMIT_PAGER_PRAGMAS)\n {/* zName:     */ \"temp_store\",\n  /* ePragTyp:  */ PragTyp_TEMP_STORE,\n  /* ePragFlg:  */ PragFlg_Result0|PragFlg_NoColumns1,\n  /* ColNames:  */ 0, 0,\n  /* iArg:      */ 0 },\n {/* zName:     */ \"temp_store_directory\",\n  /* ePragTyp:  */ PragTyp_TEMP_STORE_DIRECTORY,\n  /* ePragFlg:  */ PragFlg_NoColumns1,\n  /* ColNames:  */ 0, 0,\n  /* iArg:      */ 0 },\n#endif\n {/* zName:     */ \"threads\",\n  /* ePragTyp:  */ PragTyp_THREADS,\n  /* ePragFlg:  */ PragFlg_Result0,\n  /* ColNames:  */ 0, 0,\n  /* iArg:      */ 0 },\n#if !defined(SQLITE_OMIT_SCHEMA_VERSION_PRAGMAS)\n {/* zName:     */ \"user_version\",\n  /* ePragTyp:  */ PragTyp_HEADER_VALUE,\n  /* ePragFlg:  */ PragFlg_NoColumns1|PragFlg_Result0,\n  /* ColNames:  */ 0, 0,\n  /* iArg:      */ BTREE_USER_VERSION },\n#endif\n#if !defined(SQLITE_OMIT_FLAG_PRAGMAS)\n#if defined(SQLITE_DEBUG)\n {/* zName:     */ \"vdbe_addoptrace\",\n  /* ePragTyp:  */ PragTyp_FLAG,\n  /* ePragFlg:  */ PragFlg_Result0|PragFlg_NoColumns1,\n  /* ColNames:  */ 0, 0,\n  /* iArg:      */ SQLITE_VdbeAddopTrace },\n {/* zName:     */ \"vdbe_debug\",\n  /* ePragTyp:  */ PragTyp_FLAG,\n  /* ePragFlg:  */ PragFlg_Result0|PragFlg_NoColumns1,\n  /* ColNames:  */ 0, 0,\n  /* iArg:      */ SQLITE_SqlTrace|SQLITE_VdbeListing|SQLITE_VdbeTrace },\n {/* zName:     */ \"vdbe_eqp\",\n  /* ePragTyp:  */ PragTyp_FLAG,\n  /* ePragFlg:  */ PragFlg_Result0|PragFlg_NoColumns1,\n  /* ColNames:  */ 0, 0,\n  /* iArg:      */ SQLITE_VdbeEQP },\n {/* zName:     */ \"vdbe_listing\",\n  /* ePragTyp:  */ PragTyp_FLAG,\n  /* ePragFlg:  */ PragFlg_Result0|PragFlg_NoColumns1,\n  /* ColNames:  */ 0, 0,\n  /* iArg:      */ SQLITE_VdbeListing },\n {/* zName:     */ \"vdbe_trace\",\n  /* ePragTyp:  */ PragTyp_FLAG,\n  /* ePragFlg:  */ PragFlg_Result0|PragFlg_NoColumns1,\n  /* ColNames:  */ 0, 0,\n  /* iArg:      */ SQLITE_VdbeTrace },\n#endif\n#endif\n#if !defined(SQLITE_OMIT_WAL)\n {/* zName:     */ \"wal_autocheckpoint\",\n  /* ePragTyp:  */ PragTyp_WAL_AUTOCHECKPOINT,\n  /* ePragFlg:  */ 0,\n  /* ColNames:  */ 0, 0,\n  /* iArg:      */ 0 },\n {/* zName:     */ \"wal_checkpoint\",\n  /* ePragTyp:  */ PragTyp_WAL_CHECKPOINT,\n  /* ePragFlg:  */ PragFlg_NeedSchema,\n  /* ColNames:  */ 46, 3,\n  /* iArg:      */ 0 },\n#endif\n#if !defined(SQLITE_OMIT_FLAG_PRAGMAS)\n {/* zName:     */ \"writable_schema\",\n  /* ePragTyp:  */ PragTyp_FLAG,\n  /* ePragFlg:  */ PragFlg_Result0|PragFlg_NoColumns1,\n  /* ColNames:  */ 0, 0,\n  /* iArg:      */ SQLITE_WriteSchema },\n#endif\n};\n/* Number of pragmas: 60 on by default, 77 total. */\n\n/************** End of pragma.h **********************************************/\n/************** Continuing where we left off in pragma.c *********************/\n\n/*\n** Interpret the given string as a safety level.  Return 0 for OFF,\n** 1 for ON or NORMAL, 2 for FULL, and 3 for EXTRA.  Return 1 for an empty or \n** unrecognized string argument.  The FULL and EXTRA option is disallowed\n** if the omitFull parameter it 1.\n**\n** Note that the values returned are one less that the values that\n** should be passed into sqlite3BtreeSetSafetyLevel().  The is done\n** to support legacy SQL code.  The safety level used to be boolean\n** and older scripts may have used numbers 0 for OFF and 1 for ON.\n*/\nstatic u8 getSafetyLevel(const char *z, int omitFull, u8 dflt){\n                             /* 123456789 123456789 123 */\n  static const char zText[] = \"onoffalseyestruextrafull\";\n  static const u8 iOffset[] = {0, 1, 2,  4,    9,  12,  15,   20};\n  static const u8 iLength[] = {2, 2, 3,  5,    3,   4,   5,    4};\n  static const u8 iValue[] =  {1, 0, 0,  0,    1,   1,   3,    2};\n                            /* on no off false yes true extra full */\n  int i, n;\n  if( sqlite3Isdigit(*z) ){\n    return (u8)sqlite3Atoi(z);\n  }\n  n = sqlite3Strlen30(z);\n  for(i=0; i<ArraySize(iLength); i++){\n    if( iLength[i]==n && sqlite3StrNICmp(&zText[iOffset[i]],z,n)==0\n     && (!omitFull || iValue[i]<=1)\n    ){\n      return iValue[i];\n    }\n  }\n  return dflt;\n}\n\n/*\n** Interpret the given string as a boolean value.\n*/\nSQLITE_PRIVATE u8 sqlite3GetBoolean(const char *z, u8 dflt){\n  return getSafetyLevel(z,1,dflt)!=0;\n}\n\n/* The sqlite3GetBoolean() function is used by other modules but the\n** remainder of this file is specific to PRAGMA processing.  So omit\n** the rest of the file if PRAGMAs are omitted from the build.\n*/\n#if !defined(SQLITE_OMIT_PRAGMA)\n\n/*\n** Interpret the given string as a locking mode value.\n*/\nstatic int getLockingMode(const char *z){\n  if( z ){\n    if( 0==sqlite3StrICmp(z, \"exclusive\") ) return PAGER_LOCKINGMODE_EXCLUSIVE;\n    if( 0==sqlite3StrICmp(z, \"normal\") ) return PAGER_LOCKINGMODE_NORMAL;\n  }\n  return PAGER_LOCKINGMODE_QUERY;\n}\n\n#ifndef SQLITE_OMIT_AUTOVACUUM\n/*\n** Interpret the given string as an auto-vacuum mode value.\n**\n** The following strings, \"none\", \"full\" and \"incremental\" are \n** acceptable, as are their numeric equivalents: 0, 1 and 2 respectively.\n*/\nstatic int getAutoVacuum(const char *z){\n  int i;\n  if( 0==sqlite3StrICmp(z, \"none\") ) return BTREE_AUTOVACUUM_NONE;\n  if( 0==sqlite3StrICmp(z, \"full\") ) return BTREE_AUTOVACUUM_FULL;\n  if( 0==sqlite3StrICmp(z, \"incremental\") ) return BTREE_AUTOVACUUM_INCR;\n  i = sqlite3Atoi(z);\n  return (u8)((i>=0&&i<=2)?i:0);\n}\n#endif /* ifndef SQLITE_OMIT_AUTOVACUUM */\n\n#ifndef SQLITE_OMIT_PAGER_PRAGMAS\n/*\n** Interpret the given string as a temp db location. Return 1 for file\n** backed temporary databases, 2 for the Red-Black tree in memory database\n** and 0 to use the compile-time default.\n*/\nstatic int getTempStore(const char *z){\n  if( z[0]>='0' && z[0]<='2' ){\n    return z[0] - '0';\n  }else if( sqlite3StrICmp(z, \"file\")==0 ){\n    return 1;\n  }else if( sqlite3StrICmp(z, \"memory\")==0 ){\n    return 2;\n  }else{\n    return 0;\n  }\n}\n#endif /* SQLITE_PAGER_PRAGMAS */\n\n#ifndef SQLITE_OMIT_PAGER_PRAGMAS\n/*\n** Invalidate temp storage, either when the temp storage is changed\n** from default, or when 'file' and the temp_store_directory has changed\n*/\nstatic int invalidateTempStorage(Parse *pParse){\n  sqlite3 *db = pParse->db;\n  if( db->aDb[1].pBt!=0 ){\n    if( !db->autoCommit || sqlite3BtreeIsInReadTrans(db->aDb[1].pBt) ){\n      sqlite3ErrorMsg(pParse, \"temporary storage cannot be changed \"\n        \"from within a transaction\");\n      return SQLITE_ERROR;\n    }\n    sqlite3BtreeClose(db->aDb[1].pBt);\n    db->aDb[1].pBt = 0;\n    sqlite3ResetAllSchemasOfConnection(db);\n  }\n  return SQLITE_OK;\n}\n#endif /* SQLITE_PAGER_PRAGMAS */\n\n#ifndef SQLITE_OMIT_PAGER_PRAGMAS\n/*\n** If the TEMP database is open, close it and mark the database schema\n** as needing reloading.  This must be done when using the SQLITE_TEMP_STORE\n** or DEFAULT_TEMP_STORE pragmas.\n*/\nstatic int changeTempStorage(Parse *pParse, const char *zStorageType){\n  int ts = getTempStore(zStorageType);\n  sqlite3 *db = pParse->db;\n  if( db->temp_store==ts ) return SQLITE_OK;\n  if( invalidateTempStorage( pParse ) != SQLITE_OK ){\n    return SQLITE_ERROR;\n  }\n  db->temp_store = (u8)ts;\n  return SQLITE_OK;\n}\n#endif /* SQLITE_PAGER_PRAGMAS */\n\n/*\n** Set result column names for a pragma.\n*/\nstatic void setPragmaResultColumnNames(\n  Vdbe *v,                     /* The query under construction */\n  const PragmaName *pPragma    /* The pragma */\n){\n  u8 n = pPragma->nPragCName;\n  sqlite3VdbeSetNumCols(v, n==0 ? 1 : n);\n  if( n==0 ){\n    sqlite3VdbeSetColName(v, 0, COLNAME_NAME, pPragma->zName, SQLITE_STATIC);\n  }else{\n    int i, j;\n    for(i=0, j=pPragma->iPragCName; i<n; i++, j++){\n      sqlite3VdbeSetColName(v, i, COLNAME_NAME, pragCName[j], SQLITE_STATIC);\n    }\n  }\n}\n\n/*\n** Generate code to return a single integer value.\n*/\nstatic void returnSingleInt(Vdbe *v, i64 value){\n  sqlite3VdbeAddOp4Dup8(v, OP_Int64, 0, 1, 0, (const u8*)&value, P4_INT64);\n  sqlite3VdbeAddOp2(v, OP_ResultRow, 1, 1);\n}\n\n/*\n** Generate code to return a single text value.\n*/\nstatic void returnSingleText(\n  Vdbe *v,                /* Prepared statement under construction */\n  const char *zValue      /* Value to be returned */\n){\n  if( zValue ){\n    sqlite3VdbeLoadString(v, 1, (const char*)zValue);\n    sqlite3VdbeAddOp2(v, OP_ResultRow, 1, 1);\n  }\n}\n\n\n/*\n** Set the safety_level and pager flags for pager iDb.  Or if iDb<0\n** set these values for all pagers.\n*/\n#ifndef SQLITE_OMIT_PAGER_PRAGMAS\nstatic void setAllPagerFlags(sqlite3 *db){\n  if( db->autoCommit ){\n    Db *pDb = db->aDb;\n    int n = db->nDb;\n    assert( SQLITE_FullFSync==PAGER_FULLFSYNC );\n    assert( SQLITE_CkptFullFSync==PAGER_CKPT_FULLFSYNC );\n    assert( SQLITE_CacheSpill==PAGER_CACHESPILL );\n    assert( (PAGER_FULLFSYNC | PAGER_CKPT_FULLFSYNC | PAGER_CACHESPILL)\n             ==  PAGER_FLAGS_MASK );\n    assert( (pDb->safety_level & PAGER_SYNCHRONOUS_MASK)==pDb->safety_level );\n    while( (n--) > 0 ){\n      if( pDb->pBt ){\n        sqlite3BtreeSetPagerFlags(pDb->pBt,\n                 pDb->safety_level | (db->flags & PAGER_FLAGS_MASK) );\n      }\n      pDb++;\n    }\n  }\n}\n#else\n# define setAllPagerFlags(X)  /* no-op */\n#endif\n\n\n/*\n** Return a human-readable name for a constraint resolution action.\n*/\n#ifndef SQLITE_OMIT_FOREIGN_KEY\nstatic const char *actionName(u8 action){\n  const char *zName;\n  switch( action ){\n    case OE_SetNull:  zName = \"SET NULL\";        break;\n    case OE_SetDflt:  zName = \"SET DEFAULT\";     break;\n    case OE_Cascade:  zName = \"CASCADE\";         break;\n    case OE_Restrict: zName = \"RESTRICT\";        break;\n    default:          zName = \"NO ACTION\";  \n                      assert( action==OE_None ); break;\n  }\n  return zName;\n}\n#endif\n\n\n/*\n** Parameter eMode must be one of the PAGER_JOURNALMODE_XXX constants\n** defined in pager.h. This function returns the associated lowercase\n** journal-mode name.\n*/\nSQLITE_PRIVATE const char *sqlite3JournalModename(int eMode){\n  static char * const azModeName[] = {\n    \"delete\", \"persist\", \"off\", \"truncate\", \"memory\"\n#ifndef SQLITE_OMIT_WAL\n     , \"wal\"\n#endif\n  };\n  assert( PAGER_JOURNALMODE_DELETE==0 );\n  assert( PAGER_JOURNALMODE_PERSIST==1 );\n  assert( PAGER_JOURNALMODE_OFF==2 );\n  assert( PAGER_JOURNALMODE_TRUNCATE==3 );\n  assert( PAGER_JOURNALMODE_MEMORY==4 );\n  assert( PAGER_JOURNALMODE_WAL==5 );\n  assert( eMode>=0 && eMode<=ArraySize(azModeName) );\n\n  if( eMode==ArraySize(azModeName) ) return 0;\n  return azModeName[eMode];\n}\n\n/*\n** Locate a pragma in the aPragmaName[] array.\n*/\nstatic const PragmaName *pragmaLocate(const char *zName){\n  int upr, lwr, mid = 0, rc;\n  lwr = 0;\n  upr = ArraySize(aPragmaName)-1;\n  while( lwr<=upr ){\n    mid = (lwr+upr)/2;\n    rc = sqlite3_stricmp(zName, aPragmaName[mid].zName);\n    if( rc==0 ) break;\n    if( rc<0 ){\n      upr = mid - 1;\n    }else{\n      lwr = mid + 1;\n    }\n  }\n  return lwr>upr ? 0 : &aPragmaName[mid];\n}\n\n/*\n** Helper subroutine for PRAGMA integrity_check:\n**\n** Generate code to output a single-column result row with a value of the\n** string held in register 3.  Decrement the result count in register 1\n** and halt if the maximum number of result rows have been issued.\n*/\nstatic int integrityCheckResultRow(Vdbe *v){\n  int addr;\n  sqlite3VdbeAddOp2(v, OP_ResultRow, 3, 1);\n  addr = sqlite3VdbeAddOp3(v, OP_IfPos, 1, sqlite3VdbeCurrentAddr(v)+2, 1);\n  VdbeCoverage(v);\n  sqlite3VdbeAddOp0(v, OP_Halt);\n  return addr;\n}\n\n/*\n** Process a pragma statement.  \n**\n** Pragmas are of this form:\n**\n**      PRAGMA [schema.]id [= value]\n**\n** The identifier might also be a string.  The value is a string, and\n** identifier, or a number.  If minusFlag is true, then the value is\n** a number that was preceded by a minus sign.\n**\n** If the left side is \"database.id\" then pId1 is the database name\n** and pId2 is the id.  If the left side is just \"id\" then pId1 is the\n** id and pId2 is any empty string.\n*/\nSQLITE_PRIVATE void sqlite3Pragma(\n  Parse *pParse, \n  Token *pId1,        /* First part of [schema.]id field */\n  Token *pId2,        /* Second part of [schema.]id field, or NULL */\n  Token *pValue,      /* Token for <value>, or NULL */\n  int minusFlag       /* True if a '-' sign preceded <value> */\n){\n  char *zLeft = 0;       /* Nul-terminated UTF-8 string <id> */\n  char *zRight = 0;      /* Nul-terminated UTF-8 string <value>, or NULL */\n  const char *zDb = 0;   /* The database name */\n  Token *pId;            /* Pointer to <id> token */\n  char *aFcntl[4];       /* Argument to SQLITE_FCNTL_PRAGMA */\n  int iDb;               /* Database index for <database> */\n  int rc;                      /* return value form SQLITE_FCNTL_PRAGMA */\n  sqlite3 *db = pParse->db;    /* The database connection */\n  Db *pDb;                     /* The specific database being pragmaed */\n  Vdbe *v = sqlite3GetVdbe(pParse);  /* Prepared statement */\n  const PragmaName *pPragma;   /* The pragma */\n\n  if( v==0 ) return;\n  sqlite3VdbeRunOnlyOnce(v);\n  pParse->nMem = 2;\n\n  /* Interpret the [schema.] part of the pragma statement. iDb is the\n  ** index of the database this pragma is being applied to in db.aDb[]. */\n  iDb = sqlite3TwoPartName(pParse, pId1, pId2, &pId);\n  if( iDb<0 ) return;\n  pDb = &db->aDb[iDb];\n\n  /* If the temp database has been explicitly named as part of the \n  ** pragma, make sure it is open. \n  */\n  if( iDb==1 && sqlite3OpenTempDatabase(pParse) ){\n    return;\n  }\n\n  zLeft = sqlite3NameFromToken(db, pId);\n  if( !zLeft ) return;\n  if( minusFlag ){\n    zRight = sqlite3MPrintf(db, \"-%T\", pValue);\n  }else{\n    zRight = sqlite3NameFromToken(db, pValue);\n  }\n\n  assert( pId2 );\n  zDb = pId2->n>0 ? pDb->zDbSName : 0;\n  if( sqlite3AuthCheck(pParse, SQLITE_PRAGMA, zLeft, zRight, zDb) ){\n    goto pragma_out;\n  }\n\n  /* Send an SQLITE_FCNTL_PRAGMA file-control to the underlying VFS\n  ** connection.  If it returns SQLITE_OK, then assume that the VFS\n  ** handled the pragma and generate a no-op prepared statement.\n  **\n  ** IMPLEMENTATION-OF: R-12238-55120 Whenever a PRAGMA statement is parsed,\n  ** an SQLITE_FCNTL_PRAGMA file control is sent to the open sqlite3_file\n  ** object corresponding to the database file to which the pragma\n  ** statement refers.\n  **\n  ** IMPLEMENTATION-OF: R-29875-31678 The argument to the SQLITE_FCNTL_PRAGMA\n  ** file control is an array of pointers to strings (char**) in which the\n  ** second element of the array is the name of the pragma and the third\n  ** element is the argument to the pragma or NULL if the pragma has no\n  ** argument.\n  */\n  aFcntl[0] = 0;\n  aFcntl[1] = zLeft;\n  aFcntl[2] = zRight;\n  aFcntl[3] = 0;\n  db->busyHandler.nBusy = 0;\n  rc = sqlite3_file_control(db, zDb, SQLITE_FCNTL_PRAGMA, (void*)aFcntl);\n  if( rc==SQLITE_OK ){\n    sqlite3VdbeSetNumCols(v, 1);\n    sqlite3VdbeSetColName(v, 0, COLNAME_NAME, aFcntl[0], SQLITE_TRANSIENT);\n    returnSingleText(v, aFcntl[0]);\n    sqlite3_free(aFcntl[0]);\n    goto pragma_out;\n  }\n  if( rc!=SQLITE_NOTFOUND ){\n    if( aFcntl[0] ){\n      sqlite3ErrorMsg(pParse, \"%s\", aFcntl[0]);\n      sqlite3_free(aFcntl[0]);\n    }\n    pParse->nErr++;\n    pParse->rc = rc;\n    goto pragma_out;\n  }\n\n  /* Locate the pragma in the lookup table */\n  pPragma = pragmaLocate(zLeft);\n  if( pPragma==0 ) goto pragma_out;\n\n  /* Make sure the database schema is loaded if the pragma requires that */\n  if( (pPragma->mPragFlg & PragFlg_NeedSchema)!=0 ){\n    if( sqlite3ReadSchema(pParse) ) goto pragma_out;\n  }\n\n  /* Register the result column names for pragmas that return results */\n  if( (pPragma->mPragFlg & PragFlg_NoColumns)==0 \n   && ((pPragma->mPragFlg & PragFlg_NoColumns1)==0 || zRight==0)\n  ){\n    setPragmaResultColumnNames(v, pPragma);\n  }\n\n  /* Jump to the appropriate pragma handler */\n  switch( pPragma->ePragTyp ){\n  \n#if !defined(SQLITE_OMIT_PAGER_PRAGMAS) && !defined(SQLITE_OMIT_DEPRECATED)\n  /*\n  **  PRAGMA [schema.]default_cache_size\n  **  PRAGMA [schema.]default_cache_size=N\n  **\n  ** The first form reports the current persistent setting for the\n  ** page cache size.  The value returned is the maximum number of\n  ** pages in the page cache.  The second form sets both the current\n  ** page cache size value and the persistent page cache size value\n  ** stored in the database file.\n  **\n  ** Older versions of SQLite would set the default cache size to a\n  ** negative number to indicate synchronous=OFF.  These days, synchronous\n  ** is always on by default regardless of the sign of the default cache\n  ** size.  But continue to take the absolute value of the default cache\n  ** size of historical compatibility.\n  */\n  case PragTyp_DEFAULT_CACHE_SIZE: {\n    static const int iLn = VDBE_OFFSET_LINENO(2);\n    static const VdbeOpList getCacheSize[] = {\n      { OP_Transaction, 0, 0,        0},                         /* 0 */\n      { OP_ReadCookie,  0, 1,        BTREE_DEFAULT_CACHE_SIZE},  /* 1 */\n      { OP_IfPos,       1, 8,        0},\n      { OP_Integer,     0, 2,        0},\n      { OP_Subtract,    1, 2,        1},\n      { OP_IfPos,       1, 8,        0},\n      { OP_Integer,     0, 1,        0},                         /* 6 */\n      { OP_Noop,        0, 0,        0},\n      { OP_ResultRow,   1, 1,        0},\n    };\n    VdbeOp *aOp;\n    sqlite3VdbeUsesBtree(v, iDb);\n    if( !zRight ){\n      pParse->nMem += 2;\n      sqlite3VdbeVerifyNoMallocRequired(v, ArraySize(getCacheSize));\n      aOp = sqlite3VdbeAddOpList(v, ArraySize(getCacheSize), getCacheSize, iLn);\n      if( ONLY_IF_REALLOC_STRESS(aOp==0) ) break;\n      aOp[0].p1 = iDb;\n      aOp[1].p1 = iDb;\n      aOp[6].p1 = SQLITE_DEFAULT_CACHE_SIZE;\n    }else{\n      int size = sqlite3AbsInt32(sqlite3Atoi(zRight));\n      sqlite3BeginWriteOperation(pParse, 0, iDb);\n      sqlite3VdbeAddOp3(v, OP_SetCookie, iDb, BTREE_DEFAULT_CACHE_SIZE, size);\n      assert( sqlite3SchemaMutexHeld(db, iDb, 0) );\n      pDb->pSchema->cache_size = size;\n      sqlite3BtreeSetCacheSize(pDb->pBt, pDb->pSchema->cache_size);\n    }\n    break;\n  }\n#endif /* !SQLITE_OMIT_PAGER_PRAGMAS && !SQLITE_OMIT_DEPRECATED */\n\n#if !defined(SQLITE_OMIT_PAGER_PRAGMAS)\n  /*\n  **  PRAGMA [schema.]page_size\n  **  PRAGMA [schema.]page_size=N\n  **\n  ** The first form reports the current setting for the\n  ** database page size in bytes.  The second form sets the\n  ** database page size value.  The value can only be set if\n  ** the database has not yet been created.\n  */\n  case PragTyp_PAGE_SIZE: {\n    Btree *pBt = pDb->pBt;\n    assert( pBt!=0 );\n    if( !zRight ){\n      int size = ALWAYS(pBt) ? sqlite3BtreeGetPageSize(pBt) : 0;\n      returnSingleInt(v, size);\n    }else{\n      /* Malloc may fail when setting the page-size, as there is an internal\n      ** buffer that the pager module resizes using sqlite3_realloc().\n      */\n      db->nextPagesize = sqlite3Atoi(zRight);\n      if( SQLITE_NOMEM==sqlite3BtreeSetPageSize(pBt, db->nextPagesize,-1,0) ){\n        sqlite3OomFault(db);\n      }\n    }\n    break;\n  }\n\n  /*\n  **  PRAGMA [schema.]secure_delete\n  **  PRAGMA [schema.]secure_delete=ON/OFF/FAST\n  **\n  ** The first form reports the current setting for the\n  ** secure_delete flag.  The second form changes the secure_delete\n  ** flag setting and reports the new value.\n  */\n  case PragTyp_SECURE_DELETE: {\n    Btree *pBt = pDb->pBt;\n    int b = -1;\n    assert( pBt!=0 );\n    if( zRight ){\n      if( sqlite3_stricmp(zRight, \"fast\")==0 ){\n        b = 2;\n      }else{\n        b = sqlite3GetBoolean(zRight, 0);\n      }\n    }\n    if( pId2->n==0 && b>=0 ){\n      int ii;\n      for(ii=0; ii<db->nDb; ii++){\n        sqlite3BtreeSecureDelete(db->aDb[ii].pBt, b);\n      }\n    }\n    b = sqlite3BtreeSecureDelete(pBt, b);\n    returnSingleInt(v, b);\n    break;\n  }\n\n  /*\n  **  PRAGMA [schema.]max_page_count\n  **  PRAGMA [schema.]max_page_count=N\n  **\n  ** The first form reports the current setting for the\n  ** maximum number of pages in the database file.  The \n  ** second form attempts to change this setting.  Both\n  ** forms return the current setting.\n  **\n  ** The absolute value of N is used.  This is undocumented and might\n  ** change.  The only purpose is to provide an easy way to test\n  ** the sqlite3AbsInt32() function.\n  **\n  **  PRAGMA [schema.]page_count\n  **\n  ** Return the number of pages in the specified database.\n  */\n  case PragTyp_PAGE_COUNT: {\n    int iReg;\n    sqlite3CodeVerifySchema(pParse, iDb);\n    iReg = ++pParse->nMem;\n    if( sqlite3Tolower(zLeft[0])=='p' ){\n      sqlite3VdbeAddOp2(v, OP_Pagecount, iDb, iReg);\n    }else{\n      sqlite3VdbeAddOp3(v, OP_MaxPgcnt, iDb, iReg, \n                        sqlite3AbsInt32(sqlite3Atoi(zRight)));\n    }\n    sqlite3VdbeAddOp2(v, OP_ResultRow, iReg, 1);\n    break;\n  }\n\n  /*\n  **  PRAGMA [schema.]locking_mode\n  **  PRAGMA [schema.]locking_mode = (normal|exclusive)\n  */\n  case PragTyp_LOCKING_MODE: {\n    const char *zRet = \"normal\";\n    int eMode = getLockingMode(zRight);\n\n    if( pId2->n==0 && eMode==PAGER_LOCKINGMODE_QUERY ){\n      /* Simple \"PRAGMA locking_mode;\" statement. This is a query for\n      ** the current default locking mode (which may be different to\n      ** the locking-mode of the main database).\n      */\n      eMode = db->dfltLockMode;\n    }else{\n      Pager *pPager;\n      if( pId2->n==0 ){\n        /* This indicates that no database name was specified as part\n        ** of the PRAGMA command. In this case the locking-mode must be\n        ** set on all attached databases, as well as the main db file.\n        **\n        ** Also, the sqlite3.dfltLockMode variable is set so that\n        ** any subsequently attached databases also use the specified\n        ** locking mode.\n        */\n        int ii;\n        assert(pDb==&db->aDb[0]);\n        for(ii=2; ii<db->nDb; ii++){\n          pPager = sqlite3BtreePager(db->aDb[ii].pBt);\n          sqlite3PagerLockingMode(pPager, eMode);\n        }\n        db->dfltLockMode = (u8)eMode;\n      }\n      pPager = sqlite3BtreePager(pDb->pBt);\n      eMode = sqlite3PagerLockingMode(pPager, eMode);\n    }\n\n    assert( eMode==PAGER_LOCKINGMODE_NORMAL\n            || eMode==PAGER_LOCKINGMODE_EXCLUSIVE );\n    if( eMode==PAGER_LOCKINGMODE_EXCLUSIVE ){\n      zRet = \"exclusive\";\n    }\n    returnSingleText(v, zRet);\n    break;\n  }\n\n  /*\n  **  PRAGMA [schema.]journal_mode\n  **  PRAGMA [schema.]journal_mode =\n  **                      (delete|persist|off|truncate|memory|wal|off)\n  */\n  case PragTyp_JOURNAL_MODE: {\n    int eMode;        /* One of the PAGER_JOURNALMODE_XXX symbols */\n    int ii;           /* Loop counter */\n\n    if( zRight==0 ){\n      /* If there is no \"=MODE\" part of the pragma, do a query for the\n      ** current mode */\n      eMode = PAGER_JOURNALMODE_QUERY;\n    }else{\n      const char *zMode;\n      int n = sqlite3Strlen30(zRight);\n      for(eMode=0; (zMode = sqlite3JournalModename(eMode))!=0; eMode++){\n        if( sqlite3StrNICmp(zRight, zMode, n)==0 ) break;\n      }\n      if( !zMode ){\n        /* If the \"=MODE\" part does not match any known journal mode,\n        ** then do a query */\n        eMode = PAGER_JOURNALMODE_QUERY;\n      }\n    }\n    if( eMode==PAGER_JOURNALMODE_QUERY && pId2->n==0 ){\n      /* Convert \"PRAGMA journal_mode\" into \"PRAGMA main.journal_mode\" */\n      iDb = 0;\n      pId2->n = 1;\n    }\n    for(ii=db->nDb-1; ii>=0; ii--){\n      if( db->aDb[ii].pBt && (ii==iDb || pId2->n==0) ){\n        sqlite3VdbeUsesBtree(v, ii);\n        sqlite3VdbeAddOp3(v, OP_JournalMode, ii, 1, eMode);\n      }\n    }\n    sqlite3VdbeAddOp2(v, OP_ResultRow, 1, 1);\n    break;\n  }\n\n  /*\n  **  PRAGMA [schema.]journal_size_limit\n  **  PRAGMA [schema.]journal_size_limit=N\n  **\n  ** Get or set the size limit on rollback journal files.\n  */\n  case PragTyp_JOURNAL_SIZE_LIMIT: {\n    Pager *pPager = sqlite3BtreePager(pDb->pBt);\n    i64 iLimit = -2;\n    if( zRight ){\n      sqlite3DecOrHexToI64(zRight, &iLimit);\n      if( iLimit<-1 ) iLimit = -1;\n    }\n    iLimit = sqlite3PagerJournalSizeLimit(pPager, iLimit);\n    returnSingleInt(v, iLimit);\n    break;\n  }\n\n#endif /* SQLITE_OMIT_PAGER_PRAGMAS */\n\n  /*\n  **  PRAGMA [schema.]auto_vacuum\n  **  PRAGMA [schema.]auto_vacuum=N\n  **\n  ** Get or set the value of the database 'auto-vacuum' parameter.\n  ** The value is one of:  0 NONE 1 FULL 2 INCREMENTAL\n  */\n#ifndef SQLITE_OMIT_AUTOVACUUM\n  case PragTyp_AUTO_VACUUM: {\n    Btree *pBt = pDb->pBt;\n    assert( pBt!=0 );\n    if( !zRight ){\n      returnSingleInt(v, sqlite3BtreeGetAutoVacuum(pBt));\n    }else{\n      int eAuto = getAutoVacuum(zRight);\n      assert( eAuto>=0 && eAuto<=2 );\n      db->nextAutovac = (u8)eAuto;\n      /* Call SetAutoVacuum() to set initialize the internal auto and\n      ** incr-vacuum flags. This is required in case this connection\n      ** creates the database file. It is important that it is created\n      ** as an auto-vacuum capable db.\n      */\n      rc = sqlite3BtreeSetAutoVacuum(pBt, eAuto);\n      if( rc==SQLITE_OK && (eAuto==1 || eAuto==2) ){\n        /* When setting the auto_vacuum mode to either \"full\" or \n        ** \"incremental\", write the value of meta[6] in the database\n        ** file. Before writing to meta[6], check that meta[3] indicates\n        ** that this really is an auto-vacuum capable database.\n        */\n        static const int iLn = VDBE_OFFSET_LINENO(2);\n        static const VdbeOpList setMeta6[] = {\n          { OP_Transaction,    0,         1,                 0},    /* 0 */\n          { OP_ReadCookie,     0,         1,         BTREE_LARGEST_ROOT_PAGE},\n          { OP_If,             1,         0,                 0},    /* 2 */\n          { OP_Halt,           SQLITE_OK, OE_Abort,          0},    /* 3 */\n          { OP_SetCookie,      0,         BTREE_INCR_VACUUM, 0},    /* 4 */\n        };\n        VdbeOp *aOp;\n        int iAddr = sqlite3VdbeCurrentAddr(v);\n        sqlite3VdbeVerifyNoMallocRequired(v, ArraySize(setMeta6));\n        aOp = sqlite3VdbeAddOpList(v, ArraySize(setMeta6), setMeta6, iLn);\n        if( ONLY_IF_REALLOC_STRESS(aOp==0) ) break;\n        aOp[0].p1 = iDb;\n        aOp[1].p1 = iDb;\n        aOp[2].p2 = iAddr+4;\n        aOp[4].p1 = iDb;\n        aOp[4].p3 = eAuto - 1;\n        sqlite3VdbeUsesBtree(v, iDb);\n      }\n    }\n    break;\n  }\n#endif\n\n  /*\n  **  PRAGMA [schema.]incremental_vacuum(N)\n  **\n  ** Do N steps of incremental vacuuming on a database.\n  */\n#ifndef SQLITE_OMIT_AUTOVACUUM\n  case PragTyp_INCREMENTAL_VACUUM: {\n    int iLimit, addr;\n    if( zRight==0 || !sqlite3GetInt32(zRight, &iLimit) || iLimit<=0 ){\n      iLimit = 0x7fffffff;\n    }\n    sqlite3BeginWriteOperation(pParse, 0, iDb);\n    sqlite3VdbeAddOp2(v, OP_Integer, iLimit, 1);\n    addr = sqlite3VdbeAddOp1(v, OP_IncrVacuum, iDb); VdbeCoverage(v);\n    sqlite3VdbeAddOp1(v, OP_ResultRow, 1);\n    sqlite3VdbeAddOp2(v, OP_AddImm, 1, -1);\n    sqlite3VdbeAddOp2(v, OP_IfPos, 1, addr); VdbeCoverage(v);\n    sqlite3VdbeJumpHere(v, addr);\n    break;\n  }\n#endif\n\n#ifndef SQLITE_OMIT_PAGER_PRAGMAS\n  /*\n  **  PRAGMA [schema.]cache_size\n  **  PRAGMA [schema.]cache_size=N\n  **\n  ** The first form reports the current local setting for the\n  ** page cache size. The second form sets the local\n  ** page cache size value.  If N is positive then that is the\n  ** number of pages in the cache.  If N is negative, then the\n  ** number of pages is adjusted so that the cache uses -N kibibytes\n  ** of memory.\n  */\n  case PragTyp_CACHE_SIZE: {\n    assert( sqlite3SchemaMutexHeld(db, iDb, 0) );\n    if( !zRight ){\n      returnSingleInt(v, pDb->pSchema->cache_size);\n    }else{\n      int size = sqlite3Atoi(zRight);\n      pDb->pSchema->cache_size = size;\n      sqlite3BtreeSetCacheSize(pDb->pBt, pDb->pSchema->cache_size);\n    }\n    break;\n  }\n\n  /*\n  **  PRAGMA [schema.]cache_spill\n  **  PRAGMA cache_spill=BOOLEAN\n  **  PRAGMA [schema.]cache_spill=N\n  **\n  ** The first form reports the current local setting for the\n  ** page cache spill size. The second form turns cache spill on\n  ** or off.  When turnning cache spill on, the size is set to the\n  ** current cache_size.  The third form sets a spill size that\n  ** may be different form the cache size.\n  ** If N is positive then that is the\n  ** number of pages in the cache.  If N is negative, then the\n  ** number of pages is adjusted so that the cache uses -N kibibytes\n  ** of memory.\n  **\n  ** If the number of cache_spill pages is less then the number of\n  ** cache_size pages, no spilling occurs until the page count exceeds\n  ** the number of cache_size pages.\n  **\n  ** The cache_spill=BOOLEAN setting applies to all attached schemas,\n  ** not just the schema specified.\n  */\n  case PragTyp_CACHE_SPILL: {\n    assert( sqlite3SchemaMutexHeld(db, iDb, 0) );\n    if( !zRight ){\n      returnSingleInt(v,\n         (db->flags & SQLITE_CacheSpill)==0 ? 0 : \n            sqlite3BtreeSetSpillSize(pDb->pBt,0));\n    }else{\n      int size = 1;\n      if( sqlite3GetInt32(zRight, &size) ){\n        sqlite3BtreeSetSpillSize(pDb->pBt, size);\n      }\n      if( sqlite3GetBoolean(zRight, size!=0) ){\n        db->flags |= SQLITE_CacheSpill;\n      }else{\n        db->flags &= ~SQLITE_CacheSpill;\n      }\n      setAllPagerFlags(db);\n    }\n    break;\n  }\n\n  /*\n  **  PRAGMA [schema.]mmap_size(N)\n  **\n  ** Used to set mapping size limit. The mapping size limit is\n  ** used to limit the aggregate size of all memory mapped regions of the\n  ** database file. If this parameter is set to zero, then memory mapping\n  ** is not used at all.  If N is negative, then the default memory map\n  ** limit determined by sqlite3_config(SQLITE_CONFIG_MMAP_SIZE) is set.\n  ** The parameter N is measured in bytes.\n  **\n  ** This value is advisory.  The underlying VFS is free to memory map\n  ** as little or as much as it wants.  Except, if N is set to 0 then the\n  ** upper layers will never invoke the xFetch interfaces to the VFS.\n  */\n  case PragTyp_MMAP_SIZE: {\n    sqlite3_int64 sz;\n#if SQLITE_MAX_MMAP_SIZE>0\n    assert( sqlite3SchemaMutexHeld(db, iDb, 0) );\n    if( zRight ){\n      int ii;\n      sqlite3DecOrHexToI64(zRight, &sz);\n      if( sz<0 ) sz = sqlite3GlobalConfig.szMmap;\n      if( pId2->n==0 ) db->szMmap = sz;\n      for(ii=db->nDb-1; ii>=0; ii--){\n        if( db->aDb[ii].pBt && (ii==iDb || pId2->n==0) ){\n          sqlite3BtreeSetMmapLimit(db->aDb[ii].pBt, sz);\n        }\n      }\n    }\n    sz = -1;\n    rc = sqlite3_file_control(db, zDb, SQLITE_FCNTL_MMAP_SIZE, &sz);\n#else\n    sz = 0;\n    rc = SQLITE_OK;\n#endif\n    if( rc==SQLITE_OK ){\n      returnSingleInt(v, sz);\n    }else if( rc!=SQLITE_NOTFOUND ){\n      pParse->nErr++;\n      pParse->rc = rc;\n    }\n    break;\n  }\n\n  /*\n  **   PRAGMA temp_store\n  **   PRAGMA temp_store = \"default\"|\"memory\"|\"file\"\n  **\n  ** Return or set the local value of the temp_store flag.  Changing\n  ** the local value does not make changes to the disk file and the default\n  ** value will be restored the next time the database is opened.\n  **\n  ** Note that it is possible for the library compile-time options to\n  ** override this setting\n  */\n  case PragTyp_TEMP_STORE: {\n    if( !zRight ){\n      returnSingleInt(v, db->temp_store);\n    }else{\n      changeTempStorage(pParse, zRight);\n    }\n    break;\n  }\n\n  /*\n  **   PRAGMA temp_store_directory\n  **   PRAGMA temp_store_directory = \"\"|\"directory_name\"\n  **\n  ** Return or set the local value of the temp_store_directory flag.  Changing\n  ** the value sets a specific directory to be used for temporary files.\n  ** Setting to a null string reverts to the default temporary directory search.\n  ** If temporary directory is changed, then invalidateTempStorage.\n  **\n  */\n  case PragTyp_TEMP_STORE_DIRECTORY: {\n    if( !zRight ){\n      returnSingleText(v, sqlite3_temp_directory);\n    }else{\n#ifndef SQLITE_OMIT_WSD\n      if( zRight[0] ){\n        int res;\n        rc = sqlite3OsAccess(db->pVfs, zRight, SQLITE_ACCESS_READWRITE, &res);\n        if( rc!=SQLITE_OK || res==0 ){\n          sqlite3ErrorMsg(pParse, \"not a writable directory\");\n          goto pragma_out;\n        }\n      }\n      if( SQLITE_TEMP_STORE==0\n       || (SQLITE_TEMP_STORE==1 && db->temp_store<=1)\n       || (SQLITE_TEMP_STORE==2 && db->temp_store==1)\n      ){\n        invalidateTempStorage(pParse);\n      }\n      sqlite3_free(sqlite3_temp_directory);\n      if( zRight[0] ){\n        sqlite3_temp_directory = sqlite3_mprintf(\"%s\", zRight);\n      }else{\n        sqlite3_temp_directory = 0;\n      }\n#endif /* SQLITE_OMIT_WSD */\n    }\n    break;\n  }\n\n#if SQLITE_OS_WIN\n  /*\n  **   PRAGMA data_store_directory\n  **   PRAGMA data_store_directory = \"\"|\"directory_name\"\n  **\n  ** Return or set the local value of the data_store_directory flag.  Changing\n  ** the value sets a specific directory to be used for database files that\n  ** were specified with a relative pathname.  Setting to a null string reverts\n  ** to the default database directory, which for database files specified with\n  ** a relative path will probably be based on the current directory for the\n  ** process.  Database file specified with an absolute path are not impacted\n  ** by this setting, regardless of its value.\n  **\n  */\n  case PragTyp_DATA_STORE_DIRECTORY: {\n    if( !zRight ){\n      returnSingleText(v, sqlite3_data_directory);\n    }else{\n#ifndef SQLITE_OMIT_WSD\n      if( zRight[0] ){\n        int res;\n        rc = sqlite3OsAccess(db->pVfs, zRight, SQLITE_ACCESS_READWRITE, &res);\n        if( rc!=SQLITE_OK || res==0 ){\n          sqlite3ErrorMsg(pParse, \"not a writable directory\");\n          goto pragma_out;\n        }\n      }\n      sqlite3_free(sqlite3_data_directory);\n      if( zRight[0] ){\n        sqlite3_data_directory = sqlite3_mprintf(\"%s\", zRight);\n      }else{\n        sqlite3_data_directory = 0;\n      }\n#endif /* SQLITE_OMIT_WSD */\n    }\n    break;\n  }\n#endif\n\n#if SQLITE_ENABLE_LOCKING_STYLE\n  /*\n  **   PRAGMA [schema.]lock_proxy_file\n  **   PRAGMA [schema.]lock_proxy_file = \":auto:\"|\"lock_file_path\"\n  **\n  ** Return or set the value of the lock_proxy_file flag.  Changing\n  ** the value sets a specific file to be used for database access locks.\n  **\n  */\n  case PragTyp_LOCK_PROXY_FILE: {\n    if( !zRight ){\n      Pager *pPager = sqlite3BtreePager(pDb->pBt);\n      char *proxy_file_path = NULL;\n      sqlite3_file *pFile = sqlite3PagerFile(pPager);\n      sqlite3OsFileControlHint(pFile, SQLITE_GET_LOCKPROXYFILE, \n                           &proxy_file_path);\n      returnSingleText(v, proxy_file_path);\n    }else{\n      Pager *pPager = sqlite3BtreePager(pDb->pBt);\n      sqlite3_file *pFile = sqlite3PagerFile(pPager);\n      int res;\n      if( zRight[0] ){\n        res=sqlite3OsFileControl(pFile, SQLITE_SET_LOCKPROXYFILE, \n                                     zRight);\n      } else {\n        res=sqlite3OsFileControl(pFile, SQLITE_SET_LOCKPROXYFILE, \n                                     NULL);\n      }\n      if( res!=SQLITE_OK ){\n        sqlite3ErrorMsg(pParse, \"failed to set lock proxy file\");\n        goto pragma_out;\n      }\n    }\n    break;\n  }\n#endif /* SQLITE_ENABLE_LOCKING_STYLE */      \n    \n  /*\n  **   PRAGMA [schema.]synchronous\n  **   PRAGMA [schema.]synchronous=OFF|ON|NORMAL|FULL|EXTRA\n  **\n  ** Return or set the local value of the synchronous flag.  Changing\n  ** the local value does not make changes to the disk file and the\n  ** default value will be restored the next time the database is\n  ** opened.\n  */\n  case PragTyp_SYNCHRONOUS: {\n    if( !zRight ){\n      returnSingleInt(v, pDb->safety_level-1);\n    }else{\n      if( !db->autoCommit ){\n        sqlite3ErrorMsg(pParse, \n            \"Safety level may not be changed inside a transaction\");\n      }else if( iDb!=1 ){\n        int iLevel = (getSafetyLevel(zRight,0,1)+1) & PAGER_SYNCHRONOUS_MASK;\n        if( iLevel==0 ) iLevel = 1;\n        pDb->safety_level = iLevel;\n        pDb->bSyncSet = 1;\n        setAllPagerFlags(db);\n      }\n    }\n    break;\n  }\n#endif /* SQLITE_OMIT_PAGER_PRAGMAS */\n\n#ifndef SQLITE_OMIT_FLAG_PRAGMAS\n  case PragTyp_FLAG: {\n    if( zRight==0 ){\n      setPragmaResultColumnNames(v, pPragma);\n      returnSingleInt(v, (db->flags & pPragma->iArg)!=0 );\n    }else{\n      int mask = pPragma->iArg;    /* Mask of bits to set or clear. */\n      if( db->autoCommit==0 ){\n        /* Foreign key support may not be enabled or disabled while not\n        ** in auto-commit mode.  */\n        mask &= ~(SQLITE_ForeignKeys);\n      }\n#if SQLITE_USER_AUTHENTICATION\n      if( db->auth.authLevel==UAUTH_User ){\n        /* Do not allow non-admin users to modify the schema arbitrarily */\n        mask &= ~(SQLITE_WriteSchema);\n      }\n#endif\n\n      if( sqlite3GetBoolean(zRight, 0) ){\n        db->flags |= mask;\n      }else{\n        db->flags &= ~mask;\n        if( mask==SQLITE_DeferFKs ) db->nDeferredImmCons = 0;\n      }\n\n      /* Many of the flag-pragmas modify the code generated by the SQL \n      ** compiler (eg. count_changes). So add an opcode to expire all\n      ** compiled SQL statements after modifying a pragma value.\n      */\n      sqlite3VdbeAddOp0(v, OP_Expire);\n      setAllPagerFlags(db);\n    }\n    break;\n  }\n#endif /* SQLITE_OMIT_FLAG_PRAGMAS */\n\n#ifndef SQLITE_OMIT_SCHEMA_PRAGMAS\n  /*\n  **   PRAGMA table_info(<table>)\n  **\n  ** Return a single row for each column of the named table. The columns of\n  ** the returned data set are:\n  **\n  ** cid:        Column id (numbered from left to right, starting at 0)\n  ** name:       Column name\n  ** type:       Column declaration type.\n  ** notnull:    True if 'NOT NULL' is part of column declaration\n  ** dflt_value: The default value for the column, if any.\n  ** pk:         Non-zero for PK fields.\n  */\n  case PragTyp_TABLE_INFO: if( zRight ){\n    Table *pTab;\n    pTab = sqlite3LocateTable(pParse, LOCATE_NOERR, zRight, zDb);\n    if( pTab ){\n      int i, k;\n      int nHidden = 0;\n      Column *pCol;\n      Index *pPk = sqlite3PrimaryKeyIndex(pTab);\n      pParse->nMem = 6;\n      sqlite3CodeVerifySchema(pParse, iDb);\n      sqlite3ViewGetColumnNames(pParse, pTab);\n      for(i=0, pCol=pTab->aCol; i<pTab->nCol; i++, pCol++){\n        if( IsHiddenColumn(pCol) ){\n          nHidden++;\n          continue;\n        }\n        if( (pCol->colFlags & COLFLAG_PRIMKEY)==0 ){\n          k = 0;\n        }else if( pPk==0 ){\n          k = 1;\n        }else{\n          for(k=1; k<=pTab->nCol && pPk->aiColumn[k-1]!=i; k++){}\n        }\n        assert( pCol->pDflt==0 || pCol->pDflt->op==TK_SPAN );\n        sqlite3VdbeMultiLoad(v, 1, \"issisi\",\n               i-nHidden,\n               pCol->zName,\n               sqlite3ColumnType(pCol,\"\"),\n               pCol->notNull ? 1 : 0,\n               pCol->pDflt ? pCol->pDflt->u.zToken : 0,\n               k);\n      }\n    }\n  }\n  break;\n\n#ifdef SQLITE_DEBUG\n  case PragTyp_STATS: {\n    Index *pIdx;\n    HashElem *i;\n    pParse->nMem = 5;\n    sqlite3CodeVerifySchema(pParse, iDb);\n    for(i=sqliteHashFirst(&pDb->pSchema->tblHash); i; i=sqliteHashNext(i)){\n      Table *pTab = sqliteHashData(i);\n      sqlite3VdbeMultiLoad(v, 1, \"ssiii\",\n           pTab->zName,\n           0,\n           pTab->szTabRow,\n           pTab->nRowLogEst,\n           pTab->tabFlags);\n      for(pIdx=pTab->pIndex; pIdx; pIdx=pIdx->pNext){\n        sqlite3VdbeMultiLoad(v, 2, \"siiiX\",\n           pIdx->zName,\n           pIdx->szIdxRow,\n           pIdx->aiRowLogEst[0],\n           pIdx->hasStat1);\n        sqlite3VdbeAddOp2(v, OP_ResultRow, 1, 5);\n      }\n    }\n  }\n  break;\n#endif\n\n  case PragTyp_INDEX_INFO: if( zRight ){\n    Index *pIdx;\n    Table *pTab;\n    pIdx = sqlite3FindIndex(db, zRight, zDb);\n    if( pIdx ){\n      int i;\n      int mx;\n      if( pPragma->iArg ){\n        /* PRAGMA index_xinfo (newer version with more rows and columns) */\n        mx = pIdx->nColumn;\n        pParse->nMem = 6;\n      }else{\n        /* PRAGMA index_info (legacy version) */\n        mx = pIdx->nKeyCol;\n        pParse->nMem = 3;\n      }\n      pTab = pIdx->pTable;\n      sqlite3CodeVerifySchema(pParse, iDb);\n      assert( pParse->nMem<=pPragma->nPragCName );\n      for(i=0; i<mx; i++){\n        i16 cnum = pIdx->aiColumn[i];\n        sqlite3VdbeMultiLoad(v, 1, \"iisX\", i, cnum,\n                             cnum<0 ? 0 : pTab->aCol[cnum].zName);\n        if( pPragma->iArg ){\n          sqlite3VdbeMultiLoad(v, 4, \"isiX\",\n            pIdx->aSortOrder[i],\n            pIdx->azColl[i],\n            i<pIdx->nKeyCol);\n        }\n        sqlite3VdbeAddOp2(v, OP_ResultRow, 1, pParse->nMem);\n      }\n    }\n  }\n  break;\n\n  case PragTyp_INDEX_LIST: if( zRight ){\n    Index *pIdx;\n    Table *pTab;\n    int i;\n    pTab = sqlite3FindTable(db, zRight, zDb);\n    if( pTab ){\n      pParse->nMem = 5;\n      sqlite3CodeVerifySchema(pParse, iDb);\n      for(pIdx=pTab->pIndex, i=0; pIdx; pIdx=pIdx->pNext, i++){\n        const char *azOrigin[] = { \"c\", \"u\", \"pk\" };\n        sqlite3VdbeMultiLoad(v, 1, \"isisi\",\n           i,\n           pIdx->zName,\n           IsUniqueIndex(pIdx),\n           azOrigin[pIdx->idxType],\n           pIdx->pPartIdxWhere!=0);\n      }\n    }\n  }\n  break;\n\n  case PragTyp_DATABASE_LIST: {\n    int i;\n    pParse->nMem = 3;\n    for(i=0; i<db->nDb; i++){\n      if( db->aDb[i].pBt==0 ) continue;\n      assert( db->aDb[i].zDbSName!=0 );\n      sqlite3VdbeMultiLoad(v, 1, \"iss\",\n         i,\n         db->aDb[i].zDbSName,\n         sqlite3BtreeGetFilename(db->aDb[i].pBt));\n    }\n  }\n  break;\n\n  case PragTyp_COLLATION_LIST: {\n    int i = 0;\n    HashElem *p;\n    pParse->nMem = 2;\n    for(p=sqliteHashFirst(&db->aCollSeq); p; p=sqliteHashNext(p)){\n      CollSeq *pColl = (CollSeq *)sqliteHashData(p);\n      sqlite3VdbeMultiLoad(v, 1, \"is\", i++, pColl->zName);\n    }\n  }\n  break;\n\n#ifdef SQLITE_INTROSPECTION_PRAGMAS\n  case PragTyp_FUNCTION_LIST: {\n    int i;\n    HashElem *j;\n    FuncDef *p;\n    pParse->nMem = 2;\n    for(i=0; i<SQLITE_FUNC_HASH_SZ; i++){\n      for(p=sqlite3BuiltinFunctions.a[i]; p; p=p->u.pHash ){\n        sqlite3VdbeMultiLoad(v, 1, \"si\", p->zName, 1);\n      }\n    }\n    for(j=sqliteHashFirst(&db->aFunc); j; j=sqliteHashNext(j)){\n      p = (FuncDef*)sqliteHashData(j);\n      sqlite3VdbeMultiLoad(v, 1, \"si\", p->zName, 0);\n    }\n  }\n  break;\n\n#ifndef SQLITE_OMIT_VIRTUALTABLE\n  case PragTyp_MODULE_LIST: {\n    HashElem *j;\n    pParse->nMem = 1;\n    for(j=sqliteHashFirst(&db->aModule); j; j=sqliteHashNext(j)){\n      Module *pMod = (Module*)sqliteHashData(j);\n      sqlite3VdbeMultiLoad(v, 1, \"s\", pMod->zName);\n    }\n  }\n  break;\n#endif /* SQLITE_OMIT_VIRTUALTABLE */\n\n  case PragTyp_PRAGMA_LIST: {\n    int i;\n    for(i=0; i<ArraySize(aPragmaName); i++){\n      sqlite3VdbeMultiLoad(v, 1, \"s\", aPragmaName[i].zName);\n    }\n  }\n  break;\n#endif /* SQLITE_INTROSPECTION_PRAGMAS */\n\n#endif /* SQLITE_OMIT_SCHEMA_PRAGMAS */\n\n#ifndef SQLITE_OMIT_FOREIGN_KEY\n  case PragTyp_FOREIGN_KEY_LIST: if( zRight ){\n    FKey *pFK;\n    Table *pTab;\n    pTab = sqlite3FindTable(db, zRight, zDb);\n    if( pTab ){\n      pFK = pTab->pFKey;\n      if( pFK ){\n        int i = 0; \n        pParse->nMem = 8;\n        sqlite3CodeVerifySchema(pParse, iDb);\n        while(pFK){\n          int j;\n          for(j=0; j<pFK->nCol; j++){\n            sqlite3VdbeMultiLoad(v, 1, \"iissssss\",\n                   i,\n                   j,\n                   pFK->zTo,\n                   pTab->aCol[pFK->aCol[j].iFrom].zName,\n                   pFK->aCol[j].zCol,\n                   actionName(pFK->aAction[1]),  /* ON UPDATE */\n                   actionName(pFK->aAction[0]),  /* ON DELETE */\n                   \"NONE\");\n          }\n          ++i;\n          pFK = pFK->pNextFrom;\n        }\n      }\n    }\n  }\n  break;\n#endif /* !defined(SQLITE_OMIT_FOREIGN_KEY) */\n\n#ifndef SQLITE_OMIT_FOREIGN_KEY\n#ifndef SQLITE_OMIT_TRIGGER\n  case PragTyp_FOREIGN_KEY_CHECK: {\n    FKey *pFK;             /* A foreign key constraint */\n    Table *pTab;           /* Child table contain \"REFERENCES\" keyword */\n    Table *pParent;        /* Parent table that child points to */\n    Index *pIdx;           /* Index in the parent table */\n    int i;                 /* Loop counter:  Foreign key number for pTab */\n    int j;                 /* Loop counter:  Field of the foreign key */\n    HashElem *k;           /* Loop counter:  Next table in schema */\n    int x;                 /* result variable */\n    int regResult;         /* 3 registers to hold a result row */\n    int regKey;            /* Register to hold key for checking the FK */\n    int regRow;            /* Registers to hold a row from pTab */\n    int addrTop;           /* Top of a loop checking foreign keys */\n    int addrOk;            /* Jump here if the key is OK */\n    int *aiCols;           /* child to parent column mapping */\n\n    regResult = pParse->nMem+1;\n    pParse->nMem += 4;\n    regKey = ++pParse->nMem;\n    regRow = ++pParse->nMem;\n    sqlite3CodeVerifySchema(pParse, iDb);\n    k = sqliteHashFirst(&db->aDb[iDb].pSchema->tblHash);\n    while( k ){\n      if( zRight ){\n        pTab = sqlite3LocateTable(pParse, 0, zRight, zDb);\n        k = 0;\n      }else{\n        pTab = (Table*)sqliteHashData(k);\n        k = sqliteHashNext(k);\n      }\n      if( pTab==0 || pTab->pFKey==0 ) continue;\n      sqlite3TableLock(pParse, iDb, pTab->tnum, 0, pTab->zName);\n      if( pTab->nCol+regRow>pParse->nMem ) pParse->nMem = pTab->nCol + regRow;\n      sqlite3OpenTable(pParse, 0, iDb, pTab, OP_OpenRead);\n      sqlite3VdbeLoadString(v, regResult, pTab->zName);\n      for(i=1, pFK=pTab->pFKey; pFK; i++, pFK=pFK->pNextFrom){\n        pParent = sqlite3FindTable(db, pFK->zTo, zDb);\n        if( pParent==0 ) continue;\n        pIdx = 0;\n        sqlite3TableLock(pParse, iDb, pParent->tnum, 0, pParent->zName);\n        x = sqlite3FkLocateIndex(pParse, pParent, pFK, &pIdx, 0);\n        if( x==0 ){\n          if( pIdx==0 ){\n            sqlite3OpenTable(pParse, i, iDb, pParent, OP_OpenRead);\n          }else{\n            sqlite3VdbeAddOp3(v, OP_OpenRead, i, pIdx->tnum, iDb);\n            sqlite3VdbeSetP4KeyInfo(pParse, pIdx);\n          }\n        }else{\n          k = 0;\n          break;\n        }\n      }\n      assert( pParse->nErr>0 || pFK==0 );\n      if( pFK ) break;\n      if( pParse->nTab<i ) pParse->nTab = i;\n      addrTop = sqlite3VdbeAddOp1(v, OP_Rewind, 0); VdbeCoverage(v);\n      for(i=1, pFK=pTab->pFKey; pFK; i++, pFK=pFK->pNextFrom){\n        pParent = sqlite3FindTable(db, pFK->zTo, zDb);\n        pIdx = 0;\n        aiCols = 0;\n        if( pParent ){\n          x = sqlite3FkLocateIndex(pParse, pParent, pFK, &pIdx, &aiCols);\n          assert( x==0 );\n        }\n        addrOk = sqlite3VdbeMakeLabel(v);\n\n        /* Generate code to read the child key values into registers\n        ** regRow..regRow+n. If any of the child key values are NULL, this \n        ** row cannot cause an FK violation. Jump directly to addrOk in \n        ** this case. */\n        for(j=0; j<pFK->nCol; j++){\n          int iCol = aiCols ? aiCols[j] : pFK->aCol[j].iFrom;\n          sqlite3ExprCodeGetColumnOfTable(v, pTab, 0, iCol, regRow+j);\n          sqlite3VdbeAddOp2(v, OP_IsNull, regRow+j, addrOk); VdbeCoverage(v);\n        }\n\n        /* Generate code to query the parent index for a matching parent\n        ** key. If a match is found, jump to addrOk. */\n        if( pIdx ){\n          sqlite3VdbeAddOp4(v, OP_MakeRecord, regRow, pFK->nCol, regKey,\n              sqlite3IndexAffinityStr(db,pIdx), pFK->nCol);\n          sqlite3VdbeAddOp4Int(v, OP_Found, i, addrOk, regKey, 0);\n          VdbeCoverage(v);\n        }else if( pParent ){\n          int jmp = sqlite3VdbeCurrentAddr(v)+2;\n          sqlite3VdbeAddOp3(v, OP_SeekRowid, i, jmp, regRow); VdbeCoverage(v);\n          sqlite3VdbeGoto(v, addrOk);\n          assert( pFK->nCol==1 );\n        }\n\n        /* Generate code to report an FK violation to the caller. */\n        if( HasRowid(pTab) ){\n          sqlite3VdbeAddOp2(v, OP_Rowid, 0, regResult+1);\n        }else{\n          sqlite3VdbeAddOp2(v, OP_Null, 0, regResult+1);\n        }\n        sqlite3VdbeMultiLoad(v, regResult+2, \"siX\", pFK->zTo, i-1);\n        sqlite3VdbeAddOp2(v, OP_ResultRow, regResult, 4);\n        sqlite3VdbeResolveLabel(v, addrOk);\n        sqlite3DbFree(db, aiCols);\n      }\n      sqlite3VdbeAddOp2(v, OP_Next, 0, addrTop+1); VdbeCoverage(v);\n      sqlite3VdbeJumpHere(v, addrTop);\n    }\n  }\n  break;\n#endif /* !defined(SQLITE_OMIT_TRIGGER) */\n#endif /* !defined(SQLITE_OMIT_FOREIGN_KEY) */\n\n#ifndef NDEBUG\n  case PragTyp_PARSER_TRACE: {\n    if( zRight ){\n      if( sqlite3GetBoolean(zRight, 0) ){\n        sqlite3ParserTrace(stdout, \"parser: \");\n      }else{\n        sqlite3ParserTrace(0, 0);\n      }\n    }\n  }\n  break;\n#endif\n\n  /* Reinstall the LIKE and GLOB functions.  The variant of LIKE\n  ** used will be case sensitive or not depending on the RHS.\n  */\n  case PragTyp_CASE_SENSITIVE_LIKE: {\n    if( zRight ){\n      sqlite3RegisterLikeFunctions(db, sqlite3GetBoolean(zRight, 0));\n    }\n  }\n  break;\n\n#ifndef SQLITE_INTEGRITY_CHECK_ERROR_MAX\n# define SQLITE_INTEGRITY_CHECK_ERROR_MAX 100\n#endif\n\n#ifndef SQLITE_OMIT_INTEGRITY_CHECK\n  /*    PRAGMA integrity_check\n  **    PRAGMA integrity_check(N)\n  **    PRAGMA quick_check\n  **    PRAGMA quick_check(N)\n  **\n  ** Verify the integrity of the database.\n  **\n  ** The \"quick_check\" is reduced version of \n  ** integrity_check designed to detect most database corruption\n  ** without the overhead of cross-checking indexes.  Quick_check\n  ** is linear time wherease integrity_check is O(NlogN).\n  */\n  case PragTyp_INTEGRITY_CHECK: {\n    int i, j, addr, mxErr;\n\n    int isQuick = (sqlite3Tolower(zLeft[0])=='q');\n\n    /* If the PRAGMA command was of the form \"PRAGMA <db>.integrity_check\",\n    ** then iDb is set to the index of the database identified by <db>.\n    ** In this case, the integrity of database iDb only is verified by\n    ** the VDBE created below.\n    **\n    ** Otherwise, if the command was simply \"PRAGMA integrity_check\" (or\n    ** \"PRAGMA quick_check\"), then iDb is set to 0. In this case, set iDb\n    ** to -1 here, to indicate that the VDBE should verify the integrity\n    ** of all attached databases.  */\n    assert( iDb>=0 );\n    assert( iDb==0 || pId2->z );\n    if( pId2->z==0 ) iDb = -1;\n\n    /* Initialize the VDBE program */\n    pParse->nMem = 6;\n\n    /* Set the maximum error count */\n    mxErr = SQLITE_INTEGRITY_CHECK_ERROR_MAX;\n    if( zRight ){\n      sqlite3GetInt32(zRight, &mxErr);\n      if( mxErr<=0 ){\n        mxErr = SQLITE_INTEGRITY_CHECK_ERROR_MAX;\n      }\n    }\n    sqlite3VdbeAddOp2(v, OP_Integer, mxErr-1, 1); /* reg[1] holds errors left */\n\n    /* Do an integrity check on each database file */\n    for(i=0; i<db->nDb; i++){\n      HashElem *x;     /* For looping over tables in the schema */\n      Hash *pTbls;     /* Set of all tables in the schema */\n      int *aRoot;      /* Array of root page numbers of all btrees */\n      int cnt = 0;     /* Number of entries in aRoot[] */\n      int mxIdx = 0;   /* Maximum number of indexes for any table */\n\n      if( OMIT_TEMPDB && i==1 ) continue;\n      if( iDb>=0 && i!=iDb ) continue;\n\n      sqlite3CodeVerifySchema(pParse, i);\n\n      /* Do an integrity check of the B-Tree\n      **\n      ** Begin by finding the root pages numbers\n      ** for all tables and indices in the database.\n      */\n      assert( sqlite3SchemaMutexHeld(db, i, 0) );\n      pTbls = &db->aDb[i].pSchema->tblHash;\n      for(cnt=0, x=sqliteHashFirst(pTbls); x; x=sqliteHashNext(x)){\n        Table *pTab = sqliteHashData(x);  /* Current table */\n        Index *pIdx;                      /* An index on pTab */\n        int nIdx;                         /* Number of indexes on pTab */\n        if( HasRowid(pTab) ) cnt++;\n        for(nIdx=0, pIdx=pTab->pIndex; pIdx; pIdx=pIdx->pNext, nIdx++){ cnt++; }\n        if( nIdx>mxIdx ) mxIdx = nIdx;\n      }\n      aRoot = sqlite3DbMallocRawNN(db, sizeof(int)*(cnt+1));\n      if( aRoot==0 ) break;\n      for(cnt=0, x=sqliteHashFirst(pTbls); x; x=sqliteHashNext(x)){\n        Table *pTab = sqliteHashData(x);\n        Index *pIdx;\n        if( HasRowid(pTab) ) aRoot[++cnt] = pTab->tnum;\n        for(pIdx=pTab->pIndex; pIdx; pIdx=pIdx->pNext){\n          aRoot[++cnt] = pIdx->tnum;\n        }\n      }\n      aRoot[0] = cnt;\n\n      /* Make sure sufficient number of registers have been allocated */\n      pParse->nMem = MAX( pParse->nMem, 8+mxIdx );\n      sqlite3ClearTempRegCache(pParse);\n\n      /* Do the b-tree integrity checks */\n      sqlite3VdbeAddOp4(v, OP_IntegrityCk, 2, cnt, 1, (char*)aRoot,P4_INTARRAY);\n      sqlite3VdbeChangeP5(v, (u8)i);\n      addr = sqlite3VdbeAddOp1(v, OP_IsNull, 2); VdbeCoverage(v);\n      sqlite3VdbeAddOp4(v, OP_String8, 0, 3, 0,\n         sqlite3MPrintf(db, \"*** in database %s ***\\n\", db->aDb[i].zDbSName),\n         P4_DYNAMIC);\n      sqlite3VdbeAddOp3(v, OP_Concat, 2, 3, 3);\n      integrityCheckResultRow(v);\n      sqlite3VdbeJumpHere(v, addr);\n\n      /* Make sure all the indices are constructed correctly.\n      */\n      for(x=sqliteHashFirst(pTbls); x; x=sqliteHashNext(x)){\n        Table *pTab = sqliteHashData(x);\n        Index *pIdx, *pPk;\n        Index *pPrior = 0;\n        int loopTop;\n        int iDataCur, iIdxCur;\n        int r1 = -1;\n\n        if( pTab->tnum<1 ) continue;  /* Skip VIEWs or VIRTUAL TABLEs */\n        pPk = HasRowid(pTab) ? 0 : sqlite3PrimaryKeyIndex(pTab);\n        sqlite3ExprCacheClear(pParse);\n        sqlite3OpenTableAndIndices(pParse, pTab, OP_OpenRead, 0,\n                                   1, 0, &iDataCur, &iIdxCur);\n        /* reg[7] counts the number of entries in the table.\n        ** reg[8+i] counts the number of entries in the i-th index \n        */\n        sqlite3VdbeAddOp2(v, OP_Integer, 0, 7);\n        for(j=0, pIdx=pTab->pIndex; pIdx; pIdx=pIdx->pNext, j++){\n          sqlite3VdbeAddOp2(v, OP_Integer, 0, 8+j); /* index entries counter */\n        }\n        assert( pParse->nMem>=8+j );\n        assert( sqlite3NoTempsInRange(pParse,1,7+j) );\n        sqlite3VdbeAddOp2(v, OP_Rewind, iDataCur, 0); VdbeCoverage(v);\n        loopTop = sqlite3VdbeAddOp2(v, OP_AddImm, 7, 1);\n        /* Verify that all NOT NULL columns really are NOT NULL */\n        for(j=0; j<pTab->nCol; j++){\n          char *zErr;\n          int jmp2;\n          if( j==pTab->iPKey ) continue;\n          if( pTab->aCol[j].notNull==0 ) continue;\n          sqlite3ExprCodeGetColumnOfTable(v, pTab, iDataCur, j, 3);\n          sqlite3VdbeChangeP5(v, OPFLAG_TYPEOFARG);\n          jmp2 = sqlite3VdbeAddOp1(v, OP_NotNull, 3); VdbeCoverage(v);\n          zErr = sqlite3MPrintf(db, \"NULL value in %s.%s\", pTab->zName,\n                              pTab->aCol[j].zName);\n          sqlite3VdbeAddOp4(v, OP_String8, 0, 3, 0, zErr, P4_DYNAMIC);\n          integrityCheckResultRow(v);\n          sqlite3VdbeJumpHere(v, jmp2);\n        }\n        /* Verify CHECK constraints */\n        if( pTab->pCheck && (db->flags & SQLITE_IgnoreChecks)==0 ){\n          ExprList *pCheck = sqlite3ExprListDup(db, pTab->pCheck, 0);\n          if( db->mallocFailed==0 ){\n            int addrCkFault = sqlite3VdbeMakeLabel(v);\n            int addrCkOk = sqlite3VdbeMakeLabel(v);\n            char *zErr;\n            int k;\n            pParse->iSelfTab = iDataCur + 1;\n            sqlite3ExprCachePush(pParse);\n            for(k=pCheck->nExpr-1; k>0; k--){\n              sqlite3ExprIfFalse(pParse, pCheck->a[k].pExpr, addrCkFault, 0);\n            }\n            sqlite3ExprIfTrue(pParse, pCheck->a[0].pExpr, addrCkOk, \n                SQLITE_JUMPIFNULL);\n            sqlite3VdbeResolveLabel(v, addrCkFault);\n            pParse->iSelfTab = 0;\n            zErr = sqlite3MPrintf(db, \"CHECK constraint failed in %s\",\n                pTab->zName);\n            sqlite3VdbeAddOp4(v, OP_String8, 0, 3, 0, zErr, P4_DYNAMIC);\n            integrityCheckResultRow(v);\n            sqlite3VdbeResolveLabel(v, addrCkOk);\n            sqlite3ExprCachePop(pParse);\n          }\n          sqlite3ExprListDelete(db, pCheck);\n        }\n        if( !isQuick ){ /* Omit the remaining tests for quick_check */\n          /* Sanity check on record header decoding */\n          sqlite3VdbeAddOp3(v, OP_Column, iDataCur, pTab->nCol-1, 3);\n          sqlite3VdbeChangeP5(v, OPFLAG_TYPEOFARG);\n          /* Validate index entries for the current row */\n          for(j=0, pIdx=pTab->pIndex; pIdx; pIdx=pIdx->pNext, j++){\n            int jmp2, jmp3, jmp4, jmp5;\n            int ckUniq = sqlite3VdbeMakeLabel(v);\n            if( pPk==pIdx ) continue;\n            r1 = sqlite3GenerateIndexKey(pParse, pIdx, iDataCur, 0, 0, &jmp3,\n                                         pPrior, r1);\n            pPrior = pIdx;\n            sqlite3VdbeAddOp2(v, OP_AddImm, 8+j, 1);/* increment entry count */\n            /* Verify that an index entry exists for the current table row */\n            jmp2 = sqlite3VdbeAddOp4Int(v, OP_Found, iIdxCur+j, ckUniq, r1,\n                                        pIdx->nColumn); VdbeCoverage(v);\n            sqlite3VdbeLoadString(v, 3, \"row \");\n            sqlite3VdbeAddOp3(v, OP_Concat, 7, 3, 3);\n            sqlite3VdbeLoadString(v, 4, \" missing from index \");\n            sqlite3VdbeAddOp3(v, OP_Concat, 4, 3, 3);\n            jmp5 = sqlite3VdbeLoadString(v, 4, pIdx->zName);\n            sqlite3VdbeAddOp3(v, OP_Concat, 4, 3, 3);\n            jmp4 = integrityCheckResultRow(v);\n            sqlite3VdbeJumpHere(v, jmp2);\n            /* For UNIQUE indexes, verify that only one entry exists with the\n            ** current key.  The entry is unique if (1) any column is NULL\n            ** or (2) the next entry has a different key */\n            if( IsUniqueIndex(pIdx) ){\n              int uniqOk = sqlite3VdbeMakeLabel(v);\n              int jmp6;\n              int kk;\n              for(kk=0; kk<pIdx->nKeyCol; kk++){\n                int iCol = pIdx->aiColumn[kk];\n                assert( iCol!=XN_ROWID && iCol<pTab->nCol );\n                if( iCol>=0 && pTab->aCol[iCol].notNull ) continue;\n                sqlite3VdbeAddOp2(v, OP_IsNull, r1+kk, uniqOk);\n                VdbeCoverage(v);\n              }\n              jmp6 = sqlite3VdbeAddOp1(v, OP_Next, iIdxCur+j); VdbeCoverage(v);\n              sqlite3VdbeGoto(v, uniqOk);\n              sqlite3VdbeJumpHere(v, jmp6);\n              sqlite3VdbeAddOp4Int(v, OP_IdxGT, iIdxCur+j, uniqOk, r1,\n                                   pIdx->nKeyCol); VdbeCoverage(v);\n              sqlite3VdbeLoadString(v, 3, \"non-unique entry in index \");\n              sqlite3VdbeGoto(v, jmp5);\n              sqlite3VdbeResolveLabel(v, uniqOk);\n            }\n            sqlite3VdbeJumpHere(v, jmp4);\n            sqlite3ResolvePartIdxLabel(pParse, jmp3);\n          }\n        }\n        sqlite3VdbeAddOp2(v, OP_Next, iDataCur, loopTop); VdbeCoverage(v);\n        sqlite3VdbeJumpHere(v, loopTop-1);\n#ifndef SQLITE_OMIT_BTREECOUNT\n        if( !isQuick ){\n          sqlite3VdbeLoadString(v, 2, \"wrong # of entries in index \");\n          for(j=0, pIdx=pTab->pIndex; pIdx; pIdx=pIdx->pNext, j++){\n            if( pPk==pIdx ) continue;\n            sqlite3VdbeAddOp2(v, OP_Count, iIdxCur+j, 3);\n            addr = sqlite3VdbeAddOp3(v, OP_Eq, 8+j, 0, 3); VdbeCoverage(v);\n            sqlite3VdbeChangeP5(v, SQLITE_NOTNULL);\n            sqlite3VdbeLoadString(v, 4, pIdx->zName);\n            sqlite3VdbeAddOp3(v, OP_Concat, 4, 2, 3);\n            integrityCheckResultRow(v);\n            sqlite3VdbeJumpHere(v, addr);\n          }\n        }\n#endif /* SQLITE_OMIT_BTREECOUNT */\n      } \n    }\n    {\n      static const int iLn = VDBE_OFFSET_LINENO(2);\n      static const VdbeOpList endCode[] = {\n        { OP_AddImm,      1, 0,        0},    /* 0 */\n        { OP_IfNotZero,   1, 4,        0},    /* 1 */\n        { OP_String8,     0, 3,        0},    /* 2 */\n        { OP_ResultRow,   3, 1,        0},    /* 3 */\n        { OP_Halt,        0, 0,        0},    /* 4 */\n        { OP_String8,     0, 3,        0},    /* 5 */\n        { OP_Goto,        0, 3,        0},    /* 6 */\n      };\n      VdbeOp *aOp;\n\n      aOp = sqlite3VdbeAddOpList(v, ArraySize(endCode), endCode, iLn);\n      if( aOp ){\n        aOp[0].p2 = 1-mxErr;\n        aOp[2].p4type = P4_STATIC;\n        aOp[2].p4.z = \"ok\";\n        aOp[5].p4type = P4_STATIC;\n        aOp[5].p4.z = (char*)sqlite3ErrStr(SQLITE_CORRUPT);\n      }\n      sqlite3VdbeChangeP3(v, 0, sqlite3VdbeCurrentAddr(v)-2);\n    }\n  }\n  break;\n#endif /* SQLITE_OMIT_INTEGRITY_CHECK */\n\n#ifndef SQLITE_OMIT_UTF16\n  /*\n  **   PRAGMA encoding\n  **   PRAGMA encoding = \"utf-8\"|\"utf-16\"|\"utf-16le\"|\"utf-16be\"\n  **\n  ** In its first form, this pragma returns the encoding of the main\n  ** database. If the database is not initialized, it is initialized now.\n  **\n  ** The second form of this pragma is a no-op if the main database file\n  ** has not already been initialized. In this case it sets the default\n  ** encoding that will be used for the main database file if a new file\n  ** is created. If an existing main database file is opened, then the\n  ** default text encoding for the existing database is used.\n  ** \n  ** In all cases new databases created using the ATTACH command are\n  ** created to use the same default text encoding as the main database. If\n  ** the main database has not been initialized and/or created when ATTACH\n  ** is executed, this is done before the ATTACH operation.\n  **\n  ** In the second form this pragma sets the text encoding to be used in\n  ** new database files created using this database handle. It is only\n  ** useful if invoked immediately after the main database i\n  */\n  case PragTyp_ENCODING: {\n    static const struct EncName {\n      char *zName;\n      u8 enc;\n    } encnames[] = {\n      { \"UTF8\",     SQLITE_UTF8        },\n      { \"UTF-8\",    SQLITE_UTF8        },  /* Must be element [1] */\n      { \"UTF-16le\", SQLITE_UTF16LE     },  /* Must be element [2] */\n      { \"UTF-16be\", SQLITE_UTF16BE     },  /* Must be element [3] */\n      { \"UTF16le\",  SQLITE_UTF16LE     },\n      { \"UTF16be\",  SQLITE_UTF16BE     },\n      { \"UTF-16\",   0                  }, /* SQLITE_UTF16NATIVE */\n      { \"UTF16\",    0                  }, /* SQLITE_UTF16NATIVE */\n      { 0, 0 }\n    };\n    const struct EncName *pEnc;\n    if( !zRight ){    /* \"PRAGMA encoding\" */\n      if( sqlite3ReadSchema(pParse) ) goto pragma_out;\n      assert( encnames[SQLITE_UTF8].enc==SQLITE_UTF8 );\n      assert( encnames[SQLITE_UTF16LE].enc==SQLITE_UTF16LE );\n      assert( encnames[SQLITE_UTF16BE].enc==SQLITE_UTF16BE );\n      returnSingleText(v, encnames[ENC(pParse->db)].zName);\n    }else{                        /* \"PRAGMA encoding = XXX\" */\n      /* Only change the value of sqlite.enc if the database handle is not\n      ** initialized. If the main database exists, the new sqlite.enc value\n      ** will be overwritten when the schema is next loaded. If it does not\n      ** already exists, it will be created to use the new encoding value.\n      */\n      if( \n        !(DbHasProperty(db, 0, DB_SchemaLoaded)) || \n        DbHasProperty(db, 0, DB_Empty) \n      ){\n        for(pEnc=&encnames[0]; pEnc->zName; pEnc++){\n          if( 0==sqlite3StrICmp(zRight, pEnc->zName) ){\n            SCHEMA_ENC(db) = ENC(db) =\n                pEnc->enc ? pEnc->enc : SQLITE_UTF16NATIVE;\n            break;\n          }\n        }\n        if( !pEnc->zName ){\n          sqlite3ErrorMsg(pParse, \"unsupported encoding: %s\", zRight);\n        }\n      }\n    }\n  }\n  break;\n#endif /* SQLITE_OMIT_UTF16 */\n\n#ifndef SQLITE_OMIT_SCHEMA_VERSION_PRAGMAS\n  /*\n  **   PRAGMA [schema.]schema_version\n  **   PRAGMA [schema.]schema_version = <integer>\n  **\n  **   PRAGMA [schema.]user_version\n  **   PRAGMA [schema.]user_version = <integer>\n  **\n  **   PRAGMA [schema.]freelist_count\n  **\n  **   PRAGMA [schema.]data_version\n  **\n  **   PRAGMA [schema.]application_id\n  **   PRAGMA [schema.]application_id = <integer>\n  **\n  ** The pragma's schema_version and user_version are used to set or get\n  ** the value of the schema-version and user-version, respectively. Both\n  ** the schema-version and the user-version are 32-bit signed integers\n  ** stored in the database header.\n  **\n  ** The schema-cookie is usually only manipulated internally by SQLite. It\n  ** is incremented by SQLite whenever the database schema is modified (by\n  ** creating or dropping a table or index). The schema version is used by\n  ** SQLite each time a query is executed to ensure that the internal cache\n  ** of the schema used when compiling the SQL query matches the schema of\n  ** the database against which the compiled query is actually executed.\n  ** Subverting this mechanism by using \"PRAGMA schema_version\" to modify\n  ** the schema-version is potentially dangerous and may lead to program\n  ** crashes or database corruption. Use with caution!\n  **\n  ** The user-version is not used internally by SQLite. It may be used by\n  ** applications for any purpose.\n  */\n  case PragTyp_HEADER_VALUE: {\n    int iCookie = pPragma->iArg;  /* Which cookie to read or write */\n    sqlite3VdbeUsesBtree(v, iDb);\n    if( zRight && (pPragma->mPragFlg & PragFlg_ReadOnly)==0 ){\n      /* Write the specified cookie value */\n      static const VdbeOpList setCookie[] = {\n        { OP_Transaction,    0,  1,  0},    /* 0 */\n        { OP_SetCookie,      0,  0,  0},    /* 1 */\n      };\n      VdbeOp *aOp;\n      sqlite3VdbeVerifyNoMallocRequired(v, ArraySize(setCookie));\n      aOp = sqlite3VdbeAddOpList(v, ArraySize(setCookie), setCookie, 0);\n      if( ONLY_IF_REALLOC_STRESS(aOp==0) ) break;\n      aOp[0].p1 = iDb;\n      aOp[1].p1 = iDb;\n      aOp[1].p2 = iCookie;\n      aOp[1].p3 = sqlite3Atoi(zRight);\n    }else{\n      /* Read the specified cookie value */\n      static const VdbeOpList readCookie[] = {\n        { OP_Transaction,     0,  0,  0},    /* 0 */\n        { OP_ReadCookie,      0,  1,  0},    /* 1 */\n        { OP_ResultRow,       1,  1,  0}\n      };\n      VdbeOp *aOp;\n      sqlite3VdbeVerifyNoMallocRequired(v, ArraySize(readCookie));\n      aOp = sqlite3VdbeAddOpList(v, ArraySize(readCookie),readCookie,0);\n      if( ONLY_IF_REALLOC_STRESS(aOp==0) ) break;\n      aOp[0].p1 = iDb;\n      aOp[1].p1 = iDb;\n      aOp[1].p3 = iCookie;\n      sqlite3VdbeReusable(v);\n    }\n  }\n  break;\n#endif /* SQLITE_OMIT_SCHEMA_VERSION_PRAGMAS */\n\n#ifndef SQLITE_OMIT_COMPILEOPTION_DIAGS\n  /*\n  **   PRAGMA compile_options\n  **\n  ** Return the names of all compile-time options used in this build,\n  ** one option per row.\n  */\n  case PragTyp_COMPILE_OPTIONS: {\n    int i = 0;\n    const char *zOpt;\n    pParse->nMem = 1;\n    while( (zOpt = sqlite3_compileoption_get(i++))!=0 ){\n      sqlite3VdbeLoadString(v, 1, zOpt);\n      sqlite3VdbeAddOp2(v, OP_ResultRow, 1, 1);\n    }\n    sqlite3VdbeReusable(v);\n  }\n  break;\n#endif /* SQLITE_OMIT_COMPILEOPTION_DIAGS */\n\n#ifndef SQLITE_OMIT_WAL\n  /*\n  **   PRAGMA [schema.]wal_checkpoint = passive|full|restart|truncate\n  **\n  ** Checkpoint the database.\n  */\n  case PragTyp_WAL_CHECKPOINT: {\n    int iBt = (pId2->z?iDb:SQLITE_MAX_ATTACHED);\n    int eMode = SQLITE_CHECKPOINT_PASSIVE;\n    if( zRight ){\n      if( sqlite3StrICmp(zRight, \"full\")==0 ){\n        eMode = SQLITE_CHECKPOINT_FULL;\n      }else if( sqlite3StrICmp(zRight, \"restart\")==0 ){\n        eMode = SQLITE_CHECKPOINT_RESTART;\n      }else if( sqlite3StrICmp(zRight, \"truncate\")==0 ){\n        eMode = SQLITE_CHECKPOINT_TRUNCATE;\n      }\n    }\n    pParse->nMem = 3;\n    sqlite3VdbeAddOp3(v, OP_Checkpoint, iBt, eMode, 1);\n    sqlite3VdbeAddOp2(v, OP_ResultRow, 1, 3);\n  }\n  break;\n\n  /*\n  **   PRAGMA wal_autocheckpoint\n  **   PRAGMA wal_autocheckpoint = N\n  **\n  ** Configure a database connection to automatically checkpoint a database\n  ** after accumulating N frames in the log. Or query for the current value\n  ** of N.\n  */\n  case PragTyp_WAL_AUTOCHECKPOINT: {\n    if( zRight ){\n      sqlite3_wal_autocheckpoint(db, sqlite3Atoi(zRight));\n    }\n    returnSingleInt(v, \n       db->xWalCallback==sqlite3WalDefaultHook ? \n           SQLITE_PTR_TO_INT(db->pWalArg) : 0);\n  }\n  break;\n#endif\n\n  /*\n  **  PRAGMA shrink_memory\n  **\n  ** IMPLEMENTATION-OF: R-23445-46109 This pragma causes the database\n  ** connection on which it is invoked to free up as much memory as it\n  ** can, by calling sqlite3_db_release_memory().\n  */\n  case PragTyp_SHRINK_MEMORY: {\n    sqlite3_db_release_memory(db);\n    break;\n  }\n\n  /*\n  **  PRAGMA optimize\n  **  PRAGMA optimize(MASK)\n  **  PRAGMA schema.optimize\n  **  PRAGMA schema.optimize(MASK)\n  **\n  ** Attempt to optimize the database.  All schemas are optimized in the first\n  ** two forms, and only the specified schema is optimized in the latter two.\n  **\n  ** The details of optimizations performed by this pragma are expected\n  ** to change and improve over time.  Applications should anticipate that\n  ** this pragma will perform new optimizations in future releases.\n  **\n  ** The optional argument is a bitmask of optimizations to perform:\n  **\n  **    0x0001    Debugging mode.  Do not actually perform any optimizations\n  **              but instead return one line of text for each optimization\n  **              that would have been done.  Off by default.\n  **\n  **    0x0002    Run ANALYZE on tables that might benefit.  On by default.\n  **              See below for additional information.\n  **\n  **    0x0004    (Not yet implemented) Record usage and performance \n  **              information from the current session in the\n  **              database file so that it will be available to \"optimize\"\n  **              pragmas run by future database connections.\n  **\n  **    0x0008    (Not yet implemented) Create indexes that might have\n  **              been helpful to recent queries\n  **\n  ** The default MASK is and always shall be 0xfffe.  0xfffe means perform all\n  ** of the optimizations listed above except Debug Mode, including new\n  ** optimizations that have not yet been invented.  If new optimizations are\n  ** ever added that should be off by default, those off-by-default \n  ** optimizations will have bitmasks of 0x10000 or larger.\n  **\n  ** DETERMINATION OF WHEN TO RUN ANALYZE\n  **\n  ** In the current implementation, a table is analyzed if only if all of\n  ** the following are true:\n  **\n  ** (1) MASK bit 0x02 is set.\n  **\n  ** (2) The query planner used sqlite_stat1-style statistics for one or\n  **     more indexes of the table at some point during the lifetime of\n  **     the current connection.\n  **\n  ** (3) One or more indexes of the table are currently unanalyzed OR\n  **     the number of rows in the table has increased by 25 times or more\n  **     since the last time ANALYZE was run.\n  **\n  ** The rules for when tables are analyzed are likely to change in\n  ** future releases.\n  */\n  case PragTyp_OPTIMIZE: {\n    int iDbLast;           /* Loop termination point for the schema loop */\n    int iTabCur;           /* Cursor for a table whose size needs checking */\n    HashElem *k;           /* Loop over tables of a schema */\n    Schema *pSchema;       /* The current schema */\n    Table *pTab;           /* A table in the schema */\n    Index *pIdx;           /* An index of the table */\n    LogEst szThreshold;    /* Size threshold above which reanalysis is needd */\n    char *zSubSql;         /* SQL statement for the OP_SqlExec opcode */\n    u32 opMask;            /* Mask of operations to perform */\n\n    if( zRight ){\n      opMask = (u32)sqlite3Atoi(zRight);\n      if( (opMask & 0x02)==0 ) break;\n    }else{\n      opMask = 0xfffe;\n    }\n    iTabCur = pParse->nTab++;\n    for(iDbLast = zDb?iDb:db->nDb-1; iDb<=iDbLast; iDb++){\n      if( iDb==1 ) continue;\n      sqlite3CodeVerifySchema(pParse, iDb);\n      pSchema = db->aDb[iDb].pSchema;\n      for(k=sqliteHashFirst(&pSchema->tblHash); k; k=sqliteHashNext(k)){\n        pTab = (Table*)sqliteHashData(k);\n\n        /* If table pTab has not been used in a way that would benefit from\n        ** having analysis statistics during the current session, then skip it.\n        ** This also has the effect of skipping virtual tables and views */\n        if( (pTab->tabFlags & TF_StatsUsed)==0 ) continue;\n\n        /* Reanalyze if the table is 25 times larger than the last analysis */\n        szThreshold = pTab->nRowLogEst + 46; assert( sqlite3LogEst(25)==46 );\n        for(pIdx=pTab->pIndex; pIdx; pIdx=pIdx->pNext){\n          if( !pIdx->hasStat1 ){\n            szThreshold = 0; /* Always analyze if any index lacks statistics */\n            break;\n          }\n        }\n        if( szThreshold ){\n          sqlite3OpenTable(pParse, iTabCur, iDb, pTab, OP_OpenRead);\n          sqlite3VdbeAddOp3(v, OP_IfSmaller, iTabCur, \n                         sqlite3VdbeCurrentAddr(v)+2+(opMask&1), szThreshold);\n          VdbeCoverage(v);\n        }\n        zSubSql = sqlite3MPrintf(db, \"ANALYZE \\\"%w\\\".\\\"%w\\\"\",\n                                 db->aDb[iDb].zDbSName, pTab->zName);\n        if( opMask & 0x01 ){\n          int r1 = sqlite3GetTempReg(pParse);\n          sqlite3VdbeAddOp4(v, OP_String8, 0, r1, 0, zSubSql, P4_DYNAMIC);\n          sqlite3VdbeAddOp2(v, OP_ResultRow, r1, 1);\n        }else{\n          sqlite3VdbeAddOp4(v, OP_SqlExec, 0, 0, 0, zSubSql, P4_DYNAMIC);\n        }\n      }\n    }\n    sqlite3VdbeAddOp0(v, OP_Expire);\n    break;\n  }\n\n  /*\n  **   PRAGMA busy_timeout\n  **   PRAGMA busy_timeout = N\n  **\n  ** Call sqlite3_busy_timeout(db, N).  Return the current timeout value\n  ** if one is set.  If no busy handler or a different busy handler is set\n  ** then 0 is returned.  Setting the busy_timeout to 0 or negative\n  ** disables the timeout.\n  */\n  /*case PragTyp_BUSY_TIMEOUT*/ default: {\n    assert( pPragma->ePragTyp==PragTyp_BUSY_TIMEOUT );\n    if( zRight ){\n      sqlite3_busy_timeout(db, sqlite3Atoi(zRight));\n    }\n    returnSingleInt(v, db->busyTimeout);\n    break;\n  }\n\n  /*\n  **   PRAGMA soft_heap_limit\n  **   PRAGMA soft_heap_limit = N\n  **\n  ** IMPLEMENTATION-OF: R-26343-45930 This pragma invokes the\n  ** sqlite3_soft_heap_limit64() interface with the argument N, if N is\n  ** specified and is a non-negative integer.\n  ** IMPLEMENTATION-OF: R-64451-07163 The soft_heap_limit pragma always\n  ** returns the same integer that would be returned by the\n  ** sqlite3_soft_heap_limit64(-1) C-language function.\n  */\n  case PragTyp_SOFT_HEAP_LIMIT: {\n    sqlite3_int64 N;\n    if( zRight && sqlite3DecOrHexToI64(zRight, &N)==SQLITE_OK ){\n      sqlite3_soft_heap_limit64(N);\n    }\n    returnSingleInt(v, sqlite3_soft_heap_limit64(-1));\n    break;\n  }\n\n  /*\n  **   PRAGMA threads\n  **   PRAGMA threads = N\n  **\n  ** Configure the maximum number of worker threads.  Return the new\n  ** maximum, which might be less than requested.\n  */\n  case PragTyp_THREADS: {\n    sqlite3_int64 N;\n    if( zRight\n     && sqlite3DecOrHexToI64(zRight, &N)==SQLITE_OK\n     && N>=0\n    ){\n      sqlite3_limit(db, SQLITE_LIMIT_WORKER_THREADS, (int)(N&0x7fffffff));\n    }\n    returnSingleInt(v, sqlite3_limit(db, SQLITE_LIMIT_WORKER_THREADS, -1));\n    break;\n  }\n\n#if defined(SQLITE_DEBUG) || defined(SQLITE_TEST)\n  /*\n  ** Report the current state of file logs for all databases\n  */\n  case PragTyp_LOCK_STATUS: {\n    static const char *const azLockName[] = {\n      \"unlocked\", \"shared\", \"reserved\", \"pending\", \"exclusive\"\n    };\n    int i;\n    pParse->nMem = 2;\n    for(i=0; i<db->nDb; i++){\n      Btree *pBt;\n      const char *zState = \"unknown\";\n      int j;\n      if( db->aDb[i].zDbSName==0 ) continue;\n      pBt = db->aDb[i].pBt;\n      if( pBt==0 || sqlite3BtreePager(pBt)==0 ){\n        zState = \"closed\";\n      }else if( sqlite3_file_control(db, i ? db->aDb[i].zDbSName : 0, \n                                     SQLITE_FCNTL_LOCKSTATE, &j)==SQLITE_OK ){\n         zState = azLockName[j];\n      }\n      sqlite3VdbeMultiLoad(v, 1, \"ss\", db->aDb[i].zDbSName, zState);\n    }\n    break;\n  }\n#endif\n\n#ifdef SQLITE_HAS_CODEC\n  case PragTyp_KEY: {\n    if( zRight ) sqlite3_key_v2(db, zDb, zRight, sqlite3Strlen30(zRight));\n    break;\n  }\n  case PragTyp_REKEY: {\n    if( zRight ) sqlite3_rekey_v2(db, zDb, zRight, sqlite3Strlen30(zRight));\n    break;\n  }\n  case PragTyp_HEXKEY: {\n    if( zRight ){\n      u8 iByte;\n      int i;\n      char zKey[40];\n      for(i=0, iByte=0; i<sizeof(zKey)*2 && sqlite3Isxdigit(zRight[i]); i++){\n        iByte = (iByte<<4) + sqlite3HexToInt(zRight[i]);\n        if( (i&1)!=0 ) zKey[i/2] = iByte;\n      }\n      if( (zLeft[3] & 0xf)==0xb ){\n        sqlite3_key_v2(db, zDb, zKey, i/2);\n      }else{\n        sqlite3_rekey_v2(db, zDb, zKey, i/2);\n      }\n    }\n    break;\n  }\n#endif\n#if defined(SQLITE_HAS_CODEC) || defined(SQLITE_ENABLE_CEROD)\n  case PragTyp_ACTIVATE_EXTENSIONS: if( zRight ){\n#ifdef SQLITE_HAS_CODEC\n    if( sqlite3StrNICmp(zRight, \"see-\", 4)==0 ){\n      sqlite3_activate_see(&zRight[4]);\n    }\n#endif\n#ifdef SQLITE_ENABLE_CEROD\n    if( sqlite3StrNICmp(zRight, \"cerod-\", 6)==0 ){\n      sqlite3_activate_cerod(&zRight[6]);\n    }\n#endif\n  }\n  break;\n#endif\n\n  } /* End of the PRAGMA switch */\n\n  /* The following block is a no-op unless SQLITE_DEBUG is defined. Its only\n  ** purpose is to execute assert() statements to verify that if the\n  ** PragFlg_NoColumns1 flag is set and the caller specified an argument\n  ** to the PRAGMA, the implementation has not added any OP_ResultRow \n  ** instructions to the VM.  */\n  if( (pPragma->mPragFlg & PragFlg_NoColumns1) && zRight ){\n    sqlite3VdbeVerifyNoResultRow(v);\n  }\n\npragma_out:\n  sqlite3DbFree(db, zLeft);\n  sqlite3DbFree(db, zRight);\n}\n#ifndef SQLITE_OMIT_VIRTUALTABLE\n/*****************************************************************************\n** Implementation of an eponymous virtual table that runs a pragma.\n**\n*/\ntypedef struct PragmaVtab PragmaVtab;\ntypedef struct PragmaVtabCursor PragmaVtabCursor;\nstruct PragmaVtab {\n  sqlite3_vtab base;        /* Base class.  Must be first */\n  sqlite3 *db;              /* The database connection to which it belongs */\n  const PragmaName *pName;  /* Name of the pragma */\n  u8 nHidden;               /* Number of hidden columns */\n  u8 iHidden;               /* Index of the first hidden column */\n};\nstruct PragmaVtabCursor {\n  sqlite3_vtab_cursor base; /* Base class.  Must be first */\n  sqlite3_stmt *pPragma;    /* The pragma statement to run */\n  sqlite_int64 iRowid;      /* Current rowid */\n  char *azArg[2];           /* Value of the argument and schema */\n};\n\n/* \n** Pragma virtual table module xConnect method.\n*/\nstatic int pragmaVtabConnect(\n  sqlite3 *db,\n  void *pAux,\n  int argc, const char *const*argv,\n  sqlite3_vtab **ppVtab,\n  char **pzErr\n){\n  const PragmaName *pPragma = (const PragmaName*)pAux;\n  PragmaVtab *pTab = 0;\n  int rc;\n  int i, j;\n  char cSep = '(';\n  StrAccum acc;\n  char zBuf[200];\n\n  UNUSED_PARAMETER(argc);\n  UNUSED_PARAMETER(argv);\n  sqlite3StrAccumInit(&acc, 0, zBuf, sizeof(zBuf), 0);\n  sqlite3StrAccumAppendAll(&acc, \"CREATE TABLE x\");\n  for(i=0, j=pPragma->iPragCName; i<pPragma->nPragCName; i++, j++){\n    sqlite3XPrintf(&acc, \"%c\\\"%s\\\"\", cSep, pragCName[j]);\n    cSep = ',';\n  }\n  if( i==0 ){\n    sqlite3XPrintf(&acc, \"(\\\"%s\\\"\", pPragma->zName);\n    cSep = ',';\n    i++;\n  }\n  j = 0;\n  if( pPragma->mPragFlg & PragFlg_Result1 ){\n    sqlite3StrAccumAppendAll(&acc, \",arg HIDDEN\");\n    j++;\n  }\n  if( pPragma->mPragFlg & (PragFlg_SchemaOpt|PragFlg_SchemaReq) ){\n    sqlite3StrAccumAppendAll(&acc, \",schema HIDDEN\");\n    j++;\n  }\n  sqlite3StrAccumAppend(&acc, \")\", 1);\n  sqlite3StrAccumFinish(&acc);\n  assert( strlen(zBuf) < sizeof(zBuf)-1 );\n  rc = sqlite3_declare_vtab(db, zBuf);\n  if( rc==SQLITE_OK ){\n    pTab = (PragmaVtab*)sqlite3_malloc(sizeof(PragmaVtab));\n    if( pTab==0 ){\n      rc = SQLITE_NOMEM;\n    }else{\n      memset(pTab, 0, sizeof(PragmaVtab));\n      pTab->pName = pPragma;\n      pTab->db = db;\n      pTab->iHidden = i;\n      pTab->nHidden = j;\n    }\n  }else{\n    *pzErr = sqlite3_mprintf(\"%s\", sqlite3_errmsg(db));\n  }\n\n  *ppVtab = (sqlite3_vtab*)pTab;\n  return rc;\n}\n\n/* \n** Pragma virtual table module xDisconnect method.\n*/\nstatic int pragmaVtabDisconnect(sqlite3_vtab *pVtab){\n  PragmaVtab *pTab = (PragmaVtab*)pVtab;\n  sqlite3_free(pTab);\n  return SQLITE_OK;\n}\n\n/* Figure out the best index to use to search a pragma virtual table.\n**\n** There are not really any index choices.  But we want to encourage the\n** query planner to give == constraints on as many hidden parameters as\n** possible, and especially on the first hidden parameter.  So return a\n** high cost if hidden parameters are unconstrained.\n*/\nstatic int pragmaVtabBestIndex(sqlite3_vtab *tab, sqlite3_index_info *pIdxInfo){\n  PragmaVtab *pTab = (PragmaVtab*)tab;\n  const struct sqlite3_index_constraint *pConstraint;\n  int i, j;\n  int seen[2];\n\n  pIdxInfo->estimatedCost = (double)1;\n  if( pTab->nHidden==0 ){ return SQLITE_OK; }\n  pConstraint = pIdxInfo->aConstraint;\n  seen[0] = 0;\n  seen[1] = 0;\n  for(i=0; i<pIdxInfo->nConstraint; i++, pConstraint++){\n    if( pConstraint->usable==0 ) continue;\n    if( pConstraint->op!=SQLITE_INDEX_CONSTRAINT_EQ ) continue;\n    if( pConstraint->iColumn < pTab->iHidden ) continue;\n    j = pConstraint->iColumn - pTab->iHidden;\n    assert( j < 2 );\n    seen[j] = i+1;\n  }\n  if( seen[0]==0 ){\n    pIdxInfo->estimatedCost = (double)2147483647;\n    pIdxInfo->estimatedRows = 2147483647;\n    return SQLITE_OK;\n  }\n  j = seen[0]-1;\n  pIdxInfo->aConstraintUsage[j].argvIndex = 1;\n  pIdxInfo->aConstraintUsage[j].omit = 1;\n  if( seen[1]==0 ) return SQLITE_OK;\n  pIdxInfo->estimatedCost = (double)20;\n  pIdxInfo->estimatedRows = 20;\n  j = seen[1]-1;\n  pIdxInfo->aConstraintUsage[j].argvIndex = 2;\n  pIdxInfo->aConstraintUsage[j].omit = 1;\n  return SQLITE_OK;\n}\n\n/* Create a new cursor for the pragma virtual table */\nstatic int pragmaVtabOpen(sqlite3_vtab *pVtab, sqlite3_vtab_cursor **ppCursor){\n  PragmaVtabCursor *pCsr;\n  pCsr = (PragmaVtabCursor*)sqlite3_malloc(sizeof(*pCsr));\n  if( pCsr==0 ) return SQLITE_NOMEM;\n  memset(pCsr, 0, sizeof(PragmaVtabCursor));\n  pCsr->base.pVtab = pVtab;\n  *ppCursor = &pCsr->base;\n  return SQLITE_OK;\n}\n\n/* Clear all content from pragma virtual table cursor. */\nstatic void pragmaVtabCursorClear(PragmaVtabCursor *pCsr){\n  int i;\n  sqlite3_finalize(pCsr->pPragma);\n  pCsr->pPragma = 0;\n  for(i=0; i<ArraySize(pCsr->azArg); i++){\n    sqlite3_free(pCsr->azArg[i]);\n    pCsr->azArg[i] = 0;\n  }\n}\n\n/* Close a pragma virtual table cursor */\nstatic int pragmaVtabClose(sqlite3_vtab_cursor *cur){\n  PragmaVtabCursor *pCsr = (PragmaVtabCursor*)cur;\n  pragmaVtabCursorClear(pCsr);\n  sqlite3_free(pCsr);\n  return SQLITE_OK;\n}\n\n/* Advance the pragma virtual table cursor to the next row */\nstatic int pragmaVtabNext(sqlite3_vtab_cursor *pVtabCursor){\n  PragmaVtabCursor *pCsr = (PragmaVtabCursor*)pVtabCursor;\n  int rc = SQLITE_OK;\n\n  /* Increment the xRowid value */\n  pCsr->iRowid++;\n  assert( pCsr->pPragma );\n  if( SQLITE_ROW!=sqlite3_step(pCsr->pPragma) ){\n    rc = sqlite3_finalize(pCsr->pPragma);\n    pCsr->pPragma = 0;\n    pragmaVtabCursorClear(pCsr);\n  }\n  return rc;\n}\n\n/* \n** Pragma virtual table module xFilter method.\n*/\nstatic int pragmaVtabFilter(\n  sqlite3_vtab_cursor *pVtabCursor, \n  int idxNum, const char *idxStr,\n  int argc, sqlite3_value **argv\n){\n  PragmaVtabCursor *pCsr = (PragmaVtabCursor*)pVtabCursor;\n  PragmaVtab *pTab = (PragmaVtab*)(pVtabCursor->pVtab);\n  int rc;\n  int i, j;\n  StrAccum acc;\n  char *zSql;\n\n  UNUSED_PARAMETER(idxNum);\n  UNUSED_PARAMETER(idxStr);\n  pragmaVtabCursorClear(pCsr);\n  j = (pTab->pName->mPragFlg & PragFlg_Result1)!=0 ? 0 : 1;\n  for(i=0; i<argc; i++, j++){\n    const char *zText = (const char*)sqlite3_value_text(argv[i]);\n    assert( j<ArraySize(pCsr->azArg) );\n    assert( pCsr->azArg[j]==0 );\n    if( zText ){\n      pCsr->azArg[j] = sqlite3_mprintf(\"%s\", zText);\n      if( pCsr->azArg[j]==0 ){\n        return SQLITE_NOMEM;\n      }\n    }\n  }\n  sqlite3StrAccumInit(&acc, 0, 0, 0, pTab->db->aLimit[SQLITE_LIMIT_SQL_LENGTH]);\n  sqlite3StrAccumAppendAll(&acc, \"PRAGMA \");\n  if( pCsr->azArg[1] ){\n    sqlite3XPrintf(&acc, \"%Q.\", pCsr->azArg[1]);\n  }\n  sqlite3StrAccumAppendAll(&acc, pTab->pName->zName);\n  if( pCsr->azArg[0] ){\n    sqlite3XPrintf(&acc, \"=%Q\", pCsr->azArg[0]);\n  }\n  zSql = sqlite3StrAccumFinish(&acc);\n  if( zSql==0 ) return SQLITE_NOMEM;\n  rc = sqlite3_prepare_v2(pTab->db, zSql, -1, &pCsr->pPragma, 0);\n  sqlite3_free(zSql);\n  if( rc!=SQLITE_OK ){\n    pTab->base.zErrMsg = sqlite3_mprintf(\"%s\", sqlite3_errmsg(pTab->db));\n    return rc;\n  }\n  return pragmaVtabNext(pVtabCursor);\n}\n\n/*\n** Pragma virtual table module xEof method.\n*/\nstatic int pragmaVtabEof(sqlite3_vtab_cursor *pVtabCursor){\n  PragmaVtabCursor *pCsr = (PragmaVtabCursor*)pVtabCursor;\n  return (pCsr->pPragma==0);\n}\n\n/* The xColumn method simply returns the corresponding column from\n** the PRAGMA.  \n*/\nstatic int pragmaVtabColumn(\n  sqlite3_vtab_cursor *pVtabCursor, \n  sqlite3_context *ctx, \n  int i\n){\n  PragmaVtabCursor *pCsr = (PragmaVtabCursor*)pVtabCursor;\n  PragmaVtab *pTab = (PragmaVtab*)(pVtabCursor->pVtab);\n  if( i<pTab->iHidden ){\n    sqlite3_result_value(ctx, sqlite3_column_value(pCsr->pPragma, i));\n  }else{\n    sqlite3_result_text(ctx, pCsr->azArg[i-pTab->iHidden],-1,SQLITE_TRANSIENT);\n  }\n  return SQLITE_OK;\n}\n\n/* \n** Pragma virtual table module xRowid method.\n*/\nstatic int pragmaVtabRowid(sqlite3_vtab_cursor *pVtabCursor, sqlite_int64 *p){\n  PragmaVtabCursor *pCsr = (PragmaVtabCursor*)pVtabCursor;\n  *p = pCsr->iRowid;\n  return SQLITE_OK;\n}\n\n/* The pragma virtual table object */\nstatic const sqlite3_module pragmaVtabModule = {\n  0,                           /* iVersion */\n  0,                           /* xCreate - create a table */\n  pragmaVtabConnect,           /* xConnect - connect to an existing table */\n  pragmaVtabBestIndex,         /* xBestIndex - Determine search strategy */\n  pragmaVtabDisconnect,        /* xDisconnect - Disconnect from a table */\n  0,                           /* xDestroy - Drop a table */\n  pragmaVtabOpen,              /* xOpen - open a cursor */\n  pragmaVtabClose,             /* xClose - close a cursor */\n  pragmaVtabFilter,            /* xFilter - configure scan constraints */\n  pragmaVtabNext,              /* xNext - advance a cursor */\n  pragmaVtabEof,               /* xEof */\n  pragmaVtabColumn,            /* xColumn - read data */\n  pragmaVtabRowid,             /* xRowid - read data */\n  0,                           /* xUpdate - write data */\n  0,                           /* xBegin - begin transaction */\n  0,                           /* xSync - sync transaction */\n  0,                           /* xCommit - commit transaction */\n  0,                           /* xRollback - rollback transaction */\n  0,                           /* xFindFunction - function overloading */\n  0,                           /* xRename - rename the table */\n  0,                           /* xSavepoint */\n  0,                           /* xRelease */\n  0                            /* xRollbackTo */\n};\n\n/*\n** Check to see if zTabName is really the name of a pragma.  If it is,\n** then register an eponymous virtual table for that pragma and return\n** a pointer to the Module object for the new virtual table.\n*/\nSQLITE_PRIVATE Module *sqlite3PragmaVtabRegister(sqlite3 *db, const char *zName){\n  const PragmaName *pName;\n  assert( sqlite3_strnicmp(zName, \"pragma_\", 7)==0 );\n  pName = pragmaLocate(zName+7);\n  if( pName==0 ) return 0;\n  if( (pName->mPragFlg & (PragFlg_Result0|PragFlg_Result1))==0 ) return 0;\n  assert( sqlite3HashFind(&db->aModule, zName)==0 );\n  return sqlite3VtabCreateModule(db, zName, &pragmaVtabModule, (void*)pName, 0);\n}\n\n#endif /* SQLITE_OMIT_VIRTUALTABLE */\n\n#endif /* SQLITE_OMIT_PRAGMA */\n\n/************** End of pragma.c **********************************************/\n/************** Begin file prepare.c *****************************************/\n/*\n** 2005 May 25\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n*************************************************************************\n** This file contains the implementation of the sqlite3_prepare()\n** interface, and routines that contribute to loading the database schema\n** from disk.\n*/\n/* #include \"sqliteInt.h\" */\n\n/*\n** Fill the InitData structure with an error message that indicates\n** that the database is corrupt.\n*/\nstatic void corruptSchema(\n  InitData *pData,     /* Initialization context */\n  const char *zObj,    /* Object being parsed at the point of error */\n  const char *zExtra   /* Error information */\n){\n  sqlite3 *db = pData->db;\n  if( !db->mallocFailed && (db->flags & SQLITE_WriteSchema)==0 ){\n    char *z;\n    if( zObj==0 ) zObj = \"?\";\n    z = sqlite3MPrintf(db, \"malformed database schema (%s)\", zObj);\n    if( zExtra ) z = sqlite3MPrintf(db, \"%z - %s\", z, zExtra);\n    sqlite3DbFree(db, *pData->pzErrMsg);\n    *pData->pzErrMsg = z;\n  }\n  pData->rc = db->mallocFailed ? SQLITE_NOMEM_BKPT : SQLITE_CORRUPT_BKPT;\n}\n\n/*\n** This is the callback routine for the code that initializes the\n** database.  See sqlite3Init() below for additional information.\n** This routine is also called from the OP_ParseSchema opcode of the VDBE.\n**\n** Each callback contains the following information:\n**\n**     argv[0] = name of thing being created\n**     argv[1] = root page number for table or index. 0 for trigger or view.\n**     argv[2] = SQL text for the CREATE statement.\n**\n*/\nSQLITE_PRIVATE int sqlite3InitCallback(void *pInit, int argc, char **argv, char **NotUsed){\n  InitData *pData = (InitData*)pInit;\n  sqlite3 *db = pData->db;\n  int iDb = pData->iDb;\n\n  assert( argc==3 );\n  UNUSED_PARAMETER2(NotUsed, argc);\n  assert( sqlite3_mutex_held(db->mutex) );\n  DbClearProperty(db, iDb, DB_Empty);\n  if( db->mallocFailed ){\n    corruptSchema(pData, argv[0], 0);\n    return 1;\n  }\n\n  assert( iDb>=0 && iDb<db->nDb );\n  if( argv==0 ) return 0;   /* Might happen if EMPTY_RESULT_CALLBACKS are on */\n  if( argv[1]==0 ){\n    corruptSchema(pData, argv[0], 0);\n  }else if( sqlite3_strnicmp(argv[2],\"create \",7)==0 ){\n    /* Call the parser to process a CREATE TABLE, INDEX or VIEW.\n    ** But because db->init.busy is set to 1, no VDBE code is generated\n    ** or executed.  All the parser does is build the internal data\n    ** structures that describe the table, index, or view.\n    */\n    int rc;\n    u8 saved_iDb = db->init.iDb;\n    sqlite3_stmt *pStmt;\n    TESTONLY(int rcp);            /* Return code from sqlite3_prepare() */\n\n    assert( db->init.busy );\n    db->init.iDb = iDb;\n    db->init.newTnum = sqlite3Atoi(argv[1]);\n    db->init.orphanTrigger = 0;\n    TESTONLY(rcp = ) sqlite3_prepare(db, argv[2], -1, &pStmt, 0);\n    rc = db->errCode;\n    assert( (rc&0xFF)==(rcp&0xFF) );\n    db->init.iDb = saved_iDb;\n    assert( saved_iDb==0 || (db->mDbFlags & DBFLAG_Vacuum)!=0 );\n    if( SQLITE_OK!=rc ){\n      if( db->init.orphanTrigger ){\n        assert( iDb==1 );\n      }else{\n        pData->rc = rc;\n        if( rc==SQLITE_NOMEM ){\n          sqlite3OomFault(db);\n        }else if( rc!=SQLITE_INTERRUPT && (rc&0xFF)!=SQLITE_LOCKED ){\n          corruptSchema(pData, argv[0], sqlite3_errmsg(db));\n        }\n      }\n    }\n    sqlite3_finalize(pStmt);\n  }else if( argv[0]==0 || (argv[2]!=0 && argv[2][0]!=0) ){\n    corruptSchema(pData, argv[0], 0);\n  }else{\n    /* If the SQL column is blank it means this is an index that\n    ** was created to be the PRIMARY KEY or to fulfill a UNIQUE\n    ** constraint for a CREATE TABLE.  The index should have already\n    ** been created when we processed the CREATE TABLE.  All we have\n    ** to do here is record the root page number for that index.\n    */\n    Index *pIndex;\n    pIndex = sqlite3FindIndex(db, argv[0], db->aDb[iDb].zDbSName);\n    if( pIndex==0 ){\n      /* This can occur if there exists an index on a TEMP table which\n      ** has the same name as another index on a permanent index.  Since\n      ** the permanent table is hidden by the TEMP table, we can also\n      ** safely ignore the index on the permanent table.\n      */\n      /* Do Nothing */;\n    }else if( sqlite3GetInt32(argv[1], &pIndex->tnum)==0 ){\n      corruptSchema(pData, argv[0], \"invalid rootpage\");\n    }\n  }\n  return 0;\n}\n\n/*\n** Attempt to read the database schema and initialize internal\n** data structures for a single database file.  The index of the\n** database file is given by iDb.  iDb==0 is used for the main\n** database.  iDb==1 should never be used.  iDb>=2 is used for\n** auxiliary databases.  Return one of the SQLITE_ error codes to\n** indicate success or failure.\n*/\nstatic int sqlite3InitOne(sqlite3 *db, int iDb, char **pzErrMsg){\n  int rc;\n  int i;\n#ifndef SQLITE_OMIT_DEPRECATED\n  int size;\n#endif\n  Db *pDb;\n  char const *azArg[4];\n  int meta[5];\n  InitData initData;\n  const char *zMasterName;\n  int openedTransaction = 0;\n\n  assert( iDb>=0 && iDb<db->nDb );\n  assert( db->aDb[iDb].pSchema );\n  assert( sqlite3_mutex_held(db->mutex) );\n  assert( iDb==1 || sqlite3BtreeHoldsMutex(db->aDb[iDb].pBt) );\n\n  db->init.busy = 1;\n\n  /* Construct the in-memory representation schema tables (sqlite_master or\n  ** sqlite_temp_master) by invoking the parser directly.  The appropriate\n  ** table name will be inserted automatically by the parser so we can just\n  ** use the abbreviation \"x\" here.  The parser will also automatically tag\n  ** the schema table as read-only. */\n  azArg[0] = zMasterName = SCHEMA_TABLE(iDb);\n  azArg[1] = \"1\";\n  azArg[2] = \"CREATE TABLE x(type text,name text,tbl_name text,\"\n                            \"rootpage int,sql text)\";\n  azArg[3] = 0;\n  initData.db = db;\n  initData.iDb = iDb;\n  initData.rc = SQLITE_OK;\n  initData.pzErrMsg = pzErrMsg;\n  sqlite3InitCallback(&initData, 3, (char **)azArg, 0);\n  if( initData.rc ){\n    rc = initData.rc;\n    goto error_out;\n  }\n\n  /* Create a cursor to hold the database open\n  */\n  pDb = &db->aDb[iDb];\n  if( pDb->pBt==0 ){\n    assert( iDb==1 );\n    DbSetProperty(db, 1, DB_SchemaLoaded);\n    rc = SQLITE_OK;\n    goto error_out;\n  }\n\n  /* If there is not already a read-only (or read-write) transaction opened\n  ** on the b-tree database, open one now. If a transaction is opened, it \n  ** will be closed before this function returns.  */\n  sqlite3BtreeEnter(pDb->pBt);\n  if( !sqlite3BtreeIsInReadTrans(pDb->pBt) ){\n    rc = sqlite3BtreeBeginTrans(pDb->pBt, 0);\n    if( rc!=SQLITE_OK ){\n      sqlite3SetString(pzErrMsg, db, sqlite3ErrStr(rc));\n      goto initone_error_out;\n    }\n    openedTransaction = 1;\n  }\n\n  /* Get the database meta information.\n  **\n  ** Meta values are as follows:\n  **    meta[0]   Schema cookie.  Changes with each schema change.\n  **    meta[1]   File format of schema layer.\n  **    meta[2]   Size of the page cache.\n  **    meta[3]   Largest rootpage (auto/incr_vacuum mode)\n  **    meta[4]   Db text encoding. 1:UTF-8 2:UTF-16LE 3:UTF-16BE\n  **    meta[5]   User version\n  **    meta[6]   Incremental vacuum mode\n  **    meta[7]   unused\n  **    meta[8]   unused\n  **    meta[9]   unused\n  **\n  ** Note: The #defined SQLITE_UTF* symbols in sqliteInt.h correspond to\n  ** the possible values of meta[4].\n  */\n  for(i=0; i<ArraySize(meta); i++){\n    sqlite3BtreeGetMeta(pDb->pBt, i+1, (u32 *)&meta[i]);\n  }\n  pDb->pSchema->schema_cookie = meta[BTREE_SCHEMA_VERSION-1];\n\n  /* If opening a non-empty database, check the text encoding. For the\n  ** main database, set sqlite3.enc to the encoding of the main database.\n  ** For an attached db, it is an error if the encoding is not the same\n  ** as sqlite3.enc.\n  */\n  if( meta[BTREE_TEXT_ENCODING-1] ){  /* text encoding */\n    if( iDb==0 ){\n#ifndef SQLITE_OMIT_UTF16\n      u8 encoding;\n      /* If opening the main database, set ENC(db). */\n      encoding = (u8)meta[BTREE_TEXT_ENCODING-1] & 3;\n      if( encoding==0 ) encoding = SQLITE_UTF8;\n      ENC(db) = encoding;\n#else\n      ENC(db) = SQLITE_UTF8;\n#endif\n    }else{\n      /* If opening an attached database, the encoding much match ENC(db) */\n      if( meta[BTREE_TEXT_ENCODING-1]!=ENC(db) ){\n        sqlite3SetString(pzErrMsg, db, \"attached databases must use the same\"\n            \" text encoding as main database\");\n        rc = SQLITE_ERROR;\n        goto initone_error_out;\n      }\n    }\n  }else{\n    DbSetProperty(db, iDb, DB_Empty);\n  }\n  pDb->pSchema->enc = ENC(db);\n\n  if( pDb->pSchema->cache_size==0 ){\n#ifndef SQLITE_OMIT_DEPRECATED\n    size = sqlite3AbsInt32(meta[BTREE_DEFAULT_CACHE_SIZE-1]);\n    if( size==0 ){ size = SQLITE_DEFAULT_CACHE_SIZE; }\n    pDb->pSchema->cache_size = size;\n#else\n    pDb->pSchema->cache_size = SQLITE_DEFAULT_CACHE_SIZE;\n#endif\n    sqlite3BtreeSetCacheSize(pDb->pBt, pDb->pSchema->cache_size);\n  }\n\n  /*\n  ** file_format==1    Version 3.0.0.\n  ** file_format==2    Version 3.1.3.  // ALTER TABLE ADD COLUMN\n  ** file_format==3    Version 3.1.4.  // ditto but with non-NULL defaults\n  ** file_format==4    Version 3.3.0.  // DESC indices.  Boolean constants\n  */\n  pDb->pSchema->file_format = (u8)meta[BTREE_FILE_FORMAT-1];\n  if( pDb->pSchema->file_format==0 ){\n    pDb->pSchema->file_format = 1;\n  }\n  if( pDb->pSchema->file_format>SQLITE_MAX_FILE_FORMAT ){\n    sqlite3SetString(pzErrMsg, db, \"unsupported file format\");\n    rc = SQLITE_ERROR;\n    goto initone_error_out;\n  }\n\n  /* Ticket #2804:  When we open a database in the newer file format,\n  ** clear the legacy_file_format pragma flag so that a VACUUM will\n  ** not downgrade the database and thus invalidate any descending\n  ** indices that the user might have created.\n  */\n  if( iDb==0 && meta[BTREE_FILE_FORMAT-1]>=4 ){\n    db->flags &= ~SQLITE_LegacyFileFmt;\n  }\n\n  /* Read the schema information out of the schema tables\n  */\n  assert( db->init.busy );\n  {\n    char *zSql;\n    zSql = sqlite3MPrintf(db, \n        \"SELECT name, rootpage, sql FROM \\\"%w\\\".%s ORDER BY rowid\",\n        db->aDb[iDb].zDbSName, zMasterName);\n#ifndef SQLITE_OMIT_AUTHORIZATION\n    {\n      sqlite3_xauth xAuth;\n      xAuth = db->xAuth;\n      db->xAuth = 0;\n#endif\n      rc = sqlite3_exec(db, zSql, sqlite3InitCallback, &initData, 0);\n#ifndef SQLITE_OMIT_AUTHORIZATION\n      db->xAuth = xAuth;\n    }\n#endif\n    if( rc==SQLITE_OK ) rc = initData.rc;\n    sqlite3DbFree(db, zSql);\n#ifndef SQLITE_OMIT_ANALYZE\n    if( rc==SQLITE_OK ){\n      sqlite3AnalysisLoad(db, iDb);\n    }\n#endif\n  }\n  if( db->mallocFailed ){\n    rc = SQLITE_NOMEM_BKPT;\n    sqlite3ResetAllSchemasOfConnection(db);\n  }\n  if( rc==SQLITE_OK || (db->flags&SQLITE_WriteSchema)){\n    /* Black magic: If the SQLITE_WriteSchema flag is set, then consider\n    ** the schema loaded, even if errors occurred. In this situation the \n    ** current sqlite3_prepare() operation will fail, but the following one\n    ** will attempt to compile the supplied statement against whatever subset\n    ** of the schema was loaded before the error occurred. The primary\n    ** purpose of this is to allow access to the sqlite_master table\n    ** even when its contents have been corrupted.\n    */\n    DbSetProperty(db, iDb, DB_SchemaLoaded);\n    rc = SQLITE_OK;\n  }\n\n  /* Jump here for an error that occurs after successfully allocating\n  ** curMain and calling sqlite3BtreeEnter(). For an error that occurs\n  ** before that point, jump to error_out.\n  */\ninitone_error_out:\n  if( openedTransaction ){\n    sqlite3BtreeCommit(pDb->pBt);\n  }\n  sqlite3BtreeLeave(pDb->pBt);\n\nerror_out:\n  if( rc ){\n    if( rc==SQLITE_NOMEM || rc==SQLITE_IOERR_NOMEM ){\n      sqlite3OomFault(db);\n    }\n    sqlite3ResetOneSchema(db, iDb);\n  }\n  db->init.busy = 0;\n  return rc;\n}\n\n/*\n** Initialize all database files - the main database file, the file\n** used to store temporary tables, and any additional database files\n** created using ATTACH statements.  Return a success code.  If an\n** error occurs, write an error message into *pzErrMsg.\n**\n** After a database is initialized, the DB_SchemaLoaded bit is set\n** bit is set in the flags field of the Db structure. If the database\n** file was of zero-length, then the DB_Empty flag is also set.\n*/\nSQLITE_PRIVATE int sqlite3Init(sqlite3 *db, char **pzErrMsg){\n  int i, rc;\n  int commit_internal = !(db->mDbFlags&DBFLAG_SchemaChange);\n  \n  assert( sqlite3_mutex_held(db->mutex) );\n  assert( sqlite3BtreeHoldsMutex(db->aDb[0].pBt) );\n  assert( db->init.busy==0 );\n  ENC(db) = SCHEMA_ENC(db);\n  assert( db->nDb>0 );\n  /* Do the main schema first */\n  if( !DbHasProperty(db, 0, DB_SchemaLoaded) ){\n    rc = sqlite3InitOne(db, 0, pzErrMsg);\n    if( rc ) return rc;\n  }\n  /* All other schemas after the main schema. The \"temp\" schema must be last */\n  for(i=db->nDb-1; i>0; i--){\n    if( !DbHasProperty(db, i, DB_SchemaLoaded) ){\n      rc = sqlite3InitOne(db, i, pzErrMsg);\n      if( rc ) return rc;\n    }\n  }\n  if( commit_internal ){\n    sqlite3CommitInternalChanges(db);\n  }\n  return SQLITE_OK;\n}\n\n/*\n** This routine is a no-op if the database schema is already initialized.\n** Otherwise, the schema is loaded. An error code is returned.\n*/\nSQLITE_PRIVATE int sqlite3ReadSchema(Parse *pParse){\n  int rc = SQLITE_OK;\n  sqlite3 *db = pParse->db;\n  assert( sqlite3_mutex_held(db->mutex) );\n  if( !db->init.busy ){\n    rc = sqlite3Init(db, &pParse->zErrMsg);\n  }\n  if( rc!=SQLITE_OK ){\n    pParse->rc = rc;\n    pParse->nErr++;\n  }\n  return rc;\n}\n\n\n/*\n** Check schema cookies in all databases.  If any cookie is out\n** of date set pParse->rc to SQLITE_SCHEMA.  If all schema cookies\n** make no changes to pParse->rc.\n*/\nstatic void schemaIsValid(Parse *pParse){\n  sqlite3 *db = pParse->db;\n  int iDb;\n  int rc;\n  int cookie;\n\n  assert( pParse->checkSchema );\n  assert( sqlite3_mutex_held(db->mutex) );\n  for(iDb=0; iDb<db->nDb; iDb++){\n    int openedTransaction = 0;         /* True if a transaction is opened */\n    Btree *pBt = db->aDb[iDb].pBt;     /* Btree database to read cookie from */\n    if( pBt==0 ) continue;\n\n    /* If there is not already a read-only (or read-write) transaction opened\n    ** on the b-tree database, open one now. If a transaction is opened, it \n    ** will be closed immediately after reading the meta-value. */\n    if( !sqlite3BtreeIsInReadTrans(pBt) ){\n      rc = sqlite3BtreeBeginTrans(pBt, 0);\n      if( rc==SQLITE_NOMEM || rc==SQLITE_IOERR_NOMEM ){\n        sqlite3OomFault(db);\n      }\n      if( rc!=SQLITE_OK ) return;\n      openedTransaction = 1;\n    }\n\n    /* Read the schema cookie from the database. If it does not match the \n    ** value stored as part of the in-memory schema representation,\n    ** set Parse.rc to SQLITE_SCHEMA. */\n    sqlite3BtreeGetMeta(pBt, BTREE_SCHEMA_VERSION, (u32 *)&cookie);\n    assert( sqlite3SchemaMutexHeld(db, iDb, 0) );\n    if( cookie!=db->aDb[iDb].pSchema->schema_cookie ){\n      sqlite3ResetOneSchema(db, iDb);\n      pParse->rc = SQLITE_SCHEMA;\n    }\n\n    /* Close the transaction, if one was opened. */\n    if( openedTransaction ){\n      sqlite3BtreeCommit(pBt);\n    }\n  }\n}\n\n/*\n** Convert a schema pointer into the iDb index that indicates\n** which database file in db->aDb[] the schema refers to.\n**\n** If the same database is attached more than once, the first\n** attached database is returned.\n*/\nSQLITE_PRIVATE int sqlite3SchemaToIndex(sqlite3 *db, Schema *pSchema){\n  int i = -1000000;\n\n  /* If pSchema is NULL, then return -1000000. This happens when code in \n  ** expr.c is trying to resolve a reference to a transient table (i.e. one\n  ** created by a sub-select). In this case the return value of this \n  ** function should never be used.\n  **\n  ** We return -1000000 instead of the more usual -1 simply because using\n  ** -1000000 as the incorrect index into db->aDb[] is much \n  ** more likely to cause a segfault than -1 (of course there are assert()\n  ** statements too, but it never hurts to play the odds).\n  */\n  assert( sqlite3_mutex_held(db->mutex) );\n  if( pSchema ){\n    for(i=0; 1; i++){\n      assert( i<db->nDb );\n      if( db->aDb[i].pSchema==pSchema ){\n        break;\n      }\n    }\n    assert( i>=0 && i<db->nDb );\n  }\n  return i;\n}\n\n/*\n** Free all memory allocations in the pParse object\n*/\nSQLITE_PRIVATE void sqlite3ParserReset(Parse *pParse){\n  sqlite3 *db = pParse->db;\n  sqlite3DbFree(db, pParse->aLabel);\n  sqlite3ExprListDelete(db, pParse->pConstExpr);\n  if( db ){\n    assert( db->lookaside.bDisable >= pParse->disableLookaside );\n    db->lookaside.bDisable -= pParse->disableLookaside;\n  }\n  pParse->disableLookaside = 0;\n}\n\n/*\n** Compile the UTF-8 encoded SQL statement zSql into a statement handle.\n*/\nstatic int sqlite3Prepare(\n  sqlite3 *db,              /* Database handle. */\n  const char *zSql,         /* UTF-8 encoded SQL statement. */\n  int nBytes,               /* Length of zSql in bytes. */\n  u32 prepFlags,            /* Zero or more SQLITE_PREPARE_* flags */\n  Vdbe *pReprepare,         /* VM being reprepared */\n  sqlite3_stmt **ppStmt,    /* OUT: A pointer to the prepared statement */\n  const char **pzTail       /* OUT: End of parsed string */\n){\n  char *zErrMsg = 0;        /* Error message */\n  int rc = SQLITE_OK;       /* Result code */\n  int i;                    /* Loop counter */\n  Parse sParse;             /* Parsing context */\n\n  memset(&sParse, 0, PARSE_HDR_SZ);\n  memset(PARSE_TAIL(&sParse), 0, PARSE_TAIL_SZ);\n  sParse.pReprepare = pReprepare;\n  assert( ppStmt && *ppStmt==0 );\n  /* assert( !db->mallocFailed ); // not true with SQLITE_USE_ALLOCA */\n  assert( sqlite3_mutex_held(db->mutex) );\n\n  /* For a long-term use prepared statement avoid the use of\n  ** lookaside memory.\n  */\n  if( prepFlags & SQLITE_PREPARE_PERSISTENT ){\n    sParse.disableLookaside++;\n    db->lookaside.bDisable++;\n  }\n\n  /* Check to verify that it is possible to get a read lock on all\n  ** database schemas.  The inability to get a read lock indicates that\n  ** some other database connection is holding a write-lock, which in\n  ** turn means that the other connection has made uncommitted changes\n  ** to the schema.\n  **\n  ** Were we to proceed and prepare the statement against the uncommitted\n  ** schema changes and if those schema changes are subsequently rolled\n  ** back and different changes are made in their place, then when this\n  ** prepared statement goes to run the schema cookie would fail to detect\n  ** the schema change.  Disaster would follow.\n  **\n  ** This thread is currently holding mutexes on all Btrees (because\n  ** of the sqlite3BtreeEnterAll() in sqlite3LockAndPrepare()) so it\n  ** is not possible for another thread to start a new schema change\n  ** while this routine is running.  Hence, we do not need to hold \n  ** locks on the schema, we just need to make sure nobody else is \n  ** holding them.\n  **\n  ** Note that setting READ_UNCOMMITTED overrides most lock detection,\n  ** but it does *not* override schema lock detection, so this all still\n  ** works even if READ_UNCOMMITTED is set.\n  */\n  for(i=0; i<db->nDb; i++) {\n    Btree *pBt = db->aDb[i].pBt;\n    if( pBt ){\n      assert( sqlite3BtreeHoldsMutex(pBt) );\n      rc = sqlite3BtreeSchemaLocked(pBt);\n      if( rc ){\n        const char *zDb = db->aDb[i].zDbSName;\n        sqlite3ErrorWithMsg(db, rc, \"database schema is locked: %s\", zDb);\n        testcase( db->flags & SQLITE_ReadUncommit );\n        goto end_prepare;\n      }\n    }\n  }\n\n  sqlite3VtabUnlockList(db);\n\n  sParse.db = db;\n  if( nBytes>=0 && (nBytes==0 || zSql[nBytes-1]!=0) ){\n    char *zSqlCopy;\n    int mxLen = db->aLimit[SQLITE_LIMIT_SQL_LENGTH];\n    testcase( nBytes==mxLen );\n    testcase( nBytes==mxLen+1 );\n    if( nBytes>mxLen ){\n      sqlite3ErrorWithMsg(db, SQLITE_TOOBIG, \"statement too long\");\n      rc = sqlite3ApiExit(db, SQLITE_TOOBIG);\n      goto end_prepare;\n    }\n    zSqlCopy = sqlite3DbStrNDup(db, zSql, nBytes);\n    if( zSqlCopy ){\n      sqlite3RunParser(&sParse, zSqlCopy, &zErrMsg);\n      sParse.zTail = &zSql[sParse.zTail-zSqlCopy];\n      sqlite3DbFree(db, zSqlCopy);\n    }else{\n      sParse.zTail = &zSql[nBytes];\n    }\n  }else{\n    sqlite3RunParser(&sParse, zSql, &zErrMsg);\n  }\n  assert( 0==sParse.nQueryLoop );\n\n  if( sParse.rc==SQLITE_DONE ) sParse.rc = SQLITE_OK;\n  if( sParse.checkSchema ){\n    schemaIsValid(&sParse);\n  }\n  if( db->mallocFailed ){\n    sParse.rc = SQLITE_NOMEM_BKPT;\n  }\n  if( pzTail ){\n    *pzTail = sParse.zTail;\n  }\n  rc = sParse.rc;\n\n#ifndef SQLITE_OMIT_EXPLAIN\n  if( rc==SQLITE_OK && sParse.pVdbe && sParse.explain ){\n    static const char * const azColName[] = {\n       \"addr\", \"opcode\", \"p1\", \"p2\", \"p3\", \"p4\", \"p5\", \"comment\",\n       \"selectid\", \"order\", \"from\", \"detail\"\n    };\n    int iFirst, mx;\n    if( sParse.explain==2 ){\n      sqlite3VdbeSetNumCols(sParse.pVdbe, 4);\n      iFirst = 8;\n      mx = 12;\n    }else{\n      sqlite3VdbeSetNumCols(sParse.pVdbe, 8);\n      iFirst = 0;\n      mx = 8;\n    }\n    for(i=iFirst; i<mx; i++){\n      sqlite3VdbeSetColName(sParse.pVdbe, i-iFirst, COLNAME_NAME,\n                            azColName[i], SQLITE_STATIC);\n    }\n  }\n#endif\n\n  if( db->init.busy==0 ){\n    sqlite3VdbeSetSql(sParse.pVdbe, zSql, (int)(sParse.zTail-zSql), prepFlags);\n  }\n  if( sParse.pVdbe && (rc!=SQLITE_OK || db->mallocFailed) ){\n    sqlite3VdbeFinalize(sParse.pVdbe);\n    assert(!(*ppStmt));\n  }else{\n    *ppStmt = (sqlite3_stmt*)sParse.pVdbe;\n  }\n\n  if( zErrMsg ){\n    sqlite3ErrorWithMsg(db, rc, \"%s\", zErrMsg);\n    sqlite3DbFree(db, zErrMsg);\n  }else{\n    sqlite3Error(db, rc);\n  }\n\n  /* Delete any TriggerPrg structures allocated while parsing this statement. */\n  while( sParse.pTriggerPrg ){\n    TriggerPrg *pT = sParse.pTriggerPrg;\n    sParse.pTriggerPrg = pT->pNext;\n    sqlite3DbFree(db, pT);\n  }\n\nend_prepare:\n\n  sqlite3ParserReset(&sParse);\n  return rc;\n}\nstatic int sqlite3LockAndPrepare(\n  sqlite3 *db,              /* Database handle. */\n  const char *zSql,         /* UTF-8 encoded SQL statement. */\n  int nBytes,               /* Length of zSql in bytes. */\n  u32 prepFlags,            /* Zero or more SQLITE_PREPARE_* flags */\n  Vdbe *pOld,               /* VM being reprepared */\n  sqlite3_stmt **ppStmt,    /* OUT: A pointer to the prepared statement */\n  const char **pzTail       /* OUT: End of parsed string */\n){\n  int rc;\n  int cnt = 0;\n\n#ifdef SQLITE_ENABLE_API_ARMOR\n  if( ppStmt==0 ) return SQLITE_MISUSE_BKPT;\n#endif\n  *ppStmt = 0;\n  if( !sqlite3SafetyCheckOk(db)||zSql==0 ){\n    return SQLITE_MISUSE_BKPT;\n  }\n  sqlite3_mutex_enter(db->mutex);\n  sqlite3BtreeEnterAll(db);\n  do{\n    /* Make multiple attempts to compile the SQL, until it either succeeds\n    ** or encounters a permanent error.  A schema problem after one schema\n    ** reset is considered a permanent error. */\n    rc = sqlite3Prepare(db, zSql, nBytes, prepFlags, pOld, ppStmt, pzTail);\n    assert( rc==SQLITE_OK || *ppStmt==0 );\n  }while( rc==SQLITE_ERROR_RETRY\n       || (rc==SQLITE_SCHEMA && (sqlite3ResetOneSchema(db,-1), cnt++)==0) );\n  sqlite3BtreeLeaveAll(db);\n  rc = sqlite3ApiExit(db, rc);\n  assert( (rc&db->errMask)==rc );\n  sqlite3_mutex_leave(db->mutex);\n  return rc;\n}\n\n/*\n** Rerun the compilation of a statement after a schema change.\n**\n** If the statement is successfully recompiled, return SQLITE_OK. Otherwise,\n** if the statement cannot be recompiled because another connection has\n** locked the sqlite3_master table, return SQLITE_LOCKED. If any other error\n** occurs, return SQLITE_SCHEMA.\n*/\nSQLITE_PRIVATE int sqlite3Reprepare(Vdbe *p){\n  int rc;\n  sqlite3_stmt *pNew;\n  const char *zSql;\n  sqlite3 *db;\n  u8 prepFlags;\n\n  assert( sqlite3_mutex_held(sqlite3VdbeDb(p)->mutex) );\n  zSql = sqlite3_sql((sqlite3_stmt *)p);\n  assert( zSql!=0 );  /* Reprepare only called for prepare_v2() statements */\n  db = sqlite3VdbeDb(p);\n  assert( sqlite3_mutex_held(db->mutex) );\n  prepFlags = sqlite3VdbePrepareFlags(p);\n  rc = sqlite3LockAndPrepare(db, zSql, -1, prepFlags, p, &pNew, 0);\n  if( rc ){\n    if( rc==SQLITE_NOMEM ){\n      sqlite3OomFault(db);\n    }\n    assert( pNew==0 );\n    return rc;\n  }else{\n    assert( pNew!=0 );\n  }\n  sqlite3VdbeSwap((Vdbe*)pNew, p);\n  sqlite3TransferBindings(pNew, (sqlite3_stmt*)p);\n  sqlite3VdbeResetStepResult((Vdbe*)pNew);\n  sqlite3VdbeFinalize((Vdbe*)pNew);\n  return SQLITE_OK;\n}\n\n\n/*\n** Two versions of the official API.  Legacy and new use.  In the legacy\n** version, the original SQL text is not saved in the prepared statement\n** and so if a schema change occurs, SQLITE_SCHEMA is returned by\n** sqlite3_step().  In the new version, the original SQL text is retained\n** and the statement is automatically recompiled if an schema change\n** occurs.\n*/\nSQLITE_API int sqlite3_prepare(\n  sqlite3 *db,              /* Database handle. */\n  const char *zSql,         /* UTF-8 encoded SQL statement. */\n  int nBytes,               /* Length of zSql in bytes. */\n  sqlite3_stmt **ppStmt,    /* OUT: A pointer to the prepared statement */\n  const char **pzTail       /* OUT: End of parsed string */\n){\n  int rc;\n  rc = sqlite3LockAndPrepare(db,zSql,nBytes,0,0,ppStmt,pzTail);\n  assert( rc==SQLITE_OK || ppStmt==0 || *ppStmt==0 );  /* VERIFY: F13021 */\n  return rc;\n}\nSQLITE_API int sqlite3_prepare_v2(\n  sqlite3 *db,              /* Database handle. */\n  const char *zSql,         /* UTF-8 encoded SQL statement. */\n  int nBytes,               /* Length of zSql in bytes. */\n  sqlite3_stmt **ppStmt,    /* OUT: A pointer to the prepared statement */\n  const char **pzTail       /* OUT: End of parsed string */\n){\n  int rc;\n  /* EVIDENCE-OF: R-37923-12173 The sqlite3_prepare_v2() interface works\n  ** exactly the same as sqlite3_prepare_v3() with a zero prepFlags\n  ** parameter.\n  **\n  ** Proof in that the 5th parameter to sqlite3LockAndPrepare is 0 */\n  rc = sqlite3LockAndPrepare(db,zSql,nBytes,SQLITE_PREPARE_SAVESQL,0,\n                             ppStmt,pzTail);\n  assert( rc==SQLITE_OK || ppStmt==0 || *ppStmt==0 );\n  return rc;\n}\nSQLITE_API int sqlite3_prepare_v3(\n  sqlite3 *db,              /* Database handle. */\n  const char *zSql,         /* UTF-8 encoded SQL statement. */\n  int nBytes,               /* Length of zSql in bytes. */\n  unsigned int prepFlags,   /* Zero or more SQLITE_PREPARE_* flags */\n  sqlite3_stmt **ppStmt,    /* OUT: A pointer to the prepared statement */\n  const char **pzTail       /* OUT: End of parsed string */\n){\n  int rc;\n  /* EVIDENCE-OF: R-56861-42673 sqlite3_prepare_v3() differs from\n  ** sqlite3_prepare_v2() only in having the extra prepFlags parameter,\n  ** which is a bit array consisting of zero or more of the\n  ** SQLITE_PREPARE_* flags.\n  **\n  ** Proof by comparison to the implementation of sqlite3_prepare_v2()\n  ** directly above. */\n  rc = sqlite3LockAndPrepare(db,zSql,nBytes,\n                 SQLITE_PREPARE_SAVESQL|(prepFlags&SQLITE_PREPARE_MASK),\n                 0,ppStmt,pzTail);\n  assert( rc==SQLITE_OK || ppStmt==0 || *ppStmt==0 );\n  return rc;\n}\n\n\n#ifndef SQLITE_OMIT_UTF16\n/*\n** Compile the UTF-16 encoded SQL statement zSql into a statement handle.\n*/\nstatic int sqlite3Prepare16(\n  sqlite3 *db,              /* Database handle. */ \n  const void *zSql,         /* UTF-16 encoded SQL statement. */\n  int nBytes,               /* Length of zSql in bytes. */\n  u32 prepFlags,            /* Zero or more SQLITE_PREPARE_* flags */\n  sqlite3_stmt **ppStmt,    /* OUT: A pointer to the prepared statement */\n  const void **pzTail       /* OUT: End of parsed string */\n){\n  /* This function currently works by first transforming the UTF-16\n  ** encoded string to UTF-8, then invoking sqlite3_prepare(). The\n  ** tricky bit is figuring out the pointer to return in *pzTail.\n  */\n  char *zSql8;\n  const char *zTail8 = 0;\n  int rc = SQLITE_OK;\n\n#ifdef SQLITE_ENABLE_API_ARMOR\n  if( ppStmt==0 ) return SQLITE_MISUSE_BKPT;\n#endif\n  *ppStmt = 0;\n  if( !sqlite3SafetyCheckOk(db)||zSql==0 ){\n    return SQLITE_MISUSE_BKPT;\n  }\n  if( nBytes>=0 ){\n    int sz;\n    const char *z = (const char*)zSql;\n    for(sz=0; sz<nBytes && (z[sz]!=0 || z[sz+1]!=0); sz += 2){}\n    nBytes = sz;\n  }\n  sqlite3_mutex_enter(db->mutex);\n  zSql8 = sqlite3Utf16to8(db, zSql, nBytes, SQLITE_UTF16NATIVE);\n  if( zSql8 ){\n    rc = sqlite3LockAndPrepare(db, zSql8, -1, prepFlags, 0, ppStmt, &zTail8);\n  }\n\n  if( zTail8 && pzTail ){\n    /* If sqlite3_prepare returns a tail pointer, we calculate the\n    ** equivalent pointer into the UTF-16 string by counting the unicode\n    ** characters between zSql8 and zTail8, and then returning a pointer\n    ** the same number of characters into the UTF-16 string.\n    */\n    int chars_parsed = sqlite3Utf8CharLen(zSql8, (int)(zTail8-zSql8));\n    *pzTail = (u8 *)zSql + sqlite3Utf16ByteLen(zSql, chars_parsed);\n  }\n  sqlite3DbFree(db, zSql8); \n  rc = sqlite3ApiExit(db, rc);\n  sqlite3_mutex_leave(db->mutex);\n  return rc;\n}\n\n/*\n** Two versions of the official API.  Legacy and new use.  In the legacy\n** version, the original SQL text is not saved in the prepared statement\n** and so if a schema change occurs, SQLITE_SCHEMA is returned by\n** sqlite3_step().  In the new version, the original SQL text is retained\n** and the statement is automatically recompiled if an schema change\n** occurs.\n*/\nSQLITE_API int sqlite3_prepare16(\n  sqlite3 *db,              /* Database handle. */ \n  const void *zSql,         /* UTF-16 encoded SQL statement. */\n  int nBytes,               /* Length of zSql in bytes. */\n  sqlite3_stmt **ppStmt,    /* OUT: A pointer to the prepared statement */\n  const void **pzTail       /* OUT: End of parsed string */\n){\n  int rc;\n  rc = sqlite3Prepare16(db,zSql,nBytes,0,ppStmt,pzTail);\n  assert( rc==SQLITE_OK || ppStmt==0 || *ppStmt==0 );  /* VERIFY: F13021 */\n  return rc;\n}\nSQLITE_API int sqlite3_prepare16_v2(\n  sqlite3 *db,              /* Database handle. */ \n  const void *zSql,         /* UTF-16 encoded SQL statement. */\n  int nBytes,               /* Length of zSql in bytes. */\n  sqlite3_stmt **ppStmt,    /* OUT: A pointer to the prepared statement */\n  const void **pzTail       /* OUT: End of parsed string */\n){\n  int rc;\n  rc = sqlite3Prepare16(db,zSql,nBytes,SQLITE_PREPARE_SAVESQL,ppStmt,pzTail);\n  assert( rc==SQLITE_OK || ppStmt==0 || *ppStmt==0 );  /* VERIFY: F13021 */\n  return rc;\n}\nSQLITE_API int sqlite3_prepare16_v3(\n  sqlite3 *db,              /* Database handle. */ \n  const void *zSql,         /* UTF-16 encoded SQL statement. */\n  int nBytes,               /* Length of zSql in bytes. */\n  unsigned int prepFlags,   /* Zero or more SQLITE_PREPARE_* flags */\n  sqlite3_stmt **ppStmt,    /* OUT: A pointer to the prepared statement */\n  const void **pzTail       /* OUT: End of parsed string */\n){\n  int rc;\n  rc = sqlite3Prepare16(db,zSql,nBytes,\n         SQLITE_PREPARE_SAVESQL|(prepFlags&SQLITE_PREPARE_MASK),\n         ppStmt,pzTail);\n  assert( rc==SQLITE_OK || ppStmt==0 || *ppStmt==0 );  /* VERIFY: F13021 */\n  return rc;\n}\n\n#endif /* SQLITE_OMIT_UTF16 */\n\n/************** End of prepare.c *********************************************/\n/************** Begin file select.c ******************************************/\n/*\n** 2001 September 15\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n*************************************************************************\n** This file contains C code routines that are called by the parser\n** to handle SELECT statements in SQLite.\n*/\n/* #include \"sqliteInt.h\" */\n\n/*\n** Trace output macros\n*/\n#if SELECTTRACE_ENABLED\n/***/ int sqlite3SelectTrace = 0;\n# define SELECTTRACE(K,P,S,X)  \\\n  if(sqlite3SelectTrace&(K))   \\\n    sqlite3DebugPrintf(\"%*s%s.%p: \",(P)->nSelectIndent*2-2,\"\",\\\n        (S)->zSelName,(S)),\\\n    sqlite3DebugPrintf X\n#else\n# define SELECTTRACE(K,P,S,X)\n#endif\n\n\n/*\n** An instance of the following object is used to record information about\n** how to process the DISTINCT keyword, to simplify passing that information\n** into the selectInnerLoop() routine.\n*/\ntypedef struct DistinctCtx DistinctCtx;\nstruct DistinctCtx {\n  u8 isTnct;      /* True if the DISTINCT keyword is present */\n  u8 eTnctType;   /* One of the WHERE_DISTINCT_* operators */\n  int tabTnct;    /* Ephemeral table used for DISTINCT processing */\n  int addrTnct;   /* Address of OP_OpenEphemeral opcode for tabTnct */\n};\n\n/*\n** An instance of the following object is used to record information about\n** the ORDER BY (or GROUP BY) clause of query is being coded.\n*/\ntypedef struct SortCtx SortCtx;\nstruct SortCtx {\n  ExprList *pOrderBy;   /* The ORDER BY (or GROUP BY clause) */\n  int nOBSat;           /* Number of ORDER BY terms satisfied by indices */\n  int iECursor;         /* Cursor number for the sorter */\n  int regReturn;        /* Register holding block-output return address */\n  int labelBkOut;       /* Start label for the block-output subroutine */\n  int addrSortIndex;    /* Address of the OP_SorterOpen or OP_OpenEphemeral */\n  int labelDone;        /* Jump here when done, ex: LIMIT reached */\n  u8 sortFlags;         /* Zero or more SORTFLAG_* bits */\n  u8 bOrderedInnerLoop; /* ORDER BY correctly sorts the inner loop */\n};\n#define SORTFLAG_UseSorter  0x01   /* Use SorterOpen instead of OpenEphemeral */\n\n/*\n** Delete all the content of a Select structure.  Deallocate the structure\n** itself only if bFree is true.\n*/\nstatic void clearSelect(sqlite3 *db, Select *p, int bFree){\n  while( p ){\n    Select *pPrior = p->pPrior;\n    sqlite3ExprListDelete(db, p->pEList);\n    sqlite3SrcListDelete(db, p->pSrc);\n    sqlite3ExprDelete(db, p->pWhere);\n    sqlite3ExprListDelete(db, p->pGroupBy);\n    sqlite3ExprDelete(db, p->pHaving);\n    sqlite3ExprListDelete(db, p->pOrderBy);\n    sqlite3ExprDelete(db, p->pLimit);\n    if( OK_IF_ALWAYS_TRUE(p->pWith) ) sqlite3WithDelete(db, p->pWith);\n    if( bFree ) sqlite3DbFreeNN(db, p);\n    p = pPrior;\n    bFree = 1;\n  }\n}\n\n/*\n** Initialize a SelectDest structure.\n*/\nSQLITE_PRIVATE void sqlite3SelectDestInit(SelectDest *pDest, int eDest, int iParm){\n  pDest->eDest = (u8)eDest;\n  pDest->iSDParm = iParm;\n  pDest->zAffSdst = 0;\n  pDest->iSdst = 0;\n  pDest->nSdst = 0;\n}\n\n\n/*\n** Allocate a new Select structure and return a pointer to that\n** structure.\n*/\nSQLITE_PRIVATE Select *sqlite3SelectNew(\n  Parse *pParse,        /* Parsing context */\n  ExprList *pEList,     /* which columns to include in the result */\n  SrcList *pSrc,        /* the FROM clause -- which tables to scan */\n  Expr *pWhere,         /* the WHERE clause */\n  ExprList *pGroupBy,   /* the GROUP BY clause */\n  Expr *pHaving,        /* the HAVING clause */\n  ExprList *pOrderBy,   /* the ORDER BY clause */\n  u32 selFlags,         /* Flag parameters, such as SF_Distinct */\n  Expr *pLimit          /* LIMIT value.  NULL means not used */\n){\n  Select *pNew;\n  Select standin;\n  pNew = sqlite3DbMallocRawNN(pParse->db, sizeof(*pNew) );\n  if( pNew==0 ){\n    assert( pParse->db->mallocFailed );\n    pNew = &standin;\n  }\n  if( pEList==0 ){\n    pEList = sqlite3ExprListAppend(pParse, 0,\n                                   sqlite3Expr(pParse->db,TK_ASTERISK,0));\n  }\n  pNew->pEList = pEList;\n  pNew->op = TK_SELECT;\n  pNew->selFlags = selFlags;\n  pNew->iLimit = 0;\n  pNew->iOffset = 0;\n#if SELECTTRACE_ENABLED\n  pNew->zSelName[0] = 0;\n#endif\n  pNew->addrOpenEphm[0] = -1;\n  pNew->addrOpenEphm[1] = -1;\n  pNew->nSelectRow = 0;\n  if( pSrc==0 ) pSrc = sqlite3DbMallocZero(pParse->db, sizeof(*pSrc));\n  pNew->pSrc = pSrc;\n  pNew->pWhere = pWhere;\n  pNew->pGroupBy = pGroupBy;\n  pNew->pHaving = pHaving;\n  pNew->pOrderBy = pOrderBy;\n  pNew->pPrior = 0;\n  pNew->pNext = 0;\n  pNew->pLimit = pLimit;\n  pNew->pWith = 0;\n  if( pParse->db->mallocFailed ) {\n    clearSelect(pParse->db, pNew, pNew!=&standin);\n    pNew = 0;\n  }else{\n    assert( pNew->pSrc!=0 || pParse->nErr>0 );\n  }\n  assert( pNew!=&standin );\n  return pNew;\n}\n\n#if SELECTTRACE_ENABLED\n/*\n** Set the name of a Select object\n*/\nSQLITE_PRIVATE void sqlite3SelectSetName(Select *p, const char *zName){\n  if( p && zName ){\n    sqlite3_snprintf(sizeof(p->zSelName), p->zSelName, \"%s\", zName);\n  }\n}\n#endif\n\n\n/*\n** Delete the given Select structure and all of its substructures.\n*/\nSQLITE_PRIVATE void sqlite3SelectDelete(sqlite3 *db, Select *p){\n  if( OK_IF_ALWAYS_TRUE(p) ) clearSelect(db, p, 1);\n}\n\n/*\n** Return a pointer to the right-most SELECT statement in a compound.\n*/\nstatic Select *findRightmost(Select *p){\n  while( p->pNext ) p = p->pNext;\n  return p;\n}\n\n/*\n** Given 1 to 3 identifiers preceding the JOIN keyword, determine the\n** type of join.  Return an integer constant that expresses that type\n** in terms of the following bit values:\n**\n**     JT_INNER\n**     JT_CROSS\n**     JT_OUTER\n**     JT_NATURAL\n**     JT_LEFT\n**     JT_RIGHT\n**\n** A full outer join is the combination of JT_LEFT and JT_RIGHT.\n**\n** If an illegal or unsupported join type is seen, then still return\n** a join type, but put an error in the pParse structure.\n*/\nSQLITE_PRIVATE int sqlite3JoinType(Parse *pParse, Token *pA, Token *pB, Token *pC){\n  int jointype = 0;\n  Token *apAll[3];\n  Token *p;\n                             /*   0123456789 123456789 123456789 123 */\n  static const char zKeyText[] = \"naturaleftouterightfullinnercross\";\n  static const struct {\n    u8 i;        /* Beginning of keyword text in zKeyText[] */\n    u8 nChar;    /* Length of the keyword in characters */\n    u8 code;     /* Join type mask */\n  } aKeyword[] = {\n    /* natural */ { 0,  7, JT_NATURAL                },\n    /* left    */ { 6,  4, JT_LEFT|JT_OUTER          },\n    /* outer   */ { 10, 5, JT_OUTER                  },\n    /* right   */ { 14, 5, JT_RIGHT|JT_OUTER         },\n    /* full    */ { 19, 4, JT_LEFT|JT_RIGHT|JT_OUTER },\n    /* inner   */ { 23, 5, JT_INNER                  },\n    /* cross   */ { 28, 5, JT_INNER|JT_CROSS         },\n  };\n  int i, j;\n  apAll[0] = pA;\n  apAll[1] = pB;\n  apAll[2] = pC;\n  for(i=0; i<3 && apAll[i]; i++){\n    p = apAll[i];\n    for(j=0; j<ArraySize(aKeyword); j++){\n      if( p->n==aKeyword[j].nChar \n          && sqlite3StrNICmp((char*)p->z, &zKeyText[aKeyword[j].i], p->n)==0 ){\n        jointype |= aKeyword[j].code;\n        break;\n      }\n    }\n    testcase( j==0 || j==1 || j==2 || j==3 || j==4 || j==5 || j==6 );\n    if( j>=ArraySize(aKeyword) ){\n      jointype |= JT_ERROR;\n      break;\n    }\n  }\n  if(\n     (jointype & (JT_INNER|JT_OUTER))==(JT_INNER|JT_OUTER) ||\n     (jointype & JT_ERROR)!=0\n  ){\n    const char *zSp = \" \";\n    assert( pB!=0 );\n    if( pC==0 ){ zSp++; }\n    sqlite3ErrorMsg(pParse, \"unknown or unsupported join type: \"\n       \"%T %T%s%T\", pA, pB, zSp, pC);\n    jointype = JT_INNER;\n  }else if( (jointype & JT_OUTER)!=0 \n         && (jointype & (JT_LEFT|JT_RIGHT))!=JT_LEFT ){\n    sqlite3ErrorMsg(pParse, \n      \"RIGHT and FULL OUTER JOINs are not currently supported\");\n    jointype = JT_INNER;\n  }\n  return jointype;\n}\n\n/*\n** Return the index of a column in a table.  Return -1 if the column\n** is not contained in the table.\n*/\nstatic int columnIndex(Table *pTab, const char *zCol){\n  int i;\n  for(i=0; i<pTab->nCol; i++){\n    if( sqlite3StrICmp(pTab->aCol[i].zName, zCol)==0 ) return i;\n  }\n  return -1;\n}\n\n/*\n** Search the first N tables in pSrc, from left to right, looking for a\n** table that has a column named zCol.  \n**\n** When found, set *piTab and *piCol to the table index and column index\n** of the matching column and return TRUE.\n**\n** If not found, return FALSE.\n*/\nstatic int tableAndColumnIndex(\n  SrcList *pSrc,       /* Array of tables to search */\n  int N,               /* Number of tables in pSrc->a[] to search */\n  const char *zCol,    /* Name of the column we are looking for */\n  int *piTab,          /* Write index of pSrc->a[] here */\n  int *piCol           /* Write index of pSrc->a[*piTab].pTab->aCol[] here */\n){\n  int i;               /* For looping over tables in pSrc */\n  int iCol;            /* Index of column matching zCol */\n\n  assert( (piTab==0)==(piCol==0) );  /* Both or neither are NULL */\n  for(i=0; i<N; i++){\n    iCol = columnIndex(pSrc->a[i].pTab, zCol);\n    if( iCol>=0 ){\n      if( piTab ){\n        *piTab = i;\n        *piCol = iCol;\n      }\n      return 1;\n    }\n  }\n  return 0;\n}\n\n/*\n** This function is used to add terms implied by JOIN syntax to the\n** WHERE clause expression of a SELECT statement. The new term, which\n** is ANDed with the existing WHERE clause, is of the form:\n**\n**    (tab1.col1 = tab2.col2)\n**\n** where tab1 is the iSrc'th table in SrcList pSrc and tab2 is the \n** (iSrc+1)'th. Column col1 is column iColLeft of tab1, and col2 is\n** column iColRight of tab2.\n*/\nstatic void addWhereTerm(\n  Parse *pParse,                  /* Parsing context */\n  SrcList *pSrc,                  /* List of tables in FROM clause */\n  int iLeft,                      /* Index of first table to join in pSrc */\n  int iColLeft,                   /* Index of column in first table */\n  int iRight,                     /* Index of second table in pSrc */\n  int iColRight,                  /* Index of column in second table */\n  int isOuterJoin,                /* True if this is an OUTER join */\n  Expr **ppWhere                  /* IN/OUT: The WHERE clause to add to */\n){\n  sqlite3 *db = pParse->db;\n  Expr *pE1;\n  Expr *pE2;\n  Expr *pEq;\n\n  assert( iLeft<iRight );\n  assert( pSrc->nSrc>iRight );\n  assert( pSrc->a[iLeft].pTab );\n  assert( pSrc->a[iRight].pTab );\n\n  pE1 = sqlite3CreateColumnExpr(db, pSrc, iLeft, iColLeft);\n  pE2 = sqlite3CreateColumnExpr(db, pSrc, iRight, iColRight);\n\n  pEq = sqlite3PExpr(pParse, TK_EQ, pE1, pE2);\n  if( pEq && isOuterJoin ){\n    ExprSetProperty(pEq, EP_FromJoin);\n    assert( !ExprHasProperty(pEq, EP_TokenOnly|EP_Reduced) );\n    ExprSetVVAProperty(pEq, EP_NoReduce);\n    pEq->iRightJoinTable = (i16)pE2->iTable;\n  }\n  *ppWhere = sqlite3ExprAnd(db, *ppWhere, pEq);\n}\n\n/*\n** Set the EP_FromJoin property on all terms of the given expression.\n** And set the Expr.iRightJoinTable to iTable for every term in the\n** expression.\n**\n** The EP_FromJoin property is used on terms of an expression to tell\n** the LEFT OUTER JOIN processing logic that this term is part of the\n** join restriction specified in the ON or USING clause and not a part\n** of the more general WHERE clause.  These terms are moved over to the\n** WHERE clause during join processing but we need to remember that they\n** originated in the ON or USING clause.\n**\n** The Expr.iRightJoinTable tells the WHERE clause processing that the\n** expression depends on table iRightJoinTable even if that table is not\n** explicitly mentioned in the expression.  That information is needed\n** for cases like this:\n**\n**    SELECT * FROM t1 LEFT JOIN t2 ON t1.a=t2.b AND t1.x=5\n**\n** The where clause needs to defer the handling of the t1.x=5\n** term until after the t2 loop of the join.  In that way, a\n** NULL t2 row will be inserted whenever t1.x!=5.  If we do not\n** defer the handling of t1.x=5, it will be processed immediately\n** after the t1 loop and rows with t1.x!=5 will never appear in\n** the output, which is incorrect.\n*/\nstatic void setJoinExpr(Expr *p, int iTable){\n  while( p ){\n    ExprSetProperty(p, EP_FromJoin);\n    assert( !ExprHasProperty(p, EP_TokenOnly|EP_Reduced) );\n    ExprSetVVAProperty(p, EP_NoReduce);\n    p->iRightJoinTable = (i16)iTable;\n    if( p->op==TK_FUNCTION && p->x.pList ){\n      int i;\n      for(i=0; i<p->x.pList->nExpr; i++){\n        setJoinExpr(p->x.pList->a[i].pExpr, iTable);\n      }\n    }\n    setJoinExpr(p->pLeft, iTable);\n    p = p->pRight;\n  } \n}\n\n/*\n** This routine processes the join information for a SELECT statement.\n** ON and USING clauses are converted into extra terms of the WHERE clause.\n** NATURAL joins also create extra WHERE clause terms.\n**\n** The terms of a FROM clause are contained in the Select.pSrc structure.\n** The left most table is the first entry in Select.pSrc.  The right-most\n** table is the last entry.  The join operator is held in the entry to\n** the left.  Thus entry 0 contains the join operator for the join between\n** entries 0 and 1.  Any ON or USING clauses associated with the join are\n** also attached to the left entry.\n**\n** This routine returns the number of errors encountered.\n*/\nstatic int sqliteProcessJoin(Parse *pParse, Select *p){\n  SrcList *pSrc;                  /* All tables in the FROM clause */\n  int i, j;                       /* Loop counters */\n  struct SrcList_item *pLeft;     /* Left table being joined */\n  struct SrcList_item *pRight;    /* Right table being joined */\n\n  pSrc = p->pSrc;\n  pLeft = &pSrc->a[0];\n  pRight = &pLeft[1];\n  for(i=0; i<pSrc->nSrc-1; i++, pRight++, pLeft++){\n    Table *pRightTab = pRight->pTab;\n    int isOuter;\n\n    if( NEVER(pLeft->pTab==0 || pRightTab==0) ) continue;\n    isOuter = (pRight->fg.jointype & JT_OUTER)!=0;\n\n    /* When the NATURAL keyword is present, add WHERE clause terms for\n    ** every column that the two tables have in common.\n    */\n    if( pRight->fg.jointype & JT_NATURAL ){\n      if( pRight->pOn || pRight->pUsing ){\n        sqlite3ErrorMsg(pParse, \"a NATURAL join may not have \"\n           \"an ON or USING clause\", 0);\n        return 1;\n      }\n      for(j=0; j<pRightTab->nCol; j++){\n        char *zName;   /* Name of column in the right table */\n        int iLeft;     /* Matching left table */\n        int iLeftCol;  /* Matching column in the left table */\n\n        zName = pRightTab->aCol[j].zName;\n        if( tableAndColumnIndex(pSrc, i+1, zName, &iLeft, &iLeftCol) ){\n          addWhereTerm(pParse, pSrc, iLeft, iLeftCol, i+1, j,\n                       isOuter, &p->pWhere);\n        }\n      }\n    }\n\n    /* Disallow both ON and USING clauses in the same join\n    */\n    if( pRight->pOn && pRight->pUsing ){\n      sqlite3ErrorMsg(pParse, \"cannot have both ON and USING \"\n        \"clauses in the same join\");\n      return 1;\n    }\n\n    /* Add the ON clause to the end of the WHERE clause, connected by\n    ** an AND operator.\n    */\n    if( pRight->pOn ){\n      if( isOuter ) setJoinExpr(pRight->pOn, pRight->iCursor);\n      p->pWhere = sqlite3ExprAnd(pParse->db, p->pWhere, pRight->pOn);\n      pRight->pOn = 0;\n    }\n\n    /* Create extra terms on the WHERE clause for each column named\n    ** in the USING clause.  Example: If the two tables to be joined are \n    ** A and B and the USING clause names X, Y, and Z, then add this\n    ** to the WHERE clause:    A.X=B.X AND A.Y=B.Y AND A.Z=B.Z\n    ** Report an error if any column mentioned in the USING clause is\n    ** not contained in both tables to be joined.\n    */\n    if( pRight->pUsing ){\n      IdList *pList = pRight->pUsing;\n      for(j=0; j<pList->nId; j++){\n        char *zName;     /* Name of the term in the USING clause */\n        int iLeft;       /* Table on the left with matching column name */\n        int iLeftCol;    /* Column number of matching column on the left */\n        int iRightCol;   /* Column number of matching column on the right */\n\n        zName = pList->a[j].zName;\n        iRightCol = columnIndex(pRightTab, zName);\n        if( iRightCol<0\n         || !tableAndColumnIndex(pSrc, i+1, zName, &iLeft, &iLeftCol)\n        ){\n          sqlite3ErrorMsg(pParse, \"cannot join using column %s - column \"\n            \"not present in both tables\", zName);\n          return 1;\n        }\n        addWhereTerm(pParse, pSrc, iLeft, iLeftCol, i+1, iRightCol,\n                     isOuter, &p->pWhere);\n      }\n    }\n  }\n  return 0;\n}\n\n/* Forward reference */\nstatic KeyInfo *keyInfoFromExprList(\n  Parse *pParse,       /* Parsing context */\n  ExprList *pList,     /* Form the KeyInfo object from this ExprList */\n  int iStart,          /* Begin with this column of pList */\n  int nExtra           /* Add this many extra columns to the end */\n);\n\n/*\n** Generate code that will push the record in registers regData\n** through regData+nData-1 onto the sorter.\n*/\nstatic void pushOntoSorter(\n  Parse *pParse,         /* Parser context */\n  SortCtx *pSort,        /* Information about the ORDER BY clause */\n  Select *pSelect,       /* The whole SELECT statement */\n  int regData,           /* First register holding data to be sorted */\n  int regOrigData,       /* First register holding data before packing */\n  int nData,             /* Number of elements in the data array */\n  int nPrefixReg         /* No. of reg prior to regData available for use */\n){\n  Vdbe *v = pParse->pVdbe;                         /* Stmt under construction */\n  int bSeq = ((pSort->sortFlags & SORTFLAG_UseSorter)==0);\n  int nExpr = pSort->pOrderBy->nExpr;              /* No. of ORDER BY terms */\n  int nBase = nExpr + bSeq + nData;                /* Fields in sorter record */\n  int regBase;                                     /* Regs for sorter record */\n  int regRecord = ++pParse->nMem;                  /* Assembled sorter record */\n  int nOBSat = pSort->nOBSat;                      /* ORDER BY terms to skip */\n  int op;                            /* Opcode to add sorter record to sorter */\n  int iLimit;                        /* LIMIT counter */\n\n  assert( bSeq==0 || bSeq==1 );\n  assert( nData==1 || regData==regOrigData || regOrigData==0 );\n  if( nPrefixReg ){\n    assert( nPrefixReg==nExpr+bSeq );\n    regBase = regData - nExpr - bSeq;\n  }else{\n    regBase = pParse->nMem + 1;\n    pParse->nMem += nBase;\n  }\n  assert( pSelect->iOffset==0 || pSelect->iLimit!=0 );\n  iLimit = pSelect->iOffset ? pSelect->iOffset+1 : pSelect->iLimit;\n  pSort->labelDone = sqlite3VdbeMakeLabel(v);\n  sqlite3ExprCodeExprList(pParse, pSort->pOrderBy, regBase, regOrigData,\n                          SQLITE_ECEL_DUP | (regOrigData? SQLITE_ECEL_REF : 0));\n  if( bSeq ){\n    sqlite3VdbeAddOp2(v, OP_Sequence, pSort->iECursor, regBase+nExpr);\n  }\n  if( nPrefixReg==0 && nData>0 ){\n    sqlite3ExprCodeMove(pParse, regData, regBase+nExpr+bSeq, nData);\n  }\n  sqlite3VdbeAddOp3(v, OP_MakeRecord, regBase+nOBSat, nBase-nOBSat, regRecord);\n  if( nOBSat>0 ){\n    int regPrevKey;   /* The first nOBSat columns of the previous row */\n    int addrFirst;    /* Address of the OP_IfNot opcode */\n    int addrJmp;      /* Address of the OP_Jump opcode */\n    VdbeOp *pOp;      /* Opcode that opens the sorter */\n    int nKey;         /* Number of sorting key columns, including OP_Sequence */\n    KeyInfo *pKI;     /* Original KeyInfo on the sorter table */\n\n    regPrevKey = pParse->nMem+1;\n    pParse->nMem += pSort->nOBSat;\n    nKey = nExpr - pSort->nOBSat + bSeq;\n    if( bSeq ){\n      addrFirst = sqlite3VdbeAddOp1(v, OP_IfNot, regBase+nExpr); \n    }else{\n      addrFirst = sqlite3VdbeAddOp1(v, OP_SequenceTest, pSort->iECursor);\n    }\n    VdbeCoverage(v);\n    sqlite3VdbeAddOp3(v, OP_Compare, regPrevKey, regBase, pSort->nOBSat);\n    pOp = sqlite3VdbeGetOp(v, pSort->addrSortIndex);\n    if( pParse->db->mallocFailed ) return;\n    pOp->p2 = nKey + nData;\n    pKI = pOp->p4.pKeyInfo;\n    memset(pKI->aSortOrder, 0, pKI->nKeyField); /* Makes OP_Jump testable */\n    sqlite3VdbeChangeP4(v, -1, (char*)pKI, P4_KEYINFO);\n    testcase( pKI->nAllField > pKI->nKeyField+2 );\n    pOp->p4.pKeyInfo = keyInfoFromExprList(pParse, pSort->pOrderBy, nOBSat,\n                                           pKI->nAllField-pKI->nKeyField-1);\n    addrJmp = sqlite3VdbeCurrentAddr(v);\n    sqlite3VdbeAddOp3(v, OP_Jump, addrJmp+1, 0, addrJmp+1); VdbeCoverage(v);\n    pSort->labelBkOut = sqlite3VdbeMakeLabel(v);\n    pSort->regReturn = ++pParse->nMem;\n    sqlite3VdbeAddOp2(v, OP_Gosub, pSort->regReturn, pSort->labelBkOut);\n    sqlite3VdbeAddOp1(v, OP_ResetSorter, pSort->iECursor);\n    if( iLimit ){\n      sqlite3VdbeAddOp2(v, OP_IfNot, iLimit, pSort->labelDone);\n      VdbeCoverage(v);\n    }\n    sqlite3VdbeJumpHere(v, addrFirst);\n    sqlite3ExprCodeMove(pParse, regBase, regPrevKey, pSort->nOBSat);\n    sqlite3VdbeJumpHere(v, addrJmp);\n  }\n  if( pSort->sortFlags & SORTFLAG_UseSorter ){\n    op = OP_SorterInsert;\n  }else{\n    op = OP_IdxInsert;\n  }\n  sqlite3VdbeAddOp4Int(v, op, pSort->iECursor, regRecord,\n                       regBase+nOBSat, nBase-nOBSat);\n  if( iLimit ){\n    int addr;\n    int r1 = 0;\n    /* Fill the sorter until it contains LIMIT+OFFSET entries.  (The iLimit\n    ** register is initialized with value of LIMIT+OFFSET.)  After the sorter\n    ** fills up, delete the least entry in the sorter after each insert.\n    ** Thus we never hold more than the LIMIT+OFFSET rows in memory at once */\n    addr = sqlite3VdbeAddOp1(v, OP_IfNotZero, iLimit); VdbeCoverage(v);\n    sqlite3VdbeAddOp1(v, OP_Last, pSort->iECursor);\n    if( pSort->bOrderedInnerLoop ){\n      r1 = ++pParse->nMem;\n      sqlite3VdbeAddOp3(v, OP_Column, pSort->iECursor, nExpr, r1);\n      VdbeComment((v, \"seq\"));\n    }\n    sqlite3VdbeAddOp1(v, OP_Delete, pSort->iECursor);\n    if( pSort->bOrderedInnerLoop ){\n      /* If the inner loop is driven by an index such that values from\n      ** the same iteration of the inner loop are in sorted order, then\n      ** immediately jump to the next iteration of an inner loop if the\n      ** entry from the current iteration does not fit into the top\n      ** LIMIT+OFFSET entries of the sorter. */\n      int iBrk = sqlite3VdbeCurrentAddr(v) + 2;\n      sqlite3VdbeAddOp3(v, OP_Eq, regBase+nExpr, iBrk, r1);\n      sqlite3VdbeChangeP5(v, SQLITE_NULLEQ);\n      VdbeCoverage(v);\n    }\n    sqlite3VdbeJumpHere(v, addr);\n  }\n}\n\n/*\n** Add code to implement the OFFSET\n*/\nstatic void codeOffset(\n  Vdbe *v,          /* Generate code into this VM */\n  int iOffset,      /* Register holding the offset counter */\n  int iContinue     /* Jump here to skip the current record */\n){\n  if( iOffset>0 ){\n    sqlite3VdbeAddOp3(v, OP_IfPos, iOffset, iContinue, 1); VdbeCoverage(v);\n    VdbeComment((v, \"OFFSET\"));\n  }\n}\n\n/*\n** Add code that will check to make sure the N registers starting at iMem\n** form a distinct entry.  iTab is a sorting index that holds previously\n** seen combinations of the N values.  A new entry is made in iTab\n** if the current N values are new.\n**\n** A jump to addrRepeat is made and the N+1 values are popped from the\n** stack if the top N elements are not distinct.\n*/\nstatic void codeDistinct(\n  Parse *pParse,     /* Parsing and code generating context */\n  int iTab,          /* A sorting index used to test for distinctness */\n  int addrRepeat,    /* Jump to here if not distinct */\n  int N,             /* Number of elements */\n  int iMem           /* First element */\n){\n  Vdbe *v;\n  int r1;\n\n  v = pParse->pVdbe;\n  r1 = sqlite3GetTempReg(pParse);\n  sqlite3VdbeAddOp4Int(v, OP_Found, iTab, addrRepeat, iMem, N); VdbeCoverage(v);\n  sqlite3VdbeAddOp3(v, OP_MakeRecord, iMem, N, r1);\n  sqlite3VdbeAddOp4Int(v, OP_IdxInsert, iTab, r1, iMem, N);\n  sqlite3VdbeChangeP5(v, OPFLAG_USESEEKRESULT);\n  sqlite3ReleaseTempReg(pParse, r1);\n}\n\n/*\n** This routine generates the code for the inside of the inner loop\n** of a SELECT.\n**\n** If srcTab is negative, then the p->pEList expressions\n** are evaluated in order to get the data for this row.  If srcTab is\n** zero or more, then data is pulled from srcTab and p->pEList is used only \n** to get the number of columns and the collation sequence for each column.\n*/\nstatic void selectInnerLoop(\n  Parse *pParse,          /* The parser context */\n  Select *p,              /* The complete select statement being coded */\n  int srcTab,             /* Pull data from this table if non-negative */\n  SortCtx *pSort,         /* If not NULL, info on how to process ORDER BY */\n  DistinctCtx *pDistinct, /* If not NULL, info on how to process DISTINCT */\n  SelectDest *pDest,      /* How to dispose of the results */\n  int iContinue,          /* Jump here to continue with next row */\n  int iBreak              /* Jump here to break out of the inner loop */\n){\n  Vdbe *v = pParse->pVdbe;\n  int i;\n  int hasDistinct;            /* True if the DISTINCT keyword is present */\n  int eDest = pDest->eDest;   /* How to dispose of results */\n  int iParm = pDest->iSDParm; /* First argument to disposal method */\n  int nResultCol;             /* Number of result columns */\n  int nPrefixReg = 0;         /* Number of extra registers before regResult */\n\n  /* Usually, regResult is the first cell in an array of memory cells\n  ** containing the current result row. In this case regOrig is set to the\n  ** same value. However, if the results are being sent to the sorter, the\n  ** values for any expressions that are also part of the sort-key are omitted\n  ** from this array. In this case regOrig is set to zero.  */\n  int regResult;              /* Start of memory holding current results */\n  int regOrig;                /* Start of memory holding full result (or 0) */\n\n  assert( v );\n  assert( p->pEList!=0 );\n  hasDistinct = pDistinct ? pDistinct->eTnctType : WHERE_DISTINCT_NOOP;\n  if( pSort && pSort->pOrderBy==0 ) pSort = 0;\n  if( pSort==0 && !hasDistinct ){\n    assert( iContinue!=0 );\n    codeOffset(v, p->iOffset, iContinue);\n  }\n\n  /* Pull the requested columns.\n  */\n  nResultCol = p->pEList->nExpr;\n\n  if( pDest->iSdst==0 ){\n    if( pSort ){\n      nPrefixReg = pSort->pOrderBy->nExpr;\n      if( !(pSort->sortFlags & SORTFLAG_UseSorter) ) nPrefixReg++;\n      pParse->nMem += nPrefixReg;\n    }\n    pDest->iSdst = pParse->nMem+1;\n    pParse->nMem += nResultCol;\n  }else if( pDest->iSdst+nResultCol > pParse->nMem ){\n    /* This is an error condition that can result, for example, when a SELECT\n    ** on the right-hand side of an INSERT contains more result columns than\n    ** there are columns in the table on the left.  The error will be caught\n    ** and reported later.  But we need to make sure enough memory is allocated\n    ** to avoid other spurious errors in the meantime. */\n    pParse->nMem += nResultCol;\n  }\n  pDest->nSdst = nResultCol;\n  regOrig = regResult = pDest->iSdst;\n  if( srcTab>=0 ){\n    for(i=0; i<nResultCol; i++){\n      sqlite3VdbeAddOp3(v, OP_Column, srcTab, i, regResult+i);\n      VdbeComment((v, \"%s\", p->pEList->a[i].zName));\n    }\n  }else if( eDest!=SRT_Exists ){\n    /* If the destination is an EXISTS(...) expression, the actual\n    ** values returned by the SELECT are not required.\n    */\n    u8 ecelFlags;\n    if( eDest==SRT_Mem || eDest==SRT_Output || eDest==SRT_Coroutine ){\n      ecelFlags = SQLITE_ECEL_DUP;\n    }else{\n      ecelFlags = 0;\n    }\n    if( pSort && hasDistinct==0 && eDest!=SRT_EphemTab && eDest!=SRT_Table ){\n      /* For each expression in p->pEList that is a copy of an expression in\n      ** the ORDER BY clause (pSort->pOrderBy), set the associated \n      ** iOrderByCol value to one more than the index of the ORDER BY \n      ** expression within the sort-key that pushOntoSorter() will generate.\n      ** This allows the p->pEList field to be omitted from the sorted record,\n      ** saving space and CPU cycles.  */\n      ecelFlags |= (SQLITE_ECEL_OMITREF|SQLITE_ECEL_REF);\n      for(i=pSort->nOBSat; i<pSort->pOrderBy->nExpr; i++){\n        int j;\n        if( (j = pSort->pOrderBy->a[i].u.x.iOrderByCol)>0 ){\n          p->pEList->a[j-1].u.x.iOrderByCol = i+1-pSort->nOBSat;\n        }\n      }\n      regOrig = 0;\n      assert( eDest==SRT_Set || eDest==SRT_Mem \n           || eDest==SRT_Coroutine || eDest==SRT_Output );\n    }\n    nResultCol = sqlite3ExprCodeExprList(pParse,p->pEList,regResult,\n                                         0,ecelFlags);\n  }\n\n  /* If the DISTINCT keyword was present on the SELECT statement\n  ** and this row has been seen before, then do not make this row\n  ** part of the result.\n  */\n  if( hasDistinct ){\n    switch( pDistinct->eTnctType ){\n      case WHERE_DISTINCT_ORDERED: {\n        VdbeOp *pOp;            /* No longer required OpenEphemeral instr. */\n        int iJump;              /* Jump destination */\n        int regPrev;            /* Previous row content */\n\n        /* Allocate space for the previous row */\n        regPrev = pParse->nMem+1;\n        pParse->nMem += nResultCol;\n\n        /* Change the OP_OpenEphemeral coded earlier to an OP_Null\n        ** sets the MEM_Cleared bit on the first register of the\n        ** previous value.  This will cause the OP_Ne below to always\n        ** fail on the first iteration of the loop even if the first\n        ** row is all NULLs.\n        */\n        sqlite3VdbeChangeToNoop(v, pDistinct->addrTnct);\n        pOp = sqlite3VdbeGetOp(v, pDistinct->addrTnct);\n        pOp->opcode = OP_Null;\n        pOp->p1 = 1;\n        pOp->p2 = regPrev;\n\n        iJump = sqlite3VdbeCurrentAddr(v) + nResultCol;\n        for(i=0; i<nResultCol; i++){\n          CollSeq *pColl = sqlite3ExprCollSeq(pParse, p->pEList->a[i].pExpr);\n          if( i<nResultCol-1 ){\n            sqlite3VdbeAddOp3(v, OP_Ne, regResult+i, iJump, regPrev+i);\n            VdbeCoverage(v);\n          }else{\n            sqlite3VdbeAddOp3(v, OP_Eq, regResult+i, iContinue, regPrev+i);\n            VdbeCoverage(v);\n           }\n          sqlite3VdbeChangeP4(v, -1, (const char *)pColl, P4_COLLSEQ);\n          sqlite3VdbeChangeP5(v, SQLITE_NULLEQ);\n        }\n        assert( sqlite3VdbeCurrentAddr(v)==iJump || pParse->db->mallocFailed );\n        sqlite3VdbeAddOp3(v, OP_Copy, regResult, regPrev, nResultCol-1);\n        break;\n      }\n\n      case WHERE_DISTINCT_UNIQUE: {\n        sqlite3VdbeChangeToNoop(v, pDistinct->addrTnct);\n        break;\n      }\n\n      default: {\n        assert( pDistinct->eTnctType==WHERE_DISTINCT_UNORDERED );\n        codeDistinct(pParse, pDistinct->tabTnct, iContinue, nResultCol,\n                     regResult);\n        break;\n      }\n    }\n    if( pSort==0 ){\n      codeOffset(v, p->iOffset, iContinue);\n    }\n  }\n\n  switch( eDest ){\n    /* In this mode, write each query result to the key of the temporary\n    ** table iParm.\n    */\n#ifndef SQLITE_OMIT_COMPOUND_SELECT\n    case SRT_Union: {\n      int r1;\n      r1 = sqlite3GetTempReg(pParse);\n      sqlite3VdbeAddOp3(v, OP_MakeRecord, regResult, nResultCol, r1);\n      sqlite3VdbeAddOp4Int(v, OP_IdxInsert, iParm, r1, regResult, nResultCol);\n      sqlite3ReleaseTempReg(pParse, r1);\n      break;\n    }\n\n    /* Construct a record from the query result, but instead of\n    ** saving that record, use it as a key to delete elements from\n    ** the temporary table iParm.\n    */\n    case SRT_Except: {\n      sqlite3VdbeAddOp3(v, OP_IdxDelete, iParm, regResult, nResultCol);\n      break;\n    }\n#endif /* SQLITE_OMIT_COMPOUND_SELECT */\n\n    /* Store the result as data using a unique key.\n    */\n    case SRT_Fifo:\n    case SRT_DistFifo:\n    case SRT_Table:\n    case SRT_EphemTab: {\n      int r1 = sqlite3GetTempRange(pParse, nPrefixReg+1);\n      testcase( eDest==SRT_Table );\n      testcase( eDest==SRT_EphemTab );\n      testcase( eDest==SRT_Fifo );\n      testcase( eDest==SRT_DistFifo );\n      sqlite3VdbeAddOp3(v, OP_MakeRecord, regResult, nResultCol, r1+nPrefixReg);\n#ifndef SQLITE_OMIT_CTE\n      if( eDest==SRT_DistFifo ){\n        /* If the destination is DistFifo, then cursor (iParm+1) is open\n        ** on an ephemeral index. If the current row is already present\n        ** in the index, do not write it to the output. If not, add the\n        ** current row to the index and proceed with writing it to the\n        ** output table as well.  */\n        int addr = sqlite3VdbeCurrentAddr(v) + 4;\n        sqlite3VdbeAddOp4Int(v, OP_Found, iParm+1, addr, r1, 0);\n        VdbeCoverage(v);\n        sqlite3VdbeAddOp4Int(v, OP_IdxInsert, iParm+1, r1,regResult,nResultCol);\n        assert( pSort==0 );\n      }\n#endif\n      if( pSort ){\n        pushOntoSorter(pParse, pSort, p, r1+nPrefixReg,regResult,1,nPrefixReg);\n      }else{\n        int r2 = sqlite3GetTempReg(pParse);\n        sqlite3VdbeAddOp2(v, OP_NewRowid, iParm, r2);\n        sqlite3VdbeAddOp3(v, OP_Insert, iParm, r1, r2);\n        sqlite3VdbeChangeP5(v, OPFLAG_APPEND);\n        sqlite3ReleaseTempReg(pParse, r2);\n      }\n      sqlite3ReleaseTempRange(pParse, r1, nPrefixReg+1);\n      break;\n    }\n\n#ifndef SQLITE_OMIT_SUBQUERY\n    /* If we are creating a set for an \"expr IN (SELECT ...)\" construct,\n    ** then there should be a single item on the stack.  Write this\n    ** item into the set table with bogus data.\n    */\n    case SRT_Set: {\n      if( pSort ){\n        /* At first glance you would think we could optimize out the\n        ** ORDER BY in this case since the order of entries in the set\n        ** does not matter.  But there might be a LIMIT clause, in which\n        ** case the order does matter */\n        pushOntoSorter(\n            pParse, pSort, p, regResult, regOrig, nResultCol, nPrefixReg);\n      }else{\n        int r1 = sqlite3GetTempReg(pParse);\n        assert( sqlite3Strlen30(pDest->zAffSdst)==nResultCol );\n        sqlite3VdbeAddOp4(v, OP_MakeRecord, regResult, nResultCol, \n            r1, pDest->zAffSdst, nResultCol);\n        sqlite3ExprCacheAffinityChange(pParse, regResult, nResultCol);\n        sqlite3VdbeAddOp4Int(v, OP_IdxInsert, iParm, r1, regResult, nResultCol);\n        sqlite3ReleaseTempReg(pParse, r1);\n      }\n      break;\n    }\n\n    /* If any row exist in the result set, record that fact and abort.\n    */\n    case SRT_Exists: {\n      sqlite3VdbeAddOp2(v, OP_Integer, 1, iParm);\n      /* The LIMIT clause will terminate the loop for us */\n      break;\n    }\n\n    /* If this is a scalar select that is part of an expression, then\n    ** store the results in the appropriate memory cell or array of \n    ** memory cells and break out of the scan loop.\n    */\n    case SRT_Mem: {\n      if( pSort ){\n        assert( nResultCol<=pDest->nSdst );\n        pushOntoSorter(\n            pParse, pSort, p, regResult, regOrig, nResultCol, nPrefixReg);\n      }else{\n        assert( nResultCol==pDest->nSdst );\n        assert( regResult==iParm );\n        /* The LIMIT clause will jump out of the loop for us */\n      }\n      break;\n    }\n#endif /* #ifndef SQLITE_OMIT_SUBQUERY */\n\n    case SRT_Coroutine:       /* Send data to a co-routine */\n    case SRT_Output: {        /* Return the results */\n      testcase( eDest==SRT_Coroutine );\n      testcase( eDest==SRT_Output );\n      if( pSort ){\n        pushOntoSorter(pParse, pSort, p, regResult, regOrig, nResultCol,\n                       nPrefixReg);\n      }else if( eDest==SRT_Coroutine ){\n        sqlite3VdbeAddOp1(v, OP_Yield, pDest->iSDParm);\n      }else{\n        sqlite3VdbeAddOp2(v, OP_ResultRow, regResult, nResultCol);\n        sqlite3ExprCacheAffinityChange(pParse, regResult, nResultCol);\n      }\n      break;\n    }\n\n#ifndef SQLITE_OMIT_CTE\n    /* Write the results into a priority queue that is order according to\n    ** pDest->pOrderBy (in pSO).  pDest->iSDParm (in iParm) is the cursor for an\n    ** index with pSO->nExpr+2 columns.  Build a key using pSO for the first\n    ** pSO->nExpr columns, then make sure all keys are unique by adding a\n    ** final OP_Sequence column.  The last column is the record as a blob.\n    */\n    case SRT_DistQueue:\n    case SRT_Queue: {\n      int nKey;\n      int r1, r2, r3;\n      int addrTest = 0;\n      ExprList *pSO;\n      pSO = pDest->pOrderBy;\n      assert( pSO );\n      nKey = pSO->nExpr;\n      r1 = sqlite3GetTempReg(pParse);\n      r2 = sqlite3GetTempRange(pParse, nKey+2);\n      r3 = r2+nKey+1;\n      if( eDest==SRT_DistQueue ){\n        /* If the destination is DistQueue, then cursor (iParm+1) is open\n        ** on a second ephemeral index that holds all values every previously\n        ** added to the queue. */\n        addrTest = sqlite3VdbeAddOp4Int(v, OP_Found, iParm+1, 0, \n                                        regResult, nResultCol);\n        VdbeCoverage(v);\n      }\n      sqlite3VdbeAddOp3(v, OP_MakeRecord, regResult, nResultCol, r3);\n      if( eDest==SRT_DistQueue ){\n        sqlite3VdbeAddOp2(v, OP_IdxInsert, iParm+1, r3);\n        sqlite3VdbeChangeP5(v, OPFLAG_USESEEKRESULT);\n      }\n      for(i=0; i<nKey; i++){\n        sqlite3VdbeAddOp2(v, OP_SCopy,\n                          regResult + pSO->a[i].u.x.iOrderByCol - 1,\n                          r2+i);\n      }\n      sqlite3VdbeAddOp2(v, OP_Sequence, iParm, r2+nKey);\n      sqlite3VdbeAddOp3(v, OP_MakeRecord, r2, nKey+2, r1);\n      sqlite3VdbeAddOp4Int(v, OP_IdxInsert, iParm, r1, r2, nKey+2);\n      if( addrTest ) sqlite3VdbeJumpHere(v, addrTest);\n      sqlite3ReleaseTempReg(pParse, r1);\n      sqlite3ReleaseTempRange(pParse, r2, nKey+2);\n      break;\n    }\n#endif /* SQLITE_OMIT_CTE */\n\n\n\n#if !defined(SQLITE_OMIT_TRIGGER)\n    /* Discard the results.  This is used for SELECT statements inside\n    ** the body of a TRIGGER.  The purpose of such selects is to call\n    ** user-defined functions that have side effects.  We do not care\n    ** about the actual results of the select.\n    */\n    default: {\n      assert( eDest==SRT_Discard );\n      break;\n    }\n#endif\n  }\n\n  /* Jump to the end of the loop if the LIMIT is reached.  Except, if\n  ** there is a sorter, in which case the sorter has already limited\n  ** the output for us.\n  */\n  if( pSort==0 && p->iLimit ){\n    sqlite3VdbeAddOp2(v, OP_DecrJumpZero, p->iLimit, iBreak); VdbeCoverage(v);\n  }\n}\n\n/*\n** Allocate a KeyInfo object sufficient for an index of N key columns and\n** X extra columns.\n*/\nSQLITE_PRIVATE KeyInfo *sqlite3KeyInfoAlloc(sqlite3 *db, int N, int X){\n  int nExtra = (N+X)*(sizeof(CollSeq*)+1) - sizeof(CollSeq*);\n  KeyInfo *p = sqlite3DbMallocRawNN(db, sizeof(KeyInfo) + nExtra);\n  if( p ){\n    p->aSortOrder = (u8*)&p->aColl[N+X];\n    p->nKeyField = (u16)N;\n    p->nAllField = (u16)(N+X);\n    p->enc = ENC(db);\n    p->db = db;\n    p->nRef = 1;\n    memset(&p[1], 0, nExtra);\n  }else{\n    sqlite3OomFault(db);\n  }\n  return p;\n}\n\n/*\n** Deallocate a KeyInfo object\n*/\nSQLITE_PRIVATE void sqlite3KeyInfoUnref(KeyInfo *p){\n  if( p ){\n    assert( p->nRef>0 );\n    p->nRef--;\n    if( p->nRef==0 ) sqlite3DbFreeNN(p->db, p);\n  }\n}\n\n/*\n** Make a new pointer to a KeyInfo object\n*/\nSQLITE_PRIVATE KeyInfo *sqlite3KeyInfoRef(KeyInfo *p){\n  if( p ){\n    assert( p->nRef>0 );\n    p->nRef++;\n  }\n  return p;\n}\n\n#ifdef SQLITE_DEBUG\n/*\n** Return TRUE if a KeyInfo object can be change.  The KeyInfo object\n** can only be changed if this is just a single reference to the object.\n**\n** This routine is used only inside of assert() statements.\n*/\nSQLITE_PRIVATE int sqlite3KeyInfoIsWriteable(KeyInfo *p){ return p->nRef==1; }\n#endif /* SQLITE_DEBUG */\n\n/*\n** Given an expression list, generate a KeyInfo structure that records\n** the collating sequence for each expression in that expression list.\n**\n** If the ExprList is an ORDER BY or GROUP BY clause then the resulting\n** KeyInfo structure is appropriate for initializing a virtual index to\n** implement that clause.  If the ExprList is the result set of a SELECT\n** then the KeyInfo structure is appropriate for initializing a virtual\n** index to implement a DISTINCT test.\n**\n** Space to hold the KeyInfo structure is obtained from malloc.  The calling\n** function is responsible for seeing that this structure is eventually\n** freed.\n*/\nstatic KeyInfo *keyInfoFromExprList(\n  Parse *pParse,       /* Parsing context */\n  ExprList *pList,     /* Form the KeyInfo object from this ExprList */\n  int iStart,          /* Begin with this column of pList */\n  int nExtra           /* Add this many extra columns to the end */\n){\n  int nExpr;\n  KeyInfo *pInfo;\n  struct ExprList_item *pItem;\n  sqlite3 *db = pParse->db;\n  int i;\n\n  nExpr = pList->nExpr;\n  pInfo = sqlite3KeyInfoAlloc(db, nExpr-iStart, nExtra+1);\n  if( pInfo ){\n    assert( sqlite3KeyInfoIsWriteable(pInfo) );\n    for(i=iStart, pItem=pList->a+iStart; i<nExpr; i++, pItem++){\n      pInfo->aColl[i-iStart] = sqlite3ExprNNCollSeq(pParse, pItem->pExpr);\n      pInfo->aSortOrder[i-iStart] = pItem->sortOrder;\n    }\n  }\n  return pInfo;\n}\n\n/*\n** Name of the connection operator, used for error messages.\n*/\nstatic const char *selectOpName(int id){\n  char *z;\n  switch( id ){\n    case TK_ALL:       z = \"UNION ALL\";   break;\n    case TK_INTERSECT: z = \"INTERSECT\";   break;\n    case TK_EXCEPT:    z = \"EXCEPT\";      break;\n    default:           z = \"UNION\";       break;\n  }\n  return z;\n}\n\n#ifndef SQLITE_OMIT_EXPLAIN\n/*\n** Unless an \"EXPLAIN QUERY PLAN\" command is being processed, this function\n** is a no-op. Otherwise, it adds a single row of output to the EQP result,\n** where the caption is of the form:\n**\n**   \"USE TEMP B-TREE FOR xxx\"\n**\n** where xxx is one of \"DISTINCT\", \"ORDER BY\" or \"GROUP BY\". Exactly which\n** is determined by the zUsage argument.\n*/\nstatic void explainTempTable(Parse *pParse, const char *zUsage){\n  if( pParse->explain==2 ){\n    Vdbe *v = pParse->pVdbe;\n    char *zMsg = sqlite3MPrintf(pParse->db, \"USE TEMP B-TREE FOR %s\", zUsage);\n    sqlite3VdbeAddOp4(v, OP_Explain, pParse->iSelectId, 0, 0, zMsg, P4_DYNAMIC);\n  }\n}\n\n/*\n** Assign expression b to lvalue a. A second, no-op, version of this macro\n** is provided when SQLITE_OMIT_EXPLAIN is defined. This allows the code\n** in sqlite3Select() to assign values to structure member variables that\n** only exist if SQLITE_OMIT_EXPLAIN is not defined without polluting the\n** code with #ifndef directives.\n*/\n# define explainSetInteger(a, b) a = b\n\n#else\n/* No-op versions of the explainXXX() functions and macros. */\n# define explainTempTable(y,z)\n# define explainSetInteger(y,z)\n#endif\n\n#if !defined(SQLITE_OMIT_EXPLAIN) && !defined(SQLITE_OMIT_COMPOUND_SELECT)\n/*\n** Unless an \"EXPLAIN QUERY PLAN\" command is being processed, this function\n** is a no-op. Otherwise, it adds a single row of output to the EQP result,\n** where the caption is of one of the two forms:\n**\n**   \"COMPOSITE SUBQUERIES iSub1 and iSub2 (op)\"\n**   \"COMPOSITE SUBQUERIES iSub1 and iSub2 USING TEMP B-TREE (op)\"\n**\n** where iSub1 and iSub2 are the integers passed as the corresponding\n** function parameters, and op is the text representation of the parameter\n** of the same name. The parameter \"op\" must be one of TK_UNION, TK_EXCEPT,\n** TK_INTERSECT or TK_ALL. The first form is used if argument bUseTmp is \n** false, or the second form if it is true.\n*/\nstatic void explainComposite(\n  Parse *pParse,                  /* Parse context */\n  int op,                         /* One of TK_UNION, TK_EXCEPT etc. */\n  int iSub1,                      /* Subquery id 1 */\n  int iSub2,                      /* Subquery id 2 */\n  int bUseTmp                     /* True if a temp table was used */\n){\n  assert( op==TK_UNION || op==TK_EXCEPT || op==TK_INTERSECT || op==TK_ALL );\n  if( pParse->explain==2 ){\n    Vdbe *v = pParse->pVdbe;\n    char *zMsg = sqlite3MPrintf(\n        pParse->db, \"COMPOUND SUBQUERIES %d AND %d %s(%s)\", iSub1, iSub2,\n        bUseTmp?\"USING TEMP B-TREE \":\"\", selectOpName(op)\n    );\n    sqlite3VdbeAddOp4(v, OP_Explain, pParse->iSelectId, 0, 0, zMsg, P4_DYNAMIC);\n  }\n}\n#else\n/* No-op versions of the explainXXX() functions and macros. */\n# define explainComposite(v,w,x,y,z)\n#endif\n\n/*\n** If the inner loop was generated using a non-null pOrderBy argument,\n** then the results were placed in a sorter.  After the loop is terminated\n** we need to run the sorter and output the results.  The following\n** routine generates the code needed to do that.\n*/\nstatic void generateSortTail(\n  Parse *pParse,    /* Parsing context */\n  Select *p,        /* The SELECT statement */\n  SortCtx *pSort,   /* Information on the ORDER BY clause */\n  int nColumn,      /* Number of columns of data */\n  SelectDest *pDest /* Write the sorted results here */\n){\n  Vdbe *v = pParse->pVdbe;                     /* The prepared statement */\n  int addrBreak = pSort->labelDone;            /* Jump here to exit loop */\n  int addrContinue = sqlite3VdbeMakeLabel(v);  /* Jump here for next cycle */\n  int addr;\n  int addrOnce = 0;\n  int iTab;\n  ExprList *pOrderBy = pSort->pOrderBy;\n  int eDest = pDest->eDest;\n  int iParm = pDest->iSDParm;\n  int regRow;\n  int regRowid;\n  int iCol;\n  int nKey;\n  int iSortTab;                   /* Sorter cursor to read from */\n  int nSortData;                  /* Trailing values to read from sorter */\n  int i;\n  int bSeq;                       /* True if sorter record includes seq. no. */\n  struct ExprList_item *aOutEx = p->pEList->a;\n\n  assert( addrBreak<0 );\n  if( pSort->labelBkOut ){\n    sqlite3VdbeAddOp2(v, OP_Gosub, pSort->regReturn, pSort->labelBkOut);\n    sqlite3VdbeGoto(v, addrBreak);\n    sqlite3VdbeResolveLabel(v, pSort->labelBkOut);\n  }\n  iTab = pSort->iECursor;\n  if( eDest==SRT_Output || eDest==SRT_Coroutine || eDest==SRT_Mem ){\n    regRowid = 0;\n    regRow = pDest->iSdst;\n    nSortData = nColumn;\n  }else{\n    regRowid = sqlite3GetTempReg(pParse);\n    regRow = sqlite3GetTempRange(pParse, nColumn);\n    nSortData = nColumn;\n  }\n  nKey = pOrderBy->nExpr - pSort->nOBSat;\n  if( pSort->sortFlags & SORTFLAG_UseSorter ){\n    int regSortOut = ++pParse->nMem;\n    iSortTab = pParse->nTab++;\n    if( pSort->labelBkOut ){\n      addrOnce = sqlite3VdbeAddOp0(v, OP_Once); VdbeCoverage(v);\n    }\n    sqlite3VdbeAddOp3(v, OP_OpenPseudo, iSortTab, regSortOut, nKey+1+nSortData);\n    if( addrOnce ) sqlite3VdbeJumpHere(v, addrOnce);\n    addr = 1 + sqlite3VdbeAddOp2(v, OP_SorterSort, iTab, addrBreak);\n    VdbeCoverage(v);\n    codeOffset(v, p->iOffset, addrContinue);\n    sqlite3VdbeAddOp3(v, OP_SorterData, iTab, regSortOut, iSortTab);\n    bSeq = 0;\n  }else{\n    addr = 1 + sqlite3VdbeAddOp2(v, OP_Sort, iTab, addrBreak); VdbeCoverage(v);\n    codeOffset(v, p->iOffset, addrContinue);\n    iSortTab = iTab;\n    bSeq = 1;\n  }\n  for(i=0, iCol=nKey+bSeq-1; i<nSortData; i++){\n    if( aOutEx[i].u.x.iOrderByCol==0 ) iCol++;\n  }\n  for(i=nSortData-1; i>=0; i--){\n    int iRead;\n    if( aOutEx[i].u.x.iOrderByCol ){\n      iRead = aOutEx[i].u.x.iOrderByCol-1;\n    }else{\n      iRead = iCol--;\n    }\n    sqlite3VdbeAddOp3(v, OP_Column, iSortTab, iRead, regRow+i);\n    VdbeComment((v, \"%s\", aOutEx[i].zName ? aOutEx[i].zName : aOutEx[i].zSpan));\n  }\n  switch( eDest ){\n    case SRT_Table:\n    case SRT_EphemTab: {\n      sqlite3VdbeAddOp2(v, OP_NewRowid, iParm, regRowid);\n      sqlite3VdbeAddOp3(v, OP_Insert, iParm, regRow, regRowid);\n      sqlite3VdbeChangeP5(v, OPFLAG_APPEND);\n      break;\n    }\n#ifndef SQLITE_OMIT_SUBQUERY\n    case SRT_Set: {\n      assert( nColumn==sqlite3Strlen30(pDest->zAffSdst) );\n      sqlite3VdbeAddOp4(v, OP_MakeRecord, regRow, nColumn, regRowid,\n                        pDest->zAffSdst, nColumn);\n      sqlite3ExprCacheAffinityChange(pParse, regRow, nColumn);\n      sqlite3VdbeAddOp4Int(v, OP_IdxInsert, iParm, regRowid, regRow, nColumn);\n      break;\n    }\n    case SRT_Mem: {\n      /* The LIMIT clause will terminate the loop for us */\n      break;\n    }\n#endif\n    default: {\n      assert( eDest==SRT_Output || eDest==SRT_Coroutine ); \n      testcase( eDest==SRT_Output );\n      testcase( eDest==SRT_Coroutine );\n      if( eDest==SRT_Output ){\n        sqlite3VdbeAddOp2(v, OP_ResultRow, pDest->iSdst, nColumn);\n        sqlite3ExprCacheAffinityChange(pParse, pDest->iSdst, nColumn);\n      }else{\n        sqlite3VdbeAddOp1(v, OP_Yield, pDest->iSDParm);\n      }\n      break;\n    }\n  }\n  if( regRowid ){\n    if( eDest==SRT_Set ){\n      sqlite3ReleaseTempRange(pParse, regRow, nColumn);\n    }else{\n      sqlite3ReleaseTempReg(pParse, regRow);\n    }\n    sqlite3ReleaseTempReg(pParse, regRowid);\n  }\n  /* The bottom of the loop\n  */\n  sqlite3VdbeResolveLabel(v, addrContinue);\n  if( pSort->sortFlags & SORTFLAG_UseSorter ){\n    sqlite3VdbeAddOp2(v, OP_SorterNext, iTab, addr); VdbeCoverage(v);\n  }else{\n    sqlite3VdbeAddOp2(v, OP_Next, iTab, addr); VdbeCoverage(v);\n  }\n  if( pSort->regReturn ) sqlite3VdbeAddOp1(v, OP_Return, pSort->regReturn);\n  sqlite3VdbeResolveLabel(v, addrBreak);\n}\n\n/*\n** Return a pointer to a string containing the 'declaration type' of the\n** expression pExpr. The string may be treated as static by the caller.\n**\n** Also try to estimate the size of the returned value and return that\n** result in *pEstWidth.\n**\n** The declaration type is the exact datatype definition extracted from the\n** original CREATE TABLE statement if the expression is a column. The\n** declaration type for a ROWID field is INTEGER. Exactly when an expression\n** is considered a column can be complex in the presence of subqueries. The\n** result-set expression in all of the following SELECT statements is \n** considered a column by this function.\n**\n**   SELECT col FROM tbl;\n**   SELECT (SELECT col FROM tbl;\n**   SELECT (SELECT col FROM tbl);\n**   SELECT abc FROM (SELECT col AS abc FROM tbl);\n** \n** The declaration type for any expression other than a column is NULL.\n**\n** This routine has either 3 or 6 parameters depending on whether or not\n** the SQLITE_ENABLE_COLUMN_METADATA compile-time option is used.\n*/\n#ifdef SQLITE_ENABLE_COLUMN_METADATA\n# define columnType(A,B,C,D,E) columnTypeImpl(A,B,C,D,E)\n#else /* if !defined(SQLITE_ENABLE_COLUMN_METADATA) */\n# define columnType(A,B,C,D,E) columnTypeImpl(A,B)\n#endif\nstatic const char *columnTypeImpl(\n  NameContext *pNC, \n#ifndef SQLITE_ENABLE_COLUMN_METADATA\n  Expr *pExpr\n#else\n  Expr *pExpr,\n  const char **pzOrigDb,\n  const char **pzOrigTab,\n  const char **pzOrigCol\n#endif\n){\n  char const *zType = 0;\n  int j;\n#ifdef SQLITE_ENABLE_COLUMN_METADATA\n  char const *zOrigDb = 0;\n  char const *zOrigTab = 0;\n  char const *zOrigCol = 0;\n#endif\n\n  assert( pExpr!=0 );\n  assert( pNC->pSrcList!=0 );\n  assert( pExpr->op!=TK_AGG_COLUMN );  /* This routine runes before aggregates\n                                       ** are processed */\n  switch( pExpr->op ){\n    case TK_COLUMN: {\n      /* The expression is a column. Locate the table the column is being\n      ** extracted from in NameContext.pSrcList. This table may be real\n      ** database table or a subquery.\n      */\n      Table *pTab = 0;            /* Table structure column is extracted from */\n      Select *pS = 0;             /* Select the column is extracted from */\n      int iCol = pExpr->iColumn;  /* Index of column in pTab */\n      while( pNC && !pTab ){\n        SrcList *pTabList = pNC->pSrcList;\n        for(j=0;j<pTabList->nSrc && pTabList->a[j].iCursor!=pExpr->iTable;j++);\n        if( j<pTabList->nSrc ){\n          pTab = pTabList->a[j].pTab;\n          pS = pTabList->a[j].pSelect;\n        }else{\n          pNC = pNC->pNext;\n        }\n      }\n\n      if( pTab==0 ){\n        /* At one time, code such as \"SELECT new.x\" within a trigger would\n        ** cause this condition to run.  Since then, we have restructured how\n        ** trigger code is generated and so this condition is no longer \n        ** possible. However, it can still be true for statements like\n        ** the following:\n        **\n        **   CREATE TABLE t1(col INTEGER);\n        **   SELECT (SELECT t1.col) FROM FROM t1;\n        **\n        ** when columnType() is called on the expression \"t1.col\" in the \n        ** sub-select. In this case, set the column type to NULL, even\n        ** though it should really be \"INTEGER\".\n        **\n        ** This is not a problem, as the column type of \"t1.col\" is never\n        ** used. When columnType() is called on the expression \n        ** \"(SELECT t1.col)\", the correct type is returned (see the TK_SELECT\n        ** branch below.  */\n        break;\n      }\n\n      assert( pTab && pExpr->pTab==pTab );\n      if( pS ){\n        /* The \"table\" is actually a sub-select or a view in the FROM clause\n        ** of the SELECT statement. Return the declaration type and origin\n        ** data for the result-set column of the sub-select.\n        */\n        if( iCol>=0 && iCol<pS->pEList->nExpr ){\n          /* If iCol is less than zero, then the expression requests the\n          ** rowid of the sub-select or view. This expression is legal (see \n          ** test case misc2.2.2) - it always evaluates to NULL.\n          */\n          NameContext sNC;\n          Expr *p = pS->pEList->a[iCol].pExpr;\n          sNC.pSrcList = pS->pSrc;\n          sNC.pNext = pNC;\n          sNC.pParse = pNC->pParse;\n          zType = columnType(&sNC, p,&zOrigDb,&zOrigTab,&zOrigCol); \n        }\n      }else{\n        /* A real table or a CTE table */\n        assert( !pS );\n#ifdef SQLITE_ENABLE_COLUMN_METADATA\n        if( iCol<0 ) iCol = pTab->iPKey;\n        assert( iCol==XN_ROWID || (iCol>=0 && iCol<pTab->nCol) );\n        if( iCol<0 ){\n          zType = \"INTEGER\";\n          zOrigCol = \"rowid\";\n        }else{\n          zOrigCol = pTab->aCol[iCol].zName;\n          zType = sqlite3ColumnType(&pTab->aCol[iCol],0);\n        }\n        zOrigTab = pTab->zName;\n        if( pNC->pParse && pTab->pSchema ){\n          int iDb = sqlite3SchemaToIndex(pNC->pParse->db, pTab->pSchema);\n          zOrigDb = pNC->pParse->db->aDb[iDb].zDbSName;\n        }\n#else\n        assert( iCol==XN_ROWID || (iCol>=0 && iCol<pTab->nCol) );\n        if( iCol<0 ){\n          zType = \"INTEGER\";\n        }else{\n          zType = sqlite3ColumnType(&pTab->aCol[iCol],0);\n        }\n#endif\n      }\n      break;\n    }\n#ifndef SQLITE_OMIT_SUBQUERY\n    case TK_SELECT: {\n      /* The expression is a sub-select. Return the declaration type and\n      ** origin info for the single column in the result set of the SELECT\n      ** statement.\n      */\n      NameContext sNC;\n      Select *pS = pExpr->x.pSelect;\n      Expr *p = pS->pEList->a[0].pExpr;\n      assert( ExprHasProperty(pExpr, EP_xIsSelect) );\n      sNC.pSrcList = pS->pSrc;\n      sNC.pNext = pNC;\n      sNC.pParse = pNC->pParse;\n      zType = columnType(&sNC, p, &zOrigDb, &zOrigTab, &zOrigCol); \n      break;\n    }\n#endif\n  }\n\n#ifdef SQLITE_ENABLE_COLUMN_METADATA  \n  if( pzOrigDb ){\n    assert( pzOrigTab && pzOrigCol );\n    *pzOrigDb = zOrigDb;\n    *pzOrigTab = zOrigTab;\n    *pzOrigCol = zOrigCol;\n  }\n#endif\n  return zType;\n}\n\n/*\n** Generate code that will tell the VDBE the declaration types of columns\n** in the result set.\n*/\nstatic void generateColumnTypes(\n  Parse *pParse,      /* Parser context */\n  SrcList *pTabList,  /* List of tables */\n  ExprList *pEList    /* Expressions defining the result set */\n){\n#ifndef SQLITE_OMIT_DECLTYPE\n  Vdbe *v = pParse->pVdbe;\n  int i;\n  NameContext sNC;\n  sNC.pSrcList = pTabList;\n  sNC.pParse = pParse;\n  sNC.pNext = 0;\n  for(i=0; i<pEList->nExpr; i++){\n    Expr *p = pEList->a[i].pExpr;\n    const char *zType;\n#ifdef SQLITE_ENABLE_COLUMN_METADATA\n    const char *zOrigDb = 0;\n    const char *zOrigTab = 0;\n    const char *zOrigCol = 0;\n    zType = columnType(&sNC, p, &zOrigDb, &zOrigTab, &zOrigCol);\n\n    /* The vdbe must make its own copy of the column-type and other \n    ** column specific strings, in case the schema is reset before this\n    ** virtual machine is deleted.\n    */\n    sqlite3VdbeSetColName(v, i, COLNAME_DATABASE, zOrigDb, SQLITE_TRANSIENT);\n    sqlite3VdbeSetColName(v, i, COLNAME_TABLE, zOrigTab, SQLITE_TRANSIENT);\n    sqlite3VdbeSetColName(v, i, COLNAME_COLUMN, zOrigCol, SQLITE_TRANSIENT);\n#else\n    zType = columnType(&sNC, p, 0, 0, 0);\n#endif\n    sqlite3VdbeSetColName(v, i, COLNAME_DECLTYPE, zType, SQLITE_TRANSIENT);\n  }\n#endif /* !defined(SQLITE_OMIT_DECLTYPE) */\n}\n\n\n/*\n** Compute the column names for a SELECT statement.\n**\n** The only guarantee that SQLite makes about column names is that if the\n** column has an AS clause assigning it a name, that will be the name used.\n** That is the only documented guarantee.  However, countless applications\n** developed over the years have made baseless assumptions about column names\n** and will break if those assumptions changes.  Hence, use extreme caution\n** when modifying this routine to avoid breaking legacy.\n**\n** See Also: sqlite3ColumnsFromExprList()\n**\n** The PRAGMA short_column_names and PRAGMA full_column_names settings are\n** deprecated.  The default setting is short=ON, full=OFF.  99.9% of all\n** applications should operate this way.  Nevertheless, we need to support the\n** other modes for legacy:\n**\n**    short=OFF, full=OFF:      Column name is the text of the expression has it\n**                              originally appears in the SELECT statement.  In\n**                              other words, the zSpan of the result expression.\n**\n**    short=ON, full=OFF:       (This is the default setting).  If the result\n**                              refers directly to a table column, then the\n**                              result column name is just the table column\n**                              name: COLUMN.  Otherwise use zSpan.\n**\n**    full=ON, short=ANY:       If the result refers directly to a table column,\n**                              then the result column name with the table name\n**                              prefix, ex: TABLE.COLUMN.  Otherwise use zSpan.\n*/\nstatic void generateColumnNames(\n  Parse *pParse,      /* Parser context */\n  Select *pSelect     /* Generate column names for this SELECT statement */\n){\n  Vdbe *v = pParse->pVdbe;\n  int i;\n  Table *pTab;\n  SrcList *pTabList;\n  ExprList *pEList;\n  sqlite3 *db = pParse->db;\n  int fullName;    /* TABLE.COLUMN if no AS clause and is a direct table ref */\n  int srcName;     /* COLUMN or TABLE.COLUMN if no AS clause and is direct */\n\n#ifndef SQLITE_OMIT_EXPLAIN\n  /* If this is an EXPLAIN, skip this step */\n  if( pParse->explain ){\n    return;\n  }\n#endif\n\n  if( pParse->colNamesSet || db->mallocFailed ) return;\n  /* Column names are determined by the left-most term of a compound select */\n  while( pSelect->pPrior ) pSelect = pSelect->pPrior;\n  SELECTTRACE(1,pParse,pSelect,(\"generating column names\\n\"));\n  pTabList = pSelect->pSrc;\n  pEList = pSelect->pEList;\n  assert( v!=0 );\n  assert( pTabList!=0 );\n  pParse->colNamesSet = 1;\n  fullName = (db->flags & SQLITE_FullColNames)!=0;\n  srcName = (db->flags & SQLITE_ShortColNames)!=0 || fullName;\n  sqlite3VdbeSetNumCols(v, pEList->nExpr);\n  for(i=0; i<pEList->nExpr; i++){\n    Expr *p = pEList->a[i].pExpr;\n\n    assert( p!=0 );\n    assert( p->op!=TK_AGG_COLUMN );  /* Agg processing has not run yet */\n    assert( p->op!=TK_COLUMN || p->pTab!=0 ); /* Covering idx not yet coded */\n    if( pEList->a[i].zName ){\n      /* An AS clause always takes first priority */\n      char *zName = pEList->a[i].zName;\n      sqlite3VdbeSetColName(v, i, COLNAME_NAME, zName, SQLITE_TRANSIENT);\n    }else if( srcName && p->op==TK_COLUMN ){\n      char *zCol;\n      int iCol = p->iColumn;\n      pTab = p->pTab;\n      assert( pTab!=0 );\n      if( iCol<0 ) iCol = pTab->iPKey;\n      assert( iCol==-1 || (iCol>=0 && iCol<pTab->nCol) );\n      if( iCol<0 ){\n        zCol = \"rowid\";\n      }else{\n        zCol = pTab->aCol[iCol].zName;\n      }\n      if( fullName ){\n        char *zName = 0;\n        zName = sqlite3MPrintf(db, \"%s.%s\", pTab->zName, zCol);\n        sqlite3VdbeSetColName(v, i, COLNAME_NAME, zName, SQLITE_DYNAMIC);\n      }else{\n        sqlite3VdbeSetColName(v, i, COLNAME_NAME, zCol, SQLITE_TRANSIENT);\n      }\n    }else{\n      const char *z = pEList->a[i].zSpan;\n      z = z==0 ? sqlite3MPrintf(db, \"column%d\", i+1) : sqlite3DbStrDup(db, z);\n      sqlite3VdbeSetColName(v, i, COLNAME_NAME, z, SQLITE_DYNAMIC);\n    }\n  }\n  generateColumnTypes(pParse, pTabList, pEList);\n}\n\n/*\n** Given an expression list (which is really the list of expressions\n** that form the result set of a SELECT statement) compute appropriate\n** column names for a table that would hold the expression list.\n**\n** All column names will be unique.\n**\n** Only the column names are computed.  Column.zType, Column.zColl,\n** and other fields of Column are zeroed.\n**\n** Return SQLITE_OK on success.  If a memory allocation error occurs,\n** store NULL in *paCol and 0 in *pnCol and return SQLITE_NOMEM.\n**\n** The only guarantee that SQLite makes about column names is that if the\n** column has an AS clause assigning it a name, that will be the name used.\n** That is the only documented guarantee.  However, countless applications\n** developed over the years have made baseless assumptions about column names\n** and will break if those assumptions changes.  Hence, use extreme caution\n** when modifying this routine to avoid breaking legacy.\n**\n** See Also: generateColumnNames()\n*/\nSQLITE_PRIVATE int sqlite3ColumnsFromExprList(\n  Parse *pParse,          /* Parsing context */\n  ExprList *pEList,       /* Expr list from which to derive column names */\n  i16 *pnCol,             /* Write the number of columns here */\n  Column **paCol          /* Write the new column list here */\n){\n  sqlite3 *db = pParse->db;   /* Database connection */\n  int i, j;                   /* Loop counters */\n  u32 cnt;                    /* Index added to make the name unique */\n  Column *aCol, *pCol;        /* For looping over result columns */\n  int nCol;                   /* Number of columns in the result set */\n  char *zName;                /* Column name */\n  int nName;                  /* Size of name in zName[] */\n  Hash ht;                    /* Hash table of column names */\n\n  sqlite3HashInit(&ht);\n  if( pEList ){\n    nCol = pEList->nExpr;\n    aCol = sqlite3DbMallocZero(db, sizeof(aCol[0])*nCol);\n    testcase( aCol==0 );\n    if( nCol>32767 ) nCol = 32767;\n  }else{\n    nCol = 0;\n    aCol = 0;\n  }\n  assert( nCol==(i16)nCol );\n  *pnCol = nCol;\n  *paCol = aCol;\n\n  for(i=0, pCol=aCol; i<nCol && !db->mallocFailed; i++, pCol++){\n    /* Get an appropriate name for the column\n    */\n    if( (zName = pEList->a[i].zName)!=0 ){\n      /* If the column contains an \"AS <name>\" phrase, use <name> as the name */\n    }else{\n      Expr *pColExpr = sqlite3ExprSkipCollate(pEList->a[i].pExpr);\n      while( pColExpr->op==TK_DOT ){\n        pColExpr = pColExpr->pRight;\n        assert( pColExpr!=0 );\n      }\n      assert( pColExpr->op!=TK_AGG_COLUMN );\n      if( pColExpr->op==TK_COLUMN ){\n        /* For columns use the column name name */\n        int iCol = pColExpr->iColumn;\n        Table *pTab = pColExpr->pTab;\n        assert( pTab!=0 );\n        if( iCol<0 ) iCol = pTab->iPKey;\n        zName = iCol>=0 ? pTab->aCol[iCol].zName : \"rowid\";\n      }else if( pColExpr->op==TK_ID ){\n        assert( !ExprHasProperty(pColExpr, EP_IntValue) );\n        zName = pColExpr->u.zToken;\n      }else{\n        /* Use the original text of the column expression as its name */\n        zName = pEList->a[i].zSpan;\n      }\n    }\n    if( zName ){\n      zName = sqlite3DbStrDup(db, zName);\n    }else{\n      zName = sqlite3MPrintf(db,\"column%d\",i+1);\n    }\n\n    /* Make sure the column name is unique.  If the name is not unique,\n    ** append an integer to the name so that it becomes unique.\n    */\n    cnt = 0;\n    while( zName && sqlite3HashFind(&ht, zName)!=0 ){\n      nName = sqlite3Strlen30(zName);\n      if( nName>0 ){\n        for(j=nName-1; j>0 && sqlite3Isdigit(zName[j]); j--){}\n        if( zName[j]==':' ) nName = j;\n      }\n      zName = sqlite3MPrintf(db, \"%.*z:%u\", nName, zName, ++cnt);\n      if( cnt>3 ) sqlite3_randomness(sizeof(cnt), &cnt);\n    }\n    pCol->zName = zName;\n    sqlite3ColumnPropertiesFromName(0, pCol);\n    if( zName && sqlite3HashInsert(&ht, zName, pCol)==pCol ){\n      sqlite3OomFault(db);\n    }\n  }\n  sqlite3HashClear(&ht);\n  if( db->mallocFailed ){\n    for(j=0; j<i; j++){\n      sqlite3DbFree(db, aCol[j].zName);\n    }\n    sqlite3DbFree(db, aCol);\n    *paCol = 0;\n    *pnCol = 0;\n    return SQLITE_NOMEM_BKPT;\n  }\n  return SQLITE_OK;\n}\n\n/*\n** Add type and collation information to a column list based on\n** a SELECT statement.\n** \n** The column list presumably came from selectColumnNamesFromExprList().\n** The column list has only names, not types or collations.  This\n** routine goes through and adds the types and collations.\n**\n** This routine requires that all identifiers in the SELECT\n** statement be resolved.\n*/\nSQLITE_PRIVATE void sqlite3SelectAddColumnTypeAndCollation(\n  Parse *pParse,        /* Parsing contexts */\n  Table *pTab,          /* Add column type information to this table */\n  Select *pSelect       /* SELECT used to determine types and collations */\n){\n  sqlite3 *db = pParse->db;\n  NameContext sNC;\n  Column *pCol;\n  CollSeq *pColl;\n  int i;\n  Expr *p;\n  struct ExprList_item *a;\n\n  assert( pSelect!=0 );\n  assert( (pSelect->selFlags & SF_Resolved)!=0 );\n  assert( pTab->nCol==pSelect->pEList->nExpr || db->mallocFailed );\n  if( db->mallocFailed ) return;\n  memset(&sNC, 0, sizeof(sNC));\n  sNC.pSrcList = pSelect->pSrc;\n  a = pSelect->pEList->a;\n  for(i=0, pCol=pTab->aCol; i<pTab->nCol; i++, pCol++){\n    const char *zType;\n    int n, m;\n    p = a[i].pExpr;\n    zType = columnType(&sNC, p, 0, 0, 0);\n    /* pCol->szEst = ... // Column size est for SELECT tables never used */\n    pCol->affinity = sqlite3ExprAffinity(p);\n    if( zType ){\n      m = sqlite3Strlen30(zType);\n      n = sqlite3Strlen30(pCol->zName);\n      pCol->zName = sqlite3DbReallocOrFree(db, pCol->zName, n+m+2);\n      if( pCol->zName ){\n        memcpy(&pCol->zName[n+1], zType, m+1);\n        pCol->colFlags |= COLFLAG_HASTYPE;\n      }\n    }\n    if( pCol->affinity==0 ) pCol->affinity = SQLITE_AFF_BLOB;\n    pColl = sqlite3ExprCollSeq(pParse, p);\n    if( pColl && pCol->zColl==0 ){\n      pCol->zColl = sqlite3DbStrDup(db, pColl->zName);\n    }\n  }\n  pTab->szTabRow = 1; /* Any non-zero value works */\n}\n\n/*\n** Given a SELECT statement, generate a Table structure that describes\n** the result set of that SELECT.\n*/\nSQLITE_PRIVATE Table *sqlite3ResultSetOfSelect(Parse *pParse, Select *pSelect){\n  Table *pTab;\n  sqlite3 *db = pParse->db;\n  int savedFlags;\n\n  savedFlags = db->flags;\n  db->flags &= ~SQLITE_FullColNames;\n  db->flags |= SQLITE_ShortColNames;\n  sqlite3SelectPrep(pParse, pSelect, 0);\n  if( pParse->nErr ) return 0;\n  while( pSelect->pPrior ) pSelect = pSelect->pPrior;\n  db->flags = savedFlags;\n  pTab = sqlite3DbMallocZero(db, sizeof(Table) );\n  if( pTab==0 ){\n    return 0;\n  }\n  /* The sqlite3ResultSetOfSelect() is only used n contexts where lookaside\n  ** is disabled */\n  assert( db->lookaside.bDisable );\n  pTab->nTabRef = 1;\n  pTab->zName = 0;\n  pTab->nRowLogEst = 200; assert( 200==sqlite3LogEst(1048576) );\n  sqlite3ColumnsFromExprList(pParse, pSelect->pEList, &pTab->nCol, &pTab->aCol);\n  sqlite3SelectAddColumnTypeAndCollation(pParse, pTab, pSelect);\n  pTab->iPKey = -1;\n  if( db->mallocFailed ){\n    sqlite3DeleteTable(db, pTab);\n    return 0;\n  }\n  return pTab;\n}\n\n/*\n** Get a VDBE for the given parser context.  Create a new one if necessary.\n** If an error occurs, return NULL and leave a message in pParse.\n*/\nSQLITE_PRIVATE Vdbe *sqlite3GetVdbe(Parse *pParse){\n  if( pParse->pVdbe ){\n    return pParse->pVdbe;\n  }\n  if( pParse->pToplevel==0\n   && OptimizationEnabled(pParse->db,SQLITE_FactorOutConst)\n  ){\n    pParse->okConstFactor = 1;\n  }\n  return sqlite3VdbeCreate(pParse);\n}\n\n\n/*\n** Compute the iLimit and iOffset fields of the SELECT based on the\n** pLimit expressions.  pLimit->pLeft and pLimit->pRight hold the expressions\n** that appear in the original SQL statement after the LIMIT and OFFSET\n** keywords.  Or NULL if those keywords are omitted. iLimit and iOffset \n** are the integer memory register numbers for counters used to compute \n** the limit and offset.  If there is no limit and/or offset, then \n** iLimit and iOffset are negative.\n**\n** This routine changes the values of iLimit and iOffset only if\n** a limit or offset is defined by pLimit->pLeft and pLimit->pRight.  iLimit\n** and iOffset should have been preset to appropriate default values (zero)\n** prior to calling this routine.\n**\n** The iOffset register (if it exists) is initialized to the value\n** of the OFFSET.  The iLimit register is initialized to LIMIT.  Register\n** iOffset+1 is initialized to LIMIT+OFFSET.\n**\n** Only if pLimit->pLeft!=0 do the limit registers get\n** redefined.  The UNION ALL operator uses this property to force\n** the reuse of the same limit and offset registers across multiple\n** SELECT statements.\n*/\nstatic void computeLimitRegisters(Parse *pParse, Select *p, int iBreak){\n  Vdbe *v = 0;\n  int iLimit = 0;\n  int iOffset;\n  int n;\n  Expr *pLimit = p->pLimit;\n\n  if( p->iLimit ) return;\n\n  /* \n  ** \"LIMIT -1\" always shows all rows.  There is some\n  ** controversy about what the correct behavior should be.\n  ** The current implementation interprets \"LIMIT 0\" to mean\n  ** no rows.\n  */\n  sqlite3ExprCacheClear(pParse);\n  if( pLimit ){\n    assert( pLimit->op==TK_LIMIT );\n    assert( pLimit->pLeft!=0 );\n    p->iLimit = iLimit = ++pParse->nMem;\n    v = sqlite3GetVdbe(pParse);\n    assert( v!=0 );\n    if( sqlite3ExprIsInteger(pLimit->pLeft, &n) ){\n      sqlite3VdbeAddOp2(v, OP_Integer, n, iLimit);\n      VdbeComment((v, \"LIMIT counter\"));\n      if( n==0 ){\n        sqlite3VdbeGoto(v, iBreak);\n      }else if( n>=0 && p->nSelectRow>sqlite3LogEst((u64)n) ){\n        p->nSelectRow = sqlite3LogEst((u64)n);\n        p->selFlags |= SF_FixedLimit;\n      }\n    }else{\n      sqlite3ExprCode(pParse, pLimit->pLeft, iLimit);\n      sqlite3VdbeAddOp1(v, OP_MustBeInt, iLimit); VdbeCoverage(v);\n      VdbeComment((v, \"LIMIT counter\"));\n      sqlite3VdbeAddOp2(v, OP_IfNot, iLimit, iBreak); VdbeCoverage(v);\n    }\n    if( pLimit->pRight ){\n      p->iOffset = iOffset = ++pParse->nMem;\n      pParse->nMem++;   /* Allocate an extra register for limit+offset */\n      sqlite3ExprCode(pParse, pLimit->pRight, iOffset);\n      sqlite3VdbeAddOp1(v, OP_MustBeInt, iOffset); VdbeCoverage(v);\n      VdbeComment((v, \"OFFSET counter\"));\n      sqlite3VdbeAddOp3(v, OP_OffsetLimit, iLimit, iOffset+1, iOffset);\n      VdbeComment((v, \"LIMIT+OFFSET\"));\n    }\n  }\n}\n\n#ifndef SQLITE_OMIT_COMPOUND_SELECT\n/*\n** Return the appropriate collating sequence for the iCol-th column of\n** the result set for the compound-select statement \"p\".  Return NULL if\n** the column has no default collating sequence.\n**\n** The collating sequence for the compound select is taken from the\n** left-most term of the select that has a collating sequence.\n*/\nstatic CollSeq *multiSelectCollSeq(Parse *pParse, Select *p, int iCol){\n  CollSeq *pRet;\n  if( p->pPrior ){\n    pRet = multiSelectCollSeq(pParse, p->pPrior, iCol);\n  }else{\n    pRet = 0;\n  }\n  assert( iCol>=0 );\n  /* iCol must be less than p->pEList->nExpr.  Otherwise an error would\n  ** have been thrown during name resolution and we would not have gotten\n  ** this far */\n  if( pRet==0 && ALWAYS(iCol<p->pEList->nExpr) ){\n    pRet = sqlite3ExprCollSeq(pParse, p->pEList->a[iCol].pExpr);\n  }\n  return pRet;\n}\n\n/*\n** The select statement passed as the second parameter is a compound SELECT\n** with an ORDER BY clause. This function allocates and returns a KeyInfo\n** structure suitable for implementing the ORDER BY.\n**\n** Space to hold the KeyInfo structure is obtained from malloc. The calling\n** function is responsible for ensuring that this structure is eventually\n** freed.\n*/\nstatic KeyInfo *multiSelectOrderByKeyInfo(Parse *pParse, Select *p, int nExtra){\n  ExprList *pOrderBy = p->pOrderBy;\n  int nOrderBy = p->pOrderBy->nExpr;\n  sqlite3 *db = pParse->db;\n  KeyInfo *pRet = sqlite3KeyInfoAlloc(db, nOrderBy+nExtra, 1);\n  if( pRet ){\n    int i;\n    for(i=0; i<nOrderBy; i++){\n      struct ExprList_item *pItem = &pOrderBy->a[i];\n      Expr *pTerm = pItem->pExpr;\n      CollSeq *pColl;\n\n      if( pTerm->flags & EP_Collate ){\n        pColl = sqlite3ExprCollSeq(pParse, pTerm);\n      }else{\n        pColl = multiSelectCollSeq(pParse, p, pItem->u.x.iOrderByCol-1);\n        if( pColl==0 ) pColl = db->pDfltColl;\n        pOrderBy->a[i].pExpr =\n          sqlite3ExprAddCollateString(pParse, pTerm, pColl->zName);\n      }\n      assert( sqlite3KeyInfoIsWriteable(pRet) );\n      pRet->aColl[i] = pColl;\n      pRet->aSortOrder[i] = pOrderBy->a[i].sortOrder;\n    }\n  }\n\n  return pRet;\n}\n\n#ifndef SQLITE_OMIT_CTE\n/*\n** This routine generates VDBE code to compute the content of a WITH RECURSIVE\n** query of the form:\n**\n**   <recursive-table> AS (<setup-query> UNION [ALL] <recursive-query>)\n**                         \\___________/             \\_______________/\n**                           p->pPrior                      p\n**\n**\n** There is exactly one reference to the recursive-table in the FROM clause\n** of recursive-query, marked with the SrcList->a[].fg.isRecursive flag.\n**\n** The setup-query runs once to generate an initial set of rows that go\n** into a Queue table.  Rows are extracted from the Queue table one by\n** one.  Each row extracted from Queue is output to pDest.  Then the single\n** extracted row (now in the iCurrent table) becomes the content of the\n** recursive-table for a recursive-query run.  The output of the recursive-query\n** is added back into the Queue table.  Then another row is extracted from Queue\n** and the iteration continues until the Queue table is empty.\n**\n** If the compound query operator is UNION then no duplicate rows are ever\n** inserted into the Queue table.  The iDistinct table keeps a copy of all rows\n** that have ever been inserted into Queue and causes duplicates to be\n** discarded.  If the operator is UNION ALL, then duplicates are allowed.\n** \n** If the query has an ORDER BY, then entries in the Queue table are kept in\n** ORDER BY order and the first entry is extracted for each cycle.  Without\n** an ORDER BY, the Queue table is just a FIFO.\n**\n** If a LIMIT clause is provided, then the iteration stops after LIMIT rows\n** have been output to pDest.  A LIMIT of zero means to output no rows and a\n** negative LIMIT means to output all rows.  If there is also an OFFSET clause\n** with a positive value, then the first OFFSET outputs are discarded rather\n** than being sent to pDest.  The LIMIT count does not begin until after OFFSET\n** rows have been skipped.\n*/\nstatic void generateWithRecursiveQuery(\n  Parse *pParse,        /* Parsing context */\n  Select *p,            /* The recursive SELECT to be coded */\n  SelectDest *pDest     /* What to do with query results */\n){\n  SrcList *pSrc = p->pSrc;      /* The FROM clause of the recursive query */\n  int nCol = p->pEList->nExpr;  /* Number of columns in the recursive table */\n  Vdbe *v = pParse->pVdbe;      /* The prepared statement under construction */\n  Select *pSetup = p->pPrior;   /* The setup query */\n  int addrTop;                  /* Top of the loop */\n  int addrCont, addrBreak;      /* CONTINUE and BREAK addresses */\n  int iCurrent = 0;             /* The Current table */\n  int regCurrent;               /* Register holding Current table */\n  int iQueue;                   /* The Queue table */\n  int iDistinct = 0;            /* To ensure unique results if UNION */\n  int eDest = SRT_Fifo;         /* How to write to Queue */\n  SelectDest destQueue;         /* SelectDest targetting the Queue table */\n  int i;                        /* Loop counter */\n  int rc;                       /* Result code */\n  ExprList *pOrderBy;           /* The ORDER BY clause */\n  Expr *pLimit;                 /* Saved LIMIT and OFFSET */\n  int regLimit, regOffset;      /* Registers used by LIMIT and OFFSET */\n\n  /* Obtain authorization to do a recursive query */\n  if( sqlite3AuthCheck(pParse, SQLITE_RECURSIVE, 0, 0, 0) ) return;\n\n  /* Process the LIMIT and OFFSET clauses, if they exist */\n  addrBreak = sqlite3VdbeMakeLabel(v);\n  p->nSelectRow = 320;  /* 4 billion rows */\n  computeLimitRegisters(pParse, p, addrBreak);\n  pLimit = p->pLimit;\n  regLimit = p->iLimit;\n  regOffset = p->iOffset;\n  p->pLimit = 0;\n  p->iLimit = p->iOffset = 0;\n  pOrderBy = p->pOrderBy;\n\n  /* Locate the cursor number of the Current table */\n  for(i=0; ALWAYS(i<pSrc->nSrc); i++){\n    if( pSrc->a[i].fg.isRecursive ){\n      iCurrent = pSrc->a[i].iCursor;\n      break;\n    }\n  }\n\n  /* Allocate cursors numbers for Queue and Distinct.  The cursor number for\n  ** the Distinct table must be exactly one greater than Queue in order\n  ** for the SRT_DistFifo and SRT_DistQueue destinations to work. */\n  iQueue = pParse->nTab++;\n  if( p->op==TK_UNION ){\n    eDest = pOrderBy ? SRT_DistQueue : SRT_DistFifo;\n    iDistinct = pParse->nTab++;\n  }else{\n    eDest = pOrderBy ? SRT_Queue : SRT_Fifo;\n  }\n  sqlite3SelectDestInit(&destQueue, eDest, iQueue);\n\n  /* Allocate cursors for Current, Queue, and Distinct. */\n  regCurrent = ++pParse->nMem;\n  sqlite3VdbeAddOp3(v, OP_OpenPseudo, iCurrent, regCurrent, nCol);\n  if( pOrderBy ){\n    KeyInfo *pKeyInfo = multiSelectOrderByKeyInfo(pParse, p, 1);\n    sqlite3VdbeAddOp4(v, OP_OpenEphemeral, iQueue, pOrderBy->nExpr+2, 0,\n                      (char*)pKeyInfo, P4_KEYINFO);\n    destQueue.pOrderBy = pOrderBy;\n  }else{\n    sqlite3VdbeAddOp2(v, OP_OpenEphemeral, iQueue, nCol);\n  }\n  VdbeComment((v, \"Queue table\"));\n  if( iDistinct ){\n    p->addrOpenEphm[0] = sqlite3VdbeAddOp2(v, OP_OpenEphemeral, iDistinct, 0);\n    p->selFlags |= SF_UsesEphemeral;\n  }\n\n  /* Detach the ORDER BY clause from the compound SELECT */\n  p->pOrderBy = 0;\n\n  /* Store the results of the setup-query in Queue. */\n  pSetup->pNext = 0;\n  rc = sqlite3Select(pParse, pSetup, &destQueue);\n  pSetup->pNext = p;\n  if( rc ) goto end_of_recursive_query;\n\n  /* Find the next row in the Queue and output that row */\n  addrTop = sqlite3VdbeAddOp2(v, OP_Rewind, iQueue, addrBreak); VdbeCoverage(v);\n\n  /* Transfer the next row in Queue over to Current */\n  sqlite3VdbeAddOp1(v, OP_NullRow, iCurrent); /* To reset column cache */\n  if( pOrderBy ){\n    sqlite3VdbeAddOp3(v, OP_Column, iQueue, pOrderBy->nExpr+1, regCurrent);\n  }else{\n    sqlite3VdbeAddOp2(v, OP_RowData, iQueue, regCurrent);\n  }\n  sqlite3VdbeAddOp1(v, OP_Delete, iQueue);\n\n  /* Output the single row in Current */\n  addrCont = sqlite3VdbeMakeLabel(v);\n  codeOffset(v, regOffset, addrCont);\n  selectInnerLoop(pParse, p, iCurrent,\n      0, 0, pDest, addrCont, addrBreak);\n  if( regLimit ){\n    sqlite3VdbeAddOp2(v, OP_DecrJumpZero, regLimit, addrBreak);\n    VdbeCoverage(v);\n  }\n  sqlite3VdbeResolveLabel(v, addrCont);\n\n  /* Execute the recursive SELECT taking the single row in Current as\n  ** the value for the recursive-table. Store the results in the Queue.\n  */\n  if( p->selFlags & SF_Aggregate ){\n    sqlite3ErrorMsg(pParse, \"recursive aggregate queries not supported\");\n  }else{\n    p->pPrior = 0;\n    sqlite3Select(pParse, p, &destQueue);\n    assert( p->pPrior==0 );\n    p->pPrior = pSetup;\n  }\n\n  /* Keep running the loop until the Queue is empty */\n  sqlite3VdbeGoto(v, addrTop);\n  sqlite3VdbeResolveLabel(v, addrBreak);\n\nend_of_recursive_query:\n  sqlite3ExprListDelete(pParse->db, p->pOrderBy);\n  p->pOrderBy = pOrderBy;\n  p->pLimit = pLimit;\n  return;\n}\n#endif /* SQLITE_OMIT_CTE */\n\n/* Forward references */\nstatic int multiSelectOrderBy(\n  Parse *pParse,        /* Parsing context */\n  Select *p,            /* The right-most of SELECTs to be coded */\n  SelectDest *pDest     /* What to do with query results */\n);\n\n/*\n** Handle the special case of a compound-select that originates from a\n** VALUES clause.  By handling this as a special case, we avoid deep\n** recursion, and thus do not need to enforce the SQLITE_LIMIT_COMPOUND_SELECT\n** on a VALUES clause.\n**\n** Because the Select object originates from a VALUES clause:\n**   (1) There is no LIMIT or OFFSET or else there is a LIMIT of exactly 1\n**   (2) All terms are UNION ALL\n**   (3) There is no ORDER BY clause\n**\n** The \"LIMIT of exactly 1\" case of condition (1) comes about when a VALUES\n** clause occurs within scalar expression (ex: \"SELECT (VALUES(1),(2),(3))\").\n** The sqlite3CodeSubselect will have added the LIMIT 1 clause in tht case.\n** Since the limit is exactly 1, we only need to evalutes the left-most VALUES.\n*/\nstatic int multiSelectValues(\n  Parse *pParse,        /* Parsing context */\n  Select *p,            /* The right-most of SELECTs to be coded */\n  SelectDest *pDest     /* What to do with query results */\n){\n  Select *pPrior;\n  Select *pRightmost = p;\n  int nRow = 1;\n  int rc = 0;\n  assert( p->selFlags & SF_MultiValue );\n  do{\n    assert( p->selFlags & SF_Values );\n    assert( p->op==TK_ALL || (p->op==TK_SELECT && p->pPrior==0) );\n    assert( p->pNext==0 || p->pEList->nExpr==p->pNext->pEList->nExpr );\n    if( p->pPrior==0 ) break;\n    assert( p->pPrior->pNext==p );\n    p = p->pPrior;\n    nRow++;\n  }while(1);\n  while( p ){\n    pPrior = p->pPrior;\n    p->pPrior = 0;\n    rc = sqlite3Select(pParse, p, pDest);\n    p->pPrior = pPrior;\n    if( rc || pRightmost->pLimit ) break;\n    p->nSelectRow = nRow;\n    p = p->pNext;\n  }\n  return rc;\n}\n\n/*\n** This routine is called to process a compound query form from\n** two or more separate queries using UNION, UNION ALL, EXCEPT, or\n** INTERSECT\n**\n** \"p\" points to the right-most of the two queries.  the query on the\n** left is p->pPrior.  The left query could also be a compound query\n** in which case this routine will be called recursively. \n**\n** The results of the total query are to be written into a destination\n** of type eDest with parameter iParm.\n**\n** Example 1:  Consider a three-way compound SQL statement.\n**\n**     SELECT a FROM t1 UNION SELECT b FROM t2 UNION SELECT c FROM t3\n**\n** This statement is parsed up as follows:\n**\n**     SELECT c FROM t3\n**      |\n**      `----->  SELECT b FROM t2\n**                |\n**                `------>  SELECT a FROM t1\n**\n** The arrows in the diagram above represent the Select.pPrior pointer.\n** So if this routine is called with p equal to the t3 query, then\n** pPrior will be the t2 query.  p->op will be TK_UNION in this case.\n**\n** Notice that because of the way SQLite parses compound SELECTs, the\n** individual selects always group from left to right.\n*/\nstatic int multiSelect(\n  Parse *pParse,        /* Parsing context */\n  Select *p,            /* The right-most of SELECTs to be coded */\n  SelectDest *pDest     /* What to do with query results */\n){\n  int rc = SQLITE_OK;   /* Success code from a subroutine */\n  Select *pPrior;       /* Another SELECT immediately to our left */\n  Vdbe *v;              /* Generate code to this VDBE */\n  SelectDest dest;      /* Alternative data destination */\n  Select *pDelete = 0;  /* Chain of simple selects to delete */\n  sqlite3 *db;          /* Database connection */\n#ifndef SQLITE_OMIT_EXPLAIN\n  int iSub1 = 0;        /* EQP id of left-hand query */\n  int iSub2 = 0;        /* EQP id of right-hand query */\n#endif\n\n  /* Make sure there is no ORDER BY or LIMIT clause on prior SELECTs.  Only\n  ** the last (right-most) SELECT in the series may have an ORDER BY or LIMIT.\n  */\n  assert( p && p->pPrior );  /* Calling function guarantees this much */\n  assert( (p->selFlags & SF_Recursive)==0 || p->op==TK_ALL || p->op==TK_UNION );\n  db = pParse->db;\n  pPrior = p->pPrior;\n  dest = *pDest;\n  if( pPrior->pOrderBy || pPrior->pLimit ){\n    sqlite3ErrorMsg(pParse,\"%s clause should come after %s not before\",\n      pPrior->pOrderBy!=0 ? \"ORDER BY\" : \"LIMIT\", selectOpName(p->op));\n    rc = 1;\n    goto multi_select_end;\n  }\n\n  v = sqlite3GetVdbe(pParse);\n  assert( v!=0 );  /* The VDBE already created by calling function */\n\n  /* Create the destination temporary table if necessary\n  */\n  if( dest.eDest==SRT_EphemTab ){\n    assert( p->pEList );\n    sqlite3VdbeAddOp2(v, OP_OpenEphemeral, dest.iSDParm, p->pEList->nExpr);\n    dest.eDest = SRT_Table;\n  }\n\n  /* Special handling for a compound-select that originates as a VALUES clause.\n  */\n  if( p->selFlags & SF_MultiValue ){\n    rc = multiSelectValues(pParse, p, &dest);\n    goto multi_select_end;\n  }\n\n  /* Make sure all SELECTs in the statement have the same number of elements\n  ** in their result sets.\n  */\n  assert( p->pEList && pPrior->pEList );\n  assert( p->pEList->nExpr==pPrior->pEList->nExpr );\n\n#ifndef SQLITE_OMIT_CTE\n  if( p->selFlags & SF_Recursive ){\n    generateWithRecursiveQuery(pParse, p, &dest);\n  }else\n#endif\n\n  /* Compound SELECTs that have an ORDER BY clause are handled separately.\n  */\n  if( p->pOrderBy ){\n    return multiSelectOrderBy(pParse, p, pDest);\n  }else\n\n  /* Generate code for the left and right SELECT statements.\n  */\n  switch( p->op ){\n    case TK_ALL: {\n      int addr = 0;\n      int nLimit;\n      assert( !pPrior->pLimit );\n      pPrior->iLimit = p->iLimit;\n      pPrior->iOffset = p->iOffset;\n      pPrior->pLimit = p->pLimit;\n      explainSetInteger(iSub1, pParse->iNextSelectId);\n      rc = sqlite3Select(pParse, pPrior, &dest);\n      p->pLimit = 0;\n      if( rc ){\n        goto multi_select_end;\n      }\n      p->pPrior = 0;\n      p->iLimit = pPrior->iLimit;\n      p->iOffset = pPrior->iOffset;\n      if( p->iLimit ){\n        addr = sqlite3VdbeAddOp1(v, OP_IfNot, p->iLimit); VdbeCoverage(v);\n        VdbeComment((v, \"Jump ahead if LIMIT reached\"));\n        if( p->iOffset ){\n          sqlite3VdbeAddOp3(v, OP_OffsetLimit,\n                            p->iLimit, p->iOffset+1, p->iOffset);\n        }\n      }\n      explainSetInteger(iSub2, pParse->iNextSelectId);\n      rc = sqlite3Select(pParse, p, &dest);\n      testcase( rc!=SQLITE_OK );\n      pDelete = p->pPrior;\n      p->pPrior = pPrior;\n      p->nSelectRow = sqlite3LogEstAdd(p->nSelectRow, pPrior->nSelectRow);\n      if( pPrior->pLimit\n       && sqlite3ExprIsInteger(pPrior->pLimit->pLeft, &nLimit)\n       && nLimit>0 && p->nSelectRow > sqlite3LogEst((u64)nLimit) \n      ){\n        p->nSelectRow = sqlite3LogEst((u64)nLimit);\n      }\n      if( addr ){\n        sqlite3VdbeJumpHere(v, addr);\n      }\n      break;\n    }\n    case TK_EXCEPT:\n    case TK_UNION: {\n      int unionTab;    /* Cursor number of the temporary table holding result */\n      u8 op = 0;       /* One of the SRT_ operations to apply to self */\n      int priorOp;     /* The SRT_ operation to apply to prior selects */\n      Expr *pLimit;    /* Saved values of p->nLimit  */\n      int addr;\n      SelectDest uniondest;\n\n      testcase( p->op==TK_EXCEPT );\n      testcase( p->op==TK_UNION );\n      priorOp = SRT_Union;\n      if( dest.eDest==priorOp ){\n        /* We can reuse a temporary table generated by a SELECT to our\n        ** right.\n        */\n        assert( p->pLimit==0 );      /* Not allowed on leftward elements */\n        unionTab = dest.iSDParm;\n      }else{\n        /* We will need to create our own temporary table to hold the\n        ** intermediate results.\n        */\n        unionTab = pParse->nTab++;\n        assert( p->pOrderBy==0 );\n        addr = sqlite3VdbeAddOp2(v, OP_OpenEphemeral, unionTab, 0);\n        assert( p->addrOpenEphm[0] == -1 );\n        p->addrOpenEphm[0] = addr;\n        findRightmost(p)->selFlags |= SF_UsesEphemeral;\n        assert( p->pEList );\n      }\n\n      /* Code the SELECT statements to our left\n      */\n      assert( !pPrior->pOrderBy );\n      sqlite3SelectDestInit(&uniondest, priorOp, unionTab);\n      explainSetInteger(iSub1, pParse->iNextSelectId);\n      rc = sqlite3Select(pParse, pPrior, &uniondest);\n      if( rc ){\n        goto multi_select_end;\n      }\n\n      /* Code the current SELECT statement\n      */\n      if( p->op==TK_EXCEPT ){\n        op = SRT_Except;\n      }else{\n        assert( p->op==TK_UNION );\n        op = SRT_Union;\n      }\n      p->pPrior = 0;\n      pLimit = p->pLimit;\n      p->pLimit = 0;\n      uniondest.eDest = op;\n      explainSetInteger(iSub2, pParse->iNextSelectId);\n      rc = sqlite3Select(pParse, p, &uniondest);\n      testcase( rc!=SQLITE_OK );\n      /* Query flattening in sqlite3Select() might refill p->pOrderBy.\n      ** Be sure to delete p->pOrderBy, therefore, to avoid a memory leak. */\n      sqlite3ExprListDelete(db, p->pOrderBy);\n      pDelete = p->pPrior;\n      p->pPrior = pPrior;\n      p->pOrderBy = 0;\n      if( p->op==TK_UNION ){\n        p->nSelectRow = sqlite3LogEstAdd(p->nSelectRow, pPrior->nSelectRow);\n      }\n      sqlite3ExprDelete(db, p->pLimit);\n      p->pLimit = pLimit;\n      p->iLimit = 0;\n      p->iOffset = 0;\n\n      /* Convert the data in the temporary table into whatever form\n      ** it is that we currently need.\n      */\n      assert( unionTab==dest.iSDParm || dest.eDest!=priorOp );\n      if( dest.eDest!=priorOp ){\n        int iCont, iBreak, iStart;\n        assert( p->pEList );\n        iBreak = sqlite3VdbeMakeLabel(v);\n        iCont = sqlite3VdbeMakeLabel(v);\n        computeLimitRegisters(pParse, p, iBreak);\n        sqlite3VdbeAddOp2(v, OP_Rewind, unionTab, iBreak); VdbeCoverage(v);\n        iStart = sqlite3VdbeCurrentAddr(v);\n        selectInnerLoop(pParse, p, unionTab,\n                        0, 0, &dest, iCont, iBreak);\n        sqlite3VdbeResolveLabel(v, iCont);\n        sqlite3VdbeAddOp2(v, OP_Next, unionTab, iStart); VdbeCoverage(v);\n        sqlite3VdbeResolveLabel(v, iBreak);\n        sqlite3VdbeAddOp2(v, OP_Close, unionTab, 0);\n      }\n      break;\n    }\n    default: assert( p->op==TK_INTERSECT ); {\n      int tab1, tab2;\n      int iCont, iBreak, iStart;\n      Expr *pLimit;\n      int addr;\n      SelectDest intersectdest;\n      int r1;\n\n      /* INTERSECT is different from the others since it requires\n      ** two temporary tables.  Hence it has its own case.  Begin\n      ** by allocating the tables we will need.\n      */\n      tab1 = pParse->nTab++;\n      tab2 = pParse->nTab++;\n      assert( p->pOrderBy==0 );\n\n      addr = sqlite3VdbeAddOp2(v, OP_OpenEphemeral, tab1, 0);\n      assert( p->addrOpenEphm[0] == -1 );\n      p->addrOpenEphm[0] = addr;\n      findRightmost(p)->selFlags |= SF_UsesEphemeral;\n      assert( p->pEList );\n\n      /* Code the SELECTs to our left into temporary table \"tab1\".\n      */\n      sqlite3SelectDestInit(&intersectdest, SRT_Union, tab1);\n      explainSetInteger(iSub1, pParse->iNextSelectId);\n      rc = sqlite3Select(pParse, pPrior, &intersectdest);\n      if( rc ){\n        goto multi_select_end;\n      }\n\n      /* Code the current SELECT into temporary table \"tab2\"\n      */\n      addr = sqlite3VdbeAddOp2(v, OP_OpenEphemeral, tab2, 0);\n      assert( p->addrOpenEphm[1] == -1 );\n      p->addrOpenEphm[1] = addr;\n      p->pPrior = 0;\n      pLimit = p->pLimit;\n      p->pLimit = 0;\n      intersectdest.iSDParm = tab2;\n      explainSetInteger(iSub2, pParse->iNextSelectId);\n      rc = sqlite3Select(pParse, p, &intersectdest);\n      testcase( rc!=SQLITE_OK );\n      pDelete = p->pPrior;\n      p->pPrior = pPrior;\n      if( p->nSelectRow>pPrior->nSelectRow ) p->nSelectRow = pPrior->nSelectRow;\n      sqlite3ExprDelete(db, p->pLimit);\n      p->pLimit = pLimit;\n\n      /* Generate code to take the intersection of the two temporary\n      ** tables.\n      */\n      assert( p->pEList );\n      iBreak = sqlite3VdbeMakeLabel(v);\n      iCont = sqlite3VdbeMakeLabel(v);\n      computeLimitRegisters(pParse, p, iBreak);\n      sqlite3VdbeAddOp2(v, OP_Rewind, tab1, iBreak); VdbeCoverage(v);\n      r1 = sqlite3GetTempReg(pParse);\n      iStart = sqlite3VdbeAddOp2(v, OP_RowData, tab1, r1);\n      sqlite3VdbeAddOp4Int(v, OP_NotFound, tab2, iCont, r1, 0); VdbeCoverage(v);\n      sqlite3ReleaseTempReg(pParse, r1);\n      selectInnerLoop(pParse, p, tab1,\n                      0, 0, &dest, iCont, iBreak);\n      sqlite3VdbeResolveLabel(v, iCont);\n      sqlite3VdbeAddOp2(v, OP_Next, tab1, iStart); VdbeCoverage(v);\n      sqlite3VdbeResolveLabel(v, iBreak);\n      sqlite3VdbeAddOp2(v, OP_Close, tab2, 0);\n      sqlite3VdbeAddOp2(v, OP_Close, tab1, 0);\n      break;\n    }\n  }\n\n  explainComposite(pParse, p->op, iSub1, iSub2, p->op!=TK_ALL);\n\n  /* Compute collating sequences used by \n  ** temporary tables needed to implement the compound select.\n  ** Attach the KeyInfo structure to all temporary tables.\n  **\n  ** This section is run by the right-most SELECT statement only.\n  ** SELECT statements to the left always skip this part.  The right-most\n  ** SELECT might also skip this part if it has no ORDER BY clause and\n  ** no temp tables are required.\n  */\n  if( p->selFlags & SF_UsesEphemeral ){\n    int i;                        /* Loop counter */\n    KeyInfo *pKeyInfo;            /* Collating sequence for the result set */\n    Select *pLoop;                /* For looping through SELECT statements */\n    CollSeq **apColl;             /* For looping through pKeyInfo->aColl[] */\n    int nCol;                     /* Number of columns in result set */\n\n    assert( p->pNext==0 );\n    nCol = p->pEList->nExpr;\n    pKeyInfo = sqlite3KeyInfoAlloc(db, nCol, 1);\n    if( !pKeyInfo ){\n      rc = SQLITE_NOMEM_BKPT;\n      goto multi_select_end;\n    }\n    for(i=0, apColl=pKeyInfo->aColl; i<nCol; i++, apColl++){\n      *apColl = multiSelectCollSeq(pParse, p, i);\n      if( 0==*apColl ){\n        *apColl = db->pDfltColl;\n      }\n    }\n\n    for(pLoop=p; pLoop; pLoop=pLoop->pPrior){\n      for(i=0; i<2; i++){\n        int addr = pLoop->addrOpenEphm[i];\n        if( addr<0 ){\n          /* If [0] is unused then [1] is also unused.  So we can\n          ** always safely abort as soon as the first unused slot is found */\n          assert( pLoop->addrOpenEphm[1]<0 );\n          break;\n        }\n        sqlite3VdbeChangeP2(v, addr, nCol);\n        sqlite3VdbeChangeP4(v, addr, (char*)sqlite3KeyInfoRef(pKeyInfo),\n                            P4_KEYINFO);\n        pLoop->addrOpenEphm[i] = -1;\n      }\n    }\n    sqlite3KeyInfoUnref(pKeyInfo);\n  }\n\nmulti_select_end:\n  pDest->iSdst = dest.iSdst;\n  pDest->nSdst = dest.nSdst;\n  sqlite3SelectDelete(db, pDelete);\n  return rc;\n}\n#endif /* SQLITE_OMIT_COMPOUND_SELECT */\n\n/*\n** Error message for when two or more terms of a compound select have different\n** size result sets.\n*/\nSQLITE_PRIVATE void sqlite3SelectWrongNumTermsError(Parse *pParse, Select *p){\n  if( p->selFlags & SF_Values ){\n    sqlite3ErrorMsg(pParse, \"all VALUES must have the same number of terms\");\n  }else{\n    sqlite3ErrorMsg(pParse, \"SELECTs to the left and right of %s\"\n      \" do not have the same number of result columns\", selectOpName(p->op));\n  }\n}\n\n/*\n** Code an output subroutine for a coroutine implementation of a\n** SELECT statment.\n**\n** The data to be output is contained in pIn->iSdst.  There are\n** pIn->nSdst columns to be output.  pDest is where the output should\n** be sent.\n**\n** regReturn is the number of the register holding the subroutine\n** return address.\n**\n** If regPrev>0 then it is the first register in a vector that\n** records the previous output.  mem[regPrev] is a flag that is false\n** if there has been no previous output.  If regPrev>0 then code is\n** generated to suppress duplicates.  pKeyInfo is used for comparing\n** keys.\n**\n** If the LIMIT found in p->iLimit is reached, jump immediately to\n** iBreak.\n*/\nstatic int generateOutputSubroutine(\n  Parse *pParse,          /* Parsing context */\n  Select *p,              /* The SELECT statement */\n  SelectDest *pIn,        /* Coroutine supplying data */\n  SelectDest *pDest,      /* Where to send the data */\n  int regReturn,          /* The return address register */\n  int regPrev,            /* Previous result register.  No uniqueness if 0 */\n  KeyInfo *pKeyInfo,      /* For comparing with previous entry */\n  int iBreak              /* Jump here if we hit the LIMIT */\n){\n  Vdbe *v = pParse->pVdbe;\n  int iContinue;\n  int addr;\n\n  addr = sqlite3VdbeCurrentAddr(v);\n  iContinue = sqlite3VdbeMakeLabel(v);\n\n  /* Suppress duplicates for UNION, EXCEPT, and INTERSECT \n  */\n  if( regPrev ){\n    int addr1, addr2;\n    addr1 = sqlite3VdbeAddOp1(v, OP_IfNot, regPrev); VdbeCoverage(v);\n    addr2 = sqlite3VdbeAddOp4(v, OP_Compare, pIn->iSdst, regPrev+1, pIn->nSdst,\n                              (char*)sqlite3KeyInfoRef(pKeyInfo), P4_KEYINFO);\n    sqlite3VdbeAddOp3(v, OP_Jump, addr2+2, iContinue, addr2+2); VdbeCoverage(v);\n    sqlite3VdbeJumpHere(v, addr1);\n    sqlite3VdbeAddOp3(v, OP_Copy, pIn->iSdst, regPrev+1, pIn->nSdst-1);\n    sqlite3VdbeAddOp2(v, OP_Integer, 1, regPrev);\n  }\n  if( pParse->db->mallocFailed ) return 0;\n\n  /* Suppress the first OFFSET entries if there is an OFFSET clause\n  */\n  codeOffset(v, p->iOffset, iContinue);\n\n  assert( pDest->eDest!=SRT_Exists );\n  assert( pDest->eDest!=SRT_Table );\n  switch( pDest->eDest ){\n    /* Store the result as data using a unique key.\n    */\n    case SRT_EphemTab: {\n      int r1 = sqlite3GetTempReg(pParse);\n      int r2 = sqlite3GetTempReg(pParse);\n      sqlite3VdbeAddOp3(v, OP_MakeRecord, pIn->iSdst, pIn->nSdst, r1);\n      sqlite3VdbeAddOp2(v, OP_NewRowid, pDest->iSDParm, r2);\n      sqlite3VdbeAddOp3(v, OP_Insert, pDest->iSDParm, r1, r2);\n      sqlite3VdbeChangeP5(v, OPFLAG_APPEND);\n      sqlite3ReleaseTempReg(pParse, r2);\n      sqlite3ReleaseTempReg(pParse, r1);\n      break;\n    }\n\n#ifndef SQLITE_OMIT_SUBQUERY\n    /* If we are creating a set for an \"expr IN (SELECT ...)\".\n    */\n    case SRT_Set: {\n      int r1;\n      testcase( pIn->nSdst>1 );\n      r1 = sqlite3GetTempReg(pParse);\n      sqlite3VdbeAddOp4(v, OP_MakeRecord, pIn->iSdst, pIn->nSdst, \n          r1, pDest->zAffSdst, pIn->nSdst);\n      sqlite3ExprCacheAffinityChange(pParse, pIn->iSdst, pIn->nSdst);\n      sqlite3VdbeAddOp4Int(v, OP_IdxInsert, pDest->iSDParm, r1,\n                           pIn->iSdst, pIn->nSdst);\n      sqlite3ReleaseTempReg(pParse, r1);\n      break;\n    }\n\n    /* If this is a scalar select that is part of an expression, then\n    ** store the results in the appropriate memory cell and break out\n    ** of the scan loop.\n    */\n    case SRT_Mem: {\n      assert( pIn->nSdst==1 || pParse->nErr>0 );  testcase( pIn->nSdst!=1 );\n      sqlite3ExprCodeMove(pParse, pIn->iSdst, pDest->iSDParm, 1);\n      /* The LIMIT clause will jump out of the loop for us */\n      break;\n    }\n#endif /* #ifndef SQLITE_OMIT_SUBQUERY */\n\n    /* The results are stored in a sequence of registers\n    ** starting at pDest->iSdst.  Then the co-routine yields.\n    */\n    case SRT_Coroutine: {\n      if( pDest->iSdst==0 ){\n        pDest->iSdst = sqlite3GetTempRange(pParse, pIn->nSdst);\n        pDest->nSdst = pIn->nSdst;\n      }\n      sqlite3ExprCodeMove(pParse, pIn->iSdst, pDest->iSdst, pIn->nSdst);\n      sqlite3VdbeAddOp1(v, OP_Yield, pDest->iSDParm);\n      break;\n    }\n\n    /* If none of the above, then the result destination must be\n    ** SRT_Output.  This routine is never called with any other\n    ** destination other than the ones handled above or SRT_Output.\n    **\n    ** For SRT_Output, results are stored in a sequence of registers.  \n    ** Then the OP_ResultRow opcode is used to cause sqlite3_step() to\n    ** return the next row of result.\n    */\n    default: {\n      assert( pDest->eDest==SRT_Output );\n      sqlite3VdbeAddOp2(v, OP_ResultRow, pIn->iSdst, pIn->nSdst);\n      sqlite3ExprCacheAffinityChange(pParse, pIn->iSdst, pIn->nSdst);\n      break;\n    }\n  }\n\n  /* Jump to the end of the loop if the LIMIT is reached.\n  */\n  if( p->iLimit ){\n    sqlite3VdbeAddOp2(v, OP_DecrJumpZero, p->iLimit, iBreak); VdbeCoverage(v);\n  }\n\n  /* Generate the subroutine return\n  */\n  sqlite3VdbeResolveLabel(v, iContinue);\n  sqlite3VdbeAddOp1(v, OP_Return, regReturn);\n\n  return addr;\n}\n\n/*\n** Alternative compound select code generator for cases when there\n** is an ORDER BY clause.\n**\n** We assume a query of the following form:\n**\n**      <selectA>  <operator>  <selectB>  ORDER BY <orderbylist>\n**\n** <operator> is one of UNION ALL, UNION, EXCEPT, or INTERSECT.  The idea\n** is to code both <selectA> and <selectB> with the ORDER BY clause as\n** co-routines.  Then run the co-routines in parallel and merge the results\n** into the output.  In addition to the two coroutines (called selectA and\n** selectB) there are 7 subroutines:\n**\n**    outA:    Move the output of the selectA coroutine into the output\n**             of the compound query.\n**\n**    outB:    Move the output of the selectB coroutine into the output\n**             of the compound query.  (Only generated for UNION and\n**             UNION ALL.  EXCEPT and INSERTSECT never output a row that\n**             appears only in B.)\n**\n**    AltB:    Called when there is data from both coroutines and A<B.\n**\n**    AeqB:    Called when there is data from both coroutines and A==B.\n**\n**    AgtB:    Called when there is data from both coroutines and A>B.\n**\n**    EofA:    Called when data is exhausted from selectA.\n**\n**    EofB:    Called when data is exhausted from selectB.\n**\n** The implementation of the latter five subroutines depend on which \n** <operator> is used:\n**\n**\n**             UNION ALL         UNION            EXCEPT          INTERSECT\n**          -------------  -----------------  --------------  -----------------\n**   AltB:   outA, nextA      outA, nextA       outA, nextA         nextA\n**\n**   AeqB:   outA, nextA         nextA             nextA         outA, nextA\n**\n**   AgtB:   outB, nextB      outB, nextB          nextB            nextB\n**\n**   EofA:   outB, nextB      outB, nextB          halt             halt\n**\n**   EofB:   outA, nextA      outA, nextA       outA, nextA         halt\n**\n** In the AltB, AeqB, and AgtB subroutines, an EOF on A following nextA\n** causes an immediate jump to EofA and an EOF on B following nextB causes\n** an immediate jump to EofB.  Within EofA and EofB, and EOF on entry or\n** following nextX causes a jump to the end of the select processing.\n**\n** Duplicate removal in the UNION, EXCEPT, and INTERSECT cases is handled\n** within the output subroutine.  The regPrev register set holds the previously\n** output value.  A comparison is made against this value and the output\n** is skipped if the next results would be the same as the previous.\n**\n** The implementation plan is to implement the two coroutines and seven\n** subroutines first, then put the control logic at the bottom.  Like this:\n**\n**          goto Init\n**     coA: coroutine for left query (A)\n**     coB: coroutine for right query (B)\n**    outA: output one row of A\n**    outB: output one row of B (UNION and UNION ALL only)\n**    EofA: ...\n**    EofB: ...\n**    AltB: ...\n**    AeqB: ...\n**    AgtB: ...\n**    Init: initialize coroutine registers\n**          yield coA\n**          if eof(A) goto EofA\n**          yield coB\n**          if eof(B) goto EofB\n**    Cmpr: Compare A, B\n**          Jump AltB, AeqB, AgtB\n**     End: ...\n**\n** We call AltB, AeqB, AgtB, EofA, and EofB \"subroutines\" but they are not\n** actually called using Gosub and they do not Return.  EofA and EofB loop\n** until all data is exhausted then jump to the \"end\" labe.  AltB, AeqB,\n** and AgtB jump to either L2 or to one of EofA or EofB.\n*/\n#ifndef SQLITE_OMIT_COMPOUND_SELECT\nstatic int multiSelectOrderBy(\n  Parse *pParse,        /* Parsing context */\n  Select *p,            /* The right-most of SELECTs to be coded */\n  SelectDest *pDest     /* What to do with query results */\n){\n  int i, j;             /* Loop counters */\n  Select *pPrior;       /* Another SELECT immediately to our left */\n  Vdbe *v;              /* Generate code to this VDBE */\n  SelectDest destA;     /* Destination for coroutine A */\n  SelectDest destB;     /* Destination for coroutine B */\n  int regAddrA;         /* Address register for select-A coroutine */\n  int regAddrB;         /* Address register for select-B coroutine */\n  int addrSelectA;      /* Address of the select-A coroutine */\n  int addrSelectB;      /* Address of the select-B coroutine */\n  int regOutA;          /* Address register for the output-A subroutine */\n  int regOutB;          /* Address register for the output-B subroutine */\n  int addrOutA;         /* Address of the output-A subroutine */\n  int addrOutB = 0;     /* Address of the output-B subroutine */\n  int addrEofA;         /* Address of the select-A-exhausted subroutine */\n  int addrEofA_noB;     /* Alternate addrEofA if B is uninitialized */\n  int addrEofB;         /* Address of the select-B-exhausted subroutine */\n  int addrAltB;         /* Address of the A<B subroutine */\n  int addrAeqB;         /* Address of the A==B subroutine */\n  int addrAgtB;         /* Address of the A>B subroutine */\n  int regLimitA;        /* Limit register for select-A */\n  int regLimitB;        /* Limit register for select-A */\n  int regPrev;          /* A range of registers to hold previous output */\n  int savedLimit;       /* Saved value of p->iLimit */\n  int savedOffset;      /* Saved value of p->iOffset */\n  int labelCmpr;        /* Label for the start of the merge algorithm */\n  int labelEnd;         /* Label for the end of the overall SELECT stmt */\n  int addr1;            /* Jump instructions that get retargetted */\n  int op;               /* One of TK_ALL, TK_UNION, TK_EXCEPT, TK_INTERSECT */\n  KeyInfo *pKeyDup = 0; /* Comparison information for duplicate removal */\n  KeyInfo *pKeyMerge;   /* Comparison information for merging rows */\n  sqlite3 *db;          /* Database connection */\n  ExprList *pOrderBy;   /* The ORDER BY clause */\n  int nOrderBy;         /* Number of terms in the ORDER BY clause */\n  int *aPermute;        /* Mapping from ORDER BY terms to result set columns */\n#ifndef SQLITE_OMIT_EXPLAIN\n  int iSub1;            /* EQP id of left-hand query */\n  int iSub2;            /* EQP id of right-hand query */\n#endif\n\n  assert( p->pOrderBy!=0 );\n  assert( pKeyDup==0 ); /* \"Managed\" code needs this.  Ticket #3382. */\n  db = pParse->db;\n  v = pParse->pVdbe;\n  assert( v!=0 );       /* Already thrown the error if VDBE alloc failed */\n  labelEnd = sqlite3VdbeMakeLabel(v);\n  labelCmpr = sqlite3VdbeMakeLabel(v);\n\n\n  /* Patch up the ORDER BY clause\n  */\n  op = p->op;  \n  pPrior = p->pPrior;\n  assert( pPrior->pOrderBy==0 );\n  pOrderBy = p->pOrderBy;\n  assert( pOrderBy );\n  nOrderBy = pOrderBy->nExpr;\n\n  /* For operators other than UNION ALL we have to make sure that\n  ** the ORDER BY clause covers every term of the result set.  Add\n  ** terms to the ORDER BY clause as necessary.\n  */\n  if( op!=TK_ALL ){\n    for(i=1; db->mallocFailed==0 && i<=p->pEList->nExpr; i++){\n      struct ExprList_item *pItem;\n      for(j=0, pItem=pOrderBy->a; j<nOrderBy; j++, pItem++){\n        assert( pItem->u.x.iOrderByCol>0 );\n        if( pItem->u.x.iOrderByCol==i ) break;\n      }\n      if( j==nOrderBy ){\n        Expr *pNew = sqlite3Expr(db, TK_INTEGER, 0);\n        if( pNew==0 ) return SQLITE_NOMEM_BKPT;\n        pNew->flags |= EP_IntValue;\n        pNew->u.iValue = i;\n        p->pOrderBy = pOrderBy = sqlite3ExprListAppend(pParse, pOrderBy, pNew);\n        if( pOrderBy ) pOrderBy->a[nOrderBy++].u.x.iOrderByCol = (u16)i;\n      }\n    }\n  }\n\n  /* Compute the comparison permutation and keyinfo that is used with\n  ** the permutation used to determine if the next\n  ** row of results comes from selectA or selectB.  Also add explicit\n  ** collations to the ORDER BY clause terms so that when the subqueries\n  ** to the right and the left are evaluated, they use the correct\n  ** collation.\n  */\n  aPermute = sqlite3DbMallocRawNN(db, sizeof(int)*(nOrderBy + 1));\n  if( aPermute ){\n    struct ExprList_item *pItem;\n    aPermute[0] = nOrderBy;\n    for(i=1, pItem=pOrderBy->a; i<=nOrderBy; i++, pItem++){\n      assert( pItem->u.x.iOrderByCol>0 );\n      assert( pItem->u.x.iOrderByCol<=p->pEList->nExpr );\n      aPermute[i] = pItem->u.x.iOrderByCol - 1;\n    }\n    pKeyMerge = multiSelectOrderByKeyInfo(pParse, p, 1);\n  }else{\n    pKeyMerge = 0;\n  }\n\n  /* Reattach the ORDER BY clause to the query.\n  */\n  p->pOrderBy = pOrderBy;\n  pPrior->pOrderBy = sqlite3ExprListDup(pParse->db, pOrderBy, 0);\n\n  /* Allocate a range of temporary registers and the KeyInfo needed\n  ** for the logic that removes duplicate result rows when the\n  ** operator is UNION, EXCEPT, or INTERSECT (but not UNION ALL).\n  */\n  if( op==TK_ALL ){\n    regPrev = 0;\n  }else{\n    int nExpr = p->pEList->nExpr;\n    assert( nOrderBy>=nExpr || db->mallocFailed );\n    regPrev = pParse->nMem+1;\n    pParse->nMem += nExpr+1;\n    sqlite3VdbeAddOp2(v, OP_Integer, 0, regPrev);\n    pKeyDup = sqlite3KeyInfoAlloc(db, nExpr, 1);\n    if( pKeyDup ){\n      assert( sqlite3KeyInfoIsWriteable(pKeyDup) );\n      for(i=0; i<nExpr; i++){\n        pKeyDup->aColl[i] = multiSelectCollSeq(pParse, p, i);\n        pKeyDup->aSortOrder[i] = 0;\n      }\n    }\n  }\n \n  /* Separate the left and the right query from one another\n  */\n  p->pPrior = 0;\n  pPrior->pNext = 0;\n  sqlite3ResolveOrderGroupBy(pParse, p, p->pOrderBy, \"ORDER\");\n  if( pPrior->pPrior==0 ){\n    sqlite3ResolveOrderGroupBy(pParse, pPrior, pPrior->pOrderBy, \"ORDER\");\n  }\n\n  /* Compute the limit registers */\n  computeLimitRegisters(pParse, p, labelEnd);\n  if( p->iLimit && op==TK_ALL ){\n    regLimitA = ++pParse->nMem;\n    regLimitB = ++pParse->nMem;\n    sqlite3VdbeAddOp2(v, OP_Copy, p->iOffset ? p->iOffset+1 : p->iLimit,\n                                  regLimitA);\n    sqlite3VdbeAddOp2(v, OP_Copy, regLimitA, regLimitB);\n  }else{\n    regLimitA = regLimitB = 0;\n  }\n  sqlite3ExprDelete(db, p->pLimit);\n  p->pLimit = 0;\n\n  regAddrA = ++pParse->nMem;\n  regAddrB = ++pParse->nMem;\n  regOutA = ++pParse->nMem;\n  regOutB = ++pParse->nMem;\n  sqlite3SelectDestInit(&destA, SRT_Coroutine, regAddrA);\n  sqlite3SelectDestInit(&destB, SRT_Coroutine, regAddrB);\n\n  /* Generate a coroutine to evaluate the SELECT statement to the\n  ** left of the compound operator - the \"A\" select.\n  */\n  addrSelectA = sqlite3VdbeCurrentAddr(v) + 1;\n  addr1 = sqlite3VdbeAddOp3(v, OP_InitCoroutine, regAddrA, 0, addrSelectA);\n  VdbeComment((v, \"left SELECT\"));\n  pPrior->iLimit = regLimitA;\n  explainSetInteger(iSub1, pParse->iNextSelectId);\n  sqlite3Select(pParse, pPrior, &destA);\n  sqlite3VdbeEndCoroutine(v, regAddrA);\n  sqlite3VdbeJumpHere(v, addr1);\n\n  /* Generate a coroutine to evaluate the SELECT statement on \n  ** the right - the \"B\" select\n  */\n  addrSelectB = sqlite3VdbeCurrentAddr(v) + 1;\n  addr1 = sqlite3VdbeAddOp3(v, OP_InitCoroutine, regAddrB, 0, addrSelectB);\n  VdbeComment((v, \"right SELECT\"));\n  savedLimit = p->iLimit;\n  savedOffset = p->iOffset;\n  p->iLimit = regLimitB;\n  p->iOffset = 0;  \n  explainSetInteger(iSub2, pParse->iNextSelectId);\n  sqlite3Select(pParse, p, &destB);\n  p->iLimit = savedLimit;\n  p->iOffset = savedOffset;\n  sqlite3VdbeEndCoroutine(v, regAddrB);\n\n  /* Generate a subroutine that outputs the current row of the A\n  ** select as the next output row of the compound select.\n  */\n  VdbeNoopComment((v, \"Output routine for A\"));\n  addrOutA = generateOutputSubroutine(pParse,\n                 p, &destA, pDest, regOutA,\n                 regPrev, pKeyDup, labelEnd);\n  \n  /* Generate a subroutine that outputs the current row of the B\n  ** select as the next output row of the compound select.\n  */\n  if( op==TK_ALL || op==TK_UNION ){\n    VdbeNoopComment((v, \"Output routine for B\"));\n    addrOutB = generateOutputSubroutine(pParse,\n                 p, &destB, pDest, regOutB,\n                 regPrev, pKeyDup, labelEnd);\n  }\n  sqlite3KeyInfoUnref(pKeyDup);\n\n  /* Generate a subroutine to run when the results from select A\n  ** are exhausted and only data in select B remains.\n  */\n  if( op==TK_EXCEPT || op==TK_INTERSECT ){\n    addrEofA_noB = addrEofA = labelEnd;\n  }else{  \n    VdbeNoopComment((v, \"eof-A subroutine\"));\n    addrEofA = sqlite3VdbeAddOp2(v, OP_Gosub, regOutB, addrOutB);\n    addrEofA_noB = sqlite3VdbeAddOp2(v, OP_Yield, regAddrB, labelEnd);\n                                     VdbeCoverage(v);\n    sqlite3VdbeGoto(v, addrEofA);\n    p->nSelectRow = sqlite3LogEstAdd(p->nSelectRow, pPrior->nSelectRow);\n  }\n\n  /* Generate a subroutine to run when the results from select B\n  ** are exhausted and only data in select A remains.\n  */\n  if( op==TK_INTERSECT ){\n    addrEofB = addrEofA;\n    if( p->nSelectRow > pPrior->nSelectRow ) p->nSelectRow = pPrior->nSelectRow;\n  }else{  \n    VdbeNoopComment((v, \"eof-B subroutine\"));\n    addrEofB = sqlite3VdbeAddOp2(v, OP_Gosub, regOutA, addrOutA);\n    sqlite3VdbeAddOp2(v, OP_Yield, regAddrA, labelEnd); VdbeCoverage(v);\n    sqlite3VdbeGoto(v, addrEofB);\n  }\n\n  /* Generate code to handle the case of A<B\n  */\n  VdbeNoopComment((v, \"A-lt-B subroutine\"));\n  addrAltB = sqlite3VdbeAddOp2(v, OP_Gosub, regOutA, addrOutA);\n  sqlite3VdbeAddOp2(v, OP_Yield, regAddrA, addrEofA); VdbeCoverage(v);\n  sqlite3VdbeGoto(v, labelCmpr);\n\n  /* Generate code to handle the case of A==B\n  */\n  if( op==TK_ALL ){\n    addrAeqB = addrAltB;\n  }else if( op==TK_INTERSECT ){\n    addrAeqB = addrAltB;\n    addrAltB++;\n  }else{\n    VdbeNoopComment((v, \"A-eq-B subroutine\"));\n    addrAeqB =\n    sqlite3VdbeAddOp2(v, OP_Yield, regAddrA, addrEofA); VdbeCoverage(v);\n    sqlite3VdbeGoto(v, labelCmpr);\n  }\n\n  /* Generate code to handle the case of A>B\n  */\n  VdbeNoopComment((v, \"A-gt-B subroutine\"));\n  addrAgtB = sqlite3VdbeCurrentAddr(v);\n  if( op==TK_ALL || op==TK_UNION ){\n    sqlite3VdbeAddOp2(v, OP_Gosub, regOutB, addrOutB);\n  }\n  sqlite3VdbeAddOp2(v, OP_Yield, regAddrB, addrEofB); VdbeCoverage(v);\n  sqlite3VdbeGoto(v, labelCmpr);\n\n  /* This code runs once to initialize everything.\n  */\n  sqlite3VdbeJumpHere(v, addr1);\n  sqlite3VdbeAddOp2(v, OP_Yield, regAddrA, addrEofA_noB); VdbeCoverage(v);\n  sqlite3VdbeAddOp2(v, OP_Yield, regAddrB, addrEofB); VdbeCoverage(v);\n\n  /* Implement the main merge loop\n  */\n  sqlite3VdbeResolveLabel(v, labelCmpr);\n  sqlite3VdbeAddOp4(v, OP_Permutation, 0, 0, 0, (char*)aPermute, P4_INTARRAY);\n  sqlite3VdbeAddOp4(v, OP_Compare, destA.iSdst, destB.iSdst, nOrderBy,\n                         (char*)pKeyMerge, P4_KEYINFO);\n  sqlite3VdbeChangeP5(v, OPFLAG_PERMUTE);\n  sqlite3VdbeAddOp3(v, OP_Jump, addrAltB, addrAeqB, addrAgtB); VdbeCoverage(v);\n\n  /* Jump to the this point in order to terminate the query.\n  */\n  sqlite3VdbeResolveLabel(v, labelEnd);\n\n  /* Reassembly the compound query so that it will be freed correctly\n  ** by the calling function */\n  if( p->pPrior ){\n    sqlite3SelectDelete(db, p->pPrior);\n  }\n  p->pPrior = pPrior;\n  pPrior->pNext = p;\n\n  /*** TBD:  Insert subroutine calls to close cursors on incomplete\n  **** subqueries ****/\n  explainComposite(pParse, p->op, iSub1, iSub2, 0);\n  return pParse->nErr!=0;\n}\n#endif\n\n#if !defined(SQLITE_OMIT_SUBQUERY) || !defined(SQLITE_OMIT_VIEW)\n\n/* An instance of the SubstContext object describes an substitution edit\n** to be performed on a parse tree.\n**\n** All references to columns in table iTable are to be replaced by corresponding\n** expressions in pEList.\n*/\ntypedef struct SubstContext {\n  Parse *pParse;            /* The parsing context */\n  int iTable;               /* Replace references to this table */\n  int iNewTable;            /* New table number */\n  int isLeftJoin;           /* Add TK_IF_NULL_ROW opcodes on each replacement */\n  ExprList *pEList;         /* Replacement expressions */\n} SubstContext;\n\n/* Forward Declarations */\nstatic void substExprList(SubstContext*, ExprList*);\nstatic void substSelect(SubstContext*, Select*, int);\n\n/*\n** Scan through the expression pExpr.  Replace every reference to\n** a column in table number iTable with a copy of the iColumn-th\n** entry in pEList.  (But leave references to the ROWID column \n** unchanged.)\n**\n** This routine is part of the flattening procedure.  A subquery\n** whose result set is defined by pEList appears as entry in the\n** FROM clause of a SELECT such that the VDBE cursor assigned to that\n** FORM clause entry is iTable.  This routine makes the necessary \n** changes to pExpr so that it refers directly to the source table\n** of the subquery rather the result set of the subquery.\n*/\nstatic Expr *substExpr(\n  SubstContext *pSubst,  /* Description of the substitution */\n  Expr *pExpr            /* Expr in which substitution occurs */\n){\n  if( pExpr==0 ) return 0;\n  if( ExprHasProperty(pExpr, EP_FromJoin)\n   && pExpr->iRightJoinTable==pSubst->iTable\n  ){\n    pExpr->iRightJoinTable = pSubst->iNewTable;\n  }\n  if( pExpr->op==TK_COLUMN && pExpr->iTable==pSubst->iTable ){\n    if( pExpr->iColumn<0 ){\n      pExpr->op = TK_NULL;\n    }else{\n      Expr *pNew;\n      Expr *pCopy = pSubst->pEList->a[pExpr->iColumn].pExpr;\n      Expr ifNullRow;\n      assert( pSubst->pEList!=0 && pExpr->iColumn<pSubst->pEList->nExpr );\n      assert( pExpr->pLeft==0 && pExpr->pRight==0 );\n      if( sqlite3ExprIsVector(pCopy) ){\n        sqlite3VectorErrorMsg(pSubst->pParse, pCopy);\n      }else{\n        sqlite3 *db = pSubst->pParse->db;\n        if( pSubst->isLeftJoin && pCopy->op!=TK_COLUMN ){\n          memset(&ifNullRow, 0, sizeof(ifNullRow));\n          ifNullRow.op = TK_IF_NULL_ROW;\n          ifNullRow.pLeft = pCopy;\n          ifNullRow.iTable = pSubst->iNewTable;\n          pCopy = &ifNullRow;\n        }\n        pNew = sqlite3ExprDup(db, pCopy, 0);\n        if( pNew && pSubst->isLeftJoin ){\n          ExprSetProperty(pNew, EP_CanBeNull);\n        }\n        if( pNew && ExprHasProperty(pExpr,EP_FromJoin) ){\n          pNew->iRightJoinTable = pExpr->iRightJoinTable;\n          ExprSetProperty(pNew, EP_FromJoin);\n        }\n        sqlite3ExprDelete(db, pExpr);\n        pExpr = pNew;\n      }\n    }\n  }else{\n    if( pExpr->op==TK_IF_NULL_ROW && pExpr->iTable==pSubst->iTable ){\n      pExpr->iTable = pSubst->iNewTable;\n    }\n    pExpr->pLeft = substExpr(pSubst, pExpr->pLeft);\n    pExpr->pRight = substExpr(pSubst, pExpr->pRight);\n    if( ExprHasProperty(pExpr, EP_xIsSelect) ){\n      substSelect(pSubst, pExpr->x.pSelect, 1);\n    }else{\n      substExprList(pSubst, pExpr->x.pList);\n    }\n  }\n  return pExpr;\n}\nstatic void substExprList(\n  SubstContext *pSubst, /* Description of the substitution */\n  ExprList *pList       /* List to scan and in which to make substitutes */\n){\n  int i;\n  if( pList==0 ) return;\n  for(i=0; i<pList->nExpr; i++){\n    pList->a[i].pExpr = substExpr(pSubst, pList->a[i].pExpr);\n  }\n}\nstatic void substSelect(\n  SubstContext *pSubst, /* Description of the substitution */\n  Select *p,            /* SELECT statement in which to make substitutions */\n  int doPrior           /* Do substitutes on p->pPrior too */\n){\n  SrcList *pSrc;\n  struct SrcList_item *pItem;\n  int i;\n  if( !p ) return;\n  do{\n    substExprList(pSubst, p->pEList);\n    substExprList(pSubst, p->pGroupBy);\n    substExprList(pSubst, p->pOrderBy);\n    p->pHaving = substExpr(pSubst, p->pHaving);\n    p->pWhere = substExpr(pSubst, p->pWhere);\n    pSrc = p->pSrc;\n    assert( pSrc!=0 );\n    for(i=pSrc->nSrc, pItem=pSrc->a; i>0; i--, pItem++){\n      substSelect(pSubst, pItem->pSelect, 1);\n      if( pItem->fg.isTabFunc ){\n        substExprList(pSubst, pItem->u1.pFuncArg);\n      }\n    }\n  }while( doPrior && (p = p->pPrior)!=0 );\n}\n#endif /* !defined(SQLITE_OMIT_SUBQUERY) || !defined(SQLITE_OMIT_VIEW) */\n\n#if !defined(SQLITE_OMIT_SUBQUERY) || !defined(SQLITE_OMIT_VIEW)\n/*\n** This routine attempts to flatten subqueries as a performance optimization.\n** This routine returns 1 if it makes changes and 0 if no flattening occurs.\n**\n** To understand the concept of flattening, consider the following\n** query:\n**\n**     SELECT a FROM (SELECT x+y AS a FROM t1 WHERE z<100) WHERE a>5\n**\n** The default way of implementing this query is to execute the\n** subquery first and store the results in a temporary table, then\n** run the outer query on that temporary table.  This requires two\n** passes over the data.  Furthermore, because the temporary table\n** has no indices, the WHERE clause on the outer query cannot be\n** optimized.\n**\n** This routine attempts to rewrite queries such as the above into\n** a single flat select, like this:\n**\n**     SELECT x+y AS a FROM t1 WHERE z<100 AND a>5\n**\n** The code generated for this simplification gives the same result\n** but only has to scan the data once.  And because indices might \n** exist on the table t1, a complete scan of the data might be\n** avoided.\n**\n** Flattening is subject to the following constraints:\n**\n**  (**)  We no longer attempt to flatten aggregate subqueries. Was:\n**        The subquery and the outer query cannot both be aggregates.\n**\n**  (**)  We no longer attempt to flatten aggregate subqueries. Was:\n**        (2) If the subquery is an aggregate then\n**        (2a) the outer query must not be a join and\n**        (2b) the outer query must not use subqueries\n**             other than the one FROM-clause subquery that is a candidate\n**             for flattening.  (This is due to ticket [2f7170d73bf9abf80]\n**             from 2015-02-09.)\n**\n**   (3)  If the subquery is the right operand of a LEFT JOIN then\n**        (3a) the subquery may not be a join and\n**        (3b) the FROM clause of the subquery may not contain a virtual\n**             table and\n**        (3c) the outer query may not be an aggregate.\n**\n**   (4)  The subquery can not be DISTINCT.\n**\n**  (**)  At one point restrictions (4) and (5) defined a subset of DISTINCT\n**        sub-queries that were excluded from this optimization. Restriction \n**        (4) has since been expanded to exclude all DISTINCT subqueries.\n**\n**  (**)  We no longer attempt to flatten aggregate subqueries.  Was:\n**        If the subquery is aggregate, the outer query may not be DISTINCT.\n**\n**   (7)  The subquery must have a FROM clause.  TODO:  For subqueries without\n**        A FROM clause, consider adding a FROM clause with the special\n**        table sqlite_once that consists of a single row containing a\n**        single NULL.\n**\n**   (8)  If the subquery uses LIMIT then the outer query may not be a join.\n**\n**   (9)  If the subquery uses LIMIT then the outer query may not be aggregate.\n**\n**  (**)  Restriction (10) was removed from the code on 2005-02-05 but we\n**        accidently carried the comment forward until 2014-09-15.  Original\n**        constraint: \"If the subquery is aggregate then the outer query \n**        may not use LIMIT.\"\n**\n**  (11)  The subquery and the outer query may not both have ORDER BY clauses.\n**\n**  (**)  Not implemented.  Subsumed into restriction (3).  Was previously\n**        a separate restriction deriving from ticket #350.\n**\n**  (13)  The subquery and outer query may not both use LIMIT.\n**\n**  (14)  The subquery may not use OFFSET.\n**\n**  (15)  If the outer query is part of a compound select, then the\n**        subquery may not use LIMIT.\n**        (See ticket #2339 and ticket [02a8e81d44]).\n**\n**  (16)  If the outer query is aggregate, then the subquery may not\n**        use ORDER BY.  (Ticket #2942)  This used to not matter\n**        until we introduced the group_concat() function.  \n**\n**  (17)  If the subquery is a compound select, then\n**        (17a) all compound operators must be a UNION ALL, and\n**        (17b) no terms within the subquery compound may be aggregate\n**              or DISTINCT, and\n**        (17c) every term within the subquery compound must have a FROM clause\n**        (17d) the outer query may not be\n**              (17d1) aggregate, or\n**              (17d2) DISTINCT, or\n**              (17d3) a join.\n**\n**        The parent and sub-query may contain WHERE clauses. Subject to\n**        rules (11), (13) and (14), they may also contain ORDER BY,\n**        LIMIT and OFFSET clauses.  The subquery cannot use any compound\n**        operator other than UNION ALL because all the other compound\n**        operators have an implied DISTINCT which is disallowed by\n**        restriction (4).\n**\n**        Also, each component of the sub-query must return the same number\n**        of result columns. This is actually a requirement for any compound\n**        SELECT statement, but all the code here does is make sure that no\n**        such (illegal) sub-query is flattened. The caller will detect the\n**        syntax error and return a detailed message.\n**\n**  (18)  If the sub-query is a compound select, then all terms of the\n**        ORDER BY clause of the parent must be simple references to \n**        columns of the sub-query.\n**\n**  (19)  If the subquery uses LIMIT then the outer query may not\n**        have a WHERE clause.\n**\n**  (20)  If the sub-query is a compound select, then it must not use\n**        an ORDER BY clause.  Ticket #3773.  We could relax this constraint\n**        somewhat by saying that the terms of the ORDER BY clause must\n**        appear as unmodified result columns in the outer query.  But we\n**        have other optimizations in mind to deal with that case.\n**\n**  (21)  If the subquery uses LIMIT then the outer query may not be\n**        DISTINCT.  (See ticket [752e1646fc]).\n**\n**  (22)  The subquery may not be a recursive CTE.\n**\n**  (**)  Subsumed into restriction (17d3).  Was: If the outer query is\n**        a recursive CTE, then the sub-query may not be a compound query.\n**        This restriction is because transforming the\n**        parent to a compound query confuses the code that handles\n**        recursive queries in multiSelect().\n**\n**  (**)  We no longer attempt to flatten aggregate subqueries.  Was:\n**        The subquery may not be an aggregate that uses the built-in min() or \n**        or max() functions.  (Without this restriction, a query like:\n**        \"SELECT x FROM (SELECT max(y), x FROM t1)\" would not necessarily\n**        return the value X for which Y was maximal.)\n**\n**\n** In this routine, the \"p\" parameter is a pointer to the outer query.\n** The subquery is p->pSrc->a[iFrom].  isAgg is true if the outer query\n** uses aggregates.\n**\n** If flattening is not attempted, this routine is a no-op and returns 0.\n** If flattening is attempted this routine returns 1.\n**\n** All of the expression analysis must occur on both the outer query and\n** the subquery before this routine runs.\n*/\nstatic int flattenSubquery(\n  Parse *pParse,       /* Parsing context */\n  Select *p,           /* The parent or outer SELECT statement */\n  int iFrom,           /* Index in p->pSrc->a[] of the inner subquery */\n  int isAgg            /* True if outer SELECT uses aggregate functions */\n){\n  const char *zSavedAuthContext = pParse->zAuthContext;\n  Select *pParent;    /* Current UNION ALL term of the other query */\n  Select *pSub;       /* The inner query or \"subquery\" */\n  Select *pSub1;      /* Pointer to the rightmost select in sub-query */\n  SrcList *pSrc;      /* The FROM clause of the outer query */\n  SrcList *pSubSrc;   /* The FROM clause of the subquery */\n  int iParent;        /* VDBE cursor number of the pSub result set temp table */\n  int iNewParent = -1;/* Replacement table for iParent */\n  int isLeftJoin = 0; /* True if pSub is the right side of a LEFT JOIN */    \n  int i;              /* Loop counter */\n  Expr *pWhere;                    /* The WHERE clause */\n  struct SrcList_item *pSubitem;   /* The subquery */\n  sqlite3 *db = pParse->db;\n\n  /* Check to see if flattening is permitted.  Return 0 if not.\n  */\n  assert( p!=0 );\n  assert( p->pPrior==0 );\n  if( OptimizationDisabled(db, SQLITE_QueryFlattener) ) return 0;\n  pSrc = p->pSrc;\n  assert( pSrc && iFrom>=0 && iFrom<pSrc->nSrc );\n  pSubitem = &pSrc->a[iFrom];\n  iParent = pSubitem->iCursor;\n  pSub = pSubitem->pSelect;\n  assert( pSub!=0 );\n\n  pSubSrc = pSub->pSrc;\n  assert( pSubSrc );\n  /* Prior to version 3.1.2, when LIMIT and OFFSET had to be simple constants,\n  ** not arbitrary expressions, we allowed some combining of LIMIT and OFFSET\n  ** because they could be computed at compile-time.  But when LIMIT and OFFSET\n  ** became arbitrary expressions, we were forced to add restrictions (13)\n  ** and (14). */\n  if( pSub->pLimit && p->pLimit ) return 0;              /* Restriction (13) */\n  if( pSub->pLimit && pSub->pLimit->pRight ) return 0;   /* Restriction (14) */\n  if( (p->selFlags & SF_Compound)!=0 && pSub->pLimit ){\n    return 0;                                            /* Restriction (15) */\n  }\n  if( pSubSrc->nSrc==0 ) return 0;                       /* Restriction (7)  */\n  if( pSub->selFlags & SF_Distinct ) return 0;           /* Restriction (4)  */\n  if( pSub->pLimit && (pSrc->nSrc>1 || isAgg) ){\n     return 0;         /* Restrictions (8)(9) */\n  }\n  if( p->pOrderBy && pSub->pOrderBy ){\n     return 0;                                           /* Restriction (11) */\n  }\n  if( isAgg && pSub->pOrderBy ) return 0;                /* Restriction (16) */\n  if( pSub->pLimit && p->pWhere ) return 0;              /* Restriction (19) */\n  if( pSub->pLimit && (p->selFlags & SF_Distinct)!=0 ){\n     return 0;         /* Restriction (21) */\n  }\n  if( pSub->selFlags & (SF_Recursive) ){\n    return 0; /* Restrictions (22) */\n  }\n\n  /*\n  ** If the subquery is the right operand of a LEFT JOIN, then the\n  ** subquery may not be a join itself (3a). Example of why this is not\n  ** allowed:\n  **\n  **         t1 LEFT OUTER JOIN (t2 JOIN t3)\n  **\n  ** If we flatten the above, we would get\n  **\n  **         (t1 LEFT OUTER JOIN t2) JOIN t3\n  **\n  ** which is not at all the same thing.\n  **\n  ** If the subquery is the right operand of a LEFT JOIN, then the outer\n  ** query cannot be an aggregate. (3c)  This is an artifact of the way\n  ** aggregates are processed - there is no mechanism to determine if\n  ** the LEFT JOIN table should be all-NULL.\n  **\n  ** See also tickets #306, #350, and #3300.\n  */\n  if( (pSubitem->fg.jointype & JT_OUTER)!=0 ){\n    isLeftJoin = 1;\n    if( pSubSrc->nSrc>1 || isAgg || IsVirtual(pSubSrc->a[0].pTab) ){\n      /*  (3a)             (3c)     (3b) */\n      return 0;\n    }\n  }\n#ifdef SQLITE_EXTRA_IFNULLROW\n  else if( iFrom>0 && !isAgg ){\n    /* Setting isLeftJoin to -1 causes OP_IfNullRow opcodes to be generated for\n    ** every reference to any result column from subquery in a join, even\n    ** though they are not necessary.  This will stress-test the OP_IfNullRow \n    ** opcode. */\n    isLeftJoin = -1;\n  }\n#endif\n\n  /* Restriction (17): If the sub-query is a compound SELECT, then it must\n  ** use only the UNION ALL operator. And none of the simple select queries\n  ** that make up the compound SELECT are allowed to be aggregate or distinct\n  ** queries.\n  */\n  if( pSub->pPrior ){\n    if( pSub->pOrderBy ){\n      return 0;  /* Restriction (20) */\n    }\n    if( isAgg || (p->selFlags & SF_Distinct)!=0 || pSrc->nSrc!=1 ){\n      return 0; /* (17d1), (17d2), or (17d3) */\n    }\n    for(pSub1=pSub; pSub1; pSub1=pSub1->pPrior){\n      testcase( (pSub1->selFlags & (SF_Distinct|SF_Aggregate))==SF_Distinct );\n      testcase( (pSub1->selFlags & (SF_Distinct|SF_Aggregate))==SF_Aggregate );\n      assert( pSub->pSrc!=0 );\n      assert( pSub->pEList->nExpr==pSub1->pEList->nExpr );\n      if( (pSub1->selFlags & (SF_Distinct|SF_Aggregate))!=0    /* (17b) */\n       || (pSub1->pPrior && pSub1->op!=TK_ALL)                 /* (17a) */\n       || pSub1->pSrc->nSrc<1                                  /* (17c) */\n      ){\n        return 0;\n      }\n      testcase( pSub1->pSrc->nSrc>1 );\n    }\n\n    /* Restriction (18). */\n    if( p->pOrderBy ){\n      int ii;\n      for(ii=0; ii<p->pOrderBy->nExpr; ii++){\n        if( p->pOrderBy->a[ii].u.x.iOrderByCol==0 ) return 0;\n      }\n    }\n  }\n\n  /* Ex-restriction (23):\n  ** The only way that the recursive part of a CTE can contain a compound\n  ** subquery is for the subquery to be one term of a join.  But if the\n  ** subquery is a join, then the flattening has already been stopped by\n  ** restriction (17d3)\n  */\n  assert( (p->selFlags & SF_Recursive)==0 || pSub->pPrior==0 );\n\n  /***** If we reach this point, flattening is permitted. *****/\n  SELECTTRACE(1,pParse,p,(\"flatten %s.%p from term %d\\n\",\n                   pSub->zSelName, pSub, iFrom));\n\n  /* Authorize the subquery */\n  pParse->zAuthContext = pSubitem->zName;\n  TESTONLY(i =) sqlite3AuthCheck(pParse, SQLITE_SELECT, 0, 0, 0);\n  testcase( i==SQLITE_DENY );\n  pParse->zAuthContext = zSavedAuthContext;\n\n  /* If the sub-query is a compound SELECT statement, then (by restrictions\n  ** 17 and 18 above) it must be a UNION ALL and the parent query must \n  ** be of the form:\n  **\n  **     SELECT <expr-list> FROM (<sub-query>) <where-clause> \n  **\n  ** followed by any ORDER BY, LIMIT and/or OFFSET clauses. This block\n  ** creates N-1 copies of the parent query without any ORDER BY, LIMIT or \n  ** OFFSET clauses and joins them to the left-hand-side of the original\n  ** using UNION ALL operators. In this case N is the number of simple\n  ** select statements in the compound sub-query.\n  **\n  ** Example:\n  **\n  **     SELECT a+1 FROM (\n  **        SELECT x FROM tab\n  **        UNION ALL\n  **        SELECT y FROM tab\n  **        UNION ALL\n  **        SELECT abs(z*2) FROM tab2\n  **     ) WHERE a!=5 ORDER BY 1\n  **\n  ** Transformed into:\n  **\n  **     SELECT x+1 FROM tab WHERE x+1!=5\n  **     UNION ALL\n  **     SELECT y+1 FROM tab WHERE y+1!=5\n  **     UNION ALL\n  **     SELECT abs(z*2)+1 FROM tab2 WHERE abs(z*2)+1!=5\n  **     ORDER BY 1\n  **\n  ** We call this the \"compound-subquery flattening\".\n  */\n  for(pSub=pSub->pPrior; pSub; pSub=pSub->pPrior){\n    Select *pNew;\n    ExprList *pOrderBy = p->pOrderBy;\n    Expr *pLimit = p->pLimit;\n    Select *pPrior = p->pPrior;\n    p->pOrderBy = 0;\n    p->pSrc = 0;\n    p->pPrior = 0;\n    p->pLimit = 0;\n    pNew = sqlite3SelectDup(db, p, 0);\n    sqlite3SelectSetName(pNew, pSub->zSelName);\n    p->pLimit = pLimit;\n    p->pOrderBy = pOrderBy;\n    p->pSrc = pSrc;\n    p->op = TK_ALL;\n    if( pNew==0 ){\n      p->pPrior = pPrior;\n    }else{\n      pNew->pPrior = pPrior;\n      if( pPrior ) pPrior->pNext = pNew;\n      pNew->pNext = p;\n      p->pPrior = pNew;\n      SELECTTRACE(2,pParse,p,\n         (\"compound-subquery flattener creates %s.%p as peer\\n\",\n         pNew->zSelName, pNew));\n    }\n    if( db->mallocFailed ) return 1;\n  }\n\n  /* Begin flattening the iFrom-th entry of the FROM clause \n  ** in the outer query.\n  */\n  pSub = pSub1 = pSubitem->pSelect;\n\n  /* Delete the transient table structure associated with the\n  ** subquery\n  */\n  sqlite3DbFree(db, pSubitem->zDatabase);\n  sqlite3DbFree(db, pSubitem->zName);\n  sqlite3DbFree(db, pSubitem->zAlias);\n  pSubitem->zDatabase = 0;\n  pSubitem->zName = 0;\n  pSubitem->zAlias = 0;\n  pSubitem->pSelect = 0;\n\n  /* Defer deleting the Table object associated with the\n  ** subquery until code generation is\n  ** complete, since there may still exist Expr.pTab entries that\n  ** refer to the subquery even after flattening.  Ticket #3346.\n  **\n  ** pSubitem->pTab is always non-NULL by test restrictions and tests above.\n  */\n  if( ALWAYS(pSubitem->pTab!=0) ){\n    Table *pTabToDel = pSubitem->pTab;\n    if( pTabToDel->nTabRef==1 ){\n      Parse *pToplevel = sqlite3ParseToplevel(pParse);\n      pTabToDel->pNextZombie = pToplevel->pZombieTab;\n      pToplevel->pZombieTab = pTabToDel;\n    }else{\n      pTabToDel->nTabRef--;\n    }\n    pSubitem->pTab = 0;\n  }\n\n  /* The following loop runs once for each term in a compound-subquery\n  ** flattening (as described above).  If we are doing a different kind\n  ** of flattening - a flattening other than a compound-subquery flattening -\n  ** then this loop only runs once.\n  **\n  ** This loop moves all of the FROM elements of the subquery into the\n  ** the FROM clause of the outer query.  Before doing this, remember\n  ** the cursor number for the original outer query FROM element in\n  ** iParent.  The iParent cursor will never be used.  Subsequent code\n  ** will scan expressions looking for iParent references and replace\n  ** those references with expressions that resolve to the subquery FROM\n  ** elements we are now copying in.\n  */\n  for(pParent=p; pParent; pParent=pParent->pPrior, pSub=pSub->pPrior){\n    int nSubSrc;\n    u8 jointype = 0;\n    pSubSrc = pSub->pSrc;     /* FROM clause of subquery */\n    nSubSrc = pSubSrc->nSrc;  /* Number of terms in subquery FROM clause */\n    pSrc = pParent->pSrc;     /* FROM clause of the outer query */\n\n    if( pSrc ){\n      assert( pParent==p );  /* First time through the loop */\n      jointype = pSubitem->fg.jointype;\n    }else{\n      assert( pParent!=p );  /* 2nd and subsequent times through the loop */\n      pSrc = pParent->pSrc = sqlite3SrcListAppend(db, 0, 0, 0);\n      if( pSrc==0 ){\n        assert( db->mallocFailed );\n        break;\n      }\n    }\n\n    /* The subquery uses a single slot of the FROM clause of the outer\n    ** query.  If the subquery has more than one element in its FROM clause,\n    ** then expand the outer query to make space for it to hold all elements\n    ** of the subquery.\n    **\n    ** Example:\n    **\n    **    SELECT * FROM tabA, (SELECT * FROM sub1, sub2), tabB;\n    **\n    ** The outer query has 3 slots in its FROM clause.  One slot of the\n    ** outer query (the middle slot) is used by the subquery.  The next\n    ** block of code will expand the outer query FROM clause to 4 slots.\n    ** The middle slot is expanded to two slots in order to make space\n    ** for the two elements in the FROM clause of the subquery.\n    */\n    if( nSubSrc>1 ){\n      pParent->pSrc = pSrc = sqlite3SrcListEnlarge(db, pSrc, nSubSrc-1,iFrom+1);\n      if( db->mallocFailed ){\n        break;\n      }\n    }\n\n    /* Transfer the FROM clause terms from the subquery into the\n    ** outer query.\n    */\n    for(i=0; i<nSubSrc; i++){\n      sqlite3IdListDelete(db, pSrc->a[i+iFrom].pUsing);\n      assert( pSrc->a[i+iFrom].fg.isTabFunc==0 );\n      pSrc->a[i+iFrom] = pSubSrc->a[i];\n      iNewParent = pSubSrc->a[i].iCursor;\n      memset(&pSubSrc->a[i], 0, sizeof(pSubSrc->a[i]));\n    }\n    pSrc->a[iFrom].fg.jointype = jointype;\n  \n    /* Now begin substituting subquery result set expressions for \n    ** references to the iParent in the outer query.\n    ** \n    ** Example:\n    **\n    **   SELECT a+5, b*10 FROM (SELECT x*3 AS a, y+10 AS b FROM t1) WHERE a>b;\n    **   \\                     \\_____________ subquery __________/          /\n    **    \\_____________________ outer query ______________________________/\n    **\n    ** We look at every expression in the outer query and every place we see\n    ** \"a\" we substitute \"x*3\" and every place we see \"b\" we substitute \"y+10\".\n    */\n    if( pSub->pOrderBy ){\n      /* At this point, any non-zero iOrderByCol values indicate that the\n      ** ORDER BY column expression is identical to the iOrderByCol'th\n      ** expression returned by SELECT statement pSub. Since these values\n      ** do not necessarily correspond to columns in SELECT statement pParent,\n      ** zero them before transfering the ORDER BY clause.\n      **\n      ** Not doing this may cause an error if a subsequent call to this\n      ** function attempts to flatten a compound sub-query into pParent\n      ** (the only way this can happen is if the compound sub-query is\n      ** currently part of pSub->pSrc). See ticket [d11a6e908f].  */\n      ExprList *pOrderBy = pSub->pOrderBy;\n      for(i=0; i<pOrderBy->nExpr; i++){\n        pOrderBy->a[i].u.x.iOrderByCol = 0;\n      }\n      assert( pParent->pOrderBy==0 );\n      assert( pSub->pPrior==0 );\n      pParent->pOrderBy = pOrderBy;\n      pSub->pOrderBy = 0;\n    }\n    pWhere = sqlite3ExprDup(db, pSub->pWhere, 0);\n    if( isLeftJoin>0 ){\n      setJoinExpr(pWhere, iNewParent);\n    }\n    pParent->pWhere = sqlite3ExprAnd(db, pWhere, pParent->pWhere);\n    if( db->mallocFailed==0 ){\n      SubstContext x;\n      x.pParse = pParse;\n      x.iTable = iParent;\n      x.iNewTable = iNewParent;\n      x.isLeftJoin = isLeftJoin;\n      x.pEList = pSub->pEList;\n      substSelect(&x, pParent, 0);\n    }\n  \n    /* The flattened query is distinct if either the inner or the\n    ** outer query is distinct. \n    */\n    pParent->selFlags |= pSub->selFlags & SF_Distinct;\n  \n    /*\n    ** SELECT ... FROM (SELECT ... LIMIT a OFFSET b) LIMIT x OFFSET y;\n    **\n    ** One is tempted to try to add a and b to combine the limits.  But this\n    ** does not work if either limit is negative.\n    */\n    if( pSub->pLimit ){\n      pParent->pLimit = pSub->pLimit;\n      pSub->pLimit = 0;\n    }\n  }\n\n  /* Finially, delete what is left of the subquery and return\n  ** success.\n  */\n  sqlite3SelectDelete(db, pSub1);\n\n#if SELECTTRACE_ENABLED\n  if( sqlite3SelectTrace & 0x100 ){\n    SELECTTRACE(0x100,pParse,p,(\"After flattening:\\n\"));\n    sqlite3TreeViewSelect(0, p, 0);\n  }\n#endif\n\n  return 1;\n}\n#endif /* !defined(SQLITE_OMIT_SUBQUERY) || !defined(SQLITE_OMIT_VIEW) */\n\n\n\n#if !defined(SQLITE_OMIT_SUBQUERY) || !defined(SQLITE_OMIT_VIEW)\n/*\n** Make copies of relevant WHERE clause terms of the outer query into\n** the WHERE clause of subquery.  Example:\n**\n**    SELECT * FROM (SELECT a AS x, c-d AS y FROM t1) WHERE x=5 AND y=10;\n**\n** Transformed into:\n**\n**    SELECT * FROM (SELECT a AS x, c-d AS y FROM t1 WHERE a=5 AND c-d=10)\n**     WHERE x=5 AND y=10;\n**\n** The hope is that the terms added to the inner query will make it more\n** efficient.\n**\n** Do not attempt this optimization if:\n**\n**   (1) (** This restriction was removed on 2017-09-29.  We used to\n**           disallow this optimization for aggregate subqueries, but now\n**           it is allowed by putting the extra terms on the HAVING clause.\n**           The added HAVING clause is pointless if the subquery lacks\n**           a GROUP BY clause.  But such a HAVING clause is also harmless\n**           so there does not appear to be any reason to add extra logic\n**           to suppress it. **)\n**\n**   (2) The inner query is the recursive part of a common table expression.\n**\n**   (3) The inner query has a LIMIT clause (since the changes to the WHERE\n**       close would change the meaning of the LIMIT).\n**\n**   (4) The inner query is the right operand of a LEFT JOIN.  (The caller\n**       enforces this restriction since this routine does not have enough\n**       information to know.)\n**\n**   (5) The WHERE clause expression originates in the ON or USING clause\n**       of a LEFT JOIN.\n**\n** Return 0 if no changes are made and non-zero if one or more WHERE clause\n** terms are duplicated into the subquery.\n*/\nstatic int pushDownWhereTerms(\n  Parse *pParse,        /* Parse context (for malloc() and error reporting) */\n  Select *pSubq,        /* The subquery whose WHERE clause is to be augmented */\n  Expr *pWhere,         /* The WHERE clause of the outer query */\n  int iCursor           /* Cursor number of the subquery */\n){\n  Expr *pNew;\n  int nChng = 0;\n  if( pWhere==0 ) return 0;\n  if( pSubq->selFlags & SF_Recursive ) return 0;  /* restriction (2) */\n\n#ifdef SQLITE_DEBUG\n  /* Only the first term of a compound can have a WITH clause.  But make\n  ** sure no other terms are marked SF_Recursive in case something changes\n  ** in the future.\n  */\n  {\n    Select *pX;  \n    for(pX=pSubq; pX; pX=pX->pPrior){\n      assert( (pX->selFlags & (SF_Recursive))==0 );\n    }\n  }\n#endif\n\n  if( pSubq->pLimit!=0 ){\n    return 0; /* restriction (3) */\n  }\n  while( pWhere->op==TK_AND ){\n    nChng += pushDownWhereTerms(pParse, pSubq, pWhere->pRight, iCursor);\n    pWhere = pWhere->pLeft;\n  }\n  if( ExprHasProperty(pWhere,EP_FromJoin) ) return 0; /* restriction (5) */\n  if( sqlite3ExprIsTableConstant(pWhere, iCursor) ){\n    nChng++;\n    while( pSubq ){\n      SubstContext x;\n      pNew = sqlite3ExprDup(pParse->db, pWhere, 0);\n      x.pParse = pParse;\n      x.iTable = iCursor;\n      x.iNewTable = iCursor;\n      x.isLeftJoin = 0;\n      x.pEList = pSubq->pEList;\n      pNew = substExpr(&x, pNew);\n      if( pSubq->selFlags & SF_Aggregate ){\n        pSubq->pHaving = sqlite3ExprAnd(pParse->db, pSubq->pHaving, pNew);\n      }else{\n        pSubq->pWhere = sqlite3ExprAnd(pParse->db, pSubq->pWhere, pNew);\n      }\n      pSubq = pSubq->pPrior;\n    }\n  }\n  return nChng;\n}\n#endif /* !defined(SQLITE_OMIT_SUBQUERY) || !defined(SQLITE_OMIT_VIEW) */\n\n/*\n** The pFunc is the only aggregate function in the query.  Check to see\n** if the query is a candidate for the min/max optimization. \n**\n** If the query is a candidate for the min/max optimization, then set\n** *ppMinMax to be an ORDER BY clause to be used for the optimization\n** and return either WHERE_ORDERBY_MIN or WHERE_ORDERBY_MAX depending on\n** whether pFunc is a min() or max() function.\n**\n** If the query is not a candidate for the min/max optimization, return\n** WHERE_ORDERBY_NORMAL (which must be zero).\n**\n** This routine must be called after aggregate functions have been\n** located but before their arguments have been subjected to aggregate\n** analysis.\n*/\nstatic u8 minMaxQuery(sqlite3 *db, Expr *pFunc, ExprList **ppMinMax){\n  int eRet = WHERE_ORDERBY_NORMAL;      /* Return value */\n  ExprList *pEList = pFunc->x.pList;    /* Arguments to agg function */\n  const char *zFunc;                    /* Name of aggregate function pFunc */\n  ExprList *pOrderBy;\n  u8 sortOrder;\n\n  assert( *ppMinMax==0 );\n  assert( pFunc->op==TK_AGG_FUNCTION );\n  if( pEList==0 || pEList->nExpr!=1 ) return eRet;\n  zFunc = pFunc->u.zToken;\n  if( sqlite3StrICmp(zFunc, \"min\")==0 ){\n    eRet = WHERE_ORDERBY_MIN;\n    sortOrder = SQLITE_SO_ASC;\n  }else if( sqlite3StrICmp(zFunc, \"max\")==0 ){\n    eRet = WHERE_ORDERBY_MAX;\n    sortOrder = SQLITE_SO_DESC;\n  }else{\n    return eRet;\n  }\n  *ppMinMax = pOrderBy = sqlite3ExprListDup(db, pEList, 0);\n  assert( pOrderBy!=0 || db->mallocFailed );\n  if( pOrderBy ) pOrderBy->a[0].sortOrder = sortOrder;\n  return eRet;\n}\n\n/*\n** The select statement passed as the first argument is an aggregate query.\n** The second argument is the associated aggregate-info object. This \n** function tests if the SELECT is of the form:\n**\n**   SELECT count(*) FROM <tbl>\n**\n** where table is a database table, not a sub-select or view. If the query\n** does match this pattern, then a pointer to the Table object representing\n** <tbl> is returned. Otherwise, 0 is returned.\n*/\nstatic Table *isSimpleCount(Select *p, AggInfo *pAggInfo){\n  Table *pTab;\n  Expr *pExpr;\n\n  assert( !p->pGroupBy );\n\n  if( p->pWhere || p->pEList->nExpr!=1 \n   || p->pSrc->nSrc!=1 || p->pSrc->a[0].pSelect\n  ){\n    return 0;\n  }\n  pTab = p->pSrc->a[0].pTab;\n  pExpr = p->pEList->a[0].pExpr;\n  assert( pTab && !pTab->pSelect && pExpr );\n\n  if( IsVirtual(pTab) ) return 0;\n  if( pExpr->op!=TK_AGG_FUNCTION ) return 0;\n  if( NEVER(pAggInfo->nFunc==0) ) return 0;\n  if( (pAggInfo->aFunc[0].pFunc->funcFlags&SQLITE_FUNC_COUNT)==0 ) return 0;\n  if( pExpr->flags&EP_Distinct ) return 0;\n\n  return pTab;\n}\n\n/*\n** If the source-list item passed as an argument was augmented with an\n** INDEXED BY clause, then try to locate the specified index. If there\n** was such a clause and the named index cannot be found, return \n** SQLITE_ERROR and leave an error in pParse. Otherwise, populate \n** pFrom->pIndex and return SQLITE_OK.\n*/\nSQLITE_PRIVATE int sqlite3IndexedByLookup(Parse *pParse, struct SrcList_item *pFrom){\n  if( pFrom->pTab && pFrom->fg.isIndexedBy ){\n    Table *pTab = pFrom->pTab;\n    char *zIndexedBy = pFrom->u1.zIndexedBy;\n    Index *pIdx;\n    for(pIdx=pTab->pIndex; \n        pIdx && sqlite3StrICmp(pIdx->zName, zIndexedBy); \n        pIdx=pIdx->pNext\n    );\n    if( !pIdx ){\n      sqlite3ErrorMsg(pParse, \"no such index: %s\", zIndexedBy, 0);\n      pParse->checkSchema = 1;\n      return SQLITE_ERROR;\n    }\n    pFrom->pIBIndex = pIdx;\n  }\n  return SQLITE_OK;\n}\n/*\n** Detect compound SELECT statements that use an ORDER BY clause with \n** an alternative collating sequence.\n**\n**    SELECT ... FROM t1 EXCEPT SELECT ... FROM t2 ORDER BY .. COLLATE ...\n**\n** These are rewritten as a subquery:\n**\n**    SELECT * FROM (SELECT ... FROM t1 EXCEPT SELECT ... FROM t2)\n**     ORDER BY ... COLLATE ...\n**\n** This transformation is necessary because the multiSelectOrderBy() routine\n** above that generates the code for a compound SELECT with an ORDER BY clause\n** uses a merge algorithm that requires the same collating sequence on the\n** result columns as on the ORDER BY clause.  See ticket\n** http://www.sqlite.org/src/info/6709574d2a\n**\n** This transformation is only needed for EXCEPT, INTERSECT, and UNION.\n** The UNION ALL operator works fine with multiSelectOrderBy() even when\n** there are COLLATE terms in the ORDER BY.\n*/\nstatic int convertCompoundSelectToSubquery(Walker *pWalker, Select *p){\n  int i;\n  Select *pNew;\n  Select *pX;\n  sqlite3 *db;\n  struct ExprList_item *a;\n  SrcList *pNewSrc;\n  Parse *pParse;\n  Token dummy;\n\n  if( p->pPrior==0 ) return WRC_Continue;\n  if( p->pOrderBy==0 ) return WRC_Continue;\n  for(pX=p; pX && (pX->op==TK_ALL || pX->op==TK_SELECT); pX=pX->pPrior){}\n  if( pX==0 ) return WRC_Continue;\n  a = p->pOrderBy->a;\n  for(i=p->pOrderBy->nExpr-1; i>=0; i--){\n    if( a[i].pExpr->flags & EP_Collate ) break;\n  }\n  if( i<0 ) return WRC_Continue;\n\n  /* If we reach this point, that means the transformation is required. */\n\n  pParse = pWalker->pParse;\n  db = pParse->db;\n  pNew = sqlite3DbMallocZero(db, sizeof(*pNew) );\n  if( pNew==0 ) return WRC_Abort;\n  memset(&dummy, 0, sizeof(dummy));\n  pNewSrc = sqlite3SrcListAppendFromTerm(pParse,0,0,0,&dummy,pNew,0,0);\n  if( pNewSrc==0 ) return WRC_Abort;\n  *pNew = *p;\n  p->pSrc = pNewSrc;\n  p->pEList = sqlite3ExprListAppend(pParse, 0, sqlite3Expr(db, TK_ASTERISK, 0));\n  p->op = TK_SELECT;\n  p->pWhere = 0;\n  pNew->pGroupBy = 0;\n  pNew->pHaving = 0;\n  pNew->pOrderBy = 0;\n  p->pPrior = 0;\n  p->pNext = 0;\n  p->pWith = 0;\n  p->selFlags &= ~SF_Compound;\n  assert( (p->selFlags & SF_Converted)==0 );\n  p->selFlags |= SF_Converted;\n  assert( pNew->pPrior!=0 );\n  pNew->pPrior->pNext = pNew;\n  pNew->pLimit = 0;\n  return WRC_Continue;\n}\n\n/*\n** Check to see if the FROM clause term pFrom has table-valued function\n** arguments.  If it does, leave an error message in pParse and return\n** non-zero, since pFrom is not allowed to be a table-valued function.\n*/\nstatic int cannotBeFunction(Parse *pParse, struct SrcList_item *pFrom){\n  if( pFrom->fg.isTabFunc ){\n    sqlite3ErrorMsg(pParse, \"'%s' is not a function\", pFrom->zName);\n    return 1;\n  }\n  return 0;\n}\n\n#ifndef SQLITE_OMIT_CTE\n/*\n** Argument pWith (which may be NULL) points to a linked list of nested \n** WITH contexts, from inner to outermost. If the table identified by \n** FROM clause element pItem is really a common-table-expression (CTE) \n** then return a pointer to the CTE definition for that table. Otherwise\n** return NULL.\n**\n** If a non-NULL value is returned, set *ppContext to point to the With\n** object that the returned CTE belongs to.\n*/\nstatic struct Cte *searchWith(\n  With *pWith,                    /* Current innermost WITH clause */\n  struct SrcList_item *pItem,     /* FROM clause element to resolve */\n  With **ppContext                /* OUT: WITH clause return value belongs to */\n){\n  const char *zName;\n  if( pItem->zDatabase==0 && (zName = pItem->zName)!=0 ){\n    With *p;\n    for(p=pWith; p; p=p->pOuter){\n      int i;\n      for(i=0; i<p->nCte; i++){\n        if( sqlite3StrICmp(zName, p->a[i].zName)==0 ){\n          *ppContext = p;\n          return &p->a[i];\n        }\n      }\n    }\n  }\n  return 0;\n}\n\n/* The code generator maintains a stack of active WITH clauses\n** with the inner-most WITH clause being at the top of the stack.\n**\n** This routine pushes the WITH clause passed as the second argument\n** onto the top of the stack. If argument bFree is true, then this\n** WITH clause will never be popped from the stack. In this case it\n** should be freed along with the Parse object. In other cases, when\n** bFree==0, the With object will be freed along with the SELECT \n** statement with which it is associated.\n*/\nSQLITE_PRIVATE void sqlite3WithPush(Parse *pParse, With *pWith, u8 bFree){\n  assert( bFree==0 || (pParse->pWith==0 && pParse->pWithToFree==0) );\n  if( pWith ){\n    assert( pParse->pWith!=pWith );\n    pWith->pOuter = pParse->pWith;\n    pParse->pWith = pWith;\n    if( bFree ) pParse->pWithToFree = pWith;\n  }\n}\n\n/*\n** This function checks if argument pFrom refers to a CTE declared by \n** a WITH clause on the stack currently maintained by the parser. And,\n** if currently processing a CTE expression, if it is a recursive\n** reference to the current CTE.\n**\n** If pFrom falls into either of the two categories above, pFrom->pTab\n** and other fields are populated accordingly. The caller should check\n** (pFrom->pTab!=0) to determine whether or not a successful match\n** was found.\n**\n** Whether or not a match is found, SQLITE_OK is returned if no error\n** occurs. If an error does occur, an error message is stored in the\n** parser and some error code other than SQLITE_OK returned.\n*/\nstatic int withExpand(\n  Walker *pWalker, \n  struct SrcList_item *pFrom\n){\n  Parse *pParse = pWalker->pParse;\n  sqlite3 *db = pParse->db;\n  struct Cte *pCte;               /* Matched CTE (or NULL if no match) */\n  With *pWith;                    /* WITH clause that pCte belongs to */\n\n  assert( pFrom->pTab==0 );\n\n  pCte = searchWith(pParse->pWith, pFrom, &pWith);\n  if( pCte ){\n    Table *pTab;\n    ExprList *pEList;\n    Select *pSel;\n    Select *pLeft;                /* Left-most SELECT statement */\n    int bMayRecursive;            /* True if compound joined by UNION [ALL] */\n    With *pSavedWith;             /* Initial value of pParse->pWith */\n\n    /* If pCte->zCteErr is non-NULL at this point, then this is an illegal\n    ** recursive reference to CTE pCte. Leave an error in pParse and return\n    ** early. If pCte->zCteErr is NULL, then this is not a recursive reference.\n    ** In this case, proceed.  */\n    if( pCte->zCteErr ){\n      sqlite3ErrorMsg(pParse, pCte->zCteErr, pCte->zName);\n      return SQLITE_ERROR;\n    }\n    if( cannotBeFunction(pParse, pFrom) ) return SQLITE_ERROR;\n\n    assert( pFrom->pTab==0 );\n    pFrom->pTab = pTab = sqlite3DbMallocZero(db, sizeof(Table));\n    if( pTab==0 ) return WRC_Abort;\n    pTab->nTabRef = 1;\n    pTab->zName = sqlite3DbStrDup(db, pCte->zName);\n    pTab->iPKey = -1;\n    pTab->nRowLogEst = 200; assert( 200==sqlite3LogEst(1048576) );\n    pTab->tabFlags |= TF_Ephemeral | TF_NoVisibleRowid;\n    pFrom->pSelect = sqlite3SelectDup(db, pCte->pSelect, 0);\n    if( db->mallocFailed ) return SQLITE_NOMEM_BKPT;\n    assert( pFrom->pSelect );\n\n    /* Check if this is a recursive CTE. */\n    pSel = pFrom->pSelect;\n    bMayRecursive = ( pSel->op==TK_ALL || pSel->op==TK_UNION );\n    if( bMayRecursive ){\n      int i;\n      SrcList *pSrc = pFrom->pSelect->pSrc;\n      for(i=0; i<pSrc->nSrc; i++){\n        struct SrcList_item *pItem = &pSrc->a[i];\n        if( pItem->zDatabase==0 \n         && pItem->zName!=0 \n         && 0==sqlite3StrICmp(pItem->zName, pCte->zName)\n          ){\n          pItem->pTab = pTab;\n          pItem->fg.isRecursive = 1;\n          pTab->nTabRef++;\n          pSel->selFlags |= SF_Recursive;\n        }\n      }\n    }\n\n    /* Only one recursive reference is permitted. */ \n    if( pTab->nTabRef>2 ){\n      sqlite3ErrorMsg(\n          pParse, \"multiple references to recursive table: %s\", pCte->zName\n      );\n      return SQLITE_ERROR;\n    }\n    assert( pTab->nTabRef==1 || \n            ((pSel->selFlags&SF_Recursive) && pTab->nTabRef==2 ));\n\n    pCte->zCteErr = \"circular reference: %s\";\n    pSavedWith = pParse->pWith;\n    pParse->pWith = pWith;\n    if( bMayRecursive ){\n      Select *pPrior = pSel->pPrior;\n      assert( pPrior->pWith==0 );\n      pPrior->pWith = pSel->pWith;\n      sqlite3WalkSelect(pWalker, pPrior);\n      pPrior->pWith = 0;\n    }else{\n      sqlite3WalkSelect(pWalker, pSel);\n    }\n    pParse->pWith = pWith;\n\n    for(pLeft=pSel; pLeft->pPrior; pLeft=pLeft->pPrior);\n    pEList = pLeft->pEList;\n    if( pCte->pCols ){\n      if( pEList && pEList->nExpr!=pCte->pCols->nExpr ){\n        sqlite3ErrorMsg(pParse, \"table %s has %d values for %d columns\",\n            pCte->zName, pEList->nExpr, pCte->pCols->nExpr\n        );\n        pParse->pWith = pSavedWith;\n        return SQLITE_ERROR;\n      }\n      pEList = pCte->pCols;\n    }\n\n    sqlite3ColumnsFromExprList(pParse, pEList, &pTab->nCol, &pTab->aCol);\n    if( bMayRecursive ){\n      if( pSel->selFlags & SF_Recursive ){\n        pCte->zCteErr = \"multiple recursive references: %s\";\n      }else{\n        pCte->zCteErr = \"recursive reference in a subquery: %s\";\n      }\n      sqlite3WalkSelect(pWalker, pSel);\n    }\n    pCte->zCteErr = 0;\n    pParse->pWith = pSavedWith;\n  }\n\n  return SQLITE_OK;\n}\n#endif\n\n#ifndef SQLITE_OMIT_CTE\n/*\n** If the SELECT passed as the second argument has an associated WITH \n** clause, pop it from the stack stored as part of the Parse object.\n**\n** This function is used as the xSelectCallback2() callback by\n** sqlite3SelectExpand() when walking a SELECT tree to resolve table\n** names and other FROM clause elements. \n*/\nstatic void selectPopWith(Walker *pWalker, Select *p){\n  Parse *pParse = pWalker->pParse;\n  if( OK_IF_ALWAYS_TRUE(pParse->pWith) && p->pPrior==0 ){\n    With *pWith = findRightmost(p)->pWith;\n    if( pWith!=0 ){\n      assert( pParse->pWith==pWith );\n      pParse->pWith = pWith->pOuter;\n    }\n  }\n}\n#else\n#define selectPopWith 0\n#endif\n\n/*\n** This routine is a Walker callback for \"expanding\" a SELECT statement.\n** \"Expanding\" means to do the following:\n**\n**    (1)  Make sure VDBE cursor numbers have been assigned to every\n**         element of the FROM clause.\n**\n**    (2)  Fill in the pTabList->a[].pTab fields in the SrcList that \n**         defines FROM clause.  When views appear in the FROM clause,\n**         fill pTabList->a[].pSelect with a copy of the SELECT statement\n**         that implements the view.  A copy is made of the view's SELECT\n**         statement so that we can freely modify or delete that statement\n**         without worrying about messing up the persistent representation\n**         of the view.\n**\n**    (3)  Add terms to the WHERE clause to accommodate the NATURAL keyword\n**         on joins and the ON and USING clause of joins.\n**\n**    (4)  Scan the list of columns in the result set (pEList) looking\n**         for instances of the \"*\" operator or the TABLE.* operator.\n**         If found, expand each \"*\" to be every column in every table\n**         and TABLE.* to be every column in TABLE.\n**\n*/\nstatic int selectExpander(Walker *pWalker, Select *p){\n  Parse *pParse = pWalker->pParse;\n  int i, j, k;\n  SrcList *pTabList;\n  ExprList *pEList;\n  struct SrcList_item *pFrom;\n  sqlite3 *db = pParse->db;\n  Expr *pE, *pRight, *pExpr;\n  u16 selFlags = p->selFlags;\n  u32 elistFlags = 0;\n\n  p->selFlags |= SF_Expanded;\n  if( db->mallocFailed  ){\n    return WRC_Abort;\n  }\n  assert( p->pSrc!=0 );\n  if( (selFlags & SF_Expanded)!=0 ){\n    return WRC_Prune;\n  }\n  pTabList = p->pSrc;\n  pEList = p->pEList;\n  if( OK_IF_ALWAYS_TRUE(p->pWith) ){\n    sqlite3WithPush(pParse, p->pWith, 0);\n  }\n\n  /* Make sure cursor numbers have been assigned to all entries in\n  ** the FROM clause of the SELECT statement.\n  */\n  sqlite3SrcListAssignCursors(pParse, pTabList);\n\n  /* Look up every table named in the FROM clause of the select.  If\n  ** an entry of the FROM clause is a subquery instead of a table or view,\n  ** then create a transient table structure to describe the subquery.\n  */\n  for(i=0, pFrom=pTabList->a; i<pTabList->nSrc; i++, pFrom++){\n    Table *pTab;\n    assert( pFrom->fg.isRecursive==0 || pFrom->pTab!=0 );\n    if( pFrom->fg.isRecursive ) continue;\n    assert( pFrom->pTab==0 );\n#ifndef SQLITE_OMIT_CTE\n    if( withExpand(pWalker, pFrom) ) return WRC_Abort;\n    if( pFrom->pTab ) {} else\n#endif\n    if( pFrom->zName==0 ){\n#ifndef SQLITE_OMIT_SUBQUERY\n      Select *pSel = pFrom->pSelect;\n      /* A sub-query in the FROM clause of a SELECT */\n      assert( pSel!=0 );\n      assert( pFrom->pTab==0 );\n      if( sqlite3WalkSelect(pWalker, pSel) ) return WRC_Abort;\n      pFrom->pTab = pTab = sqlite3DbMallocZero(db, sizeof(Table));\n      if( pTab==0 ) return WRC_Abort;\n      pTab->nTabRef = 1;\n      if( pFrom->zAlias ){\n        pTab->zName = sqlite3DbStrDup(db, pFrom->zAlias);\n      }else{\n        pTab->zName = sqlite3MPrintf(db, \"subquery_%p\", (void*)pTab);\n      }\n      while( pSel->pPrior ){ pSel = pSel->pPrior; }\n      sqlite3ColumnsFromExprList(pParse, pSel->pEList,&pTab->nCol,&pTab->aCol);\n      pTab->iPKey = -1;\n      pTab->nRowLogEst = 200; assert( 200==sqlite3LogEst(1048576) );\n      pTab->tabFlags |= TF_Ephemeral;\n#endif\n    }else{\n      /* An ordinary table or view name in the FROM clause */\n      assert( pFrom->pTab==0 );\n      pFrom->pTab = pTab = sqlite3LocateTableItem(pParse, 0, pFrom);\n      if( pTab==0 ) return WRC_Abort;\n      if( pTab->nTabRef>=0xffff ){\n        sqlite3ErrorMsg(pParse, \"too many references to \\\"%s\\\": max 65535\",\n           pTab->zName);\n        pFrom->pTab = 0;\n        return WRC_Abort;\n      }\n      pTab->nTabRef++;\n      if( !IsVirtual(pTab) && cannotBeFunction(pParse, pFrom) ){\n        return WRC_Abort;\n      }\n#if !defined(SQLITE_OMIT_VIEW) || !defined (SQLITE_OMIT_VIRTUALTABLE)\n      if( IsVirtual(pTab) || pTab->pSelect ){\n        i16 nCol;\n        if( sqlite3ViewGetColumnNames(pParse, pTab) ) return WRC_Abort;\n        assert( pFrom->pSelect==0 );\n        pFrom->pSelect = sqlite3SelectDup(db, pTab->pSelect, 0);\n        sqlite3SelectSetName(pFrom->pSelect, pTab->zName);\n        nCol = pTab->nCol;\n        pTab->nCol = -1;\n        sqlite3WalkSelect(pWalker, pFrom->pSelect);\n        pTab->nCol = nCol;\n      }\n#endif\n    }\n\n    /* Locate the index named by the INDEXED BY clause, if any. */\n    if( sqlite3IndexedByLookup(pParse, pFrom) ){\n      return WRC_Abort;\n    }\n  }\n\n  /* Process NATURAL keywords, and ON and USING clauses of joins.\n  */\n  if( db->mallocFailed || sqliteProcessJoin(pParse, p) ){\n    return WRC_Abort;\n  }\n\n  /* For every \"*\" that occurs in the column list, insert the names of\n  ** all columns in all tables.  And for every TABLE.* insert the names\n  ** of all columns in TABLE.  The parser inserted a special expression\n  ** with the TK_ASTERISK operator for each \"*\" that it found in the column\n  ** list.  The following code just has to locate the TK_ASTERISK\n  ** expressions and expand each one to the list of all columns in\n  ** all tables.\n  **\n  ** The first loop just checks to see if there are any \"*\" operators\n  ** that need expanding.\n  */\n  for(k=0; k<pEList->nExpr; k++){\n    pE = pEList->a[k].pExpr;\n    if( pE->op==TK_ASTERISK ) break;\n    assert( pE->op!=TK_DOT || pE->pRight!=0 );\n    assert( pE->op!=TK_DOT || (pE->pLeft!=0 && pE->pLeft->op==TK_ID) );\n    if( pE->op==TK_DOT && pE->pRight->op==TK_ASTERISK ) break;\n    elistFlags |= pE->flags;\n  }\n  if( k<pEList->nExpr ){\n    /*\n    ** If we get here it means the result set contains one or more \"*\"\n    ** operators that need to be expanded.  Loop through each expression\n    ** in the result set and expand them one by one.\n    */\n    struct ExprList_item *a = pEList->a;\n    ExprList *pNew = 0;\n    int flags = pParse->db->flags;\n    int longNames = (flags & SQLITE_FullColNames)!=0\n                      && (flags & SQLITE_ShortColNames)==0;\n\n    for(k=0; k<pEList->nExpr; k++){\n      pE = a[k].pExpr;\n      elistFlags |= pE->flags;\n      pRight = pE->pRight;\n      assert( pE->op!=TK_DOT || pRight!=0 );\n      if( pE->op!=TK_ASTERISK\n       && (pE->op!=TK_DOT || pRight->op!=TK_ASTERISK)\n      ){\n        /* This particular expression does not need to be expanded.\n        */\n        pNew = sqlite3ExprListAppend(pParse, pNew, a[k].pExpr);\n        if( pNew ){\n          pNew->a[pNew->nExpr-1].zName = a[k].zName;\n          pNew->a[pNew->nExpr-1].zSpan = a[k].zSpan;\n          a[k].zName = 0;\n          a[k].zSpan = 0;\n        }\n        a[k].pExpr = 0;\n      }else{\n        /* This expression is a \"*\" or a \"TABLE.*\" and needs to be\n        ** expanded. */\n        int tableSeen = 0;      /* Set to 1 when TABLE matches */\n        char *zTName = 0;       /* text of name of TABLE */\n        if( pE->op==TK_DOT ){\n          assert( pE->pLeft!=0 );\n          assert( !ExprHasProperty(pE->pLeft, EP_IntValue) );\n          zTName = pE->pLeft->u.zToken;\n        }\n        for(i=0, pFrom=pTabList->a; i<pTabList->nSrc; i++, pFrom++){\n          Table *pTab = pFrom->pTab;\n          Select *pSub = pFrom->pSelect;\n          char *zTabName = pFrom->zAlias;\n          const char *zSchemaName = 0;\n          int iDb;\n          if( zTabName==0 ){\n            zTabName = pTab->zName;\n          }\n          if( db->mallocFailed ) break;\n          if( pSub==0 || (pSub->selFlags & SF_NestedFrom)==0 ){\n            pSub = 0;\n            if( zTName && sqlite3StrICmp(zTName, zTabName)!=0 ){\n              continue;\n            }\n            iDb = sqlite3SchemaToIndex(db, pTab->pSchema);\n            zSchemaName = iDb>=0 ? db->aDb[iDb].zDbSName : \"*\";\n          }\n          for(j=0; j<pTab->nCol; j++){\n            char *zName = pTab->aCol[j].zName;\n            char *zColname;  /* The computed column name */\n            char *zToFree;   /* Malloced string that needs to be freed */\n            Token sColname;  /* Computed column name as a token */\n\n            assert( zName );\n            if( zTName && pSub\n             && sqlite3MatchSpanName(pSub->pEList->a[j].zSpan, 0, zTName, 0)==0\n            ){\n              continue;\n            }\n\n            /* If a column is marked as 'hidden', omit it from the expanded\n            ** result-set list unless the SELECT has the SF_IncludeHidden\n            ** bit set.\n            */\n            if( (p->selFlags & SF_IncludeHidden)==0\n             && IsHiddenColumn(&pTab->aCol[j]) \n            ){\n              continue;\n            }\n            tableSeen = 1;\n\n            if( i>0 && zTName==0 ){\n              if( (pFrom->fg.jointype & JT_NATURAL)!=0\n                && tableAndColumnIndex(pTabList, i, zName, 0, 0)\n              ){\n                /* In a NATURAL join, omit the join columns from the \n                ** table to the right of the join */\n                continue;\n              }\n              if( sqlite3IdListIndex(pFrom->pUsing, zName)>=0 ){\n                /* In a join with a USING clause, omit columns in the\n                ** using clause from the table on the right. */\n                continue;\n              }\n            }\n            pRight = sqlite3Expr(db, TK_ID, zName);\n            zColname = zName;\n            zToFree = 0;\n            if( longNames || pTabList->nSrc>1 ){\n              Expr *pLeft;\n              pLeft = sqlite3Expr(db, TK_ID, zTabName);\n              pExpr = sqlite3PExpr(pParse, TK_DOT, pLeft, pRight);\n              if( zSchemaName ){\n                pLeft = sqlite3Expr(db, TK_ID, zSchemaName);\n                pExpr = sqlite3PExpr(pParse, TK_DOT, pLeft, pExpr);\n              }\n              if( longNames ){\n                zColname = sqlite3MPrintf(db, \"%s.%s\", zTabName, zName);\n                zToFree = zColname;\n              }\n            }else{\n              pExpr = pRight;\n            }\n            pNew = sqlite3ExprListAppend(pParse, pNew, pExpr);\n            sqlite3TokenInit(&sColname, zColname);\n            sqlite3ExprListSetName(pParse, pNew, &sColname, 0);\n            if( pNew && (p->selFlags & SF_NestedFrom)!=0 ){\n              struct ExprList_item *pX = &pNew->a[pNew->nExpr-1];\n              if( pSub ){\n                pX->zSpan = sqlite3DbStrDup(db, pSub->pEList->a[j].zSpan);\n                testcase( pX->zSpan==0 );\n              }else{\n                pX->zSpan = sqlite3MPrintf(db, \"%s.%s.%s\",\n                                           zSchemaName, zTabName, zColname);\n                testcase( pX->zSpan==0 );\n              }\n              pX->bSpanIsTab = 1;\n            }\n            sqlite3DbFree(db, zToFree);\n          }\n        }\n        if( !tableSeen ){\n          if( zTName ){\n            sqlite3ErrorMsg(pParse, \"no such table: %s\", zTName);\n          }else{\n            sqlite3ErrorMsg(pParse, \"no tables specified\");\n          }\n        }\n      }\n    }\n    sqlite3ExprListDelete(db, pEList);\n    p->pEList = pNew;\n  }\n  if( p->pEList ){\n    if( p->pEList->nExpr>db->aLimit[SQLITE_LIMIT_COLUMN] ){\n      sqlite3ErrorMsg(pParse, \"too many columns in result set\");\n      return WRC_Abort;\n    }\n    if( (elistFlags & (EP_HasFunc|EP_Subquery))!=0 ){\n      p->selFlags |= SF_ComplexResult;\n    }\n  }\n  return WRC_Continue;\n}\n\n/*\n** No-op routine for the parse-tree walker.\n**\n** When this routine is the Walker.xExprCallback then expression trees\n** are walked without any actions being taken at each node.  Presumably,\n** when this routine is used for Walker.xExprCallback then \n** Walker.xSelectCallback is set to do something useful for every \n** subquery in the parser tree.\n*/\nSQLITE_PRIVATE int sqlite3ExprWalkNoop(Walker *NotUsed, Expr *NotUsed2){\n  UNUSED_PARAMETER2(NotUsed, NotUsed2);\n  return WRC_Continue;\n}\n\n/*\n** No-op routine for the parse-tree walker for SELECT statements.\n** subquery in the parser tree.\n*/\nSQLITE_PRIVATE int sqlite3SelectWalkNoop(Walker *NotUsed, Select *NotUsed2){\n  UNUSED_PARAMETER2(NotUsed, NotUsed2);\n  return WRC_Continue;\n}\n\n#if SQLITE_DEBUG\n/*\n** Always assert.  This xSelectCallback2 implementation proves that the\n** xSelectCallback2 is never invoked.\n*/\nSQLITE_PRIVATE void sqlite3SelectWalkAssert2(Walker *NotUsed, Select *NotUsed2){\n  UNUSED_PARAMETER2(NotUsed, NotUsed2);\n  assert( 0 );\n}\n#endif\n/*\n** This routine \"expands\" a SELECT statement and all of its subqueries.\n** For additional information on what it means to \"expand\" a SELECT\n** statement, see the comment on the selectExpand worker callback above.\n**\n** Expanding a SELECT statement is the first step in processing a\n** SELECT statement.  The SELECT statement must be expanded before\n** name resolution is performed.\n**\n** If anything goes wrong, an error message is written into pParse.\n** The calling function can detect the problem by looking at pParse->nErr\n** and/or pParse->db->mallocFailed.\n*/\nstatic void sqlite3SelectExpand(Parse *pParse, Select *pSelect){\n  Walker w;\n  w.xExprCallback = sqlite3ExprWalkNoop;\n  w.pParse = pParse;\n  if( OK_IF_ALWAYS_TRUE(pParse->hasCompound) ){\n    w.xSelectCallback = convertCompoundSelectToSubquery;\n    w.xSelectCallback2 = 0;\n    sqlite3WalkSelect(&w, pSelect);\n  }\n  w.xSelectCallback = selectExpander;\n  w.xSelectCallback2 = selectPopWith;\n  sqlite3WalkSelect(&w, pSelect);\n}\n\n\n#ifndef SQLITE_OMIT_SUBQUERY\n/*\n** This is a Walker.xSelectCallback callback for the sqlite3SelectTypeInfo()\n** interface.\n**\n** For each FROM-clause subquery, add Column.zType and Column.zColl\n** information to the Table structure that represents the result set\n** of that subquery.\n**\n** The Table structure that represents the result set was constructed\n** by selectExpander() but the type and collation information was omitted\n** at that point because identifiers had not yet been resolved.  This\n** routine is called after identifier resolution.\n*/\nstatic void selectAddSubqueryTypeInfo(Walker *pWalker, Select *p){\n  Parse *pParse;\n  int i;\n  SrcList *pTabList;\n  struct SrcList_item *pFrom;\n\n  assert( p->selFlags & SF_Resolved );\n  assert( (p->selFlags & SF_HasTypeInfo)==0 );\n  p->selFlags |= SF_HasTypeInfo;\n  pParse = pWalker->pParse;\n  pTabList = p->pSrc;\n  for(i=0, pFrom=pTabList->a; i<pTabList->nSrc; i++, pFrom++){\n    Table *pTab = pFrom->pTab;\n    assert( pTab!=0 );\n    if( (pTab->tabFlags & TF_Ephemeral)!=0 ){\n      /* A sub-query in the FROM clause of a SELECT */\n      Select *pSel = pFrom->pSelect;\n      if( pSel ){\n        while( pSel->pPrior ) pSel = pSel->pPrior;\n        sqlite3SelectAddColumnTypeAndCollation(pParse, pTab, pSel);\n      }\n    }\n  }\n}\n#endif\n\n\n/*\n** This routine adds datatype and collating sequence information to\n** the Table structures of all FROM-clause subqueries in a\n** SELECT statement.\n**\n** Use this routine after name resolution.\n*/\nstatic void sqlite3SelectAddTypeInfo(Parse *pParse, Select *pSelect){\n#ifndef SQLITE_OMIT_SUBQUERY\n  Walker w;\n  w.xSelectCallback = sqlite3SelectWalkNoop;\n  w.xSelectCallback2 = selectAddSubqueryTypeInfo;\n  w.xExprCallback = sqlite3ExprWalkNoop;\n  w.pParse = pParse;\n  sqlite3WalkSelect(&w, pSelect);\n#endif\n}\n\n\n/*\n** This routine sets up a SELECT statement for processing.  The\n** following is accomplished:\n**\n**     *  VDBE Cursor numbers are assigned to all FROM-clause terms.\n**     *  Ephemeral Table objects are created for all FROM-clause subqueries.\n**     *  ON and USING clauses are shifted into WHERE statements\n**     *  Wildcards \"*\" and \"TABLE.*\" in result sets are expanded.\n**     *  Identifiers in expression are matched to tables.\n**\n** This routine acts recursively on all subqueries within the SELECT.\n*/\nSQLITE_PRIVATE void sqlite3SelectPrep(\n  Parse *pParse,         /* The parser context */\n  Select *p,             /* The SELECT statement being coded. */\n  NameContext *pOuterNC  /* Name context for container */\n){\n  assert( p!=0 || pParse->db->mallocFailed );\n  if( pParse->db->mallocFailed ) return;\n  if( p->selFlags & SF_HasTypeInfo ) return;\n  sqlite3SelectExpand(pParse, p);\n  if( pParse->nErr || pParse->db->mallocFailed ) return;\n  sqlite3ResolveSelectNames(pParse, p, pOuterNC);\n  if( pParse->nErr || pParse->db->mallocFailed ) return;\n  sqlite3SelectAddTypeInfo(pParse, p);\n}\n\n/*\n** Reset the aggregate accumulator.\n**\n** The aggregate accumulator is a set of memory cells that hold\n** intermediate results while calculating an aggregate.  This\n** routine generates code that stores NULLs in all of those memory\n** cells.\n*/\nstatic void resetAccumulator(Parse *pParse, AggInfo *pAggInfo){\n  Vdbe *v = pParse->pVdbe;\n  int i;\n  struct AggInfo_func *pFunc;\n  int nReg = pAggInfo->nFunc + pAggInfo->nColumn;\n  if( nReg==0 ) return;\n#ifdef SQLITE_DEBUG\n  /* Verify that all AggInfo registers are within the range specified by\n  ** AggInfo.mnReg..AggInfo.mxReg */\n  assert( nReg==pAggInfo->mxReg-pAggInfo->mnReg+1 );\n  for(i=0; i<pAggInfo->nColumn; i++){\n    assert( pAggInfo->aCol[i].iMem>=pAggInfo->mnReg\n         && pAggInfo->aCol[i].iMem<=pAggInfo->mxReg );\n  }\n  for(i=0; i<pAggInfo->nFunc; i++){\n    assert( pAggInfo->aFunc[i].iMem>=pAggInfo->mnReg\n         && pAggInfo->aFunc[i].iMem<=pAggInfo->mxReg );\n  }\n#endif\n  sqlite3VdbeAddOp3(v, OP_Null, 0, pAggInfo->mnReg, pAggInfo->mxReg);\n  for(pFunc=pAggInfo->aFunc, i=0; i<pAggInfo->nFunc; i++, pFunc++){\n    if( pFunc->iDistinct>=0 ){\n      Expr *pE = pFunc->pExpr;\n      assert( !ExprHasProperty(pE, EP_xIsSelect) );\n      if( pE->x.pList==0 || pE->x.pList->nExpr!=1 ){\n        sqlite3ErrorMsg(pParse, \"DISTINCT aggregates must have exactly one \"\n           \"argument\");\n        pFunc->iDistinct = -1;\n      }else{\n        KeyInfo *pKeyInfo = keyInfoFromExprList(pParse, pE->x.pList, 0, 0);\n        sqlite3VdbeAddOp4(v, OP_OpenEphemeral, pFunc->iDistinct, 0, 0,\n                          (char*)pKeyInfo, P4_KEYINFO);\n      }\n    }\n  }\n}\n\n/*\n** Invoke the OP_AggFinalize opcode for every aggregate function\n** in the AggInfo structure.\n*/\nstatic void finalizeAggFunctions(Parse *pParse, AggInfo *pAggInfo){\n  Vdbe *v = pParse->pVdbe;\n  int i;\n  struct AggInfo_func *pF;\n  for(i=0, pF=pAggInfo->aFunc; i<pAggInfo->nFunc; i++, pF++){\n    ExprList *pList = pF->pExpr->x.pList;\n    assert( !ExprHasProperty(pF->pExpr, EP_xIsSelect) );\n    sqlite3VdbeAddOp2(v, OP_AggFinal, pF->iMem, pList ? pList->nExpr : 0);\n    sqlite3VdbeAppendP4(v, pF->pFunc, P4_FUNCDEF);\n  }\n}\n\n/*\n** Update the accumulator memory cells for an aggregate based on\n** the current cursor position.\n*/\nstatic void updateAccumulator(Parse *pParse, AggInfo *pAggInfo){\n  Vdbe *v = pParse->pVdbe;\n  int i;\n  int regHit = 0;\n  int addrHitTest = 0;\n  struct AggInfo_func *pF;\n  struct AggInfo_col *pC;\n\n  pAggInfo->directMode = 1;\n  for(i=0, pF=pAggInfo->aFunc; i<pAggInfo->nFunc; i++, pF++){\n    int nArg;\n    int addrNext = 0;\n    int regAgg;\n    ExprList *pList = pF->pExpr->x.pList;\n    assert( !ExprHasProperty(pF->pExpr, EP_xIsSelect) );\n    if( pList ){\n      nArg = pList->nExpr;\n      regAgg = sqlite3GetTempRange(pParse, nArg);\n      sqlite3ExprCodeExprList(pParse, pList, regAgg, 0, SQLITE_ECEL_DUP);\n    }else{\n      nArg = 0;\n      regAgg = 0;\n    }\n    if( pF->iDistinct>=0 ){\n      addrNext = sqlite3VdbeMakeLabel(v);\n      testcase( nArg==0 );  /* Error condition */\n      testcase( nArg>1 );   /* Also an error */\n      codeDistinct(pParse, pF->iDistinct, addrNext, 1, regAgg);\n    }\n    if( pF->pFunc->funcFlags & SQLITE_FUNC_NEEDCOLL ){\n      CollSeq *pColl = 0;\n      struct ExprList_item *pItem;\n      int j;\n      assert( pList!=0 );  /* pList!=0 if pF->pFunc has NEEDCOLL */\n      for(j=0, pItem=pList->a; !pColl && j<nArg; j++, pItem++){\n        pColl = sqlite3ExprCollSeq(pParse, pItem->pExpr);\n      }\n      if( !pColl ){\n        pColl = pParse->db->pDfltColl;\n      }\n      if( regHit==0 && pAggInfo->nAccumulator ) regHit = ++pParse->nMem;\n      sqlite3VdbeAddOp4(v, OP_CollSeq, regHit, 0, 0, (char *)pColl, P4_COLLSEQ);\n    }\n    sqlite3VdbeAddOp3(v, OP_AggStep0, 0, regAgg, pF->iMem);\n    sqlite3VdbeAppendP4(v, pF->pFunc, P4_FUNCDEF);\n    sqlite3VdbeChangeP5(v, (u8)nArg);\n    sqlite3ExprCacheAffinityChange(pParse, regAgg, nArg);\n    sqlite3ReleaseTempRange(pParse, regAgg, nArg);\n    if( addrNext ){\n      sqlite3VdbeResolveLabel(v, addrNext);\n      sqlite3ExprCacheClear(pParse);\n    }\n  }\n\n  /* Before populating the accumulator registers, clear the column cache.\n  ** Otherwise, if any of the required column values are already present \n  ** in registers, sqlite3ExprCode() may use OP_SCopy to copy the value\n  ** to pC->iMem. But by the time the value is used, the original register\n  ** may have been used, invalidating the underlying buffer holding the\n  ** text or blob value. See ticket [883034dcb5].\n  **\n  ** Another solution would be to change the OP_SCopy used to copy cached\n  ** values to an OP_Copy.\n  */\n  if( regHit ){\n    addrHitTest = sqlite3VdbeAddOp1(v, OP_If, regHit); VdbeCoverage(v);\n  }\n  sqlite3ExprCacheClear(pParse);\n  for(i=0, pC=pAggInfo->aCol; i<pAggInfo->nAccumulator; i++, pC++){\n    sqlite3ExprCode(pParse, pC->pExpr, pC->iMem);\n  }\n  pAggInfo->directMode = 0;\n  sqlite3ExprCacheClear(pParse);\n  if( addrHitTest ){\n    sqlite3VdbeJumpHere(v, addrHitTest);\n  }\n}\n\n/*\n** Add a single OP_Explain instruction to the VDBE to explain a simple\n** count(*) query (\"SELECT count(*) FROM pTab\").\n*/\n#ifndef SQLITE_OMIT_EXPLAIN\nstatic void explainSimpleCount(\n  Parse *pParse,                  /* Parse context */\n  Table *pTab,                    /* Table being queried */\n  Index *pIdx                     /* Index used to optimize scan, or NULL */\n){\n  if( pParse->explain==2 ){\n    int bCover = (pIdx!=0 && (HasRowid(pTab) || !IsPrimaryKeyIndex(pIdx)));\n    char *zEqp = sqlite3MPrintf(pParse->db, \"SCAN TABLE %s%s%s\",\n        pTab->zName,\n        bCover ? \" USING COVERING INDEX \" : \"\",\n        bCover ? pIdx->zName : \"\"\n    );\n    sqlite3VdbeAddOp4(\n        pParse->pVdbe, OP_Explain, pParse->iSelectId, 0, 0, zEqp, P4_DYNAMIC\n    );\n  }\n}\n#else\n# define explainSimpleCount(a,b,c)\n#endif\n\n/*\n** Context object for havingToWhereExprCb().\n*/\nstruct HavingToWhereCtx {\n  Expr **ppWhere;\n  ExprList *pGroupBy;\n};\n\n/*\n** sqlite3WalkExpr() callback used by havingToWhere().\n**\n** If the node passed to the callback is a TK_AND node, return \n** WRC_Continue to tell sqlite3WalkExpr() to iterate through child nodes.\n**\n** Otherwise, return WRC_Prune. In this case, also check if the \n** sub-expression matches the criteria for being moved to the WHERE\n** clause. If so, add it to the WHERE clause and replace the sub-expression\n** within the HAVING expression with a constant \"1\".\n*/\nstatic int havingToWhereExprCb(Walker *pWalker, Expr *pExpr){\n  if( pExpr->op!=TK_AND ){\n    struct HavingToWhereCtx *p = pWalker->u.pHavingCtx;\n    if( sqlite3ExprIsConstantOrGroupBy(pWalker->pParse, pExpr, p->pGroupBy) ){\n      sqlite3 *db = pWalker->pParse->db;\n      Expr *pNew = sqlite3ExprAlloc(db, TK_INTEGER, &sqlite3IntTokens[1], 0);\n      if( pNew ){\n        Expr *pWhere = *(p->ppWhere);\n        SWAP(Expr, *pNew, *pExpr);\n        pNew = sqlite3ExprAnd(db, pWhere, pNew);\n        *(p->ppWhere) = pNew;\n      }\n    }\n    return WRC_Prune;\n  }\n  return WRC_Continue;\n}\n\n/*\n** Transfer eligible terms from the HAVING clause of a query, which is\n** processed after grouping, to the WHERE clause, which is processed before\n** grouping. For example, the query:\n**\n**   SELECT * FROM <tables> WHERE a=? GROUP BY b HAVING b=? AND c=?\n**\n** can be rewritten as:\n**\n**   SELECT * FROM <tables> WHERE a=? AND b=? GROUP BY b HAVING c=?\n**\n** A term of the HAVING expression is eligible for transfer if it consists\n** entirely of constants and expressions that are also GROUP BY terms that\n** use the \"BINARY\" collation sequence.\n*/\nstatic void havingToWhere(\n  Parse *pParse,\n  ExprList *pGroupBy,\n  Expr *pHaving, \n  Expr **ppWhere\n){\n  struct HavingToWhereCtx sCtx;\n  Walker sWalker;\n\n  sCtx.ppWhere = ppWhere;\n  sCtx.pGroupBy = pGroupBy;\n\n  memset(&sWalker, 0, sizeof(sWalker));\n  sWalker.pParse = pParse;\n  sWalker.xExprCallback = havingToWhereExprCb;\n  sWalker.u.pHavingCtx = &sCtx;\n  sqlite3WalkExpr(&sWalker, pHaving);\n}\n\n/*\n** Check to see if the pThis entry of pTabList is a self-join of a prior view.\n** If it is, then return the SrcList_item for the prior view.  If it is not,\n** then return 0.\n*/\nstatic struct SrcList_item *isSelfJoinView(\n  SrcList *pTabList,           /* Search for self-joins in this FROM clause */\n  struct SrcList_item *pThis   /* Search for prior reference to this subquery */\n){\n  struct SrcList_item *pItem;\n  for(pItem = pTabList->a; pItem<pThis; pItem++){\n    if( pItem->pSelect==0 ) continue;\n    if( pItem->fg.viaCoroutine ) continue;\n    if( pItem->zName==0 ) continue;\n    if( sqlite3_stricmp(pItem->zDatabase, pThis->zDatabase)!=0 ) continue;\n    if( sqlite3_stricmp(pItem->zName, pThis->zName)!=0 ) continue;\n    if( sqlite3ExprCompare(0, \n          pThis->pSelect->pWhere, pItem->pSelect->pWhere, -1) \n    ){\n      /* The view was modified by some other optimization such as\n      ** pushDownWhereTerms() */\n      continue;\n    }\n    return pItem;\n  }\n  return 0;\n}\n\n#ifdef SQLITE_COUNTOFVIEW_OPTIMIZATION\n/*\n** Attempt to transform a query of the form\n**\n**    SELECT count(*) FROM (SELECT x FROM t1 UNION ALL SELECT y FROM t2)\n**\n** Into this:\n**\n**    SELECT (SELECT count(*) FROM t1)+(SELECT count(*) FROM t2)\n**\n** The transformation only works if all of the following are true:\n**\n**   *  The subquery is a UNION ALL of two or more terms\n**   *  There is no WHERE or GROUP BY or HAVING clauses on the subqueries\n**   *  The outer query is a simple count(*)\n**\n** Return TRUE if the optimization is undertaken.\n*/\nstatic int countOfViewOptimization(Parse *pParse, Select *p){\n  Select *pSub, *pPrior;\n  Expr *pExpr;\n  Expr *pCount;\n  sqlite3 *db;\n  if( (p->selFlags & SF_Aggregate)==0 ) return 0;   /* This is an aggregate */\n  if( p->pEList->nExpr!=1 ) return 0;               /* Single result column */\n  pExpr = p->pEList->a[0].pExpr;\n  if( pExpr->op!=TK_AGG_FUNCTION ) return 0;        /* Result is an aggregate */\n  if( sqlite3_stricmp(pExpr->u.zToken,\"count\") ) return 0;  /* Is count() */\n  if( pExpr->x.pList!=0 ) return 0;                 /* Must be count(*) */\n  if( p->pSrc->nSrc!=1 ) return 0;                  /* One table in FROM  */\n  pSub = p->pSrc->a[0].pSelect;\n  if( pSub==0 ) return 0;                           /* The FROM is a subquery */\n  if( pSub->pPrior==0 ) return 0;                   /* Must be a compound ry */\n  do{\n    if( pSub->op!=TK_ALL && pSub->pPrior ) return 0;  /* Must be UNION ALL */\n    if( pSub->pWhere ) return 0;                      /* No WHERE clause */\n    if( pSub->selFlags & SF_Aggregate ) return 0;     /* Not an aggregate */\n    pSub = pSub->pPrior;                              /* Repeat over compound */\n  }while( pSub );\n\n  /* If we reach this point then it is OK to perform the transformation */\n\n  db = pParse->db;\n  pCount = pExpr;\n  pExpr = 0;\n  pSub = p->pSrc->a[0].pSelect;\n  p->pSrc->a[0].pSelect = 0;\n  sqlite3SrcListDelete(db, p->pSrc);\n  p->pSrc = sqlite3DbMallocZero(pParse->db, sizeof(*p->pSrc));\n  while( pSub ){\n    Expr *pTerm;\n    pPrior = pSub->pPrior;\n    pSub->pPrior = 0;\n    pSub->pNext = 0;\n    pSub->selFlags |= SF_Aggregate;\n    pSub->selFlags &= ~SF_Compound;\n    pSub->nSelectRow = 0;\n    sqlite3ExprListDelete(db, pSub->pEList);\n    pTerm = pPrior ? sqlite3ExprDup(db, pCount, 0) : pCount;\n    pSub->pEList = sqlite3ExprListAppend(pParse, 0, pTerm);\n    pTerm = sqlite3PExpr(pParse, TK_SELECT, 0, 0);\n    sqlite3PExprAddSelect(pParse, pTerm, pSub);\n    if( pExpr==0 ){\n      pExpr = pTerm;\n    }else{\n      pExpr = sqlite3PExpr(pParse, TK_PLUS, pTerm, pExpr);\n    }\n    pSub = pPrior;\n  }\n  p->pEList->a[0].pExpr = pExpr;\n  p->selFlags &= ~SF_Aggregate;\n\n#if SELECTTRACE_ENABLED\n  if( sqlite3SelectTrace & 0x400 ){\n    SELECTTRACE(0x400,pParse,p,(\"After count-of-view optimization:\\n\"));\n    sqlite3TreeViewSelect(0, p, 0);\n  }\n#endif\n  return 1;\n}\n#endif /* SQLITE_COUNTOFVIEW_OPTIMIZATION */\n\n/*\n** Generate code for the SELECT statement given in the p argument.  \n**\n** The results are returned according to the SelectDest structure.\n** See comments in sqliteInt.h for further information.\n**\n** This routine returns the number of errors.  If any errors are\n** encountered, then an appropriate error message is left in\n** pParse->zErrMsg.\n**\n** This routine does NOT free the Select structure passed in.  The\n** calling function needs to do that.\n*/\nSQLITE_PRIVATE int sqlite3Select(\n  Parse *pParse,         /* The parser context */\n  Select *p,             /* The SELECT statement being coded. */\n  SelectDest *pDest      /* What to do with the query results */\n){\n  int i, j;              /* Loop counters */\n  WhereInfo *pWInfo;     /* Return from sqlite3WhereBegin() */\n  Vdbe *v;               /* The virtual machine under construction */\n  int isAgg;             /* True for select lists like \"count(*)\" */\n  ExprList *pEList = 0;  /* List of columns to extract. */\n  SrcList *pTabList;     /* List of tables to select from */\n  Expr *pWhere;          /* The WHERE clause.  May be NULL */\n  ExprList *pGroupBy;    /* The GROUP BY clause.  May be NULL */\n  Expr *pHaving;         /* The HAVING clause.  May be NULL */\n  int rc = 1;            /* Value to return from this function */\n  DistinctCtx sDistinct; /* Info on how to code the DISTINCT keyword */\n  SortCtx sSort;         /* Info on how to code the ORDER BY clause */\n  AggInfo sAggInfo;      /* Information used by aggregate queries */\n  int iEnd;              /* Address of the end of the query */\n  sqlite3 *db;           /* The database connection */\n  ExprList *pMinMaxOrderBy = 0;  /* Added ORDER BY for min/max queries */\n  u8 minMaxFlag;                 /* Flag for min/max queries */\n\n#ifndef SQLITE_OMIT_EXPLAIN\n  int iRestoreSelectId = pParse->iSelectId;\n  pParse->iSelectId = pParse->iNextSelectId++;\n#endif\n\n  db = pParse->db;\n  if( p==0 || db->mallocFailed || pParse->nErr ){\n    return 1;\n  }\n  if( sqlite3AuthCheck(pParse, SQLITE_SELECT, 0, 0, 0) ) return 1;\n  memset(&sAggInfo, 0, sizeof(sAggInfo));\n#if SELECTTRACE_ENABLED\n  pParse->nSelectIndent++;\n  SELECTTRACE(1,pParse,p, (\"begin processing:\\n\"));\n  if( sqlite3SelectTrace & 0x100 ){\n    sqlite3TreeViewSelect(0, p, 0);\n  }\n#endif\n\n  assert( p->pOrderBy==0 || pDest->eDest!=SRT_DistFifo );\n  assert( p->pOrderBy==0 || pDest->eDest!=SRT_Fifo );\n  assert( p->pOrderBy==0 || pDest->eDest!=SRT_DistQueue );\n  assert( p->pOrderBy==0 || pDest->eDest!=SRT_Queue );\n  if( IgnorableOrderby(pDest) ){\n    assert(pDest->eDest==SRT_Exists || pDest->eDest==SRT_Union || \n           pDest->eDest==SRT_Except || pDest->eDest==SRT_Discard ||\n           pDest->eDest==SRT_Queue  || pDest->eDest==SRT_DistFifo ||\n           pDest->eDest==SRT_DistQueue || pDest->eDest==SRT_Fifo);\n    /* If ORDER BY makes no difference in the output then neither does\n    ** DISTINCT so it can be removed too. */\n    sqlite3ExprListDelete(db, p->pOrderBy);\n    p->pOrderBy = 0;\n    p->selFlags &= ~SF_Distinct;\n  }\n  sqlite3SelectPrep(pParse, p, 0);\n  memset(&sSort, 0, sizeof(sSort));\n  sSort.pOrderBy = p->pOrderBy;\n  pTabList = p->pSrc;\n  if( pParse->nErr || db->mallocFailed ){\n    goto select_end;\n  }\n  assert( p->pEList!=0 );\n  isAgg = (p->selFlags & SF_Aggregate)!=0;\n#if SELECTTRACE_ENABLED\n  if( sqlite3SelectTrace & 0x100 ){\n    SELECTTRACE(0x100,pParse,p, (\"after name resolution:\\n\"));\n    sqlite3TreeViewSelect(0, p, 0);\n  }\n#endif\n\n  /* Get a pointer the VDBE under construction, allocating a new VDBE if one\n  ** does not already exist */\n  v = sqlite3GetVdbe(pParse);\n  if( v==0 ) goto select_end;\n  if( pDest->eDest==SRT_Output ){\n    generateColumnNames(pParse, p);\n  }\n\n  /* Try to flatten subqueries in the FROM clause up into the main query\n  */\n#if !defined(SQLITE_OMIT_SUBQUERY) || !defined(SQLITE_OMIT_VIEW)\n  for(i=0; !p->pPrior && i<pTabList->nSrc; i++){\n    struct SrcList_item *pItem = &pTabList->a[i];\n    Select *pSub = pItem->pSelect;\n    Table *pTab = pItem->pTab;\n    if( pSub==0 ) continue;\n\n    /* Catch mismatch in the declared columns of a view and the number of\n    ** columns in the SELECT on the RHS */\n    if( pTab->nCol!=pSub->pEList->nExpr ){\n      sqlite3ErrorMsg(pParse, \"expected %d columns for '%s' but got %d\",\n                      pTab->nCol, pTab->zName, pSub->pEList->nExpr);\n      goto select_end;\n    }\n\n    /* Do not try to flatten an aggregate subquery.\n    **\n    ** Flattening an aggregate subquery is only possible if the outer query\n    ** is not a join.  But if the outer query is not a join, then the subquery\n    ** will be implemented as a co-routine and there is no advantage to\n    ** flattening in that case.\n    */\n    if( (pSub->selFlags & SF_Aggregate)!=0 ) continue;\n    assert( pSub->pGroupBy==0 );\n\n    /* If the outer query contains a \"complex\" result set (that is,\n    ** if the result set of the outer query uses functions or subqueries)\n    ** and if the subquery contains an ORDER BY clause and if\n    ** it will be implemented as a co-routine, then do not flatten.  This\n    ** restriction allows SQL constructs like this:\n    **\n    **  SELECT expensive_function(x)\n    **    FROM (SELECT x FROM tab ORDER BY y LIMIT 10);\n    **\n    ** The expensive_function() is only computed on the 10 rows that\n    ** are output, rather than every row of the table.\n    **\n    ** The requirement that the outer query have a complex result set\n    ** means that flattening does occur on simpler SQL constraints without\n    ** the expensive_function() like:\n    **\n    **  SELECT x FROM (SELECT x FROM tab ORDER BY y LIMIT 10);\n    */\n    if( pSub->pOrderBy!=0\n     && i==0\n     && (p->selFlags & SF_ComplexResult)!=0\n     && (pTabList->nSrc==1\n         || (pTabList->a[1].fg.jointype&(JT_LEFT|JT_CROSS))!=0)\n    ){\n      continue;\n    }\n\n    if( flattenSubquery(pParse, p, i, isAgg) ){\n      /* This subquery can be absorbed into its parent. */\n      i = -1;\n    }\n    pTabList = p->pSrc;\n    if( db->mallocFailed ) goto select_end;\n    if( !IgnorableOrderby(pDest) ){\n      sSort.pOrderBy = p->pOrderBy;\n    }\n  }\n#endif\n\n#ifndef SQLITE_OMIT_COMPOUND_SELECT\n  /* Handle compound SELECT statements using the separate multiSelect()\n  ** procedure.\n  */\n  if( p->pPrior ){\n    rc = multiSelect(pParse, p, pDest);\n    explainSetInteger(pParse->iSelectId, iRestoreSelectId);\n#if SELECTTRACE_ENABLED\n    SELECTTRACE(1,pParse,p,(\"end compound-select processing\\n\"));\n    pParse->nSelectIndent--;\n#endif\n    return rc;\n  }\n#endif\n\n  /* For each term in the FROM clause, do two things:\n  ** (1) Authorized unreferenced tables\n  ** (2) Generate code for all sub-queries\n  */\n  for(i=0; i<pTabList->nSrc; i++){\n    struct SrcList_item *pItem = &pTabList->a[i];\n    SelectDest dest;\n    Select *pSub;\n#if !defined(SQLITE_OMIT_SUBQUERY) || !defined(SQLITE_OMIT_VIEW)\n    const char *zSavedAuthContext;\n#endif\n\n    /* Issue SQLITE_READ authorizations with a fake column name for any\n    ** tables that are referenced but from which no values are extracted.\n    ** Examples of where these kinds of null SQLITE_READ authorizations\n    ** would occur:\n    **\n    **     SELECT count(*) FROM t1;   -- SQLITE_READ t1.\"\"\n    **     SELECT t1.* FROM t1, t2;   -- SQLITE_READ t2.\"\"\n    **\n    ** The fake column name is an empty string.  It is possible for a table to\n    ** have a column named by the empty string, in which case there is no way to\n    ** distinguish between an unreferenced table and an actual reference to the\n    ** \"\" column. The original design was for the fake column name to be a NULL,\n    ** which would be unambiguous.  But legacy authorization callbacks might\n    ** assume the column name is non-NULL and segfault.  The use of an empty\n    ** string for the fake column name seems safer.\n    */\n    if( pItem->colUsed==0 ){\n      sqlite3AuthCheck(pParse, SQLITE_READ, pItem->zName, \"\", pItem->zDatabase);\n    }\n\n#if !defined(SQLITE_OMIT_SUBQUERY) || !defined(SQLITE_OMIT_VIEW)\n    /* Generate code for all sub-queries in the FROM clause\n    */\n    pSub = pItem->pSelect;\n    if( pSub==0 ) continue;\n\n    /* Sometimes the code for a subquery will be generated more than\n    ** once, if the subquery is part of the WHERE clause in a LEFT JOIN,\n    ** for example.  In that case, do not regenerate the code to manifest\n    ** a view or the co-routine to implement a view.  The first instance\n    ** is sufficient, though the subroutine to manifest the view does need\n    ** to be invoked again. */\n    if( pItem->addrFillSub ){\n      if( pItem->fg.viaCoroutine==0 ){\n        /* The subroutine that manifests the view might be a one-time routine,\n        ** or it might need to be rerun on each iteration because it\n        ** encodes a correlated subquery. */\n        testcase( sqlite3VdbeGetOp(v, pItem->addrFillSub)->opcode==OP_Once );\n        sqlite3VdbeAddOp2(v, OP_Gosub, pItem->regReturn, pItem->addrFillSub);\n      }\n      continue;\n    }\n\n    /* Increment Parse.nHeight by the height of the largest expression\n    ** tree referred to by this, the parent select. The child select\n    ** may contain expression trees of at most\n    ** (SQLITE_MAX_EXPR_DEPTH-Parse.nHeight) height. This is a bit\n    ** more conservative than necessary, but much easier than enforcing\n    ** an exact limit.\n    */\n    pParse->nHeight += sqlite3SelectExprHeight(p);\n\n    /* Make copies of constant WHERE-clause terms in the outer query down\n    ** inside the subquery.  This can help the subquery to run more efficiently.\n    */\n    if( (pItem->fg.jointype & JT_OUTER)==0\n     && pushDownWhereTerms(pParse, pSub, p->pWhere, pItem->iCursor)\n    ){\n#if SELECTTRACE_ENABLED\n      if( sqlite3SelectTrace & 0x100 ){\n        SELECTTRACE(0x100,pParse,p,(\"After WHERE-clause push-down:\\n\"));\n        sqlite3TreeViewSelect(0, p, 0);\n      }\n#endif\n    }\n\n    zSavedAuthContext = pParse->zAuthContext;\n    pParse->zAuthContext = pItem->zName;\n\n    /* Generate code to implement the subquery\n    **\n    ** The subquery is implemented as a co-routine if the subquery is\n    ** guaranteed to be the outer loop (so that it does not need to be\n    ** computed more than once)\n    **\n    ** TODO: Are there other reasons beside (1) to use a co-routine\n    ** implementation?\n    */\n    if( i==0\n     && (pTabList->nSrc==1\n            || (pTabList->a[1].fg.jointype&(JT_LEFT|JT_CROSS))!=0)  /* (1) */\n    ){\n      /* Implement a co-routine that will return a single row of the result\n      ** set on each invocation.\n      */\n      int addrTop = sqlite3VdbeCurrentAddr(v)+1;\n     \n      pItem->regReturn = ++pParse->nMem;\n      sqlite3VdbeAddOp3(v, OP_InitCoroutine, pItem->regReturn, 0, addrTop);\n      VdbeComment((v, \"%s\", pItem->pTab->zName));\n      pItem->addrFillSub = addrTop;\n      sqlite3SelectDestInit(&dest, SRT_Coroutine, pItem->regReturn);\n      explainSetInteger(pItem->iSelectId, (u8)pParse->iNextSelectId);\n      sqlite3Select(pParse, pSub, &dest);\n      pItem->pTab->nRowLogEst = pSub->nSelectRow;\n      pItem->fg.viaCoroutine = 1;\n      pItem->regResult = dest.iSdst;\n      sqlite3VdbeEndCoroutine(v, pItem->regReturn);\n      sqlite3VdbeJumpHere(v, addrTop-1);\n      sqlite3ClearTempRegCache(pParse);\n    }else{\n      /* Generate a subroutine that will fill an ephemeral table with\n      ** the content of this subquery.  pItem->addrFillSub will point\n      ** to the address of the generated subroutine.  pItem->regReturn\n      ** is a register allocated to hold the subroutine return address\n      */\n      int topAddr;\n      int onceAddr = 0;\n      int retAddr;\n      struct SrcList_item *pPrior;\n\n      assert( pItem->addrFillSub==0 );\n      pItem->regReturn = ++pParse->nMem;\n      topAddr = sqlite3VdbeAddOp2(v, OP_Integer, 0, pItem->regReturn);\n      pItem->addrFillSub = topAddr+1;\n      if( pItem->fg.isCorrelated==0 ){\n        /* If the subquery is not correlated and if we are not inside of\n        ** a trigger, then we only need to compute the value of the subquery\n        ** once. */\n        onceAddr = sqlite3VdbeAddOp0(v, OP_Once); VdbeCoverage(v);\n        VdbeComment((v, \"materialize \\\"%s\\\"\", pItem->pTab->zName));\n      }else{\n        VdbeNoopComment((v, \"materialize \\\"%s\\\"\", pItem->pTab->zName));\n      }\n      pPrior = isSelfJoinView(pTabList, pItem);\n      if( pPrior ){\n        sqlite3VdbeAddOp2(v, OP_OpenDup, pItem->iCursor, pPrior->iCursor);\n        explainSetInteger(pItem->iSelectId, pPrior->iSelectId);\n        assert( pPrior->pSelect!=0 );\n        pSub->nSelectRow = pPrior->pSelect->nSelectRow;\n      }else{\n        sqlite3SelectDestInit(&dest, SRT_EphemTab, pItem->iCursor);\n        explainSetInteger(pItem->iSelectId, (u8)pParse->iNextSelectId);\n        sqlite3Select(pParse, pSub, &dest);\n      }\n      pItem->pTab->nRowLogEst = pSub->nSelectRow;\n      if( onceAddr ) sqlite3VdbeJumpHere(v, onceAddr);\n      retAddr = sqlite3VdbeAddOp1(v, OP_Return, pItem->regReturn);\n      VdbeComment((v, \"end %s\", pItem->pTab->zName));\n      sqlite3VdbeChangeP1(v, topAddr, retAddr);\n      sqlite3ClearTempRegCache(pParse);\n    }\n    if( db->mallocFailed ) goto select_end;\n    pParse->nHeight -= sqlite3SelectExprHeight(p);\n    pParse->zAuthContext = zSavedAuthContext;\n#endif\n  }\n\n  /* Various elements of the SELECT copied into local variables for\n  ** convenience */\n  pEList = p->pEList;\n  pWhere = p->pWhere;\n  pGroupBy = p->pGroupBy;\n  pHaving = p->pHaving;\n  sDistinct.isTnct = (p->selFlags & SF_Distinct)!=0;\n\n#if SELECTTRACE_ENABLED\n  if( sqlite3SelectTrace & 0x400 ){\n    SELECTTRACE(0x400,pParse,p,(\"After all FROM-clause analysis:\\n\"));\n    sqlite3TreeViewSelect(0, p, 0);\n  }\n#endif\n\n#ifdef SQLITE_COUNTOFVIEW_OPTIMIZATION\n  if( OptimizationEnabled(db, SQLITE_QueryFlattener|SQLITE_CountOfView)\n   && countOfViewOptimization(pParse, p)\n  ){\n    if( db->mallocFailed ) goto select_end;\n    pEList = p->pEList;\n    pTabList = p->pSrc;\n  }\n#endif\n\n  /* If the query is DISTINCT with an ORDER BY but is not an aggregate, and \n  ** if the select-list is the same as the ORDER BY list, then this query\n  ** can be rewritten as a GROUP BY. In other words, this:\n  **\n  **     SELECT DISTINCT xyz FROM ... ORDER BY xyz\n  **\n  ** is transformed to:\n  **\n  **     SELECT xyz FROM ... GROUP BY xyz ORDER BY xyz\n  **\n  ** The second form is preferred as a single index (or temp-table) may be \n  ** used for both the ORDER BY and DISTINCT processing. As originally \n  ** written the query must use a temp-table for at least one of the ORDER \n  ** BY and DISTINCT, and an index or separate temp-table for the other.\n  */\n  if( (p->selFlags & (SF_Distinct|SF_Aggregate))==SF_Distinct \n   && sqlite3ExprListCompare(sSort.pOrderBy, pEList, -1)==0\n  ){\n    p->selFlags &= ~SF_Distinct;\n    pGroupBy = p->pGroupBy = sqlite3ExprListDup(db, pEList, 0);\n    /* Notice that even thought SF_Distinct has been cleared from p->selFlags,\n    ** the sDistinct.isTnct is still set.  Hence, isTnct represents the\n    ** original setting of the SF_Distinct flag, not the current setting */\n    assert( sDistinct.isTnct );\n\n#if SELECTTRACE_ENABLED\n    if( sqlite3SelectTrace & 0x400 ){\n      SELECTTRACE(0x400,pParse,p,(\"Transform DISTINCT into GROUP BY:\\n\"));\n      sqlite3TreeViewSelect(0, p, 0);\n    }\n#endif\n  }\n\n  /* If there is an ORDER BY clause, then create an ephemeral index to\n  ** do the sorting.  But this sorting ephemeral index might end up\n  ** being unused if the data can be extracted in pre-sorted order.\n  ** If that is the case, then the OP_OpenEphemeral instruction will be\n  ** changed to an OP_Noop once we figure out that the sorting index is\n  ** not needed.  The sSort.addrSortIndex variable is used to facilitate\n  ** that change.\n  */\n  if( sSort.pOrderBy ){\n    KeyInfo *pKeyInfo;\n    pKeyInfo = keyInfoFromExprList(pParse, sSort.pOrderBy, 0, pEList->nExpr);\n    sSort.iECursor = pParse->nTab++;\n    sSort.addrSortIndex =\n      sqlite3VdbeAddOp4(v, OP_OpenEphemeral,\n          sSort.iECursor, sSort.pOrderBy->nExpr+1+pEList->nExpr, 0,\n          (char*)pKeyInfo, P4_KEYINFO\n      );\n  }else{\n    sSort.addrSortIndex = -1;\n  }\n\n  /* If the output is destined for a temporary table, open that table.\n  */\n  if( pDest->eDest==SRT_EphemTab ){\n    sqlite3VdbeAddOp2(v, OP_OpenEphemeral, pDest->iSDParm, pEList->nExpr);\n  }\n\n  /* Set the limiter.\n  */\n  iEnd = sqlite3VdbeMakeLabel(v);\n  if( (p->selFlags & SF_FixedLimit)==0 ){\n    p->nSelectRow = 320;  /* 4 billion rows */\n  }\n  computeLimitRegisters(pParse, p, iEnd);\n  if( p->iLimit==0 && sSort.addrSortIndex>=0 ){\n    sqlite3VdbeChangeOpcode(v, sSort.addrSortIndex, OP_SorterOpen);\n    sSort.sortFlags |= SORTFLAG_UseSorter;\n  }\n\n  /* Open an ephemeral index to use for the distinct set.\n  */\n  if( p->selFlags & SF_Distinct ){\n    sDistinct.tabTnct = pParse->nTab++;\n    sDistinct.addrTnct = sqlite3VdbeAddOp4(v, OP_OpenEphemeral,\n                             sDistinct.tabTnct, 0, 0,\n                             (char*)keyInfoFromExprList(pParse, p->pEList,0,0),\n                             P4_KEYINFO);\n    sqlite3VdbeChangeP5(v, BTREE_UNORDERED);\n    sDistinct.eTnctType = WHERE_DISTINCT_UNORDERED;\n  }else{\n    sDistinct.eTnctType = WHERE_DISTINCT_NOOP;\n  }\n\n  if( !isAgg && pGroupBy==0 ){\n    /* No aggregate functions and no GROUP BY clause */\n    u16 wctrlFlags = (sDistinct.isTnct ? WHERE_WANT_DISTINCT : 0);\n    assert( WHERE_USE_LIMIT==SF_FixedLimit );\n    wctrlFlags |= p->selFlags & SF_FixedLimit;\n\n    /* Begin the database scan. */\n    pWInfo = sqlite3WhereBegin(pParse, pTabList, pWhere, sSort.pOrderBy,\n                               p->pEList, wctrlFlags, p->nSelectRow);\n    if( pWInfo==0 ) goto select_end;\n    if( sqlite3WhereOutputRowCount(pWInfo) < p->nSelectRow ){\n      p->nSelectRow = sqlite3WhereOutputRowCount(pWInfo);\n    }\n    if( sDistinct.isTnct && sqlite3WhereIsDistinct(pWInfo) ){\n      sDistinct.eTnctType = sqlite3WhereIsDistinct(pWInfo);\n    }\n    if( sSort.pOrderBy ){\n      sSort.nOBSat = sqlite3WhereIsOrdered(pWInfo);\n      sSort.bOrderedInnerLoop = sqlite3WhereOrderedInnerLoop(pWInfo);\n      if( sSort.nOBSat==sSort.pOrderBy->nExpr ){\n        sSort.pOrderBy = 0;\n      }\n    }\n\n    /* If sorting index that was created by a prior OP_OpenEphemeral \n    ** instruction ended up not being needed, then change the OP_OpenEphemeral\n    ** into an OP_Noop.\n    */\n    if( sSort.addrSortIndex>=0 && sSort.pOrderBy==0 ){\n      sqlite3VdbeChangeToNoop(v, sSort.addrSortIndex);\n    }\n\n    /* Use the standard inner loop. */\n    assert( p->pEList==pEList );\n    selectInnerLoop(pParse, p, -1, &sSort, &sDistinct, pDest,\n                    sqlite3WhereContinueLabel(pWInfo),\n                    sqlite3WhereBreakLabel(pWInfo));\n\n    /* End the database scan loop.\n    */\n    sqlite3WhereEnd(pWInfo);\n  }else{\n    /* This case when there exist aggregate functions or a GROUP BY clause\n    ** or both */\n    NameContext sNC;    /* Name context for processing aggregate information */\n    int iAMem;          /* First Mem address for storing current GROUP BY */\n    int iBMem;          /* First Mem address for previous GROUP BY */\n    int iUseFlag;       /* Mem address holding flag indicating that at least\n                        ** one row of the input to the aggregator has been\n                        ** processed */\n    int iAbortFlag;     /* Mem address which causes query abort if positive */\n    int groupBySort;    /* Rows come from source in GROUP BY order */\n    int addrEnd;        /* End of processing for this SELECT */\n    int sortPTab = 0;   /* Pseudotable used to decode sorting results */\n    int sortOut = 0;    /* Output register from the sorter */\n    int orderByGrp = 0; /* True if the GROUP BY and ORDER BY are the same */\n\n    /* Remove any and all aliases between the result set and the\n    ** GROUP BY clause.\n    */\n    if( pGroupBy ){\n      int k;                        /* Loop counter */\n      struct ExprList_item *pItem;  /* For looping over expression in a list */\n\n      for(k=p->pEList->nExpr, pItem=p->pEList->a; k>0; k--, pItem++){\n        pItem->u.x.iAlias = 0;\n      }\n      for(k=pGroupBy->nExpr, pItem=pGroupBy->a; k>0; k--, pItem++){\n        pItem->u.x.iAlias = 0;\n      }\n      assert( 66==sqlite3LogEst(100) );\n      if( p->nSelectRow>66 ) p->nSelectRow = 66;\n    }else{\n      assert( 0==sqlite3LogEst(1) );\n      p->nSelectRow = 0;\n    }\n\n    /* If there is both a GROUP BY and an ORDER BY clause and they are\n    ** identical, then it may be possible to disable the ORDER BY clause \n    ** on the grounds that the GROUP BY will cause elements to come out \n    ** in the correct order. It also may not - the GROUP BY might use a\n    ** database index that causes rows to be grouped together as required\n    ** but not actually sorted. Either way, record the fact that the\n    ** ORDER BY and GROUP BY clauses are the same by setting the orderByGrp\n    ** variable.  */\n    if( sqlite3ExprListCompare(pGroupBy, sSort.pOrderBy, -1)==0 ){\n      orderByGrp = 1;\n    }\n \n    /* Create a label to jump to when we want to abort the query */\n    addrEnd = sqlite3VdbeMakeLabel(v);\n\n    /* Convert TK_COLUMN nodes into TK_AGG_COLUMN and make entries in\n    ** sAggInfo for all TK_AGG_FUNCTION nodes in expressions of the\n    ** SELECT statement.\n    */\n    memset(&sNC, 0, sizeof(sNC));\n    sNC.pParse = pParse;\n    sNC.pSrcList = pTabList;\n    sNC.pAggInfo = &sAggInfo;\n    sAggInfo.mnReg = pParse->nMem+1;\n    sAggInfo.nSortingColumn = pGroupBy ? pGroupBy->nExpr : 0;\n    sAggInfo.pGroupBy = pGroupBy;\n    sqlite3ExprAnalyzeAggList(&sNC, pEList);\n    sqlite3ExprAnalyzeAggList(&sNC, sSort.pOrderBy);\n    if( pHaving ){\n      if( pGroupBy ){\n        assert( pWhere==p->pWhere );\n        havingToWhere(pParse, pGroupBy, pHaving, &p->pWhere);\n        pWhere = p->pWhere;\n      }\n      sqlite3ExprAnalyzeAggregates(&sNC, pHaving);\n    }\n    sAggInfo.nAccumulator = sAggInfo.nColumn;\n    if( p->pGroupBy==0 && p->pHaving==0 && sAggInfo.nFunc==1 ){\n      minMaxFlag = minMaxQuery(db, sAggInfo.aFunc[0].pExpr, &pMinMaxOrderBy);\n    }else{\n      minMaxFlag = WHERE_ORDERBY_NORMAL;\n    }\n    for(i=0; i<sAggInfo.nFunc; i++){\n      assert( !ExprHasProperty(sAggInfo.aFunc[i].pExpr, EP_xIsSelect) );\n      sNC.ncFlags |= NC_InAggFunc;\n      sqlite3ExprAnalyzeAggList(&sNC, sAggInfo.aFunc[i].pExpr->x.pList);\n      sNC.ncFlags &= ~NC_InAggFunc;\n    }\n    sAggInfo.mxReg = pParse->nMem;\n    if( db->mallocFailed ) goto select_end;\n#if SELECTTRACE_ENABLED\n    if( sqlite3SelectTrace & 0x400 ){\n      int ii;\n      SELECTTRACE(0x400,pParse,p,(\"After aggregate analysis:\\n\"));\n      sqlite3TreeViewSelect(0, p, 0);\n      for(ii=0; ii<sAggInfo.nColumn; ii++){\n        sqlite3DebugPrintf(\"agg-column[%d] iMem=%d\\n\",\n            ii, sAggInfo.aCol[ii].iMem);\n        sqlite3TreeViewExpr(0, sAggInfo.aCol[ii].pExpr, 0);\n      }\n      for(ii=0; ii<sAggInfo.nFunc; ii++){\n        sqlite3DebugPrintf(\"agg-func[%d]: iMem=%d\\n\",\n            ii, sAggInfo.aFunc[ii].iMem);\n        sqlite3TreeViewExpr(0, sAggInfo.aFunc[ii].pExpr, 0);\n      }\n    }\n#endif\n\n\n    /* Processing for aggregates with GROUP BY is very different and\n    ** much more complex than aggregates without a GROUP BY.\n    */\n    if( pGroupBy ){\n      KeyInfo *pKeyInfo;  /* Keying information for the group by clause */\n      int addr1;          /* A-vs-B comparision jump */\n      int addrOutputRow;  /* Start of subroutine that outputs a result row */\n      int regOutputRow;   /* Return address register for output subroutine */\n      int addrSetAbort;   /* Set the abort flag and return */\n      int addrTopOfLoop;  /* Top of the input loop */\n      int addrSortingIdx; /* The OP_OpenEphemeral for the sorting index */\n      int addrReset;      /* Subroutine for resetting the accumulator */\n      int regReset;       /* Return address register for reset subroutine */\n\n      /* If there is a GROUP BY clause we might need a sorting index to\n      ** implement it.  Allocate that sorting index now.  If it turns out\n      ** that we do not need it after all, the OP_SorterOpen instruction\n      ** will be converted into a Noop.  \n      */\n      sAggInfo.sortingIdx = pParse->nTab++;\n      pKeyInfo = keyInfoFromExprList(pParse, pGroupBy, 0, sAggInfo.nColumn);\n      addrSortingIdx = sqlite3VdbeAddOp4(v, OP_SorterOpen, \n          sAggInfo.sortingIdx, sAggInfo.nSortingColumn, \n          0, (char*)pKeyInfo, P4_KEYINFO);\n\n      /* Initialize memory locations used by GROUP BY aggregate processing\n      */\n      iUseFlag = ++pParse->nMem;\n      iAbortFlag = ++pParse->nMem;\n      regOutputRow = ++pParse->nMem;\n      addrOutputRow = sqlite3VdbeMakeLabel(v);\n      regReset = ++pParse->nMem;\n      addrReset = sqlite3VdbeMakeLabel(v);\n      iAMem = pParse->nMem + 1;\n      pParse->nMem += pGroupBy->nExpr;\n      iBMem = pParse->nMem + 1;\n      pParse->nMem += pGroupBy->nExpr;\n      sqlite3VdbeAddOp2(v, OP_Integer, 0, iAbortFlag);\n      VdbeComment((v, \"clear abort flag\"));\n      sqlite3VdbeAddOp2(v, OP_Integer, 0, iUseFlag);\n      VdbeComment((v, \"indicate accumulator empty\"));\n      sqlite3VdbeAddOp3(v, OP_Null, 0, iAMem, iAMem+pGroupBy->nExpr-1);\n\n      /* Begin a loop that will extract all source rows in GROUP BY order.\n      ** This might involve two separate loops with an OP_Sort in between, or\n      ** it might be a single loop that uses an index to extract information\n      ** in the right order to begin with.\n      */\n      sqlite3VdbeAddOp2(v, OP_Gosub, regReset, addrReset);\n      pWInfo = sqlite3WhereBegin(pParse, pTabList, pWhere, pGroupBy, 0,\n          WHERE_GROUPBY | (orderByGrp ? WHERE_SORTBYGROUP : 0), 0\n      );\n      if( pWInfo==0 ) goto select_end;\n      if( sqlite3WhereIsOrdered(pWInfo)==pGroupBy->nExpr ){\n        /* The optimizer is able to deliver rows in group by order so\n        ** we do not have to sort.  The OP_OpenEphemeral table will be\n        ** cancelled later because we still need to use the pKeyInfo\n        */\n        groupBySort = 0;\n      }else{\n        /* Rows are coming out in undetermined order.  We have to push\n        ** each row into a sorting index, terminate the first loop,\n        ** then loop over the sorting index in order to get the output\n        ** in sorted order\n        */\n        int regBase;\n        int regRecord;\n        int nCol;\n        int nGroupBy;\n\n        explainTempTable(pParse, \n            (sDistinct.isTnct && (p->selFlags&SF_Distinct)==0) ?\n                    \"DISTINCT\" : \"GROUP BY\");\n\n        groupBySort = 1;\n        nGroupBy = pGroupBy->nExpr;\n        nCol = nGroupBy;\n        j = nGroupBy;\n        for(i=0; i<sAggInfo.nColumn; i++){\n          if( sAggInfo.aCol[i].iSorterColumn>=j ){\n            nCol++;\n            j++;\n          }\n        }\n        regBase = sqlite3GetTempRange(pParse, nCol);\n        sqlite3ExprCacheClear(pParse);\n        sqlite3ExprCodeExprList(pParse, pGroupBy, regBase, 0, 0);\n        j = nGroupBy;\n        for(i=0; i<sAggInfo.nColumn; i++){\n          struct AggInfo_col *pCol = &sAggInfo.aCol[i];\n          if( pCol->iSorterColumn>=j ){\n            int r1 = j + regBase;\n            sqlite3ExprCodeGetColumnToReg(pParse, \n                               pCol->pTab, pCol->iColumn, pCol->iTable, r1);\n            j++;\n          }\n        }\n        regRecord = sqlite3GetTempReg(pParse);\n        sqlite3VdbeAddOp3(v, OP_MakeRecord, regBase, nCol, regRecord);\n        sqlite3VdbeAddOp2(v, OP_SorterInsert, sAggInfo.sortingIdx, regRecord);\n        sqlite3ReleaseTempReg(pParse, regRecord);\n        sqlite3ReleaseTempRange(pParse, regBase, nCol);\n        sqlite3WhereEnd(pWInfo);\n        sAggInfo.sortingIdxPTab = sortPTab = pParse->nTab++;\n        sortOut = sqlite3GetTempReg(pParse);\n        sqlite3VdbeAddOp3(v, OP_OpenPseudo, sortPTab, sortOut, nCol);\n        sqlite3VdbeAddOp2(v, OP_SorterSort, sAggInfo.sortingIdx, addrEnd);\n        VdbeComment((v, \"GROUP BY sort\")); VdbeCoverage(v);\n        sAggInfo.useSortingIdx = 1;\n        sqlite3ExprCacheClear(pParse);\n\n      }\n\n      /* If the index or temporary table used by the GROUP BY sort\n      ** will naturally deliver rows in the order required by the ORDER BY\n      ** clause, cancel the ephemeral table open coded earlier.\n      **\n      ** This is an optimization - the correct answer should result regardless.\n      ** Use the SQLITE_GroupByOrder flag with SQLITE_TESTCTRL_OPTIMIZER to \n      ** disable this optimization for testing purposes.  */\n      if( orderByGrp && OptimizationEnabled(db, SQLITE_GroupByOrder) \n       && (groupBySort || sqlite3WhereIsSorted(pWInfo))\n      ){\n        sSort.pOrderBy = 0;\n        sqlite3VdbeChangeToNoop(v, sSort.addrSortIndex);\n      }\n\n      /* Evaluate the current GROUP BY terms and store in b0, b1, b2...\n      ** (b0 is memory location iBMem+0, b1 is iBMem+1, and so forth)\n      ** Then compare the current GROUP BY terms against the GROUP BY terms\n      ** from the previous row currently stored in a0, a1, a2...\n      */\n      addrTopOfLoop = sqlite3VdbeCurrentAddr(v);\n      sqlite3ExprCacheClear(pParse);\n      if( groupBySort ){\n        sqlite3VdbeAddOp3(v, OP_SorterData, sAggInfo.sortingIdx,\n                          sortOut, sortPTab);\n      }\n      for(j=0; j<pGroupBy->nExpr; j++){\n        if( groupBySort ){\n          sqlite3VdbeAddOp3(v, OP_Column, sortPTab, j, iBMem+j);\n        }else{\n          sAggInfo.directMode = 1;\n          sqlite3ExprCode(pParse, pGroupBy->a[j].pExpr, iBMem+j);\n        }\n      }\n      sqlite3VdbeAddOp4(v, OP_Compare, iAMem, iBMem, pGroupBy->nExpr,\n                          (char*)sqlite3KeyInfoRef(pKeyInfo), P4_KEYINFO);\n      addr1 = sqlite3VdbeCurrentAddr(v);\n      sqlite3VdbeAddOp3(v, OP_Jump, addr1+1, 0, addr1+1); VdbeCoverage(v);\n\n      /* Generate code that runs whenever the GROUP BY changes.\n      ** Changes in the GROUP BY are detected by the previous code\n      ** block.  If there were no changes, this block is skipped.\n      **\n      ** This code copies current group by terms in b0,b1,b2,...\n      ** over to a0,a1,a2.  It then calls the output subroutine\n      ** and resets the aggregate accumulator registers in preparation\n      ** for the next GROUP BY batch.\n      */\n      sqlite3ExprCodeMove(pParse, iBMem, iAMem, pGroupBy->nExpr);\n      sqlite3VdbeAddOp2(v, OP_Gosub, regOutputRow, addrOutputRow);\n      VdbeComment((v, \"output one row\"));\n      sqlite3VdbeAddOp2(v, OP_IfPos, iAbortFlag, addrEnd); VdbeCoverage(v);\n      VdbeComment((v, \"check abort flag\"));\n      sqlite3VdbeAddOp2(v, OP_Gosub, regReset, addrReset);\n      VdbeComment((v, \"reset accumulator\"));\n\n      /* Update the aggregate accumulators based on the content of\n      ** the current row\n      */\n      sqlite3VdbeJumpHere(v, addr1);\n      updateAccumulator(pParse, &sAggInfo);\n      sqlite3VdbeAddOp2(v, OP_Integer, 1, iUseFlag);\n      VdbeComment((v, \"indicate data in accumulator\"));\n\n      /* End of the loop\n      */\n      if( groupBySort ){\n        sqlite3VdbeAddOp2(v, OP_SorterNext, sAggInfo.sortingIdx, addrTopOfLoop);\n        VdbeCoverage(v);\n      }else{\n        sqlite3WhereEnd(pWInfo);\n        sqlite3VdbeChangeToNoop(v, addrSortingIdx);\n      }\n\n      /* Output the final row of result\n      */\n      sqlite3VdbeAddOp2(v, OP_Gosub, regOutputRow, addrOutputRow);\n      VdbeComment((v, \"output final row\"));\n\n      /* Jump over the subroutines\n      */\n      sqlite3VdbeGoto(v, addrEnd);\n\n      /* Generate a subroutine that outputs a single row of the result\n      ** set.  This subroutine first looks at the iUseFlag.  If iUseFlag\n      ** is less than or equal to zero, the subroutine is a no-op.  If\n      ** the processing calls for the query to abort, this subroutine\n      ** increments the iAbortFlag memory location before returning in\n      ** order to signal the caller to abort.\n      */\n      addrSetAbort = sqlite3VdbeCurrentAddr(v);\n      sqlite3VdbeAddOp2(v, OP_Integer, 1, iAbortFlag);\n      VdbeComment((v, \"set abort flag\"));\n      sqlite3VdbeAddOp1(v, OP_Return, regOutputRow);\n      sqlite3VdbeResolveLabel(v, addrOutputRow);\n      addrOutputRow = sqlite3VdbeCurrentAddr(v);\n      sqlite3VdbeAddOp2(v, OP_IfPos, iUseFlag, addrOutputRow+2);\n      VdbeCoverage(v);\n      VdbeComment((v, \"Groupby result generator entry point\"));\n      sqlite3VdbeAddOp1(v, OP_Return, regOutputRow);\n      finalizeAggFunctions(pParse, &sAggInfo);\n      sqlite3ExprIfFalse(pParse, pHaving, addrOutputRow+1, SQLITE_JUMPIFNULL);\n      selectInnerLoop(pParse, p, -1, &sSort,\n                      &sDistinct, pDest,\n                      addrOutputRow+1, addrSetAbort);\n      sqlite3VdbeAddOp1(v, OP_Return, regOutputRow);\n      VdbeComment((v, \"end groupby result generator\"));\n\n      /* Generate a subroutine that will reset the group-by accumulator\n      */\n      sqlite3VdbeResolveLabel(v, addrReset);\n      resetAccumulator(pParse, &sAggInfo);\n      sqlite3VdbeAddOp1(v, OP_Return, regReset);\n     \n    } /* endif pGroupBy.  Begin aggregate queries without GROUP BY: */\n    else {\n#ifndef SQLITE_OMIT_BTREECOUNT\n      Table *pTab;\n      if( (pTab = isSimpleCount(p, &sAggInfo))!=0 ){\n        /* If isSimpleCount() returns a pointer to a Table structure, then\n        ** the SQL statement is of the form:\n        **\n        **   SELECT count(*) FROM <tbl>\n        **\n        ** where the Table structure returned represents table <tbl>.\n        **\n        ** This statement is so common that it is optimized specially. The\n        ** OP_Count instruction is executed either on the intkey table that\n        ** contains the data for table <tbl> or on one of its indexes. It\n        ** is better to execute the op on an index, as indexes are almost\n        ** always spread across less pages than their corresponding tables.\n        */\n        const int iDb = sqlite3SchemaToIndex(pParse->db, pTab->pSchema);\n        const int iCsr = pParse->nTab++;     /* Cursor to scan b-tree */\n        Index *pIdx;                         /* Iterator variable */\n        KeyInfo *pKeyInfo = 0;               /* Keyinfo for scanned index */\n        Index *pBest = 0;                    /* Best index found so far */\n        int iRoot = pTab->tnum;              /* Root page of scanned b-tree */\n\n        sqlite3CodeVerifySchema(pParse, iDb);\n        sqlite3TableLock(pParse, iDb, pTab->tnum, 0, pTab->zName);\n\n        /* Search for the index that has the lowest scan cost.\n        **\n        ** (2011-04-15) Do not do a full scan of an unordered index.\n        **\n        ** (2013-10-03) Do not count the entries in a partial index.\n        **\n        ** In practice the KeyInfo structure will not be used. It is only \n        ** passed to keep OP_OpenRead happy.\n        */\n        if( !HasRowid(pTab) ) pBest = sqlite3PrimaryKeyIndex(pTab);\n        for(pIdx=pTab->pIndex; pIdx; pIdx=pIdx->pNext){\n          if( pIdx->bUnordered==0\n           && pIdx->szIdxRow<pTab->szTabRow\n           && pIdx->pPartIdxWhere==0\n           && (!pBest || pIdx->szIdxRow<pBest->szIdxRow)\n          ){\n            pBest = pIdx;\n          }\n        }\n        if( pBest ){\n          iRoot = pBest->tnum;\n          pKeyInfo = sqlite3KeyInfoOfIndex(pParse, pBest);\n        }\n\n        /* Open a read-only cursor, execute the OP_Count, close the cursor. */\n        sqlite3VdbeAddOp4Int(v, OP_OpenRead, iCsr, iRoot, iDb, 1);\n        if( pKeyInfo ){\n          sqlite3VdbeChangeP4(v, -1, (char *)pKeyInfo, P4_KEYINFO);\n        }\n        sqlite3VdbeAddOp2(v, OP_Count, iCsr, sAggInfo.aFunc[0].iMem);\n        sqlite3VdbeAddOp1(v, OP_Close, iCsr);\n        explainSimpleCount(pParse, pTab, pBest);\n      }else\n#endif /* SQLITE_OMIT_BTREECOUNT */\n      {\n        /* This case runs if the aggregate has no GROUP BY clause.  The\n        ** processing is much simpler since there is only a single row\n        ** of output.\n        */\n        assert( p->pGroupBy==0 );\n        resetAccumulator(pParse, &sAggInfo);\n\n        /* If this query is a candidate for the min/max optimization, then\n        ** minMaxFlag will have been previously set to either\n        ** WHERE_ORDERBY_MIN or WHERE_ORDERBY_MAX and pMinMaxOrderBy will\n        ** be an appropriate ORDER BY expression for the optimization.\n        */\n        assert( minMaxFlag==WHERE_ORDERBY_NORMAL || pMinMaxOrderBy!=0 );\n        assert( pMinMaxOrderBy==0 || pMinMaxOrderBy->nExpr==1 );\n\n        pWInfo = sqlite3WhereBegin(pParse, pTabList, pWhere, pMinMaxOrderBy,\n                                   0, minMaxFlag, 0);\n        if( pWInfo==0 ){\n          goto select_end;\n        }\n        updateAccumulator(pParse, &sAggInfo);\n        if( sqlite3WhereIsOrdered(pWInfo)>0 ){\n          sqlite3VdbeGoto(v, sqlite3WhereBreakLabel(pWInfo));\n          VdbeComment((v, \"%s() by index\",\n                (minMaxFlag==WHERE_ORDERBY_MIN?\"min\":\"max\")));\n        }\n        sqlite3WhereEnd(pWInfo);\n        finalizeAggFunctions(pParse, &sAggInfo);\n      }\n\n      sSort.pOrderBy = 0;\n      sqlite3ExprIfFalse(pParse, pHaving, addrEnd, SQLITE_JUMPIFNULL);\n      selectInnerLoop(pParse, p, -1, 0, 0, \n                      pDest, addrEnd, addrEnd);\n    }\n    sqlite3VdbeResolveLabel(v, addrEnd);\n    \n  } /* endif aggregate query */\n\n  if( sDistinct.eTnctType==WHERE_DISTINCT_UNORDERED ){\n    explainTempTable(pParse, \"DISTINCT\");\n  }\n\n  /* If there is an ORDER BY clause, then we need to sort the results\n  ** and send them to the callback one by one.\n  */\n  if( sSort.pOrderBy ){\n    explainTempTable(pParse,\n                     sSort.nOBSat>0 ? \"RIGHT PART OF ORDER BY\":\"ORDER BY\");\n    generateSortTail(pParse, p, &sSort, pEList->nExpr, pDest);\n  }\n\n  /* Jump here to skip this query\n  */\n  sqlite3VdbeResolveLabel(v, iEnd);\n\n  /* The SELECT has been coded. If there is an error in the Parse structure,\n  ** set the return code to 1. Otherwise 0. */\n  rc = (pParse->nErr>0);\n\n  /* Control jumps to here if an error is encountered above, or upon\n  ** successful coding of the SELECT.\n  */\nselect_end:\n  explainSetInteger(pParse->iSelectId, iRestoreSelectId);\n  sqlite3ExprListDelete(db, pMinMaxOrderBy);\n  sqlite3DbFree(db, sAggInfo.aCol);\n  sqlite3DbFree(db, sAggInfo.aFunc);\n#if SELECTTRACE_ENABLED\n  SELECTTRACE(1,pParse,p,(\"end processing\\n\"));\n  pParse->nSelectIndent--;\n#endif\n  return rc;\n}\n\n/************** End of select.c **********************************************/\n/************** Begin file table.c *******************************************/\n/*\n** 2001 September 15\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n*************************************************************************\n** This file contains the sqlite3_get_table() and sqlite3_free_table()\n** interface routines.  These are just wrappers around the main\n** interface routine of sqlite3_exec().\n**\n** These routines are in a separate files so that they will not be linked\n** if they are not used.\n*/\n/* #include \"sqliteInt.h\" */\n\n#ifndef SQLITE_OMIT_GET_TABLE\n\n/*\n** This structure is used to pass data from sqlite3_get_table() through\n** to the callback function is uses to build the result.\n*/\ntypedef struct TabResult {\n  char **azResult;   /* Accumulated output */\n  char *zErrMsg;     /* Error message text, if an error occurs */\n  u32 nAlloc;        /* Slots allocated for azResult[] */\n  u32 nRow;          /* Number of rows in the result */\n  u32 nColumn;       /* Number of columns in the result */\n  u32 nData;         /* Slots used in azResult[].  (nRow+1)*nColumn */\n  int rc;            /* Return code from sqlite3_exec() */\n} TabResult;\n\n/*\n** This routine is called once for each row in the result table.  Its job\n** is to fill in the TabResult structure appropriately, allocating new\n** memory as necessary.\n*/\nstatic int sqlite3_get_table_cb(void *pArg, int nCol, char **argv, char **colv){\n  TabResult *p = (TabResult*)pArg;  /* Result accumulator */\n  int need;                         /* Slots needed in p->azResult[] */\n  int i;                            /* Loop counter */\n  char *z;                          /* A single column of result */\n\n  /* Make sure there is enough space in p->azResult to hold everything\n  ** we need to remember from this invocation of the callback.\n  */\n  if( p->nRow==0 && argv!=0 ){\n    need = nCol*2;\n  }else{\n    need = nCol;\n  }\n  if( p->nData + need > p->nAlloc ){\n    char **azNew;\n    p->nAlloc = p->nAlloc*2 + need;\n    azNew = sqlite3_realloc64( p->azResult, sizeof(char*)*p->nAlloc );\n    if( azNew==0 ) goto malloc_failed;\n    p->azResult = azNew;\n  }\n\n  /* If this is the first row, then generate an extra row containing\n  ** the names of all columns.\n  */\n  if( p->nRow==0 ){\n    p->nColumn = nCol;\n    for(i=0; i<nCol; i++){\n      z = sqlite3_mprintf(\"%s\", colv[i]);\n      if( z==0 ) goto malloc_failed;\n      p->azResult[p->nData++] = z;\n    }\n  }else if( (int)p->nColumn!=nCol ){\n    sqlite3_free(p->zErrMsg);\n    p->zErrMsg = sqlite3_mprintf(\n       \"sqlite3_get_table() called with two or more incompatible queries\"\n    );\n    p->rc = SQLITE_ERROR;\n    return 1;\n  }\n\n  /* Copy over the row data\n  */\n  if( argv!=0 ){\n    for(i=0; i<nCol; i++){\n      if( argv[i]==0 ){\n        z = 0;\n      }else{\n        int n = sqlite3Strlen30(argv[i])+1;\n        z = sqlite3_malloc64( n );\n        if( z==0 ) goto malloc_failed;\n        memcpy(z, argv[i], n);\n      }\n      p->azResult[p->nData++] = z;\n    }\n    p->nRow++;\n  }\n  return 0;\n\nmalloc_failed:\n  p->rc = SQLITE_NOMEM_BKPT;\n  return 1;\n}\n\n/*\n** Query the database.  But instead of invoking a callback for each row,\n** malloc() for space to hold the result and return the entire results\n** at the conclusion of the call.\n**\n** The result that is written to ***pazResult is held in memory obtained\n** from malloc().  But the caller cannot free this memory directly.  \n** Instead, the entire table should be passed to sqlite3_free_table() when\n** the calling procedure is finished using it.\n*/\nSQLITE_API int sqlite3_get_table(\n  sqlite3 *db,                /* The database on which the SQL executes */\n  const char *zSql,           /* The SQL to be executed */\n  char ***pazResult,          /* Write the result table here */\n  int *pnRow,                 /* Write the number of rows in the result here */\n  int *pnColumn,              /* Write the number of columns of result here */\n  char **pzErrMsg             /* Write error messages here */\n){\n  int rc;\n  TabResult res;\n\n#ifdef SQLITE_ENABLE_API_ARMOR\n  if( !sqlite3SafetyCheckOk(db) || pazResult==0 ) return SQLITE_MISUSE_BKPT;\n#endif\n  *pazResult = 0;\n  if( pnColumn ) *pnColumn = 0;\n  if( pnRow ) *pnRow = 0;\n  if( pzErrMsg ) *pzErrMsg = 0;\n  res.zErrMsg = 0;\n  res.nRow = 0;\n  res.nColumn = 0;\n  res.nData = 1;\n  res.nAlloc = 20;\n  res.rc = SQLITE_OK;\n  res.azResult = sqlite3_malloc64(sizeof(char*)*res.nAlloc );\n  if( res.azResult==0 ){\n     db->errCode = SQLITE_NOMEM;\n     return SQLITE_NOMEM_BKPT;\n  }\n  res.azResult[0] = 0;\n  rc = sqlite3_exec(db, zSql, sqlite3_get_table_cb, &res, pzErrMsg);\n  assert( sizeof(res.azResult[0])>= sizeof(res.nData) );\n  res.azResult[0] = SQLITE_INT_TO_PTR(res.nData);\n  if( (rc&0xff)==SQLITE_ABORT ){\n    sqlite3_free_table(&res.azResult[1]);\n    if( res.zErrMsg ){\n      if( pzErrMsg ){\n        sqlite3_free(*pzErrMsg);\n        *pzErrMsg = sqlite3_mprintf(\"%s\",res.zErrMsg);\n      }\n      sqlite3_free(res.zErrMsg);\n    }\n    db->errCode = res.rc;  /* Assume 32-bit assignment is atomic */\n    return res.rc;\n  }\n  sqlite3_free(res.zErrMsg);\n  if( rc!=SQLITE_OK ){\n    sqlite3_free_table(&res.azResult[1]);\n    return rc;\n  }\n  if( res.nAlloc>res.nData ){\n    char **azNew;\n    azNew = sqlite3_realloc64( res.azResult, sizeof(char*)*res.nData );\n    if( azNew==0 ){\n      sqlite3_free_table(&res.azResult[1]);\n      db->errCode = SQLITE_NOMEM;\n      return SQLITE_NOMEM_BKPT;\n    }\n    res.azResult = azNew;\n  }\n  *pazResult = &res.azResult[1];\n  if( pnColumn ) *pnColumn = res.nColumn;\n  if( pnRow ) *pnRow = res.nRow;\n  return rc;\n}\n\n/*\n** This routine frees the space the sqlite3_get_table() malloced.\n*/\nSQLITE_API void sqlite3_free_table(\n  char **azResult            /* Result returned from sqlite3_get_table() */\n){\n  if( azResult ){\n    int i, n;\n    azResult--;\n    assert( azResult!=0 );\n    n = SQLITE_PTR_TO_INT(azResult[0]);\n    for(i=1; i<n; i++){ if( azResult[i] ) sqlite3_free(azResult[i]); }\n    sqlite3_free(azResult);\n  }\n}\n\n#endif /* SQLITE_OMIT_GET_TABLE */\n\n/************** End of table.c ***********************************************/\n/************** Begin file trigger.c *****************************************/\n/*\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n*************************************************************************\n** This file contains the implementation for TRIGGERs\n*/\n/* #include \"sqliteInt.h\" */\n\n#ifndef SQLITE_OMIT_TRIGGER\n/*\n** Delete a linked list of TriggerStep structures.\n*/\nSQLITE_PRIVATE void sqlite3DeleteTriggerStep(sqlite3 *db, TriggerStep *pTriggerStep){\n  while( pTriggerStep ){\n    TriggerStep * pTmp = pTriggerStep;\n    pTriggerStep = pTriggerStep->pNext;\n\n    sqlite3ExprDelete(db, pTmp->pWhere);\n    sqlite3ExprListDelete(db, pTmp->pExprList);\n    sqlite3SelectDelete(db, pTmp->pSelect);\n    sqlite3IdListDelete(db, pTmp->pIdList);\n    sqlite3DbFree(db, pTmp->zSpan);\n\n    sqlite3DbFree(db, pTmp);\n  }\n}\n\n/*\n** Given table pTab, return a list of all the triggers attached to \n** the table. The list is connected by Trigger.pNext pointers.\n**\n** All of the triggers on pTab that are in the same database as pTab\n** are already attached to pTab->pTrigger.  But there might be additional\n** triggers on pTab in the TEMP schema.  This routine prepends all\n** TEMP triggers on pTab to the beginning of the pTab->pTrigger list\n** and returns the combined list.\n**\n** To state it another way:  This routine returns a list of all triggers\n** that fire off of pTab.  The list will include any TEMP triggers on\n** pTab as well as the triggers lised in pTab->pTrigger.\n*/\nSQLITE_PRIVATE Trigger *sqlite3TriggerList(Parse *pParse, Table *pTab){\n  Schema * const pTmpSchema = pParse->db->aDb[1].pSchema;\n  Trigger *pList = 0;                  /* List of triggers to return */\n\n  if( pParse->disableTriggers ){\n    return 0;\n  }\n\n  if( pTmpSchema!=pTab->pSchema ){\n    HashElem *p;\n    assert( sqlite3SchemaMutexHeld(pParse->db, 0, pTmpSchema) );\n    for(p=sqliteHashFirst(&pTmpSchema->trigHash); p; p=sqliteHashNext(p)){\n      Trigger *pTrig = (Trigger *)sqliteHashData(p);\n      if( pTrig->pTabSchema==pTab->pSchema\n       && 0==sqlite3StrICmp(pTrig->table, pTab->zName) \n      ){\n        pTrig->pNext = (pList ? pList : pTab->pTrigger);\n        pList = pTrig;\n      }\n    }\n  }\n\n  return (pList ? pList : pTab->pTrigger);\n}\n\n/*\n** This is called by the parser when it sees a CREATE TRIGGER statement\n** up to the point of the BEGIN before the trigger actions.  A Trigger\n** structure is generated based on the information available and stored\n** in pParse->pNewTrigger.  After the trigger actions have been parsed, the\n** sqlite3FinishTrigger() function is called to complete the trigger\n** construction process.\n*/\nSQLITE_PRIVATE void sqlite3BeginTrigger(\n  Parse *pParse,      /* The parse context of the CREATE TRIGGER statement */\n  Token *pName1,      /* The name of the trigger */\n  Token *pName2,      /* The name of the trigger */\n  int tr_tm,          /* One of TK_BEFORE, TK_AFTER, TK_INSTEAD */\n  int op,             /* One of TK_INSERT, TK_UPDATE, TK_DELETE */\n  IdList *pColumns,   /* column list if this is an UPDATE OF trigger */\n  SrcList *pTableName,/* The name of the table/view the trigger applies to */\n  Expr *pWhen,        /* WHEN clause */\n  int isTemp,         /* True if the TEMPORARY keyword is present */\n  int noErr           /* Suppress errors if the trigger already exists */\n){\n  Trigger *pTrigger = 0;  /* The new trigger */\n  Table *pTab;            /* Table that the trigger fires off of */\n  char *zName = 0;        /* Name of the trigger */\n  sqlite3 *db = pParse->db;  /* The database connection */\n  int iDb;                /* The database to store the trigger in */\n  Token *pName;           /* The unqualified db name */\n  DbFixer sFix;           /* State vector for the DB fixer */\n\n  assert( pName1!=0 );   /* pName1->z might be NULL, but not pName1 itself */\n  assert( pName2!=0 );\n  assert( op==TK_INSERT || op==TK_UPDATE || op==TK_DELETE );\n  assert( op>0 && op<0xff );\n  if( isTemp ){\n    /* If TEMP was specified, then the trigger name may not be qualified. */\n    if( pName2->n>0 ){\n      sqlite3ErrorMsg(pParse, \"temporary trigger may not have qualified name\");\n      goto trigger_cleanup;\n    }\n    iDb = 1;\n    pName = pName1;\n  }else{\n    /* Figure out the db that the trigger will be created in */\n    iDb = sqlite3TwoPartName(pParse, pName1, pName2, &pName);\n    if( iDb<0 ){\n      goto trigger_cleanup;\n    }\n  }\n  if( !pTableName || db->mallocFailed ){\n    goto trigger_cleanup;\n  }\n\n  /* A long-standing parser bug is that this syntax was allowed:\n  **\n  **    CREATE TRIGGER attached.demo AFTER INSERT ON attached.tab ....\n  **                                                 ^^^^^^^^\n  **\n  ** To maintain backwards compatibility, ignore the database\n  ** name on pTableName if we are reparsing out of SQLITE_MASTER.\n  */\n  if( db->init.busy && iDb!=1 ){\n    sqlite3DbFree(db, pTableName->a[0].zDatabase);\n    pTableName->a[0].zDatabase = 0;\n  }\n\n  /* If the trigger name was unqualified, and the table is a temp table,\n  ** then set iDb to 1 to create the trigger in the temporary database.\n  ** If sqlite3SrcListLookup() returns 0, indicating the table does not\n  ** exist, the error is caught by the block below.\n  */\n  pTab = sqlite3SrcListLookup(pParse, pTableName);\n  if( db->init.busy==0 && pName2->n==0 && pTab\n        && pTab->pSchema==db->aDb[1].pSchema ){\n    iDb = 1;\n  }\n\n  /* Ensure the table name matches database name and that the table exists */\n  if( db->mallocFailed ) goto trigger_cleanup;\n  assert( pTableName->nSrc==1 );\n  sqlite3FixInit(&sFix, pParse, iDb, \"trigger\", pName);\n  if( sqlite3FixSrcList(&sFix, pTableName) ){\n    goto trigger_cleanup;\n  }\n  pTab = sqlite3SrcListLookup(pParse, pTableName);\n  if( !pTab ){\n    /* The table does not exist. */\n    if( db->init.iDb==1 ){\n      /* Ticket #3810.\n      ** Normally, whenever a table is dropped, all associated triggers are\n      ** dropped too.  But if a TEMP trigger is created on a non-TEMP table\n      ** and the table is dropped by a different database connection, the\n      ** trigger is not visible to the database connection that does the\n      ** drop so the trigger cannot be dropped.  This results in an\n      ** \"orphaned trigger\" - a trigger whose associated table is missing.\n      */\n      db->init.orphanTrigger = 1;\n    }\n    goto trigger_cleanup;\n  }\n  if( IsVirtual(pTab) ){\n    sqlite3ErrorMsg(pParse, \"cannot create triggers on virtual tables\");\n    goto trigger_cleanup;\n  }\n\n  /* Check that the trigger name is not reserved and that no trigger of the\n  ** specified name exists */\n  zName = sqlite3NameFromToken(db, pName);\n  if( !zName || SQLITE_OK!=sqlite3CheckObjectName(pParse, zName) ){\n    goto trigger_cleanup;\n  }\n  assert( sqlite3SchemaMutexHeld(db, iDb, 0) );\n  if( sqlite3HashFind(&(db->aDb[iDb].pSchema->trigHash),zName) ){\n    if( !noErr ){\n      sqlite3ErrorMsg(pParse, \"trigger %T already exists\", pName);\n    }else{\n      assert( !db->init.busy );\n      sqlite3CodeVerifySchema(pParse, iDb);\n    }\n    goto trigger_cleanup;\n  }\n\n  /* Do not create a trigger on a system table */\n  if( sqlite3StrNICmp(pTab->zName, \"sqlite_\", 7)==0 ){\n    sqlite3ErrorMsg(pParse, \"cannot create trigger on system table\");\n    goto trigger_cleanup;\n  }\n\n  /* INSTEAD of triggers are only for views and views only support INSTEAD\n  ** of triggers.\n  */\n  if( pTab->pSelect && tr_tm!=TK_INSTEAD ){\n    sqlite3ErrorMsg(pParse, \"cannot create %s trigger on view: %S\", \n        (tr_tm == TK_BEFORE)?\"BEFORE\":\"AFTER\", pTableName, 0);\n    goto trigger_cleanup;\n  }\n  if( !pTab->pSelect && tr_tm==TK_INSTEAD ){\n    sqlite3ErrorMsg(pParse, \"cannot create INSTEAD OF\"\n        \" trigger on table: %S\", pTableName, 0);\n    goto trigger_cleanup;\n  }\n\n#ifndef SQLITE_OMIT_AUTHORIZATION\n  {\n    int iTabDb = sqlite3SchemaToIndex(db, pTab->pSchema);\n    int code = SQLITE_CREATE_TRIGGER;\n    const char *zDb = db->aDb[iTabDb].zDbSName;\n    const char *zDbTrig = isTemp ? db->aDb[1].zDbSName : zDb;\n    if( iTabDb==1 || isTemp ) code = SQLITE_CREATE_TEMP_TRIGGER;\n    if( sqlite3AuthCheck(pParse, code, zName, pTab->zName, zDbTrig) ){\n      goto trigger_cleanup;\n    }\n    if( sqlite3AuthCheck(pParse, SQLITE_INSERT, SCHEMA_TABLE(iTabDb),0,zDb)){\n      goto trigger_cleanup;\n    }\n  }\n#endif\n\n  /* INSTEAD OF triggers can only appear on views and BEFORE triggers\n  ** cannot appear on views.  So we might as well translate every\n  ** INSTEAD OF trigger into a BEFORE trigger.  It simplifies code\n  ** elsewhere.\n  */\n  if (tr_tm == TK_INSTEAD){\n    tr_tm = TK_BEFORE;\n  }\n\n  /* Build the Trigger object */\n  pTrigger = (Trigger*)sqlite3DbMallocZero(db, sizeof(Trigger));\n  if( pTrigger==0 ) goto trigger_cleanup;\n  pTrigger->zName = zName;\n  zName = 0;\n  pTrigger->table = sqlite3DbStrDup(db, pTableName->a[0].zName);\n  pTrigger->pSchema = db->aDb[iDb].pSchema;\n  pTrigger->pTabSchema = pTab->pSchema;\n  pTrigger->op = (u8)op;\n  pTrigger->tr_tm = tr_tm==TK_BEFORE ? TRIGGER_BEFORE : TRIGGER_AFTER;\n  pTrigger->pWhen = sqlite3ExprDup(db, pWhen, EXPRDUP_REDUCE);\n  pTrigger->pColumns = sqlite3IdListDup(db, pColumns);\n  assert( pParse->pNewTrigger==0 );\n  pParse->pNewTrigger = pTrigger;\n\ntrigger_cleanup:\n  sqlite3DbFree(db, zName);\n  sqlite3SrcListDelete(db, pTableName);\n  sqlite3IdListDelete(db, pColumns);\n  sqlite3ExprDelete(db, pWhen);\n  if( !pParse->pNewTrigger ){\n    sqlite3DeleteTrigger(db, pTrigger);\n  }else{\n    assert( pParse->pNewTrigger==pTrigger );\n  }\n}\n\n/*\n** This routine is called after all of the trigger actions have been parsed\n** in order to complete the process of building the trigger.\n*/\nSQLITE_PRIVATE void sqlite3FinishTrigger(\n  Parse *pParse,          /* Parser context */\n  TriggerStep *pStepList, /* The triggered program */\n  Token *pAll             /* Token that describes the complete CREATE TRIGGER */\n){\n  Trigger *pTrig = pParse->pNewTrigger;   /* Trigger being finished */\n  char *zName;                            /* Name of trigger */\n  sqlite3 *db = pParse->db;               /* The database */\n  DbFixer sFix;                           /* Fixer object */\n  int iDb;                                /* Database containing the trigger */\n  Token nameToken;                        /* Trigger name for error reporting */\n\n  pParse->pNewTrigger = 0;\n  if( NEVER(pParse->nErr) || !pTrig ) goto triggerfinish_cleanup;\n  zName = pTrig->zName;\n  iDb = sqlite3SchemaToIndex(pParse->db, pTrig->pSchema);\n  pTrig->step_list = pStepList;\n  while( pStepList ){\n    pStepList->pTrig = pTrig;\n    pStepList = pStepList->pNext;\n  }\n  sqlite3TokenInit(&nameToken, pTrig->zName);\n  sqlite3FixInit(&sFix, pParse, iDb, \"trigger\", &nameToken);\n  if( sqlite3FixTriggerStep(&sFix, pTrig->step_list) \n   || sqlite3FixExpr(&sFix, pTrig->pWhen) \n  ){\n    goto triggerfinish_cleanup;\n  }\n\n  /* if we are not initializing,\n  ** build the sqlite_master entry\n  */\n  if( !db->init.busy ){\n    Vdbe *v;\n    char *z;\n\n    /* Make an entry in the sqlite_master table */\n    v = sqlite3GetVdbe(pParse);\n    if( v==0 ) goto triggerfinish_cleanup;\n    sqlite3BeginWriteOperation(pParse, 0, iDb);\n    z = sqlite3DbStrNDup(db, (char*)pAll->z, pAll->n);\n    testcase( z==0 );\n    sqlite3NestedParse(pParse,\n       \"INSERT INTO %Q.%s VALUES('trigger',%Q,%Q,0,'CREATE TRIGGER %q')\",\n       db->aDb[iDb].zDbSName, MASTER_NAME, zName,\n       pTrig->table, z);\n    sqlite3DbFree(db, z);\n    sqlite3ChangeCookie(pParse, iDb);\n    sqlite3VdbeAddParseSchemaOp(v, iDb,\n        sqlite3MPrintf(db, \"type='trigger' AND name='%q'\", zName));\n  }\n\n  if( db->init.busy ){\n    Trigger *pLink = pTrig;\n    Hash *pHash = &db->aDb[iDb].pSchema->trigHash;\n    assert( sqlite3SchemaMutexHeld(db, iDb, 0) );\n    pTrig = sqlite3HashInsert(pHash, zName, pTrig);\n    if( pTrig ){\n      sqlite3OomFault(db);\n    }else if( pLink->pSchema==pLink->pTabSchema ){\n      Table *pTab;\n      pTab = sqlite3HashFind(&pLink->pTabSchema->tblHash, pLink->table);\n      assert( pTab!=0 );\n      pLink->pNext = pTab->pTrigger;\n      pTab->pTrigger = pLink;\n    }\n  }\n\ntriggerfinish_cleanup:\n  sqlite3DeleteTrigger(db, pTrig);\n  assert( !pParse->pNewTrigger );\n  sqlite3DeleteTriggerStep(db, pStepList);\n}\n\n/*\n** Duplicate a range of text from an SQL statement, then convert all\n** whitespace characters into ordinary space characters.\n*/\nstatic char *triggerSpanDup(sqlite3 *db, const char *zStart, const char *zEnd){\n  char *z = sqlite3DbSpanDup(db, zStart, zEnd);\n  int i;\n  if( z ) for(i=0; z[i]; i++) if( sqlite3Isspace(z[i]) ) z[i] = ' ';\n  return z;\n}    \n\n/*\n** Turn a SELECT statement (that the pSelect parameter points to) into\n** a trigger step.  Return a pointer to a TriggerStep structure.\n**\n** The parser calls this routine when it finds a SELECT statement in\n** body of a TRIGGER.  \n*/\nSQLITE_PRIVATE TriggerStep *sqlite3TriggerSelectStep(\n  sqlite3 *db,                /* Database connection */\n  Select *pSelect,            /* The SELECT statement */\n  const char *zStart,         /* Start of SQL text */\n  const char *zEnd            /* End of SQL text */\n){\n  TriggerStep *pTriggerStep = sqlite3DbMallocZero(db, sizeof(TriggerStep));\n  if( pTriggerStep==0 ) {\n    sqlite3SelectDelete(db, pSelect);\n    return 0;\n  }\n  pTriggerStep->op = TK_SELECT;\n  pTriggerStep->pSelect = pSelect;\n  pTriggerStep->orconf = OE_Default;\n  pTriggerStep->zSpan = triggerSpanDup(db, zStart, zEnd);\n  return pTriggerStep;\n}\n\n/*\n** Allocate space to hold a new trigger step.  The allocated space\n** holds both the TriggerStep object and the TriggerStep.target.z string.\n**\n** If an OOM error occurs, NULL is returned and db->mallocFailed is set.\n*/\nstatic TriggerStep *triggerStepAllocate(\n  sqlite3 *db,                /* Database connection */\n  u8 op,                      /* Trigger opcode */\n  Token *pName,               /* The target name */\n  const char *zStart,         /* Start of SQL text */\n  const char *zEnd            /* End of SQL text */\n){\n  TriggerStep *pTriggerStep;\n\n  pTriggerStep = sqlite3DbMallocZero(db, sizeof(TriggerStep) + pName->n + 1);\n  if( pTriggerStep ){\n    char *z = (char*)&pTriggerStep[1];\n    memcpy(z, pName->z, pName->n);\n    sqlite3Dequote(z);\n    pTriggerStep->zTarget = z;\n    pTriggerStep->op = op;\n    pTriggerStep->zSpan = triggerSpanDup(db, zStart, zEnd);\n  }\n  return pTriggerStep;\n}\n\n/*\n** Build a trigger step out of an INSERT statement.  Return a pointer\n** to the new trigger step.\n**\n** The parser calls this routine when it sees an INSERT inside the\n** body of a trigger.\n*/\nSQLITE_PRIVATE TriggerStep *sqlite3TriggerInsertStep(\n  sqlite3 *db,        /* The database connection */\n  Token *pTableName,  /* Name of the table into which we insert */\n  IdList *pColumn,    /* List of columns in pTableName to insert into */\n  Select *pSelect,    /* A SELECT statement that supplies values */\n  u8 orconf,          /* The conflict algorithm (OE_Abort, OE_Replace, etc.) */\n  const char *zStart, /* Start of SQL text */\n  const char *zEnd    /* End of SQL text */\n){\n  TriggerStep *pTriggerStep;\n\n  assert(pSelect != 0 || db->mallocFailed);\n\n  pTriggerStep = triggerStepAllocate(db, TK_INSERT, pTableName, zStart, zEnd);\n  if( pTriggerStep ){\n    pTriggerStep->pSelect = sqlite3SelectDup(db, pSelect, EXPRDUP_REDUCE);\n    pTriggerStep->pIdList = pColumn;\n    pTriggerStep->orconf = orconf;\n  }else{\n    sqlite3IdListDelete(db, pColumn);\n  }\n  sqlite3SelectDelete(db, pSelect);\n\n  return pTriggerStep;\n}\n\n/*\n** Construct a trigger step that implements an UPDATE statement and return\n** a pointer to that trigger step.  The parser calls this routine when it\n** sees an UPDATE statement inside the body of a CREATE TRIGGER.\n*/\nSQLITE_PRIVATE TriggerStep *sqlite3TriggerUpdateStep(\n  sqlite3 *db,         /* The database connection */\n  Token *pTableName,   /* Name of the table to be updated */\n  ExprList *pEList,    /* The SET clause: list of column and new values */\n  Expr *pWhere,        /* The WHERE clause */\n  u8 orconf,           /* The conflict algorithm. (OE_Abort, OE_Ignore, etc) */\n  const char *zStart,  /* Start of SQL text */\n  const char *zEnd     /* End of SQL text */\n){\n  TriggerStep *pTriggerStep;\n\n  pTriggerStep = triggerStepAllocate(db, TK_UPDATE, pTableName, zStart, zEnd);\n  if( pTriggerStep ){\n    pTriggerStep->pExprList = sqlite3ExprListDup(db, pEList, EXPRDUP_REDUCE);\n    pTriggerStep->pWhere = sqlite3ExprDup(db, pWhere, EXPRDUP_REDUCE);\n    pTriggerStep->orconf = orconf;\n  }\n  sqlite3ExprListDelete(db, pEList);\n  sqlite3ExprDelete(db, pWhere);\n  return pTriggerStep;\n}\n\n/*\n** Construct a trigger step that implements a DELETE statement and return\n** a pointer to that trigger step.  The parser calls this routine when it\n** sees a DELETE statement inside the body of a CREATE TRIGGER.\n*/\nSQLITE_PRIVATE TriggerStep *sqlite3TriggerDeleteStep(\n  sqlite3 *db,            /* Database connection */\n  Token *pTableName,      /* The table from which rows are deleted */\n  Expr *pWhere,           /* The WHERE clause */\n  const char *zStart,     /* Start of SQL text */\n  const char *zEnd        /* End of SQL text */\n){\n  TriggerStep *pTriggerStep;\n\n  pTriggerStep = triggerStepAllocate(db, TK_DELETE, pTableName, zStart, zEnd);\n  if( pTriggerStep ){\n    pTriggerStep->pWhere = sqlite3ExprDup(db, pWhere, EXPRDUP_REDUCE);\n    pTriggerStep->orconf = OE_Default;\n  }\n  sqlite3ExprDelete(db, pWhere);\n  return pTriggerStep;\n}\n\n/* \n** Recursively delete a Trigger structure\n*/\nSQLITE_PRIVATE void sqlite3DeleteTrigger(sqlite3 *db, Trigger *pTrigger){\n  if( pTrigger==0 ) return;\n  sqlite3DeleteTriggerStep(db, pTrigger->step_list);\n  sqlite3DbFree(db, pTrigger->zName);\n  sqlite3DbFree(db, pTrigger->table);\n  sqlite3ExprDelete(db, pTrigger->pWhen);\n  sqlite3IdListDelete(db, pTrigger->pColumns);\n  sqlite3DbFree(db, pTrigger);\n}\n\n/*\n** This function is called to drop a trigger from the database schema. \n**\n** This may be called directly from the parser and therefore identifies\n** the trigger by name.  The sqlite3DropTriggerPtr() routine does the\n** same job as this routine except it takes a pointer to the trigger\n** instead of the trigger name.\n**/\nSQLITE_PRIVATE void sqlite3DropTrigger(Parse *pParse, SrcList *pName, int noErr){\n  Trigger *pTrigger = 0;\n  int i;\n  const char *zDb;\n  const char *zName;\n  sqlite3 *db = pParse->db;\n\n  if( db->mallocFailed ) goto drop_trigger_cleanup;\n  if( SQLITE_OK!=sqlite3ReadSchema(pParse) ){\n    goto drop_trigger_cleanup;\n  }\n\n  assert( pName->nSrc==1 );\n  zDb = pName->a[0].zDatabase;\n  zName = pName->a[0].zName;\n  assert( zDb!=0 || sqlite3BtreeHoldsAllMutexes(db) );\n  for(i=OMIT_TEMPDB; i<db->nDb; i++){\n    int j = (i<2) ? i^1 : i;  /* Search TEMP before MAIN */\n    if( zDb && sqlite3StrICmp(db->aDb[j].zDbSName, zDb) ) continue;\n    assert( sqlite3SchemaMutexHeld(db, j, 0) );\n    pTrigger = sqlite3HashFind(&(db->aDb[j].pSchema->trigHash), zName);\n    if( pTrigger ) break;\n  }\n  if( !pTrigger ){\n    if( !noErr ){\n      sqlite3ErrorMsg(pParse, \"no such trigger: %S\", pName, 0);\n    }else{\n      sqlite3CodeVerifyNamedSchema(pParse, zDb);\n    }\n    pParse->checkSchema = 1;\n    goto drop_trigger_cleanup;\n  }\n  sqlite3DropTriggerPtr(pParse, pTrigger);\n\ndrop_trigger_cleanup:\n  sqlite3SrcListDelete(db, pName);\n}\n\n/*\n** Return a pointer to the Table structure for the table that a trigger\n** is set on.\n*/\nstatic Table *tableOfTrigger(Trigger *pTrigger){\n  return sqlite3HashFind(&pTrigger->pTabSchema->tblHash, pTrigger->table);\n}\n\n\n/*\n** Drop a trigger given a pointer to that trigger. \n*/\nSQLITE_PRIVATE void sqlite3DropTriggerPtr(Parse *pParse, Trigger *pTrigger){\n  Table   *pTable;\n  Vdbe *v;\n  sqlite3 *db = pParse->db;\n  int iDb;\n\n  iDb = sqlite3SchemaToIndex(pParse->db, pTrigger->pSchema);\n  assert( iDb>=0 && iDb<db->nDb );\n  pTable = tableOfTrigger(pTrigger);\n  assert( pTable );\n  assert( pTable->pSchema==pTrigger->pSchema || iDb==1 );\n#ifndef SQLITE_OMIT_AUTHORIZATION\n  {\n    int code = SQLITE_DROP_TRIGGER;\n    const char *zDb = db->aDb[iDb].zDbSName;\n    const char *zTab = SCHEMA_TABLE(iDb);\n    if( iDb==1 ) code = SQLITE_DROP_TEMP_TRIGGER;\n    if( sqlite3AuthCheck(pParse, code, pTrigger->zName, pTable->zName, zDb) ||\n      sqlite3AuthCheck(pParse, SQLITE_DELETE, zTab, 0, zDb) ){\n      return;\n    }\n  }\n#endif\n\n  /* Generate code to destroy the database record of the trigger.\n  */\n  assert( pTable!=0 );\n  if( (v = sqlite3GetVdbe(pParse))!=0 ){\n    sqlite3NestedParse(pParse,\n       \"DELETE FROM %Q.%s WHERE name=%Q AND type='trigger'\",\n       db->aDb[iDb].zDbSName, MASTER_NAME, pTrigger->zName\n    );\n    sqlite3ChangeCookie(pParse, iDb);\n    sqlite3VdbeAddOp4(v, OP_DropTrigger, iDb, 0, 0, pTrigger->zName, 0);\n  }\n}\n\n/*\n** Remove a trigger from the hash tables of the sqlite* pointer.\n*/\nSQLITE_PRIVATE void sqlite3UnlinkAndDeleteTrigger(sqlite3 *db, int iDb, const char *zName){\n  Trigger *pTrigger;\n  Hash *pHash;\n\n  assert( sqlite3SchemaMutexHeld(db, iDb, 0) );\n  pHash = &(db->aDb[iDb].pSchema->trigHash);\n  pTrigger = sqlite3HashInsert(pHash, zName, 0);\n  if( ALWAYS(pTrigger) ){\n    if( pTrigger->pSchema==pTrigger->pTabSchema ){\n      Table *pTab = tableOfTrigger(pTrigger);\n      Trigger **pp;\n      for(pp=&pTab->pTrigger; *pp!=pTrigger; pp=&((*pp)->pNext));\n      *pp = (*pp)->pNext;\n    }\n    sqlite3DeleteTrigger(db, pTrigger);\n    db->mDbFlags |= DBFLAG_SchemaChange;\n  }\n}\n\n/*\n** pEList is the SET clause of an UPDATE statement.  Each entry\n** in pEList is of the format <id>=<expr>.  If any of the entries\n** in pEList have an <id> which matches an identifier in pIdList,\n** then return TRUE.  If pIdList==NULL, then it is considered a\n** wildcard that matches anything.  Likewise if pEList==NULL then\n** it matches anything so always return true.  Return false only\n** if there is no match.\n*/\nstatic int checkColumnOverlap(IdList *pIdList, ExprList *pEList){\n  int e;\n  if( pIdList==0 || NEVER(pEList==0) ) return 1;\n  for(e=0; e<pEList->nExpr; e++){\n    if( sqlite3IdListIndex(pIdList, pEList->a[e].zName)>=0 ) return 1;\n  }\n  return 0; \n}\n\n/*\n** Return a list of all triggers on table pTab if there exists at least\n** one trigger that must be fired when an operation of type 'op' is \n** performed on the table, and, if that operation is an UPDATE, if at\n** least one of the columns in pChanges is being modified.\n*/\nSQLITE_PRIVATE Trigger *sqlite3TriggersExist(\n  Parse *pParse,          /* Parse context */\n  Table *pTab,            /* The table the contains the triggers */\n  int op,                 /* one of TK_DELETE, TK_INSERT, TK_UPDATE */\n  ExprList *pChanges,     /* Columns that change in an UPDATE statement */\n  int *pMask              /* OUT: Mask of TRIGGER_BEFORE|TRIGGER_AFTER */\n){\n  int mask = 0;\n  Trigger *pList = 0;\n  Trigger *p;\n\n  if( (pParse->db->flags & SQLITE_EnableTrigger)!=0 ){\n    pList = sqlite3TriggerList(pParse, pTab);\n  }\n  assert( pList==0 || IsVirtual(pTab)==0 );\n  for(p=pList; p; p=p->pNext){\n    if( p->op==op && checkColumnOverlap(p->pColumns, pChanges) ){\n      mask |= p->tr_tm;\n    }\n  }\n  if( pMask ){\n    *pMask = mask;\n  }\n  return (mask ? pList : 0);\n}\n\n/*\n** Convert the pStep->zTarget string into a SrcList and return a pointer\n** to that SrcList.\n**\n** This routine adds a specific database name, if needed, to the target when\n** forming the SrcList.  This prevents a trigger in one database from\n** referring to a target in another database.  An exception is when the\n** trigger is in TEMP in which case it can refer to any other database it\n** wants.\n*/\nstatic SrcList *targetSrcList(\n  Parse *pParse,       /* The parsing context */\n  TriggerStep *pStep   /* The trigger containing the target token */\n){\n  sqlite3 *db = pParse->db;\n  int iDb;             /* Index of the database to use */\n  SrcList *pSrc;       /* SrcList to be returned */\n\n  pSrc = sqlite3SrcListAppend(db, 0, 0, 0);\n  if( pSrc ){\n    assert( pSrc->nSrc>0 );\n    pSrc->a[pSrc->nSrc-1].zName = sqlite3DbStrDup(db, pStep->zTarget);\n    iDb = sqlite3SchemaToIndex(db, pStep->pTrig->pSchema);\n    if( iDb==0 || iDb>=2 ){\n      const char *zDb;\n      assert( iDb<db->nDb );\n      zDb = db->aDb[iDb].zDbSName;\n      pSrc->a[pSrc->nSrc-1].zDatabase =  sqlite3DbStrDup(db, zDb);\n    }\n  }\n  return pSrc;\n}\n\n/*\n** Generate VDBE code for the statements inside the body of a single \n** trigger.\n*/\nstatic int codeTriggerProgram(\n  Parse *pParse,            /* The parser context */\n  TriggerStep *pStepList,   /* List of statements inside the trigger body */\n  int orconf                /* Conflict algorithm. (OE_Abort, etc) */  \n){\n  TriggerStep *pStep;\n  Vdbe *v = pParse->pVdbe;\n  sqlite3 *db = pParse->db;\n\n  assert( pParse->pTriggerTab && pParse->pToplevel );\n  assert( pStepList );\n  assert( v!=0 );\n  for(pStep=pStepList; pStep; pStep=pStep->pNext){\n    /* Figure out the ON CONFLICT policy that will be used for this step\n    ** of the trigger program. If the statement that caused this trigger\n    ** to fire had an explicit ON CONFLICT, then use it. Otherwise, use\n    ** the ON CONFLICT policy that was specified as part of the trigger\n    ** step statement. Example:\n    **\n    **   CREATE TRIGGER AFTER INSERT ON t1 BEGIN;\n    **     INSERT OR REPLACE INTO t2 VALUES(new.a, new.b);\n    **   END;\n    **\n    **   INSERT INTO t1 ... ;            -- insert into t2 uses REPLACE policy\n    **   INSERT OR IGNORE INTO t1 ... ;  -- insert into t2 uses IGNORE policy\n    */\n    pParse->eOrconf = (orconf==OE_Default)?pStep->orconf:(u8)orconf;\n    assert( pParse->okConstFactor==0 );\n\n#ifndef SQLITE_OMIT_TRACE\n    if( pStep->zSpan ){\n      sqlite3VdbeAddOp4(v, OP_Trace, 0x7fffffff, 1, 0,\n                        sqlite3MPrintf(db, \"-- %s\", pStep->zSpan),\n                        P4_DYNAMIC);\n    }\n#endif\n\n    switch( pStep->op ){\n      case TK_UPDATE: {\n        sqlite3Update(pParse, \n          targetSrcList(pParse, pStep),\n          sqlite3ExprListDup(db, pStep->pExprList, 0), \n          sqlite3ExprDup(db, pStep->pWhere, 0), \n          pParse->eOrconf, 0, 0\n        );\n        break;\n      }\n      case TK_INSERT: {\n        sqlite3Insert(pParse, \n          targetSrcList(pParse, pStep),\n          sqlite3SelectDup(db, pStep->pSelect, 0), \n          sqlite3IdListDup(db, pStep->pIdList), \n          pParse->eOrconf\n        );\n        break;\n      }\n      case TK_DELETE: {\n        sqlite3DeleteFrom(pParse, \n          targetSrcList(pParse, pStep),\n          sqlite3ExprDup(db, pStep->pWhere, 0), 0, 0\n        );\n        break;\n      }\n      default: assert( pStep->op==TK_SELECT ); {\n        SelectDest sDest;\n        Select *pSelect = sqlite3SelectDup(db, pStep->pSelect, 0);\n        sqlite3SelectDestInit(&sDest, SRT_Discard, 0);\n        sqlite3Select(pParse, pSelect, &sDest);\n        sqlite3SelectDelete(db, pSelect);\n        break;\n      }\n    } \n    if( pStep->op!=TK_SELECT ){\n      sqlite3VdbeAddOp0(v, OP_ResetCount);\n    }\n  }\n\n  return 0;\n}\n\n#ifdef SQLITE_ENABLE_EXPLAIN_COMMENTS\n/*\n** This function is used to add VdbeComment() annotations to a VDBE\n** program. It is not used in production code, only for debugging.\n*/\nstatic const char *onErrorText(int onError){\n  switch( onError ){\n    case OE_Abort:    return \"abort\";\n    case OE_Rollback: return \"rollback\";\n    case OE_Fail:     return \"fail\";\n    case OE_Replace:  return \"replace\";\n    case OE_Ignore:   return \"ignore\";\n    case OE_Default:  return \"default\";\n  }\n  return \"n/a\";\n}\n#endif\n\n/*\n** Parse context structure pFrom has just been used to create a sub-vdbe\n** (trigger program). If an error has occurred, transfer error information\n** from pFrom to pTo.\n*/\nstatic void transferParseError(Parse *pTo, Parse *pFrom){\n  assert( pFrom->zErrMsg==0 || pFrom->nErr );\n  assert( pTo->zErrMsg==0 || pTo->nErr );\n  if( pTo->nErr==0 ){\n    pTo->zErrMsg = pFrom->zErrMsg;\n    pTo->nErr = pFrom->nErr;\n    pTo->rc = pFrom->rc;\n  }else{\n    sqlite3DbFree(pFrom->db, pFrom->zErrMsg);\n  }\n}\n\n/*\n** Create and populate a new TriggerPrg object with a sub-program \n** implementing trigger pTrigger with ON CONFLICT policy orconf.\n*/\nstatic TriggerPrg *codeRowTrigger(\n  Parse *pParse,       /* Current parse context */\n  Trigger *pTrigger,   /* Trigger to code */\n  Table *pTab,         /* The table pTrigger is attached to */\n  int orconf           /* ON CONFLICT policy to code trigger program with */\n){\n  Parse *pTop = sqlite3ParseToplevel(pParse);\n  sqlite3 *db = pParse->db;   /* Database handle */\n  TriggerPrg *pPrg;           /* Value to return */\n  Expr *pWhen = 0;            /* Duplicate of trigger WHEN expression */\n  Vdbe *v;                    /* Temporary VM */\n  NameContext sNC;            /* Name context for sub-vdbe */\n  SubProgram *pProgram = 0;   /* Sub-vdbe for trigger program */\n  Parse *pSubParse;           /* Parse context for sub-vdbe */\n  int iEndTrigger = 0;        /* Label to jump to if WHEN is false */\n\n  assert( pTrigger->zName==0 || pTab==tableOfTrigger(pTrigger) );\n  assert( pTop->pVdbe );\n\n  /* Allocate the TriggerPrg and SubProgram objects. To ensure that they\n  ** are freed if an error occurs, link them into the Parse.pTriggerPrg \n  ** list of the top-level Parse object sooner rather than later.  */\n  pPrg = sqlite3DbMallocZero(db, sizeof(TriggerPrg));\n  if( !pPrg ) return 0;\n  pPrg->pNext = pTop->pTriggerPrg;\n  pTop->pTriggerPrg = pPrg;\n  pPrg->pProgram = pProgram = sqlite3DbMallocZero(db, sizeof(SubProgram));\n  if( !pProgram ) return 0;\n  sqlite3VdbeLinkSubProgram(pTop->pVdbe, pProgram);\n  pPrg->pTrigger = pTrigger;\n  pPrg->orconf = orconf;\n  pPrg->aColmask[0] = 0xffffffff;\n  pPrg->aColmask[1] = 0xffffffff;\n\n  /* Allocate and populate a new Parse context to use for coding the \n  ** trigger sub-program.  */\n  pSubParse = sqlite3StackAllocZero(db, sizeof(Parse));\n  if( !pSubParse ) return 0;\n  memset(&sNC, 0, sizeof(sNC));\n  sNC.pParse = pSubParse;\n  pSubParse->db = db;\n  pSubParse->pTriggerTab = pTab;\n  pSubParse->pToplevel = pTop;\n  pSubParse->zAuthContext = pTrigger->zName;\n  pSubParse->eTriggerOp = pTrigger->op;\n  pSubParse->nQueryLoop = pParse->nQueryLoop;\n\n  v = sqlite3GetVdbe(pSubParse);\n  if( v ){\n    VdbeComment((v, \"Start: %s.%s (%s %s%s%s ON %s)\", \n      pTrigger->zName, onErrorText(orconf),\n      (pTrigger->tr_tm==TRIGGER_BEFORE ? \"BEFORE\" : \"AFTER\"),\n        (pTrigger->op==TK_UPDATE ? \"UPDATE\" : \"\"),\n        (pTrigger->op==TK_INSERT ? \"INSERT\" : \"\"),\n        (pTrigger->op==TK_DELETE ? \"DELETE\" : \"\"),\n      pTab->zName\n    ));\n#ifndef SQLITE_OMIT_TRACE\n    if( pTrigger->zName ){\n      sqlite3VdbeChangeP4(v, -1, \n        sqlite3MPrintf(db, \"-- TRIGGER %s\", pTrigger->zName), P4_DYNAMIC\n      );\n    }\n#endif\n\n    /* If one was specified, code the WHEN clause. If it evaluates to false\n    ** (or NULL) the sub-vdbe is immediately halted by jumping to the \n    ** OP_Halt inserted at the end of the program.  */\n    if( pTrigger->pWhen ){\n      pWhen = sqlite3ExprDup(db, pTrigger->pWhen, 0);\n      if( SQLITE_OK==sqlite3ResolveExprNames(&sNC, pWhen) \n       && db->mallocFailed==0 \n      ){\n        iEndTrigger = sqlite3VdbeMakeLabel(v);\n        sqlite3ExprIfFalse(pSubParse, pWhen, iEndTrigger, SQLITE_JUMPIFNULL);\n      }\n      sqlite3ExprDelete(db, pWhen);\n    }\n\n    /* Code the trigger program into the sub-vdbe. */\n    codeTriggerProgram(pSubParse, pTrigger->step_list, orconf);\n\n    /* Insert an OP_Halt at the end of the sub-program. */\n    if( iEndTrigger ){\n      sqlite3VdbeResolveLabel(v, iEndTrigger);\n    }\n    sqlite3VdbeAddOp0(v, OP_Halt);\n    VdbeComment((v, \"End: %s.%s\", pTrigger->zName, onErrorText(orconf)));\n\n    transferParseError(pParse, pSubParse);\n    if( db->mallocFailed==0 && pParse->nErr==0 ){\n      pProgram->aOp = sqlite3VdbeTakeOpArray(v, &pProgram->nOp, &pTop->nMaxArg);\n    }\n    pProgram->nMem = pSubParse->nMem;\n    pProgram->nCsr = pSubParse->nTab;\n    pProgram->token = (void *)pTrigger;\n    pPrg->aColmask[0] = pSubParse->oldmask;\n    pPrg->aColmask[1] = pSubParse->newmask;\n    sqlite3VdbeDelete(v);\n  }\n\n  assert( !pSubParse->pAinc       && !pSubParse->pZombieTab );\n  assert( !pSubParse->pTriggerPrg && !pSubParse->nMaxArg );\n  sqlite3ParserReset(pSubParse);\n  sqlite3StackFree(db, pSubParse);\n\n  return pPrg;\n}\n    \n/*\n** Return a pointer to a TriggerPrg object containing the sub-program for\n** trigger pTrigger with default ON CONFLICT algorithm orconf. If no such\n** TriggerPrg object exists, a new object is allocated and populated before\n** being returned.\n*/\nstatic TriggerPrg *getRowTrigger(\n  Parse *pParse,       /* Current parse context */\n  Trigger *pTrigger,   /* Trigger to code */\n  Table *pTab,         /* The table trigger pTrigger is attached to */\n  int orconf           /* ON CONFLICT algorithm. */\n){\n  Parse *pRoot = sqlite3ParseToplevel(pParse);\n  TriggerPrg *pPrg;\n\n  assert( pTrigger->zName==0 || pTab==tableOfTrigger(pTrigger) );\n\n  /* It may be that this trigger has already been coded (or is in the\n  ** process of being coded). If this is the case, then an entry with\n  ** a matching TriggerPrg.pTrigger field will be present somewhere\n  ** in the Parse.pTriggerPrg list. Search for such an entry.  */\n  for(pPrg=pRoot->pTriggerPrg; \n      pPrg && (pPrg->pTrigger!=pTrigger || pPrg->orconf!=orconf); \n      pPrg=pPrg->pNext\n  );\n\n  /* If an existing TriggerPrg could not be located, create a new one. */\n  if( !pPrg ){\n    pPrg = codeRowTrigger(pParse, pTrigger, pTab, orconf);\n  }\n\n  return pPrg;\n}\n\n/*\n** Generate code for the trigger program associated with trigger p on \n** table pTab. The reg, orconf and ignoreJump parameters passed to this\n** function are the same as those described in the header function for\n** sqlite3CodeRowTrigger()\n*/\nSQLITE_PRIVATE void sqlite3CodeRowTriggerDirect(\n  Parse *pParse,       /* Parse context */\n  Trigger *p,          /* Trigger to code */\n  Table *pTab,         /* The table to code triggers from */\n  int reg,             /* Reg array containing OLD.* and NEW.* values */\n  int orconf,          /* ON CONFLICT policy */\n  int ignoreJump       /* Instruction to jump to for RAISE(IGNORE) */\n){\n  Vdbe *v = sqlite3GetVdbe(pParse); /* Main VM */\n  TriggerPrg *pPrg;\n  pPrg = getRowTrigger(pParse, p, pTab, orconf);\n  assert( pPrg || pParse->nErr || pParse->db->mallocFailed );\n\n  /* Code the OP_Program opcode in the parent VDBE. P4 of the OP_Program \n  ** is a pointer to the sub-vdbe containing the trigger program.  */\n  if( pPrg ){\n    int bRecursive = (p->zName && 0==(pParse->db->flags&SQLITE_RecTriggers));\n\n    sqlite3VdbeAddOp4(v, OP_Program, reg, ignoreJump, ++pParse->nMem,\n                      (const char *)pPrg->pProgram, P4_SUBPROGRAM);\n    VdbeComment(\n        (v, \"Call: %s.%s\", (p->zName?p->zName:\"fkey\"), onErrorText(orconf)));\n\n    /* Set the P5 operand of the OP_Program instruction to non-zero if\n    ** recursive invocation of this trigger program is disallowed. Recursive\n    ** invocation is disallowed if (a) the sub-program is really a trigger,\n    ** not a foreign key action, and (b) the flag to enable recursive triggers\n    ** is clear.  */\n    sqlite3VdbeChangeP5(v, (u8)bRecursive);\n  }\n}\n\n/*\n** This is called to code the required FOR EACH ROW triggers for an operation\n** on table pTab. The operation to code triggers for (INSERT, UPDATE or DELETE)\n** is given by the op parameter. The tr_tm parameter determines whether the\n** BEFORE or AFTER triggers are coded. If the operation is an UPDATE, then\n** parameter pChanges is passed the list of columns being modified.\n**\n** If there are no triggers that fire at the specified time for the specified\n** operation on pTab, this function is a no-op.\n**\n** The reg argument is the address of the first in an array of registers \n** that contain the values substituted for the new.* and old.* references\n** in the trigger program. If N is the number of columns in table pTab\n** (a copy of pTab->nCol), then registers are populated as follows:\n**\n**   Register       Contains\n**   ------------------------------------------------------\n**   reg+0          OLD.rowid\n**   reg+1          OLD.* value of left-most column of pTab\n**   ...            ...\n**   reg+N          OLD.* value of right-most column of pTab\n**   reg+N+1        NEW.rowid\n**   reg+N+2        OLD.* value of left-most column of pTab\n**   ...            ...\n**   reg+N+N+1      NEW.* value of right-most column of pTab\n**\n** For ON DELETE triggers, the registers containing the NEW.* values will\n** never be accessed by the trigger program, so they are not allocated or \n** populated by the caller (there is no data to populate them with anyway). \n** Similarly, for ON INSERT triggers the values stored in the OLD.* registers\n** are never accessed, and so are not allocated by the caller. So, for an\n** ON INSERT trigger, the value passed to this function as parameter reg\n** is not a readable register, although registers (reg+N) through \n** (reg+N+N+1) are.\n**\n** Parameter orconf is the default conflict resolution algorithm for the\n** trigger program to use (REPLACE, IGNORE etc.). Parameter ignoreJump\n** is the instruction that control should jump to if a trigger program\n** raises an IGNORE exception.\n*/\nSQLITE_PRIVATE void sqlite3CodeRowTrigger(\n  Parse *pParse,       /* Parse context */\n  Trigger *pTrigger,   /* List of triggers on table pTab */\n  int op,              /* One of TK_UPDATE, TK_INSERT, TK_DELETE */\n  ExprList *pChanges,  /* Changes list for any UPDATE OF triggers */\n  int tr_tm,           /* One of TRIGGER_BEFORE, TRIGGER_AFTER */\n  Table *pTab,         /* The table to code triggers from */\n  int reg,             /* The first in an array of registers (see above) */\n  int orconf,          /* ON CONFLICT policy */\n  int ignoreJump       /* Instruction to jump to for RAISE(IGNORE) */\n){\n  Trigger *p;          /* Used to iterate through pTrigger list */\n\n  assert( op==TK_UPDATE || op==TK_INSERT || op==TK_DELETE );\n  assert( tr_tm==TRIGGER_BEFORE || tr_tm==TRIGGER_AFTER );\n  assert( (op==TK_UPDATE)==(pChanges!=0) );\n\n  for(p=pTrigger; p; p=p->pNext){\n\n    /* Sanity checking:  The schema for the trigger and for the table are\n    ** always defined.  The trigger must be in the same schema as the table\n    ** or else it must be a TEMP trigger. */\n    assert( p->pSchema!=0 );\n    assert( p->pTabSchema!=0 );\n    assert( p->pSchema==p->pTabSchema \n         || p->pSchema==pParse->db->aDb[1].pSchema );\n\n    /* Determine whether we should code this trigger */\n    if( p->op==op \n     && p->tr_tm==tr_tm \n     && checkColumnOverlap(p->pColumns, pChanges)\n    ){\n      sqlite3CodeRowTriggerDirect(pParse, p, pTab, reg, orconf, ignoreJump);\n    }\n  }\n}\n\n/*\n** Triggers may access values stored in the old.* or new.* pseudo-table. \n** This function returns a 32-bit bitmask indicating which columns of the \n** old.* or new.* tables actually are used by triggers. This information \n** may be used by the caller, for example, to avoid having to load the entire\n** old.* record into memory when executing an UPDATE or DELETE command.\n**\n** Bit 0 of the returned mask is set if the left-most column of the\n** table may be accessed using an [old|new].<col> reference. Bit 1 is set if\n** the second leftmost column value is required, and so on. If there\n** are more than 32 columns in the table, and at least one of the columns\n** with an index greater than 32 may be accessed, 0xffffffff is returned.\n**\n** It is not possible to determine if the old.rowid or new.rowid column is \n** accessed by triggers. The caller must always assume that it is.\n**\n** Parameter isNew must be either 1 or 0. If it is 0, then the mask returned\n** applies to the old.* table. If 1, the new.* table.\n**\n** Parameter tr_tm must be a mask with one or both of the TRIGGER_BEFORE\n** and TRIGGER_AFTER bits set. Values accessed by BEFORE triggers are only\n** included in the returned mask if the TRIGGER_BEFORE bit is set in the\n** tr_tm parameter. Similarly, values accessed by AFTER triggers are only\n** included in the returned mask if the TRIGGER_AFTER bit is set in tr_tm.\n*/\nSQLITE_PRIVATE u32 sqlite3TriggerColmask(\n  Parse *pParse,       /* Parse context */\n  Trigger *pTrigger,   /* List of triggers on table pTab */\n  ExprList *pChanges,  /* Changes list for any UPDATE OF triggers */\n  int isNew,           /* 1 for new.* ref mask, 0 for old.* ref mask */\n  int tr_tm,           /* Mask of TRIGGER_BEFORE|TRIGGER_AFTER */\n  Table *pTab,         /* The table to code triggers from */\n  int orconf           /* Default ON CONFLICT policy for trigger steps */\n){\n  const int op = pChanges ? TK_UPDATE : TK_DELETE;\n  u32 mask = 0;\n  Trigger *p;\n\n  assert( isNew==1 || isNew==0 );\n  for(p=pTrigger; p; p=p->pNext){\n    if( p->op==op && (tr_tm&p->tr_tm)\n     && checkColumnOverlap(p->pColumns,pChanges)\n    ){\n      TriggerPrg *pPrg;\n      pPrg = getRowTrigger(pParse, p, pTab, orconf);\n      if( pPrg ){\n        mask |= pPrg->aColmask[isNew];\n      }\n    }\n  }\n\n  return mask;\n}\n\n#endif /* !defined(SQLITE_OMIT_TRIGGER) */\n\n/************** End of trigger.c *********************************************/\n/************** Begin file update.c ******************************************/\n/*\n** 2001 September 15\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n*************************************************************************\n** This file contains C code routines that are called by the parser\n** to handle UPDATE statements.\n*/\n/* #include \"sqliteInt.h\" */\n\n#ifndef SQLITE_OMIT_VIRTUALTABLE\n/* Forward declaration */\nstatic void updateVirtualTable(\n  Parse *pParse,       /* The parsing context */\n  SrcList *pSrc,       /* The virtual table to be modified */\n  Table *pTab,         /* The virtual table */\n  ExprList *pChanges,  /* The columns to change in the UPDATE statement */\n  Expr *pRowidExpr,    /* Expression used to recompute the rowid */\n  int *aXRef,          /* Mapping from columns of pTab to entries in pChanges */\n  Expr *pWhere,        /* WHERE clause of the UPDATE statement */\n  int onError          /* ON CONFLICT strategy */\n);\n#endif /* SQLITE_OMIT_VIRTUALTABLE */\n\n/*\n** The most recently coded instruction was an OP_Column to retrieve the\n** i-th column of table pTab. This routine sets the P4 parameter of the \n** OP_Column to the default value, if any.\n**\n** The default value of a column is specified by a DEFAULT clause in the \n** column definition. This was either supplied by the user when the table\n** was created, or added later to the table definition by an ALTER TABLE\n** command. If the latter, then the row-records in the table btree on disk\n** may not contain a value for the column and the default value, taken\n** from the P4 parameter of the OP_Column instruction, is returned instead.\n** If the former, then all row-records are guaranteed to include a value\n** for the column and the P4 value is not required.\n**\n** Column definitions created by an ALTER TABLE command may only have \n** literal default values specified: a number, null or a string. (If a more\n** complicated default expression value was provided, it is evaluated \n** when the ALTER TABLE is executed and one of the literal values written\n** into the sqlite_master table.)\n**\n** Therefore, the P4 parameter is only required if the default value for\n** the column is a literal number, string or null. The sqlite3ValueFromExpr()\n** function is capable of transforming these types of expressions into\n** sqlite3_value objects.\n**\n** If parameter iReg is not negative, code an OP_RealAffinity instruction\n** on register iReg. This is used when an equivalent integer value is \n** stored in place of an 8-byte floating point value in order to save \n** space.\n*/\nSQLITE_PRIVATE void sqlite3ColumnDefault(Vdbe *v, Table *pTab, int i, int iReg){\n  assert( pTab!=0 );\n  if( !pTab->pSelect ){\n    sqlite3_value *pValue = 0;\n    u8 enc = ENC(sqlite3VdbeDb(v));\n    Column *pCol = &pTab->aCol[i];\n    VdbeComment((v, \"%s.%s\", pTab->zName, pCol->zName));\n    assert( i<pTab->nCol );\n    sqlite3ValueFromExpr(sqlite3VdbeDb(v), pCol->pDflt, enc, \n                         pCol->affinity, &pValue);\n    if( pValue ){\n      sqlite3VdbeAppendP4(v, pValue, P4_MEM);\n    }\n  }\n#ifndef SQLITE_OMIT_FLOATING_POINT\n  if( pTab->aCol[i].affinity==SQLITE_AFF_REAL ){\n    sqlite3VdbeAddOp1(v, OP_RealAffinity, iReg);\n  }\n#endif\n}\n\n/*\n** Process an UPDATE statement.\n**\n**   UPDATE OR IGNORE table_wxyz SET a=b, c=d WHERE e<5 AND f NOT NULL;\n**          \\_______/ \\________/     \\______/       \\________________/\n*            onError   pTabList      pChanges             pWhere\n*/\nSQLITE_PRIVATE void sqlite3Update(\n  Parse *pParse,         /* The parser context */\n  SrcList *pTabList,     /* The table in which we should change things */\n  ExprList *pChanges,    /* Things to be changed */\n  Expr *pWhere,          /* The WHERE clause.  May be null */\n  int onError,           /* How to handle constraint errors */\n  ExprList *pOrderBy,    /* ORDER BY clause. May be null */\n  Expr *pLimit           /* LIMIT clause. May be null */\n){\n  int i, j;              /* Loop counters */\n  Table *pTab;           /* The table to be updated */\n  int addrTop = 0;       /* VDBE instruction address of the start of the loop */\n  WhereInfo *pWInfo;     /* Information about the WHERE clause */\n  Vdbe *v;               /* The virtual database engine */\n  Index *pIdx;           /* For looping over indices */\n  Index *pPk;            /* The PRIMARY KEY index for WITHOUT ROWID tables */\n  int nIdx;              /* Number of indices that need updating */\n  int iBaseCur;          /* Base cursor number */\n  int iDataCur;          /* Cursor for the canonical data btree */\n  int iIdxCur;           /* Cursor for the first index */\n  sqlite3 *db;           /* The database structure */\n  int *aRegIdx = 0;      /* First register in array assigned to each index */\n  int *aXRef = 0;        /* aXRef[i] is the index in pChanges->a[] of the\n                         ** an expression for the i-th column of the table.\n                         ** aXRef[i]==-1 if the i-th column is not changed. */\n  u8 *aToOpen;           /* 1 for tables and indices to be opened */\n  u8 chngPk;             /* PRIMARY KEY changed in a WITHOUT ROWID table */\n  u8 chngRowid;          /* Rowid changed in a normal table */\n  u8 chngKey;            /* Either chngPk or chngRowid */\n  Expr *pRowidExpr = 0;  /* Expression defining the new record number */\n  AuthContext sContext;  /* The authorization context */\n  NameContext sNC;       /* The name-context to resolve expressions in */\n  int iDb;               /* Database containing the table being updated */\n  int eOnePass;          /* ONEPASS_XXX value from where.c */\n  int hasFK;             /* True if foreign key processing is required */\n  int labelBreak;        /* Jump here to break out of UPDATE loop */\n  int labelContinue;     /* Jump here to continue next step of UPDATE loop */\n  int flags;             /* Flags for sqlite3WhereBegin() */\n\n#ifndef SQLITE_OMIT_TRIGGER\n  int isView;            /* True when updating a view (INSTEAD OF trigger) */\n  Trigger *pTrigger;     /* List of triggers on pTab, if required */\n  int tmask;             /* Mask of TRIGGER_BEFORE|TRIGGER_AFTER */\n#endif\n  int newmask;           /* Mask of NEW.* columns accessed by BEFORE triggers */\n  int iEph = 0;          /* Ephemeral table holding all primary key values */\n  int nKey = 0;          /* Number of elements in regKey for WITHOUT ROWID */\n  int aiCurOnePass[2];   /* The write cursors opened by WHERE_ONEPASS */\n  int addrOpen = 0;      /* Address of OP_OpenEphemeral */\n  int iPk = 0;           /* First of nPk cells holding PRIMARY KEY value */\n  i16 nPk = 0;           /* Number of components of the PRIMARY KEY */\n  int bReplace = 0;      /* True if REPLACE conflict resolution might happen */\n\n  /* Register Allocations */\n  int regRowCount = 0;   /* A count of rows changed */\n  int regOldRowid = 0;   /* The old rowid */\n  int regNewRowid = 0;   /* The new rowid */\n  int regNew = 0;        /* Content of the NEW.* table in triggers */\n  int regOld = 0;        /* Content of OLD.* table in triggers */\n  int regRowSet = 0;     /* Rowset of rows to be updated */\n  int regKey = 0;        /* composite PRIMARY KEY value */\n\n  memset(&sContext, 0, sizeof(sContext));\n  db = pParse->db;\n  if( pParse->nErr || db->mallocFailed ){\n    goto update_cleanup;\n  }\n  assert( pTabList->nSrc==1 );\n\n  /* Locate the table which we want to update. \n  */\n  pTab = sqlite3SrcListLookup(pParse, pTabList);\n  if( pTab==0 ) goto update_cleanup;\n  iDb = sqlite3SchemaToIndex(pParse->db, pTab->pSchema);\n\n  /* Figure out if we have any triggers and if the table being\n  ** updated is a view.\n  */\n#ifndef SQLITE_OMIT_TRIGGER\n  pTrigger = sqlite3TriggersExist(pParse, pTab, TK_UPDATE, pChanges, &tmask);\n  isView = pTab->pSelect!=0;\n  assert( pTrigger || tmask==0 );\n#else\n# define pTrigger 0\n# define isView 0\n# define tmask 0\n#endif\n#ifdef SQLITE_OMIT_VIEW\n# undef isView\n# define isView 0\n#endif\n\n#ifdef SQLITE_ENABLE_UPDATE_DELETE_LIMIT\n  if( !isView ){\n    pWhere = sqlite3LimitWhere(\n        pParse, pTabList, pWhere, pOrderBy, pLimit, \"UPDATE\"\n    );\n    pOrderBy = 0;\n    pLimit = 0;\n  }\n#endif\n\n  if( sqlite3ViewGetColumnNames(pParse, pTab) ){\n    goto update_cleanup;\n  }\n  if( sqlite3IsReadOnly(pParse, pTab, tmask) ){\n    goto update_cleanup;\n  }\n\n  /* Allocate a cursors for the main database table and for all indices.\n  ** The index cursors might not be used, but if they are used they\n  ** need to occur right after the database cursor.  So go ahead and\n  ** allocate enough space, just in case.\n  */\n  pTabList->a[0].iCursor = iBaseCur = iDataCur = pParse->nTab++;\n  iIdxCur = iDataCur+1;\n  pPk = HasRowid(pTab) ? 0 : sqlite3PrimaryKeyIndex(pTab);\n  for(nIdx=0, pIdx=pTab->pIndex; pIdx; pIdx=pIdx->pNext, nIdx++){\n    if( IsPrimaryKeyIndex(pIdx) && pPk!=0 ){\n      iDataCur = pParse->nTab;\n      pTabList->a[0].iCursor = iDataCur;\n    }\n    pParse->nTab++;\n  }\n\n  /* Allocate space for aXRef[], aRegIdx[], and aToOpen[].  \n  ** Initialize aXRef[] and aToOpen[] to their default values.\n  */\n  aXRef = sqlite3DbMallocRawNN(db, sizeof(int) * (pTab->nCol+nIdx) + nIdx+2 );\n  if( aXRef==0 ) goto update_cleanup;\n  aRegIdx = aXRef+pTab->nCol;\n  aToOpen = (u8*)(aRegIdx+nIdx);\n  memset(aToOpen, 1, nIdx+1);\n  aToOpen[nIdx+1] = 0;\n  for(i=0; i<pTab->nCol; i++) aXRef[i] = -1;\n\n  /* Initialize the name-context */\n  memset(&sNC, 0, sizeof(sNC));\n  sNC.pParse = pParse;\n  sNC.pSrcList = pTabList;\n\n  /* Resolve the column names in all the expressions of the\n  ** of the UPDATE statement.  Also find the column index\n  ** for each column to be updated in the pChanges array.  For each\n  ** column to be updated, make sure we have authorization to change\n  ** that column.\n  */\n  chngRowid = chngPk = 0;\n  for(i=0; i<pChanges->nExpr; i++){\n    if( sqlite3ResolveExprNames(&sNC, pChanges->a[i].pExpr) ){\n      goto update_cleanup;\n    }\n    for(j=0; j<pTab->nCol; j++){\n      if( sqlite3StrICmp(pTab->aCol[j].zName, pChanges->a[i].zName)==0 ){\n        if( j==pTab->iPKey ){\n          chngRowid = 1;\n          pRowidExpr = pChanges->a[i].pExpr;\n        }else if( pPk && (pTab->aCol[j].colFlags & COLFLAG_PRIMKEY)!=0 ){\n          chngPk = 1;\n        }\n        aXRef[j] = i;\n        break;\n      }\n    }\n    if( j>=pTab->nCol ){\n      if( pPk==0 && sqlite3IsRowid(pChanges->a[i].zName) ){\n        j = -1;\n        chngRowid = 1;\n        pRowidExpr = pChanges->a[i].pExpr;\n      }else{\n        sqlite3ErrorMsg(pParse, \"no such column: %s\", pChanges->a[i].zName);\n        pParse->checkSchema = 1;\n        goto update_cleanup;\n      }\n    }\n#ifndef SQLITE_OMIT_AUTHORIZATION\n    {\n      int rc;\n      rc = sqlite3AuthCheck(pParse, SQLITE_UPDATE, pTab->zName,\n                            j<0 ? \"ROWID\" : pTab->aCol[j].zName,\n                            db->aDb[iDb].zDbSName);\n      if( rc==SQLITE_DENY ){\n        goto update_cleanup;\n      }else if( rc==SQLITE_IGNORE ){\n        aXRef[j] = -1;\n      }\n    }\n#endif\n  }\n  assert( (chngRowid & chngPk)==0 );\n  assert( chngRowid==0 || chngRowid==1 );\n  assert( chngPk==0 || chngPk==1 );\n  chngKey = chngRowid + chngPk;\n\n  /* The SET expressions are not actually used inside the WHERE loop.  \n  ** So reset the colUsed mask. Unless this is a virtual table. In that\n  ** case, set all bits of the colUsed mask (to ensure that the virtual\n  ** table implementation makes all columns available).\n  */\n  pTabList->a[0].colUsed = IsVirtual(pTab) ? ALLBITS : 0;\n\n  hasFK = sqlite3FkRequired(pParse, pTab, aXRef, chngKey);\n\n  /* There is one entry in the aRegIdx[] array for each index on the table\n  ** being updated.  Fill in aRegIdx[] with a register number that will hold\n  ** the key for accessing each index.\n  **\n  ** FIXME:  Be smarter about omitting indexes that use expressions.\n  */\n  for(j=0, pIdx=pTab->pIndex; pIdx; pIdx=pIdx->pNext, j++){\n    int reg;\n    if( chngKey || hasFK>1 || pIdx->pPartIdxWhere || pIdx==pPk ){\n      reg = ++pParse->nMem;\n      pParse->nMem += pIdx->nColumn;\n    }else{\n      reg = 0;\n      for(i=0; i<pIdx->nKeyCol; i++){\n        i16 iIdxCol = pIdx->aiColumn[i];\n        if( iIdxCol<0 || aXRef[iIdxCol]>=0 ){\n          reg = ++pParse->nMem;\n          pParse->nMem += pIdx->nColumn;\n          if( (onError==OE_Replace)\n           || (onError==OE_Default && pIdx->onError==OE_Replace) \n          ){\n            bReplace = 1;\n          }\n          break;\n        }\n      }\n    }\n    if( reg==0 ) aToOpen[j+1] = 0;\n    aRegIdx[j] = reg;\n  }\n  if( bReplace ){\n    /* If REPLACE conflict resolution might be invoked, open cursors on all \n    ** indexes in case they are needed to delete records.  */\n    memset(aToOpen, 1, nIdx+1);\n  }\n\n  /* Begin generating code. */\n  v = sqlite3GetVdbe(pParse);\n  if( v==0 ) goto update_cleanup;\n  if( pParse->nested==0 ) sqlite3VdbeCountChanges(v);\n  sqlite3BeginWriteOperation(pParse, 1, iDb);\n\n  /* Allocate required registers. */\n  if( !IsVirtual(pTab) ){\n    regRowSet = ++pParse->nMem;\n    regOldRowid = regNewRowid = ++pParse->nMem;\n    if( chngPk || pTrigger || hasFK ){\n      regOld = pParse->nMem + 1;\n      pParse->nMem += pTab->nCol;\n    }\n    if( chngKey || pTrigger || hasFK ){\n      regNewRowid = ++pParse->nMem;\n    }\n    regNew = pParse->nMem + 1;\n    pParse->nMem += pTab->nCol;\n  }\n\n  /* Start the view context. */\n  if( isView ){\n    sqlite3AuthContextPush(pParse, &sContext, pTab->zName);\n  }\n\n  /* If we are trying to update a view, realize that view into\n  ** an ephemeral table.\n  */\n#if !defined(SQLITE_OMIT_VIEW) && !defined(SQLITE_OMIT_TRIGGER)\n  if( isView ){\n    sqlite3MaterializeView(pParse, pTab, \n        pWhere, pOrderBy, pLimit, iDataCur\n    );\n    pOrderBy = 0;\n    pLimit = 0;\n  }\n#endif\n\n  /* Resolve the column names in all the expressions in the\n  ** WHERE clause.\n  */\n  if( sqlite3ResolveExprNames(&sNC, pWhere) ){\n    goto update_cleanup;\n  }\n\n#ifndef SQLITE_OMIT_VIRTUALTABLE\n  /* Virtual tables must be handled separately */\n  if( IsVirtual(pTab) ){\n    updateVirtualTable(pParse, pTabList, pTab, pChanges, pRowidExpr, aXRef,\n                       pWhere, onError);\n    goto update_cleanup;\n  }\n#endif\n\n  /* Initialize the count of updated rows */\n  if( (db->flags & SQLITE_CountRows) && !pParse->pTriggerTab ){\n    regRowCount = ++pParse->nMem;\n    sqlite3VdbeAddOp2(v, OP_Integer, 0, regRowCount);\n  }\n\n  if( HasRowid(pTab) ){\n    sqlite3VdbeAddOp3(v, OP_Null, 0, regRowSet, regOldRowid);\n  }else{\n    assert( pPk!=0 );\n    nPk = pPk->nKeyCol;\n    iPk = pParse->nMem+1;\n    pParse->nMem += nPk;\n    regKey = ++pParse->nMem;\n    iEph = pParse->nTab++;\n\n    sqlite3VdbeAddOp2(v, OP_Null, 0, iPk);\n    addrOpen = sqlite3VdbeAddOp2(v, OP_OpenEphemeral, iEph, nPk);\n    sqlite3VdbeSetP4KeyInfo(pParse, pPk);\n  }\n\n  /* Begin the database scan. \n  **\n  ** Do not consider a single-pass strategy for a multi-row update if\n  ** there are any triggers or foreign keys to process, or rows may\n  ** be deleted as a result of REPLACE conflict handling. Any of these\n  ** things might disturb a cursor being used to scan through the table\n  ** or index, causing a single-pass approach to malfunction.  */\n  flags = WHERE_ONEPASS_DESIRED|WHERE_SEEK_UNIQ_TABLE;\n  if( !pParse->nested && !pTrigger && !hasFK && !chngKey && !bReplace ){\n    flags |= WHERE_ONEPASS_MULTIROW;\n  }\n  pWInfo = sqlite3WhereBegin(pParse, pTabList, pWhere, 0, 0, flags, iIdxCur);\n  if( pWInfo==0 ) goto update_cleanup;\n\n  /* A one-pass strategy that might update more than one row may not\n  ** be used if any column of the index used for the scan is being\n  ** updated. Otherwise, if there is an index on \"b\", statements like\n  ** the following could create an infinite loop:\n  **\n  **   UPDATE t1 SET b=b+1 WHERE b>?\n  **\n  ** Fall back to ONEPASS_OFF if where.c has selected a ONEPASS_MULTI\n  ** strategy that uses an index for which one or more columns are being\n  ** updated.  */\n  eOnePass = sqlite3WhereOkOnePass(pWInfo, aiCurOnePass);\n  if( eOnePass==ONEPASS_MULTI ){\n    int iCur = aiCurOnePass[1];\n    if( iCur>=0 && iCur!=iDataCur && aToOpen[iCur-iBaseCur] ){\n      eOnePass = ONEPASS_OFF;\n    }\n    assert( iCur!=iDataCur || !HasRowid(pTab) );\n  }\n  \n  if( HasRowid(pTab) ){\n    /* Read the rowid of the current row of the WHERE scan. In ONEPASS_OFF\n    ** mode, write the rowid into the FIFO. In either of the one-pass modes,\n    ** leave it in register regOldRowid.  */\n    sqlite3VdbeAddOp2(v, OP_Rowid, iDataCur, regOldRowid);\n    if( eOnePass==ONEPASS_OFF ){\n      sqlite3VdbeAddOp2(v, OP_RowSetAdd, regRowSet, regOldRowid);\n    }\n  }else{\n    /* Read the PK of the current row into an array of registers. In\n    ** ONEPASS_OFF mode, serialize the array into a record and store it in\n    ** the ephemeral table. Or, in ONEPASS_SINGLE or MULTI mode, change\n    ** the OP_OpenEphemeral instruction to a Noop (the ephemeral table \n    ** is not required) and leave the PK fields in the array of registers.  */\n    for(i=0; i<nPk; i++){\n      assert( pPk->aiColumn[i]>=0 );\n      sqlite3ExprCodeGetColumnOfTable(v, pTab, iDataCur,pPk->aiColumn[i],iPk+i);\n    }\n    if( eOnePass ){\n      sqlite3VdbeChangeToNoop(v, addrOpen);\n      nKey = nPk;\n      regKey = iPk;\n    }else{\n      sqlite3VdbeAddOp4(v, OP_MakeRecord, iPk, nPk, regKey,\n                        sqlite3IndexAffinityStr(db, pPk), nPk);\n      sqlite3VdbeAddOp4Int(v, OP_IdxInsert, iEph, regKey, iPk, nPk);\n    }\n  }\n\n  if( eOnePass!=ONEPASS_MULTI ){\n    sqlite3WhereEnd(pWInfo);\n  }\n\n  labelBreak = sqlite3VdbeMakeLabel(v);\n  if( !isView ){\n    int addrOnce = 0;\n\n    /* Open every index that needs updating. */\n    if( eOnePass!=ONEPASS_OFF ){\n      if( aiCurOnePass[0]>=0 ) aToOpen[aiCurOnePass[0]-iBaseCur] = 0;\n      if( aiCurOnePass[1]>=0 ) aToOpen[aiCurOnePass[1]-iBaseCur] = 0;\n    }\n\n    if( eOnePass==ONEPASS_MULTI && (nIdx-(aiCurOnePass[1]>=0))>0 ){\n      addrOnce = sqlite3VdbeAddOp0(v, OP_Once); VdbeCoverage(v);\n    }\n    sqlite3OpenTableAndIndices(pParse, pTab, OP_OpenWrite, 0, iBaseCur, aToOpen,\n                               0, 0);\n    if( addrOnce ) sqlite3VdbeJumpHere(v, addrOnce);\n  }\n\n  /* Top of the update loop */\n  if( eOnePass!=ONEPASS_OFF ){\n    if( !isView && aiCurOnePass[0]!=iDataCur && aiCurOnePass[1]!=iDataCur ){\n      assert( pPk );\n      sqlite3VdbeAddOp4Int(v, OP_NotFound, iDataCur, labelBreak, regKey, nKey);\n      VdbeCoverageNeverTaken(v);\n    }\n    if( eOnePass==ONEPASS_SINGLE ){\n      labelContinue = labelBreak;\n    }else{\n      labelContinue = sqlite3VdbeMakeLabel(v);\n    }\n    sqlite3VdbeAddOp2(v, OP_IsNull, pPk ? regKey : regOldRowid, labelBreak);\n    VdbeCoverageIf(v, pPk==0);\n    VdbeCoverageIf(v, pPk!=0);\n  }else if( pPk ){\n    labelContinue = sqlite3VdbeMakeLabel(v);\n    sqlite3VdbeAddOp2(v, OP_Rewind, iEph, labelBreak); VdbeCoverage(v);\n    addrTop = sqlite3VdbeAddOp2(v, OP_RowData, iEph, regKey);\n    sqlite3VdbeAddOp4Int(v, OP_NotFound, iDataCur, labelContinue, regKey, 0);\n    VdbeCoverage(v);\n  }else{\n    labelContinue = sqlite3VdbeAddOp3(v, OP_RowSetRead, regRowSet, labelBreak,\n                             regOldRowid);\n    VdbeCoverage(v);\n    sqlite3VdbeAddOp3(v, OP_NotExists, iDataCur, labelContinue, regOldRowid);\n    VdbeCoverage(v);\n  }\n\n  /* If the record number will change, set register regNewRowid to\n  ** contain the new value. If the record number is not being modified,\n  ** then regNewRowid is the same register as regOldRowid, which is\n  ** already populated.  */\n  assert( chngKey || pTrigger || hasFK || regOldRowid==regNewRowid );\n  if( chngRowid ){\n    sqlite3ExprCode(pParse, pRowidExpr, regNewRowid);\n    sqlite3VdbeAddOp1(v, OP_MustBeInt, regNewRowid); VdbeCoverage(v);\n  }\n\n  /* Compute the old pre-UPDATE content of the row being changed, if that\n  ** information is needed */\n  if( chngPk || hasFK || pTrigger ){\n    u32 oldmask = (hasFK ? sqlite3FkOldmask(pParse, pTab) : 0);\n    oldmask |= sqlite3TriggerColmask(pParse, \n        pTrigger, pChanges, 0, TRIGGER_BEFORE|TRIGGER_AFTER, pTab, onError\n    );\n    for(i=0; i<pTab->nCol; i++){\n      if( oldmask==0xffffffff\n       || (i<32 && (oldmask & MASKBIT32(i))!=0)\n       || (pTab->aCol[i].colFlags & COLFLAG_PRIMKEY)!=0\n      ){\n        testcase(  oldmask!=0xffffffff && i==31 );\n        sqlite3ExprCodeGetColumnOfTable(v, pTab, iDataCur, i, regOld+i);\n      }else{\n        sqlite3VdbeAddOp2(v, OP_Null, 0, regOld+i);\n      }\n    }\n    if( chngRowid==0 && pPk==0 ){\n      sqlite3VdbeAddOp2(v, OP_Copy, regOldRowid, regNewRowid);\n    }\n  }\n\n  /* Populate the array of registers beginning at regNew with the new\n  ** row data. This array is used to check constants, create the new\n  ** table and index records, and as the values for any new.* references\n  ** made by triggers.\n  **\n  ** If there are one or more BEFORE triggers, then do not populate the\n  ** registers associated with columns that are (a) not modified by\n  ** this UPDATE statement and (b) not accessed by new.* references. The\n  ** values for registers not modified by the UPDATE must be reloaded from \n  ** the database after the BEFORE triggers are fired anyway (as the trigger \n  ** may have modified them). So not loading those that are not going to\n  ** be used eliminates some redundant opcodes.\n  */\n  newmask = sqlite3TriggerColmask(\n      pParse, pTrigger, pChanges, 1, TRIGGER_BEFORE, pTab, onError\n  );\n  for(i=0; i<pTab->nCol; i++){\n    if( i==pTab->iPKey ){\n      sqlite3VdbeAddOp2(v, OP_Null, 0, regNew+i);\n    }else{\n      j = aXRef[i];\n      if( j>=0 ){\n        sqlite3ExprCode(pParse, pChanges->a[j].pExpr, regNew+i);\n      }else if( 0==(tmask&TRIGGER_BEFORE) || i>31 || (newmask & MASKBIT32(i)) ){\n        /* This branch loads the value of a column that will not be changed \n        ** into a register. This is done if there are no BEFORE triggers, or\n        ** if there are one or more BEFORE triggers that use this value via\n        ** a new.* reference in a trigger program.\n        */\n        testcase( i==31 );\n        testcase( i==32 );\n        sqlite3ExprCodeGetColumnToReg(pParse, pTab, i, iDataCur, regNew+i);\n      }else{\n        sqlite3VdbeAddOp2(v, OP_Null, 0, regNew+i);\n      }\n    }\n  }\n\n  /* Fire any BEFORE UPDATE triggers. This happens before constraints are\n  ** verified. One could argue that this is wrong.\n  */\n  if( tmask&TRIGGER_BEFORE ){\n    sqlite3TableAffinity(v, pTab, regNew);\n    sqlite3CodeRowTrigger(pParse, pTrigger, TK_UPDATE, pChanges, \n        TRIGGER_BEFORE, pTab, regOldRowid, onError, labelContinue);\n\n    /* The row-trigger may have deleted the row being updated. In this\n    ** case, jump to the next row. No updates or AFTER triggers are \n    ** required. This behavior - what happens when the row being updated\n    ** is deleted or renamed by a BEFORE trigger - is left undefined in the\n    ** documentation.\n    */\n    if( pPk ){\n      sqlite3VdbeAddOp4Int(v, OP_NotFound, iDataCur, labelContinue,regKey,nKey);\n      VdbeCoverage(v);\n    }else{\n      sqlite3VdbeAddOp3(v, OP_NotExists, iDataCur, labelContinue, regOldRowid);\n      VdbeCoverage(v);\n    }\n\n    /* If it did not delete it, the row-trigger may still have modified \n    ** some of the columns of the row being updated. Load the values for \n    ** all columns not modified by the update statement into their \n    ** registers in case this has happened.\n    */\n    for(i=0; i<pTab->nCol; i++){\n      if( aXRef[i]<0 && i!=pTab->iPKey ){\n        sqlite3ExprCodeGetColumnOfTable(v, pTab, iDataCur, i, regNew+i);\n      }\n    }\n  }\n\n  if( !isView ){\n    int addr1 = 0;        /* Address of jump instruction */\n\n    /* Do constraint checks. */\n    assert( regOldRowid>0 );\n    sqlite3GenerateConstraintChecks(pParse, pTab, aRegIdx, iDataCur, iIdxCur,\n        regNewRowid, regOldRowid, chngKey, onError, labelContinue, &bReplace,\n        aXRef);\n\n    /* Do FK constraint checks. */\n    if( hasFK ){\n      sqlite3FkCheck(pParse, pTab, regOldRowid, 0, aXRef, chngKey);\n    }\n\n    /* Delete the index entries associated with the current record.  */\n    if( bReplace || chngKey ){\n      if( pPk ){\n        addr1 = sqlite3VdbeAddOp4Int(v, OP_NotFound, iDataCur, 0, regKey, nKey);\n      }else{\n        addr1 = sqlite3VdbeAddOp3(v, OP_NotExists, iDataCur, 0, regOldRowid);\n      }\n      VdbeCoverageNeverTaken(v);\n    }\n    sqlite3GenerateRowIndexDelete(pParse, pTab, iDataCur, iIdxCur, aRegIdx, -1);\n\n    /* If changing the rowid value, or if there are foreign key constraints\n    ** to process, delete the old record. Otherwise, add a noop OP_Delete\n    ** to invoke the pre-update hook.\n    **\n    ** That (regNew==regnewRowid+1) is true is also important for the \n    ** pre-update hook. If the caller invokes preupdate_new(), the returned\n    ** value is copied from memory cell (regNewRowid+1+iCol), where iCol\n    ** is the column index supplied by the user.\n    */\n    assert( regNew==regNewRowid+1 );\n#ifdef SQLITE_ENABLE_PREUPDATE_HOOK\n    sqlite3VdbeAddOp3(v, OP_Delete, iDataCur,\n        OPFLAG_ISUPDATE | ((hasFK>1 || chngKey) ? 0 : OPFLAG_ISNOOP),\n        regNewRowid\n    );\n    if( eOnePass==ONEPASS_MULTI ){\n      assert( hasFK==0 && chngKey==0 );\n      sqlite3VdbeChangeP5(v, OPFLAG_SAVEPOSITION);\n    }\n    if( !pParse->nested ){\n      sqlite3VdbeAppendP4(v, pTab, P4_TABLE);\n    }\n#else\n    if( hasFK>1 || chngKey ){\n      sqlite3VdbeAddOp2(v, OP_Delete, iDataCur, 0);\n    }\n#endif\n    if( bReplace || chngKey ){\n      sqlite3VdbeJumpHere(v, addr1);\n    }\n\n    if( hasFK ){\n      sqlite3FkCheck(pParse, pTab, 0, regNewRowid, aXRef, chngKey);\n    }\n  \n    /* Insert the new index entries and the new record. */\n    sqlite3CompleteInsertion(\n        pParse, pTab, iDataCur, iIdxCur, regNewRowid, aRegIdx, \n        OPFLAG_ISUPDATE | (eOnePass==ONEPASS_MULTI ? OPFLAG_SAVEPOSITION : 0), \n        0, 0\n    );\n\n    /* Do any ON CASCADE, SET NULL or SET DEFAULT operations required to\n    ** handle rows (possibly in other tables) that refer via a foreign key\n    ** to the row just updated. */ \n    if( hasFK ){\n      sqlite3FkActions(pParse, pTab, pChanges, regOldRowid, aXRef, chngKey);\n    }\n  }\n\n  /* Increment the row counter \n  */\n  if( (db->flags & SQLITE_CountRows) && !pParse->pTriggerTab){\n    sqlite3VdbeAddOp2(v, OP_AddImm, regRowCount, 1);\n  }\n\n  sqlite3CodeRowTrigger(pParse, pTrigger, TK_UPDATE, pChanges, \n      TRIGGER_AFTER, pTab, regOldRowid, onError, labelContinue);\n\n  /* Repeat the above with the next record to be updated, until\n  ** all record selected by the WHERE clause have been updated.\n  */\n  if( eOnePass==ONEPASS_SINGLE ){\n    /* Nothing to do at end-of-loop for a single-pass */\n  }else if( eOnePass==ONEPASS_MULTI ){\n    sqlite3VdbeResolveLabel(v, labelContinue);\n    sqlite3WhereEnd(pWInfo);\n  }else if( pPk ){\n    sqlite3VdbeResolveLabel(v, labelContinue);\n    sqlite3VdbeAddOp2(v, OP_Next, iEph, addrTop); VdbeCoverage(v);\n  }else{\n    sqlite3VdbeGoto(v, labelContinue);\n  }\n  sqlite3VdbeResolveLabel(v, labelBreak);\n\n  /* Update the sqlite_sequence table by storing the content of the\n  ** maximum rowid counter values recorded while inserting into\n  ** autoincrement tables.\n  */\n  if( pParse->nested==0 && pParse->pTriggerTab==0 ){\n    sqlite3AutoincrementEnd(pParse);\n  }\n\n  /*\n  ** Return the number of rows that were changed. If this routine is \n  ** generating code because of a call to sqlite3NestedParse(), do not\n  ** invoke the callback function.\n  */\n  if( (db->flags&SQLITE_CountRows) && !pParse->pTriggerTab && !pParse->nested ){\n    sqlite3VdbeAddOp2(v, OP_ResultRow, regRowCount, 1);\n    sqlite3VdbeSetNumCols(v, 1);\n    sqlite3VdbeSetColName(v, 0, COLNAME_NAME, \"rows updated\", SQLITE_STATIC);\n  }\n\nupdate_cleanup:\n  sqlite3AuthContextPop(&sContext);\n  sqlite3DbFree(db, aXRef); /* Also frees aRegIdx[] and aToOpen[] */\n  sqlite3SrcListDelete(db, pTabList);\n  sqlite3ExprListDelete(db, pChanges);\n  sqlite3ExprDelete(db, pWhere);\n#if defined(SQLITE_ENABLE_UPDATE_DELETE_LIMIT) \n  sqlite3ExprListDelete(db, pOrderBy);\n  sqlite3ExprDelete(db, pLimit);\n#endif\n  return;\n}\n/* Make sure \"isView\" and other macros defined above are undefined. Otherwise\n** they may interfere with compilation of other functions in this file\n** (or in another file, if this file becomes part of the amalgamation).  */\n#ifdef isView\n #undef isView\n#endif\n#ifdef pTrigger\n #undef pTrigger\n#endif\n\n#ifndef SQLITE_OMIT_VIRTUALTABLE\n/*\n** Generate code for an UPDATE of a virtual table.\n**\n** There are two possible strategies - the default and the special \n** \"onepass\" strategy. Onepass is only used if the virtual table \n** implementation indicates that pWhere may match at most one row.\n**\n** The default strategy is to create an ephemeral table that contains\n** for each row to be changed:\n**\n**   (A)  The original rowid of that row.\n**   (B)  The revised rowid for the row.\n**   (C)  The content of every column in the row.\n**\n** Then loop through the contents of this ephemeral table executing a\n** VUpdate for each row. When finished, drop the ephemeral table.\n**\n** The \"onepass\" strategy does not use an ephemeral table. Instead, it\n** stores the same values (A, B and C above) in a register array and\n** makes a single invocation of VUpdate.\n*/\nstatic void updateVirtualTable(\n  Parse *pParse,       /* The parsing context */\n  SrcList *pSrc,       /* The virtual table to be modified */\n  Table *pTab,         /* The virtual table */\n  ExprList *pChanges,  /* The columns to change in the UPDATE statement */\n  Expr *pRowid,        /* Expression used to recompute the rowid */\n  int *aXRef,          /* Mapping from columns of pTab to entries in pChanges */\n  Expr *pWhere,        /* WHERE clause of the UPDATE statement */\n  int onError          /* ON CONFLICT strategy */\n){\n  Vdbe *v = pParse->pVdbe;  /* Virtual machine under construction */\n  int ephemTab;             /* Table holding the result of the SELECT */\n  int i;                    /* Loop counter */\n  sqlite3 *db = pParse->db; /* Database connection */\n  const char *pVTab = (const char*)sqlite3GetVTable(db, pTab);\n  WhereInfo *pWInfo;\n  int nArg = 2 + pTab->nCol;      /* Number of arguments to VUpdate */\n  int regArg;                     /* First register in VUpdate arg array */\n  int regRec;                     /* Register in which to assemble record */\n  int regRowid;                   /* Register for ephem table rowid */\n  int iCsr = pSrc->a[0].iCursor;  /* Cursor used for virtual table scan */\n  int aDummy[2];                  /* Unused arg for sqlite3WhereOkOnePass() */\n  int bOnePass;                   /* True to use onepass strategy */\n  int addr;                       /* Address of OP_OpenEphemeral */\n\n  /* Allocate nArg registers in which to gather the arguments for VUpdate. Then\n  ** create and open the ephemeral table in which the records created from\n  ** these arguments will be temporarily stored. */\n  assert( v );\n  ephemTab = pParse->nTab++;\n  addr= sqlite3VdbeAddOp2(v, OP_OpenEphemeral, ephemTab, nArg);\n  regArg = pParse->nMem + 1;\n  pParse->nMem += nArg;\n  regRec = ++pParse->nMem;\n  regRowid = ++pParse->nMem;\n\n  /* Start scanning the virtual table */\n  pWInfo = sqlite3WhereBegin(pParse, pSrc, pWhere, 0,0,WHERE_ONEPASS_DESIRED,0);\n  if( pWInfo==0 ) return;\n\n  /* Populate the argument registers. */\n  for(i=0; i<pTab->nCol; i++){\n    if( aXRef[i]>=0 ){\n      sqlite3ExprCode(pParse, pChanges->a[aXRef[i]].pExpr, regArg+2+i);\n    }else{\n      sqlite3VdbeAddOp3(v, OP_VColumn, iCsr, i, regArg+2+i);\n      sqlite3VdbeChangeP5(v, 1); /* Enable sqlite3_vtab_nochange() */\n    }\n  }\n  if( HasRowid(pTab) ){\n    sqlite3VdbeAddOp2(v, OP_Rowid, iCsr, regArg);\n    if( pRowid ){\n      sqlite3ExprCode(pParse, pRowid, regArg+1);\n    }else{\n      sqlite3VdbeAddOp2(v, OP_Rowid, iCsr, regArg+1);\n    }\n  }else{\n    Index *pPk;   /* PRIMARY KEY index */\n    i16 iPk;      /* PRIMARY KEY column */\n    pPk = sqlite3PrimaryKeyIndex(pTab);\n    assert( pPk!=0 );\n    assert( pPk->nKeyCol==1 );\n    iPk = pPk->aiColumn[0];\n    sqlite3VdbeAddOp3(v, OP_VColumn, iCsr, iPk, regArg);\n    sqlite3VdbeAddOp2(v, OP_SCopy, regArg+2+iPk, regArg+1);\n  }\n\n  bOnePass = sqlite3WhereOkOnePass(pWInfo, aDummy);\n\n  if( bOnePass ){\n    /* If using the onepass strategy, no-op out the OP_OpenEphemeral coded\n    ** above. Also, if this is a top-level parse (not a trigger), clear the\n    ** multi-write flag so that the VM does not open a statement journal */\n    sqlite3VdbeChangeToNoop(v, addr);\n    if( sqlite3IsToplevel(pParse) ){\n      pParse->isMultiWrite = 0;\n    }\n  }else{\n    /* Create a record from the argument register contents and insert it into\n    ** the ephemeral table. */\n    sqlite3VdbeAddOp3(v, OP_MakeRecord, regArg, nArg, regRec);\n#ifdef SQLITE_DEBUG\n    /* Signal an assert() within OP_MakeRecord that it is allowed to\n    ** accept no-change records with serial_type 10 */\n    sqlite3VdbeChangeP5(v, OPFLAG_NOCHNG_MAGIC);\n#endif\n    sqlite3VdbeAddOp2(v, OP_NewRowid, ephemTab, regRowid);\n    sqlite3VdbeAddOp3(v, OP_Insert, ephemTab, regRec, regRowid);\n  }\n\n\n  if( bOnePass==0 ){\n    /* End the virtual table scan */\n    sqlite3WhereEnd(pWInfo);\n\n    /* Begin scannning through the ephemeral table. */\n    addr = sqlite3VdbeAddOp1(v, OP_Rewind, ephemTab); VdbeCoverage(v);\n\n    /* Extract arguments from the current row of the ephemeral table and \n    ** invoke the VUpdate method.  */\n    for(i=0; i<nArg; i++){\n      sqlite3VdbeAddOp3(v, OP_Column, ephemTab, i, regArg+i);\n    }\n  }\n  sqlite3VtabMakeWritable(pParse, pTab);\n  sqlite3VdbeAddOp4(v, OP_VUpdate, 0, nArg, regArg, pVTab, P4_VTAB);\n  sqlite3VdbeChangeP5(v, onError==OE_Default ? OE_Abort : onError);\n  sqlite3MayAbort(pParse);\n\n  /* End of the ephemeral table scan. Or, if using the onepass strategy,\n  ** jump to here if the scan visited zero rows. */\n  if( bOnePass==0 ){\n    sqlite3VdbeAddOp2(v, OP_Next, ephemTab, addr+1); VdbeCoverage(v);\n    sqlite3VdbeJumpHere(v, addr);\n    sqlite3VdbeAddOp2(v, OP_Close, ephemTab, 0);\n  }else{\n    sqlite3WhereEnd(pWInfo);\n  }\n}\n#endif /* SQLITE_OMIT_VIRTUALTABLE */\n\n/************** End of update.c **********************************************/\n/************** Begin file vacuum.c ******************************************/\n/*\n** 2003 April 6\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n*************************************************************************\n** This file contains code used to implement the VACUUM command.\n**\n** Most of the code in this file may be omitted by defining the\n** SQLITE_OMIT_VACUUM macro.\n*/\n/* #include \"sqliteInt.h\" */\n/* #include \"vdbeInt.h\" */\n\n#if !defined(SQLITE_OMIT_VACUUM) && !defined(SQLITE_OMIT_ATTACH)\n\n/*\n** Execute zSql on database db.\n**\n** If zSql returns rows, then each row will have exactly one\n** column.  (This will only happen if zSql begins with \"SELECT\".)\n** Take each row of result and call execSql() again recursively.\n**\n** The execSqlF() routine does the same thing, except it accepts\n** a format string as its third argument\n*/\nstatic int execSql(sqlite3 *db, char **pzErrMsg, const char *zSql){\n  sqlite3_stmt *pStmt;\n  int rc;\n\n  /* printf(\"SQL: [%s]\\n\", zSql); fflush(stdout); */\n  rc = sqlite3_prepare_v2(db, zSql, -1, &pStmt, 0);\n  if( rc!=SQLITE_OK ) return rc;\n  while( SQLITE_ROW==(rc = sqlite3_step(pStmt)) ){\n    const char *zSubSql = (const char*)sqlite3_column_text(pStmt,0);\n    assert( sqlite3_strnicmp(zSql,\"SELECT\",6)==0 );\n    assert( sqlite3_strnicmp(zSubSql,\"SELECT\",6)!=0 || CORRUPT_DB );\n    if( zSubSql && zSubSql[0]!='S' ){\n      rc = execSql(db, pzErrMsg, zSubSql);\n      if( rc!=SQLITE_OK ) break;\n    }\n  }\n  assert( rc!=SQLITE_ROW );\n  if( rc==SQLITE_DONE ) rc = SQLITE_OK;\n  if( rc ){\n    sqlite3SetString(pzErrMsg, db, sqlite3_errmsg(db));\n  }\n  (void)sqlite3_finalize(pStmt);\n  return rc;\n}\nstatic int execSqlF(sqlite3 *db, char **pzErrMsg, const char *zSql, ...){\n  char *z;\n  va_list ap;\n  int rc;\n  va_start(ap, zSql);\n  z = sqlite3VMPrintf(db, zSql, ap);\n  va_end(ap);\n  if( z==0 ) return SQLITE_NOMEM;\n  rc = execSql(db, pzErrMsg, z);\n  sqlite3DbFree(db, z);\n  return rc;\n}\n\n/*\n** The VACUUM command is used to clean up the database,\n** collapse free space, etc.  It is modelled after the VACUUM command\n** in PostgreSQL.  The VACUUM command works as follows:\n**\n**   (1)  Create a new transient database file\n**   (2)  Copy all content from the database being vacuumed into\n**        the new transient database file\n**   (3)  Copy content from the transient database back into the\n**        original database.\n**\n** The transient database requires temporary disk space approximately\n** equal to the size of the original database.  The copy operation of\n** step (3) requires additional temporary disk space approximately equal\n** to the size of the original database for the rollback journal.\n** Hence, temporary disk space that is approximately 2x the size of the\n** original database is required.  Every page of the database is written\n** approximately 3 times:  Once for step (2) and twice for step (3).\n** Two writes per page are required in step (3) because the original\n** database content must be written into the rollback journal prior to\n** overwriting the database with the vacuumed content.\n**\n** Only 1x temporary space and only 1x writes would be required if\n** the copy of step (3) were replaced by deleting the original database\n** and renaming the transient database as the original.  But that will\n** not work if other processes are attached to the original database.\n** And a power loss in between deleting the original and renaming the\n** transient would cause the database file to appear to be deleted\n** following reboot.\n*/\nSQLITE_PRIVATE void sqlite3Vacuum(Parse *pParse, Token *pNm){\n  Vdbe *v = sqlite3GetVdbe(pParse);\n  int iDb = 0;\n  if( v==0 ) return;\n  if( pNm ){\n#ifndef SQLITE_BUG_COMPATIBLE_20160819\n    /* Default behavior:  Report an error if the argument to VACUUM is\n    ** not recognized */\n    iDb = sqlite3TwoPartName(pParse, pNm, pNm, &pNm);\n    if( iDb<0 ) return;\n#else\n    /* When SQLITE_BUG_COMPATIBLE_20160819 is defined, unrecognized arguments\n    ** to VACUUM are silently ignored.  This is a back-out of a bug fix that\n    ** occurred on 2016-08-19 (https://www.sqlite.org/src/info/083f9e6270).\n    ** The buggy behavior is required for binary compatibility with some\n    ** legacy applications. */\n    iDb = sqlite3FindDb(pParse->db, pNm);\n    if( iDb<0 ) iDb = 0;\n#endif\n  }\n  if( iDb!=1 ){\n    sqlite3VdbeAddOp1(v, OP_Vacuum, iDb);\n    sqlite3VdbeUsesBtree(v, iDb);\n  }\n  return;\n}\n\n/*\n** This routine implements the OP_Vacuum opcode of the VDBE.\n*/\nSQLITE_PRIVATE int sqlite3RunVacuum(char **pzErrMsg, sqlite3 *db, int iDb){\n  int rc = SQLITE_OK;     /* Return code from service routines */\n  Btree *pMain;           /* The database being vacuumed */\n  Btree *pTemp;           /* The temporary database we vacuum into */\n  u16 saved_mDbFlags;     /* Saved value of db->mDbFlags */\n  u32 saved_flags;        /* Saved value of db->flags */\n  int saved_nChange;      /* Saved value of db->nChange */\n  int saved_nTotalChange; /* Saved value of db->nTotalChange */\n  u8 saved_mTrace;        /* Saved trace settings */\n  Db *pDb = 0;            /* Database to detach at end of vacuum */\n  int isMemDb;            /* True if vacuuming a :memory: database */\n  int nRes;               /* Bytes of reserved space at the end of each page */\n  int nDb;                /* Number of attached databases */\n  const char *zDbMain;    /* Schema name of database to vacuum */\n\n  if( !db->autoCommit ){\n    sqlite3SetString(pzErrMsg, db, \"cannot VACUUM from within a transaction\");\n    return SQLITE_ERROR;\n  }\n  if( db->nVdbeActive>1 ){\n    sqlite3SetString(pzErrMsg, db,\"cannot VACUUM - SQL statements in progress\");\n    return SQLITE_ERROR;\n  }\n\n  /* Save the current value of the database flags so that it can be \n  ** restored before returning. Then set the writable-schema flag, and\n  ** disable CHECK and foreign key constraints.  */\n  saved_flags = db->flags;\n  saved_mDbFlags = db->mDbFlags;\n  saved_nChange = db->nChange;\n  saved_nTotalChange = db->nTotalChange;\n  saved_mTrace = db->mTrace;\n  db->flags |= SQLITE_WriteSchema | SQLITE_IgnoreChecks;\n  db->mDbFlags |= DBFLAG_PreferBuiltin | DBFLAG_Vacuum;\n  db->flags &= ~(SQLITE_ForeignKeys | SQLITE_ReverseOrder | SQLITE_CountRows);\n  db->mTrace = 0;\n\n  zDbMain = db->aDb[iDb].zDbSName;\n  pMain = db->aDb[iDb].pBt;\n  isMemDb = sqlite3PagerIsMemdb(sqlite3BtreePager(pMain));\n\n  /* Attach the temporary database as 'vacuum_db'. The synchronous pragma\n  ** can be set to 'off' for this file, as it is not recovered if a crash\n  ** occurs anyway. The integrity of the database is maintained by a\n  ** (possibly synchronous) transaction opened on the main database before\n  ** sqlite3BtreeCopyFile() is called.\n  **\n  ** An optimisation would be to use a non-journaled pager.\n  ** (Later:) I tried setting \"PRAGMA vacuum_db.journal_mode=OFF\" but\n  ** that actually made the VACUUM run slower.  Very little journalling\n  ** actually occurs when doing a vacuum since the vacuum_db is initially\n  ** empty.  Only the journal header is written.  Apparently it takes more\n  ** time to parse and run the PRAGMA to turn journalling off than it does\n  ** to write the journal header file.\n  */\n  nDb = db->nDb;\n  rc = execSql(db, pzErrMsg, \"ATTACH''AS vacuum_db\");\n  if( rc!=SQLITE_OK ) goto end_of_vacuum;\n  assert( (db->nDb-1)==nDb );\n  pDb = &db->aDb[nDb];\n  assert( strcmp(pDb->zDbSName,\"vacuum_db\")==0 );\n  pTemp = pDb->pBt;\n\n  /* The call to execSql() to attach the temp database has left the file\n  ** locked (as there was more than one active statement when the transaction\n  ** to read the schema was concluded. Unlock it here so that this doesn't\n  ** cause problems for the call to BtreeSetPageSize() below.  */\n  sqlite3BtreeCommit(pTemp);\n\n  nRes = sqlite3BtreeGetOptimalReserve(pMain);\n\n  /* A VACUUM cannot change the pagesize of an encrypted database. */\n#ifdef SQLITE_HAS_CODEC\n  if( db->nextPagesize ){\n    extern void sqlite3CodecGetKey(sqlite3*, int, void**, int*);\n    int nKey;\n    char *zKey;\n    sqlite3CodecGetKey(db, iDb, (void**)&zKey, &nKey);\n    if( nKey ) db->nextPagesize = 0;\n  }\n#endif\n\n  sqlite3BtreeSetCacheSize(pTemp, db->aDb[iDb].pSchema->cache_size);\n  sqlite3BtreeSetSpillSize(pTemp, sqlite3BtreeSetSpillSize(pMain,0));\n  sqlite3BtreeSetPagerFlags(pTemp, PAGER_SYNCHRONOUS_OFF|PAGER_CACHESPILL);\n\n  /* Begin a transaction and take an exclusive lock on the main database\n  ** file. This is done before the sqlite3BtreeGetPageSize(pMain) call below,\n  ** to ensure that we do not try to change the page-size on a WAL database.\n  */\n  rc = execSql(db, pzErrMsg, \"BEGIN\");\n  if( rc!=SQLITE_OK ) goto end_of_vacuum;\n  rc = sqlite3BtreeBeginTrans(pMain, 2);\n  if( rc!=SQLITE_OK ) goto end_of_vacuum;\n\n  /* Do not attempt to change the page size for a WAL database */\n  if( sqlite3PagerGetJournalMode(sqlite3BtreePager(pMain))\n                                               ==PAGER_JOURNALMODE_WAL ){\n    db->nextPagesize = 0;\n  }\n\n  if( sqlite3BtreeSetPageSize(pTemp, sqlite3BtreeGetPageSize(pMain), nRes, 0)\n   || (!isMemDb && sqlite3BtreeSetPageSize(pTemp, db->nextPagesize, nRes, 0))\n   || NEVER(db->mallocFailed)\n  ){\n    rc = SQLITE_NOMEM_BKPT;\n    goto end_of_vacuum;\n  }\n\n#ifndef SQLITE_OMIT_AUTOVACUUM\n  sqlite3BtreeSetAutoVacuum(pTemp, db->nextAutovac>=0 ? db->nextAutovac :\n                                           sqlite3BtreeGetAutoVacuum(pMain));\n#endif\n\n  /* Query the schema of the main database. Create a mirror schema\n  ** in the temporary database.\n  */\n  db->init.iDb = nDb; /* force new CREATE statements into vacuum_db */\n  rc = execSqlF(db, pzErrMsg,\n      \"SELECT sql FROM \\\"%w\\\".sqlite_master\"\n      \" WHERE type='table'AND name<>'sqlite_sequence'\"\n      \" AND coalesce(rootpage,1)>0\",\n      zDbMain\n  );\n  if( rc!=SQLITE_OK ) goto end_of_vacuum;\n  rc = execSqlF(db, pzErrMsg,\n      \"SELECT sql FROM \\\"%w\\\".sqlite_master\"\n      \" WHERE type='index' AND length(sql)>10\",\n      zDbMain\n  );\n  if( rc!=SQLITE_OK ) goto end_of_vacuum;\n  db->init.iDb = 0;\n\n  /* Loop through the tables in the main database. For each, do\n  ** an \"INSERT INTO vacuum_db.xxx SELECT * FROM main.xxx;\" to copy\n  ** the contents to the temporary database.\n  */\n  rc = execSqlF(db, pzErrMsg,\n      \"SELECT'INSERT INTO vacuum_db.'||quote(name)\"\n      \"||' SELECT*FROM\\\"%w\\\".'||quote(name)\"\n      \"FROM vacuum_db.sqlite_master \"\n      \"WHERE type='table'AND coalesce(rootpage,1)>0\",\n      zDbMain\n  );\n  assert( (db->mDbFlags & DBFLAG_Vacuum)!=0 );\n  db->mDbFlags &= ~DBFLAG_Vacuum;\n  if( rc!=SQLITE_OK ) goto end_of_vacuum;\n\n  /* Copy the triggers, views, and virtual tables from the main database\n  ** over to the temporary database.  None of these objects has any\n  ** associated storage, so all we have to do is copy their entries\n  ** from the SQLITE_MASTER table.\n  */\n  rc = execSqlF(db, pzErrMsg,\n      \"INSERT INTO vacuum_db.sqlite_master\"\n      \" SELECT*FROM \\\"%w\\\".sqlite_master\"\n      \" WHERE type IN('view','trigger')\"\n      \" OR(type='table'AND rootpage=0)\",\n      zDbMain\n  );\n  if( rc ) goto end_of_vacuum;\n\n  /* At this point, there is a write transaction open on both the \n  ** vacuum database and the main database. Assuming no error occurs,\n  ** both transactions are closed by this block - the main database\n  ** transaction by sqlite3BtreeCopyFile() and the other by an explicit\n  ** call to sqlite3BtreeCommit().\n  */\n  {\n    u32 meta;\n    int i;\n\n    /* This array determines which meta meta values are preserved in the\n    ** vacuum.  Even entries are the meta value number and odd entries\n    ** are an increment to apply to the meta value after the vacuum.\n    ** The increment is used to increase the schema cookie so that other\n    ** connections to the same database will know to reread the schema.\n    */\n    static const unsigned char aCopy[] = {\n       BTREE_SCHEMA_VERSION,     1,  /* Add one to the old schema cookie */\n       BTREE_DEFAULT_CACHE_SIZE, 0,  /* Preserve the default page cache size */\n       BTREE_TEXT_ENCODING,      0,  /* Preserve the text encoding */\n       BTREE_USER_VERSION,       0,  /* Preserve the user version */\n       BTREE_APPLICATION_ID,     0,  /* Preserve the application id */\n    };\n\n    assert( 1==sqlite3BtreeIsInTrans(pTemp) );\n    assert( 1==sqlite3BtreeIsInTrans(pMain) );\n\n    /* Copy Btree meta values */\n    for(i=0; i<ArraySize(aCopy); i+=2){\n      /* GetMeta() and UpdateMeta() cannot fail in this context because\n      ** we already have page 1 loaded into cache and marked dirty. */\n      sqlite3BtreeGetMeta(pMain, aCopy[i], &meta);\n      rc = sqlite3BtreeUpdateMeta(pTemp, aCopy[i], meta+aCopy[i+1]);\n      if( NEVER(rc!=SQLITE_OK) ) goto end_of_vacuum;\n    }\n\n    rc = sqlite3BtreeCopyFile(pMain, pTemp);\n    if( rc!=SQLITE_OK ) goto end_of_vacuum;\n    rc = sqlite3BtreeCommit(pTemp);\n    if( rc!=SQLITE_OK ) goto end_of_vacuum;\n#ifndef SQLITE_OMIT_AUTOVACUUM\n    sqlite3BtreeSetAutoVacuum(pMain, sqlite3BtreeGetAutoVacuum(pTemp));\n#endif\n  }\n\n  assert( rc==SQLITE_OK );\n  rc = sqlite3BtreeSetPageSize(pMain, sqlite3BtreeGetPageSize(pTemp), nRes,1);\n\nend_of_vacuum:\n  /* Restore the original value of db->flags */\n  db->init.iDb = 0;\n  db->mDbFlags = saved_mDbFlags;\n  db->flags = saved_flags;\n  db->nChange = saved_nChange;\n  db->nTotalChange = saved_nTotalChange;\n  db->mTrace = saved_mTrace;\n  sqlite3BtreeSetPageSize(pMain, -1, -1, 1);\n\n  /* Currently there is an SQL level transaction open on the vacuum\n  ** database. No locks are held on any other files (since the main file\n  ** was committed at the btree level). So it safe to end the transaction\n  ** by manually setting the autoCommit flag to true and detaching the\n  ** vacuum database. The vacuum_db journal file is deleted when the pager\n  ** is closed by the DETACH.\n  */\n  db->autoCommit = 1;\n\n  if( pDb ){\n    sqlite3BtreeClose(pDb->pBt);\n    pDb->pBt = 0;\n    pDb->pSchema = 0;\n  }\n\n  /* This both clears the schemas and reduces the size of the db->aDb[]\n  ** array. */ \n  sqlite3ResetAllSchemasOfConnection(db);\n\n  return rc;\n}\n\n#endif  /* SQLITE_OMIT_VACUUM && SQLITE_OMIT_ATTACH */\n\n/************** End of vacuum.c **********************************************/\n/************** Begin file vtab.c ********************************************/\n/*\n** 2006 June 10\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n*************************************************************************\n** This file contains code used to help implement virtual tables.\n*/\n#ifndef SQLITE_OMIT_VIRTUALTABLE\n/* #include \"sqliteInt.h\" */\n\n/*\n** Before a virtual table xCreate() or xConnect() method is invoked, the\n** sqlite3.pVtabCtx member variable is set to point to an instance of\n** this struct allocated on the stack. It is used by the implementation of \n** the sqlite3_declare_vtab() and sqlite3_vtab_config() APIs, both of which\n** are invoked only from within xCreate and xConnect methods.\n*/\nstruct VtabCtx {\n  VTable *pVTable;    /* The virtual table being constructed */\n  Table *pTab;        /* The Table object to which the virtual table belongs */\n  VtabCtx *pPrior;    /* Parent context (if any) */\n  int bDeclared;      /* True after sqlite3_declare_vtab() is called */\n};\n\n/*\n** Construct and install a Module object for a virtual table.  When this\n** routine is called, it is guaranteed that all appropriate locks are held\n** and the module is not already part of the connection.\n*/\nSQLITE_PRIVATE Module *sqlite3VtabCreateModule(\n  sqlite3 *db,                    /* Database in which module is registered */\n  const char *zName,              /* Name assigned to this module */\n  const sqlite3_module *pModule,  /* The definition of the module */\n  void *pAux,                     /* Context pointer for xCreate/xConnect */\n  void (*xDestroy)(void *)        /* Module destructor function */\n){\n  Module *pMod;\n  int nName = sqlite3Strlen30(zName);\n  pMod = (Module *)sqlite3Malloc(sizeof(Module) + nName + 1);\n  if( pMod==0 ){\n    sqlite3OomFault(db);\n  }else{\n    Module *pDel;\n    char *zCopy = (char *)(&pMod[1]);\n    memcpy(zCopy, zName, nName+1);\n    pMod->zName = zCopy;\n    pMod->pModule = pModule;\n    pMod->pAux = pAux;\n    pMod->xDestroy = xDestroy;\n    pMod->pEpoTab = 0;\n    pDel = (Module *)sqlite3HashInsert(&db->aModule,zCopy,(void*)pMod);\n    assert( pDel==0 || pDel==pMod );\n    if( pDel ){\n      sqlite3OomFault(db);\n      sqlite3DbFree(db, pDel);\n      pMod = 0;\n    }\n  }\n  return pMod;\n}\n\n/*\n** The actual function that does the work of creating a new module.\n** This function implements the sqlite3_create_module() and\n** sqlite3_create_module_v2() interfaces.\n*/\nstatic int createModule(\n  sqlite3 *db,                    /* Database in which module is registered */\n  const char *zName,              /* Name assigned to this module */\n  const sqlite3_module *pModule,  /* The definition of the module */\n  void *pAux,                     /* Context pointer for xCreate/xConnect */\n  void (*xDestroy)(void *)        /* Module destructor function */\n){\n  int rc = SQLITE_OK;\n\n  sqlite3_mutex_enter(db->mutex);\n  if( sqlite3HashFind(&db->aModule, zName) ){\n    rc = SQLITE_MISUSE_BKPT;\n  }else{\n    (void)sqlite3VtabCreateModule(db, zName, pModule, pAux, xDestroy);\n  }\n  rc = sqlite3ApiExit(db, rc);\n  if( rc!=SQLITE_OK && xDestroy ) xDestroy(pAux);\n  sqlite3_mutex_leave(db->mutex);\n  return rc;\n}\n\n\n/*\n** External API function used to create a new virtual-table module.\n*/\nSQLITE_API int sqlite3_create_module(\n  sqlite3 *db,                    /* Database in which module is registered */\n  const char *zName,              /* Name assigned to this module */\n  const sqlite3_module *pModule,  /* The definition of the module */\n  void *pAux                      /* Context pointer for xCreate/xConnect */\n){\n#ifdef SQLITE_ENABLE_API_ARMOR\n  if( !sqlite3SafetyCheckOk(db) || zName==0 ) return SQLITE_MISUSE_BKPT;\n#endif\n  return createModule(db, zName, pModule, pAux, 0);\n}\n\n/*\n** External API function used to create a new virtual-table module.\n*/\nSQLITE_API int sqlite3_create_module_v2(\n  sqlite3 *db,                    /* Database in which module is registered */\n  const char *zName,              /* Name assigned to this module */\n  const sqlite3_module *pModule,  /* The definition of the module */\n  void *pAux,                     /* Context pointer for xCreate/xConnect */\n  void (*xDestroy)(void *)        /* Module destructor function */\n){\n#ifdef SQLITE_ENABLE_API_ARMOR\n  if( !sqlite3SafetyCheckOk(db) || zName==0 ) return SQLITE_MISUSE_BKPT;\n#endif\n  return createModule(db, zName, pModule, pAux, xDestroy);\n}\n\n/*\n** Lock the virtual table so that it cannot be disconnected.\n** Locks nest.  Every lock should have a corresponding unlock.\n** If an unlock is omitted, resources leaks will occur.  \n**\n** If a disconnect is attempted while a virtual table is locked,\n** the disconnect is deferred until all locks have been removed.\n*/\nSQLITE_PRIVATE void sqlite3VtabLock(VTable *pVTab){\n  pVTab->nRef++;\n}\n\n\n/*\n** pTab is a pointer to a Table structure representing a virtual-table.\n** Return a pointer to the VTable object used by connection db to access \n** this virtual-table, if one has been created, or NULL otherwise.\n*/\nSQLITE_PRIVATE VTable *sqlite3GetVTable(sqlite3 *db, Table *pTab){\n  VTable *pVtab;\n  assert( IsVirtual(pTab) );\n  for(pVtab=pTab->pVTable; pVtab && pVtab->db!=db; pVtab=pVtab->pNext);\n  return pVtab;\n}\n\n/*\n** Decrement the ref-count on a virtual table object. When the ref-count\n** reaches zero, call the xDisconnect() method to delete the object.\n*/\nSQLITE_PRIVATE void sqlite3VtabUnlock(VTable *pVTab){\n  sqlite3 *db = pVTab->db;\n\n  assert( db );\n  assert( pVTab->nRef>0 );\n  assert( db->magic==SQLITE_MAGIC_OPEN || db->magic==SQLITE_MAGIC_ZOMBIE );\n\n  pVTab->nRef--;\n  if( pVTab->nRef==0 ){\n    sqlite3_vtab *p = pVTab->pVtab;\n    if( p ){\n      p->pModule->xDisconnect(p);\n    }\n    sqlite3DbFree(db, pVTab);\n  }\n}\n\n/*\n** Table p is a virtual table. This function moves all elements in the\n** p->pVTable list to the sqlite3.pDisconnect lists of their associated\n** database connections to be disconnected at the next opportunity. \n** Except, if argument db is not NULL, then the entry associated with\n** connection db is left in the p->pVTable list.\n*/\nstatic VTable *vtabDisconnectAll(sqlite3 *db, Table *p){\n  VTable *pRet = 0;\n  VTable *pVTable = p->pVTable;\n  p->pVTable = 0;\n\n  /* Assert that the mutex (if any) associated with the BtShared database \n  ** that contains table p is held by the caller. See header comments \n  ** above function sqlite3VtabUnlockList() for an explanation of why\n  ** this makes it safe to access the sqlite3.pDisconnect list of any\n  ** database connection that may have an entry in the p->pVTable list.\n  */\n  assert( db==0 || sqlite3SchemaMutexHeld(db, 0, p->pSchema) );\n\n  while( pVTable ){\n    sqlite3 *db2 = pVTable->db;\n    VTable *pNext = pVTable->pNext;\n    assert( db2 );\n    if( db2==db ){\n      pRet = pVTable;\n      p->pVTable = pRet;\n      pRet->pNext = 0;\n    }else{\n      pVTable->pNext = db2->pDisconnect;\n      db2->pDisconnect = pVTable;\n    }\n    pVTable = pNext;\n  }\n\n  assert( !db || pRet );\n  return pRet;\n}\n\n/*\n** Table *p is a virtual table. This function removes the VTable object\n** for table *p associated with database connection db from the linked\n** list in p->pVTab. It also decrements the VTable ref count. This is\n** used when closing database connection db to free all of its VTable\n** objects without disturbing the rest of the Schema object (which may\n** be being used by other shared-cache connections).\n*/\nSQLITE_PRIVATE void sqlite3VtabDisconnect(sqlite3 *db, Table *p){\n  VTable **ppVTab;\n\n  assert( IsVirtual(p) );\n  assert( sqlite3BtreeHoldsAllMutexes(db) );\n  assert( sqlite3_mutex_held(db->mutex) );\n\n  for(ppVTab=&p->pVTable; *ppVTab; ppVTab=&(*ppVTab)->pNext){\n    if( (*ppVTab)->db==db  ){\n      VTable *pVTab = *ppVTab;\n      *ppVTab = pVTab->pNext;\n      sqlite3VtabUnlock(pVTab);\n      break;\n    }\n  }\n}\n\n\n/*\n** Disconnect all the virtual table objects in the sqlite3.pDisconnect list.\n**\n** This function may only be called when the mutexes associated with all\n** shared b-tree databases opened using connection db are held by the \n** caller. This is done to protect the sqlite3.pDisconnect list. The\n** sqlite3.pDisconnect list is accessed only as follows:\n**\n**   1) By this function. In this case, all BtShared mutexes and the mutex\n**      associated with the database handle itself must be held.\n**\n**   2) By function vtabDisconnectAll(), when it adds a VTable entry to\n**      the sqlite3.pDisconnect list. In this case either the BtShared mutex\n**      associated with the database the virtual table is stored in is held\n**      or, if the virtual table is stored in a non-sharable database, then\n**      the database handle mutex is held.\n**\n** As a result, a sqlite3.pDisconnect cannot be accessed simultaneously \n** by multiple threads. It is thread-safe.\n*/\nSQLITE_PRIVATE void sqlite3VtabUnlockList(sqlite3 *db){\n  VTable *p = db->pDisconnect;\n  db->pDisconnect = 0;\n\n  assert( sqlite3BtreeHoldsAllMutexes(db) );\n  assert( sqlite3_mutex_held(db->mutex) );\n\n  if( p ){\n    sqlite3ExpirePreparedStatements(db);\n    do {\n      VTable *pNext = p->pNext;\n      sqlite3VtabUnlock(p);\n      p = pNext;\n    }while( p );\n  }\n}\n\n/*\n** Clear any and all virtual-table information from the Table record.\n** This routine is called, for example, just before deleting the Table\n** record.\n**\n** Since it is a virtual-table, the Table structure contains a pointer\n** to the head of a linked list of VTable structures. Each VTable \n** structure is associated with a single sqlite3* user of the schema.\n** The reference count of the VTable structure associated with database \n** connection db is decremented immediately (which may lead to the \n** structure being xDisconnected and free). Any other VTable structures\n** in the list are moved to the sqlite3.pDisconnect list of the associated \n** database connection.\n*/\nSQLITE_PRIVATE void sqlite3VtabClear(sqlite3 *db, Table *p){\n  if( !db || db->pnBytesFreed==0 ) vtabDisconnectAll(0, p);\n  if( p->azModuleArg ){\n    int i;\n    for(i=0; i<p->nModuleArg; i++){\n      if( i!=1 ) sqlite3DbFree(db, p->azModuleArg[i]);\n    }\n    sqlite3DbFree(db, p->azModuleArg);\n  }\n}\n\n/*\n** Add a new module argument to pTable->azModuleArg[].\n** The string is not copied - the pointer is stored.  The\n** string will be freed automatically when the table is\n** deleted.\n*/\nstatic void addModuleArgument(sqlite3 *db, Table *pTable, char *zArg){\n  int nBytes = sizeof(char *)*(2+pTable->nModuleArg);\n  char **azModuleArg;\n  azModuleArg = sqlite3DbRealloc(db, pTable->azModuleArg, nBytes);\n  if( azModuleArg==0 ){\n    sqlite3DbFree(db, zArg);\n  }else{\n    int i = pTable->nModuleArg++;\n    azModuleArg[i] = zArg;\n    azModuleArg[i+1] = 0;\n    pTable->azModuleArg = azModuleArg;\n  }\n}\n\n/*\n** The parser calls this routine when it first sees a CREATE VIRTUAL TABLE\n** statement.  The module name has been parsed, but the optional list\n** of parameters that follow the module name are still pending.\n*/\nSQLITE_PRIVATE void sqlite3VtabBeginParse(\n  Parse *pParse,        /* Parsing context */\n  Token *pName1,        /* Name of new table, or database name */\n  Token *pName2,        /* Name of new table or NULL */\n  Token *pModuleName,   /* Name of the module for the virtual table */\n  int ifNotExists       /* No error if the table already exists */\n){\n  int iDb;              /* The database the table is being created in */\n  Table *pTable;        /* The new virtual table */\n  sqlite3 *db;          /* Database connection */\n\n  sqlite3StartTable(pParse, pName1, pName2, 0, 0, 1, ifNotExists);\n  pTable = pParse->pNewTable;\n  if( pTable==0 ) return;\n  assert( 0==pTable->pIndex );\n\n  db = pParse->db;\n  iDb = sqlite3SchemaToIndex(db, pTable->pSchema);\n  assert( iDb>=0 );\n\n  assert( pTable->nModuleArg==0 );\n  addModuleArgument(db, pTable, sqlite3NameFromToken(db, pModuleName));\n  addModuleArgument(db, pTable, 0);\n  addModuleArgument(db, pTable, sqlite3DbStrDup(db, pTable->zName));\n  assert( (pParse->sNameToken.z==pName2->z && pName2->z!=0)\n       || (pParse->sNameToken.z==pName1->z && pName2->z==0)\n  );\n  pParse->sNameToken.n = (int)(\n      &pModuleName->z[pModuleName->n] - pParse->sNameToken.z\n  );\n\n#ifndef SQLITE_OMIT_AUTHORIZATION\n  /* Creating a virtual table invokes the authorization callback twice.\n  ** The first invocation, to obtain permission to INSERT a row into the\n  ** sqlite_master table, has already been made by sqlite3StartTable().\n  ** The second call, to obtain permission to create the table, is made now.\n  */\n  if( pTable->azModuleArg ){\n    sqlite3AuthCheck(pParse, SQLITE_CREATE_VTABLE, pTable->zName, \n            pTable->azModuleArg[0], pParse->db->aDb[iDb].zDbSName);\n  }\n#endif\n}\n\n/*\n** This routine takes the module argument that has been accumulating\n** in pParse->zArg[] and appends it to the list of arguments on the\n** virtual table currently under construction in pParse->pTable.\n*/\nstatic void addArgumentToVtab(Parse *pParse){\n  if( pParse->sArg.z && pParse->pNewTable ){\n    const char *z = (const char*)pParse->sArg.z;\n    int n = pParse->sArg.n;\n    sqlite3 *db = pParse->db;\n    addModuleArgument(db, pParse->pNewTable, sqlite3DbStrNDup(db, z, n));\n  }\n}\n\n/*\n** The parser calls this routine after the CREATE VIRTUAL TABLE statement\n** has been completely parsed.\n*/\nSQLITE_PRIVATE void sqlite3VtabFinishParse(Parse *pParse, Token *pEnd){\n  Table *pTab = pParse->pNewTable;  /* The table being constructed */\n  sqlite3 *db = pParse->db;         /* The database connection */\n\n  if( pTab==0 ) return;\n  addArgumentToVtab(pParse);\n  pParse->sArg.z = 0;\n  if( pTab->nModuleArg<1 ) return;\n  \n  /* If the CREATE VIRTUAL TABLE statement is being entered for the\n  ** first time (in other words if the virtual table is actually being\n  ** created now instead of just being read out of sqlite_master) then\n  ** do additional initialization work and store the statement text\n  ** in the sqlite_master table.\n  */\n  if( !db->init.busy ){\n    char *zStmt;\n    char *zWhere;\n    int iDb;\n    int iReg;\n    Vdbe *v;\n\n    /* Compute the complete text of the CREATE VIRTUAL TABLE statement */\n    if( pEnd ){\n      pParse->sNameToken.n = (int)(pEnd->z - pParse->sNameToken.z) + pEnd->n;\n    }\n    zStmt = sqlite3MPrintf(db, \"CREATE VIRTUAL TABLE %T\", &pParse->sNameToken);\n\n    /* A slot for the record has already been allocated in the \n    ** SQLITE_MASTER table.  We just need to update that slot with all\n    ** the information we've collected.  \n    **\n    ** The VM register number pParse->regRowid holds the rowid of an\n    ** entry in the sqlite_master table tht was created for this vtab\n    ** by sqlite3StartTable().\n    */\n    iDb = sqlite3SchemaToIndex(db, pTab->pSchema);\n    sqlite3NestedParse(pParse,\n      \"UPDATE %Q.%s \"\n         \"SET type='table', name=%Q, tbl_name=%Q, rootpage=0, sql=%Q \"\n       \"WHERE rowid=#%d\",\n      db->aDb[iDb].zDbSName, MASTER_NAME,\n      pTab->zName,\n      pTab->zName,\n      zStmt,\n      pParse->regRowid\n    );\n    sqlite3DbFree(db, zStmt);\n    v = sqlite3GetVdbe(pParse);\n    sqlite3ChangeCookie(pParse, iDb);\n\n    sqlite3VdbeAddOp0(v, OP_Expire);\n    zWhere = sqlite3MPrintf(db, \"name='%q' AND type='table'\", pTab->zName);\n    sqlite3VdbeAddParseSchemaOp(v, iDb, zWhere);\n\n    iReg = ++pParse->nMem;\n    sqlite3VdbeLoadString(v, iReg, pTab->zName);\n    sqlite3VdbeAddOp2(v, OP_VCreate, iDb, iReg);\n  }\n\n  /* If we are rereading the sqlite_master table create the in-memory\n  ** record of the table. The xConnect() method is not called until\n  ** the first time the virtual table is used in an SQL statement. This\n  ** allows a schema that contains virtual tables to be loaded before\n  ** the required virtual table implementations are registered.  */\n  else {\n    Table *pOld;\n    Schema *pSchema = pTab->pSchema;\n    const char *zName = pTab->zName;\n    assert( sqlite3SchemaMutexHeld(db, 0, pSchema) );\n    pOld = sqlite3HashInsert(&pSchema->tblHash, zName, pTab);\n    if( pOld ){\n      sqlite3OomFault(db);\n      assert( pTab==pOld );  /* Malloc must have failed inside HashInsert() */\n      return;\n    }\n    pParse->pNewTable = 0;\n  }\n}\n\n/*\n** The parser calls this routine when it sees the first token\n** of an argument to the module name in a CREATE VIRTUAL TABLE statement.\n*/\nSQLITE_PRIVATE void sqlite3VtabArgInit(Parse *pParse){\n  addArgumentToVtab(pParse);\n  pParse->sArg.z = 0;\n  pParse->sArg.n = 0;\n}\n\n/*\n** The parser calls this routine for each token after the first token\n** in an argument to the module name in a CREATE VIRTUAL TABLE statement.\n*/\nSQLITE_PRIVATE void sqlite3VtabArgExtend(Parse *pParse, Token *p){\n  Token *pArg = &pParse->sArg;\n  if( pArg->z==0 ){\n    pArg->z = p->z;\n    pArg->n = p->n;\n  }else{\n    assert(pArg->z <= p->z);\n    pArg->n = (int)(&p->z[p->n] - pArg->z);\n  }\n}\n\n/*\n** Invoke a virtual table constructor (either xCreate or xConnect). The\n** pointer to the function to invoke is passed as the fourth parameter\n** to this procedure.\n*/\nstatic int vtabCallConstructor(\n  sqlite3 *db, \n  Table *pTab,\n  Module *pMod,\n  int (*xConstruct)(sqlite3*,void*,int,const char*const*,sqlite3_vtab**,char**),\n  char **pzErr\n){\n  VtabCtx sCtx;\n  VTable *pVTable;\n  int rc;\n  const char *const*azArg = (const char *const*)pTab->azModuleArg;\n  int nArg = pTab->nModuleArg;\n  char *zErr = 0;\n  char *zModuleName;\n  int iDb;\n  VtabCtx *pCtx;\n\n  /* Check that the virtual-table is not already being initialized */\n  for(pCtx=db->pVtabCtx; pCtx; pCtx=pCtx->pPrior){\n    if( pCtx->pTab==pTab ){\n      *pzErr = sqlite3MPrintf(db, \n          \"vtable constructor called recursively: %s\", pTab->zName\n      );\n      return SQLITE_LOCKED;\n    }\n  }\n\n  zModuleName = sqlite3DbStrDup(db, pTab->zName);\n  if( !zModuleName ){\n    return SQLITE_NOMEM_BKPT;\n  }\n\n  pVTable = sqlite3MallocZero(sizeof(VTable));\n  if( !pVTable ){\n    sqlite3OomFault(db);\n    sqlite3DbFree(db, zModuleName);\n    return SQLITE_NOMEM_BKPT;\n  }\n  pVTable->db = db;\n  pVTable->pMod = pMod;\n\n  iDb = sqlite3SchemaToIndex(db, pTab->pSchema);\n  pTab->azModuleArg[1] = db->aDb[iDb].zDbSName;\n\n  /* Invoke the virtual table constructor */\n  assert( &db->pVtabCtx );\n  assert( xConstruct );\n  sCtx.pTab = pTab;\n  sCtx.pVTable = pVTable;\n  sCtx.pPrior = db->pVtabCtx;\n  sCtx.bDeclared = 0;\n  db->pVtabCtx = &sCtx;\n  rc = xConstruct(db, pMod->pAux, nArg, azArg, &pVTable->pVtab, &zErr);\n  db->pVtabCtx = sCtx.pPrior;\n  if( rc==SQLITE_NOMEM ) sqlite3OomFault(db);\n  assert( sCtx.pTab==pTab );\n\n  if( SQLITE_OK!=rc ){\n    if( zErr==0 ){\n      *pzErr = sqlite3MPrintf(db, \"vtable constructor failed: %s\", zModuleName);\n    }else {\n      *pzErr = sqlite3MPrintf(db, \"%s\", zErr);\n      sqlite3_free(zErr);\n    }\n    sqlite3DbFree(db, pVTable);\n  }else if( ALWAYS(pVTable->pVtab) ){\n    /* Justification of ALWAYS():  A correct vtab constructor must allocate\n    ** the sqlite3_vtab object if successful.  */\n    memset(pVTable->pVtab, 0, sizeof(pVTable->pVtab[0]));\n    pVTable->pVtab->pModule = pMod->pModule;\n    pVTable->nRef = 1;\n    if( sCtx.bDeclared==0 ){\n      const char *zFormat = \"vtable constructor did not declare schema: %s\";\n      *pzErr = sqlite3MPrintf(db, zFormat, pTab->zName);\n      sqlite3VtabUnlock(pVTable);\n      rc = SQLITE_ERROR;\n    }else{\n      int iCol;\n      u8 oooHidden = 0;\n      /* If everything went according to plan, link the new VTable structure\n      ** into the linked list headed by pTab->pVTable. Then loop through the \n      ** columns of the table to see if any of them contain the token \"hidden\".\n      ** If so, set the Column COLFLAG_HIDDEN flag and remove the token from\n      ** the type string.  */\n      pVTable->pNext = pTab->pVTable;\n      pTab->pVTable = pVTable;\n\n      for(iCol=0; iCol<pTab->nCol; iCol++){\n        char *zType = sqlite3ColumnType(&pTab->aCol[iCol], \"\");\n        int nType;\n        int i = 0;\n        nType = sqlite3Strlen30(zType);\n        for(i=0; i<nType; i++){\n          if( 0==sqlite3StrNICmp(\"hidden\", &zType[i], 6)\n           && (i==0 || zType[i-1]==' ')\n           && (zType[i+6]=='\\0' || zType[i+6]==' ')\n          ){\n            break;\n          }\n        }\n        if( i<nType ){\n          int j;\n          int nDel = 6 + (zType[i+6] ? 1 : 0);\n          for(j=i; (j+nDel)<=nType; j++){\n            zType[j] = zType[j+nDel];\n          }\n          if( zType[i]=='\\0' && i>0 ){\n            assert(zType[i-1]==' ');\n            zType[i-1] = '\\0';\n          }\n          pTab->aCol[iCol].colFlags |= COLFLAG_HIDDEN;\n          oooHidden = TF_OOOHidden;\n        }else{\n          pTab->tabFlags |= oooHidden;\n        }\n      }\n    }\n  }\n\n  sqlite3DbFree(db, zModuleName);\n  return rc;\n}\n\n/*\n** This function is invoked by the parser to call the xConnect() method\n** of the virtual table pTab. If an error occurs, an error code is returned \n** and an error left in pParse.\n**\n** This call is a no-op if table pTab is not a virtual table.\n*/\nSQLITE_PRIVATE int sqlite3VtabCallConnect(Parse *pParse, Table *pTab){\n  sqlite3 *db = pParse->db;\n  const char *zMod;\n  Module *pMod;\n  int rc;\n\n  assert( pTab );\n  if( !IsVirtual(pTab) || sqlite3GetVTable(db, pTab) ){\n    return SQLITE_OK;\n  }\n\n  /* Locate the required virtual table module */\n  zMod = pTab->azModuleArg[0];\n  pMod = (Module*)sqlite3HashFind(&db->aModule, zMod);\n\n  if( !pMod ){\n    const char *zModule = pTab->azModuleArg[0];\n    sqlite3ErrorMsg(pParse, \"no such module: %s\", zModule);\n    rc = SQLITE_ERROR;\n  }else{\n    char *zErr = 0;\n    rc = vtabCallConstructor(db, pTab, pMod, pMod->pModule->xConnect, &zErr);\n    if( rc!=SQLITE_OK ){\n      sqlite3ErrorMsg(pParse, \"%s\", zErr);\n      pParse->rc = rc;\n    }\n    sqlite3DbFree(db, zErr);\n  }\n\n  return rc;\n}\n/*\n** Grow the db->aVTrans[] array so that there is room for at least one\n** more v-table. Return SQLITE_NOMEM if a malloc fails, or SQLITE_OK otherwise.\n*/\nstatic int growVTrans(sqlite3 *db){\n  const int ARRAY_INCR = 5;\n\n  /* Grow the sqlite3.aVTrans array if required */\n  if( (db->nVTrans%ARRAY_INCR)==0 ){\n    VTable **aVTrans;\n    int nBytes = sizeof(sqlite3_vtab *) * (db->nVTrans + ARRAY_INCR);\n    aVTrans = sqlite3DbRealloc(db, (void *)db->aVTrans, nBytes);\n    if( !aVTrans ){\n      return SQLITE_NOMEM_BKPT;\n    }\n    memset(&aVTrans[db->nVTrans], 0, sizeof(sqlite3_vtab *)*ARRAY_INCR);\n    db->aVTrans = aVTrans;\n  }\n\n  return SQLITE_OK;\n}\n\n/*\n** Add the virtual table pVTab to the array sqlite3.aVTrans[]. Space should\n** have already been reserved using growVTrans().\n*/\nstatic void addToVTrans(sqlite3 *db, VTable *pVTab){\n  /* Add pVtab to the end of sqlite3.aVTrans */\n  db->aVTrans[db->nVTrans++] = pVTab;\n  sqlite3VtabLock(pVTab);\n}\n\n/*\n** This function is invoked by the vdbe to call the xCreate method\n** of the virtual table named zTab in database iDb. \n**\n** If an error occurs, *pzErr is set to point to an English language\n** description of the error and an SQLITE_XXX error code is returned.\n** In this case the caller must call sqlite3DbFree(db, ) on *pzErr.\n*/\nSQLITE_PRIVATE int sqlite3VtabCallCreate(sqlite3 *db, int iDb, const char *zTab, char **pzErr){\n  int rc = SQLITE_OK;\n  Table *pTab;\n  Module *pMod;\n  const char *zMod;\n\n  pTab = sqlite3FindTable(db, zTab, db->aDb[iDb].zDbSName);\n  assert( pTab && IsVirtual(pTab) && !pTab->pVTable );\n\n  /* Locate the required virtual table module */\n  zMod = pTab->azModuleArg[0];\n  pMod = (Module*)sqlite3HashFind(&db->aModule, zMod);\n\n  /* If the module has been registered and includes a Create method, \n  ** invoke it now. If the module has not been registered, return an \n  ** error. Otherwise, do nothing.\n  */\n  if( pMod==0 || pMod->pModule->xCreate==0 || pMod->pModule->xDestroy==0 ){\n    *pzErr = sqlite3MPrintf(db, \"no such module: %s\", zMod);\n    rc = SQLITE_ERROR;\n  }else{\n    rc = vtabCallConstructor(db, pTab, pMod, pMod->pModule->xCreate, pzErr);\n  }\n\n  /* Justification of ALWAYS():  The xConstructor method is required to\n  ** create a valid sqlite3_vtab if it returns SQLITE_OK. */\n  if( rc==SQLITE_OK && ALWAYS(sqlite3GetVTable(db, pTab)) ){\n    rc = growVTrans(db);\n    if( rc==SQLITE_OK ){\n      addToVTrans(db, sqlite3GetVTable(db, pTab));\n    }\n  }\n\n  return rc;\n}\n\n/*\n** This function is used to set the schema of a virtual table.  It is only\n** valid to call this function from within the xCreate() or xConnect() of a\n** virtual table module.\n*/\nSQLITE_API int sqlite3_declare_vtab(sqlite3 *db, const char *zCreateTable){\n  VtabCtx *pCtx;\n  int rc = SQLITE_OK;\n  Table *pTab;\n  char *zErr = 0;\n  Parse sParse;\n\n#ifdef SQLITE_ENABLE_API_ARMOR\n  if( !sqlite3SafetyCheckOk(db) || zCreateTable==0 ){\n    return SQLITE_MISUSE_BKPT;\n  }\n#endif\n  sqlite3_mutex_enter(db->mutex);\n  pCtx = db->pVtabCtx;\n  if( !pCtx || pCtx->bDeclared ){\n    sqlite3Error(db, SQLITE_MISUSE);\n    sqlite3_mutex_leave(db->mutex);\n    return SQLITE_MISUSE_BKPT;\n  }\n  pTab = pCtx->pTab;\n  assert( IsVirtual(pTab) );\n\n  memset(&sParse, 0, sizeof(sParse));\n  sParse.declareVtab = 1;\n  sParse.db = db;\n  sParse.nQueryLoop = 1;\n  if( SQLITE_OK==sqlite3RunParser(&sParse, zCreateTable, &zErr) \n   && sParse.pNewTable\n   && !db->mallocFailed\n   && !sParse.pNewTable->pSelect\n   && !IsVirtual(sParse.pNewTable)\n  ){\n    if( !pTab->aCol ){\n      Table *pNew = sParse.pNewTable;\n      Index *pIdx;\n      pTab->aCol = pNew->aCol;\n      pTab->nCol = pNew->nCol;\n      pTab->tabFlags |= pNew->tabFlags & (TF_WithoutRowid|TF_NoVisibleRowid);\n      pNew->nCol = 0;\n      pNew->aCol = 0;\n      assert( pTab->pIndex==0 );\n      assert( HasRowid(pNew) || sqlite3PrimaryKeyIndex(pNew)!=0 );\n      if( !HasRowid(pNew)\n       && pCtx->pVTable->pMod->pModule->xUpdate!=0\n       && sqlite3PrimaryKeyIndex(pNew)->nKeyCol!=1\n      ){\n        /* WITHOUT ROWID virtual tables must either be read-only (xUpdate==0)\n        ** or else must have a single-column PRIMARY KEY */\n        rc = SQLITE_ERROR;\n      }\n      pIdx = pNew->pIndex;\n      if( pIdx ){\n        assert( pIdx->pNext==0 );\n        pTab->pIndex = pIdx;\n        pNew->pIndex = 0;\n        pIdx->pTable = pTab;\n      }\n    }\n    pCtx->bDeclared = 1;\n  }else{\n    sqlite3ErrorWithMsg(db, SQLITE_ERROR, (zErr ? \"%s\" : 0), zErr);\n    sqlite3DbFree(db, zErr);\n    rc = SQLITE_ERROR;\n  }\n  sParse.declareVtab = 0;\n\n  if( sParse.pVdbe ){\n    sqlite3VdbeFinalize(sParse.pVdbe);\n  }\n  sqlite3DeleteTable(db, sParse.pNewTable);\n  sqlite3ParserReset(&sParse);\n\n  assert( (rc&0xff)==rc );\n  rc = sqlite3ApiExit(db, rc);\n  sqlite3_mutex_leave(db->mutex);\n  return rc;\n}\n\n/*\n** This function is invoked by the vdbe to call the xDestroy method\n** of the virtual table named zTab in database iDb. This occurs\n** when a DROP TABLE is mentioned.\n**\n** This call is a no-op if zTab is not a virtual table.\n*/\nSQLITE_PRIVATE int sqlite3VtabCallDestroy(sqlite3 *db, int iDb, const char *zTab){\n  int rc = SQLITE_OK;\n  Table *pTab;\n\n  pTab = sqlite3FindTable(db, zTab, db->aDb[iDb].zDbSName);\n  if( pTab!=0 && ALWAYS(pTab->pVTable!=0) ){\n    VTable *p;\n    int (*xDestroy)(sqlite3_vtab *);\n    for(p=pTab->pVTable; p; p=p->pNext){\n      assert( p->pVtab );\n      if( p->pVtab->nRef>0 ){\n        return SQLITE_LOCKED;\n      }\n    }\n    p = vtabDisconnectAll(db, pTab);\n    xDestroy = p->pMod->pModule->xDestroy;\n    assert( xDestroy!=0 );  /* Checked before the virtual table is created */\n    rc = xDestroy(p->pVtab);\n    /* Remove the sqlite3_vtab* from the aVTrans[] array, if applicable */\n    if( rc==SQLITE_OK ){\n      assert( pTab->pVTable==p && p->pNext==0 );\n      p->pVtab = 0;\n      pTab->pVTable = 0;\n      sqlite3VtabUnlock(p);\n    }\n  }\n\n  return rc;\n}\n\n/*\n** This function invokes either the xRollback or xCommit method\n** of each of the virtual tables in the sqlite3.aVTrans array. The method\n** called is identified by the second argument, \"offset\", which is\n** the offset of the method to call in the sqlite3_module structure.\n**\n** The array is cleared after invoking the callbacks. \n*/\nstatic void callFinaliser(sqlite3 *db, int offset){\n  int i;\n  if( db->aVTrans ){\n    VTable **aVTrans = db->aVTrans;\n    db->aVTrans = 0;\n    for(i=0; i<db->nVTrans; i++){\n      VTable *pVTab = aVTrans[i];\n      sqlite3_vtab *p = pVTab->pVtab;\n      if( p ){\n        int (*x)(sqlite3_vtab *);\n        x = *(int (**)(sqlite3_vtab *))((char *)p->pModule + offset);\n        if( x ) x(p);\n      }\n      pVTab->iSavepoint = 0;\n      sqlite3VtabUnlock(pVTab);\n    }\n    sqlite3DbFree(db, aVTrans);\n    db->nVTrans = 0;\n  }\n}\n\n/*\n** Invoke the xSync method of all virtual tables in the sqlite3.aVTrans\n** array. Return the error code for the first error that occurs, or\n** SQLITE_OK if all xSync operations are successful.\n**\n** If an error message is available, leave it in p->zErrMsg.\n*/\nSQLITE_PRIVATE int sqlite3VtabSync(sqlite3 *db, Vdbe *p){\n  int i;\n  int rc = SQLITE_OK;\n  VTable **aVTrans = db->aVTrans;\n\n  db->aVTrans = 0;\n  for(i=0; rc==SQLITE_OK && i<db->nVTrans; i++){\n    int (*x)(sqlite3_vtab *);\n    sqlite3_vtab *pVtab = aVTrans[i]->pVtab;\n    if( pVtab && (x = pVtab->pModule->xSync)!=0 ){\n      rc = x(pVtab);\n      sqlite3VtabImportErrmsg(p, pVtab);\n    }\n  }\n  db->aVTrans = aVTrans;\n  return rc;\n}\n\n/*\n** Invoke the xRollback method of all virtual tables in the \n** sqlite3.aVTrans array. Then clear the array itself.\n*/\nSQLITE_PRIVATE int sqlite3VtabRollback(sqlite3 *db){\n  callFinaliser(db, offsetof(sqlite3_module,xRollback));\n  return SQLITE_OK;\n}\n\n/*\n** Invoke the xCommit method of all virtual tables in the \n** sqlite3.aVTrans array. Then clear the array itself.\n*/\nSQLITE_PRIVATE int sqlite3VtabCommit(sqlite3 *db){\n  callFinaliser(db, offsetof(sqlite3_module,xCommit));\n  return SQLITE_OK;\n}\n\n/*\n** If the virtual table pVtab supports the transaction interface\n** (xBegin/xRollback/xCommit and optionally xSync) and a transaction is\n** not currently open, invoke the xBegin method now.\n**\n** If the xBegin call is successful, place the sqlite3_vtab pointer\n** in the sqlite3.aVTrans array.\n*/\nSQLITE_PRIVATE int sqlite3VtabBegin(sqlite3 *db, VTable *pVTab){\n  int rc = SQLITE_OK;\n  const sqlite3_module *pModule;\n\n  /* Special case: If db->aVTrans is NULL and db->nVTrans is greater\n  ** than zero, then this function is being called from within a\n  ** virtual module xSync() callback. It is illegal to write to \n  ** virtual module tables in this case, so return SQLITE_LOCKED.\n  */\n  if( sqlite3VtabInSync(db) ){\n    return SQLITE_LOCKED;\n  }\n  if( !pVTab ){\n    return SQLITE_OK;\n  } \n  pModule = pVTab->pVtab->pModule;\n\n  if( pModule->xBegin ){\n    int i;\n\n    /* If pVtab is already in the aVTrans array, return early */\n    for(i=0; i<db->nVTrans; i++){\n      if( db->aVTrans[i]==pVTab ){\n        return SQLITE_OK;\n      }\n    }\n\n    /* Invoke the xBegin method. If successful, add the vtab to the \n    ** sqlite3.aVTrans[] array. */\n    rc = growVTrans(db);\n    if( rc==SQLITE_OK ){\n      rc = pModule->xBegin(pVTab->pVtab);\n      if( rc==SQLITE_OK ){\n        int iSvpt = db->nStatement + db->nSavepoint;\n        addToVTrans(db, pVTab);\n        if( iSvpt && pModule->xSavepoint ){\n          pVTab->iSavepoint = iSvpt;\n          rc = pModule->xSavepoint(pVTab->pVtab, iSvpt-1);\n        }\n      }\n    }\n  }\n  return rc;\n}\n\n/*\n** Invoke either the xSavepoint, xRollbackTo or xRelease method of all\n** virtual tables that currently have an open transaction. Pass iSavepoint\n** as the second argument to the virtual table method invoked.\n**\n** If op is SAVEPOINT_BEGIN, the xSavepoint method is invoked. If it is\n** SAVEPOINT_ROLLBACK, the xRollbackTo method. Otherwise, if op is \n** SAVEPOINT_RELEASE, then the xRelease method of each virtual table with\n** an open transaction is invoked.\n**\n** If any virtual table method returns an error code other than SQLITE_OK, \n** processing is abandoned and the error returned to the caller of this\n** function immediately. If all calls to virtual table methods are successful,\n** SQLITE_OK is returned.\n*/\nSQLITE_PRIVATE int sqlite3VtabSavepoint(sqlite3 *db, int op, int iSavepoint){\n  int rc = SQLITE_OK;\n\n  assert( op==SAVEPOINT_RELEASE||op==SAVEPOINT_ROLLBACK||op==SAVEPOINT_BEGIN );\n  assert( iSavepoint>=-1 );\n  if( db->aVTrans ){\n    int i;\n    for(i=0; rc==SQLITE_OK && i<db->nVTrans; i++){\n      VTable *pVTab = db->aVTrans[i];\n      const sqlite3_module *pMod = pVTab->pMod->pModule;\n      if( pVTab->pVtab && pMod->iVersion>=2 ){\n        int (*xMethod)(sqlite3_vtab *, int);\n        switch( op ){\n          case SAVEPOINT_BEGIN:\n            xMethod = pMod->xSavepoint;\n            pVTab->iSavepoint = iSavepoint+1;\n            break;\n          case SAVEPOINT_ROLLBACK:\n            xMethod = pMod->xRollbackTo;\n            break;\n          default:\n            xMethod = pMod->xRelease;\n            break;\n        }\n        if( xMethod && pVTab->iSavepoint>iSavepoint ){\n          rc = xMethod(pVTab->pVtab, iSavepoint);\n        }\n      }\n    }\n  }\n  return rc;\n}\n\n/*\n** The first parameter (pDef) is a function implementation.  The\n** second parameter (pExpr) is the first argument to this function.\n** If pExpr is a column in a virtual table, then let the virtual\n** table implementation have an opportunity to overload the function.\n**\n** This routine is used to allow virtual table implementations to\n** overload MATCH, LIKE, GLOB, and REGEXP operators.\n**\n** Return either the pDef argument (indicating no change) or a \n** new FuncDef structure that is marked as ephemeral using the\n** SQLITE_FUNC_EPHEM flag.\n*/\nSQLITE_PRIVATE FuncDef *sqlite3VtabOverloadFunction(\n  sqlite3 *db,    /* Database connection for reporting malloc problems */\n  FuncDef *pDef,  /* Function to possibly overload */\n  int nArg,       /* Number of arguments to the function */\n  Expr *pExpr     /* First argument to the function */\n){\n  Table *pTab;\n  sqlite3_vtab *pVtab;\n  sqlite3_module *pMod;\n  void (*xSFunc)(sqlite3_context*,int,sqlite3_value**) = 0;\n  void *pArg = 0;\n  FuncDef *pNew;\n  int rc = 0;\n  char *zLowerName;\n  unsigned char *z;\n\n\n  /* Check to see the left operand is a column in a virtual table */\n  if( NEVER(pExpr==0) ) return pDef;\n  if( pExpr->op!=TK_COLUMN ) return pDef;\n  pTab = pExpr->pTab;\n  if( pTab==0 ) return pDef;\n  if( !IsVirtual(pTab) ) return pDef;\n  pVtab = sqlite3GetVTable(db, pTab)->pVtab;\n  assert( pVtab!=0 );\n  assert( pVtab->pModule!=0 );\n  pMod = (sqlite3_module *)pVtab->pModule;\n  if( pMod->xFindFunction==0 ) return pDef;\n \n  /* Call the xFindFunction method on the virtual table implementation\n  ** to see if the implementation wants to overload this function \n  */\n  zLowerName = sqlite3DbStrDup(db, pDef->zName);\n  if( zLowerName ){\n    for(z=(unsigned char*)zLowerName; *z; z++){\n      *z = sqlite3UpperToLower[*z];\n    }\n    rc = pMod->xFindFunction(pVtab, nArg, zLowerName, &xSFunc, &pArg);\n    sqlite3DbFree(db, zLowerName);\n  }\n  if( rc==0 ){\n    return pDef;\n  }\n\n  /* Create a new ephemeral function definition for the overloaded\n  ** function */\n  pNew = sqlite3DbMallocZero(db, sizeof(*pNew)\n                             + sqlite3Strlen30(pDef->zName) + 1);\n  if( pNew==0 ){\n    return pDef;\n  }\n  *pNew = *pDef;\n  pNew->zName = (const char*)&pNew[1];\n  memcpy((char*)&pNew[1], pDef->zName, sqlite3Strlen30(pDef->zName)+1);\n  pNew->xSFunc = xSFunc;\n  pNew->pUserData = pArg;\n  pNew->funcFlags |= SQLITE_FUNC_EPHEM;\n  return pNew;\n}\n\n/*\n** Make sure virtual table pTab is contained in the pParse->apVirtualLock[]\n** array so that an OP_VBegin will get generated for it.  Add pTab to the\n** array if it is missing.  If pTab is already in the array, this routine\n** is a no-op.\n*/\nSQLITE_PRIVATE void sqlite3VtabMakeWritable(Parse *pParse, Table *pTab){\n  Parse *pToplevel = sqlite3ParseToplevel(pParse);\n  int i, n;\n  Table **apVtabLock;\n\n  assert( IsVirtual(pTab) );\n  for(i=0; i<pToplevel->nVtabLock; i++){\n    if( pTab==pToplevel->apVtabLock[i] ) return;\n  }\n  n = (pToplevel->nVtabLock+1)*sizeof(pToplevel->apVtabLock[0]);\n  apVtabLock = sqlite3_realloc64(pToplevel->apVtabLock, n);\n  if( apVtabLock ){\n    pToplevel->apVtabLock = apVtabLock;\n    pToplevel->apVtabLock[pToplevel->nVtabLock++] = pTab;\n  }else{\n    sqlite3OomFault(pToplevel->db);\n  }\n}\n\n/*\n** Check to see if virtual table module pMod can be have an eponymous\n** virtual table instance.  If it can, create one if one does not already\n** exist. Return non-zero if the eponymous virtual table instance exists\n** when this routine returns, and return zero if it does not exist.\n**\n** An eponymous virtual table instance is one that is named after its\n** module, and more importantly, does not require a CREATE VIRTUAL TABLE\n** statement in order to come into existance.  Eponymous virtual table\n** instances always exist.  They cannot be DROP-ed.\n**\n** Any virtual table module for which xConnect and xCreate are the same\n** method can have an eponymous virtual table instance.\n*/\nSQLITE_PRIVATE int sqlite3VtabEponymousTableInit(Parse *pParse, Module *pMod){\n  const sqlite3_module *pModule = pMod->pModule;\n  Table *pTab;\n  char *zErr = 0;\n  int rc;\n  sqlite3 *db = pParse->db;\n  if( pMod->pEpoTab ) return 1;\n  if( pModule->xCreate!=0 && pModule->xCreate!=pModule->xConnect ) return 0;\n  pTab = sqlite3DbMallocZero(db, sizeof(Table));\n  if( pTab==0 ) return 0;\n  pTab->zName = sqlite3DbStrDup(db, pMod->zName);\n  if( pTab->zName==0 ){\n    sqlite3DbFree(db, pTab);\n    return 0;\n  }\n  pMod->pEpoTab = pTab;\n  pTab->nTabRef = 1;\n  pTab->pSchema = db->aDb[0].pSchema;\n  assert( pTab->nModuleArg==0 );\n  pTab->iPKey = -1;\n  addModuleArgument(db, pTab, sqlite3DbStrDup(db, pTab->zName));\n  addModuleArgument(db, pTab, 0);\n  addModuleArgument(db, pTab, sqlite3DbStrDup(db, pTab->zName));\n  rc = vtabCallConstructor(db, pTab, pMod, pModule->xConnect, &zErr);\n  if( rc ){\n    sqlite3ErrorMsg(pParse, \"%s\", zErr);\n    sqlite3DbFree(db, zErr);\n    sqlite3VtabEponymousTableClear(db, pMod);\n    return 0;\n  }\n  return 1;\n}\n\n/*\n** Erase the eponymous virtual table instance associated with\n** virtual table module pMod, if it exists.\n*/\nSQLITE_PRIVATE void sqlite3VtabEponymousTableClear(sqlite3 *db, Module *pMod){\n  Table *pTab = pMod->pEpoTab;\n  if( pTab!=0 ){\n    /* Mark the table as Ephemeral prior to deleting it, so that the\n    ** sqlite3DeleteTable() routine will know that it is not stored in \n    ** the schema. */\n    pTab->tabFlags |= TF_Ephemeral;\n    sqlite3DeleteTable(db, pTab);\n    pMod->pEpoTab = 0;\n  }\n}\n\n/*\n** Return the ON CONFLICT resolution mode in effect for the virtual\n** table update operation currently in progress.\n**\n** The results of this routine are undefined unless it is called from\n** within an xUpdate method.\n*/\nSQLITE_API int sqlite3_vtab_on_conflict(sqlite3 *db){\n  static const unsigned char aMap[] = { \n    SQLITE_ROLLBACK, SQLITE_ABORT, SQLITE_FAIL, SQLITE_IGNORE, SQLITE_REPLACE \n  };\n#ifdef SQLITE_ENABLE_API_ARMOR\n  if( !sqlite3SafetyCheckOk(db) ) return SQLITE_MISUSE_BKPT;\n#endif\n  assert( OE_Rollback==1 && OE_Abort==2 && OE_Fail==3 );\n  assert( OE_Ignore==4 && OE_Replace==5 );\n  assert( db->vtabOnConflict>=1 && db->vtabOnConflict<=5 );\n  return (int)aMap[db->vtabOnConflict-1];\n}\n\n/*\n** Call from within the xCreate() or xConnect() methods to provide \n** the SQLite core with additional information about the behavior\n** of the virtual table being implemented.\n*/\nSQLITE_API int sqlite3_vtab_config(sqlite3 *db, int op, ...){\n  va_list ap;\n  int rc = SQLITE_OK;\n\n#ifdef SQLITE_ENABLE_API_ARMOR\n  if( !sqlite3SafetyCheckOk(db) ) return SQLITE_MISUSE_BKPT;\n#endif\n  sqlite3_mutex_enter(db->mutex);\n  va_start(ap, op);\n  switch( op ){\n    case SQLITE_VTAB_CONSTRAINT_SUPPORT: {\n      VtabCtx *p = db->pVtabCtx;\n      if( !p ){\n        rc = SQLITE_MISUSE_BKPT;\n      }else{\n        assert( p->pTab==0 || IsVirtual(p->pTab) );\n        p->pVTable->bConstraint = (u8)va_arg(ap, int);\n      }\n      break;\n    }\n    default:\n      rc = SQLITE_MISUSE_BKPT;\n      break;\n  }\n  va_end(ap);\n\n  if( rc!=SQLITE_OK ) sqlite3Error(db, rc);\n  sqlite3_mutex_leave(db->mutex);\n  return rc;\n}\n\n#endif /* SQLITE_OMIT_VIRTUALTABLE */\n\n/************** End of vtab.c ************************************************/\n/************** Begin file wherecode.c ***************************************/\n/*\n** 2015-06-06\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n*************************************************************************\n** This module contains C code that generates VDBE code used to process\n** the WHERE clause of SQL statements.\n**\n** This file was split off from where.c on 2015-06-06 in order to reduce the\n** size of where.c and make it easier to edit.  This file contains the routines\n** that actually generate the bulk of the WHERE loop code.  The original where.c\n** file retains the code that does query planning and analysis.\n*/\n/* #include \"sqliteInt.h\" */\n/************** Include whereInt.h in the middle of wherecode.c **************/\n/************** Begin file whereInt.h ****************************************/\n/*\n** 2013-11-12\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n*************************************************************************\n**\n** This file contains structure and macro definitions for the query\n** planner logic in \"where.c\".  These definitions are broken out into\n** a separate source file for easier editing.\n*/\n\n/*\n** Trace output macros\n*/\n#if defined(SQLITE_TEST) || defined(SQLITE_DEBUG)\n/***/ int sqlite3WhereTrace;\n#endif\n#if defined(SQLITE_DEBUG) \\\n    && (defined(SQLITE_TEST) || defined(SQLITE_ENABLE_WHERETRACE))\n# define WHERETRACE(K,X)  if(sqlite3WhereTrace&(K)) sqlite3DebugPrintf X\n# define WHERETRACE_ENABLED 1\n#else\n# define WHERETRACE(K,X)\n#endif\n\n/* Forward references\n*/\ntypedef struct WhereClause WhereClause;\ntypedef struct WhereMaskSet WhereMaskSet;\ntypedef struct WhereOrInfo WhereOrInfo;\ntypedef struct WhereAndInfo WhereAndInfo;\ntypedef struct WhereLevel WhereLevel;\ntypedef struct WhereLoop WhereLoop;\ntypedef struct WherePath WherePath;\ntypedef struct WhereTerm WhereTerm;\ntypedef struct WhereLoopBuilder WhereLoopBuilder;\ntypedef struct WhereScan WhereScan;\ntypedef struct WhereOrCost WhereOrCost;\ntypedef struct WhereOrSet WhereOrSet;\n\n/*\n** This object contains information needed to implement a single nested\n** loop in WHERE clause.\n**\n** Contrast this object with WhereLoop.  This object describes the\n** implementation of the loop.  WhereLoop describes the algorithm.\n** This object contains a pointer to the WhereLoop algorithm as one of\n** its elements.\n**\n** The WhereInfo object contains a single instance of this object for\n** each term in the FROM clause (which is to say, for each of the\n** nested loops as implemented).  The order of WhereLevel objects determines\n** the loop nested order, with WhereInfo.a[0] being the outer loop and\n** WhereInfo.a[WhereInfo.nLevel-1] being the inner loop.\n*/\nstruct WhereLevel {\n  int iLeftJoin;        /* Memory cell used to implement LEFT OUTER JOIN */\n  int iTabCur;          /* The VDBE cursor used to access the table */\n  int iIdxCur;          /* The VDBE cursor used to access pIdx */\n  int addrBrk;          /* Jump here to break out of the loop */\n  int addrNxt;          /* Jump here to start the next IN combination */\n  int addrSkip;         /* Jump here for next iteration of skip-scan */\n  int addrCont;         /* Jump here to continue with the next loop cycle */\n  int addrFirst;        /* First instruction of interior of the loop */\n  int addrBody;         /* Beginning of the body of this loop */\n#ifndef SQLITE_LIKE_DOESNT_MATCH_BLOBS\n  u32 iLikeRepCntr;     /* LIKE range processing counter register (times 2) */\n  int addrLikeRep;      /* LIKE range processing address */\n#endif\n  u8 iFrom;             /* Which entry in the FROM clause */\n  u8 op, p3, p5;        /* Opcode, P3 & P5 of the opcode that ends the loop */\n  int p1, p2;           /* Operands of the opcode used to ends the loop */\n  union {               /* Information that depends on pWLoop->wsFlags */\n    struct {\n      int nIn;              /* Number of entries in aInLoop[] */\n      struct InLoop {\n        int iCur;              /* The VDBE cursor used by this IN operator */\n        int addrInTop;         /* Top of the IN loop */\n        u8 eEndLoopOp;         /* IN Loop terminator. OP_Next or OP_Prev */\n      } *aInLoop;           /* Information about each nested IN operator */\n    } in;                 /* Used when pWLoop->wsFlags&WHERE_IN_ABLE */\n    Index *pCovidx;       /* Possible covering index for WHERE_MULTI_OR */\n  } u;\n  struct WhereLoop *pWLoop;  /* The selected WhereLoop object */\n  Bitmask notReady;          /* FROM entries not usable at this level */\n#ifdef SQLITE_ENABLE_STMT_SCANSTATUS\n  int addrVisit;        /* Address at which row is visited */\n#endif\n};\n\n/*\n** Each instance of this object represents an algorithm for evaluating one\n** term of a join.  Every term of the FROM clause will have at least\n** one corresponding WhereLoop object (unless INDEXED BY constraints\n** prevent a query solution - which is an error) and many terms of the\n** FROM clause will have multiple WhereLoop objects, each describing a\n** potential way of implementing that FROM-clause term, together with\n** dependencies and cost estimates for using the chosen algorithm.\n**\n** Query planning consists of building up a collection of these WhereLoop\n** objects, then computing a particular sequence of WhereLoop objects, with\n** one WhereLoop object per FROM clause term, that satisfy all dependencies\n** and that minimize the overall cost.\n*/\nstruct WhereLoop {\n  Bitmask prereq;       /* Bitmask of other loops that must run first */\n  Bitmask maskSelf;     /* Bitmask identifying table iTab */\n#ifdef SQLITE_DEBUG\n  char cId;             /* Symbolic ID of this loop for debugging use */\n#endif\n  u8 iTab;              /* Position in FROM clause of table for this loop */\n  u8 iSortIdx;          /* Sorting index number.  0==None */\n  LogEst rSetup;        /* One-time setup cost (ex: create transient index) */\n  LogEst rRun;          /* Cost of running each loop */\n  LogEst nOut;          /* Estimated number of output rows */\n  union {\n    struct {               /* Information for internal btree tables */\n      u16 nEq;               /* Number of equality constraints */\n      u16 nBtm;              /* Size of BTM vector */\n      u16 nTop;              /* Size of TOP vector */\n      u16 nIdxCol;           /* Index column used for ORDER BY */\n      Index *pIndex;         /* Index used, or NULL */\n    } btree;\n    struct {               /* Information for virtual tables */\n      int idxNum;            /* Index number */\n      u8 needFree;           /* True if sqlite3_free(idxStr) is needed */\n      i8 isOrdered;          /* True if satisfies ORDER BY */\n      u16 omitMask;          /* Terms that may be omitted */\n      char *idxStr;          /* Index identifier string */\n    } vtab;\n  } u;\n  u32 wsFlags;          /* WHERE_* flags describing the plan */\n  u16 nLTerm;           /* Number of entries in aLTerm[] */\n  u16 nSkip;            /* Number of NULL aLTerm[] entries */\n  /**** whereLoopXfer() copies fields above ***********************/\n# define WHERE_LOOP_XFER_SZ offsetof(WhereLoop,nLSlot)\n  u16 nLSlot;           /* Number of slots allocated for aLTerm[] */\n  WhereTerm **aLTerm;   /* WhereTerms used */\n  WhereLoop *pNextLoop; /* Next WhereLoop object in the WhereClause */\n  WhereTerm *aLTermSpace[3];  /* Initial aLTerm[] space */\n};\n\n/* This object holds the prerequisites and the cost of running a\n** subquery on one operand of an OR operator in the WHERE clause.\n** See WhereOrSet for additional information \n*/\nstruct WhereOrCost {\n  Bitmask prereq;     /* Prerequisites */\n  LogEst rRun;        /* Cost of running this subquery */\n  LogEst nOut;        /* Number of outputs for this subquery */\n};\n\n/* The WhereOrSet object holds a set of possible WhereOrCosts that\n** correspond to the subquery(s) of OR-clause processing.  Only the\n** best N_OR_COST elements are retained.\n*/\n#define N_OR_COST 3\nstruct WhereOrSet {\n  u16 n;                      /* Number of valid a[] entries */\n  WhereOrCost a[N_OR_COST];   /* Set of best costs */\n};\n\n/*\n** Each instance of this object holds a sequence of WhereLoop objects\n** that implement some or all of a query plan.\n**\n** Think of each WhereLoop object as a node in a graph with arcs\n** showing dependencies and costs for travelling between nodes.  (That is\n** not a completely accurate description because WhereLoop costs are a\n** vector, not a scalar, and because dependencies are many-to-one, not\n** one-to-one as are graph nodes.  But it is a useful visualization aid.)\n** Then a WherePath object is a path through the graph that visits some\n** or all of the WhereLoop objects once.\n**\n** The \"solver\" works by creating the N best WherePath objects of length\n** 1.  Then using those as a basis to compute the N best WherePath objects\n** of length 2.  And so forth until the length of WherePaths equals the\n** number of nodes in the FROM clause.  The best (lowest cost) WherePath\n** at the end is the chosen query plan.\n*/\nstruct WherePath {\n  Bitmask maskLoop;     /* Bitmask of all WhereLoop objects in this path */\n  Bitmask revLoop;      /* aLoop[]s that should be reversed for ORDER BY */\n  LogEst nRow;          /* Estimated number of rows generated by this path */\n  LogEst rCost;         /* Total cost of this path */\n  LogEst rUnsorted;     /* Total cost of this path ignoring sorting costs */\n  i8 isOrdered;         /* No. of ORDER BY terms satisfied. -1 for unknown */\n  WhereLoop **aLoop;    /* Array of WhereLoop objects implementing this path */\n};\n\n/*\n** The query generator uses an array of instances of this structure to\n** help it analyze the subexpressions of the WHERE clause.  Each WHERE\n** clause subexpression is separated from the others by AND operators,\n** usually, or sometimes subexpressions separated by OR.\n**\n** All WhereTerms are collected into a single WhereClause structure.  \n** The following identity holds:\n**\n**        WhereTerm.pWC->a[WhereTerm.idx] == WhereTerm\n**\n** When a term is of the form:\n**\n**              X <op> <expr>\n**\n** where X is a column name and <op> is one of certain operators,\n** then WhereTerm.leftCursor and WhereTerm.u.leftColumn record the\n** cursor number and column number for X.  WhereTerm.eOperator records\n** the <op> using a bitmask encoding defined by WO_xxx below.  The\n** use of a bitmask encoding for the operator allows us to search\n** quickly for terms that match any of several different operators.\n**\n** A WhereTerm might also be two or more subterms connected by OR:\n**\n**         (t1.X <op> <expr>) OR (t1.Y <op> <expr>) OR ....\n**\n** In this second case, wtFlag has the TERM_ORINFO bit set and eOperator==WO_OR\n** and the WhereTerm.u.pOrInfo field points to auxiliary information that\n** is collected about the OR clause.\n**\n** If a term in the WHERE clause does not match either of the two previous\n** categories, then eOperator==0.  The WhereTerm.pExpr field is still set\n** to the original subexpression content and wtFlags is set up appropriately\n** but no other fields in the WhereTerm object are meaningful.\n**\n** When eOperator!=0, prereqRight and prereqAll record sets of cursor numbers,\n** but they do so indirectly.  A single WhereMaskSet structure translates\n** cursor number into bits and the translated bit is stored in the prereq\n** fields.  The translation is used in order to maximize the number of\n** bits that will fit in a Bitmask.  The VDBE cursor numbers might be\n** spread out over the non-negative integers.  For example, the cursor\n** numbers might be 3, 8, 9, 10, 20, 23, 41, and 45.  The WhereMaskSet\n** translates these sparse cursor numbers into consecutive integers\n** beginning with 0 in order to make the best possible use of the available\n** bits in the Bitmask.  So, in the example above, the cursor numbers\n** would be mapped into integers 0 through 7.\n**\n** The number of terms in a join is limited by the number of bits\n** in prereqRight and prereqAll.  The default is 64 bits, hence SQLite\n** is only able to process joins with 64 or fewer tables.\n*/\nstruct WhereTerm {\n  Expr *pExpr;            /* Pointer to the subexpression that is this term */\n  WhereClause *pWC;       /* The clause this term is part of */\n  LogEst truthProb;       /* Probability of truth for this expression */\n  u16 wtFlags;            /* TERM_xxx bit flags.  See below */\n  u16 eOperator;          /* A WO_xx value describing <op> */\n  u8 nChild;              /* Number of children that must disable us */\n  u8 eMatchOp;            /* Op for vtab MATCH/LIKE/GLOB/REGEXP terms */\n  int iParent;            /* Disable pWC->a[iParent] when this term disabled */\n  int leftCursor;         /* Cursor number of X in \"X <op> <expr>\" */\n  int iField;             /* Field in (?,?,?) IN (SELECT...) vector */\n  union {\n    int leftColumn;         /* Column number of X in \"X <op> <expr>\" */\n    WhereOrInfo *pOrInfo;   /* Extra information if (eOperator & WO_OR)!=0 */\n    WhereAndInfo *pAndInfo; /* Extra information if (eOperator& WO_AND)!=0 */\n  } u;\n  Bitmask prereqRight;    /* Bitmask of tables used by pExpr->pRight */\n  Bitmask prereqAll;      /* Bitmask of tables referenced by pExpr */\n};\n\n/*\n** Allowed values of WhereTerm.wtFlags\n*/\n#define TERM_DYNAMIC    0x01   /* Need to call sqlite3ExprDelete(db, pExpr) */\n#define TERM_VIRTUAL    0x02   /* Added by the optimizer.  Do not code */\n#define TERM_CODED      0x04   /* This term is already coded */\n#define TERM_COPIED     0x08   /* Has a child */\n#define TERM_ORINFO     0x10   /* Need to free the WhereTerm.u.pOrInfo object */\n#define TERM_ANDINFO    0x20   /* Need to free the WhereTerm.u.pAndInfo obj */\n#define TERM_OR_OK      0x40   /* Used during OR-clause processing */\n#ifdef SQLITE_ENABLE_STAT3_OR_STAT4\n#  define TERM_VNULL    0x80   /* Manufactured x>NULL or x<=NULL term */\n#else\n#  define TERM_VNULL    0x00   /* Disabled if not using stat3 */\n#endif\n#define TERM_LIKEOPT    0x100  /* Virtual terms from the LIKE optimization */\n#define TERM_LIKECOND   0x200  /* Conditionally this LIKE operator term */\n#define TERM_LIKE       0x400  /* The original LIKE operator */\n#define TERM_IS         0x800  /* Term.pExpr is an IS operator */\n#define TERM_VARSELECT  0x1000 /* Term.pExpr contains a correlated sub-query */\n\n/*\n** An instance of the WhereScan object is used as an iterator for locating\n** terms in the WHERE clause that are useful to the query planner.\n*/\nstruct WhereScan {\n  WhereClause *pOrigWC;      /* Original, innermost WhereClause */\n  WhereClause *pWC;          /* WhereClause currently being scanned */\n  const char *zCollName;     /* Required collating sequence, if not NULL */\n  Expr *pIdxExpr;            /* Search for this index expression */\n  char idxaff;               /* Must match this affinity, if zCollName!=NULL */\n  unsigned char nEquiv;      /* Number of entries in aEquiv[] */\n  unsigned char iEquiv;      /* Next unused slot in aEquiv[] */\n  u32 opMask;                /* Acceptable operators */\n  int k;                     /* Resume scanning at this->pWC->a[this->k] */\n  int aiCur[11];             /* Cursors in the equivalence class */\n  i16 aiColumn[11];          /* Corresponding column number in the eq-class */\n};\n\n/*\n** An instance of the following structure holds all information about a\n** WHERE clause.  Mostly this is a container for one or more WhereTerms.\n**\n** Explanation of pOuter:  For a WHERE clause of the form\n**\n**           a AND ((b AND c) OR (d AND e)) AND f\n**\n** There are separate WhereClause objects for the whole clause and for\n** the subclauses \"(b AND c)\" and \"(d AND e)\".  The pOuter field of the\n** subclauses points to the WhereClause object for the whole clause.\n*/\nstruct WhereClause {\n  WhereInfo *pWInfo;       /* WHERE clause processing context */\n  WhereClause *pOuter;     /* Outer conjunction */\n  u8 op;                   /* Split operator.  TK_AND or TK_OR */\n  int nTerm;               /* Number of terms */\n  int nSlot;               /* Number of entries in a[] */\n  WhereTerm *a;            /* Each a[] describes a term of the WHERE cluase */\n#if defined(SQLITE_SMALL_STACK)\n  WhereTerm aStatic[1];    /* Initial static space for a[] */\n#else\n  WhereTerm aStatic[8];    /* Initial static space for a[] */\n#endif\n};\n\n/*\n** A WhereTerm with eOperator==WO_OR has its u.pOrInfo pointer set to\n** a dynamically allocated instance of the following structure.\n*/\nstruct WhereOrInfo {\n  WhereClause wc;          /* Decomposition into subterms */\n  Bitmask indexable;       /* Bitmask of all indexable tables in the clause */\n};\n\n/*\n** A WhereTerm with eOperator==WO_AND has its u.pAndInfo pointer set to\n** a dynamically allocated instance of the following structure.\n*/\nstruct WhereAndInfo {\n  WhereClause wc;          /* The subexpression broken out */\n};\n\n/*\n** An instance of the following structure keeps track of a mapping\n** between VDBE cursor numbers and bits of the bitmasks in WhereTerm.\n**\n** The VDBE cursor numbers are small integers contained in \n** SrcList_item.iCursor and Expr.iTable fields.  For any given WHERE \n** clause, the cursor numbers might not begin with 0 and they might\n** contain gaps in the numbering sequence.  But we want to make maximum\n** use of the bits in our bitmasks.  This structure provides a mapping\n** from the sparse cursor numbers into consecutive integers beginning\n** with 0.\n**\n** If WhereMaskSet.ix[A]==B it means that The A-th bit of a Bitmask\n** corresponds VDBE cursor number B.  The A-th bit of a bitmask is 1<<A.\n**\n** For example, if the WHERE clause expression used these VDBE\n** cursors:  4, 5, 8, 29, 57, 73.  Then the  WhereMaskSet structure\n** would map those cursor numbers into bits 0 through 5.\n**\n** Note that the mapping is not necessarily ordered.  In the example\n** above, the mapping might go like this:  4->3, 5->1, 8->2, 29->0,\n** 57->5, 73->4.  Or one of 719 other combinations might be used. It\n** does not really matter.  What is important is that sparse cursor\n** numbers all get mapped into bit numbers that begin with 0 and contain\n** no gaps.\n*/\nstruct WhereMaskSet {\n  int bVarSelect;               /* Used by sqlite3WhereExprUsage() */\n  int n;                        /* Number of assigned cursor values */\n  int ix[BMS];                  /* Cursor assigned to each bit */\n};\n\n/*\n** Initialize a WhereMaskSet object\n*/\n#define initMaskSet(P)  (P)->n=0\n\n/*\n** This object is a convenience wrapper holding all information needed\n** to construct WhereLoop objects for a particular query.\n*/\nstruct WhereLoopBuilder {\n  WhereInfo *pWInfo;        /* Information about this WHERE */\n  WhereClause *pWC;         /* WHERE clause terms */\n  ExprList *pOrderBy;       /* ORDER BY clause */\n  WhereLoop *pNew;          /* Template WhereLoop */\n  WhereOrSet *pOrSet;       /* Record best loops here, if not NULL */\n#ifdef SQLITE_ENABLE_STAT3_OR_STAT4\n  UnpackedRecord *pRec;     /* Probe for stat4 (if required) */\n  int nRecValid;            /* Number of valid fields currently in pRec */\n#endif\n  unsigned int bldFlags;    /* SQLITE_BLDF_* flags */\n};\n\n/* Allowed values for WhereLoopBuider.bldFlags */\n#define SQLITE_BLDF_INDEXED  0x0001   /* An index is used */\n#define SQLITE_BLDF_UNIQUE   0x0002   /* All keys of a UNIQUE index used */\n\n/*\n** The WHERE clause processing routine has two halves.  The\n** first part does the start of the WHERE loop and the second\n** half does the tail of the WHERE loop.  An instance of\n** this structure is returned by the first half and passed\n** into the second half to give some continuity.\n**\n** An instance of this object holds the complete state of the query\n** planner.\n*/\nstruct WhereInfo {\n  Parse *pParse;            /* Parsing and code generating context */\n  SrcList *pTabList;        /* List of tables in the join */\n  ExprList *pOrderBy;       /* The ORDER BY clause or NULL */\n  ExprList *pResultSet;     /* Result set of the query */\n  Expr *pWhere;             /* The complete WHERE clause */\n  LogEst iLimit;            /* LIMIT if wctrlFlags has WHERE_USE_LIMIT */\n  int aiCurOnePass[2];      /* OP_OpenWrite cursors for the ONEPASS opt */\n  int iContinue;            /* Jump here to continue with next record */\n  int iBreak;               /* Jump here to break out of the loop */\n  int savedNQueryLoop;      /* pParse->nQueryLoop outside the WHERE loop */\n  u16 wctrlFlags;           /* Flags originally passed to sqlite3WhereBegin() */\n  u8 nLevel;                /* Number of nested loop */\n  i8 nOBSat;                /* Number of ORDER BY terms satisfied by indices */\n  u8 sorted;                /* True if really sorted (not just grouped) */\n  u8 eOnePass;              /* ONEPASS_OFF, or _SINGLE, or _MULTI */\n  u8 untestedTerms;         /* Not all WHERE terms resolved by outer loop */\n  u8 eDistinct;             /* One of the WHERE_DISTINCT_* values */\n  u8 bOrderedInnerLoop;     /* True if only the inner-most loop is ordered */\n  int iTop;                 /* The very beginning of the WHERE loop */\n  WhereLoop *pLoops;        /* List of all WhereLoop objects */\n  Bitmask revMask;          /* Mask of ORDER BY terms that need reversing */\n  LogEst nRowOut;           /* Estimated number of output rows */\n  WhereClause sWC;          /* Decomposition of the WHERE clause */\n  WhereMaskSet sMaskSet;    /* Map cursor numbers to bitmasks */\n  WhereLevel a[1];          /* Information about each nest loop in WHERE */\n};\n\n/*\n** Private interfaces - callable only by other where.c routines.\n**\n** where.c:\n*/\nSQLITE_PRIVATE Bitmask sqlite3WhereGetMask(WhereMaskSet*,int);\n#ifdef WHERETRACE_ENABLED\nSQLITE_PRIVATE void sqlite3WhereClausePrint(WhereClause *pWC);\n#endif\nSQLITE_PRIVATE WhereTerm *sqlite3WhereFindTerm(\n  WhereClause *pWC,     /* The WHERE clause to be searched */\n  int iCur,             /* Cursor number of LHS */\n  int iColumn,          /* Column number of LHS */\n  Bitmask notReady,     /* RHS must not overlap with this mask */\n  u32 op,               /* Mask of WO_xx values describing operator */\n  Index *pIdx           /* Must be compatible with this index, if not NULL */\n);\n\n/* wherecode.c: */\n#ifndef SQLITE_OMIT_EXPLAIN\nSQLITE_PRIVATE int sqlite3WhereExplainOneScan(\n  Parse *pParse,                  /* Parse context */\n  SrcList *pTabList,              /* Table list this loop refers to */\n  WhereLevel *pLevel,             /* Scan to write OP_Explain opcode for */\n  int iLevel,                     /* Value for \"level\" column of output */\n  int iFrom,                      /* Value for \"from\" column of output */\n  u16 wctrlFlags                  /* Flags passed to sqlite3WhereBegin() */\n);\n#else\n# define sqlite3WhereExplainOneScan(u,v,w,x,y,z) 0\n#endif /* SQLITE_OMIT_EXPLAIN */\n#ifdef SQLITE_ENABLE_STMT_SCANSTATUS\nSQLITE_PRIVATE void sqlite3WhereAddScanStatus(\n  Vdbe *v,                        /* Vdbe to add scanstatus entry to */\n  SrcList *pSrclist,              /* FROM clause pLvl reads data from */\n  WhereLevel *pLvl,               /* Level to add scanstatus() entry for */\n  int addrExplain                 /* Address of OP_Explain (or 0) */\n);\n#else\n# define sqlite3WhereAddScanStatus(a, b, c, d) ((void)d)\n#endif\nSQLITE_PRIVATE Bitmask sqlite3WhereCodeOneLoopStart(\n  WhereInfo *pWInfo,   /* Complete information about the WHERE clause */\n  int iLevel,          /* Which level of pWInfo->a[] should be coded */\n  Bitmask notReady     /* Which tables are currently available */\n);\n\n/* whereexpr.c: */\nSQLITE_PRIVATE void sqlite3WhereClauseInit(WhereClause*,WhereInfo*);\nSQLITE_PRIVATE void sqlite3WhereClauseClear(WhereClause*);\nSQLITE_PRIVATE void sqlite3WhereSplit(WhereClause*,Expr*,u8);\nSQLITE_PRIVATE Bitmask sqlite3WhereExprUsage(WhereMaskSet*, Expr*);\nSQLITE_PRIVATE Bitmask sqlite3WhereExprListUsage(WhereMaskSet*, ExprList*);\nSQLITE_PRIVATE void sqlite3WhereExprAnalyze(SrcList*, WhereClause*);\nSQLITE_PRIVATE void sqlite3WhereTabFuncArgs(Parse*, struct SrcList_item*, WhereClause*);\n\n\n\n\n\n/*\n** Bitmasks for the operators on WhereTerm objects.  These are all\n** operators that are of interest to the query planner.  An\n** OR-ed combination of these values can be used when searching for\n** particular WhereTerms within a WhereClause.\n**\n** Value constraints:\n**     WO_EQ    == SQLITE_INDEX_CONSTRAINT_EQ\n**     WO_LT    == SQLITE_INDEX_CONSTRAINT_LT\n**     WO_LE    == SQLITE_INDEX_CONSTRAINT_LE\n**     WO_GT    == SQLITE_INDEX_CONSTRAINT_GT\n**     WO_GE    == SQLITE_INDEX_CONSTRAINT_GE\n*/\n#define WO_IN     0x0001\n#define WO_EQ     0x0002\n#define WO_LT     (WO_EQ<<(TK_LT-TK_EQ))\n#define WO_LE     (WO_EQ<<(TK_LE-TK_EQ))\n#define WO_GT     (WO_EQ<<(TK_GT-TK_EQ))\n#define WO_GE     (WO_EQ<<(TK_GE-TK_EQ))\n#define WO_AUX    0x0040       /* Op useful to virtual tables only */\n#define WO_IS     0x0080\n#define WO_ISNULL 0x0100\n#define WO_OR     0x0200       /* Two or more OR-connected terms */\n#define WO_AND    0x0400       /* Two or more AND-connected terms */\n#define WO_EQUIV  0x0800       /* Of the form A==B, both columns */\n#define WO_NOOP   0x1000       /* This term does not restrict search space */\n\n#define WO_ALL    0x1fff       /* Mask of all possible WO_* values */\n#define WO_SINGLE 0x01ff       /* Mask of all non-compound WO_* values */\n\n/*\n** These are definitions of bits in the WhereLoop.wsFlags field.\n** The particular combination of bits in each WhereLoop help to\n** determine the algorithm that WhereLoop represents.\n*/\n#define WHERE_COLUMN_EQ    0x00000001  /* x=EXPR */\n#define WHERE_COLUMN_RANGE 0x00000002  /* x<EXPR and/or x>EXPR */\n#define WHERE_COLUMN_IN    0x00000004  /* x IN (...) */\n#define WHERE_COLUMN_NULL  0x00000008  /* x IS NULL */\n#define WHERE_CONSTRAINT   0x0000000f  /* Any of the WHERE_COLUMN_xxx values */\n#define WHERE_TOP_LIMIT    0x00000010  /* x<EXPR or x<=EXPR constraint */\n#define WHERE_BTM_LIMIT    0x00000020  /* x>EXPR or x>=EXPR constraint */\n#define WHERE_BOTH_LIMIT   0x00000030  /* Both x>EXPR and x<EXPR */\n#define WHERE_IDX_ONLY     0x00000040  /* Use index only - omit table */\n#define WHERE_IPK          0x00000100  /* x is the INTEGER PRIMARY KEY */\n#define WHERE_INDEXED      0x00000200  /* WhereLoop.u.btree.pIndex is valid */\n#define WHERE_VIRTUALTABLE 0x00000400  /* WhereLoop.u.vtab is valid */\n#define WHERE_IN_ABLE      0x00000800  /* Able to support an IN operator */\n#define WHERE_ONEROW       0x00001000  /* Selects no more than one row */\n#define WHERE_MULTI_OR     0x00002000  /* OR using multiple indices */\n#define WHERE_AUTO_INDEX   0x00004000  /* Uses an ephemeral index */\n#define WHERE_SKIPSCAN     0x00008000  /* Uses the skip-scan algorithm */\n#define WHERE_UNQ_WANTED   0x00010000  /* WHERE_ONEROW would have been helpful*/\n#define WHERE_PARTIALIDX   0x00020000  /* The automatic index is partial */\n\n/************** End of whereInt.h ********************************************/\n/************** Continuing where we left off in wherecode.c ******************/\n\n#ifndef SQLITE_OMIT_EXPLAIN\n\n/*\n** Return the name of the i-th column of the pIdx index.\n*/\nstatic const char *explainIndexColumnName(Index *pIdx, int i){\n  i = pIdx->aiColumn[i];\n  if( i==XN_EXPR ) return \"<expr>\";\n  if( i==XN_ROWID ) return \"rowid\";\n  return pIdx->pTable->aCol[i].zName;\n}\n\n/*\n** This routine is a helper for explainIndexRange() below\n**\n** pStr holds the text of an expression that we are building up one term\n** at a time.  This routine adds a new term to the end of the expression.\n** Terms are separated by AND so add the \"AND\" text for second and subsequent\n** terms only.\n*/\nstatic void explainAppendTerm(\n  StrAccum *pStr,             /* The text expression being built */\n  Index *pIdx,                /* Index to read column names from */\n  int nTerm,                  /* Number of terms */\n  int iTerm,                  /* Zero-based index of first term. */\n  int bAnd,                   /* Non-zero to append \" AND \" */\n  const char *zOp             /* Name of the operator */\n){\n  int i;\n\n  assert( nTerm>=1 );\n  if( bAnd ) sqlite3StrAccumAppend(pStr, \" AND \", 5);\n\n  if( nTerm>1 ) sqlite3StrAccumAppend(pStr, \"(\", 1);\n  for(i=0; i<nTerm; i++){\n    if( i ) sqlite3StrAccumAppend(pStr, \",\", 1);\n    sqlite3StrAccumAppendAll(pStr, explainIndexColumnName(pIdx, iTerm+i));\n  }\n  if( nTerm>1 ) sqlite3StrAccumAppend(pStr, \")\", 1);\n\n  sqlite3StrAccumAppend(pStr, zOp, 1);\n\n  if( nTerm>1 ) sqlite3StrAccumAppend(pStr, \"(\", 1);\n  for(i=0; i<nTerm; i++){\n    if( i ) sqlite3StrAccumAppend(pStr, \",\", 1);\n    sqlite3StrAccumAppend(pStr, \"?\", 1);\n  }\n  if( nTerm>1 ) sqlite3StrAccumAppend(pStr, \")\", 1);\n}\n\n/*\n** Argument pLevel describes a strategy for scanning table pTab. This \n** function appends text to pStr that describes the subset of table\n** rows scanned by the strategy in the form of an SQL expression.\n**\n** For example, if the query:\n**\n**   SELECT * FROM t1 WHERE a=1 AND b>2;\n**\n** is run and there is an index on (a, b), then this function returns a\n** string similar to:\n**\n**   \"a=? AND b>?\"\n*/\nstatic void explainIndexRange(StrAccum *pStr, WhereLoop *pLoop){\n  Index *pIndex = pLoop->u.btree.pIndex;\n  u16 nEq = pLoop->u.btree.nEq;\n  u16 nSkip = pLoop->nSkip;\n  int i, j;\n\n  if( nEq==0 && (pLoop->wsFlags&(WHERE_BTM_LIMIT|WHERE_TOP_LIMIT))==0 ) return;\n  sqlite3StrAccumAppend(pStr, \" (\", 2);\n  for(i=0; i<nEq; i++){\n    const char *z = explainIndexColumnName(pIndex, i);\n    if( i ) sqlite3StrAccumAppend(pStr, \" AND \", 5);\n    sqlite3XPrintf(pStr, i>=nSkip ? \"%s=?\" : \"ANY(%s)\", z);\n  }\n\n  j = i;\n  if( pLoop->wsFlags&WHERE_BTM_LIMIT ){\n    explainAppendTerm(pStr, pIndex, pLoop->u.btree.nBtm, j, i, \">\");\n    i = 1;\n  }\n  if( pLoop->wsFlags&WHERE_TOP_LIMIT ){\n    explainAppendTerm(pStr, pIndex, pLoop->u.btree.nTop, j, i, \"<\");\n  }\n  sqlite3StrAccumAppend(pStr, \")\", 1);\n}\n\n/*\n** This function is a no-op unless currently processing an EXPLAIN QUERY PLAN\n** command, or if either SQLITE_DEBUG or SQLITE_ENABLE_STMT_SCANSTATUS was\n** defined at compile-time. If it is not a no-op, a single OP_Explain opcode \n** is added to the output to describe the table scan strategy in pLevel.\n**\n** If an OP_Explain opcode is added to the VM, its address is returned.\n** Otherwise, if no OP_Explain is coded, zero is returned.\n*/\nSQLITE_PRIVATE int sqlite3WhereExplainOneScan(\n  Parse *pParse,                  /* Parse context */\n  SrcList *pTabList,              /* Table list this loop refers to */\n  WhereLevel *pLevel,             /* Scan to write OP_Explain opcode for */\n  int iLevel,                     /* Value for \"level\" column of output */\n  int iFrom,                      /* Value for \"from\" column of output */\n  u16 wctrlFlags                  /* Flags passed to sqlite3WhereBegin() */\n){\n  int ret = 0;\n#if !defined(SQLITE_DEBUG) && !defined(SQLITE_ENABLE_STMT_SCANSTATUS)\n  if( sqlite3ParseToplevel(pParse)->explain==2 )\n#endif\n  {\n    struct SrcList_item *pItem = &pTabList->a[pLevel->iFrom];\n    Vdbe *v = pParse->pVdbe;      /* VM being constructed */\n    sqlite3 *db = pParse->db;     /* Database handle */\n    int iId = pParse->iSelectId;  /* Select id (left-most output column) */\n    int isSearch;                 /* True for a SEARCH. False for SCAN. */\n    WhereLoop *pLoop;             /* The controlling WhereLoop object */\n    u32 flags;                    /* Flags that describe this loop */\n    char *zMsg;                   /* Text to add to EQP output */\n    StrAccum str;                 /* EQP output string */\n    char zBuf[100];               /* Initial space for EQP output string */\n\n    pLoop = pLevel->pWLoop;\n    flags = pLoop->wsFlags;\n    if( (flags&WHERE_MULTI_OR) || (wctrlFlags&WHERE_OR_SUBCLAUSE) ) return 0;\n\n    isSearch = (flags&(WHERE_BTM_LIMIT|WHERE_TOP_LIMIT))!=0\n            || ((flags&WHERE_VIRTUALTABLE)==0 && (pLoop->u.btree.nEq>0))\n            || (wctrlFlags&(WHERE_ORDERBY_MIN|WHERE_ORDERBY_MAX));\n\n    sqlite3StrAccumInit(&str, db, zBuf, sizeof(zBuf), SQLITE_MAX_LENGTH);\n    sqlite3StrAccumAppendAll(&str, isSearch ? \"SEARCH\" : \"SCAN\");\n    if( pItem->pSelect ){\n      sqlite3XPrintf(&str, \" SUBQUERY %d\", pItem->iSelectId);\n    }else{\n      sqlite3XPrintf(&str, \" TABLE %s\", pItem->zName);\n    }\n\n    if( pItem->zAlias ){\n      sqlite3XPrintf(&str, \" AS %s\", pItem->zAlias);\n    }\n    if( (flags & (WHERE_IPK|WHERE_VIRTUALTABLE))==0 ){\n      const char *zFmt = 0;\n      Index *pIdx;\n\n      assert( pLoop->u.btree.pIndex!=0 );\n      pIdx = pLoop->u.btree.pIndex;\n      assert( !(flags&WHERE_AUTO_INDEX) || (flags&WHERE_IDX_ONLY) );\n      if( !HasRowid(pItem->pTab) && IsPrimaryKeyIndex(pIdx) ){\n        if( isSearch ){\n          zFmt = \"PRIMARY KEY\";\n        }\n      }else if( flags & WHERE_PARTIALIDX ){\n        zFmt = \"AUTOMATIC PARTIAL COVERING INDEX\";\n      }else if( flags & WHERE_AUTO_INDEX ){\n        zFmt = \"AUTOMATIC COVERING INDEX\";\n      }else if( flags & WHERE_IDX_ONLY ){\n        zFmt = \"COVERING INDEX %s\";\n      }else{\n        zFmt = \"INDEX %s\";\n      }\n      if( zFmt ){\n        sqlite3StrAccumAppend(&str, \" USING \", 7);\n        sqlite3XPrintf(&str, zFmt, pIdx->zName);\n        explainIndexRange(&str, pLoop);\n      }\n    }else if( (flags & WHERE_IPK)!=0 && (flags & WHERE_CONSTRAINT)!=0 ){\n      const char *zRangeOp;\n      if( flags&(WHERE_COLUMN_EQ|WHERE_COLUMN_IN) ){\n        zRangeOp = \"=\";\n      }else if( (flags&WHERE_BOTH_LIMIT)==WHERE_BOTH_LIMIT ){\n        zRangeOp = \">? AND rowid<\";\n      }else if( flags&WHERE_BTM_LIMIT ){\n        zRangeOp = \">\";\n      }else{\n        assert( flags&WHERE_TOP_LIMIT);\n        zRangeOp = \"<\";\n      }\n      sqlite3XPrintf(&str, \" USING INTEGER PRIMARY KEY (rowid%s?)\",zRangeOp);\n    }\n#ifndef SQLITE_OMIT_VIRTUALTABLE\n    else if( (flags & WHERE_VIRTUALTABLE)!=0 ){\n      sqlite3XPrintf(&str, \" VIRTUAL TABLE INDEX %d:%s\",\n                  pLoop->u.vtab.idxNum, pLoop->u.vtab.idxStr);\n    }\n#endif\n#ifdef SQLITE_EXPLAIN_ESTIMATED_ROWS\n    if( pLoop->nOut>=10 ){\n      sqlite3XPrintf(&str, \" (~%llu rows)\", sqlite3LogEstToInt(pLoop->nOut));\n    }else{\n      sqlite3StrAccumAppend(&str, \" (~1 row)\", 9);\n    }\n#endif\n    zMsg = sqlite3StrAccumFinish(&str);\n    ret = sqlite3VdbeAddOp4(v, OP_Explain, iId, iLevel, iFrom, zMsg,P4_DYNAMIC);\n  }\n  return ret;\n}\n#endif /* SQLITE_OMIT_EXPLAIN */\n\n#ifdef SQLITE_ENABLE_STMT_SCANSTATUS\n/*\n** Configure the VM passed as the first argument with an\n** sqlite3_stmt_scanstatus() entry corresponding to the scan used to \n** implement level pLvl. Argument pSrclist is a pointer to the FROM \n** clause that the scan reads data from.\n**\n** If argument addrExplain is not 0, it must be the address of an \n** OP_Explain instruction that describes the same loop.\n*/\nSQLITE_PRIVATE void sqlite3WhereAddScanStatus(\n  Vdbe *v,                        /* Vdbe to add scanstatus entry to */\n  SrcList *pSrclist,              /* FROM clause pLvl reads data from */\n  WhereLevel *pLvl,               /* Level to add scanstatus() entry for */\n  int addrExplain                 /* Address of OP_Explain (or 0) */\n){\n  const char *zObj = 0;\n  WhereLoop *pLoop = pLvl->pWLoop;\n  if( (pLoop->wsFlags & WHERE_VIRTUALTABLE)==0  &&  pLoop->u.btree.pIndex!=0 ){\n    zObj = pLoop->u.btree.pIndex->zName;\n  }else{\n    zObj = pSrclist->a[pLvl->iFrom].zName;\n  }\n  sqlite3VdbeScanStatus(\n      v, addrExplain, pLvl->addrBody, pLvl->addrVisit, pLoop->nOut, zObj\n  );\n}\n#endif\n\n\n/*\n** Disable a term in the WHERE clause.  Except, do not disable the term\n** if it controls a LEFT OUTER JOIN and it did not originate in the ON\n** or USING clause of that join.\n**\n** Consider the term t2.z='ok' in the following queries:\n**\n**   (1)  SELECT * FROM t1 LEFT JOIN t2 ON t1.a=t2.x WHERE t2.z='ok'\n**   (2)  SELECT * FROM t1 LEFT JOIN t2 ON t1.a=t2.x AND t2.z='ok'\n**   (3)  SELECT * FROM t1, t2 WHERE t1.a=t2.x AND t2.z='ok'\n**\n** The t2.z='ok' is disabled in the in (2) because it originates\n** in the ON clause.  The term is disabled in (3) because it is not part\n** of a LEFT OUTER JOIN.  In (1), the term is not disabled.\n**\n** Disabling a term causes that term to not be tested in the inner loop\n** of the join.  Disabling is an optimization.  When terms are satisfied\n** by indices, we disable them to prevent redundant tests in the inner\n** loop.  We would get the correct results if nothing were ever disabled,\n** but joins might run a little slower.  The trick is to disable as much\n** as we can without disabling too much.  If we disabled in (1), we'd get\n** the wrong answer.  See ticket #813.\n**\n** If all the children of a term are disabled, then that term is also\n** automatically disabled.  In this way, terms get disabled if derived\n** virtual terms are tested first.  For example:\n**\n**      x GLOB 'abc*' AND x>='abc' AND x<'acd'\n**      \\___________/     \\______/     \\_____/\n**         parent          child1       child2\n**\n** Only the parent term was in the original WHERE clause.  The child1\n** and child2 terms were added by the LIKE optimization.  If both of\n** the virtual child terms are valid, then testing of the parent can be \n** skipped.\n**\n** Usually the parent term is marked as TERM_CODED.  But if the parent\n** term was originally TERM_LIKE, then the parent gets TERM_LIKECOND instead.\n** The TERM_LIKECOND marking indicates that the term should be coded inside\n** a conditional such that is only evaluated on the second pass of a\n** LIKE-optimization loop, when scanning BLOBs instead of strings.\n*/\nstatic void disableTerm(WhereLevel *pLevel, WhereTerm *pTerm){\n  int nLoop = 0;\n  assert( pTerm!=0 );\n  while( (pTerm->wtFlags & TERM_CODED)==0\n      && (pLevel->iLeftJoin==0 || ExprHasProperty(pTerm->pExpr, EP_FromJoin))\n      && (pLevel->notReady & pTerm->prereqAll)==0\n  ){\n    if( nLoop && (pTerm->wtFlags & TERM_LIKE)!=0 ){\n      pTerm->wtFlags |= TERM_LIKECOND;\n    }else{\n      pTerm->wtFlags |= TERM_CODED;\n    }\n    if( pTerm->iParent<0 ) break;\n    pTerm = &pTerm->pWC->a[pTerm->iParent];\n    assert( pTerm!=0 );\n    pTerm->nChild--;\n    if( pTerm->nChild!=0 ) break;\n    nLoop++;\n  }\n}\n\n/*\n** Code an OP_Affinity opcode to apply the column affinity string zAff\n** to the n registers starting at base. \n**\n** As an optimization, SQLITE_AFF_BLOB entries (which are no-ops) at the\n** beginning and end of zAff are ignored.  If all entries in zAff are\n** SQLITE_AFF_BLOB, then no code gets generated.\n**\n** This routine makes its own copy of zAff so that the caller is free\n** to modify zAff after this routine returns.\n*/\nstatic void codeApplyAffinity(Parse *pParse, int base, int n, char *zAff){\n  Vdbe *v = pParse->pVdbe;\n  if( zAff==0 ){\n    assert( pParse->db->mallocFailed );\n    return;\n  }\n  assert( v!=0 );\n\n  /* Adjust base and n to skip over SQLITE_AFF_BLOB entries at the beginning\n  ** and end of the affinity string.\n  */\n  while( n>0 && zAff[0]==SQLITE_AFF_BLOB ){\n    n--;\n    base++;\n    zAff++;\n  }\n  while( n>1 && zAff[n-1]==SQLITE_AFF_BLOB ){\n    n--;\n  }\n\n  /* Code the OP_Affinity opcode if there is anything left to do. */\n  if( n>0 ){\n    sqlite3VdbeAddOp4(v, OP_Affinity, base, n, 0, zAff, n);\n    sqlite3ExprCacheAffinityChange(pParse, base, n);\n  }\n}\n\n/*\n** Expression pRight, which is the RHS of a comparison operation, is \n** either a vector of n elements or, if n==1, a scalar expression.\n** Before the comparison operation, affinity zAff is to be applied\n** to the pRight values. This function modifies characters within the\n** affinity string to SQLITE_AFF_BLOB if either:\n**\n**   * the comparison will be performed with no affinity, or\n**   * the affinity change in zAff is guaranteed not to change the value.\n*/\nstatic void updateRangeAffinityStr(\n  Expr *pRight,                   /* RHS of comparison */\n  int n,                          /* Number of vector elements in comparison */\n  char *zAff                      /* Affinity string to modify */\n){\n  int i;\n  for(i=0; i<n; i++){\n    Expr *p = sqlite3VectorFieldSubexpr(pRight, i);\n    if( sqlite3CompareAffinity(p, zAff[i])==SQLITE_AFF_BLOB\n     || sqlite3ExprNeedsNoAffinityChange(p, zAff[i])\n    ){\n      zAff[i] = SQLITE_AFF_BLOB;\n    }\n  }\n}\n\n\n/*\n** pX is an expression of the form:  (vector) IN (SELECT ...)\n** In other words, it is a vector IN operator with a SELECT clause on the\n** LHS.  But not all terms in the vector are indexable and the terms might\n** not be in the correct order for indexing.\n**\n** This routine makes a copy of the input pX expression and then adjusts\n** the vector on the LHS with corresponding changes to the SELECT so that\n** the vector contains only index terms and those terms are in the correct\n** order.  The modified IN expression is returned.  The caller is responsible\n** for deleting the returned expression.\n**\n** Example:\n**\n**    CREATE TABLE t1(a,b,c,d,e,f);\n**    CREATE INDEX t1x1 ON t1(e,c);\n**    SELECT * FROM t1 WHERE (a,b,c,d,e) IN (SELECT v,w,x,y,z FROM t2)\n**                           \\_______________________________________/\n**                                     The pX expression\n**\n** Since only columns e and c can be used with the index, in that order,\n** the modified IN expression that is returned will be:\n**\n**        (e,c) IN (SELECT z,x FROM t2)\n**\n** The reduced pX is different from the original (obviously) and thus is\n** only used for indexing, to improve performance.  The original unaltered\n** IN expression must also be run on each output row for correctness.\n*/\nstatic Expr *removeUnindexableInClauseTerms(\n  Parse *pParse,        /* The parsing context */\n  int iEq,              /* Look at loop terms starting here */\n  WhereLoop *pLoop,     /* The current loop */\n  Expr *pX              /* The IN expression to be reduced */\n){\n  sqlite3 *db = pParse->db;\n  Expr *pNew = sqlite3ExprDup(db, pX, 0);\n  if( db->mallocFailed==0 ){\n    ExprList *pOrigRhs = pNew->x.pSelect->pEList;  /* Original unmodified RHS */\n    ExprList *pOrigLhs = pNew->pLeft->x.pList;     /* Original unmodified LHS */\n    ExprList *pRhs = 0;         /* New RHS after modifications */\n    ExprList *pLhs = 0;         /* New LHS after mods */\n    int i;                      /* Loop counter */\n    Select *pSelect;            /* Pointer to the SELECT on the RHS */\n\n    for(i=iEq; i<pLoop->nLTerm; i++){\n      if( pLoop->aLTerm[i]->pExpr==pX ){\n        int iField = pLoop->aLTerm[i]->iField - 1;\n        assert( pOrigRhs->a[iField].pExpr!=0 );\n        pRhs = sqlite3ExprListAppend(pParse, pRhs, pOrigRhs->a[iField].pExpr);\n        pOrigRhs->a[iField].pExpr = 0;\n        assert( pOrigLhs->a[iField].pExpr!=0 );\n        pLhs = sqlite3ExprListAppend(pParse, pLhs, pOrigLhs->a[iField].pExpr);\n        pOrigLhs->a[iField].pExpr = 0;\n      }\n    }\n    sqlite3ExprListDelete(db, pOrigRhs);\n    sqlite3ExprListDelete(db, pOrigLhs);\n    pNew->pLeft->x.pList = pLhs;\n    pNew->x.pSelect->pEList = pRhs;\n    if( pLhs && pLhs->nExpr==1 ){\n      /* Take care here not to generate a TK_VECTOR containing only a\n      ** single value. Since the parser never creates such a vector, some\n      ** of the subroutines do not handle this case.  */\n      Expr *p = pLhs->a[0].pExpr;\n      pLhs->a[0].pExpr = 0;\n      sqlite3ExprDelete(db, pNew->pLeft);\n      pNew->pLeft = p;\n    }\n    pSelect = pNew->x.pSelect;\n    if( pSelect->pOrderBy ){\n      /* If the SELECT statement has an ORDER BY clause, zero the \n      ** iOrderByCol variables. These are set to non-zero when an \n      ** ORDER BY term exactly matches one of the terms of the \n      ** result-set. Since the result-set of the SELECT statement may\n      ** have been modified or reordered, these variables are no longer \n      ** set correctly.  Since setting them is just an optimization, \n      ** it's easiest just to zero them here.  */\n      ExprList *pOrderBy = pSelect->pOrderBy;\n      for(i=0; i<pOrderBy->nExpr; i++){\n        pOrderBy->a[i].u.x.iOrderByCol = 0;\n      }\n    }\n\n#if 0\n    printf(\"For indexing, change the IN expr:\\n\");\n    sqlite3TreeViewExpr(0, pX, 0);\n    printf(\"Into:\\n\");\n    sqlite3TreeViewExpr(0, pNew, 0);\n#endif\n  }\n  return pNew;\n}\n\n\n/*\n** Generate code for a single equality term of the WHERE clause.  An equality\n** term can be either X=expr or X IN (...).   pTerm is the term to be \n** coded.\n**\n** The current value for the constraint is left in a register, the index\n** of which is returned.  An attempt is made store the result in iTarget but\n** this is only guaranteed for TK_ISNULL and TK_IN constraints.  If the\n** constraint is a TK_EQ or TK_IS, then the current value might be left in\n** some other register and it is the caller's responsibility to compensate.\n**\n** For a constraint of the form X=expr, the expression is evaluated in\n** straight-line code.  For constraints of the form X IN (...)\n** this routine sets up a loop that will iterate over all values of X.\n*/\nstatic int codeEqualityTerm(\n  Parse *pParse,      /* The parsing context */\n  WhereTerm *pTerm,   /* The term of the WHERE clause to be coded */\n  WhereLevel *pLevel, /* The level of the FROM clause we are working on */\n  int iEq,            /* Index of the equality term within this level */\n  int bRev,           /* True for reverse-order IN operations */\n  int iTarget         /* Attempt to leave results in this register */\n){\n  Expr *pX = pTerm->pExpr;\n  Vdbe *v = pParse->pVdbe;\n  int iReg;                  /* Register holding results */\n\n  assert( pLevel->pWLoop->aLTerm[iEq]==pTerm );\n  assert( iTarget>0 );\n  if( pX->op==TK_EQ || pX->op==TK_IS ){\n    iReg = sqlite3ExprCodeTarget(pParse, pX->pRight, iTarget);\n  }else if( pX->op==TK_ISNULL ){\n    iReg = iTarget;\n    sqlite3VdbeAddOp2(v, OP_Null, 0, iReg);\n#ifndef SQLITE_OMIT_SUBQUERY\n  }else{\n    int eType = IN_INDEX_NOOP;\n    int iTab;\n    struct InLoop *pIn;\n    WhereLoop *pLoop = pLevel->pWLoop;\n    int i;\n    int nEq = 0;\n    int *aiMap = 0;\n\n    if( (pLoop->wsFlags & WHERE_VIRTUALTABLE)==0\n      && pLoop->u.btree.pIndex!=0\n      && pLoop->u.btree.pIndex->aSortOrder[iEq]\n    ){\n      testcase( iEq==0 );\n      testcase( bRev );\n      bRev = !bRev;\n    }\n    assert( pX->op==TK_IN );\n    iReg = iTarget;\n\n    for(i=0; i<iEq; i++){\n      if( pLoop->aLTerm[i] && pLoop->aLTerm[i]->pExpr==pX ){\n        disableTerm(pLevel, pTerm);\n        return iTarget;\n      }\n    }\n    for(i=iEq;i<pLoop->nLTerm; i++){\n      assert( pLoop->aLTerm[i]!=0 );\n      if( pLoop->aLTerm[i]->pExpr==pX ) nEq++;\n    }\n\n    if( (pX->flags & EP_xIsSelect)==0 || pX->x.pSelect->pEList->nExpr==1 ){\n      eType = sqlite3FindInIndex(pParse, pX, IN_INDEX_LOOP, 0, 0);\n    }else{\n      sqlite3 *db = pParse->db;\n      pX = removeUnindexableInClauseTerms(pParse, iEq, pLoop, pX);\n\n      if( !db->mallocFailed ){\n        aiMap = (int*)sqlite3DbMallocZero(pParse->db, sizeof(int)*nEq);\n        eType = sqlite3FindInIndex(pParse, pX, IN_INDEX_LOOP, 0, aiMap);\n        pTerm->pExpr->iTable = pX->iTable;\n      }\n      sqlite3ExprDelete(db, pX);\n      pX = pTerm->pExpr;\n    }\n\n    if( eType==IN_INDEX_INDEX_DESC ){\n      testcase( bRev );\n      bRev = !bRev;\n    }\n    iTab = pX->iTable;\n    sqlite3VdbeAddOp2(v, bRev ? OP_Last : OP_Rewind, iTab, 0);\n    VdbeCoverageIf(v, bRev);\n    VdbeCoverageIf(v, !bRev);\n    assert( (pLoop->wsFlags & WHERE_MULTI_OR)==0 );\n\n    pLoop->wsFlags |= WHERE_IN_ABLE;\n    if( pLevel->u.in.nIn==0 ){\n      pLevel->addrNxt = sqlite3VdbeMakeLabel(v);\n    }\n\n    i = pLevel->u.in.nIn;\n    pLevel->u.in.nIn += nEq;\n    pLevel->u.in.aInLoop =\n       sqlite3DbReallocOrFree(pParse->db, pLevel->u.in.aInLoop,\n                              sizeof(pLevel->u.in.aInLoop[0])*pLevel->u.in.nIn);\n    pIn = pLevel->u.in.aInLoop;\n    if( pIn ){\n      int iMap = 0;               /* Index in aiMap[] */\n      pIn += i;\n      for(i=iEq;i<pLoop->nLTerm; i++){\n        if( pLoop->aLTerm[i]->pExpr==pX ){\n          int iOut = iReg + i - iEq;\n          if( eType==IN_INDEX_ROWID ){\n            testcase( nEq>1 );  /* Happens with a UNIQUE index on ROWID */\n            pIn->addrInTop = sqlite3VdbeAddOp2(v, OP_Rowid, iTab, iOut);\n          }else{\n            int iCol = aiMap ? aiMap[iMap++] : 0;\n            pIn->addrInTop = sqlite3VdbeAddOp3(v,OP_Column,iTab, iCol, iOut);\n          }\n          sqlite3VdbeAddOp1(v, OP_IsNull, iOut); VdbeCoverage(v);\n          if( i==iEq ){\n            pIn->iCur = iTab;\n            pIn->eEndLoopOp = bRev ? OP_PrevIfOpen : OP_NextIfOpen;\n          }else{\n            pIn->eEndLoopOp = OP_Noop;\n          }\n          pIn++;\n        }\n      }\n    }else{\n      pLevel->u.in.nIn = 0;\n    }\n    sqlite3DbFree(pParse->db, aiMap);\n#endif\n  }\n  disableTerm(pLevel, pTerm);\n  return iReg;\n}\n\n/*\n** Generate code that will evaluate all == and IN constraints for an\n** index scan.\n**\n** For example, consider table t1(a,b,c,d,e,f) with index i1(a,b,c).\n** Suppose the WHERE clause is this:  a==5 AND b IN (1,2,3) AND c>5 AND c<10\n** The index has as many as three equality constraints, but in this\n** example, the third \"c\" value is an inequality.  So only two \n** constraints are coded.  This routine will generate code to evaluate\n** a==5 and b IN (1,2,3).  The current values for a and b will be stored\n** in consecutive registers and the index of the first register is returned.\n**\n** In the example above nEq==2.  But this subroutine works for any value\n** of nEq including 0.  If nEq==0, this routine is nearly a no-op.\n** The only thing it does is allocate the pLevel->iMem memory cell and\n** compute the affinity string.\n**\n** The nExtraReg parameter is 0 or 1.  It is 0 if all WHERE clause constraints\n** are == or IN and are covered by the nEq.  nExtraReg is 1 if there is\n** an inequality constraint (such as the \"c>=5 AND c<10\" in the example) that\n** occurs after the nEq quality constraints.\n**\n** This routine allocates a range of nEq+nExtraReg memory cells and returns\n** the index of the first memory cell in that range. The code that\n** calls this routine will use that memory range to store keys for\n** start and termination conditions of the loop.\n** key value of the loop.  If one or more IN operators appear, then\n** this routine allocates an additional nEq memory cells for internal\n** use.\n**\n** Before returning, *pzAff is set to point to a buffer containing a\n** copy of the column affinity string of the index allocated using\n** sqlite3DbMalloc(). Except, entries in the copy of the string associated\n** with equality constraints that use BLOB or NONE affinity are set to\n** SQLITE_AFF_BLOB. This is to deal with SQL such as the following:\n**\n**   CREATE TABLE t1(a TEXT PRIMARY KEY, b);\n**   SELECT ... FROM t1 AS t2, t1 WHERE t1.a = t2.b;\n**\n** In the example above, the index on t1(a) has TEXT affinity. But since\n** the right hand side of the equality constraint (t2.b) has BLOB/NONE affinity,\n** no conversion should be attempted before using a t2.b value as part of\n** a key to search the index. Hence the first byte in the returned affinity\n** string in this example would be set to SQLITE_AFF_BLOB.\n*/\nstatic int codeAllEqualityTerms(\n  Parse *pParse,        /* Parsing context */\n  WhereLevel *pLevel,   /* Which nested loop of the FROM we are coding */\n  int bRev,             /* Reverse the order of IN operators */\n  int nExtraReg,        /* Number of extra registers to allocate */\n  char **pzAff          /* OUT: Set to point to affinity string */\n){\n  u16 nEq;                      /* The number of == or IN constraints to code */\n  u16 nSkip;                    /* Number of left-most columns to skip */\n  Vdbe *v = pParse->pVdbe;      /* The vm under construction */\n  Index *pIdx;                  /* The index being used for this loop */\n  WhereTerm *pTerm;             /* A single constraint term */\n  WhereLoop *pLoop;             /* The WhereLoop object */\n  int j;                        /* Loop counter */\n  int regBase;                  /* Base register */\n  int nReg;                     /* Number of registers to allocate */\n  char *zAff;                   /* Affinity string to return */\n\n  /* This module is only called on query plans that use an index. */\n  pLoop = pLevel->pWLoop;\n  assert( (pLoop->wsFlags & WHERE_VIRTUALTABLE)==0 );\n  nEq = pLoop->u.btree.nEq;\n  nSkip = pLoop->nSkip;\n  pIdx = pLoop->u.btree.pIndex;\n  assert( pIdx!=0 );\n\n  /* Figure out how many memory cells we will need then allocate them.\n  */\n  regBase = pParse->nMem + 1;\n  nReg = pLoop->u.btree.nEq + nExtraReg;\n  pParse->nMem += nReg;\n\n  zAff = sqlite3DbStrDup(pParse->db,sqlite3IndexAffinityStr(pParse->db,pIdx));\n  assert( zAff!=0 || pParse->db->mallocFailed );\n\n  if( nSkip ){\n    int iIdxCur = pLevel->iIdxCur;\n    sqlite3VdbeAddOp1(v, (bRev?OP_Last:OP_Rewind), iIdxCur);\n    VdbeCoverageIf(v, bRev==0);\n    VdbeCoverageIf(v, bRev!=0);\n    VdbeComment((v, \"begin skip-scan on %s\", pIdx->zName));\n    j = sqlite3VdbeAddOp0(v, OP_Goto);\n    pLevel->addrSkip = sqlite3VdbeAddOp4Int(v, (bRev?OP_SeekLT:OP_SeekGT),\n                            iIdxCur, 0, regBase, nSkip);\n    VdbeCoverageIf(v, bRev==0);\n    VdbeCoverageIf(v, bRev!=0);\n    sqlite3VdbeJumpHere(v, j);\n    for(j=0; j<nSkip; j++){\n      sqlite3VdbeAddOp3(v, OP_Column, iIdxCur, j, regBase+j);\n      testcase( pIdx->aiColumn[j]==XN_EXPR );\n      VdbeComment((v, \"%s\", explainIndexColumnName(pIdx, j)));\n    }\n  }    \n\n  /* Evaluate the equality constraints\n  */\n  assert( zAff==0 || (int)strlen(zAff)>=nEq );\n  for(j=nSkip; j<nEq; j++){\n    int r1;\n    pTerm = pLoop->aLTerm[j];\n    assert( pTerm!=0 );\n    /* The following testcase is true for indices with redundant columns. \n    ** Ex: CREATE INDEX i1 ON t1(a,b,a); SELECT * FROM t1 WHERE a=0 AND b=0; */\n    testcase( (pTerm->wtFlags & TERM_CODED)!=0 );\n    testcase( pTerm->wtFlags & TERM_VIRTUAL );\n    r1 = codeEqualityTerm(pParse, pTerm, pLevel, j, bRev, regBase+j);\n    if( r1!=regBase+j ){\n      if( nReg==1 ){\n        sqlite3ReleaseTempReg(pParse, regBase);\n        regBase = r1;\n      }else{\n        sqlite3VdbeAddOp2(v, OP_SCopy, r1, regBase+j);\n      }\n    }\n    if( pTerm->eOperator & WO_IN ){\n      if( pTerm->pExpr->flags & EP_xIsSelect ){\n        /* No affinity ever needs to be (or should be) applied to a value\n        ** from the RHS of an \"? IN (SELECT ...)\" expression. The \n        ** sqlite3FindInIndex() routine has already ensured that the \n        ** affinity of the comparison has been applied to the value.  */\n        if( zAff ) zAff[j] = SQLITE_AFF_BLOB;\n      }\n    }else if( (pTerm->eOperator & WO_ISNULL)==0 ){\n      Expr *pRight = pTerm->pExpr->pRight;\n      if( (pTerm->wtFlags & TERM_IS)==0 && sqlite3ExprCanBeNull(pRight) ){\n        sqlite3VdbeAddOp2(v, OP_IsNull, regBase+j, pLevel->addrBrk);\n        VdbeCoverage(v);\n      }\n      if( zAff ){\n        if( sqlite3CompareAffinity(pRight, zAff[j])==SQLITE_AFF_BLOB ){\n          zAff[j] = SQLITE_AFF_BLOB;\n        }\n        if( sqlite3ExprNeedsNoAffinityChange(pRight, zAff[j]) ){\n          zAff[j] = SQLITE_AFF_BLOB;\n        }\n      }\n    }\n  }\n  *pzAff = zAff;\n  return regBase;\n}\n\n#ifndef SQLITE_LIKE_DOESNT_MATCH_BLOBS\n/*\n** If the most recently coded instruction is a constant range constraint\n** (a string literal) that originated from the LIKE optimization, then \n** set P3 and P5 on the OP_String opcode so that the string will be cast\n** to a BLOB at appropriate times.\n**\n** The LIKE optimization trys to evaluate \"x LIKE 'abc%'\" as a range\n** expression: \"x>='ABC' AND x<'abd'\".  But this requires that the range\n** scan loop run twice, once for strings and a second time for BLOBs.\n** The OP_String opcodes on the second pass convert the upper and lower\n** bound string constants to blobs.  This routine makes the necessary changes\n** to the OP_String opcodes for that to happen.\n**\n** Except, of course, if SQLITE_LIKE_DOESNT_MATCH_BLOBS is defined, then\n** only the one pass through the string space is required, so this routine\n** becomes a no-op.\n*/\nstatic void whereLikeOptimizationStringFixup(\n  Vdbe *v,                /* prepared statement under construction */\n  WhereLevel *pLevel,     /* The loop that contains the LIKE operator */\n  WhereTerm *pTerm        /* The upper or lower bound just coded */\n){\n  if( pTerm->wtFlags & TERM_LIKEOPT ){\n    VdbeOp *pOp;\n    assert( pLevel->iLikeRepCntr>0 );\n    pOp = sqlite3VdbeGetOp(v, -1);\n    assert( pOp!=0 );\n    assert( pOp->opcode==OP_String8 \n            || pTerm->pWC->pWInfo->pParse->db->mallocFailed );\n    pOp->p3 = (int)(pLevel->iLikeRepCntr>>1);  /* Register holding counter */\n    pOp->p5 = (u8)(pLevel->iLikeRepCntr&1);    /* ASC or DESC */\n  }\n}\n#else\n# define whereLikeOptimizationStringFixup(A,B,C)\n#endif\n\n#ifdef SQLITE_ENABLE_CURSOR_HINTS\n/*\n** Information is passed from codeCursorHint() down to individual nodes of\n** the expression tree (by sqlite3WalkExpr()) using an instance of this\n** structure.\n*/\nstruct CCurHint {\n  int iTabCur;    /* Cursor for the main table */\n  int iIdxCur;    /* Cursor for the index, if pIdx!=0.  Unused otherwise */\n  Index *pIdx;    /* The index used to access the table */\n};\n\n/*\n** This function is called for every node of an expression that is a candidate\n** for a cursor hint on an index cursor.  For TK_COLUMN nodes that reference\n** the table CCurHint.iTabCur, verify that the same column can be\n** accessed through the index.  If it cannot, then set pWalker->eCode to 1.\n*/\nstatic int codeCursorHintCheckExpr(Walker *pWalker, Expr *pExpr){\n  struct CCurHint *pHint = pWalker->u.pCCurHint;\n  assert( pHint->pIdx!=0 );\n  if( pExpr->op==TK_COLUMN\n   && pExpr->iTable==pHint->iTabCur\n   && sqlite3ColumnOfIndex(pHint->pIdx, pExpr->iColumn)<0\n  ){\n    pWalker->eCode = 1;\n  }\n  return WRC_Continue;\n}\n\n/*\n** Test whether or not expression pExpr, which was part of a WHERE clause,\n** should be included in the cursor-hint for a table that is on the rhs\n** of a LEFT JOIN. Set Walker.eCode to non-zero before returning if the \n** expression is not suitable.\n**\n** An expression is unsuitable if it might evaluate to non NULL even if\n** a TK_COLUMN node that does affect the value of the expression is set\n** to NULL. For example:\n**\n**   col IS NULL\n**   col IS NOT NULL\n**   coalesce(col, 1)\n**   CASE WHEN col THEN 0 ELSE 1 END\n*/\nstatic int codeCursorHintIsOrFunction(Walker *pWalker, Expr *pExpr){\n  if( pExpr->op==TK_IS \n   || pExpr->op==TK_ISNULL || pExpr->op==TK_ISNOT \n   || pExpr->op==TK_NOTNULL || pExpr->op==TK_CASE \n  ){\n    pWalker->eCode = 1;\n  }else if( pExpr->op==TK_FUNCTION ){\n    int d1;\n    char d2[4];\n    if( 0==sqlite3IsLikeFunction(pWalker->pParse->db, pExpr, &d1, d2) ){\n      pWalker->eCode = 1;\n    }\n  }\n\n  return WRC_Continue;\n}\n\n\n/*\n** This function is called on every node of an expression tree used as an\n** argument to the OP_CursorHint instruction. If the node is a TK_COLUMN\n** that accesses any table other than the one identified by\n** CCurHint.iTabCur, then do the following:\n**\n**   1) allocate a register and code an OP_Column instruction to read \n**      the specified column into the new register, and\n**\n**   2) transform the expression node to a TK_REGISTER node that reads \n**      from the newly populated register.\n**\n** Also, if the node is a TK_COLUMN that does access the table idenified\n** by pCCurHint.iTabCur, and an index is being used (which we will\n** know because CCurHint.pIdx!=0) then transform the TK_COLUMN into\n** an access of the index rather than the original table.\n*/\nstatic int codeCursorHintFixExpr(Walker *pWalker, Expr *pExpr){\n  int rc = WRC_Continue;\n  struct CCurHint *pHint = pWalker->u.pCCurHint;\n  if( pExpr->op==TK_COLUMN ){\n    if( pExpr->iTable!=pHint->iTabCur ){\n      Vdbe *v = pWalker->pParse->pVdbe;\n      int reg = ++pWalker->pParse->nMem;   /* Register for column value */\n      sqlite3ExprCodeGetColumnOfTable(\n          v, pExpr->pTab, pExpr->iTable, pExpr->iColumn, reg\n      );\n      pExpr->op = TK_REGISTER;\n      pExpr->iTable = reg;\n    }else if( pHint->pIdx!=0 ){\n      pExpr->iTable = pHint->iIdxCur;\n      pExpr->iColumn = sqlite3ColumnOfIndex(pHint->pIdx, pExpr->iColumn);\n      assert( pExpr->iColumn>=0 );\n    }\n  }else if( pExpr->op==TK_AGG_FUNCTION ){\n    /* An aggregate function in the WHERE clause of a query means this must\n    ** be a correlated sub-query, and expression pExpr is an aggregate from\n    ** the parent context. Do not walk the function arguments in this case.\n    **\n    ** todo: It should be possible to replace this node with a TK_REGISTER\n    ** expression, as the result of the expression must be stored in a \n    ** register at this point. The same holds for TK_AGG_COLUMN nodes. */\n    rc = WRC_Prune;\n  }\n  return rc;\n}\n\n/*\n** Insert an OP_CursorHint instruction if it is appropriate to do so.\n*/\nstatic void codeCursorHint(\n  struct SrcList_item *pTabItem,  /* FROM clause item */\n  WhereInfo *pWInfo,    /* The where clause */\n  WhereLevel *pLevel,   /* Which loop to provide hints for */\n  WhereTerm *pEndRange  /* Hint this end-of-scan boundary term if not NULL */\n){\n  Parse *pParse = pWInfo->pParse;\n  sqlite3 *db = pParse->db;\n  Vdbe *v = pParse->pVdbe;\n  Expr *pExpr = 0;\n  WhereLoop *pLoop = pLevel->pWLoop;\n  int iCur;\n  WhereClause *pWC;\n  WhereTerm *pTerm;\n  int i, j;\n  struct CCurHint sHint;\n  Walker sWalker;\n\n  if( OptimizationDisabled(db, SQLITE_CursorHints) ) return;\n  iCur = pLevel->iTabCur;\n  assert( iCur==pWInfo->pTabList->a[pLevel->iFrom].iCursor );\n  sHint.iTabCur = iCur;\n  sHint.iIdxCur = pLevel->iIdxCur;\n  sHint.pIdx = pLoop->u.btree.pIndex;\n  memset(&sWalker, 0, sizeof(sWalker));\n  sWalker.pParse = pParse;\n  sWalker.u.pCCurHint = &sHint;\n  pWC = &pWInfo->sWC;\n  for(i=0; i<pWC->nTerm; i++){\n    pTerm = &pWC->a[i];\n    if( pTerm->wtFlags & (TERM_VIRTUAL|TERM_CODED) ) continue;\n    if( pTerm->prereqAll & pLevel->notReady ) continue;\n\n    /* Any terms specified as part of the ON(...) clause for any LEFT \n    ** JOIN for which the current table is not the rhs are omitted\n    ** from the cursor-hint. \n    **\n    ** If this table is the rhs of a LEFT JOIN, \"IS\" or \"IS NULL\" terms \n    ** that were specified as part of the WHERE clause must be excluded.\n    ** This is to address the following:\n    **\n    **   SELECT ... t1 LEFT JOIN t2 ON (t1.a=t2.b) WHERE t2.c IS NULL;\n    **\n    ** Say there is a single row in t2 that matches (t1.a=t2.b), but its\n    ** t2.c values is not NULL. If the (t2.c IS NULL) constraint is \n    ** pushed down to the cursor, this row is filtered out, causing\n    ** SQLite to synthesize a row of NULL values. Which does match the\n    ** WHERE clause, and so the query returns a row. Which is incorrect.\n    **\n    ** For the same reason, WHERE terms such as:\n    **\n    **   WHERE 1 = (t2.c IS NULL)\n    **\n    ** are also excluded. See codeCursorHintIsOrFunction() for details.\n    */\n    if( pTabItem->fg.jointype & JT_LEFT ){\n      Expr *pExpr = pTerm->pExpr;\n      if( !ExprHasProperty(pExpr, EP_FromJoin) \n       || pExpr->iRightJoinTable!=pTabItem->iCursor\n      ){\n        sWalker.eCode = 0;\n        sWalker.xExprCallback = codeCursorHintIsOrFunction;\n        sqlite3WalkExpr(&sWalker, pTerm->pExpr);\n        if( sWalker.eCode ) continue;\n      }\n    }else{\n      if( ExprHasProperty(pTerm->pExpr, EP_FromJoin) ) continue;\n    }\n\n    /* All terms in pWLoop->aLTerm[] except pEndRange are used to initialize\n    ** the cursor.  These terms are not needed as hints for a pure range\n    ** scan (that has no == terms) so omit them. */\n    if( pLoop->u.btree.nEq==0 && pTerm!=pEndRange ){\n      for(j=0; j<pLoop->nLTerm && pLoop->aLTerm[j]!=pTerm; j++){}\n      if( j<pLoop->nLTerm ) continue;\n    }\n\n    /* No subqueries or non-deterministic functions allowed */\n    if( sqlite3ExprContainsSubquery(pTerm->pExpr) ) continue;\n\n    /* For an index scan, make sure referenced columns are actually in\n    ** the index. */\n    if( sHint.pIdx!=0 ){\n      sWalker.eCode = 0;\n      sWalker.xExprCallback = codeCursorHintCheckExpr;\n      sqlite3WalkExpr(&sWalker, pTerm->pExpr);\n      if( sWalker.eCode ) continue;\n    }\n\n    /* If we survive all prior tests, that means this term is worth hinting */\n    pExpr = sqlite3ExprAnd(db, pExpr, sqlite3ExprDup(db, pTerm->pExpr, 0));\n  }\n  if( pExpr!=0 ){\n    sWalker.xExprCallback = codeCursorHintFixExpr;\n    sqlite3WalkExpr(&sWalker, pExpr);\n    sqlite3VdbeAddOp4(v, OP_CursorHint, \n                      (sHint.pIdx ? sHint.iIdxCur : sHint.iTabCur), 0, 0,\n                      (const char*)pExpr, P4_EXPR);\n  }\n}\n#else\n# define codeCursorHint(A,B,C,D)  /* No-op */\n#endif /* SQLITE_ENABLE_CURSOR_HINTS */\n\n/*\n** Cursor iCur is open on an intkey b-tree (a table). Register iRowid contains\n** a rowid value just read from cursor iIdxCur, open on index pIdx. This\n** function generates code to do a deferred seek of cursor iCur to the \n** rowid stored in register iRowid.\n**\n** Normally, this is just:\n**\n**   OP_DeferredSeek $iCur $iRowid\n**\n** However, if the scan currently being coded is a branch of an OR-loop and\n** the statement currently being coded is a SELECT, then P3 of OP_DeferredSeek\n** is set to iIdxCur and P4 is set to point to an array of integers\n** containing one entry for each column of the table cursor iCur is open \n** on. For each table column, if the column is the i'th column of the \n** index, then the corresponding array entry is set to (i+1). If the column\n** does not appear in the index at all, the array entry is set to 0.\n*/\nstatic void codeDeferredSeek(\n  WhereInfo *pWInfo,              /* Where clause context */\n  Index *pIdx,                    /* Index scan is using */\n  int iCur,                       /* Cursor for IPK b-tree */\n  int iIdxCur                     /* Index cursor */\n){\n  Parse *pParse = pWInfo->pParse; /* Parse context */\n  Vdbe *v = pParse->pVdbe;        /* Vdbe to generate code within */\n\n  assert( iIdxCur>0 );\n  assert( pIdx->aiColumn[pIdx->nColumn-1]==-1 );\n  \n  sqlite3VdbeAddOp3(v, OP_DeferredSeek, iIdxCur, 0, iCur);\n  if( (pWInfo->wctrlFlags & WHERE_OR_SUBCLAUSE)\n   && DbMaskAllZero(sqlite3ParseToplevel(pParse)->writeMask)\n  ){\n    int i;\n    Table *pTab = pIdx->pTable;\n    int *ai = (int*)sqlite3DbMallocZero(pParse->db, sizeof(int)*(pTab->nCol+1));\n    if( ai ){\n      ai[0] = pTab->nCol;\n      for(i=0; i<pIdx->nColumn-1; i++){\n        assert( pIdx->aiColumn[i]<pTab->nCol );\n        if( pIdx->aiColumn[i]>=0 ) ai[pIdx->aiColumn[i]+1] = i+1;\n      }\n      sqlite3VdbeChangeP4(v, -1, (char*)ai, P4_INTARRAY);\n    }\n  }\n}\n\n/*\n** If the expression passed as the second argument is a vector, generate\n** code to write the first nReg elements of the vector into an array\n** of registers starting with iReg.\n**\n** If the expression is not a vector, then nReg must be passed 1. In\n** this case, generate code to evaluate the expression and leave the\n** result in register iReg.\n*/\nstatic void codeExprOrVector(Parse *pParse, Expr *p, int iReg, int nReg){\n  assert( nReg>0 );\n  if( p && sqlite3ExprIsVector(p) ){\n#ifndef SQLITE_OMIT_SUBQUERY\n    if( (p->flags & EP_xIsSelect) ){\n      Vdbe *v = pParse->pVdbe;\n      int iSelect = sqlite3CodeSubselect(pParse, p, 0, 0);\n      sqlite3VdbeAddOp3(v, OP_Copy, iSelect, iReg, nReg-1);\n    }else\n#endif\n    {\n      int i;\n      ExprList *pList = p->x.pList;\n      assert( nReg<=pList->nExpr );\n      for(i=0; i<nReg; i++){\n        sqlite3ExprCode(pParse, pList->a[i].pExpr, iReg+i);\n      }\n    }\n  }else{\n    assert( nReg==1 );\n    sqlite3ExprCode(pParse, p, iReg);\n  }\n}\n\n/* An instance of the IdxExprTrans object carries information about a\n** mapping from an expression on table columns into a column in an index\n** down through the Walker.\n*/\ntypedef struct IdxExprTrans {\n  Expr *pIdxExpr;    /* The index expression */\n  int iTabCur;       /* The cursor of the corresponding table */\n  int iIdxCur;       /* The cursor for the index */\n  int iIdxCol;       /* The column for the index */\n} IdxExprTrans;\n\n/* The walker node callback used to transform matching expressions into\n** a reference to an index column for an index on an expression.\n**\n** If pExpr matches, then transform it into a reference to the index column\n** that contains the value of pExpr.\n*/\nstatic int whereIndexExprTransNode(Walker *p, Expr *pExpr){\n  IdxExprTrans *pX = p->u.pIdxTrans;\n  if( sqlite3ExprCompare(0, pExpr, pX->pIdxExpr, pX->iTabCur)==0 ){\n    pExpr->op = TK_COLUMN;\n    pExpr->iTable = pX->iIdxCur;\n    pExpr->iColumn = pX->iIdxCol;\n    pExpr->pTab = 0;\n    return WRC_Prune;\n  }else{\n    return WRC_Continue;\n  }\n}\n\n/*\n** For an indexes on expression X, locate every instance of expression X\n** in pExpr and change that subexpression into a reference to the appropriate\n** column of the index.\n*/\nstatic void whereIndexExprTrans(\n  Index *pIdx,      /* The Index */\n  int iTabCur,      /* Cursor of the table that is being indexed */\n  int iIdxCur,      /* Cursor of the index itself */\n  WhereInfo *pWInfo /* Transform expressions in this WHERE clause */\n){\n  int iIdxCol;               /* Column number of the index */\n  ExprList *aColExpr;        /* Expressions that are indexed */\n  Walker w;\n  IdxExprTrans x;\n  aColExpr = pIdx->aColExpr;\n  if( aColExpr==0 ) return;  /* Not an index on expressions */\n  memset(&w, 0, sizeof(w));\n  w.xExprCallback = whereIndexExprTransNode;\n  w.u.pIdxTrans = &x;\n  x.iTabCur = iTabCur;\n  x.iIdxCur = iIdxCur;\n  for(iIdxCol=0; iIdxCol<aColExpr->nExpr; iIdxCol++){\n    if( pIdx->aiColumn[iIdxCol]!=XN_EXPR ) continue;\n    assert( aColExpr->a[iIdxCol].pExpr!=0 );\n    x.iIdxCol = iIdxCol;\n    x.pIdxExpr = aColExpr->a[iIdxCol].pExpr;\n    sqlite3WalkExpr(&w, pWInfo->pWhere);\n    sqlite3WalkExprList(&w, pWInfo->pOrderBy);\n    sqlite3WalkExprList(&w, pWInfo->pResultSet);\n  }\n}\n\n/*\n** Generate code for the start of the iLevel-th loop in the WHERE clause\n** implementation described by pWInfo.\n*/\nSQLITE_PRIVATE Bitmask sqlite3WhereCodeOneLoopStart(\n  WhereInfo *pWInfo,   /* Complete information about the WHERE clause */\n  int iLevel,          /* Which level of pWInfo->a[] should be coded */\n  Bitmask notReady     /* Which tables are currently available */\n){\n  int j, k;            /* Loop counters */\n  int iCur;            /* The VDBE cursor for the table */\n  int addrNxt;         /* Where to jump to continue with the next IN case */\n  int omitTable;       /* True if we use the index only */\n  int bRev;            /* True if we need to scan in reverse order */\n  WhereLevel *pLevel;  /* The where level to be coded */\n  WhereLoop *pLoop;    /* The WhereLoop object being coded */\n  WhereClause *pWC;    /* Decomposition of the entire WHERE clause */\n  WhereTerm *pTerm;               /* A WHERE clause term */\n  Parse *pParse;                  /* Parsing context */\n  sqlite3 *db;                    /* Database connection */\n  Vdbe *v;                        /* The prepared stmt under constructions */\n  struct SrcList_item *pTabItem;  /* FROM clause term being coded */\n  int addrBrk;                    /* Jump here to break out of the loop */\n  int addrHalt;                   /* addrBrk for the outermost loop */\n  int addrCont;                   /* Jump here to continue with next cycle */\n  int iRowidReg = 0;        /* Rowid is stored in this register, if not zero */\n  int iReleaseReg = 0;      /* Temp register to free before returning */\n  Index *pIdx = 0;          /* Index used by loop (if any) */\n  int iLoop;                /* Iteration of constraint generator loop */\n\n  pParse = pWInfo->pParse;\n  v = pParse->pVdbe;\n  pWC = &pWInfo->sWC;\n  db = pParse->db;\n  pLevel = &pWInfo->a[iLevel];\n  pLoop = pLevel->pWLoop;\n  pTabItem = &pWInfo->pTabList->a[pLevel->iFrom];\n  iCur = pTabItem->iCursor;\n  pLevel->notReady = notReady & ~sqlite3WhereGetMask(&pWInfo->sMaskSet, iCur);\n  bRev = (pWInfo->revMask>>iLevel)&1;\n  omitTable = (pLoop->wsFlags & WHERE_IDX_ONLY)!=0 \n           && (pWInfo->wctrlFlags & WHERE_OR_SUBCLAUSE)==0;\n  VdbeModuleComment((v, \"Begin WHERE-loop%d: %s\",iLevel,pTabItem->pTab->zName));\n\n  /* Create labels for the \"break\" and \"continue\" instructions\n  ** for the current loop.  Jump to addrBrk to break out of a loop.\n  ** Jump to cont to go immediately to the next iteration of the\n  ** loop.\n  **\n  ** When there is an IN operator, we also have a \"addrNxt\" label that\n  ** means to continue with the next IN value combination.  When\n  ** there are no IN operators in the constraints, the \"addrNxt\" label\n  ** is the same as \"addrBrk\".\n  */\n  addrBrk = pLevel->addrBrk = pLevel->addrNxt = sqlite3VdbeMakeLabel(v);\n  addrCont = pLevel->addrCont = sqlite3VdbeMakeLabel(v);\n\n  /* If this is the right table of a LEFT OUTER JOIN, allocate and\n  ** initialize a memory cell that records if this table matches any\n  ** row of the left table of the join.\n  */\n  if( pLevel->iFrom>0 && (pTabItem[0].fg.jointype & JT_LEFT)!=0 ){\n    pLevel->iLeftJoin = ++pParse->nMem;\n    sqlite3VdbeAddOp2(v, OP_Integer, 0, pLevel->iLeftJoin);\n    VdbeComment((v, \"init LEFT JOIN no-match flag\"));\n  }\n\n  /* Compute a safe address to jump to if we discover that the table for\n  ** this loop is empty and can never contribute content. */\n  for(j=iLevel; j>0 && pWInfo->a[j].iLeftJoin==0; j--){}\n  addrHalt = pWInfo->a[j].addrBrk;\n\n  /* Special case of a FROM clause subquery implemented as a co-routine */\n  if( pTabItem->fg.viaCoroutine ){\n    int regYield = pTabItem->regReturn;\n    sqlite3VdbeAddOp3(v, OP_InitCoroutine, regYield, 0, pTabItem->addrFillSub);\n    pLevel->p2 =  sqlite3VdbeAddOp2(v, OP_Yield, regYield, addrBrk);\n    VdbeCoverage(v);\n    VdbeComment((v, \"next row of \\\"%s\\\"\", pTabItem->pTab->zName));\n    pLevel->op = OP_Goto;\n  }else\n\n#ifndef SQLITE_OMIT_VIRTUALTABLE\n  if(  (pLoop->wsFlags & WHERE_VIRTUALTABLE)!=0 ){\n    /* Case 1:  The table is a virtual-table.  Use the VFilter and VNext\n    **          to access the data.\n    */\n    int iReg;   /* P3 Value for OP_VFilter */\n    int addrNotFound;\n    int nConstraint = pLoop->nLTerm;\n    int iIn;    /* Counter for IN constraints */\n\n    sqlite3ExprCachePush(pParse);\n    iReg = sqlite3GetTempRange(pParse, nConstraint+2);\n    addrNotFound = pLevel->addrBrk;\n    for(j=0; j<nConstraint; j++){\n      int iTarget = iReg+j+2;\n      pTerm = pLoop->aLTerm[j];\n      if( NEVER(pTerm==0) ) continue;\n      if( pTerm->eOperator & WO_IN ){\n        codeEqualityTerm(pParse, pTerm, pLevel, j, bRev, iTarget);\n        addrNotFound = pLevel->addrNxt;\n      }else{\n        Expr *pRight = pTerm->pExpr->pRight;\n        codeExprOrVector(pParse, pRight, iTarget, 1);\n      }\n    }\n    sqlite3VdbeAddOp2(v, OP_Integer, pLoop->u.vtab.idxNum, iReg);\n    sqlite3VdbeAddOp2(v, OP_Integer, nConstraint, iReg+1);\n    sqlite3VdbeAddOp4(v, OP_VFilter, iCur, addrNotFound, iReg,\n                      pLoop->u.vtab.idxStr,\n                      pLoop->u.vtab.needFree ? P4_DYNAMIC : P4_STATIC);\n    VdbeCoverage(v);\n    pLoop->u.vtab.needFree = 0;\n    pLevel->p1 = iCur;\n    pLevel->op = pWInfo->eOnePass ? OP_Noop : OP_VNext;\n    pLevel->p2 = sqlite3VdbeCurrentAddr(v);\n    iIn = pLevel->u.in.nIn;\n    for(j=nConstraint-1; j>=0; j--){\n      pTerm = pLoop->aLTerm[j];\n      if( j<16 && (pLoop->u.vtab.omitMask>>j)&1 ){\n        disableTerm(pLevel, pTerm);\n      }else if( (pTerm->eOperator & WO_IN)!=0 ){\n        Expr *pCompare;  /* The comparison operator */\n        Expr *pRight;    /* RHS of the comparison */\n        VdbeOp *pOp;     /* Opcode to access the value of the IN constraint */\n\n        /* Reload the constraint value into reg[iReg+j+2].  The same value\n        ** was loaded into the same register prior to the OP_VFilter, but\n        ** the xFilter implementation might have changed the datatype or\n        ** encoding of the value in the register, so it *must* be reloaded. */\n        assert( pLevel->u.in.aInLoop!=0 || db->mallocFailed );\n        if( !db->mallocFailed ){\n          assert( iIn>0 );\n          pOp = sqlite3VdbeGetOp(v, pLevel->u.in.aInLoop[--iIn].addrInTop);\n          assert( pOp->opcode==OP_Column || pOp->opcode==OP_Rowid );\n          assert( pOp->opcode!=OP_Column || pOp->p3==iReg+j+2 );\n          assert( pOp->opcode!=OP_Rowid || pOp->p2==iReg+j+2 );\n          testcase( pOp->opcode==OP_Rowid );\n          sqlite3VdbeAddOp3(v, pOp->opcode, pOp->p1, pOp->p2, pOp->p3);\n        }\n\n        /* Generate code that will continue to the next row if \n        ** the IN constraint is not satisfied */\n        pCompare = sqlite3PExpr(pParse, TK_EQ, 0, 0);\n        assert( pCompare!=0 || db->mallocFailed );\n        if( pCompare ){\n          pCompare->pLeft = pTerm->pExpr->pLeft;\n          pCompare->pRight = pRight = sqlite3Expr(db, TK_REGISTER, 0);\n          if( pRight ){\n            pRight->iTable = iReg+j+2;\n            sqlite3ExprIfFalse(pParse, pCompare, pLevel->addrCont, 0);\n          }\n          pCompare->pLeft = 0;\n          sqlite3ExprDelete(db, pCompare);\n        }\n      }\n    }\n    /* These registers need to be preserved in case there is an IN operator\n    ** loop.  So we could deallocate the registers here (and potentially\n    ** reuse them later) if (pLoop->wsFlags & WHERE_IN_ABLE)==0.  But it seems\n    ** simpler and safer to simply not reuse the registers.\n    **\n    **    sqlite3ReleaseTempRange(pParse, iReg, nConstraint+2);\n    */\n    sqlite3ExprCachePop(pParse);\n  }else\n#endif /* SQLITE_OMIT_VIRTUALTABLE */\n\n  if( (pLoop->wsFlags & WHERE_IPK)!=0\n   && (pLoop->wsFlags & (WHERE_COLUMN_IN|WHERE_COLUMN_EQ))!=0\n  ){\n    /* Case 2:  We can directly reference a single row using an\n    **          equality comparison against the ROWID field.  Or\n    **          we reference multiple rows using a \"rowid IN (...)\"\n    **          construct.\n    */\n    assert( pLoop->u.btree.nEq==1 );\n    pTerm = pLoop->aLTerm[0];\n    assert( pTerm!=0 );\n    assert( pTerm->pExpr!=0 );\n    assert( omitTable==0 );\n    testcase( pTerm->wtFlags & TERM_VIRTUAL );\n    iReleaseReg = ++pParse->nMem;\n    iRowidReg = codeEqualityTerm(pParse, pTerm, pLevel, 0, bRev, iReleaseReg);\n    if( iRowidReg!=iReleaseReg ) sqlite3ReleaseTempReg(pParse, iReleaseReg);\n    addrNxt = pLevel->addrNxt;\n    sqlite3VdbeAddOp3(v, OP_SeekRowid, iCur, addrNxt, iRowidReg);\n    VdbeCoverage(v);\n    sqlite3ExprCacheAffinityChange(pParse, iRowidReg, 1);\n    sqlite3ExprCacheStore(pParse, iCur, -1, iRowidReg);\n    VdbeComment((v, \"pk\"));\n    pLevel->op = OP_Noop;\n  }else if( (pLoop->wsFlags & WHERE_IPK)!=0\n         && (pLoop->wsFlags & WHERE_COLUMN_RANGE)!=0\n  ){\n    /* Case 3:  We have an inequality comparison against the ROWID field.\n    */\n    int testOp = OP_Noop;\n    int start;\n    int memEndValue = 0;\n    WhereTerm *pStart, *pEnd;\n\n    assert( omitTable==0 );\n    j = 0;\n    pStart = pEnd = 0;\n    if( pLoop->wsFlags & WHERE_BTM_LIMIT ) pStart = pLoop->aLTerm[j++];\n    if( pLoop->wsFlags & WHERE_TOP_LIMIT ) pEnd = pLoop->aLTerm[j++];\n    assert( pStart!=0 || pEnd!=0 );\n    if( bRev ){\n      pTerm = pStart;\n      pStart = pEnd;\n      pEnd = pTerm;\n    }\n    codeCursorHint(pTabItem, pWInfo, pLevel, pEnd);\n    if( pStart ){\n      Expr *pX;             /* The expression that defines the start bound */\n      int r1, rTemp;        /* Registers for holding the start boundary */\n      int op;               /* Cursor seek operation */\n\n      /* The following constant maps TK_xx codes into corresponding \n      ** seek opcodes.  It depends on a particular ordering of TK_xx\n      */\n      const u8 aMoveOp[] = {\n           /* TK_GT */  OP_SeekGT,\n           /* TK_LE */  OP_SeekLE,\n           /* TK_LT */  OP_SeekLT,\n           /* TK_GE */  OP_SeekGE\n      };\n      assert( TK_LE==TK_GT+1 );      /* Make sure the ordering.. */\n      assert( TK_LT==TK_GT+2 );      /*  ... of the TK_xx values... */\n      assert( TK_GE==TK_GT+3 );      /*  ... is correcct. */\n\n      assert( (pStart->wtFlags & TERM_VNULL)==0 );\n      testcase( pStart->wtFlags & TERM_VIRTUAL );\n      pX = pStart->pExpr;\n      assert( pX!=0 );\n      testcase( pStart->leftCursor!=iCur ); /* transitive constraints */\n      if( sqlite3ExprIsVector(pX->pRight) ){\n        r1 = rTemp = sqlite3GetTempReg(pParse);\n        codeExprOrVector(pParse, pX->pRight, r1, 1);\n        testcase( pX->op==TK_GT );\n        testcase( pX->op==TK_GE );\n        testcase( pX->op==TK_LT );\n        testcase( pX->op==TK_LE );\n        op = aMoveOp[((pX->op - TK_GT - 1) & 0x3) | 0x1];\n        assert( pX->op!=TK_GT || op==OP_SeekGE );\n        assert( pX->op!=TK_GE || op==OP_SeekGE );\n        assert( pX->op!=TK_LT || op==OP_SeekLE );\n        assert( pX->op!=TK_LE || op==OP_SeekLE );\n      }else{\n        r1 = sqlite3ExprCodeTemp(pParse, pX->pRight, &rTemp);\n        disableTerm(pLevel, pStart);\n        op = aMoveOp[(pX->op - TK_GT)];\n      }\n      sqlite3VdbeAddOp3(v, op, iCur, addrBrk, r1);\n      VdbeComment((v, \"pk\"));\n      VdbeCoverageIf(v, pX->op==TK_GT);\n      VdbeCoverageIf(v, pX->op==TK_LE);\n      VdbeCoverageIf(v, pX->op==TK_LT);\n      VdbeCoverageIf(v, pX->op==TK_GE);\n      sqlite3ExprCacheAffinityChange(pParse, r1, 1);\n      sqlite3ReleaseTempReg(pParse, rTemp);\n    }else{\n      sqlite3VdbeAddOp2(v, bRev ? OP_Last : OP_Rewind, iCur, addrHalt);\n      VdbeCoverageIf(v, bRev==0);\n      VdbeCoverageIf(v, bRev!=0);\n    }\n    if( pEnd ){\n      Expr *pX;\n      pX = pEnd->pExpr;\n      assert( pX!=0 );\n      assert( (pEnd->wtFlags & TERM_VNULL)==0 );\n      testcase( pEnd->leftCursor!=iCur ); /* Transitive constraints */\n      testcase( pEnd->wtFlags & TERM_VIRTUAL );\n      memEndValue = ++pParse->nMem;\n      codeExprOrVector(pParse, pX->pRight, memEndValue, 1);\n      if( 0==sqlite3ExprIsVector(pX->pRight) \n       && (pX->op==TK_LT || pX->op==TK_GT) \n      ){\n        testOp = bRev ? OP_Le : OP_Ge;\n      }else{\n        testOp = bRev ? OP_Lt : OP_Gt;\n      }\n      if( 0==sqlite3ExprIsVector(pX->pRight) ){\n        disableTerm(pLevel, pEnd);\n      }\n    }\n    start = sqlite3VdbeCurrentAddr(v);\n    pLevel->op = bRev ? OP_Prev : OP_Next;\n    pLevel->p1 = iCur;\n    pLevel->p2 = start;\n    assert( pLevel->p5==0 );\n    if( testOp!=OP_Noop ){\n      iRowidReg = ++pParse->nMem;\n      sqlite3VdbeAddOp2(v, OP_Rowid, iCur, iRowidReg);\n      sqlite3ExprCacheStore(pParse, iCur, -1, iRowidReg);\n      sqlite3VdbeAddOp3(v, testOp, memEndValue, addrBrk, iRowidReg);\n      VdbeCoverageIf(v, testOp==OP_Le);\n      VdbeCoverageIf(v, testOp==OP_Lt);\n      VdbeCoverageIf(v, testOp==OP_Ge);\n      VdbeCoverageIf(v, testOp==OP_Gt);\n      sqlite3VdbeChangeP5(v, SQLITE_AFF_NUMERIC | SQLITE_JUMPIFNULL);\n    }\n  }else if( pLoop->wsFlags & WHERE_INDEXED ){\n    /* Case 4: A scan using an index.\n    **\n    **         The WHERE clause may contain zero or more equality \n    **         terms (\"==\" or \"IN\" operators) that refer to the N\n    **         left-most columns of the index. It may also contain\n    **         inequality constraints (>, <, >= or <=) on the indexed\n    **         column that immediately follows the N equalities. Only \n    **         the right-most column can be an inequality - the rest must\n    **         use the \"==\" and \"IN\" operators. For example, if the \n    **         index is on (x,y,z), then the following clauses are all \n    **         optimized:\n    **\n    **            x=5\n    **            x=5 AND y=10\n    **            x=5 AND y<10\n    **            x=5 AND y>5 AND y<10\n    **            x=5 AND y=5 AND z<=10\n    **\n    **         The z<10 term of the following cannot be used, only\n    **         the x=5 term:\n    **\n    **            x=5 AND z<10\n    **\n    **         N may be zero if there are inequality constraints.\n    **         If there are no inequality constraints, then N is at\n    **         least one.\n    **\n    **         This case is also used when there are no WHERE clause\n    **         constraints but an index is selected anyway, in order\n    **         to force the output order to conform to an ORDER BY.\n    */  \n    static const u8 aStartOp[] = {\n      0,\n      0,\n      OP_Rewind,           /* 2: (!start_constraints && startEq &&  !bRev) */\n      OP_Last,             /* 3: (!start_constraints && startEq &&   bRev) */\n      OP_SeekGT,           /* 4: (start_constraints  && !startEq && !bRev) */\n      OP_SeekLT,           /* 5: (start_constraints  && !startEq &&  bRev) */\n      OP_SeekGE,           /* 6: (start_constraints  &&  startEq && !bRev) */\n      OP_SeekLE            /* 7: (start_constraints  &&  startEq &&  bRev) */\n    };\n    static const u8 aEndOp[] = {\n      OP_IdxGE,            /* 0: (end_constraints && !bRev && !endEq) */\n      OP_IdxGT,            /* 1: (end_constraints && !bRev &&  endEq) */\n      OP_IdxLE,            /* 2: (end_constraints &&  bRev && !endEq) */\n      OP_IdxLT,            /* 3: (end_constraints &&  bRev &&  endEq) */\n    };\n    u16 nEq = pLoop->u.btree.nEq;     /* Number of == or IN terms */\n    u16 nBtm = pLoop->u.btree.nBtm;   /* Length of BTM vector */\n    u16 nTop = pLoop->u.btree.nTop;   /* Length of TOP vector */\n    int regBase;                 /* Base register holding constraint values */\n    WhereTerm *pRangeStart = 0;  /* Inequality constraint at range start */\n    WhereTerm *pRangeEnd = 0;    /* Inequality constraint at range end */\n    int startEq;                 /* True if range start uses ==, >= or <= */\n    int endEq;                   /* True if range end uses ==, >= or <= */\n    int start_constraints;       /* Start of range is constrained */\n    int nConstraint;             /* Number of constraint terms */\n    int iIdxCur;                 /* The VDBE cursor for the index */\n    int nExtraReg = 0;           /* Number of extra registers needed */\n    int op;                      /* Instruction opcode */\n    char *zStartAff;             /* Affinity for start of range constraint */\n    char *zEndAff = 0;           /* Affinity for end of range constraint */\n    u8 bSeekPastNull = 0;        /* True to seek past initial nulls */\n    u8 bStopAtNull = 0;          /* Add condition to terminate at NULLs */\n\n    pIdx = pLoop->u.btree.pIndex;\n    iIdxCur = pLevel->iIdxCur;\n    assert( nEq>=pLoop->nSkip );\n\n    /* If this loop satisfies a sort order (pOrderBy) request that \n    ** was passed to this function to implement a \"SELECT min(x) ...\" \n    ** query, then the caller will only allow the loop to run for\n    ** a single iteration. This means that the first row returned\n    ** should not have a NULL value stored in 'x'. If column 'x' is\n    ** the first one after the nEq equality constraints in the index,\n    ** this requires some special handling.\n    */\n    assert( pWInfo->pOrderBy==0\n         || pWInfo->pOrderBy->nExpr==1\n         || (pWInfo->wctrlFlags&WHERE_ORDERBY_MIN)==0 );\n    if( (pWInfo->wctrlFlags&WHERE_ORDERBY_MIN)!=0\n     && pWInfo->nOBSat>0\n     && (pIdx->nKeyCol>nEq)\n    ){\n      assert( pLoop->nSkip==0 );\n      bSeekPastNull = 1;\n      nExtraReg = 1;\n    }\n\n    /* Find any inequality constraint terms for the start and end \n    ** of the range. \n    */\n    j = nEq;\n    if( pLoop->wsFlags & WHERE_BTM_LIMIT ){\n      pRangeStart = pLoop->aLTerm[j++];\n      nExtraReg = MAX(nExtraReg, pLoop->u.btree.nBtm);\n      /* Like optimization range constraints always occur in pairs */\n      assert( (pRangeStart->wtFlags & TERM_LIKEOPT)==0 || \n              (pLoop->wsFlags & WHERE_TOP_LIMIT)!=0 );\n    }\n    if( pLoop->wsFlags & WHERE_TOP_LIMIT ){\n      pRangeEnd = pLoop->aLTerm[j++];\n      nExtraReg = MAX(nExtraReg, pLoop->u.btree.nTop);\n#ifndef SQLITE_LIKE_DOESNT_MATCH_BLOBS\n      if( (pRangeEnd->wtFlags & TERM_LIKEOPT)!=0 ){\n        assert( pRangeStart!=0 );                     /* LIKE opt constraints */\n        assert( pRangeStart->wtFlags & TERM_LIKEOPT );   /* occur in pairs */\n        pLevel->iLikeRepCntr = (u32)++pParse->nMem;\n        sqlite3VdbeAddOp2(v, OP_Integer, 1, (int)pLevel->iLikeRepCntr);\n        VdbeComment((v, \"LIKE loop counter\"));\n        pLevel->addrLikeRep = sqlite3VdbeCurrentAddr(v);\n        /* iLikeRepCntr actually stores 2x the counter register number.  The\n        ** bottom bit indicates whether the search order is ASC or DESC. */\n        testcase( bRev );\n        testcase( pIdx->aSortOrder[nEq]==SQLITE_SO_DESC );\n        assert( (bRev & ~1)==0 );\n        pLevel->iLikeRepCntr <<=1;\n        pLevel->iLikeRepCntr |= bRev ^ (pIdx->aSortOrder[nEq]==SQLITE_SO_DESC);\n      }\n#endif\n      if( pRangeStart==0 ){\n        j = pIdx->aiColumn[nEq];\n        if( (j>=0 && pIdx->pTable->aCol[j].notNull==0) || j==XN_EXPR ){\n          bSeekPastNull = 1;\n        }\n      }\n    }\n    assert( pRangeEnd==0 || (pRangeEnd->wtFlags & TERM_VNULL)==0 );\n\n    /* If we are doing a reverse order scan on an ascending index, or\n    ** a forward order scan on a descending index, interchange the \n    ** start and end terms (pRangeStart and pRangeEnd).\n    */\n    if( (nEq<pIdx->nKeyCol && bRev==(pIdx->aSortOrder[nEq]==SQLITE_SO_ASC))\n     || (bRev && pIdx->nKeyCol==nEq)\n    ){\n      SWAP(WhereTerm *, pRangeEnd, pRangeStart);\n      SWAP(u8, bSeekPastNull, bStopAtNull);\n      SWAP(u8, nBtm, nTop);\n    }\n\n    /* Generate code to evaluate all constraint terms using == or IN\n    ** and store the values of those terms in an array of registers\n    ** starting at regBase.\n    */\n    codeCursorHint(pTabItem, pWInfo, pLevel, pRangeEnd);\n    regBase = codeAllEqualityTerms(pParse,pLevel,bRev,nExtraReg,&zStartAff);\n    assert( zStartAff==0 || sqlite3Strlen30(zStartAff)>=nEq );\n    if( zStartAff && nTop ){\n      zEndAff = sqlite3DbStrDup(db, &zStartAff[nEq]);\n    }\n    addrNxt = pLevel->addrNxt;\n\n    testcase( pRangeStart && (pRangeStart->eOperator & WO_LE)!=0 );\n    testcase( pRangeStart && (pRangeStart->eOperator & WO_GE)!=0 );\n    testcase( pRangeEnd && (pRangeEnd->eOperator & WO_LE)!=0 );\n    testcase( pRangeEnd && (pRangeEnd->eOperator & WO_GE)!=0 );\n    startEq = !pRangeStart || pRangeStart->eOperator & (WO_LE|WO_GE);\n    endEq =   !pRangeEnd || pRangeEnd->eOperator & (WO_LE|WO_GE);\n    start_constraints = pRangeStart || nEq>0;\n\n    /* Seek the index cursor to the start of the range. */\n    nConstraint = nEq;\n    if( pRangeStart ){\n      Expr *pRight = pRangeStart->pExpr->pRight;\n      codeExprOrVector(pParse, pRight, regBase+nEq, nBtm);\n      whereLikeOptimizationStringFixup(v, pLevel, pRangeStart);\n      if( (pRangeStart->wtFlags & TERM_VNULL)==0\n       && sqlite3ExprCanBeNull(pRight)\n      ){\n        sqlite3VdbeAddOp2(v, OP_IsNull, regBase+nEq, addrNxt);\n        VdbeCoverage(v);\n      }\n      if( zStartAff ){\n        updateRangeAffinityStr(pRight, nBtm, &zStartAff[nEq]);\n      }  \n      nConstraint += nBtm;\n      testcase( pRangeStart->wtFlags & TERM_VIRTUAL );\n      if( sqlite3ExprIsVector(pRight)==0 ){\n        disableTerm(pLevel, pRangeStart);\n      }else{\n        startEq = 1;\n      }\n      bSeekPastNull = 0;\n    }else if( bSeekPastNull ){\n      sqlite3VdbeAddOp2(v, OP_Null, 0, regBase+nEq);\n      nConstraint++;\n      startEq = 0;\n      start_constraints = 1;\n    }\n    codeApplyAffinity(pParse, regBase, nConstraint - bSeekPastNull, zStartAff);\n    if( pLoop->nSkip>0 && nConstraint==pLoop->nSkip ){\n      /* The skip-scan logic inside the call to codeAllEqualityConstraints()\n      ** above has already left the cursor sitting on the correct row,\n      ** so no further seeking is needed */\n    }else{\n      op = aStartOp[(start_constraints<<2) + (startEq<<1) + bRev];\n      assert( op!=0 );\n      sqlite3VdbeAddOp4Int(v, op, iIdxCur, addrNxt, regBase, nConstraint);\n      VdbeCoverage(v);\n      VdbeCoverageIf(v, op==OP_Rewind);  testcase( op==OP_Rewind );\n      VdbeCoverageIf(v, op==OP_Last);    testcase( op==OP_Last );\n      VdbeCoverageIf(v, op==OP_SeekGT);  testcase( op==OP_SeekGT );\n      VdbeCoverageIf(v, op==OP_SeekGE);  testcase( op==OP_SeekGE );\n      VdbeCoverageIf(v, op==OP_SeekLE);  testcase( op==OP_SeekLE );\n      VdbeCoverageIf(v, op==OP_SeekLT);  testcase( op==OP_SeekLT );\n    }\n\n    /* Load the value for the inequality constraint at the end of the\n    ** range (if any).\n    */\n    nConstraint = nEq;\n    if( pRangeEnd ){\n      Expr *pRight = pRangeEnd->pExpr->pRight;\n      sqlite3ExprCacheRemove(pParse, regBase+nEq, 1);\n      codeExprOrVector(pParse, pRight, regBase+nEq, nTop);\n      whereLikeOptimizationStringFixup(v, pLevel, pRangeEnd);\n      if( (pRangeEnd->wtFlags & TERM_VNULL)==0\n       && sqlite3ExprCanBeNull(pRight)\n      ){\n        sqlite3VdbeAddOp2(v, OP_IsNull, regBase+nEq, addrNxt);\n        VdbeCoverage(v);\n      }\n      if( zEndAff ){\n        updateRangeAffinityStr(pRight, nTop, zEndAff);\n        codeApplyAffinity(pParse, regBase+nEq, nTop, zEndAff);\n      }else{\n        assert( pParse->db->mallocFailed );\n      }\n      nConstraint += nTop;\n      testcase( pRangeEnd->wtFlags & TERM_VIRTUAL );\n\n      if( sqlite3ExprIsVector(pRight)==0 ){\n        disableTerm(pLevel, pRangeEnd);\n      }else{\n        endEq = 1;\n      }\n    }else if( bStopAtNull ){\n      sqlite3VdbeAddOp2(v, OP_Null, 0, regBase+nEq);\n      sqlite3ExprCacheRemove(pParse, regBase+nEq, 1);\n      endEq = 0;\n      nConstraint++;\n    }\n    sqlite3DbFree(db, zStartAff);\n    sqlite3DbFree(db, zEndAff);\n\n    /* Top of the loop body */\n    pLevel->p2 = sqlite3VdbeCurrentAddr(v);\n\n    /* Check if the index cursor is past the end of the range. */\n    if( nConstraint ){\n      op = aEndOp[bRev*2 + endEq];\n      sqlite3VdbeAddOp4Int(v, op, iIdxCur, addrNxt, regBase, nConstraint);\n      testcase( op==OP_IdxGT );  VdbeCoverageIf(v, op==OP_IdxGT );\n      testcase( op==OP_IdxGE );  VdbeCoverageIf(v, op==OP_IdxGE );\n      testcase( op==OP_IdxLT );  VdbeCoverageIf(v, op==OP_IdxLT );\n      testcase( op==OP_IdxLE );  VdbeCoverageIf(v, op==OP_IdxLE );\n    }\n\n    /* Seek the table cursor, if required */\n    if( omitTable ){\n      /* pIdx is a covering index.  No need to access the main table. */\n    }else if( HasRowid(pIdx->pTable) ){\n      if( (pWInfo->wctrlFlags & WHERE_SEEK_TABLE) || (\n          (pWInfo->wctrlFlags & WHERE_SEEK_UNIQ_TABLE) \n       && (pWInfo->eOnePass==ONEPASS_SINGLE)\n      )){\n        iRowidReg = ++pParse->nMem;\n        sqlite3VdbeAddOp2(v, OP_IdxRowid, iIdxCur, iRowidReg);\n        sqlite3ExprCacheStore(pParse, iCur, -1, iRowidReg);\n        sqlite3VdbeAddOp3(v, OP_NotExists, iCur, 0, iRowidReg);\n        VdbeCoverage(v);\n      }else{\n        codeDeferredSeek(pWInfo, pIdx, iCur, iIdxCur);\n      }\n    }else if( iCur!=iIdxCur ){\n      Index *pPk = sqlite3PrimaryKeyIndex(pIdx->pTable);\n      iRowidReg = sqlite3GetTempRange(pParse, pPk->nKeyCol);\n      for(j=0; j<pPk->nKeyCol; j++){\n        k = sqlite3ColumnOfIndex(pIdx, pPk->aiColumn[j]);\n        sqlite3VdbeAddOp3(v, OP_Column, iIdxCur, k, iRowidReg+j);\n      }\n      sqlite3VdbeAddOp4Int(v, OP_NotFound, iCur, addrCont,\n                           iRowidReg, pPk->nKeyCol); VdbeCoverage(v);\n    }\n\n    /* If pIdx is an index on one or more expressions, then look through\n    ** all the expressions in pWInfo and try to transform matching expressions\n    ** into reference to index columns.\n    */\n    whereIndexExprTrans(pIdx, iCur, iIdxCur, pWInfo);\n\n\n    /* Record the instruction used to terminate the loop. */\n    if( pLoop->wsFlags & WHERE_ONEROW ){\n      pLevel->op = OP_Noop;\n    }else if( bRev ){\n      pLevel->op = OP_Prev;\n    }else{\n      pLevel->op = OP_Next;\n    }\n    pLevel->p1 = iIdxCur;\n    pLevel->p3 = (pLoop->wsFlags&WHERE_UNQ_WANTED)!=0 ? 1:0;\n    if( (pLoop->wsFlags & WHERE_CONSTRAINT)==0 ){\n      pLevel->p5 = SQLITE_STMTSTATUS_FULLSCAN_STEP;\n    }else{\n      assert( pLevel->p5==0 );\n    }\n    if( omitTable ) pIdx = 0;\n  }else\n\n#ifndef SQLITE_OMIT_OR_OPTIMIZATION\n  if( pLoop->wsFlags & WHERE_MULTI_OR ){\n    /* Case 5:  Two or more separately indexed terms connected by OR\n    **\n    ** Example:\n    **\n    **   CREATE TABLE t1(a,b,c,d);\n    **   CREATE INDEX i1 ON t1(a);\n    **   CREATE INDEX i2 ON t1(b);\n    **   CREATE INDEX i3 ON t1(c);\n    **\n    **   SELECT * FROM t1 WHERE a=5 OR b=7 OR (c=11 AND d=13)\n    **\n    ** In the example, there are three indexed terms connected by OR.\n    ** The top of the loop looks like this:\n    **\n    **          Null       1                # Zero the rowset in reg 1\n    **\n    ** Then, for each indexed term, the following. The arguments to\n    ** RowSetTest are such that the rowid of the current row is inserted\n    ** into the RowSet. If it is already present, control skips the\n    ** Gosub opcode and jumps straight to the code generated by WhereEnd().\n    **\n    **        sqlite3WhereBegin(<term>)\n    **          RowSetTest                  # Insert rowid into rowset\n    **          Gosub      2 A\n    **        sqlite3WhereEnd()\n    **\n    ** Following the above, code to terminate the loop. Label A, the target\n    ** of the Gosub above, jumps to the instruction right after the Goto.\n    **\n    **          Null       1                # Zero the rowset in reg 1\n    **          Goto       B                # The loop is finished.\n    **\n    **       A: <loop body>                 # Return data, whatever.\n    **\n    **          Return     2                # Jump back to the Gosub\n    **\n    **       B: <after the loop>\n    **\n    ** Added 2014-05-26: If the table is a WITHOUT ROWID table, then\n    ** use an ephemeral index instead of a RowSet to record the primary\n    ** keys of the rows we have already seen.\n    **\n    */\n    WhereClause *pOrWc;    /* The OR-clause broken out into subterms */\n    SrcList *pOrTab;       /* Shortened table list or OR-clause generation */\n    Index *pCov = 0;             /* Potential covering index (or NULL) */\n    int iCovCur = pParse->nTab++;  /* Cursor used for index scans (if any) */\n\n    int regReturn = ++pParse->nMem;           /* Register used with OP_Gosub */\n    int regRowset = 0;                        /* Register for RowSet object */\n    int regRowid = 0;                         /* Register holding rowid */\n    int iLoopBody = sqlite3VdbeMakeLabel(v);  /* Start of loop body */\n    int iRetInit;                             /* Address of regReturn init */\n    int untestedTerms = 0;             /* Some terms not completely tested */\n    int ii;                            /* Loop counter */\n    u16 wctrlFlags;                    /* Flags for sub-WHERE clause */\n    Expr *pAndExpr = 0;                /* An \".. AND (...)\" expression */\n    Table *pTab = pTabItem->pTab;\n\n    pTerm = pLoop->aLTerm[0];\n    assert( pTerm!=0 );\n    assert( pTerm->eOperator & WO_OR );\n    assert( (pTerm->wtFlags & TERM_ORINFO)!=0 );\n    pOrWc = &pTerm->u.pOrInfo->wc;\n    pLevel->op = OP_Return;\n    pLevel->p1 = regReturn;\n\n    /* Set up a new SrcList in pOrTab containing the table being scanned\n    ** by this loop in the a[0] slot and all notReady tables in a[1..] slots.\n    ** This becomes the SrcList in the recursive call to sqlite3WhereBegin().\n    */\n    if( pWInfo->nLevel>1 ){\n      int nNotReady;                 /* The number of notReady tables */\n      struct SrcList_item *origSrc;     /* Original list of tables */\n      nNotReady = pWInfo->nLevel - iLevel - 1;\n      pOrTab = sqlite3StackAllocRaw(db,\n                            sizeof(*pOrTab)+ nNotReady*sizeof(pOrTab->a[0]));\n      if( pOrTab==0 ) return notReady;\n      pOrTab->nAlloc = (u8)(nNotReady + 1);\n      pOrTab->nSrc = pOrTab->nAlloc;\n      memcpy(pOrTab->a, pTabItem, sizeof(*pTabItem));\n      origSrc = pWInfo->pTabList->a;\n      for(k=1; k<=nNotReady; k++){\n        memcpy(&pOrTab->a[k], &origSrc[pLevel[k].iFrom], sizeof(pOrTab->a[k]));\n      }\n    }else{\n      pOrTab = pWInfo->pTabList;\n    }\n\n    /* Initialize the rowset register to contain NULL. An SQL NULL is \n    ** equivalent to an empty rowset.  Or, create an ephemeral index\n    ** capable of holding primary keys in the case of a WITHOUT ROWID.\n    **\n    ** Also initialize regReturn to contain the address of the instruction \n    ** immediately following the OP_Return at the bottom of the loop. This\n    ** is required in a few obscure LEFT JOIN cases where control jumps\n    ** over the top of the loop into the body of it. In this case the \n    ** correct response for the end-of-loop code (the OP_Return) is to \n    ** fall through to the next instruction, just as an OP_Next does if\n    ** called on an uninitialized cursor.\n    */\n    if( (pWInfo->wctrlFlags & WHERE_DUPLICATES_OK)==0 ){\n      if( HasRowid(pTab) ){\n        regRowset = ++pParse->nMem;\n        sqlite3VdbeAddOp2(v, OP_Null, 0, regRowset);\n      }else{\n        Index *pPk = sqlite3PrimaryKeyIndex(pTab);\n        regRowset = pParse->nTab++;\n        sqlite3VdbeAddOp2(v, OP_OpenEphemeral, regRowset, pPk->nKeyCol);\n        sqlite3VdbeSetP4KeyInfo(pParse, pPk);\n      }\n      regRowid = ++pParse->nMem;\n    }\n    iRetInit = sqlite3VdbeAddOp2(v, OP_Integer, 0, regReturn);\n\n    /* If the original WHERE clause is z of the form:  (x1 OR x2 OR ...) AND y\n    ** Then for every term xN, evaluate as the subexpression: xN AND z\n    ** That way, terms in y that are factored into the disjunction will\n    ** be picked up by the recursive calls to sqlite3WhereBegin() below.\n    **\n    ** Actually, each subexpression is converted to \"xN AND w\" where w is\n    ** the \"interesting\" terms of z - terms that did not originate in the\n    ** ON or USING clause of a LEFT JOIN, and terms that are usable as \n    ** indices.\n    **\n    ** This optimization also only applies if the (x1 OR x2 OR ...) term\n    ** is not contained in the ON clause of a LEFT JOIN.\n    ** See ticket http://www.sqlite.org/src/info/f2369304e4\n    */\n    if( pWC->nTerm>1 ){\n      int iTerm;\n      for(iTerm=0; iTerm<pWC->nTerm; iTerm++){\n        Expr *pExpr = pWC->a[iTerm].pExpr;\n        if( &pWC->a[iTerm] == pTerm ) continue;\n        if( ExprHasProperty(pExpr, EP_FromJoin) ) continue;\n        testcase( pWC->a[iTerm].wtFlags & TERM_VIRTUAL );\n        testcase( pWC->a[iTerm].wtFlags & TERM_CODED );\n        if( (pWC->a[iTerm].wtFlags & (TERM_VIRTUAL|TERM_CODED))!=0 ) continue;\n        if( (pWC->a[iTerm].eOperator & WO_ALL)==0 ) continue;\n        testcase( pWC->a[iTerm].wtFlags & TERM_ORINFO );\n        pExpr = sqlite3ExprDup(db, pExpr, 0);\n        pAndExpr = sqlite3ExprAnd(db, pAndExpr, pExpr);\n      }\n      if( pAndExpr ){\n        pAndExpr = sqlite3PExpr(pParse, TK_AND|TKFLG_DONTFOLD, 0, pAndExpr);\n      }\n    }\n\n    /* Run a separate WHERE clause for each term of the OR clause.  After\n    ** eliminating duplicates from other WHERE clauses, the action for each\n    ** sub-WHERE clause is to to invoke the main loop body as a subroutine.\n    */\n    wctrlFlags =  WHERE_OR_SUBCLAUSE | (pWInfo->wctrlFlags & WHERE_SEEK_TABLE);\n    for(ii=0; ii<pOrWc->nTerm; ii++){\n      WhereTerm *pOrTerm = &pOrWc->a[ii];\n      if( pOrTerm->leftCursor==iCur || (pOrTerm->eOperator & WO_AND)!=0 ){\n        WhereInfo *pSubWInfo;           /* Info for single OR-term scan */\n        Expr *pOrExpr = pOrTerm->pExpr; /* Current OR clause term */\n        int jmp1 = 0;                   /* Address of jump operation */\n        if( pAndExpr && !ExprHasProperty(pOrExpr, EP_FromJoin) ){\n          pAndExpr->pLeft = pOrExpr;\n          pOrExpr = pAndExpr;\n        }\n        /* Loop through table entries that match term pOrTerm. */\n        WHERETRACE(0xffff, (\"Subplan for OR-clause:\\n\"));\n        pSubWInfo = sqlite3WhereBegin(pParse, pOrTab, pOrExpr, 0, 0,\n                                      wctrlFlags, iCovCur);\n        assert( pSubWInfo || pParse->nErr || db->mallocFailed );\n        if( pSubWInfo ){\n          WhereLoop *pSubLoop;\n          int addrExplain = sqlite3WhereExplainOneScan(\n              pParse, pOrTab, &pSubWInfo->a[0], iLevel, pLevel->iFrom, 0\n          );\n          sqlite3WhereAddScanStatus(v, pOrTab, &pSubWInfo->a[0], addrExplain);\n\n          /* This is the sub-WHERE clause body.  First skip over\n          ** duplicate rows from prior sub-WHERE clauses, and record the\n          ** rowid (or PRIMARY KEY) for the current row so that the same\n          ** row will be skipped in subsequent sub-WHERE clauses.\n          */\n          if( (pWInfo->wctrlFlags & WHERE_DUPLICATES_OK)==0 ){\n            int r;\n            int iSet = ((ii==pOrWc->nTerm-1)?-1:ii);\n            if( HasRowid(pTab) ){\n              r = sqlite3ExprCodeGetColumn(pParse, pTab, -1, iCur, regRowid, 0);\n              jmp1 = sqlite3VdbeAddOp4Int(v, OP_RowSetTest, regRowset, 0,\n                                           r,iSet);\n              VdbeCoverage(v);\n            }else{\n              Index *pPk = sqlite3PrimaryKeyIndex(pTab);\n              int nPk = pPk->nKeyCol;\n              int iPk;\n\n              /* Read the PK into an array of temp registers. */\n              r = sqlite3GetTempRange(pParse, nPk);\n              for(iPk=0; iPk<nPk; iPk++){\n                int iCol = pPk->aiColumn[iPk];\n                sqlite3ExprCodeGetColumnToReg(pParse, pTab, iCol, iCur, r+iPk);\n              }\n\n              /* Check if the temp table already contains this key. If so,\n              ** the row has already been included in the result set and\n              ** can be ignored (by jumping past the Gosub below). Otherwise,\n              ** insert the key into the temp table and proceed with processing\n              ** the row.\n              **\n              ** Use some of the same optimizations as OP_RowSetTest: If iSet\n              ** is zero, assume that the key cannot already be present in\n              ** the temp table. And if iSet is -1, assume that there is no \n              ** need to insert the key into the temp table, as it will never \n              ** be tested for.  */ \n              if( iSet ){\n                jmp1 = sqlite3VdbeAddOp4Int(v, OP_Found, regRowset, 0, r, nPk);\n                VdbeCoverage(v);\n              }\n              if( iSet>=0 ){\n                sqlite3VdbeAddOp3(v, OP_MakeRecord, r, nPk, regRowid);\n                sqlite3VdbeAddOp4Int(v, OP_IdxInsert, regRowset, regRowid,\n                                     r, nPk);\n                if( iSet ) sqlite3VdbeChangeP5(v, OPFLAG_USESEEKRESULT);\n              }\n\n              /* Release the array of temp registers */\n              sqlite3ReleaseTempRange(pParse, r, nPk);\n            }\n          }\n\n          /* Invoke the main loop body as a subroutine */\n          sqlite3VdbeAddOp2(v, OP_Gosub, regReturn, iLoopBody);\n\n          /* Jump here (skipping the main loop body subroutine) if the\n          ** current sub-WHERE row is a duplicate from prior sub-WHEREs. */\n          if( jmp1 ) sqlite3VdbeJumpHere(v, jmp1);\n\n          /* The pSubWInfo->untestedTerms flag means that this OR term\n          ** contained one or more AND term from a notReady table.  The\n          ** terms from the notReady table could not be tested and will\n          ** need to be tested later.\n          */\n          if( pSubWInfo->untestedTerms ) untestedTerms = 1;\n\n          /* If all of the OR-connected terms are optimized using the same\n          ** index, and the index is opened using the same cursor number\n          ** by each call to sqlite3WhereBegin() made by this loop, it may\n          ** be possible to use that index as a covering index.\n          **\n          ** If the call to sqlite3WhereBegin() above resulted in a scan that\n          ** uses an index, and this is either the first OR-connected term\n          ** processed or the index is the same as that used by all previous\n          ** terms, set pCov to the candidate covering index. Otherwise, set \n          ** pCov to NULL to indicate that no candidate covering index will \n          ** be available.\n          */\n          pSubLoop = pSubWInfo->a[0].pWLoop;\n          assert( (pSubLoop->wsFlags & WHERE_AUTO_INDEX)==0 );\n          if( (pSubLoop->wsFlags & WHERE_INDEXED)!=0\n           && (ii==0 || pSubLoop->u.btree.pIndex==pCov)\n           && (HasRowid(pTab) || !IsPrimaryKeyIndex(pSubLoop->u.btree.pIndex))\n          ){\n            assert( pSubWInfo->a[0].iIdxCur==iCovCur );\n            pCov = pSubLoop->u.btree.pIndex;\n          }else{\n            pCov = 0;\n          }\n\n          /* Finish the loop through table entries that match term pOrTerm. */\n          sqlite3WhereEnd(pSubWInfo);\n        }\n      }\n    }\n    pLevel->u.pCovidx = pCov;\n    if( pCov ) pLevel->iIdxCur = iCovCur;\n    if( pAndExpr ){\n      pAndExpr->pLeft = 0;\n      sqlite3ExprDelete(db, pAndExpr);\n    }\n    sqlite3VdbeChangeP1(v, iRetInit, sqlite3VdbeCurrentAddr(v));\n    sqlite3VdbeGoto(v, pLevel->addrBrk);\n    sqlite3VdbeResolveLabel(v, iLoopBody);\n\n    if( pWInfo->nLevel>1 ) sqlite3StackFree(db, pOrTab);\n    if( !untestedTerms ) disableTerm(pLevel, pTerm);\n  }else\n#endif /* SQLITE_OMIT_OR_OPTIMIZATION */\n\n  {\n    /* Case 6:  There is no usable index.  We must do a complete\n    **          scan of the entire table.\n    */\n    static const u8 aStep[] = { OP_Next, OP_Prev };\n    static const u8 aStart[] = { OP_Rewind, OP_Last };\n    assert( bRev==0 || bRev==1 );\n    if( pTabItem->fg.isRecursive ){\n      /* Tables marked isRecursive have only a single row that is stored in\n      ** a pseudo-cursor.  No need to Rewind or Next such cursors. */\n      pLevel->op = OP_Noop;\n    }else{\n      codeCursorHint(pTabItem, pWInfo, pLevel, 0);\n      pLevel->op = aStep[bRev];\n      pLevel->p1 = iCur;\n      pLevel->p2 = 1 + sqlite3VdbeAddOp2(v, aStart[bRev], iCur, addrHalt);\n      VdbeCoverageIf(v, bRev==0);\n      VdbeCoverageIf(v, bRev!=0);\n      pLevel->p5 = SQLITE_STMTSTATUS_FULLSCAN_STEP;\n    }\n  }\n\n#ifdef SQLITE_ENABLE_STMT_SCANSTATUS\n  pLevel->addrVisit = sqlite3VdbeCurrentAddr(v);\n#endif\n\n  /* Insert code to test every subexpression that can be completely\n  ** computed using the current set of tables.\n  **\n  ** This loop may run between one and three times, depending on the\n  ** constraints to be generated. The value of stack variable iLoop\n  ** determines the constraints coded by each iteration, as follows:\n  **\n  ** iLoop==1: Code only expressions that are entirely covered by pIdx.\n  ** iLoop==2: Code remaining expressions that do not contain correlated\n  **           sub-queries.  \n  ** iLoop==3: Code all remaining expressions.\n  **\n  ** An effort is made to skip unnecessary iterations of the loop.\n  */\n  iLoop = (pIdx ? 1 : 2);\n  do{\n    int iNext = 0;                /* Next value for iLoop */\n    for(pTerm=pWC->a, j=pWC->nTerm; j>0; j--, pTerm++){\n      Expr *pE;\n      int skipLikeAddr = 0;\n      testcase( pTerm->wtFlags & TERM_VIRTUAL );\n      testcase( pTerm->wtFlags & TERM_CODED );\n      if( pTerm->wtFlags & (TERM_VIRTUAL|TERM_CODED) ) continue;\n      if( (pTerm->prereqAll & pLevel->notReady)!=0 ){\n        testcase( pWInfo->untestedTerms==0\n            && (pWInfo->wctrlFlags & WHERE_OR_SUBCLAUSE)!=0 );\n        pWInfo->untestedTerms = 1;\n        continue;\n      }\n      pE = pTerm->pExpr;\n      assert( pE!=0 );\n      if( pLevel->iLeftJoin && !ExprHasProperty(pE, EP_FromJoin) ){\n        continue;\n      }\n      \n      if( iLoop==1 && !sqlite3ExprCoveredByIndex(pE, pLevel->iTabCur, pIdx) ){\n        iNext = 2;\n        continue;\n      }\n      if( iLoop<3 && (pTerm->wtFlags & TERM_VARSELECT) ){\n        if( iNext==0 ) iNext = 3;\n        continue;\n      }\n\n      if( pTerm->wtFlags & TERM_LIKECOND ){\n        /* If the TERM_LIKECOND flag is set, that means that the range search\n        ** is sufficient to guarantee that the LIKE operator is true, so we\n        ** can skip the call to the like(A,B) function.  But this only works\n        ** for strings.  So do not skip the call to the function on the pass\n        ** that compares BLOBs. */\n#ifdef SQLITE_LIKE_DOESNT_MATCH_BLOBS\n        continue;\n#else\n        u32 x = pLevel->iLikeRepCntr;\n        assert( x>0 );\n        skipLikeAddr = sqlite3VdbeAddOp1(v, (x&1)?OP_IfNot:OP_If, (int)(x>>1));\n        VdbeCoverage(v);\n#endif\n      }\n#ifdef WHERETRACE_ENABLED /* 0xffff */\n      if( sqlite3WhereTrace ){\n        VdbeNoopComment((v, \"WhereTerm[%d] (%p) priority=%d\",\n                         pWC->nTerm-j, pTerm, iLoop));\n      }\n#endif\n      sqlite3ExprIfFalse(pParse, pE, addrCont, SQLITE_JUMPIFNULL);\n      if( skipLikeAddr ) sqlite3VdbeJumpHere(v, skipLikeAddr);\n      pTerm->wtFlags |= TERM_CODED;\n    }\n    iLoop = iNext;\n  }while( iLoop>0 );\n\n  /* Insert code to test for implied constraints based on transitivity\n  ** of the \"==\" operator.\n  **\n  ** Example: If the WHERE clause contains \"t1.a=t2.b\" and \"t2.b=123\"\n  ** and we are coding the t1 loop and the t2 loop has not yet coded,\n  ** then we cannot use the \"t1.a=t2.b\" constraint, but we can code\n  ** the implied \"t1.a=123\" constraint.\n  */\n  for(pTerm=pWC->a, j=pWC->nTerm; j>0; j--, pTerm++){\n    Expr *pE, sEAlt;\n    WhereTerm *pAlt;\n    if( pTerm->wtFlags & (TERM_VIRTUAL|TERM_CODED) ) continue;\n    if( (pTerm->eOperator & (WO_EQ|WO_IS))==0 ) continue;\n    if( (pTerm->eOperator & WO_EQUIV)==0 ) continue;\n    if( pTerm->leftCursor!=iCur ) continue;\n    if( pLevel->iLeftJoin ) continue;\n    pE = pTerm->pExpr;\n    assert( !ExprHasProperty(pE, EP_FromJoin) );\n    assert( (pTerm->prereqRight & pLevel->notReady)!=0 );\n    pAlt = sqlite3WhereFindTerm(pWC, iCur, pTerm->u.leftColumn, notReady,\n                    WO_EQ|WO_IN|WO_IS, 0);\n    if( pAlt==0 ) continue;\n    if( pAlt->wtFlags & (TERM_CODED) ) continue;\n    if( (pAlt->eOperator & WO_IN) \n     && (pAlt->pExpr->flags & EP_xIsSelect)\n     && (pAlt->pExpr->x.pSelect->pEList->nExpr>1)\n    ){\n      continue;\n    }\n    testcase( pAlt->eOperator & WO_EQ );\n    testcase( pAlt->eOperator & WO_IS );\n    testcase( pAlt->eOperator & WO_IN );\n    VdbeModuleComment((v, \"begin transitive constraint\"));\n    sEAlt = *pAlt->pExpr;\n    sEAlt.pLeft = pE->pLeft;\n    sqlite3ExprIfFalse(pParse, &sEAlt, addrCont, SQLITE_JUMPIFNULL);\n  }\n\n  /* For a LEFT OUTER JOIN, generate code that will record the fact that\n  ** at least one row of the right table has matched the left table.  \n  */\n  if( pLevel->iLeftJoin ){\n    pLevel->addrFirst = sqlite3VdbeCurrentAddr(v);\n    sqlite3VdbeAddOp2(v, OP_Integer, 1, pLevel->iLeftJoin);\n    VdbeComment((v, \"record LEFT JOIN hit\"));\n    sqlite3ExprCacheClear(pParse);\n    for(pTerm=pWC->a, j=0; j<pWC->nTerm; j++, pTerm++){\n      testcase( pTerm->wtFlags & TERM_VIRTUAL );\n      testcase( pTerm->wtFlags & TERM_CODED );\n      if( pTerm->wtFlags & (TERM_VIRTUAL|TERM_CODED) ) continue;\n      if( (pTerm->prereqAll & pLevel->notReady)!=0 ){\n        assert( pWInfo->untestedTerms );\n        continue;\n      }\n      assert( pTerm->pExpr );\n      sqlite3ExprIfFalse(pParse, pTerm->pExpr, addrCont, SQLITE_JUMPIFNULL);\n      pTerm->wtFlags |= TERM_CODED;\n    }\n  }\n\n  return pLevel->notReady;\n}\n\n/************** End of wherecode.c *******************************************/\n/************** Begin file whereexpr.c ***************************************/\n/*\n** 2015-06-08\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n*************************************************************************\n** This module contains C code that generates VDBE code used to process\n** the WHERE clause of SQL statements.\n**\n** This file was originally part of where.c but was split out to improve\n** readability and editabiliity.  This file contains utility routines for\n** analyzing Expr objects in the WHERE clause.\n*/\n/* #include \"sqliteInt.h\" */\n/* #include \"whereInt.h\" */\n\n/* Forward declarations */\nstatic void exprAnalyze(SrcList*, WhereClause*, int);\n\n/*\n** Deallocate all memory associated with a WhereOrInfo object.\n*/\nstatic void whereOrInfoDelete(sqlite3 *db, WhereOrInfo *p){\n  sqlite3WhereClauseClear(&p->wc);\n  sqlite3DbFree(db, p);\n}\n\n/*\n** Deallocate all memory associated with a WhereAndInfo object.\n*/\nstatic void whereAndInfoDelete(sqlite3 *db, WhereAndInfo *p){\n  sqlite3WhereClauseClear(&p->wc);\n  sqlite3DbFree(db, p);\n}\n\n/*\n** Add a single new WhereTerm entry to the WhereClause object pWC.\n** The new WhereTerm object is constructed from Expr p and with wtFlags.\n** The index in pWC->a[] of the new WhereTerm is returned on success.\n** 0 is returned if the new WhereTerm could not be added due to a memory\n** allocation error.  The memory allocation failure will be recorded in\n** the db->mallocFailed flag so that higher-level functions can detect it.\n**\n** This routine will increase the size of the pWC->a[] array as necessary.\n**\n** If the wtFlags argument includes TERM_DYNAMIC, then responsibility\n** for freeing the expression p is assumed by the WhereClause object pWC.\n** This is true even if this routine fails to allocate a new WhereTerm.\n**\n** WARNING:  This routine might reallocate the space used to store\n** WhereTerms.  All pointers to WhereTerms should be invalidated after\n** calling this routine.  Such pointers may be reinitialized by referencing\n** the pWC->a[] array.\n*/\nstatic int whereClauseInsert(WhereClause *pWC, Expr *p, u16 wtFlags){\n  WhereTerm *pTerm;\n  int idx;\n  testcase( wtFlags & TERM_VIRTUAL );\n  if( pWC->nTerm>=pWC->nSlot ){\n    WhereTerm *pOld = pWC->a;\n    sqlite3 *db = pWC->pWInfo->pParse->db;\n    pWC->a = sqlite3DbMallocRawNN(db, sizeof(pWC->a[0])*pWC->nSlot*2 );\n    if( pWC->a==0 ){\n      if( wtFlags & TERM_DYNAMIC ){\n        sqlite3ExprDelete(db, p);\n      }\n      pWC->a = pOld;\n      return 0;\n    }\n    memcpy(pWC->a, pOld, sizeof(pWC->a[0])*pWC->nTerm);\n    if( pOld!=pWC->aStatic ){\n      sqlite3DbFree(db, pOld);\n    }\n    pWC->nSlot = sqlite3DbMallocSize(db, pWC->a)/sizeof(pWC->a[0]);\n  }\n  pTerm = &pWC->a[idx = pWC->nTerm++];\n  if( p && ExprHasProperty(p, EP_Unlikely) ){\n    pTerm->truthProb = sqlite3LogEst(p->iTable) - 270;\n  }else{\n    pTerm->truthProb = 1;\n  }\n  pTerm->pExpr = sqlite3ExprSkipCollate(p);\n  pTerm->wtFlags = wtFlags;\n  pTerm->pWC = pWC;\n  pTerm->iParent = -1;\n  memset(&pTerm->eOperator, 0,\n         sizeof(WhereTerm) - offsetof(WhereTerm,eOperator));\n  return idx;\n}\n\n/*\n** Return TRUE if the given operator is one of the operators that is\n** allowed for an indexable WHERE clause term.  The allowed operators are\n** \"=\", \"<\", \">\", \"<=\", \">=\", \"IN\", \"IS\", and \"IS NULL\"\n*/\nstatic int allowedOp(int op){\n  assert( TK_GT>TK_EQ && TK_GT<TK_GE );\n  assert( TK_LT>TK_EQ && TK_LT<TK_GE );\n  assert( TK_LE>TK_EQ && TK_LE<TK_GE );\n  assert( TK_GE==TK_EQ+4 );\n  return op==TK_IN || (op>=TK_EQ && op<=TK_GE) || op==TK_ISNULL || op==TK_IS;\n}\n\n/*\n** Commute a comparison operator.  Expressions of the form \"X op Y\"\n** are converted into \"Y op X\".\n**\n** If left/right precedence rules come into play when determining the\n** collating sequence, then COLLATE operators are adjusted to ensure\n** that the collating sequence does not change.  For example:\n** \"Y collate NOCASE op X\" becomes \"X op Y\" because any collation sequence on\n** the left hand side of a comparison overrides any collation sequence \n** attached to the right. For the same reason the EP_Collate flag\n** is not commuted.\n*/\nstatic void exprCommute(Parse *pParse, Expr *pExpr){\n  u16 expRight = (pExpr->pRight->flags & EP_Collate);\n  u16 expLeft = (pExpr->pLeft->flags & EP_Collate);\n  assert( allowedOp(pExpr->op) && pExpr->op!=TK_IN );\n  if( expRight==expLeft ){\n    /* Either X and Y both have COLLATE operator or neither do */\n    if( expRight ){\n      /* Both X and Y have COLLATE operators.  Make sure X is always\n      ** used by clearing the EP_Collate flag from Y. */\n      pExpr->pRight->flags &= ~EP_Collate;\n    }else if( sqlite3ExprCollSeq(pParse, pExpr->pLeft)!=0 ){\n      /* Neither X nor Y have COLLATE operators, but X has a non-default\n      ** collating sequence.  So add the EP_Collate marker on X to cause\n      ** it to be searched first. */\n      pExpr->pLeft->flags |= EP_Collate;\n    }\n  }\n  SWAP(Expr*,pExpr->pRight,pExpr->pLeft);\n  if( pExpr->op>=TK_GT ){\n    assert( TK_LT==TK_GT+2 );\n    assert( TK_GE==TK_LE+2 );\n    assert( TK_GT>TK_EQ );\n    assert( TK_GT<TK_LE );\n    assert( pExpr->op>=TK_GT && pExpr->op<=TK_GE );\n    pExpr->op = ((pExpr->op-TK_GT)^2)+TK_GT;\n  }\n}\n\n/*\n** Translate from TK_xx operator to WO_xx bitmask.\n*/\nstatic u16 operatorMask(int op){\n  u16 c;\n  assert( allowedOp(op) );\n  if( op==TK_IN ){\n    c = WO_IN;\n  }else if( op==TK_ISNULL ){\n    c = WO_ISNULL;\n  }else if( op==TK_IS ){\n    c = WO_IS;\n  }else{\n    assert( (WO_EQ<<(op-TK_EQ)) < 0x7fff );\n    c = (u16)(WO_EQ<<(op-TK_EQ));\n  }\n  assert( op!=TK_ISNULL || c==WO_ISNULL );\n  assert( op!=TK_IN || c==WO_IN );\n  assert( op!=TK_EQ || c==WO_EQ );\n  assert( op!=TK_LT || c==WO_LT );\n  assert( op!=TK_LE || c==WO_LE );\n  assert( op!=TK_GT || c==WO_GT );\n  assert( op!=TK_GE || c==WO_GE );\n  assert( op!=TK_IS || c==WO_IS );\n  return c;\n}\n\n\n#ifndef SQLITE_OMIT_LIKE_OPTIMIZATION\n/*\n** Check to see if the given expression is a LIKE or GLOB operator that\n** can be optimized using inequality constraints.  Return TRUE if it is\n** so and false if not.\n**\n** In order for the operator to be optimizible, the RHS must be a string\n** literal that does not begin with a wildcard.  The LHS must be a column\n** that may only be NULL, a string, or a BLOB, never a number. (This means\n** that virtual tables cannot participate in the LIKE optimization.)  The\n** collating sequence for the column on the LHS must be appropriate for\n** the operator.\n*/\nstatic int isLikeOrGlob(\n  Parse *pParse,    /* Parsing and code generating context */\n  Expr *pExpr,      /* Test this expression */\n  Expr **ppPrefix,  /* Pointer to TK_STRING expression with pattern prefix */\n  int *pisComplete, /* True if the only wildcard is % in the last character */\n  int *pnoCase      /* True if uppercase is equivalent to lowercase */\n){\n  const u8 *z = 0;         /* String on RHS of LIKE operator */\n  Expr *pRight, *pLeft;      /* Right and left size of LIKE operator */\n  ExprList *pList;           /* List of operands to the LIKE operator */\n  int c;                     /* One character in z[] */\n  int cnt;                   /* Number of non-wildcard prefix characters */\n  char wc[4];                /* Wildcard characters */\n  sqlite3 *db = pParse->db;  /* Database connection */\n  sqlite3_value *pVal = 0;\n  int op;                    /* Opcode of pRight */\n  int rc;                    /* Result code to return */\n\n  if( !sqlite3IsLikeFunction(db, pExpr, pnoCase, wc) ){\n    return 0;\n  }\n#ifdef SQLITE_EBCDIC\n  if( *pnoCase ) return 0;\n#endif\n  pList = pExpr->x.pList;\n  pLeft = pList->a[1].pExpr;\n\n  pRight = sqlite3ExprSkipCollate(pList->a[0].pExpr);\n  op = pRight->op;\n  if( op==TK_VARIABLE && (db->flags & SQLITE_EnableQPSG)==0 ){\n    Vdbe *pReprepare = pParse->pReprepare;\n    int iCol = pRight->iColumn;\n    pVal = sqlite3VdbeGetBoundValue(pReprepare, iCol, SQLITE_AFF_BLOB);\n    if( pVal && sqlite3_value_type(pVal)==SQLITE_TEXT ){\n      z = sqlite3_value_text(pVal);\n    }\n    sqlite3VdbeSetVarmask(pParse->pVdbe, iCol);\n    assert( pRight->op==TK_VARIABLE || pRight->op==TK_REGISTER );\n  }else if( op==TK_STRING ){\n    z = (u8*)pRight->u.zToken;\n  }\n  if( z ){\n\n    /* If the RHS begins with a digit or a minus sign, then the LHS must\n    ** be an ordinary column (not a virtual table column) with TEXT affinity.\n    ** Otherwise the LHS might be numeric and \"lhs >= rhs\" would be false\n    ** even though \"lhs LIKE rhs\" is true.  But if the RHS does not start\n    ** with a digit or '-', then \"lhs LIKE rhs\" will always be false if\n    ** the LHS is numeric and so the optimization still works.\n    */\n    if( sqlite3Isdigit(z[0]) || z[0]=='-' ){\n      if( pLeft->op!=TK_COLUMN \n       || sqlite3ExprAffinity(pLeft)!=SQLITE_AFF_TEXT \n       || IsVirtual(pLeft->pTab)  /* Value might be numeric */\n      ){\n        sqlite3ValueFree(pVal);\n        return 0;\n      }\n    }\n\n    /* Count the number of prefix characters prior to the first wildcard */\n    cnt = 0;\n    while( (c=z[cnt])!=0 && c!=wc[0] && c!=wc[1] && c!=wc[2] ){\n      cnt++;\n      if( c==wc[3] && z[cnt]!=0 ) cnt++;\n    }\n\n    /* The optimization is possible only if (1) the pattern does not begin\n    ** with a wildcard and if (2) the non-wildcard prefix does not end with\n    ** an (illegal 0xff) character.  The second condition is necessary so\n    ** that we can increment the prefix key to find an upper bound for the\n    ** range search. \n    */\n    if( cnt!=0 && 255!=(u8)z[cnt-1] ){\n      Expr *pPrefix;\n\n      /* A \"complete\" match if the pattern ends with \"*\" or \"%\" */\n      *pisComplete = c==wc[0] && z[cnt+1]==0;\n\n      /* Get the pattern prefix.  Remove all escapes from the prefix. */\n      pPrefix = sqlite3Expr(db, TK_STRING, (char*)z);\n      if( pPrefix ){\n        int iFrom, iTo;\n        char *zNew = pPrefix->u.zToken;\n        zNew[cnt] = 0;\n        for(iFrom=iTo=0; iFrom<cnt; iFrom++){\n          if( zNew[iFrom]==wc[3] ) iFrom++;\n          zNew[iTo++] = zNew[iFrom];\n        }\n        zNew[iTo] = 0;\n      }\n      *ppPrefix = pPrefix;\n\n      /* If the RHS pattern is a bound parameter, make arrangements to\n      ** reprepare the statement when that parameter is rebound */\n      if( op==TK_VARIABLE ){\n        Vdbe *v = pParse->pVdbe;\n        sqlite3VdbeSetVarmask(v, pRight->iColumn);\n        if( *pisComplete && pRight->u.zToken[1] ){\n          /* If the rhs of the LIKE expression is a variable, and the current\n          ** value of the variable means there is no need to invoke the LIKE\n          ** function, then no OP_Variable will be added to the program.\n          ** This causes problems for the sqlite3_bind_parameter_name()\n          ** API. To work around them, add a dummy OP_Variable here.\n          */ \n          int r1 = sqlite3GetTempReg(pParse);\n          sqlite3ExprCodeTarget(pParse, pRight, r1);\n          sqlite3VdbeChangeP3(v, sqlite3VdbeCurrentAddr(v)-1, 0);\n          sqlite3ReleaseTempReg(pParse, r1);\n        }\n      }\n    }else{\n      z = 0;\n    }\n  }\n\n  rc = (z!=0);\n  sqlite3ValueFree(pVal);\n  return rc;\n}\n#endif /* SQLITE_OMIT_LIKE_OPTIMIZATION */\n\n\n#ifndef SQLITE_OMIT_VIRTUALTABLE\n/*\n** Check to see if the pExpr expression is a form that needs to be passed\n** to the xBestIndex method of virtual tables.  Forms of interest include:\n**\n**          Expression                   Virtual Table Operator\n**          -----------------------      ---------------------------------\n**      1.  column MATCH expr            SQLITE_INDEX_CONSTRAINT_MATCH\n**      2.  column GLOB expr             SQLITE_INDEX_CONSTRAINT_GLOB\n**      3.  column LIKE expr             SQLITE_INDEX_CONSTRAINT_LIKE\n**      4.  column REGEXP expr           SQLITE_INDEX_CONSTRAINT_REGEXP\n**      5.  column != expr               SQLITE_INDEX_CONSTRAINT_NE\n**      6.  expr != column               SQLITE_INDEX_CONSTRAINT_NE\n**      7.  column IS NOT expr           SQLITE_INDEX_CONSTRAINT_ISNOT\n**      8.  expr IS NOT column           SQLITE_INDEX_CONSTRAINT_ISNOT\n**      9.  column IS NOT NULL           SQLITE_INDEX_CONSTRAINT_ISNOTNULL\n**\n** In every case, \"column\" must be a column of a virtual table.  If there\n** is a match, set *ppLeft to the \"column\" expression, set *ppRight to the \n** \"expr\" expression (even though in forms (6) and (8) the column is on the\n** right and the expression is on the left).  Also set *peOp2 to the\n** appropriate virtual table operator.  The return value is 1 or 2 if there\n** is a match.  The usual return is 1, but if the RHS is also a column\n** of virtual table in forms (5) or (7) then return 2.\n**\n** If the expression matches none of the patterns above, return 0.\n*/\nstatic int isAuxiliaryVtabOperator(\n  Expr *pExpr,                    /* Test this expression */\n  unsigned char *peOp2,           /* OUT: 0 for MATCH, or else an op2 value */\n  Expr **ppLeft,                  /* Column expression to left of MATCH/op2 */\n  Expr **ppRight                  /* Expression to left of MATCH/op2 */\n){\n  if( pExpr->op==TK_FUNCTION ){\n    static const struct Op2 {\n      const char *zOp;\n      unsigned char eOp2;\n    } aOp[] = {\n      { \"match\",  SQLITE_INDEX_CONSTRAINT_MATCH },\n      { \"glob\",   SQLITE_INDEX_CONSTRAINT_GLOB },\n      { \"like\",   SQLITE_INDEX_CONSTRAINT_LIKE },\n      { \"regexp\", SQLITE_INDEX_CONSTRAINT_REGEXP }\n    };\n    ExprList *pList;\n    Expr *pCol;                     /* Column reference */\n    int i;\n\n    pList = pExpr->x.pList;\n    if( pList==0 || pList->nExpr!=2 ){\n      return 0;\n    }\n    pCol = pList->a[1].pExpr;\n    if( pCol->op!=TK_COLUMN || !IsVirtual(pCol->pTab) ){\n      return 0;\n    }\n    for(i=0; i<ArraySize(aOp); i++){\n      if( sqlite3StrICmp(pExpr->u.zToken, aOp[i].zOp)==0 ){\n        *peOp2 = aOp[i].eOp2;\n        *ppRight = pList->a[0].pExpr;\n        *ppLeft = pCol;\n        return 1;\n      }\n    }\n  }else if( pExpr->op==TK_NE || pExpr->op==TK_ISNOT || pExpr->op==TK_NOTNULL ){\n    int res = 0;\n    Expr *pLeft = pExpr->pLeft;\n    Expr *pRight = pExpr->pRight;\n    if( pLeft->op==TK_COLUMN && IsVirtual(pLeft->pTab) ){\n      res++;\n    }\n    if( pRight && pRight->op==TK_COLUMN && IsVirtual(pRight->pTab) ){\n      res++;\n      SWAP(Expr*, pLeft, pRight);\n    }\n    *ppLeft = pLeft;\n    *ppRight = pRight;\n    if( pExpr->op==TK_NE ) *peOp2 = SQLITE_INDEX_CONSTRAINT_NE;\n    if( pExpr->op==TK_ISNOT ) *peOp2 = SQLITE_INDEX_CONSTRAINT_ISNOT;\n    if( pExpr->op==TK_NOTNULL ) *peOp2 = SQLITE_INDEX_CONSTRAINT_ISNOTNULL;\n    return res;\n  }\n  return 0;\n}\n#endif /* SQLITE_OMIT_VIRTUALTABLE */\n\n/*\n** If the pBase expression originated in the ON or USING clause of\n** a join, then transfer the appropriate markings over to derived.\n*/\nstatic void transferJoinMarkings(Expr *pDerived, Expr *pBase){\n  if( pDerived ){\n    pDerived->flags |= pBase->flags & EP_FromJoin;\n    pDerived->iRightJoinTable = pBase->iRightJoinTable;\n  }\n}\n\n/*\n** Mark term iChild as being a child of term iParent\n*/\nstatic void markTermAsChild(WhereClause *pWC, int iChild, int iParent){\n  pWC->a[iChild].iParent = iParent;\n  pWC->a[iChild].truthProb = pWC->a[iParent].truthProb;\n  pWC->a[iParent].nChild++;\n}\n\n/*\n** Return the N-th AND-connected subterm of pTerm.  Or if pTerm is not\n** a conjunction, then return just pTerm when N==0.  If N is exceeds\n** the number of available subterms, return NULL.\n*/\nstatic WhereTerm *whereNthSubterm(WhereTerm *pTerm, int N){\n  if( pTerm->eOperator!=WO_AND ){\n    return N==0 ? pTerm : 0;\n  }\n  if( N<pTerm->u.pAndInfo->wc.nTerm ){\n    return &pTerm->u.pAndInfo->wc.a[N];\n  }\n  return 0;\n}\n\n/*\n** Subterms pOne and pTwo are contained within WHERE clause pWC.  The\n** two subterms are in disjunction - they are OR-ed together.\n**\n** If these two terms are both of the form:  \"A op B\" with the same\n** A and B values but different operators and if the operators are\n** compatible (if one is = and the other is <, for example) then\n** add a new virtual AND term to pWC that is the combination of the\n** two.\n**\n** Some examples:\n**\n**    x<y OR x=y    -->     x<=y\n**    x=y OR x=y    -->     x=y\n**    x<=y OR x<y   -->     x<=y\n**\n** The following is NOT generated:\n**\n**    x<y OR x>y    -->     x!=y     \n*/\nstatic void whereCombineDisjuncts(\n  SrcList *pSrc,         /* the FROM clause */\n  WhereClause *pWC,      /* The complete WHERE clause */\n  WhereTerm *pOne,       /* First disjunct */\n  WhereTerm *pTwo        /* Second disjunct */\n){\n  u16 eOp = pOne->eOperator | pTwo->eOperator;\n  sqlite3 *db;           /* Database connection (for malloc) */\n  Expr *pNew;            /* New virtual expression */\n  int op;                /* Operator for the combined expression */\n  int idxNew;            /* Index in pWC of the next virtual term */\n\n  if( (pOne->eOperator & (WO_EQ|WO_LT|WO_LE|WO_GT|WO_GE))==0 ) return;\n  if( (pTwo->eOperator & (WO_EQ|WO_LT|WO_LE|WO_GT|WO_GE))==0 ) return;\n  if( (eOp & (WO_EQ|WO_LT|WO_LE))!=eOp\n   && (eOp & (WO_EQ|WO_GT|WO_GE))!=eOp ) return;\n  assert( pOne->pExpr->pLeft!=0 && pOne->pExpr->pRight!=0 );\n  assert( pTwo->pExpr->pLeft!=0 && pTwo->pExpr->pRight!=0 );\n  if( sqlite3ExprCompare(0,pOne->pExpr->pLeft, pTwo->pExpr->pLeft, -1) ) return;\n  if( sqlite3ExprCompare(0,pOne->pExpr->pRight, pTwo->pExpr->pRight,-1) )return;\n  /* If we reach this point, it means the two subterms can be combined */\n  if( (eOp & (eOp-1))!=0 ){\n    if( eOp & (WO_LT|WO_LE) ){\n      eOp = WO_LE;\n    }else{\n      assert( eOp & (WO_GT|WO_GE) );\n      eOp = WO_GE;\n    }\n  }\n  db = pWC->pWInfo->pParse->db;\n  pNew = sqlite3ExprDup(db, pOne->pExpr, 0);\n  if( pNew==0 ) return;\n  for(op=TK_EQ; eOp!=(WO_EQ<<(op-TK_EQ)); op++){ assert( op<TK_GE ); }\n  pNew->op = op;\n  idxNew = whereClauseInsert(pWC, pNew, TERM_VIRTUAL|TERM_DYNAMIC);\n  exprAnalyze(pSrc, pWC, idxNew);\n}\n\n#if !defined(SQLITE_OMIT_OR_OPTIMIZATION) && !defined(SQLITE_OMIT_SUBQUERY)\n/*\n** Analyze a term that consists of two or more OR-connected\n** subterms.  So in:\n**\n**     ... WHERE  (a=5) AND (b=7 OR c=9 OR d=13) AND (d=13)\n**                          ^^^^^^^^^^^^^^^^^^^^\n**\n** This routine analyzes terms such as the middle term in the above example.\n** A WhereOrTerm object is computed and attached to the term under\n** analysis, regardless of the outcome of the analysis.  Hence:\n**\n**     WhereTerm.wtFlags   |=  TERM_ORINFO\n**     WhereTerm.u.pOrInfo  =  a dynamically allocated WhereOrTerm object\n**\n** The term being analyzed must have two or more of OR-connected subterms.\n** A single subterm might be a set of AND-connected sub-subterms.\n** Examples of terms under analysis:\n**\n**     (A)     t1.x=t2.y OR t1.x=t2.z OR t1.y=15 OR t1.z=t3.a+5\n**     (B)     x=expr1 OR expr2=x OR x=expr3\n**     (C)     t1.x=t2.y OR (t1.x=t2.z AND t1.y=15)\n**     (D)     x=expr1 OR (y>11 AND y<22 AND z LIKE '*hello*')\n**     (E)     (p.a=1 AND q.b=2 AND r.c=3) OR (p.x=4 AND q.y=5 AND r.z=6)\n**     (F)     x>A OR (x=A AND y>=B)\n**\n** CASE 1:\n**\n** If all subterms are of the form T.C=expr for some single column of C and\n** a single table T (as shown in example B above) then create a new virtual\n** term that is an equivalent IN expression.  In other words, if the term\n** being analyzed is:\n**\n**      x = expr1  OR  expr2 = x  OR  x = expr3\n**\n** then create a new virtual term like this:\n**\n**      x IN (expr1,expr2,expr3)\n**\n** CASE 2:\n**\n** If there are exactly two disjuncts and one side has x>A and the other side\n** has x=A (for the same x and A) then add a new virtual conjunct term to the\n** WHERE clause of the form \"x>=A\".  Example:\n**\n**      x>A OR (x=A AND y>B)    adds:    x>=A\n**\n** The added conjunct can sometimes be helpful in query planning.\n**\n** CASE 3:\n**\n** If all subterms are indexable by a single table T, then set\n**\n**     WhereTerm.eOperator              =  WO_OR\n**     WhereTerm.u.pOrInfo->indexable  |=  the cursor number for table T\n**\n** A subterm is \"indexable\" if it is of the form\n** \"T.C <op> <expr>\" where C is any column of table T and \n** <op> is one of \"=\", \"<\", \"<=\", \">\", \">=\", \"IS NULL\", or \"IN\".\n** A subterm is also indexable if it is an AND of two or more\n** subsubterms at least one of which is indexable.  Indexable AND \n** subterms have their eOperator set to WO_AND and they have\n** u.pAndInfo set to a dynamically allocated WhereAndTerm object.\n**\n** From another point of view, \"indexable\" means that the subterm could\n** potentially be used with an index if an appropriate index exists.\n** This analysis does not consider whether or not the index exists; that\n** is decided elsewhere.  This analysis only looks at whether subterms\n** appropriate for indexing exist.\n**\n** All examples A through E above satisfy case 3.  But if a term\n** also satisfies case 1 (such as B) we know that the optimizer will\n** always prefer case 1, so in that case we pretend that case 3 is not\n** satisfied.\n**\n** It might be the case that multiple tables are indexable.  For example,\n** (E) above is indexable on tables P, Q, and R.\n**\n** Terms that satisfy case 3 are candidates for lookup by using\n** separate indices to find rowids for each subterm and composing\n** the union of all rowids using a RowSet object.  This is similar\n** to \"bitmap indices\" in other database engines.\n**\n** OTHERWISE:\n**\n** If none of cases 1, 2, or 3 apply, then leave the eOperator set to\n** zero.  This term is not useful for search.\n*/\nstatic void exprAnalyzeOrTerm(\n  SrcList *pSrc,            /* the FROM clause */\n  WhereClause *pWC,         /* the complete WHERE clause */\n  int idxTerm               /* Index of the OR-term to be analyzed */\n){\n  WhereInfo *pWInfo = pWC->pWInfo;        /* WHERE clause processing context */\n  Parse *pParse = pWInfo->pParse;         /* Parser context */\n  sqlite3 *db = pParse->db;               /* Database connection */\n  WhereTerm *pTerm = &pWC->a[idxTerm];    /* The term to be analyzed */\n  Expr *pExpr = pTerm->pExpr;             /* The expression of the term */\n  int i;                                  /* Loop counters */\n  WhereClause *pOrWc;       /* Breakup of pTerm into subterms */\n  WhereTerm *pOrTerm;       /* A Sub-term within the pOrWc */\n  WhereOrInfo *pOrInfo;     /* Additional information associated with pTerm */\n  Bitmask chngToIN;         /* Tables that might satisfy case 1 */\n  Bitmask indexable;        /* Tables that are indexable, satisfying case 2 */\n\n  /*\n  ** Break the OR clause into its separate subterms.  The subterms are\n  ** stored in a WhereClause structure containing within the WhereOrInfo\n  ** object that is attached to the original OR clause term.\n  */\n  assert( (pTerm->wtFlags & (TERM_DYNAMIC|TERM_ORINFO|TERM_ANDINFO))==0 );\n  assert( pExpr->op==TK_OR );\n  pTerm->u.pOrInfo = pOrInfo = sqlite3DbMallocZero(db, sizeof(*pOrInfo));\n  if( pOrInfo==0 ) return;\n  pTerm->wtFlags |= TERM_ORINFO;\n  pOrWc = &pOrInfo->wc;\n  memset(pOrWc->aStatic, 0, sizeof(pOrWc->aStatic));\n  sqlite3WhereClauseInit(pOrWc, pWInfo);\n  sqlite3WhereSplit(pOrWc, pExpr, TK_OR);\n  sqlite3WhereExprAnalyze(pSrc, pOrWc);\n  if( db->mallocFailed ) return;\n  assert( pOrWc->nTerm>=2 );\n\n  /*\n  ** Compute the set of tables that might satisfy cases 1 or 3.\n  */\n  indexable = ~(Bitmask)0;\n  chngToIN = ~(Bitmask)0;\n  for(i=pOrWc->nTerm-1, pOrTerm=pOrWc->a; i>=0 && indexable; i--, pOrTerm++){\n    if( (pOrTerm->eOperator & WO_SINGLE)==0 ){\n      WhereAndInfo *pAndInfo;\n      assert( (pOrTerm->wtFlags & (TERM_ANDINFO|TERM_ORINFO))==0 );\n      chngToIN = 0;\n      pAndInfo = sqlite3DbMallocRawNN(db, sizeof(*pAndInfo));\n      if( pAndInfo ){\n        WhereClause *pAndWC;\n        WhereTerm *pAndTerm;\n        int j;\n        Bitmask b = 0;\n        pOrTerm->u.pAndInfo = pAndInfo;\n        pOrTerm->wtFlags |= TERM_ANDINFO;\n        pOrTerm->eOperator = WO_AND;\n        pAndWC = &pAndInfo->wc;\n        memset(pAndWC->aStatic, 0, sizeof(pAndWC->aStatic));\n        sqlite3WhereClauseInit(pAndWC, pWC->pWInfo);\n        sqlite3WhereSplit(pAndWC, pOrTerm->pExpr, TK_AND);\n        sqlite3WhereExprAnalyze(pSrc, pAndWC);\n        pAndWC->pOuter = pWC;\n        if( !db->mallocFailed ){\n          for(j=0, pAndTerm=pAndWC->a; j<pAndWC->nTerm; j++, pAndTerm++){\n            assert( pAndTerm->pExpr );\n            if( allowedOp(pAndTerm->pExpr->op) \n             || pAndTerm->eOperator==WO_AUX\n            ){\n              b |= sqlite3WhereGetMask(&pWInfo->sMaskSet, pAndTerm->leftCursor);\n            }\n          }\n        }\n        indexable &= b;\n      }\n    }else if( pOrTerm->wtFlags & TERM_COPIED ){\n      /* Skip this term for now.  We revisit it when we process the\n      ** corresponding TERM_VIRTUAL term */\n    }else{\n      Bitmask b;\n      b = sqlite3WhereGetMask(&pWInfo->sMaskSet, pOrTerm->leftCursor);\n      if( pOrTerm->wtFlags & TERM_VIRTUAL ){\n        WhereTerm *pOther = &pOrWc->a[pOrTerm->iParent];\n        b |= sqlite3WhereGetMask(&pWInfo->sMaskSet, pOther->leftCursor);\n      }\n      indexable &= b;\n      if( (pOrTerm->eOperator & WO_EQ)==0 ){\n        chngToIN = 0;\n      }else{\n        chngToIN &= b;\n      }\n    }\n  }\n\n  /*\n  ** Record the set of tables that satisfy case 3.  The set might be\n  ** empty.\n  */\n  pOrInfo->indexable = indexable;\n  pTerm->eOperator = indexable==0 ? 0 : WO_OR;\n\n  /* For a two-way OR, attempt to implementation case 2.\n  */\n  if( indexable && pOrWc->nTerm==2 ){\n    int iOne = 0;\n    WhereTerm *pOne;\n    while( (pOne = whereNthSubterm(&pOrWc->a[0],iOne++))!=0 ){\n      int iTwo = 0;\n      WhereTerm *pTwo;\n      while( (pTwo = whereNthSubterm(&pOrWc->a[1],iTwo++))!=0 ){\n        whereCombineDisjuncts(pSrc, pWC, pOne, pTwo);\n      }\n    }\n  }\n\n  /*\n  ** chngToIN holds a set of tables that *might* satisfy case 1.  But\n  ** we have to do some additional checking to see if case 1 really\n  ** is satisfied.\n  **\n  ** chngToIN will hold either 0, 1, or 2 bits.  The 0-bit case means\n  ** that there is no possibility of transforming the OR clause into an\n  ** IN operator because one or more terms in the OR clause contain\n  ** something other than == on a column in the single table.  The 1-bit\n  ** case means that every term of the OR clause is of the form\n  ** \"table.column=expr\" for some single table.  The one bit that is set\n  ** will correspond to the common table.  We still need to check to make\n  ** sure the same column is used on all terms.  The 2-bit case is when\n  ** the all terms are of the form \"table1.column=table2.column\".  It\n  ** might be possible to form an IN operator with either table1.column\n  ** or table2.column as the LHS if either is common to every term of\n  ** the OR clause.\n  **\n  ** Note that terms of the form \"table.column1=table.column2\" (the\n  ** same table on both sizes of the ==) cannot be optimized.\n  */\n  if( chngToIN ){\n    int okToChngToIN = 0;     /* True if the conversion to IN is valid */\n    int iColumn = -1;         /* Column index on lhs of IN operator */\n    int iCursor = -1;         /* Table cursor common to all terms */\n    int j = 0;                /* Loop counter */\n\n    /* Search for a table and column that appears on one side or the\n    ** other of the == operator in every subterm.  That table and column\n    ** will be recorded in iCursor and iColumn.  There might not be any\n    ** such table and column.  Set okToChngToIN if an appropriate table\n    ** and column is found but leave okToChngToIN false if not found.\n    */\n    for(j=0; j<2 && !okToChngToIN; j++){\n      pOrTerm = pOrWc->a;\n      for(i=pOrWc->nTerm-1; i>=0; i--, pOrTerm++){\n        assert( pOrTerm->eOperator & WO_EQ );\n        pOrTerm->wtFlags &= ~TERM_OR_OK;\n        if( pOrTerm->leftCursor==iCursor ){\n          /* This is the 2-bit case and we are on the second iteration and\n          ** current term is from the first iteration.  So skip this term. */\n          assert( j==1 );\n          continue;\n        }\n        if( (chngToIN & sqlite3WhereGetMask(&pWInfo->sMaskSet,\n                                            pOrTerm->leftCursor))==0 ){\n          /* This term must be of the form t1.a==t2.b where t2 is in the\n          ** chngToIN set but t1 is not.  This term will be either preceded\n          ** or follwed by an inverted copy (t2.b==t1.a).  Skip this term \n          ** and use its inversion. */\n          testcase( pOrTerm->wtFlags & TERM_COPIED );\n          testcase( pOrTerm->wtFlags & TERM_VIRTUAL );\n          assert( pOrTerm->wtFlags & (TERM_COPIED|TERM_VIRTUAL) );\n          continue;\n        }\n        iColumn = pOrTerm->u.leftColumn;\n        iCursor = pOrTerm->leftCursor;\n        break;\n      }\n      if( i<0 ){\n        /* No candidate table+column was found.  This can only occur\n        ** on the second iteration */\n        assert( j==1 );\n        assert( IsPowerOfTwo(chngToIN) );\n        assert( chngToIN==sqlite3WhereGetMask(&pWInfo->sMaskSet, iCursor) );\n        break;\n      }\n      testcase( j==1 );\n\n      /* We have found a candidate table and column.  Check to see if that\n      ** table and column is common to every term in the OR clause */\n      okToChngToIN = 1;\n      for(; i>=0 && okToChngToIN; i--, pOrTerm++){\n        assert( pOrTerm->eOperator & WO_EQ );\n        if( pOrTerm->leftCursor!=iCursor ){\n          pOrTerm->wtFlags &= ~TERM_OR_OK;\n        }else if( pOrTerm->u.leftColumn!=iColumn ){\n          okToChngToIN = 0;\n        }else{\n          int affLeft, affRight;\n          /* If the right-hand side is also a column, then the affinities\n          ** of both right and left sides must be such that no type\n          ** conversions are required on the right.  (Ticket #2249)\n          */\n          affRight = sqlite3ExprAffinity(pOrTerm->pExpr->pRight);\n          affLeft = sqlite3ExprAffinity(pOrTerm->pExpr->pLeft);\n          if( affRight!=0 && affRight!=affLeft ){\n            okToChngToIN = 0;\n          }else{\n            pOrTerm->wtFlags |= TERM_OR_OK;\n          }\n        }\n      }\n    }\n\n    /* At this point, okToChngToIN is true if original pTerm satisfies\n    ** case 1.  In that case, construct a new virtual term that is \n    ** pTerm converted into an IN operator.\n    */\n    if( okToChngToIN ){\n      Expr *pDup;            /* A transient duplicate expression */\n      ExprList *pList = 0;   /* The RHS of the IN operator */\n      Expr *pLeft = 0;       /* The LHS of the IN operator */\n      Expr *pNew;            /* The complete IN operator */\n\n      for(i=pOrWc->nTerm-1, pOrTerm=pOrWc->a; i>=0; i--, pOrTerm++){\n        if( (pOrTerm->wtFlags & TERM_OR_OK)==0 ) continue;\n        assert( pOrTerm->eOperator & WO_EQ );\n        assert( pOrTerm->leftCursor==iCursor );\n        assert( pOrTerm->u.leftColumn==iColumn );\n        pDup = sqlite3ExprDup(db, pOrTerm->pExpr->pRight, 0);\n        pList = sqlite3ExprListAppend(pWInfo->pParse, pList, pDup);\n        pLeft = pOrTerm->pExpr->pLeft;\n      }\n      assert( pLeft!=0 );\n      pDup = sqlite3ExprDup(db, pLeft, 0);\n      pNew = sqlite3PExpr(pParse, TK_IN, pDup, 0);\n      if( pNew ){\n        int idxNew;\n        transferJoinMarkings(pNew, pExpr);\n        assert( !ExprHasProperty(pNew, EP_xIsSelect) );\n        pNew->x.pList = pList;\n        idxNew = whereClauseInsert(pWC, pNew, TERM_VIRTUAL|TERM_DYNAMIC);\n        testcase( idxNew==0 );\n        exprAnalyze(pSrc, pWC, idxNew);\n        pTerm = &pWC->a[idxTerm];\n        markTermAsChild(pWC, idxNew, idxTerm);\n      }else{\n        sqlite3ExprListDelete(db, pList);\n      }\n      pTerm->eOperator = WO_NOOP;  /* case 1 trumps case 3 */\n    }\n  }\n}\n#endif /* !SQLITE_OMIT_OR_OPTIMIZATION && !SQLITE_OMIT_SUBQUERY */\n\n/*\n** We already know that pExpr is a binary operator where both operands are\n** column references.  This routine checks to see if pExpr is an equivalence\n** relation:\n**   1.  The SQLITE_Transitive optimization must be enabled\n**   2.  Must be either an == or an IS operator\n**   3.  Not originating in the ON clause of an OUTER JOIN\n**   4.  The affinities of A and B must be compatible\n**   5a. Both operands use the same collating sequence OR\n**   5b. The overall collating sequence is BINARY\n** If this routine returns TRUE, that means that the RHS can be substituted\n** for the LHS anyplace else in the WHERE clause where the LHS column occurs.\n** This is an optimization.  No harm comes from returning 0.  But if 1 is\n** returned when it should not be, then incorrect answers might result.\n*/\nstatic int termIsEquivalence(Parse *pParse, Expr *pExpr){\n  char aff1, aff2;\n  CollSeq *pColl;\n  if( !OptimizationEnabled(pParse->db, SQLITE_Transitive) ) return 0;\n  if( pExpr->op!=TK_EQ && pExpr->op!=TK_IS ) return 0;\n  if( ExprHasProperty(pExpr, EP_FromJoin) ) return 0;\n  aff1 = sqlite3ExprAffinity(pExpr->pLeft);\n  aff2 = sqlite3ExprAffinity(pExpr->pRight);\n  if( aff1!=aff2\n   && (!sqlite3IsNumericAffinity(aff1) || !sqlite3IsNumericAffinity(aff2))\n  ){\n    return 0;\n  }\n  pColl = sqlite3BinaryCompareCollSeq(pParse, pExpr->pLeft, pExpr->pRight);\n  if( pColl==0 || sqlite3StrICmp(pColl->zName, \"BINARY\")==0 ) return 1;\n  return sqlite3ExprCollSeqMatch(pParse, pExpr->pLeft, pExpr->pRight);\n}\n\n/*\n** Recursively walk the expressions of a SELECT statement and generate\n** a bitmask indicating which tables are used in that expression\n** tree.\n*/\nstatic Bitmask exprSelectUsage(WhereMaskSet *pMaskSet, Select *pS){\n  Bitmask mask = 0;\n  while( pS ){\n    SrcList *pSrc = pS->pSrc;\n    mask |= sqlite3WhereExprListUsage(pMaskSet, pS->pEList);\n    mask |= sqlite3WhereExprListUsage(pMaskSet, pS->pGroupBy);\n    mask |= sqlite3WhereExprListUsage(pMaskSet, pS->pOrderBy);\n    mask |= sqlite3WhereExprUsage(pMaskSet, pS->pWhere);\n    mask |= sqlite3WhereExprUsage(pMaskSet, pS->pHaving);\n    if( ALWAYS(pSrc!=0) ){\n      int i;\n      for(i=0; i<pSrc->nSrc; i++){\n        mask |= exprSelectUsage(pMaskSet, pSrc->a[i].pSelect);\n        mask |= sqlite3WhereExprUsage(pMaskSet, pSrc->a[i].pOn);\n        if( pSrc->a[i].fg.isTabFunc ){\n          mask |= sqlite3WhereExprListUsage(pMaskSet, pSrc->a[i].u1.pFuncArg);\n        }\n      }\n    }\n    pS = pS->pPrior;\n  }\n  return mask;\n}\n\n/*\n** Expression pExpr is one operand of a comparison operator that might\n** be useful for indexing.  This routine checks to see if pExpr appears\n** in any index.  Return TRUE (1) if pExpr is an indexed term and return\n** FALSE (0) if not.  If TRUE is returned, also set aiCurCol[0] to the cursor\n** number of the table that is indexed and aiCurCol[1] to the column number\n** of the column that is indexed, or XN_EXPR (-2) if an expression is being\n** indexed.\n**\n** If pExpr is a TK_COLUMN column reference, then this routine always returns\n** true even if that particular column is not indexed, because the column\n** might be added to an automatic index later.\n*/\nstatic SQLITE_NOINLINE int exprMightBeIndexed2(\n  SrcList *pFrom,        /* The FROM clause */\n  Bitmask mPrereq,       /* Bitmask of FROM clause terms referenced by pExpr */\n  int *aiCurCol,         /* Write the referenced table cursor and column here */\n  Expr *pExpr            /* An operand of a comparison operator */\n){\n  Index *pIdx;\n  int i;\n  int iCur;\n  for(i=0; mPrereq>1; i++, mPrereq>>=1){}\n  iCur = pFrom->a[i].iCursor;\n  for(pIdx=pFrom->a[i].pTab->pIndex; pIdx; pIdx=pIdx->pNext){\n    if( pIdx->aColExpr==0 ) continue;\n    for(i=0; i<pIdx->nKeyCol; i++){\n      if( pIdx->aiColumn[i]!=XN_EXPR ) continue;\n      if( sqlite3ExprCompareSkip(pExpr, pIdx->aColExpr->a[i].pExpr, iCur)==0 ){\n        aiCurCol[0] = iCur;\n        aiCurCol[1] = XN_EXPR;\n        return 1;\n      }\n    }\n  }\n  return 0;\n}\nstatic int exprMightBeIndexed(\n  SrcList *pFrom,        /* The FROM clause */\n  Bitmask mPrereq,       /* Bitmask of FROM clause terms referenced by pExpr */\n  int *aiCurCol,         /* Write the referenced table cursor & column here */\n  Expr *pExpr,           /* An operand of a comparison operator */\n  int op                 /* The specific comparison operator */\n){\n  /* If this expression is a vector to the left or right of a \n  ** inequality constraint (>, <, >= or <=), perform the processing \n  ** on the first element of the vector.  */\n  assert( TK_GT+1==TK_LE && TK_GT+2==TK_LT && TK_GT+3==TK_GE );\n  assert( TK_IS<TK_GE && TK_ISNULL<TK_GE && TK_IN<TK_GE );\n  assert( op<=TK_GE );\n  if( pExpr->op==TK_VECTOR && (op>=TK_GT && ALWAYS(op<=TK_GE)) ){\n    pExpr = pExpr->x.pList->a[0].pExpr;\n  }\n\n  if( pExpr->op==TK_COLUMN ){\n    aiCurCol[0] = pExpr->iTable;\n    aiCurCol[1] = pExpr->iColumn;\n    return 1;\n  }\n  if( mPrereq==0 ) return 0;                 /* No table references */\n  if( (mPrereq&(mPrereq-1))!=0 ) return 0;   /* Refs more than one table */\n  return exprMightBeIndexed2(pFrom,mPrereq,aiCurCol,pExpr);\n}\n\n/*\n** The input to this routine is an WhereTerm structure with only the\n** \"pExpr\" field filled in.  The job of this routine is to analyze the\n** subexpression and populate all the other fields of the WhereTerm\n** structure.\n**\n** If the expression is of the form \"<expr> <op> X\" it gets commuted\n** to the standard form of \"X <op> <expr>\".\n**\n** If the expression is of the form \"X <op> Y\" where both X and Y are\n** columns, then the original expression is unchanged and a new virtual\n** term of the form \"Y <op> X\" is added to the WHERE clause and\n** analyzed separately.  The original term is marked with TERM_COPIED\n** and the new term is marked with TERM_DYNAMIC (because it's pExpr\n** needs to be freed with the WhereClause) and TERM_VIRTUAL (because it\n** is a commuted copy of a prior term.)  The original term has nChild=1\n** and the copy has idxParent set to the index of the original term.\n*/\nstatic void exprAnalyze(\n  SrcList *pSrc,            /* the FROM clause */\n  WhereClause *pWC,         /* the WHERE clause */\n  int idxTerm               /* Index of the term to be analyzed */\n){\n  WhereInfo *pWInfo = pWC->pWInfo; /* WHERE clause processing context */\n  WhereTerm *pTerm;                /* The term to be analyzed */\n  WhereMaskSet *pMaskSet;          /* Set of table index masks */\n  Expr *pExpr;                     /* The expression to be analyzed */\n  Bitmask prereqLeft;              /* Prerequesites of the pExpr->pLeft */\n  Bitmask prereqAll;               /* Prerequesites of pExpr */\n  Bitmask extraRight = 0;          /* Extra dependencies on LEFT JOIN */\n  Expr *pStr1 = 0;                 /* RHS of LIKE/GLOB operator */\n  int isComplete = 0;              /* RHS of LIKE/GLOB ends with wildcard */\n  int noCase = 0;                  /* uppercase equivalent to lowercase */\n  int op;                          /* Top-level operator.  pExpr->op */\n  Parse *pParse = pWInfo->pParse;  /* Parsing context */\n  sqlite3 *db = pParse->db;        /* Database connection */\n  unsigned char eOp2 = 0;          /* op2 value for LIKE/REGEXP/GLOB */\n  int nLeft;                       /* Number of elements on left side vector */\n\n  if( db->mallocFailed ){\n    return;\n  }\n  pTerm = &pWC->a[idxTerm];\n  pMaskSet = &pWInfo->sMaskSet;\n  pExpr = pTerm->pExpr;\n  assert( pExpr->op!=TK_AS && pExpr->op!=TK_COLLATE );\n  prereqLeft = sqlite3WhereExprUsage(pMaskSet, pExpr->pLeft);\n  op = pExpr->op;\n  if( op==TK_IN ){\n    assert( pExpr->pRight==0 );\n    if( sqlite3ExprCheckIN(pParse, pExpr) ) return;\n    if( ExprHasProperty(pExpr, EP_xIsSelect) ){\n      pTerm->prereqRight = exprSelectUsage(pMaskSet, pExpr->x.pSelect);\n    }else{\n      pTerm->prereqRight = sqlite3WhereExprListUsage(pMaskSet, pExpr->x.pList);\n    }\n  }else if( op==TK_ISNULL ){\n    pTerm->prereqRight = 0;\n  }else{\n    pTerm->prereqRight = sqlite3WhereExprUsage(pMaskSet, pExpr->pRight);\n  }\n  pMaskSet->bVarSelect = 0;\n  prereqAll = sqlite3WhereExprUsage(pMaskSet, pExpr);\n  if( pMaskSet->bVarSelect ) pTerm->wtFlags |= TERM_VARSELECT;\n  if( ExprHasProperty(pExpr, EP_FromJoin) ){\n    Bitmask x = sqlite3WhereGetMask(pMaskSet, pExpr->iRightJoinTable);\n    prereqAll |= x;\n    extraRight = x-1;  /* ON clause terms may not be used with an index\n                       ** on left table of a LEFT JOIN.  Ticket #3015 */\n    if( (prereqAll>>1)>=x ){\n      sqlite3ErrorMsg(pParse, \"ON clause references tables to its right\");\n      return;\n    }\n  }\n  pTerm->prereqAll = prereqAll;\n  pTerm->leftCursor = -1;\n  pTerm->iParent = -1;\n  pTerm->eOperator = 0;\n  if( allowedOp(op) ){\n    int aiCurCol[2];\n    Expr *pLeft = sqlite3ExprSkipCollate(pExpr->pLeft);\n    Expr *pRight = sqlite3ExprSkipCollate(pExpr->pRight);\n    u16 opMask = (pTerm->prereqRight & prereqLeft)==0 ? WO_ALL : WO_EQUIV;\n\n    if( pTerm->iField>0 ){\n      assert( op==TK_IN );\n      assert( pLeft->op==TK_VECTOR );\n      pLeft = pLeft->x.pList->a[pTerm->iField-1].pExpr;\n    }\n\n    if( exprMightBeIndexed(pSrc, prereqLeft, aiCurCol, pLeft, op) ){\n      pTerm->leftCursor = aiCurCol[0];\n      pTerm->u.leftColumn = aiCurCol[1];\n      pTerm->eOperator = operatorMask(op) & opMask;\n    }\n    if( op==TK_IS ) pTerm->wtFlags |= TERM_IS;\n    if( pRight \n     && exprMightBeIndexed(pSrc, pTerm->prereqRight, aiCurCol, pRight, op)\n    ){\n      WhereTerm *pNew;\n      Expr *pDup;\n      u16 eExtraOp = 0;        /* Extra bits for pNew->eOperator */\n      assert( pTerm->iField==0 );\n      if( pTerm->leftCursor>=0 ){\n        int idxNew;\n        pDup = sqlite3ExprDup(db, pExpr, 0);\n        if( db->mallocFailed ){\n          sqlite3ExprDelete(db, pDup);\n          return;\n        }\n        idxNew = whereClauseInsert(pWC, pDup, TERM_VIRTUAL|TERM_DYNAMIC);\n        if( idxNew==0 ) return;\n        pNew = &pWC->a[idxNew];\n        markTermAsChild(pWC, idxNew, idxTerm);\n        if( op==TK_IS ) pNew->wtFlags |= TERM_IS;\n        pTerm = &pWC->a[idxTerm];\n        pTerm->wtFlags |= TERM_COPIED;\n\n        if( termIsEquivalence(pParse, pDup) ){\n          pTerm->eOperator |= WO_EQUIV;\n          eExtraOp = WO_EQUIV;\n        }\n      }else{\n        pDup = pExpr;\n        pNew = pTerm;\n      }\n      exprCommute(pParse, pDup);\n      pNew->leftCursor = aiCurCol[0];\n      pNew->u.leftColumn = aiCurCol[1];\n      testcase( (prereqLeft | extraRight) != prereqLeft );\n      pNew->prereqRight = prereqLeft | extraRight;\n      pNew->prereqAll = prereqAll;\n      pNew->eOperator = (operatorMask(pDup->op) + eExtraOp) & opMask;\n    }\n  }\n\n#ifndef SQLITE_OMIT_BETWEEN_OPTIMIZATION\n  /* If a term is the BETWEEN operator, create two new virtual terms\n  ** that define the range that the BETWEEN implements.  For example:\n  **\n  **      a BETWEEN b AND c\n  **\n  ** is converted into:\n  **\n  **      (a BETWEEN b AND c) AND (a>=b) AND (a<=c)\n  **\n  ** The two new terms are added onto the end of the WhereClause object.\n  ** The new terms are \"dynamic\" and are children of the original BETWEEN\n  ** term.  That means that if the BETWEEN term is coded, the children are\n  ** skipped.  Or, if the children are satisfied by an index, the original\n  ** BETWEEN term is skipped.\n  */\n  else if( pExpr->op==TK_BETWEEN && pWC->op==TK_AND ){\n    ExprList *pList = pExpr->x.pList;\n    int i;\n    static const u8 ops[] = {TK_GE, TK_LE};\n    assert( pList!=0 );\n    assert( pList->nExpr==2 );\n    for(i=0; i<2; i++){\n      Expr *pNewExpr;\n      int idxNew;\n      pNewExpr = sqlite3PExpr(pParse, ops[i], \n                             sqlite3ExprDup(db, pExpr->pLeft, 0),\n                             sqlite3ExprDup(db, pList->a[i].pExpr, 0));\n      transferJoinMarkings(pNewExpr, pExpr);\n      idxNew = whereClauseInsert(pWC, pNewExpr, TERM_VIRTUAL|TERM_DYNAMIC);\n      testcase( idxNew==0 );\n      exprAnalyze(pSrc, pWC, idxNew);\n      pTerm = &pWC->a[idxTerm];\n      markTermAsChild(pWC, idxNew, idxTerm);\n    }\n  }\n#endif /* SQLITE_OMIT_BETWEEN_OPTIMIZATION */\n\n#if !defined(SQLITE_OMIT_OR_OPTIMIZATION) && !defined(SQLITE_OMIT_SUBQUERY)\n  /* Analyze a term that is composed of two or more subterms connected by\n  ** an OR operator.\n  */\n  else if( pExpr->op==TK_OR ){\n    assert( pWC->op==TK_AND );\n    exprAnalyzeOrTerm(pSrc, pWC, idxTerm);\n    pTerm = &pWC->a[idxTerm];\n  }\n#endif /* SQLITE_OMIT_OR_OPTIMIZATION */\n\n#ifndef SQLITE_OMIT_LIKE_OPTIMIZATION\n  /* Add constraints to reduce the search space on a LIKE or GLOB\n  ** operator.\n  **\n  ** A like pattern of the form \"x LIKE 'aBc%'\" is changed into constraints\n  **\n  **          x>='ABC' AND x<'abd' AND x LIKE 'aBc%'\n  **\n  ** The last character of the prefix \"abc\" is incremented to form the\n  ** termination condition \"abd\".  If case is not significant (the default\n  ** for LIKE) then the lower-bound is made all uppercase and the upper-\n  ** bound is made all lowercase so that the bounds also work when comparing\n  ** BLOBs.\n  */\n  if( pWC->op==TK_AND \n   && isLikeOrGlob(pParse, pExpr, &pStr1, &isComplete, &noCase)\n  ){\n    Expr *pLeft;       /* LHS of LIKE/GLOB operator */\n    Expr *pStr2;       /* Copy of pStr1 - RHS of LIKE/GLOB operator */\n    Expr *pNewExpr1;\n    Expr *pNewExpr2;\n    int idxNew1;\n    int idxNew2;\n    const char *zCollSeqName;     /* Name of collating sequence */\n    const u16 wtFlags = TERM_LIKEOPT | TERM_VIRTUAL | TERM_DYNAMIC;\n\n    pLeft = pExpr->x.pList->a[1].pExpr;\n    pStr2 = sqlite3ExprDup(db, pStr1, 0);\n\n    /* Convert the lower bound to upper-case and the upper bound to\n    ** lower-case (upper-case is less than lower-case in ASCII) so that\n    ** the range constraints also work for BLOBs\n    */\n    if( noCase && !pParse->db->mallocFailed ){\n      int i;\n      char c;\n      pTerm->wtFlags |= TERM_LIKE;\n      for(i=0; (c = pStr1->u.zToken[i])!=0; i++){\n        pStr1->u.zToken[i] = sqlite3Toupper(c);\n        pStr2->u.zToken[i] = sqlite3Tolower(c);\n      }\n    }\n\n    if( !db->mallocFailed ){\n      u8 c, *pC;       /* Last character before the first wildcard */\n      pC = (u8*)&pStr2->u.zToken[sqlite3Strlen30(pStr2->u.zToken)-1];\n      c = *pC;\n      if( noCase ){\n        /* The point is to increment the last character before the first\n        ** wildcard.  But if we increment '@', that will push it into the\n        ** alphabetic range where case conversions will mess up the \n        ** inequality.  To avoid this, make sure to also run the full\n        ** LIKE on all candidate expressions by clearing the isComplete flag\n        */\n        if( c=='A'-1 ) isComplete = 0;\n        c = sqlite3UpperToLower[c];\n      }\n      *pC = c + 1;\n    }\n    zCollSeqName = noCase ? \"NOCASE\" : \"BINARY\";\n    pNewExpr1 = sqlite3ExprDup(db, pLeft, 0);\n    pNewExpr1 = sqlite3PExpr(pParse, TK_GE,\n           sqlite3ExprAddCollateString(pParse,pNewExpr1,zCollSeqName),\n           pStr1);\n    transferJoinMarkings(pNewExpr1, pExpr);\n    idxNew1 = whereClauseInsert(pWC, pNewExpr1, wtFlags);\n    testcase( idxNew1==0 );\n    exprAnalyze(pSrc, pWC, idxNew1);\n    pNewExpr2 = sqlite3ExprDup(db, pLeft, 0);\n    pNewExpr2 = sqlite3PExpr(pParse, TK_LT,\n           sqlite3ExprAddCollateString(pParse,pNewExpr2,zCollSeqName),\n           pStr2);\n    transferJoinMarkings(pNewExpr2, pExpr);\n    idxNew2 = whereClauseInsert(pWC, pNewExpr2, wtFlags);\n    testcase( idxNew2==0 );\n    exprAnalyze(pSrc, pWC, idxNew2);\n    pTerm = &pWC->a[idxTerm];\n    if( isComplete ){\n      markTermAsChild(pWC, idxNew1, idxTerm);\n      markTermAsChild(pWC, idxNew2, idxTerm);\n    }\n  }\n#endif /* SQLITE_OMIT_LIKE_OPTIMIZATION */\n\n#ifndef SQLITE_OMIT_VIRTUALTABLE\n  /* Add a WO_AUX auxiliary term to the constraint set if the\n  ** current expression is of the form \"column OP expr\" where OP\n  ** is an operator that gets passed into virtual tables but which is\n  ** not normally optimized for ordinary tables.  In other words, OP\n  ** is one of MATCH, LIKE, GLOB, REGEXP, !=, IS, IS NOT, or NOT NULL.\n  ** This information is used by the xBestIndex methods of\n  ** virtual tables.  The native query optimizer does not attempt\n  ** to do anything with MATCH functions.\n  */\n  if( pWC->op==TK_AND ){\n    Expr *pRight = 0, *pLeft = 0;\n    int res = isAuxiliaryVtabOperator(pExpr, &eOp2, &pLeft, &pRight);\n    while( res-- > 0 ){\n      int idxNew;\n      WhereTerm *pNewTerm;\n      Bitmask prereqColumn, prereqExpr;\n\n      prereqExpr = sqlite3WhereExprUsage(pMaskSet, pRight);\n      prereqColumn = sqlite3WhereExprUsage(pMaskSet, pLeft);\n      if( (prereqExpr & prereqColumn)==0 ){\n        Expr *pNewExpr;\n        pNewExpr = sqlite3PExpr(pParse, TK_MATCH, \n            0, sqlite3ExprDup(db, pRight, 0));\n        if( ExprHasProperty(pExpr, EP_FromJoin) && pNewExpr ){\n          ExprSetProperty(pNewExpr, EP_FromJoin);\n        }\n        idxNew = whereClauseInsert(pWC, pNewExpr, TERM_VIRTUAL|TERM_DYNAMIC);\n        testcase( idxNew==0 );\n        pNewTerm = &pWC->a[idxNew];\n        pNewTerm->prereqRight = prereqExpr;\n        pNewTerm->leftCursor = pLeft->iTable;\n        pNewTerm->u.leftColumn = pLeft->iColumn;\n        pNewTerm->eOperator = WO_AUX;\n        pNewTerm->eMatchOp = eOp2;\n        markTermAsChild(pWC, idxNew, idxTerm);\n        pTerm = &pWC->a[idxTerm];\n        pTerm->wtFlags |= TERM_COPIED;\n        pNewTerm->prereqAll = pTerm->prereqAll;\n      }\n      SWAP(Expr*, pLeft, pRight);\n    }\n  }\n#endif /* SQLITE_OMIT_VIRTUALTABLE */\n\n  /* If there is a vector == or IS term - e.g. \"(a, b) == (?, ?)\" - create\n  ** new terms for each component comparison - \"a = ?\" and \"b = ?\".  The\n  ** new terms completely replace the original vector comparison, which is\n  ** no longer used.\n  **\n  ** This is only required if at least one side of the comparison operation\n  ** is not a sub-select.  */\n  if( pWC->op==TK_AND \n  && (pExpr->op==TK_EQ || pExpr->op==TK_IS)\n  && (nLeft = sqlite3ExprVectorSize(pExpr->pLeft))>1\n  && sqlite3ExprVectorSize(pExpr->pRight)==nLeft\n  && ( (pExpr->pLeft->flags & EP_xIsSelect)==0 \n    || (pExpr->pRight->flags & EP_xIsSelect)==0)\n  ){\n    int i;\n    for(i=0; i<nLeft; i++){\n      int idxNew;\n      Expr *pNew;\n      Expr *pLeft = sqlite3ExprForVectorField(pParse, pExpr->pLeft, i);\n      Expr *pRight = sqlite3ExprForVectorField(pParse, pExpr->pRight, i);\n\n      pNew = sqlite3PExpr(pParse, pExpr->op, pLeft, pRight);\n      transferJoinMarkings(pNew, pExpr);\n      idxNew = whereClauseInsert(pWC, pNew, TERM_DYNAMIC);\n      exprAnalyze(pSrc, pWC, idxNew);\n    }\n    pTerm = &pWC->a[idxTerm];\n    pTerm->wtFlags |= TERM_CODED|TERM_VIRTUAL;  /* Disable the original */\n    pTerm->eOperator = 0;\n  }\n\n  /* If there is a vector IN term - e.g. \"(a, b) IN (SELECT ...)\" - create\n  ** a virtual term for each vector component. The expression object\n  ** used by each such virtual term is pExpr (the full vector IN(...) \n  ** expression). The WhereTerm.iField variable identifies the index within\n  ** the vector on the LHS that the virtual term represents.\n  **\n  ** This only works if the RHS is a simple SELECT, not a compound\n  */\n  if( pWC->op==TK_AND && pExpr->op==TK_IN && pTerm->iField==0\n   && pExpr->pLeft->op==TK_VECTOR\n   && pExpr->x.pSelect->pPrior==0\n  ){\n    int i;\n    for(i=0; i<sqlite3ExprVectorSize(pExpr->pLeft); i++){\n      int idxNew;\n      idxNew = whereClauseInsert(pWC, pExpr, TERM_VIRTUAL);\n      pWC->a[idxNew].iField = i+1;\n      exprAnalyze(pSrc, pWC, idxNew);\n      markTermAsChild(pWC, idxNew, idxTerm);\n    }\n  }\n\n#ifdef SQLITE_ENABLE_STAT3_OR_STAT4\n  /* When sqlite_stat3 histogram data is available an operator of the\n  ** form \"x IS NOT NULL\" can sometimes be evaluated more efficiently\n  ** as \"x>NULL\" if x is not an INTEGER PRIMARY KEY.  So construct a\n  ** virtual term of that form.\n  **\n  ** Note that the virtual term must be tagged with TERM_VNULL.\n  */\n  if( pExpr->op==TK_NOTNULL\n   && pExpr->pLeft->op==TK_COLUMN\n   && pExpr->pLeft->iColumn>=0\n   && OptimizationEnabled(db, SQLITE_Stat34)\n  ){\n    Expr *pNewExpr;\n    Expr *pLeft = pExpr->pLeft;\n    int idxNew;\n    WhereTerm *pNewTerm;\n\n    pNewExpr = sqlite3PExpr(pParse, TK_GT,\n                            sqlite3ExprDup(db, pLeft, 0),\n                            sqlite3ExprAlloc(db, TK_NULL, 0, 0));\n\n    idxNew = whereClauseInsert(pWC, pNewExpr,\n                              TERM_VIRTUAL|TERM_DYNAMIC|TERM_VNULL);\n    if( idxNew ){\n      pNewTerm = &pWC->a[idxNew];\n      pNewTerm->prereqRight = 0;\n      pNewTerm->leftCursor = pLeft->iTable;\n      pNewTerm->u.leftColumn = pLeft->iColumn;\n      pNewTerm->eOperator = WO_GT;\n      markTermAsChild(pWC, idxNew, idxTerm);\n      pTerm = &pWC->a[idxTerm];\n      pTerm->wtFlags |= TERM_COPIED;\n      pNewTerm->prereqAll = pTerm->prereqAll;\n    }\n  }\n#endif /* SQLITE_ENABLE_STAT3_OR_STAT4 */\n\n  /* Prevent ON clause terms of a LEFT JOIN from being used to drive\n  ** an index for tables to the left of the join.\n  */\n  testcase( pTerm!=&pWC->a[idxTerm] );\n  pTerm = &pWC->a[idxTerm];\n  pTerm->prereqRight |= extraRight;\n}\n\n/***************************************************************************\n** Routines with file scope above.  Interface to the rest of the where.c\n** subsystem follows.\n***************************************************************************/\n\n/*\n** This routine identifies subexpressions in the WHERE clause where\n** each subexpression is separated by the AND operator or some other\n** operator specified in the op parameter.  The WhereClause structure\n** is filled with pointers to subexpressions.  For example:\n**\n**    WHERE  a=='hello' AND coalesce(b,11)<10 AND (c+12!=d OR c==22)\n**           \\________/     \\_______________/     \\________________/\n**            slot[0]            slot[1]               slot[2]\n**\n** The original WHERE clause in pExpr is unaltered.  All this routine\n** does is make slot[] entries point to substructure within pExpr.\n**\n** In the previous sentence and in the diagram, \"slot[]\" refers to\n** the WhereClause.a[] array.  The slot[] array grows as needed to contain\n** all terms of the WHERE clause.\n*/\nSQLITE_PRIVATE void sqlite3WhereSplit(WhereClause *pWC, Expr *pExpr, u8 op){\n  Expr *pE2 = sqlite3ExprSkipCollate(pExpr);\n  pWC->op = op;\n  if( pE2==0 ) return;\n  if( pE2->op!=op ){\n    whereClauseInsert(pWC, pExpr, 0);\n  }else{\n    sqlite3WhereSplit(pWC, pE2->pLeft, op);\n    sqlite3WhereSplit(pWC, pE2->pRight, op);\n  }\n}\n\n/*\n** Initialize a preallocated WhereClause structure.\n*/\nSQLITE_PRIVATE void sqlite3WhereClauseInit(\n  WhereClause *pWC,        /* The WhereClause to be initialized */\n  WhereInfo *pWInfo        /* The WHERE processing context */\n){\n  pWC->pWInfo = pWInfo;\n  pWC->pOuter = 0;\n  pWC->nTerm = 0;\n  pWC->nSlot = ArraySize(pWC->aStatic);\n  pWC->a = pWC->aStatic;\n}\n\n/*\n** Deallocate a WhereClause structure.  The WhereClause structure\n** itself is not freed.  This routine is the inverse of\n** sqlite3WhereClauseInit().\n*/\nSQLITE_PRIVATE void sqlite3WhereClauseClear(WhereClause *pWC){\n  int i;\n  WhereTerm *a;\n  sqlite3 *db = pWC->pWInfo->pParse->db;\n  for(i=pWC->nTerm-1, a=pWC->a; i>=0; i--, a++){\n    if( a->wtFlags & TERM_DYNAMIC ){\n      sqlite3ExprDelete(db, a->pExpr);\n    }\n    if( a->wtFlags & TERM_ORINFO ){\n      whereOrInfoDelete(db, a->u.pOrInfo);\n    }else if( a->wtFlags & TERM_ANDINFO ){\n      whereAndInfoDelete(db, a->u.pAndInfo);\n    }\n  }\n  if( pWC->a!=pWC->aStatic ){\n    sqlite3DbFree(db, pWC->a);\n  }\n}\n\n\n/*\n** These routines walk (recursively) an expression tree and generate\n** a bitmask indicating which tables are used in that expression\n** tree.\n*/\nSQLITE_PRIVATE Bitmask sqlite3WhereExprUsage(WhereMaskSet *pMaskSet, Expr *p){\n  Bitmask mask;\n  if( p==0 ) return 0;\n  if( p->op==TK_COLUMN ){\n    return sqlite3WhereGetMask(pMaskSet, p->iTable);\n  }\n  mask = (p->op==TK_IF_NULL_ROW) ? sqlite3WhereGetMask(pMaskSet, p->iTable) : 0;\n  assert( !ExprHasProperty(p, EP_TokenOnly) );\n  if( p->pLeft ) mask |= sqlite3WhereExprUsage(pMaskSet, p->pLeft);\n  if( p->pRight ){\n    mask |= sqlite3WhereExprUsage(pMaskSet, p->pRight);\n    assert( p->x.pList==0 );\n  }else if( ExprHasProperty(p, EP_xIsSelect) ){\n    if( ExprHasProperty(p, EP_VarSelect) ) pMaskSet->bVarSelect = 1;\n    mask |= exprSelectUsage(pMaskSet, p->x.pSelect);\n  }else if( p->x.pList ){\n    mask |= sqlite3WhereExprListUsage(pMaskSet, p->x.pList);\n  }\n  return mask;\n}\nSQLITE_PRIVATE Bitmask sqlite3WhereExprListUsage(WhereMaskSet *pMaskSet, ExprList *pList){\n  int i;\n  Bitmask mask = 0;\n  if( pList ){\n    for(i=0; i<pList->nExpr; i++){\n      mask |= sqlite3WhereExprUsage(pMaskSet, pList->a[i].pExpr);\n    }\n  }\n  return mask;\n}\n\n\n/*\n** Call exprAnalyze on all terms in a WHERE clause.  \n**\n** Note that exprAnalyze() might add new virtual terms onto the\n** end of the WHERE clause.  We do not want to analyze these new\n** virtual terms, so start analyzing at the end and work forward\n** so that the added virtual terms are never processed.\n*/\nSQLITE_PRIVATE void sqlite3WhereExprAnalyze(\n  SrcList *pTabList,       /* the FROM clause */\n  WhereClause *pWC         /* the WHERE clause to be analyzed */\n){\n  int i;\n  for(i=pWC->nTerm-1; i>=0; i--){\n    exprAnalyze(pTabList, pWC, i);\n  }\n}\n\n/*\n** For table-valued-functions, transform the function arguments into\n** new WHERE clause terms.  \n**\n** Each function argument translates into an equality constraint against\n** a HIDDEN column in the table.\n*/\nSQLITE_PRIVATE void sqlite3WhereTabFuncArgs(\n  Parse *pParse,                    /* Parsing context */\n  struct SrcList_item *pItem,       /* The FROM clause term to process */\n  WhereClause *pWC                  /* Xfer function arguments to here */\n){\n  Table *pTab;\n  int j, k;\n  ExprList *pArgs;\n  Expr *pColRef;\n  Expr *pTerm;\n  if( pItem->fg.isTabFunc==0 ) return;\n  pTab = pItem->pTab;\n  assert( pTab!=0 );\n  pArgs = pItem->u1.pFuncArg;\n  if( pArgs==0 ) return;\n  for(j=k=0; j<pArgs->nExpr; j++){\n    while( k<pTab->nCol && (pTab->aCol[k].colFlags & COLFLAG_HIDDEN)==0 ){k++;}\n    if( k>=pTab->nCol ){\n      sqlite3ErrorMsg(pParse, \"too many arguments on %s() - max %d\",\n                      pTab->zName, j);\n      return;\n    }\n    pColRef = sqlite3ExprAlloc(pParse->db, TK_COLUMN, 0, 0);\n    if( pColRef==0 ) return;\n    pColRef->iTable = pItem->iCursor;\n    pColRef->iColumn = k++;\n    pColRef->pTab = pTab;\n    pTerm = sqlite3PExpr(pParse, TK_EQ, pColRef,\n                         sqlite3ExprDup(pParse->db, pArgs->a[j].pExpr, 0));\n    whereClauseInsert(pWC, pTerm, TERM_DYNAMIC);\n  }\n}\n\n/************** End of whereexpr.c *******************************************/\n/************** Begin file where.c *******************************************/\n/*\n** 2001 September 15\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n*************************************************************************\n** This module contains C code that generates VDBE code used to process\n** the WHERE clause of SQL statements.  This module is responsible for\n** generating the code that loops through a table looking for applicable\n** rows.  Indices are selected and used to speed the search when doing\n** so is applicable.  Because this module is responsible for selecting\n** indices, you might also think of this module as the \"query optimizer\".\n*/\n/* #include \"sqliteInt.h\" */\n/* #include \"whereInt.h\" */\n\n/*\n** Extra information appended to the end of sqlite3_index_info but not\n** visible to the xBestIndex function, at least not directly.  The\n** sqlite3_vtab_collation() interface knows how to reach it, however.\n**\n** This object is not an API and can be changed from one release to the\n** next.  As long as allocateIndexInfo() and sqlite3_vtab_collation()\n** agree on the structure, all will be well.\n*/\ntypedef struct HiddenIndexInfo HiddenIndexInfo;\nstruct HiddenIndexInfo {\n  WhereClause *pWC;   /* The Where clause being analyzed */\n  Parse *pParse;      /* The parsing context */\n};\n\n/* Forward declaration of methods */\nstatic int whereLoopResize(sqlite3*, WhereLoop*, int);\n\n/* Test variable that can be set to enable WHERE tracing */\n#if defined(SQLITE_TEST) || defined(SQLITE_DEBUG)\n/***/ int sqlite3WhereTrace = 0;\n#endif\n\n\n/*\n** Return the estimated number of output rows from a WHERE clause\n*/\nSQLITE_PRIVATE LogEst sqlite3WhereOutputRowCount(WhereInfo *pWInfo){\n  return pWInfo->nRowOut;\n}\n\n/*\n** Return one of the WHERE_DISTINCT_xxxxx values to indicate how this\n** WHERE clause returns outputs for DISTINCT processing.\n*/\nSQLITE_PRIVATE int sqlite3WhereIsDistinct(WhereInfo *pWInfo){\n  return pWInfo->eDistinct;\n}\n\n/*\n** Return TRUE if the WHERE clause returns rows in ORDER BY order.\n** Return FALSE if the output needs to be sorted.\n*/\nSQLITE_PRIVATE int sqlite3WhereIsOrdered(WhereInfo *pWInfo){\n  return pWInfo->nOBSat;\n}\n\n/*\n** Return TRUE if the innermost loop of the WHERE clause implementation\n** returns rows in ORDER BY order for complete run of the inner loop.\n**\n** Across multiple iterations of outer loops, the output rows need not be\n** sorted.  As long as rows are sorted for just the innermost loop, this\n** routine can return TRUE.\n*/\nSQLITE_PRIVATE int sqlite3WhereOrderedInnerLoop(WhereInfo *pWInfo){\n  return pWInfo->bOrderedInnerLoop;\n}\n\n/*\n** Return the VDBE address or label to jump to in order to continue\n** immediately with the next row of a WHERE clause.\n*/\nSQLITE_PRIVATE int sqlite3WhereContinueLabel(WhereInfo *pWInfo){\n  assert( pWInfo->iContinue!=0 );\n  return pWInfo->iContinue;\n}\n\n/*\n** Return the VDBE address or label to jump to in order to break\n** out of a WHERE loop.\n*/\nSQLITE_PRIVATE int sqlite3WhereBreakLabel(WhereInfo *pWInfo){\n  return pWInfo->iBreak;\n}\n\n/*\n** Return ONEPASS_OFF (0) if an UPDATE or DELETE statement is unable to\n** operate directly on the rowis returned by a WHERE clause.  Return\n** ONEPASS_SINGLE (1) if the statement can operation directly because only\n** a single row is to be changed.  Return ONEPASS_MULTI (2) if the one-pass\n** optimization can be used on multiple \n**\n** If the ONEPASS optimization is used (if this routine returns true)\n** then also write the indices of open cursors used by ONEPASS\n** into aiCur[0] and aiCur[1].  iaCur[0] gets the cursor of the data\n** table and iaCur[1] gets the cursor used by an auxiliary index.\n** Either value may be -1, indicating that cursor is not used.\n** Any cursors returned will have been opened for writing.\n**\n** aiCur[0] and aiCur[1] both get -1 if the where-clause logic is\n** unable to use the ONEPASS optimization.\n*/\nSQLITE_PRIVATE int sqlite3WhereOkOnePass(WhereInfo *pWInfo, int *aiCur){\n  memcpy(aiCur, pWInfo->aiCurOnePass, sizeof(int)*2);\n#ifdef WHERETRACE_ENABLED\n  if( sqlite3WhereTrace && pWInfo->eOnePass!=ONEPASS_OFF ){\n    sqlite3DebugPrintf(\"%s cursors: %d %d\\n\",\n         pWInfo->eOnePass==ONEPASS_SINGLE ? \"ONEPASS_SINGLE\" : \"ONEPASS_MULTI\",\n         aiCur[0], aiCur[1]);\n  }\n#endif\n  return pWInfo->eOnePass;\n}\n\n/*\n** Move the content of pSrc into pDest\n*/\nstatic void whereOrMove(WhereOrSet *pDest, WhereOrSet *pSrc){\n  pDest->n = pSrc->n;\n  memcpy(pDest->a, pSrc->a, pDest->n*sizeof(pDest->a[0]));\n}\n\n/*\n** Try to insert a new prerequisite/cost entry into the WhereOrSet pSet.\n**\n** The new entry might overwrite an existing entry, or it might be\n** appended, or it might be discarded.  Do whatever is the right thing\n** so that pSet keeps the N_OR_COST best entries seen so far.\n*/\nstatic int whereOrInsert(\n  WhereOrSet *pSet,      /* The WhereOrSet to be updated */\n  Bitmask prereq,        /* Prerequisites of the new entry */\n  LogEst rRun,           /* Run-cost of the new entry */\n  LogEst nOut            /* Number of outputs for the new entry */\n){\n  u16 i;\n  WhereOrCost *p;\n  for(i=pSet->n, p=pSet->a; i>0; i--, p++){\n    if( rRun<=p->rRun && (prereq & p->prereq)==prereq ){\n      goto whereOrInsert_done;\n    }\n    if( p->rRun<=rRun && (p->prereq & prereq)==p->prereq ){\n      return 0;\n    }\n  }\n  if( pSet->n<N_OR_COST ){\n    p = &pSet->a[pSet->n++];\n    p->nOut = nOut;\n  }else{\n    p = pSet->a;\n    for(i=1; i<pSet->n; i++){\n      if( p->rRun>pSet->a[i].rRun ) p = pSet->a + i;\n    }\n    if( p->rRun<=rRun ) return 0;\n  }\nwhereOrInsert_done:\n  p->prereq = prereq;\n  p->rRun = rRun;\n  if( p->nOut>nOut ) p->nOut = nOut;\n  return 1;\n}\n\n/*\n** Return the bitmask for the given cursor number.  Return 0 if\n** iCursor is not in the set.\n*/\nSQLITE_PRIVATE Bitmask sqlite3WhereGetMask(WhereMaskSet *pMaskSet, int iCursor){\n  int i;\n  assert( pMaskSet->n<=(int)sizeof(Bitmask)*8 );\n  for(i=0; i<pMaskSet->n; i++){\n    if( pMaskSet->ix[i]==iCursor ){\n      return MASKBIT(i);\n    }\n  }\n  return 0;\n}\n\n/*\n** Create a new mask for cursor iCursor.\n**\n** There is one cursor per table in the FROM clause.  The number of\n** tables in the FROM clause is limited by a test early in the\n** sqlite3WhereBegin() routine.  So we know that the pMaskSet->ix[]\n** array will never overflow.\n*/\nstatic void createMask(WhereMaskSet *pMaskSet, int iCursor){\n  assert( pMaskSet->n < ArraySize(pMaskSet->ix) );\n  pMaskSet->ix[pMaskSet->n++] = iCursor;\n}\n\n/*\n** Advance to the next WhereTerm that matches according to the criteria\n** established when the pScan object was initialized by whereScanInit().\n** Return NULL if there are no more matching WhereTerms.\n*/\nstatic WhereTerm *whereScanNext(WhereScan *pScan){\n  int iCur;            /* The cursor on the LHS of the term */\n  i16 iColumn;         /* The column on the LHS of the term.  -1 for IPK */\n  Expr *pX;            /* An expression being tested */\n  WhereClause *pWC;    /* Shorthand for pScan->pWC */\n  WhereTerm *pTerm;    /* The term being tested */\n  int k = pScan->k;    /* Where to start scanning */\n\n  assert( pScan->iEquiv<=pScan->nEquiv );\n  pWC = pScan->pWC;\n  while(1){\n    iColumn = pScan->aiColumn[pScan->iEquiv-1];\n    iCur = pScan->aiCur[pScan->iEquiv-1];\n    assert( pWC!=0 );\n    do{\n      for(pTerm=pWC->a+k; k<pWC->nTerm; k++, pTerm++){\n        if( pTerm->leftCursor==iCur\n         && pTerm->u.leftColumn==iColumn\n         && (iColumn!=XN_EXPR\n             || sqlite3ExprCompareSkip(pTerm->pExpr->pLeft,\n                                       pScan->pIdxExpr,iCur)==0)\n         && (pScan->iEquiv<=1 || !ExprHasProperty(pTerm->pExpr, EP_FromJoin))\n        ){\n          if( (pTerm->eOperator & WO_EQUIV)!=0\n           && pScan->nEquiv<ArraySize(pScan->aiCur)\n           && (pX = sqlite3ExprSkipCollate(pTerm->pExpr->pRight))->op==TK_COLUMN\n          ){\n            int j;\n            for(j=0; j<pScan->nEquiv; j++){\n              if( pScan->aiCur[j]==pX->iTable\n               && pScan->aiColumn[j]==pX->iColumn ){\n                  break;\n              }\n            }\n            if( j==pScan->nEquiv ){\n              pScan->aiCur[j] = pX->iTable;\n              pScan->aiColumn[j] = pX->iColumn;\n              pScan->nEquiv++;\n            }\n          }\n          if( (pTerm->eOperator & pScan->opMask)!=0 ){\n            /* Verify the affinity and collating sequence match */\n            if( pScan->zCollName && (pTerm->eOperator & WO_ISNULL)==0 ){\n              CollSeq *pColl;\n              Parse *pParse = pWC->pWInfo->pParse;\n              pX = pTerm->pExpr;\n              if( !sqlite3IndexAffinityOk(pX, pScan->idxaff) ){\n                continue;\n              }\n              assert(pX->pLeft);\n              pColl = sqlite3BinaryCompareCollSeq(pParse,\n                                                  pX->pLeft, pX->pRight);\n              if( pColl==0 ) pColl = pParse->db->pDfltColl;\n              if( sqlite3StrICmp(pColl->zName, pScan->zCollName) ){\n                continue;\n              }\n            }\n            if( (pTerm->eOperator & (WO_EQ|WO_IS))!=0\n             && (pX = pTerm->pExpr->pRight)->op==TK_COLUMN\n             && pX->iTable==pScan->aiCur[0]\n             && pX->iColumn==pScan->aiColumn[0]\n            ){\n              testcase( pTerm->eOperator & WO_IS );\n              continue;\n            }\n            pScan->pWC = pWC;\n            pScan->k = k+1;\n            return pTerm;\n          }\n        }\n      }\n      pWC = pWC->pOuter;\n      k = 0;\n    }while( pWC!=0 );\n    if( pScan->iEquiv>=pScan->nEquiv ) break;\n    pWC = pScan->pOrigWC;\n    k = 0;\n    pScan->iEquiv++;\n  }\n  return 0;\n}\n\n/*\n** Initialize a WHERE clause scanner object.  Return a pointer to the\n** first match.  Return NULL if there are no matches.\n**\n** The scanner will be searching the WHERE clause pWC.  It will look\n** for terms of the form \"X <op> <expr>\" where X is column iColumn of table\n** iCur.   Or if pIdx!=0 then X is column iColumn of index pIdx.  pIdx\n** must be one of the indexes of table iCur.\n**\n** The <op> must be one of the operators described by opMask.\n**\n** If the search is for X and the WHERE clause contains terms of the\n** form X=Y then this routine might also return terms of the form\n** \"Y <op> <expr>\".  The number of levels of transitivity is limited,\n** but is enough to handle most commonly occurring SQL statements.\n**\n** If X is not the INTEGER PRIMARY KEY then X must be compatible with\n** index pIdx.\n*/\nstatic WhereTerm *whereScanInit(\n  WhereScan *pScan,       /* The WhereScan object being initialized */\n  WhereClause *pWC,       /* The WHERE clause to be scanned */\n  int iCur,               /* Cursor to scan for */\n  int iColumn,            /* Column to scan for */\n  u32 opMask,             /* Operator(s) to scan for */\n  Index *pIdx             /* Must be compatible with this index */\n){\n  pScan->pOrigWC = pWC;\n  pScan->pWC = pWC;\n  pScan->pIdxExpr = 0;\n  pScan->idxaff = 0;\n  pScan->zCollName = 0;\n  if( pIdx ){\n    int j = iColumn;\n    iColumn = pIdx->aiColumn[j];\n    if( iColumn==XN_EXPR ){\n      pScan->pIdxExpr = pIdx->aColExpr->a[j].pExpr;\n      pScan->zCollName = pIdx->azColl[j];\n    }else if( iColumn==pIdx->pTable->iPKey ){\n      iColumn = XN_ROWID;\n    }else if( iColumn>=0 ){\n      pScan->idxaff = pIdx->pTable->aCol[iColumn].affinity;\n      pScan->zCollName = pIdx->azColl[j];\n    }\n  }else if( iColumn==XN_EXPR ){\n    return 0;\n  }\n  pScan->opMask = opMask;\n  pScan->k = 0;\n  pScan->aiCur[0] = iCur;\n  pScan->aiColumn[0] = iColumn;\n  pScan->nEquiv = 1;\n  pScan->iEquiv = 1;\n  return whereScanNext(pScan);\n}\n\n/*\n** Search for a term in the WHERE clause that is of the form \"X <op> <expr>\"\n** where X is a reference to the iColumn of table iCur or of index pIdx\n** if pIdx!=0 and <op> is one of the WO_xx operator codes specified by\n** the op parameter.  Return a pointer to the term.  Return 0 if not found.\n**\n** If pIdx!=0 then it must be one of the indexes of table iCur.  \n** Search for terms matching the iColumn-th column of pIdx\n** rather than the iColumn-th column of table iCur.\n**\n** The term returned might by Y=<expr> if there is another constraint in\n** the WHERE clause that specifies that X=Y.  Any such constraints will be\n** identified by the WO_EQUIV bit in the pTerm->eOperator field.  The\n** aiCur[]/iaColumn[] arrays hold X and all its equivalents. There are 11\n** slots in aiCur[]/aiColumn[] so that means we can look for X plus up to 10\n** other equivalent values.  Hence a search for X will return <expr> if X=A1\n** and A1=A2 and A2=A3 and ... and A9=A10 and A10=<expr>.\n**\n** If there are multiple terms in the WHERE clause of the form \"X <op> <expr>\"\n** then try for the one with no dependencies on <expr> - in other words where\n** <expr> is a constant expression of some kind.  Only return entries of\n** the form \"X <op> Y\" where Y is a column in another table if no terms of\n** the form \"X <op> <const-expr>\" exist.   If no terms with a constant RHS\n** exist, try to return a term that does not use WO_EQUIV.\n*/\nSQLITE_PRIVATE WhereTerm *sqlite3WhereFindTerm(\n  WhereClause *pWC,     /* The WHERE clause to be searched */\n  int iCur,             /* Cursor number of LHS */\n  int iColumn,          /* Column number of LHS */\n  Bitmask notReady,     /* RHS must not overlap with this mask */\n  u32 op,               /* Mask of WO_xx values describing operator */\n  Index *pIdx           /* Must be compatible with this index, if not NULL */\n){\n  WhereTerm *pResult = 0;\n  WhereTerm *p;\n  WhereScan scan;\n\n  p = whereScanInit(&scan, pWC, iCur, iColumn, op, pIdx);\n  op &= WO_EQ|WO_IS;\n  while( p ){\n    if( (p->prereqRight & notReady)==0 ){\n      if( p->prereqRight==0 && (p->eOperator&op)!=0 ){\n        testcase( p->eOperator & WO_IS );\n        return p;\n      }\n      if( pResult==0 ) pResult = p;\n    }\n    p = whereScanNext(&scan);\n  }\n  return pResult;\n}\n\n/*\n** This function searches pList for an entry that matches the iCol-th column\n** of index pIdx.\n**\n** If such an expression is found, its index in pList->a[] is returned. If\n** no expression is found, -1 is returned.\n*/\nstatic int findIndexCol(\n  Parse *pParse,                  /* Parse context */\n  ExprList *pList,                /* Expression list to search */\n  int iBase,                      /* Cursor for table associated with pIdx */\n  Index *pIdx,                    /* Index to match column of */\n  int iCol                        /* Column of index to match */\n){\n  int i;\n  const char *zColl = pIdx->azColl[iCol];\n\n  for(i=0; i<pList->nExpr; i++){\n    Expr *p = sqlite3ExprSkipCollate(pList->a[i].pExpr);\n    if( p->op==TK_COLUMN\n     && p->iColumn==pIdx->aiColumn[iCol]\n     && p->iTable==iBase\n    ){\n      CollSeq *pColl = sqlite3ExprNNCollSeq(pParse, pList->a[i].pExpr);\n      if( 0==sqlite3StrICmp(pColl->zName, zColl) ){\n        return i;\n      }\n    }\n  }\n\n  return -1;\n}\n\n/*\n** Return TRUE if the iCol-th column of index pIdx is NOT NULL\n*/\nstatic int indexColumnNotNull(Index *pIdx, int iCol){\n  int j;\n  assert( pIdx!=0 );\n  assert( iCol>=0 && iCol<pIdx->nColumn );\n  j = pIdx->aiColumn[iCol];\n  if( j>=0 ){\n    return pIdx->pTable->aCol[j].notNull;\n  }else if( j==(-1) ){\n    return 1;\n  }else{\n    assert( j==(-2) );\n    return 0;  /* Assume an indexed expression can always yield a NULL */\n\n  }\n}\n\n/*\n** Return true if the DISTINCT expression-list passed as the third argument\n** is redundant.\n**\n** A DISTINCT list is redundant if any subset of the columns in the\n** DISTINCT list are collectively unique and individually non-null.\n*/\nstatic int isDistinctRedundant(\n  Parse *pParse,            /* Parsing context */\n  SrcList *pTabList,        /* The FROM clause */\n  WhereClause *pWC,         /* The WHERE clause */\n  ExprList *pDistinct       /* The result set that needs to be DISTINCT */\n){\n  Table *pTab;\n  Index *pIdx;\n  int i;                          \n  int iBase;\n\n  /* If there is more than one table or sub-select in the FROM clause of\n  ** this query, then it will not be possible to show that the DISTINCT \n  ** clause is redundant. */\n  if( pTabList->nSrc!=1 ) return 0;\n  iBase = pTabList->a[0].iCursor;\n  pTab = pTabList->a[0].pTab;\n\n  /* If any of the expressions is an IPK column on table iBase, then return \n  ** true. Note: The (p->iTable==iBase) part of this test may be false if the\n  ** current SELECT is a correlated sub-query.\n  */\n  for(i=0; i<pDistinct->nExpr; i++){\n    Expr *p = sqlite3ExprSkipCollate(pDistinct->a[i].pExpr);\n    if( p->op==TK_COLUMN && p->iTable==iBase && p->iColumn<0 ) return 1;\n  }\n\n  /* Loop through all indices on the table, checking each to see if it makes\n  ** the DISTINCT qualifier redundant. It does so if:\n  **\n  **   1. The index is itself UNIQUE, and\n  **\n  **   2. All of the columns in the index are either part of the pDistinct\n  **      list, or else the WHERE clause contains a term of the form \"col=X\",\n  **      where X is a constant value. The collation sequences of the\n  **      comparison and select-list expressions must match those of the index.\n  **\n  **   3. All of those index columns for which the WHERE clause does not\n  **      contain a \"col=X\" term are subject to a NOT NULL constraint.\n  */\n  for(pIdx=pTab->pIndex; pIdx; pIdx=pIdx->pNext){\n    if( !IsUniqueIndex(pIdx) ) continue;\n    for(i=0; i<pIdx->nKeyCol; i++){\n      if( 0==sqlite3WhereFindTerm(pWC, iBase, i, ~(Bitmask)0, WO_EQ, pIdx) ){\n        if( findIndexCol(pParse, pDistinct, iBase, pIdx, i)<0 ) break;\n        if( indexColumnNotNull(pIdx, i)==0 ) break;\n      }\n    }\n    if( i==pIdx->nKeyCol ){\n      /* This index implies that the DISTINCT qualifier is redundant. */\n      return 1;\n    }\n  }\n\n  return 0;\n}\n\n\n/*\n** Estimate the logarithm of the input value to base 2.\n*/\nstatic LogEst estLog(LogEst N){\n  return N<=10 ? 0 : sqlite3LogEst(N) - 33;\n}\n\n/*\n** Convert OP_Column opcodes to OP_Copy in previously generated code.\n**\n** This routine runs over generated VDBE code and translates OP_Column\n** opcodes into OP_Copy when the table is being accessed via co-routine \n** instead of via table lookup.\n**\n** If the bIncrRowid parameter is 0, then any OP_Rowid instructions on\n** cursor iTabCur are transformed into OP_Null. Or, if bIncrRowid is non-zero,\n** then each OP_Rowid is transformed into an instruction to increment the\n** value stored in its output register.\n*/\nstatic void translateColumnToCopy(\n  Parse *pParse,      /* Parsing context */\n  int iStart,         /* Translate from this opcode to the end */\n  int iTabCur,        /* OP_Column/OP_Rowid references to this table */\n  int iRegister,      /* The first column is in this register */\n  int bIncrRowid      /* If non-zero, transform OP_rowid to OP_AddImm(1) */\n){\n  Vdbe *v = pParse->pVdbe;\n  VdbeOp *pOp = sqlite3VdbeGetOp(v, iStart);\n  int iEnd = sqlite3VdbeCurrentAddr(v);\n  if( pParse->db->mallocFailed ) return;\n  for(; iStart<iEnd; iStart++, pOp++){\n    if( pOp->p1!=iTabCur ) continue;\n    if( pOp->opcode==OP_Column ){\n      pOp->opcode = OP_Copy;\n      pOp->p1 = pOp->p2 + iRegister;\n      pOp->p2 = pOp->p3;\n      pOp->p3 = 0;\n    }else if( pOp->opcode==OP_Rowid ){\n      if( bIncrRowid ){\n        /* Increment the value stored in the P2 operand of the OP_Rowid. */\n        pOp->opcode = OP_AddImm;\n        pOp->p1 = pOp->p2;\n        pOp->p2 = 1;\n      }else{\n        pOp->opcode = OP_Null;\n        pOp->p1 = 0;\n        pOp->p3 = 0;\n      }\n    }\n  }\n}\n\n/*\n** Two routines for printing the content of an sqlite3_index_info\n** structure.  Used for testing and debugging only.  If neither\n** SQLITE_TEST or SQLITE_DEBUG are defined, then these routines\n** are no-ops.\n*/\n#if !defined(SQLITE_OMIT_VIRTUALTABLE) && defined(WHERETRACE_ENABLED)\nstatic void TRACE_IDX_INPUTS(sqlite3_index_info *p){\n  int i;\n  if( !sqlite3WhereTrace ) return;\n  for(i=0; i<p->nConstraint; i++){\n    sqlite3DebugPrintf(\"  constraint[%d]: col=%d termid=%d op=%d usabled=%d\\n\",\n       i,\n       p->aConstraint[i].iColumn,\n       p->aConstraint[i].iTermOffset,\n       p->aConstraint[i].op,\n       p->aConstraint[i].usable);\n  }\n  for(i=0; i<p->nOrderBy; i++){\n    sqlite3DebugPrintf(\"  orderby[%d]: col=%d desc=%d\\n\",\n       i,\n       p->aOrderBy[i].iColumn,\n       p->aOrderBy[i].desc);\n  }\n}\nstatic void TRACE_IDX_OUTPUTS(sqlite3_index_info *p){\n  int i;\n  if( !sqlite3WhereTrace ) return;\n  for(i=0; i<p->nConstraint; i++){\n    sqlite3DebugPrintf(\"  usage[%d]: argvIdx=%d omit=%d\\n\",\n       i,\n       p->aConstraintUsage[i].argvIndex,\n       p->aConstraintUsage[i].omit);\n  }\n  sqlite3DebugPrintf(\"  idxNum=%d\\n\", p->idxNum);\n  sqlite3DebugPrintf(\"  idxStr=%s\\n\", p->idxStr);\n  sqlite3DebugPrintf(\"  orderByConsumed=%d\\n\", p->orderByConsumed);\n  sqlite3DebugPrintf(\"  estimatedCost=%g\\n\", p->estimatedCost);\n  sqlite3DebugPrintf(\"  estimatedRows=%lld\\n\", p->estimatedRows);\n}\n#else\n#define TRACE_IDX_INPUTS(A)\n#define TRACE_IDX_OUTPUTS(A)\n#endif\n\n#ifndef SQLITE_OMIT_AUTOMATIC_INDEX\n/*\n** Return TRUE if the WHERE clause term pTerm is of a form where it\n** could be used with an index to access pSrc, assuming an appropriate\n** index existed.\n*/\nstatic int termCanDriveIndex(\n  WhereTerm *pTerm,              /* WHERE clause term to check */\n  struct SrcList_item *pSrc,     /* Table we are trying to access */\n  Bitmask notReady               /* Tables in outer loops of the join */\n){\n  char aff;\n  if( pTerm->leftCursor!=pSrc->iCursor ) return 0;\n  if( (pTerm->eOperator & (WO_EQ|WO_IS))==0 ) return 0;\n  if( (pSrc->fg.jointype & JT_LEFT) \n   && !ExprHasProperty(pTerm->pExpr, EP_FromJoin)\n   && (pTerm->eOperator & WO_IS)\n  ){\n    /* Cannot use an IS term from the WHERE clause as an index driver for\n    ** the RHS of a LEFT JOIN. Such a term can only be used if it is from\n    ** the ON clause.  */\n    return 0;\n  }\n  if( (pTerm->prereqRight & notReady)!=0 ) return 0;\n  if( pTerm->u.leftColumn<0 ) return 0;\n  aff = pSrc->pTab->aCol[pTerm->u.leftColumn].affinity;\n  if( !sqlite3IndexAffinityOk(pTerm->pExpr, aff) ) return 0;\n  testcase( pTerm->pExpr->op==TK_IS );\n  return 1;\n}\n#endif\n\n\n#ifndef SQLITE_OMIT_AUTOMATIC_INDEX\n/*\n** Generate code to construct the Index object for an automatic index\n** and to set up the WhereLevel object pLevel so that the code generator\n** makes use of the automatic index.\n*/\nstatic void constructAutomaticIndex(\n  Parse *pParse,              /* The parsing context */\n  WhereClause *pWC,           /* The WHERE clause */\n  struct SrcList_item *pSrc,  /* The FROM clause term to get the next index */\n  Bitmask notReady,           /* Mask of cursors that are not available */\n  WhereLevel *pLevel          /* Write new index here */\n){\n  int nKeyCol;                /* Number of columns in the constructed index */\n  WhereTerm *pTerm;           /* A single term of the WHERE clause */\n  WhereTerm *pWCEnd;          /* End of pWC->a[] */\n  Index *pIdx;                /* Object describing the transient index */\n  Vdbe *v;                    /* Prepared statement under construction */\n  int addrInit;               /* Address of the initialization bypass jump */\n  Table *pTable;              /* The table being indexed */\n  int addrTop;                /* Top of the index fill loop */\n  int regRecord;              /* Register holding an index record */\n  int n;                      /* Column counter */\n  int i;                      /* Loop counter */\n  int mxBitCol;               /* Maximum column in pSrc->colUsed */\n  CollSeq *pColl;             /* Collating sequence to on a column */\n  WhereLoop *pLoop;           /* The Loop object */\n  char *zNotUsed;             /* Extra space on the end of pIdx */\n  Bitmask idxCols;            /* Bitmap of columns used for indexing */\n  Bitmask extraCols;          /* Bitmap of additional columns */\n  u8 sentWarning = 0;         /* True if a warnning has been issued */\n  Expr *pPartial = 0;         /* Partial Index Expression */\n  int iContinue = 0;          /* Jump here to skip excluded rows */\n  struct SrcList_item *pTabItem;  /* FROM clause term being indexed */\n  int addrCounter = 0;        /* Address where integer counter is initialized */\n  int regBase;                /* Array of registers where record is assembled */\n\n  /* Generate code to skip over the creation and initialization of the\n  ** transient index on 2nd and subsequent iterations of the loop. */\n  v = pParse->pVdbe;\n  assert( v!=0 );\n  addrInit = sqlite3VdbeAddOp0(v, OP_Once); VdbeCoverage(v);\n\n  /* Count the number of columns that will be added to the index\n  ** and used to match WHERE clause constraints */\n  nKeyCol = 0;\n  pTable = pSrc->pTab;\n  pWCEnd = &pWC->a[pWC->nTerm];\n  pLoop = pLevel->pWLoop;\n  idxCols = 0;\n  for(pTerm=pWC->a; pTerm<pWCEnd; pTerm++){\n    Expr *pExpr = pTerm->pExpr;\n    assert( !ExprHasProperty(pExpr, EP_FromJoin)    /* prereq always non-zero */\n         || pExpr->iRightJoinTable!=pSrc->iCursor   /*   for the right-hand   */\n         || pLoop->prereq!=0 );                     /*   table of a LEFT JOIN */\n    if( pLoop->prereq==0\n     && (pTerm->wtFlags & TERM_VIRTUAL)==0\n     && !ExprHasProperty(pExpr, EP_FromJoin)\n     && sqlite3ExprIsTableConstant(pExpr, pSrc->iCursor) ){\n      pPartial = sqlite3ExprAnd(pParse->db, pPartial,\n                                sqlite3ExprDup(pParse->db, pExpr, 0));\n    }\n    if( termCanDriveIndex(pTerm, pSrc, notReady) ){\n      int iCol = pTerm->u.leftColumn;\n      Bitmask cMask = iCol>=BMS ? MASKBIT(BMS-1) : MASKBIT(iCol);\n      testcase( iCol==BMS );\n      testcase( iCol==BMS-1 );\n      if( !sentWarning ){\n        sqlite3_log(SQLITE_WARNING_AUTOINDEX,\n            \"automatic index on %s(%s)\", pTable->zName,\n            pTable->aCol[iCol].zName);\n        sentWarning = 1;\n      }\n      if( (idxCols & cMask)==0 ){\n        if( whereLoopResize(pParse->db, pLoop, nKeyCol+1) ){\n          goto end_auto_index_create;\n        }\n        pLoop->aLTerm[nKeyCol++] = pTerm;\n        idxCols |= cMask;\n      }\n    }\n  }\n  assert( nKeyCol>0 );\n  pLoop->u.btree.nEq = pLoop->nLTerm = nKeyCol;\n  pLoop->wsFlags = WHERE_COLUMN_EQ | WHERE_IDX_ONLY | WHERE_INDEXED\n                     | WHERE_AUTO_INDEX;\n\n  /* Count the number of additional columns needed to create a\n  ** covering index.  A \"covering index\" is an index that contains all\n  ** columns that are needed by the query.  With a covering index, the\n  ** original table never needs to be accessed.  Automatic indices must\n  ** be a covering index because the index will not be updated if the\n  ** original table changes and the index and table cannot both be used\n  ** if they go out of sync.\n  */\n  extraCols = pSrc->colUsed & (~idxCols | MASKBIT(BMS-1));\n  mxBitCol = MIN(BMS-1,pTable->nCol);\n  testcase( pTable->nCol==BMS-1 );\n  testcase( pTable->nCol==BMS-2 );\n  for(i=0; i<mxBitCol; i++){\n    if( extraCols & MASKBIT(i) ) nKeyCol++;\n  }\n  if( pSrc->colUsed & MASKBIT(BMS-1) ){\n    nKeyCol += pTable->nCol - BMS + 1;\n  }\n\n  /* Construct the Index object to describe this index */\n  pIdx = sqlite3AllocateIndexObject(pParse->db, nKeyCol+1, 0, &zNotUsed);\n  if( pIdx==0 ) goto end_auto_index_create;\n  pLoop->u.btree.pIndex = pIdx;\n  pIdx->zName = \"auto-index\";\n  pIdx->pTable = pTable;\n  n = 0;\n  idxCols = 0;\n  for(pTerm=pWC->a; pTerm<pWCEnd; pTerm++){\n    if( termCanDriveIndex(pTerm, pSrc, notReady) ){\n      int iCol = pTerm->u.leftColumn;\n      Bitmask cMask = iCol>=BMS ? MASKBIT(BMS-1) : MASKBIT(iCol);\n      testcase( iCol==BMS-1 );\n      testcase( iCol==BMS );\n      if( (idxCols & cMask)==0 ){\n        Expr *pX = pTerm->pExpr;\n        idxCols |= cMask;\n        pIdx->aiColumn[n] = pTerm->u.leftColumn;\n        pColl = sqlite3BinaryCompareCollSeq(pParse, pX->pLeft, pX->pRight);\n        pIdx->azColl[n] = pColl ? pColl->zName : sqlite3StrBINARY;\n        n++;\n      }\n    }\n  }\n  assert( (u32)n==pLoop->u.btree.nEq );\n\n  /* Add additional columns needed to make the automatic index into\n  ** a covering index */\n  for(i=0; i<mxBitCol; i++){\n    if( extraCols & MASKBIT(i) ){\n      pIdx->aiColumn[n] = i;\n      pIdx->azColl[n] = sqlite3StrBINARY;\n      n++;\n    }\n  }\n  if( pSrc->colUsed & MASKBIT(BMS-1) ){\n    for(i=BMS-1; i<pTable->nCol; i++){\n      pIdx->aiColumn[n] = i;\n      pIdx->azColl[n] = sqlite3StrBINARY;\n      n++;\n    }\n  }\n  assert( n==nKeyCol );\n  pIdx->aiColumn[n] = XN_ROWID;\n  pIdx->azColl[n] = sqlite3StrBINARY;\n\n  /* Create the automatic index */\n  assert( pLevel->iIdxCur>=0 );\n  pLevel->iIdxCur = pParse->nTab++;\n  sqlite3VdbeAddOp2(v, OP_OpenAutoindex, pLevel->iIdxCur, nKeyCol+1);\n  sqlite3VdbeSetP4KeyInfo(pParse, pIdx);\n  VdbeComment((v, \"for %s\", pTable->zName));\n\n  /* Fill the automatic index with content */\n  sqlite3ExprCachePush(pParse);\n  pTabItem = &pWC->pWInfo->pTabList->a[pLevel->iFrom];\n  if( pTabItem->fg.viaCoroutine ){\n    int regYield = pTabItem->regReturn;\n    addrCounter = sqlite3VdbeAddOp2(v, OP_Integer, 0, 0);\n    sqlite3VdbeAddOp3(v, OP_InitCoroutine, regYield, 0, pTabItem->addrFillSub);\n    addrTop =  sqlite3VdbeAddOp1(v, OP_Yield, regYield);\n    VdbeCoverage(v);\n    VdbeComment((v, \"next row of \\\"%s\\\"\", pTabItem->pTab->zName));\n  }else{\n    addrTop = sqlite3VdbeAddOp1(v, OP_Rewind, pLevel->iTabCur); VdbeCoverage(v);\n  }\n  if( pPartial ){\n    iContinue = sqlite3VdbeMakeLabel(v);\n    sqlite3ExprIfFalse(pParse, pPartial, iContinue, SQLITE_JUMPIFNULL);\n    pLoop->wsFlags |= WHERE_PARTIALIDX;\n  }\n  regRecord = sqlite3GetTempReg(pParse);\n  regBase = sqlite3GenerateIndexKey(\n      pParse, pIdx, pLevel->iTabCur, regRecord, 0, 0, 0, 0\n  );\n  sqlite3VdbeAddOp2(v, OP_IdxInsert, pLevel->iIdxCur, regRecord);\n  sqlite3VdbeChangeP5(v, OPFLAG_USESEEKRESULT);\n  if( pPartial ) sqlite3VdbeResolveLabel(v, iContinue);\n  if( pTabItem->fg.viaCoroutine ){\n    sqlite3VdbeChangeP2(v, addrCounter, regBase+n);\n    testcase( pParse->db->mallocFailed );\n    translateColumnToCopy(pParse, addrTop, pLevel->iTabCur,\n                          pTabItem->regResult, 1);\n    sqlite3VdbeGoto(v, addrTop);\n    pTabItem->fg.viaCoroutine = 0;\n  }else{\n    sqlite3VdbeAddOp2(v, OP_Next, pLevel->iTabCur, addrTop+1); VdbeCoverage(v);\n  }\n  sqlite3VdbeChangeP5(v, SQLITE_STMTSTATUS_AUTOINDEX);\n  sqlite3VdbeJumpHere(v, addrTop);\n  sqlite3ReleaseTempReg(pParse, regRecord);\n  sqlite3ExprCachePop(pParse);\n  \n  /* Jump here when skipping the initialization */\n  sqlite3VdbeJumpHere(v, addrInit);\n\nend_auto_index_create:\n  sqlite3ExprDelete(pParse->db, pPartial);\n}\n#endif /* SQLITE_OMIT_AUTOMATIC_INDEX */\n\n#ifndef SQLITE_OMIT_VIRTUALTABLE\n/*\n** Allocate and populate an sqlite3_index_info structure. It is the \n** responsibility of the caller to eventually release the structure\n** by passing the pointer returned by this function to sqlite3_free().\n*/\nstatic sqlite3_index_info *allocateIndexInfo(\n  Parse *pParse,                  /* The parsing context */\n  WhereClause *pWC,               /* The WHERE clause being analyzed */\n  Bitmask mUnusable,              /* Ignore terms with these prereqs */\n  struct SrcList_item *pSrc,      /* The FROM clause term that is the vtab */\n  ExprList *pOrderBy,             /* The ORDER BY clause */\n  u16 *pmNoOmit                   /* Mask of terms not to omit */\n){\n  int i, j;\n  int nTerm;\n  struct sqlite3_index_constraint *pIdxCons;\n  struct sqlite3_index_orderby *pIdxOrderBy;\n  struct sqlite3_index_constraint_usage *pUsage;\n  struct HiddenIndexInfo *pHidden;\n  WhereTerm *pTerm;\n  int nOrderBy;\n  sqlite3_index_info *pIdxInfo;\n  u16 mNoOmit = 0;\n\n  /* Count the number of possible WHERE clause constraints referring\n  ** to this virtual table */\n  for(i=nTerm=0, pTerm=pWC->a; i<pWC->nTerm; i++, pTerm++){\n    if( pTerm->leftCursor != pSrc->iCursor ) continue;\n    if( pTerm->prereqRight & mUnusable ) continue;\n    assert( IsPowerOfTwo(pTerm->eOperator & ~WO_EQUIV) );\n    testcase( pTerm->eOperator & WO_IN );\n    testcase( pTerm->eOperator & WO_ISNULL );\n    testcase( pTerm->eOperator & WO_IS );\n    testcase( pTerm->eOperator & WO_ALL );\n    if( (pTerm->eOperator & ~(WO_EQUIV))==0 ) continue;\n    if( pTerm->wtFlags & TERM_VNULL ) continue;\n    assert( pTerm->u.leftColumn>=(-1) );\n    nTerm++;\n  }\n\n  /* If the ORDER BY clause contains only columns in the current \n  ** virtual table then allocate space for the aOrderBy part of\n  ** the sqlite3_index_info structure.\n  */\n  nOrderBy = 0;\n  if( pOrderBy ){\n    int n = pOrderBy->nExpr;\n    for(i=0; i<n; i++){\n      Expr *pExpr = pOrderBy->a[i].pExpr;\n      if( pExpr->op!=TK_COLUMN || pExpr->iTable!=pSrc->iCursor ) break;\n    }\n    if( i==n){\n      nOrderBy = n;\n    }\n  }\n\n  /* Allocate the sqlite3_index_info structure\n  */\n  pIdxInfo = sqlite3DbMallocZero(pParse->db, sizeof(*pIdxInfo)\n                           + (sizeof(*pIdxCons) + sizeof(*pUsage))*nTerm\n                           + sizeof(*pIdxOrderBy)*nOrderBy + sizeof(*pHidden) );\n  if( pIdxInfo==0 ){\n    sqlite3ErrorMsg(pParse, \"out of memory\");\n    return 0;\n  }\n\n  /* Initialize the structure.  The sqlite3_index_info structure contains\n  ** many fields that are declared \"const\" to prevent xBestIndex from\n  ** changing them.  We have to do some funky casting in order to\n  ** initialize those fields.\n  */\n  pHidden = (struct HiddenIndexInfo*)&pIdxInfo[1];\n  pIdxCons = (struct sqlite3_index_constraint*)&pHidden[1];\n  pIdxOrderBy = (struct sqlite3_index_orderby*)&pIdxCons[nTerm];\n  pUsage = (struct sqlite3_index_constraint_usage*)&pIdxOrderBy[nOrderBy];\n  *(int*)&pIdxInfo->nConstraint = nTerm;\n  *(int*)&pIdxInfo->nOrderBy = nOrderBy;\n  *(struct sqlite3_index_constraint**)&pIdxInfo->aConstraint = pIdxCons;\n  *(struct sqlite3_index_orderby**)&pIdxInfo->aOrderBy = pIdxOrderBy;\n  *(struct sqlite3_index_constraint_usage**)&pIdxInfo->aConstraintUsage =\n                                                                   pUsage;\n\n  pHidden->pWC = pWC;\n  pHidden->pParse = pParse;\n  for(i=j=0, pTerm=pWC->a; i<pWC->nTerm; i++, pTerm++){\n    u16 op;\n    if( pTerm->leftCursor != pSrc->iCursor ) continue;\n    if( pTerm->prereqRight & mUnusable ) continue;\n    assert( IsPowerOfTwo(pTerm->eOperator & ~WO_EQUIV) );\n    testcase( pTerm->eOperator & WO_IN );\n    testcase( pTerm->eOperator & WO_IS );\n    testcase( pTerm->eOperator & WO_ISNULL );\n    testcase( pTerm->eOperator & WO_ALL );\n    if( (pTerm->eOperator & ~(WO_EQUIV))==0 ) continue;\n    if( pTerm->wtFlags & TERM_VNULL ) continue;\n    assert( pTerm->u.leftColumn>=(-1) );\n    pIdxCons[j].iColumn = pTerm->u.leftColumn;\n    pIdxCons[j].iTermOffset = i;\n    op = pTerm->eOperator & WO_ALL;\n    if( op==WO_IN ) op = WO_EQ;\n    if( op==WO_AUX ){\n      pIdxCons[j].op = pTerm->eMatchOp;\n    }else if( op & (WO_ISNULL|WO_IS) ){\n      if( op==WO_ISNULL ){\n        pIdxCons[j].op = SQLITE_INDEX_CONSTRAINT_ISNULL;\n      }else{\n        pIdxCons[j].op = SQLITE_INDEX_CONSTRAINT_IS;\n      }\n    }else{\n      pIdxCons[j].op = (u8)op;\n      /* The direct assignment in the previous line is possible only because\n      ** the WO_ and SQLITE_INDEX_CONSTRAINT_ codes are identical.  The\n      ** following asserts verify this fact. */\n      assert( WO_EQ==SQLITE_INDEX_CONSTRAINT_EQ );\n      assert( WO_LT==SQLITE_INDEX_CONSTRAINT_LT );\n      assert( WO_LE==SQLITE_INDEX_CONSTRAINT_LE );\n      assert( WO_GT==SQLITE_INDEX_CONSTRAINT_GT );\n      assert( WO_GE==SQLITE_INDEX_CONSTRAINT_GE );\n      assert( pTerm->eOperator&(WO_IN|WO_EQ|WO_LT|WO_LE|WO_GT|WO_GE|WO_AUX) );\n\n      if( op & (WO_LT|WO_LE|WO_GT|WO_GE)\n       && sqlite3ExprIsVector(pTerm->pExpr->pRight) \n      ){\n        if( i<16 ) mNoOmit |= (1 << i);\n        if( op==WO_LT ) pIdxCons[j].op = WO_LE;\n        if( op==WO_GT ) pIdxCons[j].op = WO_GE;\n      }\n    }\n\n    j++;\n  }\n  for(i=0; i<nOrderBy; i++){\n    Expr *pExpr = pOrderBy->a[i].pExpr;\n    pIdxOrderBy[i].iColumn = pExpr->iColumn;\n    pIdxOrderBy[i].desc = pOrderBy->a[i].sortOrder;\n  }\n\n  *pmNoOmit = mNoOmit;\n  return pIdxInfo;\n}\n\n/*\n** The table object reference passed as the second argument to this function\n** must represent a virtual table. This function invokes the xBestIndex()\n** method of the virtual table with the sqlite3_index_info object that\n** comes in as the 3rd argument to this function.\n**\n** If an error occurs, pParse is populated with an error message and a\n** non-zero value is returned. Otherwise, 0 is returned and the output\n** part of the sqlite3_index_info structure is left populated.\n**\n** Whether or not an error is returned, it is the responsibility of the\n** caller to eventually free p->idxStr if p->needToFreeIdxStr indicates\n** that this is required.\n*/\nstatic int vtabBestIndex(Parse *pParse, Table *pTab, sqlite3_index_info *p){\n  sqlite3_vtab *pVtab = sqlite3GetVTable(pParse->db, pTab)->pVtab;\n  int rc;\n\n  TRACE_IDX_INPUTS(p);\n  rc = pVtab->pModule->xBestIndex(pVtab, p);\n  TRACE_IDX_OUTPUTS(p);\n\n  if( rc!=SQLITE_OK ){\n    if( rc==SQLITE_NOMEM ){\n      sqlite3OomFault(pParse->db);\n    }else if( !pVtab->zErrMsg ){\n      sqlite3ErrorMsg(pParse, \"%s\", sqlite3ErrStr(rc));\n    }else{\n      sqlite3ErrorMsg(pParse, \"%s\", pVtab->zErrMsg);\n    }\n  }\n  sqlite3_free(pVtab->zErrMsg);\n  pVtab->zErrMsg = 0;\n\n#if 0\n  /* This error is now caught by the caller.\n  ** Search for \"xBestIndex malfunction\" below */\n  for(i=0; i<p->nConstraint; i++){\n    if( !p->aConstraint[i].usable && p->aConstraintUsage[i].argvIndex>0 ){\n      sqlite3ErrorMsg(pParse, \n          \"table %s: xBestIndex returned an invalid plan\", pTab->zName);\n    }\n  }\n#endif\n\n  return pParse->nErr;\n}\n#endif /* !defined(SQLITE_OMIT_VIRTUALTABLE) */\n\n#ifdef SQLITE_ENABLE_STAT3_OR_STAT4\n/*\n** Estimate the location of a particular key among all keys in an\n** index.  Store the results in aStat as follows:\n**\n**    aStat[0]      Est. number of rows less than pRec\n**    aStat[1]      Est. number of rows equal to pRec\n**\n** Return the index of the sample that is the smallest sample that\n** is greater than or equal to pRec. Note that this index is not an index\n** into the aSample[] array - it is an index into a virtual set of samples\n** based on the contents of aSample[] and the number of fields in record \n** pRec. \n*/\nstatic int whereKeyStats(\n  Parse *pParse,              /* Database connection */\n  Index *pIdx,                /* Index to consider domain of */\n  UnpackedRecord *pRec,       /* Vector of values to consider */\n  int roundUp,                /* Round up if true.  Round down if false */\n  tRowcnt *aStat              /* OUT: stats written here */\n){\n  IndexSample *aSample = pIdx->aSample;\n  int iCol;                   /* Index of required stats in anEq[] etc. */\n  int i;                      /* Index of first sample >= pRec */\n  int iSample;                /* Smallest sample larger than or equal to pRec */\n  int iMin = 0;               /* Smallest sample not yet tested */\n  int iTest;                  /* Next sample to test */\n  int res;                    /* Result of comparison operation */\n  int nField;                 /* Number of fields in pRec */\n  tRowcnt iLower = 0;         /* anLt[] + anEq[] of largest sample pRec is > */\n\n#ifndef SQLITE_DEBUG\n  UNUSED_PARAMETER( pParse );\n#endif\n  assert( pRec!=0 );\n  assert( pIdx->nSample>0 );\n  assert( pRec->nField>0 && pRec->nField<=pIdx->nSampleCol );\n\n  /* Do a binary search to find the first sample greater than or equal\n  ** to pRec. If pRec contains a single field, the set of samples to search\n  ** is simply the aSample[] array. If the samples in aSample[] contain more\n  ** than one fields, all fields following the first are ignored.\n  **\n  ** If pRec contains N fields, where N is more than one, then as well as the\n  ** samples in aSample[] (truncated to N fields), the search also has to\n  ** consider prefixes of those samples. For example, if the set of samples\n  ** in aSample is:\n  **\n  **     aSample[0] = (a, 5) \n  **     aSample[1] = (a, 10) \n  **     aSample[2] = (b, 5) \n  **     aSample[3] = (c, 100) \n  **     aSample[4] = (c, 105)\n  **\n  ** Then the search space should ideally be the samples above and the \n  ** unique prefixes [a], [b] and [c]. But since that is hard to organize, \n  ** the code actually searches this set:\n  **\n  **     0: (a) \n  **     1: (a, 5) \n  **     2: (a, 10) \n  **     3: (a, 10) \n  **     4: (b) \n  **     5: (b, 5) \n  **     6: (c) \n  **     7: (c, 100) \n  **     8: (c, 105)\n  **     9: (c, 105)\n  **\n  ** For each sample in the aSample[] array, N samples are present in the\n  ** effective sample array. In the above, samples 0 and 1 are based on \n  ** sample aSample[0]. Samples 2 and 3 on aSample[1] etc.\n  **\n  ** Often, sample i of each block of N effective samples has (i+1) fields.\n  ** Except, each sample may be extended to ensure that it is greater than or\n  ** equal to the previous sample in the array. For example, in the above, \n  ** sample 2 is the first sample of a block of N samples, so at first it \n  ** appears that it should be 1 field in size. However, that would make it \n  ** smaller than sample 1, so the binary search would not work. As a result, \n  ** it is extended to two fields. The duplicates that this creates do not \n  ** cause any problems.\n  */\n  nField = pRec->nField;\n  iCol = 0;\n  iSample = pIdx->nSample * nField;\n  do{\n    int iSamp;                    /* Index in aSample[] of test sample */\n    int n;                        /* Number of fields in test sample */\n\n    iTest = (iMin+iSample)/2;\n    iSamp = iTest / nField;\n    if( iSamp>0 ){\n      /* The proposed effective sample is a prefix of sample aSample[iSamp].\n      ** Specifically, the shortest prefix of at least (1 + iTest%nField) \n      ** fields that is greater than the previous effective sample.  */\n      for(n=(iTest % nField) + 1; n<nField; n++){\n        if( aSample[iSamp-1].anLt[n-1]!=aSample[iSamp].anLt[n-1] ) break;\n      }\n    }else{\n      n = iTest + 1;\n    }\n\n    pRec->nField = n;\n    res = sqlite3VdbeRecordCompare(aSample[iSamp].n, aSample[iSamp].p, pRec);\n    if( res<0 ){\n      iLower = aSample[iSamp].anLt[n-1] + aSample[iSamp].anEq[n-1];\n      iMin = iTest+1;\n    }else if( res==0 && n<nField ){\n      iLower = aSample[iSamp].anLt[n-1];\n      iMin = iTest+1;\n      res = -1;\n    }else{\n      iSample = iTest;\n      iCol = n-1;\n    }\n  }while( res && iMin<iSample );\n  i = iSample / nField;\n\n#ifdef SQLITE_DEBUG\n  /* The following assert statements check that the binary search code\n  ** above found the right answer. This block serves no purpose other\n  ** than to invoke the asserts.  */\n  if( pParse->db->mallocFailed==0 ){\n    if( res==0 ){\n      /* If (res==0) is true, then pRec must be equal to sample i. */\n      assert( i<pIdx->nSample );\n      assert( iCol==nField-1 );\n      pRec->nField = nField;\n      assert( 0==sqlite3VdbeRecordCompare(aSample[i].n, aSample[i].p, pRec) \n           || pParse->db->mallocFailed \n      );\n    }else{\n      /* Unless i==pIdx->nSample, indicating that pRec is larger than\n      ** all samples in the aSample[] array, pRec must be smaller than the\n      ** (iCol+1) field prefix of sample i.  */\n      assert( i<=pIdx->nSample && i>=0 );\n      pRec->nField = iCol+1;\n      assert( i==pIdx->nSample \n           || sqlite3VdbeRecordCompare(aSample[i].n, aSample[i].p, pRec)>0\n           || pParse->db->mallocFailed );\n\n      /* if i==0 and iCol==0, then record pRec is smaller than all samples\n      ** in the aSample[] array. Otherwise, if (iCol>0) then pRec must\n      ** be greater than or equal to the (iCol) field prefix of sample i.\n      ** If (i>0), then pRec must also be greater than sample (i-1).  */\n      if( iCol>0 ){\n        pRec->nField = iCol;\n        assert( sqlite3VdbeRecordCompare(aSample[i].n, aSample[i].p, pRec)<=0\n             || pParse->db->mallocFailed );\n      }\n      if( i>0 ){\n        pRec->nField = nField;\n        assert( sqlite3VdbeRecordCompare(aSample[i-1].n, aSample[i-1].p, pRec)<0\n             || pParse->db->mallocFailed );\n      }\n    }\n  }\n#endif /* ifdef SQLITE_DEBUG */\n\n  if( res==0 ){\n    /* Record pRec is equal to sample i */\n    assert( iCol==nField-1 );\n    aStat[0] = aSample[i].anLt[iCol];\n    aStat[1] = aSample[i].anEq[iCol];\n  }else{\n    /* At this point, the (iCol+1) field prefix of aSample[i] is the first \n    ** sample that is greater than pRec. Or, if i==pIdx->nSample then pRec\n    ** is larger than all samples in the array. */\n    tRowcnt iUpper, iGap;\n    if( i>=pIdx->nSample ){\n      iUpper = sqlite3LogEstToInt(pIdx->aiRowLogEst[0]);\n    }else{\n      iUpper = aSample[i].anLt[iCol];\n    }\n\n    if( iLower>=iUpper ){\n      iGap = 0;\n    }else{\n      iGap = iUpper - iLower;\n    }\n    if( roundUp ){\n      iGap = (iGap*2)/3;\n    }else{\n      iGap = iGap/3;\n    }\n    aStat[0] = iLower + iGap;\n    aStat[1] = pIdx->aAvgEq[nField-1];\n  }\n\n  /* Restore the pRec->nField value before returning.  */\n  pRec->nField = nField;\n  return i;\n}\n#endif /* SQLITE_ENABLE_STAT3_OR_STAT4 */\n\n/*\n** If it is not NULL, pTerm is a term that provides an upper or lower\n** bound on a range scan. Without considering pTerm, it is estimated \n** that the scan will visit nNew rows. This function returns the number\n** estimated to be visited after taking pTerm into account.\n**\n** If the user explicitly specified a likelihood() value for this term,\n** then the return value is the likelihood multiplied by the number of\n** input rows. Otherwise, this function assumes that an \"IS NOT NULL\" term\n** has a likelihood of 0.50, and any other term a likelihood of 0.25.\n*/\nstatic LogEst whereRangeAdjust(WhereTerm *pTerm, LogEst nNew){\n  LogEst nRet = nNew;\n  if( pTerm ){\n    if( pTerm->truthProb<=0 ){\n      nRet += pTerm->truthProb;\n    }else if( (pTerm->wtFlags & TERM_VNULL)==0 ){\n      nRet -= 20;        assert( 20==sqlite3LogEst(4) );\n    }\n  }\n  return nRet;\n}\n\n\n#ifdef SQLITE_ENABLE_STAT3_OR_STAT4\n/*\n** Return the affinity for a single column of an index.\n*/\nSQLITE_PRIVATE char sqlite3IndexColumnAffinity(sqlite3 *db, Index *pIdx, int iCol){\n  assert( iCol>=0 && iCol<pIdx->nColumn );\n  if( !pIdx->zColAff ){\n    if( sqlite3IndexAffinityStr(db, pIdx)==0 ) return SQLITE_AFF_BLOB;\n  }\n  return pIdx->zColAff[iCol];\n}\n#endif\n\n\n#ifdef SQLITE_ENABLE_STAT3_OR_STAT4\n/* \n** This function is called to estimate the number of rows visited by a\n** range-scan on a skip-scan index. For example:\n**\n**   CREATE INDEX i1 ON t1(a, b, c);\n**   SELECT * FROM t1 WHERE a=? AND c BETWEEN ? AND ?;\n**\n** Value pLoop->nOut is currently set to the estimated number of rows \n** visited for scanning (a=? AND b=?). This function reduces that estimate \n** by some factor to account for the (c BETWEEN ? AND ?) expression based\n** on the stat4 data for the index. this scan will be peformed multiple \n** times (once for each (a,b) combination that matches a=?) is dealt with \n** by the caller.\n**\n** It does this by scanning through all stat4 samples, comparing values\n** extracted from pLower and pUpper with the corresponding column in each\n** sample. If L and U are the number of samples found to be less than or\n** equal to the values extracted from pLower and pUpper respectively, and\n** N is the total number of samples, the pLoop->nOut value is adjusted\n** as follows:\n**\n**   nOut = nOut * ( min(U - L, 1) / N )\n**\n** If pLower is NULL, or a value cannot be extracted from the term, L is\n** set to zero. If pUpper is NULL, or a value cannot be extracted from it,\n** U is set to N.\n**\n** Normally, this function sets *pbDone to 1 before returning. However,\n** if no value can be extracted from either pLower or pUpper (and so the\n** estimate of the number of rows delivered remains unchanged), *pbDone\n** is left as is.\n**\n** If an error occurs, an SQLite error code is returned. Otherwise, \n** SQLITE_OK.\n*/\nstatic int whereRangeSkipScanEst(\n  Parse *pParse,       /* Parsing & code generating context */\n  WhereTerm *pLower,   /* Lower bound on the range. ex: \"x>123\" Might be NULL */\n  WhereTerm *pUpper,   /* Upper bound on the range. ex: \"x<455\" Might be NULL */\n  WhereLoop *pLoop,    /* Update the .nOut value of this loop */\n  int *pbDone          /* Set to true if at least one expr. value extracted */\n){\n  Index *p = pLoop->u.btree.pIndex;\n  int nEq = pLoop->u.btree.nEq;\n  sqlite3 *db = pParse->db;\n  int nLower = -1;\n  int nUpper = p->nSample+1;\n  int rc = SQLITE_OK;\n  u8 aff = sqlite3IndexColumnAffinity(db, p, nEq);\n  CollSeq *pColl;\n  \n  sqlite3_value *p1 = 0;          /* Value extracted from pLower */\n  sqlite3_value *p2 = 0;          /* Value extracted from pUpper */\n  sqlite3_value *pVal = 0;        /* Value extracted from record */\n\n  pColl = sqlite3LocateCollSeq(pParse, p->azColl[nEq]);\n  if( pLower ){\n    rc = sqlite3Stat4ValueFromExpr(pParse, pLower->pExpr->pRight, aff, &p1);\n    nLower = 0;\n  }\n  if( pUpper && rc==SQLITE_OK ){\n    rc = sqlite3Stat4ValueFromExpr(pParse, pUpper->pExpr->pRight, aff, &p2);\n    nUpper = p2 ? 0 : p->nSample;\n  }\n\n  if( p1 || p2 ){\n    int i;\n    int nDiff;\n    for(i=0; rc==SQLITE_OK && i<p->nSample; i++){\n      rc = sqlite3Stat4Column(db, p->aSample[i].p, p->aSample[i].n, nEq, &pVal);\n      if( rc==SQLITE_OK && p1 ){\n        int res = sqlite3MemCompare(p1, pVal, pColl);\n        if( res>=0 ) nLower++;\n      }\n      if( rc==SQLITE_OK && p2 ){\n        int res = sqlite3MemCompare(p2, pVal, pColl);\n        if( res>=0 ) nUpper++;\n      }\n    }\n    nDiff = (nUpper - nLower);\n    if( nDiff<=0 ) nDiff = 1;\n\n    /* If there is both an upper and lower bound specified, and the \n    ** comparisons indicate that they are close together, use the fallback\n    ** method (assume that the scan visits 1/64 of the rows) for estimating\n    ** the number of rows visited. Otherwise, estimate the number of rows\n    ** using the method described in the header comment for this function. */\n    if( nDiff!=1 || pUpper==0 || pLower==0 ){\n      int nAdjust = (sqlite3LogEst(p->nSample) - sqlite3LogEst(nDiff));\n      pLoop->nOut -= nAdjust;\n      *pbDone = 1;\n      WHERETRACE(0x10, (\"range skip-scan regions: %u..%u  adjust=%d est=%d\\n\",\n                           nLower, nUpper, nAdjust*-1, pLoop->nOut));\n    }\n\n  }else{\n    assert( *pbDone==0 );\n  }\n\n  sqlite3ValueFree(p1);\n  sqlite3ValueFree(p2);\n  sqlite3ValueFree(pVal);\n\n  return rc;\n}\n#endif /* SQLITE_ENABLE_STAT3_OR_STAT4 */\n\n/*\n** This function is used to estimate the number of rows that will be visited\n** by scanning an index for a range of values. The range may have an upper\n** bound, a lower bound, or both. The WHERE clause terms that set the upper\n** and lower bounds are represented by pLower and pUpper respectively. For\n** example, assuming that index p is on t1(a):\n**\n**   ... FROM t1 WHERE a > ? AND a < ? ...\n**                    |_____|   |_____|\n**                       |         |\n**                     pLower    pUpper\n**\n** If either of the upper or lower bound is not present, then NULL is passed in\n** place of the corresponding WhereTerm.\n**\n** The value in (pBuilder->pNew->u.btree.nEq) is the number of the index\n** column subject to the range constraint. Or, equivalently, the number of\n** equality constraints optimized by the proposed index scan. For example,\n** assuming index p is on t1(a, b), and the SQL query is:\n**\n**   ... FROM t1 WHERE a = ? AND b > ? AND b < ? ...\n**\n** then nEq is set to 1 (as the range restricted column, b, is the second \n** left-most column of the index). Or, if the query is:\n**\n**   ... FROM t1 WHERE a > ? AND a < ? ...\n**\n** then nEq is set to 0.\n**\n** When this function is called, *pnOut is set to the sqlite3LogEst() of the\n** number of rows that the index scan is expected to visit without \n** considering the range constraints. If nEq is 0, then *pnOut is the number of \n** rows in the index. Assuming no error occurs, *pnOut is adjusted (reduced)\n** to account for the range constraints pLower and pUpper.\n** \n** In the absence of sqlite_stat4 ANALYZE data, or if such data cannot be\n** used, a single range inequality reduces the search space by a factor of 4. \n** and a pair of constraints (x>? AND x<?) reduces the expected number of\n** rows visited by a factor of 64.\n*/\nstatic int whereRangeScanEst(\n  Parse *pParse,       /* Parsing & code generating context */\n  WhereLoopBuilder *pBuilder,\n  WhereTerm *pLower,   /* Lower bound on the range. ex: \"x>123\" Might be NULL */\n  WhereTerm *pUpper,   /* Upper bound on the range. ex: \"x<455\" Might be NULL */\n  WhereLoop *pLoop     /* Modify the .nOut and maybe .rRun fields */\n){\n  int rc = SQLITE_OK;\n  int nOut = pLoop->nOut;\n  LogEst nNew;\n\n#ifdef SQLITE_ENABLE_STAT3_OR_STAT4\n  Index *p = pLoop->u.btree.pIndex;\n  int nEq = pLoop->u.btree.nEq;\n\n  if( p->nSample>0 && nEq<p->nSampleCol ){\n    if( nEq==pBuilder->nRecValid ){\n      UnpackedRecord *pRec = pBuilder->pRec;\n      tRowcnt a[2];\n      int nBtm = pLoop->u.btree.nBtm;\n      int nTop = pLoop->u.btree.nTop;\n\n      /* Variable iLower will be set to the estimate of the number of rows in \n      ** the index that are less than the lower bound of the range query. The\n      ** lower bound being the concatenation of $P and $L, where $P is the\n      ** key-prefix formed by the nEq values matched against the nEq left-most\n      ** columns of the index, and $L is the value in pLower.\n      **\n      ** Or, if pLower is NULL or $L cannot be extracted from it (because it\n      ** is not a simple variable or literal value), the lower bound of the\n      ** range is $P. Due to a quirk in the way whereKeyStats() works, even\n      ** if $L is available, whereKeyStats() is called for both ($P) and \n      ** ($P:$L) and the larger of the two returned values is used.\n      **\n      ** Similarly, iUpper is to be set to the estimate of the number of rows\n      ** less than the upper bound of the range query. Where the upper bound\n      ** is either ($P) or ($P:$U). Again, even if $U is available, both values\n      ** of iUpper are requested of whereKeyStats() and the smaller used.\n      **\n      ** The number of rows between the two bounds is then just iUpper-iLower.\n      */\n      tRowcnt iLower;     /* Rows less than the lower bound */\n      tRowcnt iUpper;     /* Rows less than the upper bound */\n      int iLwrIdx = -2;   /* aSample[] for the lower bound */\n      int iUprIdx = -1;   /* aSample[] for the upper bound */\n\n      if( pRec ){\n        testcase( pRec->nField!=pBuilder->nRecValid );\n        pRec->nField = pBuilder->nRecValid;\n      }\n      /* Determine iLower and iUpper using ($P) only. */\n      if( nEq==0 ){\n        iLower = 0;\n        iUpper = p->nRowEst0;\n      }else{\n        /* Note: this call could be optimized away - since the same values must \n        ** have been requested when testing key $P in whereEqualScanEst().  */\n        whereKeyStats(pParse, p, pRec, 0, a);\n        iLower = a[0];\n        iUpper = a[0] + a[1];\n      }\n\n      assert( pLower==0 || (pLower->eOperator & (WO_GT|WO_GE))!=0 );\n      assert( pUpper==0 || (pUpper->eOperator & (WO_LT|WO_LE))!=0 );\n      assert( p->aSortOrder!=0 );\n      if( p->aSortOrder[nEq] ){\n        /* The roles of pLower and pUpper are swapped for a DESC index */\n        SWAP(WhereTerm*, pLower, pUpper);\n        SWAP(int, nBtm, nTop);\n      }\n\n      /* If possible, improve on the iLower estimate using ($P:$L). */\n      if( pLower ){\n        int n;                    /* Values extracted from pExpr */\n        Expr *pExpr = pLower->pExpr->pRight;\n        rc = sqlite3Stat4ProbeSetValue(pParse, p, &pRec, pExpr, nBtm, nEq, &n);\n        if( rc==SQLITE_OK && n ){\n          tRowcnt iNew;\n          u16 mask = WO_GT|WO_LE;\n          if( sqlite3ExprVectorSize(pExpr)>n ) mask = (WO_LE|WO_LT);\n          iLwrIdx = whereKeyStats(pParse, p, pRec, 0, a);\n          iNew = a[0] + ((pLower->eOperator & mask) ? a[1] : 0);\n          if( iNew>iLower ) iLower = iNew;\n          nOut--;\n          pLower = 0;\n        }\n      }\n\n      /* If possible, improve on the iUpper estimate using ($P:$U). */\n      if( pUpper ){\n        int n;                    /* Values extracted from pExpr */\n        Expr *pExpr = pUpper->pExpr->pRight;\n        rc = sqlite3Stat4ProbeSetValue(pParse, p, &pRec, pExpr, nTop, nEq, &n);\n        if( rc==SQLITE_OK && n ){\n          tRowcnt iNew;\n          u16 mask = WO_GT|WO_LE;\n          if( sqlite3ExprVectorSize(pExpr)>n ) mask = (WO_LE|WO_LT);\n          iUprIdx = whereKeyStats(pParse, p, pRec, 1, a);\n          iNew = a[0] + ((pUpper->eOperator & mask) ? a[1] : 0);\n          if( iNew<iUpper ) iUpper = iNew;\n          nOut--;\n          pUpper = 0;\n        }\n      }\n\n      pBuilder->pRec = pRec;\n      if( rc==SQLITE_OK ){\n        if( iUpper>iLower ){\n          nNew = sqlite3LogEst(iUpper - iLower);\n          /* TUNING:  If both iUpper and iLower are derived from the same\n          ** sample, then assume they are 4x more selective.  This brings\n          ** the estimated selectivity more in line with what it would be\n          ** if estimated without the use of STAT3/4 tables. */\n          if( iLwrIdx==iUprIdx ) nNew -= 20;  assert( 20==sqlite3LogEst(4) );\n        }else{\n          nNew = 10;        assert( 10==sqlite3LogEst(2) );\n        }\n        if( nNew<nOut ){\n          nOut = nNew;\n        }\n        WHERETRACE(0x10, (\"STAT4 range scan: %u..%u  est=%d\\n\",\n                           (u32)iLower, (u32)iUpper, nOut));\n      }\n    }else{\n      int bDone = 0;\n      rc = whereRangeSkipScanEst(pParse, pLower, pUpper, pLoop, &bDone);\n      if( bDone ) return rc;\n    }\n  }\n#else\n  UNUSED_PARAMETER(pParse);\n  UNUSED_PARAMETER(pBuilder);\n  assert( pLower || pUpper );\n#endif\n  assert( pUpper==0 || (pUpper->wtFlags & TERM_VNULL)==0 );\n  nNew = whereRangeAdjust(pLower, nOut);\n  nNew = whereRangeAdjust(pUpper, nNew);\n\n  /* TUNING: If there is both an upper and lower limit and neither limit\n  ** has an application-defined likelihood(), assume the range is\n  ** reduced by an additional 75%. This means that, by default, an open-ended\n  ** range query (e.g. col > ?) is assumed to match 1/4 of the rows in the\n  ** index. While a closed range (e.g. col BETWEEN ? AND ?) is estimated to\n  ** match 1/64 of the index. */ \n  if( pLower && pLower->truthProb>0 && pUpper && pUpper->truthProb>0 ){\n    nNew -= 20;\n  }\n\n  nOut -= (pLower!=0) + (pUpper!=0);\n  if( nNew<10 ) nNew = 10;\n  if( nNew<nOut ) nOut = nNew;\n#if defined(WHERETRACE_ENABLED)\n  if( pLoop->nOut>nOut ){\n    WHERETRACE(0x10,(\"Range scan lowers nOut from %d to %d\\n\",\n                    pLoop->nOut, nOut));\n  }\n#endif\n  pLoop->nOut = (LogEst)nOut;\n  return rc;\n}\n\n#ifdef SQLITE_ENABLE_STAT3_OR_STAT4\n/*\n** Estimate the number of rows that will be returned based on\n** an equality constraint x=VALUE and where that VALUE occurs in\n** the histogram data.  This only works when x is the left-most\n** column of an index and sqlite_stat3 histogram data is available\n** for that index.  When pExpr==NULL that means the constraint is\n** \"x IS NULL\" instead of \"x=VALUE\".\n**\n** Write the estimated row count into *pnRow and return SQLITE_OK. \n** If unable to make an estimate, leave *pnRow unchanged and return\n** non-zero.\n**\n** This routine can fail if it is unable to load a collating sequence\n** required for string comparison, or if unable to allocate memory\n** for a UTF conversion required for comparison.  The error is stored\n** in the pParse structure.\n*/\nstatic int whereEqualScanEst(\n  Parse *pParse,       /* Parsing & code generating context */\n  WhereLoopBuilder *pBuilder,\n  Expr *pExpr,         /* Expression for VALUE in the x=VALUE constraint */\n  tRowcnt *pnRow       /* Write the revised row estimate here */\n){\n  Index *p = pBuilder->pNew->u.btree.pIndex;\n  int nEq = pBuilder->pNew->u.btree.nEq;\n  UnpackedRecord *pRec = pBuilder->pRec;\n  int rc;                   /* Subfunction return code */\n  tRowcnt a[2];             /* Statistics */\n  int bOk;\n\n  assert( nEq>=1 );\n  assert( nEq<=p->nColumn );\n  assert( p->aSample!=0 );\n  assert( p->nSample>0 );\n  assert( pBuilder->nRecValid<nEq );\n\n  /* If values are not available for all fields of the index to the left\n  ** of this one, no estimate can be made. Return SQLITE_NOTFOUND. */\n  if( pBuilder->nRecValid<(nEq-1) ){\n    return SQLITE_NOTFOUND;\n  }\n\n  /* This is an optimization only. The call to sqlite3Stat4ProbeSetValue()\n  ** below would return the same value.  */\n  if( nEq>=p->nColumn ){\n    *pnRow = 1;\n    return SQLITE_OK;\n  }\n\n  rc = sqlite3Stat4ProbeSetValue(pParse, p, &pRec, pExpr, 1, nEq-1, &bOk);\n  pBuilder->pRec = pRec;\n  if( rc!=SQLITE_OK ) return rc;\n  if( bOk==0 ) return SQLITE_NOTFOUND;\n  pBuilder->nRecValid = nEq;\n\n  whereKeyStats(pParse, p, pRec, 0, a);\n  WHERETRACE(0x10,(\"equality scan regions %s(%d): %d\\n\",\n                   p->zName, nEq-1, (int)a[1]));\n  *pnRow = a[1];\n  \n  return rc;\n}\n#endif /* SQLITE_ENABLE_STAT3_OR_STAT4 */\n\n#ifdef SQLITE_ENABLE_STAT3_OR_STAT4\n/*\n** Estimate the number of rows that will be returned based on\n** an IN constraint where the right-hand side of the IN operator\n** is a list of values.  Example:\n**\n**        WHERE x IN (1,2,3,4)\n**\n** Write the estimated row count into *pnRow and return SQLITE_OK. \n** If unable to make an estimate, leave *pnRow unchanged and return\n** non-zero.\n**\n** This routine can fail if it is unable to load a collating sequence\n** required for string comparison, or if unable to allocate memory\n** for a UTF conversion required for comparison.  The error is stored\n** in the pParse structure.\n*/\nstatic int whereInScanEst(\n  Parse *pParse,       /* Parsing & code generating context */\n  WhereLoopBuilder *pBuilder,\n  ExprList *pList,     /* The value list on the RHS of \"x IN (v1,v2,v3,...)\" */\n  tRowcnt *pnRow       /* Write the revised row estimate here */\n){\n  Index *p = pBuilder->pNew->u.btree.pIndex;\n  i64 nRow0 = sqlite3LogEstToInt(p->aiRowLogEst[0]);\n  int nRecValid = pBuilder->nRecValid;\n  int rc = SQLITE_OK;     /* Subfunction return code */\n  tRowcnt nEst;           /* Number of rows for a single term */\n  tRowcnt nRowEst = 0;    /* New estimate of the number of rows */\n  int i;                  /* Loop counter */\n\n  assert( p->aSample!=0 );\n  for(i=0; rc==SQLITE_OK && i<pList->nExpr; i++){\n    nEst = nRow0;\n    rc = whereEqualScanEst(pParse, pBuilder, pList->a[i].pExpr, &nEst);\n    nRowEst += nEst;\n    pBuilder->nRecValid = nRecValid;\n  }\n\n  if( rc==SQLITE_OK ){\n    if( nRowEst > nRow0 ) nRowEst = nRow0;\n    *pnRow = nRowEst;\n    WHERETRACE(0x10,(\"IN row estimate: est=%d\\n\", nRowEst));\n  }\n  assert( pBuilder->nRecValid==nRecValid );\n  return rc;\n}\n#endif /* SQLITE_ENABLE_STAT3_OR_STAT4 */\n\n\n#ifdef WHERETRACE_ENABLED\n/*\n** Print the content of a WhereTerm object\n*/\nstatic void whereTermPrint(WhereTerm *pTerm, int iTerm){\n  if( pTerm==0 ){\n    sqlite3DebugPrintf(\"TERM-%-3d NULL\\n\", iTerm);\n  }else{\n    char zType[4];\n    char zLeft[50];\n    memcpy(zType, \"...\", 4);\n    if( pTerm->wtFlags & TERM_VIRTUAL ) zType[0] = 'V';\n    if( pTerm->eOperator & WO_EQUIV  ) zType[1] = 'E';\n    if( ExprHasProperty(pTerm->pExpr, EP_FromJoin) ) zType[2] = 'L';\n    if( pTerm->eOperator & WO_SINGLE ){\n      sqlite3_snprintf(sizeof(zLeft),zLeft,\"left={%d:%d}\",\n                       pTerm->leftCursor, pTerm->u.leftColumn);\n    }else if( (pTerm->eOperator & WO_OR)!=0 && pTerm->u.pOrInfo!=0 ){\n      sqlite3_snprintf(sizeof(zLeft),zLeft,\"indexable=0x%lld\", \n                       pTerm->u.pOrInfo->indexable);\n    }else{\n      sqlite3_snprintf(sizeof(zLeft),zLeft,\"left=%d\", pTerm->leftCursor);\n    }\n    sqlite3DebugPrintf(\n       \"TERM-%-3d %p %s %-12s prob=%-3d op=0x%03x wtFlags=0x%04x\",\n       iTerm, pTerm, zType, zLeft, pTerm->truthProb,\n       pTerm->eOperator, pTerm->wtFlags);\n    if( pTerm->iField ){\n      sqlite3DebugPrintf(\" iField=%d\\n\", pTerm->iField);\n    }else{\n      sqlite3DebugPrintf(\"\\n\");\n    }\n    sqlite3TreeViewExpr(0, pTerm->pExpr, 0);\n  }\n}\n#endif\n\n#ifdef WHERETRACE_ENABLED\n/*\n** Show the complete content of a WhereClause\n*/\nSQLITE_PRIVATE void sqlite3WhereClausePrint(WhereClause *pWC){\n  int i;\n  for(i=0; i<pWC->nTerm; i++){\n    whereTermPrint(&pWC->a[i], i);\n  }\n}\n#endif\n\n#ifdef WHERETRACE_ENABLED\n/*\n** Print a WhereLoop object for debugging purposes\n*/\nstatic void whereLoopPrint(WhereLoop *p, WhereClause *pWC){\n  WhereInfo *pWInfo = pWC->pWInfo;\n  int nb = 1+(pWInfo->pTabList->nSrc+3)/4;\n  struct SrcList_item *pItem = pWInfo->pTabList->a + p->iTab;\n  Table *pTab = pItem->pTab;\n  Bitmask mAll = (((Bitmask)1)<<(nb*4)) - 1;\n  sqlite3DebugPrintf(\"%c%2d.%0*llx.%0*llx\", p->cId,\n                     p->iTab, nb, p->maskSelf, nb, p->prereq & mAll);\n  sqlite3DebugPrintf(\" %12s\",\n                     pItem->zAlias ? pItem->zAlias : pTab->zName);\n  if( (p->wsFlags & WHERE_VIRTUALTABLE)==0 ){\n    const char *zName;\n    if( p->u.btree.pIndex && (zName = p->u.btree.pIndex->zName)!=0 ){\n      if( strncmp(zName, \"sqlite_autoindex_\", 17)==0 ){\n        int i = sqlite3Strlen30(zName) - 1;\n        while( zName[i]!='_' ) i--;\n        zName += i;\n      }\n      sqlite3DebugPrintf(\".%-16s %2d\", zName, p->u.btree.nEq);\n    }else{\n      sqlite3DebugPrintf(\"%20s\",\"\");\n    }\n  }else{\n    char *z;\n    if( p->u.vtab.idxStr ){\n      z = sqlite3_mprintf(\"(%d,\\\"%s\\\",%x)\",\n                p->u.vtab.idxNum, p->u.vtab.idxStr, p->u.vtab.omitMask);\n    }else{\n      z = sqlite3_mprintf(\"(%d,%x)\", p->u.vtab.idxNum, p->u.vtab.omitMask);\n    }\n    sqlite3DebugPrintf(\" %-19s\", z);\n    sqlite3_free(z);\n  }\n  if( p->wsFlags & WHERE_SKIPSCAN ){\n    sqlite3DebugPrintf(\" f %05x %d-%d\", p->wsFlags, p->nLTerm,p->nSkip);\n  }else{\n    sqlite3DebugPrintf(\" f %05x N %d\", p->wsFlags, p->nLTerm);\n  }\n  sqlite3DebugPrintf(\" cost %d,%d,%d\\n\", p->rSetup, p->rRun, p->nOut);\n  if( p->nLTerm && (sqlite3WhereTrace & 0x100)!=0 ){\n    int i;\n    for(i=0; i<p->nLTerm; i++){\n      whereTermPrint(p->aLTerm[i], i);\n    }\n  }\n}\n#endif\n\n/*\n** Convert bulk memory into a valid WhereLoop that can be passed\n** to whereLoopClear harmlessly.\n*/\nstatic void whereLoopInit(WhereLoop *p){\n  p->aLTerm = p->aLTermSpace;\n  p->nLTerm = 0;\n  p->nLSlot = ArraySize(p->aLTermSpace);\n  p->wsFlags = 0;\n}\n\n/*\n** Clear the WhereLoop.u union.  Leave WhereLoop.pLTerm intact.\n*/\nstatic void whereLoopClearUnion(sqlite3 *db, WhereLoop *p){\n  if( p->wsFlags & (WHERE_VIRTUALTABLE|WHERE_AUTO_INDEX) ){\n    if( (p->wsFlags & WHERE_VIRTUALTABLE)!=0 && p->u.vtab.needFree ){\n      sqlite3_free(p->u.vtab.idxStr);\n      p->u.vtab.needFree = 0;\n      p->u.vtab.idxStr = 0;\n    }else if( (p->wsFlags & WHERE_AUTO_INDEX)!=0 && p->u.btree.pIndex!=0 ){\n      sqlite3DbFree(db, p->u.btree.pIndex->zColAff);\n      sqlite3DbFreeNN(db, p->u.btree.pIndex);\n      p->u.btree.pIndex = 0;\n    }\n  }\n}\n\n/*\n** Deallocate internal memory used by a WhereLoop object\n*/\nstatic void whereLoopClear(sqlite3 *db, WhereLoop *p){\n  if( p->aLTerm!=p->aLTermSpace ) sqlite3DbFreeNN(db, p->aLTerm);\n  whereLoopClearUnion(db, p);\n  whereLoopInit(p);\n}\n\n/*\n** Increase the memory allocation for pLoop->aLTerm[] to be at least n.\n*/\nstatic int whereLoopResize(sqlite3 *db, WhereLoop *p, int n){\n  WhereTerm **paNew;\n  if( p->nLSlot>=n ) return SQLITE_OK;\n  n = (n+7)&~7;\n  paNew = sqlite3DbMallocRawNN(db, sizeof(p->aLTerm[0])*n);\n  if( paNew==0 ) return SQLITE_NOMEM_BKPT;\n  memcpy(paNew, p->aLTerm, sizeof(p->aLTerm[0])*p->nLSlot);\n  if( p->aLTerm!=p->aLTermSpace ) sqlite3DbFreeNN(db, p->aLTerm);\n  p->aLTerm = paNew;\n  p->nLSlot = n;\n  return SQLITE_OK;\n}\n\n/*\n** Transfer content from the second pLoop into the first.\n*/\nstatic int whereLoopXfer(sqlite3 *db, WhereLoop *pTo, WhereLoop *pFrom){\n  whereLoopClearUnion(db, pTo);\n  if( whereLoopResize(db, pTo, pFrom->nLTerm) ){\n    memset(&pTo->u, 0, sizeof(pTo->u));\n    return SQLITE_NOMEM_BKPT;\n  }\n  memcpy(pTo, pFrom, WHERE_LOOP_XFER_SZ);\n  memcpy(pTo->aLTerm, pFrom->aLTerm, pTo->nLTerm*sizeof(pTo->aLTerm[0]));\n  if( pFrom->wsFlags & WHERE_VIRTUALTABLE ){\n    pFrom->u.vtab.needFree = 0;\n  }else if( (pFrom->wsFlags & WHERE_AUTO_INDEX)!=0 ){\n    pFrom->u.btree.pIndex = 0;\n  }\n  return SQLITE_OK;\n}\n\n/*\n** Delete a WhereLoop object\n*/\nstatic void whereLoopDelete(sqlite3 *db, WhereLoop *p){\n  whereLoopClear(db, p);\n  sqlite3DbFreeNN(db, p);\n}\n\n/*\n** Free a WhereInfo structure\n*/\nstatic void whereInfoFree(sqlite3 *db, WhereInfo *pWInfo){\n  int i;\n  assert( pWInfo!=0 );\n  for(i=0; i<pWInfo->nLevel; i++){\n    WhereLevel *pLevel = &pWInfo->a[i];\n    if( pLevel->pWLoop && (pLevel->pWLoop->wsFlags & WHERE_IN_ABLE) ){\n      sqlite3DbFree(db, pLevel->u.in.aInLoop);\n    }\n  }\n  sqlite3WhereClauseClear(&pWInfo->sWC);\n  while( pWInfo->pLoops ){\n    WhereLoop *p = pWInfo->pLoops;\n    pWInfo->pLoops = p->pNextLoop;\n    whereLoopDelete(db, p);\n  }\n  sqlite3DbFreeNN(db, pWInfo);\n}\n\n/*\n** Return TRUE if all of the following are true:\n**\n**   (1)  X has the same or lower cost that Y\n**   (2)  X uses fewer WHERE clause terms than Y\n**   (3)  Every WHERE clause term used by X is also used by Y\n**   (4)  X skips at least as many columns as Y\n**   (5)  If X is a covering index, than Y is too\n**\n** Conditions (2) and (3) mean that X is a \"proper subset\" of Y.\n** If X is a proper subset of Y then Y is a better choice and ought\n** to have a lower cost.  This routine returns TRUE when that cost \n** relationship is inverted and needs to be adjusted.  Constraint (4)\n** was added because if X uses skip-scan less than Y it still might\n** deserve a lower cost even if it is a proper subset of Y.  Constraint (5)\n** was added because a covering index probably deserves to have a lower cost\n** than a non-covering index even if it is a proper subset.\n*/\nstatic int whereLoopCheaperProperSubset(\n  const WhereLoop *pX,       /* First WhereLoop to compare */\n  const WhereLoop *pY        /* Compare against this WhereLoop */\n){\n  int i, j;\n  if( pX->nLTerm-pX->nSkip >= pY->nLTerm-pY->nSkip ){\n    return 0; /* X is not a subset of Y */\n  }\n  if( pY->nSkip > pX->nSkip ) return 0;\n  if( pX->rRun >= pY->rRun ){\n    if( pX->rRun > pY->rRun ) return 0;    /* X costs more than Y */\n    if( pX->nOut > pY->nOut ) return 0;    /* X costs more than Y */\n  }\n  for(i=pX->nLTerm-1; i>=0; i--){\n    if( pX->aLTerm[i]==0 ) continue;\n    for(j=pY->nLTerm-1; j>=0; j--){\n      if( pY->aLTerm[j]==pX->aLTerm[i] ) break;\n    }\n    if( j<0 ) return 0;  /* X not a subset of Y since term X[i] not used by Y */\n  }\n  if( (pX->wsFlags&WHERE_IDX_ONLY)!=0 \n   && (pY->wsFlags&WHERE_IDX_ONLY)==0 ){\n    return 0;  /* Constraint (5) */\n  }\n  return 1;  /* All conditions meet */\n}\n\n/*\n** Try to adjust the cost of WhereLoop pTemplate upwards or downwards so\n** that:\n**\n**   (1) pTemplate costs less than any other WhereLoops that are a proper\n**       subset of pTemplate\n**\n**   (2) pTemplate costs more than any other WhereLoops for which pTemplate\n**       is a proper subset.\n**\n** To say \"WhereLoop X is a proper subset of Y\" means that X uses fewer\n** WHERE clause terms than Y and that every WHERE clause term used by X is\n** also used by Y.\n*/\nstatic void whereLoopAdjustCost(const WhereLoop *p, WhereLoop *pTemplate){\n  if( (pTemplate->wsFlags & WHERE_INDEXED)==0 ) return;\n  for(; p; p=p->pNextLoop){\n    if( p->iTab!=pTemplate->iTab ) continue;\n    if( (p->wsFlags & WHERE_INDEXED)==0 ) continue;\n    if( whereLoopCheaperProperSubset(p, pTemplate) ){\n      /* Adjust pTemplate cost downward so that it is cheaper than its \n      ** subset p. */\n      WHERETRACE(0x80,(\"subset cost adjustment %d,%d to %d,%d\\n\",\n                       pTemplate->rRun, pTemplate->nOut, p->rRun, p->nOut-1));\n      pTemplate->rRun = p->rRun;\n      pTemplate->nOut = p->nOut - 1;\n    }else if( whereLoopCheaperProperSubset(pTemplate, p) ){\n      /* Adjust pTemplate cost upward so that it is costlier than p since\n      ** pTemplate is a proper subset of p */\n      WHERETRACE(0x80,(\"subset cost adjustment %d,%d to %d,%d\\n\",\n                       pTemplate->rRun, pTemplate->nOut, p->rRun, p->nOut+1));\n      pTemplate->rRun = p->rRun;\n      pTemplate->nOut = p->nOut + 1;\n    }\n  }\n}\n\n/*\n** Search the list of WhereLoops in *ppPrev looking for one that can be\n** replaced by pTemplate.\n**\n** Return NULL if pTemplate does not belong on the WhereLoop list.\n** In other words if pTemplate ought to be dropped from further consideration.\n**\n** If pX is a WhereLoop that pTemplate can replace, then return the\n** link that points to pX.\n**\n** If pTemplate cannot replace any existing element of the list but needs\n** to be added to the list as a new entry, then return a pointer to the\n** tail of the list.\n*/\nstatic WhereLoop **whereLoopFindLesser(\n  WhereLoop **ppPrev,\n  const WhereLoop *pTemplate\n){\n  WhereLoop *p;\n  for(p=(*ppPrev); p; ppPrev=&p->pNextLoop, p=*ppPrev){\n    if( p->iTab!=pTemplate->iTab || p->iSortIdx!=pTemplate->iSortIdx ){\n      /* If either the iTab or iSortIdx values for two WhereLoop are different\n      ** then those WhereLoops need to be considered separately.  Neither is\n      ** a candidate to replace the other. */\n      continue;\n    }\n    /* In the current implementation, the rSetup value is either zero\n    ** or the cost of building an automatic index (NlogN) and the NlogN\n    ** is the same for compatible WhereLoops. */\n    assert( p->rSetup==0 || pTemplate->rSetup==0 \n                 || p->rSetup==pTemplate->rSetup );\n\n    /* whereLoopAddBtree() always generates and inserts the automatic index\n    ** case first.  Hence compatible candidate WhereLoops never have a larger\n    ** rSetup. Call this SETUP-INVARIANT */\n    assert( p->rSetup>=pTemplate->rSetup );\n\n    /* Any loop using an appliation-defined index (or PRIMARY KEY or\n    ** UNIQUE constraint) with one or more == constraints is better\n    ** than an automatic index. Unless it is a skip-scan. */\n    if( (p->wsFlags & WHERE_AUTO_INDEX)!=0\n     && (pTemplate->nSkip)==0\n     && (pTemplate->wsFlags & WHERE_INDEXED)!=0\n     && (pTemplate->wsFlags & WHERE_COLUMN_EQ)!=0\n     && (p->prereq & pTemplate->prereq)==pTemplate->prereq\n    ){\n      break;\n    }\n\n    /* If existing WhereLoop p is better than pTemplate, pTemplate can be\n    ** discarded.  WhereLoop p is better if:\n    **   (1)  p has no more dependencies than pTemplate, and\n    **   (2)  p has an equal or lower cost than pTemplate\n    */\n    if( (p->prereq & pTemplate->prereq)==p->prereq    /* (1)  */\n     && p->rSetup<=pTemplate->rSetup                  /* (2a) */\n     && p->rRun<=pTemplate->rRun                      /* (2b) */\n     && p->nOut<=pTemplate->nOut                      /* (2c) */\n    ){\n      return 0;  /* Discard pTemplate */\n    }\n\n    /* If pTemplate is always better than p, then cause p to be overwritten\n    ** with pTemplate.  pTemplate is better than p if:\n    **   (1)  pTemplate has no more dependences than p, and\n    **   (2)  pTemplate has an equal or lower cost than p.\n    */\n    if( (p->prereq & pTemplate->prereq)==pTemplate->prereq   /* (1)  */\n     && p->rRun>=pTemplate->rRun                             /* (2a) */\n     && p->nOut>=pTemplate->nOut                             /* (2b) */\n    ){\n      assert( p->rSetup>=pTemplate->rSetup ); /* SETUP-INVARIANT above */\n      break;   /* Cause p to be overwritten by pTemplate */\n    }\n  }\n  return ppPrev;\n}\n\n/*\n** Insert or replace a WhereLoop entry using the template supplied.\n**\n** An existing WhereLoop entry might be overwritten if the new template\n** is better and has fewer dependencies.  Or the template will be ignored\n** and no insert will occur if an existing WhereLoop is faster and has\n** fewer dependencies than the template.  Otherwise a new WhereLoop is\n** added based on the template.\n**\n** If pBuilder->pOrSet is not NULL then we care about only the\n** prerequisites and rRun and nOut costs of the N best loops.  That\n** information is gathered in the pBuilder->pOrSet object.  This special\n** processing mode is used only for OR clause processing.\n**\n** When accumulating multiple loops (when pBuilder->pOrSet is NULL) we\n** still might overwrite similar loops with the new template if the\n** new template is better.  Loops may be overwritten if the following \n** conditions are met:\n**\n**    (1)  They have the same iTab.\n**    (2)  They have the same iSortIdx.\n**    (3)  The template has same or fewer dependencies than the current loop\n**    (4)  The template has the same or lower cost than the current loop\n*/\nstatic int whereLoopInsert(WhereLoopBuilder *pBuilder, WhereLoop *pTemplate){\n  WhereLoop **ppPrev, *p;\n  WhereInfo *pWInfo = pBuilder->pWInfo;\n  sqlite3 *db = pWInfo->pParse->db;\n  int rc;\n\n  /* If pBuilder->pOrSet is defined, then only keep track of the costs\n  ** and prereqs.\n  */\n  if( pBuilder->pOrSet!=0 ){\n    if( pTemplate->nLTerm ){\n#if WHERETRACE_ENABLED\n      u16 n = pBuilder->pOrSet->n;\n      int x =\n#endif\n      whereOrInsert(pBuilder->pOrSet, pTemplate->prereq, pTemplate->rRun,\n                                    pTemplate->nOut);\n#if WHERETRACE_ENABLED /* 0x8 */\n      if( sqlite3WhereTrace & 0x8 ){\n        sqlite3DebugPrintf(x?\"   or-%d:  \":\"   or-X:  \", n);\n        whereLoopPrint(pTemplate, pBuilder->pWC);\n      }\n#endif\n    }\n    return SQLITE_OK;\n  }\n\n  /* Look for an existing WhereLoop to replace with pTemplate\n  */\n  whereLoopAdjustCost(pWInfo->pLoops, pTemplate);\n  ppPrev = whereLoopFindLesser(&pWInfo->pLoops, pTemplate);\n\n  if( ppPrev==0 ){\n    /* There already exists a WhereLoop on the list that is better\n    ** than pTemplate, so just ignore pTemplate */\n#if WHERETRACE_ENABLED /* 0x8 */\n    if( sqlite3WhereTrace & 0x8 ){\n      sqlite3DebugPrintf(\"   skip: \");\n      whereLoopPrint(pTemplate, pBuilder->pWC);\n    }\n#endif\n    return SQLITE_OK;  \n  }else{\n    p = *ppPrev;\n  }\n\n  /* If we reach this point it means that either p[] should be overwritten\n  ** with pTemplate[] if p[] exists, or if p==NULL then allocate a new\n  ** WhereLoop and insert it.\n  */\n#if WHERETRACE_ENABLED /* 0x8 */\n  if( sqlite3WhereTrace & 0x8 ){\n    if( p!=0 ){\n      sqlite3DebugPrintf(\"replace: \");\n      whereLoopPrint(p, pBuilder->pWC);\n      sqlite3DebugPrintf(\"   with: \");\n    }else{\n      sqlite3DebugPrintf(\"    add: \");\n    }\n    whereLoopPrint(pTemplate, pBuilder->pWC);\n  }\n#endif\n  if( p==0 ){\n    /* Allocate a new WhereLoop to add to the end of the list */\n    *ppPrev = p = sqlite3DbMallocRawNN(db, sizeof(WhereLoop));\n    if( p==0 ) return SQLITE_NOMEM_BKPT;\n    whereLoopInit(p);\n    p->pNextLoop = 0;\n  }else{\n    /* We will be overwriting WhereLoop p[].  But before we do, first\n    ** go through the rest of the list and delete any other entries besides\n    ** p[] that are also supplated by pTemplate */\n    WhereLoop **ppTail = &p->pNextLoop;\n    WhereLoop *pToDel;\n    while( *ppTail ){\n      ppTail = whereLoopFindLesser(ppTail, pTemplate);\n      if( ppTail==0 ) break;\n      pToDel = *ppTail;\n      if( pToDel==0 ) break;\n      *ppTail = pToDel->pNextLoop;\n#if WHERETRACE_ENABLED /* 0x8 */\n      if( sqlite3WhereTrace & 0x8 ){\n        sqlite3DebugPrintf(\" delete: \");\n        whereLoopPrint(pToDel, pBuilder->pWC);\n      }\n#endif\n      whereLoopDelete(db, pToDel);\n    }\n  }\n  rc = whereLoopXfer(db, p, pTemplate);\n  if( (p->wsFlags & WHERE_VIRTUALTABLE)==0 ){\n    Index *pIndex = p->u.btree.pIndex;\n    if( pIndex && pIndex->tnum==0 ){\n      p->u.btree.pIndex = 0;\n    }\n  }\n  return rc;\n}\n\n/*\n** Adjust the WhereLoop.nOut value downward to account for terms of the\n** WHERE clause that reference the loop but which are not used by an\n** index.\n*\n** For every WHERE clause term that is not used by the index\n** and which has a truth probability assigned by one of the likelihood(),\n** likely(), or unlikely() SQL functions, reduce the estimated number\n** of output rows by the probability specified.\n**\n** TUNING:  For every WHERE clause term that is not used by the index\n** and which does not have an assigned truth probability, heuristics\n** described below are used to try to estimate the truth probability.\n** TODO --> Perhaps this is something that could be improved by better\n** table statistics.\n**\n** Heuristic 1:  Estimate the truth probability as 93.75%.  The 93.75%\n** value corresponds to -1 in LogEst notation, so this means decrement\n** the WhereLoop.nOut field for every such WHERE clause term.\n**\n** Heuristic 2:  If there exists one or more WHERE clause terms of the\n** form \"x==EXPR\" and EXPR is not a constant 0 or 1, then make sure the\n** final output row estimate is no greater than 1/4 of the total number\n** of rows in the table.  In other words, assume that x==EXPR will filter\n** out at least 3 out of 4 rows.  If EXPR is -1 or 0 or 1, then maybe the\n** \"x\" column is boolean or else -1 or 0 or 1 is a common default value\n** on the \"x\" column and so in that case only cap the output row estimate\n** at 1/2 instead of 1/4.\n*/\nstatic void whereLoopOutputAdjust(\n  WhereClause *pWC,      /* The WHERE clause */\n  WhereLoop *pLoop,      /* The loop to adjust downward */\n  LogEst nRow            /* Number of rows in the entire table */\n){\n  WhereTerm *pTerm, *pX;\n  Bitmask notAllowed = ~(pLoop->prereq|pLoop->maskSelf);\n  int i, j, k;\n  LogEst iReduce = 0;    /* pLoop->nOut should not exceed nRow-iReduce */\n\n  assert( (pLoop->wsFlags & WHERE_AUTO_INDEX)==0 );\n  for(i=pWC->nTerm, pTerm=pWC->a; i>0; i--, pTerm++){\n    if( (pTerm->wtFlags & TERM_VIRTUAL)!=0 ) break;\n    if( (pTerm->prereqAll & pLoop->maskSelf)==0 ) continue;\n    if( (pTerm->prereqAll & notAllowed)!=0 ) continue;\n    for(j=pLoop->nLTerm-1; j>=0; j--){\n      pX = pLoop->aLTerm[j];\n      if( pX==0 ) continue;\n      if( pX==pTerm ) break;\n      if( pX->iParent>=0 && (&pWC->a[pX->iParent])==pTerm ) break;\n    }\n    if( j<0 ){\n      if( pTerm->truthProb<=0 ){\n        /* If a truth probability is specified using the likelihood() hints,\n        ** then use the probability provided by the application. */\n        pLoop->nOut += pTerm->truthProb;\n      }else{\n        /* In the absence of explicit truth probabilities, use heuristics to\n        ** guess a reasonable truth probability. */\n        pLoop->nOut--;\n        if( pTerm->eOperator&(WO_EQ|WO_IS) ){\n          Expr *pRight = pTerm->pExpr->pRight;\n          testcase( pTerm->pExpr->op==TK_IS );\n          if( sqlite3ExprIsInteger(pRight, &k) && k>=(-1) && k<=1 ){\n            k = 10;\n          }else{\n            k = 20;\n          }\n          if( iReduce<k ) iReduce = k;\n        }\n      }\n    }\n  }\n  if( pLoop->nOut > nRow-iReduce )  pLoop->nOut = nRow - iReduce;\n}\n\n/* \n** Term pTerm is a vector range comparison operation. The first comparison\n** in the vector can be optimized using column nEq of the index. This\n** function returns the total number of vector elements that can be used\n** as part of the range comparison.\n**\n** For example, if the query is:\n**\n**   WHERE a = ? AND (b, c, d) > (?, ?, ?)\n**\n** and the index:\n**\n**   CREATE INDEX ... ON (a, b, c, d, e)\n**\n** then this function would be invoked with nEq=1. The value returned in\n** this case is 3.\n*/\nstatic int whereRangeVectorLen(\n  Parse *pParse,       /* Parsing context */\n  int iCur,            /* Cursor open on pIdx */\n  Index *pIdx,         /* The index to be used for a inequality constraint */\n  int nEq,             /* Number of prior equality constraints on same index */\n  WhereTerm *pTerm     /* The vector inequality constraint */\n){\n  int nCmp = sqlite3ExprVectorSize(pTerm->pExpr->pLeft);\n  int i;\n\n  nCmp = MIN(nCmp, (pIdx->nColumn - nEq));\n  for(i=1; i<nCmp; i++){\n    /* Test if comparison i of pTerm is compatible with column (i+nEq) \n    ** of the index. If not, exit the loop.  */\n    char aff;                     /* Comparison affinity */\n    char idxaff = 0;              /* Indexed columns affinity */\n    CollSeq *pColl;               /* Comparison collation sequence */\n    Expr *pLhs = pTerm->pExpr->pLeft->x.pList->a[i].pExpr;\n    Expr *pRhs = pTerm->pExpr->pRight;\n    if( pRhs->flags & EP_xIsSelect ){\n      pRhs = pRhs->x.pSelect->pEList->a[i].pExpr;\n    }else{\n      pRhs = pRhs->x.pList->a[i].pExpr;\n    }\n\n    /* Check that the LHS of the comparison is a column reference to\n    ** the right column of the right source table. And that the sort\n    ** order of the index column is the same as the sort order of the\n    ** leftmost index column.  */\n    if( pLhs->op!=TK_COLUMN \n     || pLhs->iTable!=iCur \n     || pLhs->iColumn!=pIdx->aiColumn[i+nEq] \n     || pIdx->aSortOrder[i+nEq]!=pIdx->aSortOrder[nEq]\n    ){\n      break;\n    }\n\n    testcase( pLhs->iColumn==XN_ROWID );\n    aff = sqlite3CompareAffinity(pRhs, sqlite3ExprAffinity(pLhs));\n    idxaff = sqlite3TableColumnAffinity(pIdx->pTable, pLhs->iColumn);\n    if( aff!=idxaff ) break;\n\n    pColl = sqlite3BinaryCompareCollSeq(pParse, pLhs, pRhs);\n    if( pColl==0 ) break;\n    if( sqlite3StrICmp(pColl->zName, pIdx->azColl[i+nEq]) ) break;\n  }\n  return i;\n}\n\n/*\n** Adjust the cost C by the costMult facter T.  This only occurs if\n** compiled with -DSQLITE_ENABLE_COSTMULT\n*/\n#ifdef SQLITE_ENABLE_COSTMULT\n# define ApplyCostMultiplier(C,T)  C += T\n#else\n# define ApplyCostMultiplier(C,T)\n#endif\n\n/*\n** We have so far matched pBuilder->pNew->u.btree.nEq terms of the \n** index pIndex. Try to match one more.\n**\n** When this function is called, pBuilder->pNew->nOut contains the \n** number of rows expected to be visited by filtering using the nEq \n** terms only. If it is modified, this value is restored before this \n** function returns.\n**\n** If pProbe->tnum==0, that means pIndex is a fake index used for the\n** INTEGER PRIMARY KEY.\n*/\nstatic int whereLoopAddBtreeIndex(\n  WhereLoopBuilder *pBuilder,     /* The WhereLoop factory */\n  struct SrcList_item *pSrc,      /* FROM clause term being analyzed */\n  Index *pProbe,                  /* An index on pSrc */\n  LogEst nInMul                   /* log(Number of iterations due to IN) */\n){\n  WhereInfo *pWInfo = pBuilder->pWInfo;  /* WHERE analyse context */\n  Parse *pParse = pWInfo->pParse;        /* Parsing context */\n  sqlite3 *db = pParse->db;       /* Database connection malloc context */\n  WhereLoop *pNew;                /* Template WhereLoop under construction */\n  WhereTerm *pTerm;               /* A WhereTerm under consideration */\n  int opMask;                     /* Valid operators for constraints */\n  WhereScan scan;                 /* Iterator for WHERE terms */\n  Bitmask saved_prereq;           /* Original value of pNew->prereq */\n  u16 saved_nLTerm;               /* Original value of pNew->nLTerm */\n  u16 saved_nEq;                  /* Original value of pNew->u.btree.nEq */\n  u16 saved_nBtm;                 /* Original value of pNew->u.btree.nBtm */\n  u16 saved_nTop;                 /* Original value of pNew->u.btree.nTop */\n  u16 saved_nSkip;                /* Original value of pNew->nSkip */\n  u32 saved_wsFlags;              /* Original value of pNew->wsFlags */\n  LogEst saved_nOut;              /* Original value of pNew->nOut */\n  int rc = SQLITE_OK;             /* Return code */\n  LogEst rSize;                   /* Number of rows in the table */\n  LogEst rLogSize;                /* Logarithm of table size */\n  WhereTerm *pTop = 0, *pBtm = 0; /* Top and bottom range constraints */\n\n  pNew = pBuilder->pNew;\n  if( db->mallocFailed ) return SQLITE_NOMEM_BKPT;\n  WHERETRACE(0x800, (\"BEGIN addBtreeIdx(%s), nEq=%d\\n\",\n                     pProbe->zName, pNew->u.btree.nEq));\n\n  assert( (pNew->wsFlags & WHERE_VIRTUALTABLE)==0 );\n  assert( (pNew->wsFlags & WHERE_TOP_LIMIT)==0 );\n  if( pNew->wsFlags & WHERE_BTM_LIMIT ){\n    opMask = WO_LT|WO_LE;\n  }else{\n    assert( pNew->u.btree.nBtm==0 );\n    opMask = WO_EQ|WO_IN|WO_GT|WO_GE|WO_LT|WO_LE|WO_ISNULL|WO_IS;\n  }\n  if( pProbe->bUnordered ) opMask &= ~(WO_GT|WO_GE|WO_LT|WO_LE);\n\n  assert( pNew->u.btree.nEq<pProbe->nColumn );\n\n  saved_nEq = pNew->u.btree.nEq;\n  saved_nBtm = pNew->u.btree.nBtm;\n  saved_nTop = pNew->u.btree.nTop;\n  saved_nSkip = pNew->nSkip;\n  saved_nLTerm = pNew->nLTerm;\n  saved_wsFlags = pNew->wsFlags;\n  saved_prereq = pNew->prereq;\n  saved_nOut = pNew->nOut;\n  pTerm = whereScanInit(&scan, pBuilder->pWC, pSrc->iCursor, saved_nEq,\n                        opMask, pProbe);\n  pNew->rSetup = 0;\n  rSize = pProbe->aiRowLogEst[0];\n  rLogSize = estLog(rSize);\n  for(; rc==SQLITE_OK && pTerm!=0; pTerm = whereScanNext(&scan)){\n    u16 eOp = pTerm->eOperator;   /* Shorthand for pTerm->eOperator */\n    LogEst rCostIdx;\n    LogEst nOutUnadjusted;        /* nOut before IN() and WHERE adjustments */\n    int nIn = 0;\n#ifdef SQLITE_ENABLE_STAT3_OR_STAT4\n    int nRecValid = pBuilder->nRecValid;\n#endif\n    if( (eOp==WO_ISNULL || (pTerm->wtFlags&TERM_VNULL)!=0)\n     && indexColumnNotNull(pProbe, saved_nEq)\n    ){\n      continue; /* ignore IS [NOT] NULL constraints on NOT NULL columns */\n    }\n    if( pTerm->prereqRight & pNew->maskSelf ) continue;\n\n    /* Do not allow the upper bound of a LIKE optimization range constraint\n    ** to mix with a lower range bound from some other source */\n    if( pTerm->wtFlags & TERM_LIKEOPT && pTerm->eOperator==WO_LT ) continue;\n\n    /* Do not allow IS constraints from the WHERE clause to be used by the\n    ** right table of a LEFT JOIN.  Only constraints in the ON clause are\n    ** allowed */\n    if( (pSrc->fg.jointype & JT_LEFT)!=0\n     && !ExprHasProperty(pTerm->pExpr, EP_FromJoin)\n     && (eOp & (WO_IS|WO_ISNULL))!=0\n    ){\n      testcase( eOp & WO_IS );\n      testcase( eOp & WO_ISNULL );\n      continue;\n    }\n\n    if( IsUniqueIndex(pProbe) && saved_nEq==pProbe->nKeyCol-1 ){\n      pBuilder->bldFlags |= SQLITE_BLDF_UNIQUE;\n    }else{\n      pBuilder->bldFlags |= SQLITE_BLDF_INDEXED;\n    }\n    pNew->wsFlags = saved_wsFlags;\n    pNew->u.btree.nEq = saved_nEq;\n    pNew->u.btree.nBtm = saved_nBtm;\n    pNew->u.btree.nTop = saved_nTop;\n    pNew->nLTerm = saved_nLTerm;\n    if( whereLoopResize(db, pNew, pNew->nLTerm+1) ) break; /* OOM */\n    pNew->aLTerm[pNew->nLTerm++] = pTerm;\n    pNew->prereq = (saved_prereq | pTerm->prereqRight) & ~pNew->maskSelf;\n\n    assert( nInMul==0\n        || (pNew->wsFlags & WHERE_COLUMN_NULL)!=0 \n        || (pNew->wsFlags & WHERE_COLUMN_IN)!=0 \n        || (pNew->wsFlags & WHERE_SKIPSCAN)!=0 \n    );\n\n    if( eOp & WO_IN ){\n      Expr *pExpr = pTerm->pExpr;\n      pNew->wsFlags |= WHERE_COLUMN_IN;\n      if( ExprHasProperty(pExpr, EP_xIsSelect) ){\n        /* \"x IN (SELECT ...)\":  TUNING: the SELECT returns 25 rows */\n        int i;\n        nIn = 46;  assert( 46==sqlite3LogEst(25) );\n\n        /* The expression may actually be of the form (x, y) IN (SELECT...).\n        ** In this case there is a separate term for each of (x) and (y).\n        ** However, the nIn multiplier should only be applied once, not once\n        ** for each such term. The following loop checks that pTerm is the\n        ** first such term in use, and sets nIn back to 0 if it is not. */\n        for(i=0; i<pNew->nLTerm-1; i++){\n          if( pNew->aLTerm[i] && pNew->aLTerm[i]->pExpr==pExpr ) nIn = 0;\n        }\n      }else if( ALWAYS(pExpr->x.pList && pExpr->x.pList->nExpr) ){\n        /* \"x IN (value, value, ...)\" */\n        nIn = sqlite3LogEst(pExpr->x.pList->nExpr);\n        assert( nIn>0 );  /* RHS always has 2 or more terms...  The parser\n                          ** changes \"x IN (?)\" into \"x=?\". */\n      }\n    }else if( eOp & (WO_EQ|WO_IS) ){\n      int iCol = pProbe->aiColumn[saved_nEq];\n      pNew->wsFlags |= WHERE_COLUMN_EQ;\n      assert( saved_nEq==pNew->u.btree.nEq );\n      if( iCol==XN_ROWID \n       || (iCol>=0 && nInMul==0 && saved_nEq==pProbe->nKeyCol-1)\n      ){\n        if( iCol==XN_ROWID || pProbe->uniqNotNull \n         || (pProbe->nKeyCol==1 && pProbe->onError && eOp==WO_EQ) \n        ){\n          pNew->wsFlags |= WHERE_ONEROW;\n        }else{\n          pNew->wsFlags |= WHERE_UNQ_WANTED;\n        }\n      }\n    }else if( eOp & WO_ISNULL ){\n      pNew->wsFlags |= WHERE_COLUMN_NULL;\n    }else if( eOp & (WO_GT|WO_GE) ){\n      testcase( eOp & WO_GT );\n      testcase( eOp & WO_GE );\n      pNew->wsFlags |= WHERE_COLUMN_RANGE|WHERE_BTM_LIMIT;\n      pNew->u.btree.nBtm = whereRangeVectorLen(\n          pParse, pSrc->iCursor, pProbe, saved_nEq, pTerm\n      );\n      pBtm = pTerm;\n      pTop = 0;\n      if( pTerm->wtFlags & TERM_LIKEOPT ){\n        /* Range contraints that come from the LIKE optimization are\n        ** always used in pairs. */\n        pTop = &pTerm[1];\n        assert( (pTop-(pTerm->pWC->a))<pTerm->pWC->nTerm );\n        assert( pTop->wtFlags & TERM_LIKEOPT );\n        assert( pTop->eOperator==WO_LT );\n        if( whereLoopResize(db, pNew, pNew->nLTerm+1) ) break; /* OOM */\n        pNew->aLTerm[pNew->nLTerm++] = pTop;\n        pNew->wsFlags |= WHERE_TOP_LIMIT;\n        pNew->u.btree.nTop = 1;\n      }\n    }else{\n      assert( eOp & (WO_LT|WO_LE) );\n      testcase( eOp & WO_LT );\n      testcase( eOp & WO_LE );\n      pNew->wsFlags |= WHERE_COLUMN_RANGE|WHERE_TOP_LIMIT;\n      pNew->u.btree.nTop = whereRangeVectorLen(\n          pParse, pSrc->iCursor, pProbe, saved_nEq, pTerm\n      );\n      pTop = pTerm;\n      pBtm = (pNew->wsFlags & WHERE_BTM_LIMIT)!=0 ?\n                     pNew->aLTerm[pNew->nLTerm-2] : 0;\n    }\n\n    /* At this point pNew->nOut is set to the number of rows expected to\n    ** be visited by the index scan before considering term pTerm, or the\n    ** values of nIn and nInMul. In other words, assuming that all \n    ** \"x IN(...)\" terms are replaced with \"x = ?\". This block updates\n    ** the value of pNew->nOut to account for pTerm (but not nIn/nInMul).  */\n    assert( pNew->nOut==saved_nOut );\n    if( pNew->wsFlags & WHERE_COLUMN_RANGE ){\n      /* Adjust nOut using stat3/stat4 data. Or, if there is no stat3/stat4\n      ** data, using some other estimate.  */\n      whereRangeScanEst(pParse, pBuilder, pBtm, pTop, pNew);\n    }else{\n      int nEq = ++pNew->u.btree.nEq;\n      assert( eOp & (WO_ISNULL|WO_EQ|WO_IN|WO_IS) );\n\n      assert( pNew->nOut==saved_nOut );\n      if( pTerm->truthProb<=0 && pProbe->aiColumn[saved_nEq]>=0 ){\n        assert( (eOp & WO_IN) || nIn==0 );\n        testcase( eOp & WO_IN );\n        pNew->nOut += pTerm->truthProb;\n        pNew->nOut -= nIn;\n      }else{\n#ifdef SQLITE_ENABLE_STAT3_OR_STAT4\n        tRowcnt nOut = 0;\n        if( nInMul==0 \n         && pProbe->nSample \n         && pNew->u.btree.nEq<=pProbe->nSampleCol\n         && ((eOp & WO_IN)==0 || !ExprHasProperty(pTerm->pExpr, EP_xIsSelect))\n        ){\n          Expr *pExpr = pTerm->pExpr;\n          if( (eOp & (WO_EQ|WO_ISNULL|WO_IS))!=0 ){\n            testcase( eOp & WO_EQ );\n            testcase( eOp & WO_IS );\n            testcase( eOp & WO_ISNULL );\n            rc = whereEqualScanEst(pParse, pBuilder, pExpr->pRight, &nOut);\n          }else{\n            rc = whereInScanEst(pParse, pBuilder, pExpr->x.pList, &nOut);\n          }\n          if( rc==SQLITE_NOTFOUND ) rc = SQLITE_OK;\n          if( rc!=SQLITE_OK ) break;          /* Jump out of the pTerm loop */\n          if( nOut ){\n            pNew->nOut = sqlite3LogEst(nOut);\n            if( pNew->nOut>saved_nOut ) pNew->nOut = saved_nOut;\n            pNew->nOut -= nIn;\n          }\n        }\n        if( nOut==0 )\n#endif\n        {\n          pNew->nOut += (pProbe->aiRowLogEst[nEq] - pProbe->aiRowLogEst[nEq-1]);\n          if( eOp & WO_ISNULL ){\n            /* TUNING: If there is no likelihood() value, assume that a \n            ** \"col IS NULL\" expression matches twice as many rows \n            ** as (col=?). */\n            pNew->nOut += 10;\n          }\n        }\n      }\n    }\n\n    /* Set rCostIdx to the cost of visiting selected rows in index. Add\n    ** it to pNew->rRun, which is currently set to the cost of the index\n    ** seek only. Then, if this is a non-covering index, add the cost of\n    ** visiting the rows in the main table.  */\n    rCostIdx = pNew->nOut + 1 + (15*pProbe->szIdxRow)/pSrc->pTab->szTabRow;\n    pNew->rRun = sqlite3LogEstAdd(rLogSize, rCostIdx);\n    if( (pNew->wsFlags & (WHERE_IDX_ONLY|WHERE_IPK))==0 ){\n      pNew->rRun = sqlite3LogEstAdd(pNew->rRun, pNew->nOut + 16);\n    }\n    ApplyCostMultiplier(pNew->rRun, pProbe->pTable->costMult);\n\n    nOutUnadjusted = pNew->nOut;\n    pNew->rRun += nInMul + nIn;\n    pNew->nOut += nInMul + nIn;\n    whereLoopOutputAdjust(pBuilder->pWC, pNew, rSize);\n    rc = whereLoopInsert(pBuilder, pNew);\n\n    if( pNew->wsFlags & WHERE_COLUMN_RANGE ){\n      pNew->nOut = saved_nOut;\n    }else{\n      pNew->nOut = nOutUnadjusted;\n    }\n\n    if( (pNew->wsFlags & WHERE_TOP_LIMIT)==0\n     && pNew->u.btree.nEq<pProbe->nColumn\n    ){\n      whereLoopAddBtreeIndex(pBuilder, pSrc, pProbe, nInMul+nIn);\n    }\n    pNew->nOut = saved_nOut;\n#ifdef SQLITE_ENABLE_STAT3_OR_STAT4\n    pBuilder->nRecValid = nRecValid;\n#endif\n  }\n  pNew->prereq = saved_prereq;\n  pNew->u.btree.nEq = saved_nEq;\n  pNew->u.btree.nBtm = saved_nBtm;\n  pNew->u.btree.nTop = saved_nTop;\n  pNew->nSkip = saved_nSkip;\n  pNew->wsFlags = saved_wsFlags;\n  pNew->nOut = saved_nOut;\n  pNew->nLTerm = saved_nLTerm;\n\n  /* Consider using a skip-scan if there are no WHERE clause constraints\n  ** available for the left-most terms of the index, and if the average\n  ** number of repeats in the left-most terms is at least 18. \n  **\n  ** The magic number 18 is selected on the basis that scanning 17 rows\n  ** is almost always quicker than an index seek (even though if the index\n  ** contains fewer than 2^17 rows we assume otherwise in other parts of\n  ** the code). And, even if it is not, it should not be too much slower. \n  ** On the other hand, the extra seeks could end up being significantly\n  ** more expensive.  */\n  assert( 42==sqlite3LogEst(18) );\n  if( saved_nEq==saved_nSkip\n   && saved_nEq+1<pProbe->nKeyCol\n   && pProbe->noSkipScan==0\n   && pProbe->aiRowLogEst[saved_nEq+1]>=42  /* TUNING: Minimum for skip-scan */\n   && (rc = whereLoopResize(db, pNew, pNew->nLTerm+1))==SQLITE_OK\n  ){\n    LogEst nIter;\n    pNew->u.btree.nEq++;\n    pNew->nSkip++;\n    pNew->aLTerm[pNew->nLTerm++] = 0;\n    pNew->wsFlags |= WHERE_SKIPSCAN;\n    nIter = pProbe->aiRowLogEst[saved_nEq] - pProbe->aiRowLogEst[saved_nEq+1];\n    pNew->nOut -= nIter;\n    /* TUNING:  Because uncertainties in the estimates for skip-scan queries,\n    ** add a 1.375 fudge factor to make skip-scan slightly less likely. */\n    nIter += 5;\n    whereLoopAddBtreeIndex(pBuilder, pSrc, pProbe, nIter + nInMul);\n    pNew->nOut = saved_nOut;\n    pNew->u.btree.nEq = saved_nEq;\n    pNew->nSkip = saved_nSkip;\n    pNew->wsFlags = saved_wsFlags;\n  }\n\n  WHERETRACE(0x800, (\"END addBtreeIdx(%s), nEq=%d, rc=%d\\n\",\n                      pProbe->zName, saved_nEq, rc));\n  return rc;\n}\n\n/*\n** Return True if it is possible that pIndex might be useful in\n** implementing the ORDER BY clause in pBuilder.\n**\n** Return False if pBuilder does not contain an ORDER BY clause or\n** if there is no way for pIndex to be useful in implementing that\n** ORDER BY clause.\n*/\nstatic int indexMightHelpWithOrderBy(\n  WhereLoopBuilder *pBuilder,\n  Index *pIndex,\n  int iCursor\n){\n  ExprList *pOB;\n  ExprList *aColExpr;\n  int ii, jj;\n\n  if( pIndex->bUnordered ) return 0;\n  if( (pOB = pBuilder->pWInfo->pOrderBy)==0 ) return 0;\n  for(ii=0; ii<pOB->nExpr; ii++){\n    Expr *pExpr = sqlite3ExprSkipCollate(pOB->a[ii].pExpr);\n    if( pExpr->op==TK_COLUMN && pExpr->iTable==iCursor ){\n      if( pExpr->iColumn<0 ) return 1;\n      for(jj=0; jj<pIndex->nKeyCol; jj++){\n        if( pExpr->iColumn==pIndex->aiColumn[jj] ) return 1;\n      }\n    }else if( (aColExpr = pIndex->aColExpr)!=0 ){\n      for(jj=0; jj<pIndex->nKeyCol; jj++){\n        if( pIndex->aiColumn[jj]!=XN_EXPR ) continue;\n        if( sqlite3ExprCompareSkip(pExpr,aColExpr->a[jj].pExpr,iCursor)==0 ){\n          return 1;\n        }\n      }\n    }\n  }\n  return 0;\n}\n\n/*\n** Return a bitmask where 1s indicate that the corresponding column of\n** the table is used by an index.  Only the first 63 columns are considered.\n*/\nstatic Bitmask columnsInIndex(Index *pIdx){\n  Bitmask m = 0;\n  int j;\n  for(j=pIdx->nColumn-1; j>=0; j--){\n    int x = pIdx->aiColumn[j];\n    if( x>=0 ){\n      testcase( x==BMS-1 );\n      testcase( x==BMS-2 );\n      if( x<BMS-1 ) m |= MASKBIT(x);\n    }\n  }\n  return m;\n}\n\n/* Check to see if a partial index with pPartIndexWhere can be used\n** in the current query.  Return true if it can be and false if not.\n*/\nstatic int whereUsablePartialIndex(int iTab, WhereClause *pWC, Expr *pWhere){\n  int i;\n  WhereTerm *pTerm;\n  Parse *pParse = pWC->pWInfo->pParse;\n  while( pWhere->op==TK_AND ){\n    if( !whereUsablePartialIndex(iTab,pWC,pWhere->pLeft) ) return 0;\n    pWhere = pWhere->pRight;\n  }\n  if( pParse->db->flags & SQLITE_EnableQPSG ) pParse = 0;\n  for(i=0, pTerm=pWC->a; i<pWC->nTerm; i++, pTerm++){\n    Expr *pExpr = pTerm->pExpr;\n    if( (!ExprHasProperty(pExpr, EP_FromJoin) || pExpr->iRightJoinTable==iTab)\n     && sqlite3ExprImpliesExpr(pParse, pExpr, pWhere, iTab) \n    ){\n      return 1;\n    }\n  }\n  return 0;\n}\n\n/*\n** Add all WhereLoop objects for a single table of the join where the table\n** is identified by pBuilder->pNew->iTab.  That table is guaranteed to be\n** a b-tree table, not a virtual table.\n**\n** The costs (WhereLoop.rRun) of the b-tree loops added by this function\n** are calculated as follows:\n**\n** For a full scan, assuming the table (or index) contains nRow rows:\n**\n**     cost = nRow * 3.0                    // full-table scan\n**     cost = nRow * K                      // scan of covering index\n**     cost = nRow * (K+3.0)                // scan of non-covering index\n**\n** where K is a value between 1.1 and 3.0 set based on the relative \n** estimated average size of the index and table records.\n**\n** For an index scan, where nVisit is the number of index rows visited\n** by the scan, and nSeek is the number of seek operations required on \n** the index b-tree:\n**\n**     cost = nSeek * (log(nRow) + K * nVisit)          // covering index\n**     cost = nSeek * (log(nRow) + (K+3.0) * nVisit)    // non-covering index\n**\n** Normally, nSeek is 1. nSeek values greater than 1 come about if the \n** WHERE clause includes \"x IN (....)\" terms used in place of \"x=?\". Or when \n** implicit \"x IN (SELECT x FROM tbl)\" terms are added for skip-scans.\n**\n** The estimated values (nRow, nVisit, nSeek) often contain a large amount\n** of uncertainty.  For this reason, scoring is designed to pick plans that\n** \"do the least harm\" if the estimates are inaccurate.  For example, a\n** log(nRow) factor is omitted from a non-covering index scan in order to\n** bias the scoring in favor of using an index, since the worst-case\n** performance of using an index is far better than the worst-case performance\n** of a full table scan.\n*/\nstatic int whereLoopAddBtree(\n  WhereLoopBuilder *pBuilder, /* WHERE clause information */\n  Bitmask mPrereq             /* Extra prerequesites for using this table */\n){\n  WhereInfo *pWInfo;          /* WHERE analysis context */\n  Index *pProbe;              /* An index we are evaluating */\n  Index sPk;                  /* A fake index object for the primary key */\n  LogEst aiRowEstPk[2];       /* The aiRowLogEst[] value for the sPk index */\n  i16 aiColumnPk = -1;        /* The aColumn[] value for the sPk index */\n  SrcList *pTabList;          /* The FROM clause */\n  struct SrcList_item *pSrc;  /* The FROM clause btree term to add */\n  WhereLoop *pNew;            /* Template WhereLoop object */\n  int rc = SQLITE_OK;         /* Return code */\n  int iSortIdx = 1;           /* Index number */\n  int b;                      /* A boolean value */\n  LogEst rSize;               /* number of rows in the table */\n  LogEst rLogSize;            /* Logarithm of the number of rows in the table */\n  WhereClause *pWC;           /* The parsed WHERE clause */\n  Table *pTab;                /* Table being queried */\n  \n  pNew = pBuilder->pNew;\n  pWInfo = pBuilder->pWInfo;\n  pTabList = pWInfo->pTabList;\n  pSrc = pTabList->a + pNew->iTab;\n  pTab = pSrc->pTab;\n  pWC = pBuilder->pWC;\n  assert( !IsVirtual(pSrc->pTab) );\n\n  if( pSrc->pIBIndex ){\n    /* An INDEXED BY clause specifies a particular index to use */\n    pProbe = pSrc->pIBIndex;\n  }else if( !HasRowid(pTab) ){\n    pProbe = pTab->pIndex;\n  }else{\n    /* There is no INDEXED BY clause.  Create a fake Index object in local\n    ** variable sPk to represent the rowid primary key index.  Make this\n    ** fake index the first in a chain of Index objects with all of the real\n    ** indices to follow */\n    Index *pFirst;                  /* First of real indices on the table */\n    memset(&sPk, 0, sizeof(Index));\n    sPk.nKeyCol = 1;\n    sPk.nColumn = 1;\n    sPk.aiColumn = &aiColumnPk;\n    sPk.aiRowLogEst = aiRowEstPk;\n    sPk.onError = OE_Replace;\n    sPk.pTable = pTab;\n    sPk.szIdxRow = pTab->szTabRow;\n    aiRowEstPk[0] = pTab->nRowLogEst;\n    aiRowEstPk[1] = 0;\n    pFirst = pSrc->pTab->pIndex;\n    if( pSrc->fg.notIndexed==0 ){\n      /* The real indices of the table are only considered if the\n      ** NOT INDEXED qualifier is omitted from the FROM clause */\n      sPk.pNext = pFirst;\n    }\n    pProbe = &sPk;\n  }\n  rSize = pTab->nRowLogEst;\n  rLogSize = estLog(rSize);\n\n#ifndef SQLITE_OMIT_AUTOMATIC_INDEX\n  /* Automatic indexes */\n  if( !pBuilder->pOrSet      /* Not part of an OR optimization */\n   && (pWInfo->wctrlFlags & WHERE_OR_SUBCLAUSE)==0\n   && (pWInfo->pParse->db->flags & SQLITE_AutoIndex)!=0\n   && pSrc->pIBIndex==0      /* Has no INDEXED BY clause */\n   && !pSrc->fg.notIndexed   /* Has no NOT INDEXED clause */\n   && HasRowid(pTab)         /* Not WITHOUT ROWID table. (FIXME: Why not?) */\n   && !pSrc->fg.isCorrelated /* Not a correlated subquery */\n   && !pSrc->fg.isRecursive  /* Not a recursive common table expression. */\n  ){\n    /* Generate auto-index WhereLoops */\n    WhereTerm *pTerm;\n    WhereTerm *pWCEnd = pWC->a + pWC->nTerm;\n    for(pTerm=pWC->a; rc==SQLITE_OK && pTerm<pWCEnd; pTerm++){\n      if( pTerm->prereqRight & pNew->maskSelf ) continue;\n      if( termCanDriveIndex(pTerm, pSrc, 0) ){\n        pNew->u.btree.nEq = 1;\n        pNew->nSkip = 0;\n        pNew->u.btree.pIndex = 0;\n        pNew->nLTerm = 1;\n        pNew->aLTerm[0] = pTerm;\n        /* TUNING: One-time cost for computing the automatic index is\n        ** estimated to be X*N*log2(N) where N is the number of rows in\n        ** the table being indexed and where X is 7 (LogEst=28) for normal\n        ** tables or 1.375 (LogEst=4) for views and subqueries.  The value\n        ** of X is smaller for views and subqueries so that the query planner\n        ** will be more aggressive about generating automatic indexes for\n        ** those objects, since there is no opportunity to add schema\n        ** indexes on subqueries and views. */\n        pNew->rSetup = rLogSize + rSize + 4;\n        if( pTab->pSelect==0 && (pTab->tabFlags & TF_Ephemeral)==0 ){\n          pNew->rSetup += 24;\n        }\n        ApplyCostMultiplier(pNew->rSetup, pTab->costMult);\n        if( pNew->rSetup<0 ) pNew->rSetup = 0;\n        /* TUNING: Each index lookup yields 20 rows in the table.  This\n        ** is more than the usual guess of 10 rows, since we have no way\n        ** of knowing how selective the index will ultimately be.  It would\n        ** not be unreasonable to make this value much larger. */\n        pNew->nOut = 43;  assert( 43==sqlite3LogEst(20) );\n        pNew->rRun = sqlite3LogEstAdd(rLogSize,pNew->nOut);\n        pNew->wsFlags = WHERE_AUTO_INDEX;\n        pNew->prereq = mPrereq | pTerm->prereqRight;\n        rc = whereLoopInsert(pBuilder, pNew);\n      }\n    }\n  }\n#endif /* SQLITE_OMIT_AUTOMATIC_INDEX */\n\n  /* Loop over all indices. If there was an INDEXED BY clause, then only \n  ** consider index pProbe.  */\n  for(; rc==SQLITE_OK && pProbe; \n      pProbe=(pSrc->pIBIndex ? 0 : pProbe->pNext), iSortIdx++\n  ){\n    if( pProbe->pPartIdxWhere!=0\n     && !whereUsablePartialIndex(pSrc->iCursor, pWC, pProbe->pPartIdxWhere) ){\n      testcase( pNew->iTab!=pSrc->iCursor );  /* See ticket [98d973b8f5] */\n      continue;  /* Partial index inappropriate for this query */\n    }\n    if( pProbe->bNoQuery ) continue;\n    rSize = pProbe->aiRowLogEst[0];\n    pNew->u.btree.nEq = 0;\n    pNew->u.btree.nBtm = 0;\n    pNew->u.btree.nTop = 0;\n    pNew->nSkip = 0;\n    pNew->nLTerm = 0;\n    pNew->iSortIdx = 0;\n    pNew->rSetup = 0;\n    pNew->prereq = mPrereq;\n    pNew->nOut = rSize;\n    pNew->u.btree.pIndex = pProbe;\n    b = indexMightHelpWithOrderBy(pBuilder, pProbe, pSrc->iCursor);\n    /* The ONEPASS_DESIRED flags never occurs together with ORDER BY */\n    assert( (pWInfo->wctrlFlags & WHERE_ONEPASS_DESIRED)==0 || b==0 );\n    if( pProbe->tnum<=0 ){\n      /* Integer primary key index */\n      pNew->wsFlags = WHERE_IPK;\n\n      /* Full table scan */\n      pNew->iSortIdx = b ? iSortIdx : 0;\n      /* TUNING: Cost of full table scan is (N*3.0). */\n      pNew->rRun = rSize + 16;\n      ApplyCostMultiplier(pNew->rRun, pTab->costMult);\n      whereLoopOutputAdjust(pWC, pNew, rSize);\n      rc = whereLoopInsert(pBuilder, pNew);\n      pNew->nOut = rSize;\n      if( rc ) break;\n    }else{\n      Bitmask m;\n      if( pProbe->isCovering ){\n        pNew->wsFlags = WHERE_IDX_ONLY | WHERE_INDEXED;\n        m = 0;\n      }else{\n        m = pSrc->colUsed & ~columnsInIndex(pProbe);\n        pNew->wsFlags = (m==0) ? (WHERE_IDX_ONLY|WHERE_INDEXED) : WHERE_INDEXED;\n      }\n\n      /* Full scan via index */\n      if( b\n       || !HasRowid(pTab)\n       || pProbe->pPartIdxWhere!=0\n       || ( m==0\n         && pProbe->bUnordered==0\n         && (pProbe->szIdxRow<pTab->szTabRow)\n         && (pWInfo->wctrlFlags & WHERE_ONEPASS_DESIRED)==0\n         && sqlite3GlobalConfig.bUseCis\n         && OptimizationEnabled(pWInfo->pParse->db, SQLITE_CoverIdxScan)\n          )\n      ){\n        pNew->iSortIdx = b ? iSortIdx : 0;\n\n        /* The cost of visiting the index rows is N*K, where K is\n        ** between 1.1 and 3.0, depending on the relative sizes of the\n        ** index and table rows. */\n        pNew->rRun = rSize + 1 + (15*pProbe->szIdxRow)/pTab->szTabRow;\n        if( m!=0 ){\n          /* If this is a non-covering index scan, add in the cost of\n          ** doing table lookups.  The cost will be 3x the number of\n          ** lookups.  Take into account WHERE clause terms that can be\n          ** satisfied using just the index, and that do not require a\n          ** table lookup. */\n          LogEst nLookup = rSize + 16;  /* Base cost:  N*3 */\n          int ii;\n          int iCur = pSrc->iCursor;\n          WhereClause *pWC2 = &pWInfo->sWC;\n          for(ii=0; ii<pWC2->nTerm; ii++){\n            WhereTerm *pTerm = &pWC2->a[ii];\n            if( !sqlite3ExprCoveredByIndex(pTerm->pExpr, iCur, pProbe) ){\n              break;\n            }\n            /* pTerm can be evaluated using just the index.  So reduce\n            ** the expected number of table lookups accordingly */\n            if( pTerm->truthProb<=0 ){\n              nLookup += pTerm->truthProb;\n            }else{\n              nLookup--;\n              if( pTerm->eOperator & (WO_EQ|WO_IS) ) nLookup -= 19;\n            }\n          }\n          \n          pNew->rRun = sqlite3LogEstAdd(pNew->rRun, nLookup);\n        }\n        ApplyCostMultiplier(pNew->rRun, pTab->costMult);\n        whereLoopOutputAdjust(pWC, pNew, rSize);\n        rc = whereLoopInsert(pBuilder, pNew);\n        pNew->nOut = rSize;\n        if( rc ) break;\n      }\n    }\n\n    pBuilder->bldFlags = 0;\n    rc = whereLoopAddBtreeIndex(pBuilder, pSrc, pProbe, 0);\n    if( pBuilder->bldFlags==SQLITE_BLDF_INDEXED ){\n      /* If a non-unique index is used, or if a prefix of the key for\n      ** unique index is used (making the index functionally non-unique)\n      ** then the sqlite_stat1 data becomes important for scoring the\n      ** plan */\n      pTab->tabFlags |= TF_StatsUsed;\n    }\n#ifdef SQLITE_ENABLE_STAT3_OR_STAT4\n    sqlite3Stat4ProbeFree(pBuilder->pRec);\n    pBuilder->nRecValid = 0;\n    pBuilder->pRec = 0;\n#endif\n  }\n  return rc;\n}\n\n#ifndef SQLITE_OMIT_VIRTUALTABLE\n\n/*\n** Argument pIdxInfo is already populated with all constraints that may\n** be used by the virtual table identified by pBuilder->pNew->iTab. This\n** function marks a subset of those constraints usable, invokes the\n** xBestIndex method and adds the returned plan to pBuilder.\n**\n** A constraint is marked usable if:\n**\n**   * Argument mUsable indicates that its prerequisites are available, and\n**\n**   * It is not one of the operators specified in the mExclude mask passed\n**     as the fourth argument (which in practice is either WO_IN or 0).\n**\n** Argument mPrereq is a mask of tables that must be scanned before the\n** virtual table in question. These are added to the plans prerequisites\n** before it is added to pBuilder.\n**\n** Output parameter *pbIn is set to true if the plan added to pBuilder\n** uses one or more WO_IN terms, or false otherwise.\n*/\nstatic int whereLoopAddVirtualOne(\n  WhereLoopBuilder *pBuilder,\n  Bitmask mPrereq,                /* Mask of tables that must be used. */\n  Bitmask mUsable,                /* Mask of usable tables */\n  u16 mExclude,                   /* Exclude terms using these operators */\n  sqlite3_index_info *pIdxInfo,   /* Populated object for xBestIndex */\n  u16 mNoOmit,                    /* Do not omit these constraints */\n  int *pbIn                       /* OUT: True if plan uses an IN(...) op */\n){\n  WhereClause *pWC = pBuilder->pWC;\n  struct sqlite3_index_constraint *pIdxCons;\n  struct sqlite3_index_constraint_usage *pUsage = pIdxInfo->aConstraintUsage;\n  int i;\n  int mxTerm;\n  int rc = SQLITE_OK;\n  WhereLoop *pNew = pBuilder->pNew;\n  Parse *pParse = pBuilder->pWInfo->pParse;\n  struct SrcList_item *pSrc = &pBuilder->pWInfo->pTabList->a[pNew->iTab];\n  int nConstraint = pIdxInfo->nConstraint;\n\n  assert( (mUsable & mPrereq)==mPrereq );\n  *pbIn = 0;\n  pNew->prereq = mPrereq;\n\n  /* Set the usable flag on the subset of constraints identified by \n  ** arguments mUsable and mExclude. */\n  pIdxCons = *(struct sqlite3_index_constraint**)&pIdxInfo->aConstraint;\n  for(i=0; i<nConstraint; i++, pIdxCons++){\n    WhereTerm *pTerm = &pWC->a[pIdxCons->iTermOffset];\n    pIdxCons->usable = 0;\n    if( (pTerm->prereqRight & mUsable)==pTerm->prereqRight \n     && (pTerm->eOperator & mExclude)==0\n    ){\n      pIdxCons->usable = 1;\n    }\n  }\n\n  /* Initialize the output fields of the sqlite3_index_info structure */\n  memset(pUsage, 0, sizeof(pUsage[0])*nConstraint);\n  assert( pIdxInfo->needToFreeIdxStr==0 );\n  pIdxInfo->idxStr = 0;\n  pIdxInfo->idxNum = 0;\n  pIdxInfo->orderByConsumed = 0;\n  pIdxInfo->estimatedCost = SQLITE_BIG_DBL / (double)2;\n  pIdxInfo->estimatedRows = 25;\n  pIdxInfo->idxFlags = 0;\n  pIdxInfo->colUsed = (sqlite3_int64)pSrc->colUsed;\n\n  /* Invoke the virtual table xBestIndex() method */\n  rc = vtabBestIndex(pParse, pSrc->pTab, pIdxInfo);\n  if( rc ) return rc;\n\n  mxTerm = -1;\n  assert( pNew->nLSlot>=nConstraint );\n  for(i=0; i<nConstraint; i++) pNew->aLTerm[i] = 0;\n  pNew->u.vtab.omitMask = 0;\n  pIdxCons = *(struct sqlite3_index_constraint**)&pIdxInfo->aConstraint;\n  for(i=0; i<nConstraint; i++, pIdxCons++){\n    int iTerm;\n    if( (iTerm = pUsage[i].argvIndex - 1)>=0 ){\n      WhereTerm *pTerm;\n      int j = pIdxCons->iTermOffset;\n      if( iTerm>=nConstraint\n       || j<0\n       || j>=pWC->nTerm\n       || pNew->aLTerm[iTerm]!=0\n       || pIdxCons->usable==0\n      ){\n        rc = SQLITE_ERROR;\n        sqlite3ErrorMsg(pParse,\"%s.xBestIndex malfunction\",pSrc->pTab->zName);\n        return rc;\n      }\n      testcase( iTerm==nConstraint-1 );\n      testcase( j==0 );\n      testcase( j==pWC->nTerm-1 );\n      pTerm = &pWC->a[j];\n      pNew->prereq |= pTerm->prereqRight;\n      assert( iTerm<pNew->nLSlot );\n      pNew->aLTerm[iTerm] = pTerm;\n      if( iTerm>mxTerm ) mxTerm = iTerm;\n      testcase( iTerm==15 );\n      testcase( iTerm==16 );\n      if( iTerm<16 && pUsage[i].omit ) pNew->u.vtab.omitMask |= 1<<iTerm;\n      if( (pTerm->eOperator & WO_IN)!=0 ){\n        /* A virtual table that is constrained by an IN clause may not\n        ** consume the ORDER BY clause because (1) the order of IN terms\n        ** is not necessarily related to the order of output terms and\n        ** (2) Multiple outputs from a single IN value will not merge\n        ** together.  */\n        pIdxInfo->orderByConsumed = 0;\n        pIdxInfo->idxFlags &= ~SQLITE_INDEX_SCAN_UNIQUE;\n        *pbIn = 1; assert( (mExclude & WO_IN)==0 );\n      }\n    }\n  }\n  pNew->u.vtab.omitMask &= ~mNoOmit;\n\n  pNew->nLTerm = mxTerm+1;\n  assert( pNew->nLTerm<=pNew->nLSlot );\n  pNew->u.vtab.idxNum = pIdxInfo->idxNum;\n  pNew->u.vtab.needFree = pIdxInfo->needToFreeIdxStr;\n  pIdxInfo->needToFreeIdxStr = 0;\n  pNew->u.vtab.idxStr = pIdxInfo->idxStr;\n  pNew->u.vtab.isOrdered = (i8)(pIdxInfo->orderByConsumed ?\n      pIdxInfo->nOrderBy : 0);\n  pNew->rSetup = 0;\n  pNew->rRun = sqlite3LogEstFromDouble(pIdxInfo->estimatedCost);\n  pNew->nOut = sqlite3LogEst(pIdxInfo->estimatedRows);\n\n  /* Set the WHERE_ONEROW flag if the xBestIndex() method indicated\n  ** that the scan will visit at most one row. Clear it otherwise. */\n  if( pIdxInfo->idxFlags & SQLITE_INDEX_SCAN_UNIQUE ){\n    pNew->wsFlags |= WHERE_ONEROW;\n  }else{\n    pNew->wsFlags &= ~WHERE_ONEROW;\n  }\n  rc = whereLoopInsert(pBuilder, pNew);\n  if( pNew->u.vtab.needFree ){\n    sqlite3_free(pNew->u.vtab.idxStr);\n    pNew->u.vtab.needFree = 0;\n  }\n  WHERETRACE(0xffff, (\"  bIn=%d prereqIn=%04llx prereqOut=%04llx\\n\",\n                      *pbIn, (sqlite3_uint64)mPrereq,\n                      (sqlite3_uint64)(pNew->prereq & ~mPrereq)));\n\n  return rc;\n}\n\n/*\n** If this function is invoked from within an xBestIndex() callback, it\n** returns a pointer to a buffer containing the name of the collation\n** sequence associated with element iCons of the sqlite3_index_info.aConstraint\n** array. Or, if iCons is out of range or there is no active xBestIndex\n** call, return NULL.\n*/\nSQLITE_API const char *sqlite3_vtab_collation(sqlite3_index_info *pIdxInfo, int iCons){\n  HiddenIndexInfo *pHidden = (HiddenIndexInfo*)&pIdxInfo[1];\n  const char *zRet = 0;\n  if( iCons>=0 && iCons<pIdxInfo->nConstraint ){\n    CollSeq *pC = 0;\n    int iTerm = pIdxInfo->aConstraint[iCons].iTermOffset;\n    Expr *pX = pHidden->pWC->a[iTerm].pExpr;\n    if( pX->pLeft ){\n      pC = sqlite3BinaryCompareCollSeq(pHidden->pParse, pX->pLeft, pX->pRight);\n    }\n    zRet = (pC ? pC->zName : \"BINARY\");\n  }\n  return zRet;\n}\n\n/*\n** Add all WhereLoop objects for a table of the join identified by\n** pBuilder->pNew->iTab.  That table is guaranteed to be a virtual table.\n**\n** If there are no LEFT or CROSS JOIN joins in the query, both mPrereq and\n** mUnusable are set to 0. Otherwise, mPrereq is a mask of all FROM clause\n** entries that occur before the virtual table in the FROM clause and are\n** separated from it by at least one LEFT or CROSS JOIN. Similarly, the\n** mUnusable mask contains all FROM clause entries that occur after the\n** virtual table and are separated from it by at least one LEFT or \n** CROSS JOIN. \n**\n** For example, if the query were:\n**\n**   ... FROM t1, t2 LEFT JOIN t3, t4, vt CROSS JOIN t5, t6;\n**\n** then mPrereq corresponds to (t1, t2) and mUnusable to (t5, t6).\n**\n** All the tables in mPrereq must be scanned before the current virtual \n** table. So any terms for which all prerequisites are satisfied by \n** mPrereq may be specified as \"usable\" in all calls to xBestIndex. \n** Conversely, all tables in mUnusable must be scanned after the current\n** virtual table, so any terms for which the prerequisites overlap with\n** mUnusable should always be configured as \"not-usable\" for xBestIndex.\n*/\nstatic int whereLoopAddVirtual(\n  WhereLoopBuilder *pBuilder,  /* WHERE clause information */\n  Bitmask mPrereq,             /* Tables that must be scanned before this one */\n  Bitmask mUnusable            /* Tables that must be scanned after this one */\n){\n  int rc = SQLITE_OK;          /* Return code */\n  WhereInfo *pWInfo;           /* WHERE analysis context */\n  Parse *pParse;               /* The parsing context */\n  WhereClause *pWC;            /* The WHERE clause */\n  struct SrcList_item *pSrc;   /* The FROM clause term to search */\n  sqlite3_index_info *p;       /* Object to pass to xBestIndex() */\n  int nConstraint;             /* Number of constraints in p */\n  int bIn;                     /* True if plan uses IN(...) operator */\n  WhereLoop *pNew;\n  Bitmask mBest;               /* Tables used by best possible plan */\n  u16 mNoOmit;\n\n  assert( (mPrereq & mUnusable)==0 );\n  pWInfo = pBuilder->pWInfo;\n  pParse = pWInfo->pParse;\n  pWC = pBuilder->pWC;\n  pNew = pBuilder->pNew;\n  pSrc = &pWInfo->pTabList->a[pNew->iTab];\n  assert( IsVirtual(pSrc->pTab) );\n  p = allocateIndexInfo(pParse, pWC, mUnusable, pSrc, pBuilder->pOrderBy, \n      &mNoOmit);\n  if( p==0 ) return SQLITE_NOMEM_BKPT;\n  pNew->rSetup = 0;\n  pNew->wsFlags = WHERE_VIRTUALTABLE;\n  pNew->nLTerm = 0;\n  pNew->u.vtab.needFree = 0;\n  nConstraint = p->nConstraint;\n  if( whereLoopResize(pParse->db, pNew, nConstraint) ){\n    sqlite3DbFree(pParse->db, p);\n    return SQLITE_NOMEM_BKPT;\n  }\n\n  /* First call xBestIndex() with all constraints usable. */\n  WHERETRACE(0x40, (\"  VirtualOne: all usable\\n\"));\n  rc = whereLoopAddVirtualOne(pBuilder, mPrereq, ALLBITS, 0, p, mNoOmit, &bIn);\n\n  /* If the call to xBestIndex() with all terms enabled produced a plan\n  ** that does not require any source tables (IOW: a plan with mBest==0),\n  ** then there is no point in making any further calls to xBestIndex() \n  ** since they will all return the same result (if the xBestIndex()\n  ** implementation is sane). */\n  if( rc==SQLITE_OK && (mBest = (pNew->prereq & ~mPrereq))!=0 ){\n    int seenZero = 0;             /* True if a plan with no prereqs seen */\n    int seenZeroNoIN = 0;         /* Plan with no prereqs and no IN(...) seen */\n    Bitmask mPrev = 0;\n    Bitmask mBestNoIn = 0;\n\n    /* If the plan produced by the earlier call uses an IN(...) term, call\n    ** xBestIndex again, this time with IN(...) terms disabled. */\n    if( bIn ){\n      WHERETRACE(0x40, (\"  VirtualOne: all usable w/o IN\\n\"));\n      rc = whereLoopAddVirtualOne(\n          pBuilder, mPrereq, ALLBITS, WO_IN, p, mNoOmit, &bIn);\n      assert( bIn==0 );\n      mBestNoIn = pNew->prereq & ~mPrereq;\n      if( mBestNoIn==0 ){\n        seenZero = 1;\n        seenZeroNoIN = 1;\n      }\n    }\n\n    /* Call xBestIndex once for each distinct value of (prereqRight & ~mPrereq) \n    ** in the set of terms that apply to the current virtual table.  */\n    while( rc==SQLITE_OK ){\n      int i;\n      Bitmask mNext = ALLBITS;\n      assert( mNext>0 );\n      for(i=0; i<nConstraint; i++){\n        Bitmask mThis = (\n            pWC->a[p->aConstraint[i].iTermOffset].prereqRight & ~mPrereq\n        );\n        if( mThis>mPrev && mThis<mNext ) mNext = mThis;\n      }\n      mPrev = mNext;\n      if( mNext==ALLBITS ) break;\n      if( mNext==mBest || mNext==mBestNoIn ) continue;\n      WHERETRACE(0x40, (\"  VirtualOne: mPrev=%04llx mNext=%04llx\\n\",\n                       (sqlite3_uint64)mPrev, (sqlite3_uint64)mNext));\n      rc = whereLoopAddVirtualOne(\n          pBuilder, mPrereq, mNext|mPrereq, 0, p, mNoOmit, &bIn);\n      if( pNew->prereq==mPrereq ){\n        seenZero = 1;\n        if( bIn==0 ) seenZeroNoIN = 1;\n      }\n    }\n\n    /* If the calls to xBestIndex() in the above loop did not find a plan\n    ** that requires no source tables at all (i.e. one guaranteed to be\n    ** usable), make a call here with all source tables disabled */\n    if( rc==SQLITE_OK && seenZero==0 ){\n      WHERETRACE(0x40, (\"  VirtualOne: all disabled\\n\"));\n      rc = whereLoopAddVirtualOne(\n          pBuilder, mPrereq, mPrereq, 0, p, mNoOmit, &bIn);\n      if( bIn==0 ) seenZeroNoIN = 1;\n    }\n\n    /* If the calls to xBestIndex() have so far failed to find a plan\n    ** that requires no source tables at all and does not use an IN(...)\n    ** operator, make a final call to obtain one here.  */\n    if( rc==SQLITE_OK && seenZeroNoIN==0 ){\n      WHERETRACE(0x40, (\"  VirtualOne: all disabled and w/o IN\\n\"));\n      rc = whereLoopAddVirtualOne(\n          pBuilder, mPrereq, mPrereq, WO_IN, p, mNoOmit, &bIn);\n    }\n  }\n\n  if( p->needToFreeIdxStr ) sqlite3_free(p->idxStr);\n  sqlite3DbFreeNN(pParse->db, p);\n  return rc;\n}\n#endif /* SQLITE_OMIT_VIRTUALTABLE */\n\n/*\n** Add WhereLoop entries to handle OR terms.  This works for either\n** btrees or virtual tables.\n*/\nstatic int whereLoopAddOr(\n  WhereLoopBuilder *pBuilder, \n  Bitmask mPrereq, \n  Bitmask mUnusable\n){\n  WhereInfo *pWInfo = pBuilder->pWInfo;\n  WhereClause *pWC;\n  WhereLoop *pNew;\n  WhereTerm *pTerm, *pWCEnd;\n  int rc = SQLITE_OK;\n  int iCur;\n  WhereClause tempWC;\n  WhereLoopBuilder sSubBuild;\n  WhereOrSet sSum, sCur;\n  struct SrcList_item *pItem;\n  \n  pWC = pBuilder->pWC;\n  pWCEnd = pWC->a + pWC->nTerm;\n  pNew = pBuilder->pNew;\n  memset(&sSum, 0, sizeof(sSum));\n  pItem = pWInfo->pTabList->a + pNew->iTab;\n  iCur = pItem->iCursor;\n\n  for(pTerm=pWC->a; pTerm<pWCEnd && rc==SQLITE_OK; pTerm++){\n    if( (pTerm->eOperator & WO_OR)!=0\n     && (pTerm->u.pOrInfo->indexable & pNew->maskSelf)!=0 \n    ){\n      WhereClause * const pOrWC = &pTerm->u.pOrInfo->wc;\n      WhereTerm * const pOrWCEnd = &pOrWC->a[pOrWC->nTerm];\n      WhereTerm *pOrTerm;\n      int once = 1;\n      int i, j;\n    \n      sSubBuild = *pBuilder;\n      sSubBuild.pOrderBy = 0;\n      sSubBuild.pOrSet = &sCur;\n\n      WHERETRACE(0x200, (\"Begin processing OR-clause %p\\n\", pTerm));\n      for(pOrTerm=pOrWC->a; pOrTerm<pOrWCEnd; pOrTerm++){\n        if( (pOrTerm->eOperator & WO_AND)!=0 ){\n          sSubBuild.pWC = &pOrTerm->u.pAndInfo->wc;\n        }else if( pOrTerm->leftCursor==iCur ){\n          tempWC.pWInfo = pWC->pWInfo;\n          tempWC.pOuter = pWC;\n          tempWC.op = TK_AND;\n          tempWC.nTerm = 1;\n          tempWC.a = pOrTerm;\n          sSubBuild.pWC = &tempWC;\n        }else{\n          continue;\n        }\n        sCur.n = 0;\n#ifdef WHERETRACE_ENABLED\n        WHERETRACE(0x200, (\"OR-term %d of %p has %d subterms:\\n\", \n                   (int)(pOrTerm-pOrWC->a), pTerm, sSubBuild.pWC->nTerm));\n        if( sqlite3WhereTrace & 0x400 ){\n          sqlite3WhereClausePrint(sSubBuild.pWC);\n        }\n#endif\n#ifndef SQLITE_OMIT_VIRTUALTABLE\n        if( IsVirtual(pItem->pTab) ){\n          rc = whereLoopAddVirtual(&sSubBuild, mPrereq, mUnusable);\n        }else\n#endif\n        {\n          rc = whereLoopAddBtree(&sSubBuild, mPrereq);\n        }\n        if( rc==SQLITE_OK ){\n          rc = whereLoopAddOr(&sSubBuild, mPrereq, mUnusable);\n        }\n        assert( rc==SQLITE_OK || sCur.n==0 );\n        if( sCur.n==0 ){\n          sSum.n = 0;\n          break;\n        }else if( once ){\n          whereOrMove(&sSum, &sCur);\n          once = 0;\n        }else{\n          WhereOrSet sPrev;\n          whereOrMove(&sPrev, &sSum);\n          sSum.n = 0;\n          for(i=0; i<sPrev.n; i++){\n            for(j=0; j<sCur.n; j++){\n              whereOrInsert(&sSum, sPrev.a[i].prereq | sCur.a[j].prereq,\n                            sqlite3LogEstAdd(sPrev.a[i].rRun, sCur.a[j].rRun),\n                            sqlite3LogEstAdd(sPrev.a[i].nOut, sCur.a[j].nOut));\n            }\n          }\n        }\n      }\n      pNew->nLTerm = 1;\n      pNew->aLTerm[0] = pTerm;\n      pNew->wsFlags = WHERE_MULTI_OR;\n      pNew->rSetup = 0;\n      pNew->iSortIdx = 0;\n      memset(&pNew->u, 0, sizeof(pNew->u));\n      for(i=0; rc==SQLITE_OK && i<sSum.n; i++){\n        /* TUNING: Currently sSum.a[i].rRun is set to the sum of the costs\n        ** of all sub-scans required by the OR-scan. However, due to rounding\n        ** errors, it may be that the cost of the OR-scan is equal to its\n        ** most expensive sub-scan. Add the smallest possible penalty \n        ** (equivalent to multiplying the cost by 1.07) to ensure that \n        ** this does not happen. Otherwise, for WHERE clauses such as the\n        ** following where there is an index on \"y\":\n        **\n        **     WHERE likelihood(x=?, 0.99) OR y=?\n        **\n        ** the planner may elect to \"OR\" together a full-table scan and an\n        ** index lookup. And other similarly odd results.  */\n        pNew->rRun = sSum.a[i].rRun + 1;\n        pNew->nOut = sSum.a[i].nOut;\n        pNew->prereq = sSum.a[i].prereq;\n        rc = whereLoopInsert(pBuilder, pNew);\n      }\n      WHERETRACE(0x200, (\"End processing OR-clause %p\\n\", pTerm));\n    }\n  }\n  return rc;\n}\n\n/*\n** Add all WhereLoop objects for all tables \n*/\nstatic int whereLoopAddAll(WhereLoopBuilder *pBuilder){\n  WhereInfo *pWInfo = pBuilder->pWInfo;\n  Bitmask mPrereq = 0;\n  Bitmask mPrior = 0;\n  int iTab;\n  SrcList *pTabList = pWInfo->pTabList;\n  struct SrcList_item *pItem;\n  struct SrcList_item *pEnd = &pTabList->a[pWInfo->nLevel];\n  sqlite3 *db = pWInfo->pParse->db;\n  int rc = SQLITE_OK;\n  WhereLoop *pNew;\n  u8 priorJointype = 0;\n\n  /* Loop over the tables in the join, from left to right */\n  pNew = pBuilder->pNew;\n  whereLoopInit(pNew);\n  for(iTab=0, pItem=pTabList->a; pItem<pEnd; iTab++, pItem++){\n    Bitmask mUnusable = 0;\n    pNew->iTab = iTab;\n    pNew->maskSelf = sqlite3WhereGetMask(&pWInfo->sMaskSet, pItem->iCursor);\n    if( ((pItem->fg.jointype|priorJointype) & (JT_LEFT|JT_CROSS))!=0 ){\n      /* This condition is true when pItem is the FROM clause term on the\n      ** right-hand-side of a LEFT or CROSS JOIN.  */\n      mPrereq = mPrior;\n    }\n    priorJointype = pItem->fg.jointype;\n#ifndef SQLITE_OMIT_VIRTUALTABLE\n    if( IsVirtual(pItem->pTab) ){\n      struct SrcList_item *p;\n      for(p=&pItem[1]; p<pEnd; p++){\n        if( mUnusable || (p->fg.jointype & (JT_LEFT|JT_CROSS)) ){\n          mUnusable |= sqlite3WhereGetMask(&pWInfo->sMaskSet, p->iCursor);\n        }\n      }\n      rc = whereLoopAddVirtual(pBuilder, mPrereq, mUnusable);\n    }else\n#endif /* SQLITE_OMIT_VIRTUALTABLE */\n    {\n      rc = whereLoopAddBtree(pBuilder, mPrereq);\n    }\n    if( rc==SQLITE_OK ){\n      rc = whereLoopAddOr(pBuilder, mPrereq, mUnusable);\n    }\n    mPrior |= pNew->maskSelf;\n    if( rc || db->mallocFailed ) break;\n  }\n\n  whereLoopClear(db, pNew);\n  return rc;\n}\n\n/*\n** Examine a WherePath (with the addition of the extra WhereLoop of the 6th\n** parameters) to see if it outputs rows in the requested ORDER BY\n** (or GROUP BY) without requiring a separate sort operation.  Return N:\n** \n**   N>0:   N terms of the ORDER BY clause are satisfied\n**   N==0:  No terms of the ORDER BY clause are satisfied\n**   N<0:   Unknown yet how many terms of ORDER BY might be satisfied.   \n**\n** Note that processing for WHERE_GROUPBY and WHERE_DISTINCTBY is not as\n** strict.  With GROUP BY and DISTINCT the only requirement is that\n** equivalent rows appear immediately adjacent to one another.  GROUP BY\n** and DISTINCT do not require rows to appear in any particular order as long\n** as equivalent rows are grouped together.  Thus for GROUP BY and DISTINCT\n** the pOrderBy terms can be matched in any order.  With ORDER BY, the \n** pOrderBy terms must be matched in strict left-to-right order.\n*/\nstatic i8 wherePathSatisfiesOrderBy(\n  WhereInfo *pWInfo,    /* The WHERE clause */\n  ExprList *pOrderBy,   /* ORDER BY or GROUP BY or DISTINCT clause to check */\n  WherePath *pPath,     /* The WherePath to check */\n  u16 wctrlFlags,       /* WHERE_GROUPBY or _DISTINCTBY or _ORDERBY_LIMIT */\n  u16 nLoop,            /* Number of entries in pPath->aLoop[] */\n  WhereLoop *pLast,     /* Add this WhereLoop to the end of pPath->aLoop[] */\n  Bitmask *pRevMask     /* OUT: Mask of WhereLoops to run in reverse order */\n){\n  u8 revSet;            /* True if rev is known */\n  u8 rev;               /* Composite sort order */\n  u8 revIdx;            /* Index sort order */\n  u8 isOrderDistinct;   /* All prior WhereLoops are order-distinct */\n  u8 distinctColumns;   /* True if the loop has UNIQUE NOT NULL columns */\n  u8 isMatch;           /* iColumn matches a term of the ORDER BY clause */\n  u16 eqOpMask;         /* Allowed equality operators */\n  u16 nKeyCol;          /* Number of key columns in pIndex */\n  u16 nColumn;          /* Total number of ordered columns in the index */\n  u16 nOrderBy;         /* Number terms in the ORDER BY clause */\n  int iLoop;            /* Index of WhereLoop in pPath being processed */\n  int i, j;             /* Loop counters */\n  int iCur;             /* Cursor number for current WhereLoop */\n  int iColumn;          /* A column number within table iCur */\n  WhereLoop *pLoop = 0; /* Current WhereLoop being processed. */\n  WhereTerm *pTerm;     /* A single term of the WHERE clause */\n  Expr *pOBExpr;        /* An expression from the ORDER BY clause */\n  CollSeq *pColl;       /* COLLATE function from an ORDER BY clause term */\n  Index *pIndex;        /* The index associated with pLoop */\n  sqlite3 *db = pWInfo->pParse->db;  /* Database connection */\n  Bitmask obSat = 0;    /* Mask of ORDER BY terms satisfied so far */\n  Bitmask obDone;       /* Mask of all ORDER BY terms */\n  Bitmask orderDistinctMask;  /* Mask of all well-ordered loops */\n  Bitmask ready;              /* Mask of inner loops */\n\n  /*\n  ** We say the WhereLoop is \"one-row\" if it generates no more than one\n  ** row of output.  A WhereLoop is one-row if all of the following are true:\n  **  (a) All index columns match with WHERE_COLUMN_EQ.\n  **  (b) The index is unique\n  ** Any WhereLoop with an WHERE_COLUMN_EQ constraint on the rowid is one-row.\n  ** Every one-row WhereLoop will have the WHERE_ONEROW bit set in wsFlags.\n  **\n  ** We say the WhereLoop is \"order-distinct\" if the set of columns from\n  ** that WhereLoop that are in the ORDER BY clause are different for every\n  ** row of the WhereLoop.  Every one-row WhereLoop is automatically\n  ** order-distinct.   A WhereLoop that has no columns in the ORDER BY clause\n  ** is not order-distinct. To be order-distinct is not quite the same as being\n  ** UNIQUE since a UNIQUE column or index can have multiple rows that \n  ** are NULL and NULL values are equivalent for the purpose of order-distinct.\n  ** To be order-distinct, the columns must be UNIQUE and NOT NULL.\n  **\n  ** The rowid for a table is always UNIQUE and NOT NULL so whenever the\n  ** rowid appears in the ORDER BY clause, the corresponding WhereLoop is\n  ** automatically order-distinct.\n  */\n\n  assert( pOrderBy!=0 );\n  if( nLoop && OptimizationDisabled(db, SQLITE_OrderByIdxJoin) ) return 0;\n\n  nOrderBy = pOrderBy->nExpr;\n  testcase( nOrderBy==BMS-1 );\n  if( nOrderBy>BMS-1 ) return 0;  /* Cannot optimize overly large ORDER BYs */\n  isOrderDistinct = 1;\n  obDone = MASKBIT(nOrderBy)-1;\n  orderDistinctMask = 0;\n  ready = 0;\n  eqOpMask = WO_EQ | WO_IS | WO_ISNULL;\n  if( wctrlFlags & WHERE_ORDERBY_LIMIT ) eqOpMask |= WO_IN;\n  for(iLoop=0; isOrderDistinct && obSat<obDone && iLoop<=nLoop; iLoop++){\n    if( iLoop>0 ) ready |= pLoop->maskSelf;\n    if( iLoop<nLoop ){\n      pLoop = pPath->aLoop[iLoop];\n      if( wctrlFlags & WHERE_ORDERBY_LIMIT ) continue;\n    }else{\n      pLoop = pLast;\n    }\n    if( pLoop->wsFlags & WHERE_VIRTUALTABLE ){\n      if( pLoop->u.vtab.isOrdered ) obSat = obDone;\n      break;\n    }else{\n      pLoop->u.btree.nIdxCol = 0;\n    }\n    iCur = pWInfo->pTabList->a[pLoop->iTab].iCursor;\n\n    /* Mark off any ORDER BY term X that is a column in the table of\n    ** the current loop for which there is term in the WHERE\n    ** clause of the form X IS NULL or X=? that reference only outer\n    ** loops.\n    */\n    for(i=0; i<nOrderBy; i++){\n      if( MASKBIT(i) & obSat ) continue;\n      pOBExpr = sqlite3ExprSkipCollate(pOrderBy->a[i].pExpr);\n      if( pOBExpr->op!=TK_COLUMN ) continue;\n      if( pOBExpr->iTable!=iCur ) continue;\n      pTerm = sqlite3WhereFindTerm(&pWInfo->sWC, iCur, pOBExpr->iColumn,\n                       ~ready, eqOpMask, 0);\n      if( pTerm==0 ) continue;\n      if( pTerm->eOperator==WO_IN ){\n        /* IN terms are only valid for sorting in the ORDER BY LIMIT \n        ** optimization, and then only if they are actually used\n        ** by the query plan */\n        assert( wctrlFlags & WHERE_ORDERBY_LIMIT );\n        for(j=0; j<pLoop->nLTerm && pTerm!=pLoop->aLTerm[j]; j++){}\n        if( j>=pLoop->nLTerm ) continue;\n      }\n      if( (pTerm->eOperator&(WO_EQ|WO_IS))!=0 && pOBExpr->iColumn>=0 ){\n        if( sqlite3ExprCollSeqMatch(pWInfo->pParse, \n                  pOrderBy->a[i].pExpr, pTerm->pExpr)==0 ){\n          continue;\n        }\n        testcase( pTerm->pExpr->op==TK_IS );\n      }\n      obSat |= MASKBIT(i);\n    }\n\n    if( (pLoop->wsFlags & WHERE_ONEROW)==0 ){\n      if( pLoop->wsFlags & WHERE_IPK ){\n        pIndex = 0;\n        nKeyCol = 0;\n        nColumn = 1;\n      }else if( (pIndex = pLoop->u.btree.pIndex)==0 || pIndex->bUnordered ){\n        return 0;\n      }else{\n        nKeyCol = pIndex->nKeyCol;\n        nColumn = pIndex->nColumn;\n        assert( nColumn==nKeyCol+1 || !HasRowid(pIndex->pTable) );\n        assert( pIndex->aiColumn[nColumn-1]==XN_ROWID\n                          || !HasRowid(pIndex->pTable));\n        isOrderDistinct = IsUniqueIndex(pIndex);\n      }\n\n      /* Loop through all columns of the index and deal with the ones\n      ** that are not constrained by == or IN.\n      */\n      rev = revSet = 0;\n      distinctColumns = 0;\n      for(j=0; j<nColumn; j++){\n        u8 bOnce = 1; /* True to run the ORDER BY search loop */\n\n        assert( j>=pLoop->u.btree.nEq \n            || (pLoop->aLTerm[j]==0)==(j<pLoop->nSkip)\n        );\n        if( j<pLoop->u.btree.nEq && j>=pLoop->nSkip ){\n          u16 eOp = pLoop->aLTerm[j]->eOperator;\n\n          /* Skip over == and IS and ISNULL terms.  (Also skip IN terms when\n          ** doing WHERE_ORDERBY_LIMIT processing). \n          **\n          ** If the current term is a column of an ((?,?) IN (SELECT...)) \n          ** expression for which the SELECT returns more than one column,\n          ** check that it is the only column used by this loop. Otherwise,\n          ** if it is one of two or more, none of the columns can be\n          ** considered to match an ORDER BY term.  */\n          if( (eOp & eqOpMask)!=0 ){\n            if( eOp & WO_ISNULL ){\n              testcase( isOrderDistinct );\n              isOrderDistinct = 0;\n            }\n            continue;  \n          }else if( ALWAYS(eOp & WO_IN) ){\n            /* ALWAYS() justification: eOp is an equality operator due to the\n            ** j<pLoop->u.btree.nEq constraint above.  Any equality other\n            ** than WO_IN is captured by the previous \"if\".  So this one\n            ** always has to be WO_IN. */\n            Expr *pX = pLoop->aLTerm[j]->pExpr;\n            for(i=j+1; i<pLoop->u.btree.nEq; i++){\n              if( pLoop->aLTerm[i]->pExpr==pX ){\n                assert( (pLoop->aLTerm[i]->eOperator & WO_IN) );\n                bOnce = 0;\n                break;\n              }\n            }\n          }\n        }\n\n        /* Get the column number in the table (iColumn) and sort order\n        ** (revIdx) for the j-th column of the index.\n        */\n        if( pIndex ){\n          iColumn = pIndex->aiColumn[j];\n          revIdx = pIndex->aSortOrder[j];\n          if( iColumn==pIndex->pTable->iPKey ) iColumn = XN_ROWID;\n        }else{\n          iColumn = XN_ROWID;\n          revIdx = 0;\n        }\n\n        /* An unconstrained column that might be NULL means that this\n        ** WhereLoop is not well-ordered\n        */\n        if( isOrderDistinct\n         && iColumn>=0\n         && j>=pLoop->u.btree.nEq\n         && pIndex->pTable->aCol[iColumn].notNull==0\n        ){\n          isOrderDistinct = 0;\n        }\n\n        /* Find the ORDER BY term that corresponds to the j-th column\n        ** of the index and mark that ORDER BY term off \n        */\n        isMatch = 0;\n        for(i=0; bOnce && i<nOrderBy; i++){\n          if( MASKBIT(i) & obSat ) continue;\n          pOBExpr = sqlite3ExprSkipCollate(pOrderBy->a[i].pExpr);\n          testcase( wctrlFlags & WHERE_GROUPBY );\n          testcase( wctrlFlags & WHERE_DISTINCTBY );\n          if( (wctrlFlags & (WHERE_GROUPBY|WHERE_DISTINCTBY))==0 ) bOnce = 0;\n          if( iColumn>=XN_ROWID ){\n            if( pOBExpr->op!=TK_COLUMN ) continue;\n            if( pOBExpr->iTable!=iCur ) continue;\n            if( pOBExpr->iColumn!=iColumn ) continue;\n          }else{\n            Expr *pIdxExpr = pIndex->aColExpr->a[j].pExpr;\n            if( sqlite3ExprCompareSkip(pOBExpr, pIdxExpr, iCur) ){\n              continue;\n            }\n          }\n          if( iColumn!=XN_ROWID ){\n            pColl = sqlite3ExprNNCollSeq(pWInfo->pParse, pOrderBy->a[i].pExpr);\n            if( sqlite3StrICmp(pColl->zName, pIndex->azColl[j])!=0 ) continue;\n          }\n          pLoop->u.btree.nIdxCol = j+1;\n          isMatch = 1;\n          break;\n        }\n        if( isMatch && (wctrlFlags & WHERE_GROUPBY)==0 ){\n          /* Make sure the sort order is compatible in an ORDER BY clause.\n          ** Sort order is irrelevant for a GROUP BY clause. */\n          if( revSet ){\n            if( (rev ^ revIdx)!=pOrderBy->a[i].sortOrder ) isMatch = 0;\n          }else{\n            rev = revIdx ^ pOrderBy->a[i].sortOrder;\n            if( rev ) *pRevMask |= MASKBIT(iLoop);\n            revSet = 1;\n          }\n        }\n        if( isMatch ){\n          if( iColumn==XN_ROWID ){\n            testcase( distinctColumns==0 );\n            distinctColumns = 1;\n          }\n          obSat |= MASKBIT(i);\n        }else{\n          /* No match found */\n          if( j==0 || j<nKeyCol ){\n            testcase( isOrderDistinct!=0 );\n            isOrderDistinct = 0;\n          }\n          break;\n        }\n      } /* end Loop over all index columns */\n      if( distinctColumns ){\n        testcase( isOrderDistinct==0 );\n        isOrderDistinct = 1;\n      }\n    } /* end-if not one-row */\n\n    /* Mark off any other ORDER BY terms that reference pLoop */\n    if( isOrderDistinct ){\n      orderDistinctMask |= pLoop->maskSelf;\n      for(i=0; i<nOrderBy; i++){\n        Expr *p;\n        Bitmask mTerm;\n        if( MASKBIT(i) & obSat ) continue;\n        p = pOrderBy->a[i].pExpr;\n        mTerm = sqlite3WhereExprUsage(&pWInfo->sMaskSet,p);\n        if( mTerm==0 && !sqlite3ExprIsConstant(p) ) continue;\n        if( (mTerm&~orderDistinctMask)==0 ){\n          obSat |= MASKBIT(i);\n        }\n      }\n    }\n  } /* End the loop over all WhereLoops from outer-most down to inner-most */\n  if( obSat==obDone ) return (i8)nOrderBy;\n  if( !isOrderDistinct ){\n    for(i=nOrderBy-1; i>0; i--){\n      Bitmask m = MASKBIT(i) - 1;\n      if( (obSat&m)==m ) return i;\n    }\n    return 0;\n  }\n  return -1;\n}\n\n\n/*\n** If the WHERE_GROUPBY flag is set in the mask passed to sqlite3WhereBegin(),\n** the planner assumes that the specified pOrderBy list is actually a GROUP\n** BY clause - and so any order that groups rows as required satisfies the\n** request.\n**\n** Normally, in this case it is not possible for the caller to determine\n** whether or not the rows are really being delivered in sorted order, or\n** just in some other order that provides the required grouping. However,\n** if the WHERE_SORTBYGROUP flag is also passed to sqlite3WhereBegin(), then\n** this function may be called on the returned WhereInfo object. It returns\n** true if the rows really will be sorted in the specified order, or false\n** otherwise.\n**\n** For example, assuming:\n**\n**   CREATE INDEX i1 ON t1(x, Y);\n**\n** then\n**\n**   SELECT * FROM t1 GROUP BY x,y ORDER BY x,y;   -- IsSorted()==1\n**   SELECT * FROM t1 GROUP BY y,x ORDER BY y,x;   -- IsSorted()==0\n*/\nSQLITE_PRIVATE int sqlite3WhereIsSorted(WhereInfo *pWInfo){\n  assert( pWInfo->wctrlFlags & WHERE_GROUPBY );\n  assert( pWInfo->wctrlFlags & WHERE_SORTBYGROUP );\n  return pWInfo->sorted;\n}\n\n#ifdef WHERETRACE_ENABLED\n/* For debugging use only: */\nstatic const char *wherePathName(WherePath *pPath, int nLoop, WhereLoop *pLast){\n  static char zName[65];\n  int i;\n  for(i=0; i<nLoop; i++){ zName[i] = pPath->aLoop[i]->cId; }\n  if( pLast ) zName[i++] = pLast->cId;\n  zName[i] = 0;\n  return zName;\n}\n#endif\n\n/*\n** Return the cost of sorting nRow rows, assuming that the keys have \n** nOrderby columns and that the first nSorted columns are already in\n** order.\n*/\nstatic LogEst whereSortingCost(\n  WhereInfo *pWInfo,\n  LogEst nRow,\n  int nOrderBy,\n  int nSorted\n){\n  /* TUNING: Estimated cost of a full external sort, where N is \n  ** the number of rows to sort is:\n  **\n  **   cost = (3.0 * N * log(N)).\n  ** \n  ** Or, if the order-by clause has X terms but only the last Y \n  ** terms are out of order, then block-sorting will reduce the \n  ** sorting cost to:\n  **\n  **   cost = (3.0 * N * log(N)) * (Y/X)\n  **\n  ** The (Y/X) term is implemented using stack variable rScale\n  ** below.  */\n  LogEst rScale, rSortCost;\n  assert( nOrderBy>0 && 66==sqlite3LogEst(100) );\n  rScale = sqlite3LogEst((nOrderBy-nSorted)*100/nOrderBy) - 66;\n  rSortCost = nRow + rScale + 16;\n\n  /* Multiple by log(M) where M is the number of output rows.\n  ** Use the LIMIT for M if it is smaller */\n  if( (pWInfo->wctrlFlags & WHERE_USE_LIMIT)!=0 && pWInfo->iLimit<nRow ){\n    nRow = pWInfo->iLimit;\n  }\n  rSortCost += estLog(nRow);\n  return rSortCost;\n}\n\n/*\n** Given the list of WhereLoop objects at pWInfo->pLoops, this routine\n** attempts to find the lowest cost path that visits each WhereLoop\n** once.  This path is then loaded into the pWInfo->a[].pWLoop fields.\n**\n** Assume that the total number of output rows that will need to be sorted\n** will be nRowEst (in the 10*log2 representation).  Or, ignore sorting\n** costs if nRowEst==0.\n**\n** Return SQLITE_OK on success or SQLITE_NOMEM of a memory allocation\n** error occurs.\n*/\nstatic int wherePathSolver(WhereInfo *pWInfo, LogEst nRowEst){\n  int mxChoice;             /* Maximum number of simultaneous paths tracked */\n  int nLoop;                /* Number of terms in the join */\n  Parse *pParse;            /* Parsing context */\n  sqlite3 *db;              /* The database connection */\n  int iLoop;                /* Loop counter over the terms of the join */\n  int ii, jj;               /* Loop counters */\n  int mxI = 0;              /* Index of next entry to replace */\n  int nOrderBy;             /* Number of ORDER BY clause terms */\n  LogEst mxCost = 0;        /* Maximum cost of a set of paths */\n  LogEst mxUnsorted = 0;    /* Maximum unsorted cost of a set of path */\n  int nTo, nFrom;           /* Number of valid entries in aTo[] and aFrom[] */\n  WherePath *aFrom;         /* All nFrom paths at the previous level */\n  WherePath *aTo;           /* The nTo best paths at the current level */\n  WherePath *pFrom;         /* An element of aFrom[] that we are working on */\n  WherePath *pTo;           /* An element of aTo[] that we are working on */\n  WhereLoop *pWLoop;        /* One of the WhereLoop objects */\n  WhereLoop **pX;           /* Used to divy up the pSpace memory */\n  LogEst *aSortCost = 0;    /* Sorting and partial sorting costs */\n  char *pSpace;             /* Temporary memory used by this routine */\n  int nSpace;               /* Bytes of space allocated at pSpace */\n\n  pParse = pWInfo->pParse;\n  db = pParse->db;\n  nLoop = pWInfo->nLevel;\n  /* TUNING: For simple queries, only the best path is tracked.\n  ** For 2-way joins, the 5 best paths are followed.\n  ** For joins of 3 or more tables, track the 10 best paths */\n  mxChoice = (nLoop<=1) ? 1 : (nLoop==2 ? 5 : 10);\n  assert( nLoop<=pWInfo->pTabList->nSrc );\n  WHERETRACE(0x002, (\"---- begin solver.  (nRowEst=%d)\\n\", nRowEst));\n\n  /* If nRowEst is zero and there is an ORDER BY clause, ignore it. In this\n  ** case the purpose of this call is to estimate the number of rows returned\n  ** by the overall query. Once this estimate has been obtained, the caller\n  ** will invoke this function a second time, passing the estimate as the\n  ** nRowEst parameter.  */\n  if( pWInfo->pOrderBy==0 || nRowEst==0 ){\n    nOrderBy = 0;\n  }else{\n    nOrderBy = pWInfo->pOrderBy->nExpr;\n  }\n\n  /* Allocate and initialize space for aTo, aFrom and aSortCost[] */\n  nSpace = (sizeof(WherePath)+sizeof(WhereLoop*)*nLoop)*mxChoice*2;\n  nSpace += sizeof(LogEst) * nOrderBy;\n  pSpace = sqlite3DbMallocRawNN(db, nSpace);\n  if( pSpace==0 ) return SQLITE_NOMEM_BKPT;\n  aTo = (WherePath*)pSpace;\n  aFrom = aTo+mxChoice;\n  memset(aFrom, 0, sizeof(aFrom[0]));\n  pX = (WhereLoop**)(aFrom+mxChoice);\n  for(ii=mxChoice*2, pFrom=aTo; ii>0; ii--, pFrom++, pX += nLoop){\n    pFrom->aLoop = pX;\n  }\n  if( nOrderBy ){\n    /* If there is an ORDER BY clause and it is not being ignored, set up\n    ** space for the aSortCost[] array. Each element of the aSortCost array\n    ** is either zero - meaning it has not yet been initialized - or the\n    ** cost of sorting nRowEst rows of data where the first X terms of\n    ** the ORDER BY clause are already in order, where X is the array \n    ** index.  */\n    aSortCost = (LogEst*)pX;\n    memset(aSortCost, 0, sizeof(LogEst) * nOrderBy);\n  }\n  assert( aSortCost==0 || &pSpace[nSpace]==(char*)&aSortCost[nOrderBy] );\n  assert( aSortCost!=0 || &pSpace[nSpace]==(char*)pX );\n\n  /* Seed the search with a single WherePath containing zero WhereLoops.\n  **\n  ** TUNING: Do not let the number of iterations go above 28.  If the cost\n  ** of computing an automatic index is not paid back within the first 28\n  ** rows, then do not use the automatic index. */\n  aFrom[0].nRow = MIN(pParse->nQueryLoop, 48);  assert( 48==sqlite3LogEst(28) );\n  nFrom = 1;\n  assert( aFrom[0].isOrdered==0 );\n  if( nOrderBy ){\n    /* If nLoop is zero, then there are no FROM terms in the query. Since\n    ** in this case the query may return a maximum of one row, the results\n    ** are already in the requested order. Set isOrdered to nOrderBy to\n    ** indicate this. Or, if nLoop is greater than zero, set isOrdered to\n    ** -1, indicating that the result set may or may not be ordered, \n    ** depending on the loops added to the current plan.  */\n    aFrom[0].isOrdered = nLoop>0 ? -1 : nOrderBy;\n  }\n\n  /* Compute successively longer WherePaths using the previous generation\n  ** of WherePaths as the basis for the next.  Keep track of the mxChoice\n  ** best paths at each generation */\n  for(iLoop=0; iLoop<nLoop; iLoop++){\n    nTo = 0;\n    for(ii=0, pFrom=aFrom; ii<nFrom; ii++, pFrom++){\n      for(pWLoop=pWInfo->pLoops; pWLoop; pWLoop=pWLoop->pNextLoop){\n        LogEst nOut;                      /* Rows visited by (pFrom+pWLoop) */\n        LogEst rCost;                     /* Cost of path (pFrom+pWLoop) */\n        LogEst rUnsorted;                 /* Unsorted cost of (pFrom+pWLoop) */\n        i8 isOrdered = pFrom->isOrdered;  /* isOrdered for (pFrom+pWLoop) */\n        Bitmask maskNew;                  /* Mask of src visited by (..) */\n        Bitmask revMask = 0;              /* Mask of rev-order loops for (..) */\n\n        if( (pWLoop->prereq & ~pFrom->maskLoop)!=0 ) continue;\n        if( (pWLoop->maskSelf & pFrom->maskLoop)!=0 ) continue;\n        if( (pWLoop->wsFlags & WHERE_AUTO_INDEX)!=0 && pFrom->nRow<10 ){\n          /* Do not use an automatic index if the this loop is expected\n          ** to run less than 2 times. */\n          assert( 10==sqlite3LogEst(2) );\n          continue;\n        }\n        /* At this point, pWLoop is a candidate to be the next loop. \n        ** Compute its cost */\n        rUnsorted = sqlite3LogEstAdd(pWLoop->rSetup,pWLoop->rRun + pFrom->nRow);\n        rUnsorted = sqlite3LogEstAdd(rUnsorted, pFrom->rUnsorted);\n        nOut = pFrom->nRow + pWLoop->nOut;\n        maskNew = pFrom->maskLoop | pWLoop->maskSelf;\n        if( isOrdered<0 ){\n          isOrdered = wherePathSatisfiesOrderBy(pWInfo,\n                       pWInfo->pOrderBy, pFrom, pWInfo->wctrlFlags,\n                       iLoop, pWLoop, &revMask);\n        }else{\n          revMask = pFrom->revLoop;\n        }\n        if( isOrdered>=0 && isOrdered<nOrderBy ){\n          if( aSortCost[isOrdered]==0 ){\n            aSortCost[isOrdered] = whereSortingCost(\n                pWInfo, nRowEst, nOrderBy, isOrdered\n            );\n          }\n          rCost = sqlite3LogEstAdd(rUnsorted, aSortCost[isOrdered]);\n\n          WHERETRACE(0x002,\n              (\"---- sort cost=%-3d (%d/%d) increases cost %3d to %-3d\\n\",\n               aSortCost[isOrdered], (nOrderBy-isOrdered), nOrderBy, \n               rUnsorted, rCost));\n        }else{\n          rCost = rUnsorted;\n          rUnsorted -= 2;  /* TUNING:  Slight bias in favor of no-sort plans */\n        }\n\n        /* Check to see if pWLoop should be added to the set of\n        ** mxChoice best-so-far paths.\n        **\n        ** First look for an existing path among best-so-far paths\n        ** that covers the same set of loops and has the same isOrdered\n        ** setting as the current path candidate.\n        **\n        ** The term \"((pTo->isOrdered^isOrdered)&0x80)==0\" is equivalent\n        ** to (pTo->isOrdered==(-1))==(isOrdered==(-1))\" for the range\n        ** of legal values for isOrdered, -1..64.\n        */\n        for(jj=0, pTo=aTo; jj<nTo; jj++, pTo++){\n          if( pTo->maskLoop==maskNew\n           && ((pTo->isOrdered^isOrdered)&0x80)==0\n          ){\n            testcase( jj==nTo-1 );\n            break;\n          }\n        }\n        if( jj>=nTo ){\n          /* None of the existing best-so-far paths match the candidate. */\n          if( nTo>=mxChoice\n           && (rCost>mxCost || (rCost==mxCost && rUnsorted>=mxUnsorted))\n          ){\n            /* The current candidate is no better than any of the mxChoice\n            ** paths currently in the best-so-far buffer.  So discard\n            ** this candidate as not viable. */\n#ifdef WHERETRACE_ENABLED /* 0x4 */\n            if( sqlite3WhereTrace&0x4 ){\n              sqlite3DebugPrintf(\"Skip   %s cost=%-3d,%3d,%3d order=%c\\n\",\n                  wherePathName(pFrom, iLoop, pWLoop), rCost, nOut, rUnsorted,\n                  isOrdered>=0 ? isOrdered+'0' : '?');\n            }\n#endif\n            continue;\n          }\n          /* If we reach this points it means that the new candidate path\n          ** needs to be added to the set of best-so-far paths. */\n          if( nTo<mxChoice ){\n            /* Increase the size of the aTo set by one */\n            jj = nTo++;\n          }else{\n            /* New path replaces the prior worst to keep count below mxChoice */\n            jj = mxI;\n          }\n          pTo = &aTo[jj];\n#ifdef WHERETRACE_ENABLED /* 0x4 */\n          if( sqlite3WhereTrace&0x4 ){\n            sqlite3DebugPrintf(\"New    %s cost=%-3d,%3d,%3d order=%c\\n\",\n                wherePathName(pFrom, iLoop, pWLoop), rCost, nOut, rUnsorted,\n                isOrdered>=0 ? isOrdered+'0' : '?');\n          }\n#endif\n        }else{\n          /* Control reaches here if best-so-far path pTo=aTo[jj] covers the\n          ** same set of loops and has the same isOrdered setting as the\n          ** candidate path.  Check to see if the candidate should replace\n          ** pTo or if the candidate should be skipped.\n          ** \n          ** The conditional is an expanded vector comparison equivalent to:\n          **   (pTo->rCost,pTo->nRow,pTo->rUnsorted) <= (rCost,nOut,rUnsorted)\n          */\n          if( pTo->rCost<rCost \n           || (pTo->rCost==rCost\n               && (pTo->nRow<nOut\n                   || (pTo->nRow==nOut && pTo->rUnsorted<=rUnsorted)\n                  )\n              )\n          ){\n#ifdef WHERETRACE_ENABLED /* 0x4 */\n            if( sqlite3WhereTrace&0x4 ){\n              sqlite3DebugPrintf(\n                  \"Skip   %s cost=%-3d,%3d,%3d order=%c\",\n                  wherePathName(pFrom, iLoop, pWLoop), rCost, nOut, rUnsorted,\n                  isOrdered>=0 ? isOrdered+'0' : '?');\n              sqlite3DebugPrintf(\"   vs %s cost=%-3d,%3d,%3d order=%c\\n\",\n                  wherePathName(pTo, iLoop+1, 0), pTo->rCost, pTo->nRow,\n                  pTo->rUnsorted, pTo->isOrdered>=0 ? pTo->isOrdered+'0' : '?');\n            }\n#endif\n            /* Discard the candidate path from further consideration */\n            testcase( pTo->rCost==rCost );\n            continue;\n          }\n          testcase( pTo->rCost==rCost+1 );\n          /* Control reaches here if the candidate path is better than the\n          ** pTo path.  Replace pTo with the candidate. */\n#ifdef WHERETRACE_ENABLED /* 0x4 */\n          if( sqlite3WhereTrace&0x4 ){\n            sqlite3DebugPrintf(\n                \"Update %s cost=%-3d,%3d,%3d order=%c\",\n                wherePathName(pFrom, iLoop, pWLoop), rCost, nOut, rUnsorted,\n                isOrdered>=0 ? isOrdered+'0' : '?');\n            sqlite3DebugPrintf(\"  was %s cost=%-3d,%3d,%3d order=%c\\n\",\n                wherePathName(pTo, iLoop+1, 0), pTo->rCost, pTo->nRow,\n                pTo->rUnsorted, pTo->isOrdered>=0 ? pTo->isOrdered+'0' : '?');\n          }\n#endif\n        }\n        /* pWLoop is a winner.  Add it to the set of best so far */\n        pTo->maskLoop = pFrom->maskLoop | pWLoop->maskSelf;\n        pTo->revLoop = revMask;\n        pTo->nRow = nOut;\n        pTo->rCost = rCost;\n        pTo->rUnsorted = rUnsorted;\n        pTo->isOrdered = isOrdered;\n        memcpy(pTo->aLoop, pFrom->aLoop, sizeof(WhereLoop*)*iLoop);\n        pTo->aLoop[iLoop] = pWLoop;\n        if( nTo>=mxChoice ){\n          mxI = 0;\n          mxCost = aTo[0].rCost;\n          mxUnsorted = aTo[0].nRow;\n          for(jj=1, pTo=&aTo[1]; jj<mxChoice; jj++, pTo++){\n            if( pTo->rCost>mxCost \n             || (pTo->rCost==mxCost && pTo->rUnsorted>mxUnsorted) \n            ){\n              mxCost = pTo->rCost;\n              mxUnsorted = pTo->rUnsorted;\n              mxI = jj;\n            }\n          }\n        }\n      }\n    }\n\n#ifdef WHERETRACE_ENABLED  /* >=2 */\n    if( sqlite3WhereTrace & 0x02 ){\n      sqlite3DebugPrintf(\"---- after round %d ----\\n\", iLoop);\n      for(ii=0, pTo=aTo; ii<nTo; ii++, pTo++){\n        sqlite3DebugPrintf(\" %s cost=%-3d nrow=%-3d order=%c\",\n           wherePathName(pTo, iLoop+1, 0), pTo->rCost, pTo->nRow,\n           pTo->isOrdered>=0 ? (pTo->isOrdered+'0') : '?');\n        if( pTo->isOrdered>0 ){\n          sqlite3DebugPrintf(\" rev=0x%llx\\n\", pTo->revLoop);\n        }else{\n          sqlite3DebugPrintf(\"\\n\");\n        }\n      }\n    }\n#endif\n\n    /* Swap the roles of aFrom and aTo for the next generation */\n    pFrom = aTo;\n    aTo = aFrom;\n    aFrom = pFrom;\n    nFrom = nTo;\n  }\n\n  if( nFrom==0 ){\n    sqlite3ErrorMsg(pParse, \"no query solution\");\n    sqlite3DbFreeNN(db, pSpace);\n    return SQLITE_ERROR;\n  }\n  \n  /* Find the lowest cost path.  pFrom will be left pointing to that path */\n  pFrom = aFrom;\n  for(ii=1; ii<nFrom; ii++){\n    if( pFrom->rCost>aFrom[ii].rCost ) pFrom = &aFrom[ii];\n  }\n  assert( pWInfo->nLevel==nLoop );\n  /* Load the lowest cost path into pWInfo */\n  for(iLoop=0; iLoop<nLoop; iLoop++){\n    WhereLevel *pLevel = pWInfo->a + iLoop;\n    pLevel->pWLoop = pWLoop = pFrom->aLoop[iLoop];\n    pLevel->iFrom = pWLoop->iTab;\n    pLevel->iTabCur = pWInfo->pTabList->a[pLevel->iFrom].iCursor;\n  }\n  if( (pWInfo->wctrlFlags & WHERE_WANT_DISTINCT)!=0\n   && (pWInfo->wctrlFlags & WHERE_DISTINCTBY)==0\n   && pWInfo->eDistinct==WHERE_DISTINCT_NOOP\n   && nRowEst\n  ){\n    Bitmask notUsed;\n    int rc = wherePathSatisfiesOrderBy(pWInfo, pWInfo->pResultSet, pFrom,\n                 WHERE_DISTINCTBY, nLoop-1, pFrom->aLoop[nLoop-1], &notUsed);\n    if( rc==pWInfo->pResultSet->nExpr ){\n      pWInfo->eDistinct = WHERE_DISTINCT_ORDERED;\n    }\n  }\n  if( pWInfo->pOrderBy ){\n    if( pWInfo->wctrlFlags & WHERE_DISTINCTBY ){\n      if( pFrom->isOrdered==pWInfo->pOrderBy->nExpr ){\n        pWInfo->eDistinct = WHERE_DISTINCT_ORDERED;\n      }\n    }else{\n      pWInfo->nOBSat = pFrom->isOrdered;\n      pWInfo->revMask = pFrom->revLoop;\n      if( pWInfo->nOBSat<=0 ){\n        pWInfo->nOBSat = 0;\n        if( nLoop>0 ){\n          u32 wsFlags = pFrom->aLoop[nLoop-1]->wsFlags;\n          if( (wsFlags & WHERE_ONEROW)==0 \n           && (wsFlags&(WHERE_IPK|WHERE_COLUMN_IN))!=(WHERE_IPK|WHERE_COLUMN_IN)\n          ){\n            Bitmask m = 0;\n            int rc = wherePathSatisfiesOrderBy(pWInfo, pWInfo->pOrderBy, pFrom,\n                      WHERE_ORDERBY_LIMIT, nLoop-1, pFrom->aLoop[nLoop-1], &m);\n            testcase( wsFlags & WHERE_IPK );\n            testcase( wsFlags & WHERE_COLUMN_IN );\n            if( rc==pWInfo->pOrderBy->nExpr ){\n              pWInfo->bOrderedInnerLoop = 1;\n              pWInfo->revMask = m;\n            }\n          }\n        }\n      }\n    }\n    if( (pWInfo->wctrlFlags & WHERE_SORTBYGROUP)\n        && pWInfo->nOBSat==pWInfo->pOrderBy->nExpr && nLoop>0\n    ){\n      Bitmask revMask = 0;\n      int nOrder = wherePathSatisfiesOrderBy(pWInfo, pWInfo->pOrderBy, \n          pFrom, 0, nLoop-1, pFrom->aLoop[nLoop-1], &revMask\n      );\n      assert( pWInfo->sorted==0 );\n      if( nOrder==pWInfo->pOrderBy->nExpr ){\n        pWInfo->sorted = 1;\n        pWInfo->revMask = revMask;\n      }\n    }\n  }\n\n\n  pWInfo->nRowOut = pFrom->nRow;\n\n  /* Free temporary memory and return success */\n  sqlite3DbFreeNN(db, pSpace);\n  return SQLITE_OK;\n}\n\n/*\n** Most queries use only a single table (they are not joins) and have\n** simple == constraints against indexed fields.  This routine attempts\n** to plan those simple cases using much less ceremony than the\n** general-purpose query planner, and thereby yield faster sqlite3_prepare()\n** times for the common case.\n**\n** Return non-zero on success, if this query can be handled by this\n** no-frills query planner.  Return zero if this query needs the \n** general-purpose query planner.\n*/\nstatic int whereShortCut(WhereLoopBuilder *pBuilder){\n  WhereInfo *pWInfo;\n  struct SrcList_item *pItem;\n  WhereClause *pWC;\n  WhereTerm *pTerm;\n  WhereLoop *pLoop;\n  int iCur;\n  int j;\n  Table *pTab;\n  Index *pIdx;\n\n  pWInfo = pBuilder->pWInfo;\n  if( pWInfo->wctrlFlags & WHERE_OR_SUBCLAUSE ) return 0;\n  assert( pWInfo->pTabList->nSrc>=1 );\n  pItem = pWInfo->pTabList->a;\n  pTab = pItem->pTab;\n  if( IsVirtual(pTab) ) return 0;\n  if( pItem->fg.isIndexedBy ) return 0;\n  iCur = pItem->iCursor;\n  pWC = &pWInfo->sWC;\n  pLoop = pBuilder->pNew;\n  pLoop->wsFlags = 0;\n  pLoop->nSkip = 0;\n  pTerm = sqlite3WhereFindTerm(pWC, iCur, -1, 0, WO_EQ|WO_IS, 0);\n  if( pTerm ){\n    testcase( pTerm->eOperator & WO_IS );\n    pLoop->wsFlags = WHERE_COLUMN_EQ|WHERE_IPK|WHERE_ONEROW;\n    pLoop->aLTerm[0] = pTerm;\n    pLoop->nLTerm = 1;\n    pLoop->u.btree.nEq = 1;\n    /* TUNING: Cost of a rowid lookup is 10 */\n    pLoop->rRun = 33;  /* 33==sqlite3LogEst(10) */\n  }else{\n    for(pIdx=pTab->pIndex; pIdx; pIdx=pIdx->pNext){\n      int opMask;\n      assert( pLoop->aLTermSpace==pLoop->aLTerm );\n      if( !IsUniqueIndex(pIdx)\n       || pIdx->pPartIdxWhere!=0 \n       || pIdx->nKeyCol>ArraySize(pLoop->aLTermSpace) \n      ) continue;\n      opMask = pIdx->uniqNotNull ? (WO_EQ|WO_IS) : WO_EQ;\n      for(j=0; j<pIdx->nKeyCol; j++){\n        pTerm = sqlite3WhereFindTerm(pWC, iCur, j, 0, opMask, pIdx);\n        if( pTerm==0 ) break;\n        testcase( pTerm->eOperator & WO_IS );\n        pLoop->aLTerm[j] = pTerm;\n      }\n      if( j!=pIdx->nKeyCol ) continue;\n      pLoop->wsFlags = WHERE_COLUMN_EQ|WHERE_ONEROW|WHERE_INDEXED;\n      if( pIdx->isCovering || (pItem->colUsed & ~columnsInIndex(pIdx))==0 ){\n        pLoop->wsFlags |= WHERE_IDX_ONLY;\n      }\n      pLoop->nLTerm = j;\n      pLoop->u.btree.nEq = j;\n      pLoop->u.btree.pIndex = pIdx;\n      /* TUNING: Cost of a unique index lookup is 15 */\n      pLoop->rRun = 39;  /* 39==sqlite3LogEst(15) */\n      break;\n    }\n  }\n  if( pLoop->wsFlags ){\n    pLoop->nOut = (LogEst)1;\n    pWInfo->a[0].pWLoop = pLoop;\n    assert( pWInfo->sMaskSet.n==1 && iCur==pWInfo->sMaskSet.ix[0] );\n    pLoop->maskSelf = 1; /* sqlite3WhereGetMask(&pWInfo->sMaskSet, iCur); */\n    pWInfo->a[0].iTabCur = iCur;\n    pWInfo->nRowOut = 1;\n    if( pWInfo->pOrderBy ) pWInfo->nOBSat =  pWInfo->pOrderBy->nExpr;\n    if( pWInfo->wctrlFlags & WHERE_WANT_DISTINCT ){\n      pWInfo->eDistinct = WHERE_DISTINCT_UNIQUE;\n    }\n#ifdef SQLITE_DEBUG\n    pLoop->cId = '0';\n#endif\n    return 1;\n  }\n  return 0;\n}\n\n/*\n** Helper function for exprIsDeterministic().\n*/\nstatic int exprNodeIsDeterministic(Walker *pWalker, Expr *pExpr){\n  if( pExpr->op==TK_FUNCTION && ExprHasProperty(pExpr, EP_ConstFunc)==0 ){\n    pWalker->eCode = 0;\n    return WRC_Abort;\n  }\n  return WRC_Continue;\n}\n\n/*\n** Return true if the expression contains no non-deterministic SQL \n** functions. Do not consider non-deterministic SQL functions that are \n** part of sub-select statements.\n*/\nstatic int exprIsDeterministic(Expr *p){\n  Walker w;\n  memset(&w, 0, sizeof(w));\n  w.eCode = 1;\n  w.xExprCallback = exprNodeIsDeterministic;\n  w.xSelectCallback = sqlite3SelectWalkFail;\n  sqlite3WalkExpr(&w, p);\n  return w.eCode;\n}\n\n/*\n** Generate the beginning of the loop used for WHERE clause processing.\n** The return value is a pointer to an opaque structure that contains\n** information needed to terminate the loop.  Later, the calling routine\n** should invoke sqlite3WhereEnd() with the return value of this function\n** in order to complete the WHERE clause processing.\n**\n** If an error occurs, this routine returns NULL.\n**\n** The basic idea is to do a nested loop, one loop for each table in\n** the FROM clause of a select.  (INSERT and UPDATE statements are the\n** same as a SELECT with only a single table in the FROM clause.)  For\n** example, if the SQL is this:\n**\n**       SELECT * FROM t1, t2, t3 WHERE ...;\n**\n** Then the code generated is conceptually like the following:\n**\n**      foreach row1 in t1 do       \\    Code generated\n**        foreach row2 in t2 do      |-- by sqlite3WhereBegin()\n**          foreach row3 in t3 do   /\n**            ...\n**          end                     \\    Code generated\n**        end                        |-- by sqlite3WhereEnd()\n**      end                         /\n**\n** Note that the loops might not be nested in the order in which they\n** appear in the FROM clause if a different order is better able to make\n** use of indices.  Note also that when the IN operator appears in\n** the WHERE clause, it might result in additional nested loops for\n** scanning through all values on the right-hand side of the IN.\n**\n** There are Btree cursors associated with each table.  t1 uses cursor\n** number pTabList->a[0].iCursor.  t2 uses the cursor pTabList->a[1].iCursor.\n** And so forth.  This routine generates code to open those VDBE cursors\n** and sqlite3WhereEnd() generates the code to close them.\n**\n** The code that sqlite3WhereBegin() generates leaves the cursors named\n** in pTabList pointing at their appropriate entries.  The [...] code\n** can use OP_Column and OP_Rowid opcodes on these cursors to extract\n** data from the various tables of the loop.\n**\n** If the WHERE clause is empty, the foreach loops must each scan their\n** entire tables.  Thus a three-way join is an O(N^3) operation.  But if\n** the tables have indices and there are terms in the WHERE clause that\n** refer to those indices, a complete table scan can be avoided and the\n** code will run much faster.  Most of the work of this routine is checking\n** to see if there are indices that can be used to speed up the loop.\n**\n** Terms of the WHERE clause are also used to limit which rows actually\n** make it to the \"...\" in the middle of the loop.  After each \"foreach\",\n** terms of the WHERE clause that use only terms in that loop and outer\n** loops are evaluated and if false a jump is made around all subsequent\n** inner loops (or around the \"...\" if the test occurs within the inner-\n** most loop)\n**\n** OUTER JOINS\n**\n** An outer join of tables t1 and t2 is conceptally coded as follows:\n**\n**    foreach row1 in t1 do\n**      flag = 0\n**      foreach row2 in t2 do\n**        start:\n**          ...\n**          flag = 1\n**      end\n**      if flag==0 then\n**        move the row2 cursor to a null row\n**        goto start\n**      fi\n**    end\n**\n** ORDER BY CLAUSE PROCESSING\n**\n** pOrderBy is a pointer to the ORDER BY clause (or the GROUP BY clause\n** if the WHERE_GROUPBY flag is set in wctrlFlags) of a SELECT statement\n** if there is one.  If there is no ORDER BY clause or if this routine\n** is called from an UPDATE or DELETE statement, then pOrderBy is NULL.\n**\n** The iIdxCur parameter is the cursor number of an index.  If \n** WHERE_OR_SUBCLAUSE is set, iIdxCur is the cursor number of an index\n** to use for OR clause processing.  The WHERE clause should use this\n** specific cursor.  If WHERE_ONEPASS_DESIRED is set, then iIdxCur is\n** the first cursor in an array of cursors for all indices.  iIdxCur should\n** be used to compute the appropriate cursor depending on which index is\n** used.\n*/\nSQLITE_PRIVATE WhereInfo *sqlite3WhereBegin(\n  Parse *pParse,          /* The parser context */\n  SrcList *pTabList,      /* FROM clause: A list of all tables to be scanned */\n  Expr *pWhere,           /* The WHERE clause */\n  ExprList *pOrderBy,     /* An ORDER BY (or GROUP BY) clause, or NULL */\n  ExprList *pResultSet,   /* Query result set.  Req'd for DISTINCT */\n  u16 wctrlFlags,         /* The WHERE_* flags defined in sqliteInt.h */\n  int iAuxArg             /* If WHERE_OR_SUBCLAUSE is set, index cursor number\n                          ** If WHERE_USE_LIMIT, then the limit amount */\n){\n  int nByteWInfo;            /* Num. bytes allocated for WhereInfo struct */\n  int nTabList;              /* Number of elements in pTabList */\n  WhereInfo *pWInfo;         /* Will become the return value of this function */\n  Vdbe *v = pParse->pVdbe;   /* The virtual database engine */\n  Bitmask notReady;          /* Cursors that are not yet positioned */\n  WhereLoopBuilder sWLB;     /* The WhereLoop builder */\n  WhereMaskSet *pMaskSet;    /* The expression mask set */\n  WhereLevel *pLevel;        /* A single level in pWInfo->a[] */\n  WhereLoop *pLoop;          /* Pointer to a single WhereLoop object */\n  int ii;                    /* Loop counter */\n  sqlite3 *db;               /* Database connection */\n  int rc;                    /* Return code */\n  u8 bFordelete = 0;         /* OPFLAG_FORDELETE or zero, as appropriate */\n\n  assert( (wctrlFlags & WHERE_ONEPASS_MULTIROW)==0 || (\n        (wctrlFlags & WHERE_ONEPASS_DESIRED)!=0 \n     && (wctrlFlags & WHERE_OR_SUBCLAUSE)==0 \n  ));\n\n  /* Only one of WHERE_OR_SUBCLAUSE or WHERE_USE_LIMIT */\n  assert( (wctrlFlags & WHERE_OR_SUBCLAUSE)==0\n            || (wctrlFlags & WHERE_USE_LIMIT)==0 );\n\n  /* Variable initialization */\n  db = pParse->db;\n  memset(&sWLB, 0, sizeof(sWLB));\n\n  /* An ORDER/GROUP BY clause of more than 63 terms cannot be optimized */\n  testcase( pOrderBy && pOrderBy->nExpr==BMS-1 );\n  if( pOrderBy && pOrderBy->nExpr>=BMS ) pOrderBy = 0;\n  sWLB.pOrderBy = pOrderBy;\n\n  /* Disable the DISTINCT optimization if SQLITE_DistinctOpt is set via\n  ** sqlite3_test_ctrl(SQLITE_TESTCTRL_OPTIMIZATIONS,...) */\n  if( OptimizationDisabled(db, SQLITE_DistinctOpt) ){\n    wctrlFlags &= ~WHERE_WANT_DISTINCT;\n  }\n\n  /* The number of tables in the FROM clause is limited by the number of\n  ** bits in a Bitmask \n  */\n  testcase( pTabList->nSrc==BMS );\n  if( pTabList->nSrc>BMS ){\n    sqlite3ErrorMsg(pParse, \"at most %d tables in a join\", BMS);\n    return 0;\n  }\n\n  /* This function normally generates a nested loop for all tables in \n  ** pTabList.  But if the WHERE_OR_SUBCLAUSE flag is set, then we should\n  ** only generate code for the first table in pTabList and assume that\n  ** any cursors associated with subsequent tables are uninitialized.\n  */\n  nTabList = (wctrlFlags & WHERE_OR_SUBCLAUSE) ? 1 : pTabList->nSrc;\n\n  /* Allocate and initialize the WhereInfo structure that will become the\n  ** return value. A single allocation is used to store the WhereInfo\n  ** struct, the contents of WhereInfo.a[], the WhereClause structure\n  ** and the WhereMaskSet structure. Since WhereClause contains an 8-byte\n  ** field (type Bitmask) it must be aligned on an 8-byte boundary on\n  ** some architectures. Hence the ROUND8() below.\n  */\n  nByteWInfo = ROUND8(sizeof(WhereInfo)+(nTabList-1)*sizeof(WhereLevel));\n  pWInfo = sqlite3DbMallocRawNN(db, nByteWInfo + sizeof(WhereLoop));\n  if( db->mallocFailed ){\n    sqlite3DbFree(db, pWInfo);\n    pWInfo = 0;\n    goto whereBeginError;\n  }\n  pWInfo->pParse = pParse;\n  pWInfo->pTabList = pTabList;\n  pWInfo->pOrderBy = pOrderBy;\n  pWInfo->pWhere = pWhere;\n  pWInfo->pResultSet = pResultSet;\n  pWInfo->aiCurOnePass[0] = pWInfo->aiCurOnePass[1] = -1;\n  pWInfo->nLevel = nTabList;\n  pWInfo->iBreak = pWInfo->iContinue = sqlite3VdbeMakeLabel(v);\n  pWInfo->wctrlFlags = wctrlFlags;\n  pWInfo->iLimit = iAuxArg;\n  pWInfo->savedNQueryLoop = pParse->nQueryLoop;\n  memset(&pWInfo->nOBSat, 0, \n         offsetof(WhereInfo,sWC) - offsetof(WhereInfo,nOBSat));\n  memset(&pWInfo->a[0], 0, sizeof(WhereLoop)+nTabList*sizeof(WhereLevel));\n  assert( pWInfo->eOnePass==ONEPASS_OFF );  /* ONEPASS defaults to OFF */\n  pMaskSet = &pWInfo->sMaskSet;\n  sWLB.pWInfo = pWInfo;\n  sWLB.pWC = &pWInfo->sWC;\n  sWLB.pNew = (WhereLoop*)(((char*)pWInfo)+nByteWInfo);\n  assert( EIGHT_BYTE_ALIGNMENT(sWLB.pNew) );\n  whereLoopInit(sWLB.pNew);\n#ifdef SQLITE_DEBUG\n  sWLB.pNew->cId = '*';\n#endif\n\n  /* Split the WHERE clause into separate subexpressions where each\n  ** subexpression is separated by an AND operator.\n  */\n  initMaskSet(pMaskSet);\n  sqlite3WhereClauseInit(&pWInfo->sWC, pWInfo);\n  sqlite3WhereSplit(&pWInfo->sWC, pWhere, TK_AND);\n    \n  /* Special case: No FROM clause\n  */\n  if( nTabList==0 ){\n    if( pOrderBy ) pWInfo->nOBSat = pOrderBy->nExpr;\n    if( wctrlFlags & WHERE_WANT_DISTINCT ){\n      pWInfo->eDistinct = WHERE_DISTINCT_UNIQUE;\n    }\n  }else{\n    /* Assign a bit from the bitmask to every term in the FROM clause.\n    **\n    ** The N-th term of the FROM clause is assigned a bitmask of 1<<N.\n    **\n    ** The rule of the previous sentence ensures thta if X is the bitmask for\n    ** a table T, then X-1 is the bitmask for all other tables to the left of T.\n    ** Knowing the bitmask for all tables to the left of a left join is\n    ** important.  Ticket #3015.\n    **\n    ** Note that bitmasks are created for all pTabList->nSrc tables in\n    ** pTabList, not just the first nTabList tables.  nTabList is normally\n    ** equal to pTabList->nSrc but might be shortened to 1 if the\n    ** WHERE_OR_SUBCLAUSE flag is set.\n    */\n    ii = 0;\n    do{\n      createMask(pMaskSet, pTabList->a[ii].iCursor);\n      sqlite3WhereTabFuncArgs(pParse, &pTabList->a[ii], &pWInfo->sWC);\n    }while( (++ii)<pTabList->nSrc );\n  #ifdef SQLITE_DEBUG\n    {\n      Bitmask mx = 0;\n      for(ii=0; ii<pTabList->nSrc; ii++){\n        Bitmask m = sqlite3WhereGetMask(pMaskSet, pTabList->a[ii].iCursor);\n        assert( m>=mx );\n        mx = m;\n      }\n    }\n  #endif\n  }\n  \n  /* Analyze all of the subexpressions. */\n  sqlite3WhereExprAnalyze(pTabList, &pWInfo->sWC);\n  if( db->mallocFailed ) goto whereBeginError;\n\n  /* Special case: WHERE terms that do not refer to any tables in the join\n  ** (constant expressions). Evaluate each such term, and jump over all the\n  ** generated code if the result is not true.  \n  **\n  ** Do not do this if the expression contains non-deterministic functions\n  ** that are not within a sub-select. This is not strictly required, but\n  ** preserves SQLite's legacy behaviour in the following two cases:\n  **\n  **   FROM ... WHERE random()>0;           -- eval random() once per row\n  **   FROM ... WHERE (SELECT random())>0;  -- eval random() once overall\n  */\n  for(ii=0; ii<sWLB.pWC->nTerm; ii++){\n    WhereTerm *pT = &sWLB.pWC->a[ii];\n    if( pT->wtFlags & TERM_VIRTUAL ) continue;\n    if( pT->prereqAll==0 && (nTabList==0 || exprIsDeterministic(pT->pExpr)) ){\n      sqlite3ExprIfFalse(pParse, pT->pExpr, pWInfo->iBreak, SQLITE_JUMPIFNULL);\n      pT->wtFlags |= TERM_CODED;\n    }\n  }\n\n  if( wctrlFlags & WHERE_WANT_DISTINCT ){\n    if( isDistinctRedundant(pParse, pTabList, &pWInfo->sWC, pResultSet) ){\n      /* The DISTINCT marking is pointless.  Ignore it. */\n      pWInfo->eDistinct = WHERE_DISTINCT_UNIQUE;\n    }else if( pOrderBy==0 ){\n      /* Try to ORDER BY the result set to make distinct processing easier */\n      pWInfo->wctrlFlags |= WHERE_DISTINCTBY;\n      pWInfo->pOrderBy = pResultSet;\n    }\n  }\n\n  /* Construct the WhereLoop objects */\n#if defined(WHERETRACE_ENABLED)\n  if( sqlite3WhereTrace & 0xffff ){\n    sqlite3DebugPrintf(\"*** Optimizer Start *** (wctrlFlags: 0x%x\",wctrlFlags);\n    if( wctrlFlags & WHERE_USE_LIMIT ){\n      sqlite3DebugPrintf(\", limit: %d\", iAuxArg);\n    }\n    sqlite3DebugPrintf(\")\\n\");\n  }\n  if( sqlite3WhereTrace & 0x100 ){ /* Display all terms of the WHERE clause */\n    sqlite3WhereClausePrint(sWLB.pWC);\n  }\n#endif\n\n  if( nTabList!=1 || whereShortCut(&sWLB)==0 ){\n    rc = whereLoopAddAll(&sWLB);\n    if( rc ) goto whereBeginError;\n  \n#ifdef WHERETRACE_ENABLED\n    if( sqlite3WhereTrace ){    /* Display all of the WhereLoop objects */\n      WhereLoop *p;\n      int i;\n      static const char zLabel[] = \"0123456789abcdefghijklmnopqrstuvwyxz\"\n                                             \"ABCDEFGHIJKLMNOPQRSTUVWYXZ\";\n      for(p=pWInfo->pLoops, i=0; p; p=p->pNextLoop, i++){\n        p->cId = zLabel[i%(sizeof(zLabel)-1)];\n        whereLoopPrint(p, sWLB.pWC);\n      }\n    }\n#endif\n  \n    wherePathSolver(pWInfo, 0);\n    if( db->mallocFailed ) goto whereBeginError;\n    if( pWInfo->pOrderBy ){\n       wherePathSolver(pWInfo, pWInfo->nRowOut+1);\n       if( db->mallocFailed ) goto whereBeginError;\n    }\n  }\n  if( pWInfo->pOrderBy==0 && (db->flags & SQLITE_ReverseOrder)!=0 ){\n     pWInfo->revMask = ALLBITS;\n  }\n  if( pParse->nErr || NEVER(db->mallocFailed) ){\n    goto whereBeginError;\n  }\n#ifdef WHERETRACE_ENABLED\n  if( sqlite3WhereTrace ){\n    sqlite3DebugPrintf(\"---- Solution nRow=%d\", pWInfo->nRowOut);\n    if( pWInfo->nOBSat>0 ){\n      sqlite3DebugPrintf(\" ORDERBY=%d,0x%llx\", pWInfo->nOBSat, pWInfo->revMask);\n    }\n    switch( pWInfo->eDistinct ){\n      case WHERE_DISTINCT_UNIQUE: {\n        sqlite3DebugPrintf(\"  DISTINCT=unique\");\n        break;\n      }\n      case WHERE_DISTINCT_ORDERED: {\n        sqlite3DebugPrintf(\"  DISTINCT=ordered\");\n        break;\n      }\n      case WHERE_DISTINCT_UNORDERED: {\n        sqlite3DebugPrintf(\"  DISTINCT=unordered\");\n        break;\n      }\n    }\n    sqlite3DebugPrintf(\"\\n\");\n    for(ii=0; ii<pWInfo->nLevel; ii++){\n      whereLoopPrint(pWInfo->a[ii].pWLoop, sWLB.pWC);\n    }\n  }\n#endif\n\n  /* Attempt to omit tables from the join that do not affect the result.\n  ** For a table to not affect the result, the following must be true:\n  **\n  **   1) The query must not be an aggregate.\n  **   2) The table must be the RHS of a LEFT JOIN.\n  **   3) Either the query must be DISTINCT, or else the ON or USING clause\n  **      must contain a constraint that limits the scan of the table to \n  **      at most a single row.\n  **   4) The table must not be referenced by any part of the query apart\n  **      from its own USING or ON clause.\n  **\n  ** For example, given:\n  **\n  **     CREATE TABLE t1(ipk INTEGER PRIMARY KEY, v1);\n  **     CREATE TABLE t2(ipk INTEGER PRIMARY KEY, v2);\n  **     CREATE TABLE t3(ipk INTEGER PRIMARY KEY, v3);\n  **\n  ** then table t2 can be omitted from the following:\n  **\n  **     SELECT v1, v3 FROM t1 \n  **       LEFT JOIN t2 USING (t1.ipk=t2.ipk)\n  **       LEFT JOIN t3 USING (t1.ipk=t3.ipk)\n  **\n  ** or from:\n  **\n  **     SELECT DISTINCT v1, v3 FROM t1 \n  **       LEFT JOIN t2\n  **       LEFT JOIN t3 USING (t1.ipk=t3.ipk)\n  */\n  notReady = ~(Bitmask)0;\n  if( pWInfo->nLevel>=2\n   && pResultSet!=0               /* guarantees condition (1) above */\n   && OptimizationEnabled(db, SQLITE_OmitNoopJoin)\n  ){\n    int i;\n    Bitmask tabUsed = sqlite3WhereExprListUsage(pMaskSet, pResultSet);\n    if( sWLB.pOrderBy ){\n      tabUsed |= sqlite3WhereExprListUsage(pMaskSet, sWLB.pOrderBy);\n    }\n    for(i=pWInfo->nLevel-1; i>=1; i--){\n      WhereTerm *pTerm, *pEnd;\n      struct SrcList_item *pItem;\n      pLoop = pWInfo->a[i].pWLoop;\n      pItem = &pWInfo->pTabList->a[pLoop->iTab];\n      if( (pItem->fg.jointype & JT_LEFT)==0 ) continue;\n      if( (wctrlFlags & WHERE_WANT_DISTINCT)==0\n       && (pLoop->wsFlags & WHERE_ONEROW)==0\n      ){\n        continue;\n      }\n      if( (tabUsed & pLoop->maskSelf)!=0 ) continue;\n      pEnd = sWLB.pWC->a + sWLB.pWC->nTerm;\n      for(pTerm=sWLB.pWC->a; pTerm<pEnd; pTerm++){\n        if( (pTerm->prereqAll & pLoop->maskSelf)!=0 ){\n          if( !ExprHasProperty(pTerm->pExpr, EP_FromJoin)\n           || pTerm->pExpr->iRightJoinTable!=pItem->iCursor\n          ){\n            break;\n          }\n        }\n      }\n      if( pTerm<pEnd ) continue;\n      WHERETRACE(0xffff, (\"-> drop loop %c not used\\n\", pLoop->cId));\n      notReady &= ~pLoop->maskSelf;\n      for(pTerm=sWLB.pWC->a; pTerm<pEnd; pTerm++){\n        if( (pTerm->prereqAll & pLoop->maskSelf)!=0 ){\n          pTerm->wtFlags |= TERM_CODED;\n        }\n      }\n      if( i!=pWInfo->nLevel-1 ){\n        int nByte = (pWInfo->nLevel-1-i) * sizeof(WhereLevel);\n        memmove(&pWInfo->a[i], &pWInfo->a[i+1], nByte);\n      }\n      pWInfo->nLevel--;\n      nTabList--;\n    }\n  }\n  WHERETRACE(0xffff,(\"*** Optimizer Finished ***\\n\"));\n  pWInfo->pParse->nQueryLoop += pWInfo->nRowOut;\n\n  /* If the caller is an UPDATE or DELETE statement that is requesting\n  ** to use a one-pass algorithm, determine if this is appropriate.\n  **\n  ** A one-pass approach can be used if the caller has requested one\n  ** and either (a) the scan visits at most one row or (b) each\n  ** of the following are true:\n  **\n  **   * the caller has indicated that a one-pass approach can be used\n  **     with multiple rows (by setting WHERE_ONEPASS_MULTIROW), and\n  **   * the table is not a virtual table, and\n  **   * either the scan does not use the OR optimization or the caller\n  **     is a DELETE operation (WHERE_DUPLICATES_OK is only specified\n  **     for DELETE).\n  **\n  ** The last qualification is because an UPDATE statement uses\n  ** WhereInfo.aiCurOnePass[1] to determine whether or not it really can\n  ** use a one-pass approach, and this is not set accurately for scans\n  ** that use the OR optimization.\n  */\n  assert( (wctrlFlags & WHERE_ONEPASS_DESIRED)==0 || pWInfo->nLevel==1 );\n  if( (wctrlFlags & WHERE_ONEPASS_DESIRED)!=0 ){\n    int wsFlags = pWInfo->a[0].pWLoop->wsFlags;\n    int bOnerow = (wsFlags & WHERE_ONEROW)!=0;\n    if( bOnerow || (\n        0!=(wctrlFlags & WHERE_ONEPASS_MULTIROW)\n     && 0==(wsFlags & WHERE_VIRTUALTABLE)\n     && (0==(wsFlags & WHERE_MULTI_OR) || (wctrlFlags & WHERE_DUPLICATES_OK))\n    )){\n      pWInfo->eOnePass = bOnerow ? ONEPASS_SINGLE : ONEPASS_MULTI;\n      if( HasRowid(pTabList->a[0].pTab) && (wsFlags & WHERE_IDX_ONLY) ){\n        if( wctrlFlags & WHERE_ONEPASS_MULTIROW ){\n          bFordelete = OPFLAG_FORDELETE;\n        }\n        pWInfo->a[0].pWLoop->wsFlags = (wsFlags & ~WHERE_IDX_ONLY);\n      }\n    }\n  }\n\n  /* Open all tables in the pTabList and any indices selected for\n  ** searching those tables.\n  */\n  for(ii=0, pLevel=pWInfo->a; ii<nTabList; ii++, pLevel++){\n    Table *pTab;     /* Table to open */\n    int iDb;         /* Index of database containing table/index */\n    struct SrcList_item *pTabItem;\n\n    pTabItem = &pTabList->a[pLevel->iFrom];\n    pTab = pTabItem->pTab;\n    iDb = sqlite3SchemaToIndex(db, pTab->pSchema);\n    pLoop = pLevel->pWLoop;\n    if( (pTab->tabFlags & TF_Ephemeral)!=0 || pTab->pSelect ){\n      /* Do nothing */\n    }else\n#ifndef SQLITE_OMIT_VIRTUALTABLE\n    if( (pLoop->wsFlags & WHERE_VIRTUALTABLE)!=0 ){\n      const char *pVTab = (const char *)sqlite3GetVTable(db, pTab);\n      int iCur = pTabItem->iCursor;\n      sqlite3VdbeAddOp4(v, OP_VOpen, iCur, 0, 0, pVTab, P4_VTAB);\n    }else if( IsVirtual(pTab) ){\n      /* noop */\n    }else\n#endif\n    if( (pLoop->wsFlags & WHERE_IDX_ONLY)==0\n         && (wctrlFlags & WHERE_OR_SUBCLAUSE)==0 ){\n      int op = OP_OpenRead;\n      if( pWInfo->eOnePass!=ONEPASS_OFF ){\n        op = OP_OpenWrite;\n        pWInfo->aiCurOnePass[0] = pTabItem->iCursor;\n      };\n      sqlite3OpenTable(pParse, pTabItem->iCursor, iDb, pTab, op);\n      assert( pTabItem->iCursor==pLevel->iTabCur );\n      testcase( pWInfo->eOnePass==ONEPASS_OFF && pTab->nCol==BMS-1 );\n      testcase( pWInfo->eOnePass==ONEPASS_OFF && pTab->nCol==BMS );\n      if( pWInfo->eOnePass==ONEPASS_OFF && pTab->nCol<BMS && HasRowid(pTab) ){\n        Bitmask b = pTabItem->colUsed;\n        int n = 0;\n        for(; b; b=b>>1, n++){}\n        sqlite3VdbeChangeP4(v, -1, SQLITE_INT_TO_PTR(n), P4_INT32);\n        assert( n<=pTab->nCol );\n      }\n#ifdef SQLITE_ENABLE_CURSOR_HINTS\n      if( pLoop->u.btree.pIndex!=0 ){\n        sqlite3VdbeChangeP5(v, OPFLAG_SEEKEQ|bFordelete);\n      }else\n#endif\n      {\n        sqlite3VdbeChangeP5(v, bFordelete);\n      }\n#ifdef SQLITE_ENABLE_COLUMN_USED_MASK\n      sqlite3VdbeAddOp4Dup8(v, OP_ColumnsUsed, pTabItem->iCursor, 0, 0,\n                            (const u8*)&pTabItem->colUsed, P4_INT64);\n#endif\n    }else{\n      sqlite3TableLock(pParse, iDb, pTab->tnum, 0, pTab->zName);\n    }\n    if( pLoop->wsFlags & WHERE_INDEXED ){\n      Index *pIx = pLoop->u.btree.pIndex;\n      int iIndexCur;\n      int op = OP_OpenRead;\n      /* iAuxArg is always set to a positive value if ONEPASS is possible */\n      assert( iAuxArg!=0 || (pWInfo->wctrlFlags & WHERE_ONEPASS_DESIRED)==0 );\n      if( !HasRowid(pTab) && IsPrimaryKeyIndex(pIx)\n       && (wctrlFlags & WHERE_OR_SUBCLAUSE)!=0\n      ){\n        /* This is one term of an OR-optimization using the PRIMARY KEY of a\n        ** WITHOUT ROWID table.  No need for a separate index */\n        iIndexCur = pLevel->iTabCur;\n        op = 0;\n      }else if( pWInfo->eOnePass!=ONEPASS_OFF ){\n        Index *pJ = pTabItem->pTab->pIndex;\n        iIndexCur = iAuxArg;\n        assert( wctrlFlags & WHERE_ONEPASS_DESIRED );\n        while( ALWAYS(pJ) && pJ!=pIx ){\n          iIndexCur++;\n          pJ = pJ->pNext;\n        }\n        op = OP_OpenWrite;\n        pWInfo->aiCurOnePass[1] = iIndexCur;\n      }else if( iAuxArg && (wctrlFlags & WHERE_OR_SUBCLAUSE)!=0 ){\n        iIndexCur = iAuxArg;\n        op = OP_ReopenIdx;\n      }else{\n        iIndexCur = pParse->nTab++;\n      }\n      pLevel->iIdxCur = iIndexCur;\n      assert( pIx->pSchema==pTab->pSchema );\n      assert( iIndexCur>=0 );\n      if( op ){\n        sqlite3VdbeAddOp3(v, op, iIndexCur, pIx->tnum, iDb);\n        sqlite3VdbeSetP4KeyInfo(pParse, pIx);\n        if( (pLoop->wsFlags & WHERE_CONSTRAINT)!=0\n         && (pLoop->wsFlags & (WHERE_COLUMN_RANGE|WHERE_SKIPSCAN))==0\n         && (pWInfo->wctrlFlags&WHERE_ORDERBY_MIN)==0\n         && pWInfo->eDistinct!=WHERE_DISTINCT_ORDERED\n        ){\n          sqlite3VdbeChangeP5(v, OPFLAG_SEEKEQ); /* Hint to COMDB2 */\n        }\n        VdbeComment((v, \"%s\", pIx->zName));\n#ifdef SQLITE_ENABLE_COLUMN_USED_MASK\n        {\n          u64 colUsed = 0;\n          int ii, jj;\n          for(ii=0; ii<pIx->nColumn; ii++){\n            jj = pIx->aiColumn[ii];\n            if( jj<0 ) continue;\n            if( jj>63 ) jj = 63;\n            if( (pTabItem->colUsed & MASKBIT(jj))==0 ) continue;\n            colUsed |= ((u64)1)<<(ii<63 ? ii : 63);\n          }\n          sqlite3VdbeAddOp4Dup8(v, OP_ColumnsUsed, iIndexCur, 0, 0,\n                                (u8*)&colUsed, P4_INT64);\n        }\n#endif /* SQLITE_ENABLE_COLUMN_USED_MASK */\n      }\n    }\n    if( iDb>=0 ) sqlite3CodeVerifySchema(pParse, iDb);\n  }\n  pWInfo->iTop = sqlite3VdbeCurrentAddr(v);\n  if( db->mallocFailed ) goto whereBeginError;\n\n  /* Generate the code to do the search.  Each iteration of the for\n  ** loop below generates code for a single nested loop of the VM\n  ** program.\n  */\n  for(ii=0; ii<nTabList; ii++){\n    int addrExplain;\n    int wsFlags;\n    pLevel = &pWInfo->a[ii];\n    wsFlags = pLevel->pWLoop->wsFlags;\n#ifndef SQLITE_OMIT_AUTOMATIC_INDEX\n    if( (pLevel->pWLoop->wsFlags & WHERE_AUTO_INDEX)!=0 ){\n      constructAutomaticIndex(pParse, &pWInfo->sWC,\n                &pTabList->a[pLevel->iFrom], notReady, pLevel);\n      if( db->mallocFailed ) goto whereBeginError;\n    }\n#endif\n    addrExplain = sqlite3WhereExplainOneScan(\n        pParse, pTabList, pLevel, ii, pLevel->iFrom, wctrlFlags\n    );\n    pLevel->addrBody = sqlite3VdbeCurrentAddr(v);\n    notReady = sqlite3WhereCodeOneLoopStart(pWInfo, ii, notReady);\n    pWInfo->iContinue = pLevel->addrCont;\n    if( (wsFlags&WHERE_MULTI_OR)==0 && (wctrlFlags&WHERE_OR_SUBCLAUSE)==0 ){\n      sqlite3WhereAddScanStatus(v, pTabList, pLevel, addrExplain);\n    }\n  }\n\n  /* Done. */\n  VdbeModuleComment((v, \"Begin WHERE-core\"));\n  return pWInfo;\n\n  /* Jump here if malloc fails */\nwhereBeginError:\n  if( pWInfo ){\n    pParse->nQueryLoop = pWInfo->savedNQueryLoop;\n    whereInfoFree(db, pWInfo);\n  }\n  return 0;\n}\n\n/*\n** Generate the end of the WHERE loop.  See comments on \n** sqlite3WhereBegin() for additional information.\n*/\nSQLITE_PRIVATE void sqlite3WhereEnd(WhereInfo *pWInfo){\n  Parse *pParse = pWInfo->pParse;\n  Vdbe *v = pParse->pVdbe;\n  int i;\n  WhereLevel *pLevel;\n  WhereLoop *pLoop;\n  SrcList *pTabList = pWInfo->pTabList;\n  sqlite3 *db = pParse->db;\n\n  /* Generate loop termination code.\n  */\n  VdbeModuleComment((v, \"End WHERE-core\"));\n  sqlite3ExprCacheClear(pParse);\n  for(i=pWInfo->nLevel-1; i>=0; i--){\n    int addr;\n    pLevel = &pWInfo->a[i];\n    pLoop = pLevel->pWLoop;\n    if( pLevel->op!=OP_Noop ){\n#ifndef SQLITE_DISABLE_SKIPAHEAD_DISTINCT\n      int addrSeek = 0;\n      Index *pIdx;\n      int n;\n      if( pWInfo->eDistinct==WHERE_DISTINCT_ORDERED\n       && i==pWInfo->nLevel-1  /* Ticket [ef9318757b152e3] 2017-10-21 */\n       && (pLoop->wsFlags & WHERE_INDEXED)!=0\n       && (pIdx = pLoop->u.btree.pIndex)->hasStat1\n       && (n = pLoop->u.btree.nIdxCol)>0\n       && pIdx->aiRowLogEst[n]>=36\n      ){\n        int r1 = pParse->nMem+1;\n        int j, op;\n        for(j=0; j<n; j++){\n          sqlite3VdbeAddOp3(v, OP_Column, pLevel->iIdxCur, j, r1+j);\n        }\n        pParse->nMem += n+1;\n        op = pLevel->op==OP_Prev ? OP_SeekLT : OP_SeekGT;\n        addrSeek = sqlite3VdbeAddOp4Int(v, op, pLevel->iIdxCur, 0, r1, n);\n        VdbeCoverageIf(v, op==OP_SeekLT);\n        VdbeCoverageIf(v, op==OP_SeekGT);\n        sqlite3VdbeAddOp2(v, OP_Goto, 1, pLevel->p2);\n      }\n#endif /* SQLITE_DISABLE_SKIPAHEAD_DISTINCT */\n      /* The common case: Advance to the next row */\n      sqlite3VdbeResolveLabel(v, pLevel->addrCont);\n      sqlite3VdbeAddOp3(v, pLevel->op, pLevel->p1, pLevel->p2, pLevel->p3);\n      sqlite3VdbeChangeP5(v, pLevel->p5);\n      VdbeCoverage(v);\n      VdbeCoverageIf(v, pLevel->op==OP_Next);\n      VdbeCoverageIf(v, pLevel->op==OP_Prev);\n      VdbeCoverageIf(v, pLevel->op==OP_VNext);\n#ifndef SQLITE_DISABLE_SKIPAHEAD_DISTINCT\n      if( addrSeek ) sqlite3VdbeJumpHere(v, addrSeek);\n#endif\n    }else{\n      sqlite3VdbeResolveLabel(v, pLevel->addrCont);\n    }\n    if( pLoop->wsFlags & WHERE_IN_ABLE && pLevel->u.in.nIn>0 ){\n      struct InLoop *pIn;\n      int j;\n      sqlite3VdbeResolveLabel(v, pLevel->addrNxt);\n      for(j=pLevel->u.in.nIn, pIn=&pLevel->u.in.aInLoop[j-1]; j>0; j--, pIn--){\n        sqlite3VdbeJumpHere(v, pIn->addrInTop+1);\n        if( pIn->eEndLoopOp!=OP_Noop ){\n          sqlite3VdbeAddOp2(v, pIn->eEndLoopOp, pIn->iCur, pIn->addrInTop);\n          VdbeCoverage(v);\n          VdbeCoverageIf(v, pIn->eEndLoopOp==OP_PrevIfOpen);\n          VdbeCoverageIf(v, pIn->eEndLoopOp==OP_NextIfOpen);\n        }\n        sqlite3VdbeJumpHere(v, pIn->addrInTop-1);\n      }\n    }\n    sqlite3VdbeResolveLabel(v, pLevel->addrBrk);\n    if( pLevel->addrSkip ){\n      sqlite3VdbeGoto(v, pLevel->addrSkip);\n      VdbeComment((v, \"next skip-scan on %s\", pLoop->u.btree.pIndex->zName));\n      sqlite3VdbeJumpHere(v, pLevel->addrSkip);\n      sqlite3VdbeJumpHere(v, pLevel->addrSkip-2);\n    }\n#ifndef SQLITE_LIKE_DOESNT_MATCH_BLOBS\n    if( pLevel->addrLikeRep ){\n      sqlite3VdbeAddOp2(v, OP_DecrJumpZero, (int)(pLevel->iLikeRepCntr>>1),\n                        pLevel->addrLikeRep);\n      VdbeCoverage(v);\n    }\n#endif\n    if( pLevel->iLeftJoin ){\n      int ws = pLoop->wsFlags;\n      addr = sqlite3VdbeAddOp1(v, OP_IfPos, pLevel->iLeftJoin); VdbeCoverage(v);\n      assert( (ws & WHERE_IDX_ONLY)==0 || (ws & WHERE_INDEXED)!=0 );\n      if( (ws & WHERE_IDX_ONLY)==0 ){\n        assert( pLevel->iTabCur==pTabList->a[pLevel->iFrom].iCursor );\n        sqlite3VdbeAddOp1(v, OP_NullRow, pLevel->iTabCur);\n      }\n      if( (ws & WHERE_INDEXED) \n       || ((ws & WHERE_MULTI_OR) && pLevel->u.pCovidx) \n      ){\n        sqlite3VdbeAddOp1(v, OP_NullRow, pLevel->iIdxCur);\n      }\n      if( pLevel->op==OP_Return ){\n        sqlite3VdbeAddOp2(v, OP_Gosub, pLevel->p1, pLevel->addrFirst);\n      }else{\n        sqlite3VdbeGoto(v, pLevel->addrFirst);\n      }\n      sqlite3VdbeJumpHere(v, addr);\n    }\n    VdbeModuleComment((v, \"End WHERE-loop%d: %s\", i,\n                     pWInfo->pTabList->a[pLevel->iFrom].pTab->zName));\n  }\n\n  /* The \"break\" point is here, just past the end of the outer loop.\n  ** Set it.\n  */\n  sqlite3VdbeResolveLabel(v, pWInfo->iBreak);\n\n  assert( pWInfo->nLevel<=pTabList->nSrc );\n  for(i=0, pLevel=pWInfo->a; i<pWInfo->nLevel; i++, pLevel++){\n    int k, last;\n    VdbeOp *pOp;\n    Index *pIdx = 0;\n    struct SrcList_item *pTabItem = &pTabList->a[pLevel->iFrom];\n    Table *pTab = pTabItem->pTab;\n    assert( pTab!=0 );\n    pLoop = pLevel->pWLoop;\n\n    /* For a co-routine, change all OP_Column references to the table of\n    ** the co-routine into OP_Copy of result contained in a register.\n    ** OP_Rowid becomes OP_Null.\n    */\n    if( pTabItem->fg.viaCoroutine ){\n      testcase( pParse->db->mallocFailed );\n      translateColumnToCopy(pParse, pLevel->addrBody, pLevel->iTabCur,\n                            pTabItem->regResult, 0);\n      continue;\n    }\n\n    /* If this scan uses an index, make VDBE code substitutions to read data\n    ** from the index instead of from the table where possible.  In some cases\n    ** this optimization prevents the table from ever being read, which can\n    ** yield a significant performance boost.\n    ** \n    ** Calls to the code generator in between sqlite3WhereBegin and\n    ** sqlite3WhereEnd will have created code that references the table\n    ** directly.  This loop scans all that code looking for opcodes\n    ** that reference the table and converts them into opcodes that\n    ** reference the index.\n    */\n    if( pLoop->wsFlags & (WHERE_INDEXED|WHERE_IDX_ONLY) ){\n      pIdx = pLoop->u.btree.pIndex;\n    }else if( pLoop->wsFlags & WHERE_MULTI_OR ){\n      pIdx = pLevel->u.pCovidx;\n    }\n    if( pIdx\n     && (pWInfo->eOnePass==ONEPASS_OFF || !HasRowid(pIdx->pTable))\n     && !db->mallocFailed\n    ){\n      last = sqlite3VdbeCurrentAddr(v);\n      k = pLevel->addrBody;\n      pOp = sqlite3VdbeGetOp(v, k);\n      for(; k<last; k++, pOp++){\n        if( pOp->p1!=pLevel->iTabCur ) continue;\n        if( pOp->opcode==OP_Column\n#ifdef SQLITE_ENABLE_OFFSET_SQL_FUNC\n         || pOp->opcode==OP_Offset\n#endif\n        ){\n          int x = pOp->p2;\n          assert( pIdx->pTable==pTab );\n          if( !HasRowid(pTab) ){\n            Index *pPk = sqlite3PrimaryKeyIndex(pTab);\n            x = pPk->aiColumn[x];\n            assert( x>=0 );\n          }\n          x = sqlite3ColumnOfIndex(pIdx, x);\n          if( x>=0 ){\n            pOp->p2 = x;\n            pOp->p1 = pLevel->iIdxCur;\n          }\n          assert( (pLoop->wsFlags & WHERE_IDX_ONLY)==0 || x>=0 \n              || pWInfo->eOnePass );\n        }else if( pOp->opcode==OP_Rowid ){\n          pOp->p1 = pLevel->iIdxCur;\n          pOp->opcode = OP_IdxRowid;\n        }else if( pOp->opcode==OP_IfNullRow ){\n          pOp->p1 = pLevel->iIdxCur;\n        }\n      }\n    }\n  }\n\n  /* Final cleanup\n  */\n  pParse->nQueryLoop = pWInfo->savedNQueryLoop;\n  whereInfoFree(db, pWInfo);\n  return;\n}\n\n/************** End of where.c ***********************************************/\n/************** Begin file parse.c *******************************************/\n/*\n** 2000-05-29\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n*************************************************************************\n** Driver template for the LEMON parser generator.\n**\n** The \"lemon\" program processes an LALR(1) input grammar file, then uses\n** this template to construct a parser.  The \"lemon\" program inserts text\n** at each \"%%\" line.  Also, any \"P-a-r-s-e\" identifer prefix (without the\n** interstitial \"-\" characters) contained in this template is changed into\n** the value of the %name directive from the grammar.  Otherwise, the content\n** of this template is copied straight through into the generate parser\n** source file.\n**\n** The following is the concatenation of all %include directives from the\n** input grammar file:\n*/\n/* #include <stdio.h> */\n/************ Begin %include sections from the grammar ************************/\n\n/* #include \"sqliteInt.h\" */\n\n/*\n** Disable all error recovery processing in the parser push-down\n** automaton.\n*/\n#define YYNOERRORRECOVERY 1\n\n/*\n** Make yytestcase() the same as testcase()\n*/\n#define yytestcase(X) testcase(X)\n\n/*\n** Indicate that sqlite3ParserFree() will never be called with a null\n** pointer.\n*/\n#define YYPARSEFREENEVERNULL 1\n\n/*\n** In the amalgamation, the parse.c file generated by lemon and the\n** tokenize.c file are concatenated.  In that case, sqlite3RunParser()\n** has access to the the size of the yyParser object and so the parser\n** engine can be allocated from stack.  In that case, only the\n** sqlite3ParserInit() and sqlite3ParserFinalize() routines are invoked\n** and the sqlite3ParserAlloc() and sqlite3ParserFree() routines can be\n** omitted.\n*/\n#ifdef SQLITE_AMALGAMATION\n# define sqlite3Parser_ENGINEALWAYSONSTACK 1\n#endif\n\n/*\n** Alternative datatype for the argument to the malloc() routine passed\n** into sqlite3ParserAlloc().  The default is size_t.\n*/\n#define YYMALLOCARGTYPE  u64\n\n/*\n** An instance of the following structure describes the event of a\n** TRIGGER.  \"a\" is the event type, one of TK_UPDATE, TK_INSERT,\n** TK_DELETE, or TK_INSTEAD.  If the event is of the form\n**\n**      UPDATE ON (a,b,c)\n**\n** Then the \"b\" IdList records the list \"a,b,c\".\n*/\nstruct TrigEvent { int a; IdList * b; };\n\n/*\n** Disable lookaside memory allocation for objects that might be\n** shared across database connections.\n*/\nstatic void disableLookaside(Parse *pParse){\n  pParse->disableLookaside++;\n  pParse->db->lookaside.bDisable++;\n}\n\n\n  /*\n  ** For a compound SELECT statement, make sure p->pPrior->pNext==p for\n  ** all elements in the list.  And make sure list length does not exceed\n  ** SQLITE_LIMIT_COMPOUND_SELECT.\n  */\n  static void parserDoubleLinkSelect(Parse *pParse, Select *p){\n    if( p->pPrior ){\n      Select *pNext = 0, *pLoop;\n      int mxSelect, cnt = 0;\n      for(pLoop=p; pLoop; pNext=pLoop, pLoop=pLoop->pPrior, cnt++){\n        pLoop->pNext = pNext;\n        pLoop->selFlags |= SF_Compound;\n      }\n      if( (p->selFlags & SF_MultiValue)==0 && \n        (mxSelect = pParse->db->aLimit[SQLITE_LIMIT_COMPOUND_SELECT])>0 &&\n        cnt>mxSelect\n      ){\n        sqlite3ErrorMsg(pParse, \"too many terms in compound SELECT\");\n      }\n    }\n  }\n\n\n  /* Construct a new Expr object from a single identifier.  Use the\n  ** new Expr to populate pOut.  Set the span of pOut to be the identifier\n  ** that created the expression.\n  */\n  static Expr *tokenExpr(Parse *pParse, int op, Token t){\n    Expr *p = sqlite3DbMallocRawNN(pParse->db, sizeof(Expr)+t.n+1);\n    if( p ){\n      memset(p, 0, sizeof(Expr));\n      p->op = (u8)op;\n      p->flags = EP_Leaf;\n      p->iAgg = -1;\n      p->u.zToken = (char*)&p[1];\n      memcpy(p->u.zToken, t.z, t.n);\n      p->u.zToken[t.n] = 0;\n      if( sqlite3Isquote(p->u.zToken[0]) ){\n        if( p->u.zToken[0]=='\"' ) p->flags |= EP_DblQuoted;\n        sqlite3Dequote(p->u.zToken);\n      }\n#if SQLITE_MAX_EXPR_DEPTH>0\n      p->nHeight = 1;\n#endif  \n    }\n    return p;\n  }\n\n  /* A routine to convert a binary TK_IS or TK_ISNOT expression into a\n  ** unary TK_ISNULL or TK_NOTNULL expression. */\n  static void binaryToUnaryIfNull(Parse *pParse, Expr *pY, Expr *pA, int op){\n    sqlite3 *db = pParse->db;\n    if( pA && pY && pY->op==TK_NULL ){\n      pA->op = (u8)op;\n      sqlite3ExprDelete(db, pA->pRight);\n      pA->pRight = 0;\n    }\n  }\n\n  /* Add a single new term to an ExprList that is used to store a\n  ** list of identifiers.  Report an error if the ID list contains\n  ** a COLLATE clause or an ASC or DESC keyword, except ignore the\n  ** error while parsing a legacy schema.\n  */\n  static ExprList *parserAddExprIdListTerm(\n    Parse *pParse,\n    ExprList *pPrior,\n    Token *pIdToken,\n    int hasCollate,\n    int sortOrder\n  ){\n    ExprList *p = sqlite3ExprListAppend(pParse, pPrior, 0);\n    if( (hasCollate || sortOrder!=SQLITE_SO_UNDEFINED)\n        && pParse->db->init.busy==0\n    ){\n      sqlite3ErrorMsg(pParse, \"syntax error after column name \\\"%.*s\\\"\",\n                         pIdToken->n, pIdToken->z);\n    }\n    sqlite3ExprListSetName(pParse, p, pIdToken, 1);\n    return p;\n  }\n/**************** End of %include directives **********************************/\n/* These constants specify the various numeric values for terminal symbols\n** in a format understandable to \"makeheaders\".  This section is blank unless\n** \"lemon\" is run with the \"-m\" command-line option.\n***************** Begin makeheaders token definitions *************************/\n/**************** End makeheaders token definitions ***************************/\n\n/* The next sections is a series of control #defines.\n** various aspects of the generated parser.\n**    YYCODETYPE         is the data type used to store the integer codes\n**                       that represent terminal and non-terminal symbols.\n**                       \"unsigned char\" is used if there are fewer than\n**                       256 symbols.  Larger types otherwise.\n**    YYNOCODE           is a number of type YYCODETYPE that is not used for\n**                       any terminal or nonterminal symbol.\n**    YYFALLBACK         If defined, this indicates that one or more tokens\n**                       (also known as: \"terminal symbols\") have fall-back\n**                       values which should be used if the original symbol\n**                       would not parse.  This permits keywords to sometimes\n**                       be used as identifiers, for example.\n**    YYACTIONTYPE       is the data type used for \"action codes\" - numbers\n**                       that indicate what to do in response to the next\n**                       token.\n**    sqlite3ParserTOKENTYPE     is the data type used for minor type for terminal\n**                       symbols.  Background: A \"minor type\" is a semantic\n**                       value associated with a terminal or non-terminal\n**                       symbols.  For example, for an \"ID\" terminal symbol,\n**                       the minor type might be the name of the identifier.\n**                       Each non-terminal can have a different minor type.\n**                       Terminal symbols all have the same minor type, though.\n**                       This macros defines the minor type for terminal \n**                       symbols.\n**    YYMINORTYPE        is the data type used for all minor types.\n**                       This is typically a union of many types, one of\n**                       which is sqlite3ParserTOKENTYPE.  The entry in the union\n**                       for terminal symbols is called \"yy0\".\n**    YYSTACKDEPTH       is the maximum depth of the parser's stack.  If\n**                       zero the stack is dynamically sized using realloc()\n**    sqlite3ParserARG_SDECL     A static variable declaration for the %extra_argument\n**    sqlite3ParserARG_PDECL     A parameter declaration for the %extra_argument\n**    sqlite3ParserARG_STORE     Code to store %extra_argument into yypParser\n**    sqlite3ParserARG_FETCH     Code to extract %extra_argument from yypParser\n**    YYERRORSYMBOL      is the code number of the error symbol.  If not\n**                       defined, then do no error processing.\n**    YYNSTATE           the combined number of states.\n**    YYNRULE            the number of rules in the grammar\n**    YYNTOKEN           Number of terminal symbols\n**    YY_MAX_SHIFT       Maximum value for shift actions\n**    YY_MIN_SHIFTREDUCE Minimum value for shift-reduce actions\n**    YY_MAX_SHIFTREDUCE Maximum value for shift-reduce actions\n**    YY_ERROR_ACTION    The yy_action[] code for syntax error\n**    YY_ACCEPT_ACTION   The yy_action[] code for accept\n**    YY_NO_ACTION       The yy_action[] code for no-op\n**    YY_MIN_REDUCE      Minimum value for reduce actions\n**    YY_MAX_REDUCE      Maximum value for reduce actions\n*/\n#ifndef INTERFACE\n# define INTERFACE 1\n#endif\n/************* Begin control #defines *****************************************/\n#define YYCODETYPE unsigned char\n#define YYNOCODE 253\n#define YYACTIONTYPE unsigned short int\n#define YYWILDCARD 83\n#define sqlite3ParserTOKENTYPE Token\ntypedef union {\n  int yyinit;\n  sqlite3ParserTOKENTYPE yy0;\n  int yy4;\n  struct TrigEvent yy90;\n  TriggerStep* yy203;\n  struct {int value; int mask;} yy215;\n  SrcList* yy259;\n  Expr* yy314;\n  ExprList* yy322;\n  const char* yy336;\n  IdList* yy384;\n  Select* yy387;\n  With* yy451;\n} YYMINORTYPE;\n#ifndef YYSTACKDEPTH\n#define YYSTACKDEPTH 100\n#endif\n#define sqlite3ParserARG_SDECL Parse *pParse;\n#define sqlite3ParserARG_PDECL ,Parse *pParse\n#define sqlite3ParserARG_FETCH Parse *pParse = yypParser->pParse\n#define sqlite3ParserARG_STORE yypParser->pParse = pParse\n#define YYFALLBACK 1\n#define YYNSTATE             466\n#define YYNRULE              330\n#define YYNTOKEN             143\n#define YY_MAX_SHIFT         465\n#define YY_MIN_SHIFTREDUCE   675\n#define YY_MAX_SHIFTREDUCE   1004\n#define YY_ERROR_ACTION      1005\n#define YY_ACCEPT_ACTION     1006\n#define YY_NO_ACTION         1007\n#define YY_MIN_REDUCE        1008\n#define YY_MAX_REDUCE        1337\n/************* End control #defines *******************************************/\n\n/* Define the yytestcase() macro to be a no-op if is not already defined\n** otherwise.\n**\n** Applications can choose to define yytestcase() in the %include section\n** to a macro that can assist in verifying code coverage.  For production\n** code the yytestcase() macro should be turned off.  But it is useful\n** for testing.\n*/\n#ifndef yytestcase\n# define yytestcase(X)\n#endif\n\n\n/* Next are the tables used to determine what action to take based on the\n** current state and lookahead token.  These tables are used to implement\n** functions that take a state number and lookahead value and return an\n** action integer.  \n**\n** Suppose the action integer is N.  Then the action is determined as\n** follows\n**\n**   0 <= N <= YY_MAX_SHIFT             Shift N.  That is, push the lookahead\n**                                      token onto the stack and goto state N.\n**\n**   N between YY_MIN_SHIFTREDUCE       Shift to an arbitrary state then\n**     and YY_MAX_SHIFTREDUCE           reduce by rule N-YY_MIN_SHIFTREDUCE.\n**\n**   N == YY_ERROR_ACTION               A syntax error has occurred.\n**\n**   N == YY_ACCEPT_ACTION              The parser accepts its input.\n**\n**   N == YY_NO_ACTION                  No such action.  Denotes unused\n**                                      slots in the yy_action[] table.\n**\n**   N between YY_MIN_REDUCE            Reduce by rule N-YY_MIN_REDUCE\n**     and YY_MAX_REDUCE\n**\n** The action table is constructed as a single large table named yy_action[].\n** Given state S and lookahead X, the action is computed as either:\n**\n**    (A)   N = yy_action[ yy_shift_ofst[S] + X ]\n**    (B)   N = yy_default[S]\n**\n** The (A) formula is preferred.  The B formula is used instead if\n** yy_lookahead[yy_shift_ofst[S]+X] is not equal to X.\n**\n** The formulas above are for computing the action when the lookahead is\n** a terminal symbol.  If the lookahead is a non-terminal (as occurs after\n** a reduce action) then the yy_reduce_ofst[] array is used in place of\n** the yy_shift_ofst[] array.\n**\n** The following are the tables generated in this section:\n**\n**  yy_action[]        A single table containing all actions.\n**  yy_lookahead[]     A table containing the lookahead for each entry in\n**                     yy_action.  Used to detect hash collisions.\n**  yy_shift_ofst[]    For each state, the offset into yy_action for\n**                     shifting terminals.\n**  yy_reduce_ofst[]   For each state, the offset into yy_action for\n**                     shifting non-terminals after a reduce.\n**  yy_default[]       Default action for each state.\n**\n*********** Begin parsing tables **********************************************/\n#define YY_ACTTAB_COUNT (1541)\nstatic const YYACTIONTYPE yy_action[] = {\n /*     0 */  1006,  156,  156,    2, 1302,   90,   87,  179,   90,   87,\n /*    10 */   179,  460, 1048,  460,  465, 1010,  460,  333, 1130,  335,\n /*    20 */   246,  330,  112,  303,  439, 1258,  304,  419, 1129, 1087,\n /*    30 */    72,  798,   50,   50,   50,   50,  331,   30,   30,  799,\n /*    40 */   951,  364,  371,   97,   98,   88,  983,  983,  859,  862,\n /*    50 */   851,  851,   95,   95,   96,   96,   96,   96,  120,  371,\n /*    60 */   370,  120,  348,   22,   90,   87,  179,  438,  423,  438,\n /*    70 */   440,  335,  420,  385,   90,   87,  179,  116,   73,  163,\n /*    80 */   848,  848,  860,  863,   94,   94,   94,   94,   93,   93,\n /*    90 */    92,   92,   92,   91,  361,   97,   98,   88,  983,  983,\n /*   100 */   859,  862,  851,  851,   95,   95,   96,   96,   96,   96,\n /*   110 */   718,  365,  339,   93,   93,   92,   92,   92,   91,  361,\n /*   120 */    99,  371,  453,  335,   94,   94,   94,   94,   93,   93,\n /*   130 */    92,   92,   92,   91,  361,  852,   94,   94,   94,   94,\n /*   140 */    93,   93,   92,   92,   92,   91,  361,   97,   98,   88,\n /*   150 */   983,  983,  859,  862,  851,  851,   95,   95,   96,   96,\n /*   160 */    96,   96,   92,   92,   92,   91,  361,  838,  132,  195,\n /*   170 */    58,  244,  412,  409,  408,  335,  457,  457,  457,  304,\n /*   180 */    59,  332,  831,  407,  394,  962,  830,  391,   94,   94,\n /*   190 */    94,   94,   93,   93,   92,   92,   92,   91,  361,   97,\n /*   200 */    98,   88,  983,  983,  859,  862,  851,  851,   95,   95,\n /*   210 */    96,   96,   96,   96,  426,  357,  460,  830,  830,  832,\n /*   220 */    91,  361,  962,  963,  964,  195,  459,  335,  412,  409,\n /*   230 */   408,  280,  361,  820,  132,   11,   11,   50,   50,  407,\n /*   240 */    94,   94,   94,   94,   93,   93,   92,   92,   92,   91,\n /*   250 */   361,   97,   98,   88,  983,  983,  859,  862,  851,  851,\n /*   260 */    95,   95,   96,   96,   96,   96,  460,  221,  460,  264,\n /*   270 */   375,  254,  438,  428, 1276, 1276,  383, 1074, 1053,  335,\n /*   280 */   245,  422,  299,  713,  271,  271, 1074,   50,   50,   50,\n /*   290 */    50,  962,   94,   94,   94,   94,   93,   93,   92,   92,\n /*   300 */    92,   91,  361,   97,   98,   88,  983,  983,  859,  862,\n /*   310 */   851,  851,   95,   95,   96,   96,   96,   96,   90,   87,\n /*   320 */   179, 1306,  438,  437,  438,  418,  368,  253,  962,  963,\n /*   330 */   964,  335,  360,  360,  360,  706,  359,  358,  324,  962,\n /*   340 */  1281,  951,  364,  230,   94,   94,   94,   94,   93,   93,\n /*   350 */    92,   92,   92,   91,  361,   97,   98,   88,  983,  983,\n /*   360 */   859,  862,  851,  851,   95,   95,   96,   96,   96,   96,\n /*   370 */   769,  460,  120,  226,  226,  366,  962,  963,  964, 1089,\n /*   380 */   990,  900,  990,  335, 1057,  425,  421,  839,  759,  759,\n /*   390 */   425,  427,   50,   50,  432,  381,   94,   94,   94,   94,\n /*   400 */    93,   93,   92,   92,   92,   91,  361,   97,   98,   88,\n /*   410 */   983,  983,  859,  862,  851,  851,   95,   95,   96,   96,\n /*   420 */    96,   96,  460,  259,  460,  120,  117,  354,  942, 1332,\n /*   430 */   942, 1333, 1332,  278, 1333,  335,  680,  681,  682,  825,\n /*   440 */   201,  176,  303,   50,   50,   49,   49,  404,   94,   94,\n /*   450 */    94,   94,   93,   93,   92,   92,   92,   91,  361,   97,\n /*   460 */    98,   88,  983,  983,  859,  862,  851,  851,   95,   95,\n /*   470 */    96,   96,   96,   96,  199,  460,  380,  265,  433,  380,\n /*   480 */   265,  383,  256,  158,  258,  319, 1003,  335,  155,  940,\n /*   490 */   177,  940,  273,  379,  276,  322,   34,   34,  302,  962,\n /*   500 */    94,   94,   94,   94,   93,   93,   92,   92,   92,   91,\n /*   510 */   361,   97,   98,   88,  983,  983,  859,  862,  851,  851,\n /*   520 */    95,   95,   96,   96,   96,   96,  905,  905,  397,  460,\n /*   530 */   301,  158,  101,  319,  941,  340,  962,  963,  964,  313,\n /*   540 */   283,  449,  335,  327,  146, 1266, 1004,  257,  234,  248,\n /*   550 */    35,   35,   94,   94,   94,   94,   93,   93,   92,   92,\n /*   560 */    92,   91,  361,  709,  785, 1227,   97,   98,   88,  983,\n /*   570 */   983,  859,  862,  851,  851,   95,   95,   96,   96,   96,\n /*   580 */    96,  962, 1227, 1229,  245,  422,  838,  198,  197,  196,\n /*   590 */  1079, 1079, 1077, 1077, 1004, 1334,  320,  335,  172,  171,\n /*   600 */   709,  831,  159,  271,  271,  830,   76,   94,   94,   94,\n /*   610 */    94,   93,   93,   92,   92,   92,   91,  361,  962,  963,\n /*   620 */   964,   97,   98,   88,  983,  983,  859,  862,  851,  851,\n /*   630 */    95,   95,   96,   96,   96,   96,  830,  830,  832, 1157,\n /*   640 */  1157,  199, 1157,  173, 1227,  231,  232, 1282,    2,  335,\n /*   650 */   271,  764,  271,  820,  271,  271,  763,  389,  389,  389,\n /*   660 */   132,   79,   94,   94,   94,   94,   93,   93,   92,   92,\n /*   670 */    92,   91,  361,   97,   98,   88,  983,  983,  859,  862,\n /*   680 */   851,  851,   95,   95,   96,   96,   96,   96,  460,  264,\n /*   690 */   223,  460, 1257,  783, 1223, 1157, 1086, 1082,   80,  271,\n /*   700 */    78,  335,  340, 1031,  341,  344,  345,  902,  346,   10,\n /*   710 */    10,  902,   25,   25,   94,   94,   94,   94,   93,   93,\n /*   720 */    92,   92,   92,   91,  361,   97,   86,   88,  983,  983,\n /*   730 */   859,  862,  851,  851,   95,   95,   96,   96,   96,   96,\n /*   740 */  1157,  270,  395,  117,  233,  263,  235,   70,  456,  341,\n /*   750 */   225,  176,  335, 1305,  342,  133,  736,  966,  980,  249,\n /*   760 */  1150,  396,  325, 1085, 1028,  178,   94,   94,   94,   94,\n /*   770 */    93,   93,   92,   92,   92,   91,  361,   98,   88,  983,\n /*   780 */   983,  859,  862,  851,  851,   95,   95,   96,   96,   96,\n /*   790 */    96,  783,  783,  132,  120,  966,  120,  120,  120,  798,\n /*   800 */   252,  937,  335,  353,  321,  429,  355,  799,  822,  692,\n /*   810 */   390,  203,  446,  450,  372,  716,  454,   94,   94,   94,\n /*   820 */    94,   93,   93,   92,   92,   92,   91,  361,   88,  983,\n /*   830 */   983,  859,  862,  851,  851,   95,   95,   96,   96,   96,\n /*   840 */    96,   84,  455, 1225,    3, 1209,  120,  120,  382,  387,\n /*   850 */   120,  203, 1271,  716,  384,  168,  266,  203,  458,   72,\n /*   860 */   260, 1246,   84,  455,  178,    3,  378,   94,   94,   94,\n /*   870 */    94,   93,   93,   92,   92,   92,   91,  361,  350,  458,\n /*   880 */  1245,  362,  430,  213,  228,  290,  415,  285,  414,  200,\n /*   890 */   783,  882,  444,  726,  725,  405,  283,  921,  209,  921,\n /*   900 */   281,  132,  362,   72,  838,  289,  147,  733,  734,  392,\n /*   910 */    81,   82,  922,  444,  922,  267,  288,   83,  362,  462,\n /*   920 */   461,  272,  132,  830,   23,  838,  388,  923, 1216,  923,\n /*   930 */  1056,   81,   82,   84,  455,  899,    3,  899,   83,  362,\n /*   940 */   462,  461,  761,  962,  830,   75,    1,  443,  275,  747,\n /*   950 */   458,    5,  962,  204,  830,  830,  832,  833,   18,  748,\n /*   960 */   229,  962,  277,   19,  153,  317,  317,  316,  216,  314,\n /*   970 */   279,  460,  689,  362, 1055,  830,  830,  832,  833,   18,\n /*   980 */   962,  963,  964,  962,  444,  181,  460,  251,  981,  962,\n /*   990 */   963,  964,    8,    8,   20,  250,  838, 1070,  962,  963,\n /*  1000 */   964,  417,   81,   82,  768,  204,  347,   36,   36,   83,\n /*  1010 */   362,  462,  461, 1054,  284,  830,   84,  455, 1123,    3,\n /*  1020 */   962,  963,  964,  460,  183,  962,  981,  764,  889, 1107,\n /*  1030 */   460,  184,  763,  458,  132,  182,   74,  455,  460,    3,\n /*  1040 */   981,  898,  834,  898,    8,    8,  830,  830,  832,  833,\n /*  1050 */    18,    8,    8,  458,  219, 1156,  362, 1103,  349,    8,\n /*  1060 */     8,  240,  962,  963,  964,  236,  889,  444,  792,  336,\n /*  1070 */   158,  203,  885,  435,  700,  209,  362,  114,  981,  838,\n /*  1080 */   834,  227,  334, 1114,  441,   81,   82,  444,  442,  305,\n /*  1090 */   784,  306,   83,  362,  462,  461,  369, 1162,  830,  838,\n /*  1100 */   460, 1037,  237, 1030,  237,   81,   82,    7,   96,   96,\n /*  1110 */    96,   96,   83,  362,  462,  461, 1019, 1018,  830, 1020,\n /*  1120 */  1289,   37,   37,  400,   96,   96,   96,   96,   89,  830,\n /*  1130 */   830,  832,  833,   18, 1100,  318,  962,  292,   94,   94,\n /*  1140 */    94,   94,   93,   93,   92,   92,   92,   91,  361,  830,\n /*  1150 */   830,  832,  833,   18,   94,   94,   94,   94,   93,   93,\n /*  1160 */    92,   92,   92,   91,  361,  359,  358,  226,  226,  727,\n /*  1170 */   294,  296,  460,  962,  963,  964,  460,  989,  160,  425,\n /*  1180 */   170, 1295,  262,  460,  987,  374,  988,  386, 1145,  255,\n /*  1190 */   326,  460,  373,   38,   38,  410,  174,   39,   39,  413,\n /*  1200 */   460,  287,  460, 1053,   40,   40,  298,  728, 1220,  990,\n /*  1210 */   445,  990,   26,   26, 1219,  460,  311,  460,  169, 1292,\n /*  1220 */   460,   27,   27,   29,   29,  998,  460,  206,  135,  995,\n /*  1230 */  1265, 1263,  460,   57,   60,  460,   41,   41,   42,   42,\n /*  1240 */   460,   43,   43,  460,  343,  351,  460,    9,    9,  460,\n /*  1250 */   144,  460,  130,   44,   44,  460,  103,  103,  460,  137,\n /*  1260 */    70,   45,   45,  460,   46,   46,  460,   31,   31, 1142,\n /*  1270 */    47,   47,   48,   48,  460,  376,   32,   32,  460,  122,\n /*  1280 */   122,  460,  157,  460,  123,  123,  139,  124,  124,  460,\n /*  1290 */   186,  460,  377,  460,  115,   54,   54,  460,  403,   33,\n /*  1300 */    33,  460,  104,  104,   51,   51,  460,  161,  460,  140,\n /*  1310 */   105,  105,  106,  106,  102,  102,  460,  141,  121,  121,\n /*  1320 */   460,  142,  119,  119,  190,  460, 1152,  110,  110,  109,\n /*  1330 */   109,  702,  460,  148,  393,   65,  460,  107,  107,  460,\n /*  1340 */   323,  108,  108,  399,  460, 1234,   53,   53, 1214,  269,\n /*  1350 */   154,  416, 1115,   55,   55,  220,  401,   52,   52,  191,\n /*  1360 */    24,   24,  274,  192,  193,   28,   28, 1021,  328,  702,\n /*  1370 */  1073,  352, 1072,  718, 1071,  431, 1111, 1064,  329, 1045,\n /*  1380 */    69,  205,    6,  291, 1044,  286, 1112, 1043, 1304, 1110,\n /*  1390 */   293,  300,  295,  297, 1063, 1200, 1109,   77,  241,  448,\n /*  1400 */   356,  452,  436,  100,  214,   71,  434, 1027, 1093,   21,\n /*  1410 */   463,  242,  243,  957,  215,  217,  218,  464,  309,  307,\n /*  1420 */   308,  310, 1016,  125, 1250, 1251, 1011, 1249,  126,  127,\n /*  1430 */  1248,  113,  676,  337,  238,  338,  134,  363,  167, 1041,\n /*  1440 */  1040,   56,  247,  367,  180,  897,  111,  895,  136, 1038,\n /*  1450 */   818,  128,  138,  750,  261,  911,  185,  143,  145,   61,\n /*  1460 */    62,   63,   64,  129,  914,  187,  188,  910,  118,   12,\n /*  1470 */   189,  903,  268,  992,  203,  162,  398,  150,  149,  691,\n /*  1480 */   402,  288,  194,  406,  151,  411,   66,   13,  729,  239,\n /*  1490 */   282,   14,   67,  131,  837,  836,  865,  758,   15,    4,\n /*  1500 */    68,  762,  175,  222,  224,  424,  152,  869,  791,  202,\n /*  1510 */   786,   75,   72,  880,  866,  864,   16,   17,  920,  207,\n /*  1520 */   919,  208,  447,  946,  164,  211,  947,  210,  165,  451,\n /*  1530 */   868,  166,  315,  835,  701,   85,  212, 1297,  312,  952,\n /*  1540 */  1296,\n};\nstatic const YYCODETYPE yy_lookahead[] = {\n /*     0 */   144,  145,  146,  147,  172,  222,  223,  224,  222,  223,\n /*    10 */   224,  152,  180,  152,  148,  149,  152,  173,  176,   19,\n /*    20 */   154,  173,  156,  152,  163,  242,  152,  163,  176,  163,\n /*    30 */    26,   31,  173,  174,  173,  174,  173,  173,  174,   39,\n /*    40 */     1,    2,  152,   43,   44,   45,   46,   47,   48,   49,\n /*    50 */    50,   51,   52,   53,   54,   55,   56,   57,  197,  169,\n /*    60 */   170,  197,  188,  197,  222,  223,  224,  208,  209,  208,\n /*    70 */   209,   19,  208,  152,  222,  223,  224,   22,   26,   24,\n /*    80 */    46,   47,   48,   49,   84,   85,   86,   87,   88,   89,\n /*    90 */    90,   91,   92,   93,   94,   43,   44,   45,   46,   47,\n /*   100 */    48,   49,   50,   51,   52,   53,   54,   55,   56,   57,\n /*   110 */   106,  245,  157,   88,   89,   90,   91,   92,   93,   94,\n /*   120 */    68,  231,  251,   19,   84,   85,   86,   87,   88,   89,\n /*   130 */    90,   91,   92,   93,   94,  101,   84,   85,   86,   87,\n /*   140 */    88,   89,   90,   91,   92,   93,   94,   43,   44,   45,\n /*   150 */    46,   47,   48,   49,   50,   51,   52,   53,   54,   55,\n /*   160 */    56,   57,   90,   91,   92,   93,   94,   82,   79,   99,\n /*   170 */    66,  200,  102,  103,  104,   19,  168,  169,  170,  152,\n /*   180 */    24,  210,   97,  113,  229,   59,  101,  232,   84,   85,\n /*   190 */    86,   87,   88,   89,   90,   91,   92,   93,   94,   43,\n /*   200 */    44,   45,   46,   47,   48,   49,   50,   51,   52,   53,\n /*   210 */    54,   55,   56,   57,  152,  188,  152,  132,  133,  134,\n /*   220 */    93,   94,   96,   97,   98,   99,  152,   19,  102,  103,\n /*   230 */   104,   23,   94,   72,   79,  173,  174,  173,  174,  113,\n /*   240 */    84,   85,   86,   87,   88,   89,   90,   91,   92,   93,\n /*   250 */    94,   43,   44,   45,   46,   47,   48,   49,   50,   51,\n /*   260 */    52,   53,   54,   55,   56,   57,  152,  171,  152,  108,\n /*   270 */   109,  110,  208,  209,  119,  120,  152,  180,  181,   19,\n /*   280 */   119,  120,  152,   23,  152,  152,  189,  173,  174,  173,\n /*   290 */   174,   59,   84,   85,   86,   87,   88,   89,   90,   91,\n /*   300 */    92,   93,   94,   43,   44,   45,   46,   47,   48,   49,\n /*   310 */    50,   51,   52,   53,   54,   55,   56,   57,  222,  223,\n /*   320 */   224,  186,  208,  209,  208,  209,  194,  194,   96,   97,\n /*   330 */    98,   19,  168,  169,  170,   23,   88,   89,  163,   59,\n /*   340 */     0,    1,    2,  219,   84,   85,   86,   87,   88,   89,\n /*   350 */    90,   91,   92,   93,   94,   43,   44,   45,   46,   47,\n /*   360 */    48,   49,   50,   51,   52,   53,   54,   55,   56,   57,\n /*   370 */    90,  152,  197,  195,  196,  243,   96,   97,   98,  196,\n /*   380 */   132,   11,  134,   19,  182,  207,  115,   23,  117,  118,\n /*   390 */   207,  163,  173,  174,  152,  220,   84,   85,   86,   87,\n /*   400 */    88,   89,   90,   91,   92,   93,   94,   43,   44,   45,\n /*   410 */    46,   47,   48,   49,   50,   51,   52,   53,   54,   55,\n /*   420 */    56,   57,  152,   16,  152,  197,  171,  208,   22,   23,\n /*   430 */    22,   23,   26,   16,   26,   19,    7,    8,    9,   23,\n /*   440 */   212,  213,  152,  173,  174,  173,  174,   19,   84,   85,\n /*   450 */    86,   87,   88,   89,   90,   91,   92,   93,   94,   43,\n /*   460 */    44,   45,   46,   47,   48,   49,   50,   51,   52,   53,\n /*   470 */    54,   55,   56,   57,   46,  152,  109,  110,  208,  109,\n /*   480 */   110,  152,   75,  152,   77,   22,   23,   19,  233,   83,\n /*   490 */   152,   83,   75,  238,   77,  164,  173,  174,  226,   59,\n /*   500 */    84,   85,   86,   87,   88,   89,   90,   91,   92,   93,\n /*   510 */    94,   43,   44,   45,   46,   47,   48,   49,   50,   51,\n /*   520 */    52,   53,   54,   55,   56,   57,  108,  109,  110,  152,\n /*   530 */   152,  152,   22,   22,   23,  107,   96,   97,   98,  160,\n /*   540 */   112,  251,   19,  164,   22,  152,   83,  140,  219,  152,\n /*   550 */   173,  174,   84,   85,   86,   87,   88,   89,   90,   91,\n /*   560 */    92,   93,   94,   59,  124,  152,   43,   44,   45,   46,\n /*   570 */    47,   48,   49,   50,   51,   52,   53,   54,   55,   56,\n /*   580 */    57,   59,  169,  170,  119,  120,   82,  108,  109,  110,\n /*   590 */   191,  192,  191,  192,   83,  248,  249,   19,   88,   89,\n /*   600 */    96,   97,   24,  152,  152,  101,  138,   84,   85,   86,\n /*   610 */    87,   88,   89,   90,   91,   92,   93,   94,   96,   97,\n /*   620 */    98,   43,   44,   45,   46,   47,   48,   49,   50,   51,\n /*   630 */    52,   53,   54,   55,   56,   57,  132,  133,  134,  152,\n /*   640 */   152,   46,  152,   26,  231,  194,  194,  146,  147,   19,\n /*   650 */   152,  116,  152,   72,  152,  152,  121,  152,  152,  152,\n /*   660 */    79,  138,   84,   85,   86,   87,   88,   89,   90,   91,\n /*   670 */    92,   93,   94,   43,   44,   45,   46,   47,   48,   49,\n /*   680 */    50,   51,   52,   53,   54,   55,   56,   57,  152,  108,\n /*   690 */    23,  152,  194,   26,  194,  152,  194,  194,  137,  152,\n /*   700 */   139,   19,  107,  166,  167,  218,  218,   29,  218,  173,\n /*   710 */   174,   33,  173,  174,   84,   85,   86,   87,   88,   89,\n /*   720 */    90,   91,   92,   93,   94,   43,   44,   45,   46,   47,\n /*   730 */    48,   49,   50,   51,   52,   53,   54,   55,   56,   57,\n /*   740 */   152,  194,   64,  171,  239,  239,  239,  130,  166,  167,\n /*   750 */   212,  213,   19,   23,  246,  247,   26,   59,   26,  152,\n /*   760 */   163,  218,  163,  163,  163,   98,   84,   85,   86,   87,\n /*   770 */    88,   89,   90,   91,   92,   93,   94,   44,   45,   46,\n /*   780 */    47,   48,   49,   50,   51,   52,   53,   54,   55,   56,\n /*   790 */    57,  124,   26,   79,  197,   97,  197,  197,  197,   31,\n /*   800 */   152,   23,   19,   19,   26,   19,  218,   39,   23,   21,\n /*   810 */   238,   26,  163,  163,  100,   59,  163,   84,   85,   86,\n /*   820 */    87,   88,   89,   90,   91,   92,   93,   94,   45,   46,\n /*   830 */    47,   48,   49,   50,   51,   52,   53,   54,   55,   56,\n /*   840 */    57,   19,   20,  152,   22,   23,  197,  197,   23,   19,\n /*   850 */   197,   26,  152,   97,   23,  123,   23,   26,   36,   26,\n /*   860 */   152,  152,   19,   20,   98,   22,   78,   84,   85,   86,\n /*   870 */    87,   88,   89,   90,   91,   92,   93,   94,   94,   36,\n /*   880 */   152,   59,   96,   99,  100,  101,  102,  103,  104,  105,\n /*   890 */   124,  103,   70,  100,  101,   23,  112,   12,   26,   12,\n /*   900 */    23,   79,   59,   26,   82,  101,   22,    7,    8,  152,\n /*   910 */    88,   89,   27,   70,   27,  152,  112,   95,   96,   97,\n /*   920 */    98,  152,   79,  101,   22,   82,   96,   42,  140,   42,\n /*   930 */   182,   88,   89,   19,   20,  132,   22,  134,   95,   96,\n /*   940 */    97,   98,   23,   59,  101,   26,   22,   62,  152,   62,\n /*   950 */    36,   22,   59,   24,  132,  133,  134,  135,  136,   72,\n /*   960 */     5,   59,  152,   22,   71,   10,   11,   12,   13,   14,\n /*   970 */   152,  152,   17,   59,  182,  132,  133,  134,  135,  136,\n /*   980 */    96,   97,   98,   59,   70,   30,  152,   32,   59,   96,\n /*   990 */    97,   98,  173,  174,   53,   40,   82,  152,   96,   97,\n /*  1000 */    98,   90,   88,   89,   90,   24,  187,  173,  174,   95,\n /*  1010 */    96,   97,   98,  152,  152,  101,   19,   20,  152,   22,\n /*  1020 */    96,   97,   98,  152,   69,   59,   97,  116,   59,  214,\n /*  1030 */   152,   76,  121,   36,   79,   80,   19,   20,  152,   22,\n /*  1040 */    59,  132,   59,  134,  173,  174,  132,  133,  134,  135,\n /*  1050 */   136,  173,  174,   36,  234,  152,   59,  152,  187,  173,\n /*  1060 */   174,  211,   96,   97,   98,  187,   97,   70,   23,  114,\n /*  1070 */   152,   26,   23,  187,   23,   26,   59,   26,   97,   82,\n /*  1080 */    97,   22,  164,  152,  152,   88,   89,   70,  192,  152,\n /*  1090 */   124,  152,   95,   96,   97,   98,  141,  152,  101,   82,\n /*  1100 */   152,  152,  184,  152,  186,   88,   89,  199,   54,   55,\n /*  1110 */    56,   57,   95,   96,   97,   98,  152,  152,  101,  152,\n /*  1120 */   152,  173,  174,  235,   54,   55,   56,   57,   58,  132,\n /*  1130 */   133,  134,  135,  136,  211,  150,   59,  211,   84,   85,\n /*  1140 */    86,   87,   88,   89,   90,   91,   92,   93,   94,  132,\n /*  1150 */   133,  134,  135,  136,   84,   85,   86,   87,   88,   89,\n /*  1160 */    90,   91,   92,   93,   94,   88,   89,  195,  196,   35,\n /*  1170 */   211,  211,  152,   96,   97,   98,  152,  100,  198,  207,\n /*  1180 */   171,  122,  240,  152,  107,  215,  109,  240,  202,  215,\n /*  1190 */   202,  152,  220,  173,  174,  177,  185,  173,  174,   65,\n /*  1200 */   152,  176,  152,  181,  173,  174,  215,   73,  176,  132,\n /*  1210 */   228,  134,  173,  174,  176,  152,  201,  152,  199,  155,\n /*  1220 */   152,  173,  174,  173,  174,   60,  152,  122,  244,   38,\n /*  1230 */   159,  159,  152,  241,  241,  152,  173,  174,  173,  174,\n /*  1240 */   152,  173,  174,  152,  159,  111,  152,  173,  174,  152,\n /*  1250 */    22,  152,   43,  173,  174,  152,  173,  174,  152,  190,\n /*  1260 */   130,  173,  174,  152,  173,  174,  152,  173,  174,  202,\n /*  1270 */   173,  174,  173,  174,  152,   18,  173,  174,  152,  173,\n /*  1280 */   174,  152,  221,  152,  173,  174,  193,  173,  174,  152,\n /*  1290 */   158,  152,  159,  152,   22,  173,  174,  152,   18,  173,\n /*  1300 */   174,  152,  173,  174,  173,  174,  152,  221,  152,  193,\n /*  1310 */   173,  174,  173,  174,  173,  174,  152,  193,  173,  174,\n /*  1320 */   152,  193,  173,  174,  158,  152,  190,  173,  174,  173,\n /*  1330 */   174,   59,  152,  190,  159,  137,  152,  173,  174,  152,\n /*  1340 */   202,  173,  174,   61,  152,  237,  173,  174,  202,  236,\n /*  1350 */    22,  107,  159,  173,  174,  159,  178,  173,  174,  158,\n /*  1360 */   173,  174,  159,  158,  158,  173,  174,  159,  178,   97,\n /*  1370 */   175,   63,  175,  106,  175,  125,  217,  183,  178,  175,\n /*  1380 */   107,  159,   22,  216,  177,  175,  217,  175,  175,  217,\n /*  1390 */   216,  159,  216,  216,  183,  225,  217,  137,  227,  178,\n /*  1400 */    94,  178,  126,  129,   25,  128,  127,  162,  206,   26,\n /*  1410 */   161,  230,  230,   13,  153,  153,    6,  151,  203,  205,\n /*  1420 */   204,  202,  151,  165,  171,  171,  151,  171,  165,  165,\n /*  1430 */   171,  179,    4,  250,  179,  250,  247,    3,   22,  171,\n /*  1440 */   171,  171,  142,   81,   15,   23,   16,   23,  131,  171,\n /*  1450 */   120,  111,  123,   20,   16,    1,  125,  123,  131,   53,\n /*  1460 */    53,   53,   53,  111,   96,   34,  122,    1,    5,   22,\n /*  1470 */   107,   67,  140,   74,   26,   24,   41,  107,   67,   20,\n /*  1480 */    19,  112,  105,   66,   22,   66,   22,   22,   28,   66,\n /*  1490 */    23,   22,   22,   37,   23,   23,   23,  116,   22,   22,\n /*  1500 */    26,   23,  122,   23,   23,   26,   22,   11,   96,   34,\n /*  1510 */   124,   26,   26,   23,   23,   23,   34,   34,   23,   26,\n /*  1520 */    23,   22,   24,   23,   22,  122,   23,   26,   22,   24,\n /*  1530 */    23,   22,   15,   23,   23,   22,  122,  122,   23,    1,\n /*  1540 */   122,  252,  252,  252,  252,  252,  252,  252,  252,  252,\n /*  1550 */   252,  252,  252,  252,  252,  252,  252,  252,  252,  252,\n /*  1560 */   252,  252,  252,  252,  252,  252,  252,  252,  252,  252,\n /*  1570 */   252,  252,  252,  252,  252,  252,  252,  252,  252,  252,\n /*  1580 */   252,  252,  252,  252,  252,  252,  252,  252,  252,  252,\n /*  1590 */   252,  252,  252,  252,  252,  252,  252,  252,  252,  252,\n /*  1600 */   252,  252,  252,  252,  252,  252,  252,  252,  252,  252,\n /*  1610 */   252,  252,  252,  252,  252,  252,  252,  252,  252,  252,\n /*  1620 */   252,  252,  252,  252,  252,  252,  252,  252,  252,  252,\n /*  1630 */   252,  252,  252,  252,  252,  252,  252,  252,  252,  252,\n /*  1640 */   252,  252,  252,  252,  252,  252,  252,  252,  252,  252,\n /*  1650 */   252,  252,  252,  252,  252,  252,  252,  252,  252,  252,\n /*  1660 */   252,  252,  252,  252,  252,  252,  252,  252,  252,  252,\n /*  1670 */   252,  252,  252,  252,  252,  252,  252,  252,  252,  252,\n /*  1680 */   252,  252,  252,  252,\n};\n#define YY_SHIFT_COUNT    (465)\n#define YY_SHIFT_MIN      (0)\n#define YY_SHIFT_MAX      (1538)\nstatic const unsigned short int yy_shift_ofst[] = {\n /*     0 */    39,  822,  955,  843,  997,  997,  997,  997,    0,    0,\n /*    10 */   104,  630,  997,  997,  997,  997,  997,  997,  997, 1077,\n /*    20 */  1077,  126,  161,  155,   52,  156,  208,  260,  312,  364,\n /*    30 */   416,  468,  523,  578,  630,  630,  630,  630,  630,  630,\n /*    40 */   630,  630,  630,  630,  630,  630,  630,  630,  630,  630,\n /*    50 */   630,  682,  630,  733,  783,  783,  914,  997,  997,  997,\n /*    60 */   997,  997,  997,  997,  997,  997,  997,  997,  997,  997,\n /*    70 */   997,  997,  997,  997,  997,  997,  997,  997,  997,  997,\n /*    80 */   997,  997,  997,  997,  997,  997,  997,  997, 1017,  997,\n /*    90 */   997,  997,  997,  997,  997,  997,  997,  997,  997,  997,\n /*   100 */   997,  997, 1070, 1054, 1054, 1054, 1054, 1054,   40,   25,\n /*   110 */    72,  232,  788,  428,  248,  248,  232,  581,  367,  127,\n /*   120 */   465,  138, 1541, 1541, 1541,  784,  784,  784,  522,  522,\n /*   130 */   887,  887,  893,  406,  408,  232,  232,  232,  232,  232,\n /*   140 */   232,  232,  232,  232,  232,  232,  232,  232,  232,  232,\n /*   150 */   232,  232,  232,  232,  232,  370,  340,  714,  698,  698,\n /*   160 */   465,   89,   89,   89,   89,   89,   89, 1541, 1541, 1541,\n /*   170 */   504,   85,   85,  884,   70,  280,  902,  440,  966,  924,\n /*   180 */   232,  232,  232,  232,  232,  232,  232,  232,  232,  232,\n /*   190 */   232,  232,  232,  232,  232,  232, 1134, 1134, 1134,  232,\n /*   200 */   232,  667,  232,  232,  232,  929,  232,  232,  885,  232,\n /*   210 */   232,  232,  232,  232,  232,  232,  232,  232,  232,  418,\n /*   220 */   678,  981,  981,  981,  981,  766,  271,  911,  510,  429,\n /*   230 */   617,  786,  786,  830,  617,  830,    4,  730,  595,  768,\n /*   240 */   786,  561,  768,  768,  732,  535,   55, 1165, 1105, 1105,\n /*   250 */  1191, 1191, 1105, 1228, 1209, 1130, 1257, 1257, 1257, 1257,\n /*   260 */  1105, 1280, 1130, 1228, 1209, 1209, 1130, 1105, 1280, 1198,\n /*   270 */  1282, 1105, 1105, 1280, 1328, 1105, 1280, 1105, 1280, 1328,\n /*   280 */  1244, 1244, 1244, 1308, 1328, 1244, 1267, 1244, 1308, 1244,\n /*   290 */  1244, 1250, 1273, 1250, 1273, 1250, 1273, 1250, 1273, 1105,\n /*   300 */  1360, 1105, 1260, 1328, 1306, 1306, 1328, 1274, 1276, 1277,\n /*   310 */  1279, 1130, 1379, 1383, 1400, 1400, 1410, 1410, 1410, 1541,\n /*   320 */  1541, 1541, 1541, 1541, 1541, 1541, 1541, 1541, 1541, 1541,\n /*   330 */  1541, 1541, 1541, 1541, 1541,   34,  407,  463,  511,  417,\n /*   340 */   479, 1272,  778,  941,  785,  825,  831,  833,  872,  877,\n /*   350 */   756,  793,  900,  804,  919, 1045,  969, 1049,  803,  909,\n /*   360 */  1051,  983, 1059, 1428, 1434, 1416, 1300, 1429, 1362, 1430,\n /*   370 */  1422, 1424, 1330, 1317, 1340, 1329, 1433, 1331, 1438, 1454,\n /*   380 */  1334, 1327, 1406, 1407, 1408, 1409, 1352, 1368, 1431, 1344,\n /*   390 */  1466, 1463, 1447, 1363, 1332, 1404, 1448, 1411, 1399, 1435,\n /*   400 */  1370, 1451, 1459, 1461, 1369, 1377, 1462, 1417, 1464, 1465,\n /*   410 */  1467, 1469, 1419, 1460, 1470, 1423, 1456, 1471, 1472, 1473,\n /*   420 */  1474, 1381, 1476, 1478, 1477, 1479, 1380, 1480, 1481, 1412,\n /*   430 */  1475, 1484, 1386, 1485, 1482, 1486, 1483, 1490, 1485, 1491,\n /*   440 */  1492, 1495, 1493, 1497, 1499, 1496, 1500, 1502, 1498, 1501,\n /*   450 */  1503, 1506, 1505, 1501, 1507, 1509, 1510, 1511, 1513, 1403,\n /*   460 */  1414, 1415, 1418, 1515, 1517, 1538,\n};\n#define YY_REDUCE_COUNT (334)\n#define YY_REDUCE_MIN   (-217)\n#define YY_REDUCE_MAX   (1278)\nstatic const short yy_reduce_ofst[] = {\n /*     0 */  -144, -139, -134, -136, -141,   64,  114,  116, -158, -148,\n /*    10 */  -217,   96,  819,  871,  878,  219,  270,  886,  272, -110,\n /*    20 */   413,  918,  972,  228, -214, -214, -214, -214, -214, -214,\n /*    30 */  -214, -214, -214, -214, -214, -214, -214, -214, -214, -214,\n /*    40 */  -214, -214, -214, -214, -214, -214, -214, -214, -214, -214,\n /*    50 */  -214, -214, -214, -214, -214, -214,   62,  323,  377,  536,\n /*    60 */   539,  834,  948, 1020, 1024, 1031, 1039, 1048, 1050, 1063,\n /*    70 */  1065, 1068, 1074, 1080, 1083, 1088, 1091, 1094, 1097, 1099,\n /*    80 */  1103, 1106, 1111, 1114, 1122, 1126, 1129, 1131, 1137, 1139,\n /*    90 */  1141, 1145, 1149, 1154, 1156, 1164, 1168, 1173, 1180, 1184,\n /*   100 */  1187, 1192, -214, -214, -214, -214, -214, -214, -214, -214,\n /*   110 */  -214,  132,  -45,   97,    8,  164,  379,  175,  255, -214,\n /*   120 */   178, -214, -214, -214, -214, -168, -168, -168,  124,  329,\n /*   130 */   399,  401, -129,  347,  347,  331,  133,  451,  452,  498,\n /*   140 */   500,  502,  503,  505,  487,  506,  488,  490,  507,  543,\n /*   150 */   547, -126,  588,  290,   27,  572,  501,  597,  537,  582,\n /*   160 */   183,  599,  600,  601,  649,  650,  653,  508,  538,  -29,\n /*   170 */  -156, -152, -137,  -79,  135,   74,  130,  242,  338,  378,\n /*   180 */   393,  397,  607,  648,  691,  700,  708,  709,  728,  757,\n /*   190 */   763,  769,  796,  810,  818,  845,  202,  748,  792,  861,\n /*   200 */   862,  815,  866,  903,  905,  850,  931,  932,  896,  937,\n /*   210 */   939,  945,   74,  949,  951,  964,  965,  967,  968,  888,\n /*   220 */   820,  923,  926,  959,  960,  815,  980,  908, 1009,  985,\n /*   230 */   986,  970,  974,  942,  988,  947, 1018, 1011, 1022, 1025,\n /*   240 */   991,  982, 1032, 1038, 1015, 1019, 1064,  984, 1071, 1072,\n /*   250 */   992,  993, 1085, 1061, 1069, 1067, 1093, 1116, 1124, 1128,\n /*   260 */  1133, 1132, 1138, 1086, 1136, 1143, 1146, 1175, 1166, 1108,\n /*   270 */  1113, 1193, 1196, 1201, 1178, 1203, 1205, 1208, 1206, 1190,\n /*   280 */  1195, 1197, 1199, 1194, 1200, 1204, 1207, 1210, 1211, 1212,\n /*   290 */  1213, 1159, 1167, 1169, 1174, 1172, 1176, 1179, 1177, 1222,\n /*   300 */  1170, 1232, 1171, 1221, 1181, 1182, 1223, 1202, 1214, 1216,\n /*   310 */  1215, 1219, 1245, 1249, 1261, 1262, 1266, 1271, 1275, 1183,\n /*   320 */  1185, 1189, 1258, 1253, 1254, 1256, 1259, 1263, 1252, 1255,\n /*   330 */  1268, 1269, 1270, 1278, 1264,\n};\nstatic const YYACTIONTYPE yy_default[] = {\n /*     0 */  1286, 1276, 1276, 1276, 1209, 1209, 1209, 1209, 1133, 1133,\n /*    10 */  1260, 1036, 1005, 1005, 1005, 1005, 1005, 1005, 1208, 1005,\n /*    20 */  1005, 1005, 1005, 1108, 1139, 1005, 1005, 1005, 1005, 1210,\n /*    30 */  1211, 1005, 1005, 1005, 1259, 1261, 1149, 1148, 1147, 1146,\n /*    40 */  1242, 1120, 1144, 1137, 1141, 1210, 1204, 1205, 1203, 1207,\n /*    50 */  1211, 1005, 1140, 1174, 1188, 1173, 1005, 1005, 1005, 1005,\n /*    60 */  1005, 1005, 1005, 1005, 1005, 1005, 1005, 1005, 1005, 1005,\n /*    70 */  1005, 1005, 1005, 1005, 1005, 1005, 1005, 1005, 1005, 1005,\n /*    80 */  1005, 1005, 1005, 1005, 1005, 1005, 1005, 1005, 1005, 1005,\n /*    90 */  1005, 1005, 1005, 1005, 1005, 1005, 1005, 1005, 1005, 1005,\n /*   100 */  1005, 1005, 1182, 1187, 1194, 1186, 1183, 1176, 1175, 1177,\n /*   110 */  1178, 1005, 1026, 1075, 1005, 1005, 1005, 1276, 1036, 1179,\n /*   120 */  1005, 1180, 1191, 1190, 1189, 1267, 1294, 1293, 1005, 1005,\n /*   130 */  1005, 1005, 1005, 1005, 1005, 1005, 1005, 1005, 1005, 1005,\n /*   140 */  1005, 1005, 1005, 1005, 1005, 1005, 1005, 1005, 1005, 1005,\n /*   150 */  1005, 1005, 1005, 1005, 1005, 1036, 1286, 1276, 1032, 1032,\n /*   160 */  1005, 1276, 1276, 1276, 1276, 1276, 1276, 1272, 1108, 1099,\n /*   170 */  1005, 1005, 1005, 1005, 1005, 1005, 1005, 1005, 1005, 1005,\n /*   180 */  1005, 1264, 1262, 1005, 1224, 1005, 1005, 1005, 1005, 1005,\n /*   190 */  1005, 1005, 1005, 1005, 1005, 1005, 1005, 1005, 1005, 1005,\n /*   200 */  1005, 1005, 1005, 1005, 1005, 1104, 1005, 1005, 1005, 1005,\n /*   210 */  1005, 1005, 1005, 1005, 1005, 1005, 1005, 1005, 1288, 1005,\n /*   220 */  1237, 1104, 1104, 1104, 1104, 1106, 1088, 1098, 1036, 1012,\n /*   230 */  1143, 1122, 1122, 1327, 1143, 1327, 1050, 1308, 1047, 1133,\n /*   240 */  1122, 1206, 1133, 1133, 1105, 1098, 1005, 1330, 1113, 1113,\n /*   250 */  1329, 1329, 1113, 1154, 1078, 1143, 1084, 1084, 1084, 1084,\n /*   260 */  1113, 1023, 1143, 1154, 1078, 1078, 1143, 1113, 1023, 1241,\n /*   270 */  1324, 1113, 1113, 1023, 1217, 1113, 1023, 1113, 1023, 1217,\n /*   280 */  1076, 1076, 1076, 1065, 1217, 1076, 1050, 1076, 1065, 1076,\n /*   290 */  1076, 1126, 1121, 1126, 1121, 1126, 1121, 1126, 1121, 1113,\n /*   300 */  1212, 1113, 1005, 1217, 1221, 1221, 1217, 1138, 1127, 1136,\n /*   310 */  1134, 1143, 1029, 1068, 1291, 1291, 1287, 1287, 1287, 1335,\n /*   320 */  1335, 1272, 1303, 1036, 1036, 1036, 1036, 1303, 1052, 1052,\n /*   330 */  1036, 1036, 1036, 1036, 1303, 1005, 1005, 1005, 1005, 1005,\n /*   340 */  1005, 1298, 1005, 1226, 1005, 1005, 1005, 1005, 1005, 1005,\n /*   350 */  1005, 1005, 1005, 1005, 1005, 1005, 1005, 1005, 1005, 1005,\n /*   360 */  1005, 1005, 1159, 1005, 1008, 1269, 1005, 1005, 1268, 1005,\n /*   370 */  1005, 1005, 1005, 1005, 1005, 1005, 1005, 1005, 1005, 1005,\n /*   380 */  1005, 1005, 1005, 1005, 1005, 1005, 1005, 1005, 1005, 1326,\n /*   390 */  1005, 1005, 1005, 1005, 1005, 1005, 1240, 1239, 1005, 1005,\n /*   400 */  1005, 1005, 1005, 1005, 1005, 1005, 1005, 1005, 1005, 1005,\n /*   410 */  1005, 1005, 1005, 1005, 1005, 1005, 1005, 1005, 1005, 1005,\n /*   420 */  1005, 1090, 1005, 1005, 1005, 1312, 1005, 1005, 1005, 1005,\n /*   430 */  1005, 1005, 1005, 1135, 1005, 1128, 1005, 1005, 1317, 1005,\n /*   440 */  1005, 1005, 1005, 1005, 1005, 1005, 1005, 1005, 1005, 1278,\n /*   450 */  1005, 1005, 1005, 1277, 1005, 1005, 1005, 1005, 1005, 1161,\n /*   460 */  1005, 1160, 1164, 1005, 1017, 1005,\n};\n/********** End of lemon-generated parsing tables *****************************/\n\n/* The next table maps tokens (terminal symbols) into fallback tokens.  \n** If a construct like the following:\n** \n**      %fallback ID X Y Z.\n**\n** appears in the grammar, then ID becomes a fallback token for X, Y,\n** and Z.  Whenever one of the tokens X, Y, or Z is input to the parser\n** but it does not parse, the type of the token is changed to ID and\n** the parse is retried before an error is thrown.\n**\n** This feature can be used, for example, to cause some keywords in a language\n** to revert to identifiers if they keyword does not apply in the context where\n** it appears.\n*/\n#ifdef YYFALLBACK\nstatic const YYCODETYPE yyFallback[] = {\n    0,  /*          $ => nothing */\n    0,  /*       SEMI => nothing */\n   59,  /*    EXPLAIN => ID */\n   59,  /*      QUERY => ID */\n   59,  /*       PLAN => ID */\n   59,  /*      BEGIN => ID */\n    0,  /* TRANSACTION => nothing */\n   59,  /*   DEFERRED => ID */\n   59,  /*  IMMEDIATE => ID */\n   59,  /*  EXCLUSIVE => ID */\n    0,  /*     COMMIT => nothing */\n   59,  /*        END => ID */\n   59,  /*   ROLLBACK => ID */\n   59,  /*  SAVEPOINT => ID */\n   59,  /*    RELEASE => ID */\n    0,  /*         TO => nothing */\n    0,  /*      TABLE => nothing */\n    0,  /*     CREATE => nothing */\n   59,  /*         IF => ID */\n    0,  /*        NOT => nothing */\n    0,  /*     EXISTS => nothing */\n   59,  /*       TEMP => ID */\n    0,  /*         LP => nothing */\n    0,  /*         RP => nothing */\n    0,  /*         AS => nothing */\n   59,  /*    WITHOUT => ID */\n    0,  /*      COMMA => nothing */\n   59,  /*      ABORT => ID */\n   59,  /*     ACTION => ID */\n   59,  /*      AFTER => ID */\n   59,  /*    ANALYZE => ID */\n   59,  /*        ASC => ID */\n   59,  /*     ATTACH => ID */\n   59,  /*     BEFORE => ID */\n   59,  /*         BY => ID */\n   59,  /*    CASCADE => ID */\n   59,  /*       CAST => ID */\n   59,  /*   CONFLICT => ID */\n   59,  /*   DATABASE => ID */\n   59,  /*       DESC => ID */\n   59,  /*     DETACH => ID */\n   59,  /*       EACH => ID */\n   59,  /*       FAIL => ID */\n    0,  /*         OR => nothing */\n    0,  /*        AND => nothing */\n    0,  /*         IS => nothing */\n   59,  /*      MATCH => ID */\n   59,  /*    LIKE_KW => ID */\n    0,  /*    BETWEEN => nothing */\n    0,  /*         IN => nothing */\n    0,  /*     ISNULL => nothing */\n    0,  /*    NOTNULL => nothing */\n    0,  /*         NE => nothing */\n    0,  /*         EQ => nothing */\n    0,  /*         GT => nothing */\n    0,  /*         LE => nothing */\n    0,  /*         LT => nothing */\n    0,  /*         GE => nothing */\n    0,  /*     ESCAPE => nothing */\n    0,  /*         ID => nothing */\n   59,  /*   COLUMNKW => ID */\n   59,  /*        FOR => ID */\n   59,  /*     IGNORE => ID */\n   59,  /*  INITIALLY => ID */\n   59,  /*    INSTEAD => ID */\n   59,  /*         NO => ID */\n   59,  /*        KEY => ID */\n   59,  /*         OF => ID */\n   59,  /*     OFFSET => ID */\n   59,  /*     PRAGMA => ID */\n   59,  /*      RAISE => ID */\n   59,  /*  RECURSIVE => ID */\n   59,  /*    REPLACE => ID */\n   59,  /*   RESTRICT => ID */\n   59,  /*        ROW => ID */\n   59,  /*    TRIGGER => ID */\n   59,  /*     VACUUM => ID */\n   59,  /*       VIEW => ID */\n   59,  /*    VIRTUAL => ID */\n   59,  /*       WITH => ID */\n   59,  /*    REINDEX => ID */\n   59,  /*     RENAME => ID */\n   59,  /*   CTIME_KW => ID */\n};\n#endif /* YYFALLBACK */\n\n/* The following structure represents a single element of the\n** parser's stack.  Information stored includes:\n**\n**   +  The state number for the parser at this level of the stack.\n**\n**   +  The value of the token stored at this level of the stack.\n**      (In other words, the \"major\" token.)\n**\n**   +  The semantic value stored at this level of the stack.  This is\n**      the information used by the action routines in the grammar.\n**      It is sometimes called the \"minor\" token.\n**\n** After the \"shift\" half of a SHIFTREDUCE action, the stateno field\n** actually contains the reduce action for the second half of the\n** SHIFTREDUCE.\n*/\nstruct yyStackEntry {\n  YYACTIONTYPE stateno;  /* The state-number, or reduce action in SHIFTREDUCE */\n  YYCODETYPE major;      /* The major token value.  This is the code\n                         ** number for the token at this stack level */\n  YYMINORTYPE minor;     /* The user-supplied minor token value.  This\n                         ** is the value of the token  */\n};\ntypedef struct yyStackEntry yyStackEntry;\n\n/* The state of the parser is completely contained in an instance of\n** the following structure */\nstruct yyParser {\n  yyStackEntry *yytos;          /* Pointer to top element of the stack */\n#ifdef YYTRACKMAXSTACKDEPTH\n  int yyhwm;                    /* High-water mark of the stack */\n#endif\n#ifndef YYNOERRORRECOVERY\n  int yyerrcnt;                 /* Shifts left before out of the error */\n#endif\n  sqlite3ParserARG_SDECL                /* A place to hold %extra_argument */\n#if YYSTACKDEPTH<=0\n  int yystksz;                  /* Current side of the stack */\n  yyStackEntry *yystack;        /* The parser's stack */\n  yyStackEntry yystk0;          /* First stack entry */\n#else\n  yyStackEntry yystack[YYSTACKDEPTH];  /* The parser's stack */\n  yyStackEntry *yystackEnd;            /* Last entry in the stack */\n#endif\n};\ntypedef struct yyParser yyParser;\n\n#ifndef NDEBUG\n/* #include <stdio.h> */\nstatic FILE *yyTraceFILE = 0;\nstatic char *yyTracePrompt = 0;\n#endif /* NDEBUG */\n\n#ifndef NDEBUG\n/* \n** Turn parser tracing on by giving a stream to which to write the trace\n** and a prompt to preface each trace message.  Tracing is turned off\n** by making either argument NULL \n**\n** Inputs:\n** <ul>\n** <li> A FILE* to which trace output should be written.\n**      If NULL, then tracing is turned off.\n** <li> A prefix string written at the beginning of every\n**      line of trace output.  If NULL, then tracing is\n**      turned off.\n** </ul>\n**\n** Outputs:\n** None.\n*/\nSQLITE_PRIVATE void sqlite3ParserTrace(FILE *TraceFILE, char *zTracePrompt){\n  yyTraceFILE = TraceFILE;\n  yyTracePrompt = zTracePrompt;\n  if( yyTraceFILE==0 ) yyTracePrompt = 0;\n  else if( yyTracePrompt==0 ) yyTraceFILE = 0;\n}\n#endif /* NDEBUG */\n\n#if defined(YYCOVERAGE) || !defined(NDEBUG)\n/* For tracing shifts, the names of all terminals and nonterminals\n** are required.  The following table supplies these names */\nstatic const char *const yyTokenName[] = { \n  /*    0 */ \"$\",\n  /*    1 */ \"SEMI\",\n  /*    2 */ \"EXPLAIN\",\n  /*    3 */ \"QUERY\",\n  /*    4 */ \"PLAN\",\n  /*    5 */ \"BEGIN\",\n  /*    6 */ \"TRANSACTION\",\n  /*    7 */ \"DEFERRED\",\n  /*    8 */ \"IMMEDIATE\",\n  /*    9 */ \"EXCLUSIVE\",\n  /*   10 */ \"COMMIT\",\n  /*   11 */ \"END\",\n  /*   12 */ \"ROLLBACK\",\n  /*   13 */ \"SAVEPOINT\",\n  /*   14 */ \"RELEASE\",\n  /*   15 */ \"TO\",\n  /*   16 */ \"TABLE\",\n  /*   17 */ \"CREATE\",\n  /*   18 */ \"IF\",\n  /*   19 */ \"NOT\",\n  /*   20 */ \"EXISTS\",\n  /*   21 */ \"TEMP\",\n  /*   22 */ \"LP\",\n  /*   23 */ \"RP\",\n  /*   24 */ \"AS\",\n  /*   25 */ \"WITHOUT\",\n  /*   26 */ \"COMMA\",\n  /*   27 */ \"ABORT\",\n  /*   28 */ \"ACTION\",\n  /*   29 */ \"AFTER\",\n  /*   30 */ \"ANALYZE\",\n  /*   31 */ \"ASC\",\n  /*   32 */ \"ATTACH\",\n  /*   33 */ \"BEFORE\",\n  /*   34 */ \"BY\",\n  /*   35 */ \"CASCADE\",\n  /*   36 */ \"CAST\",\n  /*   37 */ \"CONFLICT\",\n  /*   38 */ \"DATABASE\",\n  /*   39 */ \"DESC\",\n  /*   40 */ \"DETACH\",\n  /*   41 */ \"EACH\",\n  /*   42 */ \"FAIL\",\n  /*   43 */ \"OR\",\n  /*   44 */ \"AND\",\n  /*   45 */ \"IS\",\n  /*   46 */ \"MATCH\",\n  /*   47 */ \"LIKE_KW\",\n  /*   48 */ \"BETWEEN\",\n  /*   49 */ \"IN\",\n  /*   50 */ \"ISNULL\",\n  /*   51 */ \"NOTNULL\",\n  /*   52 */ \"NE\",\n  /*   53 */ \"EQ\",\n  /*   54 */ \"GT\",\n  /*   55 */ \"LE\",\n  /*   56 */ \"LT\",\n  /*   57 */ \"GE\",\n  /*   58 */ \"ESCAPE\",\n  /*   59 */ \"ID\",\n  /*   60 */ \"COLUMNKW\",\n  /*   61 */ \"FOR\",\n  /*   62 */ \"IGNORE\",\n  /*   63 */ \"INITIALLY\",\n  /*   64 */ \"INSTEAD\",\n  /*   65 */ \"NO\",\n  /*   66 */ \"KEY\",\n  /*   67 */ \"OF\",\n  /*   68 */ \"OFFSET\",\n  /*   69 */ \"PRAGMA\",\n  /*   70 */ \"RAISE\",\n  /*   71 */ \"RECURSIVE\",\n  /*   72 */ \"REPLACE\",\n  /*   73 */ \"RESTRICT\",\n  /*   74 */ \"ROW\",\n  /*   75 */ \"TRIGGER\",\n  /*   76 */ \"VACUUM\",\n  /*   77 */ \"VIEW\",\n  /*   78 */ \"VIRTUAL\",\n  /*   79 */ \"WITH\",\n  /*   80 */ \"REINDEX\",\n  /*   81 */ \"RENAME\",\n  /*   82 */ \"CTIME_KW\",\n  /*   83 */ \"ANY\",\n  /*   84 */ \"BITAND\",\n  /*   85 */ \"BITOR\",\n  /*   86 */ \"LSHIFT\",\n  /*   87 */ \"RSHIFT\",\n  /*   88 */ \"PLUS\",\n  /*   89 */ \"MINUS\",\n  /*   90 */ \"STAR\",\n  /*   91 */ \"SLASH\",\n  /*   92 */ \"REM\",\n  /*   93 */ \"CONCAT\",\n  /*   94 */ \"COLLATE\",\n  /*   95 */ \"BITNOT\",\n  /*   96 */ \"INDEXED\",\n  /*   97 */ \"STRING\",\n  /*   98 */ \"JOIN_KW\",\n  /*   99 */ \"CONSTRAINT\",\n  /*  100 */ \"DEFAULT\",\n  /*  101 */ \"NULL\",\n  /*  102 */ \"PRIMARY\",\n  /*  103 */ \"UNIQUE\",\n  /*  104 */ \"CHECK\",\n  /*  105 */ \"REFERENCES\",\n  /*  106 */ \"AUTOINCR\",\n  /*  107 */ \"ON\",\n  /*  108 */ \"INSERT\",\n  /*  109 */ \"DELETE\",\n  /*  110 */ \"UPDATE\",\n  /*  111 */ \"SET\",\n  /*  112 */ \"DEFERRABLE\",\n  /*  113 */ \"FOREIGN\",\n  /*  114 */ \"DROP\",\n  /*  115 */ \"UNION\",\n  /*  116 */ \"ALL\",\n  /*  117 */ \"EXCEPT\",\n  /*  118 */ \"INTERSECT\",\n  /*  119 */ \"SELECT\",\n  /*  120 */ \"VALUES\",\n  /*  121 */ \"DISTINCT\",\n  /*  122 */ \"DOT\",\n  /*  123 */ \"FROM\",\n  /*  124 */ \"JOIN\",\n  /*  125 */ \"USING\",\n  /*  126 */ \"ORDER\",\n  /*  127 */ \"GROUP\",\n  /*  128 */ \"HAVING\",\n  /*  129 */ \"LIMIT\",\n  /*  130 */ \"WHERE\",\n  /*  131 */ \"INTO\",\n  /*  132 */ \"FLOAT\",\n  /*  133 */ \"BLOB\",\n  /*  134 */ \"INTEGER\",\n  /*  135 */ \"VARIABLE\",\n  /*  136 */ \"CASE\",\n  /*  137 */ \"WHEN\",\n  /*  138 */ \"THEN\",\n  /*  139 */ \"ELSE\",\n  /*  140 */ \"INDEX\",\n  /*  141 */ \"ALTER\",\n  /*  142 */ \"ADD\",\n  /*  143 */ \"error\",\n  /*  144 */ \"input\",\n  /*  145 */ \"cmdlist\",\n  /*  146 */ \"ecmd\",\n  /*  147 */ \"explain\",\n  /*  148 */ \"cmdx\",\n  /*  149 */ \"cmd\",\n  /*  150 */ \"transtype\",\n  /*  151 */ \"trans_opt\",\n  /*  152 */ \"nm\",\n  /*  153 */ \"savepoint_opt\",\n  /*  154 */ \"create_table\",\n  /*  155 */ \"create_table_args\",\n  /*  156 */ \"createkw\",\n  /*  157 */ \"temp\",\n  /*  158 */ \"ifnotexists\",\n  /*  159 */ \"dbnm\",\n  /*  160 */ \"columnlist\",\n  /*  161 */ \"conslist_opt\",\n  /*  162 */ \"table_options\",\n  /*  163 */ \"select\",\n  /*  164 */ \"columnname\",\n  /*  165 */ \"carglist\",\n  /*  166 */ \"typetoken\",\n  /*  167 */ \"typename\",\n  /*  168 */ \"signed\",\n  /*  169 */ \"plus_num\",\n  /*  170 */ \"minus_num\",\n  /*  171 */ \"scanpt\",\n  /*  172 */ \"ccons\",\n  /*  173 */ \"term\",\n  /*  174 */ \"expr\",\n  /*  175 */ \"onconf\",\n  /*  176 */ \"sortorder\",\n  /*  177 */ \"autoinc\",\n  /*  178 */ \"eidlist_opt\",\n  /*  179 */ \"refargs\",\n  /*  180 */ \"defer_subclause\",\n  /*  181 */ \"refarg\",\n  /*  182 */ \"refact\",\n  /*  183 */ \"init_deferred_pred_opt\",\n  /*  184 */ \"conslist\",\n  /*  185 */ \"tconscomma\",\n  /*  186 */ \"tcons\",\n  /*  187 */ \"sortlist\",\n  /*  188 */ \"eidlist\",\n  /*  189 */ \"defer_subclause_opt\",\n  /*  190 */ \"orconf\",\n  /*  191 */ \"resolvetype\",\n  /*  192 */ \"raisetype\",\n  /*  193 */ \"ifexists\",\n  /*  194 */ \"fullname\",\n  /*  195 */ \"selectnowith\",\n  /*  196 */ \"oneselect\",\n  /*  197 */ \"with\",\n  /*  198 */ \"multiselect_op\",\n  /*  199 */ \"distinct\",\n  /*  200 */ \"selcollist\",\n  /*  201 */ \"from\",\n  /*  202 */ \"where_opt\",\n  /*  203 */ \"groupby_opt\",\n  /*  204 */ \"having_opt\",\n  /*  205 */ \"orderby_opt\",\n  /*  206 */ \"limit_opt\",\n  /*  207 */ \"values\",\n  /*  208 */ \"nexprlist\",\n  /*  209 */ \"exprlist\",\n  /*  210 */ \"sclp\",\n  /*  211 */ \"as\",\n  /*  212 */ \"seltablist\",\n  /*  213 */ \"stl_prefix\",\n  /*  214 */ \"joinop\",\n  /*  215 */ \"indexed_opt\",\n  /*  216 */ \"on_opt\",\n  /*  217 */ \"using_opt\",\n  /*  218 */ \"idlist\",\n  /*  219 */ \"setlist\",\n  /*  220 */ \"insert_cmd\",\n  /*  221 */ \"idlist_opt\",\n  /*  222 */ \"likeop\",\n  /*  223 */ \"between_op\",\n  /*  224 */ \"in_op\",\n  /*  225 */ \"paren_exprlist\",\n  /*  226 */ \"case_operand\",\n  /*  227 */ \"case_exprlist\",\n  /*  228 */ \"case_else\",\n  /*  229 */ \"uniqueflag\",\n  /*  230 */ \"collate\",\n  /*  231 */ \"nmnum\",\n  /*  232 */ \"trigger_decl\",\n  /*  233 */ \"trigger_cmd_list\",\n  /*  234 */ \"trigger_time\",\n  /*  235 */ \"trigger_event\",\n  /*  236 */ \"foreach_clause\",\n  /*  237 */ \"when_clause\",\n  /*  238 */ \"trigger_cmd\",\n  /*  239 */ \"trnm\",\n  /*  240 */ \"tridxby\",\n  /*  241 */ \"database_kw_opt\",\n  /*  242 */ \"key_opt\",\n  /*  243 */ \"add_column_fullname\",\n  /*  244 */ \"kwcolumn_opt\",\n  /*  245 */ \"create_vtab\",\n  /*  246 */ \"vtabarglist\",\n  /*  247 */ \"vtabarg\",\n  /*  248 */ \"vtabargtoken\",\n  /*  249 */ \"lp\",\n  /*  250 */ \"anylist\",\n  /*  251 */ \"wqlist\",\n};\n#endif /* defined(YYCOVERAGE) || !defined(NDEBUG) */\n\n#ifndef NDEBUG\n/* For tracing reduce actions, the names of all rules are required.\n*/\nstatic const char *const yyRuleName[] = {\n /*   0 */ \"explain ::= EXPLAIN\",\n /*   1 */ \"explain ::= EXPLAIN QUERY PLAN\",\n /*   2 */ \"cmdx ::= cmd\",\n /*   3 */ \"cmd ::= BEGIN transtype trans_opt\",\n /*   4 */ \"transtype ::=\",\n /*   5 */ \"transtype ::= DEFERRED\",\n /*   6 */ \"transtype ::= IMMEDIATE\",\n /*   7 */ \"transtype ::= EXCLUSIVE\",\n /*   8 */ \"cmd ::= COMMIT|END trans_opt\",\n /*   9 */ \"cmd ::= ROLLBACK trans_opt\",\n /*  10 */ \"cmd ::= SAVEPOINT nm\",\n /*  11 */ \"cmd ::= RELEASE savepoint_opt nm\",\n /*  12 */ \"cmd ::= ROLLBACK trans_opt TO savepoint_opt nm\",\n /*  13 */ \"create_table ::= createkw temp TABLE ifnotexists nm dbnm\",\n /*  14 */ \"createkw ::= CREATE\",\n /*  15 */ \"ifnotexists ::=\",\n /*  16 */ \"ifnotexists ::= IF NOT EXISTS\",\n /*  17 */ \"temp ::= TEMP\",\n /*  18 */ \"temp ::=\",\n /*  19 */ \"create_table_args ::= LP columnlist conslist_opt RP table_options\",\n /*  20 */ \"create_table_args ::= AS select\",\n /*  21 */ \"table_options ::=\",\n /*  22 */ \"table_options ::= WITHOUT nm\",\n /*  23 */ \"columnname ::= nm typetoken\",\n /*  24 */ \"typetoken ::=\",\n /*  25 */ \"typetoken ::= typename LP signed RP\",\n /*  26 */ \"typetoken ::= typename LP signed COMMA signed RP\",\n /*  27 */ \"typename ::= typename ID|STRING\",\n /*  28 */ \"scanpt ::=\",\n /*  29 */ \"ccons ::= CONSTRAINT nm\",\n /*  30 */ \"ccons ::= DEFAULT scanpt term scanpt\",\n /*  31 */ \"ccons ::= DEFAULT LP expr RP\",\n /*  32 */ \"ccons ::= DEFAULT PLUS term scanpt\",\n /*  33 */ \"ccons ::= DEFAULT MINUS term scanpt\",\n /*  34 */ \"ccons ::= DEFAULT scanpt ID|INDEXED\",\n /*  35 */ \"ccons ::= NOT NULL onconf\",\n /*  36 */ \"ccons ::= PRIMARY KEY sortorder onconf autoinc\",\n /*  37 */ \"ccons ::= UNIQUE onconf\",\n /*  38 */ \"ccons ::= CHECK LP expr RP\",\n /*  39 */ \"ccons ::= REFERENCES nm eidlist_opt refargs\",\n /*  40 */ \"ccons ::= defer_subclause\",\n /*  41 */ \"ccons ::= COLLATE ID|STRING\",\n /*  42 */ \"autoinc ::=\",\n /*  43 */ \"autoinc ::= AUTOINCR\",\n /*  44 */ \"refargs ::=\",\n /*  45 */ \"refargs ::= refargs refarg\",\n /*  46 */ \"refarg ::= MATCH nm\",\n /*  47 */ \"refarg ::= ON INSERT refact\",\n /*  48 */ \"refarg ::= ON DELETE refact\",\n /*  49 */ \"refarg ::= ON UPDATE refact\",\n /*  50 */ \"refact ::= SET NULL\",\n /*  51 */ \"refact ::= SET DEFAULT\",\n /*  52 */ \"refact ::= CASCADE\",\n /*  53 */ \"refact ::= RESTRICT\",\n /*  54 */ \"refact ::= NO ACTION\",\n /*  55 */ \"defer_subclause ::= NOT DEFERRABLE init_deferred_pred_opt\",\n /*  56 */ \"defer_subclause ::= DEFERRABLE init_deferred_pred_opt\",\n /*  57 */ \"init_deferred_pred_opt ::=\",\n /*  58 */ \"init_deferred_pred_opt ::= INITIALLY DEFERRED\",\n /*  59 */ \"init_deferred_pred_opt ::= INITIALLY IMMEDIATE\",\n /*  60 */ \"conslist_opt ::=\",\n /*  61 */ \"tconscomma ::= COMMA\",\n /*  62 */ \"tcons ::= CONSTRAINT nm\",\n /*  63 */ \"tcons ::= PRIMARY KEY LP sortlist autoinc RP onconf\",\n /*  64 */ \"tcons ::= UNIQUE LP sortlist RP onconf\",\n /*  65 */ \"tcons ::= CHECK LP expr RP onconf\",\n /*  66 */ \"tcons ::= FOREIGN KEY LP eidlist RP REFERENCES nm eidlist_opt refargs defer_subclause_opt\",\n /*  67 */ \"defer_subclause_opt ::=\",\n /*  68 */ \"onconf ::=\",\n /*  69 */ \"onconf ::= ON CONFLICT resolvetype\",\n /*  70 */ \"orconf ::=\",\n /*  71 */ \"orconf ::= OR resolvetype\",\n /*  72 */ \"resolvetype ::= IGNORE\",\n /*  73 */ \"resolvetype ::= REPLACE\",\n /*  74 */ \"cmd ::= DROP TABLE ifexists fullname\",\n /*  75 */ \"ifexists ::= IF EXISTS\",\n /*  76 */ \"ifexists ::=\",\n /*  77 */ \"cmd ::= createkw temp VIEW ifnotexists nm dbnm eidlist_opt AS select\",\n /*  78 */ \"cmd ::= DROP VIEW ifexists fullname\",\n /*  79 */ \"cmd ::= select\",\n /*  80 */ \"select ::= with selectnowith\",\n /*  81 */ \"selectnowith ::= selectnowith multiselect_op oneselect\",\n /*  82 */ \"multiselect_op ::= UNION\",\n /*  83 */ \"multiselect_op ::= UNION ALL\",\n /*  84 */ \"multiselect_op ::= EXCEPT|INTERSECT\",\n /*  85 */ \"oneselect ::= SELECT distinct selcollist from where_opt groupby_opt having_opt orderby_opt limit_opt\",\n /*  86 */ \"values ::= VALUES LP nexprlist RP\",\n /*  87 */ \"values ::= values COMMA LP exprlist RP\",\n /*  88 */ \"distinct ::= DISTINCT\",\n /*  89 */ \"distinct ::= ALL\",\n /*  90 */ \"distinct ::=\",\n /*  91 */ \"sclp ::=\",\n /*  92 */ \"selcollist ::= sclp scanpt expr scanpt as\",\n /*  93 */ \"selcollist ::= sclp scanpt STAR\",\n /*  94 */ \"selcollist ::= sclp scanpt nm DOT STAR\",\n /*  95 */ \"as ::= AS nm\",\n /*  96 */ \"as ::=\",\n /*  97 */ \"from ::=\",\n /*  98 */ \"from ::= FROM seltablist\",\n /*  99 */ \"stl_prefix ::= seltablist joinop\",\n /* 100 */ \"stl_prefix ::=\",\n /* 101 */ \"seltablist ::= stl_prefix nm dbnm as indexed_opt on_opt using_opt\",\n /* 102 */ \"seltablist ::= stl_prefix nm dbnm LP exprlist RP as on_opt using_opt\",\n /* 103 */ \"seltablist ::= stl_prefix LP select RP as on_opt using_opt\",\n /* 104 */ \"seltablist ::= stl_prefix LP seltablist RP as on_opt using_opt\",\n /* 105 */ \"dbnm ::=\",\n /* 106 */ \"dbnm ::= DOT nm\",\n /* 107 */ \"fullname ::= nm dbnm\",\n /* 108 */ \"joinop ::= COMMA|JOIN\",\n /* 109 */ \"joinop ::= JOIN_KW JOIN\",\n /* 110 */ \"joinop ::= JOIN_KW nm JOIN\",\n /* 111 */ \"joinop ::= JOIN_KW nm nm JOIN\",\n /* 112 */ \"on_opt ::= ON expr\",\n /* 113 */ \"on_opt ::=\",\n /* 114 */ \"indexed_opt ::=\",\n /* 115 */ \"indexed_opt ::= INDEXED BY nm\",\n /* 116 */ \"indexed_opt ::= NOT INDEXED\",\n /* 117 */ \"using_opt ::= USING LP idlist RP\",\n /* 118 */ \"using_opt ::=\",\n /* 119 */ \"orderby_opt ::=\",\n /* 120 */ \"orderby_opt ::= ORDER BY sortlist\",\n /* 121 */ \"sortlist ::= sortlist COMMA expr sortorder\",\n /* 122 */ \"sortlist ::= expr sortorder\",\n /* 123 */ \"sortorder ::= ASC\",\n /* 124 */ \"sortorder ::= DESC\",\n /* 125 */ \"sortorder ::=\",\n /* 126 */ \"groupby_opt ::=\",\n /* 127 */ \"groupby_opt ::= GROUP BY nexprlist\",\n /* 128 */ \"having_opt ::=\",\n /* 129 */ \"having_opt ::= HAVING expr\",\n /* 130 */ \"limit_opt ::=\",\n /* 131 */ \"limit_opt ::= LIMIT expr\",\n /* 132 */ \"limit_opt ::= LIMIT expr OFFSET expr\",\n /* 133 */ \"limit_opt ::= LIMIT expr COMMA expr\",\n /* 134 */ \"cmd ::= with DELETE FROM fullname indexed_opt where_opt\",\n /* 135 */ \"where_opt ::=\",\n /* 136 */ \"where_opt ::= WHERE expr\",\n /* 137 */ \"cmd ::= with UPDATE orconf fullname indexed_opt SET setlist where_opt\",\n /* 138 */ \"setlist ::= setlist COMMA nm EQ expr\",\n /* 139 */ \"setlist ::= setlist COMMA LP idlist RP EQ expr\",\n /* 140 */ \"setlist ::= nm EQ expr\",\n /* 141 */ \"setlist ::= LP idlist RP EQ expr\",\n /* 142 */ \"cmd ::= with insert_cmd INTO fullname idlist_opt select\",\n /* 143 */ \"cmd ::= with insert_cmd INTO fullname idlist_opt DEFAULT VALUES\",\n /* 144 */ \"insert_cmd ::= INSERT orconf\",\n /* 145 */ \"insert_cmd ::= REPLACE\",\n /* 146 */ \"idlist_opt ::=\",\n /* 147 */ \"idlist_opt ::= LP idlist RP\",\n /* 148 */ \"idlist ::= idlist COMMA nm\",\n /* 149 */ \"idlist ::= nm\",\n /* 150 */ \"expr ::= LP expr RP\",\n /* 151 */ \"expr ::= ID|INDEXED\",\n /* 152 */ \"expr ::= JOIN_KW\",\n /* 153 */ \"expr ::= nm DOT nm\",\n /* 154 */ \"expr ::= nm DOT nm DOT nm\",\n /* 155 */ \"term ::= NULL|FLOAT|BLOB\",\n /* 156 */ \"term ::= STRING\",\n /* 157 */ \"term ::= INTEGER\",\n /* 158 */ \"expr ::= VARIABLE\",\n /* 159 */ \"expr ::= expr COLLATE ID|STRING\",\n /* 160 */ \"expr ::= CAST LP expr AS typetoken RP\",\n /* 161 */ \"expr ::= ID|INDEXED LP distinct exprlist RP\",\n /* 162 */ \"expr ::= ID|INDEXED LP STAR RP\",\n /* 163 */ \"term ::= CTIME_KW\",\n /* 164 */ \"expr ::= LP nexprlist COMMA expr RP\",\n /* 165 */ \"expr ::= expr AND expr\",\n /* 166 */ \"expr ::= expr OR expr\",\n /* 167 */ \"expr ::= expr LT|GT|GE|LE expr\",\n /* 168 */ \"expr ::= expr EQ|NE expr\",\n /* 169 */ \"expr ::= expr BITAND|BITOR|LSHIFT|RSHIFT expr\",\n /* 170 */ \"expr ::= expr PLUS|MINUS expr\",\n /* 171 */ \"expr ::= expr STAR|SLASH|REM expr\",\n /* 172 */ \"expr ::= expr CONCAT expr\",\n /* 173 */ \"likeop ::= NOT LIKE_KW|MATCH\",\n /* 174 */ \"expr ::= expr likeop expr\",\n /* 175 */ \"expr ::= expr likeop expr ESCAPE expr\",\n /* 176 */ \"expr ::= expr ISNULL|NOTNULL\",\n /* 177 */ \"expr ::= expr NOT NULL\",\n /* 178 */ \"expr ::= expr IS expr\",\n /* 179 */ \"expr ::= expr IS NOT expr\",\n /* 180 */ \"expr ::= NOT expr\",\n /* 181 */ \"expr ::= BITNOT expr\",\n /* 182 */ \"expr ::= MINUS expr\",\n /* 183 */ \"expr ::= PLUS expr\",\n /* 184 */ \"between_op ::= BETWEEN\",\n /* 185 */ \"between_op ::= NOT BETWEEN\",\n /* 186 */ \"expr ::= expr between_op expr AND expr\",\n /* 187 */ \"in_op ::= IN\",\n /* 188 */ \"in_op ::= NOT IN\",\n /* 189 */ \"expr ::= expr in_op LP exprlist RP\",\n /* 190 */ \"expr ::= LP select RP\",\n /* 191 */ \"expr ::= expr in_op LP select RP\",\n /* 192 */ \"expr ::= expr in_op nm dbnm paren_exprlist\",\n /* 193 */ \"expr ::= EXISTS LP select RP\",\n /* 194 */ \"expr ::= CASE case_operand case_exprlist case_else END\",\n /* 195 */ \"case_exprlist ::= case_exprlist WHEN expr THEN expr\",\n /* 196 */ \"case_exprlist ::= WHEN expr THEN expr\",\n /* 197 */ \"case_else ::= ELSE expr\",\n /* 198 */ \"case_else ::=\",\n /* 199 */ \"case_operand ::= expr\",\n /* 200 */ \"case_operand ::=\",\n /* 201 */ \"exprlist ::=\",\n /* 202 */ \"nexprlist ::= nexprlist COMMA expr\",\n /* 203 */ \"nexprlist ::= expr\",\n /* 204 */ \"paren_exprlist ::=\",\n /* 205 */ \"paren_exprlist ::= LP exprlist RP\",\n /* 206 */ \"cmd ::= createkw uniqueflag INDEX ifnotexists nm dbnm ON nm LP sortlist RP where_opt\",\n /* 207 */ \"uniqueflag ::= UNIQUE\",\n /* 208 */ \"uniqueflag ::=\",\n /* 209 */ \"eidlist_opt ::=\",\n /* 210 */ \"eidlist_opt ::= LP eidlist RP\",\n /* 211 */ \"eidlist ::= eidlist COMMA nm collate sortorder\",\n /* 212 */ \"eidlist ::= nm collate sortorder\",\n /* 213 */ \"collate ::=\",\n /* 214 */ \"collate ::= COLLATE ID|STRING\",\n /* 215 */ \"cmd ::= DROP INDEX ifexists fullname\",\n /* 216 */ \"cmd ::= VACUUM\",\n /* 217 */ \"cmd ::= VACUUM nm\",\n /* 218 */ \"cmd ::= PRAGMA nm dbnm\",\n /* 219 */ \"cmd ::= PRAGMA nm dbnm EQ nmnum\",\n /* 220 */ \"cmd ::= PRAGMA nm dbnm LP nmnum RP\",\n /* 221 */ \"cmd ::= PRAGMA nm dbnm EQ minus_num\",\n /* 222 */ \"cmd ::= PRAGMA nm dbnm LP minus_num RP\",\n /* 223 */ \"plus_num ::= PLUS INTEGER|FLOAT\",\n /* 224 */ \"minus_num ::= MINUS INTEGER|FLOAT\",\n /* 225 */ \"cmd ::= createkw trigger_decl BEGIN trigger_cmd_list END\",\n /* 226 */ \"trigger_decl ::= temp TRIGGER ifnotexists nm dbnm trigger_time trigger_event ON fullname foreach_clause when_clause\",\n /* 227 */ \"trigger_time ::= BEFORE|AFTER\",\n /* 228 */ \"trigger_time ::= INSTEAD OF\",\n /* 229 */ \"trigger_time ::=\",\n /* 230 */ \"trigger_event ::= DELETE|INSERT\",\n /* 231 */ \"trigger_event ::= UPDATE\",\n /* 232 */ \"trigger_event ::= UPDATE OF idlist\",\n /* 233 */ \"when_clause ::=\",\n /* 234 */ \"when_clause ::= WHEN expr\",\n /* 235 */ \"trigger_cmd_list ::= trigger_cmd_list trigger_cmd SEMI\",\n /* 236 */ \"trigger_cmd_list ::= trigger_cmd SEMI\",\n /* 237 */ \"trnm ::= nm DOT nm\",\n /* 238 */ \"tridxby ::= INDEXED BY nm\",\n /* 239 */ \"tridxby ::= NOT INDEXED\",\n /* 240 */ \"trigger_cmd ::= UPDATE orconf trnm tridxby SET setlist where_opt scanpt\",\n /* 241 */ \"trigger_cmd ::= scanpt insert_cmd INTO trnm idlist_opt select scanpt\",\n /* 242 */ \"trigger_cmd ::= DELETE FROM trnm tridxby where_opt scanpt\",\n /* 243 */ \"trigger_cmd ::= scanpt select scanpt\",\n /* 244 */ \"expr ::= RAISE LP IGNORE RP\",\n /* 245 */ \"expr ::= RAISE LP raisetype COMMA nm RP\",\n /* 246 */ \"raisetype ::= ROLLBACK\",\n /* 247 */ \"raisetype ::= ABORT\",\n /* 248 */ \"raisetype ::= FAIL\",\n /* 249 */ \"cmd ::= DROP TRIGGER ifexists fullname\",\n /* 250 */ \"cmd ::= ATTACH database_kw_opt expr AS expr key_opt\",\n /* 251 */ \"cmd ::= DETACH database_kw_opt expr\",\n /* 252 */ \"key_opt ::=\",\n /* 253 */ \"key_opt ::= KEY expr\",\n /* 254 */ \"cmd ::= REINDEX\",\n /* 255 */ \"cmd ::= REINDEX nm dbnm\",\n /* 256 */ \"cmd ::= ANALYZE\",\n /* 257 */ \"cmd ::= ANALYZE nm dbnm\",\n /* 258 */ \"cmd ::= ALTER TABLE fullname RENAME TO nm\",\n /* 259 */ \"cmd ::= ALTER TABLE add_column_fullname ADD kwcolumn_opt columnname carglist\",\n /* 260 */ \"add_column_fullname ::= fullname\",\n /* 261 */ \"cmd ::= create_vtab\",\n /* 262 */ \"cmd ::= create_vtab LP vtabarglist RP\",\n /* 263 */ \"create_vtab ::= createkw VIRTUAL TABLE ifnotexists nm dbnm USING nm\",\n /* 264 */ \"vtabarg ::=\",\n /* 265 */ \"vtabargtoken ::= ANY\",\n /* 266 */ \"vtabargtoken ::= lp anylist RP\",\n /* 267 */ \"lp ::= LP\",\n /* 268 */ \"with ::=\",\n /* 269 */ \"with ::= WITH wqlist\",\n /* 270 */ \"with ::= WITH RECURSIVE wqlist\",\n /* 271 */ \"wqlist ::= nm eidlist_opt AS LP select RP\",\n /* 272 */ \"wqlist ::= wqlist COMMA nm eidlist_opt AS LP select RP\",\n /* 273 */ \"input ::= cmdlist\",\n /* 274 */ \"cmdlist ::= cmdlist ecmd\",\n /* 275 */ \"cmdlist ::= ecmd\",\n /* 276 */ \"ecmd ::= SEMI\",\n /* 277 */ \"ecmd ::= explain cmdx SEMI\",\n /* 278 */ \"explain ::=\",\n /* 279 */ \"trans_opt ::=\",\n /* 280 */ \"trans_opt ::= TRANSACTION\",\n /* 281 */ \"trans_opt ::= TRANSACTION nm\",\n /* 282 */ \"savepoint_opt ::= SAVEPOINT\",\n /* 283 */ \"savepoint_opt ::=\",\n /* 284 */ \"cmd ::= create_table create_table_args\",\n /* 285 */ \"columnlist ::= columnlist COMMA columnname carglist\",\n /* 286 */ \"columnlist ::= columnname carglist\",\n /* 287 */ \"nm ::= ID|INDEXED\",\n /* 288 */ \"nm ::= STRING\",\n /* 289 */ \"nm ::= JOIN_KW\",\n /* 290 */ \"typetoken ::= typename\",\n /* 291 */ \"typename ::= ID|STRING\",\n /* 292 */ \"signed ::= plus_num\",\n /* 293 */ \"signed ::= minus_num\",\n /* 294 */ \"carglist ::= carglist ccons\",\n /* 295 */ \"carglist ::=\",\n /* 296 */ \"ccons ::= NULL onconf\",\n /* 297 */ \"conslist_opt ::= COMMA conslist\",\n /* 298 */ \"conslist ::= conslist tconscomma tcons\",\n /* 299 */ \"conslist ::= tcons\",\n /* 300 */ \"tconscomma ::=\",\n /* 301 */ \"defer_subclause_opt ::= defer_subclause\",\n /* 302 */ \"resolvetype ::= raisetype\",\n /* 303 */ \"selectnowith ::= oneselect\",\n /* 304 */ \"oneselect ::= values\",\n /* 305 */ \"sclp ::= selcollist COMMA\",\n /* 306 */ \"as ::= ID|STRING\",\n /* 307 */ \"expr ::= term\",\n /* 308 */ \"likeop ::= LIKE_KW|MATCH\",\n /* 309 */ \"exprlist ::= nexprlist\",\n /* 310 */ \"nmnum ::= plus_num\",\n /* 311 */ \"nmnum ::= nm\",\n /* 312 */ \"nmnum ::= ON\",\n /* 313 */ \"nmnum ::= DELETE\",\n /* 314 */ \"nmnum ::= DEFAULT\",\n /* 315 */ \"plus_num ::= INTEGER|FLOAT\",\n /* 316 */ \"foreach_clause ::=\",\n /* 317 */ \"foreach_clause ::= FOR EACH ROW\",\n /* 318 */ \"trnm ::= nm\",\n /* 319 */ \"tridxby ::=\",\n /* 320 */ \"database_kw_opt ::= DATABASE\",\n /* 321 */ \"database_kw_opt ::=\",\n /* 322 */ \"kwcolumn_opt ::=\",\n /* 323 */ \"kwcolumn_opt ::= COLUMNKW\",\n /* 324 */ \"vtabarglist ::= vtabarg\",\n /* 325 */ \"vtabarglist ::= vtabarglist COMMA vtabarg\",\n /* 326 */ \"vtabarg ::= vtabarg vtabargtoken\",\n /* 327 */ \"anylist ::=\",\n /* 328 */ \"anylist ::= anylist LP anylist RP\",\n /* 329 */ \"anylist ::= anylist ANY\",\n};\n#endif /* NDEBUG */\n\n\n#if YYSTACKDEPTH<=0\n/*\n** Try to increase the size of the parser stack.  Return the number\n** of errors.  Return 0 on success.\n*/\nstatic int yyGrowStack(yyParser *p){\n  int newSize;\n  int idx;\n  yyStackEntry *pNew;\n\n  newSize = p->yystksz*2 + 100;\n  idx = p->yytos ? (int)(p->yytos - p->yystack) : 0;\n  if( p->yystack==&p->yystk0 ){\n    pNew = malloc(newSize*sizeof(pNew[0]));\n    if( pNew ) pNew[0] = p->yystk0;\n  }else{\n    pNew = realloc(p->yystack, newSize*sizeof(pNew[0]));\n  }\n  if( pNew ){\n    p->yystack = pNew;\n    p->yytos = &p->yystack[idx];\n#ifndef NDEBUG\n    if( yyTraceFILE ){\n      fprintf(yyTraceFILE,\"%sStack grows from %d to %d entries.\\n\",\n              yyTracePrompt, p->yystksz, newSize);\n    }\n#endif\n    p->yystksz = newSize;\n  }\n  return pNew==0; \n}\n#endif\n\n/* Datatype of the argument to the memory allocated passed as the\n** second argument to sqlite3ParserAlloc() below.  This can be changed by\n** putting an appropriate #define in the %include section of the input\n** grammar.\n*/\n#ifndef YYMALLOCARGTYPE\n# define YYMALLOCARGTYPE size_t\n#endif\n\n/* Initialize a new parser that has already been allocated.\n*/\nSQLITE_PRIVATE void sqlite3ParserInit(void *yypParser){\n  yyParser *pParser = (yyParser*)yypParser;\n#ifdef YYTRACKMAXSTACKDEPTH\n  pParser->yyhwm = 0;\n#endif\n#if YYSTACKDEPTH<=0\n  pParser->yytos = NULL;\n  pParser->yystack = NULL;\n  pParser->yystksz = 0;\n  if( yyGrowStack(pParser) ){\n    pParser->yystack = &pParser->yystk0;\n    pParser->yystksz = 1;\n  }\n#endif\n#ifndef YYNOERRORRECOVERY\n  pParser->yyerrcnt = -1;\n#endif\n  pParser->yytos = pParser->yystack;\n  pParser->yystack[0].stateno = 0;\n  pParser->yystack[0].major = 0;\n#if YYSTACKDEPTH>0\n  pParser->yystackEnd = &pParser->yystack[YYSTACKDEPTH-1];\n#endif\n}\n\n#ifndef sqlite3Parser_ENGINEALWAYSONSTACK\n/* \n** This function allocates a new parser.\n** The only argument is a pointer to a function which works like\n** malloc.\n**\n** Inputs:\n** A pointer to the function used to allocate memory.\n**\n** Outputs:\n** A pointer to a parser.  This pointer is used in subsequent calls\n** to sqlite3Parser and sqlite3ParserFree.\n*/\nSQLITE_PRIVATE void *sqlite3ParserAlloc(void *(*mallocProc)(YYMALLOCARGTYPE)){\n  yyParser *pParser;\n  pParser = (yyParser*)(*mallocProc)( (YYMALLOCARGTYPE)sizeof(yyParser) );\n  if( pParser ) sqlite3ParserInit(pParser);\n  return pParser;\n}\n#endif /* sqlite3Parser_ENGINEALWAYSONSTACK */\n\n\n/* The following function deletes the \"minor type\" or semantic value\n** associated with a symbol.  The symbol can be either a terminal\n** or nonterminal. \"yymajor\" is the symbol code, and \"yypminor\" is\n** a pointer to the value to be deleted.  The code used to do the \n** deletions is derived from the %destructor and/or %token_destructor\n** directives of the input grammar.\n*/\nstatic void yy_destructor(\n  yyParser *yypParser,    /* The parser */\n  YYCODETYPE yymajor,     /* Type code for object to destroy */\n  YYMINORTYPE *yypminor   /* The object to be destroyed */\n){\n  sqlite3ParserARG_FETCH;\n  switch( yymajor ){\n    /* Here is inserted the actions which take place when a\n    ** terminal or non-terminal is destroyed.  This can happen\n    ** when the symbol is popped from the stack during a\n    ** reduce or during error processing or when a parser is \n    ** being destroyed before it is finished parsing.\n    **\n    ** Note: during a reduce, the only symbols destroyed are those\n    ** which appear on the RHS of the rule, but which are *not* used\n    ** inside the C code.\n    */\n/********* Begin destructor definitions ***************************************/\n    case 163: /* select */\n    case 195: /* selectnowith */\n    case 196: /* oneselect */\n    case 207: /* values */\n{\nsqlite3SelectDelete(pParse->db, (yypminor->yy387));\n}\n      break;\n    case 173: /* term */\n    case 174: /* expr */\n    case 202: /* where_opt */\n    case 204: /* having_opt */\n    case 216: /* on_opt */\n    case 226: /* case_operand */\n    case 228: /* case_else */\n    case 237: /* when_clause */\n    case 242: /* key_opt */\n{\nsqlite3ExprDelete(pParse->db, (yypminor->yy314));\n}\n      break;\n    case 178: /* eidlist_opt */\n    case 187: /* sortlist */\n    case 188: /* eidlist */\n    case 200: /* selcollist */\n    case 203: /* groupby_opt */\n    case 205: /* orderby_opt */\n    case 208: /* nexprlist */\n    case 209: /* exprlist */\n    case 210: /* sclp */\n    case 219: /* setlist */\n    case 225: /* paren_exprlist */\n    case 227: /* case_exprlist */\n{\nsqlite3ExprListDelete(pParse->db, (yypminor->yy322));\n}\n      break;\n    case 194: /* fullname */\n    case 201: /* from */\n    case 212: /* seltablist */\n    case 213: /* stl_prefix */\n{\nsqlite3SrcListDelete(pParse->db, (yypminor->yy259));\n}\n      break;\n    case 197: /* with */\n    case 251: /* wqlist */\n{\nsqlite3WithDelete(pParse->db, (yypminor->yy451));\n}\n      break;\n    case 217: /* using_opt */\n    case 218: /* idlist */\n    case 221: /* idlist_opt */\n{\nsqlite3IdListDelete(pParse->db, (yypminor->yy384));\n}\n      break;\n    case 233: /* trigger_cmd_list */\n    case 238: /* trigger_cmd */\n{\nsqlite3DeleteTriggerStep(pParse->db, (yypminor->yy203));\n}\n      break;\n    case 235: /* trigger_event */\n{\nsqlite3IdListDelete(pParse->db, (yypminor->yy90).b);\n}\n      break;\n/********* End destructor definitions *****************************************/\n    default:  break;   /* If no destructor action specified: do nothing */\n  }\n}\n\n/*\n** Pop the parser's stack once.\n**\n** If there is a destructor routine associated with the token which\n** is popped from the stack, then call it.\n*/\nstatic void yy_pop_parser_stack(yyParser *pParser){\n  yyStackEntry *yytos;\n  assert( pParser->yytos!=0 );\n  assert( pParser->yytos > pParser->yystack );\n  yytos = pParser->yytos--;\n#ifndef NDEBUG\n  if( yyTraceFILE ){\n    fprintf(yyTraceFILE,\"%sPopping %s\\n\",\n      yyTracePrompt,\n      yyTokenName[yytos->major]);\n  }\n#endif\n  yy_destructor(pParser, yytos->major, &yytos->minor);\n}\n\n/*\n** Clear all secondary memory allocations from the parser\n*/\nSQLITE_PRIVATE void sqlite3ParserFinalize(void *p){\n  yyParser *pParser = (yyParser*)p;\n  while( pParser->yytos>pParser->yystack ) yy_pop_parser_stack(pParser);\n#if YYSTACKDEPTH<=0\n  if( pParser->yystack!=&pParser->yystk0 ) free(pParser->yystack);\n#endif\n}\n\n#ifndef sqlite3Parser_ENGINEALWAYSONSTACK\n/* \n** Deallocate and destroy a parser.  Destructors are called for\n** all stack elements before shutting the parser down.\n**\n** If the YYPARSEFREENEVERNULL macro exists (for example because it\n** is defined in a %include section of the input grammar) then it is\n** assumed that the input pointer is never NULL.\n*/\nSQLITE_PRIVATE void sqlite3ParserFree(\n  void *p,                    /* The parser to be deleted */\n  void (*freeProc)(void*)     /* Function used to reclaim memory */\n){\n#ifndef YYPARSEFREENEVERNULL\n  if( p==0 ) return;\n#endif\n  sqlite3ParserFinalize(p);\n  (*freeProc)(p);\n}\n#endif /* sqlite3Parser_ENGINEALWAYSONSTACK */\n\n/*\n** Return the peak depth of the stack for a parser.\n*/\n#ifdef YYTRACKMAXSTACKDEPTH\nSQLITE_PRIVATE int sqlite3ParserStackPeak(void *p){\n  yyParser *pParser = (yyParser*)p;\n  return pParser->yyhwm;\n}\n#endif\n\n/* This array of booleans keeps track of the parser statement\n** coverage.  The element yycoverage[X][Y] is set when the parser\n** is in state X and has a lookahead token Y.  In a well-tested\n** systems, every element of this matrix should end up being set.\n*/\n#if defined(YYCOVERAGE)\nstatic unsigned char yycoverage[YYNSTATE][YYNTOKEN];\n#endif\n\n/*\n** Write into out a description of every state/lookahead combination that\n**\n**   (1)  has not been used by the parser, and\n**   (2)  is not a syntax error.\n**\n** Return the number of missed state/lookahead combinations.\n*/\n#if defined(YYCOVERAGE)\nSQLITE_PRIVATE int sqlite3ParserCoverage(FILE *out){\n  int stateno, iLookAhead, i;\n  int nMissed = 0;\n  for(stateno=0; stateno<YYNSTATE; stateno++){\n    i = yy_shift_ofst[stateno];\n    for(iLookAhead=0; iLookAhead<YYNTOKEN; iLookAhead++){\n      if( yy_lookahead[i+iLookAhead]!=iLookAhead ) continue;\n      if( yycoverage[stateno][iLookAhead]==0 ) nMissed++;\n      if( out ){\n        fprintf(out,\"State %d lookahead %s %s\\n\", stateno,\n                yyTokenName[iLookAhead],\n                yycoverage[stateno][iLookAhead] ? \"ok\" : \"missed\");\n      }\n    }\n  }\n  return nMissed;\n}\n#endif\n\n/*\n** Find the appropriate action for a parser given the terminal\n** look-ahead token iLookAhead.\n*/\nstatic unsigned int yy_find_shift_action(\n  yyParser *pParser,        /* The parser */\n  YYCODETYPE iLookAhead     /* The look-ahead token */\n){\n  int i;\n  int stateno = pParser->yytos->stateno;\n \n  if( stateno>YY_MAX_SHIFT ) return stateno;\n  assert( stateno <= YY_SHIFT_COUNT );\n#if defined(YYCOVERAGE)\n  yycoverage[stateno][iLookAhead] = 1;\n#endif\n  do{\n    i = yy_shift_ofst[stateno];\n    assert( i>=0 );\n    assert( i+YYNTOKEN<=(int)sizeof(yy_lookahead)/sizeof(yy_lookahead[0]) );\n    assert( iLookAhead!=YYNOCODE );\n    assert( iLookAhead < YYNTOKEN );\n    i += iLookAhead;\n    if( yy_lookahead[i]!=iLookAhead ){\n#ifdef YYFALLBACK\n      YYCODETYPE iFallback;            /* Fallback token */\n      if( iLookAhead<sizeof(yyFallback)/sizeof(yyFallback[0])\n             && (iFallback = yyFallback[iLookAhead])!=0 ){\n#ifndef NDEBUG\n        if( yyTraceFILE ){\n          fprintf(yyTraceFILE, \"%sFALLBACK %s => %s\\n\",\n             yyTracePrompt, yyTokenName[iLookAhead], yyTokenName[iFallback]);\n        }\n#endif\n        assert( yyFallback[iFallback]==0 ); /* Fallback loop must terminate */\n        iLookAhead = iFallback;\n        continue;\n      }\n#endif\n#ifdef YYWILDCARD\n      {\n        int j = i - iLookAhead + YYWILDCARD;\n        if( \n#if YY_SHIFT_MIN+YYWILDCARD<0\n          j>=0 &&\n#endif\n#if YY_SHIFT_MAX+YYWILDCARD>=YY_ACTTAB_COUNT\n          j<YY_ACTTAB_COUNT &&\n#endif\n          yy_lookahead[j]==YYWILDCARD && iLookAhead>0\n        ){\n#ifndef NDEBUG\n          if( yyTraceFILE ){\n            fprintf(yyTraceFILE, \"%sWILDCARD %s => %s\\n\",\n               yyTracePrompt, yyTokenName[iLookAhead],\n               yyTokenName[YYWILDCARD]);\n          }\n#endif /* NDEBUG */\n          return yy_action[j];\n        }\n      }\n#endif /* YYWILDCARD */\n      return yy_default[stateno];\n    }else{\n      return yy_action[i];\n    }\n  }while(1);\n}\n\n/*\n** Find the appropriate action for a parser given the non-terminal\n** look-ahead token iLookAhead.\n*/\nstatic int yy_find_reduce_action(\n  int stateno,              /* Current state number */\n  YYCODETYPE iLookAhead     /* The look-ahead token */\n){\n  int i;\n#ifdef YYERRORSYMBOL\n  if( stateno>YY_REDUCE_COUNT ){\n    return yy_default[stateno];\n  }\n#else\n  assert( stateno<=YY_REDUCE_COUNT );\n#endif\n  i = yy_reduce_ofst[stateno];\n  assert( iLookAhead!=YYNOCODE );\n  i += iLookAhead;\n#ifdef YYERRORSYMBOL\n  if( i<0 || i>=YY_ACTTAB_COUNT || yy_lookahead[i]!=iLookAhead ){\n    return yy_default[stateno];\n  }\n#else\n  assert( i>=0 && i<YY_ACTTAB_COUNT );\n  assert( yy_lookahead[i]==iLookAhead );\n#endif\n  return yy_action[i];\n}\n\n/*\n** The following routine is called if the stack overflows.\n*/\nstatic void yyStackOverflow(yyParser *yypParser){\n   sqlite3ParserARG_FETCH;\n#ifndef NDEBUG\n   if( yyTraceFILE ){\n     fprintf(yyTraceFILE,\"%sStack Overflow!\\n\",yyTracePrompt);\n   }\n#endif\n   while( yypParser->yytos>yypParser->yystack ) yy_pop_parser_stack(yypParser);\n   /* Here code is inserted which will execute if the parser\n   ** stack every overflows */\n/******** Begin %stack_overflow code ******************************************/\n\n  sqlite3ErrorMsg(pParse, \"parser stack overflow\");\n/******** End %stack_overflow code ********************************************/\n   sqlite3ParserARG_STORE; /* Suppress warning about unused %extra_argument var */\n}\n\n/*\n** Print tracing information for a SHIFT action\n*/\n#ifndef NDEBUG\nstatic void yyTraceShift(yyParser *yypParser, int yyNewState, const char *zTag){\n  if( yyTraceFILE ){\n    if( yyNewState<YYNSTATE ){\n      fprintf(yyTraceFILE,\"%s%s '%s', go to state %d\\n\",\n         yyTracePrompt, zTag, yyTokenName[yypParser->yytos->major],\n         yyNewState);\n    }else{\n      fprintf(yyTraceFILE,\"%s%s '%s', pending reduce %d\\n\",\n         yyTracePrompt, zTag, yyTokenName[yypParser->yytos->major],\n         yyNewState - YY_MIN_REDUCE);\n    }\n  }\n}\n#else\n# define yyTraceShift(X,Y,Z)\n#endif\n\n/*\n** Perform a shift action.\n*/\nstatic void yy_shift(\n  yyParser *yypParser,          /* The parser to be shifted */\n  int yyNewState,               /* The new state to shift in */\n  int yyMajor,                  /* The major token to shift in */\n  sqlite3ParserTOKENTYPE yyMinor        /* The minor token to shift in */\n){\n  yyStackEntry *yytos;\n  yypParser->yytos++;\n#ifdef YYTRACKMAXSTACKDEPTH\n  if( (int)(yypParser->yytos - yypParser->yystack)>yypParser->yyhwm ){\n    yypParser->yyhwm++;\n    assert( yypParser->yyhwm == (int)(yypParser->yytos - yypParser->yystack) );\n  }\n#endif\n#if YYSTACKDEPTH>0 \n  if( yypParser->yytos>yypParser->yystackEnd ){\n    yypParser->yytos--;\n    yyStackOverflow(yypParser);\n    return;\n  }\n#else\n  if( yypParser->yytos>=&yypParser->yystack[yypParser->yystksz] ){\n    if( yyGrowStack(yypParser) ){\n      yypParser->yytos--;\n      yyStackOverflow(yypParser);\n      return;\n    }\n  }\n#endif\n  if( yyNewState > YY_MAX_SHIFT ){\n    yyNewState += YY_MIN_REDUCE - YY_MIN_SHIFTREDUCE;\n  }\n  yytos = yypParser->yytos;\n  yytos->stateno = (YYACTIONTYPE)yyNewState;\n  yytos->major = (YYCODETYPE)yyMajor;\n  yytos->minor.yy0 = yyMinor;\n  yyTraceShift(yypParser, yyNewState, \"Shift\");\n}\n\n/* The following table contains information about every rule that\n** is used during the reduce.\n*/\nstatic const struct {\n  YYCODETYPE lhs;       /* Symbol on the left-hand side of the rule */\n  signed char nrhs;     /* Negative of the number of RHS symbols in the rule */\n} yyRuleInfo[] = {\n  {  147,   -1 }, /* (0) explain ::= EXPLAIN */\n  {  147,   -3 }, /* (1) explain ::= EXPLAIN QUERY PLAN */\n  {  148,   -1 }, /* (2) cmdx ::= cmd */\n  {  149,   -3 }, /* (3) cmd ::= BEGIN transtype trans_opt */\n  {  150,    0 }, /* (4) transtype ::= */\n  {  150,   -1 }, /* (5) transtype ::= DEFERRED */\n  {  150,   -1 }, /* (6) transtype ::= IMMEDIATE */\n  {  150,   -1 }, /* (7) transtype ::= EXCLUSIVE */\n  {  149,   -2 }, /* (8) cmd ::= COMMIT|END trans_opt */\n  {  149,   -2 }, /* (9) cmd ::= ROLLBACK trans_opt */\n  {  149,   -2 }, /* (10) cmd ::= SAVEPOINT nm */\n  {  149,   -3 }, /* (11) cmd ::= RELEASE savepoint_opt nm */\n  {  149,   -5 }, /* (12) cmd ::= ROLLBACK trans_opt TO savepoint_opt nm */\n  {  154,   -6 }, /* (13) create_table ::= createkw temp TABLE ifnotexists nm dbnm */\n  {  156,   -1 }, /* (14) createkw ::= CREATE */\n  {  158,    0 }, /* (15) ifnotexists ::= */\n  {  158,   -3 }, /* (16) ifnotexists ::= IF NOT EXISTS */\n  {  157,   -1 }, /* (17) temp ::= TEMP */\n  {  157,    0 }, /* (18) temp ::= */\n  {  155,   -5 }, /* (19) create_table_args ::= LP columnlist conslist_opt RP table_options */\n  {  155,   -2 }, /* (20) create_table_args ::= AS select */\n  {  162,    0 }, /* (21) table_options ::= */\n  {  162,   -2 }, /* (22) table_options ::= WITHOUT nm */\n  {  164,   -2 }, /* (23) columnname ::= nm typetoken */\n  {  166,    0 }, /* (24) typetoken ::= */\n  {  166,   -4 }, /* (25) typetoken ::= typename LP signed RP */\n  {  166,   -6 }, /* (26) typetoken ::= typename LP signed COMMA signed RP */\n  {  167,   -2 }, /* (27) typename ::= typename ID|STRING */\n  {  171,    0 }, /* (28) scanpt ::= */\n  {  172,   -2 }, /* (29) ccons ::= CONSTRAINT nm */\n  {  172,   -4 }, /* (30) ccons ::= DEFAULT scanpt term scanpt */\n  {  172,   -4 }, /* (31) ccons ::= DEFAULT LP expr RP */\n  {  172,   -4 }, /* (32) ccons ::= DEFAULT PLUS term scanpt */\n  {  172,   -4 }, /* (33) ccons ::= DEFAULT MINUS term scanpt */\n  {  172,   -3 }, /* (34) ccons ::= DEFAULT scanpt ID|INDEXED */\n  {  172,   -3 }, /* (35) ccons ::= NOT NULL onconf */\n  {  172,   -5 }, /* (36) ccons ::= PRIMARY KEY sortorder onconf autoinc */\n  {  172,   -2 }, /* (37) ccons ::= UNIQUE onconf */\n  {  172,   -4 }, /* (38) ccons ::= CHECK LP expr RP */\n  {  172,   -4 }, /* (39) ccons ::= REFERENCES nm eidlist_opt refargs */\n  {  172,   -1 }, /* (40) ccons ::= defer_subclause */\n  {  172,   -2 }, /* (41) ccons ::= COLLATE ID|STRING */\n  {  177,    0 }, /* (42) autoinc ::= */\n  {  177,   -1 }, /* (43) autoinc ::= AUTOINCR */\n  {  179,    0 }, /* (44) refargs ::= */\n  {  179,   -2 }, /* (45) refargs ::= refargs refarg */\n  {  181,   -2 }, /* (46) refarg ::= MATCH nm */\n  {  181,   -3 }, /* (47) refarg ::= ON INSERT refact */\n  {  181,   -3 }, /* (48) refarg ::= ON DELETE refact */\n  {  181,   -3 }, /* (49) refarg ::= ON UPDATE refact */\n  {  182,   -2 }, /* (50) refact ::= SET NULL */\n  {  182,   -2 }, /* (51) refact ::= SET DEFAULT */\n  {  182,   -1 }, /* (52) refact ::= CASCADE */\n  {  182,   -1 }, /* (53) refact ::= RESTRICT */\n  {  182,   -2 }, /* (54) refact ::= NO ACTION */\n  {  180,   -3 }, /* (55) defer_subclause ::= NOT DEFERRABLE init_deferred_pred_opt */\n  {  180,   -2 }, /* (56) defer_subclause ::= DEFERRABLE init_deferred_pred_opt */\n  {  183,    0 }, /* (57) init_deferred_pred_opt ::= */\n  {  183,   -2 }, /* (58) init_deferred_pred_opt ::= INITIALLY DEFERRED */\n  {  183,   -2 }, /* (59) init_deferred_pred_opt ::= INITIALLY IMMEDIATE */\n  {  161,    0 }, /* (60) conslist_opt ::= */\n  {  185,   -1 }, /* (61) tconscomma ::= COMMA */\n  {  186,   -2 }, /* (62) tcons ::= CONSTRAINT nm */\n  {  186,   -7 }, /* (63) tcons ::= PRIMARY KEY LP sortlist autoinc RP onconf */\n  {  186,   -5 }, /* (64) tcons ::= UNIQUE LP sortlist RP onconf */\n  {  186,   -5 }, /* (65) tcons ::= CHECK LP expr RP onconf */\n  {  186,  -10 }, /* (66) tcons ::= FOREIGN KEY LP eidlist RP REFERENCES nm eidlist_opt refargs defer_subclause_opt */\n  {  189,    0 }, /* (67) defer_subclause_opt ::= */\n  {  175,    0 }, /* (68) onconf ::= */\n  {  175,   -3 }, /* (69) onconf ::= ON CONFLICT resolvetype */\n  {  190,    0 }, /* (70) orconf ::= */\n  {  190,   -2 }, /* (71) orconf ::= OR resolvetype */\n  {  191,   -1 }, /* (72) resolvetype ::= IGNORE */\n  {  191,   -1 }, /* (73) resolvetype ::= REPLACE */\n  {  149,   -4 }, /* (74) cmd ::= DROP TABLE ifexists fullname */\n  {  193,   -2 }, /* (75) ifexists ::= IF EXISTS */\n  {  193,    0 }, /* (76) ifexists ::= */\n  {  149,   -9 }, /* (77) cmd ::= createkw temp VIEW ifnotexists nm dbnm eidlist_opt AS select */\n  {  149,   -4 }, /* (78) cmd ::= DROP VIEW ifexists fullname */\n  {  149,   -1 }, /* (79) cmd ::= select */\n  {  163,   -2 }, /* (80) select ::= with selectnowith */\n  {  195,   -3 }, /* (81) selectnowith ::= selectnowith multiselect_op oneselect */\n  {  198,   -1 }, /* (82) multiselect_op ::= UNION */\n  {  198,   -2 }, /* (83) multiselect_op ::= UNION ALL */\n  {  198,   -1 }, /* (84) multiselect_op ::= EXCEPT|INTERSECT */\n  {  196,   -9 }, /* (85) oneselect ::= SELECT distinct selcollist from where_opt groupby_opt having_opt orderby_opt limit_opt */\n  {  207,   -4 }, /* (86) values ::= VALUES LP nexprlist RP */\n  {  207,   -5 }, /* (87) values ::= values COMMA LP exprlist RP */\n  {  199,   -1 }, /* (88) distinct ::= DISTINCT */\n  {  199,   -1 }, /* (89) distinct ::= ALL */\n  {  199,    0 }, /* (90) distinct ::= */\n  {  210,    0 }, /* (91) sclp ::= */\n  {  200,   -5 }, /* (92) selcollist ::= sclp scanpt expr scanpt as */\n  {  200,   -3 }, /* (93) selcollist ::= sclp scanpt STAR */\n  {  200,   -5 }, /* (94) selcollist ::= sclp scanpt nm DOT STAR */\n  {  211,   -2 }, /* (95) as ::= AS nm */\n  {  211,    0 }, /* (96) as ::= */\n  {  201,    0 }, /* (97) from ::= */\n  {  201,   -2 }, /* (98) from ::= FROM seltablist */\n  {  213,   -2 }, /* (99) stl_prefix ::= seltablist joinop */\n  {  213,    0 }, /* (100) stl_prefix ::= */\n  {  212,   -7 }, /* (101) seltablist ::= stl_prefix nm dbnm as indexed_opt on_opt using_opt */\n  {  212,   -9 }, /* (102) seltablist ::= stl_prefix nm dbnm LP exprlist RP as on_opt using_opt */\n  {  212,   -7 }, /* (103) seltablist ::= stl_prefix LP select RP as on_opt using_opt */\n  {  212,   -7 }, /* (104) seltablist ::= stl_prefix LP seltablist RP as on_opt using_opt */\n  {  159,    0 }, /* (105) dbnm ::= */\n  {  159,   -2 }, /* (106) dbnm ::= DOT nm */\n  {  194,   -2 }, /* (107) fullname ::= nm dbnm */\n  {  214,   -1 }, /* (108) joinop ::= COMMA|JOIN */\n  {  214,   -2 }, /* (109) joinop ::= JOIN_KW JOIN */\n  {  214,   -3 }, /* (110) joinop ::= JOIN_KW nm JOIN */\n  {  214,   -4 }, /* (111) joinop ::= JOIN_KW nm nm JOIN */\n  {  216,   -2 }, /* (112) on_opt ::= ON expr */\n  {  216,    0 }, /* (113) on_opt ::= */\n  {  215,    0 }, /* (114) indexed_opt ::= */\n  {  215,   -3 }, /* (115) indexed_opt ::= INDEXED BY nm */\n  {  215,   -2 }, /* (116) indexed_opt ::= NOT INDEXED */\n  {  217,   -4 }, /* (117) using_opt ::= USING LP idlist RP */\n  {  217,    0 }, /* (118) using_opt ::= */\n  {  205,    0 }, /* (119) orderby_opt ::= */\n  {  205,   -3 }, /* (120) orderby_opt ::= ORDER BY sortlist */\n  {  187,   -4 }, /* (121) sortlist ::= sortlist COMMA expr sortorder */\n  {  187,   -2 }, /* (122) sortlist ::= expr sortorder */\n  {  176,   -1 }, /* (123) sortorder ::= ASC */\n  {  176,   -1 }, /* (124) sortorder ::= DESC */\n  {  176,    0 }, /* (125) sortorder ::= */\n  {  203,    0 }, /* (126) groupby_opt ::= */\n  {  203,   -3 }, /* (127) groupby_opt ::= GROUP BY nexprlist */\n  {  204,    0 }, /* (128) having_opt ::= */\n  {  204,   -2 }, /* (129) having_opt ::= HAVING expr */\n  {  206,    0 }, /* (130) limit_opt ::= */\n  {  206,   -2 }, /* (131) limit_opt ::= LIMIT expr */\n  {  206,   -4 }, /* (132) limit_opt ::= LIMIT expr OFFSET expr */\n  {  206,   -4 }, /* (133) limit_opt ::= LIMIT expr COMMA expr */\n  {  149,   -6 }, /* (134) cmd ::= with DELETE FROM fullname indexed_opt where_opt */\n  {  202,    0 }, /* (135) where_opt ::= */\n  {  202,   -2 }, /* (136) where_opt ::= WHERE expr */\n  {  149,   -8 }, /* (137) cmd ::= with UPDATE orconf fullname indexed_opt SET setlist where_opt */\n  {  219,   -5 }, /* (138) setlist ::= setlist COMMA nm EQ expr */\n  {  219,   -7 }, /* (139) setlist ::= setlist COMMA LP idlist RP EQ expr */\n  {  219,   -3 }, /* (140) setlist ::= nm EQ expr */\n  {  219,   -5 }, /* (141) setlist ::= LP idlist RP EQ expr */\n  {  149,   -6 }, /* (142) cmd ::= with insert_cmd INTO fullname idlist_opt select */\n  {  149,   -7 }, /* (143) cmd ::= with insert_cmd INTO fullname idlist_opt DEFAULT VALUES */\n  {  220,   -2 }, /* (144) insert_cmd ::= INSERT orconf */\n  {  220,   -1 }, /* (145) insert_cmd ::= REPLACE */\n  {  221,    0 }, /* (146) idlist_opt ::= */\n  {  221,   -3 }, /* (147) idlist_opt ::= LP idlist RP */\n  {  218,   -3 }, /* (148) idlist ::= idlist COMMA nm */\n  {  218,   -1 }, /* (149) idlist ::= nm */\n  {  174,   -3 }, /* (150) expr ::= LP expr RP */\n  {  174,   -1 }, /* (151) expr ::= ID|INDEXED */\n  {  174,   -1 }, /* (152) expr ::= JOIN_KW */\n  {  174,   -3 }, /* (153) expr ::= nm DOT nm */\n  {  174,   -5 }, /* (154) expr ::= nm DOT nm DOT nm */\n  {  173,   -1 }, /* (155) term ::= NULL|FLOAT|BLOB */\n  {  173,   -1 }, /* (156) term ::= STRING */\n  {  173,   -1 }, /* (157) term ::= INTEGER */\n  {  174,   -1 }, /* (158) expr ::= VARIABLE */\n  {  174,   -3 }, /* (159) expr ::= expr COLLATE ID|STRING */\n  {  174,   -6 }, /* (160) expr ::= CAST LP expr AS typetoken RP */\n  {  174,   -5 }, /* (161) expr ::= ID|INDEXED LP distinct exprlist RP */\n  {  174,   -4 }, /* (162) expr ::= ID|INDEXED LP STAR RP */\n  {  173,   -1 }, /* (163) term ::= CTIME_KW */\n  {  174,   -5 }, /* (164) expr ::= LP nexprlist COMMA expr RP */\n  {  174,   -3 }, /* (165) expr ::= expr AND expr */\n  {  174,   -3 }, /* (166) expr ::= expr OR expr */\n  {  174,   -3 }, /* (167) expr ::= expr LT|GT|GE|LE expr */\n  {  174,   -3 }, /* (168) expr ::= expr EQ|NE expr */\n  {  174,   -3 }, /* (169) expr ::= expr BITAND|BITOR|LSHIFT|RSHIFT expr */\n  {  174,   -3 }, /* (170) expr ::= expr PLUS|MINUS expr */\n  {  174,   -3 }, /* (171) expr ::= expr STAR|SLASH|REM expr */\n  {  174,   -3 }, /* (172) expr ::= expr CONCAT expr */\n  {  222,   -2 }, /* (173) likeop ::= NOT LIKE_KW|MATCH */\n  {  174,   -3 }, /* (174) expr ::= expr likeop expr */\n  {  174,   -5 }, /* (175) expr ::= expr likeop expr ESCAPE expr */\n  {  174,   -2 }, /* (176) expr ::= expr ISNULL|NOTNULL */\n  {  174,   -3 }, /* (177) expr ::= expr NOT NULL */\n  {  174,   -3 }, /* (178) expr ::= expr IS expr */\n  {  174,   -4 }, /* (179) expr ::= expr IS NOT expr */\n  {  174,   -2 }, /* (180) expr ::= NOT expr */\n  {  174,   -2 }, /* (181) expr ::= BITNOT expr */\n  {  174,   -2 }, /* (182) expr ::= MINUS expr */\n  {  174,   -2 }, /* (183) expr ::= PLUS expr */\n  {  223,   -1 }, /* (184) between_op ::= BETWEEN */\n  {  223,   -2 }, /* (185) between_op ::= NOT BETWEEN */\n  {  174,   -5 }, /* (186) expr ::= expr between_op expr AND expr */\n  {  224,   -1 }, /* (187) in_op ::= IN */\n  {  224,   -2 }, /* (188) in_op ::= NOT IN */\n  {  174,   -5 }, /* (189) expr ::= expr in_op LP exprlist RP */\n  {  174,   -3 }, /* (190) expr ::= LP select RP */\n  {  174,   -5 }, /* (191) expr ::= expr in_op LP select RP */\n  {  174,   -5 }, /* (192) expr ::= expr in_op nm dbnm paren_exprlist */\n  {  174,   -4 }, /* (193) expr ::= EXISTS LP select RP */\n  {  174,   -5 }, /* (194) expr ::= CASE case_operand case_exprlist case_else END */\n  {  227,   -5 }, /* (195) case_exprlist ::= case_exprlist WHEN expr THEN expr */\n  {  227,   -4 }, /* (196) case_exprlist ::= WHEN expr THEN expr */\n  {  228,   -2 }, /* (197) case_else ::= ELSE expr */\n  {  228,    0 }, /* (198) case_else ::= */\n  {  226,   -1 }, /* (199) case_operand ::= expr */\n  {  226,    0 }, /* (200) case_operand ::= */\n  {  209,    0 }, /* (201) exprlist ::= */\n  {  208,   -3 }, /* (202) nexprlist ::= nexprlist COMMA expr */\n  {  208,   -1 }, /* (203) nexprlist ::= expr */\n  {  225,    0 }, /* (204) paren_exprlist ::= */\n  {  225,   -3 }, /* (205) paren_exprlist ::= LP exprlist RP */\n  {  149,  -12 }, /* (206) cmd ::= createkw uniqueflag INDEX ifnotexists nm dbnm ON nm LP sortlist RP where_opt */\n  {  229,   -1 }, /* (207) uniqueflag ::= UNIQUE */\n  {  229,    0 }, /* (208) uniqueflag ::= */\n  {  178,    0 }, /* (209) eidlist_opt ::= */\n  {  178,   -3 }, /* (210) eidlist_opt ::= LP eidlist RP */\n  {  188,   -5 }, /* (211) eidlist ::= eidlist COMMA nm collate sortorder */\n  {  188,   -3 }, /* (212) eidlist ::= nm collate sortorder */\n  {  230,    0 }, /* (213) collate ::= */\n  {  230,   -2 }, /* (214) collate ::= COLLATE ID|STRING */\n  {  149,   -4 }, /* (215) cmd ::= DROP INDEX ifexists fullname */\n  {  149,   -1 }, /* (216) cmd ::= VACUUM */\n  {  149,   -2 }, /* (217) cmd ::= VACUUM nm */\n  {  149,   -3 }, /* (218) cmd ::= PRAGMA nm dbnm */\n  {  149,   -5 }, /* (219) cmd ::= PRAGMA nm dbnm EQ nmnum */\n  {  149,   -6 }, /* (220) cmd ::= PRAGMA nm dbnm LP nmnum RP */\n  {  149,   -5 }, /* (221) cmd ::= PRAGMA nm dbnm EQ minus_num */\n  {  149,   -6 }, /* (222) cmd ::= PRAGMA nm dbnm LP minus_num RP */\n  {  169,   -2 }, /* (223) plus_num ::= PLUS INTEGER|FLOAT */\n  {  170,   -2 }, /* (224) minus_num ::= MINUS INTEGER|FLOAT */\n  {  149,   -5 }, /* (225) cmd ::= createkw trigger_decl BEGIN trigger_cmd_list END */\n  {  232,  -11 }, /* (226) trigger_decl ::= temp TRIGGER ifnotexists nm dbnm trigger_time trigger_event ON fullname foreach_clause when_clause */\n  {  234,   -1 }, /* (227) trigger_time ::= BEFORE|AFTER */\n  {  234,   -2 }, /* (228) trigger_time ::= INSTEAD OF */\n  {  234,    0 }, /* (229) trigger_time ::= */\n  {  235,   -1 }, /* (230) trigger_event ::= DELETE|INSERT */\n  {  235,   -1 }, /* (231) trigger_event ::= UPDATE */\n  {  235,   -3 }, /* (232) trigger_event ::= UPDATE OF idlist */\n  {  237,    0 }, /* (233) when_clause ::= */\n  {  237,   -2 }, /* (234) when_clause ::= WHEN expr */\n  {  233,   -3 }, /* (235) trigger_cmd_list ::= trigger_cmd_list trigger_cmd SEMI */\n  {  233,   -2 }, /* (236) trigger_cmd_list ::= trigger_cmd SEMI */\n  {  239,   -3 }, /* (237) trnm ::= nm DOT nm */\n  {  240,   -3 }, /* (238) tridxby ::= INDEXED BY nm */\n  {  240,   -2 }, /* (239) tridxby ::= NOT INDEXED */\n  {  238,   -8 }, /* (240) trigger_cmd ::= UPDATE orconf trnm tridxby SET setlist where_opt scanpt */\n  {  238,   -7 }, /* (241) trigger_cmd ::= scanpt insert_cmd INTO trnm idlist_opt select scanpt */\n  {  238,   -6 }, /* (242) trigger_cmd ::= DELETE FROM trnm tridxby where_opt scanpt */\n  {  238,   -3 }, /* (243) trigger_cmd ::= scanpt select scanpt */\n  {  174,   -4 }, /* (244) expr ::= RAISE LP IGNORE RP */\n  {  174,   -6 }, /* (245) expr ::= RAISE LP raisetype COMMA nm RP */\n  {  192,   -1 }, /* (246) raisetype ::= ROLLBACK */\n  {  192,   -1 }, /* (247) raisetype ::= ABORT */\n  {  192,   -1 }, /* (248) raisetype ::= FAIL */\n  {  149,   -4 }, /* (249) cmd ::= DROP TRIGGER ifexists fullname */\n  {  149,   -6 }, /* (250) cmd ::= ATTACH database_kw_opt expr AS expr key_opt */\n  {  149,   -3 }, /* (251) cmd ::= DETACH database_kw_opt expr */\n  {  242,    0 }, /* (252) key_opt ::= */\n  {  242,   -2 }, /* (253) key_opt ::= KEY expr */\n  {  149,   -1 }, /* (254) cmd ::= REINDEX */\n  {  149,   -3 }, /* (255) cmd ::= REINDEX nm dbnm */\n  {  149,   -1 }, /* (256) cmd ::= ANALYZE */\n  {  149,   -3 }, /* (257) cmd ::= ANALYZE nm dbnm */\n  {  149,   -6 }, /* (258) cmd ::= ALTER TABLE fullname RENAME TO nm */\n  {  149,   -7 }, /* (259) cmd ::= ALTER TABLE add_column_fullname ADD kwcolumn_opt columnname carglist */\n  {  243,   -1 }, /* (260) add_column_fullname ::= fullname */\n  {  149,   -1 }, /* (261) cmd ::= create_vtab */\n  {  149,   -4 }, /* (262) cmd ::= create_vtab LP vtabarglist RP */\n  {  245,   -8 }, /* (263) create_vtab ::= createkw VIRTUAL TABLE ifnotexists nm dbnm USING nm */\n  {  247,    0 }, /* (264) vtabarg ::= */\n  {  248,   -1 }, /* (265) vtabargtoken ::= ANY */\n  {  248,   -3 }, /* (266) vtabargtoken ::= lp anylist RP */\n  {  249,   -1 }, /* (267) lp ::= LP */\n  {  197,    0 }, /* (268) with ::= */\n  {  197,   -2 }, /* (269) with ::= WITH wqlist */\n  {  197,   -3 }, /* (270) with ::= WITH RECURSIVE wqlist */\n  {  251,   -6 }, /* (271) wqlist ::= nm eidlist_opt AS LP select RP */\n  {  251,   -8 }, /* (272) wqlist ::= wqlist COMMA nm eidlist_opt AS LP select RP */\n  {  144,   -1 }, /* (273) input ::= cmdlist */\n  {  145,   -2 }, /* (274) cmdlist ::= cmdlist ecmd */\n  {  145,   -1 }, /* (275) cmdlist ::= ecmd */\n  {  146,   -1 }, /* (276) ecmd ::= SEMI */\n  {  146,   -3 }, /* (277) ecmd ::= explain cmdx SEMI */\n  {  147,    0 }, /* (278) explain ::= */\n  {  151,    0 }, /* (279) trans_opt ::= */\n  {  151,   -1 }, /* (280) trans_opt ::= TRANSACTION */\n  {  151,   -2 }, /* (281) trans_opt ::= TRANSACTION nm */\n  {  153,   -1 }, /* (282) savepoint_opt ::= SAVEPOINT */\n  {  153,    0 }, /* (283) savepoint_opt ::= */\n  {  149,   -2 }, /* (284) cmd ::= create_table create_table_args */\n  {  160,   -4 }, /* (285) columnlist ::= columnlist COMMA columnname carglist */\n  {  160,   -2 }, /* (286) columnlist ::= columnname carglist */\n  {  152,   -1 }, /* (287) nm ::= ID|INDEXED */\n  {  152,   -1 }, /* (288) nm ::= STRING */\n  {  152,   -1 }, /* (289) nm ::= JOIN_KW */\n  {  166,   -1 }, /* (290) typetoken ::= typename */\n  {  167,   -1 }, /* (291) typename ::= ID|STRING */\n  {  168,   -1 }, /* (292) signed ::= plus_num */\n  {  168,   -1 }, /* (293) signed ::= minus_num */\n  {  165,   -2 }, /* (294) carglist ::= carglist ccons */\n  {  165,    0 }, /* (295) carglist ::= */\n  {  172,   -2 }, /* (296) ccons ::= NULL onconf */\n  {  161,   -2 }, /* (297) conslist_opt ::= COMMA conslist */\n  {  184,   -3 }, /* (298) conslist ::= conslist tconscomma tcons */\n  {  184,   -1 }, /* (299) conslist ::= tcons */\n  {  185,    0 }, /* (300) tconscomma ::= */\n  {  189,   -1 }, /* (301) defer_subclause_opt ::= defer_subclause */\n  {  191,   -1 }, /* (302) resolvetype ::= raisetype */\n  {  195,   -1 }, /* (303) selectnowith ::= oneselect */\n  {  196,   -1 }, /* (304) oneselect ::= values */\n  {  210,   -2 }, /* (305) sclp ::= selcollist COMMA */\n  {  211,   -1 }, /* (306) as ::= ID|STRING */\n  {  174,   -1 }, /* (307) expr ::= term */\n  {  222,   -1 }, /* (308) likeop ::= LIKE_KW|MATCH */\n  {  209,   -1 }, /* (309) exprlist ::= nexprlist */\n  {  231,   -1 }, /* (310) nmnum ::= plus_num */\n  {  231,   -1 }, /* (311) nmnum ::= nm */\n  {  231,   -1 }, /* (312) nmnum ::= ON */\n  {  231,   -1 }, /* (313) nmnum ::= DELETE */\n  {  231,   -1 }, /* (314) nmnum ::= DEFAULT */\n  {  169,   -1 }, /* (315) plus_num ::= INTEGER|FLOAT */\n  {  236,    0 }, /* (316) foreach_clause ::= */\n  {  236,   -3 }, /* (317) foreach_clause ::= FOR EACH ROW */\n  {  239,   -1 }, /* (318) trnm ::= nm */\n  {  240,    0 }, /* (319) tridxby ::= */\n  {  241,   -1 }, /* (320) database_kw_opt ::= DATABASE */\n  {  241,    0 }, /* (321) database_kw_opt ::= */\n  {  244,    0 }, /* (322) kwcolumn_opt ::= */\n  {  244,   -1 }, /* (323) kwcolumn_opt ::= COLUMNKW */\n  {  246,   -1 }, /* (324) vtabarglist ::= vtabarg */\n  {  246,   -3 }, /* (325) vtabarglist ::= vtabarglist COMMA vtabarg */\n  {  247,   -2 }, /* (326) vtabarg ::= vtabarg vtabargtoken */\n  {  250,    0 }, /* (327) anylist ::= */\n  {  250,   -4 }, /* (328) anylist ::= anylist LP anylist RP */\n  {  250,   -2 }, /* (329) anylist ::= anylist ANY */\n};\n\nstatic void yy_accept(yyParser*);  /* Forward Declaration */\n\n/*\n** Perform a reduce action and the shift that must immediately\n** follow the reduce.\n**\n** The yyLookahead and yyLookaheadToken parameters provide reduce actions\n** access to the lookahead token (if any).  The yyLookahead will be YYNOCODE\n** if the lookahead token has already been consumed.  As this procedure is\n** only called from one place, optimizing compilers will in-line it, which\n** means that the extra parameters have no performance impact.\n*/\nstatic void yy_reduce(\n  yyParser *yypParser,         /* The parser */\n  unsigned int yyruleno,       /* Number of the rule by which to reduce */\n  int yyLookahead,             /* Lookahead token, or YYNOCODE if none */\n  sqlite3ParserTOKENTYPE yyLookaheadToken  /* Value of the lookahead token */\n){\n  int yygoto;                     /* The next state */\n  int yyact;                      /* The next action */\n  yyStackEntry *yymsp;            /* The top of the parser's stack */\n  int yysize;                     /* Amount to pop the stack */\n  sqlite3ParserARG_FETCH;\n  (void)yyLookahead;\n  (void)yyLookaheadToken;\n  yymsp = yypParser->yytos;\n#ifndef NDEBUG\n  if( yyTraceFILE && yyruleno<(int)(sizeof(yyRuleName)/sizeof(yyRuleName[0])) ){\n    yysize = yyRuleInfo[yyruleno].nrhs;\n    if( yysize ){\n      fprintf(yyTraceFILE, \"%sReduce %d [%s], go to state %d.\\n\",\n        yyTracePrompt,\n        yyruleno, yyRuleName[yyruleno], yymsp[yysize].stateno);\n    }else{\n      fprintf(yyTraceFILE, \"%sReduce %d [%s].\\n\",\n        yyTracePrompt, yyruleno, yyRuleName[yyruleno]);\n    }\n  }\n#endif /* NDEBUG */\n\n  /* Check that the stack is large enough to grow by a single entry\n  ** if the RHS of the rule is empty.  This ensures that there is room\n  ** enough on the stack to push the LHS value */\n  if( yyRuleInfo[yyruleno].nrhs==0 ){\n#ifdef YYTRACKMAXSTACKDEPTH\n    if( (int)(yypParser->yytos - yypParser->yystack)>yypParser->yyhwm ){\n      yypParser->yyhwm++;\n      assert( yypParser->yyhwm == (int)(yypParser->yytos - yypParser->yystack));\n    }\n#endif\n#if YYSTACKDEPTH>0 \n    if( yypParser->yytos>=yypParser->yystackEnd ){\n      yyStackOverflow(yypParser);\n      return;\n    }\n#else\n    if( yypParser->yytos>=&yypParser->yystack[yypParser->yystksz-1] ){\n      if( yyGrowStack(yypParser) ){\n        yyStackOverflow(yypParser);\n        return;\n      }\n      yymsp = yypParser->yytos;\n    }\n#endif\n  }\n\n  switch( yyruleno ){\n  /* Beginning here are the reduction cases.  A typical example\n  ** follows:\n  **   case 0:\n  **  #line <lineno> <grammarfile>\n  **     { ... }           // User supplied code\n  **  #line <lineno> <thisfile>\n  **     break;\n  */\n/********** Begin reduce actions **********************************************/\n        YYMINORTYPE yylhsminor;\n      case 0: /* explain ::= EXPLAIN */\n{ pParse->explain = 1; }\n        break;\n      case 1: /* explain ::= EXPLAIN QUERY PLAN */\n{ pParse->explain = 2; }\n        break;\n      case 2: /* cmdx ::= cmd */\n{ sqlite3FinishCoding(pParse); }\n        break;\n      case 3: /* cmd ::= BEGIN transtype trans_opt */\n{sqlite3BeginTransaction(pParse, yymsp[-1].minor.yy4);}\n        break;\n      case 4: /* transtype ::= */\n{yymsp[1].minor.yy4 = TK_DEFERRED;}\n        break;\n      case 5: /* transtype ::= DEFERRED */\n      case 6: /* transtype ::= IMMEDIATE */ yytestcase(yyruleno==6);\n      case 7: /* transtype ::= EXCLUSIVE */ yytestcase(yyruleno==7);\n{yymsp[0].minor.yy4 = yymsp[0].major; /*A-overwrites-X*/}\n        break;\n      case 8: /* cmd ::= COMMIT|END trans_opt */\n      case 9: /* cmd ::= ROLLBACK trans_opt */ yytestcase(yyruleno==9);\n{sqlite3EndTransaction(pParse,yymsp[-1].major);}\n        break;\n      case 10: /* cmd ::= SAVEPOINT nm */\n{\n  sqlite3Savepoint(pParse, SAVEPOINT_BEGIN, &yymsp[0].minor.yy0);\n}\n        break;\n      case 11: /* cmd ::= RELEASE savepoint_opt nm */\n{\n  sqlite3Savepoint(pParse, SAVEPOINT_RELEASE, &yymsp[0].minor.yy0);\n}\n        break;\n      case 12: /* cmd ::= ROLLBACK trans_opt TO savepoint_opt nm */\n{\n  sqlite3Savepoint(pParse, SAVEPOINT_ROLLBACK, &yymsp[0].minor.yy0);\n}\n        break;\n      case 13: /* create_table ::= createkw temp TABLE ifnotexists nm dbnm */\n{\n   sqlite3StartTable(pParse,&yymsp[-1].minor.yy0,&yymsp[0].minor.yy0,yymsp[-4].minor.yy4,0,0,yymsp[-2].minor.yy4);\n}\n        break;\n      case 14: /* createkw ::= CREATE */\n{disableLookaside(pParse);}\n        break;\n      case 15: /* ifnotexists ::= */\n      case 18: /* temp ::= */ yytestcase(yyruleno==18);\n      case 21: /* table_options ::= */ yytestcase(yyruleno==21);\n      case 42: /* autoinc ::= */ yytestcase(yyruleno==42);\n      case 57: /* init_deferred_pred_opt ::= */ yytestcase(yyruleno==57);\n      case 67: /* defer_subclause_opt ::= */ yytestcase(yyruleno==67);\n      case 76: /* ifexists ::= */ yytestcase(yyruleno==76);\n      case 90: /* distinct ::= */ yytestcase(yyruleno==90);\n      case 213: /* collate ::= */ yytestcase(yyruleno==213);\n{yymsp[1].minor.yy4 = 0;}\n        break;\n      case 16: /* ifnotexists ::= IF NOT EXISTS */\n{yymsp[-2].minor.yy4 = 1;}\n        break;\n      case 17: /* temp ::= TEMP */\n      case 43: /* autoinc ::= AUTOINCR */ yytestcase(yyruleno==43);\n{yymsp[0].minor.yy4 = 1;}\n        break;\n      case 19: /* create_table_args ::= LP columnlist conslist_opt RP table_options */\n{\n  sqlite3EndTable(pParse,&yymsp[-2].minor.yy0,&yymsp[-1].minor.yy0,yymsp[0].minor.yy4,0);\n}\n        break;\n      case 20: /* create_table_args ::= AS select */\n{\n  sqlite3EndTable(pParse,0,0,0,yymsp[0].minor.yy387);\n  sqlite3SelectDelete(pParse->db, yymsp[0].minor.yy387);\n}\n        break;\n      case 22: /* table_options ::= WITHOUT nm */\n{\n  if( yymsp[0].minor.yy0.n==5 && sqlite3_strnicmp(yymsp[0].minor.yy0.z,\"rowid\",5)==0 ){\n    yymsp[-1].minor.yy4 = TF_WithoutRowid | TF_NoVisibleRowid;\n  }else{\n    yymsp[-1].minor.yy4 = 0;\n    sqlite3ErrorMsg(pParse, \"unknown table option: %.*s\", yymsp[0].minor.yy0.n, yymsp[0].minor.yy0.z);\n  }\n}\n        break;\n      case 23: /* columnname ::= nm typetoken */\n{sqlite3AddColumn(pParse,&yymsp[-1].minor.yy0,&yymsp[0].minor.yy0);}\n        break;\n      case 24: /* typetoken ::= */\n      case 60: /* conslist_opt ::= */ yytestcase(yyruleno==60);\n      case 96: /* as ::= */ yytestcase(yyruleno==96);\n{yymsp[1].minor.yy0.n = 0; yymsp[1].minor.yy0.z = 0;}\n        break;\n      case 25: /* typetoken ::= typename LP signed RP */\n{\n  yymsp[-3].minor.yy0.n = (int)(&yymsp[0].minor.yy0.z[yymsp[0].minor.yy0.n] - yymsp[-3].minor.yy0.z);\n}\n        break;\n      case 26: /* typetoken ::= typename LP signed COMMA signed RP */\n{\n  yymsp[-5].minor.yy0.n = (int)(&yymsp[0].minor.yy0.z[yymsp[0].minor.yy0.n] - yymsp[-5].minor.yy0.z);\n}\n        break;\n      case 27: /* typename ::= typename ID|STRING */\n{yymsp[-1].minor.yy0.n=yymsp[0].minor.yy0.n+(int)(yymsp[0].minor.yy0.z-yymsp[-1].minor.yy0.z);}\n        break;\n      case 28: /* scanpt ::= */\n{\n  assert( yyLookahead!=YYNOCODE );\n  yymsp[1].minor.yy336 = yyLookaheadToken.z;\n}\n        break;\n      case 29: /* ccons ::= CONSTRAINT nm */\n      case 62: /* tcons ::= CONSTRAINT nm */ yytestcase(yyruleno==62);\n{pParse->constraintName = yymsp[0].minor.yy0;}\n        break;\n      case 30: /* ccons ::= DEFAULT scanpt term scanpt */\n{sqlite3AddDefaultValue(pParse,yymsp[-1].minor.yy314,yymsp[-2].minor.yy336,yymsp[0].minor.yy336);}\n        break;\n      case 31: /* ccons ::= DEFAULT LP expr RP */\n{sqlite3AddDefaultValue(pParse,yymsp[-1].minor.yy314,yymsp[-2].minor.yy0.z+1,yymsp[0].minor.yy0.z);}\n        break;\n      case 32: /* ccons ::= DEFAULT PLUS term scanpt */\n{sqlite3AddDefaultValue(pParse,yymsp[-1].minor.yy314,yymsp[-2].minor.yy0.z,yymsp[0].minor.yy336);}\n        break;\n      case 33: /* ccons ::= DEFAULT MINUS term scanpt */\n{\n  Expr *p = sqlite3PExpr(pParse, TK_UMINUS, yymsp[-1].minor.yy314, 0);\n  sqlite3AddDefaultValue(pParse,p,yymsp[-2].minor.yy0.z,yymsp[0].minor.yy336);\n}\n        break;\n      case 34: /* ccons ::= DEFAULT scanpt ID|INDEXED */\n{\n  Expr *p = tokenExpr(pParse, TK_STRING, yymsp[0].minor.yy0);\n  sqlite3ExprIdToTrueFalse(p);\n  testcase( p->op==TK_TRUEFALSE && sqlite3ExprTruthValue(p) );\n  sqlite3AddDefaultValue(pParse,p,yymsp[0].minor.yy0.z,yymsp[0].minor.yy0.z+yymsp[0].minor.yy0.n);\n}\n        break;\n      case 35: /* ccons ::= NOT NULL onconf */\n{sqlite3AddNotNull(pParse, yymsp[0].minor.yy4);}\n        break;\n      case 36: /* ccons ::= PRIMARY KEY sortorder onconf autoinc */\n{sqlite3AddPrimaryKey(pParse,0,yymsp[-1].minor.yy4,yymsp[0].minor.yy4,yymsp[-2].minor.yy4);}\n        break;\n      case 37: /* ccons ::= UNIQUE onconf */\n{sqlite3CreateIndex(pParse,0,0,0,0,yymsp[0].minor.yy4,0,0,0,0,\n                                   SQLITE_IDXTYPE_UNIQUE);}\n        break;\n      case 38: /* ccons ::= CHECK LP expr RP */\n{sqlite3AddCheckConstraint(pParse,yymsp[-1].minor.yy314);}\n        break;\n      case 39: /* ccons ::= REFERENCES nm eidlist_opt refargs */\n{sqlite3CreateForeignKey(pParse,0,&yymsp[-2].minor.yy0,yymsp[-1].minor.yy322,yymsp[0].minor.yy4);}\n        break;\n      case 40: /* ccons ::= defer_subclause */\n{sqlite3DeferForeignKey(pParse,yymsp[0].minor.yy4);}\n        break;\n      case 41: /* ccons ::= COLLATE ID|STRING */\n{sqlite3AddCollateType(pParse, &yymsp[0].minor.yy0);}\n        break;\n      case 44: /* refargs ::= */\n{ yymsp[1].minor.yy4 = OE_None*0x0101; /* EV: R-19803-45884 */}\n        break;\n      case 45: /* refargs ::= refargs refarg */\n{ yymsp[-1].minor.yy4 = (yymsp[-1].minor.yy4 & ~yymsp[0].minor.yy215.mask) | yymsp[0].minor.yy215.value; }\n        break;\n      case 46: /* refarg ::= MATCH nm */\n{ yymsp[-1].minor.yy215.value = 0;     yymsp[-1].minor.yy215.mask = 0x000000; }\n        break;\n      case 47: /* refarg ::= ON INSERT refact */\n{ yymsp[-2].minor.yy215.value = 0;     yymsp[-2].minor.yy215.mask = 0x000000; }\n        break;\n      case 48: /* refarg ::= ON DELETE refact */\n{ yymsp[-2].minor.yy215.value = yymsp[0].minor.yy4;     yymsp[-2].minor.yy215.mask = 0x0000ff; }\n        break;\n      case 49: /* refarg ::= ON UPDATE refact */\n{ yymsp[-2].minor.yy215.value = yymsp[0].minor.yy4<<8;  yymsp[-2].minor.yy215.mask = 0x00ff00; }\n        break;\n      case 50: /* refact ::= SET NULL */\n{ yymsp[-1].minor.yy4 = OE_SetNull;  /* EV: R-33326-45252 */}\n        break;\n      case 51: /* refact ::= SET DEFAULT */\n{ yymsp[-1].minor.yy4 = OE_SetDflt;  /* EV: R-33326-45252 */}\n        break;\n      case 52: /* refact ::= CASCADE */\n{ yymsp[0].minor.yy4 = OE_Cascade;  /* EV: R-33326-45252 */}\n        break;\n      case 53: /* refact ::= RESTRICT */\n{ yymsp[0].minor.yy4 = OE_Restrict; /* EV: R-33326-45252 */}\n        break;\n      case 54: /* refact ::= NO ACTION */\n{ yymsp[-1].minor.yy4 = OE_None;     /* EV: R-33326-45252 */}\n        break;\n      case 55: /* defer_subclause ::= NOT DEFERRABLE init_deferred_pred_opt */\n{yymsp[-2].minor.yy4 = 0;}\n        break;\n      case 56: /* defer_subclause ::= DEFERRABLE init_deferred_pred_opt */\n      case 71: /* orconf ::= OR resolvetype */ yytestcase(yyruleno==71);\n      case 144: /* insert_cmd ::= INSERT orconf */ yytestcase(yyruleno==144);\n{yymsp[-1].minor.yy4 = yymsp[0].minor.yy4;}\n        break;\n      case 58: /* init_deferred_pred_opt ::= INITIALLY DEFERRED */\n      case 75: /* ifexists ::= IF EXISTS */ yytestcase(yyruleno==75);\n      case 185: /* between_op ::= NOT BETWEEN */ yytestcase(yyruleno==185);\n      case 188: /* in_op ::= NOT IN */ yytestcase(yyruleno==188);\n      case 214: /* collate ::= COLLATE ID|STRING */ yytestcase(yyruleno==214);\n{yymsp[-1].minor.yy4 = 1;}\n        break;\n      case 59: /* init_deferred_pred_opt ::= INITIALLY IMMEDIATE */\n{yymsp[-1].minor.yy4 = 0;}\n        break;\n      case 61: /* tconscomma ::= COMMA */\n{pParse->constraintName.n = 0;}\n        break;\n      case 63: /* tcons ::= PRIMARY KEY LP sortlist autoinc RP onconf */\n{sqlite3AddPrimaryKey(pParse,yymsp[-3].minor.yy322,yymsp[0].minor.yy4,yymsp[-2].minor.yy4,0);}\n        break;\n      case 64: /* tcons ::= UNIQUE LP sortlist RP onconf */\n{sqlite3CreateIndex(pParse,0,0,0,yymsp[-2].minor.yy322,yymsp[0].minor.yy4,0,0,0,0,\n                                       SQLITE_IDXTYPE_UNIQUE);}\n        break;\n      case 65: /* tcons ::= CHECK LP expr RP onconf */\n{sqlite3AddCheckConstraint(pParse,yymsp[-2].minor.yy314);}\n        break;\n      case 66: /* tcons ::= FOREIGN KEY LP eidlist RP REFERENCES nm eidlist_opt refargs defer_subclause_opt */\n{\n    sqlite3CreateForeignKey(pParse, yymsp[-6].minor.yy322, &yymsp[-3].minor.yy0, yymsp[-2].minor.yy322, yymsp[-1].minor.yy4);\n    sqlite3DeferForeignKey(pParse, yymsp[0].minor.yy4);\n}\n        break;\n      case 68: /* onconf ::= */\n      case 70: /* orconf ::= */ yytestcase(yyruleno==70);\n{yymsp[1].minor.yy4 = OE_Default;}\n        break;\n      case 69: /* onconf ::= ON CONFLICT resolvetype */\n{yymsp[-2].minor.yy4 = yymsp[0].minor.yy4;}\n        break;\n      case 72: /* resolvetype ::= IGNORE */\n{yymsp[0].minor.yy4 = OE_Ignore;}\n        break;\n      case 73: /* resolvetype ::= REPLACE */\n      case 145: /* insert_cmd ::= REPLACE */ yytestcase(yyruleno==145);\n{yymsp[0].minor.yy4 = OE_Replace;}\n        break;\n      case 74: /* cmd ::= DROP TABLE ifexists fullname */\n{\n  sqlite3DropTable(pParse, yymsp[0].minor.yy259, 0, yymsp[-1].minor.yy4);\n}\n        break;\n      case 77: /* cmd ::= createkw temp VIEW ifnotexists nm dbnm eidlist_opt AS select */\n{\n  sqlite3CreateView(pParse, &yymsp[-8].minor.yy0, &yymsp[-4].minor.yy0, &yymsp[-3].minor.yy0, yymsp[-2].minor.yy322, yymsp[0].minor.yy387, yymsp[-7].minor.yy4, yymsp[-5].minor.yy4);\n}\n        break;\n      case 78: /* cmd ::= DROP VIEW ifexists fullname */\n{\n  sqlite3DropTable(pParse, yymsp[0].minor.yy259, 1, yymsp[-1].minor.yy4);\n}\n        break;\n      case 79: /* cmd ::= select */\n{\n  SelectDest dest = {SRT_Output, 0, 0, 0, 0, 0};\n  sqlite3Select(pParse, yymsp[0].minor.yy387, &dest);\n  sqlite3SelectDelete(pParse->db, yymsp[0].minor.yy387);\n}\n        break;\n      case 80: /* select ::= with selectnowith */\n{\n  Select *p = yymsp[0].minor.yy387;\n  if( p ){\n    p->pWith = yymsp[-1].minor.yy451;\n    parserDoubleLinkSelect(pParse, p);\n  }else{\n    sqlite3WithDelete(pParse->db, yymsp[-1].minor.yy451);\n  }\n  yymsp[-1].minor.yy387 = p; /*A-overwrites-W*/\n}\n        break;\n      case 81: /* selectnowith ::= selectnowith multiselect_op oneselect */\n{\n  Select *pRhs = yymsp[0].minor.yy387;\n  Select *pLhs = yymsp[-2].minor.yy387;\n  if( pRhs && pRhs->pPrior ){\n    SrcList *pFrom;\n    Token x;\n    x.n = 0;\n    parserDoubleLinkSelect(pParse, pRhs);\n    pFrom = sqlite3SrcListAppendFromTerm(pParse,0,0,0,&x,pRhs,0,0);\n    pRhs = sqlite3SelectNew(pParse,0,pFrom,0,0,0,0,0,0);\n  }\n  if( pRhs ){\n    pRhs->op = (u8)yymsp[-1].minor.yy4;\n    pRhs->pPrior = pLhs;\n    if( ALWAYS(pLhs) ) pLhs->selFlags &= ~SF_MultiValue;\n    pRhs->selFlags &= ~SF_MultiValue;\n    if( yymsp[-1].minor.yy4!=TK_ALL ) pParse->hasCompound = 1;\n  }else{\n    sqlite3SelectDelete(pParse->db, pLhs);\n  }\n  yymsp[-2].minor.yy387 = pRhs;\n}\n        break;\n      case 82: /* multiselect_op ::= UNION */\n      case 84: /* multiselect_op ::= EXCEPT|INTERSECT */ yytestcase(yyruleno==84);\n{yymsp[0].minor.yy4 = yymsp[0].major; /*A-overwrites-OP*/}\n        break;\n      case 83: /* multiselect_op ::= UNION ALL */\n{yymsp[-1].minor.yy4 = TK_ALL;}\n        break;\n      case 85: /* oneselect ::= SELECT distinct selcollist from where_opt groupby_opt having_opt orderby_opt limit_opt */\n{\n#if SELECTTRACE_ENABLED\n  Token s = yymsp[-8].minor.yy0; /*A-overwrites-S*/\n#endif\n  yymsp[-8].minor.yy387 = sqlite3SelectNew(pParse,yymsp[-6].minor.yy322,yymsp[-5].minor.yy259,yymsp[-4].minor.yy314,yymsp[-3].minor.yy322,yymsp[-2].minor.yy314,yymsp[-1].minor.yy322,yymsp[-7].minor.yy4,yymsp[0].minor.yy314);\n#if SELECTTRACE_ENABLED\n  /* Populate the Select.zSelName[] string that is used to help with\n  ** query planner debugging, to differentiate between multiple Select\n  ** objects in a complex query.\n  **\n  ** If the SELECT keyword is immediately followed by a C-style comment\n  ** then extract the first few alphanumeric characters from within that\n  ** comment to be the zSelName value.  Otherwise, the label is #N where\n  ** is an integer that is incremented with each SELECT statement seen.\n  */\n  if( yymsp[-8].minor.yy387!=0 ){\n    const char *z = s.z+6;\n    int i;\n    sqlite3_snprintf(sizeof(yymsp[-8].minor.yy387->zSelName), yymsp[-8].minor.yy387->zSelName, \"#%d\",\n                     ++pParse->nSelect);\n    while( z[0]==' ' ) z++;\n    if( z[0]=='/' && z[1]=='*' ){\n      z += 2;\n      while( z[0]==' ' ) z++;\n      for(i=0; sqlite3Isalnum(z[i]); i++){}\n      sqlite3_snprintf(sizeof(yymsp[-8].minor.yy387->zSelName), yymsp[-8].minor.yy387->zSelName, \"%.*s\", i, z);\n    }\n  }\n#endif /* SELECTRACE_ENABLED */\n}\n        break;\n      case 86: /* values ::= VALUES LP nexprlist RP */\n{\n  yymsp[-3].minor.yy387 = sqlite3SelectNew(pParse,yymsp[-1].minor.yy322,0,0,0,0,0,SF_Values,0);\n}\n        break;\n      case 87: /* values ::= values COMMA LP exprlist RP */\n{\n  Select *pRight, *pLeft = yymsp[-4].minor.yy387;\n  pRight = sqlite3SelectNew(pParse,yymsp[-1].minor.yy322,0,0,0,0,0,SF_Values|SF_MultiValue,0);\n  if( ALWAYS(pLeft) ) pLeft->selFlags &= ~SF_MultiValue;\n  if( pRight ){\n    pRight->op = TK_ALL;\n    pRight->pPrior = pLeft;\n    yymsp[-4].minor.yy387 = pRight;\n  }else{\n    yymsp[-4].minor.yy387 = pLeft;\n  }\n}\n        break;\n      case 88: /* distinct ::= DISTINCT */\n{yymsp[0].minor.yy4 = SF_Distinct;}\n        break;\n      case 89: /* distinct ::= ALL */\n{yymsp[0].minor.yy4 = SF_All;}\n        break;\n      case 91: /* sclp ::= */\n      case 119: /* orderby_opt ::= */ yytestcase(yyruleno==119);\n      case 126: /* groupby_opt ::= */ yytestcase(yyruleno==126);\n      case 201: /* exprlist ::= */ yytestcase(yyruleno==201);\n      case 204: /* paren_exprlist ::= */ yytestcase(yyruleno==204);\n      case 209: /* eidlist_opt ::= */ yytestcase(yyruleno==209);\n{yymsp[1].minor.yy322 = 0;}\n        break;\n      case 92: /* selcollist ::= sclp scanpt expr scanpt as */\n{\n   yymsp[-4].minor.yy322 = sqlite3ExprListAppend(pParse, yymsp[-4].minor.yy322, yymsp[-2].minor.yy314);\n   if( yymsp[0].minor.yy0.n>0 ) sqlite3ExprListSetName(pParse, yymsp[-4].minor.yy322, &yymsp[0].minor.yy0, 1);\n   sqlite3ExprListSetSpan(pParse,yymsp[-4].minor.yy322,yymsp[-3].minor.yy336,yymsp[-1].minor.yy336);\n}\n        break;\n      case 93: /* selcollist ::= sclp scanpt STAR */\n{\n  Expr *p = sqlite3Expr(pParse->db, TK_ASTERISK, 0);\n  yymsp[-2].minor.yy322 = sqlite3ExprListAppend(pParse, yymsp[-2].minor.yy322, p);\n}\n        break;\n      case 94: /* selcollist ::= sclp scanpt nm DOT STAR */\n{\n  Expr *pRight = sqlite3PExpr(pParse, TK_ASTERISK, 0, 0);\n  Expr *pLeft = sqlite3ExprAlloc(pParse->db, TK_ID, &yymsp[-2].minor.yy0, 1);\n  Expr *pDot = sqlite3PExpr(pParse, TK_DOT, pLeft, pRight);\n  yymsp[-4].minor.yy322 = sqlite3ExprListAppend(pParse,yymsp[-4].minor.yy322, pDot);\n}\n        break;\n      case 95: /* as ::= AS nm */\n      case 106: /* dbnm ::= DOT nm */ yytestcase(yyruleno==106);\n      case 223: /* plus_num ::= PLUS INTEGER|FLOAT */ yytestcase(yyruleno==223);\n      case 224: /* minus_num ::= MINUS INTEGER|FLOAT */ yytestcase(yyruleno==224);\n{yymsp[-1].minor.yy0 = yymsp[0].minor.yy0;}\n        break;\n      case 97: /* from ::= */\n{yymsp[1].minor.yy259 = sqlite3DbMallocZero(pParse->db, sizeof(*yymsp[1].minor.yy259));}\n        break;\n      case 98: /* from ::= FROM seltablist */\n{\n  yymsp[-1].minor.yy259 = yymsp[0].minor.yy259;\n  sqlite3SrcListShiftJoinType(yymsp[-1].minor.yy259);\n}\n        break;\n      case 99: /* stl_prefix ::= seltablist joinop */\n{\n   if( ALWAYS(yymsp[-1].minor.yy259 && yymsp[-1].minor.yy259->nSrc>0) ) yymsp[-1].minor.yy259->a[yymsp[-1].minor.yy259->nSrc-1].fg.jointype = (u8)yymsp[0].minor.yy4;\n}\n        break;\n      case 100: /* stl_prefix ::= */\n{yymsp[1].minor.yy259 = 0;}\n        break;\n      case 101: /* seltablist ::= stl_prefix nm dbnm as indexed_opt on_opt using_opt */\n{\n  yymsp[-6].minor.yy259 = sqlite3SrcListAppendFromTerm(pParse,yymsp[-6].minor.yy259,&yymsp[-5].minor.yy0,&yymsp[-4].minor.yy0,&yymsp[-3].minor.yy0,0,yymsp[-1].minor.yy314,yymsp[0].minor.yy384);\n  sqlite3SrcListIndexedBy(pParse, yymsp[-6].minor.yy259, &yymsp[-2].minor.yy0);\n}\n        break;\n      case 102: /* seltablist ::= stl_prefix nm dbnm LP exprlist RP as on_opt using_opt */\n{\n  yymsp[-8].minor.yy259 = sqlite3SrcListAppendFromTerm(pParse,yymsp[-8].minor.yy259,&yymsp[-7].minor.yy0,&yymsp[-6].minor.yy0,&yymsp[-2].minor.yy0,0,yymsp[-1].minor.yy314,yymsp[0].minor.yy384);\n  sqlite3SrcListFuncArgs(pParse, yymsp[-8].minor.yy259, yymsp[-4].minor.yy322);\n}\n        break;\n      case 103: /* seltablist ::= stl_prefix LP select RP as on_opt using_opt */\n{\n    yymsp[-6].minor.yy259 = sqlite3SrcListAppendFromTerm(pParse,yymsp[-6].minor.yy259,0,0,&yymsp[-2].minor.yy0,yymsp[-4].minor.yy387,yymsp[-1].minor.yy314,yymsp[0].minor.yy384);\n  }\n        break;\n      case 104: /* seltablist ::= stl_prefix LP seltablist RP as on_opt using_opt */\n{\n    if( yymsp[-6].minor.yy259==0 && yymsp[-2].minor.yy0.n==0 && yymsp[-1].minor.yy314==0 && yymsp[0].minor.yy384==0 ){\n      yymsp[-6].minor.yy259 = yymsp[-4].minor.yy259;\n    }else if( yymsp[-4].minor.yy259->nSrc==1 ){\n      yymsp[-6].minor.yy259 = sqlite3SrcListAppendFromTerm(pParse,yymsp[-6].minor.yy259,0,0,&yymsp[-2].minor.yy0,0,yymsp[-1].minor.yy314,yymsp[0].minor.yy384);\n      if( yymsp[-6].minor.yy259 ){\n        struct SrcList_item *pNew = &yymsp[-6].minor.yy259->a[yymsp[-6].minor.yy259->nSrc-1];\n        struct SrcList_item *pOld = yymsp[-4].minor.yy259->a;\n        pNew->zName = pOld->zName;\n        pNew->zDatabase = pOld->zDatabase;\n        pNew->pSelect = pOld->pSelect;\n        pOld->zName = pOld->zDatabase = 0;\n        pOld->pSelect = 0;\n      }\n      sqlite3SrcListDelete(pParse->db, yymsp[-4].minor.yy259);\n    }else{\n      Select *pSubquery;\n      sqlite3SrcListShiftJoinType(yymsp[-4].minor.yy259);\n      pSubquery = sqlite3SelectNew(pParse,0,yymsp[-4].minor.yy259,0,0,0,0,SF_NestedFrom,0);\n      yymsp[-6].minor.yy259 = sqlite3SrcListAppendFromTerm(pParse,yymsp[-6].minor.yy259,0,0,&yymsp[-2].minor.yy0,pSubquery,yymsp[-1].minor.yy314,yymsp[0].minor.yy384);\n    }\n  }\n        break;\n      case 105: /* dbnm ::= */\n      case 114: /* indexed_opt ::= */ yytestcase(yyruleno==114);\n{yymsp[1].minor.yy0.z=0; yymsp[1].minor.yy0.n=0;}\n        break;\n      case 107: /* fullname ::= nm dbnm */\n{yymsp[-1].minor.yy259 = sqlite3SrcListAppend(pParse->db,0,&yymsp[-1].minor.yy0,&yymsp[0].minor.yy0); /*A-overwrites-X*/}\n        break;\n      case 108: /* joinop ::= COMMA|JOIN */\n{ yymsp[0].minor.yy4 = JT_INNER; }\n        break;\n      case 109: /* joinop ::= JOIN_KW JOIN */\n{yymsp[-1].minor.yy4 = sqlite3JoinType(pParse,&yymsp[-1].minor.yy0,0,0);  /*X-overwrites-A*/}\n        break;\n      case 110: /* joinop ::= JOIN_KW nm JOIN */\n{yymsp[-2].minor.yy4 = sqlite3JoinType(pParse,&yymsp[-2].minor.yy0,&yymsp[-1].minor.yy0,0); /*X-overwrites-A*/}\n        break;\n      case 111: /* joinop ::= JOIN_KW nm nm JOIN */\n{yymsp[-3].minor.yy4 = sqlite3JoinType(pParse,&yymsp[-3].minor.yy0,&yymsp[-2].minor.yy0,&yymsp[-1].minor.yy0);/*X-overwrites-A*/}\n        break;\n      case 112: /* on_opt ::= ON expr */\n      case 129: /* having_opt ::= HAVING expr */ yytestcase(yyruleno==129);\n      case 136: /* where_opt ::= WHERE expr */ yytestcase(yyruleno==136);\n      case 197: /* case_else ::= ELSE expr */ yytestcase(yyruleno==197);\n{yymsp[-1].minor.yy314 = yymsp[0].minor.yy314;}\n        break;\n      case 113: /* on_opt ::= */\n      case 128: /* having_opt ::= */ yytestcase(yyruleno==128);\n      case 130: /* limit_opt ::= */ yytestcase(yyruleno==130);\n      case 135: /* where_opt ::= */ yytestcase(yyruleno==135);\n      case 198: /* case_else ::= */ yytestcase(yyruleno==198);\n      case 200: /* case_operand ::= */ yytestcase(yyruleno==200);\n{yymsp[1].minor.yy314 = 0;}\n        break;\n      case 115: /* indexed_opt ::= INDEXED BY nm */\n{yymsp[-2].minor.yy0 = yymsp[0].minor.yy0;}\n        break;\n      case 116: /* indexed_opt ::= NOT INDEXED */\n{yymsp[-1].minor.yy0.z=0; yymsp[-1].minor.yy0.n=1;}\n        break;\n      case 117: /* using_opt ::= USING LP idlist RP */\n{yymsp[-3].minor.yy384 = yymsp[-1].minor.yy384;}\n        break;\n      case 118: /* using_opt ::= */\n      case 146: /* idlist_opt ::= */ yytestcase(yyruleno==146);\n{yymsp[1].minor.yy384 = 0;}\n        break;\n      case 120: /* orderby_opt ::= ORDER BY sortlist */\n      case 127: /* groupby_opt ::= GROUP BY nexprlist */ yytestcase(yyruleno==127);\n{yymsp[-2].minor.yy322 = yymsp[0].minor.yy322;}\n        break;\n      case 121: /* sortlist ::= sortlist COMMA expr sortorder */\n{\n  yymsp[-3].minor.yy322 = sqlite3ExprListAppend(pParse,yymsp[-3].minor.yy322,yymsp[-1].minor.yy314);\n  sqlite3ExprListSetSortOrder(yymsp[-3].minor.yy322,yymsp[0].minor.yy4);\n}\n        break;\n      case 122: /* sortlist ::= expr sortorder */\n{\n  yymsp[-1].minor.yy322 = sqlite3ExprListAppend(pParse,0,yymsp[-1].minor.yy314); /*A-overwrites-Y*/\n  sqlite3ExprListSetSortOrder(yymsp[-1].minor.yy322,yymsp[0].minor.yy4);\n}\n        break;\n      case 123: /* sortorder ::= ASC */\n{yymsp[0].minor.yy4 = SQLITE_SO_ASC;}\n        break;\n      case 124: /* sortorder ::= DESC */\n{yymsp[0].minor.yy4 = SQLITE_SO_DESC;}\n        break;\n      case 125: /* sortorder ::= */\n{yymsp[1].minor.yy4 = SQLITE_SO_UNDEFINED;}\n        break;\n      case 131: /* limit_opt ::= LIMIT expr */\n{yymsp[-1].minor.yy314 = sqlite3PExpr(pParse,TK_LIMIT,yymsp[0].minor.yy314,0);}\n        break;\n      case 132: /* limit_opt ::= LIMIT expr OFFSET expr */\n{yymsp[-3].minor.yy314 = sqlite3PExpr(pParse,TK_LIMIT,yymsp[-2].minor.yy314,yymsp[0].minor.yy314);}\n        break;\n      case 133: /* limit_opt ::= LIMIT expr COMMA expr */\n{yymsp[-3].minor.yy314 = sqlite3PExpr(pParse,TK_LIMIT,yymsp[0].minor.yy314,yymsp[-2].minor.yy314);}\n        break;\n      case 134: /* cmd ::= with DELETE FROM fullname indexed_opt where_opt */\n{\n  sqlite3WithPush(pParse, yymsp[-5].minor.yy451, 1);\n  sqlite3SrcListIndexedBy(pParse, yymsp[-2].minor.yy259, &yymsp[-1].minor.yy0);\n  sqlite3DeleteFrom(pParse,yymsp[-2].minor.yy259,yymsp[0].minor.yy314,0,0);\n}\n        break;\n      case 137: /* cmd ::= with UPDATE orconf fullname indexed_opt SET setlist where_opt */\n{\n  sqlite3WithPush(pParse, yymsp[-7].minor.yy451, 1);\n  sqlite3SrcListIndexedBy(pParse, yymsp[-4].minor.yy259, &yymsp[-3].minor.yy0);\n  sqlite3ExprListCheckLength(pParse,yymsp[-1].minor.yy322,\"set list\"); \n  sqlite3Update(pParse,yymsp[-4].minor.yy259,yymsp[-1].minor.yy322,yymsp[0].minor.yy314,yymsp[-5].minor.yy4,0,0);\n}\n        break;\n      case 138: /* setlist ::= setlist COMMA nm EQ expr */\n{\n  yymsp[-4].minor.yy322 = sqlite3ExprListAppend(pParse, yymsp[-4].minor.yy322, yymsp[0].minor.yy314);\n  sqlite3ExprListSetName(pParse, yymsp[-4].minor.yy322, &yymsp[-2].minor.yy0, 1);\n}\n        break;\n      case 139: /* setlist ::= setlist COMMA LP idlist RP EQ expr */\n{\n  yymsp[-6].minor.yy322 = sqlite3ExprListAppendVector(pParse, yymsp[-6].minor.yy322, yymsp[-3].minor.yy384, yymsp[0].minor.yy314);\n}\n        break;\n      case 140: /* setlist ::= nm EQ expr */\n{\n  yylhsminor.yy322 = sqlite3ExprListAppend(pParse, 0, yymsp[0].minor.yy314);\n  sqlite3ExprListSetName(pParse, yylhsminor.yy322, &yymsp[-2].minor.yy0, 1);\n}\n  yymsp[-2].minor.yy322 = yylhsminor.yy322;\n        break;\n      case 141: /* setlist ::= LP idlist RP EQ expr */\n{\n  yymsp[-4].minor.yy322 = sqlite3ExprListAppendVector(pParse, 0, yymsp[-3].minor.yy384, yymsp[0].minor.yy314);\n}\n        break;\n      case 142: /* cmd ::= with insert_cmd INTO fullname idlist_opt select */\n{\n  sqlite3WithPush(pParse, yymsp[-5].minor.yy451, 1);\n  sqlite3Insert(pParse, yymsp[-2].minor.yy259, yymsp[0].minor.yy387, yymsp[-1].minor.yy384, yymsp[-4].minor.yy4);\n}\n        break;\n      case 143: /* cmd ::= with insert_cmd INTO fullname idlist_opt DEFAULT VALUES */\n{\n  sqlite3WithPush(pParse, yymsp[-6].minor.yy451, 1);\n  sqlite3Insert(pParse, yymsp[-3].minor.yy259, 0, yymsp[-2].minor.yy384, yymsp[-5].minor.yy4);\n}\n        break;\n      case 147: /* idlist_opt ::= LP idlist RP */\n{yymsp[-2].minor.yy384 = yymsp[-1].minor.yy384;}\n        break;\n      case 148: /* idlist ::= idlist COMMA nm */\n{yymsp[-2].minor.yy384 = sqlite3IdListAppend(pParse->db,yymsp[-2].minor.yy384,&yymsp[0].minor.yy0);}\n        break;\n      case 149: /* idlist ::= nm */\n{yymsp[0].minor.yy384 = sqlite3IdListAppend(pParse->db,0,&yymsp[0].minor.yy0); /*A-overwrites-Y*/}\n        break;\n      case 150: /* expr ::= LP expr RP */\n{yymsp[-2].minor.yy314 = yymsp[-1].minor.yy314;}\n        break;\n      case 151: /* expr ::= ID|INDEXED */\n      case 152: /* expr ::= JOIN_KW */ yytestcase(yyruleno==152);\n{yymsp[0].minor.yy314=tokenExpr(pParse,TK_ID,yymsp[0].minor.yy0); /*A-overwrites-X*/}\n        break;\n      case 153: /* expr ::= nm DOT nm */\n{\n  Expr *temp1 = sqlite3ExprAlloc(pParse->db, TK_ID, &yymsp[-2].minor.yy0, 1);\n  Expr *temp2 = sqlite3ExprAlloc(pParse->db, TK_ID, &yymsp[0].minor.yy0, 1);\n  yylhsminor.yy314 = sqlite3PExpr(pParse, TK_DOT, temp1, temp2);\n}\n  yymsp[-2].minor.yy314 = yylhsminor.yy314;\n        break;\n      case 154: /* expr ::= nm DOT nm DOT nm */\n{\n  Expr *temp1 = sqlite3ExprAlloc(pParse->db, TK_ID, &yymsp[-4].minor.yy0, 1);\n  Expr *temp2 = sqlite3ExprAlloc(pParse->db, TK_ID, &yymsp[-2].minor.yy0, 1);\n  Expr *temp3 = sqlite3ExprAlloc(pParse->db, TK_ID, &yymsp[0].minor.yy0, 1);\n  Expr *temp4 = sqlite3PExpr(pParse, TK_DOT, temp2, temp3);\n  yylhsminor.yy314 = sqlite3PExpr(pParse, TK_DOT, temp1, temp4);\n}\n  yymsp[-4].minor.yy314 = yylhsminor.yy314;\n        break;\n      case 155: /* term ::= NULL|FLOAT|BLOB */\n      case 156: /* term ::= STRING */ yytestcase(yyruleno==156);\n{yymsp[0].minor.yy314=tokenExpr(pParse,yymsp[0].major,yymsp[0].minor.yy0); /*A-overwrites-X*/}\n        break;\n      case 157: /* term ::= INTEGER */\n{\n  yylhsminor.yy314 = sqlite3ExprAlloc(pParse->db, TK_INTEGER, &yymsp[0].minor.yy0, 1);\n}\n  yymsp[0].minor.yy314 = yylhsminor.yy314;\n        break;\n      case 158: /* expr ::= VARIABLE */\n{\n  if( !(yymsp[0].minor.yy0.z[0]=='#' && sqlite3Isdigit(yymsp[0].minor.yy0.z[1])) ){\n    u32 n = yymsp[0].minor.yy0.n;\n    yymsp[0].minor.yy314 = tokenExpr(pParse, TK_VARIABLE, yymsp[0].minor.yy0);\n    sqlite3ExprAssignVarNumber(pParse, yymsp[0].minor.yy314, n);\n  }else{\n    /* When doing a nested parse, one can include terms in an expression\n    ** that look like this:   #1 #2 ...  These terms refer to registers\n    ** in the virtual machine.  #N is the N-th register. */\n    Token t = yymsp[0].minor.yy0; /*A-overwrites-X*/\n    assert( t.n>=2 );\n    if( pParse->nested==0 ){\n      sqlite3ErrorMsg(pParse, \"near \\\"%T\\\": syntax error\", &t);\n      yymsp[0].minor.yy314 = 0;\n    }else{\n      yymsp[0].minor.yy314 = sqlite3PExpr(pParse, TK_REGISTER, 0, 0);\n      if( yymsp[0].minor.yy314 ) sqlite3GetInt32(&t.z[1], &yymsp[0].minor.yy314->iTable);\n    }\n  }\n}\n        break;\n      case 159: /* expr ::= expr COLLATE ID|STRING */\n{\n  yymsp[-2].minor.yy314 = sqlite3ExprAddCollateToken(pParse, yymsp[-2].minor.yy314, &yymsp[0].minor.yy0, 1);\n}\n        break;\n      case 160: /* expr ::= CAST LP expr AS typetoken RP */\n{\n  yymsp[-5].minor.yy314 = sqlite3ExprAlloc(pParse->db, TK_CAST, &yymsp[-1].minor.yy0, 1);\n  sqlite3ExprAttachSubtrees(pParse->db, yymsp[-5].minor.yy314, yymsp[-3].minor.yy314, 0);\n}\n        break;\n      case 161: /* expr ::= ID|INDEXED LP distinct exprlist RP */\n{\n  if( yymsp[-1].minor.yy322 && yymsp[-1].minor.yy322->nExpr>pParse->db->aLimit[SQLITE_LIMIT_FUNCTION_ARG] ){\n    sqlite3ErrorMsg(pParse, \"too many arguments on function %T\", &yymsp[-4].minor.yy0);\n  }\n  yylhsminor.yy314 = sqlite3ExprFunction(pParse, yymsp[-1].minor.yy322, &yymsp[-4].minor.yy0);\n  if( yymsp[-2].minor.yy4==SF_Distinct && yylhsminor.yy314 ){\n    yylhsminor.yy314->flags |= EP_Distinct;\n  }\n}\n  yymsp[-4].minor.yy314 = yylhsminor.yy314;\n        break;\n      case 162: /* expr ::= ID|INDEXED LP STAR RP */\n{\n  yylhsminor.yy314 = sqlite3ExprFunction(pParse, 0, &yymsp[-3].minor.yy0);\n}\n  yymsp[-3].minor.yy314 = yylhsminor.yy314;\n        break;\n      case 163: /* term ::= CTIME_KW */\n{\n  yylhsminor.yy314 = sqlite3ExprFunction(pParse, 0, &yymsp[0].minor.yy0);\n}\n  yymsp[0].minor.yy314 = yylhsminor.yy314;\n        break;\n      case 164: /* expr ::= LP nexprlist COMMA expr RP */\n{\n  ExprList *pList = sqlite3ExprListAppend(pParse, yymsp[-3].minor.yy322, yymsp[-1].minor.yy314);\n  yymsp[-4].minor.yy314 = sqlite3PExpr(pParse, TK_VECTOR, 0, 0);\n  if( yymsp[-4].minor.yy314 ){\n    yymsp[-4].minor.yy314->x.pList = pList;\n  }else{\n    sqlite3ExprListDelete(pParse->db, pList);\n  }\n}\n        break;\n      case 165: /* expr ::= expr AND expr */\n      case 166: /* expr ::= expr OR expr */ yytestcase(yyruleno==166);\n      case 167: /* expr ::= expr LT|GT|GE|LE expr */ yytestcase(yyruleno==167);\n      case 168: /* expr ::= expr EQ|NE expr */ yytestcase(yyruleno==168);\n      case 169: /* expr ::= expr BITAND|BITOR|LSHIFT|RSHIFT expr */ yytestcase(yyruleno==169);\n      case 170: /* expr ::= expr PLUS|MINUS expr */ yytestcase(yyruleno==170);\n      case 171: /* expr ::= expr STAR|SLASH|REM expr */ yytestcase(yyruleno==171);\n      case 172: /* expr ::= expr CONCAT expr */ yytestcase(yyruleno==172);\n{yymsp[-2].minor.yy314=sqlite3PExpr(pParse,yymsp[-1].major,yymsp[-2].minor.yy314,yymsp[0].minor.yy314);}\n        break;\n      case 173: /* likeop ::= NOT LIKE_KW|MATCH */\n{yymsp[-1].minor.yy0=yymsp[0].minor.yy0; yymsp[-1].minor.yy0.n|=0x80000000; /*yymsp[-1].minor.yy0-overwrite-yymsp[0].minor.yy0*/}\n        break;\n      case 174: /* expr ::= expr likeop expr */\n{\n  ExprList *pList;\n  int bNot = yymsp[-1].minor.yy0.n & 0x80000000;\n  yymsp[-1].minor.yy0.n &= 0x7fffffff;\n  pList = sqlite3ExprListAppend(pParse,0, yymsp[0].minor.yy314);\n  pList = sqlite3ExprListAppend(pParse,pList, yymsp[-2].minor.yy314);\n  yymsp[-2].minor.yy314 = sqlite3ExprFunction(pParse, pList, &yymsp[-1].minor.yy0);\n  if( bNot ) yymsp[-2].minor.yy314 = sqlite3PExpr(pParse, TK_NOT, yymsp[-2].minor.yy314, 0);\n  if( yymsp[-2].minor.yy314 ) yymsp[-2].minor.yy314->flags |= EP_InfixFunc;\n}\n        break;\n      case 175: /* expr ::= expr likeop expr ESCAPE expr */\n{\n  ExprList *pList;\n  int bNot = yymsp[-3].minor.yy0.n & 0x80000000;\n  yymsp[-3].minor.yy0.n &= 0x7fffffff;\n  pList = sqlite3ExprListAppend(pParse,0, yymsp[-2].minor.yy314);\n  pList = sqlite3ExprListAppend(pParse,pList, yymsp[-4].minor.yy314);\n  pList = sqlite3ExprListAppend(pParse,pList, yymsp[0].minor.yy314);\n  yymsp[-4].minor.yy314 = sqlite3ExprFunction(pParse, pList, &yymsp[-3].minor.yy0);\n  if( bNot ) yymsp[-4].minor.yy314 = sqlite3PExpr(pParse, TK_NOT, yymsp[-4].minor.yy314, 0);\n  if( yymsp[-4].minor.yy314 ) yymsp[-4].minor.yy314->flags |= EP_InfixFunc;\n}\n        break;\n      case 176: /* expr ::= expr ISNULL|NOTNULL */\n{yymsp[-1].minor.yy314 = sqlite3PExpr(pParse,yymsp[0].major,yymsp[-1].minor.yy314,0);}\n        break;\n      case 177: /* expr ::= expr NOT NULL */\n{yymsp[-2].minor.yy314 = sqlite3PExpr(pParse,TK_NOTNULL,yymsp[-2].minor.yy314,0);}\n        break;\n      case 178: /* expr ::= expr IS expr */\n{\n  yymsp[-2].minor.yy314 = sqlite3PExpr(pParse,TK_IS,yymsp[-2].minor.yy314,yymsp[0].minor.yy314);\n  binaryToUnaryIfNull(pParse, yymsp[0].minor.yy314, yymsp[-2].minor.yy314, TK_ISNULL);\n}\n        break;\n      case 179: /* expr ::= expr IS NOT expr */\n{\n  yymsp[-3].minor.yy314 = sqlite3PExpr(pParse,TK_ISNOT,yymsp[-3].minor.yy314,yymsp[0].minor.yy314);\n  binaryToUnaryIfNull(pParse, yymsp[0].minor.yy314, yymsp[-3].minor.yy314, TK_NOTNULL);\n}\n        break;\n      case 180: /* expr ::= NOT expr */\n      case 181: /* expr ::= BITNOT expr */ yytestcase(yyruleno==181);\n{yymsp[-1].minor.yy314 = sqlite3PExpr(pParse, yymsp[-1].major, yymsp[0].minor.yy314, 0);/*A-overwrites-B*/}\n        break;\n      case 182: /* expr ::= MINUS expr */\n{yymsp[-1].minor.yy314 = sqlite3PExpr(pParse, TK_UMINUS, yymsp[0].minor.yy314, 0);}\n        break;\n      case 183: /* expr ::= PLUS expr */\n{yymsp[-1].minor.yy314 = sqlite3PExpr(pParse, TK_UPLUS, yymsp[0].minor.yy314, 0);}\n        break;\n      case 184: /* between_op ::= BETWEEN */\n      case 187: /* in_op ::= IN */ yytestcase(yyruleno==187);\n{yymsp[0].minor.yy4 = 0;}\n        break;\n      case 186: /* expr ::= expr between_op expr AND expr */\n{\n  ExprList *pList = sqlite3ExprListAppend(pParse,0, yymsp[-2].minor.yy314);\n  pList = sqlite3ExprListAppend(pParse,pList, yymsp[0].minor.yy314);\n  yymsp[-4].minor.yy314 = sqlite3PExpr(pParse, TK_BETWEEN, yymsp[-4].minor.yy314, 0);\n  if( yymsp[-4].minor.yy314 ){\n    yymsp[-4].minor.yy314->x.pList = pList;\n  }else{\n    sqlite3ExprListDelete(pParse->db, pList);\n  } \n  if( yymsp[-3].minor.yy4 ) yymsp[-4].minor.yy314 = sqlite3PExpr(pParse, TK_NOT, yymsp[-4].minor.yy314, 0);\n}\n        break;\n      case 189: /* expr ::= expr in_op LP exprlist RP */\n{\n    if( yymsp[-1].minor.yy322==0 ){\n      /* Expressions of the form\n      **\n      **      expr1 IN ()\n      **      expr1 NOT IN ()\n      **\n      ** simplify to constants 0 (false) and 1 (true), respectively,\n      ** regardless of the value of expr1.\n      */\n      sqlite3ExprDelete(pParse->db, yymsp[-4].minor.yy314);\n      yymsp[-4].minor.yy314 = sqlite3ExprAlloc(pParse->db, TK_INTEGER,&sqlite3IntTokens[yymsp[-3].minor.yy4],1);\n    }else if( yymsp[-1].minor.yy322->nExpr==1 ){\n      /* Expressions of the form:\n      **\n      **      expr1 IN (?1)\n      **      expr1 NOT IN (?2)\n      **\n      ** with exactly one value on the RHS can be simplified to something\n      ** like this:\n      **\n      **      expr1 == ?1\n      **      expr1 <> ?2\n      **\n      ** But, the RHS of the == or <> is marked with the EP_Generic flag\n      ** so that it may not contribute to the computation of comparison\n      ** affinity or the collating sequence to use for comparison.  Otherwise,\n      ** the semantics would be subtly different from IN or NOT IN.\n      */\n      Expr *pRHS = yymsp[-1].minor.yy322->a[0].pExpr;\n      yymsp[-1].minor.yy322->a[0].pExpr = 0;\n      sqlite3ExprListDelete(pParse->db, yymsp[-1].minor.yy322);\n      /* pRHS cannot be NULL because a malloc error would have been detected\n      ** before now and control would have never reached this point */\n      if( ALWAYS(pRHS) ){\n        pRHS->flags &= ~EP_Collate;\n        pRHS->flags |= EP_Generic;\n      }\n      yymsp[-4].minor.yy314 = sqlite3PExpr(pParse, yymsp[-3].minor.yy4 ? TK_NE : TK_EQ, yymsp[-4].minor.yy314, pRHS);\n    }else{\n      yymsp[-4].minor.yy314 = sqlite3PExpr(pParse, TK_IN, yymsp[-4].minor.yy314, 0);\n      if( yymsp[-4].minor.yy314 ){\n        yymsp[-4].minor.yy314->x.pList = yymsp[-1].minor.yy322;\n        sqlite3ExprSetHeightAndFlags(pParse, yymsp[-4].minor.yy314);\n      }else{\n        sqlite3ExprListDelete(pParse->db, yymsp[-1].minor.yy322);\n      }\n      if( yymsp[-3].minor.yy4 ) yymsp[-4].minor.yy314 = sqlite3PExpr(pParse, TK_NOT, yymsp[-4].minor.yy314, 0);\n    }\n  }\n        break;\n      case 190: /* expr ::= LP select RP */\n{\n    yymsp[-2].minor.yy314 = sqlite3PExpr(pParse, TK_SELECT, 0, 0);\n    sqlite3PExprAddSelect(pParse, yymsp[-2].minor.yy314, yymsp[-1].minor.yy387);\n  }\n        break;\n      case 191: /* expr ::= expr in_op LP select RP */\n{\n    yymsp[-4].minor.yy314 = sqlite3PExpr(pParse, TK_IN, yymsp[-4].minor.yy314, 0);\n    sqlite3PExprAddSelect(pParse, yymsp[-4].minor.yy314, yymsp[-1].minor.yy387);\n    if( yymsp[-3].minor.yy4 ) yymsp[-4].minor.yy314 = sqlite3PExpr(pParse, TK_NOT, yymsp[-4].minor.yy314, 0);\n  }\n        break;\n      case 192: /* expr ::= expr in_op nm dbnm paren_exprlist */\n{\n    SrcList *pSrc = sqlite3SrcListAppend(pParse->db, 0,&yymsp[-2].minor.yy0,&yymsp[-1].minor.yy0);\n    Select *pSelect = sqlite3SelectNew(pParse, 0,pSrc,0,0,0,0,0,0);\n    if( yymsp[0].minor.yy322 )  sqlite3SrcListFuncArgs(pParse, pSelect ? pSrc : 0, yymsp[0].minor.yy322);\n    yymsp[-4].minor.yy314 = sqlite3PExpr(pParse, TK_IN, yymsp[-4].minor.yy314, 0);\n    sqlite3PExprAddSelect(pParse, yymsp[-4].minor.yy314, pSelect);\n    if( yymsp[-3].minor.yy4 ) yymsp[-4].minor.yy314 = sqlite3PExpr(pParse, TK_NOT, yymsp[-4].minor.yy314, 0);\n  }\n        break;\n      case 193: /* expr ::= EXISTS LP select RP */\n{\n    Expr *p;\n    p = yymsp[-3].minor.yy314 = sqlite3PExpr(pParse, TK_EXISTS, 0, 0);\n    sqlite3PExprAddSelect(pParse, p, yymsp[-1].minor.yy387);\n  }\n        break;\n      case 194: /* expr ::= CASE case_operand case_exprlist case_else END */\n{\n  yymsp[-4].minor.yy314 = sqlite3PExpr(pParse, TK_CASE, yymsp[-3].minor.yy314, 0);\n  if( yymsp[-4].minor.yy314 ){\n    yymsp[-4].minor.yy314->x.pList = yymsp[-1].minor.yy314 ? sqlite3ExprListAppend(pParse,yymsp[-2].minor.yy322,yymsp[-1].minor.yy314) : yymsp[-2].minor.yy322;\n    sqlite3ExprSetHeightAndFlags(pParse, yymsp[-4].minor.yy314);\n  }else{\n    sqlite3ExprListDelete(pParse->db, yymsp[-2].minor.yy322);\n    sqlite3ExprDelete(pParse->db, yymsp[-1].minor.yy314);\n  }\n}\n        break;\n      case 195: /* case_exprlist ::= case_exprlist WHEN expr THEN expr */\n{\n  yymsp[-4].minor.yy322 = sqlite3ExprListAppend(pParse,yymsp[-4].minor.yy322, yymsp[-2].minor.yy314);\n  yymsp[-4].minor.yy322 = sqlite3ExprListAppend(pParse,yymsp[-4].minor.yy322, yymsp[0].minor.yy314);\n}\n        break;\n      case 196: /* case_exprlist ::= WHEN expr THEN expr */\n{\n  yymsp[-3].minor.yy322 = sqlite3ExprListAppend(pParse,0, yymsp[-2].minor.yy314);\n  yymsp[-3].minor.yy322 = sqlite3ExprListAppend(pParse,yymsp[-3].minor.yy322, yymsp[0].minor.yy314);\n}\n        break;\n      case 199: /* case_operand ::= expr */\n{yymsp[0].minor.yy314 = yymsp[0].minor.yy314; /*A-overwrites-X*/}\n        break;\n      case 202: /* nexprlist ::= nexprlist COMMA expr */\n{yymsp[-2].minor.yy322 = sqlite3ExprListAppend(pParse,yymsp[-2].minor.yy322,yymsp[0].minor.yy314);}\n        break;\n      case 203: /* nexprlist ::= expr */\n{yymsp[0].minor.yy322 = sqlite3ExprListAppend(pParse,0,yymsp[0].minor.yy314); /*A-overwrites-Y*/}\n        break;\n      case 205: /* paren_exprlist ::= LP exprlist RP */\n      case 210: /* eidlist_opt ::= LP eidlist RP */ yytestcase(yyruleno==210);\n{yymsp[-2].minor.yy322 = yymsp[-1].minor.yy322;}\n        break;\n      case 206: /* cmd ::= createkw uniqueflag INDEX ifnotexists nm dbnm ON nm LP sortlist RP where_opt */\n{\n  sqlite3CreateIndex(pParse, &yymsp[-7].minor.yy0, &yymsp[-6].minor.yy0, \n                     sqlite3SrcListAppend(pParse->db,0,&yymsp[-4].minor.yy0,0), yymsp[-2].minor.yy322, yymsp[-10].minor.yy4,\n                      &yymsp[-11].minor.yy0, yymsp[0].minor.yy314, SQLITE_SO_ASC, yymsp[-8].minor.yy4, SQLITE_IDXTYPE_APPDEF);\n}\n        break;\n      case 207: /* uniqueflag ::= UNIQUE */\n      case 247: /* raisetype ::= ABORT */ yytestcase(yyruleno==247);\n{yymsp[0].minor.yy4 = OE_Abort;}\n        break;\n      case 208: /* uniqueflag ::= */\n{yymsp[1].minor.yy4 = OE_None;}\n        break;\n      case 211: /* eidlist ::= eidlist COMMA nm collate sortorder */\n{\n  yymsp[-4].minor.yy322 = parserAddExprIdListTerm(pParse, yymsp[-4].minor.yy322, &yymsp[-2].minor.yy0, yymsp[-1].minor.yy4, yymsp[0].minor.yy4);\n}\n        break;\n      case 212: /* eidlist ::= nm collate sortorder */\n{\n  yymsp[-2].minor.yy322 = parserAddExprIdListTerm(pParse, 0, &yymsp[-2].minor.yy0, yymsp[-1].minor.yy4, yymsp[0].minor.yy4); /*A-overwrites-Y*/\n}\n        break;\n      case 215: /* cmd ::= DROP INDEX ifexists fullname */\n{sqlite3DropIndex(pParse, yymsp[0].minor.yy259, yymsp[-1].minor.yy4);}\n        break;\n      case 216: /* cmd ::= VACUUM */\n{sqlite3Vacuum(pParse,0);}\n        break;\n      case 217: /* cmd ::= VACUUM nm */\n{sqlite3Vacuum(pParse,&yymsp[0].minor.yy0);}\n        break;\n      case 218: /* cmd ::= PRAGMA nm dbnm */\n{sqlite3Pragma(pParse,&yymsp[-1].minor.yy0,&yymsp[0].minor.yy0,0,0);}\n        break;\n      case 219: /* cmd ::= PRAGMA nm dbnm EQ nmnum */\n{sqlite3Pragma(pParse,&yymsp[-3].minor.yy0,&yymsp[-2].minor.yy0,&yymsp[0].minor.yy0,0);}\n        break;\n      case 220: /* cmd ::= PRAGMA nm dbnm LP nmnum RP */\n{sqlite3Pragma(pParse,&yymsp[-4].minor.yy0,&yymsp[-3].minor.yy0,&yymsp[-1].minor.yy0,0);}\n        break;\n      case 221: /* cmd ::= PRAGMA nm dbnm EQ minus_num */\n{sqlite3Pragma(pParse,&yymsp[-3].minor.yy0,&yymsp[-2].minor.yy0,&yymsp[0].minor.yy0,1);}\n        break;\n      case 222: /* cmd ::= PRAGMA nm dbnm LP minus_num RP */\n{sqlite3Pragma(pParse,&yymsp[-4].minor.yy0,&yymsp[-3].minor.yy0,&yymsp[-1].minor.yy0,1);}\n        break;\n      case 225: /* cmd ::= createkw trigger_decl BEGIN trigger_cmd_list END */\n{\n  Token all;\n  all.z = yymsp[-3].minor.yy0.z;\n  all.n = (int)(yymsp[0].minor.yy0.z - yymsp[-3].minor.yy0.z) + yymsp[0].minor.yy0.n;\n  sqlite3FinishTrigger(pParse, yymsp[-1].minor.yy203, &all);\n}\n        break;\n      case 226: /* trigger_decl ::= temp TRIGGER ifnotexists nm dbnm trigger_time trigger_event ON fullname foreach_clause when_clause */\n{\n  sqlite3BeginTrigger(pParse, &yymsp[-7].minor.yy0, &yymsp[-6].minor.yy0, yymsp[-5].minor.yy4, yymsp[-4].minor.yy90.a, yymsp[-4].minor.yy90.b, yymsp[-2].minor.yy259, yymsp[0].minor.yy314, yymsp[-10].minor.yy4, yymsp[-8].minor.yy4);\n  yymsp[-10].minor.yy0 = (yymsp[-6].minor.yy0.n==0?yymsp[-7].minor.yy0:yymsp[-6].minor.yy0); /*A-overwrites-T*/\n}\n        break;\n      case 227: /* trigger_time ::= BEFORE|AFTER */\n{ yymsp[0].minor.yy4 = yymsp[0].major; /*A-overwrites-X*/ }\n        break;\n      case 228: /* trigger_time ::= INSTEAD OF */\n{ yymsp[-1].minor.yy4 = TK_INSTEAD;}\n        break;\n      case 229: /* trigger_time ::= */\n{ yymsp[1].minor.yy4 = TK_BEFORE; }\n        break;\n      case 230: /* trigger_event ::= DELETE|INSERT */\n      case 231: /* trigger_event ::= UPDATE */ yytestcase(yyruleno==231);\n{yymsp[0].minor.yy90.a = yymsp[0].major; /*A-overwrites-X*/ yymsp[0].minor.yy90.b = 0;}\n        break;\n      case 232: /* trigger_event ::= UPDATE OF idlist */\n{yymsp[-2].minor.yy90.a = TK_UPDATE; yymsp[-2].minor.yy90.b = yymsp[0].minor.yy384;}\n        break;\n      case 233: /* when_clause ::= */\n      case 252: /* key_opt ::= */ yytestcase(yyruleno==252);\n{ yymsp[1].minor.yy314 = 0; }\n        break;\n      case 234: /* when_clause ::= WHEN expr */\n      case 253: /* key_opt ::= KEY expr */ yytestcase(yyruleno==253);\n{ yymsp[-1].minor.yy314 = yymsp[0].minor.yy314; }\n        break;\n      case 235: /* trigger_cmd_list ::= trigger_cmd_list trigger_cmd SEMI */\n{\n  assert( yymsp[-2].minor.yy203!=0 );\n  yymsp[-2].minor.yy203->pLast->pNext = yymsp[-1].minor.yy203;\n  yymsp[-2].minor.yy203->pLast = yymsp[-1].minor.yy203;\n}\n        break;\n      case 236: /* trigger_cmd_list ::= trigger_cmd SEMI */\n{ \n  assert( yymsp[-1].minor.yy203!=0 );\n  yymsp[-1].minor.yy203->pLast = yymsp[-1].minor.yy203;\n}\n        break;\n      case 237: /* trnm ::= nm DOT nm */\n{\n  yymsp[-2].minor.yy0 = yymsp[0].minor.yy0;\n  sqlite3ErrorMsg(pParse, \n        \"qualified table names are not allowed on INSERT, UPDATE, and DELETE \"\n        \"statements within triggers\");\n}\n        break;\n      case 238: /* tridxby ::= INDEXED BY nm */\n{\n  sqlite3ErrorMsg(pParse,\n        \"the INDEXED BY clause is not allowed on UPDATE or DELETE statements \"\n        \"within triggers\");\n}\n        break;\n      case 239: /* tridxby ::= NOT INDEXED */\n{\n  sqlite3ErrorMsg(pParse,\n        \"the NOT INDEXED clause is not allowed on UPDATE or DELETE statements \"\n        \"within triggers\");\n}\n        break;\n      case 240: /* trigger_cmd ::= UPDATE orconf trnm tridxby SET setlist where_opt scanpt */\n{yylhsminor.yy203 = sqlite3TriggerUpdateStep(pParse->db, &yymsp[-5].minor.yy0, yymsp[-2].minor.yy322, yymsp[-1].minor.yy314, yymsp[-6].minor.yy4, yymsp[-7].minor.yy0.z, yymsp[0].minor.yy336);}\n  yymsp[-7].minor.yy203 = yylhsminor.yy203;\n        break;\n      case 241: /* trigger_cmd ::= scanpt insert_cmd INTO trnm idlist_opt select scanpt */\n{yylhsminor.yy203 = sqlite3TriggerInsertStep(pParse->db,&yymsp[-3].minor.yy0,yymsp[-2].minor.yy384,yymsp[-1].minor.yy387,yymsp[-5].minor.yy4,yymsp[-6].minor.yy336,yymsp[0].minor.yy336);/*yylhsminor.yy203-overwrites-yymsp[-5].minor.yy4*/}\n  yymsp[-6].minor.yy203 = yylhsminor.yy203;\n        break;\n      case 242: /* trigger_cmd ::= DELETE FROM trnm tridxby where_opt scanpt */\n{yylhsminor.yy203 = sqlite3TriggerDeleteStep(pParse->db, &yymsp[-3].minor.yy0, yymsp[-1].minor.yy314, yymsp[-5].minor.yy0.z, yymsp[0].minor.yy336);}\n  yymsp[-5].minor.yy203 = yylhsminor.yy203;\n        break;\n      case 243: /* trigger_cmd ::= scanpt select scanpt */\n{yylhsminor.yy203 = sqlite3TriggerSelectStep(pParse->db, yymsp[-1].minor.yy387, yymsp[-2].minor.yy336, yymsp[0].minor.yy336); /*yylhsminor.yy203-overwrites-yymsp[-1].minor.yy387*/}\n  yymsp[-2].minor.yy203 = yylhsminor.yy203;\n        break;\n      case 244: /* expr ::= RAISE LP IGNORE RP */\n{\n  yymsp[-3].minor.yy314 = sqlite3PExpr(pParse, TK_RAISE, 0, 0); \n  if( yymsp[-3].minor.yy314 ){\n    yymsp[-3].minor.yy314->affinity = OE_Ignore;\n  }\n}\n        break;\n      case 245: /* expr ::= RAISE LP raisetype COMMA nm RP */\n{\n  yymsp[-5].minor.yy314 = sqlite3ExprAlloc(pParse->db, TK_RAISE, &yymsp[-1].minor.yy0, 1); \n  if( yymsp[-5].minor.yy314 ) {\n    yymsp[-5].minor.yy314->affinity = (char)yymsp[-3].minor.yy4;\n  }\n}\n        break;\n      case 246: /* raisetype ::= ROLLBACK */\n{yymsp[0].minor.yy4 = OE_Rollback;}\n        break;\n      case 248: /* raisetype ::= FAIL */\n{yymsp[0].minor.yy4 = OE_Fail;}\n        break;\n      case 249: /* cmd ::= DROP TRIGGER ifexists fullname */\n{\n  sqlite3DropTrigger(pParse,yymsp[0].minor.yy259,yymsp[-1].minor.yy4);\n}\n        break;\n      case 250: /* cmd ::= ATTACH database_kw_opt expr AS expr key_opt */\n{\n  sqlite3Attach(pParse, yymsp[-3].minor.yy314, yymsp[-1].minor.yy314, yymsp[0].minor.yy314);\n}\n        break;\n      case 251: /* cmd ::= DETACH database_kw_opt expr */\n{\n  sqlite3Detach(pParse, yymsp[0].minor.yy314);\n}\n        break;\n      case 254: /* cmd ::= REINDEX */\n{sqlite3Reindex(pParse, 0, 0);}\n        break;\n      case 255: /* cmd ::= REINDEX nm dbnm */\n{sqlite3Reindex(pParse, &yymsp[-1].minor.yy0, &yymsp[0].minor.yy0);}\n        break;\n      case 256: /* cmd ::= ANALYZE */\n{sqlite3Analyze(pParse, 0, 0);}\n        break;\n      case 257: /* cmd ::= ANALYZE nm dbnm */\n{sqlite3Analyze(pParse, &yymsp[-1].minor.yy0, &yymsp[0].minor.yy0);}\n        break;\n      case 258: /* cmd ::= ALTER TABLE fullname RENAME TO nm */\n{\n  sqlite3AlterRenameTable(pParse,yymsp[-3].minor.yy259,&yymsp[0].minor.yy0);\n}\n        break;\n      case 259: /* cmd ::= ALTER TABLE add_column_fullname ADD kwcolumn_opt columnname carglist */\n{\n  yymsp[-1].minor.yy0.n = (int)(pParse->sLastToken.z-yymsp[-1].minor.yy0.z) + pParse->sLastToken.n;\n  sqlite3AlterFinishAddColumn(pParse, &yymsp[-1].minor.yy0);\n}\n        break;\n      case 260: /* add_column_fullname ::= fullname */\n{\n  disableLookaside(pParse);\n  sqlite3AlterBeginAddColumn(pParse, yymsp[0].minor.yy259);\n}\n        break;\n      case 261: /* cmd ::= create_vtab */\n{sqlite3VtabFinishParse(pParse,0);}\n        break;\n      case 262: /* cmd ::= create_vtab LP vtabarglist RP */\n{sqlite3VtabFinishParse(pParse,&yymsp[0].minor.yy0);}\n        break;\n      case 263: /* create_vtab ::= createkw VIRTUAL TABLE ifnotexists nm dbnm USING nm */\n{\n    sqlite3VtabBeginParse(pParse, &yymsp[-3].minor.yy0, &yymsp[-2].minor.yy0, &yymsp[0].minor.yy0, yymsp[-4].minor.yy4);\n}\n        break;\n      case 264: /* vtabarg ::= */\n{sqlite3VtabArgInit(pParse);}\n        break;\n      case 265: /* vtabargtoken ::= ANY */\n      case 266: /* vtabargtoken ::= lp anylist RP */ yytestcase(yyruleno==266);\n      case 267: /* lp ::= LP */ yytestcase(yyruleno==267);\n{sqlite3VtabArgExtend(pParse,&yymsp[0].minor.yy0);}\n        break;\n      case 268: /* with ::= */\n{yymsp[1].minor.yy451 = 0;}\n        break;\n      case 269: /* with ::= WITH wqlist */\n{ yymsp[-1].minor.yy451 = yymsp[0].minor.yy451; }\n        break;\n      case 270: /* with ::= WITH RECURSIVE wqlist */\n{ yymsp[-2].minor.yy451 = yymsp[0].minor.yy451; }\n        break;\n      case 271: /* wqlist ::= nm eidlist_opt AS LP select RP */\n{\n  yymsp[-5].minor.yy451 = sqlite3WithAdd(pParse, 0, &yymsp[-5].minor.yy0, yymsp[-4].minor.yy322, yymsp[-1].minor.yy387); /*A-overwrites-X*/\n}\n        break;\n      case 272: /* wqlist ::= wqlist COMMA nm eidlist_opt AS LP select RP */\n{\n  yymsp[-7].minor.yy451 = sqlite3WithAdd(pParse, yymsp[-7].minor.yy451, &yymsp[-5].minor.yy0, yymsp[-4].minor.yy322, yymsp[-1].minor.yy387);\n}\n        break;\n      default:\n      /* (273) input ::= cmdlist */ yytestcase(yyruleno==273);\n      /* (274) cmdlist ::= cmdlist ecmd */ yytestcase(yyruleno==274);\n      /* (275) cmdlist ::= ecmd (OPTIMIZED OUT) */ assert(yyruleno!=275);\n      /* (276) ecmd ::= SEMI */ yytestcase(yyruleno==276);\n      /* (277) ecmd ::= explain cmdx SEMI */ yytestcase(yyruleno==277);\n      /* (278) explain ::= */ yytestcase(yyruleno==278);\n      /* (279) trans_opt ::= */ yytestcase(yyruleno==279);\n      /* (280) trans_opt ::= TRANSACTION */ yytestcase(yyruleno==280);\n      /* (281) trans_opt ::= TRANSACTION nm */ yytestcase(yyruleno==281);\n      /* (282) savepoint_opt ::= SAVEPOINT */ yytestcase(yyruleno==282);\n      /* (283) savepoint_opt ::= */ yytestcase(yyruleno==283);\n      /* (284) cmd ::= create_table create_table_args */ yytestcase(yyruleno==284);\n      /* (285) columnlist ::= columnlist COMMA columnname carglist */ yytestcase(yyruleno==285);\n      /* (286) columnlist ::= columnname carglist */ yytestcase(yyruleno==286);\n      /* (287) nm ::= ID|INDEXED */ yytestcase(yyruleno==287);\n      /* (288) nm ::= STRING */ yytestcase(yyruleno==288);\n      /* (289) nm ::= JOIN_KW */ yytestcase(yyruleno==289);\n      /* (290) typetoken ::= typename */ yytestcase(yyruleno==290);\n      /* (291) typename ::= ID|STRING */ yytestcase(yyruleno==291);\n      /* (292) signed ::= plus_num (OPTIMIZED OUT) */ assert(yyruleno!=292);\n      /* (293) signed ::= minus_num (OPTIMIZED OUT) */ assert(yyruleno!=293);\n      /* (294) carglist ::= carglist ccons */ yytestcase(yyruleno==294);\n      /* (295) carglist ::= */ yytestcase(yyruleno==295);\n      /* (296) ccons ::= NULL onconf */ yytestcase(yyruleno==296);\n      /* (297) conslist_opt ::= COMMA conslist */ yytestcase(yyruleno==297);\n      /* (298) conslist ::= conslist tconscomma tcons */ yytestcase(yyruleno==298);\n      /* (299) conslist ::= tcons (OPTIMIZED OUT) */ assert(yyruleno!=299);\n      /* (300) tconscomma ::= */ yytestcase(yyruleno==300);\n      /* (301) defer_subclause_opt ::= defer_subclause (OPTIMIZED OUT) */ assert(yyruleno!=301);\n      /* (302) resolvetype ::= raisetype (OPTIMIZED OUT) */ assert(yyruleno!=302);\n      /* (303) selectnowith ::= oneselect (OPTIMIZED OUT) */ assert(yyruleno!=303);\n      /* (304) oneselect ::= values */ yytestcase(yyruleno==304);\n      /* (305) sclp ::= selcollist COMMA */ yytestcase(yyruleno==305);\n      /* (306) as ::= ID|STRING */ yytestcase(yyruleno==306);\n      /* (307) expr ::= term (OPTIMIZED OUT) */ assert(yyruleno!=307);\n      /* (308) likeop ::= LIKE_KW|MATCH */ yytestcase(yyruleno==308);\n      /* (309) exprlist ::= nexprlist */ yytestcase(yyruleno==309);\n      /* (310) nmnum ::= plus_num (OPTIMIZED OUT) */ assert(yyruleno!=310);\n      /* (311) nmnum ::= nm (OPTIMIZED OUT) */ assert(yyruleno!=311);\n      /* (312) nmnum ::= ON */ yytestcase(yyruleno==312);\n      /* (313) nmnum ::= DELETE */ yytestcase(yyruleno==313);\n      /* (314) nmnum ::= DEFAULT */ yytestcase(yyruleno==314);\n      /* (315) plus_num ::= INTEGER|FLOAT */ yytestcase(yyruleno==315);\n      /* (316) foreach_clause ::= */ yytestcase(yyruleno==316);\n      /* (317) foreach_clause ::= FOR EACH ROW */ yytestcase(yyruleno==317);\n      /* (318) trnm ::= nm */ yytestcase(yyruleno==318);\n      /* (319) tridxby ::= */ yytestcase(yyruleno==319);\n      /* (320) database_kw_opt ::= DATABASE */ yytestcase(yyruleno==320);\n      /* (321) database_kw_opt ::= */ yytestcase(yyruleno==321);\n      /* (322) kwcolumn_opt ::= */ yytestcase(yyruleno==322);\n      /* (323) kwcolumn_opt ::= COLUMNKW */ yytestcase(yyruleno==323);\n      /* (324) vtabarglist ::= vtabarg */ yytestcase(yyruleno==324);\n      /* (325) vtabarglist ::= vtabarglist COMMA vtabarg */ yytestcase(yyruleno==325);\n      /* (326) vtabarg ::= vtabarg vtabargtoken */ yytestcase(yyruleno==326);\n      /* (327) anylist ::= */ yytestcase(yyruleno==327);\n      /* (328) anylist ::= anylist LP anylist RP */ yytestcase(yyruleno==328);\n      /* (329) anylist ::= anylist ANY */ yytestcase(yyruleno==329);\n        break;\n/********** End reduce actions ************************************************/\n  };\n  assert( yyruleno<sizeof(yyRuleInfo)/sizeof(yyRuleInfo[0]) );\n  yygoto = yyRuleInfo[yyruleno].lhs;\n  yysize = yyRuleInfo[yyruleno].nrhs;\n  yyact = yy_find_reduce_action(yymsp[yysize].stateno,(YYCODETYPE)yygoto);\n\n  /* There are no SHIFTREDUCE actions on nonterminals because the table\n  ** generator has simplified them to pure REDUCE actions. */\n  assert( !(yyact>YY_MAX_SHIFT && yyact<=YY_MAX_SHIFTREDUCE) );\n\n  /* It is not possible for a REDUCE to be followed by an error */\n  assert( yyact!=YY_ERROR_ACTION );\n\n  yymsp += yysize+1;\n  yypParser->yytos = yymsp;\n  yymsp->stateno = (YYACTIONTYPE)yyact;\n  yymsp->major = (YYCODETYPE)yygoto;\n  yyTraceShift(yypParser, yyact, \"... then shift\");\n}\n\n/*\n** The following code executes when the parse fails\n*/\n#ifndef YYNOERRORRECOVERY\nstatic void yy_parse_failed(\n  yyParser *yypParser           /* The parser */\n){\n  sqlite3ParserARG_FETCH;\n#ifndef NDEBUG\n  if( yyTraceFILE ){\n    fprintf(yyTraceFILE,\"%sFail!\\n\",yyTracePrompt);\n  }\n#endif\n  while( yypParser->yytos>yypParser->yystack ) yy_pop_parser_stack(yypParser);\n  /* Here code is inserted which will be executed whenever the\n  ** parser fails */\n/************ Begin %parse_failure code ***************************************/\n/************ End %parse_failure code *****************************************/\n  sqlite3ParserARG_STORE; /* Suppress warning about unused %extra_argument variable */\n}\n#endif /* YYNOERRORRECOVERY */\n\n/*\n** The following code executes when a syntax error first occurs.\n*/\nstatic void yy_syntax_error(\n  yyParser *yypParser,           /* The parser */\n  int yymajor,                   /* The major type of the error token */\n  sqlite3ParserTOKENTYPE yyminor         /* The minor type of the error token */\n){\n  sqlite3ParserARG_FETCH;\n#define TOKEN yyminor\n/************ Begin %syntax_error code ****************************************/\n\n  UNUSED_PARAMETER(yymajor);  /* Silence some compiler warnings */\n  if( TOKEN.z[0] ){\n    sqlite3ErrorMsg(pParse, \"near \\\"%T\\\": syntax error\", &TOKEN);\n  }else{\n    sqlite3ErrorMsg(pParse, \"incomplete input\");\n  }\n/************ End %syntax_error code ******************************************/\n  sqlite3ParserARG_STORE; /* Suppress warning about unused %extra_argument variable */\n}\n\n/*\n** The following is executed when the parser accepts\n*/\nstatic void yy_accept(\n  yyParser *yypParser           /* The parser */\n){\n  sqlite3ParserARG_FETCH;\n#ifndef NDEBUG\n  if( yyTraceFILE ){\n    fprintf(yyTraceFILE,\"%sAccept!\\n\",yyTracePrompt);\n  }\n#endif\n#ifndef YYNOERRORRECOVERY\n  yypParser->yyerrcnt = -1;\n#endif\n  assert( yypParser->yytos==yypParser->yystack );\n  /* Here code is inserted which will be executed whenever the\n  ** parser accepts */\n/*********** Begin %parse_accept code *****************************************/\n/*********** End %parse_accept code *******************************************/\n  sqlite3ParserARG_STORE; /* Suppress warning about unused %extra_argument variable */\n}\n\n/* The main parser program.\n** The first argument is a pointer to a structure obtained from\n** \"sqlite3ParserAlloc\" which describes the current state of the parser.\n** The second argument is the major token number.  The third is\n** the minor token.  The fourth optional argument is whatever the\n** user wants (and specified in the grammar) and is available for\n** use by the action routines.\n**\n** Inputs:\n** <ul>\n** <li> A pointer to the parser (an opaque structure.)\n** <li> The major token number.\n** <li> The minor token number.\n** <li> An option argument of a grammar-specified type.\n** </ul>\n**\n** Outputs:\n** None.\n*/\nSQLITE_PRIVATE void sqlite3Parser(\n  void *yyp,                   /* The parser */\n  int yymajor,                 /* The major token code number */\n  sqlite3ParserTOKENTYPE yyminor       /* The value for the token */\n  sqlite3ParserARG_PDECL               /* Optional %extra_argument parameter */\n){\n  YYMINORTYPE yyminorunion;\n  unsigned int yyact;   /* The parser action. */\n#if !defined(YYERRORSYMBOL) && !defined(YYNOERRORRECOVERY)\n  int yyendofinput;     /* True if we are at the end of input */\n#endif\n#ifdef YYERRORSYMBOL\n  int yyerrorhit = 0;   /* True if yymajor has invoked an error */\n#endif\n  yyParser *yypParser;  /* The parser */\n\n  yypParser = (yyParser*)yyp;\n  assert( yypParser->yytos!=0 );\n#if !defined(YYERRORSYMBOL) && !defined(YYNOERRORRECOVERY)\n  yyendofinput = (yymajor==0);\n#endif\n  sqlite3ParserARG_STORE;\n\n#ifndef NDEBUG\n  if( yyTraceFILE ){\n    int stateno = yypParser->yytos->stateno;\n    if( stateno < YY_MIN_REDUCE ){\n      fprintf(yyTraceFILE,\"%sInput '%s' in state %d\\n\",\n              yyTracePrompt,yyTokenName[yymajor],stateno);\n    }else{\n      fprintf(yyTraceFILE,\"%sInput '%s' with pending reduce %d\\n\",\n              yyTracePrompt,yyTokenName[yymajor],stateno-YY_MIN_REDUCE);\n    }\n  }\n#endif\n\n  do{\n    yyact = yy_find_shift_action(yypParser,(YYCODETYPE)yymajor);\n    if( yyact >= YY_MIN_REDUCE ){\n      yy_reduce(yypParser,yyact-YY_MIN_REDUCE,yymajor,yyminor);\n    }else if( yyact <= YY_MAX_SHIFTREDUCE ){\n      yy_shift(yypParser,yyact,yymajor,yyminor);\n#ifndef YYNOERRORRECOVERY\n      yypParser->yyerrcnt--;\n#endif\n      yymajor = YYNOCODE;\n    }else if( yyact==YY_ACCEPT_ACTION ){\n      yypParser->yytos--;\n      yy_accept(yypParser);\n      return;\n    }else{\n      assert( yyact == YY_ERROR_ACTION );\n      yyminorunion.yy0 = yyminor;\n#ifdef YYERRORSYMBOL\n      int yymx;\n#endif\n#ifndef NDEBUG\n      if( yyTraceFILE ){\n        fprintf(yyTraceFILE,\"%sSyntax Error!\\n\",yyTracePrompt);\n      }\n#endif\n#ifdef YYERRORSYMBOL\n      /* A syntax error has occurred.\n      ** The response to an error depends upon whether or not the\n      ** grammar defines an error token \"ERROR\".  \n      **\n      ** This is what we do if the grammar does define ERROR:\n      **\n      **  * Call the %syntax_error function.\n      **\n      **  * Begin popping the stack until we enter a state where\n      **    it is legal to shift the error symbol, then shift\n      **    the error symbol.\n      **\n      **  * Set the error count to three.\n      **\n      **  * Begin accepting and shifting new tokens.  No new error\n      **    processing will occur until three tokens have been\n      **    shifted successfully.\n      **\n      */\n      if( yypParser->yyerrcnt<0 ){\n        yy_syntax_error(yypParser,yymajor,yyminor);\n      }\n      yymx = yypParser->yytos->major;\n      if( yymx==YYERRORSYMBOL || yyerrorhit ){\n#ifndef NDEBUG\n        if( yyTraceFILE ){\n          fprintf(yyTraceFILE,\"%sDiscard input token %s\\n\",\n             yyTracePrompt,yyTokenName[yymajor]);\n        }\n#endif\n        yy_destructor(yypParser, (YYCODETYPE)yymajor, &yyminorunion);\n        yymajor = YYNOCODE;\n      }else{\n        while( yypParser->yytos >= yypParser->yystack\n            && yymx != YYERRORSYMBOL\n            && (yyact = yy_find_reduce_action(\n                        yypParser->yytos->stateno,\n                        YYERRORSYMBOL)) >= YY_MIN_REDUCE\n        ){\n          yy_pop_parser_stack(yypParser);\n        }\n        if( yypParser->yytos < yypParser->yystack || yymajor==0 ){\n          yy_destructor(yypParser,(YYCODETYPE)yymajor,&yyminorunion);\n          yy_parse_failed(yypParser);\n#ifndef YYNOERRORRECOVERY\n          yypParser->yyerrcnt = -1;\n#endif\n          yymajor = YYNOCODE;\n        }else if( yymx!=YYERRORSYMBOL ){\n          yy_shift(yypParser,yyact,YYERRORSYMBOL,yyminor);\n        }\n      }\n      yypParser->yyerrcnt = 3;\n      yyerrorhit = 1;\n#elif defined(YYNOERRORRECOVERY)\n      /* If the YYNOERRORRECOVERY macro is defined, then do not attempt to\n      ** do any kind of error recovery.  Instead, simply invoke the syntax\n      ** error routine and continue going as if nothing had happened.\n      **\n      ** Applications can set this macro (for example inside %include) if\n      ** they intend to abandon the parse upon the first syntax error seen.\n      */\n      yy_syntax_error(yypParser,yymajor, yyminor);\n      yy_destructor(yypParser,(YYCODETYPE)yymajor,&yyminorunion);\n      yymajor = YYNOCODE;\n      \n#else  /* YYERRORSYMBOL is not defined */\n      /* This is what we do if the grammar does not define ERROR:\n      **\n      **  * Report an error message, and throw away the input token.\n      **\n      **  * If the input token is $, then fail the parse.\n      **\n      ** As before, subsequent error messages are suppressed until\n      ** three input tokens have been successfully shifted.\n      */\n      if( yypParser->yyerrcnt<=0 ){\n        yy_syntax_error(yypParser,yymajor, yyminor);\n      }\n      yypParser->yyerrcnt = 3;\n      yy_destructor(yypParser,(YYCODETYPE)yymajor,&yyminorunion);\n      if( yyendofinput ){\n        yy_parse_failed(yypParser);\n#ifndef YYNOERRORRECOVERY\n        yypParser->yyerrcnt = -1;\n#endif\n      }\n      yymajor = YYNOCODE;\n#endif\n    }\n  }while( yymajor!=YYNOCODE && yypParser->yytos>yypParser->yystack );\n#ifndef NDEBUG\n  if( yyTraceFILE ){\n    yyStackEntry *i;\n    char cDiv = '[';\n    fprintf(yyTraceFILE,\"%sReturn. Stack=\",yyTracePrompt);\n    for(i=&yypParser->yystack[1]; i<=yypParser->yytos; i++){\n      fprintf(yyTraceFILE,\"%c%s\", cDiv, yyTokenName[i->major]);\n      cDiv = ' ';\n    }\n    fprintf(yyTraceFILE,\"]\\n\");\n  }\n#endif\n  return;\n}\n\n/************** End of parse.c ***********************************************/\n/************** Begin file tokenize.c ****************************************/\n/*\n** 2001 September 15\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n*************************************************************************\n** An tokenizer for SQL\n**\n** This file contains C code that splits an SQL input string up into\n** individual tokens and sends those tokens one-by-one over to the\n** parser for analysis.\n*/\n/* #include \"sqliteInt.h\" */\n/* #include <stdlib.h> */\n\n/* Character classes for tokenizing\n**\n** In the sqlite3GetToken() function, a switch() on aiClass[c] is implemented\n** using a lookup table, whereas a switch() directly on c uses a binary search.\n** The lookup table is much faster.  To maximize speed, and to ensure that\n** a lookup table is used, all of the classes need to be small integers and\n** all of them need to be used within the switch.\n*/\n#define CC_X          0    /* The letter 'x', or start of BLOB literal */\n#define CC_KYWD       1    /* Alphabetics or '_'.  Usable in a keyword */\n#define CC_ID         2    /* unicode characters usable in IDs */\n#define CC_DIGIT      3    /* Digits */\n#define CC_DOLLAR     4    /* '$' */\n#define CC_VARALPHA   5    /* '@', '#', ':'.  Alphabetic SQL variables */\n#define CC_VARNUM     6    /* '?'.  Numeric SQL variables */\n#define CC_SPACE      7    /* Space characters */\n#define CC_QUOTE      8    /* '\"', '\\'', or '`'.  String literals, quoted ids */\n#define CC_QUOTE2     9    /* '['.   [...] style quoted ids */\n#define CC_PIPE      10    /* '|'.   Bitwise OR or concatenate */\n#define CC_MINUS     11    /* '-'.  Minus or SQL-style comment */\n#define CC_LT        12    /* '<'.  Part of < or <= or <> */\n#define CC_GT        13    /* '>'.  Part of > or >= */\n#define CC_EQ        14    /* '='.  Part of = or == */\n#define CC_BANG      15    /* '!'.  Part of != */\n#define CC_SLASH     16    /* '/'.  / or c-style comment */\n#define CC_LP        17    /* '(' */\n#define CC_RP        18    /* ')' */\n#define CC_SEMI      19    /* ';' */\n#define CC_PLUS      20    /* '+' */\n#define CC_STAR      21    /* '*' */\n#define CC_PERCENT   22    /* '%' */\n#define CC_COMMA     23    /* ',' */\n#define CC_AND       24    /* '&' */\n#define CC_TILDA     25    /* '~' */\n#define CC_DOT       26    /* '.' */\n#define CC_ILLEGAL   27    /* Illegal character */\n\nstatic const unsigned char aiClass[] = {\n#ifdef SQLITE_ASCII\n/*         x0  x1  x2  x3  x4  x5  x6  x7  x8  x9  xa  xb  xc  xd  xe  xf */\n/* 0x */   27, 27, 27, 27, 27, 27, 27, 27, 27,  7,  7, 27,  7,  7, 27, 27,\n/* 1x */   27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27,\n/* 2x */    7, 15,  8,  5,  4, 22, 24,  8, 17, 18, 21, 20, 23, 11, 26, 16,\n/* 3x */    3,  3,  3,  3,  3,  3,  3,  3,  3,  3,  5, 19, 12, 14, 13,  6,\n/* 4x */    5,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,\n/* 5x */    1,  1,  1,  1,  1,  1,  1,  1,  0,  1,  1,  9, 27, 27, 27,  1,\n/* 6x */    8,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,\n/* 7x */    1,  1,  1,  1,  1,  1,  1,  1,  0,  1,  1, 27, 10, 27, 25, 27,\n/* 8x */    2,  2,  2,  2,  2,  2,  2,  2,  2,  2,  2,  2,  2,  2,  2,  2,\n/* 9x */    2,  2,  2,  2,  2,  2,  2,  2,  2,  2,  2,  2,  2,  2,  2,  2,\n/* Ax */    2,  2,  2,  2,  2,  2,  2,  2,  2,  2,  2,  2,  2,  2,  2,  2,\n/* Bx */    2,  2,  2,  2,  2,  2,  2,  2,  2,  2,  2,  2,  2,  2,  2,  2,\n/* Cx */    2,  2,  2,  2,  2,  2,  2,  2,  2,  2,  2,  2,  2,  2,  2,  2,\n/* Dx */    2,  2,  2,  2,  2,  2,  2,  2,  2,  2,  2,  2,  2,  2,  2,  2,\n/* Ex */    2,  2,  2,  2,  2,  2,  2,  2,  2,  2,  2,  2,  2,  2,  2,  2,\n/* Fx */    2,  2,  2,  2,  2,  2,  2,  2,  2,  2,  2,  2,  2,  2,  2,  2\n#endif\n#ifdef SQLITE_EBCDIC\n/*         x0  x1  x2  x3  x4  x5  x6  x7  x8  x9  xa  xb  xc  xd  xe  xf */\n/* 0x */   27, 27, 27, 27, 27,  7, 27, 27, 27, 27, 27, 27,  7,  7, 27, 27,\n/* 1x */   27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27,\n/* 2x */   27, 27, 27, 27, 27,  7, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27,\n/* 3x */   27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27,\n/* 4x */    7, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 26, 12, 17, 20, 10,\n/* 5x */   24, 27, 27, 27, 27, 27, 27, 27, 27, 27, 15,  4, 21, 18, 19, 27,\n/* 6x */   11, 16, 27, 27, 27, 27, 27, 27, 27, 27, 27, 23, 22,  1, 13,  6,\n/* 7x */   27, 27, 27, 27, 27, 27, 27, 27, 27,  8,  5,  5,  5,  8, 14,  8,\n/* 8x */   27,  1,  1,  1,  1,  1,  1,  1,  1,  1, 27, 27, 27, 27, 27, 27,\n/* 9x */   27,  1,  1,  1,  1,  1,  1,  1,  1,  1, 27, 27, 27, 27, 27, 27,\n/* Ax */   27, 25,  1,  1,  1,  1,  1,  0,  1,  1, 27, 27, 27, 27, 27, 27,\n/* Bx */   27, 27, 27, 27, 27, 27, 27, 27, 27, 27,  9, 27, 27, 27, 27, 27,\n/* Cx */   27,  1,  1,  1,  1,  1,  1,  1,  1,  1, 27, 27, 27, 27, 27, 27,\n/* Dx */   27,  1,  1,  1,  1,  1,  1,  1,  1,  1, 27, 27, 27, 27, 27, 27,\n/* Ex */   27, 27,  1,  1,  1,  1,  1,  0,  1,  1, 27, 27, 27, 27, 27, 27,\n/* Fx */    3,  3,  3,  3,  3,  3,  3,  3,  3,  3, 27, 27, 27, 27, 27, 27,\n#endif\n};\n\n/*\n** The charMap() macro maps alphabetic characters (only) into their\n** lower-case ASCII equivalent.  On ASCII machines, this is just\n** an upper-to-lower case map.  On EBCDIC machines we also need\n** to adjust the encoding.  The mapping is only valid for alphabetics\n** which are the only characters for which this feature is used. \n**\n** Used by keywordhash.h\n*/\n#ifdef SQLITE_ASCII\n# define charMap(X) sqlite3UpperToLower[(unsigned char)X]\n#endif\n#ifdef SQLITE_EBCDIC\n# define charMap(X) ebcdicToAscii[(unsigned char)X]\nconst unsigned char ebcdicToAscii[] = {\n/* 0   1   2   3   4   5   6   7   8   9   A   B   C   D   E   F */\n   0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  /* 0x */\n   0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  /* 1x */\n   0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  /* 2x */\n   0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  /* 3x */\n   0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  /* 4x */\n   0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  /* 5x */\n   0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0, 95,  0,  0,  /* 6x */\n   0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  /* 7x */\n   0, 97, 98, 99,100,101,102,103,104,105,  0,  0,  0,  0,  0,  0,  /* 8x */\n   0,106,107,108,109,110,111,112,113,114,  0,  0,  0,  0,  0,  0,  /* 9x */\n   0,  0,115,116,117,118,119,120,121,122,  0,  0,  0,  0,  0,  0,  /* Ax */\n   0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  /* Bx */\n   0, 97, 98, 99,100,101,102,103,104,105,  0,  0,  0,  0,  0,  0,  /* Cx */\n   0,106,107,108,109,110,111,112,113,114,  0,  0,  0,  0,  0,  0,  /* Dx */\n   0,  0,115,116,117,118,119,120,121,122,  0,  0,  0,  0,  0,  0,  /* Ex */\n   0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  /* Fx */\n};\n#endif\n\n/*\n** The sqlite3KeywordCode function looks up an identifier to determine if\n** it is a keyword.  If it is a keyword, the token code of that keyword is \n** returned.  If the input is not a keyword, TK_ID is returned.\n**\n** The implementation of this routine was generated by a program,\n** mkkeywordhash.c, located in the tool subdirectory of the distribution.\n** The output of the mkkeywordhash.c program is written into a file\n** named keywordhash.h and then included into this source file by\n** the #include below.\n*/\n/************** Include keywordhash.h in the middle of tokenize.c ************/\n/************** Begin file keywordhash.h *************************************/\n/***** This file contains automatically generated code ******\n**\n** The code in this file has been automatically generated by\n**\n**   sqlite/tool/mkkeywordhash.c\n**\n** The code in this file implements a function that determines whether\n** or not a given identifier is really an SQL keyword.  The same thing\n** might be implemented more directly using a hand-written hash table.\n** But by using this automatically generated code, the size of the code\n** is substantially reduced.  This is important for embedded applications\n** on platforms with limited memory.\n*/\n/* Hash score: 182 */\n/* zKWText[] encodes 834 bytes of keyword text in 554 bytes */\n/*   REINDEXEDESCAPEACHECKEYBEFOREIGNOREGEXPLAINSTEADDATABASELECT       */\n/*   ABLEFTHENDEFERRABLELSEXCEPTRANSACTIONATURALTERAISEXCLUSIVE         */\n/*   XISTSAVEPOINTERSECTRIGGEREFERENCESCONSTRAINTOFFSETEMPORARY         */\n/*   UNIQUERYWITHOUTERELEASEATTACHAVINGROUPDATEBEGINNERECURSIVE         */\n/*   BETWEENOTNULLIKECASCADELETECASECOLLATECREATECURRENT_DATEDETACH     */\n/*   IMMEDIATEJOINSERTMATCHPLANALYZEPRAGMABORTVALUESVIRTUALIMITWHEN     */\n/*   WHERENAMEAFTEREPLACEANDEFAULTAUTOINCREMENTCASTCOLUMNCOMMIT         */\n/*   CONFLICTCROSSCURRENT_TIMESTAMPRIMARYDEFERREDISTINCTDROPFAIL        */\n/*   FROMFULLGLOBYIFISNULLORDERESTRICTRIGHTROLLBACKROWUNIONUSING        */\n/*   VACUUMVIEWINITIALLY                                                */\nstatic const char zKWText[553] = {\n  'R','E','I','N','D','E','X','E','D','E','S','C','A','P','E','A','C','H',\n  'E','C','K','E','Y','B','E','F','O','R','E','I','G','N','O','R','E','G',\n  'E','X','P','L','A','I','N','S','T','E','A','D','D','A','T','A','B','A',\n  'S','E','L','E','C','T','A','B','L','E','F','T','H','E','N','D','E','F',\n  'E','R','R','A','B','L','E','L','S','E','X','C','E','P','T','R','A','N',\n  'S','A','C','T','I','O','N','A','T','U','R','A','L','T','E','R','A','I',\n  'S','E','X','C','L','U','S','I','V','E','X','I','S','T','S','A','V','E',\n  'P','O','I','N','T','E','R','S','E','C','T','R','I','G','G','E','R','E',\n  'F','E','R','E','N','C','E','S','C','O','N','S','T','R','A','I','N','T',\n  'O','F','F','S','E','T','E','M','P','O','R','A','R','Y','U','N','I','Q',\n  'U','E','R','Y','W','I','T','H','O','U','T','E','R','E','L','E','A','S',\n  'E','A','T','T','A','C','H','A','V','I','N','G','R','O','U','P','D','A',\n  'T','E','B','E','G','I','N','N','E','R','E','C','U','R','S','I','V','E',\n  'B','E','T','W','E','E','N','O','T','N','U','L','L','I','K','E','C','A',\n  'S','C','A','D','E','L','E','T','E','C','A','S','E','C','O','L','L','A',\n  'T','E','C','R','E','A','T','E','C','U','R','R','E','N','T','_','D','A',\n  'T','E','D','E','T','A','C','H','I','M','M','E','D','I','A','T','E','J',\n  'O','I','N','S','E','R','T','M','A','T','C','H','P','L','A','N','A','L',\n  'Y','Z','E','P','R','A','G','M','A','B','O','R','T','V','A','L','U','E',\n  'S','V','I','R','T','U','A','L','I','M','I','T','W','H','E','N','W','H',\n  'E','R','E','N','A','M','E','A','F','T','E','R','E','P','L','A','C','E',\n  'A','N','D','E','F','A','U','L','T','A','U','T','O','I','N','C','R','E',\n  'M','E','N','T','C','A','S','T','C','O','L','U','M','N','C','O','M','M',\n  'I','T','C','O','N','F','L','I','C','T','C','R','O','S','S','C','U','R',\n  'R','E','N','T','_','T','I','M','E','S','T','A','M','P','R','I','M','A',\n  'R','Y','D','E','F','E','R','R','E','D','I','S','T','I','N','C','T','D',\n  'R','O','P','F','A','I','L','F','R','O','M','F','U','L','L','G','L','O',\n  'B','Y','I','F','I','S','N','U','L','L','O','R','D','E','R','E','S','T',\n  'R','I','C','T','R','I','G','H','T','R','O','L','L','B','A','C','K','R',\n  'O','W','U','N','I','O','N','U','S','I','N','G','V','A','C','U','U','M',\n  'V','I','E','W','I','N','I','T','I','A','L','L','Y',\n};\n/* aKWHash[i] is the hash value for the i-th keyword */\nstatic const unsigned char aKWHash[127] = {\n    76, 105, 117,  74,   0,  45,   0,   0,  82,   0,  77,   0,   0,\n    42,  12,  78,  15,   0, 116,  85,  54, 112,   0,  19,   0,   0,\n   121,   0, 119, 115,   0,  22,  93,   0,   9,   0,   0,  70,  71,\n     0,  69,   6,   0,  48,  90, 102,   0, 118, 101,   0,   0,  44,\n     0, 103,  24,   0,  17,   0, 122,  53,  23,   0,   5, 110,  25,\n    96,   0,   0, 124, 106,  60, 123,  57,  28,  55,   0,  91,   0,\n   100,  26,   0,  99,   0,   0,   0,  95,  92,  97,  88, 109,  14,\n    39, 108,   0,  81,   0,  18,  89, 111,  32,   0, 120,  80, 113,\n    62,  46,  84,   0,   0,  94,  40,  59, 114,   0,  36,   0,   0,\n    29,   0,  86,  63,  64,   0,  20,  61,   0,  56,\n};\n/* aKWNext[] forms the hash collision chain.  If aKWHash[i]==0\n** then the i-th keyword has no more hash collisions.  Otherwise,\n** the next keyword with the same hash is aKWHash[i]-1. */\nstatic const unsigned char aKWNext[124] = {\n     0,   0,   0,   0,   4,   0,   0,   0,   0,   0,   0,   0,   0,\n     0,   2,   0,   0,   0,   0,   0,   0,  13,   0,   0,   0,   0,\n     0,   7,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,\n     0,   0,   0,   0,  33,   0,  21,   0,   0,   0,   0,   0,  50,\n     0,  43,   3,  47,   0,   0,   0,   0,  30,   0,  58,   0,  38,\n     0,   0,   0,   1,  66,   0,   0,  67,   0,  41,   0,   0,   0,\n     0,   0,   0,  49,  65,   0,   0,   0,   0,  31,  52,  16,  34,\n    10,   0,   0,   0,   0,   0,   0,   0,  11,  72,  79,   0,   8,\n     0, 104,  98,   0, 107,   0,  87,   0,  75,  51,   0,  27,  37,\n    73,  83,   0,  35,  68,   0,   0,\n};\n/* aKWLen[i] is the length (in bytes) of the i-th keyword */\nstatic const unsigned char aKWLen[124] = {\n     7,   7,   5,   4,   6,   4,   5,   3,   6,   7,   3,   6,   6,\n     7,   7,   3,   8,   2,   6,   5,   4,   4,   3,  10,   4,   6,\n    11,   6,   2,   7,   5,   5,   9,   6,   9,   9,   7,  10,  10,\n     4,   6,   2,   3,   9,   4,   2,   6,   5,   7,   4,   5,   7,\n     6,   6,   5,   6,   5,   5,   9,   7,   7,   3,   2,   4,   4,\n     7,   3,   6,   4,   7,   6,  12,   6,   9,   4,   6,   5,   4,\n     7,   6,   5,   6,   7,   5,   4,   5,   6,   5,   7,   3,   7,\n    13,   2,   2,   4,   6,   6,   8,   5,  17,  12,   7,   8,   8,\n     2,   4,   4,   4,   4,   4,   2,   2,   6,   5,   8,   5,   8,\n     3,   5,   5,   6,   4,   9,   3,\n};\n/* aKWOffset[i] is the index into zKWText[] of the start of\n** the text for the i-th keyword. */\nstatic const unsigned short int aKWOffset[124] = {\n     0,   2,   2,   8,   9,  14,  16,  20,  23,  25,  25,  29,  33,\n    36,  41,  46,  48,  53,  54,  59,  62,  65,  67,  69,  78,  81,\n    86,  91,  95,  96, 101, 105, 109, 117, 122, 128, 136, 142, 152,\n   159, 162, 162, 165, 167, 167, 171, 176, 179, 184, 184, 188, 192,\n   199, 204, 209, 212, 218, 221, 225, 234, 240, 240, 240, 243, 246,\n   250, 251, 255, 261, 265, 272, 278, 290, 296, 305, 307, 313, 318,\n   320, 327, 332, 337, 343, 349, 354, 358, 361, 367, 371, 378, 380,\n   387, 389, 391, 400, 404, 410, 416, 424, 429, 429, 445, 452, 459,\n   460, 467, 471, 475, 479, 483, 486, 488, 490, 496, 500, 508, 513,\n   521, 524, 529, 534, 540, 544, 549,\n};\n/* aKWCode[i] is the parser symbol code for the i-th keyword */\nstatic const unsigned char aKWCode[124] = {\n  TK_REINDEX,    TK_INDEXED,    TK_INDEX,      TK_DESC,       TK_ESCAPE,     \n  TK_EACH,       TK_CHECK,      TK_KEY,        TK_BEFORE,     TK_FOREIGN,    \n  TK_FOR,        TK_IGNORE,     TK_LIKE_KW,    TK_EXPLAIN,    TK_INSTEAD,    \n  TK_ADD,        TK_DATABASE,   TK_AS,         TK_SELECT,     TK_TABLE,      \n  TK_JOIN_KW,    TK_THEN,       TK_END,        TK_DEFERRABLE, TK_ELSE,       \n  TK_EXCEPT,     TK_TRANSACTION,TK_ACTION,     TK_ON,         TK_JOIN_KW,    \n  TK_ALTER,      TK_RAISE,      TK_EXCLUSIVE,  TK_EXISTS,     TK_SAVEPOINT,  \n  TK_INTERSECT,  TK_TRIGGER,    TK_REFERENCES, TK_CONSTRAINT, TK_INTO,       \n  TK_OFFSET,     TK_OF,         TK_SET,        TK_TEMP,       TK_TEMP,       \n  TK_OR,         TK_UNIQUE,     TK_QUERY,      TK_WITHOUT,    TK_WITH,       \n  TK_JOIN_KW,    TK_RELEASE,    TK_ATTACH,     TK_HAVING,     TK_GROUP,      \n  TK_UPDATE,     TK_BEGIN,      TK_JOIN_KW,    TK_RECURSIVE,  TK_BETWEEN,    \n  TK_NOTNULL,    TK_NOT,        TK_NO,         TK_NULL,       TK_LIKE_KW,    \n  TK_CASCADE,    TK_ASC,        TK_DELETE,     TK_CASE,       TK_COLLATE,    \n  TK_CREATE,     TK_CTIME_KW,   TK_DETACH,     TK_IMMEDIATE,  TK_JOIN,       \n  TK_INSERT,     TK_MATCH,      TK_PLAN,       TK_ANALYZE,    TK_PRAGMA,     \n  TK_ABORT,      TK_VALUES,     TK_VIRTUAL,    TK_LIMIT,      TK_WHEN,       \n  TK_WHERE,      TK_RENAME,     TK_AFTER,      TK_REPLACE,    TK_AND,        \n  TK_DEFAULT,    TK_AUTOINCR,   TK_TO,         TK_IN,         TK_CAST,       \n  TK_COLUMNKW,   TK_COMMIT,     TK_CONFLICT,   TK_JOIN_KW,    TK_CTIME_KW,   \n  TK_CTIME_KW,   TK_PRIMARY,    TK_DEFERRED,   TK_DISTINCT,   TK_IS,         \n  TK_DROP,       TK_FAIL,       TK_FROM,       TK_JOIN_KW,    TK_LIKE_KW,    \n  TK_BY,         TK_IF,         TK_ISNULL,     TK_ORDER,      TK_RESTRICT,   \n  TK_JOIN_KW,    TK_ROLLBACK,   TK_ROW,        TK_UNION,      TK_USING,      \n  TK_VACUUM,     TK_VIEW,       TK_INITIALLY,  TK_ALL,        \n};\n/* Check to see if z[0..n-1] is a keyword. If it is, write the\n** parser symbol code for that keyword into *pType.  Always\n** return the integer n (the length of the token). */\nstatic int keywordCode(const char *z, int n, int *pType){\n  int i, j;\n  const char *zKW;\n  if( n>=2 ){\n    i = ((charMap(z[0])*4) ^ (charMap(z[n-1])*3) ^ n) % 127;\n    for(i=((int)aKWHash[i])-1; i>=0; i=((int)aKWNext[i])-1){\n      if( aKWLen[i]!=n ) continue;\n      j = 0;\n      zKW = &zKWText[aKWOffset[i]];\n#ifdef SQLITE_ASCII\n      while( j<n && (z[j]&~0x20)==zKW[j] ){ j++; }\n#endif\n#ifdef SQLITE_EBCDIC\n      while( j<n && toupper(z[j])==zKW[j] ){ j++; }\n#endif\n      if( j<n ) continue;\n      testcase( i==0 ); /* REINDEX */\n      testcase( i==1 ); /* INDEXED */\n      testcase( i==2 ); /* INDEX */\n      testcase( i==3 ); /* DESC */\n      testcase( i==4 ); /* ESCAPE */\n      testcase( i==5 ); /* EACH */\n      testcase( i==6 ); /* CHECK */\n      testcase( i==7 ); /* KEY */\n      testcase( i==8 ); /* BEFORE */\n      testcase( i==9 ); /* FOREIGN */\n      testcase( i==10 ); /* FOR */\n      testcase( i==11 ); /* IGNORE */\n      testcase( i==12 ); /* REGEXP */\n      testcase( i==13 ); /* EXPLAIN */\n      testcase( i==14 ); /* INSTEAD */\n      testcase( i==15 ); /* ADD */\n      testcase( i==16 ); /* DATABASE */\n      testcase( i==17 ); /* AS */\n      testcase( i==18 ); /* SELECT */\n      testcase( i==19 ); /* TABLE */\n      testcase( i==20 ); /* LEFT */\n      testcase( i==21 ); /* THEN */\n      testcase( i==22 ); /* END */\n      testcase( i==23 ); /* DEFERRABLE */\n      testcase( i==24 ); /* ELSE */\n      testcase( i==25 ); /* EXCEPT */\n      testcase( i==26 ); /* TRANSACTION */\n      testcase( i==27 ); /* ACTION */\n      testcase( i==28 ); /* ON */\n      testcase( i==29 ); /* NATURAL */\n      testcase( i==30 ); /* ALTER */\n      testcase( i==31 ); /* RAISE */\n      testcase( i==32 ); /* EXCLUSIVE */\n      testcase( i==33 ); /* EXISTS */\n      testcase( i==34 ); /* SAVEPOINT */\n      testcase( i==35 ); /* INTERSECT */\n      testcase( i==36 ); /* TRIGGER */\n      testcase( i==37 ); /* REFERENCES */\n      testcase( i==38 ); /* CONSTRAINT */\n      testcase( i==39 ); /* INTO */\n      testcase( i==40 ); /* OFFSET */\n      testcase( i==41 ); /* OF */\n      testcase( i==42 ); /* SET */\n      testcase( i==43 ); /* TEMPORARY */\n      testcase( i==44 ); /* TEMP */\n      testcase( i==45 ); /* OR */\n      testcase( i==46 ); /* UNIQUE */\n      testcase( i==47 ); /* QUERY */\n      testcase( i==48 ); /* WITHOUT */\n      testcase( i==49 ); /* WITH */\n      testcase( i==50 ); /* OUTER */\n      testcase( i==51 ); /* RELEASE */\n      testcase( i==52 ); /* ATTACH */\n      testcase( i==53 ); /* HAVING */\n      testcase( i==54 ); /* GROUP */\n      testcase( i==55 ); /* UPDATE */\n      testcase( i==56 ); /* BEGIN */\n      testcase( i==57 ); /* INNER */\n      testcase( i==58 ); /* RECURSIVE */\n      testcase( i==59 ); /* BETWEEN */\n      testcase( i==60 ); /* NOTNULL */\n      testcase( i==61 ); /* NOT */\n      testcase( i==62 ); /* NO */\n      testcase( i==63 ); /* NULL */\n      testcase( i==64 ); /* LIKE */\n      testcase( i==65 ); /* CASCADE */\n      testcase( i==66 ); /* ASC */\n      testcase( i==67 ); /* DELETE */\n      testcase( i==68 ); /* CASE */\n      testcase( i==69 ); /* COLLATE */\n      testcase( i==70 ); /* CREATE */\n      testcase( i==71 ); /* CURRENT_DATE */\n      testcase( i==72 ); /* DETACH */\n      testcase( i==73 ); /* IMMEDIATE */\n      testcase( i==74 ); /* JOIN */\n      testcase( i==75 ); /* INSERT */\n      testcase( i==76 ); /* MATCH */\n      testcase( i==77 ); /* PLAN */\n      testcase( i==78 ); /* ANALYZE */\n      testcase( i==79 ); /* PRAGMA */\n      testcase( i==80 ); /* ABORT */\n      testcase( i==81 ); /* VALUES */\n      testcase( i==82 ); /* VIRTUAL */\n      testcase( i==83 ); /* LIMIT */\n      testcase( i==84 ); /* WHEN */\n      testcase( i==85 ); /* WHERE */\n      testcase( i==86 ); /* RENAME */\n      testcase( i==87 ); /* AFTER */\n      testcase( i==88 ); /* REPLACE */\n      testcase( i==89 ); /* AND */\n      testcase( i==90 ); /* DEFAULT */\n      testcase( i==91 ); /* AUTOINCREMENT */\n      testcase( i==92 ); /* TO */\n      testcase( i==93 ); /* IN */\n      testcase( i==94 ); /* CAST */\n      testcase( i==95 ); /* COLUMN */\n      testcase( i==96 ); /* COMMIT */\n      testcase( i==97 ); /* CONFLICT */\n      testcase( i==98 ); /* CROSS */\n      testcase( i==99 ); /* CURRENT_TIMESTAMP */\n      testcase( i==100 ); /* CURRENT_TIME */\n      testcase( i==101 ); /* PRIMARY */\n      testcase( i==102 ); /* DEFERRED */\n      testcase( i==103 ); /* DISTINCT */\n      testcase( i==104 ); /* IS */\n      testcase( i==105 ); /* DROP */\n      testcase( i==106 ); /* FAIL */\n      testcase( i==107 ); /* FROM */\n      testcase( i==108 ); /* FULL */\n      testcase( i==109 ); /* GLOB */\n      testcase( i==110 ); /* BY */\n      testcase( i==111 ); /* IF */\n      testcase( i==112 ); /* ISNULL */\n      testcase( i==113 ); /* ORDER */\n      testcase( i==114 ); /* RESTRICT */\n      testcase( i==115 ); /* RIGHT */\n      testcase( i==116 ); /* ROLLBACK */\n      testcase( i==117 ); /* ROW */\n      testcase( i==118 ); /* UNION */\n      testcase( i==119 ); /* USING */\n      testcase( i==120 ); /* VACUUM */\n      testcase( i==121 ); /* VIEW */\n      testcase( i==122 ); /* INITIALLY */\n      testcase( i==123 ); /* ALL */\n      *pType = aKWCode[i];\n      break;\n    }\n  }\n  return n;\n}\nSQLITE_PRIVATE int sqlite3KeywordCode(const unsigned char *z, int n){\n  int id = TK_ID;\n  keywordCode((char*)z, n, &id);\n  return id;\n}\n#define SQLITE_N_KEYWORD 124\n\n/************** End of keywordhash.h *****************************************/\n/************** Continuing where we left off in tokenize.c *******************/\n\n\n/*\n** If X is a character that can be used in an identifier then\n** IdChar(X) will be true.  Otherwise it is false.\n**\n** For ASCII, any character with the high-order bit set is\n** allowed in an identifier.  For 7-bit characters, \n** sqlite3IsIdChar[X] must be 1.\n**\n** For EBCDIC, the rules are more complex but have the same\n** end result.\n**\n** Ticket #1066.  the SQL standard does not allow '$' in the\n** middle of identifiers.  But many SQL implementations do. \n** SQLite will allow '$' in identifiers for compatibility.\n** But the feature is undocumented.\n*/\n#ifdef SQLITE_ASCII\n#define IdChar(C)  ((sqlite3CtypeMap[(unsigned char)C]&0x46)!=0)\n#endif\n#ifdef SQLITE_EBCDIC\nSQLITE_PRIVATE const char sqlite3IsEbcdicIdChar[] = {\n/* x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 xA xB xC xD xE xF */\n    0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0,  /* 4x */\n    0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0,  /* 5x */\n    0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0,  /* 6x */\n    0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0,  /* 7x */\n    0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0,  /* 8x */\n    0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 0,  /* 9x */\n    1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0,  /* Ax */\n    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,  /* Bx */\n    0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1,  /* Cx */\n    0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1,  /* Dx */\n    0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1,  /* Ex */\n    1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0,  /* Fx */\n};\n#define IdChar(C)  (((c=C)>=0x42 && sqlite3IsEbcdicIdChar[c-0x40]))\n#endif\n\n/* Make the IdChar function accessible from ctime.c */\n#ifndef SQLITE_OMIT_COMPILEOPTION_DIAGS\nSQLITE_PRIVATE int sqlite3IsIdChar(u8 c){ return IdChar(c); }\n#endif\n\n\n/*\n** Return the length (in bytes) of the token that begins at z[0]. \n** Store the token type in *tokenType before returning.\n*/\nSQLITE_PRIVATE int sqlite3GetToken(const unsigned char *z, int *tokenType){\n  int i, c;\n  switch( aiClass[*z] ){  /* Switch on the character-class of the first byte\n                          ** of the token. See the comment on the CC_ defines\n                          ** above. */\n    case CC_SPACE: {\n      testcase( z[0]==' ' );\n      testcase( z[0]=='\\t' );\n      testcase( z[0]=='\\n' );\n      testcase( z[0]=='\\f' );\n      testcase( z[0]=='\\r' );\n      for(i=1; sqlite3Isspace(z[i]); i++){}\n      *tokenType = TK_SPACE;\n      return i;\n    }\n    case CC_MINUS: {\n      if( z[1]=='-' ){\n        for(i=2; (c=z[i])!=0 && c!='\\n'; i++){}\n        *tokenType = TK_SPACE;   /* IMP: R-22934-25134 */\n        return i;\n      }\n      *tokenType = TK_MINUS;\n      return 1;\n    }\n    case CC_LP: {\n      *tokenType = TK_LP;\n      return 1;\n    }\n    case CC_RP: {\n      *tokenType = TK_RP;\n      return 1;\n    }\n    case CC_SEMI: {\n      *tokenType = TK_SEMI;\n      return 1;\n    }\n    case CC_PLUS: {\n      *tokenType = TK_PLUS;\n      return 1;\n    }\n    case CC_STAR: {\n      *tokenType = TK_STAR;\n      return 1;\n    }\n    case CC_SLASH: {\n      if( z[1]!='*' || z[2]==0 ){\n        *tokenType = TK_SLASH;\n        return 1;\n      }\n      for(i=3, c=z[2]; (c!='*' || z[i]!='/') && (c=z[i])!=0; i++){}\n      if( c ) i++;\n      *tokenType = TK_SPACE;   /* IMP: R-22934-25134 */\n      return i;\n    }\n    case CC_PERCENT: {\n      *tokenType = TK_REM;\n      return 1;\n    }\n    case CC_EQ: {\n      *tokenType = TK_EQ;\n      return 1 + (z[1]=='=');\n    }\n    case CC_LT: {\n      if( (c=z[1])=='=' ){\n        *tokenType = TK_LE;\n        return 2;\n      }else if( c=='>' ){\n        *tokenType = TK_NE;\n        return 2;\n      }else if( c=='<' ){\n        *tokenType = TK_LSHIFT;\n        return 2;\n      }else{\n        *tokenType = TK_LT;\n        return 1;\n      }\n    }\n    case CC_GT: {\n      if( (c=z[1])=='=' ){\n        *tokenType = TK_GE;\n        return 2;\n      }else if( c=='>' ){\n        *tokenType = TK_RSHIFT;\n        return 2;\n      }else{\n        *tokenType = TK_GT;\n        return 1;\n      }\n    }\n    case CC_BANG: {\n      if( z[1]!='=' ){\n        *tokenType = TK_ILLEGAL;\n        return 1;\n      }else{\n        *tokenType = TK_NE;\n        return 2;\n      }\n    }\n    case CC_PIPE: {\n      if( z[1]!='|' ){\n        *tokenType = TK_BITOR;\n        return 1;\n      }else{\n        *tokenType = TK_CONCAT;\n        return 2;\n      }\n    }\n    case CC_COMMA: {\n      *tokenType = TK_COMMA;\n      return 1;\n    }\n    case CC_AND: {\n      *tokenType = TK_BITAND;\n      return 1;\n    }\n    case CC_TILDA: {\n      *tokenType = TK_BITNOT;\n      return 1;\n    }\n    case CC_QUOTE: {\n      int delim = z[0];\n      testcase( delim=='`' );\n      testcase( delim=='\\'' );\n      testcase( delim=='\"' );\n      for(i=1; (c=z[i])!=0; i++){\n        if( c==delim ){\n          if( z[i+1]==delim ){\n            i++;\n          }else{\n            break;\n          }\n        }\n      }\n      if( c=='\\'' ){\n        *tokenType = TK_STRING;\n        return i+1;\n      }else if( c!=0 ){\n        *tokenType = TK_ID;\n        return i+1;\n      }else{\n        *tokenType = TK_ILLEGAL;\n        return i;\n      }\n    }\n    case CC_DOT: {\n#ifndef SQLITE_OMIT_FLOATING_POINT\n      if( !sqlite3Isdigit(z[1]) )\n#endif\n      {\n        *tokenType = TK_DOT;\n        return 1;\n      }\n      /* If the next character is a digit, this is a floating point\n      ** number that begins with \".\".  Fall thru into the next case */\n    }\n    case CC_DIGIT: {\n      testcase( z[0]=='0' );  testcase( z[0]=='1' );  testcase( z[0]=='2' );\n      testcase( z[0]=='3' );  testcase( z[0]=='4' );  testcase( z[0]=='5' );\n      testcase( z[0]=='6' );  testcase( z[0]=='7' );  testcase( z[0]=='8' );\n      testcase( z[0]=='9' );\n      *tokenType = TK_INTEGER;\n#ifndef SQLITE_OMIT_HEX_INTEGER\n      if( z[0]=='0' && (z[1]=='x' || z[1]=='X') && sqlite3Isxdigit(z[2]) ){\n        for(i=3; sqlite3Isxdigit(z[i]); i++){}\n        return i;\n      }\n#endif\n      for(i=0; sqlite3Isdigit(z[i]); i++){}\n#ifndef SQLITE_OMIT_FLOATING_POINT\n      if( z[i]=='.' ){\n        i++;\n        while( sqlite3Isdigit(z[i]) ){ i++; }\n        *tokenType = TK_FLOAT;\n      }\n      if( (z[i]=='e' || z[i]=='E') &&\n           ( sqlite3Isdigit(z[i+1]) \n            || ((z[i+1]=='+' || z[i+1]=='-') && sqlite3Isdigit(z[i+2]))\n           )\n      ){\n        i += 2;\n        while( sqlite3Isdigit(z[i]) ){ i++; }\n        *tokenType = TK_FLOAT;\n      }\n#endif\n      while( IdChar(z[i]) ){\n        *tokenType = TK_ILLEGAL;\n        i++;\n      }\n      return i;\n    }\n    case CC_QUOTE2: {\n      for(i=1, c=z[0]; c!=']' && (c=z[i])!=0; i++){}\n      *tokenType = c==']' ? TK_ID : TK_ILLEGAL;\n      return i;\n    }\n    case CC_VARNUM: {\n      *tokenType = TK_VARIABLE;\n      for(i=1; sqlite3Isdigit(z[i]); i++){}\n      return i;\n    }\n    case CC_DOLLAR:\n    case CC_VARALPHA: {\n      int n = 0;\n      testcase( z[0]=='$' );  testcase( z[0]=='@' );\n      testcase( z[0]==':' );  testcase( z[0]=='#' );\n      *tokenType = TK_VARIABLE;\n      for(i=1; (c=z[i])!=0; i++){\n        if( IdChar(c) ){\n          n++;\n#ifndef SQLITE_OMIT_TCL_VARIABLE\n        }else if( c=='(' && n>0 ){\n          do{\n            i++;\n          }while( (c=z[i])!=0 && !sqlite3Isspace(c) && c!=')' );\n          if( c==')' ){\n            i++;\n          }else{\n            *tokenType = TK_ILLEGAL;\n          }\n          break;\n        }else if( c==':' && z[i+1]==':' ){\n          i++;\n#endif\n        }else{\n          break;\n        }\n      }\n      if( n==0 ) *tokenType = TK_ILLEGAL;\n      return i;\n    }\n    case CC_KYWD: {\n      for(i=1; aiClass[z[i]]<=CC_KYWD; i++){}\n      if( IdChar(z[i]) ){\n        /* This token started out using characters that can appear in keywords,\n        ** but z[i] is a character not allowed within keywords, so this must\n        ** be an identifier instead */\n        i++;\n        break;\n      }\n      *tokenType = TK_ID;\n      return keywordCode((char*)z, i, tokenType);\n    }\n    case CC_X: {\n#ifndef SQLITE_OMIT_BLOB_LITERAL\n      testcase( z[0]=='x' ); testcase( z[0]=='X' );\n      if( z[1]=='\\'' ){\n        *tokenType = TK_BLOB;\n        for(i=2; sqlite3Isxdigit(z[i]); i++){}\n        if( z[i]!='\\'' || i%2 ){\n          *tokenType = TK_ILLEGAL;\n          while( z[i] && z[i]!='\\'' ){ i++; }\n        }\n        if( z[i] ) i++;\n        return i;\n      }\n#endif\n      /* If it is not a BLOB literal, then it must be an ID, since no\n      ** SQL keywords start with the letter 'x'.  Fall through */\n    }\n    case CC_ID: {\n      i = 1;\n      break;\n    }\n    default: {\n      *tokenType = TK_ILLEGAL;\n      return 1;\n    }\n  }\n  while( IdChar(z[i]) ){ i++; }\n  *tokenType = TK_ID;\n  return i;\n}\n\n/*\n** Run the parser on the given SQL string.  The parser structure is\n** passed in.  An SQLITE_ status code is returned.  If an error occurs\n** then an and attempt is made to write an error message into \n** memory obtained from sqlite3_malloc() and to make *pzErrMsg point to that\n** error message.\n*/\nSQLITE_PRIVATE int sqlite3RunParser(Parse *pParse, const char *zSql, char **pzErrMsg){\n  int nErr = 0;                   /* Number of errors encountered */\n  void *pEngine;                  /* The LEMON-generated LALR(1) parser */\n  int n = 0;                      /* Length of the next token token */\n  int tokenType;                  /* type of the next token */\n  int lastTokenParsed = -1;       /* type of the previous token */\n  sqlite3 *db = pParse->db;       /* The database connection */\n  int mxSqlLen;                   /* Max length of an SQL string */\n#ifdef sqlite3Parser_ENGINEALWAYSONSTACK\n  yyParser sEngine;    /* Space to hold the Lemon-generated Parser object */\n#endif\n\n  assert( zSql!=0 );\n  mxSqlLen = db->aLimit[SQLITE_LIMIT_SQL_LENGTH];\n  if( db->nVdbeActive==0 ){\n    db->u1.isInterrupted = 0;\n  }\n  pParse->rc = SQLITE_OK;\n  pParse->zTail = zSql;\n  assert( pzErrMsg!=0 );\n  /* sqlite3ParserTrace(stdout, \"parser: \"); */\n#ifdef sqlite3Parser_ENGINEALWAYSONSTACK\n  pEngine = &sEngine;\n  sqlite3ParserInit(pEngine);\n#else\n  pEngine = sqlite3ParserAlloc(sqlite3Malloc);\n  if( pEngine==0 ){\n    sqlite3OomFault(db);\n    return SQLITE_NOMEM_BKPT;\n  }\n#endif\n  assert( pParse->pNewTable==0 );\n  assert( pParse->pNewTrigger==0 );\n  assert( pParse->nVar==0 );\n  assert( pParse->pVList==0 );\n  while( 1 ){\n    if( zSql[0]!=0 ){\n      n = sqlite3GetToken((u8*)zSql, &tokenType);\n      mxSqlLen -= n;\n      if( mxSqlLen<0 ){\n        pParse->rc = SQLITE_TOOBIG;\n        break;\n      }\n    }else{\n      /* Upon reaching the end of input, call the parser two more times\n      ** with tokens TK_SEMI and 0, in that order. */\n      if( lastTokenParsed==TK_SEMI ){\n        tokenType = 0;\n      }else if( lastTokenParsed==0 ){\n        break;\n      }else{\n        tokenType = TK_SEMI;\n      }\n      n = 0;\n    }\n    if( tokenType>=TK_SPACE ){\n      assert( tokenType==TK_SPACE || tokenType==TK_ILLEGAL );\n      if( db->u1.isInterrupted ){\n        pParse->rc = SQLITE_INTERRUPT;\n        break;\n      }\n      if( tokenType==TK_ILLEGAL ){\n        sqlite3ErrorMsg(pParse, \"unrecognized token: \\\"%.*s\\\"\", n, zSql);\n        break;\n      }\n      zSql += n;\n    }else{\n      pParse->sLastToken.z = zSql;\n      pParse->sLastToken.n = n;\n      sqlite3Parser(pEngine, tokenType, pParse->sLastToken, pParse);\n      lastTokenParsed = tokenType;\n      zSql += n;\n      if( pParse->rc!=SQLITE_OK || db->mallocFailed ) break;\n    }\n  }\n  assert( nErr==0 );\n  pParse->zTail = zSql;\n#ifdef YYTRACKMAXSTACKDEPTH\n  sqlite3_mutex_enter(sqlite3MallocMutex());\n  sqlite3StatusHighwater(SQLITE_STATUS_PARSER_STACK,\n      sqlite3ParserStackPeak(pEngine)\n  );\n  sqlite3_mutex_leave(sqlite3MallocMutex());\n#endif /* YYDEBUG */\n#ifdef sqlite3Parser_ENGINEALWAYSONSTACK\n  sqlite3ParserFinalize(pEngine);\n#else\n  sqlite3ParserFree(pEngine, sqlite3_free);\n#endif\n  if( db->mallocFailed ){\n    pParse->rc = SQLITE_NOMEM_BKPT;\n  }\n  if( pParse->rc!=SQLITE_OK && pParse->rc!=SQLITE_DONE && pParse->zErrMsg==0 ){\n    pParse->zErrMsg = sqlite3MPrintf(db, \"%s\", sqlite3ErrStr(pParse->rc));\n  }\n  assert( pzErrMsg!=0 );\n  if( pParse->zErrMsg ){\n    *pzErrMsg = pParse->zErrMsg;\n    sqlite3_log(pParse->rc, \"%s\", *pzErrMsg);\n    pParse->zErrMsg = 0;\n    nErr++;\n  }\n  if( pParse->pVdbe && pParse->nErr>0 && pParse->nested==0 ){\n    sqlite3VdbeDelete(pParse->pVdbe);\n    pParse->pVdbe = 0;\n  }\n#ifndef SQLITE_OMIT_SHARED_CACHE\n  if( pParse->nested==0 ){\n    sqlite3DbFree(db, pParse->aTableLock);\n    pParse->aTableLock = 0;\n    pParse->nTableLock = 0;\n  }\n#endif\n#ifndef SQLITE_OMIT_VIRTUALTABLE\n  sqlite3_free(pParse->apVtabLock);\n#endif\n\n  if( !IN_DECLARE_VTAB ){\n    /* If the pParse->declareVtab flag is set, do not delete any table \n    ** structure built up in pParse->pNewTable. The calling code (see vtab.c)\n    ** will take responsibility for freeing the Table structure.\n    */\n    sqlite3DeleteTable(db, pParse->pNewTable);\n  }\n\n  if( pParse->pWithToFree ) sqlite3WithDelete(db, pParse->pWithToFree);\n  sqlite3DeleteTrigger(db, pParse->pNewTrigger);\n  sqlite3DbFree(db, pParse->pVList);\n  while( pParse->pAinc ){\n    AutoincInfo *p = pParse->pAinc;\n    pParse->pAinc = p->pNext;\n    sqlite3DbFreeNN(db, p);\n  }\n  while( pParse->pZombieTab ){\n    Table *p = pParse->pZombieTab;\n    pParse->pZombieTab = p->pNextZombie;\n    sqlite3DeleteTable(db, p);\n  }\n  assert( nErr==0 || pParse->rc!=SQLITE_OK );\n  return nErr;\n}\n\n/************** End of tokenize.c ********************************************/\n/************** Begin file complete.c ****************************************/\n/*\n** 2001 September 15\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n*************************************************************************\n** An tokenizer for SQL\n**\n** This file contains C code that implements the sqlite3_complete() API.\n** This code used to be part of the tokenizer.c source file.  But by\n** separating it out, the code will be automatically omitted from\n** static links that do not use it.\n*/\n/* #include \"sqliteInt.h\" */\n#ifndef SQLITE_OMIT_COMPLETE\n\n/*\n** This is defined in tokenize.c.  We just have to import the definition.\n*/\n#ifndef SQLITE_AMALGAMATION\n#ifdef SQLITE_ASCII\n#define IdChar(C)  ((sqlite3CtypeMap[(unsigned char)C]&0x46)!=0)\n#endif\n#ifdef SQLITE_EBCDIC\nSQLITE_PRIVATE const char sqlite3IsEbcdicIdChar[];\n#define IdChar(C)  (((c=C)>=0x42 && sqlite3IsEbcdicIdChar[c-0x40]))\n#endif\n#endif /* SQLITE_AMALGAMATION */\n\n\n/*\n** Token types used by the sqlite3_complete() routine.  See the header\n** comments on that procedure for additional information.\n*/\n#define tkSEMI    0\n#define tkWS      1\n#define tkOTHER   2\n#ifndef SQLITE_OMIT_TRIGGER\n#define tkEXPLAIN 3\n#define tkCREATE  4\n#define tkTEMP    5\n#define tkTRIGGER 6\n#define tkEND     7\n#endif\n\n/*\n** Return TRUE if the given SQL string ends in a semicolon.\n**\n** Special handling is require for CREATE TRIGGER statements.\n** Whenever the CREATE TRIGGER keywords are seen, the statement\n** must end with \";END;\".\n**\n** This implementation uses a state machine with 8 states:\n**\n**   (0) INVALID   We have not yet seen a non-whitespace character.\n**\n**   (1) START     At the beginning or end of an SQL statement.  This routine\n**                 returns 1 if it ends in the START state and 0 if it ends\n**                 in any other state.\n**\n**   (2) NORMAL    We are in the middle of statement which ends with a single\n**                 semicolon.\n**\n**   (3) EXPLAIN   The keyword EXPLAIN has been seen at the beginning of \n**                 a statement.\n**\n**   (4) CREATE    The keyword CREATE has been seen at the beginning of a\n**                 statement, possibly preceded by EXPLAIN and/or followed by\n**                 TEMP or TEMPORARY\n**\n**   (5) TRIGGER   We are in the middle of a trigger definition that must be\n**                 ended by a semicolon, the keyword END, and another semicolon.\n**\n**   (6) SEMI      We've seen the first semicolon in the \";END;\" that occurs at\n**                 the end of a trigger definition.\n**\n**   (7) END       We've seen the \";END\" of the \";END;\" that occurs at the end\n**                 of a trigger definition.\n**\n** Transitions between states above are determined by tokens extracted\n** from the input.  The following tokens are significant:\n**\n**   (0) tkSEMI      A semicolon.\n**   (1) tkWS        Whitespace.\n**   (2) tkOTHER     Any other SQL token.\n**   (3) tkEXPLAIN   The \"explain\" keyword.\n**   (4) tkCREATE    The \"create\" keyword.\n**   (5) tkTEMP      The \"temp\" or \"temporary\" keyword.\n**   (6) tkTRIGGER   The \"trigger\" keyword.\n**   (7) tkEND       The \"end\" keyword.\n**\n** Whitespace never causes a state transition and is always ignored.\n** This means that a SQL string of all whitespace is invalid.\n**\n** If we compile with SQLITE_OMIT_TRIGGER, all of the computation needed\n** to recognize the end of a trigger can be omitted.  All we have to do\n** is look for a semicolon that is not part of an string or comment.\n*/\nSQLITE_API int sqlite3_complete(const char *zSql){\n  u8 state = 0;   /* Current state, using numbers defined in header comment */\n  u8 token;       /* Value of the next token */\n\n#ifndef SQLITE_OMIT_TRIGGER\n  /* A complex statement machine used to detect the end of a CREATE TRIGGER\n  ** statement.  This is the normal case.\n  */\n  static const u8 trans[8][8] = {\n                     /* Token:                                                */\n     /* State:       **  SEMI  WS  OTHER  EXPLAIN  CREATE  TEMP  TRIGGER  END */\n     /* 0 INVALID: */ {    1,  0,     2,       3,      4,    2,       2,   2, },\n     /* 1   START: */ {    1,  1,     2,       3,      4,    2,       2,   2, },\n     /* 2  NORMAL: */ {    1,  2,     2,       2,      2,    2,       2,   2, },\n     /* 3 EXPLAIN: */ {    1,  3,     3,       2,      4,    2,       2,   2, },\n     /* 4  CREATE: */ {    1,  4,     2,       2,      2,    4,       5,   2, },\n     /* 5 TRIGGER: */ {    6,  5,     5,       5,      5,    5,       5,   5, },\n     /* 6    SEMI: */ {    6,  6,     5,       5,      5,    5,       5,   7, },\n     /* 7     END: */ {    1,  7,     5,       5,      5,    5,       5,   5, },\n  };\n#else\n  /* If triggers are not supported by this compile then the statement machine\n  ** used to detect the end of a statement is much simpler\n  */\n  static const u8 trans[3][3] = {\n                     /* Token:           */\n     /* State:       **  SEMI  WS  OTHER */\n     /* 0 INVALID: */ {    1,  0,     2, },\n     /* 1   START: */ {    1,  1,     2, },\n     /* 2  NORMAL: */ {    1,  2,     2, },\n  };\n#endif /* SQLITE_OMIT_TRIGGER */\n\n#ifdef SQLITE_ENABLE_API_ARMOR\n  if( zSql==0 ){\n    (void)SQLITE_MISUSE_BKPT;\n    return 0;\n  }\n#endif\n\n  while( *zSql ){\n    switch( *zSql ){\n      case ';': {  /* A semicolon */\n        token = tkSEMI;\n        break;\n      }\n      case ' ':\n      case '\\r':\n      case '\\t':\n      case '\\n':\n      case '\\f': {  /* White space is ignored */\n        token = tkWS;\n        break;\n      }\n      case '/': {   /* C-style comments */\n        if( zSql[1]!='*' ){\n          token = tkOTHER;\n          break;\n        }\n        zSql += 2;\n        while( zSql[0] && (zSql[0]!='*' || zSql[1]!='/') ){ zSql++; }\n        if( zSql[0]==0 ) return 0;\n        zSql++;\n        token = tkWS;\n        break;\n      }\n      case '-': {   /* SQL-style comments from \"--\" to end of line */\n        if( zSql[1]!='-' ){\n          token = tkOTHER;\n          break;\n        }\n        while( *zSql && *zSql!='\\n' ){ zSql++; }\n        if( *zSql==0 ) return state==1;\n        token = tkWS;\n        break;\n      }\n      case '[': {   /* Microsoft-style identifiers in [...] */\n        zSql++;\n        while( *zSql && *zSql!=']' ){ zSql++; }\n        if( *zSql==0 ) return 0;\n        token = tkOTHER;\n        break;\n      }\n      case '`':     /* Grave-accent quoted symbols used by MySQL */\n      case '\"':     /* single- and double-quoted strings */\n      case '\\'': {\n        int c = *zSql;\n        zSql++;\n        while( *zSql && *zSql!=c ){ zSql++; }\n        if( *zSql==0 ) return 0;\n        token = tkOTHER;\n        break;\n      }\n      default: {\n#ifdef SQLITE_EBCDIC\n        unsigned char c;\n#endif\n        if( IdChar((u8)*zSql) ){\n          /* Keywords and unquoted identifiers */\n          int nId;\n          for(nId=1; IdChar(zSql[nId]); nId++){}\n#ifdef SQLITE_OMIT_TRIGGER\n          token = tkOTHER;\n#else\n          switch( *zSql ){\n            case 'c': case 'C': {\n              if( nId==6 && sqlite3StrNICmp(zSql, \"create\", 6)==0 ){\n                token = tkCREATE;\n              }else{\n                token = tkOTHER;\n              }\n              break;\n            }\n            case 't': case 'T': {\n              if( nId==7 && sqlite3StrNICmp(zSql, \"trigger\", 7)==0 ){\n                token = tkTRIGGER;\n              }else if( nId==4 && sqlite3StrNICmp(zSql, \"temp\", 4)==0 ){\n                token = tkTEMP;\n              }else if( nId==9 && sqlite3StrNICmp(zSql, \"temporary\", 9)==0 ){\n                token = tkTEMP;\n              }else{\n                token = tkOTHER;\n              }\n              break;\n            }\n            case 'e':  case 'E': {\n              if( nId==3 && sqlite3StrNICmp(zSql, \"end\", 3)==0 ){\n                token = tkEND;\n              }else\n#ifndef SQLITE_OMIT_EXPLAIN\n              if( nId==7 && sqlite3StrNICmp(zSql, \"explain\", 7)==0 ){\n                token = tkEXPLAIN;\n              }else\n#endif\n              {\n                token = tkOTHER;\n              }\n              break;\n            }\n            default: {\n              token = tkOTHER;\n              break;\n            }\n          }\n#endif /* SQLITE_OMIT_TRIGGER */\n          zSql += nId-1;\n        }else{\n          /* Operators and special symbols */\n          token = tkOTHER;\n        }\n        break;\n      }\n    }\n    state = trans[state][token];\n    zSql++;\n  }\n  return state==1;\n}\n\n#ifndef SQLITE_OMIT_UTF16\n/*\n** This routine is the same as the sqlite3_complete() routine described\n** above, except that the parameter is required to be UTF-16 encoded, not\n** UTF-8.\n*/\nSQLITE_API int sqlite3_complete16(const void *zSql){\n  sqlite3_value *pVal;\n  char const *zSql8;\n  int rc;\n\n#ifndef SQLITE_OMIT_AUTOINIT\n  rc = sqlite3_initialize();\n  if( rc ) return rc;\n#endif\n  pVal = sqlite3ValueNew(0);\n  sqlite3ValueSetStr(pVal, -1, zSql, SQLITE_UTF16NATIVE, SQLITE_STATIC);\n  zSql8 = sqlite3ValueText(pVal, SQLITE_UTF8);\n  if( zSql8 ){\n    rc = sqlite3_complete(zSql8);\n  }else{\n    rc = SQLITE_NOMEM_BKPT;\n  }\n  sqlite3ValueFree(pVal);\n  return rc & 0xff;\n}\n#endif /* SQLITE_OMIT_UTF16 */\n#endif /* SQLITE_OMIT_COMPLETE */\n\n/************** End of complete.c ********************************************/\n/************** Begin file main.c ********************************************/\n/*\n** 2001 September 15\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n*************************************************************************\n** Main file for the SQLite library.  The routines in this file\n** implement the programmer interface to the library.  Routines in\n** other files are for internal use by SQLite and should not be\n** accessed by users of the library.\n*/\n/* #include \"sqliteInt.h\" */\n\n#ifdef SQLITE_ENABLE_FTS3\n/************** Include fts3.h in the middle of main.c ***********************/\n/************** Begin file fts3.h ********************************************/\n/*\n** 2006 Oct 10\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n******************************************************************************\n**\n** This header file is used by programs that want to link against the\n** FTS3 library.  All it does is declare the sqlite3Fts3Init() interface.\n*/\n/* #include \"sqlite3.h\" */\n\n#if 0\nextern \"C\" {\n#endif  /* __cplusplus */\n\nSQLITE_PRIVATE int sqlite3Fts3Init(sqlite3 *db);\n\n#if 0\n}  /* extern \"C\" */\n#endif  /* __cplusplus */\n\n/************** End of fts3.h ************************************************/\n/************** Continuing where we left off in main.c ***********************/\n#endif\n#ifdef SQLITE_ENABLE_RTREE\n/************** Include rtree.h in the middle of main.c **********************/\n/************** Begin file rtree.h *******************************************/\n/*\n** 2008 May 26\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n******************************************************************************\n**\n** This header file is used by programs that want to link against the\n** RTREE library.  All it does is declare the sqlite3RtreeInit() interface.\n*/\n/* #include \"sqlite3.h\" */\n\n#ifdef SQLITE_OMIT_VIRTUALTABLE\n# undef SQLITE_ENABLE_RTREE\n#endif\n\n#if 0\nextern \"C\" {\n#endif  /* __cplusplus */\n\nSQLITE_PRIVATE int sqlite3RtreeInit(sqlite3 *db);\n\n#if 0\n}  /* extern \"C\" */\n#endif  /* __cplusplus */\n\n/************** End of rtree.h ***********************************************/\n/************** Continuing where we left off in main.c ***********************/\n#endif\n#if defined(SQLITE_ENABLE_ICU) || defined(SQLITE_ENABLE_ICU_COLLATIONS)\n/************** Include sqliteicu.h in the middle of main.c ******************/\n/************** Begin file sqliteicu.h ***************************************/\n/*\n** 2008 May 26\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n******************************************************************************\n**\n** This header file is used by programs that want to link against the\n** ICU extension.  All it does is declare the sqlite3IcuInit() interface.\n*/\n/* #include \"sqlite3.h\" */\n\n#if 0\nextern \"C\" {\n#endif  /* __cplusplus */\n\nSQLITE_PRIVATE int sqlite3IcuInit(sqlite3 *db);\n\n#if 0\n}  /* extern \"C\" */\n#endif  /* __cplusplus */\n\n\n/************** End of sqliteicu.h *******************************************/\n/************** Continuing where we left off in main.c ***********************/\n#endif\n#ifdef SQLITE_ENABLE_JSON1\nSQLITE_PRIVATE int sqlite3Json1Init(sqlite3*);\n#endif\n#ifdef SQLITE_ENABLE_STMTVTAB\nSQLITE_PRIVATE int sqlite3StmtVtabInit(sqlite3*);\n#endif\n#ifdef SQLITE_ENABLE_FTS5\nSQLITE_PRIVATE int sqlite3Fts5Init(sqlite3*);\n#endif\n\n#ifndef SQLITE_AMALGAMATION\n/* IMPLEMENTATION-OF: R-46656-45156 The sqlite3_version[] string constant\n** contains the text of SQLITE_VERSION macro. \n*/\nSQLITE_API const char sqlite3_version[] = SQLITE_VERSION;\n#endif\n\n/* IMPLEMENTATION-OF: R-53536-42575 The sqlite3_libversion() function returns\n** a pointer to the to the sqlite3_version[] string constant. \n*/\nSQLITE_API const char *sqlite3_libversion(void){ return sqlite3_version; }\n\n/* IMPLEMENTATION-OF: R-25063-23286 The sqlite3_sourceid() function returns a\n** pointer to a string constant whose value is the same as the\n** SQLITE_SOURCE_ID C preprocessor macro. Except if SQLite is built using\n** an edited copy of the amalgamation, then the last four characters of\n** the hash might be different from SQLITE_SOURCE_ID.\n*/\n/* SQLITE_API const char *sqlite3_sourceid(void){ return SQLITE_SOURCE_ID; } */\n\n/* IMPLEMENTATION-OF: R-35210-63508 The sqlite3_libversion_number() function\n** returns an integer equal to SQLITE_VERSION_NUMBER.\n*/\nSQLITE_API int sqlite3_libversion_number(void){ return SQLITE_VERSION_NUMBER; }\n\n/* IMPLEMENTATION-OF: R-20790-14025 The sqlite3_threadsafe() function returns\n** zero if and only if SQLite was compiled with mutexing code omitted due to\n** the SQLITE_THREADSAFE compile-time option being set to 0.\n*/\nSQLITE_API int sqlite3_threadsafe(void){ return SQLITE_THREADSAFE; }\n\n/*\n** When compiling the test fixture or with debugging enabled (on Win32),\n** this variable being set to non-zero will cause OSTRACE macros to emit\n** extra diagnostic information.\n*/\n#ifdef SQLITE_HAVE_OS_TRACE\n# ifndef SQLITE_DEBUG_OS_TRACE\n#   define SQLITE_DEBUG_OS_TRACE 0\n# endif\n  int sqlite3OSTrace = SQLITE_DEBUG_OS_TRACE;\n#endif\n\n#if !defined(SQLITE_OMIT_TRACE) && defined(SQLITE_ENABLE_IOTRACE)\n/*\n** If the following function pointer is not NULL and if\n** SQLITE_ENABLE_IOTRACE is enabled, then messages describing\n** I/O active are written using this function.  These messages\n** are intended for debugging activity only.\n*/\nSQLITE_API void (SQLITE_CDECL *sqlite3IoTrace)(const char*, ...) = 0;\n#endif\n\n/*\n** If the following global variable points to a string which is the\n** name of a directory, then that directory will be used to store\n** temporary files.\n**\n** See also the \"PRAGMA temp_store_directory\" SQL command.\n*/\nSQLITE_API char *sqlite3_temp_directory = 0;\n\n/*\n** If the following global variable points to a string which is the\n** name of a directory, then that directory will be used to store\n** all database files specified with a relative pathname.\n**\n** See also the \"PRAGMA data_store_directory\" SQL command.\n*/\nSQLITE_API char *sqlite3_data_directory = 0;\n\n/*\n** Initialize SQLite.  \n**\n** This routine must be called to initialize the memory allocation,\n** VFS, and mutex subsystems prior to doing any serious work with\n** SQLite.  But as long as you do not compile with SQLITE_OMIT_AUTOINIT\n** this routine will be called automatically by key routines such as\n** sqlite3_open().  \n**\n** This routine is a no-op except on its very first call for the process,\n** or for the first call after a call to sqlite3_shutdown.\n**\n** The first thread to call this routine runs the initialization to\n** completion.  If subsequent threads call this routine before the first\n** thread has finished the initialization process, then the subsequent\n** threads must block until the first thread finishes with the initialization.\n**\n** The first thread might call this routine recursively.  Recursive\n** calls to this routine should not block, of course.  Otherwise the\n** initialization process would never complete.\n**\n** Let X be the first thread to enter this routine.  Let Y be some other\n** thread.  Then while the initial invocation of this routine by X is\n** incomplete, it is required that:\n**\n**    *  Calls to this routine from Y must block until the outer-most\n**       call by X completes.\n**\n**    *  Recursive calls to this routine from thread X return immediately\n**       without blocking.\n*/\nSQLITE_API int sqlite3_initialize(void){\n  MUTEX_LOGIC( sqlite3_mutex *pMaster; )       /* The main static mutex */\n  int rc;                                      /* Result code */\n#ifdef SQLITE_EXTRA_INIT\n  int bRunExtraInit = 0;                       /* Extra initialization needed */\n#endif\n\n#ifdef SQLITE_OMIT_WSD\n  rc = sqlite3_wsd_init(4096, 24);\n  if( rc!=SQLITE_OK ){\n    return rc;\n  }\n#endif\n\n  /* If the following assert() fails on some obscure processor/compiler\n  ** combination, the work-around is to set the correct pointer\n  ** size at compile-time using -DSQLITE_PTRSIZE=n compile-time option */\n  assert( SQLITE_PTRSIZE==sizeof(char*) );\n\n  /* If SQLite is already completely initialized, then this call\n  ** to sqlite3_initialize() should be a no-op.  But the initialization\n  ** must be complete.  So isInit must not be set until the very end\n  ** of this routine.\n  */\n  if( sqlite3GlobalConfig.isInit ) return SQLITE_OK;\n\n  /* Make sure the mutex subsystem is initialized.  If unable to \n  ** initialize the mutex subsystem, return early with the error.\n  ** If the system is so sick that we are unable to allocate a mutex,\n  ** there is not much SQLite is going to be able to do.\n  **\n  ** The mutex subsystem must take care of serializing its own\n  ** initialization.\n  */\n  rc = sqlite3MutexInit();\n  if( rc ) return rc;\n\n  /* Initialize the malloc() system and the recursive pInitMutex mutex.\n  ** This operation is protected by the STATIC_MASTER mutex.  Note that\n  ** MutexAlloc() is called for a static mutex prior to initializing the\n  ** malloc subsystem - this implies that the allocation of a static\n  ** mutex must not require support from the malloc subsystem.\n  */\n  MUTEX_LOGIC( pMaster = sqlite3MutexAlloc(SQLITE_MUTEX_STATIC_MASTER); )\n  sqlite3_mutex_enter(pMaster);\n  sqlite3GlobalConfig.isMutexInit = 1;\n  if( !sqlite3GlobalConfig.isMallocInit ){\n    rc = sqlite3MallocInit();\n  }\n  if( rc==SQLITE_OK ){\n    sqlite3GlobalConfig.isMallocInit = 1;\n    if( !sqlite3GlobalConfig.pInitMutex ){\n      sqlite3GlobalConfig.pInitMutex =\n           sqlite3MutexAlloc(SQLITE_MUTEX_RECURSIVE);\n      if( sqlite3GlobalConfig.bCoreMutex && !sqlite3GlobalConfig.pInitMutex ){\n        rc = SQLITE_NOMEM_BKPT;\n      }\n    }\n  }\n  if( rc==SQLITE_OK ){\n    sqlite3GlobalConfig.nRefInitMutex++;\n  }\n  sqlite3_mutex_leave(pMaster);\n\n  /* If rc is not SQLITE_OK at this point, then either the malloc\n  ** subsystem could not be initialized or the system failed to allocate\n  ** the pInitMutex mutex. Return an error in either case.  */\n  if( rc!=SQLITE_OK ){\n    return rc;\n  }\n\n  /* Do the rest of the initialization under the recursive mutex so\n  ** that we will be able to handle recursive calls into\n  ** sqlite3_initialize().  The recursive calls normally come through\n  ** sqlite3_os_init() when it invokes sqlite3_vfs_register(), but other\n  ** recursive calls might also be possible.\n  **\n  ** IMPLEMENTATION-OF: R-00140-37445 SQLite automatically serializes calls\n  ** to the xInit method, so the xInit method need not be threadsafe.\n  **\n  ** The following mutex is what serializes access to the appdef pcache xInit\n  ** methods.  The sqlite3_pcache_methods.xInit() all is embedded in the\n  ** call to sqlite3PcacheInitialize().\n  */\n  sqlite3_mutex_enter(sqlite3GlobalConfig.pInitMutex);\n  if( sqlite3GlobalConfig.isInit==0 && sqlite3GlobalConfig.inProgress==0 ){\n    sqlite3GlobalConfig.inProgress = 1;\n#ifdef SQLITE_ENABLE_SQLLOG\n    {\n      extern void sqlite3_init_sqllog(void);\n      sqlite3_init_sqllog();\n    }\n#endif\n    memset(&sqlite3BuiltinFunctions, 0, sizeof(sqlite3BuiltinFunctions));\n    sqlite3RegisterBuiltinFunctions();\n    if( sqlite3GlobalConfig.isPCacheInit==0 ){\n      rc = sqlite3PcacheInitialize();\n    }\n    if( rc==SQLITE_OK ){\n      sqlite3GlobalConfig.isPCacheInit = 1;\n      rc = sqlite3OsInit();\n    }\n    if( rc==SQLITE_OK ){\n      sqlite3PCacheBufferSetup( sqlite3GlobalConfig.pPage, \n          sqlite3GlobalConfig.szPage, sqlite3GlobalConfig.nPage);\n      sqlite3GlobalConfig.isInit = 1;\n#ifdef SQLITE_EXTRA_INIT\n      bRunExtraInit = 1;\n#endif\n    }\n    sqlite3GlobalConfig.inProgress = 0;\n  }\n  sqlite3_mutex_leave(sqlite3GlobalConfig.pInitMutex);\n\n  /* Go back under the static mutex and clean up the recursive\n  ** mutex to prevent a resource leak.\n  */\n  sqlite3_mutex_enter(pMaster);\n  sqlite3GlobalConfig.nRefInitMutex--;\n  if( sqlite3GlobalConfig.nRefInitMutex<=0 ){\n    assert( sqlite3GlobalConfig.nRefInitMutex==0 );\n    sqlite3_mutex_free(sqlite3GlobalConfig.pInitMutex);\n    sqlite3GlobalConfig.pInitMutex = 0;\n  }\n  sqlite3_mutex_leave(pMaster);\n\n  /* The following is just a sanity check to make sure SQLite has\n  ** been compiled correctly.  It is important to run this code, but\n  ** we don't want to run it too often and soak up CPU cycles for no\n  ** reason.  So we run it once during initialization.\n  */\n#ifndef NDEBUG\n#ifndef SQLITE_OMIT_FLOATING_POINT\n  /* This section of code's only \"output\" is via assert() statements. */\n  if ( rc==SQLITE_OK ){\n    u64 x = (((u64)1)<<63)-1;\n    double y;\n    assert(sizeof(x)==8);\n    assert(sizeof(x)==sizeof(y));\n    memcpy(&y, &x, 8);\n    assert( sqlite3IsNaN(y) );\n  }\n#endif\n#endif\n\n  /* Do extra initialization steps requested by the SQLITE_EXTRA_INIT\n  ** compile-time option.\n  */\n#ifdef SQLITE_EXTRA_INIT\n  if( bRunExtraInit ){\n    int SQLITE_EXTRA_INIT(const char*);\n    rc = SQLITE_EXTRA_INIT(0);\n  }\n#endif\n\n  return rc;\n}\n\n/*\n** Undo the effects of sqlite3_initialize().  Must not be called while\n** there are outstanding database connections or memory allocations or\n** while any part of SQLite is otherwise in use in any thread.  This\n** routine is not threadsafe.  But it is safe to invoke this routine\n** on when SQLite is already shut down.  If SQLite is already shut down\n** when this routine is invoked, then this routine is a harmless no-op.\n*/\nSQLITE_API int sqlite3_shutdown(void){\n#ifdef SQLITE_OMIT_WSD\n  int rc = sqlite3_wsd_init(4096, 24);\n  if( rc!=SQLITE_OK ){\n    return rc;\n  }\n#endif\n\n  if( sqlite3GlobalConfig.isInit ){\n#ifdef SQLITE_EXTRA_SHUTDOWN\n    void SQLITE_EXTRA_SHUTDOWN(void);\n    SQLITE_EXTRA_SHUTDOWN();\n#endif\n    sqlite3_os_end();\n    sqlite3_reset_auto_extension();\n    sqlite3GlobalConfig.isInit = 0;\n  }\n  if( sqlite3GlobalConfig.isPCacheInit ){\n    sqlite3PcacheShutdown();\n    sqlite3GlobalConfig.isPCacheInit = 0;\n  }\n  if( sqlite3GlobalConfig.isMallocInit ){\n    sqlite3MallocEnd();\n    sqlite3GlobalConfig.isMallocInit = 0;\n\n#ifndef SQLITE_OMIT_SHUTDOWN_DIRECTORIES\n    /* The heap subsystem has now been shutdown and these values are supposed\n    ** to be NULL or point to memory that was obtained from sqlite3_malloc(),\n    ** which would rely on that heap subsystem; therefore, make sure these\n    ** values cannot refer to heap memory that was just invalidated when the\n    ** heap subsystem was shutdown.  This is only done if the current call to\n    ** this function resulted in the heap subsystem actually being shutdown.\n    */\n    sqlite3_data_directory = 0;\n    sqlite3_temp_directory = 0;\n#endif\n  }\n  if( sqlite3GlobalConfig.isMutexInit ){\n    sqlite3MutexEnd();\n    sqlite3GlobalConfig.isMutexInit = 0;\n  }\n\n  return SQLITE_OK;\n}\n\n/*\n** This API allows applications to modify the global configuration of\n** the SQLite library at run-time.\n**\n** This routine should only be called when there are no outstanding\n** database connections or memory allocations.  This routine is not\n** threadsafe.  Failure to heed these warnings can lead to unpredictable\n** behavior.\n*/\nSQLITE_API int sqlite3_config(int op, ...){\n  va_list ap;\n  int rc = SQLITE_OK;\n\n  /* sqlite3_config() shall return SQLITE_MISUSE if it is invoked while\n  ** the SQLite library is in use. */\n  if( sqlite3GlobalConfig.isInit ) return SQLITE_MISUSE_BKPT;\n\n  va_start(ap, op);\n  switch( op ){\n\n    /* Mutex configuration options are only available in a threadsafe\n    ** compile.\n    */\n#if defined(SQLITE_THREADSAFE) && SQLITE_THREADSAFE>0  /* IMP: R-54466-46756 */\n    case SQLITE_CONFIG_SINGLETHREAD: {\n      /* EVIDENCE-OF: R-02748-19096 This option sets the threading mode to\n      ** Single-thread. */\n      sqlite3GlobalConfig.bCoreMutex = 0;  /* Disable mutex on core */\n      sqlite3GlobalConfig.bFullMutex = 0;  /* Disable mutex on connections */\n      break;\n    }\n#endif\n#if defined(SQLITE_THREADSAFE) && SQLITE_THREADSAFE>0 /* IMP: R-20520-54086 */\n    case SQLITE_CONFIG_MULTITHREAD: {\n      /* EVIDENCE-OF: R-14374-42468 This option sets the threading mode to\n      ** Multi-thread. */\n      sqlite3GlobalConfig.bCoreMutex = 1;  /* Enable mutex on core */\n      sqlite3GlobalConfig.bFullMutex = 0;  /* Disable mutex on connections */\n      break;\n    }\n#endif\n#if defined(SQLITE_THREADSAFE) && SQLITE_THREADSAFE>0 /* IMP: R-59593-21810 */\n    case SQLITE_CONFIG_SERIALIZED: {\n      /* EVIDENCE-OF: R-41220-51800 This option sets the threading mode to\n      ** Serialized. */\n      sqlite3GlobalConfig.bCoreMutex = 1;  /* Enable mutex on core */\n      sqlite3GlobalConfig.bFullMutex = 1;  /* Enable mutex on connections */\n      break;\n    }\n#endif\n#if defined(SQLITE_THREADSAFE) && SQLITE_THREADSAFE>0 /* IMP: R-63666-48755 */\n    case SQLITE_CONFIG_MUTEX: {\n      /* Specify an alternative mutex implementation */\n      sqlite3GlobalConfig.mutex = *va_arg(ap, sqlite3_mutex_methods*);\n      break;\n    }\n#endif\n#if defined(SQLITE_THREADSAFE) && SQLITE_THREADSAFE>0 /* IMP: R-14450-37597 */\n    case SQLITE_CONFIG_GETMUTEX: {\n      /* Retrieve the current mutex implementation */\n      *va_arg(ap, sqlite3_mutex_methods*) = sqlite3GlobalConfig.mutex;\n      break;\n    }\n#endif\n\n    case SQLITE_CONFIG_MALLOC: {\n      /* EVIDENCE-OF: R-55594-21030 The SQLITE_CONFIG_MALLOC option takes a\n      ** single argument which is a pointer to an instance of the\n      ** sqlite3_mem_methods structure. The argument specifies alternative\n      ** low-level memory allocation routines to be used in place of the memory\n      ** allocation routines built into SQLite. */\n      sqlite3GlobalConfig.m = *va_arg(ap, sqlite3_mem_methods*);\n      break;\n    }\n    case SQLITE_CONFIG_GETMALLOC: {\n      /* EVIDENCE-OF: R-51213-46414 The SQLITE_CONFIG_GETMALLOC option takes a\n      ** single argument which is a pointer to an instance of the\n      ** sqlite3_mem_methods structure. The sqlite3_mem_methods structure is\n      ** filled with the currently defined memory allocation routines. */\n      if( sqlite3GlobalConfig.m.xMalloc==0 ) sqlite3MemSetDefault();\n      *va_arg(ap, sqlite3_mem_methods*) = sqlite3GlobalConfig.m;\n      break;\n    }\n    case SQLITE_CONFIG_MEMSTATUS: {\n      /* EVIDENCE-OF: R-61275-35157 The SQLITE_CONFIG_MEMSTATUS option takes\n      ** single argument of type int, interpreted as a boolean, which enables\n      ** or disables the collection of memory allocation statistics. */\n      sqlite3GlobalConfig.bMemstat = va_arg(ap, int);\n      break;\n    }\n    case SQLITE_CONFIG_SMALL_MALLOC: {\n      sqlite3GlobalConfig.bSmallMalloc = va_arg(ap, int);\n      break;\n    }\n    case SQLITE_CONFIG_PAGECACHE: {\n      /* EVIDENCE-OF: R-18761-36601 There are three arguments to\n      ** SQLITE_CONFIG_PAGECACHE: A pointer to 8-byte aligned memory (pMem),\n      ** the size of each page cache line (sz), and the number of cache lines\n      ** (N). */\n      sqlite3GlobalConfig.pPage = va_arg(ap, void*);\n      sqlite3GlobalConfig.szPage = va_arg(ap, int);\n      sqlite3GlobalConfig.nPage = va_arg(ap, int);\n      break;\n    }\n    case SQLITE_CONFIG_PCACHE_HDRSZ: {\n      /* EVIDENCE-OF: R-39100-27317 The SQLITE_CONFIG_PCACHE_HDRSZ option takes\n      ** a single parameter which is a pointer to an integer and writes into\n      ** that integer the number of extra bytes per page required for each page\n      ** in SQLITE_CONFIG_PAGECACHE. */\n      *va_arg(ap, int*) = \n          sqlite3HeaderSizeBtree() +\n          sqlite3HeaderSizePcache() +\n          sqlite3HeaderSizePcache1();\n      break;\n    }\n\n    case SQLITE_CONFIG_PCACHE: {\n      /* no-op */\n      break;\n    }\n    case SQLITE_CONFIG_GETPCACHE: {\n      /* now an error */\n      rc = SQLITE_ERROR;\n      break;\n    }\n\n    case SQLITE_CONFIG_PCACHE2: {\n      /* EVIDENCE-OF: R-63325-48378 The SQLITE_CONFIG_PCACHE2 option takes a\n      ** single argument which is a pointer to an sqlite3_pcache_methods2\n      ** object. This object specifies the interface to a custom page cache\n      ** implementation. */\n      sqlite3GlobalConfig.pcache2 = *va_arg(ap, sqlite3_pcache_methods2*);\n      break;\n    }\n    case SQLITE_CONFIG_GETPCACHE2: {\n      /* EVIDENCE-OF: R-22035-46182 The SQLITE_CONFIG_GETPCACHE2 option takes a\n      ** single argument which is a pointer to an sqlite3_pcache_methods2\n      ** object. SQLite copies of the current page cache implementation into\n      ** that object. */\n      if( sqlite3GlobalConfig.pcache2.xInit==0 ){\n        sqlite3PCacheSetDefault();\n      }\n      *va_arg(ap, sqlite3_pcache_methods2*) = sqlite3GlobalConfig.pcache2;\n      break;\n    }\n\n/* EVIDENCE-OF: R-06626-12911 The SQLITE_CONFIG_HEAP option is only\n** available if SQLite is compiled with either SQLITE_ENABLE_MEMSYS3 or\n** SQLITE_ENABLE_MEMSYS5 and returns SQLITE_ERROR if invoked otherwise. */\n#if defined(SQLITE_ENABLE_MEMSYS3) || defined(SQLITE_ENABLE_MEMSYS5)\n    case SQLITE_CONFIG_HEAP: {\n      /* EVIDENCE-OF: R-19854-42126 There are three arguments to\n      ** SQLITE_CONFIG_HEAP: An 8-byte aligned pointer to the memory, the\n      ** number of bytes in the memory buffer, and the minimum allocation size.\n      */\n      sqlite3GlobalConfig.pHeap = va_arg(ap, void*);\n      sqlite3GlobalConfig.nHeap = va_arg(ap, int);\n      sqlite3GlobalConfig.mnReq = va_arg(ap, int);\n\n      if( sqlite3GlobalConfig.mnReq<1 ){\n        sqlite3GlobalConfig.mnReq = 1;\n      }else if( sqlite3GlobalConfig.mnReq>(1<<12) ){\n        /* cap min request size at 2^12 */\n        sqlite3GlobalConfig.mnReq = (1<<12);\n      }\n\n      if( sqlite3GlobalConfig.pHeap==0 ){\n        /* EVIDENCE-OF: R-49920-60189 If the first pointer (the memory pointer)\n        ** is NULL, then SQLite reverts to using its default memory allocator\n        ** (the system malloc() implementation), undoing any prior invocation of\n        ** SQLITE_CONFIG_MALLOC.\n        **\n        ** Setting sqlite3GlobalConfig.m to all zeros will cause malloc to\n        ** revert to its default implementation when sqlite3_initialize() is run\n        */\n        memset(&sqlite3GlobalConfig.m, 0, sizeof(sqlite3GlobalConfig.m));\n      }else{\n        /* EVIDENCE-OF: R-61006-08918 If the memory pointer is not NULL then the\n        ** alternative memory allocator is engaged to handle all of SQLites\n        ** memory allocation needs. */\n#ifdef SQLITE_ENABLE_MEMSYS3\n        sqlite3GlobalConfig.m = *sqlite3MemGetMemsys3();\n#endif\n#ifdef SQLITE_ENABLE_MEMSYS5\n        sqlite3GlobalConfig.m = *sqlite3MemGetMemsys5();\n#endif\n      }\n      break;\n    }\n#endif\n\n    case SQLITE_CONFIG_LOOKASIDE: {\n      sqlite3GlobalConfig.szLookaside = va_arg(ap, int);\n      sqlite3GlobalConfig.nLookaside = va_arg(ap, int);\n      break;\n    }\n    \n    /* Record a pointer to the logger function and its first argument.\n    ** The default is NULL.  Logging is disabled if the function pointer is\n    ** NULL.\n    */\n    case SQLITE_CONFIG_LOG: {\n      /* MSVC is picky about pulling func ptrs from va lists.\n      ** http://support.microsoft.com/kb/47961\n      ** sqlite3GlobalConfig.xLog = va_arg(ap, void(*)(void*,int,const char*));\n      */\n      typedef void(*LOGFUNC_t)(void*,int,const char*);\n      sqlite3GlobalConfig.xLog = va_arg(ap, LOGFUNC_t);\n      sqlite3GlobalConfig.pLogArg = va_arg(ap, void*);\n      break;\n    }\n\n    /* EVIDENCE-OF: R-55548-33817 The compile-time setting for URI filenames\n    ** can be changed at start-time using the\n    ** sqlite3_config(SQLITE_CONFIG_URI,1) or\n    ** sqlite3_config(SQLITE_CONFIG_URI,0) configuration calls.\n    */\n    case SQLITE_CONFIG_URI: {\n      /* EVIDENCE-OF: R-25451-61125 The SQLITE_CONFIG_URI option takes a single\n      ** argument of type int. If non-zero, then URI handling is globally\n      ** enabled. If the parameter is zero, then URI handling is globally\n      ** disabled. */\n      sqlite3GlobalConfig.bOpenUri = va_arg(ap, int);\n      break;\n    }\n\n    case SQLITE_CONFIG_COVERING_INDEX_SCAN: {\n      /* EVIDENCE-OF: R-36592-02772 The SQLITE_CONFIG_COVERING_INDEX_SCAN\n      ** option takes a single integer argument which is interpreted as a\n      ** boolean in order to enable or disable the use of covering indices for\n      ** full table scans in the query optimizer. */\n      sqlite3GlobalConfig.bUseCis = va_arg(ap, int);\n      break;\n    }\n\n#ifdef SQLITE_ENABLE_SQLLOG\n    case SQLITE_CONFIG_SQLLOG: {\n      typedef void(*SQLLOGFUNC_t)(void*, sqlite3*, const char*, int);\n      sqlite3GlobalConfig.xSqllog = va_arg(ap, SQLLOGFUNC_t);\n      sqlite3GlobalConfig.pSqllogArg = va_arg(ap, void *);\n      break;\n    }\n#endif\n\n    case SQLITE_CONFIG_MMAP_SIZE: {\n      /* EVIDENCE-OF: R-58063-38258 SQLITE_CONFIG_MMAP_SIZE takes two 64-bit\n      ** integer (sqlite3_int64) values that are the default mmap size limit\n      ** (the default setting for PRAGMA mmap_size) and the maximum allowed\n      ** mmap size limit. */\n      sqlite3_int64 szMmap = va_arg(ap, sqlite3_int64);\n      sqlite3_int64 mxMmap = va_arg(ap, sqlite3_int64);\n      /* EVIDENCE-OF: R-53367-43190 If either argument to this option is\n      ** negative, then that argument is changed to its compile-time default.\n      **\n      ** EVIDENCE-OF: R-34993-45031 The maximum allowed mmap size will be\n      ** silently truncated if necessary so that it does not exceed the\n      ** compile-time maximum mmap size set by the SQLITE_MAX_MMAP_SIZE\n      ** compile-time option.\n      */\n      if( mxMmap<0 || mxMmap>SQLITE_MAX_MMAP_SIZE ){\n        mxMmap = SQLITE_MAX_MMAP_SIZE;\n      }\n      if( szMmap<0 ) szMmap = SQLITE_DEFAULT_MMAP_SIZE;\n      if( szMmap>mxMmap) szMmap = mxMmap;\n      sqlite3GlobalConfig.mxMmap = mxMmap;\n      sqlite3GlobalConfig.szMmap = szMmap;\n      break;\n    }\n\n#if SQLITE_OS_WIN && defined(SQLITE_WIN32_MALLOC) /* IMP: R-04780-55815 */\n    case SQLITE_CONFIG_WIN32_HEAPSIZE: {\n      /* EVIDENCE-OF: R-34926-03360 SQLITE_CONFIG_WIN32_HEAPSIZE takes a 32-bit\n      ** unsigned integer value that specifies the maximum size of the created\n      ** heap. */\n      sqlite3GlobalConfig.nHeap = va_arg(ap, int);\n      break;\n    }\n#endif\n\n    case SQLITE_CONFIG_PMASZ: {\n      sqlite3GlobalConfig.szPma = va_arg(ap, unsigned int);\n      break;\n    }\n\n    case SQLITE_CONFIG_STMTJRNL_SPILL: {\n      sqlite3GlobalConfig.nStmtSpill = va_arg(ap, int);\n      break;\n    }\n\n    default: {\n      rc = SQLITE_ERROR;\n      break;\n    }\n  }\n  va_end(ap);\n  return rc;\n}\n\n/*\n** Set up the lookaside buffers for a database connection.\n** Return SQLITE_OK on success.  \n** If lookaside is already active, return SQLITE_BUSY.\n**\n** The sz parameter is the number of bytes in each lookaside slot.\n** The cnt parameter is the number of slots.  If pStart is NULL the\n** space for the lookaside memory is obtained from sqlite3_malloc().\n** If pStart is not NULL then it is sz*cnt bytes of memory to use for\n** the lookaside memory.\n*/\nstatic int setupLookaside(sqlite3 *db, void *pBuf, int sz, int cnt){\n#ifndef SQLITE_OMIT_LOOKASIDE\n  void *pStart;\n  \n  if( sqlite3LookasideUsed(db,0)>0 ){\n    return SQLITE_BUSY;\n  }\n  /* Free any existing lookaside buffer for this handle before\n  ** allocating a new one so we don't have to have space for \n  ** both at the same time.\n  */\n  if( db->lookaside.bMalloced ){\n    sqlite3_free(db->lookaside.pStart);\n  }\n  /* The size of a lookaside slot after ROUNDDOWN8 needs to be larger\n  ** than a pointer to be useful.\n  */\n  sz = ROUNDDOWN8(sz);  /* IMP: R-33038-09382 */\n  if( sz<=(int)sizeof(LookasideSlot*) ) sz = 0;\n  if( cnt<0 ) cnt = 0;\n  if( sz==0 || cnt==0 ){\n    sz = 0;\n    pStart = 0;\n  }else if( pBuf==0 ){\n    sqlite3BeginBenignMalloc();\n    pStart = sqlite3Malloc( sz*cnt );  /* IMP: R-61949-35727 */\n    sqlite3EndBenignMalloc();\n    if( pStart ) cnt = sqlite3MallocSize(pStart)/sz;\n  }else{\n    pStart = pBuf;\n  }\n  db->lookaside.pStart = pStart;\n  db->lookaside.pInit = 0;\n  db->lookaside.pFree = 0;\n  db->lookaside.sz = (u16)sz;\n  if( pStart ){\n    int i;\n    LookasideSlot *p;\n    assert( sz > (int)sizeof(LookasideSlot*) );\n    db->lookaside.nSlot = cnt;\n    p = (LookasideSlot*)pStart;\n    for(i=cnt-1; i>=0; i--){\n      p->pNext = db->lookaside.pInit;\n      db->lookaside.pInit = p;\n      p = (LookasideSlot*)&((u8*)p)[sz];\n    }\n    db->lookaside.pEnd = p;\n    db->lookaside.bDisable = 0;\n    db->lookaside.bMalloced = pBuf==0 ?1:0;\n  }else{\n    db->lookaside.pStart = db;\n    db->lookaside.pEnd = db;\n    db->lookaside.bDisable = 1;\n    db->lookaside.bMalloced = 0;\n    db->lookaside.nSlot = 0;\n  }\n#endif /* SQLITE_OMIT_LOOKASIDE */\n  return SQLITE_OK;\n}\n\n/*\n** Return the mutex associated with a database connection.\n*/\nSQLITE_API sqlite3_mutex *sqlite3_db_mutex(sqlite3 *db){\n#ifdef SQLITE_ENABLE_API_ARMOR\n  if( !sqlite3SafetyCheckOk(db) ){\n    (void)SQLITE_MISUSE_BKPT;\n    return 0;\n  }\n#endif\n  return db->mutex;\n}\n\n/*\n** Free up as much memory as we can from the given database\n** connection.\n*/\nSQLITE_API int sqlite3_db_release_memory(sqlite3 *db){\n  int i;\n\n#ifdef SQLITE_ENABLE_API_ARMOR\n  if( !sqlite3SafetyCheckOk(db) ) return SQLITE_MISUSE_BKPT;\n#endif\n  sqlite3_mutex_enter(db->mutex);\n  sqlite3BtreeEnterAll(db);\n  for(i=0; i<db->nDb; i++){\n    Btree *pBt = db->aDb[i].pBt;\n    if( pBt ){\n      Pager *pPager = sqlite3BtreePager(pBt);\n      sqlite3PagerShrink(pPager);\n    }\n  }\n  sqlite3BtreeLeaveAll(db);\n  sqlite3_mutex_leave(db->mutex);\n  return SQLITE_OK;\n}\n\n/*\n** Flush any dirty pages in the pager-cache for any attached database\n** to disk.\n*/\nSQLITE_API int sqlite3_db_cacheflush(sqlite3 *db){\n  int i;\n  int rc = SQLITE_OK;\n  int bSeenBusy = 0;\n\n#ifdef SQLITE_ENABLE_API_ARMOR\n  if( !sqlite3SafetyCheckOk(db) ) return SQLITE_MISUSE_BKPT;\n#endif\n  sqlite3_mutex_enter(db->mutex);\n  sqlite3BtreeEnterAll(db);\n  for(i=0; rc==SQLITE_OK && i<db->nDb; i++){\n    Btree *pBt = db->aDb[i].pBt;\n    if( pBt && sqlite3BtreeIsInTrans(pBt) ){\n      Pager *pPager = sqlite3BtreePager(pBt);\n      rc = sqlite3PagerFlush(pPager);\n      if( rc==SQLITE_BUSY ){\n        bSeenBusy = 1;\n        rc = SQLITE_OK;\n      }\n    }\n  }\n  sqlite3BtreeLeaveAll(db);\n  sqlite3_mutex_leave(db->mutex);\n  return ((rc==SQLITE_OK && bSeenBusy) ? SQLITE_BUSY : rc);\n}\n\n/*\n** Configuration settings for an individual database connection\n*/\nSQLITE_API int sqlite3_db_config(sqlite3 *db, int op, ...){\n  va_list ap;\n  int rc;\n  va_start(ap, op);\n  switch( op ){\n    case SQLITE_DBCONFIG_MAINDBNAME: {\n      /* IMP: R-06824-28531 */\n      /* IMP: R-36257-52125 */\n      db->aDb[0].zDbSName = va_arg(ap,char*);\n      rc = SQLITE_OK;\n      break;\n    }\n    case SQLITE_DBCONFIG_LOOKASIDE: {\n      void *pBuf = va_arg(ap, void*); /* IMP: R-26835-10964 */\n      int sz = va_arg(ap, int);       /* IMP: R-47871-25994 */\n      int cnt = va_arg(ap, int);      /* IMP: R-04460-53386 */\n      rc = setupLookaside(db, pBuf, sz, cnt);\n      break;\n    }\n    default: {\n      static const struct {\n        int op;      /* The opcode */\n        u32 mask;    /* Mask of the bit in sqlite3.flags to set/clear */\n      } aFlagOp[] = {\n        { SQLITE_DBCONFIG_ENABLE_FKEY,           SQLITE_ForeignKeys    },\n        { SQLITE_DBCONFIG_ENABLE_TRIGGER,        SQLITE_EnableTrigger  },\n        { SQLITE_DBCONFIG_ENABLE_FTS3_TOKENIZER, SQLITE_Fts3Tokenizer  },\n        { SQLITE_DBCONFIG_ENABLE_LOAD_EXTENSION, SQLITE_LoadExtension  },\n        { SQLITE_DBCONFIG_NO_CKPT_ON_CLOSE,      SQLITE_NoCkptOnClose  },\n        { SQLITE_DBCONFIG_ENABLE_QPSG,           SQLITE_EnableQPSG     },\n        { SQLITE_DBCONFIG_TRIGGER_EQP,           SQLITE_TriggerEQP     },\n      };\n      unsigned int i;\n      rc = SQLITE_ERROR; /* IMP: R-42790-23372 */\n      for(i=0; i<ArraySize(aFlagOp); i++){\n        if( aFlagOp[i].op==op ){\n          int onoff = va_arg(ap, int);\n          int *pRes = va_arg(ap, int*);\n          u32 oldFlags = db->flags;\n          if( onoff>0 ){\n            db->flags |= aFlagOp[i].mask;\n          }else if( onoff==0 ){\n            db->flags &= ~aFlagOp[i].mask;\n          }\n          if( oldFlags!=db->flags ){\n            sqlite3ExpirePreparedStatements(db);\n          }\n          if( pRes ){\n            *pRes = (db->flags & aFlagOp[i].mask)!=0;\n          }\n          rc = SQLITE_OK;\n          break;\n        }\n      }\n      break;\n    }\n  }\n  va_end(ap);\n  return rc;\n}\n\n\n/*\n** Return true if the buffer z[0..n-1] contains all spaces.\n*/\nstatic int allSpaces(const char *z, int n){\n  while( n>0 && z[n-1]==' ' ){ n--; }\n  return n==0;\n}\n\n/*\n** This is the default collating function named \"BINARY\" which is always\n** available.\n**\n** If the padFlag argument is not NULL then space padding at the end\n** of strings is ignored.  This implements the RTRIM collation.\n*/\nstatic int binCollFunc(\n  void *padFlag,\n  int nKey1, const void *pKey1,\n  int nKey2, const void *pKey2\n){\n  int rc, n;\n  n = nKey1<nKey2 ? nKey1 : nKey2;\n  /* EVIDENCE-OF: R-65033-28449 The built-in BINARY collation compares\n  ** strings byte by byte using the memcmp() function from the standard C\n  ** library. */\n  assert( pKey1 && pKey2 );\n  rc = memcmp(pKey1, pKey2, n);\n  if( rc==0 ){\n    if( padFlag\n     && allSpaces(((char*)pKey1)+n, nKey1-n)\n     && allSpaces(((char*)pKey2)+n, nKey2-n)\n    ){\n      /* EVIDENCE-OF: R-31624-24737 RTRIM is like BINARY except that extra\n      ** spaces at the end of either string do not change the result. In other\n      ** words, strings will compare equal to one another as long as they\n      ** differ only in the number of spaces at the end.\n      */\n    }else{\n      rc = nKey1 - nKey2;\n    }\n  }\n  return rc;\n}\n\n/*\n** Another built-in collating sequence: NOCASE. \n**\n** This collating sequence is intended to be used for \"case independent\n** comparison\". SQLite's knowledge of upper and lower case equivalents\n** extends only to the 26 characters used in the English language.\n**\n** At the moment there is only a UTF-8 implementation.\n*/\nstatic int nocaseCollatingFunc(\n  void *NotUsed,\n  int nKey1, const void *pKey1,\n  int nKey2, const void *pKey2\n){\n  int r = sqlite3StrNICmp(\n      (const char *)pKey1, (const char *)pKey2, (nKey1<nKey2)?nKey1:nKey2);\n  UNUSED_PARAMETER(NotUsed);\n  if( 0==r ){\n    r = nKey1-nKey2;\n  }\n  return r;\n}\n\n/*\n** Return the ROWID of the most recent insert\n*/\nSQLITE_API sqlite_int64 sqlite3_last_insert_rowid(sqlite3 *db){\n#ifdef SQLITE_ENABLE_API_ARMOR\n  if( !sqlite3SafetyCheckOk(db) ){\n    (void)SQLITE_MISUSE_BKPT;\n    return 0;\n  }\n#endif\n  return db->lastRowid;\n}\n\n/*\n** Set the value returned by the sqlite3_last_insert_rowid() API function.\n*/\nSQLITE_API void sqlite3_set_last_insert_rowid(sqlite3 *db, sqlite3_int64 iRowid){\n#ifdef SQLITE_ENABLE_API_ARMOR\n  if( !sqlite3SafetyCheckOk(db) ){\n    (void)SQLITE_MISUSE_BKPT;\n    return;\n  }\n#endif\n  sqlite3_mutex_enter(db->mutex);\n  db->lastRowid = iRowid;\n  sqlite3_mutex_leave(db->mutex);\n}\n\n/*\n** Return the number of changes in the most recent call to sqlite3_exec().\n*/\nSQLITE_API int sqlite3_changes(sqlite3 *db){\n#ifdef SQLITE_ENABLE_API_ARMOR\n  if( !sqlite3SafetyCheckOk(db) ){\n    (void)SQLITE_MISUSE_BKPT;\n    return 0;\n  }\n#endif\n  return db->nChange;\n}\n\n/*\n** Return the number of changes since the database handle was opened.\n*/\nSQLITE_API int sqlite3_total_changes(sqlite3 *db){\n#ifdef SQLITE_ENABLE_API_ARMOR\n  if( !sqlite3SafetyCheckOk(db) ){\n    (void)SQLITE_MISUSE_BKPT;\n    return 0;\n  }\n#endif\n  return db->nTotalChange;\n}\n\n/*\n** Close all open savepoints. This function only manipulates fields of the\n** database handle object, it does not close any savepoints that may be open\n** at the b-tree/pager level.\n*/\nSQLITE_PRIVATE void sqlite3CloseSavepoints(sqlite3 *db){\n  while( db->pSavepoint ){\n    Savepoint *pTmp = db->pSavepoint;\n    db->pSavepoint = pTmp->pNext;\n    sqlite3DbFree(db, pTmp);\n  }\n  db->nSavepoint = 0;\n  db->nStatement = 0;\n  db->isTransactionSavepoint = 0;\n}\n\n/*\n** Invoke the destructor function associated with FuncDef p, if any. Except,\n** if this is not the last copy of the function, do not invoke it. Multiple\n** copies of a single function are created when create_function() is called\n** with SQLITE_ANY as the encoding.\n*/\nstatic void functionDestroy(sqlite3 *db, FuncDef *p){\n  FuncDestructor *pDestructor = p->u.pDestructor;\n  if( pDestructor ){\n    pDestructor->nRef--;\n    if( pDestructor->nRef==0 ){\n      pDestructor->xDestroy(pDestructor->pUserData);\n      sqlite3DbFree(db, pDestructor);\n    }\n  }\n}\n\n/*\n** Disconnect all sqlite3_vtab objects that belong to database connection\n** db. This is called when db is being closed.\n*/\nstatic void disconnectAllVtab(sqlite3 *db){\n#ifndef SQLITE_OMIT_VIRTUALTABLE\n  int i;\n  HashElem *p;\n  sqlite3BtreeEnterAll(db);\n  for(i=0; i<db->nDb; i++){\n    Schema *pSchema = db->aDb[i].pSchema;\n    if( db->aDb[i].pSchema ){\n      for(p=sqliteHashFirst(&pSchema->tblHash); p; p=sqliteHashNext(p)){\n        Table *pTab = (Table *)sqliteHashData(p);\n        if( IsVirtual(pTab) ) sqlite3VtabDisconnect(db, pTab);\n      }\n    }\n  }\n  for(p=sqliteHashFirst(&db->aModule); p; p=sqliteHashNext(p)){\n    Module *pMod = (Module *)sqliteHashData(p);\n    if( pMod->pEpoTab ){\n      sqlite3VtabDisconnect(db, pMod->pEpoTab);\n    }\n  }\n  sqlite3VtabUnlockList(db);\n  sqlite3BtreeLeaveAll(db);\n#else\n  UNUSED_PARAMETER(db);\n#endif\n}\n\n/*\n** Return TRUE if database connection db has unfinalized prepared\n** statements or unfinished sqlite3_backup objects.  \n*/\nstatic int connectionIsBusy(sqlite3 *db){\n  int j;\n  assert( sqlite3_mutex_held(db->mutex) );\n  if( db->pVdbe ) return 1;\n  for(j=0; j<db->nDb; j++){\n    Btree *pBt = db->aDb[j].pBt;\n    if( pBt && sqlite3BtreeIsInBackup(pBt) ) return 1;\n  }\n  return 0;\n}\n\n/*\n** Close an existing SQLite database\n*/\nstatic int sqlite3Close(sqlite3 *db, int forceZombie){\n  if( !db ){\n    /* EVIDENCE-OF: R-63257-11740 Calling sqlite3_close() or\n    ** sqlite3_close_v2() with a NULL pointer argument is a harmless no-op. */\n    return SQLITE_OK;\n  }\n  if( !sqlite3SafetyCheckSickOrOk(db) ){\n    return SQLITE_MISUSE_BKPT;\n  }\n  sqlite3_mutex_enter(db->mutex);\n  if( db->mTrace & SQLITE_TRACE_CLOSE ){\n    db->xTrace(SQLITE_TRACE_CLOSE, db->pTraceArg, db, 0);\n  }\n\n  /* Force xDisconnect calls on all virtual tables */\n  disconnectAllVtab(db);\n\n  /* If a transaction is open, the disconnectAllVtab() call above\n  ** will not have called the xDisconnect() method on any virtual\n  ** tables in the db->aVTrans[] array. The following sqlite3VtabRollback()\n  ** call will do so. We need to do this before the check for active\n  ** SQL statements below, as the v-table implementation may be storing\n  ** some prepared statements internally.\n  */\n  sqlite3VtabRollback(db);\n\n  /* Legacy behavior (sqlite3_close() behavior) is to return\n  ** SQLITE_BUSY if the connection can not be closed immediately.\n  */\n  if( !forceZombie && connectionIsBusy(db) ){\n    sqlite3ErrorWithMsg(db, SQLITE_BUSY, \"unable to close due to unfinalized \"\n       \"statements or unfinished backups\");\n    sqlite3_mutex_leave(db->mutex);\n    return SQLITE_BUSY;\n  }\n\n#ifdef SQLITE_ENABLE_SQLLOG\n  if( sqlite3GlobalConfig.xSqllog ){\n    /* Closing the handle. Fourth parameter is passed the value 2. */\n    sqlite3GlobalConfig.xSqllog(sqlite3GlobalConfig.pSqllogArg, db, 0, 2);\n  }\n#endif\n\n  /* Convert the connection into a zombie and then close it.\n  */\n  db->magic = SQLITE_MAGIC_ZOMBIE;\n  sqlite3LeaveMutexAndCloseZombie(db);\n  return SQLITE_OK;\n}\n\n/*\n** Two variations on the public interface for closing a database\n** connection. The sqlite3_close() version returns SQLITE_BUSY and\n** leaves the connection option if there are unfinalized prepared\n** statements or unfinished sqlite3_backups.  The sqlite3_close_v2()\n** version forces the connection to become a zombie if there are\n** unclosed resources, and arranges for deallocation when the last\n** prepare statement or sqlite3_backup closes.\n*/\nSQLITE_API int sqlite3_close(sqlite3 *db){ return sqlite3Close(db,0); }\nSQLITE_API int sqlite3_close_v2(sqlite3 *db){ return sqlite3Close(db,1); }\n\n\n/*\n** Close the mutex on database connection db.\n**\n** Furthermore, if database connection db is a zombie (meaning that there\n** has been a prior call to sqlite3_close(db) or sqlite3_close_v2(db)) and\n** every sqlite3_stmt has now been finalized and every sqlite3_backup has\n** finished, then free all resources.\n*/\nSQLITE_PRIVATE void sqlite3LeaveMutexAndCloseZombie(sqlite3 *db){\n  HashElem *i;                    /* Hash table iterator */\n  int j;\n\n  /* If there are outstanding sqlite3_stmt or sqlite3_backup objects\n  ** or if the connection has not yet been closed by sqlite3_close_v2(),\n  ** then just leave the mutex and return.\n  */\n  if( db->magic!=SQLITE_MAGIC_ZOMBIE || connectionIsBusy(db) ){\n    sqlite3_mutex_leave(db->mutex);\n    return;\n  }\n\n  /* If we reach this point, it means that the database connection has\n  ** closed all sqlite3_stmt and sqlite3_backup objects and has been\n  ** passed to sqlite3_close (meaning that it is a zombie).  Therefore,\n  ** go ahead and free all resources.\n  */\n\n  /* If a transaction is open, roll it back. This also ensures that if\n  ** any database schemas have been modified by an uncommitted transaction\n  ** they are reset. And that the required b-tree mutex is held to make\n  ** the pager rollback and schema reset an atomic operation. */\n  sqlite3RollbackAll(db, SQLITE_OK);\n\n  /* Free any outstanding Savepoint structures. */\n  sqlite3CloseSavepoints(db);\n\n  /* Close all database connections */\n  for(j=0; j<db->nDb; j++){\n    struct Db *pDb = &db->aDb[j];\n    if( pDb->pBt ){\n      sqlite3BtreeClose(pDb->pBt);\n      pDb->pBt = 0;\n      if( j!=1 ){\n        pDb->pSchema = 0;\n      }\n    }\n  }\n  /* Clear the TEMP schema separately and last */\n  if( db->aDb[1].pSchema ){\n    sqlite3SchemaClear(db->aDb[1].pSchema);\n  }\n  sqlite3VtabUnlockList(db);\n\n  /* Free up the array of auxiliary databases */\n  sqlite3CollapseDatabaseArray(db);\n  assert( db->nDb<=2 );\n  assert( db->aDb==db->aDbStatic );\n\n  /* Tell the code in notify.c that the connection no longer holds any\n  ** locks and does not require any further unlock-notify callbacks.\n  */\n  sqlite3ConnectionClosed(db);\n\n  for(i=sqliteHashFirst(&db->aFunc); i; i=sqliteHashNext(i)){\n    FuncDef *pNext, *p;\n    p = sqliteHashData(i);\n    do{\n      functionDestroy(db, p);\n      pNext = p->pNext;\n      sqlite3DbFree(db, p);\n      p = pNext;\n    }while( p );\n  }\n  sqlite3HashClear(&db->aFunc);\n  for(i=sqliteHashFirst(&db->aCollSeq); i; i=sqliteHashNext(i)){\n    CollSeq *pColl = (CollSeq *)sqliteHashData(i);\n    /* Invoke any destructors registered for collation sequence user data. */\n    for(j=0; j<3; j++){\n      if( pColl[j].xDel ){\n        pColl[j].xDel(pColl[j].pUser);\n      }\n    }\n    sqlite3DbFree(db, pColl);\n  }\n  sqlite3HashClear(&db->aCollSeq);\n#ifndef SQLITE_OMIT_VIRTUALTABLE\n  for(i=sqliteHashFirst(&db->aModule); i; i=sqliteHashNext(i)){\n    Module *pMod = (Module *)sqliteHashData(i);\n    if( pMod->xDestroy ){\n      pMod->xDestroy(pMod->pAux);\n    }\n    sqlite3VtabEponymousTableClear(db, pMod);\n    sqlite3DbFree(db, pMod);\n  }\n  sqlite3HashClear(&db->aModule);\n#endif\n\n  sqlite3Error(db, SQLITE_OK); /* Deallocates any cached error strings. */\n  sqlite3ValueFree(db->pErr);\n  sqlite3CloseExtensions(db);\n#if SQLITE_USER_AUTHENTICATION\n  sqlite3_free(db->auth.zAuthUser);\n  sqlite3_free(db->auth.zAuthPW);\n#endif\n\n  db->magic = SQLITE_MAGIC_ERROR;\n\n  /* The temp-database schema is allocated differently from the other schema\n  ** objects (using sqliteMalloc() directly, instead of sqlite3BtreeSchema()).\n  ** So it needs to be freed here. Todo: Why not roll the temp schema into\n  ** the same sqliteMalloc() as the one that allocates the database \n  ** structure?\n  */\n  sqlite3DbFree(db, db->aDb[1].pSchema);\n  sqlite3_mutex_leave(db->mutex);\n  db->magic = SQLITE_MAGIC_CLOSED;\n  sqlite3_mutex_free(db->mutex);\n  assert( sqlite3LookasideUsed(db,0)==0 );\n  if( db->lookaside.bMalloced ){\n    sqlite3_free(db->lookaside.pStart);\n  }\n  sqlite3_free(db);\n}\n\n/*\n** Rollback all database files.  If tripCode is not SQLITE_OK, then\n** any write cursors are invalidated (\"tripped\" - as in \"tripping a circuit\n** breaker\") and made to return tripCode if there are any further\n** attempts to use that cursor.  Read cursors remain open and valid\n** but are \"saved\" in case the table pages are moved around.\n*/\nSQLITE_PRIVATE void sqlite3RollbackAll(sqlite3 *db, int tripCode){\n  int i;\n  int inTrans = 0;\n  int schemaChange;\n  assert( sqlite3_mutex_held(db->mutex) );\n  sqlite3BeginBenignMalloc();\n\n  /* Obtain all b-tree mutexes before making any calls to BtreeRollback(). \n  ** This is important in case the transaction being rolled back has\n  ** modified the database schema. If the b-tree mutexes are not taken\n  ** here, then another shared-cache connection might sneak in between\n  ** the database rollback and schema reset, which can cause false\n  ** corruption reports in some cases.  */\n  sqlite3BtreeEnterAll(db);\n  schemaChange = (db->mDbFlags & DBFLAG_SchemaChange)!=0 && db->init.busy==0;\n\n  for(i=0; i<db->nDb; i++){\n    Btree *p = db->aDb[i].pBt;\n    if( p ){\n      if( sqlite3BtreeIsInTrans(p) ){\n        inTrans = 1;\n      }\n      sqlite3BtreeRollback(p, tripCode, !schemaChange);\n    }\n  }\n  sqlite3VtabRollback(db);\n  sqlite3EndBenignMalloc();\n\n  if( (db->mDbFlags&DBFLAG_SchemaChange)!=0 && db->init.busy==0 ){\n    sqlite3ExpirePreparedStatements(db);\n    sqlite3ResetAllSchemasOfConnection(db);\n  }\n  sqlite3BtreeLeaveAll(db);\n\n  /* Any deferred constraint violations have now been resolved. */\n  db->nDeferredCons = 0;\n  db->nDeferredImmCons = 0;\n  db->flags &= ~SQLITE_DeferFKs;\n\n  /* If one has been configured, invoke the rollback-hook callback */\n  if( db->xRollbackCallback && (inTrans || !db->autoCommit) ){\n    db->xRollbackCallback(db->pRollbackArg);\n  }\n}\n\n/*\n** Return a static string containing the name corresponding to the error code\n** specified in the argument.\n*/\n#if defined(SQLITE_NEED_ERR_NAME)\nSQLITE_PRIVATE const char *sqlite3ErrName(int rc){\n  const char *zName = 0;\n  int i, origRc = rc;\n  for(i=0; i<2 && zName==0; i++, rc &= 0xff){\n    switch( rc ){\n      case SQLITE_OK:                 zName = \"SQLITE_OK\";                break;\n      case SQLITE_ERROR:              zName = \"SQLITE_ERROR\";             break;\n      case SQLITE_INTERNAL:           zName = \"SQLITE_INTERNAL\";          break;\n      case SQLITE_PERM:               zName = \"SQLITE_PERM\";              break;\n      case SQLITE_ABORT:              zName = \"SQLITE_ABORT\";             break;\n      case SQLITE_ABORT_ROLLBACK:     zName = \"SQLITE_ABORT_ROLLBACK\";    break;\n      case SQLITE_BUSY:               zName = \"SQLITE_BUSY\";              break;\n      case SQLITE_BUSY_RECOVERY:      zName = \"SQLITE_BUSY_RECOVERY\";     break;\n      case SQLITE_BUSY_SNAPSHOT:      zName = \"SQLITE_BUSY_SNAPSHOT\";     break;\n      case SQLITE_LOCKED:             zName = \"SQLITE_LOCKED\";            break;\n      case SQLITE_LOCKED_SHAREDCACHE: zName = \"SQLITE_LOCKED_SHAREDCACHE\";break;\n      case SQLITE_NOMEM:              zName = \"SQLITE_NOMEM\";             break;\n      case SQLITE_READONLY:           zName = \"SQLITE_READONLY\";          break;\n      case SQLITE_READONLY_RECOVERY:  zName = \"SQLITE_READONLY_RECOVERY\"; break;\n      case SQLITE_READONLY_CANTINIT:  zName = \"SQLITE_READONLY_CANTINIT\"; break;\n      case SQLITE_READONLY_ROLLBACK:  zName = \"SQLITE_READONLY_ROLLBACK\"; break;\n      case SQLITE_READONLY_DBMOVED:   zName = \"SQLITE_READONLY_DBMOVED\";  break;\n      case SQLITE_READONLY_DIRECTORY: zName = \"SQLITE_READONLY_DIRECTORY\";break;\n      case SQLITE_INTERRUPT:          zName = \"SQLITE_INTERRUPT\";         break;\n      case SQLITE_IOERR:              zName = \"SQLITE_IOERR\";             break;\n      case SQLITE_IOERR_READ:         zName = \"SQLITE_IOERR_READ\";        break;\n      case SQLITE_IOERR_SHORT_READ:   zName = \"SQLITE_IOERR_SHORT_READ\";  break;\n      case SQLITE_IOERR_WRITE:        zName = \"SQLITE_IOERR_WRITE\";       break;\n      case SQLITE_IOERR_FSYNC:        zName = \"SQLITE_IOERR_FSYNC\";       break;\n      case SQLITE_IOERR_DIR_FSYNC:    zName = \"SQLITE_IOERR_DIR_FSYNC\";   break;\n      case SQLITE_IOERR_TRUNCATE:     zName = \"SQLITE_IOERR_TRUNCATE\";    break;\n      case SQLITE_IOERR_FSTAT:        zName = \"SQLITE_IOERR_FSTAT\";       break;\n      case SQLITE_IOERR_UNLOCK:       zName = \"SQLITE_IOERR_UNLOCK\";      break;\n      case SQLITE_IOERR_RDLOCK:       zName = \"SQLITE_IOERR_RDLOCK\";      break;\n      case SQLITE_IOERR_DELETE:       zName = \"SQLITE_IOERR_DELETE\";      break;\n      case SQLITE_IOERR_NOMEM:        zName = \"SQLITE_IOERR_NOMEM\";       break;\n      case SQLITE_IOERR_ACCESS:       zName = \"SQLITE_IOERR_ACCESS\";      break;\n      case SQLITE_IOERR_CHECKRESERVEDLOCK:\n                                zName = \"SQLITE_IOERR_CHECKRESERVEDLOCK\"; break;\n      case SQLITE_IOERR_LOCK:         zName = \"SQLITE_IOERR_LOCK\";        break;\n      case SQLITE_IOERR_CLOSE:        zName = \"SQLITE_IOERR_CLOSE\";       break;\n      case SQLITE_IOERR_DIR_CLOSE:    zName = \"SQLITE_IOERR_DIR_CLOSE\";   break;\n      case SQLITE_IOERR_SHMOPEN:      zName = \"SQLITE_IOERR_SHMOPEN\";     break;\n      case SQLITE_IOERR_SHMSIZE:      zName = \"SQLITE_IOERR_SHMSIZE\";     break;\n      case SQLITE_IOERR_SHMLOCK:      zName = \"SQLITE_IOERR_SHMLOCK\";     break;\n      case SQLITE_IOERR_SHMMAP:       zName = \"SQLITE_IOERR_SHMMAP\";      break;\n      case SQLITE_IOERR_SEEK:         zName = \"SQLITE_IOERR_SEEK\";        break;\n      case SQLITE_IOERR_DELETE_NOENT: zName = \"SQLITE_IOERR_DELETE_NOENT\";break;\n      case SQLITE_IOERR_MMAP:         zName = \"SQLITE_IOERR_MMAP\";        break;\n      case SQLITE_IOERR_GETTEMPPATH:  zName = \"SQLITE_IOERR_GETTEMPPATH\"; break;\n      case SQLITE_IOERR_CONVPATH:     zName = \"SQLITE_IOERR_CONVPATH\";    break;\n      case SQLITE_CORRUPT:            zName = \"SQLITE_CORRUPT\";           break;\n      case SQLITE_CORRUPT_VTAB:       zName = \"SQLITE_CORRUPT_VTAB\";      break;\n      case SQLITE_NOTFOUND:           zName = \"SQLITE_NOTFOUND\";          break;\n      case SQLITE_FULL:               zName = \"SQLITE_FULL\";              break;\n      case SQLITE_CANTOPEN:           zName = \"SQLITE_CANTOPEN\";          break;\n      case SQLITE_CANTOPEN_NOTEMPDIR: zName = \"SQLITE_CANTOPEN_NOTEMPDIR\";break;\n      case SQLITE_CANTOPEN_ISDIR:     zName = \"SQLITE_CANTOPEN_ISDIR\";    break;\n      case SQLITE_CANTOPEN_FULLPATH:  zName = \"SQLITE_CANTOPEN_FULLPATH\"; break;\n      case SQLITE_CANTOPEN_CONVPATH:  zName = \"SQLITE_CANTOPEN_CONVPATH\"; break;\n      case SQLITE_PROTOCOL:           zName = \"SQLITE_PROTOCOL\";          break;\n      case SQLITE_EMPTY:              zName = \"SQLITE_EMPTY\";             break;\n      case SQLITE_SCHEMA:             zName = \"SQLITE_SCHEMA\";            break;\n      case SQLITE_TOOBIG:             zName = \"SQLITE_TOOBIG\";            break;\n      case SQLITE_CONSTRAINT:         zName = \"SQLITE_CONSTRAINT\";        break;\n      case SQLITE_CONSTRAINT_UNIQUE:  zName = \"SQLITE_CONSTRAINT_UNIQUE\"; break;\n      case SQLITE_CONSTRAINT_TRIGGER: zName = \"SQLITE_CONSTRAINT_TRIGGER\";break;\n      case SQLITE_CONSTRAINT_FOREIGNKEY:\n                                zName = \"SQLITE_CONSTRAINT_FOREIGNKEY\";   break;\n      case SQLITE_CONSTRAINT_CHECK:   zName = \"SQLITE_CONSTRAINT_CHECK\";  break;\n      case SQLITE_CONSTRAINT_PRIMARYKEY:\n                                zName = \"SQLITE_CONSTRAINT_PRIMARYKEY\";   break;\n      case SQLITE_CONSTRAINT_NOTNULL: zName = \"SQLITE_CONSTRAINT_NOTNULL\";break;\n      case SQLITE_CONSTRAINT_COMMITHOOK:\n                                zName = \"SQLITE_CONSTRAINT_COMMITHOOK\";   break;\n      case SQLITE_CONSTRAINT_VTAB:    zName = \"SQLITE_CONSTRAINT_VTAB\";   break;\n      case SQLITE_CONSTRAINT_FUNCTION:\n                                zName = \"SQLITE_CONSTRAINT_FUNCTION\";     break;\n      case SQLITE_CONSTRAINT_ROWID:   zName = \"SQLITE_CONSTRAINT_ROWID\";  break;\n      case SQLITE_MISMATCH:           zName = \"SQLITE_MISMATCH\";          break;\n      case SQLITE_MISUSE:             zName = \"SQLITE_MISUSE\";            break;\n      case SQLITE_NOLFS:              zName = \"SQLITE_NOLFS\";             break;\n      case SQLITE_AUTH:               zName = \"SQLITE_AUTH\";              break;\n      case SQLITE_FORMAT:             zName = \"SQLITE_FORMAT\";            break;\n      case SQLITE_RANGE:              zName = \"SQLITE_RANGE\";             break;\n      case SQLITE_NOTADB:             zName = \"SQLITE_NOTADB\";            break;\n      case SQLITE_ROW:                zName = \"SQLITE_ROW\";               break;\n      case SQLITE_NOTICE:             zName = \"SQLITE_NOTICE\";            break;\n      case SQLITE_NOTICE_RECOVER_WAL: zName = \"SQLITE_NOTICE_RECOVER_WAL\";break;\n      case SQLITE_NOTICE_RECOVER_ROLLBACK:\n                                zName = \"SQLITE_NOTICE_RECOVER_ROLLBACK\"; break;\n      case SQLITE_WARNING:            zName = \"SQLITE_WARNING\";           break;\n      case SQLITE_WARNING_AUTOINDEX:  zName = \"SQLITE_WARNING_AUTOINDEX\"; break;\n      case SQLITE_DONE:               zName = \"SQLITE_DONE\";              break;\n    }\n  }\n  if( zName==0 ){\n    static char zBuf[50];\n    sqlite3_snprintf(sizeof(zBuf), zBuf, \"SQLITE_UNKNOWN(%d)\", origRc);\n    zName = zBuf;\n  }\n  return zName;\n}\n#endif\n\n/*\n** Return a static string that describes the kind of error specified in the\n** argument.\n*/\nSQLITE_PRIVATE const char *sqlite3ErrStr(int rc){\n  static const char* const aMsg[] = {\n    /* SQLITE_OK          */ \"not an error\",\n    /* SQLITE_ERROR       */ \"SQL logic error\",\n    /* SQLITE_INTERNAL    */ 0,\n    /* SQLITE_PERM        */ \"access permission denied\",\n    /* SQLITE_ABORT       */ \"query aborted\",\n    /* SQLITE_BUSY        */ \"database is locked\",\n    /* SQLITE_LOCKED      */ \"database table is locked\",\n    /* SQLITE_NOMEM       */ \"out of memory\",\n    /* SQLITE_READONLY    */ \"attempt to write a readonly database\",\n    /* SQLITE_INTERRUPT   */ \"interrupted\",\n    /* SQLITE_IOERR       */ \"disk I/O error\",\n    /* SQLITE_CORRUPT     */ \"database disk image is malformed\",\n    /* SQLITE_NOTFOUND    */ \"unknown operation\",\n    /* SQLITE_FULL        */ \"database or disk is full\",\n    /* SQLITE_CANTOPEN    */ \"unable to open database file\",\n    /* SQLITE_PROTOCOL    */ \"locking protocol\",\n    /* SQLITE_EMPTY       */ 0,\n    /* SQLITE_SCHEMA      */ \"database schema has changed\",\n    /* SQLITE_TOOBIG      */ \"string or blob too big\",\n    /* SQLITE_CONSTRAINT  */ \"constraint failed\",\n    /* SQLITE_MISMATCH    */ \"datatype mismatch\",\n    /* SQLITE_MISUSE      */ \"bad parameter or other API misuse\",\n#ifdef SQLITE_DISABLE_LFS\n    /* SQLITE_NOLFS       */ \"large file support is disabled\",\n#else\n    /* SQLITE_NOLFS       */ 0,\n#endif\n    /* SQLITE_AUTH        */ \"authorization denied\",\n    /* SQLITE_FORMAT      */ 0,\n    /* SQLITE_RANGE       */ \"column index out of range\",\n    /* SQLITE_NOTADB      */ \"file is not a database\",\n    /* SQLITE_NOTICE      */ \"notification message\",\n    /* SQLITE_WARNING     */ \"warning message\",\n  };\n  const char *zErr = \"unknown error\";\n  switch( rc ){\n    case SQLITE_ABORT_ROLLBACK: {\n      zErr = \"abort due to ROLLBACK\";\n      break;\n    }\n    case SQLITE_ROW: {\n      zErr = \"another row available\";\n      break;\n    }\n    case SQLITE_DONE: {\n      zErr = \"no more rows available\";\n      break;\n    }\n    default: {\n      rc &= 0xff;\n      if( ALWAYS(rc>=0) && rc<ArraySize(aMsg) && aMsg[rc]!=0 ){\n        zErr = aMsg[rc];\n      }\n      break;\n    }\n  }\n  return zErr;\n}\n\n/*\n** This routine implements a busy callback that sleeps and tries\n** again until a timeout value is reached.  The timeout value is\n** an integer number of milliseconds passed in as the first\n** argument.\n*/\nstatic int sqliteDefaultBusyCallback(\n void *ptr,               /* Database connection */\n int count                /* Number of times table has been busy */\n){\n#if SQLITE_OS_WIN || HAVE_USLEEP\n  static const u8 delays[] =\n     { 1, 2, 5, 10, 15, 20, 25, 25,  25,  50,  50, 100 };\n  static const u8 totals[] =\n     { 0, 1, 3,  8, 18, 33, 53, 78, 103, 128, 178, 228 };\n# define NDELAY ArraySize(delays)\n  sqlite3 *db = (sqlite3 *)ptr;\n  int timeout = db->busyTimeout;\n  int delay, prior;\n\n  assert( count>=0 );\n  if( count < NDELAY ){\n    delay = delays[count];\n    prior = totals[count];\n  }else{\n    delay = delays[NDELAY-1];\n    prior = totals[NDELAY-1] + delay*(count-(NDELAY-1));\n  }\n  if( prior + delay > timeout ){\n    delay = timeout - prior;\n    if( delay<=0 ) return 0;\n  }\n  sqlite3OsSleep(db->pVfs, delay*1000);\n  return 1;\n#else\n  sqlite3 *db = (sqlite3 *)ptr;\n  int timeout = ((sqlite3 *)ptr)->busyTimeout;\n  if( (count+1)*1000 > timeout ){\n    return 0;\n  }\n  sqlite3OsSleep(db->pVfs, 1000000);\n  return 1;\n#endif\n}\n\n/*\n** Invoke the given busy handler.\n**\n** This routine is called when an operation failed with a lock.\n** If this routine returns non-zero, the lock is retried.  If it\n** returns 0, the operation aborts with an SQLITE_BUSY error.\n*/\nSQLITE_PRIVATE int sqlite3InvokeBusyHandler(BusyHandler *p){\n  int rc;\n  if( NEVER(p==0) || p->xFunc==0 || p->nBusy<0 ) return 0;\n  rc = p->xFunc(p->pArg, p->nBusy);\n  if( rc==0 ){\n    p->nBusy = -1;\n  }else{\n    p->nBusy++;\n  }\n  return rc; \n}\n\n/*\n** This routine sets the busy callback for an Sqlite database to the\n** given callback function with the given argument.\n*/\nSQLITE_API int sqlite3_busy_handler(\n  sqlite3 *db,\n  int (*xBusy)(void*,int),\n  void *pArg\n){\n#ifdef SQLITE_ENABLE_API_ARMOR\n  if( !sqlite3SafetyCheckOk(db) ) return SQLITE_MISUSE_BKPT;\n#endif\n  sqlite3_mutex_enter(db->mutex);\n  db->busyHandler.xFunc = xBusy;\n  db->busyHandler.pArg = pArg;\n  db->busyHandler.nBusy = 0;\n  db->busyTimeout = 0;\n  sqlite3_mutex_leave(db->mutex);\n  return SQLITE_OK;\n}\n\n#ifndef SQLITE_OMIT_PROGRESS_CALLBACK\n/*\n** This routine sets the progress callback for an Sqlite database to the\n** given callback function with the given argument. The progress callback will\n** be invoked every nOps opcodes.\n*/\nSQLITE_API void sqlite3_progress_handler(\n  sqlite3 *db, \n  int nOps,\n  int (*xProgress)(void*), \n  void *pArg\n){\n#ifdef SQLITE_ENABLE_API_ARMOR\n  if( !sqlite3SafetyCheckOk(db) ){\n    (void)SQLITE_MISUSE_BKPT;\n    return;\n  }\n#endif\n  sqlite3_mutex_enter(db->mutex);\n  if( nOps>0 ){\n    db->xProgress = xProgress;\n    db->nProgressOps = (unsigned)nOps;\n    db->pProgressArg = pArg;\n  }else{\n    db->xProgress = 0;\n    db->nProgressOps = 0;\n    db->pProgressArg = 0;\n  }\n  sqlite3_mutex_leave(db->mutex);\n}\n#endif\n\n\n/*\n** This routine installs a default busy handler that waits for the\n** specified number of milliseconds before returning 0.\n*/\nSQLITE_API int sqlite3_busy_timeout(sqlite3 *db, int ms){\n#ifdef SQLITE_ENABLE_API_ARMOR\n  if( !sqlite3SafetyCheckOk(db) ) return SQLITE_MISUSE_BKPT;\n#endif\n  if( ms>0 ){\n    sqlite3_busy_handler(db, sqliteDefaultBusyCallback, (void*)db);\n    db->busyTimeout = ms;\n  }else{\n    sqlite3_busy_handler(db, 0, 0);\n  }\n  return SQLITE_OK;\n}\n\n/*\n** Cause any pending operation to stop at its earliest opportunity.\n*/\nSQLITE_API void sqlite3_interrupt(sqlite3 *db){\n#ifdef SQLITE_ENABLE_API_ARMOR\n  if( !sqlite3SafetyCheckOk(db) && (db==0 || db->magic!=SQLITE_MAGIC_ZOMBIE) ){\n    (void)SQLITE_MISUSE_BKPT;\n    return;\n  }\n#endif\n  db->u1.isInterrupted = 1;\n}\n\n\n/*\n** This function is exactly the same as sqlite3_create_function(), except\n** that it is designed to be called by internal code. The difference is\n** that if a malloc() fails in sqlite3_create_function(), an error code\n** is returned and the mallocFailed flag cleared. \n*/\nSQLITE_PRIVATE int sqlite3CreateFunc(\n  sqlite3 *db,\n  const char *zFunctionName,\n  int nArg,\n  int enc,\n  void *pUserData,\n  void (*xSFunc)(sqlite3_context*,int,sqlite3_value **),\n  void (*xStep)(sqlite3_context*,int,sqlite3_value **),\n  void (*xFinal)(sqlite3_context*),\n  FuncDestructor *pDestructor\n){\n  FuncDef *p;\n  int nName;\n  int extraFlags;\n\n  assert( sqlite3_mutex_held(db->mutex) );\n  if( zFunctionName==0 ||\n      (xSFunc && (xFinal || xStep)) || \n      (!xSFunc && (xFinal && !xStep)) ||\n      (!xSFunc && (!xFinal && xStep)) ||\n      (nArg<-1 || nArg>SQLITE_MAX_FUNCTION_ARG) ||\n      (255<(nName = sqlite3Strlen30( zFunctionName))) ){\n    return SQLITE_MISUSE_BKPT;\n  }\n\n  assert( SQLITE_FUNC_CONSTANT==SQLITE_DETERMINISTIC );\n  extraFlags = enc &  SQLITE_DETERMINISTIC;\n  enc &= (SQLITE_FUNC_ENCMASK|SQLITE_ANY);\n  \n#ifndef SQLITE_OMIT_UTF16\n  /* If SQLITE_UTF16 is specified as the encoding type, transform this\n  ** to one of SQLITE_UTF16LE or SQLITE_UTF16BE using the\n  ** SQLITE_UTF16NATIVE macro. SQLITE_UTF16 is not used internally.\n  **\n  ** If SQLITE_ANY is specified, add three versions of the function\n  ** to the hash table.\n  */\n  if( enc==SQLITE_UTF16 ){\n    enc = SQLITE_UTF16NATIVE;\n  }else if( enc==SQLITE_ANY ){\n    int rc;\n    rc = sqlite3CreateFunc(db, zFunctionName, nArg, SQLITE_UTF8|extraFlags,\n         pUserData, xSFunc, xStep, xFinal, pDestructor);\n    if( rc==SQLITE_OK ){\n      rc = sqlite3CreateFunc(db, zFunctionName, nArg, SQLITE_UTF16LE|extraFlags,\n          pUserData, xSFunc, xStep, xFinal, pDestructor);\n    }\n    if( rc!=SQLITE_OK ){\n      return rc;\n    }\n    enc = SQLITE_UTF16BE;\n  }\n#else\n  enc = SQLITE_UTF8;\n#endif\n  \n  /* Check if an existing function is being overridden or deleted. If so,\n  ** and there are active VMs, then return SQLITE_BUSY. If a function\n  ** is being overridden/deleted but there are no active VMs, allow the\n  ** operation to continue but invalidate all precompiled statements.\n  */\n  p = sqlite3FindFunction(db, zFunctionName, nArg, (u8)enc, 0);\n  if( p && (p->funcFlags & SQLITE_FUNC_ENCMASK)==enc && p->nArg==nArg ){\n    if( db->nVdbeActive ){\n      sqlite3ErrorWithMsg(db, SQLITE_BUSY, \n        \"unable to delete/modify user-function due to active statements\");\n      assert( !db->mallocFailed );\n      return SQLITE_BUSY;\n    }else{\n      sqlite3ExpirePreparedStatements(db);\n    }\n  }\n\n  p = sqlite3FindFunction(db, zFunctionName, nArg, (u8)enc, 1);\n  assert(p || db->mallocFailed);\n  if( !p ){\n    return SQLITE_NOMEM_BKPT;\n  }\n\n  /* If an older version of the function with a configured destructor is\n  ** being replaced invoke the destructor function here. */\n  functionDestroy(db, p);\n\n  if( pDestructor ){\n    pDestructor->nRef++;\n  }\n  p->u.pDestructor = pDestructor;\n  p->funcFlags = (p->funcFlags & SQLITE_FUNC_ENCMASK) | extraFlags;\n  testcase( p->funcFlags & SQLITE_DETERMINISTIC );\n  p->xSFunc = xSFunc ? xSFunc : xStep;\n  p->xFinalize = xFinal;\n  p->pUserData = pUserData;\n  p->nArg = (u16)nArg;\n  return SQLITE_OK;\n}\n\n/*\n** Create new user functions.\n*/\nSQLITE_API int sqlite3_create_function(\n  sqlite3 *db,\n  const char *zFunc,\n  int nArg,\n  int enc,\n  void *p,\n  void (*xSFunc)(sqlite3_context*,int,sqlite3_value **),\n  void (*xStep)(sqlite3_context*,int,sqlite3_value **),\n  void (*xFinal)(sqlite3_context*)\n){\n  return sqlite3_create_function_v2(db, zFunc, nArg, enc, p, xSFunc, xStep,\n                                    xFinal, 0);\n}\n\nSQLITE_API int sqlite3_create_function_v2(\n  sqlite3 *db,\n  const char *zFunc,\n  int nArg,\n  int enc,\n  void *p,\n  void (*xSFunc)(sqlite3_context*,int,sqlite3_value **),\n  void (*xStep)(sqlite3_context*,int,sqlite3_value **),\n  void (*xFinal)(sqlite3_context*),\n  void (*xDestroy)(void *)\n){\n  int rc = SQLITE_ERROR;\n  FuncDestructor *pArg = 0;\n\n#ifdef SQLITE_ENABLE_API_ARMOR\n  if( !sqlite3SafetyCheckOk(db) ){\n    return SQLITE_MISUSE_BKPT;\n  }\n#endif\n  sqlite3_mutex_enter(db->mutex);\n  if( xDestroy ){\n    pArg = (FuncDestructor *)sqlite3DbMallocZero(db, sizeof(FuncDestructor));\n    if( !pArg ){\n      xDestroy(p);\n      goto out;\n    }\n    pArg->xDestroy = xDestroy;\n    pArg->pUserData = p;\n  }\n  rc = sqlite3CreateFunc(db, zFunc, nArg, enc, p, xSFunc, xStep, xFinal, pArg);\n  if( pArg && pArg->nRef==0 ){\n    assert( rc!=SQLITE_OK );\n    xDestroy(p);\n    sqlite3DbFree(db, pArg);\n  }\n\n out:\n  rc = sqlite3ApiExit(db, rc);\n  sqlite3_mutex_leave(db->mutex);\n  return rc;\n}\n\n#ifndef SQLITE_OMIT_UTF16\nSQLITE_API int sqlite3_create_function16(\n  sqlite3 *db,\n  const void *zFunctionName,\n  int nArg,\n  int eTextRep,\n  void *p,\n  void (*xSFunc)(sqlite3_context*,int,sqlite3_value**),\n  void (*xStep)(sqlite3_context*,int,sqlite3_value**),\n  void (*xFinal)(sqlite3_context*)\n){\n  int rc;\n  char *zFunc8;\n\n#ifdef SQLITE_ENABLE_API_ARMOR\n  if( !sqlite3SafetyCheckOk(db) || zFunctionName==0 ) return SQLITE_MISUSE_BKPT;\n#endif\n  sqlite3_mutex_enter(db->mutex);\n  assert( !db->mallocFailed );\n  zFunc8 = sqlite3Utf16to8(db, zFunctionName, -1, SQLITE_UTF16NATIVE);\n  rc = sqlite3CreateFunc(db, zFunc8, nArg, eTextRep, p, xSFunc,xStep,xFinal,0);\n  sqlite3DbFree(db, zFunc8);\n  rc = sqlite3ApiExit(db, rc);\n  sqlite3_mutex_leave(db->mutex);\n  return rc;\n}\n#endif\n\n\n/*\n** Declare that a function has been overloaded by a virtual table.\n**\n** If the function already exists as a regular global function, then\n** this routine is a no-op.  If the function does not exist, then create\n** a new one that always throws a run-time error.  \n**\n** When virtual tables intend to provide an overloaded function, they\n** should call this routine to make sure the global function exists.\n** A global function must exist in order for name resolution to work\n** properly.\n*/\nSQLITE_API int sqlite3_overload_function(\n  sqlite3 *db,\n  const char *zName,\n  int nArg\n){\n  int rc = SQLITE_OK;\n\n#ifdef SQLITE_ENABLE_API_ARMOR\n  if( !sqlite3SafetyCheckOk(db) || zName==0 || nArg<-2 ){\n    return SQLITE_MISUSE_BKPT;\n  }\n#endif\n  sqlite3_mutex_enter(db->mutex);\n  if( sqlite3FindFunction(db, zName, nArg, SQLITE_UTF8, 0)==0 ){\n    rc = sqlite3CreateFunc(db, zName, nArg, SQLITE_UTF8,\n                           0, sqlite3InvalidFunction, 0, 0, 0);\n  }\n  rc = sqlite3ApiExit(db, rc);\n  sqlite3_mutex_leave(db->mutex);\n  return rc;\n}\n\n#ifndef SQLITE_OMIT_TRACE\n/*\n** Register a trace function.  The pArg from the previously registered trace\n** is returned.  \n**\n** A NULL trace function means that no tracing is executes.  A non-NULL\n** trace is a pointer to a function that is invoked at the start of each\n** SQL statement.\n*/\n#ifndef SQLITE_OMIT_DEPRECATED\nSQLITE_API void *sqlite3_trace(sqlite3 *db, void(*xTrace)(void*,const char*), void *pArg){\n  void *pOld;\n\n#ifdef SQLITE_ENABLE_API_ARMOR\n  if( !sqlite3SafetyCheckOk(db) ){\n    (void)SQLITE_MISUSE_BKPT;\n    return 0;\n  }\n#endif\n  sqlite3_mutex_enter(db->mutex);\n  pOld = db->pTraceArg;\n  db->mTrace = xTrace ? SQLITE_TRACE_LEGACY : 0;\n  db->xTrace = (int(*)(u32,void*,void*,void*))xTrace;\n  db->pTraceArg = pArg;\n  sqlite3_mutex_leave(db->mutex);\n  return pOld;\n}\n#endif /* SQLITE_OMIT_DEPRECATED */\n\n/* Register a trace callback using the version-2 interface.\n*/\nSQLITE_API int sqlite3_trace_v2(\n  sqlite3 *db,                               /* Trace this connection */\n  unsigned mTrace,                           /* Mask of events to be traced */\n  int(*xTrace)(unsigned,void*,void*,void*),  /* Callback to invoke */\n  void *pArg                                 /* Context */\n){\n#ifdef SQLITE_ENABLE_API_ARMOR\n  if( !sqlite3SafetyCheckOk(db) ){\n    return SQLITE_MISUSE_BKPT;\n  }\n#endif\n  sqlite3_mutex_enter(db->mutex);\n  if( mTrace==0 ) xTrace = 0;\n  if( xTrace==0 ) mTrace = 0;\n  db->mTrace = mTrace;\n  db->xTrace = xTrace;\n  db->pTraceArg = pArg;\n  sqlite3_mutex_leave(db->mutex);\n  return SQLITE_OK;\n}\n\n#ifndef SQLITE_OMIT_DEPRECATED\n/*\n** Register a profile function.  The pArg from the previously registered \n** profile function is returned.  \n**\n** A NULL profile function means that no profiling is executes.  A non-NULL\n** profile is a pointer to a function that is invoked at the conclusion of\n** each SQL statement that is run.\n*/\nSQLITE_API void *sqlite3_profile(\n  sqlite3 *db,\n  void (*xProfile)(void*,const char*,sqlite_uint64),\n  void *pArg\n){\n  void *pOld;\n\n#ifdef SQLITE_ENABLE_API_ARMOR\n  if( !sqlite3SafetyCheckOk(db) ){\n    (void)SQLITE_MISUSE_BKPT;\n    return 0;\n  }\n#endif\n  sqlite3_mutex_enter(db->mutex);\n  pOld = db->pProfileArg;\n  db->xProfile = xProfile;\n  db->pProfileArg = pArg;\n  sqlite3_mutex_leave(db->mutex);\n  return pOld;\n}\n#endif /* SQLITE_OMIT_DEPRECATED */\n#endif /* SQLITE_OMIT_TRACE */\n\n/*\n** Register a function to be invoked when a transaction commits.\n** If the invoked function returns non-zero, then the commit becomes a\n** rollback.\n*/\nSQLITE_API void *sqlite3_commit_hook(\n  sqlite3 *db,              /* Attach the hook to this database */\n  int (*xCallback)(void*),  /* Function to invoke on each commit */\n  void *pArg                /* Argument to the function */\n){\n  void *pOld;\n\n#ifdef SQLITE_ENABLE_API_ARMOR\n  if( !sqlite3SafetyCheckOk(db) ){\n    (void)SQLITE_MISUSE_BKPT;\n    return 0;\n  }\n#endif\n  sqlite3_mutex_enter(db->mutex);\n  pOld = db->pCommitArg;\n  db->xCommitCallback = xCallback;\n  db->pCommitArg = pArg;\n  sqlite3_mutex_leave(db->mutex);\n  return pOld;\n}\n\n/*\n** Register a callback to be invoked each time a row is updated,\n** inserted or deleted using this database connection.\n*/\nSQLITE_API void *sqlite3_update_hook(\n  sqlite3 *db,              /* Attach the hook to this database */\n  void (*xCallback)(void*,int,char const *,char const *,sqlite_int64),\n  void *pArg                /* Argument to the function */\n){\n  void *pRet;\n\n#ifdef SQLITE_ENABLE_API_ARMOR\n  if( !sqlite3SafetyCheckOk(db) ){\n    (void)SQLITE_MISUSE_BKPT;\n    return 0;\n  }\n#endif\n  sqlite3_mutex_enter(db->mutex);\n  pRet = db->pUpdateArg;\n  db->xUpdateCallback = xCallback;\n  db->pUpdateArg = pArg;\n  sqlite3_mutex_leave(db->mutex);\n  return pRet;\n}\n\n/*\n** Register a callback to be invoked each time a transaction is rolled\n** back by this database connection.\n*/\nSQLITE_API void *sqlite3_rollback_hook(\n  sqlite3 *db,              /* Attach the hook to this database */\n  void (*xCallback)(void*), /* Callback function */\n  void *pArg                /* Argument to the function */\n){\n  void *pRet;\n\n#ifdef SQLITE_ENABLE_API_ARMOR\n  if( !sqlite3SafetyCheckOk(db) ){\n    (void)SQLITE_MISUSE_BKPT;\n    return 0;\n  }\n#endif\n  sqlite3_mutex_enter(db->mutex);\n  pRet = db->pRollbackArg;\n  db->xRollbackCallback = xCallback;\n  db->pRollbackArg = pArg;\n  sqlite3_mutex_leave(db->mutex);\n  return pRet;\n}\n\n#ifdef SQLITE_ENABLE_PREUPDATE_HOOK\n/*\n** Register a callback to be invoked each time a row is updated,\n** inserted or deleted using this database connection.\n*/\nSQLITE_API void *sqlite3_preupdate_hook(\n  sqlite3 *db,              /* Attach the hook to this database */\n  void(*xCallback)(         /* Callback function */\n    void*,sqlite3*,int,char const*,char const*,sqlite3_int64,sqlite3_int64),\n  void *pArg                /* First callback argument */\n){\n  void *pRet;\n  sqlite3_mutex_enter(db->mutex);\n  pRet = db->pPreUpdateArg;\n  db->xPreUpdateCallback = xCallback;\n  db->pPreUpdateArg = pArg;\n  sqlite3_mutex_leave(db->mutex);\n  return pRet;\n}\n#endif /* SQLITE_ENABLE_PREUPDATE_HOOK */\n\n#ifndef SQLITE_OMIT_WAL\n/*\n** The sqlite3_wal_hook() callback registered by sqlite3_wal_autocheckpoint().\n** Invoke sqlite3_wal_checkpoint if the number of frames in the log file\n** is greater than sqlite3.pWalArg cast to an integer (the value configured by\n** wal_autocheckpoint()).\n*/ \nSQLITE_PRIVATE int sqlite3WalDefaultHook(\n  void *pClientData,     /* Argument */\n  sqlite3 *db,           /* Connection */\n  const char *zDb,       /* Database */\n  int nFrame             /* Size of WAL */\n){\n  if( nFrame>=SQLITE_PTR_TO_INT(pClientData) ){\n    sqlite3BeginBenignMalloc();\n    sqlite3_wal_checkpoint(db, zDb);\n    sqlite3EndBenignMalloc();\n  }\n  return SQLITE_OK;\n}\n#endif /* SQLITE_OMIT_WAL */\n\n/*\n** Configure an sqlite3_wal_hook() callback to automatically checkpoint\n** a database after committing a transaction if there are nFrame or\n** more frames in the log file. Passing zero or a negative value as the\n** nFrame parameter disables automatic checkpoints entirely.\n**\n** The callback registered by this function replaces any existing callback\n** registered using sqlite3_wal_hook(). Likewise, registering a callback\n** using sqlite3_wal_hook() disables the automatic checkpoint mechanism\n** configured by this function.\n*/\nSQLITE_API int sqlite3_wal_autocheckpoint(sqlite3 *db, int nFrame){\n#ifdef SQLITE_OMIT_WAL\n  UNUSED_PARAMETER(db);\n  UNUSED_PARAMETER(nFrame);\n#else\n#ifdef SQLITE_ENABLE_API_ARMOR\n  if( !sqlite3SafetyCheckOk(db) ) return SQLITE_MISUSE_BKPT;\n#endif\n  if( nFrame>0 ){\n    sqlite3_wal_hook(db, sqlite3WalDefaultHook, SQLITE_INT_TO_PTR(nFrame));\n  }else{\n    sqlite3_wal_hook(db, 0, 0);\n  }\n#endif\n  return SQLITE_OK;\n}\n\n/*\n** Register a callback to be invoked each time a transaction is written\n** into the write-ahead-log by this database connection.\n*/\nSQLITE_API void *sqlite3_wal_hook(\n  sqlite3 *db,                    /* Attach the hook to this db handle */\n  int(*xCallback)(void *, sqlite3*, const char*, int),\n  void *pArg                      /* First argument passed to xCallback() */\n){\n#ifndef SQLITE_OMIT_WAL\n  void *pRet;\n#ifdef SQLITE_ENABLE_API_ARMOR\n  if( !sqlite3SafetyCheckOk(db) ){\n    (void)SQLITE_MISUSE_BKPT;\n    return 0;\n  }\n#endif\n  sqlite3_mutex_enter(db->mutex);\n  pRet = db->pWalArg;\n  db->xWalCallback = xCallback;\n  db->pWalArg = pArg;\n  sqlite3_mutex_leave(db->mutex);\n  return pRet;\n#else\n  return 0;\n#endif\n}\n\n/*\n** Checkpoint database zDb.\n*/\nSQLITE_API int sqlite3_wal_checkpoint_v2(\n  sqlite3 *db,                    /* Database handle */\n  const char *zDb,                /* Name of attached database (or NULL) */\n  int eMode,                      /* SQLITE_CHECKPOINT_* value */\n  int *pnLog,                     /* OUT: Size of WAL log in frames */\n  int *pnCkpt                     /* OUT: Total number of frames checkpointed */\n){\n#ifdef SQLITE_OMIT_WAL\n  return SQLITE_OK;\n#else\n  int rc;                         /* Return code */\n  int iDb = SQLITE_MAX_ATTACHED;  /* sqlite3.aDb[] index of db to checkpoint */\n\n#ifdef SQLITE_ENABLE_API_ARMOR\n  if( !sqlite3SafetyCheckOk(db) ) return SQLITE_MISUSE_BKPT;\n#endif\n\n  /* Initialize the output variables to -1 in case an error occurs. */\n  if( pnLog ) *pnLog = -1;\n  if( pnCkpt ) *pnCkpt = -1;\n\n  assert( SQLITE_CHECKPOINT_PASSIVE==0 );\n  assert( SQLITE_CHECKPOINT_FULL==1 );\n  assert( SQLITE_CHECKPOINT_RESTART==2 );\n  assert( SQLITE_CHECKPOINT_TRUNCATE==3 );\n  if( eMode<SQLITE_CHECKPOINT_PASSIVE || eMode>SQLITE_CHECKPOINT_TRUNCATE ){\n    /* EVIDENCE-OF: R-03996-12088 The M parameter must be a valid checkpoint\n    ** mode: */\n    return SQLITE_MISUSE;\n  }\n\n  sqlite3_mutex_enter(db->mutex);\n  if( zDb && zDb[0] ){\n    iDb = sqlite3FindDbName(db, zDb);\n  }\n  if( iDb<0 ){\n    rc = SQLITE_ERROR;\n    sqlite3ErrorWithMsg(db, SQLITE_ERROR, \"unknown database: %s\", zDb);\n  }else{\n    db->busyHandler.nBusy = 0;\n    rc = sqlite3Checkpoint(db, iDb, eMode, pnLog, pnCkpt);\n    sqlite3Error(db, rc);\n  }\n  rc = sqlite3ApiExit(db, rc);\n\n  /* If there are no active statements, clear the interrupt flag at this\n  ** point.  */\n  if( db->nVdbeActive==0 ){\n    db->u1.isInterrupted = 0;\n  }\n\n  sqlite3_mutex_leave(db->mutex);\n  return rc;\n#endif\n}\n\n\n/*\n** Checkpoint database zDb. If zDb is NULL, or if the buffer zDb points\n** to contains a zero-length string, all attached databases are \n** checkpointed.\n*/\nSQLITE_API int sqlite3_wal_checkpoint(sqlite3 *db, const char *zDb){\n  /* EVIDENCE-OF: R-41613-20553 The sqlite3_wal_checkpoint(D,X) is equivalent to\n  ** sqlite3_wal_checkpoint_v2(D,X,SQLITE_CHECKPOINT_PASSIVE,0,0). */\n  return sqlite3_wal_checkpoint_v2(db,zDb,SQLITE_CHECKPOINT_PASSIVE,0,0);\n}\n\n#ifndef SQLITE_OMIT_WAL\n/*\n** Run a checkpoint on database iDb. This is a no-op if database iDb is\n** not currently open in WAL mode.\n**\n** If a transaction is open on the database being checkpointed, this \n** function returns SQLITE_LOCKED and a checkpoint is not attempted. If \n** an error occurs while running the checkpoint, an SQLite error code is \n** returned (i.e. SQLITE_IOERR). Otherwise, SQLITE_OK.\n**\n** The mutex on database handle db should be held by the caller. The mutex\n** associated with the specific b-tree being checkpointed is taken by\n** this function while the checkpoint is running.\n**\n** If iDb is passed SQLITE_MAX_ATTACHED, then all attached databases are\n** checkpointed. If an error is encountered it is returned immediately -\n** no attempt is made to checkpoint any remaining databases.\n**\n** Parameter eMode is one of SQLITE_CHECKPOINT_PASSIVE, FULL, RESTART\n** or TRUNCATE.\n*/\nSQLITE_PRIVATE int sqlite3Checkpoint(sqlite3 *db, int iDb, int eMode, int *pnLog, int *pnCkpt){\n  int rc = SQLITE_OK;             /* Return code */\n  int i;                          /* Used to iterate through attached dbs */\n  int bBusy = 0;                  /* True if SQLITE_BUSY has been encountered */\n\n  assert( sqlite3_mutex_held(db->mutex) );\n  assert( !pnLog || *pnLog==-1 );\n  assert( !pnCkpt || *pnCkpt==-1 );\n\n  for(i=0; i<db->nDb && rc==SQLITE_OK; i++){\n    if( i==iDb || iDb==SQLITE_MAX_ATTACHED ){\n      rc = sqlite3BtreeCheckpoint(db->aDb[i].pBt, eMode, pnLog, pnCkpt);\n      pnLog = 0;\n      pnCkpt = 0;\n      if( rc==SQLITE_BUSY ){\n        bBusy = 1;\n        rc = SQLITE_OK;\n      }\n    }\n  }\n\n  return (rc==SQLITE_OK && bBusy) ? SQLITE_BUSY : rc;\n}\n#endif /* SQLITE_OMIT_WAL */\n\n/*\n** This function returns true if main-memory should be used instead of\n** a temporary file for transient pager files and statement journals.\n** The value returned depends on the value of db->temp_store (runtime\n** parameter) and the compile time value of SQLITE_TEMP_STORE. The\n** following table describes the relationship between these two values\n** and this functions return value.\n**\n**   SQLITE_TEMP_STORE     db->temp_store     Location of temporary database\n**   -----------------     --------------     ------------------------------\n**   0                     any                file      (return 0)\n**   1                     1                  file      (return 0)\n**   1                     2                  memory    (return 1)\n**   1                     0                  file      (return 0)\n**   2                     1                  file      (return 0)\n**   2                     2                  memory    (return 1)\n**   2                     0                  memory    (return 1)\n**   3                     any                memory    (return 1)\n*/\nSQLITE_PRIVATE int sqlite3TempInMemory(const sqlite3 *db){\n#if SQLITE_TEMP_STORE==1\n  return ( db->temp_store==2 );\n#endif\n#if SQLITE_TEMP_STORE==2\n  return ( db->temp_store!=1 );\n#endif\n#if SQLITE_TEMP_STORE==3\n  UNUSED_PARAMETER(db);\n  return 1;\n#endif\n#if SQLITE_TEMP_STORE<1 || SQLITE_TEMP_STORE>3\n  UNUSED_PARAMETER(db);\n  return 0;\n#endif\n}\n\n/*\n** Return UTF-8 encoded English language explanation of the most recent\n** error.\n*/\nSQLITE_API const char *sqlite3_errmsg(sqlite3 *db){\n  const char *z;\n  if( !db ){\n    return sqlite3ErrStr(SQLITE_NOMEM_BKPT);\n  }\n  if( !sqlite3SafetyCheckSickOrOk(db) ){\n    return sqlite3ErrStr(SQLITE_MISUSE_BKPT);\n  }\n  sqlite3_mutex_enter(db->mutex);\n  if( db->mallocFailed ){\n    z = sqlite3ErrStr(SQLITE_NOMEM_BKPT);\n  }else{\n    testcase( db->pErr==0 );\n    z = (char*)sqlite3_value_text(db->pErr);\n    assert( !db->mallocFailed );\n    if( z==0 ){\n      z = sqlite3ErrStr(db->errCode);\n    }\n  }\n  sqlite3_mutex_leave(db->mutex);\n  return z;\n}\n\n#ifndef SQLITE_OMIT_UTF16\n/*\n** Return UTF-16 encoded English language explanation of the most recent\n** error.\n*/\nSQLITE_API const void *sqlite3_errmsg16(sqlite3 *db){\n  static const u16 outOfMem[] = {\n    'o', 'u', 't', ' ', 'o', 'f', ' ', 'm', 'e', 'm', 'o', 'r', 'y', 0\n  };\n  static const u16 misuse[] = {\n    'b', 'a', 'd', ' ', 'p', 'a', 'r', 'a', 'm', 'e', 't', 'e', 'r', ' ',\n    'o', 'r', ' ', 'o', 't', 'h', 'e', 'r', ' ', 'A', 'P', 'I', ' ',\n    'm', 'i', 's', 'u', 's', 'e', 0\n  };\n\n  const void *z;\n  if( !db ){\n    return (void *)outOfMem;\n  }\n  if( !sqlite3SafetyCheckSickOrOk(db) ){\n    return (void *)misuse;\n  }\n  sqlite3_mutex_enter(db->mutex);\n  if( db->mallocFailed ){\n    z = (void *)outOfMem;\n  }else{\n    z = sqlite3_value_text16(db->pErr);\n    if( z==0 ){\n      sqlite3ErrorWithMsg(db, db->errCode, sqlite3ErrStr(db->errCode));\n      z = sqlite3_value_text16(db->pErr);\n    }\n    /* A malloc() may have failed within the call to sqlite3_value_text16()\n    ** above. If this is the case, then the db->mallocFailed flag needs to\n    ** be cleared before returning. Do this directly, instead of via\n    ** sqlite3ApiExit(), to avoid setting the database handle error message.\n    */\n    sqlite3OomClear(db);\n  }\n  sqlite3_mutex_leave(db->mutex);\n  return z;\n}\n#endif /* SQLITE_OMIT_UTF16 */\n\n/*\n** Return the most recent error code generated by an SQLite routine. If NULL is\n** passed to this function, we assume a malloc() failed during sqlite3_open().\n*/\nSQLITE_API int sqlite3_errcode(sqlite3 *db){\n  if( db && !sqlite3SafetyCheckSickOrOk(db) ){\n    return SQLITE_MISUSE_BKPT;\n  }\n  if( !db || db->mallocFailed ){\n    return SQLITE_NOMEM_BKPT;\n  }\n  return db->errCode & db->errMask;\n}\nSQLITE_API int sqlite3_extended_errcode(sqlite3 *db){\n  if( db && !sqlite3SafetyCheckSickOrOk(db) ){\n    return SQLITE_MISUSE_BKPT;\n  }\n  if( !db || db->mallocFailed ){\n    return SQLITE_NOMEM_BKPT;\n  }\n  return db->errCode;\n}\nSQLITE_API int sqlite3_system_errno(sqlite3 *db){\n  return db ? db->iSysErrno : 0;\n}  \n\n/*\n** Return a string that describes the kind of error specified in the\n** argument.  For now, this simply calls the internal sqlite3ErrStr()\n** function.\n*/\nSQLITE_API const char *sqlite3_errstr(int rc){\n  return sqlite3ErrStr(rc);\n}\n\n/*\n** Create a new collating function for database \"db\".  The name is zName\n** and the encoding is enc.\n*/\nstatic int createCollation(\n  sqlite3* db,\n  const char *zName, \n  u8 enc,\n  void* pCtx,\n  int(*xCompare)(void*,int,const void*,int,const void*),\n  void(*xDel)(void*)\n){\n  CollSeq *pColl;\n  int enc2;\n  \n  assert( sqlite3_mutex_held(db->mutex) );\n\n  /* If SQLITE_UTF16 is specified as the encoding type, transform this\n  ** to one of SQLITE_UTF16LE or SQLITE_UTF16BE using the\n  ** SQLITE_UTF16NATIVE macro. SQLITE_UTF16 is not used internally.\n  */\n  enc2 = enc;\n  testcase( enc2==SQLITE_UTF16 );\n  testcase( enc2==SQLITE_UTF16_ALIGNED );\n  if( enc2==SQLITE_UTF16 || enc2==SQLITE_UTF16_ALIGNED ){\n    enc2 = SQLITE_UTF16NATIVE;\n  }\n  if( enc2<SQLITE_UTF8 || enc2>SQLITE_UTF16BE ){\n    return SQLITE_MISUSE_BKPT;\n  }\n\n  /* Check if this call is removing or replacing an existing collation \n  ** sequence. If so, and there are active VMs, return busy. If there\n  ** are no active VMs, invalidate any pre-compiled statements.\n  */\n  pColl = sqlite3FindCollSeq(db, (u8)enc2, zName, 0);\n  if( pColl && pColl->xCmp ){\n    if( db->nVdbeActive ){\n      sqlite3ErrorWithMsg(db, SQLITE_BUSY, \n        \"unable to delete/modify collation sequence due to active statements\");\n      return SQLITE_BUSY;\n    }\n    sqlite3ExpirePreparedStatements(db);\n\n    /* If collation sequence pColl was created directly by a call to\n    ** sqlite3_create_collation, and not generated by synthCollSeq(),\n    ** then any copies made by synthCollSeq() need to be invalidated.\n    ** Also, collation destructor - CollSeq.xDel() - function may need\n    ** to be called.\n    */ \n    if( (pColl->enc & ~SQLITE_UTF16_ALIGNED)==enc2 ){\n      CollSeq *aColl = sqlite3HashFind(&db->aCollSeq, zName);\n      int j;\n      for(j=0; j<3; j++){\n        CollSeq *p = &aColl[j];\n        if( p->enc==pColl->enc ){\n          if( p->xDel ){\n            p->xDel(p->pUser);\n          }\n          p->xCmp = 0;\n        }\n      }\n    }\n  }\n\n  pColl = sqlite3FindCollSeq(db, (u8)enc2, zName, 1);\n  if( pColl==0 ) return SQLITE_NOMEM_BKPT;\n  pColl->xCmp = xCompare;\n  pColl->pUser = pCtx;\n  pColl->xDel = xDel;\n  pColl->enc = (u8)(enc2 | (enc & SQLITE_UTF16_ALIGNED));\n  sqlite3Error(db, SQLITE_OK);\n  return SQLITE_OK;\n}\n\n\n/*\n** This array defines hard upper bounds on limit values.  The\n** initializer must be kept in sync with the SQLITE_LIMIT_*\n** #defines in sqlite3.h.\n*/\nstatic const int aHardLimit[] = {\n  SQLITE_MAX_LENGTH,\n  SQLITE_MAX_SQL_LENGTH,\n  SQLITE_MAX_COLUMN,\n  SQLITE_MAX_EXPR_DEPTH,\n  SQLITE_MAX_COMPOUND_SELECT,\n  SQLITE_MAX_VDBE_OP,\n  SQLITE_MAX_FUNCTION_ARG,\n  SQLITE_MAX_ATTACHED,\n  SQLITE_MAX_LIKE_PATTERN_LENGTH,\n  SQLITE_MAX_VARIABLE_NUMBER,      /* IMP: R-38091-32352 */\n  SQLITE_MAX_TRIGGER_DEPTH,\n  SQLITE_MAX_WORKER_THREADS,\n};\n\n/*\n** Make sure the hard limits are set to reasonable values\n*/\n#if SQLITE_MAX_LENGTH<100\n# error SQLITE_MAX_LENGTH must be at least 100\n#endif\n#if SQLITE_MAX_SQL_LENGTH<100\n# error SQLITE_MAX_SQL_LENGTH must be at least 100\n#endif\n#if SQLITE_MAX_SQL_LENGTH>SQLITE_MAX_LENGTH\n# error SQLITE_MAX_SQL_LENGTH must not be greater than SQLITE_MAX_LENGTH\n#endif\n#if SQLITE_MAX_COMPOUND_SELECT<2\n# error SQLITE_MAX_COMPOUND_SELECT must be at least 2\n#endif\n#if SQLITE_MAX_VDBE_OP<40\n# error SQLITE_MAX_VDBE_OP must be at least 40\n#endif\n#if SQLITE_MAX_FUNCTION_ARG<0 || SQLITE_MAX_FUNCTION_ARG>127\n# error SQLITE_MAX_FUNCTION_ARG must be between 0 and 127\n#endif\n#if SQLITE_MAX_ATTACHED<0 || SQLITE_MAX_ATTACHED>125\n# error SQLITE_MAX_ATTACHED must be between 0 and 125\n#endif\n#if SQLITE_MAX_LIKE_PATTERN_LENGTH<1\n# error SQLITE_MAX_LIKE_PATTERN_LENGTH must be at least 1\n#endif\n#if SQLITE_MAX_COLUMN>32767\n# error SQLITE_MAX_COLUMN must not exceed 32767\n#endif\n#if SQLITE_MAX_TRIGGER_DEPTH<1\n# error SQLITE_MAX_TRIGGER_DEPTH must be at least 1\n#endif\n#if SQLITE_MAX_WORKER_THREADS<0 || SQLITE_MAX_WORKER_THREADS>50\n# error SQLITE_MAX_WORKER_THREADS must be between 0 and 50\n#endif\n\n\n/*\n** Change the value of a limit.  Report the old value.\n** If an invalid limit index is supplied, report -1.\n** Make no changes but still report the old value if the\n** new limit is negative.\n**\n** A new lower limit does not shrink existing constructs.\n** It merely prevents new constructs that exceed the limit\n** from forming.\n*/\nSQLITE_API int sqlite3_limit(sqlite3 *db, int limitId, int newLimit){\n  int oldLimit;\n\n#ifdef SQLITE_ENABLE_API_ARMOR\n  if( !sqlite3SafetyCheckOk(db) ){\n    (void)SQLITE_MISUSE_BKPT;\n    return -1;\n  }\n#endif\n\n  /* EVIDENCE-OF: R-30189-54097 For each limit category SQLITE_LIMIT_NAME\n  ** there is a hard upper bound set at compile-time by a C preprocessor\n  ** macro called SQLITE_MAX_NAME. (The \"_LIMIT_\" in the name is changed to\n  ** \"_MAX_\".)\n  */\n  assert( aHardLimit[SQLITE_LIMIT_LENGTH]==SQLITE_MAX_LENGTH );\n  assert( aHardLimit[SQLITE_LIMIT_SQL_LENGTH]==SQLITE_MAX_SQL_LENGTH );\n  assert( aHardLimit[SQLITE_LIMIT_COLUMN]==SQLITE_MAX_COLUMN );\n  assert( aHardLimit[SQLITE_LIMIT_EXPR_DEPTH]==SQLITE_MAX_EXPR_DEPTH );\n  assert( aHardLimit[SQLITE_LIMIT_COMPOUND_SELECT]==SQLITE_MAX_COMPOUND_SELECT);\n  assert( aHardLimit[SQLITE_LIMIT_VDBE_OP]==SQLITE_MAX_VDBE_OP );\n  assert( aHardLimit[SQLITE_LIMIT_FUNCTION_ARG]==SQLITE_MAX_FUNCTION_ARG );\n  assert( aHardLimit[SQLITE_LIMIT_ATTACHED]==SQLITE_MAX_ATTACHED );\n  assert( aHardLimit[SQLITE_LIMIT_LIKE_PATTERN_LENGTH]==\n                                               SQLITE_MAX_LIKE_PATTERN_LENGTH );\n  assert( aHardLimit[SQLITE_LIMIT_VARIABLE_NUMBER]==SQLITE_MAX_VARIABLE_NUMBER);\n  assert( aHardLimit[SQLITE_LIMIT_TRIGGER_DEPTH]==SQLITE_MAX_TRIGGER_DEPTH );\n  assert( aHardLimit[SQLITE_LIMIT_WORKER_THREADS]==SQLITE_MAX_WORKER_THREADS );\n  assert( SQLITE_LIMIT_WORKER_THREADS==(SQLITE_N_LIMIT-1) );\n\n\n  if( limitId<0 || limitId>=SQLITE_N_LIMIT ){\n    return -1;\n  }\n  oldLimit = db->aLimit[limitId];\n  if( newLimit>=0 ){                   /* IMP: R-52476-28732 */\n    if( newLimit>aHardLimit[limitId] ){\n      newLimit = aHardLimit[limitId];  /* IMP: R-51463-25634 */\n    }\n    db->aLimit[limitId] = newLimit;\n  }\n  return oldLimit;                     /* IMP: R-53341-35419 */\n}\n\n/*\n** This function is used to parse both URIs and non-URI filenames passed by the\n** user to API functions sqlite3_open() or sqlite3_open_v2(), and for database\n** URIs specified as part of ATTACH statements.\n**\n** The first argument to this function is the name of the VFS to use (or\n** a NULL to signify the default VFS) if the URI does not contain a \"vfs=xxx\"\n** query parameter. The second argument contains the URI (or non-URI filename)\n** itself. When this function is called the *pFlags variable should contain\n** the default flags to open the database handle with. The value stored in\n** *pFlags may be updated before returning if the URI filename contains \n** \"cache=xxx\" or \"mode=xxx\" query parameters.\n**\n** If successful, SQLITE_OK is returned. In this case *ppVfs is set to point to\n** the VFS that should be used to open the database file. *pzFile is set to\n** point to a buffer containing the name of the file to open. It is the \n** responsibility of the caller to eventually call sqlite3_free() to release\n** this buffer.\n**\n** If an error occurs, then an SQLite error code is returned and *pzErrMsg\n** may be set to point to a buffer containing an English language error \n** message. It is the responsibility of the caller to eventually release\n** this buffer by calling sqlite3_free().\n*/\nSQLITE_PRIVATE int sqlite3ParseUri(\n  const char *zDefaultVfs,        /* VFS to use if no \"vfs=xxx\" query option */\n  const char *zUri,               /* Nul-terminated URI to parse */\n  unsigned int *pFlags,           /* IN/OUT: SQLITE_OPEN_XXX flags */\n  sqlite3_vfs **ppVfs,            /* OUT: VFS to use */ \n  char **pzFile,                  /* OUT: Filename component of URI */\n  char **pzErrMsg                 /* OUT: Error message (if rc!=SQLITE_OK) */\n){\n  int rc = SQLITE_OK;\n  unsigned int flags = *pFlags;\n  const char *zVfs = zDefaultVfs;\n  char *zFile;\n  char c;\n  int nUri = sqlite3Strlen30(zUri);\n\n  assert( *pzErrMsg==0 );\n\n  if( ((flags & SQLITE_OPEN_URI)             /* IMP: R-48725-32206 */\n            || sqlite3GlobalConfig.bOpenUri) /* IMP: R-51689-46548 */\n   && nUri>=5 && memcmp(zUri, \"file:\", 5)==0 /* IMP: R-57884-37496 */\n  ){\n    char *zOpt;\n    int eState;                   /* Parser state when parsing URI */\n    int iIn;                      /* Input character index */\n    int iOut = 0;                 /* Output character index */\n    u64 nByte = nUri+2;           /* Bytes of space to allocate */\n\n    /* Make sure the SQLITE_OPEN_URI flag is set to indicate to the VFS xOpen \n    ** method that there may be extra parameters following the file-name.  */\n    flags |= SQLITE_OPEN_URI;\n\n    for(iIn=0; iIn<nUri; iIn++) nByte += (zUri[iIn]=='&');\n    zFile = sqlite3_malloc64(nByte);\n    if( !zFile ) return SQLITE_NOMEM_BKPT;\n\n    iIn = 5;\n#ifdef SQLITE_ALLOW_URI_AUTHORITY\n    if( strncmp(zUri+5, \"///\", 3)==0 ){\n      iIn = 7;\n      /* The following condition causes URIs with five leading / characters\n      ** like file://///host/path to be converted into UNCs like //host/path.\n      ** The correct URI for that UNC has only two or four leading / characters\n      ** file://host/path or file:////host/path.  But 5 leading slashes is a \n      ** common error, we are told, so we handle it as a special case. */\n      if( strncmp(zUri+7, \"///\", 3)==0 ){ iIn++; }\n    }else if( strncmp(zUri+5, \"//localhost/\", 12)==0 ){\n      iIn = 16;\n    }\n#else\n    /* Discard the scheme and authority segments of the URI. */\n    if( zUri[5]=='/' && zUri[6]=='/' ){\n      iIn = 7;\n      while( zUri[iIn] && zUri[iIn]!='/' ) iIn++;\n      if( iIn!=7 && (iIn!=16 || memcmp(\"localhost\", &zUri[7], 9)) ){\n        *pzErrMsg = sqlite3_mprintf(\"invalid uri authority: %.*s\", \n            iIn-7, &zUri[7]);\n        rc = SQLITE_ERROR;\n        goto parse_uri_out;\n      }\n    }\n#endif\n\n    /* Copy the filename and any query parameters into the zFile buffer. \n    ** Decode %HH escape codes along the way. \n    **\n    ** Within this loop, variable eState may be set to 0, 1 or 2, depending\n    ** on the parsing context. As follows:\n    **\n    **   0: Parsing file-name.\n    **   1: Parsing name section of a name=value query parameter.\n    **   2: Parsing value section of a name=value query parameter.\n    */\n    eState = 0;\n    while( (c = zUri[iIn])!=0 && c!='#' ){\n      iIn++;\n      if( c=='%' \n       && sqlite3Isxdigit(zUri[iIn]) \n       && sqlite3Isxdigit(zUri[iIn+1]) \n      ){\n        int octet = (sqlite3HexToInt(zUri[iIn++]) << 4);\n        octet += sqlite3HexToInt(zUri[iIn++]);\n\n        assert( octet>=0 && octet<256 );\n        if( octet==0 ){\n#ifndef SQLITE_ENABLE_URI_00_ERROR\n          /* This branch is taken when \"%00\" appears within the URI. In this\n          ** case we ignore all text in the remainder of the path, name or\n          ** value currently being parsed. So ignore the current character\n          ** and skip to the next \"?\", \"=\" or \"&\", as appropriate. */\n          while( (c = zUri[iIn])!=0 && c!='#' \n              && (eState!=0 || c!='?')\n              && (eState!=1 || (c!='=' && c!='&'))\n              && (eState!=2 || c!='&')\n          ){\n            iIn++;\n          }\n          continue;\n#else\n          /* If ENABLE_URI_00_ERROR is defined, \"%00\" in a URI is an error. */\n          *pzErrMsg = sqlite3_mprintf(\"unexpected %%00 in uri\");\n          rc = SQLITE_ERROR;\n          goto parse_uri_out;\n#endif\n        }\n        c = octet;\n      }else if( eState==1 && (c=='&' || c=='=') ){\n        if( zFile[iOut-1]==0 ){\n          /* An empty option name. Ignore this option altogether. */\n          while( zUri[iIn] && zUri[iIn]!='#' && zUri[iIn-1]!='&' ) iIn++;\n          continue;\n        }\n        if( c=='&' ){\n          zFile[iOut++] = '\\0';\n        }else{\n          eState = 2;\n        }\n        c = 0;\n      }else if( (eState==0 && c=='?') || (eState==2 && c=='&') ){\n        c = 0;\n        eState = 1;\n      }\n      zFile[iOut++] = c;\n    }\n    if( eState==1 ) zFile[iOut++] = '\\0';\n    zFile[iOut++] = '\\0';\n    zFile[iOut++] = '\\0';\n\n    /* Check if there were any options specified that should be interpreted \n    ** here. Options that are interpreted here include \"vfs\" and those that\n    ** correspond to flags that may be passed to the sqlite3_open_v2()\n    ** method. */\n    zOpt = &zFile[sqlite3Strlen30(zFile)+1];\n    while( zOpt[0] ){\n      int nOpt = sqlite3Strlen30(zOpt);\n      char *zVal = &zOpt[nOpt+1];\n      int nVal = sqlite3Strlen30(zVal);\n\n      if( nOpt==3 && memcmp(\"vfs\", zOpt, 3)==0 ){\n        zVfs = zVal;\n      }else{\n        struct OpenMode {\n          const char *z;\n          int mode;\n        } *aMode = 0;\n        char *zModeType = 0;\n        int mask = 0;\n        int limit = 0;\n\n        if( nOpt==5 && memcmp(\"cache\", zOpt, 5)==0 ){\n          static struct OpenMode aCacheMode[] = {\n            { \"shared\",  SQLITE_OPEN_SHAREDCACHE },\n            { \"private\", SQLITE_OPEN_PRIVATECACHE },\n            { 0, 0 }\n          };\n\n          mask = SQLITE_OPEN_SHAREDCACHE|SQLITE_OPEN_PRIVATECACHE;\n          aMode = aCacheMode;\n          limit = mask;\n          zModeType = \"cache\";\n        }\n        if( nOpt==4 && memcmp(\"mode\", zOpt, 4)==0 ){\n          static struct OpenMode aOpenMode[] = {\n            { \"ro\",  SQLITE_OPEN_READONLY },\n            { \"rw\",  SQLITE_OPEN_READWRITE }, \n            { \"rwc\", SQLITE_OPEN_READWRITE | SQLITE_OPEN_CREATE },\n            { \"memory\", SQLITE_OPEN_MEMORY },\n            { 0, 0 }\n          };\n\n          mask = SQLITE_OPEN_READONLY | SQLITE_OPEN_READWRITE\n                   | SQLITE_OPEN_CREATE | SQLITE_OPEN_MEMORY;\n          aMode = aOpenMode;\n          limit = mask & flags;\n          zModeType = \"access\";\n        }\n\n        if( aMode ){\n          int i;\n          int mode = 0;\n          for(i=0; aMode[i].z; i++){\n            const char *z = aMode[i].z;\n            if( nVal==sqlite3Strlen30(z) && 0==memcmp(zVal, z, nVal) ){\n              mode = aMode[i].mode;\n              break;\n            }\n          }\n          if( mode==0 ){\n            *pzErrMsg = sqlite3_mprintf(\"no such %s mode: %s\", zModeType, zVal);\n            rc = SQLITE_ERROR;\n            goto parse_uri_out;\n          }\n          if( (mode & ~SQLITE_OPEN_MEMORY)>limit ){\n            *pzErrMsg = sqlite3_mprintf(\"%s mode not allowed: %s\",\n                                        zModeType, zVal);\n            rc = SQLITE_PERM;\n            goto parse_uri_out;\n          }\n          flags = (flags & ~mask) | mode;\n        }\n      }\n\n      zOpt = &zVal[nVal+1];\n    }\n\n  }else{\n    zFile = sqlite3_malloc64(nUri+2);\n    if( !zFile ) return SQLITE_NOMEM_BKPT;\n    if( nUri ){\n      memcpy(zFile, zUri, nUri);\n    }\n    zFile[nUri] = '\\0';\n    zFile[nUri+1] = '\\0';\n    flags &= ~SQLITE_OPEN_URI;\n  }\n\n  *ppVfs = sqlite3_vfs_find(zVfs);\n  if( *ppVfs==0 ){\n    *pzErrMsg = sqlite3_mprintf(\"no such vfs: %s\", zVfs);\n    rc = SQLITE_ERROR;\n  }\n parse_uri_out:\n  if( rc!=SQLITE_OK ){\n    sqlite3_free(zFile);\n    zFile = 0;\n  }\n  *pFlags = flags;\n  *pzFile = zFile;\n  return rc;\n}\n\n\n/*\n** This routine does the work of opening a database on behalf of\n** sqlite3_open() and sqlite3_open16(). The database filename \"zFilename\"  \n** is UTF-8 encoded.\n*/\nstatic int openDatabase(\n  const char *zFilename, /* Database filename UTF-8 encoded */\n  sqlite3 **ppDb,        /* OUT: Returned database handle */\n  unsigned int flags,    /* Operational flags */\n  const char *zVfs       /* Name of the VFS to use */\n){\n  sqlite3 *db;                    /* Store allocated handle here */\n  int rc;                         /* Return code */\n  int isThreadsafe;               /* True for threadsafe connections */\n  char *zOpen = 0;                /* Filename argument to pass to BtreeOpen() */\n  char *zErrMsg = 0;              /* Error message from sqlite3ParseUri() */\n\n#ifdef SQLITE_ENABLE_API_ARMOR\n  if( ppDb==0 ) return SQLITE_MISUSE_BKPT;\n#endif\n  *ppDb = 0;\n#ifndef SQLITE_OMIT_AUTOINIT\n  rc = sqlite3_initialize();\n  if( rc ) return rc;\n#endif\n\n  if( sqlite3GlobalConfig.bCoreMutex==0 ){\n    isThreadsafe = 0;\n  }else if( flags & SQLITE_OPEN_NOMUTEX ){\n    isThreadsafe = 0;\n  }else if( flags & SQLITE_OPEN_FULLMUTEX ){\n    isThreadsafe = 1;\n  }else{\n    isThreadsafe = sqlite3GlobalConfig.bFullMutex;\n  }\n\n  if( flags & SQLITE_OPEN_PRIVATECACHE ){\n    flags &= ~SQLITE_OPEN_SHAREDCACHE;\n  }else if( sqlite3GlobalConfig.sharedCacheEnabled ){\n    flags |= SQLITE_OPEN_SHAREDCACHE;\n  }\n\n  /* Remove harmful bits from the flags parameter\n  **\n  ** The SQLITE_OPEN_NOMUTEX and SQLITE_OPEN_FULLMUTEX flags were\n  ** dealt with in the previous code block.  Besides these, the only\n  ** valid input flags for sqlite3_open_v2() are SQLITE_OPEN_READONLY,\n  ** SQLITE_OPEN_READWRITE, SQLITE_OPEN_CREATE, SQLITE_OPEN_SHAREDCACHE,\n  ** SQLITE_OPEN_PRIVATECACHE, and some reserved bits.  Silently mask\n  ** off all other flags.\n  */\n  flags &=  ~( SQLITE_OPEN_DELETEONCLOSE |\n               SQLITE_OPEN_EXCLUSIVE |\n               SQLITE_OPEN_MAIN_DB |\n               SQLITE_OPEN_TEMP_DB | \n               SQLITE_OPEN_TRANSIENT_DB | \n               SQLITE_OPEN_MAIN_JOURNAL | \n               SQLITE_OPEN_TEMP_JOURNAL | \n               SQLITE_OPEN_SUBJOURNAL | \n               SQLITE_OPEN_MASTER_JOURNAL |\n               SQLITE_OPEN_NOMUTEX |\n               SQLITE_OPEN_FULLMUTEX |\n               SQLITE_OPEN_WAL\n             );\n\n  /* Allocate the sqlite data structure */\n  db = sqlite3MallocZero( sizeof(sqlite3) );\n  if( db==0 ) goto opendb_out;\n  if( isThreadsafe \n#ifdef SQLITE_ENABLE_MULTITHREADED_CHECKS\n   || sqlite3GlobalConfig.bCoreMutex\n#endif\n  ){\n    db->mutex = sqlite3MutexAlloc(SQLITE_MUTEX_RECURSIVE);\n    if( db->mutex==0 ){\n      sqlite3_free(db);\n      db = 0;\n      goto opendb_out;\n    }\n    if( isThreadsafe==0 ){\n      sqlite3MutexWarnOnContention(db->mutex);\n    }\n  }\n  sqlite3_mutex_enter(db->mutex);\n  db->errMask = 0xff;\n  db->nDb = 2;\n  db->magic = SQLITE_MAGIC_BUSY;\n  db->aDb = db->aDbStatic;\n\n  assert( sizeof(db->aLimit)==sizeof(aHardLimit) );\n  memcpy(db->aLimit, aHardLimit, sizeof(db->aLimit));\n  db->aLimit[SQLITE_LIMIT_WORKER_THREADS] = SQLITE_DEFAULT_WORKER_THREADS;\n  db->autoCommit = 1;\n  db->nextAutovac = -1;\n  db->szMmap = sqlite3GlobalConfig.szMmap;\n  db->nextPagesize = 0;\n  db->nMaxSorterMmap = 0x7FFFFFFF;\n  db->flags |= SQLITE_ShortColNames | SQLITE_EnableTrigger | SQLITE_CacheSpill\n#if !defined(SQLITE_DEFAULT_AUTOMATIC_INDEX) || SQLITE_DEFAULT_AUTOMATIC_INDEX\n                 | SQLITE_AutoIndex\n#endif\n#if SQLITE_DEFAULT_CKPTFULLFSYNC\n                 | SQLITE_CkptFullFSync\n#endif\n#if SQLITE_DEFAULT_FILE_FORMAT<4\n                 | SQLITE_LegacyFileFmt\n#endif\n#ifdef SQLITE_ENABLE_LOAD_EXTENSION\n                 | SQLITE_LoadExtension\n#endif\n#if SQLITE_DEFAULT_RECURSIVE_TRIGGERS\n                 | SQLITE_RecTriggers\n#endif\n#if defined(SQLITE_DEFAULT_FOREIGN_KEYS) && SQLITE_DEFAULT_FOREIGN_KEYS\n                 | SQLITE_ForeignKeys\n#endif\n#if defined(SQLITE_REVERSE_UNORDERED_SELECTS)\n                 | SQLITE_ReverseOrder\n#endif\n#if defined(SQLITE_ENABLE_OVERSIZE_CELL_CHECK)\n                 | SQLITE_CellSizeCk\n#endif\n#if defined(SQLITE_ENABLE_FTS3_TOKENIZER)\n                 | SQLITE_Fts3Tokenizer\n#endif\n#if defined(SQLITE_ENABLE_QPSG)\n                 | SQLITE_EnableQPSG\n#endif\n      ;\n  sqlite3HashInit(&db->aCollSeq);\n#ifndef SQLITE_OMIT_VIRTUALTABLE\n  sqlite3HashInit(&db->aModule);\n#endif\n\n  /* Add the default collation sequence BINARY. BINARY works for both UTF-8\n  ** and UTF-16, so add a version for each to avoid any unnecessary\n  ** conversions. The only error that can occur here is a malloc() failure.\n  **\n  ** EVIDENCE-OF: R-52786-44878 SQLite defines three built-in collating\n  ** functions:\n  */\n  createCollation(db, sqlite3StrBINARY, SQLITE_UTF8, 0, binCollFunc, 0);\n  createCollation(db, sqlite3StrBINARY, SQLITE_UTF16BE, 0, binCollFunc, 0);\n  createCollation(db, sqlite3StrBINARY, SQLITE_UTF16LE, 0, binCollFunc, 0);\n  createCollation(db, \"NOCASE\", SQLITE_UTF8, 0, nocaseCollatingFunc, 0);\n  createCollation(db, \"RTRIM\", SQLITE_UTF8, (void*)1, binCollFunc, 0);\n  if( db->mallocFailed ){\n    goto opendb_out;\n  }\n  /* EVIDENCE-OF: R-08308-17224 The default collating function for all\n  ** strings is BINARY. \n  */\n  db->pDfltColl = sqlite3FindCollSeq(db, SQLITE_UTF8, sqlite3StrBINARY, 0);\n  assert( db->pDfltColl!=0 );\n\n  /* Parse the filename/URI argument\n  **\n  ** Only allow sensible combinations of bits in the flags argument.  \n  ** Throw an error if any non-sense combination is used.  If we\n  ** do not block illegal combinations here, it could trigger\n  ** assert() statements in deeper layers.  Sensible combinations\n  ** are:\n  **\n  **  1:  SQLITE_OPEN_READONLY\n  **  2:  SQLITE_OPEN_READWRITE\n  **  6:  SQLITE_OPEN_READWRITE | SQLITE_OPEN_CREATE\n  */\n  db->openFlags = flags;\n  assert( SQLITE_OPEN_READONLY  == 0x01 );\n  assert( SQLITE_OPEN_READWRITE == 0x02 );\n  assert( SQLITE_OPEN_CREATE    == 0x04 );\n  testcase( (1<<(flags&7))==0x02 ); /* READONLY */\n  testcase( (1<<(flags&7))==0x04 ); /* READWRITE */\n  testcase( (1<<(flags&7))==0x40 ); /* READWRITE | CREATE */\n  if( ((1<<(flags&7)) & 0x46)==0 ){\n    rc = SQLITE_MISUSE_BKPT;  /* IMP: R-65497-44594 */\n  }else{\n    rc = sqlite3ParseUri(zVfs, zFilename, &flags, &db->pVfs, &zOpen, &zErrMsg);\n  }\n  if( rc!=SQLITE_OK ){\n    if( rc==SQLITE_NOMEM ) sqlite3OomFault(db);\n    sqlite3ErrorWithMsg(db, rc, zErrMsg ? \"%s\" : 0, zErrMsg);\n    sqlite3_free(zErrMsg);\n    goto opendb_out;\n  }\n\n  /* Open the backend database driver */\n  rc = sqlite3BtreeOpen(db->pVfs, zOpen, db, &db->aDb[0].pBt, 0,\n                        flags | SQLITE_OPEN_MAIN_DB);\n  if( rc!=SQLITE_OK ){\n    if( rc==SQLITE_IOERR_NOMEM ){\n      rc = SQLITE_NOMEM_BKPT;\n    }\n    sqlite3Error(db, rc);\n    goto opendb_out;\n  }\n  sqlite3BtreeEnter(db->aDb[0].pBt);\n  db->aDb[0].pSchema = sqlite3SchemaGet(db, db->aDb[0].pBt);\n  if( !db->mallocFailed ) ENC(db) = SCHEMA_ENC(db);\n  sqlite3BtreeLeave(db->aDb[0].pBt);\n  db->aDb[1].pSchema = sqlite3SchemaGet(db, 0);\n\n  /* The default safety_level for the main database is FULL; for the temp\n  ** database it is OFF. This matches the pager layer defaults.  \n  */\n  db->aDb[0].zDbSName = \"main\";\n  db->aDb[0].safety_level = SQLITE_DEFAULT_SYNCHRONOUS+1;\n  db->aDb[1].zDbSName = \"temp\";\n  db->aDb[1].safety_level = PAGER_SYNCHRONOUS_OFF;\n\n  db->magic = SQLITE_MAGIC_OPEN;\n  if( db->mallocFailed ){\n    goto opendb_out;\n  }\n\n  /* Register all built-in functions, but do not attempt to read the\n  ** database schema yet. This is delayed until the first time the database\n  ** is accessed.\n  */\n  sqlite3Error(db, SQLITE_OK);\n  sqlite3RegisterPerConnectionBuiltinFunctions(db);\n  rc = sqlite3_errcode(db);\n\n#ifdef SQLITE_ENABLE_FTS5\n  /* Register any built-in FTS5 module before loading the automatic\n  ** extensions. This allows automatic extensions to register FTS5 \n  ** tokenizers and auxiliary functions.  */\n  if( !db->mallocFailed && rc==SQLITE_OK ){\n    rc = sqlite3Fts5Init(db);\n  }\n#endif\n\n  /* Load automatic extensions - extensions that have been registered\n  ** using the sqlite3_automatic_extension() API.\n  */\n  if( rc==SQLITE_OK ){\n    sqlite3AutoLoadExtensions(db);\n    rc = sqlite3_errcode(db);\n    if( rc!=SQLITE_OK ){\n      goto opendb_out;\n    }\n  }\n\n#ifdef SQLITE_ENABLE_FTS1\n  if( !db->mallocFailed ){\n    extern int sqlite3Fts1Init(sqlite3*);\n    rc = sqlite3Fts1Init(db);\n  }\n#endif\n\n#ifdef SQLITE_ENABLE_FTS2\n  if( !db->mallocFailed && rc==SQLITE_OK ){\n    extern int sqlite3Fts2Init(sqlite3*);\n    rc = sqlite3Fts2Init(db);\n  }\n#endif\n\n#ifdef SQLITE_ENABLE_FTS3 /* automatically defined by SQLITE_ENABLE_FTS4 */\n  if( !db->mallocFailed && rc==SQLITE_OK ){\n    rc = sqlite3Fts3Init(db);\n  }\n#endif\n\n#if defined(SQLITE_ENABLE_ICU) || defined(SQLITE_ENABLE_ICU_COLLATIONS)\n  if( !db->mallocFailed && rc==SQLITE_OK ){\n    rc = sqlite3IcuInit(db);\n  }\n#endif\n\n#ifdef SQLITE_ENABLE_RTREE\n  if( !db->mallocFailed && rc==SQLITE_OK){\n    rc = sqlite3RtreeInit(db);\n  }\n#endif\n\n#ifdef SQLITE_ENABLE_DBPAGE_VTAB\n  if( !db->mallocFailed && rc==SQLITE_OK){\n    rc = sqlite3DbpageRegister(db);\n  }\n#endif\n\n#ifdef SQLITE_ENABLE_DBSTAT_VTAB\n  if( !db->mallocFailed && rc==SQLITE_OK){\n    rc = sqlite3DbstatRegister(db);\n  }\n#endif\n\n#ifdef SQLITE_ENABLE_JSON1\n  if( !db->mallocFailed && rc==SQLITE_OK){\n    rc = sqlite3Json1Init(db);\n  }\n#endif\n\n#ifdef SQLITE_ENABLE_STMTVTAB\n  if( !db->mallocFailed && rc==SQLITE_OK){\n    rc = sqlite3StmtVtabInit(db);\n  }\n#endif\n\n  /* -DSQLITE_DEFAULT_LOCKING_MODE=1 makes EXCLUSIVE the default locking\n  ** mode.  -DSQLITE_DEFAULT_LOCKING_MODE=0 make NORMAL the default locking\n  ** mode.  Doing nothing at all also makes NORMAL the default.\n  */\n#ifdef SQLITE_DEFAULT_LOCKING_MODE\n  db->dfltLockMode = SQLITE_DEFAULT_LOCKING_MODE;\n  sqlite3PagerLockingMode(sqlite3BtreePager(db->aDb[0].pBt),\n                          SQLITE_DEFAULT_LOCKING_MODE);\n#endif\n\n  if( rc ) sqlite3Error(db, rc);\n\n  /* Enable the lookaside-malloc subsystem */\n  setupLookaside(db, 0, sqlite3GlobalConfig.szLookaside,\n                        sqlite3GlobalConfig.nLookaside);\n\n  sqlite3_wal_autocheckpoint(db, SQLITE_DEFAULT_WAL_AUTOCHECKPOINT);\n\nopendb_out:\n  if( db ){\n    assert( db->mutex!=0 || isThreadsafe==0\n           || sqlite3GlobalConfig.bFullMutex==0 );\n    sqlite3_mutex_leave(db->mutex);\n  }\n  rc = sqlite3_errcode(db);\n  assert( db!=0 || rc==SQLITE_NOMEM );\n  if( rc==SQLITE_NOMEM ){\n    sqlite3_close(db);\n    db = 0;\n  }else if( rc!=SQLITE_OK ){\n    db->magic = SQLITE_MAGIC_SICK;\n  }\n  *ppDb = db;\n#ifdef SQLITE_ENABLE_SQLLOG\n  if( sqlite3GlobalConfig.xSqllog ){\n    /* Opening a db handle. Fourth parameter is passed 0. */\n    void *pArg = sqlite3GlobalConfig.pSqllogArg;\n    sqlite3GlobalConfig.xSqllog(pArg, db, zFilename, 0);\n  }\n#endif\n#if defined(SQLITE_HAS_CODEC)\n  if( rc==SQLITE_OK ){\n    const char *zKey;\n    if( (zKey = sqlite3_uri_parameter(zOpen, \"hexkey\"))!=0 && zKey[0] ){\n      u8 iByte;\n      int i;\n      char zDecoded[40];\n      for(i=0, iByte=0; i<sizeof(zDecoded)*2 && sqlite3Isxdigit(zKey[i]); i++){\n        iByte = (iByte<<4) + sqlite3HexToInt(zKey[i]);\n        if( (i&1)!=0 ) zDecoded[i/2] = iByte;\n      }\n      sqlite3_key_v2(db, 0, zDecoded, i/2);\n    }else if( (zKey = sqlite3_uri_parameter(zOpen, \"key\"))!=0 ){\n      sqlite3_key_v2(db, 0, zKey, sqlite3Strlen30(zKey));\n    }\n  }\n#endif\n  sqlite3_free(zOpen);\n  return rc & 0xff;\n}\n\n/*\n** Open a new database handle.\n*/\nSQLITE_API int sqlite3_open(\n  const char *zFilename, \n  sqlite3 **ppDb \n){\n  return openDatabase(zFilename, ppDb,\n                      SQLITE_OPEN_READWRITE | SQLITE_OPEN_CREATE, 0);\n}\nSQLITE_API int sqlite3_open_v2(\n  const char *filename,   /* Database filename (UTF-8) */\n  sqlite3 **ppDb,         /* OUT: SQLite db handle */\n  int flags,              /* Flags */\n  const char *zVfs        /* Name of VFS module to use */\n){\n  return openDatabase(filename, ppDb, (unsigned int)flags, zVfs);\n}\n\n#ifndef SQLITE_OMIT_UTF16\n/*\n** Open a new database handle.\n*/\nSQLITE_API int sqlite3_open16(\n  const void *zFilename, \n  sqlite3 **ppDb\n){\n  char const *zFilename8;   /* zFilename encoded in UTF-8 instead of UTF-16 */\n  sqlite3_value *pVal;\n  int rc;\n\n#ifdef SQLITE_ENABLE_API_ARMOR\n  if( ppDb==0 ) return SQLITE_MISUSE_BKPT;\n#endif\n  *ppDb = 0;\n#ifndef SQLITE_OMIT_AUTOINIT\n  rc = sqlite3_initialize();\n  if( rc ) return rc;\n#endif\n  if( zFilename==0 ) zFilename = \"\\000\\000\";\n  pVal = sqlite3ValueNew(0);\n  sqlite3ValueSetStr(pVal, -1, zFilename, SQLITE_UTF16NATIVE, SQLITE_STATIC);\n  zFilename8 = sqlite3ValueText(pVal, SQLITE_UTF8);\n  if( zFilename8 ){\n    rc = openDatabase(zFilename8, ppDb,\n                      SQLITE_OPEN_READWRITE | SQLITE_OPEN_CREATE, 0);\n    assert( *ppDb || rc==SQLITE_NOMEM );\n    if( rc==SQLITE_OK && !DbHasProperty(*ppDb, 0, DB_SchemaLoaded) ){\n      SCHEMA_ENC(*ppDb) = ENC(*ppDb) = SQLITE_UTF16NATIVE;\n    }\n  }else{\n    rc = SQLITE_NOMEM_BKPT;\n  }\n  sqlite3ValueFree(pVal);\n\n  return rc & 0xff;\n}\n#endif /* SQLITE_OMIT_UTF16 */\n\n/*\n** Register a new collation sequence with the database handle db.\n*/\nSQLITE_API int sqlite3_create_collation(\n  sqlite3* db, \n  const char *zName, \n  int enc, \n  void* pCtx,\n  int(*xCompare)(void*,int,const void*,int,const void*)\n){\n  return sqlite3_create_collation_v2(db, zName, enc, pCtx, xCompare, 0);\n}\n\n/*\n** Register a new collation sequence with the database handle db.\n*/\nSQLITE_API int sqlite3_create_collation_v2(\n  sqlite3* db, \n  const char *zName, \n  int enc, \n  void* pCtx,\n  int(*xCompare)(void*,int,const void*,int,const void*),\n  void(*xDel)(void*)\n){\n  int rc;\n\n#ifdef SQLITE_ENABLE_API_ARMOR\n  if( !sqlite3SafetyCheckOk(db) || zName==0 ) return SQLITE_MISUSE_BKPT;\n#endif\n  sqlite3_mutex_enter(db->mutex);\n  assert( !db->mallocFailed );\n  rc = createCollation(db, zName, (u8)enc, pCtx, xCompare, xDel);\n  rc = sqlite3ApiExit(db, rc);\n  sqlite3_mutex_leave(db->mutex);\n  return rc;\n}\n\n#ifndef SQLITE_OMIT_UTF16\n/*\n** Register a new collation sequence with the database handle db.\n*/\nSQLITE_API int sqlite3_create_collation16(\n  sqlite3* db, \n  const void *zName,\n  int enc, \n  void* pCtx,\n  int(*xCompare)(void*,int,const void*,int,const void*)\n){\n  int rc = SQLITE_OK;\n  char *zName8;\n\n#ifdef SQLITE_ENABLE_API_ARMOR\n  if( !sqlite3SafetyCheckOk(db) || zName==0 ) return SQLITE_MISUSE_BKPT;\n#endif\n  sqlite3_mutex_enter(db->mutex);\n  assert( !db->mallocFailed );\n  zName8 = sqlite3Utf16to8(db, zName, -1, SQLITE_UTF16NATIVE);\n  if( zName8 ){\n    rc = createCollation(db, zName8, (u8)enc, pCtx, xCompare, 0);\n    sqlite3DbFree(db, zName8);\n  }\n  rc = sqlite3ApiExit(db, rc);\n  sqlite3_mutex_leave(db->mutex);\n  return rc;\n}\n#endif /* SQLITE_OMIT_UTF16 */\n\n/*\n** Register a collation sequence factory callback with the database handle\n** db. Replace any previously installed collation sequence factory.\n*/\nSQLITE_API int sqlite3_collation_needed(\n  sqlite3 *db, \n  void *pCollNeededArg, \n  void(*xCollNeeded)(void*,sqlite3*,int eTextRep,const char*)\n){\n#ifdef SQLITE_ENABLE_API_ARMOR\n  if( !sqlite3SafetyCheckOk(db) ) return SQLITE_MISUSE_BKPT;\n#endif\n  sqlite3_mutex_enter(db->mutex);\n  db->xCollNeeded = xCollNeeded;\n  db->xCollNeeded16 = 0;\n  db->pCollNeededArg = pCollNeededArg;\n  sqlite3_mutex_leave(db->mutex);\n  return SQLITE_OK;\n}\n\n#ifndef SQLITE_OMIT_UTF16\n/*\n** Register a collation sequence factory callback with the database handle\n** db. Replace any previously installed collation sequence factory.\n*/\nSQLITE_API int sqlite3_collation_needed16(\n  sqlite3 *db, \n  void *pCollNeededArg, \n  void(*xCollNeeded16)(void*,sqlite3*,int eTextRep,const void*)\n){\n#ifdef SQLITE_ENABLE_API_ARMOR\n  if( !sqlite3SafetyCheckOk(db) ) return SQLITE_MISUSE_BKPT;\n#endif\n  sqlite3_mutex_enter(db->mutex);\n  db->xCollNeeded = 0;\n  db->xCollNeeded16 = xCollNeeded16;\n  db->pCollNeededArg = pCollNeededArg;\n  sqlite3_mutex_leave(db->mutex);\n  return SQLITE_OK;\n}\n#endif /* SQLITE_OMIT_UTF16 */\n\n#ifndef SQLITE_OMIT_DEPRECATED\n/*\n** This function is now an anachronism. It used to be used to recover from a\n** malloc() failure, but SQLite now does this automatically.\n*/\nSQLITE_API int sqlite3_global_recover(void){\n  return SQLITE_OK;\n}\n#endif\n\n/*\n** Test to see whether or not the database connection is in autocommit\n** mode.  Return TRUE if it is and FALSE if not.  Autocommit mode is on\n** by default.  Autocommit is disabled by a BEGIN statement and reenabled\n** by the next COMMIT or ROLLBACK.\n*/\nSQLITE_API int sqlite3_get_autocommit(sqlite3 *db){\n#ifdef SQLITE_ENABLE_API_ARMOR\n  if( !sqlite3SafetyCheckOk(db) ){\n    (void)SQLITE_MISUSE_BKPT;\n    return 0;\n  }\n#endif\n  return db->autoCommit;\n}\n\n/*\n** The following routines are substitutes for constants SQLITE_CORRUPT,\n** SQLITE_MISUSE, SQLITE_CANTOPEN, SQLITE_NOMEM and possibly other error\n** constants.  They serve two purposes:\n**\n**   1.  Serve as a convenient place to set a breakpoint in a debugger\n**       to detect when version error conditions occurs.\n**\n**   2.  Invoke sqlite3_log() to provide the source code location where\n**       a low-level error is first detected.\n*/\nSQLITE_PRIVATE int sqlite3ReportError(int iErr, int lineno, const char *zType){\n  sqlite3_log(iErr, \"%s at line %d of [%.10s]\",\n              zType, lineno, 20+sqlite3_sourceid());\n  return iErr;\n}\nSQLITE_PRIVATE int sqlite3CorruptError(int lineno){\n  testcase( sqlite3GlobalConfig.xLog!=0 );\n  return sqlite3ReportError(SQLITE_CORRUPT, lineno, \"database corruption\");\n}\nSQLITE_PRIVATE int sqlite3MisuseError(int lineno){\n  testcase( sqlite3GlobalConfig.xLog!=0 );\n  return sqlite3ReportError(SQLITE_MISUSE, lineno, \"misuse\");\n}\nSQLITE_PRIVATE int sqlite3CantopenError(int lineno){\n  testcase( sqlite3GlobalConfig.xLog!=0 );\n  return sqlite3ReportError(SQLITE_CANTOPEN, lineno, \"cannot open file\");\n}\n#ifdef SQLITE_DEBUG\nSQLITE_PRIVATE int sqlite3CorruptPgnoError(int lineno, Pgno pgno){\n  char zMsg[100];\n  sqlite3_snprintf(sizeof(zMsg), zMsg, \"database corruption page %d\", pgno);\n  testcase( sqlite3GlobalConfig.xLog!=0 );\n  return sqlite3ReportError(SQLITE_CORRUPT, lineno, zMsg);\n}\nSQLITE_PRIVATE int sqlite3NomemError(int lineno){\n  testcase( sqlite3GlobalConfig.xLog!=0 );\n  return sqlite3ReportError(SQLITE_NOMEM, lineno, \"OOM\");\n}\nSQLITE_PRIVATE int sqlite3IoerrnomemError(int lineno){\n  testcase( sqlite3GlobalConfig.xLog!=0 );\n  return sqlite3ReportError(SQLITE_IOERR_NOMEM, lineno, \"I/O OOM error\");\n}\n#endif\n\n#ifndef SQLITE_OMIT_DEPRECATED\n/*\n** This is a convenience routine that makes sure that all thread-specific\n** data for this thread has been deallocated.\n**\n** SQLite no longer uses thread-specific data so this routine is now a\n** no-op.  It is retained for historical compatibility.\n*/\nSQLITE_API void sqlite3_thread_cleanup(void){\n}\n#endif\n\n/*\n** Return meta information about a specific column of a database table.\n** See comment in sqlite3.h (sqlite.h.in) for details.\n*/\nSQLITE_API int sqlite3_table_column_metadata(\n  sqlite3 *db,                /* Connection handle */\n  const char *zDbName,        /* Database name or NULL */\n  const char *zTableName,     /* Table name */\n  const char *zColumnName,    /* Column name */\n  char const **pzDataType,    /* OUTPUT: Declared data type */\n  char const **pzCollSeq,     /* OUTPUT: Collation sequence name */\n  int *pNotNull,              /* OUTPUT: True if NOT NULL constraint exists */\n  int *pPrimaryKey,           /* OUTPUT: True if column part of PK */\n  int *pAutoinc               /* OUTPUT: True if column is auto-increment */\n){\n  int rc;\n  char *zErrMsg = 0;\n  Table *pTab = 0;\n  Column *pCol = 0;\n  int iCol = 0;\n  char const *zDataType = 0;\n  char const *zCollSeq = 0;\n  int notnull = 0;\n  int primarykey = 0;\n  int autoinc = 0;\n\n\n#ifdef SQLITE_ENABLE_API_ARMOR\n  if( !sqlite3SafetyCheckOk(db) || zTableName==0 ){\n    return SQLITE_MISUSE_BKPT;\n  }\n#endif\n\n  /* Ensure the database schema has been loaded */\n  sqlite3_mutex_enter(db->mutex);\n  sqlite3BtreeEnterAll(db);\n  rc = sqlite3Init(db, &zErrMsg);\n  if( SQLITE_OK!=rc ){\n    goto error_out;\n  }\n\n  /* Locate the table in question */\n  pTab = sqlite3FindTable(db, zTableName, zDbName);\n  if( !pTab || pTab->pSelect ){\n    pTab = 0;\n    goto error_out;\n  }\n\n  /* Find the column for which info is requested */\n  if( zColumnName==0 ){\n    /* Query for existance of table only */\n  }else{\n    for(iCol=0; iCol<pTab->nCol; iCol++){\n      pCol = &pTab->aCol[iCol];\n      if( 0==sqlite3StrICmp(pCol->zName, zColumnName) ){\n        break;\n      }\n    }\n    if( iCol==pTab->nCol ){\n      if( HasRowid(pTab) && sqlite3IsRowid(zColumnName) ){\n        iCol = pTab->iPKey;\n        pCol = iCol>=0 ? &pTab->aCol[iCol] : 0;\n      }else{\n        pTab = 0;\n        goto error_out;\n      }\n    }\n  }\n\n  /* The following block stores the meta information that will be returned\n  ** to the caller in local variables zDataType, zCollSeq, notnull, primarykey\n  ** and autoinc. At this point there are two possibilities:\n  ** \n  **     1. The specified column name was rowid\", \"oid\" or \"_rowid_\" \n  **        and there is no explicitly declared IPK column. \n  **\n  **     2. The table is not a view and the column name identified an \n  **        explicitly declared column. Copy meta information from *pCol.\n  */ \n  if( pCol ){\n    zDataType = sqlite3ColumnType(pCol,0);\n    zCollSeq = pCol->zColl;\n    notnull = pCol->notNull!=0;\n    primarykey  = (pCol->colFlags & COLFLAG_PRIMKEY)!=0;\n    autoinc = pTab->iPKey==iCol && (pTab->tabFlags & TF_Autoincrement)!=0;\n  }else{\n    zDataType = \"INTEGER\";\n    primarykey = 1;\n  }\n  if( !zCollSeq ){\n    zCollSeq = sqlite3StrBINARY;\n  }\n\nerror_out:\n  sqlite3BtreeLeaveAll(db);\n\n  /* Whether the function call succeeded or failed, set the output parameters\n  ** to whatever their local counterparts contain. If an error did occur,\n  ** this has the effect of zeroing all output parameters.\n  */\n  if( pzDataType ) *pzDataType = zDataType;\n  if( pzCollSeq ) *pzCollSeq = zCollSeq;\n  if( pNotNull ) *pNotNull = notnull;\n  if( pPrimaryKey ) *pPrimaryKey = primarykey;\n  if( pAutoinc ) *pAutoinc = autoinc;\n\n  if( SQLITE_OK==rc && !pTab ){\n    sqlite3DbFree(db, zErrMsg);\n    zErrMsg = sqlite3MPrintf(db, \"no such table column: %s.%s\", zTableName,\n        zColumnName);\n    rc = SQLITE_ERROR;\n  }\n  sqlite3ErrorWithMsg(db, rc, (zErrMsg?\"%s\":0), zErrMsg);\n  sqlite3DbFree(db, zErrMsg);\n  rc = sqlite3ApiExit(db, rc);\n  sqlite3_mutex_leave(db->mutex);\n  return rc;\n}\n\n/*\n** Sleep for a little while.  Return the amount of time slept.\n*/\nSQLITE_API int sqlite3_sleep(int ms){\n  sqlite3_vfs *pVfs;\n  int rc;\n  pVfs = sqlite3_vfs_find(0);\n  if( pVfs==0 ) return 0;\n\n  /* This function works in milliseconds, but the underlying OsSleep() \n  ** API uses microseconds. Hence the 1000's.\n  */\n  rc = (sqlite3OsSleep(pVfs, 1000*ms)/1000);\n  return rc;\n}\n\n/*\n** Enable or disable the extended result codes.\n*/\nSQLITE_API int sqlite3_extended_result_codes(sqlite3 *db, int onoff){\n#ifdef SQLITE_ENABLE_API_ARMOR\n  if( !sqlite3SafetyCheckOk(db) ) return SQLITE_MISUSE_BKPT;\n#endif\n  sqlite3_mutex_enter(db->mutex);\n  db->errMask = onoff ? 0xffffffff : 0xff;\n  sqlite3_mutex_leave(db->mutex);\n  return SQLITE_OK;\n}\n\n/*\n** Invoke the xFileControl method on a particular database.\n*/\nSQLITE_API int sqlite3_file_control(sqlite3 *db, const char *zDbName, int op, void *pArg){\n  int rc = SQLITE_ERROR;\n  Btree *pBtree;\n\n#ifdef SQLITE_ENABLE_API_ARMOR\n  if( !sqlite3SafetyCheckOk(db) ) return SQLITE_MISUSE_BKPT;\n#endif\n  sqlite3_mutex_enter(db->mutex);\n  pBtree = sqlite3DbNameToBtree(db, zDbName);\n  if( pBtree ){\n    Pager *pPager;\n    sqlite3_file *fd;\n    sqlite3BtreeEnter(pBtree);\n    pPager = sqlite3BtreePager(pBtree);\n    assert( pPager!=0 );\n    fd = sqlite3PagerFile(pPager);\n    assert( fd!=0 );\n    if( op==SQLITE_FCNTL_FILE_POINTER ){\n      *(sqlite3_file**)pArg = fd;\n      rc = SQLITE_OK;\n    }else if( op==SQLITE_FCNTL_VFS_POINTER ){\n      *(sqlite3_vfs**)pArg = sqlite3PagerVfs(pPager);\n      rc = SQLITE_OK;\n    }else if( op==SQLITE_FCNTL_JOURNAL_POINTER ){\n      *(sqlite3_file**)pArg = sqlite3PagerJrnlFile(pPager);\n      rc = SQLITE_OK;\n    }else if( fd->pMethods ){\n      rc = sqlite3OsFileControl(fd, op, pArg);\n    }else{\n      rc = SQLITE_NOTFOUND;\n    }\n    sqlite3BtreeLeave(pBtree);\n  }\n  sqlite3_mutex_leave(db->mutex);\n  return rc;\n}\n\n/*\n** Interface to the testing logic.\n*/\nSQLITE_API int sqlite3_test_control(int op, ...){\n  int rc = 0;\n#ifdef SQLITE_UNTESTABLE\n  UNUSED_PARAMETER(op);\n#else\n  va_list ap;\n  va_start(ap, op);\n  switch( op ){\n\n    /*\n    ** Save the current state of the PRNG.\n    */\n    case SQLITE_TESTCTRL_PRNG_SAVE: {\n      sqlite3PrngSaveState();\n      break;\n    }\n\n    /*\n    ** Restore the state of the PRNG to the last state saved using\n    ** PRNG_SAVE.  If PRNG_SAVE has never before been called, then\n    ** this verb acts like PRNG_RESET.\n    */\n    case SQLITE_TESTCTRL_PRNG_RESTORE: {\n      sqlite3PrngRestoreState();\n      break;\n    }\n\n    /*\n    ** Reset the PRNG back to its uninitialized state.  The next call\n    ** to sqlite3_randomness() will reseed the PRNG using a single call\n    ** to the xRandomness method of the default VFS.\n    */\n    case SQLITE_TESTCTRL_PRNG_RESET: {\n      sqlite3_randomness(0,0);\n      break;\n    }\n\n    /*\n    **  sqlite3_test_control(BITVEC_TEST, size, program)\n    **\n    ** Run a test against a Bitvec object of size.  The program argument\n    ** is an array of integers that defines the test.  Return -1 on a\n    ** memory allocation error, 0 on success, or non-zero for an error.\n    ** See the sqlite3BitvecBuiltinTest() for additional information.\n    */\n    case SQLITE_TESTCTRL_BITVEC_TEST: {\n      int sz = va_arg(ap, int);\n      int *aProg = va_arg(ap, int*);\n      rc = sqlite3BitvecBuiltinTest(sz, aProg);\n      break;\n    }\n\n    /*\n    **  sqlite3_test_control(FAULT_INSTALL, xCallback)\n    **\n    ** Arrange to invoke xCallback() whenever sqlite3FaultSim() is called,\n    ** if xCallback is not NULL.\n    **\n    ** As a test of the fault simulator mechanism itself, sqlite3FaultSim(0)\n    ** is called immediately after installing the new callback and the return\n    ** value from sqlite3FaultSim(0) becomes the return from\n    ** sqlite3_test_control().\n    */\n    case SQLITE_TESTCTRL_FAULT_INSTALL: {\n      /* MSVC is picky about pulling func ptrs from va lists.\n      ** http://support.microsoft.com/kb/47961\n      ** sqlite3GlobalConfig.xTestCallback = va_arg(ap, int(*)(int));\n      */\n      typedef int(*TESTCALLBACKFUNC_t)(int);\n      sqlite3GlobalConfig.xTestCallback = va_arg(ap, TESTCALLBACKFUNC_t);\n      rc = sqlite3FaultSim(0);\n      break;\n    }\n\n    /*\n    **  sqlite3_test_control(BENIGN_MALLOC_HOOKS, xBegin, xEnd)\n    **\n    ** Register hooks to call to indicate which malloc() failures \n    ** are benign.\n    */\n    case SQLITE_TESTCTRL_BENIGN_MALLOC_HOOKS: {\n      typedef void (*void_function)(void);\n      void_function xBenignBegin;\n      void_function xBenignEnd;\n      xBenignBegin = va_arg(ap, void_function);\n      xBenignEnd = va_arg(ap, void_function);\n      sqlite3BenignMallocHooks(xBenignBegin, xBenignEnd);\n      break;\n    }\n\n    /*\n    **  sqlite3_test_control(SQLITE_TESTCTRL_PENDING_BYTE, unsigned int X)\n    **\n    ** Set the PENDING byte to the value in the argument, if X>0.\n    ** Make no changes if X==0.  Return the value of the pending byte\n    ** as it existing before this routine was called.\n    **\n    ** IMPORTANT:  Changing the PENDING byte from 0x40000000 results in\n    ** an incompatible database file format.  Changing the PENDING byte\n    ** while any database connection is open results in undefined and\n    ** deleterious behavior.\n    */\n    case SQLITE_TESTCTRL_PENDING_BYTE: {\n      rc = PENDING_BYTE;\n#ifndef SQLITE_OMIT_WSD\n      {\n        unsigned int newVal = va_arg(ap, unsigned int);\n        if( newVal ) sqlite3PendingByte = newVal;\n      }\n#endif\n      break;\n    }\n\n    /*\n    **  sqlite3_test_control(SQLITE_TESTCTRL_ASSERT, int X)\n    **\n    ** This action provides a run-time test to see whether or not\n    ** assert() was enabled at compile-time.  If X is true and assert()\n    ** is enabled, then the return value is true.  If X is true and\n    ** assert() is disabled, then the return value is zero.  If X is\n    ** false and assert() is enabled, then the assertion fires and the\n    ** process aborts.  If X is false and assert() is disabled, then the\n    ** return value is zero.\n    */\n    case SQLITE_TESTCTRL_ASSERT: {\n      volatile int x = 0;\n      assert( /*side-effects-ok*/ (x = va_arg(ap,int))!=0 );\n      rc = x;\n      break;\n    }\n\n\n    /*\n    **  sqlite3_test_control(SQLITE_TESTCTRL_ALWAYS, int X)\n    **\n    ** This action provides a run-time test to see how the ALWAYS and\n    ** NEVER macros were defined at compile-time.\n    **\n    ** The return value is ALWAYS(X) if X is true, or 0 if X is false.\n    **\n    ** The recommended test is X==2.  If the return value is 2, that means\n    ** ALWAYS() and NEVER() are both no-op pass-through macros, which is the\n    ** default setting.  If the return value is 1, then ALWAYS() is either\n    ** hard-coded to true or else it asserts if its argument is false.\n    ** The first behavior (hard-coded to true) is the case if\n    ** SQLITE_TESTCTRL_ASSERT shows that assert() is disabled and the second\n    ** behavior (assert if the argument to ALWAYS() is false) is the case if\n    ** SQLITE_TESTCTRL_ASSERT shows that assert() is enabled.\n    **\n    ** The run-time test procedure might look something like this:\n    **\n    **    if( sqlite3_test_control(SQLITE_TESTCTRL_ALWAYS, 2)==2 ){\n    **      // ALWAYS() and NEVER() are no-op pass-through macros\n    **    }else if( sqlite3_test_control(SQLITE_TESTCTRL_ASSERT, 1) ){\n    **      // ALWAYS(x) asserts that x is true. NEVER(x) asserts x is false.\n    **    }else{\n    **      // ALWAYS(x) is a constant 1.  NEVER(x) is a constant 0.\n    **    }\n    */\n    case SQLITE_TESTCTRL_ALWAYS: {\n      int x = va_arg(ap,int);\n      rc = x ? ALWAYS(x) : 0;\n      break;\n    }\n\n    /*\n    **   sqlite3_test_control(SQLITE_TESTCTRL_BYTEORDER);\n    **\n    ** The integer returned reveals the byte-order of the computer on which\n    ** SQLite is running:\n    **\n    **       1     big-endian,    determined at run-time\n    **      10     little-endian, determined at run-time\n    **  432101     big-endian,    determined at compile-time\n    **  123410     little-endian, determined at compile-time\n    */ \n    case SQLITE_TESTCTRL_BYTEORDER: {\n      rc = SQLITE_BYTEORDER*100 + SQLITE_LITTLEENDIAN*10 + SQLITE_BIGENDIAN;\n      break;\n    }\n\n    /*   sqlite3_test_control(SQLITE_TESTCTRL_RESERVE, sqlite3 *db, int N)\n    **\n    ** Set the nReserve size to N for the main database on the database\n    ** connection db.\n    */\n    case SQLITE_TESTCTRL_RESERVE: {\n      sqlite3 *db = va_arg(ap, sqlite3*);\n      int x = va_arg(ap,int);\n      sqlite3_mutex_enter(db->mutex);\n      sqlite3BtreeSetPageSize(db->aDb[0].pBt, 0, x, 0);\n      sqlite3_mutex_leave(db->mutex);\n      break;\n    }\n\n    /*  sqlite3_test_control(SQLITE_TESTCTRL_OPTIMIZATIONS, sqlite3 *db, int N)\n    **\n    ** Enable or disable various optimizations for testing purposes.  The \n    ** argument N is a bitmask of optimizations to be disabled.  For normal\n    ** operation N should be 0.  The idea is that a test program (like the\n    ** SQL Logic Test or SLT test module) can run the same SQL multiple times\n    ** with various optimizations disabled to verify that the same answer\n    ** is obtained in every case.\n    */\n    case SQLITE_TESTCTRL_OPTIMIZATIONS: {\n      sqlite3 *db = va_arg(ap, sqlite3*);\n      db->dbOptFlags = (u16)(va_arg(ap, int) & 0xffff);\n      break;\n    }\n\n#ifdef SQLITE_N_KEYWORD\n    /* sqlite3_test_control(SQLITE_TESTCTRL_ISKEYWORD, const char *zWord)\n    **\n    ** If zWord is a keyword recognized by the parser, then return the\n    ** number of keywords.  Or if zWord is not a keyword, return 0.\n    ** \n    ** This test feature is only available in the amalgamation since\n    ** the SQLITE_N_KEYWORD macro is not defined in this file if SQLite\n    ** is built using separate source files.\n    */\n    case SQLITE_TESTCTRL_ISKEYWORD: {\n      const char *zWord = va_arg(ap, const char*);\n      int n = sqlite3Strlen30(zWord);\n      rc = (sqlite3KeywordCode((u8*)zWord, n)!=TK_ID) ? SQLITE_N_KEYWORD : 0;\n      break;\n    }\n#endif \n\n    /*   sqlite3_test_control(SQLITE_TESTCTRL_LOCALTIME_FAULT, int onoff);\n    **\n    ** If parameter onoff is non-zero, configure the wrappers so that all\n    ** subsequent calls to localtime() and variants fail. If onoff is zero,\n    ** undo this setting.\n    */\n    case SQLITE_TESTCTRL_LOCALTIME_FAULT: {\n      sqlite3GlobalConfig.bLocaltimeFault = va_arg(ap, int);\n      break;\n    }\n\n    /*   sqlite3_test_control(SQLITE_TESTCTRL_NEVER_CORRUPT, int);\n    **\n    ** Set or clear a flag that indicates that the database file is always well-\n    ** formed and never corrupt.  This flag is clear by default, indicating that\n    ** database files might have arbitrary corruption.  Setting the flag during\n    ** testing causes certain assert() statements in the code to be activated\n    ** that demonstrat invariants on well-formed database files.\n    */\n    case SQLITE_TESTCTRL_NEVER_CORRUPT: {\n      sqlite3GlobalConfig.neverCorrupt = va_arg(ap, int);\n      break;\n    }\n\n    /* Set the threshold at which OP_Once counters reset back to zero.\n    ** By default this is 0x7ffffffe (over 2 billion), but that value is\n    ** too big to test in a reasonable amount of time, so this control is\n    ** provided to set a small and easily reachable reset value.\n    */\n    case SQLITE_TESTCTRL_ONCE_RESET_THRESHOLD: {\n      sqlite3GlobalConfig.iOnceResetThreshold = va_arg(ap, int);\n      break;\n    }\n\n    /*   sqlite3_test_control(SQLITE_TESTCTRL_VDBE_COVERAGE, xCallback, ptr);\n    **\n    ** Set the VDBE coverage callback function to xCallback with context \n    ** pointer ptr.\n    */\n    case SQLITE_TESTCTRL_VDBE_COVERAGE: {\n#ifdef SQLITE_VDBE_COVERAGE\n      typedef void (*branch_callback)(void*,int,u8,u8);\n      sqlite3GlobalConfig.xVdbeBranch = va_arg(ap,branch_callback);\n      sqlite3GlobalConfig.pVdbeBranchArg = va_arg(ap,void*);\n#endif\n      break;\n    }\n\n    /*   sqlite3_test_control(SQLITE_TESTCTRL_SORTER_MMAP, db, nMax); */\n    case SQLITE_TESTCTRL_SORTER_MMAP: {\n      sqlite3 *db = va_arg(ap, sqlite3*);\n      db->nMaxSorterMmap = va_arg(ap, int);\n      break;\n    }\n\n    /*   sqlite3_test_control(SQLITE_TESTCTRL_ISINIT);\n    **\n    ** Return SQLITE_OK if SQLite has been initialized and SQLITE_ERROR if\n    ** not.\n    */\n    case SQLITE_TESTCTRL_ISINIT: {\n      if( sqlite3GlobalConfig.isInit==0 ) rc = SQLITE_ERROR;\n      break;\n    }\n\n    /*  sqlite3_test_control(SQLITE_TESTCTRL_IMPOSTER, db, dbName, onOff, tnum);\n    **\n    ** This test control is used to create imposter tables.  \"db\" is a pointer\n    ** to the database connection.  dbName is the database name (ex: \"main\" or\n    ** \"temp\") which will receive the imposter.  \"onOff\" turns imposter mode on\n    ** or off.  \"tnum\" is the root page of the b-tree to which the imposter\n    ** table should connect.\n    **\n    ** Enable imposter mode only when the schema has already been parsed.  Then\n    ** run a single CREATE TABLE statement to construct the imposter table in\n    ** the parsed schema.  Then turn imposter mode back off again.\n    **\n    ** If onOff==0 and tnum>0 then reset the schema for all databases, causing\n    ** the schema to be reparsed the next time it is needed.  This has the\n    ** effect of erasing all imposter tables.\n    */\n    case SQLITE_TESTCTRL_IMPOSTER: {\n      sqlite3 *db = va_arg(ap, sqlite3*);\n      sqlite3_mutex_enter(db->mutex);\n      db->init.iDb = sqlite3FindDbName(db, va_arg(ap,const char*));\n      db->init.busy = db->init.imposterTable = va_arg(ap,int);\n      db->init.newTnum = va_arg(ap,int);\n      if( db->init.busy==0 && db->init.newTnum>0 ){\n        sqlite3ResetAllSchemasOfConnection(db);\n      }\n      sqlite3_mutex_leave(db->mutex);\n      break;\n    }\n\n#if defined(YYCOVERAGE)\n    /*  sqlite3_test_control(SQLITE_TESTCTRL_PARSER_COVERAGE, FILE *out)\n    **\n    ** This test control (only available when SQLite is compiled with\n    ** -DYYCOVERAGE) writes a report onto \"out\" that shows all\n    ** state/lookahead combinations in the parser state machine\n    ** which are never exercised.  If any state is missed, make the\n    ** return code SQLITE_ERROR.\n    */\n    case SQLITE_TESTCTRL_PARSER_COVERAGE: {\n      FILE *out = va_arg(ap, FILE*);\n      if( sqlite3ParserCoverage(out) ) rc = SQLITE_ERROR;\n      break;\n    }\n#endif /* defined(YYCOVERAGE) */\n  }\n  va_end(ap);\n#endif /* SQLITE_UNTESTABLE */\n  return rc;\n}\n\n/*\n** This is a utility routine, useful to VFS implementations, that checks\n** to see if a database file was a URI that contained a specific query \n** parameter, and if so obtains the value of the query parameter.\n**\n** The zFilename argument is the filename pointer passed into the xOpen()\n** method of a VFS implementation.  The zParam argument is the name of the\n** query parameter we seek.  This routine returns the value of the zParam\n** parameter if it exists.  If the parameter does not exist, this routine\n** returns a NULL pointer.\n*/\nSQLITE_API const char *sqlite3_uri_parameter(const char *zFilename, const char *zParam){\n  if( zFilename==0 || zParam==0 ) return 0;\n  zFilename += sqlite3Strlen30(zFilename) + 1;\n  while( zFilename[0] ){\n    int x = strcmp(zFilename, zParam);\n    zFilename += sqlite3Strlen30(zFilename) + 1;\n    if( x==0 ) return zFilename;\n    zFilename += sqlite3Strlen30(zFilename) + 1;\n  }\n  return 0;\n}\n\n/*\n** Return a boolean value for a query parameter.\n*/\nSQLITE_API int sqlite3_uri_boolean(const char *zFilename, const char *zParam, int bDflt){\n  const char *z = sqlite3_uri_parameter(zFilename, zParam);\n  bDflt = bDflt!=0;\n  return z ? sqlite3GetBoolean(z, bDflt) : bDflt;\n}\n\n/*\n** Return a 64-bit integer value for a query parameter.\n*/\nSQLITE_API sqlite3_int64 sqlite3_uri_int64(\n  const char *zFilename,    /* Filename as passed to xOpen */\n  const char *zParam,       /* URI parameter sought */\n  sqlite3_int64 bDflt       /* return if parameter is missing */\n){\n  const char *z = sqlite3_uri_parameter(zFilename, zParam);\n  sqlite3_int64 v;\n  if( z && sqlite3DecOrHexToI64(z, &v)==0 ){\n    bDflt = v;\n  }\n  return bDflt;\n}\n\n/*\n** Return the Btree pointer identified by zDbName.  Return NULL if not found.\n*/\nSQLITE_PRIVATE Btree *sqlite3DbNameToBtree(sqlite3 *db, const char *zDbName){\n  int iDb = zDbName ? sqlite3FindDbName(db, zDbName) : 0;\n  return iDb<0 ? 0 : db->aDb[iDb].pBt;\n}\n\n/*\n** Return the filename of the database associated with a database\n** connection.\n*/\nSQLITE_API const char *sqlite3_db_filename(sqlite3 *db, const char *zDbName){\n  Btree *pBt;\n#ifdef SQLITE_ENABLE_API_ARMOR\n  if( !sqlite3SafetyCheckOk(db) ){\n    (void)SQLITE_MISUSE_BKPT;\n    return 0;\n  }\n#endif\n  pBt = sqlite3DbNameToBtree(db, zDbName);\n  return pBt ? sqlite3BtreeGetFilename(pBt) : 0;\n}\n\n/*\n** Return 1 if database is read-only or 0 if read/write.  Return -1 if\n** no such database exists.\n*/\nSQLITE_API int sqlite3_db_readonly(sqlite3 *db, const char *zDbName){\n  Btree *pBt;\n#ifdef SQLITE_ENABLE_API_ARMOR\n  if( !sqlite3SafetyCheckOk(db) ){\n    (void)SQLITE_MISUSE_BKPT;\n    return -1;\n  }\n#endif\n  pBt = sqlite3DbNameToBtree(db, zDbName);\n  return pBt ? sqlite3BtreeIsReadonly(pBt) : -1;\n}\n\n#ifdef SQLITE_ENABLE_SNAPSHOT\n/*\n** Obtain a snapshot handle for the snapshot of database zDb currently \n** being read by handle db.\n*/\nSQLITE_API int sqlite3_snapshot_get(\n  sqlite3 *db, \n  const char *zDb,\n  sqlite3_snapshot **ppSnapshot\n){\n  int rc = SQLITE_ERROR;\n#ifndef SQLITE_OMIT_WAL\n\n#ifdef SQLITE_ENABLE_API_ARMOR\n  if( !sqlite3SafetyCheckOk(db) ){\n    return SQLITE_MISUSE_BKPT;\n  }\n#endif\n  sqlite3_mutex_enter(db->mutex);\n\n  if( db->autoCommit==0 ){\n    int iDb = sqlite3FindDbName(db, zDb);\n    if( iDb==0 || iDb>1 ){\n      Btree *pBt = db->aDb[iDb].pBt;\n      if( 0==sqlite3BtreeIsInTrans(pBt) ){\n        rc = sqlite3BtreeBeginTrans(pBt, 0);\n        if( rc==SQLITE_OK ){\n          rc = sqlite3PagerSnapshotGet(sqlite3BtreePager(pBt), ppSnapshot);\n        }\n      }\n    }\n  }\n\n  sqlite3_mutex_leave(db->mutex);\n#endif   /* SQLITE_OMIT_WAL */\n  return rc;\n}\n\n/*\n** Open a read-transaction on the snapshot idendified by pSnapshot.\n*/\nSQLITE_API int sqlite3_snapshot_open(\n  sqlite3 *db, \n  const char *zDb, \n  sqlite3_snapshot *pSnapshot\n){\n  int rc = SQLITE_ERROR;\n#ifndef SQLITE_OMIT_WAL\n\n#ifdef SQLITE_ENABLE_API_ARMOR\n  if( !sqlite3SafetyCheckOk(db) ){\n    return SQLITE_MISUSE_BKPT;\n  }\n#endif\n  sqlite3_mutex_enter(db->mutex);\n  if( db->autoCommit==0 ){\n    int iDb;\n    iDb = sqlite3FindDbName(db, zDb);\n    if( iDb==0 || iDb>1 ){\n      Btree *pBt = db->aDb[iDb].pBt;\n      if( 0==sqlite3BtreeIsInReadTrans(pBt) ){\n        rc = sqlite3PagerSnapshotOpen(sqlite3BtreePager(pBt), pSnapshot);\n        if( rc==SQLITE_OK ){\n          rc = sqlite3BtreeBeginTrans(pBt, 0);\n          sqlite3PagerSnapshotOpen(sqlite3BtreePager(pBt), 0);\n        }\n      }\n    }\n  }\n\n  sqlite3_mutex_leave(db->mutex);\n#endif   /* SQLITE_OMIT_WAL */\n  return rc;\n}\n\n/*\n** Recover as many snapshots as possible from the wal file associated with\n** schema zDb of database db.\n*/\nSQLITE_API int sqlite3_snapshot_recover(sqlite3 *db, const char *zDb){\n  int rc = SQLITE_ERROR;\n  int iDb;\n#ifndef SQLITE_OMIT_WAL\n\n#ifdef SQLITE_ENABLE_API_ARMOR\n  if( !sqlite3SafetyCheckOk(db) ){\n    return SQLITE_MISUSE_BKPT;\n  }\n#endif\n\n  sqlite3_mutex_enter(db->mutex);\n  iDb = sqlite3FindDbName(db, zDb);\n  if( iDb==0 || iDb>1 ){\n    Btree *pBt = db->aDb[iDb].pBt;\n    if( 0==sqlite3BtreeIsInReadTrans(pBt) ){\n      rc = sqlite3BtreeBeginTrans(pBt, 0);\n      if( rc==SQLITE_OK ){\n        rc = sqlite3PagerSnapshotRecover(sqlite3BtreePager(pBt));\n        sqlite3BtreeCommit(pBt);\n      }\n    }\n  }\n  sqlite3_mutex_leave(db->mutex);\n#endif   /* SQLITE_OMIT_WAL */\n  return rc;\n}\n\n/*\n** Free a snapshot handle obtained from sqlite3_snapshot_get().\n*/\nSQLITE_API void sqlite3_snapshot_free(sqlite3_snapshot *pSnapshot){\n  sqlite3_free(pSnapshot);\n}\n#endif /* SQLITE_ENABLE_SNAPSHOT */\n\n#ifndef SQLITE_OMIT_COMPILEOPTION_DIAGS\n/*\n** Given the name of a compile-time option, return true if that option\n** was used and false if not.\n**\n** The name can optionally begin with \"SQLITE_\" but the \"SQLITE_\" prefix\n** is not required for a match.\n*/\nSQLITE_API int sqlite3_compileoption_used(const char *zOptName){\n  int i, n;\n  int nOpt;\n  const char **azCompileOpt;\n \n#if SQLITE_ENABLE_API_ARMOR\n  if( zOptName==0 ){\n    (void)SQLITE_MISUSE_BKPT;\n    return 0;\n  }\n#endif\n\n  azCompileOpt = sqlite3CompileOptions(&nOpt);\n\n  if( sqlite3StrNICmp(zOptName, \"SQLITE_\", 7)==0 ) zOptName += 7;\n  n = sqlite3Strlen30(zOptName);\n\n  /* Since nOpt is normally in single digits, a linear search is \n  ** adequate. No need for a binary search. */\n  for(i=0; i<nOpt; i++){\n    if( sqlite3StrNICmp(zOptName, azCompileOpt[i], n)==0\n     && sqlite3IsIdChar((unsigned char)azCompileOpt[i][n])==0\n    ){\n      return 1;\n    }\n  }\n  return 0;\n}\n\n/*\n** Return the N-th compile-time option string.  If N is out of range,\n** return a NULL pointer.\n*/\nSQLITE_API const char *sqlite3_compileoption_get(int N){\n  int nOpt;\n  const char **azCompileOpt;\n  azCompileOpt = sqlite3CompileOptions(&nOpt);\n  if( N>=0 && N<nOpt ){\n    return azCompileOpt[N];\n  }\n  return 0;\n}\n#endif /* SQLITE_OMIT_COMPILEOPTION_DIAGS */\n\n/************** End of main.c ************************************************/\n/************** Begin file notify.c ******************************************/\n/*\n** 2009 March 3\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n*************************************************************************\n**\n** This file contains the implementation of the sqlite3_unlock_notify()\n** API method and its associated functionality.\n*/\n/* #include \"sqliteInt.h\" */\n/* #include \"btreeInt.h\" */\n\n/* Omit this entire file if SQLITE_ENABLE_UNLOCK_NOTIFY is not defined. */\n#ifdef SQLITE_ENABLE_UNLOCK_NOTIFY\n\n/*\n** Public interfaces:\n**\n**   sqlite3ConnectionBlocked()\n**   sqlite3ConnectionUnlocked()\n**   sqlite3ConnectionClosed()\n**   sqlite3_unlock_notify()\n*/\n\n#define assertMutexHeld() \\\n  assert( sqlite3_mutex_held(sqlite3MutexAlloc(SQLITE_MUTEX_STATIC_MASTER)) )\n\n/*\n** Head of a linked list of all sqlite3 objects created by this process\n** for which either sqlite3.pBlockingConnection or sqlite3.pUnlockConnection\n** is not NULL. This variable may only accessed while the STATIC_MASTER\n** mutex is held.\n*/\nstatic sqlite3 *SQLITE_WSD sqlite3BlockedList = 0;\n\n#ifndef NDEBUG\n/*\n** This function is a complex assert() that verifies the following \n** properties of the blocked connections list:\n**\n**   1) Each entry in the list has a non-NULL value for either \n**      pUnlockConnection or pBlockingConnection, or both.\n**\n**   2) All entries in the list that share a common value for \n**      xUnlockNotify are grouped together.\n**\n**   3) If the argument db is not NULL, then none of the entries in the\n**      blocked connections list have pUnlockConnection or pBlockingConnection\n**      set to db. This is used when closing connection db.\n*/\nstatic void checkListProperties(sqlite3 *db){\n  sqlite3 *p;\n  for(p=sqlite3BlockedList; p; p=p->pNextBlocked){\n    int seen = 0;\n    sqlite3 *p2;\n\n    /* Verify property (1) */\n    assert( p->pUnlockConnection || p->pBlockingConnection );\n\n    /* Verify property (2) */\n    for(p2=sqlite3BlockedList; p2!=p; p2=p2->pNextBlocked){\n      if( p2->xUnlockNotify==p->xUnlockNotify ) seen = 1;\n      assert( p2->xUnlockNotify==p->xUnlockNotify || !seen );\n      assert( db==0 || p->pUnlockConnection!=db );\n      assert( db==0 || p->pBlockingConnection!=db );\n    }\n  }\n}\n#else\n# define checkListProperties(x)\n#endif\n\n/*\n** Remove connection db from the blocked connections list. If connection\n** db is not currently a part of the list, this function is a no-op.\n*/\nstatic void removeFromBlockedList(sqlite3 *db){\n  sqlite3 **pp;\n  assertMutexHeld();\n  for(pp=&sqlite3BlockedList; *pp; pp = &(*pp)->pNextBlocked){\n    if( *pp==db ){\n      *pp = (*pp)->pNextBlocked;\n      break;\n    }\n  }\n}\n\n/*\n** Add connection db to the blocked connections list. It is assumed\n** that it is not already a part of the list.\n*/\nstatic void addToBlockedList(sqlite3 *db){\n  sqlite3 **pp;\n  assertMutexHeld();\n  for(\n    pp=&sqlite3BlockedList; \n    *pp && (*pp)->xUnlockNotify!=db->xUnlockNotify; \n    pp=&(*pp)->pNextBlocked\n  );\n  db->pNextBlocked = *pp;\n  *pp = db;\n}\n\n/*\n** Obtain the STATIC_MASTER mutex.\n*/\nstatic void enterMutex(void){\n  sqlite3_mutex_enter(sqlite3MutexAlloc(SQLITE_MUTEX_STATIC_MASTER));\n  checkListProperties(0);\n}\n\n/*\n** Release the STATIC_MASTER mutex.\n*/\nstatic void leaveMutex(void){\n  assertMutexHeld();\n  checkListProperties(0);\n  sqlite3_mutex_leave(sqlite3MutexAlloc(SQLITE_MUTEX_STATIC_MASTER));\n}\n\n/*\n** Register an unlock-notify callback.\n**\n** This is called after connection \"db\" has attempted some operation\n** but has received an SQLITE_LOCKED error because another connection\n** (call it pOther) in the same process was busy using the same shared\n** cache.  pOther is found by looking at db->pBlockingConnection.\n**\n** If there is no blocking connection, the callback is invoked immediately,\n** before this routine returns.\n**\n** If pOther is already blocked on db, then report SQLITE_LOCKED, to indicate\n** a deadlock.\n**\n** Otherwise, make arrangements to invoke xNotify when pOther drops\n** its locks.\n**\n** Each call to this routine overrides any prior callbacks registered\n** on the same \"db\".  If xNotify==0 then any prior callbacks are immediately\n** cancelled.\n*/\nSQLITE_API int sqlite3_unlock_notify(\n  sqlite3 *db,\n  void (*xNotify)(void **, int),\n  void *pArg\n){\n  int rc = SQLITE_OK;\n\n  sqlite3_mutex_enter(db->mutex);\n  enterMutex();\n\n  if( xNotify==0 ){\n    removeFromBlockedList(db);\n    db->pBlockingConnection = 0;\n    db->pUnlockConnection = 0;\n    db->xUnlockNotify = 0;\n    db->pUnlockArg = 0;\n  }else if( 0==db->pBlockingConnection ){\n    /* The blocking transaction has been concluded. Or there never was a \n    ** blocking transaction. In either case, invoke the notify callback\n    ** immediately. \n    */\n    xNotify(&pArg, 1);\n  }else{\n    sqlite3 *p;\n\n    for(p=db->pBlockingConnection; p && p!=db; p=p->pUnlockConnection){}\n    if( p ){\n      rc = SQLITE_LOCKED;              /* Deadlock detected. */\n    }else{\n      db->pUnlockConnection = db->pBlockingConnection;\n      db->xUnlockNotify = xNotify;\n      db->pUnlockArg = pArg;\n      removeFromBlockedList(db);\n      addToBlockedList(db);\n    }\n  }\n\n  leaveMutex();\n  assert( !db->mallocFailed );\n  sqlite3ErrorWithMsg(db, rc, (rc?\"database is deadlocked\":0));\n  sqlite3_mutex_leave(db->mutex);\n  return rc;\n}\n\n/*\n** This function is called while stepping or preparing a statement \n** associated with connection db. The operation will return SQLITE_LOCKED\n** to the user because it requires a lock that will not be available\n** until connection pBlocker concludes its current transaction.\n*/\nSQLITE_PRIVATE void sqlite3ConnectionBlocked(sqlite3 *db, sqlite3 *pBlocker){\n  enterMutex();\n  if( db->pBlockingConnection==0 && db->pUnlockConnection==0 ){\n    addToBlockedList(db);\n  }\n  db->pBlockingConnection = pBlocker;\n  leaveMutex();\n}\n\n/*\n** This function is called when\n** the transaction opened by database db has just finished. Locks held \n** by database connection db have been released.\n**\n** This function loops through each entry in the blocked connections\n** list and does the following:\n**\n**   1) If the sqlite3.pBlockingConnection member of a list entry is\n**      set to db, then set pBlockingConnection=0.\n**\n**   2) If the sqlite3.pUnlockConnection member of a list entry is\n**      set to db, then invoke the configured unlock-notify callback and\n**      set pUnlockConnection=0.\n**\n**   3) If the two steps above mean that pBlockingConnection==0 and\n**      pUnlockConnection==0, remove the entry from the blocked connections\n**      list.\n*/\nSQLITE_PRIVATE void sqlite3ConnectionUnlocked(sqlite3 *db){\n  void (*xUnlockNotify)(void **, int) = 0; /* Unlock-notify cb to invoke */\n  int nArg = 0;                            /* Number of entries in aArg[] */\n  sqlite3 **pp;                            /* Iterator variable */\n  void **aArg;               /* Arguments to the unlock callback */\n  void **aDyn = 0;           /* Dynamically allocated space for aArg[] */\n  void *aStatic[16];         /* Starter space for aArg[].  No malloc required */\n\n  aArg = aStatic;\n  enterMutex();         /* Enter STATIC_MASTER mutex */\n\n  /* This loop runs once for each entry in the blocked-connections list. */\n  for(pp=&sqlite3BlockedList; *pp; /* no-op */ ){\n    sqlite3 *p = *pp;\n\n    /* Step 1. */\n    if( p->pBlockingConnection==db ){\n      p->pBlockingConnection = 0;\n    }\n\n    /* Step 2. */\n    if( p->pUnlockConnection==db ){\n      assert( p->xUnlockNotify );\n      if( p->xUnlockNotify!=xUnlockNotify && nArg!=0 ){\n        xUnlockNotify(aArg, nArg);\n        nArg = 0;\n      }\n\n      sqlite3BeginBenignMalloc();\n      assert( aArg==aDyn || (aDyn==0 && aArg==aStatic) );\n      assert( nArg<=(int)ArraySize(aStatic) || aArg==aDyn );\n      if( (!aDyn && nArg==(int)ArraySize(aStatic))\n       || (aDyn && nArg==(int)(sqlite3MallocSize(aDyn)/sizeof(void*)))\n      ){\n        /* The aArg[] array needs to grow. */\n        void **pNew = (void **)sqlite3Malloc(nArg*sizeof(void *)*2);\n        if( pNew ){\n          memcpy(pNew, aArg, nArg*sizeof(void *));\n          sqlite3_free(aDyn);\n          aDyn = aArg = pNew;\n        }else{\n          /* This occurs when the array of context pointers that need to\n          ** be passed to the unlock-notify callback is larger than the\n          ** aStatic[] array allocated on the stack and the attempt to \n          ** allocate a larger array from the heap has failed.\n          **\n          ** This is a difficult situation to handle. Returning an error\n          ** code to the caller is insufficient, as even if an error code\n          ** is returned the transaction on connection db will still be\n          ** closed and the unlock-notify callbacks on blocked connections\n          ** will go unissued. This might cause the application to wait\n          ** indefinitely for an unlock-notify callback that will never \n          ** arrive.\n          **\n          ** Instead, invoke the unlock-notify callback with the context\n          ** array already accumulated. We can then clear the array and\n          ** begin accumulating any further context pointers without \n          ** requiring any dynamic allocation. This is sub-optimal because\n          ** it means that instead of one callback with a large array of\n          ** context pointers the application will receive two or more\n          ** callbacks with smaller arrays of context pointers, which will\n          ** reduce the applications ability to prioritize multiple \n          ** connections. But it is the best that can be done under the\n          ** circumstances.\n          */\n          xUnlockNotify(aArg, nArg);\n          nArg = 0;\n        }\n      }\n      sqlite3EndBenignMalloc();\n\n      aArg[nArg++] = p->pUnlockArg;\n      xUnlockNotify = p->xUnlockNotify;\n      p->pUnlockConnection = 0;\n      p->xUnlockNotify = 0;\n      p->pUnlockArg = 0;\n    }\n\n    /* Step 3. */\n    if( p->pBlockingConnection==0 && p->pUnlockConnection==0 ){\n      /* Remove connection p from the blocked connections list. */\n      *pp = p->pNextBlocked;\n      p->pNextBlocked = 0;\n    }else{\n      pp = &p->pNextBlocked;\n    }\n  }\n\n  if( nArg!=0 ){\n    xUnlockNotify(aArg, nArg);\n  }\n  sqlite3_free(aDyn);\n  leaveMutex();         /* Leave STATIC_MASTER mutex */\n}\n\n/*\n** This is called when the database connection passed as an argument is \n** being closed. The connection is removed from the blocked list.\n*/\nSQLITE_PRIVATE void sqlite3ConnectionClosed(sqlite3 *db){\n  sqlite3ConnectionUnlocked(db);\n  enterMutex();\n  removeFromBlockedList(db);\n  checkListProperties(db);\n  leaveMutex();\n}\n#endif\n\n/************** End of notify.c **********************************************/\n/************** Begin file fts3.c ********************************************/\n/*\n** 2006 Oct 10\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n******************************************************************************\n**\n** This is an SQLite module implementing full-text search.\n*/\n\n/*\n** The code in this file is only compiled if:\n**\n**     * The FTS3 module is being built as an extension\n**       (in which case SQLITE_CORE is not defined), or\n**\n**     * The FTS3 module is being built into the core of\n**       SQLite (in which case SQLITE_ENABLE_FTS3 is defined).\n*/\n\n/* The full-text index is stored in a series of b+tree (-like)\n** structures called segments which map terms to doclists.  The\n** structures are like b+trees in layout, but are constructed from the\n** bottom up in optimal fashion and are not updatable.  Since trees\n** are built from the bottom up, things will be described from the\n** bottom up.\n**\n**\n**** Varints ****\n** The basic unit of encoding is a variable-length integer called a\n** varint.  We encode variable-length integers in little-endian order\n** using seven bits * per byte as follows:\n**\n** KEY:\n**         A = 0xxxxxxx    7 bits of data and one flag bit\n**         B = 1xxxxxxx    7 bits of data and one flag bit\n**\n**  7 bits - A\n** 14 bits - BA\n** 21 bits - BBA\n** and so on.\n**\n** This is similar in concept to how sqlite encodes \"varints\" but\n** the encoding is not the same.  SQLite varints are big-endian\n** are are limited to 9 bytes in length whereas FTS3 varints are\n** little-endian and can be up to 10 bytes in length (in theory).\n**\n** Example encodings:\n**\n**     1:    0x01\n**   127:    0x7f\n**   128:    0x81 0x00\n**\n**\n**** Document lists ****\n** A doclist (document list) holds a docid-sorted list of hits for a\n** given term.  Doclists hold docids and associated token positions.\n** A docid is the unique integer identifier for a single document.\n** A position is the index of a word within the document.  The first \n** word of the document has a position of 0.\n**\n** FTS3 used to optionally store character offsets using a compile-time\n** option.  But that functionality is no longer supported.\n**\n** A doclist is stored like this:\n**\n** array {\n**   varint docid;          (delta from previous doclist)\n**   array {                (position list for column 0)\n**     varint position;     (2 more than the delta from previous position)\n**   }\n**   array {\n**     varint POS_COLUMN;   (marks start of position list for new column)\n**     varint column;       (index of new column)\n**     array {\n**       varint position;   (2 more than the delta from previous position)\n**     }\n**   }\n**   varint POS_END;        (marks end of positions for this document.\n** }\n**\n** Here, array { X } means zero or more occurrences of X, adjacent in\n** memory.  A \"position\" is an index of a token in the token stream\n** generated by the tokenizer. Note that POS_END and POS_COLUMN occur \n** in the same logical place as the position element, and act as sentinals\n** ending a position list array.  POS_END is 0.  POS_COLUMN is 1.\n** The positions numbers are not stored literally but rather as two more\n** than the difference from the prior position, or the just the position plus\n** 2 for the first position.  Example:\n**\n**   label:       A B C D E  F  G H   I  J K\n**   value:     123 5 9 1 1 14 35 0 234 72 0\n**\n** The 123 value is the first docid.  For column zero in this document\n** there are two matches at positions 3 and 10 (5-2 and 9-2+3).  The 1\n** at D signals the start of a new column; the 1 at E indicates that the\n** new column is column number 1.  There are two positions at 12 and 45\n** (14-2 and 35-2+12).  The 0 at H indicate the end-of-document.  The\n** 234 at I is the delta to next docid (357).  It has one position 70\n** (72-2) and then terminates with the 0 at K.\n**\n** A \"position-list\" is the list of positions for multiple columns for\n** a single docid.  A \"column-list\" is the set of positions for a single\n** column.  Hence, a position-list consists of one or more column-lists,\n** a document record consists of a docid followed by a position-list and\n** a doclist consists of one or more document records.\n**\n** A bare doclist omits the position information, becoming an \n** array of varint-encoded docids.\n**\n**** Segment leaf nodes ****\n** Segment leaf nodes store terms and doclists, ordered by term.  Leaf\n** nodes are written using LeafWriter, and read using LeafReader (to\n** iterate through a single leaf node's data) and LeavesReader (to\n** iterate through a segment's entire leaf layer).  Leaf nodes have\n** the format:\n**\n** varint iHeight;             (height from leaf level, always 0)\n** varint nTerm;               (length of first term)\n** char pTerm[nTerm];          (content of first term)\n** varint nDoclist;            (length of term's associated doclist)\n** char pDoclist[nDoclist];    (content of doclist)\n** array {\n**                             (further terms are delta-encoded)\n**   varint nPrefix;           (length of prefix shared with previous term)\n**   varint nSuffix;           (length of unshared suffix)\n**   char pTermSuffix[nSuffix];(unshared suffix of next term)\n**   varint nDoclist;          (length of term's associated doclist)\n**   char pDoclist[nDoclist];  (content of doclist)\n** }\n**\n** Here, array { X } means zero or more occurrences of X, adjacent in\n** memory.\n**\n** Leaf nodes are broken into blocks which are stored contiguously in\n** the %_segments table in sorted order.  This means that when the end\n** of a node is reached, the next term is in the node with the next\n** greater node id.\n**\n** New data is spilled to a new leaf node when the current node\n** exceeds LEAF_MAX bytes (default 2048).  New data which itself is\n** larger than STANDALONE_MIN (default 1024) is placed in a standalone\n** node (a leaf node with a single term and doclist).  The goal of\n** these settings is to pack together groups of small doclists while\n** making it efficient to directly access large doclists.  The\n** assumption is that large doclists represent terms which are more\n** likely to be query targets.\n**\n** TODO(shess) It may be useful for blocking decisions to be more\n** dynamic.  For instance, it may make more sense to have a 2.5k leaf\n** node rather than splitting into 2k and .5k nodes.  My intuition is\n** that this might extend through 2x or 4x the pagesize.\n**\n**\n**** Segment interior nodes ****\n** Segment interior nodes store blockids for subtree nodes and terms\n** to describe what data is stored by the each subtree.  Interior\n** nodes are written using InteriorWriter, and read using\n** InteriorReader.  InteriorWriters are created as needed when\n** SegmentWriter creates new leaf nodes, or when an interior node\n** itself grows too big and must be split.  The format of interior\n** nodes:\n**\n** varint iHeight;           (height from leaf level, always >0)\n** varint iBlockid;          (block id of node's leftmost subtree)\n** optional {\n**   varint nTerm;           (length of first term)\n**   char pTerm[nTerm];      (content of first term)\n**   array {\n**                                (further terms are delta-encoded)\n**     varint nPrefix;            (length of shared prefix with previous term)\n**     varint nSuffix;            (length of unshared suffix)\n**     char pTermSuffix[nSuffix]; (unshared suffix of next term)\n**   }\n** }\n**\n** Here, optional { X } means an optional element, while array { X }\n** means zero or more occurrences of X, adjacent in memory.\n**\n** An interior node encodes n terms separating n+1 subtrees.  The\n** subtree blocks are contiguous, so only the first subtree's blockid\n** is encoded.  The subtree at iBlockid will contain all terms less\n** than the first term encoded (or all terms if no term is encoded).\n** Otherwise, for terms greater than or equal to pTerm[i] but less\n** than pTerm[i+1], the subtree for that term will be rooted at\n** iBlockid+i.  Interior nodes only store enough term data to\n** distinguish adjacent children (if the rightmost term of the left\n** child is \"something\", and the leftmost term of the right child is\n** \"wicked\", only \"w\" is stored).\n**\n** New data is spilled to a new interior node at the same height when\n** the current node exceeds INTERIOR_MAX bytes (default 2048).\n** INTERIOR_MIN_TERMS (default 7) keeps large terms from monopolizing\n** interior nodes and making the tree too skinny.  The interior nodes\n** at a given height are naturally tracked by interior nodes at\n** height+1, and so on.\n**\n**\n**** Segment directory ****\n** The segment directory in table %_segdir stores meta-information for\n** merging and deleting segments, and also the root node of the\n** segment's tree.\n**\n** The root node is the top node of the segment's tree after encoding\n** the entire segment, restricted to ROOT_MAX bytes (default 1024).\n** This could be either a leaf node or an interior node.  If the top\n** node requires more than ROOT_MAX bytes, it is flushed to %_segments\n** and a new root interior node is generated (which should always fit\n** within ROOT_MAX because it only needs space for 2 varints, the\n** height and the blockid of the previous root).\n**\n** The meta-information in the segment directory is:\n**   level               - segment level (see below)\n**   idx                 - index within level\n**                       - (level,idx uniquely identify a segment)\n**   start_block         - first leaf node\n**   leaves_end_block    - last leaf node\n**   end_block           - last block (including interior nodes)\n**   root                - contents of root node\n**\n** If the root node is a leaf node, then start_block,\n** leaves_end_block, and end_block are all 0.\n**\n**\n**** Segment merging ****\n** To amortize update costs, segments are grouped into levels and\n** merged in batches.  Each increase in level represents exponentially\n** more documents.\n**\n** New documents (actually, document updates) are tokenized and\n** written individually (using LeafWriter) to a level 0 segment, with\n** incrementing idx.  When idx reaches MERGE_COUNT (default 16), all\n** level 0 segments are merged into a single level 1 segment.  Level 1\n** is populated like level 0, and eventually MERGE_COUNT level 1\n** segments are merged to a single level 2 segment (representing\n** MERGE_COUNT^2 updates), and so on.\n**\n** A segment merge traverses all segments at a given level in\n** parallel, performing a straightforward sorted merge.  Since segment\n** leaf nodes are written in to the %_segments table in order, this\n** merge traverses the underlying sqlite disk structures efficiently.\n** After the merge, all segment blocks from the merged level are\n** deleted.\n**\n** MERGE_COUNT controls how often we merge segments.  16 seems to be\n** somewhat of a sweet spot for insertion performance.  32 and 64 show\n** very similar performance numbers to 16 on insertion, though they're\n** a tiny bit slower (perhaps due to more overhead in merge-time\n** sorting).  8 is about 20% slower than 16, 4 about 50% slower than\n** 16, 2 about 66% slower than 16.\n**\n** At query time, high MERGE_COUNT increases the number of segments\n** which need to be scanned and merged.  For instance, with 100k docs\n** inserted:\n**\n**    MERGE_COUNT   segments\n**       16           25\n**        8           12\n**        4           10\n**        2            6\n**\n** This appears to have only a moderate impact on queries for very\n** frequent terms (which are somewhat dominated by segment merge\n** costs), and infrequent and non-existent terms still seem to be fast\n** even with many segments.\n**\n** TODO(shess) That said, it would be nice to have a better query-side\n** argument for MERGE_COUNT of 16.  Also, it is possible/likely that\n** optimizations to things like doclist merging will swing the sweet\n** spot around.\n**\n**\n**\n**** Handling of deletions and updates ****\n** Since we're using a segmented structure, with no docid-oriented\n** index into the term index, we clearly cannot simply update the term\n** index when a document is deleted or updated.  For deletions, we\n** write an empty doclist (varint(docid) varint(POS_END)), for updates\n** we simply write the new doclist.  Segment merges overwrite older\n** data for a particular docid with newer data, so deletes or updates\n** will eventually overtake the earlier data and knock it out.  The\n** query logic likewise merges doclists so that newer data knocks out\n** older data.\n*/\n\n/************** Include fts3Int.h in the middle of fts3.c ********************/\n/************** Begin file fts3Int.h *****************************************/\n/*\n** 2009 Nov 12\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n******************************************************************************\n**\n*/\n#ifndef _FTSINT_H\n#define _FTSINT_H\n\n#if !defined(NDEBUG) && !defined(SQLITE_DEBUG) \n# define NDEBUG 1\n#endif\n\n/* FTS3/FTS4 require virtual tables */\n#ifdef SQLITE_OMIT_VIRTUALTABLE\n# undef SQLITE_ENABLE_FTS3\n# undef SQLITE_ENABLE_FTS4\n#endif\n\n/*\n** FTS4 is really an extension for FTS3.  It is enabled using the\n** SQLITE_ENABLE_FTS3 macro.  But to avoid confusion we also all\n** the SQLITE_ENABLE_FTS4 macro to serve as an alisse for SQLITE_ENABLE_FTS3.\n*/\n#if defined(SQLITE_ENABLE_FTS4) && !defined(SQLITE_ENABLE_FTS3)\n# define SQLITE_ENABLE_FTS3\n#endif\n\n#if !defined(SQLITE_CORE) || defined(SQLITE_ENABLE_FTS3)\n\n/* If not building as part of the core, include sqlite3ext.h. */\n#ifndef SQLITE_CORE\n/* # include \"sqlite3ext.h\"  */\nSQLITE_EXTENSION_INIT3\n#endif\n\n/* #include \"sqlite3.h\" */\n/************** Include fts3_tokenizer.h in the middle of fts3Int.h **********/\n/************** Begin file fts3_tokenizer.h **********************************/\n/*\n** 2006 July 10\n**\n** The author disclaims copyright to this source code.\n**\n*************************************************************************\n** Defines the interface to tokenizers used by fulltext-search.  There\n** are three basic components:\n**\n** sqlite3_tokenizer_module is a singleton defining the tokenizer\n** interface functions.  This is essentially the class structure for\n** tokenizers.\n**\n** sqlite3_tokenizer is used to define a particular tokenizer, perhaps\n** including customization information defined at creation time.\n**\n** sqlite3_tokenizer_cursor is generated by a tokenizer to generate\n** tokens from a particular input.\n*/\n#ifndef _FTS3_TOKENIZER_H_\n#define _FTS3_TOKENIZER_H_\n\n/* TODO(shess) Only used for SQLITE_OK and SQLITE_DONE at this time.\n** If tokenizers are to be allowed to call sqlite3_*() functions, then\n** we will need a way to register the API consistently.\n*/\n/* #include \"sqlite3.h\" */\n\n/*\n** Structures used by the tokenizer interface. When a new tokenizer\n** implementation is registered, the caller provides a pointer to\n** an sqlite3_tokenizer_module containing pointers to the callback\n** functions that make up an implementation.\n**\n** When an fts3 table is created, it passes any arguments passed to\n** the tokenizer clause of the CREATE VIRTUAL TABLE statement to the\n** sqlite3_tokenizer_module.xCreate() function of the requested tokenizer\n** implementation. The xCreate() function in turn returns an \n** sqlite3_tokenizer structure representing the specific tokenizer to\n** be used for the fts3 table (customized by the tokenizer clause arguments).\n**\n** To tokenize an input buffer, the sqlite3_tokenizer_module.xOpen()\n** method is called. It returns an sqlite3_tokenizer_cursor object\n** that may be used to tokenize a specific input buffer based on\n** the tokenization rules supplied by a specific sqlite3_tokenizer\n** object.\n*/\ntypedef struct sqlite3_tokenizer_module sqlite3_tokenizer_module;\ntypedef struct sqlite3_tokenizer sqlite3_tokenizer;\ntypedef struct sqlite3_tokenizer_cursor sqlite3_tokenizer_cursor;\n\nstruct sqlite3_tokenizer_module {\n\n  /*\n  ** Structure version. Should always be set to 0 or 1.\n  */\n  int iVersion;\n\n  /*\n  ** Create a new tokenizer. The values in the argv[] array are the\n  ** arguments passed to the \"tokenizer\" clause of the CREATE VIRTUAL\n  ** TABLE statement that created the fts3 table. For example, if\n  ** the following SQL is executed:\n  **\n  **   CREATE .. USING fts3( ... , tokenizer <tokenizer-name> arg1 arg2)\n  **\n  ** then argc is set to 2, and the argv[] array contains pointers\n  ** to the strings \"arg1\" and \"arg2\".\n  **\n  ** This method should return either SQLITE_OK (0), or an SQLite error \n  ** code. If SQLITE_OK is returned, then *ppTokenizer should be set\n  ** to point at the newly created tokenizer structure. The generic\n  ** sqlite3_tokenizer.pModule variable should not be initialized by\n  ** this callback. The caller will do so.\n  */\n  int (*xCreate)(\n    int argc,                           /* Size of argv array */\n    const char *const*argv,             /* Tokenizer argument strings */\n    sqlite3_tokenizer **ppTokenizer     /* OUT: Created tokenizer */\n  );\n\n  /*\n  ** Destroy an existing tokenizer. The fts3 module calls this method\n  ** exactly once for each successful call to xCreate().\n  */\n  int (*xDestroy)(sqlite3_tokenizer *pTokenizer);\n\n  /*\n  ** Create a tokenizer cursor to tokenize an input buffer. The caller\n  ** is responsible for ensuring that the input buffer remains valid\n  ** until the cursor is closed (using the xClose() method). \n  */\n  int (*xOpen)(\n    sqlite3_tokenizer *pTokenizer,       /* Tokenizer object */\n    const char *pInput, int nBytes,      /* Input buffer */\n    sqlite3_tokenizer_cursor **ppCursor  /* OUT: Created tokenizer cursor */\n  );\n\n  /*\n  ** Destroy an existing tokenizer cursor. The fts3 module calls this \n  ** method exactly once for each successful call to xOpen().\n  */\n  int (*xClose)(sqlite3_tokenizer_cursor *pCursor);\n\n  /*\n  ** Retrieve the next token from the tokenizer cursor pCursor. This\n  ** method should either return SQLITE_OK and set the values of the\n  ** \"OUT\" variables identified below, or SQLITE_DONE to indicate that\n  ** the end of the buffer has been reached, or an SQLite error code.\n  **\n  ** *ppToken should be set to point at a buffer containing the \n  ** normalized version of the token (i.e. after any case-folding and/or\n  ** stemming has been performed). *pnBytes should be set to the length\n  ** of this buffer in bytes. The input text that generated the token is\n  ** identified by the byte offsets returned in *piStartOffset and\n  ** *piEndOffset. *piStartOffset should be set to the index of the first\n  ** byte of the token in the input buffer. *piEndOffset should be set\n  ** to the index of the first byte just past the end of the token in\n  ** the input buffer.\n  **\n  ** The buffer *ppToken is set to point at is managed by the tokenizer\n  ** implementation. It is only required to be valid until the next call\n  ** to xNext() or xClose(). \n  */\n  /* TODO(shess) current implementation requires pInput to be\n  ** nul-terminated.  This should either be fixed, or pInput/nBytes\n  ** should be converted to zInput.\n  */\n  int (*xNext)(\n    sqlite3_tokenizer_cursor *pCursor,   /* Tokenizer cursor */\n    const char **ppToken, int *pnBytes,  /* OUT: Normalized text for token */\n    int *piStartOffset,  /* OUT: Byte offset of token in input buffer */\n    int *piEndOffset,    /* OUT: Byte offset of end of token in input buffer */\n    int *piPosition      /* OUT: Number of tokens returned before this one */\n  );\n\n  /***********************************************************************\n  ** Methods below this point are only available if iVersion>=1.\n  */\n\n  /* \n  ** Configure the language id of a tokenizer cursor.\n  */\n  int (*xLanguageid)(sqlite3_tokenizer_cursor *pCsr, int iLangid);\n};\n\nstruct sqlite3_tokenizer {\n  const sqlite3_tokenizer_module *pModule;  /* The module for this tokenizer */\n  /* Tokenizer implementations will typically add additional fields */\n};\n\nstruct sqlite3_tokenizer_cursor {\n  sqlite3_tokenizer *pTokenizer;       /* Tokenizer for this cursor. */\n  /* Tokenizer implementations will typically add additional fields */\n};\n\nint fts3_global_term_cnt(int iTerm, int iCol);\nint fts3_term_cnt(int iTerm, int iCol);\n\n\n#endif /* _FTS3_TOKENIZER_H_ */\n\n/************** End of fts3_tokenizer.h **************************************/\n/************** Continuing where we left off in fts3Int.h ********************/\n/************** Include fts3_hash.h in the middle of fts3Int.h ***************/\n/************** Begin file fts3_hash.h ***************************************/\n/*\n** 2001 September 22\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n*************************************************************************\n** This is the header file for the generic hash-table implementation\n** used in SQLite.  We've modified it slightly to serve as a standalone\n** hash table implementation for the full-text indexing module.\n**\n*/\n#ifndef _FTS3_HASH_H_\n#define _FTS3_HASH_H_\n\n/* Forward declarations of structures. */\ntypedef struct Fts3Hash Fts3Hash;\ntypedef struct Fts3HashElem Fts3HashElem;\n\n/* A complete hash table is an instance of the following structure.\n** The internals of this structure are intended to be opaque -- client\n** code should not attempt to access or modify the fields of this structure\n** directly.  Change this structure only by using the routines below.\n** However, many of the \"procedures\" and \"functions\" for modifying and\n** accessing this structure are really macros, so we can't really make\n** this structure opaque.\n*/\nstruct Fts3Hash {\n  char keyClass;          /* HASH_INT, _POINTER, _STRING, _BINARY */\n  char copyKey;           /* True if copy of key made on insert */\n  int count;              /* Number of entries in this table */\n  Fts3HashElem *first;    /* The first element of the array */\n  int htsize;             /* Number of buckets in the hash table */\n  struct _fts3ht {        /* the hash table */\n    int count;               /* Number of entries with this hash */\n    Fts3HashElem *chain;     /* Pointer to first entry with this hash */\n  } *ht;\n};\n\n/* Each element in the hash table is an instance of the following \n** structure.  All elements are stored on a single doubly-linked list.\n**\n** Again, this structure is intended to be opaque, but it can't really\n** be opaque because it is used by macros.\n*/\nstruct Fts3HashElem {\n  Fts3HashElem *next, *prev; /* Next and previous elements in the table */\n  void *data;                /* Data associated with this element */\n  void *pKey; int nKey;      /* Key associated with this element */\n};\n\n/*\n** There are 2 different modes of operation for a hash table:\n**\n**   FTS3_HASH_STRING        pKey points to a string that is nKey bytes long\n**                           (including the null-terminator, if any).  Case\n**                           is respected in comparisons.\n**\n**   FTS3_HASH_BINARY        pKey points to binary data nKey bytes long. \n**                           memcmp() is used to compare keys.\n**\n** A copy of the key is made if the copyKey parameter to fts3HashInit is 1.  \n*/\n#define FTS3_HASH_STRING    1\n#define FTS3_HASH_BINARY    2\n\n/*\n** Access routines.  To delete, insert a NULL pointer.\n*/\nSQLITE_PRIVATE void sqlite3Fts3HashInit(Fts3Hash *pNew, char keyClass, char copyKey);\nSQLITE_PRIVATE void *sqlite3Fts3HashInsert(Fts3Hash*, const void *pKey, int nKey, void *pData);\nSQLITE_PRIVATE void *sqlite3Fts3HashFind(const Fts3Hash*, const void *pKey, int nKey);\nSQLITE_PRIVATE void sqlite3Fts3HashClear(Fts3Hash*);\nSQLITE_PRIVATE Fts3HashElem *sqlite3Fts3HashFindElem(const Fts3Hash *, const void *, int);\n\n/*\n** Shorthand for the functions above\n*/\n#define fts3HashInit     sqlite3Fts3HashInit\n#define fts3HashInsert   sqlite3Fts3HashInsert\n#define fts3HashFind     sqlite3Fts3HashFind\n#define fts3HashClear    sqlite3Fts3HashClear\n#define fts3HashFindElem sqlite3Fts3HashFindElem\n\n/*\n** Macros for looping over all elements of a hash table.  The idiom is\n** like this:\n**\n**   Fts3Hash h;\n**   Fts3HashElem *p;\n**   ...\n**   for(p=fts3HashFirst(&h); p; p=fts3HashNext(p)){\n**     SomeStructure *pData = fts3HashData(p);\n**     // do something with pData\n**   }\n*/\n#define fts3HashFirst(H)  ((H)->first)\n#define fts3HashNext(E)   ((E)->next)\n#define fts3HashData(E)   ((E)->data)\n#define fts3HashKey(E)    ((E)->pKey)\n#define fts3HashKeysize(E) ((E)->nKey)\n\n/*\n** Number of entries in a hash table\n*/\n#define fts3HashCount(H)  ((H)->count)\n\n#endif /* _FTS3_HASH_H_ */\n\n/************** End of fts3_hash.h *******************************************/\n/************** Continuing where we left off in fts3Int.h ********************/\n\n/*\n** This constant determines the maximum depth of an FTS expression tree\n** that the library will create and use. FTS uses recursion to perform \n** various operations on the query tree, so the disadvantage of a large\n** limit is that it may allow very large queries to use large amounts\n** of stack space (perhaps causing a stack overflow).\n*/\n#ifndef SQLITE_FTS3_MAX_EXPR_DEPTH\n# define SQLITE_FTS3_MAX_EXPR_DEPTH 12\n#endif\n\n\n/*\n** This constant controls how often segments are merged. Once there are\n** FTS3_MERGE_COUNT segments of level N, they are merged into a single\n** segment of level N+1.\n*/\n#define FTS3_MERGE_COUNT 16\n\n/*\n** This is the maximum amount of data (in bytes) to store in the \n** Fts3Table.pendingTerms hash table. Normally, the hash table is\n** populated as documents are inserted/updated/deleted in a transaction\n** and used to create a new segment when the transaction is committed.\n** However if this limit is reached midway through a transaction, a new \n** segment is created and the hash table cleared immediately.\n*/\n#define FTS3_MAX_PENDING_DATA (1*1024*1024)\n\n/*\n** Macro to return the number of elements in an array. SQLite has a\n** similar macro called ArraySize(). Use a different name to avoid\n** a collision when building an amalgamation with built-in FTS3.\n*/\n#define SizeofArray(X) ((int)(sizeof(X)/sizeof(X[0])))\n\n\n#ifndef MIN\n# define MIN(x,y) ((x)<(y)?(x):(y))\n#endif\n#ifndef MAX\n# define MAX(x,y) ((x)>(y)?(x):(y))\n#endif\n\n/*\n** Maximum length of a varint encoded integer. The varint format is different\n** from that used by SQLite, so the maximum length is 10, not 9.\n*/\n#define FTS3_VARINT_MAX 10\n\n/*\n** FTS4 virtual tables may maintain multiple indexes - one index of all terms\n** in the document set and zero or more prefix indexes. All indexes are stored\n** as one or more b+-trees in the %_segments and %_segdir tables. \n**\n** It is possible to determine which index a b+-tree belongs to based on the\n** value stored in the \"%_segdir.level\" column. Given this value L, the index\n** that the b+-tree belongs to is (L<<10). In other words, all b+-trees with\n** level values between 0 and 1023 (inclusive) belong to index 0, all levels\n** between 1024 and 2047 to index 1, and so on.\n**\n** It is considered impossible for an index to use more than 1024 levels. In \n** theory though this may happen, but only after at least \n** (FTS3_MERGE_COUNT^1024) separate flushes of the pending-terms tables.\n*/\n#define FTS3_SEGDIR_MAXLEVEL      1024\n#define FTS3_SEGDIR_MAXLEVEL_STR \"1024\"\n\n/*\n** The testcase() macro is only used by the amalgamation.  If undefined,\n** make it a no-op.\n*/\n#ifndef testcase\n# define testcase(X)\n#endif\n\n/*\n** Terminator values for position-lists and column-lists.\n*/\n#define POS_COLUMN  (1)     /* Column-list terminator */\n#define POS_END     (0)     /* Position-list terminator */ \n\n/*\n** This section provides definitions to allow the\n** FTS3 extension to be compiled outside of the \n** amalgamation.\n*/\n#ifndef SQLITE_AMALGAMATION\n/*\n** Macros indicating that conditional expressions are always true or\n** false.\n*/\n#ifdef SQLITE_COVERAGE_TEST\n# define ALWAYS(x) (1)\n# define NEVER(X)  (0)\n#elif defined(SQLITE_DEBUG)\n# define ALWAYS(x) sqlite3Fts3Always((x)!=0)\n# define NEVER(x) sqlite3Fts3Never((x)!=0)\nSQLITE_PRIVATE int sqlite3Fts3Always(int b);\nSQLITE_PRIVATE int sqlite3Fts3Never(int b);\n#else\n# define ALWAYS(x) (x)\n# define NEVER(x)  (x)\n#endif\n\n/*\n** Internal types used by SQLite.\n*/\ntypedef unsigned char u8;         /* 1-byte (or larger) unsigned integer */\ntypedef short int i16;            /* 2-byte (or larger) signed integer */\ntypedef unsigned int u32;         /* 4-byte unsigned integer */\ntypedef sqlite3_uint64 u64;       /* 8-byte unsigned integer */\ntypedef sqlite3_int64 i64;        /* 8-byte signed integer */\n\n/*\n** Macro used to suppress compiler warnings for unused parameters.\n*/\n#define UNUSED_PARAMETER(x) (void)(x)\n\n/*\n** Activate assert() only if SQLITE_TEST is enabled.\n*/\n#if !defined(NDEBUG) && !defined(SQLITE_DEBUG) \n# define NDEBUG 1\n#endif\n\n/*\n** The TESTONLY macro is used to enclose variable declarations or\n** other bits of code that are needed to support the arguments\n** within testcase() and assert() macros.\n*/\n#if defined(SQLITE_DEBUG) || defined(SQLITE_COVERAGE_TEST)\n# define TESTONLY(X)  X\n#else\n# define TESTONLY(X)\n#endif\n\n#endif /* SQLITE_AMALGAMATION */\n\n#ifdef SQLITE_DEBUG\nSQLITE_PRIVATE int sqlite3Fts3Corrupt(void);\n# define FTS_CORRUPT_VTAB sqlite3Fts3Corrupt()\n#else\n# define FTS_CORRUPT_VTAB SQLITE_CORRUPT_VTAB\n#endif\n\ntypedef struct Fts3Table Fts3Table;\ntypedef struct Fts3Cursor Fts3Cursor;\ntypedef struct Fts3Expr Fts3Expr;\ntypedef struct Fts3Phrase Fts3Phrase;\ntypedef struct Fts3PhraseToken Fts3PhraseToken;\n\ntypedef struct Fts3Doclist Fts3Doclist;\ntypedef struct Fts3SegFilter Fts3SegFilter;\ntypedef struct Fts3DeferredToken Fts3DeferredToken;\ntypedef struct Fts3SegReader Fts3SegReader;\ntypedef struct Fts3MultiSegReader Fts3MultiSegReader;\n\ntypedef struct MatchinfoBuffer MatchinfoBuffer;\n\n/*\n** A connection to a fulltext index is an instance of the following\n** structure. The xCreate and xConnect methods create an instance\n** of this structure and xDestroy and xDisconnect free that instance.\n** All other methods receive a pointer to the structure as one of their\n** arguments.\n*/\nstruct Fts3Table {\n  sqlite3_vtab base;              /* Base class used by SQLite core */\n  sqlite3 *db;                    /* The database connection */\n  const char *zDb;                /* logical database name */\n  const char *zName;              /* virtual table name */\n  int nColumn;                    /* number of named columns in virtual table */\n  char **azColumn;                /* column names.  malloced */\n  u8 *abNotindexed;               /* True for 'notindexed' columns */\n  sqlite3_tokenizer *pTokenizer;  /* tokenizer for inserts and queries */\n  char *zContentTbl;              /* content=xxx option, or NULL */\n  char *zLanguageid;              /* languageid=xxx option, or NULL */\n  int nAutoincrmerge;             /* Value configured by 'automerge' */\n  u32 nLeafAdd;                   /* Number of leaf blocks added this trans */\n\n  /* Precompiled statements used by the implementation. Each of these \n  ** statements is run and reset within a single virtual table API call. \n  */\n  sqlite3_stmt *aStmt[40];\n  sqlite3_stmt *pSeekStmt;        /* Cache for fts3CursorSeekStmt() */\n\n  char *zReadExprlist;\n  char *zWriteExprlist;\n\n  int nNodeSize;                  /* Soft limit for node size */\n  u8 bFts4;                       /* True for FTS4, false for FTS3 */\n  u8 bHasStat;                    /* True if %_stat table exists (2==unknown) */\n  u8 bHasDocsize;                 /* True if %_docsize table exists */\n  u8 bDescIdx;                    /* True if doclists are in reverse order */\n  u8 bIgnoreSavepoint;            /* True to ignore xSavepoint invocations */\n  int nPgsz;                      /* Page size for host database */\n  char *zSegmentsTbl;             /* Name of %_segments table */\n  sqlite3_blob *pSegments;        /* Blob handle open on %_segments table */\n\n  /* \n  ** The following array of hash tables is used to buffer pending index \n  ** updates during transactions. All pending updates buffered at any one\n  ** time must share a common language-id (see the FTS4 langid= feature).\n  ** The current language id is stored in variable iPrevLangid.\n  **\n  ** A single FTS4 table may have multiple full-text indexes. For each index\n  ** there is an entry in the aIndex[] array. Index 0 is an index of all the\n  ** terms that appear in the document set. Each subsequent index in aIndex[]\n  ** is an index of prefixes of a specific length.\n  **\n  ** Variable nPendingData contains an estimate the memory consumed by the \n  ** pending data structures, including hash table overhead, but not including\n  ** malloc overhead.  When nPendingData exceeds nMaxPendingData, all hash\n  ** tables are flushed to disk. Variable iPrevDocid is the docid of the most \n  ** recently inserted record.\n  */\n  int nIndex;                     /* Size of aIndex[] */\n  struct Fts3Index {\n    int nPrefix;                  /* Prefix length (0 for main terms index) */\n    Fts3Hash hPending;            /* Pending terms table for this index */\n  } *aIndex;\n  int nMaxPendingData;            /* Max pending data before flush to disk */\n  int nPendingData;               /* Current bytes of pending data */\n  sqlite_int64 iPrevDocid;        /* Docid of most recently inserted document */\n  int iPrevLangid;                /* Langid of recently inserted document */\n  int bPrevDelete;                /* True if last operation was a delete */\n\n#if defined(SQLITE_DEBUG) || defined(SQLITE_COVERAGE_TEST)\n  /* State variables used for validating that the transaction control\n  ** methods of the virtual table are called at appropriate times.  These\n  ** values do not contribute to FTS functionality; they are used for\n  ** verifying the operation of the SQLite core.\n  */\n  int inTransaction;     /* True after xBegin but before xCommit/xRollback */\n  int mxSavepoint;       /* Largest valid xSavepoint integer */\n#endif\n\n#ifdef SQLITE_TEST\n  /* True to disable the incremental doclist optimization. This is controled\n  ** by special insert command 'test-no-incr-doclist'.  */\n  int bNoIncrDoclist;\n#endif\n};\n\n/*\n** When the core wants to read from the virtual table, it creates a\n** virtual table cursor (an instance of the following structure) using\n** the xOpen method. Cursors are destroyed using the xClose method.\n*/\nstruct Fts3Cursor {\n  sqlite3_vtab_cursor base;       /* Base class used by SQLite core */\n  i16 eSearch;                    /* Search strategy (see below) */\n  u8 isEof;                       /* True if at End Of Results */\n  u8 isRequireSeek;               /* True if must seek pStmt to %_content row */\n  u8 bSeekStmt;                   /* True if pStmt is a seek */\n  sqlite3_stmt *pStmt;            /* Prepared statement in use by the cursor */\n  Fts3Expr *pExpr;                /* Parsed MATCH query string */\n  int iLangid;                    /* Language being queried for */\n  int nPhrase;                    /* Number of matchable phrases in query */\n  Fts3DeferredToken *pDeferred;   /* Deferred search tokens, if any */\n  sqlite3_int64 iPrevId;          /* Previous id read from aDoclist */\n  char *pNextId;                  /* Pointer into the body of aDoclist */\n  char *aDoclist;                 /* List of docids for full-text queries */\n  int nDoclist;                   /* Size of buffer at aDoclist */\n  u8 bDesc;                       /* True to sort in descending order */\n  int eEvalmode;                  /* An FTS3_EVAL_XX constant */\n  int nRowAvg;                    /* Average size of database rows, in pages */\n  sqlite3_int64 nDoc;             /* Documents in table */\n  i64 iMinDocid;                  /* Minimum docid to return */\n  i64 iMaxDocid;                  /* Maximum docid to return */\n  int isMatchinfoNeeded;          /* True when aMatchinfo[] needs filling in */\n  MatchinfoBuffer *pMIBuffer;     /* Buffer for matchinfo data */\n};\n\n#define FTS3_EVAL_FILTER    0\n#define FTS3_EVAL_NEXT      1\n#define FTS3_EVAL_MATCHINFO 2\n\n/*\n** The Fts3Cursor.eSearch member is always set to one of the following.\n** Actualy, Fts3Cursor.eSearch can be greater than or equal to\n** FTS3_FULLTEXT_SEARCH.  If so, then Fts3Cursor.eSearch - 2 is the index\n** of the column to be searched.  For example, in\n**\n**     CREATE VIRTUAL TABLE ex1 USING fts3(a,b,c,d);\n**     SELECT docid FROM ex1 WHERE b MATCH 'one two three';\n** \n** Because the LHS of the MATCH operator is 2nd column \"b\",\n** Fts3Cursor.eSearch will be set to FTS3_FULLTEXT_SEARCH+1.  (+0 for a,\n** +1 for b, +2 for c, +3 for d.)  If the LHS of MATCH were \"ex1\" \n** indicating that all columns should be searched,\n** then eSearch would be set to FTS3_FULLTEXT_SEARCH+4.\n*/\n#define FTS3_FULLSCAN_SEARCH 0    /* Linear scan of %_content table */\n#define FTS3_DOCID_SEARCH    1    /* Lookup by rowid on %_content table */\n#define FTS3_FULLTEXT_SEARCH 2    /* Full-text index search */\n\n/*\n** The lower 16-bits of the sqlite3_index_info.idxNum value set by\n** the xBestIndex() method contains the Fts3Cursor.eSearch value described\n** above. The upper 16-bits contain a combination of the following\n** bits, used to describe extra constraints on full-text searches.\n*/\n#define FTS3_HAVE_LANGID    0x00010000      /* languageid=? */\n#define FTS3_HAVE_DOCID_GE  0x00020000      /* docid>=? */\n#define FTS3_HAVE_DOCID_LE  0x00040000      /* docid<=? */\n\nstruct Fts3Doclist {\n  char *aAll;                    /* Array containing doclist (or NULL) */\n  int nAll;                      /* Size of a[] in bytes */\n  char *pNextDocid;              /* Pointer to next docid */\n\n  sqlite3_int64 iDocid;          /* Current docid (if pList!=0) */\n  int bFreeList;                 /* True if pList should be sqlite3_free()d */\n  char *pList;                   /* Pointer to position list following iDocid */\n  int nList;                     /* Length of position list */\n};\n\n/*\n** A \"phrase\" is a sequence of one or more tokens that must match in\n** sequence.  A single token is the base case and the most common case.\n** For a sequence of tokens contained in double-quotes (i.e. \"one two three\")\n** nToken will be the number of tokens in the string.\n*/\nstruct Fts3PhraseToken {\n  char *z;                        /* Text of the token */\n  int n;                          /* Number of bytes in buffer z */\n  int isPrefix;                   /* True if token ends with a \"*\" character */\n  int bFirst;                     /* True if token must appear at position 0 */\n\n  /* Variables above this point are populated when the expression is\n  ** parsed (by code in fts3_expr.c). Below this point the variables are\n  ** used when evaluating the expression. */\n  Fts3DeferredToken *pDeferred;   /* Deferred token object for this token */\n  Fts3MultiSegReader *pSegcsr;    /* Segment-reader for this token */\n};\n\nstruct Fts3Phrase {\n  /* Cache of doclist for this phrase. */\n  Fts3Doclist doclist;\n  int bIncr;                 /* True if doclist is loaded incrementally */\n  int iDoclistToken;\n\n  /* Used by sqlite3Fts3EvalPhrasePoslist() if this is a descendent of an\n  ** OR condition.  */\n  char *pOrPoslist;\n  i64 iOrDocid;\n\n  /* Variables below this point are populated by fts3_expr.c when parsing \n  ** a MATCH expression. Everything above is part of the evaluation phase. \n  */\n  int nToken;                /* Number of tokens in the phrase */\n  int iColumn;               /* Index of column this phrase must match */\n  Fts3PhraseToken aToken[1]; /* One entry for each token in the phrase */\n};\n\n/*\n** A tree of these objects forms the RHS of a MATCH operator.\n**\n** If Fts3Expr.eType is FTSQUERY_PHRASE and isLoaded is true, then aDoclist \n** points to a malloced buffer, size nDoclist bytes, containing the results \n** of this phrase query in FTS3 doclist format. As usual, the initial \n** \"Length\" field found in doclists stored on disk is omitted from this \n** buffer.\n**\n** Variable aMI is used only for FTSQUERY_NEAR nodes to store the global\n** matchinfo data. If it is not NULL, it points to an array of size nCol*3,\n** where nCol is the number of columns in the queried FTS table. The array\n** is populated as follows:\n**\n**   aMI[iCol*3 + 0] = Undefined\n**   aMI[iCol*3 + 1] = Number of occurrences\n**   aMI[iCol*3 + 2] = Number of rows containing at least one instance\n**\n** The aMI array is allocated using sqlite3_malloc(). It should be freed \n** when the expression node is.\n*/\nstruct Fts3Expr {\n  int eType;                 /* One of the FTSQUERY_XXX values defined below */\n  int nNear;                 /* Valid if eType==FTSQUERY_NEAR */\n  Fts3Expr *pParent;         /* pParent->pLeft==this or pParent->pRight==this */\n  Fts3Expr *pLeft;           /* Left operand */\n  Fts3Expr *pRight;          /* Right operand */\n  Fts3Phrase *pPhrase;       /* Valid if eType==FTSQUERY_PHRASE */\n\n  /* The following are used by the fts3_eval.c module. */\n  sqlite3_int64 iDocid;      /* Current docid */\n  u8 bEof;                   /* True this expression is at EOF already */\n  u8 bStart;                 /* True if iDocid is valid */\n  u8 bDeferred;              /* True if this expression is entirely deferred */\n\n  /* The following are used by the fts3_snippet.c module. */\n  int iPhrase;               /* Index of this phrase in matchinfo() results */\n  u32 *aMI;                  /* See above */\n};\n\n/*\n** Candidate values for Fts3Query.eType. Note that the order of the first\n** four values is in order of precedence when parsing expressions. For \n** example, the following:\n**\n**   \"a OR b AND c NOT d NEAR e\"\n**\n** is equivalent to:\n**\n**   \"a OR (b AND (c NOT (d NEAR e)))\"\n*/\n#define FTSQUERY_NEAR   1\n#define FTSQUERY_NOT    2\n#define FTSQUERY_AND    3\n#define FTSQUERY_OR     4\n#define FTSQUERY_PHRASE 5\n\n\n/* fts3_write.c */\nSQLITE_PRIVATE int sqlite3Fts3UpdateMethod(sqlite3_vtab*,int,sqlite3_value**,sqlite3_int64*);\nSQLITE_PRIVATE int sqlite3Fts3PendingTermsFlush(Fts3Table *);\nSQLITE_PRIVATE void sqlite3Fts3PendingTermsClear(Fts3Table *);\nSQLITE_PRIVATE int sqlite3Fts3Optimize(Fts3Table *);\nSQLITE_PRIVATE int sqlite3Fts3SegReaderNew(int, int, sqlite3_int64,\n  sqlite3_int64, sqlite3_int64, const char *, int, Fts3SegReader**);\nSQLITE_PRIVATE int sqlite3Fts3SegReaderPending(\n  Fts3Table*,int,const char*,int,int,Fts3SegReader**);\nSQLITE_PRIVATE void sqlite3Fts3SegReaderFree(Fts3SegReader *);\nSQLITE_PRIVATE int sqlite3Fts3AllSegdirs(Fts3Table*, int, int, int, sqlite3_stmt **);\nSQLITE_PRIVATE int sqlite3Fts3ReadBlock(Fts3Table*, sqlite3_int64, char **, int*, int*);\n\nSQLITE_PRIVATE int sqlite3Fts3SelectDoctotal(Fts3Table *, sqlite3_stmt **);\nSQLITE_PRIVATE int sqlite3Fts3SelectDocsize(Fts3Table *, sqlite3_int64, sqlite3_stmt **);\n\n#ifndef SQLITE_DISABLE_FTS4_DEFERRED\nSQLITE_PRIVATE void sqlite3Fts3FreeDeferredTokens(Fts3Cursor *);\nSQLITE_PRIVATE int sqlite3Fts3DeferToken(Fts3Cursor *, Fts3PhraseToken *, int);\nSQLITE_PRIVATE int sqlite3Fts3CacheDeferredDoclists(Fts3Cursor *);\nSQLITE_PRIVATE void sqlite3Fts3FreeDeferredDoclists(Fts3Cursor *);\nSQLITE_PRIVATE int sqlite3Fts3DeferredTokenList(Fts3DeferredToken *, char **, int *);\n#else\n# define sqlite3Fts3FreeDeferredTokens(x)\n# define sqlite3Fts3DeferToken(x,y,z) SQLITE_OK\n# define sqlite3Fts3CacheDeferredDoclists(x) SQLITE_OK\n# define sqlite3Fts3FreeDeferredDoclists(x)\n# define sqlite3Fts3DeferredTokenList(x,y,z) SQLITE_OK\n#endif\n\nSQLITE_PRIVATE void sqlite3Fts3SegmentsClose(Fts3Table *);\nSQLITE_PRIVATE int sqlite3Fts3MaxLevel(Fts3Table *, int *);\n\n/* Special values interpreted by sqlite3SegReaderCursor() */\n#define FTS3_SEGCURSOR_PENDING        -1\n#define FTS3_SEGCURSOR_ALL            -2\n\nSQLITE_PRIVATE int sqlite3Fts3SegReaderStart(Fts3Table*, Fts3MultiSegReader*, Fts3SegFilter*);\nSQLITE_PRIVATE int sqlite3Fts3SegReaderStep(Fts3Table *, Fts3MultiSegReader *);\nSQLITE_PRIVATE void sqlite3Fts3SegReaderFinish(Fts3MultiSegReader *);\n\nSQLITE_PRIVATE int sqlite3Fts3SegReaderCursor(Fts3Table *, \n    int, int, int, const char *, int, int, int, Fts3MultiSegReader *);\n\n/* Flags allowed as part of the 4th argument to SegmentReaderIterate() */\n#define FTS3_SEGMENT_REQUIRE_POS   0x00000001\n#define FTS3_SEGMENT_IGNORE_EMPTY  0x00000002\n#define FTS3_SEGMENT_COLUMN_FILTER 0x00000004\n#define FTS3_SEGMENT_PREFIX        0x00000008\n#define FTS3_SEGMENT_SCAN          0x00000010\n#define FTS3_SEGMENT_FIRST         0x00000020\n\n/* Type passed as 4th argument to SegmentReaderIterate() */\nstruct Fts3SegFilter {\n  const char *zTerm;\n  int nTerm;\n  int iCol;\n  int flags;\n};\n\nstruct Fts3MultiSegReader {\n  /* Used internally by sqlite3Fts3SegReaderXXX() calls */\n  Fts3SegReader **apSegment;      /* Array of Fts3SegReader objects */\n  int nSegment;                   /* Size of apSegment array */\n  int nAdvance;                   /* How many seg-readers to advance */\n  Fts3SegFilter *pFilter;         /* Pointer to filter object */\n  char *aBuffer;                  /* Buffer to merge doclists in */\n  int nBuffer;                    /* Allocated size of aBuffer[] in bytes */\n\n  int iColFilter;                 /* If >=0, filter for this column */\n  int bRestart;\n\n  /* Used by fts3.c only. */\n  int nCost;                      /* Cost of running iterator */\n  int bLookup;                    /* True if a lookup of a single entry. */\n\n  /* Output values. Valid only after Fts3SegReaderStep() returns SQLITE_ROW. */\n  char *zTerm;                    /* Pointer to term buffer */\n  int nTerm;                      /* Size of zTerm in bytes */\n  char *aDoclist;                 /* Pointer to doclist buffer */\n  int nDoclist;                   /* Size of aDoclist[] in bytes */\n};\n\nSQLITE_PRIVATE int sqlite3Fts3Incrmerge(Fts3Table*,int,int);\n\n#define fts3GetVarint32(p, piVal) (                                           \\\n  (*(u8*)(p)&0x80) ? sqlite3Fts3GetVarint32(p, piVal) : (*piVal=*(u8*)(p), 1) \\\n)\n\n/* fts3.c */\nSQLITE_PRIVATE void sqlite3Fts3ErrMsg(char**,const char*,...);\nSQLITE_PRIVATE int sqlite3Fts3PutVarint(char *, sqlite3_int64);\nSQLITE_PRIVATE int sqlite3Fts3GetVarint(const char *, sqlite_int64 *);\nSQLITE_PRIVATE int sqlite3Fts3GetVarint32(const char *, int *);\nSQLITE_PRIVATE int sqlite3Fts3VarintLen(sqlite3_uint64);\nSQLITE_PRIVATE void sqlite3Fts3Dequote(char *);\nSQLITE_PRIVATE void sqlite3Fts3DoclistPrev(int,char*,int,char**,sqlite3_int64*,int*,u8*);\nSQLITE_PRIVATE int sqlite3Fts3EvalPhraseStats(Fts3Cursor *, Fts3Expr *, u32 *);\nSQLITE_PRIVATE int sqlite3Fts3FirstFilter(sqlite3_int64, char *, int, char *);\nSQLITE_PRIVATE void sqlite3Fts3CreateStatTable(int*, Fts3Table*);\nSQLITE_PRIVATE int sqlite3Fts3EvalTestDeferred(Fts3Cursor *pCsr, int *pRc);\n\n/* fts3_tokenizer.c */\nSQLITE_PRIVATE const char *sqlite3Fts3NextToken(const char *, int *);\nSQLITE_PRIVATE int sqlite3Fts3InitHashTable(sqlite3 *, Fts3Hash *, const char *);\nSQLITE_PRIVATE int sqlite3Fts3InitTokenizer(Fts3Hash *pHash, const char *, \n    sqlite3_tokenizer **, char **\n);\nSQLITE_PRIVATE int sqlite3Fts3IsIdChar(char);\n\n/* fts3_snippet.c */\nSQLITE_PRIVATE void sqlite3Fts3Offsets(sqlite3_context*, Fts3Cursor*);\nSQLITE_PRIVATE void sqlite3Fts3Snippet(sqlite3_context *, Fts3Cursor *, const char *,\n  const char *, const char *, int, int\n);\nSQLITE_PRIVATE void sqlite3Fts3Matchinfo(sqlite3_context *, Fts3Cursor *, const char *);\nSQLITE_PRIVATE void sqlite3Fts3MIBufferFree(MatchinfoBuffer *p);\n\n/* fts3_expr.c */\nSQLITE_PRIVATE int sqlite3Fts3ExprParse(sqlite3_tokenizer *, int,\n  char **, int, int, int, const char *, int, Fts3Expr **, char **\n);\nSQLITE_PRIVATE void sqlite3Fts3ExprFree(Fts3Expr *);\n#ifdef SQLITE_TEST\nSQLITE_PRIVATE int sqlite3Fts3ExprInitTestInterface(sqlite3 *db);\nSQLITE_PRIVATE int sqlite3Fts3InitTerm(sqlite3 *db);\n#endif\n\nSQLITE_PRIVATE int sqlite3Fts3OpenTokenizer(sqlite3_tokenizer *, int, const char *, int,\n  sqlite3_tokenizer_cursor **\n);\n\n/* fts3_aux.c */\nSQLITE_PRIVATE int sqlite3Fts3InitAux(sqlite3 *db);\n\nSQLITE_PRIVATE void sqlite3Fts3EvalPhraseCleanup(Fts3Phrase *);\n\nSQLITE_PRIVATE int sqlite3Fts3MsrIncrStart(\n    Fts3Table*, Fts3MultiSegReader*, int, const char*, int);\nSQLITE_PRIVATE int sqlite3Fts3MsrIncrNext(\n    Fts3Table *, Fts3MultiSegReader *, sqlite3_int64 *, char **, int *);\nSQLITE_PRIVATE int sqlite3Fts3EvalPhrasePoslist(Fts3Cursor *, Fts3Expr *, int iCol, char **); \nSQLITE_PRIVATE int sqlite3Fts3MsrOvfl(Fts3Cursor *, Fts3MultiSegReader *, int *);\nSQLITE_PRIVATE int sqlite3Fts3MsrIncrRestart(Fts3MultiSegReader *pCsr);\n\n/* fts3_tokenize_vtab.c */\nSQLITE_PRIVATE int sqlite3Fts3InitTok(sqlite3*, Fts3Hash *);\n\n/* fts3_unicode2.c (functions generated by parsing unicode text files) */\n#ifndef SQLITE_DISABLE_FTS3_UNICODE\nSQLITE_PRIVATE int sqlite3FtsUnicodeFold(int, int);\nSQLITE_PRIVATE int sqlite3FtsUnicodeIsalnum(int);\nSQLITE_PRIVATE int sqlite3FtsUnicodeIsdiacritic(int);\n#endif\n\n#endif /* !SQLITE_CORE || SQLITE_ENABLE_FTS3 */\n#endif /* _FTSINT_H */\n\n/************** End of fts3Int.h *********************************************/\n/************** Continuing where we left off in fts3.c ***********************/\n#if !defined(SQLITE_CORE) || defined(SQLITE_ENABLE_FTS3)\n\n#if defined(SQLITE_ENABLE_FTS3) && !defined(SQLITE_CORE)\n# define SQLITE_CORE 1\n#endif\n\n/* #include <assert.h> */\n/* #include <stdlib.h> */\n/* #include <stddef.h> */\n/* #include <stdio.h> */\n/* #include <string.h> */\n/* #include <stdarg.h> */\n\n/* #include \"fts3.h\" */\n#ifndef SQLITE_CORE \n/* # include \"sqlite3ext.h\" */\n  SQLITE_EXTENSION_INIT1\n#endif\n\nstatic int fts3EvalNext(Fts3Cursor *pCsr);\nstatic int fts3EvalStart(Fts3Cursor *pCsr);\nstatic int fts3TermSegReaderCursor(\n    Fts3Cursor *, const char *, int, int, Fts3MultiSegReader **);\n\n#ifndef SQLITE_AMALGAMATION\n# if defined(SQLITE_DEBUG)\nSQLITE_PRIVATE int sqlite3Fts3Always(int b) { assert( b ); return b; }\nSQLITE_PRIVATE int sqlite3Fts3Never(int b)  { assert( !b ); return b; }\n# endif\n#endif\n\n/* \n** Write a 64-bit variable-length integer to memory starting at p[0].\n** The length of data written will be between 1 and FTS3_VARINT_MAX bytes.\n** The number of bytes written is returned.\n*/\nSQLITE_PRIVATE int sqlite3Fts3PutVarint(char *p, sqlite_int64 v){\n  unsigned char *q = (unsigned char *) p;\n  sqlite_uint64 vu = v;\n  do{\n    *q++ = (unsigned char) ((vu & 0x7f) | 0x80);\n    vu >>= 7;\n  }while( vu!=0 );\n  q[-1] &= 0x7f;  /* turn off high bit in final byte */\n  assert( q - (unsigned char *)p <= FTS3_VARINT_MAX );\n  return (int) (q - (unsigned char *)p);\n}\n\n#define GETVARINT_STEP(v, ptr, shift, mask1, mask2, var, ret) \\\n  v = (v & mask1) | ( (*ptr++) << shift );                    \\\n  if( (v & mask2)==0 ){ var = v; return ret; }\n#define GETVARINT_INIT(v, ptr, shift, mask1, mask2, var, ret) \\\n  v = (*ptr++);                                               \\\n  if( (v & mask2)==0 ){ var = v; return ret; }\n\n/* \n** Read a 64-bit variable-length integer from memory starting at p[0].\n** Return the number of bytes read, or 0 on error.\n** The value is stored in *v.\n*/\nSQLITE_PRIVATE int sqlite3Fts3GetVarint(const char *pBuf, sqlite_int64 *v){\n  const unsigned char *p = (const unsigned char*)pBuf;\n  const unsigned char *pStart = p;\n  u32 a;\n  u64 b;\n  int shift;\n\n  GETVARINT_INIT(a, p, 0,  0x00,     0x80, *v, 1);\n  GETVARINT_STEP(a, p, 7,  0x7F,     0x4000, *v, 2);\n  GETVARINT_STEP(a, p, 14, 0x3FFF,   0x200000, *v, 3);\n  GETVARINT_STEP(a, p, 21, 0x1FFFFF, 0x10000000, *v, 4);\n  b = (a & 0x0FFFFFFF );\n\n  for(shift=28; shift<=63; shift+=7){\n    u64 c = *p++;\n    b += (c&0x7F) << shift;\n    if( (c & 0x80)==0 ) break;\n  }\n  *v = b;\n  return (int)(p - pStart);\n}\n\n/*\n** Similar to sqlite3Fts3GetVarint(), except that the output is truncated to \n** a non-negative 32-bit integer before it is returned.\n*/\nSQLITE_PRIVATE int sqlite3Fts3GetVarint32(const char *p, int *pi){\n  u32 a;\n\n#ifndef fts3GetVarint32\n  GETVARINT_INIT(a, p, 0,  0x00,     0x80, *pi, 1);\n#else\n  a = (*p++);\n  assert( a & 0x80 );\n#endif\n\n  GETVARINT_STEP(a, p, 7,  0x7F,     0x4000, *pi, 2);\n  GETVARINT_STEP(a, p, 14, 0x3FFF,   0x200000, *pi, 3);\n  GETVARINT_STEP(a, p, 21, 0x1FFFFF, 0x10000000, *pi, 4);\n  a = (a & 0x0FFFFFFF );\n  *pi = (int)(a | ((u32)(*p & 0x07) << 28));\n  assert( 0==(a & 0x80000000) );\n  assert( *pi>=0 );\n  return 5;\n}\n\n/*\n** Return the number of bytes required to encode v as a varint\n*/\nSQLITE_PRIVATE int sqlite3Fts3VarintLen(sqlite3_uint64 v){\n  int i = 0;\n  do{\n    i++;\n    v >>= 7;\n  }while( v!=0 );\n  return i;\n}\n\n/*\n** Convert an SQL-style quoted string into a normal string by removing\n** the quote characters.  The conversion is done in-place.  If the\n** input does not begin with a quote character, then this routine\n** is a no-op.\n**\n** Examples:\n**\n**     \"abc\"   becomes   abc\n**     'xyz'   becomes   xyz\n**     [pqr]   becomes   pqr\n**     `mno`   becomes   mno\n**\n*/\nSQLITE_PRIVATE void sqlite3Fts3Dequote(char *z){\n  char quote;                     /* Quote character (if any ) */\n\n  quote = z[0];\n  if( quote=='[' || quote=='\\'' || quote=='\"' || quote=='`' ){\n    int iIn = 1;                  /* Index of next byte to read from input */\n    int iOut = 0;                 /* Index of next byte to write to output */\n\n    /* If the first byte was a '[', then the close-quote character is a ']' */\n    if( quote=='[' ) quote = ']';  \n\n    while( z[iIn] ){\n      if( z[iIn]==quote ){\n        if( z[iIn+1]!=quote ) break;\n        z[iOut++] = quote;\n        iIn += 2;\n      }else{\n        z[iOut++] = z[iIn++];\n      }\n    }\n    z[iOut] = '\\0';\n  }\n}\n\n/*\n** Read a single varint from the doclist at *pp and advance *pp to point\n** to the first byte past the end of the varint.  Add the value of the varint\n** to *pVal.\n*/\nstatic void fts3GetDeltaVarint(char **pp, sqlite3_int64 *pVal){\n  sqlite3_int64 iVal;\n  *pp += sqlite3Fts3GetVarint(*pp, &iVal);\n  *pVal += iVal;\n}\n\n/*\n** When this function is called, *pp points to the first byte following a\n** varint that is part of a doclist (or position-list, or any other list\n** of varints). This function moves *pp to point to the start of that varint,\n** and sets *pVal by the varint value.\n**\n** Argument pStart points to the first byte of the doclist that the\n** varint is part of.\n*/\nstatic void fts3GetReverseVarint(\n  char **pp, \n  char *pStart, \n  sqlite3_int64 *pVal\n){\n  sqlite3_int64 iVal;\n  char *p;\n\n  /* Pointer p now points at the first byte past the varint we are \n  ** interested in. So, unless the doclist is corrupt, the 0x80 bit is\n  ** clear on character p[-1]. */\n  for(p = (*pp)-2; p>=pStart && *p&0x80; p--);\n  p++;\n  *pp = p;\n\n  sqlite3Fts3GetVarint(p, &iVal);\n  *pVal = iVal;\n}\n\n/*\n** The xDisconnect() virtual table method.\n*/\nstatic int fts3DisconnectMethod(sqlite3_vtab *pVtab){\n  Fts3Table *p = (Fts3Table *)pVtab;\n  int i;\n\n  assert( p->nPendingData==0 );\n  assert( p->pSegments==0 );\n\n  /* Free any prepared statements held */\n  sqlite3_finalize(p->pSeekStmt);\n  for(i=0; i<SizeofArray(p->aStmt); i++){\n    sqlite3_finalize(p->aStmt[i]);\n  }\n  sqlite3_free(p->zSegmentsTbl);\n  sqlite3_free(p->zReadExprlist);\n  sqlite3_free(p->zWriteExprlist);\n  sqlite3_free(p->zContentTbl);\n  sqlite3_free(p->zLanguageid);\n\n  /* Invoke the tokenizer destructor to free the tokenizer. */\n  p->pTokenizer->pModule->xDestroy(p->pTokenizer);\n\n  sqlite3_free(p);\n  return SQLITE_OK;\n}\n\n/*\n** Write an error message into *pzErr\n*/\nSQLITE_PRIVATE void sqlite3Fts3ErrMsg(char **pzErr, const char *zFormat, ...){\n  va_list ap;\n  sqlite3_free(*pzErr);\n  va_start(ap, zFormat);\n  *pzErr = sqlite3_vmprintf(zFormat, ap);\n  va_end(ap);\n}\n\n/*\n** Construct one or more SQL statements from the format string given\n** and then evaluate those statements. The success code is written\n** into *pRc.\n**\n** If *pRc is initially non-zero then this routine is a no-op.\n*/\nstatic void fts3DbExec(\n  int *pRc,              /* Success code */\n  sqlite3 *db,           /* Database in which to run SQL */\n  const char *zFormat,   /* Format string for SQL */\n  ...                    /* Arguments to the format string */\n){\n  va_list ap;\n  char *zSql;\n  if( *pRc ) return;\n  va_start(ap, zFormat);\n  zSql = sqlite3_vmprintf(zFormat, ap);\n  va_end(ap);\n  if( zSql==0 ){\n    *pRc = SQLITE_NOMEM;\n  }else{\n    *pRc = sqlite3_exec(db, zSql, 0, 0, 0);\n    sqlite3_free(zSql);\n  }\n}\n\n/*\n** The xDestroy() virtual table method.\n*/\nstatic int fts3DestroyMethod(sqlite3_vtab *pVtab){\n  Fts3Table *p = (Fts3Table *)pVtab;\n  int rc = SQLITE_OK;              /* Return code */\n  const char *zDb = p->zDb;        /* Name of database (e.g. \"main\", \"temp\") */\n  sqlite3 *db = p->db;             /* Database handle */\n\n  /* Drop the shadow tables */\n  if( p->zContentTbl==0 ){\n    fts3DbExec(&rc, db, \"DROP TABLE IF EXISTS %Q.'%q_content'\", zDb, p->zName);\n  }\n  fts3DbExec(&rc, db, \"DROP TABLE IF EXISTS %Q.'%q_segments'\", zDb,p->zName);\n  fts3DbExec(&rc, db, \"DROP TABLE IF EXISTS %Q.'%q_segdir'\", zDb, p->zName);\n  fts3DbExec(&rc, db, \"DROP TABLE IF EXISTS %Q.'%q_docsize'\", zDb, p->zName);\n  fts3DbExec(&rc, db, \"DROP TABLE IF EXISTS %Q.'%q_stat'\", zDb, p->zName);\n\n  /* If everything has worked, invoke fts3DisconnectMethod() to free the\n  ** memory associated with the Fts3Table structure and return SQLITE_OK.\n  ** Otherwise, return an SQLite error code.\n  */\n  return (rc==SQLITE_OK ? fts3DisconnectMethod(pVtab) : rc);\n}\n\n\n/*\n** Invoke sqlite3_declare_vtab() to declare the schema for the FTS3 table\n** passed as the first argument. This is done as part of the xConnect()\n** and xCreate() methods.\n**\n** If *pRc is non-zero when this function is called, it is a no-op. \n** Otherwise, if an error occurs, an SQLite error code is stored in *pRc\n** before returning.\n*/\nstatic void fts3DeclareVtab(int *pRc, Fts3Table *p){\n  if( *pRc==SQLITE_OK ){\n    int i;                        /* Iterator variable */\n    int rc;                       /* Return code */\n    char *zSql;                   /* SQL statement passed to declare_vtab() */\n    char *zCols;                  /* List of user defined columns */\n    const char *zLanguageid;\n\n    zLanguageid = (p->zLanguageid ? p->zLanguageid : \"__langid\");\n    sqlite3_vtab_config(p->db, SQLITE_VTAB_CONSTRAINT_SUPPORT, 1);\n\n    /* Create a list of user columns for the virtual table */\n    zCols = sqlite3_mprintf(\"%Q, \", p->azColumn[0]);\n    for(i=1; zCols && i<p->nColumn; i++){\n      zCols = sqlite3_mprintf(\"%z%Q, \", zCols, p->azColumn[i]);\n    }\n\n    /* Create the whole \"CREATE TABLE\" statement to pass to SQLite */\n    zSql = sqlite3_mprintf(\n        \"CREATE TABLE x(%s %Q HIDDEN, docid HIDDEN, %Q HIDDEN)\", \n        zCols, p->zName, zLanguageid\n    );\n    if( !zCols || !zSql ){\n      rc = SQLITE_NOMEM;\n    }else{\n      rc = sqlite3_declare_vtab(p->db, zSql);\n    }\n\n    sqlite3_free(zSql);\n    sqlite3_free(zCols);\n    *pRc = rc;\n  }\n}\n\n/*\n** Create the %_stat table if it does not already exist.\n*/\nSQLITE_PRIVATE void sqlite3Fts3CreateStatTable(int *pRc, Fts3Table *p){\n  fts3DbExec(pRc, p->db, \n      \"CREATE TABLE IF NOT EXISTS %Q.'%q_stat'\"\n          \"(id INTEGER PRIMARY KEY, value BLOB);\",\n      p->zDb, p->zName\n  );\n  if( (*pRc)==SQLITE_OK ) p->bHasStat = 1;\n}\n\n/*\n** Create the backing store tables (%_content, %_segments and %_segdir)\n** required by the FTS3 table passed as the only argument. This is done\n** as part of the vtab xCreate() method.\n**\n** If the p->bHasDocsize boolean is true (indicating that this is an\n** FTS4 table, not an FTS3 table) then also create the %_docsize and\n** %_stat tables required by FTS4.\n*/\nstatic int fts3CreateTables(Fts3Table *p){\n  int rc = SQLITE_OK;             /* Return code */\n  int i;                          /* Iterator variable */\n  sqlite3 *db = p->db;            /* The database connection */\n\n  if( p->zContentTbl==0 ){\n    const char *zLanguageid = p->zLanguageid;\n    char *zContentCols;           /* Columns of %_content table */\n\n    /* Create a list of user columns for the content table */\n    zContentCols = sqlite3_mprintf(\"docid INTEGER PRIMARY KEY\");\n    for(i=0; zContentCols && i<p->nColumn; i++){\n      char *z = p->azColumn[i];\n      zContentCols = sqlite3_mprintf(\"%z, 'c%d%q'\", zContentCols, i, z);\n    }\n    if( zLanguageid && zContentCols ){\n      zContentCols = sqlite3_mprintf(\"%z, langid\", zContentCols, zLanguageid);\n    }\n    if( zContentCols==0 ) rc = SQLITE_NOMEM;\n  \n    /* Create the content table */\n    fts3DbExec(&rc, db, \n       \"CREATE TABLE %Q.'%q_content'(%s)\",\n       p->zDb, p->zName, zContentCols\n    );\n    sqlite3_free(zContentCols);\n  }\n\n  /* Create other tables */\n  fts3DbExec(&rc, db, \n      \"CREATE TABLE %Q.'%q_segments'(blockid INTEGER PRIMARY KEY, block BLOB);\",\n      p->zDb, p->zName\n  );\n  fts3DbExec(&rc, db, \n      \"CREATE TABLE %Q.'%q_segdir'(\"\n        \"level INTEGER,\"\n        \"idx INTEGER,\"\n        \"start_block INTEGER,\"\n        \"leaves_end_block INTEGER,\"\n        \"end_block INTEGER,\"\n        \"root BLOB,\"\n        \"PRIMARY KEY(level, idx)\"\n      \");\",\n      p->zDb, p->zName\n  );\n  if( p->bHasDocsize ){\n    fts3DbExec(&rc, db, \n        \"CREATE TABLE %Q.'%q_docsize'(docid INTEGER PRIMARY KEY, size BLOB);\",\n        p->zDb, p->zName\n    );\n  }\n  assert( p->bHasStat==p->bFts4 );\n  if( p->bHasStat ){\n    sqlite3Fts3CreateStatTable(&rc, p);\n  }\n  return rc;\n}\n\n/*\n** Store the current database page-size in bytes in p->nPgsz.\n**\n** If *pRc is non-zero when this function is called, it is a no-op. \n** Otherwise, if an error occurs, an SQLite error code is stored in *pRc\n** before returning.\n*/\nstatic void fts3DatabasePageSize(int *pRc, Fts3Table *p){\n  if( *pRc==SQLITE_OK ){\n    int rc;                       /* Return code */\n    char *zSql;                   /* SQL text \"PRAGMA %Q.page_size\" */\n    sqlite3_stmt *pStmt;          /* Compiled \"PRAGMA %Q.page_size\" statement */\n  \n    zSql = sqlite3_mprintf(\"PRAGMA %Q.page_size\", p->zDb);\n    if( !zSql ){\n      rc = SQLITE_NOMEM;\n    }else{\n      rc = sqlite3_prepare(p->db, zSql, -1, &pStmt, 0);\n      if( rc==SQLITE_OK ){\n        sqlite3_step(pStmt);\n        p->nPgsz = sqlite3_column_int(pStmt, 0);\n        rc = sqlite3_finalize(pStmt);\n      }else if( rc==SQLITE_AUTH ){\n        p->nPgsz = 1024;\n        rc = SQLITE_OK;\n      }\n    }\n    assert( p->nPgsz>0 || rc!=SQLITE_OK );\n    sqlite3_free(zSql);\n    *pRc = rc;\n  }\n}\n\n/*\n** \"Special\" FTS4 arguments are column specifications of the following form:\n**\n**   <key> = <value>\n**\n** There may not be whitespace surrounding the \"=\" character. The <value> \n** term may be quoted, but the <key> may not.\n*/\nstatic int fts3IsSpecialColumn(\n  const char *z, \n  int *pnKey,\n  char **pzValue\n){\n  char *zValue;\n  const char *zCsr = z;\n\n  while( *zCsr!='=' ){\n    if( *zCsr=='\\0' ) return 0;\n    zCsr++;\n  }\n\n  *pnKey = (int)(zCsr-z);\n  zValue = sqlite3_mprintf(\"%s\", &zCsr[1]);\n  if( zValue ){\n    sqlite3Fts3Dequote(zValue);\n  }\n  *pzValue = zValue;\n  return 1;\n}\n\n/*\n** Append the output of a printf() style formatting to an existing string.\n*/\nstatic void fts3Appendf(\n  int *pRc,                       /* IN/OUT: Error code */\n  char **pz,                      /* IN/OUT: Pointer to string buffer */\n  const char *zFormat,            /* Printf format string to append */\n  ...                             /* Arguments for printf format string */\n){\n  if( *pRc==SQLITE_OK ){\n    va_list ap;\n    char *z;\n    va_start(ap, zFormat);\n    z = sqlite3_vmprintf(zFormat, ap);\n    va_end(ap);\n    if( z && *pz ){\n      char *z2 = sqlite3_mprintf(\"%s%s\", *pz, z);\n      sqlite3_free(z);\n      z = z2;\n    }\n    if( z==0 ) *pRc = SQLITE_NOMEM;\n    sqlite3_free(*pz);\n    *pz = z;\n  }\n}\n\n/*\n** Return a copy of input string zInput enclosed in double-quotes (\") and\n** with all double quote characters escaped. For example:\n**\n**     fts3QuoteId(\"un \\\"zip\\\"\")   ->    \"un \\\"\\\"zip\\\"\\\"\"\n**\n** The pointer returned points to memory obtained from sqlite3_malloc(). It\n** is the callers responsibility to call sqlite3_free() to release this\n** memory.\n*/\nstatic char *fts3QuoteId(char const *zInput){\n  int nRet;\n  char *zRet;\n  nRet = 2 + (int)strlen(zInput)*2 + 1;\n  zRet = sqlite3_malloc(nRet);\n  if( zRet ){\n    int i;\n    char *z = zRet;\n    *(z++) = '\"';\n    for(i=0; zInput[i]; i++){\n      if( zInput[i]=='\"' ) *(z++) = '\"';\n      *(z++) = zInput[i];\n    }\n    *(z++) = '\"';\n    *(z++) = '\\0';\n  }\n  return zRet;\n}\n\n/*\n** Return a list of comma separated SQL expressions and a FROM clause that \n** could be used in a SELECT statement such as the following:\n**\n**     SELECT <list of expressions> FROM %_content AS x ...\n**\n** to return the docid, followed by each column of text data in order\n** from left to write. If parameter zFunc is not NULL, then instead of\n** being returned directly each column of text data is passed to an SQL\n** function named zFunc first. For example, if zFunc is \"unzip\" and the\n** table has the three user-defined columns \"a\", \"b\", and \"c\", the following\n** string is returned:\n**\n**     \"docid, unzip(x.'a'), unzip(x.'b'), unzip(x.'c') FROM %_content AS x\"\n**\n** The pointer returned points to a buffer allocated by sqlite3_malloc(). It\n** is the responsibility of the caller to eventually free it.\n**\n** If *pRc is not SQLITE_OK when this function is called, it is a no-op (and\n** a NULL pointer is returned). Otherwise, if an OOM error is encountered\n** by this function, NULL is returned and *pRc is set to SQLITE_NOMEM. If\n** no error occurs, *pRc is left unmodified.\n*/\nstatic char *fts3ReadExprList(Fts3Table *p, const char *zFunc, int *pRc){\n  char *zRet = 0;\n  char *zFree = 0;\n  char *zFunction;\n  int i;\n\n  if( p->zContentTbl==0 ){\n    if( !zFunc ){\n      zFunction = \"\";\n    }else{\n      zFree = zFunction = fts3QuoteId(zFunc);\n    }\n    fts3Appendf(pRc, &zRet, \"docid\");\n    for(i=0; i<p->nColumn; i++){\n      fts3Appendf(pRc, &zRet, \",%s(x.'c%d%q')\", zFunction, i, p->azColumn[i]);\n    }\n    if( p->zLanguageid ){\n      fts3Appendf(pRc, &zRet, \", x.%Q\", \"langid\");\n    }\n    sqlite3_free(zFree);\n  }else{\n    fts3Appendf(pRc, &zRet, \"rowid\");\n    for(i=0; i<p->nColumn; i++){\n      fts3Appendf(pRc, &zRet, \", x.'%q'\", p->azColumn[i]);\n    }\n    if( p->zLanguageid ){\n      fts3Appendf(pRc, &zRet, \", x.%Q\", p->zLanguageid);\n    }\n  }\n  fts3Appendf(pRc, &zRet, \" FROM '%q'.'%q%s' AS x\", \n      p->zDb,\n      (p->zContentTbl ? p->zContentTbl : p->zName),\n      (p->zContentTbl ? \"\" : \"_content\")\n  );\n  return zRet;\n}\n\n/*\n** Return a list of N comma separated question marks, where N is the number\n** of columns in the %_content table (one for the docid plus one for each\n** user-defined text column).\n**\n** If argument zFunc is not NULL, then all but the first question mark\n** is preceded by zFunc and an open bracket, and followed by a closed\n** bracket. For example, if zFunc is \"zip\" and the FTS3 table has three \n** user-defined text columns, the following string is returned:\n**\n**     \"?, zip(?), zip(?), zip(?)\"\n**\n** The pointer returned points to a buffer allocated by sqlite3_malloc(). It\n** is the responsibility of the caller to eventually free it.\n**\n** If *pRc is not SQLITE_OK when this function is called, it is a no-op (and\n** a NULL pointer is returned). Otherwise, if an OOM error is encountered\n** by this function, NULL is returned and *pRc is set to SQLITE_NOMEM. If\n** no error occurs, *pRc is left unmodified.\n*/\nstatic char *fts3WriteExprList(Fts3Table *p, const char *zFunc, int *pRc){\n  char *zRet = 0;\n  char *zFree = 0;\n  char *zFunction;\n  int i;\n\n  if( !zFunc ){\n    zFunction = \"\";\n  }else{\n    zFree = zFunction = fts3QuoteId(zFunc);\n  }\n  fts3Appendf(pRc, &zRet, \"?\");\n  for(i=0; i<p->nColumn; i++){\n    fts3Appendf(pRc, &zRet, \",%s(?)\", zFunction);\n  }\n  if( p->zLanguageid ){\n    fts3Appendf(pRc, &zRet, \", ?\");\n  }\n  sqlite3_free(zFree);\n  return zRet;\n}\n\n/*\n** This function interprets the string at (*pp) as a non-negative integer\n** value. It reads the integer and sets *pnOut to the value read, then \n** sets *pp to point to the byte immediately following the last byte of\n** the integer value.\n**\n** Only decimal digits ('0'..'9') may be part of an integer value. \n**\n** If *pp does not being with a decimal digit SQLITE_ERROR is returned and\n** the output value undefined. Otherwise SQLITE_OK is returned.\n**\n** This function is used when parsing the \"prefix=\" FTS4 parameter.\n*/\nstatic int fts3GobbleInt(const char **pp, int *pnOut){\n  const int MAX_NPREFIX = 10000000;\n  const char *p;                  /* Iterator pointer */\n  int nInt = 0;                   /* Output value */\n\n  for(p=*pp; p[0]>='0' && p[0]<='9'; p++){\n    nInt = nInt * 10 + (p[0] - '0');\n    if( nInt>MAX_NPREFIX ){\n      nInt = 0;\n      break;\n    }\n  }\n  if( p==*pp ) return SQLITE_ERROR;\n  *pnOut = nInt;\n  *pp = p;\n  return SQLITE_OK;\n}\n\n/*\n** This function is called to allocate an array of Fts3Index structures\n** representing the indexes maintained by the current FTS table. FTS tables\n** always maintain the main \"terms\" index, but may also maintain one or\n** more \"prefix\" indexes, depending on the value of the \"prefix=\" parameter\n** (if any) specified as part of the CREATE VIRTUAL TABLE statement.\n**\n** Argument zParam is passed the value of the \"prefix=\" option if one was\n** specified, or NULL otherwise.\n**\n** If no error occurs, SQLITE_OK is returned and *apIndex set to point to\n** the allocated array. *pnIndex is set to the number of elements in the\n** array. If an error does occur, an SQLite error code is returned.\n**\n** Regardless of whether or not an error is returned, it is the responsibility\n** of the caller to call sqlite3_free() on the output array to free it.\n*/\nstatic int fts3PrefixParameter(\n  const char *zParam,             /* ABC in prefix=ABC parameter to parse */\n  int *pnIndex,                   /* OUT: size of *apIndex[] array */\n  struct Fts3Index **apIndex      /* OUT: Array of indexes for this table */\n){\n  struct Fts3Index *aIndex;       /* Allocated array */\n  int nIndex = 1;                 /* Number of entries in array */\n\n  if( zParam && zParam[0] ){\n    const char *p;\n    nIndex++;\n    for(p=zParam; *p; p++){\n      if( *p==',' ) nIndex++;\n    }\n  }\n\n  aIndex = sqlite3_malloc(sizeof(struct Fts3Index) * nIndex);\n  *apIndex = aIndex;\n  if( !aIndex ){\n    return SQLITE_NOMEM;\n  }\n\n  memset(aIndex, 0, sizeof(struct Fts3Index) * nIndex);\n  if( zParam ){\n    const char *p = zParam;\n    int i;\n    for(i=1; i<nIndex; i++){\n      int nPrefix = 0;\n      if( fts3GobbleInt(&p, &nPrefix) ) return SQLITE_ERROR;\n      assert( nPrefix>=0 );\n      if( nPrefix==0 ){\n        nIndex--;\n        i--;\n      }else{\n        aIndex[i].nPrefix = nPrefix;\n      }\n      p++;\n    }\n  }\n\n  *pnIndex = nIndex;\n  return SQLITE_OK;\n}\n\n/*\n** This function is called when initializing an FTS4 table that uses the\n** content=xxx option. It determines the number of and names of the columns\n** of the new FTS4 table.\n**\n** The third argument passed to this function is the value passed to the\n** config=xxx option (i.e. \"xxx\"). This function queries the database for\n** a table of that name. If found, the output variables are populated\n** as follows:\n**\n**   *pnCol:   Set to the number of columns table xxx has,\n**\n**   *pnStr:   Set to the total amount of space required to store a copy\n**             of each columns name, including the nul-terminator.\n**\n**   *pazCol:  Set to point to an array of *pnCol strings. Each string is\n**             the name of the corresponding column in table xxx. The array\n**             and its contents are allocated using a single allocation. It\n**             is the responsibility of the caller to free this allocation\n**             by eventually passing the *pazCol value to sqlite3_free().\n**\n** If the table cannot be found, an error code is returned and the output\n** variables are undefined. Or, if an OOM is encountered, SQLITE_NOMEM is\n** returned (and the output variables are undefined).\n*/\nstatic int fts3ContentColumns(\n  sqlite3 *db,                    /* Database handle */\n  const char *zDb,                /* Name of db (i.e. \"main\", \"temp\" etc.) */\n  const char *zTbl,               /* Name of content table */\n  const char ***pazCol,           /* OUT: Malloc'd array of column names */\n  int *pnCol,                     /* OUT: Size of array *pazCol */\n  int *pnStr,                     /* OUT: Bytes of string content */\n  char **pzErr                    /* OUT: error message */\n){\n  int rc = SQLITE_OK;             /* Return code */\n  char *zSql;                     /* \"SELECT *\" statement on zTbl */  \n  sqlite3_stmt *pStmt = 0;        /* Compiled version of zSql */\n\n  zSql = sqlite3_mprintf(\"SELECT * FROM %Q.%Q\", zDb, zTbl);\n  if( !zSql ){\n    rc = SQLITE_NOMEM;\n  }else{\n    rc = sqlite3_prepare(db, zSql, -1, &pStmt, 0);\n    if( rc!=SQLITE_OK ){\n      sqlite3Fts3ErrMsg(pzErr, \"%s\", sqlite3_errmsg(db));\n    }\n  }\n  sqlite3_free(zSql);\n\n  if( rc==SQLITE_OK ){\n    const char **azCol;           /* Output array */\n    int nStr = 0;                 /* Size of all column names (incl. 0x00) */\n    int nCol;                     /* Number of table columns */\n    int i;                        /* Used to iterate through columns */\n\n    /* Loop through the returned columns. Set nStr to the number of bytes of\n    ** space required to store a copy of each column name, including the\n    ** nul-terminator byte.  */\n    nCol = sqlite3_column_count(pStmt);\n    for(i=0; i<nCol; i++){\n      const char *zCol = sqlite3_column_name(pStmt, i);\n      nStr += (int)strlen(zCol) + 1;\n    }\n\n    /* Allocate and populate the array to return. */\n    azCol = (const char **)sqlite3_malloc(sizeof(char *) * nCol + nStr);\n    if( azCol==0 ){\n      rc = SQLITE_NOMEM;\n    }else{\n      char *p = (char *)&azCol[nCol];\n      for(i=0; i<nCol; i++){\n        const char *zCol = sqlite3_column_name(pStmt, i);\n        int n = (int)strlen(zCol)+1;\n        memcpy(p, zCol, n);\n        azCol[i] = p;\n        p += n;\n      }\n    }\n    sqlite3_finalize(pStmt);\n\n    /* Set the output variables. */\n    *pnCol = nCol;\n    *pnStr = nStr;\n    *pazCol = azCol;\n  }\n\n  return rc;\n}\n\n/*\n** This function is the implementation of both the xConnect and xCreate\n** methods of the FTS3 virtual table.\n**\n** The argv[] array contains the following:\n**\n**   argv[0]   -> module name  (\"fts3\" or \"fts4\")\n**   argv[1]   -> database name\n**   argv[2]   -> table name\n**   argv[...] -> \"column name\" and other module argument fields.\n*/\nstatic int fts3InitVtab(\n  int isCreate,                   /* True for xCreate, false for xConnect */\n  sqlite3 *db,                    /* The SQLite database connection */\n  void *pAux,                     /* Hash table containing tokenizers */\n  int argc,                       /* Number of elements in argv array */\n  const char * const *argv,       /* xCreate/xConnect argument array */\n  sqlite3_vtab **ppVTab,          /* Write the resulting vtab structure here */\n  char **pzErr                    /* Write any error message here */\n){\n  Fts3Hash *pHash = (Fts3Hash *)pAux;\n  Fts3Table *p = 0;               /* Pointer to allocated vtab */\n  int rc = SQLITE_OK;             /* Return code */\n  int i;                          /* Iterator variable */\n  int nByte;                      /* Size of allocation used for *p */\n  int iCol;                       /* Column index */\n  int nString = 0;                /* Bytes required to hold all column names */\n  int nCol = 0;                   /* Number of columns in the FTS table */\n  char *zCsr;                     /* Space for holding column names */\n  int nDb;                        /* Bytes required to hold database name */\n  int nName;                      /* Bytes required to hold table name */\n  int isFts4 = (argv[0][3]=='4'); /* True for FTS4, false for FTS3 */\n  const char **aCol;              /* Array of column names */\n  sqlite3_tokenizer *pTokenizer = 0;        /* Tokenizer for this table */\n\n  int nIndex = 0;                 /* Size of aIndex[] array */\n  struct Fts3Index *aIndex = 0;   /* Array of indexes for this table */\n\n  /* The results of parsing supported FTS4 key=value options: */\n  int bNoDocsize = 0;             /* True to omit %_docsize table */\n  int bDescIdx = 0;               /* True to store descending indexes */\n  char *zPrefix = 0;              /* Prefix parameter value (or NULL) */\n  char *zCompress = 0;            /* compress=? parameter (or NULL) */\n  char *zUncompress = 0;          /* uncompress=? parameter (or NULL) */\n  char *zContent = 0;             /* content=? parameter (or NULL) */\n  char *zLanguageid = 0;          /* languageid=? parameter (or NULL) */\n  char **azNotindexed = 0;        /* The set of notindexed= columns */\n  int nNotindexed = 0;            /* Size of azNotindexed[] array */\n\n  assert( strlen(argv[0])==4 );\n  assert( (sqlite3_strnicmp(argv[0], \"fts4\", 4)==0 && isFts4)\n       || (sqlite3_strnicmp(argv[0], \"fts3\", 4)==0 && !isFts4)\n  );\n\n  nDb = (int)strlen(argv[1]) + 1;\n  nName = (int)strlen(argv[2]) + 1;\n\n  nByte = sizeof(const char *) * (argc-2);\n  aCol = (const char **)sqlite3_malloc(nByte);\n  if( aCol ){\n    memset((void*)aCol, 0, nByte);\n    azNotindexed = (char **)sqlite3_malloc(nByte);\n  }\n  if( azNotindexed ){\n    memset(azNotindexed, 0, nByte);\n  }\n  if( !aCol || !azNotindexed ){\n    rc = SQLITE_NOMEM;\n    goto fts3_init_out;\n  }\n\n  /* Loop through all of the arguments passed by the user to the FTS3/4\n  ** module (i.e. all the column names and special arguments). This loop\n  ** does the following:\n  **\n  **   + Figures out the number of columns the FTSX table will have, and\n  **     the number of bytes of space that must be allocated to store copies\n  **     of the column names.\n  **\n  **   + If there is a tokenizer specification included in the arguments,\n  **     initializes the tokenizer pTokenizer.\n  */\n  for(i=3; rc==SQLITE_OK && i<argc; i++){\n    char const *z = argv[i];\n    int nKey;\n    char *zVal;\n\n    /* Check if this is a tokenizer specification */\n    if( !pTokenizer \n     && strlen(z)>8\n     && 0==sqlite3_strnicmp(z, \"tokenize\", 8) \n     && 0==sqlite3Fts3IsIdChar(z[8])\n    ){\n      rc = sqlite3Fts3InitTokenizer(pHash, &z[9], &pTokenizer, pzErr);\n    }\n\n    /* Check if it is an FTS4 special argument. */\n    else if( isFts4 && fts3IsSpecialColumn(z, &nKey, &zVal) ){\n      struct Fts4Option {\n        const char *zOpt;\n        int nOpt;\n      } aFts4Opt[] = {\n        { \"matchinfo\",   9 },     /* 0 -> MATCHINFO */\n        { \"prefix\",      6 },     /* 1 -> PREFIX */\n        { \"compress\",    8 },     /* 2 -> COMPRESS */\n        { \"uncompress\", 10 },     /* 3 -> UNCOMPRESS */\n        { \"order\",       5 },     /* 4 -> ORDER */\n        { \"content\",     7 },     /* 5 -> CONTENT */\n        { \"languageid\", 10 },     /* 6 -> LANGUAGEID */\n        { \"notindexed\", 10 }      /* 7 -> NOTINDEXED */\n      };\n\n      int iOpt;\n      if( !zVal ){\n        rc = SQLITE_NOMEM;\n      }else{\n        for(iOpt=0; iOpt<SizeofArray(aFts4Opt); iOpt++){\n          struct Fts4Option *pOp = &aFts4Opt[iOpt];\n          if( nKey==pOp->nOpt && !sqlite3_strnicmp(z, pOp->zOpt, pOp->nOpt) ){\n            break;\n          }\n        }\n        switch( iOpt ){\n          case 0:               /* MATCHINFO */\n            if( strlen(zVal)!=4 || sqlite3_strnicmp(zVal, \"fts3\", 4) ){\n              sqlite3Fts3ErrMsg(pzErr, \"unrecognized matchinfo: %s\", zVal);\n              rc = SQLITE_ERROR;\n            }\n            bNoDocsize = 1;\n            break;\n\n          case 1:               /* PREFIX */\n            sqlite3_free(zPrefix);\n            zPrefix = zVal;\n            zVal = 0;\n            break;\n\n          case 2:               /* COMPRESS */\n            sqlite3_free(zCompress);\n            zCompress = zVal;\n            zVal = 0;\n            break;\n\n          case 3:               /* UNCOMPRESS */\n            sqlite3_free(zUncompress);\n            zUncompress = zVal;\n            zVal = 0;\n            break;\n\n          case 4:               /* ORDER */\n            if( (strlen(zVal)!=3 || sqlite3_strnicmp(zVal, \"asc\", 3)) \n             && (strlen(zVal)!=4 || sqlite3_strnicmp(zVal, \"desc\", 4)) \n            ){\n              sqlite3Fts3ErrMsg(pzErr, \"unrecognized order: %s\", zVal);\n              rc = SQLITE_ERROR;\n            }\n            bDescIdx = (zVal[0]=='d' || zVal[0]=='D');\n            break;\n\n          case 5:              /* CONTENT */\n            sqlite3_free(zContent);\n            zContent = zVal;\n            zVal = 0;\n            break;\n\n          case 6:              /* LANGUAGEID */\n            assert( iOpt==6 );\n            sqlite3_free(zLanguageid);\n            zLanguageid = zVal;\n            zVal = 0;\n            break;\n\n          case 7:              /* NOTINDEXED */\n            azNotindexed[nNotindexed++] = zVal;\n            zVal = 0;\n            break;\n\n          default:\n            assert( iOpt==SizeofArray(aFts4Opt) );\n            sqlite3Fts3ErrMsg(pzErr, \"unrecognized parameter: %s\", z);\n            rc = SQLITE_ERROR;\n            break;\n        }\n        sqlite3_free(zVal);\n      }\n    }\n\n    /* Otherwise, the argument is a column name. */\n    else {\n      nString += (int)(strlen(z) + 1);\n      aCol[nCol++] = z;\n    }\n  }\n\n  /* If a content=xxx option was specified, the following:\n  **\n  **   1. Ignore any compress= and uncompress= options.\n  **\n  **   2. If no column names were specified as part of the CREATE VIRTUAL\n  **      TABLE statement, use all columns from the content table.\n  */\n  if( rc==SQLITE_OK && zContent ){\n    sqlite3_free(zCompress); \n    sqlite3_free(zUncompress); \n    zCompress = 0;\n    zUncompress = 0;\n    if( nCol==0 ){\n      sqlite3_free((void*)aCol); \n      aCol = 0;\n      rc = fts3ContentColumns(db, argv[1], zContent,&aCol,&nCol,&nString,pzErr);\n\n      /* If a languageid= option was specified, remove the language id\n      ** column from the aCol[] array. */ \n      if( rc==SQLITE_OK && zLanguageid ){\n        int j;\n        for(j=0; j<nCol; j++){\n          if( sqlite3_stricmp(zLanguageid, aCol[j])==0 ){\n            int k;\n            for(k=j; k<nCol; k++) aCol[k] = aCol[k+1];\n            nCol--;\n            break;\n          }\n        }\n      }\n    }\n  }\n  if( rc!=SQLITE_OK ) goto fts3_init_out;\n\n  if( nCol==0 ){\n    assert( nString==0 );\n    aCol[0] = \"content\";\n    nString = 8;\n    nCol = 1;\n  }\n\n  if( pTokenizer==0 ){\n    rc = sqlite3Fts3InitTokenizer(pHash, \"simple\", &pTokenizer, pzErr);\n    if( rc!=SQLITE_OK ) goto fts3_init_out;\n  }\n  assert( pTokenizer );\n\n  rc = fts3PrefixParameter(zPrefix, &nIndex, &aIndex);\n  if( rc==SQLITE_ERROR ){\n    assert( zPrefix );\n    sqlite3Fts3ErrMsg(pzErr, \"error parsing prefix parameter: %s\", zPrefix);\n  }\n  if( rc!=SQLITE_OK ) goto fts3_init_out;\n\n  /* Allocate and populate the Fts3Table structure. */\n  nByte = sizeof(Fts3Table) +                  /* Fts3Table */\n          nCol * sizeof(char *) +              /* azColumn */\n          nIndex * sizeof(struct Fts3Index) +  /* aIndex */\n          nCol * sizeof(u8) +                  /* abNotindexed */\n          nName +                              /* zName */\n          nDb +                                /* zDb */\n          nString;                             /* Space for azColumn strings */\n  p = (Fts3Table*)sqlite3_malloc(nByte);\n  if( p==0 ){\n    rc = SQLITE_NOMEM;\n    goto fts3_init_out;\n  }\n  memset(p, 0, nByte);\n  p->db = db;\n  p->nColumn = nCol;\n  p->nPendingData = 0;\n  p->azColumn = (char **)&p[1];\n  p->pTokenizer = pTokenizer;\n  p->nMaxPendingData = FTS3_MAX_PENDING_DATA;\n  p->bHasDocsize = (isFts4 && bNoDocsize==0);\n  p->bHasStat = (u8)isFts4;\n  p->bFts4 = (u8)isFts4;\n  p->bDescIdx = (u8)bDescIdx;\n  p->nAutoincrmerge = 0xff;   /* 0xff means setting unknown */\n  p->zContentTbl = zContent;\n  p->zLanguageid = zLanguageid;\n  zContent = 0;\n  zLanguageid = 0;\n  TESTONLY( p->inTransaction = -1 );\n  TESTONLY( p->mxSavepoint = -1 );\n\n  p->aIndex = (struct Fts3Index *)&p->azColumn[nCol];\n  memcpy(p->aIndex, aIndex, sizeof(struct Fts3Index) * nIndex);\n  p->nIndex = nIndex;\n  for(i=0; i<nIndex; i++){\n    fts3HashInit(&p->aIndex[i].hPending, FTS3_HASH_STRING, 1);\n  }\n  p->abNotindexed = (u8 *)&p->aIndex[nIndex];\n\n  /* Fill in the zName and zDb fields of the vtab structure. */\n  zCsr = (char *)&p->abNotindexed[nCol];\n  p->zName = zCsr;\n  memcpy(zCsr, argv[2], nName);\n  zCsr += nName;\n  p->zDb = zCsr;\n  memcpy(zCsr, argv[1], nDb);\n  zCsr += nDb;\n\n  /* Fill in the azColumn array */\n  for(iCol=0; iCol<nCol; iCol++){\n    char *z; \n    int n = 0;\n    z = (char *)sqlite3Fts3NextToken(aCol[iCol], &n);\n    if( n>0 ){\n      memcpy(zCsr, z, n);\n    }\n    zCsr[n] = '\\0';\n    sqlite3Fts3Dequote(zCsr);\n    p->azColumn[iCol] = zCsr;\n    zCsr += n+1;\n    assert( zCsr <= &((char *)p)[nByte] );\n  }\n\n  /* Fill in the abNotindexed array */\n  for(iCol=0; iCol<nCol; iCol++){\n    int n = (int)strlen(p->azColumn[iCol]);\n    for(i=0; i<nNotindexed; i++){\n      char *zNot = azNotindexed[i];\n      if( zNot && n==(int)strlen(zNot)\n       && 0==sqlite3_strnicmp(p->azColumn[iCol], zNot, n) \n      ){\n        p->abNotindexed[iCol] = 1;\n        sqlite3_free(zNot);\n        azNotindexed[i] = 0;\n      }\n    }\n  }\n  for(i=0; i<nNotindexed; i++){\n    if( azNotindexed[i] ){\n      sqlite3Fts3ErrMsg(pzErr, \"no such column: %s\", azNotindexed[i]);\n      rc = SQLITE_ERROR;\n    }\n  }\n\n  if( rc==SQLITE_OK && (zCompress==0)!=(zUncompress==0) ){\n    char const *zMiss = (zCompress==0 ? \"compress\" : \"uncompress\");\n    rc = SQLITE_ERROR;\n    sqlite3Fts3ErrMsg(pzErr, \"missing %s parameter in fts4 constructor\", zMiss);\n  }\n  p->zReadExprlist = fts3ReadExprList(p, zUncompress, &rc);\n  p->zWriteExprlist = fts3WriteExprList(p, zCompress, &rc);\n  if( rc!=SQLITE_OK ) goto fts3_init_out;\n\n  /* If this is an xCreate call, create the underlying tables in the \n  ** database. TODO: For xConnect(), it could verify that said tables exist.\n  */\n  if( isCreate ){\n    rc = fts3CreateTables(p);\n  }\n\n  /* Check to see if a legacy fts3 table has been \"upgraded\" by the\n  ** addition of a %_stat table so that it can use incremental merge.\n  */\n  if( !isFts4 && !isCreate ){\n    p->bHasStat = 2;\n  }\n\n  /* Figure out the page-size for the database. This is required in order to\n  ** estimate the cost of loading large doclists from the database.  */\n  fts3DatabasePageSize(&rc, p);\n  p->nNodeSize = p->nPgsz-35;\n\n  /* Declare the table schema to SQLite. */\n  fts3DeclareVtab(&rc, p);\n\nfts3_init_out:\n  sqlite3_free(zPrefix);\n  sqlite3_free(aIndex);\n  sqlite3_free(zCompress);\n  sqlite3_free(zUncompress);\n  sqlite3_free(zContent);\n  sqlite3_free(zLanguageid);\n  for(i=0; i<nNotindexed; i++) sqlite3_free(azNotindexed[i]);\n  sqlite3_free((void *)aCol);\n  sqlite3_free((void *)azNotindexed);\n  if( rc!=SQLITE_OK ){\n    if( p ){\n      fts3DisconnectMethod((sqlite3_vtab *)p);\n    }else if( pTokenizer ){\n      pTokenizer->pModule->xDestroy(pTokenizer);\n    }\n  }else{\n    assert( p->pSegments==0 );\n    *ppVTab = &p->base;\n  }\n  return rc;\n}\n\n/*\n** The xConnect() and xCreate() methods for the virtual table. All the\n** work is done in function fts3InitVtab().\n*/\nstatic int fts3ConnectMethod(\n  sqlite3 *db,                    /* Database connection */\n  void *pAux,                     /* Pointer to tokenizer hash table */\n  int argc,                       /* Number of elements in argv array */\n  const char * const *argv,       /* xCreate/xConnect argument array */\n  sqlite3_vtab **ppVtab,          /* OUT: New sqlite3_vtab object */\n  char **pzErr                    /* OUT: sqlite3_malloc'd error message */\n){\n  return fts3InitVtab(0, db, pAux, argc, argv, ppVtab, pzErr);\n}\nstatic int fts3CreateMethod(\n  sqlite3 *db,                    /* Database connection */\n  void *pAux,                     /* Pointer to tokenizer hash table */\n  int argc,                       /* Number of elements in argv array */\n  const char * const *argv,       /* xCreate/xConnect argument array */\n  sqlite3_vtab **ppVtab,          /* OUT: New sqlite3_vtab object */\n  char **pzErr                    /* OUT: sqlite3_malloc'd error message */\n){\n  return fts3InitVtab(1, db, pAux, argc, argv, ppVtab, pzErr);\n}\n\n/*\n** Set the pIdxInfo->estimatedRows variable to nRow. Unless this\n** extension is currently being used by a version of SQLite too old to\n** support estimatedRows. In that case this function is a no-op.\n*/\nstatic void fts3SetEstimatedRows(sqlite3_index_info *pIdxInfo, i64 nRow){\n#if SQLITE_VERSION_NUMBER>=3008002\n  if( sqlite3_libversion_number()>=3008002 ){\n    pIdxInfo->estimatedRows = nRow;\n  }\n#endif\n}\n\n/*\n** Set the SQLITE_INDEX_SCAN_UNIQUE flag in pIdxInfo->flags. Unless this\n** extension is currently being used by a version of SQLite too old to\n** support index-info flags. In that case this function is a no-op.\n*/\nstatic void fts3SetUniqueFlag(sqlite3_index_info *pIdxInfo){\n#if SQLITE_VERSION_NUMBER>=3008012\n  if( sqlite3_libversion_number()>=3008012 ){\n    pIdxInfo->idxFlags |= SQLITE_INDEX_SCAN_UNIQUE;\n  }\n#endif\n}\n\n/* \n** Implementation of the xBestIndex method for FTS3 tables. There\n** are three possible strategies, in order of preference:\n**\n**   1. Direct lookup by rowid or docid. \n**   2. Full-text search using a MATCH operator on a non-docid column.\n**   3. Linear scan of %_content table.\n*/\nstatic int fts3BestIndexMethod(sqlite3_vtab *pVTab, sqlite3_index_info *pInfo){\n  Fts3Table *p = (Fts3Table *)pVTab;\n  int i;                          /* Iterator variable */\n  int iCons = -1;                 /* Index of constraint to use */\n\n  int iLangidCons = -1;           /* Index of langid=x constraint, if present */\n  int iDocidGe = -1;              /* Index of docid>=x constraint, if present */\n  int iDocidLe = -1;              /* Index of docid<=x constraint, if present */\n  int iIdx;\n\n  /* By default use a full table scan. This is an expensive option,\n  ** so search through the constraints to see if a more efficient \n  ** strategy is possible.\n  */\n  pInfo->idxNum = FTS3_FULLSCAN_SEARCH;\n  pInfo->estimatedCost = 5000000;\n  for(i=0; i<pInfo->nConstraint; i++){\n    int bDocid;                 /* True if this constraint is on docid */\n    struct sqlite3_index_constraint *pCons = &pInfo->aConstraint[i];\n    if( pCons->usable==0 ){\n      if( pCons->op==SQLITE_INDEX_CONSTRAINT_MATCH ){\n        /* There exists an unusable MATCH constraint. This means that if\n        ** the planner does elect to use the results of this call as part\n        ** of the overall query plan the user will see an \"unable to use\n        ** function MATCH in the requested context\" error. To discourage\n        ** this, return a very high cost here.  */\n        pInfo->idxNum = FTS3_FULLSCAN_SEARCH;\n        pInfo->estimatedCost = 1e50;\n        fts3SetEstimatedRows(pInfo, ((sqlite3_int64)1) << 50);\n        return SQLITE_OK;\n      }\n      continue;\n    }\n\n    bDocid = (pCons->iColumn<0 || pCons->iColumn==p->nColumn+1);\n\n    /* A direct lookup on the rowid or docid column. Assign a cost of 1.0. */\n    if( iCons<0 && pCons->op==SQLITE_INDEX_CONSTRAINT_EQ && bDocid ){\n      pInfo->idxNum = FTS3_DOCID_SEARCH;\n      pInfo->estimatedCost = 1.0;\n      iCons = i;\n    }\n\n    /* A MATCH constraint. Use a full-text search.\n    **\n    ** If there is more than one MATCH constraint available, use the first\n    ** one encountered. If there is both a MATCH constraint and a direct\n    ** rowid/docid lookup, prefer the MATCH strategy. This is done even \n    ** though the rowid/docid lookup is faster than a MATCH query, selecting\n    ** it would lead to an \"unable to use function MATCH in the requested \n    ** context\" error.\n    */\n    if( pCons->op==SQLITE_INDEX_CONSTRAINT_MATCH \n     && pCons->iColumn>=0 && pCons->iColumn<=p->nColumn\n    ){\n      pInfo->idxNum = FTS3_FULLTEXT_SEARCH + pCons->iColumn;\n      pInfo->estimatedCost = 2.0;\n      iCons = i;\n    }\n\n    /* Equality constraint on the langid column */\n    if( pCons->op==SQLITE_INDEX_CONSTRAINT_EQ \n     && pCons->iColumn==p->nColumn + 2\n    ){\n      iLangidCons = i;\n    }\n\n    if( bDocid ){\n      switch( pCons->op ){\n        case SQLITE_INDEX_CONSTRAINT_GE:\n        case SQLITE_INDEX_CONSTRAINT_GT:\n          iDocidGe = i;\n          break;\n\n        case SQLITE_INDEX_CONSTRAINT_LE:\n        case SQLITE_INDEX_CONSTRAINT_LT:\n          iDocidLe = i;\n          break;\n      }\n    }\n  }\n\n  /* If using a docid=? or rowid=? strategy, set the UNIQUE flag. */\n  if( pInfo->idxNum==FTS3_DOCID_SEARCH ) fts3SetUniqueFlag(pInfo);\n\n  iIdx = 1;\n  if( iCons>=0 ){\n    pInfo->aConstraintUsage[iCons].argvIndex = iIdx++;\n    pInfo->aConstraintUsage[iCons].omit = 1;\n  } \n  if( iLangidCons>=0 ){\n    pInfo->idxNum |= FTS3_HAVE_LANGID;\n    pInfo->aConstraintUsage[iLangidCons].argvIndex = iIdx++;\n  } \n  if( iDocidGe>=0 ){\n    pInfo->idxNum |= FTS3_HAVE_DOCID_GE;\n    pInfo->aConstraintUsage[iDocidGe].argvIndex = iIdx++;\n  } \n  if( iDocidLe>=0 ){\n    pInfo->idxNum |= FTS3_HAVE_DOCID_LE;\n    pInfo->aConstraintUsage[iDocidLe].argvIndex = iIdx++;\n  } \n\n  /* Regardless of the strategy selected, FTS can deliver rows in rowid (or\n  ** docid) order. Both ascending and descending are possible. \n  */\n  if( pInfo->nOrderBy==1 ){\n    struct sqlite3_index_orderby *pOrder = &pInfo->aOrderBy[0];\n    if( pOrder->iColumn<0 || pOrder->iColumn==p->nColumn+1 ){\n      if( pOrder->desc ){\n        pInfo->idxStr = \"DESC\";\n      }else{\n        pInfo->idxStr = \"ASC\";\n      }\n      pInfo->orderByConsumed = 1;\n    }\n  }\n\n  assert( p->pSegments==0 );\n  return SQLITE_OK;\n}\n\n/*\n** Implementation of xOpen method.\n*/\nstatic int fts3OpenMethod(sqlite3_vtab *pVTab, sqlite3_vtab_cursor **ppCsr){\n  sqlite3_vtab_cursor *pCsr;               /* Allocated cursor */\n\n  UNUSED_PARAMETER(pVTab);\n\n  /* Allocate a buffer large enough for an Fts3Cursor structure. If the\n  ** allocation succeeds, zero it and return SQLITE_OK. Otherwise, \n  ** if the allocation fails, return SQLITE_NOMEM.\n  */\n  *ppCsr = pCsr = (sqlite3_vtab_cursor *)sqlite3_malloc(sizeof(Fts3Cursor));\n  if( !pCsr ){\n    return SQLITE_NOMEM;\n  }\n  memset(pCsr, 0, sizeof(Fts3Cursor));\n  return SQLITE_OK;\n}\n\n/*\n** Finalize the statement handle at pCsr->pStmt.\n**\n** Or, if that statement handle is one created by fts3CursorSeekStmt(),\n** and the Fts3Table.pSeekStmt slot is currently NULL, save the statement\n** pointer there instead of finalizing it.\n*/\nstatic void fts3CursorFinalizeStmt(Fts3Cursor *pCsr){\n  if( pCsr->bSeekStmt ){\n    Fts3Table *p = (Fts3Table *)pCsr->base.pVtab;\n    if( p->pSeekStmt==0 ){\n      p->pSeekStmt = pCsr->pStmt;\n      sqlite3_reset(pCsr->pStmt);\n      pCsr->pStmt = 0;\n    }\n    pCsr->bSeekStmt = 0;\n  }\n  sqlite3_finalize(pCsr->pStmt);\n}\n\n/*\n** Free all resources currently held by the cursor passed as the only\n** argument.\n*/\nstatic void fts3ClearCursor(Fts3Cursor *pCsr){\n  fts3CursorFinalizeStmt(pCsr);\n  sqlite3Fts3FreeDeferredTokens(pCsr);\n  sqlite3_free(pCsr->aDoclist);\n  sqlite3Fts3MIBufferFree(pCsr->pMIBuffer);\n  sqlite3Fts3ExprFree(pCsr->pExpr);\n  memset(&(&pCsr->base)[1], 0, sizeof(Fts3Cursor)-sizeof(sqlite3_vtab_cursor));\n}\n\n/*\n** Close the cursor.  For additional information see the documentation\n** on the xClose method of the virtual table interface.\n*/\nstatic int fts3CloseMethod(sqlite3_vtab_cursor *pCursor){\n  Fts3Cursor *pCsr = (Fts3Cursor *)pCursor;\n  assert( ((Fts3Table *)pCsr->base.pVtab)->pSegments==0 );\n  fts3ClearCursor(pCsr);\n  assert( ((Fts3Table *)pCsr->base.pVtab)->pSegments==0 );\n  sqlite3_free(pCsr);\n  return SQLITE_OK;\n}\n\n/*\n** If pCsr->pStmt has not been prepared (i.e. if pCsr->pStmt==0), then\n** compose and prepare an SQL statement of the form:\n**\n**    \"SELECT <columns> FROM %_content WHERE rowid = ?\"\n**\n** (or the equivalent for a content=xxx table) and set pCsr->pStmt to\n** it. If an error occurs, return an SQLite error code.\n*/\nstatic int fts3CursorSeekStmt(Fts3Cursor *pCsr){\n  int rc = SQLITE_OK;\n  if( pCsr->pStmt==0 ){\n    Fts3Table *p = (Fts3Table *)pCsr->base.pVtab;\n    char *zSql;\n    if( p->pSeekStmt ){\n      pCsr->pStmt = p->pSeekStmt;\n      p->pSeekStmt = 0;\n    }else{\n      zSql = sqlite3_mprintf(\"SELECT %s WHERE rowid = ?\", p->zReadExprlist);\n      if( !zSql ) return SQLITE_NOMEM;\n      rc = sqlite3_prepare_v3(p->db, zSql,-1,SQLITE_PREPARE_PERSISTENT,&pCsr->pStmt,0);\n      sqlite3_free(zSql);\n    }\n    if( rc==SQLITE_OK ) pCsr->bSeekStmt = 1;\n  }\n  return rc;\n}\n\n/*\n** Position the pCsr->pStmt statement so that it is on the row\n** of the %_content table that contains the last match.  Return\n** SQLITE_OK on success.  \n*/\nstatic int fts3CursorSeek(sqlite3_context *pContext, Fts3Cursor *pCsr){\n  int rc = SQLITE_OK;\n  if( pCsr->isRequireSeek ){\n    rc = fts3CursorSeekStmt(pCsr);\n    if( rc==SQLITE_OK ){\n      sqlite3_bind_int64(pCsr->pStmt, 1, pCsr->iPrevId);\n      pCsr->isRequireSeek = 0;\n      if( SQLITE_ROW==sqlite3_step(pCsr->pStmt) ){\n        return SQLITE_OK;\n      }else{\n        rc = sqlite3_reset(pCsr->pStmt);\n        if( rc==SQLITE_OK && ((Fts3Table *)pCsr->base.pVtab)->zContentTbl==0 ){\n          /* If no row was found and no error has occurred, then the %_content\n          ** table is missing a row that is present in the full-text index.\n          ** The data structures are corrupt.  */\n          rc = FTS_CORRUPT_VTAB;\n          pCsr->isEof = 1;\n        }\n      }\n    }\n  }\n\n  if( rc!=SQLITE_OK && pContext ){\n    sqlite3_result_error_code(pContext, rc);\n  }\n  return rc;\n}\n\n/*\n** This function is used to process a single interior node when searching\n** a b-tree for a term or term prefix. The node data is passed to this \n** function via the zNode/nNode parameters. The term to search for is\n** passed in zTerm/nTerm.\n**\n** If piFirst is not NULL, then this function sets *piFirst to the blockid\n** of the child node that heads the sub-tree that may contain the term.\n**\n** If piLast is not NULL, then *piLast is set to the right-most child node\n** that heads a sub-tree that may contain a term for which zTerm/nTerm is\n** a prefix.\n**\n** If an OOM error occurs, SQLITE_NOMEM is returned. Otherwise, SQLITE_OK.\n*/\nstatic int fts3ScanInteriorNode(\n  const char *zTerm,              /* Term to select leaves for */\n  int nTerm,                      /* Size of term zTerm in bytes */\n  const char *zNode,              /* Buffer containing segment interior node */\n  int nNode,                      /* Size of buffer at zNode */\n  sqlite3_int64 *piFirst,         /* OUT: Selected child node */\n  sqlite3_int64 *piLast           /* OUT: Selected child node */\n){\n  int rc = SQLITE_OK;             /* Return code */\n  const char *zCsr = zNode;       /* Cursor to iterate through node */\n  const char *zEnd = &zCsr[nNode];/* End of interior node buffer */\n  char *zBuffer = 0;              /* Buffer to load terms into */\n  int nAlloc = 0;                 /* Size of allocated buffer */\n  int isFirstTerm = 1;            /* True when processing first term on page */\n  sqlite3_int64 iChild;           /* Block id of child node to descend to */\n\n  /* Skip over the 'height' varint that occurs at the start of every \n  ** interior node. Then load the blockid of the left-child of the b-tree\n  ** node into variable iChild.  \n  **\n  ** Even if the data structure on disk is corrupted, this (reading two\n  ** varints from the buffer) does not risk an overread. If zNode is a\n  ** root node, then the buffer comes from a SELECT statement. SQLite does\n  ** not make this guarantee explicitly, but in practice there are always\n  ** either more than 20 bytes of allocated space following the nNode bytes of\n  ** contents, or two zero bytes. Or, if the node is read from the %_segments\n  ** table, then there are always 20 bytes of zeroed padding following the\n  ** nNode bytes of content (see sqlite3Fts3ReadBlock() for details).\n  */\n  zCsr += sqlite3Fts3GetVarint(zCsr, &iChild);\n  zCsr += sqlite3Fts3GetVarint(zCsr, &iChild);\n  if( zCsr>zEnd ){\n    return FTS_CORRUPT_VTAB;\n  }\n  \n  while( zCsr<zEnd && (piFirst || piLast) ){\n    int cmp;                      /* memcmp() result */\n    int nSuffix;                  /* Size of term suffix */\n    int nPrefix = 0;              /* Size of term prefix */\n    int nBuffer;                  /* Total term size */\n  \n    /* Load the next term on the node into zBuffer. Use realloc() to expand\n    ** the size of zBuffer if required.  */\n    if( !isFirstTerm ){\n      zCsr += fts3GetVarint32(zCsr, &nPrefix);\n    }\n    isFirstTerm = 0;\n    zCsr += fts3GetVarint32(zCsr, &nSuffix);\n    \n    assert( nPrefix>=0 && nSuffix>=0 );\n    if( &zCsr[nSuffix]>zEnd ){\n      rc = FTS_CORRUPT_VTAB;\n      goto finish_scan;\n    }\n    if( nPrefix+nSuffix>nAlloc ){\n      char *zNew;\n      nAlloc = (nPrefix+nSuffix) * 2;\n      zNew = (char *)sqlite3_realloc(zBuffer, nAlloc);\n      if( !zNew ){\n        rc = SQLITE_NOMEM;\n        goto finish_scan;\n      }\n      zBuffer = zNew;\n    }\n    assert( zBuffer );\n    memcpy(&zBuffer[nPrefix], zCsr, nSuffix);\n    nBuffer = nPrefix + nSuffix;\n    zCsr += nSuffix;\n\n    /* Compare the term we are searching for with the term just loaded from\n    ** the interior node. If the specified term is greater than or equal\n    ** to the term from the interior node, then all terms on the sub-tree \n    ** headed by node iChild are smaller than zTerm. No need to search \n    ** iChild.\n    **\n    ** If the interior node term is larger than the specified term, then\n    ** the tree headed by iChild may contain the specified term.\n    */\n    cmp = memcmp(zTerm, zBuffer, (nBuffer>nTerm ? nTerm : nBuffer));\n    if( piFirst && (cmp<0 || (cmp==0 && nBuffer>nTerm)) ){\n      *piFirst = iChild;\n      piFirst = 0;\n    }\n\n    if( piLast && cmp<0 ){\n      *piLast = iChild;\n      piLast = 0;\n    }\n\n    iChild++;\n  };\n\n  if( piFirst ) *piFirst = iChild;\n  if( piLast ) *piLast = iChild;\n\n finish_scan:\n  sqlite3_free(zBuffer);\n  return rc;\n}\n\n\n/*\n** The buffer pointed to by argument zNode (size nNode bytes) contains an\n** interior node of a b-tree segment. The zTerm buffer (size nTerm bytes)\n** contains a term. This function searches the sub-tree headed by the zNode\n** node for the range of leaf nodes that may contain the specified term\n** or terms for which the specified term is a prefix.\n**\n** If piLeaf is not NULL, then *piLeaf is set to the blockid of the \n** left-most leaf node in the tree that may contain the specified term.\n** If piLeaf2 is not NULL, then *piLeaf2 is set to the blockid of the\n** right-most leaf node that may contain a term for which the specified\n** term is a prefix.\n**\n** It is possible that the range of returned leaf nodes does not contain \n** the specified term or any terms for which it is a prefix. However, if the \n** segment does contain any such terms, they are stored within the identified\n** range. Because this function only inspects interior segment nodes (and\n** never loads leaf nodes into memory), it is not possible to be sure.\n**\n** If an error occurs, an error code other than SQLITE_OK is returned.\n*/ \nstatic int fts3SelectLeaf(\n  Fts3Table *p,                   /* Virtual table handle */\n  const char *zTerm,              /* Term to select leaves for */\n  int nTerm,                      /* Size of term zTerm in bytes */\n  const char *zNode,              /* Buffer containing segment interior node */\n  int nNode,                      /* Size of buffer at zNode */\n  sqlite3_int64 *piLeaf,          /* Selected leaf node */\n  sqlite3_int64 *piLeaf2          /* Selected leaf node */\n){\n  int rc = SQLITE_OK;             /* Return code */\n  int iHeight;                    /* Height of this node in tree */\n\n  assert( piLeaf || piLeaf2 );\n\n  fts3GetVarint32(zNode, &iHeight);\n  rc = fts3ScanInteriorNode(zTerm, nTerm, zNode, nNode, piLeaf, piLeaf2);\n  assert( !piLeaf2 || !piLeaf || rc!=SQLITE_OK || (*piLeaf<=*piLeaf2) );\n\n  if( rc==SQLITE_OK && iHeight>1 ){\n    char *zBlob = 0;              /* Blob read from %_segments table */\n    int nBlob = 0;                /* Size of zBlob in bytes */\n\n    if( piLeaf && piLeaf2 && (*piLeaf!=*piLeaf2) ){\n      rc = sqlite3Fts3ReadBlock(p, *piLeaf, &zBlob, &nBlob, 0);\n      if( rc==SQLITE_OK ){\n        rc = fts3SelectLeaf(p, zTerm, nTerm, zBlob, nBlob, piLeaf, 0);\n      }\n      sqlite3_free(zBlob);\n      piLeaf = 0;\n      zBlob = 0;\n    }\n\n    if( rc==SQLITE_OK ){\n      rc = sqlite3Fts3ReadBlock(p, piLeaf?*piLeaf:*piLeaf2, &zBlob, &nBlob, 0);\n    }\n    if( rc==SQLITE_OK ){\n      rc = fts3SelectLeaf(p, zTerm, nTerm, zBlob, nBlob, piLeaf, piLeaf2);\n    }\n    sqlite3_free(zBlob);\n  }\n\n  return rc;\n}\n\n/*\n** This function is used to create delta-encoded serialized lists of FTS3 \n** varints. Each call to this function appends a single varint to a list.\n*/\nstatic void fts3PutDeltaVarint(\n  char **pp,                      /* IN/OUT: Output pointer */\n  sqlite3_int64 *piPrev,          /* IN/OUT: Previous value written to list */\n  sqlite3_int64 iVal              /* Write this value to the list */\n){\n  assert( iVal-*piPrev > 0 || (*piPrev==0 && iVal==0) );\n  *pp += sqlite3Fts3PutVarint(*pp, iVal-*piPrev);\n  *piPrev = iVal;\n}\n\n/*\n** When this function is called, *ppPoslist is assumed to point to the \n** start of a position-list. After it returns, *ppPoslist points to the\n** first byte after the position-list.\n**\n** A position list is list of positions (delta encoded) and columns for \n** a single document record of a doclist.  So, in other words, this\n** routine advances *ppPoslist so that it points to the next docid in\n** the doclist, or to the first byte past the end of the doclist.\n**\n** If pp is not NULL, then the contents of the position list are copied\n** to *pp. *pp is set to point to the first byte past the last byte copied\n** before this function returns.\n*/\nstatic void fts3PoslistCopy(char **pp, char **ppPoslist){\n  char *pEnd = *ppPoslist;\n  char c = 0;\n\n  /* The end of a position list is marked by a zero encoded as an FTS3 \n  ** varint. A single POS_END (0) byte. Except, if the 0 byte is preceded by\n  ** a byte with the 0x80 bit set, then it is not a varint 0, but the tail\n  ** of some other, multi-byte, value.\n  **\n  ** The following while-loop moves pEnd to point to the first byte that is not \n  ** immediately preceded by a byte with the 0x80 bit set. Then increments\n  ** pEnd once more so that it points to the byte immediately following the\n  ** last byte in the position-list.\n  */\n  while( *pEnd | c ){\n    c = *pEnd++ & 0x80;\n    testcase( c!=0 && (*pEnd)==0 );\n  }\n  pEnd++;  /* Advance past the POS_END terminator byte */\n\n  if( pp ){\n    int n = (int)(pEnd - *ppPoslist);\n    char *p = *pp;\n    memcpy(p, *ppPoslist, n);\n    p += n;\n    *pp = p;\n  }\n  *ppPoslist = pEnd;\n}\n\n/*\n** When this function is called, *ppPoslist is assumed to point to the \n** start of a column-list. After it returns, *ppPoslist points to the\n** to the terminator (POS_COLUMN or POS_END) byte of the column-list.\n**\n** A column-list is list of delta-encoded positions for a single column\n** within a single document within a doclist.\n**\n** The column-list is terminated either by a POS_COLUMN varint (1) or\n** a POS_END varint (0).  This routine leaves *ppPoslist pointing to\n** the POS_COLUMN or POS_END that terminates the column-list.\n**\n** If pp is not NULL, then the contents of the column-list are copied\n** to *pp. *pp is set to point to the first byte past the last byte copied\n** before this function returns.  The POS_COLUMN or POS_END terminator\n** is not copied into *pp.\n*/\nstatic void fts3ColumnlistCopy(char **pp, char **ppPoslist){\n  char *pEnd = *ppPoslist;\n  char c = 0;\n\n  /* A column-list is terminated by either a 0x01 or 0x00 byte that is\n  ** not part of a multi-byte varint.\n  */\n  while( 0xFE & (*pEnd | c) ){\n    c = *pEnd++ & 0x80;\n    testcase( c!=0 && ((*pEnd)&0xfe)==0 );\n  }\n  if( pp ){\n    int n = (int)(pEnd - *ppPoslist);\n    char *p = *pp;\n    memcpy(p, *ppPoslist, n);\n    p += n;\n    *pp = p;\n  }\n  *ppPoslist = pEnd;\n}\n\n/*\n** Value used to signify the end of an position-list. This is safe because\n** it is not possible to have a document with 2^31 terms.\n*/\n#define POSITION_LIST_END 0x7fffffff\n\n/*\n** This function is used to help parse position-lists. When this function is\n** called, *pp may point to the start of the next varint in the position-list\n** being parsed, or it may point to 1 byte past the end of the position-list\n** (in which case **pp will be a terminator bytes POS_END (0) or\n** (1)).\n**\n** If *pp points past the end of the current position-list, set *pi to \n** POSITION_LIST_END and return. Otherwise, read the next varint from *pp,\n** increment the current value of *pi by the value read, and set *pp to\n** point to the next value before returning.\n**\n** Before calling this routine *pi must be initialized to the value of\n** the previous position, or zero if we are reading the first position\n** in the position-list.  Because positions are delta-encoded, the value\n** of the previous position is needed in order to compute the value of\n** the next position.\n*/\nstatic void fts3ReadNextPos(\n  char **pp,                    /* IN/OUT: Pointer into position-list buffer */\n  sqlite3_int64 *pi             /* IN/OUT: Value read from position-list */\n){\n  if( (**pp)&0xFE ){\n    fts3GetDeltaVarint(pp, pi);\n    *pi -= 2;\n  }else{\n    *pi = POSITION_LIST_END;\n  }\n}\n\n/*\n** If parameter iCol is not 0, write an POS_COLUMN (1) byte followed by\n** the value of iCol encoded as a varint to *pp.   This will start a new\n** column list.\n**\n** Set *pp to point to the byte just after the last byte written before \n** returning (do not modify it if iCol==0). Return the total number of bytes\n** written (0 if iCol==0).\n*/\nstatic int fts3PutColNumber(char **pp, int iCol){\n  int n = 0;                      /* Number of bytes written */\n  if( iCol ){\n    char *p = *pp;                /* Output pointer */\n    n = 1 + sqlite3Fts3PutVarint(&p[1], iCol);\n    *p = 0x01;\n    *pp = &p[n];\n  }\n  return n;\n}\n\n/*\n** Compute the union of two position lists.  The output written\n** into *pp contains all positions of both *pp1 and *pp2 in sorted\n** order and with any duplicates removed.  All pointers are\n** updated appropriately.   The caller is responsible for insuring\n** that there is enough space in *pp to hold the complete output.\n*/\nstatic void fts3PoslistMerge(\n  char **pp,                      /* Output buffer */\n  char **pp1,                     /* Left input list */\n  char **pp2                      /* Right input list */\n){\n  char *p = *pp;\n  char *p1 = *pp1;\n  char *p2 = *pp2;\n\n  while( *p1 || *p2 ){\n    int iCol1;         /* The current column index in pp1 */\n    int iCol2;         /* The current column index in pp2 */\n\n    if( *p1==POS_COLUMN ) fts3GetVarint32(&p1[1], &iCol1);\n    else if( *p1==POS_END ) iCol1 = POSITION_LIST_END;\n    else iCol1 = 0;\n\n    if( *p2==POS_COLUMN ) fts3GetVarint32(&p2[1], &iCol2);\n    else if( *p2==POS_END ) iCol2 = POSITION_LIST_END;\n    else iCol2 = 0;\n\n    if( iCol1==iCol2 ){\n      sqlite3_int64 i1 = 0;       /* Last position from pp1 */\n      sqlite3_int64 i2 = 0;       /* Last position from pp2 */\n      sqlite3_int64 iPrev = 0;\n      int n = fts3PutColNumber(&p, iCol1);\n      p1 += n;\n      p2 += n;\n\n      /* At this point, both p1 and p2 point to the start of column-lists\n      ** for the same column (the column with index iCol1 and iCol2).\n      ** A column-list is a list of non-negative delta-encoded varints, each \n      ** incremented by 2 before being stored. Each list is terminated by a\n      ** POS_END (0) or POS_COLUMN (1). The following block merges the two lists\n      ** and writes the results to buffer p. p is left pointing to the byte\n      ** after the list written. No terminator (POS_END or POS_COLUMN) is\n      ** written to the output.\n      */\n      fts3GetDeltaVarint(&p1, &i1);\n      fts3GetDeltaVarint(&p2, &i2);\n      do {\n        fts3PutDeltaVarint(&p, &iPrev, (i1<i2) ? i1 : i2); \n        iPrev -= 2;\n        if( i1==i2 ){\n          fts3ReadNextPos(&p1, &i1);\n          fts3ReadNextPos(&p2, &i2);\n        }else if( i1<i2 ){\n          fts3ReadNextPos(&p1, &i1);\n        }else{\n          fts3ReadNextPos(&p2, &i2);\n        }\n      }while( i1!=POSITION_LIST_END || i2!=POSITION_LIST_END );\n    }else if( iCol1<iCol2 ){\n      p1 += fts3PutColNumber(&p, iCol1);\n      fts3ColumnlistCopy(&p, &p1);\n    }else{\n      p2 += fts3PutColNumber(&p, iCol2);\n      fts3ColumnlistCopy(&p, &p2);\n    }\n  }\n\n  *p++ = POS_END;\n  *pp = p;\n  *pp1 = p1 + 1;\n  *pp2 = p2 + 1;\n}\n\n/*\n** This function is used to merge two position lists into one. When it is\n** called, *pp1 and *pp2 must both point to position lists. A position-list is\n** the part of a doclist that follows each document id. For example, if a row\n** contains:\n**\n**     'a b c'|'x y z'|'a b b a'\n**\n** Then the position list for this row for token 'b' would consist of:\n**\n**     0x02 0x01 0x02 0x03 0x03 0x00\n**\n** When this function returns, both *pp1 and *pp2 are left pointing to the\n** byte following the 0x00 terminator of their respective position lists.\n**\n** If isSaveLeft is 0, an entry is added to the output position list for \n** each position in *pp2 for which there exists one or more positions in\n** *pp1 so that (pos(*pp2)>pos(*pp1) && pos(*pp2)-pos(*pp1)<=nToken). i.e.\n** when the *pp1 token appears before the *pp2 token, but not more than nToken\n** slots before it.\n**\n** e.g. nToken==1 searches for adjacent positions.\n*/\nstatic int fts3PoslistPhraseMerge(\n  char **pp,                      /* IN/OUT: Preallocated output buffer */\n  int nToken,                     /* Maximum difference in token positions */\n  int isSaveLeft,                 /* Save the left position */\n  int isExact,                    /* If *pp1 is exactly nTokens before *pp2 */\n  char **pp1,                     /* IN/OUT: Left input list */\n  char **pp2                      /* IN/OUT: Right input list */\n){\n  char *p = *pp;\n  char *p1 = *pp1;\n  char *p2 = *pp2;\n  int iCol1 = 0;\n  int iCol2 = 0;\n\n  /* Never set both isSaveLeft and isExact for the same invocation. */\n  assert( isSaveLeft==0 || isExact==0 );\n\n  assert( p!=0 && *p1!=0 && *p2!=0 );\n  if( *p1==POS_COLUMN ){ \n    p1++;\n    p1 += fts3GetVarint32(p1, &iCol1);\n  }\n  if( *p2==POS_COLUMN ){ \n    p2++;\n    p2 += fts3GetVarint32(p2, &iCol2);\n  }\n\n  while( 1 ){\n    if( iCol1==iCol2 ){\n      char *pSave = p;\n      sqlite3_int64 iPrev = 0;\n      sqlite3_int64 iPos1 = 0;\n      sqlite3_int64 iPos2 = 0;\n\n      if( iCol1 ){\n        *p++ = POS_COLUMN;\n        p += sqlite3Fts3PutVarint(p, iCol1);\n      }\n\n      assert( *p1!=POS_END && *p1!=POS_COLUMN );\n      assert( *p2!=POS_END && *p2!=POS_COLUMN );\n      fts3GetDeltaVarint(&p1, &iPos1); iPos1 -= 2;\n      fts3GetDeltaVarint(&p2, &iPos2); iPos2 -= 2;\n\n      while( 1 ){\n        if( iPos2==iPos1+nToken \n         || (isExact==0 && iPos2>iPos1 && iPos2<=iPos1+nToken) \n        ){\n          sqlite3_int64 iSave;\n          iSave = isSaveLeft ? iPos1 : iPos2;\n          fts3PutDeltaVarint(&p, &iPrev, iSave+2); iPrev -= 2;\n          pSave = 0;\n          assert( p );\n        }\n        if( (!isSaveLeft && iPos2<=(iPos1+nToken)) || iPos2<=iPos1 ){\n          if( (*p2&0xFE)==0 ) break;\n          fts3GetDeltaVarint(&p2, &iPos2); iPos2 -= 2;\n        }else{\n          if( (*p1&0xFE)==0 ) break;\n          fts3GetDeltaVarint(&p1, &iPos1); iPos1 -= 2;\n        }\n      }\n\n      if( pSave ){\n        assert( pp && p );\n        p = pSave;\n      }\n\n      fts3ColumnlistCopy(0, &p1);\n      fts3ColumnlistCopy(0, &p2);\n      assert( (*p1&0xFE)==0 && (*p2&0xFE)==0 );\n      if( 0==*p1 || 0==*p2 ) break;\n\n      p1++;\n      p1 += fts3GetVarint32(p1, &iCol1);\n      p2++;\n      p2 += fts3GetVarint32(p2, &iCol2);\n    }\n\n    /* Advance pointer p1 or p2 (whichever corresponds to the smaller of\n    ** iCol1 and iCol2) so that it points to either the 0x00 that marks the\n    ** end of the position list, or the 0x01 that precedes the next \n    ** column-number in the position list. \n    */\n    else if( iCol1<iCol2 ){\n      fts3ColumnlistCopy(0, &p1);\n      if( 0==*p1 ) break;\n      p1++;\n      p1 += fts3GetVarint32(p1, &iCol1);\n    }else{\n      fts3ColumnlistCopy(0, &p2);\n      if( 0==*p2 ) break;\n      p2++;\n      p2 += fts3GetVarint32(p2, &iCol2);\n    }\n  }\n\n  fts3PoslistCopy(0, &p2);\n  fts3PoslistCopy(0, &p1);\n  *pp1 = p1;\n  *pp2 = p2;\n  if( *pp==p ){\n    return 0;\n  }\n  *p++ = 0x00;\n  *pp = p;\n  return 1;\n}\n\n/*\n** Merge two position-lists as required by the NEAR operator. The argument\n** position lists correspond to the left and right phrases of an expression \n** like:\n**\n**     \"phrase 1\" NEAR \"phrase number 2\"\n**\n** Position list *pp1 corresponds to the left-hand side of the NEAR \n** expression and *pp2 to the right. As usual, the indexes in the position \n** lists are the offsets of the last token in each phrase (tokens \"1\" and \"2\" \n** in the example above).\n**\n** The output position list - written to *pp - is a copy of *pp2 with those\n** entries that are not sufficiently NEAR entries in *pp1 removed.\n*/\nstatic int fts3PoslistNearMerge(\n  char **pp,                      /* Output buffer */\n  char *aTmp,                     /* Temporary buffer space */\n  int nRight,                     /* Maximum difference in token positions */\n  int nLeft,                      /* Maximum difference in token positions */\n  char **pp1,                     /* IN/OUT: Left input list */\n  char **pp2                      /* IN/OUT: Right input list */\n){\n  char *p1 = *pp1;\n  char *p2 = *pp2;\n\n  char *pTmp1 = aTmp;\n  char *pTmp2;\n  char *aTmp2;\n  int res = 1;\n\n  fts3PoslistPhraseMerge(&pTmp1, nRight, 0, 0, pp1, pp2);\n  aTmp2 = pTmp2 = pTmp1;\n  *pp1 = p1;\n  *pp2 = p2;\n  fts3PoslistPhraseMerge(&pTmp2, nLeft, 1, 0, pp2, pp1);\n  if( pTmp1!=aTmp && pTmp2!=aTmp2 ){\n    fts3PoslistMerge(pp, &aTmp, &aTmp2);\n  }else if( pTmp1!=aTmp ){\n    fts3PoslistCopy(pp, &aTmp);\n  }else if( pTmp2!=aTmp2 ){\n    fts3PoslistCopy(pp, &aTmp2);\n  }else{\n    res = 0;\n  }\n\n  return res;\n}\n\n/* \n** An instance of this function is used to merge together the (potentially\n** large number of) doclists for each term that matches a prefix query.\n** See function fts3TermSelectMerge() for details.\n*/\ntypedef struct TermSelect TermSelect;\nstruct TermSelect {\n  char *aaOutput[16];             /* Malloc'd output buffers */\n  int anOutput[16];               /* Size each output buffer in bytes */\n};\n\n/*\n** This function is used to read a single varint from a buffer. Parameter\n** pEnd points 1 byte past the end of the buffer. When this function is\n** called, if *pp points to pEnd or greater, then the end of the buffer\n** has been reached. In this case *pp is set to 0 and the function returns.\n**\n** If *pp does not point to or past pEnd, then a single varint is read\n** from *pp. *pp is then set to point 1 byte past the end of the read varint.\n**\n** If bDescIdx is false, the value read is added to *pVal before returning.\n** If it is true, the value read is subtracted from *pVal before this \n** function returns.\n*/\nstatic void fts3GetDeltaVarint3(\n  char **pp,                      /* IN/OUT: Point to read varint from */\n  char *pEnd,                     /* End of buffer */\n  int bDescIdx,                   /* True if docids are descending */\n  sqlite3_int64 *pVal             /* IN/OUT: Integer value */\n){\n  if( *pp>=pEnd ){\n    *pp = 0;\n  }else{\n    sqlite3_int64 iVal;\n    *pp += sqlite3Fts3GetVarint(*pp, &iVal);\n    if( bDescIdx ){\n      *pVal -= iVal;\n    }else{\n      *pVal += iVal;\n    }\n  }\n}\n\n/*\n** This function is used to write a single varint to a buffer. The varint\n** is written to *pp. Before returning, *pp is set to point 1 byte past the\n** end of the value written.\n**\n** If *pbFirst is zero when this function is called, the value written to\n** the buffer is that of parameter iVal. \n**\n** If *pbFirst is non-zero when this function is called, then the value \n** written is either (iVal-*piPrev) (if bDescIdx is zero) or (*piPrev-iVal)\n** (if bDescIdx is non-zero).\n**\n** Before returning, this function always sets *pbFirst to 1 and *piPrev\n** to the value of parameter iVal.\n*/\nstatic void fts3PutDeltaVarint3(\n  char **pp,                      /* IN/OUT: Output pointer */\n  int bDescIdx,                   /* True for descending docids */\n  sqlite3_int64 *piPrev,          /* IN/OUT: Previous value written to list */\n  int *pbFirst,                   /* IN/OUT: True after first int written */\n  sqlite3_int64 iVal              /* Write this value to the list */\n){\n  sqlite3_int64 iWrite;\n  if( bDescIdx==0 || *pbFirst==0 ){\n    iWrite = iVal - *piPrev;\n  }else{\n    iWrite = *piPrev - iVal;\n  }\n  assert( *pbFirst || *piPrev==0 );\n  assert( *pbFirst==0 || iWrite>0 );\n  *pp += sqlite3Fts3PutVarint(*pp, iWrite);\n  *piPrev = iVal;\n  *pbFirst = 1;\n}\n\n\n/*\n** This macro is used by various functions that merge doclists. The two\n** arguments are 64-bit docid values. If the value of the stack variable\n** bDescDoclist is 0 when this macro is invoked, then it returns (i1-i2). \n** Otherwise, (i2-i1).\n**\n** Using this makes it easier to write code that can merge doclists that are\n** sorted in either ascending or descending order.\n*/\n#define DOCID_CMP(i1, i2) ((bDescDoclist?-1:1) * (i1-i2))\n\n/*\n** This function does an \"OR\" merge of two doclists (output contains all\n** positions contained in either argument doclist). If the docids in the \n** input doclists are sorted in ascending order, parameter bDescDoclist\n** should be false. If they are sorted in ascending order, it should be\n** passed a non-zero value.\n**\n** If no error occurs, *paOut is set to point at an sqlite3_malloc'd buffer\n** containing the output doclist and SQLITE_OK is returned. In this case\n** *pnOut is set to the number of bytes in the output doclist.\n**\n** If an error occurs, an SQLite error code is returned. The output values\n** are undefined in this case.\n*/\nstatic int fts3DoclistOrMerge(\n  int bDescDoclist,               /* True if arguments are desc */\n  char *a1, int n1,               /* First doclist */\n  char *a2, int n2,               /* Second doclist */\n  char **paOut, int *pnOut        /* OUT: Malloc'd doclist */\n){\n  sqlite3_int64 i1 = 0;\n  sqlite3_int64 i2 = 0;\n  sqlite3_int64 iPrev = 0;\n  char *pEnd1 = &a1[n1];\n  char *pEnd2 = &a2[n2];\n  char *p1 = a1;\n  char *p2 = a2;\n  char *p;\n  char *aOut;\n  int bFirstOut = 0;\n\n  *paOut = 0;\n  *pnOut = 0;\n\n  /* Allocate space for the output. Both the input and output doclists\n  ** are delta encoded. If they are in ascending order (bDescDoclist==0),\n  ** then the first docid in each list is simply encoded as a varint. For\n  ** each subsequent docid, the varint stored is the difference between the\n  ** current and previous docid (a positive number - since the list is in\n  ** ascending order).\n  **\n  ** The first docid written to the output is therefore encoded using the \n  ** same number of bytes as it is in whichever of the input lists it is\n  ** read from. And each subsequent docid read from the same input list \n  ** consumes either the same or less bytes as it did in the input (since\n  ** the difference between it and the previous value in the output must\n  ** be a positive value less than or equal to the delta value read from \n  ** the input list). The same argument applies to all but the first docid\n  ** read from the 'other' list. And to the contents of all position lists\n  ** that will be copied and merged from the input to the output.\n  **\n  ** However, if the first docid copied to the output is a negative number,\n  ** then the encoding of the first docid from the 'other' input list may\n  ** be larger in the output than it was in the input (since the delta value\n  ** may be a larger positive integer than the actual docid).\n  **\n  ** The space required to store the output is therefore the sum of the\n  ** sizes of the two inputs, plus enough space for exactly one of the input\n  ** docids to grow. \n  **\n  ** A symetric argument may be made if the doclists are in descending \n  ** order.\n  */\n  aOut = sqlite3_malloc(n1+n2+FTS3_VARINT_MAX-1);\n  if( !aOut ) return SQLITE_NOMEM;\n\n  p = aOut;\n  fts3GetDeltaVarint3(&p1, pEnd1, 0, &i1);\n  fts3GetDeltaVarint3(&p2, pEnd2, 0, &i2);\n  while( p1 || p2 ){\n    sqlite3_int64 iDiff = DOCID_CMP(i1, i2);\n\n    if( p2 && p1 && iDiff==0 ){\n      fts3PutDeltaVarint3(&p, bDescDoclist, &iPrev, &bFirstOut, i1);\n      fts3PoslistMerge(&p, &p1, &p2);\n      fts3GetDeltaVarint3(&p1, pEnd1, bDescDoclist, &i1);\n      fts3GetDeltaVarint3(&p2, pEnd2, bDescDoclist, &i2);\n    }else if( !p2 || (p1 && iDiff<0) ){\n      fts3PutDeltaVarint3(&p, bDescDoclist, &iPrev, &bFirstOut, i1);\n      fts3PoslistCopy(&p, &p1);\n      fts3GetDeltaVarint3(&p1, pEnd1, bDescDoclist, &i1);\n    }else{\n      fts3PutDeltaVarint3(&p, bDescDoclist, &iPrev, &bFirstOut, i2);\n      fts3PoslistCopy(&p, &p2);\n      fts3GetDeltaVarint3(&p2, pEnd2, bDescDoclist, &i2);\n    }\n  }\n\n  *paOut = aOut;\n  *pnOut = (int)(p-aOut);\n  assert( *pnOut<=n1+n2+FTS3_VARINT_MAX-1 );\n  return SQLITE_OK;\n}\n\n/*\n** This function does a \"phrase\" merge of two doclists. In a phrase merge,\n** the output contains a copy of each position from the right-hand input\n** doclist for which there is a position in the left-hand input doclist\n** exactly nDist tokens before it.\n**\n** If the docids in the input doclists are sorted in ascending order,\n** parameter bDescDoclist should be false. If they are sorted in ascending \n** order, it should be passed a non-zero value.\n**\n** The right-hand input doclist is overwritten by this function.\n*/\nstatic int fts3DoclistPhraseMerge(\n  int bDescDoclist,               /* True if arguments are desc */\n  int nDist,                      /* Distance from left to right (1=adjacent) */\n  char *aLeft, int nLeft,         /* Left doclist */\n  char **paRight, int *pnRight    /* IN/OUT: Right/output doclist */\n){\n  sqlite3_int64 i1 = 0;\n  sqlite3_int64 i2 = 0;\n  sqlite3_int64 iPrev = 0;\n  char *aRight = *paRight;\n  char *pEnd1 = &aLeft[nLeft];\n  char *pEnd2 = &aRight[*pnRight];\n  char *p1 = aLeft;\n  char *p2 = aRight;\n  char *p;\n  int bFirstOut = 0;\n  char *aOut;\n\n  assert( nDist>0 );\n  if( bDescDoclist ){\n    aOut = sqlite3_malloc(*pnRight + FTS3_VARINT_MAX);\n    if( aOut==0 ) return SQLITE_NOMEM;\n  }else{\n    aOut = aRight;\n  }\n  p = aOut;\n\n  fts3GetDeltaVarint3(&p1, pEnd1, 0, &i1);\n  fts3GetDeltaVarint3(&p2, pEnd2, 0, &i2);\n\n  while( p1 && p2 ){\n    sqlite3_int64 iDiff = DOCID_CMP(i1, i2);\n    if( iDiff==0 ){\n      char *pSave = p;\n      sqlite3_int64 iPrevSave = iPrev;\n      int bFirstOutSave = bFirstOut;\n\n      fts3PutDeltaVarint3(&p, bDescDoclist, &iPrev, &bFirstOut, i1);\n      if( 0==fts3PoslistPhraseMerge(&p, nDist, 0, 1, &p1, &p2) ){\n        p = pSave;\n        iPrev = iPrevSave;\n        bFirstOut = bFirstOutSave;\n      }\n      fts3GetDeltaVarint3(&p1, pEnd1, bDescDoclist, &i1);\n      fts3GetDeltaVarint3(&p2, pEnd2, bDescDoclist, &i2);\n    }else if( iDiff<0 ){\n      fts3PoslistCopy(0, &p1);\n      fts3GetDeltaVarint3(&p1, pEnd1, bDescDoclist, &i1);\n    }else{\n      fts3PoslistCopy(0, &p2);\n      fts3GetDeltaVarint3(&p2, pEnd2, bDescDoclist, &i2);\n    }\n  }\n\n  *pnRight = (int)(p - aOut);\n  if( bDescDoclist ){\n    sqlite3_free(aRight);\n    *paRight = aOut;\n  }\n\n  return SQLITE_OK;\n}\n\n/*\n** Argument pList points to a position list nList bytes in size. This\n** function checks to see if the position list contains any entries for\n** a token in position 0 (of any column). If so, it writes argument iDelta\n** to the output buffer pOut, followed by a position list consisting only\n** of the entries from pList at position 0, and terminated by an 0x00 byte.\n** The value returned is the number of bytes written to pOut (if any).\n*/\nSQLITE_PRIVATE int sqlite3Fts3FirstFilter(\n  sqlite3_int64 iDelta,           /* Varint that may be written to pOut */\n  char *pList,                    /* Position list (no 0x00 term) */\n  int nList,                      /* Size of pList in bytes */\n  char *pOut                      /* Write output here */\n){\n  int nOut = 0;\n  int bWritten = 0;               /* True once iDelta has been written */\n  char *p = pList;\n  char *pEnd = &pList[nList];\n\n  if( *p!=0x01 ){\n    if( *p==0x02 ){\n      nOut += sqlite3Fts3PutVarint(&pOut[nOut], iDelta);\n      pOut[nOut++] = 0x02;\n      bWritten = 1;\n    }\n    fts3ColumnlistCopy(0, &p);\n  }\n\n  while( p<pEnd ){\n    sqlite3_int64 iCol;\n    p++;\n    p += sqlite3Fts3GetVarint(p, &iCol);\n    if( *p==0x02 ){\n      if( bWritten==0 ){\n        nOut += sqlite3Fts3PutVarint(&pOut[nOut], iDelta);\n        bWritten = 1;\n      }\n      pOut[nOut++] = 0x01;\n      nOut += sqlite3Fts3PutVarint(&pOut[nOut], iCol);\n      pOut[nOut++] = 0x02;\n    }\n    fts3ColumnlistCopy(0, &p);\n  }\n  if( bWritten ){\n    pOut[nOut++] = 0x00;\n  }\n\n  return nOut;\n}\n\n\n/*\n** Merge all doclists in the TermSelect.aaOutput[] array into a single\n** doclist stored in TermSelect.aaOutput[0]. If successful, delete all\n** other doclists (except the aaOutput[0] one) and return SQLITE_OK.\n**\n** If an OOM error occurs, return SQLITE_NOMEM. In this case it is\n** the responsibility of the caller to free any doclists left in the\n** TermSelect.aaOutput[] array.\n*/\nstatic int fts3TermSelectFinishMerge(Fts3Table *p, TermSelect *pTS){\n  char *aOut = 0;\n  int nOut = 0;\n  int i;\n\n  /* Loop through the doclists in the aaOutput[] array. Merge them all\n  ** into a single doclist.\n  */\n  for(i=0; i<SizeofArray(pTS->aaOutput); i++){\n    if( pTS->aaOutput[i] ){\n      if( !aOut ){\n        aOut = pTS->aaOutput[i];\n        nOut = pTS->anOutput[i];\n        pTS->aaOutput[i] = 0;\n      }else{\n        int nNew;\n        char *aNew;\n\n        int rc = fts3DoclistOrMerge(p->bDescIdx, \n            pTS->aaOutput[i], pTS->anOutput[i], aOut, nOut, &aNew, &nNew\n        );\n        if( rc!=SQLITE_OK ){\n          sqlite3_free(aOut);\n          return rc;\n        }\n\n        sqlite3_free(pTS->aaOutput[i]);\n        sqlite3_free(aOut);\n        pTS->aaOutput[i] = 0;\n        aOut = aNew;\n        nOut = nNew;\n      }\n    }\n  }\n\n  pTS->aaOutput[0] = aOut;\n  pTS->anOutput[0] = nOut;\n  return SQLITE_OK;\n}\n\n/*\n** Merge the doclist aDoclist/nDoclist into the TermSelect object passed\n** as the first argument. The merge is an \"OR\" merge (see function\n** fts3DoclistOrMerge() for details).\n**\n** This function is called with the doclist for each term that matches\n** a queried prefix. It merges all these doclists into one, the doclist\n** for the specified prefix. Since there can be a very large number of\n** doclists to merge, the merging is done pair-wise using the TermSelect\n** object.\n**\n** This function returns SQLITE_OK if the merge is successful, or an\n** SQLite error code (SQLITE_NOMEM) if an error occurs.\n*/\nstatic int fts3TermSelectMerge(\n  Fts3Table *p,                   /* FTS table handle */\n  TermSelect *pTS,                /* TermSelect object to merge into */\n  char *aDoclist,                 /* Pointer to doclist */\n  int nDoclist                    /* Size of aDoclist in bytes */\n){\n  if( pTS->aaOutput[0]==0 ){\n    /* If this is the first term selected, copy the doclist to the output\n    ** buffer using memcpy(). \n    **\n    ** Add FTS3_VARINT_MAX bytes of unused space to the end of the \n    ** allocation. This is so as to ensure that the buffer is big enough\n    ** to hold the current doclist AND'd with any other doclist. If the\n    ** doclists are stored in order=ASC order, this padding would not be\n    ** required (since the size of [doclistA AND doclistB] is always less\n    ** than or equal to the size of [doclistA] in that case). But this is\n    ** not true for order=DESC. For example, a doclist containing (1, -1) \n    ** may be smaller than (-1), as in the first example the -1 may be stored\n    ** as a single-byte delta, whereas in the second it must be stored as a\n    ** FTS3_VARINT_MAX byte varint.\n    **\n    ** Similar padding is added in the fts3DoclistOrMerge() function.\n    */\n    pTS->aaOutput[0] = sqlite3_malloc(nDoclist + FTS3_VARINT_MAX + 1);\n    pTS->anOutput[0] = nDoclist;\n    if( pTS->aaOutput[0] ){\n      memcpy(pTS->aaOutput[0], aDoclist, nDoclist);\n    }else{\n      return SQLITE_NOMEM;\n    }\n  }else{\n    char *aMerge = aDoclist;\n    int nMerge = nDoclist;\n    int iOut;\n\n    for(iOut=0; iOut<SizeofArray(pTS->aaOutput); iOut++){\n      if( pTS->aaOutput[iOut]==0 ){\n        assert( iOut>0 );\n        pTS->aaOutput[iOut] = aMerge;\n        pTS->anOutput[iOut] = nMerge;\n        break;\n      }else{\n        char *aNew;\n        int nNew;\n\n        int rc = fts3DoclistOrMerge(p->bDescIdx, aMerge, nMerge, \n            pTS->aaOutput[iOut], pTS->anOutput[iOut], &aNew, &nNew\n        );\n        if( rc!=SQLITE_OK ){\n          if( aMerge!=aDoclist ) sqlite3_free(aMerge);\n          return rc;\n        }\n\n        if( aMerge!=aDoclist ) sqlite3_free(aMerge);\n        sqlite3_free(pTS->aaOutput[iOut]);\n        pTS->aaOutput[iOut] = 0;\n  \n        aMerge = aNew;\n        nMerge = nNew;\n        if( (iOut+1)==SizeofArray(pTS->aaOutput) ){\n          pTS->aaOutput[iOut] = aMerge;\n          pTS->anOutput[iOut] = nMerge;\n        }\n      }\n    }\n  }\n  return SQLITE_OK;\n}\n\n/*\n** Append SegReader object pNew to the end of the pCsr->apSegment[] array.\n*/\nstatic int fts3SegReaderCursorAppend(\n  Fts3MultiSegReader *pCsr, \n  Fts3SegReader *pNew\n){\n  if( (pCsr->nSegment%16)==0 ){\n    Fts3SegReader **apNew;\n    int nByte = (pCsr->nSegment + 16)*sizeof(Fts3SegReader*);\n    apNew = (Fts3SegReader **)sqlite3_realloc(pCsr->apSegment, nByte);\n    if( !apNew ){\n      sqlite3Fts3SegReaderFree(pNew);\n      return SQLITE_NOMEM;\n    }\n    pCsr->apSegment = apNew;\n  }\n  pCsr->apSegment[pCsr->nSegment++] = pNew;\n  return SQLITE_OK;\n}\n\n/*\n** Add seg-reader objects to the Fts3MultiSegReader object passed as the\n** 8th argument.\n**\n** This function returns SQLITE_OK if successful, or an SQLite error code\n** otherwise.\n*/\nstatic int fts3SegReaderCursor(\n  Fts3Table *p,                   /* FTS3 table handle */\n  int iLangid,                    /* Language id */\n  int iIndex,                     /* Index to search (from 0 to p->nIndex-1) */\n  int iLevel,                     /* Level of segments to scan */\n  const char *zTerm,              /* Term to query for */\n  int nTerm,                      /* Size of zTerm in bytes */\n  int isPrefix,                   /* True for a prefix search */\n  int isScan,                     /* True to scan from zTerm to EOF */\n  Fts3MultiSegReader *pCsr        /* Cursor object to populate */\n){\n  int rc = SQLITE_OK;             /* Error code */\n  sqlite3_stmt *pStmt = 0;        /* Statement to iterate through segments */\n  int rc2;                        /* Result of sqlite3_reset() */\n\n  /* If iLevel is less than 0 and this is not a scan, include a seg-reader \n  ** for the pending-terms. If this is a scan, then this call must be being\n  ** made by an fts4aux module, not an FTS table. In this case calling\n  ** Fts3SegReaderPending might segfault, as the data structures used by \n  ** fts4aux are not completely populated. So it's easiest to filter these\n  ** calls out here.  */\n  if( iLevel<0 && p->aIndex ){\n    Fts3SegReader *pSeg = 0;\n    rc = sqlite3Fts3SegReaderPending(p, iIndex, zTerm, nTerm, isPrefix||isScan, &pSeg);\n    if( rc==SQLITE_OK && pSeg ){\n      rc = fts3SegReaderCursorAppend(pCsr, pSeg);\n    }\n  }\n\n  if( iLevel!=FTS3_SEGCURSOR_PENDING ){\n    if( rc==SQLITE_OK ){\n      rc = sqlite3Fts3AllSegdirs(p, iLangid, iIndex, iLevel, &pStmt);\n    }\n\n    while( rc==SQLITE_OK && SQLITE_ROW==(rc = sqlite3_step(pStmt)) ){\n      Fts3SegReader *pSeg = 0;\n\n      /* Read the values returned by the SELECT into local variables. */\n      sqlite3_int64 iStartBlock = sqlite3_column_int64(pStmt, 1);\n      sqlite3_int64 iLeavesEndBlock = sqlite3_column_int64(pStmt, 2);\n      sqlite3_int64 iEndBlock = sqlite3_column_int64(pStmt, 3);\n      int nRoot = sqlite3_column_bytes(pStmt, 4);\n      char const *zRoot = sqlite3_column_blob(pStmt, 4);\n\n      /* If zTerm is not NULL, and this segment is not stored entirely on its\n      ** root node, the range of leaves scanned can be reduced. Do this. */\n      if( iStartBlock && zTerm ){\n        sqlite3_int64 *pi = (isPrefix ? &iLeavesEndBlock : 0);\n        rc = fts3SelectLeaf(p, zTerm, nTerm, zRoot, nRoot, &iStartBlock, pi);\n        if( rc!=SQLITE_OK ) goto finished;\n        if( isPrefix==0 && isScan==0 ) iLeavesEndBlock = iStartBlock;\n      }\n \n      rc = sqlite3Fts3SegReaderNew(pCsr->nSegment+1, \n          (isPrefix==0 && isScan==0),\n          iStartBlock, iLeavesEndBlock, \n          iEndBlock, zRoot, nRoot, &pSeg\n      );\n      if( rc!=SQLITE_OK ) goto finished;\n      rc = fts3SegReaderCursorAppend(pCsr, pSeg);\n    }\n  }\n\n finished:\n  rc2 = sqlite3_reset(pStmt);\n  if( rc==SQLITE_DONE ) rc = rc2;\n\n  return rc;\n}\n\n/*\n** Set up a cursor object for iterating through a full-text index or a \n** single level therein.\n*/\nSQLITE_PRIVATE int sqlite3Fts3SegReaderCursor(\n  Fts3Table *p,                   /* FTS3 table handle */\n  int iLangid,                    /* Language-id to search */\n  int iIndex,                     /* Index to search (from 0 to p->nIndex-1) */\n  int iLevel,                     /* Level of segments to scan */\n  const char *zTerm,              /* Term to query for */\n  int nTerm,                      /* Size of zTerm in bytes */\n  int isPrefix,                   /* True for a prefix search */\n  int isScan,                     /* True to scan from zTerm to EOF */\n  Fts3MultiSegReader *pCsr       /* Cursor object to populate */\n){\n  assert( iIndex>=0 && iIndex<p->nIndex );\n  assert( iLevel==FTS3_SEGCURSOR_ALL\n      ||  iLevel==FTS3_SEGCURSOR_PENDING \n      ||  iLevel>=0\n  );\n  assert( iLevel<FTS3_SEGDIR_MAXLEVEL );\n  assert( FTS3_SEGCURSOR_ALL<0 && FTS3_SEGCURSOR_PENDING<0 );\n  assert( isPrefix==0 || isScan==0 );\n\n  memset(pCsr, 0, sizeof(Fts3MultiSegReader));\n  return fts3SegReaderCursor(\n      p, iLangid, iIndex, iLevel, zTerm, nTerm, isPrefix, isScan, pCsr\n  );\n}\n\n/*\n** In addition to its current configuration, have the Fts3MultiSegReader\n** passed as the 4th argument also scan the doclist for term zTerm/nTerm.\n**\n** SQLITE_OK is returned if no error occurs, otherwise an SQLite error code.\n*/\nstatic int fts3SegReaderCursorAddZero(\n  Fts3Table *p,                   /* FTS virtual table handle */\n  int iLangid,\n  const char *zTerm,              /* Term to scan doclist of */\n  int nTerm,                      /* Number of bytes in zTerm */\n  Fts3MultiSegReader *pCsr        /* Fts3MultiSegReader to modify */\n){\n  return fts3SegReaderCursor(p, \n      iLangid, 0, FTS3_SEGCURSOR_ALL, zTerm, nTerm, 0, 0,pCsr\n  );\n}\n\n/*\n** Open an Fts3MultiSegReader to scan the doclist for term zTerm/nTerm. Or,\n** if isPrefix is true, to scan the doclist for all terms for which \n** zTerm/nTerm is a prefix. If successful, return SQLITE_OK and write\n** a pointer to the new Fts3MultiSegReader to *ppSegcsr. Otherwise, return\n** an SQLite error code.\n**\n** It is the responsibility of the caller to free this object by eventually\n** passing it to fts3SegReaderCursorFree() \n**\n** SQLITE_OK is returned if no error occurs, otherwise an SQLite error code.\n** Output parameter *ppSegcsr is set to 0 if an error occurs.\n*/\nstatic int fts3TermSegReaderCursor(\n  Fts3Cursor *pCsr,               /* Virtual table cursor handle */\n  const char *zTerm,              /* Term to query for */\n  int nTerm,                      /* Size of zTerm in bytes */\n  int isPrefix,                   /* True for a prefix search */\n  Fts3MultiSegReader **ppSegcsr   /* OUT: Allocated seg-reader cursor */\n){\n  Fts3MultiSegReader *pSegcsr;    /* Object to allocate and return */\n  int rc = SQLITE_NOMEM;          /* Return code */\n\n  pSegcsr = sqlite3_malloc(sizeof(Fts3MultiSegReader));\n  if( pSegcsr ){\n    int i;\n    int bFound = 0;               /* True once an index has been found */\n    Fts3Table *p = (Fts3Table *)pCsr->base.pVtab;\n\n    if( isPrefix ){\n      for(i=1; bFound==0 && i<p->nIndex; i++){\n        if( p->aIndex[i].nPrefix==nTerm ){\n          bFound = 1;\n          rc = sqlite3Fts3SegReaderCursor(p, pCsr->iLangid, \n              i, FTS3_SEGCURSOR_ALL, zTerm, nTerm, 0, 0, pSegcsr\n          );\n          pSegcsr->bLookup = 1;\n        }\n      }\n\n      for(i=1; bFound==0 && i<p->nIndex; i++){\n        if( p->aIndex[i].nPrefix==nTerm+1 ){\n          bFound = 1;\n          rc = sqlite3Fts3SegReaderCursor(p, pCsr->iLangid, \n              i, FTS3_SEGCURSOR_ALL, zTerm, nTerm, 1, 0, pSegcsr\n          );\n          if( rc==SQLITE_OK ){\n            rc = fts3SegReaderCursorAddZero(\n                p, pCsr->iLangid, zTerm, nTerm, pSegcsr\n            );\n          }\n        }\n      }\n    }\n\n    if( bFound==0 ){\n      rc = sqlite3Fts3SegReaderCursor(p, pCsr->iLangid, \n          0, FTS3_SEGCURSOR_ALL, zTerm, nTerm, isPrefix, 0, pSegcsr\n      );\n      pSegcsr->bLookup = !isPrefix;\n    }\n  }\n\n  *ppSegcsr = pSegcsr;\n  return rc;\n}\n\n/*\n** Free an Fts3MultiSegReader allocated by fts3TermSegReaderCursor().\n*/\nstatic void fts3SegReaderCursorFree(Fts3MultiSegReader *pSegcsr){\n  sqlite3Fts3SegReaderFinish(pSegcsr);\n  sqlite3_free(pSegcsr);\n}\n\n/*\n** This function retrieves the doclist for the specified term (or term\n** prefix) from the database.\n*/\nstatic int fts3TermSelect(\n  Fts3Table *p,                   /* Virtual table handle */\n  Fts3PhraseToken *pTok,          /* Token to query for */\n  int iColumn,                    /* Column to query (or -ve for all columns) */\n  int *pnOut,                     /* OUT: Size of buffer at *ppOut */\n  char **ppOut                    /* OUT: Malloced result buffer */\n){\n  int rc;                         /* Return code */\n  Fts3MultiSegReader *pSegcsr;    /* Seg-reader cursor for this term */\n  TermSelect tsc;                 /* Object for pair-wise doclist merging */\n  Fts3SegFilter filter;           /* Segment term filter configuration */\n\n  pSegcsr = pTok->pSegcsr;\n  memset(&tsc, 0, sizeof(TermSelect));\n\n  filter.flags = FTS3_SEGMENT_IGNORE_EMPTY | FTS3_SEGMENT_REQUIRE_POS\n        | (pTok->isPrefix ? FTS3_SEGMENT_PREFIX : 0)\n        | (pTok->bFirst ? FTS3_SEGMENT_FIRST : 0)\n        | (iColumn<p->nColumn ? FTS3_SEGMENT_COLUMN_FILTER : 0);\n  filter.iCol = iColumn;\n  filter.zTerm = pTok->z;\n  filter.nTerm = pTok->n;\n\n  rc = sqlite3Fts3SegReaderStart(p, pSegcsr, &filter);\n  while( SQLITE_OK==rc\n      && SQLITE_ROW==(rc = sqlite3Fts3SegReaderStep(p, pSegcsr)) \n  ){\n    rc = fts3TermSelectMerge(p, &tsc, pSegcsr->aDoclist, pSegcsr->nDoclist);\n  }\n\n  if( rc==SQLITE_OK ){\n    rc = fts3TermSelectFinishMerge(p, &tsc);\n  }\n  if( rc==SQLITE_OK ){\n    *ppOut = tsc.aaOutput[0];\n    *pnOut = tsc.anOutput[0];\n  }else{\n    int i;\n    for(i=0; i<SizeofArray(tsc.aaOutput); i++){\n      sqlite3_free(tsc.aaOutput[i]);\n    }\n  }\n\n  fts3SegReaderCursorFree(pSegcsr);\n  pTok->pSegcsr = 0;\n  return rc;\n}\n\n/*\n** This function counts the total number of docids in the doclist stored\n** in buffer aList[], size nList bytes.\n**\n** If the isPoslist argument is true, then it is assumed that the doclist\n** contains a position-list following each docid. Otherwise, it is assumed\n** that the doclist is simply a list of docids stored as delta encoded \n** varints.\n*/\nstatic int fts3DoclistCountDocids(char *aList, int nList){\n  int nDoc = 0;                   /* Return value */\n  if( aList ){\n    char *aEnd = &aList[nList];   /* Pointer to one byte after EOF */\n    char *p = aList;              /* Cursor */\n    while( p<aEnd ){\n      nDoc++;\n      while( (*p++)&0x80 );     /* Skip docid varint */\n      fts3PoslistCopy(0, &p);   /* Skip over position list */\n    }\n  }\n\n  return nDoc;\n}\n\n/*\n** Advance the cursor to the next row in the %_content table that\n** matches the search criteria.  For a MATCH search, this will be\n** the next row that matches. For a full-table scan, this will be\n** simply the next row in the %_content table.  For a docid lookup,\n** this routine simply sets the EOF flag.\n**\n** Return SQLITE_OK if nothing goes wrong.  SQLITE_OK is returned\n** even if we reach end-of-file.  The fts3EofMethod() will be called\n** subsequently to determine whether or not an EOF was hit.\n*/\nstatic int fts3NextMethod(sqlite3_vtab_cursor *pCursor){\n  int rc;\n  Fts3Cursor *pCsr = (Fts3Cursor *)pCursor;\n  if( pCsr->eSearch==FTS3_DOCID_SEARCH || pCsr->eSearch==FTS3_FULLSCAN_SEARCH ){\n    if( SQLITE_ROW!=sqlite3_step(pCsr->pStmt) ){\n      pCsr->isEof = 1;\n      rc = sqlite3_reset(pCsr->pStmt);\n    }else{\n      pCsr->iPrevId = sqlite3_column_int64(pCsr->pStmt, 0);\n      rc = SQLITE_OK;\n    }\n  }else{\n    rc = fts3EvalNext((Fts3Cursor *)pCursor);\n  }\n  assert( ((Fts3Table *)pCsr->base.pVtab)->pSegments==0 );\n  return rc;\n}\n\n/*\n** The following are copied from sqliteInt.h.\n**\n** Constants for the largest and smallest possible 64-bit signed integers.\n** These macros are designed to work correctly on both 32-bit and 64-bit\n** compilers.\n*/\n#ifndef SQLITE_AMALGAMATION\n# define LARGEST_INT64  (0xffffffff|(((sqlite3_int64)0x7fffffff)<<32))\n# define SMALLEST_INT64 (((sqlite3_int64)-1) - LARGEST_INT64)\n#endif\n\n/*\n** If the numeric type of argument pVal is \"integer\", then return it\n** converted to a 64-bit signed integer. Otherwise, return a copy of\n** the second parameter, iDefault.\n*/\nstatic sqlite3_int64 fts3DocidRange(sqlite3_value *pVal, i64 iDefault){\n  if( pVal ){\n    int eType = sqlite3_value_numeric_type(pVal);\n    if( eType==SQLITE_INTEGER ){\n      return sqlite3_value_int64(pVal);\n    }\n  }\n  return iDefault;\n}\n\n/*\n** This is the xFilter interface for the virtual table.  See\n** the virtual table xFilter method documentation for additional\n** information.\n**\n** If idxNum==FTS3_FULLSCAN_SEARCH then do a full table scan against\n** the %_content table.\n**\n** If idxNum==FTS3_DOCID_SEARCH then do a docid lookup for a single entry\n** in the %_content table.\n**\n** If idxNum>=FTS3_FULLTEXT_SEARCH then use the full text index.  The\n** column on the left-hand side of the MATCH operator is column\n** number idxNum-FTS3_FULLTEXT_SEARCH, 0 indexed.  argv[0] is the right-hand\n** side of the MATCH operator.\n*/\nstatic int fts3FilterMethod(\n  sqlite3_vtab_cursor *pCursor,   /* The cursor used for this query */\n  int idxNum,                     /* Strategy index */\n  const char *idxStr,             /* Unused */\n  int nVal,                       /* Number of elements in apVal */\n  sqlite3_value **apVal           /* Arguments for the indexing scheme */\n){\n  int rc = SQLITE_OK;\n  char *zSql;                     /* SQL statement used to access %_content */\n  int eSearch;\n  Fts3Table *p = (Fts3Table *)pCursor->pVtab;\n  Fts3Cursor *pCsr = (Fts3Cursor *)pCursor;\n\n  sqlite3_value *pCons = 0;       /* The MATCH or rowid constraint, if any */\n  sqlite3_value *pLangid = 0;     /* The \"langid = ?\" constraint, if any */\n  sqlite3_value *pDocidGe = 0;    /* The \"docid >= ?\" constraint, if any */\n  sqlite3_value *pDocidLe = 0;    /* The \"docid <= ?\" constraint, if any */\n  int iIdx;\n\n  UNUSED_PARAMETER(idxStr);\n  UNUSED_PARAMETER(nVal);\n\n  eSearch = (idxNum & 0x0000FFFF);\n  assert( eSearch>=0 && eSearch<=(FTS3_FULLTEXT_SEARCH+p->nColumn) );\n  assert( p->pSegments==0 );\n\n  /* Collect arguments into local variables */\n  iIdx = 0;\n  if( eSearch!=FTS3_FULLSCAN_SEARCH ) pCons = apVal[iIdx++];\n  if( idxNum & FTS3_HAVE_LANGID ) pLangid = apVal[iIdx++];\n  if( idxNum & FTS3_HAVE_DOCID_GE ) pDocidGe = apVal[iIdx++];\n  if( idxNum & FTS3_HAVE_DOCID_LE ) pDocidLe = apVal[iIdx++];\n  assert( iIdx==nVal );\n\n  /* In case the cursor has been used before, clear it now. */\n  fts3ClearCursor(pCsr);\n\n  /* Set the lower and upper bounds on docids to return */\n  pCsr->iMinDocid = fts3DocidRange(pDocidGe, SMALLEST_INT64);\n  pCsr->iMaxDocid = fts3DocidRange(pDocidLe, LARGEST_INT64);\n\n  if( idxStr ){\n    pCsr->bDesc = (idxStr[0]=='D');\n  }else{\n    pCsr->bDesc = p->bDescIdx;\n  }\n  pCsr->eSearch = (i16)eSearch;\n\n  if( eSearch!=FTS3_DOCID_SEARCH && eSearch!=FTS3_FULLSCAN_SEARCH ){\n    int iCol = eSearch-FTS3_FULLTEXT_SEARCH;\n    const char *zQuery = (const char *)sqlite3_value_text(pCons);\n\n    if( zQuery==0 && sqlite3_value_type(pCons)!=SQLITE_NULL ){\n      return SQLITE_NOMEM;\n    }\n\n    pCsr->iLangid = 0;\n    if( pLangid ) pCsr->iLangid = sqlite3_value_int(pLangid);\n\n    assert( p->base.zErrMsg==0 );\n    rc = sqlite3Fts3ExprParse(p->pTokenizer, pCsr->iLangid,\n        p->azColumn, p->bFts4, p->nColumn, iCol, zQuery, -1, &pCsr->pExpr, \n        &p->base.zErrMsg\n    );\n    if( rc!=SQLITE_OK ){\n      return rc;\n    }\n\n    rc = fts3EvalStart(pCsr);\n    sqlite3Fts3SegmentsClose(p);\n    if( rc!=SQLITE_OK ) return rc;\n    pCsr->pNextId = pCsr->aDoclist;\n    pCsr->iPrevId = 0;\n  }\n\n  /* Compile a SELECT statement for this cursor. For a full-table-scan, the\n  ** statement loops through all rows of the %_content table. For a\n  ** full-text query or docid lookup, the statement retrieves a single\n  ** row by docid.\n  */\n  if( eSearch==FTS3_FULLSCAN_SEARCH ){\n    if( pDocidGe || pDocidLe ){\n      zSql = sqlite3_mprintf(\n          \"SELECT %s WHERE rowid BETWEEN %lld AND %lld ORDER BY rowid %s\",\n          p->zReadExprlist, pCsr->iMinDocid, pCsr->iMaxDocid,\n          (pCsr->bDesc ? \"DESC\" : \"ASC\")\n      );\n    }else{\n      zSql = sqlite3_mprintf(\"SELECT %s ORDER BY rowid %s\", \n          p->zReadExprlist, (pCsr->bDesc ? \"DESC\" : \"ASC\")\n      );\n    }\n    if( zSql ){\n      rc = sqlite3_prepare_v3(p->db,zSql,-1,SQLITE_PREPARE_PERSISTENT,&pCsr->pStmt,0);\n      sqlite3_free(zSql);\n    }else{\n      rc = SQLITE_NOMEM;\n    }\n  }else if( eSearch==FTS3_DOCID_SEARCH ){\n    rc = fts3CursorSeekStmt(pCsr);\n    if( rc==SQLITE_OK ){\n      rc = sqlite3_bind_value(pCsr->pStmt, 1, pCons);\n    }\n  }\n  if( rc!=SQLITE_OK ) return rc;\n\n  return fts3NextMethod(pCursor);\n}\n\n/* \n** This is the xEof method of the virtual table. SQLite calls this \n** routine to find out if it has reached the end of a result set.\n*/\nstatic int fts3EofMethod(sqlite3_vtab_cursor *pCursor){\n  Fts3Cursor *pCsr = (Fts3Cursor*)pCursor;\n  if( pCsr->isEof ){\n    fts3ClearCursor(pCsr);\n    pCsr->isEof = 1;\n  }\n  return pCsr->isEof;\n}\n\n/* \n** This is the xRowid method. The SQLite core calls this routine to\n** retrieve the rowid for the current row of the result set. fts3\n** exposes %_content.docid as the rowid for the virtual table. The\n** rowid should be written to *pRowid.\n*/\nstatic int fts3RowidMethod(sqlite3_vtab_cursor *pCursor, sqlite_int64 *pRowid){\n  Fts3Cursor *pCsr = (Fts3Cursor *) pCursor;\n  *pRowid = pCsr->iPrevId;\n  return SQLITE_OK;\n}\n\n/* \n** This is the xColumn method, called by SQLite to request a value from\n** the row that the supplied cursor currently points to.\n**\n** If:\n**\n**   (iCol <  p->nColumn)   -> The value of the iCol'th user column.\n**   (iCol == p->nColumn)   -> Magic column with the same name as the table.\n**   (iCol == p->nColumn+1) -> Docid column\n**   (iCol == p->nColumn+2) -> Langid column\n*/\nstatic int fts3ColumnMethod(\n  sqlite3_vtab_cursor *pCursor,   /* Cursor to retrieve value from */\n  sqlite3_context *pCtx,          /* Context for sqlite3_result_xxx() calls */\n  int iCol                        /* Index of column to read value from */\n){\n  int rc = SQLITE_OK;             /* Return Code */\n  Fts3Cursor *pCsr = (Fts3Cursor *) pCursor;\n  Fts3Table *p = (Fts3Table *)pCursor->pVtab;\n\n  /* The column value supplied by SQLite must be in range. */\n  assert( iCol>=0 && iCol<=p->nColumn+2 );\n\n  switch( iCol-p->nColumn ){\n    case 0:\n      /* The special 'table-name' column */\n      sqlite3_result_pointer(pCtx, pCsr, \"fts3cursor\", 0);\n      break;\n\n    case 1:\n      /* The docid column */\n      sqlite3_result_int64(pCtx, pCsr->iPrevId);\n      break;\n\n    case 2:\n      if( pCsr->pExpr ){\n        sqlite3_result_int64(pCtx, pCsr->iLangid);\n        break;\n      }else if( p->zLanguageid==0 ){\n        sqlite3_result_int(pCtx, 0);\n        break;\n      }else{\n        iCol = p->nColumn;\n        /* fall-through */\n      }\n\n    default:\n      /* A user column. Or, if this is a full-table scan, possibly the\n      ** language-id column. Seek the cursor. */\n      rc = fts3CursorSeek(0, pCsr);\n      if( rc==SQLITE_OK && sqlite3_data_count(pCsr->pStmt)-1>iCol ){\n        sqlite3_result_value(pCtx, sqlite3_column_value(pCsr->pStmt, iCol+1));\n      }\n      break;\n  }\n\n  assert( ((Fts3Table *)pCsr->base.pVtab)->pSegments==0 );\n  return rc;\n}\n\n/* \n** This function is the implementation of the xUpdate callback used by \n** FTS3 virtual tables. It is invoked by SQLite each time a row is to be\n** inserted, updated or deleted.\n*/\nstatic int fts3UpdateMethod(\n  sqlite3_vtab *pVtab,            /* Virtual table handle */\n  int nArg,                       /* Size of argument array */\n  sqlite3_value **apVal,          /* Array of arguments */\n  sqlite_int64 *pRowid            /* OUT: The affected (or effected) rowid */\n){\n  return sqlite3Fts3UpdateMethod(pVtab, nArg, apVal, pRowid);\n}\n\n/*\n** Implementation of xSync() method. Flush the contents of the pending-terms\n** hash-table to the database.\n*/\nstatic int fts3SyncMethod(sqlite3_vtab *pVtab){\n\n  /* Following an incremental-merge operation, assuming that the input\n  ** segments are not completely consumed (the usual case), they are updated\n  ** in place to remove the entries that have already been merged. This\n  ** involves updating the leaf block that contains the smallest unmerged\n  ** entry and each block (if any) between the leaf and the root node. So\n  ** if the height of the input segment b-trees is N, and input segments\n  ** are merged eight at a time, updating the input segments at the end\n  ** of an incremental-merge requires writing (8*(1+N)) blocks. N is usually\n  ** small - often between 0 and 2. So the overhead of the incremental\n  ** merge is somewhere between 8 and 24 blocks. To avoid this overhead\n  ** dwarfing the actual productive work accomplished, the incremental merge\n  ** is only attempted if it will write at least 64 leaf blocks. Hence\n  ** nMinMerge.\n  **\n  ** Of course, updating the input segments also involves deleting a bunch\n  ** of blocks from the segments table. But this is not considered overhead\n  ** as it would also be required by a crisis-merge that used the same input \n  ** segments.\n  */\n  const u32 nMinMerge = 64;       /* Minimum amount of incr-merge work to do */\n\n  Fts3Table *p = (Fts3Table*)pVtab;\n  int rc;\n  i64 iLastRowid = sqlite3_last_insert_rowid(p->db);\n\n  rc = sqlite3Fts3PendingTermsFlush(p);\n  if( rc==SQLITE_OK \n   && p->nLeafAdd>(nMinMerge/16) \n   && p->nAutoincrmerge && p->nAutoincrmerge!=0xff\n  ){\n    int mxLevel = 0;              /* Maximum relative level value in db */\n    int A;                        /* Incr-merge parameter A */\n\n    rc = sqlite3Fts3MaxLevel(p, &mxLevel);\n    assert( rc==SQLITE_OK || mxLevel==0 );\n    A = p->nLeafAdd * mxLevel;\n    A += (A/2);\n    if( A>(int)nMinMerge ) rc = sqlite3Fts3Incrmerge(p, A, p->nAutoincrmerge);\n  }\n  sqlite3Fts3SegmentsClose(p);\n  sqlite3_set_last_insert_rowid(p->db, iLastRowid);\n  return rc;\n}\n\n/*\n** If it is currently unknown whether or not the FTS table has an %_stat\n** table (if p->bHasStat==2), attempt to determine this (set p->bHasStat\n** to 0 or 1). Return SQLITE_OK if successful, or an SQLite error code\n** if an error occurs.\n*/\nstatic int fts3SetHasStat(Fts3Table *p){\n  int rc = SQLITE_OK;\n  if( p->bHasStat==2 ){\n    char *zTbl = sqlite3_mprintf(\"%s_stat\", p->zName);\n    if( zTbl ){\n      int res = sqlite3_table_column_metadata(p->db, p->zDb, zTbl, 0,0,0,0,0,0);\n      sqlite3_free(zTbl);\n      p->bHasStat = (res==SQLITE_OK);\n    }else{\n      rc = SQLITE_NOMEM;\n    }\n  }\n  return rc;\n}\n\n/*\n** Implementation of xBegin() method. \n*/\nstatic int fts3BeginMethod(sqlite3_vtab *pVtab){\n  Fts3Table *p = (Fts3Table*)pVtab;\n  UNUSED_PARAMETER(pVtab);\n  assert( p->pSegments==0 );\n  assert( p->nPendingData==0 );\n  assert( p->inTransaction!=1 );\n  TESTONLY( p->inTransaction = 1 );\n  TESTONLY( p->mxSavepoint = -1; );\n  p->nLeafAdd = 0;\n  return fts3SetHasStat(p);\n}\n\n/*\n** Implementation of xCommit() method. This is a no-op. The contents of\n** the pending-terms hash-table have already been flushed into the database\n** by fts3SyncMethod().\n*/\nstatic int fts3CommitMethod(sqlite3_vtab *pVtab){\n  TESTONLY( Fts3Table *p = (Fts3Table*)pVtab );\n  UNUSED_PARAMETER(pVtab);\n  assert( p->nPendingData==0 );\n  assert( p->inTransaction!=0 );\n  assert( p->pSegments==0 );\n  TESTONLY( p->inTransaction = 0 );\n  TESTONLY( p->mxSavepoint = -1; );\n  return SQLITE_OK;\n}\n\n/*\n** Implementation of xRollback(). Discard the contents of the pending-terms\n** hash-table. Any changes made to the database are reverted by SQLite.\n*/\nstatic int fts3RollbackMethod(sqlite3_vtab *pVtab){\n  Fts3Table *p = (Fts3Table*)pVtab;\n  sqlite3Fts3PendingTermsClear(p);\n  assert( p->inTransaction!=0 );\n  TESTONLY( p->inTransaction = 0 );\n  TESTONLY( p->mxSavepoint = -1; );\n  return SQLITE_OK;\n}\n\n/*\n** When called, *ppPoslist must point to the byte immediately following the\n** end of a position-list. i.e. ( (*ppPoslist)[-1]==POS_END ). This function\n** moves *ppPoslist so that it instead points to the first byte of the\n** same position list.\n*/\nstatic void fts3ReversePoslist(char *pStart, char **ppPoslist){\n  char *p = &(*ppPoslist)[-2];\n  char c = 0;\n\n  /* Skip backwards passed any trailing 0x00 bytes added by NearTrim() */\n  while( p>pStart && (c=*p--)==0 );\n\n  /* Search backwards for a varint with value zero (the end of the previous \n  ** poslist). This is an 0x00 byte preceded by some byte that does not\n  ** have the 0x80 bit set.  */\n  while( p>pStart && (*p & 0x80) | c ){ \n    c = *p--; \n  }\n  assert( p==pStart || c==0 );\n\n  /* At this point p points to that preceding byte without the 0x80 bit\n  ** set. So to find the start of the poslist, skip forward 2 bytes then\n  ** over a varint. \n  **\n  ** Normally. The other case is that p==pStart and the poslist to return\n  ** is the first in the doclist. In this case do not skip forward 2 bytes.\n  ** The second part of the if condition (c==0 && *ppPoslist>&p[2])\n  ** is required for cases where the first byte of a doclist and the\n  ** doclist is empty. For example, if the first docid is 10, a doclist\n  ** that begins with:\n  **\n  **   0x0A 0x00 <next docid delta varint>\n  */\n  if( p>pStart || (c==0 && *ppPoslist>&p[2]) ){ p = &p[2]; }\n  while( *p++&0x80 );\n  *ppPoslist = p;\n}\n\n/*\n** Helper function used by the implementation of the overloaded snippet(),\n** offsets() and optimize() SQL functions.\n**\n** If the value passed as the third argument is a blob of size\n** sizeof(Fts3Cursor*), then the blob contents are copied to the \n** output variable *ppCsr and SQLITE_OK is returned. Otherwise, an error\n** message is written to context pContext and SQLITE_ERROR returned. The\n** string passed via zFunc is used as part of the error message.\n*/\nstatic int fts3FunctionArg(\n  sqlite3_context *pContext,      /* SQL function call context */\n  const char *zFunc,              /* Function name */\n  sqlite3_value *pVal,            /* argv[0] passed to function */\n  Fts3Cursor **ppCsr              /* OUT: Store cursor handle here */\n){\n  int rc;\n  *ppCsr = (Fts3Cursor*)sqlite3_value_pointer(pVal, \"fts3cursor\");\n  if( (*ppCsr)!=0 ){\n    rc = SQLITE_OK;\n  }else{\n    char *zErr = sqlite3_mprintf(\"illegal first argument to %s\", zFunc);\n    sqlite3_result_error(pContext, zErr, -1);\n    sqlite3_free(zErr);\n    rc = SQLITE_ERROR;\n  }\n  return rc;\n}\n\n/*\n** Implementation of the snippet() function for FTS3\n*/\nstatic void fts3SnippetFunc(\n  sqlite3_context *pContext,      /* SQLite function call context */\n  int nVal,                       /* Size of apVal[] array */\n  sqlite3_value **apVal           /* Array of arguments */\n){\n  Fts3Cursor *pCsr;               /* Cursor handle passed through apVal[0] */\n  const char *zStart = \"<b>\";\n  const char *zEnd = \"</b>\";\n  const char *zEllipsis = \"<b>...</b>\";\n  int iCol = -1;\n  int nToken = 15;                /* Default number of tokens in snippet */\n\n  /* There must be at least one argument passed to this function (otherwise\n  ** the non-overloaded version would have been called instead of this one).\n  */\n  assert( nVal>=1 );\n\n  if( nVal>6 ){\n    sqlite3_result_error(pContext, \n        \"wrong number of arguments to function snippet()\", -1);\n    return;\n  }\n  if( fts3FunctionArg(pContext, \"snippet\", apVal[0], &pCsr) ) return;\n\n  switch( nVal ){\n    case 6: nToken = sqlite3_value_int(apVal[5]);\n    case 5: iCol = sqlite3_value_int(apVal[4]);\n    case 4: zEllipsis = (const char*)sqlite3_value_text(apVal[3]);\n    case 3: zEnd = (const char*)sqlite3_value_text(apVal[2]);\n    case 2: zStart = (const char*)sqlite3_value_text(apVal[1]);\n  }\n  if( !zEllipsis || !zEnd || !zStart ){\n    sqlite3_result_error_nomem(pContext);\n  }else if( nToken==0 ){\n    sqlite3_result_text(pContext, \"\", -1, SQLITE_STATIC);\n  }else if( SQLITE_OK==fts3CursorSeek(pContext, pCsr) ){\n    sqlite3Fts3Snippet(pContext, pCsr, zStart, zEnd, zEllipsis, iCol, nToken);\n  }\n}\n\n/*\n** Implementation of the offsets() function for FTS3\n*/\nstatic void fts3OffsetsFunc(\n  sqlite3_context *pContext,      /* SQLite function call context */\n  int nVal,                       /* Size of argument array */\n  sqlite3_value **apVal           /* Array of arguments */\n){\n  Fts3Cursor *pCsr;               /* Cursor handle passed through apVal[0] */\n\n  UNUSED_PARAMETER(nVal);\n\n  assert( nVal==1 );\n  if( fts3FunctionArg(pContext, \"offsets\", apVal[0], &pCsr) ) return;\n  assert( pCsr );\n  if( SQLITE_OK==fts3CursorSeek(pContext, pCsr) ){\n    sqlite3Fts3Offsets(pContext, pCsr);\n  }\n}\n\n/* \n** Implementation of the special optimize() function for FTS3. This \n** function merges all segments in the database to a single segment.\n** Example usage is:\n**\n**   SELECT optimize(t) FROM t LIMIT 1;\n**\n** where 't' is the name of an FTS3 table.\n*/\nstatic void fts3OptimizeFunc(\n  sqlite3_context *pContext,      /* SQLite function call context */\n  int nVal,                       /* Size of argument array */\n  sqlite3_value **apVal           /* Array of arguments */\n){\n  int rc;                         /* Return code */\n  Fts3Table *p;                   /* Virtual table handle */\n  Fts3Cursor *pCursor;            /* Cursor handle passed through apVal[0] */\n\n  UNUSED_PARAMETER(nVal);\n\n  assert( nVal==1 );\n  if( fts3FunctionArg(pContext, \"optimize\", apVal[0], &pCursor) ) return;\n  p = (Fts3Table *)pCursor->base.pVtab;\n  assert( p );\n\n  rc = sqlite3Fts3Optimize(p);\n\n  switch( rc ){\n    case SQLITE_OK:\n      sqlite3_result_text(pContext, \"Index optimized\", -1, SQLITE_STATIC);\n      break;\n    case SQLITE_DONE:\n      sqlite3_result_text(pContext, \"Index already optimal\", -1, SQLITE_STATIC);\n      break;\n    default:\n      sqlite3_result_error_code(pContext, rc);\n      break;\n  }\n}\n\n/*\n** Implementation of the matchinfo() function for FTS3\n*/\nstatic void fts3MatchinfoFunc(\n  sqlite3_context *pContext,      /* SQLite function call context */\n  int nVal,                       /* Size of argument array */\n  sqlite3_value **apVal           /* Array of arguments */\n){\n  Fts3Cursor *pCsr;               /* Cursor handle passed through apVal[0] */\n  assert( nVal==1 || nVal==2 );\n  if( SQLITE_OK==fts3FunctionArg(pContext, \"matchinfo\", apVal[0], &pCsr) ){\n    const char *zArg = 0;\n    if( nVal>1 ){\n      zArg = (const char *)sqlite3_value_text(apVal[1]);\n    }\n    sqlite3Fts3Matchinfo(pContext, pCsr, zArg);\n  }\n}\n\n/*\n** This routine implements the xFindFunction method for the FTS3\n** virtual table.\n*/\nstatic int fts3FindFunctionMethod(\n  sqlite3_vtab *pVtab,            /* Virtual table handle */\n  int nArg,                       /* Number of SQL function arguments */\n  const char *zName,              /* Name of SQL function */\n  void (**pxFunc)(sqlite3_context*,int,sqlite3_value**), /* OUT: Result */\n  void **ppArg                    /* Unused */\n){\n  struct Overloaded {\n    const char *zName;\n    void (*xFunc)(sqlite3_context*,int,sqlite3_value**);\n  } aOverload[] = {\n    { \"snippet\", fts3SnippetFunc },\n    { \"offsets\", fts3OffsetsFunc },\n    { \"optimize\", fts3OptimizeFunc },\n    { \"matchinfo\", fts3MatchinfoFunc },\n  };\n  int i;                          /* Iterator variable */\n\n  UNUSED_PARAMETER(pVtab);\n  UNUSED_PARAMETER(nArg);\n  UNUSED_PARAMETER(ppArg);\n\n  for(i=0; i<SizeofArray(aOverload); i++){\n    if( strcmp(zName, aOverload[i].zName)==0 ){\n      *pxFunc = aOverload[i].xFunc;\n      return 1;\n    }\n  }\n\n  /* No function of the specified name was found. Return 0. */\n  return 0;\n}\n\n/*\n** Implementation of FTS3 xRename method. Rename an fts3 table.\n*/\nstatic int fts3RenameMethod(\n  sqlite3_vtab *pVtab,            /* Virtual table handle */\n  const char *zName               /* New name of table */\n){\n  Fts3Table *p = (Fts3Table *)pVtab;\n  sqlite3 *db = p->db;            /* Database connection */\n  int rc;                         /* Return Code */\n\n  /* At this point it must be known if the %_stat table exists or not.\n  ** So bHasStat may not be 2.  */\n  rc = fts3SetHasStat(p);\n  \n  /* As it happens, the pending terms table is always empty here. This is\n  ** because an \"ALTER TABLE RENAME TABLE\" statement inside a transaction \n  ** always opens a savepoint transaction. And the xSavepoint() method \n  ** flushes the pending terms table. But leave the (no-op) call to\n  ** PendingTermsFlush() in in case that changes.\n  */\n  assert( p->nPendingData==0 );\n  if( rc==SQLITE_OK ){\n    rc = sqlite3Fts3PendingTermsFlush(p);\n  }\n\n  if( p->zContentTbl==0 ){\n    fts3DbExec(&rc, db,\n      \"ALTER TABLE %Q.'%q_content'  RENAME TO '%q_content';\",\n      p->zDb, p->zName, zName\n    );\n  }\n\n  if( p->bHasDocsize ){\n    fts3DbExec(&rc, db,\n      \"ALTER TABLE %Q.'%q_docsize'  RENAME TO '%q_docsize';\",\n      p->zDb, p->zName, zName\n    );\n  }\n  if( p->bHasStat ){\n    fts3DbExec(&rc, db,\n      \"ALTER TABLE %Q.'%q_stat'  RENAME TO '%q_stat';\",\n      p->zDb, p->zName, zName\n    );\n  }\n  fts3DbExec(&rc, db,\n    \"ALTER TABLE %Q.'%q_segments' RENAME TO '%q_segments';\",\n    p->zDb, p->zName, zName\n  );\n  fts3DbExec(&rc, db,\n    \"ALTER TABLE %Q.'%q_segdir'   RENAME TO '%q_segdir';\",\n    p->zDb, p->zName, zName\n  );\n  return rc;\n}\n\n/*\n** The xSavepoint() method.\n**\n** Flush the contents of the pending-terms table to disk.\n*/\nstatic int fts3SavepointMethod(sqlite3_vtab *pVtab, int iSavepoint){\n  int rc = SQLITE_OK;\n  UNUSED_PARAMETER(iSavepoint);\n  assert( ((Fts3Table *)pVtab)->inTransaction );\n  assert( ((Fts3Table *)pVtab)->mxSavepoint < iSavepoint );\n  TESTONLY( ((Fts3Table *)pVtab)->mxSavepoint = iSavepoint );\n  if( ((Fts3Table *)pVtab)->bIgnoreSavepoint==0 ){\n    rc = fts3SyncMethod(pVtab);\n  }\n  return rc;\n}\n\n/*\n** The xRelease() method.\n**\n** This is a no-op.\n*/\nstatic int fts3ReleaseMethod(sqlite3_vtab *pVtab, int iSavepoint){\n  TESTONLY( Fts3Table *p = (Fts3Table*)pVtab );\n  UNUSED_PARAMETER(iSavepoint);\n  UNUSED_PARAMETER(pVtab);\n  assert( p->inTransaction );\n  assert( p->mxSavepoint >= iSavepoint );\n  TESTONLY( p->mxSavepoint = iSavepoint-1 );\n  return SQLITE_OK;\n}\n\n/*\n** The xRollbackTo() method.\n**\n** Discard the contents of the pending terms table.\n*/\nstatic int fts3RollbackToMethod(sqlite3_vtab *pVtab, int iSavepoint){\n  Fts3Table *p = (Fts3Table*)pVtab;\n  UNUSED_PARAMETER(iSavepoint);\n  assert( p->inTransaction );\n  assert( p->mxSavepoint >= iSavepoint );\n  TESTONLY( p->mxSavepoint = iSavepoint );\n  sqlite3Fts3PendingTermsClear(p);\n  return SQLITE_OK;\n}\n\nstatic const sqlite3_module fts3Module = {\n  /* iVersion      */ 2,\n  /* xCreate       */ fts3CreateMethod,\n  /* xConnect      */ fts3ConnectMethod,\n  /* xBestIndex    */ fts3BestIndexMethod,\n  /* xDisconnect   */ fts3DisconnectMethod,\n  /* xDestroy      */ fts3DestroyMethod,\n  /* xOpen         */ fts3OpenMethod,\n  /* xClose        */ fts3CloseMethod,\n  /* xFilter       */ fts3FilterMethod,\n  /* xNext         */ fts3NextMethod,\n  /* xEof          */ fts3EofMethod,\n  /* xColumn       */ fts3ColumnMethod,\n  /* xRowid        */ fts3RowidMethod,\n  /* xUpdate       */ fts3UpdateMethod,\n  /* xBegin        */ fts3BeginMethod,\n  /* xSync         */ fts3SyncMethod,\n  /* xCommit       */ fts3CommitMethod,\n  /* xRollback     */ fts3RollbackMethod,\n  /* xFindFunction */ fts3FindFunctionMethod,\n  /* xRename */       fts3RenameMethod,\n  /* xSavepoint    */ fts3SavepointMethod,\n  /* xRelease      */ fts3ReleaseMethod,\n  /* xRollbackTo   */ fts3RollbackToMethod,\n};\n\n/*\n** This function is registered as the module destructor (called when an\n** FTS3 enabled database connection is closed). It frees the memory\n** allocated for the tokenizer hash table.\n*/\nstatic void hashDestroy(void *p){\n  Fts3Hash *pHash = (Fts3Hash *)p;\n  sqlite3Fts3HashClear(pHash);\n  sqlite3_free(pHash);\n}\n\n/*\n** The fts3 built-in tokenizers - \"simple\", \"porter\" and \"icu\"- are \n** implemented in files fts3_tokenizer1.c, fts3_porter.c and fts3_icu.c\n** respectively. The following three forward declarations are for functions\n** declared in these files used to retrieve the respective implementations.\n**\n** Calling sqlite3Fts3SimpleTokenizerModule() sets the value pointed\n** to by the argument to point to the \"simple\" tokenizer implementation.\n** And so on.\n*/\nSQLITE_PRIVATE void sqlite3Fts3SimpleTokenizerModule(sqlite3_tokenizer_module const**ppModule);\nSQLITE_PRIVATE void sqlite3Fts3PorterTokenizerModule(sqlite3_tokenizer_module const**ppModule);\n#ifndef SQLITE_DISABLE_FTS3_UNICODE\nSQLITE_PRIVATE void sqlite3Fts3UnicodeTokenizer(sqlite3_tokenizer_module const**ppModule);\n#endif\n#ifdef SQLITE_ENABLE_ICU\nSQLITE_PRIVATE void sqlite3Fts3IcuTokenizerModule(sqlite3_tokenizer_module const**ppModule);\n#endif\n\n/*\n** Initialize the fts3 extension. If this extension is built as part\n** of the sqlite library, then this function is called directly by\n** SQLite. If fts3 is built as a dynamically loadable extension, this\n** function is called by the sqlite3_extension_init() entry point.\n*/\nSQLITE_PRIVATE int sqlite3Fts3Init(sqlite3 *db){\n  int rc = SQLITE_OK;\n  Fts3Hash *pHash = 0;\n  const sqlite3_tokenizer_module *pSimple = 0;\n  const sqlite3_tokenizer_module *pPorter = 0;\n#ifndef SQLITE_DISABLE_FTS3_UNICODE\n  const sqlite3_tokenizer_module *pUnicode = 0;\n#endif\n\n#ifdef SQLITE_ENABLE_ICU\n  const sqlite3_tokenizer_module *pIcu = 0;\n  sqlite3Fts3IcuTokenizerModule(&pIcu);\n#endif\n\n#ifndef SQLITE_DISABLE_FTS3_UNICODE\n  sqlite3Fts3UnicodeTokenizer(&pUnicode);\n#endif\n\n#ifdef SQLITE_TEST\n  rc = sqlite3Fts3InitTerm(db);\n  if( rc!=SQLITE_OK ) return rc;\n#endif\n\n  rc = sqlite3Fts3InitAux(db);\n  if( rc!=SQLITE_OK ) return rc;\n\n  sqlite3Fts3SimpleTokenizerModule(&pSimple);\n  sqlite3Fts3PorterTokenizerModule(&pPorter);\n\n  /* Allocate and initialize the hash-table used to store tokenizers. */\n  pHash = sqlite3_malloc(sizeof(Fts3Hash));\n  if( !pHash ){\n    rc = SQLITE_NOMEM;\n  }else{\n    sqlite3Fts3HashInit(pHash, FTS3_HASH_STRING, 1);\n  }\n\n  /* Load the built-in tokenizers into the hash table */\n  if( rc==SQLITE_OK ){\n    if( sqlite3Fts3HashInsert(pHash, \"simple\", 7, (void *)pSimple)\n     || sqlite3Fts3HashInsert(pHash, \"porter\", 7, (void *)pPorter) \n\n#ifndef SQLITE_DISABLE_FTS3_UNICODE\n     || sqlite3Fts3HashInsert(pHash, \"unicode61\", 10, (void *)pUnicode) \n#endif\n#ifdef SQLITE_ENABLE_ICU\n     || (pIcu && sqlite3Fts3HashInsert(pHash, \"icu\", 4, (void *)pIcu))\n#endif\n    ){\n      rc = SQLITE_NOMEM;\n    }\n  }\n\n#ifdef SQLITE_TEST\n  if( rc==SQLITE_OK ){\n    rc = sqlite3Fts3ExprInitTestInterface(db);\n  }\n#endif\n\n  /* Create the virtual table wrapper around the hash-table and overload \n  ** the four scalar functions. If this is successful, register the\n  ** module with sqlite.\n  */\n  if( SQLITE_OK==rc \n   && SQLITE_OK==(rc = sqlite3Fts3InitHashTable(db, pHash, \"fts3_tokenizer\"))\n   && SQLITE_OK==(rc = sqlite3_overload_function(db, \"snippet\", -1))\n   && SQLITE_OK==(rc = sqlite3_overload_function(db, \"offsets\", 1))\n   && SQLITE_OK==(rc = sqlite3_overload_function(db, \"matchinfo\", 1))\n   && SQLITE_OK==(rc = sqlite3_overload_function(db, \"matchinfo\", 2))\n   && SQLITE_OK==(rc = sqlite3_overload_function(db, \"optimize\", 1))\n  ){\n    rc = sqlite3_create_module_v2(\n        db, \"fts3\", &fts3Module, (void *)pHash, hashDestroy\n    );\n    if( rc==SQLITE_OK ){\n      rc = sqlite3_create_module_v2(\n          db, \"fts4\", &fts3Module, (void *)pHash, 0\n      );\n    }\n    if( rc==SQLITE_OK ){\n      rc = sqlite3Fts3InitTok(db, (void *)pHash);\n    }\n    return rc;\n  }\n\n\n  /* An error has occurred. Delete the hash table and return the error code. */\n  assert( rc!=SQLITE_OK );\n  if( pHash ){\n    sqlite3Fts3HashClear(pHash);\n    sqlite3_free(pHash);\n  }\n  return rc;\n}\n\n/*\n** Allocate an Fts3MultiSegReader for each token in the expression headed\n** by pExpr. \n**\n** An Fts3SegReader object is a cursor that can seek or scan a range of\n** entries within a single segment b-tree. An Fts3MultiSegReader uses multiple\n** Fts3SegReader objects internally to provide an interface to seek or scan\n** within the union of all segments of a b-tree. Hence the name.\n**\n** If the allocated Fts3MultiSegReader just seeks to a single entry in a\n** segment b-tree (if the term is not a prefix or it is a prefix for which\n** there exists prefix b-tree of the right length) then it may be traversed\n** and merged incrementally. Otherwise, it has to be merged into an in-memory \n** doclist and then traversed.\n*/\nstatic void fts3EvalAllocateReaders(\n  Fts3Cursor *pCsr,               /* FTS cursor handle */\n  Fts3Expr *pExpr,                /* Allocate readers for this expression */\n  int *pnToken,                   /* OUT: Total number of tokens in phrase. */\n  int *pnOr,                      /* OUT: Total number of OR nodes in expr. */\n  int *pRc                        /* IN/OUT: Error code */\n){\n  if( pExpr && SQLITE_OK==*pRc ){\n    if( pExpr->eType==FTSQUERY_PHRASE ){\n      int i;\n      int nToken = pExpr->pPhrase->nToken;\n      *pnToken += nToken;\n      for(i=0; i<nToken; i++){\n        Fts3PhraseToken *pToken = &pExpr->pPhrase->aToken[i];\n        int rc = fts3TermSegReaderCursor(pCsr, \n            pToken->z, pToken->n, pToken->isPrefix, &pToken->pSegcsr\n        );\n        if( rc!=SQLITE_OK ){\n          *pRc = rc;\n          return;\n        }\n      }\n      assert( pExpr->pPhrase->iDoclistToken==0 );\n      pExpr->pPhrase->iDoclistToken = -1;\n    }else{\n      *pnOr += (pExpr->eType==FTSQUERY_OR);\n      fts3EvalAllocateReaders(pCsr, pExpr->pLeft, pnToken, pnOr, pRc);\n      fts3EvalAllocateReaders(pCsr, pExpr->pRight, pnToken, pnOr, pRc);\n    }\n  }\n}\n\n/*\n** Arguments pList/nList contain the doclist for token iToken of phrase p.\n** It is merged into the main doclist stored in p->doclist.aAll/nAll.\n**\n** This function assumes that pList points to a buffer allocated using\n** sqlite3_malloc(). This function takes responsibility for eventually\n** freeing the buffer.\n**\n** SQLITE_OK is returned if successful, or SQLITE_NOMEM if an error occurs.\n*/\nstatic int fts3EvalPhraseMergeToken(\n  Fts3Table *pTab,                /* FTS Table pointer */\n  Fts3Phrase *p,                  /* Phrase to merge pList/nList into */\n  int iToken,                     /* Token pList/nList corresponds to */\n  char *pList,                    /* Pointer to doclist */\n  int nList                       /* Number of bytes in pList */\n){\n  int rc = SQLITE_OK;\n  assert( iToken!=p->iDoclistToken );\n\n  if( pList==0 ){\n    sqlite3_free(p->doclist.aAll);\n    p->doclist.aAll = 0;\n    p->doclist.nAll = 0;\n  }\n\n  else if( p->iDoclistToken<0 ){\n    p->doclist.aAll = pList;\n    p->doclist.nAll = nList;\n  }\n\n  else if( p->doclist.aAll==0 ){\n    sqlite3_free(pList);\n  }\n\n  else {\n    char *pLeft;\n    char *pRight;\n    int nLeft;\n    int nRight;\n    int nDiff;\n\n    if( p->iDoclistToken<iToken ){\n      pLeft = p->doclist.aAll;\n      nLeft = p->doclist.nAll;\n      pRight = pList;\n      nRight = nList;\n      nDiff = iToken - p->iDoclistToken;\n    }else{\n      pRight = p->doclist.aAll;\n      nRight = p->doclist.nAll;\n      pLeft = pList;\n      nLeft = nList;\n      nDiff = p->iDoclistToken - iToken;\n    }\n\n    rc = fts3DoclistPhraseMerge(\n        pTab->bDescIdx, nDiff, pLeft, nLeft, &pRight, &nRight\n    );\n    sqlite3_free(pLeft);\n    p->doclist.aAll = pRight;\n    p->doclist.nAll = nRight;\n  }\n\n  if( iToken>p->iDoclistToken ) p->iDoclistToken = iToken;\n  return rc;\n}\n\n/*\n** Load the doclist for phrase p into p->doclist.aAll/nAll. The loaded doclist\n** does not take deferred tokens into account.\n**\n** SQLITE_OK is returned if no error occurs, otherwise an SQLite error code.\n*/\nstatic int fts3EvalPhraseLoad(\n  Fts3Cursor *pCsr,               /* FTS Cursor handle */\n  Fts3Phrase *p                   /* Phrase object */\n){\n  Fts3Table *pTab = (Fts3Table *)pCsr->base.pVtab;\n  int iToken;\n  int rc = SQLITE_OK;\n\n  for(iToken=0; rc==SQLITE_OK && iToken<p->nToken; iToken++){\n    Fts3PhraseToken *pToken = &p->aToken[iToken];\n    assert( pToken->pDeferred==0 || pToken->pSegcsr==0 );\n\n    if( pToken->pSegcsr ){\n      int nThis = 0;\n      char *pThis = 0;\n      rc = fts3TermSelect(pTab, pToken, p->iColumn, &nThis, &pThis);\n      if( rc==SQLITE_OK ){\n        rc = fts3EvalPhraseMergeToken(pTab, p, iToken, pThis, nThis);\n      }\n    }\n    assert( pToken->pSegcsr==0 );\n  }\n\n  return rc;\n}\n\n/*\n** This function is called on each phrase after the position lists for\n** any deferred tokens have been loaded into memory. It updates the phrases\n** current position list to include only those positions that are really\n** instances of the phrase (after considering deferred tokens). If this\n** means that the phrase does not appear in the current row, doclist.pList\n** and doclist.nList are both zeroed.\n**\n** SQLITE_OK is returned if no error occurs, otherwise an SQLite error code.\n*/\nstatic int fts3EvalDeferredPhrase(Fts3Cursor *pCsr, Fts3Phrase *pPhrase){\n  int iToken;                     /* Used to iterate through phrase tokens */\n  char *aPoslist = 0;             /* Position list for deferred tokens */\n  int nPoslist = 0;               /* Number of bytes in aPoslist */\n  int iPrev = -1;                 /* Token number of previous deferred token */\n\n  assert( pPhrase->doclist.bFreeList==0 );\n\n  for(iToken=0; iToken<pPhrase->nToken; iToken++){\n    Fts3PhraseToken *pToken = &pPhrase->aToken[iToken];\n    Fts3DeferredToken *pDeferred = pToken->pDeferred;\n\n    if( pDeferred ){\n      char *pList;\n      int nList;\n      int rc = sqlite3Fts3DeferredTokenList(pDeferred, &pList, &nList);\n      if( rc!=SQLITE_OK ) return rc;\n\n      if( pList==0 ){\n        sqlite3_free(aPoslist);\n        pPhrase->doclist.pList = 0;\n        pPhrase->doclist.nList = 0;\n        return SQLITE_OK;\n\n      }else if( aPoslist==0 ){\n        aPoslist = pList;\n        nPoslist = nList;\n\n      }else{\n        char *aOut = pList;\n        char *p1 = aPoslist;\n        char *p2 = aOut;\n\n        assert( iPrev>=0 );\n        fts3PoslistPhraseMerge(&aOut, iToken-iPrev, 0, 1, &p1, &p2);\n        sqlite3_free(aPoslist);\n        aPoslist = pList;\n        nPoslist = (int)(aOut - aPoslist);\n        if( nPoslist==0 ){\n          sqlite3_free(aPoslist);\n          pPhrase->doclist.pList = 0;\n          pPhrase->doclist.nList = 0;\n          return SQLITE_OK;\n        }\n      }\n      iPrev = iToken;\n    }\n  }\n\n  if( iPrev>=0 ){\n    int nMaxUndeferred = pPhrase->iDoclistToken;\n    if( nMaxUndeferred<0 ){\n      pPhrase->doclist.pList = aPoslist;\n      pPhrase->doclist.nList = nPoslist;\n      pPhrase->doclist.iDocid = pCsr->iPrevId;\n      pPhrase->doclist.bFreeList = 1;\n    }else{\n      int nDistance;\n      char *p1;\n      char *p2;\n      char *aOut;\n\n      if( nMaxUndeferred>iPrev ){\n        p1 = aPoslist;\n        p2 = pPhrase->doclist.pList;\n        nDistance = nMaxUndeferred - iPrev;\n      }else{\n        p1 = pPhrase->doclist.pList;\n        p2 = aPoslist;\n        nDistance = iPrev - nMaxUndeferred;\n      }\n\n      aOut = (char *)sqlite3_malloc(nPoslist+8);\n      if( !aOut ){\n        sqlite3_free(aPoslist);\n        return SQLITE_NOMEM;\n      }\n      \n      pPhrase->doclist.pList = aOut;\n      if( fts3PoslistPhraseMerge(&aOut, nDistance, 0, 1, &p1, &p2) ){\n        pPhrase->doclist.bFreeList = 1;\n        pPhrase->doclist.nList = (int)(aOut - pPhrase->doclist.pList);\n      }else{\n        sqlite3_free(aOut);\n        pPhrase->doclist.pList = 0;\n        pPhrase->doclist.nList = 0;\n      }\n      sqlite3_free(aPoslist);\n    }\n  }\n\n  return SQLITE_OK;\n}\n\n/*\n** Maximum number of tokens a phrase may have to be considered for the\n** incremental doclists strategy.\n*/\n#define MAX_INCR_PHRASE_TOKENS 4\n\n/*\n** This function is called for each Fts3Phrase in a full-text query \n** expression to initialize the mechanism for returning rows. Once this\n** function has been called successfully on an Fts3Phrase, it may be\n** used with fts3EvalPhraseNext() to iterate through the matching docids.\n**\n** If parameter bOptOk is true, then the phrase may (or may not) use the\n** incremental loading strategy. Otherwise, the entire doclist is loaded into\n** memory within this call.\n**\n** SQLITE_OK is returned if no error occurs, otherwise an SQLite error code.\n*/\nstatic int fts3EvalPhraseStart(Fts3Cursor *pCsr, int bOptOk, Fts3Phrase *p){\n  Fts3Table *pTab = (Fts3Table *)pCsr->base.pVtab;\n  int rc = SQLITE_OK;             /* Error code */\n  int i;\n\n  /* Determine if doclists may be loaded from disk incrementally. This is\n  ** possible if the bOptOk argument is true, the FTS doclists will be\n  ** scanned in forward order, and the phrase consists of \n  ** MAX_INCR_PHRASE_TOKENS or fewer tokens, none of which are are \"^first\"\n  ** tokens or prefix tokens that cannot use a prefix-index.  */\n  int bHaveIncr = 0;\n  int bIncrOk = (bOptOk \n   && pCsr->bDesc==pTab->bDescIdx \n   && p->nToken<=MAX_INCR_PHRASE_TOKENS && p->nToken>0\n#ifdef SQLITE_TEST\n   && pTab->bNoIncrDoclist==0\n#endif\n  );\n  for(i=0; bIncrOk==1 && i<p->nToken; i++){\n    Fts3PhraseToken *pToken = &p->aToken[i];\n    if( pToken->bFirst || (pToken->pSegcsr!=0 && !pToken->pSegcsr->bLookup) ){\n      bIncrOk = 0;\n    }\n    if( pToken->pSegcsr ) bHaveIncr = 1;\n  }\n\n  if( bIncrOk && bHaveIncr ){\n    /* Use the incremental approach. */\n    int iCol = (p->iColumn >= pTab->nColumn ? -1 : p->iColumn);\n    for(i=0; rc==SQLITE_OK && i<p->nToken; i++){\n      Fts3PhraseToken *pToken = &p->aToken[i];\n      Fts3MultiSegReader *pSegcsr = pToken->pSegcsr;\n      if( pSegcsr ){\n        rc = sqlite3Fts3MsrIncrStart(pTab, pSegcsr, iCol, pToken->z, pToken->n);\n      }\n    }\n    p->bIncr = 1;\n  }else{\n    /* Load the full doclist for the phrase into memory. */\n    rc = fts3EvalPhraseLoad(pCsr, p);\n    p->bIncr = 0;\n  }\n\n  assert( rc!=SQLITE_OK || p->nToken<1 || p->aToken[0].pSegcsr==0 || p->bIncr );\n  return rc;\n}\n\n/*\n** This function is used to iterate backwards (from the end to start) \n** through doclists. It is used by this module to iterate through phrase\n** doclists in reverse and by the fts3_write.c module to iterate through\n** pending-terms lists when writing to databases with \"order=desc\".\n**\n** The doclist may be sorted in ascending (parameter bDescIdx==0) or \n** descending (parameter bDescIdx==1) order of docid. Regardless, this\n** function iterates from the end of the doclist to the beginning.\n*/\nSQLITE_PRIVATE void sqlite3Fts3DoclistPrev(\n  int bDescIdx,                   /* True if the doclist is desc */\n  char *aDoclist,                 /* Pointer to entire doclist */\n  int nDoclist,                   /* Length of aDoclist in bytes */\n  char **ppIter,                  /* IN/OUT: Iterator pointer */\n  sqlite3_int64 *piDocid,         /* IN/OUT: Docid pointer */\n  int *pnList,                    /* OUT: List length pointer */\n  u8 *pbEof                       /* OUT: End-of-file flag */\n){\n  char *p = *ppIter;\n\n  assert( nDoclist>0 );\n  assert( *pbEof==0 );\n  assert( p || *piDocid==0 );\n  assert( !p || (p>aDoclist && p<&aDoclist[nDoclist]) );\n\n  if( p==0 ){\n    sqlite3_int64 iDocid = 0;\n    char *pNext = 0;\n    char *pDocid = aDoclist;\n    char *pEnd = &aDoclist[nDoclist];\n    int iMul = 1;\n\n    while( pDocid<pEnd ){\n      sqlite3_int64 iDelta;\n      pDocid += sqlite3Fts3GetVarint(pDocid, &iDelta);\n      iDocid += (iMul * iDelta);\n      pNext = pDocid;\n      fts3PoslistCopy(0, &pDocid);\n      while( pDocid<pEnd && *pDocid==0 ) pDocid++;\n      iMul = (bDescIdx ? -1 : 1);\n    }\n\n    *pnList = (int)(pEnd - pNext);\n    *ppIter = pNext;\n    *piDocid = iDocid;\n  }else{\n    int iMul = (bDescIdx ? -1 : 1);\n    sqlite3_int64 iDelta;\n    fts3GetReverseVarint(&p, aDoclist, &iDelta);\n    *piDocid -= (iMul * iDelta);\n\n    if( p==aDoclist ){\n      *pbEof = 1;\n    }else{\n      char *pSave = p;\n      fts3ReversePoslist(aDoclist, &p);\n      *pnList = (int)(pSave - p);\n    }\n    *ppIter = p;\n  }\n}\n\n/*\n** Iterate forwards through a doclist.\n*/\nSQLITE_PRIVATE void sqlite3Fts3DoclistNext(\n  int bDescIdx,                   /* True if the doclist is desc */\n  char *aDoclist,                 /* Pointer to entire doclist */\n  int nDoclist,                   /* Length of aDoclist in bytes */\n  char **ppIter,                  /* IN/OUT: Iterator pointer */\n  sqlite3_int64 *piDocid,         /* IN/OUT: Docid pointer */\n  u8 *pbEof                       /* OUT: End-of-file flag */\n){\n  char *p = *ppIter;\n\n  assert( nDoclist>0 );\n  assert( *pbEof==0 );\n  assert( p || *piDocid==0 );\n  assert( !p || (p>=aDoclist && p<=&aDoclist[nDoclist]) );\n\n  if( p==0 ){\n    p = aDoclist;\n    p += sqlite3Fts3GetVarint(p, piDocid);\n  }else{\n    fts3PoslistCopy(0, &p);\n    while( p<&aDoclist[nDoclist] && *p==0 ) p++; \n    if( p>=&aDoclist[nDoclist] ){\n      *pbEof = 1;\n    }else{\n      sqlite3_int64 iVar;\n      p += sqlite3Fts3GetVarint(p, &iVar);\n      *piDocid += ((bDescIdx ? -1 : 1) * iVar);\n    }\n  }\n\n  *ppIter = p;\n}\n\n/*\n** Advance the iterator pDL to the next entry in pDL->aAll/nAll. Set *pbEof\n** to true if EOF is reached.\n*/\nstatic void fts3EvalDlPhraseNext(\n  Fts3Table *pTab,\n  Fts3Doclist *pDL,\n  u8 *pbEof\n){\n  char *pIter;                            /* Used to iterate through aAll */\n  char *pEnd = &pDL->aAll[pDL->nAll];     /* 1 byte past end of aAll */\n \n  if( pDL->pNextDocid ){\n    pIter = pDL->pNextDocid;\n  }else{\n    pIter = pDL->aAll;\n  }\n\n  if( pIter>=pEnd ){\n    /* We have already reached the end of this doclist. EOF. */\n    *pbEof = 1;\n  }else{\n    sqlite3_int64 iDelta;\n    pIter += sqlite3Fts3GetVarint(pIter, &iDelta);\n    if( pTab->bDescIdx==0 || pDL->pNextDocid==0 ){\n      pDL->iDocid += iDelta;\n    }else{\n      pDL->iDocid -= iDelta;\n    }\n    pDL->pList = pIter;\n    fts3PoslistCopy(0, &pIter);\n    pDL->nList = (int)(pIter - pDL->pList);\n\n    /* pIter now points just past the 0x00 that terminates the position-\n    ** list for document pDL->iDocid. However, if this position-list was\n    ** edited in place by fts3EvalNearTrim(), then pIter may not actually\n    ** point to the start of the next docid value. The following line deals\n    ** with this case by advancing pIter past the zero-padding added by\n    ** fts3EvalNearTrim().  */\n    while( pIter<pEnd && *pIter==0 ) pIter++;\n\n    pDL->pNextDocid = pIter;\n    assert( pIter>=&pDL->aAll[pDL->nAll] || *pIter );\n    *pbEof = 0;\n  }\n}\n\n/*\n** Helper type used by fts3EvalIncrPhraseNext() and incrPhraseTokenNext().\n*/\ntypedef struct TokenDoclist TokenDoclist;\nstruct TokenDoclist {\n  int bIgnore;\n  sqlite3_int64 iDocid;\n  char *pList;\n  int nList;\n};\n\n/*\n** Token pToken is an incrementally loaded token that is part of a \n** multi-token phrase. Advance it to the next matching document in the\n** database and populate output variable *p with the details of the new\n** entry. Or, if the iterator has reached EOF, set *pbEof to true.\n**\n** If an error occurs, return an SQLite error code. Otherwise, return \n** SQLITE_OK.\n*/\nstatic int incrPhraseTokenNext(\n  Fts3Table *pTab,                /* Virtual table handle */\n  Fts3Phrase *pPhrase,            /* Phrase to advance token of */\n  int iToken,                     /* Specific token to advance */\n  TokenDoclist *p,                /* OUT: Docid and doclist for new entry */\n  u8 *pbEof                       /* OUT: True if iterator is at EOF */\n){\n  int rc = SQLITE_OK;\n\n  if( pPhrase->iDoclistToken==iToken ){\n    assert( p->bIgnore==0 );\n    assert( pPhrase->aToken[iToken].pSegcsr==0 );\n    fts3EvalDlPhraseNext(pTab, &pPhrase->doclist, pbEof);\n    p->pList = pPhrase->doclist.pList;\n    p->nList = pPhrase->doclist.nList;\n    p->iDocid = pPhrase->doclist.iDocid;\n  }else{\n    Fts3PhraseToken *pToken = &pPhrase->aToken[iToken];\n    assert( pToken->pDeferred==0 );\n    assert( pToken->pSegcsr || pPhrase->iDoclistToken>=0 );\n    if( pToken->pSegcsr ){\n      assert( p->bIgnore==0 );\n      rc = sqlite3Fts3MsrIncrNext(\n          pTab, pToken->pSegcsr, &p->iDocid, &p->pList, &p->nList\n      );\n      if( p->pList==0 ) *pbEof = 1;\n    }else{\n      p->bIgnore = 1;\n    }\n  }\n\n  return rc;\n}\n\n\n/*\n** The phrase iterator passed as the second argument:\n**\n**   * features at least one token that uses an incremental doclist, and \n**\n**   * does not contain any deferred tokens.\n**\n** Advance it to the next matching documnent in the database and populate\n** the Fts3Doclist.pList and nList fields. \n**\n** If there is no \"next\" entry and no error occurs, then *pbEof is set to\n** 1 before returning. Otherwise, if no error occurs and the iterator is\n** successfully advanced, *pbEof is set to 0.\n**\n** If an error occurs, return an SQLite error code. Otherwise, return \n** SQLITE_OK.\n*/\nstatic int fts3EvalIncrPhraseNext(\n  Fts3Cursor *pCsr,               /* FTS Cursor handle */\n  Fts3Phrase *p,                  /* Phrase object to advance to next docid */\n  u8 *pbEof                       /* OUT: Set to 1 if EOF */\n){\n  int rc = SQLITE_OK;\n  Fts3Doclist *pDL = &p->doclist;\n  Fts3Table *pTab = (Fts3Table *)pCsr->base.pVtab;\n  u8 bEof = 0;\n\n  /* This is only called if it is guaranteed that the phrase has at least\n  ** one incremental token. In which case the bIncr flag is set. */\n  assert( p->bIncr==1 );\n\n  if( p->nToken==1 ){\n    rc = sqlite3Fts3MsrIncrNext(pTab, p->aToken[0].pSegcsr, \n        &pDL->iDocid, &pDL->pList, &pDL->nList\n    );\n    if( pDL->pList==0 ) bEof = 1;\n  }else{\n    int bDescDoclist = pCsr->bDesc;\n    struct TokenDoclist a[MAX_INCR_PHRASE_TOKENS];\n\n    memset(a, 0, sizeof(a));\n    assert( p->nToken<=MAX_INCR_PHRASE_TOKENS );\n    assert( p->iDoclistToken<MAX_INCR_PHRASE_TOKENS );\n\n    while( bEof==0 ){\n      int bMaxSet = 0;\n      sqlite3_int64 iMax = 0;     /* Largest docid for all iterators */\n      int i;                      /* Used to iterate through tokens */\n\n      /* Advance the iterator for each token in the phrase once. */\n      for(i=0; rc==SQLITE_OK && i<p->nToken && bEof==0; i++){\n        rc = incrPhraseTokenNext(pTab, p, i, &a[i], &bEof);\n        if( a[i].bIgnore==0 && (bMaxSet==0 || DOCID_CMP(iMax, a[i].iDocid)<0) ){\n          iMax = a[i].iDocid;\n          bMaxSet = 1;\n        }\n      }\n      assert( rc!=SQLITE_OK || (p->nToken>=1 && a[p->nToken-1].bIgnore==0) );\n      assert( rc!=SQLITE_OK || bMaxSet );\n\n      /* Keep advancing iterators until they all point to the same document */\n      for(i=0; i<p->nToken; i++){\n        while( rc==SQLITE_OK && bEof==0 \n            && a[i].bIgnore==0 && DOCID_CMP(a[i].iDocid, iMax)<0 \n        ){\n          rc = incrPhraseTokenNext(pTab, p, i, &a[i], &bEof);\n          if( DOCID_CMP(a[i].iDocid, iMax)>0 ){\n            iMax = a[i].iDocid;\n            i = 0;\n          }\n        }\n      }\n\n      /* Check if the current entries really are a phrase match */\n      if( bEof==0 ){\n        int nList = 0;\n        int nByte = a[p->nToken-1].nList;\n        char *aDoclist = sqlite3_malloc(nByte+1);\n        if( !aDoclist ) return SQLITE_NOMEM;\n        memcpy(aDoclist, a[p->nToken-1].pList, nByte+1);\n\n        for(i=0; i<(p->nToken-1); i++){\n          if( a[i].bIgnore==0 ){\n            char *pL = a[i].pList;\n            char *pR = aDoclist;\n            char *pOut = aDoclist;\n            int nDist = p->nToken-1-i;\n            int res = fts3PoslistPhraseMerge(&pOut, nDist, 0, 1, &pL, &pR);\n            if( res==0 ) break;\n            nList = (int)(pOut - aDoclist);\n          }\n        }\n        if( i==(p->nToken-1) ){\n          pDL->iDocid = iMax;\n          pDL->pList = aDoclist;\n          pDL->nList = nList;\n          pDL->bFreeList = 1;\n          break;\n        }\n        sqlite3_free(aDoclist);\n      }\n    }\n  }\n\n  *pbEof = bEof;\n  return rc;\n}\n\n/*\n** Attempt to move the phrase iterator to point to the next matching docid. \n** If an error occurs, return an SQLite error code. Otherwise, return \n** SQLITE_OK.\n**\n** If there is no \"next\" entry and no error occurs, then *pbEof is set to\n** 1 before returning. Otherwise, if no error occurs and the iterator is\n** successfully advanced, *pbEof is set to 0.\n*/\nstatic int fts3EvalPhraseNext(\n  Fts3Cursor *pCsr,               /* FTS Cursor handle */\n  Fts3Phrase *p,                  /* Phrase object to advance to next docid */\n  u8 *pbEof                       /* OUT: Set to 1 if EOF */\n){\n  int rc = SQLITE_OK;\n  Fts3Doclist *pDL = &p->doclist;\n  Fts3Table *pTab = (Fts3Table *)pCsr->base.pVtab;\n\n  if( p->bIncr ){\n    rc = fts3EvalIncrPhraseNext(pCsr, p, pbEof);\n  }else if( pCsr->bDesc!=pTab->bDescIdx && pDL->nAll ){\n    sqlite3Fts3DoclistPrev(pTab->bDescIdx, pDL->aAll, pDL->nAll, \n        &pDL->pNextDocid, &pDL->iDocid, &pDL->nList, pbEof\n    );\n    pDL->pList = pDL->pNextDocid;\n  }else{\n    fts3EvalDlPhraseNext(pTab, pDL, pbEof);\n  }\n\n  return rc;\n}\n\n/*\n**\n** If *pRc is not SQLITE_OK when this function is called, it is a no-op.\n** Otherwise, fts3EvalPhraseStart() is called on all phrases within the\n** expression. Also the Fts3Expr.bDeferred variable is set to true for any\n** expressions for which all descendent tokens are deferred.\n**\n** If parameter bOptOk is zero, then it is guaranteed that the\n** Fts3Phrase.doclist.aAll/nAll variables contain the entire doclist for\n** each phrase in the expression (subject to deferred token processing).\n** Or, if bOptOk is non-zero, then one or more tokens within the expression\n** may be loaded incrementally, meaning doclist.aAll/nAll is not available.\n**\n** If an error occurs within this function, *pRc is set to an SQLite error\n** code before returning.\n*/\nstatic void fts3EvalStartReaders(\n  Fts3Cursor *pCsr,               /* FTS Cursor handle */\n  Fts3Expr *pExpr,                /* Expression to initialize phrases in */\n  int *pRc                        /* IN/OUT: Error code */\n){\n  if( pExpr && SQLITE_OK==*pRc ){\n    if( pExpr->eType==FTSQUERY_PHRASE ){\n      int nToken = pExpr->pPhrase->nToken;\n      if( nToken ){\n        int i;\n        for(i=0; i<nToken; i++){\n          if( pExpr->pPhrase->aToken[i].pDeferred==0 ) break;\n        }\n        pExpr->bDeferred = (i==nToken);\n      }\n      *pRc = fts3EvalPhraseStart(pCsr, 1, pExpr->pPhrase);\n    }else{\n      fts3EvalStartReaders(pCsr, pExpr->pLeft, pRc);\n      fts3EvalStartReaders(pCsr, pExpr->pRight, pRc);\n      pExpr->bDeferred = (pExpr->pLeft->bDeferred && pExpr->pRight->bDeferred);\n    }\n  }\n}\n\n/*\n** An array of the following structures is assembled as part of the process\n** of selecting tokens to defer before the query starts executing (as part\n** of the xFilter() method). There is one element in the array for each\n** token in the FTS expression.\n**\n** Tokens are divided into AND/NEAR clusters. All tokens in a cluster belong\n** to phrases that are connected only by AND and NEAR operators (not OR or\n** NOT). When determining tokens to defer, each AND/NEAR cluster is considered\n** separately. The root of a tokens AND/NEAR cluster is stored in \n** Fts3TokenAndCost.pRoot.\n*/\ntypedef struct Fts3TokenAndCost Fts3TokenAndCost;\nstruct Fts3TokenAndCost {\n  Fts3Phrase *pPhrase;            /* The phrase the token belongs to */\n  int iToken;                     /* Position of token in phrase */\n  Fts3PhraseToken *pToken;        /* The token itself */\n  Fts3Expr *pRoot;                /* Root of NEAR/AND cluster */\n  int nOvfl;                      /* Number of overflow pages to load doclist */\n  int iCol;                       /* The column the token must match */\n};\n\n/*\n** This function is used to populate an allocated Fts3TokenAndCost array.\n**\n** If *pRc is not SQLITE_OK when this function is called, it is a no-op.\n** Otherwise, if an error occurs during execution, *pRc is set to an\n** SQLite error code.\n*/\nstatic void fts3EvalTokenCosts(\n  Fts3Cursor *pCsr,               /* FTS Cursor handle */\n  Fts3Expr *pRoot,                /* Root of current AND/NEAR cluster */\n  Fts3Expr *pExpr,                /* Expression to consider */\n  Fts3TokenAndCost **ppTC,        /* Write new entries to *(*ppTC)++ */\n  Fts3Expr ***ppOr,               /* Write new OR root to *(*ppOr)++ */\n  int *pRc                        /* IN/OUT: Error code */\n){\n  if( *pRc==SQLITE_OK ){\n    if( pExpr->eType==FTSQUERY_PHRASE ){\n      Fts3Phrase *pPhrase = pExpr->pPhrase;\n      int i;\n      for(i=0; *pRc==SQLITE_OK && i<pPhrase->nToken; i++){\n        Fts3TokenAndCost *pTC = (*ppTC)++;\n        pTC->pPhrase = pPhrase;\n        pTC->iToken = i;\n        pTC->pRoot = pRoot;\n        pTC->pToken = &pPhrase->aToken[i];\n        pTC->iCol = pPhrase->iColumn;\n        *pRc = sqlite3Fts3MsrOvfl(pCsr, pTC->pToken->pSegcsr, &pTC->nOvfl);\n      }\n    }else if( pExpr->eType!=FTSQUERY_NOT ){\n      assert( pExpr->eType==FTSQUERY_OR\n           || pExpr->eType==FTSQUERY_AND\n           || pExpr->eType==FTSQUERY_NEAR\n      );\n      assert( pExpr->pLeft && pExpr->pRight );\n      if( pExpr->eType==FTSQUERY_OR ){\n        pRoot = pExpr->pLeft;\n        **ppOr = pRoot;\n        (*ppOr)++;\n      }\n      fts3EvalTokenCosts(pCsr, pRoot, pExpr->pLeft, ppTC, ppOr, pRc);\n      if( pExpr->eType==FTSQUERY_OR ){\n        pRoot = pExpr->pRight;\n        **ppOr = pRoot;\n        (*ppOr)++;\n      }\n      fts3EvalTokenCosts(pCsr, pRoot, pExpr->pRight, ppTC, ppOr, pRc);\n    }\n  }\n}\n\n/*\n** Determine the average document (row) size in pages. If successful,\n** write this value to *pnPage and return SQLITE_OK. Otherwise, return\n** an SQLite error code.\n**\n** The average document size in pages is calculated by first calculating \n** determining the average size in bytes, B. If B is less than the amount\n** of data that will fit on a single leaf page of an intkey table in\n** this database, then the average docsize is 1. Otherwise, it is 1 plus\n** the number of overflow pages consumed by a record B bytes in size.\n*/\nstatic int fts3EvalAverageDocsize(Fts3Cursor *pCsr, int *pnPage){\n  int rc = SQLITE_OK;\n  if( pCsr->nRowAvg==0 ){\n    /* The average document size, which is required to calculate the cost\n    ** of each doclist, has not yet been determined. Read the required \n    ** data from the %_stat table to calculate it.\n    **\n    ** Entry 0 of the %_stat table is a blob containing (nCol+1) FTS3 \n    ** varints, where nCol is the number of columns in the FTS3 table.\n    ** The first varint is the number of documents currently stored in\n    ** the table. The following nCol varints contain the total amount of\n    ** data stored in all rows of each column of the table, from left\n    ** to right.\n    */\n    Fts3Table *p = (Fts3Table*)pCsr->base.pVtab;\n    sqlite3_stmt *pStmt;\n    sqlite3_int64 nDoc = 0;\n    sqlite3_int64 nByte = 0;\n    const char *pEnd;\n    const char *a;\n\n    rc = sqlite3Fts3SelectDoctotal(p, &pStmt);\n    if( rc!=SQLITE_OK ) return rc;\n    a = sqlite3_column_blob(pStmt, 0);\n    assert( a );\n\n    pEnd = &a[sqlite3_column_bytes(pStmt, 0)];\n    a += sqlite3Fts3GetVarint(a, &nDoc);\n    while( a<pEnd ){\n      a += sqlite3Fts3GetVarint(a, &nByte);\n    }\n    if( nDoc==0 || nByte==0 ){\n      sqlite3_reset(pStmt);\n      return FTS_CORRUPT_VTAB;\n    }\n\n    pCsr->nDoc = nDoc;\n    pCsr->nRowAvg = (int)(((nByte / nDoc) + p->nPgsz) / p->nPgsz);\n    assert( pCsr->nRowAvg>0 ); \n    rc = sqlite3_reset(pStmt);\n  }\n\n  *pnPage = pCsr->nRowAvg;\n  return rc;\n}\n\n/*\n** This function is called to select the tokens (if any) that will be \n** deferred. The array aTC[] has already been populated when this is\n** called.\n**\n** This function is called once for each AND/NEAR cluster in the \n** expression. Each invocation determines which tokens to defer within\n** the cluster with root node pRoot. See comments above the definition\n** of struct Fts3TokenAndCost for more details.\n**\n** If no error occurs, SQLITE_OK is returned and sqlite3Fts3DeferToken()\n** called on each token to defer. Otherwise, an SQLite error code is\n** returned.\n*/\nstatic int fts3EvalSelectDeferred(\n  Fts3Cursor *pCsr,               /* FTS Cursor handle */\n  Fts3Expr *pRoot,                /* Consider tokens with this root node */\n  Fts3TokenAndCost *aTC,          /* Array of expression tokens and costs */\n  int nTC                         /* Number of entries in aTC[] */\n){\n  Fts3Table *pTab = (Fts3Table *)pCsr->base.pVtab;\n  int nDocSize = 0;               /* Number of pages per doc loaded */\n  int rc = SQLITE_OK;             /* Return code */\n  int ii;                         /* Iterator variable for various purposes */\n  int nOvfl = 0;                  /* Total overflow pages used by doclists */\n  int nToken = 0;                 /* Total number of tokens in cluster */\n\n  int nMinEst = 0;                /* The minimum count for any phrase so far. */\n  int nLoad4 = 1;                 /* (Phrases that will be loaded)^4. */\n\n  /* Tokens are never deferred for FTS tables created using the content=xxx\n  ** option. The reason being that it is not guaranteed that the content\n  ** table actually contains the same data as the index. To prevent this from\n  ** causing any problems, the deferred token optimization is completely\n  ** disabled for content=xxx tables. */\n  if( pTab->zContentTbl ){\n    return SQLITE_OK;\n  }\n\n  /* Count the tokens in this AND/NEAR cluster. If none of the doclists\n  ** associated with the tokens spill onto overflow pages, or if there is\n  ** only 1 token, exit early. No tokens to defer in this case. */\n  for(ii=0; ii<nTC; ii++){\n    if( aTC[ii].pRoot==pRoot ){\n      nOvfl += aTC[ii].nOvfl;\n      nToken++;\n    }\n  }\n  if( nOvfl==0 || nToken<2 ) return SQLITE_OK;\n\n  /* Obtain the average docsize (in pages). */\n  rc = fts3EvalAverageDocsize(pCsr, &nDocSize);\n  assert( rc!=SQLITE_OK || nDocSize>0 );\n\n\n  /* Iterate through all tokens in this AND/NEAR cluster, in ascending order \n  ** of the number of overflow pages that will be loaded by the pager layer \n  ** to retrieve the entire doclist for the token from the full-text index.\n  ** Load the doclists for tokens that are either:\n  **\n  **   a. The cheapest token in the entire query (i.e. the one visited by the\n  **      first iteration of this loop), or\n  **\n  **   b. Part of a multi-token phrase.\n  **\n  ** After each token doclist is loaded, merge it with the others from the\n  ** same phrase and count the number of documents that the merged doclist\n  ** contains. Set variable \"nMinEst\" to the smallest number of documents in \n  ** any phrase doclist for which 1 or more token doclists have been loaded.\n  ** Let nOther be the number of other phrases for which it is certain that\n  ** one or more tokens will not be deferred.\n  **\n  ** Then, for each token, defer it if loading the doclist would result in\n  ** loading N or more overflow pages into memory, where N is computed as:\n  **\n  **    (nMinEst + 4^nOther - 1) / (4^nOther)\n  */\n  for(ii=0; ii<nToken && rc==SQLITE_OK; ii++){\n    int iTC;                      /* Used to iterate through aTC[] array. */\n    Fts3TokenAndCost *pTC = 0;    /* Set to cheapest remaining token. */\n\n    /* Set pTC to point to the cheapest remaining token. */\n    for(iTC=0; iTC<nTC; iTC++){\n      if( aTC[iTC].pToken && aTC[iTC].pRoot==pRoot \n       && (!pTC || aTC[iTC].nOvfl<pTC->nOvfl) \n      ){\n        pTC = &aTC[iTC];\n      }\n    }\n    assert( pTC );\n\n    if( ii && pTC->nOvfl>=((nMinEst+(nLoad4/4)-1)/(nLoad4/4))*nDocSize ){\n      /* The number of overflow pages to load for this (and therefore all\n      ** subsequent) tokens is greater than the estimated number of pages \n      ** that will be loaded if all subsequent tokens are deferred.\n      */\n      Fts3PhraseToken *pToken = pTC->pToken;\n      rc = sqlite3Fts3DeferToken(pCsr, pToken, pTC->iCol);\n      fts3SegReaderCursorFree(pToken->pSegcsr);\n      pToken->pSegcsr = 0;\n    }else{\n      /* Set nLoad4 to the value of (4^nOther) for the next iteration of the\n      ** for-loop. Except, limit the value to 2^24 to prevent it from \n      ** overflowing the 32-bit integer it is stored in. */\n      if( ii<12 ) nLoad4 = nLoad4*4;\n\n      if( ii==0 || (pTC->pPhrase->nToken>1 && ii!=nToken-1) ){\n        /* Either this is the cheapest token in the entire query, or it is\n        ** part of a multi-token phrase. Either way, the entire doclist will\n        ** (eventually) be loaded into memory. It may as well be now. */\n        Fts3PhraseToken *pToken = pTC->pToken;\n        int nList = 0;\n        char *pList = 0;\n        rc = fts3TermSelect(pTab, pToken, pTC->iCol, &nList, &pList);\n        assert( rc==SQLITE_OK || pList==0 );\n        if( rc==SQLITE_OK ){\n          rc = fts3EvalPhraseMergeToken(\n              pTab, pTC->pPhrase, pTC->iToken,pList,nList\n          );\n        }\n        if( rc==SQLITE_OK ){\n          int nCount;\n          nCount = fts3DoclistCountDocids(\n              pTC->pPhrase->doclist.aAll, pTC->pPhrase->doclist.nAll\n          );\n          if( ii==0 || nCount<nMinEst ) nMinEst = nCount;\n        }\n      }\n    }\n    pTC->pToken = 0;\n  }\n\n  return rc;\n}\n\n/*\n** This function is called from within the xFilter method. It initializes\n** the full-text query currently stored in pCsr->pExpr. To iterate through\n** the results of a query, the caller does:\n**\n**    fts3EvalStart(pCsr);\n**    while( 1 ){\n**      fts3EvalNext(pCsr);\n**      if( pCsr->bEof ) break;\n**      ... return row pCsr->iPrevId to the caller ...\n**    }\n*/\nstatic int fts3EvalStart(Fts3Cursor *pCsr){\n  Fts3Table *pTab = (Fts3Table *)pCsr->base.pVtab;\n  int rc = SQLITE_OK;\n  int nToken = 0;\n  int nOr = 0;\n\n  /* Allocate a MultiSegReader for each token in the expression. */\n  fts3EvalAllocateReaders(pCsr, pCsr->pExpr, &nToken, &nOr, &rc);\n\n  /* Determine which, if any, tokens in the expression should be deferred. */\n#ifndef SQLITE_DISABLE_FTS4_DEFERRED\n  if( rc==SQLITE_OK && nToken>1 && pTab->bFts4 ){\n    Fts3TokenAndCost *aTC;\n    Fts3Expr **apOr;\n    aTC = (Fts3TokenAndCost *)sqlite3_malloc(\n        sizeof(Fts3TokenAndCost) * nToken\n      + sizeof(Fts3Expr *) * nOr * 2\n    );\n    apOr = (Fts3Expr **)&aTC[nToken];\n\n    if( !aTC ){\n      rc = SQLITE_NOMEM;\n    }else{\n      int ii;\n      Fts3TokenAndCost *pTC = aTC;\n      Fts3Expr **ppOr = apOr;\n\n      fts3EvalTokenCosts(pCsr, 0, pCsr->pExpr, &pTC, &ppOr, &rc);\n      nToken = (int)(pTC-aTC);\n      nOr = (int)(ppOr-apOr);\n\n      if( rc==SQLITE_OK ){\n        rc = fts3EvalSelectDeferred(pCsr, 0, aTC, nToken);\n        for(ii=0; rc==SQLITE_OK && ii<nOr; ii++){\n          rc = fts3EvalSelectDeferred(pCsr, apOr[ii], aTC, nToken);\n        }\n      }\n\n      sqlite3_free(aTC);\n    }\n  }\n#endif\n\n  fts3EvalStartReaders(pCsr, pCsr->pExpr, &rc);\n  return rc;\n}\n\n/*\n** Invalidate the current position list for phrase pPhrase.\n*/\nstatic void fts3EvalInvalidatePoslist(Fts3Phrase *pPhrase){\n  if( pPhrase->doclist.bFreeList ){\n    sqlite3_free(pPhrase->doclist.pList);\n  }\n  pPhrase->doclist.pList = 0;\n  pPhrase->doclist.nList = 0;\n  pPhrase->doclist.bFreeList = 0;\n}\n\n/*\n** This function is called to edit the position list associated with\n** the phrase object passed as the fifth argument according to a NEAR\n** condition. For example:\n**\n**     abc NEAR/5 \"def ghi\"\n**\n** Parameter nNear is passed the NEAR distance of the expression (5 in\n** the example above). When this function is called, *paPoslist points to\n** the position list, and *pnToken is the number of phrase tokens in, the\n** phrase on the other side of the NEAR operator to pPhrase. For example,\n** if pPhrase refers to the \"def ghi\" phrase, then *paPoslist points to\n** the position list associated with phrase \"abc\".\n**\n** All positions in the pPhrase position list that are not sufficiently\n** close to a position in the *paPoslist position list are removed. If this\n** leaves 0 positions, zero is returned. Otherwise, non-zero.\n**\n** Before returning, *paPoslist is set to point to the position lsit \n** associated with pPhrase. And *pnToken is set to the number of tokens in\n** pPhrase.\n*/\nstatic int fts3EvalNearTrim(\n  int nNear,                      /* NEAR distance. As in \"NEAR/nNear\". */\n  char *aTmp,                     /* Temporary space to use */\n  char **paPoslist,               /* IN/OUT: Position list */\n  int *pnToken,                   /* IN/OUT: Tokens in phrase of *paPoslist */\n  Fts3Phrase *pPhrase             /* The phrase object to trim the doclist of */\n){\n  int nParam1 = nNear + pPhrase->nToken;\n  int nParam2 = nNear + *pnToken;\n  int nNew;\n  char *p2; \n  char *pOut; \n  int res;\n\n  assert( pPhrase->doclist.pList );\n\n  p2 = pOut = pPhrase->doclist.pList;\n  res = fts3PoslistNearMerge(\n    &pOut, aTmp, nParam1, nParam2, paPoslist, &p2\n  );\n  if( res ){\n    nNew = (int)(pOut - pPhrase->doclist.pList) - 1;\n    assert( pPhrase->doclist.pList[nNew]=='\\0' );\n    assert( nNew<=pPhrase->doclist.nList && nNew>0 );\n    memset(&pPhrase->doclist.pList[nNew], 0, pPhrase->doclist.nList - nNew);\n    pPhrase->doclist.nList = nNew;\n    *paPoslist = pPhrase->doclist.pList;\n    *pnToken = pPhrase->nToken;\n  }\n\n  return res;\n}\n\n/*\n** This function is a no-op if *pRc is other than SQLITE_OK when it is called.\n** Otherwise, it advances the expression passed as the second argument to\n** point to the next matching row in the database. Expressions iterate through\n** matching rows in docid order. Ascending order if Fts3Cursor.bDesc is zero,\n** or descending if it is non-zero.\n**\n** If an error occurs, *pRc is set to an SQLite error code. Otherwise, if\n** successful, the following variables in pExpr are set:\n**\n**   Fts3Expr.bEof                (non-zero if EOF - there is no next row)\n**   Fts3Expr.iDocid              (valid if bEof==0. The docid of the next row)\n**\n** If the expression is of type FTSQUERY_PHRASE, and the expression is not\n** at EOF, then the following variables are populated with the position list\n** for the phrase for the visited row:\n**\n**   FTs3Expr.pPhrase->doclist.nList        (length of pList in bytes)\n**   FTs3Expr.pPhrase->doclist.pList        (pointer to position list)\n**\n** It says above that this function advances the expression to the next\n** matching row. This is usually true, but there are the following exceptions:\n**\n**   1. Deferred tokens are not taken into account. If a phrase consists\n**      entirely of deferred tokens, it is assumed to match every row in\n**      the db. In this case the position-list is not populated at all. \n**\n**      Or, if a phrase contains one or more deferred tokens and one or\n**      more non-deferred tokens, then the expression is advanced to the \n**      next possible match, considering only non-deferred tokens. In other\n**      words, if the phrase is \"A B C\", and \"B\" is deferred, the expression\n**      is advanced to the next row that contains an instance of \"A * C\", \n**      where \"*\" may match any single token. The position list in this case\n**      is populated as for \"A * C\" before returning.\n**\n**   2. NEAR is treated as AND. If the expression is \"x NEAR y\", it is \n**      advanced to point to the next row that matches \"x AND y\".\n** \n** See sqlite3Fts3EvalTestDeferred() for details on testing if a row is\n** really a match, taking into account deferred tokens and NEAR operators.\n*/\nstatic void fts3EvalNextRow(\n  Fts3Cursor *pCsr,               /* FTS Cursor handle */\n  Fts3Expr *pExpr,                /* Expr. to advance to next matching row */\n  int *pRc                        /* IN/OUT: Error code */\n){\n  if( *pRc==SQLITE_OK ){\n    int bDescDoclist = pCsr->bDesc;         /* Used by DOCID_CMP() macro */\n    assert( pExpr->bEof==0 );\n    pExpr->bStart = 1;\n\n    switch( pExpr->eType ){\n      case FTSQUERY_NEAR:\n      case FTSQUERY_AND: {\n        Fts3Expr *pLeft = pExpr->pLeft;\n        Fts3Expr *pRight = pExpr->pRight;\n        assert( !pLeft->bDeferred || !pRight->bDeferred );\n\n        if( pLeft->bDeferred ){\n          /* LHS is entirely deferred. So we assume it matches every row.\n          ** Advance the RHS iterator to find the next row visited. */\n          fts3EvalNextRow(pCsr, pRight, pRc);\n          pExpr->iDocid = pRight->iDocid;\n          pExpr->bEof = pRight->bEof;\n        }else if( pRight->bDeferred ){\n          /* RHS is entirely deferred. So we assume it matches every row.\n          ** Advance the LHS iterator to find the next row visited. */\n          fts3EvalNextRow(pCsr, pLeft, pRc);\n          pExpr->iDocid = pLeft->iDocid;\n          pExpr->bEof = pLeft->bEof;\n        }else{\n          /* Neither the RHS or LHS are deferred. */\n          fts3EvalNextRow(pCsr, pLeft, pRc);\n          fts3EvalNextRow(pCsr, pRight, pRc);\n          while( !pLeft->bEof && !pRight->bEof && *pRc==SQLITE_OK ){\n            sqlite3_int64 iDiff = DOCID_CMP(pLeft->iDocid, pRight->iDocid);\n            if( iDiff==0 ) break;\n            if( iDiff<0 ){\n              fts3EvalNextRow(pCsr, pLeft, pRc);\n            }else{\n              fts3EvalNextRow(pCsr, pRight, pRc);\n            }\n          }\n          pExpr->iDocid = pLeft->iDocid;\n          pExpr->bEof = (pLeft->bEof || pRight->bEof);\n          if( pExpr->eType==FTSQUERY_NEAR && pExpr->bEof ){\n            assert( pRight->eType==FTSQUERY_PHRASE );\n            if( pRight->pPhrase->doclist.aAll ){\n              Fts3Doclist *pDl = &pRight->pPhrase->doclist;\n              while( *pRc==SQLITE_OK && pRight->bEof==0 ){\n                memset(pDl->pList, 0, pDl->nList);\n                fts3EvalNextRow(pCsr, pRight, pRc);\n              }\n            }\n            if( pLeft->pPhrase && pLeft->pPhrase->doclist.aAll ){\n              Fts3Doclist *pDl = &pLeft->pPhrase->doclist;\n              while( *pRc==SQLITE_OK && pLeft->bEof==0 ){\n                memset(pDl->pList, 0, pDl->nList);\n                fts3EvalNextRow(pCsr, pLeft, pRc);\n              }\n            }\n          }\n        }\n        break;\n      }\n  \n      case FTSQUERY_OR: {\n        Fts3Expr *pLeft = pExpr->pLeft;\n        Fts3Expr *pRight = pExpr->pRight;\n        sqlite3_int64 iCmp = DOCID_CMP(pLeft->iDocid, pRight->iDocid);\n\n        assert( pLeft->bStart || pLeft->iDocid==pRight->iDocid );\n        assert( pRight->bStart || pLeft->iDocid==pRight->iDocid );\n\n        if( pRight->bEof || (pLeft->bEof==0 && iCmp<0) ){\n          fts3EvalNextRow(pCsr, pLeft, pRc);\n        }else if( pLeft->bEof || iCmp>0 ){\n          fts3EvalNextRow(pCsr, pRight, pRc);\n        }else{\n          fts3EvalNextRow(pCsr, pLeft, pRc);\n          fts3EvalNextRow(pCsr, pRight, pRc);\n        }\n\n        pExpr->bEof = (pLeft->bEof && pRight->bEof);\n        iCmp = DOCID_CMP(pLeft->iDocid, pRight->iDocid);\n        if( pRight->bEof || (pLeft->bEof==0 &&  iCmp<0) ){\n          pExpr->iDocid = pLeft->iDocid;\n        }else{\n          pExpr->iDocid = pRight->iDocid;\n        }\n\n        break;\n      }\n\n      case FTSQUERY_NOT: {\n        Fts3Expr *pLeft = pExpr->pLeft;\n        Fts3Expr *pRight = pExpr->pRight;\n\n        if( pRight->bStart==0 ){\n          fts3EvalNextRow(pCsr, pRight, pRc);\n          assert( *pRc!=SQLITE_OK || pRight->bStart );\n        }\n\n        fts3EvalNextRow(pCsr, pLeft, pRc);\n        if( pLeft->bEof==0 ){\n          while( !*pRc \n              && !pRight->bEof \n              && DOCID_CMP(pLeft->iDocid, pRight->iDocid)>0 \n          ){\n            fts3EvalNextRow(pCsr, pRight, pRc);\n          }\n        }\n        pExpr->iDocid = pLeft->iDocid;\n        pExpr->bEof = pLeft->bEof;\n        break;\n      }\n\n      default: {\n        Fts3Phrase *pPhrase = pExpr->pPhrase;\n        fts3EvalInvalidatePoslist(pPhrase);\n        *pRc = fts3EvalPhraseNext(pCsr, pPhrase, &pExpr->bEof);\n        pExpr->iDocid = pPhrase->doclist.iDocid;\n        break;\n      }\n    }\n  }\n}\n\n/*\n** If *pRc is not SQLITE_OK, or if pExpr is not the root node of a NEAR\n** cluster, then this function returns 1 immediately.\n**\n** Otherwise, it checks if the current row really does match the NEAR \n** expression, using the data currently stored in the position lists \n** (Fts3Expr->pPhrase.doclist.pList/nList) for each phrase in the expression. \n**\n** If the current row is a match, the position list associated with each\n** phrase in the NEAR expression is edited in place to contain only those\n** phrase instances sufficiently close to their peers to satisfy all NEAR\n** constraints. In this case it returns 1. If the NEAR expression does not \n** match the current row, 0 is returned. The position lists may or may not\n** be edited if 0 is returned.\n*/\nstatic int fts3EvalNearTest(Fts3Expr *pExpr, int *pRc){\n  int res = 1;\n\n  /* The following block runs if pExpr is the root of a NEAR query.\n  ** For example, the query:\n  **\n  **         \"w\" NEAR \"x\" NEAR \"y\" NEAR \"z\"\n  **\n  ** which is represented in tree form as:\n  **\n  **                               |\n  **                          +--NEAR--+      <-- root of NEAR query\n  **                          |        |\n  **                     +--NEAR--+   \"z\"\n  **                     |        |\n  **                +--NEAR--+   \"y\"\n  **                |        |\n  **               \"w\"      \"x\"\n  **\n  ** The right-hand child of a NEAR node is always a phrase. The \n  ** left-hand child may be either a phrase or a NEAR node. There are\n  ** no exceptions to this - it's the way the parser in fts3_expr.c works.\n  */\n  if( *pRc==SQLITE_OK \n   && pExpr->eType==FTSQUERY_NEAR \n   && (pExpr->pParent==0 || pExpr->pParent->eType!=FTSQUERY_NEAR)\n  ){\n    Fts3Expr *p; \n    int nTmp = 0;                 /* Bytes of temp space */\n    char *aTmp;                   /* Temp space for PoslistNearMerge() */\n\n    /* Allocate temporary working space. */\n    for(p=pExpr; p->pLeft; p=p->pLeft){\n      assert( p->pRight->pPhrase->doclist.nList>0 );\n      nTmp += p->pRight->pPhrase->doclist.nList;\n    }\n    nTmp += p->pPhrase->doclist.nList;\n    aTmp = sqlite3_malloc(nTmp*2);\n    if( !aTmp ){\n      *pRc = SQLITE_NOMEM;\n      res = 0;\n    }else{\n      char *aPoslist = p->pPhrase->doclist.pList;\n      int nToken = p->pPhrase->nToken;\n\n      for(p=p->pParent;res && p && p->eType==FTSQUERY_NEAR; p=p->pParent){\n        Fts3Phrase *pPhrase = p->pRight->pPhrase;\n        int nNear = p->nNear;\n        res = fts3EvalNearTrim(nNear, aTmp, &aPoslist, &nToken, pPhrase);\n      }\n\n      aPoslist = pExpr->pRight->pPhrase->doclist.pList;\n      nToken = pExpr->pRight->pPhrase->nToken;\n      for(p=pExpr->pLeft; p && res; p=p->pLeft){\n        int nNear;\n        Fts3Phrase *pPhrase;\n        assert( p->pParent && p->pParent->pLeft==p );\n        nNear = p->pParent->nNear;\n        pPhrase = (\n            p->eType==FTSQUERY_NEAR ? p->pRight->pPhrase : p->pPhrase\n        );\n        res = fts3EvalNearTrim(nNear, aTmp, &aPoslist, &nToken, pPhrase);\n      }\n    }\n\n    sqlite3_free(aTmp);\n  }\n\n  return res;\n}\n\n/*\n** This function is a helper function for sqlite3Fts3EvalTestDeferred().\n** Assuming no error occurs or has occurred, It returns non-zero if the\n** expression passed as the second argument matches the row that pCsr \n** currently points to, or zero if it does not.\n**\n** If *pRc is not SQLITE_OK when this function is called, it is a no-op.\n** If an error occurs during execution of this function, *pRc is set to \n** the appropriate SQLite error code. In this case the returned value is \n** undefined.\n*/\nstatic int fts3EvalTestExpr(\n  Fts3Cursor *pCsr,               /* FTS cursor handle */\n  Fts3Expr *pExpr,                /* Expr to test. May or may not be root. */\n  int *pRc                        /* IN/OUT: Error code */\n){\n  int bHit = 1;                   /* Return value */\n  if( *pRc==SQLITE_OK ){\n    switch( pExpr->eType ){\n      case FTSQUERY_NEAR:\n      case FTSQUERY_AND:\n        bHit = (\n            fts3EvalTestExpr(pCsr, pExpr->pLeft, pRc)\n         && fts3EvalTestExpr(pCsr, pExpr->pRight, pRc)\n         && fts3EvalNearTest(pExpr, pRc)\n        );\n\n        /* If the NEAR expression does not match any rows, zero the doclist for \n        ** all phrases involved in the NEAR. This is because the snippet(),\n        ** offsets() and matchinfo() functions are not supposed to recognize \n        ** any instances of phrases that are part of unmatched NEAR queries. \n        ** For example if this expression:\n        **\n        **    ... MATCH 'a OR (b NEAR c)'\n        **\n        ** is matched against a row containing:\n        **\n        **        'a b d e'\n        **\n        ** then any snippet() should ony highlight the \"a\" term, not the \"b\"\n        ** (as \"b\" is part of a non-matching NEAR clause).\n        */\n        if( bHit==0 \n         && pExpr->eType==FTSQUERY_NEAR \n         && (pExpr->pParent==0 || pExpr->pParent->eType!=FTSQUERY_NEAR)\n        ){\n          Fts3Expr *p;\n          for(p=pExpr; p->pPhrase==0; p=p->pLeft){\n            if( p->pRight->iDocid==pCsr->iPrevId ){\n              fts3EvalInvalidatePoslist(p->pRight->pPhrase);\n            }\n          }\n          if( p->iDocid==pCsr->iPrevId ){\n            fts3EvalInvalidatePoslist(p->pPhrase);\n          }\n        }\n\n        break;\n\n      case FTSQUERY_OR: {\n        int bHit1 = fts3EvalTestExpr(pCsr, pExpr->pLeft, pRc);\n        int bHit2 = fts3EvalTestExpr(pCsr, pExpr->pRight, pRc);\n        bHit = bHit1 || bHit2;\n        break;\n      }\n\n      case FTSQUERY_NOT:\n        bHit = (\n            fts3EvalTestExpr(pCsr, pExpr->pLeft, pRc)\n         && !fts3EvalTestExpr(pCsr, pExpr->pRight, pRc)\n        );\n        break;\n\n      default: {\n#ifndef SQLITE_DISABLE_FTS4_DEFERRED\n        if( pCsr->pDeferred \n         && (pExpr->iDocid==pCsr->iPrevId || pExpr->bDeferred)\n        ){\n          Fts3Phrase *pPhrase = pExpr->pPhrase;\n          assert( pExpr->bDeferred || pPhrase->doclist.bFreeList==0 );\n          if( pExpr->bDeferred ){\n            fts3EvalInvalidatePoslist(pPhrase);\n          }\n          *pRc = fts3EvalDeferredPhrase(pCsr, pPhrase);\n          bHit = (pPhrase->doclist.pList!=0);\n          pExpr->iDocid = pCsr->iPrevId;\n        }else\n#endif\n        {\n          bHit = (pExpr->bEof==0 && pExpr->iDocid==pCsr->iPrevId);\n        }\n        break;\n      }\n    }\n  }\n  return bHit;\n}\n\n/*\n** This function is called as the second part of each xNext operation when\n** iterating through the results of a full-text query. At this point the\n** cursor points to a row that matches the query expression, with the\n** following caveats:\n**\n**   * Up until this point, \"NEAR\" operators in the expression have been\n**     treated as \"AND\".\n**\n**   * Deferred tokens have not yet been considered.\n**\n** If *pRc is not SQLITE_OK when this function is called, it immediately\n** returns 0. Otherwise, it tests whether or not after considering NEAR\n** operators and deferred tokens the current row is still a match for the\n** expression. It returns 1 if both of the following are true:\n**\n**   1. *pRc is SQLITE_OK when this function returns, and\n**\n**   2. After scanning the current FTS table row for the deferred tokens,\n**      it is determined that the row does *not* match the query.\n**\n** Or, if no error occurs and it seems the current row does match the FTS\n** query, return 0.\n*/\nSQLITE_PRIVATE int sqlite3Fts3EvalTestDeferred(Fts3Cursor *pCsr, int *pRc){\n  int rc = *pRc;\n  int bMiss = 0;\n  if( rc==SQLITE_OK ){\n\n    /* If there are one or more deferred tokens, load the current row into\n    ** memory and scan it to determine the position list for each deferred\n    ** token. Then, see if this row is really a match, considering deferred\n    ** tokens and NEAR operators (neither of which were taken into account\n    ** earlier, by fts3EvalNextRow()). \n    */\n    if( pCsr->pDeferred ){\n      rc = fts3CursorSeek(0, pCsr);\n      if( rc==SQLITE_OK ){\n        rc = sqlite3Fts3CacheDeferredDoclists(pCsr);\n      }\n    }\n    bMiss = (0==fts3EvalTestExpr(pCsr, pCsr->pExpr, &rc));\n\n    /* Free the position-lists accumulated for each deferred token above. */\n    sqlite3Fts3FreeDeferredDoclists(pCsr);\n    *pRc = rc;\n  }\n  return (rc==SQLITE_OK && bMiss);\n}\n\n/*\n** Advance to the next document that matches the FTS expression in\n** Fts3Cursor.pExpr.\n*/\nstatic int fts3EvalNext(Fts3Cursor *pCsr){\n  int rc = SQLITE_OK;             /* Return Code */\n  Fts3Expr *pExpr = pCsr->pExpr;\n  assert( pCsr->isEof==0 );\n  if( pExpr==0 ){\n    pCsr->isEof = 1;\n  }else{\n    do {\n      if( pCsr->isRequireSeek==0 ){\n        sqlite3_reset(pCsr->pStmt);\n      }\n      assert( sqlite3_data_count(pCsr->pStmt)==0 );\n      fts3EvalNextRow(pCsr, pExpr, &rc);\n      pCsr->isEof = pExpr->bEof;\n      pCsr->isRequireSeek = 1;\n      pCsr->isMatchinfoNeeded = 1;\n      pCsr->iPrevId = pExpr->iDocid;\n    }while( pCsr->isEof==0 && sqlite3Fts3EvalTestDeferred(pCsr, &rc) );\n  }\n\n  /* Check if the cursor is past the end of the docid range specified\n  ** by Fts3Cursor.iMinDocid/iMaxDocid. If so, set the EOF flag.  */\n  if( rc==SQLITE_OK && (\n        (pCsr->bDesc==0 && pCsr->iPrevId>pCsr->iMaxDocid)\n     || (pCsr->bDesc!=0 && pCsr->iPrevId<pCsr->iMinDocid)\n  )){\n    pCsr->isEof = 1;\n  }\n\n  return rc;\n}\n\n/*\n** Restart interation for expression pExpr so that the next call to\n** fts3EvalNext() visits the first row. Do not allow incremental \n** loading or merging of phrase doclists for this iteration.\n**\n** If *pRc is other than SQLITE_OK when this function is called, it is\n** a no-op. If an error occurs within this function, *pRc is set to an\n** SQLite error code before returning.\n*/\nstatic void fts3EvalRestart(\n  Fts3Cursor *pCsr,\n  Fts3Expr *pExpr,\n  int *pRc\n){\n  if( pExpr && *pRc==SQLITE_OK ){\n    Fts3Phrase *pPhrase = pExpr->pPhrase;\n\n    if( pPhrase ){\n      fts3EvalInvalidatePoslist(pPhrase);\n      if( pPhrase->bIncr ){\n        int i;\n        for(i=0; i<pPhrase->nToken; i++){\n          Fts3PhraseToken *pToken = &pPhrase->aToken[i];\n          assert( pToken->pDeferred==0 );\n          if( pToken->pSegcsr ){\n            sqlite3Fts3MsrIncrRestart(pToken->pSegcsr);\n          }\n        }\n        *pRc = fts3EvalPhraseStart(pCsr, 0, pPhrase);\n      }\n      pPhrase->doclist.pNextDocid = 0;\n      pPhrase->doclist.iDocid = 0;\n      pPhrase->pOrPoslist = 0;\n    }\n\n    pExpr->iDocid = 0;\n    pExpr->bEof = 0;\n    pExpr->bStart = 0;\n\n    fts3EvalRestart(pCsr, pExpr->pLeft, pRc);\n    fts3EvalRestart(pCsr, pExpr->pRight, pRc);\n  }\n}\n\n/*\n** After allocating the Fts3Expr.aMI[] array for each phrase in the \n** expression rooted at pExpr, the cursor iterates through all rows matched\n** by pExpr, calling this function for each row. This function increments\n** the values in Fts3Expr.aMI[] according to the position-list currently\n** found in Fts3Expr.pPhrase->doclist.pList for each of the phrase \n** expression nodes.\n*/\nstatic void fts3EvalUpdateCounts(Fts3Expr *pExpr){\n  if( pExpr ){\n    Fts3Phrase *pPhrase = pExpr->pPhrase;\n    if( pPhrase && pPhrase->doclist.pList ){\n      int iCol = 0;\n      char *p = pPhrase->doclist.pList;\n\n      assert( *p );\n      while( 1 ){\n        u8 c = 0;\n        int iCnt = 0;\n        while( 0xFE & (*p | c) ){\n          if( (c&0x80)==0 ) iCnt++;\n          c = *p++ & 0x80;\n        }\n\n        /* aMI[iCol*3 + 1] = Number of occurrences\n        ** aMI[iCol*3 + 2] = Number of rows containing at least one instance\n        */\n        pExpr->aMI[iCol*3 + 1] += iCnt;\n        pExpr->aMI[iCol*3 + 2] += (iCnt>0);\n        if( *p==0x00 ) break;\n        p++;\n        p += fts3GetVarint32(p, &iCol);\n      }\n    }\n\n    fts3EvalUpdateCounts(pExpr->pLeft);\n    fts3EvalUpdateCounts(pExpr->pRight);\n  }\n}\n\n/*\n** Expression pExpr must be of type FTSQUERY_PHRASE.\n**\n** If it is not already allocated and populated, this function allocates and\n** populates the Fts3Expr.aMI[] array for expression pExpr. If pExpr is part\n** of a NEAR expression, then it also allocates and populates the same array\n** for all other phrases that are part of the NEAR expression.\n**\n** SQLITE_OK is returned if the aMI[] array is successfully allocated and\n** populated. Otherwise, if an error occurs, an SQLite error code is returned.\n*/\nstatic int fts3EvalGatherStats(\n  Fts3Cursor *pCsr,               /* Cursor object */\n  Fts3Expr *pExpr                 /* FTSQUERY_PHRASE expression */\n){\n  int rc = SQLITE_OK;             /* Return code */\n\n  assert( pExpr->eType==FTSQUERY_PHRASE );\n  if( pExpr->aMI==0 ){\n    Fts3Table *pTab = (Fts3Table *)pCsr->base.pVtab;\n    Fts3Expr *pRoot;                /* Root of NEAR expression */\n    Fts3Expr *p;                    /* Iterator used for several purposes */\n\n    sqlite3_int64 iPrevId = pCsr->iPrevId;\n    sqlite3_int64 iDocid;\n    u8 bEof;\n\n    /* Find the root of the NEAR expression */\n    pRoot = pExpr;\n    while( pRoot->pParent && pRoot->pParent->eType==FTSQUERY_NEAR ){\n      pRoot = pRoot->pParent;\n    }\n    iDocid = pRoot->iDocid;\n    bEof = pRoot->bEof;\n    assert( pRoot->bStart );\n\n    /* Allocate space for the aMSI[] array of each FTSQUERY_PHRASE node */\n    for(p=pRoot; p; p=p->pLeft){\n      Fts3Expr *pE = (p->eType==FTSQUERY_PHRASE?p:p->pRight);\n      assert( pE->aMI==0 );\n      pE->aMI = (u32 *)sqlite3_malloc(pTab->nColumn * 3 * sizeof(u32));\n      if( !pE->aMI ) return SQLITE_NOMEM;\n      memset(pE->aMI, 0, pTab->nColumn * 3 * sizeof(u32));\n    }\n\n    fts3EvalRestart(pCsr, pRoot, &rc);\n\n    while( pCsr->isEof==0 && rc==SQLITE_OK ){\n\n      do {\n        /* Ensure the %_content statement is reset. */\n        if( pCsr->isRequireSeek==0 ) sqlite3_reset(pCsr->pStmt);\n        assert( sqlite3_data_count(pCsr->pStmt)==0 );\n\n        /* Advance to the next document */\n        fts3EvalNextRow(pCsr, pRoot, &rc);\n        pCsr->isEof = pRoot->bEof;\n        pCsr->isRequireSeek = 1;\n        pCsr->isMatchinfoNeeded = 1;\n        pCsr->iPrevId = pRoot->iDocid;\n      }while( pCsr->isEof==0 \n           && pRoot->eType==FTSQUERY_NEAR \n           && sqlite3Fts3EvalTestDeferred(pCsr, &rc) \n      );\n\n      if( rc==SQLITE_OK && pCsr->isEof==0 ){\n        fts3EvalUpdateCounts(pRoot);\n      }\n    }\n\n    pCsr->isEof = 0;\n    pCsr->iPrevId = iPrevId;\n\n    if( bEof ){\n      pRoot->bEof = bEof;\n    }else{\n      /* Caution: pRoot may iterate through docids in ascending or descending\n      ** order. For this reason, even though it seems more defensive, the \n      ** do loop can not be written:\n      **\n      **   do {...} while( pRoot->iDocid<iDocid && rc==SQLITE_OK );\n      */\n      fts3EvalRestart(pCsr, pRoot, &rc);\n      do {\n        fts3EvalNextRow(pCsr, pRoot, &rc);\n        assert( pRoot->bEof==0 );\n      }while( pRoot->iDocid!=iDocid && rc==SQLITE_OK );\n    }\n  }\n  return rc;\n}\n\n/*\n** This function is used by the matchinfo() module to query a phrase \n** expression node for the following information:\n**\n**   1. The total number of occurrences of the phrase in each column of \n**      the FTS table (considering all rows), and\n**\n**   2. For each column, the number of rows in the table for which the\n**      column contains at least one instance of the phrase.\n**\n** If no error occurs, SQLITE_OK is returned and the values for each column\n** written into the array aiOut as follows:\n**\n**   aiOut[iCol*3 + 1] = Number of occurrences\n**   aiOut[iCol*3 + 2] = Number of rows containing at least one instance\n**\n** Caveats:\n**\n**   * If a phrase consists entirely of deferred tokens, then all output \n**     values are set to the number of documents in the table. In other\n**     words we assume that very common tokens occur exactly once in each \n**     column of each row of the table.\n**\n**   * If a phrase contains some deferred tokens (and some non-deferred \n**     tokens), count the potential occurrence identified by considering\n**     the non-deferred tokens instead of actual phrase occurrences.\n**\n**   * If the phrase is part of a NEAR expression, then only phrase instances\n**     that meet the NEAR constraint are included in the counts.\n*/\nSQLITE_PRIVATE int sqlite3Fts3EvalPhraseStats(\n  Fts3Cursor *pCsr,               /* FTS cursor handle */\n  Fts3Expr *pExpr,                /* Phrase expression */\n  u32 *aiOut                      /* Array to write results into (see above) */\n){\n  Fts3Table *pTab = (Fts3Table *)pCsr->base.pVtab;\n  int rc = SQLITE_OK;\n  int iCol;\n\n  if( pExpr->bDeferred && pExpr->pParent->eType!=FTSQUERY_NEAR ){\n    assert( pCsr->nDoc>0 );\n    for(iCol=0; iCol<pTab->nColumn; iCol++){\n      aiOut[iCol*3 + 1] = (u32)pCsr->nDoc;\n      aiOut[iCol*3 + 2] = (u32)pCsr->nDoc;\n    }\n  }else{\n    rc = fts3EvalGatherStats(pCsr, pExpr);\n    if( rc==SQLITE_OK ){\n      assert( pExpr->aMI );\n      for(iCol=0; iCol<pTab->nColumn; iCol++){\n        aiOut[iCol*3 + 1] = pExpr->aMI[iCol*3 + 1];\n        aiOut[iCol*3 + 2] = pExpr->aMI[iCol*3 + 2];\n      }\n    }\n  }\n\n  return rc;\n}\n\n/*\n** The expression pExpr passed as the second argument to this function\n** must be of type FTSQUERY_PHRASE. \n**\n** The returned value is either NULL or a pointer to a buffer containing\n** a position-list indicating the occurrences of the phrase in column iCol\n** of the current row. \n**\n** More specifically, the returned buffer contains 1 varint for each \n** occurrence of the phrase in the column, stored using the normal (delta+2) \n** compression and is terminated by either an 0x01 or 0x00 byte. For example,\n** if the requested column contains \"a b X c d X X\" and the position-list\n** for 'X' is requested, the buffer returned may contain:\n**\n**     0x04 0x05 0x03 0x01   or   0x04 0x05 0x03 0x00\n**\n** This function works regardless of whether or not the phrase is deferred,\n** incremental, or neither.\n*/\nSQLITE_PRIVATE int sqlite3Fts3EvalPhrasePoslist(\n  Fts3Cursor *pCsr,               /* FTS3 cursor object */\n  Fts3Expr *pExpr,                /* Phrase to return doclist for */\n  int iCol,                       /* Column to return position list for */\n  char **ppOut                    /* OUT: Pointer to position list */\n){\n  Fts3Phrase *pPhrase = pExpr->pPhrase;\n  Fts3Table *pTab = (Fts3Table *)pCsr->base.pVtab;\n  char *pIter;\n  int iThis;\n  sqlite3_int64 iDocid;\n\n  /* If this phrase is applies specifically to some column other than \n  ** column iCol, return a NULL pointer.  */\n  *ppOut = 0;\n  assert( iCol>=0 && iCol<pTab->nColumn );\n  if( (pPhrase->iColumn<pTab->nColumn && pPhrase->iColumn!=iCol) ){\n    return SQLITE_OK;\n  }\n\n  iDocid = pExpr->iDocid;\n  pIter = pPhrase->doclist.pList;\n  if( iDocid!=pCsr->iPrevId || pExpr->bEof ){\n    int rc = SQLITE_OK;\n    int bDescDoclist = pTab->bDescIdx;      /* For DOCID_CMP macro */\n    int bOr = 0;\n    u8 bTreeEof = 0;\n    Fts3Expr *p;                  /* Used to iterate from pExpr to root */\n    Fts3Expr *pNear;              /* Most senior NEAR ancestor (or pExpr) */\n    int bMatch;\n\n    /* Check if this phrase descends from an OR expression node. If not, \n    ** return NULL. Otherwise, the entry that corresponds to docid \n    ** pCsr->iPrevId may lie earlier in the doclist buffer. Or, if the\n    ** tree that the node is part of has been marked as EOF, but the node\n    ** itself is not EOF, then it may point to an earlier entry. */\n    pNear = pExpr;\n    for(p=pExpr->pParent; p; p=p->pParent){\n      if( p->eType==FTSQUERY_OR ) bOr = 1;\n      if( p->eType==FTSQUERY_NEAR ) pNear = p;\n      if( p->bEof ) bTreeEof = 1;\n    }\n    if( bOr==0 ) return SQLITE_OK;\n\n    /* This is the descendent of an OR node. In this case we cannot use\n    ** an incremental phrase. Load the entire doclist for the phrase\n    ** into memory in this case.  */\n    if( pPhrase->bIncr ){\n      int bEofSave = pNear->bEof;\n      fts3EvalRestart(pCsr, pNear, &rc);\n      while( rc==SQLITE_OK && !pNear->bEof ){\n        fts3EvalNextRow(pCsr, pNear, &rc);\n        if( bEofSave==0 && pNear->iDocid==iDocid ) break;\n      }\n      assert( rc!=SQLITE_OK || pPhrase->bIncr==0 );\n    }\n    if( bTreeEof ){\n      while( rc==SQLITE_OK && !pNear->bEof ){\n        fts3EvalNextRow(pCsr, pNear, &rc);\n      }\n    }\n    if( rc!=SQLITE_OK ) return rc;\n\n    bMatch = 1;\n    for(p=pNear; p; p=p->pLeft){\n      u8 bEof = 0;\n      Fts3Expr *pTest = p;\n      Fts3Phrase *pPh;\n      assert( pTest->eType==FTSQUERY_NEAR || pTest->eType==FTSQUERY_PHRASE );\n      if( pTest->eType==FTSQUERY_NEAR ) pTest = pTest->pRight;\n      assert( pTest->eType==FTSQUERY_PHRASE );\n      pPh = pTest->pPhrase;\n\n      pIter = pPh->pOrPoslist;\n      iDocid = pPh->iOrDocid;\n      if( pCsr->bDesc==bDescDoclist ){\n        bEof = !pPh->doclist.nAll ||\n          (pIter >= (pPh->doclist.aAll + pPh->doclist.nAll));\n        while( (pIter==0 || DOCID_CMP(iDocid, pCsr->iPrevId)<0 ) && bEof==0 ){\n          sqlite3Fts3DoclistNext(\n              bDescDoclist, pPh->doclist.aAll, pPh->doclist.nAll, \n              &pIter, &iDocid, &bEof\n          );\n        }\n      }else{\n        bEof = !pPh->doclist.nAll || (pIter && pIter<=pPh->doclist.aAll);\n        while( (pIter==0 || DOCID_CMP(iDocid, pCsr->iPrevId)>0 ) && bEof==0 ){\n          int dummy;\n          sqlite3Fts3DoclistPrev(\n              bDescDoclist, pPh->doclist.aAll, pPh->doclist.nAll, \n              &pIter, &iDocid, &dummy, &bEof\n              );\n        }\n      }\n      pPh->pOrPoslist = pIter;\n      pPh->iOrDocid = iDocid;\n      if( bEof || iDocid!=pCsr->iPrevId ) bMatch = 0;\n    }\n\n    if( bMatch ){\n      pIter = pPhrase->pOrPoslist;\n    }else{\n      pIter = 0;\n    }\n  }\n  if( pIter==0 ) return SQLITE_OK;\n\n  if( *pIter==0x01 ){\n    pIter++;\n    pIter += fts3GetVarint32(pIter, &iThis);\n  }else{\n    iThis = 0;\n  }\n  while( iThis<iCol ){\n    fts3ColumnlistCopy(0, &pIter);\n    if( *pIter==0x00 ) return SQLITE_OK;\n    pIter++;\n    pIter += fts3GetVarint32(pIter, &iThis);\n  }\n  if( *pIter==0x00 ){\n    pIter = 0;\n  }\n\n  *ppOut = ((iCol==iThis)?pIter:0);\n  return SQLITE_OK;\n}\n\n/*\n** Free all components of the Fts3Phrase structure that were allocated by\n** the eval module. Specifically, this means to free:\n**\n**   * the contents of pPhrase->doclist, and\n**   * any Fts3MultiSegReader objects held by phrase tokens.\n*/\nSQLITE_PRIVATE void sqlite3Fts3EvalPhraseCleanup(Fts3Phrase *pPhrase){\n  if( pPhrase ){\n    int i;\n    sqlite3_free(pPhrase->doclist.aAll);\n    fts3EvalInvalidatePoslist(pPhrase);\n    memset(&pPhrase->doclist, 0, sizeof(Fts3Doclist));\n    for(i=0; i<pPhrase->nToken; i++){\n      fts3SegReaderCursorFree(pPhrase->aToken[i].pSegcsr);\n      pPhrase->aToken[i].pSegcsr = 0;\n    }\n  }\n}\n\n\n/*\n** Return SQLITE_CORRUPT_VTAB.\n*/\n#ifdef SQLITE_DEBUG\nSQLITE_PRIVATE int sqlite3Fts3Corrupt(){\n  return SQLITE_CORRUPT_VTAB;\n}\n#endif\n\n#if !SQLITE_CORE\n/*\n** Initialize API pointer table, if required.\n*/\n#ifdef _WIN32\n__declspec(dllexport)\n#endif\nSQLITE_API int sqlite3_fts3_init(\n  sqlite3 *db, \n  char **pzErrMsg,\n  const sqlite3_api_routines *pApi\n){\n  SQLITE_EXTENSION_INIT2(pApi)\n  return sqlite3Fts3Init(db);\n}\n#endif\n\n#endif\n\n/************** End of fts3.c ************************************************/\n/************** Begin file fts3_aux.c ****************************************/\n/*\n** 2011 Jan 27\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n******************************************************************************\n**\n*/\n/* #include \"fts3Int.h\" */\n#if !defined(SQLITE_CORE) || defined(SQLITE_ENABLE_FTS3)\n\n/* #include <string.h> */\n/* #include <assert.h> */\n\ntypedef struct Fts3auxTable Fts3auxTable;\ntypedef struct Fts3auxCursor Fts3auxCursor;\n\nstruct Fts3auxTable {\n  sqlite3_vtab base;              /* Base class used by SQLite core */\n  Fts3Table *pFts3Tab;\n};\n\nstruct Fts3auxCursor {\n  sqlite3_vtab_cursor base;       /* Base class used by SQLite core */\n  Fts3MultiSegReader csr;        /* Must be right after \"base\" */\n  Fts3SegFilter filter;\n  char *zStop;\n  int nStop;                      /* Byte-length of string zStop */\n  int iLangid;                    /* Language id to query */\n  int isEof;                      /* True if cursor is at EOF */\n  sqlite3_int64 iRowid;           /* Current rowid */\n\n  int iCol;                       /* Current value of 'col' column */\n  int nStat;                      /* Size of aStat[] array */\n  struct Fts3auxColstats {\n    sqlite3_int64 nDoc;           /* 'documents' values for current csr row */\n    sqlite3_int64 nOcc;           /* 'occurrences' values for current csr row */\n  } *aStat;\n};\n\n/*\n** Schema of the terms table.\n*/\n#define FTS3_AUX_SCHEMA \\\n  \"CREATE TABLE x(term, col, documents, occurrences, languageid HIDDEN)\"\n\n/*\n** This function does all the work for both the xConnect and xCreate methods.\n** These tables have no persistent representation of their own, so xConnect\n** and xCreate are identical operations.\n*/\nstatic int fts3auxConnectMethod(\n  sqlite3 *db,                    /* Database connection */\n  void *pUnused,                  /* Unused */\n  int argc,                       /* Number of elements in argv array */\n  const char * const *argv,       /* xCreate/xConnect argument array */\n  sqlite3_vtab **ppVtab,          /* OUT: New sqlite3_vtab object */\n  char **pzErr                    /* OUT: sqlite3_malloc'd error message */\n){\n  char const *zDb;                /* Name of database (e.g. \"main\") */\n  char const *zFts3;              /* Name of fts3 table */\n  int nDb;                        /* Result of strlen(zDb) */\n  int nFts3;                      /* Result of strlen(zFts3) */\n  int nByte;                      /* Bytes of space to allocate here */\n  int rc;                         /* value returned by declare_vtab() */\n  Fts3auxTable *p;                /* Virtual table object to return */\n\n  UNUSED_PARAMETER(pUnused);\n\n  /* The user should invoke this in one of two forms:\n  **\n  **     CREATE VIRTUAL TABLE xxx USING fts4aux(fts4-table);\n  **     CREATE VIRTUAL TABLE xxx USING fts4aux(fts4-table-db, fts4-table);\n  */\n  if( argc!=4 && argc!=5 ) goto bad_args;\n\n  zDb = argv[1]; \n  nDb = (int)strlen(zDb);\n  if( argc==5 ){\n    if( nDb==4 && 0==sqlite3_strnicmp(\"temp\", zDb, 4) ){\n      zDb = argv[3]; \n      nDb = (int)strlen(zDb);\n      zFts3 = argv[4];\n    }else{\n      goto bad_args;\n    }\n  }else{\n    zFts3 = argv[3];\n  }\n  nFts3 = (int)strlen(zFts3);\n\n  rc = sqlite3_declare_vtab(db, FTS3_AUX_SCHEMA);\n  if( rc!=SQLITE_OK ) return rc;\n\n  nByte = sizeof(Fts3auxTable) + sizeof(Fts3Table) + nDb + nFts3 + 2;\n  p = (Fts3auxTable *)sqlite3_malloc(nByte);\n  if( !p ) return SQLITE_NOMEM;\n  memset(p, 0, nByte);\n\n  p->pFts3Tab = (Fts3Table *)&p[1];\n  p->pFts3Tab->zDb = (char *)&p->pFts3Tab[1];\n  p->pFts3Tab->zName = &p->pFts3Tab->zDb[nDb+1];\n  p->pFts3Tab->db = db;\n  p->pFts3Tab->nIndex = 1;\n\n  memcpy((char *)p->pFts3Tab->zDb, zDb, nDb);\n  memcpy((char *)p->pFts3Tab->zName, zFts3, nFts3);\n  sqlite3Fts3Dequote((char *)p->pFts3Tab->zName);\n\n  *ppVtab = (sqlite3_vtab *)p;\n  return SQLITE_OK;\n\n bad_args:\n  sqlite3Fts3ErrMsg(pzErr, \"invalid arguments to fts4aux constructor\");\n  return SQLITE_ERROR;\n}\n\n/*\n** This function does the work for both the xDisconnect and xDestroy methods.\n** These tables have no persistent representation of their own, so xDisconnect\n** and xDestroy are identical operations.\n*/\nstatic int fts3auxDisconnectMethod(sqlite3_vtab *pVtab){\n  Fts3auxTable *p = (Fts3auxTable *)pVtab;\n  Fts3Table *pFts3 = p->pFts3Tab;\n  int i;\n\n  /* Free any prepared statements held */\n  for(i=0; i<SizeofArray(pFts3->aStmt); i++){\n    sqlite3_finalize(pFts3->aStmt[i]);\n  }\n  sqlite3_free(pFts3->zSegmentsTbl);\n  sqlite3_free(p);\n  return SQLITE_OK;\n}\n\n#define FTS4AUX_EQ_CONSTRAINT 1\n#define FTS4AUX_GE_CONSTRAINT 2\n#define FTS4AUX_LE_CONSTRAINT 4\n\n/*\n** xBestIndex - Analyze a WHERE and ORDER BY clause.\n*/\nstatic int fts3auxBestIndexMethod(\n  sqlite3_vtab *pVTab, \n  sqlite3_index_info *pInfo\n){\n  int i;\n  int iEq = -1;\n  int iGe = -1;\n  int iLe = -1;\n  int iLangid = -1;\n  int iNext = 1;                  /* Next free argvIndex value */\n\n  UNUSED_PARAMETER(pVTab);\n\n  /* This vtab delivers always results in \"ORDER BY term ASC\" order. */\n  if( pInfo->nOrderBy==1 \n   && pInfo->aOrderBy[0].iColumn==0 \n   && pInfo->aOrderBy[0].desc==0\n  ){\n    pInfo->orderByConsumed = 1;\n  }\n\n  /* Search for equality and range constraints on the \"term\" column. \n  ** And equality constraints on the hidden \"languageid\" column. */\n  for(i=0; i<pInfo->nConstraint; i++){\n    if( pInfo->aConstraint[i].usable ){\n      int op = pInfo->aConstraint[i].op;\n      int iCol = pInfo->aConstraint[i].iColumn;\n\n      if( iCol==0 ){\n        if( op==SQLITE_INDEX_CONSTRAINT_EQ ) iEq = i;\n        if( op==SQLITE_INDEX_CONSTRAINT_LT ) iLe = i;\n        if( op==SQLITE_INDEX_CONSTRAINT_LE ) iLe = i;\n        if( op==SQLITE_INDEX_CONSTRAINT_GT ) iGe = i;\n        if( op==SQLITE_INDEX_CONSTRAINT_GE ) iGe = i;\n      }\n      if( iCol==4 ){\n        if( op==SQLITE_INDEX_CONSTRAINT_EQ ) iLangid = i;\n      }\n    }\n  }\n\n  if( iEq>=0 ){\n    pInfo->idxNum = FTS4AUX_EQ_CONSTRAINT;\n    pInfo->aConstraintUsage[iEq].argvIndex = iNext++;\n    pInfo->estimatedCost = 5;\n  }else{\n    pInfo->idxNum = 0;\n    pInfo->estimatedCost = 20000;\n    if( iGe>=0 ){\n      pInfo->idxNum += FTS4AUX_GE_CONSTRAINT;\n      pInfo->aConstraintUsage[iGe].argvIndex = iNext++;\n      pInfo->estimatedCost /= 2;\n    }\n    if( iLe>=0 ){\n      pInfo->idxNum += FTS4AUX_LE_CONSTRAINT;\n      pInfo->aConstraintUsage[iLe].argvIndex = iNext++;\n      pInfo->estimatedCost /= 2;\n    }\n  }\n  if( iLangid>=0 ){\n    pInfo->aConstraintUsage[iLangid].argvIndex = iNext++;\n    pInfo->estimatedCost--;\n  }\n\n  return SQLITE_OK;\n}\n\n/*\n** xOpen - Open a cursor.\n*/\nstatic int fts3auxOpenMethod(sqlite3_vtab *pVTab, sqlite3_vtab_cursor **ppCsr){\n  Fts3auxCursor *pCsr;            /* Pointer to cursor object to return */\n\n  UNUSED_PARAMETER(pVTab);\n\n  pCsr = (Fts3auxCursor *)sqlite3_malloc(sizeof(Fts3auxCursor));\n  if( !pCsr ) return SQLITE_NOMEM;\n  memset(pCsr, 0, sizeof(Fts3auxCursor));\n\n  *ppCsr = (sqlite3_vtab_cursor *)pCsr;\n  return SQLITE_OK;\n}\n\n/*\n** xClose - Close a cursor.\n*/\nstatic int fts3auxCloseMethod(sqlite3_vtab_cursor *pCursor){\n  Fts3Table *pFts3 = ((Fts3auxTable *)pCursor->pVtab)->pFts3Tab;\n  Fts3auxCursor *pCsr = (Fts3auxCursor *)pCursor;\n\n  sqlite3Fts3SegmentsClose(pFts3);\n  sqlite3Fts3SegReaderFinish(&pCsr->csr);\n  sqlite3_free((void *)pCsr->filter.zTerm);\n  sqlite3_free(pCsr->zStop);\n  sqlite3_free(pCsr->aStat);\n  sqlite3_free(pCsr);\n  return SQLITE_OK;\n}\n\nstatic int fts3auxGrowStatArray(Fts3auxCursor *pCsr, int nSize){\n  if( nSize>pCsr->nStat ){\n    struct Fts3auxColstats *aNew;\n    aNew = (struct Fts3auxColstats *)sqlite3_realloc(pCsr->aStat, \n        sizeof(struct Fts3auxColstats) * nSize\n    );\n    if( aNew==0 ) return SQLITE_NOMEM;\n    memset(&aNew[pCsr->nStat], 0, \n        sizeof(struct Fts3auxColstats) * (nSize - pCsr->nStat)\n    );\n    pCsr->aStat = aNew;\n    pCsr->nStat = nSize;\n  }\n  return SQLITE_OK;\n}\n\n/*\n** xNext - Advance the cursor to the next row, if any.\n*/\nstatic int fts3auxNextMethod(sqlite3_vtab_cursor *pCursor){\n  Fts3auxCursor *pCsr = (Fts3auxCursor *)pCursor;\n  Fts3Table *pFts3 = ((Fts3auxTable *)pCursor->pVtab)->pFts3Tab;\n  int rc;\n\n  /* Increment our pretend rowid value. */\n  pCsr->iRowid++;\n\n  for(pCsr->iCol++; pCsr->iCol<pCsr->nStat; pCsr->iCol++){\n    if( pCsr->aStat[pCsr->iCol].nDoc>0 ) return SQLITE_OK;\n  }\n\n  rc = sqlite3Fts3SegReaderStep(pFts3, &pCsr->csr);\n  if( rc==SQLITE_ROW ){\n    int i = 0;\n    int nDoclist = pCsr->csr.nDoclist;\n    char *aDoclist = pCsr->csr.aDoclist;\n    int iCol;\n\n    int eState = 0;\n\n    if( pCsr->zStop ){\n      int n = (pCsr->nStop<pCsr->csr.nTerm) ? pCsr->nStop : pCsr->csr.nTerm;\n      int mc = memcmp(pCsr->zStop, pCsr->csr.zTerm, n);\n      if( mc<0 || (mc==0 && pCsr->csr.nTerm>pCsr->nStop) ){\n        pCsr->isEof = 1;\n        return SQLITE_OK;\n      }\n    }\n\n    if( fts3auxGrowStatArray(pCsr, 2) ) return SQLITE_NOMEM;\n    memset(pCsr->aStat, 0, sizeof(struct Fts3auxColstats) * pCsr->nStat);\n    iCol = 0;\n\n    while( i<nDoclist ){\n      sqlite3_int64 v = 0;\n\n      i += sqlite3Fts3GetVarint(&aDoclist[i], &v);\n      switch( eState ){\n        /* State 0. In this state the integer just read was a docid. */\n        case 0:\n          pCsr->aStat[0].nDoc++;\n          eState = 1;\n          iCol = 0;\n          break;\n\n        /* State 1. In this state we are expecting either a 1, indicating\n        ** that the following integer will be a column number, or the\n        ** start of a position list for column 0.  \n        ** \n        ** The only difference between state 1 and state 2 is that if the\n        ** integer encountered in state 1 is not 0 or 1, then we need to\n        ** increment the column 0 \"nDoc\" count for this term.\n        */\n        case 1:\n          assert( iCol==0 );\n          if( v>1 ){\n            pCsr->aStat[1].nDoc++;\n          }\n          eState = 2;\n          /* fall through */\n\n        case 2:\n          if( v==0 ){       /* 0x00. Next integer will be a docid. */\n            eState = 0;\n          }else if( v==1 ){ /* 0x01. Next integer will be a column number. */\n            eState = 3;\n          }else{            /* 2 or greater. A position. */\n            pCsr->aStat[iCol+1].nOcc++;\n            pCsr->aStat[0].nOcc++;\n          }\n          break;\n\n        /* State 3. The integer just read is a column number. */\n        default: assert( eState==3 );\n          iCol = (int)v;\n          if( fts3auxGrowStatArray(pCsr, iCol+2) ) return SQLITE_NOMEM;\n          pCsr->aStat[iCol+1].nDoc++;\n          eState = 2;\n          break;\n      }\n    }\n\n    pCsr->iCol = 0;\n    rc = SQLITE_OK;\n  }else{\n    pCsr->isEof = 1;\n  }\n  return rc;\n}\n\n/*\n** xFilter - Initialize a cursor to point at the start of its data.\n*/\nstatic int fts3auxFilterMethod(\n  sqlite3_vtab_cursor *pCursor,   /* The cursor used for this query */\n  int idxNum,                     /* Strategy index */\n  const char *idxStr,             /* Unused */\n  int nVal,                       /* Number of elements in apVal */\n  sqlite3_value **apVal           /* Arguments for the indexing scheme */\n){\n  Fts3auxCursor *pCsr = (Fts3auxCursor *)pCursor;\n  Fts3Table *pFts3 = ((Fts3auxTable *)pCursor->pVtab)->pFts3Tab;\n  int rc;\n  int isScan = 0;\n  int iLangVal = 0;               /* Language id to query */\n\n  int iEq = -1;                   /* Index of term=? value in apVal */\n  int iGe = -1;                   /* Index of term>=? value in apVal */\n  int iLe = -1;                   /* Index of term<=? value in apVal */\n  int iLangid = -1;               /* Index of languageid=? value in apVal */\n  int iNext = 0;\n\n  UNUSED_PARAMETER(nVal);\n  UNUSED_PARAMETER(idxStr);\n\n  assert( idxStr==0 );\n  assert( idxNum==FTS4AUX_EQ_CONSTRAINT || idxNum==0\n       || idxNum==FTS4AUX_LE_CONSTRAINT || idxNum==FTS4AUX_GE_CONSTRAINT\n       || idxNum==(FTS4AUX_LE_CONSTRAINT|FTS4AUX_GE_CONSTRAINT)\n  );\n\n  if( idxNum==FTS4AUX_EQ_CONSTRAINT ){\n    iEq = iNext++;\n  }else{\n    isScan = 1;\n    if( idxNum & FTS4AUX_GE_CONSTRAINT ){\n      iGe = iNext++;\n    }\n    if( idxNum & FTS4AUX_LE_CONSTRAINT ){\n      iLe = iNext++;\n    }\n  }\n  if( iNext<nVal ){\n    iLangid = iNext++;\n  }\n\n  /* In case this cursor is being reused, close and zero it. */\n  testcase(pCsr->filter.zTerm);\n  sqlite3Fts3SegReaderFinish(&pCsr->csr);\n  sqlite3_free((void *)pCsr->filter.zTerm);\n  sqlite3_free(pCsr->aStat);\n  memset(&pCsr->csr, 0, ((u8*)&pCsr[1]) - (u8*)&pCsr->csr);\n\n  pCsr->filter.flags = FTS3_SEGMENT_REQUIRE_POS|FTS3_SEGMENT_IGNORE_EMPTY;\n  if( isScan ) pCsr->filter.flags |= FTS3_SEGMENT_SCAN;\n\n  if( iEq>=0 || iGe>=0 ){\n    const unsigned char *zStr = sqlite3_value_text(apVal[0]);\n    assert( (iEq==0 && iGe==-1) || (iEq==-1 && iGe==0) );\n    if( zStr ){\n      pCsr->filter.zTerm = sqlite3_mprintf(\"%s\", zStr);\n      pCsr->filter.nTerm = sqlite3_value_bytes(apVal[0]);\n      if( pCsr->filter.zTerm==0 ) return SQLITE_NOMEM;\n    }\n  }\n\n  if( iLe>=0 ){\n    pCsr->zStop = sqlite3_mprintf(\"%s\", sqlite3_value_text(apVal[iLe]));\n    pCsr->nStop = sqlite3_value_bytes(apVal[iLe]);\n    if( pCsr->zStop==0 ) return SQLITE_NOMEM;\n  }\n  \n  if( iLangid>=0 ){\n    iLangVal = sqlite3_value_int(apVal[iLangid]);\n\n    /* If the user specified a negative value for the languageid, use zero\n    ** instead. This works, as the \"languageid=?\" constraint will also\n    ** be tested by the VDBE layer. The test will always be false (since\n    ** this module will not return a row with a negative languageid), and\n    ** so the overall query will return zero rows.  */\n    if( iLangVal<0 ) iLangVal = 0;\n  }\n  pCsr->iLangid = iLangVal;\n\n  rc = sqlite3Fts3SegReaderCursor(pFts3, iLangVal, 0, FTS3_SEGCURSOR_ALL,\n      pCsr->filter.zTerm, pCsr->filter.nTerm, 0, isScan, &pCsr->csr\n  );\n  if( rc==SQLITE_OK ){\n    rc = sqlite3Fts3SegReaderStart(pFts3, &pCsr->csr, &pCsr->filter);\n  }\n\n  if( rc==SQLITE_OK ) rc = fts3auxNextMethod(pCursor);\n  return rc;\n}\n\n/*\n** xEof - Return true if the cursor is at EOF, or false otherwise.\n*/\nstatic int fts3auxEofMethod(sqlite3_vtab_cursor *pCursor){\n  Fts3auxCursor *pCsr = (Fts3auxCursor *)pCursor;\n  return pCsr->isEof;\n}\n\n/*\n** xColumn - Return a column value.\n*/\nstatic int fts3auxColumnMethod(\n  sqlite3_vtab_cursor *pCursor,   /* Cursor to retrieve value from */\n  sqlite3_context *pCtx,          /* Context for sqlite3_result_xxx() calls */\n  int iCol                        /* Index of column to read value from */\n){\n  Fts3auxCursor *p = (Fts3auxCursor *)pCursor;\n\n  assert( p->isEof==0 );\n  switch( iCol ){\n    case 0: /* term */\n      sqlite3_result_text(pCtx, p->csr.zTerm, p->csr.nTerm, SQLITE_TRANSIENT);\n      break;\n\n    case 1: /* col */\n      if( p->iCol ){\n        sqlite3_result_int(pCtx, p->iCol-1);\n      }else{\n        sqlite3_result_text(pCtx, \"*\", -1, SQLITE_STATIC);\n      }\n      break;\n\n    case 2: /* documents */\n      sqlite3_result_int64(pCtx, p->aStat[p->iCol].nDoc);\n      break;\n\n    case 3: /* occurrences */\n      sqlite3_result_int64(pCtx, p->aStat[p->iCol].nOcc);\n      break;\n\n    default: /* languageid */\n      assert( iCol==4 );\n      sqlite3_result_int(pCtx, p->iLangid);\n      break;\n  }\n\n  return SQLITE_OK;\n}\n\n/*\n** xRowid - Return the current rowid for the cursor.\n*/\nstatic int fts3auxRowidMethod(\n  sqlite3_vtab_cursor *pCursor,   /* Cursor to retrieve value from */\n  sqlite_int64 *pRowid            /* OUT: Rowid value */\n){\n  Fts3auxCursor *pCsr = (Fts3auxCursor *)pCursor;\n  *pRowid = pCsr->iRowid;\n  return SQLITE_OK;\n}\n\n/*\n** Register the fts3aux module with database connection db. Return SQLITE_OK\n** if successful or an error code if sqlite3_create_module() fails.\n*/\nSQLITE_PRIVATE int sqlite3Fts3InitAux(sqlite3 *db){\n  static const sqlite3_module fts3aux_module = {\n     0,                           /* iVersion      */\n     fts3auxConnectMethod,        /* xCreate       */\n     fts3auxConnectMethod,        /* xConnect      */\n     fts3auxBestIndexMethod,      /* xBestIndex    */\n     fts3auxDisconnectMethod,     /* xDisconnect   */\n     fts3auxDisconnectMethod,     /* xDestroy      */\n     fts3auxOpenMethod,           /* xOpen         */\n     fts3auxCloseMethod,          /* xClose        */\n     fts3auxFilterMethod,         /* xFilter       */\n     fts3auxNextMethod,           /* xNext         */\n     fts3auxEofMethod,            /* xEof          */\n     fts3auxColumnMethod,         /* xColumn       */\n     fts3auxRowidMethod,          /* xRowid        */\n     0,                           /* xUpdate       */\n     0,                           /* xBegin        */\n     0,                           /* xSync         */\n     0,                           /* xCommit       */\n     0,                           /* xRollback     */\n     0,                           /* xFindFunction */\n     0,                           /* xRename       */\n     0,                           /* xSavepoint    */\n     0,                           /* xRelease      */\n     0                            /* xRollbackTo   */\n  };\n  int rc;                         /* Return code */\n\n  rc = sqlite3_create_module(db, \"fts4aux\", &fts3aux_module, 0);\n  return rc;\n}\n\n#endif /* !defined(SQLITE_CORE) || defined(SQLITE_ENABLE_FTS3) */\n\n/************** End of fts3_aux.c ********************************************/\n/************** Begin file fts3_expr.c ***************************************/\n/*\n** 2008 Nov 28\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n******************************************************************************\n**\n** This module contains code that implements a parser for fts3 query strings\n** (the right-hand argument to the MATCH operator). Because the supported \n** syntax is relatively simple, the whole tokenizer/parser system is\n** hand-coded. \n*/\n/* #include \"fts3Int.h\" */\n#if !defined(SQLITE_CORE) || defined(SQLITE_ENABLE_FTS3)\n\n/*\n** By default, this module parses the legacy syntax that has been \n** traditionally used by fts3. Or, if SQLITE_ENABLE_FTS3_PARENTHESIS\n** is defined, then it uses the new syntax. The differences between\n** the new and the old syntaxes are:\n**\n**  a) The new syntax supports parenthesis. The old does not.\n**\n**  b) The new syntax supports the AND and NOT operators. The old does not.\n**\n**  c) The old syntax supports the \"-\" token qualifier. This is not \n**     supported by the new syntax (it is replaced by the NOT operator).\n**\n**  d) When using the old syntax, the OR operator has a greater precedence\n**     than an implicit AND. When using the new, both implicity and explicit\n**     AND operators have a higher precedence than OR.\n**\n** If compiled with SQLITE_TEST defined, then this module exports the\n** symbol \"int sqlite3_fts3_enable_parentheses\". Setting this variable\n** to zero causes the module to use the old syntax. If it is set to \n** non-zero the new syntax is activated. This is so both syntaxes can\n** be tested using a single build of testfixture.\n**\n** The following describes the syntax supported by the fts3 MATCH\n** operator in a similar format to that used by the lemon parser\n** generator. This module does not use actually lemon, it uses a\n** custom parser.\n**\n**   query ::= andexpr (OR andexpr)*.\n**\n**   andexpr ::= notexpr (AND? notexpr)*.\n**\n**   notexpr ::= nearexpr (NOT nearexpr|-TOKEN)*.\n**   notexpr ::= LP query RP.\n**\n**   nearexpr ::= phrase (NEAR distance_opt nearexpr)*.\n**\n**   distance_opt ::= .\n**   distance_opt ::= / INTEGER.\n**\n**   phrase ::= TOKEN.\n**   phrase ::= COLUMN:TOKEN.\n**   phrase ::= \"TOKEN TOKEN TOKEN...\".\n*/\n\n#ifdef SQLITE_TEST\nSQLITE_API int sqlite3_fts3_enable_parentheses = 0;\n#else\n# ifdef SQLITE_ENABLE_FTS3_PARENTHESIS \n#  define sqlite3_fts3_enable_parentheses 1\n# else\n#  define sqlite3_fts3_enable_parentheses 0\n# endif\n#endif\n\n/*\n** Default span for NEAR operators.\n*/\n#define SQLITE_FTS3_DEFAULT_NEAR_PARAM 10\n\n/* #include <string.h> */\n/* #include <assert.h> */\n\n/*\n** isNot:\n**   This variable is used by function getNextNode(). When getNextNode() is\n**   called, it sets ParseContext.isNot to true if the 'next node' is a \n**   FTSQUERY_PHRASE with a unary \"-\" attached to it. i.e. \"mysql\" in the\n**   FTS3 query \"sqlite -mysql\". Otherwise, ParseContext.isNot is set to\n**   zero.\n*/\ntypedef struct ParseContext ParseContext;\nstruct ParseContext {\n  sqlite3_tokenizer *pTokenizer;      /* Tokenizer module */\n  int iLangid;                        /* Language id used with tokenizer */\n  const char **azCol;                 /* Array of column names for fts3 table */\n  int bFts4;                          /* True to allow FTS4-only syntax */\n  int nCol;                           /* Number of entries in azCol[] */\n  int iDefaultCol;                    /* Default column to query */\n  int isNot;                          /* True if getNextNode() sees a unary - */\n  sqlite3_context *pCtx;              /* Write error message here */\n  int nNest;                          /* Number of nested brackets */\n};\n\n/*\n** This function is equivalent to the standard isspace() function. \n**\n** The standard isspace() can be awkward to use safely, because although it\n** is defined to accept an argument of type int, its behavior when passed\n** an integer that falls outside of the range of the unsigned char type\n** is undefined (and sometimes, \"undefined\" means segfault). This wrapper\n** is defined to accept an argument of type char, and always returns 0 for\n** any values that fall outside of the range of the unsigned char type (i.e.\n** negative values).\n*/\nstatic int fts3isspace(char c){\n  return c==' ' || c=='\\t' || c=='\\n' || c=='\\r' || c=='\\v' || c=='\\f';\n}\n\n/*\n** Allocate nByte bytes of memory using sqlite3_malloc(). If successful,\n** zero the memory before returning a pointer to it. If unsuccessful, \n** return NULL.\n*/\nstatic void *fts3MallocZero(int nByte){\n  void *pRet = sqlite3_malloc(nByte);\n  if( pRet ) memset(pRet, 0, nByte);\n  return pRet;\n}\n\nSQLITE_PRIVATE int sqlite3Fts3OpenTokenizer(\n  sqlite3_tokenizer *pTokenizer,\n  int iLangid,\n  const char *z,\n  int n,\n  sqlite3_tokenizer_cursor **ppCsr\n){\n  sqlite3_tokenizer_module const *pModule = pTokenizer->pModule;\n  sqlite3_tokenizer_cursor *pCsr = 0;\n  int rc;\n\n  rc = pModule->xOpen(pTokenizer, z, n, &pCsr);\n  assert( rc==SQLITE_OK || pCsr==0 );\n  if( rc==SQLITE_OK ){\n    pCsr->pTokenizer = pTokenizer;\n    if( pModule->iVersion>=1 ){\n      rc = pModule->xLanguageid(pCsr, iLangid);\n      if( rc!=SQLITE_OK ){\n        pModule->xClose(pCsr);\n        pCsr = 0;\n      }\n    }\n  }\n  *ppCsr = pCsr;\n  return rc;\n}\n\n/*\n** Function getNextNode(), which is called by fts3ExprParse(), may itself\n** call fts3ExprParse(). So this forward declaration is required.\n*/\nstatic int fts3ExprParse(ParseContext *, const char *, int, Fts3Expr **, int *);\n\n/*\n** Extract the next token from buffer z (length n) using the tokenizer\n** and other information (column names etc.) in pParse. Create an Fts3Expr\n** structure of type FTSQUERY_PHRASE containing a phrase consisting of this\n** single token and set *ppExpr to point to it. If the end of the buffer is\n** reached before a token is found, set *ppExpr to zero. It is the\n** responsibility of the caller to eventually deallocate the allocated \n** Fts3Expr structure (if any) by passing it to sqlite3_free().\n**\n** Return SQLITE_OK if successful, or SQLITE_NOMEM if a memory allocation\n** fails.\n*/\nstatic int getNextToken(\n  ParseContext *pParse,                   /* fts3 query parse context */\n  int iCol,                               /* Value for Fts3Phrase.iColumn */\n  const char *z, int n,                   /* Input string */\n  Fts3Expr **ppExpr,                      /* OUT: expression */\n  int *pnConsumed                         /* OUT: Number of bytes consumed */\n){\n  sqlite3_tokenizer *pTokenizer = pParse->pTokenizer;\n  sqlite3_tokenizer_module const *pModule = pTokenizer->pModule;\n  int rc;\n  sqlite3_tokenizer_cursor *pCursor;\n  Fts3Expr *pRet = 0;\n  int i = 0;\n\n  /* Set variable i to the maximum number of bytes of input to tokenize. */\n  for(i=0; i<n; i++){\n    if( sqlite3_fts3_enable_parentheses && (z[i]=='(' || z[i]==')') ) break;\n    if( z[i]=='\"' ) break;\n  }\n\n  *pnConsumed = i;\n  rc = sqlite3Fts3OpenTokenizer(pTokenizer, pParse->iLangid, z, i, &pCursor);\n  if( rc==SQLITE_OK ){\n    const char *zToken;\n    int nToken = 0, iStart = 0, iEnd = 0, iPosition = 0;\n    int nByte;                               /* total space to allocate */\n\n    rc = pModule->xNext(pCursor, &zToken, &nToken, &iStart, &iEnd, &iPosition);\n    if( rc==SQLITE_OK ){\n      nByte = sizeof(Fts3Expr) + sizeof(Fts3Phrase) + nToken;\n      pRet = (Fts3Expr *)fts3MallocZero(nByte);\n      if( !pRet ){\n        rc = SQLITE_NOMEM;\n      }else{\n        pRet->eType = FTSQUERY_PHRASE;\n        pRet->pPhrase = (Fts3Phrase *)&pRet[1];\n        pRet->pPhrase->nToken = 1;\n        pRet->pPhrase->iColumn = iCol;\n        pRet->pPhrase->aToken[0].n = nToken;\n        pRet->pPhrase->aToken[0].z = (char *)&pRet->pPhrase[1];\n        memcpy(pRet->pPhrase->aToken[0].z, zToken, nToken);\n\n        if( iEnd<n && z[iEnd]=='*' ){\n          pRet->pPhrase->aToken[0].isPrefix = 1;\n          iEnd++;\n        }\n\n        while( 1 ){\n          if( !sqlite3_fts3_enable_parentheses \n           && iStart>0 && z[iStart-1]=='-' \n          ){\n            pParse->isNot = 1;\n            iStart--;\n          }else if( pParse->bFts4 && iStart>0 && z[iStart-1]=='^' ){\n            pRet->pPhrase->aToken[0].bFirst = 1;\n            iStart--;\n          }else{\n            break;\n          }\n        }\n\n      }\n      *pnConsumed = iEnd;\n    }else if( i && rc==SQLITE_DONE ){\n      rc = SQLITE_OK;\n    }\n\n    pModule->xClose(pCursor);\n  }\n  \n  *ppExpr = pRet;\n  return rc;\n}\n\n\n/*\n** Enlarge a memory allocation.  If an out-of-memory allocation occurs,\n** then free the old allocation.\n*/\nstatic void *fts3ReallocOrFree(void *pOrig, int nNew){\n  void *pRet = sqlite3_realloc(pOrig, nNew);\n  if( !pRet ){\n    sqlite3_free(pOrig);\n  }\n  return pRet;\n}\n\n/*\n** Buffer zInput, length nInput, contains the contents of a quoted string\n** that appeared as part of an fts3 query expression. Neither quote character\n** is included in the buffer. This function attempts to tokenize the entire\n** input buffer and create an Fts3Expr structure of type FTSQUERY_PHRASE \n** containing the results.\n**\n** If successful, SQLITE_OK is returned and *ppExpr set to point at the\n** allocated Fts3Expr structure. Otherwise, either SQLITE_NOMEM (out of memory\n** error) or SQLITE_ERROR (tokenization error) is returned and *ppExpr set\n** to 0.\n*/\nstatic int getNextString(\n  ParseContext *pParse,                   /* fts3 query parse context */\n  const char *zInput, int nInput,         /* Input string */\n  Fts3Expr **ppExpr                       /* OUT: expression */\n){\n  sqlite3_tokenizer *pTokenizer = pParse->pTokenizer;\n  sqlite3_tokenizer_module const *pModule = pTokenizer->pModule;\n  int rc;\n  Fts3Expr *p = 0;\n  sqlite3_tokenizer_cursor *pCursor = 0;\n  char *zTemp = 0;\n  int nTemp = 0;\n\n  const int nSpace = sizeof(Fts3Expr) + sizeof(Fts3Phrase);\n  int nToken = 0;\n\n  /* The final Fts3Expr data structure, including the Fts3Phrase,\n  ** Fts3PhraseToken structures token buffers are all stored as a single \n  ** allocation so that the expression can be freed with a single call to\n  ** sqlite3_free(). Setting this up requires a two pass approach.\n  **\n  ** The first pass, in the block below, uses a tokenizer cursor to iterate\n  ** through the tokens in the expression. This pass uses fts3ReallocOrFree()\n  ** to assemble data in two dynamic buffers:\n  **\n  **   Buffer p: Points to the Fts3Expr structure, followed by the Fts3Phrase\n  **             structure, followed by the array of Fts3PhraseToken \n  **             structures. This pass only populates the Fts3PhraseToken array.\n  **\n  **   Buffer zTemp: Contains copies of all tokens.\n  **\n  ** The second pass, in the block that begins \"if( rc==SQLITE_DONE )\" below,\n  ** appends buffer zTemp to buffer p, and fills in the Fts3Expr and Fts3Phrase\n  ** structures.\n  */\n  rc = sqlite3Fts3OpenTokenizer(\n      pTokenizer, pParse->iLangid, zInput, nInput, &pCursor);\n  if( rc==SQLITE_OK ){\n    int ii;\n    for(ii=0; rc==SQLITE_OK; ii++){\n      const char *zByte;\n      int nByte = 0, iBegin = 0, iEnd = 0, iPos = 0;\n      rc = pModule->xNext(pCursor, &zByte, &nByte, &iBegin, &iEnd, &iPos);\n      if( rc==SQLITE_OK ){\n        Fts3PhraseToken *pToken;\n\n        p = fts3ReallocOrFree(p, nSpace + ii*sizeof(Fts3PhraseToken));\n        if( !p ) goto no_mem;\n\n        zTemp = fts3ReallocOrFree(zTemp, nTemp + nByte);\n        if( !zTemp ) goto no_mem;\n\n        assert( nToken==ii );\n        pToken = &((Fts3Phrase *)(&p[1]))->aToken[ii];\n        memset(pToken, 0, sizeof(Fts3PhraseToken));\n\n        memcpy(&zTemp[nTemp], zByte, nByte);\n        nTemp += nByte;\n\n        pToken->n = nByte;\n        pToken->isPrefix = (iEnd<nInput && zInput[iEnd]=='*');\n        pToken->bFirst = (iBegin>0 && zInput[iBegin-1]=='^');\n        nToken = ii+1;\n      }\n    }\n\n    pModule->xClose(pCursor);\n    pCursor = 0;\n  }\n\n  if( rc==SQLITE_DONE ){\n    int jj;\n    char *zBuf = 0;\n\n    p = fts3ReallocOrFree(p, nSpace + nToken*sizeof(Fts3PhraseToken) + nTemp);\n    if( !p ) goto no_mem;\n    memset(p, 0, (char *)&(((Fts3Phrase *)&p[1])->aToken[0])-(char *)p);\n    p->eType = FTSQUERY_PHRASE;\n    p->pPhrase = (Fts3Phrase *)&p[1];\n    p->pPhrase->iColumn = pParse->iDefaultCol;\n    p->pPhrase->nToken = nToken;\n\n    zBuf = (char *)&p->pPhrase->aToken[nToken];\n    if( zTemp ){\n      memcpy(zBuf, zTemp, nTemp);\n      sqlite3_free(zTemp);\n    }else{\n      assert( nTemp==0 );\n    }\n\n    for(jj=0; jj<p->pPhrase->nToken; jj++){\n      p->pPhrase->aToken[jj].z = zBuf;\n      zBuf += p->pPhrase->aToken[jj].n;\n    }\n    rc = SQLITE_OK;\n  }\n\n  *ppExpr = p;\n  return rc;\nno_mem:\n\n  if( pCursor ){\n    pModule->xClose(pCursor);\n  }\n  sqlite3_free(zTemp);\n  sqlite3_free(p);\n  *ppExpr = 0;\n  return SQLITE_NOMEM;\n}\n\n/*\n** The output variable *ppExpr is populated with an allocated Fts3Expr \n** structure, or set to 0 if the end of the input buffer is reached.\n**\n** Returns an SQLite error code. SQLITE_OK if everything works, SQLITE_NOMEM\n** if a malloc failure occurs, or SQLITE_ERROR if a parse error is encountered.\n** If SQLITE_ERROR is returned, pContext is populated with an error message.\n*/\nstatic int getNextNode(\n  ParseContext *pParse,                   /* fts3 query parse context */\n  const char *z, int n,                   /* Input string */\n  Fts3Expr **ppExpr,                      /* OUT: expression */\n  int *pnConsumed                         /* OUT: Number of bytes consumed */\n){\n  static const struct Fts3Keyword {\n    char *z;                              /* Keyword text */\n    unsigned char n;                      /* Length of the keyword */\n    unsigned char parenOnly;              /* Only valid in paren mode */\n    unsigned char eType;                  /* Keyword code */\n  } aKeyword[] = {\n    { \"OR\" ,  2, 0, FTSQUERY_OR   },\n    { \"AND\",  3, 1, FTSQUERY_AND  },\n    { \"NOT\",  3, 1, FTSQUERY_NOT  },\n    { \"NEAR\", 4, 0, FTSQUERY_NEAR }\n  };\n  int ii;\n  int iCol;\n  int iColLen;\n  int rc;\n  Fts3Expr *pRet = 0;\n\n  const char *zInput = z;\n  int nInput = n;\n\n  pParse->isNot = 0;\n\n  /* Skip over any whitespace before checking for a keyword, an open or\n  ** close bracket, or a quoted string. \n  */\n  while( nInput>0 && fts3isspace(*zInput) ){\n    nInput--;\n    zInput++;\n  }\n  if( nInput==0 ){\n    return SQLITE_DONE;\n  }\n\n  /* See if we are dealing with a keyword. */\n  for(ii=0; ii<(int)(sizeof(aKeyword)/sizeof(struct Fts3Keyword)); ii++){\n    const struct Fts3Keyword *pKey = &aKeyword[ii];\n\n    if( (pKey->parenOnly & ~sqlite3_fts3_enable_parentheses)!=0 ){\n      continue;\n    }\n\n    if( nInput>=pKey->n && 0==memcmp(zInput, pKey->z, pKey->n) ){\n      int nNear = SQLITE_FTS3_DEFAULT_NEAR_PARAM;\n      int nKey = pKey->n;\n      char cNext;\n\n      /* If this is a \"NEAR\" keyword, check for an explicit nearness. */\n      if( pKey->eType==FTSQUERY_NEAR ){\n        assert( nKey==4 );\n        if( zInput[4]=='/' && zInput[5]>='0' && zInput[5]<='9' ){\n          nNear = 0;\n          for(nKey=5; zInput[nKey]>='0' && zInput[nKey]<='9'; nKey++){\n            nNear = nNear * 10 + (zInput[nKey] - '0');\n          }\n        }\n      }\n\n      /* At this point this is probably a keyword. But for that to be true,\n      ** the next byte must contain either whitespace, an open or close\n      ** parenthesis, a quote character, or EOF. \n      */\n      cNext = zInput[nKey];\n      if( fts3isspace(cNext) \n       || cNext=='\"' || cNext=='(' || cNext==')' || cNext==0\n      ){\n        pRet = (Fts3Expr *)fts3MallocZero(sizeof(Fts3Expr));\n        if( !pRet ){\n          return SQLITE_NOMEM;\n        }\n        pRet->eType = pKey->eType;\n        pRet->nNear = nNear;\n        *ppExpr = pRet;\n        *pnConsumed = (int)((zInput - z) + nKey);\n        return SQLITE_OK;\n      }\n\n      /* Turns out that wasn't a keyword after all. This happens if the\n      ** user has supplied a token such as \"ORacle\". Continue.\n      */\n    }\n  }\n\n  /* See if we are dealing with a quoted phrase. If this is the case, then\n  ** search for the closing quote and pass the whole string to getNextString()\n  ** for processing. This is easy to do, as fts3 has no syntax for escaping\n  ** a quote character embedded in a string.\n  */\n  if( *zInput=='\"' ){\n    for(ii=1; ii<nInput && zInput[ii]!='\"'; ii++);\n    *pnConsumed = (int)((zInput - z) + ii + 1);\n    if( ii==nInput ){\n      return SQLITE_ERROR;\n    }\n    return getNextString(pParse, &zInput[1], ii-1, ppExpr);\n  }\n\n  if( sqlite3_fts3_enable_parentheses ){\n    if( *zInput=='(' ){\n      int nConsumed = 0;\n      pParse->nNest++;\n      rc = fts3ExprParse(pParse, zInput+1, nInput-1, ppExpr, &nConsumed);\n      if( rc==SQLITE_OK && !*ppExpr ){ rc = SQLITE_DONE; }\n      *pnConsumed = (int)(zInput - z) + 1 + nConsumed;\n      return rc;\n    }else if( *zInput==')' ){\n      pParse->nNest--;\n      *pnConsumed = (int)((zInput - z) + 1);\n      *ppExpr = 0;\n      return SQLITE_DONE;\n    }\n  }\n\n  /* If control flows to this point, this must be a regular token, or \n  ** the end of the input. Read a regular token using the sqlite3_tokenizer\n  ** interface. Before doing so, figure out if there is an explicit\n  ** column specifier for the token. \n  **\n  ** TODO: Strangely, it is not possible to associate a column specifier\n  ** with a quoted phrase, only with a single token. Not sure if this was\n  ** an implementation artifact or an intentional decision when fts3 was\n  ** first implemented. Whichever it was, this module duplicates the \n  ** limitation.\n  */\n  iCol = pParse->iDefaultCol;\n  iColLen = 0;\n  for(ii=0; ii<pParse->nCol; ii++){\n    const char *zStr = pParse->azCol[ii];\n    int nStr = (int)strlen(zStr);\n    if( nInput>nStr && zInput[nStr]==':' \n     && sqlite3_strnicmp(zStr, zInput, nStr)==0 \n    ){\n      iCol = ii;\n      iColLen = (int)((zInput - z) + nStr + 1);\n      break;\n    }\n  }\n  rc = getNextToken(pParse, iCol, &z[iColLen], n-iColLen, ppExpr, pnConsumed);\n  *pnConsumed += iColLen;\n  return rc;\n}\n\n/*\n** The argument is an Fts3Expr structure for a binary operator (any type\n** except an FTSQUERY_PHRASE). Return an integer value representing the\n** precedence of the operator. Lower values have a higher precedence (i.e.\n** group more tightly). For example, in the C language, the == operator\n** groups more tightly than ||, and would therefore have a higher precedence.\n**\n** When using the new fts3 query syntax (when SQLITE_ENABLE_FTS3_PARENTHESIS\n** is defined), the order of the operators in precedence from highest to\n** lowest is:\n**\n**   NEAR\n**   NOT\n**   AND (including implicit ANDs)\n**   OR\n**\n** Note that when using the old query syntax, the OR operator has a higher\n** precedence than the AND operator.\n*/\nstatic int opPrecedence(Fts3Expr *p){\n  assert( p->eType!=FTSQUERY_PHRASE );\n  if( sqlite3_fts3_enable_parentheses ){\n    return p->eType;\n  }else if( p->eType==FTSQUERY_NEAR ){\n    return 1;\n  }else if( p->eType==FTSQUERY_OR ){\n    return 2;\n  }\n  assert( p->eType==FTSQUERY_AND );\n  return 3;\n}\n\n/*\n** Argument ppHead contains a pointer to the current head of a query \n** expression tree being parsed. pPrev is the expression node most recently\n** inserted into the tree. This function adds pNew, which is always a binary\n** operator node, into the expression tree based on the relative precedence\n** of pNew and the existing nodes of the tree. This may result in the head\n** of the tree changing, in which case *ppHead is set to the new root node.\n*/\nstatic void insertBinaryOperator(\n  Fts3Expr **ppHead,       /* Pointer to the root node of a tree */\n  Fts3Expr *pPrev,         /* Node most recently inserted into the tree */\n  Fts3Expr *pNew           /* New binary node to insert into expression tree */\n){\n  Fts3Expr *pSplit = pPrev;\n  while( pSplit->pParent && opPrecedence(pSplit->pParent)<=opPrecedence(pNew) ){\n    pSplit = pSplit->pParent;\n  }\n\n  if( pSplit->pParent ){\n    assert( pSplit->pParent->pRight==pSplit );\n    pSplit->pParent->pRight = pNew;\n    pNew->pParent = pSplit->pParent;\n  }else{\n    *ppHead = pNew;\n  }\n  pNew->pLeft = pSplit;\n  pSplit->pParent = pNew;\n}\n\n/*\n** Parse the fts3 query expression found in buffer z, length n. This function\n** returns either when the end of the buffer is reached or an unmatched \n** closing bracket - ')' - is encountered.\n**\n** If successful, SQLITE_OK is returned, *ppExpr is set to point to the\n** parsed form of the expression and *pnConsumed is set to the number of\n** bytes read from buffer z. Otherwise, *ppExpr is set to 0 and SQLITE_NOMEM\n** (out of memory error) or SQLITE_ERROR (parse error) is returned.\n*/\nstatic int fts3ExprParse(\n  ParseContext *pParse,                   /* fts3 query parse context */\n  const char *z, int n,                   /* Text of MATCH query */\n  Fts3Expr **ppExpr,                      /* OUT: Parsed query structure */\n  int *pnConsumed                         /* OUT: Number of bytes consumed */\n){\n  Fts3Expr *pRet = 0;\n  Fts3Expr *pPrev = 0;\n  Fts3Expr *pNotBranch = 0;               /* Only used in legacy parse mode */\n  int nIn = n;\n  const char *zIn = z;\n  int rc = SQLITE_OK;\n  int isRequirePhrase = 1;\n\n  while( rc==SQLITE_OK ){\n    Fts3Expr *p = 0;\n    int nByte = 0;\n\n    rc = getNextNode(pParse, zIn, nIn, &p, &nByte);\n    assert( nByte>0 || (rc!=SQLITE_OK && p==0) );\n    if( rc==SQLITE_OK ){\n      if( p ){\n        int isPhrase;\n\n        if( !sqlite3_fts3_enable_parentheses \n            && p->eType==FTSQUERY_PHRASE && pParse->isNot \n        ){\n          /* Create an implicit NOT operator. */\n          Fts3Expr *pNot = fts3MallocZero(sizeof(Fts3Expr));\n          if( !pNot ){\n            sqlite3Fts3ExprFree(p);\n            rc = SQLITE_NOMEM;\n            goto exprparse_out;\n          }\n          pNot->eType = FTSQUERY_NOT;\n          pNot->pRight = p;\n          p->pParent = pNot;\n          if( pNotBranch ){\n            pNot->pLeft = pNotBranch;\n            pNotBranch->pParent = pNot;\n          }\n          pNotBranch = pNot;\n          p = pPrev;\n        }else{\n          int eType = p->eType;\n          isPhrase = (eType==FTSQUERY_PHRASE || p->pLeft);\n\n          /* The isRequirePhrase variable is set to true if a phrase or\n          ** an expression contained in parenthesis is required. If a\n          ** binary operator (AND, OR, NOT or NEAR) is encounted when\n          ** isRequirePhrase is set, this is a syntax error.\n          */\n          if( !isPhrase && isRequirePhrase ){\n            sqlite3Fts3ExprFree(p);\n            rc = SQLITE_ERROR;\n            goto exprparse_out;\n          }\n\n          if( isPhrase && !isRequirePhrase ){\n            /* Insert an implicit AND operator. */\n            Fts3Expr *pAnd;\n            assert( pRet && pPrev );\n            pAnd = fts3MallocZero(sizeof(Fts3Expr));\n            if( !pAnd ){\n              sqlite3Fts3ExprFree(p);\n              rc = SQLITE_NOMEM;\n              goto exprparse_out;\n            }\n            pAnd->eType = FTSQUERY_AND;\n            insertBinaryOperator(&pRet, pPrev, pAnd);\n            pPrev = pAnd;\n          }\n\n          /* This test catches attempts to make either operand of a NEAR\n           ** operator something other than a phrase. For example, either of\n           ** the following:\n           **\n           **    (bracketed expression) NEAR phrase\n           **    phrase NEAR (bracketed expression)\n           **\n           ** Return an error in either case.\n           */\n          if( pPrev && (\n            (eType==FTSQUERY_NEAR && !isPhrase && pPrev->eType!=FTSQUERY_PHRASE)\n         || (eType!=FTSQUERY_PHRASE && isPhrase && pPrev->eType==FTSQUERY_NEAR)\n          )){\n            sqlite3Fts3ExprFree(p);\n            rc = SQLITE_ERROR;\n            goto exprparse_out;\n          }\n\n          if( isPhrase ){\n            if( pRet ){\n              assert( pPrev && pPrev->pLeft && pPrev->pRight==0 );\n              pPrev->pRight = p;\n              p->pParent = pPrev;\n            }else{\n              pRet = p;\n            }\n          }else{\n            insertBinaryOperator(&pRet, pPrev, p);\n          }\n          isRequirePhrase = !isPhrase;\n        }\n        pPrev = p;\n      }\n      assert( nByte>0 );\n    }\n    assert( rc!=SQLITE_OK || (nByte>0 && nByte<=nIn) );\n    nIn -= nByte;\n    zIn += nByte;\n  }\n\n  if( rc==SQLITE_DONE && pRet && isRequirePhrase ){\n    rc = SQLITE_ERROR;\n  }\n\n  if( rc==SQLITE_DONE ){\n    rc = SQLITE_OK;\n    if( !sqlite3_fts3_enable_parentheses && pNotBranch ){\n      if( !pRet ){\n        rc = SQLITE_ERROR;\n      }else{\n        Fts3Expr *pIter = pNotBranch;\n        while( pIter->pLeft ){\n          pIter = pIter->pLeft;\n        }\n        pIter->pLeft = pRet;\n        pRet->pParent = pIter;\n        pRet = pNotBranch;\n      }\n    }\n  }\n  *pnConsumed = n - nIn;\n\nexprparse_out:\n  if( rc!=SQLITE_OK ){\n    sqlite3Fts3ExprFree(pRet);\n    sqlite3Fts3ExprFree(pNotBranch);\n    pRet = 0;\n  }\n  *ppExpr = pRet;\n  return rc;\n}\n\n/*\n** Return SQLITE_ERROR if the maximum depth of the expression tree passed \n** as the only argument is more than nMaxDepth.\n*/\nstatic int fts3ExprCheckDepth(Fts3Expr *p, int nMaxDepth){\n  int rc = SQLITE_OK;\n  if( p ){\n    if( nMaxDepth<0 ){ \n      rc = SQLITE_TOOBIG;\n    }else{\n      rc = fts3ExprCheckDepth(p->pLeft, nMaxDepth-1);\n      if( rc==SQLITE_OK ){\n        rc = fts3ExprCheckDepth(p->pRight, nMaxDepth-1);\n      }\n    }\n  }\n  return rc;\n}\n\n/*\n** This function attempts to transform the expression tree at (*pp) to\n** an equivalent but more balanced form. The tree is modified in place.\n** If successful, SQLITE_OK is returned and (*pp) set to point to the \n** new root expression node. \n**\n** nMaxDepth is the maximum allowable depth of the balanced sub-tree.\n**\n** Otherwise, if an error occurs, an SQLite error code is returned and \n** expression (*pp) freed.\n*/\nstatic int fts3ExprBalance(Fts3Expr **pp, int nMaxDepth){\n  int rc = SQLITE_OK;             /* Return code */\n  Fts3Expr *pRoot = *pp;          /* Initial root node */\n  Fts3Expr *pFree = 0;            /* List of free nodes. Linked by pParent. */\n  int eType = pRoot->eType;       /* Type of node in this tree */\n\n  if( nMaxDepth==0 ){\n    rc = SQLITE_ERROR;\n  }\n\n  if( rc==SQLITE_OK ){\n    if( (eType==FTSQUERY_AND || eType==FTSQUERY_OR) ){\n      Fts3Expr **apLeaf;\n      apLeaf = (Fts3Expr **)sqlite3_malloc(sizeof(Fts3Expr *) * nMaxDepth);\n      if( 0==apLeaf ){\n        rc = SQLITE_NOMEM;\n      }else{\n        memset(apLeaf, 0, sizeof(Fts3Expr *) * nMaxDepth);\n      }\n\n      if( rc==SQLITE_OK ){\n        int i;\n        Fts3Expr *p;\n\n        /* Set $p to point to the left-most leaf in the tree of eType nodes. */\n        for(p=pRoot; p->eType==eType; p=p->pLeft){\n          assert( p->pParent==0 || p->pParent->pLeft==p );\n          assert( p->pLeft && p->pRight );\n        }\n\n        /* This loop runs once for each leaf in the tree of eType nodes. */\n        while( 1 ){\n          int iLvl;\n          Fts3Expr *pParent = p->pParent;     /* Current parent of p */\n\n          assert( pParent==0 || pParent->pLeft==p );\n          p->pParent = 0;\n          if( pParent ){\n            pParent->pLeft = 0;\n          }else{\n            pRoot = 0;\n          }\n          rc = fts3ExprBalance(&p, nMaxDepth-1);\n          if( rc!=SQLITE_OK ) break;\n\n          for(iLvl=0; p && iLvl<nMaxDepth; iLvl++){\n            if( apLeaf[iLvl]==0 ){\n              apLeaf[iLvl] = p;\n              p = 0;\n            }else{\n              assert( pFree );\n              pFree->pLeft = apLeaf[iLvl];\n              pFree->pRight = p;\n              pFree->pLeft->pParent = pFree;\n              pFree->pRight->pParent = pFree;\n\n              p = pFree;\n              pFree = pFree->pParent;\n              p->pParent = 0;\n              apLeaf[iLvl] = 0;\n            }\n          }\n          if( p ){\n            sqlite3Fts3ExprFree(p);\n            rc = SQLITE_TOOBIG;\n            break;\n          }\n\n          /* If that was the last leaf node, break out of the loop */\n          if( pParent==0 ) break;\n\n          /* Set $p to point to the next leaf in the tree of eType nodes */\n          for(p=pParent->pRight; p->eType==eType; p=p->pLeft);\n\n          /* Remove pParent from the original tree. */\n          assert( pParent->pParent==0 || pParent->pParent->pLeft==pParent );\n          pParent->pRight->pParent = pParent->pParent;\n          if( pParent->pParent ){\n            pParent->pParent->pLeft = pParent->pRight;\n          }else{\n            assert( pParent==pRoot );\n            pRoot = pParent->pRight;\n          }\n\n          /* Link pParent into the free node list. It will be used as an\n          ** internal node of the new tree.  */\n          pParent->pParent = pFree;\n          pFree = pParent;\n        }\n\n        if( rc==SQLITE_OK ){\n          p = 0;\n          for(i=0; i<nMaxDepth; i++){\n            if( apLeaf[i] ){\n              if( p==0 ){\n                p = apLeaf[i];\n                p->pParent = 0;\n              }else{\n                assert( pFree!=0 );\n                pFree->pRight = p;\n                pFree->pLeft = apLeaf[i];\n                pFree->pLeft->pParent = pFree;\n                pFree->pRight->pParent = pFree;\n\n                p = pFree;\n                pFree = pFree->pParent;\n                p->pParent = 0;\n              }\n            }\n          }\n          pRoot = p;\n        }else{\n          /* An error occurred. Delete the contents of the apLeaf[] array \n          ** and pFree list. Everything else is cleaned up by the call to\n          ** sqlite3Fts3ExprFree(pRoot) below.  */\n          Fts3Expr *pDel;\n          for(i=0; i<nMaxDepth; i++){\n            sqlite3Fts3ExprFree(apLeaf[i]);\n          }\n          while( (pDel=pFree)!=0 ){\n            pFree = pDel->pParent;\n            sqlite3_free(pDel);\n          }\n        }\n\n        assert( pFree==0 );\n        sqlite3_free( apLeaf );\n      }\n    }else if( eType==FTSQUERY_NOT ){\n      Fts3Expr *pLeft = pRoot->pLeft;\n      Fts3Expr *pRight = pRoot->pRight;\n\n      pRoot->pLeft = 0;\n      pRoot->pRight = 0;\n      pLeft->pParent = 0;\n      pRight->pParent = 0;\n\n      rc = fts3ExprBalance(&pLeft, nMaxDepth-1);\n      if( rc==SQLITE_OK ){\n        rc = fts3ExprBalance(&pRight, nMaxDepth-1);\n      }\n\n      if( rc!=SQLITE_OK ){\n        sqlite3Fts3ExprFree(pRight);\n        sqlite3Fts3ExprFree(pLeft);\n      }else{\n        assert( pLeft && pRight );\n        pRoot->pLeft = pLeft;\n        pLeft->pParent = pRoot;\n        pRoot->pRight = pRight;\n        pRight->pParent = pRoot;\n      }\n    }\n  }\n  \n  if( rc!=SQLITE_OK ){\n    sqlite3Fts3ExprFree(pRoot);\n    pRoot = 0;\n  }\n  *pp = pRoot;\n  return rc;\n}\n\n/*\n** This function is similar to sqlite3Fts3ExprParse(), with the following\n** differences:\n**\n**   1. It does not do expression rebalancing.\n**   2. It does not check that the expression does not exceed the \n**      maximum allowable depth.\n**   3. Even if it fails, *ppExpr may still be set to point to an \n**      expression tree. It should be deleted using sqlite3Fts3ExprFree()\n**      in this case.\n*/\nstatic int fts3ExprParseUnbalanced(\n  sqlite3_tokenizer *pTokenizer,      /* Tokenizer module */\n  int iLangid,                        /* Language id for tokenizer */\n  char **azCol,                       /* Array of column names for fts3 table */\n  int bFts4,                          /* True to allow FTS4-only syntax */\n  int nCol,                           /* Number of entries in azCol[] */\n  int iDefaultCol,                    /* Default column to query */\n  const char *z, int n,               /* Text of MATCH query */\n  Fts3Expr **ppExpr                   /* OUT: Parsed query structure */\n){\n  int nParsed;\n  int rc;\n  ParseContext sParse;\n\n  memset(&sParse, 0, sizeof(ParseContext));\n  sParse.pTokenizer = pTokenizer;\n  sParse.iLangid = iLangid;\n  sParse.azCol = (const char **)azCol;\n  sParse.nCol = nCol;\n  sParse.iDefaultCol = iDefaultCol;\n  sParse.bFts4 = bFts4;\n  if( z==0 ){\n    *ppExpr = 0;\n    return SQLITE_OK;\n  }\n  if( n<0 ){\n    n = (int)strlen(z);\n  }\n  rc = fts3ExprParse(&sParse, z, n, ppExpr, &nParsed);\n  assert( rc==SQLITE_OK || *ppExpr==0 );\n\n  /* Check for mismatched parenthesis */\n  if( rc==SQLITE_OK && sParse.nNest ){\n    rc = SQLITE_ERROR;\n  }\n  \n  return rc;\n}\n\n/*\n** Parameters z and n contain a pointer to and length of a buffer containing\n** an fts3 query expression, respectively. This function attempts to parse the\n** query expression and create a tree of Fts3Expr structures representing the\n** parsed expression. If successful, *ppExpr is set to point to the head\n** of the parsed expression tree and SQLITE_OK is returned. If an error\n** occurs, either SQLITE_NOMEM (out-of-memory error) or SQLITE_ERROR (parse\n** error) is returned and *ppExpr is set to 0.\n**\n** If parameter n is a negative number, then z is assumed to point to a\n** nul-terminated string and the length is determined using strlen().\n**\n** The first parameter, pTokenizer, is passed the fts3 tokenizer module to\n** use to normalize query tokens while parsing the expression. The azCol[]\n** array, which is assumed to contain nCol entries, should contain the names\n** of each column in the target fts3 table, in order from left to right. \n** Column names must be nul-terminated strings.\n**\n** The iDefaultCol parameter should be passed the index of the table column\n** that appears on the left-hand-side of the MATCH operator (the default\n** column to match against for tokens for which a column name is not explicitly\n** specified as part of the query string), or -1 if tokens may by default\n** match any table column.\n*/\nSQLITE_PRIVATE int sqlite3Fts3ExprParse(\n  sqlite3_tokenizer *pTokenizer,      /* Tokenizer module */\n  int iLangid,                        /* Language id for tokenizer */\n  char **azCol,                       /* Array of column names for fts3 table */\n  int bFts4,                          /* True to allow FTS4-only syntax */\n  int nCol,                           /* Number of entries in azCol[] */\n  int iDefaultCol,                    /* Default column to query */\n  const char *z, int n,               /* Text of MATCH query */\n  Fts3Expr **ppExpr,                  /* OUT: Parsed query structure */\n  char **pzErr                        /* OUT: Error message (sqlite3_malloc) */\n){\n  int rc = fts3ExprParseUnbalanced(\n      pTokenizer, iLangid, azCol, bFts4, nCol, iDefaultCol, z, n, ppExpr\n  );\n  \n  /* Rebalance the expression. And check that its depth does not exceed\n  ** SQLITE_FTS3_MAX_EXPR_DEPTH.  */\n  if( rc==SQLITE_OK && *ppExpr ){\n    rc = fts3ExprBalance(ppExpr, SQLITE_FTS3_MAX_EXPR_DEPTH);\n    if( rc==SQLITE_OK ){\n      rc = fts3ExprCheckDepth(*ppExpr, SQLITE_FTS3_MAX_EXPR_DEPTH);\n    }\n  }\n\n  if( rc!=SQLITE_OK ){\n    sqlite3Fts3ExprFree(*ppExpr);\n    *ppExpr = 0;\n    if( rc==SQLITE_TOOBIG ){\n      sqlite3Fts3ErrMsg(pzErr,\n          \"FTS expression tree is too large (maximum depth %d)\", \n          SQLITE_FTS3_MAX_EXPR_DEPTH\n      );\n      rc = SQLITE_ERROR;\n    }else if( rc==SQLITE_ERROR ){\n      sqlite3Fts3ErrMsg(pzErr, \"malformed MATCH expression: [%s]\", z);\n    }\n  }\n\n  return rc;\n}\n\n/*\n** Free a single node of an expression tree.\n*/\nstatic void fts3FreeExprNode(Fts3Expr *p){\n  assert( p->eType==FTSQUERY_PHRASE || p->pPhrase==0 );\n  sqlite3Fts3EvalPhraseCleanup(p->pPhrase);\n  sqlite3_free(p->aMI);\n  sqlite3_free(p);\n}\n\n/*\n** Free a parsed fts3 query expression allocated by sqlite3Fts3ExprParse().\n**\n** This function would be simpler if it recursively called itself. But\n** that would mean passing a sufficiently large expression to ExprParse()\n** could cause a stack overflow.\n*/\nSQLITE_PRIVATE void sqlite3Fts3ExprFree(Fts3Expr *pDel){\n  Fts3Expr *p;\n  assert( pDel==0 || pDel->pParent==0 );\n  for(p=pDel; p && (p->pLeft||p->pRight); p=(p->pLeft ? p->pLeft : p->pRight)){\n    assert( p->pParent==0 || p==p->pParent->pRight || p==p->pParent->pLeft );\n  }\n  while( p ){\n    Fts3Expr *pParent = p->pParent;\n    fts3FreeExprNode(p);\n    if( pParent && p==pParent->pLeft && pParent->pRight ){\n      p = pParent->pRight;\n      while( p && (p->pLeft || p->pRight) ){\n        assert( p==p->pParent->pRight || p==p->pParent->pLeft );\n        p = (p->pLeft ? p->pLeft : p->pRight);\n      }\n    }else{\n      p = pParent;\n    }\n  }\n}\n\n/****************************************************************************\n*****************************************************************************\n** Everything after this point is just test code.\n*/\n\n#ifdef SQLITE_TEST\n\n/* #include <stdio.h> */\n\n/*\n** Function to query the hash-table of tokenizers (see README.tokenizers).\n*/\nstatic int queryTestTokenizer(\n  sqlite3 *db, \n  const char *zName,  \n  const sqlite3_tokenizer_module **pp\n){\n  int rc;\n  sqlite3_stmt *pStmt;\n  const char zSql[] = \"SELECT fts3_tokenizer(?)\";\n\n  *pp = 0;\n  rc = sqlite3_prepare_v2(db, zSql, -1, &pStmt, 0);\n  if( rc!=SQLITE_OK ){\n    return rc;\n  }\n\n  sqlite3_bind_text(pStmt, 1, zName, -1, SQLITE_STATIC);\n  if( SQLITE_ROW==sqlite3_step(pStmt) ){\n    if( sqlite3_column_type(pStmt, 0)==SQLITE_BLOB ){\n      memcpy((void *)pp, sqlite3_column_blob(pStmt, 0), sizeof(*pp));\n    }\n  }\n\n  return sqlite3_finalize(pStmt);\n}\n\n/*\n** Return a pointer to a buffer containing a text representation of the\n** expression passed as the first argument. The buffer is obtained from\n** sqlite3_malloc(). It is the responsibility of the caller to use \n** sqlite3_free() to release the memory. If an OOM condition is encountered,\n** NULL is returned.\n**\n** If the second argument is not NULL, then its contents are prepended to \n** the returned expression text and then freed using sqlite3_free().\n*/\nstatic char *exprToString(Fts3Expr *pExpr, char *zBuf){\n  if( pExpr==0 ){\n    return sqlite3_mprintf(\"\");\n  }\n  switch( pExpr->eType ){\n    case FTSQUERY_PHRASE: {\n      Fts3Phrase *pPhrase = pExpr->pPhrase;\n      int i;\n      zBuf = sqlite3_mprintf(\n          \"%zPHRASE %d 0\", zBuf, pPhrase->iColumn);\n      for(i=0; zBuf && i<pPhrase->nToken; i++){\n        zBuf = sqlite3_mprintf(\"%z %.*s%s\", zBuf, \n            pPhrase->aToken[i].n, pPhrase->aToken[i].z,\n            (pPhrase->aToken[i].isPrefix?\"+\":\"\")\n        );\n      }\n      return zBuf;\n    }\n\n    case FTSQUERY_NEAR:\n      zBuf = sqlite3_mprintf(\"%zNEAR/%d \", zBuf, pExpr->nNear);\n      break;\n    case FTSQUERY_NOT:\n      zBuf = sqlite3_mprintf(\"%zNOT \", zBuf);\n      break;\n    case FTSQUERY_AND:\n      zBuf = sqlite3_mprintf(\"%zAND \", zBuf);\n      break;\n    case FTSQUERY_OR:\n      zBuf = sqlite3_mprintf(\"%zOR \", zBuf);\n      break;\n  }\n\n  if( zBuf ) zBuf = sqlite3_mprintf(\"%z{\", zBuf);\n  if( zBuf ) zBuf = exprToString(pExpr->pLeft, zBuf);\n  if( zBuf ) zBuf = sqlite3_mprintf(\"%z} {\", zBuf);\n\n  if( zBuf ) zBuf = exprToString(pExpr->pRight, zBuf);\n  if( zBuf ) zBuf = sqlite3_mprintf(\"%z}\", zBuf);\n\n  return zBuf;\n}\n\n/*\n** This is the implementation of a scalar SQL function used to test the \n** expression parser. It should be called as follows:\n**\n**   fts3_exprtest(<tokenizer>, <expr>, <column 1>, ...);\n**\n** The first argument, <tokenizer>, is the name of the fts3 tokenizer used\n** to parse the query expression (see README.tokenizers). The second argument\n** is the query expression to parse. Each subsequent argument is the name\n** of a column of the fts3 table that the query expression may refer to.\n** For example:\n**\n**   SELECT fts3_exprtest('simple', 'Bill col2:Bloggs', 'col1', 'col2');\n*/\nstatic void fts3ExprTest(\n  sqlite3_context *context,\n  int argc,\n  sqlite3_value **argv\n){\n  sqlite3_tokenizer_module const *pModule = 0;\n  sqlite3_tokenizer *pTokenizer = 0;\n  int rc;\n  char **azCol = 0;\n  const char *zExpr;\n  int nExpr;\n  int nCol;\n  int ii;\n  Fts3Expr *pExpr;\n  char *zBuf = 0;\n  sqlite3 *db = sqlite3_context_db_handle(context);\n\n  if( argc<3 ){\n    sqlite3_result_error(context, \n        \"Usage: fts3_exprtest(tokenizer, expr, col1, ...\", -1\n    );\n    return;\n  }\n\n  rc = queryTestTokenizer(db,\n                          (const char *)sqlite3_value_text(argv[0]), &pModule);\n  if( rc==SQLITE_NOMEM ){\n    sqlite3_result_error_nomem(context);\n    goto exprtest_out;\n  }else if( !pModule ){\n    sqlite3_result_error(context, \"No such tokenizer module\", -1);\n    goto exprtest_out;\n  }\n\n  rc = pModule->xCreate(0, 0, &pTokenizer);\n  assert( rc==SQLITE_NOMEM || rc==SQLITE_OK );\n  if( rc==SQLITE_NOMEM ){\n    sqlite3_result_error_nomem(context);\n    goto exprtest_out;\n  }\n  pTokenizer->pModule = pModule;\n\n  zExpr = (const char *)sqlite3_value_text(argv[1]);\n  nExpr = sqlite3_value_bytes(argv[1]);\n  nCol = argc-2;\n  azCol = (char **)sqlite3_malloc(nCol*sizeof(char *));\n  if( !azCol ){\n    sqlite3_result_error_nomem(context);\n    goto exprtest_out;\n  }\n  for(ii=0; ii<nCol; ii++){\n    azCol[ii] = (char *)sqlite3_value_text(argv[ii+2]);\n  }\n\n  if( sqlite3_user_data(context) ){\n    char *zDummy = 0;\n    rc = sqlite3Fts3ExprParse(\n        pTokenizer, 0, azCol, 0, nCol, nCol, zExpr, nExpr, &pExpr, &zDummy\n    );\n    assert( rc==SQLITE_OK || pExpr==0 );\n    sqlite3_free(zDummy);\n  }else{\n    rc = fts3ExprParseUnbalanced(\n        pTokenizer, 0, azCol, 0, nCol, nCol, zExpr, nExpr, &pExpr\n    );\n  }\n\n  if( rc!=SQLITE_OK && rc!=SQLITE_NOMEM ){\n    sqlite3Fts3ExprFree(pExpr);\n    sqlite3_result_error(context, \"Error parsing expression\", -1);\n  }else if( rc==SQLITE_NOMEM || !(zBuf = exprToString(pExpr, 0)) ){\n    sqlite3_result_error_nomem(context);\n  }else{\n    sqlite3_result_text(context, zBuf, -1, SQLITE_TRANSIENT);\n    sqlite3_free(zBuf);\n  }\n\n  sqlite3Fts3ExprFree(pExpr);\n\nexprtest_out:\n  if( pModule && pTokenizer ){\n    rc = pModule->xDestroy(pTokenizer);\n  }\n  sqlite3_free(azCol);\n}\n\n/*\n** Register the query expression parser test function fts3_exprtest() \n** with database connection db. \n*/\nSQLITE_PRIVATE int sqlite3Fts3ExprInitTestInterface(sqlite3* db){\n  int rc = sqlite3_create_function(\n      db, \"fts3_exprtest\", -1, SQLITE_UTF8, 0, fts3ExprTest, 0, 0\n  );\n  if( rc==SQLITE_OK ){\n    rc = sqlite3_create_function(db, \"fts3_exprtest_rebalance\", \n        -1, SQLITE_UTF8, (void *)1, fts3ExprTest, 0, 0\n    );\n  }\n  return rc;\n}\n\n#endif\n#endif /* !defined(SQLITE_CORE) || defined(SQLITE_ENABLE_FTS3) */\n\n/************** End of fts3_expr.c *******************************************/\n/************** Begin file fts3_hash.c ***************************************/\n/*\n** 2001 September 22\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n*************************************************************************\n** This is the implementation of generic hash-tables used in SQLite.\n** We've modified it slightly to serve as a standalone hash table\n** implementation for the full-text indexing module.\n*/\n\n/*\n** The code in this file is only compiled if:\n**\n**     * The FTS3 module is being built as an extension\n**       (in which case SQLITE_CORE is not defined), or\n**\n**     * The FTS3 module is being built into the core of\n**       SQLite (in which case SQLITE_ENABLE_FTS3 is defined).\n*/\n/* #include \"fts3Int.h\" */\n#if !defined(SQLITE_CORE) || defined(SQLITE_ENABLE_FTS3)\n\n/* #include <assert.h> */\n/* #include <stdlib.h> */\n/* #include <string.h> */\n\n/* #include \"fts3_hash.h\" */\n\n/*\n** Malloc and Free functions\n*/\nstatic void *fts3HashMalloc(int n){\n  void *p = sqlite3_malloc(n);\n  if( p ){\n    memset(p, 0, n);\n  }\n  return p;\n}\nstatic void fts3HashFree(void *p){\n  sqlite3_free(p);\n}\n\n/* Turn bulk memory into a hash table object by initializing the\n** fields of the Hash structure.\n**\n** \"pNew\" is a pointer to the hash table that is to be initialized.\n** keyClass is one of the constants \n** FTS3_HASH_BINARY or FTS3_HASH_STRING.  The value of keyClass \n** determines what kind of key the hash table will use.  \"copyKey\" is\n** true if the hash table should make its own private copy of keys and\n** false if it should just use the supplied pointer.\n*/\nSQLITE_PRIVATE void sqlite3Fts3HashInit(Fts3Hash *pNew, char keyClass, char copyKey){\n  assert( pNew!=0 );\n  assert( keyClass>=FTS3_HASH_STRING && keyClass<=FTS3_HASH_BINARY );\n  pNew->keyClass = keyClass;\n  pNew->copyKey = copyKey;\n  pNew->first = 0;\n  pNew->count = 0;\n  pNew->htsize = 0;\n  pNew->ht = 0;\n}\n\n/* Remove all entries from a hash table.  Reclaim all memory.\n** Call this routine to delete a hash table or to reset a hash table\n** to the empty state.\n*/\nSQLITE_PRIVATE void sqlite3Fts3HashClear(Fts3Hash *pH){\n  Fts3HashElem *elem;         /* For looping over all elements of the table */\n\n  assert( pH!=0 );\n  elem = pH->first;\n  pH->first = 0;\n  fts3HashFree(pH->ht);\n  pH->ht = 0;\n  pH->htsize = 0;\n  while( elem ){\n    Fts3HashElem *next_elem = elem->next;\n    if( pH->copyKey && elem->pKey ){\n      fts3HashFree(elem->pKey);\n    }\n    fts3HashFree(elem);\n    elem = next_elem;\n  }\n  pH->count = 0;\n}\n\n/*\n** Hash and comparison functions when the mode is FTS3_HASH_STRING\n*/\nstatic int fts3StrHash(const void *pKey, int nKey){\n  const char *z = (const char *)pKey;\n  unsigned h = 0;\n  if( nKey<=0 ) nKey = (int) strlen(z);\n  while( nKey > 0  ){\n    h = (h<<3) ^ h ^ *z++;\n    nKey--;\n  }\n  return (int)(h & 0x7fffffff);\n}\nstatic int fts3StrCompare(const void *pKey1, int n1, const void *pKey2, int n2){\n  if( n1!=n2 ) return 1;\n  return strncmp((const char*)pKey1,(const char*)pKey2,n1);\n}\n\n/*\n** Hash and comparison functions when the mode is FTS3_HASH_BINARY\n*/\nstatic int fts3BinHash(const void *pKey, int nKey){\n  int h = 0;\n  const char *z = (const char *)pKey;\n  while( nKey-- > 0 ){\n    h = (h<<3) ^ h ^ *(z++);\n  }\n  return h & 0x7fffffff;\n}\nstatic int fts3BinCompare(const void *pKey1, int n1, const void *pKey2, int n2){\n  if( n1!=n2 ) return 1;\n  return memcmp(pKey1,pKey2,n1);\n}\n\n/*\n** Return a pointer to the appropriate hash function given the key class.\n**\n** The C syntax in this function definition may be unfamilar to some \n** programmers, so we provide the following additional explanation:\n**\n** The name of the function is \"ftsHashFunction\".  The function takes a\n** single parameter \"keyClass\".  The return value of ftsHashFunction()\n** is a pointer to another function.  Specifically, the return value\n** of ftsHashFunction() is a pointer to a function that takes two parameters\n** with types \"const void*\" and \"int\" and returns an \"int\".\n*/\nstatic int (*ftsHashFunction(int keyClass))(const void*,int){\n  if( keyClass==FTS3_HASH_STRING ){\n    return &fts3StrHash;\n  }else{\n    assert( keyClass==FTS3_HASH_BINARY );\n    return &fts3BinHash;\n  }\n}\n\n/*\n** Return a pointer to the appropriate hash function given the key class.\n**\n** For help in interpreted the obscure C code in the function definition,\n** see the header comment on the previous function.\n*/\nstatic int (*ftsCompareFunction(int keyClass))(const void*,int,const void*,int){\n  if( keyClass==FTS3_HASH_STRING ){\n    return &fts3StrCompare;\n  }else{\n    assert( keyClass==FTS3_HASH_BINARY );\n    return &fts3BinCompare;\n  }\n}\n\n/* Link an element into the hash table\n*/\nstatic void fts3HashInsertElement(\n  Fts3Hash *pH,            /* The complete hash table */\n  struct _fts3ht *pEntry,  /* The entry into which pNew is inserted */\n  Fts3HashElem *pNew       /* The element to be inserted */\n){\n  Fts3HashElem *pHead;     /* First element already in pEntry */\n  pHead = pEntry->chain;\n  if( pHead ){\n    pNew->next = pHead;\n    pNew->prev = pHead->prev;\n    if( pHead->prev ){ pHead->prev->next = pNew; }\n    else             { pH->first = pNew; }\n    pHead->prev = pNew;\n  }else{\n    pNew->next = pH->first;\n    if( pH->first ){ pH->first->prev = pNew; }\n    pNew->prev = 0;\n    pH->first = pNew;\n  }\n  pEntry->count++;\n  pEntry->chain = pNew;\n}\n\n\n/* Resize the hash table so that it cantains \"new_size\" buckets.\n** \"new_size\" must be a power of 2.  The hash table might fail \n** to resize if sqliteMalloc() fails.\n**\n** Return non-zero if a memory allocation error occurs.\n*/\nstatic int fts3Rehash(Fts3Hash *pH, int new_size){\n  struct _fts3ht *new_ht;          /* The new hash table */\n  Fts3HashElem *elem, *next_elem;  /* For looping over existing elements */\n  int (*xHash)(const void*,int);   /* The hash function */\n\n  assert( (new_size & (new_size-1))==0 );\n  new_ht = (struct _fts3ht *)fts3HashMalloc( new_size*sizeof(struct _fts3ht) );\n  if( new_ht==0 ) return 1;\n  fts3HashFree(pH->ht);\n  pH->ht = new_ht;\n  pH->htsize = new_size;\n  xHash = ftsHashFunction(pH->keyClass);\n  for(elem=pH->first, pH->first=0; elem; elem = next_elem){\n    int h = (*xHash)(elem->pKey, elem->nKey) & (new_size-1);\n    next_elem = elem->next;\n    fts3HashInsertElement(pH, &new_ht[h], elem);\n  }\n  return 0;\n}\n\n/* This function (for internal use only) locates an element in an\n** hash table that matches the given key.  The hash for this key has\n** already been computed and is passed as the 4th parameter.\n*/\nstatic Fts3HashElem *fts3FindElementByHash(\n  const Fts3Hash *pH, /* The pH to be searched */\n  const void *pKey,   /* The key we are searching for */\n  int nKey,\n  int h               /* The hash for this key. */\n){\n  Fts3HashElem *elem;            /* Used to loop thru the element list */\n  int count;                     /* Number of elements left to test */\n  int (*xCompare)(const void*,int,const void*,int);  /* comparison function */\n\n  if( pH->ht ){\n    struct _fts3ht *pEntry = &pH->ht[h];\n    elem = pEntry->chain;\n    count = pEntry->count;\n    xCompare = ftsCompareFunction(pH->keyClass);\n    while( count-- && elem ){\n      if( (*xCompare)(elem->pKey,elem->nKey,pKey,nKey)==0 ){ \n        return elem;\n      }\n      elem = elem->next;\n    }\n  }\n  return 0;\n}\n\n/* Remove a single entry from the hash table given a pointer to that\n** element and a hash on the element's key.\n*/\nstatic void fts3RemoveElementByHash(\n  Fts3Hash *pH,         /* The pH containing \"elem\" */\n  Fts3HashElem* elem,   /* The element to be removed from the pH */\n  int h                 /* Hash value for the element */\n){\n  struct _fts3ht *pEntry;\n  if( elem->prev ){\n    elem->prev->next = elem->next; \n  }else{\n    pH->first = elem->next;\n  }\n  if( elem->next ){\n    elem->next->prev = elem->prev;\n  }\n  pEntry = &pH->ht[h];\n  if( pEntry->chain==elem ){\n    pEntry->chain = elem->next;\n  }\n  pEntry->count--;\n  if( pEntry->count<=0 ){\n    pEntry->chain = 0;\n  }\n  if( pH->copyKey && elem->pKey ){\n    fts3HashFree(elem->pKey);\n  }\n  fts3HashFree( elem );\n  pH->count--;\n  if( pH->count<=0 ){\n    assert( pH->first==0 );\n    assert( pH->count==0 );\n    fts3HashClear(pH);\n  }\n}\n\nSQLITE_PRIVATE Fts3HashElem *sqlite3Fts3HashFindElem(\n  const Fts3Hash *pH, \n  const void *pKey, \n  int nKey\n){\n  int h;                          /* A hash on key */\n  int (*xHash)(const void*,int);  /* The hash function */\n\n  if( pH==0 || pH->ht==0 ) return 0;\n  xHash = ftsHashFunction(pH->keyClass);\n  assert( xHash!=0 );\n  h = (*xHash)(pKey,nKey);\n  assert( (pH->htsize & (pH->htsize-1))==0 );\n  return fts3FindElementByHash(pH,pKey,nKey, h & (pH->htsize-1));\n}\n\n/* \n** Attempt to locate an element of the hash table pH with a key\n** that matches pKey,nKey.  Return the data for this element if it is\n** found, or NULL if there is no match.\n*/\nSQLITE_PRIVATE void *sqlite3Fts3HashFind(const Fts3Hash *pH, const void *pKey, int nKey){\n  Fts3HashElem *pElem;            /* The element that matches key (if any) */\n\n  pElem = sqlite3Fts3HashFindElem(pH, pKey, nKey);\n  return pElem ? pElem->data : 0;\n}\n\n/* Insert an element into the hash table pH.  The key is pKey,nKey\n** and the data is \"data\".\n**\n** If no element exists with a matching key, then a new\n** element is created.  A copy of the key is made if the copyKey\n** flag is set.  NULL is returned.\n**\n** If another element already exists with the same key, then the\n** new data replaces the old data and the old data is returned.\n** The key is not copied in this instance.  If a malloc fails, then\n** the new data is returned and the hash table is unchanged.\n**\n** If the \"data\" parameter to this function is NULL, then the\n** element corresponding to \"key\" is removed from the hash table.\n*/\nSQLITE_PRIVATE void *sqlite3Fts3HashInsert(\n  Fts3Hash *pH,        /* The hash table to insert into */\n  const void *pKey,    /* The key */\n  int nKey,            /* Number of bytes in the key */\n  void *data           /* The data */\n){\n  int hraw;                 /* Raw hash value of the key */\n  int h;                    /* the hash of the key modulo hash table size */\n  Fts3HashElem *elem;       /* Used to loop thru the element list */\n  Fts3HashElem *new_elem;   /* New element added to the pH */\n  int (*xHash)(const void*,int);  /* The hash function */\n\n  assert( pH!=0 );\n  xHash = ftsHashFunction(pH->keyClass);\n  assert( xHash!=0 );\n  hraw = (*xHash)(pKey, nKey);\n  assert( (pH->htsize & (pH->htsize-1))==0 );\n  h = hraw & (pH->htsize-1);\n  elem = fts3FindElementByHash(pH,pKey,nKey,h);\n  if( elem ){\n    void *old_data = elem->data;\n    if( data==0 ){\n      fts3RemoveElementByHash(pH,elem,h);\n    }else{\n      elem->data = data;\n    }\n    return old_data;\n  }\n  if( data==0 ) return 0;\n  if( (pH->htsize==0 && fts3Rehash(pH,8))\n   || (pH->count>=pH->htsize && fts3Rehash(pH, pH->htsize*2))\n  ){\n    pH->count = 0;\n    return data;\n  }\n  assert( pH->htsize>0 );\n  new_elem = (Fts3HashElem*)fts3HashMalloc( sizeof(Fts3HashElem) );\n  if( new_elem==0 ) return data;\n  if( pH->copyKey && pKey!=0 ){\n    new_elem->pKey = fts3HashMalloc( nKey );\n    if( new_elem->pKey==0 ){\n      fts3HashFree(new_elem);\n      return data;\n    }\n    memcpy((void*)new_elem->pKey, pKey, nKey);\n  }else{\n    new_elem->pKey = (void*)pKey;\n  }\n  new_elem->nKey = nKey;\n  pH->count++;\n  assert( pH->htsize>0 );\n  assert( (pH->htsize & (pH->htsize-1))==0 );\n  h = hraw & (pH->htsize-1);\n  fts3HashInsertElement(pH, &pH->ht[h], new_elem);\n  new_elem->data = data;\n  return 0;\n}\n\n#endif /* !defined(SQLITE_CORE) || defined(SQLITE_ENABLE_FTS3) */\n\n/************** End of fts3_hash.c *******************************************/\n/************** Begin file fts3_porter.c *************************************/\n/*\n** 2006 September 30\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n*************************************************************************\n** Implementation of the full-text-search tokenizer that implements\n** a Porter stemmer.\n*/\n\n/*\n** The code in this file is only compiled if:\n**\n**     * The FTS3 module is being built as an extension\n**       (in which case SQLITE_CORE is not defined), or\n**\n**     * The FTS3 module is being built into the core of\n**       SQLite (in which case SQLITE_ENABLE_FTS3 is defined).\n*/\n/* #include \"fts3Int.h\" */\n#if !defined(SQLITE_CORE) || defined(SQLITE_ENABLE_FTS3)\n\n/* #include <assert.h> */\n/* #include <stdlib.h> */\n/* #include <stdio.h> */\n/* #include <string.h> */\n\n/* #include \"fts3_tokenizer.h\" */\n\n/*\n** Class derived from sqlite3_tokenizer\n*/\ntypedef struct porter_tokenizer {\n  sqlite3_tokenizer base;      /* Base class */\n} porter_tokenizer;\n\n/*\n** Class derived from sqlite3_tokenizer_cursor\n*/\ntypedef struct porter_tokenizer_cursor {\n  sqlite3_tokenizer_cursor base;\n  const char *zInput;          /* input we are tokenizing */\n  int nInput;                  /* size of the input */\n  int iOffset;                 /* current position in zInput */\n  int iToken;                  /* index of next token to be returned */\n  char *zToken;                /* storage for current token */\n  int nAllocated;              /* space allocated to zToken buffer */\n} porter_tokenizer_cursor;\n\n\n/*\n** Create a new tokenizer instance.\n*/\nstatic int porterCreate(\n  int argc, const char * const *argv,\n  sqlite3_tokenizer **ppTokenizer\n){\n  porter_tokenizer *t;\n\n  UNUSED_PARAMETER(argc);\n  UNUSED_PARAMETER(argv);\n\n  t = (porter_tokenizer *) sqlite3_malloc(sizeof(*t));\n  if( t==NULL ) return SQLITE_NOMEM;\n  memset(t, 0, sizeof(*t));\n  *ppTokenizer = &t->base;\n  return SQLITE_OK;\n}\n\n/*\n** Destroy a tokenizer\n*/\nstatic int porterDestroy(sqlite3_tokenizer *pTokenizer){\n  sqlite3_free(pTokenizer);\n  return SQLITE_OK;\n}\n\n/*\n** Prepare to begin tokenizing a particular string.  The input\n** string to be tokenized is zInput[0..nInput-1].  A cursor\n** used to incrementally tokenize this string is returned in \n** *ppCursor.\n*/\nstatic int porterOpen(\n  sqlite3_tokenizer *pTokenizer,         /* The tokenizer */\n  const char *zInput, int nInput,        /* String to be tokenized */\n  sqlite3_tokenizer_cursor **ppCursor    /* OUT: Tokenization cursor */\n){\n  porter_tokenizer_cursor *c;\n\n  UNUSED_PARAMETER(pTokenizer);\n\n  c = (porter_tokenizer_cursor *) sqlite3_malloc(sizeof(*c));\n  if( c==NULL ) return SQLITE_NOMEM;\n\n  c->zInput = zInput;\n  if( zInput==0 ){\n    c->nInput = 0;\n  }else if( nInput<0 ){\n    c->nInput = (int)strlen(zInput);\n  }else{\n    c->nInput = nInput;\n  }\n  c->iOffset = 0;                 /* start tokenizing at the beginning */\n  c->iToken = 0;\n  c->zToken = NULL;               /* no space allocated, yet. */\n  c->nAllocated = 0;\n\n  *ppCursor = &c->base;\n  return SQLITE_OK;\n}\n\n/*\n** Close a tokenization cursor previously opened by a call to\n** porterOpen() above.\n*/\nstatic int porterClose(sqlite3_tokenizer_cursor *pCursor){\n  porter_tokenizer_cursor *c = (porter_tokenizer_cursor *) pCursor;\n  sqlite3_free(c->zToken);\n  sqlite3_free(c);\n  return SQLITE_OK;\n}\n/*\n** Vowel or consonant\n*/\nstatic const char cType[] = {\n   0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0,\n   1, 1, 1, 2, 1\n};\n\n/*\n** isConsonant() and isVowel() determine if their first character in\n** the string they point to is a consonant or a vowel, according\n** to Porter ruls.  \n**\n** A consonate is any letter other than 'a', 'e', 'i', 'o', or 'u'.\n** 'Y' is a consonant unless it follows another consonant,\n** in which case it is a vowel.\n**\n** In these routine, the letters are in reverse order.  So the 'y' rule\n** is that 'y' is a consonant unless it is followed by another\n** consonent.\n*/\nstatic int isVowel(const char*);\nstatic int isConsonant(const char *z){\n  int j;\n  char x = *z;\n  if( x==0 ) return 0;\n  assert( x>='a' && x<='z' );\n  j = cType[x-'a'];\n  if( j<2 ) return j;\n  return z[1]==0 || isVowel(z + 1);\n}\nstatic int isVowel(const char *z){\n  int j;\n  char x = *z;\n  if( x==0 ) return 0;\n  assert( x>='a' && x<='z' );\n  j = cType[x-'a'];\n  if( j<2 ) return 1-j;\n  return isConsonant(z + 1);\n}\n\n/*\n** Let any sequence of one or more vowels be represented by V and let\n** C be sequence of one or more consonants.  Then every word can be\n** represented as:\n**\n**           [C] (VC){m} [V]\n**\n** In prose:  A word is an optional consonant followed by zero or\n** vowel-consonant pairs followed by an optional vowel.  \"m\" is the\n** number of vowel consonant pairs.  This routine computes the value\n** of m for the first i bytes of a word.\n**\n** Return true if the m-value for z is 1 or more.  In other words,\n** return true if z contains at least one vowel that is followed\n** by a consonant.\n**\n** In this routine z[] is in reverse order.  So we are really looking\n** for an instance of a consonant followed by a vowel.\n*/\nstatic int m_gt_0(const char *z){\n  while( isVowel(z) ){ z++; }\n  if( *z==0 ) return 0;\n  while( isConsonant(z) ){ z++; }\n  return *z!=0;\n}\n\n/* Like mgt0 above except we are looking for a value of m which is\n** exactly 1\n*/\nstatic int m_eq_1(const char *z){\n  while( isVowel(z) ){ z++; }\n  if( *z==0 ) return 0;\n  while( isConsonant(z) ){ z++; }\n  if( *z==0 ) return 0;\n  while( isVowel(z) ){ z++; }\n  if( *z==0 ) return 1;\n  while( isConsonant(z) ){ z++; }\n  return *z==0;\n}\n\n/* Like mgt0 above except we are looking for a value of m>1 instead\n** or m>0\n*/\nstatic int m_gt_1(const char *z){\n  while( isVowel(z) ){ z++; }\n  if( *z==0 ) return 0;\n  while( isConsonant(z) ){ z++; }\n  if( *z==0 ) return 0;\n  while( isVowel(z) ){ z++; }\n  if( *z==0 ) return 0;\n  while( isConsonant(z) ){ z++; }\n  return *z!=0;\n}\n\n/*\n** Return TRUE if there is a vowel anywhere within z[0..n-1]\n*/\nstatic int hasVowel(const char *z){\n  while( isConsonant(z) ){ z++; }\n  return *z!=0;\n}\n\n/*\n** Return TRUE if the word ends in a double consonant.\n**\n** The text is reversed here. So we are really looking at\n** the first two characters of z[].\n*/\nstatic int doubleConsonant(const char *z){\n  return isConsonant(z) && z[0]==z[1];\n}\n\n/*\n** Return TRUE if the word ends with three letters which\n** are consonant-vowel-consonent and where the final consonant\n** is not 'w', 'x', or 'y'.\n**\n** The word is reversed here.  So we are really checking the\n** first three letters and the first one cannot be in [wxy].\n*/\nstatic int star_oh(const char *z){\n  return\n    isConsonant(z) &&\n    z[0]!='w' && z[0]!='x' && z[0]!='y' &&\n    isVowel(z+1) &&\n    isConsonant(z+2);\n}\n\n/*\n** If the word ends with zFrom and xCond() is true for the stem\n** of the word that preceeds the zFrom ending, then change the \n** ending to zTo.\n**\n** The input word *pz and zFrom are both in reverse order.  zTo\n** is in normal order. \n**\n** Return TRUE if zFrom matches.  Return FALSE if zFrom does not\n** match.  Not that TRUE is returned even if xCond() fails and\n** no substitution occurs.\n*/\nstatic int stem(\n  char **pz,             /* The word being stemmed (Reversed) */\n  const char *zFrom,     /* If the ending matches this... (Reversed) */\n  const char *zTo,       /* ... change the ending to this (not reversed) */\n  int (*xCond)(const char*)   /* Condition that must be true */\n){\n  char *z = *pz;\n  while( *zFrom && *zFrom==*z ){ z++; zFrom++; }\n  if( *zFrom!=0 ) return 0;\n  if( xCond && !xCond(z) ) return 1;\n  while( *zTo ){\n    *(--z) = *(zTo++);\n  }\n  *pz = z;\n  return 1;\n}\n\n/*\n** This is the fallback stemmer used when the porter stemmer is\n** inappropriate.  The input word is copied into the output with\n** US-ASCII case folding.  If the input word is too long (more\n** than 20 bytes if it contains no digits or more than 6 bytes if\n** it contains digits) then word is truncated to 20 or 6 bytes\n** by taking 10 or 3 bytes from the beginning and end.\n*/\nstatic void copy_stemmer(const char *zIn, int nIn, char *zOut, int *pnOut){\n  int i, mx, j;\n  int hasDigit = 0;\n  for(i=0; i<nIn; i++){\n    char c = zIn[i];\n    if( c>='A' && c<='Z' ){\n      zOut[i] = c - 'A' + 'a';\n    }else{\n      if( c>='0' && c<='9' ) hasDigit = 1;\n      zOut[i] = c;\n    }\n  }\n  mx = hasDigit ? 3 : 10;\n  if( nIn>mx*2 ){\n    for(j=mx, i=nIn-mx; i<nIn; i++, j++){\n      zOut[j] = zOut[i];\n    }\n    i = j;\n  }\n  zOut[i] = 0;\n  *pnOut = i;\n}\n\n\n/*\n** Stem the input word zIn[0..nIn-1].  Store the output in zOut.\n** zOut is at least big enough to hold nIn bytes.  Write the actual\n** size of the output word (exclusive of the '\\0' terminator) into *pnOut.\n**\n** Any upper-case characters in the US-ASCII character set ([A-Z])\n** are converted to lower case.  Upper-case UTF characters are\n** unchanged.\n**\n** Words that are longer than about 20 bytes are stemmed by retaining\n** a few bytes from the beginning and the end of the word.  If the\n** word contains digits, 3 bytes are taken from the beginning and\n** 3 bytes from the end.  For long words without digits, 10 bytes\n** are taken from each end.  US-ASCII case folding still applies.\n** \n** If the input word contains not digits but does characters not \n** in [a-zA-Z] then no stemming is attempted and this routine just \n** copies the input into the input into the output with US-ASCII\n** case folding.\n**\n** Stemming never increases the length of the word.  So there is\n** no chance of overflowing the zOut buffer.\n*/\nstatic void porter_stemmer(const char *zIn, int nIn, char *zOut, int *pnOut){\n  int i, j;\n  char zReverse[28];\n  char *z, *z2;\n  if( nIn<3 || nIn>=(int)sizeof(zReverse)-7 ){\n    /* The word is too big or too small for the porter stemmer.\n    ** Fallback to the copy stemmer */\n    copy_stemmer(zIn, nIn, zOut, pnOut);\n    return;\n  }\n  for(i=0, j=sizeof(zReverse)-6; i<nIn; i++, j--){\n    char c = zIn[i];\n    if( c>='A' && c<='Z' ){\n      zReverse[j] = c + 'a' - 'A';\n    }else if( c>='a' && c<='z' ){\n      zReverse[j] = c;\n    }else{\n      /* The use of a character not in [a-zA-Z] means that we fallback\n      ** to the copy stemmer */\n      copy_stemmer(zIn, nIn, zOut, pnOut);\n      return;\n    }\n  }\n  memset(&zReverse[sizeof(zReverse)-5], 0, 5);\n  z = &zReverse[j+1];\n\n\n  /* Step 1a */\n  if( z[0]=='s' ){\n    if(\n     !stem(&z, \"sess\", \"ss\", 0) &&\n     !stem(&z, \"sei\", \"i\", 0)  &&\n     !stem(&z, \"ss\", \"ss\", 0)\n    ){\n      z++;\n    }\n  }\n\n  /* Step 1b */  \n  z2 = z;\n  if( stem(&z, \"dee\", \"ee\", m_gt_0) ){\n    /* Do nothing.  The work was all in the test */\n  }else if( \n     (stem(&z, \"gni\", \"\", hasVowel) || stem(&z, \"de\", \"\", hasVowel))\n      && z!=z2\n  ){\n     if( stem(&z, \"ta\", \"ate\", 0) ||\n         stem(&z, \"lb\", \"ble\", 0) ||\n         stem(&z, \"zi\", \"ize\", 0) ){\n       /* Do nothing.  The work was all in the test */\n     }else if( doubleConsonant(z) && (*z!='l' && *z!='s' && *z!='z') ){\n       z++;\n     }else if( m_eq_1(z) && star_oh(z) ){\n       *(--z) = 'e';\n     }\n  }\n\n  /* Step 1c */\n  if( z[0]=='y' && hasVowel(z+1) ){\n    z[0] = 'i';\n  }\n\n  /* Step 2 */\n  switch( z[1] ){\n   case 'a':\n     if( !stem(&z, \"lanoita\", \"ate\", m_gt_0) ){\n       stem(&z, \"lanoit\", \"tion\", m_gt_0);\n     }\n     break;\n   case 'c':\n     if( !stem(&z, \"icne\", \"ence\", m_gt_0) ){\n       stem(&z, \"icna\", \"ance\", m_gt_0);\n     }\n     break;\n   case 'e':\n     stem(&z, \"rezi\", \"ize\", m_gt_0);\n     break;\n   case 'g':\n     stem(&z, \"igol\", \"log\", m_gt_0);\n     break;\n   case 'l':\n     if( !stem(&z, \"ilb\", \"ble\", m_gt_0) \n      && !stem(&z, \"illa\", \"al\", m_gt_0)\n      && !stem(&z, \"iltne\", \"ent\", m_gt_0)\n      && !stem(&z, \"ile\", \"e\", m_gt_0)\n     ){\n       stem(&z, \"ilsuo\", \"ous\", m_gt_0);\n     }\n     break;\n   case 'o':\n     if( !stem(&z, \"noitazi\", \"ize\", m_gt_0)\n      && !stem(&z, \"noita\", \"ate\", m_gt_0)\n     ){\n       stem(&z, \"rota\", \"ate\", m_gt_0);\n     }\n     break;\n   case 's':\n     if( !stem(&z, \"msila\", \"al\", m_gt_0)\n      && !stem(&z, \"ssenevi\", \"ive\", m_gt_0)\n      && !stem(&z, \"ssenluf\", \"ful\", m_gt_0)\n     ){\n       stem(&z, \"ssensuo\", \"ous\", m_gt_0);\n     }\n     break;\n   case 't':\n     if( !stem(&z, \"itila\", \"al\", m_gt_0)\n      && !stem(&z, \"itivi\", \"ive\", m_gt_0)\n     ){\n       stem(&z, \"itilib\", \"ble\", m_gt_0);\n     }\n     break;\n  }\n\n  /* Step 3 */\n  switch( z[0] ){\n   case 'e':\n     if( !stem(&z, \"etaci\", \"ic\", m_gt_0)\n      && !stem(&z, \"evita\", \"\", m_gt_0)\n     ){\n       stem(&z, \"ezila\", \"al\", m_gt_0);\n     }\n     break;\n   case 'i':\n     stem(&z, \"itici\", \"ic\", m_gt_0);\n     break;\n   case 'l':\n     if( !stem(&z, \"laci\", \"ic\", m_gt_0) ){\n       stem(&z, \"luf\", \"\", m_gt_0);\n     }\n     break;\n   case 's':\n     stem(&z, \"ssen\", \"\", m_gt_0);\n     break;\n  }\n\n  /* Step 4 */\n  switch( z[1] ){\n   case 'a':\n     if( z[0]=='l' && m_gt_1(z+2) ){\n       z += 2;\n     }\n     break;\n   case 'c':\n     if( z[0]=='e' && z[2]=='n' && (z[3]=='a' || z[3]=='e')  && m_gt_1(z+4)  ){\n       z += 4;\n     }\n     break;\n   case 'e':\n     if( z[0]=='r' && m_gt_1(z+2) ){\n       z += 2;\n     }\n     break;\n   case 'i':\n     if( z[0]=='c' && m_gt_1(z+2) ){\n       z += 2;\n     }\n     break;\n   case 'l':\n     if( z[0]=='e' && z[2]=='b' && (z[3]=='a' || z[3]=='i') && m_gt_1(z+4) ){\n       z += 4;\n     }\n     break;\n   case 'n':\n     if( z[0]=='t' ){\n       if( z[2]=='a' ){\n         if( m_gt_1(z+3) ){\n           z += 3;\n         }\n       }else if( z[2]=='e' ){\n         if( !stem(&z, \"tneme\", \"\", m_gt_1)\n          && !stem(&z, \"tnem\", \"\", m_gt_1)\n         ){\n           stem(&z, \"tne\", \"\", m_gt_1);\n         }\n       }\n     }\n     break;\n   case 'o':\n     if( z[0]=='u' ){\n       if( m_gt_1(z+2) ){\n         z += 2;\n       }\n     }else if( z[3]=='s' || z[3]=='t' ){\n       stem(&z, \"noi\", \"\", m_gt_1);\n     }\n     break;\n   case 's':\n     if( z[0]=='m' && z[2]=='i' && m_gt_1(z+3) ){\n       z += 3;\n     }\n     break;\n   case 't':\n     if( !stem(&z, \"eta\", \"\", m_gt_1) ){\n       stem(&z, \"iti\", \"\", m_gt_1);\n     }\n     break;\n   case 'u':\n     if( z[0]=='s' && z[2]=='o' && m_gt_1(z+3) ){\n       z += 3;\n     }\n     break;\n   case 'v':\n   case 'z':\n     if( z[0]=='e' && z[2]=='i' && m_gt_1(z+3) ){\n       z += 3;\n     }\n     break;\n  }\n\n  /* Step 5a */\n  if( z[0]=='e' ){\n    if( m_gt_1(z+1) ){\n      z++;\n    }else if( m_eq_1(z+1) && !star_oh(z+1) ){\n      z++;\n    }\n  }\n\n  /* Step 5b */\n  if( m_gt_1(z) && z[0]=='l' && z[1]=='l' ){\n    z++;\n  }\n\n  /* z[] is now the stemmed word in reverse order.  Flip it back\n  ** around into forward order and return.\n  */\n  *pnOut = i = (int)strlen(z);\n  zOut[i] = 0;\n  while( *z ){\n    zOut[--i] = *(z++);\n  }\n}\n\n/*\n** Characters that can be part of a token.  We assume any character\n** whose value is greater than 0x80 (any UTF character) can be\n** part of a token.  In other words, delimiters all must have\n** values of 0x7f or lower.\n*/\nstatic const char porterIdChar[] = {\n/* x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 xA xB xC xD xE xF */\n    1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0,  /* 3x */\n    0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,  /* 4x */\n    1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1,  /* 5x */\n    0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,  /* 6x */\n    1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0,  /* 7x */\n};\n#define isDelim(C) (((ch=C)&0x80)==0 && (ch<0x30 || !porterIdChar[ch-0x30]))\n\n/*\n** Extract the next token from a tokenization cursor.  The cursor must\n** have been opened by a prior call to porterOpen().\n*/\nstatic int porterNext(\n  sqlite3_tokenizer_cursor *pCursor,  /* Cursor returned by porterOpen */\n  const char **pzToken,               /* OUT: *pzToken is the token text */\n  int *pnBytes,                       /* OUT: Number of bytes in token */\n  int *piStartOffset,                 /* OUT: Starting offset of token */\n  int *piEndOffset,                   /* OUT: Ending offset of token */\n  int *piPosition                     /* OUT: Position integer of token */\n){\n  porter_tokenizer_cursor *c = (porter_tokenizer_cursor *) pCursor;\n  const char *z = c->zInput;\n\n  while( c->iOffset<c->nInput ){\n    int iStartOffset, ch;\n\n    /* Scan past delimiter characters */\n    while( c->iOffset<c->nInput && isDelim(z[c->iOffset]) ){\n      c->iOffset++;\n    }\n\n    /* Count non-delimiter characters. */\n    iStartOffset = c->iOffset;\n    while( c->iOffset<c->nInput && !isDelim(z[c->iOffset]) ){\n      c->iOffset++;\n    }\n\n    if( c->iOffset>iStartOffset ){\n      int n = c->iOffset-iStartOffset;\n      if( n>c->nAllocated ){\n        char *pNew;\n        c->nAllocated = n+20;\n        pNew = sqlite3_realloc(c->zToken, c->nAllocated);\n        if( !pNew ) return SQLITE_NOMEM;\n        c->zToken = pNew;\n      }\n      porter_stemmer(&z[iStartOffset], n, c->zToken, pnBytes);\n      *pzToken = c->zToken;\n      *piStartOffset = iStartOffset;\n      *piEndOffset = c->iOffset;\n      *piPosition = c->iToken++;\n      return SQLITE_OK;\n    }\n  }\n  return SQLITE_DONE;\n}\n\n/*\n** The set of routines that implement the porter-stemmer tokenizer\n*/\nstatic const sqlite3_tokenizer_module porterTokenizerModule = {\n  0,\n  porterCreate,\n  porterDestroy,\n  porterOpen,\n  porterClose,\n  porterNext,\n  0\n};\n\n/*\n** Allocate a new porter tokenizer.  Return a pointer to the new\n** tokenizer in *ppModule\n*/\nSQLITE_PRIVATE void sqlite3Fts3PorterTokenizerModule(\n  sqlite3_tokenizer_module const**ppModule\n){\n  *ppModule = &porterTokenizerModule;\n}\n\n#endif /* !defined(SQLITE_CORE) || defined(SQLITE_ENABLE_FTS3) */\n\n/************** End of fts3_porter.c *****************************************/\n/************** Begin file fts3_tokenizer.c **********************************/\n/*\n** 2007 June 22\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n******************************************************************************\n**\n** This is part of an SQLite module implementing full-text search.\n** This particular file implements the generic tokenizer interface.\n*/\n\n/*\n** The code in this file is only compiled if:\n**\n**     * The FTS3 module is being built as an extension\n**       (in which case SQLITE_CORE is not defined), or\n**\n**     * The FTS3 module is being built into the core of\n**       SQLite (in which case SQLITE_ENABLE_FTS3 is defined).\n*/\n/* #include \"fts3Int.h\" */\n#if !defined(SQLITE_CORE) || defined(SQLITE_ENABLE_FTS3)\n\n/* #include <assert.h> */\n/* #include <string.h> */\n\n/*\n** Return true if the two-argument version of fts3_tokenizer()\n** has been activated via a prior call to sqlite3_db_config(db,\n** SQLITE_DBCONFIG_ENABLE_FTS3_TOKENIZER, 1, 0);\n*/\nstatic int fts3TokenizerEnabled(sqlite3_context *context){\n  sqlite3 *db = sqlite3_context_db_handle(context);\n  int isEnabled = 0;\n  sqlite3_db_config(db,SQLITE_DBCONFIG_ENABLE_FTS3_TOKENIZER,-1,&isEnabled);\n  return isEnabled;\n}\n\n/*\n** Implementation of the SQL scalar function for accessing the underlying \n** hash table. This function may be called as follows:\n**\n**   SELECT <function-name>(<key-name>);\n**   SELECT <function-name>(<key-name>, <pointer>);\n**\n** where <function-name> is the name passed as the second argument\n** to the sqlite3Fts3InitHashTable() function (e.g. 'fts3_tokenizer').\n**\n** If the <pointer> argument is specified, it must be a blob value\n** containing a pointer to be stored as the hash data corresponding\n** to the string <key-name>. If <pointer> is not specified, then\n** the string <key-name> must already exist in the has table. Otherwise,\n** an error is returned.\n**\n** Whether or not the <pointer> argument is specified, the value returned\n** is a blob containing the pointer stored as the hash data corresponding\n** to string <key-name> (after the hash-table is updated, if applicable).\n*/\nstatic void fts3TokenizerFunc(\n  sqlite3_context *context,\n  int argc,\n  sqlite3_value **argv\n){\n  Fts3Hash *pHash;\n  void *pPtr = 0;\n  const unsigned char *zName;\n  int nName;\n\n  assert( argc==1 || argc==2 );\n\n  pHash = (Fts3Hash *)sqlite3_user_data(context);\n\n  zName = sqlite3_value_text(argv[0]);\n  nName = sqlite3_value_bytes(argv[0])+1;\n\n  if( argc==2 ){\n    if( fts3TokenizerEnabled(context) ){\n      void *pOld;\n      int n = sqlite3_value_bytes(argv[1]);\n      if( zName==0 || n!=sizeof(pPtr) ){\n        sqlite3_result_error(context, \"argument type mismatch\", -1);\n        return;\n      }\n      pPtr = *(void **)sqlite3_value_blob(argv[1]);\n      pOld = sqlite3Fts3HashInsert(pHash, (void *)zName, nName, pPtr);\n      if( pOld==pPtr ){\n        sqlite3_result_error(context, \"out of memory\", -1);\n      }\n    }else{\n      sqlite3_result_error(context, \"fts3tokenize disabled\", -1);\n      return;\n    }\n  }else{\n    if( zName ){\n      pPtr = sqlite3Fts3HashFind(pHash, zName, nName);\n    }\n    if( !pPtr ){\n      char *zErr = sqlite3_mprintf(\"unknown tokenizer: %s\", zName);\n      sqlite3_result_error(context, zErr, -1);\n      sqlite3_free(zErr);\n      return;\n    }\n  }\n  sqlite3_result_blob(context, (void *)&pPtr, sizeof(pPtr), SQLITE_TRANSIENT);\n}\n\nSQLITE_PRIVATE int sqlite3Fts3IsIdChar(char c){\n  static const char isFtsIdChar[] = {\n      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,  /* 0x */\n      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,  /* 1x */\n      0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,  /* 2x */\n      1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0,  /* 3x */\n      0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,  /* 4x */\n      1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1,  /* 5x */\n      0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,  /* 6x */\n      1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0,  /* 7x */\n  };\n  return (c&0x80 || isFtsIdChar[(int)(c)]);\n}\n\nSQLITE_PRIVATE const char *sqlite3Fts3NextToken(const char *zStr, int *pn){\n  const char *z1;\n  const char *z2 = 0;\n\n  /* Find the start of the next token. */\n  z1 = zStr;\n  while( z2==0 ){\n    char c = *z1;\n    switch( c ){\n      case '\\0': return 0;        /* No more tokens here */\n      case '\\'':\n      case '\"':\n      case '`': {\n        z2 = z1;\n        while( *++z2 && (*z2!=c || *++z2==c) );\n        break;\n      }\n      case '[':\n        z2 = &z1[1];\n        while( *z2 && z2[0]!=']' ) z2++;\n        if( *z2 ) z2++;\n        break;\n\n      default:\n        if( sqlite3Fts3IsIdChar(*z1) ){\n          z2 = &z1[1];\n          while( sqlite3Fts3IsIdChar(*z2) ) z2++;\n        }else{\n          z1++;\n        }\n    }\n  }\n\n  *pn = (int)(z2-z1);\n  return z1;\n}\n\nSQLITE_PRIVATE int sqlite3Fts3InitTokenizer(\n  Fts3Hash *pHash,                /* Tokenizer hash table */\n  const char *zArg,               /* Tokenizer name */\n  sqlite3_tokenizer **ppTok,      /* OUT: Tokenizer (if applicable) */\n  char **pzErr                    /* OUT: Set to malloced error message */\n){\n  int rc;\n  char *z = (char *)zArg;\n  int n = 0;\n  char *zCopy;\n  char *zEnd;                     /* Pointer to nul-term of zCopy */\n  sqlite3_tokenizer_module *m;\n\n  zCopy = sqlite3_mprintf(\"%s\", zArg);\n  if( !zCopy ) return SQLITE_NOMEM;\n  zEnd = &zCopy[strlen(zCopy)];\n\n  z = (char *)sqlite3Fts3NextToken(zCopy, &n);\n  if( z==0 ){\n    assert( n==0 );\n    z = zCopy;\n  }\n  z[n] = '\\0';\n  sqlite3Fts3Dequote(z);\n\n  m = (sqlite3_tokenizer_module *)sqlite3Fts3HashFind(pHash,z,(int)strlen(z)+1);\n  if( !m ){\n    sqlite3Fts3ErrMsg(pzErr, \"unknown tokenizer: %s\", z);\n    rc = SQLITE_ERROR;\n  }else{\n    char const **aArg = 0;\n    int iArg = 0;\n    z = &z[n+1];\n    while( z<zEnd && (NULL!=(z = (char *)sqlite3Fts3NextToken(z, &n))) ){\n      int nNew = sizeof(char *)*(iArg+1);\n      char const **aNew = (const char **)sqlite3_realloc((void *)aArg, nNew);\n      if( !aNew ){\n        sqlite3_free(zCopy);\n        sqlite3_free((void *)aArg);\n        return SQLITE_NOMEM;\n      }\n      aArg = aNew;\n      aArg[iArg++] = z;\n      z[n] = '\\0';\n      sqlite3Fts3Dequote(z);\n      z = &z[n+1];\n    }\n    rc = m->xCreate(iArg, aArg, ppTok);\n    assert( rc!=SQLITE_OK || *ppTok );\n    if( rc!=SQLITE_OK ){\n      sqlite3Fts3ErrMsg(pzErr, \"unknown tokenizer\");\n    }else{\n      (*ppTok)->pModule = m; \n    }\n    sqlite3_free((void *)aArg);\n  }\n\n  sqlite3_free(zCopy);\n  return rc;\n}\n\n\n#ifdef SQLITE_TEST\n\n#if defined(INCLUDE_SQLITE_TCL_H)\n#  include \"sqlite_tcl.h\"\n#else\n#  include \"tcl.h\"\n#endif\n/* #include <string.h> */\n\n/*\n** Implementation of a special SQL scalar function for testing tokenizers \n** designed to be used in concert with the Tcl testing framework. This\n** function must be called with two or more arguments:\n**\n**   SELECT <function-name>(<key-name>, ..., <input-string>);\n**\n** where <function-name> is the name passed as the second argument\n** to the sqlite3Fts3InitHashTable() function (e.g. 'fts3_tokenizer')\n** concatenated with the string '_test' (e.g. 'fts3_tokenizer_test').\n**\n** The return value is a string that may be interpreted as a Tcl\n** list. For each token in the <input-string>, three elements are\n** added to the returned list. The first is the token position, the \n** second is the token text (folded, stemmed, etc.) and the third is the\n** substring of <input-string> associated with the token. For example, \n** using the built-in \"simple\" tokenizer:\n**\n**   SELECT fts_tokenizer_test('simple', 'I don't see how');\n**\n** will return the string:\n**\n**   \"{0 i I 1 dont don't 2 see see 3 how how}\"\n**   \n*/\nstatic void testFunc(\n  sqlite3_context *context,\n  int argc,\n  sqlite3_value **argv\n){\n  Fts3Hash *pHash;\n  sqlite3_tokenizer_module *p;\n  sqlite3_tokenizer *pTokenizer = 0;\n  sqlite3_tokenizer_cursor *pCsr = 0;\n\n  const char *zErr = 0;\n\n  const char *zName;\n  int nName;\n  const char *zInput;\n  int nInput;\n\n  const char *azArg[64];\n\n  const char *zToken;\n  int nToken = 0;\n  int iStart = 0;\n  int iEnd = 0;\n  int iPos = 0;\n  int i;\n\n  Tcl_Obj *pRet;\n\n  if( argc<2 ){\n    sqlite3_result_error(context, \"insufficient arguments\", -1);\n    return;\n  }\n\n  nName = sqlite3_value_bytes(argv[0]);\n  zName = (const char *)sqlite3_value_text(argv[0]);\n  nInput = sqlite3_value_bytes(argv[argc-1]);\n  zInput = (const char *)sqlite3_value_text(argv[argc-1]);\n\n  pHash = (Fts3Hash *)sqlite3_user_data(context);\n  p = (sqlite3_tokenizer_module *)sqlite3Fts3HashFind(pHash, zName, nName+1);\n\n  if( !p ){\n    char *zErr2 = sqlite3_mprintf(\"unknown tokenizer: %s\", zName);\n    sqlite3_result_error(context, zErr2, -1);\n    sqlite3_free(zErr2);\n    return;\n  }\n\n  pRet = Tcl_NewObj();\n  Tcl_IncrRefCount(pRet);\n\n  for(i=1; i<argc-1; i++){\n    azArg[i-1] = (const char *)sqlite3_value_text(argv[i]);\n  }\n\n  if( SQLITE_OK!=p->xCreate(argc-2, azArg, &pTokenizer) ){\n    zErr = \"error in xCreate()\";\n    goto finish;\n  }\n  pTokenizer->pModule = p;\n  if( sqlite3Fts3OpenTokenizer(pTokenizer, 0, zInput, nInput, &pCsr) ){\n    zErr = \"error in xOpen()\";\n    goto finish;\n  }\n\n  while( SQLITE_OK==p->xNext(pCsr, &zToken, &nToken, &iStart, &iEnd, &iPos) ){\n    Tcl_ListObjAppendElement(0, pRet, Tcl_NewIntObj(iPos));\n    Tcl_ListObjAppendElement(0, pRet, Tcl_NewStringObj(zToken, nToken));\n    zToken = &zInput[iStart];\n    nToken = iEnd-iStart;\n    Tcl_ListObjAppendElement(0, pRet, Tcl_NewStringObj(zToken, nToken));\n  }\n\n  if( SQLITE_OK!=p->xClose(pCsr) ){\n    zErr = \"error in xClose()\";\n    goto finish;\n  }\n  if( SQLITE_OK!=p->xDestroy(pTokenizer) ){\n    zErr = \"error in xDestroy()\";\n    goto finish;\n  }\n\nfinish:\n  if( zErr ){\n    sqlite3_result_error(context, zErr, -1);\n  }else{\n    sqlite3_result_text(context, Tcl_GetString(pRet), -1, SQLITE_TRANSIENT);\n  }\n  Tcl_DecrRefCount(pRet);\n}\n\nstatic\nint registerTokenizer(\n  sqlite3 *db, \n  char *zName, \n  const sqlite3_tokenizer_module *p\n){\n  int rc;\n  sqlite3_stmt *pStmt;\n  const char zSql[] = \"SELECT fts3_tokenizer(?, ?)\";\n\n  rc = sqlite3_prepare_v2(db, zSql, -1, &pStmt, 0);\n  if( rc!=SQLITE_OK ){\n    return rc;\n  }\n\n  sqlite3_bind_text(pStmt, 1, zName, -1, SQLITE_STATIC);\n  sqlite3_bind_blob(pStmt, 2, &p, sizeof(p), SQLITE_STATIC);\n  sqlite3_step(pStmt);\n\n  return sqlite3_finalize(pStmt);\n}\n\n\nstatic\nint queryTokenizer(\n  sqlite3 *db, \n  char *zName,  \n  const sqlite3_tokenizer_module **pp\n){\n  int rc;\n  sqlite3_stmt *pStmt;\n  const char zSql[] = \"SELECT fts3_tokenizer(?)\";\n\n  *pp = 0;\n  rc = sqlite3_prepare_v2(db, zSql, -1, &pStmt, 0);\n  if( rc!=SQLITE_OK ){\n    return rc;\n  }\n\n  sqlite3_bind_text(pStmt, 1, zName, -1, SQLITE_STATIC);\n  if( SQLITE_ROW==sqlite3_step(pStmt) ){\n    if( sqlite3_column_type(pStmt, 0)==SQLITE_BLOB ){\n      memcpy((void *)pp, sqlite3_column_blob(pStmt, 0), sizeof(*pp));\n    }\n  }\n\n  return sqlite3_finalize(pStmt);\n}\n\nSQLITE_PRIVATE void sqlite3Fts3SimpleTokenizerModule(sqlite3_tokenizer_module const**ppModule);\n\n/*\n** Implementation of the scalar function fts3_tokenizer_internal_test().\n** This function is used for testing only, it is not included in the\n** build unless SQLITE_TEST is defined.\n**\n** The purpose of this is to test that the fts3_tokenizer() function\n** can be used as designed by the C-code in the queryTokenizer and\n** registerTokenizer() functions above. These two functions are repeated\n** in the README.tokenizer file as an example, so it is important to\n** test them.\n**\n** To run the tests, evaluate the fts3_tokenizer_internal_test() scalar\n** function with no arguments. An assert() will fail if a problem is\n** detected. i.e.:\n**\n**     SELECT fts3_tokenizer_internal_test();\n**\n*/\nstatic void intTestFunc(\n  sqlite3_context *context,\n  int argc,\n  sqlite3_value **argv\n){\n  int rc;\n  const sqlite3_tokenizer_module *p1;\n  const sqlite3_tokenizer_module *p2;\n  sqlite3 *db = (sqlite3 *)sqlite3_user_data(context);\n\n  UNUSED_PARAMETER(argc);\n  UNUSED_PARAMETER(argv);\n\n  /* Test the query function */\n  sqlite3Fts3SimpleTokenizerModule(&p1);\n  rc = queryTokenizer(db, \"simple\", &p2);\n  assert( rc==SQLITE_OK );\n  assert( p1==p2 );\n  rc = queryTokenizer(db, \"nosuchtokenizer\", &p2);\n  assert( rc==SQLITE_ERROR );\n  assert( p2==0 );\n  assert( 0==strcmp(sqlite3_errmsg(db), \"unknown tokenizer: nosuchtokenizer\") );\n\n  /* Test the storage function */\n  if( fts3TokenizerEnabled(context) ){\n    rc = registerTokenizer(db, \"nosuchtokenizer\", p1);\n    assert( rc==SQLITE_OK );\n    rc = queryTokenizer(db, \"nosuchtokenizer\", &p2);\n    assert( rc==SQLITE_OK );\n    assert( p2==p1 );\n  }\n\n  sqlite3_result_text(context, \"ok\", -1, SQLITE_STATIC);\n}\n\n#endif\n\n/*\n** Set up SQL objects in database db used to access the contents of\n** the hash table pointed to by argument pHash. The hash table must\n** been initialized to use string keys, and to take a private copy \n** of the key when a value is inserted. i.e. by a call similar to:\n**\n**    sqlite3Fts3HashInit(pHash, FTS3_HASH_STRING, 1);\n**\n** This function adds a scalar function (see header comment above\n** fts3TokenizerFunc() in this file for details) and, if ENABLE_TABLE is\n** defined at compilation time, a temporary virtual table (see header \n** comment above struct HashTableVtab) to the database schema. Both \n** provide read/write access to the contents of *pHash.\n**\n** The third argument to this function, zName, is used as the name\n** of both the scalar and, if created, the virtual table.\n*/\nSQLITE_PRIVATE int sqlite3Fts3InitHashTable(\n  sqlite3 *db, \n  Fts3Hash *pHash, \n  const char *zName\n){\n  int rc = SQLITE_OK;\n  void *p = (void *)pHash;\n  const int any = SQLITE_ANY;\n\n#ifdef SQLITE_TEST\n  char *zTest = 0;\n  char *zTest2 = 0;\n  void *pdb = (void *)db;\n  zTest = sqlite3_mprintf(\"%s_test\", zName);\n  zTest2 = sqlite3_mprintf(\"%s_internal_test\", zName);\n  if( !zTest || !zTest2 ){\n    rc = SQLITE_NOMEM;\n  }\n#endif\n\n  if( SQLITE_OK==rc ){\n    rc = sqlite3_create_function(db, zName, 1, any, p, fts3TokenizerFunc, 0, 0);\n  }\n  if( SQLITE_OK==rc ){\n    rc = sqlite3_create_function(db, zName, 2, any, p, fts3TokenizerFunc, 0, 0);\n  }\n#ifdef SQLITE_TEST\n  if( SQLITE_OK==rc ){\n    rc = sqlite3_create_function(db, zTest, -1, any, p, testFunc, 0, 0);\n  }\n  if( SQLITE_OK==rc ){\n    rc = sqlite3_create_function(db, zTest2, 0, any, pdb, intTestFunc, 0, 0);\n  }\n#endif\n\n#ifdef SQLITE_TEST\n  sqlite3_free(zTest);\n  sqlite3_free(zTest2);\n#endif\n\n  return rc;\n}\n\n#endif /* !defined(SQLITE_CORE) || defined(SQLITE_ENABLE_FTS3) */\n\n/************** End of fts3_tokenizer.c **************************************/\n/************** Begin file fts3_tokenizer1.c *********************************/\n/*\n** 2006 Oct 10\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n******************************************************************************\n**\n** Implementation of the \"simple\" full-text-search tokenizer.\n*/\n\n/*\n** The code in this file is only compiled if:\n**\n**     * The FTS3 module is being built as an extension\n**       (in which case SQLITE_CORE is not defined), or\n**\n**     * The FTS3 module is being built into the core of\n**       SQLite (in which case SQLITE_ENABLE_FTS3 is defined).\n*/\n/* #include \"fts3Int.h\" */\n#if !defined(SQLITE_CORE) || defined(SQLITE_ENABLE_FTS3)\n\n/* #include <assert.h> */\n/* #include <stdlib.h> */\n/* #include <stdio.h> */\n/* #include <string.h> */\n\n/* #include \"fts3_tokenizer.h\" */\n\ntypedef struct simple_tokenizer {\n  sqlite3_tokenizer base;\n  char delim[128];             /* flag ASCII delimiters */\n} simple_tokenizer;\n\ntypedef struct simple_tokenizer_cursor {\n  sqlite3_tokenizer_cursor base;\n  const char *pInput;          /* input we are tokenizing */\n  int nBytes;                  /* size of the input */\n  int iOffset;                 /* current position in pInput */\n  int iToken;                  /* index of next token to be returned */\n  char *pToken;                /* storage for current token */\n  int nTokenAllocated;         /* space allocated to zToken buffer */\n} simple_tokenizer_cursor;\n\n\nstatic int simpleDelim(simple_tokenizer *t, unsigned char c){\n  return c<0x80 && t->delim[c];\n}\nstatic int fts3_isalnum(int x){\n  return (x>='0' && x<='9') || (x>='A' && x<='Z') || (x>='a' && x<='z');\n}\n\n/*\n** Create a new tokenizer instance.\n*/\nstatic int simpleCreate(\n  int argc, const char * const *argv,\n  sqlite3_tokenizer **ppTokenizer\n){\n  simple_tokenizer *t;\n\n  t = (simple_tokenizer *) sqlite3_malloc(sizeof(*t));\n  if( t==NULL ) return SQLITE_NOMEM;\n  memset(t, 0, sizeof(*t));\n\n  /* TODO(shess) Delimiters need to remain the same from run to run,\n  ** else we need to reindex.  One solution would be a meta-table to\n  ** track such information in the database, then we'd only want this\n  ** information on the initial create.\n  */\n  if( argc>1 ){\n    int i, n = (int)strlen(argv[1]);\n    for(i=0; i<n; i++){\n      unsigned char ch = argv[1][i];\n      /* We explicitly don't support UTF-8 delimiters for now. */\n      if( ch>=0x80 ){\n        sqlite3_free(t);\n        return SQLITE_ERROR;\n      }\n      t->delim[ch] = 1;\n    }\n  } else {\n    /* Mark non-alphanumeric ASCII characters as delimiters */\n    int i;\n    for(i=1; i<0x80; i++){\n      t->delim[i] = !fts3_isalnum(i) ? -1 : 0;\n    }\n  }\n\n  *ppTokenizer = &t->base;\n  return SQLITE_OK;\n}\n\n/*\n** Destroy a tokenizer\n*/\nstatic int simpleDestroy(sqlite3_tokenizer *pTokenizer){\n  sqlite3_free(pTokenizer);\n  return SQLITE_OK;\n}\n\n/*\n** Prepare to begin tokenizing a particular string.  The input\n** string to be tokenized is pInput[0..nBytes-1].  A cursor\n** used to incrementally tokenize this string is returned in \n** *ppCursor.\n*/\nstatic int simpleOpen(\n  sqlite3_tokenizer *pTokenizer,         /* The tokenizer */\n  const char *pInput, int nBytes,        /* String to be tokenized */\n  sqlite3_tokenizer_cursor **ppCursor    /* OUT: Tokenization cursor */\n){\n  simple_tokenizer_cursor *c;\n\n  UNUSED_PARAMETER(pTokenizer);\n\n  c = (simple_tokenizer_cursor *) sqlite3_malloc(sizeof(*c));\n  if( c==NULL ) return SQLITE_NOMEM;\n\n  c->pInput = pInput;\n  if( pInput==0 ){\n    c->nBytes = 0;\n  }else if( nBytes<0 ){\n    c->nBytes = (int)strlen(pInput);\n  }else{\n    c->nBytes = nBytes;\n  }\n  c->iOffset = 0;                 /* start tokenizing at the beginning */\n  c->iToken = 0;\n  c->pToken = NULL;               /* no space allocated, yet. */\n  c->nTokenAllocated = 0;\n\n  *ppCursor = &c->base;\n  return SQLITE_OK;\n}\n\n/*\n** Close a tokenization cursor previously opened by a call to\n** simpleOpen() above.\n*/\nstatic int simpleClose(sqlite3_tokenizer_cursor *pCursor){\n  simple_tokenizer_cursor *c = (simple_tokenizer_cursor *) pCursor;\n  sqlite3_free(c->pToken);\n  sqlite3_free(c);\n  return SQLITE_OK;\n}\n\n/*\n** Extract the next token from a tokenization cursor.  The cursor must\n** have been opened by a prior call to simpleOpen().\n*/\nstatic int simpleNext(\n  sqlite3_tokenizer_cursor *pCursor,  /* Cursor returned by simpleOpen */\n  const char **ppToken,               /* OUT: *ppToken is the token text */\n  int *pnBytes,                       /* OUT: Number of bytes in token */\n  int *piStartOffset,                 /* OUT: Starting offset of token */\n  int *piEndOffset,                   /* OUT: Ending offset of token */\n  int *piPosition                     /* OUT: Position integer of token */\n){\n  simple_tokenizer_cursor *c = (simple_tokenizer_cursor *) pCursor;\n  simple_tokenizer *t = (simple_tokenizer *) pCursor->pTokenizer;\n  unsigned char *p = (unsigned char *)c->pInput;\n\n  while( c->iOffset<c->nBytes ){\n    int iStartOffset;\n\n    /* Scan past delimiter characters */\n    while( c->iOffset<c->nBytes && simpleDelim(t, p[c->iOffset]) ){\n      c->iOffset++;\n    }\n\n    /* Count non-delimiter characters. */\n    iStartOffset = c->iOffset;\n    while( c->iOffset<c->nBytes && !simpleDelim(t, p[c->iOffset]) ){\n      c->iOffset++;\n    }\n\n    if( c->iOffset>iStartOffset ){\n      int i, n = c->iOffset-iStartOffset;\n      if( n>c->nTokenAllocated ){\n        char *pNew;\n        c->nTokenAllocated = n+20;\n        pNew = sqlite3_realloc(c->pToken, c->nTokenAllocated);\n        if( !pNew ) return SQLITE_NOMEM;\n        c->pToken = pNew;\n      }\n      for(i=0; i<n; i++){\n        /* TODO(shess) This needs expansion to handle UTF-8\n        ** case-insensitivity.\n        */\n        unsigned char ch = p[iStartOffset+i];\n        c->pToken[i] = (char)((ch>='A' && ch<='Z') ? ch-'A'+'a' : ch);\n      }\n      *ppToken = c->pToken;\n      *pnBytes = n;\n      *piStartOffset = iStartOffset;\n      *piEndOffset = c->iOffset;\n      *piPosition = c->iToken++;\n\n      return SQLITE_OK;\n    }\n  }\n  return SQLITE_DONE;\n}\n\n/*\n** The set of routines that implement the simple tokenizer\n*/\nstatic const sqlite3_tokenizer_module simpleTokenizerModule = {\n  0,\n  simpleCreate,\n  simpleDestroy,\n  simpleOpen,\n  simpleClose,\n  simpleNext,\n  0,\n};\n\n/*\n** Allocate a new simple tokenizer.  Return a pointer to the new\n** tokenizer in *ppModule\n*/\nSQLITE_PRIVATE void sqlite3Fts3SimpleTokenizerModule(\n  sqlite3_tokenizer_module const**ppModule\n){\n  *ppModule = &simpleTokenizerModule;\n}\n\n#endif /* !defined(SQLITE_CORE) || defined(SQLITE_ENABLE_FTS3) */\n\n/************** End of fts3_tokenizer1.c *************************************/\n/************** Begin file fts3_tokenize_vtab.c ******************************/\n/*\n** 2013 Apr 22\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n******************************************************************************\n**\n** This file contains code for the \"fts3tokenize\" virtual table module.\n** An fts3tokenize virtual table is created as follows:\n**\n**   CREATE VIRTUAL TABLE <tbl> USING fts3tokenize(\n**       <tokenizer-name>, <arg-1>, ...\n**   );\n**\n** The table created has the following schema:\n**\n**   CREATE TABLE <tbl>(input, token, start, end, position)\n**\n** When queried, the query must include a WHERE clause of type:\n**\n**   input = <string>\n**\n** The virtual table module tokenizes this <string>, using the FTS3 \n** tokenizer specified by the arguments to the CREATE VIRTUAL TABLE \n** statement and returns one row for each token in the result. With\n** fields set as follows:\n**\n**   input:   Always set to a copy of <string>\n**   token:   A token from the input.\n**   start:   Byte offset of the token within the input <string>.\n**   end:     Byte offset of the byte immediately following the end of the\n**            token within the input string.\n**   pos:     Token offset of token within input.\n**\n*/\n/* #include \"fts3Int.h\" */\n#if !defined(SQLITE_CORE) || defined(SQLITE_ENABLE_FTS3)\n\n/* #include <string.h> */\n/* #include <assert.h> */\n\ntypedef struct Fts3tokTable Fts3tokTable;\ntypedef struct Fts3tokCursor Fts3tokCursor;\n\n/*\n** Virtual table structure.\n*/\nstruct Fts3tokTable {\n  sqlite3_vtab base;              /* Base class used by SQLite core */\n  const sqlite3_tokenizer_module *pMod;\n  sqlite3_tokenizer *pTok;\n};\n\n/*\n** Virtual table cursor structure.\n*/\nstruct Fts3tokCursor {\n  sqlite3_vtab_cursor base;       /* Base class used by SQLite core */\n  char *zInput;                   /* Input string */\n  sqlite3_tokenizer_cursor *pCsr; /* Cursor to iterate through zInput */\n  int iRowid;                     /* Current 'rowid' value */\n  const char *zToken;             /* Current 'token' value */\n  int nToken;                     /* Size of zToken in bytes */\n  int iStart;                     /* Current 'start' value */\n  int iEnd;                       /* Current 'end' value */\n  int iPos;                       /* Current 'pos' value */\n};\n\n/*\n** Query FTS for the tokenizer implementation named zName.\n*/\nstatic int fts3tokQueryTokenizer(\n  Fts3Hash *pHash,\n  const char *zName,\n  const sqlite3_tokenizer_module **pp,\n  char **pzErr\n){\n  sqlite3_tokenizer_module *p;\n  int nName = (int)strlen(zName);\n\n  p = (sqlite3_tokenizer_module *)sqlite3Fts3HashFind(pHash, zName, nName+1);\n  if( !p ){\n    sqlite3Fts3ErrMsg(pzErr, \"unknown tokenizer: %s\", zName);\n    return SQLITE_ERROR;\n  }\n\n  *pp = p;\n  return SQLITE_OK;\n}\n\n/*\n** The second argument, argv[], is an array of pointers to nul-terminated\n** strings. This function makes a copy of the array and strings into a \n** single block of memory. It then dequotes any of the strings that appear\n** to be quoted.\n**\n** If successful, output parameter *pazDequote is set to point at the\n** array of dequoted strings and SQLITE_OK is returned. The caller is\n** responsible for eventually calling sqlite3_free() to free the array\n** in this case. Or, if an error occurs, an SQLite error code is returned.\n** The final value of *pazDequote is undefined in this case.\n*/\nstatic int fts3tokDequoteArray(\n  int argc,                       /* Number of elements in argv[] */\n  const char * const *argv,       /* Input array */\n  char ***pazDequote              /* Output array */\n){\n  int rc = SQLITE_OK;             /* Return code */\n  if( argc==0 ){\n    *pazDequote = 0;\n  }else{\n    int i;\n    int nByte = 0;\n    char **azDequote;\n\n    for(i=0; i<argc; i++){\n      nByte += (int)(strlen(argv[i]) + 1);\n    }\n\n    *pazDequote = azDequote = sqlite3_malloc(sizeof(char *)*argc + nByte);\n    if( azDequote==0 ){\n      rc = SQLITE_NOMEM;\n    }else{\n      char *pSpace = (char *)&azDequote[argc];\n      for(i=0; i<argc; i++){\n        int n = (int)strlen(argv[i]);\n        azDequote[i] = pSpace;\n        memcpy(pSpace, argv[i], n+1);\n        sqlite3Fts3Dequote(pSpace);\n        pSpace += (n+1);\n      }\n    }\n  }\n\n  return rc;\n}\n\n/*\n** Schema of the tokenizer table.\n*/\n#define FTS3_TOK_SCHEMA \"CREATE TABLE x(input, token, start, end, position)\"\n\n/*\n** This function does all the work for both the xConnect and xCreate methods.\n** These tables have no persistent representation of their own, so xConnect\n** and xCreate are identical operations.\n**\n**   argv[0]: module name\n**   argv[1]: database name \n**   argv[2]: table name\n**   argv[3]: first argument (tokenizer name)\n*/\nstatic int fts3tokConnectMethod(\n  sqlite3 *db,                    /* Database connection */\n  void *pHash,                    /* Hash table of tokenizers */\n  int argc,                       /* Number of elements in argv array */\n  const char * const *argv,       /* xCreate/xConnect argument array */\n  sqlite3_vtab **ppVtab,          /* OUT: New sqlite3_vtab object */\n  char **pzErr                    /* OUT: sqlite3_malloc'd error message */\n){\n  Fts3tokTable *pTab = 0;\n  const sqlite3_tokenizer_module *pMod = 0;\n  sqlite3_tokenizer *pTok = 0;\n  int rc;\n  char **azDequote = 0;\n  int nDequote;\n\n  rc = sqlite3_declare_vtab(db, FTS3_TOK_SCHEMA);\n  if( rc!=SQLITE_OK ) return rc;\n\n  nDequote = argc-3;\n  rc = fts3tokDequoteArray(nDequote, &argv[3], &azDequote);\n\n  if( rc==SQLITE_OK ){\n    const char *zModule;\n    if( nDequote<1 ){\n      zModule = \"simple\";\n    }else{\n      zModule = azDequote[0];\n    }\n    rc = fts3tokQueryTokenizer((Fts3Hash*)pHash, zModule, &pMod, pzErr);\n  }\n\n  assert( (rc==SQLITE_OK)==(pMod!=0) );\n  if( rc==SQLITE_OK ){\n    const char * const *azArg = (const char * const *)&azDequote[1];\n    rc = pMod->xCreate((nDequote>1 ? nDequote-1 : 0), azArg, &pTok);\n  }\n\n  if( rc==SQLITE_OK ){\n    pTab = (Fts3tokTable *)sqlite3_malloc(sizeof(Fts3tokTable));\n    if( pTab==0 ){\n      rc = SQLITE_NOMEM;\n    }\n  }\n\n  if( rc==SQLITE_OK ){\n    memset(pTab, 0, sizeof(Fts3tokTable));\n    pTab->pMod = pMod;\n    pTab->pTok = pTok;\n    *ppVtab = &pTab->base;\n  }else{\n    if( pTok ){\n      pMod->xDestroy(pTok);\n    }\n  }\n\n  sqlite3_free(azDequote);\n  return rc;\n}\n\n/*\n** This function does the work for both the xDisconnect and xDestroy methods.\n** These tables have no persistent representation of their own, so xDisconnect\n** and xDestroy are identical operations.\n*/\nstatic int fts3tokDisconnectMethod(sqlite3_vtab *pVtab){\n  Fts3tokTable *pTab = (Fts3tokTable *)pVtab;\n\n  pTab->pMod->xDestroy(pTab->pTok);\n  sqlite3_free(pTab);\n  return SQLITE_OK;\n}\n\n/*\n** xBestIndex - Analyze a WHERE and ORDER BY clause.\n*/\nstatic int fts3tokBestIndexMethod(\n  sqlite3_vtab *pVTab, \n  sqlite3_index_info *pInfo\n){\n  int i;\n  UNUSED_PARAMETER(pVTab);\n\n  for(i=0; i<pInfo->nConstraint; i++){\n    if( pInfo->aConstraint[i].usable \n     && pInfo->aConstraint[i].iColumn==0 \n     && pInfo->aConstraint[i].op==SQLITE_INDEX_CONSTRAINT_EQ \n    ){\n      pInfo->idxNum = 1;\n      pInfo->aConstraintUsage[i].argvIndex = 1;\n      pInfo->aConstraintUsage[i].omit = 1;\n      pInfo->estimatedCost = 1;\n      return SQLITE_OK;\n    }\n  }\n\n  pInfo->idxNum = 0;\n  assert( pInfo->estimatedCost>1000000.0 );\n\n  return SQLITE_OK;\n}\n\n/*\n** xOpen - Open a cursor.\n*/\nstatic int fts3tokOpenMethod(sqlite3_vtab *pVTab, sqlite3_vtab_cursor **ppCsr){\n  Fts3tokCursor *pCsr;\n  UNUSED_PARAMETER(pVTab);\n\n  pCsr = (Fts3tokCursor *)sqlite3_malloc(sizeof(Fts3tokCursor));\n  if( pCsr==0 ){\n    return SQLITE_NOMEM;\n  }\n  memset(pCsr, 0, sizeof(Fts3tokCursor));\n\n  *ppCsr = (sqlite3_vtab_cursor *)pCsr;\n  return SQLITE_OK;\n}\n\n/*\n** Reset the tokenizer cursor passed as the only argument. As if it had\n** just been returned by fts3tokOpenMethod().\n*/\nstatic void fts3tokResetCursor(Fts3tokCursor *pCsr){\n  if( pCsr->pCsr ){\n    Fts3tokTable *pTab = (Fts3tokTable *)(pCsr->base.pVtab);\n    pTab->pMod->xClose(pCsr->pCsr);\n    pCsr->pCsr = 0;\n  }\n  sqlite3_free(pCsr->zInput);\n  pCsr->zInput = 0;\n  pCsr->zToken = 0;\n  pCsr->nToken = 0;\n  pCsr->iStart = 0;\n  pCsr->iEnd = 0;\n  pCsr->iPos = 0;\n  pCsr->iRowid = 0;\n}\n\n/*\n** xClose - Close a cursor.\n*/\nstatic int fts3tokCloseMethod(sqlite3_vtab_cursor *pCursor){\n  Fts3tokCursor *pCsr = (Fts3tokCursor *)pCursor;\n\n  fts3tokResetCursor(pCsr);\n  sqlite3_free(pCsr);\n  return SQLITE_OK;\n}\n\n/*\n** xNext - Advance the cursor to the next row, if any.\n*/\nstatic int fts3tokNextMethod(sqlite3_vtab_cursor *pCursor){\n  Fts3tokCursor *pCsr = (Fts3tokCursor *)pCursor;\n  Fts3tokTable *pTab = (Fts3tokTable *)(pCursor->pVtab);\n  int rc;                         /* Return code */\n\n  pCsr->iRowid++;\n  rc = pTab->pMod->xNext(pCsr->pCsr,\n      &pCsr->zToken, &pCsr->nToken,\n      &pCsr->iStart, &pCsr->iEnd, &pCsr->iPos\n  );\n\n  if( rc!=SQLITE_OK ){\n    fts3tokResetCursor(pCsr);\n    if( rc==SQLITE_DONE ) rc = SQLITE_OK;\n  }\n\n  return rc;\n}\n\n/*\n** xFilter - Initialize a cursor to point at the start of its data.\n*/\nstatic int fts3tokFilterMethod(\n  sqlite3_vtab_cursor *pCursor,   /* The cursor used for this query */\n  int idxNum,                     /* Strategy index */\n  const char *idxStr,             /* Unused */\n  int nVal,                       /* Number of elements in apVal */\n  sqlite3_value **apVal           /* Arguments for the indexing scheme */\n){\n  int rc = SQLITE_ERROR;\n  Fts3tokCursor *pCsr = (Fts3tokCursor *)pCursor;\n  Fts3tokTable *pTab = (Fts3tokTable *)(pCursor->pVtab);\n  UNUSED_PARAMETER(idxStr);\n  UNUSED_PARAMETER(nVal);\n\n  fts3tokResetCursor(pCsr);\n  if( idxNum==1 ){\n    const char *zByte = (const char *)sqlite3_value_text(apVal[0]);\n    int nByte = sqlite3_value_bytes(apVal[0]);\n    pCsr->zInput = sqlite3_malloc(nByte+1);\n    if( pCsr->zInput==0 ){\n      rc = SQLITE_NOMEM;\n    }else{\n      memcpy(pCsr->zInput, zByte, nByte);\n      pCsr->zInput[nByte] = 0;\n      rc = pTab->pMod->xOpen(pTab->pTok, pCsr->zInput, nByte, &pCsr->pCsr);\n      if( rc==SQLITE_OK ){\n        pCsr->pCsr->pTokenizer = pTab->pTok;\n      }\n    }\n  }\n\n  if( rc!=SQLITE_OK ) return rc;\n  return fts3tokNextMethod(pCursor);\n}\n\n/*\n** xEof - Return true if the cursor is at EOF, or false otherwise.\n*/\nstatic int fts3tokEofMethod(sqlite3_vtab_cursor *pCursor){\n  Fts3tokCursor *pCsr = (Fts3tokCursor *)pCursor;\n  return (pCsr->zToken==0);\n}\n\n/*\n** xColumn - Return a column value.\n*/\nstatic int fts3tokColumnMethod(\n  sqlite3_vtab_cursor *pCursor,   /* Cursor to retrieve value from */\n  sqlite3_context *pCtx,          /* Context for sqlite3_result_xxx() calls */\n  int iCol                        /* Index of column to read value from */\n){\n  Fts3tokCursor *pCsr = (Fts3tokCursor *)pCursor;\n\n  /* CREATE TABLE x(input, token, start, end, position) */\n  switch( iCol ){\n    case 0:\n      sqlite3_result_text(pCtx, pCsr->zInput, -1, SQLITE_TRANSIENT);\n      break;\n    case 1:\n      sqlite3_result_text(pCtx, pCsr->zToken, pCsr->nToken, SQLITE_TRANSIENT);\n      break;\n    case 2:\n      sqlite3_result_int(pCtx, pCsr->iStart);\n      break;\n    case 3:\n      sqlite3_result_int(pCtx, pCsr->iEnd);\n      break;\n    default:\n      assert( iCol==4 );\n      sqlite3_result_int(pCtx, pCsr->iPos);\n      break;\n  }\n  return SQLITE_OK;\n}\n\n/*\n** xRowid - Return the current rowid for the cursor.\n*/\nstatic int fts3tokRowidMethod(\n  sqlite3_vtab_cursor *pCursor,   /* Cursor to retrieve value from */\n  sqlite_int64 *pRowid            /* OUT: Rowid value */\n){\n  Fts3tokCursor *pCsr = (Fts3tokCursor *)pCursor;\n  *pRowid = (sqlite3_int64)pCsr->iRowid;\n  return SQLITE_OK;\n}\n\n/*\n** Register the fts3tok module with database connection db. Return SQLITE_OK\n** if successful or an error code if sqlite3_create_module() fails.\n*/\nSQLITE_PRIVATE int sqlite3Fts3InitTok(sqlite3 *db, Fts3Hash *pHash){\n  static const sqlite3_module fts3tok_module = {\n     0,                           /* iVersion      */\n     fts3tokConnectMethod,        /* xCreate       */\n     fts3tokConnectMethod,        /* xConnect      */\n     fts3tokBestIndexMethod,      /* xBestIndex    */\n     fts3tokDisconnectMethod,     /* xDisconnect   */\n     fts3tokDisconnectMethod,     /* xDestroy      */\n     fts3tokOpenMethod,           /* xOpen         */\n     fts3tokCloseMethod,          /* xClose        */\n     fts3tokFilterMethod,         /* xFilter       */\n     fts3tokNextMethod,           /* xNext         */\n     fts3tokEofMethod,            /* xEof          */\n     fts3tokColumnMethod,         /* xColumn       */\n     fts3tokRowidMethod,          /* xRowid        */\n     0,                           /* xUpdate       */\n     0,                           /* xBegin        */\n     0,                           /* xSync         */\n     0,                           /* xCommit       */\n     0,                           /* xRollback     */\n     0,                           /* xFindFunction */\n     0,                           /* xRename       */\n     0,                           /* xSavepoint    */\n     0,                           /* xRelease      */\n     0                            /* xRollbackTo   */\n  };\n  int rc;                         /* Return code */\n\n  rc = sqlite3_create_module(db, \"fts3tokenize\", &fts3tok_module, (void*)pHash);\n  return rc;\n}\n\n#endif /* !defined(SQLITE_CORE) || defined(SQLITE_ENABLE_FTS3) */\n\n/************** End of fts3_tokenize_vtab.c **********************************/\n/************** Begin file fts3_write.c **************************************/\n/*\n** 2009 Oct 23\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n******************************************************************************\n**\n** This file is part of the SQLite FTS3 extension module. Specifically,\n** this file contains code to insert, update and delete rows from FTS3\n** tables. It also contains code to merge FTS3 b-tree segments. Some\n** of the sub-routines used to merge segments are also used by the query \n** code in fts3.c.\n*/\n\n/* #include \"fts3Int.h\" */\n#if !defined(SQLITE_CORE) || defined(SQLITE_ENABLE_FTS3)\n\n/* #include <string.h> */\n/* #include <assert.h> */\n/* #include <stdlib.h> */\n\n\n#define FTS_MAX_APPENDABLE_HEIGHT 16\n\n/*\n** When full-text index nodes are loaded from disk, the buffer that they\n** are loaded into has the following number of bytes of padding at the end \n** of it. i.e. if a full-text index node is 900 bytes in size, then a buffer\n** of 920 bytes is allocated for it.\n**\n** This means that if we have a pointer into a buffer containing node data,\n** it is always safe to read up to two varints from it without risking an\n** overread, even if the node data is corrupted.\n*/\n#define FTS3_NODE_PADDING (FTS3_VARINT_MAX*2)\n\n/*\n** Under certain circumstances, b-tree nodes (doclists) can be loaded into\n** memory incrementally instead of all at once. This can be a big performance\n** win (reduced IO and CPU) if SQLite stops calling the virtual table xNext()\n** method before retrieving all query results (as may happen, for example,\n** if a query has a LIMIT clause).\n**\n** Incremental loading is used for b-tree nodes FTS3_NODE_CHUNK_THRESHOLD \n** bytes and larger. Nodes are loaded in chunks of FTS3_NODE_CHUNKSIZE bytes.\n** The code is written so that the hard lower-limit for each of these values \n** is 1. Clearly such small values would be inefficient, but can be useful \n** for testing purposes.\n**\n** If this module is built with SQLITE_TEST defined, these constants may\n** be overridden at runtime for testing purposes. File fts3_test.c contains\n** a Tcl interface to read and write the values.\n*/\n#ifdef SQLITE_TEST\nint test_fts3_node_chunksize = (4*1024);\nint test_fts3_node_chunk_threshold = (4*1024)*4;\n# define FTS3_NODE_CHUNKSIZE       test_fts3_node_chunksize\n# define FTS3_NODE_CHUNK_THRESHOLD test_fts3_node_chunk_threshold\n#else\n# define FTS3_NODE_CHUNKSIZE (4*1024) \n# define FTS3_NODE_CHUNK_THRESHOLD (FTS3_NODE_CHUNKSIZE*4)\n#endif\n\n/*\n** The two values that may be meaningfully bound to the :1 parameter in\n** statements SQL_REPLACE_STAT and SQL_SELECT_STAT.\n*/\n#define FTS_STAT_DOCTOTAL      0\n#define FTS_STAT_INCRMERGEHINT 1\n#define FTS_STAT_AUTOINCRMERGE 2\n\n/*\n** If FTS_LOG_MERGES is defined, call sqlite3_log() to report each automatic\n** and incremental merge operation that takes place. This is used for \n** debugging FTS only, it should not usually be turned on in production\n** systems.\n*/\n#ifdef FTS3_LOG_MERGES\nstatic void fts3LogMerge(int nMerge, sqlite3_int64 iAbsLevel){\n  sqlite3_log(SQLITE_OK, \"%d-way merge from level %d\", nMerge, (int)iAbsLevel);\n}\n#else\n#define fts3LogMerge(x, y)\n#endif\n\n\ntypedef struct PendingList PendingList;\ntypedef struct SegmentNode SegmentNode;\ntypedef struct SegmentWriter SegmentWriter;\n\n/*\n** An instance of the following data structure is used to build doclists\n** incrementally. See function fts3PendingListAppend() for details.\n*/\nstruct PendingList {\n  int nData;\n  char *aData;\n  int nSpace;\n  sqlite3_int64 iLastDocid;\n  sqlite3_int64 iLastCol;\n  sqlite3_int64 iLastPos;\n};\n\n\n/*\n** Each cursor has a (possibly empty) linked list of the following objects.\n*/\nstruct Fts3DeferredToken {\n  Fts3PhraseToken *pToken;        /* Pointer to corresponding expr token */\n  int iCol;                       /* Column token must occur in */\n  Fts3DeferredToken *pNext;       /* Next in list of deferred tokens */\n  PendingList *pList;             /* Doclist is assembled here */\n};\n\n/*\n** An instance of this structure is used to iterate through the terms on\n** a contiguous set of segment b-tree leaf nodes. Although the details of\n** this structure are only manipulated by code in this file, opaque handles\n** of type Fts3SegReader* are also used by code in fts3.c to iterate through\n** terms when querying the full-text index. See functions:\n**\n**   sqlite3Fts3SegReaderNew()\n**   sqlite3Fts3SegReaderFree()\n**   sqlite3Fts3SegReaderIterate()\n**\n** Methods used to manipulate Fts3SegReader structures:\n**\n**   fts3SegReaderNext()\n**   fts3SegReaderFirstDocid()\n**   fts3SegReaderNextDocid()\n*/\nstruct Fts3SegReader {\n  int iIdx;                       /* Index within level, or 0x7FFFFFFF for PT */\n  u8 bLookup;                     /* True for a lookup only */\n  u8 rootOnly;                    /* True for a root-only reader */\n\n  sqlite3_int64 iStartBlock;      /* Rowid of first leaf block to traverse */\n  sqlite3_int64 iLeafEndBlock;    /* Rowid of final leaf block to traverse */\n  sqlite3_int64 iEndBlock;        /* Rowid of final block in segment (or 0) */\n  sqlite3_int64 iCurrentBlock;    /* Current leaf block (or 0) */\n\n  char *aNode;                    /* Pointer to node data (or NULL) */\n  int nNode;                      /* Size of buffer at aNode (or 0) */\n  int nPopulate;                  /* If >0, bytes of buffer aNode[] loaded */\n  sqlite3_blob *pBlob;            /* If not NULL, blob handle to read node */\n\n  Fts3HashElem **ppNextElem;\n\n  /* Variables set by fts3SegReaderNext(). These may be read directly\n  ** by the caller. They are valid from the time SegmentReaderNew() returns\n  ** until SegmentReaderNext() returns something other than SQLITE_OK\n  ** (i.e. SQLITE_DONE).\n  */\n  int nTerm;                      /* Number of bytes in current term */\n  char *zTerm;                    /* Pointer to current term */\n  int nTermAlloc;                 /* Allocated size of zTerm buffer */\n  char *aDoclist;                 /* Pointer to doclist of current entry */\n  int nDoclist;                   /* Size of doclist in current entry */\n\n  /* The following variables are used by fts3SegReaderNextDocid() to iterate \n  ** through the current doclist (aDoclist/nDoclist).\n  */\n  char *pOffsetList;\n  int nOffsetList;                /* For descending pending seg-readers only */\n  sqlite3_int64 iDocid;\n};\n\n#define fts3SegReaderIsPending(p) ((p)->ppNextElem!=0)\n#define fts3SegReaderIsRootOnly(p) ((p)->rootOnly!=0)\n\n/*\n** An instance of this structure is used to create a segment b-tree in the\n** database. The internal details of this type are only accessed by the\n** following functions:\n**\n**   fts3SegWriterAdd()\n**   fts3SegWriterFlush()\n**   fts3SegWriterFree()\n*/\nstruct SegmentWriter {\n  SegmentNode *pTree;             /* Pointer to interior tree structure */\n  sqlite3_int64 iFirst;           /* First slot in %_segments written */\n  sqlite3_int64 iFree;            /* Next free slot in %_segments */\n  char *zTerm;                    /* Pointer to previous term buffer */\n  int nTerm;                      /* Number of bytes in zTerm */\n  int nMalloc;                    /* Size of malloc'd buffer at zMalloc */\n  char *zMalloc;                  /* Malloc'd space (possibly) used for zTerm */\n  int nSize;                      /* Size of allocation at aData */\n  int nData;                      /* Bytes of data in aData */\n  char *aData;                    /* Pointer to block from malloc() */\n  i64 nLeafData;                  /* Number of bytes of leaf data written */\n};\n\n/*\n** Type SegmentNode is used by the following three functions to create\n** the interior part of the segment b+-tree structures (everything except\n** the leaf nodes). These functions and type are only ever used by code\n** within the fts3SegWriterXXX() family of functions described above.\n**\n**   fts3NodeAddTerm()\n**   fts3NodeWrite()\n**   fts3NodeFree()\n**\n** When a b+tree is written to the database (either as a result of a merge\n** or the pending-terms table being flushed), leaves are written into the \n** database file as soon as they are completely populated. The interior of\n** the tree is assembled in memory and written out only once all leaves have\n** been populated and stored. This is Ok, as the b+-tree fanout is usually\n** very large, meaning that the interior of the tree consumes relatively \n** little memory.\n*/\nstruct SegmentNode {\n  SegmentNode *pParent;           /* Parent node (or NULL for root node) */\n  SegmentNode *pRight;            /* Pointer to right-sibling */\n  SegmentNode *pLeftmost;         /* Pointer to left-most node of this depth */\n  int nEntry;                     /* Number of terms written to node so far */\n  char *zTerm;                    /* Pointer to previous term buffer */\n  int nTerm;                      /* Number of bytes in zTerm */\n  int nMalloc;                    /* Size of malloc'd buffer at zMalloc */\n  char *zMalloc;                  /* Malloc'd space (possibly) used for zTerm */\n  int nData;                      /* Bytes of valid data so far */\n  char *aData;                    /* Node data */\n};\n\n/*\n** Valid values for the second argument to fts3SqlStmt().\n*/\n#define SQL_DELETE_CONTENT             0\n#define SQL_IS_EMPTY                   1\n#define SQL_DELETE_ALL_CONTENT         2 \n#define SQL_DELETE_ALL_SEGMENTS        3\n#define SQL_DELETE_ALL_SEGDIR          4\n#define SQL_DELETE_ALL_DOCSIZE         5\n#define SQL_DELETE_ALL_STAT            6\n#define SQL_SELECT_CONTENT_BY_ROWID    7\n#define SQL_NEXT_SEGMENT_INDEX         8\n#define SQL_INSERT_SEGMENTS            9\n#define SQL_NEXT_SEGMENTS_ID          10\n#define SQL_INSERT_SEGDIR             11\n#define SQL_SELECT_LEVEL              12\n#define SQL_SELECT_LEVEL_RANGE        13\n#define SQL_SELECT_LEVEL_COUNT        14\n#define SQL_SELECT_SEGDIR_MAX_LEVEL   15\n#define SQL_DELETE_SEGDIR_LEVEL       16\n#define SQL_DELETE_SEGMENTS_RANGE     17\n#define SQL_CONTENT_INSERT            18\n#define SQL_DELETE_DOCSIZE            19\n#define SQL_REPLACE_DOCSIZE           20\n#define SQL_SELECT_DOCSIZE            21\n#define SQL_SELECT_STAT               22\n#define SQL_REPLACE_STAT              23\n\n#define SQL_SELECT_ALL_PREFIX_LEVEL   24\n#define SQL_DELETE_ALL_TERMS_SEGDIR   25\n#define SQL_DELETE_SEGDIR_RANGE       26\n#define SQL_SELECT_ALL_LANGID         27\n#define SQL_FIND_MERGE_LEVEL          28\n#define SQL_MAX_LEAF_NODE_ESTIMATE    29\n#define SQL_DELETE_SEGDIR_ENTRY       30\n#define SQL_SHIFT_SEGDIR_ENTRY        31\n#define SQL_SELECT_SEGDIR             32\n#define SQL_CHOMP_SEGDIR              33\n#define SQL_SEGMENT_IS_APPENDABLE     34\n#define SQL_SELECT_INDEXES            35\n#define SQL_SELECT_MXLEVEL            36\n\n#define SQL_SELECT_LEVEL_RANGE2       37\n#define SQL_UPDATE_LEVEL_IDX          38\n#define SQL_UPDATE_LEVEL              39\n\n/*\n** This function is used to obtain an SQLite prepared statement handle\n** for the statement identified by the second argument. If successful,\n** *pp is set to the requested statement handle and SQLITE_OK returned.\n** Otherwise, an SQLite error code is returned and *pp is set to 0.\n**\n** If argument apVal is not NULL, then it must point to an array with\n** at least as many entries as the requested statement has bound \n** parameters. The values are bound to the statements parameters before\n** returning.\n*/\nstatic int fts3SqlStmt(\n  Fts3Table *p,                   /* Virtual table handle */\n  int eStmt,                      /* One of the SQL_XXX constants above */\n  sqlite3_stmt **pp,              /* OUT: Statement handle */\n  sqlite3_value **apVal           /* Values to bind to statement */\n){\n  const char *azSql[] = {\n/* 0  */  \"DELETE FROM %Q.'%q_content' WHERE rowid = ?\",\n/* 1  */  \"SELECT NOT EXISTS(SELECT docid FROM %Q.'%q_content' WHERE rowid!=?)\",\n/* 2  */  \"DELETE FROM %Q.'%q_content'\",\n/* 3  */  \"DELETE FROM %Q.'%q_segments'\",\n/* 4  */  \"DELETE FROM %Q.'%q_segdir'\",\n/* 5  */  \"DELETE FROM %Q.'%q_docsize'\",\n/* 6  */  \"DELETE FROM %Q.'%q_stat'\",\n/* 7  */  \"SELECT %s WHERE rowid=?\",\n/* 8  */  \"SELECT (SELECT max(idx) FROM %Q.'%q_segdir' WHERE level = ?) + 1\",\n/* 9  */  \"REPLACE INTO %Q.'%q_segments'(blockid, block) VALUES(?, ?)\",\n/* 10 */  \"SELECT coalesce((SELECT max(blockid) FROM %Q.'%q_segments') + 1, 1)\",\n/* 11 */  \"REPLACE INTO %Q.'%q_segdir' VALUES(?,?,?,?,?,?)\",\n\n          /* Return segments in order from oldest to newest.*/ \n/* 12 */  \"SELECT idx, start_block, leaves_end_block, end_block, root \"\n            \"FROM %Q.'%q_segdir' WHERE level = ? ORDER BY idx ASC\",\n/* 13 */  \"SELECT idx, start_block, leaves_end_block, end_block, root \"\n            \"FROM %Q.'%q_segdir' WHERE level BETWEEN ? AND ?\"\n            \"ORDER BY level DESC, idx ASC\",\n\n/* 14 */  \"SELECT count(*) FROM %Q.'%q_segdir' WHERE level = ?\",\n/* 15 */  \"SELECT max(level) FROM %Q.'%q_segdir' WHERE level BETWEEN ? AND ?\",\n\n/* 16 */  \"DELETE FROM %Q.'%q_segdir' WHERE level = ?\",\n/* 17 */  \"DELETE FROM %Q.'%q_segments' WHERE blockid BETWEEN ? AND ?\",\n/* 18 */  \"INSERT INTO %Q.'%q_content' VALUES(%s)\",\n/* 19 */  \"DELETE FROM %Q.'%q_docsize' WHERE docid = ?\",\n/* 20 */  \"REPLACE INTO %Q.'%q_docsize' VALUES(?,?)\",\n/* 21 */  \"SELECT size FROM %Q.'%q_docsize' WHERE docid=?\",\n/* 22 */  \"SELECT value FROM %Q.'%q_stat' WHERE id=?\",\n/* 23 */  \"REPLACE INTO %Q.'%q_stat' VALUES(?,?)\",\n/* 24 */  \"\",\n/* 25 */  \"\",\n\n/* 26 */ \"DELETE FROM %Q.'%q_segdir' WHERE level BETWEEN ? AND ?\",\n/* 27 */ \"SELECT ? UNION SELECT level / (1024 * ?) FROM %Q.'%q_segdir'\",\n\n/* This statement is used to determine which level to read the input from\n** when performing an incremental merge. It returns the absolute level number\n** of the oldest level in the db that contains at least ? segments. Or,\n** if no level in the FTS index contains more than ? segments, the statement\n** returns zero rows.  */\n/* 28 */ \"SELECT level, count(*) AS cnt FROM %Q.'%q_segdir' \"\n         \"  GROUP BY level HAVING cnt>=?\"\n         \"  ORDER BY (level %% 1024) ASC LIMIT 1\",\n\n/* Estimate the upper limit on the number of leaf nodes in a new segment\n** created by merging the oldest :2 segments from absolute level :1. See \n** function sqlite3Fts3Incrmerge() for details.  */\n/* 29 */ \"SELECT 2 * total(1 + leaves_end_block - start_block) \"\n         \"  FROM %Q.'%q_segdir' WHERE level = ? AND idx < ?\",\n\n/* SQL_DELETE_SEGDIR_ENTRY\n**   Delete the %_segdir entry on absolute level :1 with index :2.  */\n/* 30 */ \"DELETE FROM %Q.'%q_segdir' WHERE level = ? AND idx = ?\",\n\n/* SQL_SHIFT_SEGDIR_ENTRY\n**   Modify the idx value for the segment with idx=:3 on absolute level :2\n**   to :1.  */\n/* 31 */ \"UPDATE %Q.'%q_segdir' SET idx = ? WHERE level=? AND idx=?\",\n\n/* SQL_SELECT_SEGDIR\n**   Read a single entry from the %_segdir table. The entry from absolute \n**   level :1 with index value :2.  */\n/* 32 */  \"SELECT idx, start_block, leaves_end_block, end_block, root \"\n            \"FROM %Q.'%q_segdir' WHERE level = ? AND idx = ?\",\n\n/* SQL_CHOMP_SEGDIR\n**   Update the start_block (:1) and root (:2) fields of the %_segdir\n**   entry located on absolute level :3 with index :4.  */\n/* 33 */  \"UPDATE %Q.'%q_segdir' SET start_block = ?, root = ?\"\n            \"WHERE level = ? AND idx = ?\",\n\n/* SQL_SEGMENT_IS_APPENDABLE\n**   Return a single row if the segment with end_block=? is appendable. Or\n**   no rows otherwise.  */\n/* 34 */  \"SELECT 1 FROM %Q.'%q_segments' WHERE blockid=? AND block IS NULL\",\n\n/* SQL_SELECT_INDEXES\n**   Return the list of valid segment indexes for absolute level ?  */\n/* 35 */  \"SELECT idx FROM %Q.'%q_segdir' WHERE level=? ORDER BY 1 ASC\",\n\n/* SQL_SELECT_MXLEVEL\n**   Return the largest relative level in the FTS index or indexes.  */\n/* 36 */  \"SELECT max( level %% 1024 ) FROM %Q.'%q_segdir'\",\n\n          /* Return segments in order from oldest to newest.*/ \n/* 37 */  \"SELECT level, idx, end_block \"\n            \"FROM %Q.'%q_segdir' WHERE level BETWEEN ? AND ? \"\n            \"ORDER BY level DESC, idx ASC\",\n\n          /* Update statements used while promoting segments */\n/* 38 */  \"UPDATE OR FAIL %Q.'%q_segdir' SET level=-1,idx=? \"\n            \"WHERE level=? AND idx=?\",\n/* 39 */  \"UPDATE OR FAIL %Q.'%q_segdir' SET level=? WHERE level=-1\"\n\n  };\n  int rc = SQLITE_OK;\n  sqlite3_stmt *pStmt;\n\n  assert( SizeofArray(azSql)==SizeofArray(p->aStmt) );\n  assert( eStmt<SizeofArray(azSql) && eStmt>=0 );\n  \n  pStmt = p->aStmt[eStmt];\n  if( !pStmt ){\n    char *zSql;\n    if( eStmt==SQL_CONTENT_INSERT ){\n      zSql = sqlite3_mprintf(azSql[eStmt], p->zDb, p->zName, p->zWriteExprlist);\n    }else if( eStmt==SQL_SELECT_CONTENT_BY_ROWID ){\n      zSql = sqlite3_mprintf(azSql[eStmt], p->zReadExprlist);\n    }else{\n      zSql = sqlite3_mprintf(azSql[eStmt], p->zDb, p->zName);\n    }\n    if( !zSql ){\n      rc = SQLITE_NOMEM;\n    }else{\n      rc = sqlite3_prepare_v3(p->db, zSql, -1, SQLITE_PREPARE_PERSISTENT,\n                              &pStmt, NULL);\n      sqlite3_free(zSql);\n      assert( rc==SQLITE_OK || pStmt==0 );\n      p->aStmt[eStmt] = pStmt;\n    }\n  }\n  if( apVal ){\n    int i;\n    int nParam = sqlite3_bind_parameter_count(pStmt);\n    for(i=0; rc==SQLITE_OK && i<nParam; i++){\n      rc = sqlite3_bind_value(pStmt, i+1, apVal[i]);\n    }\n  }\n  *pp = pStmt;\n  return rc;\n}\n\n\nstatic int fts3SelectDocsize(\n  Fts3Table *pTab,                /* FTS3 table handle */\n  sqlite3_int64 iDocid,           /* Docid to bind for SQL_SELECT_DOCSIZE */\n  sqlite3_stmt **ppStmt           /* OUT: Statement handle */\n){\n  sqlite3_stmt *pStmt = 0;        /* Statement requested from fts3SqlStmt() */\n  int rc;                         /* Return code */\n\n  rc = fts3SqlStmt(pTab, SQL_SELECT_DOCSIZE, &pStmt, 0);\n  if( rc==SQLITE_OK ){\n    sqlite3_bind_int64(pStmt, 1, iDocid);\n    rc = sqlite3_step(pStmt);\n    if( rc!=SQLITE_ROW || sqlite3_column_type(pStmt, 0)!=SQLITE_BLOB ){\n      rc = sqlite3_reset(pStmt);\n      if( rc==SQLITE_OK ) rc = FTS_CORRUPT_VTAB;\n      pStmt = 0;\n    }else{\n      rc = SQLITE_OK;\n    }\n  }\n\n  *ppStmt = pStmt;\n  return rc;\n}\n\nSQLITE_PRIVATE int sqlite3Fts3SelectDoctotal(\n  Fts3Table *pTab,                /* Fts3 table handle */\n  sqlite3_stmt **ppStmt           /* OUT: Statement handle */\n){\n  sqlite3_stmt *pStmt = 0;\n  int rc;\n  rc = fts3SqlStmt(pTab, SQL_SELECT_STAT, &pStmt, 0);\n  if( rc==SQLITE_OK ){\n    sqlite3_bind_int(pStmt, 1, FTS_STAT_DOCTOTAL);\n    if( sqlite3_step(pStmt)!=SQLITE_ROW\n     || sqlite3_column_type(pStmt, 0)!=SQLITE_BLOB\n    ){\n      rc = sqlite3_reset(pStmt);\n      if( rc==SQLITE_OK ) rc = FTS_CORRUPT_VTAB;\n      pStmt = 0;\n    }\n  }\n  *ppStmt = pStmt;\n  return rc;\n}\n\nSQLITE_PRIVATE int sqlite3Fts3SelectDocsize(\n  Fts3Table *pTab,                /* Fts3 table handle */\n  sqlite3_int64 iDocid,           /* Docid to read size data for */\n  sqlite3_stmt **ppStmt           /* OUT: Statement handle */\n){\n  return fts3SelectDocsize(pTab, iDocid, ppStmt);\n}\n\n/*\n** Similar to fts3SqlStmt(). Except, after binding the parameters in\n** array apVal[] to the SQL statement identified by eStmt, the statement\n** is executed.\n**\n** Returns SQLITE_OK if the statement is successfully executed, or an\n** SQLite error code otherwise.\n*/\nstatic void fts3SqlExec(\n  int *pRC,                /* Result code */\n  Fts3Table *p,            /* The FTS3 table */\n  int eStmt,               /* Index of statement to evaluate */\n  sqlite3_value **apVal    /* Parameters to bind */\n){\n  sqlite3_stmt *pStmt;\n  int rc;\n  if( *pRC ) return;\n  rc = fts3SqlStmt(p, eStmt, &pStmt, apVal); \n  if( rc==SQLITE_OK ){\n    sqlite3_step(pStmt);\n    rc = sqlite3_reset(pStmt);\n  }\n  *pRC = rc;\n}\n\n\n/*\n** This function ensures that the caller has obtained an exclusive \n** shared-cache table-lock on the %_segdir table. This is required before \n** writing data to the fts3 table. If this lock is not acquired first, then\n** the caller may end up attempting to take this lock as part of committing\n** a transaction, causing SQLite to return SQLITE_LOCKED or \n** LOCKED_SHAREDCACHEto a COMMIT command.\n**\n** It is best to avoid this because if FTS3 returns any error when \n** committing a transaction, the whole transaction will be rolled back. \n** And this is not what users expect when they get SQLITE_LOCKED_SHAREDCACHE. \n** It can still happen if the user locks the underlying tables directly \n** instead of accessing them via FTS.\n*/\nstatic int fts3Writelock(Fts3Table *p){\n  int rc = SQLITE_OK;\n  \n  if( p->nPendingData==0 ){\n    sqlite3_stmt *pStmt;\n    rc = fts3SqlStmt(p, SQL_DELETE_SEGDIR_LEVEL, &pStmt, 0);\n    if( rc==SQLITE_OK ){\n      sqlite3_bind_null(pStmt, 1);\n      sqlite3_step(pStmt);\n      rc = sqlite3_reset(pStmt);\n    }\n  }\n\n  return rc;\n}\n\n/*\n** FTS maintains a separate indexes for each language-id (a 32-bit integer).\n** Within each language id, a separate index is maintained to store the\n** document terms, and each configured prefix size (configured the FTS \n** \"prefix=\" option). And each index consists of multiple levels (\"relative\n** levels\").\n**\n** All three of these values (the language id, the specific index and the\n** level within the index) are encoded in 64-bit integer values stored\n** in the %_segdir table on disk. This function is used to convert three\n** separate component values into the single 64-bit integer value that\n** can be used to query the %_segdir table.\n**\n** Specifically, each language-id/index combination is allocated 1024 \n** 64-bit integer level values (\"absolute levels\"). The main terms index\n** for language-id 0 is allocate values 0-1023. The first prefix index\n** (if any) for language-id 0 is allocated values 1024-2047. And so on.\n** Language 1 indexes are allocated immediately following language 0.\n**\n** So, for a system with nPrefix prefix indexes configured, the block of\n** absolute levels that corresponds to language-id iLangid and index \n** iIndex starts at absolute level ((iLangid * (nPrefix+1) + iIndex) * 1024).\n*/\nstatic sqlite3_int64 getAbsoluteLevel(\n  Fts3Table *p,                   /* FTS3 table handle */\n  int iLangid,                    /* Language id */\n  int iIndex,                     /* Index in p->aIndex[] */\n  int iLevel                      /* Level of segments */\n){\n  sqlite3_int64 iBase;            /* First absolute level for iLangid/iIndex */\n  assert( iLangid>=0 );\n  assert( p->nIndex>0 );\n  assert( iIndex>=0 && iIndex<p->nIndex );\n\n  iBase = ((sqlite3_int64)iLangid * p->nIndex + iIndex) * FTS3_SEGDIR_MAXLEVEL;\n  return iBase + iLevel;\n}\n\n/*\n** Set *ppStmt to a statement handle that may be used to iterate through\n** all rows in the %_segdir table, from oldest to newest. If successful,\n** return SQLITE_OK. If an error occurs while preparing the statement, \n** return an SQLite error code.\n**\n** There is only ever one instance of this SQL statement compiled for\n** each FTS3 table.\n**\n** The statement returns the following columns from the %_segdir table:\n**\n**   0: idx\n**   1: start_block\n**   2: leaves_end_block\n**   3: end_block\n**   4: root\n*/\nSQLITE_PRIVATE int sqlite3Fts3AllSegdirs(\n  Fts3Table *p,                   /* FTS3 table */\n  int iLangid,                    /* Language being queried */\n  int iIndex,                     /* Index for p->aIndex[] */\n  int iLevel,                     /* Level to select (relative level) */\n  sqlite3_stmt **ppStmt           /* OUT: Compiled statement */\n){\n  int rc;\n  sqlite3_stmt *pStmt = 0;\n\n  assert( iLevel==FTS3_SEGCURSOR_ALL || iLevel>=0 );\n  assert( iLevel<FTS3_SEGDIR_MAXLEVEL );\n  assert( iIndex>=0 && iIndex<p->nIndex );\n\n  if( iLevel<0 ){\n    /* \"SELECT * FROM %_segdir WHERE level BETWEEN ? AND ? ORDER BY ...\" */\n    rc = fts3SqlStmt(p, SQL_SELECT_LEVEL_RANGE, &pStmt, 0);\n    if( rc==SQLITE_OK ){ \n      sqlite3_bind_int64(pStmt, 1, getAbsoluteLevel(p, iLangid, iIndex, 0));\n      sqlite3_bind_int64(pStmt, 2, \n          getAbsoluteLevel(p, iLangid, iIndex, FTS3_SEGDIR_MAXLEVEL-1)\n      );\n    }\n  }else{\n    /* \"SELECT * FROM %_segdir WHERE level = ? ORDER BY ...\" */\n    rc = fts3SqlStmt(p, SQL_SELECT_LEVEL, &pStmt, 0);\n    if( rc==SQLITE_OK ){ \n      sqlite3_bind_int64(pStmt, 1, getAbsoluteLevel(p, iLangid, iIndex,iLevel));\n    }\n  }\n  *ppStmt = pStmt;\n  return rc;\n}\n\n\n/*\n** Append a single varint to a PendingList buffer. SQLITE_OK is returned\n** if successful, or an SQLite error code otherwise.\n**\n** This function also serves to allocate the PendingList structure itself.\n** For example, to create a new PendingList structure containing two\n** varints:\n**\n**   PendingList *p = 0;\n**   fts3PendingListAppendVarint(&p, 1);\n**   fts3PendingListAppendVarint(&p, 2);\n*/\nstatic int fts3PendingListAppendVarint(\n  PendingList **pp,               /* IN/OUT: Pointer to PendingList struct */\n  sqlite3_int64 i                 /* Value to append to data */\n){\n  PendingList *p = *pp;\n\n  /* Allocate or grow the PendingList as required. */\n  if( !p ){\n    p = sqlite3_malloc(sizeof(*p) + 100);\n    if( !p ){\n      return SQLITE_NOMEM;\n    }\n    p->nSpace = 100;\n    p->aData = (char *)&p[1];\n    p->nData = 0;\n  }\n  else if( p->nData+FTS3_VARINT_MAX+1>p->nSpace ){\n    int nNew = p->nSpace * 2;\n    p = sqlite3_realloc(p, sizeof(*p) + nNew);\n    if( !p ){\n      sqlite3_free(*pp);\n      *pp = 0;\n      return SQLITE_NOMEM;\n    }\n    p->nSpace = nNew;\n    p->aData = (char *)&p[1];\n  }\n\n  /* Append the new serialized varint to the end of the list. */\n  p->nData += sqlite3Fts3PutVarint(&p->aData[p->nData], i);\n  p->aData[p->nData] = '\\0';\n  *pp = p;\n  return SQLITE_OK;\n}\n\n/*\n** Add a docid/column/position entry to a PendingList structure. Non-zero\n** is returned if the structure is sqlite3_realloced as part of adding\n** the entry. Otherwise, zero.\n**\n** If an OOM error occurs, *pRc is set to SQLITE_NOMEM before returning.\n** Zero is always returned in this case. Otherwise, if no OOM error occurs,\n** it is set to SQLITE_OK.\n*/\nstatic int fts3PendingListAppend(\n  PendingList **pp,               /* IN/OUT: PendingList structure */\n  sqlite3_int64 iDocid,           /* Docid for entry to add */\n  sqlite3_int64 iCol,             /* Column for entry to add */\n  sqlite3_int64 iPos,             /* Position of term for entry to add */\n  int *pRc                        /* OUT: Return code */\n){\n  PendingList *p = *pp;\n  int rc = SQLITE_OK;\n\n  assert( !p || p->iLastDocid<=iDocid );\n\n  if( !p || p->iLastDocid!=iDocid ){\n    sqlite3_int64 iDelta = iDocid - (p ? p->iLastDocid : 0);\n    if( p ){\n      assert( p->nData<p->nSpace );\n      assert( p->aData[p->nData]==0 );\n      p->nData++;\n    }\n    if( SQLITE_OK!=(rc = fts3PendingListAppendVarint(&p, iDelta)) ){\n      goto pendinglistappend_out;\n    }\n    p->iLastCol = -1;\n    p->iLastPos = 0;\n    p->iLastDocid = iDocid;\n  }\n  if( iCol>0 && p->iLastCol!=iCol ){\n    if( SQLITE_OK!=(rc = fts3PendingListAppendVarint(&p, 1))\n     || SQLITE_OK!=(rc = fts3PendingListAppendVarint(&p, iCol))\n    ){\n      goto pendinglistappend_out;\n    }\n    p->iLastCol = iCol;\n    p->iLastPos = 0;\n  }\n  if( iCol>=0 ){\n    assert( iPos>p->iLastPos || (iPos==0 && p->iLastPos==0) );\n    rc = fts3PendingListAppendVarint(&p, 2+iPos-p->iLastPos);\n    if( rc==SQLITE_OK ){\n      p->iLastPos = iPos;\n    }\n  }\n\n pendinglistappend_out:\n  *pRc = rc;\n  if( p!=*pp ){\n    *pp = p;\n    return 1;\n  }\n  return 0;\n}\n\n/*\n** Free a PendingList object allocated by fts3PendingListAppend().\n*/\nstatic void fts3PendingListDelete(PendingList *pList){\n  sqlite3_free(pList);\n}\n\n/*\n** Add an entry to one of the pending-terms hash tables.\n*/\nstatic int fts3PendingTermsAddOne(\n  Fts3Table *p,\n  int iCol,\n  int iPos,\n  Fts3Hash *pHash,                /* Pending terms hash table to add entry to */\n  const char *zToken,\n  int nToken\n){\n  PendingList *pList;\n  int rc = SQLITE_OK;\n\n  pList = (PendingList *)fts3HashFind(pHash, zToken, nToken);\n  if( pList ){\n    p->nPendingData -= (pList->nData + nToken + sizeof(Fts3HashElem));\n  }\n  if( fts3PendingListAppend(&pList, p->iPrevDocid, iCol, iPos, &rc) ){\n    if( pList==fts3HashInsert(pHash, zToken, nToken, pList) ){\n      /* Malloc failed while inserting the new entry. This can only \n      ** happen if there was no previous entry for this token.\n      */\n      assert( 0==fts3HashFind(pHash, zToken, nToken) );\n      sqlite3_free(pList);\n      rc = SQLITE_NOMEM;\n    }\n  }\n  if( rc==SQLITE_OK ){\n    p->nPendingData += (pList->nData + nToken + sizeof(Fts3HashElem));\n  }\n  return rc;\n}\n\n/*\n** Tokenize the nul-terminated string zText and add all tokens to the\n** pending-terms hash-table. The docid used is that currently stored in\n** p->iPrevDocid, and the column is specified by argument iCol.\n**\n** If successful, SQLITE_OK is returned. Otherwise, an SQLite error code.\n*/\nstatic int fts3PendingTermsAdd(\n  Fts3Table *p,                   /* Table into which text will be inserted */\n  int iLangid,                    /* Language id to use */\n  const char *zText,              /* Text of document to be inserted */\n  int iCol,                       /* Column into which text is being inserted */\n  u32 *pnWord                     /* IN/OUT: Incr. by number tokens inserted */\n){\n  int rc;\n  int iStart = 0;\n  int iEnd = 0;\n  int iPos = 0;\n  int nWord = 0;\n\n  char const *zToken;\n  int nToken = 0;\n\n  sqlite3_tokenizer *pTokenizer = p->pTokenizer;\n  sqlite3_tokenizer_module const *pModule = pTokenizer->pModule;\n  sqlite3_tokenizer_cursor *pCsr;\n  int (*xNext)(sqlite3_tokenizer_cursor *pCursor,\n      const char**,int*,int*,int*,int*);\n\n  assert( pTokenizer && pModule );\n\n  /* If the user has inserted a NULL value, this function may be called with\n  ** zText==0. In this case, add zero token entries to the hash table and \n  ** return early. */\n  if( zText==0 ){\n    *pnWord = 0;\n    return SQLITE_OK;\n  }\n\n  rc = sqlite3Fts3OpenTokenizer(pTokenizer, iLangid, zText, -1, &pCsr);\n  if( rc!=SQLITE_OK ){\n    return rc;\n  }\n\n  xNext = pModule->xNext;\n  while( SQLITE_OK==rc\n      && SQLITE_OK==(rc = xNext(pCsr, &zToken, &nToken, &iStart, &iEnd, &iPos))\n  ){\n    int i;\n    if( iPos>=nWord ) nWord = iPos+1;\n\n    /* Positions cannot be negative; we use -1 as a terminator internally.\n    ** Tokens must have a non-zero length.\n    */\n    if( iPos<0 || !zToken || nToken<=0 ){\n      rc = SQLITE_ERROR;\n      break;\n    }\n\n    /* Add the term to the terms index */\n    rc = fts3PendingTermsAddOne(\n        p, iCol, iPos, &p->aIndex[0].hPending, zToken, nToken\n    );\n    \n    /* Add the term to each of the prefix indexes that it is not too \n    ** short for. */\n    for(i=1; rc==SQLITE_OK && i<p->nIndex; i++){\n      struct Fts3Index *pIndex = &p->aIndex[i];\n      if( nToken<pIndex->nPrefix ) continue;\n      rc = fts3PendingTermsAddOne(\n          p, iCol, iPos, &pIndex->hPending, zToken, pIndex->nPrefix\n      );\n    }\n  }\n\n  pModule->xClose(pCsr);\n  *pnWord += nWord;\n  return (rc==SQLITE_DONE ? SQLITE_OK : rc);\n}\n\n/* \n** Calling this function indicates that subsequent calls to \n** fts3PendingTermsAdd() are to add term/position-list pairs for the\n** contents of the document with docid iDocid.\n*/\nstatic int fts3PendingTermsDocid(\n  Fts3Table *p,                   /* Full-text table handle */\n  int bDelete,                    /* True if this op is a delete */\n  int iLangid,                    /* Language id of row being written */\n  sqlite_int64 iDocid             /* Docid of row being written */\n){\n  assert( iLangid>=0 );\n  assert( bDelete==1 || bDelete==0 );\n\n  /* TODO(shess) Explore whether partially flushing the buffer on\n  ** forced-flush would provide better performance.  I suspect that if\n  ** we ordered the doclists by size and flushed the largest until the\n  ** buffer was half empty, that would let the less frequent terms\n  ** generate longer doclists.\n  */\n  if( iDocid<p->iPrevDocid \n   || (iDocid==p->iPrevDocid && p->bPrevDelete==0)\n   || p->iPrevLangid!=iLangid\n   || p->nPendingData>p->nMaxPendingData \n  ){\n    int rc = sqlite3Fts3PendingTermsFlush(p);\n    if( rc!=SQLITE_OK ) return rc;\n  }\n  p->iPrevDocid = iDocid;\n  p->iPrevLangid = iLangid;\n  p->bPrevDelete = bDelete;\n  return SQLITE_OK;\n}\n\n/*\n** Discard the contents of the pending-terms hash tables. \n*/\nSQLITE_PRIVATE void sqlite3Fts3PendingTermsClear(Fts3Table *p){\n  int i;\n  for(i=0; i<p->nIndex; i++){\n    Fts3HashElem *pElem;\n    Fts3Hash *pHash = &p->aIndex[i].hPending;\n    for(pElem=fts3HashFirst(pHash); pElem; pElem=fts3HashNext(pElem)){\n      PendingList *pList = (PendingList *)fts3HashData(pElem);\n      fts3PendingListDelete(pList);\n    }\n    fts3HashClear(pHash);\n  }\n  p->nPendingData = 0;\n}\n\n/*\n** This function is called by the xUpdate() method as part of an INSERT\n** operation. It adds entries for each term in the new record to the\n** pendingTerms hash table.\n**\n** Argument apVal is the same as the similarly named argument passed to\n** fts3InsertData(). Parameter iDocid is the docid of the new row.\n*/\nstatic int fts3InsertTerms(\n  Fts3Table *p, \n  int iLangid, \n  sqlite3_value **apVal, \n  u32 *aSz\n){\n  int i;                          /* Iterator variable */\n  for(i=2; i<p->nColumn+2; i++){\n    int iCol = i-2;\n    if( p->abNotindexed[iCol]==0 ){\n      const char *zText = (const char *)sqlite3_value_text(apVal[i]);\n      int rc = fts3PendingTermsAdd(p, iLangid, zText, iCol, &aSz[iCol]);\n      if( rc!=SQLITE_OK ){\n        return rc;\n      }\n      aSz[p->nColumn] += sqlite3_value_bytes(apVal[i]);\n    }\n  }\n  return SQLITE_OK;\n}\n\n/*\n** This function is called by the xUpdate() method for an INSERT operation.\n** The apVal parameter is passed a copy of the apVal argument passed by\n** SQLite to the xUpdate() method. i.e:\n**\n**   apVal[0]                Not used for INSERT.\n**   apVal[1]                rowid\n**   apVal[2]                Left-most user-defined column\n**   ...\n**   apVal[p->nColumn+1]     Right-most user-defined column\n**   apVal[p->nColumn+2]     Hidden column with same name as table\n**   apVal[p->nColumn+3]     Hidden \"docid\" column (alias for rowid)\n**   apVal[p->nColumn+4]     Hidden languageid column\n*/\nstatic int fts3InsertData(\n  Fts3Table *p,                   /* Full-text table */\n  sqlite3_value **apVal,          /* Array of values to insert */\n  sqlite3_int64 *piDocid          /* OUT: Docid for row just inserted */\n){\n  int rc;                         /* Return code */\n  sqlite3_stmt *pContentInsert;   /* INSERT INTO %_content VALUES(...) */\n\n  if( p->zContentTbl ){\n    sqlite3_value *pRowid = apVal[p->nColumn+3];\n    if( sqlite3_value_type(pRowid)==SQLITE_NULL ){\n      pRowid = apVal[1];\n    }\n    if( sqlite3_value_type(pRowid)!=SQLITE_INTEGER ){\n      return SQLITE_CONSTRAINT;\n    }\n    *piDocid = sqlite3_value_int64(pRowid);\n    return SQLITE_OK;\n  }\n\n  /* Locate the statement handle used to insert data into the %_content\n  ** table. The SQL for this statement is:\n  **\n  **   INSERT INTO %_content VALUES(?, ?, ?, ...)\n  **\n  ** The statement features N '?' variables, where N is the number of user\n  ** defined columns in the FTS3 table, plus one for the docid field.\n  */\n  rc = fts3SqlStmt(p, SQL_CONTENT_INSERT, &pContentInsert, &apVal[1]);\n  if( rc==SQLITE_OK && p->zLanguageid ){\n    rc = sqlite3_bind_int(\n        pContentInsert, p->nColumn+2, \n        sqlite3_value_int(apVal[p->nColumn+4])\n    );\n  }\n  if( rc!=SQLITE_OK ) return rc;\n\n  /* There is a quirk here. The users INSERT statement may have specified\n  ** a value for the \"rowid\" field, for the \"docid\" field, or for both.\n  ** Which is a problem, since \"rowid\" and \"docid\" are aliases for the\n  ** same value. For example:\n  **\n  **   INSERT INTO fts3tbl(rowid, docid) VALUES(1, 2);\n  **\n  ** In FTS3, this is an error. It is an error to specify non-NULL values\n  ** for both docid and some other rowid alias.\n  */\n  if( SQLITE_NULL!=sqlite3_value_type(apVal[3+p->nColumn]) ){\n    if( SQLITE_NULL==sqlite3_value_type(apVal[0])\n     && SQLITE_NULL!=sqlite3_value_type(apVal[1])\n    ){\n      /* A rowid/docid conflict. */\n      return SQLITE_ERROR;\n    }\n    rc = sqlite3_bind_value(pContentInsert, 1, apVal[3+p->nColumn]);\n    if( rc!=SQLITE_OK ) return rc;\n  }\n\n  /* Execute the statement to insert the record. Set *piDocid to the \n  ** new docid value. \n  */\n  sqlite3_step(pContentInsert);\n  rc = sqlite3_reset(pContentInsert);\n\n  *piDocid = sqlite3_last_insert_rowid(p->db);\n  return rc;\n}\n\n\n\n/*\n** Remove all data from the FTS3 table. Clear the hash table containing\n** pending terms.\n*/\nstatic int fts3DeleteAll(Fts3Table *p, int bContent){\n  int rc = SQLITE_OK;             /* Return code */\n\n  /* Discard the contents of the pending-terms hash table. */\n  sqlite3Fts3PendingTermsClear(p);\n\n  /* Delete everything from the shadow tables. Except, leave %_content as\n  ** is if bContent is false.  */\n  assert( p->zContentTbl==0 || bContent==0 );\n  if( bContent ) fts3SqlExec(&rc, p, SQL_DELETE_ALL_CONTENT, 0);\n  fts3SqlExec(&rc, p, SQL_DELETE_ALL_SEGMENTS, 0);\n  fts3SqlExec(&rc, p, SQL_DELETE_ALL_SEGDIR, 0);\n  if( p->bHasDocsize ){\n    fts3SqlExec(&rc, p, SQL_DELETE_ALL_DOCSIZE, 0);\n  }\n  if( p->bHasStat ){\n    fts3SqlExec(&rc, p, SQL_DELETE_ALL_STAT, 0);\n  }\n  return rc;\n}\n\n/*\n**\n*/\nstatic int langidFromSelect(Fts3Table *p, sqlite3_stmt *pSelect){\n  int iLangid = 0;\n  if( p->zLanguageid ) iLangid = sqlite3_column_int(pSelect, p->nColumn+1);\n  return iLangid;\n}\n\n/*\n** The first element in the apVal[] array is assumed to contain the docid\n** (an integer) of a row about to be deleted. Remove all terms from the\n** full-text index.\n*/\nstatic void fts3DeleteTerms( \n  int *pRC,               /* Result code */\n  Fts3Table *p,           /* The FTS table to delete from */\n  sqlite3_value *pRowid,  /* The docid to be deleted */\n  u32 *aSz,               /* Sizes of deleted document written here */\n  int *pbFound            /* OUT: Set to true if row really does exist */\n){\n  int rc;\n  sqlite3_stmt *pSelect;\n\n  assert( *pbFound==0 );\n  if( *pRC ) return;\n  rc = fts3SqlStmt(p, SQL_SELECT_CONTENT_BY_ROWID, &pSelect, &pRowid);\n  if( rc==SQLITE_OK ){\n    if( SQLITE_ROW==sqlite3_step(pSelect) ){\n      int i;\n      int iLangid = langidFromSelect(p, pSelect);\n      i64 iDocid = sqlite3_column_int64(pSelect, 0);\n      rc = fts3PendingTermsDocid(p, 1, iLangid, iDocid);\n      for(i=1; rc==SQLITE_OK && i<=p->nColumn; i++){\n        int iCol = i-1;\n        if( p->abNotindexed[iCol]==0 ){\n          const char *zText = (const char *)sqlite3_column_text(pSelect, i);\n          rc = fts3PendingTermsAdd(p, iLangid, zText, -1, &aSz[iCol]);\n          aSz[p->nColumn] += sqlite3_column_bytes(pSelect, i);\n        }\n      }\n      if( rc!=SQLITE_OK ){\n        sqlite3_reset(pSelect);\n        *pRC = rc;\n        return;\n      }\n      *pbFound = 1;\n    }\n    rc = sqlite3_reset(pSelect);\n  }else{\n    sqlite3_reset(pSelect);\n  }\n  *pRC = rc;\n}\n\n/*\n** Forward declaration to account for the circular dependency between\n** functions fts3SegmentMerge() and fts3AllocateSegdirIdx().\n*/\nstatic int fts3SegmentMerge(Fts3Table *, int, int, int);\n\n/* \n** This function allocates a new level iLevel index in the segdir table.\n** Usually, indexes are allocated within a level sequentially starting\n** with 0, so the allocated index is one greater than the value returned\n** by:\n**\n**   SELECT max(idx) FROM %_segdir WHERE level = :iLevel\n**\n** However, if there are already FTS3_MERGE_COUNT indexes at the requested\n** level, they are merged into a single level (iLevel+1) segment and the \n** allocated index is 0.\n**\n** If successful, *piIdx is set to the allocated index slot and SQLITE_OK\n** returned. Otherwise, an SQLite error code is returned.\n*/\nstatic int fts3AllocateSegdirIdx(\n  Fts3Table *p, \n  int iLangid,                    /* Language id */\n  int iIndex,                     /* Index for p->aIndex */\n  int iLevel, \n  int *piIdx\n){\n  int rc;                         /* Return Code */\n  sqlite3_stmt *pNextIdx;         /* Query for next idx at level iLevel */\n  int iNext = 0;                  /* Result of query pNextIdx */\n\n  assert( iLangid>=0 );\n  assert( p->nIndex>=1 );\n\n  /* Set variable iNext to the next available segdir index at level iLevel. */\n  rc = fts3SqlStmt(p, SQL_NEXT_SEGMENT_INDEX, &pNextIdx, 0);\n  if( rc==SQLITE_OK ){\n    sqlite3_bind_int64(\n        pNextIdx, 1, getAbsoluteLevel(p, iLangid, iIndex, iLevel)\n    );\n    if( SQLITE_ROW==sqlite3_step(pNextIdx) ){\n      iNext = sqlite3_column_int(pNextIdx, 0);\n    }\n    rc = sqlite3_reset(pNextIdx);\n  }\n\n  if( rc==SQLITE_OK ){\n    /* If iNext is FTS3_MERGE_COUNT, indicating that level iLevel is already\n    ** full, merge all segments in level iLevel into a single iLevel+1\n    ** segment and allocate (newly freed) index 0 at level iLevel. Otherwise,\n    ** if iNext is less than FTS3_MERGE_COUNT, allocate index iNext.\n    */\n    if( iNext>=FTS3_MERGE_COUNT ){\n      fts3LogMerge(16, getAbsoluteLevel(p, iLangid, iIndex, iLevel));\n      rc = fts3SegmentMerge(p, iLangid, iIndex, iLevel);\n      *piIdx = 0;\n    }else{\n      *piIdx = iNext;\n    }\n  }\n\n  return rc;\n}\n\n/*\n** The %_segments table is declared as follows:\n**\n**   CREATE TABLE %_segments(blockid INTEGER PRIMARY KEY, block BLOB)\n**\n** This function reads data from a single row of the %_segments table. The\n** specific row is identified by the iBlockid parameter. If paBlob is not\n** NULL, then a buffer is allocated using sqlite3_malloc() and populated\n** with the contents of the blob stored in the \"block\" column of the \n** identified table row is. Whether or not paBlob is NULL, *pnBlob is set\n** to the size of the blob in bytes before returning.\n**\n** If an error occurs, or the table does not contain the specified row,\n** an SQLite error code is returned. Otherwise, SQLITE_OK is returned. If\n** paBlob is non-NULL, then it is the responsibility of the caller to\n** eventually free the returned buffer.\n**\n** This function may leave an open sqlite3_blob* handle in the\n** Fts3Table.pSegments variable. This handle is reused by subsequent calls\n** to this function. The handle may be closed by calling the\n** sqlite3Fts3SegmentsClose() function. Reusing a blob handle is a handy\n** performance improvement, but the blob handle should always be closed\n** before control is returned to the user (to prevent a lock being held\n** on the database file for longer than necessary). Thus, any virtual table\n** method (xFilter etc.) that may directly or indirectly call this function\n** must call sqlite3Fts3SegmentsClose() before returning.\n*/\nSQLITE_PRIVATE int sqlite3Fts3ReadBlock(\n  Fts3Table *p,                   /* FTS3 table handle */\n  sqlite3_int64 iBlockid,         /* Access the row with blockid=$iBlockid */\n  char **paBlob,                  /* OUT: Blob data in malloc'd buffer */\n  int *pnBlob,                    /* OUT: Size of blob data */\n  int *pnLoad                     /* OUT: Bytes actually loaded */\n){\n  int rc;                         /* Return code */\n\n  /* pnBlob must be non-NULL. paBlob may be NULL or non-NULL. */\n  assert( pnBlob );\n\n  if( p->pSegments ){\n    rc = sqlite3_blob_reopen(p->pSegments, iBlockid);\n  }else{\n    if( 0==p->zSegmentsTbl ){\n      p->zSegmentsTbl = sqlite3_mprintf(\"%s_segments\", p->zName);\n      if( 0==p->zSegmentsTbl ) return SQLITE_NOMEM;\n    }\n    rc = sqlite3_blob_open(\n       p->db, p->zDb, p->zSegmentsTbl, \"block\", iBlockid, 0, &p->pSegments\n    );\n  }\n\n  if( rc==SQLITE_OK ){\n    int nByte = sqlite3_blob_bytes(p->pSegments);\n    *pnBlob = nByte;\n    if( paBlob ){\n      char *aByte = sqlite3_malloc(nByte + FTS3_NODE_PADDING);\n      if( !aByte ){\n        rc = SQLITE_NOMEM;\n      }else{\n        if( pnLoad && nByte>(FTS3_NODE_CHUNK_THRESHOLD) ){\n          nByte = FTS3_NODE_CHUNKSIZE;\n          *pnLoad = nByte;\n        }\n        rc = sqlite3_blob_read(p->pSegments, aByte, nByte, 0);\n        memset(&aByte[nByte], 0, FTS3_NODE_PADDING);\n        if( rc!=SQLITE_OK ){\n          sqlite3_free(aByte);\n          aByte = 0;\n        }\n      }\n      *paBlob = aByte;\n    }\n  }\n\n  return rc;\n}\n\n/*\n** Close the blob handle at p->pSegments, if it is open. See comments above\n** the sqlite3Fts3ReadBlock() function for details.\n*/\nSQLITE_PRIVATE void sqlite3Fts3SegmentsClose(Fts3Table *p){\n  sqlite3_blob_close(p->pSegments);\n  p->pSegments = 0;\n}\n    \nstatic int fts3SegReaderIncrRead(Fts3SegReader *pReader){\n  int nRead;                      /* Number of bytes to read */\n  int rc;                         /* Return code */\n\n  nRead = MIN(pReader->nNode - pReader->nPopulate, FTS3_NODE_CHUNKSIZE);\n  rc = sqlite3_blob_read(\n      pReader->pBlob, \n      &pReader->aNode[pReader->nPopulate],\n      nRead,\n      pReader->nPopulate\n  );\n\n  if( rc==SQLITE_OK ){\n    pReader->nPopulate += nRead;\n    memset(&pReader->aNode[pReader->nPopulate], 0, FTS3_NODE_PADDING);\n    if( pReader->nPopulate==pReader->nNode ){\n      sqlite3_blob_close(pReader->pBlob);\n      pReader->pBlob = 0;\n      pReader->nPopulate = 0;\n    }\n  }\n  return rc;\n}\n\nstatic int fts3SegReaderRequire(Fts3SegReader *pReader, char *pFrom, int nByte){\n  int rc = SQLITE_OK;\n  assert( !pReader->pBlob \n       || (pFrom>=pReader->aNode && pFrom<&pReader->aNode[pReader->nNode])\n  );\n  while( pReader->pBlob && rc==SQLITE_OK \n     &&  (pFrom - pReader->aNode + nByte)>pReader->nPopulate\n  ){\n    rc = fts3SegReaderIncrRead(pReader);\n  }\n  return rc;\n}\n\n/*\n** Set an Fts3SegReader cursor to point at EOF.\n*/\nstatic void fts3SegReaderSetEof(Fts3SegReader *pSeg){\n  if( !fts3SegReaderIsRootOnly(pSeg) ){\n    sqlite3_free(pSeg->aNode);\n    sqlite3_blob_close(pSeg->pBlob);\n    pSeg->pBlob = 0;\n  }\n  pSeg->aNode = 0;\n}\n\n/*\n** Move the iterator passed as the first argument to the next term in the\n** segment. If successful, SQLITE_OK is returned. If there is no next term,\n** SQLITE_DONE. Otherwise, an SQLite error code.\n*/\nstatic int fts3SegReaderNext(\n  Fts3Table *p, \n  Fts3SegReader *pReader,\n  int bIncr\n){\n  int rc;                         /* Return code of various sub-routines */\n  char *pNext;                    /* Cursor variable */\n  int nPrefix;                    /* Number of bytes in term prefix */\n  int nSuffix;                    /* Number of bytes in term suffix */\n\n  if( !pReader->aDoclist ){\n    pNext = pReader->aNode;\n  }else{\n    pNext = &pReader->aDoclist[pReader->nDoclist];\n  }\n\n  if( !pNext || pNext>=&pReader->aNode[pReader->nNode] ){\n\n    if( fts3SegReaderIsPending(pReader) ){\n      Fts3HashElem *pElem = *(pReader->ppNextElem);\n      sqlite3_free(pReader->aNode);\n      pReader->aNode = 0;\n      if( pElem ){\n        char *aCopy;\n        PendingList *pList = (PendingList *)fts3HashData(pElem);\n        int nCopy = pList->nData+1;\n        pReader->zTerm = (char *)fts3HashKey(pElem);\n        pReader->nTerm = fts3HashKeysize(pElem);\n        aCopy = (char*)sqlite3_malloc(nCopy);\n        if( !aCopy ) return SQLITE_NOMEM;\n        memcpy(aCopy, pList->aData, nCopy);\n        pReader->nNode = pReader->nDoclist = nCopy;\n        pReader->aNode = pReader->aDoclist = aCopy;\n        pReader->ppNextElem++;\n        assert( pReader->aNode );\n      }\n      return SQLITE_OK;\n    }\n\n    fts3SegReaderSetEof(pReader);\n\n    /* If iCurrentBlock>=iLeafEndBlock, this is an EOF condition. All leaf \n    ** blocks have already been traversed.  */\n    assert( pReader->iCurrentBlock<=pReader->iLeafEndBlock );\n    if( pReader->iCurrentBlock>=pReader->iLeafEndBlock ){\n      return SQLITE_OK;\n    }\n\n    rc = sqlite3Fts3ReadBlock(\n        p, ++pReader->iCurrentBlock, &pReader->aNode, &pReader->nNode, \n        (bIncr ? &pReader->nPopulate : 0)\n    );\n    if( rc!=SQLITE_OK ) return rc;\n    assert( pReader->pBlob==0 );\n    if( bIncr && pReader->nPopulate<pReader->nNode ){\n      pReader->pBlob = p->pSegments;\n      p->pSegments = 0;\n    }\n    pNext = pReader->aNode;\n  }\n\n  assert( !fts3SegReaderIsPending(pReader) );\n\n  rc = fts3SegReaderRequire(pReader, pNext, FTS3_VARINT_MAX*2);\n  if( rc!=SQLITE_OK ) return rc;\n  \n  /* Because of the FTS3_NODE_PADDING bytes of padding, the following is \n  ** safe (no risk of overread) even if the node data is corrupted. */\n  pNext += fts3GetVarint32(pNext, &nPrefix);\n  pNext += fts3GetVarint32(pNext, &nSuffix);\n  if( nPrefix<0 || nSuffix<=0 \n   || &pNext[nSuffix]>&pReader->aNode[pReader->nNode] \n  ){\n    return FTS_CORRUPT_VTAB;\n  }\n\n  if( nPrefix+nSuffix>pReader->nTermAlloc ){\n    int nNew = (nPrefix+nSuffix)*2;\n    char *zNew = sqlite3_realloc(pReader->zTerm, nNew);\n    if( !zNew ){\n      return SQLITE_NOMEM;\n    }\n    pReader->zTerm = zNew;\n    pReader->nTermAlloc = nNew;\n  }\n\n  rc = fts3SegReaderRequire(pReader, pNext, nSuffix+FTS3_VARINT_MAX);\n  if( rc!=SQLITE_OK ) return rc;\n\n  memcpy(&pReader->zTerm[nPrefix], pNext, nSuffix);\n  pReader->nTerm = nPrefix+nSuffix;\n  pNext += nSuffix;\n  pNext += fts3GetVarint32(pNext, &pReader->nDoclist);\n  pReader->aDoclist = pNext;\n  pReader->pOffsetList = 0;\n\n  /* Check that the doclist does not appear to extend past the end of the\n  ** b-tree node. And that the final byte of the doclist is 0x00. If either \n  ** of these statements is untrue, then the data structure is corrupt.\n  */\n  if( &pReader->aDoclist[pReader->nDoclist]>&pReader->aNode[pReader->nNode] \n   || (pReader->nPopulate==0 && pReader->aDoclist[pReader->nDoclist-1])\n  ){\n    return FTS_CORRUPT_VTAB;\n  }\n  return SQLITE_OK;\n}\n\n/*\n** Set the SegReader to point to the first docid in the doclist associated\n** with the current term.\n*/\nstatic int fts3SegReaderFirstDocid(Fts3Table *pTab, Fts3SegReader *pReader){\n  int rc = SQLITE_OK;\n  assert( pReader->aDoclist );\n  assert( !pReader->pOffsetList );\n  if( pTab->bDescIdx && fts3SegReaderIsPending(pReader) ){\n    u8 bEof = 0;\n    pReader->iDocid = 0;\n    pReader->nOffsetList = 0;\n    sqlite3Fts3DoclistPrev(0,\n        pReader->aDoclist, pReader->nDoclist, &pReader->pOffsetList, \n        &pReader->iDocid, &pReader->nOffsetList, &bEof\n    );\n  }else{\n    rc = fts3SegReaderRequire(pReader, pReader->aDoclist, FTS3_VARINT_MAX);\n    if( rc==SQLITE_OK ){\n      int n = sqlite3Fts3GetVarint(pReader->aDoclist, &pReader->iDocid);\n      pReader->pOffsetList = &pReader->aDoclist[n];\n    }\n  }\n  return rc;\n}\n\n/*\n** Advance the SegReader to point to the next docid in the doclist\n** associated with the current term.\n** \n** If arguments ppOffsetList and pnOffsetList are not NULL, then \n** *ppOffsetList is set to point to the first column-offset list\n** in the doclist entry (i.e. immediately past the docid varint).\n** *pnOffsetList is set to the length of the set of column-offset\n** lists, not including the nul-terminator byte. For example:\n*/\nstatic int fts3SegReaderNextDocid(\n  Fts3Table *pTab,\n  Fts3SegReader *pReader,         /* Reader to advance to next docid */\n  char **ppOffsetList,            /* OUT: Pointer to current position-list */\n  int *pnOffsetList               /* OUT: Length of *ppOffsetList in bytes */\n){\n  int rc = SQLITE_OK;\n  char *p = pReader->pOffsetList;\n  char c = 0;\n\n  assert( p );\n\n  if( pTab->bDescIdx && fts3SegReaderIsPending(pReader) ){\n    /* A pending-terms seg-reader for an FTS4 table that uses order=desc.\n    ** Pending-terms doclists are always built up in ascending order, so\n    ** we have to iterate through them backwards here. */\n    u8 bEof = 0;\n    if( ppOffsetList ){\n      *ppOffsetList = pReader->pOffsetList;\n      *pnOffsetList = pReader->nOffsetList - 1;\n    }\n    sqlite3Fts3DoclistPrev(0,\n        pReader->aDoclist, pReader->nDoclist, &p, &pReader->iDocid,\n        &pReader->nOffsetList, &bEof\n    );\n    if( bEof ){\n      pReader->pOffsetList = 0;\n    }else{\n      pReader->pOffsetList = p;\n    }\n  }else{\n    char *pEnd = &pReader->aDoclist[pReader->nDoclist];\n\n    /* Pointer p currently points at the first byte of an offset list. The\n    ** following block advances it to point one byte past the end of\n    ** the same offset list. */\n    while( 1 ){\n  \n      /* The following line of code (and the \"p++\" below the while() loop) is\n      ** normally all that is required to move pointer p to the desired \n      ** position. The exception is if this node is being loaded from disk\n      ** incrementally and pointer \"p\" now points to the first byte past\n      ** the populated part of pReader->aNode[].\n      */\n      while( *p | c ) c = *p++ & 0x80;\n      assert( *p==0 );\n  \n      if( pReader->pBlob==0 || p<&pReader->aNode[pReader->nPopulate] ) break;\n      rc = fts3SegReaderIncrRead(pReader);\n      if( rc!=SQLITE_OK ) return rc;\n    }\n    p++;\n  \n    /* If required, populate the output variables with a pointer to and the\n    ** size of the previous offset-list.\n    */\n    if( ppOffsetList ){\n      *ppOffsetList = pReader->pOffsetList;\n      *pnOffsetList = (int)(p - pReader->pOffsetList - 1);\n    }\n\n    /* List may have been edited in place by fts3EvalNearTrim() */\n    while( p<pEnd && *p==0 ) p++;\n  \n    /* If there are no more entries in the doclist, set pOffsetList to\n    ** NULL. Otherwise, set Fts3SegReader.iDocid to the next docid and\n    ** Fts3SegReader.pOffsetList to point to the next offset list before\n    ** returning.\n    */\n    if( p>=pEnd ){\n      pReader->pOffsetList = 0;\n    }else{\n      rc = fts3SegReaderRequire(pReader, p, FTS3_VARINT_MAX);\n      if( rc==SQLITE_OK ){\n        sqlite3_int64 iDelta;\n        pReader->pOffsetList = p + sqlite3Fts3GetVarint(p, &iDelta);\n        if( pTab->bDescIdx ){\n          pReader->iDocid -= iDelta;\n        }else{\n          pReader->iDocid += iDelta;\n        }\n      }\n    }\n  }\n\n  return SQLITE_OK;\n}\n\n\nSQLITE_PRIVATE int sqlite3Fts3MsrOvfl(\n  Fts3Cursor *pCsr, \n  Fts3MultiSegReader *pMsr,\n  int *pnOvfl\n){\n  Fts3Table *p = (Fts3Table*)pCsr->base.pVtab;\n  int nOvfl = 0;\n  int ii;\n  int rc = SQLITE_OK;\n  int pgsz = p->nPgsz;\n\n  assert( p->bFts4 );\n  assert( pgsz>0 );\n\n  for(ii=0; rc==SQLITE_OK && ii<pMsr->nSegment; ii++){\n    Fts3SegReader *pReader = pMsr->apSegment[ii];\n    if( !fts3SegReaderIsPending(pReader) \n     && !fts3SegReaderIsRootOnly(pReader) \n    ){\n      sqlite3_int64 jj;\n      for(jj=pReader->iStartBlock; jj<=pReader->iLeafEndBlock; jj++){\n        int nBlob;\n        rc = sqlite3Fts3ReadBlock(p, jj, 0, &nBlob, 0);\n        if( rc!=SQLITE_OK ) break;\n        if( (nBlob+35)>pgsz ){\n          nOvfl += (nBlob + 34)/pgsz;\n        }\n      }\n    }\n  }\n  *pnOvfl = nOvfl;\n  return rc;\n}\n\n/*\n** Free all allocations associated with the iterator passed as the \n** second argument.\n*/\nSQLITE_PRIVATE void sqlite3Fts3SegReaderFree(Fts3SegReader *pReader){\n  if( pReader ){\n    if( !fts3SegReaderIsPending(pReader) ){\n      sqlite3_free(pReader->zTerm);\n    }\n    if( !fts3SegReaderIsRootOnly(pReader) ){\n      sqlite3_free(pReader->aNode);\n    }\n    sqlite3_blob_close(pReader->pBlob);\n  }\n  sqlite3_free(pReader);\n}\n\n/*\n** Allocate a new SegReader object.\n*/\nSQLITE_PRIVATE int sqlite3Fts3SegReaderNew(\n  int iAge,                       /* Segment \"age\". */\n  int bLookup,                    /* True for a lookup only */\n  sqlite3_int64 iStartLeaf,       /* First leaf to traverse */\n  sqlite3_int64 iEndLeaf,         /* Final leaf to traverse */\n  sqlite3_int64 iEndBlock,        /* Final block of segment */\n  const char *zRoot,              /* Buffer containing root node */\n  int nRoot,                      /* Size of buffer containing root node */\n  Fts3SegReader **ppReader        /* OUT: Allocated Fts3SegReader */\n){\n  Fts3SegReader *pReader;         /* Newly allocated SegReader object */\n  int nExtra = 0;                 /* Bytes to allocate segment root node */\n\n  assert( iStartLeaf<=iEndLeaf );\n  if( iStartLeaf==0 ){\n    nExtra = nRoot + FTS3_NODE_PADDING;\n  }\n\n  pReader = (Fts3SegReader *)sqlite3_malloc(sizeof(Fts3SegReader) + nExtra);\n  if( !pReader ){\n    return SQLITE_NOMEM;\n  }\n  memset(pReader, 0, sizeof(Fts3SegReader));\n  pReader->iIdx = iAge;\n  pReader->bLookup = bLookup!=0;\n  pReader->iStartBlock = iStartLeaf;\n  pReader->iLeafEndBlock = iEndLeaf;\n  pReader->iEndBlock = iEndBlock;\n\n  if( nExtra ){\n    /* The entire segment is stored in the root node. */\n    pReader->aNode = (char *)&pReader[1];\n    pReader->rootOnly = 1;\n    pReader->nNode = nRoot;\n    memcpy(pReader->aNode, zRoot, nRoot);\n    memset(&pReader->aNode[nRoot], 0, FTS3_NODE_PADDING);\n  }else{\n    pReader->iCurrentBlock = iStartLeaf-1;\n  }\n  *ppReader = pReader;\n  return SQLITE_OK;\n}\n\n/*\n** This is a comparison function used as a qsort() callback when sorting\n** an array of pending terms by term. This occurs as part of flushing\n** the contents of the pending-terms hash table to the database.\n*/\nstatic int SQLITE_CDECL fts3CompareElemByTerm(\n  const void *lhs,\n  const void *rhs\n){\n  char *z1 = fts3HashKey(*(Fts3HashElem **)lhs);\n  char *z2 = fts3HashKey(*(Fts3HashElem **)rhs);\n  int n1 = fts3HashKeysize(*(Fts3HashElem **)lhs);\n  int n2 = fts3HashKeysize(*(Fts3HashElem **)rhs);\n\n  int n = (n1<n2 ? n1 : n2);\n  int c = memcmp(z1, z2, n);\n  if( c==0 ){\n    c = n1 - n2;\n  }\n  return c;\n}\n\n/*\n** This function is used to allocate an Fts3SegReader that iterates through\n** a subset of the terms stored in the Fts3Table.pendingTerms array.\n**\n** If the isPrefixIter parameter is zero, then the returned SegReader iterates\n** through each term in the pending-terms table. Or, if isPrefixIter is\n** non-zero, it iterates through each term and its prefixes. For example, if\n** the pending terms hash table contains the terms \"sqlite\", \"mysql\" and\n** \"firebird\", then the iterator visits the following 'terms' (in the order\n** shown):\n**\n**   f fi fir fire fireb firebi firebir firebird\n**   m my mys mysq mysql\n**   s sq sql sqli sqlit sqlite\n**\n** Whereas if isPrefixIter is zero, the terms visited are:\n**\n**   firebird mysql sqlite\n*/\nSQLITE_PRIVATE int sqlite3Fts3SegReaderPending(\n  Fts3Table *p,                   /* Virtual table handle */\n  int iIndex,                     /* Index for p->aIndex */\n  const char *zTerm,              /* Term to search for */\n  int nTerm,                      /* Size of buffer zTerm */\n  int bPrefix,                    /* True for a prefix iterator */\n  Fts3SegReader **ppReader        /* OUT: SegReader for pending-terms */\n){\n  Fts3SegReader *pReader = 0;     /* Fts3SegReader object to return */\n  Fts3HashElem *pE;               /* Iterator variable */\n  Fts3HashElem **aElem = 0;       /* Array of term hash entries to scan */\n  int nElem = 0;                  /* Size of array at aElem */\n  int rc = SQLITE_OK;             /* Return Code */\n  Fts3Hash *pHash;\n\n  pHash = &p->aIndex[iIndex].hPending;\n  if( bPrefix ){\n    int nAlloc = 0;               /* Size of allocated array at aElem */\n\n    for(pE=fts3HashFirst(pHash); pE; pE=fts3HashNext(pE)){\n      char *zKey = (char *)fts3HashKey(pE);\n      int nKey = fts3HashKeysize(pE);\n      if( nTerm==0 || (nKey>=nTerm && 0==memcmp(zKey, zTerm, nTerm)) ){\n        if( nElem==nAlloc ){\n          Fts3HashElem **aElem2;\n          nAlloc += 16;\n          aElem2 = (Fts3HashElem **)sqlite3_realloc(\n              aElem, nAlloc*sizeof(Fts3HashElem *)\n          );\n          if( !aElem2 ){\n            rc = SQLITE_NOMEM;\n            nElem = 0;\n            break;\n          }\n          aElem = aElem2;\n        }\n\n        aElem[nElem++] = pE;\n      }\n    }\n\n    /* If more than one term matches the prefix, sort the Fts3HashElem\n    ** objects in term order using qsort(). This uses the same comparison\n    ** callback as is used when flushing terms to disk.\n    */\n    if( nElem>1 ){\n      qsort(aElem, nElem, sizeof(Fts3HashElem *), fts3CompareElemByTerm);\n    }\n\n  }else{\n    /* The query is a simple term lookup that matches at most one term in\n    ** the index. All that is required is a straight hash-lookup. \n    **\n    ** Because the stack address of pE may be accessed via the aElem pointer\n    ** below, the \"Fts3HashElem *pE\" must be declared so that it is valid\n    ** within this entire function, not just this \"else{...}\" block.\n    */\n    pE = fts3HashFindElem(pHash, zTerm, nTerm);\n    if( pE ){\n      aElem = &pE;\n      nElem = 1;\n    }\n  }\n\n  if( nElem>0 ){\n    int nByte = sizeof(Fts3SegReader) + (nElem+1)*sizeof(Fts3HashElem *);\n    pReader = (Fts3SegReader *)sqlite3_malloc(nByte);\n    if( !pReader ){\n      rc = SQLITE_NOMEM;\n    }else{\n      memset(pReader, 0, nByte);\n      pReader->iIdx = 0x7FFFFFFF;\n      pReader->ppNextElem = (Fts3HashElem **)&pReader[1];\n      memcpy(pReader->ppNextElem, aElem, nElem*sizeof(Fts3HashElem *));\n    }\n  }\n\n  if( bPrefix ){\n    sqlite3_free(aElem);\n  }\n  *ppReader = pReader;\n  return rc;\n}\n\n/*\n** Compare the entries pointed to by two Fts3SegReader structures. \n** Comparison is as follows:\n**\n**   1) EOF is greater than not EOF.\n**\n**   2) The current terms (if any) are compared using memcmp(). If one\n**      term is a prefix of another, the longer term is considered the\n**      larger.\n**\n**   3) By segment age. An older segment is considered larger.\n*/\nstatic int fts3SegReaderCmp(Fts3SegReader *pLhs, Fts3SegReader *pRhs){\n  int rc;\n  if( pLhs->aNode && pRhs->aNode ){\n    int rc2 = pLhs->nTerm - pRhs->nTerm;\n    if( rc2<0 ){\n      rc = memcmp(pLhs->zTerm, pRhs->zTerm, pLhs->nTerm);\n    }else{\n      rc = memcmp(pLhs->zTerm, pRhs->zTerm, pRhs->nTerm);\n    }\n    if( rc==0 ){\n      rc = rc2;\n    }\n  }else{\n    rc = (pLhs->aNode==0) - (pRhs->aNode==0);\n  }\n  if( rc==0 ){\n    rc = pRhs->iIdx - pLhs->iIdx;\n  }\n  assert( rc!=0 );\n  return rc;\n}\n\n/*\n** A different comparison function for SegReader structures. In this\n** version, it is assumed that each SegReader points to an entry in\n** a doclist for identical terms. Comparison is made as follows:\n**\n**   1) EOF (end of doclist in this case) is greater than not EOF.\n**\n**   2) By current docid.\n**\n**   3) By segment age. An older segment is considered larger.\n*/\nstatic int fts3SegReaderDoclistCmp(Fts3SegReader *pLhs, Fts3SegReader *pRhs){\n  int rc = (pLhs->pOffsetList==0)-(pRhs->pOffsetList==0);\n  if( rc==0 ){\n    if( pLhs->iDocid==pRhs->iDocid ){\n      rc = pRhs->iIdx - pLhs->iIdx;\n    }else{\n      rc = (pLhs->iDocid > pRhs->iDocid) ? 1 : -1;\n    }\n  }\n  assert( pLhs->aNode && pRhs->aNode );\n  return rc;\n}\nstatic int fts3SegReaderDoclistCmpRev(Fts3SegReader *pLhs, Fts3SegReader *pRhs){\n  int rc = (pLhs->pOffsetList==0)-(pRhs->pOffsetList==0);\n  if( rc==0 ){\n    if( pLhs->iDocid==pRhs->iDocid ){\n      rc = pRhs->iIdx - pLhs->iIdx;\n    }else{\n      rc = (pLhs->iDocid < pRhs->iDocid) ? 1 : -1;\n    }\n  }\n  assert( pLhs->aNode && pRhs->aNode );\n  return rc;\n}\n\n/*\n** Compare the term that the Fts3SegReader object passed as the first argument\n** points to with the term specified by arguments zTerm and nTerm. \n**\n** If the pSeg iterator is already at EOF, return 0. Otherwise, return\n** -ve if the pSeg term is less than zTerm/nTerm, 0 if the two terms are\n** equal, or +ve if the pSeg term is greater than zTerm/nTerm.\n*/\nstatic int fts3SegReaderTermCmp(\n  Fts3SegReader *pSeg,            /* Segment reader object */\n  const char *zTerm,              /* Term to compare to */\n  int nTerm                       /* Size of term zTerm in bytes */\n){\n  int res = 0;\n  if( pSeg->aNode ){\n    if( pSeg->nTerm>nTerm ){\n      res = memcmp(pSeg->zTerm, zTerm, nTerm);\n    }else{\n      res = memcmp(pSeg->zTerm, zTerm, pSeg->nTerm);\n    }\n    if( res==0 ){\n      res = pSeg->nTerm-nTerm;\n    }\n  }\n  return res;\n}\n\n/*\n** Argument apSegment is an array of nSegment elements. It is known that\n** the final (nSegment-nSuspect) members are already in sorted order\n** (according to the comparison function provided). This function shuffles\n** the array around until all entries are in sorted order.\n*/\nstatic void fts3SegReaderSort(\n  Fts3SegReader **apSegment,                     /* Array to sort entries of */\n  int nSegment,                                  /* Size of apSegment array */\n  int nSuspect,                                  /* Unsorted entry count */\n  int (*xCmp)(Fts3SegReader *, Fts3SegReader *)  /* Comparison function */\n){\n  int i;                          /* Iterator variable */\n\n  assert( nSuspect<=nSegment );\n\n  if( nSuspect==nSegment ) nSuspect--;\n  for(i=nSuspect-1; i>=0; i--){\n    int j;\n    for(j=i; j<(nSegment-1); j++){\n      Fts3SegReader *pTmp;\n      if( xCmp(apSegment[j], apSegment[j+1])<0 ) break;\n      pTmp = apSegment[j+1];\n      apSegment[j+1] = apSegment[j];\n      apSegment[j] = pTmp;\n    }\n  }\n\n#ifndef NDEBUG\n  /* Check that the list really is sorted now. */\n  for(i=0; i<(nSuspect-1); i++){\n    assert( xCmp(apSegment[i], apSegment[i+1])<0 );\n  }\n#endif\n}\n\n/* \n** Insert a record into the %_segments table.\n*/\nstatic int fts3WriteSegment(\n  Fts3Table *p,                   /* Virtual table handle */\n  sqlite3_int64 iBlock,           /* Block id for new block */\n  char *z,                        /* Pointer to buffer containing block data */\n  int n                           /* Size of buffer z in bytes */\n){\n  sqlite3_stmt *pStmt;\n  int rc = fts3SqlStmt(p, SQL_INSERT_SEGMENTS, &pStmt, 0);\n  if( rc==SQLITE_OK ){\n    sqlite3_bind_int64(pStmt, 1, iBlock);\n    sqlite3_bind_blob(pStmt, 2, z, n, SQLITE_STATIC);\n    sqlite3_step(pStmt);\n    rc = sqlite3_reset(pStmt);\n    sqlite3_bind_null(pStmt, 2);\n  }\n  return rc;\n}\n\n/*\n** Find the largest relative level number in the table. If successful, set\n** *pnMax to this value and return SQLITE_OK. Otherwise, if an error occurs,\n** set *pnMax to zero and return an SQLite error code.\n*/\nSQLITE_PRIVATE int sqlite3Fts3MaxLevel(Fts3Table *p, int *pnMax){\n  int rc;\n  int mxLevel = 0;\n  sqlite3_stmt *pStmt = 0;\n\n  rc = fts3SqlStmt(p, SQL_SELECT_MXLEVEL, &pStmt, 0);\n  if( rc==SQLITE_OK ){\n    if( SQLITE_ROW==sqlite3_step(pStmt) ){\n      mxLevel = sqlite3_column_int(pStmt, 0);\n    }\n    rc = sqlite3_reset(pStmt);\n  }\n  *pnMax = mxLevel;\n  return rc;\n}\n\n/* \n** Insert a record into the %_segdir table.\n*/\nstatic int fts3WriteSegdir(\n  Fts3Table *p,                   /* Virtual table handle */\n  sqlite3_int64 iLevel,           /* Value for \"level\" field (absolute level) */\n  int iIdx,                       /* Value for \"idx\" field */\n  sqlite3_int64 iStartBlock,      /* Value for \"start_block\" field */\n  sqlite3_int64 iLeafEndBlock,    /* Value for \"leaves_end_block\" field */\n  sqlite3_int64 iEndBlock,        /* Value for \"end_block\" field */\n  sqlite3_int64 nLeafData,        /* Bytes of leaf data in segment */\n  char *zRoot,                    /* Blob value for \"root\" field */\n  int nRoot                       /* Number of bytes in buffer zRoot */\n){\n  sqlite3_stmt *pStmt;\n  int rc = fts3SqlStmt(p, SQL_INSERT_SEGDIR, &pStmt, 0);\n  if( rc==SQLITE_OK ){\n    sqlite3_bind_int64(pStmt, 1, iLevel);\n    sqlite3_bind_int(pStmt, 2, iIdx);\n    sqlite3_bind_int64(pStmt, 3, iStartBlock);\n    sqlite3_bind_int64(pStmt, 4, iLeafEndBlock);\n    if( nLeafData==0 ){\n      sqlite3_bind_int64(pStmt, 5, iEndBlock);\n    }else{\n      char *zEnd = sqlite3_mprintf(\"%lld %lld\", iEndBlock, nLeafData);\n      if( !zEnd ) return SQLITE_NOMEM;\n      sqlite3_bind_text(pStmt, 5, zEnd, -1, sqlite3_free);\n    }\n    sqlite3_bind_blob(pStmt, 6, zRoot, nRoot, SQLITE_STATIC);\n    sqlite3_step(pStmt);\n    rc = sqlite3_reset(pStmt);\n    sqlite3_bind_null(pStmt, 6);\n  }\n  return rc;\n}\n\n/*\n** Return the size of the common prefix (if any) shared by zPrev and\n** zNext, in bytes. For example, \n**\n**   fts3PrefixCompress(\"abc\", 3, \"abcdef\", 6)   // returns 3\n**   fts3PrefixCompress(\"abX\", 3, \"abcdef\", 6)   // returns 2\n**   fts3PrefixCompress(\"abX\", 3, \"Xbcdef\", 6)   // returns 0\n*/\nstatic int fts3PrefixCompress(\n  const char *zPrev,              /* Buffer containing previous term */\n  int nPrev,                      /* Size of buffer zPrev in bytes */\n  const char *zNext,              /* Buffer containing next term */\n  int nNext                       /* Size of buffer zNext in bytes */\n){\n  int n;\n  UNUSED_PARAMETER(nNext);\n  for(n=0; n<nPrev && zPrev[n]==zNext[n]; n++);\n  return n;\n}\n\n/*\n** Add term zTerm to the SegmentNode. It is guaranteed that zTerm is larger\n** (according to memcmp) than the previous term.\n*/\nstatic int fts3NodeAddTerm(\n  Fts3Table *p,                   /* Virtual table handle */\n  SegmentNode **ppTree,           /* IN/OUT: SegmentNode handle */ \n  int isCopyTerm,                 /* True if zTerm/nTerm is transient */\n  const char *zTerm,              /* Pointer to buffer containing term */\n  int nTerm                       /* Size of term in bytes */\n){\n  SegmentNode *pTree = *ppTree;\n  int rc;\n  SegmentNode *pNew;\n\n  /* First try to append the term to the current node. Return early if \n  ** this is possible.\n  */\n  if( pTree ){\n    int nData = pTree->nData;     /* Current size of node in bytes */\n    int nReq = nData;             /* Required space after adding zTerm */\n    int nPrefix;                  /* Number of bytes of prefix compression */\n    int nSuffix;                  /* Suffix length */\n\n    nPrefix = fts3PrefixCompress(pTree->zTerm, pTree->nTerm, zTerm, nTerm);\n    nSuffix = nTerm-nPrefix;\n\n    nReq += sqlite3Fts3VarintLen(nPrefix)+sqlite3Fts3VarintLen(nSuffix)+nSuffix;\n    if( nReq<=p->nNodeSize || !pTree->zTerm ){\n\n      if( nReq>p->nNodeSize ){\n        /* An unusual case: this is the first term to be added to the node\n        ** and the static node buffer (p->nNodeSize bytes) is not large\n        ** enough. Use a separately malloced buffer instead This wastes\n        ** p->nNodeSize bytes, but since this scenario only comes about when\n        ** the database contain two terms that share a prefix of almost 2KB, \n        ** this is not expected to be a serious problem. \n        */\n        assert( pTree->aData==(char *)&pTree[1] );\n        pTree->aData = (char *)sqlite3_malloc(nReq);\n        if( !pTree->aData ){\n          return SQLITE_NOMEM;\n        }\n      }\n\n      if( pTree->zTerm ){\n        /* There is no prefix-length field for first term in a node */\n        nData += sqlite3Fts3PutVarint(&pTree->aData[nData], nPrefix);\n      }\n\n      nData += sqlite3Fts3PutVarint(&pTree->aData[nData], nSuffix);\n      memcpy(&pTree->aData[nData], &zTerm[nPrefix], nSuffix);\n      pTree->nData = nData + nSuffix;\n      pTree->nEntry++;\n\n      if( isCopyTerm ){\n        if( pTree->nMalloc<nTerm ){\n          char *zNew = sqlite3_realloc(pTree->zMalloc, nTerm*2);\n          if( !zNew ){\n            return SQLITE_NOMEM;\n          }\n          pTree->nMalloc = nTerm*2;\n          pTree->zMalloc = zNew;\n        }\n        pTree->zTerm = pTree->zMalloc;\n        memcpy(pTree->zTerm, zTerm, nTerm);\n        pTree->nTerm = nTerm;\n      }else{\n        pTree->zTerm = (char *)zTerm;\n        pTree->nTerm = nTerm;\n      }\n      return SQLITE_OK;\n    }\n  }\n\n  /* If control flows to here, it was not possible to append zTerm to the\n  ** current node. Create a new node (a right-sibling of the current node).\n  ** If this is the first node in the tree, the term is added to it.\n  **\n  ** Otherwise, the term is not added to the new node, it is left empty for\n  ** now. Instead, the term is inserted into the parent of pTree. If pTree \n  ** has no parent, one is created here.\n  */\n  pNew = (SegmentNode *)sqlite3_malloc(sizeof(SegmentNode) + p->nNodeSize);\n  if( !pNew ){\n    return SQLITE_NOMEM;\n  }\n  memset(pNew, 0, sizeof(SegmentNode));\n  pNew->nData = 1 + FTS3_VARINT_MAX;\n  pNew->aData = (char *)&pNew[1];\n\n  if( pTree ){\n    SegmentNode *pParent = pTree->pParent;\n    rc = fts3NodeAddTerm(p, &pParent, isCopyTerm, zTerm, nTerm);\n    if( pTree->pParent==0 ){\n      pTree->pParent = pParent;\n    }\n    pTree->pRight = pNew;\n    pNew->pLeftmost = pTree->pLeftmost;\n    pNew->pParent = pParent;\n    pNew->zMalloc = pTree->zMalloc;\n    pNew->nMalloc = pTree->nMalloc;\n    pTree->zMalloc = 0;\n  }else{\n    pNew->pLeftmost = pNew;\n    rc = fts3NodeAddTerm(p, &pNew, isCopyTerm, zTerm, nTerm); \n  }\n\n  *ppTree = pNew;\n  return rc;\n}\n\n/*\n** Helper function for fts3NodeWrite().\n*/\nstatic int fts3TreeFinishNode(\n  SegmentNode *pTree, \n  int iHeight, \n  sqlite3_int64 iLeftChild\n){\n  int nStart;\n  assert( iHeight>=1 && iHeight<128 );\n  nStart = FTS3_VARINT_MAX - sqlite3Fts3VarintLen(iLeftChild);\n  pTree->aData[nStart] = (char)iHeight;\n  sqlite3Fts3PutVarint(&pTree->aData[nStart+1], iLeftChild);\n  return nStart;\n}\n\n/*\n** Write the buffer for the segment node pTree and all of its peers to the\n** database. Then call this function recursively to write the parent of \n** pTree and its peers to the database. \n**\n** Except, if pTree is a root node, do not write it to the database. Instead,\n** set output variables *paRoot and *pnRoot to contain the root node.\n**\n** If successful, SQLITE_OK is returned and output variable *piLast is\n** set to the largest blockid written to the database (or zero if no\n** blocks were written to the db). Otherwise, an SQLite error code is \n** returned.\n*/\nstatic int fts3NodeWrite(\n  Fts3Table *p,                   /* Virtual table handle */\n  SegmentNode *pTree,             /* SegmentNode handle */\n  int iHeight,                    /* Height of this node in tree */\n  sqlite3_int64 iLeaf,            /* Block id of first leaf node */\n  sqlite3_int64 iFree,            /* Block id of next free slot in %_segments */\n  sqlite3_int64 *piLast,          /* OUT: Block id of last entry written */\n  char **paRoot,                  /* OUT: Data for root node */\n  int *pnRoot                     /* OUT: Size of root node in bytes */\n){\n  int rc = SQLITE_OK;\n\n  if( !pTree->pParent ){\n    /* Root node of the tree. */\n    int nStart = fts3TreeFinishNode(pTree, iHeight, iLeaf);\n    *piLast = iFree-1;\n    *pnRoot = pTree->nData - nStart;\n    *paRoot = &pTree->aData[nStart];\n  }else{\n    SegmentNode *pIter;\n    sqlite3_int64 iNextFree = iFree;\n    sqlite3_int64 iNextLeaf = iLeaf;\n    for(pIter=pTree->pLeftmost; pIter && rc==SQLITE_OK; pIter=pIter->pRight){\n      int nStart = fts3TreeFinishNode(pIter, iHeight, iNextLeaf);\n      int nWrite = pIter->nData - nStart;\n  \n      rc = fts3WriteSegment(p, iNextFree, &pIter->aData[nStart], nWrite);\n      iNextFree++;\n      iNextLeaf += (pIter->nEntry+1);\n    }\n    if( rc==SQLITE_OK ){\n      assert( iNextLeaf==iFree );\n      rc = fts3NodeWrite(\n          p, pTree->pParent, iHeight+1, iFree, iNextFree, piLast, paRoot, pnRoot\n      );\n    }\n  }\n\n  return rc;\n}\n\n/*\n** Free all memory allocations associated with the tree pTree.\n*/\nstatic void fts3NodeFree(SegmentNode *pTree){\n  if( pTree ){\n    SegmentNode *p = pTree->pLeftmost;\n    fts3NodeFree(p->pParent);\n    while( p ){\n      SegmentNode *pRight = p->pRight;\n      if( p->aData!=(char *)&p[1] ){\n        sqlite3_free(p->aData);\n      }\n      assert( pRight==0 || p->zMalloc==0 );\n      sqlite3_free(p->zMalloc);\n      sqlite3_free(p);\n      p = pRight;\n    }\n  }\n}\n\n/*\n** Add a term to the segment being constructed by the SegmentWriter object\n** *ppWriter. When adding the first term to a segment, *ppWriter should\n** be passed NULL. This function will allocate a new SegmentWriter object\n** and return it via the input/output variable *ppWriter in this case.\n**\n** If successful, SQLITE_OK is returned. Otherwise, an SQLite error code.\n*/\nstatic int fts3SegWriterAdd(\n  Fts3Table *p,                   /* Virtual table handle */\n  SegmentWriter **ppWriter,       /* IN/OUT: SegmentWriter handle */ \n  int isCopyTerm,                 /* True if buffer zTerm must be copied */\n  const char *zTerm,              /* Pointer to buffer containing term */\n  int nTerm,                      /* Size of term in bytes */\n  const char *aDoclist,           /* Pointer to buffer containing doclist */\n  int nDoclist                    /* Size of doclist in bytes */\n){\n  int nPrefix;                    /* Size of term prefix in bytes */\n  int nSuffix;                    /* Size of term suffix in bytes */\n  int nReq;                       /* Number of bytes required on leaf page */\n  int nData;\n  SegmentWriter *pWriter = *ppWriter;\n\n  if( !pWriter ){\n    int rc;\n    sqlite3_stmt *pStmt;\n\n    /* Allocate the SegmentWriter structure */\n    pWriter = (SegmentWriter *)sqlite3_malloc(sizeof(SegmentWriter));\n    if( !pWriter ) return SQLITE_NOMEM;\n    memset(pWriter, 0, sizeof(SegmentWriter));\n    *ppWriter = pWriter;\n\n    /* Allocate a buffer in which to accumulate data */\n    pWriter->aData = (char *)sqlite3_malloc(p->nNodeSize);\n    if( !pWriter->aData ) return SQLITE_NOMEM;\n    pWriter->nSize = p->nNodeSize;\n\n    /* Find the next free blockid in the %_segments table */\n    rc = fts3SqlStmt(p, SQL_NEXT_SEGMENTS_ID, &pStmt, 0);\n    if( rc!=SQLITE_OK ) return rc;\n    if( SQLITE_ROW==sqlite3_step(pStmt) ){\n      pWriter->iFree = sqlite3_column_int64(pStmt, 0);\n      pWriter->iFirst = pWriter->iFree;\n    }\n    rc = sqlite3_reset(pStmt);\n    if( rc!=SQLITE_OK ) return rc;\n  }\n  nData = pWriter->nData;\n\n  nPrefix = fts3PrefixCompress(pWriter->zTerm, pWriter->nTerm, zTerm, nTerm);\n  nSuffix = nTerm-nPrefix;\n\n  /* Figure out how many bytes are required by this new entry */\n  nReq = sqlite3Fts3VarintLen(nPrefix) +    /* varint containing prefix size */\n    sqlite3Fts3VarintLen(nSuffix) +         /* varint containing suffix size */\n    nSuffix +                               /* Term suffix */\n    sqlite3Fts3VarintLen(nDoclist) +        /* Size of doclist */\n    nDoclist;                               /* Doclist data */\n\n  if( nData>0 && nData+nReq>p->nNodeSize ){\n    int rc;\n\n    /* The current leaf node is full. Write it out to the database. */\n    rc = fts3WriteSegment(p, pWriter->iFree++, pWriter->aData, nData);\n    if( rc!=SQLITE_OK ) return rc;\n    p->nLeafAdd++;\n\n    /* Add the current term to the interior node tree. The term added to\n    ** the interior tree must:\n    **\n    **   a) be greater than the largest term on the leaf node just written\n    **      to the database (still available in pWriter->zTerm), and\n    **\n    **   b) be less than or equal to the term about to be added to the new\n    **      leaf node (zTerm/nTerm).\n    **\n    ** In other words, it must be the prefix of zTerm 1 byte longer than\n    ** the common prefix (if any) of zTerm and pWriter->zTerm.\n    */\n    assert( nPrefix<nTerm );\n    rc = fts3NodeAddTerm(p, &pWriter->pTree, isCopyTerm, zTerm, nPrefix+1);\n    if( rc!=SQLITE_OK ) return rc;\n\n    nData = 0;\n    pWriter->nTerm = 0;\n\n    nPrefix = 0;\n    nSuffix = nTerm;\n    nReq = 1 +                              /* varint containing prefix size */\n      sqlite3Fts3VarintLen(nTerm) +         /* varint containing suffix size */\n      nTerm +                               /* Term suffix */\n      sqlite3Fts3VarintLen(nDoclist) +      /* Size of doclist */\n      nDoclist;                             /* Doclist data */\n  }\n\n  /* Increase the total number of bytes written to account for the new entry. */\n  pWriter->nLeafData += nReq;\n\n  /* If the buffer currently allocated is too small for this entry, realloc\n  ** the buffer to make it large enough.\n  */\n  if( nReq>pWriter->nSize ){\n    char *aNew = sqlite3_realloc(pWriter->aData, nReq);\n    if( !aNew ) return SQLITE_NOMEM;\n    pWriter->aData = aNew;\n    pWriter->nSize = nReq;\n  }\n  assert( nData+nReq<=pWriter->nSize );\n\n  /* Append the prefix-compressed term and doclist to the buffer. */\n  nData += sqlite3Fts3PutVarint(&pWriter->aData[nData], nPrefix);\n  nData += sqlite3Fts3PutVarint(&pWriter->aData[nData], nSuffix);\n  memcpy(&pWriter->aData[nData], &zTerm[nPrefix], nSuffix);\n  nData += nSuffix;\n  nData += sqlite3Fts3PutVarint(&pWriter->aData[nData], nDoclist);\n  memcpy(&pWriter->aData[nData], aDoclist, nDoclist);\n  pWriter->nData = nData + nDoclist;\n\n  /* Save the current term so that it can be used to prefix-compress the next.\n  ** If the isCopyTerm parameter is true, then the buffer pointed to by\n  ** zTerm is transient, so take a copy of the term data. Otherwise, just\n  ** store a copy of the pointer.\n  */\n  if( isCopyTerm ){\n    if( nTerm>pWriter->nMalloc ){\n      char *zNew = sqlite3_realloc(pWriter->zMalloc, nTerm*2);\n      if( !zNew ){\n        return SQLITE_NOMEM;\n      }\n      pWriter->nMalloc = nTerm*2;\n      pWriter->zMalloc = zNew;\n      pWriter->zTerm = zNew;\n    }\n    assert( pWriter->zTerm==pWriter->zMalloc );\n    memcpy(pWriter->zTerm, zTerm, nTerm);\n  }else{\n    pWriter->zTerm = (char *)zTerm;\n  }\n  pWriter->nTerm = nTerm;\n\n  return SQLITE_OK;\n}\n\n/*\n** Flush all data associated with the SegmentWriter object pWriter to the\n** database. This function must be called after all terms have been added\n** to the segment using fts3SegWriterAdd(). If successful, SQLITE_OK is\n** returned. Otherwise, an SQLite error code.\n*/\nstatic int fts3SegWriterFlush(\n  Fts3Table *p,                   /* Virtual table handle */\n  SegmentWriter *pWriter,         /* SegmentWriter to flush to the db */\n  sqlite3_int64 iLevel,           /* Value for 'level' column of %_segdir */\n  int iIdx                        /* Value for 'idx' column of %_segdir */\n){\n  int rc;                         /* Return code */\n  if( pWriter->pTree ){\n    sqlite3_int64 iLast = 0;      /* Largest block id written to database */\n    sqlite3_int64 iLastLeaf;      /* Largest leaf block id written to db */\n    char *zRoot = NULL;           /* Pointer to buffer containing root node */\n    int nRoot = 0;                /* Size of buffer zRoot */\n\n    iLastLeaf = pWriter->iFree;\n    rc = fts3WriteSegment(p, pWriter->iFree++, pWriter->aData, pWriter->nData);\n    if( rc==SQLITE_OK ){\n      rc = fts3NodeWrite(p, pWriter->pTree, 1,\n          pWriter->iFirst, pWriter->iFree, &iLast, &zRoot, &nRoot);\n    }\n    if( rc==SQLITE_OK ){\n      rc = fts3WriteSegdir(p, iLevel, iIdx, \n          pWriter->iFirst, iLastLeaf, iLast, pWriter->nLeafData, zRoot, nRoot);\n    }\n  }else{\n    /* The entire tree fits on the root node. Write it to the segdir table. */\n    rc = fts3WriteSegdir(p, iLevel, iIdx, \n        0, 0, 0, pWriter->nLeafData, pWriter->aData, pWriter->nData);\n  }\n  p->nLeafAdd++;\n  return rc;\n}\n\n/*\n** Release all memory held by the SegmentWriter object passed as the \n** first argument.\n*/\nstatic void fts3SegWriterFree(SegmentWriter *pWriter){\n  if( pWriter ){\n    sqlite3_free(pWriter->aData);\n    sqlite3_free(pWriter->zMalloc);\n    fts3NodeFree(pWriter->pTree);\n    sqlite3_free(pWriter);\n  }\n}\n\n/*\n** The first value in the apVal[] array is assumed to contain an integer.\n** This function tests if there exist any documents with docid values that\n** are different from that integer. i.e. if deleting the document with docid\n** pRowid would mean the FTS3 table were empty.\n**\n** If successful, *pisEmpty is set to true if the table is empty except for\n** document pRowid, or false otherwise, and SQLITE_OK is returned. If an\n** error occurs, an SQLite error code is returned.\n*/\nstatic int fts3IsEmpty(Fts3Table *p, sqlite3_value *pRowid, int *pisEmpty){\n  sqlite3_stmt *pStmt;\n  int rc;\n  if( p->zContentTbl ){\n    /* If using the content=xxx option, assume the table is never empty */\n    *pisEmpty = 0;\n    rc = SQLITE_OK;\n  }else{\n    rc = fts3SqlStmt(p, SQL_IS_EMPTY, &pStmt, &pRowid);\n    if( rc==SQLITE_OK ){\n      if( SQLITE_ROW==sqlite3_step(pStmt) ){\n        *pisEmpty = sqlite3_column_int(pStmt, 0);\n      }\n      rc = sqlite3_reset(pStmt);\n    }\n  }\n  return rc;\n}\n\n/*\n** Set *pnMax to the largest segment level in the database for the index\n** iIndex.\n**\n** Segment levels are stored in the 'level' column of the %_segdir table.\n**\n** Return SQLITE_OK if successful, or an SQLite error code if not.\n*/\nstatic int fts3SegmentMaxLevel(\n  Fts3Table *p, \n  int iLangid,\n  int iIndex, \n  sqlite3_int64 *pnMax\n){\n  sqlite3_stmt *pStmt;\n  int rc;\n  assert( iIndex>=0 && iIndex<p->nIndex );\n\n  /* Set pStmt to the compiled version of:\n  **\n  **   SELECT max(level) FROM %Q.'%q_segdir' WHERE level BETWEEN ? AND ?\n  **\n  ** (1024 is actually the value of macro FTS3_SEGDIR_PREFIXLEVEL_STR).\n  */\n  rc = fts3SqlStmt(p, SQL_SELECT_SEGDIR_MAX_LEVEL, &pStmt, 0);\n  if( rc!=SQLITE_OK ) return rc;\n  sqlite3_bind_int64(pStmt, 1, getAbsoluteLevel(p, iLangid, iIndex, 0));\n  sqlite3_bind_int64(pStmt, 2, \n      getAbsoluteLevel(p, iLangid, iIndex, FTS3_SEGDIR_MAXLEVEL-1)\n  );\n  if( SQLITE_ROW==sqlite3_step(pStmt) ){\n    *pnMax = sqlite3_column_int64(pStmt, 0);\n  }\n  return sqlite3_reset(pStmt);\n}\n\n/*\n** iAbsLevel is an absolute level that may be assumed to exist within\n** the database. This function checks if it is the largest level number\n** within its index. Assuming no error occurs, *pbMax is set to 1 if\n** iAbsLevel is indeed the largest level, or 0 otherwise, and SQLITE_OK\n** is returned. If an error occurs, an error code is returned and the\n** final value of *pbMax is undefined.\n*/\nstatic int fts3SegmentIsMaxLevel(Fts3Table *p, i64 iAbsLevel, int *pbMax){\n\n  /* Set pStmt to the compiled version of:\n  **\n  **   SELECT max(level) FROM %Q.'%q_segdir' WHERE level BETWEEN ? AND ?\n  **\n  ** (1024 is actually the value of macro FTS3_SEGDIR_PREFIXLEVEL_STR).\n  */\n  sqlite3_stmt *pStmt;\n  int rc = fts3SqlStmt(p, SQL_SELECT_SEGDIR_MAX_LEVEL, &pStmt, 0);\n  if( rc!=SQLITE_OK ) return rc;\n  sqlite3_bind_int64(pStmt, 1, iAbsLevel+1);\n  sqlite3_bind_int64(pStmt, 2, \n      ((iAbsLevel/FTS3_SEGDIR_MAXLEVEL)+1) * FTS3_SEGDIR_MAXLEVEL\n  );\n\n  *pbMax = 0;\n  if( SQLITE_ROW==sqlite3_step(pStmt) ){\n    *pbMax = sqlite3_column_type(pStmt, 0)==SQLITE_NULL;\n  }\n  return sqlite3_reset(pStmt);\n}\n\n/*\n** Delete all entries in the %_segments table associated with the segment\n** opened with seg-reader pSeg. This function does not affect the contents\n** of the %_segdir table.\n*/\nstatic int fts3DeleteSegment(\n  Fts3Table *p,                   /* FTS table handle */\n  Fts3SegReader *pSeg             /* Segment to delete */\n){\n  int rc = SQLITE_OK;             /* Return code */\n  if( pSeg->iStartBlock ){\n    sqlite3_stmt *pDelete;        /* SQL statement to delete rows */\n    rc = fts3SqlStmt(p, SQL_DELETE_SEGMENTS_RANGE, &pDelete, 0);\n    if( rc==SQLITE_OK ){\n      sqlite3_bind_int64(pDelete, 1, pSeg->iStartBlock);\n      sqlite3_bind_int64(pDelete, 2, pSeg->iEndBlock);\n      sqlite3_step(pDelete);\n      rc = sqlite3_reset(pDelete);\n    }\n  }\n  return rc;\n}\n\n/*\n** This function is used after merging multiple segments into a single large\n** segment to delete the old, now redundant, segment b-trees. Specifically,\n** it:\n** \n**   1) Deletes all %_segments entries for the segments associated with \n**      each of the SegReader objects in the array passed as the third \n**      argument, and\n**\n**   2) deletes all %_segdir entries with level iLevel, or all %_segdir\n**      entries regardless of level if (iLevel<0).\n**\n** SQLITE_OK is returned if successful, otherwise an SQLite error code.\n*/\nstatic int fts3DeleteSegdir(\n  Fts3Table *p,                   /* Virtual table handle */\n  int iLangid,                    /* Language id */\n  int iIndex,                     /* Index for p->aIndex */\n  int iLevel,                     /* Level of %_segdir entries to delete */\n  Fts3SegReader **apSegment,      /* Array of SegReader objects */\n  int nReader                     /* Size of array apSegment */\n){\n  int rc = SQLITE_OK;             /* Return Code */\n  int i;                          /* Iterator variable */\n  sqlite3_stmt *pDelete = 0;      /* SQL statement to delete rows */\n\n  for(i=0; rc==SQLITE_OK && i<nReader; i++){\n    rc = fts3DeleteSegment(p, apSegment[i]);\n  }\n  if( rc!=SQLITE_OK ){\n    return rc;\n  }\n\n  assert( iLevel>=0 || iLevel==FTS3_SEGCURSOR_ALL );\n  if( iLevel==FTS3_SEGCURSOR_ALL ){\n    rc = fts3SqlStmt(p, SQL_DELETE_SEGDIR_RANGE, &pDelete, 0);\n    if( rc==SQLITE_OK ){\n      sqlite3_bind_int64(pDelete, 1, getAbsoluteLevel(p, iLangid, iIndex, 0));\n      sqlite3_bind_int64(pDelete, 2, \n          getAbsoluteLevel(p, iLangid, iIndex, FTS3_SEGDIR_MAXLEVEL-1)\n      );\n    }\n  }else{\n    rc = fts3SqlStmt(p, SQL_DELETE_SEGDIR_LEVEL, &pDelete, 0);\n    if( rc==SQLITE_OK ){\n      sqlite3_bind_int64(\n          pDelete, 1, getAbsoluteLevel(p, iLangid, iIndex, iLevel)\n      );\n    }\n  }\n\n  if( rc==SQLITE_OK ){\n    sqlite3_step(pDelete);\n    rc = sqlite3_reset(pDelete);\n  }\n\n  return rc;\n}\n\n/*\n** When this function is called, buffer *ppList (size *pnList bytes) contains \n** a position list that may (or may not) feature multiple columns. This\n** function adjusts the pointer *ppList and the length *pnList so that they\n** identify the subset of the position list that corresponds to column iCol.\n**\n** If there are no entries in the input position list for column iCol, then\n** *pnList is set to zero before returning.\n**\n** If parameter bZero is non-zero, then any part of the input list following\n** the end of the output list is zeroed before returning.\n*/\nstatic void fts3ColumnFilter(\n  int iCol,                       /* Column to filter on */\n  int bZero,                      /* Zero out anything following *ppList */\n  char **ppList,                  /* IN/OUT: Pointer to position list */\n  int *pnList                     /* IN/OUT: Size of buffer *ppList in bytes */\n){\n  char *pList = *ppList;\n  int nList = *pnList;\n  char *pEnd = &pList[nList];\n  int iCurrent = 0;\n  char *p = pList;\n\n  assert( iCol>=0 );\n  while( 1 ){\n    char c = 0;\n    while( p<pEnd && (c | *p)&0xFE ) c = *p++ & 0x80;\n  \n    if( iCol==iCurrent ){\n      nList = (int)(p - pList);\n      break;\n    }\n\n    nList -= (int)(p - pList);\n    pList = p;\n    if( nList==0 ){\n      break;\n    }\n    p = &pList[1];\n    p += fts3GetVarint32(p, &iCurrent);\n  }\n\n  if( bZero && &pList[nList]!=pEnd ){\n    memset(&pList[nList], 0, pEnd - &pList[nList]);\n  }\n  *ppList = pList;\n  *pnList = nList;\n}\n\n/*\n** Cache data in the Fts3MultiSegReader.aBuffer[] buffer (overwriting any\n** existing data). Grow the buffer if required.\n**\n** If successful, return SQLITE_OK. Otherwise, if an OOM error is encountered\n** trying to resize the buffer, return SQLITE_NOMEM.\n*/\nstatic int fts3MsrBufferData(\n  Fts3MultiSegReader *pMsr,       /* Multi-segment-reader handle */\n  char *pList,\n  int nList\n){\n  if( nList>pMsr->nBuffer ){\n    char *pNew;\n    pMsr->nBuffer = nList*2;\n    pNew = (char *)sqlite3_realloc(pMsr->aBuffer, pMsr->nBuffer);\n    if( !pNew ) return SQLITE_NOMEM;\n    pMsr->aBuffer = pNew;\n  }\n\n  memcpy(pMsr->aBuffer, pList, nList);\n  return SQLITE_OK;\n}\n\nSQLITE_PRIVATE int sqlite3Fts3MsrIncrNext(\n  Fts3Table *p,                   /* Virtual table handle */\n  Fts3MultiSegReader *pMsr,       /* Multi-segment-reader handle */\n  sqlite3_int64 *piDocid,         /* OUT: Docid value */\n  char **paPoslist,               /* OUT: Pointer to position list */\n  int *pnPoslist                  /* OUT: Size of position list in bytes */\n){\n  int nMerge = pMsr->nAdvance;\n  Fts3SegReader **apSegment = pMsr->apSegment;\n  int (*xCmp)(Fts3SegReader *, Fts3SegReader *) = (\n    p->bDescIdx ? fts3SegReaderDoclistCmpRev : fts3SegReaderDoclistCmp\n  );\n\n  if( nMerge==0 ){\n    *paPoslist = 0;\n    return SQLITE_OK;\n  }\n\n  while( 1 ){\n    Fts3SegReader *pSeg;\n    pSeg = pMsr->apSegment[0];\n\n    if( pSeg->pOffsetList==0 ){\n      *paPoslist = 0;\n      break;\n    }else{\n      int rc;\n      char *pList;\n      int nList;\n      int j;\n      sqlite3_int64 iDocid = apSegment[0]->iDocid;\n\n      rc = fts3SegReaderNextDocid(p, apSegment[0], &pList, &nList);\n      j = 1;\n      while( rc==SQLITE_OK \n        && j<nMerge\n        && apSegment[j]->pOffsetList\n        && apSegment[j]->iDocid==iDocid\n      ){\n        rc = fts3SegReaderNextDocid(p, apSegment[j], 0, 0);\n        j++;\n      }\n      if( rc!=SQLITE_OK ) return rc;\n      fts3SegReaderSort(pMsr->apSegment, nMerge, j, xCmp);\n\n      if( nList>0 && fts3SegReaderIsPending(apSegment[0]) ){\n        rc = fts3MsrBufferData(pMsr, pList, nList+1);\n        if( rc!=SQLITE_OK ) return rc;\n        assert( (pMsr->aBuffer[nList] & 0xFE)==0x00 );\n        pList = pMsr->aBuffer;\n      }\n\n      if( pMsr->iColFilter>=0 ){\n        fts3ColumnFilter(pMsr->iColFilter, 1, &pList, &nList);\n      }\n\n      if( nList>0 ){\n        *paPoslist = pList;\n        *piDocid = iDocid;\n        *pnPoslist = nList;\n        break;\n      }\n    }\n  }\n\n  return SQLITE_OK;\n}\n\nstatic int fts3SegReaderStart(\n  Fts3Table *p,                   /* Virtual table handle */\n  Fts3MultiSegReader *pCsr,       /* Cursor object */\n  const char *zTerm,              /* Term searched for (or NULL) */\n  int nTerm                       /* Length of zTerm in bytes */\n){\n  int i;\n  int nSeg = pCsr->nSegment;\n\n  /* If the Fts3SegFilter defines a specific term (or term prefix) to search \n  ** for, then advance each segment iterator until it points to a term of\n  ** equal or greater value than the specified term. This prevents many\n  ** unnecessary merge/sort operations for the case where single segment\n  ** b-tree leaf nodes contain more than one term.\n  */\n  for(i=0; pCsr->bRestart==0 && i<pCsr->nSegment; i++){\n    int res = 0;\n    Fts3SegReader *pSeg = pCsr->apSegment[i];\n    do {\n      int rc = fts3SegReaderNext(p, pSeg, 0);\n      if( rc!=SQLITE_OK ) return rc;\n    }while( zTerm && (res = fts3SegReaderTermCmp(pSeg, zTerm, nTerm))<0 );\n\n    if( pSeg->bLookup && res!=0 ){\n      fts3SegReaderSetEof(pSeg);\n    }\n  }\n  fts3SegReaderSort(pCsr->apSegment, nSeg, nSeg, fts3SegReaderCmp);\n\n  return SQLITE_OK;\n}\n\nSQLITE_PRIVATE int sqlite3Fts3SegReaderStart(\n  Fts3Table *p,                   /* Virtual table handle */\n  Fts3MultiSegReader *pCsr,       /* Cursor object */\n  Fts3SegFilter *pFilter          /* Restrictions on range of iteration */\n){\n  pCsr->pFilter = pFilter;\n  return fts3SegReaderStart(p, pCsr, pFilter->zTerm, pFilter->nTerm);\n}\n\nSQLITE_PRIVATE int sqlite3Fts3MsrIncrStart(\n  Fts3Table *p,                   /* Virtual table handle */\n  Fts3MultiSegReader *pCsr,       /* Cursor object */\n  int iCol,                       /* Column to match on. */\n  const char *zTerm,              /* Term to iterate through a doclist for */\n  int nTerm                       /* Number of bytes in zTerm */\n){\n  int i;\n  int rc;\n  int nSegment = pCsr->nSegment;\n  int (*xCmp)(Fts3SegReader *, Fts3SegReader *) = (\n    p->bDescIdx ? fts3SegReaderDoclistCmpRev : fts3SegReaderDoclistCmp\n  );\n\n  assert( pCsr->pFilter==0 );\n  assert( zTerm && nTerm>0 );\n\n  /* Advance each segment iterator until it points to the term zTerm/nTerm. */\n  rc = fts3SegReaderStart(p, pCsr, zTerm, nTerm);\n  if( rc!=SQLITE_OK ) return rc;\n\n  /* Determine how many of the segments actually point to zTerm/nTerm. */\n  for(i=0; i<nSegment; i++){\n    Fts3SegReader *pSeg = pCsr->apSegment[i];\n    if( !pSeg->aNode || fts3SegReaderTermCmp(pSeg, zTerm, nTerm) ){\n      break;\n    }\n  }\n  pCsr->nAdvance = i;\n\n  /* Advance each of the segments to point to the first docid. */\n  for(i=0; i<pCsr->nAdvance; i++){\n    rc = fts3SegReaderFirstDocid(p, pCsr->apSegment[i]);\n    if( rc!=SQLITE_OK ) return rc;\n  }\n  fts3SegReaderSort(pCsr->apSegment, i, i, xCmp);\n\n  assert( iCol<0 || iCol<p->nColumn );\n  pCsr->iColFilter = iCol;\n\n  return SQLITE_OK;\n}\n\n/*\n** This function is called on a MultiSegReader that has been started using\n** sqlite3Fts3MsrIncrStart(). One or more calls to MsrIncrNext() may also\n** have been made. Calling this function puts the MultiSegReader in such\n** a state that if the next two calls are:\n**\n**   sqlite3Fts3SegReaderStart()\n**   sqlite3Fts3SegReaderStep()\n**\n** then the entire doclist for the term is available in \n** MultiSegReader.aDoclist/nDoclist.\n*/\nSQLITE_PRIVATE int sqlite3Fts3MsrIncrRestart(Fts3MultiSegReader *pCsr){\n  int i;                          /* Used to iterate through segment-readers */\n\n  assert( pCsr->zTerm==0 );\n  assert( pCsr->nTerm==0 );\n  assert( pCsr->aDoclist==0 );\n  assert( pCsr->nDoclist==0 );\n\n  pCsr->nAdvance = 0;\n  pCsr->bRestart = 1;\n  for(i=0; i<pCsr->nSegment; i++){\n    pCsr->apSegment[i]->pOffsetList = 0;\n    pCsr->apSegment[i]->nOffsetList = 0;\n    pCsr->apSegment[i]->iDocid = 0;\n  }\n\n  return SQLITE_OK;\n}\n\n\nSQLITE_PRIVATE int sqlite3Fts3SegReaderStep(\n  Fts3Table *p,                   /* Virtual table handle */\n  Fts3MultiSegReader *pCsr        /* Cursor object */\n){\n  int rc = SQLITE_OK;\n\n  int isIgnoreEmpty =  (pCsr->pFilter->flags & FTS3_SEGMENT_IGNORE_EMPTY);\n  int isRequirePos =   (pCsr->pFilter->flags & FTS3_SEGMENT_REQUIRE_POS);\n  int isColFilter =    (pCsr->pFilter->flags & FTS3_SEGMENT_COLUMN_FILTER);\n  int isPrefix =       (pCsr->pFilter->flags & FTS3_SEGMENT_PREFIX);\n  int isScan =         (pCsr->pFilter->flags & FTS3_SEGMENT_SCAN);\n  int isFirst =        (pCsr->pFilter->flags & FTS3_SEGMENT_FIRST);\n\n  Fts3SegReader **apSegment = pCsr->apSegment;\n  int nSegment = pCsr->nSegment;\n  Fts3SegFilter *pFilter = pCsr->pFilter;\n  int (*xCmp)(Fts3SegReader *, Fts3SegReader *) = (\n    p->bDescIdx ? fts3SegReaderDoclistCmpRev : fts3SegReaderDoclistCmp\n  );\n\n  if( pCsr->nSegment==0 ) return SQLITE_OK;\n\n  do {\n    int nMerge;\n    int i;\n  \n    /* Advance the first pCsr->nAdvance entries in the apSegment[] array\n    ** forward. Then sort the list in order of current term again.  \n    */\n    for(i=0; i<pCsr->nAdvance; i++){\n      Fts3SegReader *pSeg = apSegment[i];\n      if( pSeg->bLookup ){\n        fts3SegReaderSetEof(pSeg);\n      }else{\n        rc = fts3SegReaderNext(p, pSeg, 0);\n      }\n      if( rc!=SQLITE_OK ) return rc;\n    }\n    fts3SegReaderSort(apSegment, nSegment, pCsr->nAdvance, fts3SegReaderCmp);\n    pCsr->nAdvance = 0;\n\n    /* If all the seg-readers are at EOF, we're finished. return SQLITE_OK. */\n    assert( rc==SQLITE_OK );\n    if( apSegment[0]->aNode==0 ) break;\n\n    pCsr->nTerm = apSegment[0]->nTerm;\n    pCsr->zTerm = apSegment[0]->zTerm;\n\n    /* If this is a prefix-search, and if the term that apSegment[0] points\n    ** to does not share a suffix with pFilter->zTerm/nTerm, then all \n    ** required callbacks have been made. In this case exit early.\n    **\n    ** Similarly, if this is a search for an exact match, and the first term\n    ** of segment apSegment[0] is not a match, exit early.\n    */\n    if( pFilter->zTerm && !isScan ){\n      if( pCsr->nTerm<pFilter->nTerm \n       || (!isPrefix && pCsr->nTerm>pFilter->nTerm)\n       || memcmp(pCsr->zTerm, pFilter->zTerm, pFilter->nTerm) \n      ){\n        break;\n      }\n    }\n\n    nMerge = 1;\n    while( nMerge<nSegment \n        && apSegment[nMerge]->aNode\n        && apSegment[nMerge]->nTerm==pCsr->nTerm \n        && 0==memcmp(pCsr->zTerm, apSegment[nMerge]->zTerm, pCsr->nTerm)\n    ){\n      nMerge++;\n    }\n\n    assert( isIgnoreEmpty || (isRequirePos && !isColFilter) );\n    if( nMerge==1 \n     && !isIgnoreEmpty \n     && !isFirst \n     && (p->bDescIdx==0 || fts3SegReaderIsPending(apSegment[0])==0)\n    ){\n      pCsr->nDoclist = apSegment[0]->nDoclist;\n      if( fts3SegReaderIsPending(apSegment[0]) ){\n        rc = fts3MsrBufferData(pCsr, apSegment[0]->aDoclist, pCsr->nDoclist);\n        pCsr->aDoclist = pCsr->aBuffer;\n      }else{\n        pCsr->aDoclist = apSegment[0]->aDoclist;\n      }\n      if( rc==SQLITE_OK ) rc = SQLITE_ROW;\n    }else{\n      int nDoclist = 0;           /* Size of doclist */\n      sqlite3_int64 iPrev = 0;    /* Previous docid stored in doclist */\n\n      /* The current term of the first nMerge entries in the array\n      ** of Fts3SegReader objects is the same. The doclists must be merged\n      ** and a single term returned with the merged doclist.\n      */\n      for(i=0; i<nMerge; i++){\n        fts3SegReaderFirstDocid(p, apSegment[i]);\n      }\n      fts3SegReaderSort(apSegment, nMerge, nMerge, xCmp);\n      while( apSegment[0]->pOffsetList ){\n        int j;                    /* Number of segments that share a docid */\n        char *pList = 0;\n        int nList = 0;\n        int nByte;\n        sqlite3_int64 iDocid = apSegment[0]->iDocid;\n        fts3SegReaderNextDocid(p, apSegment[0], &pList, &nList);\n        j = 1;\n        while( j<nMerge\n            && apSegment[j]->pOffsetList\n            && apSegment[j]->iDocid==iDocid\n        ){\n          fts3SegReaderNextDocid(p, apSegment[j], 0, 0);\n          j++;\n        }\n\n        if( isColFilter ){\n          fts3ColumnFilter(pFilter->iCol, 0, &pList, &nList);\n        }\n\n        if( !isIgnoreEmpty || nList>0 ){\n\n          /* Calculate the 'docid' delta value to write into the merged \n          ** doclist. */\n          sqlite3_int64 iDelta;\n          if( p->bDescIdx && nDoclist>0 ){\n            iDelta = iPrev - iDocid;\n          }else{\n            iDelta = iDocid - iPrev;\n          }\n          assert( iDelta>0 || (nDoclist==0 && iDelta==iDocid) );\n          assert( nDoclist>0 || iDelta==iDocid );\n\n          nByte = sqlite3Fts3VarintLen(iDelta) + (isRequirePos?nList+1:0);\n          if( nDoclist+nByte>pCsr->nBuffer ){\n            char *aNew;\n            pCsr->nBuffer = (nDoclist+nByte)*2;\n            aNew = sqlite3_realloc(pCsr->aBuffer, pCsr->nBuffer);\n            if( !aNew ){\n              return SQLITE_NOMEM;\n            }\n            pCsr->aBuffer = aNew;\n          }\n\n          if( isFirst ){\n            char *a = &pCsr->aBuffer[nDoclist];\n            int nWrite;\n           \n            nWrite = sqlite3Fts3FirstFilter(iDelta, pList, nList, a);\n            if( nWrite ){\n              iPrev = iDocid;\n              nDoclist += nWrite;\n            }\n          }else{\n            nDoclist += sqlite3Fts3PutVarint(&pCsr->aBuffer[nDoclist], iDelta);\n            iPrev = iDocid;\n            if( isRequirePos ){\n              memcpy(&pCsr->aBuffer[nDoclist], pList, nList);\n              nDoclist += nList;\n              pCsr->aBuffer[nDoclist++] = '\\0';\n            }\n          }\n        }\n\n        fts3SegReaderSort(apSegment, nMerge, j, xCmp);\n      }\n      if( nDoclist>0 ){\n        pCsr->aDoclist = pCsr->aBuffer;\n        pCsr->nDoclist = nDoclist;\n        rc = SQLITE_ROW;\n      }\n    }\n    pCsr->nAdvance = nMerge;\n  }while( rc==SQLITE_OK );\n\n  return rc;\n}\n\n\nSQLITE_PRIVATE void sqlite3Fts3SegReaderFinish(\n  Fts3MultiSegReader *pCsr       /* Cursor object */\n){\n  if( pCsr ){\n    int i;\n    for(i=0; i<pCsr->nSegment; i++){\n      sqlite3Fts3SegReaderFree(pCsr->apSegment[i]);\n    }\n    sqlite3_free(pCsr->apSegment);\n    sqlite3_free(pCsr->aBuffer);\n\n    pCsr->nSegment = 0;\n    pCsr->apSegment = 0;\n    pCsr->aBuffer = 0;\n  }\n}\n\n/*\n** Decode the \"end_block\" field, selected by column iCol of the SELECT \n** statement passed as the first argument. \n**\n** The \"end_block\" field may contain either an integer, or a text field\n** containing the text representation of two non-negative integers separated \n** by one or more space (0x20) characters. In the first case, set *piEndBlock \n** to the integer value and *pnByte to zero before returning. In the second, \n** set *piEndBlock to the first value and *pnByte to the second.\n*/\nstatic void fts3ReadEndBlockField(\n  sqlite3_stmt *pStmt, \n  int iCol, \n  i64 *piEndBlock,\n  i64 *pnByte\n){\n  const unsigned char *zText = sqlite3_column_text(pStmt, iCol);\n  if( zText ){\n    int i;\n    int iMul = 1;\n    i64 iVal = 0;\n    for(i=0; zText[i]>='0' && zText[i]<='9'; i++){\n      iVal = iVal*10 + (zText[i] - '0');\n    }\n    *piEndBlock = iVal;\n    while( zText[i]==' ' ) i++;\n    iVal = 0;\n    if( zText[i]=='-' ){\n      i++;\n      iMul = -1;\n    }\n    for(/* no-op */; zText[i]>='0' && zText[i]<='9'; i++){\n      iVal = iVal*10 + (zText[i] - '0');\n    }\n    *pnByte = (iVal * (i64)iMul);\n  }\n}\n\n\n/*\n** A segment of size nByte bytes has just been written to absolute level\n** iAbsLevel. Promote any segments that should be promoted as a result.\n*/\nstatic int fts3PromoteSegments(\n  Fts3Table *p,                   /* FTS table handle */\n  sqlite3_int64 iAbsLevel,        /* Absolute level just updated */\n  sqlite3_int64 nByte             /* Size of new segment at iAbsLevel */\n){\n  int rc = SQLITE_OK;\n  sqlite3_stmt *pRange;\n\n  rc = fts3SqlStmt(p, SQL_SELECT_LEVEL_RANGE2, &pRange, 0);\n\n  if( rc==SQLITE_OK ){\n    int bOk = 0;\n    i64 iLast = (iAbsLevel/FTS3_SEGDIR_MAXLEVEL + 1) * FTS3_SEGDIR_MAXLEVEL - 1;\n    i64 nLimit = (nByte*3)/2;\n\n    /* Loop through all entries in the %_segdir table corresponding to \n    ** segments in this index on levels greater than iAbsLevel. If there is\n    ** at least one such segment, and it is possible to determine that all \n    ** such segments are smaller than nLimit bytes in size, they will be \n    ** promoted to level iAbsLevel.  */\n    sqlite3_bind_int64(pRange, 1, iAbsLevel+1);\n    sqlite3_bind_int64(pRange, 2, iLast);\n    while( SQLITE_ROW==sqlite3_step(pRange) ){\n      i64 nSize = 0, dummy;\n      fts3ReadEndBlockField(pRange, 2, &dummy, &nSize);\n      if( nSize<=0 || nSize>nLimit ){\n        /* If nSize==0, then the %_segdir.end_block field does not not \n        ** contain a size value. This happens if it was written by an\n        ** old version of FTS. In this case it is not possible to determine\n        ** the size of the segment, and so segment promotion does not\n        ** take place.  */\n        bOk = 0;\n        break;\n      }\n      bOk = 1;\n    }\n    rc = sqlite3_reset(pRange);\n\n    if( bOk ){\n      int iIdx = 0;\n      sqlite3_stmt *pUpdate1 = 0;\n      sqlite3_stmt *pUpdate2 = 0;\n\n      if( rc==SQLITE_OK ){\n        rc = fts3SqlStmt(p, SQL_UPDATE_LEVEL_IDX, &pUpdate1, 0);\n      }\n      if( rc==SQLITE_OK ){\n        rc = fts3SqlStmt(p, SQL_UPDATE_LEVEL, &pUpdate2, 0);\n      }\n\n      if( rc==SQLITE_OK ){\n\n        /* Loop through all %_segdir entries for segments in this index with\n        ** levels equal to or greater than iAbsLevel. As each entry is visited,\n        ** updated it to set (level = -1) and (idx = N), where N is 0 for the\n        ** oldest segment in the range, 1 for the next oldest, and so on.\n        **\n        ** In other words, move all segments being promoted to level -1,\n        ** setting the \"idx\" fields as appropriate to keep them in the same\n        ** order. The contents of level -1 (which is never used, except\n        ** transiently here), will be moved back to level iAbsLevel below.  */\n        sqlite3_bind_int64(pRange, 1, iAbsLevel);\n        while( SQLITE_ROW==sqlite3_step(pRange) ){\n          sqlite3_bind_int(pUpdate1, 1, iIdx++);\n          sqlite3_bind_int(pUpdate1, 2, sqlite3_column_int(pRange, 0));\n          sqlite3_bind_int(pUpdate1, 3, sqlite3_column_int(pRange, 1));\n          sqlite3_step(pUpdate1);\n          rc = sqlite3_reset(pUpdate1);\n          if( rc!=SQLITE_OK ){\n            sqlite3_reset(pRange);\n            break;\n          }\n        }\n      }\n      if( rc==SQLITE_OK ){\n        rc = sqlite3_reset(pRange);\n      }\n\n      /* Move level -1 to level iAbsLevel */\n      if( rc==SQLITE_OK ){\n        sqlite3_bind_int64(pUpdate2, 1, iAbsLevel);\n        sqlite3_step(pUpdate2);\n        rc = sqlite3_reset(pUpdate2);\n      }\n    }\n  }\n\n\n  return rc;\n}\n\n/*\n** Merge all level iLevel segments in the database into a single \n** iLevel+1 segment. Or, if iLevel<0, merge all segments into a\n** single segment with a level equal to the numerically largest level \n** currently present in the database.\n**\n** If this function is called with iLevel<0, but there is only one\n** segment in the database, SQLITE_DONE is returned immediately. \n** Otherwise, if successful, SQLITE_OK is returned. If an error occurs, \n** an SQLite error code is returned.\n*/\nstatic int fts3SegmentMerge(\n  Fts3Table *p, \n  int iLangid,                    /* Language id to merge */\n  int iIndex,                     /* Index in p->aIndex[] to merge */\n  int iLevel                      /* Level to merge */\n){\n  int rc;                         /* Return code */\n  int iIdx = 0;                   /* Index of new segment */\n  sqlite3_int64 iNewLevel = 0;    /* Level/index to create new segment at */\n  SegmentWriter *pWriter = 0;     /* Used to write the new, merged, segment */\n  Fts3SegFilter filter;           /* Segment term filter condition */\n  Fts3MultiSegReader csr;         /* Cursor to iterate through level(s) */\n  int bIgnoreEmpty = 0;           /* True to ignore empty segments */\n  i64 iMaxLevel = 0;              /* Max level number for this index/langid */\n\n  assert( iLevel==FTS3_SEGCURSOR_ALL\n       || iLevel==FTS3_SEGCURSOR_PENDING\n       || iLevel>=0\n  );\n  assert( iLevel<FTS3_SEGDIR_MAXLEVEL );\n  assert( iIndex>=0 && iIndex<p->nIndex );\n\n  rc = sqlite3Fts3SegReaderCursor(p, iLangid, iIndex, iLevel, 0, 0, 1, 0, &csr);\n  if( rc!=SQLITE_OK || csr.nSegment==0 ) goto finished;\n\n  if( iLevel!=FTS3_SEGCURSOR_PENDING ){\n    rc = fts3SegmentMaxLevel(p, iLangid, iIndex, &iMaxLevel);\n    if( rc!=SQLITE_OK ) goto finished;\n  }\n\n  if( iLevel==FTS3_SEGCURSOR_ALL ){\n    /* This call is to merge all segments in the database to a single\n    ** segment. The level of the new segment is equal to the numerically\n    ** greatest segment level currently present in the database for this\n    ** index. The idx of the new segment is always 0.  */\n    if( csr.nSegment==1 && 0==fts3SegReaderIsPending(csr.apSegment[0]) ){\n      rc = SQLITE_DONE;\n      goto finished;\n    }\n    iNewLevel = iMaxLevel;\n    bIgnoreEmpty = 1;\n\n  }else{\n    /* This call is to merge all segments at level iLevel. find the next\n    ** available segment index at level iLevel+1. The call to\n    ** fts3AllocateSegdirIdx() will merge the segments at level iLevel+1 to \n    ** a single iLevel+2 segment if necessary.  */\n    assert( FTS3_SEGCURSOR_PENDING==-1 );\n    iNewLevel = getAbsoluteLevel(p, iLangid, iIndex, iLevel+1);\n    rc = fts3AllocateSegdirIdx(p, iLangid, iIndex, iLevel+1, &iIdx);\n    bIgnoreEmpty = (iLevel!=FTS3_SEGCURSOR_PENDING) && (iNewLevel>iMaxLevel);\n  }\n  if( rc!=SQLITE_OK ) goto finished;\n\n  assert( csr.nSegment>0 );\n  assert( iNewLevel>=getAbsoluteLevel(p, iLangid, iIndex, 0) );\n  assert( iNewLevel<getAbsoluteLevel(p, iLangid, iIndex,FTS3_SEGDIR_MAXLEVEL) );\n\n  memset(&filter, 0, sizeof(Fts3SegFilter));\n  filter.flags = FTS3_SEGMENT_REQUIRE_POS;\n  filter.flags |= (bIgnoreEmpty ? FTS3_SEGMENT_IGNORE_EMPTY : 0);\n\n  rc = sqlite3Fts3SegReaderStart(p, &csr, &filter);\n  while( SQLITE_OK==rc ){\n    rc = sqlite3Fts3SegReaderStep(p, &csr);\n    if( rc!=SQLITE_ROW ) break;\n    rc = fts3SegWriterAdd(p, &pWriter, 1, \n        csr.zTerm, csr.nTerm, csr.aDoclist, csr.nDoclist);\n  }\n  if( rc!=SQLITE_OK ) goto finished;\n  assert( pWriter || bIgnoreEmpty );\n\n  if( iLevel!=FTS3_SEGCURSOR_PENDING ){\n    rc = fts3DeleteSegdir(\n        p, iLangid, iIndex, iLevel, csr.apSegment, csr.nSegment\n    );\n    if( rc!=SQLITE_OK ) goto finished;\n  }\n  if( pWriter ){\n    rc = fts3SegWriterFlush(p, pWriter, iNewLevel, iIdx);\n    if( rc==SQLITE_OK ){\n      if( iLevel==FTS3_SEGCURSOR_PENDING || iNewLevel<iMaxLevel ){\n        rc = fts3PromoteSegments(p, iNewLevel, pWriter->nLeafData);\n      }\n    }\n  }\n\n finished:\n  fts3SegWriterFree(pWriter);\n  sqlite3Fts3SegReaderFinish(&csr);\n  return rc;\n}\n\n\n/* \n** Flush the contents of pendingTerms to level 0 segments. \n*/\nSQLITE_PRIVATE int sqlite3Fts3PendingTermsFlush(Fts3Table *p){\n  int rc = SQLITE_OK;\n  int i;\n        \n  for(i=0; rc==SQLITE_OK && i<p->nIndex; i++){\n    rc = fts3SegmentMerge(p, p->iPrevLangid, i, FTS3_SEGCURSOR_PENDING);\n    if( rc==SQLITE_DONE ) rc = SQLITE_OK;\n  }\n  sqlite3Fts3PendingTermsClear(p);\n\n  /* Determine the auto-incr-merge setting if unknown.  If enabled,\n  ** estimate the number of leaf blocks of content to be written\n  */\n  if( rc==SQLITE_OK && p->bHasStat\n   && p->nAutoincrmerge==0xff && p->nLeafAdd>0\n  ){\n    sqlite3_stmt *pStmt = 0;\n    rc = fts3SqlStmt(p, SQL_SELECT_STAT, &pStmt, 0);\n    if( rc==SQLITE_OK ){\n      sqlite3_bind_int(pStmt, 1, FTS_STAT_AUTOINCRMERGE);\n      rc = sqlite3_step(pStmt);\n      if( rc==SQLITE_ROW ){\n        p->nAutoincrmerge = sqlite3_column_int(pStmt, 0);\n        if( p->nAutoincrmerge==1 ) p->nAutoincrmerge = 8;\n      }else if( rc==SQLITE_DONE ){\n        p->nAutoincrmerge = 0;\n      }\n      rc = sqlite3_reset(pStmt);\n    }\n  }\n  return rc;\n}\n\n/*\n** Encode N integers as varints into a blob.\n*/\nstatic void fts3EncodeIntArray(\n  int N,             /* The number of integers to encode */\n  u32 *a,            /* The integer values */\n  char *zBuf,        /* Write the BLOB here */\n  int *pNBuf         /* Write number of bytes if zBuf[] used here */\n){\n  int i, j;\n  for(i=j=0; i<N; i++){\n    j += sqlite3Fts3PutVarint(&zBuf[j], (sqlite3_int64)a[i]);\n  }\n  *pNBuf = j;\n}\n\n/*\n** Decode a blob of varints into N integers\n*/\nstatic void fts3DecodeIntArray(\n  int N,             /* The number of integers to decode */\n  u32 *a,            /* Write the integer values */\n  const char *zBuf,  /* The BLOB containing the varints */\n  int nBuf           /* size of the BLOB */\n){\n  int i, j;\n  UNUSED_PARAMETER(nBuf);\n  for(i=j=0; i<N; i++){\n    sqlite3_int64 x;\n    j += sqlite3Fts3GetVarint(&zBuf[j], &x);\n    assert(j<=nBuf);\n    a[i] = (u32)(x & 0xffffffff);\n  }\n}\n\n/*\n** Insert the sizes (in tokens) for each column of the document\n** with docid equal to p->iPrevDocid.  The sizes are encoded as\n** a blob of varints.\n*/\nstatic void fts3InsertDocsize(\n  int *pRC,                       /* Result code */\n  Fts3Table *p,                   /* Table into which to insert */\n  u32 *aSz                        /* Sizes of each column, in tokens */\n){\n  char *pBlob;             /* The BLOB encoding of the document size */\n  int nBlob;               /* Number of bytes in the BLOB */\n  sqlite3_stmt *pStmt;     /* Statement used to insert the encoding */\n  int rc;                  /* Result code from subfunctions */\n\n  if( *pRC ) return;\n  pBlob = sqlite3_malloc( 10*p->nColumn );\n  if( pBlob==0 ){\n    *pRC = SQLITE_NOMEM;\n    return;\n  }\n  fts3EncodeIntArray(p->nColumn, aSz, pBlob, &nBlob);\n  rc = fts3SqlStmt(p, SQL_REPLACE_DOCSIZE, &pStmt, 0);\n  if( rc ){\n    sqlite3_free(pBlob);\n    *pRC = rc;\n    return;\n  }\n  sqlite3_bind_int64(pStmt, 1, p->iPrevDocid);\n  sqlite3_bind_blob(pStmt, 2, pBlob, nBlob, sqlite3_free);\n  sqlite3_step(pStmt);\n  *pRC = sqlite3_reset(pStmt);\n}\n\n/*\n** Record 0 of the %_stat table contains a blob consisting of N varints,\n** where N is the number of user defined columns in the fts3 table plus\n** two. If nCol is the number of user defined columns, then values of the \n** varints are set as follows:\n**\n**   Varint 0:       Total number of rows in the table.\n**\n**   Varint 1..nCol: For each column, the total number of tokens stored in\n**                   the column for all rows of the table.\n**\n**   Varint 1+nCol:  The total size, in bytes, of all text values in all\n**                   columns of all rows of the table.\n**\n*/\nstatic void fts3UpdateDocTotals(\n  int *pRC,                       /* The result code */\n  Fts3Table *p,                   /* Table being updated */\n  u32 *aSzIns,                    /* Size increases */\n  u32 *aSzDel,                    /* Size decreases */\n  int nChng                       /* Change in the number of documents */\n){\n  char *pBlob;             /* Storage for BLOB written into %_stat */\n  int nBlob;               /* Size of BLOB written into %_stat */\n  u32 *a;                  /* Array of integers that becomes the BLOB */\n  sqlite3_stmt *pStmt;     /* Statement for reading and writing */\n  int i;                   /* Loop counter */\n  int rc;                  /* Result code from subfunctions */\n\n  const int nStat = p->nColumn+2;\n\n  if( *pRC ) return;\n  a = sqlite3_malloc( (sizeof(u32)+10)*nStat );\n  if( a==0 ){\n    *pRC = SQLITE_NOMEM;\n    return;\n  }\n  pBlob = (char*)&a[nStat];\n  rc = fts3SqlStmt(p, SQL_SELECT_STAT, &pStmt, 0);\n  if( rc ){\n    sqlite3_free(a);\n    *pRC = rc;\n    return;\n  }\n  sqlite3_bind_int(pStmt, 1, FTS_STAT_DOCTOTAL);\n  if( sqlite3_step(pStmt)==SQLITE_ROW ){\n    fts3DecodeIntArray(nStat, a,\n         sqlite3_column_blob(pStmt, 0),\n         sqlite3_column_bytes(pStmt, 0));\n  }else{\n    memset(a, 0, sizeof(u32)*(nStat) );\n  }\n  rc = sqlite3_reset(pStmt);\n  if( rc!=SQLITE_OK ){\n    sqlite3_free(a);\n    *pRC = rc;\n    return;\n  }\n  if( nChng<0 && a[0]<(u32)(-nChng) ){\n    a[0] = 0;\n  }else{\n    a[0] += nChng;\n  }\n  for(i=0; i<p->nColumn+1; i++){\n    u32 x = a[i+1];\n    if( x+aSzIns[i] < aSzDel[i] ){\n      x = 0;\n    }else{\n      x = x + aSzIns[i] - aSzDel[i];\n    }\n    a[i+1] = x;\n  }\n  fts3EncodeIntArray(nStat, a, pBlob, &nBlob);\n  rc = fts3SqlStmt(p, SQL_REPLACE_STAT, &pStmt, 0);\n  if( rc ){\n    sqlite3_free(a);\n    *pRC = rc;\n    return;\n  }\n  sqlite3_bind_int(pStmt, 1, FTS_STAT_DOCTOTAL);\n  sqlite3_bind_blob(pStmt, 2, pBlob, nBlob, SQLITE_STATIC);\n  sqlite3_step(pStmt);\n  *pRC = sqlite3_reset(pStmt);\n  sqlite3_bind_null(pStmt, 2);\n  sqlite3_free(a);\n}\n\n/*\n** Merge the entire database so that there is one segment for each \n** iIndex/iLangid combination.\n*/\nstatic int fts3DoOptimize(Fts3Table *p, int bReturnDone){\n  int bSeenDone = 0;\n  int rc;\n  sqlite3_stmt *pAllLangid = 0;\n\n  rc = fts3SqlStmt(p, SQL_SELECT_ALL_LANGID, &pAllLangid, 0);\n  if( rc==SQLITE_OK ){\n    int rc2;\n    sqlite3_bind_int(pAllLangid, 1, p->iPrevLangid);\n    sqlite3_bind_int(pAllLangid, 2, p->nIndex);\n    while( sqlite3_step(pAllLangid)==SQLITE_ROW ){\n      int i;\n      int iLangid = sqlite3_column_int(pAllLangid, 0);\n      for(i=0; rc==SQLITE_OK && i<p->nIndex; i++){\n        rc = fts3SegmentMerge(p, iLangid, i, FTS3_SEGCURSOR_ALL);\n        if( rc==SQLITE_DONE ){\n          bSeenDone = 1;\n          rc = SQLITE_OK;\n        }\n      }\n    }\n    rc2 = sqlite3_reset(pAllLangid);\n    if( rc==SQLITE_OK ) rc = rc2;\n  }\n\n  sqlite3Fts3SegmentsClose(p);\n  sqlite3Fts3PendingTermsClear(p);\n\n  return (rc==SQLITE_OK && bReturnDone && bSeenDone) ? SQLITE_DONE : rc;\n}\n\n/*\n** This function is called when the user executes the following statement:\n**\n**     INSERT INTO <tbl>(<tbl>) VALUES('rebuild');\n**\n** The entire FTS index is discarded and rebuilt. If the table is one \n** created using the content=xxx option, then the new index is based on\n** the current contents of the xxx table. Otherwise, it is rebuilt based\n** on the contents of the %_content table.\n*/\nstatic int fts3DoRebuild(Fts3Table *p){\n  int rc;                         /* Return Code */\n\n  rc = fts3DeleteAll(p, 0);\n  if( rc==SQLITE_OK ){\n    u32 *aSz = 0;\n    u32 *aSzIns = 0;\n    u32 *aSzDel = 0;\n    sqlite3_stmt *pStmt = 0;\n    int nEntry = 0;\n\n    /* Compose and prepare an SQL statement to loop through the content table */\n    char *zSql = sqlite3_mprintf(\"SELECT %s\" , p->zReadExprlist);\n    if( !zSql ){\n      rc = SQLITE_NOMEM;\n    }else{\n      rc = sqlite3_prepare_v2(p->db, zSql, -1, &pStmt, 0);\n      sqlite3_free(zSql);\n    }\n\n    if( rc==SQLITE_OK ){\n      int nByte = sizeof(u32) * (p->nColumn+1)*3;\n      aSz = (u32 *)sqlite3_malloc(nByte);\n      if( aSz==0 ){\n        rc = SQLITE_NOMEM;\n      }else{\n        memset(aSz, 0, nByte);\n        aSzIns = &aSz[p->nColumn+1];\n        aSzDel = &aSzIns[p->nColumn+1];\n      }\n    }\n\n    while( rc==SQLITE_OK && SQLITE_ROW==sqlite3_step(pStmt) ){\n      int iCol;\n      int iLangid = langidFromSelect(p, pStmt);\n      rc = fts3PendingTermsDocid(p, 0, iLangid, sqlite3_column_int64(pStmt, 0));\n      memset(aSz, 0, sizeof(aSz[0]) * (p->nColumn+1));\n      for(iCol=0; rc==SQLITE_OK && iCol<p->nColumn; iCol++){\n        if( p->abNotindexed[iCol]==0 ){\n          const char *z = (const char *) sqlite3_column_text(pStmt, iCol+1);\n          rc = fts3PendingTermsAdd(p, iLangid, z, iCol, &aSz[iCol]);\n          aSz[p->nColumn] += sqlite3_column_bytes(pStmt, iCol+1);\n        }\n      }\n      if( p->bHasDocsize ){\n        fts3InsertDocsize(&rc, p, aSz);\n      }\n      if( rc!=SQLITE_OK ){\n        sqlite3_finalize(pStmt);\n        pStmt = 0;\n      }else{\n        nEntry++;\n        for(iCol=0; iCol<=p->nColumn; iCol++){\n          aSzIns[iCol] += aSz[iCol];\n        }\n      }\n    }\n    if( p->bFts4 ){\n      fts3UpdateDocTotals(&rc, p, aSzIns, aSzDel, nEntry);\n    }\n    sqlite3_free(aSz);\n\n    if( pStmt ){\n      int rc2 = sqlite3_finalize(pStmt);\n      if( rc==SQLITE_OK ){\n        rc = rc2;\n      }\n    }\n  }\n\n  return rc;\n}\n\n\n/*\n** This function opens a cursor used to read the input data for an \n** incremental merge operation. Specifically, it opens a cursor to scan\n** the oldest nSeg segments (idx=0 through idx=(nSeg-1)) in absolute \n** level iAbsLevel.\n*/\nstatic int fts3IncrmergeCsr(\n  Fts3Table *p,                   /* FTS3 table handle */\n  sqlite3_int64 iAbsLevel,        /* Absolute level to open */\n  int nSeg,                       /* Number of segments to merge */\n  Fts3MultiSegReader *pCsr        /* Cursor object to populate */\n){\n  int rc;                         /* Return Code */\n  sqlite3_stmt *pStmt = 0;        /* Statement used to read %_segdir entry */  \n  int nByte;                      /* Bytes allocated at pCsr->apSegment[] */\n\n  /* Allocate space for the Fts3MultiSegReader.aCsr[] array */\n  memset(pCsr, 0, sizeof(*pCsr));\n  nByte = sizeof(Fts3SegReader *) * nSeg;\n  pCsr->apSegment = (Fts3SegReader **)sqlite3_malloc(nByte);\n\n  if( pCsr->apSegment==0 ){\n    rc = SQLITE_NOMEM;\n  }else{\n    memset(pCsr->apSegment, 0, nByte);\n    rc = fts3SqlStmt(p, SQL_SELECT_LEVEL, &pStmt, 0);\n  }\n  if( rc==SQLITE_OK ){\n    int i;\n    int rc2;\n    sqlite3_bind_int64(pStmt, 1, iAbsLevel);\n    assert( pCsr->nSegment==0 );\n    for(i=0; rc==SQLITE_OK && sqlite3_step(pStmt)==SQLITE_ROW && i<nSeg; i++){\n      rc = sqlite3Fts3SegReaderNew(i, 0,\n          sqlite3_column_int64(pStmt, 1),        /* segdir.start_block */\n          sqlite3_column_int64(pStmt, 2),        /* segdir.leaves_end_block */\n          sqlite3_column_int64(pStmt, 3),        /* segdir.end_block */\n          sqlite3_column_blob(pStmt, 4),         /* segdir.root */\n          sqlite3_column_bytes(pStmt, 4),        /* segdir.root */\n          &pCsr->apSegment[i]\n      );\n      pCsr->nSegment++;\n    }\n    rc2 = sqlite3_reset(pStmt);\n    if( rc==SQLITE_OK ) rc = rc2;\n  }\n\n  return rc;\n}\n\ntypedef struct IncrmergeWriter IncrmergeWriter;\ntypedef struct NodeWriter NodeWriter;\ntypedef struct Blob Blob;\ntypedef struct NodeReader NodeReader;\n\n/*\n** An instance of the following structure is used as a dynamic buffer\n** to build up nodes or other blobs of data in.\n**\n** The function blobGrowBuffer() is used to extend the allocation.\n*/\nstruct Blob {\n  char *a;                        /* Pointer to allocation */\n  int n;                          /* Number of valid bytes of data in a[] */\n  int nAlloc;                     /* Allocated size of a[] (nAlloc>=n) */\n};\n\n/*\n** This structure is used to build up buffers containing segment b-tree \n** nodes (blocks).\n*/\nstruct NodeWriter {\n  sqlite3_int64 iBlock;           /* Current block id */\n  Blob key;                       /* Last key written to the current block */\n  Blob block;                     /* Current block image */\n};\n\n/*\n** An object of this type contains the state required to create or append\n** to an appendable b-tree segment.\n*/\nstruct IncrmergeWriter {\n  int nLeafEst;                   /* Space allocated for leaf blocks */\n  int nWork;                      /* Number of leaf pages flushed */\n  sqlite3_int64 iAbsLevel;        /* Absolute level of input segments */\n  int iIdx;                       /* Index of *output* segment in iAbsLevel+1 */\n  sqlite3_int64 iStart;           /* Block number of first allocated block */\n  sqlite3_int64 iEnd;             /* Block number of last allocated block */\n  sqlite3_int64 nLeafData;        /* Bytes of leaf page data so far */\n  u8 bNoLeafData;                 /* If true, store 0 for segment size */\n  NodeWriter aNodeWriter[FTS_MAX_APPENDABLE_HEIGHT];\n};\n\n/*\n** An object of the following type is used to read data from a single\n** FTS segment node. See the following functions:\n**\n**     nodeReaderInit()\n**     nodeReaderNext()\n**     nodeReaderRelease()\n*/\nstruct NodeReader {\n  const char *aNode;\n  int nNode;\n  int iOff;                       /* Current offset within aNode[] */\n\n  /* Output variables. Containing the current node entry. */\n  sqlite3_int64 iChild;           /* Pointer to child node */\n  Blob term;                      /* Current term */\n  const char *aDoclist;           /* Pointer to doclist */\n  int nDoclist;                   /* Size of doclist in bytes */\n};\n\n/*\n** If *pRc is not SQLITE_OK when this function is called, it is a no-op.\n** Otherwise, if the allocation at pBlob->a is not already at least nMin\n** bytes in size, extend (realloc) it to be so.\n**\n** If an OOM error occurs, set *pRc to SQLITE_NOMEM and leave pBlob->a\n** unmodified. Otherwise, if the allocation succeeds, update pBlob->nAlloc\n** to reflect the new size of the pBlob->a[] buffer.\n*/\nstatic void blobGrowBuffer(Blob *pBlob, int nMin, int *pRc){\n  if( *pRc==SQLITE_OK && nMin>pBlob->nAlloc ){\n    int nAlloc = nMin;\n    char *a = (char *)sqlite3_realloc(pBlob->a, nAlloc);\n    if( a ){\n      pBlob->nAlloc = nAlloc;\n      pBlob->a = a;\n    }else{\n      *pRc = SQLITE_NOMEM;\n    }\n  }\n}\n\n/*\n** Attempt to advance the node-reader object passed as the first argument to\n** the next entry on the node. \n**\n** Return an error code if an error occurs (SQLITE_NOMEM is possible). \n** Otherwise return SQLITE_OK. If there is no next entry on the node\n** (e.g. because the current entry is the last) set NodeReader->aNode to\n** NULL to indicate EOF. Otherwise, populate the NodeReader structure output \n** variables for the new entry.\n*/\nstatic int nodeReaderNext(NodeReader *p){\n  int bFirst = (p->term.n==0);    /* True for first term on the node */\n  int nPrefix = 0;                /* Bytes to copy from previous term */\n  int nSuffix = 0;                /* Bytes to append to the prefix */\n  int rc = SQLITE_OK;             /* Return code */\n\n  assert( p->aNode );\n  if( p->iChild && bFirst==0 ) p->iChild++;\n  if( p->iOff>=p->nNode ){\n    /* EOF */\n    p->aNode = 0;\n  }else{\n    if( bFirst==0 ){\n      p->iOff += fts3GetVarint32(&p->aNode[p->iOff], &nPrefix);\n    }\n    p->iOff += fts3GetVarint32(&p->aNode[p->iOff], &nSuffix);\n\n    blobGrowBuffer(&p->term, nPrefix+nSuffix, &rc);\n    if( rc==SQLITE_OK ){\n      memcpy(&p->term.a[nPrefix], &p->aNode[p->iOff], nSuffix);\n      p->term.n = nPrefix+nSuffix;\n      p->iOff += nSuffix;\n      if( p->iChild==0 ){\n        p->iOff += fts3GetVarint32(&p->aNode[p->iOff], &p->nDoclist);\n        p->aDoclist = &p->aNode[p->iOff];\n        p->iOff += p->nDoclist;\n      }\n    }\n  }\n\n  assert( p->iOff<=p->nNode );\n\n  return rc;\n}\n\n/*\n** Release all dynamic resources held by node-reader object *p.\n*/\nstatic void nodeReaderRelease(NodeReader *p){\n  sqlite3_free(p->term.a);\n}\n\n/*\n** Initialize a node-reader object to read the node in buffer aNode/nNode.\n**\n** If successful, SQLITE_OK is returned and the NodeReader object set to \n** point to the first entry on the node (if any). Otherwise, an SQLite\n** error code is returned.\n*/\nstatic int nodeReaderInit(NodeReader *p, const char *aNode, int nNode){\n  memset(p, 0, sizeof(NodeReader));\n  p->aNode = aNode;\n  p->nNode = nNode;\n\n  /* Figure out if this is a leaf or an internal node. */\n  if( p->aNode[0] ){\n    /* An internal node. */\n    p->iOff = 1 + sqlite3Fts3GetVarint(&p->aNode[1], &p->iChild);\n  }else{\n    p->iOff = 1;\n  }\n\n  return nodeReaderNext(p);\n}\n\n/*\n** This function is called while writing an FTS segment each time a leaf o\n** node is finished and written to disk. The key (zTerm/nTerm) is guaranteed\n** to be greater than the largest key on the node just written, but smaller\n** than or equal to the first key that will be written to the next leaf\n** node.\n**\n** The block id of the leaf node just written to disk may be found in\n** (pWriter->aNodeWriter[0].iBlock) when this function is called.\n*/\nstatic int fts3IncrmergePush(\n  Fts3Table *p,                   /* Fts3 table handle */\n  IncrmergeWriter *pWriter,       /* Writer object */\n  const char *zTerm,              /* Term to write to internal node */\n  int nTerm                       /* Bytes at zTerm */\n){\n  sqlite3_int64 iPtr = pWriter->aNodeWriter[0].iBlock;\n  int iLayer;\n\n  assert( nTerm>0 );\n  for(iLayer=1; ALWAYS(iLayer<FTS_MAX_APPENDABLE_HEIGHT); iLayer++){\n    sqlite3_int64 iNextPtr = 0;\n    NodeWriter *pNode = &pWriter->aNodeWriter[iLayer];\n    int rc = SQLITE_OK;\n    int nPrefix;\n    int nSuffix;\n    int nSpace;\n\n    /* Figure out how much space the key will consume if it is written to\n    ** the current node of layer iLayer. Due to the prefix compression, \n    ** the space required changes depending on which node the key is to\n    ** be added to.  */\n    nPrefix = fts3PrefixCompress(pNode->key.a, pNode->key.n, zTerm, nTerm);\n    nSuffix = nTerm - nPrefix;\n    nSpace  = sqlite3Fts3VarintLen(nPrefix);\n    nSpace += sqlite3Fts3VarintLen(nSuffix) + nSuffix;\n\n    if( pNode->key.n==0 || (pNode->block.n + nSpace)<=p->nNodeSize ){ \n      /* If the current node of layer iLayer contains zero keys, or if adding\n      ** the key to it will not cause it to grow to larger than nNodeSize \n      ** bytes in size, write the key here.  */\n\n      Blob *pBlk = &pNode->block;\n      if( pBlk->n==0 ){\n        blobGrowBuffer(pBlk, p->nNodeSize, &rc);\n        if( rc==SQLITE_OK ){\n          pBlk->a[0] = (char)iLayer;\n          pBlk->n = 1 + sqlite3Fts3PutVarint(&pBlk->a[1], iPtr);\n        }\n      }\n      blobGrowBuffer(pBlk, pBlk->n + nSpace, &rc);\n      blobGrowBuffer(&pNode->key, nTerm, &rc);\n\n      if( rc==SQLITE_OK ){\n        if( pNode->key.n ){\n          pBlk->n += sqlite3Fts3PutVarint(&pBlk->a[pBlk->n], nPrefix);\n        }\n        pBlk->n += sqlite3Fts3PutVarint(&pBlk->a[pBlk->n], nSuffix);\n        memcpy(&pBlk->a[pBlk->n], &zTerm[nPrefix], nSuffix);\n        pBlk->n += nSuffix;\n\n        memcpy(pNode->key.a, zTerm, nTerm);\n        pNode->key.n = nTerm;\n      }\n    }else{\n      /* Otherwise, flush the current node of layer iLayer to disk.\n      ** Then allocate a new, empty sibling node. The key will be written\n      ** into the parent of this node. */\n      rc = fts3WriteSegment(p, pNode->iBlock, pNode->block.a, pNode->block.n);\n\n      assert( pNode->block.nAlloc>=p->nNodeSize );\n      pNode->block.a[0] = (char)iLayer;\n      pNode->block.n = 1 + sqlite3Fts3PutVarint(&pNode->block.a[1], iPtr+1);\n\n      iNextPtr = pNode->iBlock;\n      pNode->iBlock++;\n      pNode->key.n = 0;\n    }\n\n    if( rc!=SQLITE_OK || iNextPtr==0 ) return rc;\n    iPtr = iNextPtr;\n  }\n\n  assert( 0 );\n  return 0;\n}\n\n/*\n** Append a term and (optionally) doclist to the FTS segment node currently\n** stored in blob *pNode. The node need not contain any terms, but the\n** header must be written before this function is called.\n**\n** A node header is a single 0x00 byte for a leaf node, or a height varint\n** followed by the left-hand-child varint for an internal node.\n**\n** The term to be appended is passed via arguments zTerm/nTerm. For a \n** leaf node, the doclist is passed as aDoclist/nDoclist. For an internal\n** node, both aDoclist and nDoclist must be passed 0.\n**\n** If the size of the value in blob pPrev is zero, then this is the first\n** term written to the node. Otherwise, pPrev contains a copy of the \n** previous term. Before this function returns, it is updated to contain a\n** copy of zTerm/nTerm.\n**\n** It is assumed that the buffer associated with pNode is already large\n** enough to accommodate the new entry. The buffer associated with pPrev\n** is extended by this function if requrired.\n**\n** If an error (i.e. OOM condition) occurs, an SQLite error code is\n** returned. Otherwise, SQLITE_OK.\n*/\nstatic int fts3AppendToNode(\n  Blob *pNode,                    /* Current node image to append to */\n  Blob *pPrev,                    /* Buffer containing previous term written */\n  const char *zTerm,              /* New term to write */\n  int nTerm,                      /* Size of zTerm in bytes */\n  const char *aDoclist,           /* Doclist (or NULL) to write */\n  int nDoclist                    /* Size of aDoclist in bytes */ \n){\n  int rc = SQLITE_OK;             /* Return code */\n  int bFirst = (pPrev->n==0);     /* True if this is the first term written */\n  int nPrefix;                    /* Size of term prefix in bytes */\n  int nSuffix;                    /* Size of term suffix in bytes */\n\n  /* Node must have already been started. There must be a doclist for a\n  ** leaf node, and there must not be a doclist for an internal node.  */\n  assert( pNode->n>0 );\n  assert( (pNode->a[0]=='\\0')==(aDoclist!=0) );\n\n  blobGrowBuffer(pPrev, nTerm, &rc);\n  if( rc!=SQLITE_OK ) return rc;\n\n  nPrefix = fts3PrefixCompress(pPrev->a, pPrev->n, zTerm, nTerm);\n  nSuffix = nTerm - nPrefix;\n  memcpy(pPrev->a, zTerm, nTerm);\n  pPrev->n = nTerm;\n\n  if( bFirst==0 ){\n    pNode->n += sqlite3Fts3PutVarint(&pNode->a[pNode->n], nPrefix);\n  }\n  pNode->n += sqlite3Fts3PutVarint(&pNode->a[pNode->n], nSuffix);\n  memcpy(&pNode->a[pNode->n], &zTerm[nPrefix], nSuffix);\n  pNode->n += nSuffix;\n\n  if( aDoclist ){\n    pNode->n += sqlite3Fts3PutVarint(&pNode->a[pNode->n], nDoclist);\n    memcpy(&pNode->a[pNode->n], aDoclist, nDoclist);\n    pNode->n += nDoclist;\n  }\n\n  assert( pNode->n<=pNode->nAlloc );\n\n  return SQLITE_OK;\n}\n\n/*\n** Append the current term and doclist pointed to by cursor pCsr to the\n** appendable b-tree segment opened for writing by pWriter.\n**\n** Return SQLITE_OK if successful, or an SQLite error code otherwise.\n*/\nstatic int fts3IncrmergeAppend(\n  Fts3Table *p,                   /* Fts3 table handle */\n  IncrmergeWriter *pWriter,       /* Writer object */\n  Fts3MultiSegReader *pCsr        /* Cursor containing term and doclist */\n){\n  const char *zTerm = pCsr->zTerm;\n  int nTerm = pCsr->nTerm;\n  const char *aDoclist = pCsr->aDoclist;\n  int nDoclist = pCsr->nDoclist;\n  int rc = SQLITE_OK;           /* Return code */\n  int nSpace;                   /* Total space in bytes required on leaf */\n  int nPrefix;                  /* Size of prefix shared with previous term */\n  int nSuffix;                  /* Size of suffix (nTerm - nPrefix) */\n  NodeWriter *pLeaf;            /* Object used to write leaf nodes */\n\n  pLeaf = &pWriter->aNodeWriter[0];\n  nPrefix = fts3PrefixCompress(pLeaf->key.a, pLeaf->key.n, zTerm, nTerm);\n  nSuffix = nTerm - nPrefix;\n\n  nSpace  = sqlite3Fts3VarintLen(nPrefix);\n  nSpace += sqlite3Fts3VarintLen(nSuffix) + nSuffix;\n  nSpace += sqlite3Fts3VarintLen(nDoclist) + nDoclist;\n\n  /* If the current block is not empty, and if adding this term/doclist\n  ** to the current block would make it larger than Fts3Table.nNodeSize\n  ** bytes, write this block out to the database. */\n  if( pLeaf->block.n>0 && (pLeaf->block.n + nSpace)>p->nNodeSize ){\n    rc = fts3WriteSegment(p, pLeaf->iBlock, pLeaf->block.a, pLeaf->block.n);\n    pWriter->nWork++;\n\n    /* Add the current term to the parent node. The term added to the \n    ** parent must:\n    **\n    **   a) be greater than the largest term on the leaf node just written\n    **      to the database (still available in pLeaf->key), and\n    **\n    **   b) be less than or equal to the term about to be added to the new\n    **      leaf node (zTerm/nTerm).\n    **\n    ** In other words, it must be the prefix of zTerm 1 byte longer than\n    ** the common prefix (if any) of zTerm and pWriter->zTerm.\n    */\n    if( rc==SQLITE_OK ){\n      rc = fts3IncrmergePush(p, pWriter, zTerm, nPrefix+1);\n    }\n\n    /* Advance to the next output block */\n    pLeaf->iBlock++;\n    pLeaf->key.n = 0;\n    pLeaf->block.n = 0;\n\n    nSuffix = nTerm;\n    nSpace  = 1;\n    nSpace += sqlite3Fts3VarintLen(nSuffix) + nSuffix;\n    nSpace += sqlite3Fts3VarintLen(nDoclist) + nDoclist;\n  }\n\n  pWriter->nLeafData += nSpace;\n  blobGrowBuffer(&pLeaf->block, pLeaf->block.n + nSpace, &rc);\n  if( rc==SQLITE_OK ){\n    if( pLeaf->block.n==0 ){\n      pLeaf->block.n = 1;\n      pLeaf->block.a[0] = '\\0';\n    }\n    rc = fts3AppendToNode(\n        &pLeaf->block, &pLeaf->key, zTerm, nTerm, aDoclist, nDoclist\n    );\n  }\n\n  return rc;\n}\n\n/*\n** This function is called to release all dynamic resources held by the\n** merge-writer object pWriter, and if no error has occurred, to flush\n** all outstanding node buffers held by pWriter to disk.\n**\n** If *pRc is not SQLITE_OK when this function is called, then no attempt\n** is made to write any data to disk. Instead, this function serves only\n** to release outstanding resources.\n**\n** Otherwise, if *pRc is initially SQLITE_OK and an error occurs while\n** flushing buffers to disk, *pRc is set to an SQLite error code before\n** returning.\n*/\nstatic void fts3IncrmergeRelease(\n  Fts3Table *p,                   /* FTS3 table handle */\n  IncrmergeWriter *pWriter,       /* Merge-writer object */\n  int *pRc                        /* IN/OUT: Error code */\n){\n  int i;                          /* Used to iterate through non-root layers */\n  int iRoot;                      /* Index of root in pWriter->aNodeWriter */\n  NodeWriter *pRoot;              /* NodeWriter for root node */\n  int rc = *pRc;                  /* Error code */\n\n  /* Set iRoot to the index in pWriter->aNodeWriter[] of the output segment \n  ** root node. If the segment fits entirely on a single leaf node, iRoot\n  ** will be set to 0. If the root node is the parent of the leaves, iRoot\n  ** will be 1. And so on.  */\n  for(iRoot=FTS_MAX_APPENDABLE_HEIGHT-1; iRoot>=0; iRoot--){\n    NodeWriter *pNode = &pWriter->aNodeWriter[iRoot];\n    if( pNode->block.n>0 ) break;\n    assert( *pRc || pNode->block.nAlloc==0 );\n    assert( *pRc || pNode->key.nAlloc==0 );\n    sqlite3_free(pNode->block.a);\n    sqlite3_free(pNode->key.a);\n  }\n\n  /* Empty output segment. This is a no-op. */\n  if( iRoot<0 ) return;\n\n  /* The entire output segment fits on a single node. Normally, this means\n  ** the node would be stored as a blob in the \"root\" column of the %_segdir\n  ** table. However, this is not permitted in this case. The problem is that \n  ** space has already been reserved in the %_segments table, and so the \n  ** start_block and end_block fields of the %_segdir table must be populated. \n  ** And, by design or by accident, released versions of FTS cannot handle \n  ** segments that fit entirely on the root node with start_block!=0.\n  **\n  ** Instead, create a synthetic root node that contains nothing but a \n  ** pointer to the single content node. So that the segment consists of a\n  ** single leaf and a single interior (root) node.\n  **\n  ** Todo: Better might be to defer allocating space in the %_segments \n  ** table until we are sure it is needed.\n  */\n  if( iRoot==0 ){\n    Blob *pBlock = &pWriter->aNodeWriter[1].block;\n    blobGrowBuffer(pBlock, 1 + FTS3_VARINT_MAX, &rc);\n    if( rc==SQLITE_OK ){\n      pBlock->a[0] = 0x01;\n      pBlock->n = 1 + sqlite3Fts3PutVarint(\n          &pBlock->a[1], pWriter->aNodeWriter[0].iBlock\n      );\n    }\n    iRoot = 1;\n  }\n  pRoot = &pWriter->aNodeWriter[iRoot];\n\n  /* Flush all currently outstanding nodes to disk. */\n  for(i=0; i<iRoot; i++){\n    NodeWriter *pNode = &pWriter->aNodeWriter[i];\n    if( pNode->block.n>0 && rc==SQLITE_OK ){\n      rc = fts3WriteSegment(p, pNode->iBlock, pNode->block.a, pNode->block.n);\n    }\n    sqlite3_free(pNode->block.a);\n    sqlite3_free(pNode->key.a);\n  }\n\n  /* Write the %_segdir record. */\n  if( rc==SQLITE_OK ){\n    rc = fts3WriteSegdir(p, \n        pWriter->iAbsLevel+1,               /* level */\n        pWriter->iIdx,                      /* idx */\n        pWriter->iStart,                    /* start_block */\n        pWriter->aNodeWriter[0].iBlock,     /* leaves_end_block */\n        pWriter->iEnd,                      /* end_block */\n        (pWriter->bNoLeafData==0 ? pWriter->nLeafData : 0),   /* end_block */\n        pRoot->block.a, pRoot->block.n      /* root */\n    );\n  }\n  sqlite3_free(pRoot->block.a);\n  sqlite3_free(pRoot->key.a);\n\n  *pRc = rc;\n}\n\n/*\n** Compare the term in buffer zLhs (size in bytes nLhs) with that in\n** zRhs (size in bytes nRhs) using memcmp. If one term is a prefix of\n** the other, it is considered to be smaller than the other.\n**\n** Return -ve if zLhs is smaller than zRhs, 0 if it is equal, or +ve\n** if it is greater.\n*/\nstatic int fts3TermCmp(\n  const char *zLhs, int nLhs,     /* LHS of comparison */\n  const char *zRhs, int nRhs      /* RHS of comparison */\n){\n  int nCmp = MIN(nLhs, nRhs);\n  int res;\n\n  res = memcmp(zLhs, zRhs, nCmp);\n  if( res==0 ) res = nLhs - nRhs;\n\n  return res;\n}\n\n\n/*\n** Query to see if the entry in the %_segments table with blockid iEnd is \n** NULL. If no error occurs and the entry is NULL, set *pbRes 1 before\n** returning. Otherwise, set *pbRes to 0. \n**\n** Or, if an error occurs while querying the database, return an SQLite \n** error code. The final value of *pbRes is undefined in this case.\n**\n** This is used to test if a segment is an \"appendable\" segment. If it\n** is, then a NULL entry has been inserted into the %_segments table\n** with blockid %_segdir.end_block.\n*/\nstatic int fts3IsAppendable(Fts3Table *p, sqlite3_int64 iEnd, int *pbRes){\n  int bRes = 0;                   /* Result to set *pbRes to */\n  sqlite3_stmt *pCheck = 0;       /* Statement to query database with */\n  int rc;                         /* Return code */\n\n  rc = fts3SqlStmt(p, SQL_SEGMENT_IS_APPENDABLE, &pCheck, 0);\n  if( rc==SQLITE_OK ){\n    sqlite3_bind_int64(pCheck, 1, iEnd);\n    if( SQLITE_ROW==sqlite3_step(pCheck) ) bRes = 1;\n    rc = sqlite3_reset(pCheck);\n  }\n  \n  *pbRes = bRes;\n  return rc;\n}\n\n/*\n** This function is called when initializing an incremental-merge operation.\n** It checks if the existing segment with index value iIdx at absolute level \n** (iAbsLevel+1) can be appended to by the incremental merge. If it can, the\n** merge-writer object *pWriter is initialized to write to it.\n**\n** An existing segment can be appended to by an incremental merge if:\n**\n**   * It was initially created as an appendable segment (with all required\n**     space pre-allocated), and\n**\n**   * The first key read from the input (arguments zKey and nKey) is \n**     greater than the largest key currently stored in the potential\n**     output segment.\n*/\nstatic int fts3IncrmergeLoad(\n  Fts3Table *p,                   /* Fts3 table handle */\n  sqlite3_int64 iAbsLevel,        /* Absolute level of input segments */\n  int iIdx,                       /* Index of candidate output segment */\n  const char *zKey,               /* First key to write */\n  int nKey,                       /* Number of bytes in nKey */\n  IncrmergeWriter *pWriter        /* Populate this object */\n){\n  int rc;                         /* Return code */\n  sqlite3_stmt *pSelect = 0;      /* SELECT to read %_segdir entry */\n\n  rc = fts3SqlStmt(p, SQL_SELECT_SEGDIR, &pSelect, 0);\n  if( rc==SQLITE_OK ){\n    sqlite3_int64 iStart = 0;     /* Value of %_segdir.start_block */\n    sqlite3_int64 iLeafEnd = 0;   /* Value of %_segdir.leaves_end_block */\n    sqlite3_int64 iEnd = 0;       /* Value of %_segdir.end_block */\n    const char *aRoot = 0;        /* Pointer to %_segdir.root buffer */\n    int nRoot = 0;                /* Size of aRoot[] in bytes */\n    int rc2;                      /* Return code from sqlite3_reset() */\n    int bAppendable = 0;          /* Set to true if segment is appendable */\n\n    /* Read the %_segdir entry for index iIdx absolute level (iAbsLevel+1) */\n    sqlite3_bind_int64(pSelect, 1, iAbsLevel+1);\n    sqlite3_bind_int(pSelect, 2, iIdx);\n    if( sqlite3_step(pSelect)==SQLITE_ROW ){\n      iStart = sqlite3_column_int64(pSelect, 1);\n      iLeafEnd = sqlite3_column_int64(pSelect, 2);\n      fts3ReadEndBlockField(pSelect, 3, &iEnd, &pWriter->nLeafData);\n      if( pWriter->nLeafData<0 ){\n        pWriter->nLeafData = pWriter->nLeafData * -1;\n      }\n      pWriter->bNoLeafData = (pWriter->nLeafData==0);\n      nRoot = sqlite3_column_bytes(pSelect, 4);\n      aRoot = sqlite3_column_blob(pSelect, 4);\n    }else{\n      return sqlite3_reset(pSelect);\n    }\n\n    /* Check for the zero-length marker in the %_segments table */\n    rc = fts3IsAppendable(p, iEnd, &bAppendable);\n\n    /* Check that zKey/nKey is larger than the largest key the candidate */\n    if( rc==SQLITE_OK && bAppendable ){\n      char *aLeaf = 0;\n      int nLeaf = 0;\n\n      rc = sqlite3Fts3ReadBlock(p, iLeafEnd, &aLeaf, &nLeaf, 0);\n      if( rc==SQLITE_OK ){\n        NodeReader reader;\n        for(rc = nodeReaderInit(&reader, aLeaf, nLeaf);\n            rc==SQLITE_OK && reader.aNode;\n            rc = nodeReaderNext(&reader)\n        ){\n          assert( reader.aNode );\n        }\n        if( fts3TermCmp(zKey, nKey, reader.term.a, reader.term.n)<=0 ){\n          bAppendable = 0;\n        }\n        nodeReaderRelease(&reader);\n      }\n      sqlite3_free(aLeaf);\n    }\n\n    if( rc==SQLITE_OK && bAppendable ){\n      /* It is possible to append to this segment. Set up the IncrmergeWriter\n      ** object to do so.  */\n      int i;\n      int nHeight = (int)aRoot[0];\n      NodeWriter *pNode;\n\n      pWriter->nLeafEst = (int)((iEnd - iStart) + 1)/FTS_MAX_APPENDABLE_HEIGHT;\n      pWriter->iStart = iStart;\n      pWriter->iEnd = iEnd;\n      pWriter->iAbsLevel = iAbsLevel;\n      pWriter->iIdx = iIdx;\n\n      for(i=nHeight+1; i<FTS_MAX_APPENDABLE_HEIGHT; i++){\n        pWriter->aNodeWriter[i].iBlock = pWriter->iStart + i*pWriter->nLeafEst;\n      }\n\n      pNode = &pWriter->aNodeWriter[nHeight];\n      pNode->iBlock = pWriter->iStart + pWriter->nLeafEst*nHeight;\n      blobGrowBuffer(&pNode->block, MAX(nRoot, p->nNodeSize), &rc);\n      if( rc==SQLITE_OK ){\n        memcpy(pNode->block.a, aRoot, nRoot);\n        pNode->block.n = nRoot;\n      }\n\n      for(i=nHeight; i>=0 && rc==SQLITE_OK; i--){\n        NodeReader reader;\n        pNode = &pWriter->aNodeWriter[i];\n\n        rc = nodeReaderInit(&reader, pNode->block.a, pNode->block.n);\n        while( reader.aNode && rc==SQLITE_OK ) rc = nodeReaderNext(&reader);\n        blobGrowBuffer(&pNode->key, reader.term.n, &rc);\n        if( rc==SQLITE_OK ){\n          memcpy(pNode->key.a, reader.term.a, reader.term.n);\n          pNode->key.n = reader.term.n;\n          if( i>0 ){\n            char *aBlock = 0;\n            int nBlock = 0;\n            pNode = &pWriter->aNodeWriter[i-1];\n            pNode->iBlock = reader.iChild;\n            rc = sqlite3Fts3ReadBlock(p, reader.iChild, &aBlock, &nBlock, 0);\n            blobGrowBuffer(&pNode->block, MAX(nBlock, p->nNodeSize), &rc);\n            if( rc==SQLITE_OK ){\n              memcpy(pNode->block.a, aBlock, nBlock);\n              pNode->block.n = nBlock;\n            }\n            sqlite3_free(aBlock);\n          }\n        }\n        nodeReaderRelease(&reader);\n      }\n    }\n\n    rc2 = sqlite3_reset(pSelect);\n    if( rc==SQLITE_OK ) rc = rc2;\n  }\n\n  return rc;\n}\n\n/*\n** Determine the largest segment index value that exists within absolute\n** level iAbsLevel+1. If no error occurs, set *piIdx to this value plus\n** one before returning SQLITE_OK. Or, if there are no segments at all \n** within level iAbsLevel, set *piIdx to zero.\n**\n** If an error occurs, return an SQLite error code. The final value of\n** *piIdx is undefined in this case.\n*/\nstatic int fts3IncrmergeOutputIdx( \n  Fts3Table *p,                   /* FTS Table handle */\n  sqlite3_int64 iAbsLevel,        /* Absolute index of input segments */\n  int *piIdx                      /* OUT: Next free index at iAbsLevel+1 */\n){\n  int rc;\n  sqlite3_stmt *pOutputIdx = 0;   /* SQL used to find output index */\n\n  rc = fts3SqlStmt(p, SQL_NEXT_SEGMENT_INDEX, &pOutputIdx, 0);\n  if( rc==SQLITE_OK ){\n    sqlite3_bind_int64(pOutputIdx, 1, iAbsLevel+1);\n    sqlite3_step(pOutputIdx);\n    *piIdx = sqlite3_column_int(pOutputIdx, 0);\n    rc = sqlite3_reset(pOutputIdx);\n  }\n\n  return rc;\n}\n\n/* \n** Allocate an appendable output segment on absolute level iAbsLevel+1\n** with idx value iIdx.\n**\n** In the %_segdir table, a segment is defined by the values in three\n** columns:\n**\n**     start_block\n**     leaves_end_block\n**     end_block\n**\n** When an appendable segment is allocated, it is estimated that the\n** maximum number of leaf blocks that may be required is the sum of the\n** number of leaf blocks consumed by the input segments, plus the number\n** of input segments, multiplied by two. This value is stored in stack \n** variable nLeafEst.\n**\n** A total of 16*nLeafEst blocks are allocated when an appendable segment\n** is created ((1 + end_block - start_block)==16*nLeafEst). The contiguous\n** array of leaf nodes starts at the first block allocated. The array\n** of interior nodes that are parents of the leaf nodes start at block\n** (start_block + (1 + end_block - start_block) / 16). And so on.\n**\n** In the actual code below, the value \"16\" is replaced with the \n** pre-processor macro FTS_MAX_APPENDABLE_HEIGHT.\n*/\nstatic int fts3IncrmergeWriter( \n  Fts3Table *p,                   /* Fts3 table handle */\n  sqlite3_int64 iAbsLevel,        /* Absolute level of input segments */\n  int iIdx,                       /* Index of new output segment */\n  Fts3MultiSegReader *pCsr,       /* Cursor that data will be read from */\n  IncrmergeWriter *pWriter        /* Populate this object */\n){\n  int rc;                         /* Return Code */\n  int i;                          /* Iterator variable */\n  int nLeafEst = 0;               /* Blocks allocated for leaf nodes */\n  sqlite3_stmt *pLeafEst = 0;     /* SQL used to determine nLeafEst */\n  sqlite3_stmt *pFirstBlock = 0;  /* SQL used to determine first block */\n\n  /* Calculate nLeafEst. */\n  rc = fts3SqlStmt(p, SQL_MAX_LEAF_NODE_ESTIMATE, &pLeafEst, 0);\n  if( rc==SQLITE_OK ){\n    sqlite3_bind_int64(pLeafEst, 1, iAbsLevel);\n    sqlite3_bind_int64(pLeafEst, 2, pCsr->nSegment);\n    if( SQLITE_ROW==sqlite3_step(pLeafEst) ){\n      nLeafEst = sqlite3_column_int(pLeafEst, 0);\n    }\n    rc = sqlite3_reset(pLeafEst);\n  }\n  if( rc!=SQLITE_OK ) return rc;\n\n  /* Calculate the first block to use in the output segment */\n  rc = fts3SqlStmt(p, SQL_NEXT_SEGMENTS_ID, &pFirstBlock, 0);\n  if( rc==SQLITE_OK ){\n    if( SQLITE_ROW==sqlite3_step(pFirstBlock) ){\n      pWriter->iStart = sqlite3_column_int64(pFirstBlock, 0);\n      pWriter->iEnd = pWriter->iStart - 1;\n      pWriter->iEnd += nLeafEst * FTS_MAX_APPENDABLE_HEIGHT;\n    }\n    rc = sqlite3_reset(pFirstBlock);\n  }\n  if( rc!=SQLITE_OK ) return rc;\n\n  /* Insert the marker in the %_segments table to make sure nobody tries\n  ** to steal the space just allocated. This is also used to identify \n  ** appendable segments.  */\n  rc = fts3WriteSegment(p, pWriter->iEnd, 0, 0);\n  if( rc!=SQLITE_OK ) return rc;\n\n  pWriter->iAbsLevel = iAbsLevel;\n  pWriter->nLeafEst = nLeafEst;\n  pWriter->iIdx = iIdx;\n\n  /* Set up the array of NodeWriter objects */\n  for(i=0; i<FTS_MAX_APPENDABLE_HEIGHT; i++){\n    pWriter->aNodeWriter[i].iBlock = pWriter->iStart + i*pWriter->nLeafEst;\n  }\n  return SQLITE_OK;\n}\n\n/*\n** Remove an entry from the %_segdir table. This involves running the \n** following two statements:\n**\n**   DELETE FROM %_segdir WHERE level = :iAbsLevel AND idx = :iIdx\n**   UPDATE %_segdir SET idx = idx - 1 WHERE level = :iAbsLevel AND idx > :iIdx\n**\n** The DELETE statement removes the specific %_segdir level. The UPDATE \n** statement ensures that the remaining segments have contiguously allocated\n** idx values.\n*/\nstatic int fts3RemoveSegdirEntry(\n  Fts3Table *p,                   /* FTS3 table handle */\n  sqlite3_int64 iAbsLevel,        /* Absolute level to delete from */\n  int iIdx                        /* Index of %_segdir entry to delete */\n){\n  int rc;                         /* Return code */\n  sqlite3_stmt *pDelete = 0;      /* DELETE statement */\n\n  rc = fts3SqlStmt(p, SQL_DELETE_SEGDIR_ENTRY, &pDelete, 0);\n  if( rc==SQLITE_OK ){\n    sqlite3_bind_int64(pDelete, 1, iAbsLevel);\n    sqlite3_bind_int(pDelete, 2, iIdx);\n    sqlite3_step(pDelete);\n    rc = sqlite3_reset(pDelete);\n  }\n\n  return rc;\n}\n\n/*\n** One or more segments have just been removed from absolute level iAbsLevel.\n** Update the 'idx' values of the remaining segments in the level so that\n** the idx values are a contiguous sequence starting from 0.\n*/\nstatic int fts3RepackSegdirLevel(\n  Fts3Table *p,                   /* FTS3 table handle */\n  sqlite3_int64 iAbsLevel         /* Absolute level to repack */\n){\n  int rc;                         /* Return code */\n  int *aIdx = 0;                  /* Array of remaining idx values */\n  int nIdx = 0;                   /* Valid entries in aIdx[] */\n  int nAlloc = 0;                 /* Allocated size of aIdx[] */\n  int i;                          /* Iterator variable */\n  sqlite3_stmt *pSelect = 0;      /* Select statement to read idx values */\n  sqlite3_stmt *pUpdate = 0;      /* Update statement to modify idx values */\n\n  rc = fts3SqlStmt(p, SQL_SELECT_INDEXES, &pSelect, 0);\n  if( rc==SQLITE_OK ){\n    int rc2;\n    sqlite3_bind_int64(pSelect, 1, iAbsLevel);\n    while( SQLITE_ROW==sqlite3_step(pSelect) ){\n      if( nIdx>=nAlloc ){\n        int *aNew;\n        nAlloc += 16;\n        aNew = sqlite3_realloc(aIdx, nAlloc*sizeof(int));\n        if( !aNew ){\n          rc = SQLITE_NOMEM;\n          break;\n        }\n        aIdx = aNew;\n      }\n      aIdx[nIdx++] = sqlite3_column_int(pSelect, 0);\n    }\n    rc2 = sqlite3_reset(pSelect);\n    if( rc==SQLITE_OK ) rc = rc2;\n  }\n\n  if( rc==SQLITE_OK ){\n    rc = fts3SqlStmt(p, SQL_SHIFT_SEGDIR_ENTRY, &pUpdate, 0);\n  }\n  if( rc==SQLITE_OK ){\n    sqlite3_bind_int64(pUpdate, 2, iAbsLevel);\n  }\n\n  assert( p->bIgnoreSavepoint==0 );\n  p->bIgnoreSavepoint = 1;\n  for(i=0; rc==SQLITE_OK && i<nIdx; i++){\n    if( aIdx[i]!=i ){\n      sqlite3_bind_int(pUpdate, 3, aIdx[i]);\n      sqlite3_bind_int(pUpdate, 1, i);\n      sqlite3_step(pUpdate);\n      rc = sqlite3_reset(pUpdate);\n    }\n  }\n  p->bIgnoreSavepoint = 0;\n\n  sqlite3_free(aIdx);\n  return rc;\n}\n\nstatic void fts3StartNode(Blob *pNode, int iHeight, sqlite3_int64 iChild){\n  pNode->a[0] = (char)iHeight;\n  if( iChild ){\n    assert( pNode->nAlloc>=1+sqlite3Fts3VarintLen(iChild) );\n    pNode->n = 1 + sqlite3Fts3PutVarint(&pNode->a[1], iChild);\n  }else{\n    assert( pNode->nAlloc>=1 );\n    pNode->n = 1;\n  }\n}\n\n/*\n** The first two arguments are a pointer to and the size of a segment b-tree\n** node. The node may be a leaf or an internal node.\n**\n** This function creates a new node image in blob object *pNew by copying\n** all terms that are greater than or equal to zTerm/nTerm (for leaf nodes)\n** or greater than zTerm/nTerm (for internal nodes) from aNode/nNode.\n*/\nstatic int fts3TruncateNode(\n  const char *aNode,              /* Current node image */\n  int nNode,                      /* Size of aNode in bytes */\n  Blob *pNew,                     /* OUT: Write new node image here */\n  const char *zTerm,              /* Omit all terms smaller than this */\n  int nTerm,                      /* Size of zTerm in bytes */\n  sqlite3_int64 *piBlock          /* OUT: Block number in next layer down */\n){\n  NodeReader reader;              /* Reader object */\n  Blob prev = {0, 0, 0};          /* Previous term written to new node */\n  int rc = SQLITE_OK;             /* Return code */\n  int bLeaf = aNode[0]=='\\0';     /* True for a leaf node */\n\n  /* Allocate required output space */\n  blobGrowBuffer(pNew, nNode, &rc);\n  if( rc!=SQLITE_OK ) return rc;\n  pNew->n = 0;\n\n  /* Populate new node buffer */\n  for(rc = nodeReaderInit(&reader, aNode, nNode); \n      rc==SQLITE_OK && reader.aNode; \n      rc = nodeReaderNext(&reader)\n  ){\n    if( pNew->n==0 ){\n      int res = fts3TermCmp(reader.term.a, reader.term.n, zTerm, nTerm);\n      if( res<0 || (bLeaf==0 && res==0) ) continue;\n      fts3StartNode(pNew, (int)aNode[0], reader.iChild);\n      *piBlock = reader.iChild;\n    }\n    rc = fts3AppendToNode(\n        pNew, &prev, reader.term.a, reader.term.n,\n        reader.aDoclist, reader.nDoclist\n    );\n    if( rc!=SQLITE_OK ) break;\n  }\n  if( pNew->n==0 ){\n    fts3StartNode(pNew, (int)aNode[0], reader.iChild);\n    *piBlock = reader.iChild;\n  }\n  assert( pNew->n<=pNew->nAlloc );\n\n  nodeReaderRelease(&reader);\n  sqlite3_free(prev.a);\n  return rc;\n}\n\n/*\n** Remove all terms smaller than zTerm/nTerm from segment iIdx in absolute \n** level iAbsLevel. This may involve deleting entries from the %_segments\n** table, and modifying existing entries in both the %_segments and %_segdir\n** tables.\n**\n** SQLITE_OK is returned if the segment is updated successfully. Or an\n** SQLite error code otherwise.\n*/\nstatic int fts3TruncateSegment(\n  Fts3Table *p,                   /* FTS3 table handle */\n  sqlite3_int64 iAbsLevel,        /* Absolute level of segment to modify */\n  int iIdx,                       /* Index within level of segment to modify */\n  const char *zTerm,              /* Remove terms smaller than this */\n  int nTerm                      /* Number of bytes in buffer zTerm */\n){\n  int rc = SQLITE_OK;             /* Return code */\n  Blob root = {0,0,0};            /* New root page image */\n  Blob block = {0,0,0};           /* Buffer used for any other block */\n  sqlite3_int64 iBlock = 0;       /* Block id */\n  sqlite3_int64 iNewStart = 0;    /* New value for iStartBlock */\n  sqlite3_int64 iOldStart = 0;    /* Old value for iStartBlock */\n  sqlite3_stmt *pFetch = 0;       /* Statement used to fetch segdir */\n\n  rc = fts3SqlStmt(p, SQL_SELECT_SEGDIR, &pFetch, 0);\n  if( rc==SQLITE_OK ){\n    int rc2;                      /* sqlite3_reset() return code */\n    sqlite3_bind_int64(pFetch, 1, iAbsLevel);\n    sqlite3_bind_int(pFetch, 2, iIdx);\n    if( SQLITE_ROW==sqlite3_step(pFetch) ){\n      const char *aRoot = sqlite3_column_blob(pFetch, 4);\n      int nRoot = sqlite3_column_bytes(pFetch, 4);\n      iOldStart = sqlite3_column_int64(pFetch, 1);\n      rc = fts3TruncateNode(aRoot, nRoot, &root, zTerm, nTerm, &iBlock);\n    }\n    rc2 = sqlite3_reset(pFetch);\n    if( rc==SQLITE_OK ) rc = rc2;\n  }\n\n  while( rc==SQLITE_OK && iBlock ){\n    char *aBlock = 0;\n    int nBlock = 0;\n    iNewStart = iBlock;\n\n    rc = sqlite3Fts3ReadBlock(p, iBlock, &aBlock, &nBlock, 0);\n    if( rc==SQLITE_OK ){\n      rc = fts3TruncateNode(aBlock, nBlock, &block, zTerm, nTerm, &iBlock);\n    }\n    if( rc==SQLITE_OK ){\n      rc = fts3WriteSegment(p, iNewStart, block.a, block.n);\n    }\n    sqlite3_free(aBlock);\n  }\n\n  /* Variable iNewStart now contains the first valid leaf node. */\n  if( rc==SQLITE_OK && iNewStart ){\n    sqlite3_stmt *pDel = 0;\n    rc = fts3SqlStmt(p, SQL_DELETE_SEGMENTS_RANGE, &pDel, 0);\n    if( rc==SQLITE_OK ){\n      sqlite3_bind_int64(pDel, 1, iOldStart);\n      sqlite3_bind_int64(pDel, 2, iNewStart-1);\n      sqlite3_step(pDel);\n      rc = sqlite3_reset(pDel);\n    }\n  }\n\n  if( rc==SQLITE_OK ){\n    sqlite3_stmt *pChomp = 0;\n    rc = fts3SqlStmt(p, SQL_CHOMP_SEGDIR, &pChomp, 0);\n    if( rc==SQLITE_OK ){\n      sqlite3_bind_int64(pChomp, 1, iNewStart);\n      sqlite3_bind_blob(pChomp, 2, root.a, root.n, SQLITE_STATIC);\n      sqlite3_bind_int64(pChomp, 3, iAbsLevel);\n      sqlite3_bind_int(pChomp, 4, iIdx);\n      sqlite3_step(pChomp);\n      rc = sqlite3_reset(pChomp);\n      sqlite3_bind_null(pChomp, 2);\n    }\n  }\n\n  sqlite3_free(root.a);\n  sqlite3_free(block.a);\n  return rc;\n}\n\n/*\n** This function is called after an incrmental-merge operation has run to\n** merge (or partially merge) two or more segments from absolute level\n** iAbsLevel.\n**\n** Each input segment is either removed from the db completely (if all of\n** its data was copied to the output segment by the incrmerge operation)\n** or modified in place so that it no longer contains those entries that\n** have been duplicated in the output segment.\n*/\nstatic int fts3IncrmergeChomp(\n  Fts3Table *p,                   /* FTS table handle */\n  sqlite3_int64 iAbsLevel,        /* Absolute level containing segments */\n  Fts3MultiSegReader *pCsr,       /* Chomp all segments opened by this cursor */\n  int *pnRem                      /* Number of segments not deleted */\n){\n  int i;\n  int nRem = 0;\n  int rc = SQLITE_OK;\n\n  for(i=pCsr->nSegment-1; i>=0 && rc==SQLITE_OK; i--){\n    Fts3SegReader *pSeg = 0;\n    int j;\n\n    /* Find the Fts3SegReader object with Fts3SegReader.iIdx==i. It is hiding\n    ** somewhere in the pCsr->apSegment[] array.  */\n    for(j=0; ALWAYS(j<pCsr->nSegment); j++){\n      pSeg = pCsr->apSegment[j];\n      if( pSeg->iIdx==i ) break;\n    }\n    assert( j<pCsr->nSegment && pSeg->iIdx==i );\n\n    if( pSeg->aNode==0 ){\n      /* Seg-reader is at EOF. Remove the entire input segment. */\n      rc = fts3DeleteSegment(p, pSeg);\n      if( rc==SQLITE_OK ){\n        rc = fts3RemoveSegdirEntry(p, iAbsLevel, pSeg->iIdx);\n      }\n      *pnRem = 0;\n    }else{\n      /* The incremental merge did not copy all the data from this \n      ** segment to the upper level. The segment is modified in place\n      ** so that it contains no keys smaller than zTerm/nTerm. */ \n      const char *zTerm = pSeg->zTerm;\n      int nTerm = pSeg->nTerm;\n      rc = fts3TruncateSegment(p, iAbsLevel, pSeg->iIdx, zTerm, nTerm);\n      nRem++;\n    }\n  }\n\n  if( rc==SQLITE_OK && nRem!=pCsr->nSegment ){\n    rc = fts3RepackSegdirLevel(p, iAbsLevel);\n  }\n\n  *pnRem = nRem;\n  return rc;\n}\n\n/*\n** Store an incr-merge hint in the database.\n*/\nstatic int fts3IncrmergeHintStore(Fts3Table *p, Blob *pHint){\n  sqlite3_stmt *pReplace = 0;\n  int rc;                         /* Return code */\n\n  rc = fts3SqlStmt(p, SQL_REPLACE_STAT, &pReplace, 0);\n  if( rc==SQLITE_OK ){\n    sqlite3_bind_int(pReplace, 1, FTS_STAT_INCRMERGEHINT);\n    sqlite3_bind_blob(pReplace, 2, pHint->a, pHint->n, SQLITE_STATIC);\n    sqlite3_step(pReplace);\n    rc = sqlite3_reset(pReplace);\n    sqlite3_bind_null(pReplace, 2);\n  }\n\n  return rc;\n}\n\n/*\n** Load an incr-merge hint from the database. The incr-merge hint, if one \n** exists, is stored in the rowid==1 row of the %_stat table.\n**\n** If successful, populate blob *pHint with the value read from the %_stat\n** table and return SQLITE_OK. Otherwise, if an error occurs, return an\n** SQLite error code.\n*/\nstatic int fts3IncrmergeHintLoad(Fts3Table *p, Blob *pHint){\n  sqlite3_stmt *pSelect = 0;\n  int rc;\n\n  pHint->n = 0;\n  rc = fts3SqlStmt(p, SQL_SELECT_STAT, &pSelect, 0);\n  if( rc==SQLITE_OK ){\n    int rc2;\n    sqlite3_bind_int(pSelect, 1, FTS_STAT_INCRMERGEHINT);\n    if( SQLITE_ROW==sqlite3_step(pSelect) ){\n      const char *aHint = sqlite3_column_blob(pSelect, 0);\n      int nHint = sqlite3_column_bytes(pSelect, 0);\n      if( aHint ){\n        blobGrowBuffer(pHint, nHint, &rc);\n        if( rc==SQLITE_OK ){\n          memcpy(pHint->a, aHint, nHint);\n          pHint->n = nHint;\n        }\n      }\n    }\n    rc2 = sqlite3_reset(pSelect);\n    if( rc==SQLITE_OK ) rc = rc2;\n  }\n\n  return rc;\n}\n\n/*\n** If *pRc is not SQLITE_OK when this function is called, it is a no-op.\n** Otherwise, append an entry to the hint stored in blob *pHint. Each entry\n** consists of two varints, the absolute level number of the input segments \n** and the number of input segments.\n**\n** If successful, leave *pRc set to SQLITE_OK and return. If an error occurs,\n** set *pRc to an SQLite error code before returning.\n*/\nstatic void fts3IncrmergeHintPush(\n  Blob *pHint,                    /* Hint blob to append to */\n  i64 iAbsLevel,                  /* First varint to store in hint */\n  int nInput,                     /* Second varint to store in hint */\n  int *pRc                        /* IN/OUT: Error code */\n){\n  blobGrowBuffer(pHint, pHint->n + 2*FTS3_VARINT_MAX, pRc);\n  if( *pRc==SQLITE_OK ){\n    pHint->n += sqlite3Fts3PutVarint(&pHint->a[pHint->n], iAbsLevel);\n    pHint->n += sqlite3Fts3PutVarint(&pHint->a[pHint->n], (i64)nInput);\n  }\n}\n\n/*\n** Read the last entry (most recently pushed) from the hint blob *pHint\n** and then remove the entry. Write the two values read to *piAbsLevel and \n** *pnInput before returning.\n**\n** If no error occurs, return SQLITE_OK. If the hint blob in *pHint does\n** not contain at least two valid varints, return SQLITE_CORRUPT_VTAB.\n*/\nstatic int fts3IncrmergeHintPop(Blob *pHint, i64 *piAbsLevel, int *pnInput){\n  const int nHint = pHint->n;\n  int i;\n\n  i = pHint->n-2;\n  while( i>0 && (pHint->a[i-1] & 0x80) ) i--;\n  while( i>0 && (pHint->a[i-1] & 0x80) ) i--;\n\n  pHint->n = i;\n  i += sqlite3Fts3GetVarint(&pHint->a[i], piAbsLevel);\n  i += fts3GetVarint32(&pHint->a[i], pnInput);\n  if( i!=nHint ) return FTS_CORRUPT_VTAB;\n\n  return SQLITE_OK;\n}\n\n\n/*\n** Attempt an incremental merge that writes nMerge leaf blocks.\n**\n** Incremental merges happen nMin segments at a time. The segments \n** to be merged are the nMin oldest segments (the ones with the smallest \n** values for the _segdir.idx field) in the highest level that contains \n** at least nMin segments. Multiple merges might occur in an attempt to \n** write the quota of nMerge leaf blocks.\n*/\nSQLITE_PRIVATE int sqlite3Fts3Incrmerge(Fts3Table *p, int nMerge, int nMin){\n  int rc;                         /* Return code */\n  int nRem = nMerge;              /* Number of leaf pages yet to  be written */\n  Fts3MultiSegReader *pCsr;       /* Cursor used to read input data */\n  Fts3SegFilter *pFilter;         /* Filter used with cursor pCsr */\n  IncrmergeWriter *pWriter;       /* Writer object */\n  int nSeg = 0;                   /* Number of input segments */\n  sqlite3_int64 iAbsLevel = 0;    /* Absolute level number to work on */\n  Blob hint = {0, 0, 0};          /* Hint read from %_stat table */\n  int bDirtyHint = 0;             /* True if blob 'hint' has been modified */\n\n  /* Allocate space for the cursor, filter and writer objects */\n  const int nAlloc = sizeof(*pCsr) + sizeof(*pFilter) + sizeof(*pWriter);\n  pWriter = (IncrmergeWriter *)sqlite3_malloc(nAlloc);\n  if( !pWriter ) return SQLITE_NOMEM;\n  pFilter = (Fts3SegFilter *)&pWriter[1];\n  pCsr = (Fts3MultiSegReader *)&pFilter[1];\n\n  rc = fts3IncrmergeHintLoad(p, &hint);\n  while( rc==SQLITE_OK && nRem>0 ){\n    const i64 nMod = FTS3_SEGDIR_MAXLEVEL * p->nIndex;\n    sqlite3_stmt *pFindLevel = 0; /* SQL used to determine iAbsLevel */\n    int bUseHint = 0;             /* True if attempting to append */\n    int iIdx = 0;                 /* Largest idx in level (iAbsLevel+1) */\n\n    /* Search the %_segdir table for the absolute level with the smallest\n    ** relative level number that contains at least nMin segments, if any.\n    ** If one is found, set iAbsLevel to the absolute level number and\n    ** nSeg to nMin. If no level with at least nMin segments can be found, \n    ** set nSeg to -1.\n    */\n    rc = fts3SqlStmt(p, SQL_FIND_MERGE_LEVEL, &pFindLevel, 0);\n    sqlite3_bind_int(pFindLevel, 1, MAX(2, nMin));\n    if( sqlite3_step(pFindLevel)==SQLITE_ROW ){\n      iAbsLevel = sqlite3_column_int64(pFindLevel, 0);\n      nSeg = sqlite3_column_int(pFindLevel, 1);\n      assert( nSeg>=2 );\n    }else{\n      nSeg = -1;\n    }\n    rc = sqlite3_reset(pFindLevel);\n\n    /* If the hint read from the %_stat table is not empty, check if the\n    ** last entry in it specifies a relative level smaller than or equal\n    ** to the level identified by the block above (if any). If so, this \n    ** iteration of the loop will work on merging at the hinted level.\n    */\n    if( rc==SQLITE_OK && hint.n ){\n      int nHint = hint.n;\n      sqlite3_int64 iHintAbsLevel = 0;      /* Hint level */\n      int nHintSeg = 0;                     /* Hint number of segments */\n\n      rc = fts3IncrmergeHintPop(&hint, &iHintAbsLevel, &nHintSeg);\n      if( nSeg<0 || (iAbsLevel % nMod) >= (iHintAbsLevel % nMod) ){\n        iAbsLevel = iHintAbsLevel;\n        nSeg = nHintSeg;\n        bUseHint = 1;\n        bDirtyHint = 1;\n      }else{\n        /* This undoes the effect of the HintPop() above - so that no entry\n        ** is removed from the hint blob.  */\n        hint.n = nHint;\n      }\n    }\n\n    /* If nSeg is less that zero, then there is no level with at least\n    ** nMin segments and no hint in the %_stat table. No work to do.\n    ** Exit early in this case.  */\n    if( nSeg<0 ) break;\n\n    /* Open a cursor to iterate through the contents of the oldest nSeg \n    ** indexes of absolute level iAbsLevel. If this cursor is opened using \n    ** the 'hint' parameters, it is possible that there are less than nSeg\n    ** segments available in level iAbsLevel. In this case, no work is\n    ** done on iAbsLevel - fall through to the next iteration of the loop \n    ** to start work on some other level.  */\n    memset(pWriter, 0, nAlloc);\n    pFilter->flags = FTS3_SEGMENT_REQUIRE_POS;\n\n    if( rc==SQLITE_OK ){\n      rc = fts3IncrmergeOutputIdx(p, iAbsLevel, &iIdx);\n      assert( bUseHint==1 || bUseHint==0 );\n      if( iIdx==0 || (bUseHint && iIdx==1) ){\n        int bIgnore = 0;\n        rc = fts3SegmentIsMaxLevel(p, iAbsLevel+1, &bIgnore);\n        if( bIgnore ){\n          pFilter->flags |= FTS3_SEGMENT_IGNORE_EMPTY;\n        }\n      }\n    }\n\n    if( rc==SQLITE_OK ){\n      rc = fts3IncrmergeCsr(p, iAbsLevel, nSeg, pCsr);\n    }\n    if( SQLITE_OK==rc && pCsr->nSegment==nSeg\n     && SQLITE_OK==(rc = sqlite3Fts3SegReaderStart(p, pCsr, pFilter))\n     && SQLITE_ROW==(rc = sqlite3Fts3SegReaderStep(p, pCsr))\n    ){\n      if( bUseHint && iIdx>0 ){\n        const char *zKey = pCsr->zTerm;\n        int nKey = pCsr->nTerm;\n        rc = fts3IncrmergeLoad(p, iAbsLevel, iIdx-1, zKey, nKey, pWriter);\n      }else{\n        rc = fts3IncrmergeWriter(p, iAbsLevel, iIdx, pCsr, pWriter);\n      }\n\n      if( rc==SQLITE_OK && pWriter->nLeafEst ){\n        fts3LogMerge(nSeg, iAbsLevel);\n        do {\n          rc = fts3IncrmergeAppend(p, pWriter, pCsr);\n          if( rc==SQLITE_OK ) rc = sqlite3Fts3SegReaderStep(p, pCsr);\n          if( pWriter->nWork>=nRem && rc==SQLITE_ROW ) rc = SQLITE_OK;\n        }while( rc==SQLITE_ROW );\n\n        /* Update or delete the input segments */\n        if( rc==SQLITE_OK ){\n          nRem -= (1 + pWriter->nWork);\n          rc = fts3IncrmergeChomp(p, iAbsLevel, pCsr, &nSeg);\n          if( nSeg!=0 ){\n            bDirtyHint = 1;\n            fts3IncrmergeHintPush(&hint, iAbsLevel, nSeg, &rc);\n          }\n        }\n      }\n\n      if( nSeg!=0 ){\n        pWriter->nLeafData = pWriter->nLeafData * -1;\n      }\n      fts3IncrmergeRelease(p, pWriter, &rc);\n      if( nSeg==0 && pWriter->bNoLeafData==0 ){\n        fts3PromoteSegments(p, iAbsLevel+1, pWriter->nLeafData);\n      }\n    }\n\n    sqlite3Fts3SegReaderFinish(pCsr);\n  }\n\n  /* Write the hint values into the %_stat table for the next incr-merger */\n  if( bDirtyHint && rc==SQLITE_OK ){\n    rc = fts3IncrmergeHintStore(p, &hint);\n  }\n\n  sqlite3_free(pWriter);\n  sqlite3_free(hint.a);\n  return rc;\n}\n\n/*\n** Convert the text beginning at *pz into an integer and return\n** its value.  Advance *pz to point to the first character past\n** the integer.\n**\n** This function used for parameters to merge= and incrmerge=\n** commands. \n*/\nstatic int fts3Getint(const char **pz){\n  const char *z = *pz;\n  int i = 0;\n  while( (*z)>='0' && (*z)<='9' && i<214748363 ) i = 10*i + *(z++) - '0';\n  *pz = z;\n  return i;\n}\n\n/*\n** Process statements of the form:\n**\n**    INSERT INTO table(table) VALUES('merge=A,B');\n**\n** A and B are integers that decode to be the number of leaf pages\n** written for the merge, and the minimum number of segments on a level\n** before it will be selected for a merge, respectively.\n*/\nstatic int fts3DoIncrmerge(\n  Fts3Table *p,                   /* FTS3 table handle */\n  const char *zParam              /* Nul-terminated string containing \"A,B\" */\n){\n  int rc;\n  int nMin = (FTS3_MERGE_COUNT / 2);\n  int nMerge = 0;\n  const char *z = zParam;\n\n  /* Read the first integer value */\n  nMerge = fts3Getint(&z);\n\n  /* If the first integer value is followed by a ',',  read the second\n  ** integer value. */\n  if( z[0]==',' && z[1]!='\\0' ){\n    z++;\n    nMin = fts3Getint(&z);\n  }\n\n  if( z[0]!='\\0' || nMin<2 ){\n    rc = SQLITE_ERROR;\n  }else{\n    rc = SQLITE_OK;\n    if( !p->bHasStat ){\n      assert( p->bFts4==0 );\n      sqlite3Fts3CreateStatTable(&rc, p);\n    }\n    if( rc==SQLITE_OK ){\n      rc = sqlite3Fts3Incrmerge(p, nMerge, nMin);\n    }\n    sqlite3Fts3SegmentsClose(p);\n  }\n  return rc;\n}\n\n/*\n** Process statements of the form:\n**\n**    INSERT INTO table(table) VALUES('automerge=X');\n**\n** where X is an integer.  X==0 means to turn automerge off.  X!=0 means\n** turn it on.  The setting is persistent.\n*/\nstatic int fts3DoAutoincrmerge(\n  Fts3Table *p,                   /* FTS3 table handle */\n  const char *zParam              /* Nul-terminated string containing boolean */\n){\n  int rc = SQLITE_OK;\n  sqlite3_stmt *pStmt = 0;\n  p->nAutoincrmerge = fts3Getint(&zParam);\n  if( p->nAutoincrmerge==1 || p->nAutoincrmerge>FTS3_MERGE_COUNT ){\n    p->nAutoincrmerge = 8;\n  }\n  if( !p->bHasStat ){\n    assert( p->bFts4==0 );\n    sqlite3Fts3CreateStatTable(&rc, p);\n    if( rc ) return rc;\n  }\n  rc = fts3SqlStmt(p, SQL_REPLACE_STAT, &pStmt, 0);\n  if( rc ) return rc;\n  sqlite3_bind_int(pStmt, 1, FTS_STAT_AUTOINCRMERGE);\n  sqlite3_bind_int(pStmt, 2, p->nAutoincrmerge);\n  sqlite3_step(pStmt);\n  rc = sqlite3_reset(pStmt);\n  return rc;\n}\n\n/*\n** Return a 64-bit checksum for the FTS index entry specified by the\n** arguments to this function.\n*/\nstatic u64 fts3ChecksumEntry(\n  const char *zTerm,              /* Pointer to buffer containing term */\n  int nTerm,                      /* Size of zTerm in bytes */\n  int iLangid,                    /* Language id for current row */\n  int iIndex,                     /* Index (0..Fts3Table.nIndex-1) */\n  i64 iDocid,                     /* Docid for current row. */\n  int iCol,                       /* Column number */\n  int iPos                        /* Position */\n){\n  int i;\n  u64 ret = (u64)iDocid;\n\n  ret += (ret<<3) + iLangid;\n  ret += (ret<<3) + iIndex;\n  ret += (ret<<3) + iCol;\n  ret += (ret<<3) + iPos;\n  for(i=0; i<nTerm; i++) ret += (ret<<3) + zTerm[i];\n\n  return ret;\n}\n\n/*\n** Return a checksum of all entries in the FTS index that correspond to\n** language id iLangid. The checksum is calculated by XORing the checksums\n** of each individual entry (see fts3ChecksumEntry()) together.\n**\n** If successful, the checksum value is returned and *pRc set to SQLITE_OK.\n** Otherwise, if an error occurs, *pRc is set to an SQLite error code. The\n** return value is undefined in this case.\n*/\nstatic u64 fts3ChecksumIndex(\n  Fts3Table *p,                   /* FTS3 table handle */\n  int iLangid,                    /* Language id to return cksum for */\n  int iIndex,                     /* Index to cksum (0..p->nIndex-1) */\n  int *pRc                        /* OUT: Return code */\n){\n  Fts3SegFilter filter;\n  Fts3MultiSegReader csr;\n  int rc;\n  u64 cksum = 0;\n\n  assert( *pRc==SQLITE_OK );\n\n  memset(&filter, 0, sizeof(filter));\n  memset(&csr, 0, sizeof(csr));\n  filter.flags =  FTS3_SEGMENT_REQUIRE_POS|FTS3_SEGMENT_IGNORE_EMPTY;\n  filter.flags |= FTS3_SEGMENT_SCAN;\n\n  rc = sqlite3Fts3SegReaderCursor(\n      p, iLangid, iIndex, FTS3_SEGCURSOR_ALL, 0, 0, 0, 1,&csr\n  );\n  if( rc==SQLITE_OK ){\n    rc = sqlite3Fts3SegReaderStart(p, &csr, &filter);\n  }\n\n  if( rc==SQLITE_OK ){\n    while( SQLITE_ROW==(rc = sqlite3Fts3SegReaderStep(p, &csr)) ){\n      char *pCsr = csr.aDoclist;\n      char *pEnd = &pCsr[csr.nDoclist];\n\n      i64 iDocid = 0;\n      i64 iCol = 0;\n      i64 iPos = 0;\n\n      pCsr += sqlite3Fts3GetVarint(pCsr, &iDocid);\n      while( pCsr<pEnd ){\n        i64 iVal = 0;\n        pCsr += sqlite3Fts3GetVarint(pCsr, &iVal);\n        if( pCsr<pEnd ){\n          if( iVal==0 || iVal==1 ){\n            iCol = 0;\n            iPos = 0;\n            if( iVal ){\n              pCsr += sqlite3Fts3GetVarint(pCsr, &iCol);\n            }else{\n              pCsr += sqlite3Fts3GetVarint(pCsr, &iVal);\n              iDocid += iVal;\n            }\n          }else{\n            iPos += (iVal - 2);\n            cksum = cksum ^ fts3ChecksumEntry(\n                csr.zTerm, csr.nTerm, iLangid, iIndex, iDocid,\n                (int)iCol, (int)iPos\n            );\n          }\n        }\n      }\n    }\n  }\n  sqlite3Fts3SegReaderFinish(&csr);\n\n  *pRc = rc;\n  return cksum;\n}\n\n/*\n** Check if the contents of the FTS index match the current contents of the\n** content table. If no error occurs and the contents do match, set *pbOk\n** to true and return SQLITE_OK. Or if the contents do not match, set *pbOk\n** to false before returning.\n**\n** If an error occurs (e.g. an OOM or IO error), return an SQLite error \n** code. The final value of *pbOk is undefined in this case.\n*/\nstatic int fts3IntegrityCheck(Fts3Table *p, int *pbOk){\n  int rc = SQLITE_OK;             /* Return code */\n  u64 cksum1 = 0;                 /* Checksum based on FTS index contents */\n  u64 cksum2 = 0;                 /* Checksum based on %_content contents */\n  sqlite3_stmt *pAllLangid = 0;   /* Statement to return all language-ids */\n\n  /* This block calculates the checksum according to the FTS index. */\n  rc = fts3SqlStmt(p, SQL_SELECT_ALL_LANGID, &pAllLangid, 0);\n  if( rc==SQLITE_OK ){\n    int rc2;\n    sqlite3_bind_int(pAllLangid, 1, p->iPrevLangid);\n    sqlite3_bind_int(pAllLangid, 2, p->nIndex);\n    while( rc==SQLITE_OK && sqlite3_step(pAllLangid)==SQLITE_ROW ){\n      int iLangid = sqlite3_column_int(pAllLangid, 0);\n      int i;\n      for(i=0; i<p->nIndex; i++){\n        cksum1 = cksum1 ^ fts3ChecksumIndex(p, iLangid, i, &rc);\n      }\n    }\n    rc2 = sqlite3_reset(pAllLangid);\n    if( rc==SQLITE_OK ) rc = rc2;\n  }\n\n  /* This block calculates the checksum according to the %_content table */\n  if( rc==SQLITE_OK ){\n    sqlite3_tokenizer_module const *pModule = p->pTokenizer->pModule;\n    sqlite3_stmt *pStmt = 0;\n    char *zSql;\n   \n    zSql = sqlite3_mprintf(\"SELECT %s\" , p->zReadExprlist);\n    if( !zSql ){\n      rc = SQLITE_NOMEM;\n    }else{\n      rc = sqlite3_prepare_v2(p->db, zSql, -1, &pStmt, 0);\n      sqlite3_free(zSql);\n    }\n\n    while( rc==SQLITE_OK && SQLITE_ROW==sqlite3_step(pStmt) ){\n      i64 iDocid = sqlite3_column_int64(pStmt, 0);\n      int iLang = langidFromSelect(p, pStmt);\n      int iCol;\n\n      for(iCol=0; rc==SQLITE_OK && iCol<p->nColumn; iCol++){\n        if( p->abNotindexed[iCol]==0 ){\n          const char *zText = (const char *)sqlite3_column_text(pStmt, iCol+1);\n          int nText = sqlite3_column_bytes(pStmt, iCol+1);\n          sqlite3_tokenizer_cursor *pT = 0;\n\n          rc = sqlite3Fts3OpenTokenizer(p->pTokenizer, iLang, zText, nText,&pT);\n          while( rc==SQLITE_OK ){\n            char const *zToken;       /* Buffer containing token */\n            int nToken = 0;           /* Number of bytes in token */\n            int iDum1 = 0, iDum2 = 0; /* Dummy variables */\n            int iPos = 0;             /* Position of token in zText */\n\n            rc = pModule->xNext(pT, &zToken, &nToken, &iDum1, &iDum2, &iPos);\n            if( rc==SQLITE_OK ){\n              int i;\n              cksum2 = cksum2 ^ fts3ChecksumEntry(\n                  zToken, nToken, iLang, 0, iDocid, iCol, iPos\n              );\n              for(i=1; i<p->nIndex; i++){\n                if( p->aIndex[i].nPrefix<=nToken ){\n                  cksum2 = cksum2 ^ fts3ChecksumEntry(\n                      zToken, p->aIndex[i].nPrefix, iLang, i, iDocid, iCol, iPos\n                  );\n                }\n              }\n            }\n          }\n          if( pT ) pModule->xClose(pT);\n          if( rc==SQLITE_DONE ) rc = SQLITE_OK;\n        }\n      }\n    }\n\n    sqlite3_finalize(pStmt);\n  }\n\n  *pbOk = (cksum1==cksum2);\n  return rc;\n}\n\n/*\n** Run the integrity-check. If no error occurs and the current contents of\n** the FTS index are correct, return SQLITE_OK. Or, if the contents of the\n** FTS index are incorrect, return SQLITE_CORRUPT_VTAB.\n**\n** Or, if an error (e.g. an OOM or IO error) occurs, return an SQLite \n** error code.\n**\n** The integrity-check works as follows. For each token and indexed token\n** prefix in the document set, a 64-bit checksum is calculated (by code\n** in fts3ChecksumEntry()) based on the following:\n**\n**     + The index number (0 for the main index, 1 for the first prefix\n**       index etc.),\n**     + The token (or token prefix) text itself, \n**     + The language-id of the row it appears in,\n**     + The docid of the row it appears in,\n**     + The column it appears in, and\n**     + The tokens position within that column.\n**\n** The checksums for all entries in the index are XORed together to create\n** a single checksum for the entire index.\n**\n** The integrity-check code calculates the same checksum in two ways:\n**\n**     1. By scanning the contents of the FTS index, and \n**     2. By scanning and tokenizing the content table.\n**\n** If the two checksums are identical, the integrity-check is deemed to have\n** passed.\n*/\nstatic int fts3DoIntegrityCheck(\n  Fts3Table *p                    /* FTS3 table handle */\n){\n  int rc;\n  int bOk = 0;\n  rc = fts3IntegrityCheck(p, &bOk);\n  if( rc==SQLITE_OK && bOk==0 ) rc = FTS_CORRUPT_VTAB;\n  return rc;\n}\n\n/*\n** Handle a 'special' INSERT of the form:\n**\n**   \"INSERT INTO tbl(tbl) VALUES(<expr>)\"\n**\n** Argument pVal contains the result of <expr>. Currently the only \n** meaningful value to insert is the text 'optimize'.\n*/\nstatic int fts3SpecialInsert(Fts3Table *p, sqlite3_value *pVal){\n  int rc;                         /* Return Code */\n  const char *zVal = (const char *)sqlite3_value_text(pVal);\n  int nVal = sqlite3_value_bytes(pVal);\n\n  if( !zVal ){\n    return SQLITE_NOMEM;\n  }else if( nVal==8 && 0==sqlite3_strnicmp(zVal, \"optimize\", 8) ){\n    rc = fts3DoOptimize(p, 0);\n  }else if( nVal==7 && 0==sqlite3_strnicmp(zVal, \"rebuild\", 7) ){\n    rc = fts3DoRebuild(p);\n  }else if( nVal==15 && 0==sqlite3_strnicmp(zVal, \"integrity-check\", 15) ){\n    rc = fts3DoIntegrityCheck(p);\n  }else if( nVal>6 && 0==sqlite3_strnicmp(zVal, \"merge=\", 6) ){\n    rc = fts3DoIncrmerge(p, &zVal[6]);\n  }else if( nVal>10 && 0==sqlite3_strnicmp(zVal, \"automerge=\", 10) ){\n    rc = fts3DoAutoincrmerge(p, &zVal[10]);\n#ifdef SQLITE_TEST\n  }else if( nVal>9 && 0==sqlite3_strnicmp(zVal, \"nodesize=\", 9) ){\n    p->nNodeSize = atoi(&zVal[9]);\n    rc = SQLITE_OK;\n  }else if( nVal>11 && 0==sqlite3_strnicmp(zVal, \"maxpending=\", 9) ){\n    p->nMaxPendingData = atoi(&zVal[11]);\n    rc = SQLITE_OK;\n  }else if( nVal>21 && 0==sqlite3_strnicmp(zVal, \"test-no-incr-doclist=\", 21) ){\n    p->bNoIncrDoclist = atoi(&zVal[21]);\n    rc = SQLITE_OK;\n#endif\n  }else{\n    rc = SQLITE_ERROR;\n  }\n\n  return rc;\n}\n\n#ifndef SQLITE_DISABLE_FTS4_DEFERRED\n/*\n** Delete all cached deferred doclists. Deferred doclists are cached\n** (allocated) by the sqlite3Fts3CacheDeferredDoclists() function.\n*/\nSQLITE_PRIVATE void sqlite3Fts3FreeDeferredDoclists(Fts3Cursor *pCsr){\n  Fts3DeferredToken *pDef;\n  for(pDef=pCsr->pDeferred; pDef; pDef=pDef->pNext){\n    fts3PendingListDelete(pDef->pList);\n    pDef->pList = 0;\n  }\n}\n\n/*\n** Free all entries in the pCsr->pDeffered list. Entries are added to \n** this list using sqlite3Fts3DeferToken().\n*/\nSQLITE_PRIVATE void sqlite3Fts3FreeDeferredTokens(Fts3Cursor *pCsr){\n  Fts3DeferredToken *pDef;\n  Fts3DeferredToken *pNext;\n  for(pDef=pCsr->pDeferred; pDef; pDef=pNext){\n    pNext = pDef->pNext;\n    fts3PendingListDelete(pDef->pList);\n    sqlite3_free(pDef);\n  }\n  pCsr->pDeferred = 0;\n}\n\n/*\n** Generate deferred-doclists for all tokens in the pCsr->pDeferred list\n** based on the row that pCsr currently points to.\n**\n** A deferred-doclist is like any other doclist with position information\n** included, except that it only contains entries for a single row of the\n** table, not for all rows.\n*/\nSQLITE_PRIVATE int sqlite3Fts3CacheDeferredDoclists(Fts3Cursor *pCsr){\n  int rc = SQLITE_OK;             /* Return code */\n  if( pCsr->pDeferred ){\n    int i;                        /* Used to iterate through table columns */\n    sqlite3_int64 iDocid;         /* Docid of the row pCsr points to */\n    Fts3DeferredToken *pDef;      /* Used to iterate through deferred tokens */\n  \n    Fts3Table *p = (Fts3Table *)pCsr->base.pVtab;\n    sqlite3_tokenizer *pT = p->pTokenizer;\n    sqlite3_tokenizer_module const *pModule = pT->pModule;\n   \n    assert( pCsr->isRequireSeek==0 );\n    iDocid = sqlite3_column_int64(pCsr->pStmt, 0);\n  \n    for(i=0; i<p->nColumn && rc==SQLITE_OK; i++){\n      if( p->abNotindexed[i]==0 ){\n        const char *zText = (const char *)sqlite3_column_text(pCsr->pStmt, i+1);\n        sqlite3_tokenizer_cursor *pTC = 0;\n\n        rc = sqlite3Fts3OpenTokenizer(pT, pCsr->iLangid, zText, -1, &pTC);\n        while( rc==SQLITE_OK ){\n          char const *zToken;       /* Buffer containing token */\n          int nToken = 0;           /* Number of bytes in token */\n          int iDum1 = 0, iDum2 = 0; /* Dummy variables */\n          int iPos = 0;             /* Position of token in zText */\n\n          rc = pModule->xNext(pTC, &zToken, &nToken, &iDum1, &iDum2, &iPos);\n          for(pDef=pCsr->pDeferred; pDef && rc==SQLITE_OK; pDef=pDef->pNext){\n            Fts3PhraseToken *pPT = pDef->pToken;\n            if( (pDef->iCol>=p->nColumn || pDef->iCol==i)\n                && (pPT->bFirst==0 || iPos==0)\n                && (pPT->n==nToken || (pPT->isPrefix && pPT->n<nToken))\n                && (0==memcmp(zToken, pPT->z, pPT->n))\n              ){\n              fts3PendingListAppend(&pDef->pList, iDocid, i, iPos, &rc);\n            }\n          }\n        }\n        if( pTC ) pModule->xClose(pTC);\n        if( rc==SQLITE_DONE ) rc = SQLITE_OK;\n      }\n    }\n\n    for(pDef=pCsr->pDeferred; pDef && rc==SQLITE_OK; pDef=pDef->pNext){\n      if( pDef->pList ){\n        rc = fts3PendingListAppendVarint(&pDef->pList, 0);\n      }\n    }\n  }\n\n  return rc;\n}\n\nSQLITE_PRIVATE int sqlite3Fts3DeferredTokenList(\n  Fts3DeferredToken *p, \n  char **ppData, \n  int *pnData\n){\n  char *pRet;\n  int nSkip;\n  sqlite3_int64 dummy;\n\n  *ppData = 0;\n  *pnData = 0;\n\n  if( p->pList==0 ){\n    return SQLITE_OK;\n  }\n\n  pRet = (char *)sqlite3_malloc(p->pList->nData);\n  if( !pRet ) return SQLITE_NOMEM;\n\n  nSkip = sqlite3Fts3GetVarint(p->pList->aData, &dummy);\n  *pnData = p->pList->nData - nSkip;\n  *ppData = pRet;\n  \n  memcpy(pRet, &p->pList->aData[nSkip], *pnData);\n  return SQLITE_OK;\n}\n\n/*\n** Add an entry for token pToken to the pCsr->pDeferred list.\n*/\nSQLITE_PRIVATE int sqlite3Fts3DeferToken(\n  Fts3Cursor *pCsr,               /* Fts3 table cursor */\n  Fts3PhraseToken *pToken,        /* Token to defer */\n  int iCol                        /* Column that token must appear in (or -1) */\n){\n  Fts3DeferredToken *pDeferred;\n  pDeferred = sqlite3_malloc(sizeof(*pDeferred));\n  if( !pDeferred ){\n    return SQLITE_NOMEM;\n  }\n  memset(pDeferred, 0, sizeof(*pDeferred));\n  pDeferred->pToken = pToken;\n  pDeferred->pNext = pCsr->pDeferred; \n  pDeferred->iCol = iCol;\n  pCsr->pDeferred = pDeferred;\n\n  assert( pToken->pDeferred==0 );\n  pToken->pDeferred = pDeferred;\n\n  return SQLITE_OK;\n}\n#endif\n\n/*\n** SQLite value pRowid contains the rowid of a row that may or may not be\n** present in the FTS3 table. If it is, delete it and adjust the contents\n** of subsiduary data structures accordingly.\n*/\nstatic int fts3DeleteByRowid(\n  Fts3Table *p, \n  sqlite3_value *pRowid, \n  int *pnChng,                    /* IN/OUT: Decrement if row is deleted */\n  u32 *aSzDel\n){\n  int rc = SQLITE_OK;             /* Return code */\n  int bFound = 0;                 /* True if *pRowid really is in the table */\n\n  fts3DeleteTerms(&rc, p, pRowid, aSzDel, &bFound);\n  if( bFound && rc==SQLITE_OK ){\n    int isEmpty = 0;              /* Deleting *pRowid leaves the table empty */\n    rc = fts3IsEmpty(p, pRowid, &isEmpty);\n    if( rc==SQLITE_OK ){\n      if( isEmpty ){\n        /* Deleting this row means the whole table is empty. In this case\n        ** delete the contents of all three tables and throw away any\n        ** data in the pendingTerms hash table.  */\n        rc = fts3DeleteAll(p, 1);\n        *pnChng = 0;\n        memset(aSzDel, 0, sizeof(u32) * (p->nColumn+1) * 2);\n      }else{\n        *pnChng = *pnChng - 1;\n        if( p->zContentTbl==0 ){\n          fts3SqlExec(&rc, p, SQL_DELETE_CONTENT, &pRowid);\n        }\n        if( p->bHasDocsize ){\n          fts3SqlExec(&rc, p, SQL_DELETE_DOCSIZE, &pRowid);\n        }\n      }\n    }\n  }\n\n  return rc;\n}\n\n/*\n** This function does the work for the xUpdate method of FTS3 virtual\n** tables. The schema of the virtual table being:\n**\n**     CREATE TABLE <table name>( \n**       <user columns>,\n**       <table name> HIDDEN, \n**       docid HIDDEN, \n**       <langid> HIDDEN\n**     );\n**\n** \n*/\nSQLITE_PRIVATE int sqlite3Fts3UpdateMethod(\n  sqlite3_vtab *pVtab,            /* FTS3 vtab object */\n  int nArg,                       /* Size of argument array */\n  sqlite3_value **apVal,          /* Array of arguments */\n  sqlite_int64 *pRowid            /* OUT: The affected (or effected) rowid */\n){\n  Fts3Table *p = (Fts3Table *)pVtab;\n  int rc = SQLITE_OK;             /* Return Code */\n  u32 *aSzIns = 0;                /* Sizes of inserted documents */\n  u32 *aSzDel = 0;                /* Sizes of deleted documents */\n  int nChng = 0;                  /* Net change in number of documents */\n  int bInsertDone = 0;\n\n  /* At this point it must be known if the %_stat table exists or not.\n  ** So bHasStat may not be 2.  */\n  assert( p->bHasStat==0 || p->bHasStat==1 );\n\n  assert( p->pSegments==0 );\n  assert( \n      nArg==1                     /* DELETE operations */\n   || nArg==(2 + p->nColumn + 3)  /* INSERT or UPDATE operations */\n  );\n\n  /* Check for a \"special\" INSERT operation. One of the form:\n  **\n  **   INSERT INTO xyz(xyz) VALUES('command');\n  */\n  if( nArg>1 \n   && sqlite3_value_type(apVal[0])==SQLITE_NULL \n   && sqlite3_value_type(apVal[p->nColumn+2])!=SQLITE_NULL \n  ){\n    rc = fts3SpecialInsert(p, apVal[p->nColumn+2]);\n    goto update_out;\n  }\n\n  if( nArg>1 && sqlite3_value_int(apVal[2 + p->nColumn + 2])<0 ){\n    rc = SQLITE_CONSTRAINT;\n    goto update_out;\n  }\n\n  /* Allocate space to hold the change in document sizes */\n  aSzDel = sqlite3_malloc( sizeof(aSzDel[0])*(p->nColumn+1)*2 );\n  if( aSzDel==0 ){\n    rc = SQLITE_NOMEM;\n    goto update_out;\n  }\n  aSzIns = &aSzDel[p->nColumn+1];\n  memset(aSzDel, 0, sizeof(aSzDel[0])*(p->nColumn+1)*2);\n\n  rc = fts3Writelock(p);\n  if( rc!=SQLITE_OK ) goto update_out;\n\n  /* If this is an INSERT operation, or an UPDATE that modifies the rowid\n  ** value, then this operation requires constraint handling.\n  **\n  ** If the on-conflict mode is REPLACE, this means that the existing row\n  ** should be deleted from the database before inserting the new row. Or,\n  ** if the on-conflict mode is other than REPLACE, then this method must\n  ** detect the conflict and return SQLITE_CONSTRAINT before beginning to\n  ** modify the database file.\n  */\n  if( nArg>1 && p->zContentTbl==0 ){\n    /* Find the value object that holds the new rowid value. */\n    sqlite3_value *pNewRowid = apVal[3+p->nColumn];\n    if( sqlite3_value_type(pNewRowid)==SQLITE_NULL ){\n      pNewRowid = apVal[1];\n    }\n\n    if( sqlite3_value_type(pNewRowid)!=SQLITE_NULL && ( \n        sqlite3_value_type(apVal[0])==SQLITE_NULL\n     || sqlite3_value_int64(apVal[0])!=sqlite3_value_int64(pNewRowid)\n    )){\n      /* The new rowid is not NULL (in this case the rowid will be\n      ** automatically assigned and there is no chance of a conflict), and \n      ** the statement is either an INSERT or an UPDATE that modifies the\n      ** rowid column. So if the conflict mode is REPLACE, then delete any\n      ** existing row with rowid=pNewRowid. \n      **\n      ** Or, if the conflict mode is not REPLACE, insert the new record into \n      ** the %_content table. If we hit the duplicate rowid constraint (or any\n      ** other error) while doing so, return immediately.\n      **\n      ** This branch may also run if pNewRowid contains a value that cannot\n      ** be losslessly converted to an integer. In this case, the eventual \n      ** call to fts3InsertData() (either just below or further on in this\n      ** function) will return SQLITE_MISMATCH. If fts3DeleteByRowid is \n      ** invoked, it will delete zero rows (since no row will have\n      ** docid=$pNewRowid if $pNewRowid is not an integer value).\n      */\n      if( sqlite3_vtab_on_conflict(p->db)==SQLITE_REPLACE ){\n        rc = fts3DeleteByRowid(p, pNewRowid, &nChng, aSzDel);\n      }else{\n        rc = fts3InsertData(p, apVal, pRowid);\n        bInsertDone = 1;\n      }\n    }\n  }\n  if( rc!=SQLITE_OK ){\n    goto update_out;\n  }\n\n  /* If this is a DELETE or UPDATE operation, remove the old record. */\n  if( sqlite3_value_type(apVal[0])!=SQLITE_NULL ){\n    assert( sqlite3_value_type(apVal[0])==SQLITE_INTEGER );\n    rc = fts3DeleteByRowid(p, apVal[0], &nChng, aSzDel);\n  }\n  \n  /* If this is an INSERT or UPDATE operation, insert the new record. */\n  if( nArg>1 && rc==SQLITE_OK ){\n    int iLangid = sqlite3_value_int(apVal[2 + p->nColumn + 2]);\n    if( bInsertDone==0 ){\n      rc = fts3InsertData(p, apVal, pRowid);\n      if( rc==SQLITE_CONSTRAINT && p->zContentTbl==0 ){\n        rc = FTS_CORRUPT_VTAB;\n      }\n    }\n    if( rc==SQLITE_OK ){\n      rc = fts3PendingTermsDocid(p, 0, iLangid, *pRowid);\n    }\n    if( rc==SQLITE_OK ){\n      assert( p->iPrevDocid==*pRowid );\n      rc = fts3InsertTerms(p, iLangid, apVal, aSzIns);\n    }\n    if( p->bHasDocsize ){\n      fts3InsertDocsize(&rc, p, aSzIns);\n    }\n    nChng++;\n  }\n\n  if( p->bFts4 ){\n    fts3UpdateDocTotals(&rc, p, aSzIns, aSzDel, nChng);\n  }\n\n update_out:\n  sqlite3_free(aSzDel);\n  sqlite3Fts3SegmentsClose(p);\n  return rc;\n}\n\n/* \n** Flush any data in the pending-terms hash table to disk. If successful,\n** merge all segments in the database (including the new segment, if \n** there was any data to flush) into a single segment. \n*/\nSQLITE_PRIVATE int sqlite3Fts3Optimize(Fts3Table *p){\n  int rc;\n  rc = sqlite3_exec(p->db, \"SAVEPOINT fts3\", 0, 0, 0);\n  if( rc==SQLITE_OK ){\n    rc = fts3DoOptimize(p, 1);\n    if( rc==SQLITE_OK || rc==SQLITE_DONE ){\n      int rc2 = sqlite3_exec(p->db, \"RELEASE fts3\", 0, 0, 0);\n      if( rc2!=SQLITE_OK ) rc = rc2;\n    }else{\n      sqlite3_exec(p->db, \"ROLLBACK TO fts3\", 0, 0, 0);\n      sqlite3_exec(p->db, \"RELEASE fts3\", 0, 0, 0);\n    }\n  }\n  sqlite3Fts3SegmentsClose(p);\n  return rc;\n}\n\n#endif\n\n/************** End of fts3_write.c ******************************************/\n/************** Begin file fts3_snippet.c ************************************/\n/*\n** 2009 Oct 23\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n******************************************************************************\n*/\n\n/* #include \"fts3Int.h\" */\n#if !defined(SQLITE_CORE) || defined(SQLITE_ENABLE_FTS3)\n\n/* #include <string.h> */\n/* #include <assert.h> */\n\n/*\n** Characters that may appear in the second argument to matchinfo().\n*/\n#define FTS3_MATCHINFO_NPHRASE   'p'        /* 1 value */\n#define FTS3_MATCHINFO_NCOL      'c'        /* 1 value */\n#define FTS3_MATCHINFO_NDOC      'n'        /* 1 value */\n#define FTS3_MATCHINFO_AVGLENGTH 'a'        /* nCol values */\n#define FTS3_MATCHINFO_LENGTH    'l'        /* nCol values */\n#define FTS3_MATCHINFO_LCS       's'        /* nCol values */\n#define FTS3_MATCHINFO_HITS      'x'        /* 3*nCol*nPhrase values */\n#define FTS3_MATCHINFO_LHITS     'y'        /* nCol*nPhrase values */\n#define FTS3_MATCHINFO_LHITS_BM  'b'        /* nCol*nPhrase values */\n\n/*\n** The default value for the second argument to matchinfo(). \n*/\n#define FTS3_MATCHINFO_DEFAULT   \"pcx\"\n\n\n/*\n** Used as an fts3ExprIterate() context when loading phrase doclists to\n** Fts3Expr.aDoclist[]/nDoclist.\n*/\ntypedef struct LoadDoclistCtx LoadDoclistCtx;\nstruct LoadDoclistCtx {\n  Fts3Cursor *pCsr;               /* FTS3 Cursor */\n  int nPhrase;                    /* Number of phrases seen so far */\n  int nToken;                     /* Number of tokens seen so far */\n};\n\n/*\n** The following types are used as part of the implementation of the \n** fts3BestSnippet() routine.\n*/\ntypedef struct SnippetIter SnippetIter;\ntypedef struct SnippetPhrase SnippetPhrase;\ntypedef struct SnippetFragment SnippetFragment;\n\nstruct SnippetIter {\n  Fts3Cursor *pCsr;               /* Cursor snippet is being generated from */\n  int iCol;                       /* Extract snippet from this column */\n  int nSnippet;                   /* Requested snippet length (in tokens) */\n  int nPhrase;                    /* Number of phrases in query */\n  SnippetPhrase *aPhrase;         /* Array of size nPhrase */\n  int iCurrent;                   /* First token of current snippet */\n};\n\nstruct SnippetPhrase {\n  int nToken;                     /* Number of tokens in phrase */\n  char *pList;                    /* Pointer to start of phrase position list */\n  int iHead;                      /* Next value in position list */\n  char *pHead;                    /* Position list data following iHead */\n  int iTail;                      /* Next value in trailing position list */\n  char *pTail;                    /* Position list data following iTail */\n};\n\nstruct SnippetFragment {\n  int iCol;                       /* Column snippet is extracted from */\n  int iPos;                       /* Index of first token in snippet */\n  u64 covered;                    /* Mask of query phrases covered */\n  u64 hlmask;                     /* Mask of snippet terms to highlight */\n};\n\n/*\n** This type is used as an fts3ExprIterate() context object while \n** accumulating the data returned by the matchinfo() function.\n*/\ntypedef struct MatchInfo MatchInfo;\nstruct MatchInfo {\n  Fts3Cursor *pCursor;            /* FTS3 Cursor */\n  int nCol;                       /* Number of columns in table */\n  int nPhrase;                    /* Number of matchable phrases in query */\n  sqlite3_int64 nDoc;             /* Number of docs in database */\n  char flag;\n  u32 *aMatchinfo;                /* Pre-allocated buffer */\n};\n\n/*\n** An instance of this structure is used to manage a pair of buffers, each\n** (nElem * sizeof(u32)) bytes in size. See the MatchinfoBuffer code below\n** for details.\n*/\nstruct MatchinfoBuffer {\n  u8 aRef[3];\n  int nElem;\n  int bGlobal;                    /* Set if global data is loaded */\n  char *zMatchinfo;\n  u32 aMatchinfo[1];\n};\n\n\n/*\n** The snippet() and offsets() functions both return text values. An instance\n** of the following structure is used to accumulate those values while the\n** functions are running. See fts3StringAppend() for details.\n*/\ntypedef struct StrBuffer StrBuffer;\nstruct StrBuffer {\n  char *z;                        /* Pointer to buffer containing string */\n  int n;                          /* Length of z in bytes (excl. nul-term) */\n  int nAlloc;                     /* Allocated size of buffer z in bytes */\n};\n\n\n/*************************************************************************\n** Start of MatchinfoBuffer code.\n*/\n\n/*\n** Allocate a two-slot MatchinfoBuffer object.\n*/\nstatic MatchinfoBuffer *fts3MIBufferNew(int nElem, const char *zMatchinfo){\n  MatchinfoBuffer *pRet;\n  int nByte = sizeof(u32) * (2*nElem + 1) + sizeof(MatchinfoBuffer);\n  int nStr = (int)strlen(zMatchinfo);\n\n  pRet = sqlite3_malloc(nByte + nStr+1);\n  if( pRet ){\n    memset(pRet, 0, nByte);\n    pRet->aMatchinfo[0] = (u8*)(&pRet->aMatchinfo[1]) - (u8*)pRet;\n    pRet->aMatchinfo[1+nElem] = pRet->aMatchinfo[0] + sizeof(u32)*(nElem+1);\n    pRet->nElem = nElem;\n    pRet->zMatchinfo = ((char*)pRet) + nByte;\n    memcpy(pRet->zMatchinfo, zMatchinfo, nStr+1);\n    pRet->aRef[0] = 1;\n  }\n\n  return pRet;\n}\n\nstatic void fts3MIBufferFree(void *p){\n  MatchinfoBuffer *pBuf = (MatchinfoBuffer*)((u8*)p - ((u32*)p)[-1]);\n\n  assert( (u32*)p==&pBuf->aMatchinfo[1] \n       || (u32*)p==&pBuf->aMatchinfo[pBuf->nElem+2] \n  );\n  if( (u32*)p==&pBuf->aMatchinfo[1] ){\n    pBuf->aRef[1] = 0;\n  }else{\n    pBuf->aRef[2] = 0;\n  }\n\n  if( pBuf->aRef[0]==0 && pBuf->aRef[1]==0 && pBuf->aRef[2]==0 ){\n    sqlite3_free(pBuf);\n  }\n}\n\nstatic void (*fts3MIBufferAlloc(MatchinfoBuffer *p, u32 **paOut))(void*){\n  void (*xRet)(void*) = 0;\n  u32 *aOut = 0;\n\n  if( p->aRef[1]==0 ){\n    p->aRef[1] = 1;\n    aOut = &p->aMatchinfo[1];\n    xRet = fts3MIBufferFree;\n  }\n  else if( p->aRef[2]==0 ){\n    p->aRef[2] = 1;\n    aOut = &p->aMatchinfo[p->nElem+2];\n    xRet = fts3MIBufferFree;\n  }else{\n    aOut = (u32*)sqlite3_malloc(p->nElem * sizeof(u32));\n    if( aOut ){\n      xRet = sqlite3_free;\n      if( p->bGlobal ) memcpy(aOut, &p->aMatchinfo[1], p->nElem*sizeof(u32));\n    }\n  }\n\n  *paOut = aOut;\n  return xRet;\n}\n\nstatic void fts3MIBufferSetGlobal(MatchinfoBuffer *p){\n  p->bGlobal = 1;\n  memcpy(&p->aMatchinfo[2+p->nElem], &p->aMatchinfo[1], p->nElem*sizeof(u32));\n}\n\n/*\n** Free a MatchinfoBuffer object allocated using fts3MIBufferNew()\n*/\nSQLITE_PRIVATE void sqlite3Fts3MIBufferFree(MatchinfoBuffer *p){\n  if( p ){\n    assert( p->aRef[0]==1 );\n    p->aRef[0] = 0;\n    if( p->aRef[0]==0 && p->aRef[1]==0 && p->aRef[2]==0 ){\n      sqlite3_free(p);\n    }\n  }\n}\n\n/* \n** End of MatchinfoBuffer code.\n*************************************************************************/\n\n\n/*\n** This function is used to help iterate through a position-list. A position\n** list is a list of unique integers, sorted from smallest to largest. Each\n** element of the list is represented by an FTS3 varint that takes the value\n** of the difference between the current element and the previous one plus\n** two. For example, to store the position-list:\n**\n**     4 9 113\n**\n** the three varints:\n**\n**     6 7 106\n**\n** are encoded.\n**\n** When this function is called, *pp points to the start of an element of\n** the list. *piPos contains the value of the previous entry in the list.\n** After it returns, *piPos contains the value of the next element of the\n** list and *pp is advanced to the following varint.\n*/\nstatic void fts3GetDeltaPosition(char **pp, int *piPos){\n  int iVal;\n  *pp += fts3GetVarint32(*pp, &iVal);\n  *piPos += (iVal-2);\n}\n\n/*\n** Helper function for fts3ExprIterate() (see below).\n*/\nstatic int fts3ExprIterate2(\n  Fts3Expr *pExpr,                /* Expression to iterate phrases of */\n  int *piPhrase,                  /* Pointer to phrase counter */\n  int (*x)(Fts3Expr*,int,void*),  /* Callback function to invoke for phrases */\n  void *pCtx                      /* Second argument to pass to callback */\n){\n  int rc;                         /* Return code */\n  int eType = pExpr->eType;     /* Type of expression node pExpr */\n\n  if( eType!=FTSQUERY_PHRASE ){\n    assert( pExpr->pLeft && pExpr->pRight );\n    rc = fts3ExprIterate2(pExpr->pLeft, piPhrase, x, pCtx);\n    if( rc==SQLITE_OK && eType!=FTSQUERY_NOT ){\n      rc = fts3ExprIterate2(pExpr->pRight, piPhrase, x, pCtx);\n    }\n  }else{\n    rc = x(pExpr, *piPhrase, pCtx);\n    (*piPhrase)++;\n  }\n  return rc;\n}\n\n/*\n** Iterate through all phrase nodes in an FTS3 query, except those that\n** are part of a sub-tree that is the right-hand-side of a NOT operator.\n** For each phrase node found, the supplied callback function is invoked.\n**\n** If the callback function returns anything other than SQLITE_OK, \n** the iteration is abandoned and the error code returned immediately.\n** Otherwise, SQLITE_OK is returned after a callback has been made for\n** all eligible phrase nodes.\n*/\nstatic int fts3ExprIterate(\n  Fts3Expr *pExpr,                /* Expression to iterate phrases of */\n  int (*x)(Fts3Expr*,int,void*),  /* Callback function to invoke for phrases */\n  void *pCtx                      /* Second argument to pass to callback */\n){\n  int iPhrase = 0;                /* Variable used as the phrase counter */\n  return fts3ExprIterate2(pExpr, &iPhrase, x, pCtx);\n}\n\n\n/*\n** This is an fts3ExprIterate() callback used while loading the doclists\n** for each phrase into Fts3Expr.aDoclist[]/nDoclist. See also\n** fts3ExprLoadDoclists().\n*/\nstatic int fts3ExprLoadDoclistsCb(Fts3Expr *pExpr, int iPhrase, void *ctx){\n  int rc = SQLITE_OK;\n  Fts3Phrase *pPhrase = pExpr->pPhrase;\n  LoadDoclistCtx *p = (LoadDoclistCtx *)ctx;\n\n  UNUSED_PARAMETER(iPhrase);\n\n  p->nPhrase++;\n  p->nToken += pPhrase->nToken;\n\n  return rc;\n}\n\n/*\n** Load the doclists for each phrase in the query associated with FTS3 cursor\n** pCsr. \n**\n** If pnPhrase is not NULL, then *pnPhrase is set to the number of matchable \n** phrases in the expression (all phrases except those directly or \n** indirectly descended from the right-hand-side of a NOT operator). If \n** pnToken is not NULL, then it is set to the number of tokens in all\n** matchable phrases of the expression.\n*/\nstatic int fts3ExprLoadDoclists(\n  Fts3Cursor *pCsr,               /* Fts3 cursor for current query */\n  int *pnPhrase,                  /* OUT: Number of phrases in query */\n  int *pnToken                    /* OUT: Number of tokens in query */\n){\n  int rc;                         /* Return Code */\n  LoadDoclistCtx sCtx = {0,0,0};  /* Context for fts3ExprIterate() */\n  sCtx.pCsr = pCsr;\n  rc = fts3ExprIterate(pCsr->pExpr, fts3ExprLoadDoclistsCb, (void *)&sCtx);\n  if( pnPhrase ) *pnPhrase = sCtx.nPhrase;\n  if( pnToken ) *pnToken = sCtx.nToken;\n  return rc;\n}\n\nstatic int fts3ExprPhraseCountCb(Fts3Expr *pExpr, int iPhrase, void *ctx){\n  (*(int *)ctx)++;\n  pExpr->iPhrase = iPhrase;\n  return SQLITE_OK;\n}\nstatic int fts3ExprPhraseCount(Fts3Expr *pExpr){\n  int nPhrase = 0;\n  (void)fts3ExprIterate(pExpr, fts3ExprPhraseCountCb, (void *)&nPhrase);\n  return nPhrase;\n}\n\n/*\n** Advance the position list iterator specified by the first two \n** arguments so that it points to the first element with a value greater\n** than or equal to parameter iNext.\n*/\nstatic void fts3SnippetAdvance(char **ppIter, int *piIter, int iNext){\n  char *pIter = *ppIter;\n  if( pIter ){\n    int iIter = *piIter;\n\n    while( iIter<iNext ){\n      if( 0==(*pIter & 0xFE) ){\n        iIter = -1;\n        pIter = 0;\n        break;\n      }\n      fts3GetDeltaPosition(&pIter, &iIter);\n    }\n\n    *piIter = iIter;\n    *ppIter = pIter;\n  }\n}\n\n/*\n** Advance the snippet iterator to the next candidate snippet.\n*/\nstatic int fts3SnippetNextCandidate(SnippetIter *pIter){\n  int i;                          /* Loop counter */\n\n  if( pIter->iCurrent<0 ){\n    /* The SnippetIter object has just been initialized. The first snippet\n    ** candidate always starts at offset 0 (even if this candidate has a\n    ** score of 0.0).\n    */\n    pIter->iCurrent = 0;\n\n    /* Advance the 'head' iterator of each phrase to the first offset that\n    ** is greater than or equal to (iNext+nSnippet).\n    */\n    for(i=0; i<pIter->nPhrase; i++){\n      SnippetPhrase *pPhrase = &pIter->aPhrase[i];\n      fts3SnippetAdvance(&pPhrase->pHead, &pPhrase->iHead, pIter->nSnippet);\n    }\n  }else{\n    int iStart;\n    int iEnd = 0x7FFFFFFF;\n\n    for(i=0; i<pIter->nPhrase; i++){\n      SnippetPhrase *pPhrase = &pIter->aPhrase[i];\n      if( pPhrase->pHead && pPhrase->iHead<iEnd ){\n        iEnd = pPhrase->iHead;\n      }\n    }\n    if( iEnd==0x7FFFFFFF ){\n      return 1;\n    }\n\n    pIter->iCurrent = iStart = iEnd - pIter->nSnippet + 1;\n    for(i=0; i<pIter->nPhrase; i++){\n      SnippetPhrase *pPhrase = &pIter->aPhrase[i];\n      fts3SnippetAdvance(&pPhrase->pHead, &pPhrase->iHead, iEnd+1);\n      fts3SnippetAdvance(&pPhrase->pTail, &pPhrase->iTail, iStart);\n    }\n  }\n\n  return 0;\n}\n\n/*\n** Retrieve information about the current candidate snippet of snippet \n** iterator pIter.\n*/\nstatic void fts3SnippetDetails(\n  SnippetIter *pIter,             /* Snippet iterator */\n  u64 mCovered,                   /* Bitmask of phrases already covered */\n  int *piToken,                   /* OUT: First token of proposed snippet */\n  int *piScore,                   /* OUT: \"Score\" for this snippet */\n  u64 *pmCover,                   /* OUT: Bitmask of phrases covered */\n  u64 *pmHighlight                /* OUT: Bitmask of terms to highlight */\n){\n  int iStart = pIter->iCurrent;   /* First token of snippet */\n  int iScore = 0;                 /* Score of this snippet */\n  int i;                          /* Loop counter */\n  u64 mCover = 0;                 /* Mask of phrases covered by this snippet */\n  u64 mHighlight = 0;             /* Mask of tokens to highlight in snippet */\n\n  for(i=0; i<pIter->nPhrase; i++){\n    SnippetPhrase *pPhrase = &pIter->aPhrase[i];\n    if( pPhrase->pTail ){\n      char *pCsr = pPhrase->pTail;\n      int iCsr = pPhrase->iTail;\n\n      while( iCsr<(iStart+pIter->nSnippet) ){\n        int j;\n        u64 mPhrase = (u64)1 << i;\n        u64 mPos = (u64)1 << (iCsr - iStart);\n        assert( iCsr>=iStart );\n        if( (mCover|mCovered)&mPhrase ){\n          iScore++;\n        }else{\n          iScore += 1000;\n        }\n        mCover |= mPhrase;\n\n        for(j=0; j<pPhrase->nToken; j++){\n          mHighlight |= (mPos>>j);\n        }\n\n        if( 0==(*pCsr & 0x0FE) ) break;\n        fts3GetDeltaPosition(&pCsr, &iCsr);\n      }\n    }\n  }\n\n  /* Set the output variables before returning. */\n  *piToken = iStart;\n  *piScore = iScore;\n  *pmCover = mCover;\n  *pmHighlight = mHighlight;\n}\n\n/*\n** This function is an fts3ExprIterate() callback used by fts3BestSnippet().\n** Each invocation populates an element of the SnippetIter.aPhrase[] array.\n*/\nstatic int fts3SnippetFindPositions(Fts3Expr *pExpr, int iPhrase, void *ctx){\n  SnippetIter *p = (SnippetIter *)ctx;\n  SnippetPhrase *pPhrase = &p->aPhrase[iPhrase];\n  char *pCsr;\n  int rc;\n\n  pPhrase->nToken = pExpr->pPhrase->nToken;\n  rc = sqlite3Fts3EvalPhrasePoslist(p->pCsr, pExpr, p->iCol, &pCsr);\n  assert( rc==SQLITE_OK || pCsr==0 );\n  if( pCsr ){\n    int iFirst = 0;\n    pPhrase->pList = pCsr;\n    fts3GetDeltaPosition(&pCsr, &iFirst);\n    assert( iFirst>=0 );\n    pPhrase->pHead = pCsr;\n    pPhrase->pTail = pCsr;\n    pPhrase->iHead = iFirst;\n    pPhrase->iTail = iFirst;\n  }else{\n    assert( rc!=SQLITE_OK || (\n       pPhrase->pList==0 && pPhrase->pHead==0 && pPhrase->pTail==0 \n    ));\n  }\n\n  return rc;\n}\n\n/*\n** Select the fragment of text consisting of nFragment contiguous tokens \n** from column iCol that represent the \"best\" snippet. The best snippet\n** is the snippet with the highest score, where scores are calculated\n** by adding:\n**\n**   (a) +1 point for each occurrence of a matchable phrase in the snippet.\n**\n**   (b) +1000 points for the first occurrence of each matchable phrase in \n**       the snippet for which the corresponding mCovered bit is not set.\n**\n** The selected snippet parameters are stored in structure *pFragment before\n** returning. The score of the selected snippet is stored in *piScore\n** before returning.\n*/\nstatic int fts3BestSnippet(\n  int nSnippet,                   /* Desired snippet length */\n  Fts3Cursor *pCsr,               /* Cursor to create snippet for */\n  int iCol,                       /* Index of column to create snippet from */\n  u64 mCovered,                   /* Mask of phrases already covered */\n  u64 *pmSeen,                    /* IN/OUT: Mask of phrases seen */\n  SnippetFragment *pFragment,     /* OUT: Best snippet found */\n  int *piScore                    /* OUT: Score of snippet pFragment */\n){\n  int rc;                         /* Return Code */\n  int nList;                      /* Number of phrases in expression */\n  SnippetIter sIter;              /* Iterates through snippet candidates */\n  int nByte;                      /* Number of bytes of space to allocate */\n  int iBestScore = -1;            /* Best snippet score found so far */\n  int i;                          /* Loop counter */\n\n  memset(&sIter, 0, sizeof(sIter));\n\n  /* Iterate through the phrases in the expression to count them. The same\n  ** callback makes sure the doclists are loaded for each phrase.\n  */\n  rc = fts3ExprLoadDoclists(pCsr, &nList, 0);\n  if( rc!=SQLITE_OK ){\n    return rc;\n  }\n\n  /* Now that it is known how many phrases there are, allocate and zero\n  ** the required space using malloc().\n  */\n  nByte = sizeof(SnippetPhrase) * nList;\n  sIter.aPhrase = (SnippetPhrase *)sqlite3_malloc(nByte);\n  if( !sIter.aPhrase ){\n    return SQLITE_NOMEM;\n  }\n  memset(sIter.aPhrase, 0, nByte);\n\n  /* Initialize the contents of the SnippetIter object. Then iterate through\n  ** the set of phrases in the expression to populate the aPhrase[] array.\n  */\n  sIter.pCsr = pCsr;\n  sIter.iCol = iCol;\n  sIter.nSnippet = nSnippet;\n  sIter.nPhrase = nList;\n  sIter.iCurrent = -1;\n  rc = fts3ExprIterate(pCsr->pExpr, fts3SnippetFindPositions, (void*)&sIter);\n  if( rc==SQLITE_OK ){\n\n    /* Set the *pmSeen output variable. */\n    for(i=0; i<nList; i++){\n      if( sIter.aPhrase[i].pHead ){\n        *pmSeen |= (u64)1 << i;\n      }\n    }\n\n    /* Loop through all candidate snippets. Store the best snippet in \n     ** *pFragment. Store its associated 'score' in iBestScore.\n     */\n    pFragment->iCol = iCol;\n    while( !fts3SnippetNextCandidate(&sIter) ){\n      int iPos;\n      int iScore;\n      u64 mCover;\n      u64 mHighlite;\n      fts3SnippetDetails(&sIter, mCovered, &iPos, &iScore, &mCover,&mHighlite);\n      assert( iScore>=0 );\n      if( iScore>iBestScore ){\n        pFragment->iPos = iPos;\n        pFragment->hlmask = mHighlite;\n        pFragment->covered = mCover;\n        iBestScore = iScore;\n      }\n    }\n\n    *piScore = iBestScore;\n  }\n  sqlite3_free(sIter.aPhrase);\n  return rc;\n}\n\n\n/*\n** Append a string to the string-buffer passed as the first argument.\n**\n** If nAppend is negative, then the length of the string zAppend is\n** determined using strlen().\n*/\nstatic int fts3StringAppend(\n  StrBuffer *pStr,                /* Buffer to append to */\n  const char *zAppend,            /* Pointer to data to append to buffer */\n  int nAppend                     /* Size of zAppend in bytes (or -1) */\n){\n  if( nAppend<0 ){\n    nAppend = (int)strlen(zAppend);\n  }\n\n  /* If there is insufficient space allocated at StrBuffer.z, use realloc()\n  ** to grow the buffer until so that it is big enough to accomadate the\n  ** appended data.\n  */\n  if( pStr->n+nAppend+1>=pStr->nAlloc ){\n    int nAlloc = pStr->nAlloc+nAppend+100;\n    char *zNew = sqlite3_realloc(pStr->z, nAlloc);\n    if( !zNew ){\n      return SQLITE_NOMEM;\n    }\n    pStr->z = zNew;\n    pStr->nAlloc = nAlloc;\n  }\n  assert( pStr->z!=0 && (pStr->nAlloc >= pStr->n+nAppend+1) );\n\n  /* Append the data to the string buffer. */\n  memcpy(&pStr->z[pStr->n], zAppend, nAppend);\n  pStr->n += nAppend;\n  pStr->z[pStr->n] = '\\0';\n\n  return SQLITE_OK;\n}\n\n/*\n** The fts3BestSnippet() function often selects snippets that end with a\n** query term. That is, the final term of the snippet is always a term\n** that requires highlighting. For example, if 'X' is a highlighted term\n** and '.' is a non-highlighted term, BestSnippet() may select:\n**\n**     ........X.....X\n**\n** This function \"shifts\" the beginning of the snippet forward in the \n** document so that there are approximately the same number of \n** non-highlighted terms to the right of the final highlighted term as there\n** are to the left of the first highlighted term. For example, to this:\n**\n**     ....X.....X....\n**\n** This is done as part of extracting the snippet text, not when selecting\n** the snippet. Snippet selection is done based on doclists only, so there\n** is no way for fts3BestSnippet() to know whether or not the document \n** actually contains terms that follow the final highlighted term. \n*/\nstatic int fts3SnippetShift(\n  Fts3Table *pTab,                /* FTS3 table snippet comes from */\n  int iLangid,                    /* Language id to use in tokenizing */\n  int nSnippet,                   /* Number of tokens desired for snippet */\n  const char *zDoc,               /* Document text to extract snippet from */\n  int nDoc,                       /* Size of buffer zDoc in bytes */\n  int *piPos,                     /* IN/OUT: First token of snippet */\n  u64 *pHlmask                    /* IN/OUT: Mask of tokens to highlight */\n){\n  u64 hlmask = *pHlmask;          /* Local copy of initial highlight-mask */\n\n  if( hlmask ){\n    int nLeft;                    /* Tokens to the left of first highlight */\n    int nRight;                   /* Tokens to the right of last highlight */\n    int nDesired;                 /* Ideal number of tokens to shift forward */\n\n    for(nLeft=0; !(hlmask & ((u64)1 << nLeft)); nLeft++);\n    for(nRight=0; !(hlmask & ((u64)1 << (nSnippet-1-nRight))); nRight++);\n    nDesired = (nLeft-nRight)/2;\n\n    /* Ideally, the start of the snippet should be pushed forward in the\n    ** document nDesired tokens. This block checks if there are actually\n    ** nDesired tokens to the right of the snippet. If so, *piPos and\n    ** *pHlMask are updated to shift the snippet nDesired tokens to the\n    ** right. Otherwise, the snippet is shifted by the number of tokens\n    ** available.\n    */\n    if( nDesired>0 ){\n      int nShift;                 /* Number of tokens to shift snippet by */\n      int iCurrent = 0;           /* Token counter */\n      int rc;                     /* Return Code */\n      sqlite3_tokenizer_module *pMod;\n      sqlite3_tokenizer_cursor *pC;\n      pMod = (sqlite3_tokenizer_module *)pTab->pTokenizer->pModule;\n\n      /* Open a cursor on zDoc/nDoc. Check if there are (nSnippet+nDesired)\n      ** or more tokens in zDoc/nDoc.\n      */\n      rc = sqlite3Fts3OpenTokenizer(pTab->pTokenizer, iLangid, zDoc, nDoc, &pC);\n      if( rc!=SQLITE_OK ){\n        return rc;\n      }\n      while( rc==SQLITE_OK && iCurrent<(nSnippet+nDesired) ){\n        const char *ZDUMMY; int DUMMY1 = 0, DUMMY2 = 0, DUMMY3 = 0;\n        rc = pMod->xNext(pC, &ZDUMMY, &DUMMY1, &DUMMY2, &DUMMY3, &iCurrent);\n      }\n      pMod->xClose(pC);\n      if( rc!=SQLITE_OK && rc!=SQLITE_DONE ){ return rc; }\n\n      nShift = (rc==SQLITE_DONE)+iCurrent-nSnippet;\n      assert( nShift<=nDesired );\n      if( nShift>0 ){\n        *piPos += nShift;\n        *pHlmask = hlmask >> nShift;\n      }\n    }\n  }\n  return SQLITE_OK;\n}\n\n/*\n** Extract the snippet text for fragment pFragment from cursor pCsr and\n** append it to string buffer pOut.\n*/\nstatic int fts3SnippetText(\n  Fts3Cursor *pCsr,               /* FTS3 Cursor */\n  SnippetFragment *pFragment,     /* Snippet to extract */\n  int iFragment,                  /* Fragment number */\n  int isLast,                     /* True for final fragment in snippet */\n  int nSnippet,                   /* Number of tokens in extracted snippet */\n  const char *zOpen,              /* String inserted before highlighted term */\n  const char *zClose,             /* String inserted after highlighted term */\n  const char *zEllipsis,          /* String inserted between snippets */\n  StrBuffer *pOut                 /* Write output here */\n){\n  Fts3Table *pTab = (Fts3Table *)pCsr->base.pVtab;\n  int rc;                         /* Return code */\n  const char *zDoc;               /* Document text to extract snippet from */\n  int nDoc;                       /* Size of zDoc in bytes */\n  int iCurrent = 0;               /* Current token number of document */\n  int iEnd = 0;                   /* Byte offset of end of current token */\n  int isShiftDone = 0;            /* True after snippet is shifted */\n  int iPos = pFragment->iPos;     /* First token of snippet */\n  u64 hlmask = pFragment->hlmask; /* Highlight-mask for snippet */\n  int iCol = pFragment->iCol+1;   /* Query column to extract text from */\n  sqlite3_tokenizer_module *pMod; /* Tokenizer module methods object */\n  sqlite3_tokenizer_cursor *pC;   /* Tokenizer cursor open on zDoc/nDoc */\n  \n  zDoc = (const char *)sqlite3_column_text(pCsr->pStmt, iCol);\n  if( zDoc==0 ){\n    if( sqlite3_column_type(pCsr->pStmt, iCol)!=SQLITE_NULL ){\n      return SQLITE_NOMEM;\n    }\n    return SQLITE_OK;\n  }\n  nDoc = sqlite3_column_bytes(pCsr->pStmt, iCol);\n\n  /* Open a token cursor on the document. */\n  pMod = (sqlite3_tokenizer_module *)pTab->pTokenizer->pModule;\n  rc = sqlite3Fts3OpenTokenizer(pTab->pTokenizer, pCsr->iLangid, zDoc,nDoc,&pC);\n  if( rc!=SQLITE_OK ){\n    return rc;\n  }\n\n  while( rc==SQLITE_OK ){\n    const char *ZDUMMY;           /* Dummy argument used with tokenizer */\n    int DUMMY1 = -1;              /* Dummy argument used with tokenizer */\n    int iBegin = 0;               /* Offset in zDoc of start of token */\n    int iFin = 0;                 /* Offset in zDoc of end of token */\n    int isHighlight = 0;          /* True for highlighted terms */\n\n    /* Variable DUMMY1 is initialized to a negative value above. Elsewhere\n    ** in the FTS code the variable that the third argument to xNext points to\n    ** is initialized to zero before the first (*but not necessarily\n    ** subsequent*) call to xNext(). This is done for a particular application\n    ** that needs to know whether or not the tokenizer is being used for\n    ** snippet generation or for some other purpose.\n    **\n    ** Extreme care is required when writing code to depend on this\n    ** initialization. It is not a documented part of the tokenizer interface.\n    ** If a tokenizer is used directly by any code outside of FTS, this\n    ** convention might not be respected.  */\n    rc = pMod->xNext(pC, &ZDUMMY, &DUMMY1, &iBegin, &iFin, &iCurrent);\n    if( rc!=SQLITE_OK ){\n      if( rc==SQLITE_DONE ){\n        /* Special case - the last token of the snippet is also the last token\n        ** of the column. Append any punctuation that occurred between the end\n        ** of the previous token and the end of the document to the output. \n        ** Then break out of the loop. */\n        rc = fts3StringAppend(pOut, &zDoc[iEnd], -1);\n      }\n      break;\n    }\n    if( iCurrent<iPos ){ continue; }\n\n    if( !isShiftDone ){\n      int n = nDoc - iBegin;\n      rc = fts3SnippetShift(\n          pTab, pCsr->iLangid, nSnippet, &zDoc[iBegin], n, &iPos, &hlmask\n      );\n      isShiftDone = 1;\n\n      /* Now that the shift has been done, check if the initial \"...\" are\n      ** required. They are required if (a) this is not the first fragment,\n      ** or (b) this fragment does not begin at position 0 of its column. \n      */\n      if( rc==SQLITE_OK ){\n        if( iPos>0 || iFragment>0 ){\n          rc = fts3StringAppend(pOut, zEllipsis, -1);\n        }else if( iBegin ){\n          rc = fts3StringAppend(pOut, zDoc, iBegin);\n        }\n      }\n      if( rc!=SQLITE_OK || iCurrent<iPos ) continue;\n    }\n\n    if( iCurrent>=(iPos+nSnippet) ){\n      if( isLast ){\n        rc = fts3StringAppend(pOut, zEllipsis, -1);\n      }\n      break;\n    }\n\n    /* Set isHighlight to true if this term should be highlighted. */\n    isHighlight = (hlmask & ((u64)1 << (iCurrent-iPos)))!=0;\n\n    if( iCurrent>iPos ) rc = fts3StringAppend(pOut, &zDoc[iEnd], iBegin-iEnd);\n    if( rc==SQLITE_OK && isHighlight ) rc = fts3StringAppend(pOut, zOpen, -1);\n    if( rc==SQLITE_OK ) rc = fts3StringAppend(pOut, &zDoc[iBegin], iFin-iBegin);\n    if( rc==SQLITE_OK && isHighlight ) rc = fts3StringAppend(pOut, zClose, -1);\n\n    iEnd = iFin;\n  }\n\n  pMod->xClose(pC);\n  return rc;\n}\n\n\n/*\n** This function is used to count the entries in a column-list (a \n** delta-encoded list of term offsets within a single column of a single \n** row). When this function is called, *ppCollist should point to the\n** beginning of the first varint in the column-list (the varint that\n** contains the position of the first matching term in the column data).\n** Before returning, *ppCollist is set to point to the first byte after\n** the last varint in the column-list (either the 0x00 signifying the end\n** of the position-list, or the 0x01 that precedes the column number of\n** the next column in the position-list).\n**\n** The number of elements in the column-list is returned.\n*/\nstatic int fts3ColumnlistCount(char **ppCollist){\n  char *pEnd = *ppCollist;\n  char c = 0;\n  int nEntry = 0;\n\n  /* A column-list is terminated by either a 0x01 or 0x00. */\n  while( 0xFE & (*pEnd | c) ){\n    c = *pEnd++ & 0x80;\n    if( !c ) nEntry++;\n  }\n\n  *ppCollist = pEnd;\n  return nEntry;\n}\n\n/*\n** This function gathers 'y' or 'b' data for a single phrase.\n*/\nstatic void fts3ExprLHits(\n  Fts3Expr *pExpr,                /* Phrase expression node */\n  MatchInfo *p                    /* Matchinfo context */\n){\n  Fts3Table *pTab = (Fts3Table *)p->pCursor->base.pVtab;\n  int iStart;\n  Fts3Phrase *pPhrase = pExpr->pPhrase;\n  char *pIter = pPhrase->doclist.pList;\n  int iCol = 0;\n\n  assert( p->flag==FTS3_MATCHINFO_LHITS_BM || p->flag==FTS3_MATCHINFO_LHITS );\n  if( p->flag==FTS3_MATCHINFO_LHITS ){\n    iStart = pExpr->iPhrase * p->nCol;\n  }else{\n    iStart = pExpr->iPhrase * ((p->nCol + 31) / 32);\n  }\n\n  while( 1 ){\n    int nHit = fts3ColumnlistCount(&pIter);\n    if( (pPhrase->iColumn>=pTab->nColumn || pPhrase->iColumn==iCol) ){\n      if( p->flag==FTS3_MATCHINFO_LHITS ){\n        p->aMatchinfo[iStart + iCol] = (u32)nHit;\n      }else if( nHit ){\n        p->aMatchinfo[iStart + (iCol+1)/32] |= (1 << (iCol&0x1F));\n      }\n    }\n    assert( *pIter==0x00 || *pIter==0x01 );\n    if( *pIter!=0x01 ) break;\n    pIter++;\n    pIter += fts3GetVarint32(pIter, &iCol);\n  }\n}\n\n/*\n** Gather the results for matchinfo directives 'y' and 'b'.\n*/\nstatic void fts3ExprLHitGather(\n  Fts3Expr *pExpr,\n  MatchInfo *p\n){\n  assert( (pExpr->pLeft==0)==(pExpr->pRight==0) );\n  if( pExpr->bEof==0 && pExpr->iDocid==p->pCursor->iPrevId ){\n    if( pExpr->pLeft ){\n      fts3ExprLHitGather(pExpr->pLeft, p);\n      fts3ExprLHitGather(pExpr->pRight, p);\n    }else{\n      fts3ExprLHits(pExpr, p);\n    }\n  }\n}\n\n/*\n** fts3ExprIterate() callback used to collect the \"global\" matchinfo stats\n** for a single query. \n**\n** fts3ExprIterate() callback to load the 'global' elements of a\n** FTS3_MATCHINFO_HITS matchinfo array. The global stats are those elements \n** of the matchinfo array that are constant for all rows returned by the \n** current query.\n**\n** Argument pCtx is actually a pointer to a struct of type MatchInfo. This\n** function populates Matchinfo.aMatchinfo[] as follows:\n**\n**   for(iCol=0; iCol<nCol; iCol++){\n**     aMatchinfo[3*iPhrase*nCol + 3*iCol + 1] = X;\n**     aMatchinfo[3*iPhrase*nCol + 3*iCol + 2] = Y;\n**   }\n**\n** where X is the number of matches for phrase iPhrase is column iCol of all\n** rows of the table. Y is the number of rows for which column iCol contains\n** at least one instance of phrase iPhrase.\n**\n** If the phrase pExpr consists entirely of deferred tokens, then all X and\n** Y values are set to nDoc, where nDoc is the number of documents in the \n** file system. This is done because the full-text index doclist is required\n** to calculate these values properly, and the full-text index doclist is\n** not available for deferred tokens.\n*/\nstatic int fts3ExprGlobalHitsCb(\n  Fts3Expr *pExpr,                /* Phrase expression node */\n  int iPhrase,                    /* Phrase number (numbered from zero) */\n  void *pCtx                      /* Pointer to MatchInfo structure */\n){\n  MatchInfo *p = (MatchInfo *)pCtx;\n  return sqlite3Fts3EvalPhraseStats(\n      p->pCursor, pExpr, &p->aMatchinfo[3*iPhrase*p->nCol]\n  );\n}\n\n/*\n** fts3ExprIterate() callback used to collect the \"local\" part of the\n** FTS3_MATCHINFO_HITS array. The local stats are those elements of the \n** array that are different for each row returned by the query.\n*/\nstatic int fts3ExprLocalHitsCb(\n  Fts3Expr *pExpr,                /* Phrase expression node */\n  int iPhrase,                    /* Phrase number */\n  void *pCtx                      /* Pointer to MatchInfo structure */\n){\n  int rc = SQLITE_OK;\n  MatchInfo *p = (MatchInfo *)pCtx;\n  int iStart = iPhrase * p->nCol * 3;\n  int i;\n\n  for(i=0; i<p->nCol && rc==SQLITE_OK; i++){\n    char *pCsr;\n    rc = sqlite3Fts3EvalPhrasePoslist(p->pCursor, pExpr, i, &pCsr);\n    if( pCsr ){\n      p->aMatchinfo[iStart+i*3] = fts3ColumnlistCount(&pCsr);\n    }else{\n      p->aMatchinfo[iStart+i*3] = 0;\n    }\n  }\n\n  return rc;\n}\n\nstatic int fts3MatchinfoCheck(\n  Fts3Table *pTab, \n  char cArg,\n  char **pzErr\n){\n  if( (cArg==FTS3_MATCHINFO_NPHRASE)\n   || (cArg==FTS3_MATCHINFO_NCOL)\n   || (cArg==FTS3_MATCHINFO_NDOC && pTab->bFts4)\n   || (cArg==FTS3_MATCHINFO_AVGLENGTH && pTab->bFts4)\n   || (cArg==FTS3_MATCHINFO_LENGTH && pTab->bHasDocsize)\n   || (cArg==FTS3_MATCHINFO_LCS)\n   || (cArg==FTS3_MATCHINFO_HITS)\n   || (cArg==FTS3_MATCHINFO_LHITS)\n   || (cArg==FTS3_MATCHINFO_LHITS_BM)\n  ){\n    return SQLITE_OK;\n  }\n  sqlite3Fts3ErrMsg(pzErr, \"unrecognized matchinfo request: %c\", cArg);\n  return SQLITE_ERROR;\n}\n\nstatic int fts3MatchinfoSize(MatchInfo *pInfo, char cArg){\n  int nVal;                       /* Number of integers output by cArg */\n\n  switch( cArg ){\n    case FTS3_MATCHINFO_NDOC:\n    case FTS3_MATCHINFO_NPHRASE: \n    case FTS3_MATCHINFO_NCOL: \n      nVal = 1;\n      break;\n\n    case FTS3_MATCHINFO_AVGLENGTH:\n    case FTS3_MATCHINFO_LENGTH:\n    case FTS3_MATCHINFO_LCS:\n      nVal = pInfo->nCol;\n      break;\n\n    case FTS3_MATCHINFO_LHITS:\n      nVal = pInfo->nCol * pInfo->nPhrase;\n      break;\n\n    case FTS3_MATCHINFO_LHITS_BM:\n      nVal = pInfo->nPhrase * ((pInfo->nCol + 31) / 32);\n      break;\n\n    default:\n      assert( cArg==FTS3_MATCHINFO_HITS );\n      nVal = pInfo->nCol * pInfo->nPhrase * 3;\n      break;\n  }\n\n  return nVal;\n}\n\nstatic int fts3MatchinfoSelectDoctotal(\n  Fts3Table *pTab,\n  sqlite3_stmt **ppStmt,\n  sqlite3_int64 *pnDoc,\n  const char **paLen\n){\n  sqlite3_stmt *pStmt;\n  const char *a;\n  sqlite3_int64 nDoc;\n\n  if( !*ppStmt ){\n    int rc = sqlite3Fts3SelectDoctotal(pTab, ppStmt);\n    if( rc!=SQLITE_OK ) return rc;\n  }\n  pStmt = *ppStmt;\n  assert( sqlite3_data_count(pStmt)==1 );\n\n  a = sqlite3_column_blob(pStmt, 0);\n  a += sqlite3Fts3GetVarint(a, &nDoc);\n  if( nDoc==0 ) return FTS_CORRUPT_VTAB;\n  *pnDoc = (u32)nDoc;\n\n  if( paLen ) *paLen = a;\n  return SQLITE_OK;\n}\n\n/*\n** An instance of the following structure is used to store state while \n** iterating through a multi-column position-list corresponding to the\n** hits for a single phrase on a single row in order to calculate the\n** values for a matchinfo() FTS3_MATCHINFO_LCS request.\n*/\ntypedef struct LcsIterator LcsIterator;\nstruct LcsIterator {\n  Fts3Expr *pExpr;                /* Pointer to phrase expression */\n  int iPosOffset;                 /* Tokens count up to end of this phrase */\n  char *pRead;                    /* Cursor used to iterate through aDoclist */\n  int iPos;                       /* Current position */\n};\n\n/* \n** If LcsIterator.iCol is set to the following value, the iterator has\n** finished iterating through all offsets for all columns.\n*/\n#define LCS_ITERATOR_FINISHED 0x7FFFFFFF;\n\nstatic int fts3MatchinfoLcsCb(\n  Fts3Expr *pExpr,                /* Phrase expression node */\n  int iPhrase,                    /* Phrase number (numbered from zero) */\n  void *pCtx                      /* Pointer to MatchInfo structure */\n){\n  LcsIterator *aIter = (LcsIterator *)pCtx;\n  aIter[iPhrase].pExpr = pExpr;\n  return SQLITE_OK;\n}\n\n/*\n** Advance the iterator passed as an argument to the next position. Return\n** 1 if the iterator is at EOF or if it now points to the start of the\n** position list for the next column.\n*/\nstatic int fts3LcsIteratorAdvance(LcsIterator *pIter){\n  char *pRead = pIter->pRead;\n  sqlite3_int64 iRead;\n  int rc = 0;\n\n  pRead += sqlite3Fts3GetVarint(pRead, &iRead);\n  if( iRead==0 || iRead==1 ){\n    pRead = 0;\n    rc = 1;\n  }else{\n    pIter->iPos += (int)(iRead-2);\n  }\n\n  pIter->pRead = pRead;\n  return rc;\n}\n  \n/*\n** This function implements the FTS3_MATCHINFO_LCS matchinfo() flag. \n**\n** If the call is successful, the longest-common-substring lengths for each\n** column are written into the first nCol elements of the pInfo->aMatchinfo[] \n** array before returning. SQLITE_OK is returned in this case.\n**\n** Otherwise, if an error occurs, an SQLite error code is returned and the\n** data written to the first nCol elements of pInfo->aMatchinfo[] is \n** undefined.\n*/\nstatic int fts3MatchinfoLcs(Fts3Cursor *pCsr, MatchInfo *pInfo){\n  LcsIterator *aIter;\n  int i;\n  int iCol;\n  int nToken = 0;\n\n  /* Allocate and populate the array of LcsIterator objects. The array\n  ** contains one element for each matchable phrase in the query.\n  **/\n  aIter = sqlite3_malloc(sizeof(LcsIterator) * pCsr->nPhrase);\n  if( !aIter ) return SQLITE_NOMEM;\n  memset(aIter, 0, sizeof(LcsIterator) * pCsr->nPhrase);\n  (void)fts3ExprIterate(pCsr->pExpr, fts3MatchinfoLcsCb, (void*)aIter);\n\n  for(i=0; i<pInfo->nPhrase; i++){\n    LcsIterator *pIter = &aIter[i];\n    nToken -= pIter->pExpr->pPhrase->nToken;\n    pIter->iPosOffset = nToken;\n  }\n\n  for(iCol=0; iCol<pInfo->nCol; iCol++){\n    int nLcs = 0;                 /* LCS value for this column */\n    int nLive = 0;                /* Number of iterators in aIter not at EOF */\n\n    for(i=0; i<pInfo->nPhrase; i++){\n      int rc;\n      LcsIterator *pIt = &aIter[i];\n      rc = sqlite3Fts3EvalPhrasePoslist(pCsr, pIt->pExpr, iCol, &pIt->pRead);\n      if( rc!=SQLITE_OK ) return rc;\n      if( pIt->pRead ){\n        pIt->iPos = pIt->iPosOffset;\n        fts3LcsIteratorAdvance(&aIter[i]);\n        nLive++;\n      }\n    }\n\n    while( nLive>0 ){\n      LcsIterator *pAdv = 0;      /* The iterator to advance by one position */\n      int nThisLcs = 0;           /* LCS for the current iterator positions */\n\n      for(i=0; i<pInfo->nPhrase; i++){\n        LcsIterator *pIter = &aIter[i];\n        if( pIter->pRead==0 ){\n          /* This iterator is already at EOF for this column. */\n          nThisLcs = 0;\n        }else{\n          if( pAdv==0 || pIter->iPos<pAdv->iPos ){\n            pAdv = pIter;\n          }\n          if( nThisLcs==0 || pIter->iPos==pIter[-1].iPos ){\n            nThisLcs++;\n          }else{\n            nThisLcs = 1;\n          }\n          if( nThisLcs>nLcs ) nLcs = nThisLcs;\n        }\n      }\n      if( fts3LcsIteratorAdvance(pAdv) ) nLive--;\n    }\n\n    pInfo->aMatchinfo[iCol] = nLcs;\n  }\n\n  sqlite3_free(aIter);\n  return SQLITE_OK;\n}\n\n/*\n** Populate the buffer pInfo->aMatchinfo[] with an array of integers to\n** be returned by the matchinfo() function. Argument zArg contains the \n** format string passed as the second argument to matchinfo (or the\n** default value \"pcx\" if no second argument was specified). The format\n** string has already been validated and the pInfo->aMatchinfo[] array\n** is guaranteed to be large enough for the output.\n**\n** If bGlobal is true, then populate all fields of the matchinfo() output.\n** If it is false, then assume that those fields that do not change between\n** rows (i.e. FTS3_MATCHINFO_NPHRASE, NCOL, NDOC, AVGLENGTH and part of HITS)\n** have already been populated.\n**\n** Return SQLITE_OK if successful, or an SQLite error code if an error \n** occurs. If a value other than SQLITE_OK is returned, the state the\n** pInfo->aMatchinfo[] buffer is left in is undefined.\n*/\nstatic int fts3MatchinfoValues(\n  Fts3Cursor *pCsr,               /* FTS3 cursor object */\n  int bGlobal,                    /* True to grab the global stats */\n  MatchInfo *pInfo,               /* Matchinfo context object */\n  const char *zArg                /* Matchinfo format string */\n){\n  int rc = SQLITE_OK;\n  int i;\n  Fts3Table *pTab = (Fts3Table *)pCsr->base.pVtab;\n  sqlite3_stmt *pSelect = 0;\n\n  for(i=0; rc==SQLITE_OK && zArg[i]; i++){\n    pInfo->flag = zArg[i];\n    switch( zArg[i] ){\n      case FTS3_MATCHINFO_NPHRASE:\n        if( bGlobal ) pInfo->aMatchinfo[0] = pInfo->nPhrase;\n        break;\n\n      case FTS3_MATCHINFO_NCOL:\n        if( bGlobal ) pInfo->aMatchinfo[0] = pInfo->nCol;\n        break;\n        \n      case FTS3_MATCHINFO_NDOC:\n        if( bGlobal ){\n          sqlite3_int64 nDoc = 0;\n          rc = fts3MatchinfoSelectDoctotal(pTab, &pSelect, &nDoc, 0);\n          pInfo->aMatchinfo[0] = (u32)nDoc;\n        }\n        break;\n\n      case FTS3_MATCHINFO_AVGLENGTH: \n        if( bGlobal ){\n          sqlite3_int64 nDoc;     /* Number of rows in table */\n          const char *a;          /* Aggregate column length array */\n\n          rc = fts3MatchinfoSelectDoctotal(pTab, &pSelect, &nDoc, &a);\n          if( rc==SQLITE_OK ){\n            int iCol;\n            for(iCol=0; iCol<pInfo->nCol; iCol++){\n              u32 iVal;\n              sqlite3_int64 nToken;\n              a += sqlite3Fts3GetVarint(a, &nToken);\n              iVal = (u32)(((u32)(nToken&0xffffffff)+nDoc/2)/nDoc);\n              pInfo->aMatchinfo[iCol] = iVal;\n            }\n          }\n        }\n        break;\n\n      case FTS3_MATCHINFO_LENGTH: {\n        sqlite3_stmt *pSelectDocsize = 0;\n        rc = sqlite3Fts3SelectDocsize(pTab, pCsr->iPrevId, &pSelectDocsize);\n        if( rc==SQLITE_OK ){\n          int iCol;\n          const char *a = sqlite3_column_blob(pSelectDocsize, 0);\n          for(iCol=0; iCol<pInfo->nCol; iCol++){\n            sqlite3_int64 nToken;\n            a += sqlite3Fts3GetVarint(a, &nToken);\n            pInfo->aMatchinfo[iCol] = (u32)nToken;\n          }\n        }\n        sqlite3_reset(pSelectDocsize);\n        break;\n      }\n\n      case FTS3_MATCHINFO_LCS:\n        rc = fts3ExprLoadDoclists(pCsr, 0, 0);\n        if( rc==SQLITE_OK ){\n          rc = fts3MatchinfoLcs(pCsr, pInfo);\n        }\n        break;\n\n      case FTS3_MATCHINFO_LHITS_BM:\n      case FTS3_MATCHINFO_LHITS: {\n        int nZero = fts3MatchinfoSize(pInfo, zArg[i]) * sizeof(u32);\n        memset(pInfo->aMatchinfo, 0, nZero);\n        fts3ExprLHitGather(pCsr->pExpr, pInfo);\n        break;\n      }\n\n      default: {\n        Fts3Expr *pExpr;\n        assert( zArg[i]==FTS3_MATCHINFO_HITS );\n        pExpr = pCsr->pExpr;\n        rc = fts3ExprLoadDoclists(pCsr, 0, 0);\n        if( rc!=SQLITE_OK ) break;\n        if( bGlobal ){\n          if( pCsr->pDeferred ){\n            rc = fts3MatchinfoSelectDoctotal(pTab, &pSelect, &pInfo->nDoc, 0);\n            if( rc!=SQLITE_OK ) break;\n          }\n          rc = fts3ExprIterate(pExpr, fts3ExprGlobalHitsCb,(void*)pInfo);\n          sqlite3Fts3EvalTestDeferred(pCsr, &rc);\n          if( rc!=SQLITE_OK ) break;\n        }\n        (void)fts3ExprIterate(pExpr, fts3ExprLocalHitsCb,(void*)pInfo);\n        break;\n      }\n    }\n\n    pInfo->aMatchinfo += fts3MatchinfoSize(pInfo, zArg[i]);\n  }\n\n  sqlite3_reset(pSelect);\n  return rc;\n}\n\n\n/*\n** Populate pCsr->aMatchinfo[] with data for the current row. The \n** 'matchinfo' data is an array of 32-bit unsigned integers (C type u32).\n*/\nstatic void fts3GetMatchinfo(\n  sqlite3_context *pCtx,        /* Return results here */\n  Fts3Cursor *pCsr,               /* FTS3 Cursor object */\n  const char *zArg                /* Second argument to matchinfo() function */\n){\n  MatchInfo sInfo;\n  Fts3Table *pTab = (Fts3Table *)pCsr->base.pVtab;\n  int rc = SQLITE_OK;\n  int bGlobal = 0;                /* Collect 'global' stats as well as local */\n\n  u32 *aOut = 0;\n  void (*xDestroyOut)(void*) = 0;\n\n  memset(&sInfo, 0, sizeof(MatchInfo));\n  sInfo.pCursor = pCsr;\n  sInfo.nCol = pTab->nColumn;\n\n  /* If there is cached matchinfo() data, but the format string for the \n  ** cache does not match the format string for this request, discard \n  ** the cached data. */\n  if( pCsr->pMIBuffer && strcmp(pCsr->pMIBuffer->zMatchinfo, zArg) ){\n    sqlite3Fts3MIBufferFree(pCsr->pMIBuffer);\n    pCsr->pMIBuffer = 0;\n  }\n\n  /* If Fts3Cursor.pMIBuffer is NULL, then this is the first time the\n  ** matchinfo function has been called for this query. In this case \n  ** allocate the array used to accumulate the matchinfo data and\n  ** initialize those elements that are constant for every row.\n  */\n  if( pCsr->pMIBuffer==0 ){\n    int nMatchinfo = 0;           /* Number of u32 elements in match-info */\n    int i;                        /* Used to iterate through zArg */\n\n    /* Determine the number of phrases in the query */\n    pCsr->nPhrase = fts3ExprPhraseCount(pCsr->pExpr);\n    sInfo.nPhrase = pCsr->nPhrase;\n\n    /* Determine the number of integers in the buffer returned by this call. */\n    for(i=0; zArg[i]; i++){\n      char *zErr = 0;\n      if( fts3MatchinfoCheck(pTab, zArg[i], &zErr) ){\n        sqlite3_result_error(pCtx, zErr, -1);\n        sqlite3_free(zErr);\n        return;\n      }\n      nMatchinfo += fts3MatchinfoSize(&sInfo, zArg[i]);\n    }\n\n    /* Allocate space for Fts3Cursor.aMatchinfo[] and Fts3Cursor.zMatchinfo. */\n    pCsr->pMIBuffer = fts3MIBufferNew(nMatchinfo, zArg);\n    if( !pCsr->pMIBuffer ) rc = SQLITE_NOMEM;\n\n    pCsr->isMatchinfoNeeded = 1;\n    bGlobal = 1;\n  }\n\n  if( rc==SQLITE_OK ){\n    xDestroyOut = fts3MIBufferAlloc(pCsr->pMIBuffer, &aOut);\n    if( xDestroyOut==0 ){\n      rc = SQLITE_NOMEM;\n    }\n  }\n\n  if( rc==SQLITE_OK ){\n    sInfo.aMatchinfo = aOut;\n    sInfo.nPhrase = pCsr->nPhrase;\n    rc = fts3MatchinfoValues(pCsr, bGlobal, &sInfo, zArg);\n    if( bGlobal ){\n      fts3MIBufferSetGlobal(pCsr->pMIBuffer);\n    }\n  }\n\n  if( rc!=SQLITE_OK ){\n    sqlite3_result_error_code(pCtx, rc);\n    if( xDestroyOut ) xDestroyOut(aOut);\n  }else{\n    int n = pCsr->pMIBuffer->nElem * sizeof(u32);\n    sqlite3_result_blob(pCtx, aOut, n, xDestroyOut);\n  }\n}\n\n/*\n** Implementation of snippet() function.\n*/\nSQLITE_PRIVATE void sqlite3Fts3Snippet(\n  sqlite3_context *pCtx,          /* SQLite function call context */\n  Fts3Cursor *pCsr,               /* Cursor object */\n  const char *zStart,             /* Snippet start text - \"<b>\" */\n  const char *zEnd,               /* Snippet end text - \"</b>\" */\n  const char *zEllipsis,          /* Snippet ellipsis text - \"<b>...</b>\" */\n  int iCol,                       /* Extract snippet from this column */\n  int nToken                      /* Approximate number of tokens in snippet */\n){\n  Fts3Table *pTab = (Fts3Table *)pCsr->base.pVtab;\n  int rc = SQLITE_OK;\n  int i;\n  StrBuffer res = {0, 0, 0};\n\n  /* The returned text includes up to four fragments of text extracted from\n  ** the data in the current row. The first iteration of the for(...) loop\n  ** below attempts to locate a single fragment of text nToken tokens in \n  ** size that contains at least one instance of all phrases in the query\n  ** expression that appear in the current row. If such a fragment of text\n  ** cannot be found, the second iteration of the loop attempts to locate\n  ** a pair of fragments, and so on.\n  */\n  int nSnippet = 0;               /* Number of fragments in this snippet */\n  SnippetFragment aSnippet[4];    /* Maximum of 4 fragments per snippet */\n  int nFToken = -1;               /* Number of tokens in each fragment */\n\n  if( !pCsr->pExpr ){\n    sqlite3_result_text(pCtx, \"\", 0, SQLITE_STATIC);\n    return;\n  }\n\n  for(nSnippet=1; 1; nSnippet++){\n\n    int iSnip;                    /* Loop counter 0..nSnippet-1 */\n    u64 mCovered = 0;             /* Bitmask of phrases covered by snippet */\n    u64 mSeen = 0;                /* Bitmask of phrases seen by BestSnippet() */\n\n    if( nToken>=0 ){\n      nFToken = (nToken+nSnippet-1) / nSnippet;\n    }else{\n      nFToken = -1 * nToken;\n    }\n\n    for(iSnip=0; iSnip<nSnippet; iSnip++){\n      int iBestScore = -1;        /* Best score of columns checked so far */\n      int iRead;                  /* Used to iterate through columns */\n      SnippetFragment *pFragment = &aSnippet[iSnip];\n\n      memset(pFragment, 0, sizeof(*pFragment));\n\n      /* Loop through all columns of the table being considered for snippets.\n      ** If the iCol argument to this function was negative, this means all\n      ** columns of the FTS3 table. Otherwise, only column iCol is considered.\n      */\n      for(iRead=0; iRead<pTab->nColumn; iRead++){\n        SnippetFragment sF = {0, 0, 0, 0};\n        int iS = 0;\n        if( iCol>=0 && iRead!=iCol ) continue;\n\n        /* Find the best snippet of nFToken tokens in column iRead. */\n        rc = fts3BestSnippet(nFToken, pCsr, iRead, mCovered, &mSeen, &sF, &iS);\n        if( rc!=SQLITE_OK ){\n          goto snippet_out;\n        }\n        if( iS>iBestScore ){\n          *pFragment = sF;\n          iBestScore = iS;\n        }\n      }\n\n      mCovered |= pFragment->covered;\n    }\n\n    /* If all query phrases seen by fts3BestSnippet() are present in at least\n    ** one of the nSnippet snippet fragments, break out of the loop.\n    */\n    assert( (mCovered&mSeen)==mCovered );\n    if( mSeen==mCovered || nSnippet==SizeofArray(aSnippet) ) break;\n  }\n\n  assert( nFToken>0 );\n\n  for(i=0; i<nSnippet && rc==SQLITE_OK; i++){\n    rc = fts3SnippetText(pCsr, &aSnippet[i], \n        i, (i==nSnippet-1), nFToken, zStart, zEnd, zEllipsis, &res\n    );\n  }\n\n snippet_out:\n  sqlite3Fts3SegmentsClose(pTab);\n  if( rc!=SQLITE_OK ){\n    sqlite3_result_error_code(pCtx, rc);\n    sqlite3_free(res.z);\n  }else{\n    sqlite3_result_text(pCtx, res.z, -1, sqlite3_free);\n  }\n}\n\n\ntypedef struct TermOffset TermOffset;\ntypedef struct TermOffsetCtx TermOffsetCtx;\n\nstruct TermOffset {\n  char *pList;                    /* Position-list */\n  int iPos;                       /* Position just read from pList */\n  int iOff;                       /* Offset of this term from read positions */\n};\n\nstruct TermOffsetCtx {\n  Fts3Cursor *pCsr;\n  int iCol;                       /* Column of table to populate aTerm for */\n  int iTerm;\n  sqlite3_int64 iDocid;\n  TermOffset *aTerm;\n};\n\n/*\n** This function is an fts3ExprIterate() callback used by sqlite3Fts3Offsets().\n*/\nstatic int fts3ExprTermOffsetInit(Fts3Expr *pExpr, int iPhrase, void *ctx){\n  TermOffsetCtx *p = (TermOffsetCtx *)ctx;\n  int nTerm;                      /* Number of tokens in phrase */\n  int iTerm;                      /* For looping through nTerm phrase terms */\n  char *pList;                    /* Pointer to position list for phrase */\n  int iPos = 0;                   /* First position in position-list */\n  int rc;\n\n  UNUSED_PARAMETER(iPhrase);\n  rc = sqlite3Fts3EvalPhrasePoslist(p->pCsr, pExpr, p->iCol, &pList);\n  nTerm = pExpr->pPhrase->nToken;\n  if( pList ){\n    fts3GetDeltaPosition(&pList, &iPos);\n    assert( iPos>=0 );\n  }\n\n  for(iTerm=0; iTerm<nTerm; iTerm++){\n    TermOffset *pT = &p->aTerm[p->iTerm++];\n    pT->iOff = nTerm-iTerm-1;\n    pT->pList = pList;\n    pT->iPos = iPos;\n  }\n\n  return rc;\n}\n\n/*\n** Implementation of offsets() function.\n*/\nSQLITE_PRIVATE void sqlite3Fts3Offsets(\n  sqlite3_context *pCtx,          /* SQLite function call context */\n  Fts3Cursor *pCsr                /* Cursor object */\n){\n  Fts3Table *pTab = (Fts3Table *)pCsr->base.pVtab;\n  sqlite3_tokenizer_module const *pMod = pTab->pTokenizer->pModule;\n  int rc;                         /* Return Code */\n  int nToken;                     /* Number of tokens in query */\n  int iCol;                       /* Column currently being processed */\n  StrBuffer res = {0, 0, 0};      /* Result string */\n  TermOffsetCtx sCtx;             /* Context for fts3ExprTermOffsetInit() */\n\n  if( !pCsr->pExpr ){\n    sqlite3_result_text(pCtx, \"\", 0, SQLITE_STATIC);\n    return;\n  }\n\n  memset(&sCtx, 0, sizeof(sCtx));\n  assert( pCsr->isRequireSeek==0 );\n\n  /* Count the number of terms in the query */\n  rc = fts3ExprLoadDoclists(pCsr, 0, &nToken);\n  if( rc!=SQLITE_OK ) goto offsets_out;\n\n  /* Allocate the array of TermOffset iterators. */\n  sCtx.aTerm = (TermOffset *)sqlite3_malloc(sizeof(TermOffset)*nToken);\n  if( 0==sCtx.aTerm ){\n    rc = SQLITE_NOMEM;\n    goto offsets_out;\n  }\n  sCtx.iDocid = pCsr->iPrevId;\n  sCtx.pCsr = pCsr;\n\n  /* Loop through the table columns, appending offset information to \n  ** string-buffer res for each column.\n  */\n  for(iCol=0; iCol<pTab->nColumn; iCol++){\n    sqlite3_tokenizer_cursor *pC; /* Tokenizer cursor */\n    const char *ZDUMMY;           /* Dummy argument used with xNext() */\n    int NDUMMY = 0;               /* Dummy argument used with xNext() */\n    int iStart = 0;\n    int iEnd = 0;\n    int iCurrent = 0;\n    const char *zDoc;\n    int nDoc;\n\n    /* Initialize the contents of sCtx.aTerm[] for column iCol. There is \n    ** no way that this operation can fail, so the return code from\n    ** fts3ExprIterate() can be discarded.\n    */\n    sCtx.iCol = iCol;\n    sCtx.iTerm = 0;\n    (void)fts3ExprIterate(pCsr->pExpr, fts3ExprTermOffsetInit, (void*)&sCtx);\n\n    /* Retreive the text stored in column iCol. If an SQL NULL is stored \n    ** in column iCol, jump immediately to the next iteration of the loop.\n    ** If an OOM occurs while retrieving the data (this can happen if SQLite\n    ** needs to transform the data from utf-16 to utf-8), return SQLITE_NOMEM \n    ** to the caller. \n    */\n    zDoc = (const char *)sqlite3_column_text(pCsr->pStmt, iCol+1);\n    nDoc = sqlite3_column_bytes(pCsr->pStmt, iCol+1);\n    if( zDoc==0 ){\n      if( sqlite3_column_type(pCsr->pStmt, iCol+1)==SQLITE_NULL ){\n        continue;\n      }\n      rc = SQLITE_NOMEM;\n      goto offsets_out;\n    }\n\n    /* Initialize a tokenizer iterator to iterate through column iCol. */\n    rc = sqlite3Fts3OpenTokenizer(pTab->pTokenizer, pCsr->iLangid,\n        zDoc, nDoc, &pC\n    );\n    if( rc!=SQLITE_OK ) goto offsets_out;\n\n    rc = pMod->xNext(pC, &ZDUMMY, &NDUMMY, &iStart, &iEnd, &iCurrent);\n    while( rc==SQLITE_OK ){\n      int i;                      /* Used to loop through terms */\n      int iMinPos = 0x7FFFFFFF;   /* Position of next token */\n      TermOffset *pTerm = 0;      /* TermOffset associated with next token */\n\n      for(i=0; i<nToken; i++){\n        TermOffset *pT = &sCtx.aTerm[i];\n        if( pT->pList && (pT->iPos-pT->iOff)<iMinPos ){\n          iMinPos = pT->iPos-pT->iOff;\n          pTerm = pT;\n        }\n      }\n\n      if( !pTerm ){\n        /* All offsets for this column have been gathered. */\n        rc = SQLITE_DONE;\n      }else{\n        assert( iCurrent<=iMinPos );\n        if( 0==(0xFE&*pTerm->pList) ){\n          pTerm->pList = 0;\n        }else{\n          fts3GetDeltaPosition(&pTerm->pList, &pTerm->iPos);\n        }\n        while( rc==SQLITE_OK && iCurrent<iMinPos ){\n          rc = pMod->xNext(pC, &ZDUMMY, &NDUMMY, &iStart, &iEnd, &iCurrent);\n        }\n        if( rc==SQLITE_OK ){\n          char aBuffer[64];\n          sqlite3_snprintf(sizeof(aBuffer), aBuffer, \n              \"%d %d %d %d \", iCol, pTerm-sCtx.aTerm, iStart, iEnd-iStart\n          );\n          rc = fts3StringAppend(&res, aBuffer, -1);\n        }else if( rc==SQLITE_DONE && pTab->zContentTbl==0 ){\n          rc = FTS_CORRUPT_VTAB;\n        }\n      }\n    }\n    if( rc==SQLITE_DONE ){\n      rc = SQLITE_OK;\n    }\n\n    pMod->xClose(pC);\n    if( rc!=SQLITE_OK ) goto offsets_out;\n  }\n\n offsets_out:\n  sqlite3_free(sCtx.aTerm);\n  assert( rc!=SQLITE_DONE );\n  sqlite3Fts3SegmentsClose(pTab);\n  if( rc!=SQLITE_OK ){\n    sqlite3_result_error_code(pCtx,  rc);\n    sqlite3_free(res.z);\n  }else{\n    sqlite3_result_text(pCtx, res.z, res.n-1, sqlite3_free);\n  }\n  return;\n}\n\n/*\n** Implementation of matchinfo() function.\n*/\nSQLITE_PRIVATE void sqlite3Fts3Matchinfo(\n  sqlite3_context *pContext,      /* Function call context */\n  Fts3Cursor *pCsr,               /* FTS3 table cursor */\n  const char *zArg                /* Second arg to matchinfo() function */\n){\n  Fts3Table *pTab = (Fts3Table *)pCsr->base.pVtab;\n  const char *zFormat;\n\n  if( zArg ){\n    zFormat = zArg;\n  }else{\n    zFormat = FTS3_MATCHINFO_DEFAULT;\n  }\n\n  if( !pCsr->pExpr ){\n    sqlite3_result_blob(pContext, \"\", 0, SQLITE_STATIC);\n    return;\n  }else{\n    /* Retrieve matchinfo() data. */\n    fts3GetMatchinfo(pContext, pCsr, zFormat);\n    sqlite3Fts3SegmentsClose(pTab);\n  }\n}\n\n#endif\n\n/************** End of fts3_snippet.c ****************************************/\n/************** Begin file fts3_unicode.c ************************************/\n/*\n** 2012 May 24\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n******************************************************************************\n**\n** Implementation of the \"unicode\" full-text-search tokenizer.\n*/\n\n#ifndef SQLITE_DISABLE_FTS3_UNICODE\n\n/* #include \"fts3Int.h\" */\n#if !defined(SQLITE_CORE) || defined(SQLITE_ENABLE_FTS3)\n\n/* #include <assert.h> */\n/* #include <stdlib.h> */\n/* #include <stdio.h> */\n/* #include <string.h> */\n\n/* #include \"fts3_tokenizer.h\" */\n\n/*\n** The following two macros - READ_UTF8 and WRITE_UTF8 - have been copied\n** from the sqlite3 source file utf.c. If this file is compiled as part\n** of the amalgamation, they are not required.\n*/\n#ifndef SQLITE_AMALGAMATION\n\nstatic const unsigned char sqlite3Utf8Trans1[] = {\n  0x00, 0x01, 0x02, 0x03, 0x04, 0x05, 0x06, 0x07,\n  0x08, 0x09, 0x0a, 0x0b, 0x0c, 0x0d, 0x0e, 0x0f,\n  0x10, 0x11, 0x12, 0x13, 0x14, 0x15, 0x16, 0x17,\n  0x18, 0x19, 0x1a, 0x1b, 0x1c, 0x1d, 0x1e, 0x1f,\n  0x00, 0x01, 0x02, 0x03, 0x04, 0x05, 0x06, 0x07,\n  0x08, 0x09, 0x0a, 0x0b, 0x0c, 0x0d, 0x0e, 0x0f,\n  0x00, 0x01, 0x02, 0x03, 0x04, 0x05, 0x06, 0x07,\n  0x00, 0x01, 0x02, 0x03, 0x00, 0x01, 0x00, 0x00,\n};\n\n#define READ_UTF8(zIn, zTerm, c)                           \\\n  c = *(zIn++);                                            \\\n  if( c>=0xc0 ){                                           \\\n    c = sqlite3Utf8Trans1[c-0xc0];                         \\\n    while( zIn!=zTerm && (*zIn & 0xc0)==0x80 ){            \\\n      c = (c<<6) + (0x3f & *(zIn++));                      \\\n    }                                                      \\\n    if( c<0x80                                             \\\n        || (c&0xFFFFF800)==0xD800                          \\\n        || (c&0xFFFFFFFE)==0xFFFE ){  c = 0xFFFD; }        \\\n  }\n\n#define WRITE_UTF8(zOut, c) {                          \\\n  if( c<0x00080 ){                                     \\\n    *zOut++ = (u8)(c&0xFF);                            \\\n  }                                                    \\\n  else if( c<0x00800 ){                                \\\n    *zOut++ = 0xC0 + (u8)((c>>6)&0x1F);                \\\n    *zOut++ = 0x80 + (u8)(c & 0x3F);                   \\\n  }                                                    \\\n  else if( c<0x10000 ){                                \\\n    *zOut++ = 0xE0 + (u8)((c>>12)&0x0F);               \\\n    *zOut++ = 0x80 + (u8)((c>>6) & 0x3F);              \\\n    *zOut++ = 0x80 + (u8)(c & 0x3F);                   \\\n  }else{                                               \\\n    *zOut++ = 0xF0 + (u8)((c>>18) & 0x07);             \\\n    *zOut++ = 0x80 + (u8)((c>>12) & 0x3F);             \\\n    *zOut++ = 0x80 + (u8)((c>>6) & 0x3F);              \\\n    *zOut++ = 0x80 + (u8)(c & 0x3F);                   \\\n  }                                                    \\\n}\n\n#endif /* ifndef SQLITE_AMALGAMATION */\n\ntypedef struct unicode_tokenizer unicode_tokenizer;\ntypedef struct unicode_cursor unicode_cursor;\n\nstruct unicode_tokenizer {\n  sqlite3_tokenizer base;\n  int bRemoveDiacritic;\n  int nException;\n  int *aiException;\n};\n\nstruct unicode_cursor {\n  sqlite3_tokenizer_cursor base;\n  const unsigned char *aInput;    /* Input text being tokenized */\n  int nInput;                     /* Size of aInput[] in bytes */\n  int iOff;                       /* Current offset within aInput[] */\n  int iToken;                     /* Index of next token to be returned */\n  char *zToken;                   /* storage for current token */\n  int nAlloc;                     /* space allocated at zToken */\n};\n\n\n/*\n** Destroy a tokenizer allocated by unicodeCreate().\n*/\nstatic int unicodeDestroy(sqlite3_tokenizer *pTokenizer){\n  if( pTokenizer ){\n    unicode_tokenizer *p = (unicode_tokenizer *)pTokenizer;\n    sqlite3_free(p->aiException);\n    sqlite3_free(p);\n  }\n  return SQLITE_OK;\n}\n\n/*\n** As part of a tokenchars= or separators= option, the CREATE VIRTUAL TABLE\n** statement has specified that the tokenizer for this table shall consider\n** all characters in string zIn/nIn to be separators (if bAlnum==0) or\n** token characters (if bAlnum==1).\n**\n** For each codepoint in the zIn/nIn string, this function checks if the\n** sqlite3FtsUnicodeIsalnum() function already returns the desired result.\n** If so, no action is taken. Otherwise, the codepoint is added to the \n** unicode_tokenizer.aiException[] array. For the purposes of tokenization,\n** the return value of sqlite3FtsUnicodeIsalnum() is inverted for all\n** codepoints in the aiException[] array.\n**\n** If a standalone diacritic mark (one that sqlite3FtsUnicodeIsdiacritic()\n** identifies as a diacritic) occurs in the zIn/nIn string it is ignored.\n** It is not possible to change the behavior of the tokenizer with respect\n** to these codepoints.\n*/\nstatic int unicodeAddExceptions(\n  unicode_tokenizer *p,           /* Tokenizer to add exceptions to */\n  int bAlnum,                     /* Replace Isalnum() return value with this */\n  const char *zIn,                /* Array of characters to make exceptions */\n  int nIn                         /* Length of z in bytes */\n){\n  const unsigned char *z = (const unsigned char *)zIn;\n  const unsigned char *zTerm = &z[nIn];\n  unsigned int iCode;\n  int nEntry = 0;\n\n  assert( bAlnum==0 || bAlnum==1 );\n\n  while( z<zTerm ){\n    READ_UTF8(z, zTerm, iCode);\n    assert( (sqlite3FtsUnicodeIsalnum((int)iCode) & 0xFFFFFFFE)==0 );\n    if( sqlite3FtsUnicodeIsalnum((int)iCode)!=bAlnum \n     && sqlite3FtsUnicodeIsdiacritic((int)iCode)==0 \n    ){\n      nEntry++;\n    }\n  }\n\n  if( nEntry ){\n    int *aNew;                    /* New aiException[] array */\n    int nNew;                     /* Number of valid entries in array aNew[] */\n\n    aNew = sqlite3_realloc(p->aiException, (p->nException+nEntry)*sizeof(int));\n    if( aNew==0 ) return SQLITE_NOMEM;\n    nNew = p->nException;\n\n    z = (const unsigned char *)zIn;\n    while( z<zTerm ){\n      READ_UTF8(z, zTerm, iCode);\n      if( sqlite3FtsUnicodeIsalnum((int)iCode)!=bAlnum \n       && sqlite3FtsUnicodeIsdiacritic((int)iCode)==0\n      ){\n        int i, j;\n        for(i=0; i<nNew && aNew[i]<(int)iCode; i++);\n        for(j=nNew; j>i; j--) aNew[j] = aNew[j-1];\n        aNew[i] = (int)iCode;\n        nNew++;\n      }\n    }\n    p->aiException = aNew;\n    p->nException = nNew;\n  }\n\n  return SQLITE_OK;\n}\n\n/*\n** Return true if the p->aiException[] array contains the value iCode.\n*/\nstatic int unicodeIsException(unicode_tokenizer *p, int iCode){\n  if( p->nException>0 ){\n    int *a = p->aiException;\n    int iLo = 0;\n    int iHi = p->nException-1;\n\n    while( iHi>=iLo ){\n      int iTest = (iHi + iLo) / 2;\n      if( iCode==a[iTest] ){\n        return 1;\n      }else if( iCode>a[iTest] ){\n        iLo = iTest+1;\n      }else{\n        iHi = iTest-1;\n      }\n    }\n  }\n\n  return 0;\n}\n\n/*\n** Return true if, for the purposes of tokenization, codepoint iCode is\n** considered a token character (not a separator).\n*/\nstatic int unicodeIsAlnum(unicode_tokenizer *p, int iCode){\n  assert( (sqlite3FtsUnicodeIsalnum(iCode) & 0xFFFFFFFE)==0 );\n  return sqlite3FtsUnicodeIsalnum(iCode) ^ unicodeIsException(p, iCode);\n}\n\n/*\n** Create a new tokenizer instance.\n*/\nstatic int unicodeCreate(\n  int nArg,                       /* Size of array argv[] */\n  const char * const *azArg,      /* Tokenizer creation arguments */\n  sqlite3_tokenizer **pp          /* OUT: New tokenizer handle */\n){\n  unicode_tokenizer *pNew;        /* New tokenizer object */\n  int i;\n  int rc = SQLITE_OK;\n\n  pNew = (unicode_tokenizer *) sqlite3_malloc(sizeof(unicode_tokenizer));\n  if( pNew==NULL ) return SQLITE_NOMEM;\n  memset(pNew, 0, sizeof(unicode_tokenizer));\n  pNew->bRemoveDiacritic = 1;\n\n  for(i=0; rc==SQLITE_OK && i<nArg; i++){\n    const char *z = azArg[i];\n    int n = (int)strlen(z);\n\n    if( n==19 && memcmp(\"remove_diacritics=1\", z, 19)==0 ){\n      pNew->bRemoveDiacritic = 1;\n    }\n    else if( n==19 && memcmp(\"remove_diacritics=0\", z, 19)==0 ){\n      pNew->bRemoveDiacritic = 0;\n    }\n    else if( n>=11 && memcmp(\"tokenchars=\", z, 11)==0 ){\n      rc = unicodeAddExceptions(pNew, 1, &z[11], n-11);\n    }\n    else if( n>=11 && memcmp(\"separators=\", z, 11)==0 ){\n      rc = unicodeAddExceptions(pNew, 0, &z[11], n-11);\n    }\n    else{\n      /* Unrecognized argument */\n      rc  = SQLITE_ERROR;\n    }\n  }\n\n  if( rc!=SQLITE_OK ){\n    unicodeDestroy((sqlite3_tokenizer *)pNew);\n    pNew = 0;\n  }\n  *pp = (sqlite3_tokenizer *)pNew;\n  return rc;\n}\n\n/*\n** Prepare to begin tokenizing a particular string.  The input\n** string to be tokenized is pInput[0..nBytes-1].  A cursor\n** used to incrementally tokenize this string is returned in \n** *ppCursor.\n*/\nstatic int unicodeOpen(\n  sqlite3_tokenizer *p,           /* The tokenizer */\n  const char *aInput,             /* Input string */\n  int nInput,                     /* Size of string aInput in bytes */\n  sqlite3_tokenizer_cursor **pp   /* OUT: New cursor object */\n){\n  unicode_cursor *pCsr;\n\n  pCsr = (unicode_cursor *)sqlite3_malloc(sizeof(unicode_cursor));\n  if( pCsr==0 ){\n    return SQLITE_NOMEM;\n  }\n  memset(pCsr, 0, sizeof(unicode_cursor));\n\n  pCsr->aInput = (const unsigned char *)aInput;\n  if( aInput==0 ){\n    pCsr->nInput = 0;\n  }else if( nInput<0 ){\n    pCsr->nInput = (int)strlen(aInput);\n  }else{\n    pCsr->nInput = nInput;\n  }\n\n  *pp = &pCsr->base;\n  UNUSED_PARAMETER(p);\n  return SQLITE_OK;\n}\n\n/*\n** Close a tokenization cursor previously opened by a call to\n** simpleOpen() above.\n*/\nstatic int unicodeClose(sqlite3_tokenizer_cursor *pCursor){\n  unicode_cursor *pCsr = (unicode_cursor *) pCursor;\n  sqlite3_free(pCsr->zToken);\n  sqlite3_free(pCsr);\n  return SQLITE_OK;\n}\n\n/*\n** Extract the next token from a tokenization cursor.  The cursor must\n** have been opened by a prior call to simpleOpen().\n*/\nstatic int unicodeNext(\n  sqlite3_tokenizer_cursor *pC,   /* Cursor returned by simpleOpen */\n  const char **paToken,           /* OUT: Token text */\n  int *pnToken,                   /* OUT: Number of bytes at *paToken */\n  int *piStart,                   /* OUT: Starting offset of token */\n  int *piEnd,                     /* OUT: Ending offset of token */\n  int *piPos                      /* OUT: Position integer of token */\n){\n  unicode_cursor *pCsr = (unicode_cursor *)pC;\n  unicode_tokenizer *p = ((unicode_tokenizer *)pCsr->base.pTokenizer);\n  unsigned int iCode = 0;\n  char *zOut;\n  const unsigned char *z = &pCsr->aInput[pCsr->iOff];\n  const unsigned char *zStart = z;\n  const unsigned char *zEnd;\n  const unsigned char *zTerm = &pCsr->aInput[pCsr->nInput];\n\n  /* Scan past any delimiter characters before the start of the next token.\n  ** Return SQLITE_DONE early if this takes us all the way to the end of \n  ** the input.  */\n  while( z<zTerm ){\n    READ_UTF8(z, zTerm, iCode);\n    if( unicodeIsAlnum(p, (int)iCode) ) break;\n    zStart = z;\n  }\n  if( zStart>=zTerm ) return SQLITE_DONE;\n\n  zOut = pCsr->zToken;\n  do {\n    int iOut;\n\n    /* Grow the output buffer if required. */\n    if( (zOut-pCsr->zToken)>=(pCsr->nAlloc-4) ){\n      char *zNew = sqlite3_realloc(pCsr->zToken, pCsr->nAlloc+64);\n      if( !zNew ) return SQLITE_NOMEM;\n      zOut = &zNew[zOut - pCsr->zToken];\n      pCsr->zToken = zNew;\n      pCsr->nAlloc += 64;\n    }\n\n    /* Write the folded case of the last character read to the output */\n    zEnd = z;\n    iOut = sqlite3FtsUnicodeFold((int)iCode, p->bRemoveDiacritic);\n    if( iOut ){\n      WRITE_UTF8(zOut, iOut);\n    }\n\n    /* If the cursor is not at EOF, read the next character */\n    if( z>=zTerm ) break;\n    READ_UTF8(z, zTerm, iCode);\n  }while( unicodeIsAlnum(p, (int)iCode) \n       || sqlite3FtsUnicodeIsdiacritic((int)iCode)\n  );\n\n  /* Set the output variables and return. */\n  pCsr->iOff = (int)(z - pCsr->aInput);\n  *paToken = pCsr->zToken;\n  *pnToken = (int)(zOut - pCsr->zToken);\n  *piStart = (int)(zStart - pCsr->aInput);\n  *piEnd = (int)(zEnd - pCsr->aInput);\n  *piPos = pCsr->iToken++;\n  return SQLITE_OK;\n}\n\n/*\n** Set *ppModule to a pointer to the sqlite3_tokenizer_module \n** structure for the unicode tokenizer.\n*/\nSQLITE_PRIVATE void sqlite3Fts3UnicodeTokenizer(sqlite3_tokenizer_module const **ppModule){\n  static const sqlite3_tokenizer_module module = {\n    0,\n    unicodeCreate,\n    unicodeDestroy,\n    unicodeOpen,\n    unicodeClose,\n    unicodeNext,\n    0,\n  };\n  *ppModule = &module;\n}\n\n#endif /* !defined(SQLITE_CORE) || defined(SQLITE_ENABLE_FTS3) */\n#endif /* ifndef SQLITE_DISABLE_FTS3_UNICODE */\n\n/************** End of fts3_unicode.c ****************************************/\n/************** Begin file fts3_unicode2.c ***********************************/\n/*\n** 2012 May 25\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n******************************************************************************\n*/\n\n/*\n** DO NOT EDIT THIS MACHINE GENERATED FILE.\n*/\n\n#ifndef SQLITE_DISABLE_FTS3_UNICODE\n#if defined(SQLITE_ENABLE_FTS3) || defined(SQLITE_ENABLE_FTS4)\n\n/* #include <assert.h> */\n\n/*\n** Return true if the argument corresponds to a unicode codepoint\n** classified as either a letter or a number. Otherwise false.\n**\n** The results are undefined if the value passed to this function\n** is less than zero.\n*/\nSQLITE_PRIVATE int sqlite3FtsUnicodeIsalnum(int c){\n  /* Each unsigned integer in the following array corresponds to a contiguous\n  ** range of unicode codepoints that are not either letters or numbers (i.e.\n  ** codepoints for which this function should return 0).\n  **\n  ** The most significant 22 bits in each 32-bit value contain the first \n  ** codepoint in the range. The least significant 10 bits are used to store\n  ** the size of the range (always at least 1). In other words, the value \n  ** ((C<<22) + N) represents a range of N codepoints starting with codepoint \n  ** C. It is not possible to represent a range larger than 1023 codepoints \n  ** using this format.\n  */\n  static const unsigned int aEntry[] = {\n    0x00000030, 0x0000E807, 0x00016C06, 0x0001EC2F, 0x0002AC07,\n    0x0002D001, 0x0002D803, 0x0002EC01, 0x0002FC01, 0x00035C01,\n    0x0003DC01, 0x000B0804, 0x000B480E, 0x000B9407, 0x000BB401,\n    0x000BBC81, 0x000DD401, 0x000DF801, 0x000E1002, 0x000E1C01,\n    0x000FD801, 0x00120808, 0x00156806, 0x00162402, 0x00163C01,\n    0x00164437, 0x0017CC02, 0x00180005, 0x00181816, 0x00187802,\n    0x00192C15, 0x0019A804, 0x0019C001, 0x001B5001, 0x001B580F,\n    0x001B9C07, 0x001BF402, 0x001C000E, 0x001C3C01, 0x001C4401,\n    0x001CC01B, 0x001E980B, 0x001FAC09, 0x001FD804, 0x00205804,\n    0x00206C09, 0x00209403, 0x0020A405, 0x0020C00F, 0x00216403,\n    0x00217801, 0x0023901B, 0x00240004, 0x0024E803, 0x0024F812,\n    0x00254407, 0x00258804, 0x0025C001, 0x00260403, 0x0026F001,\n    0x0026F807, 0x00271C02, 0x00272C03, 0x00275C01, 0x00278802,\n    0x0027C802, 0x0027E802, 0x00280403, 0x0028F001, 0x0028F805,\n    0x00291C02, 0x00292C03, 0x00294401, 0x0029C002, 0x0029D401,\n    0x002A0403, 0x002AF001, 0x002AF808, 0x002B1C03, 0x002B2C03,\n    0x002B8802, 0x002BC002, 0x002C0403, 0x002CF001, 0x002CF807,\n    0x002D1C02, 0x002D2C03, 0x002D5802, 0x002D8802, 0x002DC001,\n    0x002E0801, 0x002EF805, 0x002F1803, 0x002F2804, 0x002F5C01,\n    0x002FCC08, 0x00300403, 0x0030F807, 0x00311803, 0x00312804,\n    0x00315402, 0x00318802, 0x0031FC01, 0x00320802, 0x0032F001,\n    0x0032F807, 0x00331803, 0x00332804, 0x00335402, 0x00338802,\n    0x00340802, 0x0034F807, 0x00351803, 0x00352804, 0x00355C01,\n    0x00358802, 0x0035E401, 0x00360802, 0x00372801, 0x00373C06,\n    0x00375801, 0x00376008, 0x0037C803, 0x0038C401, 0x0038D007,\n    0x0038FC01, 0x00391C09, 0x00396802, 0x003AC401, 0x003AD006,\n    0x003AEC02, 0x003B2006, 0x003C041F, 0x003CD00C, 0x003DC417,\n    0x003E340B, 0x003E6424, 0x003EF80F, 0x003F380D, 0x0040AC14,\n    0x00412806, 0x00415804, 0x00417803, 0x00418803, 0x00419C07,\n    0x0041C404, 0x0042080C, 0x00423C01, 0x00426806, 0x0043EC01,\n    0x004D740C, 0x004E400A, 0x00500001, 0x0059B402, 0x005A0001,\n    0x005A6C02, 0x005BAC03, 0x005C4803, 0x005CC805, 0x005D4802,\n    0x005DC802, 0x005ED023, 0x005F6004, 0x005F7401, 0x0060000F,\n    0x0062A401, 0x0064800C, 0x0064C00C, 0x00650001, 0x00651002,\n    0x0066C011, 0x00672002, 0x00677822, 0x00685C05, 0x00687802,\n    0x0069540A, 0x0069801D, 0x0069FC01, 0x006A8007, 0x006AA006,\n    0x006C0005, 0x006CD011, 0x006D6823, 0x006E0003, 0x006E840D,\n    0x006F980E, 0x006FF004, 0x00709014, 0x0070EC05, 0x0071F802,\n    0x00730008, 0x00734019, 0x0073B401, 0x0073C803, 0x00770027,\n    0x0077F004, 0x007EF401, 0x007EFC03, 0x007F3403, 0x007F7403,\n    0x007FB403, 0x007FF402, 0x00800065, 0x0081A806, 0x0081E805,\n    0x00822805, 0x0082801A, 0x00834021, 0x00840002, 0x00840C04,\n    0x00842002, 0x00845001, 0x00845803, 0x00847806, 0x00849401,\n    0x00849C01, 0x0084A401, 0x0084B801, 0x0084E802, 0x00850005,\n    0x00852804, 0x00853C01, 0x00864264, 0x00900027, 0x0091000B,\n    0x0092704E, 0x00940200, 0x009C0475, 0x009E53B9, 0x00AD400A,\n    0x00B39406, 0x00B3BC03, 0x00B3E404, 0x00B3F802, 0x00B5C001,\n    0x00B5FC01, 0x00B7804F, 0x00B8C00C, 0x00BA001A, 0x00BA6C59,\n    0x00BC00D6, 0x00BFC00C, 0x00C00005, 0x00C02019, 0x00C0A807,\n    0x00C0D802, 0x00C0F403, 0x00C26404, 0x00C28001, 0x00C3EC01,\n    0x00C64002, 0x00C6580A, 0x00C70024, 0x00C8001F, 0x00C8A81E,\n    0x00C94001, 0x00C98020, 0x00CA2827, 0x00CB003F, 0x00CC0100,\n    0x01370040, 0x02924037, 0x0293F802, 0x02983403, 0x0299BC10,\n    0x029A7C01, 0x029BC008, 0x029C0017, 0x029C8002, 0x029E2402,\n    0x02A00801, 0x02A01801, 0x02A02C01, 0x02A08C09, 0x02A0D804,\n    0x02A1D004, 0x02A20002, 0x02A2D011, 0x02A33802, 0x02A38012,\n    0x02A3E003, 0x02A4980A, 0x02A51C0D, 0x02A57C01, 0x02A60004,\n    0x02A6CC1B, 0x02A77802, 0x02A8A40E, 0x02A90C01, 0x02A93002,\n    0x02A97004, 0x02A9DC03, 0x02A9EC01, 0x02AAC001, 0x02AAC803,\n    0x02AADC02, 0x02AAF802, 0x02AB0401, 0x02AB7802, 0x02ABAC07,\n    0x02ABD402, 0x02AF8C0B, 0x03600001, 0x036DFC02, 0x036FFC02,\n    0x037FFC01, 0x03EC7801, 0x03ECA401, 0x03EEC810, 0x03F4F802,\n    0x03F7F002, 0x03F8001A, 0x03F88007, 0x03F8C023, 0x03F95013,\n    0x03F9A004, 0x03FBFC01, 0x03FC040F, 0x03FC6807, 0x03FCEC06,\n    0x03FD6C0B, 0x03FF8007, 0x03FFA007, 0x03FFE405, 0x04040003,\n    0x0404DC09, 0x0405E411, 0x0406400C, 0x0407402E, 0x040E7C01,\n    0x040F4001, 0x04215C01, 0x04247C01, 0x0424FC01, 0x04280403,\n    0x04281402, 0x04283004, 0x0428E003, 0x0428FC01, 0x04294009,\n    0x0429FC01, 0x042CE407, 0x04400003, 0x0440E016, 0x04420003,\n    0x0442C012, 0x04440003, 0x04449C0E, 0x04450004, 0x04460003,\n    0x0446CC0E, 0x04471404, 0x045AAC0D, 0x0491C004, 0x05BD442E,\n    0x05BE3C04, 0x074000F6, 0x07440027, 0x0744A4B5, 0x07480046,\n    0x074C0057, 0x075B0401, 0x075B6C01, 0x075BEC01, 0x075C5401,\n    0x075CD401, 0x075D3C01, 0x075DBC01, 0x075E2401, 0x075EA401,\n    0x075F0C01, 0x07BBC002, 0x07C0002C, 0x07C0C064, 0x07C2800F,\n    0x07C2C40E, 0x07C3040F, 0x07C3440F, 0x07C4401F, 0x07C4C03C,\n    0x07C5C02B, 0x07C7981D, 0x07C8402B, 0x07C90009, 0x07C94002,\n    0x07CC0021, 0x07CCC006, 0x07CCDC46, 0x07CE0014, 0x07CE8025,\n    0x07CF1805, 0x07CF8011, 0x07D0003F, 0x07D10001, 0x07D108B6,\n    0x07D3E404, 0x07D4003E, 0x07D50004, 0x07D54018, 0x07D7EC46,\n    0x07D9140B, 0x07DA0046, 0x07DC0074, 0x38000401, 0x38008060,\n    0x380400F0,\n  };\n  static const unsigned int aAscii[4] = {\n    0xFFFFFFFF, 0xFC00FFFF, 0xF8000001, 0xF8000001,\n  };\n\n  if( (unsigned int)c<128 ){\n    return ( (aAscii[c >> 5] & ((unsigned int)1 << (c & 0x001F)))==0 );\n  }else if( (unsigned int)c<(1<<22) ){\n    unsigned int key = (((unsigned int)c)<<10) | 0x000003FF;\n    int iRes = 0;\n    int iHi = sizeof(aEntry)/sizeof(aEntry[0]) - 1;\n    int iLo = 0;\n    while( iHi>=iLo ){\n      int iTest = (iHi + iLo) / 2;\n      if( key >= aEntry[iTest] ){\n        iRes = iTest;\n        iLo = iTest+1;\n      }else{\n        iHi = iTest-1;\n      }\n    }\n    assert( aEntry[0]<key );\n    assert( key>=aEntry[iRes] );\n    return (((unsigned int)c) >= ((aEntry[iRes]>>10) + (aEntry[iRes]&0x3FF)));\n  }\n  return 1;\n}\n\n\n/*\n** If the argument is a codepoint corresponding to a lowercase letter\n** in the ASCII range with a diacritic added, return the codepoint\n** of the ASCII letter only. For example, if passed 235 - \"LATIN\n** SMALL LETTER E WITH DIAERESIS\" - return 65 (\"LATIN SMALL LETTER\n** E\"). The resuls of passing a codepoint that corresponds to an\n** uppercase letter are undefined.\n*/\nstatic int remove_diacritic(int c){\n  unsigned short aDia[] = {\n        0,  1797,  1848,  1859,  1891,  1928,  1940,  1995, \n     2024,  2040,  2060,  2110,  2168,  2206,  2264,  2286, \n     2344,  2383,  2472,  2488,  2516,  2596,  2668,  2732, \n     2782,  2842,  2894,  2954,  2984,  3000,  3028,  3336, \n     3456,  3696,  3712,  3728,  3744,  3896,  3912,  3928, \n     3968,  4008,  4040,  4106,  4138,  4170,  4202,  4234, \n     4266,  4296,  4312,  4344,  4408,  4424,  4472,  4504, \n     6148,  6198,  6264,  6280,  6360,  6429,  6505,  6529, \n    61448, 61468, 61534, 61592, 61642, 61688, 61704, 61726, \n    61784, 61800, 61836, 61880, 61914, 61948, 61998, 62122, \n    62154, 62200, 62218, 62302, 62364, 62442, 62478, 62536, \n    62554, 62584, 62604, 62640, 62648, 62656, 62664, 62730, \n    62924, 63050, 63082, 63274, 63390, \n  };\n  char aChar[] = {\n    '\\0', 'a',  'c',  'e',  'i',  'n',  'o',  'u',  'y',  'y',  'a',  'c',  \n    'd',  'e',  'e',  'g',  'h',  'i',  'j',  'k',  'l',  'n',  'o',  'r',  \n    's',  't',  'u',  'u',  'w',  'y',  'z',  'o',  'u',  'a',  'i',  'o',  \n    'u',  'g',  'k',  'o',  'j',  'g',  'n',  'a',  'e',  'i',  'o',  'r',  \n    'u',  's',  't',  'h',  'a',  'e',  'o',  'y',  '\\0', '\\0', '\\0', '\\0', \n    '\\0', '\\0', '\\0', '\\0', 'a',  'b',  'd',  'd',  'e',  'f',  'g',  'h',  \n    'h',  'i',  'k',  'l',  'l',  'm',  'n',  'p',  'r',  'r',  's',  't',  \n    'u',  'v',  'w',  'w',  'x',  'y',  'z',  'h',  't',  'w',  'y',  'a',  \n    'e',  'i',  'o',  'u',  'y',  \n  };\n\n  unsigned int key = (((unsigned int)c)<<3) | 0x00000007;\n  int iRes = 0;\n  int iHi = sizeof(aDia)/sizeof(aDia[0]) - 1;\n  int iLo = 0;\n  while( iHi>=iLo ){\n    int iTest = (iHi + iLo) / 2;\n    if( key >= aDia[iTest] ){\n      iRes = iTest;\n      iLo = iTest+1;\n    }else{\n      iHi = iTest-1;\n    }\n  }\n  assert( key>=aDia[iRes] );\n  return ((c > (aDia[iRes]>>3) + (aDia[iRes]&0x07)) ? c : (int)aChar[iRes]);\n}\n\n\n/*\n** Return true if the argument interpreted as a unicode codepoint\n** is a diacritical modifier character.\n*/\nSQLITE_PRIVATE int sqlite3FtsUnicodeIsdiacritic(int c){\n  unsigned int mask0 = 0x08029FDF;\n  unsigned int mask1 = 0x000361F8;\n  if( c<768 || c>817 ) return 0;\n  return (c < 768+32) ?\n      (mask0 & (1 << (c-768))) :\n      (mask1 & (1 << (c-768-32)));\n}\n\n\n/*\n** Interpret the argument as a unicode codepoint. If the codepoint\n** is an upper case character that has a lower case equivalent,\n** return the codepoint corresponding to the lower case version.\n** Otherwise, return a copy of the argument.\n**\n** The results are undefined if the value passed to this function\n** is less than zero.\n*/\nSQLITE_PRIVATE int sqlite3FtsUnicodeFold(int c, int bRemoveDiacritic){\n  /* Each entry in the following array defines a rule for folding a range\n  ** of codepoints to lower case. The rule applies to a range of nRange\n  ** codepoints starting at codepoint iCode.\n  **\n  ** If the least significant bit in flags is clear, then the rule applies\n  ** to all nRange codepoints (i.e. all nRange codepoints are upper case and\n  ** need to be folded). Or, if it is set, then the rule only applies to\n  ** every second codepoint in the range, starting with codepoint C.\n  **\n  ** The 7 most significant bits in flags are an index into the aiOff[]\n  ** array. If a specific codepoint C does require folding, then its lower\n  ** case equivalent is ((C + aiOff[flags>>1]) & 0xFFFF).\n  **\n  ** The contents of this array are generated by parsing the CaseFolding.txt\n  ** file distributed as part of the \"Unicode Character Database\". See\n  ** http://www.unicode.org for details.\n  */\n  static const struct TableEntry {\n    unsigned short iCode;\n    unsigned char flags;\n    unsigned char nRange;\n  } aEntry[] = {\n    {65, 14, 26},          {181, 64, 1},          {192, 14, 23},\n    {216, 14, 7},          {256, 1, 48},          {306, 1, 6},\n    {313, 1, 16},          {330, 1, 46},          {376, 116, 1},\n    {377, 1, 6},           {383, 104, 1},         {385, 50, 1},\n    {386, 1, 4},           {390, 44, 1},          {391, 0, 1},\n    {393, 42, 2},          {395, 0, 1},           {398, 32, 1},\n    {399, 38, 1},          {400, 40, 1},          {401, 0, 1},\n    {403, 42, 1},          {404, 46, 1},          {406, 52, 1},\n    {407, 48, 1},          {408, 0, 1},           {412, 52, 1},\n    {413, 54, 1},          {415, 56, 1},          {416, 1, 6},\n    {422, 60, 1},          {423, 0, 1},           {425, 60, 1},\n    {428, 0, 1},           {430, 60, 1},          {431, 0, 1},\n    {433, 58, 2},          {435, 1, 4},           {439, 62, 1},\n    {440, 0, 1},           {444, 0, 1},           {452, 2, 1},\n    {453, 0, 1},           {455, 2, 1},           {456, 0, 1},\n    {458, 2, 1},           {459, 1, 18},          {478, 1, 18},\n    {497, 2, 1},           {498, 1, 4},           {502, 122, 1},\n    {503, 134, 1},         {504, 1, 40},          {544, 110, 1},\n    {546, 1, 18},          {570, 70, 1},          {571, 0, 1},\n    {573, 108, 1},         {574, 68, 1},          {577, 0, 1},\n    {579, 106, 1},         {580, 28, 1},          {581, 30, 1},\n    {582, 1, 10},          {837, 36, 1},          {880, 1, 4},\n    {886, 0, 1},           {902, 18, 1},          {904, 16, 3},\n    {908, 26, 1},          {910, 24, 2},          {913, 14, 17},\n    {931, 14, 9},          {962, 0, 1},           {975, 4, 1},\n    {976, 140, 1},         {977, 142, 1},         {981, 146, 1},\n    {982, 144, 1},         {984, 1, 24},          {1008, 136, 1},\n    {1009, 138, 1},        {1012, 130, 1},        {1013, 128, 1},\n    {1015, 0, 1},          {1017, 152, 1},        {1018, 0, 1},\n    {1021, 110, 3},        {1024, 34, 16},        {1040, 14, 32},\n    {1120, 1, 34},         {1162, 1, 54},         {1216, 6, 1},\n    {1217, 1, 14},         {1232, 1, 88},         {1329, 22, 38},\n    {4256, 66, 38},        {4295, 66, 1},         {4301, 66, 1},\n    {7680, 1, 150},        {7835, 132, 1},        {7838, 96, 1},\n    {7840, 1, 96},         {7944, 150, 8},        {7960, 150, 6},\n    {7976, 150, 8},        {7992, 150, 8},        {8008, 150, 6},\n    {8025, 151, 8},        {8040, 150, 8},        {8072, 150, 8},\n    {8088, 150, 8},        {8104, 150, 8},        {8120, 150, 2},\n    {8122, 126, 2},        {8124, 148, 1},        {8126, 100, 1},\n    {8136, 124, 4},        {8140, 148, 1},        {8152, 150, 2},\n    {8154, 120, 2},        {8168, 150, 2},        {8170, 118, 2},\n    {8172, 152, 1},        {8184, 112, 2},        {8186, 114, 2},\n    {8188, 148, 1},        {8486, 98, 1},         {8490, 92, 1},\n    {8491, 94, 1},         {8498, 12, 1},         {8544, 8, 16},\n    {8579, 0, 1},          {9398, 10, 26},        {11264, 22, 47},\n    {11360, 0, 1},         {11362, 88, 1},        {11363, 102, 1},\n    {11364, 90, 1},        {11367, 1, 6},         {11373, 84, 1},\n    {11374, 86, 1},        {11375, 80, 1},        {11376, 82, 1},\n    {11378, 0, 1},         {11381, 0, 1},         {11390, 78, 2},\n    {11392, 1, 100},       {11499, 1, 4},         {11506, 0, 1},\n    {42560, 1, 46},        {42624, 1, 24},        {42786, 1, 14},\n    {42802, 1, 62},        {42873, 1, 4},         {42877, 76, 1},\n    {42878, 1, 10},        {42891, 0, 1},         {42893, 74, 1},\n    {42896, 1, 4},         {42912, 1, 10},        {42922, 72, 1},\n    {65313, 14, 26},       \n  };\n  static const unsigned short aiOff[] = {\n   1,     2,     8,     15,    16,    26,    28,    32,    \n   37,    38,    40,    48,    63,    64,    69,    71,    \n   79,    80,    116,   202,   203,   205,   206,   207,   \n   209,   210,   211,   213,   214,   217,   218,   219,   \n   775,   7264,  10792, 10795, 23228, 23256, 30204, 54721, \n   54753, 54754, 54756, 54787, 54793, 54809, 57153, 57274, \n   57921, 58019, 58363, 61722, 65268, 65341, 65373, 65406, \n   65408, 65410, 65415, 65424, 65436, 65439, 65450, 65462, \n   65472, 65476, 65478, 65480, 65482, 65488, 65506, 65511, \n   65514, 65521, 65527, 65528, 65529, \n  };\n\n  int ret = c;\n\n  assert( sizeof(unsigned short)==2 && sizeof(unsigned char)==1 );\n\n  if( c<128 ){\n    if( c>='A' && c<='Z' ) ret = c + ('a' - 'A');\n  }else if( c<65536 ){\n    const struct TableEntry *p;\n    int iHi = sizeof(aEntry)/sizeof(aEntry[0]) - 1;\n    int iLo = 0;\n    int iRes = -1;\n\n    assert( c>aEntry[0].iCode );\n    while( iHi>=iLo ){\n      int iTest = (iHi + iLo) / 2;\n      int cmp = (c - aEntry[iTest].iCode);\n      if( cmp>=0 ){\n        iRes = iTest;\n        iLo = iTest+1;\n      }else{\n        iHi = iTest-1;\n      }\n    }\n\n    assert( iRes>=0 && c>=aEntry[iRes].iCode );\n    p = &aEntry[iRes];\n    if( c<(p->iCode + p->nRange) && 0==(0x01 & p->flags & (p->iCode ^ c)) ){\n      ret = (c + (aiOff[p->flags>>1])) & 0x0000FFFF;\n      assert( ret>0 );\n    }\n\n    if( bRemoveDiacritic ) ret = remove_diacritic(ret);\n  }\n  \n  else if( c>=66560 && c<66600 ){\n    ret = c + 40;\n  }\n\n  return ret;\n}\n#endif /* defined(SQLITE_ENABLE_FTS3) || defined(SQLITE_ENABLE_FTS4) */\n#endif /* !defined(SQLITE_DISABLE_FTS3_UNICODE) */\n\n/************** End of fts3_unicode2.c ***************************************/\n/************** Begin file rtree.c *******************************************/\n/*\n** 2001 September 15\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n*************************************************************************\n** This file contains code for implementations of the r-tree and r*-tree\n** algorithms packaged as an SQLite virtual table module.\n*/\n\n/*\n** Database Format of R-Tree Tables\n** --------------------------------\n**\n** The data structure for a single virtual r-tree table is stored in three \n** native SQLite tables declared as follows. In each case, the '%' character\n** in the table name is replaced with the user-supplied name of the r-tree\n** table.\n**\n**   CREATE TABLE %_node(nodeno INTEGER PRIMARY KEY, data BLOB)\n**   CREATE TABLE %_parent(nodeno INTEGER PRIMARY KEY, parentnode INTEGER)\n**   CREATE TABLE %_rowid(rowid INTEGER PRIMARY KEY, nodeno INTEGER)\n**\n** The data for each node of the r-tree structure is stored in the %_node\n** table. For each node that is not the root node of the r-tree, there is\n** an entry in the %_parent table associating the node with its parent.\n** And for each row of data in the table, there is an entry in the %_rowid\n** table that maps from the entries rowid to the id of the node that it\n** is stored on.\n**\n** The root node of an r-tree always exists, even if the r-tree table is\n** empty. The nodeno of the root node is always 1. All other nodes in the\n** table must be the same size as the root node. The content of each node\n** is formatted as follows:\n**\n**   1. If the node is the root node (node 1), then the first 2 bytes\n**      of the node contain the tree depth as a big-endian integer.\n**      For non-root nodes, the first 2 bytes are left unused.\n**\n**   2. The next 2 bytes contain the number of entries currently \n**      stored in the node.\n**\n**   3. The remainder of the node contains the node entries. Each entry\n**      consists of a single 8-byte integer followed by an even number\n**      of 4-byte coordinates. For leaf nodes the integer is the rowid\n**      of a record. For internal nodes it is the node number of a\n**      child page.\n*/\n\n#if !defined(SQLITE_CORE) \\\n  || (defined(SQLITE_ENABLE_RTREE) && !defined(SQLITE_OMIT_VIRTUALTABLE))\n\n#ifndef SQLITE_CORE\n/*   #include \"sqlite3ext.h\" */\n  SQLITE_EXTENSION_INIT1\n#else\n/*   #include \"sqlite3.h\" */\n#endif\n\n/* #include <string.h> */\n/* #include <assert.h> */\n/* #include <stdio.h> */\n\n#ifndef SQLITE_AMALGAMATION\n#include \"sqlite3rtree.h\"\ntypedef sqlite3_int64 i64;\ntypedef sqlite3_uint64 u64;\ntypedef unsigned char u8;\ntypedef unsigned short u16;\ntypedef unsigned int u32;\n#endif\n\n/*  The following macro is used to suppress compiler warnings.\n*/\n#ifndef UNUSED_PARAMETER\n# define UNUSED_PARAMETER(x) (void)(x)\n#endif\n\ntypedef struct Rtree Rtree;\ntypedef struct RtreeCursor RtreeCursor;\ntypedef struct RtreeNode RtreeNode;\ntypedef struct RtreeCell RtreeCell;\ntypedef struct RtreeConstraint RtreeConstraint;\ntypedef struct RtreeMatchArg RtreeMatchArg;\ntypedef struct RtreeGeomCallback RtreeGeomCallback;\ntypedef union RtreeCoord RtreeCoord;\ntypedef struct RtreeSearchPoint RtreeSearchPoint;\n\n/* The rtree may have between 1 and RTREE_MAX_DIMENSIONS dimensions. */\n#define RTREE_MAX_DIMENSIONS 5\n\n/* Size of hash table Rtree.aHash. This hash table is not expected to\n** ever contain very many entries, so a fixed number of buckets is \n** used.\n*/\n#define HASHSIZE 97\n\n/* The xBestIndex method of this virtual table requires an estimate of\n** the number of rows in the virtual table to calculate the costs of\n** various strategies. If possible, this estimate is loaded from the\n** sqlite_stat1 table (with RTREE_MIN_ROWEST as a hard-coded minimum).\n** Otherwise, if no sqlite_stat1 entry is available, use \n** RTREE_DEFAULT_ROWEST.\n*/\n#define RTREE_DEFAULT_ROWEST 1048576\n#define RTREE_MIN_ROWEST         100\n\n/* \n** An rtree virtual-table object.\n*/\nstruct Rtree {\n  sqlite3_vtab base;          /* Base class.  Must be first */\n  sqlite3 *db;                /* Host database connection */\n  int iNodeSize;              /* Size in bytes of each node in the node table */\n  u8 nDim;                    /* Number of dimensions */\n  u8 nDim2;                   /* Twice the number of dimensions */\n  u8 eCoordType;              /* RTREE_COORD_REAL32 or RTREE_COORD_INT32 */\n  u8 nBytesPerCell;           /* Bytes consumed per cell */\n  u8 inWrTrans;               /* True if inside write transaction */\n  int iDepth;                 /* Current depth of the r-tree structure */\n  char *zDb;                  /* Name of database containing r-tree table */\n  char *zName;                /* Name of r-tree table */ \n  u32 nBusy;                  /* Current number of users of this structure */\n  i64 nRowEst;                /* Estimated number of rows in this table */\n  u32 nCursor;                /* Number of open cursors */\n\n  /* List of nodes removed during a CondenseTree operation. List is\n  ** linked together via the pointer normally used for hash chains -\n  ** RtreeNode.pNext. RtreeNode.iNode stores the depth of the sub-tree \n  ** headed by the node (leaf nodes have RtreeNode.iNode==0).\n  */\n  RtreeNode *pDeleted;\n  int iReinsertHeight;        /* Height of sub-trees Reinsert() has run on */\n\n  /* Blob I/O on xxx_node */\n  sqlite3_blob *pNodeBlob;\n\n  /* Statements to read/write/delete a record from xxx_node */\n  sqlite3_stmt *pWriteNode;\n  sqlite3_stmt *pDeleteNode;\n\n  /* Statements to read/write/delete a record from xxx_rowid */\n  sqlite3_stmt *pReadRowid;\n  sqlite3_stmt *pWriteRowid;\n  sqlite3_stmt *pDeleteRowid;\n\n  /* Statements to read/write/delete a record from xxx_parent */\n  sqlite3_stmt *pReadParent;\n  sqlite3_stmt *pWriteParent;\n  sqlite3_stmt *pDeleteParent;\n\n  RtreeNode *aHash[HASHSIZE]; /* Hash table of in-memory nodes. */ \n};\n\n/* Possible values for Rtree.eCoordType: */\n#define RTREE_COORD_REAL32 0\n#define RTREE_COORD_INT32  1\n\n/*\n** If SQLITE_RTREE_INT_ONLY is defined, then this virtual table will\n** only deal with integer coordinates.  No floating point operations\n** will be done.\n*/\n#ifdef SQLITE_RTREE_INT_ONLY\n  typedef sqlite3_int64 RtreeDValue;       /* High accuracy coordinate */\n  typedef int RtreeValue;                  /* Low accuracy coordinate */\n# define RTREE_ZERO 0\n#else\n  typedef double RtreeDValue;              /* High accuracy coordinate */\n  typedef float RtreeValue;                /* Low accuracy coordinate */\n# define RTREE_ZERO 0.0\n#endif\n\n/*\n** When doing a search of an r-tree, instances of the following structure\n** record intermediate results from the tree walk.\n**\n** The id is always a node-id.  For iLevel>=1 the id is the node-id of\n** the node that the RtreeSearchPoint represents.  When iLevel==0, however,\n** the id is of the parent node and the cell that RtreeSearchPoint\n** represents is the iCell-th entry in the parent node.\n*/\nstruct RtreeSearchPoint {\n  RtreeDValue rScore;    /* The score for this node.  Smallest goes first. */\n  sqlite3_int64 id;      /* Node ID */\n  u8 iLevel;             /* 0=entries.  1=leaf node.  2+ for higher */\n  u8 eWithin;            /* PARTLY_WITHIN or FULLY_WITHIN */\n  u8 iCell;              /* Cell index within the node */\n};\n\n/*\n** The minimum number of cells allowed for a node is a third of the \n** maximum. In Gutman's notation:\n**\n**     m = M/3\n**\n** If an R*-tree \"Reinsert\" operation is required, the same number of\n** cells are removed from the overfull node and reinserted into the tree.\n*/\n#define RTREE_MINCELLS(p) ((((p)->iNodeSize-4)/(p)->nBytesPerCell)/3)\n#define RTREE_REINSERT(p) RTREE_MINCELLS(p)\n#define RTREE_MAXCELLS 51\n\n/*\n** The smallest possible node-size is (512-64)==448 bytes. And the largest\n** supported cell size is 48 bytes (8 byte rowid + ten 4 byte coordinates).\n** Therefore all non-root nodes must contain at least 3 entries. Since \n** 3^40 is greater than 2^64, an r-tree structure always has a depth of\n** 40 or less.\n*/\n#define RTREE_MAX_DEPTH 40\n\n\n/*\n** Number of entries in the cursor RtreeNode cache.  The first entry is\n** used to cache the RtreeNode for RtreeCursor.sPoint.  The remaining\n** entries cache the RtreeNode for the first elements of the priority queue.\n*/\n#define RTREE_CACHE_SZ  5\n\n/* \n** An rtree cursor object.\n*/\nstruct RtreeCursor {\n  sqlite3_vtab_cursor base;         /* Base class.  Must be first */\n  u8 atEOF;                         /* True if at end of search */\n  u8 bPoint;                        /* True if sPoint is valid */\n  int iStrategy;                    /* Copy of idxNum search parameter */\n  int nConstraint;                  /* Number of entries in aConstraint */\n  RtreeConstraint *aConstraint;     /* Search constraints. */\n  int nPointAlloc;                  /* Number of slots allocated for aPoint[] */\n  int nPoint;                       /* Number of slots used in aPoint[] */\n  int mxLevel;                      /* iLevel value for root of the tree */\n  RtreeSearchPoint *aPoint;         /* Priority queue for search points */\n  RtreeSearchPoint sPoint;          /* Cached next search point */\n  RtreeNode *aNode[RTREE_CACHE_SZ]; /* Rtree node cache */\n  u32 anQueue[RTREE_MAX_DEPTH+1];   /* Number of queued entries by iLevel */\n};\n\n/* Return the Rtree of a RtreeCursor */\n#define RTREE_OF_CURSOR(X)   ((Rtree*)((X)->base.pVtab))\n\n/*\n** A coordinate can be either a floating point number or a integer.  All\n** coordinates within a single R-Tree are always of the same time.\n*/\nunion RtreeCoord {\n  RtreeValue f;      /* Floating point value */\n  int i;             /* Integer value */\n  u32 u;             /* Unsigned for byte-order conversions */\n};\n\n/*\n** The argument is an RtreeCoord. Return the value stored within the RtreeCoord\n** formatted as a RtreeDValue (double or int64). This macro assumes that local\n** variable pRtree points to the Rtree structure associated with the\n** RtreeCoord.\n*/\n#ifdef SQLITE_RTREE_INT_ONLY\n# define DCOORD(coord) ((RtreeDValue)coord.i)\n#else\n# define DCOORD(coord) (                           \\\n    (pRtree->eCoordType==RTREE_COORD_REAL32) ?      \\\n      ((double)coord.f) :                           \\\n      ((double)coord.i)                             \\\n  )\n#endif\n\n/*\n** A search constraint.\n*/\nstruct RtreeConstraint {\n  int iCoord;                     /* Index of constrained coordinate */\n  int op;                         /* Constraining operation */\n  union {\n    RtreeDValue rValue;             /* Constraint value. */\n    int (*xGeom)(sqlite3_rtree_geometry*,int,RtreeDValue*,int*);\n    int (*xQueryFunc)(sqlite3_rtree_query_info*);\n  } u;\n  sqlite3_rtree_query_info *pInfo;  /* xGeom and xQueryFunc argument */\n};\n\n/* Possible values for RtreeConstraint.op */\n#define RTREE_EQ    0x41  /* A */\n#define RTREE_LE    0x42  /* B */\n#define RTREE_LT    0x43  /* C */\n#define RTREE_GE    0x44  /* D */\n#define RTREE_GT    0x45  /* E */\n#define RTREE_MATCH 0x46  /* F: Old-style sqlite3_rtree_geometry_callback() */\n#define RTREE_QUERY 0x47  /* G: New-style sqlite3_rtree_query_callback() */\n\n\n/* \n** An rtree structure node.\n*/\nstruct RtreeNode {\n  RtreeNode *pParent;         /* Parent node */\n  i64 iNode;                  /* The node number */\n  int nRef;                   /* Number of references to this node */\n  int isDirty;                /* True if the node needs to be written to disk */\n  u8 *zData;                  /* Content of the node, as should be on disk */\n  RtreeNode *pNext;           /* Next node in this hash collision chain */\n};\n\n/* Return the number of cells in a node  */\n#define NCELL(pNode) readInt16(&(pNode)->zData[2])\n\n/* \n** A single cell from a node, deserialized\n*/\nstruct RtreeCell {\n  i64 iRowid;                                 /* Node or entry ID */\n  RtreeCoord aCoord[RTREE_MAX_DIMENSIONS*2];  /* Bounding box coordinates */\n};\n\n\n/*\n** This object becomes the sqlite3_user_data() for the SQL functions\n** that are created by sqlite3_rtree_geometry_callback() and\n** sqlite3_rtree_query_callback() and which appear on the right of MATCH\n** operators in order to constrain a search.\n**\n** xGeom and xQueryFunc are the callback functions.  Exactly one of \n** xGeom and xQueryFunc fields is non-NULL, depending on whether the\n** SQL function was created using sqlite3_rtree_geometry_callback() or\n** sqlite3_rtree_query_callback().\n** \n** This object is deleted automatically by the destructor mechanism in\n** sqlite3_create_function_v2().\n*/\nstruct RtreeGeomCallback {\n  int (*xGeom)(sqlite3_rtree_geometry*, int, RtreeDValue*, int*);\n  int (*xQueryFunc)(sqlite3_rtree_query_info*);\n  void (*xDestructor)(void*);\n  void *pContext;\n};\n\n/*\n** An instance of this structure (in the form of a BLOB) is returned by\n** the SQL functions that sqlite3_rtree_geometry_callback() and\n** sqlite3_rtree_query_callback() create, and is read as the right-hand\n** operand to the MATCH operator of an R-Tree.\n*/\nstruct RtreeMatchArg {\n  u32 iSize;                  /* Size of this object */\n  RtreeGeomCallback cb;       /* Info about the callback functions */\n  int nParam;                 /* Number of parameters to the SQL function */\n  sqlite3_value **apSqlParam; /* Original SQL parameter values */\n  RtreeDValue aParam[1];      /* Values for parameters to the SQL function */\n};\n\n#ifndef MAX\n# define MAX(x,y) ((x) < (y) ? (y) : (x))\n#endif\n#ifndef MIN\n# define MIN(x,y) ((x) > (y) ? (y) : (x))\n#endif\n\n/* What version of GCC is being used.  0 means GCC is not being used .\n** Note that the GCC_VERSION macro will also be set correctly when using\n** clang, since clang works hard to be gcc compatible.  So the gcc\n** optimizations will also work when compiling with clang.\n*/\n#ifndef GCC_VERSION\n#if defined(__GNUC__) && !defined(SQLITE_DISABLE_INTRINSIC)\n# define GCC_VERSION (__GNUC__*1000000+__GNUC_MINOR__*1000+__GNUC_PATCHLEVEL__)\n#else\n# define GCC_VERSION 0\n#endif\n#endif\n\n/* The testcase() macro should already be defined in the amalgamation.  If\n** it is not, make it a no-op.\n*/\n#ifndef SQLITE_AMALGAMATION\n# define testcase(X)\n#endif\n\n/*\n** Macros to determine whether the machine is big or little endian,\n** and whether or not that determination is run-time or compile-time.\n**\n** For best performance, an attempt is made to guess at the byte-order\n** using C-preprocessor macros.  If that is unsuccessful, or if\n** -DSQLITE_RUNTIME_BYTEORDER=1 is set, then byte-order is determined\n** at run-time.\n*/\n#ifndef SQLITE_BYTEORDER\n#if defined(i386)     || defined(__i386__)   || defined(_M_IX86) ||    \\\n    defined(__x86_64) || defined(__x86_64__) || defined(_M_X64)  ||    \\\n    defined(_M_AMD64) || defined(_M_ARM)     || defined(__x86)   ||    \\\n    defined(__arm__)\n# define SQLITE_BYTEORDER    1234\n#elif defined(sparc)    || defined(__ppc__)\n# define SQLITE_BYTEORDER    4321\n#else\n# define SQLITE_BYTEORDER    0     /* 0 means \"unknown at compile-time\" */\n#endif\n#endif\n\n\n/* What version of MSVC is being used.  0 means MSVC is not being used */\n#ifndef MSVC_VERSION\n#if defined(_MSC_VER) && !defined(SQLITE_DISABLE_INTRINSIC)\n# define MSVC_VERSION _MSC_VER\n#else\n# define MSVC_VERSION 0\n#endif\n#endif\n\n/*\n** Functions to deserialize a 16 bit integer, 32 bit real number and\n** 64 bit integer. The deserialized value is returned.\n*/\nstatic int readInt16(u8 *p){\n  return (p[0]<<8) + p[1];\n}\nstatic void readCoord(u8 *p, RtreeCoord *pCoord){\n  assert( ((((char*)p) - (char*)0)&3)==0 );  /* p is always 4-byte aligned */\n#if SQLITE_BYTEORDER==1234 && MSVC_VERSION>=1300\n  pCoord->u = _byteswap_ulong(*(u32*)p);\n#elif SQLITE_BYTEORDER==1234 && GCC_VERSION>=4003000\n  pCoord->u = __builtin_bswap32(*(u32*)p);\n#elif SQLITE_BYTEORDER==4321\n  pCoord->u = *(u32*)p;\n#else\n  pCoord->u = (\n    (((u32)p[0]) << 24) + \n    (((u32)p[1]) << 16) + \n    (((u32)p[2]) <<  8) + \n    (((u32)p[3]) <<  0)\n  );\n#endif\n}\nstatic i64 readInt64(u8 *p){\n#if SQLITE_BYTEORDER==1234 && MSVC_VERSION>=1300\n  u64 x;\n  memcpy(&x, p, 8);\n  return (i64)_byteswap_uint64(x);\n#elif SQLITE_BYTEORDER==1234 && GCC_VERSION>=4003000\n  u64 x;\n  memcpy(&x, p, 8);\n  return (i64)__builtin_bswap64(x);\n#elif SQLITE_BYTEORDER==4321\n  i64 x;\n  memcpy(&x, p, 8);\n  return x;\n#else\n  return (i64)(\n    (((u64)p[0]) << 56) + \n    (((u64)p[1]) << 48) + \n    (((u64)p[2]) << 40) + \n    (((u64)p[3]) << 32) + \n    (((u64)p[4]) << 24) + \n    (((u64)p[5]) << 16) + \n    (((u64)p[6]) <<  8) + \n    (((u64)p[7]) <<  0)\n  );\n#endif\n}\n\n/*\n** Functions to serialize a 16 bit integer, 32 bit real number and\n** 64 bit integer. The value returned is the number of bytes written\n** to the argument buffer (always 2, 4 and 8 respectively).\n*/\nstatic void writeInt16(u8 *p, int i){\n  p[0] = (i>> 8)&0xFF;\n  p[1] = (i>> 0)&0xFF;\n}\nstatic int writeCoord(u8 *p, RtreeCoord *pCoord){\n  u32 i;\n  assert( ((((char*)p) - (char*)0)&3)==0 );  /* p is always 4-byte aligned */\n  assert( sizeof(RtreeCoord)==4 );\n  assert( sizeof(u32)==4 );\n#if SQLITE_BYTEORDER==1234 && GCC_VERSION>=4003000\n  i = __builtin_bswap32(pCoord->u);\n  memcpy(p, &i, 4);\n#elif SQLITE_BYTEORDER==1234 && MSVC_VERSION>=1300\n  i = _byteswap_ulong(pCoord->u);\n  memcpy(p, &i, 4);\n#elif SQLITE_BYTEORDER==4321\n  i = pCoord->u;\n  memcpy(p, &i, 4);\n#else\n  i = pCoord->u;\n  p[0] = (i>>24)&0xFF;\n  p[1] = (i>>16)&0xFF;\n  p[2] = (i>> 8)&0xFF;\n  p[3] = (i>> 0)&0xFF;\n#endif\n  return 4;\n}\nstatic int writeInt64(u8 *p, i64 i){\n#if SQLITE_BYTEORDER==1234 && GCC_VERSION>=4003000\n  i = (i64)__builtin_bswap64((u64)i);\n  memcpy(p, &i, 8);\n#elif SQLITE_BYTEORDER==1234 && MSVC_VERSION>=1300\n  i = (i64)_byteswap_uint64((u64)i);\n  memcpy(p, &i, 8);\n#elif SQLITE_BYTEORDER==4321\n  memcpy(p, &i, 8);\n#else\n  p[0] = (i>>56)&0xFF;\n  p[1] = (i>>48)&0xFF;\n  p[2] = (i>>40)&0xFF;\n  p[3] = (i>>32)&0xFF;\n  p[4] = (i>>24)&0xFF;\n  p[5] = (i>>16)&0xFF;\n  p[6] = (i>> 8)&0xFF;\n  p[7] = (i>> 0)&0xFF;\n#endif\n  return 8;\n}\n\n/*\n** Increment the reference count of node p.\n*/\nstatic void nodeReference(RtreeNode *p){\n  if( p ){\n    p->nRef++;\n  }\n}\n\n/*\n** Clear the content of node p (set all bytes to 0x00).\n*/\nstatic void nodeZero(Rtree *pRtree, RtreeNode *p){\n  memset(&p->zData[2], 0, pRtree->iNodeSize-2);\n  p->isDirty = 1;\n}\n\n/*\n** Given a node number iNode, return the corresponding key to use\n** in the Rtree.aHash table.\n*/\nstatic int nodeHash(i64 iNode){\n  return iNode % HASHSIZE;\n}\n\n/*\n** Search the node hash table for node iNode. If found, return a pointer\n** to it. Otherwise, return 0.\n*/\nstatic RtreeNode *nodeHashLookup(Rtree *pRtree, i64 iNode){\n  RtreeNode *p;\n  for(p=pRtree->aHash[nodeHash(iNode)]; p && p->iNode!=iNode; p=p->pNext);\n  return p;\n}\n\n/*\n** Add node pNode to the node hash table.\n*/\nstatic void nodeHashInsert(Rtree *pRtree, RtreeNode *pNode){\n  int iHash;\n  assert( pNode->pNext==0 );\n  iHash = nodeHash(pNode->iNode);\n  pNode->pNext = pRtree->aHash[iHash];\n  pRtree->aHash[iHash] = pNode;\n}\n\n/*\n** Remove node pNode from the node hash table.\n*/\nstatic void nodeHashDelete(Rtree *pRtree, RtreeNode *pNode){\n  RtreeNode **pp;\n  if( pNode->iNode!=0 ){\n    pp = &pRtree->aHash[nodeHash(pNode->iNode)];\n    for( ; (*pp)!=pNode; pp = &(*pp)->pNext){ assert(*pp); }\n    *pp = pNode->pNext;\n    pNode->pNext = 0;\n  }\n}\n\n/*\n** Allocate and return new r-tree node. Initially, (RtreeNode.iNode==0),\n** indicating that node has not yet been assigned a node number. It is\n** assigned a node number when nodeWrite() is called to write the\n** node contents out to the database.\n*/\nstatic RtreeNode *nodeNew(Rtree *pRtree, RtreeNode *pParent){\n  RtreeNode *pNode;\n  pNode = (RtreeNode *)sqlite3_malloc(sizeof(RtreeNode) + pRtree->iNodeSize);\n  if( pNode ){\n    memset(pNode, 0, sizeof(RtreeNode) + pRtree->iNodeSize);\n    pNode->zData = (u8 *)&pNode[1];\n    pNode->nRef = 1;\n    pNode->pParent = pParent;\n    pNode->isDirty = 1;\n    nodeReference(pParent);\n  }\n  return pNode;\n}\n\n/*\n** Clear the Rtree.pNodeBlob object\n*/\nstatic void nodeBlobReset(Rtree *pRtree){\n  if( pRtree->pNodeBlob && pRtree->inWrTrans==0 && pRtree->nCursor==0 ){\n    sqlite3_blob *pBlob = pRtree->pNodeBlob;\n    pRtree->pNodeBlob = 0;\n    sqlite3_blob_close(pBlob);\n  }\n}\n\n/*\n** Obtain a reference to an r-tree node.\n*/\nstatic int nodeAcquire(\n  Rtree *pRtree,             /* R-tree structure */\n  i64 iNode,                 /* Node number to load */\n  RtreeNode *pParent,        /* Either the parent node or NULL */\n  RtreeNode **ppNode         /* OUT: Acquired node */\n){\n  int rc = SQLITE_OK;\n  RtreeNode *pNode = 0;\n\n  /* Check if the requested node is already in the hash table. If so,\n  ** increase its reference count and return it.\n  */\n  if( (pNode = nodeHashLookup(pRtree, iNode)) ){\n    assert( !pParent || !pNode->pParent || pNode->pParent==pParent );\n    if( pParent && !pNode->pParent ){\n      nodeReference(pParent);\n      pNode->pParent = pParent;\n    }\n    pNode->nRef++;\n    *ppNode = pNode;\n    return SQLITE_OK;\n  }\n\n  if( pRtree->pNodeBlob ){\n    sqlite3_blob *pBlob = pRtree->pNodeBlob;\n    pRtree->pNodeBlob = 0;\n    rc = sqlite3_blob_reopen(pBlob, iNode);\n    pRtree->pNodeBlob = pBlob;\n    if( rc ){\n      nodeBlobReset(pRtree);\n      if( rc==SQLITE_NOMEM ) return SQLITE_NOMEM;\n    }\n  }\n  if( pRtree->pNodeBlob==0 ){\n    char *zTab = sqlite3_mprintf(\"%s_node\", pRtree->zName);\n    if( zTab==0 ) return SQLITE_NOMEM;\n    rc = sqlite3_blob_open(pRtree->db, pRtree->zDb, zTab, \"data\", iNode, 0,\n                           &pRtree->pNodeBlob);\n    sqlite3_free(zTab);\n  }\n  if( rc ){\n    nodeBlobReset(pRtree);\n    *ppNode = 0;\n    /* If unable to open an sqlite3_blob on the desired row, that can only\n    ** be because the shadow tables hold erroneous data. */\n    if( rc==SQLITE_ERROR ) rc = SQLITE_CORRUPT_VTAB;\n  }else if( pRtree->iNodeSize==sqlite3_blob_bytes(pRtree->pNodeBlob) ){\n    pNode = (RtreeNode *)sqlite3_malloc(sizeof(RtreeNode)+pRtree->iNodeSize);\n    if( !pNode ){\n      rc = SQLITE_NOMEM;\n    }else{\n      pNode->pParent = pParent;\n      pNode->zData = (u8 *)&pNode[1];\n      pNode->nRef = 1;\n      pNode->iNode = iNode;\n      pNode->isDirty = 0;\n      pNode->pNext = 0;\n      rc = sqlite3_blob_read(pRtree->pNodeBlob, pNode->zData,\n                             pRtree->iNodeSize, 0);\n      nodeReference(pParent);\n    }\n  }\n\n  /* If the root node was just loaded, set pRtree->iDepth to the height\n  ** of the r-tree structure. A height of zero means all data is stored on\n  ** the root node. A height of one means the children of the root node\n  ** are the leaves, and so on. If the depth as specified on the root node\n  ** is greater than RTREE_MAX_DEPTH, the r-tree structure must be corrupt.\n  */\n  if( pNode && iNode==1 ){\n    pRtree->iDepth = readInt16(pNode->zData);\n    if( pRtree->iDepth>RTREE_MAX_DEPTH ){\n      rc = SQLITE_CORRUPT_VTAB;\n    }\n  }\n\n  /* If no error has occurred so far, check if the \"number of entries\"\n  ** field on the node is too large. If so, set the return code to \n  ** SQLITE_CORRUPT_VTAB.\n  */\n  if( pNode && rc==SQLITE_OK ){\n    if( NCELL(pNode)>((pRtree->iNodeSize-4)/pRtree->nBytesPerCell) ){\n      rc = SQLITE_CORRUPT_VTAB;\n    }\n  }\n\n  if( rc==SQLITE_OK ){\n    if( pNode!=0 ){\n      nodeHashInsert(pRtree, pNode);\n    }else{\n      rc = SQLITE_CORRUPT_VTAB;\n    }\n    *ppNode = pNode;\n  }else{\n    sqlite3_free(pNode);\n    *ppNode = 0;\n  }\n\n  return rc;\n}\n\n/*\n** Overwrite cell iCell of node pNode with the contents of pCell.\n*/\nstatic void nodeOverwriteCell(\n  Rtree *pRtree,             /* The overall R-Tree */\n  RtreeNode *pNode,          /* The node into which the cell is to be written */\n  RtreeCell *pCell,          /* The cell to write */\n  int iCell                  /* Index into pNode into which pCell is written */\n){\n  int ii;\n  u8 *p = &pNode->zData[4 + pRtree->nBytesPerCell*iCell];\n  p += writeInt64(p, pCell->iRowid);\n  for(ii=0; ii<pRtree->nDim2; ii++){\n    p += writeCoord(p, &pCell->aCoord[ii]);\n  }\n  pNode->isDirty = 1;\n}\n\n/*\n** Remove the cell with index iCell from node pNode.\n*/\nstatic void nodeDeleteCell(Rtree *pRtree, RtreeNode *pNode, int iCell){\n  u8 *pDst = &pNode->zData[4 + pRtree->nBytesPerCell*iCell];\n  u8 *pSrc = &pDst[pRtree->nBytesPerCell];\n  int nByte = (NCELL(pNode) - iCell - 1) * pRtree->nBytesPerCell;\n  memmove(pDst, pSrc, nByte);\n  writeInt16(&pNode->zData[2], NCELL(pNode)-1);\n  pNode->isDirty = 1;\n}\n\n/*\n** Insert the contents of cell pCell into node pNode. If the insert\n** is successful, return SQLITE_OK.\n**\n** If there is not enough free space in pNode, return SQLITE_FULL.\n*/\nstatic int nodeInsertCell(\n  Rtree *pRtree,                /* The overall R-Tree */\n  RtreeNode *pNode,             /* Write new cell into this node */\n  RtreeCell *pCell              /* The cell to be inserted */\n){\n  int nCell;                    /* Current number of cells in pNode */\n  int nMaxCell;                 /* Maximum number of cells for pNode */\n\n  nMaxCell = (pRtree->iNodeSize-4)/pRtree->nBytesPerCell;\n  nCell = NCELL(pNode);\n\n  assert( nCell<=nMaxCell );\n  if( nCell<nMaxCell ){\n    nodeOverwriteCell(pRtree, pNode, pCell, nCell);\n    writeInt16(&pNode->zData[2], nCell+1);\n    pNode->isDirty = 1;\n  }\n\n  return (nCell==nMaxCell);\n}\n\n/*\n** If the node is dirty, write it out to the database.\n*/\nstatic int nodeWrite(Rtree *pRtree, RtreeNode *pNode){\n  int rc = SQLITE_OK;\n  if( pNode->isDirty ){\n    sqlite3_stmt *p = pRtree->pWriteNode;\n    if( pNode->iNode ){\n      sqlite3_bind_int64(p, 1, pNode->iNode);\n    }else{\n      sqlite3_bind_null(p, 1);\n    }\n    sqlite3_bind_blob(p, 2, pNode->zData, pRtree->iNodeSize, SQLITE_STATIC);\n    sqlite3_step(p);\n    pNode->isDirty = 0;\n    rc = sqlite3_reset(p);\n    sqlite3_bind_null(p, 2);\n    if( pNode->iNode==0 && rc==SQLITE_OK ){\n      pNode->iNode = sqlite3_last_insert_rowid(pRtree->db);\n      nodeHashInsert(pRtree, pNode);\n    }\n  }\n  return rc;\n}\n\n/*\n** Release a reference to a node. If the node is dirty and the reference\n** count drops to zero, the node data is written to the database.\n*/\nstatic int nodeRelease(Rtree *pRtree, RtreeNode *pNode){\n  int rc = SQLITE_OK;\n  if( pNode ){\n    assert( pNode->nRef>0 );\n    pNode->nRef--;\n    if( pNode->nRef==0 ){\n      if( pNode->iNode==1 ){\n        pRtree->iDepth = -1;\n      }\n      if( pNode->pParent ){\n        rc = nodeRelease(pRtree, pNode->pParent);\n      }\n      if( rc==SQLITE_OK ){\n        rc = nodeWrite(pRtree, pNode);\n      }\n      nodeHashDelete(pRtree, pNode);\n      sqlite3_free(pNode);\n    }\n  }\n  return rc;\n}\n\n/*\n** Return the 64-bit integer value associated with cell iCell of\n** node pNode. If pNode is a leaf node, this is a rowid. If it is\n** an internal node, then the 64-bit integer is a child page number.\n*/\nstatic i64 nodeGetRowid(\n  Rtree *pRtree,       /* The overall R-Tree */\n  RtreeNode *pNode,    /* The node from which to extract the ID */\n  int iCell            /* The cell index from which to extract the ID */\n){\n  assert( iCell<NCELL(pNode) );\n  return readInt64(&pNode->zData[4 + pRtree->nBytesPerCell*iCell]);\n}\n\n/*\n** Return coordinate iCoord from cell iCell in node pNode.\n*/\nstatic void nodeGetCoord(\n  Rtree *pRtree,               /* The overall R-Tree */\n  RtreeNode *pNode,            /* The node from which to extract a coordinate */\n  int iCell,                   /* The index of the cell within the node */\n  int iCoord,                  /* Which coordinate to extract */\n  RtreeCoord *pCoord           /* OUT: Space to write result to */\n){\n  readCoord(&pNode->zData[12 + pRtree->nBytesPerCell*iCell + 4*iCoord], pCoord);\n}\n\n/*\n** Deserialize cell iCell of node pNode. Populate the structure pointed\n** to by pCell with the results.\n*/\nstatic void nodeGetCell(\n  Rtree *pRtree,               /* The overall R-Tree */\n  RtreeNode *pNode,            /* The node containing the cell to be read */\n  int iCell,                   /* Index of the cell within the node */\n  RtreeCell *pCell             /* OUT: Write the cell contents here */\n){\n  u8 *pData;\n  RtreeCoord *pCoord;\n  int ii = 0;\n  pCell->iRowid = nodeGetRowid(pRtree, pNode, iCell);\n  pData = pNode->zData + (12 + pRtree->nBytesPerCell*iCell);\n  pCoord = pCell->aCoord;\n  do{\n    readCoord(pData, &pCoord[ii]);\n    readCoord(pData+4, &pCoord[ii+1]);\n    pData += 8;\n    ii += 2;\n  }while( ii<pRtree->nDim2 );\n}\n\n\n/* Forward declaration for the function that does the work of\n** the virtual table module xCreate() and xConnect() methods.\n*/\nstatic int rtreeInit(\n  sqlite3 *, void *, int, const char *const*, sqlite3_vtab **, char **, int\n);\n\n/* \n** Rtree virtual table module xCreate method.\n*/\nstatic int rtreeCreate(\n  sqlite3 *db,\n  void *pAux,\n  int argc, const char *const*argv,\n  sqlite3_vtab **ppVtab,\n  char **pzErr\n){\n  return rtreeInit(db, pAux, argc, argv, ppVtab, pzErr, 1);\n}\n\n/* \n** Rtree virtual table module xConnect method.\n*/\nstatic int rtreeConnect(\n  sqlite3 *db,\n  void *pAux,\n  int argc, const char *const*argv,\n  sqlite3_vtab **ppVtab,\n  char **pzErr\n){\n  return rtreeInit(db, pAux, argc, argv, ppVtab, pzErr, 0);\n}\n\n/*\n** Increment the r-tree reference count.\n*/\nstatic void rtreeReference(Rtree *pRtree){\n  pRtree->nBusy++;\n}\n\n/*\n** Decrement the r-tree reference count. When the reference count reaches\n** zero the structure is deleted.\n*/\nstatic void rtreeRelease(Rtree *pRtree){\n  pRtree->nBusy--;\n  if( pRtree->nBusy==0 ){\n    pRtree->inWrTrans = 0;\n    pRtree->nCursor = 0;\n    nodeBlobReset(pRtree);\n    sqlite3_finalize(pRtree->pWriteNode);\n    sqlite3_finalize(pRtree->pDeleteNode);\n    sqlite3_finalize(pRtree->pReadRowid);\n    sqlite3_finalize(pRtree->pWriteRowid);\n    sqlite3_finalize(pRtree->pDeleteRowid);\n    sqlite3_finalize(pRtree->pReadParent);\n    sqlite3_finalize(pRtree->pWriteParent);\n    sqlite3_finalize(pRtree->pDeleteParent);\n    sqlite3_free(pRtree);\n  }\n}\n\n/* \n** Rtree virtual table module xDisconnect method.\n*/\nstatic int rtreeDisconnect(sqlite3_vtab *pVtab){\n  rtreeRelease((Rtree *)pVtab);\n  return SQLITE_OK;\n}\n\n/* \n** Rtree virtual table module xDestroy method.\n*/\nstatic int rtreeDestroy(sqlite3_vtab *pVtab){\n  Rtree *pRtree = (Rtree *)pVtab;\n  int rc;\n  char *zCreate = sqlite3_mprintf(\n    \"DROP TABLE '%q'.'%q_node';\"\n    \"DROP TABLE '%q'.'%q_rowid';\"\n    \"DROP TABLE '%q'.'%q_parent';\",\n    pRtree->zDb, pRtree->zName, \n    pRtree->zDb, pRtree->zName,\n    pRtree->zDb, pRtree->zName\n  );\n  if( !zCreate ){\n    rc = SQLITE_NOMEM;\n  }else{\n    nodeBlobReset(pRtree);\n    rc = sqlite3_exec(pRtree->db, zCreate, 0, 0, 0);\n    sqlite3_free(zCreate);\n  }\n  if( rc==SQLITE_OK ){\n    rtreeRelease(pRtree);\n  }\n\n  return rc;\n}\n\n/* \n** Rtree virtual table module xOpen method.\n*/\nstatic int rtreeOpen(sqlite3_vtab *pVTab, sqlite3_vtab_cursor **ppCursor){\n  int rc = SQLITE_NOMEM;\n  Rtree *pRtree = (Rtree *)pVTab;\n  RtreeCursor *pCsr;\n\n  pCsr = (RtreeCursor *)sqlite3_malloc(sizeof(RtreeCursor));\n  if( pCsr ){\n    memset(pCsr, 0, sizeof(RtreeCursor));\n    pCsr->base.pVtab = pVTab;\n    rc = SQLITE_OK;\n    pRtree->nCursor++;\n  }\n  *ppCursor = (sqlite3_vtab_cursor *)pCsr;\n\n  return rc;\n}\n\n\n/*\n** Free the RtreeCursor.aConstraint[] array and its contents.\n*/\nstatic void freeCursorConstraints(RtreeCursor *pCsr){\n  if( pCsr->aConstraint ){\n    int i;                        /* Used to iterate through constraint array */\n    for(i=0; i<pCsr->nConstraint; i++){\n      sqlite3_rtree_query_info *pInfo = pCsr->aConstraint[i].pInfo;\n      if( pInfo ){\n        if( pInfo->xDelUser ) pInfo->xDelUser(pInfo->pUser);\n        sqlite3_free(pInfo);\n      }\n    }\n    sqlite3_free(pCsr->aConstraint);\n    pCsr->aConstraint = 0;\n  }\n}\n\n/* \n** Rtree virtual table module xClose method.\n*/\nstatic int rtreeClose(sqlite3_vtab_cursor *cur){\n  Rtree *pRtree = (Rtree *)(cur->pVtab);\n  int ii;\n  RtreeCursor *pCsr = (RtreeCursor *)cur;\n  assert( pRtree->nCursor>0 );\n  freeCursorConstraints(pCsr);\n  sqlite3_free(pCsr->aPoint);\n  for(ii=0; ii<RTREE_CACHE_SZ; ii++) nodeRelease(pRtree, pCsr->aNode[ii]);\n  sqlite3_free(pCsr);\n  pRtree->nCursor--;\n  nodeBlobReset(pRtree);\n  return SQLITE_OK;\n}\n\n/*\n** Rtree virtual table module xEof method.\n**\n** Return non-zero if the cursor does not currently point to a valid \n** record (i.e if the scan has finished), or zero otherwise.\n*/\nstatic int rtreeEof(sqlite3_vtab_cursor *cur){\n  RtreeCursor *pCsr = (RtreeCursor *)cur;\n  return pCsr->atEOF;\n}\n\n/*\n** Convert raw bits from the on-disk RTree record into a coordinate value.\n** The on-disk format is big-endian and needs to be converted for little-\n** endian platforms.  The on-disk record stores integer coordinates if\n** eInt is true and it stores 32-bit floating point records if eInt is\n** false.  a[] is the four bytes of the on-disk record to be decoded.\n** Store the results in \"r\".\n**\n** There are five versions of this macro.  The last one is generic.  The\n** other four are various architectures-specific optimizations.\n*/\n#if SQLITE_BYTEORDER==1234 && MSVC_VERSION>=1300\n#define RTREE_DECODE_COORD(eInt, a, r) {                        \\\n    RtreeCoord c;    /* Coordinate decoded */                   \\\n    c.u = _byteswap_ulong(*(u32*)a);                            \\\n    r = eInt ? (sqlite3_rtree_dbl)c.i : (sqlite3_rtree_dbl)c.f; \\\n}\n#elif SQLITE_BYTEORDER==1234 && GCC_VERSION>=4003000\n#define RTREE_DECODE_COORD(eInt, a, r) {                        \\\n    RtreeCoord c;    /* Coordinate decoded */                   \\\n    c.u = __builtin_bswap32(*(u32*)a);                          \\\n    r = eInt ? (sqlite3_rtree_dbl)c.i : (sqlite3_rtree_dbl)c.f; \\\n}\n#elif SQLITE_BYTEORDER==1234\n#define RTREE_DECODE_COORD(eInt, a, r) {                        \\\n    RtreeCoord c;    /* Coordinate decoded */                   \\\n    memcpy(&c.u,a,4);                                           \\\n    c.u = ((c.u>>24)&0xff)|((c.u>>8)&0xff00)|                   \\\n          ((c.u&0xff)<<24)|((c.u&0xff00)<<8);                   \\\n    r = eInt ? (sqlite3_rtree_dbl)c.i : (sqlite3_rtree_dbl)c.f; \\\n}\n#elif SQLITE_BYTEORDER==4321\n#define RTREE_DECODE_COORD(eInt, a, r) {                        \\\n    RtreeCoord c;    /* Coordinate decoded */                   \\\n    memcpy(&c.u,a,4);                                           \\\n    r = eInt ? (sqlite3_rtree_dbl)c.i : (sqlite3_rtree_dbl)c.f; \\\n}\n#else\n#define RTREE_DECODE_COORD(eInt, a, r) {                        \\\n    RtreeCoord c;    /* Coordinate decoded */                   \\\n    c.u = ((u32)a[0]<<24) + ((u32)a[1]<<16)                     \\\n           +((u32)a[2]<<8) + a[3];                              \\\n    r = eInt ? (sqlite3_rtree_dbl)c.i : (sqlite3_rtree_dbl)c.f; \\\n}\n#endif\n\n/*\n** Check the RTree node or entry given by pCellData and p against the MATCH\n** constraint pConstraint.  \n*/\nstatic int rtreeCallbackConstraint(\n  RtreeConstraint *pConstraint,  /* The constraint to test */\n  int eInt,                      /* True if RTree holding integer coordinates */\n  u8 *pCellData,                 /* Raw cell content */\n  RtreeSearchPoint *pSearch,     /* Container of this cell */\n  sqlite3_rtree_dbl *prScore,    /* OUT: score for the cell */\n  int *peWithin                  /* OUT: visibility of the cell */\n){\n  sqlite3_rtree_query_info *pInfo = pConstraint->pInfo; /* Callback info */\n  int nCoord = pInfo->nCoord;                           /* No. of coordinates */\n  int rc;                                             /* Callback return code */\n  RtreeCoord c;                                       /* Translator union */\n  sqlite3_rtree_dbl aCoord[RTREE_MAX_DIMENSIONS*2];   /* Decoded coordinates */\n\n  assert( pConstraint->op==RTREE_MATCH || pConstraint->op==RTREE_QUERY );\n  assert( nCoord==2 || nCoord==4 || nCoord==6 || nCoord==8 || nCoord==10 );\n\n  if( pConstraint->op==RTREE_QUERY && pSearch->iLevel==1 ){\n    pInfo->iRowid = readInt64(pCellData);\n  }\n  pCellData += 8;\n#ifndef SQLITE_RTREE_INT_ONLY\n  if( eInt==0 ){\n    switch( nCoord ){\n      case 10:  readCoord(pCellData+36, &c); aCoord[9] = c.f;\n                readCoord(pCellData+32, &c); aCoord[8] = c.f;\n      case 8:   readCoord(pCellData+28, &c); aCoord[7] = c.f;\n                readCoord(pCellData+24, &c); aCoord[6] = c.f;\n      case 6:   readCoord(pCellData+20, &c); aCoord[5] = c.f;\n                readCoord(pCellData+16, &c); aCoord[4] = c.f;\n      case 4:   readCoord(pCellData+12, &c); aCoord[3] = c.f;\n                readCoord(pCellData+8,  &c); aCoord[2] = c.f;\n      default:  readCoord(pCellData+4,  &c); aCoord[1] = c.f;\n                readCoord(pCellData,    &c); aCoord[0] = c.f;\n    }\n  }else\n#endif\n  {\n    switch( nCoord ){\n      case 10:  readCoord(pCellData+36, &c); aCoord[9] = c.i;\n                readCoord(pCellData+32, &c); aCoord[8] = c.i;\n      case 8:   readCoord(pCellData+28, &c); aCoord[7] = c.i;\n                readCoord(pCellData+24, &c); aCoord[6] = c.i;\n      case 6:   readCoord(pCellData+20, &c); aCoord[5] = c.i;\n                readCoord(pCellData+16, &c); aCoord[4] = c.i;\n      case 4:   readCoord(pCellData+12, &c); aCoord[3] = c.i;\n                readCoord(pCellData+8,  &c); aCoord[2] = c.i;\n      default:  readCoord(pCellData+4,  &c); aCoord[1] = c.i;\n                readCoord(pCellData,    &c); aCoord[0] = c.i;\n    }\n  }\n  if( pConstraint->op==RTREE_MATCH ){\n    int eWithin = 0;\n    rc = pConstraint->u.xGeom((sqlite3_rtree_geometry*)pInfo,\n                              nCoord, aCoord, &eWithin);\n    if( eWithin==0 ) *peWithin = NOT_WITHIN;\n    *prScore = RTREE_ZERO;\n  }else{\n    pInfo->aCoord = aCoord;\n    pInfo->iLevel = pSearch->iLevel - 1;\n    pInfo->rScore = pInfo->rParentScore = pSearch->rScore;\n    pInfo->eWithin = pInfo->eParentWithin = pSearch->eWithin;\n    rc = pConstraint->u.xQueryFunc(pInfo);\n    if( pInfo->eWithin<*peWithin ) *peWithin = pInfo->eWithin;\n    if( pInfo->rScore<*prScore || *prScore<RTREE_ZERO ){\n      *prScore = pInfo->rScore;\n    }\n  }\n  return rc;\n}\n\n/* \n** Check the internal RTree node given by pCellData against constraint p.\n** If this constraint cannot be satisfied by any child within the node,\n** set *peWithin to NOT_WITHIN.\n*/\nstatic void rtreeNonleafConstraint(\n  RtreeConstraint *p,        /* The constraint to test */\n  int eInt,                  /* True if RTree holds integer coordinates */\n  u8 *pCellData,             /* Raw cell content as appears on disk */\n  int *peWithin              /* Adjust downward, as appropriate */\n){\n  sqlite3_rtree_dbl val;     /* Coordinate value convert to a double */\n\n  /* p->iCoord might point to either a lower or upper bound coordinate\n  ** in a coordinate pair.  But make pCellData point to the lower bound.\n  */\n  pCellData += 8 + 4*(p->iCoord&0xfe);\n\n  assert(p->op==RTREE_LE || p->op==RTREE_LT || p->op==RTREE_GE \n      || p->op==RTREE_GT || p->op==RTREE_EQ );\n  assert( ((((char*)pCellData) - (char*)0)&3)==0 );  /* 4-byte aligned */\n  switch( p->op ){\n    case RTREE_LE:\n    case RTREE_LT:\n    case RTREE_EQ:\n      RTREE_DECODE_COORD(eInt, pCellData, val);\n      /* val now holds the lower bound of the coordinate pair */\n      if( p->u.rValue>=val ) return;\n      if( p->op!=RTREE_EQ ) break;  /* RTREE_LE and RTREE_LT end here */\n      /* Fall through for the RTREE_EQ case */\n\n    default: /* RTREE_GT or RTREE_GE,  or fallthrough of RTREE_EQ */\n      pCellData += 4;\n      RTREE_DECODE_COORD(eInt, pCellData, val);\n      /* val now holds the upper bound of the coordinate pair */\n      if( p->u.rValue<=val ) return;\n  }\n  *peWithin = NOT_WITHIN;\n}\n\n/*\n** Check the leaf RTree cell given by pCellData against constraint p.\n** If this constraint is not satisfied, set *peWithin to NOT_WITHIN.\n** If the constraint is satisfied, leave *peWithin unchanged.\n**\n** The constraint is of the form:  xN op $val\n**\n** The op is given by p->op.  The xN is p->iCoord-th coordinate in\n** pCellData.  $val is given by p->u.rValue.\n*/\nstatic void rtreeLeafConstraint(\n  RtreeConstraint *p,        /* The constraint to test */\n  int eInt,                  /* True if RTree holds integer coordinates */\n  u8 *pCellData,             /* Raw cell content as appears on disk */\n  int *peWithin              /* Adjust downward, as appropriate */\n){\n  RtreeDValue xN;      /* Coordinate value converted to a double */\n\n  assert(p->op==RTREE_LE || p->op==RTREE_LT || p->op==RTREE_GE \n      || p->op==RTREE_GT || p->op==RTREE_EQ );\n  pCellData += 8 + p->iCoord*4;\n  assert( ((((char*)pCellData) - (char*)0)&3)==0 );  /* 4-byte aligned */\n  RTREE_DECODE_COORD(eInt, pCellData, xN);\n  switch( p->op ){\n    case RTREE_LE: if( xN <= p->u.rValue ) return;  break;\n    case RTREE_LT: if( xN <  p->u.rValue ) return;  break;\n    case RTREE_GE: if( xN >= p->u.rValue ) return;  break;\n    case RTREE_GT: if( xN >  p->u.rValue ) return;  break;\n    default:       if( xN == p->u.rValue ) return;  break;\n  }\n  *peWithin = NOT_WITHIN;\n}\n\n/*\n** One of the cells in node pNode is guaranteed to have a 64-bit \n** integer value equal to iRowid. Return the index of this cell.\n*/\nstatic int nodeRowidIndex(\n  Rtree *pRtree, \n  RtreeNode *pNode, \n  i64 iRowid,\n  int *piIndex\n){\n  int ii;\n  int nCell = NCELL(pNode);\n  assert( nCell<200 );\n  for(ii=0; ii<nCell; ii++){\n    if( nodeGetRowid(pRtree, pNode, ii)==iRowid ){\n      *piIndex = ii;\n      return SQLITE_OK;\n    }\n  }\n  return SQLITE_CORRUPT_VTAB;\n}\n\n/*\n** Return the index of the cell containing a pointer to node pNode\n** in its parent. If pNode is the root node, return -1.\n*/\nstatic int nodeParentIndex(Rtree *pRtree, RtreeNode *pNode, int *piIndex){\n  RtreeNode *pParent = pNode->pParent;\n  if( pParent ){\n    return nodeRowidIndex(pRtree, pParent, pNode->iNode, piIndex);\n  }\n  *piIndex = -1;\n  return SQLITE_OK;\n}\n\n/*\n** Compare two search points.  Return negative, zero, or positive if the first\n** is less than, equal to, or greater than the second.\n**\n** The rScore is the primary key.  Smaller rScore values come first.\n** If the rScore is a tie, then use iLevel as the tie breaker with smaller\n** iLevel values coming first.  In this way, if rScore is the same for all\n** SearchPoints, then iLevel becomes the deciding factor and the result\n** is a depth-first search, which is the desired default behavior.\n*/\nstatic int rtreeSearchPointCompare(\n  const RtreeSearchPoint *pA,\n  const RtreeSearchPoint *pB\n){\n  if( pA->rScore<pB->rScore ) return -1;\n  if( pA->rScore>pB->rScore ) return +1;\n  if( pA->iLevel<pB->iLevel ) return -1;\n  if( pA->iLevel>pB->iLevel ) return +1;\n  return 0;\n}\n\n/*\n** Interchange two search points in a cursor.\n*/\nstatic void rtreeSearchPointSwap(RtreeCursor *p, int i, int j){\n  RtreeSearchPoint t = p->aPoint[i];\n  assert( i<j );\n  p->aPoint[i] = p->aPoint[j];\n  p->aPoint[j] = t;\n  i++; j++;\n  if( i<RTREE_CACHE_SZ ){\n    if( j>=RTREE_CACHE_SZ ){\n      nodeRelease(RTREE_OF_CURSOR(p), p->aNode[i]);\n      p->aNode[i] = 0;\n    }else{\n      RtreeNode *pTemp = p->aNode[i];\n      p->aNode[i] = p->aNode[j];\n      p->aNode[j] = pTemp;\n    }\n  }\n}\n\n/*\n** Return the search point with the lowest current score.\n*/\nstatic RtreeSearchPoint *rtreeSearchPointFirst(RtreeCursor *pCur){\n  return pCur->bPoint ? &pCur->sPoint : pCur->nPoint ? pCur->aPoint : 0;\n}\n\n/*\n** Get the RtreeNode for the search point with the lowest score.\n*/\nstatic RtreeNode *rtreeNodeOfFirstSearchPoint(RtreeCursor *pCur, int *pRC){\n  sqlite3_int64 id;\n  int ii = 1 - pCur->bPoint;\n  assert( ii==0 || ii==1 );\n  assert( pCur->bPoint || pCur->nPoint );\n  if( pCur->aNode[ii]==0 ){\n    assert( pRC!=0 );\n    id = ii ? pCur->aPoint[0].id : pCur->sPoint.id;\n    *pRC = nodeAcquire(RTREE_OF_CURSOR(pCur), id, 0, &pCur->aNode[ii]);\n  }\n  return pCur->aNode[ii];\n}\n\n/*\n** Push a new element onto the priority queue\n*/\nstatic RtreeSearchPoint *rtreeEnqueue(\n  RtreeCursor *pCur,    /* The cursor */\n  RtreeDValue rScore,   /* Score for the new search point */\n  u8 iLevel             /* Level for the new search point */\n){\n  int i, j;\n  RtreeSearchPoint *pNew;\n  if( pCur->nPoint>=pCur->nPointAlloc ){\n    int nNew = pCur->nPointAlloc*2 + 8;\n    pNew = sqlite3_realloc(pCur->aPoint, nNew*sizeof(pCur->aPoint[0]));\n    if( pNew==0 ) return 0;\n    pCur->aPoint = pNew;\n    pCur->nPointAlloc = nNew;\n  }\n  i = pCur->nPoint++;\n  pNew = pCur->aPoint + i;\n  pNew->rScore = rScore;\n  pNew->iLevel = iLevel;\n  assert( iLevel<=RTREE_MAX_DEPTH );\n  while( i>0 ){\n    RtreeSearchPoint *pParent;\n    j = (i-1)/2;\n    pParent = pCur->aPoint + j;\n    if( rtreeSearchPointCompare(pNew, pParent)>=0 ) break;\n    rtreeSearchPointSwap(pCur, j, i);\n    i = j;\n    pNew = pParent;\n  }\n  return pNew;\n}\n\n/*\n** Allocate a new RtreeSearchPoint and return a pointer to it.  Return\n** NULL if malloc fails.\n*/\nstatic RtreeSearchPoint *rtreeSearchPointNew(\n  RtreeCursor *pCur,    /* The cursor */\n  RtreeDValue rScore,   /* Score for the new search point */\n  u8 iLevel             /* Level for the new search point */\n){\n  RtreeSearchPoint *pNew, *pFirst;\n  pFirst = rtreeSearchPointFirst(pCur);\n  pCur->anQueue[iLevel]++;\n  if( pFirst==0\n   || pFirst->rScore>rScore \n   || (pFirst->rScore==rScore && pFirst->iLevel>iLevel)\n  ){\n    if( pCur->bPoint ){\n      int ii;\n      pNew = rtreeEnqueue(pCur, rScore, iLevel);\n      if( pNew==0 ) return 0;\n      ii = (int)(pNew - pCur->aPoint) + 1;\n      if( ii<RTREE_CACHE_SZ ){\n        assert( pCur->aNode[ii]==0 );\n        pCur->aNode[ii] = pCur->aNode[0];\n       }else{\n        nodeRelease(RTREE_OF_CURSOR(pCur), pCur->aNode[0]);\n      }\n      pCur->aNode[0] = 0;\n      *pNew = pCur->sPoint;\n    }\n    pCur->sPoint.rScore = rScore;\n    pCur->sPoint.iLevel = iLevel;\n    pCur->bPoint = 1;\n    return &pCur->sPoint;\n  }else{\n    return rtreeEnqueue(pCur, rScore, iLevel);\n  }\n}\n\n#if 0\n/* Tracing routines for the RtreeSearchPoint queue */\nstatic void tracePoint(RtreeSearchPoint *p, int idx, RtreeCursor *pCur){\n  if( idx<0 ){ printf(\" s\"); }else{ printf(\"%2d\", idx); }\n  printf(\" %d.%05lld.%02d %g %d\",\n    p->iLevel, p->id, p->iCell, p->rScore, p->eWithin\n  );\n  idx++;\n  if( idx<RTREE_CACHE_SZ ){\n    printf(\" %p\\n\", pCur->aNode[idx]);\n  }else{\n    printf(\"\\n\");\n  }\n}\nstatic void traceQueue(RtreeCursor *pCur, const char *zPrefix){\n  int ii;\n  printf(\"=== %9s \", zPrefix);\n  if( pCur->bPoint ){\n    tracePoint(&pCur->sPoint, -1, pCur);\n  }\n  for(ii=0; ii<pCur->nPoint; ii++){\n    if( ii>0 || pCur->bPoint ) printf(\"              \");\n    tracePoint(&pCur->aPoint[ii], ii, pCur);\n  }\n}\n# define RTREE_QUEUE_TRACE(A,B) traceQueue(A,B)\n#else\n# define RTREE_QUEUE_TRACE(A,B)   /* no-op */\n#endif\n\n/* Remove the search point with the lowest current score.\n*/\nstatic void rtreeSearchPointPop(RtreeCursor *p){\n  int i, j, k, n;\n  i = 1 - p->bPoint;\n  assert( i==0 || i==1 );\n  if( p->aNode[i] ){\n    nodeRelease(RTREE_OF_CURSOR(p), p->aNode[i]);\n    p->aNode[i] = 0;\n  }\n  if( p->bPoint ){\n    p->anQueue[p->sPoint.iLevel]--;\n    p->bPoint = 0;\n  }else if( p->nPoint ){\n    p->anQueue[p->aPoint[0].iLevel]--;\n    n = --p->nPoint;\n    p->aPoint[0] = p->aPoint[n];\n    if( n<RTREE_CACHE_SZ-1 ){\n      p->aNode[1] = p->aNode[n+1];\n      p->aNode[n+1] = 0;\n    }\n    i = 0;\n    while( (j = i*2+1)<n ){\n      k = j+1;\n      if( k<n && rtreeSearchPointCompare(&p->aPoint[k], &p->aPoint[j])<0 ){\n        if( rtreeSearchPointCompare(&p->aPoint[k], &p->aPoint[i])<0 ){\n          rtreeSearchPointSwap(p, i, k);\n          i = k;\n        }else{\n          break;\n        }\n      }else{\n        if( rtreeSearchPointCompare(&p->aPoint[j], &p->aPoint[i])<0 ){\n          rtreeSearchPointSwap(p, i, j);\n          i = j;\n        }else{\n          break;\n        }\n      }\n    }\n  }\n}\n\n\n/*\n** Continue the search on cursor pCur until the front of the queue\n** contains an entry suitable for returning as a result-set row,\n** or until the RtreeSearchPoint queue is empty, indicating that the\n** query has completed.\n*/\nstatic int rtreeStepToLeaf(RtreeCursor *pCur){\n  RtreeSearchPoint *p;\n  Rtree *pRtree = RTREE_OF_CURSOR(pCur);\n  RtreeNode *pNode;\n  int eWithin;\n  int rc = SQLITE_OK;\n  int nCell;\n  int nConstraint = pCur->nConstraint;\n  int ii;\n  int eInt;\n  RtreeSearchPoint x;\n\n  eInt = pRtree->eCoordType==RTREE_COORD_INT32;\n  while( (p = rtreeSearchPointFirst(pCur))!=0 && p->iLevel>0 ){\n    pNode = rtreeNodeOfFirstSearchPoint(pCur, &rc);\n    if( rc ) return rc;\n    nCell = NCELL(pNode);\n    assert( nCell<200 );\n    while( p->iCell<nCell ){\n      sqlite3_rtree_dbl rScore = (sqlite3_rtree_dbl)-1;\n      u8 *pCellData = pNode->zData + (4+pRtree->nBytesPerCell*p->iCell);\n      eWithin = FULLY_WITHIN;\n      for(ii=0; ii<nConstraint; ii++){\n        RtreeConstraint *pConstraint = pCur->aConstraint + ii;\n        if( pConstraint->op>=RTREE_MATCH ){\n          rc = rtreeCallbackConstraint(pConstraint, eInt, pCellData, p,\n                                       &rScore, &eWithin);\n          if( rc ) return rc;\n        }else if( p->iLevel==1 ){\n          rtreeLeafConstraint(pConstraint, eInt, pCellData, &eWithin);\n        }else{\n          rtreeNonleafConstraint(pConstraint, eInt, pCellData, &eWithin);\n        }\n        if( eWithin==NOT_WITHIN ) break;\n      }\n      p->iCell++;\n      if( eWithin==NOT_WITHIN ) continue;\n      x.iLevel = p->iLevel - 1;\n      if( x.iLevel ){\n        x.id = readInt64(pCellData);\n        x.iCell = 0;\n      }else{\n        x.id = p->id;\n        x.iCell = p->iCell - 1;\n      }\n      if( p->iCell>=nCell ){\n        RTREE_QUEUE_TRACE(pCur, \"POP-S:\");\n        rtreeSearchPointPop(pCur);\n      }\n      if( rScore<RTREE_ZERO ) rScore = RTREE_ZERO;\n      p = rtreeSearchPointNew(pCur, rScore, x.iLevel);\n      if( p==0 ) return SQLITE_NOMEM;\n      p->eWithin = (u8)eWithin;\n      p->id = x.id;\n      p->iCell = x.iCell;\n      RTREE_QUEUE_TRACE(pCur, \"PUSH-S:\");\n      break;\n    }\n    if( p->iCell>=nCell ){\n      RTREE_QUEUE_TRACE(pCur, \"POP-Se:\");\n      rtreeSearchPointPop(pCur);\n    }\n  }\n  pCur->atEOF = p==0;\n  return SQLITE_OK;\n}\n\n/* \n** Rtree virtual table module xNext method.\n*/\nstatic int rtreeNext(sqlite3_vtab_cursor *pVtabCursor){\n  RtreeCursor *pCsr = (RtreeCursor *)pVtabCursor;\n  int rc = SQLITE_OK;\n\n  /* Move to the next entry that matches the configured constraints. */\n  RTREE_QUEUE_TRACE(pCsr, \"POP-Nx:\");\n  rtreeSearchPointPop(pCsr);\n  rc = rtreeStepToLeaf(pCsr);\n  return rc;\n}\n\n/* \n** Rtree virtual table module xRowid method.\n*/\nstatic int rtreeRowid(sqlite3_vtab_cursor *pVtabCursor, sqlite_int64 *pRowid){\n  RtreeCursor *pCsr = (RtreeCursor *)pVtabCursor;\n  RtreeSearchPoint *p = rtreeSearchPointFirst(pCsr);\n  int rc = SQLITE_OK;\n  RtreeNode *pNode = rtreeNodeOfFirstSearchPoint(pCsr, &rc);\n  if( rc==SQLITE_OK && p ){\n    *pRowid = nodeGetRowid(RTREE_OF_CURSOR(pCsr), pNode, p->iCell);\n  }\n  return rc;\n}\n\n/* \n** Rtree virtual table module xColumn method.\n*/\nstatic int rtreeColumn(sqlite3_vtab_cursor *cur, sqlite3_context *ctx, int i){\n  Rtree *pRtree = (Rtree *)cur->pVtab;\n  RtreeCursor *pCsr = (RtreeCursor *)cur;\n  RtreeSearchPoint *p = rtreeSearchPointFirst(pCsr);\n  RtreeCoord c;\n  int rc = SQLITE_OK;\n  RtreeNode *pNode = rtreeNodeOfFirstSearchPoint(pCsr, &rc);\n\n  if( rc ) return rc;\n  if( p==0 ) return SQLITE_OK;\n  if( i==0 ){\n    sqlite3_result_int64(ctx, nodeGetRowid(pRtree, pNode, p->iCell));\n  }else{\n    nodeGetCoord(pRtree, pNode, p->iCell, i-1, &c);\n#ifndef SQLITE_RTREE_INT_ONLY\n    if( pRtree->eCoordType==RTREE_COORD_REAL32 ){\n      sqlite3_result_double(ctx, c.f);\n    }else\n#endif\n    {\n      assert( pRtree->eCoordType==RTREE_COORD_INT32 );\n      sqlite3_result_int(ctx, c.i);\n    }\n  }\n  return SQLITE_OK;\n}\n\n/* \n** Use nodeAcquire() to obtain the leaf node containing the record with \n** rowid iRowid. If successful, set *ppLeaf to point to the node and\n** return SQLITE_OK. If there is no such record in the table, set\n** *ppLeaf to 0 and return SQLITE_OK. If an error occurs, set *ppLeaf\n** to zero and return an SQLite error code.\n*/\nstatic int findLeafNode(\n  Rtree *pRtree,              /* RTree to search */\n  i64 iRowid,                 /* The rowid searching for */\n  RtreeNode **ppLeaf,         /* Write the node here */\n  sqlite3_int64 *piNode       /* Write the node-id here */\n){\n  int rc;\n  *ppLeaf = 0;\n  sqlite3_bind_int64(pRtree->pReadRowid, 1, iRowid);\n  if( sqlite3_step(pRtree->pReadRowid)==SQLITE_ROW ){\n    i64 iNode = sqlite3_column_int64(pRtree->pReadRowid, 0);\n    if( piNode ) *piNode = iNode;\n    rc = nodeAcquire(pRtree, iNode, 0, ppLeaf);\n    sqlite3_reset(pRtree->pReadRowid);\n  }else{\n    rc = sqlite3_reset(pRtree->pReadRowid);\n  }\n  return rc;\n}\n\n/*\n** This function is called to configure the RtreeConstraint object passed\n** as the second argument for a MATCH constraint. The value passed as the\n** first argument to this function is the right-hand operand to the MATCH\n** operator.\n*/\nstatic int deserializeGeometry(sqlite3_value *pValue, RtreeConstraint *pCons){\n  RtreeMatchArg *pBlob, *pSrc;       /* BLOB returned by geometry function */\n  sqlite3_rtree_query_info *pInfo;   /* Callback information */\n\n  pSrc = sqlite3_value_pointer(pValue, \"RtreeMatchArg\");\n  if( pSrc==0 ) return SQLITE_ERROR;\n  pInfo = (sqlite3_rtree_query_info*)\n                sqlite3_malloc64( sizeof(*pInfo)+pSrc->iSize );\n  if( !pInfo ) return SQLITE_NOMEM;\n  memset(pInfo, 0, sizeof(*pInfo));\n  pBlob = (RtreeMatchArg*)&pInfo[1];\n  memcpy(pBlob, pSrc, pSrc->iSize);\n  pInfo->pContext = pBlob->cb.pContext;\n  pInfo->nParam = pBlob->nParam;\n  pInfo->aParam = pBlob->aParam;\n  pInfo->apSqlParam = pBlob->apSqlParam;\n\n  if( pBlob->cb.xGeom ){\n    pCons->u.xGeom = pBlob->cb.xGeom;\n  }else{\n    pCons->op = RTREE_QUERY;\n    pCons->u.xQueryFunc = pBlob->cb.xQueryFunc;\n  }\n  pCons->pInfo = pInfo;\n  return SQLITE_OK;\n}\n\n/* \n** Rtree virtual table module xFilter method.\n*/\nstatic int rtreeFilter(\n  sqlite3_vtab_cursor *pVtabCursor, \n  int idxNum, const char *idxStr,\n  int argc, sqlite3_value **argv\n){\n  Rtree *pRtree = (Rtree *)pVtabCursor->pVtab;\n  RtreeCursor *pCsr = (RtreeCursor *)pVtabCursor;\n  RtreeNode *pRoot = 0;\n  int ii;\n  int rc = SQLITE_OK;\n  int iCell = 0;\n\n  rtreeReference(pRtree);\n\n  /* Reset the cursor to the same state as rtreeOpen() leaves it in. */\n  freeCursorConstraints(pCsr);\n  sqlite3_free(pCsr->aPoint);\n  memset(pCsr, 0, sizeof(RtreeCursor));\n  pCsr->base.pVtab = (sqlite3_vtab*)pRtree;\n\n  pCsr->iStrategy = idxNum;\n  if( idxNum==1 ){\n    /* Special case - lookup by rowid. */\n    RtreeNode *pLeaf;        /* Leaf on which the required cell resides */\n    RtreeSearchPoint *p;     /* Search point for the leaf */\n    i64 iRowid = sqlite3_value_int64(argv[0]);\n    i64 iNode = 0;\n    rc = findLeafNode(pRtree, iRowid, &pLeaf, &iNode);\n    if( rc==SQLITE_OK && pLeaf!=0 ){\n      p = rtreeSearchPointNew(pCsr, RTREE_ZERO, 0);\n      assert( p!=0 );  /* Always returns pCsr->sPoint */\n      pCsr->aNode[0] = pLeaf;\n      p->id = iNode;\n      p->eWithin = PARTLY_WITHIN;\n      rc = nodeRowidIndex(pRtree, pLeaf, iRowid, &iCell);\n      p->iCell = (u8)iCell;\n      RTREE_QUEUE_TRACE(pCsr, \"PUSH-F1:\");\n    }else{\n      pCsr->atEOF = 1;\n    }\n  }else{\n    /* Normal case - r-tree scan. Set up the RtreeCursor.aConstraint array \n    ** with the configured constraints. \n    */\n    rc = nodeAcquire(pRtree, 1, 0, &pRoot);\n    if( rc==SQLITE_OK && argc>0 ){\n      pCsr->aConstraint = sqlite3_malloc(sizeof(RtreeConstraint)*argc);\n      pCsr->nConstraint = argc;\n      if( !pCsr->aConstraint ){\n        rc = SQLITE_NOMEM;\n      }else{\n        memset(pCsr->aConstraint, 0, sizeof(RtreeConstraint)*argc);\n        memset(pCsr->anQueue, 0, sizeof(u32)*(pRtree->iDepth + 1));\n        assert( (idxStr==0 && argc==0)\n                || (idxStr && (int)strlen(idxStr)==argc*2) );\n        for(ii=0; ii<argc; ii++){\n          RtreeConstraint *p = &pCsr->aConstraint[ii];\n          p->op = idxStr[ii*2];\n          p->iCoord = idxStr[ii*2+1]-'0';\n          if( p->op>=RTREE_MATCH ){\n            /* A MATCH operator. The right-hand-side must be a blob that\n            ** can be cast into an RtreeMatchArg object. One created using\n            ** an sqlite3_rtree_geometry_callback() SQL user function.\n            */\n            rc = deserializeGeometry(argv[ii], p);\n            if( rc!=SQLITE_OK ){\n              break;\n            }\n            p->pInfo->nCoord = pRtree->nDim2;\n            p->pInfo->anQueue = pCsr->anQueue;\n            p->pInfo->mxLevel = pRtree->iDepth + 1;\n          }else{\n#ifdef SQLITE_RTREE_INT_ONLY\n            p->u.rValue = sqlite3_value_int64(argv[ii]);\n#else\n            p->u.rValue = sqlite3_value_double(argv[ii]);\n#endif\n          }\n        }\n      }\n    }\n    if( rc==SQLITE_OK ){\n      RtreeSearchPoint *pNew;\n      pNew = rtreeSearchPointNew(pCsr, RTREE_ZERO, (u8)(pRtree->iDepth+1));\n      if( pNew==0 ) return SQLITE_NOMEM;\n      pNew->id = 1;\n      pNew->iCell = 0;\n      pNew->eWithin = PARTLY_WITHIN;\n      assert( pCsr->bPoint==1 );\n      pCsr->aNode[0] = pRoot;\n      pRoot = 0;\n      RTREE_QUEUE_TRACE(pCsr, \"PUSH-Fm:\");\n      rc = rtreeStepToLeaf(pCsr);\n    }\n  }\n\n  nodeRelease(pRtree, pRoot);\n  rtreeRelease(pRtree);\n  return rc;\n}\n\n/*\n** Rtree virtual table module xBestIndex method. There are three\n** table scan strategies to choose from (in order from most to \n** least desirable):\n**\n**   idxNum     idxStr        Strategy\n**   ------------------------------------------------\n**     1        Unused        Direct lookup by rowid.\n**     2        See below     R-tree query or full-table scan.\n**   ------------------------------------------------\n**\n** If strategy 1 is used, then idxStr is not meaningful. If strategy\n** 2 is used, idxStr is formatted to contain 2 bytes for each \n** constraint used. The first two bytes of idxStr correspond to \n** the constraint in sqlite3_index_info.aConstraintUsage[] with\n** (argvIndex==1) etc.\n**\n** The first of each pair of bytes in idxStr identifies the constraint\n** operator as follows:\n**\n**   Operator    Byte Value\n**   ----------------------\n**      =        0x41 ('A')\n**     <=        0x42 ('B')\n**      <        0x43 ('C')\n**     >=        0x44 ('D')\n**      >        0x45 ('E')\n**   MATCH       0x46 ('F')\n**   ----------------------\n**\n** The second of each pair of bytes identifies the coordinate column\n** to which the constraint applies. The leftmost coordinate column\n** is 'a', the second from the left 'b' etc.\n*/\nstatic int rtreeBestIndex(sqlite3_vtab *tab, sqlite3_index_info *pIdxInfo){\n  Rtree *pRtree = (Rtree*)tab;\n  int rc = SQLITE_OK;\n  int ii;\n  int bMatch = 0;                 /* True if there exists a MATCH constraint */\n  i64 nRow;                       /* Estimated rows returned by this scan */\n\n  int iIdx = 0;\n  char zIdxStr[RTREE_MAX_DIMENSIONS*8+1];\n  memset(zIdxStr, 0, sizeof(zIdxStr));\n\n  /* Check if there exists a MATCH constraint - even an unusable one. If there\n  ** is, do not consider the lookup-by-rowid plan as using such a plan would\n  ** require the VDBE to evaluate the MATCH constraint, which is not currently\n  ** possible. */\n  for(ii=0; ii<pIdxInfo->nConstraint; ii++){\n    if( pIdxInfo->aConstraint[ii].op==SQLITE_INDEX_CONSTRAINT_MATCH ){\n      bMatch = 1;\n    }\n  }\n\n  assert( pIdxInfo->idxStr==0 );\n  for(ii=0; ii<pIdxInfo->nConstraint && iIdx<(int)(sizeof(zIdxStr)-1); ii++){\n    struct sqlite3_index_constraint *p = &pIdxInfo->aConstraint[ii];\n\n    if( bMatch==0 && p->usable \n     && p->iColumn==0 && p->op==SQLITE_INDEX_CONSTRAINT_EQ \n    ){\n      /* We have an equality constraint on the rowid. Use strategy 1. */\n      int jj;\n      for(jj=0; jj<ii; jj++){\n        pIdxInfo->aConstraintUsage[jj].argvIndex = 0;\n        pIdxInfo->aConstraintUsage[jj].omit = 0;\n      }\n      pIdxInfo->idxNum = 1;\n      pIdxInfo->aConstraintUsage[ii].argvIndex = 1;\n      pIdxInfo->aConstraintUsage[jj].omit = 1;\n\n      /* This strategy involves a two rowid lookups on an B-Tree structures\n      ** and then a linear search of an R-Tree node. This should be \n      ** considered almost as quick as a direct rowid lookup (for which \n      ** sqlite uses an internal cost of 0.0). It is expected to return\n      ** a single row.\n      */ \n      pIdxInfo->estimatedCost = 30.0;\n      pIdxInfo->estimatedRows = 1;\n      return SQLITE_OK;\n    }\n\n    if( p->usable && (p->iColumn>0 || p->op==SQLITE_INDEX_CONSTRAINT_MATCH) ){\n      u8 op;\n      switch( p->op ){\n        case SQLITE_INDEX_CONSTRAINT_EQ: op = RTREE_EQ; break;\n        case SQLITE_INDEX_CONSTRAINT_GT: op = RTREE_GT; break;\n        case SQLITE_INDEX_CONSTRAINT_LE: op = RTREE_LE; break;\n        case SQLITE_INDEX_CONSTRAINT_LT: op = RTREE_LT; break;\n        case SQLITE_INDEX_CONSTRAINT_GE: op = RTREE_GE; break;\n        default:\n          assert( p->op==SQLITE_INDEX_CONSTRAINT_MATCH );\n          op = RTREE_MATCH; \n          break;\n      }\n      zIdxStr[iIdx++] = op;\n      zIdxStr[iIdx++] = (char)(p->iColumn - 1 + '0');\n      pIdxInfo->aConstraintUsage[ii].argvIndex = (iIdx/2);\n      pIdxInfo->aConstraintUsage[ii].omit = 1;\n    }\n  }\n\n  pIdxInfo->idxNum = 2;\n  pIdxInfo->needToFreeIdxStr = 1;\n  if( iIdx>0 && 0==(pIdxInfo->idxStr = sqlite3_mprintf(\"%s\", zIdxStr)) ){\n    return SQLITE_NOMEM;\n  }\n\n  nRow = pRtree->nRowEst >> (iIdx/2);\n  pIdxInfo->estimatedCost = (double)6.0 * (double)nRow;\n  pIdxInfo->estimatedRows = nRow;\n\n  return rc;\n}\n\n/*\n** Return the N-dimensional volumn of the cell stored in *p.\n*/\nstatic RtreeDValue cellArea(Rtree *pRtree, RtreeCell *p){\n  RtreeDValue area = (RtreeDValue)1;\n  assert( pRtree->nDim>=1 && pRtree->nDim<=5 );\n#ifndef SQLITE_RTREE_INT_ONLY\n  if( pRtree->eCoordType==RTREE_COORD_REAL32 ){\n    switch( pRtree->nDim ){\n      case 5:  area  = p->aCoord[9].f - p->aCoord[8].f;\n      case 4:  area *= p->aCoord[7].f - p->aCoord[6].f;\n      case 3:  area *= p->aCoord[5].f - p->aCoord[4].f;\n      case 2:  area *= p->aCoord[3].f - p->aCoord[2].f;\n      default: area *= p->aCoord[1].f - p->aCoord[0].f;\n    }\n  }else\n#endif\n  {\n    switch( pRtree->nDim ){\n      case 5:  area  = p->aCoord[9].i - p->aCoord[8].i;\n      case 4:  area *= p->aCoord[7].i - p->aCoord[6].i;\n      case 3:  area *= p->aCoord[5].i - p->aCoord[4].i;\n      case 2:  area *= p->aCoord[3].i - p->aCoord[2].i;\n      default: area *= p->aCoord[1].i - p->aCoord[0].i;\n    }\n  }\n  return area;\n}\n\n/*\n** Return the margin length of cell p. The margin length is the sum\n** of the objects size in each dimension.\n*/\nstatic RtreeDValue cellMargin(Rtree *pRtree, RtreeCell *p){\n  RtreeDValue margin = 0;\n  int ii = pRtree->nDim2 - 2;\n  do{\n    margin += (DCOORD(p->aCoord[ii+1]) - DCOORD(p->aCoord[ii]));\n    ii -= 2;\n  }while( ii>=0 );\n  return margin;\n}\n\n/*\n** Store the union of cells p1 and p2 in p1.\n*/\nstatic void cellUnion(Rtree *pRtree, RtreeCell *p1, RtreeCell *p2){\n  int ii = 0;\n  if( pRtree->eCoordType==RTREE_COORD_REAL32 ){\n    do{\n      p1->aCoord[ii].f = MIN(p1->aCoord[ii].f, p2->aCoord[ii].f);\n      p1->aCoord[ii+1].f = MAX(p1->aCoord[ii+1].f, p2->aCoord[ii+1].f);\n      ii += 2;\n    }while( ii<pRtree->nDim2 );\n  }else{\n    do{\n      p1->aCoord[ii].i = MIN(p1->aCoord[ii].i, p2->aCoord[ii].i);\n      p1->aCoord[ii+1].i = MAX(p1->aCoord[ii+1].i, p2->aCoord[ii+1].i);\n      ii += 2;\n    }while( ii<pRtree->nDim2 );\n  }\n}\n\n/*\n** Return true if the area covered by p2 is a subset of the area covered\n** by p1. False otherwise.\n*/\nstatic int cellContains(Rtree *pRtree, RtreeCell *p1, RtreeCell *p2){\n  int ii;\n  int isInt = (pRtree->eCoordType==RTREE_COORD_INT32);\n  for(ii=0; ii<pRtree->nDim2; ii+=2){\n    RtreeCoord *a1 = &p1->aCoord[ii];\n    RtreeCoord *a2 = &p2->aCoord[ii];\n    if( (!isInt && (a2[0].f<a1[0].f || a2[1].f>a1[1].f)) \n     || ( isInt && (a2[0].i<a1[0].i || a2[1].i>a1[1].i)) \n    ){\n      return 0;\n    }\n  }\n  return 1;\n}\n\n/*\n** Return the amount cell p would grow by if it were unioned with pCell.\n*/\nstatic RtreeDValue cellGrowth(Rtree *pRtree, RtreeCell *p, RtreeCell *pCell){\n  RtreeDValue area;\n  RtreeCell cell;\n  memcpy(&cell, p, sizeof(RtreeCell));\n  area = cellArea(pRtree, &cell);\n  cellUnion(pRtree, &cell, pCell);\n  return (cellArea(pRtree, &cell)-area);\n}\n\nstatic RtreeDValue cellOverlap(\n  Rtree *pRtree, \n  RtreeCell *p, \n  RtreeCell *aCell, \n  int nCell\n){\n  int ii;\n  RtreeDValue overlap = RTREE_ZERO;\n  for(ii=0; ii<nCell; ii++){\n    int jj;\n    RtreeDValue o = (RtreeDValue)1;\n    for(jj=0; jj<pRtree->nDim2; jj+=2){\n      RtreeDValue x1, x2;\n      x1 = MAX(DCOORD(p->aCoord[jj]), DCOORD(aCell[ii].aCoord[jj]));\n      x2 = MIN(DCOORD(p->aCoord[jj+1]), DCOORD(aCell[ii].aCoord[jj+1]));\n      if( x2<x1 ){\n        o = (RtreeDValue)0;\n        break;\n      }else{\n        o = o * (x2-x1);\n      }\n    }\n    overlap += o;\n  }\n  return overlap;\n}\n\n\n/*\n** This function implements the ChooseLeaf algorithm from Gutman[84].\n** ChooseSubTree in r*tree terminology.\n*/\nstatic int ChooseLeaf(\n  Rtree *pRtree,               /* Rtree table */\n  RtreeCell *pCell,            /* Cell to insert into rtree */\n  int iHeight,                 /* Height of sub-tree rooted at pCell */\n  RtreeNode **ppLeaf           /* OUT: Selected leaf page */\n){\n  int rc;\n  int ii;\n  RtreeNode *pNode = 0;\n  rc = nodeAcquire(pRtree, 1, 0, &pNode);\n\n  for(ii=0; rc==SQLITE_OK && ii<(pRtree->iDepth-iHeight); ii++){\n    int iCell;\n    sqlite3_int64 iBest = 0;\n\n    RtreeDValue fMinGrowth = RTREE_ZERO;\n    RtreeDValue fMinArea = RTREE_ZERO;\n\n    int nCell = NCELL(pNode);\n    RtreeCell cell;\n    RtreeNode *pChild;\n\n    RtreeCell *aCell = 0;\n\n    /* Select the child node which will be enlarged the least if pCell\n    ** is inserted into it. Resolve ties by choosing the entry with\n    ** the smallest area.\n    */\n    for(iCell=0; iCell<nCell; iCell++){\n      int bBest = 0;\n      RtreeDValue growth;\n      RtreeDValue area;\n      nodeGetCell(pRtree, pNode, iCell, &cell);\n      growth = cellGrowth(pRtree, &cell, pCell);\n      area = cellArea(pRtree, &cell);\n      if( iCell==0||growth<fMinGrowth||(growth==fMinGrowth && area<fMinArea) ){\n        bBest = 1;\n      }\n      if( bBest ){\n        fMinGrowth = growth;\n        fMinArea = area;\n        iBest = cell.iRowid;\n      }\n    }\n\n    sqlite3_free(aCell);\n    rc = nodeAcquire(pRtree, iBest, pNode, &pChild);\n    nodeRelease(pRtree, pNode);\n    pNode = pChild;\n  }\n\n  *ppLeaf = pNode;\n  return rc;\n}\n\n/*\n** A cell with the same content as pCell has just been inserted into\n** the node pNode. This function updates the bounding box cells in\n** all ancestor elements.\n*/\nstatic int AdjustTree(\n  Rtree *pRtree,                    /* Rtree table */\n  RtreeNode *pNode,                 /* Adjust ancestry of this node. */\n  RtreeCell *pCell                  /* This cell was just inserted */\n){\n  RtreeNode *p = pNode;\n  while( p->pParent ){\n    RtreeNode *pParent = p->pParent;\n    RtreeCell cell;\n    int iCell;\n\n    if( nodeParentIndex(pRtree, p, &iCell) ){\n      return SQLITE_CORRUPT_VTAB;\n    }\n\n    nodeGetCell(pRtree, pParent, iCell, &cell);\n    if( !cellContains(pRtree, &cell, pCell) ){\n      cellUnion(pRtree, &cell, pCell);\n      nodeOverwriteCell(pRtree, pParent, &cell, iCell);\n    }\n \n    p = pParent;\n  }\n  return SQLITE_OK;\n}\n\n/*\n** Write mapping (iRowid->iNode) to the <rtree>_rowid table.\n*/\nstatic int rowidWrite(Rtree *pRtree, sqlite3_int64 iRowid, sqlite3_int64 iNode){\n  sqlite3_bind_int64(pRtree->pWriteRowid, 1, iRowid);\n  sqlite3_bind_int64(pRtree->pWriteRowid, 2, iNode);\n  sqlite3_step(pRtree->pWriteRowid);\n  return sqlite3_reset(pRtree->pWriteRowid);\n}\n\n/*\n** Write mapping (iNode->iPar) to the <rtree>_parent table.\n*/\nstatic int parentWrite(Rtree *pRtree, sqlite3_int64 iNode, sqlite3_int64 iPar){\n  sqlite3_bind_int64(pRtree->pWriteParent, 1, iNode);\n  sqlite3_bind_int64(pRtree->pWriteParent, 2, iPar);\n  sqlite3_step(pRtree->pWriteParent);\n  return sqlite3_reset(pRtree->pWriteParent);\n}\n\nstatic int rtreeInsertCell(Rtree *, RtreeNode *, RtreeCell *, int);\n\n\n/*\n** Arguments aIdx, aDistance and aSpare all point to arrays of size\n** nIdx. The aIdx array contains the set of integers from 0 to \n** (nIdx-1) in no particular order. This function sorts the values\n** in aIdx according to the indexed values in aDistance. For\n** example, assuming the inputs:\n**\n**   aIdx      = { 0,   1,   2,   3 }\n**   aDistance = { 5.0, 2.0, 7.0, 6.0 }\n**\n** this function sets the aIdx array to contain:\n**\n**   aIdx      = { 0,   1,   2,   3 }\n**\n** The aSpare array is used as temporary working space by the\n** sorting algorithm.\n*/\nstatic void SortByDistance(\n  int *aIdx, \n  int nIdx, \n  RtreeDValue *aDistance, \n  int *aSpare\n){\n  if( nIdx>1 ){\n    int iLeft = 0;\n    int iRight = 0;\n\n    int nLeft = nIdx/2;\n    int nRight = nIdx-nLeft;\n    int *aLeft = aIdx;\n    int *aRight = &aIdx[nLeft];\n\n    SortByDistance(aLeft, nLeft, aDistance, aSpare);\n    SortByDistance(aRight, nRight, aDistance, aSpare);\n\n    memcpy(aSpare, aLeft, sizeof(int)*nLeft);\n    aLeft = aSpare;\n\n    while( iLeft<nLeft || iRight<nRight ){\n      if( iLeft==nLeft ){\n        aIdx[iLeft+iRight] = aRight[iRight];\n        iRight++;\n      }else if( iRight==nRight ){\n        aIdx[iLeft+iRight] = aLeft[iLeft];\n        iLeft++;\n      }else{\n        RtreeDValue fLeft = aDistance[aLeft[iLeft]];\n        RtreeDValue fRight = aDistance[aRight[iRight]];\n        if( fLeft<fRight ){\n          aIdx[iLeft+iRight] = aLeft[iLeft];\n          iLeft++;\n        }else{\n          aIdx[iLeft+iRight] = aRight[iRight];\n          iRight++;\n        }\n      }\n    }\n\n#if 0\n    /* Check that the sort worked */\n    {\n      int jj;\n      for(jj=1; jj<nIdx; jj++){\n        RtreeDValue left = aDistance[aIdx[jj-1]];\n        RtreeDValue right = aDistance[aIdx[jj]];\n        assert( left<=right );\n      }\n    }\n#endif\n  }\n}\n\n/*\n** Arguments aIdx, aCell and aSpare all point to arrays of size\n** nIdx. The aIdx array contains the set of integers from 0 to \n** (nIdx-1) in no particular order. This function sorts the values\n** in aIdx according to dimension iDim of the cells in aCell. The\n** minimum value of dimension iDim is considered first, the\n** maximum used to break ties.\n**\n** The aSpare array is used as temporary working space by the\n** sorting algorithm.\n*/\nstatic void SortByDimension(\n  Rtree *pRtree,\n  int *aIdx, \n  int nIdx, \n  int iDim, \n  RtreeCell *aCell, \n  int *aSpare\n){\n  if( nIdx>1 ){\n\n    int iLeft = 0;\n    int iRight = 0;\n\n    int nLeft = nIdx/2;\n    int nRight = nIdx-nLeft;\n    int *aLeft = aIdx;\n    int *aRight = &aIdx[nLeft];\n\n    SortByDimension(pRtree, aLeft, nLeft, iDim, aCell, aSpare);\n    SortByDimension(pRtree, aRight, nRight, iDim, aCell, aSpare);\n\n    memcpy(aSpare, aLeft, sizeof(int)*nLeft);\n    aLeft = aSpare;\n    while( iLeft<nLeft || iRight<nRight ){\n      RtreeDValue xleft1 = DCOORD(aCell[aLeft[iLeft]].aCoord[iDim*2]);\n      RtreeDValue xleft2 = DCOORD(aCell[aLeft[iLeft]].aCoord[iDim*2+1]);\n      RtreeDValue xright1 = DCOORD(aCell[aRight[iRight]].aCoord[iDim*2]);\n      RtreeDValue xright2 = DCOORD(aCell[aRight[iRight]].aCoord[iDim*2+1]);\n      if( (iLeft!=nLeft) && ((iRight==nRight)\n       || (xleft1<xright1)\n       || (xleft1==xright1 && xleft2<xright2)\n      )){\n        aIdx[iLeft+iRight] = aLeft[iLeft];\n        iLeft++;\n      }else{\n        aIdx[iLeft+iRight] = aRight[iRight];\n        iRight++;\n      }\n    }\n\n#if 0\n    /* Check that the sort worked */\n    {\n      int jj;\n      for(jj=1; jj<nIdx; jj++){\n        RtreeDValue xleft1 = aCell[aIdx[jj-1]].aCoord[iDim*2];\n        RtreeDValue xleft2 = aCell[aIdx[jj-1]].aCoord[iDim*2+1];\n        RtreeDValue xright1 = aCell[aIdx[jj]].aCoord[iDim*2];\n        RtreeDValue xright2 = aCell[aIdx[jj]].aCoord[iDim*2+1];\n        assert( xleft1<=xright1 && (xleft1<xright1 || xleft2<=xright2) );\n      }\n    }\n#endif\n  }\n}\n\n/*\n** Implementation of the R*-tree variant of SplitNode from Beckman[1990].\n*/\nstatic int splitNodeStartree(\n  Rtree *pRtree,\n  RtreeCell *aCell,\n  int nCell,\n  RtreeNode *pLeft,\n  RtreeNode *pRight,\n  RtreeCell *pBboxLeft,\n  RtreeCell *pBboxRight\n){\n  int **aaSorted;\n  int *aSpare;\n  int ii;\n\n  int iBestDim = 0;\n  int iBestSplit = 0;\n  RtreeDValue fBestMargin = RTREE_ZERO;\n\n  int nByte = (pRtree->nDim+1)*(sizeof(int*)+nCell*sizeof(int));\n\n  aaSorted = (int **)sqlite3_malloc(nByte);\n  if( !aaSorted ){\n    return SQLITE_NOMEM;\n  }\n\n  aSpare = &((int *)&aaSorted[pRtree->nDim])[pRtree->nDim*nCell];\n  memset(aaSorted, 0, nByte);\n  for(ii=0; ii<pRtree->nDim; ii++){\n    int jj;\n    aaSorted[ii] = &((int *)&aaSorted[pRtree->nDim])[ii*nCell];\n    for(jj=0; jj<nCell; jj++){\n      aaSorted[ii][jj] = jj;\n    }\n    SortByDimension(pRtree, aaSorted[ii], nCell, ii, aCell, aSpare);\n  }\n\n  for(ii=0; ii<pRtree->nDim; ii++){\n    RtreeDValue margin = RTREE_ZERO;\n    RtreeDValue fBestOverlap = RTREE_ZERO;\n    RtreeDValue fBestArea = RTREE_ZERO;\n    int iBestLeft = 0;\n    int nLeft;\n\n    for(\n      nLeft=RTREE_MINCELLS(pRtree); \n      nLeft<=(nCell-RTREE_MINCELLS(pRtree)); \n      nLeft++\n    ){\n      RtreeCell left;\n      RtreeCell right;\n      int kk;\n      RtreeDValue overlap;\n      RtreeDValue area;\n\n      memcpy(&left, &aCell[aaSorted[ii][0]], sizeof(RtreeCell));\n      memcpy(&right, &aCell[aaSorted[ii][nCell-1]], sizeof(RtreeCell));\n      for(kk=1; kk<(nCell-1); kk++){\n        if( kk<nLeft ){\n          cellUnion(pRtree, &left, &aCell[aaSorted[ii][kk]]);\n        }else{\n          cellUnion(pRtree, &right, &aCell[aaSorted[ii][kk]]);\n        }\n      }\n      margin += cellMargin(pRtree, &left);\n      margin += cellMargin(pRtree, &right);\n      overlap = cellOverlap(pRtree, &left, &right, 1);\n      area = cellArea(pRtree, &left) + cellArea(pRtree, &right);\n      if( (nLeft==RTREE_MINCELLS(pRtree))\n       || (overlap<fBestOverlap)\n       || (overlap==fBestOverlap && area<fBestArea)\n      ){\n        iBestLeft = nLeft;\n        fBestOverlap = overlap;\n        fBestArea = area;\n      }\n    }\n\n    if( ii==0 || margin<fBestMargin ){\n      iBestDim = ii;\n      fBestMargin = margin;\n      iBestSplit = iBestLeft;\n    }\n  }\n\n  memcpy(pBboxLeft, &aCell[aaSorted[iBestDim][0]], sizeof(RtreeCell));\n  memcpy(pBboxRight, &aCell[aaSorted[iBestDim][iBestSplit]], sizeof(RtreeCell));\n  for(ii=0; ii<nCell; ii++){\n    RtreeNode *pTarget = (ii<iBestSplit)?pLeft:pRight;\n    RtreeCell *pBbox = (ii<iBestSplit)?pBboxLeft:pBboxRight;\n    RtreeCell *pCell = &aCell[aaSorted[iBestDim][ii]];\n    nodeInsertCell(pRtree, pTarget, pCell);\n    cellUnion(pRtree, pBbox, pCell);\n  }\n\n  sqlite3_free(aaSorted);\n  return SQLITE_OK;\n}\n\n\nstatic int updateMapping(\n  Rtree *pRtree, \n  i64 iRowid, \n  RtreeNode *pNode, \n  int iHeight\n){\n  int (*xSetMapping)(Rtree *, sqlite3_int64, sqlite3_int64);\n  xSetMapping = ((iHeight==0)?rowidWrite:parentWrite);\n  if( iHeight>0 ){\n    RtreeNode *pChild = nodeHashLookup(pRtree, iRowid);\n    if( pChild ){\n      nodeRelease(pRtree, pChild->pParent);\n      nodeReference(pNode);\n      pChild->pParent = pNode;\n    }\n  }\n  return xSetMapping(pRtree, iRowid, pNode->iNode);\n}\n\nstatic int SplitNode(\n  Rtree *pRtree,\n  RtreeNode *pNode,\n  RtreeCell *pCell,\n  int iHeight\n){\n  int i;\n  int newCellIsRight = 0;\n\n  int rc = SQLITE_OK;\n  int nCell = NCELL(pNode);\n  RtreeCell *aCell;\n  int *aiUsed;\n\n  RtreeNode *pLeft = 0;\n  RtreeNode *pRight = 0;\n\n  RtreeCell leftbbox;\n  RtreeCell rightbbox;\n\n  /* Allocate an array and populate it with a copy of pCell and \n  ** all cells from node pLeft. Then zero the original node.\n  */\n  aCell = sqlite3_malloc((sizeof(RtreeCell)+sizeof(int))*(nCell+1));\n  if( !aCell ){\n    rc = SQLITE_NOMEM;\n    goto splitnode_out;\n  }\n  aiUsed = (int *)&aCell[nCell+1];\n  memset(aiUsed, 0, sizeof(int)*(nCell+1));\n  for(i=0; i<nCell; i++){\n    nodeGetCell(pRtree, pNode, i, &aCell[i]);\n  }\n  nodeZero(pRtree, pNode);\n  memcpy(&aCell[nCell], pCell, sizeof(RtreeCell));\n  nCell++;\n\n  if( pNode->iNode==1 ){\n    pRight = nodeNew(pRtree, pNode);\n    pLeft = nodeNew(pRtree, pNode);\n    pRtree->iDepth++;\n    pNode->isDirty = 1;\n    writeInt16(pNode->zData, pRtree->iDepth);\n  }else{\n    pLeft = pNode;\n    pRight = nodeNew(pRtree, pLeft->pParent);\n    nodeReference(pLeft);\n  }\n\n  if( !pLeft || !pRight ){\n    rc = SQLITE_NOMEM;\n    goto splitnode_out;\n  }\n\n  memset(pLeft->zData, 0, pRtree->iNodeSize);\n  memset(pRight->zData, 0, pRtree->iNodeSize);\n\n  rc = splitNodeStartree(pRtree, aCell, nCell, pLeft, pRight,\n                         &leftbbox, &rightbbox);\n  if( rc!=SQLITE_OK ){\n    goto splitnode_out;\n  }\n\n  /* Ensure both child nodes have node numbers assigned to them by calling\n  ** nodeWrite(). Node pRight always needs a node number, as it was created\n  ** by nodeNew() above. But node pLeft sometimes already has a node number.\n  ** In this case avoid the all to nodeWrite().\n  */\n  if( SQLITE_OK!=(rc = nodeWrite(pRtree, pRight))\n   || (0==pLeft->iNode && SQLITE_OK!=(rc = nodeWrite(pRtree, pLeft)))\n  ){\n    goto splitnode_out;\n  }\n\n  rightbbox.iRowid = pRight->iNode;\n  leftbbox.iRowid = pLeft->iNode;\n\n  if( pNode->iNode==1 ){\n    rc = rtreeInsertCell(pRtree, pLeft->pParent, &leftbbox, iHeight+1);\n    if( rc!=SQLITE_OK ){\n      goto splitnode_out;\n    }\n  }else{\n    RtreeNode *pParent = pLeft->pParent;\n    int iCell;\n    rc = nodeParentIndex(pRtree, pLeft, &iCell);\n    if( rc==SQLITE_OK ){\n      nodeOverwriteCell(pRtree, pParent, &leftbbox, iCell);\n      rc = AdjustTree(pRtree, pParent, &leftbbox);\n    }\n    if( rc!=SQLITE_OK ){\n      goto splitnode_out;\n    }\n  }\n  if( (rc = rtreeInsertCell(pRtree, pRight->pParent, &rightbbox, iHeight+1)) ){\n    goto splitnode_out;\n  }\n\n  for(i=0; i<NCELL(pRight); i++){\n    i64 iRowid = nodeGetRowid(pRtree, pRight, i);\n    rc = updateMapping(pRtree, iRowid, pRight, iHeight);\n    if( iRowid==pCell->iRowid ){\n      newCellIsRight = 1;\n    }\n    if( rc!=SQLITE_OK ){\n      goto splitnode_out;\n    }\n  }\n  if( pNode->iNode==1 ){\n    for(i=0; i<NCELL(pLeft); i++){\n      i64 iRowid = nodeGetRowid(pRtree, pLeft, i);\n      rc = updateMapping(pRtree, iRowid, pLeft, iHeight);\n      if( rc!=SQLITE_OK ){\n        goto splitnode_out;\n      }\n    }\n  }else if( newCellIsRight==0 ){\n    rc = updateMapping(pRtree, pCell->iRowid, pLeft, iHeight);\n  }\n\n  if( rc==SQLITE_OK ){\n    rc = nodeRelease(pRtree, pRight);\n    pRight = 0;\n  }\n  if( rc==SQLITE_OK ){\n    rc = nodeRelease(pRtree, pLeft);\n    pLeft = 0;\n  }\n\nsplitnode_out:\n  nodeRelease(pRtree, pRight);\n  nodeRelease(pRtree, pLeft);\n  sqlite3_free(aCell);\n  return rc;\n}\n\n/*\n** If node pLeaf is not the root of the r-tree and its pParent pointer is \n** still NULL, load all ancestor nodes of pLeaf into memory and populate\n** the pLeaf->pParent chain all the way up to the root node.\n**\n** This operation is required when a row is deleted (or updated - an update\n** is implemented as a delete followed by an insert). SQLite provides the\n** rowid of the row to delete, which can be used to find the leaf on which\n** the entry resides (argument pLeaf). Once the leaf is located, this \n** function is called to determine its ancestry.\n*/\nstatic int fixLeafParent(Rtree *pRtree, RtreeNode *pLeaf){\n  int rc = SQLITE_OK;\n  RtreeNode *pChild = pLeaf;\n  while( rc==SQLITE_OK && pChild->iNode!=1 && pChild->pParent==0 ){\n    int rc2 = SQLITE_OK;          /* sqlite3_reset() return code */\n    sqlite3_bind_int64(pRtree->pReadParent, 1, pChild->iNode);\n    rc = sqlite3_step(pRtree->pReadParent);\n    if( rc==SQLITE_ROW ){\n      RtreeNode *pTest;           /* Used to test for reference loops */\n      i64 iNode;                  /* Node number of parent node */\n\n      /* Before setting pChild->pParent, test that we are not creating a\n      ** loop of references (as we would if, say, pChild==pParent). We don't\n      ** want to do this as it leads to a memory leak when trying to delete\n      ** the referenced counted node structures.\n      */\n      iNode = sqlite3_column_int64(pRtree->pReadParent, 0);\n      for(pTest=pLeaf; pTest && pTest->iNode!=iNode; pTest=pTest->pParent);\n      if( !pTest ){\n        rc2 = nodeAcquire(pRtree, iNode, 0, &pChild->pParent);\n      }\n    }\n    rc = sqlite3_reset(pRtree->pReadParent);\n    if( rc==SQLITE_OK ) rc = rc2;\n    if( rc==SQLITE_OK && !pChild->pParent ) rc = SQLITE_CORRUPT_VTAB;\n    pChild = pChild->pParent;\n  }\n  return rc;\n}\n\nstatic int deleteCell(Rtree *, RtreeNode *, int, int);\n\nstatic int removeNode(Rtree *pRtree, RtreeNode *pNode, int iHeight){\n  int rc;\n  int rc2;\n  RtreeNode *pParent = 0;\n  int iCell;\n\n  assert( pNode->nRef==1 );\n\n  /* Remove the entry in the parent cell. */\n  rc = nodeParentIndex(pRtree, pNode, &iCell);\n  if( rc==SQLITE_OK ){\n    pParent = pNode->pParent;\n    pNode->pParent = 0;\n    rc = deleteCell(pRtree, pParent, iCell, iHeight+1);\n  }\n  rc2 = nodeRelease(pRtree, pParent);\n  if( rc==SQLITE_OK ){\n    rc = rc2;\n  }\n  if( rc!=SQLITE_OK ){\n    return rc;\n  }\n\n  /* Remove the xxx_node entry. */\n  sqlite3_bind_int64(pRtree->pDeleteNode, 1, pNode->iNode);\n  sqlite3_step(pRtree->pDeleteNode);\n  if( SQLITE_OK!=(rc = sqlite3_reset(pRtree->pDeleteNode)) ){\n    return rc;\n  }\n\n  /* Remove the xxx_parent entry. */\n  sqlite3_bind_int64(pRtree->pDeleteParent, 1, pNode->iNode);\n  sqlite3_step(pRtree->pDeleteParent);\n  if( SQLITE_OK!=(rc = sqlite3_reset(pRtree->pDeleteParent)) ){\n    return rc;\n  }\n  \n  /* Remove the node from the in-memory hash table and link it into\n  ** the Rtree.pDeleted list. Its contents will be re-inserted later on.\n  */\n  nodeHashDelete(pRtree, pNode);\n  pNode->iNode = iHeight;\n  pNode->pNext = pRtree->pDeleted;\n  pNode->nRef++;\n  pRtree->pDeleted = pNode;\n\n  return SQLITE_OK;\n}\n\nstatic int fixBoundingBox(Rtree *pRtree, RtreeNode *pNode){\n  RtreeNode *pParent = pNode->pParent;\n  int rc = SQLITE_OK; \n  if( pParent ){\n    int ii; \n    int nCell = NCELL(pNode);\n    RtreeCell box;                            /* Bounding box for pNode */\n    nodeGetCell(pRtree, pNode, 0, &box);\n    for(ii=1; ii<nCell; ii++){\n      RtreeCell cell;\n      nodeGetCell(pRtree, pNode, ii, &cell);\n      cellUnion(pRtree, &box, &cell);\n    }\n    box.iRowid = pNode->iNode;\n    rc = nodeParentIndex(pRtree, pNode, &ii);\n    if( rc==SQLITE_OK ){\n      nodeOverwriteCell(pRtree, pParent, &box, ii);\n      rc = fixBoundingBox(pRtree, pParent);\n    }\n  }\n  return rc;\n}\n\n/*\n** Delete the cell at index iCell of node pNode. After removing the\n** cell, adjust the r-tree data structure if required.\n*/\nstatic int deleteCell(Rtree *pRtree, RtreeNode *pNode, int iCell, int iHeight){\n  RtreeNode *pParent;\n  int rc;\n\n  if( SQLITE_OK!=(rc = fixLeafParent(pRtree, pNode)) ){\n    return rc;\n  }\n\n  /* Remove the cell from the node. This call just moves bytes around\n  ** the in-memory node image, so it cannot fail.\n  */\n  nodeDeleteCell(pRtree, pNode, iCell);\n\n  /* If the node is not the tree root and now has less than the minimum\n  ** number of cells, remove it from the tree. Otherwise, update the\n  ** cell in the parent node so that it tightly contains the updated\n  ** node.\n  */\n  pParent = pNode->pParent;\n  assert( pParent || pNode->iNode==1 );\n  if( pParent ){\n    if( NCELL(pNode)<RTREE_MINCELLS(pRtree) ){\n      rc = removeNode(pRtree, pNode, iHeight);\n    }else{\n      rc = fixBoundingBox(pRtree, pNode);\n    }\n  }\n\n  return rc;\n}\n\nstatic int Reinsert(\n  Rtree *pRtree, \n  RtreeNode *pNode, \n  RtreeCell *pCell, \n  int iHeight\n){\n  int *aOrder;\n  int *aSpare;\n  RtreeCell *aCell;\n  RtreeDValue *aDistance;\n  int nCell;\n  RtreeDValue aCenterCoord[RTREE_MAX_DIMENSIONS];\n  int iDim;\n  int ii;\n  int rc = SQLITE_OK;\n  int n;\n\n  memset(aCenterCoord, 0, sizeof(RtreeDValue)*RTREE_MAX_DIMENSIONS);\n\n  nCell = NCELL(pNode)+1;\n  n = (nCell+1)&(~1);\n\n  /* Allocate the buffers used by this operation. The allocation is\n  ** relinquished before this function returns.\n  */\n  aCell = (RtreeCell *)sqlite3_malloc(n * (\n    sizeof(RtreeCell)     +         /* aCell array */\n    sizeof(int)           +         /* aOrder array */\n    sizeof(int)           +         /* aSpare array */\n    sizeof(RtreeDValue)             /* aDistance array */\n  ));\n  if( !aCell ){\n    return SQLITE_NOMEM;\n  }\n  aOrder    = (int *)&aCell[n];\n  aSpare    = (int *)&aOrder[n];\n  aDistance = (RtreeDValue *)&aSpare[n];\n\n  for(ii=0; ii<nCell; ii++){\n    if( ii==(nCell-1) ){\n      memcpy(&aCell[ii], pCell, sizeof(RtreeCell));\n    }else{\n      nodeGetCell(pRtree, pNode, ii, &aCell[ii]);\n    }\n    aOrder[ii] = ii;\n    for(iDim=0; iDim<pRtree->nDim; iDim++){\n      aCenterCoord[iDim] += DCOORD(aCell[ii].aCoord[iDim*2]);\n      aCenterCoord[iDim] += DCOORD(aCell[ii].aCoord[iDim*2+1]);\n    }\n  }\n  for(iDim=0; iDim<pRtree->nDim; iDim++){\n    aCenterCoord[iDim] = (aCenterCoord[iDim]/(nCell*(RtreeDValue)2));\n  }\n\n  for(ii=0; ii<nCell; ii++){\n    aDistance[ii] = RTREE_ZERO;\n    for(iDim=0; iDim<pRtree->nDim; iDim++){\n      RtreeDValue coord = (DCOORD(aCell[ii].aCoord[iDim*2+1]) - \n                               DCOORD(aCell[ii].aCoord[iDim*2]));\n      aDistance[ii] += (coord-aCenterCoord[iDim])*(coord-aCenterCoord[iDim]);\n    }\n  }\n\n  SortByDistance(aOrder, nCell, aDistance, aSpare);\n  nodeZero(pRtree, pNode);\n\n  for(ii=0; rc==SQLITE_OK && ii<(nCell-(RTREE_MINCELLS(pRtree)+1)); ii++){\n    RtreeCell *p = &aCell[aOrder[ii]];\n    nodeInsertCell(pRtree, pNode, p);\n    if( p->iRowid==pCell->iRowid ){\n      if( iHeight==0 ){\n        rc = rowidWrite(pRtree, p->iRowid, pNode->iNode);\n      }else{\n        rc = parentWrite(pRtree, p->iRowid, pNode->iNode);\n      }\n    }\n  }\n  if( rc==SQLITE_OK ){\n    rc = fixBoundingBox(pRtree, pNode);\n  }\n  for(; rc==SQLITE_OK && ii<nCell; ii++){\n    /* Find a node to store this cell in. pNode->iNode currently contains\n    ** the height of the sub-tree headed by the cell.\n    */\n    RtreeNode *pInsert;\n    RtreeCell *p = &aCell[aOrder[ii]];\n    rc = ChooseLeaf(pRtree, p, iHeight, &pInsert);\n    if( rc==SQLITE_OK ){\n      int rc2;\n      rc = rtreeInsertCell(pRtree, pInsert, p, iHeight);\n      rc2 = nodeRelease(pRtree, pInsert);\n      if( rc==SQLITE_OK ){\n        rc = rc2;\n      }\n    }\n  }\n\n  sqlite3_free(aCell);\n  return rc;\n}\n\n/*\n** Insert cell pCell into node pNode. Node pNode is the head of a \n** subtree iHeight high (leaf nodes have iHeight==0).\n*/\nstatic int rtreeInsertCell(\n  Rtree *pRtree,\n  RtreeNode *pNode,\n  RtreeCell *pCell,\n  int iHeight\n){\n  int rc = SQLITE_OK;\n  if( iHeight>0 ){\n    RtreeNode *pChild = nodeHashLookup(pRtree, pCell->iRowid);\n    if( pChild ){\n      nodeRelease(pRtree, pChild->pParent);\n      nodeReference(pNode);\n      pChild->pParent = pNode;\n    }\n  }\n  if( nodeInsertCell(pRtree, pNode, pCell) ){\n    if( iHeight<=pRtree->iReinsertHeight || pNode->iNode==1){\n      rc = SplitNode(pRtree, pNode, pCell, iHeight);\n    }else{\n      pRtree->iReinsertHeight = iHeight;\n      rc = Reinsert(pRtree, pNode, pCell, iHeight);\n    }\n  }else{\n    rc = AdjustTree(pRtree, pNode, pCell);\n    if( rc==SQLITE_OK ){\n      if( iHeight==0 ){\n        rc = rowidWrite(pRtree, pCell->iRowid, pNode->iNode);\n      }else{\n        rc = parentWrite(pRtree, pCell->iRowid, pNode->iNode);\n      }\n    }\n  }\n  return rc;\n}\n\nstatic int reinsertNodeContent(Rtree *pRtree, RtreeNode *pNode){\n  int ii;\n  int rc = SQLITE_OK;\n  int nCell = NCELL(pNode);\n\n  for(ii=0; rc==SQLITE_OK && ii<nCell; ii++){\n    RtreeNode *pInsert;\n    RtreeCell cell;\n    nodeGetCell(pRtree, pNode, ii, &cell);\n\n    /* Find a node to store this cell in. pNode->iNode currently contains\n    ** the height of the sub-tree headed by the cell.\n    */\n    rc = ChooseLeaf(pRtree, &cell, (int)pNode->iNode, &pInsert);\n    if( rc==SQLITE_OK ){\n      int rc2;\n      rc = rtreeInsertCell(pRtree, pInsert, &cell, (int)pNode->iNode);\n      rc2 = nodeRelease(pRtree, pInsert);\n      if( rc==SQLITE_OK ){\n        rc = rc2;\n      }\n    }\n  }\n  return rc;\n}\n\n/*\n** Select a currently unused rowid for a new r-tree record.\n*/\nstatic int newRowid(Rtree *pRtree, i64 *piRowid){\n  int rc;\n  sqlite3_bind_null(pRtree->pWriteRowid, 1);\n  sqlite3_bind_null(pRtree->pWriteRowid, 2);\n  sqlite3_step(pRtree->pWriteRowid);\n  rc = sqlite3_reset(pRtree->pWriteRowid);\n  *piRowid = sqlite3_last_insert_rowid(pRtree->db);\n  return rc;\n}\n\n/*\n** Remove the entry with rowid=iDelete from the r-tree structure.\n*/\nstatic int rtreeDeleteRowid(Rtree *pRtree, sqlite3_int64 iDelete){\n  int rc;                         /* Return code */\n  RtreeNode *pLeaf = 0;           /* Leaf node containing record iDelete */\n  int iCell;                      /* Index of iDelete cell in pLeaf */\n  RtreeNode *pRoot = 0;           /* Root node of rtree structure */\n\n\n  /* Obtain a reference to the root node to initialize Rtree.iDepth */\n  rc = nodeAcquire(pRtree, 1, 0, &pRoot);\n\n  /* Obtain a reference to the leaf node that contains the entry \n  ** about to be deleted. \n  */\n  if( rc==SQLITE_OK ){\n    rc = findLeafNode(pRtree, iDelete, &pLeaf, 0);\n  }\n\n  /* Delete the cell in question from the leaf node. */\n  if( rc==SQLITE_OK ){\n    int rc2;\n    rc = nodeRowidIndex(pRtree, pLeaf, iDelete, &iCell);\n    if( rc==SQLITE_OK ){\n      rc = deleteCell(pRtree, pLeaf, iCell, 0);\n    }\n    rc2 = nodeRelease(pRtree, pLeaf);\n    if( rc==SQLITE_OK ){\n      rc = rc2;\n    }\n  }\n\n  /* Delete the corresponding entry in the <rtree>_rowid table. */\n  if( rc==SQLITE_OK ){\n    sqlite3_bind_int64(pRtree->pDeleteRowid, 1, iDelete);\n    sqlite3_step(pRtree->pDeleteRowid);\n    rc = sqlite3_reset(pRtree->pDeleteRowid);\n  }\n\n  /* Check if the root node now has exactly one child. If so, remove\n  ** it, schedule the contents of the child for reinsertion and \n  ** reduce the tree height by one.\n  **\n  ** This is equivalent to copying the contents of the child into\n  ** the root node (the operation that Gutman's paper says to perform \n  ** in this scenario).\n  */\n  if( rc==SQLITE_OK && pRtree->iDepth>0 && NCELL(pRoot)==1 ){\n    int rc2;\n    RtreeNode *pChild = 0;\n    i64 iChild = nodeGetRowid(pRtree, pRoot, 0);\n    rc = nodeAcquire(pRtree, iChild, pRoot, &pChild);\n    if( rc==SQLITE_OK ){\n      rc = removeNode(pRtree, pChild, pRtree->iDepth-1);\n    }\n    rc2 = nodeRelease(pRtree, pChild);\n    if( rc==SQLITE_OK ) rc = rc2;\n    if( rc==SQLITE_OK ){\n      pRtree->iDepth--;\n      writeInt16(pRoot->zData, pRtree->iDepth);\n      pRoot->isDirty = 1;\n    }\n  }\n\n  /* Re-insert the contents of any underfull nodes removed from the tree. */\n  for(pLeaf=pRtree->pDeleted; pLeaf; pLeaf=pRtree->pDeleted){\n    if( rc==SQLITE_OK ){\n      rc = reinsertNodeContent(pRtree, pLeaf);\n    }\n    pRtree->pDeleted = pLeaf->pNext;\n    sqlite3_free(pLeaf);\n  }\n\n  /* Release the reference to the root node. */\n  if( rc==SQLITE_OK ){\n    rc = nodeRelease(pRtree, pRoot);\n  }else{\n    nodeRelease(pRtree, pRoot);\n  }\n\n  return rc;\n}\n\n/*\n** Rounding constants for float->double conversion.\n*/\n#define RNDTOWARDS  (1.0 - 1.0/8388608.0)  /* Round towards zero */\n#define RNDAWAY     (1.0 + 1.0/8388608.0)  /* Round away from zero */\n\n#if !defined(SQLITE_RTREE_INT_ONLY)\n/*\n** Convert an sqlite3_value into an RtreeValue (presumably a float)\n** while taking care to round toward negative or positive, respectively.\n*/\nstatic RtreeValue rtreeValueDown(sqlite3_value *v){\n  double d = sqlite3_value_double(v);\n  float f = (float)d;\n  if( f>d ){\n    f = (float)(d*(d<0 ? RNDAWAY : RNDTOWARDS));\n  }\n  return f;\n}\nstatic RtreeValue rtreeValueUp(sqlite3_value *v){\n  double d = sqlite3_value_double(v);\n  float f = (float)d;\n  if( f<d ){\n    f = (float)(d*(d<0 ? RNDTOWARDS : RNDAWAY));\n  }\n  return f;\n}\n#endif /* !defined(SQLITE_RTREE_INT_ONLY) */\n\n/*\n** A constraint has failed while inserting a row into an rtree table. \n** Assuming no OOM error occurs, this function sets the error message \n** (at pRtree->base.zErrMsg) to an appropriate value and returns\n** SQLITE_CONSTRAINT.\n**\n** Parameter iCol is the index of the leftmost column involved in the\n** constraint failure. If it is 0, then the constraint that failed is\n** the unique constraint on the id column. Otherwise, it is the rtree\n** (c1<=c2) constraint on columns iCol and iCol+1 that has failed.\n**\n** If an OOM occurs, SQLITE_NOMEM is returned instead of SQLITE_CONSTRAINT.\n*/\nstatic int rtreeConstraintError(Rtree *pRtree, int iCol){\n  sqlite3_stmt *pStmt = 0;\n  char *zSql; \n  int rc;\n\n  assert( iCol==0 || iCol%2 );\n  zSql = sqlite3_mprintf(\"SELECT * FROM %Q.%Q\", pRtree->zDb, pRtree->zName);\n  if( zSql ){\n    rc = sqlite3_prepare_v2(pRtree->db, zSql, -1, &pStmt, 0);\n  }else{\n    rc = SQLITE_NOMEM;\n  }\n  sqlite3_free(zSql);\n\n  if( rc==SQLITE_OK ){\n    if( iCol==0 ){\n      const char *zCol = sqlite3_column_name(pStmt, 0);\n      pRtree->base.zErrMsg = sqlite3_mprintf(\n          \"UNIQUE constraint failed: %s.%s\", pRtree->zName, zCol\n      );\n    }else{\n      const char *zCol1 = sqlite3_column_name(pStmt, iCol);\n      const char *zCol2 = sqlite3_column_name(pStmt, iCol+1);\n      pRtree->base.zErrMsg = sqlite3_mprintf(\n          \"rtree constraint failed: %s.(%s<=%s)\", pRtree->zName, zCol1, zCol2\n      );\n    }\n  }\n\n  sqlite3_finalize(pStmt);\n  return (rc==SQLITE_OK ? SQLITE_CONSTRAINT : rc);\n}\n\n\n\n/*\n** The xUpdate method for rtree module virtual tables.\n*/\nstatic int rtreeUpdate(\n  sqlite3_vtab *pVtab, \n  int nData, \n  sqlite3_value **azData, \n  sqlite_int64 *pRowid\n){\n  Rtree *pRtree = (Rtree *)pVtab;\n  int rc = SQLITE_OK;\n  RtreeCell cell;                 /* New cell to insert if nData>1 */\n  int bHaveRowid = 0;             /* Set to 1 after new rowid is determined */\n\n  rtreeReference(pRtree);\n  assert(nData>=1);\n\n  cell.iRowid = 0;  /* Used only to suppress a compiler warning */\n\n  /* Constraint handling. A write operation on an r-tree table may return\n  ** SQLITE_CONSTRAINT for two reasons:\n  **\n  **   1. A duplicate rowid value, or\n  **   2. The supplied data violates the \"x2>=x1\" constraint.\n  **\n  ** In the first case, if the conflict-handling mode is REPLACE, then\n  ** the conflicting row can be removed before proceeding. In the second\n  ** case, SQLITE_CONSTRAINT must be returned regardless of the\n  ** conflict-handling mode specified by the user.\n  */\n  if( nData>1 ){\n    int ii;\n\n    /* Populate the cell.aCoord[] array. The first coordinate is azData[3].\n    **\n    ** NB: nData can only be less than nDim*2+3 if the rtree is mis-declared\n    ** with \"column\" that are interpreted as table constraints.\n    ** Example:  CREATE VIRTUAL TABLE bad USING rtree(x,y,CHECK(y>5));\n    ** This problem was discovered after years of use, so we silently ignore\n    ** these kinds of misdeclared tables to avoid breaking any legacy.\n    */\n    assert( nData<=(pRtree->nDim2 + 3) );\n\n#ifndef SQLITE_RTREE_INT_ONLY\n    if( pRtree->eCoordType==RTREE_COORD_REAL32 ){\n      for(ii=0; ii<nData-4; ii+=2){\n        cell.aCoord[ii].f = rtreeValueDown(azData[ii+3]);\n        cell.aCoord[ii+1].f = rtreeValueUp(azData[ii+4]);\n        if( cell.aCoord[ii].f>cell.aCoord[ii+1].f ){\n          rc = rtreeConstraintError(pRtree, ii+1);\n          goto constraint;\n        }\n      }\n    }else\n#endif\n    {\n      for(ii=0; ii<nData-4; ii+=2){\n        cell.aCoord[ii].i = sqlite3_value_int(azData[ii+3]);\n        cell.aCoord[ii+1].i = sqlite3_value_int(azData[ii+4]);\n        if( cell.aCoord[ii].i>cell.aCoord[ii+1].i ){\n          rc = rtreeConstraintError(pRtree, ii+1);\n          goto constraint;\n        }\n      }\n    }\n\n    /* If a rowid value was supplied, check if it is already present in \n    ** the table. If so, the constraint has failed. */\n    if( sqlite3_value_type(azData[2])!=SQLITE_NULL ){\n      cell.iRowid = sqlite3_value_int64(azData[2]);\n      if( sqlite3_value_type(azData[0])==SQLITE_NULL\n       || sqlite3_value_int64(azData[0])!=cell.iRowid\n      ){\n        int steprc;\n        sqlite3_bind_int64(pRtree->pReadRowid, 1, cell.iRowid);\n        steprc = sqlite3_step(pRtree->pReadRowid);\n        rc = sqlite3_reset(pRtree->pReadRowid);\n        if( SQLITE_ROW==steprc ){\n          if( sqlite3_vtab_on_conflict(pRtree->db)==SQLITE_REPLACE ){\n            rc = rtreeDeleteRowid(pRtree, cell.iRowid);\n          }else{\n            rc = rtreeConstraintError(pRtree, 0);\n            goto constraint;\n          }\n        }\n      }\n      bHaveRowid = 1;\n    }\n  }\n\n  /* If azData[0] is not an SQL NULL value, it is the rowid of a\n  ** record to delete from the r-tree table. The following block does\n  ** just that.\n  */\n  if( sqlite3_value_type(azData[0])!=SQLITE_NULL ){\n    rc = rtreeDeleteRowid(pRtree, sqlite3_value_int64(azData[0]));\n  }\n\n  /* If the azData[] array contains more than one element, elements\n  ** (azData[2]..azData[argc-1]) contain a new record to insert into\n  ** the r-tree structure.\n  */\n  if( rc==SQLITE_OK && nData>1 ){\n    /* Insert the new record into the r-tree */\n    RtreeNode *pLeaf = 0;\n\n    /* Figure out the rowid of the new row. */\n    if( bHaveRowid==0 ){\n      rc = newRowid(pRtree, &cell.iRowid);\n    }\n    *pRowid = cell.iRowid;\n\n    if( rc==SQLITE_OK ){\n      rc = ChooseLeaf(pRtree, &cell, 0, &pLeaf);\n    }\n    if( rc==SQLITE_OK ){\n      int rc2;\n      pRtree->iReinsertHeight = -1;\n      rc = rtreeInsertCell(pRtree, pLeaf, &cell, 0);\n      rc2 = nodeRelease(pRtree, pLeaf);\n      if( rc==SQLITE_OK ){\n        rc = rc2;\n      }\n    }\n  }\n\nconstraint:\n  rtreeRelease(pRtree);\n  return rc;\n}\n\n/*\n** Called when a transaction starts.\n*/\nstatic int rtreeBeginTransaction(sqlite3_vtab *pVtab){\n  Rtree *pRtree = (Rtree *)pVtab;\n  assert( pRtree->inWrTrans==0 );\n  pRtree->inWrTrans++;\n  return SQLITE_OK;\n}\n\n/*\n** Called when a transaction completes (either by COMMIT or ROLLBACK).\n** The sqlite3_blob object should be released at this point.\n*/\nstatic int rtreeEndTransaction(sqlite3_vtab *pVtab){\n  Rtree *pRtree = (Rtree *)pVtab;\n  pRtree->inWrTrans = 0;\n  nodeBlobReset(pRtree);\n  return SQLITE_OK;\n}\n\n/*\n** The xRename method for rtree module virtual tables.\n*/\nstatic int rtreeRename(sqlite3_vtab *pVtab, const char *zNewName){\n  Rtree *pRtree = (Rtree *)pVtab;\n  int rc = SQLITE_NOMEM;\n  char *zSql = sqlite3_mprintf(\n    \"ALTER TABLE %Q.'%q_node'   RENAME TO \\\"%w_node\\\";\"\n    \"ALTER TABLE %Q.'%q_parent' RENAME TO \\\"%w_parent\\\";\"\n    \"ALTER TABLE %Q.'%q_rowid'  RENAME TO \\\"%w_rowid\\\";\"\n    , pRtree->zDb, pRtree->zName, zNewName \n    , pRtree->zDb, pRtree->zName, zNewName \n    , pRtree->zDb, pRtree->zName, zNewName\n  );\n  if( zSql ){\n    nodeBlobReset(pRtree);\n    rc = sqlite3_exec(pRtree->db, zSql, 0, 0, 0);\n    sqlite3_free(zSql);\n  }\n  return rc;\n}\n\n/*\n** The xSavepoint method.\n**\n** This module does not need to do anything to support savepoints. However,\n** it uses this hook to close any open blob handle. This is done because a \n** DROP TABLE command - which fortunately always opens a savepoint - cannot \n** succeed if there are any open blob handles. i.e. if the blob handle were\n** not closed here, the following would fail:\n**\n**   BEGIN;\n**     INSERT INTO rtree...\n**     DROP TABLE <tablename>;    -- Would fail with SQLITE_LOCKED\n**   COMMIT;\n*/\nstatic int rtreeSavepoint(sqlite3_vtab *pVtab, int iSavepoint){\n  Rtree *pRtree = (Rtree *)pVtab;\n  int iwt = pRtree->inWrTrans;\n  UNUSED_PARAMETER(iSavepoint);\n  pRtree->inWrTrans = 0;\n  nodeBlobReset(pRtree);\n  pRtree->inWrTrans = iwt;\n  return SQLITE_OK;\n}\n\n/*\n** This function populates the pRtree->nRowEst variable with an estimate\n** of the number of rows in the virtual table. If possible, this is based\n** on sqlite_stat1 data. Otherwise, use RTREE_DEFAULT_ROWEST.\n*/\nstatic int rtreeQueryStat1(sqlite3 *db, Rtree *pRtree){\n  const char *zFmt = \"SELECT stat FROM %Q.sqlite_stat1 WHERE tbl = '%q_rowid'\";\n  char *zSql;\n  sqlite3_stmt *p;\n  int rc;\n  i64 nRow = 0;\n\n  rc = sqlite3_table_column_metadata(\n      db, pRtree->zDb, \"sqlite_stat1\",0,0,0,0,0,0\n  );\n  if( rc!=SQLITE_OK ){\n    pRtree->nRowEst = RTREE_DEFAULT_ROWEST;\n    return rc==SQLITE_ERROR ? SQLITE_OK : rc;\n  }\n  zSql = sqlite3_mprintf(zFmt, pRtree->zDb, pRtree->zName);\n  if( zSql==0 ){\n    rc = SQLITE_NOMEM;\n  }else{\n    rc = sqlite3_prepare_v2(db, zSql, -1, &p, 0);\n    if( rc==SQLITE_OK ){\n      if( sqlite3_step(p)==SQLITE_ROW ) nRow = sqlite3_column_int64(p, 0);\n      rc = sqlite3_finalize(p);\n    }else if( rc!=SQLITE_NOMEM ){\n      rc = SQLITE_OK;\n    }\n\n    if( rc==SQLITE_OK ){\n      if( nRow==0 ){\n        pRtree->nRowEst = RTREE_DEFAULT_ROWEST;\n      }else{\n        pRtree->nRowEst = MAX(nRow, RTREE_MIN_ROWEST);\n      }\n    }\n    sqlite3_free(zSql);\n  }\n\n  return rc;\n}\n\nstatic sqlite3_module rtreeModule = {\n  2,                          /* iVersion */\n  rtreeCreate,                /* xCreate - create a table */\n  rtreeConnect,               /* xConnect - connect to an existing table */\n  rtreeBestIndex,             /* xBestIndex - Determine search strategy */\n  rtreeDisconnect,            /* xDisconnect - Disconnect from a table */\n  rtreeDestroy,               /* xDestroy - Drop a table */\n  rtreeOpen,                  /* xOpen - open a cursor */\n  rtreeClose,                 /* xClose - close a cursor */\n  rtreeFilter,                /* xFilter - configure scan constraints */\n  rtreeNext,                  /* xNext - advance a cursor */\n  rtreeEof,                   /* xEof */\n  rtreeColumn,                /* xColumn - read data */\n  rtreeRowid,                 /* xRowid - read data */\n  rtreeUpdate,                /* xUpdate - write data */\n  rtreeBeginTransaction,      /* xBegin - begin transaction */\n  rtreeEndTransaction,        /* xSync - sync transaction */\n  rtreeEndTransaction,        /* xCommit - commit transaction */\n  rtreeEndTransaction,        /* xRollback - rollback transaction */\n  0,                          /* xFindFunction - function overloading */\n  rtreeRename,                /* xRename - rename the table */\n  rtreeSavepoint,             /* xSavepoint */\n  0,                          /* xRelease */\n  0,                          /* xRollbackTo */\n};\n\nstatic int rtreeSqlInit(\n  Rtree *pRtree, \n  sqlite3 *db, \n  const char *zDb, \n  const char *zPrefix, \n  int isCreate\n){\n  int rc = SQLITE_OK;\n\n  #define N_STATEMENT 8\n  static const char *azSql[N_STATEMENT] = {\n    /* Write the xxx_node table */\n    \"INSERT OR REPLACE INTO '%q'.'%q_node' VALUES(:1, :2)\",\n    \"DELETE FROM '%q'.'%q_node' WHERE nodeno = :1\",\n\n    /* Read and write the xxx_rowid table */\n    \"SELECT nodeno FROM '%q'.'%q_rowid' WHERE rowid = :1\",\n    \"INSERT OR REPLACE INTO '%q'.'%q_rowid' VALUES(:1, :2)\",\n    \"DELETE FROM '%q'.'%q_rowid' WHERE rowid = :1\",\n\n    /* Read and write the xxx_parent table */\n    \"SELECT parentnode FROM '%q'.'%q_parent' WHERE nodeno = :1\",\n    \"INSERT OR REPLACE INTO '%q'.'%q_parent' VALUES(:1, :2)\",\n    \"DELETE FROM '%q'.'%q_parent' WHERE nodeno = :1\"\n  };\n  sqlite3_stmt **appStmt[N_STATEMENT];\n  int i;\n\n  pRtree->db = db;\n\n  if( isCreate ){\n    char *zCreate = sqlite3_mprintf(\n\"CREATE TABLE \\\"%w\\\".\\\"%w_node\\\"(nodeno INTEGER PRIMARY KEY, data BLOB);\"\n\"CREATE TABLE \\\"%w\\\".\\\"%w_rowid\\\"(rowid INTEGER PRIMARY KEY, nodeno INTEGER);\"\n\"CREATE TABLE \\\"%w\\\".\\\"%w_parent\\\"(nodeno INTEGER PRIMARY KEY,\"\n                                  \" parentnode INTEGER);\"\n\"INSERT INTO '%q'.'%q_node' VALUES(1, zeroblob(%d))\",\n      zDb, zPrefix, zDb, zPrefix, zDb, zPrefix, zDb, zPrefix, pRtree->iNodeSize\n    );\n    if( !zCreate ){\n      return SQLITE_NOMEM;\n    }\n    rc = sqlite3_exec(db, zCreate, 0, 0, 0);\n    sqlite3_free(zCreate);\n    if( rc!=SQLITE_OK ){\n      return rc;\n    }\n  }\n\n  appStmt[0] = &pRtree->pWriteNode;\n  appStmt[1] = &pRtree->pDeleteNode;\n  appStmt[2] = &pRtree->pReadRowid;\n  appStmt[3] = &pRtree->pWriteRowid;\n  appStmt[4] = &pRtree->pDeleteRowid;\n  appStmt[5] = &pRtree->pReadParent;\n  appStmt[6] = &pRtree->pWriteParent;\n  appStmt[7] = &pRtree->pDeleteParent;\n\n  rc = rtreeQueryStat1(db, pRtree);\n  for(i=0; i<N_STATEMENT && rc==SQLITE_OK; i++){\n    char *zSql = sqlite3_mprintf(azSql[i], zDb, zPrefix);\n    if( zSql ){\n      rc = sqlite3_prepare_v3(db, zSql, -1, SQLITE_PREPARE_PERSISTENT,\n                              appStmt[i], 0); \n    }else{\n      rc = SQLITE_NOMEM;\n    }\n    sqlite3_free(zSql);\n  }\n\n  return rc;\n}\n\n/*\n** The second argument to this function contains the text of an SQL statement\n** that returns a single integer value. The statement is compiled and executed\n** using database connection db. If successful, the integer value returned\n** is written to *piVal and SQLITE_OK returned. Otherwise, an SQLite error\n** code is returned and the value of *piVal after returning is not defined.\n*/\nstatic int getIntFromStmt(sqlite3 *db, const char *zSql, int *piVal){\n  int rc = SQLITE_NOMEM;\n  if( zSql ){\n    sqlite3_stmt *pStmt = 0;\n    rc = sqlite3_prepare_v2(db, zSql, -1, &pStmt, 0);\n    if( rc==SQLITE_OK ){\n      if( SQLITE_ROW==sqlite3_step(pStmt) ){\n        *piVal = sqlite3_column_int(pStmt, 0);\n      }\n      rc = sqlite3_finalize(pStmt);\n    }\n  }\n  return rc;\n}\n\n/*\n** This function is called from within the xConnect() or xCreate() method to\n** determine the node-size used by the rtree table being created or connected\n** to. If successful, pRtree->iNodeSize is populated and SQLITE_OK returned.\n** Otherwise, an SQLite error code is returned.\n**\n** If this function is being called as part of an xConnect(), then the rtree\n** table already exists. In this case the node-size is determined by inspecting\n** the root node of the tree.\n**\n** Otherwise, for an xCreate(), use 64 bytes less than the database page-size. \n** This ensures that each node is stored on a single database page. If the \n** database page-size is so large that more than RTREE_MAXCELLS entries \n** would fit in a single node, use a smaller node-size.\n*/\nstatic int getNodeSize(\n  sqlite3 *db,                    /* Database handle */\n  Rtree *pRtree,                  /* Rtree handle */\n  int isCreate,                   /* True for xCreate, false for xConnect */\n  char **pzErr                    /* OUT: Error message, if any */\n){\n  int rc;\n  char *zSql;\n  if( isCreate ){\n    int iPageSize = 0;\n    zSql = sqlite3_mprintf(\"PRAGMA %Q.page_size\", pRtree->zDb);\n    rc = getIntFromStmt(db, zSql, &iPageSize);\n    if( rc==SQLITE_OK ){\n      pRtree->iNodeSize = iPageSize-64;\n      if( (4+pRtree->nBytesPerCell*RTREE_MAXCELLS)<pRtree->iNodeSize ){\n        pRtree->iNodeSize = 4+pRtree->nBytesPerCell*RTREE_MAXCELLS;\n      }\n    }else{\n      *pzErr = sqlite3_mprintf(\"%s\", sqlite3_errmsg(db));\n    }\n  }else{\n    zSql = sqlite3_mprintf(\n        \"SELECT length(data) FROM '%q'.'%q_node' WHERE nodeno = 1\",\n        pRtree->zDb, pRtree->zName\n    );\n    rc = getIntFromStmt(db, zSql, &pRtree->iNodeSize);\n    if( rc!=SQLITE_OK ){\n      *pzErr = sqlite3_mprintf(\"%s\", sqlite3_errmsg(db));\n    }else if( pRtree->iNodeSize<(512-64) ){\n      rc = SQLITE_CORRUPT_VTAB;\n      *pzErr = sqlite3_mprintf(\"undersize RTree blobs in \\\"%q_node\\\"\",\n                               pRtree->zName);\n    }\n  }\n\n  sqlite3_free(zSql);\n  return rc;\n}\n\n/* \n** This function is the implementation of both the xConnect and xCreate\n** methods of the r-tree virtual table.\n**\n**   argv[0]   -> module name\n**   argv[1]   -> database name\n**   argv[2]   -> table name\n**   argv[...] -> column names...\n*/\nstatic int rtreeInit(\n  sqlite3 *db,                        /* Database connection */\n  void *pAux,                         /* One of the RTREE_COORD_* constants */\n  int argc, const char *const*argv,   /* Parameters to CREATE TABLE statement */\n  sqlite3_vtab **ppVtab,              /* OUT: New virtual table */\n  char **pzErr,                       /* OUT: Error message, if any */\n  int isCreate                        /* True for xCreate, false for xConnect */\n){\n  int rc = SQLITE_OK;\n  Rtree *pRtree;\n  int nDb;              /* Length of string argv[1] */\n  int nName;            /* Length of string argv[2] */\n  int eCoordType = (pAux ? RTREE_COORD_INT32 : RTREE_COORD_REAL32);\n\n  const char *aErrMsg[] = {\n    0,                                                    /* 0 */\n    \"Wrong number of columns for an rtree table\",         /* 1 */\n    \"Too few columns for an rtree table\",                 /* 2 */\n    \"Too many columns for an rtree table\"                 /* 3 */\n  };\n\n  int iErr = (argc<6) ? 2 : argc>(RTREE_MAX_DIMENSIONS*2+4) ? 3 : argc%2;\n  if( aErrMsg[iErr] ){\n    *pzErr = sqlite3_mprintf(\"%s\", aErrMsg[iErr]);\n    return SQLITE_ERROR;\n  }\n\n  sqlite3_vtab_config(db, SQLITE_VTAB_CONSTRAINT_SUPPORT, 1);\n\n  /* Allocate the sqlite3_vtab structure */\n  nDb = (int)strlen(argv[1]);\n  nName = (int)strlen(argv[2]);\n  pRtree = (Rtree *)sqlite3_malloc(sizeof(Rtree)+nDb+nName+2);\n  if( !pRtree ){\n    return SQLITE_NOMEM;\n  }\n  memset(pRtree, 0, sizeof(Rtree)+nDb+nName+2);\n  pRtree->nBusy = 1;\n  pRtree->base.pModule = &rtreeModule;\n  pRtree->zDb = (char *)&pRtree[1];\n  pRtree->zName = &pRtree->zDb[nDb+1];\n  pRtree->nDim = (u8)((argc-4)/2);\n  pRtree->nDim2 = pRtree->nDim*2;\n  pRtree->nBytesPerCell = 8 + pRtree->nDim2*4;\n  pRtree->eCoordType = (u8)eCoordType;\n  memcpy(pRtree->zDb, argv[1], nDb);\n  memcpy(pRtree->zName, argv[2], nName);\n\n  /* Figure out the node size to use. */\n  rc = getNodeSize(db, pRtree, isCreate, pzErr);\n\n  /* Create/Connect to the underlying relational database schema. If\n  ** that is successful, call sqlite3_declare_vtab() to configure\n  ** the r-tree table schema.\n  */\n  if( rc==SQLITE_OK ){\n    if( (rc = rtreeSqlInit(pRtree, db, argv[1], argv[2], isCreate)) ){\n      *pzErr = sqlite3_mprintf(\"%s\", sqlite3_errmsg(db));\n    }else{\n      char *zSql = sqlite3_mprintf(\"CREATE TABLE x(%s\", argv[3]);\n      char *zTmp;\n      int ii;\n      for(ii=4; zSql && ii<argc; ii++){\n        zTmp = zSql;\n        zSql = sqlite3_mprintf(\"%s, %s\", zTmp, argv[ii]);\n        sqlite3_free(zTmp);\n      }\n      if( zSql ){\n        zTmp = zSql;\n        zSql = sqlite3_mprintf(\"%s);\", zTmp);\n        sqlite3_free(zTmp);\n      }\n      if( !zSql ){\n        rc = SQLITE_NOMEM;\n      }else if( SQLITE_OK!=(rc = sqlite3_declare_vtab(db, zSql)) ){\n        *pzErr = sqlite3_mprintf(\"%s\", sqlite3_errmsg(db));\n      }\n      sqlite3_free(zSql);\n    }\n  }\n\n  if( rc==SQLITE_OK ){\n    *ppVtab = (sqlite3_vtab *)pRtree;\n  }else{\n    assert( *ppVtab==0 );\n    assert( pRtree->nBusy==1 );\n    rtreeRelease(pRtree);\n  }\n  return rc;\n}\n\n\n/*\n** Implementation of a scalar function that decodes r-tree nodes to\n** human readable strings. This can be used for debugging and analysis.\n**\n** The scalar function takes two arguments: (1) the number of dimensions\n** to the rtree (between 1 and 5, inclusive) and (2) a blob of data containing\n** an r-tree node.  For a two-dimensional r-tree structure called \"rt\", to\n** deserialize all nodes, a statement like:\n**\n**   SELECT rtreenode(2, data) FROM rt_node;\n**\n** The human readable string takes the form of a Tcl list with one\n** entry for each cell in the r-tree node. Each entry is itself a\n** list, containing the 8-byte rowid/pageno followed by the \n** <num-dimension>*2 coordinates.\n*/\nstatic void rtreenode(sqlite3_context *ctx, int nArg, sqlite3_value **apArg){\n  char *zText = 0;\n  RtreeNode node;\n  Rtree tree;\n  int ii;\n\n  UNUSED_PARAMETER(nArg);\n  memset(&node, 0, sizeof(RtreeNode));\n  memset(&tree, 0, sizeof(Rtree));\n  tree.nDim = (u8)sqlite3_value_int(apArg[0]);\n  tree.nDim2 = tree.nDim*2;\n  tree.nBytesPerCell = 8 + 8 * tree.nDim;\n  node.zData = (u8 *)sqlite3_value_blob(apArg[1]);\n\n  for(ii=0; ii<NCELL(&node); ii++){\n    char zCell[512];\n    int nCell = 0;\n    RtreeCell cell;\n    int jj;\n\n    nodeGetCell(&tree, &node, ii, &cell);\n    sqlite3_snprintf(512-nCell,&zCell[nCell],\"%lld\", cell.iRowid);\n    nCell = (int)strlen(zCell);\n    for(jj=0; jj<tree.nDim2; jj++){\n#ifndef SQLITE_RTREE_INT_ONLY\n      sqlite3_snprintf(512-nCell,&zCell[nCell], \" %g\",\n                       (double)cell.aCoord[jj].f);\n#else\n      sqlite3_snprintf(512-nCell,&zCell[nCell], \" %d\",\n                       cell.aCoord[jj].i);\n#endif\n      nCell = (int)strlen(zCell);\n    }\n\n    if( zText ){\n      char *zTextNew = sqlite3_mprintf(\"%s {%s}\", zText, zCell);\n      sqlite3_free(zText);\n      zText = zTextNew;\n    }else{\n      zText = sqlite3_mprintf(\"{%s}\", zCell);\n    }\n  }\n  \n  sqlite3_result_text(ctx, zText, -1, sqlite3_free);\n}\n\n/* This routine implements an SQL function that returns the \"depth\" parameter\n** from the front of a blob that is an r-tree node.  For example:\n**\n**     SELECT rtreedepth(data) FROM rt_node WHERE nodeno=1;\n**\n** The depth value is 0 for all nodes other than the root node, and the root\n** node always has nodeno=1, so the example above is the primary use for this\n** routine.  This routine is intended for testing and analysis only.\n*/\nstatic void rtreedepth(sqlite3_context *ctx, int nArg, sqlite3_value **apArg){\n  UNUSED_PARAMETER(nArg);\n  if( sqlite3_value_type(apArg[0])!=SQLITE_BLOB \n   || sqlite3_value_bytes(apArg[0])<2\n  ){\n    sqlite3_result_error(ctx, \"Invalid argument to rtreedepth()\", -1); \n  }else{\n    u8 *zBlob = (u8 *)sqlite3_value_blob(apArg[0]);\n    sqlite3_result_int(ctx, readInt16(zBlob));\n  }\n}\n\n/*\n** Context object passed between the various routines that make up the\n** implementation of integrity-check function rtreecheck().\n*/\ntypedef struct RtreeCheck RtreeCheck;\nstruct RtreeCheck {\n  sqlite3 *db;                    /* Database handle */\n  const char *zDb;                /* Database containing rtree table */\n  const char *zTab;               /* Name of rtree table */\n  int bInt;                       /* True for rtree_i32 table */\n  int nDim;                       /* Number of dimensions for this rtree tbl */\n  sqlite3_stmt *pGetNode;         /* Statement used to retrieve nodes */\n  sqlite3_stmt *aCheckMapping[2]; /* Statements to query %_parent/%_rowid */\n  int nLeaf;                      /* Number of leaf cells in table */\n  int nNonLeaf;                   /* Number of non-leaf cells in table */\n  int rc;                         /* Return code */\n  char *zReport;                  /* Message to report */\n  int nErr;                       /* Number of lines in zReport */\n};\n\n#define RTREE_CHECK_MAX_ERROR 100\n\n/*\n** Reset SQL statement pStmt. If the sqlite3_reset() call returns an error,\n** and RtreeCheck.rc==SQLITE_OK, set RtreeCheck.rc to the error code.\n*/\nstatic void rtreeCheckReset(RtreeCheck *pCheck, sqlite3_stmt *pStmt){\n  int rc = sqlite3_reset(pStmt);\n  if( pCheck->rc==SQLITE_OK ) pCheck->rc = rc;\n}\n\n/*\n** The second and subsequent arguments to this function are a format string\n** and printf style arguments. This function formats the string and attempts\n** to compile it as an SQL statement.\n**\n** If successful, a pointer to the new SQL statement is returned. Otherwise,\n** NULL is returned and an error code left in RtreeCheck.rc.\n*/\nstatic sqlite3_stmt *rtreeCheckPrepare(\n  RtreeCheck *pCheck,             /* RtreeCheck object */\n  const char *zFmt, ...           /* Format string and trailing args */\n){\n  va_list ap;\n  char *z;\n  sqlite3_stmt *pRet = 0;\n\n  va_start(ap, zFmt);\n  z = sqlite3_vmprintf(zFmt, ap);\n\n  if( pCheck->rc==SQLITE_OK ){\n    if( z==0 ){\n      pCheck->rc = SQLITE_NOMEM;\n    }else{\n      pCheck->rc = sqlite3_prepare_v2(pCheck->db, z, -1, &pRet, 0);\n    }\n  }\n\n  sqlite3_free(z);\n  va_end(ap);\n  return pRet;\n}\n\n/*\n** The second and subsequent arguments to this function are a printf()\n** style format string and arguments. This function formats the string and\n** appends it to the report being accumuated in pCheck.\n*/\nstatic void rtreeCheckAppendMsg(RtreeCheck *pCheck, const char *zFmt, ...){\n  va_list ap;\n  va_start(ap, zFmt);\n  if( pCheck->rc==SQLITE_OK && pCheck->nErr<RTREE_CHECK_MAX_ERROR ){\n    char *z = sqlite3_vmprintf(zFmt, ap);\n    if( z==0 ){\n      pCheck->rc = SQLITE_NOMEM;\n    }else{\n      pCheck->zReport = sqlite3_mprintf(\"%z%s%z\", \n          pCheck->zReport, (pCheck->zReport ? \"\\n\" : \"\"), z\n      );\n      if( pCheck->zReport==0 ){\n        pCheck->rc = SQLITE_NOMEM;\n      }\n    }\n    pCheck->nErr++;\n  }\n  va_end(ap);\n}\n\n/*\n** This function is a no-op if there is already an error code stored\n** in the RtreeCheck object indicated by the first argument. NULL is\n** returned in this case.\n**\n** Otherwise, the contents of rtree table node iNode are loaded from\n** the database and copied into a buffer obtained from sqlite3_malloc().\n** If no error occurs, a pointer to the buffer is returned and (*pnNode)\n** is set to the size of the buffer in bytes.\n**\n** Or, if an error does occur, NULL is returned and an error code left\n** in the RtreeCheck object. The final value of *pnNode is undefined in\n** this case.\n*/\nstatic u8 *rtreeCheckGetNode(RtreeCheck *pCheck, i64 iNode, int *pnNode){\n  u8 *pRet = 0;                   /* Return value */\n\n  assert( pCheck->rc==SQLITE_OK );\n  if( pCheck->pGetNode==0 ){\n    pCheck->pGetNode = rtreeCheckPrepare(pCheck,\n        \"SELECT data FROM %Q.'%q_node' WHERE nodeno=?\", \n        pCheck->zDb, pCheck->zTab\n    );\n  }\n\n  if( pCheck->rc==SQLITE_OK ){\n    sqlite3_bind_int64(pCheck->pGetNode, 1, iNode);\n    if( sqlite3_step(pCheck->pGetNode)==SQLITE_ROW ){\n      int nNode = sqlite3_column_bytes(pCheck->pGetNode, 0);\n      const u8 *pNode = (const u8*)sqlite3_column_blob(pCheck->pGetNode, 0);\n      pRet = sqlite3_malloc(nNode);\n      if( pRet==0 ){\n        pCheck->rc = SQLITE_NOMEM;\n      }else{\n        memcpy(pRet, pNode, nNode);\n        *pnNode = nNode;\n      }\n    }\n    rtreeCheckReset(pCheck, pCheck->pGetNode);\n    if( pCheck->rc==SQLITE_OK && pRet==0 ){\n      rtreeCheckAppendMsg(pCheck, \"Node %lld missing from database\", iNode);\n    }\n  }\n\n  return pRet;\n}\n\n/*\n** This function is used to check that the %_parent (if bLeaf==0) or %_rowid\n** (if bLeaf==1) table contains a specified entry. The schemas of the\n** two tables are:\n**\n**   CREATE TABLE %_parent(nodeno INTEGER PRIMARY KEY, parentnode INTEGER)\n**   CREATE TABLE %_rowid(rowid INTEGER PRIMARY KEY, nodeno INTEGER)\n**\n** In both cases, this function checks that there exists an entry with\n** IPK value iKey and the second column set to iVal.\n**\n*/\nstatic void rtreeCheckMapping(\n  RtreeCheck *pCheck,             /* RtreeCheck object */\n  int bLeaf,                      /* True for a leaf cell, false for interior */\n  i64 iKey,                       /* Key for mapping */\n  i64 iVal                        /* Expected value for mapping */\n){\n  int rc;\n  sqlite3_stmt *pStmt;\n  const char *azSql[2] = {\n    \"SELECT parentnode FROM %Q.'%q_parent' WHERE nodeno=?\",\n    \"SELECT nodeno FROM %Q.'%q_rowid' WHERE rowid=?\"\n  };\n\n  assert( bLeaf==0 || bLeaf==1 );\n  if( pCheck->aCheckMapping[bLeaf]==0 ){\n    pCheck->aCheckMapping[bLeaf] = rtreeCheckPrepare(pCheck,\n        azSql[bLeaf], pCheck->zDb, pCheck->zTab\n    );\n  }\n  if( pCheck->rc!=SQLITE_OK ) return;\n\n  pStmt = pCheck->aCheckMapping[bLeaf];\n  sqlite3_bind_int64(pStmt, 1, iKey);\n  rc = sqlite3_step(pStmt);\n  if( rc==SQLITE_DONE ){\n    rtreeCheckAppendMsg(pCheck, \"Mapping (%lld -> %lld) missing from %s table\",\n        iKey, iVal, (bLeaf ? \"%_rowid\" : \"%_parent\")\n    );\n  }else if( rc==SQLITE_ROW ){\n    i64 ii = sqlite3_column_int64(pStmt, 0);\n    if( ii!=iVal ){\n      rtreeCheckAppendMsg(pCheck, \n          \"Found (%lld -> %lld) in %s table, expected (%lld -> %lld)\",\n          iKey, ii, (bLeaf ? \"%_rowid\" : \"%_parent\"), iKey, iVal\n      );\n    }\n  }\n  rtreeCheckReset(pCheck, pStmt);\n}\n\n/*\n** Argument pCell points to an array of coordinates stored on an rtree page.\n** This function checks that the coordinates are internally consistent (no\n** x1>x2 conditions) and adds an error message to the RtreeCheck object\n** if they are not.\n**\n** Additionally, if pParent is not NULL, then it is assumed to point to\n** the array of coordinates on the parent page that bound the page \n** containing pCell. In this case it is also verified that the two\n** sets of coordinates are mutually consistent and an error message added\n** to the RtreeCheck object if they are not.\n*/\nstatic void rtreeCheckCellCoord(\n  RtreeCheck *pCheck, \n  i64 iNode,                      /* Node id to use in error messages */\n  int iCell,                      /* Cell number to use in error messages */\n  u8 *pCell,                      /* Pointer to cell coordinates */\n  u8 *pParent                     /* Pointer to parent coordinates */\n){\n  RtreeCoord c1, c2;\n  RtreeCoord p1, p2;\n  int i;\n\n  for(i=0; i<pCheck->nDim; i++){\n    readCoord(&pCell[4*2*i], &c1);\n    readCoord(&pCell[4*(2*i + 1)], &c2);\n\n    /* printf(\"%e, %e\\n\", c1.u.f, c2.u.f); */\n    if( pCheck->bInt ? c1.i>c2.i : c1.f>c2.f ){\n      rtreeCheckAppendMsg(pCheck, \n          \"Dimension %d of cell %d on node %lld is corrupt\", i, iCell, iNode\n      );\n    }\n\n    if( pParent ){\n      readCoord(&pParent[4*2*i], &p1);\n      readCoord(&pParent[4*(2*i + 1)], &p2);\n\n      if( (pCheck->bInt ? c1.i<p1.i : c1.f<p1.f) \n       || (pCheck->bInt ? c2.i>p2.i : c2.f>p2.f)\n      ){\n        rtreeCheckAppendMsg(pCheck, \n            \"Dimension %d of cell %d on node %lld is corrupt relative to parent\"\n            , i, iCell, iNode\n        );\n      }\n    }\n  }\n}\n\n/*\n** Run rtreecheck() checks on node iNode, which is at depth iDepth within\n** the r-tree structure. Argument aParent points to the array of coordinates\n** that bound node iNode on the parent node.\n**\n** If any problems are discovered, an error message is appended to the\n** report accumulated in the RtreeCheck object.\n*/\nstatic void rtreeCheckNode(\n  RtreeCheck *pCheck,\n  int iDepth,                     /* Depth of iNode (0==leaf) */\n  u8 *aParent,                    /* Buffer containing parent coords */\n  i64 iNode                       /* Node to check */\n){\n  u8 *aNode = 0;\n  int nNode = 0;\n\n  assert( iNode==1 || aParent!=0 );\n  assert( pCheck->nDim>0 );\n\n  aNode = rtreeCheckGetNode(pCheck, iNode, &nNode);\n  if( aNode ){\n    if( nNode<4 ){\n      rtreeCheckAppendMsg(pCheck, \n          \"Node %lld is too small (%d bytes)\", iNode, nNode\n      );\n    }else{\n      int nCell;                  /* Number of cells on page */\n      int i;                      /* Used to iterate through cells */\n      if( aParent==0 ){\n        iDepth = readInt16(aNode);\n        if( iDepth>RTREE_MAX_DEPTH ){\n          rtreeCheckAppendMsg(pCheck, \"Rtree depth out of range (%d)\", iDepth);\n          sqlite3_free(aNode);\n          return;\n        }\n      }\n      nCell = readInt16(&aNode[2]);\n      if( (4 + nCell*(8 + pCheck->nDim*2*4))>nNode ){\n        rtreeCheckAppendMsg(pCheck, \n            \"Node %lld is too small for cell count of %d (%d bytes)\", \n            iNode, nCell, nNode\n        );\n      }else{\n        for(i=0; i<nCell; i++){\n          u8 *pCell = &aNode[4 + i*(8 + pCheck->nDim*2*4)];\n          i64 iVal = readInt64(pCell);\n          rtreeCheckCellCoord(pCheck, iNode, i, &pCell[8], aParent);\n\n          if( iDepth>0 ){\n            rtreeCheckMapping(pCheck, 0, iVal, iNode);\n            rtreeCheckNode(pCheck, iDepth-1, &pCell[8], iVal);\n            pCheck->nNonLeaf++;\n          }else{\n            rtreeCheckMapping(pCheck, 1, iVal, iNode);\n            pCheck->nLeaf++;\n          }\n        }\n      }\n    }\n    sqlite3_free(aNode);\n  }\n}\n\n/*\n** The second argument to this function must be either \"_rowid\" or\n** \"_parent\". This function checks that the number of entries in the\n** %_rowid or %_parent table is exactly nExpect. If not, it adds\n** an error message to the report in the RtreeCheck object indicated\n** by the first argument.\n*/\nstatic void rtreeCheckCount(RtreeCheck *pCheck, const char *zTbl, i64 nExpect){\n  if( pCheck->rc==SQLITE_OK ){\n    sqlite3_stmt *pCount;\n    pCount = rtreeCheckPrepare(pCheck, \"SELECT count(*) FROM %Q.'%q%s'\",\n        pCheck->zDb, pCheck->zTab, zTbl\n    );\n    if( pCount ){\n      if( sqlite3_step(pCount)==SQLITE_ROW ){\n        i64 nActual = sqlite3_column_int64(pCount, 0);\n        if( nActual!=nExpect ){\n          rtreeCheckAppendMsg(pCheck, \"Wrong number of entries in %%%s table\"\n              \" - expected %lld, actual %lld\" , zTbl, nExpect, nActual\n          );\n        }\n      }\n      pCheck->rc = sqlite3_finalize(pCount);\n    }\n  }\n}\n\n/*\n** This function does the bulk of the work for the rtree integrity-check.\n** It is called by rtreecheck(), which is the SQL function implementation.\n*/\nstatic int rtreeCheckTable(\n  sqlite3 *db,                    /* Database handle to access db through */\n  const char *zDb,                /* Name of db (\"main\", \"temp\" etc.) */\n  const char *zTab,               /* Name of rtree table to check */\n  char **pzReport                 /* OUT: sqlite3_malloc'd report text */\n){\n  RtreeCheck check;               /* Common context for various routines */\n  sqlite3_stmt *pStmt = 0;        /* Used to find column count of rtree table */\n  int bEnd = 0;                   /* True if transaction should be closed */\n\n  /* Initialize the context object */\n  memset(&check, 0, sizeof(check));\n  check.db = db;\n  check.zDb = zDb;\n  check.zTab = zTab;\n\n  /* If there is not already an open transaction, open one now. This is\n  ** to ensure that the queries run as part of this integrity-check operate\n  ** on a consistent snapshot.  */\n  if( sqlite3_get_autocommit(db) ){\n    check.rc = sqlite3_exec(db, \"BEGIN\", 0, 0, 0);\n    bEnd = 1;\n  }\n\n  /* Find number of dimensions in the rtree table. */\n  pStmt = rtreeCheckPrepare(&check, \"SELECT * FROM %Q.%Q\", zDb, zTab);\n  if( pStmt ){\n    int rc;\n    check.nDim = (sqlite3_column_count(pStmt) - 1) / 2;\n    if( check.nDim<1 ){\n      rtreeCheckAppendMsg(&check, \"Schema corrupt or not an rtree\");\n    }else if( SQLITE_ROW==sqlite3_step(pStmt) ){\n      check.bInt = (sqlite3_column_type(pStmt, 1)==SQLITE_INTEGER);\n    }\n    rc = sqlite3_finalize(pStmt);\n    if( rc!=SQLITE_CORRUPT ) check.rc = rc;\n  }\n\n  /* Do the actual integrity-check */\n  if( check.nDim>=1 ){\n    if( check.rc==SQLITE_OK ){\n      rtreeCheckNode(&check, 0, 0, 1);\n    }\n    rtreeCheckCount(&check, \"_rowid\", check.nLeaf);\n    rtreeCheckCount(&check, \"_parent\", check.nNonLeaf);\n  }\n\n  /* Finalize SQL statements used by the integrity-check */\n  sqlite3_finalize(check.pGetNode);\n  sqlite3_finalize(check.aCheckMapping[0]);\n  sqlite3_finalize(check.aCheckMapping[1]);\n\n  /* If one was opened, close the transaction */\n  if( bEnd ){\n    int rc = sqlite3_exec(db, \"END\", 0, 0, 0);\n    if( check.rc==SQLITE_OK ) check.rc = rc;\n  }\n  *pzReport = check.zReport;\n  return check.rc;\n}\n\n/*\n** Usage:\n**\n**   rtreecheck(<rtree-table>);\n**   rtreecheck(<database>, <rtree-table>);\n**\n** Invoking this SQL function runs an integrity-check on the named rtree\n** table. The integrity-check verifies the following:\n**\n**   1. For each cell in the r-tree structure (%_node table), that:\n**\n**       a) for each dimension, (coord1 <= coord2).\n**\n**       b) unless the cell is on the root node, that the cell is bounded\n**          by the parent cell on the parent node.\n**\n**       c) for leaf nodes, that there is an entry in the %_rowid \n**          table corresponding to the cell's rowid value that \n**          points to the correct node.\n**\n**       d) for cells on non-leaf nodes, that there is an entry in the \n**          %_parent table mapping from the cell's child node to the\n**          node that it resides on.\n**\n**   2. That there are the same number of entries in the %_rowid table\n**      as there are leaf cells in the r-tree structure, and that there\n**      is a leaf cell that corresponds to each entry in the %_rowid table.\n**\n**   3. That there are the same number of entries in the %_parent table\n**      as there are non-leaf cells in the r-tree structure, and that \n**      there is a non-leaf cell that corresponds to each entry in the \n**      %_parent table.\n*/\nstatic void rtreecheck(\n  sqlite3_context *ctx, \n  int nArg, \n  sqlite3_value **apArg\n){\n  if( nArg!=1 && nArg!=2 ){\n    sqlite3_result_error(ctx, \n        \"wrong number of arguments to function rtreecheck()\", -1\n    );\n  }else{\n    int rc;\n    char *zReport = 0;\n    const char *zDb = (const char*)sqlite3_value_text(apArg[0]);\n    const char *zTab;\n    if( nArg==1 ){\n      zTab = zDb;\n      zDb = \"main\";\n    }else{\n      zTab = (const char*)sqlite3_value_text(apArg[1]);\n    }\n    rc = rtreeCheckTable(sqlite3_context_db_handle(ctx), zDb, zTab, &zReport);\n    if( rc==SQLITE_OK ){\n      sqlite3_result_text(ctx, zReport ? zReport : \"ok\", -1, SQLITE_TRANSIENT);\n    }else{\n      sqlite3_result_error_code(ctx, rc);\n    }\n    sqlite3_free(zReport);\n  }\n}\n\n\n/*\n** Register the r-tree module with database handle db. This creates the\n** virtual table module \"rtree\" and the debugging/analysis scalar \n** function \"rtreenode\".\n*/\nSQLITE_PRIVATE int sqlite3RtreeInit(sqlite3 *db){\n  const int utf8 = SQLITE_UTF8;\n  int rc;\n\n  rc = sqlite3_create_function(db, \"rtreenode\", 2, utf8, 0, rtreenode, 0, 0);\n  if( rc==SQLITE_OK ){\n    rc = sqlite3_create_function(db, \"rtreedepth\", 1, utf8, 0,rtreedepth, 0, 0);\n  }\n  if( rc==SQLITE_OK ){\n    rc = sqlite3_create_function(db, \"rtreecheck\", -1, utf8, 0,rtreecheck, 0,0);\n  }\n  if( rc==SQLITE_OK ){\n#ifdef SQLITE_RTREE_INT_ONLY\n    void *c = (void *)RTREE_COORD_INT32;\n#else\n    void *c = (void *)RTREE_COORD_REAL32;\n#endif\n    rc = sqlite3_create_module_v2(db, \"rtree\", &rtreeModule, c, 0);\n  }\n  if( rc==SQLITE_OK ){\n    void *c = (void *)RTREE_COORD_INT32;\n    rc = sqlite3_create_module_v2(db, \"rtree_i32\", &rtreeModule, c, 0);\n  }\n\n  return rc;\n}\n\n/*\n** This routine deletes the RtreeGeomCallback object that was attached\n** one of the SQL functions create by sqlite3_rtree_geometry_callback()\n** or sqlite3_rtree_query_callback().  In other words, this routine is the\n** destructor for an RtreeGeomCallback objecct.  This routine is called when\n** the corresponding SQL function is deleted.\n*/\nstatic void rtreeFreeCallback(void *p){\n  RtreeGeomCallback *pInfo = (RtreeGeomCallback*)p;\n  if( pInfo->xDestructor ) pInfo->xDestructor(pInfo->pContext);\n  sqlite3_free(p);\n}\n\n/*\n** This routine frees the BLOB that is returned by geomCallback().\n*/\nstatic void rtreeMatchArgFree(void *pArg){\n  int i;\n  RtreeMatchArg *p = (RtreeMatchArg*)pArg;\n  for(i=0; i<p->nParam; i++){\n    sqlite3_value_free(p->apSqlParam[i]);\n  }\n  sqlite3_free(p);\n}\n\n/*\n** Each call to sqlite3_rtree_geometry_callback() or\n** sqlite3_rtree_query_callback() creates an ordinary SQLite\n** scalar function that is implemented by this routine.\n**\n** All this function does is construct an RtreeMatchArg object that\n** contains the geometry-checking callback routines and a list of\n** parameters to this function, then return that RtreeMatchArg object\n** as a BLOB.\n**\n** The R-Tree MATCH operator will read the returned BLOB, deserialize\n** the RtreeMatchArg object, and use the RtreeMatchArg object to figure\n** out which elements of the R-Tree should be returned by the query.\n*/\nstatic void geomCallback(sqlite3_context *ctx, int nArg, sqlite3_value **aArg){\n  RtreeGeomCallback *pGeomCtx = (RtreeGeomCallback *)sqlite3_user_data(ctx);\n  RtreeMatchArg *pBlob;\n  int nBlob;\n  int memErr = 0;\n\n  nBlob = sizeof(RtreeMatchArg) + (nArg-1)*sizeof(RtreeDValue)\n           + nArg*sizeof(sqlite3_value*);\n  pBlob = (RtreeMatchArg *)sqlite3_malloc(nBlob);\n  if( !pBlob ){\n    sqlite3_result_error_nomem(ctx);\n  }else{\n    int i;\n    pBlob->iSize = nBlob;\n    pBlob->cb = pGeomCtx[0];\n    pBlob->apSqlParam = (sqlite3_value**)&pBlob->aParam[nArg];\n    pBlob->nParam = nArg;\n    for(i=0; i<nArg; i++){\n      pBlob->apSqlParam[i] = sqlite3_value_dup(aArg[i]);\n      if( pBlob->apSqlParam[i]==0 ) memErr = 1;\n#ifdef SQLITE_RTREE_INT_ONLY\n      pBlob->aParam[i] = sqlite3_value_int64(aArg[i]);\n#else\n      pBlob->aParam[i] = sqlite3_value_double(aArg[i]);\n#endif\n    }\n    if( memErr ){\n      sqlite3_result_error_nomem(ctx);\n      rtreeMatchArgFree(pBlob);\n    }else{\n      sqlite3_result_pointer(ctx, pBlob, \"RtreeMatchArg\", rtreeMatchArgFree);\n    }\n  }\n}\n\n/*\n** Register a new geometry function for use with the r-tree MATCH operator.\n*/\nSQLITE_API int sqlite3_rtree_geometry_callback(\n  sqlite3 *db,                  /* Register SQL function on this connection */\n  const char *zGeom,            /* Name of the new SQL function */\n  int (*xGeom)(sqlite3_rtree_geometry*,int,RtreeDValue*,int*), /* Callback */\n  void *pContext                /* Extra data associated with the callback */\n){\n  RtreeGeomCallback *pGeomCtx;      /* Context object for new user-function */\n\n  /* Allocate and populate the context object. */\n  pGeomCtx = (RtreeGeomCallback *)sqlite3_malloc(sizeof(RtreeGeomCallback));\n  if( !pGeomCtx ) return SQLITE_NOMEM;\n  pGeomCtx->xGeom = xGeom;\n  pGeomCtx->xQueryFunc = 0;\n  pGeomCtx->xDestructor = 0;\n  pGeomCtx->pContext = pContext;\n  return sqlite3_create_function_v2(db, zGeom, -1, SQLITE_ANY, \n      (void *)pGeomCtx, geomCallback, 0, 0, rtreeFreeCallback\n  );\n}\n\n/*\n** Register a new 2nd-generation geometry function for use with the\n** r-tree MATCH operator.\n*/\nSQLITE_API int sqlite3_rtree_query_callback(\n  sqlite3 *db,                 /* Register SQL function on this connection */\n  const char *zQueryFunc,      /* Name of new SQL function */\n  int (*xQueryFunc)(sqlite3_rtree_query_info*), /* Callback */\n  void *pContext,              /* Extra data passed into the callback */\n  void (*xDestructor)(void*)   /* Destructor for the extra data */\n){\n  RtreeGeomCallback *pGeomCtx;      /* Context object for new user-function */\n\n  /* Allocate and populate the context object. */\n  pGeomCtx = (RtreeGeomCallback *)sqlite3_malloc(sizeof(RtreeGeomCallback));\n  if( !pGeomCtx ) return SQLITE_NOMEM;\n  pGeomCtx->xGeom = 0;\n  pGeomCtx->xQueryFunc = xQueryFunc;\n  pGeomCtx->xDestructor = xDestructor;\n  pGeomCtx->pContext = pContext;\n  return sqlite3_create_function_v2(db, zQueryFunc, -1, SQLITE_ANY, \n      (void *)pGeomCtx, geomCallback, 0, 0, rtreeFreeCallback\n  );\n}\n\n#if !SQLITE_CORE\n#ifdef _WIN32\n__declspec(dllexport)\n#endif\nSQLITE_API int sqlite3_rtree_init(\n  sqlite3 *db,\n  char **pzErrMsg,\n  const sqlite3_api_routines *pApi\n){\n  SQLITE_EXTENSION_INIT2(pApi)\n  return sqlite3RtreeInit(db);\n}\n#endif\n\n#endif\n\n/************** End of rtree.c ***********************************************/\n/************** Begin file icu.c *********************************************/\n/*\n** 2007 May 6\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n*************************************************************************\n** $Id: icu.c,v 1.7 2007/12/13 21:54:11 drh Exp $\n**\n** This file implements an integration between the ICU library \n** (\"International Components for Unicode\", an open-source library \n** for handling unicode data) and SQLite. The integration uses \n** ICU to provide the following to SQLite:\n**\n**   * An implementation of the SQL regexp() function (and hence REGEXP\n**     operator) using the ICU uregex_XX() APIs.\n**\n**   * Implementations of the SQL scalar upper() and lower() functions\n**     for case mapping.\n**\n**   * Integration of ICU and SQLite collation sequences.\n**\n**   * An implementation of the LIKE operator that uses ICU to \n**     provide case-independent matching.\n*/\n\n#if !defined(SQLITE_CORE)                  \\\n || defined(SQLITE_ENABLE_ICU)             \\\n || defined(SQLITE_ENABLE_ICU_COLLATIONS)\n\n/* Include ICU headers */\n#include <unicode/utypes.h>\n#include <unicode/uregex.h>\n#include <unicode/ustring.h>\n#include <unicode/ucol.h>\n\n/* #include <assert.h> */\n\n#ifndef SQLITE_CORE\n/*   #include \"sqlite3ext.h\" */\n  SQLITE_EXTENSION_INIT1\n#else\n/*   #include \"sqlite3.h\" */\n#endif\n\n/*\n** This function is called when an ICU function called from within\n** the implementation of an SQL scalar function returns an error.\n**\n** The scalar function context passed as the first argument is \n** loaded with an error message based on the following two args.\n*/\nstatic void icuFunctionError(\n  sqlite3_context *pCtx,       /* SQLite scalar function context */\n  const char *zName,           /* Name of ICU function that failed */\n  UErrorCode e                 /* Error code returned by ICU function */\n){\n  char zBuf[128];\n  sqlite3_snprintf(128, zBuf, \"ICU error: %s(): %s\", zName, u_errorName(e));\n  zBuf[127] = '\\0';\n  sqlite3_result_error(pCtx, zBuf, -1);\n}\n\n#if !defined(SQLITE_CORE) || defined(SQLITE_ENABLE_ICU)\n\n/*\n** Maximum length (in bytes) of the pattern in a LIKE or GLOB\n** operator.\n*/\n#ifndef SQLITE_MAX_LIKE_PATTERN_LENGTH\n# define SQLITE_MAX_LIKE_PATTERN_LENGTH 50000\n#endif\n\n/*\n** Version of sqlite3_free() that is always a function, never a macro.\n*/\nstatic void xFree(void *p){\n  sqlite3_free(p);\n}\n\n/*\n** This lookup table is used to help decode the first byte of\n** a multi-byte UTF8 character. It is copied here from SQLite source\n** code file utf8.c.\n*/\nstatic const unsigned char icuUtf8Trans1[] = {\n  0x00, 0x01, 0x02, 0x03, 0x04, 0x05, 0x06, 0x07,\n  0x08, 0x09, 0x0a, 0x0b, 0x0c, 0x0d, 0x0e, 0x0f,\n  0x10, 0x11, 0x12, 0x13, 0x14, 0x15, 0x16, 0x17,\n  0x18, 0x19, 0x1a, 0x1b, 0x1c, 0x1d, 0x1e, 0x1f,\n  0x00, 0x01, 0x02, 0x03, 0x04, 0x05, 0x06, 0x07,\n  0x08, 0x09, 0x0a, 0x0b, 0x0c, 0x0d, 0x0e, 0x0f,\n  0x00, 0x01, 0x02, 0x03, 0x04, 0x05, 0x06, 0x07,\n  0x00, 0x01, 0x02, 0x03, 0x00, 0x01, 0x00, 0x00,\n};\n\n#define SQLITE_ICU_READ_UTF8(zIn, c)                       \\\n  c = *(zIn++);                                            \\\n  if( c>=0xc0 ){                                           \\\n    c = icuUtf8Trans1[c-0xc0];                             \\\n    while( (*zIn & 0xc0)==0x80 ){                          \\\n      c = (c<<6) + (0x3f & *(zIn++));                      \\\n    }                                                      \\\n  }\n\n#define SQLITE_ICU_SKIP_UTF8(zIn)                          \\\n  assert( *zIn );                                          \\\n  if( *(zIn++)>=0xc0 ){                                    \\\n    while( (*zIn & 0xc0)==0x80 ){zIn++;}                   \\\n  }\n\n\n/*\n** Compare two UTF-8 strings for equality where the first string is\n** a \"LIKE\" expression. Return true (1) if they are the same and \n** false (0) if they are different.\n*/\nstatic int icuLikeCompare(\n  const uint8_t *zPattern,   /* LIKE pattern */\n  const uint8_t *zString,    /* The UTF-8 string to compare against */\n  const UChar32 uEsc         /* The escape character */\n){\n  static const uint32_t MATCH_ONE = (uint32_t)'_';\n  static const uint32_t MATCH_ALL = (uint32_t)'%';\n\n  int prevEscape = 0;     /* True if the previous character was uEsc */\n\n  while( 1 ){\n\n    /* Read (and consume) the next character from the input pattern. */\n    uint32_t uPattern;\n    SQLITE_ICU_READ_UTF8(zPattern, uPattern);\n    if( uPattern==0 ) break;\n\n    /* There are now 4 possibilities:\n    **\n    **     1. uPattern is an unescaped match-all character \"%\",\n    **     2. uPattern is an unescaped match-one character \"_\",\n    **     3. uPattern is an unescaped escape character, or\n    **     4. uPattern is to be handled as an ordinary character\n    */\n    if( !prevEscape && uPattern==MATCH_ALL ){\n      /* Case 1. */\n      uint8_t c;\n\n      /* Skip any MATCH_ALL or MATCH_ONE characters that follow a\n      ** MATCH_ALL. For each MATCH_ONE, skip one character in the \n      ** test string.\n      */\n      while( (c=*zPattern) == MATCH_ALL || c == MATCH_ONE ){\n        if( c==MATCH_ONE ){\n          if( *zString==0 ) return 0;\n          SQLITE_ICU_SKIP_UTF8(zString);\n        }\n        zPattern++;\n      }\n\n      if( *zPattern==0 ) return 1;\n\n      while( *zString ){\n        if( icuLikeCompare(zPattern, zString, uEsc) ){\n          return 1;\n        }\n        SQLITE_ICU_SKIP_UTF8(zString);\n      }\n      return 0;\n\n    }else if( !prevEscape && uPattern==MATCH_ONE ){\n      /* Case 2. */\n      if( *zString==0 ) return 0;\n      SQLITE_ICU_SKIP_UTF8(zString);\n\n    }else if( !prevEscape && uPattern==(uint32_t)uEsc){\n      /* Case 3. */\n      prevEscape = 1;\n\n    }else{\n      /* Case 4. */\n      uint32_t uString;\n      SQLITE_ICU_READ_UTF8(zString, uString);\n      uString = (uint32_t)u_foldCase((UChar32)uString, U_FOLD_CASE_DEFAULT);\n      uPattern = (uint32_t)u_foldCase((UChar32)uPattern, U_FOLD_CASE_DEFAULT);\n      if( uString!=uPattern ){\n        return 0;\n      }\n      prevEscape = 0;\n    }\n  }\n\n  return *zString==0;\n}\n\n/*\n** Implementation of the like() SQL function.  This function implements\n** the build-in LIKE operator.  The first argument to the function is the\n** pattern and the second argument is the string.  So, the SQL statements:\n**\n**       A LIKE B\n**\n** is implemented as like(B, A). If there is an escape character E, \n**\n**       A LIKE B ESCAPE E\n**\n** is mapped to like(B, A, E).\n*/\nstatic void icuLikeFunc(\n  sqlite3_context *context, \n  int argc, \n  sqlite3_value **argv\n){\n  const unsigned char *zA = sqlite3_value_text(argv[0]);\n  const unsigned char *zB = sqlite3_value_text(argv[1]);\n  UChar32 uEsc = 0;\n\n  /* Limit the length of the LIKE or GLOB pattern to avoid problems\n  ** of deep recursion and N*N behavior in patternCompare().\n  */\n  if( sqlite3_value_bytes(argv[0])>SQLITE_MAX_LIKE_PATTERN_LENGTH ){\n    sqlite3_result_error(context, \"LIKE or GLOB pattern too complex\", -1);\n    return;\n  }\n\n\n  if( argc==3 ){\n    /* The escape character string must consist of a single UTF-8 character.\n    ** Otherwise, return an error.\n    */\n    int nE= sqlite3_value_bytes(argv[2]);\n    const unsigned char *zE = sqlite3_value_text(argv[2]);\n    int i = 0;\n    if( zE==0 ) return;\n    U8_NEXT(zE, i, nE, uEsc);\n    if( i!=nE){\n      sqlite3_result_error(context, \n          \"ESCAPE expression must be a single character\", -1);\n      return;\n    }\n  }\n\n  if( zA && zB ){\n    sqlite3_result_int(context, icuLikeCompare(zA, zB, uEsc));\n  }\n}\n\n/*\n** Function to delete compiled regexp objects. Registered as\n** a destructor function with sqlite3_set_auxdata().\n*/\nstatic void icuRegexpDelete(void *p){\n  URegularExpression *pExpr = (URegularExpression *)p;\n  uregex_close(pExpr);\n}\n\n/*\n** Implementation of SQLite REGEXP operator. This scalar function takes\n** two arguments. The first is a regular expression pattern to compile\n** the second is a string to match against that pattern. If either \n** argument is an SQL NULL, then NULL Is returned. Otherwise, the result\n** is 1 if the string matches the pattern, or 0 otherwise.\n**\n** SQLite maps the regexp() function to the regexp() operator such\n** that the following two are equivalent:\n**\n**     zString REGEXP zPattern\n**     regexp(zPattern, zString)\n**\n** Uses the following ICU regexp APIs:\n**\n**     uregex_open()\n**     uregex_matches()\n**     uregex_close()\n*/\nstatic void icuRegexpFunc(sqlite3_context *p, int nArg, sqlite3_value **apArg){\n  UErrorCode status = U_ZERO_ERROR;\n  URegularExpression *pExpr;\n  UBool res;\n  const UChar *zString = sqlite3_value_text16(apArg[1]);\n\n  (void)nArg;  /* Unused parameter */\n\n  /* If the left hand side of the regexp operator is NULL, \n  ** then the result is also NULL. \n  */\n  if( !zString ){\n    return;\n  }\n\n  pExpr = sqlite3_get_auxdata(p, 0);\n  if( !pExpr ){\n    const UChar *zPattern = sqlite3_value_text16(apArg[0]);\n    if( !zPattern ){\n      return;\n    }\n    pExpr = uregex_open(zPattern, -1, 0, 0, &status);\n\n    if( U_SUCCESS(status) ){\n      sqlite3_set_auxdata(p, 0, pExpr, icuRegexpDelete);\n    }else{\n      assert(!pExpr);\n      icuFunctionError(p, \"uregex_open\", status);\n      return;\n    }\n  }\n\n  /* Configure the text that the regular expression operates on. */\n  uregex_setText(pExpr, zString, -1, &status);\n  if( !U_SUCCESS(status) ){\n    icuFunctionError(p, \"uregex_setText\", status);\n    return;\n  }\n\n  /* Attempt the match */\n  res = uregex_matches(pExpr, 0, &status);\n  if( !U_SUCCESS(status) ){\n    icuFunctionError(p, \"uregex_matches\", status);\n    return;\n  }\n\n  /* Set the text that the regular expression operates on to a NULL\n  ** pointer. This is not really necessary, but it is tidier than \n  ** leaving the regular expression object configured with an invalid\n  ** pointer after this function returns.\n  */\n  uregex_setText(pExpr, 0, 0, &status);\n\n  /* Return 1 or 0. */\n  sqlite3_result_int(p, res ? 1 : 0);\n}\n\n/*\n** Implementations of scalar functions for case mapping - upper() and \n** lower(). Function upper() converts its input to upper-case (ABC).\n** Function lower() converts to lower-case (abc).\n**\n** ICU provides two types of case mapping, \"general\" case mapping and\n** \"language specific\". Refer to ICU documentation for the differences\n** between the two.\n**\n** To utilise \"general\" case mapping, the upper() or lower() scalar \n** functions are invoked with one argument:\n**\n**     upper('ABC') -> 'abc'\n**     lower('abc') -> 'ABC'\n**\n** To access ICU \"language specific\" case mapping, upper() or lower()\n** should be invoked with two arguments. The second argument is the name\n** of the locale to use. Passing an empty string (\"\") or SQL NULL value\n** as the second argument is the same as invoking the 1 argument version\n** of upper() or lower().\n**\n**     lower('I', 'en_us') -> 'i'\n**     lower('I', 'tr_tr') -> '\\u131' (small dotless i)\n**\n** http://www.icu-project.org/userguide/posix.html#case_mappings\n*/\nstatic void icuCaseFunc16(sqlite3_context *p, int nArg, sqlite3_value **apArg){\n  const UChar *zInput;            /* Pointer to input string */\n  UChar *zOutput = 0;             /* Pointer to output buffer */\n  int nInput;                     /* Size of utf-16 input string in bytes */\n  int nOut;                       /* Size of output buffer in bytes */\n  int cnt;\n  int bToUpper;                   /* True for toupper(), false for tolower() */\n  UErrorCode status;\n  const char *zLocale = 0;\n\n  assert(nArg==1 || nArg==2);\n  bToUpper = (sqlite3_user_data(p)!=0);\n  if( nArg==2 ){\n    zLocale = (const char *)sqlite3_value_text(apArg[1]);\n  }\n\n  zInput = sqlite3_value_text16(apArg[0]);\n  if( !zInput ){\n    return;\n  }\n  nOut = nInput = sqlite3_value_bytes16(apArg[0]);\n  if( nOut==0 ){\n    sqlite3_result_text16(p, \"\", 0, SQLITE_STATIC);\n    return;\n  }\n\n  for(cnt=0; cnt<2; cnt++){\n    UChar *zNew = sqlite3_realloc(zOutput, nOut);\n    if( zNew==0 ){\n      sqlite3_free(zOutput);\n      sqlite3_result_error_nomem(p);\n      return;\n    }\n    zOutput = zNew;\n    status = U_ZERO_ERROR;\n    if( bToUpper ){\n      nOut = 2*u_strToUpper(zOutput,nOut/2,zInput,nInput/2,zLocale,&status);\n    }else{\n      nOut = 2*u_strToLower(zOutput,nOut/2,zInput,nInput/2,zLocale,&status);\n    }\n\n    if( U_SUCCESS(status) ){\n      sqlite3_result_text16(p, zOutput, nOut, xFree);\n    }else if( status==U_BUFFER_OVERFLOW_ERROR ){\n      assert( cnt==0 );\n      continue;\n    }else{\n      icuFunctionError(p, bToUpper ? \"u_strToUpper\" : \"u_strToLower\", status);\n    }\n    return;\n  }\n  assert( 0 );     /* Unreachable */\n}\n\n#endif /* !defined(SQLITE_CORE) || defined(SQLITE_ENABLE_ICU) */\n\n/*\n** Collation sequence destructor function. The pCtx argument points to\n** a UCollator structure previously allocated using ucol_open().\n*/\nstatic void icuCollationDel(void *pCtx){\n  UCollator *p = (UCollator *)pCtx;\n  ucol_close(p);\n}\n\n/*\n** Collation sequence comparison function. The pCtx argument points to\n** a UCollator structure previously allocated using ucol_open().\n*/\nstatic int icuCollationColl(\n  void *pCtx,\n  int nLeft,\n  const void *zLeft,\n  int nRight,\n  const void *zRight\n){\n  UCollationResult res;\n  UCollator *p = (UCollator *)pCtx;\n  res = ucol_strcoll(p, (UChar *)zLeft, nLeft/2, (UChar *)zRight, nRight/2);\n  switch( res ){\n    case UCOL_LESS:    return -1;\n    case UCOL_GREATER: return +1;\n    case UCOL_EQUAL:   return 0;\n  }\n  assert(!\"Unexpected return value from ucol_strcoll()\");\n  return 0;\n}\n\n/*\n** Implementation of the scalar function icu_load_collation().\n**\n** This scalar function is used to add ICU collation based collation \n** types to an SQLite database connection. It is intended to be called\n** as follows:\n**\n**     SELECT icu_load_collation(<locale>, <collation-name>);\n**\n** Where <locale> is a string containing an ICU locale identifier (i.e.\n** \"en_AU\", \"tr_TR\" etc.) and <collation-name> is the name of the\n** collation sequence to create.\n*/\nstatic void icuLoadCollation(\n  sqlite3_context *p, \n  int nArg, \n  sqlite3_value **apArg\n){\n  sqlite3 *db = (sqlite3 *)sqlite3_user_data(p);\n  UErrorCode status = U_ZERO_ERROR;\n  const char *zLocale;      /* Locale identifier - (eg. \"jp_JP\") */\n  const char *zName;        /* SQL Collation sequence name (eg. \"japanese\") */\n  UCollator *pUCollator;    /* ICU library collation object */\n  int rc;                   /* Return code from sqlite3_create_collation_x() */\n\n  assert(nArg==2);\n  (void)nArg; /* Unused parameter */\n  zLocale = (const char *)sqlite3_value_text(apArg[0]);\n  zName = (const char *)sqlite3_value_text(apArg[1]);\n\n  if( !zLocale || !zName ){\n    return;\n  }\n\n  pUCollator = ucol_open(zLocale, &status);\n  if( !U_SUCCESS(status) ){\n    icuFunctionError(p, \"ucol_open\", status);\n    return;\n  }\n  assert(p);\n\n  rc = sqlite3_create_collation_v2(db, zName, SQLITE_UTF16, (void *)pUCollator, \n      icuCollationColl, icuCollationDel\n  );\n  if( rc!=SQLITE_OK ){\n    ucol_close(pUCollator);\n    sqlite3_result_error(p, \"Error registering collation function\", -1);\n  }\n}\n\n/*\n** Register the ICU extension functions with database db.\n*/\nSQLITE_PRIVATE int sqlite3IcuInit(sqlite3 *db){\n  static const struct IcuScalar {\n    const char *zName;                        /* Function name */\n    unsigned char nArg;                       /* Number of arguments */\n    unsigned short enc;                       /* Optimal text encoding */\n    unsigned char iContext;                   /* sqlite3_user_data() context */\n    void (*xFunc)(sqlite3_context*,int,sqlite3_value**);\n  } scalars[] = {\n    {\"icu_load_collation\",  2, SQLITE_UTF8,                1, icuLoadCollation},\n#if !defined(SQLITE_CORE) || defined(SQLITE_ENABLE_ICU)\n    {\"regexp\", 2, SQLITE_ANY|SQLITE_DETERMINISTIC,         0, icuRegexpFunc},\n    {\"lower\",  1, SQLITE_UTF16|SQLITE_DETERMINISTIC,       0, icuCaseFunc16},\n    {\"lower\",  2, SQLITE_UTF16|SQLITE_DETERMINISTIC,       0, icuCaseFunc16},\n    {\"upper\",  1, SQLITE_UTF16|SQLITE_DETERMINISTIC,       1, icuCaseFunc16},\n    {\"upper\",  2, SQLITE_UTF16|SQLITE_DETERMINISTIC,       1, icuCaseFunc16},\n    {\"lower\",  1, SQLITE_UTF8|SQLITE_DETERMINISTIC,        0, icuCaseFunc16},\n    {\"lower\",  2, SQLITE_UTF8|SQLITE_DETERMINISTIC,        0, icuCaseFunc16},\n    {\"upper\",  1, SQLITE_UTF8|SQLITE_DETERMINISTIC,        1, icuCaseFunc16},\n    {\"upper\",  2, SQLITE_UTF8|SQLITE_DETERMINISTIC,        1, icuCaseFunc16},\n    {\"like\",   2, SQLITE_UTF8|SQLITE_DETERMINISTIC,        0, icuLikeFunc},\n    {\"like\",   3, SQLITE_UTF8|SQLITE_DETERMINISTIC,        0, icuLikeFunc},\n#endif /* !defined(SQLITE_CORE) || defined(SQLITE_ENABLE_ICU) */\n  };\n  int rc = SQLITE_OK;\n  int i;\n  \n  for(i=0; rc==SQLITE_OK && i<(int)(sizeof(scalars)/sizeof(scalars[0])); i++){\n    const struct IcuScalar *p = &scalars[i];\n    rc = sqlite3_create_function(\n        db, p->zName, p->nArg, p->enc, \n        p->iContext ? (void*)db : (void*)0,\n        p->xFunc, 0, 0\n    );\n  }\n\n  return rc;\n}\n\n#if !SQLITE_CORE\n#ifdef _WIN32\n__declspec(dllexport)\n#endif\nSQLITE_API int sqlite3_icu_init(\n  sqlite3 *db, \n  char **pzErrMsg,\n  const sqlite3_api_routines *pApi\n){\n  SQLITE_EXTENSION_INIT2(pApi)\n  return sqlite3IcuInit(db);\n}\n#endif\n\n#endif\n\n/************** End of icu.c *************************************************/\n/************** Begin file fts3_icu.c ****************************************/\n/*\n** 2007 June 22\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n*************************************************************************\n** This file implements a tokenizer for fts3 based on the ICU library.\n*/\n/* #include \"fts3Int.h\" */\n#if !defined(SQLITE_CORE) || defined(SQLITE_ENABLE_FTS3)\n#ifdef SQLITE_ENABLE_ICU\n\n/* #include <assert.h> */\n/* #include <string.h> */\n/* #include \"fts3_tokenizer.h\" */\n\n#include <unicode/ubrk.h>\n/* #include <unicode/ucol.h> */\n/* #include <unicode/ustring.h> */\n#include <unicode/utf16.h>\n\ntypedef struct IcuTokenizer IcuTokenizer;\ntypedef struct IcuCursor IcuCursor;\n\nstruct IcuTokenizer {\n  sqlite3_tokenizer base;\n  char *zLocale;\n};\n\nstruct IcuCursor {\n  sqlite3_tokenizer_cursor base;\n\n  UBreakIterator *pIter;      /* ICU break-iterator object */\n  int nChar;                  /* Number of UChar elements in pInput */\n  UChar *aChar;               /* Copy of input using utf-16 encoding */\n  int *aOffset;               /* Offsets of each character in utf-8 input */\n\n  int nBuffer;\n  char *zBuffer;\n\n  int iToken;\n};\n\n/*\n** Create a new tokenizer instance.\n*/\nstatic int icuCreate(\n  int argc,                            /* Number of entries in argv[] */\n  const char * const *argv,            /* Tokenizer creation arguments */\n  sqlite3_tokenizer **ppTokenizer      /* OUT: Created tokenizer */\n){\n  IcuTokenizer *p;\n  int n = 0;\n\n  if( argc>0 ){\n    n = strlen(argv[0])+1;\n  }\n  p = (IcuTokenizer *)sqlite3_malloc(sizeof(IcuTokenizer)+n);\n  if( !p ){\n    return SQLITE_NOMEM;\n  }\n  memset(p, 0, sizeof(IcuTokenizer));\n\n  if( n ){\n    p->zLocale = (char *)&p[1];\n    memcpy(p->zLocale, argv[0], n);\n  }\n\n  *ppTokenizer = (sqlite3_tokenizer *)p;\n\n  return SQLITE_OK;\n}\n\n/*\n** Destroy a tokenizer\n*/\nstatic int icuDestroy(sqlite3_tokenizer *pTokenizer){\n  IcuTokenizer *p = (IcuTokenizer *)pTokenizer;\n  sqlite3_free(p);\n  return SQLITE_OK;\n}\n\n/*\n** Prepare to begin tokenizing a particular string.  The input\n** string to be tokenized is pInput[0..nBytes-1].  A cursor\n** used to incrementally tokenize this string is returned in \n** *ppCursor.\n*/\nstatic int icuOpen(\n  sqlite3_tokenizer *pTokenizer,         /* The tokenizer */\n  const char *zInput,                    /* Input string */\n  int nInput,                            /* Length of zInput in bytes */\n  sqlite3_tokenizer_cursor **ppCursor    /* OUT: Tokenization cursor */\n){\n  IcuTokenizer *p = (IcuTokenizer *)pTokenizer;\n  IcuCursor *pCsr;\n\n  const int32_t opt = U_FOLD_CASE_DEFAULT;\n  UErrorCode status = U_ZERO_ERROR;\n  int nChar;\n\n  UChar32 c;\n  int iInput = 0;\n  int iOut = 0;\n\n  *ppCursor = 0;\n\n  if( zInput==0 ){\n    nInput = 0;\n    zInput = \"\";\n  }else if( nInput<0 ){\n    nInput = strlen(zInput);\n  }\n  nChar = nInput+1;\n  pCsr = (IcuCursor *)sqlite3_malloc(\n      sizeof(IcuCursor) +                /* IcuCursor */\n      ((nChar+3)&~3) * sizeof(UChar) +   /* IcuCursor.aChar[] */\n      (nChar+1) * sizeof(int)            /* IcuCursor.aOffset[] */\n  );\n  if( !pCsr ){\n    return SQLITE_NOMEM;\n  }\n  memset(pCsr, 0, sizeof(IcuCursor));\n  pCsr->aChar = (UChar *)&pCsr[1];\n  pCsr->aOffset = (int *)&pCsr->aChar[(nChar+3)&~3];\n\n  pCsr->aOffset[iOut] = iInput;\n  U8_NEXT(zInput, iInput, nInput, c); \n  while( c>0 ){\n    int isError = 0;\n    c = u_foldCase(c, opt);\n    U16_APPEND(pCsr->aChar, iOut, nChar, c, isError);\n    if( isError ){\n      sqlite3_free(pCsr);\n      return SQLITE_ERROR;\n    }\n    pCsr->aOffset[iOut] = iInput;\n\n    if( iInput<nInput ){\n      U8_NEXT(zInput, iInput, nInput, c);\n    }else{\n      c = 0;\n    }\n  }\n\n  pCsr->pIter = ubrk_open(UBRK_WORD, p->zLocale, pCsr->aChar, iOut, &status);\n  if( !U_SUCCESS(status) ){\n    sqlite3_free(pCsr);\n    return SQLITE_ERROR;\n  }\n  pCsr->nChar = iOut;\n\n  ubrk_first(pCsr->pIter);\n  *ppCursor = (sqlite3_tokenizer_cursor *)pCsr;\n  return SQLITE_OK;\n}\n\n/*\n** Close a tokenization cursor previously opened by a call to icuOpen().\n*/\nstatic int icuClose(sqlite3_tokenizer_cursor *pCursor){\n  IcuCursor *pCsr = (IcuCursor *)pCursor;\n  ubrk_close(pCsr->pIter);\n  sqlite3_free(pCsr->zBuffer);\n  sqlite3_free(pCsr);\n  return SQLITE_OK;\n}\n\n/*\n** Extract the next token from a tokenization cursor.\n*/\nstatic int icuNext(\n  sqlite3_tokenizer_cursor *pCursor,  /* Cursor returned by simpleOpen */\n  const char **ppToken,               /* OUT: *ppToken is the token text */\n  int *pnBytes,                       /* OUT: Number of bytes in token */\n  int *piStartOffset,                 /* OUT: Starting offset of token */\n  int *piEndOffset,                   /* OUT: Ending offset of token */\n  int *piPosition                     /* OUT: Position integer of token */\n){\n  IcuCursor *pCsr = (IcuCursor *)pCursor;\n\n  int iStart = 0;\n  int iEnd = 0;\n  int nByte = 0;\n\n  while( iStart==iEnd ){\n    UChar32 c;\n\n    iStart = ubrk_current(pCsr->pIter);\n    iEnd = ubrk_next(pCsr->pIter);\n    if( iEnd==UBRK_DONE ){\n      return SQLITE_DONE;\n    }\n\n    while( iStart<iEnd ){\n      int iWhite = iStart;\n      U16_NEXT(pCsr->aChar, iWhite, pCsr->nChar, c);\n      if( u_isspace(c) ){\n        iStart = iWhite;\n      }else{\n        break;\n      }\n    }\n    assert(iStart<=iEnd);\n  }\n\n  do {\n    UErrorCode status = U_ZERO_ERROR;\n    if( nByte ){\n      char *zNew = sqlite3_realloc(pCsr->zBuffer, nByte);\n      if( !zNew ){\n        return SQLITE_NOMEM;\n      }\n      pCsr->zBuffer = zNew;\n      pCsr->nBuffer = nByte;\n    }\n\n    u_strToUTF8(\n        pCsr->zBuffer, pCsr->nBuffer, &nByte,    /* Output vars */\n        &pCsr->aChar[iStart], iEnd-iStart,       /* Input vars */\n        &status                                  /* Output success/failure */\n    );\n  } while( nByte>pCsr->nBuffer );\n\n  *ppToken = pCsr->zBuffer;\n  *pnBytes = nByte;\n  *piStartOffset = pCsr->aOffset[iStart];\n  *piEndOffset = pCsr->aOffset[iEnd];\n  *piPosition = pCsr->iToken++;\n\n  return SQLITE_OK;\n}\n\n/*\n** The set of routines that implement the simple tokenizer\n*/\nstatic const sqlite3_tokenizer_module icuTokenizerModule = {\n  0,                           /* iVersion    */\n  icuCreate,                   /* xCreate     */\n  icuDestroy,                  /* xCreate     */\n  icuOpen,                     /* xOpen       */\n  icuClose,                    /* xClose      */\n  icuNext,                     /* xNext       */\n  0,                           /* xLanguageid */\n};\n\n/*\n** Set *ppModule to point at the implementation of the ICU tokenizer.\n*/\nSQLITE_PRIVATE void sqlite3Fts3IcuTokenizerModule(\n  sqlite3_tokenizer_module const**ppModule\n){\n  *ppModule = &icuTokenizerModule;\n}\n\n#endif /* defined(SQLITE_ENABLE_ICU) */\n#endif /* !defined(SQLITE_CORE) || defined(SQLITE_ENABLE_FTS3) */\n\n/************** End of fts3_icu.c ********************************************/\n/************** Begin file sqlite3rbu.c **************************************/\n/*\n** 2014 August 30\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n*************************************************************************\n**\n**\n** OVERVIEW \n**\n**  The RBU extension requires that the RBU update be packaged as an\n**  SQLite database. The tables it expects to find are described in\n**  sqlite3rbu.h.  Essentially, for each table xyz in the target database\n**  that the user wishes to write to, a corresponding data_xyz table is\n**  created in the RBU database and populated with one row for each row to\n**  update, insert or delete from the target table.\n** \n**  The update proceeds in three stages:\n** \n**  1) The database is updated. The modified database pages are written\n**     to a *-oal file. A *-oal file is just like a *-wal file, except\n**     that it is named \"<database>-oal\" instead of \"<database>-wal\".\n**     Because regular SQLite clients do not look for file named\n**     \"<database>-oal\", they go on using the original database in\n**     rollback mode while the *-oal file is being generated.\n** \n**     During this stage RBU does not update the database by writing\n**     directly to the target tables. Instead it creates \"imposter\"\n**     tables using the SQLITE_TESTCTRL_IMPOSTER interface that it uses\n**     to update each b-tree individually. All updates required by each\n**     b-tree are completed before moving on to the next, and all\n**     updates are done in sorted key order.\n** \n**  2) The \"<database>-oal\" file is moved to the equivalent \"<database>-wal\"\n**     location using a call to rename(2). Before doing this the RBU\n**     module takes an EXCLUSIVE lock on the database file, ensuring\n**     that there are no other active readers.\n** \n**     Once the EXCLUSIVE lock is released, any other database readers\n**     detect the new *-wal file and read the database in wal mode. At\n**     this point they see the new version of the database - including\n**     the updates made as part of the RBU update.\n** \n**  3) The new *-wal file is checkpointed. This proceeds in the same way \n**     as a regular database checkpoint, except that a single frame is\n**     checkpointed each time sqlite3rbu_step() is called. If the RBU\n**     handle is closed before the entire *-wal file is checkpointed,\n**     the checkpoint progress is saved in the RBU database and the\n**     checkpoint can be resumed by another RBU client at some point in\n**     the future.\n**\n** POTENTIAL PROBLEMS\n** \n**  The rename() call might not be portable. And RBU is not currently\n**  syncing the directory after renaming the file.\n**\n**  When state is saved, any commit to the *-oal file and the commit to\n**  the RBU update database are not atomic. So if the power fails at the\n**  wrong moment they might get out of sync. As the main database will be\n**  committed before the RBU update database this will likely either just\n**  pass unnoticed, or result in SQLITE_CONSTRAINT errors (due to UNIQUE\n**  constraint violations).\n**\n**  If some client does modify the target database mid RBU update, or some\n**  other error occurs, the RBU extension will keep throwing errors. It's\n**  not really clear how to get out of this state. The system could just\n**  by delete the RBU update database and *-oal file and have the device\n**  download the update again and start over.\n**\n**  At present, for an UPDATE, both the new.* and old.* records are\n**  collected in the rbu_xyz table. And for both UPDATEs and DELETEs all\n**  fields are collected.  This means we're probably writing a lot more\n**  data to disk when saving the state of an ongoing update to the RBU\n**  update database than is strictly necessary.\n** \n*/\n\n/* #include <assert.h> */\n/* #include <string.h> */\n/* #include <stdio.h> */\n\n/* #include \"sqlite3.h\" */\n\n#if !defined(SQLITE_CORE) || defined(SQLITE_ENABLE_RBU)\n/************** Include sqlite3rbu.h in the middle of sqlite3rbu.c ***********/\n/************** Begin file sqlite3rbu.h **************************************/\n/*\n** 2014 August 30\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n*************************************************************************\n**\n** This file contains the public interface for the RBU extension. \n*/\n\n/*\n** SUMMARY\n**\n** Writing a transaction containing a large number of operations on \n** b-tree indexes that are collectively larger than the available cache\n** memory can be very inefficient. \n**\n** The problem is that in order to update a b-tree, the leaf page (at least)\n** containing the entry being inserted or deleted must be modified. If the\n** working set of leaves is larger than the available cache memory, then a \n** single leaf that is modified more than once as part of the transaction \n** may be loaded from or written to the persistent media multiple times.\n** Additionally, because the index updates are likely to be applied in\n** random order, access to pages within the database is also likely to be in \n** random order, which is itself quite inefficient.\n**\n** One way to improve the situation is to sort the operations on each index\n** by index key before applying them to the b-tree. This leads to an IO\n** pattern that resembles a single linear scan through the index b-tree,\n** and all but guarantees each modified leaf page is loaded and stored \n** exactly once. SQLite uses this trick to improve the performance of\n** CREATE INDEX commands. This extension allows it to be used to improve\n** the performance of large transactions on existing databases.\n**\n** Additionally, this extension allows the work involved in writing the \n** large transaction to be broken down into sub-transactions performed \n** sequentially by separate processes. This is useful if the system cannot \n** guarantee that a single update process will run for long enough to apply \n** the entire update, for example because the update is being applied on a \n** mobile device that is frequently rebooted. Even after the writer process \n** has committed one or more sub-transactions, other database clients continue\n** to read from the original database snapshot. In other words, partially \n** applied transactions are not visible to other clients. \n**\n** \"RBU\" stands for \"Resumable Bulk Update\". As in a large database update\n** transmitted via a wireless network to a mobile device. A transaction\n** applied using this extension is hence refered to as an \"RBU update\".\n**\n**\n** LIMITATIONS\n**\n** An \"RBU update\" transaction is subject to the following limitations:\n**\n**   * The transaction must consist of INSERT, UPDATE and DELETE operations\n**     only.\n**\n**   * INSERT statements may not use any default values.\n**\n**   * UPDATE and DELETE statements must identify their target rows by \n**     non-NULL PRIMARY KEY values. Rows with NULL values stored in PRIMARY\n**     KEY fields may not be updated or deleted. If the table being written \n**     has no PRIMARY KEY, affected rows must be identified by rowid.\n**\n**   * UPDATE statements may not modify PRIMARY KEY columns.\n**\n**   * No triggers will be fired.\n**\n**   * No foreign key violations are detected or reported.\n**\n**   * CHECK constraints are not enforced.\n**\n**   * No constraint handling mode except for \"OR ROLLBACK\" is supported.\n**\n**\n** PREPARATION\n**\n** An \"RBU update\" is stored as a separate SQLite database. A database\n** containing an RBU update is an \"RBU database\". For each table in the \n** target database to be updated, the RBU database should contain a table\n** named \"data_<target name>\" containing the same set of columns as the\n** target table, and one more - \"rbu_control\". The data_% table should \n** have no PRIMARY KEY or UNIQUE constraints, but each column should have\n** the same type as the corresponding column in the target database.\n** The \"rbu_control\" column should have no type at all. For example, if\n** the target database contains:\n**\n**   CREATE TABLE t1(a INTEGER PRIMARY KEY, b TEXT, c UNIQUE);\n**\n** Then the RBU database should contain:\n**\n**   CREATE TABLE data_t1(a INTEGER, b TEXT, c, rbu_control);\n**\n** The order of the columns in the data_% table does not matter.\n**\n** Instead of a regular table, the RBU database may also contain virtual\n** tables or view named using the data_<target> naming scheme. \n**\n** Instead of the plain data_<target> naming scheme, RBU database tables \n** may also be named data<integer>_<target>, where <integer> is any sequence\n** of zero or more numeric characters (0-9). This can be significant because\n** tables within the RBU database are always processed in order sorted by \n** name. By judicious selection of the <integer> portion of the names\n** of the RBU tables the user can therefore control the order in which they\n** are processed. This can be useful, for example, to ensure that \"external\n** content\" FTS4 tables are updated before their underlying content tables.\n**\n** If the target database table is a virtual table or a table that has no\n** PRIMARY KEY declaration, the data_% table must also contain a column \n** named \"rbu_rowid\". This column is mapped to the tables implicit primary \n** key column - \"rowid\". Virtual tables for which the \"rowid\" column does \n** not function like a primary key value cannot be updated using RBU. For \n** example, if the target db contains either of the following:\n**\n**   CREATE VIRTUAL TABLE x1 USING fts3(a, b);\n**   CREATE TABLE x1(a, b)\n**\n** then the RBU database should contain:\n**\n**   CREATE TABLE data_x1(a, b, rbu_rowid, rbu_control);\n**\n** All non-hidden columns (i.e. all columns matched by \"SELECT *\") of the\n** target table must be present in the input table. For virtual tables,\n** hidden columns are optional - they are updated by RBU if present in\n** the input table, or not otherwise. For example, to write to an fts4\n** table with a hidden languageid column such as:\n**\n**   CREATE VIRTUAL TABLE ft1 USING fts4(a, b, languageid='langid');\n**\n** Either of the following input table schemas may be used:\n**\n**   CREATE TABLE data_ft1(a, b, langid, rbu_rowid, rbu_control);\n**   CREATE TABLE data_ft1(a, b, rbu_rowid, rbu_control);\n**\n** For each row to INSERT into the target database as part of the RBU \n** update, the corresponding data_% table should contain a single record\n** with the \"rbu_control\" column set to contain integer value 0. The\n** other columns should be set to the values that make up the new record \n** to insert. \n**\n** If the target database table has an INTEGER PRIMARY KEY, it is not \n** possible to insert a NULL value into the IPK column. Attempting to \n** do so results in an SQLITE_MISMATCH error.\n**\n** For each row to DELETE from the target database as part of the RBU \n** update, the corresponding data_% table should contain a single record\n** with the \"rbu_control\" column set to contain integer value 1. The\n** real primary key values of the row to delete should be stored in the\n** corresponding columns of the data_% table. The values stored in the\n** other columns are not used.\n**\n** For each row to UPDATE from the target database as part of the RBU \n** update, the corresponding data_% table should contain a single record\n** with the \"rbu_control\" column set to contain a value of type text.\n** The real primary key values identifying the row to update should be \n** stored in the corresponding columns of the data_% table row, as should\n** the new values of all columns being update. The text value in the \n** \"rbu_control\" column must contain the same number of characters as\n** there are columns in the target database table, and must consist entirely\n** of 'x' and '.' characters (or in some special cases 'd' - see below). For \n** each column that is being updated, the corresponding character is set to\n** 'x'. For those that remain as they are, the corresponding character of the\n** rbu_control value should be set to '.'. For example, given the tables \n** above, the update statement:\n**\n**   UPDATE t1 SET c = 'usa' WHERE a = 4;\n**\n** is represented by the data_t1 row created by:\n**\n**   INSERT INTO data_t1(a, b, c, rbu_control) VALUES(4, NULL, 'usa', '..x');\n**\n** Instead of an 'x' character, characters of the rbu_control value specified\n** for UPDATEs may also be set to 'd'. In this case, instead of updating the\n** target table with the value stored in the corresponding data_% column, the\n** user-defined SQL function \"rbu_delta()\" is invoked and the result stored in\n** the target table column. rbu_delta() is invoked with two arguments - the\n** original value currently stored in the target table column and the \n** value specified in the data_xxx table.\n**\n** For example, this row:\n**\n**   INSERT INTO data_t1(a, b, c, rbu_control) VALUES(4, NULL, 'usa', '..d');\n**\n** is similar to an UPDATE statement such as: \n**\n**   UPDATE t1 SET c = rbu_delta(c, 'usa') WHERE a = 4;\n**\n** Finally, if an 'f' character appears in place of a 'd' or 's' in an \n** ota_control string, the contents of the data_xxx table column is assumed\n** to be a \"fossil delta\" - a patch to be applied to a blob value in the\n** format used by the fossil source-code management system. In this case\n** the existing value within the target database table must be of type BLOB. \n** It is replaced by the result of applying the specified fossil delta to\n** itself.\n**\n** If the target database table is a virtual table or a table with no PRIMARY\n** KEY, the rbu_control value should not include a character corresponding \n** to the rbu_rowid value. For example, this:\n**\n**   INSERT INTO data_ft1(a, b, rbu_rowid, rbu_control) \n**       VALUES(NULL, 'usa', 12, '.x');\n**\n** causes a result similar to:\n**\n**   UPDATE ft1 SET b = 'usa' WHERE rowid = 12;\n**\n** The data_xxx tables themselves should have no PRIMARY KEY declarations.\n** However, RBU is more efficient if reading the rows in from each data_xxx\n** table in \"rowid\" order is roughly the same as reading them sorted by\n** the PRIMARY KEY of the corresponding target database table. In other \n** words, rows should be sorted using the destination table PRIMARY KEY \n** fields before they are inserted into the data_xxx tables.\n**\n** USAGE\n**\n** The API declared below allows an application to apply an RBU update \n** stored on disk to an existing target database. Essentially, the \n** application:\n**\n**     1) Opens an RBU handle using the sqlite3rbu_open() function.\n**\n**     2) Registers any required virtual table modules with the database\n**        handle returned by sqlite3rbu_db(). Also, if required, register\n**        the rbu_delta() implementation.\n**\n**     3) Calls the sqlite3rbu_step() function one or more times on\n**        the new handle. Each call to sqlite3rbu_step() performs a single\n**        b-tree operation, so thousands of calls may be required to apply \n**        a complete update.\n**\n**     4) Calls sqlite3rbu_close() to close the RBU update handle. If\n**        sqlite3rbu_step() has been called enough times to completely\n**        apply the update to the target database, then the RBU database\n**        is marked as fully applied. Otherwise, the state of the RBU \n**        update application is saved in the RBU database for later \n**        resumption.\n**\n** See comments below for more detail on APIs.\n**\n** If an update is only partially applied to the target database by the\n** time sqlite3rbu_close() is called, various state information is saved \n** within the RBU database. This allows subsequent processes to automatically\n** resume the RBU update from where it left off.\n**\n** To remove all RBU extension state information, returning an RBU database \n** to its original contents, it is sufficient to drop all tables that begin\n** with the prefix \"rbu_\"\n**\n** DATABASE LOCKING\n**\n** An RBU update may not be applied to a database in WAL mode. Attempting\n** to do so is an error (SQLITE_ERROR).\n**\n** While an RBU handle is open, a SHARED lock may be held on the target\n** database file. This means it is possible for other clients to read the\n** database, but not to write it.\n**\n** If an RBU update is started and then suspended before it is completed,\n** then an external client writes to the database, then attempting to resume\n** the suspended RBU update is also an error (SQLITE_BUSY).\n*/\n\n#ifndef _SQLITE3RBU_H\n#define _SQLITE3RBU_H\n\n/* #include \"sqlite3.h\"              ** Required for error code definitions ** */\n\n#if 0\nextern \"C\" {\n#endif\n\ntypedef struct sqlite3rbu sqlite3rbu;\n\n/*\n** Open an RBU handle.\n**\n** Argument zTarget is the path to the target database. Argument zRbu is\n** the path to the RBU database. Each call to this function must be matched\n** by a call to sqlite3rbu_close(). When opening the databases, RBU passes\n** the SQLITE_CONFIG_URI flag to sqlite3_open_v2(). So if either zTarget\n** or zRbu begin with \"file:\", it will be interpreted as an SQLite \n** database URI, not a regular file name.\n**\n** If the zState argument is passed a NULL value, the RBU extension stores \n** the current state of the update (how many rows have been updated, which \n** indexes are yet to be updated etc.) within the RBU database itself. This\n** can be convenient, as it means that the RBU application does not need to\n** organize removing a separate state file after the update is concluded. \n** Or, if zState is non-NULL, it must be a path to a database file in which \n** the RBU extension can store the state of the update.\n**\n** When resuming an RBU update, the zState argument must be passed the same\n** value as when the RBU update was started.\n**\n** Once the RBU update is finished, the RBU extension does not \n** automatically remove any zState database file, even if it created it.\n**\n** By default, RBU uses the default VFS to access the files on disk. To\n** use a VFS other than the default, an SQLite \"file:\" URI containing a\n** \"vfs=...\" option may be passed as the zTarget option.\n**\n** IMPORTANT NOTE FOR ZIPVFS USERS: The RBU extension works with all of\n** SQLite's built-in VFSs, including the multiplexor VFS. However it does\n** not work out of the box with zipvfs. Refer to the comment describing\n** the zipvfs_create_vfs() API below for details on using RBU with zipvfs.\n*/\nSQLITE_API sqlite3rbu *sqlite3rbu_open(\n  const char *zTarget, \n  const char *zRbu,\n  const char *zState\n);\n\n/*\n** Open an RBU handle to perform an RBU vacuum on database file zTarget.\n** An RBU vacuum is similar to SQLite's built-in VACUUM command, except\n** that it can be suspended and resumed like an RBU update.\n**\n** The second argument to this function identifies a database in which \n** to store the state of the RBU vacuum operation if it is suspended. The \n** first time sqlite3rbu_vacuum() is called, to start an RBU vacuum\n** operation, the state database should either not exist or be empty\n** (contain no tables). If an RBU vacuum is suspended by calling \n** sqlite3rbu_close() on the RBU handle before sqlite3rbu_step() has\n** returned SQLITE_DONE, the vacuum state is stored in the state database. \n** The vacuum can be resumed by calling this function to open a new RBU\n** handle specifying the same target and state databases.\n**\n** If the second argument passed to this function is NULL, then the\n** name of the state database is \"<database>-vacuum\", where <database>\n** is the name of the target database file. In this case, on UNIX, if the\n** state database is not already present in the file-system, it is created\n** with the same permissions as the target db is made.\n**\n** This function does not delete the state database after an RBU vacuum\n** is completed, even if it created it. However, if the call to\n** sqlite3rbu_close() returns any value other than SQLITE_OK, the contents\n** of the state tables within the state database are zeroed. This way,\n** the next call to sqlite3rbu_vacuum() opens a handle that starts a \n** new RBU vacuum operation.\n**\n** As with sqlite3rbu_open(), Zipvfs users should rever to the comment\n** describing the sqlite3rbu_create_vfs() API function below for \n** a description of the complications associated with using RBU with \n** zipvfs databases.\n*/\nSQLITE_API sqlite3rbu *sqlite3rbu_vacuum(\n  const char *zTarget, \n  const char *zState\n);\n\n/*\n** Configure a limit for the amount of temp space that may be used by\n** the RBU handle passed as the first argument. The new limit is specified\n** in bytes by the second parameter. If it is positive, the limit is updated.\n** If the second parameter to this function is passed zero, then the limit\n** is removed entirely. If the second parameter is negative, the limit is\n** not modified (this is useful for querying the current limit).\n**\n** In all cases the returned value is the current limit in bytes (zero \n** indicates unlimited).\n**\n** If the temp space limit is exceeded during operation, an SQLITE_FULL\n** error is returned.\n*/\nSQLITE_API sqlite3_int64 sqlite3rbu_temp_size_limit(sqlite3rbu*, sqlite3_int64);\n\n/*\n** Return the current amount of temp file space, in bytes, currently used by \n** the RBU handle passed as the only argument.\n*/\nSQLITE_API sqlite3_int64 sqlite3rbu_temp_size(sqlite3rbu*);\n\n/*\n** Internally, each RBU connection uses a separate SQLite database \n** connection to access the target and rbu update databases. This\n** API allows the application direct access to these database handles.\n**\n** The first argument passed to this function must be a valid, open, RBU\n** handle. The second argument should be passed zero to access the target\n** database handle, or non-zero to access the rbu update database handle.\n** Accessing the underlying database handles may be useful in the\n** following scenarios:\n**\n**   * If any target tables are virtual tables, it may be necessary to\n**     call sqlite3_create_module() on the target database handle to \n**     register the required virtual table implementations.\n**\n**   * If the data_xxx tables in the RBU source database are virtual \n**     tables, the application may need to call sqlite3_create_module() on\n**     the rbu update db handle to any required virtual table\n**     implementations.\n**\n**   * If the application uses the \"rbu_delta()\" feature described above,\n**     it must use sqlite3_create_function() or similar to register the\n**     rbu_delta() implementation with the target database handle.\n**\n** If an error has occurred, either while opening or stepping the RBU object,\n** this function may return NULL. The error code and message may be collected\n** when sqlite3rbu_close() is called.\n**\n** Database handles returned by this function remain valid until the next\n** call to any sqlite3rbu_xxx() function other than sqlite3rbu_db().\n*/\nSQLITE_API sqlite3 *sqlite3rbu_db(sqlite3rbu*, int bRbu);\n\n/*\n** Do some work towards applying the RBU update to the target db. \n**\n** Return SQLITE_DONE if the update has been completely applied, or \n** SQLITE_OK if no error occurs but there remains work to do to apply\n** the RBU update. If an error does occur, some other error code is \n** returned. \n**\n** Once a call to sqlite3rbu_step() has returned a value other than\n** SQLITE_OK, all subsequent calls on the same RBU handle are no-ops\n** that immediately return the same value.\n*/\nSQLITE_API int sqlite3rbu_step(sqlite3rbu *pRbu);\n\n/*\n** Force RBU to save its state to disk.\n**\n** If a power failure or application crash occurs during an update, following\n** system recovery RBU may resume the update from the point at which the state\n** was last saved. In other words, from the most recent successful call to \n** sqlite3rbu_close() or this function.\n**\n** SQLITE_OK is returned if successful, or an SQLite error code otherwise.\n*/\nSQLITE_API int sqlite3rbu_savestate(sqlite3rbu *pRbu);\n\n/*\n** Close an RBU handle. \n**\n** If the RBU update has been completely applied, mark the RBU database\n** as fully applied. Otherwise, assuming no error has occurred, save the\n** current state of the RBU update appliation to the RBU database.\n**\n** If an error has already occurred as part of an sqlite3rbu_step()\n** or sqlite3rbu_open() call, or if one occurs within this function, an\n** SQLite error code is returned. Additionally, if pzErrmsg is not NULL,\n** *pzErrmsg may be set to point to a buffer containing a utf-8 formatted\n** English language error message. It is the responsibility of the caller to\n** eventually free any such buffer using sqlite3_free().\n**\n** Otherwise, if no error occurs, this function returns SQLITE_OK if the\n** update has been partially applied, or SQLITE_DONE if it has been \n** completely applied.\n*/\nSQLITE_API int sqlite3rbu_close(sqlite3rbu *pRbu, char **pzErrmsg);\n\n/*\n** Return the total number of key-value operations (inserts, deletes or \n** updates) that have been performed on the target database since the\n** current RBU update was started.\n*/\nSQLITE_API sqlite3_int64 sqlite3rbu_progress(sqlite3rbu *pRbu);\n\n/*\n** Obtain permyriadage (permyriadage is to 10000 as percentage is to 100) \n** progress indications for the two stages of an RBU update. This API may\n** be useful for driving GUI progress indicators and similar.\n**\n** An RBU update is divided into two stages:\n**\n**   * Stage 1, in which changes are accumulated in an oal/wal file, and\n**   * Stage 2, in which the contents of the wal file are copied into the\n**     main database.\n**\n** The update is visible to non-RBU clients during stage 2. During stage 1\n** non-RBU reader clients may see the original database.\n**\n** If this API is called during stage 2 of the update, output variable \n** (*pnOne) is set to 10000 to indicate that stage 1 has finished and (*pnTwo)\n** to a value between 0 and 10000 to indicate the permyriadage progress of\n** stage 2. A value of 5000 indicates that stage 2 is half finished, \n** 9000 indicates that it is 90% finished, and so on.\n**\n** If this API is called during stage 1 of the update, output variable \n** (*pnTwo) is set to 0 to indicate that stage 2 has not yet started. The\n** value to which (*pnOne) is set depends on whether or not the RBU \n** database contains an \"rbu_count\" table. The rbu_count table, if it \n** exists, must contain the same columns as the following:\n**\n**   CREATE TABLE rbu_count(tbl TEXT PRIMARY KEY, cnt INTEGER) WITHOUT ROWID;\n**\n** There must be one row in the table for each source (data_xxx) table within\n** the RBU database. The 'tbl' column should contain the name of the source\n** table. The 'cnt' column should contain the number of rows within the\n** source table.\n**\n** If the rbu_count table is present and populated correctly and this\n** API is called during stage 1, the *pnOne output variable is set to the\n** permyriadage progress of the same stage. If the rbu_count table does\n** not exist, then (*pnOne) is set to -1 during stage 1. If the rbu_count\n** table exists but is not correctly populated, the value of the *pnOne\n** output variable during stage 1 is undefined.\n*/\nSQLITE_API void sqlite3rbu_bp_progress(sqlite3rbu *pRbu, int *pnOne, int*pnTwo);\n\n/*\n** Obtain an indication as to the current stage of an RBU update or vacuum.\n** This function always returns one of the SQLITE_RBU_STATE_XXX constants\n** defined in this file. Return values should be interpreted as follows:\n**\n** SQLITE_RBU_STATE_OAL:\n**   RBU is currently building a *-oal file. The next call to sqlite3rbu_step()\n**   may either add further data to the *-oal file, or compute data that will\n**   be added by a subsequent call.\n**\n** SQLITE_RBU_STATE_MOVE:\n**   RBU has finished building the *-oal file. The next call to sqlite3rbu_step()\n**   will move the *-oal file to the equivalent *-wal path. If the current\n**   operation is an RBU update, then the updated version of the database\n**   file will become visible to ordinary SQLite clients following the next\n**   call to sqlite3rbu_step().\n**\n** SQLITE_RBU_STATE_CHECKPOINT:\n**   RBU is currently performing an incremental checkpoint. The next call to\n**   sqlite3rbu_step() will copy a page of data from the *-wal file into\n**   the target database file.\n**\n** SQLITE_RBU_STATE_DONE:\n**   The RBU operation has finished. Any subsequent calls to sqlite3rbu_step()\n**   will immediately return SQLITE_DONE.\n**\n** SQLITE_RBU_STATE_ERROR:\n**   An error has occurred. Any subsequent calls to sqlite3rbu_step() will\n**   immediately return the SQLite error code associated with the error.\n*/\n#define SQLITE_RBU_STATE_OAL        1\n#define SQLITE_RBU_STATE_MOVE       2\n#define SQLITE_RBU_STATE_CHECKPOINT 3\n#define SQLITE_RBU_STATE_DONE       4\n#define SQLITE_RBU_STATE_ERROR      5\n\nSQLITE_API int sqlite3rbu_state(sqlite3rbu *pRbu);\n\n/*\n** Create an RBU VFS named zName that accesses the underlying file-system\n** via existing VFS zParent. Or, if the zParent parameter is passed NULL, \n** then the new RBU VFS uses the default system VFS to access the file-system.\n** The new object is registered as a non-default VFS with SQLite before \n** returning.\n**\n** Part of the RBU implementation uses a custom VFS object. Usually, this\n** object is created and deleted automatically by RBU. \n**\n** The exception is for applications that also use zipvfs. In this case,\n** the custom VFS must be explicitly created by the user before the RBU\n** handle is opened. The RBU VFS should be installed so that the zipvfs\n** VFS uses the RBU VFS, which in turn uses any other VFS layers in use \n** (for example multiplexor) to access the file-system. For example,\n** to assemble an RBU enabled VFS stack that uses both zipvfs and \n** multiplexor (error checking omitted):\n**\n**     // Create a VFS named \"multiplex\" (not the default).\n**     sqlite3_multiplex_initialize(0, 0);\n**\n**     // Create an rbu VFS named \"rbu\" that uses multiplexor. If the\n**     // second argument were replaced with NULL, the \"rbu\" VFS would\n**     // access the file-system via the system default VFS, bypassing the\n**     // multiplexor.\n**     sqlite3rbu_create_vfs(\"rbu\", \"multiplex\");\n**\n**     // Create a zipvfs VFS named \"zipvfs\" that uses rbu.\n**     zipvfs_create_vfs_v3(\"zipvfs\", \"rbu\", 0, xCompressorAlgorithmDetector);\n**\n**     // Make zipvfs the default VFS.\n**     sqlite3_vfs_register(sqlite3_vfs_find(\"zipvfs\"), 1);\n**\n** Because the default VFS created above includes a RBU functionality, it\n** may be used by RBU clients. Attempting to use RBU with a zipvfs VFS stack\n** that does not include the RBU layer results in an error.\n**\n** The overhead of adding the \"rbu\" VFS to the system is negligible for \n** non-RBU users. There is no harm in an application accessing the \n** file-system via \"rbu\" all the time, even if it only uses RBU functionality \n** occasionally.\n*/\nSQLITE_API int sqlite3rbu_create_vfs(const char *zName, const char *zParent);\n\n/*\n** Deregister and destroy an RBU vfs created by an earlier call to\n** sqlite3rbu_create_vfs().\n**\n** VFS objects are not reference counted. If a VFS object is destroyed\n** before all database handles that use it have been closed, the results\n** are undefined.\n*/\nSQLITE_API void sqlite3rbu_destroy_vfs(const char *zName);\n\n#if 0\n}  /* end of the 'extern \"C\"' block */\n#endif\n\n#endif /* _SQLITE3RBU_H */\n\n/************** End of sqlite3rbu.h ******************************************/\n/************** Continuing where we left off in sqlite3rbu.c *****************/\n\n#if defined(_WIN32_WCE)\n/* #include \"windows.h\" */\n#endif\n\n/* Maximum number of prepared UPDATE statements held by this module */\n#define SQLITE_RBU_UPDATE_CACHESIZE 16\n\n/* Delta checksums disabled by default.  Compile with -DRBU_ENABLE_DELTA_CKSUM\n** to enable checksum verification.\n*/\n#ifndef RBU_ENABLE_DELTA_CKSUM\n# define RBU_ENABLE_DELTA_CKSUM 0\n#endif\n\n/*\n** Swap two objects of type TYPE.\n*/\n#if !defined(SQLITE_AMALGAMATION)\n# define SWAP(TYPE,A,B) {TYPE t=A; A=B; B=t;}\n#endif\n\n/*\n** The rbu_state table is used to save the state of a partially applied\n** update so that it can be resumed later. The table consists of integer\n** keys mapped to values as follows:\n**\n** RBU_STATE_STAGE:\n**   May be set to integer values 1, 2, 4 or 5. As follows:\n**       1: the *-rbu file is currently under construction.\n**       2: the *-rbu file has been constructed, but not yet moved \n**          to the *-wal path.\n**       4: the checkpoint is underway.\n**       5: the rbu update has been checkpointed.\n**\n** RBU_STATE_TBL:\n**   Only valid if STAGE==1. The target database name of the table \n**   currently being written.\n**\n** RBU_STATE_IDX:\n**   Only valid if STAGE==1. The target database name of the index \n**   currently being written, or NULL if the main table is currently being\n**   updated.\n**\n** RBU_STATE_ROW:\n**   Only valid if STAGE==1. Number of rows already processed for the current\n**   table/index.\n**\n** RBU_STATE_PROGRESS:\n**   Trbul number of sqlite3rbu_step() calls made so far as part of this\n**   rbu update.\n**\n** RBU_STATE_CKPT:\n**   Valid if STAGE==4. The 64-bit checksum associated with the wal-index\n**   header created by recovering the *-wal file. This is used to detect\n**   cases when another client appends frames to the *-wal file in the\n**   middle of an incremental checkpoint (an incremental checkpoint cannot\n**   be continued if this happens).\n**\n** RBU_STATE_COOKIE:\n**   Valid if STAGE==1. The current change-counter cookie value in the \n**   target db file.\n**\n** RBU_STATE_OALSZ:\n**   Valid if STAGE==1. The size in bytes of the *-oal file.\n*/\n#define RBU_STATE_STAGE        1\n#define RBU_STATE_TBL          2\n#define RBU_STATE_IDX          3\n#define RBU_STATE_ROW          4\n#define RBU_STATE_PROGRESS     5\n#define RBU_STATE_CKPT         6\n#define RBU_STATE_COOKIE       7\n#define RBU_STATE_OALSZ        8\n#define RBU_STATE_PHASEONESTEP 9\n\n#define RBU_STAGE_OAL         1\n#define RBU_STAGE_MOVE        2\n#define RBU_STAGE_CAPTURE     3\n#define RBU_STAGE_CKPT        4\n#define RBU_STAGE_DONE        5\n\n\n#define RBU_CREATE_STATE \\\n  \"CREATE TABLE IF NOT EXISTS %s.rbu_state(k INTEGER PRIMARY KEY, v)\"\n\ntypedef struct RbuFrame RbuFrame;\ntypedef struct RbuObjIter RbuObjIter;\ntypedef struct RbuState RbuState;\ntypedef struct rbu_vfs rbu_vfs;\ntypedef struct rbu_file rbu_file;\ntypedef struct RbuUpdateStmt RbuUpdateStmt;\n\n#if !defined(SQLITE_AMALGAMATION)\ntypedef unsigned int u32;\ntypedef unsigned short u16;\ntypedef unsigned char u8;\ntypedef sqlite3_int64 i64;\n#endif\n\n/*\n** These values must match the values defined in wal.c for the equivalent\n** locks. These are not magic numbers as they are part of the SQLite file\n** format.\n*/\n#define WAL_LOCK_WRITE  0\n#define WAL_LOCK_CKPT   1\n#define WAL_LOCK_READ0  3\n\n#define SQLITE_FCNTL_RBUCNT    5149216\n\n/*\n** A structure to store values read from the rbu_state table in memory.\n*/\nstruct RbuState {\n  int eStage;\n  char *zTbl;\n  char *zIdx;\n  i64 iWalCksum;\n  int nRow;\n  i64 nProgress;\n  u32 iCookie;\n  i64 iOalSz;\n  i64 nPhaseOneStep;\n};\n\nstruct RbuUpdateStmt {\n  char *zMask;                    /* Copy of update mask used with pUpdate */\n  sqlite3_stmt *pUpdate;          /* Last update statement (or NULL) */\n  RbuUpdateStmt *pNext;\n};\n\n/*\n** An iterator of this type is used to iterate through all objects in\n** the target database that require updating. For each such table, the\n** iterator visits, in order:\n**\n**     * the table itself, \n**     * each index of the table (zero or more points to visit), and\n**     * a special \"cleanup table\" state.\n**\n** abIndexed:\n**   If the table has no indexes on it, abIndexed is set to NULL. Otherwise,\n**   it points to an array of flags nTblCol elements in size. The flag is\n**   set for each column that is either a part of the PK or a part of an\n**   index. Or clear otherwise.\n**   \n*/\nstruct RbuObjIter {\n  sqlite3_stmt *pTblIter;         /* Iterate through tables */\n  sqlite3_stmt *pIdxIter;         /* Index iterator */\n  int nTblCol;                    /* Size of azTblCol[] array */\n  char **azTblCol;                /* Array of unquoted target column names */\n  char **azTblType;               /* Array of target column types */\n  int *aiSrcOrder;                /* src table col -> target table col */\n  u8 *abTblPk;                    /* Array of flags, set on target PK columns */\n  u8 *abNotNull;                  /* Array of flags, set on NOT NULL columns */\n  u8 *abIndexed;                  /* Array of flags, set on indexed & PK cols */\n  int eType;                      /* Table type - an RBU_PK_XXX value */\n\n  /* Output variables. zTbl==0 implies EOF. */\n  int bCleanup;                   /* True in \"cleanup\" state */\n  const char *zTbl;               /* Name of target db table */\n  const char *zDataTbl;           /* Name of rbu db table (or null) */\n  const char *zIdx;               /* Name of target db index (or null) */\n  int iTnum;                      /* Root page of current object */\n  int iPkTnum;                    /* If eType==EXTERNAL, root of PK index */\n  int bUnique;                    /* Current index is unique */\n  int nIndex;                     /* Number of aux. indexes on table zTbl */\n\n  /* Statements created by rbuObjIterPrepareAll() */\n  int nCol;                       /* Number of columns in current object */\n  sqlite3_stmt *pSelect;          /* Source data */\n  sqlite3_stmt *pInsert;          /* Statement for INSERT operations */\n  sqlite3_stmt *pDelete;          /* Statement for DELETE ops */\n  sqlite3_stmt *pTmpInsert;       /* Insert into rbu_tmp_$zDataTbl */\n\n  /* Last UPDATE used (for PK b-tree updates only), or NULL. */\n  RbuUpdateStmt *pRbuUpdate;\n};\n\n/*\n** Values for RbuObjIter.eType\n**\n**     0: Table does not exist (error)\n**     1: Table has an implicit rowid.\n**     2: Table has an explicit IPK column.\n**     3: Table has an external PK index.\n**     4: Table is WITHOUT ROWID.\n**     5: Table is a virtual table.\n*/\n#define RBU_PK_NOTABLE        0\n#define RBU_PK_NONE           1\n#define RBU_PK_IPK            2\n#define RBU_PK_EXTERNAL       3\n#define RBU_PK_WITHOUT_ROWID  4\n#define RBU_PK_VTAB           5\n\n\n/*\n** Within the RBU_STAGE_OAL stage, each call to sqlite3rbu_step() performs\n** one of the following operations.\n*/\n#define RBU_INSERT     1          /* Insert on a main table b-tree */\n#define RBU_DELETE     2          /* Delete a row from a main table b-tree */\n#define RBU_REPLACE    3          /* Delete and then insert a row */\n#define RBU_IDX_DELETE 4          /* Delete a row from an aux. index b-tree */\n#define RBU_IDX_INSERT 5          /* Insert on an aux. index b-tree */\n\n#define RBU_UPDATE     6          /* Update a row in a main table b-tree */\n\n/*\n** A single step of an incremental checkpoint - frame iWalFrame of the wal\n** file should be copied to page iDbPage of the database file.\n*/\nstruct RbuFrame {\n  u32 iDbPage;\n  u32 iWalFrame;\n};\n\n/*\n** RBU handle.\n**\n** nPhaseOneStep:\n**   If the RBU database contains an rbu_count table, this value is set to\n**   a running estimate of the number of b-tree operations required to \n**   finish populating the *-oal file. This allows the sqlite3_bp_progress()\n**   API to calculate the permyriadage progress of populating the *-oal file\n**   using the formula:\n**\n**     permyriadage = (10000 * nProgress) / nPhaseOneStep\n**\n**   nPhaseOneStep is initialized to the sum of:\n**\n**     nRow * (nIndex + 1)\n**\n**   for all source tables in the RBU database, where nRow is the number\n**   of rows in the source table and nIndex the number of indexes on the\n**   corresponding target database table.\n**\n**   This estimate is accurate if the RBU update consists entirely of\n**   INSERT operations. However, it is inaccurate if:\n**\n**     * the RBU update contains any UPDATE operations. If the PK specified\n**       for an UPDATE operation does not exist in the target table, then\n**       no b-tree operations are required on index b-trees. Or if the \n**       specified PK does exist, then (nIndex*2) such operations are\n**       required (one delete and one insert on each index b-tree).\n**\n**     * the RBU update contains any DELETE operations for which the specified\n**       PK does not exist. In this case no operations are required on index\n**       b-trees.\n**\n**     * the RBU update contains REPLACE operations. These are similar to\n**       UPDATE operations.\n**\n**   nPhaseOneStep is updated to account for the conditions above during the\n**   first pass of each source table. The updated nPhaseOneStep value is\n**   stored in the rbu_state table if the RBU update is suspended.\n*/\nstruct sqlite3rbu {\n  int eStage;                     /* Value of RBU_STATE_STAGE field */\n  sqlite3 *dbMain;                /* target database handle */\n  sqlite3 *dbRbu;                 /* rbu database handle */\n  char *zTarget;                  /* Path to target db */\n  char *zRbu;                     /* Path to rbu db */\n  char *zState;                   /* Path to state db (or NULL if zRbu) */\n  char zStateDb[5];               /* Db name for state (\"stat\" or \"main\") */\n  int rc;                         /* Value returned by last rbu_step() call */\n  char *zErrmsg;                  /* Error message if rc!=SQLITE_OK */\n  int nStep;                      /* Rows processed for current object */\n  int nProgress;                  /* Rows processed for all objects */\n  RbuObjIter objiter;             /* Iterator for skipping through tbl/idx */\n  const char *zVfsName;           /* Name of automatically created rbu vfs */\n  rbu_file *pTargetFd;            /* File handle open on target db */\n  int nPagePerSector;             /* Pages per sector for pTargetFd */\n  i64 iOalSz;\n  i64 nPhaseOneStep;\n\n  /* The following state variables are used as part of the incremental\n  ** checkpoint stage (eStage==RBU_STAGE_CKPT). See comments surrounding\n  ** function rbuSetupCheckpoint() for details.  */\n  u32 iMaxFrame;                  /* Largest iWalFrame value in aFrame[] */\n  u32 mLock;\n  int nFrame;                     /* Entries in aFrame[] array */\n  int nFrameAlloc;                /* Allocated size of aFrame[] array */\n  RbuFrame *aFrame;\n  int pgsz;\n  u8 *aBuf;\n  i64 iWalCksum;\n  i64 szTemp;                     /* Current size of all temp files in use */\n  i64 szTempLimit;                /* Total size limit for temp files */\n\n  /* Used in RBU vacuum mode only */\n  int nRbu;                       /* Number of RBU VFS in the stack */\n  rbu_file *pRbuFd;               /* Fd for main db of dbRbu */\n};\n\n/*\n** An rbu VFS is implemented using an instance of this structure.\n**\n** Variable pRbu is only non-NULL for automatically created RBU VFS objects.\n** It is NULL for RBU VFS objects created explicitly using\n** sqlite3rbu_create_vfs(). It is used to track the total amount of temp\n** space used by the RBU handle.\n*/\nstruct rbu_vfs {\n  sqlite3_vfs base;               /* rbu VFS shim methods */\n  sqlite3_vfs *pRealVfs;          /* Underlying VFS */\n  sqlite3_mutex *mutex;           /* Mutex to protect pMain */\n  sqlite3rbu *pRbu;               /* Owner RBU object */\n  rbu_file *pMain;                /* Linked list of main db files */\n};\n\n/*\n** Each file opened by an rbu VFS is represented by an instance of\n** the following structure.\n**\n** If this is a temporary file (pRbu!=0 && flags&DELETE_ON_CLOSE), variable\n** \"sz\" is set to the current size of the database file.\n*/\nstruct rbu_file {\n  sqlite3_file base;              /* sqlite3_file methods */\n  sqlite3_file *pReal;            /* Underlying file handle */\n  rbu_vfs *pRbuVfs;               /* Pointer to the rbu_vfs object */\n  sqlite3rbu *pRbu;               /* Pointer to rbu object (rbu target only) */\n  i64 sz;                         /* Size of file in bytes (temp only) */\n\n  int openFlags;                  /* Flags this file was opened with */\n  u32 iCookie;                    /* Cookie value for main db files */\n  u8 iWriteVer;                   /* \"write-version\" value for main db files */\n  u8 bNolock;                     /* True to fail EXCLUSIVE locks */\n\n  int nShm;                       /* Number of entries in apShm[] array */\n  char **apShm;                   /* Array of mmap'd *-shm regions */\n  char *zDel;                     /* Delete this when closing file */\n\n  const char *zWal;               /* Wal filename for this main db file */\n  rbu_file *pWalFd;               /* Wal file descriptor for this main db */\n  rbu_file *pMainNext;            /* Next MAIN_DB file */\n};\n\n/*\n** True for an RBU vacuum handle, or false otherwise.\n*/\n#define rbuIsVacuum(p) ((p)->zTarget==0)\n\n\n/*************************************************************************\n** The following three functions, found below:\n**\n**   rbuDeltaGetInt()\n**   rbuDeltaChecksum()\n**   rbuDeltaApply()\n**\n** are lifted from the fossil source code (http://fossil-scm.org). They\n** are used to implement the scalar SQL function rbu_fossil_delta().\n*/\n\n/*\n** Read bytes from *pz and convert them into a positive integer.  When\n** finished, leave *pz pointing to the first character past the end of\n** the integer.  The *pLen parameter holds the length of the string\n** in *pz and is decremented once for each character in the integer.\n*/\nstatic unsigned int rbuDeltaGetInt(const char **pz, int *pLen){\n  static const signed char zValue[] = {\n    -1, -1, -1, -1, -1, -1, -1, -1,   -1, -1, -1, -1, -1, -1, -1, -1,\n    -1, -1, -1, -1, -1, -1, -1, -1,   -1, -1, -1, -1, -1, -1, -1, -1,\n    -1, -1, -1, -1, -1, -1, -1, -1,   -1, -1, -1, -1, -1, -1, -1, -1,\n     0,  1,  2,  3,  4,  5,  6,  7,    8,  9, -1, -1, -1, -1, -1, -1,\n    -1, 10, 11, 12, 13, 14, 15, 16,   17, 18, 19, 20, 21, 22, 23, 24,\n    25, 26, 27, 28, 29, 30, 31, 32,   33, 34, 35, -1, -1, -1, -1, 36,\n    -1, 37, 38, 39, 40, 41, 42, 43,   44, 45, 46, 47, 48, 49, 50, 51,\n    52, 53, 54, 55, 56, 57, 58, 59,   60, 61, 62, -1, -1, -1, 63, -1,\n  };\n  unsigned int v = 0;\n  int c;\n  unsigned char *z = (unsigned char*)*pz;\n  unsigned char *zStart = z;\n  while( (c = zValue[0x7f&*(z++)])>=0 ){\n     v = (v<<6) + c;\n  }\n  z--;\n  *pLen -= z - zStart;\n  *pz = (char*)z;\n  return v;\n}\n\n#if RBU_ENABLE_DELTA_CKSUM\n/*\n** Compute a 32-bit checksum on the N-byte buffer.  Return the result.\n*/\nstatic unsigned int rbuDeltaChecksum(const char *zIn, size_t N){\n  const unsigned char *z = (const unsigned char *)zIn;\n  unsigned sum0 = 0;\n  unsigned sum1 = 0;\n  unsigned sum2 = 0;\n  unsigned sum3 = 0;\n  while(N >= 16){\n    sum0 += ((unsigned)z[0] + z[4] + z[8] + z[12]);\n    sum1 += ((unsigned)z[1] + z[5] + z[9] + z[13]);\n    sum2 += ((unsigned)z[2] + z[6] + z[10]+ z[14]);\n    sum3 += ((unsigned)z[3] + z[7] + z[11]+ z[15]);\n    z += 16;\n    N -= 16;\n  }\n  while(N >= 4){\n    sum0 += z[0];\n    sum1 += z[1];\n    sum2 += z[2];\n    sum3 += z[3];\n    z += 4;\n    N -= 4;\n  }\n  sum3 += (sum2 << 8) + (sum1 << 16) + (sum0 << 24);\n  switch(N){\n    case 3:   sum3 += (z[2] << 8);\n    case 2:   sum3 += (z[1] << 16);\n    case 1:   sum3 += (z[0] << 24);\n    default:  ;\n  }\n  return sum3;\n}\n#endif\n\n/*\n** Apply a delta.\n**\n** The output buffer should be big enough to hold the whole output\n** file and a NUL terminator at the end.  The delta_output_size()\n** routine will determine this size for you.\n**\n** The delta string should be null-terminated.  But the delta string\n** may contain embedded NUL characters (if the input and output are\n** binary files) so we also have to pass in the length of the delta in\n** the lenDelta parameter.\n**\n** This function returns the size of the output file in bytes (excluding\n** the final NUL terminator character).  Except, if the delta string is\n** malformed or intended for use with a source file other than zSrc,\n** then this routine returns -1.\n**\n** Refer to the delta_create() documentation above for a description\n** of the delta file format.\n*/\nstatic int rbuDeltaApply(\n  const char *zSrc,      /* The source or pattern file */\n  int lenSrc,            /* Length of the source file */\n  const char *zDelta,    /* Delta to apply to the pattern */\n  int lenDelta,          /* Length of the delta */\n  char *zOut             /* Write the output into this preallocated buffer */\n){\n  unsigned int limit;\n  unsigned int total = 0;\n#if RBU_ENABLE_DELTA_CKSUM\n  char *zOrigOut = zOut;\n#endif\n\n  limit = rbuDeltaGetInt(&zDelta, &lenDelta);\n  if( *zDelta!='\\n' ){\n    /* ERROR: size integer not terminated by \"\\n\" */\n    return -1;\n  }\n  zDelta++; lenDelta--;\n  while( *zDelta && lenDelta>0 ){\n    unsigned int cnt, ofst;\n    cnt = rbuDeltaGetInt(&zDelta, &lenDelta);\n    switch( zDelta[0] ){\n      case '@': {\n        zDelta++; lenDelta--;\n        ofst = rbuDeltaGetInt(&zDelta, &lenDelta);\n        if( lenDelta>0 && zDelta[0]!=',' ){\n          /* ERROR: copy command not terminated by ',' */\n          return -1;\n        }\n        zDelta++; lenDelta--;\n        total += cnt;\n        if( total>limit ){\n          /* ERROR: copy exceeds output file size */\n          return -1;\n        }\n        if( (int)(ofst+cnt) > lenSrc ){\n          /* ERROR: copy extends past end of input */\n          return -1;\n        }\n        memcpy(zOut, &zSrc[ofst], cnt);\n        zOut += cnt;\n        break;\n      }\n      case ':': {\n        zDelta++; lenDelta--;\n        total += cnt;\n        if( total>limit ){\n          /* ERROR:  insert command gives an output larger than predicted */\n          return -1;\n        }\n        if( (int)cnt>lenDelta ){\n          /* ERROR: insert count exceeds size of delta */\n          return -1;\n        }\n        memcpy(zOut, zDelta, cnt);\n        zOut += cnt;\n        zDelta += cnt;\n        lenDelta -= cnt;\n        break;\n      }\n      case ';': {\n        zDelta++; lenDelta--;\n        zOut[0] = 0;\n#if RBU_ENABLE_DELTA_CKSUM\n        if( cnt!=rbuDeltaChecksum(zOrigOut, total) ){\n          /* ERROR:  bad checksum */\n          return -1;\n        }\n#endif\n        if( total!=limit ){\n          /* ERROR: generated size does not match predicted size */\n          return -1;\n        }\n        return total;\n      }\n      default: {\n        /* ERROR: unknown delta operator */\n        return -1;\n      }\n    }\n  }\n  /* ERROR: unterminated delta */\n  return -1;\n}\n\nstatic int rbuDeltaOutputSize(const char *zDelta, int lenDelta){\n  int size;\n  size = rbuDeltaGetInt(&zDelta, &lenDelta);\n  if( *zDelta!='\\n' ){\n    /* ERROR: size integer not terminated by \"\\n\" */\n    return -1;\n  }\n  return size;\n}\n\n/*\n** End of code taken from fossil.\n*************************************************************************/\n\n/*\n** Implementation of SQL scalar function rbu_fossil_delta().\n**\n** This function applies a fossil delta patch to a blob. Exactly two\n** arguments must be passed to this function. The first is the blob to\n** patch and the second the patch to apply. If no error occurs, this\n** function returns the patched blob.\n*/\nstatic void rbuFossilDeltaFunc(\n  sqlite3_context *context,\n  int argc,\n  sqlite3_value **argv\n){\n  const char *aDelta;\n  int nDelta;\n  const char *aOrig;\n  int nOrig;\n\n  int nOut;\n  int nOut2;\n  char *aOut;\n\n  assert( argc==2 );\n\n  nOrig = sqlite3_value_bytes(argv[0]);\n  aOrig = (const char*)sqlite3_value_blob(argv[0]);\n  nDelta = sqlite3_value_bytes(argv[1]);\n  aDelta = (const char*)sqlite3_value_blob(argv[1]);\n\n  /* Figure out the size of the output */\n  nOut = rbuDeltaOutputSize(aDelta, nDelta);\n  if( nOut<0 ){\n    sqlite3_result_error(context, \"corrupt fossil delta\", -1);\n    return;\n  }\n\n  aOut = sqlite3_malloc(nOut+1);\n  if( aOut==0 ){\n    sqlite3_result_error_nomem(context);\n  }else{\n    nOut2 = rbuDeltaApply(aOrig, nOrig, aDelta, nDelta, aOut);\n    if( nOut2!=nOut ){\n      sqlite3_result_error(context, \"corrupt fossil delta\", -1);\n    }else{\n      sqlite3_result_blob(context, aOut, nOut, sqlite3_free);\n    }\n  }\n}\n\n\n/*\n** Prepare the SQL statement in buffer zSql against database handle db.\n** If successful, set *ppStmt to point to the new statement and return\n** SQLITE_OK. \n**\n** Otherwise, if an error does occur, set *ppStmt to NULL and return\n** an SQLite error code. Additionally, set output variable *pzErrmsg to\n** point to a buffer containing an error message. It is the responsibility\n** of the caller to (eventually) free this buffer using sqlite3_free().\n*/\nstatic int prepareAndCollectError(\n  sqlite3 *db, \n  sqlite3_stmt **ppStmt,\n  char **pzErrmsg,\n  const char *zSql\n){\n  int rc = sqlite3_prepare_v2(db, zSql, -1, ppStmt, 0);\n  if( rc!=SQLITE_OK ){\n    *pzErrmsg = sqlite3_mprintf(\"%s\", sqlite3_errmsg(db));\n    *ppStmt = 0;\n  }\n  return rc;\n}\n\n/*\n** Reset the SQL statement passed as the first argument. Return a copy\n** of the value returned by sqlite3_reset().\n**\n** If an error has occurred, then set *pzErrmsg to point to a buffer\n** containing an error message. It is the responsibility of the caller\n** to eventually free this buffer using sqlite3_free().\n*/\nstatic int resetAndCollectError(sqlite3_stmt *pStmt, char **pzErrmsg){\n  int rc = sqlite3_reset(pStmt);\n  if( rc!=SQLITE_OK ){\n    *pzErrmsg = sqlite3_mprintf(\"%s\", sqlite3_errmsg(sqlite3_db_handle(pStmt)));\n  }\n  return rc;\n}\n\n/*\n** Unless it is NULL, argument zSql points to a buffer allocated using\n** sqlite3_malloc containing an SQL statement. This function prepares the SQL\n** statement against database db and frees the buffer. If statement \n** compilation is successful, *ppStmt is set to point to the new statement \n** handle and SQLITE_OK is returned. \n**\n** Otherwise, if an error occurs, *ppStmt is set to NULL and an error code\n** returned. In this case, *pzErrmsg may also be set to point to an error\n** message. It is the responsibility of the caller to free this error message\n** buffer using sqlite3_free().\n**\n** If argument zSql is NULL, this function assumes that an OOM has occurred.\n** In this case SQLITE_NOMEM is returned and *ppStmt set to NULL.\n*/\nstatic int prepareFreeAndCollectError(\n  sqlite3 *db, \n  sqlite3_stmt **ppStmt,\n  char **pzErrmsg,\n  char *zSql\n){\n  int rc;\n  assert( *pzErrmsg==0 );\n  if( zSql==0 ){\n    rc = SQLITE_NOMEM;\n    *ppStmt = 0;\n  }else{\n    rc = prepareAndCollectError(db, ppStmt, pzErrmsg, zSql);\n    sqlite3_free(zSql);\n  }\n  return rc;\n}\n\n/*\n** Free the RbuObjIter.azTblCol[] and RbuObjIter.abTblPk[] arrays allocated\n** by an earlier call to rbuObjIterCacheTableInfo().\n*/\nstatic void rbuObjIterFreeCols(RbuObjIter *pIter){\n  int i;\n  for(i=0; i<pIter->nTblCol; i++){\n    sqlite3_free(pIter->azTblCol[i]);\n    sqlite3_free(pIter->azTblType[i]);\n  }\n  sqlite3_free(pIter->azTblCol);\n  pIter->azTblCol = 0;\n  pIter->azTblType = 0;\n  pIter->aiSrcOrder = 0;\n  pIter->abTblPk = 0;\n  pIter->abNotNull = 0;\n  pIter->nTblCol = 0;\n  pIter->eType = 0;               /* Invalid value */\n}\n\n/*\n** Finalize all statements and free all allocations that are specific to\n** the current object (table/index pair).\n*/\nstatic void rbuObjIterClearStatements(RbuObjIter *pIter){\n  RbuUpdateStmt *pUp;\n\n  sqlite3_finalize(pIter->pSelect);\n  sqlite3_finalize(pIter->pInsert);\n  sqlite3_finalize(pIter->pDelete);\n  sqlite3_finalize(pIter->pTmpInsert);\n  pUp = pIter->pRbuUpdate;\n  while( pUp ){\n    RbuUpdateStmt *pTmp = pUp->pNext;\n    sqlite3_finalize(pUp->pUpdate);\n    sqlite3_free(pUp);\n    pUp = pTmp;\n  }\n  \n  pIter->pSelect = 0;\n  pIter->pInsert = 0;\n  pIter->pDelete = 0;\n  pIter->pRbuUpdate = 0;\n  pIter->pTmpInsert = 0;\n  pIter->nCol = 0;\n}\n\n/*\n** Clean up any resources allocated as part of the iterator object passed\n** as the only argument.\n*/\nstatic void rbuObjIterFinalize(RbuObjIter *pIter){\n  rbuObjIterClearStatements(pIter);\n  sqlite3_finalize(pIter->pTblIter);\n  sqlite3_finalize(pIter->pIdxIter);\n  rbuObjIterFreeCols(pIter);\n  memset(pIter, 0, sizeof(RbuObjIter));\n}\n\n/*\n** Advance the iterator to the next position.\n**\n** If no error occurs, SQLITE_OK is returned and the iterator is left \n** pointing to the next entry. Otherwise, an error code and message is \n** left in the RBU handle passed as the first argument. A copy of the \n** error code is returned.\n*/\nstatic int rbuObjIterNext(sqlite3rbu *p, RbuObjIter *pIter){\n  int rc = p->rc;\n  if( rc==SQLITE_OK ){\n\n    /* Free any SQLite statements used while processing the previous object */ \n    rbuObjIterClearStatements(pIter);\n    if( pIter->zIdx==0 ){\n      rc = sqlite3_exec(p->dbMain,\n          \"DROP TRIGGER IF EXISTS temp.rbu_insert_tr;\"\n          \"DROP TRIGGER IF EXISTS temp.rbu_update1_tr;\"\n          \"DROP TRIGGER IF EXISTS temp.rbu_update2_tr;\"\n          \"DROP TRIGGER IF EXISTS temp.rbu_delete_tr;\"\n          , 0, 0, &p->zErrmsg\n      );\n    }\n\n    if( rc==SQLITE_OK ){\n      if( pIter->bCleanup ){\n        rbuObjIterFreeCols(pIter);\n        pIter->bCleanup = 0;\n        rc = sqlite3_step(pIter->pTblIter);\n        if( rc!=SQLITE_ROW ){\n          rc = resetAndCollectError(pIter->pTblIter, &p->zErrmsg);\n          pIter->zTbl = 0;\n        }else{\n          pIter->zTbl = (const char*)sqlite3_column_text(pIter->pTblIter, 0);\n          pIter->zDataTbl = (const char*)sqlite3_column_text(pIter->pTblIter,1);\n          rc = (pIter->zDataTbl && pIter->zTbl) ? SQLITE_OK : SQLITE_NOMEM;\n        }\n      }else{\n        if( pIter->zIdx==0 ){\n          sqlite3_stmt *pIdx = pIter->pIdxIter;\n          rc = sqlite3_bind_text(pIdx, 1, pIter->zTbl, -1, SQLITE_STATIC);\n        }\n        if( rc==SQLITE_OK ){\n          rc = sqlite3_step(pIter->pIdxIter);\n          if( rc!=SQLITE_ROW ){\n            rc = resetAndCollectError(pIter->pIdxIter, &p->zErrmsg);\n            pIter->bCleanup = 1;\n            pIter->zIdx = 0;\n          }else{\n            pIter->zIdx = (const char*)sqlite3_column_text(pIter->pIdxIter, 0);\n            pIter->iTnum = sqlite3_column_int(pIter->pIdxIter, 1);\n            pIter->bUnique = sqlite3_column_int(pIter->pIdxIter, 2);\n            rc = pIter->zIdx ? SQLITE_OK : SQLITE_NOMEM;\n          }\n        }\n      }\n    }\n  }\n\n  if( rc!=SQLITE_OK ){\n    rbuObjIterFinalize(pIter);\n    p->rc = rc;\n  }\n  return rc;\n}\n\n\n/*\n** The implementation of the rbu_target_name() SQL function. This function\n** accepts one or two arguments. The first argument is the name of a table -\n** the name of a table in the RBU database.  The second, if it is present, is 1\n** for a view or 0 for a table. \n**\n** For a non-vacuum RBU handle, if the table name matches the pattern:\n**\n**     data[0-9]_<name>\n**\n** where <name> is any sequence of 1 or more characters, <name> is returned.\n** Otherwise, if the only argument does not match the above pattern, an SQL\n** NULL is returned.\n**\n**     \"data_t1\"     -> \"t1\"\n**     \"data0123_t2\" -> \"t2\"\n**     \"dataAB_t3\"   -> NULL\n**\n** For an rbu vacuum handle, a copy of the first argument is returned if\n** the second argument is either missing or 0 (not a view).\n*/\nstatic void rbuTargetNameFunc(\n  sqlite3_context *pCtx,\n  int argc,\n  sqlite3_value **argv\n){\n  sqlite3rbu *p = sqlite3_user_data(pCtx);\n  const char *zIn;\n  assert( argc==1 || argc==2 );\n\n  zIn = (const char*)sqlite3_value_text(argv[0]);\n  if( zIn ){\n    if( rbuIsVacuum(p) ){\n      if( argc==1 || 0==sqlite3_value_int(argv[1]) ){\n        sqlite3_result_text(pCtx, zIn, -1, SQLITE_STATIC);\n      }\n    }else{\n      if( strlen(zIn)>4 && memcmp(\"data\", zIn, 4)==0 ){\n        int i;\n        for(i=4; zIn[i]>='0' && zIn[i]<='9'; i++);\n        if( zIn[i]=='_' && zIn[i+1] ){\n          sqlite3_result_text(pCtx, &zIn[i+1], -1, SQLITE_STATIC);\n        }\n      }\n    }\n  }\n}\n\n/*\n** Initialize the iterator structure passed as the second argument.\n**\n** If no error occurs, SQLITE_OK is returned and the iterator is left \n** pointing to the first entry. Otherwise, an error code and message is \n** left in the RBU handle passed as the first argument. A copy of the \n** error code is returned.\n*/\nstatic int rbuObjIterFirst(sqlite3rbu *p, RbuObjIter *pIter){\n  int rc;\n  memset(pIter, 0, sizeof(RbuObjIter));\n\n  rc = prepareFreeAndCollectError(p->dbRbu, &pIter->pTblIter, &p->zErrmsg, \n    sqlite3_mprintf(\n      \"SELECT rbu_target_name(name, type='view') AS target, name \"\n      \"FROM sqlite_master \"\n      \"WHERE type IN ('table', 'view') AND target IS NOT NULL \"\n      \" %s \"\n      \"ORDER BY name\"\n  , rbuIsVacuum(p) ? \"AND rootpage!=0 AND rootpage IS NOT NULL\" : \"\"));\n\n  if( rc==SQLITE_OK ){\n    rc = prepareAndCollectError(p->dbMain, &pIter->pIdxIter, &p->zErrmsg,\n        \"SELECT name, rootpage, sql IS NULL OR substr(8, 6)=='UNIQUE' \"\n        \"  FROM main.sqlite_master \"\n        \"  WHERE type='index' AND tbl_name = ?\"\n    );\n  }\n\n  pIter->bCleanup = 1;\n  p->rc = rc;\n  return rbuObjIterNext(p, pIter);\n}\n\n/*\n** This is a wrapper around \"sqlite3_mprintf(zFmt, ...)\". If an OOM occurs,\n** an error code is stored in the RBU handle passed as the first argument.\n**\n** If an error has already occurred (p->rc is already set to something other\n** than SQLITE_OK), then this function returns NULL without modifying the\n** stored error code. In this case it still calls sqlite3_free() on any \n** printf() parameters associated with %z conversions.\n*/\nstatic char *rbuMPrintf(sqlite3rbu *p, const char *zFmt, ...){\n  char *zSql = 0;\n  va_list ap;\n  va_start(ap, zFmt);\n  zSql = sqlite3_vmprintf(zFmt, ap);\n  if( p->rc==SQLITE_OK ){\n    if( zSql==0 ) p->rc = SQLITE_NOMEM;\n  }else{\n    sqlite3_free(zSql);\n    zSql = 0;\n  }\n  va_end(ap);\n  return zSql;\n}\n\n/*\n** Argument zFmt is a sqlite3_mprintf() style format string. The trailing\n** arguments are the usual subsitution values. This function performs\n** the printf() style substitutions and executes the result as an SQL\n** statement on the RBU handles database.\n**\n** If an error occurs, an error code and error message is stored in the\n** RBU handle. If an error has already occurred when this function is\n** called, it is a no-op.\n*/\nstatic int rbuMPrintfExec(sqlite3rbu *p, sqlite3 *db, const char *zFmt, ...){\n  va_list ap;\n  char *zSql;\n  va_start(ap, zFmt);\n  zSql = sqlite3_vmprintf(zFmt, ap);\n  if( p->rc==SQLITE_OK ){\n    if( zSql==0 ){\n      p->rc = SQLITE_NOMEM;\n    }else{\n      p->rc = sqlite3_exec(db, zSql, 0, 0, &p->zErrmsg);\n    }\n  }\n  sqlite3_free(zSql);\n  va_end(ap);\n  return p->rc;\n}\n\n/*\n** Attempt to allocate and return a pointer to a zeroed block of nByte \n** bytes. \n**\n** If an error (i.e. an OOM condition) occurs, return NULL and leave an \n** error code in the rbu handle passed as the first argument. Or, if an \n** error has already occurred when this function is called, return NULL \n** immediately without attempting the allocation or modifying the stored\n** error code.\n*/\nstatic void *rbuMalloc(sqlite3rbu *p, int nByte){\n  void *pRet = 0;\n  if( p->rc==SQLITE_OK ){\n    assert( nByte>0 );\n    pRet = sqlite3_malloc64(nByte);\n    if( pRet==0 ){\n      p->rc = SQLITE_NOMEM;\n    }else{\n      memset(pRet, 0, nByte);\n    }\n  }\n  return pRet;\n}\n\n\n/*\n** Allocate and zero the pIter->azTblCol[] and abTblPk[] arrays so that\n** there is room for at least nCol elements. If an OOM occurs, store an\n** error code in the RBU handle passed as the first argument.\n*/\nstatic void rbuAllocateIterArrays(sqlite3rbu *p, RbuObjIter *pIter, int nCol){\n  int nByte = (2*sizeof(char*) + sizeof(int) + 3*sizeof(u8)) * nCol;\n  char **azNew;\n\n  azNew = (char**)rbuMalloc(p, nByte);\n  if( azNew ){\n    pIter->azTblCol = azNew;\n    pIter->azTblType = &azNew[nCol];\n    pIter->aiSrcOrder = (int*)&pIter->azTblType[nCol];\n    pIter->abTblPk = (u8*)&pIter->aiSrcOrder[nCol];\n    pIter->abNotNull = (u8*)&pIter->abTblPk[nCol];\n    pIter->abIndexed = (u8*)&pIter->abNotNull[nCol];\n  }\n}\n\n/*\n** The first argument must be a nul-terminated string. This function\n** returns a copy of the string in memory obtained from sqlite3_malloc().\n** It is the responsibility of the caller to eventually free this memory\n** using sqlite3_free().\n**\n** If an OOM condition is encountered when attempting to allocate memory,\n** output variable (*pRc) is set to SQLITE_NOMEM before returning. Otherwise,\n** if the allocation succeeds, (*pRc) is left unchanged.\n*/\nstatic char *rbuStrndup(const char *zStr, int *pRc){\n  char *zRet = 0;\n\n  assert( *pRc==SQLITE_OK );\n  if( zStr ){\n    size_t nCopy = strlen(zStr) + 1;\n    zRet = (char*)sqlite3_malloc64(nCopy);\n    if( zRet ){\n      memcpy(zRet, zStr, nCopy);\n    }else{\n      *pRc = SQLITE_NOMEM;\n    }\n  }\n\n  return zRet;\n}\n\n/*\n** Finalize the statement passed as the second argument.\n**\n** If the sqlite3_finalize() call indicates that an error occurs, and the\n** rbu handle error code is not already set, set the error code and error\n** message accordingly.\n*/\nstatic void rbuFinalize(sqlite3rbu *p, sqlite3_stmt *pStmt){\n  sqlite3 *db = sqlite3_db_handle(pStmt);\n  int rc = sqlite3_finalize(pStmt);\n  if( p->rc==SQLITE_OK && rc!=SQLITE_OK ){\n    p->rc = rc;\n    p->zErrmsg = sqlite3_mprintf(\"%s\", sqlite3_errmsg(db));\n  }\n}\n\n/* Determine the type of a table.\n**\n**   peType is of type (int*), a pointer to an output parameter of type\n**   (int). This call sets the output parameter as follows, depending\n**   on the type of the table specified by parameters dbName and zTbl.\n**\n**     RBU_PK_NOTABLE:       No such table.\n**     RBU_PK_NONE:          Table has an implicit rowid.\n**     RBU_PK_IPK:           Table has an explicit IPK column.\n**     RBU_PK_EXTERNAL:      Table has an external PK index.\n**     RBU_PK_WITHOUT_ROWID: Table is WITHOUT ROWID.\n**     RBU_PK_VTAB:          Table is a virtual table.\n**\n**   Argument *piPk is also of type (int*), and also points to an output\n**   parameter. Unless the table has an external primary key index \n**   (i.e. unless *peType is set to 3), then *piPk is set to zero. Or,\n**   if the table does have an external primary key index, then *piPk\n**   is set to the root page number of the primary key index before\n**   returning.\n**\n** ALGORITHM:\n**\n**   if( no entry exists in sqlite_master ){\n**     return RBU_PK_NOTABLE\n**   }else if( sql for the entry starts with \"CREATE VIRTUAL\" ){\n**     return RBU_PK_VTAB\n**   }else if( \"PRAGMA index_list()\" for the table contains a \"pk\" index ){\n**     if( the index that is the pk exists in sqlite_master ){\n**       *piPK = rootpage of that index.\n**       return RBU_PK_EXTERNAL\n**     }else{\n**       return RBU_PK_WITHOUT_ROWID\n**     }\n**   }else if( \"PRAGMA table_info()\" lists one or more \"pk\" columns ){\n**     return RBU_PK_IPK\n**   }else{\n**     return RBU_PK_NONE\n**   }\n*/\nstatic void rbuTableType(\n  sqlite3rbu *p,\n  const char *zTab,\n  int *peType,\n  int *piTnum,\n  int *piPk\n){\n  /*\n  ** 0) SELECT count(*) FROM sqlite_master where name=%Q AND IsVirtual(%Q)\n  ** 1) PRAGMA index_list = ?\n  ** 2) SELECT count(*) FROM sqlite_master where name=%Q \n  ** 3) PRAGMA table_info = ?\n  */\n  sqlite3_stmt *aStmt[4] = {0, 0, 0, 0};\n\n  *peType = RBU_PK_NOTABLE;\n  *piPk = 0;\n\n  assert( p->rc==SQLITE_OK );\n  p->rc = prepareFreeAndCollectError(p->dbMain, &aStmt[0], &p->zErrmsg, \n    sqlite3_mprintf(\n          \"SELECT (sql LIKE 'create virtual%%'), rootpage\"\n          \"  FROM sqlite_master\"\n          \" WHERE name=%Q\", zTab\n  ));\n  if( p->rc!=SQLITE_OK || sqlite3_step(aStmt[0])!=SQLITE_ROW ){\n    /* Either an error, or no such table. */\n    goto rbuTableType_end;\n  }\n  if( sqlite3_column_int(aStmt[0], 0) ){\n    *peType = RBU_PK_VTAB;                     /* virtual table */\n    goto rbuTableType_end;\n  }\n  *piTnum = sqlite3_column_int(aStmt[0], 1);\n\n  p->rc = prepareFreeAndCollectError(p->dbMain, &aStmt[1], &p->zErrmsg, \n    sqlite3_mprintf(\"PRAGMA index_list=%Q\",zTab)\n  );\n  if( p->rc ) goto rbuTableType_end;\n  while( sqlite3_step(aStmt[1])==SQLITE_ROW ){\n    const u8 *zOrig = sqlite3_column_text(aStmt[1], 3);\n    const u8 *zIdx = sqlite3_column_text(aStmt[1], 1);\n    if( zOrig && zIdx && zOrig[0]=='p' ){\n      p->rc = prepareFreeAndCollectError(p->dbMain, &aStmt[2], &p->zErrmsg, \n          sqlite3_mprintf(\n            \"SELECT rootpage FROM sqlite_master WHERE name = %Q\", zIdx\n      ));\n      if( p->rc==SQLITE_OK ){\n        if( sqlite3_step(aStmt[2])==SQLITE_ROW ){\n          *piPk = sqlite3_column_int(aStmt[2], 0);\n          *peType = RBU_PK_EXTERNAL;\n        }else{\n          *peType = RBU_PK_WITHOUT_ROWID;\n        }\n      }\n      goto rbuTableType_end;\n    }\n  }\n\n  p->rc = prepareFreeAndCollectError(p->dbMain, &aStmt[3], &p->zErrmsg, \n    sqlite3_mprintf(\"PRAGMA table_info=%Q\",zTab)\n  );\n  if( p->rc==SQLITE_OK ){\n    while( sqlite3_step(aStmt[3])==SQLITE_ROW ){\n      if( sqlite3_column_int(aStmt[3],5)>0 ){\n        *peType = RBU_PK_IPK;                /* explicit IPK column */\n        goto rbuTableType_end;\n      }\n    }\n    *peType = RBU_PK_NONE;\n  }\n\nrbuTableType_end: {\n    unsigned int i;\n    for(i=0; i<sizeof(aStmt)/sizeof(aStmt[0]); i++){\n      rbuFinalize(p, aStmt[i]);\n    }\n  }\n}\n\n/*\n** This is a helper function for rbuObjIterCacheTableInfo(). It populates\n** the pIter->abIndexed[] array.\n*/\nstatic void rbuObjIterCacheIndexedCols(sqlite3rbu *p, RbuObjIter *pIter){\n  sqlite3_stmt *pList = 0;\n  int bIndex = 0;\n\n  if( p->rc==SQLITE_OK ){\n    memcpy(pIter->abIndexed, pIter->abTblPk, sizeof(u8)*pIter->nTblCol);\n    p->rc = prepareFreeAndCollectError(p->dbMain, &pList, &p->zErrmsg,\n        sqlite3_mprintf(\"PRAGMA main.index_list = %Q\", pIter->zTbl)\n    );\n  }\n\n  pIter->nIndex = 0;\n  while( p->rc==SQLITE_OK && SQLITE_ROW==sqlite3_step(pList) ){\n    const char *zIdx = (const char*)sqlite3_column_text(pList, 1);\n    sqlite3_stmt *pXInfo = 0;\n    if( zIdx==0 ) break;\n    p->rc = prepareFreeAndCollectError(p->dbMain, &pXInfo, &p->zErrmsg,\n        sqlite3_mprintf(\"PRAGMA main.index_xinfo = %Q\", zIdx)\n    );\n    while( p->rc==SQLITE_OK && SQLITE_ROW==sqlite3_step(pXInfo) ){\n      int iCid = sqlite3_column_int(pXInfo, 1);\n      if( iCid>=0 ) pIter->abIndexed[iCid] = 1;\n    }\n    rbuFinalize(p, pXInfo);\n    bIndex = 1;\n    pIter->nIndex++;\n  }\n\n  if( pIter->eType==RBU_PK_WITHOUT_ROWID ){\n    /* \"PRAGMA index_list\" includes the main PK b-tree */\n    pIter->nIndex--;\n  }\n\n  rbuFinalize(p, pList);\n  if( bIndex==0 ) pIter->abIndexed = 0;\n}\n\n\n/*\n** If they are not already populated, populate the pIter->azTblCol[],\n** pIter->abTblPk[], pIter->nTblCol and pIter->bRowid variables according to\n** the table (not index) that the iterator currently points to.\n**\n** Return SQLITE_OK if successful, or an SQLite error code otherwise. If\n** an error does occur, an error code and error message are also left in \n** the RBU handle.\n*/\nstatic int rbuObjIterCacheTableInfo(sqlite3rbu *p, RbuObjIter *pIter){\n  if( pIter->azTblCol==0 ){\n    sqlite3_stmt *pStmt = 0;\n    int nCol = 0;\n    int i;                        /* for() loop iterator variable */\n    int bRbuRowid = 0;            /* If input table has column \"rbu_rowid\" */\n    int iOrder = 0;\n    int iTnum = 0;\n\n    /* Figure out the type of table this step will deal with. */\n    assert( pIter->eType==0 );\n    rbuTableType(p, pIter->zTbl, &pIter->eType, &iTnum, &pIter->iPkTnum);\n    if( p->rc==SQLITE_OK && pIter->eType==RBU_PK_NOTABLE ){\n      p->rc = SQLITE_ERROR;\n      p->zErrmsg = sqlite3_mprintf(\"no such table: %s\", pIter->zTbl);\n    }\n    if( p->rc ) return p->rc;\n    if( pIter->zIdx==0 ) pIter->iTnum = iTnum;\n\n    assert( pIter->eType==RBU_PK_NONE || pIter->eType==RBU_PK_IPK \n         || pIter->eType==RBU_PK_EXTERNAL || pIter->eType==RBU_PK_WITHOUT_ROWID\n         || pIter->eType==RBU_PK_VTAB\n    );\n\n    /* Populate the azTblCol[] and nTblCol variables based on the columns\n    ** of the input table. Ignore any input table columns that begin with\n    ** \"rbu_\".  */\n    p->rc = prepareFreeAndCollectError(p->dbRbu, &pStmt, &p->zErrmsg, \n        sqlite3_mprintf(\"SELECT * FROM '%q'\", pIter->zDataTbl)\n    );\n    if( p->rc==SQLITE_OK ){\n      nCol = sqlite3_column_count(pStmt);\n      rbuAllocateIterArrays(p, pIter, nCol);\n    }\n    for(i=0; p->rc==SQLITE_OK && i<nCol; i++){\n      const char *zName = (const char*)sqlite3_column_name(pStmt, i);\n      if( sqlite3_strnicmp(\"rbu_\", zName, 4) ){\n        char *zCopy = rbuStrndup(zName, &p->rc);\n        pIter->aiSrcOrder[pIter->nTblCol] = pIter->nTblCol;\n        pIter->azTblCol[pIter->nTblCol++] = zCopy;\n      }\n      else if( 0==sqlite3_stricmp(\"rbu_rowid\", zName) ){\n        bRbuRowid = 1;\n      }\n    }\n    sqlite3_finalize(pStmt);\n    pStmt = 0;\n\n    if( p->rc==SQLITE_OK\n     && rbuIsVacuum(p)==0\n     && bRbuRowid!=(pIter->eType==RBU_PK_VTAB || pIter->eType==RBU_PK_NONE)\n    ){\n      p->rc = SQLITE_ERROR;\n      p->zErrmsg = sqlite3_mprintf(\n          \"table %q %s rbu_rowid column\", pIter->zDataTbl,\n          (bRbuRowid ? \"may not have\" : \"requires\")\n      );\n    }\n\n    /* Check that all non-HIDDEN columns in the destination table are also\n    ** present in the input table. Populate the abTblPk[], azTblType[] and\n    ** aiTblOrder[] arrays at the same time.  */\n    if( p->rc==SQLITE_OK ){\n      p->rc = prepareFreeAndCollectError(p->dbMain, &pStmt, &p->zErrmsg, \n          sqlite3_mprintf(\"PRAGMA table_info(%Q)\", pIter->zTbl)\n      );\n    }\n    while( p->rc==SQLITE_OK && SQLITE_ROW==sqlite3_step(pStmt) ){\n      const char *zName = (const char*)sqlite3_column_text(pStmt, 1);\n      if( zName==0 ) break;  /* An OOM - finalize() below returns S_NOMEM */\n      for(i=iOrder; i<pIter->nTblCol; i++){\n        if( 0==strcmp(zName, pIter->azTblCol[i]) ) break;\n      }\n      if( i==pIter->nTblCol ){\n        p->rc = SQLITE_ERROR;\n        p->zErrmsg = sqlite3_mprintf(\"column missing from %q: %s\",\n            pIter->zDataTbl, zName\n        );\n      }else{\n        int iPk = sqlite3_column_int(pStmt, 5);\n        int bNotNull = sqlite3_column_int(pStmt, 3);\n        const char *zType = (const char*)sqlite3_column_text(pStmt, 2);\n\n        if( i!=iOrder ){\n          SWAP(int, pIter->aiSrcOrder[i], pIter->aiSrcOrder[iOrder]);\n          SWAP(char*, pIter->azTblCol[i], pIter->azTblCol[iOrder]);\n        }\n\n        pIter->azTblType[iOrder] = rbuStrndup(zType, &p->rc);\n        pIter->abTblPk[iOrder] = (iPk!=0);\n        pIter->abNotNull[iOrder] = (u8)bNotNull || (iPk!=0);\n        iOrder++;\n      }\n    }\n\n    rbuFinalize(p, pStmt);\n    rbuObjIterCacheIndexedCols(p, pIter);\n    assert( pIter->eType!=RBU_PK_VTAB || pIter->abIndexed==0 );\n    assert( pIter->eType!=RBU_PK_VTAB || pIter->nIndex==0 );\n  }\n\n  return p->rc;\n}\n\n/*\n** This function constructs and returns a pointer to a nul-terminated \n** string containing some SQL clause or list based on one or more of the \n** column names currently stored in the pIter->azTblCol[] array.\n*/\nstatic char *rbuObjIterGetCollist(\n  sqlite3rbu *p,                  /* RBU object */\n  RbuObjIter *pIter               /* Object iterator for column names */\n){\n  char *zList = 0;\n  const char *zSep = \"\";\n  int i;\n  for(i=0; i<pIter->nTblCol; i++){\n    const char *z = pIter->azTblCol[i];\n    zList = rbuMPrintf(p, \"%z%s\\\"%w\\\"\", zList, zSep, z);\n    zSep = \", \";\n  }\n  return zList;\n}\n\n/*\n** This function is used to create a SELECT list (the list of SQL \n** expressions that follows a SELECT keyword) for a SELECT statement \n** used to read from an data_xxx or rbu_tmp_xxx table while updating the \n** index object currently indicated by the iterator object passed as the \n** second argument. A \"PRAGMA index_xinfo = <idxname>\" statement is used \n** to obtain the required information.\n**\n** If the index is of the following form:\n**\n**   CREATE INDEX i1 ON t1(c, b COLLATE nocase);\n**\n** and \"t1\" is a table with an explicit INTEGER PRIMARY KEY column \n** \"ipk\", the returned string is:\n**\n**   \"`c` COLLATE 'BINARY', `b` COLLATE 'NOCASE', `ipk` COLLATE 'BINARY'\"\n**\n** As well as the returned string, three other malloc'd strings are \n** returned via output parameters. As follows:\n**\n**   pzImposterCols: ...\n**   pzImposterPk: ...\n**   pzWhere: ...\n*/\nstatic char *rbuObjIterGetIndexCols(\n  sqlite3rbu *p,                  /* RBU object */\n  RbuObjIter *pIter,              /* Object iterator for column names */\n  char **pzImposterCols,          /* OUT: Columns for imposter table */\n  char **pzImposterPk,            /* OUT: Imposter PK clause */\n  char **pzWhere,                 /* OUT: WHERE clause */\n  int *pnBind                     /* OUT: Trbul number of columns */\n){\n  int rc = p->rc;                 /* Error code */\n  int rc2;                        /* sqlite3_finalize() return code */\n  char *zRet = 0;                 /* String to return */\n  char *zImpCols = 0;             /* String to return via *pzImposterCols */\n  char *zImpPK = 0;               /* String to return via *pzImposterPK */\n  char *zWhere = 0;               /* String to return via *pzWhere */\n  int nBind = 0;                  /* Value to return via *pnBind */\n  const char *zCom = \"\";          /* Set to \", \" later on */\n  const char *zAnd = \"\";          /* Set to \" AND \" later on */\n  sqlite3_stmt *pXInfo = 0;       /* PRAGMA index_xinfo = ? */\n\n  if( rc==SQLITE_OK ){\n    assert( p->zErrmsg==0 );\n    rc = prepareFreeAndCollectError(p->dbMain, &pXInfo, &p->zErrmsg,\n        sqlite3_mprintf(\"PRAGMA main.index_xinfo = %Q\", pIter->zIdx)\n    );\n  }\n\n  while( rc==SQLITE_OK && SQLITE_ROW==sqlite3_step(pXInfo) ){\n    int iCid = sqlite3_column_int(pXInfo, 1);\n    int bDesc = sqlite3_column_int(pXInfo, 3);\n    const char *zCollate = (const char*)sqlite3_column_text(pXInfo, 4);\n    const char *zCol;\n    const char *zType;\n\n    if( iCid<0 ){\n      /* An integer primary key. If the table has an explicit IPK, use\n      ** its name. Otherwise, use \"rbu_rowid\".  */\n      if( pIter->eType==RBU_PK_IPK ){\n        int i;\n        for(i=0; pIter->abTblPk[i]==0; i++);\n        assert( i<pIter->nTblCol );\n        zCol = pIter->azTblCol[i];\n      }else if( rbuIsVacuum(p) ){\n        zCol = \"_rowid_\";\n      }else{\n        zCol = \"rbu_rowid\";\n      }\n      zType = \"INTEGER\";\n    }else{\n      zCol = pIter->azTblCol[iCid];\n      zType = pIter->azTblType[iCid];\n    }\n\n    zRet = sqlite3_mprintf(\"%z%s\\\"%w\\\" COLLATE %Q\", zRet, zCom, zCol, zCollate);\n    if( pIter->bUnique==0 || sqlite3_column_int(pXInfo, 5) ){\n      const char *zOrder = (bDesc ? \" DESC\" : \"\");\n      zImpPK = sqlite3_mprintf(\"%z%s\\\"rbu_imp_%d%w\\\"%s\", \n          zImpPK, zCom, nBind, zCol, zOrder\n      );\n    }\n    zImpCols = sqlite3_mprintf(\"%z%s\\\"rbu_imp_%d%w\\\" %s COLLATE %Q\", \n        zImpCols, zCom, nBind, zCol, zType, zCollate\n    );\n    zWhere = sqlite3_mprintf(\n        \"%z%s\\\"rbu_imp_%d%w\\\" IS ?\", zWhere, zAnd, nBind, zCol\n    );\n    if( zRet==0 || zImpPK==0 || zImpCols==0 || zWhere==0 ) rc = SQLITE_NOMEM;\n    zCom = \", \";\n    zAnd = \" AND \";\n    nBind++;\n  }\n\n  rc2 = sqlite3_finalize(pXInfo);\n  if( rc==SQLITE_OK ) rc = rc2;\n\n  if( rc!=SQLITE_OK ){\n    sqlite3_free(zRet);\n    sqlite3_free(zImpCols);\n    sqlite3_free(zImpPK);\n    sqlite3_free(zWhere);\n    zRet = 0;\n    zImpCols = 0;\n    zImpPK = 0;\n    zWhere = 0;\n    p->rc = rc;\n  }\n\n  *pzImposterCols = zImpCols;\n  *pzImposterPk = zImpPK;\n  *pzWhere = zWhere;\n  *pnBind = nBind;\n  return zRet;\n}\n\n/*\n** Assuming the current table columns are \"a\", \"b\" and \"c\", and the zObj\n** paramter is passed \"old\", return a string of the form:\n**\n**     \"old.a, old.b, old.b\"\n**\n** With the column names escaped.\n**\n** For tables with implicit rowids - RBU_PK_EXTERNAL and RBU_PK_NONE, append\n** the text \", old._rowid_\" to the returned value.\n*/\nstatic char *rbuObjIterGetOldlist(\n  sqlite3rbu *p, \n  RbuObjIter *pIter,\n  const char *zObj\n){\n  char *zList = 0;\n  if( p->rc==SQLITE_OK && pIter->abIndexed ){\n    const char *zS = \"\";\n    int i;\n    for(i=0; i<pIter->nTblCol; i++){\n      if( pIter->abIndexed[i] ){\n        const char *zCol = pIter->azTblCol[i];\n        zList = sqlite3_mprintf(\"%z%s%s.\\\"%w\\\"\", zList, zS, zObj, zCol);\n      }else{\n        zList = sqlite3_mprintf(\"%z%sNULL\", zList, zS);\n      }\n      zS = \", \";\n      if( zList==0 ){\n        p->rc = SQLITE_NOMEM;\n        break;\n      }\n    }\n\n    /* For a table with implicit rowids, append \"old._rowid_\" to the list. */\n    if( pIter->eType==RBU_PK_EXTERNAL || pIter->eType==RBU_PK_NONE ){\n      zList = rbuMPrintf(p, \"%z, %s._rowid_\", zList, zObj);\n    }\n  }\n  return zList;\n}\n\n/*\n** Return an expression that can be used in a WHERE clause to match the\n** primary key of the current table. For example, if the table is:\n**\n**   CREATE TABLE t1(a, b, c, PRIMARY KEY(b, c));\n**\n** Return the string:\n**\n**   \"b = ?1 AND c = ?2\"\n*/\nstatic char *rbuObjIterGetWhere(\n  sqlite3rbu *p, \n  RbuObjIter *pIter\n){\n  char *zList = 0;\n  if( pIter->eType==RBU_PK_VTAB || pIter->eType==RBU_PK_NONE ){\n    zList = rbuMPrintf(p, \"_rowid_ = ?%d\", pIter->nTblCol+1);\n  }else if( pIter->eType==RBU_PK_EXTERNAL ){\n    const char *zSep = \"\";\n    int i;\n    for(i=0; i<pIter->nTblCol; i++){\n      if( pIter->abTblPk[i] ){\n        zList = rbuMPrintf(p, \"%z%sc%d=?%d\", zList, zSep, i, i+1);\n        zSep = \" AND \";\n      }\n    }\n    zList = rbuMPrintf(p, \n        \"_rowid_ = (SELECT id FROM rbu_imposter2 WHERE %z)\", zList\n    );\n\n  }else{\n    const char *zSep = \"\";\n    int i;\n    for(i=0; i<pIter->nTblCol; i++){\n      if( pIter->abTblPk[i] ){\n        const char *zCol = pIter->azTblCol[i];\n        zList = rbuMPrintf(p, \"%z%s\\\"%w\\\"=?%d\", zList, zSep, zCol, i+1);\n        zSep = \" AND \";\n      }\n    }\n  }\n  return zList;\n}\n\n/*\n** The SELECT statement iterating through the keys for the current object\n** (p->objiter.pSelect) currently points to a valid row. However, there\n** is something wrong with the rbu_control value in the rbu_control value\n** stored in the (p->nCol+1)'th column. Set the error code and error message\n** of the RBU handle to something reflecting this.\n*/\nstatic void rbuBadControlError(sqlite3rbu *p){\n  p->rc = SQLITE_ERROR;\n  p->zErrmsg = sqlite3_mprintf(\"invalid rbu_control value\");\n}\n\n\n/*\n** Return a nul-terminated string containing the comma separated list of\n** assignments that should be included following the \"SET\" keyword of\n** an UPDATE statement used to update the table object that the iterator\n** passed as the second argument currently points to if the rbu_control\n** column of the data_xxx table entry is set to zMask.\n**\n** The memory for the returned string is obtained from sqlite3_malloc().\n** It is the responsibility of the caller to eventually free it using\n** sqlite3_free(). \n**\n** If an OOM error is encountered when allocating space for the new\n** string, an error code is left in the rbu handle passed as the first\n** argument and NULL is returned. Or, if an error has already occurred\n** when this function is called, NULL is returned immediately, without\n** attempting the allocation or modifying the stored error code.\n*/\nstatic char *rbuObjIterGetSetlist(\n  sqlite3rbu *p,\n  RbuObjIter *pIter,\n  const char *zMask\n){\n  char *zList = 0;\n  if( p->rc==SQLITE_OK ){\n    int i;\n\n    if( (int)strlen(zMask)!=pIter->nTblCol ){\n      rbuBadControlError(p);\n    }else{\n      const char *zSep = \"\";\n      for(i=0; i<pIter->nTblCol; i++){\n        char c = zMask[pIter->aiSrcOrder[i]];\n        if( c=='x' ){\n          zList = rbuMPrintf(p, \"%z%s\\\"%w\\\"=?%d\", \n              zList, zSep, pIter->azTblCol[i], i+1\n          );\n          zSep = \", \";\n        }\n        else if( c=='d' ){\n          zList = rbuMPrintf(p, \"%z%s\\\"%w\\\"=rbu_delta(\\\"%w\\\", ?%d)\", \n              zList, zSep, pIter->azTblCol[i], pIter->azTblCol[i], i+1\n          );\n          zSep = \", \";\n        }\n        else if( c=='f' ){\n          zList = rbuMPrintf(p, \"%z%s\\\"%w\\\"=rbu_fossil_delta(\\\"%w\\\", ?%d)\", \n              zList, zSep, pIter->azTblCol[i], pIter->azTblCol[i], i+1\n          );\n          zSep = \", \";\n        }\n      }\n    }\n  }\n  return zList;\n}\n\n/*\n** Return a nul-terminated string consisting of nByte comma separated\n** \"?\" expressions. For example, if nByte is 3, return a pointer to\n** a buffer containing the string \"?,?,?\".\n**\n** The memory for the returned string is obtained from sqlite3_malloc().\n** It is the responsibility of the caller to eventually free it using\n** sqlite3_free(). \n**\n** If an OOM error is encountered when allocating space for the new\n** string, an error code is left in the rbu handle passed as the first\n** argument and NULL is returned. Or, if an error has already occurred\n** when this function is called, NULL is returned immediately, without\n** attempting the allocation or modifying the stored error code.\n*/\nstatic char *rbuObjIterGetBindlist(sqlite3rbu *p, int nBind){\n  char *zRet = 0;\n  int nByte = nBind*2 + 1;\n\n  zRet = (char*)rbuMalloc(p, nByte);\n  if( zRet ){\n    int i;\n    for(i=0; i<nBind; i++){\n      zRet[i*2] = '?';\n      zRet[i*2+1] = (i+1==nBind) ? '\\0' : ',';\n    }\n  }\n  return zRet;\n}\n\n/*\n** The iterator currently points to a table (not index) of type \n** RBU_PK_WITHOUT_ROWID. This function creates the PRIMARY KEY \n** declaration for the corresponding imposter table. For example,\n** if the iterator points to a table created as:\n**\n**   CREATE TABLE t1(a, b, c, PRIMARY KEY(b, a DESC)) WITHOUT ROWID\n**\n** this function returns:\n**\n**   PRIMARY KEY(\"b\", \"a\" DESC)\n*/\nstatic char *rbuWithoutRowidPK(sqlite3rbu *p, RbuObjIter *pIter){\n  char *z = 0;\n  assert( pIter->zIdx==0 );\n  if( p->rc==SQLITE_OK ){\n    const char *zSep = \"PRIMARY KEY(\";\n    sqlite3_stmt *pXList = 0;     /* PRAGMA index_list = (pIter->zTbl) */\n    sqlite3_stmt *pXInfo = 0;     /* PRAGMA index_xinfo = <pk-index> */\n   \n    p->rc = prepareFreeAndCollectError(p->dbMain, &pXList, &p->zErrmsg,\n        sqlite3_mprintf(\"PRAGMA main.index_list = %Q\", pIter->zTbl)\n    );\n    while( p->rc==SQLITE_OK && SQLITE_ROW==sqlite3_step(pXList) ){\n      const char *zOrig = (const char*)sqlite3_column_text(pXList,3);\n      if( zOrig && strcmp(zOrig, \"pk\")==0 ){\n        const char *zIdx = (const char*)sqlite3_column_text(pXList,1);\n        if( zIdx ){\n          p->rc = prepareFreeAndCollectError(p->dbMain, &pXInfo, &p->zErrmsg,\n              sqlite3_mprintf(\"PRAGMA main.index_xinfo = %Q\", zIdx)\n          );\n        }\n        break;\n      }\n    }\n    rbuFinalize(p, pXList);\n\n    while( p->rc==SQLITE_OK && SQLITE_ROW==sqlite3_step(pXInfo) ){\n      if( sqlite3_column_int(pXInfo, 5) ){\n        /* int iCid = sqlite3_column_int(pXInfo, 0); */\n        const char *zCol = (const char*)sqlite3_column_text(pXInfo, 2);\n        const char *zDesc = sqlite3_column_int(pXInfo, 3) ? \" DESC\" : \"\";\n        z = rbuMPrintf(p, \"%z%s\\\"%w\\\"%s\", z, zSep, zCol, zDesc);\n        zSep = \", \";\n      }\n    }\n    z = rbuMPrintf(p, \"%z)\", z);\n    rbuFinalize(p, pXInfo);\n  }\n  return z;\n}\n\n/*\n** This function creates the second imposter table used when writing to\n** a table b-tree where the table has an external primary key. If the\n** iterator passed as the second argument does not currently point to\n** a table (not index) with an external primary key, this function is a\n** no-op. \n**\n** Assuming the iterator does point to a table with an external PK, this\n** function creates a WITHOUT ROWID imposter table named \"rbu_imposter2\"\n** used to access that PK index. For example, if the target table is\n** declared as follows:\n**\n**   CREATE TABLE t1(a, b TEXT, c REAL, PRIMARY KEY(b, c));\n**\n** then the imposter table schema is:\n**\n**   CREATE TABLE rbu_imposter2(c1 TEXT, c2 REAL, id INTEGER) WITHOUT ROWID;\n**\n*/\nstatic void rbuCreateImposterTable2(sqlite3rbu *p, RbuObjIter *pIter){\n  if( p->rc==SQLITE_OK && pIter->eType==RBU_PK_EXTERNAL ){\n    int tnum = pIter->iPkTnum;    /* Root page of PK index */\n    sqlite3_stmt *pQuery = 0;     /* SELECT name ... WHERE rootpage = $tnum */\n    const char *zIdx = 0;         /* Name of PK index */\n    sqlite3_stmt *pXInfo = 0;     /* PRAGMA main.index_xinfo = $zIdx */\n    const char *zComma = \"\";\n    char *zCols = 0;              /* Used to build up list of table cols */\n    char *zPk = 0;                /* Used to build up table PK declaration */\n\n    /* Figure out the name of the primary key index for the current table.\n    ** This is needed for the argument to \"PRAGMA index_xinfo\". Set\n    ** zIdx to point to a nul-terminated string containing this name. */\n    p->rc = prepareAndCollectError(p->dbMain, &pQuery, &p->zErrmsg, \n        \"SELECT name FROM sqlite_master WHERE rootpage = ?\"\n    );\n    if( p->rc==SQLITE_OK ){\n      sqlite3_bind_int(pQuery, 1, tnum);\n      if( SQLITE_ROW==sqlite3_step(pQuery) ){\n        zIdx = (const char*)sqlite3_column_text(pQuery, 0);\n      }\n    }\n    if( zIdx ){\n      p->rc = prepareFreeAndCollectError(p->dbMain, &pXInfo, &p->zErrmsg,\n          sqlite3_mprintf(\"PRAGMA main.index_xinfo = %Q\", zIdx)\n      );\n    }\n    rbuFinalize(p, pQuery);\n\n    while( p->rc==SQLITE_OK && SQLITE_ROW==sqlite3_step(pXInfo) ){\n      int bKey = sqlite3_column_int(pXInfo, 5);\n      if( bKey ){\n        int iCid = sqlite3_column_int(pXInfo, 1);\n        int bDesc = sqlite3_column_int(pXInfo, 3);\n        const char *zCollate = (const char*)sqlite3_column_text(pXInfo, 4);\n        zCols = rbuMPrintf(p, \"%z%sc%d %s COLLATE %s\", zCols, zComma, \n            iCid, pIter->azTblType[iCid], zCollate\n        );\n        zPk = rbuMPrintf(p, \"%z%sc%d%s\", zPk, zComma, iCid, bDesc?\" DESC\":\"\");\n        zComma = \", \";\n      }\n    }\n    zCols = rbuMPrintf(p, \"%z, id INTEGER\", zCols);\n    rbuFinalize(p, pXInfo);\n\n    sqlite3_test_control(SQLITE_TESTCTRL_IMPOSTER, p->dbMain, \"main\", 1, tnum);\n    rbuMPrintfExec(p, p->dbMain,\n        \"CREATE TABLE rbu_imposter2(%z, PRIMARY KEY(%z)) WITHOUT ROWID\", \n        zCols, zPk\n    );\n    sqlite3_test_control(SQLITE_TESTCTRL_IMPOSTER, p->dbMain, \"main\", 0, 0);\n  }\n}\n\n/*\n** If an error has already occurred when this function is called, it \n** immediately returns zero (without doing any work). Or, if an error\n** occurs during the execution of this function, it sets the error code\n** in the sqlite3rbu object indicated by the first argument and returns\n** zero.\n**\n** The iterator passed as the second argument is guaranteed to point to\n** a table (not an index) when this function is called. This function\n** attempts to create any imposter table required to write to the main\n** table b-tree of the table before returning. Non-zero is returned if\n** an imposter table are created, or zero otherwise.\n**\n** An imposter table is required in all cases except RBU_PK_VTAB. Only\n** virtual tables are written to directly. The imposter table has the \n** same schema as the actual target table (less any UNIQUE constraints). \n** More precisely, the \"same schema\" means the same columns, types, \n** collation sequences. For tables that do not have an external PRIMARY\n** KEY, it also means the same PRIMARY KEY declaration.\n*/\nstatic void rbuCreateImposterTable(sqlite3rbu *p, RbuObjIter *pIter){\n  if( p->rc==SQLITE_OK && pIter->eType!=RBU_PK_VTAB ){\n    int tnum = pIter->iTnum;\n    const char *zComma = \"\";\n    char *zSql = 0;\n    int iCol;\n    sqlite3_test_control(SQLITE_TESTCTRL_IMPOSTER, p->dbMain, \"main\", 0, 1);\n\n    for(iCol=0; p->rc==SQLITE_OK && iCol<pIter->nTblCol; iCol++){\n      const char *zPk = \"\";\n      const char *zCol = pIter->azTblCol[iCol];\n      const char *zColl = 0;\n\n      p->rc = sqlite3_table_column_metadata(\n          p->dbMain, \"main\", pIter->zTbl, zCol, 0, &zColl, 0, 0, 0\n      );\n\n      if( pIter->eType==RBU_PK_IPK && pIter->abTblPk[iCol] ){\n        /* If the target table column is an \"INTEGER PRIMARY KEY\", add\n        ** \"PRIMARY KEY\" to the imposter table column declaration. */\n        zPk = \"PRIMARY KEY \";\n      }\n      zSql = rbuMPrintf(p, \"%z%s\\\"%w\\\" %s %sCOLLATE %s%s\", \n          zSql, zComma, zCol, pIter->azTblType[iCol], zPk, zColl,\n          (pIter->abNotNull[iCol] ? \" NOT NULL\" : \"\")\n      );\n      zComma = \", \";\n    }\n\n    if( pIter->eType==RBU_PK_WITHOUT_ROWID ){\n      char *zPk = rbuWithoutRowidPK(p, pIter);\n      if( zPk ){\n        zSql = rbuMPrintf(p, \"%z, %z\", zSql, zPk);\n      }\n    }\n\n    sqlite3_test_control(SQLITE_TESTCTRL_IMPOSTER, p->dbMain, \"main\", 1, tnum);\n    rbuMPrintfExec(p, p->dbMain, \"CREATE TABLE \\\"rbu_imp_%w\\\"(%z)%s\", \n        pIter->zTbl, zSql, \n        (pIter->eType==RBU_PK_WITHOUT_ROWID ? \" WITHOUT ROWID\" : \"\")\n    );\n    sqlite3_test_control(SQLITE_TESTCTRL_IMPOSTER, p->dbMain, \"main\", 0, 0);\n  }\n}\n\n/*\n** Prepare a statement used to insert rows into the \"rbu_tmp_xxx\" table.\n** Specifically a statement of the form:\n**\n**     INSERT INTO rbu_tmp_xxx VALUES(?, ?, ? ...);\n**\n** The number of bound variables is equal to the number of columns in\n** the target table, plus one (for the rbu_control column), plus one more \n** (for the rbu_rowid column) if the target table is an implicit IPK or \n** virtual table.\n*/\nstatic void rbuObjIterPrepareTmpInsert(\n  sqlite3rbu *p, \n  RbuObjIter *pIter,\n  const char *zCollist,\n  const char *zRbuRowid\n){\n  int bRbuRowid = (pIter->eType==RBU_PK_EXTERNAL || pIter->eType==RBU_PK_NONE);\n  char *zBind = rbuObjIterGetBindlist(p, pIter->nTblCol + 1 + bRbuRowid);\n  if( zBind ){\n    assert( pIter->pTmpInsert==0 );\n    p->rc = prepareFreeAndCollectError(\n        p->dbRbu, &pIter->pTmpInsert, &p->zErrmsg, sqlite3_mprintf(\n          \"INSERT INTO %s.'rbu_tmp_%q'(rbu_control,%s%s) VALUES(%z)\", \n          p->zStateDb, pIter->zDataTbl, zCollist, zRbuRowid, zBind\n    ));\n  }\n}\n\nstatic void rbuTmpInsertFunc(\n  sqlite3_context *pCtx, \n  int nVal,\n  sqlite3_value **apVal\n){\n  sqlite3rbu *p = sqlite3_user_data(pCtx);\n  int rc = SQLITE_OK;\n  int i;\n\n  assert( sqlite3_value_int(apVal[0])!=0\n      || p->objiter.eType==RBU_PK_EXTERNAL \n      || p->objiter.eType==RBU_PK_NONE \n  );\n  if( sqlite3_value_int(apVal[0])!=0 ){\n    p->nPhaseOneStep += p->objiter.nIndex;\n  }\n\n  for(i=0; rc==SQLITE_OK && i<nVal; i++){\n    rc = sqlite3_bind_value(p->objiter.pTmpInsert, i+1, apVal[i]);\n  }\n  if( rc==SQLITE_OK ){\n    sqlite3_step(p->objiter.pTmpInsert);\n    rc = sqlite3_reset(p->objiter.pTmpInsert);\n  }\n\n  if( rc!=SQLITE_OK ){\n    sqlite3_result_error_code(pCtx, rc);\n  }\n}\n\n/*\n** Ensure that the SQLite statement handles required to update the \n** target database object currently indicated by the iterator passed \n** as the second argument are available.\n*/\nstatic int rbuObjIterPrepareAll(\n  sqlite3rbu *p, \n  RbuObjIter *pIter,\n  int nOffset                     /* Add \"LIMIT -1 OFFSET $nOffset\" to SELECT */\n){\n  assert( pIter->bCleanup==0 );\n  if( pIter->pSelect==0 && rbuObjIterCacheTableInfo(p, pIter)==SQLITE_OK ){\n    const int tnum = pIter->iTnum;\n    char *zCollist = 0;           /* List of indexed columns */\n    char **pz = &p->zErrmsg;\n    const char *zIdx = pIter->zIdx;\n    char *zLimit = 0;\n\n    if( nOffset ){\n      zLimit = sqlite3_mprintf(\" LIMIT -1 OFFSET %d\", nOffset);\n      if( !zLimit ) p->rc = SQLITE_NOMEM;\n    }\n\n    if( zIdx ){\n      const char *zTbl = pIter->zTbl;\n      char *zImposterCols = 0;    /* Columns for imposter table */\n      char *zImposterPK = 0;      /* Primary key declaration for imposter */\n      char *zWhere = 0;           /* WHERE clause on PK columns */\n      char *zBind = 0;\n      int nBind = 0;\n\n      assert( pIter->eType!=RBU_PK_VTAB );\n      zCollist = rbuObjIterGetIndexCols(\n          p, pIter, &zImposterCols, &zImposterPK, &zWhere, &nBind\n      );\n      zBind = rbuObjIterGetBindlist(p, nBind);\n\n      /* Create the imposter table used to write to this index. */\n      sqlite3_test_control(SQLITE_TESTCTRL_IMPOSTER, p->dbMain, \"main\", 0, 1);\n      sqlite3_test_control(SQLITE_TESTCTRL_IMPOSTER, p->dbMain, \"main\", 1,tnum);\n      rbuMPrintfExec(p, p->dbMain,\n          \"CREATE TABLE \\\"rbu_imp_%w\\\"( %s, PRIMARY KEY( %s ) ) WITHOUT ROWID\",\n          zTbl, zImposterCols, zImposterPK\n      );\n      sqlite3_test_control(SQLITE_TESTCTRL_IMPOSTER, p->dbMain, \"main\", 0, 0);\n\n      /* Create the statement to insert index entries */\n      pIter->nCol = nBind;\n      if( p->rc==SQLITE_OK ){\n        p->rc = prepareFreeAndCollectError(\n            p->dbMain, &pIter->pInsert, &p->zErrmsg,\n          sqlite3_mprintf(\"INSERT INTO \\\"rbu_imp_%w\\\" VALUES(%s)\", zTbl, zBind)\n        );\n      }\n\n      /* And to delete index entries */\n      if( rbuIsVacuum(p)==0 && p->rc==SQLITE_OK ){\n        p->rc = prepareFreeAndCollectError(\n            p->dbMain, &pIter->pDelete, &p->zErrmsg,\n          sqlite3_mprintf(\"DELETE FROM \\\"rbu_imp_%w\\\" WHERE %s\", zTbl, zWhere)\n        );\n      }\n\n      /* Create the SELECT statement to read keys in sorted order */\n      if( p->rc==SQLITE_OK ){\n        char *zSql;\n        if( rbuIsVacuum(p) ){\n          zSql = sqlite3_mprintf(\n              \"SELECT %s, 0 AS rbu_control FROM '%q' ORDER BY %s%s\",\n              zCollist, \n              pIter->zDataTbl,\n              zCollist, zLimit\n          );\n        }else\n\n        if( pIter->eType==RBU_PK_EXTERNAL || pIter->eType==RBU_PK_NONE ){\n          zSql = sqlite3_mprintf(\n              \"SELECT %s, rbu_control FROM %s.'rbu_tmp_%q' ORDER BY %s%s\",\n              zCollist, p->zStateDb, pIter->zDataTbl,\n              zCollist, zLimit\n          );\n        }else{\n          zSql = sqlite3_mprintf(\n              \"SELECT %s, rbu_control FROM %s.'rbu_tmp_%q' \"\n              \"UNION ALL \"\n              \"SELECT %s, rbu_control FROM '%q' \"\n              \"WHERE typeof(rbu_control)='integer' AND rbu_control!=1 \"\n              \"ORDER BY %s%s\",\n              zCollist, p->zStateDb, pIter->zDataTbl, \n              zCollist, pIter->zDataTbl, \n              zCollist, zLimit\n          );\n        }\n        p->rc = prepareFreeAndCollectError(p->dbRbu, &pIter->pSelect, pz, zSql);\n      }\n\n      sqlite3_free(zImposterCols);\n      sqlite3_free(zImposterPK);\n      sqlite3_free(zWhere);\n      sqlite3_free(zBind);\n    }else{\n      int bRbuRowid = (pIter->eType==RBU_PK_VTAB)\n                    ||(pIter->eType==RBU_PK_NONE)\n                    ||(pIter->eType==RBU_PK_EXTERNAL && rbuIsVacuum(p));\n      const char *zTbl = pIter->zTbl;       /* Table this step applies to */\n      const char *zWrite;                   /* Imposter table name */\n\n      char *zBindings = rbuObjIterGetBindlist(p, pIter->nTblCol + bRbuRowid);\n      char *zWhere = rbuObjIterGetWhere(p, pIter);\n      char *zOldlist = rbuObjIterGetOldlist(p, pIter, \"old\");\n      char *zNewlist = rbuObjIterGetOldlist(p, pIter, \"new\");\n\n      zCollist = rbuObjIterGetCollist(p, pIter);\n      pIter->nCol = pIter->nTblCol;\n\n      /* Create the imposter table or tables (if required). */\n      rbuCreateImposterTable(p, pIter);\n      rbuCreateImposterTable2(p, pIter);\n      zWrite = (pIter->eType==RBU_PK_VTAB ? \"\" : \"rbu_imp_\");\n\n      /* Create the INSERT statement to write to the target PK b-tree */\n      if( p->rc==SQLITE_OK ){\n        p->rc = prepareFreeAndCollectError(p->dbMain, &pIter->pInsert, pz,\n            sqlite3_mprintf(\n              \"INSERT INTO \\\"%s%w\\\"(%s%s) VALUES(%s)\", \n              zWrite, zTbl, zCollist, (bRbuRowid ? \", _rowid_\" : \"\"), zBindings\n            )\n        );\n      }\n\n      /* Create the DELETE statement to write to the target PK b-tree.\n      ** Because it only performs INSERT operations, this is not required for\n      ** an rbu vacuum handle.  */\n      if( rbuIsVacuum(p)==0 && p->rc==SQLITE_OK ){\n        p->rc = prepareFreeAndCollectError(p->dbMain, &pIter->pDelete, pz,\n            sqlite3_mprintf(\n              \"DELETE FROM \\\"%s%w\\\" WHERE %s\", zWrite, zTbl, zWhere\n            )\n        );\n      }\n\n      if( rbuIsVacuum(p)==0 && pIter->abIndexed ){\n        const char *zRbuRowid = \"\";\n        if( pIter->eType==RBU_PK_EXTERNAL || pIter->eType==RBU_PK_NONE ){\n          zRbuRowid = \", rbu_rowid\";\n        }\n\n        /* Create the rbu_tmp_xxx table and the triggers to populate it. */\n        rbuMPrintfExec(p, p->dbRbu,\n            \"CREATE TABLE IF NOT EXISTS %s.'rbu_tmp_%q' AS \"\n            \"SELECT *%s FROM '%q' WHERE 0;\"\n            , p->zStateDb, pIter->zDataTbl\n            , (pIter->eType==RBU_PK_EXTERNAL ? \", 0 AS rbu_rowid\" : \"\")\n            , pIter->zDataTbl\n        );\n\n        rbuMPrintfExec(p, p->dbMain,\n            \"CREATE TEMP TRIGGER rbu_delete_tr BEFORE DELETE ON \\\"%s%w\\\" \"\n            \"BEGIN \"\n            \"  SELECT rbu_tmp_insert(3, %s);\"\n            \"END;\"\n\n            \"CREATE TEMP TRIGGER rbu_update1_tr BEFORE UPDATE ON \\\"%s%w\\\" \"\n            \"BEGIN \"\n            \"  SELECT rbu_tmp_insert(3, %s);\"\n            \"END;\"\n\n            \"CREATE TEMP TRIGGER rbu_update2_tr AFTER UPDATE ON \\\"%s%w\\\" \"\n            \"BEGIN \"\n            \"  SELECT rbu_tmp_insert(4, %s);\"\n            \"END;\",\n            zWrite, zTbl, zOldlist,\n            zWrite, zTbl, zOldlist,\n            zWrite, zTbl, zNewlist\n        );\n\n        if( pIter->eType==RBU_PK_EXTERNAL || pIter->eType==RBU_PK_NONE ){\n          rbuMPrintfExec(p, p->dbMain,\n              \"CREATE TEMP TRIGGER rbu_insert_tr AFTER INSERT ON \\\"%s%w\\\" \"\n              \"BEGIN \"\n              \"  SELECT rbu_tmp_insert(0, %s);\"\n              \"END;\",\n              zWrite, zTbl, zNewlist\n          );\n        }\n\n        rbuObjIterPrepareTmpInsert(p, pIter, zCollist, zRbuRowid);\n      }\n\n      /* Create the SELECT statement to read keys from data_xxx */\n      if( p->rc==SQLITE_OK ){\n        const char *zRbuRowid = \"\";\n        if( bRbuRowid ){\n          zRbuRowid = rbuIsVacuum(p) ? \",_rowid_ \" : \",rbu_rowid\";\n        }\n        p->rc = prepareFreeAndCollectError(p->dbRbu, &pIter->pSelect, pz,\n            sqlite3_mprintf(\n              \"SELECT %s,%s rbu_control%s FROM '%q'%s\", \n              zCollist, \n              (rbuIsVacuum(p) ? \"0 AS \" : \"\"),\n              zRbuRowid,\n              pIter->zDataTbl, zLimit\n            )\n        );\n      }\n\n      sqlite3_free(zWhere);\n      sqlite3_free(zOldlist);\n      sqlite3_free(zNewlist);\n      sqlite3_free(zBindings);\n    }\n    sqlite3_free(zCollist);\n    sqlite3_free(zLimit);\n  }\n  \n  return p->rc;\n}\n\n/*\n** Set output variable *ppStmt to point to an UPDATE statement that may\n** be used to update the imposter table for the main table b-tree of the\n** table object that pIter currently points to, assuming that the \n** rbu_control column of the data_xyz table contains zMask.\n** \n** If the zMask string does not specify any columns to update, then this\n** is not an error. Output variable *ppStmt is set to NULL in this case.\n*/\nstatic int rbuGetUpdateStmt(\n  sqlite3rbu *p,                  /* RBU handle */\n  RbuObjIter *pIter,              /* Object iterator */\n  const char *zMask,              /* rbu_control value ('x.x.') */\n  sqlite3_stmt **ppStmt           /* OUT: UPDATE statement handle */\n){\n  RbuUpdateStmt **pp;\n  RbuUpdateStmt *pUp = 0;\n  int nUp = 0;\n\n  /* In case an error occurs */\n  *ppStmt = 0;\n\n  /* Search for an existing statement. If one is found, shift it to the front\n  ** of the LRU queue and return immediately. Otherwise, leave nUp pointing\n  ** to the number of statements currently in the cache and pUp to the\n  ** last object in the list.  */\n  for(pp=&pIter->pRbuUpdate; *pp; pp=&((*pp)->pNext)){\n    pUp = *pp;\n    if( strcmp(pUp->zMask, zMask)==0 ){\n      *pp = pUp->pNext;\n      pUp->pNext = pIter->pRbuUpdate;\n      pIter->pRbuUpdate = pUp;\n      *ppStmt = pUp->pUpdate; \n      return SQLITE_OK;\n    }\n    nUp++;\n  }\n  assert( pUp==0 || pUp->pNext==0 );\n\n  if( nUp>=SQLITE_RBU_UPDATE_CACHESIZE ){\n    for(pp=&pIter->pRbuUpdate; *pp!=pUp; pp=&((*pp)->pNext));\n    *pp = 0;\n    sqlite3_finalize(pUp->pUpdate);\n    pUp->pUpdate = 0;\n  }else{\n    pUp = (RbuUpdateStmt*)rbuMalloc(p, sizeof(RbuUpdateStmt)+pIter->nTblCol+1);\n  }\n\n  if( pUp ){\n    char *zWhere = rbuObjIterGetWhere(p, pIter);\n    char *zSet = rbuObjIterGetSetlist(p, pIter, zMask);\n    char *zUpdate = 0;\n\n    pUp->zMask = (char*)&pUp[1];\n    memcpy(pUp->zMask, zMask, pIter->nTblCol);\n    pUp->pNext = pIter->pRbuUpdate;\n    pIter->pRbuUpdate = pUp;\n\n    if( zSet ){\n      const char *zPrefix = \"\";\n\n      if( pIter->eType!=RBU_PK_VTAB ) zPrefix = \"rbu_imp_\";\n      zUpdate = sqlite3_mprintf(\"UPDATE \\\"%s%w\\\" SET %s WHERE %s\", \n          zPrefix, pIter->zTbl, zSet, zWhere\n      );\n      p->rc = prepareFreeAndCollectError(\n          p->dbMain, &pUp->pUpdate, &p->zErrmsg, zUpdate\n      );\n      *ppStmt = pUp->pUpdate;\n    }\n    sqlite3_free(zWhere);\n    sqlite3_free(zSet);\n  }\n\n  return p->rc;\n}\n\nstatic sqlite3 *rbuOpenDbhandle(\n  sqlite3rbu *p, \n  const char *zName, \n  int bUseVfs\n){\n  sqlite3 *db = 0;\n  if( p->rc==SQLITE_OK ){\n    const int flags = SQLITE_OPEN_READWRITE|SQLITE_OPEN_CREATE|SQLITE_OPEN_URI;\n    p->rc = sqlite3_open_v2(zName, &db, flags, bUseVfs ? p->zVfsName : 0);\n    if( p->rc ){\n      p->zErrmsg = sqlite3_mprintf(\"%s\", sqlite3_errmsg(db));\n      sqlite3_close(db);\n      db = 0;\n    }\n  }\n  return db;\n}\n\n/*\n** Free an RbuState object allocated by rbuLoadState().\n*/\nstatic void rbuFreeState(RbuState *p){\n  if( p ){\n    sqlite3_free(p->zTbl);\n    sqlite3_free(p->zIdx);\n    sqlite3_free(p);\n  }\n}\n\n/*\n** Allocate an RbuState object and load the contents of the rbu_state \n** table into it. Return a pointer to the new object. It is the \n** responsibility of the caller to eventually free the object using\n** sqlite3_free().\n**\n** If an error occurs, leave an error code and message in the rbu handle\n** and return NULL.\n*/\nstatic RbuState *rbuLoadState(sqlite3rbu *p){\n  RbuState *pRet = 0;\n  sqlite3_stmt *pStmt = 0;\n  int rc;\n  int rc2;\n\n  pRet = (RbuState*)rbuMalloc(p, sizeof(RbuState));\n  if( pRet==0 ) return 0;\n\n  rc = prepareFreeAndCollectError(p->dbRbu, &pStmt, &p->zErrmsg, \n      sqlite3_mprintf(\"SELECT k, v FROM %s.rbu_state\", p->zStateDb)\n  );\n  while( rc==SQLITE_OK && SQLITE_ROW==sqlite3_step(pStmt) ){\n    switch( sqlite3_column_int(pStmt, 0) ){\n      case RBU_STATE_STAGE:\n        pRet->eStage = sqlite3_column_int(pStmt, 1);\n        if( pRet->eStage!=RBU_STAGE_OAL\n         && pRet->eStage!=RBU_STAGE_MOVE\n         && pRet->eStage!=RBU_STAGE_CKPT\n        ){\n          p->rc = SQLITE_CORRUPT;\n        }\n        break;\n\n      case RBU_STATE_TBL:\n        pRet->zTbl = rbuStrndup((char*)sqlite3_column_text(pStmt, 1), &rc);\n        break;\n\n      case RBU_STATE_IDX:\n        pRet->zIdx = rbuStrndup((char*)sqlite3_column_text(pStmt, 1), &rc);\n        break;\n\n      case RBU_STATE_ROW:\n        pRet->nRow = sqlite3_column_int(pStmt, 1);\n        break;\n\n      case RBU_STATE_PROGRESS:\n        pRet->nProgress = sqlite3_column_int64(pStmt, 1);\n        break;\n\n      case RBU_STATE_CKPT:\n        pRet->iWalCksum = sqlite3_column_int64(pStmt, 1);\n        break;\n\n      case RBU_STATE_COOKIE:\n        pRet->iCookie = (u32)sqlite3_column_int64(pStmt, 1);\n        break;\n\n      case RBU_STATE_OALSZ:\n        pRet->iOalSz = (u32)sqlite3_column_int64(pStmt, 1);\n        break;\n\n      case RBU_STATE_PHASEONESTEP:\n        pRet->nPhaseOneStep = sqlite3_column_int64(pStmt, 1);\n        break;\n\n      default:\n        rc = SQLITE_CORRUPT;\n        break;\n    }\n  }\n  rc2 = sqlite3_finalize(pStmt);\n  if( rc==SQLITE_OK ) rc = rc2;\n\n  p->rc = rc;\n  return pRet;\n}\n\n\n/*\n** Open the database handle and attach the RBU database as \"rbu\". If an\n** error occurs, leave an error code and message in the RBU handle.\n*/\nstatic void rbuOpenDatabase(sqlite3rbu *p, int *pbRetry){\n  assert( p->rc || (p->dbMain==0 && p->dbRbu==0) );\n  assert( p->rc || rbuIsVacuum(p) || p->zTarget!=0 );\n\n  /* Open the RBU database */\n  p->dbRbu = rbuOpenDbhandle(p, p->zRbu, 1);\n\n  if( p->rc==SQLITE_OK && rbuIsVacuum(p) ){\n    sqlite3_file_control(p->dbRbu, \"main\", SQLITE_FCNTL_RBUCNT, (void*)p);\n    if( p->zState==0 ){\n      const char *zFile = sqlite3_db_filename(p->dbRbu, \"main\");\n      p->zState = rbuMPrintf(p, \"file://%s-vacuum?modeof=%s\", zFile, zFile);\n    }\n  }\n\n  /* If using separate RBU and state databases, attach the state database to\n  ** the RBU db handle now.  */\n  if( p->zState ){\n    rbuMPrintfExec(p, p->dbRbu, \"ATTACH %Q AS stat\", p->zState);\n    memcpy(p->zStateDb, \"stat\", 4);\n  }else{\n    memcpy(p->zStateDb, \"main\", 4);\n  }\n\n#if 0\n  if( p->rc==SQLITE_OK && rbuIsVacuum(p) ){\n    p->rc = sqlite3_exec(p->dbRbu, \"BEGIN\", 0, 0, 0);\n  }\n#endif\n\n  /* If it has not already been created, create the rbu_state table */\n  rbuMPrintfExec(p, p->dbRbu, RBU_CREATE_STATE, p->zStateDb);\n\n#if 0\n  if( rbuIsVacuum(p) ){\n    if( p->rc==SQLITE_OK ){\n      int rc2;\n      int bOk = 0;\n      sqlite3_stmt *pCnt = 0;\n      p->rc = prepareAndCollectError(p->dbRbu, &pCnt, &p->zErrmsg,\n          \"SELECT count(*) FROM stat.sqlite_master\"\n      );\n      if( p->rc==SQLITE_OK \n       && sqlite3_step(pCnt)==SQLITE_ROW\n       && 1==sqlite3_column_int(pCnt, 0)\n      ){\n        bOk = 1;\n      }\n      rc2 = sqlite3_finalize(pCnt);\n      if( p->rc==SQLITE_OK ) p->rc = rc2;\n\n      if( p->rc==SQLITE_OK && bOk==0 ){\n        p->rc = SQLITE_ERROR;\n        p->zErrmsg = sqlite3_mprintf(\"invalid state database\");\n      }\n    \n      if( p->rc==SQLITE_OK ){\n        p->rc = sqlite3_exec(p->dbRbu, \"COMMIT\", 0, 0, 0);\n      }\n    }\n  }\n#endif\n\n  if( p->rc==SQLITE_OK && rbuIsVacuum(p) ){\n    int bOpen = 0;\n    int rc;\n    p->nRbu = 0;\n    p->pRbuFd = 0;\n    rc = sqlite3_file_control(p->dbRbu, \"main\", SQLITE_FCNTL_RBUCNT, (void*)p);\n    if( rc!=SQLITE_NOTFOUND ) p->rc = rc;\n    if( p->eStage>=RBU_STAGE_MOVE ){\n      bOpen = 1;\n    }else{\n      RbuState *pState = rbuLoadState(p);\n      if( pState ){\n        bOpen = (pState->eStage>=RBU_STAGE_MOVE);\n        rbuFreeState(pState);\n      }\n    }\n    if( bOpen ) p->dbMain = rbuOpenDbhandle(p, p->zRbu, p->nRbu<=1);\n  }\n\n  p->eStage = 0;\n  if( p->rc==SQLITE_OK && p->dbMain==0 ){\n    if( !rbuIsVacuum(p) ){\n      p->dbMain = rbuOpenDbhandle(p, p->zTarget, 1);\n    }else if( p->pRbuFd->pWalFd ){\n      if( pbRetry ){\n        p->pRbuFd->bNolock = 0;\n        sqlite3_close(p->dbRbu);\n        sqlite3_close(p->dbMain);\n        p->dbMain = 0;\n        p->dbRbu = 0;\n        *pbRetry = 1;\n        return;\n      }\n      p->rc = SQLITE_ERROR;\n      p->zErrmsg = sqlite3_mprintf(\"cannot vacuum wal mode database\");\n    }else{\n      char *zTarget;\n      char *zExtra = 0;\n      if( strlen(p->zRbu)>=5 && 0==memcmp(\"file:\", p->zRbu, 5) ){\n        zExtra = &p->zRbu[5];\n        while( *zExtra ){\n          if( *zExtra++=='?' ) break;\n        }\n        if( *zExtra=='\\0' ) zExtra = 0;\n      }\n\n      zTarget = sqlite3_mprintf(\"file:%s-vacuum?rbu_memory=1%s%s\", \n          sqlite3_db_filename(p->dbRbu, \"main\"),\n          (zExtra==0 ? \"\" : \"&\"), (zExtra==0 ? \"\" : zExtra)\n      );\n\n      if( zTarget==0 ){\n        p->rc = SQLITE_NOMEM;\n        return;\n      }\n      p->dbMain = rbuOpenDbhandle(p, zTarget, p->nRbu<=1);\n      sqlite3_free(zTarget);\n    }\n  }\n\n  if( p->rc==SQLITE_OK ){\n    p->rc = sqlite3_create_function(p->dbMain, \n        \"rbu_tmp_insert\", -1, SQLITE_UTF8, (void*)p, rbuTmpInsertFunc, 0, 0\n    );\n  }\n\n  if( p->rc==SQLITE_OK ){\n    p->rc = sqlite3_create_function(p->dbMain, \n        \"rbu_fossil_delta\", 2, SQLITE_UTF8, 0, rbuFossilDeltaFunc, 0, 0\n    );\n  }\n\n  if( p->rc==SQLITE_OK ){\n    p->rc = sqlite3_create_function(p->dbRbu, \n        \"rbu_target_name\", -1, SQLITE_UTF8, (void*)p, rbuTargetNameFunc, 0, 0\n    );\n  }\n\n  if( p->rc==SQLITE_OK ){\n    p->rc = sqlite3_file_control(p->dbMain, \"main\", SQLITE_FCNTL_RBU, (void*)p);\n  }\n  rbuMPrintfExec(p, p->dbMain, \"SELECT * FROM sqlite_master\");\n\n  /* Mark the database file just opened as an RBU target database. If \n  ** this call returns SQLITE_NOTFOUND, then the RBU vfs is not in use.\n  ** This is an error.  */\n  if( p->rc==SQLITE_OK ){\n    p->rc = sqlite3_file_control(p->dbMain, \"main\", SQLITE_FCNTL_RBU, (void*)p);\n  }\n\n  if( p->rc==SQLITE_NOTFOUND ){\n    p->rc = SQLITE_ERROR;\n    p->zErrmsg = sqlite3_mprintf(\"rbu vfs not found\");\n  }\n}\n\n/*\n** This routine is a copy of the sqlite3FileSuffix3() routine from the core.\n** It is a no-op unless SQLITE_ENABLE_8_3_NAMES is defined.\n**\n** If SQLITE_ENABLE_8_3_NAMES is set at compile-time and if the database\n** filename in zBaseFilename is a URI with the \"8_3_names=1\" parameter and\n** if filename in z[] has a suffix (a.k.a. \"extension\") that is longer than\n** three characters, then shorten the suffix on z[] to be the last three\n** characters of the original suffix.\n**\n** If SQLITE_ENABLE_8_3_NAMES is set to 2 at compile-time, then always\n** do the suffix shortening regardless of URI parameter.\n**\n** Examples:\n**\n**     test.db-journal    =>   test.nal\n**     test.db-wal        =>   test.wal\n**     test.db-shm        =>   test.shm\n**     test.db-mj7f3319fa =>   test.9fa\n*/\nstatic void rbuFileSuffix3(const char *zBase, char *z){\n#ifdef SQLITE_ENABLE_8_3_NAMES\n#if SQLITE_ENABLE_8_3_NAMES<2\n  if( sqlite3_uri_boolean(zBase, \"8_3_names\", 0) )\n#endif\n  {\n    int i, sz;\n    sz = (int)strlen(z)&0xffffff;\n    for(i=sz-1; i>0 && z[i]!='/' && z[i]!='.'; i--){}\n    if( z[i]=='.' && sz>i+4 ) memmove(&z[i+1], &z[sz-3], 4);\n  }\n#endif\n}\n\n/*\n** Return the current wal-index header checksum for the target database \n** as a 64-bit integer.\n**\n** The checksum is store in the first page of xShmMap memory as an 8-byte \n** blob starting at byte offset 40.\n*/\nstatic i64 rbuShmChecksum(sqlite3rbu *p){\n  i64 iRet = 0;\n  if( p->rc==SQLITE_OK ){\n    sqlite3_file *pDb = p->pTargetFd->pReal;\n    u32 volatile *ptr;\n    p->rc = pDb->pMethods->xShmMap(pDb, 0, 32*1024, 0, (void volatile**)&ptr);\n    if( p->rc==SQLITE_OK ){\n      iRet = ((i64)ptr[10] << 32) + ptr[11];\n    }\n  }\n  return iRet;\n}\n\n/*\n** This function is called as part of initializing or reinitializing an\n** incremental checkpoint. \n**\n** It populates the sqlite3rbu.aFrame[] array with the set of \n** (wal frame -> db page) copy operations required to checkpoint the \n** current wal file, and obtains the set of shm locks required to safely \n** perform the copy operations directly on the file-system.\n**\n** If argument pState is not NULL, then the incremental checkpoint is\n** being resumed. In this case, if the checksum of the wal-index-header\n** following recovery is not the same as the checksum saved in the RbuState\n** object, then the rbu handle is set to DONE state. This occurs if some\n** other client appends a transaction to the wal file in the middle of\n** an incremental checkpoint.\n*/\nstatic void rbuSetupCheckpoint(sqlite3rbu *p, RbuState *pState){\n\n  /* If pState is NULL, then the wal file may not have been opened and\n  ** recovered. Running a read-statement here to ensure that doing so\n  ** does not interfere with the \"capture\" process below.  */\n  if( pState==0 ){\n    p->eStage = 0;\n    if( p->rc==SQLITE_OK ){\n      p->rc = sqlite3_exec(p->dbMain, \"SELECT * FROM sqlite_master\", 0, 0, 0);\n    }\n  }\n\n  /* Assuming no error has occurred, run a \"restart\" checkpoint with the\n  ** sqlite3rbu.eStage variable set to CAPTURE. This turns on the following\n  ** special behaviour in the rbu VFS:\n  **\n  **   * If the exclusive shm WRITER or READ0 lock cannot be obtained,\n  **     the checkpoint fails with SQLITE_BUSY (normally SQLite would\n  **     proceed with running a passive checkpoint instead of failing).\n  **\n  **   * Attempts to read from the *-wal file or write to the database file\n  **     do not perform any IO. Instead, the frame/page combinations that\n  **     would be read/written are recorded in the sqlite3rbu.aFrame[]\n  **     array.\n  **\n  **   * Calls to xShmLock(UNLOCK) to release the exclusive shm WRITER, \n  **     READ0 and CHECKPOINT locks taken as part of the checkpoint are\n  **     no-ops. These locks will not be released until the connection\n  **     is closed.\n  **\n  **   * Attempting to xSync() the database file causes an SQLITE_INTERNAL \n  **     error.\n  **\n  ** As a result, unless an error (i.e. OOM or SQLITE_BUSY) occurs, the\n  ** checkpoint below fails with SQLITE_INTERNAL, and leaves the aFrame[]\n  ** array populated with a set of (frame -> page) mappings. Because the \n  ** WRITER, CHECKPOINT and READ0 locks are still held, it is safe to copy \n  ** data from the wal file into the database file according to the \n  ** contents of aFrame[].\n  */\n  if( p->rc==SQLITE_OK ){\n    int rc2;\n    p->eStage = RBU_STAGE_CAPTURE;\n    rc2 = sqlite3_exec(p->dbMain, \"PRAGMA main.wal_checkpoint=restart\", 0, 0,0);\n    if( rc2!=SQLITE_INTERNAL ) p->rc = rc2;\n  }\n\n  if( p->rc==SQLITE_OK && p->nFrame>0 ){\n    p->eStage = RBU_STAGE_CKPT;\n    p->nStep = (pState ? pState->nRow : 0);\n    p->aBuf = rbuMalloc(p, p->pgsz);\n    p->iWalCksum = rbuShmChecksum(p);\n  }\n\n  if( p->rc==SQLITE_OK ){\n    if( p->nFrame==0 || (pState && pState->iWalCksum!=p->iWalCksum) ){\n      p->rc = SQLITE_DONE;\n      p->eStage = RBU_STAGE_DONE;\n    }else{\n      int nSectorSize;\n      sqlite3_file *pDb = p->pTargetFd->pReal;\n      sqlite3_file *pWal = p->pTargetFd->pWalFd->pReal;\n      assert( p->nPagePerSector==0 );\n      nSectorSize = pDb->pMethods->xSectorSize(pDb);\n      if( nSectorSize>p->pgsz ){\n        p->nPagePerSector = nSectorSize / p->pgsz;\n      }else{\n        p->nPagePerSector = 1;\n      }\n\n      /* Call xSync() on the wal file. This causes SQLite to sync the \n      ** directory in which the target database and the wal file reside, in \n      ** case it has not been synced since the rename() call in \n      ** rbuMoveOalFile(). */\n      p->rc = pWal->pMethods->xSync(pWal, SQLITE_SYNC_NORMAL);\n    }\n  }\n}\n\n/*\n** Called when iAmt bytes are read from offset iOff of the wal file while\n** the rbu object is in capture mode. Record the frame number of the frame\n** being read in the aFrame[] array.\n*/\nstatic int rbuCaptureWalRead(sqlite3rbu *pRbu, i64 iOff, int iAmt){\n  const u32 mReq = (1<<WAL_LOCK_WRITE)|(1<<WAL_LOCK_CKPT)|(1<<WAL_LOCK_READ0);\n  u32 iFrame;\n\n  if( pRbu->mLock!=mReq ){\n    pRbu->rc = SQLITE_BUSY;\n    return SQLITE_INTERNAL;\n  }\n\n  pRbu->pgsz = iAmt;\n  if( pRbu->nFrame==pRbu->nFrameAlloc ){\n    int nNew = (pRbu->nFrameAlloc ? pRbu->nFrameAlloc : 64) * 2;\n    RbuFrame *aNew;\n    aNew = (RbuFrame*)sqlite3_realloc64(pRbu->aFrame, nNew * sizeof(RbuFrame));\n    if( aNew==0 ) return SQLITE_NOMEM;\n    pRbu->aFrame = aNew;\n    pRbu->nFrameAlloc = nNew;\n  }\n\n  iFrame = (u32)((iOff-32) / (i64)(iAmt+24)) + 1;\n  if( pRbu->iMaxFrame<iFrame ) pRbu->iMaxFrame = iFrame;\n  pRbu->aFrame[pRbu->nFrame].iWalFrame = iFrame;\n  pRbu->aFrame[pRbu->nFrame].iDbPage = 0;\n  pRbu->nFrame++;\n  return SQLITE_OK;\n}\n\n/*\n** Called when a page of data is written to offset iOff of the database\n** file while the rbu handle is in capture mode. Record the page number \n** of the page being written in the aFrame[] array.\n*/\nstatic int rbuCaptureDbWrite(sqlite3rbu *pRbu, i64 iOff){\n  pRbu->aFrame[pRbu->nFrame-1].iDbPage = (u32)(iOff / pRbu->pgsz) + 1;\n  return SQLITE_OK;\n}\n\n/*\n** This is called as part of an incremental checkpoint operation. Copy\n** a single frame of data from the wal file into the database file, as\n** indicated by the RbuFrame object.\n*/\nstatic void rbuCheckpointFrame(sqlite3rbu *p, RbuFrame *pFrame){\n  sqlite3_file *pWal = p->pTargetFd->pWalFd->pReal;\n  sqlite3_file *pDb = p->pTargetFd->pReal;\n  i64 iOff;\n\n  assert( p->rc==SQLITE_OK );\n  iOff = (i64)(pFrame->iWalFrame-1) * (p->pgsz + 24) + 32 + 24;\n  p->rc = pWal->pMethods->xRead(pWal, p->aBuf, p->pgsz, iOff);\n  if( p->rc ) return;\n\n  iOff = (i64)(pFrame->iDbPage-1) * p->pgsz;\n  p->rc = pDb->pMethods->xWrite(pDb, p->aBuf, p->pgsz, iOff);\n}\n\n\n/*\n** Take an EXCLUSIVE lock on the database file.\n*/\nstatic void rbuLockDatabase(sqlite3rbu *p){\n  sqlite3_file *pReal = p->pTargetFd->pReal;\n  assert( p->rc==SQLITE_OK );\n  p->rc = pReal->pMethods->xLock(pReal, SQLITE_LOCK_SHARED);\n  if( p->rc==SQLITE_OK ){\n    p->rc = pReal->pMethods->xLock(pReal, SQLITE_LOCK_EXCLUSIVE);\n  }\n}\n\n#if defined(_WIN32_WCE)\nstatic LPWSTR rbuWinUtf8ToUnicode(const char *zFilename){\n  int nChar;\n  LPWSTR zWideFilename;\n\n  nChar = MultiByteToWideChar(CP_UTF8, 0, zFilename, -1, NULL, 0);\n  if( nChar==0 ){\n    return 0;\n  }\n  zWideFilename = sqlite3_malloc64( nChar*sizeof(zWideFilename[0]) );\n  if( zWideFilename==0 ){\n    return 0;\n  }\n  memset(zWideFilename, 0, nChar*sizeof(zWideFilename[0]));\n  nChar = MultiByteToWideChar(CP_UTF8, 0, zFilename, -1, zWideFilename,\n                                nChar);\n  if( nChar==0 ){\n    sqlite3_free(zWideFilename);\n    zWideFilename = 0;\n  }\n  return zWideFilename;\n}\n#endif\n\n/*\n** The RBU handle is currently in RBU_STAGE_OAL state, with a SHARED lock\n** on the database file. This proc moves the *-oal file to the *-wal path,\n** then reopens the database file (this time in vanilla, non-oal, WAL mode).\n** If an error occurs, leave an error code and error message in the rbu \n** handle.\n*/\nstatic void rbuMoveOalFile(sqlite3rbu *p){\n  const char *zBase = sqlite3_db_filename(p->dbMain, \"main\");\n  const char *zMove = zBase;\n  char *zOal;\n  char *zWal;\n\n  if( rbuIsVacuum(p) ){\n    zMove = sqlite3_db_filename(p->dbRbu, \"main\");\n  }\n  zOal = sqlite3_mprintf(\"%s-oal\", zMove);\n  zWal = sqlite3_mprintf(\"%s-wal\", zMove);\n\n  assert( p->eStage==RBU_STAGE_MOVE );\n  assert( p->rc==SQLITE_OK && p->zErrmsg==0 );\n  if( zWal==0 || zOal==0 ){\n    p->rc = SQLITE_NOMEM;\n  }else{\n    /* Move the *-oal file to *-wal. At this point connection p->db is\n    ** holding a SHARED lock on the target database file (because it is\n    ** in WAL mode). So no other connection may be writing the db. \n    **\n    ** In order to ensure that there are no database readers, an EXCLUSIVE\n    ** lock is obtained here before the *-oal is moved to *-wal.\n    */\n    rbuLockDatabase(p);\n    if( p->rc==SQLITE_OK ){\n      rbuFileSuffix3(zBase, zWal);\n      rbuFileSuffix3(zBase, zOal);\n\n      /* Re-open the databases. */\n      rbuObjIterFinalize(&p->objiter);\n      sqlite3_close(p->dbRbu);\n      sqlite3_close(p->dbMain);\n      p->dbMain = 0;\n      p->dbRbu = 0;\n\n#if defined(_WIN32_WCE)\n      {\n        LPWSTR zWideOal;\n        LPWSTR zWideWal;\n\n        zWideOal = rbuWinUtf8ToUnicode(zOal);\n        if( zWideOal ){\n          zWideWal = rbuWinUtf8ToUnicode(zWal);\n          if( zWideWal ){\n            if( MoveFileW(zWideOal, zWideWal) ){\n              p->rc = SQLITE_OK;\n            }else{\n              p->rc = SQLITE_IOERR;\n            }\n            sqlite3_free(zWideWal);\n          }else{\n            p->rc = SQLITE_IOERR_NOMEM;\n          }\n          sqlite3_free(zWideOal);\n        }else{\n          p->rc = SQLITE_IOERR_NOMEM;\n        }\n      }\n#else\n      p->rc = rename(zOal, zWal) ? SQLITE_IOERR : SQLITE_OK;\n#endif\n\n      if( p->rc==SQLITE_OK ){\n        rbuOpenDatabase(p, 0);\n        rbuSetupCheckpoint(p, 0);\n      }\n    }\n  }\n\n  sqlite3_free(zWal);\n  sqlite3_free(zOal);\n}\n\n/*\n** The SELECT statement iterating through the keys for the current object\n** (p->objiter.pSelect) currently points to a valid row. This function\n** determines the type of operation requested by this row and returns\n** one of the following values to indicate the result:\n**\n**     * RBU_INSERT\n**     * RBU_DELETE\n**     * RBU_IDX_DELETE\n**     * RBU_UPDATE\n**\n** If RBU_UPDATE is returned, then output variable *pzMask is set to\n** point to the text value indicating the columns to update.\n**\n** If the rbu_control field contains an invalid value, an error code and\n** message are left in the RBU handle and zero returned.\n*/\nstatic int rbuStepType(sqlite3rbu *p, const char **pzMask){\n  int iCol = p->objiter.nCol;     /* Index of rbu_control column */\n  int res = 0;                    /* Return value */\n\n  switch( sqlite3_column_type(p->objiter.pSelect, iCol) ){\n    case SQLITE_INTEGER: {\n      int iVal = sqlite3_column_int(p->objiter.pSelect, iCol);\n      switch( iVal ){\n        case 0: res = RBU_INSERT;     break;\n        case 1: res = RBU_DELETE;     break;\n        case 2: res = RBU_REPLACE;    break;\n        case 3: res = RBU_IDX_DELETE; break;\n        case 4: res = RBU_IDX_INSERT; break;\n      }\n      break;\n    }\n\n    case SQLITE_TEXT: {\n      const unsigned char *z = sqlite3_column_text(p->objiter.pSelect, iCol);\n      if( z==0 ){\n        p->rc = SQLITE_NOMEM;\n      }else{\n        *pzMask = (const char*)z;\n      }\n      res = RBU_UPDATE;\n\n      break;\n    }\n\n    default:\n      break;\n  }\n\n  if( res==0 ){\n    rbuBadControlError(p);\n  }\n  return res;\n}\n\n#ifdef SQLITE_DEBUG\n/*\n** Assert that column iCol of statement pStmt is named zName.\n*/\nstatic void assertColumnName(sqlite3_stmt *pStmt, int iCol, const char *zName){\n  const char *zCol = sqlite3_column_name(pStmt, iCol);\n  assert( 0==sqlite3_stricmp(zName, zCol) );\n}\n#else\n# define assertColumnName(x,y,z)\n#endif\n\n/*\n** Argument eType must be one of RBU_INSERT, RBU_DELETE, RBU_IDX_INSERT or\n** RBU_IDX_DELETE. This function performs the work of a single\n** sqlite3rbu_step() call for the type of operation specified by eType.\n*/\nstatic void rbuStepOneOp(sqlite3rbu *p, int eType){\n  RbuObjIter *pIter = &p->objiter;\n  sqlite3_value *pVal;\n  sqlite3_stmt *pWriter;\n  int i;\n\n  assert( p->rc==SQLITE_OK );\n  assert( eType!=RBU_DELETE || pIter->zIdx==0 );\n  assert( eType==RBU_DELETE || eType==RBU_IDX_DELETE\n       || eType==RBU_INSERT || eType==RBU_IDX_INSERT\n  );\n\n  /* If this is a delete, decrement nPhaseOneStep by nIndex. If the DELETE\n  ** statement below does actually delete a row, nPhaseOneStep will be\n  ** incremented by the same amount when SQL function rbu_tmp_insert()\n  ** is invoked by the trigger.  */\n  if( eType==RBU_DELETE ){\n    p->nPhaseOneStep -= p->objiter.nIndex;\n  }\n\n  if( eType==RBU_IDX_DELETE || eType==RBU_DELETE ){\n    pWriter = pIter->pDelete;\n  }else{\n    pWriter = pIter->pInsert;\n  }\n\n  for(i=0; i<pIter->nCol; i++){\n    /* If this is an INSERT into a table b-tree and the table has an\n    ** explicit INTEGER PRIMARY KEY, check that this is not an attempt\n    ** to write a NULL into the IPK column. That is not permitted.  */\n    if( eType==RBU_INSERT \n     && pIter->zIdx==0 && pIter->eType==RBU_PK_IPK && pIter->abTblPk[i] \n     && sqlite3_column_type(pIter->pSelect, i)==SQLITE_NULL\n    ){\n      p->rc = SQLITE_MISMATCH;\n      p->zErrmsg = sqlite3_mprintf(\"datatype mismatch\");\n      return;\n    }\n\n    if( eType==RBU_DELETE && pIter->abTblPk[i]==0 ){\n      continue;\n    }\n\n    pVal = sqlite3_column_value(pIter->pSelect, i);\n    p->rc = sqlite3_bind_value(pWriter, i+1, pVal);\n    if( p->rc ) return;\n  }\n  if( pIter->zIdx==0 ){\n    if( pIter->eType==RBU_PK_VTAB \n     || pIter->eType==RBU_PK_NONE \n     || (pIter->eType==RBU_PK_EXTERNAL && rbuIsVacuum(p)) \n    ){\n      /* For a virtual table, or a table with no primary key, the \n      ** SELECT statement is:\n      **\n      **   SELECT <cols>, rbu_control, rbu_rowid FROM ....\n      **\n      ** Hence column_value(pIter->nCol+1).\n      */\n      assertColumnName(pIter->pSelect, pIter->nCol+1, \n          rbuIsVacuum(p) ? \"rowid\" : \"rbu_rowid\"\n      );\n      pVal = sqlite3_column_value(pIter->pSelect, pIter->nCol+1);\n      p->rc = sqlite3_bind_value(pWriter, pIter->nCol+1, pVal);\n    }\n  }\n  if( p->rc==SQLITE_OK ){\n    sqlite3_step(pWriter);\n    p->rc = resetAndCollectError(pWriter, &p->zErrmsg);\n  }\n}\n\n/*\n** This function does the work for an sqlite3rbu_step() call.\n**\n** The object-iterator (p->objiter) currently points to a valid object,\n** and the input cursor (p->objiter.pSelect) currently points to a valid\n** input row. Perform whatever processing is required and return.\n**\n** If no  error occurs, SQLITE_OK is returned. Otherwise, an error code\n** and message is left in the RBU handle and a copy of the error code\n** returned.\n*/\nstatic int rbuStep(sqlite3rbu *p){\n  RbuObjIter *pIter = &p->objiter;\n  const char *zMask = 0;\n  int eType = rbuStepType(p, &zMask);\n\n  if( eType ){\n    assert( eType==RBU_INSERT     || eType==RBU_DELETE\n         || eType==RBU_REPLACE    || eType==RBU_IDX_DELETE\n         || eType==RBU_IDX_INSERT || eType==RBU_UPDATE\n    );\n    assert( eType!=RBU_UPDATE || pIter->zIdx==0 );\n\n    if( pIter->zIdx==0 && (eType==RBU_IDX_DELETE || eType==RBU_IDX_INSERT) ){\n      rbuBadControlError(p);\n    }\n    else if( eType==RBU_REPLACE ){\n      if( pIter->zIdx==0 ){\n        p->nPhaseOneStep += p->objiter.nIndex;\n        rbuStepOneOp(p, RBU_DELETE);\n      }\n      if( p->rc==SQLITE_OK ) rbuStepOneOp(p, RBU_INSERT);\n    }\n    else if( eType!=RBU_UPDATE ){\n      rbuStepOneOp(p, eType);\n    }\n    else{\n      sqlite3_value *pVal;\n      sqlite3_stmt *pUpdate = 0;\n      assert( eType==RBU_UPDATE );\n      p->nPhaseOneStep -= p->objiter.nIndex;\n      rbuGetUpdateStmt(p, pIter, zMask, &pUpdate);\n      if( pUpdate ){\n        int i;\n        for(i=0; p->rc==SQLITE_OK && i<pIter->nCol; i++){\n          char c = zMask[pIter->aiSrcOrder[i]];\n          pVal = sqlite3_column_value(pIter->pSelect, i);\n          if( pIter->abTblPk[i] || c!='.' ){\n            p->rc = sqlite3_bind_value(pUpdate, i+1, pVal);\n          }\n        }\n        if( p->rc==SQLITE_OK \n         && (pIter->eType==RBU_PK_VTAB || pIter->eType==RBU_PK_NONE) \n        ){\n          /* Bind the rbu_rowid value to column _rowid_ */\n          assertColumnName(pIter->pSelect, pIter->nCol+1, \"rbu_rowid\");\n          pVal = sqlite3_column_value(pIter->pSelect, pIter->nCol+1);\n          p->rc = sqlite3_bind_value(pUpdate, pIter->nCol+1, pVal);\n        }\n        if( p->rc==SQLITE_OK ){\n          sqlite3_step(pUpdate);\n          p->rc = resetAndCollectError(pUpdate, &p->zErrmsg);\n        }\n      }\n    }\n  }\n  return p->rc;\n}\n\n/*\n** Increment the schema cookie of the main database opened by p->dbMain.\n**\n** Or, if this is an RBU vacuum, set the schema cookie of the main db\n** opened by p->dbMain to one more than the schema cookie of the main\n** db opened by p->dbRbu.\n*/\nstatic void rbuIncrSchemaCookie(sqlite3rbu *p){\n  if( p->rc==SQLITE_OK ){\n    sqlite3 *dbread = (rbuIsVacuum(p) ? p->dbRbu : p->dbMain);\n    int iCookie = 1000000;\n    sqlite3_stmt *pStmt;\n\n    p->rc = prepareAndCollectError(dbread, &pStmt, &p->zErrmsg, \n        \"PRAGMA schema_version\"\n    );\n    if( p->rc==SQLITE_OK ){\n      /* Coverage: it may be that this sqlite3_step() cannot fail. There\n      ** is already a transaction open, so the prepared statement cannot\n      ** throw an SQLITE_SCHEMA exception. The only database page the\n      ** statement reads is page 1, which is guaranteed to be in the cache.\n      ** And no memory allocations are required.  */\n      if( SQLITE_ROW==sqlite3_step(pStmt) ){\n        iCookie = sqlite3_column_int(pStmt, 0);\n      }\n      rbuFinalize(p, pStmt);\n    }\n    if( p->rc==SQLITE_OK ){\n      rbuMPrintfExec(p, p->dbMain, \"PRAGMA schema_version = %d\", iCookie+1);\n    }\n  }\n}\n\n/*\n** Update the contents of the rbu_state table within the rbu database. The\n** value stored in the RBU_STATE_STAGE column is eStage. All other values\n** are determined by inspecting the rbu handle passed as the first argument.\n*/\nstatic void rbuSaveState(sqlite3rbu *p, int eStage){\n  if( p->rc==SQLITE_OK || p->rc==SQLITE_DONE ){\n    sqlite3_stmt *pInsert = 0;\n    rbu_file *pFd = (rbuIsVacuum(p) ? p->pRbuFd : p->pTargetFd);\n    int rc;\n\n    assert( p->zErrmsg==0 );\n    rc = prepareFreeAndCollectError(p->dbRbu, &pInsert, &p->zErrmsg, \n        sqlite3_mprintf(\n          \"INSERT OR REPLACE INTO %s.rbu_state(k, v) VALUES \"\n          \"(%d, %d), \"\n          \"(%d, %Q), \"\n          \"(%d, %Q), \"\n          \"(%d, %d), \"\n          \"(%d, %d), \"\n          \"(%d, %lld), \"\n          \"(%d, %lld), \"\n          \"(%d, %lld), \"\n          \"(%d, %lld) \",\n          p->zStateDb,\n          RBU_STATE_STAGE, eStage,\n          RBU_STATE_TBL, p->objiter.zTbl, \n          RBU_STATE_IDX, p->objiter.zIdx, \n          RBU_STATE_ROW, p->nStep, \n          RBU_STATE_PROGRESS, p->nProgress,\n          RBU_STATE_CKPT, p->iWalCksum,\n          RBU_STATE_COOKIE, (i64)pFd->iCookie,\n          RBU_STATE_OALSZ, p->iOalSz,\n          RBU_STATE_PHASEONESTEP, p->nPhaseOneStep\n      )\n    );\n    assert( pInsert==0 || rc==SQLITE_OK );\n\n    if( rc==SQLITE_OK ){\n      sqlite3_step(pInsert);\n      rc = sqlite3_finalize(pInsert);\n    }\n    if( rc!=SQLITE_OK ) p->rc = rc;\n  }\n}\n\n\n/*\n** The second argument passed to this function is the name of a PRAGMA \n** setting - \"page_size\", \"auto_vacuum\", \"user_version\" or \"application_id\".\n** This function executes the following on sqlite3rbu.dbRbu:\n**\n**   \"PRAGMA main.$zPragma\"\n**\n** where $zPragma is the string passed as the second argument, then\n** on sqlite3rbu.dbMain:\n**\n**   \"PRAGMA main.$zPragma = $val\"\n**\n** where $val is the value returned by the first PRAGMA invocation.\n**\n** In short, it copies the value  of the specified PRAGMA setting from\n** dbRbu to dbMain.\n*/\nstatic void rbuCopyPragma(sqlite3rbu *p, const char *zPragma){\n  if( p->rc==SQLITE_OK ){\n    sqlite3_stmt *pPragma = 0;\n    p->rc = prepareFreeAndCollectError(p->dbRbu, &pPragma, &p->zErrmsg, \n        sqlite3_mprintf(\"PRAGMA main.%s\", zPragma)\n    );\n    if( p->rc==SQLITE_OK && SQLITE_ROW==sqlite3_step(pPragma) ){\n      p->rc = rbuMPrintfExec(p, p->dbMain, \"PRAGMA main.%s = %d\",\n          zPragma, sqlite3_column_int(pPragma, 0)\n      );\n    }\n    rbuFinalize(p, pPragma);\n  }\n}\n\n/*\n** The RBU handle passed as the only argument has just been opened and \n** the state database is empty. If this RBU handle was opened for an\n** RBU vacuum operation, create the schema in the target db.\n*/\nstatic void rbuCreateTargetSchema(sqlite3rbu *p){\n  sqlite3_stmt *pSql = 0;\n  sqlite3_stmt *pInsert = 0;\n\n  assert( rbuIsVacuum(p) );\n  p->rc = sqlite3_exec(p->dbMain, \"PRAGMA writable_schema=1\", 0,0, &p->zErrmsg);\n  if( p->rc==SQLITE_OK ){\n    p->rc = prepareAndCollectError(p->dbRbu, &pSql, &p->zErrmsg, \n      \"SELECT sql FROM sqlite_master WHERE sql!='' AND rootpage!=0\"\n      \" AND name!='sqlite_sequence' \"\n      \" ORDER BY type DESC\"\n    );\n  }\n\n  while( p->rc==SQLITE_OK && sqlite3_step(pSql)==SQLITE_ROW ){\n    const char *zSql = (const char*)sqlite3_column_text(pSql, 0);\n    p->rc = sqlite3_exec(p->dbMain, zSql, 0, 0, &p->zErrmsg);\n  }\n  rbuFinalize(p, pSql);\n  if( p->rc!=SQLITE_OK ) return;\n\n  if( p->rc==SQLITE_OK ){\n    p->rc = prepareAndCollectError(p->dbRbu, &pSql, &p->zErrmsg, \n        \"SELECT * FROM sqlite_master WHERE rootpage=0 OR rootpage IS NULL\" \n    );\n  }\n\n  if( p->rc==SQLITE_OK ){\n    p->rc = prepareAndCollectError(p->dbMain, &pInsert, &p->zErrmsg, \n        \"INSERT INTO sqlite_master VALUES(?,?,?,?,?)\"\n    );\n  }\n\n  while( p->rc==SQLITE_OK && sqlite3_step(pSql)==SQLITE_ROW ){\n    int i;\n    for(i=0; i<5; i++){\n      sqlite3_bind_value(pInsert, i+1, sqlite3_column_value(pSql, i));\n    }\n    sqlite3_step(pInsert);\n    p->rc = sqlite3_reset(pInsert);\n  }\n  if( p->rc==SQLITE_OK ){\n    p->rc = sqlite3_exec(p->dbMain, \"PRAGMA writable_schema=0\",0,0,&p->zErrmsg);\n  }\n\n  rbuFinalize(p, pSql);\n  rbuFinalize(p, pInsert);\n}\n\n/*\n** Step the RBU object.\n*/\nSQLITE_API int sqlite3rbu_step(sqlite3rbu *p){\n  if( p ){\n    switch( p->eStage ){\n      case RBU_STAGE_OAL: {\n        RbuObjIter *pIter = &p->objiter;\n\n        /* If this is an RBU vacuum operation and the state table was empty\n        ** when this handle was opened, create the target database schema. */\n        if( rbuIsVacuum(p) && p->nProgress==0 && p->rc==SQLITE_OK ){\n          rbuCreateTargetSchema(p);\n          rbuCopyPragma(p, \"user_version\");\n          rbuCopyPragma(p, \"application_id\");\n        }\n\n        while( p->rc==SQLITE_OK && pIter->zTbl ){\n\n          if( pIter->bCleanup ){\n            /* Clean up the rbu_tmp_xxx table for the previous table. It \n            ** cannot be dropped as there are currently active SQL statements.\n            ** But the contents can be deleted.  */\n            if( rbuIsVacuum(p)==0 && pIter->abIndexed ){\n              rbuMPrintfExec(p, p->dbRbu, \n                  \"DELETE FROM %s.'rbu_tmp_%q'\", p->zStateDb, pIter->zDataTbl\n              );\n            }\n          }else{\n            rbuObjIterPrepareAll(p, pIter, 0);\n\n            /* Advance to the next row to process. */\n            if( p->rc==SQLITE_OK ){\n              int rc = sqlite3_step(pIter->pSelect);\n              if( rc==SQLITE_ROW ){\n                p->nProgress++;\n                p->nStep++;\n                return rbuStep(p);\n              }\n              p->rc = sqlite3_reset(pIter->pSelect);\n              p->nStep = 0;\n            }\n          }\n\n          rbuObjIterNext(p, pIter);\n        }\n\n        if( p->rc==SQLITE_OK ){\n          assert( pIter->zTbl==0 );\n          rbuSaveState(p, RBU_STAGE_MOVE);\n          rbuIncrSchemaCookie(p);\n          if( p->rc==SQLITE_OK ){\n            p->rc = sqlite3_exec(p->dbMain, \"COMMIT\", 0, 0, &p->zErrmsg);\n          }\n          if( p->rc==SQLITE_OK ){\n            p->rc = sqlite3_exec(p->dbRbu, \"COMMIT\", 0, 0, &p->zErrmsg);\n          }\n          p->eStage = RBU_STAGE_MOVE;\n        }\n        break;\n      }\n\n      case RBU_STAGE_MOVE: {\n        if( p->rc==SQLITE_OK ){\n          rbuMoveOalFile(p);\n          p->nProgress++;\n        }\n        break;\n      }\n\n      case RBU_STAGE_CKPT: {\n        if( p->rc==SQLITE_OK ){\n          if( p->nStep>=p->nFrame ){\n            sqlite3_file *pDb = p->pTargetFd->pReal;\n  \n            /* Sync the db file */\n            p->rc = pDb->pMethods->xSync(pDb, SQLITE_SYNC_NORMAL);\n  \n            /* Update nBackfill */\n            if( p->rc==SQLITE_OK ){\n              void volatile *ptr;\n              p->rc = pDb->pMethods->xShmMap(pDb, 0, 32*1024, 0, &ptr);\n              if( p->rc==SQLITE_OK ){\n                ((u32 volatile*)ptr)[24] = p->iMaxFrame;\n              }\n            }\n  \n            if( p->rc==SQLITE_OK ){\n              p->eStage = RBU_STAGE_DONE;\n              p->rc = SQLITE_DONE;\n            }\n          }else{\n            /* At one point the following block copied a single frame from the\n            ** wal file to the database file. So that one call to sqlite3rbu_step()\n            ** checkpointed a single frame. \n            **\n            ** However, if the sector-size is larger than the page-size, and the\n            ** application calls sqlite3rbu_savestate() or close() immediately\n            ** after this step, then rbu_step() again, then a power failure occurs,\n            ** then the database page written here may be damaged. Work around\n            ** this by checkpointing frames until the next page in the aFrame[]\n            ** lies on a different disk sector to the current one. */\n            u32 iSector;\n            do{\n              RbuFrame *pFrame = &p->aFrame[p->nStep];\n              iSector = (pFrame->iDbPage-1) / p->nPagePerSector;\n              rbuCheckpointFrame(p, pFrame);\n              p->nStep++;\n            }while( p->nStep<p->nFrame \n                 && iSector==((p->aFrame[p->nStep].iDbPage-1) / p->nPagePerSector)\n                 && p->rc==SQLITE_OK\n            );\n          }\n          p->nProgress++;\n        }\n        break;\n      }\n\n      default:\n        break;\n    }\n    return p->rc;\n  }else{\n    return SQLITE_NOMEM;\n  }\n}\n\n/*\n** Compare strings z1 and z2, returning 0 if they are identical, or non-zero\n** otherwise. Either or both argument may be NULL. Two NULL values are\n** considered equal, and NULL is considered distinct from all other values.\n*/\nstatic int rbuStrCompare(const char *z1, const char *z2){\n  if( z1==0 && z2==0 ) return 0;\n  if( z1==0 || z2==0 ) return 1;\n  return (sqlite3_stricmp(z1, z2)!=0);\n}\n\n/*\n** This function is called as part of sqlite3rbu_open() when initializing\n** an rbu handle in OAL stage. If the rbu update has not started (i.e.\n** the rbu_state table was empty) it is a no-op. Otherwise, it arranges\n** things so that the next call to sqlite3rbu_step() continues on from\n** where the previous rbu handle left off.\n**\n** If an error occurs, an error code and error message are left in the\n** rbu handle passed as the first argument.\n*/\nstatic void rbuSetupOal(sqlite3rbu *p, RbuState *pState){\n  assert( p->rc==SQLITE_OK );\n  if( pState->zTbl ){\n    RbuObjIter *pIter = &p->objiter;\n    int rc = SQLITE_OK;\n\n    while( rc==SQLITE_OK && pIter->zTbl && (pIter->bCleanup \n       || rbuStrCompare(pIter->zIdx, pState->zIdx)\n       || rbuStrCompare(pIter->zTbl, pState->zTbl) \n    )){\n      rc = rbuObjIterNext(p, pIter);\n    }\n\n    if( rc==SQLITE_OK && !pIter->zTbl ){\n      rc = SQLITE_ERROR;\n      p->zErrmsg = sqlite3_mprintf(\"rbu_state mismatch error\");\n    }\n\n    if( rc==SQLITE_OK ){\n      p->nStep = pState->nRow;\n      rc = rbuObjIterPrepareAll(p, &p->objiter, p->nStep);\n    }\n\n    p->rc = rc;\n  }\n}\n\n/*\n** If there is a \"*-oal\" file in the file-system corresponding to the\n** target database in the file-system, delete it. If an error occurs,\n** leave an error code and error message in the rbu handle.\n*/\nstatic void rbuDeleteOalFile(sqlite3rbu *p){\n  char *zOal = rbuMPrintf(p, \"%s-oal\", p->zTarget);\n  if( zOal ){\n    sqlite3_vfs *pVfs = sqlite3_vfs_find(0);\n    assert( pVfs && p->rc==SQLITE_OK && p->zErrmsg==0 );\n    pVfs->xDelete(pVfs, zOal, 0);\n    sqlite3_free(zOal);\n  }\n}\n\n/*\n** Allocate a private rbu VFS for the rbu handle passed as the only\n** argument. This VFS will be used unless the call to sqlite3rbu_open()\n** specified a URI with a vfs=? option in place of a target database\n** file name.\n*/\nstatic void rbuCreateVfs(sqlite3rbu *p){\n  int rnd;\n  char zRnd[64];\n\n  assert( p->rc==SQLITE_OK );\n  sqlite3_randomness(sizeof(int), (void*)&rnd);\n  sqlite3_snprintf(sizeof(zRnd), zRnd, \"rbu_vfs_%d\", rnd);\n  p->rc = sqlite3rbu_create_vfs(zRnd, 0);\n  if( p->rc==SQLITE_OK ){\n    sqlite3_vfs *pVfs = sqlite3_vfs_find(zRnd);\n    assert( pVfs );\n    p->zVfsName = pVfs->zName;\n    ((rbu_vfs*)pVfs)->pRbu = p;\n  }\n}\n\n/*\n** Destroy the private VFS created for the rbu handle passed as the only\n** argument by an earlier call to rbuCreateVfs().\n*/\nstatic void rbuDeleteVfs(sqlite3rbu *p){\n  if( p->zVfsName ){\n    sqlite3rbu_destroy_vfs(p->zVfsName);\n    p->zVfsName = 0;\n  }\n}\n\n/*\n** This user-defined SQL function is invoked with a single argument - the\n** name of a table expected to appear in the target database. It returns\n** the number of auxilliary indexes on the table.\n*/\nstatic void rbuIndexCntFunc(\n  sqlite3_context *pCtx, \n  int nVal,\n  sqlite3_value **apVal\n){\n  sqlite3rbu *p = (sqlite3rbu*)sqlite3_user_data(pCtx);\n  sqlite3_stmt *pStmt = 0;\n  char *zErrmsg = 0;\n  int rc;\n\n  assert( nVal==1 );\n  \n  rc = prepareFreeAndCollectError(p->dbMain, &pStmt, &zErrmsg, \n      sqlite3_mprintf(\"SELECT count(*) FROM sqlite_master \"\n        \"WHERE type='index' AND tbl_name = %Q\", sqlite3_value_text(apVal[0]))\n  );\n  if( rc!=SQLITE_OK ){\n    sqlite3_result_error(pCtx, zErrmsg, -1);\n  }else{\n    int nIndex = 0;\n    if( SQLITE_ROW==sqlite3_step(pStmt) ){\n      nIndex = sqlite3_column_int(pStmt, 0);\n    }\n    rc = sqlite3_finalize(pStmt);\n    if( rc==SQLITE_OK ){\n      sqlite3_result_int(pCtx, nIndex);\n    }else{\n      sqlite3_result_error(pCtx, sqlite3_errmsg(p->dbMain), -1);\n    }\n  }\n\n  sqlite3_free(zErrmsg);\n}\n\n/*\n** If the RBU database contains the rbu_count table, use it to initialize\n** the sqlite3rbu.nPhaseOneStep variable. The schema of the rbu_count table\n** is assumed to contain the same columns as:\n**\n**   CREATE TABLE rbu_count(tbl TEXT PRIMARY KEY, cnt INTEGER) WITHOUT ROWID;\n**\n** There should be one row in the table for each data_xxx table in the\n** database. The 'tbl' column should contain the name of a data_xxx table,\n** and the cnt column the number of rows it contains.\n**\n** sqlite3rbu.nPhaseOneStep is initialized to the sum of (1 + nIndex) * cnt\n** for all rows in the rbu_count table, where nIndex is the number of \n** indexes on the corresponding target database table.\n*/\nstatic void rbuInitPhaseOneSteps(sqlite3rbu *p){\n  if( p->rc==SQLITE_OK ){\n    sqlite3_stmt *pStmt = 0;\n    int bExists = 0;                /* True if rbu_count exists */\n\n    p->nPhaseOneStep = -1;\n\n    p->rc = sqlite3_create_function(p->dbRbu, \n        \"rbu_index_cnt\", 1, SQLITE_UTF8, (void*)p, rbuIndexCntFunc, 0, 0\n    );\n  \n    /* Check for the rbu_count table. If it does not exist, or if an error\n    ** occurs, nPhaseOneStep will be left set to -1. */\n    if( p->rc==SQLITE_OK ){\n      p->rc = prepareAndCollectError(p->dbRbu, &pStmt, &p->zErrmsg,\n          \"SELECT 1 FROM sqlite_master WHERE tbl_name = 'rbu_count'\"\n      );\n    }\n    if( p->rc==SQLITE_OK ){\n      if( SQLITE_ROW==sqlite3_step(pStmt) ){\n        bExists = 1;\n      }\n      p->rc = sqlite3_finalize(pStmt);\n    }\n  \n    if( p->rc==SQLITE_OK && bExists ){\n      p->rc = prepareAndCollectError(p->dbRbu, &pStmt, &p->zErrmsg,\n          \"SELECT sum(cnt * (1 + rbu_index_cnt(rbu_target_name(tbl))))\"\n          \"FROM rbu_count\"\n      );\n      if( p->rc==SQLITE_OK ){\n        if( SQLITE_ROW==sqlite3_step(pStmt) ){\n          p->nPhaseOneStep = sqlite3_column_int64(pStmt, 0);\n        }\n        p->rc = sqlite3_finalize(pStmt);\n      }\n    }\n  }\n}\n\n\nstatic sqlite3rbu *openRbuHandle(\n  const char *zTarget, \n  const char *zRbu,\n  const char *zState\n){\n  sqlite3rbu *p;\n  size_t nTarget = zTarget ? strlen(zTarget) : 0;\n  size_t nRbu = strlen(zRbu);\n  size_t nByte = sizeof(sqlite3rbu) + nTarget+1 + nRbu+1;\n\n  p = (sqlite3rbu*)sqlite3_malloc64(nByte);\n  if( p ){\n    RbuState *pState = 0;\n\n    /* Create the custom VFS. */\n    memset(p, 0, sizeof(sqlite3rbu));\n    rbuCreateVfs(p);\n\n    /* Open the target, RBU and state databases */\n    if( p->rc==SQLITE_OK ){\n      char *pCsr = (char*)&p[1];\n      int bRetry = 0;\n      if( zTarget ){\n        p->zTarget = pCsr;\n        memcpy(p->zTarget, zTarget, nTarget+1);\n        pCsr += nTarget+1;\n      }\n      p->zRbu = pCsr;\n      memcpy(p->zRbu, zRbu, nRbu+1);\n      pCsr += nRbu+1;\n      if( zState ){\n        p->zState = rbuMPrintf(p, \"%s\", zState);\n      }\n\n      /* If the first attempt to open the database file fails and the bRetry\n      ** flag it set, this means that the db was not opened because it seemed\n      ** to be a wal-mode db. But, this may have happened due to an earlier\n      ** RBU vacuum operation leaving an old wal file in the directory.\n      ** If this is the case, it will have been checkpointed and deleted\n      ** when the handle was closed and a second attempt to open the \n      ** database may succeed.  */\n      rbuOpenDatabase(p, &bRetry);\n      if( bRetry ){\n        rbuOpenDatabase(p, 0);\n      }\n    }\n\n    if( p->rc==SQLITE_OK ){\n      pState = rbuLoadState(p);\n      assert( pState || p->rc!=SQLITE_OK );\n      if( p->rc==SQLITE_OK ){\n\n        if( pState->eStage==0 ){ \n          rbuDeleteOalFile(p);\n          rbuInitPhaseOneSteps(p);\n          p->eStage = RBU_STAGE_OAL;\n        }else{\n          p->eStage = pState->eStage;\n          p->nPhaseOneStep = pState->nPhaseOneStep;\n        }\n        p->nProgress = pState->nProgress;\n        p->iOalSz = pState->iOalSz;\n      }\n    }\n    assert( p->rc!=SQLITE_OK || p->eStage!=0 );\n\n    if( p->rc==SQLITE_OK && p->pTargetFd->pWalFd ){\n      if( p->eStage==RBU_STAGE_OAL ){\n        p->rc = SQLITE_ERROR;\n        p->zErrmsg = sqlite3_mprintf(\"cannot update wal mode database\");\n      }else if( p->eStage==RBU_STAGE_MOVE ){\n        p->eStage = RBU_STAGE_CKPT;\n        p->nStep = 0;\n      }\n    }\n\n    if( p->rc==SQLITE_OK \n     && (p->eStage==RBU_STAGE_OAL || p->eStage==RBU_STAGE_MOVE)\n     && pState->eStage!=0\n    ){\n      rbu_file *pFd = (rbuIsVacuum(p) ? p->pRbuFd : p->pTargetFd);\n      if( pFd->iCookie!=pState->iCookie ){   \n        /* At this point (pTargetFd->iCookie) contains the value of the\n        ** change-counter cookie (the thing that gets incremented when a \n        ** transaction is committed in rollback mode) currently stored on \n        ** page 1 of the database file. */\n        p->rc = SQLITE_BUSY;\n        p->zErrmsg = sqlite3_mprintf(\"database modified during rbu %s\",\n            (rbuIsVacuum(p) ? \"vacuum\" : \"update\")\n        );\n      }\n    }\n\n    if( p->rc==SQLITE_OK ){\n      if( p->eStage==RBU_STAGE_OAL ){\n        sqlite3 *db = p->dbMain;\n        p->rc = sqlite3_exec(p->dbRbu, \"BEGIN\", 0, 0, &p->zErrmsg);\n\n        /* Point the object iterator at the first object */\n        if( p->rc==SQLITE_OK ){\n          p->rc = rbuObjIterFirst(p, &p->objiter);\n        }\n\n        /* If the RBU database contains no data_xxx tables, declare the RBU\n        ** update finished.  */\n        if( p->rc==SQLITE_OK && p->objiter.zTbl==0 ){\n          p->rc = SQLITE_DONE;\n          p->eStage = RBU_STAGE_DONE;\n        }else{\n          if( p->rc==SQLITE_OK && pState->eStage==0 && rbuIsVacuum(p) ){\n            rbuCopyPragma(p, \"page_size\");\n            rbuCopyPragma(p, \"auto_vacuum\");\n          }\n\n          /* Open transactions both databases. The *-oal file is opened or\n          ** created at this point. */\n          if( p->rc==SQLITE_OK ){\n            p->rc = sqlite3_exec(db, \"BEGIN IMMEDIATE\", 0, 0, &p->zErrmsg);\n          }\n\n          /* Check if the main database is a zipvfs db. If it is, set the upper\n          ** level pager to use \"journal_mode=off\". This prevents it from \n          ** generating a large journal using a temp file.  */\n          if( p->rc==SQLITE_OK ){\n            int frc = sqlite3_file_control(db, \"main\", SQLITE_FCNTL_ZIPVFS, 0);\n            if( frc==SQLITE_OK ){\n              p->rc = sqlite3_exec(\n                db, \"PRAGMA journal_mode=off\",0,0,&p->zErrmsg);\n            }\n          }\n\n          if( p->rc==SQLITE_OK ){\n            rbuSetupOal(p, pState);\n          }\n        }\n      }else if( p->eStage==RBU_STAGE_MOVE ){\n        /* no-op */\n      }else if( p->eStage==RBU_STAGE_CKPT ){\n        rbuSetupCheckpoint(p, pState);\n      }else if( p->eStage==RBU_STAGE_DONE ){\n        p->rc = SQLITE_DONE;\n      }else{\n        p->rc = SQLITE_CORRUPT;\n      }\n    }\n\n    rbuFreeState(pState);\n  }\n\n  return p;\n}\n\n/*\n** Allocate and return an RBU handle with all fields zeroed except for the\n** error code, which is set to SQLITE_MISUSE.\n*/\nstatic sqlite3rbu *rbuMisuseError(void){\n  sqlite3rbu *pRet;\n  pRet = sqlite3_malloc64(sizeof(sqlite3rbu));\n  if( pRet ){\n    memset(pRet, 0, sizeof(sqlite3rbu));\n    pRet->rc = SQLITE_MISUSE;\n  }\n  return pRet;\n}\n\n/*\n** Open and return a new RBU handle. \n*/\nSQLITE_API sqlite3rbu *sqlite3rbu_open(\n  const char *zTarget, \n  const char *zRbu,\n  const char *zState\n){\n  if( zTarget==0 || zRbu==0 ){ return rbuMisuseError(); }\n  /* TODO: Check that zTarget and zRbu are non-NULL */\n  return openRbuHandle(zTarget, zRbu, zState);\n}\n\n/*\n** Open a handle to begin or resume an RBU VACUUM operation.\n*/\nSQLITE_API sqlite3rbu *sqlite3rbu_vacuum(\n  const char *zTarget, \n  const char *zState\n){\n  if( zTarget==0 ){ return rbuMisuseError(); }\n  /* TODO: Check that both arguments are non-NULL */\n  return openRbuHandle(0, zTarget, zState);\n}\n\n/*\n** Return the database handle used by pRbu.\n*/\nSQLITE_API sqlite3 *sqlite3rbu_db(sqlite3rbu *pRbu, int bRbu){\n  sqlite3 *db = 0;\n  if( pRbu ){\n    db = (bRbu ? pRbu->dbRbu : pRbu->dbMain);\n  }\n  return db;\n}\n\n\n/*\n** If the error code currently stored in the RBU handle is SQLITE_CONSTRAINT,\n** then edit any error message string so as to remove all occurrences of\n** the pattern \"rbu_imp_[0-9]*\".\n*/\nstatic void rbuEditErrmsg(sqlite3rbu *p){\n  if( p->rc==SQLITE_CONSTRAINT && p->zErrmsg ){\n    unsigned int i;\n    size_t nErrmsg = strlen(p->zErrmsg);\n    for(i=0; i<(nErrmsg-8); i++){\n      if( memcmp(&p->zErrmsg[i], \"rbu_imp_\", 8)==0 ){\n        int nDel = 8;\n        while( p->zErrmsg[i+nDel]>='0' && p->zErrmsg[i+nDel]<='9' ) nDel++;\n        memmove(&p->zErrmsg[i], &p->zErrmsg[i+nDel], nErrmsg + 1 - i - nDel);\n        nErrmsg -= nDel;\n      }\n    }\n  }\n}\n\n/*\n** Close the RBU handle.\n*/\nSQLITE_API int sqlite3rbu_close(sqlite3rbu *p, char **pzErrmsg){\n  int rc;\n  if( p ){\n\n    /* Commit the transaction to the *-oal file. */\n    if( p->rc==SQLITE_OK && p->eStage==RBU_STAGE_OAL ){\n      p->rc = sqlite3_exec(p->dbMain, \"COMMIT\", 0, 0, &p->zErrmsg);\n    }\n\n    /* Sync the db file if currently doing an incremental checkpoint */\n    if( p->rc==SQLITE_OK && p->eStage==RBU_STAGE_CKPT ){\n      sqlite3_file *pDb = p->pTargetFd->pReal;\n      p->rc = pDb->pMethods->xSync(pDb, SQLITE_SYNC_NORMAL);\n    }\n\n    rbuSaveState(p, p->eStage);\n\n    if( p->rc==SQLITE_OK && p->eStage==RBU_STAGE_OAL ){\n      p->rc = sqlite3_exec(p->dbRbu, \"COMMIT\", 0, 0, &p->zErrmsg);\n    }\n\n    /* Close any open statement handles. */\n    rbuObjIterFinalize(&p->objiter);\n\n    /* If this is an RBU vacuum handle and the vacuum has either finished\n    ** successfully or encountered an error, delete the contents of the \n    ** state table. This causes the next call to sqlite3rbu_vacuum() \n    ** specifying the current target and state databases to start a new\n    ** vacuum from scratch.  */\n    if( rbuIsVacuum(p) && p->rc!=SQLITE_OK && p->dbRbu ){\n      int rc2 = sqlite3_exec(p->dbRbu, \"DELETE FROM stat.rbu_state\", 0, 0, 0);\n      if( p->rc==SQLITE_DONE && rc2!=SQLITE_OK ) p->rc = rc2;\n    }\n\n    /* Close the open database handle and VFS object. */\n    sqlite3_close(p->dbRbu);\n    sqlite3_close(p->dbMain);\n    assert( p->szTemp==0 );\n    rbuDeleteVfs(p);\n    sqlite3_free(p->aBuf);\n    sqlite3_free(p->aFrame);\n\n    rbuEditErrmsg(p);\n    rc = p->rc;\n    if( pzErrmsg ){\n      *pzErrmsg = p->zErrmsg;\n    }else{\n      sqlite3_free(p->zErrmsg);\n    }\n    sqlite3_free(p->zState);\n    sqlite3_free(p);\n  }else{\n    rc = SQLITE_NOMEM;\n    *pzErrmsg = 0;\n  }\n  return rc;\n}\n\n/*\n** Return the total number of key-value operations (inserts, deletes or \n** updates) that have been performed on the target database since the\n** current RBU update was started.\n*/\nSQLITE_API sqlite3_int64 sqlite3rbu_progress(sqlite3rbu *pRbu){\n  return pRbu->nProgress;\n}\n\n/*\n** Return permyriadage progress indications for the two main stages of\n** an RBU update.\n*/\nSQLITE_API void sqlite3rbu_bp_progress(sqlite3rbu *p, int *pnOne, int *pnTwo){\n  const int MAX_PROGRESS = 10000;\n  switch( p->eStage ){\n    case RBU_STAGE_OAL:\n      if( p->nPhaseOneStep>0 ){\n        *pnOne = (int)(MAX_PROGRESS * (i64)p->nProgress/(i64)p->nPhaseOneStep);\n      }else{\n        *pnOne = -1;\n      }\n      *pnTwo = 0;\n      break;\n\n    case RBU_STAGE_MOVE:\n      *pnOne = MAX_PROGRESS;\n      *pnTwo = 0;\n      break;\n\n    case RBU_STAGE_CKPT:\n      *pnOne = MAX_PROGRESS;\n      *pnTwo = (int)(MAX_PROGRESS * (i64)p->nStep / (i64)p->nFrame);\n      break;\n\n    case RBU_STAGE_DONE:\n      *pnOne = MAX_PROGRESS;\n      *pnTwo = MAX_PROGRESS;\n      break;\n\n    default:\n      assert( 0 );\n  }\n}\n\n/*\n** Return the current state of the RBU vacuum or update operation.\n*/\nSQLITE_API int sqlite3rbu_state(sqlite3rbu *p){\n  int aRes[] = {\n    0, SQLITE_RBU_STATE_OAL, SQLITE_RBU_STATE_MOVE,\n    0, SQLITE_RBU_STATE_CHECKPOINT, SQLITE_RBU_STATE_DONE\n  };\n\n  assert( RBU_STAGE_OAL==1 );\n  assert( RBU_STAGE_MOVE==2 );\n  assert( RBU_STAGE_CKPT==4 );\n  assert( RBU_STAGE_DONE==5 );\n  assert( aRes[RBU_STAGE_OAL]==SQLITE_RBU_STATE_OAL );\n  assert( aRes[RBU_STAGE_MOVE]==SQLITE_RBU_STATE_MOVE );\n  assert( aRes[RBU_STAGE_CKPT]==SQLITE_RBU_STATE_CHECKPOINT );\n  assert( aRes[RBU_STAGE_DONE]==SQLITE_RBU_STATE_DONE );\n\n  if( p->rc!=SQLITE_OK && p->rc!=SQLITE_DONE ){\n    return SQLITE_RBU_STATE_ERROR;\n  }else{\n    assert( p->rc!=SQLITE_DONE || p->eStage==RBU_STAGE_DONE );\n    assert( p->eStage==RBU_STAGE_OAL\n         || p->eStage==RBU_STAGE_MOVE\n         || p->eStage==RBU_STAGE_CKPT\n         || p->eStage==RBU_STAGE_DONE\n    );\n    return aRes[p->eStage];\n  }\n}\n\nSQLITE_API int sqlite3rbu_savestate(sqlite3rbu *p){\n  int rc = p->rc;\n  if( rc==SQLITE_DONE ) return SQLITE_OK;\n\n  assert( p->eStage>=RBU_STAGE_OAL && p->eStage<=RBU_STAGE_DONE );\n  if( p->eStage==RBU_STAGE_OAL ){\n    assert( rc!=SQLITE_DONE );\n    if( rc==SQLITE_OK ) rc = sqlite3_exec(p->dbMain, \"COMMIT\", 0, 0, 0);\n  }\n\n  /* Sync the db file */\n  if( rc==SQLITE_OK && p->eStage==RBU_STAGE_CKPT ){\n    sqlite3_file *pDb = p->pTargetFd->pReal;\n    rc = pDb->pMethods->xSync(pDb, SQLITE_SYNC_NORMAL);\n  }\n\n  p->rc = rc;\n  rbuSaveState(p, p->eStage);\n  rc = p->rc;\n\n  if( p->eStage==RBU_STAGE_OAL ){\n    assert( rc!=SQLITE_DONE );\n    if( rc==SQLITE_OK ) rc = sqlite3_exec(p->dbRbu, \"COMMIT\", 0, 0, 0);\n    if( rc==SQLITE_OK ) rc = sqlite3_exec(p->dbRbu, \"BEGIN IMMEDIATE\", 0, 0, 0);\n    if( rc==SQLITE_OK ) rc = sqlite3_exec(p->dbMain, \"BEGIN IMMEDIATE\", 0, 0,0);\n  }\n\n  p->rc = rc;\n  return rc;\n}\n\n/**************************************************************************\n** Beginning of RBU VFS shim methods. The VFS shim modifies the behaviour\n** of a standard VFS in the following ways:\n**\n** 1. Whenever the first page of a main database file is read or \n**    written, the value of the change-counter cookie is stored in\n**    rbu_file.iCookie. Similarly, the value of the \"write-version\"\n**    database header field is stored in rbu_file.iWriteVer. This ensures\n**    that the values are always trustworthy within an open transaction.\n**\n** 2. Whenever an SQLITE_OPEN_WAL file is opened, the (rbu_file.pWalFd)\n**    member variable of the associated database file descriptor is set\n**    to point to the new file. A mutex protected linked list of all main \n**    db fds opened using a particular RBU VFS is maintained at \n**    rbu_vfs.pMain to facilitate this.\n**\n** 3. Using a new file-control \"SQLITE_FCNTL_RBU\", a main db rbu_file \n**    object can be marked as the target database of an RBU update. This\n**    turns on the following extra special behaviour:\n**\n** 3a. If xAccess() is called to check if there exists a *-wal file \n**     associated with an RBU target database currently in RBU_STAGE_OAL\n**     stage (preparing the *-oal file), the following special handling\n**     applies:\n**\n**      * if the *-wal file does exist, return SQLITE_CANTOPEN. An RBU\n**        target database may not be in wal mode already.\n**\n**      * if the *-wal file does not exist, set the output parameter to\n**        non-zero (to tell SQLite that it does exist) anyway.\n**\n**     Then, when xOpen() is called to open the *-wal file associated with\n**     the RBU target in RBU_STAGE_OAL stage, instead of opening the *-wal\n**     file, the rbu vfs opens the corresponding *-oal file instead. \n**\n** 3b. The *-shm pages returned by xShmMap() for a target db file in\n**     RBU_STAGE_OAL mode are actually stored in heap memory. This is to\n**     avoid creating a *-shm file on disk. Additionally, xShmLock() calls\n**     are no-ops on target database files in RBU_STAGE_OAL mode. This is\n**     because assert() statements in some VFS implementations fail if \n**     xShmLock() is called before xShmMap().\n**\n** 3c. If an EXCLUSIVE lock is attempted on a target database file in any\n**     mode except RBU_STAGE_DONE (all work completed and checkpointed), it \n**     fails with an SQLITE_BUSY error. This is to stop RBU connections\n**     from automatically checkpointing a *-wal (or *-oal) file from within\n**     sqlite3_close().\n**\n** 3d. In RBU_STAGE_CAPTURE mode, all xRead() calls on the wal file, and\n**     all xWrite() calls on the target database file perform no IO. \n**     Instead the frame and page numbers that would be read and written\n**     are recorded. Additionally, successful attempts to obtain exclusive\n**     xShmLock() WRITER, CHECKPOINTER and READ0 locks on the target \n**     database file are recorded. xShmLock() calls to unlock the same\n**     locks are no-ops (so that once obtained, these locks are never\n**     relinquished). Finally, calls to xSync() on the target database\n**     file fail with SQLITE_INTERNAL errors.\n*/\n\nstatic void rbuUnlockShm(rbu_file *p){\n  assert( p->openFlags & SQLITE_OPEN_MAIN_DB );\n  if( p->pRbu ){\n    int (*xShmLock)(sqlite3_file*,int,int,int) = p->pReal->pMethods->xShmLock;\n    int i;\n    for(i=0; i<SQLITE_SHM_NLOCK;i++){\n      if( (1<<i) & p->pRbu->mLock ){\n        xShmLock(p->pReal, i, 1, SQLITE_SHM_UNLOCK|SQLITE_SHM_EXCLUSIVE);\n      }\n    }\n    p->pRbu->mLock = 0;\n  }\n}\n\n/*\n*/\nstatic int rbuUpdateTempSize(rbu_file *pFd, sqlite3_int64 nNew){\n  sqlite3rbu *pRbu = pFd->pRbu;\n  i64 nDiff = nNew - pFd->sz;\n  pRbu->szTemp += nDiff;\n  pFd->sz = nNew;\n  assert( pRbu->szTemp>=0 );\n  if( pRbu->szTempLimit && pRbu->szTemp>pRbu->szTempLimit ) return SQLITE_FULL;\n  return SQLITE_OK;\n}\n\n/*\n** Close an rbu file.\n*/\nstatic int rbuVfsClose(sqlite3_file *pFile){\n  rbu_file *p = (rbu_file*)pFile;\n  int rc;\n  int i;\n\n  /* Free the contents of the apShm[] array. And the array itself. */\n  for(i=0; i<p->nShm; i++){\n    sqlite3_free(p->apShm[i]);\n  }\n  sqlite3_free(p->apShm);\n  p->apShm = 0;\n  sqlite3_free(p->zDel);\n\n  if( p->openFlags & SQLITE_OPEN_MAIN_DB ){\n    rbu_file **pp;\n    sqlite3_mutex_enter(p->pRbuVfs->mutex);\n    for(pp=&p->pRbuVfs->pMain; *pp!=p; pp=&((*pp)->pMainNext));\n    *pp = p->pMainNext;\n    sqlite3_mutex_leave(p->pRbuVfs->mutex);\n    rbuUnlockShm(p);\n    p->pReal->pMethods->xShmUnmap(p->pReal, 0);\n  }\n  else if( (p->openFlags & SQLITE_OPEN_DELETEONCLOSE) && p->pRbu ){\n    rbuUpdateTempSize(p, 0);\n  }\n\n  /* Close the underlying file handle */\n  rc = p->pReal->pMethods->xClose(p->pReal);\n  return rc;\n}\n\n\n/*\n** Read and return an unsigned 32-bit big-endian integer from the buffer \n** passed as the only argument.\n*/\nstatic u32 rbuGetU32(u8 *aBuf){\n  return ((u32)aBuf[0] << 24)\n       + ((u32)aBuf[1] << 16)\n       + ((u32)aBuf[2] <<  8)\n       + ((u32)aBuf[3]);\n}\n\n/*\n** Write an unsigned 32-bit value in big-endian format to the supplied\n** buffer.\n*/\nstatic void rbuPutU32(u8 *aBuf, u32 iVal){\n  aBuf[0] = (iVal >> 24) & 0xFF;\n  aBuf[1] = (iVal >> 16) & 0xFF;\n  aBuf[2] = (iVal >>  8) & 0xFF;\n  aBuf[3] = (iVal >>  0) & 0xFF;\n}\n\nstatic void rbuPutU16(u8 *aBuf, u16 iVal){\n  aBuf[0] = (iVal >>  8) & 0xFF;\n  aBuf[1] = (iVal >>  0) & 0xFF;\n}\n\n/*\n** Read data from an rbuVfs-file.\n*/\nstatic int rbuVfsRead(\n  sqlite3_file *pFile, \n  void *zBuf, \n  int iAmt, \n  sqlite_int64 iOfst\n){\n  rbu_file *p = (rbu_file*)pFile;\n  sqlite3rbu *pRbu = p->pRbu;\n  int rc;\n\n  if( pRbu && pRbu->eStage==RBU_STAGE_CAPTURE ){\n    assert( p->openFlags & SQLITE_OPEN_WAL );\n    rc = rbuCaptureWalRead(p->pRbu, iOfst, iAmt);\n  }else{\n    if( pRbu && pRbu->eStage==RBU_STAGE_OAL \n     && (p->openFlags & SQLITE_OPEN_WAL) \n     && iOfst>=pRbu->iOalSz \n    ){\n      rc = SQLITE_OK;\n      memset(zBuf, 0, iAmt);\n    }else{\n      rc = p->pReal->pMethods->xRead(p->pReal, zBuf, iAmt, iOfst);\n#if 1\n      /* If this is being called to read the first page of the target \n      ** database as part of an rbu vacuum operation, synthesize the \n      ** contents of the first page if it does not yet exist. Otherwise,\n      ** SQLite will not check for a *-wal file.  */\n      if( pRbu && rbuIsVacuum(pRbu) \n          && rc==SQLITE_IOERR_SHORT_READ && iOfst==0\n          && (p->openFlags & SQLITE_OPEN_MAIN_DB)\n          && pRbu->rc==SQLITE_OK\n      ){\n        sqlite3_file *pFd = (sqlite3_file*)pRbu->pRbuFd;\n        rc = pFd->pMethods->xRead(pFd, zBuf, iAmt, iOfst);\n        if( rc==SQLITE_OK ){\n          u8 *aBuf = (u8*)zBuf;\n          u32 iRoot = rbuGetU32(&aBuf[52]) ? 1 : 0;\n          rbuPutU32(&aBuf[52], iRoot);      /* largest root page number */\n          rbuPutU32(&aBuf[36], 0);          /* number of free pages */\n          rbuPutU32(&aBuf[32], 0);          /* first page on free list trunk */\n          rbuPutU32(&aBuf[28], 1);          /* size of db file in pages */\n          rbuPutU32(&aBuf[24], pRbu->pRbuFd->iCookie+1);  /* Change counter */\n\n          if( iAmt>100 ){\n            memset(&aBuf[100], 0, iAmt-100);\n            rbuPutU16(&aBuf[105], iAmt & 0xFFFF);\n            aBuf[100] = 0x0D;\n          }\n        }\n      }\n#endif\n    }\n    if( rc==SQLITE_OK && iOfst==0 && (p->openFlags & SQLITE_OPEN_MAIN_DB) ){\n      /* These look like magic numbers. But they are stable, as they are part\n       ** of the definition of the SQLite file format, which may not change. */\n      u8 *pBuf = (u8*)zBuf;\n      p->iCookie = rbuGetU32(&pBuf[24]);\n      p->iWriteVer = pBuf[19];\n    }\n  }\n  return rc;\n}\n\n/*\n** Write data to an rbuVfs-file.\n*/\nstatic int rbuVfsWrite(\n  sqlite3_file *pFile, \n  const void *zBuf, \n  int iAmt, \n  sqlite_int64 iOfst\n){\n  rbu_file *p = (rbu_file*)pFile;\n  sqlite3rbu *pRbu = p->pRbu;\n  int rc;\n\n  if( pRbu && pRbu->eStage==RBU_STAGE_CAPTURE ){\n    assert( p->openFlags & SQLITE_OPEN_MAIN_DB );\n    rc = rbuCaptureDbWrite(p->pRbu, iOfst);\n  }else{\n    if( pRbu ){\n      if( pRbu->eStage==RBU_STAGE_OAL \n       && (p->openFlags & SQLITE_OPEN_WAL) \n       && iOfst>=pRbu->iOalSz\n      ){\n        pRbu->iOalSz = iAmt + iOfst;\n      }else if( p->openFlags & SQLITE_OPEN_DELETEONCLOSE ){\n        i64 szNew = iAmt+iOfst;\n        if( szNew>p->sz ){\n          rc = rbuUpdateTempSize(p, szNew);\n          if( rc!=SQLITE_OK ) return rc;\n        }\n      }\n    }\n    rc = p->pReal->pMethods->xWrite(p->pReal, zBuf, iAmt, iOfst);\n    if( rc==SQLITE_OK && iOfst==0 && (p->openFlags & SQLITE_OPEN_MAIN_DB) ){\n      /* These look like magic numbers. But they are stable, as they are part\n      ** of the definition of the SQLite file format, which may not change. */\n      u8 *pBuf = (u8*)zBuf;\n      p->iCookie = rbuGetU32(&pBuf[24]);\n      p->iWriteVer = pBuf[19];\n    }\n  }\n  return rc;\n}\n\n/*\n** Truncate an rbuVfs-file.\n*/\nstatic int rbuVfsTruncate(sqlite3_file *pFile, sqlite_int64 size){\n  rbu_file *p = (rbu_file*)pFile;\n  if( (p->openFlags & SQLITE_OPEN_DELETEONCLOSE) && p->pRbu ){\n    int rc = rbuUpdateTempSize(p, size);\n    if( rc!=SQLITE_OK ) return rc;\n  }\n  return p->pReal->pMethods->xTruncate(p->pReal, size);\n}\n\n/*\n** Sync an rbuVfs-file.\n*/\nstatic int rbuVfsSync(sqlite3_file *pFile, int flags){\n  rbu_file *p = (rbu_file *)pFile;\n  if( p->pRbu && p->pRbu->eStage==RBU_STAGE_CAPTURE ){\n    if( p->openFlags & SQLITE_OPEN_MAIN_DB ){\n      return SQLITE_INTERNAL;\n    }\n    return SQLITE_OK;\n  }\n  return p->pReal->pMethods->xSync(p->pReal, flags);\n}\n\n/*\n** Return the current file-size of an rbuVfs-file.\n*/\nstatic int rbuVfsFileSize(sqlite3_file *pFile, sqlite_int64 *pSize){\n  rbu_file *p = (rbu_file *)pFile;\n  int rc;\n  rc = p->pReal->pMethods->xFileSize(p->pReal, pSize);\n\n  /* If this is an RBU vacuum operation and this is the target database,\n  ** pretend that it has at least one page. Otherwise, SQLite will not\n  ** check for the existance of a *-wal file. rbuVfsRead() contains \n  ** similar logic.  */\n  if( rc==SQLITE_OK && *pSize==0 \n   && p->pRbu && rbuIsVacuum(p->pRbu) \n   && (p->openFlags & SQLITE_OPEN_MAIN_DB)\n  ){\n    *pSize = 1024;\n  }\n  return rc;\n}\n\n/*\n** Lock an rbuVfs-file.\n*/\nstatic int rbuVfsLock(sqlite3_file *pFile, int eLock){\n  rbu_file *p = (rbu_file*)pFile;\n  sqlite3rbu *pRbu = p->pRbu;\n  int rc = SQLITE_OK;\n\n  assert( p->openFlags & (SQLITE_OPEN_MAIN_DB|SQLITE_OPEN_TEMP_DB) );\n  if( eLock==SQLITE_LOCK_EXCLUSIVE \n   && (p->bNolock || (pRbu && pRbu->eStage!=RBU_STAGE_DONE))\n  ){\n    /* Do not allow EXCLUSIVE locks. Preventing SQLite from taking this \n    ** prevents it from checkpointing the database from sqlite3_close(). */\n    rc = SQLITE_BUSY;\n  }else{\n    rc = p->pReal->pMethods->xLock(p->pReal, eLock);\n  }\n\n  return rc;\n}\n\n/*\n** Unlock an rbuVfs-file.\n*/\nstatic int rbuVfsUnlock(sqlite3_file *pFile, int eLock){\n  rbu_file *p = (rbu_file *)pFile;\n  return p->pReal->pMethods->xUnlock(p->pReal, eLock);\n}\n\n/*\n** Check if another file-handle holds a RESERVED lock on an rbuVfs-file.\n*/\nstatic int rbuVfsCheckReservedLock(sqlite3_file *pFile, int *pResOut){\n  rbu_file *p = (rbu_file *)pFile;\n  return p->pReal->pMethods->xCheckReservedLock(p->pReal, pResOut);\n}\n\n/*\n** File control method. For custom operations on an rbuVfs-file.\n*/\nstatic int rbuVfsFileControl(sqlite3_file *pFile, int op, void *pArg){\n  rbu_file *p = (rbu_file *)pFile;\n  int (*xControl)(sqlite3_file*,int,void*) = p->pReal->pMethods->xFileControl;\n  int rc;\n\n  assert( p->openFlags & (SQLITE_OPEN_MAIN_DB|SQLITE_OPEN_TEMP_DB)\n       || p->openFlags & (SQLITE_OPEN_TRANSIENT_DB|SQLITE_OPEN_TEMP_JOURNAL)\n  );\n  if( op==SQLITE_FCNTL_RBU ){\n    sqlite3rbu *pRbu = (sqlite3rbu*)pArg;\n\n    /* First try to find another RBU vfs lower down in the vfs stack. If\n    ** one is found, this vfs will operate in pass-through mode. The lower\n    ** level vfs will do the special RBU handling.  */\n    rc = xControl(p->pReal, op, pArg);\n\n    if( rc==SQLITE_NOTFOUND ){\n      /* Now search for a zipvfs instance lower down in the VFS stack. If\n      ** one is found, this is an error.  */\n      void *dummy = 0;\n      rc = xControl(p->pReal, SQLITE_FCNTL_ZIPVFS, &dummy);\n      if( rc==SQLITE_OK ){\n        rc = SQLITE_ERROR;\n        pRbu->zErrmsg = sqlite3_mprintf(\"rbu/zipvfs setup error\");\n      }else if( rc==SQLITE_NOTFOUND ){\n        pRbu->pTargetFd = p;\n        p->pRbu = pRbu;\n        if( p->pWalFd ) p->pWalFd->pRbu = pRbu;\n        rc = SQLITE_OK;\n      }\n    }\n    return rc;\n  }\n  else if( op==SQLITE_FCNTL_RBUCNT ){\n    sqlite3rbu *pRbu = (sqlite3rbu*)pArg;\n    pRbu->nRbu++;\n    pRbu->pRbuFd = p;\n    p->bNolock = 1;\n  }\n\n  rc = xControl(p->pReal, op, pArg);\n  if( rc==SQLITE_OK && op==SQLITE_FCNTL_VFSNAME ){\n    rbu_vfs *pRbuVfs = p->pRbuVfs;\n    char *zIn = *(char**)pArg;\n    char *zOut = sqlite3_mprintf(\"rbu(%s)/%z\", pRbuVfs->base.zName, zIn);\n    *(char**)pArg = zOut;\n    if( zOut==0 ) rc = SQLITE_NOMEM;\n  }\n\n  return rc;\n}\n\n/*\n** Return the sector-size in bytes for an rbuVfs-file.\n*/\nstatic int rbuVfsSectorSize(sqlite3_file *pFile){\n  rbu_file *p = (rbu_file *)pFile;\n  return p->pReal->pMethods->xSectorSize(p->pReal);\n}\n\n/*\n** Return the device characteristic flags supported by an rbuVfs-file.\n*/\nstatic int rbuVfsDeviceCharacteristics(sqlite3_file *pFile){\n  rbu_file *p = (rbu_file *)pFile;\n  return p->pReal->pMethods->xDeviceCharacteristics(p->pReal);\n}\n\n/*\n** Take or release a shared-memory lock.\n*/\nstatic int rbuVfsShmLock(sqlite3_file *pFile, int ofst, int n, int flags){\n  rbu_file *p = (rbu_file*)pFile;\n  sqlite3rbu *pRbu = p->pRbu;\n  int rc = SQLITE_OK;\n\n#ifdef SQLITE_AMALGAMATION\n    assert( WAL_CKPT_LOCK==1 );\n#endif\n\n  assert( p->openFlags & (SQLITE_OPEN_MAIN_DB|SQLITE_OPEN_TEMP_DB) );\n  if( pRbu && (pRbu->eStage==RBU_STAGE_OAL || pRbu->eStage==RBU_STAGE_MOVE) ){\n    /* Magic number 1 is the WAL_CKPT_LOCK lock. Preventing SQLite from\n    ** taking this lock also prevents any checkpoints from occurring. \n    ** todo: really, it's not clear why this might occur, as \n    ** wal_autocheckpoint ought to be turned off.  */\n    if( ofst==WAL_LOCK_CKPT && n==1 ) rc = SQLITE_BUSY;\n  }else{\n    int bCapture = 0;\n    if( n==1 && (flags & SQLITE_SHM_EXCLUSIVE)\n     && pRbu && pRbu->eStage==RBU_STAGE_CAPTURE\n     && (ofst==WAL_LOCK_WRITE || ofst==WAL_LOCK_CKPT || ofst==WAL_LOCK_READ0)\n    ){\n      bCapture = 1;\n    }\n\n    if( bCapture==0 || 0==(flags & SQLITE_SHM_UNLOCK) ){\n      rc = p->pReal->pMethods->xShmLock(p->pReal, ofst, n, flags);\n      if( bCapture && rc==SQLITE_OK ){\n        pRbu->mLock |= (1 << ofst);\n      }\n    }\n  }\n\n  return rc;\n}\n\n/*\n** Obtain a pointer to a mapping of a single 32KiB page of the *-shm file.\n*/\nstatic int rbuVfsShmMap(\n  sqlite3_file *pFile, \n  int iRegion, \n  int szRegion, \n  int isWrite, \n  void volatile **pp\n){\n  rbu_file *p = (rbu_file*)pFile;\n  int rc = SQLITE_OK;\n  int eStage = (p->pRbu ? p->pRbu->eStage : 0);\n\n  /* If not in RBU_STAGE_OAL, allow this call to pass through. Or, if this\n  ** rbu is in the RBU_STAGE_OAL state, use heap memory for *-shm space \n  ** instead of a file on disk.  */\n  assert( p->openFlags & (SQLITE_OPEN_MAIN_DB|SQLITE_OPEN_TEMP_DB) );\n  if( eStage==RBU_STAGE_OAL || eStage==RBU_STAGE_MOVE ){\n    if( iRegion<=p->nShm ){\n      int nByte = (iRegion+1) * sizeof(char*);\n      char **apNew = (char**)sqlite3_realloc64(p->apShm, nByte);\n      if( apNew==0 ){\n        rc = SQLITE_NOMEM;\n      }else{\n        memset(&apNew[p->nShm], 0, sizeof(char*) * (1 + iRegion - p->nShm));\n        p->apShm = apNew;\n        p->nShm = iRegion+1;\n      }\n    }\n\n    if( rc==SQLITE_OK && p->apShm[iRegion]==0 ){\n      char *pNew = (char*)sqlite3_malloc64(szRegion);\n      if( pNew==0 ){\n        rc = SQLITE_NOMEM;\n      }else{\n        memset(pNew, 0, szRegion);\n        p->apShm[iRegion] = pNew;\n      }\n    }\n\n    if( rc==SQLITE_OK ){\n      *pp = p->apShm[iRegion];\n    }else{\n      *pp = 0;\n    }\n  }else{\n    assert( p->apShm==0 );\n    rc = p->pReal->pMethods->xShmMap(p->pReal, iRegion, szRegion, isWrite, pp);\n  }\n\n  return rc;\n}\n\n/*\n** Memory barrier.\n*/\nstatic void rbuVfsShmBarrier(sqlite3_file *pFile){\n  rbu_file *p = (rbu_file *)pFile;\n  p->pReal->pMethods->xShmBarrier(p->pReal);\n}\n\n/*\n** The xShmUnmap method.\n*/\nstatic int rbuVfsShmUnmap(sqlite3_file *pFile, int delFlag){\n  rbu_file *p = (rbu_file*)pFile;\n  int rc = SQLITE_OK;\n  int eStage = (p->pRbu ? p->pRbu->eStage : 0);\n\n  assert( p->openFlags & (SQLITE_OPEN_MAIN_DB|SQLITE_OPEN_TEMP_DB) );\n  if( eStage==RBU_STAGE_OAL || eStage==RBU_STAGE_MOVE ){\n    /* no-op */\n  }else{\n    /* Release the checkpointer and writer locks */\n    rbuUnlockShm(p);\n    rc = p->pReal->pMethods->xShmUnmap(p->pReal, delFlag);\n  }\n  return rc;\n}\n\n/*\n** Given that zWal points to a buffer containing a wal file name passed to \n** either the xOpen() or xAccess() VFS method, return a pointer to the\n** file-handle opened by the same database connection on the corresponding\n** database file.\n*/\nstatic rbu_file *rbuFindMaindb(rbu_vfs *pRbuVfs, const char *zWal){\n  rbu_file *pDb;\n  sqlite3_mutex_enter(pRbuVfs->mutex);\n  for(pDb=pRbuVfs->pMain; pDb && pDb->zWal!=zWal; pDb=pDb->pMainNext){}\n  sqlite3_mutex_leave(pRbuVfs->mutex);\n  return pDb;\n}\n\n/* \n** A main database named zName has just been opened. The following \n** function returns a pointer to a buffer owned by SQLite that contains\n** the name of the *-wal file this db connection will use. SQLite\n** happens to pass a pointer to this buffer when using xAccess()\n** or xOpen() to operate on the *-wal file.  \n*/\nstatic const char *rbuMainToWal(const char *zName, int flags){\n  int n = (int)strlen(zName);\n  const char *z = &zName[n];\n  if( flags & SQLITE_OPEN_URI ){\n    int odd = 0;\n    while( 1 ){\n      if( z[0]==0 ){\n        odd = 1 - odd;\n        if( odd && z[1]==0 ) break;\n      }\n      z++;\n    }\n    z += 2;\n  }else{\n    while( *z==0 ) z++;\n  }\n  z += (n + 8 + 1);\n  return z;\n}\n\n/*\n** Open an rbu file handle.\n*/\nstatic int rbuVfsOpen(\n  sqlite3_vfs *pVfs,\n  const char *zName,\n  sqlite3_file *pFile,\n  int flags,\n  int *pOutFlags\n){\n  static sqlite3_io_methods rbuvfs_io_methods = {\n    2,                            /* iVersion */\n    rbuVfsClose,                  /* xClose */\n    rbuVfsRead,                   /* xRead */\n    rbuVfsWrite,                  /* xWrite */\n    rbuVfsTruncate,               /* xTruncate */\n    rbuVfsSync,                   /* xSync */\n    rbuVfsFileSize,               /* xFileSize */\n    rbuVfsLock,                   /* xLock */\n    rbuVfsUnlock,                 /* xUnlock */\n    rbuVfsCheckReservedLock,      /* xCheckReservedLock */\n    rbuVfsFileControl,            /* xFileControl */\n    rbuVfsSectorSize,             /* xSectorSize */\n    rbuVfsDeviceCharacteristics,  /* xDeviceCharacteristics */\n    rbuVfsShmMap,                 /* xShmMap */\n    rbuVfsShmLock,                /* xShmLock */\n    rbuVfsShmBarrier,             /* xShmBarrier */\n    rbuVfsShmUnmap,               /* xShmUnmap */\n    0, 0                          /* xFetch, xUnfetch */\n  };\n  rbu_vfs *pRbuVfs = (rbu_vfs*)pVfs;\n  sqlite3_vfs *pRealVfs = pRbuVfs->pRealVfs;\n  rbu_file *pFd = (rbu_file *)pFile;\n  int rc = SQLITE_OK;\n  const char *zOpen = zName;\n  int oflags = flags;\n\n  memset(pFd, 0, sizeof(rbu_file));\n  pFd->pReal = (sqlite3_file*)&pFd[1];\n  pFd->pRbuVfs = pRbuVfs;\n  pFd->openFlags = flags;\n  if( zName ){\n    if( flags & SQLITE_OPEN_MAIN_DB ){\n      /* A main database has just been opened. The following block sets\n      ** (pFd->zWal) to point to a buffer owned by SQLite that contains\n      ** the name of the *-wal file this db connection will use. SQLite\n      ** happens to pass a pointer to this buffer when using xAccess()\n      ** or xOpen() to operate on the *-wal file.  */\n      pFd->zWal = rbuMainToWal(zName, flags);\n    }\n    else if( flags & SQLITE_OPEN_WAL ){\n      rbu_file *pDb = rbuFindMaindb(pRbuVfs, zName);\n      if( pDb ){\n        if( pDb->pRbu && pDb->pRbu->eStage==RBU_STAGE_OAL ){\n          /* This call is to open a *-wal file. Intead, open the *-oal. This\n          ** code ensures that the string passed to xOpen() is terminated by a\n          ** pair of '\\0' bytes in case the VFS attempts to extract a URI \n          ** parameter from it.  */\n          const char *zBase = zName;\n          size_t nCopy;\n          char *zCopy;\n          if( rbuIsVacuum(pDb->pRbu) ){\n            zBase = sqlite3_db_filename(pDb->pRbu->dbRbu, \"main\");\n            zBase = rbuMainToWal(zBase, SQLITE_OPEN_URI);\n          }\n          nCopy = strlen(zBase);\n          zCopy = sqlite3_malloc64(nCopy+2);\n          if( zCopy ){\n            memcpy(zCopy, zBase, nCopy);\n            zCopy[nCopy-3] = 'o';\n            zCopy[nCopy] = '\\0';\n            zCopy[nCopy+1] = '\\0';\n            zOpen = (const char*)(pFd->zDel = zCopy);\n          }else{\n            rc = SQLITE_NOMEM;\n          }\n          pFd->pRbu = pDb->pRbu;\n        }\n        pDb->pWalFd = pFd;\n      }\n    }\n  }else{\n    pFd->pRbu = pRbuVfs->pRbu;\n  }\n\n  if( oflags & SQLITE_OPEN_MAIN_DB \n   && sqlite3_uri_boolean(zName, \"rbu_memory\", 0) \n  ){\n    assert( oflags & SQLITE_OPEN_MAIN_DB );\n    oflags =  SQLITE_OPEN_TEMP_DB | SQLITE_OPEN_READWRITE | SQLITE_OPEN_CREATE |\n              SQLITE_OPEN_EXCLUSIVE | SQLITE_OPEN_DELETEONCLOSE;\n    zOpen = 0;\n  }\n\n  if( rc==SQLITE_OK ){\n    rc = pRealVfs->xOpen(pRealVfs, zOpen, pFd->pReal, oflags, pOutFlags);\n  }\n  if( pFd->pReal->pMethods ){\n    /* The xOpen() operation has succeeded. Set the sqlite3_file.pMethods\n    ** pointer and, if the file is a main database file, link it into the\n    ** mutex protected linked list of all such files.  */\n    pFile->pMethods = &rbuvfs_io_methods;\n    if( flags & SQLITE_OPEN_MAIN_DB ){\n      sqlite3_mutex_enter(pRbuVfs->mutex);\n      pFd->pMainNext = pRbuVfs->pMain;\n      pRbuVfs->pMain = pFd;\n      sqlite3_mutex_leave(pRbuVfs->mutex);\n    }\n  }else{\n    sqlite3_free(pFd->zDel);\n  }\n\n  return rc;\n}\n\n/*\n** Delete the file located at zPath.\n*/\nstatic int rbuVfsDelete(sqlite3_vfs *pVfs, const char *zPath, int dirSync){\n  sqlite3_vfs *pRealVfs = ((rbu_vfs*)pVfs)->pRealVfs;\n  return pRealVfs->xDelete(pRealVfs, zPath, dirSync);\n}\n\n/*\n** Test for access permissions. Return true if the requested permission\n** is available, or false otherwise.\n*/\nstatic int rbuVfsAccess(\n  sqlite3_vfs *pVfs, \n  const char *zPath, \n  int flags, \n  int *pResOut\n){\n  rbu_vfs *pRbuVfs = (rbu_vfs*)pVfs;\n  sqlite3_vfs *pRealVfs = pRbuVfs->pRealVfs;\n  int rc;\n\n  rc = pRealVfs->xAccess(pRealVfs, zPath, flags, pResOut);\n\n  /* If this call is to check if a *-wal file associated with an RBU target\n  ** database connection exists, and the RBU update is in RBU_STAGE_OAL,\n  ** the following special handling is activated:\n  **\n  **   a) if the *-wal file does exist, return SQLITE_CANTOPEN. This\n  **      ensures that the RBU extension never tries to update a database\n  **      in wal mode, even if the first page of the database file has\n  **      been damaged. \n  **\n  **   b) if the *-wal file does not exist, claim that it does anyway,\n  **      causing SQLite to call xOpen() to open it. This call will also\n  **      be intercepted (see the rbuVfsOpen() function) and the *-oal\n  **      file opened instead.\n  */\n  if( rc==SQLITE_OK && flags==SQLITE_ACCESS_EXISTS ){\n    rbu_file *pDb = rbuFindMaindb(pRbuVfs, zPath);\n    if( pDb && pDb->pRbu && pDb->pRbu->eStage==RBU_STAGE_OAL ){\n      if( *pResOut ){\n        rc = SQLITE_CANTOPEN;\n      }else{\n        sqlite3_int64 sz = 0;\n        rc = rbuVfsFileSize(&pDb->base, &sz);\n        *pResOut = (sz>0);\n      }\n    }\n  }\n\n  return rc;\n}\n\n/*\n** Populate buffer zOut with the full canonical pathname corresponding\n** to the pathname in zPath. zOut is guaranteed to point to a buffer\n** of at least (DEVSYM_MAX_PATHNAME+1) bytes.\n*/\nstatic int rbuVfsFullPathname(\n  sqlite3_vfs *pVfs, \n  const char *zPath, \n  int nOut, \n  char *zOut\n){\n  sqlite3_vfs *pRealVfs = ((rbu_vfs*)pVfs)->pRealVfs;\n  return pRealVfs->xFullPathname(pRealVfs, zPath, nOut, zOut);\n}\n\n#ifndef SQLITE_OMIT_LOAD_EXTENSION\n/*\n** Open the dynamic library located at zPath and return a handle.\n*/\nstatic void *rbuVfsDlOpen(sqlite3_vfs *pVfs, const char *zPath){\n  sqlite3_vfs *pRealVfs = ((rbu_vfs*)pVfs)->pRealVfs;\n  return pRealVfs->xDlOpen(pRealVfs, zPath);\n}\n\n/*\n** Populate the buffer zErrMsg (size nByte bytes) with a human readable\n** utf-8 string describing the most recent error encountered associated \n** with dynamic libraries.\n*/\nstatic void rbuVfsDlError(sqlite3_vfs *pVfs, int nByte, char *zErrMsg){\n  sqlite3_vfs *pRealVfs = ((rbu_vfs*)pVfs)->pRealVfs;\n  pRealVfs->xDlError(pRealVfs, nByte, zErrMsg);\n}\n\n/*\n** Return a pointer to the symbol zSymbol in the dynamic library pHandle.\n*/\nstatic void (*rbuVfsDlSym(\n  sqlite3_vfs *pVfs, \n  void *pArg, \n  const char *zSym\n))(void){\n  sqlite3_vfs *pRealVfs = ((rbu_vfs*)pVfs)->pRealVfs;\n  return pRealVfs->xDlSym(pRealVfs, pArg, zSym);\n}\n\n/*\n** Close the dynamic library handle pHandle.\n*/\nstatic void rbuVfsDlClose(sqlite3_vfs *pVfs, void *pHandle){\n  sqlite3_vfs *pRealVfs = ((rbu_vfs*)pVfs)->pRealVfs;\n  pRealVfs->xDlClose(pRealVfs, pHandle);\n}\n#endif /* SQLITE_OMIT_LOAD_EXTENSION */\n\n/*\n** Populate the buffer pointed to by zBufOut with nByte bytes of \n** random data.\n*/\nstatic int rbuVfsRandomness(sqlite3_vfs *pVfs, int nByte, char *zBufOut){\n  sqlite3_vfs *pRealVfs = ((rbu_vfs*)pVfs)->pRealVfs;\n  return pRealVfs->xRandomness(pRealVfs, nByte, zBufOut);\n}\n\n/*\n** Sleep for nMicro microseconds. Return the number of microseconds \n** actually slept.\n*/\nstatic int rbuVfsSleep(sqlite3_vfs *pVfs, int nMicro){\n  sqlite3_vfs *pRealVfs = ((rbu_vfs*)pVfs)->pRealVfs;\n  return pRealVfs->xSleep(pRealVfs, nMicro);\n}\n\n/*\n** Return the current time as a Julian Day number in *pTimeOut.\n*/\nstatic int rbuVfsCurrentTime(sqlite3_vfs *pVfs, double *pTimeOut){\n  sqlite3_vfs *pRealVfs = ((rbu_vfs*)pVfs)->pRealVfs;\n  return pRealVfs->xCurrentTime(pRealVfs, pTimeOut);\n}\n\n/*\n** No-op.\n*/\nstatic int rbuVfsGetLastError(sqlite3_vfs *pVfs, int a, char *b){\n  return 0;\n}\n\n/*\n** Deregister and destroy an RBU vfs created by an earlier call to\n** sqlite3rbu_create_vfs().\n*/\nSQLITE_API void sqlite3rbu_destroy_vfs(const char *zName){\n  sqlite3_vfs *pVfs = sqlite3_vfs_find(zName);\n  if( pVfs && pVfs->xOpen==rbuVfsOpen ){\n    sqlite3_mutex_free(((rbu_vfs*)pVfs)->mutex);\n    sqlite3_vfs_unregister(pVfs);\n    sqlite3_free(pVfs);\n  }\n}\n\n/*\n** Create an RBU VFS named zName that accesses the underlying file-system\n** via existing VFS zParent. The new object is registered as a non-default\n** VFS with SQLite before returning.\n*/\nSQLITE_API int sqlite3rbu_create_vfs(const char *zName, const char *zParent){\n\n  /* Template for VFS */\n  static sqlite3_vfs vfs_template = {\n    1,                            /* iVersion */\n    0,                            /* szOsFile */\n    0,                            /* mxPathname */\n    0,                            /* pNext */\n    0,                            /* zName */\n    0,                            /* pAppData */\n    rbuVfsOpen,                   /* xOpen */\n    rbuVfsDelete,                 /* xDelete */\n    rbuVfsAccess,                 /* xAccess */\n    rbuVfsFullPathname,           /* xFullPathname */\n\n#ifndef SQLITE_OMIT_LOAD_EXTENSION\n    rbuVfsDlOpen,                 /* xDlOpen */\n    rbuVfsDlError,                /* xDlError */\n    rbuVfsDlSym,                  /* xDlSym */\n    rbuVfsDlClose,                /* xDlClose */\n#else\n    0, 0, 0, 0,\n#endif\n\n    rbuVfsRandomness,             /* xRandomness */\n    rbuVfsSleep,                  /* xSleep */\n    rbuVfsCurrentTime,            /* xCurrentTime */\n    rbuVfsGetLastError,           /* xGetLastError */\n    0,                            /* xCurrentTimeInt64 (version 2) */\n    0, 0, 0                       /* Unimplemented version 3 methods */\n  };\n\n  rbu_vfs *pNew = 0;              /* Newly allocated VFS */\n  int rc = SQLITE_OK;\n  size_t nName;\n  size_t nByte;\n\n  nName = strlen(zName);\n  nByte = sizeof(rbu_vfs) + nName + 1;\n  pNew = (rbu_vfs*)sqlite3_malloc64(nByte);\n  if( pNew==0 ){\n    rc = SQLITE_NOMEM;\n  }else{\n    sqlite3_vfs *pParent;           /* Parent VFS */\n    memset(pNew, 0, nByte);\n    pParent = sqlite3_vfs_find(zParent);\n    if( pParent==0 ){\n      rc = SQLITE_NOTFOUND;\n    }else{\n      char *zSpace;\n      memcpy(&pNew->base, &vfs_template, sizeof(sqlite3_vfs));\n      pNew->base.mxPathname = pParent->mxPathname;\n      pNew->base.szOsFile = sizeof(rbu_file) + pParent->szOsFile;\n      pNew->pRealVfs = pParent;\n      pNew->base.zName = (const char*)(zSpace = (char*)&pNew[1]);\n      memcpy(zSpace, zName, nName);\n\n      /* Allocate the mutex and register the new VFS (not as the default) */\n      pNew->mutex = sqlite3_mutex_alloc(SQLITE_MUTEX_RECURSIVE);\n      if( pNew->mutex==0 ){\n        rc = SQLITE_NOMEM;\n      }else{\n        rc = sqlite3_vfs_register(&pNew->base, 0);\n      }\n    }\n\n    if( rc!=SQLITE_OK ){\n      sqlite3_mutex_free(pNew->mutex);\n      sqlite3_free(pNew);\n    }\n  }\n\n  return rc;\n}\n\n/*\n** Configure the aggregate temp file size limit for this RBU handle.\n*/\nSQLITE_API sqlite3_int64 sqlite3rbu_temp_size_limit(sqlite3rbu *pRbu, sqlite3_int64 n){\n  if( n>=0 ){\n    pRbu->szTempLimit = n;\n  }\n  return pRbu->szTempLimit;\n}\n\nSQLITE_API sqlite3_int64 sqlite3rbu_temp_size(sqlite3rbu *pRbu){\n  return pRbu->szTemp;\n}\n\n\n/**************************************************************************/\n\n#endif /* !defined(SQLITE_CORE) || defined(SQLITE_ENABLE_RBU) */\n\n/************** End of sqlite3rbu.c ******************************************/\n/************** Begin file dbstat.c ******************************************/\n/*\n** 2010 July 12\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n******************************************************************************\n**\n** This file contains an implementation of the \"dbstat\" virtual table.\n**\n** The dbstat virtual table is used to extract low-level formatting\n** information from an SQLite database in order to implement the\n** \"sqlite3_analyzer\" utility.  See the ../tool/spaceanal.tcl script\n** for an example implementation.\n**\n** Additional information is available on the \"dbstat.html\" page of the\n** official SQLite documentation.\n*/\n\n/* #include \"sqliteInt.h\"   ** Requires access to internal data structures ** */\n#if (defined(SQLITE_ENABLE_DBSTAT_VTAB) || defined(SQLITE_TEST)) \\\n    && !defined(SQLITE_OMIT_VIRTUALTABLE)\n\n/*\n** Page paths:\n** \n**   The value of the 'path' column describes the path taken from the \n**   root-node of the b-tree structure to each page. The value of the \n**   root-node path is '/'.\n**\n**   The value of the path for the left-most child page of the root of\n**   a b-tree is '/000/'. (Btrees store content ordered from left to right\n**   so the pages to the left have smaller keys than the pages to the right.)\n**   The next to left-most child of the root page is\n**   '/001', and so on, each sibling page identified by a 3-digit hex \n**   value. The children of the 451st left-most sibling have paths such\n**   as '/1c2/000/, '/1c2/001/' etc.\n**\n**   Overflow pages are specified by appending a '+' character and a \n**   six-digit hexadecimal value to the path to the cell they are linked\n**   from. For example, the three overflow pages in a chain linked from \n**   the left-most cell of the 450th child of the root page are identified\n**   by the paths:\n**\n**      '/1c2/000+000000'         // First page in overflow chain\n**      '/1c2/000+000001'         // Second page in overflow chain\n**      '/1c2/000+000002'         // Third page in overflow chain\n**\n**   If the paths are sorted using the BINARY collation sequence, then\n**   the overflow pages associated with a cell will appear earlier in the\n**   sort-order than its child page:\n**\n**      '/1c2/000/'               // Left-most child of 451st child of root\n*/\n#define VTAB_SCHEMA                                                         \\\n  \"CREATE TABLE xx( \"                                                       \\\n  \"  name       TEXT,             /* Name of table or index */\"             \\\n  \"  path       TEXT,             /* Path to page from root */\"             \\\n  \"  pageno     INTEGER,          /* Page number */\"                        \\\n  \"  pagetype   TEXT,             /* 'internal', 'leaf' or 'overflow' */\"   \\\n  \"  ncell      INTEGER,          /* Cells on page (0 for overflow) */\"     \\\n  \"  payload    INTEGER,          /* Bytes of payload on this page */\"      \\\n  \"  unused     INTEGER,          /* Bytes of unused space on this page */\" \\\n  \"  mx_payload INTEGER,          /* Largest payload size of all cells */\"  \\\n  \"  pgoffset   INTEGER,          /* Offset of page in file */\"             \\\n  \"  pgsize     INTEGER,          /* Size of the page */\"                   \\\n  \"  schema     TEXT HIDDEN       /* Database schema being analyzed */\"     \\\n  \");\"\n\n\ntypedef struct StatTable StatTable;\ntypedef struct StatCursor StatCursor;\ntypedef struct StatPage StatPage;\ntypedef struct StatCell StatCell;\n\nstruct StatCell {\n  int nLocal;                     /* Bytes of local payload */\n  u32 iChildPg;                   /* Child node (or 0 if this is a leaf) */\n  int nOvfl;                      /* Entries in aOvfl[] */\n  u32 *aOvfl;                     /* Array of overflow page numbers */\n  int nLastOvfl;                  /* Bytes of payload on final overflow page */\n  int iOvfl;                      /* Iterates through aOvfl[] */\n};\n\nstruct StatPage {\n  u32 iPgno;\n  DbPage *pPg;\n  int iCell;\n\n  char *zPath;                    /* Path to this page */\n\n  /* Variables populated by statDecodePage(): */\n  u8 flags;                       /* Copy of flags byte */\n  int nCell;                      /* Number of cells on page */\n  int nUnused;                    /* Number of unused bytes on page */\n  StatCell *aCell;                /* Array of parsed cells */\n  u32 iRightChildPg;              /* Right-child page number (or 0) */\n  int nMxPayload;                 /* Largest payload of any cell on this page */\n};\n\nstruct StatCursor {\n  sqlite3_vtab_cursor base;\n  sqlite3_stmt *pStmt;            /* Iterates through set of root pages */\n  int isEof;                      /* After pStmt has returned SQLITE_DONE */\n  int iDb;                        /* Schema used for this query */\n\n  StatPage aPage[32];\n  int iPage;                      /* Current entry in aPage[] */\n\n  /* Values to return. */\n  char *zName;                    /* Value of 'name' column */\n  char *zPath;                    /* Value of 'path' column */\n  u32 iPageno;                    /* Value of 'pageno' column */\n  char *zPagetype;                /* Value of 'pagetype' column */\n  int nCell;                      /* Value of 'ncell' column */\n  int nPayload;                   /* Value of 'payload' column */\n  int nUnused;                    /* Value of 'unused' column */\n  int nMxPayload;                 /* Value of 'mx_payload' column */\n  i64 iOffset;                    /* Value of 'pgOffset' column */\n  int szPage;                     /* Value of 'pgSize' column */\n};\n\nstruct StatTable {\n  sqlite3_vtab base;\n  sqlite3 *db;\n  int iDb;                        /* Index of database to analyze */\n};\n\n#ifndef get2byte\n# define get2byte(x)   ((x)[0]<<8 | (x)[1])\n#endif\n\n/*\n** Connect to or create a statvfs virtual table.\n*/\nstatic int statConnect(\n  sqlite3 *db,\n  void *pAux,\n  int argc, const char *const*argv,\n  sqlite3_vtab **ppVtab,\n  char **pzErr\n){\n  StatTable *pTab = 0;\n  int rc = SQLITE_OK;\n  int iDb;\n\n  if( argc>=4 ){\n    Token nm;\n    sqlite3TokenInit(&nm, (char*)argv[3]);\n    iDb = sqlite3FindDb(db, &nm);\n    if( iDb<0 ){\n      *pzErr = sqlite3_mprintf(\"no such database: %s\", argv[3]);\n      return SQLITE_ERROR;\n    }\n  }else{\n    iDb = 0;\n  }\n  rc = sqlite3_declare_vtab(db, VTAB_SCHEMA);\n  if( rc==SQLITE_OK ){\n    pTab = (StatTable *)sqlite3_malloc64(sizeof(StatTable));\n    if( pTab==0 ) rc = SQLITE_NOMEM_BKPT;\n  }\n\n  assert( rc==SQLITE_OK || pTab==0 );\n  if( rc==SQLITE_OK ){\n    memset(pTab, 0, sizeof(StatTable));\n    pTab->db = db;\n    pTab->iDb = iDb;\n  }\n\n  *ppVtab = (sqlite3_vtab*)pTab;\n  return rc;\n}\n\n/*\n** Disconnect from or destroy a statvfs virtual table.\n*/\nstatic int statDisconnect(sqlite3_vtab *pVtab){\n  sqlite3_free(pVtab);\n  return SQLITE_OK;\n}\n\n/*\n** There is no \"best-index\". This virtual table always does a linear\n** scan.  However, a schema=? constraint should cause this table to\n** operate on a different database schema, so check for it.\n**\n** idxNum is normally 0, but will be 1 if a schema=? constraint exists.\n*/\nstatic int statBestIndex(sqlite3_vtab *tab, sqlite3_index_info *pIdxInfo){\n  int i;\n\n  pIdxInfo->estimatedCost = 1.0e6;  /* Initial cost estimate */\n\n  /* Look for a valid schema=? constraint.  If found, change the idxNum to\n  ** 1 and request the value of that constraint be sent to xFilter.  And\n  ** lower the cost estimate to encourage the constrained version to be\n  ** used.\n  */\n  for(i=0; i<pIdxInfo->nConstraint; i++){\n    if( pIdxInfo->aConstraint[i].usable==0 ) continue;\n    if( pIdxInfo->aConstraint[i].op!=SQLITE_INDEX_CONSTRAINT_EQ ) continue;\n    if( pIdxInfo->aConstraint[i].iColumn!=10 ) continue;\n    pIdxInfo->idxNum = 1;\n    pIdxInfo->estimatedCost = 1.0;\n    pIdxInfo->aConstraintUsage[i].argvIndex = 1;\n    pIdxInfo->aConstraintUsage[i].omit = 1;\n    break;\n  }\n\n\n  /* Records are always returned in ascending order of (name, path). \n  ** If this will satisfy the client, set the orderByConsumed flag so that \n  ** SQLite does not do an external sort.\n  */\n  if( ( pIdxInfo->nOrderBy==1\n     && pIdxInfo->aOrderBy[0].iColumn==0\n     && pIdxInfo->aOrderBy[0].desc==0\n     ) ||\n      ( pIdxInfo->nOrderBy==2\n     && pIdxInfo->aOrderBy[0].iColumn==0\n     && pIdxInfo->aOrderBy[0].desc==0\n     && pIdxInfo->aOrderBy[1].iColumn==1\n     && pIdxInfo->aOrderBy[1].desc==0\n     )\n  ){\n    pIdxInfo->orderByConsumed = 1;\n  }\n\n  return SQLITE_OK;\n}\n\n/*\n** Open a new statvfs cursor.\n*/\nstatic int statOpen(sqlite3_vtab *pVTab, sqlite3_vtab_cursor **ppCursor){\n  StatTable *pTab = (StatTable *)pVTab;\n  StatCursor *pCsr;\n\n  pCsr = (StatCursor *)sqlite3_malloc64(sizeof(StatCursor));\n  if( pCsr==0 ){\n    return SQLITE_NOMEM_BKPT;\n  }else{\n    memset(pCsr, 0, sizeof(StatCursor));\n    pCsr->base.pVtab = pVTab;\n    pCsr->iDb = pTab->iDb;\n  }\n\n  *ppCursor = (sqlite3_vtab_cursor *)pCsr;\n  return SQLITE_OK;\n}\n\nstatic void statClearPage(StatPage *p){\n  int i;\n  if( p->aCell ){\n    for(i=0; i<p->nCell; i++){\n      sqlite3_free(p->aCell[i].aOvfl);\n    }\n    sqlite3_free(p->aCell);\n  }\n  sqlite3PagerUnref(p->pPg);\n  sqlite3_free(p->zPath);\n  memset(p, 0, sizeof(StatPage));\n}\n\nstatic void statResetCsr(StatCursor *pCsr){\n  int i;\n  sqlite3_reset(pCsr->pStmt);\n  for(i=0; i<ArraySize(pCsr->aPage); i++){\n    statClearPage(&pCsr->aPage[i]);\n  }\n  pCsr->iPage = 0;\n  sqlite3_free(pCsr->zPath);\n  pCsr->zPath = 0;\n  pCsr->isEof = 0;\n}\n\n/*\n** Close a statvfs cursor.\n*/\nstatic int statClose(sqlite3_vtab_cursor *pCursor){\n  StatCursor *pCsr = (StatCursor *)pCursor;\n  statResetCsr(pCsr);\n  sqlite3_finalize(pCsr->pStmt);\n  sqlite3_free(pCsr);\n  return SQLITE_OK;\n}\n\nstatic void getLocalPayload(\n  int nUsable,                    /* Usable bytes per page */\n  u8 flags,                       /* Page flags */\n  int nTotal,                     /* Total record (payload) size */\n  int *pnLocal                    /* OUT: Bytes stored locally */\n){\n  int nLocal;\n  int nMinLocal;\n  int nMaxLocal;\n \n  if( flags==0x0D ){              /* Table leaf node */\n    nMinLocal = (nUsable - 12) * 32 / 255 - 23;\n    nMaxLocal = nUsable - 35;\n  }else{                          /* Index interior and leaf nodes */\n    nMinLocal = (nUsable - 12) * 32 / 255 - 23;\n    nMaxLocal = (nUsable - 12) * 64 / 255 - 23;\n  }\n\n  nLocal = nMinLocal + (nTotal - nMinLocal) % (nUsable - 4);\n  if( nLocal>nMaxLocal ) nLocal = nMinLocal;\n  *pnLocal = nLocal;\n}\n\nstatic int statDecodePage(Btree *pBt, StatPage *p){\n  int nUnused;\n  int iOff;\n  int nHdr;\n  int isLeaf;\n  int szPage;\n\n  u8 *aData = sqlite3PagerGetData(p->pPg);\n  u8 *aHdr = &aData[p->iPgno==1 ? 100 : 0];\n\n  p->flags = aHdr[0];\n  p->nCell = get2byte(&aHdr[3]);\n  p->nMxPayload = 0;\n\n  isLeaf = (p->flags==0x0A || p->flags==0x0D);\n  nHdr = 12 - isLeaf*4 + (p->iPgno==1)*100;\n\n  nUnused = get2byte(&aHdr[5]) - nHdr - 2*p->nCell;\n  nUnused += (int)aHdr[7];\n  iOff = get2byte(&aHdr[1]);\n  while( iOff ){\n    nUnused += get2byte(&aData[iOff+2]);\n    iOff = get2byte(&aData[iOff]);\n  }\n  p->nUnused = nUnused;\n  p->iRightChildPg = isLeaf ? 0 : sqlite3Get4byte(&aHdr[8]);\n  szPage = sqlite3BtreeGetPageSize(pBt);\n\n  if( p->nCell ){\n    int i;                        /* Used to iterate through cells */\n    int nUsable;                  /* Usable bytes per page */\n\n    sqlite3BtreeEnter(pBt);\n    nUsable = szPage - sqlite3BtreeGetReserveNoMutex(pBt);\n    sqlite3BtreeLeave(pBt);\n    p->aCell = sqlite3_malloc64((p->nCell+1) * sizeof(StatCell));\n    if( p->aCell==0 ) return SQLITE_NOMEM_BKPT;\n    memset(p->aCell, 0, (p->nCell+1) * sizeof(StatCell));\n\n    for(i=0; i<p->nCell; i++){\n      StatCell *pCell = &p->aCell[i];\n\n      iOff = get2byte(&aData[nHdr+i*2]);\n      if( !isLeaf ){\n        pCell->iChildPg = sqlite3Get4byte(&aData[iOff]);\n        iOff += 4;\n      }\n      if( p->flags==0x05 ){\n        /* A table interior node. nPayload==0. */\n      }else{\n        u32 nPayload;             /* Bytes of payload total (local+overflow) */\n        int nLocal;               /* Bytes of payload stored locally */\n        iOff += getVarint32(&aData[iOff], nPayload);\n        if( p->flags==0x0D ){\n          u64 dummy;\n          iOff += sqlite3GetVarint(&aData[iOff], &dummy);\n        }\n        if( nPayload>(u32)p->nMxPayload ) p->nMxPayload = nPayload;\n        getLocalPayload(nUsable, p->flags, nPayload, &nLocal);\n        pCell->nLocal = nLocal;\n        assert( nLocal>=0 );\n        assert( nPayload>=(u32)nLocal );\n        assert( nLocal<=(nUsable-35) );\n        if( nPayload>(u32)nLocal ){\n          int j;\n          int nOvfl = ((nPayload - nLocal) + nUsable-4 - 1) / (nUsable - 4);\n          pCell->nLastOvfl = (nPayload-nLocal) - (nOvfl-1) * (nUsable-4);\n          pCell->nOvfl = nOvfl;\n          pCell->aOvfl = sqlite3_malloc64(sizeof(u32)*nOvfl);\n          if( pCell->aOvfl==0 ) return SQLITE_NOMEM_BKPT;\n          pCell->aOvfl[0] = sqlite3Get4byte(&aData[iOff+nLocal]);\n          for(j=1; j<nOvfl; j++){\n            int rc;\n            u32 iPrev = pCell->aOvfl[j-1];\n            DbPage *pPg = 0;\n            rc = sqlite3PagerGet(sqlite3BtreePager(pBt), iPrev, &pPg, 0);\n            if( rc!=SQLITE_OK ){\n              assert( pPg==0 );\n              return rc;\n            } \n            pCell->aOvfl[j] = sqlite3Get4byte(sqlite3PagerGetData(pPg));\n            sqlite3PagerUnref(pPg);\n          }\n        }\n      }\n    }\n  }\n\n  return SQLITE_OK;\n}\n\n/*\n** Populate the pCsr->iOffset and pCsr->szPage member variables. Based on\n** the current value of pCsr->iPageno.\n*/\nstatic void statSizeAndOffset(StatCursor *pCsr){\n  StatTable *pTab = (StatTable *)((sqlite3_vtab_cursor *)pCsr)->pVtab;\n  Btree *pBt = pTab->db->aDb[pTab->iDb].pBt;\n  Pager *pPager = sqlite3BtreePager(pBt);\n  sqlite3_file *fd;\n  sqlite3_int64 x[2];\n\n  /* The default page size and offset */\n  pCsr->szPage = sqlite3BtreeGetPageSize(pBt);\n  pCsr->iOffset = (i64)pCsr->szPage * (pCsr->iPageno - 1);\n\n  /* If connected to a ZIPVFS backend, override the page size and\n  ** offset with actual values obtained from ZIPVFS.\n  */\n  fd = sqlite3PagerFile(pPager);\n  x[0] = pCsr->iPageno;\n  if( fd->pMethods!=0 && sqlite3OsFileControl(fd, 230440, &x)==SQLITE_OK ){\n    pCsr->iOffset = x[0];\n    pCsr->szPage = (int)x[1];\n  }\n}\n\n/*\n** Move a statvfs cursor to the next entry in the file.\n*/\nstatic int statNext(sqlite3_vtab_cursor *pCursor){\n  int rc;\n  int nPayload;\n  char *z;\n  StatCursor *pCsr = (StatCursor *)pCursor;\n  StatTable *pTab = (StatTable *)pCursor->pVtab;\n  Btree *pBt = pTab->db->aDb[pCsr->iDb].pBt;\n  Pager *pPager = sqlite3BtreePager(pBt);\n\n  sqlite3_free(pCsr->zPath);\n  pCsr->zPath = 0;\n\nstatNextRestart:\n  if( pCsr->aPage[0].pPg==0 ){\n    rc = sqlite3_step(pCsr->pStmt);\n    if( rc==SQLITE_ROW ){\n      int nPage;\n      u32 iRoot = (u32)sqlite3_column_int64(pCsr->pStmt, 1);\n      sqlite3PagerPagecount(pPager, &nPage);\n      if( nPage==0 ){\n        pCsr->isEof = 1;\n        return sqlite3_reset(pCsr->pStmt);\n      }\n      rc = sqlite3PagerGet(pPager, iRoot, &pCsr->aPage[0].pPg, 0);\n      pCsr->aPage[0].iPgno = iRoot;\n      pCsr->aPage[0].iCell = 0;\n      pCsr->aPage[0].zPath = z = sqlite3_mprintf(\"/\");\n      pCsr->iPage = 0;\n      if( z==0 ) rc = SQLITE_NOMEM_BKPT;\n    }else{\n      pCsr->isEof = 1;\n      return sqlite3_reset(pCsr->pStmt);\n    }\n  }else{\n\n    /* Page p itself has already been visited. */\n    StatPage *p = &pCsr->aPage[pCsr->iPage];\n\n    while( p->iCell<p->nCell ){\n      StatCell *pCell = &p->aCell[p->iCell];\n      if( pCell->iOvfl<pCell->nOvfl ){\n        int nUsable;\n        sqlite3BtreeEnter(pBt);\n        nUsable = sqlite3BtreeGetPageSize(pBt) - \n                        sqlite3BtreeGetReserveNoMutex(pBt);\n        sqlite3BtreeLeave(pBt);\n        pCsr->zName = (char *)sqlite3_column_text(pCsr->pStmt, 0);\n        pCsr->iPageno = pCell->aOvfl[pCell->iOvfl];\n        pCsr->zPagetype = \"overflow\";\n        pCsr->nCell = 0;\n        pCsr->nMxPayload = 0;\n        pCsr->zPath = z = sqlite3_mprintf(\n            \"%s%.3x+%.6x\", p->zPath, p->iCell, pCell->iOvfl\n        );\n        if( pCell->iOvfl<pCell->nOvfl-1 ){\n          pCsr->nUnused = 0;\n          pCsr->nPayload = nUsable - 4;\n        }else{\n          pCsr->nPayload = pCell->nLastOvfl;\n          pCsr->nUnused = nUsable - 4 - pCsr->nPayload;\n        }\n        pCell->iOvfl++;\n        statSizeAndOffset(pCsr);\n        return z==0 ? SQLITE_NOMEM_BKPT : SQLITE_OK;\n      }\n      if( p->iRightChildPg ) break;\n      p->iCell++;\n    }\n\n    if( !p->iRightChildPg || p->iCell>p->nCell ){\n      statClearPage(p);\n      if( pCsr->iPage==0 ) return statNext(pCursor);\n      pCsr->iPage--;\n      goto statNextRestart; /* Tail recursion */\n    }\n    pCsr->iPage++;\n    assert( p==&pCsr->aPage[pCsr->iPage-1] );\n\n    if( p->iCell==p->nCell ){\n      p[1].iPgno = p->iRightChildPg;\n    }else{\n      p[1].iPgno = p->aCell[p->iCell].iChildPg;\n    }\n    rc = sqlite3PagerGet(pPager, p[1].iPgno, &p[1].pPg, 0);\n    p[1].iCell = 0;\n    p[1].zPath = z = sqlite3_mprintf(\"%s%.3x/\", p->zPath, p->iCell);\n    p->iCell++;\n    if( z==0 ) rc = SQLITE_NOMEM_BKPT;\n  }\n\n\n  /* Populate the StatCursor fields with the values to be returned\n  ** by the xColumn() and xRowid() methods.\n  */\n  if( rc==SQLITE_OK ){\n    int i;\n    StatPage *p = &pCsr->aPage[pCsr->iPage];\n    pCsr->zName = (char *)sqlite3_column_text(pCsr->pStmt, 0);\n    pCsr->iPageno = p->iPgno;\n\n    rc = statDecodePage(pBt, p);\n    if( rc==SQLITE_OK ){\n      statSizeAndOffset(pCsr);\n\n      switch( p->flags ){\n        case 0x05:             /* table internal */\n        case 0x02:             /* index internal */\n          pCsr->zPagetype = \"internal\";\n          break;\n        case 0x0D:             /* table leaf */\n        case 0x0A:             /* index leaf */\n          pCsr->zPagetype = \"leaf\";\n          break;\n        default:\n          pCsr->zPagetype = \"corrupted\";\n          break;\n      }\n      pCsr->nCell = p->nCell;\n      pCsr->nUnused = p->nUnused;\n      pCsr->nMxPayload = p->nMxPayload;\n      pCsr->zPath = z = sqlite3_mprintf(\"%s\", p->zPath);\n      if( z==0 ) rc = SQLITE_NOMEM_BKPT;\n      nPayload = 0;\n      for(i=0; i<p->nCell; i++){\n        nPayload += p->aCell[i].nLocal;\n      }\n      pCsr->nPayload = nPayload;\n    }\n  }\n\n  return rc;\n}\n\nstatic int statEof(sqlite3_vtab_cursor *pCursor){\n  StatCursor *pCsr = (StatCursor *)pCursor;\n  return pCsr->isEof;\n}\n\nstatic int statFilter(\n  sqlite3_vtab_cursor *pCursor, \n  int idxNum, const char *idxStr,\n  int argc, sqlite3_value **argv\n){\n  StatCursor *pCsr = (StatCursor *)pCursor;\n  StatTable *pTab = (StatTable*)(pCursor->pVtab);\n  char *zSql;\n  int rc = SQLITE_OK;\n  char *zMaster;\n\n  if( idxNum==1 ){\n    const char *zDbase = (const char*)sqlite3_value_text(argv[0]);\n    pCsr->iDb = sqlite3FindDbName(pTab->db, zDbase);\n    if( pCsr->iDb<0 ){\n      sqlite3_free(pCursor->pVtab->zErrMsg);\n      pCursor->pVtab->zErrMsg = sqlite3_mprintf(\"no such schema: %s\", zDbase);\n      return pCursor->pVtab->zErrMsg ? SQLITE_ERROR : SQLITE_NOMEM_BKPT;\n    }\n  }else{\n    pCsr->iDb = pTab->iDb;\n  }\n  statResetCsr(pCsr);\n  sqlite3_finalize(pCsr->pStmt);\n  pCsr->pStmt = 0;\n  zMaster = pCsr->iDb==1 ? \"sqlite_temp_master\" : \"sqlite_master\";\n  zSql = sqlite3_mprintf(\n      \"SELECT 'sqlite_master' AS name, 1 AS rootpage, 'table' AS type\"\n      \"  UNION ALL  \"\n      \"SELECT name, rootpage, type\"\n      \"  FROM \\\"%w\\\".%s WHERE rootpage!=0\"\n      \"  ORDER BY name\", pTab->db->aDb[pCsr->iDb].zDbSName, zMaster);\n  if( zSql==0 ){\n    return SQLITE_NOMEM_BKPT;\n  }else{\n    rc = sqlite3_prepare_v2(pTab->db, zSql, -1, &pCsr->pStmt, 0);\n    sqlite3_free(zSql);\n  }\n\n  if( rc==SQLITE_OK ){\n    rc = statNext(pCursor);\n  }\n  return rc;\n}\n\nstatic int statColumn(\n  sqlite3_vtab_cursor *pCursor, \n  sqlite3_context *ctx, \n  int i\n){\n  StatCursor *pCsr = (StatCursor *)pCursor;\n  switch( i ){\n    case 0:            /* name */\n      sqlite3_result_text(ctx, pCsr->zName, -1, SQLITE_TRANSIENT);\n      break;\n    case 1:            /* path */\n      sqlite3_result_text(ctx, pCsr->zPath, -1, SQLITE_TRANSIENT);\n      break;\n    case 2:            /* pageno */\n      sqlite3_result_int64(ctx, pCsr->iPageno);\n      break;\n    case 3:            /* pagetype */\n      sqlite3_result_text(ctx, pCsr->zPagetype, -1, SQLITE_STATIC);\n      break;\n    case 4:            /* ncell */\n      sqlite3_result_int(ctx, pCsr->nCell);\n      break;\n    case 5:            /* payload */\n      sqlite3_result_int(ctx, pCsr->nPayload);\n      break;\n    case 6:            /* unused */\n      sqlite3_result_int(ctx, pCsr->nUnused);\n      break;\n    case 7:            /* mx_payload */\n      sqlite3_result_int(ctx, pCsr->nMxPayload);\n      break;\n    case 8:            /* pgoffset */\n      sqlite3_result_int64(ctx, pCsr->iOffset);\n      break;\n    case 9:            /* pgsize */\n      sqlite3_result_int(ctx, pCsr->szPage);\n      break;\n    default: {          /* schema */\n      sqlite3 *db = sqlite3_context_db_handle(ctx);\n      int iDb = pCsr->iDb;\n      sqlite3_result_text(ctx, db->aDb[iDb].zDbSName, -1, SQLITE_STATIC);\n      break;\n    }\n  }\n  return SQLITE_OK;\n}\n\nstatic int statRowid(sqlite3_vtab_cursor *pCursor, sqlite_int64 *pRowid){\n  StatCursor *pCsr = (StatCursor *)pCursor;\n  *pRowid = pCsr->iPageno;\n  return SQLITE_OK;\n}\n\n/*\n** Invoke this routine to register the \"dbstat\" virtual table module\n*/\nSQLITE_PRIVATE int sqlite3DbstatRegister(sqlite3 *db){\n  static sqlite3_module dbstat_module = {\n    0,                            /* iVersion */\n    statConnect,                  /* xCreate */\n    statConnect,                  /* xConnect */\n    statBestIndex,                /* xBestIndex */\n    statDisconnect,               /* xDisconnect */\n    statDisconnect,               /* xDestroy */\n    statOpen,                     /* xOpen - open a cursor */\n    statClose,                    /* xClose - close a cursor */\n    statFilter,                   /* xFilter - configure scan constraints */\n    statNext,                     /* xNext - advance a cursor */\n    statEof,                      /* xEof - check for end of scan */\n    statColumn,                   /* xColumn - read data */\n    statRowid,                    /* xRowid - read data */\n    0,                            /* xUpdate */\n    0,                            /* xBegin */\n    0,                            /* xSync */\n    0,                            /* xCommit */\n    0,                            /* xRollback */\n    0,                            /* xFindMethod */\n    0,                            /* xRename */\n    0,                            /* xSavepoint */\n    0,                            /* xRelease */\n    0,                            /* xRollbackTo */\n  };\n  return sqlite3_create_module(db, \"dbstat\", &dbstat_module, 0);\n}\n#elif defined(SQLITE_ENABLE_DBSTAT_VTAB)\nSQLITE_PRIVATE int sqlite3DbstatRegister(sqlite3 *db){ return SQLITE_OK; }\n#endif /* SQLITE_ENABLE_DBSTAT_VTAB */\n\n/************** End of dbstat.c **********************************************/\n/************** Begin file dbpage.c ******************************************/\n/*\n** 2017-10-11\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n******************************************************************************\n**\n** This file contains an implementation of the \"sqlite_dbpage\" virtual table.\n**\n** The sqlite_dbpage virtual table is used to read or write whole raw\n** pages of the database file.  The pager interface is used so that \n** uncommitted changes and changes recorded in the WAL file are correctly\n** retrieved.\n**\n** Usage example:\n**\n**    SELECT data FROM sqlite_dbpage('aux1') WHERE pgno=123;\n**\n** This is an eponymous virtual table so it does not need to be created before\n** use.  The optional argument to the sqlite_dbpage() table name is the\n** schema for the database file that is to be read.  The default schema is\n** \"main\".\n**\n** The data field of sqlite_dbpage table can be updated.  The new\n** value must be a BLOB which is the correct page size, otherwise the\n** update fails.  Rows may not be deleted or inserted.\n*/\n\n/* #include \"sqliteInt.h\"   ** Requires access to internal data structures ** */\n#if (defined(SQLITE_ENABLE_DBPAGE_VTAB) || defined(SQLITE_TEST)) \\\n    && !defined(SQLITE_OMIT_VIRTUALTABLE)\n\ntypedef struct DbpageTable DbpageTable;\ntypedef struct DbpageCursor DbpageCursor;\n\nstruct DbpageCursor {\n  sqlite3_vtab_cursor base;       /* Base class.  Must be first */\n  int pgno;                       /* Current page number */\n  int mxPgno;                     /* Last page to visit on this scan */\n  Pager *pPager;                  /* Pager being read/written */\n  DbPage *pPage1;                 /* Page 1 of the database */\n  int iDb;                        /* Index of database to analyze */\n  int szPage;                     /* Size of each page in bytes */\n};\n\nstruct DbpageTable {\n  sqlite3_vtab base;              /* Base class.  Must be first */\n  sqlite3 *db;                    /* The database */\n};\n\n/* Columns */\n#define DBPAGE_COLUMN_PGNO    0\n#define DBPAGE_COLUMN_DATA    1\n#define DBPAGE_COLUMN_SCHEMA  2\n\n\n\n/*\n** Connect to or create a dbpagevfs virtual table.\n*/\nstatic int dbpageConnect(\n  sqlite3 *db,\n  void *pAux,\n  int argc, const char *const*argv,\n  sqlite3_vtab **ppVtab,\n  char **pzErr\n){\n  DbpageTable *pTab = 0;\n  int rc = SQLITE_OK;\n\n  rc = sqlite3_declare_vtab(db, \n          \"CREATE TABLE x(pgno INTEGER PRIMARY KEY, data BLOB, schema HIDDEN)\");\n  if( rc==SQLITE_OK ){\n    pTab = (DbpageTable *)sqlite3_malloc64(sizeof(DbpageTable));\n    if( pTab==0 ) rc = SQLITE_NOMEM_BKPT;\n  }\n\n  assert( rc==SQLITE_OK || pTab==0 );\n  if( rc==SQLITE_OK ){\n    memset(pTab, 0, sizeof(DbpageTable));\n    pTab->db = db;\n  }\n\n  *ppVtab = (sqlite3_vtab*)pTab;\n  return rc;\n}\n\n/*\n** Disconnect from or destroy a dbpagevfs virtual table.\n*/\nstatic int dbpageDisconnect(sqlite3_vtab *pVtab){\n  sqlite3_free(pVtab);\n  return SQLITE_OK;\n}\n\n/*\n** idxNum:\n**\n**     0     schema=main, full table scan\n**     1     schema=main, pgno=?1\n**     2     schema=?1, full table scan\n**     3     schema=?1, pgno=?2\n*/\nstatic int dbpageBestIndex(sqlite3_vtab *tab, sqlite3_index_info *pIdxInfo){\n  int i;\n  int iPlan = 0;\n\n  /* If there is a schema= constraint, it must be honored.  Report a\n  ** ridiculously large estimated cost if the schema= constraint is\n  ** unavailable\n  */\n  for(i=0; i<pIdxInfo->nConstraint; i++){\n    struct sqlite3_index_constraint *p = &pIdxInfo->aConstraint[i];\n    if( p->iColumn!=DBPAGE_COLUMN_SCHEMA ) continue;\n    if( p->op!=SQLITE_INDEX_CONSTRAINT_EQ ) continue;\n    if( !p->usable ){\n      /* No solution.  Use the default SQLITE_BIG_DBL cost */\n      pIdxInfo->estimatedRows = 0x7fffffff;\n      return SQLITE_OK;\n    }\n    iPlan = 2;\n    pIdxInfo->aConstraintUsage[i].argvIndex = 1;\n    pIdxInfo->aConstraintUsage[i].omit = 1;\n    break;\n  }\n\n  /* If we reach this point, it means that either there is no schema=\n  ** constraint (in which case we use the \"main\" schema) or else the\n  ** schema constraint was accepted.  Lower the estimated cost accordingly\n  */\n  pIdxInfo->estimatedCost = 1.0e6;\n\n  /* Check for constraints against pgno */\n  for(i=0; i<pIdxInfo->nConstraint; i++){\n    struct sqlite3_index_constraint *p = &pIdxInfo->aConstraint[i];\n    if( p->usable && p->iColumn<=0 && p->op==SQLITE_INDEX_CONSTRAINT_EQ ){\n      pIdxInfo->estimatedRows = 1;\n      pIdxInfo->idxFlags = SQLITE_INDEX_SCAN_UNIQUE;\n      pIdxInfo->estimatedCost = 1.0;\n      pIdxInfo->aConstraintUsage[i].argvIndex = iPlan ? 2 : 1;\n      pIdxInfo->aConstraintUsage[i].omit = 1;\n      iPlan |= 1;\n      break;\n    }\n  }\n  pIdxInfo->idxNum = iPlan;\n\n  if( pIdxInfo->nOrderBy>=1\n   && pIdxInfo->aOrderBy[0].iColumn<=0\n   && pIdxInfo->aOrderBy[0].desc==0\n  ){\n    pIdxInfo->orderByConsumed = 1;\n  }\n  return SQLITE_OK;\n}\n\n/*\n** Open a new dbpagevfs cursor.\n*/\nstatic int dbpageOpen(sqlite3_vtab *pVTab, sqlite3_vtab_cursor **ppCursor){\n  DbpageCursor *pCsr;\n\n  pCsr = (DbpageCursor *)sqlite3_malloc64(sizeof(DbpageCursor));\n  if( pCsr==0 ){\n    return SQLITE_NOMEM_BKPT;\n  }else{\n    memset(pCsr, 0, sizeof(DbpageCursor));\n    pCsr->base.pVtab = pVTab;\n    pCsr->pgno = -1;\n  }\n\n  *ppCursor = (sqlite3_vtab_cursor *)pCsr;\n  return SQLITE_OK;\n}\n\n/*\n** Close a dbpagevfs cursor.\n*/\nstatic int dbpageClose(sqlite3_vtab_cursor *pCursor){\n  DbpageCursor *pCsr = (DbpageCursor *)pCursor;\n  if( pCsr->pPage1 ) sqlite3PagerUnrefPageOne(pCsr->pPage1);\n  sqlite3_free(pCsr);\n  return SQLITE_OK;\n}\n\n/*\n** Move a dbpagevfs cursor to the next entry in the file.\n*/\nstatic int dbpageNext(sqlite3_vtab_cursor *pCursor){\n  int rc = SQLITE_OK;\n  DbpageCursor *pCsr = (DbpageCursor *)pCursor;\n  pCsr->pgno++;\n  return rc;\n}\n\nstatic int dbpageEof(sqlite3_vtab_cursor *pCursor){\n  DbpageCursor *pCsr = (DbpageCursor *)pCursor;\n  return pCsr->pgno > pCsr->mxPgno;\n}\n\n/*\n** idxNum:\n**\n**     0     schema=main, full table scan\n**     1     schema=main, pgno=?1\n**     2     schema=?1, full table scan\n**     3     schema=?1, pgno=?2\n**\n** idxStr is not used\n*/\nstatic int dbpageFilter(\n  sqlite3_vtab_cursor *pCursor, \n  int idxNum, const char *idxStr,\n  int argc, sqlite3_value **argv\n){\n  DbpageCursor *pCsr = (DbpageCursor *)pCursor;\n  DbpageTable *pTab = (DbpageTable *)pCursor->pVtab;\n  int rc;\n  sqlite3 *db = pTab->db;\n  Btree *pBt;\n\n  /* Default setting is no rows of result */\n  pCsr->pgno = 1; \n  pCsr->mxPgno = 0;\n\n  if( idxNum & 2 ){\n    const char *zSchema;\n    assert( argc>=1 );\n    zSchema = (const char*)sqlite3_value_text(argv[0]);\n    pCsr->iDb = sqlite3FindDbName(db, zSchema);\n    if( pCsr->iDb<0 ) return SQLITE_OK;\n  }else{\n    pCsr->iDb = 0;\n  }\n  pBt = db->aDb[pCsr->iDb].pBt;\n  if( pBt==0 ) return SQLITE_OK;\n  pCsr->pPager = sqlite3BtreePager(pBt);\n  pCsr->szPage = sqlite3BtreeGetPageSize(pBt);\n  pCsr->mxPgno = sqlite3BtreeLastPage(pBt);\n  if( idxNum & 1 ){\n    assert( argc>(idxNum>>1) );\n    pCsr->pgno = sqlite3_value_int(argv[idxNum>>1]);\n    if( pCsr->pgno<1 || pCsr->pgno>pCsr->mxPgno ){\n      pCsr->pgno = 1;\n      pCsr->mxPgno = 0;\n    }else{\n      pCsr->mxPgno = pCsr->pgno;\n    }\n  }else{\n    assert( pCsr->pgno==1 );\n  }\n  if( pCsr->pPage1 ) sqlite3PagerUnrefPageOne(pCsr->pPage1);\n  rc = sqlite3PagerGet(pCsr->pPager, 1, &pCsr->pPage1, 0);\n  return rc;\n}\n\nstatic int dbpageColumn(\n  sqlite3_vtab_cursor *pCursor, \n  sqlite3_context *ctx, \n  int i\n){\n  DbpageCursor *pCsr = (DbpageCursor *)pCursor;\n  int rc = SQLITE_OK;\n  switch( i ){\n    case 0: {           /* pgno */\n      sqlite3_result_int(ctx, pCsr->pgno);\n      break;\n    }\n    case 1: {           /* data */\n      DbPage *pDbPage = 0;\n      rc = sqlite3PagerGet(pCsr->pPager, pCsr->pgno, (DbPage**)&pDbPage, 0);\n      if( rc==SQLITE_OK ){\n        sqlite3_result_blob(ctx, sqlite3PagerGetData(pDbPage), pCsr->szPage,\n                            SQLITE_TRANSIENT);\n      }\n      sqlite3PagerUnref(pDbPage);\n      break;\n    }\n    default: {          /* schema */\n      sqlite3 *db = sqlite3_context_db_handle(ctx);\n      sqlite3_result_text(ctx, db->aDb[pCsr->iDb].zDbSName, -1, SQLITE_STATIC);\n      break;\n    }\n  }\n  return SQLITE_OK;\n}\n\nstatic int dbpageRowid(sqlite3_vtab_cursor *pCursor, sqlite_int64 *pRowid){\n  DbpageCursor *pCsr = (DbpageCursor *)pCursor;\n  *pRowid = pCsr->pgno;\n  return SQLITE_OK;\n}\n\nstatic int dbpageUpdate(\n  sqlite3_vtab *pVtab,\n  int argc,\n  sqlite3_value **argv,\n  sqlite_int64 *pRowid\n){\n  DbpageTable *pTab = (DbpageTable *)pVtab;\n  Pgno pgno;\n  DbPage *pDbPage = 0;\n  int rc = SQLITE_OK;\n  char *zErr = 0;\n  const char *zSchema;\n  int iDb;\n  Btree *pBt;\n  Pager *pPager;\n  int szPage;\n\n  if( argc==1 ){\n    zErr = \"cannot delete\";\n    goto update_fail;\n  }\n  pgno = sqlite3_value_int(argv[0]);\n  if( (Pgno)sqlite3_value_int(argv[1])!=pgno ){\n    zErr = \"cannot insert\";\n    goto update_fail;\n  }\n  zSchema = (const char*)sqlite3_value_text(argv[4]);\n  iDb = zSchema ? sqlite3FindDbName(pTab->db, zSchema) : -1;\n  if( iDb<0 ){\n    zErr = \"no such schema\";\n    goto update_fail;\n  }\n  pBt = pTab->db->aDb[iDb].pBt;\n  if( pgno<1 || pBt==0 || pgno>(int)sqlite3BtreeLastPage(pBt) ){\n    zErr = \"bad page number\";\n    goto update_fail;\n  }\n  szPage = sqlite3BtreeGetPageSize(pBt);\n  if( sqlite3_value_type(argv[3])!=SQLITE_BLOB \n   || sqlite3_value_bytes(argv[3])!=szPage\n  ){\n    zErr = \"bad page value\";\n    goto update_fail;\n  }\n  pPager = sqlite3BtreePager(pBt);\n  rc = sqlite3PagerGet(pPager, pgno, (DbPage**)&pDbPage, 0);\n  if( rc==SQLITE_OK ){\n    rc = sqlite3PagerWrite(pDbPage);\n    if( rc==SQLITE_OK ){\n      memcpy(sqlite3PagerGetData(pDbPage),\n             sqlite3_value_blob(argv[3]),\n             szPage);\n    }\n  }\n  sqlite3PagerUnref(pDbPage);\n  return rc;\n\nupdate_fail:\n  sqlite3_free(pVtab->zErrMsg);\n  pVtab->zErrMsg = sqlite3_mprintf(\"%s\", zErr);\n  return SQLITE_ERROR;\n}\n\n/* Since we do not know in advance which database files will be\n** written by the sqlite_dbpage virtual table, start a write transaction\n** on them all.\n*/\nstatic int dbpageBegin(sqlite3_vtab *pVtab){\n  DbpageTable *pTab = (DbpageTable *)pVtab;\n  sqlite3 *db = pTab->db;\n  int i;\n  for(i=0; i<db->nDb; i++){\n    Btree *pBt = db->aDb[i].pBt;\n    if( pBt ) sqlite3BtreeBeginTrans(pBt, 1);\n  }\n  return SQLITE_OK;\n}\n\n\n/*\n** Invoke this routine to register the \"dbpage\" virtual table module\n*/\nSQLITE_PRIVATE int sqlite3DbpageRegister(sqlite3 *db){\n  static sqlite3_module dbpage_module = {\n    0,                            /* iVersion */\n    dbpageConnect,                /* xCreate */\n    dbpageConnect,                /* xConnect */\n    dbpageBestIndex,              /* xBestIndex */\n    dbpageDisconnect,             /* xDisconnect */\n    dbpageDisconnect,             /* xDestroy */\n    dbpageOpen,                   /* xOpen - open a cursor */\n    dbpageClose,                  /* xClose - close a cursor */\n    dbpageFilter,                 /* xFilter - configure scan constraints */\n    dbpageNext,                   /* xNext - advance a cursor */\n    dbpageEof,                    /* xEof - check for end of scan */\n    dbpageColumn,                 /* xColumn - read data */\n    dbpageRowid,                  /* xRowid - read data */\n    dbpageUpdate,                 /* xUpdate */\n    dbpageBegin,                  /* xBegin */\n    0,                            /* xSync */\n    0,                            /* xCommit */\n    0,                            /* xRollback */\n    0,                            /* xFindMethod */\n    0,                            /* xRename */\n    0,                            /* xSavepoint */\n    0,                            /* xRelease */\n    0,                            /* xRollbackTo */\n  };\n  return sqlite3_create_module(db, \"sqlite_dbpage\", &dbpage_module, 0);\n}\n#elif defined(SQLITE_ENABLE_DBPAGE_VTAB)\nSQLITE_PRIVATE int sqlite3DbpageRegister(sqlite3 *db){ return SQLITE_OK; }\n#endif /* SQLITE_ENABLE_DBSTAT_VTAB */\n\n/************** End of dbpage.c **********************************************/\n/************** Begin file sqlite3session.c **********************************/\n\n#if defined(SQLITE_ENABLE_SESSION) && defined(SQLITE_ENABLE_PREUPDATE_HOOK)\n/* #include \"sqlite3session.h\" */\n/* #include <assert.h> */\n/* #include <string.h> */\n\n#ifndef SQLITE_AMALGAMATION\n/* # include \"sqliteInt.h\" */\n/* # include \"vdbeInt.h\" */\n#endif\n\ntypedef struct SessionTable SessionTable;\ntypedef struct SessionChange SessionChange;\ntypedef struct SessionBuffer SessionBuffer;\ntypedef struct SessionInput SessionInput;\n\n/*\n** Minimum chunk size used by streaming versions of functions.\n*/\n#ifndef SESSIONS_STRM_CHUNK_SIZE\n# ifdef SQLITE_TEST\n#   define SESSIONS_STRM_CHUNK_SIZE 64\n# else\n#   define SESSIONS_STRM_CHUNK_SIZE 1024\n# endif\n#endif\n\ntypedef struct SessionHook SessionHook;\nstruct SessionHook {\n  void *pCtx;\n  int (*xOld)(void*,int,sqlite3_value**);\n  int (*xNew)(void*,int,sqlite3_value**);\n  int (*xCount)(void*);\n  int (*xDepth)(void*);\n};\n\n/*\n** Session handle structure.\n*/\nstruct sqlite3_session {\n  sqlite3 *db;                    /* Database handle session is attached to */\n  char *zDb;                      /* Name of database session is attached to */\n  int bEnable;                    /* True if currently recording */\n  int bIndirect;                  /* True if all changes are indirect */\n  int bAutoAttach;                /* True to auto-attach tables */\n  int rc;                         /* Non-zero if an error has occurred */\n  void *pFilterCtx;               /* First argument to pass to xTableFilter */\n  int (*xTableFilter)(void *pCtx, const char *zTab);\n  sqlite3_value *pZeroBlob;       /* Value containing X'' */\n  sqlite3_session *pNext;         /* Next session object on same db. */\n  SessionTable *pTable;           /* List of attached tables */\n  SessionHook hook;               /* APIs to grab new and old data with */\n};\n\n/*\n** Instances of this structure are used to build strings or binary records.\n*/\nstruct SessionBuffer {\n  u8 *aBuf;                       /* Pointer to changeset buffer */\n  int nBuf;                       /* Size of buffer aBuf */\n  int nAlloc;                     /* Size of allocation containing aBuf */\n};\n\n/*\n** An object of this type is used internally as an abstraction for \n** input data. Input data may be supplied either as a single large buffer\n** (e.g. sqlite3changeset_start()) or using a stream function (e.g.\n**  sqlite3changeset_start_strm()).\n*/\nstruct SessionInput {\n  int bNoDiscard;                 /* If true, discard no data */\n  int iCurrent;                   /* Offset in aData[] of current change */\n  int iNext;                      /* Offset in aData[] of next change */\n  u8 *aData;                      /* Pointer to buffer containing changeset */\n  int nData;                      /* Number of bytes in aData */\n\n  SessionBuffer buf;              /* Current read buffer */\n  int (*xInput)(void*, void*, int*);        /* Input stream call (or NULL) */\n  void *pIn;                                /* First argument to xInput */\n  int bEof;                       /* Set to true after xInput finished */\n};\n\n/*\n** Structure for changeset iterators.\n*/\nstruct sqlite3_changeset_iter {\n  SessionInput in;                /* Input buffer or stream */\n  SessionBuffer tblhdr;           /* Buffer to hold apValue/zTab/abPK/ */\n  int bPatchset;                  /* True if this is a patchset */\n  int rc;                         /* Iterator error code */\n  sqlite3_stmt *pConflict;        /* Points to conflicting row, if any */\n  char *zTab;                     /* Current table */\n  int nCol;                       /* Number of columns in zTab */\n  int op;                         /* Current operation */\n  int bIndirect;                  /* True if current change was indirect */\n  u8 *abPK;                       /* Primary key array */\n  sqlite3_value **apValue;        /* old.* and new.* values */\n};\n\n/*\n** Each session object maintains a set of the following structures, one\n** for each table the session object is monitoring. The structures are\n** stored in a linked list starting at sqlite3_session.pTable.\n**\n** The keys of the SessionTable.aChange[] hash table are all rows that have\n** been modified in any way since the session object was attached to the\n** table.\n**\n** The data associated with each hash-table entry is a structure containing\n** a subset of the initial values that the modified row contained at the\n** start of the session. Or no initial values if the row was inserted.\n*/\nstruct SessionTable {\n  SessionTable *pNext;\n  char *zName;                    /* Local name of table */\n  int nCol;                       /* Number of columns in table zName */\n  int bStat1;                     /* True if this is sqlite_stat1 */\n  const char **azCol;             /* Column names */\n  u8 *abPK;                       /* Array of primary key flags */\n  int nEntry;                     /* Total number of entries in hash table */\n  int nChange;                    /* Size of apChange[] array */\n  SessionChange **apChange;       /* Hash table buckets */\n};\n\n/* \n** RECORD FORMAT:\n**\n** The following record format is similar to (but not compatible with) that \n** used in SQLite database files. This format is used as part of the \n** change-set binary format, and so must be architecture independent.\n**\n** Unlike the SQLite database record format, each field is self-contained -\n** there is no separation of header and data. Each field begins with a\n** single byte describing its type, as follows:\n**\n**       0x00: Undefined value.\n**       0x01: Integer value.\n**       0x02: Real value.\n**       0x03: Text value.\n**       0x04: Blob value.\n**       0x05: SQL NULL value.\n**\n** Note that the above match the definitions of SQLITE_INTEGER, SQLITE_TEXT\n** and so on in sqlite3.h. For undefined and NULL values, the field consists\n** only of the single type byte. For other types of values, the type byte\n** is followed by:\n**\n**   Text values:\n**     A varint containing the number of bytes in the value (encoded using\n**     UTF-8). Followed by a buffer containing the UTF-8 representation\n**     of the text value. There is no nul terminator.\n**\n**   Blob values:\n**     A varint containing the number of bytes in the value, followed by\n**     a buffer containing the value itself.\n**\n**   Integer values:\n**     An 8-byte big-endian integer value.\n**\n**   Real values:\n**     An 8-byte big-endian IEEE 754-2008 real value.\n**\n** Varint values are encoded in the same way as varints in the SQLite \n** record format.\n**\n** CHANGESET FORMAT:\n**\n** A changeset is a collection of DELETE, UPDATE and INSERT operations on\n** one or more tables. Operations on a single table are grouped together,\n** but may occur in any order (i.e. deletes, updates and inserts are all\n** mixed together).\n**\n** Each group of changes begins with a table header:\n**\n**   1 byte: Constant 0x54 (capital 'T')\n**   Varint: Number of columns in the table.\n**   nCol bytes: 0x01 for PK columns, 0x00 otherwise.\n**   N bytes: Unqualified table name (encoded using UTF-8). Nul-terminated.\n**\n** Followed by one or more changes to the table.\n**\n**   1 byte: Either SQLITE_INSERT (0x12), UPDATE (0x17) or DELETE (0x09).\n**   1 byte: The \"indirect-change\" flag.\n**   old.* record: (delete and update only)\n**   new.* record: (insert and update only)\n**\n** The \"old.*\" and \"new.*\" records, if present, are N field records in the\n** format described above under \"RECORD FORMAT\", where N is the number of\n** columns in the table. The i'th field of each record is associated with\n** the i'th column of the table, counting from left to right in the order\n** in which columns were declared in the CREATE TABLE statement.\n**\n** The new.* record that is part of each INSERT change contains the values\n** that make up the new row. Similarly, the old.* record that is part of each\n** DELETE change contains the values that made up the row that was deleted \n** from the database. In the changeset format, the records that are part\n** of INSERT or DELETE changes never contain any undefined (type byte 0x00)\n** fields.\n**\n** Within the old.* record associated with an UPDATE change, all fields\n** associated with table columns that are not PRIMARY KEY columns and are\n** not modified by the UPDATE change are set to \"undefined\". Other fields\n** are set to the values that made up the row before the UPDATE that the\n** change records took place. Within the new.* record, fields associated \n** with table columns modified by the UPDATE change contain the new \n** values. Fields associated with table columns that are not modified\n** are set to \"undefined\".\n**\n** PATCHSET FORMAT:\n**\n** A patchset is also a collection of changes. It is similar to a changeset,\n** but leaves undefined those fields that are not useful if no conflict\n** resolution is required when applying the changeset.\n**\n** Each group of changes begins with a table header:\n**\n**   1 byte: Constant 0x50 (capital 'P')\n**   Varint: Number of columns in the table.\n**   nCol bytes: 0x01 for PK columns, 0x00 otherwise.\n**   N bytes: Unqualified table name (encoded using UTF-8). Nul-terminated.\n**\n** Followed by one or more changes to the table.\n**\n**   1 byte: Either SQLITE_INSERT (0x12), UPDATE (0x17) or DELETE (0x09).\n**   1 byte: The \"indirect-change\" flag.\n**   single record: (PK fields for DELETE, PK and modified fields for UPDATE,\n**                   full record for INSERT).\n**\n** As in the changeset format, each field of the single record that is part\n** of a patchset change is associated with the correspondingly positioned\n** table column, counting from left to right within the CREATE TABLE \n** statement.\n**\n** For a DELETE change, all fields within the record except those associated\n** with PRIMARY KEY columns are set to \"undefined\". The PRIMARY KEY fields\n** contain the values identifying the row to delete.\n**\n** For an UPDATE change, all fields except those associated with PRIMARY KEY\n** columns and columns that are modified by the UPDATE are set to \"undefined\".\n** PRIMARY KEY fields contain the values identifying the table row to update,\n** and fields associated with modified columns contain the new column values.\n**\n** The records associated with INSERT changes are in the same format as for\n** changesets. It is not possible for a record associated with an INSERT\n** change to contain a field set to \"undefined\".\n*/\n\n/*\n** For each row modified during a session, there exists a single instance of\n** this structure stored in a SessionTable.aChange[] hash table.\n*/\nstruct SessionChange {\n  int op;                         /* One of UPDATE, DELETE, INSERT */\n  int bIndirect;                  /* True if this change is \"indirect\" */\n  int nRecord;                    /* Number of bytes in buffer aRecord[] */\n  u8 *aRecord;                    /* Buffer containing old.* record */\n  SessionChange *pNext;           /* For hash-table collisions */\n};\n\n/*\n** Write a varint with value iVal into the buffer at aBuf. Return the \n** number of bytes written.\n*/\nstatic int sessionVarintPut(u8 *aBuf, int iVal){\n  return putVarint32(aBuf, iVal);\n}\n\n/*\n** Return the number of bytes required to store value iVal as a varint.\n*/\nstatic int sessionVarintLen(int iVal){\n  return sqlite3VarintLen(iVal);\n}\n\n/*\n** Read a varint value from aBuf[] into *piVal. Return the number of \n** bytes read.\n*/\nstatic int sessionVarintGet(u8 *aBuf, int *piVal){\n  return getVarint32(aBuf, *piVal);\n}\n\n/* Load an unaligned and unsigned 32-bit integer */\n#define SESSION_UINT32(x) (((u32)(x)[0]<<24)|((x)[1]<<16)|((x)[2]<<8)|(x)[3])\n\n/*\n** Read a 64-bit big-endian integer value from buffer aRec[]. Return\n** the value read.\n*/\nstatic sqlite3_int64 sessionGetI64(u8 *aRec){\n  u64 x = SESSION_UINT32(aRec);\n  u32 y = SESSION_UINT32(aRec+4);\n  x = (x<<32) + y;\n  return (sqlite3_int64)x;\n}\n\n/*\n** Write a 64-bit big-endian integer value to the buffer aBuf[].\n*/\nstatic void sessionPutI64(u8 *aBuf, sqlite3_int64 i){\n  aBuf[0] = (i>>56) & 0xFF;\n  aBuf[1] = (i>>48) & 0xFF;\n  aBuf[2] = (i>>40) & 0xFF;\n  aBuf[3] = (i>>32) & 0xFF;\n  aBuf[4] = (i>>24) & 0xFF;\n  aBuf[5] = (i>>16) & 0xFF;\n  aBuf[6] = (i>> 8) & 0xFF;\n  aBuf[7] = (i>> 0) & 0xFF;\n}\n\n/*\n** This function is used to serialize the contents of value pValue (see\n** comment titled \"RECORD FORMAT\" above).\n**\n** If it is non-NULL, the serialized form of the value is written to \n** buffer aBuf. *pnWrite is set to the number of bytes written before\n** returning. Or, if aBuf is NULL, the only thing this function does is\n** set *pnWrite.\n**\n** If no error occurs, SQLITE_OK is returned. Or, if an OOM error occurs\n** within a call to sqlite3_value_text() (may fail if the db is utf-16)) \n** SQLITE_NOMEM is returned.\n*/\nstatic int sessionSerializeValue(\n  u8 *aBuf,                       /* If non-NULL, write serialized value here */\n  sqlite3_value *pValue,          /* Value to serialize */\n  int *pnWrite                    /* IN/OUT: Increment by bytes written */\n){\n  int nByte;                      /* Size of serialized value in bytes */\n\n  if( pValue ){\n    int eType;                    /* Value type (SQLITE_NULL, TEXT etc.) */\n  \n    eType = sqlite3_value_type(pValue);\n    if( aBuf ) aBuf[0] = eType;\n  \n    switch( eType ){\n      case SQLITE_NULL: \n        nByte = 1;\n        break;\n  \n      case SQLITE_INTEGER: \n      case SQLITE_FLOAT:\n        if( aBuf ){\n          /* TODO: SQLite does something special to deal with mixed-endian\n          ** floating point values (e.g. ARM7). This code probably should\n          ** too.  */\n          u64 i;\n          if( eType==SQLITE_INTEGER ){\n            i = (u64)sqlite3_value_int64(pValue);\n          }else{\n            double r;\n            assert( sizeof(double)==8 && sizeof(u64)==8 );\n            r = sqlite3_value_double(pValue);\n            memcpy(&i, &r, 8);\n          }\n          sessionPutI64(&aBuf[1], i);\n        }\n        nByte = 9; \n        break;\n  \n      default: {\n        u8 *z;\n        int n;\n        int nVarint;\n  \n        assert( eType==SQLITE_TEXT || eType==SQLITE_BLOB );\n        if( eType==SQLITE_TEXT ){\n          z = (u8 *)sqlite3_value_text(pValue);\n        }else{\n          z = (u8 *)sqlite3_value_blob(pValue);\n        }\n        n = sqlite3_value_bytes(pValue);\n        if( z==0 && (eType!=SQLITE_BLOB || n>0) ) return SQLITE_NOMEM;\n        nVarint = sessionVarintLen(n);\n  \n        if( aBuf ){\n          sessionVarintPut(&aBuf[1], n);\n          if( n ) memcpy(&aBuf[nVarint + 1], z, n);\n        }\n  \n        nByte = 1 + nVarint + n;\n        break;\n      }\n    }\n  }else{\n    nByte = 1;\n    if( aBuf ) aBuf[0] = '\\0';\n  }\n\n  if( pnWrite ) *pnWrite += nByte;\n  return SQLITE_OK;\n}\n\n\n/*\n** This macro is used to calculate hash key values for data structures. In\n** order to use this macro, the entire data structure must be represented\n** as a series of unsigned integers. In order to calculate a hash-key value\n** for a data structure represented as three such integers, the macro may\n** then be used as follows:\n**\n**    int hash_key_value;\n**    hash_key_value = HASH_APPEND(0, <value 1>);\n**    hash_key_value = HASH_APPEND(hash_key_value, <value 2>);\n**    hash_key_value = HASH_APPEND(hash_key_value, <value 3>);\n**\n** In practice, the data structures this macro is used for are the primary\n** key values of modified rows.\n*/\n#define HASH_APPEND(hash, add) ((hash) << 3) ^ (hash) ^ (unsigned int)(add)\n\n/*\n** Append the hash of the 64-bit integer passed as the second argument to the\n** hash-key value passed as the first. Return the new hash-key value.\n*/\nstatic unsigned int sessionHashAppendI64(unsigned int h, i64 i){\n  h = HASH_APPEND(h, i & 0xFFFFFFFF);\n  return HASH_APPEND(h, (i>>32)&0xFFFFFFFF);\n}\n\n/*\n** Append the hash of the blob passed via the second and third arguments to \n** the hash-key value passed as the first. Return the new hash-key value.\n*/\nstatic unsigned int sessionHashAppendBlob(unsigned int h, int n, const u8 *z){\n  int i;\n  for(i=0; i<n; i++) h = HASH_APPEND(h, z[i]);\n  return h;\n}\n\n/*\n** Append the hash of the data type passed as the second argument to the\n** hash-key value passed as the first. Return the new hash-key value.\n*/\nstatic unsigned int sessionHashAppendType(unsigned int h, int eType){\n  return HASH_APPEND(h, eType);\n}\n\n/*\n** This function may only be called from within a pre-update callback.\n** It calculates a hash based on the primary key values of the old.* or \n** new.* row currently available and, assuming no error occurs, writes it to\n** *piHash before returning. If the primary key contains one or more NULL\n** values, *pbNullPK is set to true before returning.\n**\n** If an error occurs, an SQLite error code is returned and the final values\n** of *piHash asn *pbNullPK are undefined. Otherwise, SQLITE_OK is returned\n** and the output variables are set as described above.\n*/\nstatic int sessionPreupdateHash(\n  sqlite3_session *pSession,      /* Session object that owns pTab */\n  SessionTable *pTab,             /* Session table handle */\n  int bNew,                       /* True to hash the new.* PK */\n  int *piHash,                    /* OUT: Hash value */\n  int *pbNullPK                   /* OUT: True if there are NULL values in PK */\n){\n  unsigned int h = 0;             /* Hash value to return */\n  int i;                          /* Used to iterate through columns */\n\n  assert( *pbNullPK==0 );\n  assert( pTab->nCol==pSession->hook.xCount(pSession->hook.pCtx) );\n  for(i=0; i<pTab->nCol; i++){\n    if( pTab->abPK[i] ){\n      int rc;\n      int eType;\n      sqlite3_value *pVal;\n\n      if( bNew ){\n        rc = pSession->hook.xNew(pSession->hook.pCtx, i, &pVal);\n      }else{\n        rc = pSession->hook.xOld(pSession->hook.pCtx, i, &pVal);\n      }\n      if( rc!=SQLITE_OK ) return rc;\n\n      eType = sqlite3_value_type(pVal);\n      h = sessionHashAppendType(h, eType);\n      if( eType==SQLITE_INTEGER || eType==SQLITE_FLOAT ){\n        i64 iVal;\n        if( eType==SQLITE_INTEGER ){\n          iVal = sqlite3_value_int64(pVal);\n        }else{\n          double rVal = sqlite3_value_double(pVal);\n          assert( sizeof(iVal)==8 && sizeof(rVal)==8 );\n          memcpy(&iVal, &rVal, 8);\n        }\n        h = sessionHashAppendI64(h, iVal);\n      }else if( eType==SQLITE_TEXT || eType==SQLITE_BLOB ){\n        const u8 *z;\n        int n;\n        if( eType==SQLITE_TEXT ){\n          z = (const u8 *)sqlite3_value_text(pVal);\n        }else{\n          z = (const u8 *)sqlite3_value_blob(pVal);\n        }\n        n = sqlite3_value_bytes(pVal);\n        if( !z && (eType!=SQLITE_BLOB || n>0) ) return SQLITE_NOMEM;\n        h = sessionHashAppendBlob(h, n, z);\n      }else{\n        assert( eType==SQLITE_NULL );\n        assert( pTab->bStat1==0 || i!=1 );\n        *pbNullPK = 1;\n      }\n    }\n  }\n\n  *piHash = (h % pTab->nChange);\n  return SQLITE_OK;\n}\n\n/*\n** The buffer that the argument points to contains a serialized SQL value.\n** Return the number of bytes of space occupied by the value (including\n** the type byte).\n*/\nstatic int sessionSerialLen(u8 *a){\n  int e = *a;\n  int n;\n  if( e==0 ) return 1;\n  if( e==SQLITE_NULL ) return 1;\n  if( e==SQLITE_INTEGER || e==SQLITE_FLOAT ) return 9;\n  return sessionVarintGet(&a[1], &n) + 1 + n;\n}\n\n/*\n** Based on the primary key values stored in change aRecord, calculate a\n** hash key. Assume the has table has nBucket buckets. The hash keys\n** calculated by this function are compatible with those calculated by\n** sessionPreupdateHash().\n**\n** The bPkOnly argument is non-zero if the record at aRecord[] is from\n** a patchset DELETE. In this case the non-PK fields are omitted entirely.\n*/\nstatic unsigned int sessionChangeHash(\n  SessionTable *pTab,             /* Table handle */\n  int bPkOnly,                    /* Record consists of PK fields only */\n  u8 *aRecord,                    /* Change record */\n  int nBucket                     /* Assume this many buckets in hash table */\n){\n  unsigned int h = 0;             /* Value to return */\n  int i;                          /* Used to iterate through columns */\n  u8 *a = aRecord;                /* Used to iterate through change record */\n\n  for(i=0; i<pTab->nCol; i++){\n    int eType = *a;\n    int isPK = pTab->abPK[i];\n    if( bPkOnly && isPK==0 ) continue;\n\n    /* It is not possible for eType to be SQLITE_NULL here. The session \n    ** module does not record changes for rows with NULL values stored in\n    ** primary key columns. */\n    assert( eType==SQLITE_INTEGER || eType==SQLITE_FLOAT \n         || eType==SQLITE_TEXT || eType==SQLITE_BLOB \n         || eType==SQLITE_NULL || eType==0 \n    );\n    assert( !isPK || (eType!=0 && eType!=SQLITE_NULL) );\n\n    if( isPK ){\n      a++;\n      h = sessionHashAppendType(h, eType);\n      if( eType==SQLITE_INTEGER || eType==SQLITE_FLOAT ){\n        h = sessionHashAppendI64(h, sessionGetI64(a));\n        a += 8;\n      }else{\n        int n; \n        a += sessionVarintGet(a, &n);\n        h = sessionHashAppendBlob(h, n, a);\n        a += n;\n      }\n    }else{\n      a += sessionSerialLen(a);\n    }\n  }\n  return (h % nBucket);\n}\n\n/*\n** Arguments aLeft and aRight are pointers to change records for table pTab.\n** This function returns true if the two records apply to the same row (i.e.\n** have the same values stored in the primary key columns), or false \n** otherwise.\n*/\nstatic int sessionChangeEqual(\n  SessionTable *pTab,             /* Table used for PK definition */\n  int bLeftPkOnly,                /* True if aLeft[] contains PK fields only */\n  u8 *aLeft,                      /* Change record */\n  int bRightPkOnly,               /* True if aRight[] contains PK fields only */\n  u8 *aRight                      /* Change record */\n){\n  u8 *a1 = aLeft;                 /* Cursor to iterate through aLeft */\n  u8 *a2 = aRight;                /* Cursor to iterate through aRight */\n  int iCol;                       /* Used to iterate through table columns */\n\n  for(iCol=0; iCol<pTab->nCol; iCol++){\n    if( pTab->abPK[iCol] ){\n      int n1 = sessionSerialLen(a1);\n      int n2 = sessionSerialLen(a2);\n\n      if( pTab->abPK[iCol] && (n1!=n2 || memcmp(a1, a2, n1)) ){\n        return 0;\n      }\n      a1 += n1;\n      a2 += n2;\n    }else{\n      if( bLeftPkOnly==0 ) a1 += sessionSerialLen(a1);\n      if( bRightPkOnly==0 ) a2 += sessionSerialLen(a2);\n    }\n  }\n\n  return 1;\n}\n\n/*\n** Arguments aLeft and aRight both point to buffers containing change\n** records with nCol columns. This function \"merges\" the two records into\n** a single records which is written to the buffer at *paOut. *paOut is\n** then set to point to one byte after the last byte written before \n** returning.\n**\n** The merging of records is done as follows: For each column, if the \n** aRight record contains a value for the column, copy the value from\n** their. Otherwise, if aLeft contains a value, copy it. If neither\n** record contains a value for a given column, then neither does the\n** output record.\n*/\nstatic void sessionMergeRecord(\n  u8 **paOut, \n  int nCol,\n  u8 *aLeft,\n  u8 *aRight\n){\n  u8 *a1 = aLeft;                 /* Cursor used to iterate through aLeft */\n  u8 *a2 = aRight;                /* Cursor used to iterate through aRight */\n  u8 *aOut = *paOut;              /* Output cursor */\n  int iCol;                       /* Used to iterate from 0 to nCol */\n\n  for(iCol=0; iCol<nCol; iCol++){\n    int n1 = sessionSerialLen(a1);\n    int n2 = sessionSerialLen(a2);\n    if( *a2 ){\n      memcpy(aOut, a2, n2);\n      aOut += n2;\n    }else{\n      memcpy(aOut, a1, n1);\n      aOut += n1;\n    }\n    a1 += n1;\n    a2 += n2;\n  }\n\n  *paOut = aOut;\n}\n\n/*\n** This is a helper function used by sessionMergeUpdate().\n**\n** When this function is called, both *paOne and *paTwo point to a value \n** within a change record. Before it returns, both have been advanced so \n** as to point to the next value in the record.\n**\n** If, when this function is called, *paTwo points to a valid value (i.e.\n** *paTwo[0] is not 0x00 - the \"no value\" placeholder), a copy of the *paTwo\n** pointer is returned and *pnVal is set to the number of bytes in the \n** serialized value. Otherwise, a copy of *paOne is returned and *pnVal\n** set to the number of bytes in the value at *paOne. If *paOne points\n** to the \"no value\" placeholder, *pnVal is set to 1. In other words:\n**\n**   if( *paTwo is valid ) return *paTwo;\n**   return *paOne;\n**\n*/\nstatic u8 *sessionMergeValue(\n  u8 **paOne,                     /* IN/OUT: Left-hand buffer pointer */\n  u8 **paTwo,                     /* IN/OUT: Right-hand buffer pointer */\n  int *pnVal                      /* OUT: Bytes in returned value */\n){\n  u8 *a1 = *paOne;\n  u8 *a2 = *paTwo;\n  u8 *pRet = 0;\n  int n1;\n\n  assert( a1 );\n  if( a2 ){\n    int n2 = sessionSerialLen(a2);\n    if( *a2 ){\n      *pnVal = n2;\n      pRet = a2;\n    }\n    *paTwo = &a2[n2];\n  }\n\n  n1 = sessionSerialLen(a1);\n  if( pRet==0 ){\n    *pnVal = n1;\n    pRet = a1;\n  }\n  *paOne = &a1[n1];\n\n  return pRet;\n}\n\n/*\n** This function is used by changeset_concat() to merge two UPDATE changes\n** on the same row.\n*/\nstatic int sessionMergeUpdate(\n  u8 **paOut,                     /* IN/OUT: Pointer to output buffer */\n  SessionTable *pTab,             /* Table change pertains to */\n  int bPatchset,                  /* True if records are patchset records */\n  u8 *aOldRecord1,                /* old.* record for first change */\n  u8 *aOldRecord2,                /* old.* record for second change */\n  u8 *aNewRecord1,                /* new.* record for first change */\n  u8 *aNewRecord2                 /* new.* record for second change */\n){\n  u8 *aOld1 = aOldRecord1;\n  u8 *aOld2 = aOldRecord2;\n  u8 *aNew1 = aNewRecord1;\n  u8 *aNew2 = aNewRecord2;\n\n  u8 *aOut = *paOut;\n  int i;\n\n  if( bPatchset==0 ){\n    int bRequired = 0;\n\n    assert( aOldRecord1 && aNewRecord1 );\n\n    /* Write the old.* vector first. */\n    for(i=0; i<pTab->nCol; i++){\n      int nOld;\n      u8 *aOld;\n      int nNew;\n      u8 *aNew;\n\n      aOld = sessionMergeValue(&aOld1, &aOld2, &nOld);\n      aNew = sessionMergeValue(&aNew1, &aNew2, &nNew);\n      if( pTab->abPK[i] || nOld!=nNew || memcmp(aOld, aNew, nNew) ){\n        if( pTab->abPK[i]==0 ) bRequired = 1;\n        memcpy(aOut, aOld, nOld);\n        aOut += nOld;\n      }else{\n        *(aOut++) = '\\0';\n      }\n    }\n\n    if( !bRequired ) return 0;\n  }\n\n  /* Write the new.* vector */\n  aOld1 = aOldRecord1;\n  aOld2 = aOldRecord2;\n  aNew1 = aNewRecord1;\n  aNew2 = aNewRecord2;\n  for(i=0; i<pTab->nCol; i++){\n    int nOld;\n    u8 *aOld;\n    int nNew;\n    u8 *aNew;\n\n    aOld = sessionMergeValue(&aOld1, &aOld2, &nOld);\n    aNew = sessionMergeValue(&aNew1, &aNew2, &nNew);\n    if( bPatchset==0 \n     && (pTab->abPK[i] || (nOld==nNew && 0==memcmp(aOld, aNew, nNew))) \n    ){\n      *(aOut++) = '\\0';\n    }else{\n      memcpy(aOut, aNew, nNew);\n      aOut += nNew;\n    }\n  }\n\n  *paOut = aOut;\n  return 1;\n}\n\n/*\n** This function is only called from within a pre-update-hook callback.\n** It determines if the current pre-update-hook change affects the same row\n** as the change stored in argument pChange. If so, it returns true. Otherwise\n** if the pre-update-hook does not affect the same row as pChange, it returns\n** false.\n*/\nstatic int sessionPreupdateEqual(\n  sqlite3_session *pSession,      /* Session object that owns SessionTable */\n  SessionTable *pTab,             /* Table associated with change */\n  SessionChange *pChange,         /* Change to compare to */\n  int op                          /* Current pre-update operation */\n){\n  int iCol;                       /* Used to iterate through columns */\n  u8 *a = pChange->aRecord;       /* Cursor used to scan change record */\n\n  assert( op==SQLITE_INSERT || op==SQLITE_UPDATE || op==SQLITE_DELETE );\n  for(iCol=0; iCol<pTab->nCol; iCol++){\n    if( !pTab->abPK[iCol] ){\n      a += sessionSerialLen(a);\n    }else{\n      sqlite3_value *pVal;        /* Value returned by preupdate_new/old */\n      int rc;                     /* Error code from preupdate_new/old */\n      int eType = *a++;           /* Type of value from change record */\n\n      /* The following calls to preupdate_new() and preupdate_old() can not\n      ** fail. This is because they cache their return values, and by the\n      ** time control flows to here they have already been called once from\n      ** within sessionPreupdateHash(). The first two asserts below verify\n      ** this (that the method has already been called). */\n      if( op==SQLITE_INSERT ){\n        /* assert( db->pPreUpdate->pNewUnpacked || db->pPreUpdate->aNew ); */\n        rc = pSession->hook.xNew(pSession->hook.pCtx, iCol, &pVal);\n      }else{\n        /* assert( db->pPreUpdate->pUnpacked ); */\n        rc = pSession->hook.xOld(pSession->hook.pCtx, iCol, &pVal);\n      }\n      assert( rc==SQLITE_OK );\n      if( sqlite3_value_type(pVal)!=eType ) return 0;\n\n      /* A SessionChange object never has a NULL value in a PK column */\n      assert( eType==SQLITE_INTEGER || eType==SQLITE_FLOAT\n           || eType==SQLITE_BLOB    || eType==SQLITE_TEXT\n      );\n\n      if( eType==SQLITE_INTEGER || eType==SQLITE_FLOAT ){\n        i64 iVal = sessionGetI64(a);\n        a += 8;\n        if( eType==SQLITE_INTEGER ){\n          if( sqlite3_value_int64(pVal)!=iVal ) return 0;\n        }else{\n          double rVal;\n          assert( sizeof(iVal)==8 && sizeof(rVal)==8 );\n          memcpy(&rVal, &iVal, 8);\n          if( sqlite3_value_double(pVal)!=rVal ) return 0;\n        }\n      }else{\n        int n;\n        const u8 *z;\n        a += sessionVarintGet(a, &n);\n        if( sqlite3_value_bytes(pVal)!=n ) return 0;\n        if( eType==SQLITE_TEXT ){\n          z = sqlite3_value_text(pVal);\n        }else{\n          z = sqlite3_value_blob(pVal);\n        }\n        if( memcmp(a, z, n) ) return 0;\n        a += n;\n      }\n    }\n  }\n\n  return 1;\n}\n\n/*\n** If required, grow the hash table used to store changes on table pTab \n** (part of the session pSession). If a fatal OOM error occurs, set the\n** session object to failed and return SQLITE_ERROR. Otherwise, return\n** SQLITE_OK.\n**\n** It is possible that a non-fatal OOM error occurs in this function. In\n** that case the hash-table does not grow, but SQLITE_OK is returned anyway.\n** Growing the hash table in this case is a performance optimization only,\n** it is not required for correct operation.\n*/\nstatic int sessionGrowHash(int bPatchset, SessionTable *pTab){\n  if( pTab->nChange==0 || pTab->nEntry>=(pTab->nChange/2) ){\n    int i;\n    SessionChange **apNew;\n    int nNew = (pTab->nChange ? pTab->nChange : 128) * 2;\n\n    apNew = (SessionChange **)sqlite3_malloc(sizeof(SessionChange *) * nNew);\n    if( apNew==0 ){\n      if( pTab->nChange==0 ){\n        return SQLITE_ERROR;\n      }\n      return SQLITE_OK;\n    }\n    memset(apNew, 0, sizeof(SessionChange *) * nNew);\n\n    for(i=0; i<pTab->nChange; i++){\n      SessionChange *p;\n      SessionChange *pNext;\n      for(p=pTab->apChange[i]; p; p=pNext){\n        int bPkOnly = (p->op==SQLITE_DELETE && bPatchset);\n        int iHash = sessionChangeHash(pTab, bPkOnly, p->aRecord, nNew);\n        pNext = p->pNext;\n        p->pNext = apNew[iHash];\n        apNew[iHash] = p;\n      }\n    }\n\n    sqlite3_free(pTab->apChange);\n    pTab->nChange = nNew;\n    pTab->apChange = apNew;\n  }\n\n  return SQLITE_OK;\n}\n\n/*\n** This function queries the database for the names of the columns of table\n** zThis, in schema zDb.\n**\n** Otherwise, if they are not NULL, variable *pnCol is set to the number\n** of columns in the database table and variable *pzTab is set to point to a\n** nul-terminated copy of the table name. *pazCol (if not NULL) is set to\n** point to an array of pointers to column names. And *pabPK (again, if not\n** NULL) is set to point to an array of booleans - true if the corresponding\n** column is part of the primary key.\n**\n** For example, if the table is declared as:\n**\n**     CREATE TABLE tbl1(w, x, y, z, PRIMARY KEY(w, z));\n**\n** Then the four output variables are populated as follows:\n**\n**     *pnCol  = 4\n**     *pzTab  = \"tbl1\"\n**     *pazCol = {\"w\", \"x\", \"y\", \"z\"}\n**     *pabPK  = {1, 0, 0, 1}\n**\n** All returned buffers are part of the same single allocation, which must\n** be freed using sqlite3_free() by the caller\n*/\nstatic int sessionTableInfo(\n  sqlite3 *db,                    /* Database connection */\n  const char *zDb,                /* Name of attached database (e.g. \"main\") */\n  const char *zThis,              /* Table name */\n  int *pnCol,                     /* OUT: number of columns */\n  const char **pzTab,             /* OUT: Copy of zThis */\n  const char ***pazCol,           /* OUT: Array of column names for table */\n  u8 **pabPK                      /* OUT: Array of booleans - true for PK col */\n){\n  char *zPragma;\n  sqlite3_stmt *pStmt;\n  int rc;\n  int nByte;\n  int nDbCol = 0;\n  int nThis;\n  int i;\n  u8 *pAlloc = 0;\n  char **azCol = 0;\n  u8 *abPK = 0;\n\n  assert( pazCol && pabPK );\n\n  nThis = sqlite3Strlen30(zThis);\n  if( nThis==12 && 0==sqlite3_stricmp(\"sqlite_stat1\", zThis) ){\n    rc = sqlite3_table_column_metadata(db, zDb, zThis, 0, 0, 0, 0, 0, 0);\n    if( rc==SQLITE_OK ){\n      /* For sqlite_stat1, pretend that (tbl,idx) is the PRIMARY KEY. */\n      zPragma = sqlite3_mprintf(\n          \"SELECT 0, 'tbl',  '', 0, '', 1     UNION ALL \"\n          \"SELECT 1, 'idx',  '', 0, '', 2     UNION ALL \"\n          \"SELECT 2, 'stat', '', 0, '', 0\"\n      );\n    }else if( rc==SQLITE_ERROR ){\n      zPragma = sqlite3_mprintf(\"\");\n    }else{\n      return rc;\n    }\n  }else{\n    zPragma = sqlite3_mprintf(\"PRAGMA '%q'.table_info('%q')\", zDb, zThis);\n  }\n  if( !zPragma ) return SQLITE_NOMEM;\n\n  rc = sqlite3_prepare_v2(db, zPragma, -1, &pStmt, 0);\n  sqlite3_free(zPragma);\n  if( rc!=SQLITE_OK ) return rc;\n\n  nByte = nThis + 1;\n  while( SQLITE_ROW==sqlite3_step(pStmt) ){\n    nByte += sqlite3_column_bytes(pStmt, 1);\n    nDbCol++;\n  }\n  rc = sqlite3_reset(pStmt);\n\n  if( rc==SQLITE_OK ){\n    nByte += nDbCol * (sizeof(const char *) + sizeof(u8) + 1);\n    pAlloc = sqlite3_malloc(nByte);\n    if( pAlloc==0 ){\n      rc = SQLITE_NOMEM;\n    }\n  }\n  if( rc==SQLITE_OK ){\n    azCol = (char **)pAlloc;\n    pAlloc = (u8 *)&azCol[nDbCol];\n    abPK = (u8 *)pAlloc;\n    pAlloc = &abPK[nDbCol];\n    if( pzTab ){\n      memcpy(pAlloc, zThis, nThis+1);\n      *pzTab = (char *)pAlloc;\n      pAlloc += nThis+1;\n    }\n  \n    i = 0;\n    while( SQLITE_ROW==sqlite3_step(pStmt) ){\n      int nName = sqlite3_column_bytes(pStmt, 1);\n      const unsigned char *zName = sqlite3_column_text(pStmt, 1);\n      if( zName==0 ) break;\n      memcpy(pAlloc, zName, nName+1);\n      azCol[i] = (char *)pAlloc;\n      pAlloc += nName+1;\n      abPK[i] = sqlite3_column_int(pStmt, 5);\n      i++;\n    }\n    rc = sqlite3_reset(pStmt);\n  \n  }\n\n  /* If successful, populate the output variables. Otherwise, zero them and\n  ** free any allocation made. An error code will be returned in this case.\n  */\n  if( rc==SQLITE_OK ){\n    *pazCol = (const char **)azCol;\n    *pabPK = abPK;\n    *pnCol = nDbCol;\n  }else{\n    *pazCol = 0;\n    *pabPK = 0;\n    *pnCol = 0;\n    if( pzTab ) *pzTab = 0;\n    sqlite3_free(azCol);\n  }\n  sqlite3_finalize(pStmt);\n  return rc;\n}\n\n/*\n** This function is only called from within a pre-update handler for a\n** write to table pTab, part of session pSession. If this is the first\n** write to this table, initalize the SessionTable.nCol, azCol[] and\n** abPK[] arrays accordingly.\n**\n** If an error occurs, an error code is stored in sqlite3_session.rc and\n** non-zero returned. Or, if no error occurs but the table has no primary\n** key, sqlite3_session.rc is left set to SQLITE_OK and non-zero returned to\n** indicate that updates on this table should be ignored. SessionTable.abPK \n** is set to NULL in this case.\n*/\nstatic int sessionInitTable(sqlite3_session *pSession, SessionTable *pTab){\n  if( pTab->nCol==0 ){\n    u8 *abPK;\n    assert( pTab->azCol==0 || pTab->abPK==0 );\n    pSession->rc = sessionTableInfo(pSession->db, pSession->zDb, \n        pTab->zName, &pTab->nCol, 0, &pTab->azCol, &abPK\n    );\n    if( pSession->rc==SQLITE_OK ){\n      int i;\n      for(i=0; i<pTab->nCol; i++){\n        if( abPK[i] ){\n          pTab->abPK = abPK;\n          break;\n        }\n      }\n      if( 0==sqlite3_stricmp(\"sqlite_stat1\", pTab->zName) ){\n        pTab->bStat1 = 1;\n      }\n    }\n  }\n  return (pSession->rc || pTab->abPK==0);\n}\n\n/*\n** Versions of the four methods in object SessionHook for use with the\n** sqlite_stat1 table. The purpose of this is to substitute a zero-length\n** blob each time a NULL value is read from the \"idx\" column of the\n** sqlite_stat1 table.\n*/\ntypedef struct SessionStat1Ctx SessionStat1Ctx;\nstruct SessionStat1Ctx {\n  SessionHook hook;\n  sqlite3_session *pSession;\n};\nstatic int sessionStat1Old(void *pCtx, int iCol, sqlite3_value **ppVal){\n  SessionStat1Ctx *p = (SessionStat1Ctx*)pCtx;\n  sqlite3_value *pVal = 0;\n  int rc = p->hook.xOld(p->hook.pCtx, iCol, &pVal);\n  if( rc==SQLITE_OK && iCol==1 && sqlite3_value_type(pVal)==SQLITE_NULL ){\n    pVal = p->pSession->pZeroBlob;\n  }\n  *ppVal = pVal;\n  return rc;\n}\nstatic int sessionStat1New(void *pCtx, int iCol, sqlite3_value **ppVal){\n  SessionStat1Ctx *p = (SessionStat1Ctx*)pCtx;\n  sqlite3_value *pVal = 0;\n  int rc = p->hook.xNew(p->hook.pCtx, iCol, &pVal);\n  if( rc==SQLITE_OK && iCol==1 && sqlite3_value_type(pVal)==SQLITE_NULL ){\n    pVal = p->pSession->pZeroBlob;\n  }\n  *ppVal = pVal;\n  return rc;\n}\nstatic int sessionStat1Count(void *pCtx){\n  SessionStat1Ctx *p = (SessionStat1Ctx*)pCtx;\n  return p->hook.xCount(p->hook.pCtx);\n}\nstatic int sessionStat1Depth(void *pCtx){\n  SessionStat1Ctx *p = (SessionStat1Ctx*)pCtx;\n  return p->hook.xDepth(p->hook.pCtx);\n}\n\n\n/*\n** This function is only called from with a pre-update-hook reporting a \n** change on table pTab (attached to session pSession). The type of change\n** (UPDATE, INSERT, DELETE) is specified by the first argument.\n**\n** Unless one is already present or an error occurs, an entry is added\n** to the changed-rows hash table associated with table pTab.\n*/\nstatic void sessionPreupdateOneChange(\n  int op,                         /* One of SQLITE_UPDATE, INSERT, DELETE */\n  sqlite3_session *pSession,      /* Session object pTab is attached to */\n  SessionTable *pTab              /* Table that change applies to */\n){\n  int iHash; \n  int bNull = 0; \n  int rc = SQLITE_OK;\n  SessionStat1Ctx stat1 = {0};\n\n  if( pSession->rc ) return;\n\n  /* Load table details if required */\n  if( sessionInitTable(pSession, pTab) ) return;\n\n  /* Check the number of columns in this xPreUpdate call matches the \n  ** number of columns in the table.  */\n  if( pTab->nCol!=pSession->hook.xCount(pSession->hook.pCtx) ){\n    pSession->rc = SQLITE_SCHEMA;\n    return;\n  }\n\n  /* Grow the hash table if required */\n  if( sessionGrowHash(0, pTab) ){\n    pSession->rc = SQLITE_NOMEM;\n    return;\n  }\n\n  if( pTab->bStat1 ){\n    stat1.hook = pSession->hook;\n    stat1.pSession = pSession;\n    pSession->hook.pCtx = (void*)&stat1;\n    pSession->hook.xNew = sessionStat1New;\n    pSession->hook.xOld = sessionStat1Old;\n    pSession->hook.xCount = sessionStat1Count;\n    pSession->hook.xDepth = sessionStat1Depth;\n    if( pSession->pZeroBlob==0 ){\n      sqlite3_value *p = sqlite3ValueNew(0);\n      if( p==0 ){\n        rc = SQLITE_NOMEM;\n        goto error_out;\n      }\n      sqlite3ValueSetStr(p, 0, \"\", 0, SQLITE_STATIC);\n      pSession->pZeroBlob = p;\n    }\n  }\n\n  /* Calculate the hash-key for this change. If the primary key of the row\n  ** includes a NULL value, exit early. Such changes are ignored by the\n  ** session module. */\n  rc = sessionPreupdateHash(pSession, pTab, op==SQLITE_INSERT, &iHash, &bNull);\n  if( rc!=SQLITE_OK ) goto error_out;\n\n  if( bNull==0 ){\n    /* Search the hash table for an existing record for this row. */\n    SessionChange *pC;\n    for(pC=pTab->apChange[iHash]; pC; pC=pC->pNext){\n      if( sessionPreupdateEqual(pSession, pTab, pC, op) ) break;\n    }\n\n    if( pC==0 ){\n      /* Create a new change object containing all the old values (if\n      ** this is an SQLITE_UPDATE or SQLITE_DELETE), or just the PK\n      ** values (if this is an INSERT). */\n      SessionChange *pChange; /* New change object */\n      int nByte;              /* Number of bytes to allocate */\n      int i;                  /* Used to iterate through columns */\n  \n      assert( rc==SQLITE_OK );\n      pTab->nEntry++;\n  \n      /* Figure out how large an allocation is required */\n      nByte = sizeof(SessionChange);\n      for(i=0; i<pTab->nCol; i++){\n        sqlite3_value *p = 0;\n        if( op!=SQLITE_INSERT ){\n          TESTONLY(int trc = ) pSession->hook.xOld(pSession->hook.pCtx, i, &p);\n          assert( trc==SQLITE_OK );\n        }else if( pTab->abPK[i] ){\n          TESTONLY(int trc = ) pSession->hook.xNew(pSession->hook.pCtx, i, &p);\n          assert( trc==SQLITE_OK );\n        }\n\n        /* This may fail if SQLite value p contains a utf-16 string that must\n        ** be converted to utf-8 and an OOM error occurs while doing so. */\n        rc = sessionSerializeValue(0, p, &nByte);\n        if( rc!=SQLITE_OK ) goto error_out;\n      }\n  \n      /* Allocate the change object */\n      pChange = (SessionChange *)sqlite3_malloc(nByte);\n      if( !pChange ){\n        rc = SQLITE_NOMEM;\n        goto error_out;\n      }else{\n        memset(pChange, 0, sizeof(SessionChange));\n        pChange->aRecord = (u8 *)&pChange[1];\n      }\n  \n      /* Populate the change object. None of the preupdate_old(),\n      ** preupdate_new() or SerializeValue() calls below may fail as all\n      ** required values and encodings have already been cached in memory.\n      ** It is not possible for an OOM to occur in this block. */\n      nByte = 0;\n      for(i=0; i<pTab->nCol; i++){\n        sqlite3_value *p = 0;\n        if( op!=SQLITE_INSERT ){\n          pSession->hook.xOld(pSession->hook.pCtx, i, &p);\n        }else if( pTab->abPK[i] ){\n          pSession->hook.xNew(pSession->hook.pCtx, i, &p);\n        }\n        sessionSerializeValue(&pChange->aRecord[nByte], p, &nByte);\n      }\n\n      /* Add the change to the hash-table */\n      if( pSession->bIndirect || pSession->hook.xDepth(pSession->hook.pCtx) ){\n        pChange->bIndirect = 1;\n      }\n      pChange->nRecord = nByte;\n      pChange->op = op;\n      pChange->pNext = pTab->apChange[iHash];\n      pTab->apChange[iHash] = pChange;\n\n    }else if( pC->bIndirect ){\n      /* If the existing change is considered \"indirect\", but this current\n      ** change is \"direct\", mark the change object as direct. */\n      if( pSession->hook.xDepth(pSession->hook.pCtx)==0 \n       && pSession->bIndirect==0 \n      ){\n        pC->bIndirect = 0;\n      }\n    }\n  }\n\n  /* If an error has occurred, mark the session object as failed. */\n error_out:\n  if( pTab->bStat1 ){\n    pSession->hook = stat1.hook;\n  }\n  if( rc!=SQLITE_OK ){\n    pSession->rc = rc;\n  }\n}\n\nstatic int sessionFindTable(\n  sqlite3_session *pSession, \n  const char *zName,\n  SessionTable **ppTab\n){\n  int rc = SQLITE_OK;\n  int nName = sqlite3Strlen30(zName);\n  SessionTable *pRet;\n\n  /* Search for an existing table */\n  for(pRet=pSession->pTable; pRet; pRet=pRet->pNext){\n    if( 0==sqlite3_strnicmp(pRet->zName, zName, nName+1) ) break;\n  }\n\n  if( pRet==0 && pSession->bAutoAttach ){\n    /* If there is a table-filter configured, invoke it. If it returns 0,\n    ** do not automatically add the new table. */\n    if( pSession->xTableFilter==0\n     || pSession->xTableFilter(pSession->pFilterCtx, zName) \n    ){\n      rc = sqlite3session_attach(pSession, zName);\n      if( rc==SQLITE_OK ){\n        for(pRet=pSession->pTable; pRet->pNext; pRet=pRet->pNext);\n        assert( 0==sqlite3_strnicmp(pRet->zName, zName, nName+1) );\n      }\n    }\n  }\n\n  assert( rc==SQLITE_OK || pRet==0 );\n  *ppTab = pRet;\n  return rc;\n}\n\n/*\n** The 'pre-update' hook registered by this module with SQLite databases.\n*/\nstatic void xPreUpdate(\n  void *pCtx,                     /* Copy of third arg to preupdate_hook() */\n  sqlite3 *db,                    /* Database handle */\n  int op,                         /* SQLITE_UPDATE, DELETE or INSERT */\n  char const *zDb,                /* Database name */\n  char const *zName,              /* Table name */\n  sqlite3_int64 iKey1,            /* Rowid of row about to be deleted/updated */\n  sqlite3_int64 iKey2             /* New rowid value (for a rowid UPDATE) */\n){\n  sqlite3_session *pSession;\n  int nDb = sqlite3Strlen30(zDb);\n\n  assert( sqlite3_mutex_held(db->mutex) );\n\n  for(pSession=(sqlite3_session *)pCtx; pSession; pSession=pSession->pNext){\n    SessionTable *pTab;\n\n    /* If this session is attached to a different database (\"main\", \"temp\" \n    ** etc.), or if it is not currently enabled, there is nothing to do. Skip \n    ** to the next session object attached to this database. */\n    if( pSession->bEnable==0 ) continue;\n    if( pSession->rc ) continue;\n    if( sqlite3_strnicmp(zDb, pSession->zDb, nDb+1) ) continue;\n\n    pSession->rc = sessionFindTable(pSession, zName, &pTab);\n    if( pTab ){\n      assert( pSession->rc==SQLITE_OK );\n      sessionPreupdateOneChange(op, pSession, pTab);\n      if( op==SQLITE_UPDATE ){\n        sessionPreupdateOneChange(SQLITE_INSERT, pSession, pTab);\n      }\n    }\n  }\n}\n\n/*\n** The pre-update hook implementations.\n*/\nstatic int sessionPreupdateOld(void *pCtx, int iVal, sqlite3_value **ppVal){\n  return sqlite3_preupdate_old((sqlite3*)pCtx, iVal, ppVal);\n}\nstatic int sessionPreupdateNew(void *pCtx, int iVal, sqlite3_value **ppVal){\n  return sqlite3_preupdate_new((sqlite3*)pCtx, iVal, ppVal);\n}\nstatic int sessionPreupdateCount(void *pCtx){\n  return sqlite3_preupdate_count((sqlite3*)pCtx);\n}\nstatic int sessionPreupdateDepth(void *pCtx){\n  return sqlite3_preupdate_depth((sqlite3*)pCtx);\n}\n\n/*\n** Install the pre-update hooks on the session object passed as the only\n** argument.\n*/\nstatic void sessionPreupdateHooks(\n  sqlite3_session *pSession\n){\n  pSession->hook.pCtx = (void*)pSession->db;\n  pSession->hook.xOld = sessionPreupdateOld;\n  pSession->hook.xNew = sessionPreupdateNew;\n  pSession->hook.xCount = sessionPreupdateCount;\n  pSession->hook.xDepth = sessionPreupdateDepth;\n}\n\ntypedef struct SessionDiffCtx SessionDiffCtx;\nstruct SessionDiffCtx {\n  sqlite3_stmt *pStmt;\n  int nOldOff;\n};\n\n/*\n** The diff hook implementations.\n*/\nstatic int sessionDiffOld(void *pCtx, int iVal, sqlite3_value **ppVal){\n  SessionDiffCtx *p = (SessionDiffCtx*)pCtx;\n  *ppVal = sqlite3_column_value(p->pStmt, iVal+p->nOldOff);\n  return SQLITE_OK;\n}\nstatic int sessionDiffNew(void *pCtx, int iVal, sqlite3_value **ppVal){\n  SessionDiffCtx *p = (SessionDiffCtx*)pCtx;\n  *ppVal = sqlite3_column_value(p->pStmt, iVal);\n   return SQLITE_OK;\n}\nstatic int sessionDiffCount(void *pCtx){\n  SessionDiffCtx *p = (SessionDiffCtx*)pCtx;\n  return p->nOldOff ? p->nOldOff : sqlite3_column_count(p->pStmt);\n}\nstatic int sessionDiffDepth(void *pCtx){\n  return 0;\n}\n\n/*\n** Install the diff hooks on the session object passed as the only\n** argument.\n*/\nstatic void sessionDiffHooks(\n  sqlite3_session *pSession,\n  SessionDiffCtx *pDiffCtx\n){\n  pSession->hook.pCtx = (void*)pDiffCtx;\n  pSession->hook.xOld = sessionDiffOld;\n  pSession->hook.xNew = sessionDiffNew;\n  pSession->hook.xCount = sessionDiffCount;\n  pSession->hook.xDepth = sessionDiffDepth;\n}\n\nstatic char *sessionExprComparePK(\n  int nCol,\n  const char *zDb1, const char *zDb2, \n  const char *zTab,\n  const char **azCol, u8 *abPK\n){\n  int i;\n  const char *zSep = \"\";\n  char *zRet = 0;\n\n  for(i=0; i<nCol; i++){\n    if( abPK[i] ){\n      zRet = sqlite3_mprintf(\"%z%s\\\"%w\\\".\\\"%w\\\".\\\"%w\\\"=\\\"%w\\\".\\\"%w\\\".\\\"%w\\\"\",\n          zRet, zSep, zDb1, zTab, azCol[i], zDb2, zTab, azCol[i]\n      );\n      zSep = \" AND \";\n      if( zRet==0 ) break;\n    }\n  }\n\n  return zRet;\n}\n\nstatic char *sessionExprCompareOther(\n  int nCol,\n  const char *zDb1, const char *zDb2, \n  const char *zTab,\n  const char **azCol, u8 *abPK\n){\n  int i;\n  const char *zSep = \"\";\n  char *zRet = 0;\n  int bHave = 0;\n\n  for(i=0; i<nCol; i++){\n    if( abPK[i]==0 ){\n      bHave = 1;\n      zRet = sqlite3_mprintf(\n          \"%z%s\\\"%w\\\".\\\"%w\\\".\\\"%w\\\" IS NOT \\\"%w\\\".\\\"%w\\\".\\\"%w\\\"\",\n          zRet, zSep, zDb1, zTab, azCol[i], zDb2, zTab, azCol[i]\n      );\n      zSep = \" OR \";\n      if( zRet==0 ) break;\n    }\n  }\n\n  if( bHave==0 ){\n    assert( zRet==0 );\n    zRet = sqlite3_mprintf(\"0\");\n  }\n\n  return zRet;\n}\n\nstatic char *sessionSelectFindNew(\n  int nCol,\n  const char *zDb1,      /* Pick rows in this db only */\n  const char *zDb2,      /* But not in this one */\n  const char *zTbl,      /* Table name */\n  const char *zExpr\n){\n  char *zRet = sqlite3_mprintf(\n      \"SELECT * FROM \\\"%w\\\".\\\"%w\\\" WHERE NOT EXISTS (\"\n      \"  SELECT 1 FROM \\\"%w\\\".\\\"%w\\\" WHERE %s\"\n      \")\",\n      zDb1, zTbl, zDb2, zTbl, zExpr\n  );\n  return zRet;\n}\n\nstatic int sessionDiffFindNew(\n  int op,\n  sqlite3_session *pSession,\n  SessionTable *pTab,\n  const char *zDb1,\n  const char *zDb2,\n  char *zExpr\n){\n  int rc = SQLITE_OK;\n  char *zStmt = sessionSelectFindNew(pTab->nCol, zDb1, zDb2, pTab->zName,zExpr);\n\n  if( zStmt==0 ){\n    rc = SQLITE_NOMEM;\n  }else{\n    sqlite3_stmt *pStmt;\n    rc = sqlite3_prepare(pSession->db, zStmt, -1, &pStmt, 0);\n    if( rc==SQLITE_OK ){\n      SessionDiffCtx *pDiffCtx = (SessionDiffCtx*)pSession->hook.pCtx;\n      pDiffCtx->pStmt = pStmt;\n      pDiffCtx->nOldOff = 0;\n      while( SQLITE_ROW==sqlite3_step(pStmt) ){\n        sessionPreupdateOneChange(op, pSession, pTab);\n      }\n      rc = sqlite3_finalize(pStmt);\n    }\n    sqlite3_free(zStmt);\n  }\n\n  return rc;\n}\n\nstatic int sessionDiffFindModified(\n  sqlite3_session *pSession, \n  SessionTable *pTab, \n  const char *zFrom, \n  const char *zExpr\n){\n  int rc = SQLITE_OK;\n\n  char *zExpr2 = sessionExprCompareOther(pTab->nCol,\n      pSession->zDb, zFrom, pTab->zName, pTab->azCol, pTab->abPK\n  );\n  if( zExpr2==0 ){\n    rc = SQLITE_NOMEM;\n  }else{\n    char *zStmt = sqlite3_mprintf(\n        \"SELECT * FROM \\\"%w\\\".\\\"%w\\\", \\\"%w\\\".\\\"%w\\\" WHERE %s AND (%z)\",\n        pSession->zDb, pTab->zName, zFrom, pTab->zName, zExpr, zExpr2\n    );\n    if( zStmt==0 ){\n      rc = SQLITE_NOMEM;\n    }else{\n      sqlite3_stmt *pStmt;\n      rc = sqlite3_prepare(pSession->db, zStmt, -1, &pStmt, 0);\n\n      if( rc==SQLITE_OK ){\n        SessionDiffCtx *pDiffCtx = (SessionDiffCtx*)pSession->hook.pCtx;\n        pDiffCtx->pStmt = pStmt;\n        pDiffCtx->nOldOff = pTab->nCol;\n        while( SQLITE_ROW==sqlite3_step(pStmt) ){\n          sessionPreupdateOneChange(SQLITE_UPDATE, pSession, pTab);\n        }\n        rc = sqlite3_finalize(pStmt);\n      }\n      sqlite3_free(zStmt);\n    }\n  }\n\n  return rc;\n}\n\nSQLITE_API int sqlite3session_diff(\n  sqlite3_session *pSession,\n  const char *zFrom,\n  const char *zTbl,\n  char **pzErrMsg\n){\n  const char *zDb = pSession->zDb;\n  int rc = pSession->rc;\n  SessionDiffCtx d;\n\n  memset(&d, 0, sizeof(d));\n  sessionDiffHooks(pSession, &d);\n\n  sqlite3_mutex_enter(sqlite3_db_mutex(pSession->db));\n  if( pzErrMsg ) *pzErrMsg = 0;\n  if( rc==SQLITE_OK ){\n    char *zExpr = 0;\n    sqlite3 *db = pSession->db;\n    SessionTable *pTo;            /* Table zTbl */\n\n    /* Locate and if necessary initialize the target table object */\n    rc = sessionFindTable(pSession, zTbl, &pTo);\n    if( pTo==0 ) goto diff_out;\n    if( sessionInitTable(pSession, pTo) ){\n      rc = pSession->rc;\n      goto diff_out;\n    }\n\n    /* Check the table schemas match */\n    if( rc==SQLITE_OK ){\n      int bHasPk = 0;\n      int bMismatch = 0;\n      int nCol;                   /* Columns in zFrom.zTbl */\n      u8 *abPK;\n      const char **azCol = 0;\n      rc = sessionTableInfo(db, zFrom, zTbl, &nCol, 0, &azCol, &abPK);\n      if( rc==SQLITE_OK ){\n        if( pTo->nCol!=nCol ){\n          bMismatch = 1;\n        }else{\n          int i;\n          for(i=0; i<nCol; i++){\n            if( pTo->abPK[i]!=abPK[i] ) bMismatch = 1;\n            if( sqlite3_stricmp(azCol[i], pTo->azCol[i]) ) bMismatch = 1;\n            if( abPK[i] ) bHasPk = 1;\n          }\n        }\n      }\n      sqlite3_free((char*)azCol);\n      if( bMismatch ){\n        *pzErrMsg = sqlite3_mprintf(\"table schemas do not match\");\n        rc = SQLITE_SCHEMA;\n      }\n      if( bHasPk==0 ){\n        /* Ignore tables with no primary keys */\n        goto diff_out;\n      }\n    }\n\n    if( rc==SQLITE_OK ){\n      zExpr = sessionExprComparePK(pTo->nCol, \n          zDb, zFrom, pTo->zName, pTo->azCol, pTo->abPK\n      );\n    }\n\n    /* Find new rows */\n    if( rc==SQLITE_OK ){\n      rc = sessionDiffFindNew(SQLITE_INSERT, pSession, pTo, zDb, zFrom, zExpr);\n    }\n\n    /* Find old rows */\n    if( rc==SQLITE_OK ){\n      rc = sessionDiffFindNew(SQLITE_DELETE, pSession, pTo, zFrom, zDb, zExpr);\n    }\n\n    /* Find modified rows */\n    if( rc==SQLITE_OK ){\n      rc = sessionDiffFindModified(pSession, pTo, zFrom, zExpr);\n    }\n\n    sqlite3_free(zExpr);\n  }\n\n diff_out:\n  sessionPreupdateHooks(pSession);\n  sqlite3_mutex_leave(sqlite3_db_mutex(pSession->db));\n  return rc;\n}\n\n/*\n** Create a session object. This session object will record changes to\n** database zDb attached to connection db.\n*/\nSQLITE_API int sqlite3session_create(\n  sqlite3 *db,                    /* Database handle */\n  const char *zDb,                /* Name of db (e.g. \"main\") */\n  sqlite3_session **ppSession     /* OUT: New session object */\n){\n  sqlite3_session *pNew;          /* Newly allocated session object */\n  sqlite3_session *pOld;          /* Session object already attached to db */\n  int nDb = sqlite3Strlen30(zDb); /* Length of zDb in bytes */\n\n  /* Zero the output value in case an error occurs. */\n  *ppSession = 0;\n\n  /* Allocate and populate the new session object. */\n  pNew = (sqlite3_session *)sqlite3_malloc(sizeof(sqlite3_session) + nDb + 1);\n  if( !pNew ) return SQLITE_NOMEM;\n  memset(pNew, 0, sizeof(sqlite3_session));\n  pNew->db = db;\n  pNew->zDb = (char *)&pNew[1];\n  pNew->bEnable = 1;\n  memcpy(pNew->zDb, zDb, nDb+1);\n  sessionPreupdateHooks(pNew);\n\n  /* Add the new session object to the linked list of session objects \n  ** attached to database handle $db. Do this under the cover of the db\n  ** handle mutex.  */\n  sqlite3_mutex_enter(sqlite3_db_mutex(db));\n  pOld = (sqlite3_session*)sqlite3_preupdate_hook(db, xPreUpdate, (void*)pNew);\n  pNew->pNext = pOld;\n  sqlite3_mutex_leave(sqlite3_db_mutex(db));\n\n  *ppSession = pNew;\n  return SQLITE_OK;\n}\n\n/*\n** Free the list of table objects passed as the first argument. The contents\n** of the changed-rows hash tables are also deleted.\n*/\nstatic void sessionDeleteTable(SessionTable *pList){\n  SessionTable *pNext;\n  SessionTable *pTab;\n\n  for(pTab=pList; pTab; pTab=pNext){\n    int i;\n    pNext = pTab->pNext;\n    for(i=0; i<pTab->nChange; i++){\n      SessionChange *p;\n      SessionChange *pNextChange;\n      for(p=pTab->apChange[i]; p; p=pNextChange){\n        pNextChange = p->pNext;\n        sqlite3_free(p);\n      }\n    }\n    sqlite3_free((char*)pTab->azCol);  /* cast works around VC++ bug */\n    sqlite3_free(pTab->apChange);\n    sqlite3_free(pTab);\n  }\n}\n\n/*\n** Delete a session object previously allocated using sqlite3session_create().\n*/\nSQLITE_API void sqlite3session_delete(sqlite3_session *pSession){\n  sqlite3 *db = pSession->db;\n  sqlite3_session *pHead;\n  sqlite3_session **pp;\n\n  /* Unlink the session from the linked list of sessions attached to the\n  ** database handle. Hold the db mutex while doing so.  */\n  sqlite3_mutex_enter(sqlite3_db_mutex(db));\n  pHead = (sqlite3_session*)sqlite3_preupdate_hook(db, 0, 0);\n  for(pp=&pHead; ALWAYS((*pp)!=0); pp=&((*pp)->pNext)){\n    if( (*pp)==pSession ){\n      *pp = (*pp)->pNext;\n      if( pHead ) sqlite3_preupdate_hook(db, xPreUpdate, (void*)pHead);\n      break;\n    }\n  }\n  sqlite3_mutex_leave(sqlite3_db_mutex(db));\n  sqlite3ValueFree(pSession->pZeroBlob);\n\n  /* Delete all attached table objects. And the contents of their \n  ** associated hash-tables. */\n  sessionDeleteTable(pSession->pTable);\n\n  /* Free the session object itself. */\n  sqlite3_free(pSession);\n}\n\n/*\n** Set a table filter on a Session Object.\n*/\nSQLITE_API void sqlite3session_table_filter(\n  sqlite3_session *pSession, \n  int(*xFilter)(void*, const char*),\n  void *pCtx                      /* First argument passed to xFilter */\n){\n  pSession->bAutoAttach = 1;\n  pSession->pFilterCtx = pCtx;\n  pSession->xTableFilter = xFilter;\n}\n\n/*\n** Attach a table to a session. All subsequent changes made to the table\n** while the session object is enabled will be recorded.\n**\n** Only tables that have a PRIMARY KEY defined may be attached. It does\n** not matter if the PRIMARY KEY is an \"INTEGER PRIMARY KEY\" (rowid alias)\n** or not.\n*/\nSQLITE_API int sqlite3session_attach(\n  sqlite3_session *pSession,      /* Session object */\n  const char *zName               /* Table name */\n){\n  int rc = SQLITE_OK;\n  sqlite3_mutex_enter(sqlite3_db_mutex(pSession->db));\n\n  if( !zName ){\n    pSession->bAutoAttach = 1;\n  }else{\n    SessionTable *pTab;           /* New table object (if required) */\n    int nName;                    /* Number of bytes in string zName */\n\n    /* First search for an existing entry. If one is found, this call is\n    ** a no-op. Return early. */\n    nName = sqlite3Strlen30(zName);\n    for(pTab=pSession->pTable; pTab; pTab=pTab->pNext){\n      if( 0==sqlite3_strnicmp(pTab->zName, zName, nName+1) ) break;\n    }\n\n    if( !pTab ){\n      /* Allocate new SessionTable object. */\n      pTab = (SessionTable *)sqlite3_malloc(sizeof(SessionTable) + nName + 1);\n      if( !pTab ){\n        rc = SQLITE_NOMEM;\n      }else{\n        /* Populate the new SessionTable object and link it into the list.\n        ** The new object must be linked onto the end of the list, not \n        ** simply added to the start of it in order to ensure that tables\n        ** appear in the correct order when a changeset or patchset is\n        ** eventually generated. */\n        SessionTable **ppTab;\n        memset(pTab, 0, sizeof(SessionTable));\n        pTab->zName = (char *)&pTab[1];\n        memcpy(pTab->zName, zName, nName+1);\n        for(ppTab=&pSession->pTable; *ppTab; ppTab=&(*ppTab)->pNext);\n        *ppTab = pTab;\n      }\n    }\n  }\n\n  sqlite3_mutex_leave(sqlite3_db_mutex(pSession->db));\n  return rc;\n}\n\n/*\n** Ensure that there is room in the buffer to append nByte bytes of data.\n** If not, use sqlite3_realloc() to grow the buffer so that there is.\n**\n** If successful, return zero. Otherwise, if an OOM condition is encountered,\n** set *pRc to SQLITE_NOMEM and return non-zero.\n*/\nstatic int sessionBufferGrow(SessionBuffer *p, int nByte, int *pRc){\n  if( *pRc==SQLITE_OK && p->nAlloc-p->nBuf<nByte ){\n    u8 *aNew;\n    int nNew = p->nAlloc ? p->nAlloc : 128;\n    do {\n      nNew = nNew*2;\n    }while( nNew<(p->nBuf+nByte) );\n\n    aNew = (u8 *)sqlite3_realloc(p->aBuf, nNew);\n    if( 0==aNew ){\n      *pRc = SQLITE_NOMEM;\n    }else{\n      p->aBuf = aNew;\n      p->nAlloc = nNew;\n    }\n  }\n  return (*pRc!=SQLITE_OK);\n}\n\n/*\n** Append the value passed as the second argument to the buffer passed\n** as the first.\n**\n** This function is a no-op if *pRc is non-zero when it is called.\n** Otherwise, if an error occurs, *pRc is set to an SQLite error code\n** before returning.\n*/\nstatic void sessionAppendValue(SessionBuffer *p, sqlite3_value *pVal, int *pRc){\n  int rc = *pRc;\n  if( rc==SQLITE_OK ){\n    int nByte = 0;\n    rc = sessionSerializeValue(0, pVal, &nByte);\n    sessionBufferGrow(p, nByte, &rc);\n    if( rc==SQLITE_OK ){\n      rc = sessionSerializeValue(&p->aBuf[p->nBuf], pVal, 0);\n      p->nBuf += nByte;\n    }else{\n      *pRc = rc;\n    }\n  }\n}\n\n/*\n** This function is a no-op if *pRc is other than SQLITE_OK when it is \n** called. Otherwise, append a single byte to the buffer. \n**\n** If an OOM condition is encountered, set *pRc to SQLITE_NOMEM before\n** returning.\n*/\nstatic void sessionAppendByte(SessionBuffer *p, u8 v, int *pRc){\n  if( 0==sessionBufferGrow(p, 1, pRc) ){\n    p->aBuf[p->nBuf++] = v;\n  }\n}\n\n/*\n** This function is a no-op if *pRc is other than SQLITE_OK when it is \n** called. Otherwise, append a single varint to the buffer. \n**\n** If an OOM condition is encountered, set *pRc to SQLITE_NOMEM before\n** returning.\n*/\nstatic void sessionAppendVarint(SessionBuffer *p, int v, int *pRc){\n  if( 0==sessionBufferGrow(p, 9, pRc) ){\n    p->nBuf += sessionVarintPut(&p->aBuf[p->nBuf], v);\n  }\n}\n\n/*\n** This function is a no-op if *pRc is other than SQLITE_OK when it is \n** called. Otherwise, append a blob of data to the buffer. \n**\n** If an OOM condition is encountered, set *pRc to SQLITE_NOMEM before\n** returning.\n*/\nstatic void sessionAppendBlob(\n  SessionBuffer *p, \n  const u8 *aBlob, \n  int nBlob, \n  int *pRc\n){\n  if( nBlob>0 && 0==sessionBufferGrow(p, nBlob, pRc) ){\n    memcpy(&p->aBuf[p->nBuf], aBlob, nBlob);\n    p->nBuf += nBlob;\n  }\n}\n\n/*\n** This function is a no-op if *pRc is other than SQLITE_OK when it is \n** called. Otherwise, append a string to the buffer. All bytes in the string\n** up to (but not including) the nul-terminator are written to the buffer.\n**\n** If an OOM condition is encountered, set *pRc to SQLITE_NOMEM before\n** returning.\n*/\nstatic void sessionAppendStr(\n  SessionBuffer *p, \n  const char *zStr, \n  int *pRc\n){\n  int nStr = sqlite3Strlen30(zStr);\n  if( 0==sessionBufferGrow(p, nStr, pRc) ){\n    memcpy(&p->aBuf[p->nBuf], zStr, nStr);\n    p->nBuf += nStr;\n  }\n}\n\n/*\n** This function is a no-op if *pRc is other than SQLITE_OK when it is \n** called. Otherwise, append the string representation of integer iVal\n** to the buffer. No nul-terminator is written.\n**\n** If an OOM condition is encountered, set *pRc to SQLITE_NOMEM before\n** returning.\n*/\nstatic void sessionAppendInteger(\n  SessionBuffer *p,               /* Buffer to append to */\n  int iVal,                       /* Value to write the string rep. of */\n  int *pRc                        /* IN/OUT: Error code */\n){\n  char aBuf[24];\n  sqlite3_snprintf(sizeof(aBuf)-1, aBuf, \"%d\", iVal);\n  sessionAppendStr(p, aBuf, pRc);\n}\n\n/*\n** This function is a no-op if *pRc is other than SQLITE_OK when it is \n** called. Otherwise, append the string zStr enclosed in quotes (\") and\n** with any embedded quote characters escaped to the buffer. No \n** nul-terminator byte is written.\n**\n** If an OOM condition is encountered, set *pRc to SQLITE_NOMEM before\n** returning.\n*/\nstatic void sessionAppendIdent(\n  SessionBuffer *p,               /* Buffer to a append to */\n  const char *zStr,               /* String to quote, escape and append */\n  int *pRc                        /* IN/OUT: Error code */\n){\n  int nStr = sqlite3Strlen30(zStr)*2 + 2 + 1;\n  if( 0==sessionBufferGrow(p, nStr, pRc) ){\n    char *zOut = (char *)&p->aBuf[p->nBuf];\n    const char *zIn = zStr;\n    *zOut++ = '\"';\n    while( *zIn ){\n      if( *zIn=='\"' ) *zOut++ = '\"';\n      *zOut++ = *(zIn++);\n    }\n    *zOut++ = '\"';\n    p->nBuf = (int)((u8 *)zOut - p->aBuf);\n  }\n}\n\n/*\n** This function is a no-op if *pRc is other than SQLITE_OK when it is\n** called. Otherwse, it appends the serialized version of the value stored\n** in column iCol of the row that SQL statement pStmt currently points\n** to to the buffer.\n*/\nstatic void sessionAppendCol(\n  SessionBuffer *p,               /* Buffer to append to */\n  sqlite3_stmt *pStmt,            /* Handle pointing to row containing value */\n  int iCol,                       /* Column to read value from */\n  int *pRc                        /* IN/OUT: Error code */\n){\n  if( *pRc==SQLITE_OK ){\n    int eType = sqlite3_column_type(pStmt, iCol);\n    sessionAppendByte(p, (u8)eType, pRc);\n    if( eType==SQLITE_INTEGER || eType==SQLITE_FLOAT ){\n      sqlite3_int64 i;\n      u8 aBuf[8];\n      if( eType==SQLITE_INTEGER ){\n        i = sqlite3_column_int64(pStmt, iCol);\n      }else{\n        double r = sqlite3_column_double(pStmt, iCol);\n        memcpy(&i, &r, 8);\n      }\n      sessionPutI64(aBuf, i);\n      sessionAppendBlob(p, aBuf, 8, pRc);\n    }\n    if( eType==SQLITE_BLOB || eType==SQLITE_TEXT ){\n      u8 *z;\n      int nByte;\n      if( eType==SQLITE_BLOB ){\n        z = (u8 *)sqlite3_column_blob(pStmt, iCol);\n      }else{\n        z = (u8 *)sqlite3_column_text(pStmt, iCol);\n      }\n      nByte = sqlite3_column_bytes(pStmt, iCol);\n      if( z || (eType==SQLITE_BLOB && nByte==0) ){\n        sessionAppendVarint(p, nByte, pRc);\n        sessionAppendBlob(p, z, nByte, pRc);\n      }else{\n        *pRc = SQLITE_NOMEM;\n      }\n    }\n  }\n}\n\n/*\n**\n** This function appends an update change to the buffer (see the comments \n** under \"CHANGESET FORMAT\" at the top of the file). An update change \n** consists of:\n**\n**   1 byte:  SQLITE_UPDATE (0x17)\n**   n bytes: old.* record (see RECORD FORMAT)\n**   m bytes: new.* record (see RECORD FORMAT)\n**\n** The SessionChange object passed as the third argument contains the\n** values that were stored in the row when the session began (the old.*\n** values). The statement handle passed as the second argument points\n** at the current version of the row (the new.* values).\n**\n** If all of the old.* values are equal to their corresponding new.* value\n** (i.e. nothing has changed), then no data at all is appended to the buffer.\n**\n** Otherwise, the old.* record contains all primary key values and the \n** original values of any fields that have been modified. The new.* record \n** contains the new values of only those fields that have been modified.\n*/ \nstatic int sessionAppendUpdate(\n  SessionBuffer *pBuf,            /* Buffer to append to */\n  int bPatchset,                  /* True for \"patchset\", 0 for \"changeset\" */\n  sqlite3_stmt *pStmt,            /* Statement handle pointing at new row */\n  SessionChange *p,               /* Object containing old values */\n  u8 *abPK                        /* Boolean array - true for PK columns */\n){\n  int rc = SQLITE_OK;\n  SessionBuffer buf2 = {0,0,0}; /* Buffer to accumulate new.* record in */\n  int bNoop = 1;                /* Set to zero if any values are modified */\n  int nRewind = pBuf->nBuf;     /* Set to zero if any values are modified */\n  int i;                        /* Used to iterate through columns */\n  u8 *pCsr = p->aRecord;        /* Used to iterate through old.* values */\n\n  sessionAppendByte(pBuf, SQLITE_UPDATE, &rc);\n  sessionAppendByte(pBuf, p->bIndirect, &rc);\n  for(i=0; i<sqlite3_column_count(pStmt); i++){\n    int bChanged = 0;\n    int nAdvance;\n    int eType = *pCsr;\n    switch( eType ){\n      case SQLITE_NULL:\n        nAdvance = 1;\n        if( sqlite3_column_type(pStmt, i)!=SQLITE_NULL ){\n          bChanged = 1;\n        }\n        break;\n\n      case SQLITE_FLOAT:\n      case SQLITE_INTEGER: {\n        nAdvance = 9;\n        if( eType==sqlite3_column_type(pStmt, i) ){\n          sqlite3_int64 iVal = sessionGetI64(&pCsr[1]);\n          if( eType==SQLITE_INTEGER ){\n            if( iVal==sqlite3_column_int64(pStmt, i) ) break;\n          }else{\n            double dVal;\n            memcpy(&dVal, &iVal, 8);\n            if( dVal==sqlite3_column_double(pStmt, i) ) break;\n          }\n        }\n        bChanged = 1;\n        break;\n      }\n\n      default: {\n        int n;\n        int nHdr = 1 + sessionVarintGet(&pCsr[1], &n);\n        assert( eType==SQLITE_TEXT || eType==SQLITE_BLOB );\n        nAdvance = nHdr + n;\n        if( eType==sqlite3_column_type(pStmt, i) \n         && n==sqlite3_column_bytes(pStmt, i) \n         && (n==0 || 0==memcmp(&pCsr[nHdr], sqlite3_column_blob(pStmt, i), n))\n        ){\n          break;\n        }\n        bChanged = 1;\n      }\n    }\n\n    /* If at least one field has been modified, this is not a no-op. */\n    if( bChanged ) bNoop = 0;\n\n    /* Add a field to the old.* record. This is omitted if this modules is\n    ** currently generating a patchset. */\n    if( bPatchset==0 ){\n      if( bChanged || abPK[i] ){\n        sessionAppendBlob(pBuf, pCsr, nAdvance, &rc);\n      }else{\n        sessionAppendByte(pBuf, 0, &rc);\n      }\n    }\n\n    /* Add a field to the new.* record. Or the only record if currently\n    ** generating a patchset.  */\n    if( bChanged || (bPatchset && abPK[i]) ){\n      sessionAppendCol(&buf2, pStmt, i, &rc);\n    }else{\n      sessionAppendByte(&buf2, 0, &rc);\n    }\n\n    pCsr += nAdvance;\n  }\n\n  if( bNoop ){\n    pBuf->nBuf = nRewind;\n  }else{\n    sessionAppendBlob(pBuf, buf2.aBuf, buf2.nBuf, &rc);\n  }\n  sqlite3_free(buf2.aBuf);\n\n  return rc;\n}\n\n/*\n** Append a DELETE change to the buffer passed as the first argument. Use\n** the changeset format if argument bPatchset is zero, or the patchset\n** format otherwise.\n*/\nstatic int sessionAppendDelete(\n  SessionBuffer *pBuf,            /* Buffer to append to */\n  int bPatchset,                  /* True for \"patchset\", 0 for \"changeset\" */\n  SessionChange *p,               /* Object containing old values */\n  int nCol,                       /* Number of columns in table */\n  u8 *abPK                        /* Boolean array - true for PK columns */\n){\n  int rc = SQLITE_OK;\n\n  sessionAppendByte(pBuf, SQLITE_DELETE, &rc);\n  sessionAppendByte(pBuf, p->bIndirect, &rc);\n\n  if( bPatchset==0 ){\n    sessionAppendBlob(pBuf, p->aRecord, p->nRecord, &rc);\n  }else{\n    int i;\n    u8 *a = p->aRecord;\n    for(i=0; i<nCol; i++){\n      u8 *pStart = a;\n      int eType = *a++;\n\n      switch( eType ){\n        case 0:\n        case SQLITE_NULL:\n          assert( abPK[i]==0 );\n          break;\n\n        case SQLITE_FLOAT:\n        case SQLITE_INTEGER:\n          a += 8;\n          break;\n\n        default: {\n          int n;\n          a += sessionVarintGet(a, &n);\n          a += n;\n          break;\n        }\n      }\n      if( abPK[i] ){\n        sessionAppendBlob(pBuf, pStart, (int)(a-pStart), &rc);\n      }\n    }\n    assert( (a - p->aRecord)==p->nRecord );\n  }\n\n  return rc;\n}\n\n/*\n** Formulate and prepare a SELECT statement to retrieve a row from table\n** zTab in database zDb based on its primary key. i.e.\n**\n**   SELECT * FROM zDb.zTab WHERE pk1 = ? AND pk2 = ? AND ...\n*/\nstatic int sessionSelectStmt(\n  sqlite3 *db,                    /* Database handle */\n  const char *zDb,                /* Database name */\n  const char *zTab,               /* Table name */\n  int nCol,                       /* Number of columns in table */\n  const char **azCol,             /* Names of table columns */\n  u8 *abPK,                       /* PRIMARY KEY  array */\n  sqlite3_stmt **ppStmt           /* OUT: Prepared SELECT statement */\n){\n  int rc = SQLITE_OK;\n  char *zSql = 0;\n  int nSql = -1;\n\n  if( 0==sqlite3_stricmp(\"sqlite_stat1\", zTab) ){\n    zSql = sqlite3_mprintf(\n        \"SELECT tbl, ?2, stat FROM %Q.sqlite_stat1 WHERE tbl IS ?1 AND \"\n        \"idx IS (CASE WHEN ?2=X'' THEN NULL ELSE ?2 END)\", zDb\n    );\n  }else{\n    int i;\n    const char *zSep = \"\";\n    SessionBuffer buf = {0, 0, 0};\n\n    sessionAppendStr(&buf, \"SELECT * FROM \", &rc);\n    sessionAppendIdent(&buf, zDb, &rc);\n    sessionAppendStr(&buf, \".\", &rc);\n    sessionAppendIdent(&buf, zTab, &rc);\n    sessionAppendStr(&buf, \" WHERE \", &rc);\n    for(i=0; i<nCol; i++){\n      if( abPK[i] ){\n        sessionAppendStr(&buf, zSep, &rc);\n        sessionAppendIdent(&buf, azCol[i], &rc);\n        sessionAppendStr(&buf, \" IS ?\", &rc);\n        sessionAppendInteger(&buf, i+1, &rc);\n        zSep = \" AND \";\n      }\n    }\n    zSql = (char*)buf.aBuf;\n    nSql = buf.nBuf;\n  }\n\n  if( rc==SQLITE_OK ){\n    rc = sqlite3_prepare_v2(db, zSql, nSql, ppStmt, 0);\n  }\n  sqlite3_free(zSql);\n  return rc;\n}\n\n/*\n** Bind the PRIMARY KEY values from the change passed in argument pChange\n** to the SELECT statement passed as the first argument. The SELECT statement\n** is as prepared by function sessionSelectStmt().\n**\n** Return SQLITE_OK if all PK values are successfully bound, or an SQLite\n** error code (e.g. SQLITE_NOMEM) otherwise.\n*/\nstatic int sessionSelectBind(\n  sqlite3_stmt *pSelect,          /* SELECT from sessionSelectStmt() */\n  int nCol,                       /* Number of columns in table */\n  u8 *abPK,                       /* PRIMARY KEY array */\n  SessionChange *pChange          /* Change structure */\n){\n  int i;\n  int rc = SQLITE_OK;\n  u8 *a = pChange->aRecord;\n\n  for(i=0; i<nCol && rc==SQLITE_OK; i++){\n    int eType = *a++;\n\n    switch( eType ){\n      case 0:\n      case SQLITE_NULL:\n        assert( abPK[i]==0 );\n        break;\n\n      case SQLITE_INTEGER: {\n        if( abPK[i] ){\n          i64 iVal = sessionGetI64(a);\n          rc = sqlite3_bind_int64(pSelect, i+1, iVal);\n        }\n        a += 8;\n        break;\n      }\n\n      case SQLITE_FLOAT: {\n        if( abPK[i] ){\n          double rVal;\n          i64 iVal = sessionGetI64(a);\n          memcpy(&rVal, &iVal, 8);\n          rc = sqlite3_bind_double(pSelect, i+1, rVal);\n        }\n        a += 8;\n        break;\n      }\n\n      case SQLITE_TEXT: {\n        int n;\n        a += sessionVarintGet(a, &n);\n        if( abPK[i] ){\n          rc = sqlite3_bind_text(pSelect, i+1, (char *)a, n, SQLITE_TRANSIENT);\n        }\n        a += n;\n        break;\n      }\n\n      default: {\n        int n;\n        assert( eType==SQLITE_BLOB );\n        a += sessionVarintGet(a, &n);\n        if( abPK[i] ){\n          rc = sqlite3_bind_blob(pSelect, i+1, a, n, SQLITE_TRANSIENT);\n        }\n        a += n;\n        break;\n      }\n    }\n  }\n\n  return rc;\n}\n\n/*\n** This function is a no-op if *pRc is set to other than SQLITE_OK when it\n** is called. Otherwise, append a serialized table header (part of the binary \n** changeset format) to buffer *pBuf. If an error occurs, set *pRc to an\n** SQLite error code before returning.\n*/\nstatic void sessionAppendTableHdr(\n  SessionBuffer *pBuf,            /* Append header to this buffer */\n  int bPatchset,                  /* Use the patchset format if true */\n  SessionTable *pTab,             /* Table object to append header for */\n  int *pRc                        /* IN/OUT: Error code */\n){\n  /* Write a table header */\n  sessionAppendByte(pBuf, (bPatchset ? 'P' : 'T'), pRc);\n  sessionAppendVarint(pBuf, pTab->nCol, pRc);\n  sessionAppendBlob(pBuf, pTab->abPK, pTab->nCol, pRc);\n  sessionAppendBlob(pBuf, (u8 *)pTab->zName, (int)strlen(pTab->zName)+1, pRc);\n}\n\n/*\n** Generate either a changeset (if argument bPatchset is zero) or a patchset\n** (if it is non-zero) based on the current contents of the session object\n** passed as the first argument.\n**\n** If no error occurs, SQLITE_OK is returned and the new changeset/patchset\n** stored in output variables *pnChangeset and *ppChangeset. Or, if an error\n** occurs, an SQLite error code is returned and both output variables set \n** to 0.\n*/\nstatic int sessionGenerateChangeset(\n  sqlite3_session *pSession,      /* Session object */\n  int bPatchset,                  /* True for patchset, false for changeset */\n  int (*xOutput)(void *pOut, const void *pData, int nData),\n  void *pOut,                     /* First argument for xOutput */\n  int *pnChangeset,               /* OUT: Size of buffer at *ppChangeset */\n  void **ppChangeset              /* OUT: Buffer containing changeset */\n){\n  sqlite3 *db = pSession->db;     /* Source database handle */\n  SessionTable *pTab;             /* Used to iterate through attached tables */\n  SessionBuffer buf = {0,0,0};    /* Buffer in which to accumlate changeset */\n  int rc;                         /* Return code */\n\n  assert( xOutput==0 || (pnChangeset==0 && ppChangeset==0 ) );\n\n  /* Zero the output variables in case an error occurs. If this session\n  ** object is already in the error state (sqlite3_session.rc != SQLITE_OK),\n  ** this call will be a no-op.  */\n  if( xOutput==0 ){\n    *pnChangeset = 0;\n    *ppChangeset = 0;\n  }\n\n  if( pSession->rc ) return pSession->rc;\n  rc = sqlite3_exec(pSession->db, \"SAVEPOINT changeset\", 0, 0, 0);\n  if( rc!=SQLITE_OK ) return rc;\n\n  sqlite3_mutex_enter(sqlite3_db_mutex(db));\n\n  for(pTab=pSession->pTable; rc==SQLITE_OK && pTab; pTab=pTab->pNext){\n    if( pTab->nEntry ){\n      const char *zName = pTab->zName;\n      int nCol;                   /* Number of columns in table */\n      u8 *abPK;                   /* Primary key array */\n      const char **azCol = 0;     /* Table columns */\n      int i;                      /* Used to iterate through hash buckets */\n      sqlite3_stmt *pSel = 0;     /* SELECT statement to query table pTab */\n      int nRewind = buf.nBuf;     /* Initial size of write buffer */\n      int nNoop;                  /* Size of buffer after writing tbl header */\n\n      /* Check the table schema is still Ok. */\n      rc = sessionTableInfo(db, pSession->zDb, zName, &nCol, 0, &azCol, &abPK);\n      if( !rc && (pTab->nCol!=nCol || memcmp(abPK, pTab->abPK, nCol)) ){\n        rc = SQLITE_SCHEMA;\n      }\n\n      /* Write a table header */\n      sessionAppendTableHdr(&buf, bPatchset, pTab, &rc);\n\n      /* Build and compile a statement to execute: */\n      if( rc==SQLITE_OK ){\n        rc = sessionSelectStmt(\n            db, pSession->zDb, zName, nCol, azCol, abPK, &pSel);\n      }\n\n      nNoop = buf.nBuf;\n      for(i=0; i<pTab->nChange && rc==SQLITE_OK; i++){\n        SessionChange *p;         /* Used to iterate through changes */\n\n        for(p=pTab->apChange[i]; rc==SQLITE_OK && p; p=p->pNext){\n          rc = sessionSelectBind(pSel, nCol, abPK, p);\n          if( rc!=SQLITE_OK ) continue;\n          if( sqlite3_step(pSel)==SQLITE_ROW ){\n            if( p->op==SQLITE_INSERT ){\n              int iCol;\n              sessionAppendByte(&buf, SQLITE_INSERT, &rc);\n              sessionAppendByte(&buf, p->bIndirect, &rc);\n              for(iCol=0; iCol<nCol; iCol++){\n                sessionAppendCol(&buf, pSel, iCol, &rc);\n              }\n            }else{\n              rc = sessionAppendUpdate(&buf, bPatchset, pSel, p, abPK);\n            }\n          }else if( p->op!=SQLITE_INSERT ){\n            rc = sessionAppendDelete(&buf, bPatchset, p, nCol, abPK);\n          }\n          if( rc==SQLITE_OK ){\n            rc = sqlite3_reset(pSel);\n          }\n\n          /* If the buffer is now larger than SESSIONS_STRM_CHUNK_SIZE, pass\n          ** its contents to the xOutput() callback. */\n          if( xOutput \n           && rc==SQLITE_OK \n           && buf.nBuf>nNoop \n           && buf.nBuf>SESSIONS_STRM_CHUNK_SIZE \n          ){\n            rc = xOutput(pOut, (void*)buf.aBuf, buf.nBuf);\n            nNoop = -1;\n            buf.nBuf = 0;\n          }\n\n        }\n      }\n\n      sqlite3_finalize(pSel);\n      if( buf.nBuf==nNoop ){\n        buf.nBuf = nRewind;\n      }\n      sqlite3_free((char*)azCol);  /* cast works around VC++ bug */\n    }\n  }\n\n  if( rc==SQLITE_OK ){\n    if( xOutput==0 ){\n      *pnChangeset = buf.nBuf;\n      *ppChangeset = buf.aBuf;\n      buf.aBuf = 0;\n    }else if( buf.nBuf>0 ){\n      rc = xOutput(pOut, (void*)buf.aBuf, buf.nBuf);\n    }\n  }\n\n  sqlite3_free(buf.aBuf);\n  sqlite3_exec(db, \"RELEASE changeset\", 0, 0, 0);\n  sqlite3_mutex_leave(sqlite3_db_mutex(db));\n  return rc;\n}\n\n/*\n** Obtain a changeset object containing all changes recorded by the \n** session object passed as the first argument.\n**\n** It is the responsibility of the caller to eventually free the buffer \n** using sqlite3_free().\n*/\nSQLITE_API int sqlite3session_changeset(\n  sqlite3_session *pSession,      /* Session object */\n  int *pnChangeset,               /* OUT: Size of buffer at *ppChangeset */\n  void **ppChangeset              /* OUT: Buffer containing changeset */\n){\n  return sessionGenerateChangeset(pSession, 0, 0, 0, pnChangeset, ppChangeset);\n}\n\n/*\n** Streaming version of sqlite3session_changeset().\n*/\nSQLITE_API int sqlite3session_changeset_strm(\n  sqlite3_session *pSession,\n  int (*xOutput)(void *pOut, const void *pData, int nData),\n  void *pOut\n){\n  return sessionGenerateChangeset(pSession, 0, xOutput, pOut, 0, 0);\n}\n\n/*\n** Streaming version of sqlite3session_patchset().\n*/\nSQLITE_API int sqlite3session_patchset_strm(\n  sqlite3_session *pSession,\n  int (*xOutput)(void *pOut, const void *pData, int nData),\n  void *pOut\n){\n  return sessionGenerateChangeset(pSession, 1, xOutput, pOut, 0, 0);\n}\n\n/*\n** Obtain a patchset object containing all changes recorded by the \n** session object passed as the first argument.\n**\n** It is the responsibility of the caller to eventually free the buffer \n** using sqlite3_free().\n*/\nSQLITE_API int sqlite3session_patchset(\n  sqlite3_session *pSession,      /* Session object */\n  int *pnPatchset,                /* OUT: Size of buffer at *ppChangeset */\n  void **ppPatchset               /* OUT: Buffer containing changeset */\n){\n  return sessionGenerateChangeset(pSession, 1, 0, 0, pnPatchset, ppPatchset);\n}\n\n/*\n** Enable or disable the session object passed as the first argument.\n*/\nSQLITE_API int sqlite3session_enable(sqlite3_session *pSession, int bEnable){\n  int ret;\n  sqlite3_mutex_enter(sqlite3_db_mutex(pSession->db));\n  if( bEnable>=0 ){\n    pSession->bEnable = bEnable;\n  }\n  ret = pSession->bEnable;\n  sqlite3_mutex_leave(sqlite3_db_mutex(pSession->db));\n  return ret;\n}\n\n/*\n** Enable or disable the session object passed as the first argument.\n*/\nSQLITE_API int sqlite3session_indirect(sqlite3_session *pSession, int bIndirect){\n  int ret;\n  sqlite3_mutex_enter(sqlite3_db_mutex(pSession->db));\n  if( bIndirect>=0 ){\n    pSession->bIndirect = bIndirect;\n  }\n  ret = pSession->bIndirect;\n  sqlite3_mutex_leave(sqlite3_db_mutex(pSession->db));\n  return ret;\n}\n\n/*\n** Return true if there have been no changes to monitored tables recorded\n** by the session object passed as the only argument.\n*/\nSQLITE_API int sqlite3session_isempty(sqlite3_session *pSession){\n  int ret = 0;\n  SessionTable *pTab;\n\n  sqlite3_mutex_enter(sqlite3_db_mutex(pSession->db));\n  for(pTab=pSession->pTable; pTab && ret==0; pTab=pTab->pNext){\n    ret = (pTab->nEntry>0);\n  }\n  sqlite3_mutex_leave(sqlite3_db_mutex(pSession->db));\n\n  return (ret==0);\n}\n\n/*\n** Do the work for either sqlite3changeset_start() or start_strm().\n*/\nstatic int sessionChangesetStart(\n  sqlite3_changeset_iter **pp,    /* OUT: Changeset iterator handle */\n  int (*xInput)(void *pIn, void *pData, int *pnData),\n  void *pIn,\n  int nChangeset,                 /* Size of buffer pChangeset in bytes */\n  void *pChangeset                /* Pointer to buffer containing changeset */\n){\n  sqlite3_changeset_iter *pRet;   /* Iterator to return */\n  int nByte;                      /* Number of bytes to allocate for iterator */\n\n  assert( xInput==0 || (pChangeset==0 && nChangeset==0) );\n\n  /* Zero the output variable in case an error occurs. */\n  *pp = 0;\n\n  /* Allocate and initialize the iterator structure. */\n  nByte = sizeof(sqlite3_changeset_iter);\n  pRet = (sqlite3_changeset_iter *)sqlite3_malloc(nByte);\n  if( !pRet ) return SQLITE_NOMEM;\n  memset(pRet, 0, sizeof(sqlite3_changeset_iter));\n  pRet->in.aData = (u8 *)pChangeset;\n  pRet->in.nData = nChangeset;\n  pRet->in.xInput = xInput;\n  pRet->in.pIn = pIn;\n  pRet->in.bEof = (xInput ? 0 : 1);\n\n  /* Populate the output variable and return success. */\n  *pp = pRet;\n  return SQLITE_OK;\n}\n\n/*\n** Create an iterator used to iterate through the contents of a changeset.\n*/\nSQLITE_API int sqlite3changeset_start(\n  sqlite3_changeset_iter **pp,    /* OUT: Changeset iterator handle */\n  int nChangeset,                 /* Size of buffer pChangeset in bytes */\n  void *pChangeset                /* Pointer to buffer containing changeset */\n){\n  return sessionChangesetStart(pp, 0, 0, nChangeset, pChangeset);\n}\n\n/*\n** Streaming version of sqlite3changeset_start().\n*/\nSQLITE_API int sqlite3changeset_start_strm(\n  sqlite3_changeset_iter **pp,    /* OUT: Changeset iterator handle */\n  int (*xInput)(void *pIn, void *pData, int *pnData),\n  void *pIn\n){\n  return sessionChangesetStart(pp, xInput, pIn, 0, 0);\n}\n\n/*\n** If the SessionInput object passed as the only argument is a streaming\n** object and the buffer is full, discard some data to free up space.\n*/\nstatic void sessionDiscardData(SessionInput *pIn){\n  if( pIn->bEof && pIn->xInput && pIn->iNext>=SESSIONS_STRM_CHUNK_SIZE ){\n    int nMove = pIn->buf.nBuf - pIn->iNext;\n    assert( nMove>=0 );\n    if( nMove>0 ){\n      memmove(pIn->buf.aBuf, &pIn->buf.aBuf[pIn->iNext], nMove);\n    }\n    pIn->buf.nBuf -= pIn->iNext;\n    pIn->iNext = 0;\n    pIn->nData = pIn->buf.nBuf;\n  }\n}\n\n/*\n** Ensure that there are at least nByte bytes available in the buffer. Or,\n** if there are not nByte bytes remaining in the input, that all available\n** data is in the buffer.\n**\n** Return an SQLite error code if an error occurs, or SQLITE_OK otherwise.\n*/\nstatic int sessionInputBuffer(SessionInput *pIn, int nByte){\n  int rc = SQLITE_OK;\n  if( pIn->xInput ){\n    while( !pIn->bEof && (pIn->iNext+nByte)>=pIn->nData && rc==SQLITE_OK ){\n      int nNew = SESSIONS_STRM_CHUNK_SIZE;\n\n      if( pIn->bNoDiscard==0 ) sessionDiscardData(pIn);\n      if( SQLITE_OK==sessionBufferGrow(&pIn->buf, nNew, &rc) ){\n        rc = pIn->xInput(pIn->pIn, &pIn->buf.aBuf[pIn->buf.nBuf], &nNew);\n        if( nNew==0 ){\n          pIn->bEof = 1;\n        }else{\n          pIn->buf.nBuf += nNew;\n        }\n      }\n\n      pIn->aData = pIn->buf.aBuf;\n      pIn->nData = pIn->buf.nBuf;\n    }\n  }\n  return rc;\n}\n\n/*\n** When this function is called, *ppRec points to the start of a record\n** that contains nCol values. This function advances the pointer *ppRec\n** until it points to the byte immediately following that record.\n*/\nstatic void sessionSkipRecord(\n  u8 **ppRec,                     /* IN/OUT: Record pointer */\n  int nCol                        /* Number of values in record */\n){\n  u8 *aRec = *ppRec;\n  int i;\n  for(i=0; i<nCol; i++){\n    int eType = *aRec++;\n    if( eType==SQLITE_TEXT || eType==SQLITE_BLOB ){\n      int nByte;\n      aRec += sessionVarintGet((u8*)aRec, &nByte);\n      aRec += nByte;\n    }else if( eType==SQLITE_INTEGER || eType==SQLITE_FLOAT ){\n      aRec += 8;\n    }\n  }\n\n  *ppRec = aRec;\n}\n\n/*\n** This function sets the value of the sqlite3_value object passed as the\n** first argument to a copy of the string or blob held in the aData[] \n** buffer. SQLITE_OK is returned if successful, or SQLITE_NOMEM if an OOM\n** error occurs.\n*/\nstatic int sessionValueSetStr(\n  sqlite3_value *pVal,            /* Set the value of this object */\n  u8 *aData,                      /* Buffer containing string or blob data */\n  int nData,                      /* Size of buffer aData[] in bytes */\n  u8 enc                          /* String encoding (0 for blobs) */\n){\n  /* In theory this code could just pass SQLITE_TRANSIENT as the final\n  ** argument to sqlite3ValueSetStr() and have the copy created \n  ** automatically. But doing so makes it difficult to detect any OOM\n  ** error. Hence the code to create the copy externally. */\n  u8 *aCopy = sqlite3_malloc(nData+1);\n  if( aCopy==0 ) return SQLITE_NOMEM;\n  memcpy(aCopy, aData, nData);\n  sqlite3ValueSetStr(pVal, nData, (char*)aCopy, enc, sqlite3_free);\n  return SQLITE_OK;\n}\n\n/*\n** Deserialize a single record from a buffer in memory. See \"RECORD FORMAT\"\n** for details.\n**\n** When this function is called, *paChange points to the start of the record\n** to deserialize. Assuming no error occurs, *paChange is set to point to\n** one byte after the end of the same record before this function returns.\n** If the argument abPK is NULL, then the record contains nCol values. Or,\n** if abPK is other than NULL, then the record contains only the PK fields\n** (in other words, it is a patchset DELETE record).\n**\n** If successful, each element of the apOut[] array (allocated by the caller)\n** is set to point to an sqlite3_value object containing the value read\n** from the corresponding position in the record. If that value is not\n** included in the record (i.e. because the record is part of an UPDATE change\n** and the field was not modified), the corresponding element of apOut[] is\n** set to NULL.\n**\n** It is the responsibility of the caller to free all sqlite_value structures\n** using sqlite3_free().\n**\n** If an error occurs, an SQLite error code (e.g. SQLITE_NOMEM) is returned.\n** The apOut[] array may have been partially populated in this case.\n*/\nstatic int sessionReadRecord(\n  SessionInput *pIn,              /* Input data */\n  int nCol,                       /* Number of values in record */\n  u8 *abPK,                       /* Array of primary key flags, or NULL */\n  sqlite3_value **apOut           /* Write values to this array */\n){\n  int i;                          /* Used to iterate through columns */\n  int rc = SQLITE_OK;\n\n  for(i=0; i<nCol && rc==SQLITE_OK; i++){\n    int eType = 0;                /* Type of value (SQLITE_NULL, TEXT etc.) */\n    if( abPK && abPK[i]==0 ) continue;\n    rc = sessionInputBuffer(pIn, 9);\n    if( rc==SQLITE_OK ){\n      eType = pIn->aData[pIn->iNext++];\n    }\n\n    assert( apOut[i]==0 );\n    if( eType ){\n      apOut[i] = sqlite3ValueNew(0);\n      if( !apOut[i] ) rc = SQLITE_NOMEM;\n    }\n\n    if( rc==SQLITE_OK ){\n      u8 *aVal = &pIn->aData[pIn->iNext];\n      if( eType==SQLITE_TEXT || eType==SQLITE_BLOB ){\n        int nByte;\n        pIn->iNext += sessionVarintGet(aVal, &nByte);\n        rc = sessionInputBuffer(pIn, nByte);\n        if( rc==SQLITE_OK ){\n          u8 enc = (eType==SQLITE_TEXT ? SQLITE_UTF8 : 0);\n          rc = sessionValueSetStr(apOut[i],&pIn->aData[pIn->iNext],nByte,enc);\n        }\n        pIn->iNext += nByte;\n      }\n      if( eType==SQLITE_INTEGER || eType==SQLITE_FLOAT ){\n        sqlite3_int64 v = sessionGetI64(aVal);\n        if( eType==SQLITE_INTEGER ){\n          sqlite3VdbeMemSetInt64(apOut[i], v);\n        }else{\n          double d;\n          memcpy(&d, &v, 8);\n          sqlite3VdbeMemSetDouble(apOut[i], d);\n        }\n        pIn->iNext += 8;\n      }\n    }\n  }\n\n  return rc;\n}\n\n/*\n** The input pointer currently points to the second byte of a table-header.\n** Specifically, to the following:\n**\n**   + number of columns in table (varint)\n**   + array of PK flags (1 byte per column),\n**   + table name (nul terminated).\n**\n** This function ensures that all of the above is present in the input \n** buffer (i.e. that it can be accessed without any calls to xInput()).\n** If successful, SQLITE_OK is returned. Otherwise, an SQLite error code.\n** The input pointer is not moved.\n*/\nstatic int sessionChangesetBufferTblhdr(SessionInput *pIn, int *pnByte){\n  int rc = SQLITE_OK;\n  int nCol = 0;\n  int nRead = 0;\n\n  rc = sessionInputBuffer(pIn, 9);\n  if( rc==SQLITE_OK ){\n    nRead += sessionVarintGet(&pIn->aData[pIn->iNext + nRead], &nCol);\n    rc = sessionInputBuffer(pIn, nRead+nCol+100);\n    nRead += nCol;\n  }\n\n  while( rc==SQLITE_OK ){\n    while( (pIn->iNext + nRead)<pIn->nData && pIn->aData[pIn->iNext + nRead] ){\n      nRead++;\n    }\n    if( (pIn->iNext + nRead)<pIn->nData ) break;\n    rc = sessionInputBuffer(pIn, nRead + 100);\n  }\n  *pnByte = nRead+1;\n  return rc;\n}\n\n/*\n** The input pointer currently points to the first byte of the first field\n** of a record consisting of nCol columns. This function ensures the entire\n** record is buffered. It does not move the input pointer.\n**\n** If successful, SQLITE_OK is returned and *pnByte is set to the size of\n** the record in bytes. Otherwise, an SQLite error code is returned. The\n** final value of *pnByte is undefined in this case.\n*/\nstatic int sessionChangesetBufferRecord(\n  SessionInput *pIn,              /* Input data */\n  int nCol,                       /* Number of columns in record */\n  int *pnByte                     /* OUT: Size of record in bytes */\n){\n  int rc = SQLITE_OK;\n  int nByte = 0;\n  int i;\n  for(i=0; rc==SQLITE_OK && i<nCol; i++){\n    int eType;\n    rc = sessionInputBuffer(pIn, nByte + 10);\n    if( rc==SQLITE_OK ){\n      eType = pIn->aData[pIn->iNext + nByte++];\n      if( eType==SQLITE_TEXT || eType==SQLITE_BLOB ){\n        int n;\n        nByte += sessionVarintGet(&pIn->aData[pIn->iNext+nByte], &n);\n        nByte += n;\n        rc = sessionInputBuffer(pIn, nByte);\n      }else if( eType==SQLITE_INTEGER || eType==SQLITE_FLOAT ){\n        nByte += 8;\n      }\n    }\n  }\n  *pnByte = nByte;\n  return rc;\n}\n\n/*\n** The input pointer currently points to the second byte of a table-header.\n** Specifically, to the following:\n**\n**   + number of columns in table (varint)\n**   + array of PK flags (1 byte per column),\n**   + table name (nul terminated).\n**\n** This function decodes the table-header and populates the p->nCol, \n** p->zTab and p->abPK[] variables accordingly. The p->apValue[] array is \n** also allocated or resized according to the new value of p->nCol. The\n** input pointer is left pointing to the byte following the table header.\n**\n** If successful, SQLITE_OK is returned. Otherwise, an SQLite error code\n** is returned and the final values of the various fields enumerated above\n** are undefined.\n*/\nstatic int sessionChangesetReadTblhdr(sqlite3_changeset_iter *p){\n  int rc;\n  int nCopy;\n  assert( p->rc==SQLITE_OK );\n\n  rc = sessionChangesetBufferTblhdr(&p->in, &nCopy);\n  if( rc==SQLITE_OK ){\n    int nByte;\n    int nVarint;\n    nVarint = sessionVarintGet(&p->in.aData[p->in.iNext], &p->nCol);\n    nCopy -= nVarint;\n    p->in.iNext += nVarint;\n    nByte = p->nCol * sizeof(sqlite3_value*) * 2 + nCopy;\n    p->tblhdr.nBuf = 0;\n    sessionBufferGrow(&p->tblhdr, nByte, &rc);\n  }\n\n  if( rc==SQLITE_OK ){\n    int iPK = sizeof(sqlite3_value*)*p->nCol*2;\n    memset(p->tblhdr.aBuf, 0, iPK);\n    memcpy(&p->tblhdr.aBuf[iPK], &p->in.aData[p->in.iNext], nCopy);\n    p->in.iNext += nCopy;\n  }\n\n  p->apValue = (sqlite3_value**)p->tblhdr.aBuf;\n  p->abPK = (u8*)&p->apValue[p->nCol*2];\n  p->zTab = (char*)&p->abPK[p->nCol];\n  return (p->rc = rc);\n}\n\n/*\n** Advance the changeset iterator to the next change.\n**\n** If both paRec and pnRec are NULL, then this function works like the public\n** API sqlite3changeset_next(). If SQLITE_ROW is returned, then the\n** sqlite3changeset_new() and old() APIs may be used to query for values.\n**\n** Otherwise, if paRec and pnRec are not NULL, then a pointer to the change\n** record is written to *paRec before returning and the number of bytes in\n** the record to *pnRec.\n**\n** Either way, this function returns SQLITE_ROW if the iterator is \n** successfully advanced to the next change in the changeset, an SQLite \n** error code if an error occurs, or SQLITE_DONE if there are no further \n** changes in the changeset.\n*/\nstatic int sessionChangesetNext(\n  sqlite3_changeset_iter *p,      /* Changeset iterator */\n  u8 **paRec,                     /* If non-NULL, store record pointer here */\n  int *pnRec                      /* If non-NULL, store size of record here */\n){\n  int i;\n  u8 op;\n\n  assert( (paRec==0 && pnRec==0) || (paRec && pnRec) );\n\n  /* If the iterator is in the error-state, return immediately. */\n  if( p->rc!=SQLITE_OK ) return p->rc;\n\n  /* Free the current contents of p->apValue[], if any. */\n  if( p->apValue ){\n    for(i=0; i<p->nCol*2; i++){\n      sqlite3ValueFree(p->apValue[i]);\n    }\n    memset(p->apValue, 0, sizeof(sqlite3_value*)*p->nCol*2);\n  }\n\n  /* Make sure the buffer contains at least 10 bytes of input data, or all\n  ** remaining data if there are less than 10 bytes available. This is\n  ** sufficient either for the 'T' or 'P' byte and the varint that follows\n  ** it, or for the two single byte values otherwise. */\n  p->rc = sessionInputBuffer(&p->in, 2);\n  if( p->rc!=SQLITE_OK ) return p->rc;\n\n  /* If the iterator is already at the end of the changeset, return DONE. */\n  if( p->in.iNext>=p->in.nData ){\n    return SQLITE_DONE;\n  }\n\n  sessionDiscardData(&p->in);\n  p->in.iCurrent = p->in.iNext;\n\n  op = p->in.aData[p->in.iNext++];\n  while( op=='T' || op=='P' ){\n    p->bPatchset = (op=='P');\n    if( sessionChangesetReadTblhdr(p) ) return p->rc;\n    if( (p->rc = sessionInputBuffer(&p->in, 2)) ) return p->rc;\n    p->in.iCurrent = p->in.iNext;\n    if( p->in.iNext>=p->in.nData ) return SQLITE_DONE;\n    op = p->in.aData[p->in.iNext++];\n  }\n\n  p->op = op;\n  p->bIndirect = p->in.aData[p->in.iNext++];\n  if( p->op!=SQLITE_UPDATE && p->op!=SQLITE_DELETE && p->op!=SQLITE_INSERT ){\n    return (p->rc = SQLITE_CORRUPT_BKPT);\n  }\n\n  if( paRec ){ \n    int nVal;                     /* Number of values to buffer */\n    if( p->bPatchset==0 && op==SQLITE_UPDATE ){\n      nVal = p->nCol * 2;\n    }else if( p->bPatchset && op==SQLITE_DELETE ){\n      nVal = 0;\n      for(i=0; i<p->nCol; i++) if( p->abPK[i] ) nVal++;\n    }else{\n      nVal = p->nCol;\n    }\n    p->rc = sessionChangesetBufferRecord(&p->in, nVal, pnRec);\n    if( p->rc!=SQLITE_OK ) return p->rc;\n    *paRec = &p->in.aData[p->in.iNext];\n    p->in.iNext += *pnRec;\n  }else{\n\n    /* If this is an UPDATE or DELETE, read the old.* record. */\n    if( p->op!=SQLITE_INSERT && (p->bPatchset==0 || p->op==SQLITE_DELETE) ){\n      u8 *abPK = p->bPatchset ? p->abPK : 0;\n      p->rc = sessionReadRecord(&p->in, p->nCol, abPK, p->apValue);\n      if( p->rc!=SQLITE_OK ) return p->rc;\n    }\n\n    /* If this is an INSERT or UPDATE, read the new.* record. */\n    if( p->op!=SQLITE_DELETE ){\n      p->rc = sessionReadRecord(&p->in, p->nCol, 0, &p->apValue[p->nCol]);\n      if( p->rc!=SQLITE_OK ) return p->rc;\n    }\n\n    if( p->bPatchset && p->op==SQLITE_UPDATE ){\n      /* If this is an UPDATE that is part of a patchset, then all PK and\n      ** modified fields are present in the new.* record. The old.* record\n      ** is currently completely empty. This block shifts the PK fields from\n      ** new.* to old.*, to accommodate the code that reads these arrays.  */\n      for(i=0; i<p->nCol; i++){\n        assert( p->apValue[i]==0 );\n        assert( p->abPK[i]==0 || p->apValue[i+p->nCol] );\n        if( p->abPK[i] ){\n          p->apValue[i] = p->apValue[i+p->nCol];\n          p->apValue[i+p->nCol] = 0;\n        }\n      }\n    }\n  }\n\n  return SQLITE_ROW;\n}\n\n/*\n** Advance an iterator created by sqlite3changeset_start() to the next\n** change in the changeset. This function may return SQLITE_ROW, SQLITE_DONE\n** or SQLITE_CORRUPT.\n**\n** This function may not be called on iterators passed to a conflict handler\n** callback by changeset_apply().\n*/\nSQLITE_API int sqlite3changeset_next(sqlite3_changeset_iter *p){\n  return sessionChangesetNext(p, 0, 0);\n}\n\n/*\n** The following function extracts information on the current change\n** from a changeset iterator. It may only be called after changeset_next()\n** has returned SQLITE_ROW.\n*/\nSQLITE_API int sqlite3changeset_op(\n  sqlite3_changeset_iter *pIter,  /* Iterator handle */\n  const char **pzTab,             /* OUT: Pointer to table name */\n  int *pnCol,                     /* OUT: Number of columns in table */\n  int *pOp,                       /* OUT: SQLITE_INSERT, DELETE or UPDATE */\n  int *pbIndirect                 /* OUT: True if change is indirect */\n){\n  *pOp = pIter->op;\n  *pnCol = pIter->nCol;\n  *pzTab = pIter->zTab;\n  if( pbIndirect ) *pbIndirect = pIter->bIndirect;\n  return SQLITE_OK;\n}\n\n/*\n** Return information regarding the PRIMARY KEY and number of columns in\n** the database table affected by the change that pIter currently points\n** to. This function may only be called after changeset_next() returns\n** SQLITE_ROW.\n*/\nSQLITE_API int sqlite3changeset_pk(\n  sqlite3_changeset_iter *pIter,  /* Iterator object */\n  unsigned char **pabPK,          /* OUT: Array of boolean - true for PK cols */\n  int *pnCol                      /* OUT: Number of entries in output array */\n){\n  *pabPK = pIter->abPK;\n  if( pnCol ) *pnCol = pIter->nCol;\n  return SQLITE_OK;\n}\n\n/*\n** This function may only be called while the iterator is pointing to an\n** SQLITE_UPDATE or SQLITE_DELETE change (see sqlite3changeset_op()).\n** Otherwise, SQLITE_MISUSE is returned.\n**\n** It sets *ppValue to point to an sqlite3_value structure containing the\n** iVal'th value in the old.* record. Or, if that particular value is not\n** included in the record (because the change is an UPDATE and the field\n** was not modified and is not a PK column), set *ppValue to NULL.\n**\n** If value iVal is out-of-range, SQLITE_RANGE is returned and *ppValue is\n** not modified. Otherwise, SQLITE_OK.\n*/\nSQLITE_API int sqlite3changeset_old(\n  sqlite3_changeset_iter *pIter,  /* Changeset iterator */\n  int iVal,                       /* Index of old.* value to retrieve */\n  sqlite3_value **ppValue         /* OUT: Old value (or NULL pointer) */\n){\n  if( pIter->op!=SQLITE_UPDATE && pIter->op!=SQLITE_DELETE ){\n    return SQLITE_MISUSE;\n  }\n  if( iVal<0 || iVal>=pIter->nCol ){\n    return SQLITE_RANGE;\n  }\n  *ppValue = pIter->apValue[iVal];\n  return SQLITE_OK;\n}\n\n/*\n** This function may only be called while the iterator is pointing to an\n** SQLITE_UPDATE or SQLITE_INSERT change (see sqlite3changeset_op()).\n** Otherwise, SQLITE_MISUSE is returned.\n**\n** It sets *ppValue to point to an sqlite3_value structure containing the\n** iVal'th value in the new.* record. Or, if that particular value is not\n** included in the record (because the change is an UPDATE and the field\n** was not modified), set *ppValue to NULL.\n**\n** If value iVal is out-of-range, SQLITE_RANGE is returned and *ppValue is\n** not modified. Otherwise, SQLITE_OK.\n*/\nSQLITE_API int sqlite3changeset_new(\n  sqlite3_changeset_iter *pIter,  /* Changeset iterator */\n  int iVal,                       /* Index of new.* value to retrieve */\n  sqlite3_value **ppValue         /* OUT: New value (or NULL pointer) */\n){\n  if( pIter->op!=SQLITE_UPDATE && pIter->op!=SQLITE_INSERT ){\n    return SQLITE_MISUSE;\n  }\n  if( iVal<0 || iVal>=pIter->nCol ){\n    return SQLITE_RANGE;\n  }\n  *ppValue = pIter->apValue[pIter->nCol+iVal];\n  return SQLITE_OK;\n}\n\n/*\n** The following two macros are used internally. They are similar to the\n** sqlite3changeset_new() and sqlite3changeset_old() functions, except that\n** they omit all error checking and return a pointer to the requested value.\n*/\n#define sessionChangesetNew(pIter, iVal) (pIter)->apValue[(pIter)->nCol+(iVal)]\n#define sessionChangesetOld(pIter, iVal) (pIter)->apValue[(iVal)]\n\n/*\n** This function may only be called with a changeset iterator that has been\n** passed to an SQLITE_CHANGESET_DATA or SQLITE_CHANGESET_CONFLICT \n** conflict-handler function. Otherwise, SQLITE_MISUSE is returned.\n**\n** If successful, *ppValue is set to point to an sqlite3_value structure\n** containing the iVal'th value of the conflicting record.\n**\n** If value iVal is out-of-range or some other error occurs, an SQLite error\n** code is returned. Otherwise, SQLITE_OK.\n*/\nSQLITE_API int sqlite3changeset_conflict(\n  sqlite3_changeset_iter *pIter,  /* Changeset iterator */\n  int iVal,                       /* Index of conflict record value to fetch */\n  sqlite3_value **ppValue         /* OUT: Value from conflicting row */\n){\n  if( !pIter->pConflict ){\n    return SQLITE_MISUSE;\n  }\n  if( iVal<0 || iVal>=pIter->nCol ){\n    return SQLITE_RANGE;\n  }\n  *ppValue = sqlite3_column_value(pIter->pConflict, iVal);\n  return SQLITE_OK;\n}\n\n/*\n** This function may only be called with an iterator passed to an\n** SQLITE_CHANGESET_FOREIGN_KEY conflict handler callback. In this case\n** it sets the output variable to the total number of known foreign key\n** violations in the destination database and returns SQLITE_OK.\n**\n** In all other cases this function returns SQLITE_MISUSE.\n*/\nSQLITE_API int sqlite3changeset_fk_conflicts(\n  sqlite3_changeset_iter *pIter,  /* Changeset iterator */\n  int *pnOut                      /* OUT: Number of FK violations */\n){\n  if( pIter->pConflict || pIter->apValue ){\n    return SQLITE_MISUSE;\n  }\n  *pnOut = pIter->nCol;\n  return SQLITE_OK;\n}\n\n\n/*\n** Finalize an iterator allocated with sqlite3changeset_start().\n**\n** This function may not be called on iterators passed to a conflict handler\n** callback by changeset_apply().\n*/\nSQLITE_API int sqlite3changeset_finalize(sqlite3_changeset_iter *p){\n  int rc = SQLITE_OK;\n  if( p ){\n    int i;                        /* Used to iterate through p->apValue[] */\n    rc = p->rc;\n    if( p->apValue ){\n      for(i=0; i<p->nCol*2; i++) sqlite3ValueFree(p->apValue[i]);\n    }\n    sqlite3_free(p->tblhdr.aBuf);\n    sqlite3_free(p->in.buf.aBuf);\n    sqlite3_free(p);\n  }\n  return rc;\n}\n\nstatic int sessionChangesetInvert(\n  SessionInput *pInput,           /* Input changeset */\n  int (*xOutput)(void *pOut, const void *pData, int nData),\n  void *pOut,\n  int *pnInverted,                /* OUT: Number of bytes in output changeset */\n  void **ppInverted               /* OUT: Inverse of pChangeset */\n){\n  int rc = SQLITE_OK;             /* Return value */\n  SessionBuffer sOut;             /* Output buffer */\n  int nCol = 0;                   /* Number of cols in current table */\n  u8 *abPK = 0;                   /* PK array for current table */\n  sqlite3_value **apVal = 0;      /* Space for values for UPDATE inversion */\n  SessionBuffer sPK = {0, 0, 0};  /* PK array for current table */\n\n  /* Initialize the output buffer */\n  memset(&sOut, 0, sizeof(SessionBuffer));\n\n  /* Zero the output variables in case an error occurs. */\n  if( ppInverted ){\n    *ppInverted = 0;\n    *pnInverted = 0;\n  }\n\n  while( 1 ){\n    u8 eType;\n\n    /* Test for EOF. */\n    if( (rc = sessionInputBuffer(pInput, 2)) ) goto finished_invert;\n    if( pInput->iNext>=pInput->nData ) break;\n    eType = pInput->aData[pInput->iNext];\n\n    switch( eType ){\n      case 'T': {\n        /* A 'table' record consists of:\n        **\n        **   * A constant 'T' character,\n        **   * Number of columns in said table (a varint),\n        **   * An array of nCol bytes (sPK),\n        **   * A nul-terminated table name.\n        */\n        int nByte;\n        int nVar;\n        pInput->iNext++;\n        if( (rc = sessionChangesetBufferTblhdr(pInput, &nByte)) ){\n          goto finished_invert;\n        }\n        nVar = sessionVarintGet(&pInput->aData[pInput->iNext], &nCol);\n        sPK.nBuf = 0;\n        sessionAppendBlob(&sPK, &pInput->aData[pInput->iNext+nVar], nCol, &rc);\n        sessionAppendByte(&sOut, eType, &rc);\n        sessionAppendBlob(&sOut, &pInput->aData[pInput->iNext], nByte, &rc);\n        if( rc ) goto finished_invert;\n\n        pInput->iNext += nByte;\n        sqlite3_free(apVal);\n        apVal = 0;\n        abPK = sPK.aBuf;\n        break;\n      }\n\n      case SQLITE_INSERT:\n      case SQLITE_DELETE: {\n        int nByte;\n        int bIndirect = pInput->aData[pInput->iNext+1];\n        int eType2 = (eType==SQLITE_DELETE ? SQLITE_INSERT : SQLITE_DELETE);\n        pInput->iNext += 2;\n        assert( rc==SQLITE_OK );\n        rc = sessionChangesetBufferRecord(pInput, nCol, &nByte);\n        sessionAppendByte(&sOut, eType2, &rc);\n        sessionAppendByte(&sOut, bIndirect, &rc);\n        sessionAppendBlob(&sOut, &pInput->aData[pInput->iNext], nByte, &rc);\n        pInput->iNext += nByte;\n        if( rc ) goto finished_invert;\n        break;\n      }\n\n      case SQLITE_UPDATE: {\n        int iCol;\n\n        if( 0==apVal ){\n          apVal = (sqlite3_value **)sqlite3_malloc(sizeof(apVal[0])*nCol*2);\n          if( 0==apVal ){\n            rc = SQLITE_NOMEM;\n            goto finished_invert;\n          }\n          memset(apVal, 0, sizeof(apVal[0])*nCol*2);\n        }\n\n        /* Write the header for the new UPDATE change. Same as the original. */\n        sessionAppendByte(&sOut, eType, &rc);\n        sessionAppendByte(&sOut, pInput->aData[pInput->iNext+1], &rc);\n\n        /* Read the old.* and new.* records for the update change. */\n        pInput->iNext += 2;\n        rc = sessionReadRecord(pInput, nCol, 0, &apVal[0]);\n        if( rc==SQLITE_OK ){\n          rc = sessionReadRecord(pInput, nCol, 0, &apVal[nCol]);\n        }\n\n        /* Write the new old.* record. Consists of the PK columns from the\n        ** original old.* record, and the other values from the original\n        ** new.* record. */\n        for(iCol=0; iCol<nCol; iCol++){\n          sqlite3_value *pVal = apVal[iCol + (abPK[iCol] ? 0 : nCol)];\n          sessionAppendValue(&sOut, pVal, &rc);\n        }\n\n        /* Write the new new.* record. Consists of a copy of all values\n        ** from the original old.* record, except for the PK columns, which\n        ** are set to \"undefined\". */\n        for(iCol=0; iCol<nCol; iCol++){\n          sqlite3_value *pVal = (abPK[iCol] ? 0 : apVal[iCol]);\n          sessionAppendValue(&sOut, pVal, &rc);\n        }\n\n        for(iCol=0; iCol<nCol*2; iCol++){\n          sqlite3ValueFree(apVal[iCol]);\n        }\n        memset(apVal, 0, sizeof(apVal[0])*nCol*2);\n        if( rc!=SQLITE_OK ){\n          goto finished_invert;\n        }\n\n        break;\n      }\n\n      default:\n        rc = SQLITE_CORRUPT_BKPT;\n        goto finished_invert;\n    }\n\n    assert( rc==SQLITE_OK );\n    if( xOutput && sOut.nBuf>=SESSIONS_STRM_CHUNK_SIZE ){\n      rc = xOutput(pOut, sOut.aBuf, sOut.nBuf);\n      sOut.nBuf = 0;\n      if( rc!=SQLITE_OK ) goto finished_invert;\n    }\n  }\n\n  assert( rc==SQLITE_OK );\n  if( pnInverted ){\n    *pnInverted = sOut.nBuf;\n    *ppInverted = sOut.aBuf;\n    sOut.aBuf = 0;\n  }else if( sOut.nBuf>0 ){\n    rc = xOutput(pOut, sOut.aBuf, sOut.nBuf);\n  }\n\n finished_invert:\n  sqlite3_free(sOut.aBuf);\n  sqlite3_free(apVal);\n  sqlite3_free(sPK.aBuf);\n  return rc;\n}\n\n\n/*\n** Invert a changeset object.\n*/\nSQLITE_API int sqlite3changeset_invert(\n  int nChangeset,                 /* Number of bytes in input */\n  const void *pChangeset,         /* Input changeset */\n  int *pnInverted,                /* OUT: Number of bytes in output changeset */\n  void **ppInverted               /* OUT: Inverse of pChangeset */\n){\n  SessionInput sInput;\n\n  /* Set up the input stream */\n  memset(&sInput, 0, sizeof(SessionInput));\n  sInput.nData = nChangeset;\n  sInput.aData = (u8*)pChangeset;\n\n  return sessionChangesetInvert(&sInput, 0, 0, pnInverted, ppInverted);\n}\n\n/*\n** Streaming version of sqlite3changeset_invert().\n*/\nSQLITE_API int sqlite3changeset_invert_strm(\n  int (*xInput)(void *pIn, void *pData, int *pnData),\n  void *pIn,\n  int (*xOutput)(void *pOut, const void *pData, int nData),\n  void *pOut\n){\n  SessionInput sInput;\n  int rc;\n\n  /* Set up the input stream */\n  memset(&sInput, 0, sizeof(SessionInput));\n  sInput.xInput = xInput;\n  sInput.pIn = pIn;\n\n  rc = sessionChangesetInvert(&sInput, xOutput, pOut, 0, 0);\n  sqlite3_free(sInput.buf.aBuf);\n  return rc;\n}\n\ntypedef struct SessionApplyCtx SessionApplyCtx;\nstruct SessionApplyCtx {\n  sqlite3 *db;\n  sqlite3_stmt *pDelete;          /* DELETE statement */\n  sqlite3_stmt *pUpdate;          /* UPDATE statement */\n  sqlite3_stmt *pInsert;          /* INSERT statement */\n  sqlite3_stmt *pSelect;          /* SELECT statement */\n  int nCol;                       /* Size of azCol[] and abPK[] arrays */\n  const char **azCol;             /* Array of column names */\n  u8 *abPK;                       /* Boolean array - true if column is in PK */\n  int bStat1;                     /* True if table is sqlite_stat1 */\n  int bDeferConstraints;          /* True to defer constraints */\n  SessionBuffer constraints;      /* Deferred constraints are stored here */\n};\n\n/*\n** Formulate a statement to DELETE a row from database db. Assuming a table\n** structure like this:\n**\n**     CREATE TABLE x(a, b, c, d, PRIMARY KEY(a, c));\n**\n** The DELETE statement looks like this:\n**\n**     DELETE FROM x WHERE a = :1 AND c = :3 AND (:5 OR b IS :2 AND d IS :4)\n**\n** Variable :5 (nCol+1) is a boolean. It should be set to 0 if we require\n** matching b and d values, or 1 otherwise. The second case comes up if the\n** conflict handler is invoked with NOTFOUND and returns CHANGESET_REPLACE.\n**\n** If successful, SQLITE_OK is returned and SessionApplyCtx.pDelete is left\n** pointing to the prepared version of the SQL statement.\n*/\nstatic int sessionDeleteRow(\n  sqlite3 *db,                    /* Database handle */\n  const char *zTab,               /* Table name */\n  SessionApplyCtx *p              /* Session changeset-apply context */\n){\n  int i;\n  const char *zSep = \"\";\n  int rc = SQLITE_OK;\n  SessionBuffer buf = {0, 0, 0};\n  int nPk = 0;\n\n  sessionAppendStr(&buf, \"DELETE FROM \", &rc);\n  sessionAppendIdent(&buf, zTab, &rc);\n  sessionAppendStr(&buf, \" WHERE \", &rc);\n\n  for(i=0; i<p->nCol; i++){\n    if( p->abPK[i] ){\n      nPk++;\n      sessionAppendStr(&buf, zSep, &rc);\n      sessionAppendIdent(&buf, p->azCol[i], &rc);\n      sessionAppendStr(&buf, \" = ?\", &rc);\n      sessionAppendInteger(&buf, i+1, &rc);\n      zSep = \" AND \";\n    }\n  }\n\n  if( nPk<p->nCol ){\n    sessionAppendStr(&buf, \" AND (?\", &rc);\n    sessionAppendInteger(&buf, p->nCol+1, &rc);\n    sessionAppendStr(&buf, \" OR \", &rc);\n\n    zSep = \"\";\n    for(i=0; i<p->nCol; i++){\n      if( !p->abPK[i] ){\n        sessionAppendStr(&buf, zSep, &rc);\n        sessionAppendIdent(&buf, p->azCol[i], &rc);\n        sessionAppendStr(&buf, \" IS ?\", &rc);\n        sessionAppendInteger(&buf, i+1, &rc);\n        zSep = \"AND \";\n      }\n    }\n    sessionAppendStr(&buf, \")\", &rc);\n  }\n\n  if( rc==SQLITE_OK ){\n    rc = sqlite3_prepare_v2(db, (char *)buf.aBuf, buf.nBuf, &p->pDelete, 0);\n  }\n  sqlite3_free(buf.aBuf);\n\n  return rc;\n}\n\n/*\n** Formulate and prepare a statement to UPDATE a row from database db. \n** Assuming a table structure like this:\n**\n**     CREATE TABLE x(a, b, c, d, PRIMARY KEY(a, c));\n**\n** The UPDATE statement looks like this:\n**\n**     UPDATE x SET\n**     a = CASE WHEN ?2  THEN ?3  ELSE a END,\n**     b = CASE WHEN ?5  THEN ?6  ELSE b END,\n**     c = CASE WHEN ?8  THEN ?9  ELSE c END,\n**     d = CASE WHEN ?11 THEN ?12 ELSE d END\n**     WHERE a = ?1 AND c = ?7 AND (?13 OR \n**       (?5==0 OR b IS ?4) AND (?11==0 OR d IS ?10) AND\n**     )\n**\n** For each column in the table, there are three variables to bind:\n**\n**     ?(i*3+1)    The old.* value of the column, if any.\n**     ?(i*3+2)    A boolean flag indicating that the value is being modified.\n**     ?(i*3+3)    The new.* value of the column, if any.\n**\n** Also, a boolean flag that, if set to true, causes the statement to update\n** a row even if the non-PK values do not match. This is required if the\n** conflict-handler is invoked with CHANGESET_DATA and returns\n** CHANGESET_REPLACE. This is variable \"?(nCol*3+1)\".\n**\n** If successful, SQLITE_OK is returned and SessionApplyCtx.pUpdate is left\n** pointing to the prepared version of the SQL statement.\n*/\nstatic int sessionUpdateRow(\n  sqlite3 *db,                    /* Database handle */\n  const char *zTab,               /* Table name */\n  SessionApplyCtx *p              /* Session changeset-apply context */\n){\n  int rc = SQLITE_OK;\n  int i;\n  const char *zSep = \"\";\n  SessionBuffer buf = {0, 0, 0};\n\n  /* Append \"UPDATE tbl SET \" */\n  sessionAppendStr(&buf, \"UPDATE \", &rc);\n  sessionAppendIdent(&buf, zTab, &rc);\n  sessionAppendStr(&buf, \" SET \", &rc);\n\n  /* Append the assignments */\n  for(i=0; i<p->nCol; i++){\n    sessionAppendStr(&buf, zSep, &rc);\n    sessionAppendIdent(&buf, p->azCol[i], &rc);\n    sessionAppendStr(&buf, \" = CASE WHEN ?\", &rc);\n    sessionAppendInteger(&buf, i*3+2, &rc);\n    sessionAppendStr(&buf, \" THEN ?\", &rc);\n    sessionAppendInteger(&buf, i*3+3, &rc);\n    sessionAppendStr(&buf, \" ELSE \", &rc);\n    sessionAppendIdent(&buf, p->azCol[i], &rc);\n    sessionAppendStr(&buf, \" END\", &rc);\n    zSep = \", \";\n  }\n\n  /* Append the PK part of the WHERE clause */\n  sessionAppendStr(&buf, \" WHERE \", &rc);\n  for(i=0; i<p->nCol; i++){\n    if( p->abPK[i] ){\n      sessionAppendIdent(&buf, p->azCol[i], &rc);\n      sessionAppendStr(&buf, \" = ?\", &rc);\n      sessionAppendInteger(&buf, i*3+1, &rc);\n      sessionAppendStr(&buf, \" AND \", &rc);\n    }\n  }\n\n  /* Append the non-PK part of the WHERE clause */\n  sessionAppendStr(&buf, \" (?\", &rc);\n  sessionAppendInteger(&buf, p->nCol*3+1, &rc);\n  sessionAppendStr(&buf, \" OR 1\", &rc);\n  for(i=0; i<p->nCol; i++){\n    if( !p->abPK[i] ){\n      sessionAppendStr(&buf, \" AND (?\", &rc);\n      sessionAppendInteger(&buf, i*3+2, &rc);\n      sessionAppendStr(&buf, \"=0 OR \", &rc);\n      sessionAppendIdent(&buf, p->azCol[i], &rc);\n      sessionAppendStr(&buf, \" IS ?\", &rc);\n      sessionAppendInteger(&buf, i*3+1, &rc);\n      sessionAppendStr(&buf, \")\", &rc);\n    }\n  }\n  sessionAppendStr(&buf, \")\", &rc);\n\n  if( rc==SQLITE_OK ){\n    rc = sqlite3_prepare_v2(db, (char *)buf.aBuf, buf.nBuf, &p->pUpdate, 0);\n  }\n  sqlite3_free(buf.aBuf);\n\n  return rc;\n}\n\n\n/*\n** Formulate and prepare an SQL statement to query table zTab by primary\n** key. Assuming the following table structure:\n**\n**     CREATE TABLE x(a, b, c, d, PRIMARY KEY(a, c));\n**\n** The SELECT statement looks like this:\n**\n**     SELECT * FROM x WHERE a = ?1 AND c = ?3\n**\n** If successful, SQLITE_OK is returned and SessionApplyCtx.pSelect is left\n** pointing to the prepared version of the SQL statement.\n*/\nstatic int sessionSelectRow(\n  sqlite3 *db,                    /* Database handle */\n  const char *zTab,               /* Table name */\n  SessionApplyCtx *p              /* Session changeset-apply context */\n){\n  return sessionSelectStmt(\n      db, \"main\", zTab, p->nCol, p->azCol, p->abPK, &p->pSelect);\n}\n\n/*\n** Formulate and prepare an INSERT statement to add a record to table zTab.\n** For example:\n**\n**     INSERT INTO main.\"zTab\" VALUES(?1, ?2, ?3 ...);\n**\n** If successful, SQLITE_OK is returned and SessionApplyCtx.pInsert is left\n** pointing to the prepared version of the SQL statement.\n*/\nstatic int sessionInsertRow(\n  sqlite3 *db,                    /* Database handle */\n  const char *zTab,               /* Table name */\n  SessionApplyCtx *p              /* Session changeset-apply context */\n){\n  int rc = SQLITE_OK;\n  int i;\n  SessionBuffer buf = {0, 0, 0};\n\n  sessionAppendStr(&buf, \"INSERT INTO main.\", &rc);\n  sessionAppendIdent(&buf, zTab, &rc);\n  sessionAppendStr(&buf, \"(\", &rc);\n  for(i=0; i<p->nCol; i++){\n    if( i!=0 ) sessionAppendStr(&buf, \", \", &rc);\n    sessionAppendIdent(&buf, p->azCol[i], &rc);\n  }\n\n  sessionAppendStr(&buf, \") VALUES(?\", &rc);\n  for(i=1; i<p->nCol; i++){\n    sessionAppendStr(&buf, \", ?\", &rc);\n  }\n  sessionAppendStr(&buf, \")\", &rc);\n\n  if( rc==SQLITE_OK ){\n    rc = sqlite3_prepare_v2(db, (char *)buf.aBuf, buf.nBuf, &p->pInsert, 0);\n  }\n  sqlite3_free(buf.aBuf);\n  return rc;\n}\n\nstatic int sessionPrepare(sqlite3 *db, sqlite3_stmt **pp, const char *zSql){\n  return sqlite3_prepare_v2(db, zSql, -1, pp, 0);\n}\n\n/*\n** Prepare statements for applying changes to the sqlite_stat1 table.\n** These are similar to those created by sessionSelectRow(),\n** sessionInsertRow(), sessionUpdateRow() and sessionDeleteRow() for \n** other tables.\n*/\nstatic int sessionStat1Sql(sqlite3 *db, SessionApplyCtx *p){\n  int rc = sessionSelectRow(db, \"sqlite_stat1\", p);\n  if( rc==SQLITE_OK ){\n    rc = sessionPrepare(db, &p->pInsert,\n        \"INSERT INTO main.sqlite_stat1 VALUES(?1, \"\n        \"CASE WHEN length(?2)=0 AND typeof(?2)='blob' THEN NULL ELSE ?2 END, \"\n        \"?3)\"\n    );\n  }\n  if( rc==SQLITE_OK ){\n    rc = sessionPrepare(db, &p->pUpdate,\n        \"UPDATE main.sqlite_stat1 SET \"\n        \"tbl = CASE WHEN ?2 THEN ?3 ELSE tbl END, \"\n        \"idx = CASE WHEN ?5 THEN ?6 ELSE idx END, \"\n        \"stat = CASE WHEN ?8 THEN ?9 ELSE stat END  \"\n        \"WHERE tbl=?1 AND idx IS \"\n        \"CASE WHEN length(?4)=0 AND typeof(?4)='blob' THEN NULL ELSE ?4 END \"\n        \"AND (?10 OR ?8=0 OR stat IS ?7)\"\n    );\n  }\n  if( rc==SQLITE_OK ){\n    rc = sessionPrepare(db, &p->pDelete,\n        \"DELETE FROM main.sqlite_stat1 WHERE tbl=?1 AND idx IS \"\n        \"CASE WHEN length(?2)=0 AND typeof(?2)='blob' THEN NULL ELSE ?2 END \"\n        \"AND (?4 OR stat IS ?3)\"\n    );\n  }\n  assert( rc==SQLITE_OK );\n  return rc;\n}\n\n/*\n** A wrapper around sqlite3_bind_value() that detects an extra problem. \n** See comments in the body of this function for details.\n*/\nstatic int sessionBindValue(\n  sqlite3_stmt *pStmt,            /* Statement to bind value to */\n  int i,                          /* Parameter number to bind to */\n  sqlite3_value *pVal             /* Value to bind */\n){\n  int eType = sqlite3_value_type(pVal);\n  /* COVERAGE: The (pVal->z==0) branch is never true using current versions\n  ** of SQLite. If a malloc fails in an sqlite3_value_xxx() function, either\n  ** the (pVal->z) variable remains as it was or the type of the value is\n  ** set to SQLITE_NULL.  */\n  if( (eType==SQLITE_TEXT || eType==SQLITE_BLOB) && pVal->z==0 ){\n    /* This condition occurs when an earlier OOM in a call to\n    ** sqlite3_value_text() or sqlite3_value_blob() (perhaps from within\n    ** a conflict-handler) has zeroed the pVal->z pointer. Return NOMEM. */\n    return SQLITE_NOMEM;\n  }\n  return sqlite3_bind_value(pStmt, i, pVal);\n}\n\n/*\n** Iterator pIter must point to an SQLITE_INSERT entry. This function \n** transfers new.* values from the current iterator entry to statement\n** pStmt. The table being inserted into has nCol columns.\n**\n** New.* value $i from the iterator is bound to variable ($i+1) of \n** statement pStmt. If parameter abPK is NULL, all values from 0 to (nCol-1)\n** are transfered to the statement. Otherwise, if abPK is not NULL, it points\n** to an array nCol elements in size. In this case only those values for \n** which abPK[$i] is true are read from the iterator and bound to the \n** statement.\n**\n** An SQLite error code is returned if an error occurs. Otherwise, SQLITE_OK.\n*/\nstatic int sessionBindRow(\n  sqlite3_changeset_iter *pIter,  /* Iterator to read values from */\n  int(*xValue)(sqlite3_changeset_iter *, int, sqlite3_value **),\n  int nCol,                       /* Number of columns */\n  u8 *abPK,                       /* If not NULL, bind only if true */\n  sqlite3_stmt *pStmt             /* Bind values to this statement */\n){\n  int i;\n  int rc = SQLITE_OK;\n\n  /* Neither sqlite3changeset_old or sqlite3changeset_new can fail if the\n  ** argument iterator points to a suitable entry. Make sure that xValue \n  ** is one of these to guarantee that it is safe to ignore the return \n  ** in the code below. */\n  assert( xValue==sqlite3changeset_old || xValue==sqlite3changeset_new );\n\n  for(i=0; rc==SQLITE_OK && i<nCol; i++){\n    if( !abPK || abPK[i] ){\n      sqlite3_value *pVal;\n      (void)xValue(pIter, i, &pVal);\n      rc = sessionBindValue(pStmt, i+1, pVal);\n    }\n  }\n  return rc;\n}\n\n/*\n** SQL statement pSelect is as generated by the sessionSelectRow() function.\n** This function binds the primary key values from the change that changeset\n** iterator pIter points to to the SELECT and attempts to seek to the table\n** entry. If a row is found, the SELECT statement left pointing at the row \n** and SQLITE_ROW is returned. Otherwise, if no row is found and no error\n** has occured, the statement is reset and SQLITE_OK is returned. If an\n** error occurs, the statement is reset and an SQLite error code is returned.\n**\n** If this function returns SQLITE_ROW, the caller must eventually reset() \n** statement pSelect. If any other value is returned, the statement does\n** not require a reset().\n**\n** If the iterator currently points to an INSERT record, bind values from the\n** new.* record to the SELECT statement. Or, if it points to a DELETE or\n** UPDATE, bind values from the old.* record. \n*/\nstatic int sessionSeekToRow(\n  sqlite3 *db,                    /* Database handle */\n  sqlite3_changeset_iter *pIter,  /* Changeset iterator */\n  u8 *abPK,                       /* Primary key flags array */\n  sqlite3_stmt *pSelect           /* SELECT statement from sessionSelectRow() */\n){\n  int rc;                         /* Return code */\n  int nCol;                       /* Number of columns in table */\n  int op;                         /* Changset operation (SQLITE_UPDATE etc.) */\n  const char *zDummy;             /* Unused */\n\n  sqlite3changeset_op(pIter, &zDummy, &nCol, &op, 0);\n  rc = sessionBindRow(pIter, \n      op==SQLITE_INSERT ? sqlite3changeset_new : sqlite3changeset_old,\n      nCol, abPK, pSelect\n  );\n\n  if( rc==SQLITE_OK ){\n    rc = sqlite3_step(pSelect);\n    if( rc!=SQLITE_ROW ) rc = sqlite3_reset(pSelect);\n  }\n\n  return rc;\n}\n\n/*\n** Invoke the conflict handler for the change that the changeset iterator\n** currently points to.\n**\n** Argument eType must be either CHANGESET_DATA or CHANGESET_CONFLICT.\n** If argument pbReplace is NULL, then the type of conflict handler invoked\n** depends solely on eType, as follows:\n**\n**    eType value                 Value passed to xConflict\n**    -------------------------------------------------\n**    CHANGESET_DATA              CHANGESET_NOTFOUND\n**    CHANGESET_CONFLICT          CHANGESET_CONSTRAINT\n**\n** Or, if pbReplace is not NULL, then an attempt is made to find an existing\n** record with the same primary key as the record about to be deleted, updated\n** or inserted. If such a record can be found, it is available to the conflict\n** handler as the \"conflicting\" record. In this case the type of conflict\n** handler invoked is as follows:\n**\n**    eType value         PK Record found?   Value passed to xConflict\n**    ----------------------------------------------------------------\n**    CHANGESET_DATA      Yes                CHANGESET_DATA\n**    CHANGESET_DATA      No                 CHANGESET_NOTFOUND\n**    CHANGESET_CONFLICT  Yes                CHANGESET_CONFLICT\n**    CHANGESET_CONFLICT  No                 CHANGESET_CONSTRAINT\n**\n** If pbReplace is not NULL, and a record with a matching PK is found, and\n** the conflict handler function returns SQLITE_CHANGESET_REPLACE, *pbReplace\n** is set to non-zero before returning SQLITE_OK.\n**\n** If the conflict handler returns SQLITE_CHANGESET_ABORT, SQLITE_ABORT is\n** returned. Or, if the conflict handler returns an invalid value, \n** SQLITE_MISUSE. If the conflict handler returns SQLITE_CHANGESET_OMIT,\n** this function returns SQLITE_OK.\n*/\nstatic int sessionConflictHandler(\n  int eType,                      /* Either CHANGESET_DATA or CONFLICT */\n  SessionApplyCtx *p,             /* changeset_apply() context */\n  sqlite3_changeset_iter *pIter,  /* Changeset iterator */\n  int(*xConflict)(void *, int, sqlite3_changeset_iter*),\n  void *pCtx,                     /* First argument for conflict handler */\n  int *pbReplace                  /* OUT: Set to true if PK row is found */\n){\n  int res = 0;                    /* Value returned by conflict handler */\n  int rc;\n  int nCol;\n  int op;\n  const char *zDummy;\n\n  sqlite3changeset_op(pIter, &zDummy, &nCol, &op, 0);\n\n  assert( eType==SQLITE_CHANGESET_CONFLICT || eType==SQLITE_CHANGESET_DATA );\n  assert( SQLITE_CHANGESET_CONFLICT+1==SQLITE_CHANGESET_CONSTRAINT );\n  assert( SQLITE_CHANGESET_DATA+1==SQLITE_CHANGESET_NOTFOUND );\n\n  /* Bind the new.* PRIMARY KEY values to the SELECT statement. */\n  if( pbReplace ){\n    rc = sessionSeekToRow(p->db, pIter, p->abPK, p->pSelect);\n  }else{\n    rc = SQLITE_OK;\n  }\n\n  if( rc==SQLITE_ROW ){\n    /* There exists another row with the new.* primary key. */\n    pIter->pConflict = p->pSelect;\n    res = xConflict(pCtx, eType, pIter);\n    pIter->pConflict = 0;\n    rc = sqlite3_reset(p->pSelect);\n  }else if( rc==SQLITE_OK ){\n    if( p->bDeferConstraints && eType==SQLITE_CHANGESET_CONFLICT ){\n      /* Instead of invoking the conflict handler, append the change blob\n      ** to the SessionApplyCtx.constraints buffer. */\n      u8 *aBlob = &pIter->in.aData[pIter->in.iCurrent];\n      int nBlob = pIter->in.iNext - pIter->in.iCurrent;\n      sessionAppendBlob(&p->constraints, aBlob, nBlob, &rc);\n      res = SQLITE_CHANGESET_OMIT;\n    }else{\n      /* No other row with the new.* primary key. */\n      res = xConflict(pCtx, eType+1, pIter);\n      if( res==SQLITE_CHANGESET_REPLACE ) rc = SQLITE_MISUSE;\n    }\n  }\n\n  if( rc==SQLITE_OK ){\n    switch( res ){\n      case SQLITE_CHANGESET_REPLACE:\n        assert( pbReplace );\n        *pbReplace = 1;\n        break;\n\n      case SQLITE_CHANGESET_OMIT:\n        break;\n\n      case SQLITE_CHANGESET_ABORT:\n        rc = SQLITE_ABORT;\n        break;\n\n      default:\n        rc = SQLITE_MISUSE;\n        break;\n    }\n  }\n\n  return rc;\n}\n\n/*\n** Attempt to apply the change that the iterator passed as the first argument\n** currently points to to the database. If a conflict is encountered, invoke\n** the conflict handler callback.\n**\n** If argument pbRetry is NULL, then ignore any CHANGESET_DATA conflict. If\n** one is encountered, update or delete the row with the matching primary key\n** instead. Or, if pbRetry is not NULL and a CHANGESET_DATA conflict occurs,\n** invoke the conflict handler. If it returns CHANGESET_REPLACE, set *pbRetry\n** to true before returning. In this case the caller will invoke this function\n** again, this time with pbRetry set to NULL.\n**\n** If argument pbReplace is NULL and a CHANGESET_CONFLICT conflict is \n** encountered invoke the conflict handler with CHANGESET_CONSTRAINT instead.\n** Or, if pbReplace is not NULL, invoke it with CHANGESET_CONFLICT. If such\n** an invocation returns SQLITE_CHANGESET_REPLACE, set *pbReplace to true\n** before retrying. In this case the caller attempts to remove the conflicting\n** row before invoking this function again, this time with pbReplace set \n** to NULL.\n**\n** If any conflict handler returns SQLITE_CHANGESET_ABORT, this function\n** returns SQLITE_ABORT. Otherwise, if no error occurs, SQLITE_OK is \n** returned.\n*/\nstatic int sessionApplyOneOp(\n  sqlite3_changeset_iter *pIter,  /* Changeset iterator */\n  SessionApplyCtx *p,             /* changeset_apply() context */\n  int(*xConflict)(void *, int, sqlite3_changeset_iter *),\n  void *pCtx,                     /* First argument for the conflict handler */\n  int *pbReplace,                 /* OUT: True to remove PK row and retry */\n  int *pbRetry                    /* OUT: True to retry. */\n){\n  const char *zDummy;\n  int op;\n  int nCol;\n  int rc = SQLITE_OK;\n\n  assert( p->pDelete && p->pUpdate && p->pInsert && p->pSelect );\n  assert( p->azCol && p->abPK );\n  assert( !pbReplace || *pbReplace==0 );\n\n  sqlite3changeset_op(pIter, &zDummy, &nCol, &op, 0);\n\n  if( op==SQLITE_DELETE ){\n\n    /* Bind values to the DELETE statement. If conflict handling is required,\n    ** bind values for all columns and set bound variable (nCol+1) to true.\n    ** Or, if conflict handling is not required, bind just the PK column\n    ** values and, if it exists, set (nCol+1) to false. Conflict handling\n    ** is not required if:\n    **\n    **   * this is a patchset, or\n    **   * (pbRetry==0), or\n    **   * all columns of the table are PK columns (in this case there is\n    **     no (nCol+1) variable to bind to).\n    */\n    u8 *abPK = (pIter->bPatchset ? p->abPK : 0);\n    rc = sessionBindRow(pIter, sqlite3changeset_old, nCol, abPK, p->pDelete);\n    if( rc==SQLITE_OK && sqlite3_bind_parameter_count(p->pDelete)>nCol ){\n      rc = sqlite3_bind_int(p->pDelete, nCol+1, (pbRetry==0 || abPK));\n    }\n    if( rc!=SQLITE_OK ) return rc;\n\n    sqlite3_step(p->pDelete);\n    rc = sqlite3_reset(p->pDelete);\n    if( rc==SQLITE_OK && sqlite3_changes(p->db)==0 ){\n      rc = sessionConflictHandler(\n          SQLITE_CHANGESET_DATA, p, pIter, xConflict, pCtx, pbRetry\n      );\n    }else if( (rc&0xff)==SQLITE_CONSTRAINT ){\n      rc = sessionConflictHandler(\n          SQLITE_CHANGESET_CONFLICT, p, pIter, xConflict, pCtx, 0\n      );\n    }\n\n  }else if( op==SQLITE_UPDATE ){\n    int i;\n\n    /* Bind values to the UPDATE statement. */\n    for(i=0; rc==SQLITE_OK && i<nCol; i++){\n      sqlite3_value *pOld = sessionChangesetOld(pIter, i);\n      sqlite3_value *pNew = sessionChangesetNew(pIter, i);\n\n      sqlite3_bind_int(p->pUpdate, i*3+2, !!pNew);\n      if( pOld ){\n        rc = sessionBindValue(p->pUpdate, i*3+1, pOld);\n      }\n      if( rc==SQLITE_OK && pNew ){\n        rc = sessionBindValue(p->pUpdate, i*3+3, pNew);\n      }\n    }\n    if( rc==SQLITE_OK ){\n      sqlite3_bind_int(p->pUpdate, nCol*3+1, pbRetry==0 || pIter->bPatchset);\n    }\n    if( rc!=SQLITE_OK ) return rc;\n\n    /* Attempt the UPDATE. In the case of a NOTFOUND or DATA conflict,\n    ** the result will be SQLITE_OK with 0 rows modified. */\n    sqlite3_step(p->pUpdate);\n    rc = sqlite3_reset(p->pUpdate);\n\n    if( rc==SQLITE_OK && sqlite3_changes(p->db)==0 ){\n      /* A NOTFOUND or DATA error. Search the table to see if it contains\n      ** a row with a matching primary key. If so, this is a DATA conflict.\n      ** Otherwise, if there is no primary key match, it is a NOTFOUND. */\n\n      rc = sessionConflictHandler(\n          SQLITE_CHANGESET_DATA, p, pIter, xConflict, pCtx, pbRetry\n      );\n\n    }else if( (rc&0xff)==SQLITE_CONSTRAINT ){\n      /* This is always a CONSTRAINT conflict. */\n      rc = sessionConflictHandler(\n          SQLITE_CHANGESET_CONFLICT, p, pIter, xConflict, pCtx, 0\n      );\n    }\n\n  }else{\n    assert( op==SQLITE_INSERT );\n    if( p->bStat1 ){\n      /* Check if there is a conflicting row. For sqlite_stat1, this needs\n      ** to be done using a SELECT, as there is no PRIMARY KEY in the \n      ** database schema to throw an exception if a duplicate is inserted.  */\n      rc = sessionSeekToRow(p->db, pIter, p->abPK, p->pSelect);\n      if( rc==SQLITE_ROW ){\n        rc = SQLITE_CONSTRAINT;\n        sqlite3_reset(p->pSelect);\n      }\n    }\n\n    if( rc==SQLITE_OK ){\n      rc = sessionBindRow(pIter, sqlite3changeset_new, nCol, 0, p->pInsert);\n      if( rc!=SQLITE_OK ) return rc;\n\n      sqlite3_step(p->pInsert);\n      rc = sqlite3_reset(p->pInsert);\n    }\n\n    if( (rc&0xff)==SQLITE_CONSTRAINT ){\n      rc = sessionConflictHandler(\n          SQLITE_CHANGESET_CONFLICT, p, pIter, xConflict, pCtx, pbReplace\n      );\n    }\n  }\n\n  return rc;\n}\n\n/*\n** Attempt to apply the change that the iterator passed as the first argument\n** currently points to to the database. If a conflict is encountered, invoke\n** the conflict handler callback.\n**\n** The difference between this function and sessionApplyOne() is that this\n** function handles the case where the conflict-handler is invoked and \n** returns SQLITE_CHANGESET_REPLACE - indicating that the change should be\n** retried in some manner.\n*/\nstatic int sessionApplyOneWithRetry(\n  sqlite3 *db,                    /* Apply change to \"main\" db of this handle */\n  sqlite3_changeset_iter *pIter,  /* Changeset iterator to read change from */\n  SessionApplyCtx *pApply,        /* Apply context */\n  int(*xConflict)(void*, int, sqlite3_changeset_iter*),\n  void *pCtx                      /* First argument passed to xConflict */\n){\n  int bReplace = 0;\n  int bRetry = 0;\n  int rc;\n\n  rc = sessionApplyOneOp(pIter, pApply, xConflict, pCtx, &bReplace, &bRetry);\n  assert( rc==SQLITE_OK || (bRetry==0 && bReplace==0) );\n\n  /* If the bRetry flag is set, the change has not been applied due to an\n  ** SQLITE_CHANGESET_DATA problem (i.e. this is an UPDATE or DELETE and\n  ** a row with the correct PK is present in the db, but one or more other\n  ** fields do not contain the expected values) and the conflict handler \n  ** returned SQLITE_CHANGESET_REPLACE. In this case retry the operation,\n  ** but pass NULL as the final argument so that sessionApplyOneOp() ignores\n  ** the SQLITE_CHANGESET_DATA problem.  */\n  if( bRetry ){\n    assert( pIter->op==SQLITE_UPDATE || pIter->op==SQLITE_DELETE );\n    rc = sessionApplyOneOp(pIter, pApply, xConflict, pCtx, 0, 0);\n  }\n\n  /* If the bReplace flag is set, the change is an INSERT that has not\n  ** been performed because the database already contains a row with the\n  ** specified primary key and the conflict handler returned\n  ** SQLITE_CHANGESET_REPLACE. In this case remove the conflicting row\n  ** before reattempting the INSERT.  */\n  else if( bReplace ){\n    assert( pIter->op==SQLITE_INSERT );\n    rc = sqlite3_exec(db, \"SAVEPOINT replace_op\", 0, 0, 0);\n    if( rc==SQLITE_OK ){\n      rc = sessionBindRow(pIter, \n          sqlite3changeset_new, pApply->nCol, pApply->abPK, pApply->pDelete);\n      sqlite3_bind_int(pApply->pDelete, pApply->nCol+1, 1);\n    }\n    if( rc==SQLITE_OK ){\n      sqlite3_step(pApply->pDelete);\n      rc = sqlite3_reset(pApply->pDelete);\n    }\n    if( rc==SQLITE_OK ){\n      rc = sessionApplyOneOp(pIter, pApply, xConflict, pCtx, 0, 0);\n    }\n    if( rc==SQLITE_OK ){\n      rc = sqlite3_exec(db, \"RELEASE replace_op\", 0, 0, 0);\n    }\n  }\n\n  return rc;\n}\n\n/*\n** Retry the changes accumulated in the pApply->constraints buffer.\n*/\nstatic int sessionRetryConstraints(\n  sqlite3 *db, \n  int bPatchset,\n  const char *zTab,\n  SessionApplyCtx *pApply,\n  int(*xConflict)(void*, int, sqlite3_changeset_iter*),\n  void *pCtx                      /* First argument passed to xConflict */\n){\n  int rc = SQLITE_OK;\n\n  while( pApply->constraints.nBuf ){\n    sqlite3_changeset_iter *pIter2 = 0;\n    SessionBuffer cons = pApply->constraints;\n    memset(&pApply->constraints, 0, sizeof(SessionBuffer));\n\n    rc = sessionChangesetStart(&pIter2, 0, 0, cons.nBuf, cons.aBuf);\n    if( rc==SQLITE_OK ){\n      int nByte = 2*pApply->nCol*sizeof(sqlite3_value*);\n      int rc2;\n      pIter2->bPatchset = bPatchset;\n      pIter2->zTab = (char*)zTab;\n      pIter2->nCol = pApply->nCol;\n      pIter2->abPK = pApply->abPK;\n      sessionBufferGrow(&pIter2->tblhdr, nByte, &rc);\n      pIter2->apValue = (sqlite3_value**)pIter2->tblhdr.aBuf;\n      if( rc==SQLITE_OK ) memset(pIter2->apValue, 0, nByte);\n\n      while( rc==SQLITE_OK && SQLITE_ROW==sqlite3changeset_next(pIter2) ){\n        rc = sessionApplyOneWithRetry(db, pIter2, pApply, xConflict, pCtx);\n      }\n\n      rc2 = sqlite3changeset_finalize(pIter2);\n      if( rc==SQLITE_OK ) rc = rc2;\n    }\n    assert( pApply->bDeferConstraints || pApply->constraints.nBuf==0 );\n\n    sqlite3_free(cons.aBuf);\n    if( rc!=SQLITE_OK ) break;\n    if( pApply->constraints.nBuf>=cons.nBuf ){\n      /* No progress was made on the last round. */\n      pApply->bDeferConstraints = 0;\n    }\n  }\n\n  return rc;\n}\n\n/*\n** Argument pIter is a changeset iterator that has been initialized, but\n** not yet passed to sqlite3changeset_next(). This function applies the \n** changeset to the main database attached to handle \"db\". The supplied\n** conflict handler callback is invoked to resolve any conflicts encountered\n** while applying the change.\n*/\nstatic int sessionChangesetApply(\n  sqlite3 *db,                    /* Apply change to \"main\" db of this handle */\n  sqlite3_changeset_iter *pIter,  /* Changeset to apply */\n  int(*xFilter)(\n    void *pCtx,                   /* Copy of sixth arg to _apply() */\n    const char *zTab              /* Table name */\n  ),\n  int(*xConflict)(\n    void *pCtx,                   /* Copy of fifth arg to _apply() */\n    int eConflict,                /* DATA, MISSING, CONFLICT, CONSTRAINT */\n    sqlite3_changeset_iter *p     /* Handle describing change and conflict */\n  ),\n  void *pCtx                      /* First argument passed to xConflict */\n){\n  int schemaMismatch = 0;\n  int rc;                         /* Return code */\n  const char *zTab = 0;           /* Name of current table */\n  int nTab = 0;                   /* Result of sqlite3Strlen30(zTab) */\n  SessionApplyCtx sApply;         /* changeset_apply() context object */\n  int bPatchset;\n\n  assert( xConflict!=0 );\n\n  pIter->in.bNoDiscard = 1;\n  memset(&sApply, 0, sizeof(sApply));\n  sqlite3_mutex_enter(sqlite3_db_mutex(db));\n  rc = sqlite3_exec(db, \"SAVEPOINT changeset_apply\", 0, 0, 0);\n  if( rc==SQLITE_OK ){\n    rc = sqlite3_exec(db, \"PRAGMA defer_foreign_keys = 1\", 0, 0, 0);\n  }\n  while( rc==SQLITE_OK && SQLITE_ROW==sqlite3changeset_next(pIter) ){\n    int nCol;\n    int op;\n    const char *zNew;\n    \n    sqlite3changeset_op(pIter, &zNew, &nCol, &op, 0);\n\n    if( zTab==0 || sqlite3_strnicmp(zNew, zTab, nTab+1) ){\n      u8 *abPK;\n\n      rc = sessionRetryConstraints(\n          db, pIter->bPatchset, zTab, &sApply, xConflict, pCtx\n      );\n      if( rc!=SQLITE_OK ) break;\n\n      sqlite3_free((char*)sApply.azCol);  /* cast works around VC++ bug */\n      sqlite3_finalize(sApply.pDelete);\n      sqlite3_finalize(sApply.pUpdate); \n      sqlite3_finalize(sApply.pInsert);\n      sqlite3_finalize(sApply.pSelect);\n      memset(&sApply, 0, sizeof(sApply));\n      sApply.db = db;\n      sApply.bDeferConstraints = 1;\n\n      /* If an xFilter() callback was specified, invoke it now. If the \n      ** xFilter callback returns zero, skip this table. If it returns\n      ** non-zero, proceed. */\n      schemaMismatch = (xFilter && (0==xFilter(pCtx, zNew)));\n      if( schemaMismatch ){\n        zTab = sqlite3_mprintf(\"%s\", zNew);\n        if( zTab==0 ){\n          rc = SQLITE_NOMEM;\n          break;\n        }\n        nTab = (int)strlen(zTab);\n        sApply.azCol = (const char **)zTab;\n      }else{\n        int nMinCol = 0;\n        int i;\n\n        sqlite3changeset_pk(pIter, &abPK, 0);\n        rc = sessionTableInfo(\n            db, \"main\", zNew, &sApply.nCol, &zTab, &sApply.azCol, &sApply.abPK\n        );\n        if( rc!=SQLITE_OK ) break;\n        for(i=0; i<sApply.nCol; i++){\n          if( sApply.abPK[i] ) nMinCol = i+1;\n        }\n  \n        if( sApply.nCol==0 ){\n          schemaMismatch = 1;\n          sqlite3_log(SQLITE_SCHEMA, \n              \"sqlite3changeset_apply(): no such table: %s\", zTab\n          );\n        }\n        else if( sApply.nCol<nCol ){\n          schemaMismatch = 1;\n          sqlite3_log(SQLITE_SCHEMA, \n              \"sqlite3changeset_apply(): table %s has %d columns, \"\n              \"expected %d or more\", \n              zTab, sApply.nCol, nCol\n          );\n        }\n        else if( nCol<nMinCol || memcmp(sApply.abPK, abPK, nCol)!=0 ){\n          schemaMismatch = 1;\n          sqlite3_log(SQLITE_SCHEMA, \"sqlite3changeset_apply(): \"\n              \"primary key mismatch for table %s\", zTab\n          );\n        }\n        else{\n          sApply.nCol = nCol;\n          if( 0==sqlite3_stricmp(zTab, \"sqlite_stat1\") ){\n            if( (rc = sessionStat1Sql(db, &sApply) ) ){\n              break;\n            }\n            sApply.bStat1 = 1;\n          }else{\n            if((rc = sessionSelectRow(db, zTab, &sApply))\n                || (rc = sessionUpdateRow(db, zTab, &sApply))\n                || (rc = sessionDeleteRow(db, zTab, &sApply))\n                || (rc = sessionInsertRow(db, zTab, &sApply))\n              ){\n              break;\n            }\n            sApply.bStat1 = 0;\n          }\n        }\n        nTab = sqlite3Strlen30(zTab);\n      }\n    }\n\n    /* If there is a schema mismatch on the current table, proceed to the\n    ** next change. A log message has already been issued. */\n    if( schemaMismatch ) continue;\n\n    rc = sessionApplyOneWithRetry(db, pIter, &sApply, xConflict, pCtx);\n  }\n\n  bPatchset = pIter->bPatchset;\n  if( rc==SQLITE_OK ){\n    rc = sqlite3changeset_finalize(pIter);\n  }else{\n    sqlite3changeset_finalize(pIter);\n  }\n\n  if( rc==SQLITE_OK ){\n    rc = sessionRetryConstraints(db, bPatchset, zTab, &sApply, xConflict, pCtx);\n  }\n\n  if( rc==SQLITE_OK ){\n    int nFk, notUsed;\n    sqlite3_db_status(db, SQLITE_DBSTATUS_DEFERRED_FKS, &nFk, &notUsed, 0);\n    if( nFk!=0 ){\n      int res = SQLITE_CHANGESET_ABORT;\n      sqlite3_changeset_iter sIter;\n      memset(&sIter, 0, sizeof(sIter));\n      sIter.nCol = nFk;\n      res = xConflict(pCtx, SQLITE_CHANGESET_FOREIGN_KEY, &sIter);\n      if( res!=SQLITE_CHANGESET_OMIT ){\n        rc = SQLITE_CONSTRAINT;\n      }\n    }\n  }\n  sqlite3_exec(db, \"PRAGMA defer_foreign_keys = 0\", 0, 0, 0);\n\n  if( rc==SQLITE_OK ){\n    rc = sqlite3_exec(db, \"RELEASE changeset_apply\", 0, 0, 0);\n  }else{\n    sqlite3_exec(db, \"ROLLBACK TO changeset_apply\", 0, 0, 0);\n    sqlite3_exec(db, \"RELEASE changeset_apply\", 0, 0, 0);\n  }\n\n  sqlite3_finalize(sApply.pInsert);\n  sqlite3_finalize(sApply.pDelete);\n  sqlite3_finalize(sApply.pUpdate);\n  sqlite3_finalize(sApply.pSelect);\n  sqlite3_free((char*)sApply.azCol);  /* cast works around VC++ bug */\n  sqlite3_free((char*)sApply.constraints.aBuf);\n  sqlite3_mutex_leave(sqlite3_db_mutex(db));\n  return rc;\n}\n\n/*\n** Apply the changeset passed via pChangeset/nChangeset to the main database\n** attached to handle \"db\". Invoke the supplied conflict handler callback\n** to resolve any conflicts encountered while applying the change.\n*/\nSQLITE_API int sqlite3changeset_apply(\n  sqlite3 *db,                    /* Apply change to \"main\" db of this handle */\n  int nChangeset,                 /* Size of changeset in bytes */\n  void *pChangeset,               /* Changeset blob */\n  int(*xFilter)(\n    void *pCtx,                   /* Copy of sixth arg to _apply() */\n    const char *zTab              /* Table name */\n  ),\n  int(*xConflict)(\n    void *pCtx,                   /* Copy of fifth arg to _apply() */\n    int eConflict,                /* DATA, MISSING, CONFLICT, CONSTRAINT */\n    sqlite3_changeset_iter *p     /* Handle describing change and conflict */\n  ),\n  void *pCtx                      /* First argument passed to xConflict */\n){\n  sqlite3_changeset_iter *pIter;  /* Iterator to skip through changeset */  \n  int rc = sqlite3changeset_start(&pIter, nChangeset, pChangeset);\n  if( rc==SQLITE_OK ){\n    rc = sessionChangesetApply(db, pIter, xFilter, xConflict, pCtx);\n  }\n  return rc;\n}\n\n/*\n** Apply the changeset passed via xInput/pIn to the main database\n** attached to handle \"db\". Invoke the supplied conflict handler callback\n** to resolve any conflicts encountered while applying the change.\n*/\nSQLITE_API int sqlite3changeset_apply_strm(\n  sqlite3 *db,                    /* Apply change to \"main\" db of this handle */\n  int (*xInput)(void *pIn, void *pData, int *pnData), /* Input function */\n  void *pIn,                                          /* First arg for xInput */\n  int(*xFilter)(\n    void *pCtx,                   /* Copy of sixth arg to _apply() */\n    const char *zTab              /* Table name */\n  ),\n  int(*xConflict)(\n    void *pCtx,                   /* Copy of sixth arg to _apply() */\n    int eConflict,                /* DATA, MISSING, CONFLICT, CONSTRAINT */\n    sqlite3_changeset_iter *p     /* Handle describing change and conflict */\n  ),\n  void *pCtx                      /* First argument passed to xConflict */\n){\n  sqlite3_changeset_iter *pIter;  /* Iterator to skip through changeset */  \n  int rc = sqlite3changeset_start_strm(&pIter, xInput, pIn);\n  if( rc==SQLITE_OK ){\n    rc = sessionChangesetApply(db, pIter, xFilter, xConflict, pCtx);\n  }\n  return rc;\n}\n\n/*\n** sqlite3_changegroup handle.\n*/\nstruct sqlite3_changegroup {\n  int rc;                         /* Error code */\n  int bPatch;                     /* True to accumulate patchsets */\n  SessionTable *pList;            /* List of tables in current patch */\n};\n\n/*\n** This function is called to merge two changes to the same row together as\n** part of an sqlite3changeset_concat() operation. A new change object is\n** allocated and a pointer to it stored in *ppNew.\n*/\nstatic int sessionChangeMerge(\n  SessionTable *pTab,             /* Table structure */\n  int bPatchset,                  /* True for patchsets */\n  SessionChange *pExist,          /* Existing change */\n  int op2,                        /* Second change operation */\n  int bIndirect,                  /* True if second change is indirect */\n  u8 *aRec,                       /* Second change record */\n  int nRec,                       /* Number of bytes in aRec */\n  SessionChange **ppNew           /* OUT: Merged change */\n){\n  SessionChange *pNew = 0;\n\n  if( !pExist ){\n    pNew = (SessionChange *)sqlite3_malloc(sizeof(SessionChange) + nRec);\n    if( !pNew ){\n      return SQLITE_NOMEM;\n    }\n    memset(pNew, 0, sizeof(SessionChange));\n    pNew->op = op2;\n    pNew->bIndirect = bIndirect;\n    pNew->nRecord = nRec;\n    pNew->aRecord = (u8*)&pNew[1];\n    memcpy(pNew->aRecord, aRec, nRec);\n  }else{\n    int op1 = pExist->op;\n\n    /* \n    **   op1=INSERT, op2=INSERT      ->      Unsupported. Discard op2.\n    **   op1=INSERT, op2=UPDATE      ->      INSERT.\n    **   op1=INSERT, op2=DELETE      ->      (none)\n    **\n    **   op1=UPDATE, op2=INSERT      ->      Unsupported. Discard op2.\n    **   op1=UPDATE, op2=UPDATE      ->      UPDATE.\n    **   op1=UPDATE, op2=DELETE      ->      DELETE.\n    **\n    **   op1=DELETE, op2=INSERT      ->      UPDATE.\n    **   op1=DELETE, op2=UPDATE      ->      Unsupported. Discard op2.\n    **   op1=DELETE, op2=DELETE      ->      Unsupported. Discard op2.\n    */   \n    if( (op1==SQLITE_INSERT && op2==SQLITE_INSERT)\n     || (op1==SQLITE_UPDATE && op2==SQLITE_INSERT)\n     || (op1==SQLITE_DELETE && op2==SQLITE_UPDATE)\n     || (op1==SQLITE_DELETE && op2==SQLITE_DELETE)\n    ){\n      pNew = pExist;\n    }else if( op1==SQLITE_INSERT && op2==SQLITE_DELETE ){\n      sqlite3_free(pExist);\n      assert( pNew==0 );\n    }else{\n      u8 *aExist = pExist->aRecord;\n      int nByte;\n      u8 *aCsr;\n\n      /* Allocate a new SessionChange object. Ensure that the aRecord[]\n      ** buffer of the new object is large enough to hold any record that\n      ** may be generated by combining the input records.  */\n      nByte = sizeof(SessionChange) + pExist->nRecord + nRec;\n      pNew = (SessionChange *)sqlite3_malloc(nByte);\n      if( !pNew ){\n        sqlite3_free(pExist);\n        return SQLITE_NOMEM;\n      }\n      memset(pNew, 0, sizeof(SessionChange));\n      pNew->bIndirect = (bIndirect && pExist->bIndirect);\n      aCsr = pNew->aRecord = (u8 *)&pNew[1];\n\n      if( op1==SQLITE_INSERT ){             /* INSERT + UPDATE */\n        u8 *a1 = aRec;\n        assert( op2==SQLITE_UPDATE );\n        pNew->op = SQLITE_INSERT;\n        if( bPatchset==0 ) sessionSkipRecord(&a1, pTab->nCol);\n        sessionMergeRecord(&aCsr, pTab->nCol, aExist, a1);\n      }else if( op1==SQLITE_DELETE ){       /* DELETE + INSERT */\n        assert( op2==SQLITE_INSERT );\n        pNew->op = SQLITE_UPDATE;\n        if( bPatchset ){\n          memcpy(aCsr, aRec, nRec);\n          aCsr += nRec;\n        }else{\n          if( 0==sessionMergeUpdate(&aCsr, pTab, bPatchset, aExist, 0,aRec,0) ){\n            sqlite3_free(pNew);\n            pNew = 0;\n          }\n        }\n      }else if( op2==SQLITE_UPDATE ){       /* UPDATE + UPDATE */\n        u8 *a1 = aExist;\n        u8 *a2 = aRec;\n        assert( op1==SQLITE_UPDATE );\n        if( bPatchset==0 ){\n          sessionSkipRecord(&a1, pTab->nCol);\n          sessionSkipRecord(&a2, pTab->nCol);\n        }\n        pNew->op = SQLITE_UPDATE;\n        if( 0==sessionMergeUpdate(&aCsr, pTab, bPatchset, aRec, aExist,a1,a2) ){\n          sqlite3_free(pNew);\n          pNew = 0;\n        }\n      }else{                                /* UPDATE + DELETE */\n        assert( op1==SQLITE_UPDATE && op2==SQLITE_DELETE );\n        pNew->op = SQLITE_DELETE;\n        if( bPatchset ){\n          memcpy(aCsr, aRec, nRec);\n          aCsr += nRec;\n        }else{\n          sessionMergeRecord(&aCsr, pTab->nCol, aRec, aExist);\n        }\n      }\n\n      if( pNew ){\n        pNew->nRecord = (int)(aCsr - pNew->aRecord);\n      }\n      sqlite3_free(pExist);\n    }\n  }\n\n  *ppNew = pNew;\n  return SQLITE_OK;\n}\n\n/*\n** Add all changes in the changeset traversed by the iterator passed as\n** the first argument to the changegroup hash tables.\n*/\nstatic int sessionChangesetToHash(\n  sqlite3_changeset_iter *pIter,   /* Iterator to read from */\n  sqlite3_changegroup *pGrp        /* Changegroup object to add changeset to */\n){\n  u8 *aRec;\n  int nRec;\n  int rc = SQLITE_OK;\n  SessionTable *pTab = 0;\n\n\n  while( SQLITE_ROW==sessionChangesetNext(pIter, &aRec, &nRec) ){\n    const char *zNew;\n    int nCol;\n    int op;\n    int iHash;\n    int bIndirect;\n    SessionChange *pChange;\n    SessionChange *pExist = 0;\n    SessionChange **pp;\n\n    if( pGrp->pList==0 ){\n      pGrp->bPatch = pIter->bPatchset;\n    }else if( pIter->bPatchset!=pGrp->bPatch ){\n      rc = SQLITE_ERROR;\n      break;\n    }\n\n    sqlite3changeset_op(pIter, &zNew, &nCol, &op, &bIndirect);\n    if( !pTab || sqlite3_stricmp(zNew, pTab->zName) ){\n      /* Search the list for a matching table */\n      int nNew = (int)strlen(zNew);\n      u8 *abPK;\n\n      sqlite3changeset_pk(pIter, &abPK, 0);\n      for(pTab = pGrp->pList; pTab; pTab=pTab->pNext){\n        if( 0==sqlite3_strnicmp(pTab->zName, zNew, nNew+1) ) break;\n      }\n      if( !pTab ){\n        SessionTable **ppTab;\n\n        pTab = sqlite3_malloc(sizeof(SessionTable) + nCol + nNew+1);\n        if( !pTab ){\n          rc = SQLITE_NOMEM;\n          break;\n        }\n        memset(pTab, 0, sizeof(SessionTable));\n        pTab->nCol = nCol;\n        pTab->abPK = (u8*)&pTab[1];\n        memcpy(pTab->abPK, abPK, nCol);\n        pTab->zName = (char*)&pTab->abPK[nCol];\n        memcpy(pTab->zName, zNew, nNew+1);\n\n        /* The new object must be linked on to the end of the list, not\n        ** simply added to the start of it. This is to ensure that the\n        ** tables within the output of sqlite3changegroup_output() are in \n        ** the right order.  */\n        for(ppTab=&pGrp->pList; *ppTab; ppTab=&(*ppTab)->pNext);\n        *ppTab = pTab;\n      }else if( pTab->nCol!=nCol || memcmp(pTab->abPK, abPK, nCol) ){\n        rc = SQLITE_SCHEMA;\n        break;\n      }\n    }\n\n    if( sessionGrowHash(pIter->bPatchset, pTab) ){\n      rc = SQLITE_NOMEM;\n      break;\n    }\n    iHash = sessionChangeHash(\n        pTab, (pIter->bPatchset && op==SQLITE_DELETE), aRec, pTab->nChange\n    );\n\n    /* Search for existing entry. If found, remove it from the hash table. \n    ** Code below may link it back in.\n    */\n    for(pp=&pTab->apChange[iHash]; *pp; pp=&(*pp)->pNext){\n      int bPkOnly1 = 0;\n      int bPkOnly2 = 0;\n      if( pIter->bPatchset ){\n        bPkOnly1 = (*pp)->op==SQLITE_DELETE;\n        bPkOnly2 = op==SQLITE_DELETE;\n      }\n      if( sessionChangeEqual(pTab, bPkOnly1, (*pp)->aRecord, bPkOnly2, aRec) ){\n        pExist = *pp;\n        *pp = (*pp)->pNext;\n        pTab->nEntry--;\n        break;\n      }\n    }\n\n    rc = sessionChangeMerge(pTab, \n        pIter->bPatchset, pExist, op, bIndirect, aRec, nRec, &pChange\n    );\n    if( rc ) break;\n    if( pChange ){\n      pChange->pNext = pTab->apChange[iHash];\n      pTab->apChange[iHash] = pChange;\n      pTab->nEntry++;\n    }\n  }\n\n  if( rc==SQLITE_OK ) rc = pIter->rc;\n  return rc;\n}\n\n/*\n** Serialize a changeset (or patchset) based on all changesets (or patchsets)\n** added to the changegroup object passed as the first argument.\n**\n** If xOutput is not NULL, then the changeset/patchset is returned to the\n** user via one or more calls to xOutput, as with the other streaming\n** interfaces. \n**\n** Or, if xOutput is NULL, then (*ppOut) is populated with a pointer to a\n** buffer containing the output changeset before this function returns. In\n** this case (*pnOut) is set to the size of the output buffer in bytes. It\n** is the responsibility of the caller to free the output buffer using\n** sqlite3_free() when it is no longer required.\n**\n** If successful, SQLITE_OK is returned. Or, if an error occurs, an SQLite\n** error code. If an error occurs and xOutput is NULL, (*ppOut) and (*pnOut)\n** are both set to 0 before returning.\n*/\nstatic int sessionChangegroupOutput(\n  sqlite3_changegroup *pGrp,\n  int (*xOutput)(void *pOut, const void *pData, int nData),\n  void *pOut,\n  int *pnOut,\n  void **ppOut\n){\n  int rc = SQLITE_OK;\n  SessionBuffer buf = {0, 0, 0};\n  SessionTable *pTab;\n  assert( xOutput==0 || (ppOut==0 && pnOut==0) );\n\n  /* Create the serialized output changeset based on the contents of the\n  ** hash tables attached to the SessionTable objects in list p->pList. \n  */\n  for(pTab=pGrp->pList; rc==SQLITE_OK && pTab; pTab=pTab->pNext){\n    int i;\n    if( pTab->nEntry==0 ) continue;\n\n    sessionAppendTableHdr(&buf, pGrp->bPatch, pTab, &rc);\n    for(i=0; i<pTab->nChange; i++){\n      SessionChange *p;\n      for(p=pTab->apChange[i]; p; p=p->pNext){\n        sessionAppendByte(&buf, p->op, &rc);\n        sessionAppendByte(&buf, p->bIndirect, &rc);\n        sessionAppendBlob(&buf, p->aRecord, p->nRecord, &rc);\n      }\n    }\n\n    if( rc==SQLITE_OK && xOutput && buf.nBuf>=SESSIONS_STRM_CHUNK_SIZE ){\n      rc = xOutput(pOut, buf.aBuf, buf.nBuf);\n      buf.nBuf = 0;\n    }\n  }\n\n  if( rc==SQLITE_OK ){\n    if( xOutput ){\n      if( buf.nBuf>0 ) rc = xOutput(pOut, buf.aBuf, buf.nBuf);\n    }else{\n      *ppOut = buf.aBuf;\n      *pnOut = buf.nBuf;\n      buf.aBuf = 0;\n    }\n  }\n  sqlite3_free(buf.aBuf);\n\n  return rc;\n}\n\n/*\n** Allocate a new, empty, sqlite3_changegroup.\n*/\nSQLITE_API int sqlite3changegroup_new(sqlite3_changegroup **pp){\n  int rc = SQLITE_OK;             /* Return code */\n  sqlite3_changegroup *p;         /* New object */\n  p = (sqlite3_changegroup*)sqlite3_malloc(sizeof(sqlite3_changegroup));\n  if( p==0 ){\n    rc = SQLITE_NOMEM;\n  }else{\n    memset(p, 0, sizeof(sqlite3_changegroup));\n  }\n  *pp = p;\n  return rc;\n}\n\n/*\n** Add the changeset currently stored in buffer pData, size nData bytes,\n** to changeset-group p.\n*/\nSQLITE_API int sqlite3changegroup_add(sqlite3_changegroup *pGrp, int nData, void *pData){\n  sqlite3_changeset_iter *pIter;  /* Iterator opened on pData/nData */\n  int rc;                         /* Return code */\n\n  rc = sqlite3changeset_start(&pIter, nData, pData);\n  if( rc==SQLITE_OK ){\n    rc = sessionChangesetToHash(pIter, pGrp);\n  }\n  sqlite3changeset_finalize(pIter);\n  return rc;\n}\n\n/*\n** Obtain a buffer containing a changeset representing the concatenation\n** of all changesets added to the group so far.\n*/\nSQLITE_API int sqlite3changegroup_output(\n    sqlite3_changegroup *pGrp,\n    int *pnData,\n    void **ppData\n){\n  return sessionChangegroupOutput(pGrp, 0, 0, pnData, ppData);\n}\n\n/*\n** Streaming versions of changegroup_add().\n*/\nSQLITE_API int sqlite3changegroup_add_strm(\n  sqlite3_changegroup *pGrp,\n  int (*xInput)(void *pIn, void *pData, int *pnData),\n  void *pIn\n){\n  sqlite3_changeset_iter *pIter;  /* Iterator opened on pData/nData */\n  int rc;                         /* Return code */\n\n  rc = sqlite3changeset_start_strm(&pIter, xInput, pIn);\n  if( rc==SQLITE_OK ){\n    rc = sessionChangesetToHash(pIter, pGrp);\n  }\n  sqlite3changeset_finalize(pIter);\n  return rc;\n}\n\n/*\n** Streaming versions of changegroup_output().\n*/\nSQLITE_API int sqlite3changegroup_output_strm(\n  sqlite3_changegroup *pGrp,\n  int (*xOutput)(void *pOut, const void *pData, int nData), \n  void *pOut\n){\n  return sessionChangegroupOutput(pGrp, xOutput, pOut, 0, 0);\n}\n\n/*\n** Delete a changegroup object.\n*/\nSQLITE_API void sqlite3changegroup_delete(sqlite3_changegroup *pGrp){\n  if( pGrp ){\n    sessionDeleteTable(pGrp->pList);\n    sqlite3_free(pGrp);\n  }\n}\n\n/* \n** Combine two changesets together.\n*/\nSQLITE_API int sqlite3changeset_concat(\n  int nLeft,                      /* Number of bytes in lhs input */\n  void *pLeft,                    /* Lhs input changeset */\n  int nRight                      /* Number of bytes in rhs input */,\n  void *pRight,                   /* Rhs input changeset */\n  int *pnOut,                     /* OUT: Number of bytes in output changeset */\n  void **ppOut                    /* OUT: changeset (left <concat> right) */\n){\n  sqlite3_changegroup *pGrp;\n  int rc;\n\n  rc = sqlite3changegroup_new(&pGrp);\n  if( rc==SQLITE_OK ){\n    rc = sqlite3changegroup_add(pGrp, nLeft, pLeft);\n  }\n  if( rc==SQLITE_OK ){\n    rc = sqlite3changegroup_add(pGrp, nRight, pRight);\n  }\n  if( rc==SQLITE_OK ){\n    rc = sqlite3changegroup_output(pGrp, pnOut, ppOut);\n  }\n  sqlite3changegroup_delete(pGrp);\n\n  return rc;\n}\n\n/*\n** Streaming version of sqlite3changeset_concat().\n*/\nSQLITE_API int sqlite3changeset_concat_strm(\n  int (*xInputA)(void *pIn, void *pData, int *pnData),\n  void *pInA,\n  int (*xInputB)(void *pIn, void *pData, int *pnData),\n  void *pInB,\n  int (*xOutput)(void *pOut, const void *pData, int nData),\n  void *pOut\n){\n  sqlite3_changegroup *pGrp;\n  int rc;\n\n  rc = sqlite3changegroup_new(&pGrp);\n  if( rc==SQLITE_OK ){\n    rc = sqlite3changegroup_add_strm(pGrp, xInputA, pInA);\n  }\n  if( rc==SQLITE_OK ){\n    rc = sqlite3changegroup_add_strm(pGrp, xInputB, pInB);\n  }\n  if( rc==SQLITE_OK ){\n    rc = sqlite3changegroup_output_strm(pGrp, xOutput, pOut);\n  }\n  sqlite3changegroup_delete(pGrp);\n\n  return rc;\n}\n\n#endif /* SQLITE_ENABLE_SESSION && SQLITE_ENABLE_PREUPDATE_HOOK */\n\n/************** End of sqlite3session.c **************************************/\n/************** Begin file json1.c *******************************************/\n/*\n** 2015-08-12\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n******************************************************************************\n**\n** This SQLite extension implements JSON functions.  The interface is\n** modeled after MySQL JSON functions:\n**\n**     https://dev.mysql.com/doc/refman/5.7/en/json.html\n**\n** For the time being, all JSON is stored as pure text.  (We might add\n** a JSONB type in the future which stores a binary encoding of JSON in\n** a BLOB, but there is no support for JSONB in the current implementation.\n** This implementation parses JSON text at 250 MB/s, so it is hard to see\n** how JSONB might improve on that.)\n*/\n#if !defined(SQLITE_CORE) || defined(SQLITE_ENABLE_JSON1)\n#if !defined(SQLITEINT_H)\n/* #include \"sqlite3ext.h\" */\n#endif\nSQLITE_EXTENSION_INIT1\n/* #include <assert.h> */\n/* #include <string.h> */\n/* #include <stdlib.h> */\n/* #include <stdarg.h> */\n\n/* Mark a function parameter as unused, to suppress nuisance compiler\n** warnings. */\n#ifndef UNUSED_PARAM\n# define UNUSED_PARAM(X)  (void)(X)\n#endif\n\n#ifndef LARGEST_INT64\n# define LARGEST_INT64  (0xffffffff|(((sqlite3_int64)0x7fffffff)<<32))\n# define SMALLEST_INT64 (((sqlite3_int64)-1) - LARGEST_INT64)\n#endif\n\n/*\n** Versions of isspace(), isalnum() and isdigit() to which it is safe\n** to pass signed char values.\n*/\n#ifdef sqlite3Isdigit\n   /* Use the SQLite core versions if this routine is part of the\n   ** SQLite amalgamation */\n#  define safe_isdigit(x)  sqlite3Isdigit(x)\n#  define safe_isalnum(x)  sqlite3Isalnum(x)\n#  define safe_isxdigit(x) sqlite3Isxdigit(x)\n#else\n   /* Use the standard library for separate compilation */\n#include <ctype.h>  /* amalgamator: keep */\n#  define safe_isdigit(x)  isdigit((unsigned char)(x))\n#  define safe_isalnum(x)  isalnum((unsigned char)(x))\n#  define safe_isxdigit(x) isxdigit((unsigned char)(x))\n#endif\n\n/*\n** Growing our own isspace() routine this way is twice as fast as\n** the library isspace() function, resulting in a 7% overall performance\n** increase for the parser.  (Ubuntu14.10 gcc 4.8.4 x64 with -Os).\n*/\nstatic const char jsonIsSpace[] = {\n  0, 0, 0, 0, 0, 0, 0, 0,     0, 1, 1, 0, 0, 1, 0, 0,\n  0, 0, 0, 0, 0, 0, 0, 0,     0, 0, 0, 0, 0, 0, 0, 0,\n  1, 0, 0, 0, 0, 0, 0, 0,     0, 0, 0, 0, 0, 0, 0, 0,\n  0, 0, 0, 0, 0, 0, 0, 0,     0, 0, 0, 0, 0, 0, 0, 0,\n  0, 0, 0, 0, 0, 0, 0, 0,     0, 0, 0, 0, 0, 0, 0, 0,\n  0, 0, 0, 0, 0, 0, 0, 0,     0, 0, 0, 0, 0, 0, 0, 0,\n  0, 0, 0, 0, 0, 0, 0, 0,     0, 0, 0, 0, 0, 0, 0, 0,\n  0, 0, 0, 0, 0, 0, 0, 0,     0, 0, 0, 0, 0, 0, 0, 0,\n  0, 0, 0, 0, 0, 0, 0, 0,     0, 0, 0, 0, 0, 0, 0, 0,\n  0, 0, 0, 0, 0, 0, 0, 0,     0, 0, 0, 0, 0, 0, 0, 0,\n  0, 0, 0, 0, 0, 0, 0, 0,     0, 0, 0, 0, 0, 0, 0, 0,\n  0, 0, 0, 0, 0, 0, 0, 0,     0, 0, 0, 0, 0, 0, 0, 0,\n  0, 0, 0, 0, 0, 0, 0, 0,     0, 0, 0, 0, 0, 0, 0, 0,\n  0, 0, 0, 0, 0, 0, 0, 0,     0, 0, 0, 0, 0, 0, 0, 0,\n  0, 0, 0, 0, 0, 0, 0, 0,     0, 0, 0, 0, 0, 0, 0, 0,\n  0, 0, 0, 0, 0, 0, 0, 0,     0, 0, 0, 0, 0, 0, 0, 0,\n};\n#define safe_isspace(x) (jsonIsSpace[(unsigned char)x])\n\n#ifndef SQLITE_AMALGAMATION\n  /* Unsigned integer types.  These are already defined in the sqliteInt.h,\n  ** but the definitions need to be repeated for separate compilation. */\n  typedef sqlite3_uint64 u64;\n  typedef unsigned int u32;\n  typedef unsigned short int u16;\n  typedef unsigned char u8;\n#endif\n\n/* Objects */\ntypedef struct JsonString JsonString;\ntypedef struct JsonNode JsonNode;\ntypedef struct JsonParse JsonParse;\n\n/* An instance of this object represents a JSON string\n** under construction.  Really, this is a generic string accumulator\n** that can be and is used to create strings other than JSON.\n*/\nstruct JsonString {\n  sqlite3_context *pCtx;   /* Function context - put error messages here */\n  char *zBuf;              /* Append JSON content here */\n  u64 nAlloc;              /* Bytes of storage available in zBuf[] */\n  u64 nUsed;               /* Bytes of zBuf[] currently used */\n  u8 bStatic;              /* True if zBuf is static space */\n  u8 bErr;                 /* True if an error has been encountered */\n  char zSpace[100];        /* Initial static space */\n};\n\n/* JSON type values\n*/\n#define JSON_NULL     0\n#define JSON_TRUE     1\n#define JSON_FALSE    2\n#define JSON_INT      3\n#define JSON_REAL     4\n#define JSON_STRING   5\n#define JSON_ARRAY    6\n#define JSON_OBJECT   7\n\n/* The \"subtype\" set for JSON values */\n#define JSON_SUBTYPE  74    /* Ascii for \"J\" */\n\n/*\n** Names of the various JSON types:\n*/\nstatic const char * const jsonType[] = {\n  \"null\", \"true\", \"false\", \"integer\", \"real\", \"text\", \"array\", \"object\"\n};\n\n/* Bit values for the JsonNode.jnFlag field\n*/\n#define JNODE_RAW     0x01         /* Content is raw, not JSON encoded */\n#define JNODE_ESCAPE  0x02         /* Content is text with \\ escapes */\n#define JNODE_REMOVE  0x04         /* Do not output */\n#define JNODE_REPLACE 0x08         /* Replace with JsonNode.u.iReplace */\n#define JNODE_PATCH   0x10         /* Patch with JsonNode.u.pPatch */\n#define JNODE_APPEND  0x20         /* More ARRAY/OBJECT entries at u.iAppend */\n#define JNODE_LABEL   0x40         /* Is a label of an object */\n\n\n/* A single node of parsed JSON\n*/\nstruct JsonNode {\n  u8 eType;              /* One of the JSON_ type values */\n  u8 jnFlags;            /* JNODE flags */\n  u32 n;                 /* Bytes of content, or number of sub-nodes */\n  union {\n    const char *zJContent; /* Content for INT, REAL, and STRING */\n    u32 iAppend;           /* More terms for ARRAY and OBJECT */\n    u32 iKey;              /* Key for ARRAY objects in json_tree() */\n    u32 iReplace;          /* Replacement content for JNODE_REPLACE */\n    JsonNode *pPatch;      /* Node chain of patch for JNODE_PATCH */\n  } u;\n};\n\n/* A completely parsed JSON string\n*/\nstruct JsonParse {\n  u32 nNode;         /* Number of slots of aNode[] used */\n  u32 nAlloc;        /* Number of slots of aNode[] allocated */\n  JsonNode *aNode;   /* Array of nodes containing the parse */\n  const char *zJson; /* Original JSON string */\n  u32 *aUp;          /* Index of parent of each node */\n  u8 oom;            /* Set to true if out of memory */\n  u8 nErr;           /* Number of errors seen */\n  u16 iDepth;        /* Nesting depth */\n  int nJson;         /* Length of the zJson string in bytes */\n};\n\n/*\n** Maximum nesting depth of JSON for this implementation.\n**\n** This limit is needed to avoid a stack overflow in the recursive\n** descent parser.  A depth of 2000 is far deeper than any sane JSON\n** should go.\n*/\n#define JSON_MAX_DEPTH  2000\n\n/**************************************************************************\n** Utility routines for dealing with JsonString objects\n**************************************************************************/\n\n/* Set the JsonString object to an empty string\n*/\nstatic void jsonZero(JsonString *p){\n  p->zBuf = p->zSpace;\n  p->nAlloc = sizeof(p->zSpace);\n  p->nUsed = 0;\n  p->bStatic = 1;\n}\n\n/* Initialize the JsonString object\n*/\nstatic void jsonInit(JsonString *p, sqlite3_context *pCtx){\n  p->pCtx = pCtx;\n  p->bErr = 0;\n  jsonZero(p);\n}\n\n\n/* Free all allocated memory and reset the JsonString object back to its\n** initial state.\n*/\nstatic void jsonReset(JsonString *p){\n  if( !p->bStatic ) sqlite3_free(p->zBuf);\n  jsonZero(p);\n}\n\n\n/* Report an out-of-memory (OOM) condition \n*/\nstatic void jsonOom(JsonString *p){\n  p->bErr = 1;\n  sqlite3_result_error_nomem(p->pCtx);\n  jsonReset(p);\n}\n\n/* Enlarge pJson->zBuf so that it can hold at least N more bytes.\n** Return zero on success.  Return non-zero on an OOM error\n*/\nstatic int jsonGrow(JsonString *p, u32 N){\n  u64 nTotal = N<p->nAlloc ? p->nAlloc*2 : p->nAlloc+N+10;\n  char *zNew;\n  if( p->bStatic ){\n    if( p->bErr ) return 1;\n    zNew = sqlite3_malloc64(nTotal);\n    if( zNew==0 ){\n      jsonOom(p);\n      return SQLITE_NOMEM;\n    }\n    memcpy(zNew, p->zBuf, (size_t)p->nUsed);\n    p->zBuf = zNew;\n    p->bStatic = 0;\n  }else{\n    zNew = sqlite3_realloc64(p->zBuf, nTotal);\n    if( zNew==0 ){\n      jsonOom(p);\n      return SQLITE_NOMEM;\n    }\n    p->zBuf = zNew;\n  }\n  p->nAlloc = nTotal;\n  return SQLITE_OK;\n}\n\n/* Append N bytes from zIn onto the end of the JsonString string.\n*/\nstatic void jsonAppendRaw(JsonString *p, const char *zIn, u32 N){\n  if( (N+p->nUsed >= p->nAlloc) && jsonGrow(p,N)!=0 ) return;\n  memcpy(p->zBuf+p->nUsed, zIn, N);\n  p->nUsed += N;\n}\n\n/* Append formatted text (not to exceed N bytes) to the JsonString.\n*/\nstatic void jsonPrintf(int N, JsonString *p, const char *zFormat, ...){\n  va_list ap;\n  if( (p->nUsed + N >= p->nAlloc) && jsonGrow(p, N) ) return;\n  va_start(ap, zFormat);\n  sqlite3_vsnprintf(N, p->zBuf+p->nUsed, zFormat, ap);\n  va_end(ap);\n  p->nUsed += (int)strlen(p->zBuf+p->nUsed);\n}\n\n/* Append a single character\n*/\nstatic void jsonAppendChar(JsonString *p, char c){\n  if( p->nUsed>=p->nAlloc && jsonGrow(p,1)!=0 ) return;\n  p->zBuf[p->nUsed++] = c;\n}\n\n/* Append a comma separator to the output buffer, if the previous\n** character is not '[' or '{'.\n*/\nstatic void jsonAppendSeparator(JsonString *p){\n  char c;\n  if( p->nUsed==0 ) return;\n  c = p->zBuf[p->nUsed-1];\n  if( c!='[' && c!='{' ) jsonAppendChar(p, ',');\n}\n\n/* Append the N-byte string in zIn to the end of the JsonString string\n** under construction.  Enclose the string in \"...\" and escape\n** any double-quotes or backslash characters contained within the\n** string.\n*/\nstatic void jsonAppendString(JsonString *p, const char *zIn, u32 N){\n  u32 i;\n  if( (N+p->nUsed+2 >= p->nAlloc) && jsonGrow(p,N+2)!=0 ) return;\n  p->zBuf[p->nUsed++] = '\"';\n  for(i=0; i<N; i++){\n    unsigned char c = ((unsigned const char*)zIn)[i];\n    if( c=='\"' || c=='\\\\' ){\n      json_simple_escape:\n      if( (p->nUsed+N+3-i > p->nAlloc) && jsonGrow(p,N+3-i)!=0 ) return;\n      p->zBuf[p->nUsed++] = '\\\\';\n    }else if( c<=0x1f ){\n      static const char aSpecial[] = {\n         0, 0, 0, 0, 0, 0, 0, 0, 'b', 't', 'n', 0, 'f', 'r', 0, 0,\n         0, 0, 0, 0, 0, 0, 0, 0,   0,   0,   0, 0,   0,   0, 0, 0\n      };\n      assert( sizeof(aSpecial)==32 );\n      assert( aSpecial['\\b']=='b' );\n      assert( aSpecial['\\f']=='f' );\n      assert( aSpecial['\\n']=='n' );\n      assert( aSpecial['\\r']=='r' );\n      assert( aSpecial['\\t']=='t' );\n      if( aSpecial[c] ){\n        c = aSpecial[c];\n        goto json_simple_escape;\n      }\n      if( (p->nUsed+N+7+i > p->nAlloc) && jsonGrow(p,N+7-i)!=0 ) return;\n      p->zBuf[p->nUsed++] = '\\\\';\n      p->zBuf[p->nUsed++] = 'u';\n      p->zBuf[p->nUsed++] = '0';\n      p->zBuf[p->nUsed++] = '0';\n      p->zBuf[p->nUsed++] = '0' + (c>>4);\n      c = \"0123456789abcdef\"[c&0xf];\n    }\n    p->zBuf[p->nUsed++] = c;\n  }\n  p->zBuf[p->nUsed++] = '\"';\n  assert( p->nUsed<p->nAlloc );\n}\n\n/*\n** Append a function parameter value to the JSON string under \n** construction.\n*/\nstatic void jsonAppendValue(\n  JsonString *p,                 /* Append to this JSON string */\n  sqlite3_value *pValue          /* Value to append */\n){\n  switch( sqlite3_value_type(pValue) ){\n    case SQLITE_NULL: {\n      jsonAppendRaw(p, \"null\", 4);\n      break;\n    }\n    case SQLITE_INTEGER:\n    case SQLITE_FLOAT: {\n      const char *z = (const char*)sqlite3_value_text(pValue);\n      u32 n = (u32)sqlite3_value_bytes(pValue);\n      jsonAppendRaw(p, z, n);\n      break;\n    }\n    case SQLITE_TEXT: {\n      const char *z = (const char*)sqlite3_value_text(pValue);\n      u32 n = (u32)sqlite3_value_bytes(pValue);\n      if( sqlite3_value_subtype(pValue)==JSON_SUBTYPE ){\n        jsonAppendRaw(p, z, n);\n      }else{\n        jsonAppendString(p, z, n);\n      }\n      break;\n    }\n    default: {\n      if( p->bErr==0 ){\n        sqlite3_result_error(p->pCtx, \"JSON cannot hold BLOB values\", -1);\n        p->bErr = 2;\n        jsonReset(p);\n      }\n      break;\n    }\n  }\n}\n\n\n/* Make the JSON in p the result of the SQL function.\n*/\nstatic void jsonResult(JsonString *p){\n  if( p->bErr==0 ){\n    sqlite3_result_text64(p->pCtx, p->zBuf, p->nUsed, \n                          p->bStatic ? SQLITE_TRANSIENT : sqlite3_free,\n                          SQLITE_UTF8);\n    jsonZero(p);\n  }\n  assert( p->bStatic );\n}\n\n/**************************************************************************\n** Utility routines for dealing with JsonNode and JsonParse objects\n**************************************************************************/\n\n/*\n** Return the number of consecutive JsonNode slots need to represent\n** the parsed JSON at pNode.  The minimum answer is 1.  For ARRAY and\n** OBJECT types, the number might be larger.\n**\n** Appended elements are not counted.  The value returned is the number\n** by which the JsonNode counter should increment in order to go to the\n** next peer value.\n*/\nstatic u32 jsonNodeSize(JsonNode *pNode){\n  return pNode->eType>=JSON_ARRAY ? pNode->n+1 : 1;\n}\n\n/*\n** Reclaim all memory allocated by a JsonParse object.  But do not\n** delete the JsonParse object itself.\n*/\nstatic void jsonParseReset(JsonParse *pParse){\n  sqlite3_free(pParse->aNode);\n  pParse->aNode = 0;\n  pParse->nNode = 0;\n  pParse->nAlloc = 0;\n  sqlite3_free(pParse->aUp);\n  pParse->aUp = 0;\n}\n\n/*\n** Free a JsonParse object that was obtained from sqlite3_malloc().\n*/\nstatic void jsonParseFree(JsonParse *pParse){\n  jsonParseReset(pParse);\n  sqlite3_free(pParse);\n}\n\n/*\n** Convert the JsonNode pNode into a pure JSON string and\n** append to pOut.  Subsubstructure is also included.  Return\n** the number of JsonNode objects that are encoded.\n*/\nstatic void jsonRenderNode(\n  JsonNode *pNode,               /* The node to render */\n  JsonString *pOut,              /* Write JSON here */\n  sqlite3_value **aReplace       /* Replacement values */\n){\n  if( pNode->jnFlags & (JNODE_REPLACE|JNODE_PATCH) ){\n    if( pNode->jnFlags & JNODE_REPLACE ){\n      jsonAppendValue(pOut, aReplace[pNode->u.iReplace]);\n      return;\n    }\n    pNode = pNode->u.pPatch;\n  }\n  switch( pNode->eType ){\n    default: {\n      assert( pNode->eType==JSON_NULL );\n      jsonAppendRaw(pOut, \"null\", 4);\n      break;\n    }\n    case JSON_TRUE: {\n      jsonAppendRaw(pOut, \"true\", 4);\n      break;\n    }\n    case JSON_FALSE: {\n      jsonAppendRaw(pOut, \"false\", 5);\n      break;\n    }\n    case JSON_STRING: {\n      if( pNode->jnFlags & JNODE_RAW ){\n        jsonAppendString(pOut, pNode->u.zJContent, pNode->n);\n        break;\n      }\n      /* Fall through into the next case */\n    }\n    case JSON_REAL:\n    case JSON_INT: {\n      jsonAppendRaw(pOut, pNode->u.zJContent, pNode->n);\n      break;\n    }\n    case JSON_ARRAY: {\n      u32 j = 1;\n      jsonAppendChar(pOut, '[');\n      for(;;){\n        while( j<=pNode->n ){\n          if( (pNode[j].jnFlags & JNODE_REMOVE)==0 ){\n            jsonAppendSeparator(pOut);\n            jsonRenderNode(&pNode[j], pOut, aReplace);\n          }\n          j += jsonNodeSize(&pNode[j]);\n        }\n        if( (pNode->jnFlags & JNODE_APPEND)==0 ) break;\n        pNode = &pNode[pNode->u.iAppend];\n        j = 1;\n      }\n      jsonAppendChar(pOut, ']');\n      break;\n    }\n    case JSON_OBJECT: {\n      u32 j = 1;\n      jsonAppendChar(pOut, '{');\n      for(;;){\n        while( j<=pNode->n ){\n          if( (pNode[j+1].jnFlags & JNODE_REMOVE)==0 ){\n            jsonAppendSeparator(pOut);\n            jsonRenderNode(&pNode[j], pOut, aReplace);\n            jsonAppendChar(pOut, ':');\n            jsonRenderNode(&pNode[j+1], pOut, aReplace);\n          }\n          j += 1 + jsonNodeSize(&pNode[j+1]);\n        }\n        if( (pNode->jnFlags & JNODE_APPEND)==0 ) break;\n        pNode = &pNode[pNode->u.iAppend];\n        j = 1;\n      }\n      jsonAppendChar(pOut, '}');\n      break;\n    }\n  }\n}\n\n/*\n** Return a JsonNode and all its descendents as a JSON string.\n*/\nstatic void jsonReturnJson(\n  JsonNode *pNode,            /* Node to return */\n  sqlite3_context *pCtx,      /* Return value for this function */\n  sqlite3_value **aReplace    /* Array of replacement values */\n){\n  JsonString s;\n  jsonInit(&s, pCtx);\n  jsonRenderNode(pNode, &s, aReplace);\n  jsonResult(&s);\n  sqlite3_result_subtype(pCtx, JSON_SUBTYPE);\n}\n\n/*\n** Make the JsonNode the return value of the function.\n*/\nstatic void jsonReturn(\n  JsonNode *pNode,            /* Node to return */\n  sqlite3_context *pCtx,      /* Return value for this function */\n  sqlite3_value **aReplace    /* Array of replacement values */\n){\n  switch( pNode->eType ){\n    default: {\n      assert( pNode->eType==JSON_NULL );\n      sqlite3_result_null(pCtx);\n      break;\n    }\n    case JSON_TRUE: {\n      sqlite3_result_int(pCtx, 1);\n      break;\n    }\n    case JSON_FALSE: {\n      sqlite3_result_int(pCtx, 0);\n      break;\n    }\n    case JSON_INT: {\n      sqlite3_int64 i = 0;\n      const char *z = pNode->u.zJContent;\n      if( z[0]=='-' ){ z++; }\n      while( z[0]>='0' && z[0]<='9' ){\n        unsigned v = *(z++) - '0';\n        if( i>=LARGEST_INT64/10 ){\n          if( i>LARGEST_INT64/10 ) goto int_as_real;\n          if( z[0]>='0' && z[0]<='9' ) goto int_as_real;\n          if( v==9 ) goto int_as_real;\n          if( v==8 ){\n            if( pNode->u.zJContent[0]=='-' ){\n              sqlite3_result_int64(pCtx, SMALLEST_INT64);\n              goto int_done;\n            }else{\n              goto int_as_real;\n            }\n          }\n        }\n        i = i*10 + v;\n      }\n      if( pNode->u.zJContent[0]=='-' ){ i = -i; }\n      sqlite3_result_int64(pCtx, i);\n      int_done:\n      break;\n      int_as_real: /* fall through to real */;\n    }\n    case JSON_REAL: {\n      double r;\n#ifdef SQLITE_AMALGAMATION\n      const char *z = pNode->u.zJContent;\n      sqlite3AtoF(z, &r, sqlite3Strlen30(z), SQLITE_UTF8);\n#else\n      r = strtod(pNode->u.zJContent, 0);\n#endif\n      sqlite3_result_double(pCtx, r);\n      break;\n    }\n    case JSON_STRING: {\n#if 0 /* Never happens because JNODE_RAW is only set by json_set(),\n      ** json_insert() and json_replace() and those routines do not\n      ** call jsonReturn() */\n      if( pNode->jnFlags & JNODE_RAW ){\n        sqlite3_result_text(pCtx, pNode->u.zJContent, pNode->n,\n                            SQLITE_TRANSIENT);\n      }else \n#endif\n      assert( (pNode->jnFlags & JNODE_RAW)==0 );\n      if( (pNode->jnFlags & JNODE_ESCAPE)==0 ){\n        /* JSON formatted without any backslash-escapes */\n        sqlite3_result_text(pCtx, pNode->u.zJContent+1, pNode->n-2,\n                            SQLITE_TRANSIENT);\n      }else{\n        /* Translate JSON formatted string into raw text */\n        u32 i;\n        u32 n = pNode->n;\n        const char *z = pNode->u.zJContent;\n        char *zOut;\n        u32 j;\n        zOut = sqlite3_malloc( n+1 );\n        if( zOut==0 ){\n          sqlite3_result_error_nomem(pCtx);\n          break;\n        }\n        for(i=1, j=0; i<n-1; i++){\n          char c = z[i];\n          if( c!='\\\\' ){\n            zOut[j++] = c;\n          }else{\n            c = z[++i];\n            if( c=='u' ){\n              u32 v = 0, k;\n              for(k=0; k<4; i++, k++){\n                assert( i<n-2 );\n                c = z[i+1];\n                assert( safe_isxdigit(c) );\n                if( c<='9' ) v = v*16 + c - '0';\n                else if( c<='F' ) v = v*16 + c - 'A' + 10;\n                else v = v*16 + c - 'a' + 10;\n              }\n              if( v==0 ) break;\n              if( v<=0x7f ){\n                zOut[j++] = (char)v;\n              }else if( v<=0x7ff ){\n                zOut[j++] = (char)(0xc0 | (v>>6));\n                zOut[j++] = 0x80 | (v&0x3f);\n              }else{\n                zOut[j++] = (char)(0xe0 | (v>>12));\n                zOut[j++] = 0x80 | ((v>>6)&0x3f);\n                zOut[j++] = 0x80 | (v&0x3f);\n              }\n            }else{\n              if( c=='b' ){\n                c = '\\b';\n              }else if( c=='f' ){\n                c = '\\f';\n              }else if( c=='n' ){\n                c = '\\n';\n              }else if( c=='r' ){\n                c = '\\r';\n              }else if( c=='t' ){\n                c = '\\t';\n              }\n              zOut[j++] = c;\n            }\n          }\n        }\n        zOut[j] = 0;\n        sqlite3_result_text(pCtx, zOut, j, sqlite3_free);\n      }\n      break;\n    }\n    case JSON_ARRAY:\n    case JSON_OBJECT: {\n      jsonReturnJson(pNode, pCtx, aReplace);\n      break;\n    }\n  }\n}\n\n/* Forward reference */\nstatic int jsonParseAddNode(JsonParse*,u32,u32,const char*);\n\n/*\n** A macro to hint to the compiler that a function should not be\n** inlined.\n*/\n#if defined(__GNUC__)\n#  define JSON_NOINLINE  __attribute__((noinline))\n#elif defined(_MSC_VER) && _MSC_VER>=1310\n#  define JSON_NOINLINE  __declspec(noinline)\n#else\n#  define JSON_NOINLINE\n#endif\n\n\nstatic JSON_NOINLINE int jsonParseAddNodeExpand(\n  JsonParse *pParse,        /* Append the node to this object */\n  u32 eType,                /* Node type */\n  u32 n,                    /* Content size or sub-node count */\n  const char *zContent      /* Content */\n){\n  u32 nNew;\n  JsonNode *pNew;\n  assert( pParse->nNode>=pParse->nAlloc );\n  if( pParse->oom ) return -1;\n  nNew = pParse->nAlloc*2 + 10;\n  pNew = sqlite3_realloc(pParse->aNode, sizeof(JsonNode)*nNew);\n  if( pNew==0 ){\n    pParse->oom = 1;\n    return -1;\n  }\n  pParse->nAlloc = nNew;\n  pParse->aNode = pNew;\n  assert( pParse->nNode<pParse->nAlloc );\n  return jsonParseAddNode(pParse, eType, n, zContent);\n}\n\n/*\n** Create a new JsonNode instance based on the arguments and append that\n** instance to the JsonParse.  Return the index in pParse->aNode[] of the\n** new node, or -1 if a memory allocation fails.\n*/\nstatic int jsonParseAddNode(\n  JsonParse *pParse,        /* Append the node to this object */\n  u32 eType,                /* Node type */\n  u32 n,                    /* Content size or sub-node count */\n  const char *zContent      /* Content */\n){\n  JsonNode *p;\n  if( pParse->nNode>=pParse->nAlloc ){\n    return jsonParseAddNodeExpand(pParse, eType, n, zContent);\n  }\n  p = &pParse->aNode[pParse->nNode];\n  p->eType = (u8)eType;\n  p->jnFlags = 0;\n  p->n = n;\n  p->u.zJContent = zContent;\n  return pParse->nNode++;\n}\n\n/*\n** Return true if z[] begins with 4 (or more) hexadecimal digits\n*/\nstatic int jsonIs4Hex(const char *z){\n  int i;\n  for(i=0; i<4; i++) if( !safe_isxdigit(z[i]) ) return 0;\n  return 1;\n}\n\n/*\n** Parse a single JSON value which begins at pParse->zJson[i].  Return the\n** index of the first character past the end of the value parsed.\n**\n** Return negative for a syntax error.  Special cases:  return -2 if the\n** first non-whitespace character is '}' and return -3 if the first\n** non-whitespace character is ']'.\n*/\nstatic int jsonParseValue(JsonParse *pParse, u32 i){\n  char c;\n  u32 j;\n  int iThis;\n  int x;\n  JsonNode *pNode;\n  const char *z = pParse->zJson;\n  while( safe_isspace(z[i]) ){ i++; }\n  if( (c = z[i])=='{' ){\n    /* Parse object */\n    iThis = jsonParseAddNode(pParse, JSON_OBJECT, 0, 0);\n    if( iThis<0 ) return -1;\n    for(j=i+1;;j++){\n      while( safe_isspace(z[j]) ){ j++; }\n      if( ++pParse->iDepth > JSON_MAX_DEPTH ) return -1;\n      x = jsonParseValue(pParse, j);\n      if( x<0 ){\n        pParse->iDepth--;\n        if( x==(-2) && pParse->nNode==(u32)iThis+1 ) return j+1;\n        return -1;\n      }\n      if( pParse->oom ) return -1;\n      pNode = &pParse->aNode[pParse->nNode-1];\n      if( pNode->eType!=JSON_STRING ) return -1;\n      pNode->jnFlags |= JNODE_LABEL;\n      j = x;\n      while( safe_isspace(z[j]) ){ j++; }\n      if( z[j]!=':' ) return -1;\n      j++;\n      x = jsonParseValue(pParse, j);\n      pParse->iDepth--;\n      if( x<0 ) return -1;\n      j = x;\n      while( safe_isspace(z[j]) ){ j++; }\n      c = z[j];\n      if( c==',' ) continue;\n      if( c!='}' ) return -1;\n      break;\n    }\n    pParse->aNode[iThis].n = pParse->nNode - (u32)iThis - 1;\n    return j+1;\n  }else if( c=='[' ){\n    /* Parse array */\n    iThis = jsonParseAddNode(pParse, JSON_ARRAY, 0, 0);\n    if( iThis<0 ) return -1;\n    for(j=i+1;;j++){\n      while( safe_isspace(z[j]) ){ j++; }\n      if( ++pParse->iDepth > JSON_MAX_DEPTH ) return -1;\n      x = jsonParseValue(pParse, j);\n      pParse->iDepth--;\n      if( x<0 ){\n        if( x==(-3) && pParse->nNode==(u32)iThis+1 ) return j+1;\n        return -1;\n      }\n      j = x;\n      while( safe_isspace(z[j]) ){ j++; }\n      c = z[j];\n      if( c==',' ) continue;\n      if( c!=']' ) return -1;\n      break;\n    }\n    pParse->aNode[iThis].n = pParse->nNode - (u32)iThis - 1;\n    return j+1;\n  }else if( c=='\"' ){\n    /* Parse string */\n    u8 jnFlags = 0;\n    j = i+1;\n    for(;;){\n      c = z[j];\n      if( (c & ~0x1f)==0 ){\n        /* Control characters are not allowed in strings */\n        return -1;\n      }\n      if( c=='\\\\' ){\n        c = z[++j];\n        if( c=='\"' || c=='\\\\' || c=='/' || c=='b' || c=='f'\n           || c=='n' || c=='r' || c=='t'\n           || (c=='u' && jsonIs4Hex(z+j+1)) ){\n          jnFlags = JNODE_ESCAPE;\n        }else{\n          return -1;\n        }\n      }else if( c=='\"' ){\n        break;\n      }\n      j++;\n    }\n    jsonParseAddNode(pParse, JSON_STRING, j+1-i, &z[i]);\n    if( !pParse->oom ) pParse->aNode[pParse->nNode-1].jnFlags = jnFlags;\n    return j+1;\n  }else if( c=='n'\n         && strncmp(z+i,\"null\",4)==0\n         && !safe_isalnum(z[i+4]) ){\n    jsonParseAddNode(pParse, JSON_NULL, 0, 0);\n    return i+4;\n  }else if( c=='t'\n         && strncmp(z+i,\"true\",4)==0\n         && !safe_isalnum(z[i+4]) ){\n    jsonParseAddNode(pParse, JSON_TRUE, 0, 0);\n    return i+4;\n  }else if( c=='f'\n         && strncmp(z+i,\"false\",5)==0\n         && !safe_isalnum(z[i+5]) ){\n    jsonParseAddNode(pParse, JSON_FALSE, 0, 0);\n    return i+5;\n  }else if( c=='-' || (c>='0' && c<='9') ){\n    /* Parse number */\n    u8 seenDP = 0;\n    u8 seenE = 0;\n    assert( '-' < '0' );\n    if( c<='0' ){\n      j = c=='-' ? i+1 : i;\n      if( z[j]=='0' && z[j+1]>='0' && z[j+1]<='9' ) return -1;\n    }\n    j = i+1;\n    for(;; j++){\n      c = z[j];\n      if( c>='0' && c<='9' ) continue;\n      if( c=='.' ){\n        if( z[j-1]=='-' ) return -1;\n        if( seenDP ) return -1;\n        seenDP = 1;\n        continue;\n      }\n      if( c=='e' || c=='E' ){\n        if( z[j-1]<'0' ) return -1;\n        if( seenE ) return -1;\n        seenDP = seenE = 1;\n        c = z[j+1];\n        if( c=='+' || c=='-' ){\n          j++;\n          c = z[j+1];\n        }\n        if( c<'0' || c>'9' ) return -1;\n        continue;\n      }\n      break;\n    }\n    if( z[j-1]<'0' ) return -1;\n    jsonParseAddNode(pParse, seenDP ? JSON_REAL : JSON_INT,\n                        j - i, &z[i]);\n    return j;\n  }else if( c=='}' ){\n    return -2;  /* End of {...} */\n  }else if( c==']' ){\n    return -3;  /* End of [...] */\n  }else if( c==0 ){\n    return 0;   /* End of file */\n  }else{\n    return -1;  /* Syntax error */\n  }\n}\n\n/*\n** Parse a complete JSON string.  Return 0 on success or non-zero if there\n** are any errors.  If an error occurs, free all memory associated with\n** pParse.\n**\n** pParse is uninitialized when this routine is called.\n*/\nstatic int jsonParse(\n  JsonParse *pParse,           /* Initialize and fill this JsonParse object */\n  sqlite3_context *pCtx,       /* Report errors here */\n  const char *zJson            /* Input JSON text to be parsed */\n){\n  int i;\n  memset(pParse, 0, sizeof(*pParse));\n  if( zJson==0 ) return 1;\n  pParse->zJson = zJson;\n  i = jsonParseValue(pParse, 0);\n  if( pParse->oom ) i = -1;\n  if( i>0 ){\n    assert( pParse->iDepth==0 );\n    while( safe_isspace(zJson[i]) ) i++;\n    if( zJson[i] ) i = -1;\n  }\n  if( i<=0 ){\n    if( pCtx!=0 ){\n      if( pParse->oom ){\n        sqlite3_result_error_nomem(pCtx);\n      }else{\n        sqlite3_result_error(pCtx, \"malformed JSON\", -1);\n      }\n    }\n    jsonParseReset(pParse);\n    return 1;\n  }\n  return 0;\n}\n\n/* Mark node i of pParse as being a child of iParent.  Call recursively\n** to fill in all the descendants of node i.\n*/\nstatic void jsonParseFillInParentage(JsonParse *pParse, u32 i, u32 iParent){\n  JsonNode *pNode = &pParse->aNode[i];\n  u32 j;\n  pParse->aUp[i] = iParent;\n  switch( pNode->eType ){\n    case JSON_ARRAY: {\n      for(j=1; j<=pNode->n; j += jsonNodeSize(pNode+j)){\n        jsonParseFillInParentage(pParse, i+j, i);\n      }\n      break;\n    }\n    case JSON_OBJECT: {\n      for(j=1; j<=pNode->n; j += jsonNodeSize(pNode+j+1)+1){\n        pParse->aUp[i+j] = i;\n        jsonParseFillInParentage(pParse, i+j+1, i);\n      }\n      break;\n    }\n    default: {\n      break;\n    }\n  }\n}\n\n/*\n** Compute the parentage of all nodes in a completed parse.\n*/\nstatic int jsonParseFindParents(JsonParse *pParse){\n  u32 *aUp;\n  assert( pParse->aUp==0 );\n  aUp = pParse->aUp = sqlite3_malloc( sizeof(u32)*pParse->nNode );\n  if( aUp==0 ){\n    pParse->oom = 1;\n    return SQLITE_NOMEM;\n  }\n  jsonParseFillInParentage(pParse, 0, 0);\n  return SQLITE_OK;\n}\n\n/*\n** Magic number used for the JSON parse cache in sqlite3_get_auxdata()\n*/\n#define JSON_CACHE_ID  (-429938)\n\n/*\n** Obtain a complete parse of the JSON found in the first argument\n** of the argv array.  Use the sqlite3_get_auxdata() cache for this\n** parse if it is available.  If the cache is not available or if it\n** is no longer valid, parse the JSON again and return the new parse,\n** and also register the new parse so that it will be available for\n** future sqlite3_get_auxdata() calls.\n*/\nstatic JsonParse *jsonParseCached(\n  sqlite3_context *pCtx,\n  sqlite3_value **argv\n){\n  const char *zJson = (const char*)sqlite3_value_text(argv[0]);\n  int nJson = sqlite3_value_bytes(argv[0]);\n  JsonParse *p;\n  if( zJson==0 ) return 0;\n  p = (JsonParse*)sqlite3_get_auxdata(pCtx, JSON_CACHE_ID);\n  if( p && p->nJson==nJson && memcmp(p->zJson,zJson,nJson)==0 ){\n    p->nErr = 0;\n    return p; /* The cached entry matches, so return it */\n  }\n  p = sqlite3_malloc( sizeof(*p) + nJson + 1 );\n  if( p==0 ){\n    sqlite3_result_error_nomem(pCtx);\n    return 0;\n  }\n  memset(p, 0, sizeof(*p));\n  p->zJson = (char*)&p[1];\n  memcpy((char*)p->zJson, zJson, nJson+1);\n  if( jsonParse(p, pCtx, p->zJson) ){\n    sqlite3_free(p);\n    return 0;\n  }\n  p->nJson = nJson;\n  sqlite3_set_auxdata(pCtx, JSON_CACHE_ID, p, (void(*)(void*))jsonParseFree);\n  return (JsonParse*)sqlite3_get_auxdata(pCtx, JSON_CACHE_ID);\n}\n\n/*\n** Compare the OBJECT label at pNode against zKey,nKey.  Return true on\n** a match.\n*/\nstatic int jsonLabelCompare(JsonNode *pNode, const char *zKey, u32 nKey){\n  if( pNode->jnFlags & JNODE_RAW ){\n    if( pNode->n!=nKey ) return 0;\n    return strncmp(pNode->u.zJContent, zKey, nKey)==0;\n  }else{\n    if( pNode->n!=nKey+2 ) return 0;\n    return strncmp(pNode->u.zJContent+1, zKey, nKey)==0;\n  }\n}\n\n/* forward declaration */\nstatic JsonNode *jsonLookupAppend(JsonParse*,const char*,int*,const char**);\n\n/*\n** Search along zPath to find the node specified.  Return a pointer\n** to that node, or NULL if zPath is malformed or if there is no such\n** node.\n**\n** If pApnd!=0, then try to append new nodes to complete zPath if it is\n** possible to do so and if no existing node corresponds to zPath.  If\n** new nodes are appended *pApnd is set to 1.\n*/\nstatic JsonNode *jsonLookupStep(\n  JsonParse *pParse,      /* The JSON to search */\n  u32 iRoot,              /* Begin the search at this node */\n  const char *zPath,      /* The path to search */\n  int *pApnd,             /* Append nodes to complete path if not NULL */\n  const char **pzErr      /* Make *pzErr point to any syntax error in zPath */\n){\n  u32 i, j, nKey;\n  const char *zKey;\n  JsonNode *pRoot = &pParse->aNode[iRoot];\n  if( zPath[0]==0 ) return pRoot;\n  if( zPath[0]=='.' ){\n    if( pRoot->eType!=JSON_OBJECT ) return 0;\n    zPath++;\n    if( zPath[0]=='\"' ){\n      zKey = zPath + 1;\n      for(i=1; zPath[i] && zPath[i]!='\"'; i++){}\n      nKey = i-1;\n      if( zPath[i] ){\n        i++;\n      }else{\n        *pzErr = zPath;\n        return 0;\n      }\n    }else{\n      zKey = zPath;\n      for(i=0; zPath[i] && zPath[i]!='.' && zPath[i]!='['; i++){}\n      nKey = i;\n    }\n    if( nKey==0 ){\n      *pzErr = zPath;\n      return 0;\n    }\n    j = 1;\n    for(;;){\n      while( j<=pRoot->n ){\n        if( jsonLabelCompare(pRoot+j, zKey, nKey) ){\n          return jsonLookupStep(pParse, iRoot+j+1, &zPath[i], pApnd, pzErr);\n        }\n        j++;\n        j += jsonNodeSize(&pRoot[j]);\n      }\n      if( (pRoot->jnFlags & JNODE_APPEND)==0 ) break;\n      iRoot += pRoot->u.iAppend;\n      pRoot = &pParse->aNode[iRoot];\n      j = 1;\n    }\n    if( pApnd ){\n      u32 iStart, iLabel;\n      JsonNode *pNode;\n      iStart = jsonParseAddNode(pParse, JSON_OBJECT, 2, 0);\n      iLabel = jsonParseAddNode(pParse, JSON_STRING, i, zPath);\n      zPath += i;\n      pNode = jsonLookupAppend(pParse, zPath, pApnd, pzErr);\n      if( pParse->oom ) return 0;\n      if( pNode ){\n        pRoot = &pParse->aNode[iRoot];\n        pRoot->u.iAppend = iStart - iRoot;\n        pRoot->jnFlags |= JNODE_APPEND;\n        pParse->aNode[iLabel].jnFlags |= JNODE_RAW;\n      }\n      return pNode;\n    }\n  }else if( zPath[0]=='[' && safe_isdigit(zPath[1]) ){\n    if( pRoot->eType!=JSON_ARRAY ) return 0;\n    i = 0;\n    j = 1;\n    while( safe_isdigit(zPath[j]) ){\n      i = i*10 + zPath[j] - '0';\n      j++;\n    }\n    if( zPath[j]!=']' ){\n      *pzErr = zPath;\n      return 0;\n    }\n    zPath += j + 1;\n    j = 1;\n    for(;;){\n      while( j<=pRoot->n && (i>0 || (pRoot[j].jnFlags & JNODE_REMOVE)!=0) ){\n        if( (pRoot[j].jnFlags & JNODE_REMOVE)==0 ) i--;\n        j += jsonNodeSize(&pRoot[j]);\n      }\n      if( (pRoot->jnFlags & JNODE_APPEND)==0 ) break;\n      iRoot += pRoot->u.iAppend;\n      pRoot = &pParse->aNode[iRoot];\n      j = 1;\n    }\n    if( j<=pRoot->n ){\n      return jsonLookupStep(pParse, iRoot+j, zPath, pApnd, pzErr);\n    }\n    if( i==0 && pApnd ){\n      u32 iStart;\n      JsonNode *pNode;\n      iStart = jsonParseAddNode(pParse, JSON_ARRAY, 1, 0);\n      pNode = jsonLookupAppend(pParse, zPath, pApnd, pzErr);\n      if( pParse->oom ) return 0;\n      if( pNode ){\n        pRoot = &pParse->aNode[iRoot];\n        pRoot->u.iAppend = iStart - iRoot;\n        pRoot->jnFlags |= JNODE_APPEND;\n      }\n      return pNode;\n    }\n  }else{\n    *pzErr = zPath;\n  }\n  return 0;\n}\n\n/*\n** Append content to pParse that will complete zPath.  Return a pointer\n** to the inserted node, or return NULL if the append fails.\n*/\nstatic JsonNode *jsonLookupAppend(\n  JsonParse *pParse,     /* Append content to the JSON parse */\n  const char *zPath,     /* Description of content to append */\n  int *pApnd,            /* Set this flag to 1 */\n  const char **pzErr     /* Make this point to any syntax error */\n){\n  *pApnd = 1;\n  if( zPath[0]==0 ){\n    jsonParseAddNode(pParse, JSON_NULL, 0, 0);\n    return pParse->oom ? 0 : &pParse->aNode[pParse->nNode-1];\n  }\n  if( zPath[0]=='.' ){\n    jsonParseAddNode(pParse, JSON_OBJECT, 0, 0);\n  }else if( strncmp(zPath,\"[0]\",3)==0 ){\n    jsonParseAddNode(pParse, JSON_ARRAY, 0, 0);\n  }else{\n    return 0;\n  }\n  if( pParse->oom ) return 0;\n  return jsonLookupStep(pParse, pParse->nNode-1, zPath, pApnd, pzErr);\n}\n\n/*\n** Return the text of a syntax error message on a JSON path.  Space is\n** obtained from sqlite3_malloc().\n*/\nstatic char *jsonPathSyntaxError(const char *zErr){\n  return sqlite3_mprintf(\"JSON path error near '%q'\", zErr);\n}\n\n/*\n** Do a node lookup using zPath.  Return a pointer to the node on success.\n** Return NULL if not found or if there is an error.\n**\n** On an error, write an error message into pCtx and increment the\n** pParse->nErr counter.\n**\n** If pApnd!=NULL then try to append missing nodes and set *pApnd = 1 if\n** nodes are appended.\n*/\nstatic JsonNode *jsonLookup(\n  JsonParse *pParse,      /* The JSON to search */\n  const char *zPath,      /* The path to search */\n  int *pApnd,             /* Append nodes to complete path if not NULL */\n  sqlite3_context *pCtx   /* Report errors here, if not NULL */\n){\n  const char *zErr = 0;\n  JsonNode *pNode = 0;\n  char *zMsg;\n\n  if( zPath==0 ) return 0;\n  if( zPath[0]!='$' ){\n    zErr = zPath;\n    goto lookup_err;\n  }\n  zPath++;\n  pNode = jsonLookupStep(pParse, 0, zPath, pApnd, &zErr);\n  if( zErr==0 ) return pNode;\n\nlookup_err:\n  pParse->nErr++;\n  assert( zErr!=0 && pCtx!=0 );\n  zMsg = jsonPathSyntaxError(zErr);\n  if( zMsg ){\n    sqlite3_result_error(pCtx, zMsg, -1);\n    sqlite3_free(zMsg);\n  }else{\n    sqlite3_result_error_nomem(pCtx);\n  }\n  return 0;\n}\n\n\n/*\n** Report the wrong number of arguments for json_insert(), json_replace()\n** or json_set().\n*/\nstatic void jsonWrongNumArgs(\n  sqlite3_context *pCtx,\n  const char *zFuncName\n){\n  char *zMsg = sqlite3_mprintf(\"json_%s() needs an odd number of arguments\",\n                               zFuncName);\n  sqlite3_result_error(pCtx, zMsg, -1);\n  sqlite3_free(zMsg);     \n}\n\n/*\n** Mark all NULL entries in the Object passed in as JNODE_REMOVE.\n*/\nstatic void jsonRemoveAllNulls(JsonNode *pNode){\n  int i, n;\n  assert( pNode->eType==JSON_OBJECT );\n  n = pNode->n;\n  for(i=2; i<=n; i += jsonNodeSize(&pNode[i])+1){\n    switch( pNode[i].eType ){\n      case JSON_NULL:\n        pNode[i].jnFlags |= JNODE_REMOVE;\n        break;\n      case JSON_OBJECT:\n        jsonRemoveAllNulls(&pNode[i]);\n        break;\n    }\n  }\n}\n\n\n/****************************************************************************\n** SQL functions used for testing and debugging\n****************************************************************************/\n\n#ifdef SQLITE_DEBUG\n/*\n** The json_parse(JSON) function returns a string which describes\n** a parse of the JSON provided.  Or it returns NULL if JSON is not\n** well-formed.\n*/\nstatic void jsonParseFunc(\n  sqlite3_context *ctx,\n  int argc,\n  sqlite3_value **argv\n){\n  JsonString s;       /* Output string - not real JSON */\n  JsonParse x;        /* The parse */\n  u32 i;\n\n  assert( argc==1 );\n  if( jsonParse(&x, ctx, (const char*)sqlite3_value_text(argv[0])) ) return;\n  jsonParseFindParents(&x);\n  jsonInit(&s, ctx);\n  for(i=0; i<x.nNode; i++){\n    const char *zType;\n    if( x.aNode[i].jnFlags & JNODE_LABEL ){\n      assert( x.aNode[i].eType==JSON_STRING );\n      zType = \"label\";\n    }else{\n      zType = jsonType[x.aNode[i].eType];\n    }\n    jsonPrintf(100, &s,\"node %3u: %7s n=%-4d up=%-4d\",\n               i, zType, x.aNode[i].n, x.aUp[i]);\n    if( x.aNode[i].u.zJContent!=0 ){\n      jsonAppendRaw(&s, \" \", 1);\n      jsonAppendRaw(&s, x.aNode[i].u.zJContent, x.aNode[i].n);\n    }\n    jsonAppendRaw(&s, \"\\n\", 1);\n  }\n  jsonParseReset(&x);\n  jsonResult(&s);\n}\n\n/*\n** The json_test1(JSON) function return true (1) if the input is JSON\n** text generated by another json function.  It returns (0) if the input\n** is not known to be JSON.\n*/\nstatic void jsonTest1Func(\n  sqlite3_context *ctx,\n  int argc,\n  sqlite3_value **argv\n){\n  UNUSED_PARAM(argc);\n  sqlite3_result_int(ctx, sqlite3_value_subtype(argv[0])==JSON_SUBTYPE);\n}\n#endif /* SQLITE_DEBUG */\n\n/****************************************************************************\n** Scalar SQL function implementations\n****************************************************************************/\n\n/*\n** Implementation of the json_QUOTE(VALUE) function.  Return a JSON value\n** corresponding to the SQL value input.  Mostly this means putting \n** double-quotes around strings and returning the unquoted string \"null\"\n** when given a NULL input.\n*/\nstatic void jsonQuoteFunc(\n  sqlite3_context *ctx,\n  int argc,\n  sqlite3_value **argv\n){\n  JsonString jx;\n  UNUSED_PARAM(argc);\n\n  jsonInit(&jx, ctx);\n  jsonAppendValue(&jx, argv[0]);\n  jsonResult(&jx);\n  sqlite3_result_subtype(ctx, JSON_SUBTYPE);\n}\n\n/*\n** Implementation of the json_array(VALUE,...) function.  Return a JSON\n** array that contains all values given in arguments.  Or if any argument\n** is a BLOB, throw an error.\n*/\nstatic void jsonArrayFunc(\n  sqlite3_context *ctx,\n  int argc,\n  sqlite3_value **argv\n){\n  int i;\n  JsonString jx;\n\n  jsonInit(&jx, ctx);\n  jsonAppendChar(&jx, '[');\n  for(i=0; i<argc; i++){\n    jsonAppendSeparator(&jx);\n    jsonAppendValue(&jx, argv[i]);\n  }\n  jsonAppendChar(&jx, ']');\n  jsonResult(&jx);\n  sqlite3_result_subtype(ctx, JSON_SUBTYPE);\n}\n\n\n/*\n** json_array_length(JSON)\n** json_array_length(JSON, PATH)\n**\n** Return the number of elements in the top-level JSON array.  \n** Return 0 if the input is not a well-formed JSON array.\n*/\nstatic void jsonArrayLengthFunc(\n  sqlite3_context *ctx,\n  int argc,\n  sqlite3_value **argv\n){\n  JsonParse *p;          /* The parse */\n  sqlite3_int64 n = 0;\n  u32 i;\n  JsonNode *pNode;\n\n  p = jsonParseCached(ctx, argv);\n  if( p==0 ) return;\n  assert( p->nNode );\n  if( argc==2 ){\n    const char *zPath = (const char*)sqlite3_value_text(argv[1]);\n    pNode = jsonLookup(p, zPath, 0, ctx);\n  }else{\n    pNode = p->aNode;\n  }\n  if( pNode==0 ){\n    return;\n  }\n  if( pNode->eType==JSON_ARRAY ){\n    assert( (pNode->jnFlags & JNODE_APPEND)==0 );\n    for(i=1; i<=pNode->n; n++){\n      i += jsonNodeSize(&pNode[i]);\n    }\n  }\n  sqlite3_result_int64(ctx, n);\n}\n\n/*\n** json_extract(JSON, PATH, ...)\n**\n** Return the element described by PATH.  Return NULL if there is no\n** PATH element.  If there are multiple PATHs, then return a JSON array\n** with the result from each path.  Throw an error if the JSON or any PATH\n** is malformed.\n*/\nstatic void jsonExtractFunc(\n  sqlite3_context *ctx,\n  int argc,\n  sqlite3_value **argv\n){\n  JsonParse *p;          /* The parse */\n  JsonNode *pNode;\n  const char *zPath;\n  JsonString jx;\n  int i;\n\n  if( argc<2 ) return;\n  p = jsonParseCached(ctx, argv);\n  if( p==0 ) return;\n  jsonInit(&jx, ctx);\n  jsonAppendChar(&jx, '[');\n  for(i=1; i<argc; i++){\n    zPath = (const char*)sqlite3_value_text(argv[i]);\n    pNode = jsonLookup(p, zPath, 0, ctx);\n    if( p->nErr ) break;\n    if( argc>2 ){\n      jsonAppendSeparator(&jx);\n      if( pNode ){\n        jsonRenderNode(pNode, &jx, 0);\n      }else{\n        jsonAppendRaw(&jx, \"null\", 4);\n      }\n    }else if( pNode ){\n      jsonReturn(pNode, ctx, 0);\n    }\n  }\n  if( argc>2 && i==argc ){\n    jsonAppendChar(&jx, ']');\n    jsonResult(&jx);\n    sqlite3_result_subtype(ctx, JSON_SUBTYPE);\n  }\n  jsonReset(&jx);\n}\n\n/* This is the RFC 7396 MergePatch algorithm.\n*/\nstatic JsonNode *jsonMergePatch(\n  JsonParse *pParse,   /* The JSON parser that contains the TARGET */\n  u32 iTarget,         /* Node of the TARGET in pParse */\n  JsonNode *pPatch     /* The PATCH */\n){\n  u32 i, j;\n  u32 iRoot;\n  JsonNode *pTarget;\n  if( pPatch->eType!=JSON_OBJECT ){\n    return pPatch;\n  }\n  assert( iTarget>=0 && iTarget<pParse->nNode );\n  pTarget = &pParse->aNode[iTarget];\n  assert( (pPatch->jnFlags & JNODE_APPEND)==0 );\n  if( pTarget->eType!=JSON_OBJECT ){\n    jsonRemoveAllNulls(pPatch);\n    return pPatch;\n  }\n  iRoot = iTarget;\n  for(i=1; i<pPatch->n; i += jsonNodeSize(&pPatch[i+1])+1){\n    u32 nKey;\n    const char *zKey;\n    assert( pPatch[i].eType==JSON_STRING );\n    assert( pPatch[i].jnFlags & JNODE_LABEL );\n    nKey = pPatch[i].n;\n    zKey = pPatch[i].u.zJContent;\n    assert( (pPatch[i].jnFlags & JNODE_RAW)==0 );\n    for(j=1; j<pTarget->n; j += jsonNodeSize(&pTarget[j+1])+1 ){\n      assert( pTarget[j].eType==JSON_STRING );\n      assert( pTarget[j].jnFlags & JNODE_LABEL );\n      assert( (pPatch[i].jnFlags & JNODE_RAW)==0 );\n      if( pTarget[j].n==nKey && strncmp(pTarget[j].u.zJContent,zKey,nKey)==0 ){\n        if( pTarget[j+1].jnFlags & (JNODE_REMOVE|JNODE_PATCH) ) break;\n        if( pPatch[i+1].eType==JSON_NULL ){\n          pTarget[j+1].jnFlags |= JNODE_REMOVE;\n        }else{\n          JsonNode *pNew = jsonMergePatch(pParse, iTarget+j+1, &pPatch[i+1]);\n          if( pNew==0 ) return 0;\n          pTarget = &pParse->aNode[iTarget];\n          if( pNew!=&pTarget[j+1] ){\n            pTarget[j+1].u.pPatch = pNew;\n            pTarget[j+1].jnFlags |= JNODE_PATCH;\n          }\n        }\n        break;\n      }\n    }\n    if( j>=pTarget->n && pPatch[i+1].eType!=JSON_NULL ){\n      int iStart, iPatch;\n      iStart = jsonParseAddNode(pParse, JSON_OBJECT, 2, 0);\n      jsonParseAddNode(pParse, JSON_STRING, nKey, zKey);\n      iPatch = jsonParseAddNode(pParse, JSON_TRUE, 0, 0);\n      if( pParse->oom ) return 0;\n      jsonRemoveAllNulls(pPatch);\n      pTarget = &pParse->aNode[iTarget];\n      pParse->aNode[iRoot].jnFlags |= JNODE_APPEND;\n      pParse->aNode[iRoot].u.iAppend = iStart - iRoot;\n      iRoot = iStart;\n      pParse->aNode[iPatch].jnFlags |= JNODE_PATCH;\n      pParse->aNode[iPatch].u.pPatch = &pPatch[i+1];\n    }\n  }\n  return pTarget;\n}\n\n/*\n** Implementation of the json_mergepatch(JSON1,JSON2) function.  Return a JSON\n** object that is the result of running the RFC 7396 MergePatch() algorithm\n** on the two arguments.\n*/\nstatic void jsonPatchFunc(\n  sqlite3_context *ctx,\n  int argc,\n  sqlite3_value **argv\n){\n  JsonParse x;     /* The JSON that is being patched */\n  JsonParse y;     /* The patch */\n  JsonNode *pResult;   /* The result of the merge */\n\n  UNUSED_PARAM(argc);\n  if( jsonParse(&x, ctx, (const char*)sqlite3_value_text(argv[0])) ) return;\n  if( jsonParse(&y, ctx, (const char*)sqlite3_value_text(argv[1])) ){\n    jsonParseReset(&x);\n    return;\n  }\n  pResult = jsonMergePatch(&x, 0, y.aNode);\n  assert( pResult!=0 || x.oom );\n  if( pResult ){\n    jsonReturnJson(pResult, ctx, 0);\n  }else{\n    sqlite3_result_error_nomem(ctx);\n  }\n  jsonParseReset(&x);\n  jsonParseReset(&y);\n}\n\n\n/*\n** Implementation of the json_object(NAME,VALUE,...) function.  Return a JSON\n** object that contains all name/value given in arguments.  Or if any name\n** is not a string or if any value is a BLOB, throw an error.\n*/\nstatic void jsonObjectFunc(\n  sqlite3_context *ctx,\n  int argc,\n  sqlite3_value **argv\n){\n  int i;\n  JsonString jx;\n  const char *z;\n  u32 n;\n\n  if( argc&1 ){\n    sqlite3_result_error(ctx, \"json_object() requires an even number \"\n                                  \"of arguments\", -1);\n    return;\n  }\n  jsonInit(&jx, ctx);\n  jsonAppendChar(&jx, '{');\n  for(i=0; i<argc; i+=2){\n    if( sqlite3_value_type(argv[i])!=SQLITE_TEXT ){\n      sqlite3_result_error(ctx, \"json_object() labels must be TEXT\", -1);\n      jsonReset(&jx);\n      return;\n    }\n    jsonAppendSeparator(&jx);\n    z = (const char*)sqlite3_value_text(argv[i]);\n    n = (u32)sqlite3_value_bytes(argv[i]);\n    jsonAppendString(&jx, z, n);\n    jsonAppendChar(&jx, ':');\n    jsonAppendValue(&jx, argv[i+1]);\n  }\n  jsonAppendChar(&jx, '}');\n  jsonResult(&jx);\n  sqlite3_result_subtype(ctx, JSON_SUBTYPE);\n}\n\n\n/*\n** json_remove(JSON, PATH, ...)\n**\n** Remove the named elements from JSON and return the result.  malformed\n** JSON or PATH arguments result in an error.\n*/\nstatic void jsonRemoveFunc(\n  sqlite3_context *ctx,\n  int argc,\n  sqlite3_value **argv\n){\n  JsonParse x;          /* The parse */\n  JsonNode *pNode;\n  const char *zPath;\n  u32 i;\n\n  if( argc<1 ) return;\n  if( jsonParse(&x, ctx, (const char*)sqlite3_value_text(argv[0])) ) return;\n  assert( x.nNode );\n  for(i=1; i<(u32)argc; i++){\n    zPath = (const char*)sqlite3_value_text(argv[i]);\n    if( zPath==0 ) goto remove_done;\n    pNode = jsonLookup(&x, zPath, 0, ctx);\n    if( x.nErr ) goto remove_done;\n    if( pNode ) pNode->jnFlags |= JNODE_REMOVE;\n  }\n  if( (x.aNode[0].jnFlags & JNODE_REMOVE)==0 ){\n    jsonReturnJson(x.aNode, ctx, 0);\n  }\nremove_done:\n  jsonParseReset(&x);\n}\n\n/*\n** json_replace(JSON, PATH, VALUE, ...)\n**\n** Replace the value at PATH with VALUE.  If PATH does not already exist,\n** this routine is a no-op.  If JSON or PATH is malformed, throw an error.\n*/\nstatic void jsonReplaceFunc(\n  sqlite3_context *ctx,\n  int argc,\n  sqlite3_value **argv\n){\n  JsonParse x;          /* The parse */\n  JsonNode *pNode;\n  const char *zPath;\n  u32 i;\n\n  if( argc<1 ) return;\n  if( (argc&1)==0 ) {\n    jsonWrongNumArgs(ctx, \"replace\");\n    return;\n  }\n  if( jsonParse(&x, ctx, (const char*)sqlite3_value_text(argv[0])) ) return;\n  assert( x.nNode );\n  for(i=1; i<(u32)argc; i+=2){\n    zPath = (const char*)sqlite3_value_text(argv[i]);\n    pNode = jsonLookup(&x, zPath, 0, ctx);\n    if( x.nErr ) goto replace_err;\n    if( pNode ){\n      pNode->jnFlags |= (u8)JNODE_REPLACE;\n      pNode->u.iReplace = i + 1;\n    }\n  }\n  if( x.aNode[0].jnFlags & JNODE_REPLACE ){\n    sqlite3_result_value(ctx, argv[x.aNode[0].u.iReplace]);\n  }else{\n    jsonReturnJson(x.aNode, ctx, argv);\n  }\nreplace_err:\n  jsonParseReset(&x);\n}\n\n/*\n** json_set(JSON, PATH, VALUE, ...)\n**\n** Set the value at PATH to VALUE.  Create the PATH if it does not already\n** exist.  Overwrite existing values that do exist.\n** If JSON or PATH is malformed, throw an error.\n**\n** json_insert(JSON, PATH, VALUE, ...)\n**\n** Create PATH and initialize it to VALUE.  If PATH already exists, this\n** routine is a no-op.  If JSON or PATH is malformed, throw an error.\n*/\nstatic void jsonSetFunc(\n  sqlite3_context *ctx,\n  int argc,\n  sqlite3_value **argv\n){\n  JsonParse x;          /* The parse */\n  JsonNode *pNode;\n  const char *zPath;\n  u32 i;\n  int bApnd;\n  int bIsSet = *(int*)sqlite3_user_data(ctx);\n\n  if( argc<1 ) return;\n  if( (argc&1)==0 ) {\n    jsonWrongNumArgs(ctx, bIsSet ? \"set\" : \"insert\");\n    return;\n  }\n  if( jsonParse(&x, ctx, (const char*)sqlite3_value_text(argv[0])) ) return;\n  assert( x.nNode );\n  for(i=1; i<(u32)argc; i+=2){\n    zPath = (const char*)sqlite3_value_text(argv[i]);\n    bApnd = 0;\n    pNode = jsonLookup(&x, zPath, &bApnd, ctx);\n    if( x.oom ){\n      sqlite3_result_error_nomem(ctx);\n      goto jsonSetDone;\n    }else if( x.nErr ){\n      goto jsonSetDone;\n    }else if( pNode && (bApnd || bIsSet) ){\n      pNode->jnFlags |= (u8)JNODE_REPLACE;\n      pNode->u.iReplace = i + 1;\n    }\n  }\n  if( x.aNode[0].jnFlags & JNODE_REPLACE ){\n    sqlite3_result_value(ctx, argv[x.aNode[0].u.iReplace]);\n  }else{\n    jsonReturnJson(x.aNode, ctx, argv);\n  }\njsonSetDone:\n  jsonParseReset(&x);\n}\n\n/*\n** json_type(JSON)\n** json_type(JSON, PATH)\n**\n** Return the top-level \"type\" of a JSON string.  Throw an error if\n** either the JSON or PATH inputs are not well-formed.\n*/\nstatic void jsonTypeFunc(\n  sqlite3_context *ctx,\n  int argc,\n  sqlite3_value **argv\n){\n  JsonParse x;          /* The parse */\n  const char *zPath;\n  JsonNode *pNode;\n\n  if( jsonParse(&x, ctx, (const char*)sqlite3_value_text(argv[0])) ) return;\n  assert( x.nNode );\n  if( argc==2 ){\n    zPath = (const char*)sqlite3_value_text(argv[1]);\n    pNode = jsonLookup(&x, zPath, 0, ctx);\n  }else{\n    pNode = x.aNode;\n  }\n  if( pNode ){\n    sqlite3_result_text(ctx, jsonType[pNode->eType], -1, SQLITE_STATIC);\n  }\n  jsonParseReset(&x);\n}\n\n/*\n** json_valid(JSON)\n**\n** Return 1 if JSON is a well-formed JSON string according to RFC-7159.\n** Return 0 otherwise.\n*/\nstatic void jsonValidFunc(\n  sqlite3_context *ctx,\n  int argc,\n  sqlite3_value **argv\n){\n  JsonParse x;          /* The parse */\n  int rc = 0;\n\n  UNUSED_PARAM(argc);\n  if( jsonParse(&x, 0, (const char*)sqlite3_value_text(argv[0]))==0 ){\n    rc = 1;\n  }\n  jsonParseReset(&x);\n  sqlite3_result_int(ctx, rc);\n}\n\n\n/****************************************************************************\n** Aggregate SQL function implementations\n****************************************************************************/\n/*\n** json_group_array(VALUE)\n**\n** Return a JSON array composed of all values in the aggregate.\n*/\nstatic void jsonArrayStep(\n  sqlite3_context *ctx,\n  int argc,\n  sqlite3_value **argv\n){\n  JsonString *pStr;\n  UNUSED_PARAM(argc);\n  pStr = (JsonString*)sqlite3_aggregate_context(ctx, sizeof(*pStr));\n  if( pStr ){\n    if( pStr->zBuf==0 ){\n      jsonInit(pStr, ctx);\n      jsonAppendChar(pStr, '[');\n    }else{\n      jsonAppendChar(pStr, ',');\n      pStr->pCtx = ctx;\n    }\n    jsonAppendValue(pStr, argv[0]);\n  }\n}\nstatic void jsonArrayFinal(sqlite3_context *ctx){\n  JsonString *pStr;\n  pStr = (JsonString*)sqlite3_aggregate_context(ctx, 0);\n  if( pStr ){\n    pStr->pCtx = ctx;\n    jsonAppendChar(pStr, ']');\n    if( pStr->bErr ){\n      if( pStr->bErr==1 ) sqlite3_result_error_nomem(ctx);\n      assert( pStr->bStatic );\n    }else{\n      sqlite3_result_text(ctx, pStr->zBuf, pStr->nUsed,\n                          pStr->bStatic ? SQLITE_TRANSIENT : sqlite3_free);\n      pStr->bStatic = 1;\n    }\n  }else{\n    sqlite3_result_text(ctx, \"[]\", 2, SQLITE_STATIC);\n  }\n  sqlite3_result_subtype(ctx, JSON_SUBTYPE);\n}\n\n/*\n** json_group_obj(NAME,VALUE)\n**\n** Return a JSON object composed of all names and values in the aggregate.\n*/\nstatic void jsonObjectStep(\n  sqlite3_context *ctx,\n  int argc,\n  sqlite3_value **argv\n){\n  JsonString *pStr;\n  const char *z;\n  u32 n;\n  UNUSED_PARAM(argc);\n  pStr = (JsonString*)sqlite3_aggregate_context(ctx, sizeof(*pStr));\n  if( pStr ){\n    if( pStr->zBuf==0 ){\n      jsonInit(pStr, ctx);\n      jsonAppendChar(pStr, '{');\n    }else{\n      jsonAppendChar(pStr, ',');\n      pStr->pCtx = ctx;\n    }\n    z = (const char*)sqlite3_value_text(argv[0]);\n    n = (u32)sqlite3_value_bytes(argv[0]);\n    jsonAppendString(pStr, z, n);\n    jsonAppendChar(pStr, ':');\n    jsonAppendValue(pStr, argv[1]);\n  }\n}\nstatic void jsonObjectFinal(sqlite3_context *ctx){\n  JsonString *pStr;\n  pStr = (JsonString*)sqlite3_aggregate_context(ctx, 0);\n  if( pStr ){\n    jsonAppendChar(pStr, '}');\n    if( pStr->bErr ){\n      if( pStr->bErr==1 ) sqlite3_result_error_nomem(ctx);\n      assert( pStr->bStatic );\n    }else{\n      sqlite3_result_text(ctx, pStr->zBuf, pStr->nUsed,\n                          pStr->bStatic ? SQLITE_TRANSIENT : sqlite3_free);\n      pStr->bStatic = 1;\n    }\n  }else{\n    sqlite3_result_text(ctx, \"{}\", 2, SQLITE_STATIC);\n  }\n  sqlite3_result_subtype(ctx, JSON_SUBTYPE);\n}\n\n\n#ifndef SQLITE_OMIT_VIRTUALTABLE\n/****************************************************************************\n** The json_each virtual table\n****************************************************************************/\ntypedef struct JsonEachCursor JsonEachCursor;\nstruct JsonEachCursor {\n  sqlite3_vtab_cursor base;  /* Base class - must be first */\n  u32 iRowid;                /* The rowid */\n  u32 iBegin;                /* The first node of the scan */\n  u32 i;                     /* Index in sParse.aNode[] of current row */\n  u32 iEnd;                  /* EOF when i equals or exceeds this value */\n  u8 eType;                  /* Type of top-level element */\n  u8 bRecursive;             /* True for json_tree().  False for json_each() */\n  char *zJson;               /* Input JSON */\n  char *zRoot;               /* Path by which to filter zJson */\n  JsonParse sParse;          /* Parse of the input JSON */\n};\n\n/* Constructor for the json_each virtual table */\nstatic int jsonEachConnect(\n  sqlite3 *db,\n  void *pAux,\n  int argc, const char *const*argv,\n  sqlite3_vtab **ppVtab,\n  char **pzErr\n){\n  sqlite3_vtab *pNew;\n  int rc;\n\n/* Column numbers */\n#define JEACH_KEY     0\n#define JEACH_VALUE   1\n#define JEACH_TYPE    2\n#define JEACH_ATOM    3\n#define JEACH_ID      4\n#define JEACH_PARENT  5\n#define JEACH_FULLKEY 6\n#define JEACH_PATH    7\n#define JEACH_JSON    8\n#define JEACH_ROOT    9\n\n  UNUSED_PARAM(pzErr);\n  UNUSED_PARAM(argv);\n  UNUSED_PARAM(argc);\n  UNUSED_PARAM(pAux);\n  rc = sqlite3_declare_vtab(db, \n     \"CREATE TABLE x(key,value,type,atom,id,parent,fullkey,path,\"\n                    \"json HIDDEN,root HIDDEN)\");\n  if( rc==SQLITE_OK ){\n    pNew = *ppVtab = sqlite3_malloc( sizeof(*pNew) );\n    if( pNew==0 ) return SQLITE_NOMEM;\n    memset(pNew, 0, sizeof(*pNew));\n  }\n  return rc;\n}\n\n/* destructor for json_each virtual table */\nstatic int jsonEachDisconnect(sqlite3_vtab *pVtab){\n  sqlite3_free(pVtab);\n  return SQLITE_OK;\n}\n\n/* constructor for a JsonEachCursor object for json_each(). */\nstatic int jsonEachOpenEach(sqlite3_vtab *p, sqlite3_vtab_cursor **ppCursor){\n  JsonEachCursor *pCur;\n\n  UNUSED_PARAM(p);\n  pCur = sqlite3_malloc( sizeof(*pCur) );\n  if( pCur==0 ) return SQLITE_NOMEM;\n  memset(pCur, 0, sizeof(*pCur));\n  *ppCursor = &pCur->base;\n  return SQLITE_OK;\n}\n\n/* constructor for a JsonEachCursor object for json_tree(). */\nstatic int jsonEachOpenTree(sqlite3_vtab *p, sqlite3_vtab_cursor **ppCursor){\n  int rc = jsonEachOpenEach(p, ppCursor);\n  if( rc==SQLITE_OK ){\n    JsonEachCursor *pCur = (JsonEachCursor*)*ppCursor;\n    pCur->bRecursive = 1;\n  }\n  return rc;\n}\n\n/* Reset a JsonEachCursor back to its original state.  Free any memory\n** held. */\nstatic void jsonEachCursorReset(JsonEachCursor *p){\n  sqlite3_free(p->zJson);\n  sqlite3_free(p->zRoot);\n  jsonParseReset(&p->sParse);\n  p->iRowid = 0;\n  p->i = 0;\n  p->iEnd = 0;\n  p->eType = 0;\n  p->zJson = 0;\n  p->zRoot = 0;\n}\n\n/* Destructor for a jsonEachCursor object */\nstatic int jsonEachClose(sqlite3_vtab_cursor *cur){\n  JsonEachCursor *p = (JsonEachCursor*)cur;\n  jsonEachCursorReset(p);\n  sqlite3_free(cur);\n  return SQLITE_OK;\n}\n\n/* Return TRUE if the jsonEachCursor object has been advanced off the end\n** of the JSON object */\nstatic int jsonEachEof(sqlite3_vtab_cursor *cur){\n  JsonEachCursor *p = (JsonEachCursor*)cur;\n  return p->i >= p->iEnd;\n}\n\n/* Advance the cursor to the next element for json_tree() */\nstatic int jsonEachNext(sqlite3_vtab_cursor *cur){\n  JsonEachCursor *p = (JsonEachCursor*)cur;\n  if( p->bRecursive ){\n    if( p->sParse.aNode[p->i].jnFlags & JNODE_LABEL ) p->i++;\n    p->i++;\n    p->iRowid++;\n    if( p->i<p->iEnd ){\n      u32 iUp = p->sParse.aUp[p->i];\n      JsonNode *pUp = &p->sParse.aNode[iUp];\n      p->eType = pUp->eType;\n      if( pUp->eType==JSON_ARRAY ){\n        if( iUp==p->i-1 ){\n          pUp->u.iKey = 0;\n        }else{\n          pUp->u.iKey++;\n        }\n      }\n    }\n  }else{\n    switch( p->eType ){\n      case JSON_ARRAY: {\n        p->i += jsonNodeSize(&p->sParse.aNode[p->i]);\n        p->iRowid++;\n        break;\n      }\n      case JSON_OBJECT: {\n        p->i += 1 + jsonNodeSize(&p->sParse.aNode[p->i+1]);\n        p->iRowid++;\n        break;\n      }\n      default: {\n        p->i = p->iEnd;\n        break;\n      }\n    }\n  }\n  return SQLITE_OK;\n}\n\n/* Append the name of the path for element i to pStr\n*/\nstatic void jsonEachComputePath(\n  JsonEachCursor *p,       /* The cursor */\n  JsonString *pStr,        /* Write the path here */\n  u32 i                    /* Path to this element */\n){\n  JsonNode *pNode, *pUp;\n  u32 iUp;\n  if( i==0 ){\n    jsonAppendChar(pStr, '$');\n    return;\n  }\n  iUp = p->sParse.aUp[i];\n  jsonEachComputePath(p, pStr, iUp);\n  pNode = &p->sParse.aNode[i];\n  pUp = &p->sParse.aNode[iUp];\n  if( pUp->eType==JSON_ARRAY ){\n    jsonPrintf(30, pStr, \"[%d]\", pUp->u.iKey);\n  }else{\n    assert( pUp->eType==JSON_OBJECT );\n    if( (pNode->jnFlags & JNODE_LABEL)==0 ) pNode--;\n    assert( pNode->eType==JSON_STRING );\n    assert( pNode->jnFlags & JNODE_LABEL );\n    jsonPrintf(pNode->n+1, pStr, \".%.*s\", pNode->n-2, pNode->u.zJContent+1);\n  }\n}\n\n/* Return the value of a column */\nstatic int jsonEachColumn(\n  sqlite3_vtab_cursor *cur,   /* The cursor */\n  sqlite3_context *ctx,       /* First argument to sqlite3_result_...() */\n  int i                       /* Which column to return */\n){\n  JsonEachCursor *p = (JsonEachCursor*)cur;\n  JsonNode *pThis = &p->sParse.aNode[p->i];\n  switch( i ){\n    case JEACH_KEY: {\n      if( p->i==0 ) break;\n      if( p->eType==JSON_OBJECT ){\n        jsonReturn(pThis, ctx, 0);\n      }else if( p->eType==JSON_ARRAY ){\n        u32 iKey;\n        if( p->bRecursive ){\n          if( p->iRowid==0 ) break;\n          iKey = p->sParse.aNode[p->sParse.aUp[p->i]].u.iKey;\n        }else{\n          iKey = p->iRowid;\n        }\n        sqlite3_result_int64(ctx, (sqlite3_int64)iKey);\n      }\n      break;\n    }\n    case JEACH_VALUE: {\n      if( pThis->jnFlags & JNODE_LABEL ) pThis++;\n      jsonReturn(pThis, ctx, 0);\n      break;\n    }\n    case JEACH_TYPE: {\n      if( pThis->jnFlags & JNODE_LABEL ) pThis++;\n      sqlite3_result_text(ctx, jsonType[pThis->eType], -1, SQLITE_STATIC);\n      break;\n    }\n    case JEACH_ATOM: {\n      if( pThis->jnFlags & JNODE_LABEL ) pThis++;\n      if( pThis->eType>=JSON_ARRAY ) break;\n      jsonReturn(pThis, ctx, 0);\n      break;\n    }\n    case JEACH_ID: {\n      sqlite3_result_int64(ctx, \n         (sqlite3_int64)p->i + ((pThis->jnFlags & JNODE_LABEL)!=0));\n      break;\n    }\n    case JEACH_PARENT: {\n      if( p->i>p->iBegin && p->bRecursive ){\n        sqlite3_result_int64(ctx, (sqlite3_int64)p->sParse.aUp[p->i]);\n      }\n      break;\n    }\n    case JEACH_FULLKEY: {\n      JsonString x;\n      jsonInit(&x, ctx);\n      if( p->bRecursive ){\n        jsonEachComputePath(p, &x, p->i);\n      }else{\n        if( p->zRoot ){\n          jsonAppendRaw(&x, p->zRoot, (int)strlen(p->zRoot));\n        }else{\n          jsonAppendChar(&x, '$');\n        }\n        if( p->eType==JSON_ARRAY ){\n          jsonPrintf(30, &x, \"[%d]\", p->iRowid);\n        }else{\n          jsonPrintf(pThis->n, &x, \".%.*s\", pThis->n-2, pThis->u.zJContent+1);\n        }\n      }\n      jsonResult(&x);\n      break;\n    }\n    case JEACH_PATH: {\n      if( p->bRecursive ){\n        JsonString x;\n        jsonInit(&x, ctx);\n        jsonEachComputePath(p, &x, p->sParse.aUp[p->i]);\n        jsonResult(&x);\n        break;\n      }\n      /* For json_each() path and root are the same so fall through\n      ** into the root case */\n    }\n    default: {\n      const char *zRoot = p->zRoot;\n      if( zRoot==0 ) zRoot = \"$\";\n      sqlite3_result_text(ctx, zRoot, -1, SQLITE_STATIC);\n      break;\n    }\n    case JEACH_JSON: {\n      assert( i==JEACH_JSON );\n      sqlite3_result_text(ctx, p->sParse.zJson, -1, SQLITE_STATIC);\n      break;\n    }\n  }\n  return SQLITE_OK;\n}\n\n/* Return the current rowid value */\nstatic int jsonEachRowid(sqlite3_vtab_cursor *cur, sqlite_int64 *pRowid){\n  JsonEachCursor *p = (JsonEachCursor*)cur;\n  *pRowid = p->iRowid;\n  return SQLITE_OK;\n}\n\n/* The query strategy is to look for an equality constraint on the json\n** column.  Without such a constraint, the table cannot operate.  idxNum is\n** 1 if the constraint is found, 3 if the constraint and zRoot are found,\n** and 0 otherwise.\n*/\nstatic int jsonEachBestIndex(\n  sqlite3_vtab *tab,\n  sqlite3_index_info *pIdxInfo\n){\n  int i;\n  int jsonIdx = -1;\n  int rootIdx = -1;\n  const struct sqlite3_index_constraint *pConstraint;\n\n  UNUSED_PARAM(tab);\n  pConstraint = pIdxInfo->aConstraint;\n  for(i=0; i<pIdxInfo->nConstraint; i++, pConstraint++){\n    if( pConstraint->usable==0 ) continue;\n    if( pConstraint->op!=SQLITE_INDEX_CONSTRAINT_EQ ) continue;\n    switch( pConstraint->iColumn ){\n      case JEACH_JSON:   jsonIdx = i;    break;\n      case JEACH_ROOT:   rootIdx = i;    break;\n      default:           /* no-op */     break;\n    }\n  }\n  if( jsonIdx<0 ){\n    pIdxInfo->idxNum = 0;\n    pIdxInfo->estimatedCost = 1e99;\n  }else{\n    pIdxInfo->estimatedCost = 1.0;\n    pIdxInfo->aConstraintUsage[jsonIdx].argvIndex = 1;\n    pIdxInfo->aConstraintUsage[jsonIdx].omit = 1;\n    if( rootIdx<0 ){\n      pIdxInfo->idxNum = 1;\n    }else{\n      pIdxInfo->aConstraintUsage[rootIdx].argvIndex = 2;\n      pIdxInfo->aConstraintUsage[rootIdx].omit = 1;\n      pIdxInfo->idxNum = 3;\n    }\n  }\n  return SQLITE_OK;\n}\n\n/* Start a search on a new JSON string */\nstatic int jsonEachFilter(\n  sqlite3_vtab_cursor *cur,\n  int idxNum, const char *idxStr,\n  int argc, sqlite3_value **argv\n){\n  JsonEachCursor *p = (JsonEachCursor*)cur;\n  const char *z;\n  const char *zRoot = 0;\n  sqlite3_int64 n;\n\n  UNUSED_PARAM(idxStr);\n  UNUSED_PARAM(argc);\n  jsonEachCursorReset(p);\n  if( idxNum==0 ) return SQLITE_OK;\n  z = (const char*)sqlite3_value_text(argv[0]);\n  if( z==0 ) return SQLITE_OK;\n  n = sqlite3_value_bytes(argv[0]);\n  p->zJson = sqlite3_malloc64( n+1 );\n  if( p->zJson==0 ) return SQLITE_NOMEM;\n  memcpy(p->zJson, z, (size_t)n+1);\n  if( jsonParse(&p->sParse, 0, p->zJson) ){\n    int rc = SQLITE_NOMEM;\n    if( p->sParse.oom==0 ){\n      sqlite3_free(cur->pVtab->zErrMsg);\n      cur->pVtab->zErrMsg = sqlite3_mprintf(\"malformed JSON\");\n      if( cur->pVtab->zErrMsg ) rc = SQLITE_ERROR;\n    }\n    jsonEachCursorReset(p);\n    return rc;\n  }else if( p->bRecursive && jsonParseFindParents(&p->sParse) ){\n    jsonEachCursorReset(p);\n    return SQLITE_NOMEM;\n  }else{\n    JsonNode *pNode = 0;\n    if( idxNum==3 ){\n      const char *zErr = 0;\n      zRoot = (const char*)sqlite3_value_text(argv[1]);\n      if( zRoot==0 ) return SQLITE_OK;\n      n = sqlite3_value_bytes(argv[1]);\n      p->zRoot = sqlite3_malloc64( n+1 );\n      if( p->zRoot==0 ) return SQLITE_NOMEM;\n      memcpy(p->zRoot, zRoot, (size_t)n+1);\n      if( zRoot[0]!='$' ){\n        zErr = zRoot;\n      }else{\n        pNode = jsonLookupStep(&p->sParse, 0, p->zRoot+1, 0, &zErr);\n      }\n      if( zErr ){\n        sqlite3_free(cur->pVtab->zErrMsg);\n        cur->pVtab->zErrMsg = jsonPathSyntaxError(zErr);\n        jsonEachCursorReset(p);\n        return cur->pVtab->zErrMsg ? SQLITE_ERROR : SQLITE_NOMEM;\n      }else if( pNode==0 ){\n        return SQLITE_OK;\n      }\n    }else{\n      pNode = p->sParse.aNode;\n    }\n    p->iBegin = p->i = (int)(pNode - p->sParse.aNode);\n    p->eType = pNode->eType;\n    if( p->eType>=JSON_ARRAY ){\n      pNode->u.iKey = 0;\n      p->iEnd = p->i + pNode->n + 1;\n      if( p->bRecursive ){\n        p->eType = p->sParse.aNode[p->sParse.aUp[p->i]].eType;\n        if( p->i>0 && (p->sParse.aNode[p->i-1].jnFlags & JNODE_LABEL)!=0 ){\n          p->i--;\n        }\n      }else{\n        p->i++;\n      }\n    }else{\n      p->iEnd = p->i+1;\n    }\n  }\n  return SQLITE_OK;\n}\n\n/* The methods of the json_each virtual table */\nstatic sqlite3_module jsonEachModule = {\n  0,                         /* iVersion */\n  0,                         /* xCreate */\n  jsonEachConnect,           /* xConnect */\n  jsonEachBestIndex,         /* xBestIndex */\n  jsonEachDisconnect,        /* xDisconnect */\n  0,                         /* xDestroy */\n  jsonEachOpenEach,          /* xOpen - open a cursor */\n  jsonEachClose,             /* xClose - close a cursor */\n  jsonEachFilter,            /* xFilter - configure scan constraints */\n  jsonEachNext,              /* xNext - advance a cursor */\n  jsonEachEof,               /* xEof - check for end of scan */\n  jsonEachColumn,            /* xColumn - read data */\n  jsonEachRowid,             /* xRowid - read data */\n  0,                         /* xUpdate */\n  0,                         /* xBegin */\n  0,                         /* xSync */\n  0,                         /* xCommit */\n  0,                         /* xRollback */\n  0,                         /* xFindMethod */\n  0,                         /* xRename */\n  0,                         /* xSavepoint */\n  0,                         /* xRelease */\n  0                          /* xRollbackTo */\n};\n\n/* The methods of the json_tree virtual table. */\nstatic sqlite3_module jsonTreeModule = {\n  0,                         /* iVersion */\n  0,                         /* xCreate */\n  jsonEachConnect,           /* xConnect */\n  jsonEachBestIndex,         /* xBestIndex */\n  jsonEachDisconnect,        /* xDisconnect */\n  0,                         /* xDestroy */\n  jsonEachOpenTree,          /* xOpen - open a cursor */\n  jsonEachClose,             /* xClose - close a cursor */\n  jsonEachFilter,            /* xFilter - configure scan constraints */\n  jsonEachNext,              /* xNext - advance a cursor */\n  jsonEachEof,               /* xEof - check for end of scan */\n  jsonEachColumn,            /* xColumn - read data */\n  jsonEachRowid,             /* xRowid - read data */\n  0,                         /* xUpdate */\n  0,                         /* xBegin */\n  0,                         /* xSync */\n  0,                         /* xCommit */\n  0,                         /* xRollback */\n  0,                         /* xFindMethod */\n  0,                         /* xRename */\n  0,                         /* xSavepoint */\n  0,                         /* xRelease */\n  0                          /* xRollbackTo */\n};\n#endif /* SQLITE_OMIT_VIRTUALTABLE */\n\n/****************************************************************************\n** The following routines are the only publically visible identifiers in this\n** file.  Call the following routines in order to register the various SQL\n** functions and the virtual table implemented by this file.\n****************************************************************************/\n\nSQLITE_PRIVATE int sqlite3Json1Init(sqlite3 *db){\n  int rc = SQLITE_OK;\n  unsigned int i;\n  static const struct {\n     const char *zName;\n     int nArg;\n     int flag;\n     void (*xFunc)(sqlite3_context*,int,sqlite3_value**);\n  } aFunc[] = {\n    { \"json\",                 1, 0,   jsonRemoveFunc        },\n    { \"json_array\",          -1, 0,   jsonArrayFunc         },\n    { \"json_array_length\",    1, 0,   jsonArrayLengthFunc   },\n    { \"json_array_length\",    2, 0,   jsonArrayLengthFunc   },\n    { \"json_extract\",        -1, 0,   jsonExtractFunc       },\n    { \"json_insert\",         -1, 0,   jsonSetFunc           },\n    { \"json_object\",         -1, 0,   jsonObjectFunc        },\n    { \"json_patch\",           2, 0,   jsonPatchFunc         },\n    { \"json_quote\",           1, 0,   jsonQuoteFunc         },\n    { \"json_remove\",         -1, 0,   jsonRemoveFunc        },\n    { \"json_replace\",        -1, 0,   jsonReplaceFunc       },\n    { \"json_set\",            -1, 1,   jsonSetFunc           },\n    { \"json_type\",            1, 0,   jsonTypeFunc          },\n    { \"json_type\",            2, 0,   jsonTypeFunc          },\n    { \"json_valid\",           1, 0,   jsonValidFunc         },\n\n#if SQLITE_DEBUG\n    /* DEBUG and TESTING functions */\n    { \"json_parse\",           1, 0,   jsonParseFunc         },\n    { \"json_test1\",           1, 0,   jsonTest1Func         },\n#endif\n  };\n  static const struct {\n     const char *zName;\n     int nArg;\n     void (*xStep)(sqlite3_context*,int,sqlite3_value**);\n     void (*xFinal)(sqlite3_context*);\n  } aAgg[] = {\n    { \"json_group_array\",     1,   jsonArrayStep,   jsonArrayFinal  },\n    { \"json_group_object\",    2,   jsonObjectStep,  jsonObjectFinal },\n  };\n#ifndef SQLITE_OMIT_VIRTUALTABLE\n  static const struct {\n     const char *zName;\n     sqlite3_module *pModule;\n  } aMod[] = {\n    { \"json_each\",            &jsonEachModule               },\n    { \"json_tree\",            &jsonTreeModule               },\n  };\n#endif\n  for(i=0; i<sizeof(aFunc)/sizeof(aFunc[0]) && rc==SQLITE_OK; i++){\n    rc = sqlite3_create_function(db, aFunc[i].zName, aFunc[i].nArg,\n                                 SQLITE_UTF8 | SQLITE_DETERMINISTIC, \n                                 (void*)&aFunc[i].flag,\n                                 aFunc[i].xFunc, 0, 0);\n  }\n  for(i=0; i<sizeof(aAgg)/sizeof(aAgg[0]) && rc==SQLITE_OK; i++){\n    rc = sqlite3_create_function(db, aAgg[i].zName, aAgg[i].nArg,\n                                 SQLITE_UTF8 | SQLITE_DETERMINISTIC, 0,\n                                 0, aAgg[i].xStep, aAgg[i].xFinal);\n  }\n#ifndef SQLITE_OMIT_VIRTUALTABLE\n  for(i=0; i<sizeof(aMod)/sizeof(aMod[0]) && rc==SQLITE_OK; i++){\n    rc = sqlite3_create_module(db, aMod[i].zName, aMod[i].pModule, 0);\n  }\n#endif\n  return rc;\n}\n\n\n#ifndef SQLITE_CORE\n#ifdef _WIN32\n__declspec(dllexport)\n#endif\nSQLITE_API int sqlite3_json_init(\n  sqlite3 *db, \n  char **pzErrMsg, \n  const sqlite3_api_routines *pApi\n){\n  SQLITE_EXTENSION_INIT2(pApi);\n  (void)pzErrMsg;  /* Unused parameter */\n  return sqlite3Json1Init(db);\n}\n#endif\n#endif /* !defined(SQLITE_CORE) || defined(SQLITE_ENABLE_JSON1) */\n\n/************** End of json1.c ***********************************************/\n/************** Begin file fts5.c ********************************************/\n\n\n#if !defined(SQLITE_CORE) || defined(SQLITE_ENABLE_FTS5) \n\n#if !defined(NDEBUG) && !defined(SQLITE_DEBUG) \n# define NDEBUG 1\n#endif\n#if defined(NDEBUG) && defined(SQLITE_DEBUG)\n# undef NDEBUG\n#endif\n\n/*\n** 2014 May 31\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n******************************************************************************\n**\n** Interfaces to extend FTS5. Using the interfaces defined in this file, \n** FTS5 may be extended with:\n**\n**     * custom tokenizers, and\n**     * custom auxiliary functions.\n*/\n\n\n#ifndef _FTS5_H\n#define _FTS5_H\n\n/* #include \"sqlite3.h\" */\n\n#if 0\nextern \"C\" {\n#endif\n\n/*************************************************************************\n** CUSTOM AUXILIARY FUNCTIONS\n**\n** Virtual table implementations may overload SQL functions by implementing\n** the sqlite3_module.xFindFunction() method.\n*/\n\ntypedef struct Fts5ExtensionApi Fts5ExtensionApi;\ntypedef struct Fts5Context Fts5Context;\ntypedef struct Fts5PhraseIter Fts5PhraseIter;\n\ntypedef void (*fts5_extension_function)(\n  const Fts5ExtensionApi *pApi,   /* API offered by current FTS version */\n  Fts5Context *pFts,              /* First arg to pass to pApi functions */\n  sqlite3_context *pCtx,          /* Context for returning result/error */\n  int nVal,                       /* Number of values in apVal[] array */\n  sqlite3_value **apVal           /* Array of trailing arguments */\n);\n\nstruct Fts5PhraseIter {\n  const unsigned char *a;\n  const unsigned char *b;\n};\n\n/*\n** EXTENSION API FUNCTIONS\n**\n** xUserData(pFts):\n**   Return a copy of the context pointer the extension function was \n**   registered with.\n**\n** xColumnTotalSize(pFts, iCol, pnToken):\n**   If parameter iCol is less than zero, set output variable *pnToken\n**   to the total number of tokens in the FTS5 table. Or, if iCol is\n**   non-negative but less than the number of columns in the table, return\n**   the total number of tokens in column iCol, considering all rows in \n**   the FTS5 table.\n**\n**   If parameter iCol is greater than or equal to the number of columns\n**   in the table, SQLITE_RANGE is returned. Or, if an error occurs (e.g.\n**   an OOM condition or IO error), an appropriate SQLite error code is \n**   returned.\n**\n** xColumnCount(pFts):\n**   Return the number of columns in the table.\n**\n** xColumnSize(pFts, iCol, pnToken):\n**   If parameter iCol is less than zero, set output variable *pnToken\n**   to the total number of tokens in the current row. Or, if iCol is\n**   non-negative but less than the number of columns in the table, set\n**   *pnToken to the number of tokens in column iCol of the current row.\n**\n**   If parameter iCol is greater than or equal to the number of columns\n**   in the table, SQLITE_RANGE is returned. Or, if an error occurs (e.g.\n**   an OOM condition or IO error), an appropriate SQLite error code is \n**   returned.\n**\n**   This function may be quite inefficient if used with an FTS5 table\n**   created with the \"columnsize=0\" option.\n**\n** xColumnText:\n**   This function attempts to retrieve the text of column iCol of the\n**   current document. If successful, (*pz) is set to point to a buffer\n**   containing the text in utf-8 encoding, (*pn) is set to the size in bytes\n**   (not characters) of the buffer and SQLITE_OK is returned. Otherwise,\n**   if an error occurs, an SQLite error code is returned and the final values\n**   of (*pz) and (*pn) are undefined.\n**\n** xPhraseCount:\n**   Returns the number of phrases in the current query expression.\n**\n** xPhraseSize:\n**   Returns the number of tokens in phrase iPhrase of the query. Phrases\n**   are numbered starting from zero.\n**\n** xInstCount:\n**   Set *pnInst to the total number of occurrences of all phrases within\n**   the query within the current row. Return SQLITE_OK if successful, or\n**   an error code (i.e. SQLITE_NOMEM) if an error occurs.\n**\n**   This API can be quite slow if used with an FTS5 table created with the\n**   \"detail=none\" or \"detail=column\" option. If the FTS5 table is created \n**   with either \"detail=none\" or \"detail=column\" and \"content=\" option \n**   (i.e. if it is a contentless table), then this API always returns 0.\n**\n** xInst:\n**   Query for the details of phrase match iIdx within the current row.\n**   Phrase matches are numbered starting from zero, so the iIdx argument\n**   should be greater than or equal to zero and smaller than the value\n**   output by xInstCount().\n**\n**   Usually, output parameter *piPhrase is set to the phrase number, *piCol\n**   to the column in which it occurs and *piOff the token offset of the\n**   first token of the phrase. The exception is if the table was created\n**   with the offsets=0 option specified. In this case *piOff is always\n**   set to -1.\n**\n**   Returns SQLITE_OK if successful, or an error code (i.e. SQLITE_NOMEM) \n**   if an error occurs.\n**\n**   This API can be quite slow if used with an FTS5 table created with the\n**   \"detail=none\" or \"detail=column\" option. \n**\n** xRowid:\n**   Returns the rowid of the current row.\n**\n** xTokenize:\n**   Tokenize text using the tokenizer belonging to the FTS5 table.\n**\n** xQueryPhrase(pFts5, iPhrase, pUserData, xCallback):\n**   This API function is used to query the FTS table for phrase iPhrase\n**   of the current query. Specifically, a query equivalent to:\n**\n**       ... FROM ftstable WHERE ftstable MATCH $p ORDER BY rowid\n**\n**   with $p set to a phrase equivalent to the phrase iPhrase of the\n**   current query is executed. Any column filter that applies to\n**   phrase iPhrase of the current query is included in $p. For each \n**   row visited, the callback function passed as the fourth argument \n**   is invoked. The context and API objects passed to the callback \n**   function may be used to access the properties of each matched row.\n**   Invoking Api.xUserData() returns a copy of the pointer passed as \n**   the third argument to pUserData.\n**\n**   If the callback function returns any value other than SQLITE_OK, the\n**   query is abandoned and the xQueryPhrase function returns immediately.\n**   If the returned value is SQLITE_DONE, xQueryPhrase returns SQLITE_OK.\n**   Otherwise, the error code is propagated upwards.\n**\n**   If the query runs to completion without incident, SQLITE_OK is returned.\n**   Or, if some error occurs before the query completes or is aborted by\n**   the callback, an SQLite error code is returned.\n**\n**\n** xSetAuxdata(pFts5, pAux, xDelete)\n**\n**   Save the pointer passed as the second argument as the extension functions \n**   \"auxiliary data\". The pointer may then be retrieved by the current or any\n**   future invocation of the same fts5 extension function made as part of\n**   of the same MATCH query using the xGetAuxdata() API.\n**\n**   Each extension function is allocated a single auxiliary data slot for\n**   each FTS query (MATCH expression). If the extension function is invoked \n**   more than once for a single FTS query, then all invocations share a \n**   single auxiliary data context.\n**\n**   If there is already an auxiliary data pointer when this function is\n**   invoked, then it is replaced by the new pointer. If an xDelete callback\n**   was specified along with the original pointer, it is invoked at this\n**   point.\n**\n**   The xDelete callback, if one is specified, is also invoked on the\n**   auxiliary data pointer after the FTS5 query has finished.\n**\n**   If an error (e.g. an OOM condition) occurs within this function, an\n**   the auxiliary data is set to NULL and an error code returned. If the\n**   xDelete parameter was not NULL, it is invoked on the auxiliary data\n**   pointer before returning.\n**\n**\n** xGetAuxdata(pFts5, bClear)\n**\n**   Returns the current auxiliary data pointer for the fts5 extension \n**   function. See the xSetAuxdata() method for details.\n**\n**   If the bClear argument is non-zero, then the auxiliary data is cleared\n**   (set to NULL) before this function returns. In this case the xDelete,\n**   if any, is not invoked.\n**\n**\n** xRowCount(pFts5, pnRow)\n**\n**   This function is used to retrieve the total number of rows in the table.\n**   In other words, the same value that would be returned by:\n**\n**        SELECT count(*) FROM ftstable;\n**\n** xPhraseFirst()\n**   This function is used, along with type Fts5PhraseIter and the xPhraseNext\n**   method, to iterate through all instances of a single query phrase within\n**   the current row. This is the same information as is accessible via the\n**   xInstCount/xInst APIs. While the xInstCount/xInst APIs are more convenient\n**   to use, this API may be faster under some circumstances. To iterate \n**   through instances of phrase iPhrase, use the following code:\n**\n**       Fts5PhraseIter iter;\n**       int iCol, iOff;\n**       for(pApi->xPhraseFirst(pFts, iPhrase, &iter, &iCol, &iOff);\n**           iCol>=0;\n**           pApi->xPhraseNext(pFts, &iter, &iCol, &iOff)\n**       ){\n**         // An instance of phrase iPhrase at offset iOff of column iCol\n**       }\n**\n**   The Fts5PhraseIter structure is defined above. Applications should not\n**   modify this structure directly - it should only be used as shown above\n**   with the xPhraseFirst() and xPhraseNext() API methods (and by\n**   xPhraseFirstColumn() and xPhraseNextColumn() as illustrated below).\n**\n**   This API can be quite slow if used with an FTS5 table created with the\n**   \"detail=none\" or \"detail=column\" option. If the FTS5 table is created \n**   with either \"detail=none\" or \"detail=column\" and \"content=\" option \n**   (i.e. if it is a contentless table), then this API always iterates\n**   through an empty set (all calls to xPhraseFirst() set iCol to -1).\n**\n** xPhraseNext()\n**   See xPhraseFirst above.\n**\n** xPhraseFirstColumn()\n**   This function and xPhraseNextColumn() are similar to the xPhraseFirst()\n**   and xPhraseNext() APIs described above. The difference is that instead\n**   of iterating through all instances of a phrase in the current row, these\n**   APIs are used to iterate through the set of columns in the current row\n**   that contain one or more instances of a specified phrase. For example:\n**\n**       Fts5PhraseIter iter;\n**       int iCol;\n**       for(pApi->xPhraseFirstColumn(pFts, iPhrase, &iter, &iCol);\n**           iCol>=0;\n**           pApi->xPhraseNextColumn(pFts, &iter, &iCol)\n**       ){\n**         // Column iCol contains at least one instance of phrase iPhrase\n**       }\n**\n**   This API can be quite slow if used with an FTS5 table created with the\n**   \"detail=none\" option. If the FTS5 table is created with either \n**   \"detail=none\" \"content=\" option (i.e. if it is a contentless table), \n**   then this API always iterates through an empty set (all calls to \n**   xPhraseFirstColumn() set iCol to -1).\n**\n**   The information accessed using this API and its companion\n**   xPhraseFirstColumn() may also be obtained using xPhraseFirst/xPhraseNext\n**   (or xInst/xInstCount). The chief advantage of this API is that it is\n**   significantly more efficient than those alternatives when used with\n**   \"detail=column\" tables.  \n**\n** xPhraseNextColumn()\n**   See xPhraseFirstColumn above.\n*/\nstruct Fts5ExtensionApi {\n  int iVersion;                   /* Currently always set to 3 */\n\n  void *(*xUserData)(Fts5Context*);\n\n  int (*xColumnCount)(Fts5Context*);\n  int (*xRowCount)(Fts5Context*, sqlite3_int64 *pnRow);\n  int (*xColumnTotalSize)(Fts5Context*, int iCol, sqlite3_int64 *pnToken);\n\n  int (*xTokenize)(Fts5Context*, \n    const char *pText, int nText, /* Text to tokenize */\n    void *pCtx,                   /* Context passed to xToken() */\n    int (*xToken)(void*, int, const char*, int, int, int)       /* Callback */\n  );\n\n  int (*xPhraseCount)(Fts5Context*);\n  int (*xPhraseSize)(Fts5Context*, int iPhrase);\n\n  int (*xInstCount)(Fts5Context*, int *pnInst);\n  int (*xInst)(Fts5Context*, int iIdx, int *piPhrase, int *piCol, int *piOff);\n\n  sqlite3_int64 (*xRowid)(Fts5Context*);\n  int (*xColumnText)(Fts5Context*, int iCol, const char **pz, int *pn);\n  int (*xColumnSize)(Fts5Context*, int iCol, int *pnToken);\n\n  int (*xQueryPhrase)(Fts5Context*, int iPhrase, void *pUserData,\n    int(*)(const Fts5ExtensionApi*,Fts5Context*,void*)\n  );\n  int (*xSetAuxdata)(Fts5Context*, void *pAux, void(*xDelete)(void*));\n  void *(*xGetAuxdata)(Fts5Context*, int bClear);\n\n  int (*xPhraseFirst)(Fts5Context*, int iPhrase, Fts5PhraseIter*, int*, int*);\n  void (*xPhraseNext)(Fts5Context*, Fts5PhraseIter*, int *piCol, int *piOff);\n\n  int (*xPhraseFirstColumn)(Fts5Context*, int iPhrase, Fts5PhraseIter*, int*);\n  void (*xPhraseNextColumn)(Fts5Context*, Fts5PhraseIter*, int *piCol);\n};\n\n/* \n** CUSTOM AUXILIARY FUNCTIONS\n*************************************************************************/\n\n/*************************************************************************\n** CUSTOM TOKENIZERS\n**\n** Applications may also register custom tokenizer types. A tokenizer \n** is registered by providing fts5 with a populated instance of the \n** following structure. All structure methods must be defined, setting\n** any member of the fts5_tokenizer struct to NULL leads to undefined\n** behaviour. The structure methods are expected to function as follows:\n**\n** xCreate:\n**   This function is used to allocate and initialize a tokenizer instance.\n**   A tokenizer instance is required to actually tokenize text.\n**\n**   The first argument passed to this function is a copy of the (void*)\n**   pointer provided by the application when the fts5_tokenizer object\n**   was registered with FTS5 (the third argument to xCreateTokenizer()). \n**   The second and third arguments are an array of nul-terminated strings\n**   containing the tokenizer arguments, if any, specified following the\n**   tokenizer name as part of the CREATE VIRTUAL TABLE statement used\n**   to create the FTS5 table.\n**\n**   The final argument is an output variable. If successful, (*ppOut) \n**   should be set to point to the new tokenizer handle and SQLITE_OK\n**   returned. If an error occurs, some value other than SQLITE_OK should\n**   be returned. In this case, fts5 assumes that the final value of *ppOut \n**   is undefined.\n**\n** xDelete:\n**   This function is invoked to delete a tokenizer handle previously\n**   allocated using xCreate(). Fts5 guarantees that this function will\n**   be invoked exactly once for each successful call to xCreate().\n**\n** xTokenize:\n**   This function is expected to tokenize the nText byte string indicated \n**   by argument pText. pText may or may not be nul-terminated. The first\n**   argument passed to this function is a pointer to an Fts5Tokenizer object\n**   returned by an earlier call to xCreate().\n**\n**   The second argument indicates the reason that FTS5 is requesting\n**   tokenization of the supplied text. This is always one of the following\n**   four values:\n**\n**   <ul><li> <b>FTS5_TOKENIZE_DOCUMENT</b> - A document is being inserted into\n**            or removed from the FTS table. The tokenizer is being invoked to\n**            determine the set of tokens to add to (or delete from) the\n**            FTS index.\n**\n**       <li> <b>FTS5_TOKENIZE_QUERY</b> - A MATCH query is being executed \n**            against the FTS index. The tokenizer is being called to tokenize \n**            a bareword or quoted string specified as part of the query.\n**\n**       <li> <b>(FTS5_TOKENIZE_QUERY | FTS5_TOKENIZE_PREFIX)</b> - Same as\n**            FTS5_TOKENIZE_QUERY, except that the bareword or quoted string is\n**            followed by a \"*\" character, indicating that the last token\n**            returned by the tokenizer will be treated as a token prefix.\n**\n**       <li> <b>FTS5_TOKENIZE_AUX</b> - The tokenizer is being invoked to \n**            satisfy an fts5_api.xTokenize() request made by an auxiliary\n**            function. Or an fts5_api.xColumnSize() request made by the same\n**            on a columnsize=0 database.  \n**   </ul>\n**\n**   For each token in the input string, the supplied callback xToken() must\n**   be invoked. The first argument to it should be a copy of the pointer\n**   passed as the second argument to xTokenize(). The third and fourth\n**   arguments are a pointer to a buffer containing the token text, and the\n**   size of the token in bytes. The 4th and 5th arguments are the byte offsets\n**   of the first byte of and first byte immediately following the text from\n**   which the token is derived within the input.\n**\n**   The second argument passed to the xToken() callback (\"tflags\") should\n**   normally be set to 0. The exception is if the tokenizer supports \n**   synonyms. In this case see the discussion below for details.\n**\n**   FTS5 assumes the xToken() callback is invoked for each token in the \n**   order that they occur within the input text.\n**\n**   If an xToken() callback returns any value other than SQLITE_OK, then\n**   the tokenization should be abandoned and the xTokenize() method should\n**   immediately return a copy of the xToken() return value. Or, if the\n**   input buffer is exhausted, xTokenize() should return SQLITE_OK. Finally,\n**   if an error occurs with the xTokenize() implementation itself, it\n**   may abandon the tokenization and return any error code other than\n**   SQLITE_OK or SQLITE_DONE.\n**\n** SYNONYM SUPPORT\n**\n**   Custom tokenizers may also support synonyms. Consider a case in which a\n**   user wishes to query for a phrase such as \"first place\". Using the \n**   built-in tokenizers, the FTS5 query 'first + place' will match instances\n**   of \"first place\" within the document set, but not alternative forms\n**   such as \"1st place\". In some applications, it would be better to match\n**   all instances of \"first place\" or \"1st place\" regardless of which form\n**   the user specified in the MATCH query text.\n**\n**   There are several ways to approach this in FTS5:\n**\n**   <ol><li> By mapping all synonyms to a single token. In this case, the \n**            In the above example, this means that the tokenizer returns the\n**            same token for inputs \"first\" and \"1st\". Say that token is in\n**            fact \"first\", so that when the user inserts the document \"I won\n**            1st place\" entries are added to the index for tokens \"i\", \"won\",\n**            \"first\" and \"place\". If the user then queries for '1st + place',\n**            the tokenizer substitutes \"first\" for \"1st\" and the query works\n**            as expected.\n**\n**       <li> By adding multiple synonyms for a single term to the FTS index.\n**            In this case, when tokenizing query text, the tokenizer may \n**            provide multiple synonyms for a single term within the document.\n**            FTS5 then queries the index for each synonym individually. For\n**            example, faced with the query:\n**\n**   <codeblock>\n**     ... MATCH 'first place'</codeblock>\n**\n**            the tokenizer offers both \"1st\" and \"first\" as synonyms for the\n**            first token in the MATCH query and FTS5 effectively runs a query \n**            similar to:\n**\n**   <codeblock>\n**     ... MATCH '(first OR 1st) place'</codeblock>\n**\n**            except that, for the purposes of auxiliary functions, the query\n**            still appears to contain just two phrases - \"(first OR 1st)\" \n**            being treated as a single phrase.\n**\n**       <li> By adding multiple synonyms for a single term to the FTS index.\n**            Using this method, when tokenizing document text, the tokenizer\n**            provides multiple synonyms for each token. So that when a \n**            document such as \"I won first place\" is tokenized, entries are\n**            added to the FTS index for \"i\", \"won\", \"first\", \"1st\" and\n**            \"place\".\n**\n**            This way, even if the tokenizer does not provide synonyms\n**            when tokenizing query text (it should not - to do would be\n**            inefficient), it doesn't matter if the user queries for \n**            'first + place' or '1st + place', as there are entires in the\n**            FTS index corresponding to both forms of the first token.\n**   </ol>\n**\n**   Whether it is parsing document or query text, any call to xToken that\n**   specifies a <i>tflags</i> argument with the FTS5_TOKEN_COLOCATED bit\n**   is considered to supply a synonym for the previous token. For example,\n**   when parsing the document \"I won first place\", a tokenizer that supports\n**   synonyms would call xToken() 5 times, as follows:\n**\n**   <codeblock>\n**       xToken(pCtx, 0, \"i\",                      1,  0,  1);\n**       xToken(pCtx, 0, \"won\",                    3,  2,  5);\n**       xToken(pCtx, 0, \"first\",                  5,  6, 11);\n**       xToken(pCtx, FTS5_TOKEN_COLOCATED, \"1st\", 3,  6, 11);\n**       xToken(pCtx, 0, \"place\",                  5, 12, 17);\n**</codeblock>\n**\n**   It is an error to specify the FTS5_TOKEN_COLOCATED flag the first time\n**   xToken() is called. Multiple synonyms may be specified for a single token\n**   by making multiple calls to xToken(FTS5_TOKEN_COLOCATED) in sequence. \n**   There is no limit to the number of synonyms that may be provided for a\n**   single token.\n**\n**   In many cases, method (1) above is the best approach. It does not add \n**   extra data to the FTS index or require FTS5 to query for multiple terms,\n**   so it is efficient in terms of disk space and query speed. However, it\n**   does not support prefix queries very well. If, as suggested above, the\n**   token \"first\" is subsituted for \"1st\" by the tokenizer, then the query:\n**\n**   <codeblock>\n**     ... MATCH '1s*'</codeblock>\n**\n**   will not match documents that contain the token \"1st\" (as the tokenizer\n**   will probably not map \"1s\" to any prefix of \"first\").\n**\n**   For full prefix support, method (3) may be preferred. In this case, \n**   because the index contains entries for both \"first\" and \"1st\", prefix\n**   queries such as 'fi*' or '1s*' will match correctly. However, because\n**   extra entries are added to the FTS index, this method uses more space\n**   within the database.\n**\n**   Method (2) offers a midpoint between (1) and (3). Using this method,\n**   a query such as '1s*' will match documents that contain the literal \n**   token \"1st\", but not \"first\" (assuming the tokenizer is not able to\n**   provide synonyms for prefixes). However, a non-prefix query like '1st'\n**   will match against \"1st\" and \"first\". This method does not require\n**   extra disk space, as no extra entries are added to the FTS index. \n**   On the other hand, it may require more CPU cycles to run MATCH queries,\n**   as separate queries of the FTS index are required for each synonym.\n**\n**   When using methods (2) or (3), it is important that the tokenizer only\n**   provide synonyms when tokenizing document text (method (2)) or query\n**   text (method (3)), not both. Doing so will not cause any errors, but is\n**   inefficient.\n*/\ntypedef struct Fts5Tokenizer Fts5Tokenizer;\ntypedef struct fts5_tokenizer fts5_tokenizer;\nstruct fts5_tokenizer {\n  int (*xCreate)(void*, const char **azArg, int nArg, Fts5Tokenizer **ppOut);\n  void (*xDelete)(Fts5Tokenizer*);\n  int (*xTokenize)(Fts5Tokenizer*, \n      void *pCtx,\n      int flags,            /* Mask of FTS5_TOKENIZE_* flags */\n      const char *pText, int nText, \n      int (*xToken)(\n        void *pCtx,         /* Copy of 2nd argument to xTokenize() */\n        int tflags,         /* Mask of FTS5_TOKEN_* flags */\n        const char *pToken, /* Pointer to buffer containing token */\n        int nToken,         /* Size of token in bytes */\n        int iStart,         /* Byte offset of token within input text */\n        int iEnd            /* Byte offset of end of token within input text */\n      )\n  );\n};\n\n/* Flags that may be passed as the third argument to xTokenize() */\n#define FTS5_TOKENIZE_QUERY     0x0001\n#define FTS5_TOKENIZE_PREFIX    0x0002\n#define FTS5_TOKENIZE_DOCUMENT  0x0004\n#define FTS5_TOKENIZE_AUX       0x0008\n\n/* Flags that may be passed by the tokenizer implementation back to FTS5\n** as the third argument to the supplied xToken callback. */\n#define FTS5_TOKEN_COLOCATED    0x0001      /* Same position as prev. token */\n\n/*\n** END OF CUSTOM TOKENIZERS\n*************************************************************************/\n\n/*************************************************************************\n** FTS5 EXTENSION REGISTRATION API\n*/\ntypedef struct fts5_api fts5_api;\nstruct fts5_api {\n  int iVersion;                   /* Currently always set to 2 */\n\n  /* Create a new tokenizer */\n  int (*xCreateTokenizer)(\n    fts5_api *pApi,\n    const char *zName,\n    void *pContext,\n    fts5_tokenizer *pTokenizer,\n    void (*xDestroy)(void*)\n  );\n\n  /* Find an existing tokenizer */\n  int (*xFindTokenizer)(\n    fts5_api *pApi,\n    const char *zName,\n    void **ppContext,\n    fts5_tokenizer *pTokenizer\n  );\n\n  /* Create a new auxiliary function */\n  int (*xCreateFunction)(\n    fts5_api *pApi,\n    const char *zName,\n    void *pContext,\n    fts5_extension_function xFunction,\n    void (*xDestroy)(void*)\n  );\n};\n\n/*\n** END OF REGISTRATION API\n*************************************************************************/\n\n#if 0\n}  /* end of the 'extern \"C\"' block */\n#endif\n\n#endif /* _FTS5_H */\n\n/*\n** 2014 May 31\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n******************************************************************************\n**\n*/\n#ifndef _FTS5INT_H\n#define _FTS5INT_H\n\n/* #include \"fts5.h\" */\n/* #include \"sqlite3ext.h\" */\nSQLITE_EXTENSION_INIT1\n\n/* #include <string.h> */\n/* #include <assert.h> */\n\n#ifndef SQLITE_AMALGAMATION\n\ntypedef unsigned char  u8;\ntypedef unsigned int   u32;\ntypedef unsigned short u16;\ntypedef short i16;\ntypedef sqlite3_int64 i64;\ntypedef sqlite3_uint64 u64;\n\n#ifndef ArraySize\n# define ArraySize(x) ((int)(sizeof(x) / sizeof(x[0])))\n#endif\n\n#define testcase(x)\n#define ALWAYS(x) 1\n#define NEVER(x) 0\n\n#define MIN(x,y) (((x) < (y)) ? (x) : (y))\n#define MAX(x,y) (((x) > (y)) ? (x) : (y))\n\n/*\n** Constants for the largest and smallest possible 64-bit signed integers.\n*/\n# define LARGEST_INT64  (0xffffffff|(((i64)0x7fffffff)<<32))\n# define SMALLEST_INT64 (((i64)-1) - LARGEST_INT64)\n\n#endif\n\n/* Truncate very long tokens to this many bytes. Hard limit is \n** (65536-1-1-4-9)==65521 bytes. The limiting factor is the 16-bit offset\n** field that occurs at the start of each leaf page (see fts5_index.c). */\n#define FTS5_MAX_TOKEN_SIZE 32768\n\n/*\n** Maximum number of prefix indexes on single FTS5 table. This must be\n** less than 32. If it is set to anything large than that, an #error\n** directive in fts5_index.c will cause the build to fail.\n*/\n#define FTS5_MAX_PREFIX_INDEXES 31\n\n#define FTS5_DEFAULT_NEARDIST 10\n#define FTS5_DEFAULT_RANK     \"bm25\"\n\n/* Name of rank and rowid columns */\n#define FTS5_RANK_NAME \"rank\"\n#define FTS5_ROWID_NAME \"rowid\"\n\n#ifdef SQLITE_DEBUG\n# define FTS5_CORRUPT sqlite3Fts5Corrupt()\nstatic int sqlite3Fts5Corrupt(void);\n#else\n# define FTS5_CORRUPT SQLITE_CORRUPT_VTAB\n#endif\n\n/*\n** The assert_nc() macro is similar to the assert() macro, except that it\n** is used for assert() conditions that are true only if it can be \n** guranteed that the database is not corrupt.\n*/\n#ifdef SQLITE_DEBUG\nSQLITE_API extern int sqlite3_fts5_may_be_corrupt;\n# define assert_nc(x) assert(sqlite3_fts5_may_be_corrupt || (x))\n#else\n# define assert_nc(x) assert(x)\n#endif\n\n/* Mark a function parameter as unused, to suppress nuisance compiler\n** warnings. */\n#ifndef UNUSED_PARAM\n# define UNUSED_PARAM(X)  (void)(X)\n#endif\n\n#ifndef UNUSED_PARAM2\n# define UNUSED_PARAM2(X, Y)  (void)(X), (void)(Y)\n#endif\n\ntypedef struct Fts5Global Fts5Global;\ntypedef struct Fts5Colset Fts5Colset;\n\n/* If a NEAR() clump or phrase may only match a specific set of columns, \n** then an object of the following type is used to record the set of columns.\n** Each entry in the aiCol[] array is a column that may be matched.\n**\n** This object is used by fts5_expr.c and fts5_index.c.\n*/\nstruct Fts5Colset {\n  int nCol;\n  int aiCol[1];\n};\n\n\n\n/**************************************************************************\n** Interface to code in fts5_config.c. fts5_config.c contains contains code\n** to parse the arguments passed to the CREATE VIRTUAL TABLE statement.\n*/\n\ntypedef struct Fts5Config Fts5Config;\n\n/*\n** An instance of the following structure encodes all information that can\n** be gleaned from the CREATE VIRTUAL TABLE statement.\n**\n** And all information loaded from the %_config table.\n**\n** nAutomerge:\n**   The minimum number of segments that an auto-merge operation should\n**   attempt to merge together. A value of 1 sets the object to use the \n**   compile time default. Zero disables auto-merge altogether.\n**\n** zContent:\n**\n** zContentRowid:\n**   The value of the content_rowid= option, if one was specified. Or \n**   the string \"rowid\" otherwise. This text is not quoted - if it is\n**   used as part of an SQL statement it needs to be quoted appropriately.\n**\n** zContentExprlist:\n**\n** pzErrmsg:\n**   This exists in order to allow the fts5_index.c module to return a \n**   decent error message if it encounters a file-format version it does\n**   not understand.\n**\n** bColumnsize:\n**   True if the %_docsize table is created.\n**\n** bPrefixIndex:\n**   This is only used for debugging. If set to false, any prefix indexes\n**   are ignored. This value is configured using:\n**\n**       INSERT INTO tbl(tbl, rank) VALUES('prefix-index', $bPrefixIndex);\n**\n*/\nstruct Fts5Config {\n  sqlite3 *db;                    /* Database handle */\n  char *zDb;                      /* Database holding FTS index (e.g. \"main\") */\n  char *zName;                    /* Name of FTS index */\n  int nCol;                       /* Number of columns */\n  char **azCol;                   /* Column names */\n  u8 *abUnindexed;                /* True for unindexed columns */\n  int nPrefix;                    /* Number of prefix indexes */\n  int *aPrefix;                   /* Sizes in bytes of nPrefix prefix indexes */\n  int eContent;                   /* An FTS5_CONTENT value */\n  char *zContent;                 /* content table */ \n  char *zContentRowid;            /* \"content_rowid=\" option value */ \n  int bColumnsize;                /* \"columnsize=\" option value (dflt==1) */\n  int eDetail;                    /* FTS5_DETAIL_XXX value */\n  char *zContentExprlist;\n  Fts5Tokenizer *pTok;\n  fts5_tokenizer *pTokApi;\n\n  /* Values loaded from the %_config table */\n  int iCookie;                    /* Incremented when %_config is modified */\n  int pgsz;                       /* Approximate page size used in %_data */\n  int nAutomerge;                 /* 'automerge' setting */\n  int nCrisisMerge;               /* Maximum allowed segments per level */\n  int nUsermerge;                 /* 'usermerge' setting */\n  int nHashSize;                  /* Bytes of memory for in-memory hash */\n  char *zRank;                    /* Name of rank function */\n  char *zRankArgs;                /* Arguments to rank function */\n\n  /* If non-NULL, points to sqlite3_vtab.base.zErrmsg. Often NULL. */\n  char **pzErrmsg;\n\n#ifdef SQLITE_DEBUG\n  int bPrefixIndex;               /* True to use prefix-indexes */\n#endif\n};\n\n/* Current expected value of %_config table 'version' field */\n#define FTS5_CURRENT_VERSION 4\n\n#define FTS5_CONTENT_NORMAL   0\n#define FTS5_CONTENT_NONE     1\n#define FTS5_CONTENT_EXTERNAL 2\n\n#define FTS5_DETAIL_FULL    0\n#define FTS5_DETAIL_NONE    1\n#define FTS5_DETAIL_COLUMNS 2\n\n\n\nstatic int sqlite3Fts5ConfigParse(\n    Fts5Global*, sqlite3*, int, const char **, Fts5Config**, char**\n);\nstatic void sqlite3Fts5ConfigFree(Fts5Config*);\n\nstatic int sqlite3Fts5ConfigDeclareVtab(Fts5Config *pConfig);\n\nstatic int sqlite3Fts5Tokenize(\n  Fts5Config *pConfig,            /* FTS5 Configuration object */\n  int flags,                      /* FTS5_TOKENIZE_* flags */\n  const char *pText, int nText,   /* Text to tokenize */\n  void *pCtx,                     /* Context passed to xToken() */\n  int (*xToken)(void*, int, const char*, int, int, int)    /* Callback */\n);\n\nstatic void sqlite3Fts5Dequote(char *z);\n\n/* Load the contents of the %_config table */\nstatic int sqlite3Fts5ConfigLoad(Fts5Config*, int);\n\n/* Set the value of a single config attribute */\nstatic int sqlite3Fts5ConfigSetValue(Fts5Config*, const char*, sqlite3_value*, int*);\n\nstatic int sqlite3Fts5ConfigParseRank(const char*, char**, char**);\n\n/*\n** End of interface to code in fts5_config.c.\n**************************************************************************/\n\n/**************************************************************************\n** Interface to code in fts5_buffer.c.\n*/\n\n/*\n** Buffer object for the incremental building of string data.\n*/\ntypedef struct Fts5Buffer Fts5Buffer;\nstruct Fts5Buffer {\n  u8 *p;\n  int n;\n  int nSpace;\n};\n\nstatic int sqlite3Fts5BufferSize(int*, Fts5Buffer*, u32);\nstatic void sqlite3Fts5BufferAppendVarint(int*, Fts5Buffer*, i64);\nstatic void sqlite3Fts5BufferAppendBlob(int*, Fts5Buffer*, u32, const u8*);\nstatic void sqlite3Fts5BufferAppendString(int *, Fts5Buffer*, const char*);\nstatic void sqlite3Fts5BufferFree(Fts5Buffer*);\nstatic void sqlite3Fts5BufferZero(Fts5Buffer*);\nstatic void sqlite3Fts5BufferSet(int*, Fts5Buffer*, int, const u8*);\nstatic void sqlite3Fts5BufferAppendPrintf(int *, Fts5Buffer*, char *zFmt, ...);\n\nstatic char *sqlite3Fts5Mprintf(int *pRc, const char *zFmt, ...);\n\n#define fts5BufferZero(x)             sqlite3Fts5BufferZero(x)\n#define fts5BufferAppendVarint(a,b,c) sqlite3Fts5BufferAppendVarint(a,b,c)\n#define fts5BufferFree(a)             sqlite3Fts5BufferFree(a)\n#define fts5BufferAppendBlob(a,b,c,d) sqlite3Fts5BufferAppendBlob(a,b,c,d)\n#define fts5BufferSet(a,b,c,d)        sqlite3Fts5BufferSet(a,b,c,d)\n\n#define fts5BufferGrow(pRc,pBuf,nn) ( \\\n  (u32)((pBuf)->n) + (u32)(nn) <= (u32)((pBuf)->nSpace) ? 0 : \\\n    sqlite3Fts5BufferSize((pRc),(pBuf),(nn)+(pBuf)->n) \\\n)\n\n/* Write and decode big-endian 32-bit integer values */\nstatic void sqlite3Fts5Put32(u8*, int);\nstatic int sqlite3Fts5Get32(const u8*);\n\n#define FTS5_POS2COLUMN(iPos) (int)(iPos >> 32)\n#define FTS5_POS2OFFSET(iPos) (int)(iPos & 0xFFFFFFFF)\n\ntypedef struct Fts5PoslistReader Fts5PoslistReader;\nstruct Fts5PoslistReader {\n  /* Variables used only by sqlite3Fts5PoslistIterXXX() functions. */\n  const u8 *a;                    /* Position list to iterate through */\n  int n;                          /* Size of buffer at a[] in bytes */\n  int i;                          /* Current offset in a[] */\n\n  u8 bFlag;                       /* For client use (any custom purpose) */\n\n  /* Output variables */\n  u8 bEof;                        /* Set to true at EOF */\n  i64 iPos;                       /* (iCol<<32) + iPos */\n};\nstatic int sqlite3Fts5PoslistReaderInit(\n  const u8 *a, int n,             /* Poslist buffer to iterate through */\n  Fts5PoslistReader *pIter        /* Iterator object to initialize */\n);\nstatic int sqlite3Fts5PoslistReaderNext(Fts5PoslistReader*);\n\ntypedef struct Fts5PoslistWriter Fts5PoslistWriter;\nstruct Fts5PoslistWriter {\n  i64 iPrev;\n};\nstatic int sqlite3Fts5PoslistWriterAppend(Fts5Buffer*, Fts5PoslistWriter*, i64);\nstatic void sqlite3Fts5PoslistSafeAppend(Fts5Buffer*, i64*, i64);\n\nstatic int sqlite3Fts5PoslistNext64(\n  const u8 *a, int n,             /* Buffer containing poslist */\n  int *pi,                        /* IN/OUT: Offset within a[] */\n  i64 *piOff                      /* IN/OUT: Current offset */\n);\n\n/* Malloc utility */\nstatic void *sqlite3Fts5MallocZero(int *pRc, int nByte);\nstatic char *sqlite3Fts5Strndup(int *pRc, const char *pIn, int nIn);\n\n/* Character set tests (like isspace(), isalpha() etc.) */\nstatic int sqlite3Fts5IsBareword(char t);\n\n\n/* Bucket of terms object used by the integrity-check in offsets=0 mode. */\ntypedef struct Fts5Termset Fts5Termset;\nstatic int sqlite3Fts5TermsetNew(Fts5Termset**);\nstatic int sqlite3Fts5TermsetAdd(Fts5Termset*, int, const char*, int, int *pbPresent);\nstatic void sqlite3Fts5TermsetFree(Fts5Termset*);\n\n/*\n** End of interface to code in fts5_buffer.c.\n**************************************************************************/\n\n/**************************************************************************\n** Interface to code in fts5_index.c. fts5_index.c contains contains code\n** to access the data stored in the %_data table.\n*/\n\ntypedef struct Fts5Index Fts5Index;\ntypedef struct Fts5IndexIter Fts5IndexIter;\n\nstruct Fts5IndexIter {\n  i64 iRowid;\n  const u8 *pData;\n  int nData;\n  u8 bEof;\n};\n\n#define sqlite3Fts5IterEof(x) ((x)->bEof)\n\n/*\n** Values used as part of the flags argument passed to IndexQuery().\n*/\n#define FTS5INDEX_QUERY_PREFIX     0x0001   /* Prefix query */\n#define FTS5INDEX_QUERY_DESC       0x0002   /* Docs in descending rowid order */\n#define FTS5INDEX_QUERY_TEST_NOIDX 0x0004   /* Do not use prefix index */\n#define FTS5INDEX_QUERY_SCAN       0x0008   /* Scan query (fts5vocab) */\n\n/* The following are used internally by the fts5_index.c module. They are\n** defined here only to make it easier to avoid clashes with the flags\n** above. */\n#define FTS5INDEX_QUERY_SKIPEMPTY  0x0010\n#define FTS5INDEX_QUERY_NOOUTPUT   0x0020\n\n/*\n** Create/destroy an Fts5Index object.\n*/\nstatic int sqlite3Fts5IndexOpen(Fts5Config *pConfig, int bCreate, Fts5Index**, char**);\nstatic int sqlite3Fts5IndexClose(Fts5Index *p);\n\n/*\n** Return a simple checksum value based on the arguments.\n*/\nstatic u64 sqlite3Fts5IndexEntryCksum(\n  i64 iRowid, \n  int iCol, \n  int iPos, \n  int iIdx,\n  const char *pTerm,\n  int nTerm\n);\n\n/*\n** Argument p points to a buffer containing utf-8 text that is n bytes in \n** size. Return the number of bytes in the nChar character prefix of the\n** buffer, or 0 if there are less than nChar characters in total.\n*/\nstatic int sqlite3Fts5IndexCharlenToBytelen(\n  const char *p, \n  int nByte, \n  int nChar\n);\n\n/*\n** Open a new iterator to iterate though all rowids that match the \n** specified token or token prefix.\n*/\nstatic int sqlite3Fts5IndexQuery(\n  Fts5Index *p,                   /* FTS index to query */\n  const char *pToken, int nToken, /* Token (or prefix) to query for */\n  int flags,                      /* Mask of FTS5INDEX_QUERY_X flags */\n  Fts5Colset *pColset,            /* Match these columns only */\n  Fts5IndexIter **ppIter          /* OUT: New iterator object */\n);\n\n/*\n** The various operations on open token or token prefix iterators opened\n** using sqlite3Fts5IndexQuery().\n*/\nstatic int sqlite3Fts5IterNext(Fts5IndexIter*);\nstatic int sqlite3Fts5IterNextFrom(Fts5IndexIter*, i64 iMatch);\n\n/*\n** Close an iterator opened by sqlite3Fts5IndexQuery().\n*/\nstatic void sqlite3Fts5IterClose(Fts5IndexIter*);\n\n/*\n** This interface is used by the fts5vocab module.\n*/\nstatic const char *sqlite3Fts5IterTerm(Fts5IndexIter*, int*);\nstatic int sqlite3Fts5IterNextScan(Fts5IndexIter*);\n\n\n/*\n** Insert or remove data to or from the index. Each time a document is \n** added to or removed from the index, this function is called one or more\n** times.\n**\n** For an insert, it must be called once for each token in the new document.\n** If the operation is a delete, it must be called (at least) once for each\n** unique token in the document with an iCol value less than zero. The iPos\n** argument is ignored for a delete.\n*/\nstatic int sqlite3Fts5IndexWrite(\n  Fts5Index *p,                   /* Index to write to */\n  int iCol,                       /* Column token appears in (-ve -> delete) */\n  int iPos,                       /* Position of token within column */\n  const char *pToken, int nToken  /* Token to add or remove to or from index */\n);\n\n/*\n** Indicate that subsequent calls to sqlite3Fts5IndexWrite() pertain to\n** document iDocid.\n*/\nstatic int sqlite3Fts5IndexBeginWrite(\n  Fts5Index *p,                   /* Index to write to */\n  int bDelete,                    /* True if current operation is a delete */\n  i64 iDocid                      /* Docid to add or remove data from */\n);\n\n/*\n** Flush any data stored in the in-memory hash tables to the database.\n** Also close any open blob handles.\n*/\nstatic int sqlite3Fts5IndexSync(Fts5Index *p);\n\n/*\n** Discard any data stored in the in-memory hash tables. Do not write it\n** to the database. Additionally, assume that the contents of the %_data\n** table may have changed on disk. So any in-memory caches of %_data \n** records must be invalidated.\n*/\nstatic int sqlite3Fts5IndexRollback(Fts5Index *p);\n\n/*\n** Get or set the \"averages\" values.\n*/\nstatic int sqlite3Fts5IndexGetAverages(Fts5Index *p, i64 *pnRow, i64 *anSize);\nstatic int sqlite3Fts5IndexSetAverages(Fts5Index *p, const u8*, int);\n\n/*\n** Functions called by the storage module as part of integrity-check.\n*/\nstatic int sqlite3Fts5IndexIntegrityCheck(Fts5Index*, u64 cksum);\n\n/* \n** Called during virtual module initialization to register UDF \n** fts5_decode() with SQLite \n*/\nstatic int sqlite3Fts5IndexInit(sqlite3*);\n\nstatic int sqlite3Fts5IndexSetCookie(Fts5Index*, int);\n\n/*\n** Return the total number of entries read from the %_data table by \n** this connection since it was created.\n*/\nstatic int sqlite3Fts5IndexReads(Fts5Index *p);\n\nstatic int sqlite3Fts5IndexReinit(Fts5Index *p);\nstatic int sqlite3Fts5IndexOptimize(Fts5Index *p);\nstatic int sqlite3Fts5IndexMerge(Fts5Index *p, int nMerge);\nstatic int sqlite3Fts5IndexReset(Fts5Index *p);\n\nstatic int sqlite3Fts5IndexLoadConfig(Fts5Index *p);\n\n/*\n** End of interface to code in fts5_index.c.\n**************************************************************************/\n\n/**************************************************************************\n** Interface to code in fts5_varint.c. \n*/\nstatic int sqlite3Fts5GetVarint32(const unsigned char *p, u32 *v);\nstatic int sqlite3Fts5GetVarintLen(u32 iVal);\nstatic u8 sqlite3Fts5GetVarint(const unsigned char*, u64*);\nstatic int sqlite3Fts5PutVarint(unsigned char *p, u64 v);\n\n#define fts5GetVarint32(a,b) sqlite3Fts5GetVarint32(a,(u32*)&b)\n#define fts5GetVarint    sqlite3Fts5GetVarint\n\n#define fts5FastGetVarint32(a, iOff, nVal) {      \\\n  nVal = (a)[iOff++];                             \\\n  if( nVal & 0x80 ){                              \\\n    iOff--;                                       \\\n    iOff += fts5GetVarint32(&(a)[iOff], nVal);    \\\n  }                                               \\\n}\n\n\n/*\n** End of interface to code in fts5_varint.c.\n**************************************************************************/\n\n\n/**************************************************************************\n** Interface to code in fts5.c. \n*/\n\nstatic int sqlite3Fts5GetTokenizer(\n  Fts5Global*, \n  const char **azArg,\n  int nArg,\n  Fts5Tokenizer**,\n  fts5_tokenizer**,\n  char **pzErr\n);\n\nstatic Fts5Index *sqlite3Fts5IndexFromCsrid(Fts5Global*, i64, Fts5Config **);\n\n/*\n** End of interface to code in fts5.c.\n**************************************************************************/\n\n/**************************************************************************\n** Interface to code in fts5_hash.c. \n*/\ntypedef struct Fts5Hash Fts5Hash;\n\n/*\n** Create a hash table, free a hash table.\n*/\nstatic int sqlite3Fts5HashNew(Fts5Config*, Fts5Hash**, int *pnSize);\nstatic void sqlite3Fts5HashFree(Fts5Hash*);\n\nstatic int sqlite3Fts5HashWrite(\n  Fts5Hash*,\n  i64 iRowid,                     /* Rowid for this entry */\n  int iCol,                       /* Column token appears in (-ve -> delete) */\n  int iPos,                       /* Position of token within column */\n  char bByte,\n  const char *pToken, int nToken  /* Token to add or remove to or from index */\n);\n\n/*\n** Empty (but do not delete) a hash table.\n*/\nstatic void sqlite3Fts5HashClear(Fts5Hash*);\n\nstatic int sqlite3Fts5HashQuery(\n  Fts5Hash*,                      /* Hash table to query */\n  const char *pTerm, int nTerm,   /* Query term */\n  const u8 **ppDoclist,           /* OUT: Pointer to doclist for pTerm */\n  int *pnDoclist                  /* OUT: Size of doclist in bytes */\n);\n\nstatic int sqlite3Fts5HashScanInit(\n  Fts5Hash*,                      /* Hash table to query */\n  const char *pTerm, int nTerm    /* Query prefix */\n);\nstatic void sqlite3Fts5HashScanNext(Fts5Hash*);\nstatic int sqlite3Fts5HashScanEof(Fts5Hash*);\nstatic void sqlite3Fts5HashScanEntry(Fts5Hash *,\n  const char **pzTerm,            /* OUT: term (nul-terminated) */\n  const u8 **ppDoclist,           /* OUT: pointer to doclist */\n  int *pnDoclist                  /* OUT: size of doclist in bytes */\n);\n\n\n/*\n** End of interface to code in fts5_hash.c.\n**************************************************************************/\n\n/**************************************************************************\n** Interface to code in fts5_storage.c. fts5_storage.c contains contains \n** code to access the data stored in the %_content and %_docsize tables.\n*/\n\n#define FTS5_STMT_SCAN_ASC  0     /* SELECT rowid, * FROM ... ORDER BY 1 ASC */\n#define FTS5_STMT_SCAN_DESC 1     /* SELECT rowid, * FROM ... ORDER BY 1 DESC */\n#define FTS5_STMT_LOOKUP    2     /* SELECT rowid, * FROM ... WHERE rowid=? */\n\ntypedef struct Fts5Storage Fts5Storage;\n\nstatic int sqlite3Fts5StorageOpen(Fts5Config*, Fts5Index*, int, Fts5Storage**, char**);\nstatic int sqlite3Fts5StorageClose(Fts5Storage *p);\nstatic int sqlite3Fts5StorageRename(Fts5Storage*, const char *zName);\n\nstatic int sqlite3Fts5DropAll(Fts5Config*);\nstatic int sqlite3Fts5CreateTable(Fts5Config*, const char*, const char*, int, char **);\n\nstatic int sqlite3Fts5StorageDelete(Fts5Storage *p, i64, sqlite3_value**);\nstatic int sqlite3Fts5StorageContentInsert(Fts5Storage *p, sqlite3_value**, i64*);\nstatic int sqlite3Fts5StorageIndexInsert(Fts5Storage *p, sqlite3_value**, i64);\n\nstatic int sqlite3Fts5StorageIntegrity(Fts5Storage *p);\n\nstatic int sqlite3Fts5StorageStmt(Fts5Storage *p, int eStmt, sqlite3_stmt**, char**);\nstatic void sqlite3Fts5StorageStmtRelease(Fts5Storage *p, int eStmt, sqlite3_stmt*);\n\nstatic int sqlite3Fts5StorageDocsize(Fts5Storage *p, i64 iRowid, int *aCol);\nstatic int sqlite3Fts5StorageSize(Fts5Storage *p, int iCol, i64 *pnAvg);\nstatic int sqlite3Fts5StorageRowCount(Fts5Storage *p, i64 *pnRow);\n\nstatic int sqlite3Fts5StorageSync(Fts5Storage *p);\nstatic int sqlite3Fts5StorageRollback(Fts5Storage *p);\n\nstatic int sqlite3Fts5StorageConfigValue(\n    Fts5Storage *p, const char*, sqlite3_value*, int\n);\n\nstatic int sqlite3Fts5StorageDeleteAll(Fts5Storage *p);\nstatic int sqlite3Fts5StorageRebuild(Fts5Storage *p);\nstatic int sqlite3Fts5StorageOptimize(Fts5Storage *p);\nstatic int sqlite3Fts5StorageMerge(Fts5Storage *p, int nMerge);\nstatic int sqlite3Fts5StorageReset(Fts5Storage *p);\n\n/*\n** End of interface to code in fts5_storage.c.\n**************************************************************************/\n\n\n/**************************************************************************\n** Interface to code in fts5_expr.c. \n*/\ntypedef struct Fts5Expr Fts5Expr;\ntypedef struct Fts5ExprNode Fts5ExprNode;\ntypedef struct Fts5Parse Fts5Parse;\ntypedef struct Fts5Token Fts5Token;\ntypedef struct Fts5ExprPhrase Fts5ExprPhrase;\ntypedef struct Fts5ExprNearset Fts5ExprNearset;\n\nstruct Fts5Token {\n  const char *p;                  /* Token text (not NULL terminated) */\n  int n;                          /* Size of buffer p in bytes */\n};\n\n/* Parse a MATCH expression. */\nstatic int sqlite3Fts5ExprNew(\n  Fts5Config *pConfig, \n  int iCol,                       /* Column on LHS of MATCH operator */\n  const char *zExpr,\n  Fts5Expr **ppNew, \n  char **pzErr\n);\n\n/*\n** for(rc = sqlite3Fts5ExprFirst(pExpr, pIdx, bDesc);\n**     rc==SQLITE_OK && 0==sqlite3Fts5ExprEof(pExpr);\n**     rc = sqlite3Fts5ExprNext(pExpr)\n** ){\n**   // The document with rowid iRowid matches the expression!\n**   i64 iRowid = sqlite3Fts5ExprRowid(pExpr);\n** }\n*/\nstatic int sqlite3Fts5ExprFirst(Fts5Expr*, Fts5Index *pIdx, i64 iMin, int bDesc);\nstatic int sqlite3Fts5ExprNext(Fts5Expr*, i64 iMax);\nstatic int sqlite3Fts5ExprEof(Fts5Expr*);\nstatic i64 sqlite3Fts5ExprRowid(Fts5Expr*);\n\nstatic void sqlite3Fts5ExprFree(Fts5Expr*);\n\n/* Called during startup to register a UDF with SQLite */\nstatic int sqlite3Fts5ExprInit(Fts5Global*, sqlite3*);\n\nstatic int sqlite3Fts5ExprPhraseCount(Fts5Expr*);\nstatic int sqlite3Fts5ExprPhraseSize(Fts5Expr*, int iPhrase);\nstatic int sqlite3Fts5ExprPoslist(Fts5Expr*, int, const u8 **);\n\ntypedef struct Fts5PoslistPopulator Fts5PoslistPopulator;\nstatic Fts5PoslistPopulator *sqlite3Fts5ExprClearPoslists(Fts5Expr*, int);\nstatic int sqlite3Fts5ExprPopulatePoslists(\n    Fts5Config*, Fts5Expr*, Fts5PoslistPopulator*, int, const char*, int\n);\nstatic void sqlite3Fts5ExprCheckPoslists(Fts5Expr*, i64);\n\nstatic int sqlite3Fts5ExprClonePhrase(Fts5Expr*, int, Fts5Expr**);\n\nstatic int sqlite3Fts5ExprPhraseCollist(Fts5Expr *, int, const u8 **, int *);\n\n/*******************************************\n** The fts5_expr.c API above this point is used by the other hand-written\n** C code in this module. The interfaces below this point are called by\n** the parser code in fts5parse.y.  */\n\nstatic void sqlite3Fts5ParseError(Fts5Parse *pParse, const char *zFmt, ...);\n\nstatic Fts5ExprNode *sqlite3Fts5ParseNode(\n  Fts5Parse *pParse,\n  int eType,\n  Fts5ExprNode *pLeft,\n  Fts5ExprNode *pRight,\n  Fts5ExprNearset *pNear\n);\n\nstatic Fts5ExprNode *sqlite3Fts5ParseImplicitAnd(\n  Fts5Parse *pParse,\n  Fts5ExprNode *pLeft,\n  Fts5ExprNode *pRight\n);\n\nstatic Fts5ExprPhrase *sqlite3Fts5ParseTerm(\n  Fts5Parse *pParse, \n  Fts5ExprPhrase *pPhrase, \n  Fts5Token *pToken,\n  int bPrefix\n);\n\nstatic void sqlite3Fts5ParseSetCaret(Fts5ExprPhrase*);\n\nstatic Fts5ExprNearset *sqlite3Fts5ParseNearset(\n  Fts5Parse*, \n  Fts5ExprNearset*,\n  Fts5ExprPhrase* \n);\n\nstatic Fts5Colset *sqlite3Fts5ParseColset(\n  Fts5Parse*, \n  Fts5Colset*, \n  Fts5Token *\n);\n\nstatic void sqlite3Fts5ParsePhraseFree(Fts5ExprPhrase*);\nstatic void sqlite3Fts5ParseNearsetFree(Fts5ExprNearset*);\nstatic void sqlite3Fts5ParseNodeFree(Fts5ExprNode*);\n\nstatic void sqlite3Fts5ParseSetDistance(Fts5Parse*, Fts5ExprNearset*, Fts5Token*);\nstatic void sqlite3Fts5ParseSetColset(Fts5Parse*, Fts5ExprNode*, Fts5Colset*);\nstatic Fts5Colset *sqlite3Fts5ParseColsetInvert(Fts5Parse*, Fts5Colset*);\nstatic void sqlite3Fts5ParseFinished(Fts5Parse *pParse, Fts5ExprNode *p);\nstatic void sqlite3Fts5ParseNear(Fts5Parse *pParse, Fts5Token*);\n\n/*\n** End of interface to code in fts5_expr.c.\n**************************************************************************/\n\n\n\n/**************************************************************************\n** Interface to code in fts5_aux.c. \n*/\n\nstatic int sqlite3Fts5AuxInit(fts5_api*);\n/*\n** End of interface to code in fts5_aux.c.\n**************************************************************************/\n\n/**************************************************************************\n** Interface to code in fts5_tokenizer.c. \n*/\n\nstatic int sqlite3Fts5TokenizerInit(fts5_api*);\n/*\n** End of interface to code in fts5_tokenizer.c.\n**************************************************************************/\n\n/**************************************************************************\n** Interface to code in fts5_vocab.c. \n*/\n\nstatic int sqlite3Fts5VocabInit(Fts5Global*, sqlite3*);\n\n/*\n** End of interface to code in fts5_vocab.c.\n**************************************************************************/\n\n\n/**************************************************************************\n** Interface to automatically generated code in fts5_unicode2.c. \n*/\nstatic int sqlite3Fts5UnicodeIsalnum(int c);\nstatic int sqlite3Fts5UnicodeIsdiacritic(int c);\nstatic int sqlite3Fts5UnicodeFold(int c, int bRemoveDiacritic);\n/*\n** End of interface to code in fts5_unicode2.c.\n**************************************************************************/\n\n#endif\n\n#define FTS5_OR                               1\n#define FTS5_AND                              2\n#define FTS5_NOT                              3\n#define FTS5_TERM                             4\n#define FTS5_COLON                            5\n#define FTS5_MINUS                            6\n#define FTS5_LCP                              7\n#define FTS5_RCP                              8\n#define FTS5_STRING                           9\n#define FTS5_LP                              10\n#define FTS5_RP                              11\n#define FTS5_CARET                           12\n#define FTS5_COMMA                           13\n#define FTS5_PLUS                            14\n#define FTS5_STAR                            15\n\n/*\n** 2000-05-29\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n*************************************************************************\n** Driver template for the LEMON parser generator.\n**\n** The \"lemon\" program processes an LALR(1) input grammar file, then uses\n** this template to construct a parser.  The \"lemon\" program inserts text\n** at each \"%%\" line.  Also, any \"P-a-r-s-e\" identifer prefix (without the\n** interstitial \"-\" characters) contained in this template is changed into\n** the value of the %name directive from the grammar.  Otherwise, the content\n** of this template is copied straight through into the generate parser\n** source file.\n**\n** The following is the concatenation of all %include directives from the\n** input grammar file:\n*/\n/* #include <stdio.h> */\n/************ Begin %include sections from the grammar ************************/\n\n/* #include \"fts5Int.h\" */\n/* #include \"fts5parse.h\" */\n\n/*\n** Disable all error recovery processing in the parser push-down\n** automaton.\n*/\n#define fts5YYNOERRORRECOVERY 1\n\n/*\n** Make fts5yytestcase() the same as testcase()\n*/\n#define fts5yytestcase(X) testcase(X)\n\n/*\n** Indicate that sqlite3ParserFree() will never be called with a null\n** pointer.\n*/\n#define fts5YYPARSEFREENOTNULL 1\n\n/*\n** Alternative datatype for the argument to the malloc() routine passed\n** into sqlite3ParserAlloc().  The default is size_t.\n*/\n#define fts5YYMALLOCARGTYPE  u64\n\n/**************** End of %include directives **********************************/\n/* These constants specify the various numeric values for terminal symbols\n** in a format understandable to \"makeheaders\".  This section is blank unless\n** \"lemon\" is run with the \"-m\" command-line option.\n***************** Begin makeheaders token definitions *************************/\n/**************** End makeheaders token definitions ***************************/\n\n/* The next sections is a series of control #defines.\n** various aspects of the generated parser.\n**    fts5YYCODETYPE         is the data type used to store the integer codes\n**                       that represent terminal and non-terminal symbols.\n**                       \"unsigned char\" is used if there are fewer than\n**                       256 symbols.  Larger types otherwise.\n**    fts5YYNOCODE           is a number of type fts5YYCODETYPE that is not used for\n**                       any terminal or nonterminal symbol.\n**    fts5YYFALLBACK         If defined, this indicates that one or more tokens\n**                       (also known as: \"terminal symbols\") have fall-back\n**                       values which should be used if the original symbol\n**                       would not parse.  This permits keywords to sometimes\n**                       be used as identifiers, for example.\n**    fts5YYACTIONTYPE       is the data type used for \"action codes\" - numbers\n**                       that indicate what to do in response to the next\n**                       token.\n**    sqlite3Fts5ParserFTS5TOKENTYPE     is the data type used for minor type for terminal\n**                       symbols.  Background: A \"minor type\" is a semantic\n**                       value associated with a terminal or non-terminal\n**                       symbols.  For example, for an \"ID\" terminal symbol,\n**                       the minor type might be the name of the identifier.\n**                       Each non-terminal can have a different minor type.\n**                       Terminal symbols all have the same minor type, though.\n**                       This macros defines the minor type for terminal \n**                       symbols.\n**    fts5YYMINORTYPE        is the data type used for all minor types.\n**                       This is typically a union of many types, one of\n**                       which is sqlite3Fts5ParserFTS5TOKENTYPE.  The entry in the union\n**                       for terminal symbols is called \"fts5yy0\".\n**    fts5YYSTACKDEPTH       is the maximum depth of the parser's stack.  If\n**                       zero the stack is dynamically sized using realloc()\n**    sqlite3Fts5ParserARG_SDECL     A static variable declaration for the %extra_argument\n**    sqlite3Fts5ParserARG_PDECL     A parameter declaration for the %extra_argument\n**    sqlite3Fts5ParserARG_STORE     Code to store %extra_argument into fts5yypParser\n**    sqlite3Fts5ParserARG_FETCH     Code to extract %extra_argument from fts5yypParser\n**    fts5YYERRORSYMBOL      is the code number of the error symbol.  If not\n**                       defined, then do no error processing.\n**    fts5YYNSTATE           the combined number of states.\n**    fts5YYNRULE            the number of rules in the grammar\n**    fts5YYNFTS5TOKEN           Number of terminal symbols\n**    fts5YY_MAX_SHIFT       Maximum value for shift actions\n**    fts5YY_MIN_SHIFTREDUCE Minimum value for shift-reduce actions\n**    fts5YY_MAX_SHIFTREDUCE Maximum value for shift-reduce actions\n**    fts5YY_ERROR_ACTION    The fts5yy_action[] code for syntax error\n**    fts5YY_ACCEPT_ACTION   The fts5yy_action[] code for accept\n**    fts5YY_NO_ACTION       The fts5yy_action[] code for no-op\n**    fts5YY_MIN_REDUCE      Minimum value for reduce actions\n**    fts5YY_MAX_REDUCE      Maximum value for reduce actions\n*/\n#ifndef INTERFACE\n# define INTERFACE 1\n#endif\n/************* Begin control #defines *****************************************/\n#define fts5YYCODETYPE unsigned char\n#define fts5YYNOCODE 29\n#define fts5YYACTIONTYPE unsigned char\n#define sqlite3Fts5ParserFTS5TOKENTYPE Fts5Token\ntypedef union {\n  int fts5yyinit;\n  sqlite3Fts5ParserFTS5TOKENTYPE fts5yy0;\n  int fts5yy4;\n  Fts5ExprPhrase* fts5yy11;\n  Fts5ExprNearset* fts5yy14;\n  Fts5Colset* fts5yy43;\n  Fts5ExprNode* fts5yy54;\n} fts5YYMINORTYPE;\n#ifndef fts5YYSTACKDEPTH\n#define fts5YYSTACKDEPTH 100\n#endif\n#define sqlite3Fts5ParserARG_SDECL Fts5Parse *pParse;\n#define sqlite3Fts5ParserARG_PDECL ,Fts5Parse *pParse\n#define sqlite3Fts5ParserARG_FETCH Fts5Parse *pParse = fts5yypParser->pParse\n#define sqlite3Fts5ParserARG_STORE fts5yypParser->pParse = pParse\n#define fts5YYNSTATE             35\n#define fts5YYNRULE              28\n#define fts5YYNFTS5TOKEN             16\n#define fts5YY_MAX_SHIFT         34\n#define fts5YY_MIN_SHIFTREDUCE   52\n#define fts5YY_MAX_SHIFTREDUCE   79\n#define fts5YY_ERROR_ACTION      80\n#define fts5YY_ACCEPT_ACTION     81\n#define fts5YY_NO_ACTION         82\n#define fts5YY_MIN_REDUCE        83\n#define fts5YY_MAX_REDUCE        110\n/************* End control #defines *******************************************/\n\n/* Define the fts5yytestcase() macro to be a no-op if is not already defined\n** otherwise.\n**\n** Applications can choose to define fts5yytestcase() in the %include section\n** to a macro that can assist in verifying code coverage.  For production\n** code the fts5yytestcase() macro should be turned off.  But it is useful\n** for testing.\n*/\n#ifndef fts5yytestcase\n# define fts5yytestcase(X)\n#endif\n\n\n/* Next are the tables used to determine what action to take based on the\n** current state and lookahead token.  These tables are used to implement\n** functions that take a state number and lookahead value and return an\n** action integer.  \n**\n** Suppose the action integer is N.  Then the action is determined as\n** follows\n**\n**   0 <= N <= fts5YY_MAX_SHIFT             Shift N.  That is, push the lookahead\n**                                      token onto the stack and goto state N.\n**\n**   N between fts5YY_MIN_SHIFTREDUCE       Shift to an arbitrary state then\n**     and fts5YY_MAX_SHIFTREDUCE           reduce by rule N-fts5YY_MIN_SHIFTREDUCE.\n**\n**   N == fts5YY_ERROR_ACTION               A syntax error has occurred.\n**\n**   N == fts5YY_ACCEPT_ACTION              The parser accepts its input.\n**\n**   N == fts5YY_NO_ACTION                  No such action.  Denotes unused\n**                                      slots in the fts5yy_action[] table.\n**\n**   N between fts5YY_MIN_REDUCE            Reduce by rule N-fts5YY_MIN_REDUCE\n**     and fts5YY_MAX_REDUCE\n**\n** The action table is constructed as a single large table named fts5yy_action[].\n** Given state S and lookahead X, the action is computed as either:\n**\n**    (A)   N = fts5yy_action[ fts5yy_shift_ofst[S] + X ]\n**    (B)   N = fts5yy_default[S]\n**\n** The (A) formula is preferred.  The B formula is used instead if\n** fts5yy_lookahead[fts5yy_shift_ofst[S]+X] is not equal to X.\n**\n** The formulas above are for computing the action when the lookahead is\n** a terminal symbol.  If the lookahead is a non-terminal (as occurs after\n** a reduce action) then the fts5yy_reduce_ofst[] array is used in place of\n** the fts5yy_shift_ofst[] array.\n**\n** The following are the tables generated in this section:\n**\n**  fts5yy_action[]        A single table containing all actions.\n**  fts5yy_lookahead[]     A table containing the lookahead for each entry in\n**                     fts5yy_action.  Used to detect hash collisions.\n**  fts5yy_shift_ofst[]    For each state, the offset into fts5yy_action for\n**                     shifting terminals.\n**  fts5yy_reduce_ofst[]   For each state, the offset into fts5yy_action for\n**                     shifting non-terminals after a reduce.\n**  fts5yy_default[]       Default action for each state.\n**\n*********** Begin parsing tables **********************************************/\n#define fts5YY_ACTTAB_COUNT (105)\nstatic const fts5YYACTIONTYPE fts5yy_action[] = {\n /*     0 */    81,   20,   96,    6,   28,   99,   98,   26,   26,   18,\n /*    10 */    96,    6,   28,   17,   98,   56,   26,   19,   96,    6,\n /*    20 */    28,   14,   98,  108,   26,   92,   96,    6,   28,   25,\n /*    30 */    98,   78,   26,   21,   96,    6,   28,  107,   98,   58,\n /*    40 */    26,   29,   96,    6,   28,   32,   98,   22,   26,   24,\n /*    50 */    16,   23,   11,    1,   14,   13,   24,   16,   31,   11,\n /*    60 */     3,   97,   13,   27,    8,   98,   82,   26,    7,    4,\n /*    70 */     5,    3,    4,    5,    3,   83,    4,    5,    3,   63,\n /*    80 */    33,   34,   62,   12,    2,   86,   13,   10,   12,   71,\n /*    90 */    10,   13,   78,    5,    3,   78,    9,   30,   75,   82,\n /*   100 */    54,   57,   53,   57,   15,\n};\nstatic const fts5YYCODETYPE fts5yy_lookahead[] = {\n /*     0 */    17,   18,   19,   20,   21,   23,   23,   25,   25,   18,\n /*    10 */    19,   20,   21,    7,   23,    9,   25,   18,   19,   20,\n /*    20 */    21,    9,   23,   27,   25,   18,   19,   20,   21,   25,\n /*    30 */    23,   15,   25,   18,   19,   20,   21,   27,   23,    9,\n /*    40 */    25,   18,   19,   20,   21,   14,   23,   22,   25,    6,\n /*    50 */     7,   22,    9,   10,    9,   12,    6,    7,   13,    9,\n /*    60 */     3,   19,   12,   21,    5,   23,   28,   25,    5,    1,\n /*    70 */     2,    3,    1,    2,    3,    0,    1,    2,    3,   11,\n /*    80 */    25,   26,   11,    9,   10,    5,   12,   10,    9,   11,\n /*    90 */    10,   12,   15,    2,    3,   15,   24,   25,    9,   28,\n /*   100 */     8,    9,    8,    9,    9,   28,   28,   28,   28,   28,\n /*   110 */    28,   28,   28,   28,   28,   28,   28,   28,   28,   28,\n /*   120 */    28,\n};\n#define fts5YY_SHIFT_COUNT    (34)\n#define fts5YY_SHIFT_MIN      (0)\n#define fts5YY_SHIFT_MAX      (95)\nstatic const unsigned char fts5yy_shift_ofst[] = {\n /*     0 */    43,   43,   43,   43,   43,   43,   50,   74,   79,   45,\n /*    10 */    12,   80,   77,   12,   16,   16,   30,   30,   68,   71,\n /*    20 */    75,   91,   92,   94,    6,   31,   31,   59,   63,   57,\n /*    30 */    31,   89,   95,   31,   78,\n};\n#define fts5YY_REDUCE_COUNT (17)\n#define fts5YY_REDUCE_MIN   (-18)\n#define fts5YY_REDUCE_MAX   (72)\nstatic const signed char fts5yy_reduce_ofst[] = {\n /*     0 */   -17,   -9,   -1,    7,   15,   23,   42,  -18,  -18,   55,\n /*    10 */    72,   -4,   -4,    4,   -4,   10,   25,   29,\n};\nstatic const fts5YYACTIONTYPE fts5yy_default[] = {\n /*     0 */    80,   80,   80,   80,   80,   80,   95,   80,   80,  105,\n /*    10 */    80,  110,  110,   80,  110,  110,   80,   80,   80,   80,\n /*    20 */    80,   91,   80,   80,   80,  101,  100,   80,   80,   90,\n /*    30 */   103,   80,   80,  104,   80,\n};\n/********** End of lemon-generated parsing tables *****************************/\n\n/* The next table maps tokens (terminal symbols) into fallback tokens.  \n** If a construct like the following:\n** \n**      %fallback ID X Y Z.\n**\n** appears in the grammar, then ID becomes a fallback token for X, Y,\n** and Z.  Whenever one of the tokens X, Y, or Z is input to the parser\n** but it does not parse, the type of the token is changed to ID and\n** the parse is retried before an error is thrown.\n**\n** This feature can be used, for example, to cause some keywords in a language\n** to revert to identifiers if they keyword does not apply in the context where\n** it appears.\n*/\n#ifdef fts5YYFALLBACK\nstatic const fts5YYCODETYPE fts5yyFallback[] = {\n};\n#endif /* fts5YYFALLBACK */\n\n/* The following structure represents a single element of the\n** parser's stack.  Information stored includes:\n**\n**   +  The state number for the parser at this level of the stack.\n**\n**   +  The value of the token stored at this level of the stack.\n**      (In other words, the \"major\" token.)\n**\n**   +  The semantic value stored at this level of the stack.  This is\n**      the information used by the action routines in the grammar.\n**      It is sometimes called the \"minor\" token.\n**\n** After the \"shift\" half of a SHIFTREDUCE action, the stateno field\n** actually contains the reduce action for the second half of the\n** SHIFTREDUCE.\n*/\nstruct fts5yyStackEntry {\n  fts5YYACTIONTYPE stateno;  /* The state-number, or reduce action in SHIFTREDUCE */\n  fts5YYCODETYPE major;      /* The major token value.  This is the code\n                         ** number for the token at this stack level */\n  fts5YYMINORTYPE minor;     /* The user-supplied minor token value.  This\n                         ** is the value of the token  */\n};\ntypedef struct fts5yyStackEntry fts5yyStackEntry;\n\n/* The state of the parser is completely contained in an instance of\n** the following structure */\nstruct fts5yyParser {\n  fts5yyStackEntry *fts5yytos;          /* Pointer to top element of the stack */\n#ifdef fts5YYTRACKMAXSTACKDEPTH\n  int fts5yyhwm;                    /* High-water mark of the stack */\n#endif\n#ifndef fts5YYNOERRORRECOVERY\n  int fts5yyerrcnt;                 /* Shifts left before out of the error */\n#endif\n  sqlite3Fts5ParserARG_SDECL                /* A place to hold %extra_argument */\n#if fts5YYSTACKDEPTH<=0\n  int fts5yystksz;                  /* Current side of the stack */\n  fts5yyStackEntry *fts5yystack;        /* The parser's stack */\n  fts5yyStackEntry fts5yystk0;          /* First stack entry */\n#else\n  fts5yyStackEntry fts5yystack[fts5YYSTACKDEPTH];  /* The parser's stack */\n  fts5yyStackEntry *fts5yystackEnd;            /* Last entry in the stack */\n#endif\n};\ntypedef struct fts5yyParser fts5yyParser;\n\n#ifndef NDEBUG\n/* #include <stdio.h> */\nstatic FILE *fts5yyTraceFILE = 0;\nstatic char *fts5yyTracePrompt = 0;\n#endif /* NDEBUG */\n\n#ifndef NDEBUG\n/* \n** Turn parser tracing on by giving a stream to which to write the trace\n** and a prompt to preface each trace message.  Tracing is turned off\n** by making either argument NULL \n**\n** Inputs:\n** <ul>\n** <li> A FILE* to which trace output should be written.\n**      If NULL, then tracing is turned off.\n** <li> A prefix string written at the beginning of every\n**      line of trace output.  If NULL, then tracing is\n**      turned off.\n** </ul>\n**\n** Outputs:\n** None.\n*/\nstatic void sqlite3Fts5ParserTrace(FILE *TraceFILE, char *zTracePrompt){\n  fts5yyTraceFILE = TraceFILE;\n  fts5yyTracePrompt = zTracePrompt;\n  if( fts5yyTraceFILE==0 ) fts5yyTracePrompt = 0;\n  else if( fts5yyTracePrompt==0 ) fts5yyTraceFILE = 0;\n}\n#endif /* NDEBUG */\n\n#if defined(fts5YYCOVERAGE) || !defined(NDEBUG)\n/* For tracing shifts, the names of all terminals and nonterminals\n** are required.  The following table supplies these names */\nstatic const char *const fts5yyTokenName[] = { \n  /*    0 */ \"$\",\n  /*    1 */ \"OR\",\n  /*    2 */ \"AND\",\n  /*    3 */ \"NOT\",\n  /*    4 */ \"TERM\",\n  /*    5 */ \"COLON\",\n  /*    6 */ \"MINUS\",\n  /*    7 */ \"LCP\",\n  /*    8 */ \"RCP\",\n  /*    9 */ \"STRING\",\n  /*   10 */ \"LP\",\n  /*   11 */ \"RP\",\n  /*   12 */ \"CARET\",\n  /*   13 */ \"COMMA\",\n  /*   14 */ \"PLUS\",\n  /*   15 */ \"STAR\",\n  /*   16 */ \"error\",\n  /*   17 */ \"input\",\n  /*   18 */ \"expr\",\n  /*   19 */ \"cnearset\",\n  /*   20 */ \"exprlist\",\n  /*   21 */ \"colset\",\n  /*   22 */ \"colsetlist\",\n  /*   23 */ \"nearset\",\n  /*   24 */ \"nearphrases\",\n  /*   25 */ \"phrase\",\n  /*   26 */ \"neardist_opt\",\n  /*   27 */ \"star_opt\",\n};\n#endif /* defined(fts5YYCOVERAGE) || !defined(NDEBUG) */\n\n#ifndef NDEBUG\n/* For tracing reduce actions, the names of all rules are required.\n*/\nstatic const char *const fts5yyRuleName[] = {\n /*   0 */ \"input ::= expr\",\n /*   1 */ \"colset ::= MINUS LCP colsetlist RCP\",\n /*   2 */ \"colset ::= LCP colsetlist RCP\",\n /*   3 */ \"colset ::= STRING\",\n /*   4 */ \"colset ::= MINUS STRING\",\n /*   5 */ \"colsetlist ::= colsetlist STRING\",\n /*   6 */ \"colsetlist ::= STRING\",\n /*   7 */ \"expr ::= expr AND expr\",\n /*   8 */ \"expr ::= expr OR expr\",\n /*   9 */ \"expr ::= expr NOT expr\",\n /*  10 */ \"expr ::= colset COLON LP expr RP\",\n /*  11 */ \"expr ::= LP expr RP\",\n /*  12 */ \"expr ::= exprlist\",\n /*  13 */ \"exprlist ::= cnearset\",\n /*  14 */ \"exprlist ::= exprlist cnearset\",\n /*  15 */ \"cnearset ::= nearset\",\n /*  16 */ \"cnearset ::= colset COLON nearset\",\n /*  17 */ \"nearset ::= phrase\",\n /*  18 */ \"nearset ::= CARET phrase\",\n /*  19 */ \"nearset ::= STRING LP nearphrases neardist_opt RP\",\n /*  20 */ \"nearphrases ::= phrase\",\n /*  21 */ \"nearphrases ::= nearphrases phrase\",\n /*  22 */ \"neardist_opt ::=\",\n /*  23 */ \"neardist_opt ::= COMMA STRING\",\n /*  24 */ \"phrase ::= phrase PLUS STRING star_opt\",\n /*  25 */ \"phrase ::= STRING star_opt\",\n /*  26 */ \"star_opt ::= STAR\",\n /*  27 */ \"star_opt ::=\",\n};\n#endif /* NDEBUG */\n\n\n#if fts5YYSTACKDEPTH<=0\n/*\n** Try to increase the size of the parser stack.  Return the number\n** of errors.  Return 0 on success.\n*/\nstatic int fts5yyGrowStack(fts5yyParser *p){\n  int newSize;\n  int idx;\n  fts5yyStackEntry *pNew;\n\n  newSize = p->fts5yystksz*2 + 100;\n  idx = p->fts5yytos ? (int)(p->fts5yytos - p->fts5yystack) : 0;\n  if( p->fts5yystack==&p->fts5yystk0 ){\n    pNew = malloc(newSize*sizeof(pNew[0]));\n    if( pNew ) pNew[0] = p->fts5yystk0;\n  }else{\n    pNew = realloc(p->fts5yystack, newSize*sizeof(pNew[0]));\n  }\n  if( pNew ){\n    p->fts5yystack = pNew;\n    p->fts5yytos = &p->fts5yystack[idx];\n#ifndef NDEBUG\n    if( fts5yyTraceFILE ){\n      fprintf(fts5yyTraceFILE,\"%sStack grows from %d to %d entries.\\n\",\n              fts5yyTracePrompt, p->fts5yystksz, newSize);\n    }\n#endif\n    p->fts5yystksz = newSize;\n  }\n  return pNew==0; \n}\n#endif\n\n/* Datatype of the argument to the memory allocated passed as the\n** second argument to sqlite3Fts5ParserAlloc() below.  This can be changed by\n** putting an appropriate #define in the %include section of the input\n** grammar.\n*/\n#ifndef fts5YYMALLOCARGTYPE\n# define fts5YYMALLOCARGTYPE size_t\n#endif\n\n/* Initialize a new parser that has already been allocated.\n*/\nstatic void sqlite3Fts5ParserInit(void *fts5yypParser){\n  fts5yyParser *pParser = (fts5yyParser*)fts5yypParser;\n#ifdef fts5YYTRACKMAXSTACKDEPTH\n  pParser->fts5yyhwm = 0;\n#endif\n#if fts5YYSTACKDEPTH<=0\n  pParser->fts5yytos = NULL;\n  pParser->fts5yystack = NULL;\n  pParser->fts5yystksz = 0;\n  if( fts5yyGrowStack(pParser) ){\n    pParser->fts5yystack = &pParser->fts5yystk0;\n    pParser->fts5yystksz = 1;\n  }\n#endif\n#ifndef fts5YYNOERRORRECOVERY\n  pParser->fts5yyerrcnt = -1;\n#endif\n  pParser->fts5yytos = pParser->fts5yystack;\n  pParser->fts5yystack[0].stateno = 0;\n  pParser->fts5yystack[0].major = 0;\n#if fts5YYSTACKDEPTH>0\n  pParser->fts5yystackEnd = &pParser->fts5yystack[fts5YYSTACKDEPTH-1];\n#endif\n}\n\n#ifndef sqlite3Fts5Parser_ENGINEALWAYSONSTACK\n/* \n** This function allocates a new parser.\n** The only argument is a pointer to a function which works like\n** malloc.\n**\n** Inputs:\n** A pointer to the function used to allocate memory.\n**\n** Outputs:\n** A pointer to a parser.  This pointer is used in subsequent calls\n** to sqlite3Fts5Parser and sqlite3Fts5ParserFree.\n*/\nstatic void *sqlite3Fts5ParserAlloc(void *(*mallocProc)(fts5YYMALLOCARGTYPE)){\n  fts5yyParser *pParser;\n  pParser = (fts5yyParser*)(*mallocProc)( (fts5YYMALLOCARGTYPE)sizeof(fts5yyParser) );\n  if( pParser ) sqlite3Fts5ParserInit(pParser);\n  return pParser;\n}\n#endif /* sqlite3Fts5Parser_ENGINEALWAYSONSTACK */\n\n\n/* The following function deletes the \"minor type\" or semantic value\n** associated with a symbol.  The symbol can be either a terminal\n** or nonterminal. \"fts5yymajor\" is the symbol code, and \"fts5yypminor\" is\n** a pointer to the value to be deleted.  The code used to do the \n** deletions is derived from the %destructor and/or %token_destructor\n** directives of the input grammar.\n*/\nstatic void fts5yy_destructor(\n  fts5yyParser *fts5yypParser,    /* The parser */\n  fts5YYCODETYPE fts5yymajor,     /* Type code for object to destroy */\n  fts5YYMINORTYPE *fts5yypminor   /* The object to be destroyed */\n){\n  sqlite3Fts5ParserARG_FETCH;\n  switch( fts5yymajor ){\n    /* Here is inserted the actions which take place when a\n    ** terminal or non-terminal is destroyed.  This can happen\n    ** when the symbol is popped from the stack during a\n    ** reduce or during error processing or when a parser is \n    ** being destroyed before it is finished parsing.\n    **\n    ** Note: during a reduce, the only symbols destroyed are those\n    ** which appear on the RHS of the rule, but which are *not* used\n    ** inside the C code.\n    */\n/********* Begin destructor definitions ***************************************/\n    case 17: /* input */\n{\n (void)pParse; \n}\n      break;\n    case 18: /* expr */\n    case 19: /* cnearset */\n    case 20: /* exprlist */\n{\n sqlite3Fts5ParseNodeFree((fts5yypminor->fts5yy54)); \n}\n      break;\n    case 21: /* colset */\n    case 22: /* colsetlist */\n{\n sqlite3_free((fts5yypminor->fts5yy43)); \n}\n      break;\n    case 23: /* nearset */\n    case 24: /* nearphrases */\n{\n sqlite3Fts5ParseNearsetFree((fts5yypminor->fts5yy14)); \n}\n      break;\n    case 25: /* phrase */\n{\n sqlite3Fts5ParsePhraseFree((fts5yypminor->fts5yy11)); \n}\n      break;\n/********* End destructor definitions *****************************************/\n    default:  break;   /* If no destructor action specified: do nothing */\n  }\n}\n\n/*\n** Pop the parser's stack once.\n**\n** If there is a destructor routine associated with the token which\n** is popped from the stack, then call it.\n*/\nstatic void fts5yy_pop_parser_stack(fts5yyParser *pParser){\n  fts5yyStackEntry *fts5yytos;\n  assert( pParser->fts5yytos!=0 );\n  assert( pParser->fts5yytos > pParser->fts5yystack );\n  fts5yytos = pParser->fts5yytos--;\n#ifndef NDEBUG\n  if( fts5yyTraceFILE ){\n    fprintf(fts5yyTraceFILE,\"%sPopping %s\\n\",\n      fts5yyTracePrompt,\n      fts5yyTokenName[fts5yytos->major]);\n  }\n#endif\n  fts5yy_destructor(pParser, fts5yytos->major, &fts5yytos->minor);\n}\n\n/*\n** Clear all secondary memory allocations from the parser\n*/\nstatic void sqlite3Fts5ParserFinalize(void *p){\n  fts5yyParser *pParser = (fts5yyParser*)p;\n  while( pParser->fts5yytos>pParser->fts5yystack ) fts5yy_pop_parser_stack(pParser);\n#if fts5YYSTACKDEPTH<=0\n  if( pParser->fts5yystack!=&pParser->fts5yystk0 ) free(pParser->fts5yystack);\n#endif\n}\n\n#ifndef sqlite3Fts5Parser_ENGINEALWAYSONSTACK\n/* \n** Deallocate and destroy a parser.  Destructors are called for\n** all stack elements before shutting the parser down.\n**\n** If the fts5YYPARSEFREENEVERNULL macro exists (for example because it\n** is defined in a %include section of the input grammar) then it is\n** assumed that the input pointer is never NULL.\n*/\nstatic void sqlite3Fts5ParserFree(\n  void *p,                    /* The parser to be deleted */\n  void (*freeProc)(void*)     /* Function used to reclaim memory */\n){\n#ifndef fts5YYPARSEFREENEVERNULL\n  if( p==0 ) return;\n#endif\n  sqlite3Fts5ParserFinalize(p);\n  (*freeProc)(p);\n}\n#endif /* sqlite3Fts5Parser_ENGINEALWAYSONSTACK */\n\n/*\n** Return the peak depth of the stack for a parser.\n*/\n#ifdef fts5YYTRACKMAXSTACKDEPTH\nstatic int sqlite3Fts5ParserStackPeak(void *p){\n  fts5yyParser *pParser = (fts5yyParser*)p;\n  return pParser->fts5yyhwm;\n}\n#endif\n\n/* This array of booleans keeps track of the parser statement\n** coverage.  The element fts5yycoverage[X][Y] is set when the parser\n** is in state X and has a lookahead token Y.  In a well-tested\n** systems, every element of this matrix should end up being set.\n*/\n#if defined(fts5YYCOVERAGE)\nstatic unsigned char fts5yycoverage[fts5YYNSTATE][fts5YYNFTS5TOKEN];\n#endif\n\n/*\n** Write into out a description of every state/lookahead combination that\n**\n**   (1)  has not been used by the parser, and\n**   (2)  is not a syntax error.\n**\n** Return the number of missed state/lookahead combinations.\n*/\n#if defined(fts5YYCOVERAGE)\nstatic int sqlite3Fts5ParserCoverage(FILE *out){\n  int stateno, iLookAhead, i;\n  int nMissed = 0;\n  for(stateno=0; stateno<fts5YYNSTATE; stateno++){\n    i = fts5yy_shift_ofst[stateno];\n    for(iLookAhead=0; iLookAhead<fts5YYNFTS5TOKEN; iLookAhead++){\n      if( fts5yy_lookahead[i+iLookAhead]!=iLookAhead ) continue;\n      if( fts5yycoverage[stateno][iLookAhead]==0 ) nMissed++;\n      if( out ){\n        fprintf(out,\"State %d lookahead %s %s\\n\", stateno,\n                fts5yyTokenName[iLookAhead],\n                fts5yycoverage[stateno][iLookAhead] ? \"ok\" : \"missed\");\n      }\n    }\n  }\n  return nMissed;\n}\n#endif\n\n/*\n** Find the appropriate action for a parser given the terminal\n** look-ahead token iLookAhead.\n*/\nstatic unsigned int fts5yy_find_shift_action(\n  fts5yyParser *pParser,        /* The parser */\n  fts5YYCODETYPE iLookAhead     /* The look-ahead token */\n){\n  int i;\n  int stateno = pParser->fts5yytos->stateno;\n \n  if( stateno>fts5YY_MAX_SHIFT ) return stateno;\n  assert( stateno <= fts5YY_SHIFT_COUNT );\n#if defined(fts5YYCOVERAGE)\n  fts5yycoverage[stateno][iLookAhead] = 1;\n#endif\n  do{\n    i = fts5yy_shift_ofst[stateno];\n    assert( i>=0 );\n    assert( i+fts5YYNFTS5TOKEN<=(int)sizeof(fts5yy_lookahead)/sizeof(fts5yy_lookahead[0]) );\n    assert( iLookAhead!=fts5YYNOCODE );\n    assert( iLookAhead < fts5YYNFTS5TOKEN );\n    i += iLookAhead;\n    if( fts5yy_lookahead[i]!=iLookAhead ){\n#ifdef fts5YYFALLBACK\n      fts5YYCODETYPE iFallback;            /* Fallback token */\n      if( iLookAhead<sizeof(fts5yyFallback)/sizeof(fts5yyFallback[0])\n             && (iFallback = fts5yyFallback[iLookAhead])!=0 ){\n#ifndef NDEBUG\n        if( fts5yyTraceFILE ){\n          fprintf(fts5yyTraceFILE, \"%sFALLBACK %s => %s\\n\",\n             fts5yyTracePrompt, fts5yyTokenName[iLookAhead], fts5yyTokenName[iFallback]);\n        }\n#endif\n        assert( fts5yyFallback[iFallback]==0 ); /* Fallback loop must terminate */\n        iLookAhead = iFallback;\n        continue;\n      }\n#endif\n#ifdef fts5YYWILDCARD\n      {\n        int j = i - iLookAhead + fts5YYWILDCARD;\n        if( \n#if fts5YY_SHIFT_MIN+fts5YYWILDCARD<0\n          j>=0 &&\n#endif\n#if fts5YY_SHIFT_MAX+fts5YYWILDCARD>=fts5YY_ACTTAB_COUNT\n          j<fts5YY_ACTTAB_COUNT &&\n#endif\n          fts5yy_lookahead[j]==fts5YYWILDCARD && iLookAhead>0\n        ){\n#ifndef NDEBUG\n          if( fts5yyTraceFILE ){\n            fprintf(fts5yyTraceFILE, \"%sWILDCARD %s => %s\\n\",\n               fts5yyTracePrompt, fts5yyTokenName[iLookAhead],\n               fts5yyTokenName[fts5YYWILDCARD]);\n          }\n#endif /* NDEBUG */\n          return fts5yy_action[j];\n        }\n      }\n#endif /* fts5YYWILDCARD */\n      return fts5yy_default[stateno];\n    }else{\n      return fts5yy_action[i];\n    }\n  }while(1);\n}\n\n/*\n** Find the appropriate action for a parser given the non-terminal\n** look-ahead token iLookAhead.\n*/\nstatic int fts5yy_find_reduce_action(\n  int stateno,              /* Current state number */\n  fts5YYCODETYPE iLookAhead     /* The look-ahead token */\n){\n  int i;\n#ifdef fts5YYERRORSYMBOL\n  if( stateno>fts5YY_REDUCE_COUNT ){\n    return fts5yy_default[stateno];\n  }\n#else\n  assert( stateno<=fts5YY_REDUCE_COUNT );\n#endif\n  i = fts5yy_reduce_ofst[stateno];\n  assert( iLookAhead!=fts5YYNOCODE );\n  i += iLookAhead;\n#ifdef fts5YYERRORSYMBOL\n  if( i<0 || i>=fts5YY_ACTTAB_COUNT || fts5yy_lookahead[i]!=iLookAhead ){\n    return fts5yy_default[stateno];\n  }\n#else\n  assert( i>=0 && i<fts5YY_ACTTAB_COUNT );\n  assert( fts5yy_lookahead[i]==iLookAhead );\n#endif\n  return fts5yy_action[i];\n}\n\n/*\n** The following routine is called if the stack overflows.\n*/\nstatic void fts5yyStackOverflow(fts5yyParser *fts5yypParser){\n   sqlite3Fts5ParserARG_FETCH;\n#ifndef NDEBUG\n   if( fts5yyTraceFILE ){\n     fprintf(fts5yyTraceFILE,\"%sStack Overflow!\\n\",fts5yyTracePrompt);\n   }\n#endif\n   while( fts5yypParser->fts5yytos>fts5yypParser->fts5yystack ) fts5yy_pop_parser_stack(fts5yypParser);\n   /* Here code is inserted which will execute if the parser\n   ** stack every overflows */\n/******** Begin %stack_overflow code ******************************************/\n\n  sqlite3Fts5ParseError(pParse, \"fts5: parser stack overflow\");\n/******** End %stack_overflow code ********************************************/\n   sqlite3Fts5ParserARG_STORE; /* Suppress warning about unused %extra_argument var */\n}\n\n/*\n** Print tracing information for a SHIFT action\n*/\n#ifndef NDEBUG\nstatic void fts5yyTraceShift(fts5yyParser *fts5yypParser, int fts5yyNewState, const char *zTag){\n  if( fts5yyTraceFILE ){\n    if( fts5yyNewState<fts5YYNSTATE ){\n      fprintf(fts5yyTraceFILE,\"%s%s '%s', go to state %d\\n\",\n         fts5yyTracePrompt, zTag, fts5yyTokenName[fts5yypParser->fts5yytos->major],\n         fts5yyNewState);\n    }else{\n      fprintf(fts5yyTraceFILE,\"%s%s '%s', pending reduce %d\\n\",\n         fts5yyTracePrompt, zTag, fts5yyTokenName[fts5yypParser->fts5yytos->major],\n         fts5yyNewState - fts5YY_MIN_REDUCE);\n    }\n  }\n}\n#else\n# define fts5yyTraceShift(X,Y,Z)\n#endif\n\n/*\n** Perform a shift action.\n*/\nstatic void fts5yy_shift(\n  fts5yyParser *fts5yypParser,          /* The parser to be shifted */\n  int fts5yyNewState,               /* The new state to shift in */\n  int fts5yyMajor,                  /* The major token to shift in */\n  sqlite3Fts5ParserFTS5TOKENTYPE fts5yyMinor        /* The minor token to shift in */\n){\n  fts5yyStackEntry *fts5yytos;\n  fts5yypParser->fts5yytos++;\n#ifdef fts5YYTRACKMAXSTACKDEPTH\n  if( (int)(fts5yypParser->fts5yytos - fts5yypParser->fts5yystack)>fts5yypParser->fts5yyhwm ){\n    fts5yypParser->fts5yyhwm++;\n    assert( fts5yypParser->fts5yyhwm == (int)(fts5yypParser->fts5yytos - fts5yypParser->fts5yystack) );\n  }\n#endif\n#if fts5YYSTACKDEPTH>0 \n  if( fts5yypParser->fts5yytos>fts5yypParser->fts5yystackEnd ){\n    fts5yypParser->fts5yytos--;\n    fts5yyStackOverflow(fts5yypParser);\n    return;\n  }\n#else\n  if( fts5yypParser->fts5yytos>=&fts5yypParser->fts5yystack[fts5yypParser->fts5yystksz] ){\n    if( fts5yyGrowStack(fts5yypParser) ){\n      fts5yypParser->fts5yytos--;\n      fts5yyStackOverflow(fts5yypParser);\n      return;\n    }\n  }\n#endif\n  if( fts5yyNewState > fts5YY_MAX_SHIFT ){\n    fts5yyNewState += fts5YY_MIN_REDUCE - fts5YY_MIN_SHIFTREDUCE;\n  }\n  fts5yytos = fts5yypParser->fts5yytos;\n  fts5yytos->stateno = (fts5YYACTIONTYPE)fts5yyNewState;\n  fts5yytos->major = (fts5YYCODETYPE)fts5yyMajor;\n  fts5yytos->minor.fts5yy0 = fts5yyMinor;\n  fts5yyTraceShift(fts5yypParser, fts5yyNewState, \"Shift\");\n}\n\n/* The following table contains information about every rule that\n** is used during the reduce.\n*/\nstatic const struct {\n  fts5YYCODETYPE lhs;       /* Symbol on the left-hand side of the rule */\n  signed char nrhs;     /* Negative of the number of RHS symbols in the rule */\n} fts5yyRuleInfo[] = {\n  {   17,   -1 }, /* (0) input ::= expr */\n  {   21,   -4 }, /* (1) colset ::= MINUS LCP colsetlist RCP */\n  {   21,   -3 }, /* (2) colset ::= LCP colsetlist RCP */\n  {   21,   -1 }, /* (3) colset ::= STRING */\n  {   21,   -2 }, /* (4) colset ::= MINUS STRING */\n  {   22,   -2 }, /* (5) colsetlist ::= colsetlist STRING */\n  {   22,   -1 }, /* (6) colsetlist ::= STRING */\n  {   18,   -3 }, /* (7) expr ::= expr AND expr */\n  {   18,   -3 }, /* (8) expr ::= expr OR expr */\n  {   18,   -3 }, /* (9) expr ::= expr NOT expr */\n  {   18,   -5 }, /* (10) expr ::= colset COLON LP expr RP */\n  {   18,   -3 }, /* (11) expr ::= LP expr RP */\n  {   18,   -1 }, /* (12) expr ::= exprlist */\n  {   20,   -1 }, /* (13) exprlist ::= cnearset */\n  {   20,   -2 }, /* (14) exprlist ::= exprlist cnearset */\n  {   19,   -1 }, /* (15) cnearset ::= nearset */\n  {   19,   -3 }, /* (16) cnearset ::= colset COLON nearset */\n  {   23,   -1 }, /* (17) nearset ::= phrase */\n  {   23,   -2 }, /* (18) nearset ::= CARET phrase */\n  {   23,   -5 }, /* (19) nearset ::= STRING LP nearphrases neardist_opt RP */\n  {   24,   -1 }, /* (20) nearphrases ::= phrase */\n  {   24,   -2 }, /* (21) nearphrases ::= nearphrases phrase */\n  {   26,    0 }, /* (22) neardist_opt ::= */\n  {   26,   -2 }, /* (23) neardist_opt ::= COMMA STRING */\n  {   25,   -4 }, /* (24) phrase ::= phrase PLUS STRING star_opt */\n  {   25,   -2 }, /* (25) phrase ::= STRING star_opt */\n  {   27,   -1 }, /* (26) star_opt ::= STAR */\n  {   27,    0 }, /* (27) star_opt ::= */\n};\n\nstatic void fts5yy_accept(fts5yyParser*);  /* Forward Declaration */\n\n/*\n** Perform a reduce action and the shift that must immediately\n** follow the reduce.\n**\n** The fts5yyLookahead and fts5yyLookaheadToken parameters provide reduce actions\n** access to the lookahead token (if any).  The fts5yyLookahead will be fts5YYNOCODE\n** if the lookahead token has already been consumed.  As this procedure is\n** only called from one place, optimizing compilers will in-line it, which\n** means that the extra parameters have no performance impact.\n*/\nstatic void fts5yy_reduce(\n  fts5yyParser *fts5yypParser,         /* The parser */\n  unsigned int fts5yyruleno,       /* Number of the rule by which to reduce */\n  int fts5yyLookahead,             /* Lookahead token, or fts5YYNOCODE if none */\n  sqlite3Fts5ParserFTS5TOKENTYPE fts5yyLookaheadToken  /* Value of the lookahead token */\n){\n  int fts5yygoto;                     /* The next state */\n  int fts5yyact;                      /* The next action */\n  fts5yyStackEntry *fts5yymsp;            /* The top of the parser's stack */\n  int fts5yysize;                     /* Amount to pop the stack */\n  sqlite3Fts5ParserARG_FETCH;\n  (void)fts5yyLookahead;\n  (void)fts5yyLookaheadToken;\n  fts5yymsp = fts5yypParser->fts5yytos;\n#ifndef NDEBUG\n  if( fts5yyTraceFILE && fts5yyruleno<(int)(sizeof(fts5yyRuleName)/sizeof(fts5yyRuleName[0])) ){\n    fts5yysize = fts5yyRuleInfo[fts5yyruleno].nrhs;\n    if( fts5yysize ){\n      fprintf(fts5yyTraceFILE, \"%sReduce %d [%s], go to state %d.\\n\",\n        fts5yyTracePrompt,\n        fts5yyruleno, fts5yyRuleName[fts5yyruleno], fts5yymsp[fts5yysize].stateno);\n    }else{\n      fprintf(fts5yyTraceFILE, \"%sReduce %d [%s].\\n\",\n        fts5yyTracePrompt, fts5yyruleno, fts5yyRuleName[fts5yyruleno]);\n    }\n  }\n#endif /* NDEBUG */\n\n  /* Check that the stack is large enough to grow by a single entry\n  ** if the RHS of the rule is empty.  This ensures that there is room\n  ** enough on the stack to push the LHS value */\n  if( fts5yyRuleInfo[fts5yyruleno].nrhs==0 ){\n#ifdef fts5YYTRACKMAXSTACKDEPTH\n    if( (int)(fts5yypParser->fts5yytos - fts5yypParser->fts5yystack)>fts5yypParser->fts5yyhwm ){\n      fts5yypParser->fts5yyhwm++;\n      assert( fts5yypParser->fts5yyhwm == (int)(fts5yypParser->fts5yytos - fts5yypParser->fts5yystack));\n    }\n#endif\n#if fts5YYSTACKDEPTH>0 \n    if( fts5yypParser->fts5yytos>=fts5yypParser->fts5yystackEnd ){\n      fts5yyStackOverflow(fts5yypParser);\n      return;\n    }\n#else\n    if( fts5yypParser->fts5yytos>=&fts5yypParser->fts5yystack[fts5yypParser->fts5yystksz-1] ){\n      if( fts5yyGrowStack(fts5yypParser) ){\n        fts5yyStackOverflow(fts5yypParser);\n        return;\n      }\n      fts5yymsp = fts5yypParser->fts5yytos;\n    }\n#endif\n  }\n\n  switch( fts5yyruleno ){\n  /* Beginning here are the reduction cases.  A typical example\n  ** follows:\n  **   case 0:\n  **  #line <lineno> <grammarfile>\n  **     { ... }           // User supplied code\n  **  #line <lineno> <thisfile>\n  **     break;\n  */\n/********** Begin reduce actions **********************************************/\n        fts5YYMINORTYPE fts5yylhsminor;\n      case 0: /* input ::= expr */\n{ sqlite3Fts5ParseFinished(pParse, fts5yymsp[0].minor.fts5yy54); }\n        break;\n      case 1: /* colset ::= MINUS LCP colsetlist RCP */\n{ \n    fts5yymsp[-3].minor.fts5yy43 = sqlite3Fts5ParseColsetInvert(pParse, fts5yymsp[-1].minor.fts5yy43);\n}\n        break;\n      case 2: /* colset ::= LCP colsetlist RCP */\n{ fts5yymsp[-2].minor.fts5yy43 = fts5yymsp[-1].minor.fts5yy43; }\n        break;\n      case 3: /* colset ::= STRING */\n{\n  fts5yylhsminor.fts5yy43 = sqlite3Fts5ParseColset(pParse, 0, &fts5yymsp[0].minor.fts5yy0);\n}\n  fts5yymsp[0].minor.fts5yy43 = fts5yylhsminor.fts5yy43;\n        break;\n      case 4: /* colset ::= MINUS STRING */\n{\n  fts5yymsp[-1].minor.fts5yy43 = sqlite3Fts5ParseColset(pParse, 0, &fts5yymsp[0].minor.fts5yy0);\n  fts5yymsp[-1].minor.fts5yy43 = sqlite3Fts5ParseColsetInvert(pParse, fts5yymsp[-1].minor.fts5yy43);\n}\n        break;\n      case 5: /* colsetlist ::= colsetlist STRING */\n{ \n  fts5yylhsminor.fts5yy43 = sqlite3Fts5ParseColset(pParse, fts5yymsp[-1].minor.fts5yy43, &fts5yymsp[0].minor.fts5yy0); }\n  fts5yymsp[-1].minor.fts5yy43 = fts5yylhsminor.fts5yy43;\n        break;\n      case 6: /* colsetlist ::= STRING */\n{ \n  fts5yylhsminor.fts5yy43 = sqlite3Fts5ParseColset(pParse, 0, &fts5yymsp[0].minor.fts5yy0); \n}\n  fts5yymsp[0].minor.fts5yy43 = fts5yylhsminor.fts5yy43;\n        break;\n      case 7: /* expr ::= expr AND expr */\n{\n  fts5yylhsminor.fts5yy54 = sqlite3Fts5ParseNode(pParse, FTS5_AND, fts5yymsp[-2].minor.fts5yy54, fts5yymsp[0].minor.fts5yy54, 0);\n}\n  fts5yymsp[-2].minor.fts5yy54 = fts5yylhsminor.fts5yy54;\n        break;\n      case 8: /* expr ::= expr OR expr */\n{\n  fts5yylhsminor.fts5yy54 = sqlite3Fts5ParseNode(pParse, FTS5_OR, fts5yymsp[-2].minor.fts5yy54, fts5yymsp[0].minor.fts5yy54, 0);\n}\n  fts5yymsp[-2].minor.fts5yy54 = fts5yylhsminor.fts5yy54;\n        break;\n      case 9: /* expr ::= expr NOT expr */\n{\n  fts5yylhsminor.fts5yy54 = sqlite3Fts5ParseNode(pParse, FTS5_NOT, fts5yymsp[-2].minor.fts5yy54, fts5yymsp[0].minor.fts5yy54, 0);\n}\n  fts5yymsp[-2].minor.fts5yy54 = fts5yylhsminor.fts5yy54;\n        break;\n      case 10: /* expr ::= colset COLON LP expr RP */\n{\n  sqlite3Fts5ParseSetColset(pParse, fts5yymsp[-1].minor.fts5yy54, fts5yymsp[-4].minor.fts5yy43);\n  fts5yylhsminor.fts5yy54 = fts5yymsp[-1].minor.fts5yy54;\n}\n  fts5yymsp[-4].minor.fts5yy54 = fts5yylhsminor.fts5yy54;\n        break;\n      case 11: /* expr ::= LP expr RP */\n{fts5yymsp[-2].minor.fts5yy54 = fts5yymsp[-1].minor.fts5yy54;}\n        break;\n      case 12: /* expr ::= exprlist */\n      case 13: /* exprlist ::= cnearset */ fts5yytestcase(fts5yyruleno==13);\n{fts5yylhsminor.fts5yy54 = fts5yymsp[0].minor.fts5yy54;}\n  fts5yymsp[0].minor.fts5yy54 = fts5yylhsminor.fts5yy54;\n        break;\n      case 14: /* exprlist ::= exprlist cnearset */\n{\n  fts5yylhsminor.fts5yy54 = sqlite3Fts5ParseImplicitAnd(pParse, fts5yymsp[-1].minor.fts5yy54, fts5yymsp[0].minor.fts5yy54);\n}\n  fts5yymsp[-1].minor.fts5yy54 = fts5yylhsminor.fts5yy54;\n        break;\n      case 15: /* cnearset ::= nearset */\n{ \n  fts5yylhsminor.fts5yy54 = sqlite3Fts5ParseNode(pParse, FTS5_STRING, 0, 0, fts5yymsp[0].minor.fts5yy14); \n}\n  fts5yymsp[0].minor.fts5yy54 = fts5yylhsminor.fts5yy54;\n        break;\n      case 16: /* cnearset ::= colset COLON nearset */\n{ \n  fts5yylhsminor.fts5yy54 = sqlite3Fts5ParseNode(pParse, FTS5_STRING, 0, 0, fts5yymsp[0].minor.fts5yy14); \n  sqlite3Fts5ParseSetColset(pParse, fts5yylhsminor.fts5yy54, fts5yymsp[-2].minor.fts5yy43);\n}\n  fts5yymsp[-2].minor.fts5yy54 = fts5yylhsminor.fts5yy54;\n        break;\n      case 17: /* nearset ::= phrase */\n{ fts5yylhsminor.fts5yy14 = sqlite3Fts5ParseNearset(pParse, 0, fts5yymsp[0].minor.fts5yy11); }\n  fts5yymsp[0].minor.fts5yy14 = fts5yylhsminor.fts5yy14;\n        break;\n      case 18: /* nearset ::= CARET phrase */\n{ \n  sqlite3Fts5ParseSetCaret(fts5yymsp[0].minor.fts5yy11);\n  fts5yymsp[-1].minor.fts5yy14 = sqlite3Fts5ParseNearset(pParse, 0, fts5yymsp[0].minor.fts5yy11); \n}\n        break;\n      case 19: /* nearset ::= STRING LP nearphrases neardist_opt RP */\n{\n  sqlite3Fts5ParseNear(pParse, &fts5yymsp[-4].minor.fts5yy0);\n  sqlite3Fts5ParseSetDistance(pParse, fts5yymsp[-2].minor.fts5yy14, &fts5yymsp[-1].minor.fts5yy0);\n  fts5yylhsminor.fts5yy14 = fts5yymsp[-2].minor.fts5yy14;\n}\n  fts5yymsp[-4].minor.fts5yy14 = fts5yylhsminor.fts5yy14;\n        break;\n      case 20: /* nearphrases ::= phrase */\n{ \n  fts5yylhsminor.fts5yy14 = sqlite3Fts5ParseNearset(pParse, 0, fts5yymsp[0].minor.fts5yy11); \n}\n  fts5yymsp[0].minor.fts5yy14 = fts5yylhsminor.fts5yy14;\n        break;\n      case 21: /* nearphrases ::= nearphrases phrase */\n{\n  fts5yylhsminor.fts5yy14 = sqlite3Fts5ParseNearset(pParse, fts5yymsp[-1].minor.fts5yy14, fts5yymsp[0].minor.fts5yy11);\n}\n  fts5yymsp[-1].minor.fts5yy14 = fts5yylhsminor.fts5yy14;\n        break;\n      case 22: /* neardist_opt ::= */\n{ fts5yymsp[1].minor.fts5yy0.p = 0; fts5yymsp[1].minor.fts5yy0.n = 0; }\n        break;\n      case 23: /* neardist_opt ::= COMMA STRING */\n{ fts5yymsp[-1].minor.fts5yy0 = fts5yymsp[0].minor.fts5yy0; }\n        break;\n      case 24: /* phrase ::= phrase PLUS STRING star_opt */\n{ \n  fts5yylhsminor.fts5yy11 = sqlite3Fts5ParseTerm(pParse, fts5yymsp[-3].minor.fts5yy11, &fts5yymsp[-1].minor.fts5yy0, fts5yymsp[0].minor.fts5yy4);\n}\n  fts5yymsp[-3].minor.fts5yy11 = fts5yylhsminor.fts5yy11;\n        break;\n      case 25: /* phrase ::= STRING star_opt */\n{ \n  fts5yylhsminor.fts5yy11 = sqlite3Fts5ParseTerm(pParse, 0, &fts5yymsp[-1].minor.fts5yy0, fts5yymsp[0].minor.fts5yy4);\n}\n  fts5yymsp[-1].minor.fts5yy11 = fts5yylhsminor.fts5yy11;\n        break;\n      case 26: /* star_opt ::= STAR */\n{ fts5yymsp[0].minor.fts5yy4 = 1; }\n        break;\n      case 27: /* star_opt ::= */\n{ fts5yymsp[1].minor.fts5yy4 = 0; }\n        break;\n      default:\n        break;\n/********** End reduce actions ************************************************/\n  };\n  assert( fts5yyruleno<sizeof(fts5yyRuleInfo)/sizeof(fts5yyRuleInfo[0]) );\n  fts5yygoto = fts5yyRuleInfo[fts5yyruleno].lhs;\n  fts5yysize = fts5yyRuleInfo[fts5yyruleno].nrhs;\n  fts5yyact = fts5yy_find_reduce_action(fts5yymsp[fts5yysize].stateno,(fts5YYCODETYPE)fts5yygoto);\n\n  /* There are no SHIFTREDUCE actions on nonterminals because the table\n  ** generator has simplified them to pure REDUCE actions. */\n  assert( !(fts5yyact>fts5YY_MAX_SHIFT && fts5yyact<=fts5YY_MAX_SHIFTREDUCE) );\n\n  /* It is not possible for a REDUCE to be followed by an error */\n  assert( fts5yyact!=fts5YY_ERROR_ACTION );\n\n  fts5yymsp += fts5yysize+1;\n  fts5yypParser->fts5yytos = fts5yymsp;\n  fts5yymsp->stateno = (fts5YYACTIONTYPE)fts5yyact;\n  fts5yymsp->major = (fts5YYCODETYPE)fts5yygoto;\n  fts5yyTraceShift(fts5yypParser, fts5yyact, \"... then shift\");\n}\n\n/*\n** The following code executes when the parse fails\n*/\n#ifndef fts5YYNOERRORRECOVERY\nstatic void fts5yy_parse_failed(\n  fts5yyParser *fts5yypParser           /* The parser */\n){\n  sqlite3Fts5ParserARG_FETCH;\n#ifndef NDEBUG\n  if( fts5yyTraceFILE ){\n    fprintf(fts5yyTraceFILE,\"%sFail!\\n\",fts5yyTracePrompt);\n  }\n#endif\n  while( fts5yypParser->fts5yytos>fts5yypParser->fts5yystack ) fts5yy_pop_parser_stack(fts5yypParser);\n  /* Here code is inserted which will be executed whenever the\n  ** parser fails */\n/************ Begin %parse_failure code ***************************************/\n/************ End %parse_failure code *****************************************/\n  sqlite3Fts5ParserARG_STORE; /* Suppress warning about unused %extra_argument variable */\n}\n#endif /* fts5YYNOERRORRECOVERY */\n\n/*\n** The following code executes when a syntax error first occurs.\n*/\nstatic void fts5yy_syntax_error(\n  fts5yyParser *fts5yypParser,           /* The parser */\n  int fts5yymajor,                   /* The major type of the error token */\n  sqlite3Fts5ParserFTS5TOKENTYPE fts5yyminor         /* The minor type of the error token */\n){\n  sqlite3Fts5ParserARG_FETCH;\n#define FTS5TOKEN fts5yyminor\n/************ Begin %syntax_error code ****************************************/\n\n  UNUSED_PARAM(fts5yymajor); /* Silence a compiler warning */\n  sqlite3Fts5ParseError(\n    pParse, \"fts5: syntax error near \\\"%.*s\\\"\",FTS5TOKEN.n,FTS5TOKEN.p\n  );\n/************ End %syntax_error code ******************************************/\n  sqlite3Fts5ParserARG_STORE; /* Suppress warning about unused %extra_argument variable */\n}\n\n/*\n** The following is executed when the parser accepts\n*/\nstatic void fts5yy_accept(\n  fts5yyParser *fts5yypParser           /* The parser */\n){\n  sqlite3Fts5ParserARG_FETCH;\n#ifndef NDEBUG\n  if( fts5yyTraceFILE ){\n    fprintf(fts5yyTraceFILE,\"%sAccept!\\n\",fts5yyTracePrompt);\n  }\n#endif\n#ifndef fts5YYNOERRORRECOVERY\n  fts5yypParser->fts5yyerrcnt = -1;\n#endif\n  assert( fts5yypParser->fts5yytos==fts5yypParser->fts5yystack );\n  /* Here code is inserted which will be executed whenever the\n  ** parser accepts */\n/*********** Begin %parse_accept code *****************************************/\n/*********** End %parse_accept code *******************************************/\n  sqlite3Fts5ParserARG_STORE; /* Suppress warning about unused %extra_argument variable */\n}\n\n/* The main parser program.\n** The first argument is a pointer to a structure obtained from\n** \"sqlite3Fts5ParserAlloc\" which describes the current state of the parser.\n** The second argument is the major token number.  The third is\n** the minor token.  The fourth optional argument is whatever the\n** user wants (and specified in the grammar) and is available for\n** use by the action routines.\n**\n** Inputs:\n** <ul>\n** <li> A pointer to the parser (an opaque structure.)\n** <li> The major token number.\n** <li> The minor token number.\n** <li> An option argument of a grammar-specified type.\n** </ul>\n**\n** Outputs:\n** None.\n*/\nstatic void sqlite3Fts5Parser(\n  void *fts5yyp,                   /* The parser */\n  int fts5yymajor,                 /* The major token code number */\n  sqlite3Fts5ParserFTS5TOKENTYPE fts5yyminor       /* The value for the token */\n  sqlite3Fts5ParserARG_PDECL               /* Optional %extra_argument parameter */\n){\n  fts5YYMINORTYPE fts5yyminorunion;\n  unsigned int fts5yyact;   /* The parser action. */\n#if !defined(fts5YYERRORSYMBOL) && !defined(fts5YYNOERRORRECOVERY)\n  int fts5yyendofinput;     /* True if we are at the end of input */\n#endif\n#ifdef fts5YYERRORSYMBOL\n  int fts5yyerrorhit = 0;   /* True if fts5yymajor has invoked an error */\n#endif\n  fts5yyParser *fts5yypParser;  /* The parser */\n\n  fts5yypParser = (fts5yyParser*)fts5yyp;\n  assert( fts5yypParser->fts5yytos!=0 );\n#if !defined(fts5YYERRORSYMBOL) && !defined(fts5YYNOERRORRECOVERY)\n  fts5yyendofinput = (fts5yymajor==0);\n#endif\n  sqlite3Fts5ParserARG_STORE;\n\n#ifndef NDEBUG\n  if( fts5yyTraceFILE ){\n    int stateno = fts5yypParser->fts5yytos->stateno;\n    if( stateno < fts5YY_MIN_REDUCE ){\n      fprintf(fts5yyTraceFILE,\"%sInput '%s' in state %d\\n\",\n              fts5yyTracePrompt,fts5yyTokenName[fts5yymajor],stateno);\n    }else{\n      fprintf(fts5yyTraceFILE,\"%sInput '%s' with pending reduce %d\\n\",\n              fts5yyTracePrompt,fts5yyTokenName[fts5yymajor],stateno-fts5YY_MIN_REDUCE);\n    }\n  }\n#endif\n\n  do{\n    fts5yyact = fts5yy_find_shift_action(fts5yypParser,(fts5YYCODETYPE)fts5yymajor);\n    if( fts5yyact >= fts5YY_MIN_REDUCE ){\n      fts5yy_reduce(fts5yypParser,fts5yyact-fts5YY_MIN_REDUCE,fts5yymajor,fts5yyminor);\n    }else if( fts5yyact <= fts5YY_MAX_SHIFTREDUCE ){\n      fts5yy_shift(fts5yypParser,fts5yyact,fts5yymajor,fts5yyminor);\n#ifndef fts5YYNOERRORRECOVERY\n      fts5yypParser->fts5yyerrcnt--;\n#endif\n      fts5yymajor = fts5YYNOCODE;\n    }else if( fts5yyact==fts5YY_ACCEPT_ACTION ){\n      fts5yypParser->fts5yytos--;\n      fts5yy_accept(fts5yypParser);\n      return;\n    }else{\n      assert( fts5yyact == fts5YY_ERROR_ACTION );\n      fts5yyminorunion.fts5yy0 = fts5yyminor;\n#ifdef fts5YYERRORSYMBOL\n      int fts5yymx;\n#endif\n#ifndef NDEBUG\n      if( fts5yyTraceFILE ){\n        fprintf(fts5yyTraceFILE,\"%sSyntax Error!\\n\",fts5yyTracePrompt);\n      }\n#endif\n#ifdef fts5YYERRORSYMBOL\n      /* A syntax error has occurred.\n      ** The response to an error depends upon whether or not the\n      ** grammar defines an error token \"ERROR\".  \n      **\n      ** This is what we do if the grammar does define ERROR:\n      **\n      **  * Call the %syntax_error function.\n      **\n      **  * Begin popping the stack until we enter a state where\n      **    it is legal to shift the error symbol, then shift\n      **    the error symbol.\n      **\n      **  * Set the error count to three.\n      **\n      **  * Begin accepting and shifting new tokens.  No new error\n      **    processing will occur until three tokens have been\n      **    shifted successfully.\n      **\n      */\n      if( fts5yypParser->fts5yyerrcnt<0 ){\n        fts5yy_syntax_error(fts5yypParser,fts5yymajor,fts5yyminor);\n      }\n      fts5yymx = fts5yypParser->fts5yytos->major;\n      if( fts5yymx==fts5YYERRORSYMBOL || fts5yyerrorhit ){\n#ifndef NDEBUG\n        if( fts5yyTraceFILE ){\n          fprintf(fts5yyTraceFILE,\"%sDiscard input token %s\\n\",\n             fts5yyTracePrompt,fts5yyTokenName[fts5yymajor]);\n        }\n#endif\n        fts5yy_destructor(fts5yypParser, (fts5YYCODETYPE)fts5yymajor, &fts5yyminorunion);\n        fts5yymajor = fts5YYNOCODE;\n      }else{\n        while( fts5yypParser->fts5yytos >= fts5yypParser->fts5yystack\n            && fts5yymx != fts5YYERRORSYMBOL\n            && (fts5yyact = fts5yy_find_reduce_action(\n                        fts5yypParser->fts5yytos->stateno,\n                        fts5YYERRORSYMBOL)) >= fts5YY_MIN_REDUCE\n        ){\n          fts5yy_pop_parser_stack(fts5yypParser);\n        }\n        if( fts5yypParser->fts5yytos < fts5yypParser->fts5yystack || fts5yymajor==0 ){\n          fts5yy_destructor(fts5yypParser,(fts5YYCODETYPE)fts5yymajor,&fts5yyminorunion);\n          fts5yy_parse_failed(fts5yypParser);\n#ifndef fts5YYNOERRORRECOVERY\n          fts5yypParser->fts5yyerrcnt = -1;\n#endif\n          fts5yymajor = fts5YYNOCODE;\n        }else if( fts5yymx!=fts5YYERRORSYMBOL ){\n          fts5yy_shift(fts5yypParser,fts5yyact,fts5YYERRORSYMBOL,fts5yyminor);\n        }\n      }\n      fts5yypParser->fts5yyerrcnt = 3;\n      fts5yyerrorhit = 1;\n#elif defined(fts5YYNOERRORRECOVERY)\n      /* If the fts5YYNOERRORRECOVERY macro is defined, then do not attempt to\n      ** do any kind of error recovery.  Instead, simply invoke the syntax\n      ** error routine and continue going as if nothing had happened.\n      **\n      ** Applications can set this macro (for example inside %include) if\n      ** they intend to abandon the parse upon the first syntax error seen.\n      */\n      fts5yy_syntax_error(fts5yypParser,fts5yymajor, fts5yyminor);\n      fts5yy_destructor(fts5yypParser,(fts5YYCODETYPE)fts5yymajor,&fts5yyminorunion);\n      fts5yymajor = fts5YYNOCODE;\n      \n#else  /* fts5YYERRORSYMBOL is not defined */\n      /* This is what we do if the grammar does not define ERROR:\n      **\n      **  * Report an error message, and throw away the input token.\n      **\n      **  * If the input token is $, then fail the parse.\n      **\n      ** As before, subsequent error messages are suppressed until\n      ** three input tokens have been successfully shifted.\n      */\n      if( fts5yypParser->fts5yyerrcnt<=0 ){\n        fts5yy_syntax_error(fts5yypParser,fts5yymajor, fts5yyminor);\n      }\n      fts5yypParser->fts5yyerrcnt = 3;\n      fts5yy_destructor(fts5yypParser,(fts5YYCODETYPE)fts5yymajor,&fts5yyminorunion);\n      if( fts5yyendofinput ){\n        fts5yy_parse_failed(fts5yypParser);\n#ifndef fts5YYNOERRORRECOVERY\n        fts5yypParser->fts5yyerrcnt = -1;\n#endif\n      }\n      fts5yymajor = fts5YYNOCODE;\n#endif\n    }\n  }while( fts5yymajor!=fts5YYNOCODE && fts5yypParser->fts5yytos>fts5yypParser->fts5yystack );\n#ifndef NDEBUG\n  if( fts5yyTraceFILE ){\n    fts5yyStackEntry *i;\n    char cDiv = '[';\n    fprintf(fts5yyTraceFILE,\"%sReturn. Stack=\",fts5yyTracePrompt);\n    for(i=&fts5yypParser->fts5yystack[1]; i<=fts5yypParser->fts5yytos; i++){\n      fprintf(fts5yyTraceFILE,\"%c%s\", cDiv, fts5yyTokenName[i->major]);\n      cDiv = ' ';\n    }\n    fprintf(fts5yyTraceFILE,\"]\\n\");\n  }\n#endif\n  return;\n}\n\n/*\n** 2014 May 31\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n******************************************************************************\n*/\n\n\n/* #include \"fts5Int.h\" */\n#include <math.h>                 /* amalgamator: keep */\n\n/*\n** Object used to iterate through all \"coalesced phrase instances\" in \n** a single column of the current row. If the phrase instances in the\n** column being considered do not overlap, this object simply iterates\n** through them. Or, if they do overlap (share one or more tokens in\n** common), each set of overlapping instances is treated as a single\n** match. See documentation for the highlight() auxiliary function for\n** details.\n**\n** Usage is:\n**\n**   for(rc = fts5CInstIterNext(pApi, pFts, iCol, &iter);\n**      (rc==SQLITE_OK && 0==fts5CInstIterEof(&iter);\n**      rc = fts5CInstIterNext(&iter)\n**   ){\n**     printf(\"instance starts at %d, ends at %d\\n\", iter.iStart, iter.iEnd);\n**   }\n**\n*/\ntypedef struct CInstIter CInstIter;\nstruct CInstIter {\n  const Fts5ExtensionApi *pApi;   /* API offered by current FTS version */\n  Fts5Context *pFts;              /* First arg to pass to pApi functions */\n  int iCol;                       /* Column to search */\n  int iInst;                      /* Next phrase instance index */\n  int nInst;                      /* Total number of phrase instances */\n\n  /* Output variables */\n  int iStart;                     /* First token in coalesced phrase instance */\n  int iEnd;                       /* Last token in coalesced phrase instance */\n};\n\n/*\n** Advance the iterator to the next coalesced phrase instance. Return\n** an SQLite error code if an error occurs, or SQLITE_OK otherwise.\n*/\nstatic int fts5CInstIterNext(CInstIter *pIter){\n  int rc = SQLITE_OK;\n  pIter->iStart = -1;\n  pIter->iEnd = -1;\n\n  while( rc==SQLITE_OK && pIter->iInst<pIter->nInst ){\n    int ip; int ic; int io;\n    rc = pIter->pApi->xInst(pIter->pFts, pIter->iInst, &ip, &ic, &io);\n    if( rc==SQLITE_OK ){\n      if( ic==pIter->iCol ){\n        int iEnd = io - 1 + pIter->pApi->xPhraseSize(pIter->pFts, ip);\n        if( pIter->iStart<0 ){\n          pIter->iStart = io;\n          pIter->iEnd = iEnd;\n        }else if( io<=pIter->iEnd ){\n          if( iEnd>pIter->iEnd ) pIter->iEnd = iEnd;\n        }else{\n          break;\n        }\n      }\n      pIter->iInst++;\n    }\n  }\n\n  return rc;\n}\n\n/*\n** Initialize the iterator object indicated by the final parameter to \n** iterate through coalesced phrase instances in column iCol.\n*/\nstatic int fts5CInstIterInit(\n  const Fts5ExtensionApi *pApi,\n  Fts5Context *pFts,\n  int iCol,\n  CInstIter *pIter\n){\n  int rc;\n\n  memset(pIter, 0, sizeof(CInstIter));\n  pIter->pApi = pApi;\n  pIter->pFts = pFts;\n  pIter->iCol = iCol;\n  rc = pApi->xInstCount(pFts, &pIter->nInst);\n\n  if( rc==SQLITE_OK ){\n    rc = fts5CInstIterNext(pIter);\n  }\n\n  return rc;\n}\n\n\n\n/*************************************************************************\n** Start of highlight() implementation.\n*/\ntypedef struct HighlightContext HighlightContext;\nstruct HighlightContext {\n  CInstIter iter;                 /* Coalesced Instance Iterator */\n  int iPos;                       /* Current token offset in zIn[] */\n  int iRangeStart;                /* First token to include */\n  int iRangeEnd;                  /* If non-zero, last token to include */\n  const char *zOpen;              /* Opening highlight */\n  const char *zClose;             /* Closing highlight */\n  const char *zIn;                /* Input text */\n  int nIn;                        /* Size of input text in bytes */\n  int iOff;                       /* Current offset within zIn[] */\n  char *zOut;                     /* Output value */\n};\n\n/*\n** Append text to the HighlightContext output string - p->zOut. Argument\n** z points to a buffer containing n bytes of text to append. If n is \n** negative, everything up until the first '\\0' is appended to the output.\n**\n** If *pRc is set to any value other than SQLITE_OK when this function is \n** called, it is a no-op. If an error (i.e. an OOM condition) is encountered, \n** *pRc is set to an error code before returning. \n*/\nstatic void fts5HighlightAppend(\n  int *pRc, \n  HighlightContext *p, \n  const char *z, int n\n){\n  if( *pRc==SQLITE_OK ){\n    if( n<0 ) n = (int)strlen(z);\n    p->zOut = sqlite3_mprintf(\"%z%.*s\", p->zOut, n, z);\n    if( p->zOut==0 ) *pRc = SQLITE_NOMEM;\n  }\n}\n\n/*\n** Tokenizer callback used by implementation of highlight() function.\n*/\nstatic int fts5HighlightCb(\n  void *pContext,                 /* Pointer to HighlightContext object */\n  int tflags,                     /* Mask of FTS5_TOKEN_* flags */\n  const char *pToken,             /* Buffer containing token */\n  int nToken,                     /* Size of token in bytes */\n  int iStartOff,                  /* Start offset of token */\n  int iEndOff                     /* End offset of token */\n){\n  HighlightContext *p = (HighlightContext*)pContext;\n  int rc = SQLITE_OK;\n  int iPos;\n\n  UNUSED_PARAM2(pToken, nToken);\n\n  if( tflags & FTS5_TOKEN_COLOCATED ) return SQLITE_OK;\n  iPos = p->iPos++;\n\n  if( p->iRangeEnd>0 ){\n    if( iPos<p->iRangeStart || iPos>p->iRangeEnd ) return SQLITE_OK;\n    if( p->iRangeStart && iPos==p->iRangeStart ) p->iOff = iStartOff;\n  }\n\n  if( iPos==p->iter.iStart ){\n    fts5HighlightAppend(&rc, p, &p->zIn[p->iOff], iStartOff - p->iOff);\n    fts5HighlightAppend(&rc, p, p->zOpen, -1);\n    p->iOff = iStartOff;\n  }\n\n  if( iPos==p->iter.iEnd ){\n    if( p->iRangeEnd && p->iter.iStart<p->iRangeStart ){\n      fts5HighlightAppend(&rc, p, p->zOpen, -1);\n    }\n    fts5HighlightAppend(&rc, p, &p->zIn[p->iOff], iEndOff - p->iOff);\n    fts5HighlightAppend(&rc, p, p->zClose, -1);\n    p->iOff = iEndOff;\n    if( rc==SQLITE_OK ){\n      rc = fts5CInstIterNext(&p->iter);\n    }\n  }\n\n  if( p->iRangeEnd>0 && iPos==p->iRangeEnd ){\n    fts5HighlightAppend(&rc, p, &p->zIn[p->iOff], iEndOff - p->iOff);\n    p->iOff = iEndOff;\n    if( iPos>=p->iter.iStart && iPos<p->iter.iEnd ){\n      fts5HighlightAppend(&rc, p, p->zClose, -1);\n    }\n  }\n\n  return rc;\n}\n\n/*\n** Implementation of highlight() function.\n*/\nstatic void fts5HighlightFunction(\n  const Fts5ExtensionApi *pApi,   /* API offered by current FTS version */\n  Fts5Context *pFts,              /* First arg to pass to pApi functions */\n  sqlite3_context *pCtx,          /* Context for returning result/error */\n  int nVal,                       /* Number of values in apVal[] array */\n  sqlite3_value **apVal           /* Array of trailing arguments */\n){\n  HighlightContext ctx;\n  int rc;\n  int iCol;\n\n  if( nVal!=3 ){\n    const char *zErr = \"wrong number of arguments to function highlight()\";\n    sqlite3_result_error(pCtx, zErr, -1);\n    return;\n  }\n\n  iCol = sqlite3_value_int(apVal[0]);\n  memset(&ctx, 0, sizeof(HighlightContext));\n  ctx.zOpen = (const char*)sqlite3_value_text(apVal[1]);\n  ctx.zClose = (const char*)sqlite3_value_text(apVal[2]);\n  rc = pApi->xColumnText(pFts, iCol, &ctx.zIn, &ctx.nIn);\n\n  if( ctx.zIn ){\n    if( rc==SQLITE_OK ){\n      rc = fts5CInstIterInit(pApi, pFts, iCol, &ctx.iter);\n    }\n\n    if( rc==SQLITE_OK ){\n      rc = pApi->xTokenize(pFts, ctx.zIn, ctx.nIn, (void*)&ctx,fts5HighlightCb);\n    }\n    fts5HighlightAppend(&rc, &ctx, &ctx.zIn[ctx.iOff], ctx.nIn - ctx.iOff);\n\n    if( rc==SQLITE_OK ){\n      sqlite3_result_text(pCtx, (const char*)ctx.zOut, -1, SQLITE_TRANSIENT);\n    }\n    sqlite3_free(ctx.zOut);\n  }\n  if( rc!=SQLITE_OK ){\n    sqlite3_result_error_code(pCtx, rc);\n  }\n}\n/*\n** End of highlight() implementation.\n**************************************************************************/\n\n/*\n** Context object passed to the fts5SentenceFinderCb() function.\n*/\ntypedef struct Fts5SFinder Fts5SFinder;\nstruct Fts5SFinder {\n  int iPos;                       /* Current token position */\n  int nFirstAlloc;                /* Allocated size of aFirst[] */\n  int nFirst;                     /* Number of entries in aFirst[] */\n  int *aFirst;                    /* Array of first token in each sentence */\n  const char *zDoc;               /* Document being tokenized */\n};\n\n/*\n** Add an entry to the Fts5SFinder.aFirst[] array. Grow the array if\n** necessary. Return SQLITE_OK if successful, or SQLITE_NOMEM if an\n** error occurs.\n*/\nstatic int fts5SentenceFinderAdd(Fts5SFinder *p, int iAdd){\n  if( p->nFirstAlloc==p->nFirst ){\n    int nNew = p->nFirstAlloc ? p->nFirstAlloc*2 : 64;\n    int *aNew;\n\n    aNew = (int*)sqlite3_realloc(p->aFirst, nNew*sizeof(int));\n    if( aNew==0 ) return SQLITE_NOMEM;\n    p->aFirst = aNew;\n    p->nFirstAlloc = nNew;\n  }\n  p->aFirst[p->nFirst++] = iAdd;\n  return SQLITE_OK;\n}\n\n/*\n** This function is an xTokenize() callback used by the auxiliary snippet()\n** function. Its job is to identify tokens that are the first in a sentence.\n** For each such token, an entry is added to the SFinder.aFirst[] array.\n*/\nstatic int fts5SentenceFinderCb(\n  void *pContext,                 /* Pointer to HighlightContext object */\n  int tflags,                     /* Mask of FTS5_TOKEN_* flags */\n  const char *pToken,             /* Buffer containing token */\n  int nToken,                     /* Size of token in bytes */\n  int iStartOff,                  /* Start offset of token */\n  int iEndOff                     /* End offset of token */\n){\n  int rc = SQLITE_OK;\n\n  UNUSED_PARAM2(pToken, nToken);\n  UNUSED_PARAM(iEndOff);\n\n  if( (tflags & FTS5_TOKEN_COLOCATED)==0 ){\n    Fts5SFinder *p = (Fts5SFinder*)pContext;\n    if( p->iPos>0 ){\n      int i;\n      char c = 0;\n      for(i=iStartOff-1; i>=0; i--){\n        c = p->zDoc[i];\n        if( c!=' ' && c!='\\t' && c!='\\n' && c!='\\r' ) break;\n      }\n      if( i!=iStartOff-1 && (c=='.' || c==':') ){\n        rc = fts5SentenceFinderAdd(p, p->iPos);\n      }\n    }else{\n      rc = fts5SentenceFinderAdd(p, 0);\n    }\n    p->iPos++;\n  }\n  return rc;\n}\n\nstatic int fts5SnippetScore(\n  const Fts5ExtensionApi *pApi,   /* API offered by current FTS version */\n  Fts5Context *pFts,              /* First arg to pass to pApi functions */\n  int nDocsize,                   /* Size of column in tokens */\n  unsigned char *aSeen,           /* Array with one element per query phrase */\n  int iCol,                       /* Column to score */\n  int iPos,                       /* Starting offset to score */\n  int nToken,                     /* Max tokens per snippet */\n  int *pnScore,                   /* OUT: Score */\n  int *piPos                      /* OUT: Adjusted offset */\n){\n  int rc;\n  int i;\n  int ip = 0;\n  int ic = 0;\n  int iOff = 0;\n  int iFirst = -1;\n  int nInst;\n  int nScore = 0;\n  int iLast = 0;\n\n  rc = pApi->xInstCount(pFts, &nInst);\n  for(i=0; i<nInst && rc==SQLITE_OK; i++){\n    rc = pApi->xInst(pFts, i, &ip, &ic, &iOff);\n    if( rc==SQLITE_OK && ic==iCol && iOff>=iPos && iOff<(iPos+nToken) ){\n      nScore += (aSeen[ip] ? 1 : 1000);\n      aSeen[ip] = 1;\n      if( iFirst<0 ) iFirst = iOff;\n      iLast = iOff + pApi->xPhraseSize(pFts, ip);\n    }\n  }\n\n  *pnScore = nScore;\n  if( piPos ){\n    int iAdj = iFirst - (nToken - (iLast-iFirst)) / 2;\n    if( (iAdj+nToken)>nDocsize ) iAdj = nDocsize - nToken;\n    if( iAdj<0 ) iAdj = 0;\n    *piPos = iAdj;\n  }\n\n  return rc;\n}\n\n/*\n** Return the value in pVal interpreted as utf-8 text. Except, if pVal \n** contains a NULL value, return a pointer to a static string zero\n** bytes in length instead of a NULL pointer.\n*/\nstatic const char *fts5ValueToText(sqlite3_value *pVal){\n  const char *zRet = (const char*)sqlite3_value_text(pVal);\n  return zRet ? zRet : \"\";\n}\n\n/*\n** Implementation of snippet() function.\n*/\nstatic void fts5SnippetFunction(\n  const Fts5ExtensionApi *pApi,   /* API offered by current FTS version */\n  Fts5Context *pFts,              /* First arg to pass to pApi functions */\n  sqlite3_context *pCtx,          /* Context for returning result/error */\n  int nVal,                       /* Number of values in apVal[] array */\n  sqlite3_value **apVal           /* Array of trailing arguments */\n){\n  HighlightContext ctx;\n  int rc = SQLITE_OK;             /* Return code */\n  int iCol;                       /* 1st argument to snippet() */\n  const char *zEllips;            /* 4th argument to snippet() */\n  int nToken;                     /* 5th argument to snippet() */\n  int nInst = 0;                  /* Number of instance matches this row */\n  int i;                          /* Used to iterate through instances */\n  int nPhrase;                    /* Number of phrases in query */\n  unsigned char *aSeen;           /* Array of \"seen instance\" flags */\n  int iBestCol;                   /* Column containing best snippet */\n  int iBestStart = 0;             /* First token of best snippet */\n  int nBestScore = 0;             /* Score of best snippet */\n  int nColSize = 0;               /* Total size of iBestCol in tokens */\n  Fts5SFinder sFinder;            /* Used to find the beginnings of sentences */\n  int nCol;\n\n  if( nVal!=5 ){\n    const char *zErr = \"wrong number of arguments to function snippet()\";\n    sqlite3_result_error(pCtx, zErr, -1);\n    return;\n  }\n\n  nCol = pApi->xColumnCount(pFts);\n  memset(&ctx, 0, sizeof(HighlightContext));\n  iCol = sqlite3_value_int(apVal[0]);\n  ctx.zOpen = fts5ValueToText(apVal[1]);\n  ctx.zClose = fts5ValueToText(apVal[2]);\n  zEllips = fts5ValueToText(apVal[3]);\n  nToken = sqlite3_value_int(apVal[4]);\n\n  iBestCol = (iCol>=0 ? iCol : 0);\n  nPhrase = pApi->xPhraseCount(pFts);\n  aSeen = sqlite3_malloc(nPhrase);\n  if( aSeen==0 ){\n    rc = SQLITE_NOMEM;\n  }\n  if( rc==SQLITE_OK ){\n    rc = pApi->xInstCount(pFts, &nInst);\n  }\n\n  memset(&sFinder, 0, sizeof(Fts5SFinder));\n  for(i=0; i<nCol; i++){\n    if( iCol<0 || iCol==i ){\n      int nDoc;\n      int nDocsize;\n      int ii;\n      sFinder.iPos = 0;\n      sFinder.nFirst = 0;\n      rc = pApi->xColumnText(pFts, i, &sFinder.zDoc, &nDoc);\n      if( rc!=SQLITE_OK ) break;\n      rc = pApi->xTokenize(pFts, \n          sFinder.zDoc, nDoc, (void*)&sFinder,fts5SentenceFinderCb\n      );\n      if( rc!=SQLITE_OK ) break;\n      rc = pApi->xColumnSize(pFts, i, &nDocsize);\n      if( rc!=SQLITE_OK ) break;\n\n      for(ii=0; rc==SQLITE_OK && ii<nInst; ii++){\n        int ip, ic, io;\n        int iAdj;\n        int nScore;\n        int jj;\n\n        rc = pApi->xInst(pFts, ii, &ip, &ic, &io);\n        if( ic!=i || rc!=SQLITE_OK ) continue;\n        memset(aSeen, 0, nPhrase);\n        rc = fts5SnippetScore(pApi, pFts, nDocsize, aSeen, i,\n            io, nToken, &nScore, &iAdj\n        );\n        if( rc==SQLITE_OK && nScore>nBestScore ){\n          nBestScore = nScore;\n          iBestCol = i;\n          iBestStart = iAdj;\n          nColSize = nDocsize;\n        }\n\n        if( rc==SQLITE_OK && sFinder.nFirst && nDocsize>nToken ){\n          for(jj=0; jj<(sFinder.nFirst-1); jj++){\n            if( sFinder.aFirst[jj+1]>io ) break;\n          }\n\n          if( sFinder.aFirst[jj]<io ){\n            memset(aSeen, 0, nPhrase);\n            rc = fts5SnippetScore(pApi, pFts, nDocsize, aSeen, i, \n              sFinder.aFirst[jj], nToken, &nScore, 0\n            );\n\n            nScore += (sFinder.aFirst[jj]==0 ? 120 : 100);\n            if( rc==SQLITE_OK && nScore>nBestScore ){\n              nBestScore = nScore;\n              iBestCol = i;\n              iBestStart = sFinder.aFirst[jj];\n              nColSize = nDocsize;\n            }\n          }\n        }\n      }\n    }\n  }\n\n  if( rc==SQLITE_OK ){\n    rc = pApi->xColumnText(pFts, iBestCol, &ctx.zIn, &ctx.nIn);\n  }\n  if( rc==SQLITE_OK && nColSize==0 ){\n    rc = pApi->xColumnSize(pFts, iBestCol, &nColSize);\n  }\n  if( ctx.zIn ){\n    if( rc==SQLITE_OK ){\n      rc = fts5CInstIterInit(pApi, pFts, iBestCol, &ctx.iter);\n    }\n\n    ctx.iRangeStart = iBestStart;\n    ctx.iRangeEnd = iBestStart + nToken - 1;\n\n    if( iBestStart>0 ){\n      fts5HighlightAppend(&rc, &ctx, zEllips, -1);\n    }\n\n    /* Advance iterator ctx.iter so that it points to the first coalesced\n    ** phrase instance at or following position iBestStart. */\n    while( ctx.iter.iStart>=0 && ctx.iter.iStart<iBestStart && rc==SQLITE_OK ){\n      rc = fts5CInstIterNext(&ctx.iter);\n    }\n\n    if( rc==SQLITE_OK ){\n      rc = pApi->xTokenize(pFts, ctx.zIn, ctx.nIn, (void*)&ctx,fts5HighlightCb);\n    }\n    if( ctx.iRangeEnd>=(nColSize-1) ){\n      fts5HighlightAppend(&rc, &ctx, &ctx.zIn[ctx.iOff], ctx.nIn - ctx.iOff);\n    }else{\n      fts5HighlightAppend(&rc, &ctx, zEllips, -1);\n    }\n  }\n  if( rc==SQLITE_OK ){\n    sqlite3_result_text(pCtx, (const char*)ctx.zOut, -1, SQLITE_TRANSIENT);\n  }else{\n    sqlite3_result_error_code(pCtx, rc);\n  }\n  sqlite3_free(ctx.zOut);\n  sqlite3_free(aSeen);\n  sqlite3_free(sFinder.aFirst);\n}\n\n/************************************************************************/\n\n/*\n** The first time the bm25() function is called for a query, an instance\n** of the following structure is allocated and populated.\n*/\ntypedef struct Fts5Bm25Data Fts5Bm25Data;\nstruct Fts5Bm25Data {\n  int nPhrase;                    /* Number of phrases in query */\n  double avgdl;                   /* Average number of tokens in each row */\n  double *aIDF;                   /* IDF for each phrase */\n  double *aFreq;                  /* Array used to calculate phrase freq. */\n};\n\n/*\n** Callback used by fts5Bm25GetData() to count the number of rows in the\n** table matched by each individual phrase within the query.\n*/\nstatic int fts5CountCb(\n  const Fts5ExtensionApi *pApi, \n  Fts5Context *pFts,\n  void *pUserData                 /* Pointer to sqlite3_int64 variable */\n){\n  sqlite3_int64 *pn = (sqlite3_int64*)pUserData;\n  UNUSED_PARAM2(pApi, pFts);\n  (*pn)++;\n  return SQLITE_OK;\n}\n\n/*\n** Set *ppData to point to the Fts5Bm25Data object for the current query. \n** If the object has not already been allocated, allocate and populate it\n** now.\n*/\nstatic int fts5Bm25GetData(\n  const Fts5ExtensionApi *pApi, \n  Fts5Context *pFts,\n  Fts5Bm25Data **ppData           /* OUT: bm25-data object for this query */\n){\n  int rc = SQLITE_OK;             /* Return code */\n  Fts5Bm25Data *p;                /* Object to return */\n\n  p = pApi->xGetAuxdata(pFts, 0);\n  if( p==0 ){\n    int nPhrase;                  /* Number of phrases in query */\n    sqlite3_int64 nRow = 0;       /* Number of rows in table */\n    sqlite3_int64 nToken = 0;     /* Number of tokens in table */\n    int nByte;                    /* Bytes of space to allocate */\n    int i;\n\n    /* Allocate the Fts5Bm25Data object */\n    nPhrase = pApi->xPhraseCount(pFts);\n    nByte = sizeof(Fts5Bm25Data) + nPhrase*2*sizeof(double);\n    p = (Fts5Bm25Data*)sqlite3_malloc(nByte);\n    if( p==0 ){\n      rc = SQLITE_NOMEM;\n    }else{\n      memset(p, 0, nByte);\n      p->nPhrase = nPhrase;\n      p->aIDF = (double*)&p[1];\n      p->aFreq = &p->aIDF[nPhrase];\n    }\n\n    /* Calculate the average document length for this FTS5 table */\n    if( rc==SQLITE_OK ) rc = pApi->xRowCount(pFts, &nRow);\n    if( rc==SQLITE_OK ) rc = pApi->xColumnTotalSize(pFts, -1, &nToken);\n    if( rc==SQLITE_OK ) p->avgdl = (double)nToken  / (double)nRow;\n\n    /* Calculate an IDF for each phrase in the query */\n    for(i=0; rc==SQLITE_OK && i<nPhrase; i++){\n      sqlite3_int64 nHit = 0;\n      rc = pApi->xQueryPhrase(pFts, i, (void*)&nHit, fts5CountCb);\n      if( rc==SQLITE_OK ){\n        /* Calculate the IDF (Inverse Document Frequency) for phrase i.\n        ** This is done using the standard BM25 formula as found on wikipedia:\n        **\n        **   IDF = log( (N - nHit + 0.5) / (nHit + 0.5) )\n        **\n        ** where \"N\" is the total number of documents in the set and nHit\n        ** is the number that contain at least one instance of the phrase\n        ** under consideration.\n        **\n        ** The problem with this is that if (N < 2*nHit), the IDF is \n        ** negative. Which is undesirable. So the mimimum allowable IDF is\n        ** (1e-6) - roughly the same as a term that appears in just over\n        ** half of set of 5,000,000 documents.  */\n        double idf = log( (nRow - nHit + 0.5) / (nHit + 0.5) );\n        if( idf<=0.0 ) idf = 1e-6;\n        p->aIDF[i] = idf;\n      }\n    }\n\n    if( rc!=SQLITE_OK ){\n      sqlite3_free(p);\n    }else{\n      rc = pApi->xSetAuxdata(pFts, p, sqlite3_free);\n    }\n    if( rc!=SQLITE_OK ) p = 0;\n  }\n  *ppData = p;\n  return rc;\n}\n\n/*\n** Implementation of bm25() function.\n*/\nstatic void fts5Bm25Function(\n  const Fts5ExtensionApi *pApi,   /* API offered by current FTS version */\n  Fts5Context *pFts,              /* First arg to pass to pApi functions */\n  sqlite3_context *pCtx,          /* Context for returning result/error */\n  int nVal,                       /* Number of values in apVal[] array */\n  sqlite3_value **apVal           /* Array of trailing arguments */\n){\n  const double k1 = 1.2;          /* Constant \"k1\" from BM25 formula */\n  const double b = 0.75;          /* Constant \"b\" from BM25 formula */\n  int rc = SQLITE_OK;             /* Error code */\n  double score = 0.0;             /* SQL function return value */\n  Fts5Bm25Data *pData;            /* Values allocated/calculated once only */\n  int i;                          /* Iterator variable */\n  int nInst = 0;                  /* Value returned by xInstCount() */\n  double D = 0.0;                 /* Total number of tokens in row */\n  double *aFreq = 0;              /* Array of phrase freq. for current row */\n\n  /* Calculate the phrase frequency (symbol \"f(qi,D)\" in the documentation)\n  ** for each phrase in the query for the current row. */\n  rc = fts5Bm25GetData(pApi, pFts, &pData);\n  if( rc==SQLITE_OK ){\n    aFreq = pData->aFreq;\n    memset(aFreq, 0, sizeof(double) * pData->nPhrase);\n    rc = pApi->xInstCount(pFts, &nInst);\n  }\n  for(i=0; rc==SQLITE_OK && i<nInst; i++){\n    int ip; int ic; int io;\n    rc = pApi->xInst(pFts, i, &ip, &ic, &io);\n    if( rc==SQLITE_OK ){\n      double w = (nVal > ic) ? sqlite3_value_double(apVal[ic]) : 1.0;\n      aFreq[ip] += w;\n    }\n  }\n\n  /* Figure out the total size of the current row in tokens. */\n  if( rc==SQLITE_OK ){\n    int nTok;\n    rc = pApi->xColumnSize(pFts, -1, &nTok);\n    D = (double)nTok;\n  }\n\n  /* Determine the BM25 score for the current row. */\n  for(i=0; rc==SQLITE_OK && i<pData->nPhrase; i++){\n    score += pData->aIDF[i] * (\n      ( aFreq[i] * (k1 + 1.0) ) / \n      ( aFreq[i] + k1 * (1 - b + b * D / pData->avgdl) )\n    );\n  }\n  \n  /* If no error has occurred, return the calculated score. Otherwise,\n  ** throw an SQL exception.  */\n  if( rc==SQLITE_OK ){\n    sqlite3_result_double(pCtx, -1.0 * score);\n  }else{\n    sqlite3_result_error_code(pCtx, rc);\n  }\n}\n\nstatic int sqlite3Fts5AuxInit(fts5_api *pApi){\n  struct Builtin {\n    const char *zFunc;            /* Function name (nul-terminated) */\n    void *pUserData;              /* User-data pointer */\n    fts5_extension_function xFunc;/* Callback function */\n    void (*xDestroy)(void*);      /* Destructor function */\n  } aBuiltin [] = {\n    { \"snippet\",   0, fts5SnippetFunction, 0 },\n    { \"highlight\", 0, fts5HighlightFunction, 0 },\n    { \"bm25\",      0, fts5Bm25Function,    0 },\n  };\n  int rc = SQLITE_OK;             /* Return code */\n  int i;                          /* To iterate through builtin functions */\n\n  for(i=0; rc==SQLITE_OK && i<ArraySize(aBuiltin); i++){\n    rc = pApi->xCreateFunction(pApi,\n        aBuiltin[i].zFunc,\n        aBuiltin[i].pUserData,\n        aBuiltin[i].xFunc,\n        aBuiltin[i].xDestroy\n    );\n  }\n\n  return rc;\n}\n\n\n\n/*\n** 2014 May 31\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n******************************************************************************\n*/\n\n\n\n/* #include \"fts5Int.h\" */\n\nstatic int sqlite3Fts5BufferSize(int *pRc, Fts5Buffer *pBuf, u32 nByte){\n  if( (u32)pBuf->nSpace<nByte ){\n    u32 nNew = pBuf->nSpace ? pBuf->nSpace : 64;\n    u8 *pNew;\n    while( nNew<nByte ){\n      nNew = nNew * 2;\n    }\n    pNew = sqlite3_realloc(pBuf->p, nNew);\n    if( pNew==0 ){\n      *pRc = SQLITE_NOMEM;\n      return 1;\n    }else{\n      pBuf->nSpace = nNew;\n      pBuf->p = pNew;\n    }\n  }\n  return 0;\n}\n\n\n/*\n** Encode value iVal as an SQLite varint and append it to the buffer object\n** pBuf. If an OOM error occurs, set the error code in p.\n*/\nstatic void sqlite3Fts5BufferAppendVarint(int *pRc, Fts5Buffer *pBuf, i64 iVal){\n  if( fts5BufferGrow(pRc, pBuf, 9) ) return;\n  pBuf->n += sqlite3Fts5PutVarint(&pBuf->p[pBuf->n], iVal);\n}\n\nstatic void sqlite3Fts5Put32(u8 *aBuf, int iVal){\n  aBuf[0] = (iVal>>24) & 0x00FF;\n  aBuf[1] = (iVal>>16) & 0x00FF;\n  aBuf[2] = (iVal>> 8) & 0x00FF;\n  aBuf[3] = (iVal>> 0) & 0x00FF;\n}\n\nstatic int sqlite3Fts5Get32(const u8 *aBuf){\n  return (aBuf[0] << 24) + (aBuf[1] << 16) + (aBuf[2] << 8) + aBuf[3];\n}\n\n/*\n** Append buffer nData/pData to buffer pBuf. If an OOM error occurs, set \n** the error code in p. If an error has already occurred when this function\n** is called, it is a no-op.\n*/\nstatic void sqlite3Fts5BufferAppendBlob(\n  int *pRc,\n  Fts5Buffer *pBuf, \n  u32 nData, \n  const u8 *pData\n){\n  assert_nc( *pRc || nData>=0 );\n  if( nData ){\n    if( fts5BufferGrow(pRc, pBuf, nData) ) return;\n    memcpy(&pBuf->p[pBuf->n], pData, nData);\n    pBuf->n += nData;\n  }\n}\n\n/*\n** Append the nul-terminated string zStr to the buffer pBuf. This function\n** ensures that the byte following the buffer data is set to 0x00, even \n** though this byte is not included in the pBuf->n count.\n*/\nstatic void sqlite3Fts5BufferAppendString(\n  int *pRc,\n  Fts5Buffer *pBuf, \n  const char *zStr\n){\n  int nStr = (int)strlen(zStr);\n  sqlite3Fts5BufferAppendBlob(pRc, pBuf, nStr+1, (const u8*)zStr);\n  pBuf->n--;\n}\n\n/*\n** Argument zFmt is a printf() style format string. This function performs\n** the printf() style processing, then appends the results to buffer pBuf.\n**\n** Like sqlite3Fts5BufferAppendString(), this function ensures that the byte \n** following the buffer data is set to 0x00, even though this byte is not\n** included in the pBuf->n count.\n*/ \nstatic void sqlite3Fts5BufferAppendPrintf(\n  int *pRc,\n  Fts5Buffer *pBuf, \n  char *zFmt, ...\n){\n  if( *pRc==SQLITE_OK ){\n    char *zTmp;\n    va_list ap;\n    va_start(ap, zFmt);\n    zTmp = sqlite3_vmprintf(zFmt, ap);\n    va_end(ap);\n\n    if( zTmp==0 ){\n      *pRc = SQLITE_NOMEM;\n    }else{\n      sqlite3Fts5BufferAppendString(pRc, pBuf, zTmp);\n      sqlite3_free(zTmp);\n    }\n  }\n}\n\nstatic char *sqlite3Fts5Mprintf(int *pRc, const char *zFmt, ...){\n  char *zRet = 0;\n  if( *pRc==SQLITE_OK ){\n    va_list ap;\n    va_start(ap, zFmt);\n    zRet = sqlite3_vmprintf(zFmt, ap);\n    va_end(ap);\n    if( zRet==0 ){\n      *pRc = SQLITE_NOMEM; \n    }\n  }\n  return zRet;\n}\n \n\n/*\n** Free any buffer allocated by pBuf. Zero the structure before returning.\n*/\nstatic void sqlite3Fts5BufferFree(Fts5Buffer *pBuf){\n  sqlite3_free(pBuf->p);\n  memset(pBuf, 0, sizeof(Fts5Buffer));\n}\n\n/*\n** Zero the contents of the buffer object. But do not free the associated \n** memory allocation.\n*/\nstatic void sqlite3Fts5BufferZero(Fts5Buffer *pBuf){\n  pBuf->n = 0;\n}\n\n/*\n** Set the buffer to contain nData/pData. If an OOM error occurs, leave an\n** the error code in p. If an error has already occurred when this function\n** is called, it is a no-op.\n*/\nstatic void sqlite3Fts5BufferSet(\n  int *pRc,\n  Fts5Buffer *pBuf, \n  int nData, \n  const u8 *pData\n){\n  pBuf->n = 0;\n  sqlite3Fts5BufferAppendBlob(pRc, pBuf, nData, pData);\n}\n\nstatic int sqlite3Fts5PoslistNext64(\n  const u8 *a, int n,             /* Buffer containing poslist */\n  int *pi,                        /* IN/OUT: Offset within a[] */\n  i64 *piOff                      /* IN/OUT: Current offset */\n){\n  int i = *pi;\n  if( i>=n ){\n    /* EOF */\n    *piOff = -1;\n    return 1;  \n  }else{\n    i64 iOff = *piOff;\n    int iVal;\n    fts5FastGetVarint32(a, i, iVal);\n    if( iVal==1 ){\n      fts5FastGetVarint32(a, i, iVal);\n      iOff = ((i64)iVal) << 32;\n      fts5FastGetVarint32(a, i, iVal);\n    }\n    *piOff = iOff + (iVal-2);\n    *pi = i;\n    return 0;\n  }\n}\n\n\n/*\n** Advance the iterator object passed as the only argument. Return true\n** if the iterator reaches EOF, or false otherwise.\n*/\nstatic int sqlite3Fts5PoslistReaderNext(Fts5PoslistReader *pIter){\n  if( sqlite3Fts5PoslistNext64(pIter->a, pIter->n, &pIter->i, &pIter->iPos) ){\n    pIter->bEof = 1;\n  }\n  return pIter->bEof;\n}\n\nstatic int sqlite3Fts5PoslistReaderInit(\n  const u8 *a, int n,             /* Poslist buffer to iterate through */\n  Fts5PoslistReader *pIter        /* Iterator object to initialize */\n){\n  memset(pIter, 0, sizeof(*pIter));\n  pIter->a = a;\n  pIter->n = n;\n  sqlite3Fts5PoslistReaderNext(pIter);\n  return pIter->bEof;\n}\n\n/*\n** Append position iPos to the position list being accumulated in buffer\n** pBuf, which must be already be large enough to hold the new data.\n** The previous position written to this list is *piPrev. *piPrev is set\n** to iPos before returning.\n*/\nstatic void sqlite3Fts5PoslistSafeAppend(\n  Fts5Buffer *pBuf, \n  i64 *piPrev, \n  i64 iPos\n){\n  static const i64 colmask = ((i64)(0x7FFFFFFF)) << 32;\n  if( (iPos & colmask) != (*piPrev & colmask) ){\n    pBuf->p[pBuf->n++] = 1;\n    pBuf->n += sqlite3Fts5PutVarint(&pBuf->p[pBuf->n], (iPos>>32));\n    *piPrev = (iPos & colmask);\n  }\n  pBuf->n += sqlite3Fts5PutVarint(&pBuf->p[pBuf->n], (iPos-*piPrev)+2);\n  *piPrev = iPos;\n}\n\nstatic int sqlite3Fts5PoslistWriterAppend(\n  Fts5Buffer *pBuf, \n  Fts5PoslistWriter *pWriter,\n  i64 iPos\n){\n  int rc = 0;   /* Initialized only to suppress erroneous warning from Clang */\n  if( fts5BufferGrow(&rc, pBuf, 5+5+5) ) return rc;\n  sqlite3Fts5PoslistSafeAppend(pBuf, &pWriter->iPrev, iPos);\n  return SQLITE_OK;\n}\n\nstatic void *sqlite3Fts5MallocZero(int *pRc, int nByte){\n  void *pRet = 0;\n  if( *pRc==SQLITE_OK ){\n    pRet = sqlite3_malloc(nByte);\n    if( pRet==0 ){\n      if( nByte>0 ) *pRc = SQLITE_NOMEM;\n    }else{\n      memset(pRet, 0, nByte);\n    }\n  }\n  return pRet;\n}\n\n/*\n** Return a nul-terminated copy of the string indicated by pIn. If nIn\n** is non-negative, then it is the length of the string in bytes. Otherwise,\n** the length of the string is determined using strlen().\n**\n** It is the responsibility of the caller to eventually free the returned\n** buffer using sqlite3_free(). If an OOM error occurs, NULL is returned. \n*/\nstatic char *sqlite3Fts5Strndup(int *pRc, const char *pIn, int nIn){\n  char *zRet = 0;\n  if( *pRc==SQLITE_OK ){\n    if( nIn<0 ){\n      nIn = (int)strlen(pIn);\n    }\n    zRet = (char*)sqlite3_malloc(nIn+1);\n    if( zRet ){\n      memcpy(zRet, pIn, nIn);\n      zRet[nIn] = '\\0';\n    }else{\n      *pRc = SQLITE_NOMEM;\n    }\n  }\n  return zRet;\n}\n\n\n/*\n** Return true if character 't' may be part of an FTS5 bareword, or false\n** otherwise. Characters that may be part of barewords:\n**\n**   * All non-ASCII characters,\n**   * The 52 upper and lower case ASCII characters, and\n**   * The 10 integer ASCII characters.\n**   * The underscore character \"_\" (0x5F).\n**   * The unicode \"subsitute\" character (0x1A).\n*/\nstatic int sqlite3Fts5IsBareword(char t){\n  u8 aBareword[128] = {\n    0, 0, 0, 0, 0, 0, 0, 0,    0, 0, 0, 0, 0, 0, 0, 0,   /* 0x00 .. 0x0F */\n    0, 0, 0, 0, 0, 0, 0, 0,    0, 0, 1, 0, 0, 0, 0, 0,   /* 0x10 .. 0x1F */\n    0, 0, 0, 0, 0, 0, 0, 0,    0, 0, 0, 0, 0, 0, 0, 0,   /* 0x20 .. 0x2F */\n    1, 1, 1, 1, 1, 1, 1, 1,    1, 1, 0, 0, 0, 0, 0, 0,   /* 0x30 .. 0x3F */\n    0, 1, 1, 1, 1, 1, 1, 1,    1, 1, 1, 1, 1, 1, 1, 1,   /* 0x40 .. 0x4F */\n    1, 1, 1, 1, 1, 1, 1, 1,    1, 1, 1, 0, 0, 0, 0, 1,   /* 0x50 .. 0x5F */\n    0, 1, 1, 1, 1, 1, 1, 1,    1, 1, 1, 1, 1, 1, 1, 1,   /* 0x60 .. 0x6F */\n    1, 1, 1, 1, 1, 1, 1, 1,    1, 1, 1, 0, 0, 0, 0, 0    /* 0x70 .. 0x7F */\n  };\n\n  return (t & 0x80) || aBareword[(int)t];\n}\n\n\n/*************************************************************************\n*/\ntypedef struct Fts5TermsetEntry Fts5TermsetEntry;\nstruct Fts5TermsetEntry {\n  char *pTerm;\n  int nTerm;\n  int iIdx;                       /* Index (main or aPrefix[] entry) */\n  Fts5TermsetEntry *pNext;\n};\n\nstruct Fts5Termset {\n  Fts5TermsetEntry *apHash[512];\n};\n\nstatic int sqlite3Fts5TermsetNew(Fts5Termset **pp){\n  int rc = SQLITE_OK;\n  *pp = sqlite3Fts5MallocZero(&rc, sizeof(Fts5Termset));\n  return rc;\n}\n\nstatic int sqlite3Fts5TermsetAdd(\n  Fts5Termset *p, \n  int iIdx,\n  const char *pTerm, int nTerm, \n  int *pbPresent\n){\n  int rc = SQLITE_OK;\n  *pbPresent = 0;\n  if( p ){\n    int i;\n    u32 hash = 13;\n    Fts5TermsetEntry *pEntry;\n\n    /* Calculate a hash value for this term. This is the same hash checksum\n    ** used by the fts5_hash.c module. This is not important for correct\n    ** operation of the module, but is necessary to ensure that some tests\n    ** designed to produce hash table collisions really do work.  */\n    for(i=nTerm-1; i>=0; i--){\n      hash = (hash << 3) ^ hash ^ pTerm[i];\n    }\n    hash = (hash << 3) ^ hash ^ iIdx;\n    hash = hash % ArraySize(p->apHash);\n\n    for(pEntry=p->apHash[hash]; pEntry; pEntry=pEntry->pNext){\n      if( pEntry->iIdx==iIdx \n          && pEntry->nTerm==nTerm \n          && memcmp(pEntry->pTerm, pTerm, nTerm)==0 \n      ){\n        *pbPresent = 1;\n        break;\n      }\n    }\n\n    if( pEntry==0 ){\n      pEntry = sqlite3Fts5MallocZero(&rc, sizeof(Fts5TermsetEntry) + nTerm);\n      if( pEntry ){\n        pEntry->pTerm = (char*)&pEntry[1];\n        pEntry->nTerm = nTerm;\n        pEntry->iIdx = iIdx;\n        memcpy(pEntry->pTerm, pTerm, nTerm);\n        pEntry->pNext = p->apHash[hash];\n        p->apHash[hash] = pEntry;\n      }\n    }\n  }\n\n  return rc;\n}\n\nstatic void sqlite3Fts5TermsetFree(Fts5Termset *p){\n  if( p ){\n    u32 i;\n    for(i=0; i<ArraySize(p->apHash); i++){\n      Fts5TermsetEntry *pEntry = p->apHash[i];\n      while( pEntry ){\n        Fts5TermsetEntry *pDel = pEntry;\n        pEntry = pEntry->pNext;\n        sqlite3_free(pDel);\n      }\n    }\n    sqlite3_free(p);\n  }\n}\n\n/*\n** 2014 Jun 09\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n******************************************************************************\n**\n** This is an SQLite module implementing full-text search.\n*/\n\n\n/* #include \"fts5Int.h\" */\n\n#define FTS5_DEFAULT_PAGE_SIZE   4050\n#define FTS5_DEFAULT_AUTOMERGE      4\n#define FTS5_DEFAULT_USERMERGE      4\n#define FTS5_DEFAULT_CRISISMERGE   16\n#define FTS5_DEFAULT_HASHSIZE    (1024*1024)\n\n/* Maximum allowed page size */\n#define FTS5_MAX_PAGE_SIZE (128*1024)\n\nstatic int fts5_iswhitespace(char x){\n  return (x==' ');\n}\n\nstatic int fts5_isopenquote(char x){\n  return (x=='\"' || x=='\\'' || x=='[' || x=='`');\n}\n\n/*\n** Argument pIn points to a character that is part of a nul-terminated \n** string. Return a pointer to the first character following *pIn in \n** the string that is not a white-space character.\n*/\nstatic const char *fts5ConfigSkipWhitespace(const char *pIn){\n  const char *p = pIn;\n  if( p ){\n    while( fts5_iswhitespace(*p) ){ p++; }\n  }\n  return p;\n}\n\n/*\n** Argument pIn points to a character that is part of a nul-terminated \n** string. Return a pointer to the first character following *pIn in \n** the string that is not a \"bareword\" character.\n*/\nstatic const char *fts5ConfigSkipBareword(const char *pIn){\n  const char *p = pIn;\n  while ( sqlite3Fts5IsBareword(*p) ) p++;\n  if( p==pIn ) p = 0;\n  return p;\n}\n\nstatic int fts5_isdigit(char a){\n  return (a>='0' && a<='9');\n}\n\n\n\nstatic const char *fts5ConfigSkipLiteral(const char *pIn){\n  const char *p = pIn;\n  switch( *p ){\n    case 'n': case 'N':\n      if( sqlite3_strnicmp(\"null\", p, 4)==0 ){\n        p = &p[4];\n      }else{\n        p = 0;\n      }\n      break;\n\n    case 'x': case 'X':\n      p++;\n      if( *p=='\\'' ){\n        p++;\n        while( (*p>='a' && *p<='f') \n            || (*p>='A' && *p<='F') \n            || (*p>='0' && *p<='9') \n            ){\n          p++;\n        }\n        if( *p=='\\'' && 0==((p-pIn)%2) ){\n          p++;\n        }else{\n          p = 0;\n        }\n      }else{\n        p = 0;\n      }\n      break;\n\n    case '\\'':\n      p++;\n      while( p ){\n        if( *p=='\\'' ){\n          p++;\n          if( *p!='\\'' ) break;\n        }\n        p++;\n        if( *p==0 ) p = 0;\n      }\n      break;\n\n    default:\n      /* maybe a number */\n      if( *p=='+' || *p=='-' ) p++;\n      while( fts5_isdigit(*p) ) p++;\n\n      /* At this point, if the literal was an integer, the parse is \n      ** finished. Or, if it is a floating point value, it may continue\n      ** with either a decimal point or an 'E' character. */\n      if( *p=='.' && fts5_isdigit(p[1]) ){\n        p += 2;\n        while( fts5_isdigit(*p) ) p++;\n      }\n      if( p==pIn ) p = 0;\n\n      break;\n  }\n\n  return p;\n}\n\n/*\n** The first character of the string pointed to by argument z is guaranteed\n** to be an open-quote character (see function fts5_isopenquote()).\n**\n** This function searches for the corresponding close-quote character within\n** the string and, if found, dequotes the string in place and adds a new\n** nul-terminator byte.\n**\n** If the close-quote is found, the value returned is the byte offset of\n** the character immediately following it. Or, if the close-quote is not \n** found, -1 is returned. If -1 is returned, the buffer is left in an \n** undefined state.\n*/\nstatic int fts5Dequote(char *z){\n  char q;\n  int iIn = 1;\n  int iOut = 0;\n  q = z[0];\n\n  /* Set stack variable q to the close-quote character */\n  assert( q=='[' || q=='\\'' || q=='\"' || q=='`' );\n  if( q=='[' ) q = ']';  \n\n  while( ALWAYS(z[iIn]) ){\n    if( z[iIn]==q ){\n      if( z[iIn+1]!=q ){\n        /* Character iIn was the close quote. */\n        iIn++;\n        break;\n      }else{\n        /* Character iIn and iIn+1 form an escaped quote character. Skip\n        ** the input cursor past both and copy a single quote character \n        ** to the output buffer. */\n        iIn += 2;\n        z[iOut++] = q;\n      }\n    }else{\n      z[iOut++] = z[iIn++];\n    }\n  }\n\n  z[iOut] = '\\0';\n  return iIn;\n}\n\n/*\n** Convert an SQL-style quoted string into a normal string by removing\n** the quote characters.  The conversion is done in-place.  If the\n** input does not begin with a quote character, then this routine\n** is a no-op.\n**\n** Examples:\n**\n**     \"abc\"   becomes   abc\n**     'xyz'   becomes   xyz\n**     [pqr]   becomes   pqr\n**     `mno`   becomes   mno\n*/\nstatic void sqlite3Fts5Dequote(char *z){\n  char quote;                     /* Quote character (if any ) */\n\n  assert( 0==fts5_iswhitespace(z[0]) );\n  quote = z[0];\n  if( quote=='[' || quote=='\\'' || quote=='\"' || quote=='`' ){\n    fts5Dequote(z);\n  }\n}\n\n\nstruct Fts5Enum {\n  const char *zName;\n  int eVal;\n};\ntypedef struct Fts5Enum Fts5Enum;\n\nstatic int fts5ConfigSetEnum(\n  const Fts5Enum *aEnum, \n  const char *zEnum, \n  int *peVal\n){\n  int nEnum = (int)strlen(zEnum);\n  int i;\n  int iVal = -1;\n\n  for(i=0; aEnum[i].zName; i++){\n    if( sqlite3_strnicmp(aEnum[i].zName, zEnum, nEnum)==0 ){\n      if( iVal>=0 ) return SQLITE_ERROR;\n      iVal = aEnum[i].eVal;\n    }\n  }\n\n  *peVal = iVal;\n  return iVal<0 ? SQLITE_ERROR : SQLITE_OK;\n}\n\n/*\n** Parse a \"special\" CREATE VIRTUAL TABLE directive and update\n** configuration object pConfig as appropriate.\n**\n** If successful, object pConfig is updated and SQLITE_OK returned. If\n** an error occurs, an SQLite error code is returned and an error message\n** may be left in *pzErr. It is the responsibility of the caller to\n** eventually free any such error message using sqlite3_free().\n*/\nstatic int fts5ConfigParseSpecial(\n  Fts5Global *pGlobal,\n  Fts5Config *pConfig,            /* Configuration object to update */\n  const char *zCmd,               /* Special command to parse */\n  const char *zArg,               /* Argument to parse */\n  char **pzErr                    /* OUT: Error message */\n){\n  int rc = SQLITE_OK;\n  int nCmd = (int)strlen(zCmd);\n  if( sqlite3_strnicmp(\"prefix\", zCmd, nCmd)==0 ){\n    const int nByte = sizeof(int) * FTS5_MAX_PREFIX_INDEXES;\n    const char *p;\n    int bFirst = 1;\n    if( pConfig->aPrefix==0 ){\n      pConfig->aPrefix = sqlite3Fts5MallocZero(&rc, nByte);\n      if( rc ) return rc;\n    }\n\n    p = zArg;\n    while( 1 ){\n      int nPre = 0;\n\n      while( p[0]==' ' ) p++;\n      if( bFirst==0 && p[0]==',' ){\n        p++;\n        while( p[0]==' ' ) p++;\n      }else if( p[0]=='\\0' ){\n        break;\n      }\n      if( p[0]<'0' || p[0]>'9' ){\n        *pzErr = sqlite3_mprintf(\"malformed prefix=... directive\");\n        rc = SQLITE_ERROR;\n        break;\n      }\n\n      if( pConfig->nPrefix==FTS5_MAX_PREFIX_INDEXES ){\n        *pzErr = sqlite3_mprintf(\n            \"too many prefix indexes (max %d)\", FTS5_MAX_PREFIX_INDEXES\n        );\n        rc = SQLITE_ERROR;\n        break;\n      }\n\n      while( p[0]>='0' && p[0]<='9' && nPre<1000 ){\n        nPre = nPre*10 + (p[0] - '0');\n        p++;\n      }\n\n      if( nPre<=0 || nPre>=1000 ){\n        *pzErr = sqlite3_mprintf(\"prefix length out of range (max 999)\");\n        rc = SQLITE_ERROR;\n        break;\n      }\n\n      pConfig->aPrefix[pConfig->nPrefix] = nPre;\n      pConfig->nPrefix++;\n      bFirst = 0;\n    }\n    assert( pConfig->nPrefix<=FTS5_MAX_PREFIX_INDEXES );\n    return rc;\n  }\n\n  if( sqlite3_strnicmp(\"tokenize\", zCmd, nCmd)==0 ){\n    const char *p = (const char*)zArg;\n    int nArg = (int)strlen(zArg) + 1;\n    char **azArg = sqlite3Fts5MallocZero(&rc, sizeof(char*) * nArg);\n    char *pDel = sqlite3Fts5MallocZero(&rc, nArg * 2);\n    char *pSpace = pDel;\n\n    if( azArg && pSpace ){\n      if( pConfig->pTok ){\n        *pzErr = sqlite3_mprintf(\"multiple tokenize=... directives\");\n        rc = SQLITE_ERROR;\n      }else{\n        for(nArg=0; p && *p; nArg++){\n          const char *p2 = fts5ConfigSkipWhitespace(p);\n          if( *p2=='\\'' ){\n            p = fts5ConfigSkipLiteral(p2);\n          }else{\n            p = fts5ConfigSkipBareword(p2);\n          }\n          if( p ){\n            memcpy(pSpace, p2, p-p2);\n            azArg[nArg] = pSpace;\n            sqlite3Fts5Dequote(pSpace);\n            pSpace += (p - p2) + 1;\n            p = fts5ConfigSkipWhitespace(p);\n          }\n        }\n        if( p==0 ){\n          *pzErr = sqlite3_mprintf(\"parse error in tokenize directive\");\n          rc = SQLITE_ERROR;\n        }else{\n          rc = sqlite3Fts5GetTokenizer(pGlobal, \n              (const char**)azArg, nArg, &pConfig->pTok, &pConfig->pTokApi,\n              pzErr\n          );\n        }\n      }\n    }\n\n    sqlite3_free(azArg);\n    sqlite3_free(pDel);\n    return rc;\n  }\n\n  if( sqlite3_strnicmp(\"content\", zCmd, nCmd)==0 ){\n    if( pConfig->eContent!=FTS5_CONTENT_NORMAL ){\n      *pzErr = sqlite3_mprintf(\"multiple content=... directives\");\n      rc = SQLITE_ERROR;\n    }else{\n      if( zArg[0] ){\n        pConfig->eContent = FTS5_CONTENT_EXTERNAL;\n        pConfig->zContent = sqlite3Fts5Mprintf(&rc, \"%Q.%Q\", pConfig->zDb,zArg);\n      }else{\n        pConfig->eContent = FTS5_CONTENT_NONE;\n      }\n    }\n    return rc;\n  }\n\n  if( sqlite3_strnicmp(\"content_rowid\", zCmd, nCmd)==0 ){\n    if( pConfig->zContentRowid ){\n      *pzErr = sqlite3_mprintf(\"multiple content_rowid=... directives\");\n      rc = SQLITE_ERROR;\n    }else{\n      pConfig->zContentRowid = sqlite3Fts5Strndup(&rc, zArg, -1);\n    }\n    return rc;\n  }\n\n  if( sqlite3_strnicmp(\"columnsize\", zCmd, nCmd)==0 ){\n    if( (zArg[0]!='0' && zArg[0]!='1') || zArg[1]!='\\0' ){\n      *pzErr = sqlite3_mprintf(\"malformed columnsize=... directive\");\n      rc = SQLITE_ERROR;\n    }else{\n      pConfig->bColumnsize = (zArg[0]=='1');\n    }\n    return rc;\n  }\n\n  if( sqlite3_strnicmp(\"detail\", zCmd, nCmd)==0 ){\n    const Fts5Enum aDetail[] = {\n      { \"none\", FTS5_DETAIL_NONE },\n      { \"full\", FTS5_DETAIL_FULL },\n      { \"columns\", FTS5_DETAIL_COLUMNS },\n      { 0, 0 }\n    };\n\n    if( (rc = fts5ConfigSetEnum(aDetail, zArg, &pConfig->eDetail)) ){\n      *pzErr = sqlite3_mprintf(\"malformed detail=... directive\");\n    }\n    return rc;\n  }\n\n  *pzErr = sqlite3_mprintf(\"unrecognized option: \\\"%.*s\\\"\", nCmd, zCmd);\n  return SQLITE_ERROR;\n}\n\n/*\n** Allocate an instance of the default tokenizer (\"simple\") at \n** Fts5Config.pTokenizer. Return SQLITE_OK if successful, or an SQLite error\n** code if an error occurs.\n*/\nstatic int fts5ConfigDefaultTokenizer(Fts5Global *pGlobal, Fts5Config *pConfig){\n  assert( pConfig->pTok==0 && pConfig->pTokApi==0 );\n  return sqlite3Fts5GetTokenizer(\n      pGlobal, 0, 0, &pConfig->pTok, &pConfig->pTokApi, 0\n  );\n}\n\n/*\n** Gobble up the first bareword or quoted word from the input buffer zIn.\n** Return a pointer to the character immediately following the last in\n** the gobbled word if successful, or a NULL pointer otherwise (failed\n** to find close-quote character).\n**\n** Before returning, set pzOut to point to a new buffer containing a\n** nul-terminated, dequoted copy of the gobbled word. If the word was\n** quoted, *pbQuoted is also set to 1 before returning.\n**\n** If *pRc is other than SQLITE_OK when this function is called, it is\n** a no-op (NULL is returned). Otherwise, if an OOM occurs within this\n** function, *pRc is set to SQLITE_NOMEM before returning. *pRc is *not*\n** set if a parse error (failed to find close quote) occurs.\n*/\nstatic const char *fts5ConfigGobbleWord(\n  int *pRc,                       /* IN/OUT: Error code */\n  const char *zIn,                /* Buffer to gobble string/bareword from */\n  char **pzOut,                   /* OUT: malloc'd buffer containing str/bw */\n  int *pbQuoted                   /* OUT: Set to true if dequoting required */\n){\n  const char *zRet = 0;\n\n  int nIn = (int)strlen(zIn);\n  char *zOut = sqlite3_malloc(nIn+1);\n\n  assert( *pRc==SQLITE_OK );\n  *pbQuoted = 0;\n  *pzOut = 0;\n\n  if( zOut==0 ){\n    *pRc = SQLITE_NOMEM;\n  }else{\n    memcpy(zOut, zIn, nIn+1);\n    if( fts5_isopenquote(zOut[0]) ){\n      int ii = fts5Dequote(zOut);\n      zRet = &zIn[ii];\n      *pbQuoted = 1;\n    }else{\n      zRet = fts5ConfigSkipBareword(zIn);\n      if( zRet ){\n        zOut[zRet-zIn] = '\\0';\n      }\n    }\n  }\n\n  if( zRet==0 ){\n    sqlite3_free(zOut);\n  }else{\n    *pzOut = zOut;\n  }\n\n  return zRet;\n}\n\nstatic int fts5ConfigParseColumn(\n  Fts5Config *p, \n  char *zCol, \n  char *zArg, \n  char **pzErr\n){\n  int rc = SQLITE_OK;\n  if( 0==sqlite3_stricmp(zCol, FTS5_RANK_NAME) \n   || 0==sqlite3_stricmp(zCol, FTS5_ROWID_NAME) \n  ){\n    *pzErr = sqlite3_mprintf(\"reserved fts5 column name: %s\", zCol);\n    rc = SQLITE_ERROR;\n  }else if( zArg ){\n    if( 0==sqlite3_stricmp(zArg, \"unindexed\") ){\n      p->abUnindexed[p->nCol] = 1;\n    }else{\n      *pzErr = sqlite3_mprintf(\"unrecognized column option: %s\", zArg);\n      rc = SQLITE_ERROR;\n    }\n  }\n\n  p->azCol[p->nCol++] = zCol;\n  return rc;\n}\n\n/*\n** Populate the Fts5Config.zContentExprlist string.\n*/\nstatic int fts5ConfigMakeExprlist(Fts5Config *p){\n  int i;\n  int rc = SQLITE_OK;\n  Fts5Buffer buf = {0, 0, 0};\n\n  sqlite3Fts5BufferAppendPrintf(&rc, &buf, \"T.%Q\", p->zContentRowid);\n  if( p->eContent!=FTS5_CONTENT_NONE ){\n    for(i=0; i<p->nCol; i++){\n      if( p->eContent==FTS5_CONTENT_EXTERNAL ){\n        sqlite3Fts5BufferAppendPrintf(&rc, &buf, \", T.%Q\", p->azCol[i]);\n      }else{\n        sqlite3Fts5BufferAppendPrintf(&rc, &buf, \", T.c%d\", i);\n      }\n    }\n  }\n\n  assert( p->zContentExprlist==0 );\n  p->zContentExprlist = (char*)buf.p;\n  return rc;\n}\n\n/*\n** Arguments nArg/azArg contain the string arguments passed to the xCreate\n** or xConnect method of the virtual table. This function attempts to \n** allocate an instance of Fts5Config containing the results of parsing\n** those arguments.\n**\n** If successful, SQLITE_OK is returned and *ppOut is set to point to the\n** new Fts5Config object. If an error occurs, an SQLite error code is \n** returned, *ppOut is set to NULL and an error message may be left in\n** *pzErr. It is the responsibility of the caller to eventually free any \n** such error message using sqlite3_free().\n*/\nstatic int sqlite3Fts5ConfigParse(\n  Fts5Global *pGlobal,\n  sqlite3 *db,\n  int nArg,                       /* Number of arguments */\n  const char **azArg,             /* Array of nArg CREATE VIRTUAL TABLE args */\n  Fts5Config **ppOut,             /* OUT: Results of parse */\n  char **pzErr                    /* OUT: Error message */\n){\n  int rc = SQLITE_OK;             /* Return code */\n  Fts5Config *pRet;               /* New object to return */\n  int i;\n  int nByte;\n\n  *ppOut = pRet = (Fts5Config*)sqlite3_malloc(sizeof(Fts5Config));\n  if( pRet==0 ) return SQLITE_NOMEM;\n  memset(pRet, 0, sizeof(Fts5Config));\n  pRet->db = db;\n  pRet->iCookie = -1;\n\n  nByte = nArg * (sizeof(char*) + sizeof(u8));\n  pRet->azCol = (char**)sqlite3Fts5MallocZero(&rc, nByte);\n  pRet->abUnindexed = (u8*)&pRet->azCol[nArg];\n  pRet->zDb = sqlite3Fts5Strndup(&rc, azArg[1], -1);\n  pRet->zName = sqlite3Fts5Strndup(&rc, azArg[2], -1);\n  pRet->bColumnsize = 1;\n  pRet->eDetail = FTS5_DETAIL_FULL;\n#ifdef SQLITE_DEBUG\n  pRet->bPrefixIndex = 1;\n#endif\n  if( rc==SQLITE_OK && sqlite3_stricmp(pRet->zName, FTS5_RANK_NAME)==0 ){\n    *pzErr = sqlite3_mprintf(\"reserved fts5 table name: %s\", pRet->zName);\n    rc = SQLITE_ERROR;\n  }\n\n  for(i=3; rc==SQLITE_OK && i<nArg; i++){\n    const char *zOrig = azArg[i];\n    const char *z;\n    char *zOne = 0;\n    char *zTwo = 0;\n    int bOption = 0;\n    int bMustBeCol = 0;\n\n    z = fts5ConfigGobbleWord(&rc, zOrig, &zOne, &bMustBeCol);\n    z = fts5ConfigSkipWhitespace(z);\n    if( z && *z=='=' ){\n      bOption = 1;\n      z++;\n      if( bMustBeCol ) z = 0;\n    }\n    z = fts5ConfigSkipWhitespace(z);\n    if( z && z[0] ){\n      int bDummy;\n      z = fts5ConfigGobbleWord(&rc, z, &zTwo, &bDummy);\n      if( z && z[0] ) z = 0;\n    }\n\n    if( rc==SQLITE_OK ){\n      if( z==0 ){\n        *pzErr = sqlite3_mprintf(\"parse error in \\\"%s\\\"\", zOrig);\n        rc = SQLITE_ERROR;\n      }else{\n        if( bOption ){\n          rc = fts5ConfigParseSpecial(pGlobal, pRet, zOne, zTwo?zTwo:\"\", pzErr);\n        }else{\n          rc = fts5ConfigParseColumn(pRet, zOne, zTwo, pzErr);\n          zOne = 0;\n        }\n      }\n    }\n\n    sqlite3_free(zOne);\n    sqlite3_free(zTwo);\n  }\n\n  /* If a tokenizer= option was successfully parsed, the tokenizer has\n  ** already been allocated. Otherwise, allocate an instance of the default\n  ** tokenizer (unicode61) now.  */\n  if( rc==SQLITE_OK && pRet->pTok==0 ){\n    rc = fts5ConfigDefaultTokenizer(pGlobal, pRet);\n  }\n\n  /* If no zContent option was specified, fill in the default values. */\n  if( rc==SQLITE_OK && pRet->zContent==0 ){\n    const char *zTail = 0;\n    assert( pRet->eContent==FTS5_CONTENT_NORMAL \n         || pRet->eContent==FTS5_CONTENT_NONE \n    );\n    if( pRet->eContent==FTS5_CONTENT_NORMAL ){\n      zTail = \"content\";\n    }else if( pRet->bColumnsize ){\n      zTail = \"docsize\";\n    }\n\n    if( zTail ){\n      pRet->zContent = sqlite3Fts5Mprintf(\n          &rc, \"%Q.'%q_%s'\", pRet->zDb, pRet->zName, zTail\n      );\n    }\n  }\n\n  if( rc==SQLITE_OK && pRet->zContentRowid==0 ){\n    pRet->zContentRowid = sqlite3Fts5Strndup(&rc, \"rowid\", -1);\n  }\n\n  /* Formulate the zContentExprlist text */\n  if( rc==SQLITE_OK ){\n    rc = fts5ConfigMakeExprlist(pRet);\n  }\n\n  if( rc!=SQLITE_OK ){\n    sqlite3Fts5ConfigFree(pRet);\n    *ppOut = 0;\n  }\n  return rc;\n}\n\n/*\n** Free the configuration object passed as the only argument.\n*/\nstatic void sqlite3Fts5ConfigFree(Fts5Config *pConfig){\n  if( pConfig ){\n    int i;\n    if( pConfig->pTok ){\n      pConfig->pTokApi->xDelete(pConfig->pTok);\n    }\n    sqlite3_free(pConfig->zDb);\n    sqlite3_free(pConfig->zName);\n    for(i=0; i<pConfig->nCol; i++){\n      sqlite3_free(pConfig->azCol[i]);\n    }\n    sqlite3_free(pConfig->azCol);\n    sqlite3_free(pConfig->aPrefix);\n    sqlite3_free(pConfig->zRank);\n    sqlite3_free(pConfig->zRankArgs);\n    sqlite3_free(pConfig->zContent);\n    sqlite3_free(pConfig->zContentRowid);\n    sqlite3_free(pConfig->zContentExprlist);\n    sqlite3_free(pConfig);\n  }\n}\n\n/*\n** Call sqlite3_declare_vtab() based on the contents of the configuration\n** object passed as the only argument. Return SQLITE_OK if successful, or\n** an SQLite error code if an error occurs.\n*/\nstatic int sqlite3Fts5ConfigDeclareVtab(Fts5Config *pConfig){\n  int i;\n  int rc = SQLITE_OK;\n  char *zSql;\n\n  zSql = sqlite3Fts5Mprintf(&rc, \"CREATE TABLE x(\");\n  for(i=0; zSql && i<pConfig->nCol; i++){\n    const char *zSep = (i==0?\"\":\", \");\n    zSql = sqlite3Fts5Mprintf(&rc, \"%z%s%Q\", zSql, zSep, pConfig->azCol[i]);\n  }\n  zSql = sqlite3Fts5Mprintf(&rc, \"%z, %Q HIDDEN, %s HIDDEN)\", \n      zSql, pConfig->zName, FTS5_RANK_NAME\n  );\n\n  assert( zSql || rc==SQLITE_NOMEM );\n  if( zSql ){\n    rc = sqlite3_declare_vtab(pConfig->db, zSql);\n    sqlite3_free(zSql);\n  }\n  \n  return rc;\n}\n\n/*\n** Tokenize the text passed via the second and third arguments.\n**\n** The callback is invoked once for each token in the input text. The\n** arguments passed to it are, in order:\n**\n**     void *pCtx          // Copy of 4th argument to sqlite3Fts5Tokenize()\n**     const char *pToken  // Pointer to buffer containing token\n**     int nToken          // Size of token in bytes\n**     int iStart          // Byte offset of start of token within input text\n**     int iEnd            // Byte offset of end of token within input text\n**     int iPos            // Position of token in input (first token is 0)\n**\n** If the callback returns a non-zero value the tokenization is abandoned\n** and no further callbacks are issued. \n**\n** This function returns SQLITE_OK if successful or an SQLite error code\n** if an error occurs. If the tokenization was abandoned early because\n** the callback returned SQLITE_DONE, this is not an error and this function\n** still returns SQLITE_OK. Or, if the tokenization was abandoned early\n** because the callback returned another non-zero value, it is assumed\n** to be an SQLite error code and returned to the caller.\n*/\nstatic int sqlite3Fts5Tokenize(\n  Fts5Config *pConfig,            /* FTS5 Configuration object */\n  int flags,                      /* FTS5_TOKENIZE_* flags */\n  const char *pText, int nText,   /* Text to tokenize */\n  void *pCtx,                     /* Context passed to xToken() */\n  int (*xToken)(void*, int, const char*, int, int, int)    /* Callback */\n){\n  if( pText==0 ) return SQLITE_OK;\n  return pConfig->pTokApi->xTokenize(\n      pConfig->pTok, pCtx, flags, pText, nText, xToken\n  );\n}\n\n/*\n** Argument pIn points to the first character in what is expected to be\n** a comma-separated list of SQL literals followed by a ')' character.\n** If it actually is this, return a pointer to the ')'. Otherwise, return\n** NULL to indicate a parse error.\n*/\nstatic const char *fts5ConfigSkipArgs(const char *pIn){\n  const char *p = pIn;\n  \n  while( 1 ){\n    p = fts5ConfigSkipWhitespace(p);\n    p = fts5ConfigSkipLiteral(p);\n    p = fts5ConfigSkipWhitespace(p);\n    if( p==0 || *p==')' ) break;\n    if( *p!=',' ){\n      p = 0;\n      break;\n    }\n    p++;\n  }\n\n  return p;\n}\n\n/*\n** Parameter zIn contains a rank() function specification. The format of \n** this is:\n**\n**   + Bareword (function name)\n**   + Open parenthesis - \"(\"\n**   + Zero or more SQL literals in a comma separated list\n**   + Close parenthesis - \")\"\n*/\nstatic int sqlite3Fts5ConfigParseRank(\n  const char *zIn,                /* Input string */\n  char **pzRank,                  /* OUT: Rank function name */\n  char **pzRankArgs               /* OUT: Rank function arguments */\n){\n  const char *p = zIn;\n  const char *pRank;\n  char *zRank = 0;\n  char *zRankArgs = 0;\n  int rc = SQLITE_OK;\n\n  *pzRank = 0;\n  *pzRankArgs = 0;\n\n  if( p==0 ){\n    rc = SQLITE_ERROR;\n  }else{\n    p = fts5ConfigSkipWhitespace(p);\n    pRank = p;\n    p = fts5ConfigSkipBareword(p);\n\n    if( p ){\n      zRank = sqlite3Fts5MallocZero(&rc, 1 + p - pRank);\n      if( zRank ) memcpy(zRank, pRank, p-pRank);\n    }else{\n      rc = SQLITE_ERROR;\n    }\n\n    if( rc==SQLITE_OK ){\n      p = fts5ConfigSkipWhitespace(p);\n      if( *p!='(' ) rc = SQLITE_ERROR;\n      p++;\n    }\n    if( rc==SQLITE_OK ){\n      const char *pArgs; \n      p = fts5ConfigSkipWhitespace(p);\n      pArgs = p;\n      if( *p!=')' ){\n        p = fts5ConfigSkipArgs(p);\n        if( p==0 ){\n          rc = SQLITE_ERROR;\n        }else{\n          zRankArgs = sqlite3Fts5MallocZero(&rc, 1 + p - pArgs);\n          if( zRankArgs ) memcpy(zRankArgs, pArgs, p-pArgs);\n        }\n      }\n    }\n  }\n\n  if( rc!=SQLITE_OK ){\n    sqlite3_free(zRank);\n    assert( zRankArgs==0 );\n  }else{\n    *pzRank = zRank;\n    *pzRankArgs = zRankArgs;\n  }\n  return rc;\n}\n\nstatic int sqlite3Fts5ConfigSetValue(\n  Fts5Config *pConfig, \n  const char *zKey, \n  sqlite3_value *pVal,\n  int *pbBadkey\n){\n  int rc = SQLITE_OK;\n\n  if( 0==sqlite3_stricmp(zKey, \"pgsz\") ){\n    int pgsz = 0;\n    if( SQLITE_INTEGER==sqlite3_value_numeric_type(pVal) ){\n      pgsz = sqlite3_value_int(pVal);\n    }\n    if( pgsz<=0 || pgsz>FTS5_MAX_PAGE_SIZE ){\n      *pbBadkey = 1;\n    }else{\n      pConfig->pgsz = pgsz;\n    }\n  }\n\n  else if( 0==sqlite3_stricmp(zKey, \"hashsize\") ){\n    int nHashSize = -1;\n    if( SQLITE_INTEGER==sqlite3_value_numeric_type(pVal) ){\n      nHashSize = sqlite3_value_int(pVal);\n    }\n    if( nHashSize<=0 ){\n      *pbBadkey = 1;\n    }else{\n      pConfig->nHashSize = nHashSize;\n    }\n  }\n\n  else if( 0==sqlite3_stricmp(zKey, \"automerge\") ){\n    int nAutomerge = -1;\n    if( SQLITE_INTEGER==sqlite3_value_numeric_type(pVal) ){\n      nAutomerge = sqlite3_value_int(pVal);\n    }\n    if( nAutomerge<0 || nAutomerge>64 ){\n      *pbBadkey = 1;\n    }else{\n      if( nAutomerge==1 ) nAutomerge = FTS5_DEFAULT_AUTOMERGE;\n      pConfig->nAutomerge = nAutomerge;\n    }\n  }\n\n  else if( 0==sqlite3_stricmp(zKey, \"usermerge\") ){\n    int nUsermerge = -1;\n    if( SQLITE_INTEGER==sqlite3_value_numeric_type(pVal) ){\n      nUsermerge = sqlite3_value_int(pVal);\n    }\n    if( nUsermerge<2 || nUsermerge>16 ){\n      *pbBadkey = 1;\n    }else{\n      pConfig->nUsermerge = nUsermerge;\n    }\n  }\n\n  else if( 0==sqlite3_stricmp(zKey, \"crisismerge\") ){\n    int nCrisisMerge = -1;\n    if( SQLITE_INTEGER==sqlite3_value_numeric_type(pVal) ){\n      nCrisisMerge = sqlite3_value_int(pVal);\n    }\n    if( nCrisisMerge<0 ){\n      *pbBadkey = 1;\n    }else{\n      if( nCrisisMerge<=1 ) nCrisisMerge = FTS5_DEFAULT_CRISISMERGE;\n      pConfig->nCrisisMerge = nCrisisMerge;\n    }\n  }\n\n  else if( 0==sqlite3_stricmp(zKey, \"rank\") ){\n    const char *zIn = (const char*)sqlite3_value_text(pVal);\n    char *zRank;\n    char *zRankArgs;\n    rc = sqlite3Fts5ConfigParseRank(zIn, &zRank, &zRankArgs);\n    if( rc==SQLITE_OK ){\n      sqlite3_free(pConfig->zRank);\n      sqlite3_free(pConfig->zRankArgs);\n      pConfig->zRank = zRank;\n      pConfig->zRankArgs = zRankArgs;\n    }else if( rc==SQLITE_ERROR ){\n      rc = SQLITE_OK;\n      *pbBadkey = 1;\n    }\n  }else{\n    *pbBadkey = 1;\n  }\n  return rc;\n}\n\n/*\n** Load the contents of the %_config table into memory.\n*/\nstatic int sqlite3Fts5ConfigLoad(Fts5Config *pConfig, int iCookie){\n  const char *zSelect = \"SELECT k, v FROM %Q.'%q_config'\";\n  char *zSql;\n  sqlite3_stmt *p = 0;\n  int rc = SQLITE_OK;\n  int iVersion = 0;\n\n  /* Set default values */\n  pConfig->pgsz = FTS5_DEFAULT_PAGE_SIZE;\n  pConfig->nAutomerge = FTS5_DEFAULT_AUTOMERGE;\n  pConfig->nUsermerge = FTS5_DEFAULT_USERMERGE;\n  pConfig->nCrisisMerge = FTS5_DEFAULT_CRISISMERGE;\n  pConfig->nHashSize = FTS5_DEFAULT_HASHSIZE;\n\n  zSql = sqlite3Fts5Mprintf(&rc, zSelect, pConfig->zDb, pConfig->zName);\n  if( zSql ){\n    rc = sqlite3_prepare_v2(pConfig->db, zSql, -1, &p, 0);\n    sqlite3_free(zSql);\n  }\n\n  assert( rc==SQLITE_OK || p==0 );\n  if( rc==SQLITE_OK ){\n    while( SQLITE_ROW==sqlite3_step(p) ){\n      const char *zK = (const char*)sqlite3_column_text(p, 0);\n      sqlite3_value *pVal = sqlite3_column_value(p, 1);\n      if( 0==sqlite3_stricmp(zK, \"version\") ){\n        iVersion = sqlite3_value_int(pVal);\n      }else{\n        int bDummy = 0;\n        sqlite3Fts5ConfigSetValue(pConfig, zK, pVal, &bDummy);\n      }\n    }\n    rc = sqlite3_finalize(p);\n  }\n  \n  if( rc==SQLITE_OK && iVersion!=FTS5_CURRENT_VERSION ){\n    rc = SQLITE_ERROR;\n    if( pConfig->pzErrmsg ){\n      assert( 0==*pConfig->pzErrmsg );\n      *pConfig->pzErrmsg = sqlite3_mprintf(\n          \"invalid fts5 file format (found %d, expected %d) - run 'rebuild'\",\n          iVersion, FTS5_CURRENT_VERSION\n      );\n    }\n  }\n\n  if( rc==SQLITE_OK ){\n    pConfig->iCookie = iCookie;\n  }\n  return rc;\n}\n\n/*\n** 2014 May 31\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n******************************************************************************\n**\n*/\n\n\n\n/* #include \"fts5Int.h\" */\n/* #include \"fts5parse.h\" */\n\n/*\n** All token types in the generated fts5parse.h file are greater than 0.\n*/\n#define FTS5_EOF 0\n\n#define FTS5_LARGEST_INT64  (0xffffffff|(((i64)0x7fffffff)<<32))\n\ntypedef struct Fts5ExprTerm Fts5ExprTerm;\n\n/*\n** Functions generated by lemon from fts5parse.y.\n*/\nstatic void *sqlite3Fts5ParserAlloc(void *(*mallocProc)(u64));\nstatic void sqlite3Fts5ParserFree(void*, void (*freeProc)(void*));\nstatic void sqlite3Fts5Parser(void*, int, Fts5Token, Fts5Parse*);\n#ifndef NDEBUG\n/* #include <stdio.h> */\nstatic void sqlite3Fts5ParserTrace(FILE*, char*);\n#endif\n\n\nstruct Fts5Expr {\n  Fts5Index *pIndex;\n  Fts5Config *pConfig;\n  Fts5ExprNode *pRoot;\n  int bDesc;                      /* Iterate in descending rowid order */\n  int nPhrase;                    /* Number of phrases in expression */\n  Fts5ExprPhrase **apExprPhrase;  /* Pointers to phrase objects */\n};\n\n/*\n** eType:\n**   Expression node type. Always one of:\n**\n**       FTS5_AND                 (nChild, apChild valid)\n**       FTS5_OR                  (nChild, apChild valid)\n**       FTS5_NOT                 (nChild, apChild valid)\n**       FTS5_STRING              (pNear valid)\n**       FTS5_TERM                (pNear valid)\n*/\nstruct Fts5ExprNode {\n  int eType;                      /* Node type */\n  int bEof;                       /* True at EOF */\n  int bNomatch;                   /* True if entry is not a match */\n\n  /* Next method for this node. */\n  int (*xNext)(Fts5Expr*, Fts5ExprNode*, int, i64);\n\n  i64 iRowid;                     /* Current rowid */\n  Fts5ExprNearset *pNear;         /* For FTS5_STRING - cluster of phrases */\n\n  /* Child nodes. For a NOT node, this array always contains 2 entries. For \n  ** AND or OR nodes, it contains 2 or more entries.  */\n  int nChild;                     /* Number of child nodes */\n  Fts5ExprNode *apChild[1];       /* Array of child nodes */\n};\n\n#define Fts5NodeIsString(p) ((p)->eType==FTS5_TERM || (p)->eType==FTS5_STRING)\n\n/*\n** Invoke the xNext method of an Fts5ExprNode object. This macro should be\n** used as if it has the same signature as the xNext() methods themselves.\n*/\n#define fts5ExprNodeNext(a,b,c,d) (b)->xNext((a), (b), (c), (d))\n\n/*\n** An instance of the following structure represents a single search term\n** or term prefix.\n*/\nstruct Fts5ExprTerm {\n  u8 bPrefix;                     /* True for a prefix term */\n  u8 bFirst;                      /* True if token must be first in column */\n  char *zTerm;                    /* nul-terminated term */\n  Fts5IndexIter *pIter;           /* Iterator for this term */\n  Fts5ExprTerm *pSynonym;         /* Pointer to first in list of synonyms */\n};\n\n/*\n** A phrase. One or more terms that must appear in a contiguous sequence\n** within a document for it to match.\n*/\nstruct Fts5ExprPhrase {\n  Fts5ExprNode *pNode;            /* FTS5_STRING node this phrase is part of */\n  Fts5Buffer poslist;             /* Current position list */\n  int nTerm;                      /* Number of entries in aTerm[] */\n  Fts5ExprTerm aTerm[1];          /* Terms that make up this phrase */\n};\n\n/*\n** One or more phrases that must appear within a certain token distance of\n** each other within each matching document.\n*/\nstruct Fts5ExprNearset {\n  int nNear;                      /* NEAR parameter */\n  Fts5Colset *pColset;            /* Columns to search (NULL -> all columns) */\n  int nPhrase;                    /* Number of entries in aPhrase[] array */\n  Fts5ExprPhrase *apPhrase[1];    /* Array of phrase pointers */\n};\n\n\n/*\n** Parse context.\n*/\nstruct Fts5Parse {\n  Fts5Config *pConfig;\n  char *zErr;\n  int rc;\n  int nPhrase;                    /* Size of apPhrase array */\n  Fts5ExprPhrase **apPhrase;      /* Array of all phrases */\n  Fts5ExprNode *pExpr;            /* Result of a successful parse */\n};\n\nstatic void sqlite3Fts5ParseError(Fts5Parse *pParse, const char *zFmt, ...){\n  va_list ap;\n  va_start(ap, zFmt);\n  if( pParse->rc==SQLITE_OK ){\n    pParse->zErr = sqlite3_vmprintf(zFmt, ap);\n    pParse->rc = SQLITE_ERROR;\n  }\n  va_end(ap);\n}\n\nstatic int fts5ExprIsspace(char t){\n  return t==' ' || t=='\\t' || t=='\\n' || t=='\\r';\n}\n\n/*\n** Read the first token from the nul-terminated string at *pz.\n*/\nstatic int fts5ExprGetToken(\n  Fts5Parse *pParse, \n  const char **pz,                /* IN/OUT: Pointer into buffer */\n  Fts5Token *pToken\n){\n  const char *z = *pz;\n  int tok;\n\n  /* Skip past any whitespace */\n  while( fts5ExprIsspace(*z) ) z++;\n\n  pToken->p = z;\n  pToken->n = 1;\n  switch( *z ){\n    case '(':  tok = FTS5_LP;    break;\n    case ')':  tok = FTS5_RP;    break;\n    case '{':  tok = FTS5_LCP;   break;\n    case '}':  tok = FTS5_RCP;   break;\n    case ':':  tok = FTS5_COLON; break;\n    case ',':  tok = FTS5_COMMA; break;\n    case '+':  tok = FTS5_PLUS;  break;\n    case '*':  tok = FTS5_STAR;  break;\n    case '-':  tok = FTS5_MINUS; break;\n    case '^':  tok = FTS5_CARET; break;\n    case '\\0': tok = FTS5_EOF;   break;\n\n    case '\"': {\n      const char *z2;\n      tok = FTS5_STRING;\n\n      for(z2=&z[1]; 1; z2++){\n        if( z2[0]=='\"' ){\n          z2++;\n          if( z2[0]!='\"' ) break;\n        }\n        if( z2[0]=='\\0' ){\n          sqlite3Fts5ParseError(pParse, \"unterminated string\");\n          return FTS5_EOF;\n        }\n      }\n      pToken->n = (z2 - z);\n      break;\n    }\n\n    default: {\n      const char *z2;\n      if( sqlite3Fts5IsBareword(z[0])==0 ){\n        sqlite3Fts5ParseError(pParse, \"fts5: syntax error near \\\"%.1s\\\"\", z);\n        return FTS5_EOF;\n      }\n      tok = FTS5_STRING;\n      for(z2=&z[1]; sqlite3Fts5IsBareword(*z2); z2++);\n      pToken->n = (z2 - z);\n      if( pToken->n==2 && memcmp(pToken->p, \"OR\", 2)==0 )  tok = FTS5_OR;\n      if( pToken->n==3 && memcmp(pToken->p, \"NOT\", 3)==0 ) tok = FTS5_NOT;\n      if( pToken->n==3 && memcmp(pToken->p, \"AND\", 3)==0 ) tok = FTS5_AND;\n      break;\n    }\n  }\n\n  *pz = &pToken->p[pToken->n];\n  return tok;\n}\n\nstatic void *fts5ParseAlloc(u64 t){ return sqlite3_malloc((int)t); }\nstatic void fts5ParseFree(void *p){ sqlite3_free(p); }\n\nstatic int sqlite3Fts5ExprNew(\n  Fts5Config *pConfig,            /* FTS5 Configuration */\n  int iCol,\n  const char *zExpr,              /* Expression text */\n  Fts5Expr **ppNew, \n  char **pzErr\n){\n  Fts5Parse sParse;\n  Fts5Token token;\n  const char *z = zExpr;\n  int t;                          /* Next token type */\n  void *pEngine;\n  Fts5Expr *pNew;\n\n  *ppNew = 0;\n  *pzErr = 0;\n  memset(&sParse, 0, sizeof(sParse));\n  pEngine = sqlite3Fts5ParserAlloc(fts5ParseAlloc);\n  if( pEngine==0 ){ return SQLITE_NOMEM; }\n  sParse.pConfig = pConfig;\n\n  do {\n    t = fts5ExprGetToken(&sParse, &z, &token);\n    sqlite3Fts5Parser(pEngine, t, token, &sParse);\n  }while( sParse.rc==SQLITE_OK && t!=FTS5_EOF );\n  sqlite3Fts5ParserFree(pEngine, fts5ParseFree);\n\n  /* If the LHS of the MATCH expression was a user column, apply the\n  ** implicit column-filter.  */\n  if( iCol<pConfig->nCol && sParse.pExpr && sParse.rc==SQLITE_OK ){\n    int n = sizeof(Fts5Colset);\n    Fts5Colset *pColset = (Fts5Colset*)sqlite3Fts5MallocZero(&sParse.rc, n);\n    if( pColset ){\n      pColset->nCol = 1;\n      pColset->aiCol[0] = iCol;\n      sqlite3Fts5ParseSetColset(&sParse, sParse.pExpr, pColset);\n    }\n  }\n\n  assert( sParse.rc!=SQLITE_OK || sParse.zErr==0 );\n  if( sParse.rc==SQLITE_OK ){\n    *ppNew = pNew = sqlite3_malloc(sizeof(Fts5Expr));\n    if( pNew==0 ){\n      sParse.rc = SQLITE_NOMEM;\n      sqlite3Fts5ParseNodeFree(sParse.pExpr);\n    }else{\n      if( !sParse.pExpr ){\n        const int nByte = sizeof(Fts5ExprNode);\n        pNew->pRoot = (Fts5ExprNode*)sqlite3Fts5MallocZero(&sParse.rc, nByte);\n        if( pNew->pRoot ){\n          pNew->pRoot->bEof = 1;\n        }\n      }else{\n        pNew->pRoot = sParse.pExpr;\n      }\n      pNew->pIndex = 0;\n      pNew->pConfig = pConfig;\n      pNew->apExprPhrase = sParse.apPhrase;\n      pNew->nPhrase = sParse.nPhrase;\n      sParse.apPhrase = 0;\n    }\n  }else{\n    sqlite3Fts5ParseNodeFree(sParse.pExpr);\n  }\n\n  sqlite3_free(sParse.apPhrase);\n  *pzErr = sParse.zErr;\n  return sParse.rc;\n}\n\n/*\n** Free the expression node object passed as the only argument.\n*/\nstatic void sqlite3Fts5ParseNodeFree(Fts5ExprNode *p){\n  if( p ){\n    int i;\n    for(i=0; i<p->nChild; i++){\n      sqlite3Fts5ParseNodeFree(p->apChild[i]);\n    }\n    sqlite3Fts5ParseNearsetFree(p->pNear);\n    sqlite3_free(p);\n  }\n}\n\n/*\n** Free the expression object passed as the only argument.\n*/\nstatic void sqlite3Fts5ExprFree(Fts5Expr *p){\n  if( p ){\n    sqlite3Fts5ParseNodeFree(p->pRoot);\n    sqlite3_free(p->apExprPhrase);\n    sqlite3_free(p);\n  }\n}\n\n/*\n** Argument pTerm must be a synonym iterator. Return the current rowid\n** that it points to.\n*/\nstatic i64 fts5ExprSynonymRowid(Fts5ExprTerm *pTerm, int bDesc, int *pbEof){\n  i64 iRet = 0;\n  int bRetValid = 0;\n  Fts5ExprTerm *p;\n\n  assert( pTerm->pSynonym );\n  assert( bDesc==0 || bDesc==1 );\n  for(p=pTerm; p; p=p->pSynonym){\n    if( 0==sqlite3Fts5IterEof(p->pIter) ){\n      i64 iRowid = p->pIter->iRowid;\n      if( bRetValid==0 || (bDesc!=(iRowid<iRet)) ){\n        iRet = iRowid;\n        bRetValid = 1;\n      }\n    }\n  }\n\n  if( pbEof && bRetValid==0 ) *pbEof = 1;\n  return iRet;\n}\n\n/*\n** Argument pTerm must be a synonym iterator.\n*/\nstatic int fts5ExprSynonymList(\n  Fts5ExprTerm *pTerm, \n  i64 iRowid,\n  Fts5Buffer *pBuf,               /* Use this buffer for space if required */\n  u8 **pa, int *pn\n){\n  Fts5PoslistReader aStatic[4];\n  Fts5PoslistReader *aIter = aStatic;\n  int nIter = 0;\n  int nAlloc = 4;\n  int rc = SQLITE_OK;\n  Fts5ExprTerm *p;\n\n  assert( pTerm->pSynonym );\n  for(p=pTerm; p; p=p->pSynonym){\n    Fts5IndexIter *pIter = p->pIter;\n    if( sqlite3Fts5IterEof(pIter)==0 && pIter->iRowid==iRowid ){\n      if( pIter->nData==0 ) continue;\n      if( nIter==nAlloc ){\n        int nByte = sizeof(Fts5PoslistReader) * nAlloc * 2;\n        Fts5PoslistReader *aNew = (Fts5PoslistReader*)sqlite3_malloc(nByte);\n        if( aNew==0 ){\n          rc = SQLITE_NOMEM;\n          goto synonym_poslist_out;\n        }\n        memcpy(aNew, aIter, sizeof(Fts5PoslistReader) * nIter);\n        nAlloc = nAlloc*2;\n        if( aIter!=aStatic ) sqlite3_free(aIter);\n        aIter = aNew;\n      }\n      sqlite3Fts5PoslistReaderInit(pIter->pData, pIter->nData, &aIter[nIter]);\n      assert( aIter[nIter].bEof==0 );\n      nIter++;\n    }\n  }\n\n  if( nIter==1 ){\n    *pa = (u8*)aIter[0].a;\n    *pn = aIter[0].n;\n  }else{\n    Fts5PoslistWriter writer = {0};\n    i64 iPrev = -1;\n    fts5BufferZero(pBuf);\n    while( 1 ){\n      int i;\n      i64 iMin = FTS5_LARGEST_INT64;\n      for(i=0; i<nIter; i++){\n        if( aIter[i].bEof==0 ){\n          if( aIter[i].iPos==iPrev ){\n            if( sqlite3Fts5PoslistReaderNext(&aIter[i]) ) continue;\n          }\n          if( aIter[i].iPos<iMin ){\n            iMin = aIter[i].iPos;\n          }\n        }\n      }\n      if( iMin==FTS5_LARGEST_INT64 || rc!=SQLITE_OK ) break;\n      rc = sqlite3Fts5PoslistWriterAppend(pBuf, &writer, iMin);\n      iPrev = iMin;\n    }\n    if( rc==SQLITE_OK ){\n      *pa = pBuf->p;\n      *pn = pBuf->n;\n    }\n  }\n\n synonym_poslist_out:\n  if( aIter!=aStatic ) sqlite3_free(aIter);\n  return rc;\n}\n\n\n/*\n** All individual term iterators in pPhrase are guaranteed to be valid and\n** pointing to the same rowid when this function is called. This function \n** checks if the current rowid really is a match, and if so populates\n** the pPhrase->poslist buffer accordingly. Output parameter *pbMatch\n** is set to true if this is really a match, or false otherwise.\n**\n** SQLITE_OK is returned if an error occurs, or an SQLite error code \n** otherwise. It is not considered an error code if the current rowid is \n** not a match.\n*/\nstatic int fts5ExprPhraseIsMatch(\n  Fts5ExprNode *pNode,            /* Node pPhrase belongs to */\n  Fts5ExprPhrase *pPhrase,        /* Phrase object to initialize */\n  int *pbMatch                    /* OUT: Set to true if really a match */\n){\n  Fts5PoslistWriter writer = {0};\n  Fts5PoslistReader aStatic[4];\n  Fts5PoslistReader *aIter = aStatic;\n  int i;\n  int rc = SQLITE_OK;\n  int bFirst = pPhrase->aTerm[0].bFirst;\n  \n  fts5BufferZero(&pPhrase->poslist);\n\n  /* If the aStatic[] array is not large enough, allocate a large array\n  ** using sqlite3_malloc(). This approach could be improved upon. */\n  if( pPhrase->nTerm>ArraySize(aStatic) ){\n    int nByte = sizeof(Fts5PoslistReader) * pPhrase->nTerm;\n    aIter = (Fts5PoslistReader*)sqlite3_malloc(nByte);\n    if( !aIter ) return SQLITE_NOMEM;\n  }\n  memset(aIter, 0, sizeof(Fts5PoslistReader) * pPhrase->nTerm);\n\n  /* Initialize a term iterator for each term in the phrase */\n  for(i=0; i<pPhrase->nTerm; i++){\n    Fts5ExprTerm *pTerm = &pPhrase->aTerm[i];\n    int n = 0;\n    int bFlag = 0;\n    u8 *a = 0;\n    if( pTerm->pSynonym ){\n      Fts5Buffer buf = {0, 0, 0};\n      rc = fts5ExprSynonymList(pTerm, pNode->iRowid, &buf, &a, &n);\n      if( rc ){\n        sqlite3_free(a);\n        goto ismatch_out;\n      }\n      if( a==buf.p ) bFlag = 1;\n    }else{\n      a = (u8*)pTerm->pIter->pData;\n      n = pTerm->pIter->nData;\n    }\n    sqlite3Fts5PoslistReaderInit(a, n, &aIter[i]);\n    aIter[i].bFlag = (u8)bFlag;\n    if( aIter[i].bEof ) goto ismatch_out;\n  }\n\n  while( 1 ){\n    int bMatch;\n    i64 iPos = aIter[0].iPos;\n    do {\n      bMatch = 1;\n      for(i=0; i<pPhrase->nTerm; i++){\n        Fts5PoslistReader *pPos = &aIter[i];\n        i64 iAdj = iPos + i;\n        if( pPos->iPos!=iAdj ){\n          bMatch = 0;\n          while( pPos->iPos<iAdj ){\n            if( sqlite3Fts5PoslistReaderNext(pPos) ) goto ismatch_out;\n          }\n          if( pPos->iPos>iAdj ) iPos = pPos->iPos-i;\n        }\n      }\n    }while( bMatch==0 );\n\n    /* Append position iPos to the output */\n    if( bFirst==0 || FTS5_POS2OFFSET(iPos)==0 ){\n      rc = sqlite3Fts5PoslistWriterAppend(&pPhrase->poslist, &writer, iPos);\n      if( rc!=SQLITE_OK ) goto ismatch_out;\n    }\n\n    for(i=0; i<pPhrase->nTerm; i++){\n      if( sqlite3Fts5PoslistReaderNext(&aIter[i]) ) goto ismatch_out;\n    }\n  }\n\n ismatch_out:\n  *pbMatch = (pPhrase->poslist.n>0);\n  for(i=0; i<pPhrase->nTerm; i++){\n    if( aIter[i].bFlag ) sqlite3_free((u8*)aIter[i].a);\n  }\n  if( aIter!=aStatic ) sqlite3_free(aIter);\n  return rc;\n}\n\ntypedef struct Fts5LookaheadReader Fts5LookaheadReader;\nstruct Fts5LookaheadReader {\n  const u8 *a;                    /* Buffer containing position list */\n  int n;                          /* Size of buffer a[] in bytes */\n  int i;                          /* Current offset in position list */\n  i64 iPos;                       /* Current position */\n  i64 iLookahead;                 /* Next position */\n};\n\n#define FTS5_LOOKAHEAD_EOF (((i64)1) << 62)\n\nstatic int fts5LookaheadReaderNext(Fts5LookaheadReader *p){\n  p->iPos = p->iLookahead;\n  if( sqlite3Fts5PoslistNext64(p->a, p->n, &p->i, &p->iLookahead) ){\n    p->iLookahead = FTS5_LOOKAHEAD_EOF;\n  }\n  return (p->iPos==FTS5_LOOKAHEAD_EOF);\n}\n\nstatic int fts5LookaheadReaderInit(\n  const u8 *a, int n,             /* Buffer to read position list from */\n  Fts5LookaheadReader *p          /* Iterator object to initialize */\n){\n  memset(p, 0, sizeof(Fts5LookaheadReader));\n  p->a = a;\n  p->n = n;\n  fts5LookaheadReaderNext(p);\n  return fts5LookaheadReaderNext(p);\n}\n\ntypedef struct Fts5NearTrimmer Fts5NearTrimmer;\nstruct Fts5NearTrimmer {\n  Fts5LookaheadReader reader;     /* Input iterator */\n  Fts5PoslistWriter writer;       /* Writer context */\n  Fts5Buffer *pOut;               /* Output poslist */\n};\n\n/*\n** The near-set object passed as the first argument contains more than\n** one phrase. All phrases currently point to the same row. The\n** Fts5ExprPhrase.poslist buffers are populated accordingly. This function\n** tests if the current row contains instances of each phrase sufficiently\n** close together to meet the NEAR constraint. Non-zero is returned if it\n** does, or zero otherwise.\n**\n** If in/out parameter (*pRc) is set to other than SQLITE_OK when this\n** function is called, it is a no-op. Or, if an error (e.g. SQLITE_NOMEM)\n** occurs within this function (*pRc) is set accordingly before returning.\n** The return value is undefined in both these cases.\n** \n** If no error occurs and non-zero (a match) is returned, the position-list\n** of each phrase object is edited to contain only those entries that\n** meet the constraint before returning.\n*/\nstatic int fts5ExprNearIsMatch(int *pRc, Fts5ExprNearset *pNear){\n  Fts5NearTrimmer aStatic[4];\n  Fts5NearTrimmer *a = aStatic;\n  Fts5ExprPhrase **apPhrase = pNear->apPhrase;\n\n  int i;\n  int rc = *pRc;\n  int bMatch;\n\n  assert( pNear->nPhrase>1 );\n\n  /* If the aStatic[] array is not large enough, allocate a large array\n  ** using sqlite3_malloc(). This approach could be improved upon. */\n  if( pNear->nPhrase>ArraySize(aStatic) ){\n    int nByte = sizeof(Fts5NearTrimmer) * pNear->nPhrase;\n    a = (Fts5NearTrimmer*)sqlite3Fts5MallocZero(&rc, nByte);\n  }else{\n    memset(aStatic, 0, sizeof(aStatic));\n  }\n  if( rc!=SQLITE_OK ){\n    *pRc = rc;\n    return 0;\n  }\n\n  /* Initialize a lookahead iterator for each phrase. After passing the\n  ** buffer and buffer size to the lookaside-reader init function, zero\n  ** the phrase poslist buffer. The new poslist for the phrase (containing\n  ** the same entries as the original with some entries removed on account \n  ** of the NEAR constraint) is written over the original even as it is\n  ** being read. This is safe as the entries for the new poslist are a\n  ** subset of the old, so it is not possible for data yet to be read to\n  ** be overwritten.  */\n  for(i=0; i<pNear->nPhrase; i++){\n    Fts5Buffer *pPoslist = &apPhrase[i]->poslist;\n    fts5LookaheadReaderInit(pPoslist->p, pPoslist->n, &a[i].reader);\n    pPoslist->n = 0;\n    a[i].pOut = pPoslist;\n  }\n\n  while( 1 ){\n    int iAdv;\n    i64 iMin;\n    i64 iMax;\n\n    /* This block advances the phrase iterators until they point to a set of\n    ** entries that together comprise a match.  */\n    iMax = a[0].reader.iPos;\n    do {\n      bMatch = 1;\n      for(i=0; i<pNear->nPhrase; i++){\n        Fts5LookaheadReader *pPos = &a[i].reader;\n        iMin = iMax - pNear->apPhrase[i]->nTerm - pNear->nNear;\n        if( pPos->iPos<iMin || pPos->iPos>iMax ){\n          bMatch = 0;\n          while( pPos->iPos<iMin ){\n            if( fts5LookaheadReaderNext(pPos) ) goto ismatch_out;\n          }\n          if( pPos->iPos>iMax ) iMax = pPos->iPos;\n        }\n      }\n    }while( bMatch==0 );\n\n    /* Add an entry to each output position list */\n    for(i=0; i<pNear->nPhrase; i++){\n      i64 iPos = a[i].reader.iPos;\n      Fts5PoslistWriter *pWriter = &a[i].writer;\n      if( a[i].pOut->n==0 || iPos!=pWriter->iPrev ){\n        sqlite3Fts5PoslistWriterAppend(a[i].pOut, pWriter, iPos);\n      }\n    }\n\n    iAdv = 0;\n    iMin = a[0].reader.iLookahead;\n    for(i=0; i<pNear->nPhrase; i++){\n      if( a[i].reader.iLookahead < iMin ){\n        iMin = a[i].reader.iLookahead;\n        iAdv = i;\n      }\n    }\n    if( fts5LookaheadReaderNext(&a[iAdv].reader) ) goto ismatch_out;\n  }\n\n  ismatch_out: {\n    int bRet = a[0].pOut->n>0;\n    *pRc = rc;\n    if( a!=aStatic ) sqlite3_free(a);\n    return bRet;\n  }\n}\n\n/*\n** Advance iterator pIter until it points to a value equal to or laster\n** than the initial value of *piLast. If this means the iterator points\n** to a value laster than *piLast, update *piLast to the new lastest value.\n**\n** If the iterator reaches EOF, set *pbEof to true before returning. If\n** an error occurs, set *pRc to an error code. If either *pbEof or *pRc\n** are set, return a non-zero value. Otherwise, return zero.\n*/\nstatic int fts5ExprAdvanceto(\n  Fts5IndexIter *pIter,           /* Iterator to advance */\n  int bDesc,                      /* True if iterator is \"rowid DESC\" */\n  i64 *piLast,                    /* IN/OUT: Lastest rowid seen so far */\n  int *pRc,                       /* OUT: Error code */\n  int *pbEof                      /* OUT: Set to true if EOF */\n){\n  i64 iLast = *piLast;\n  i64 iRowid;\n\n  iRowid = pIter->iRowid;\n  if( (bDesc==0 && iLast>iRowid) || (bDesc && iLast<iRowid) ){\n    int rc = sqlite3Fts5IterNextFrom(pIter, iLast);\n    if( rc || sqlite3Fts5IterEof(pIter) ){\n      *pRc = rc;\n      *pbEof = 1;\n      return 1;\n    }\n    iRowid = pIter->iRowid;\n    assert( (bDesc==0 && iRowid>=iLast) || (bDesc==1 && iRowid<=iLast) );\n  }\n  *piLast = iRowid;\n\n  return 0;\n}\n\nstatic int fts5ExprSynonymAdvanceto(\n  Fts5ExprTerm *pTerm,            /* Term iterator to advance */\n  int bDesc,                      /* True if iterator is \"rowid DESC\" */\n  i64 *piLast,                    /* IN/OUT: Lastest rowid seen so far */\n  int *pRc                        /* OUT: Error code */\n){\n  int rc = SQLITE_OK;\n  i64 iLast = *piLast;\n  Fts5ExprTerm *p;\n  int bEof = 0;\n\n  for(p=pTerm; rc==SQLITE_OK && p; p=p->pSynonym){\n    if( sqlite3Fts5IterEof(p->pIter)==0 ){\n      i64 iRowid = p->pIter->iRowid;\n      if( (bDesc==0 && iLast>iRowid) || (bDesc && iLast<iRowid) ){\n        rc = sqlite3Fts5IterNextFrom(p->pIter, iLast);\n      }\n    }\n  }\n\n  if( rc!=SQLITE_OK ){\n    *pRc = rc;\n    bEof = 1;\n  }else{\n    *piLast = fts5ExprSynonymRowid(pTerm, bDesc, &bEof);\n  }\n  return bEof;\n}\n\n\nstatic int fts5ExprNearTest(\n  int *pRc,\n  Fts5Expr *pExpr,                /* Expression that pNear is a part of */\n  Fts5ExprNode *pNode             /* The \"NEAR\" node (FTS5_STRING) */\n){\n  Fts5ExprNearset *pNear = pNode->pNear;\n  int rc = *pRc;\n\n  if( pExpr->pConfig->eDetail!=FTS5_DETAIL_FULL ){\n    Fts5ExprTerm *pTerm;\n    Fts5ExprPhrase *pPhrase = pNear->apPhrase[0];\n    pPhrase->poslist.n = 0;\n    for(pTerm=&pPhrase->aTerm[0]; pTerm; pTerm=pTerm->pSynonym){\n      Fts5IndexIter *pIter = pTerm->pIter;\n      if( sqlite3Fts5IterEof(pIter)==0 ){\n        if( pIter->iRowid==pNode->iRowid && pIter->nData>0 ){\n          pPhrase->poslist.n = 1;\n        }\n      }\n    }\n    return pPhrase->poslist.n;\n  }else{\n    int i;\n\n    /* Check that each phrase in the nearset matches the current row.\n    ** Populate the pPhrase->poslist buffers at the same time. If any\n    ** phrase is not a match, break out of the loop early.  */\n    for(i=0; rc==SQLITE_OK && i<pNear->nPhrase; i++){\n      Fts5ExprPhrase *pPhrase = pNear->apPhrase[i];\n      if( pPhrase->nTerm>1 || pPhrase->aTerm[0].pSynonym \n       || pNear->pColset || pPhrase->aTerm[0].bFirst\n      ){\n        int bMatch = 0;\n        rc = fts5ExprPhraseIsMatch(pNode, pPhrase, &bMatch);\n        if( bMatch==0 ) break;\n      }else{\n        Fts5IndexIter *pIter = pPhrase->aTerm[0].pIter;\n        fts5BufferSet(&rc, &pPhrase->poslist, pIter->nData, pIter->pData);\n      }\n    }\n\n    *pRc = rc;\n    if( i==pNear->nPhrase && (i==1 || fts5ExprNearIsMatch(pRc, pNear)) ){\n      return 1;\n    }\n    return 0;\n  }\n}\n\n\n/*\n** Initialize all term iterators in the pNear object. If any term is found\n** to match no documents at all, return immediately without initializing any\n** further iterators.\n**\n** If an error occurs, return an SQLite error code. Otherwise, return\n** SQLITE_OK. It is not considered an error if some term matches zero\n** documents.\n*/\nstatic int fts5ExprNearInitAll(\n  Fts5Expr *pExpr,\n  Fts5ExprNode *pNode\n){\n  Fts5ExprNearset *pNear = pNode->pNear;\n  int i;\n\n  assert( pNode->bNomatch==0 );\n  for(i=0; i<pNear->nPhrase; i++){\n    Fts5ExprPhrase *pPhrase = pNear->apPhrase[i];\n    if( pPhrase->nTerm==0 ){\n      pNode->bEof = 1;\n      return SQLITE_OK;\n    }else{\n      int j;\n      for(j=0; j<pPhrase->nTerm; j++){\n        Fts5ExprTerm *pTerm = &pPhrase->aTerm[j];\n        Fts5ExprTerm *p;\n        int bHit = 0;\n\n        for(p=pTerm; p; p=p->pSynonym){\n          int rc;\n          if( p->pIter ){\n            sqlite3Fts5IterClose(p->pIter);\n            p->pIter = 0;\n          }\n          rc = sqlite3Fts5IndexQuery(\n              pExpr->pIndex, p->zTerm, (int)strlen(p->zTerm),\n              (pTerm->bPrefix ? FTS5INDEX_QUERY_PREFIX : 0) |\n              (pExpr->bDesc ? FTS5INDEX_QUERY_DESC : 0),\n              pNear->pColset,\n              &p->pIter\n          );\n          assert( (rc==SQLITE_OK)==(p->pIter!=0) );\n          if( rc!=SQLITE_OK ) return rc;\n          if( 0==sqlite3Fts5IterEof(p->pIter) ){\n            bHit = 1;\n          }\n        }\n\n        if( bHit==0 ){\n          pNode->bEof = 1;\n          return SQLITE_OK;\n        }\n      }\n    }\n  }\n\n  pNode->bEof = 0;\n  return SQLITE_OK;\n}\n\n/*\n** If pExpr is an ASC iterator, this function returns a value with the\n** same sign as:\n**\n**   (iLhs - iRhs)\n**\n** Otherwise, if this is a DESC iterator, the opposite is returned:\n**\n**   (iRhs - iLhs)\n*/\nstatic int fts5RowidCmp(\n  Fts5Expr *pExpr,\n  i64 iLhs,\n  i64 iRhs\n){\n  assert( pExpr->bDesc==0 || pExpr->bDesc==1 );\n  if( pExpr->bDesc==0 ){\n    if( iLhs<iRhs ) return -1;\n    return (iLhs > iRhs);\n  }else{\n    if( iLhs>iRhs ) return -1;\n    return (iLhs < iRhs);\n  }\n}\n\nstatic void fts5ExprSetEof(Fts5ExprNode *pNode){\n  int i;\n  pNode->bEof = 1;\n  pNode->bNomatch = 0;\n  for(i=0; i<pNode->nChild; i++){\n    fts5ExprSetEof(pNode->apChild[i]);\n  }\n}\n\nstatic void fts5ExprNodeZeroPoslist(Fts5ExprNode *pNode){\n  if( pNode->eType==FTS5_STRING || pNode->eType==FTS5_TERM ){\n    Fts5ExprNearset *pNear = pNode->pNear;\n    int i;\n    for(i=0; i<pNear->nPhrase; i++){\n      Fts5ExprPhrase *pPhrase = pNear->apPhrase[i];\n      pPhrase->poslist.n = 0;\n    }\n  }else{\n    int i;\n    for(i=0; i<pNode->nChild; i++){\n      fts5ExprNodeZeroPoslist(pNode->apChild[i]);\n    }\n  }\n}\n\n\n\n/*\n** Compare the values currently indicated by the two nodes as follows:\n**\n**    res = (*p1) - (*p2)\n**\n** Nodes that point to values that come later in the iteration order are\n** considered to be larger. Nodes at EOF are the largest of all.\n**\n** This means that if the iteration order is ASC, then numerically larger\n** rowids are considered larger. Or if it is the default DESC, numerically\n** smaller rowids are larger.\n*/\nstatic int fts5NodeCompare(\n  Fts5Expr *pExpr,\n  Fts5ExprNode *p1, \n  Fts5ExprNode *p2\n){\n  if( p2->bEof ) return -1;\n  if( p1->bEof ) return +1;\n  return fts5RowidCmp(pExpr, p1->iRowid, p2->iRowid);\n}\n\n/*\n** All individual term iterators in pNear are guaranteed to be valid when\n** this function is called. This function checks if all term iterators\n** point to the same rowid, and if not, advances them until they do.\n** If an EOF is reached before this happens, *pbEof is set to true before\n** returning.\n**\n** SQLITE_OK is returned if an error occurs, or an SQLite error code \n** otherwise. It is not considered an error code if an iterator reaches\n** EOF.\n*/\nstatic int fts5ExprNodeTest_STRING(\n  Fts5Expr *pExpr,                /* Expression pPhrase belongs to */\n  Fts5ExprNode *pNode\n){\n  Fts5ExprNearset *pNear = pNode->pNear;\n  Fts5ExprPhrase *pLeft = pNear->apPhrase[0];\n  int rc = SQLITE_OK;\n  i64 iLast;                      /* Lastest rowid any iterator points to */\n  int i, j;                       /* Phrase and token index, respectively */\n  int bMatch;                     /* True if all terms are at the same rowid */\n  const int bDesc = pExpr->bDesc;\n\n  /* Check that this node should not be FTS5_TERM */\n  assert( pNear->nPhrase>1 \n       || pNear->apPhrase[0]->nTerm>1 \n       || pNear->apPhrase[0]->aTerm[0].pSynonym\n       || pNear->apPhrase[0]->aTerm[0].bFirst\n  );\n\n  /* Initialize iLast, the \"lastest\" rowid any iterator points to. If the\n  ** iterator skips through rowids in the default ascending order, this means\n  ** the maximum rowid. Or, if the iterator is \"ORDER BY rowid DESC\", then it\n  ** means the minimum rowid.  */\n  if( pLeft->aTerm[0].pSynonym ){\n    iLast = fts5ExprSynonymRowid(&pLeft->aTerm[0], bDesc, 0);\n  }else{\n    iLast = pLeft->aTerm[0].pIter->iRowid;\n  }\n\n  do {\n    bMatch = 1;\n    for(i=0; i<pNear->nPhrase; i++){\n      Fts5ExprPhrase *pPhrase = pNear->apPhrase[i];\n      for(j=0; j<pPhrase->nTerm; j++){\n        Fts5ExprTerm *pTerm = &pPhrase->aTerm[j];\n        if( pTerm->pSynonym ){\n          i64 iRowid = fts5ExprSynonymRowid(pTerm, bDesc, 0);\n          if( iRowid==iLast ) continue;\n          bMatch = 0;\n          if( fts5ExprSynonymAdvanceto(pTerm, bDesc, &iLast, &rc) ){\n            pNode->bNomatch = 0;\n            pNode->bEof = 1;\n            return rc;\n          }\n        }else{\n          Fts5IndexIter *pIter = pPhrase->aTerm[j].pIter;\n          if( pIter->iRowid==iLast || pIter->bEof ) continue;\n          bMatch = 0;\n          if( fts5ExprAdvanceto(pIter, bDesc, &iLast, &rc, &pNode->bEof) ){\n            return rc;\n          }\n        }\n      }\n    }\n  }while( bMatch==0 );\n\n  pNode->iRowid = iLast;\n  pNode->bNomatch = ((0==fts5ExprNearTest(&rc, pExpr, pNode)) && rc==SQLITE_OK);\n  assert( pNode->bEof==0 || pNode->bNomatch==0 );\n\n  return rc;\n}\n\n/*\n** Advance the first term iterator in the first phrase of pNear. Set output\n** variable *pbEof to true if it reaches EOF or if an error occurs.\n**\n** Return SQLITE_OK if successful, or an SQLite error code if an error\n** occurs.\n*/\nstatic int fts5ExprNodeNext_STRING(\n  Fts5Expr *pExpr,                /* Expression pPhrase belongs to */\n  Fts5ExprNode *pNode,            /* FTS5_STRING or FTS5_TERM node */\n  int bFromValid,\n  i64 iFrom \n){\n  Fts5ExprTerm *pTerm = &pNode->pNear->apPhrase[0]->aTerm[0];\n  int rc = SQLITE_OK;\n\n  pNode->bNomatch = 0;\n  if( pTerm->pSynonym ){\n    int bEof = 1;\n    Fts5ExprTerm *p;\n\n    /* Find the firstest rowid any synonym points to. */\n    i64 iRowid = fts5ExprSynonymRowid(pTerm, pExpr->bDesc, 0);\n\n    /* Advance each iterator that currently points to iRowid. Or, if iFrom\n    ** is valid - each iterator that points to a rowid before iFrom.  */\n    for(p=pTerm; p; p=p->pSynonym){\n      if( sqlite3Fts5IterEof(p->pIter)==0 ){\n        i64 ii = p->pIter->iRowid;\n        if( ii==iRowid \n         || (bFromValid && ii!=iFrom && (ii>iFrom)==pExpr->bDesc) \n        ){\n          if( bFromValid ){\n            rc = sqlite3Fts5IterNextFrom(p->pIter, iFrom);\n          }else{\n            rc = sqlite3Fts5IterNext(p->pIter);\n          }\n          if( rc!=SQLITE_OK ) break;\n          if( sqlite3Fts5IterEof(p->pIter)==0 ){\n            bEof = 0;\n          }\n        }else{\n          bEof = 0;\n        }\n      }\n    }\n\n    /* Set the EOF flag if either all synonym iterators are at EOF or an\n    ** error has occurred.  */\n    pNode->bEof = (rc || bEof);\n  }else{\n    Fts5IndexIter *pIter = pTerm->pIter;\n\n    assert( Fts5NodeIsString(pNode) );\n    if( bFromValid ){\n      rc = sqlite3Fts5IterNextFrom(pIter, iFrom);\n    }else{\n      rc = sqlite3Fts5IterNext(pIter);\n    }\n\n    pNode->bEof = (rc || sqlite3Fts5IterEof(pIter));\n  }\n\n  if( pNode->bEof==0 ){\n    assert( rc==SQLITE_OK );\n    rc = fts5ExprNodeTest_STRING(pExpr, pNode);\n  }\n\n  return rc;\n}\n\n\nstatic int fts5ExprNodeTest_TERM(\n  Fts5Expr *pExpr,                /* Expression that pNear is a part of */\n  Fts5ExprNode *pNode             /* The \"NEAR\" node (FTS5_TERM) */\n){\n  /* As this \"NEAR\" object is actually a single phrase that consists \n  ** of a single term only, grab pointers into the poslist managed by the\n  ** fts5_index.c iterator object. This is much faster than synthesizing \n  ** a new poslist the way we have to for more complicated phrase or NEAR\n  ** expressions.  */\n  Fts5ExprPhrase *pPhrase = pNode->pNear->apPhrase[0];\n  Fts5IndexIter *pIter = pPhrase->aTerm[0].pIter;\n\n  assert( pNode->eType==FTS5_TERM );\n  assert( pNode->pNear->nPhrase==1 && pPhrase->nTerm==1 );\n  assert( pPhrase->aTerm[0].pSynonym==0 );\n\n  pPhrase->poslist.n = pIter->nData;\n  if( pExpr->pConfig->eDetail==FTS5_DETAIL_FULL ){\n    pPhrase->poslist.p = (u8*)pIter->pData;\n  }\n  pNode->iRowid = pIter->iRowid;\n  pNode->bNomatch = (pPhrase->poslist.n==0);\n  return SQLITE_OK;\n}\n\n/*\n** xNext() method for a node of type FTS5_TERM.\n*/\nstatic int fts5ExprNodeNext_TERM(\n  Fts5Expr *pExpr, \n  Fts5ExprNode *pNode,\n  int bFromValid,\n  i64 iFrom\n){\n  int rc;\n  Fts5IndexIter *pIter = pNode->pNear->apPhrase[0]->aTerm[0].pIter;\n\n  assert( pNode->bEof==0 );\n  if( bFromValid ){\n    rc = sqlite3Fts5IterNextFrom(pIter, iFrom);\n  }else{\n    rc = sqlite3Fts5IterNext(pIter);\n  }\n  if( rc==SQLITE_OK && sqlite3Fts5IterEof(pIter)==0 ){\n    rc = fts5ExprNodeTest_TERM(pExpr, pNode);\n  }else{\n    pNode->bEof = 1;\n    pNode->bNomatch = 0;\n  }\n  return rc;\n}\n\nstatic void fts5ExprNodeTest_OR(\n  Fts5Expr *pExpr,                /* Expression of which pNode is a part */\n  Fts5ExprNode *pNode             /* Expression node to test */\n){\n  Fts5ExprNode *pNext = pNode->apChild[0];\n  int i;\n\n  for(i=1; i<pNode->nChild; i++){\n    Fts5ExprNode *pChild = pNode->apChild[i];\n    int cmp = fts5NodeCompare(pExpr, pNext, pChild);\n    if( cmp>0 || (cmp==0 && pChild->bNomatch==0) ){\n      pNext = pChild;\n    }\n  }\n  pNode->iRowid = pNext->iRowid;\n  pNode->bEof = pNext->bEof;\n  pNode->bNomatch = pNext->bNomatch;\n}\n\nstatic int fts5ExprNodeNext_OR(\n  Fts5Expr *pExpr, \n  Fts5ExprNode *pNode,\n  int bFromValid,\n  i64 iFrom\n){\n  int i;\n  i64 iLast = pNode->iRowid;\n\n  for(i=0; i<pNode->nChild; i++){\n    Fts5ExprNode *p1 = pNode->apChild[i];\n    assert( p1->bEof || fts5RowidCmp(pExpr, p1->iRowid, iLast)>=0 );\n    if( p1->bEof==0 ){\n      if( (p1->iRowid==iLast) \n       || (bFromValid && fts5RowidCmp(pExpr, p1->iRowid, iFrom)<0)\n      ){\n        int rc = fts5ExprNodeNext(pExpr, p1, bFromValid, iFrom);\n        if( rc!=SQLITE_OK ){\n          pNode->bNomatch = 0;\n          return rc;\n        }\n      }\n    }\n  }\n\n  fts5ExprNodeTest_OR(pExpr, pNode);\n  return SQLITE_OK;\n}\n\n/*\n** Argument pNode is an FTS5_AND node.\n*/\nstatic int fts5ExprNodeTest_AND(\n  Fts5Expr *pExpr,                /* Expression pPhrase belongs to */\n  Fts5ExprNode *pAnd              /* FTS5_AND node to advance */\n){\n  int iChild;\n  i64 iLast = pAnd->iRowid;\n  int rc = SQLITE_OK;\n  int bMatch;\n\n  assert( pAnd->bEof==0 );\n  do {\n    pAnd->bNomatch = 0;\n    bMatch = 1;\n    for(iChild=0; iChild<pAnd->nChild; iChild++){\n      Fts5ExprNode *pChild = pAnd->apChild[iChild];\n      int cmp = fts5RowidCmp(pExpr, iLast, pChild->iRowid);\n      if( cmp>0 ){\n        /* Advance pChild until it points to iLast or laster */\n        rc = fts5ExprNodeNext(pExpr, pChild, 1, iLast);\n        if( rc!=SQLITE_OK ){\n          pAnd->bNomatch = 0;\n          return rc;\n        }\n      }\n\n      /* If the child node is now at EOF, so is the parent AND node. Otherwise,\n      ** the child node is guaranteed to have advanced at least as far as\n      ** rowid iLast. So if it is not at exactly iLast, pChild->iRowid is the\n      ** new lastest rowid seen so far.  */\n      assert( pChild->bEof || fts5RowidCmp(pExpr, iLast, pChild->iRowid)<=0 );\n      if( pChild->bEof ){\n        fts5ExprSetEof(pAnd);\n        bMatch = 1;\n        break;\n      }else if( iLast!=pChild->iRowid ){\n        bMatch = 0;\n        iLast = pChild->iRowid;\n      }\n\n      if( pChild->bNomatch ){\n        pAnd->bNomatch = 1;\n      }\n    }\n  }while( bMatch==0 );\n\n  if( pAnd->bNomatch && pAnd!=pExpr->pRoot ){\n    fts5ExprNodeZeroPoslist(pAnd);\n  }\n  pAnd->iRowid = iLast;\n  return SQLITE_OK;\n}\n\nstatic int fts5ExprNodeNext_AND(\n  Fts5Expr *pExpr, \n  Fts5ExprNode *pNode,\n  int bFromValid,\n  i64 iFrom\n){\n  int rc = fts5ExprNodeNext(pExpr, pNode->apChild[0], bFromValid, iFrom);\n  if( rc==SQLITE_OK ){\n    rc = fts5ExprNodeTest_AND(pExpr, pNode);\n  }else{\n    pNode->bNomatch = 0;\n  }\n  return rc;\n}\n\nstatic int fts5ExprNodeTest_NOT(\n  Fts5Expr *pExpr,                /* Expression pPhrase belongs to */\n  Fts5ExprNode *pNode             /* FTS5_NOT node to advance */\n){\n  int rc = SQLITE_OK;\n  Fts5ExprNode *p1 = pNode->apChild[0];\n  Fts5ExprNode *p2 = pNode->apChild[1];\n  assert( pNode->nChild==2 );\n\n  while( rc==SQLITE_OK && p1->bEof==0 ){\n    int cmp = fts5NodeCompare(pExpr, p1, p2);\n    if( cmp>0 ){\n      rc = fts5ExprNodeNext(pExpr, p2, 1, p1->iRowid);\n      cmp = fts5NodeCompare(pExpr, p1, p2);\n    }\n    assert( rc!=SQLITE_OK || cmp<=0 );\n    if( cmp || p2->bNomatch ) break;\n    rc = fts5ExprNodeNext(pExpr, p1, 0, 0);\n  }\n  pNode->bEof = p1->bEof;\n  pNode->bNomatch = p1->bNomatch;\n  pNode->iRowid = p1->iRowid;\n  if( p1->bEof ){\n    fts5ExprNodeZeroPoslist(p2);\n  }\n  return rc;\n}\n\nstatic int fts5ExprNodeNext_NOT(\n  Fts5Expr *pExpr, \n  Fts5ExprNode *pNode,\n  int bFromValid,\n  i64 iFrom\n){\n  int rc = fts5ExprNodeNext(pExpr, pNode->apChild[0], bFromValid, iFrom);\n  if( rc==SQLITE_OK ){\n    rc = fts5ExprNodeTest_NOT(pExpr, pNode);\n  }\n  if( rc!=SQLITE_OK ){\n    pNode->bNomatch = 0;\n  }\n  return rc;\n}\n\n/*\n** If pNode currently points to a match, this function returns SQLITE_OK\n** without modifying it. Otherwise, pNode is advanced until it does point\n** to a match or EOF is reached.\n*/\nstatic int fts5ExprNodeTest(\n  Fts5Expr *pExpr,                /* Expression of which pNode is a part */\n  Fts5ExprNode *pNode             /* Expression node to test */\n){\n  int rc = SQLITE_OK;\n  if( pNode->bEof==0 ){\n    switch( pNode->eType ){\n\n      case FTS5_STRING: {\n        rc = fts5ExprNodeTest_STRING(pExpr, pNode);\n        break;\n      }\n\n      case FTS5_TERM: {\n        rc = fts5ExprNodeTest_TERM(pExpr, pNode);\n        break;\n      }\n\n      case FTS5_AND: {\n        rc = fts5ExprNodeTest_AND(pExpr, pNode);\n        break;\n      }\n\n      case FTS5_OR: {\n        fts5ExprNodeTest_OR(pExpr, pNode);\n        break;\n      }\n\n      default: assert( pNode->eType==FTS5_NOT ); {\n        rc = fts5ExprNodeTest_NOT(pExpr, pNode);\n        break;\n      }\n    }\n  }\n  return rc;\n}\n\n \n/*\n** Set node pNode, which is part of expression pExpr, to point to the first\n** match. If there are no matches, set the Node.bEof flag to indicate EOF.\n**\n** Return an SQLite error code if an error occurs, or SQLITE_OK otherwise.\n** It is not an error if there are no matches.\n*/\nstatic int fts5ExprNodeFirst(Fts5Expr *pExpr, Fts5ExprNode *pNode){\n  int rc = SQLITE_OK;\n  pNode->bEof = 0;\n  pNode->bNomatch = 0;\n\n  if( Fts5NodeIsString(pNode) ){\n    /* Initialize all term iterators in the NEAR object. */\n    rc = fts5ExprNearInitAll(pExpr, pNode);\n  }else if( pNode->xNext==0 ){\n    pNode->bEof = 1;\n  }else{\n    int i;\n    int nEof = 0;\n    for(i=0; i<pNode->nChild && rc==SQLITE_OK; i++){\n      Fts5ExprNode *pChild = pNode->apChild[i];\n      rc = fts5ExprNodeFirst(pExpr, pNode->apChild[i]);\n      assert( pChild->bEof==0 || pChild->bEof==1 );\n      nEof += pChild->bEof;\n    }\n    pNode->iRowid = pNode->apChild[0]->iRowid;\n\n    switch( pNode->eType ){\n      case FTS5_AND:\n        if( nEof>0 ) fts5ExprSetEof(pNode);\n        break;\n\n      case FTS5_OR:\n        if( pNode->nChild==nEof ) fts5ExprSetEof(pNode);\n        break;\n\n      default:\n        assert( pNode->eType==FTS5_NOT );\n        pNode->bEof = pNode->apChild[0]->bEof;\n        break;\n    }\n  }\n\n  if( rc==SQLITE_OK ){\n    rc = fts5ExprNodeTest(pExpr, pNode);\n  }\n  return rc;\n}\n\n\n/*\n** Begin iterating through the set of documents in index pIdx matched by\n** the MATCH expression passed as the first argument. If the \"bDesc\" \n** parameter is passed a non-zero value, iteration is in descending rowid \n** order. Or, if it is zero, in ascending order.\n**\n** If iterating in ascending rowid order (bDesc==0), the first document\n** visited is that with the smallest rowid that is larger than or equal\n** to parameter iFirst. Or, if iterating in ascending order (bDesc==1),\n** then the first document visited must have a rowid smaller than or\n** equal to iFirst.\n**\n** Return SQLITE_OK if successful, or an SQLite error code otherwise. It\n** is not considered an error if the query does not match any documents.\n*/\nstatic int sqlite3Fts5ExprFirst(Fts5Expr *p, Fts5Index *pIdx, i64 iFirst, int bDesc){\n  Fts5ExprNode *pRoot = p->pRoot;\n  int rc;                         /* Return code */\n\n  p->pIndex = pIdx;\n  p->bDesc = bDesc;\n  rc = fts5ExprNodeFirst(p, pRoot);\n\n  /* If not at EOF but the current rowid occurs earlier than iFirst in\n  ** the iteration order, move to document iFirst or later. */\n  if( rc==SQLITE_OK \n   && 0==pRoot->bEof \n   && fts5RowidCmp(p, pRoot->iRowid, iFirst)<0 \n  ){\n    rc = fts5ExprNodeNext(p, pRoot, 1, iFirst);\n  }\n\n  /* If the iterator is not at a real match, skip forward until it is. */\n  while( pRoot->bNomatch ){\n    assert( pRoot->bEof==0 && rc==SQLITE_OK );\n    rc = fts5ExprNodeNext(p, pRoot, 0, 0);\n  }\n  return rc;\n}\n\n/*\n** Move to the next document \n**\n** Return SQLITE_OK if successful, or an SQLite error code otherwise. It\n** is not considered an error if the query does not match any documents.\n*/\nstatic int sqlite3Fts5ExprNext(Fts5Expr *p, i64 iLast){\n  int rc;\n  Fts5ExprNode *pRoot = p->pRoot;\n  assert( pRoot->bEof==0 && pRoot->bNomatch==0 );\n  do {\n    rc = fts5ExprNodeNext(p, pRoot, 0, 0);\n    assert( pRoot->bNomatch==0 || (rc==SQLITE_OK && pRoot->bEof==0) );\n  }while( pRoot->bNomatch );\n  if( fts5RowidCmp(p, pRoot->iRowid, iLast)>0 ){\n    pRoot->bEof = 1;\n  }\n  return rc;\n}\n\nstatic int sqlite3Fts5ExprEof(Fts5Expr *p){\n  return p->pRoot->bEof;\n}\n\nstatic i64 sqlite3Fts5ExprRowid(Fts5Expr *p){\n  return p->pRoot->iRowid;\n}\n\nstatic int fts5ParseStringFromToken(Fts5Token *pToken, char **pz){\n  int rc = SQLITE_OK;\n  *pz = sqlite3Fts5Strndup(&rc, pToken->p, pToken->n);\n  return rc;\n}\n\n/*\n** Free the phrase object passed as the only argument.\n*/\nstatic void fts5ExprPhraseFree(Fts5ExprPhrase *pPhrase){\n  if( pPhrase ){\n    int i;\n    for(i=0; i<pPhrase->nTerm; i++){\n      Fts5ExprTerm *pSyn;\n      Fts5ExprTerm *pNext;\n      Fts5ExprTerm *pTerm = &pPhrase->aTerm[i];\n      sqlite3_free(pTerm->zTerm);\n      sqlite3Fts5IterClose(pTerm->pIter);\n      for(pSyn=pTerm->pSynonym; pSyn; pSyn=pNext){\n        pNext = pSyn->pSynonym;\n        sqlite3Fts5IterClose(pSyn->pIter);\n        fts5BufferFree((Fts5Buffer*)&pSyn[1]);\n        sqlite3_free(pSyn);\n      }\n    }\n    if( pPhrase->poslist.nSpace>0 ) fts5BufferFree(&pPhrase->poslist);\n    sqlite3_free(pPhrase);\n  }\n}\n\n/*\n** Set the \"bFirst\" flag on the first token of the phrase passed as the\n** only argument.\n*/\nstatic void sqlite3Fts5ParseSetCaret(Fts5ExprPhrase *pPhrase){\n  if( pPhrase && pPhrase->nTerm ){\n    pPhrase->aTerm[0].bFirst = 1;\n  }\n}\n\n/*\n** If argument pNear is NULL, then a new Fts5ExprNearset object is allocated\n** and populated with pPhrase. Or, if pNear is not NULL, phrase pPhrase is\n** appended to it and the results returned.\n**\n** If an OOM error occurs, both the pNear and pPhrase objects are freed and\n** NULL returned.\n*/\nstatic Fts5ExprNearset *sqlite3Fts5ParseNearset(\n  Fts5Parse *pParse,              /* Parse context */\n  Fts5ExprNearset *pNear,         /* Existing nearset, or NULL */\n  Fts5ExprPhrase *pPhrase         /* Recently parsed phrase */\n){\n  const int SZALLOC = 8;\n  Fts5ExprNearset *pRet = 0;\n\n  if( pParse->rc==SQLITE_OK ){\n    if( pPhrase==0 ){\n      return pNear;\n    }\n    if( pNear==0 ){\n      int nByte = sizeof(Fts5ExprNearset) + SZALLOC * sizeof(Fts5ExprPhrase*);\n      pRet = sqlite3_malloc(nByte);\n      if( pRet==0 ){\n        pParse->rc = SQLITE_NOMEM;\n      }else{\n        memset(pRet, 0, nByte);\n      }\n    }else if( (pNear->nPhrase % SZALLOC)==0 ){\n      int nNew = pNear->nPhrase + SZALLOC;\n      int nByte = sizeof(Fts5ExprNearset) + nNew * sizeof(Fts5ExprPhrase*);\n\n      pRet = (Fts5ExprNearset*)sqlite3_realloc(pNear, nByte);\n      if( pRet==0 ){\n        pParse->rc = SQLITE_NOMEM;\n      }\n    }else{\n      pRet = pNear;\n    }\n  }\n\n  if( pRet==0 ){\n    assert( pParse->rc!=SQLITE_OK );\n    sqlite3Fts5ParseNearsetFree(pNear);\n    sqlite3Fts5ParsePhraseFree(pPhrase);\n  }else{\n    if( pRet->nPhrase>0 ){\n      Fts5ExprPhrase *pLast = pRet->apPhrase[pRet->nPhrase-1];\n      assert( pLast==pParse->apPhrase[pParse->nPhrase-2] );\n      if( pPhrase->nTerm==0 ){\n        fts5ExprPhraseFree(pPhrase);\n        pRet->nPhrase--;\n        pParse->nPhrase--;\n        pPhrase = pLast;\n      }else if( pLast->nTerm==0 ){\n        fts5ExprPhraseFree(pLast);\n        pParse->apPhrase[pParse->nPhrase-2] = pPhrase;\n        pParse->nPhrase--;\n        pRet->nPhrase--;\n      }\n    }\n    pRet->apPhrase[pRet->nPhrase++] = pPhrase;\n  }\n  return pRet;\n}\n\ntypedef struct TokenCtx TokenCtx;\nstruct TokenCtx {\n  Fts5ExprPhrase *pPhrase;\n  int rc;\n};\n\n/*\n** Callback for tokenizing terms used by ParseTerm().\n*/\nstatic int fts5ParseTokenize(\n  void *pContext,                 /* Pointer to Fts5InsertCtx object */\n  int tflags,                     /* Mask of FTS5_TOKEN_* flags */\n  const char *pToken,             /* Buffer containing token */\n  int nToken,                     /* Size of token in bytes */\n  int iUnused1,                   /* Start offset of token */\n  int iUnused2                    /* End offset of token */\n){\n  int rc = SQLITE_OK;\n  const int SZALLOC = 8;\n  TokenCtx *pCtx = (TokenCtx*)pContext;\n  Fts5ExprPhrase *pPhrase = pCtx->pPhrase;\n\n  UNUSED_PARAM2(iUnused1, iUnused2);\n\n  /* If an error has already occurred, this is a no-op */\n  if( pCtx->rc!=SQLITE_OK ) return pCtx->rc;\n  if( nToken>FTS5_MAX_TOKEN_SIZE ) nToken = FTS5_MAX_TOKEN_SIZE;\n\n  if( pPhrase && pPhrase->nTerm>0 && (tflags & FTS5_TOKEN_COLOCATED) ){\n    Fts5ExprTerm *pSyn;\n    int nByte = sizeof(Fts5ExprTerm) + sizeof(Fts5Buffer) + nToken+1;\n    pSyn = (Fts5ExprTerm*)sqlite3_malloc(nByte);\n    if( pSyn==0 ){\n      rc = SQLITE_NOMEM;\n    }else{\n      memset(pSyn, 0, nByte);\n      pSyn->zTerm = ((char*)pSyn) + sizeof(Fts5ExprTerm) + sizeof(Fts5Buffer);\n      memcpy(pSyn->zTerm, pToken, nToken);\n      pSyn->pSynonym = pPhrase->aTerm[pPhrase->nTerm-1].pSynonym;\n      pPhrase->aTerm[pPhrase->nTerm-1].pSynonym = pSyn;\n    }\n  }else{\n    Fts5ExprTerm *pTerm;\n    if( pPhrase==0 || (pPhrase->nTerm % SZALLOC)==0 ){\n      Fts5ExprPhrase *pNew;\n      int nNew = SZALLOC + (pPhrase ? pPhrase->nTerm : 0);\n\n      pNew = (Fts5ExprPhrase*)sqlite3_realloc(pPhrase, \n          sizeof(Fts5ExprPhrase) + sizeof(Fts5ExprTerm) * nNew\n      );\n      if( pNew==0 ){\n        rc = SQLITE_NOMEM;\n      }else{\n        if( pPhrase==0 ) memset(pNew, 0, sizeof(Fts5ExprPhrase));\n        pCtx->pPhrase = pPhrase = pNew;\n        pNew->nTerm = nNew - SZALLOC;\n      }\n    }\n\n    if( rc==SQLITE_OK ){\n      pTerm = &pPhrase->aTerm[pPhrase->nTerm++];\n      memset(pTerm, 0, sizeof(Fts5ExprTerm));\n      pTerm->zTerm = sqlite3Fts5Strndup(&rc, pToken, nToken);\n    }\n  }\n\n  pCtx->rc = rc;\n  return rc;\n}\n\n\n/*\n** Free the phrase object passed as the only argument.\n*/\nstatic void sqlite3Fts5ParsePhraseFree(Fts5ExprPhrase *pPhrase){\n  fts5ExprPhraseFree(pPhrase);\n}\n\n/*\n** Free the phrase object passed as the second argument.\n*/\nstatic void sqlite3Fts5ParseNearsetFree(Fts5ExprNearset *pNear){\n  if( pNear ){\n    int i;\n    for(i=0; i<pNear->nPhrase; i++){\n      fts5ExprPhraseFree(pNear->apPhrase[i]);\n    }\n    sqlite3_free(pNear->pColset);\n    sqlite3_free(pNear);\n  }\n}\n\nstatic void sqlite3Fts5ParseFinished(Fts5Parse *pParse, Fts5ExprNode *p){\n  assert( pParse->pExpr==0 );\n  pParse->pExpr = p;\n}\n\n/*\n** This function is called by the parser to process a string token. The\n** string may or may not be quoted. In any case it is tokenized and a\n** phrase object consisting of all tokens returned.\n*/\nstatic Fts5ExprPhrase *sqlite3Fts5ParseTerm(\n  Fts5Parse *pParse,              /* Parse context */\n  Fts5ExprPhrase *pAppend,        /* Phrase to append to */\n  Fts5Token *pToken,              /* String to tokenize */\n  int bPrefix                     /* True if there is a trailing \"*\" */\n){\n  Fts5Config *pConfig = pParse->pConfig;\n  TokenCtx sCtx;                  /* Context object passed to callback */\n  int rc;                         /* Tokenize return code */\n  char *z = 0;\n\n  memset(&sCtx, 0, sizeof(TokenCtx));\n  sCtx.pPhrase = pAppend;\n\n  rc = fts5ParseStringFromToken(pToken, &z);\n  if( rc==SQLITE_OK ){\n    int flags = FTS5_TOKENIZE_QUERY | (bPrefix ? FTS5_TOKENIZE_PREFIX : 0);\n    int n;\n    sqlite3Fts5Dequote(z);\n    n = (int)strlen(z);\n    rc = sqlite3Fts5Tokenize(pConfig, flags, z, n, &sCtx, fts5ParseTokenize);\n  }\n  sqlite3_free(z);\n  if( rc || (rc = sCtx.rc) ){\n    pParse->rc = rc;\n    fts5ExprPhraseFree(sCtx.pPhrase);\n    sCtx.pPhrase = 0;\n  }else{\n\n    if( pAppend==0 ){\n      if( (pParse->nPhrase % 8)==0 ){\n        int nByte = sizeof(Fts5ExprPhrase*) * (pParse->nPhrase + 8);\n        Fts5ExprPhrase **apNew;\n        apNew = (Fts5ExprPhrase**)sqlite3_realloc(pParse->apPhrase, nByte);\n        if( apNew==0 ){\n          pParse->rc = SQLITE_NOMEM;\n          fts5ExprPhraseFree(sCtx.pPhrase);\n          return 0;\n        }\n        pParse->apPhrase = apNew;\n      }\n      pParse->nPhrase++;\n    }\n\n    if( sCtx.pPhrase==0 ){\n      /* This happens when parsing a token or quoted phrase that contains\n      ** no token characters at all. (e.g ... MATCH '\"\"'). */\n      sCtx.pPhrase = sqlite3Fts5MallocZero(&pParse->rc, sizeof(Fts5ExprPhrase));\n    }else if( sCtx.pPhrase->nTerm ){\n      sCtx.pPhrase->aTerm[sCtx.pPhrase->nTerm-1].bPrefix = bPrefix;\n    }\n    pParse->apPhrase[pParse->nPhrase-1] = sCtx.pPhrase;\n  }\n\n  return sCtx.pPhrase;\n}\n\n/*\n** Create a new FTS5 expression by cloning phrase iPhrase of the\n** expression passed as the second argument.\n*/\nstatic int sqlite3Fts5ExprClonePhrase(\n  Fts5Expr *pExpr, \n  int iPhrase, \n  Fts5Expr **ppNew\n){\n  int rc = SQLITE_OK;             /* Return code */\n  Fts5ExprPhrase *pOrig;          /* The phrase extracted from pExpr */\n  Fts5Expr *pNew = 0;             /* Expression to return via *ppNew */\n  TokenCtx sCtx = {0,0};          /* Context object for fts5ParseTokenize */\n\n  pOrig = pExpr->apExprPhrase[iPhrase];\n  pNew = (Fts5Expr*)sqlite3Fts5MallocZero(&rc, sizeof(Fts5Expr));\n  if( rc==SQLITE_OK ){\n    pNew->apExprPhrase = (Fts5ExprPhrase**)sqlite3Fts5MallocZero(&rc, \n        sizeof(Fts5ExprPhrase*));\n  }\n  if( rc==SQLITE_OK ){\n    pNew->pRoot = (Fts5ExprNode*)sqlite3Fts5MallocZero(&rc, \n        sizeof(Fts5ExprNode));\n  }\n  if( rc==SQLITE_OK ){\n    pNew->pRoot->pNear = (Fts5ExprNearset*)sqlite3Fts5MallocZero(&rc, \n        sizeof(Fts5ExprNearset) + sizeof(Fts5ExprPhrase*));\n  }\n  if( rc==SQLITE_OK ){\n    Fts5Colset *pColsetOrig = pOrig->pNode->pNear->pColset;\n    if( pColsetOrig ){\n      int nByte = sizeof(Fts5Colset) + (pColsetOrig->nCol-1) * sizeof(int);\n      Fts5Colset *pColset = (Fts5Colset*)sqlite3Fts5MallocZero(&rc, nByte);\n      if( pColset ){ \n        memcpy(pColset, pColsetOrig, nByte);\n      }\n      pNew->pRoot->pNear->pColset = pColset;\n    }\n  }\n\n  if( pOrig->nTerm ){\n    int i;                          /* Used to iterate through phrase terms */\n    for(i=0; rc==SQLITE_OK && i<pOrig->nTerm; i++){\n      int tflags = 0;\n      Fts5ExprTerm *p;\n      for(p=&pOrig->aTerm[i]; p && rc==SQLITE_OK; p=p->pSynonym){\n        const char *zTerm = p->zTerm;\n        rc = fts5ParseTokenize((void*)&sCtx, tflags, zTerm, (int)strlen(zTerm),\n            0, 0);\n        tflags = FTS5_TOKEN_COLOCATED;\n      }\n      if( rc==SQLITE_OK ){\n        sCtx.pPhrase->aTerm[i].bPrefix = pOrig->aTerm[i].bPrefix;\n        sCtx.pPhrase->aTerm[i].bFirst = pOrig->aTerm[i].bFirst;\n      }\n    }\n  }else{\n    /* This happens when parsing a token or quoted phrase that contains\n    ** no token characters at all. (e.g ... MATCH '\"\"'). */\n    sCtx.pPhrase = sqlite3Fts5MallocZero(&rc, sizeof(Fts5ExprPhrase));\n  }\n\n  if( rc==SQLITE_OK ){\n    /* All the allocations succeeded. Put the expression object together. */\n    pNew->pIndex = pExpr->pIndex;\n    pNew->pConfig = pExpr->pConfig;\n    pNew->nPhrase = 1;\n    pNew->apExprPhrase[0] = sCtx.pPhrase;\n    pNew->pRoot->pNear->apPhrase[0] = sCtx.pPhrase;\n    pNew->pRoot->pNear->nPhrase = 1;\n    sCtx.pPhrase->pNode = pNew->pRoot;\n\n    if( pOrig->nTerm==1 \n     && pOrig->aTerm[0].pSynonym==0 \n     && pOrig->aTerm[0].bFirst==0 \n    ){\n      pNew->pRoot->eType = FTS5_TERM;\n      pNew->pRoot->xNext = fts5ExprNodeNext_TERM;\n    }else{\n      pNew->pRoot->eType = FTS5_STRING;\n      pNew->pRoot->xNext = fts5ExprNodeNext_STRING;\n    }\n  }else{\n    sqlite3Fts5ExprFree(pNew);\n    fts5ExprPhraseFree(sCtx.pPhrase);\n    pNew = 0;\n  }\n\n  *ppNew = pNew;\n  return rc;\n}\n\n\n/*\n** Token pTok has appeared in a MATCH expression where the NEAR operator\n** is expected. If token pTok does not contain \"NEAR\", store an error\n** in the pParse object.\n*/\nstatic void sqlite3Fts5ParseNear(Fts5Parse *pParse, Fts5Token *pTok){\n  if( pTok->n!=4 || memcmp(\"NEAR\", pTok->p, 4) ){\n    sqlite3Fts5ParseError(\n        pParse, \"fts5: syntax error near \\\"%.*s\\\"\", pTok->n, pTok->p\n    );\n  }\n}\n\nstatic void sqlite3Fts5ParseSetDistance(\n  Fts5Parse *pParse, \n  Fts5ExprNearset *pNear,\n  Fts5Token *p\n){\n  if( pNear ){\n    int nNear = 0;\n    int i;\n    if( p->n ){\n      for(i=0; i<p->n; i++){\n        char c = (char)p->p[i];\n        if( c<'0' || c>'9' ){\n          sqlite3Fts5ParseError(\n              pParse, \"expected integer, got \\\"%.*s\\\"\", p->n, p->p\n              );\n          return;\n        }\n        nNear = nNear * 10 + (p->p[i] - '0');\n      }\n    }else{\n      nNear = FTS5_DEFAULT_NEARDIST;\n    }\n    pNear->nNear = nNear;\n  }\n}\n\n/*\n** The second argument passed to this function may be NULL, or it may be\n** an existing Fts5Colset object. This function returns a pointer to\n** a new colset object containing the contents of (p) with new value column\n** number iCol appended. \n**\n** If an OOM error occurs, store an error code in pParse and return NULL.\n** The old colset object (if any) is not freed in this case.\n*/\nstatic Fts5Colset *fts5ParseColset(\n  Fts5Parse *pParse,              /* Store SQLITE_NOMEM here if required */\n  Fts5Colset *p,                  /* Existing colset object */\n  int iCol                        /* New column to add to colset object */\n){\n  int nCol = p ? p->nCol : 0;     /* Num. columns already in colset object */\n  Fts5Colset *pNew;               /* New colset object to return */\n\n  assert( pParse->rc==SQLITE_OK );\n  assert( iCol>=0 && iCol<pParse->pConfig->nCol );\n\n  pNew = sqlite3_realloc(p, sizeof(Fts5Colset) + sizeof(int)*nCol);\n  if( pNew==0 ){\n    pParse->rc = SQLITE_NOMEM;\n  }else{\n    int *aiCol = pNew->aiCol;\n    int i, j;\n    for(i=0; i<nCol; i++){\n      if( aiCol[i]==iCol ) return pNew;\n      if( aiCol[i]>iCol ) break;\n    }\n    for(j=nCol; j>i; j--){\n      aiCol[j] = aiCol[j-1];\n    }\n    aiCol[i] = iCol;\n    pNew->nCol = nCol+1;\n\n#ifndef NDEBUG\n    /* Check that the array is in order and contains no duplicate entries. */\n    for(i=1; i<pNew->nCol; i++) assert( pNew->aiCol[i]>pNew->aiCol[i-1] );\n#endif\n  }\n\n  return pNew;\n}\n\n/*\n** Allocate and return an Fts5Colset object specifying the inverse of\n** the colset passed as the second argument. Free the colset passed\n** as the second argument before returning.\n*/\nstatic Fts5Colset *sqlite3Fts5ParseColsetInvert(Fts5Parse *pParse, Fts5Colset *p){\n  Fts5Colset *pRet;\n  int nCol = pParse->pConfig->nCol;\n\n  pRet = (Fts5Colset*)sqlite3Fts5MallocZero(&pParse->rc, \n      sizeof(Fts5Colset) + sizeof(int)*nCol\n  );\n  if( pRet ){\n    int i;\n    int iOld = 0;\n    for(i=0; i<nCol; i++){\n      if( iOld>=p->nCol || p->aiCol[iOld]!=i ){\n        pRet->aiCol[pRet->nCol++] = i;\n      }else{\n        iOld++;\n      }\n    }\n  }\n\n  sqlite3_free(p);\n  return pRet;\n}\n\nstatic Fts5Colset *sqlite3Fts5ParseColset(\n  Fts5Parse *pParse,              /* Store SQLITE_NOMEM here if required */\n  Fts5Colset *pColset,            /* Existing colset object */\n  Fts5Token *p\n){\n  Fts5Colset *pRet = 0;\n  int iCol;\n  char *z;                        /* Dequoted copy of token p */\n\n  z = sqlite3Fts5Strndup(&pParse->rc, p->p, p->n);\n  if( pParse->rc==SQLITE_OK ){\n    Fts5Config *pConfig = pParse->pConfig;\n    sqlite3Fts5Dequote(z);\n    for(iCol=0; iCol<pConfig->nCol; iCol++){\n      if( 0==sqlite3_stricmp(pConfig->azCol[iCol], z) ) break;\n    }\n    if( iCol==pConfig->nCol ){\n      sqlite3Fts5ParseError(pParse, \"no such column: %s\", z);\n    }else{\n      pRet = fts5ParseColset(pParse, pColset, iCol);\n    }\n    sqlite3_free(z);\n  }\n\n  if( pRet==0 ){\n    assert( pParse->rc!=SQLITE_OK );\n    sqlite3_free(pColset);\n  }\n\n  return pRet;\n}\n\n/*\n** If argument pOrig is NULL, or if (*pRc) is set to anything other than\n** SQLITE_OK when this function is called, NULL is returned. \n**\n** Otherwise, a copy of (*pOrig) is made into memory obtained from\n** sqlite3Fts5MallocZero() and a pointer to it returned. If the allocation\n** fails, (*pRc) is set to SQLITE_NOMEM and NULL is returned.\n*/\nstatic Fts5Colset *fts5CloneColset(int *pRc, Fts5Colset *pOrig){\n  Fts5Colset *pRet;\n  if( pOrig ){\n    int nByte = sizeof(Fts5Colset) + (pOrig->nCol-1) * sizeof(int);\n    pRet = (Fts5Colset*)sqlite3Fts5MallocZero(pRc, nByte);\n    if( pRet ){ \n      memcpy(pRet, pOrig, nByte);\n    }\n  }else{\n    pRet = 0;\n  }\n  return pRet;\n}\n\n/*\n** Remove from colset pColset any columns that are not also in colset pMerge.\n*/\nstatic void fts5MergeColset(Fts5Colset *pColset, Fts5Colset *pMerge){\n  int iIn = 0;          /* Next input in pColset */\n  int iMerge = 0;       /* Next input in pMerge */\n  int iOut = 0;         /* Next output slot in pColset */\n\n  while( iIn<pColset->nCol && iMerge<pMerge->nCol ){\n    int iDiff = pColset->aiCol[iIn] - pMerge->aiCol[iMerge];\n    if( iDiff==0 ){\n      pColset->aiCol[iOut++] = pMerge->aiCol[iMerge];\n      iMerge++;\n      iIn++;\n    }else if( iDiff>0 ){\n      iMerge++;\n    }else{\n      iIn++;\n    }\n  }\n  pColset->nCol = iOut;\n}\n\n/*\n** Recursively apply colset pColset to expression node pNode and all of\n** its decendents. If (*ppFree) is not NULL, it contains a spare copy\n** of pColset. This function may use the spare copy and set (*ppFree) to\n** zero, or it may create copies of pColset using fts5CloneColset().\n*/\nstatic void fts5ParseSetColset(\n  Fts5Parse *pParse, \n  Fts5ExprNode *pNode, \n  Fts5Colset *pColset,\n  Fts5Colset **ppFree\n){\n  if( pParse->rc==SQLITE_OK ){\n    assert( pNode->eType==FTS5_TERM || pNode->eType==FTS5_STRING \n         || pNode->eType==FTS5_AND  || pNode->eType==FTS5_OR\n         || pNode->eType==FTS5_NOT  || pNode->eType==FTS5_EOF\n    );\n    if( pNode->eType==FTS5_STRING || pNode->eType==FTS5_TERM ){\n      Fts5ExprNearset *pNear = pNode->pNear;\n      if( pNear->pColset ){\n        fts5MergeColset(pNear->pColset, pColset);\n        if( pNear->pColset->nCol==0 ){\n          pNode->eType = FTS5_EOF;\n          pNode->xNext = 0;\n        }\n      }else if( *ppFree ){\n        pNear->pColset = pColset;\n        *ppFree = 0;\n      }else{\n        pNear->pColset = fts5CloneColset(&pParse->rc, pColset);\n      }\n    }else{\n      int i;\n      assert( pNode->eType!=FTS5_EOF || pNode->nChild==0 );\n      for(i=0; i<pNode->nChild; i++){\n        fts5ParseSetColset(pParse, pNode->apChild[i], pColset, ppFree);\n      }\n    }\n  }\n}\n\n/*\n** Apply colset pColset to expression node pExpr and all of its descendents.\n*/\nstatic void sqlite3Fts5ParseSetColset(\n  Fts5Parse *pParse, \n  Fts5ExprNode *pExpr, \n  Fts5Colset *pColset \n){\n  Fts5Colset *pFree = pColset;\n  if( pParse->pConfig->eDetail==FTS5_DETAIL_NONE ){\n    pParse->rc = SQLITE_ERROR;\n    pParse->zErr = sqlite3_mprintf(\n      \"fts5: column queries are not supported (detail=none)\"\n    );\n  }else{\n    fts5ParseSetColset(pParse, pExpr, pColset, &pFree);\n  }\n  sqlite3_free(pFree);\n}\n\nstatic void fts5ExprAssignXNext(Fts5ExprNode *pNode){\n  switch( pNode->eType ){\n    case FTS5_STRING: {\n      Fts5ExprNearset *pNear = pNode->pNear;\n      if( pNear->nPhrase==1 && pNear->apPhrase[0]->nTerm==1 \n       && pNear->apPhrase[0]->aTerm[0].pSynonym==0\n       && pNear->apPhrase[0]->aTerm[0].bFirst==0\n      ){\n        pNode->eType = FTS5_TERM;\n        pNode->xNext = fts5ExprNodeNext_TERM;\n      }else{\n        pNode->xNext = fts5ExprNodeNext_STRING;\n      }\n      break;\n    };\n\n    case FTS5_OR: {\n      pNode->xNext = fts5ExprNodeNext_OR;\n      break;\n    };\n\n    case FTS5_AND: {\n      pNode->xNext = fts5ExprNodeNext_AND;\n      break;\n    };\n\n    default: assert( pNode->eType==FTS5_NOT ); {\n      pNode->xNext = fts5ExprNodeNext_NOT;\n      break;\n    };\n  }\n}\n\nstatic void fts5ExprAddChildren(Fts5ExprNode *p, Fts5ExprNode *pSub){\n  if( p->eType!=FTS5_NOT && pSub->eType==p->eType ){\n    int nByte = sizeof(Fts5ExprNode*) * pSub->nChild;\n    memcpy(&p->apChild[p->nChild], pSub->apChild, nByte);\n    p->nChild += pSub->nChild;\n    sqlite3_free(pSub);\n  }else{\n    p->apChild[p->nChild++] = pSub;\n  }\n}\n\n/*\n** Allocate and return a new expression object. If anything goes wrong (i.e.\n** OOM error), leave an error code in pParse and return NULL.\n*/\nstatic Fts5ExprNode *sqlite3Fts5ParseNode(\n  Fts5Parse *pParse,              /* Parse context */\n  int eType,                      /* FTS5_STRING, AND, OR or NOT */\n  Fts5ExprNode *pLeft,            /* Left hand child expression */\n  Fts5ExprNode *pRight,           /* Right hand child expression */\n  Fts5ExprNearset *pNear          /* For STRING expressions, the near cluster */\n){\n  Fts5ExprNode *pRet = 0;\n\n  if( pParse->rc==SQLITE_OK ){\n    int nChild = 0;               /* Number of children of returned node */\n    int nByte;                    /* Bytes of space to allocate for this node */\n \n    assert( (eType!=FTS5_STRING && !pNear)\n         || (eType==FTS5_STRING && !pLeft && !pRight)\n    );\n    if( eType==FTS5_STRING && pNear==0 ) return 0;\n    if( eType!=FTS5_STRING && pLeft==0 ) return pRight;\n    if( eType!=FTS5_STRING && pRight==0 ) return pLeft;\n\n    if( eType==FTS5_NOT ){\n      nChild = 2;\n    }else if( eType==FTS5_AND || eType==FTS5_OR ){\n      nChild = 2;\n      if( pLeft->eType==eType ) nChild += pLeft->nChild-1;\n      if( pRight->eType==eType ) nChild += pRight->nChild-1;\n    }\n\n    nByte = sizeof(Fts5ExprNode) + sizeof(Fts5ExprNode*)*(nChild-1);\n    pRet = (Fts5ExprNode*)sqlite3Fts5MallocZero(&pParse->rc, nByte);\n\n    if( pRet ){\n      pRet->eType = eType;\n      pRet->pNear = pNear;\n      fts5ExprAssignXNext(pRet);\n      if( eType==FTS5_STRING ){\n        int iPhrase;\n        for(iPhrase=0; iPhrase<pNear->nPhrase; iPhrase++){\n          pNear->apPhrase[iPhrase]->pNode = pRet;\n          if( pNear->apPhrase[iPhrase]->nTerm==0 ){\n            pRet->xNext = 0;\n            pRet->eType = FTS5_EOF;\n          }\n        }\n\n        if( pParse->pConfig->eDetail!=FTS5_DETAIL_FULL ){\n          Fts5ExprPhrase *pPhrase = pNear->apPhrase[0];\n          if( pNear->nPhrase!=1 \n           || pPhrase->nTerm>1\n           || (pPhrase->nTerm>0 && pPhrase->aTerm[0].bFirst)\n          ){\n            assert( pParse->rc==SQLITE_OK );\n            pParse->rc = SQLITE_ERROR;\n            assert( pParse->zErr==0 );\n            pParse->zErr = sqlite3_mprintf(\n                \"fts5: %s queries are not supported (detail!=full)\", \n                pNear->nPhrase==1 ? \"phrase\": \"NEAR\"\n                );\n            sqlite3_free(pRet);\n            pRet = 0;\n          }\n        }\n      }else{\n        fts5ExprAddChildren(pRet, pLeft);\n        fts5ExprAddChildren(pRet, pRight);\n      }\n    }\n  }\n\n  if( pRet==0 ){\n    assert( pParse->rc!=SQLITE_OK );\n    sqlite3Fts5ParseNodeFree(pLeft);\n    sqlite3Fts5ParseNodeFree(pRight);\n    sqlite3Fts5ParseNearsetFree(pNear);\n  }\n  return pRet;\n}\n\nstatic Fts5ExprNode *sqlite3Fts5ParseImplicitAnd(\n  Fts5Parse *pParse,              /* Parse context */\n  Fts5ExprNode *pLeft,            /* Left hand child expression */\n  Fts5ExprNode *pRight            /* Right hand child expression */\n){\n  Fts5ExprNode *pRet = 0;\n  Fts5ExprNode *pPrev;\n\n  if( pParse->rc ){\n    sqlite3Fts5ParseNodeFree(pLeft);\n    sqlite3Fts5ParseNodeFree(pRight);\n  }else{\n\n    assert( pLeft->eType==FTS5_STRING \n        || pLeft->eType==FTS5_TERM\n        || pLeft->eType==FTS5_EOF\n        || pLeft->eType==FTS5_AND\n    );\n    assert( pRight->eType==FTS5_STRING \n        || pRight->eType==FTS5_TERM \n        || pRight->eType==FTS5_EOF \n    );\n\n    if( pLeft->eType==FTS5_AND ){\n      pPrev = pLeft->apChild[pLeft->nChild-1];\n    }else{\n      pPrev = pLeft;\n    }\n    assert( pPrev->eType==FTS5_STRING \n        || pPrev->eType==FTS5_TERM \n        || pPrev->eType==FTS5_EOF \n        );\n\n    if( pRight->eType==FTS5_EOF ){\n      assert( pParse->apPhrase[pParse->nPhrase-1]==pRight->pNear->apPhrase[0] );\n      sqlite3Fts5ParseNodeFree(pRight);\n      pRet = pLeft;\n      pParse->nPhrase--;\n    }\n    else if( pPrev->eType==FTS5_EOF ){\n      Fts5ExprPhrase **ap;\n\n      if( pPrev==pLeft ){\n        pRet = pRight;\n      }else{\n        pLeft->apChild[pLeft->nChild-1] = pRight;\n        pRet = pLeft;\n      }\n\n      ap = &pParse->apPhrase[pParse->nPhrase-1-pRight->pNear->nPhrase];\n      assert( ap[0]==pPrev->pNear->apPhrase[0] );\n      memmove(ap, &ap[1], sizeof(Fts5ExprPhrase*)*pRight->pNear->nPhrase);\n      pParse->nPhrase--;\n\n      sqlite3Fts5ParseNodeFree(pPrev);\n    }\n    else{\n      pRet = sqlite3Fts5ParseNode(pParse, FTS5_AND, pLeft, pRight, 0);\n    }\n  }\n\n  return pRet;\n}\n\nstatic char *fts5ExprTermPrint(Fts5ExprTerm *pTerm){\n  int nByte = 0;\n  Fts5ExprTerm *p;\n  char *zQuoted;\n\n  /* Determine the maximum amount of space required. */\n  for(p=pTerm; p; p=p->pSynonym){\n    nByte += (int)strlen(pTerm->zTerm) * 2 + 3 + 2;\n  }\n  zQuoted = sqlite3_malloc(nByte);\n\n  if( zQuoted ){\n    int i = 0;\n    for(p=pTerm; p; p=p->pSynonym){\n      char *zIn = p->zTerm;\n      zQuoted[i++] = '\"';\n      while( *zIn ){\n        if( *zIn=='\"' ) zQuoted[i++] = '\"';\n        zQuoted[i++] = *zIn++;\n      }\n      zQuoted[i++] = '\"';\n      if( p->pSynonym ) zQuoted[i++] = '|';\n    }\n    if( pTerm->bPrefix ){\n      zQuoted[i++] = ' ';\n      zQuoted[i++] = '*';\n    }\n    zQuoted[i++] = '\\0';\n  }\n  return zQuoted;\n}\n\nstatic char *fts5PrintfAppend(char *zApp, const char *zFmt, ...){\n  char *zNew;\n  va_list ap;\n  va_start(ap, zFmt);\n  zNew = sqlite3_vmprintf(zFmt, ap);\n  va_end(ap);\n  if( zApp && zNew ){\n    char *zNew2 = sqlite3_mprintf(\"%s%s\", zApp, zNew);\n    sqlite3_free(zNew);\n    zNew = zNew2;\n  }\n  sqlite3_free(zApp);\n  return zNew;\n}\n\n/*\n** Compose a tcl-readable representation of expression pExpr. Return a \n** pointer to a buffer containing that representation. It is the \n** responsibility of the caller to at some point free the buffer using \n** sqlite3_free().\n*/\nstatic char *fts5ExprPrintTcl(\n  Fts5Config *pConfig, \n  const char *zNearsetCmd,\n  Fts5ExprNode *pExpr\n){\n  char *zRet = 0;\n  if( pExpr->eType==FTS5_STRING || pExpr->eType==FTS5_TERM ){\n    Fts5ExprNearset *pNear = pExpr->pNear;\n    int i; \n    int iTerm;\n\n    zRet = fts5PrintfAppend(zRet, \"%s \", zNearsetCmd);\n    if( zRet==0 ) return 0;\n    if( pNear->pColset ){\n      int *aiCol = pNear->pColset->aiCol;\n      int nCol = pNear->pColset->nCol;\n      if( nCol==1 ){\n        zRet = fts5PrintfAppend(zRet, \"-col %d \", aiCol[0]);\n      }else{\n        zRet = fts5PrintfAppend(zRet, \"-col {%d\", aiCol[0]);\n        for(i=1; i<pNear->pColset->nCol; i++){\n          zRet = fts5PrintfAppend(zRet, \" %d\", aiCol[i]);\n        }\n        zRet = fts5PrintfAppend(zRet, \"} \");\n      }\n      if( zRet==0 ) return 0;\n    }\n\n    if( pNear->nPhrase>1 ){\n      zRet = fts5PrintfAppend(zRet, \"-near %d \", pNear->nNear);\n      if( zRet==0 ) return 0;\n    }\n\n    zRet = fts5PrintfAppend(zRet, \"--\");\n    if( zRet==0 ) return 0;\n\n    for(i=0; i<pNear->nPhrase; i++){\n      Fts5ExprPhrase *pPhrase = pNear->apPhrase[i];\n\n      zRet = fts5PrintfAppend(zRet, \" {\");\n      for(iTerm=0; zRet && iTerm<pPhrase->nTerm; iTerm++){\n        char *zTerm = pPhrase->aTerm[iTerm].zTerm;\n        zRet = fts5PrintfAppend(zRet, \"%s%s\", iTerm==0?\"\":\" \", zTerm);\n        if( pPhrase->aTerm[iTerm].bPrefix ){\n          zRet = fts5PrintfAppend(zRet, \"*\");\n        }\n      }\n\n      if( zRet ) zRet = fts5PrintfAppend(zRet, \"}\");\n      if( zRet==0 ) return 0;\n    }\n\n  }else{\n    char const *zOp = 0;\n    int i;\n    switch( pExpr->eType ){\n      case FTS5_AND: zOp = \"AND\"; break;\n      case FTS5_NOT: zOp = \"NOT\"; break;\n      default: \n        assert( pExpr->eType==FTS5_OR );\n        zOp = \"OR\"; \n        break;\n    }\n\n    zRet = sqlite3_mprintf(\"%s\", zOp);\n    for(i=0; zRet && i<pExpr->nChild; i++){\n      char *z = fts5ExprPrintTcl(pConfig, zNearsetCmd, pExpr->apChild[i]);\n      if( !z ){\n        sqlite3_free(zRet);\n        zRet = 0;\n      }else{\n        zRet = fts5PrintfAppend(zRet, \" [%z]\", z);\n      }\n    }\n  }\n\n  return zRet;\n}\n\nstatic char *fts5ExprPrint(Fts5Config *pConfig, Fts5ExprNode *pExpr){\n  char *zRet = 0;\n  if( pExpr->eType==0 ){\n    return sqlite3_mprintf(\"\\\"\\\"\");\n  }else\n  if( pExpr->eType==FTS5_STRING || pExpr->eType==FTS5_TERM ){\n    Fts5ExprNearset *pNear = pExpr->pNear;\n    int i; \n    int iTerm;\n\n    if( pNear->pColset ){\n      int iCol = pNear->pColset->aiCol[0];\n      zRet = fts5PrintfAppend(zRet, \"%s : \", pConfig->azCol[iCol]);\n      if( zRet==0 ) return 0;\n    }\n\n    if( pNear->nPhrase>1 ){\n      zRet = fts5PrintfAppend(zRet, \"NEAR(\");\n      if( zRet==0 ) return 0;\n    }\n\n    for(i=0; i<pNear->nPhrase; i++){\n      Fts5ExprPhrase *pPhrase = pNear->apPhrase[i];\n      if( i!=0 ){\n        zRet = fts5PrintfAppend(zRet, \" \");\n        if( zRet==0 ) return 0;\n      }\n      for(iTerm=0; iTerm<pPhrase->nTerm; iTerm++){\n        char *zTerm = fts5ExprTermPrint(&pPhrase->aTerm[iTerm]);\n        if( zTerm ){\n          zRet = fts5PrintfAppend(zRet, \"%s%s\", iTerm==0?\"\":\" + \", zTerm);\n          sqlite3_free(zTerm);\n        }\n        if( zTerm==0 || zRet==0 ){\n          sqlite3_free(zRet);\n          return 0;\n        }\n      }\n    }\n\n    if( pNear->nPhrase>1 ){\n      zRet = fts5PrintfAppend(zRet, \", %d)\", pNear->nNear);\n      if( zRet==0 ) return 0;\n    }\n\n  }else{\n    char const *zOp = 0;\n    int i;\n\n    switch( pExpr->eType ){\n      case FTS5_AND: zOp = \" AND \"; break;\n      case FTS5_NOT: zOp = \" NOT \"; break;\n      default:  \n        assert( pExpr->eType==FTS5_OR );\n        zOp = \" OR \"; \n        break;\n    }\n\n    for(i=0; i<pExpr->nChild; i++){\n      char *z = fts5ExprPrint(pConfig, pExpr->apChild[i]);\n      if( z==0 ){\n        sqlite3_free(zRet);\n        zRet = 0;\n      }else{\n        int e = pExpr->apChild[i]->eType;\n        int b = (e!=FTS5_STRING && e!=FTS5_TERM && e!=FTS5_EOF);\n        zRet = fts5PrintfAppend(zRet, \"%s%s%z%s\", \n            (i==0 ? \"\" : zOp),\n            (b?\"(\":\"\"), z, (b?\")\":\"\")\n        );\n      }\n      if( zRet==0 ) break;\n    }\n  }\n\n  return zRet;\n}\n\n/*\n** The implementation of user-defined scalar functions fts5_expr() (bTcl==0)\n** and fts5_expr_tcl() (bTcl!=0).\n*/\nstatic void fts5ExprFunction(\n  sqlite3_context *pCtx,          /* Function call context */\n  int nArg,                       /* Number of args */\n  sqlite3_value **apVal,          /* Function arguments */\n  int bTcl\n){\n  Fts5Global *pGlobal = (Fts5Global*)sqlite3_user_data(pCtx);\n  sqlite3 *db = sqlite3_context_db_handle(pCtx);\n  const char *zExpr = 0;\n  char *zErr = 0;\n  Fts5Expr *pExpr = 0;\n  int rc;\n  int i;\n\n  const char **azConfig;          /* Array of arguments for Fts5Config */\n  const char *zNearsetCmd = \"nearset\";\n  int nConfig;                    /* Size of azConfig[] */\n  Fts5Config *pConfig = 0;\n  int iArg = 1;\n\n  if( nArg<1 ){\n    zErr = sqlite3_mprintf(\"wrong number of arguments to function %s\",\n        bTcl ? \"fts5_expr_tcl\" : \"fts5_expr\"\n    );\n    sqlite3_result_error(pCtx, zErr, -1);\n    sqlite3_free(zErr);\n    return;\n  }\n\n  if( bTcl && nArg>1 ){\n    zNearsetCmd = (const char*)sqlite3_value_text(apVal[1]);\n    iArg = 2;\n  }\n\n  nConfig = 3 + (nArg-iArg);\n  azConfig = (const char**)sqlite3_malloc(sizeof(char*) * nConfig);\n  if( azConfig==0 ){\n    sqlite3_result_error_nomem(pCtx);\n    return;\n  }\n  azConfig[0] = 0;\n  azConfig[1] = \"main\";\n  azConfig[2] = \"tbl\";\n  for(i=3; iArg<nArg; iArg++){\n    azConfig[i++] = (const char*)sqlite3_value_text(apVal[iArg]);\n  }\n\n  zExpr = (const char*)sqlite3_value_text(apVal[0]);\n\n  rc = sqlite3Fts5ConfigParse(pGlobal, db, nConfig, azConfig, &pConfig, &zErr);\n  if( rc==SQLITE_OK ){\n    rc = sqlite3Fts5ExprNew(pConfig, pConfig->nCol, zExpr, &pExpr, &zErr);\n  }\n  if( rc==SQLITE_OK ){\n    char *zText;\n    if( pExpr->pRoot->xNext==0 ){\n      zText = sqlite3_mprintf(\"\");\n    }else if( bTcl ){\n      zText = fts5ExprPrintTcl(pConfig, zNearsetCmd, pExpr->pRoot);\n    }else{\n      zText = fts5ExprPrint(pConfig, pExpr->pRoot);\n    }\n    if( zText==0 ){\n      rc = SQLITE_NOMEM;\n    }else{\n      sqlite3_result_text(pCtx, zText, -1, SQLITE_TRANSIENT);\n      sqlite3_free(zText);\n    }\n  }\n\n  if( rc!=SQLITE_OK ){\n    if( zErr ){\n      sqlite3_result_error(pCtx, zErr, -1);\n      sqlite3_free(zErr);\n    }else{\n      sqlite3_result_error_code(pCtx, rc);\n    }\n  }\n  sqlite3_free((void *)azConfig);\n  sqlite3Fts5ConfigFree(pConfig);\n  sqlite3Fts5ExprFree(pExpr);\n}\n\nstatic void fts5ExprFunctionHr(\n  sqlite3_context *pCtx,          /* Function call context */\n  int nArg,                       /* Number of args */\n  sqlite3_value **apVal           /* Function arguments */\n){\n  fts5ExprFunction(pCtx, nArg, apVal, 0);\n}\nstatic void fts5ExprFunctionTcl(\n  sqlite3_context *pCtx,          /* Function call context */\n  int nArg,                       /* Number of args */\n  sqlite3_value **apVal           /* Function arguments */\n){\n  fts5ExprFunction(pCtx, nArg, apVal, 1);\n}\n\n/*\n** The implementation of an SQLite user-defined-function that accepts a\n** single integer as an argument. If the integer is an alpha-numeric \n** unicode code point, 1 is returned. Otherwise 0.\n*/\nstatic void fts5ExprIsAlnum(\n  sqlite3_context *pCtx,          /* Function call context */\n  int nArg,                       /* Number of args */\n  sqlite3_value **apVal           /* Function arguments */\n){\n  int iCode;\n  if( nArg!=1 ){\n    sqlite3_result_error(pCtx, \n        \"wrong number of arguments to function fts5_isalnum\", -1\n    );\n    return;\n  }\n  iCode = sqlite3_value_int(apVal[0]);\n  sqlite3_result_int(pCtx, sqlite3Fts5UnicodeIsalnum(iCode));\n}\n\nstatic void fts5ExprFold(\n  sqlite3_context *pCtx,          /* Function call context */\n  int nArg,                       /* Number of args */\n  sqlite3_value **apVal           /* Function arguments */\n){\n  if( nArg!=1 && nArg!=2 ){\n    sqlite3_result_error(pCtx, \n        \"wrong number of arguments to function fts5_fold\", -1\n    );\n  }else{\n    int iCode;\n    int bRemoveDiacritics = 0;\n    iCode = sqlite3_value_int(apVal[0]);\n    if( nArg==2 ) bRemoveDiacritics = sqlite3_value_int(apVal[1]);\n    sqlite3_result_int(pCtx, sqlite3Fts5UnicodeFold(iCode, bRemoveDiacritics));\n  }\n}\n\n/*\n** This is called during initialization to register the fts5_expr() scalar\n** UDF with the SQLite handle passed as the only argument.\n*/\nstatic int sqlite3Fts5ExprInit(Fts5Global *pGlobal, sqlite3 *db){\n  struct Fts5ExprFunc {\n    const char *z;\n    void (*x)(sqlite3_context*,int,sqlite3_value**);\n  } aFunc[] = {\n    { \"fts5_expr\",     fts5ExprFunctionHr },\n    { \"fts5_expr_tcl\", fts5ExprFunctionTcl },\n    { \"fts5_isalnum\",  fts5ExprIsAlnum },\n    { \"fts5_fold\",     fts5ExprFold },\n  };\n  int i;\n  int rc = SQLITE_OK;\n  void *pCtx = (void*)pGlobal;\n\n  for(i=0; rc==SQLITE_OK && i<ArraySize(aFunc); i++){\n    struct Fts5ExprFunc *p = &aFunc[i];\n    rc = sqlite3_create_function(db, p->z, -1, SQLITE_UTF8, pCtx, p->x, 0, 0);\n  }\n\n  /* Avoid a warning indicating that sqlite3Fts5ParserTrace() is unused */\n#ifndef NDEBUG\n  (void)sqlite3Fts5ParserTrace;\n#endif\n\n  return rc;\n}\n\n/*\n** Return the number of phrases in expression pExpr.\n*/\nstatic int sqlite3Fts5ExprPhraseCount(Fts5Expr *pExpr){\n  return (pExpr ? pExpr->nPhrase : 0);\n}\n\n/*\n** Return the number of terms in the iPhrase'th phrase in pExpr.\n*/\nstatic int sqlite3Fts5ExprPhraseSize(Fts5Expr *pExpr, int iPhrase){\n  if( iPhrase<0 || iPhrase>=pExpr->nPhrase ) return 0;\n  return pExpr->apExprPhrase[iPhrase]->nTerm;\n}\n\n/*\n** This function is used to access the current position list for phrase\n** iPhrase.\n*/\nstatic int sqlite3Fts5ExprPoslist(Fts5Expr *pExpr, int iPhrase, const u8 **pa){\n  int nRet;\n  Fts5ExprPhrase *pPhrase = pExpr->apExprPhrase[iPhrase];\n  Fts5ExprNode *pNode = pPhrase->pNode;\n  if( pNode->bEof==0 && pNode->iRowid==pExpr->pRoot->iRowid ){\n    *pa = pPhrase->poslist.p;\n    nRet = pPhrase->poslist.n;\n  }else{\n    *pa = 0;\n    nRet = 0;\n  }\n  return nRet;\n}\n\nstruct Fts5PoslistPopulator {\n  Fts5PoslistWriter writer;\n  int bOk;                        /* True if ok to populate */\n  int bMiss;\n};\n\nstatic Fts5PoslistPopulator *sqlite3Fts5ExprClearPoslists(Fts5Expr *pExpr, int bLive){\n  Fts5PoslistPopulator *pRet;\n  pRet = sqlite3_malloc(sizeof(Fts5PoslistPopulator)*pExpr->nPhrase);\n  if( pRet ){\n    int i;\n    memset(pRet, 0, sizeof(Fts5PoslistPopulator)*pExpr->nPhrase);\n    for(i=0; i<pExpr->nPhrase; i++){\n      Fts5Buffer *pBuf = &pExpr->apExprPhrase[i]->poslist;\n      Fts5ExprNode *pNode = pExpr->apExprPhrase[i]->pNode;\n      assert( pExpr->apExprPhrase[i]->nTerm==1 );\n      if( bLive && \n          (pBuf->n==0 || pNode->iRowid!=pExpr->pRoot->iRowid || pNode->bEof)\n      ){\n        pRet[i].bMiss = 1;\n      }else{\n        pBuf->n = 0;\n      }\n    }\n  }\n  return pRet;\n}\n\nstruct Fts5ExprCtx {\n  Fts5Expr *pExpr;\n  Fts5PoslistPopulator *aPopulator;\n  i64 iOff;\n};\ntypedef struct Fts5ExprCtx Fts5ExprCtx;\n\n/*\n** TODO: Make this more efficient!\n*/\nstatic int fts5ExprColsetTest(Fts5Colset *pColset, int iCol){\n  int i;\n  for(i=0; i<pColset->nCol; i++){\n    if( pColset->aiCol[i]==iCol ) return 1;\n  }\n  return 0;\n}\n\nstatic int fts5ExprPopulatePoslistsCb(\n  void *pCtx,                /* Copy of 2nd argument to xTokenize() */\n  int tflags,                /* Mask of FTS5_TOKEN_* flags */\n  const char *pToken,        /* Pointer to buffer containing token */\n  int nToken,                /* Size of token in bytes */\n  int iUnused1,              /* Byte offset of token within input text */\n  int iUnused2               /* Byte offset of end of token within input text */\n){\n  Fts5ExprCtx *p = (Fts5ExprCtx*)pCtx;\n  Fts5Expr *pExpr = p->pExpr;\n  int i;\n\n  UNUSED_PARAM2(iUnused1, iUnused2);\n\n  if( nToken>FTS5_MAX_TOKEN_SIZE ) nToken = FTS5_MAX_TOKEN_SIZE;\n  if( (tflags & FTS5_TOKEN_COLOCATED)==0 ) p->iOff++;\n  for(i=0; i<pExpr->nPhrase; i++){\n    Fts5ExprTerm *pTerm;\n    if( p->aPopulator[i].bOk==0 ) continue;\n    for(pTerm=&pExpr->apExprPhrase[i]->aTerm[0]; pTerm; pTerm=pTerm->pSynonym){\n      int nTerm = (int)strlen(pTerm->zTerm);\n      if( (nTerm==nToken || (nTerm<nToken && pTerm->bPrefix))\n       && memcmp(pTerm->zTerm, pToken, nTerm)==0\n      ){\n        int rc = sqlite3Fts5PoslistWriterAppend(\n            &pExpr->apExprPhrase[i]->poslist, &p->aPopulator[i].writer, p->iOff\n        );\n        if( rc ) return rc;\n        break;\n      }\n    }\n  }\n  return SQLITE_OK;\n}\n\nstatic int sqlite3Fts5ExprPopulatePoslists(\n  Fts5Config *pConfig,\n  Fts5Expr *pExpr, \n  Fts5PoslistPopulator *aPopulator,\n  int iCol, \n  const char *z, int n\n){\n  int i;\n  Fts5ExprCtx sCtx;\n  sCtx.pExpr = pExpr;\n  sCtx.aPopulator = aPopulator;\n  sCtx.iOff = (((i64)iCol) << 32) - 1;\n\n  for(i=0; i<pExpr->nPhrase; i++){\n    Fts5ExprNode *pNode = pExpr->apExprPhrase[i]->pNode;\n    Fts5Colset *pColset = pNode->pNear->pColset;\n    if( (pColset && 0==fts5ExprColsetTest(pColset, iCol)) \n     || aPopulator[i].bMiss\n    ){\n      aPopulator[i].bOk = 0;\n    }else{\n      aPopulator[i].bOk = 1;\n    }\n  }\n\n  return sqlite3Fts5Tokenize(pConfig, \n      FTS5_TOKENIZE_DOCUMENT, z, n, (void*)&sCtx, fts5ExprPopulatePoslistsCb\n  );\n}\n\nstatic void fts5ExprClearPoslists(Fts5ExprNode *pNode){\n  if( pNode->eType==FTS5_TERM || pNode->eType==FTS5_STRING ){\n    pNode->pNear->apPhrase[0]->poslist.n = 0;\n  }else{\n    int i;\n    for(i=0; i<pNode->nChild; i++){\n      fts5ExprClearPoslists(pNode->apChild[i]);\n    }\n  }\n}\n\nstatic int fts5ExprCheckPoslists(Fts5ExprNode *pNode, i64 iRowid){\n  pNode->iRowid = iRowid;\n  pNode->bEof = 0;\n  switch( pNode->eType ){\n    case FTS5_TERM:\n    case FTS5_STRING:\n      return (pNode->pNear->apPhrase[0]->poslist.n>0);\n\n    case FTS5_AND: {\n      int i;\n      for(i=0; i<pNode->nChild; i++){\n        if( fts5ExprCheckPoslists(pNode->apChild[i], iRowid)==0 ){\n          fts5ExprClearPoslists(pNode);\n          return 0;\n        }\n      }\n      break;\n    }\n\n    case FTS5_OR: {\n      int i;\n      int bRet = 0;\n      for(i=0; i<pNode->nChild; i++){\n        if( fts5ExprCheckPoslists(pNode->apChild[i], iRowid) ){\n          bRet = 1;\n        }\n      }\n      return bRet;\n    }\n\n    default: {\n      assert( pNode->eType==FTS5_NOT );\n      if( 0==fts5ExprCheckPoslists(pNode->apChild[0], iRowid)\n          || 0!=fts5ExprCheckPoslists(pNode->apChild[1], iRowid)\n        ){\n        fts5ExprClearPoslists(pNode);\n        return 0;\n      }\n      break;\n    }\n  }\n  return 1;\n}\n\nstatic void sqlite3Fts5ExprCheckPoslists(Fts5Expr *pExpr, i64 iRowid){\n  fts5ExprCheckPoslists(pExpr->pRoot, iRowid);\n}\n\n/*\n** This function is only called for detail=columns tables. \n*/\nstatic int sqlite3Fts5ExprPhraseCollist(\n  Fts5Expr *pExpr, \n  int iPhrase, \n  const u8 **ppCollist, \n  int *pnCollist\n){\n  Fts5ExprPhrase *pPhrase = pExpr->apExprPhrase[iPhrase];\n  Fts5ExprNode *pNode = pPhrase->pNode;\n  int rc = SQLITE_OK;\n\n  assert( iPhrase>=0 && iPhrase<pExpr->nPhrase );\n  assert( pExpr->pConfig->eDetail==FTS5_DETAIL_COLUMNS );\n\n  if( pNode->bEof==0 \n   && pNode->iRowid==pExpr->pRoot->iRowid \n   && pPhrase->poslist.n>0\n  ){\n    Fts5ExprTerm *pTerm = &pPhrase->aTerm[0];\n    if( pTerm->pSynonym ){\n      Fts5Buffer *pBuf = (Fts5Buffer*)&pTerm->pSynonym[1];\n      rc = fts5ExprSynonymList(\n          pTerm, pNode->iRowid, pBuf, (u8**)ppCollist, pnCollist\n      );\n    }else{\n      *ppCollist = pPhrase->aTerm[0].pIter->pData;\n      *pnCollist = pPhrase->aTerm[0].pIter->nData;\n    }\n  }else{\n    *ppCollist = 0;\n    *pnCollist = 0;\n  }\n\n  return rc;\n}\n\n\n/*\n** 2014 August 11\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n******************************************************************************\n**\n*/\n\n\n\n/* #include \"fts5Int.h\" */\n\ntypedef struct Fts5HashEntry Fts5HashEntry;\n\n/*\n** This file contains the implementation of an in-memory hash table used\n** to accumuluate \"term -> doclist\" content before it is flused to a level-0\n** segment.\n*/\n\n\nstruct Fts5Hash {\n  int eDetail;                    /* Copy of Fts5Config.eDetail */\n  int *pnByte;                    /* Pointer to bytes counter */\n  int nEntry;                     /* Number of entries currently in hash */\n  int nSlot;                      /* Size of aSlot[] array */\n  Fts5HashEntry *pScan;           /* Current ordered scan item */\n  Fts5HashEntry **aSlot;          /* Array of hash slots */\n};\n\n/*\n** Each entry in the hash table is represented by an object of the \n** following type. Each object, its key (a nul-terminated string) and \n** its current data are stored in a single memory allocation. The \n** key immediately follows the object in memory. The position list\n** data immediately follows the key data in memory.\n**\n** The data that follows the key is in a similar, but not identical format\n** to the doclist data stored in the database. It is:\n**\n**   * Rowid, as a varint\n**   * Position list, without 0x00 terminator.\n**   * Size of previous position list and rowid, as a 4 byte\n**     big-endian integer.\n**\n** iRowidOff:\n**   Offset of last rowid written to data area. Relative to first byte of\n**   structure.\n**\n** nData:\n**   Bytes of data written since iRowidOff.\n*/\nstruct Fts5HashEntry {\n  Fts5HashEntry *pHashNext;       /* Next hash entry with same hash-key */\n  Fts5HashEntry *pScanNext;       /* Next entry in sorted order */\n  \n  int nAlloc;                     /* Total size of allocation */\n  int iSzPoslist;                 /* Offset of space for 4-byte poslist size */\n  int nData;                      /* Total bytes of data (incl. structure) */\n  int nKey;                       /* Length of key in bytes */\n  u8 bDel;                        /* Set delete-flag @ iSzPoslist */\n  u8 bContent;                    /* Set content-flag (detail=none mode) */\n  i16 iCol;                       /* Column of last value written */\n  int iPos;                       /* Position of last value written */\n  i64 iRowid;                     /* Rowid of last value written */\n};\n\n/*\n** Eqivalent to:\n**\n**   char *fts5EntryKey(Fts5HashEntry *pEntry){ return zKey; }\n*/\n#define fts5EntryKey(p) ( ((char *)(&(p)[1])) )\n\n\n/*\n** Allocate a new hash table.\n*/\nstatic int sqlite3Fts5HashNew(Fts5Config *pConfig, Fts5Hash **ppNew, int *pnByte){\n  int rc = SQLITE_OK;\n  Fts5Hash *pNew;\n\n  *ppNew = pNew = (Fts5Hash*)sqlite3_malloc(sizeof(Fts5Hash));\n  if( pNew==0 ){\n    rc = SQLITE_NOMEM;\n  }else{\n    int nByte;\n    memset(pNew, 0, sizeof(Fts5Hash));\n    pNew->pnByte = pnByte;\n    pNew->eDetail = pConfig->eDetail;\n\n    pNew->nSlot = 1024;\n    nByte = sizeof(Fts5HashEntry*) * pNew->nSlot;\n    pNew->aSlot = (Fts5HashEntry**)sqlite3_malloc(nByte);\n    if( pNew->aSlot==0 ){\n      sqlite3_free(pNew);\n      *ppNew = 0;\n      rc = SQLITE_NOMEM;\n    }else{\n      memset(pNew->aSlot, 0, nByte);\n    }\n  }\n  return rc;\n}\n\n/*\n** Free a hash table object.\n*/\nstatic void sqlite3Fts5HashFree(Fts5Hash *pHash){\n  if( pHash ){\n    sqlite3Fts5HashClear(pHash);\n    sqlite3_free(pHash->aSlot);\n    sqlite3_free(pHash);\n  }\n}\n\n/*\n** Empty (but do not delete) a hash table.\n*/\nstatic void sqlite3Fts5HashClear(Fts5Hash *pHash){\n  int i;\n  for(i=0; i<pHash->nSlot; i++){\n    Fts5HashEntry *pNext;\n    Fts5HashEntry *pSlot;\n    for(pSlot=pHash->aSlot[i]; pSlot; pSlot=pNext){\n      pNext = pSlot->pHashNext;\n      sqlite3_free(pSlot);\n    }\n  }\n  memset(pHash->aSlot, 0, pHash->nSlot * sizeof(Fts5HashEntry*));\n  pHash->nEntry = 0;\n}\n\nstatic unsigned int fts5HashKey(int nSlot, const u8 *p, int n){\n  int i;\n  unsigned int h = 13;\n  for(i=n-1; i>=0; i--){\n    h = (h << 3) ^ h ^ p[i];\n  }\n  return (h % nSlot);\n}\n\nstatic unsigned int fts5HashKey2(int nSlot, u8 b, const u8 *p, int n){\n  int i;\n  unsigned int h = 13;\n  for(i=n-1; i>=0; i--){\n    h = (h << 3) ^ h ^ p[i];\n  }\n  h = (h << 3) ^ h ^ b;\n  return (h % nSlot);\n}\n\n/*\n** Resize the hash table by doubling the number of slots.\n*/\nstatic int fts5HashResize(Fts5Hash *pHash){\n  int nNew = pHash->nSlot*2;\n  int i;\n  Fts5HashEntry **apNew;\n  Fts5HashEntry **apOld = pHash->aSlot;\n\n  apNew = (Fts5HashEntry**)sqlite3_malloc(nNew*sizeof(Fts5HashEntry*));\n  if( !apNew ) return SQLITE_NOMEM;\n  memset(apNew, 0, nNew*sizeof(Fts5HashEntry*));\n\n  for(i=0; i<pHash->nSlot; i++){\n    while( apOld[i] ){\n      unsigned int iHash;\n      Fts5HashEntry *p = apOld[i];\n      apOld[i] = p->pHashNext;\n      iHash = fts5HashKey(nNew, (u8*)fts5EntryKey(p),\n                          (int)strlen(fts5EntryKey(p)));\n      p->pHashNext = apNew[iHash];\n      apNew[iHash] = p;\n    }\n  }\n\n  sqlite3_free(apOld);\n  pHash->nSlot = nNew;\n  pHash->aSlot = apNew;\n  return SQLITE_OK;\n}\n\nstatic void fts5HashAddPoslistSize(Fts5Hash *pHash, Fts5HashEntry *p){\n  if( p->iSzPoslist ){\n    u8 *pPtr = (u8*)p;\n    if( pHash->eDetail==FTS5_DETAIL_NONE ){\n      assert( p->nData==p->iSzPoslist );\n      if( p->bDel ){\n        pPtr[p->nData++] = 0x00;\n        if( p->bContent ){\n          pPtr[p->nData++] = 0x00;\n        }\n      }\n    }else{\n      int nSz = (p->nData - p->iSzPoslist - 1);       /* Size in bytes */\n      int nPos = nSz*2 + p->bDel;                     /* Value of nPos field */\n\n      assert( p->bDel==0 || p->bDel==1 );\n      if( nPos<=127 ){\n        pPtr[p->iSzPoslist] = (u8)nPos;\n      }else{\n        int nByte = sqlite3Fts5GetVarintLen((u32)nPos);\n        memmove(&pPtr[p->iSzPoslist + nByte], &pPtr[p->iSzPoslist + 1], nSz);\n        sqlite3Fts5PutVarint(&pPtr[p->iSzPoslist], nPos);\n        p->nData += (nByte-1);\n      }\n    }\n\n    p->iSzPoslist = 0;\n    p->bDel = 0;\n    p->bContent = 0;\n  }\n}\n\n/*\n** Add an entry to the in-memory hash table. The key is the concatenation\n** of bByte and (pToken/nToken). The value is (iRowid/iCol/iPos).\n**\n**     (bByte || pToken) -> (iRowid,iCol,iPos)\n**\n** Or, if iCol is negative, then the value is a delete marker.\n*/\nstatic int sqlite3Fts5HashWrite(\n  Fts5Hash *pHash,\n  i64 iRowid,                     /* Rowid for this entry */\n  int iCol,                       /* Column token appears in (-ve -> delete) */\n  int iPos,                       /* Position of token within column */\n  char bByte,                     /* First byte of token */\n  const char *pToken, int nToken  /* Token to add or remove to or from index */\n){\n  unsigned int iHash;\n  Fts5HashEntry *p;\n  u8 *pPtr;\n  int nIncr = 0;                  /* Amount to increment (*pHash->pnByte) by */\n  int bNew;                       /* If non-delete entry should be written */\n  \n  bNew = (pHash->eDetail==FTS5_DETAIL_FULL);\n\n  /* Attempt to locate an existing hash entry */\n  iHash = fts5HashKey2(pHash->nSlot, (u8)bByte, (const u8*)pToken, nToken);\n  for(p=pHash->aSlot[iHash]; p; p=p->pHashNext){\n    char *zKey = fts5EntryKey(p);\n    if( zKey[0]==bByte \n     && p->nKey==nToken\n     && memcmp(&zKey[1], pToken, nToken)==0 \n    ){\n      break;\n    }\n  }\n\n  /* If an existing hash entry cannot be found, create a new one. */\n  if( p==0 ){\n    /* Figure out how much space to allocate */\n    char *zKey;\n    int nByte = sizeof(Fts5HashEntry) + (nToken+1) + 1 + 64;\n    if( nByte<128 ) nByte = 128;\n\n    /* Grow the Fts5Hash.aSlot[] array if necessary. */\n    if( (pHash->nEntry*2)>=pHash->nSlot ){\n      int rc = fts5HashResize(pHash);\n      if( rc!=SQLITE_OK ) return rc;\n      iHash = fts5HashKey2(pHash->nSlot, (u8)bByte, (const u8*)pToken, nToken);\n    }\n\n    /* Allocate new Fts5HashEntry and add it to the hash table. */\n    p = (Fts5HashEntry*)sqlite3_malloc(nByte);\n    if( !p ) return SQLITE_NOMEM;\n    memset(p, 0, sizeof(Fts5HashEntry));\n    p->nAlloc = nByte;\n    zKey = fts5EntryKey(p);\n    zKey[0] = bByte;\n    memcpy(&zKey[1], pToken, nToken);\n    assert( iHash==fts5HashKey(pHash->nSlot, (u8*)zKey, nToken+1) );\n    p->nKey = nToken;\n    zKey[nToken+1] = '\\0';\n    p->nData = nToken+1 + 1 + sizeof(Fts5HashEntry);\n    p->pHashNext = pHash->aSlot[iHash];\n    pHash->aSlot[iHash] = p;\n    pHash->nEntry++;\n\n    /* Add the first rowid field to the hash-entry */\n    p->nData += sqlite3Fts5PutVarint(&((u8*)p)[p->nData], iRowid);\n    p->iRowid = iRowid;\n\n    p->iSzPoslist = p->nData;\n    if( pHash->eDetail!=FTS5_DETAIL_NONE ){\n      p->nData += 1;\n      p->iCol = (pHash->eDetail==FTS5_DETAIL_FULL ? 0 : -1);\n    }\n\n    nIncr += p->nData;\n  }else{\n\n    /* Appending to an existing hash-entry. Check that there is enough \n    ** space to append the largest possible new entry. Worst case scenario \n    ** is:\n    **\n    **     + 9 bytes for a new rowid,\n    **     + 4 byte reserved for the \"poslist size\" varint.\n    **     + 1 byte for a \"new column\" byte,\n    **     + 3 bytes for a new column number (16-bit max) as a varint,\n    **     + 5 bytes for the new position offset (32-bit max).\n    */\n    if( (p->nAlloc - p->nData) < (9 + 4 + 1 + 3 + 5) ){\n      int nNew = p->nAlloc * 2;\n      Fts5HashEntry *pNew;\n      Fts5HashEntry **pp;\n      pNew = (Fts5HashEntry*)sqlite3_realloc(p, nNew);\n      if( pNew==0 ) return SQLITE_NOMEM;\n      pNew->nAlloc = nNew;\n      for(pp=&pHash->aSlot[iHash]; *pp!=p; pp=&(*pp)->pHashNext);\n      *pp = pNew;\n      p = pNew;\n    }\n    nIncr -= p->nData;\n  }\n  assert( (p->nAlloc - p->nData) >= (9 + 4 + 1 + 3 + 5) );\n\n  pPtr = (u8*)p;\n\n  /* If this is a new rowid, append the 4-byte size field for the previous\n  ** entry, and the new rowid for this entry.  */\n  if( iRowid!=p->iRowid ){\n    fts5HashAddPoslistSize(pHash, p);\n    p->nData += sqlite3Fts5PutVarint(&pPtr[p->nData], iRowid - p->iRowid);\n    p->iRowid = iRowid;\n    bNew = 1;\n    p->iSzPoslist = p->nData;\n    if( pHash->eDetail!=FTS5_DETAIL_NONE ){\n      p->nData += 1;\n      p->iCol = (pHash->eDetail==FTS5_DETAIL_FULL ? 0 : -1);\n      p->iPos = 0;\n    }\n  }\n\n  if( iCol>=0 ){\n    if( pHash->eDetail==FTS5_DETAIL_NONE ){\n      p->bContent = 1;\n    }else{\n      /* Append a new column value, if necessary */\n      assert( iCol>=p->iCol );\n      if( iCol!=p->iCol ){\n        if( pHash->eDetail==FTS5_DETAIL_FULL ){\n          pPtr[p->nData++] = 0x01;\n          p->nData += sqlite3Fts5PutVarint(&pPtr[p->nData], iCol);\n          p->iCol = (i16)iCol;\n          p->iPos = 0;\n        }else{\n          bNew = 1;\n          p->iCol = (i16)(iPos = iCol);\n        }\n      }\n\n      /* Append the new position offset, if necessary */\n      if( bNew ){\n        p->nData += sqlite3Fts5PutVarint(&pPtr[p->nData], iPos - p->iPos + 2);\n        p->iPos = iPos;\n      }\n    }\n  }else{\n    /* This is a delete. Set the delete flag. */\n    p->bDel = 1;\n  }\n\n  nIncr += p->nData;\n  *pHash->pnByte += nIncr;\n  return SQLITE_OK;\n}\n\n\n/*\n** Arguments pLeft and pRight point to linked-lists of hash-entry objects,\n** each sorted in key order. This function merges the two lists into a\n** single list and returns a pointer to its first element.\n*/\nstatic Fts5HashEntry *fts5HashEntryMerge(\n  Fts5HashEntry *pLeft,\n  Fts5HashEntry *pRight\n){\n  Fts5HashEntry *p1 = pLeft;\n  Fts5HashEntry *p2 = pRight;\n  Fts5HashEntry *pRet = 0;\n  Fts5HashEntry **ppOut = &pRet;\n\n  while( p1 || p2 ){\n    if( p1==0 ){\n      *ppOut = p2;\n      p2 = 0;\n    }else if( p2==0 ){\n      *ppOut = p1;\n      p1 = 0;\n    }else{\n      int i = 0;\n      char *zKey1 = fts5EntryKey(p1);\n      char *zKey2 = fts5EntryKey(p2);\n      while( zKey1[i]==zKey2[i] ) i++;\n\n      if( ((u8)zKey1[i])>((u8)zKey2[i]) ){\n        /* p2 is smaller */\n        *ppOut = p2;\n        ppOut = &p2->pScanNext;\n        p2 = p2->pScanNext;\n      }else{\n        /* p1 is smaller */\n        *ppOut = p1;\n        ppOut = &p1->pScanNext;\n        p1 = p1->pScanNext;\n      }\n      *ppOut = 0;\n    }\n  }\n\n  return pRet;\n}\n\n/*\n** Extract all tokens from hash table iHash and link them into a list\n** in sorted order. The hash table is cleared before returning. It is\n** the responsibility of the caller to free the elements of the returned\n** list.\n*/\nstatic int fts5HashEntrySort(\n  Fts5Hash *pHash, \n  const char *pTerm, int nTerm,   /* Query prefix, if any */\n  Fts5HashEntry **ppSorted\n){\n  const int nMergeSlot = 32;\n  Fts5HashEntry **ap;\n  Fts5HashEntry *pList;\n  int iSlot;\n  int i;\n\n  *ppSorted = 0;\n  ap = sqlite3_malloc(sizeof(Fts5HashEntry*) * nMergeSlot);\n  if( !ap ) return SQLITE_NOMEM;\n  memset(ap, 0, sizeof(Fts5HashEntry*) * nMergeSlot);\n\n  for(iSlot=0; iSlot<pHash->nSlot; iSlot++){\n    Fts5HashEntry *pIter;\n    for(pIter=pHash->aSlot[iSlot]; pIter; pIter=pIter->pHashNext){\n      if( pTerm==0 || 0==memcmp(fts5EntryKey(pIter), pTerm, nTerm) ){\n        Fts5HashEntry *pEntry = pIter;\n        pEntry->pScanNext = 0;\n        for(i=0; ap[i]; i++){\n          pEntry = fts5HashEntryMerge(pEntry, ap[i]);\n          ap[i] = 0;\n        }\n        ap[i] = pEntry;\n      }\n    }\n  }\n\n  pList = 0;\n  for(i=0; i<nMergeSlot; i++){\n    pList = fts5HashEntryMerge(pList, ap[i]);\n  }\n\n  pHash->nEntry = 0;\n  sqlite3_free(ap);\n  *ppSorted = pList;\n  return SQLITE_OK;\n}\n\n/*\n** Query the hash table for a doclist associated with term pTerm/nTerm.\n*/\nstatic int sqlite3Fts5HashQuery(\n  Fts5Hash *pHash,                /* Hash table to query */\n  const char *pTerm, int nTerm,   /* Query term */\n  const u8 **ppDoclist,           /* OUT: Pointer to doclist for pTerm */\n  int *pnDoclist                  /* OUT: Size of doclist in bytes */\n){\n  unsigned int iHash = fts5HashKey(pHash->nSlot, (const u8*)pTerm, nTerm);\n  char *zKey = 0;\n  Fts5HashEntry *p;\n\n  for(p=pHash->aSlot[iHash]; p; p=p->pHashNext){\n    zKey = fts5EntryKey(p);\n    if( memcmp(zKey, pTerm, nTerm)==0 && zKey[nTerm]==0 ) break;\n  }\n\n  if( p ){\n    fts5HashAddPoslistSize(pHash, p);\n    *ppDoclist = (const u8*)&zKey[nTerm+1];\n    *pnDoclist = p->nData - (sizeof(Fts5HashEntry) + nTerm + 1);\n  }else{\n    *ppDoclist = 0;\n    *pnDoclist = 0;\n  }\n\n  return SQLITE_OK;\n}\n\nstatic int sqlite3Fts5HashScanInit(\n  Fts5Hash *p,                    /* Hash table to query */\n  const char *pTerm, int nTerm    /* Query prefix */\n){\n  return fts5HashEntrySort(p, pTerm, nTerm, &p->pScan);\n}\n\nstatic void sqlite3Fts5HashScanNext(Fts5Hash *p){\n  assert( !sqlite3Fts5HashScanEof(p) );\n  p->pScan = p->pScan->pScanNext;\n}\n\nstatic int sqlite3Fts5HashScanEof(Fts5Hash *p){\n  return (p->pScan==0);\n}\n\nstatic void sqlite3Fts5HashScanEntry(\n  Fts5Hash *pHash,\n  const char **pzTerm,            /* OUT: term (nul-terminated) */\n  const u8 **ppDoclist,           /* OUT: pointer to doclist */\n  int *pnDoclist                  /* OUT: size of doclist in bytes */\n){\n  Fts5HashEntry *p;\n  if( (p = pHash->pScan) ){\n    char *zKey = fts5EntryKey(p);\n    int nTerm = (int)strlen(zKey);\n    fts5HashAddPoslistSize(pHash, p);\n    *pzTerm = zKey;\n    *ppDoclist = (const u8*)&zKey[nTerm+1];\n    *pnDoclist = p->nData - (sizeof(Fts5HashEntry) + nTerm + 1);\n  }else{\n    *pzTerm = 0;\n    *ppDoclist = 0;\n    *pnDoclist = 0;\n  }\n}\n\n\n/*\n** 2014 May 31\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n******************************************************************************\n**\n** Low level access to the FTS index stored in the database file. The \n** routines in this file file implement all read and write access to the\n** %_data table. Other parts of the system access this functionality via\n** the interface defined in fts5Int.h.\n*/\n\n\n/* #include \"fts5Int.h\" */\n\n/*\n** Overview:\n**\n** The %_data table contains all the FTS indexes for an FTS5 virtual table.\n** As well as the main term index, there may be up to 31 prefix indexes.\n** The format is similar to FTS3/4, except that:\n**\n**   * all segment b-tree leaf data is stored in fixed size page records \n**     (e.g. 1000 bytes). A single doclist may span multiple pages. Care is \n**     taken to ensure it is possible to iterate in either direction through \n**     the entries in a doclist, or to seek to a specific entry within a \n**     doclist, without loading it into memory.\n**\n**   * large doclists that span many pages have associated \"doclist index\"\n**     records that contain a copy of the first rowid on each page spanned by\n**     the doclist. This is used to speed up seek operations, and merges of\n**     large doclists with very small doclists.\n**\n**   * extra fields in the \"structure record\" record the state of ongoing\n**     incremental merge operations.\n**\n*/\n\n\n#define FTS5_OPT_WORK_UNIT  1000  /* Number of leaf pages per optimize step */\n#define FTS5_WORK_UNIT      64    /* Number of leaf pages in unit of work */\n\n#define FTS5_MIN_DLIDX_SIZE 4     /* Add dlidx if this many empty pages */\n\n#define FTS5_MAIN_PREFIX '0'\n\n#if FTS5_MAX_PREFIX_INDEXES > 31\n# error \"FTS5_MAX_PREFIX_INDEXES is too large\"\n#endif\n\n/*\n** Details:\n**\n** The %_data table managed by this module,\n**\n**     CREATE TABLE %_data(id INTEGER PRIMARY KEY, block BLOB);\n**\n** , contains the following 5 types of records. See the comments surrounding\n** the FTS5_*_ROWID macros below for a description of how %_data rowids are \n** assigned to each fo them.\n**\n** 1. Structure Records:\n**\n**   The set of segments that make up an index - the index structure - are\n**   recorded in a single record within the %_data table. The record consists\n**   of a single 32-bit configuration cookie value followed by a list of \n**   SQLite varints. If the FTS table features more than one index (because\n**   there are one or more prefix indexes), it is guaranteed that all share\n**   the same cookie value.\n**\n**   Immediately following the configuration cookie, the record begins with\n**   three varints:\n**\n**     + number of levels,\n**     + total number of segments on all levels,\n**     + value of write counter.\n**\n**   Then, for each level from 0 to nMax:\n**\n**     + number of input segments in ongoing merge.\n**     + total number of segments in level.\n**     + for each segment from oldest to newest:\n**         + segment id (always > 0)\n**         + first leaf page number (often 1, always greater than 0)\n**         + final leaf page number\n**\n** 2. The Averages Record:\n**\n**   A single record within the %_data table. The data is a list of varints.\n**   The first value is the number of rows in the index. Then, for each column\n**   from left to right, the total number of tokens in the column for all\n**   rows of the table.\n**\n** 3. Segment leaves:\n**\n**   TERM/DOCLIST FORMAT:\n**\n**     Most of each segment leaf is taken up by term/doclist data. The \n**     general format of term/doclist, starting with the first term\n**     on the leaf page, is:\n**\n**         varint : size of first term\n**         blob:    first term data\n**         doclist: first doclist\n**         zero-or-more {\n**           varint:  number of bytes in common with previous term\n**           varint:  number of bytes of new term data (nNew)\n**           blob:    nNew bytes of new term data\n**           doclist: next doclist\n**         }\n**\n**     doclist format:\n**\n**         varint:  first rowid\n**         poslist: first poslist\n**         zero-or-more {\n**           varint:  rowid delta (always > 0)\n**           poslist: next poslist\n**         }\n**\n**     poslist format:\n**\n**         varint: size of poslist in bytes multiplied by 2, not including\n**                 this field. Plus 1 if this entry carries the \"delete\" flag.\n**         collist: collist for column 0\n**         zero-or-more {\n**           0x01 byte\n**           varint: column number (I)\n**           collist: collist for column I\n**         }\n**\n**     collist format:\n**\n**         varint: first offset + 2\n**         zero-or-more {\n**           varint: offset delta + 2\n**         }\n**\n**   PAGE FORMAT\n**\n**     Each leaf page begins with a 4-byte header containing 2 16-bit \n**     unsigned integer fields in big-endian format. They are:\n**\n**       * The byte offset of the first rowid on the page, if it exists\n**         and occurs before the first term (otherwise 0).\n**\n**       * The byte offset of the start of the page footer. If the page\n**         footer is 0 bytes in size, then this field is the same as the\n**         size of the leaf page in bytes.\n**\n**     The page footer consists of a single varint for each term located\n**     on the page. Each varint is the byte offset of the current term\n**     within the page, delta-compressed against the previous value. In\n**     other words, the first varint in the footer is the byte offset of\n**     the first term, the second is the byte offset of the second less that\n**     of the first, and so on.\n**\n**     The term/doclist format described above is accurate if the entire\n**     term/doclist data fits on a single leaf page. If this is not the case,\n**     the format is changed in two ways:\n**\n**       + if the first rowid on a page occurs before the first term, it\n**         is stored as a literal value:\n**\n**             varint:  first rowid\n**\n**       + the first term on each page is stored in the same way as the\n**         very first term of the segment:\n**\n**             varint : size of first term\n**             blob:    first term data\n**\n** 5. Segment doclist indexes:\n**\n**   Doclist indexes are themselves b-trees, however they usually consist of\n**   a single leaf record only. The format of each doclist index leaf page \n**   is:\n**\n**     * Flags byte. Bits are:\n**         0x01: Clear if leaf is also the root page, otherwise set.\n**\n**     * Page number of fts index leaf page. As a varint.\n**\n**     * First rowid on page indicated by previous field. As a varint.\n**\n**     * A list of varints, one for each subsequent termless page. A \n**       positive delta if the termless page contains at least one rowid, \n**       or an 0x00 byte otherwise.\n**\n**   Internal doclist index nodes are:\n**\n**     * Flags byte. Bits are:\n**         0x01: Clear for root page, otherwise set.\n**\n**     * Page number of first child page. As a varint.\n**\n**     * Copy of first rowid on page indicated by previous field. As a varint.\n**\n**     * A list of delta-encoded varints - the first rowid on each subsequent\n**       child page. \n**\n*/\n\n/*\n** Rowids for the averages and structure records in the %_data table.\n*/\n#define FTS5_AVERAGES_ROWID     1    /* Rowid used for the averages record */\n#define FTS5_STRUCTURE_ROWID   10    /* The structure record */\n\n/*\n** Macros determining the rowids used by segment leaves and dlidx leaves\n** and nodes. All nodes and leaves are stored in the %_data table with large\n** positive rowids.\n**\n** Each segment has a unique non-zero 16-bit id.\n**\n** The rowid for each segment leaf is found by passing the segment id and \n** the leaf page number to the FTS5_SEGMENT_ROWID macro. Leaves are numbered\n** sequentially starting from 1.\n*/\n#define FTS5_DATA_ID_B     16     /* Max seg id number 65535 */\n#define FTS5_DATA_DLI_B     1     /* Doclist-index flag (1 bit) */\n#define FTS5_DATA_HEIGHT_B  5     /* Max dlidx tree height of 32 */\n#define FTS5_DATA_PAGE_B   31     /* Max page number of 2147483648 */\n\n#define fts5_dri(segid, dlidx, height, pgno) (                                 \\\n ((i64)(segid)  << (FTS5_DATA_PAGE_B+FTS5_DATA_HEIGHT_B+FTS5_DATA_DLI_B)) +    \\\n ((i64)(dlidx)  << (FTS5_DATA_PAGE_B + FTS5_DATA_HEIGHT_B)) +                  \\\n ((i64)(height) << (FTS5_DATA_PAGE_B)) +                                       \\\n ((i64)(pgno))                                                                 \\\n)\n\n#define FTS5_SEGMENT_ROWID(segid, pgno)       fts5_dri(segid, 0, 0, pgno)\n#define FTS5_DLIDX_ROWID(segid, height, pgno) fts5_dri(segid, 1, height, pgno)\n\n/*\n** Maximum segments permitted in a single index \n*/\n#define FTS5_MAX_SEGMENT 2000\n\n#ifdef SQLITE_DEBUG\nstatic int sqlite3Fts5Corrupt() { return SQLITE_CORRUPT_VTAB; }\n#endif\n\n\n/*\n** Each time a blob is read from the %_data table, it is padded with this\n** many zero bytes. This makes it easier to decode the various record formats\n** without overreading if the records are corrupt.\n*/\n#define FTS5_DATA_ZERO_PADDING 8\n#define FTS5_DATA_PADDING 20\n\ntypedef struct Fts5Data Fts5Data;\ntypedef struct Fts5DlidxIter Fts5DlidxIter;\ntypedef struct Fts5DlidxLvl Fts5DlidxLvl;\ntypedef struct Fts5DlidxWriter Fts5DlidxWriter;\ntypedef struct Fts5Iter Fts5Iter;\ntypedef struct Fts5PageWriter Fts5PageWriter;\ntypedef struct Fts5SegIter Fts5SegIter;\ntypedef struct Fts5DoclistIter Fts5DoclistIter;\ntypedef struct Fts5SegWriter Fts5SegWriter;\ntypedef struct Fts5Structure Fts5Structure;\ntypedef struct Fts5StructureLevel Fts5StructureLevel;\ntypedef struct Fts5StructureSegment Fts5StructureSegment;\n\nstruct Fts5Data {\n  u8 *p;                          /* Pointer to buffer containing record */\n  int nn;                         /* Size of record in bytes */\n  int szLeaf;                     /* Size of leaf without page-index */\n};\n\n/*\n** One object per %_data table.\n*/\nstruct Fts5Index {\n  Fts5Config *pConfig;            /* Virtual table configuration */\n  char *zDataTbl;                 /* Name of %_data table */\n  int nWorkUnit;                  /* Leaf pages in a \"unit\" of work */\n\n  /*\n  ** Variables related to the accumulation of tokens and doclists within the\n  ** in-memory hash tables before they are flushed to disk.\n  */\n  Fts5Hash *pHash;                /* Hash table for in-memory data */\n  int nPendingData;               /* Current bytes of pending data */\n  i64 iWriteRowid;                /* Rowid for current doc being written */\n  int bDelete;                    /* Current write is a delete */\n\n  /* Error state. */\n  int rc;                         /* Current error code */\n\n  /* State used by the fts5DataXXX() functions. */\n  sqlite3_blob *pReader;          /* RO incr-blob open on %_data table */\n  sqlite3_stmt *pWriter;          /* \"INSERT ... %_data VALUES(?,?)\" */\n  sqlite3_stmt *pDeleter;         /* \"DELETE FROM %_data ... id>=? AND id<=?\" */\n  sqlite3_stmt *pIdxWriter;       /* \"INSERT ... %_idx VALUES(?,?,?,?)\" */\n  sqlite3_stmt *pIdxDeleter;      /* \"DELETE FROM %_idx WHERE segid=? */\n  sqlite3_stmt *pIdxSelect;\n  int nRead;                      /* Total number of blocks read */\n\n  sqlite3_stmt *pDataVersion;\n  i64 iStructVersion;             /* data_version when pStruct read */\n  Fts5Structure *pStruct;         /* Current db structure (or NULL) */\n};\n\nstruct Fts5DoclistIter {\n  u8 *aEof;                       /* Pointer to 1 byte past end of doclist */\n\n  /* Output variables. aPoslist==0 at EOF */\n  i64 iRowid;\n  u8 *aPoslist;\n  int nPoslist;\n  int nSize;\n};\n\n/*\n** The contents of the \"structure\" record for each index are represented\n** using an Fts5Structure record in memory. Which uses instances of the \n** other Fts5StructureXXX types as components.\n*/\nstruct Fts5StructureSegment {\n  int iSegid;                     /* Segment id */\n  int pgnoFirst;                  /* First leaf page number in segment */\n  int pgnoLast;                   /* Last leaf page number in segment */\n};\nstruct Fts5StructureLevel {\n  int nMerge;                     /* Number of segments in incr-merge */\n  int nSeg;                       /* Total number of segments on level */\n  Fts5StructureSegment *aSeg;     /* Array of segments. aSeg[0] is oldest. */\n};\nstruct Fts5Structure {\n  int nRef;                       /* Object reference count */\n  u64 nWriteCounter;              /* Total leaves written to level 0 */\n  int nSegment;                   /* Total segments in this structure */\n  int nLevel;                     /* Number of levels in this index */\n  Fts5StructureLevel aLevel[1];   /* Array of nLevel level objects */\n};\n\n/*\n** An object of type Fts5SegWriter is used to write to segments.\n*/\nstruct Fts5PageWriter {\n  int pgno;                       /* Page number for this page */\n  int iPrevPgidx;                 /* Previous value written into pgidx */\n  Fts5Buffer buf;                 /* Buffer containing leaf data */\n  Fts5Buffer pgidx;               /* Buffer containing page-index */\n  Fts5Buffer term;                /* Buffer containing previous term on page */\n};\nstruct Fts5DlidxWriter {\n  int pgno;                       /* Page number for this page */\n  int bPrevValid;                 /* True if iPrev is valid */\n  i64 iPrev;                      /* Previous rowid value written to page */\n  Fts5Buffer buf;                 /* Buffer containing page data */\n};\nstruct Fts5SegWriter {\n  int iSegid;                     /* Segid to write to */\n  Fts5PageWriter writer;          /* PageWriter object */\n  i64 iPrevRowid;                 /* Previous rowid written to current leaf */\n  u8 bFirstRowidInDoclist;        /* True if next rowid is first in doclist */\n  u8 bFirstRowidInPage;           /* True if next rowid is first in page */\n  /* TODO1: Can use (writer.pgidx.n==0) instead of bFirstTermInPage */\n  u8 bFirstTermInPage;            /* True if next term will be first in leaf */\n  int nLeafWritten;               /* Number of leaf pages written */\n  int nEmpty;                     /* Number of contiguous term-less nodes */\n\n  int nDlidx;                     /* Allocated size of aDlidx[] array */\n  Fts5DlidxWriter *aDlidx;        /* Array of Fts5DlidxWriter objects */\n\n  /* Values to insert into the %_idx table */\n  Fts5Buffer btterm;              /* Next term to insert into %_idx table */\n  int iBtPage;                    /* Page number corresponding to btterm */\n};\n\ntypedef struct Fts5CResult Fts5CResult;\nstruct Fts5CResult {\n  u16 iFirst;                     /* aSeg[] index of firstest iterator */\n  u8 bTermEq;                     /* True if the terms are equal */\n};\n\n/*\n** Object for iterating through a single segment, visiting each term/rowid\n** pair in the segment.\n**\n** pSeg:\n**   The segment to iterate through.\n**\n** iLeafPgno:\n**   Current leaf page number within segment.\n**\n** iLeafOffset:\n**   Byte offset within the current leaf that is the first byte of the \n**   position list data (one byte passed the position-list size field).\n**   rowid field of the current entry. Usually this is the size field of the\n**   position list data. The exception is if the rowid for the current entry \n**   is the last thing on the leaf page.\n**\n** pLeaf:\n**   Buffer containing current leaf page data. Set to NULL at EOF.\n**\n** iTermLeafPgno, iTermLeafOffset:\n**   Leaf page number containing the last term read from the segment. And\n**   the offset immediately following the term data.\n**\n** flags:\n**   Mask of FTS5_SEGITER_XXX values. Interpreted as follows:\n**\n**   FTS5_SEGITER_ONETERM:\n**     If set, set the iterator to point to EOF after the current doclist \n**     has been exhausted. Do not proceed to the next term in the segment.\n**\n**   FTS5_SEGITER_REVERSE:\n**     This flag is only ever set if FTS5_SEGITER_ONETERM is also set. If\n**     it is set, iterate through rowid in descending order instead of the\n**     default ascending order.\n**\n** iRowidOffset/nRowidOffset/aRowidOffset:\n**     These are used if the FTS5_SEGITER_REVERSE flag is set.\n**\n**     For each rowid on the page corresponding to the current term, the\n**     corresponding aRowidOffset[] entry is set to the byte offset of the\n**     start of the \"position-list-size\" field within the page.\n**\n** iTermIdx:\n**     Index of current term on iTermLeafPgno.\n*/\nstruct Fts5SegIter {\n  Fts5StructureSegment *pSeg;     /* Segment to iterate through */\n  int flags;                      /* Mask of configuration flags */\n  int iLeafPgno;                  /* Current leaf page number */\n  Fts5Data *pLeaf;                /* Current leaf data */\n  Fts5Data *pNextLeaf;            /* Leaf page (iLeafPgno+1) */\n  int iLeafOffset;                /* Byte offset within current leaf */\n\n  /* Next method */\n  void (*xNext)(Fts5Index*, Fts5SegIter*, int*);\n\n  /* The page and offset from which the current term was read. The offset \n  ** is the offset of the first rowid in the current doclist.  */\n  int iTermLeafPgno;\n  int iTermLeafOffset;\n\n  int iPgidxOff;                  /* Next offset in pgidx */\n  int iEndofDoclist;\n\n  /* The following are only used if the FTS5_SEGITER_REVERSE flag is set. */\n  int iRowidOffset;               /* Current entry in aRowidOffset[] */\n  int nRowidOffset;               /* Allocated size of aRowidOffset[] array */\n  int *aRowidOffset;              /* Array of offset to rowid fields */\n\n  Fts5DlidxIter *pDlidx;          /* If there is a doclist-index */\n\n  /* Variables populated based on current entry. */\n  Fts5Buffer term;                /* Current term */\n  i64 iRowid;                     /* Current rowid */\n  int nPos;                       /* Number of bytes in current position list */\n  u8 bDel;                        /* True if the delete flag is set */\n};\n\n/*\n** Argument is a pointer to an Fts5Data structure that contains a \n** leaf page.\n*/\n#define ASSERT_SZLEAF_OK(x) assert( \\\n    (x)->szLeaf==(x)->nn || (x)->szLeaf==fts5GetU16(&(x)->p[2]) \\\n)\n\n#define FTS5_SEGITER_ONETERM 0x01\n#define FTS5_SEGITER_REVERSE 0x02\n\n/* \n** Argument is a pointer to an Fts5Data structure that contains a leaf\n** page. This macro evaluates to true if the leaf contains no terms, or\n** false if it contains at least one term.\n*/\n#define fts5LeafIsTermless(x) ((x)->szLeaf >= (x)->nn)\n\n#define fts5LeafTermOff(x, i) (fts5GetU16(&(x)->p[(x)->szLeaf + (i)*2]))\n\n#define fts5LeafFirstRowidOff(x) (fts5GetU16((x)->p))\n\n/*\n** Object for iterating through the merged results of one or more segments,\n** visiting each term/rowid pair in the merged data.\n**\n** nSeg is always a power of two greater than or equal to the number of\n** segments that this object is merging data from. Both the aSeg[] and\n** aFirst[] arrays are sized at nSeg entries. The aSeg[] array is padded\n** with zeroed objects - these are handled as if they were iterators opened\n** on empty segments.\n**\n** The results of comparing segments aSeg[N] and aSeg[N+1], where N is an\n** even number, is stored in aFirst[(nSeg+N)/2]. The \"result\" of the \n** comparison in this context is the index of the iterator that currently\n** points to the smaller term/rowid combination. Iterators at EOF are\n** considered to be greater than all other iterators.\n**\n** aFirst[1] contains the index in aSeg[] of the iterator that points to\n** the smallest key overall. aFirst[0] is unused. \n**\n** poslist:\n**   Used by sqlite3Fts5IterPoslist() when the poslist needs to be buffered.\n**   There is no way to tell if this is populated or not.\n*/\nstruct Fts5Iter {\n  Fts5IndexIter base;             /* Base class containing output vars */\n\n  Fts5Index *pIndex;              /* Index that owns this iterator */\n  Fts5Structure *pStruct;         /* Database structure for this iterator */\n  Fts5Buffer poslist;             /* Buffer containing current poslist */\n  Fts5Colset *pColset;            /* Restrict matches to these columns */\n\n  /* Invoked to set output variables. */\n  void (*xSetOutputs)(Fts5Iter*, Fts5SegIter*);\n\n  int nSeg;                       /* Size of aSeg[] array */\n  int bRev;                       /* True to iterate in reverse order */\n  u8 bSkipEmpty;                  /* True to skip deleted entries */\n\n  i64 iSwitchRowid;               /* Firstest rowid of other than aFirst[1] */\n  Fts5CResult *aFirst;            /* Current merge state (see above) */\n  Fts5SegIter aSeg[1];            /* Array of segment iterators */\n};\n\n\n/*\n** An instance of the following type is used to iterate through the contents\n** of a doclist-index record.\n**\n** pData:\n**   Record containing the doclist-index data.\n**\n** bEof:\n**   Set to true once iterator has reached EOF.\n**\n** iOff:\n**   Set to the current offset within record pData.\n*/\nstruct Fts5DlidxLvl {\n  Fts5Data *pData;              /* Data for current page of this level */\n  int iOff;                     /* Current offset into pData */\n  int bEof;                     /* At EOF already */\n  int iFirstOff;                /* Used by reverse iterators */\n\n  /* Output variables */\n  int iLeafPgno;                /* Page number of current leaf page */\n  i64 iRowid;                   /* First rowid on leaf iLeafPgno */\n};\nstruct Fts5DlidxIter {\n  int nLvl;\n  int iSegid;\n  Fts5DlidxLvl aLvl[1];\n};\n\nstatic void fts5PutU16(u8 *aOut, u16 iVal){\n  aOut[0] = (iVal>>8);\n  aOut[1] = (iVal&0xFF);\n}\n\nstatic u16 fts5GetU16(const u8 *aIn){\n  return ((u16)aIn[0] << 8) + aIn[1];\n} \n\n/*\n** Allocate and return a buffer at least nByte bytes in size.\n**\n** If an OOM error is encountered, return NULL and set the error code in\n** the Fts5Index handle passed as the first argument.\n*/\nstatic void *fts5IdxMalloc(Fts5Index *p, int nByte){\n  return sqlite3Fts5MallocZero(&p->rc, nByte);\n}\n\n/*\n** Compare the contents of the pLeft buffer with the pRight/nRight blob.\n**\n** Return -ve if pLeft is smaller than pRight, 0 if they are equal or\n** +ve if pRight is smaller than pLeft. In other words:\n**\n**     res = *pLeft - *pRight\n*/\n#ifdef SQLITE_DEBUG\nstatic int fts5BufferCompareBlob(\n  Fts5Buffer *pLeft,              /* Left hand side of comparison */\n  const u8 *pRight, int nRight    /* Right hand side of comparison */\n){\n  int nCmp = MIN(pLeft->n, nRight);\n  int res = memcmp(pLeft->p, pRight, nCmp);\n  return (res==0 ? (pLeft->n - nRight) : res);\n}\n#endif\n\n/*\n** Compare the contents of the two buffers using memcmp(). If one buffer\n** is a prefix of the other, it is considered the lesser.\n**\n** Return -ve if pLeft is smaller than pRight, 0 if they are equal or\n** +ve if pRight is smaller than pLeft. In other words:\n**\n**     res = *pLeft - *pRight\n*/\nstatic int fts5BufferCompare(Fts5Buffer *pLeft, Fts5Buffer *pRight){\n  int nCmp = MIN(pLeft->n, pRight->n);\n  int res = memcmp(pLeft->p, pRight->p, nCmp);\n  return (res==0 ? (pLeft->n - pRight->n) : res);\n}\n\nstatic int fts5LeafFirstTermOff(Fts5Data *pLeaf){\n  int ret;\n  fts5GetVarint32(&pLeaf->p[pLeaf->szLeaf], ret);\n  return ret;\n}\n\n/*\n** Close the read-only blob handle, if it is open.\n*/\nstatic void fts5CloseReader(Fts5Index *p){\n  if( p->pReader ){\n    sqlite3_blob *pReader = p->pReader;\n    p->pReader = 0;\n    sqlite3_blob_close(pReader);\n  }\n}\n\n/*\n** Retrieve a record from the %_data table.\n**\n** If an error occurs, NULL is returned and an error left in the \n** Fts5Index object.\n*/\nstatic Fts5Data *fts5DataRead(Fts5Index *p, i64 iRowid){\n  Fts5Data *pRet = 0;\n  if( p->rc==SQLITE_OK ){\n    int rc = SQLITE_OK;\n\n    if( p->pReader ){\n      /* This call may return SQLITE_ABORT if there has been a savepoint\n      ** rollback since it was last used. In this case a new blob handle\n      ** is required.  */\n      sqlite3_blob *pBlob = p->pReader;\n      p->pReader = 0;\n      rc = sqlite3_blob_reopen(pBlob, iRowid);\n      assert( p->pReader==0 );\n      p->pReader = pBlob;\n      if( rc!=SQLITE_OK ){\n        fts5CloseReader(p);\n      }\n      if( rc==SQLITE_ABORT ) rc = SQLITE_OK;\n    }\n\n    /* If the blob handle is not open at this point, open it and seek \n    ** to the requested entry.  */\n    if( p->pReader==0 && rc==SQLITE_OK ){\n      Fts5Config *pConfig = p->pConfig;\n      rc = sqlite3_blob_open(pConfig->db, \n          pConfig->zDb, p->zDataTbl, \"block\", iRowid, 0, &p->pReader\n      );\n    }\n\n    /* If either of the sqlite3_blob_open() or sqlite3_blob_reopen() calls\n    ** above returned SQLITE_ERROR, return SQLITE_CORRUPT_VTAB instead.\n    ** All the reasons those functions might return SQLITE_ERROR - missing\n    ** table, missing row, non-blob/text in block column - indicate \n    ** backing store corruption.  */\n    if( rc==SQLITE_ERROR ) rc = FTS5_CORRUPT;\n\n    if( rc==SQLITE_OK ){\n      u8 *aOut = 0;               /* Read blob data into this buffer */\n      int nByte = sqlite3_blob_bytes(p->pReader);\n      int nAlloc = sizeof(Fts5Data) + nByte + FTS5_DATA_PADDING;\n      pRet = (Fts5Data*)sqlite3_malloc(nAlloc);\n      if( pRet ){\n        pRet->nn = nByte;\n        aOut = pRet->p = (u8*)&pRet[1];\n      }else{\n        rc = SQLITE_NOMEM;\n      }\n\n      if( rc==SQLITE_OK ){\n        rc = sqlite3_blob_read(p->pReader, aOut, nByte, 0);\n      }\n      if( rc!=SQLITE_OK ){\n        sqlite3_free(pRet);\n        pRet = 0;\n      }else{\n        /* TODO1: Fix this */\n        pRet->szLeaf = fts5GetU16(&pRet->p[2]);\n      }\n    }\n    p->rc = rc;\n    p->nRead++;\n  }\n\n  assert( (pRet==0)==(p->rc!=SQLITE_OK) );\n  return pRet;\n}\n\n/*\n** Release a reference to data record returned by an earlier call to\n** fts5DataRead().\n*/\nstatic void fts5DataRelease(Fts5Data *pData){\n  sqlite3_free(pData);\n}\n\nstatic Fts5Data *fts5LeafRead(Fts5Index *p, i64 iRowid){\n  Fts5Data *pRet = fts5DataRead(p, iRowid);\n  if( pRet ){\n    if( pRet->szLeaf>pRet->nn ){\n      p->rc = FTS5_CORRUPT;\n      fts5DataRelease(pRet);\n      pRet = 0;\n    }\n  }\n  return pRet;\n}\n\nstatic int fts5IndexPrepareStmt(\n  Fts5Index *p,\n  sqlite3_stmt **ppStmt,\n  char *zSql\n){\n  if( p->rc==SQLITE_OK ){\n    if( zSql ){\n      p->rc = sqlite3_prepare_v3(p->pConfig->db, zSql, -1,\n                                 SQLITE_PREPARE_PERSISTENT, ppStmt, 0);\n    }else{\n      p->rc = SQLITE_NOMEM;\n    }\n  }\n  sqlite3_free(zSql);\n  return p->rc;\n}\n\n\n/*\n** INSERT OR REPLACE a record into the %_data table.\n*/\nstatic void fts5DataWrite(Fts5Index *p, i64 iRowid, const u8 *pData, int nData){\n  if( p->rc!=SQLITE_OK ) return;\n\n  if( p->pWriter==0 ){\n    Fts5Config *pConfig = p->pConfig;\n    fts5IndexPrepareStmt(p, &p->pWriter, sqlite3_mprintf(\n          \"REPLACE INTO '%q'.'%q_data'(id, block) VALUES(?,?)\", \n          pConfig->zDb, pConfig->zName\n    ));\n    if( p->rc ) return;\n  }\n\n  sqlite3_bind_int64(p->pWriter, 1, iRowid);\n  sqlite3_bind_blob(p->pWriter, 2, pData, nData, SQLITE_STATIC);\n  sqlite3_step(p->pWriter);\n  p->rc = sqlite3_reset(p->pWriter);\n  sqlite3_bind_null(p->pWriter, 2);\n}\n\n/*\n** Execute the following SQL:\n**\n**     DELETE FROM %_data WHERE id BETWEEN $iFirst AND $iLast\n*/\nstatic void fts5DataDelete(Fts5Index *p, i64 iFirst, i64 iLast){\n  if( p->rc!=SQLITE_OK ) return;\n\n  if( p->pDeleter==0 ){\n    int rc;\n    Fts5Config *pConfig = p->pConfig;\n    char *zSql = sqlite3_mprintf(\n        \"DELETE FROM '%q'.'%q_data' WHERE id>=? AND id<=?\", \n          pConfig->zDb, pConfig->zName\n    );\n    if( zSql==0 ){\n      rc = SQLITE_NOMEM;\n    }else{\n      rc = sqlite3_prepare_v3(pConfig->db, zSql, -1,\n                              SQLITE_PREPARE_PERSISTENT, &p->pDeleter, 0);\n      sqlite3_free(zSql);\n    }\n    if( rc!=SQLITE_OK ){\n      p->rc = rc;\n      return;\n    }\n  }\n\n  sqlite3_bind_int64(p->pDeleter, 1, iFirst);\n  sqlite3_bind_int64(p->pDeleter, 2, iLast);\n  sqlite3_step(p->pDeleter);\n  p->rc = sqlite3_reset(p->pDeleter);\n}\n\n/*\n** Remove all records associated with segment iSegid.\n*/\nstatic void fts5DataRemoveSegment(Fts5Index *p, int iSegid){\n  i64 iFirst = FTS5_SEGMENT_ROWID(iSegid, 0);\n  i64 iLast = FTS5_SEGMENT_ROWID(iSegid+1, 0)-1;\n  fts5DataDelete(p, iFirst, iLast);\n  if( p->pIdxDeleter==0 ){\n    Fts5Config *pConfig = p->pConfig;\n    fts5IndexPrepareStmt(p, &p->pIdxDeleter, sqlite3_mprintf(\n          \"DELETE FROM '%q'.'%q_idx' WHERE segid=?\",\n          pConfig->zDb, pConfig->zName\n    ));\n  }\n  if( p->rc==SQLITE_OK ){\n    sqlite3_bind_int(p->pIdxDeleter, 1, iSegid);\n    sqlite3_step(p->pIdxDeleter);\n    p->rc = sqlite3_reset(p->pIdxDeleter);\n  }\n}\n\n/*\n** Release a reference to an Fts5Structure object returned by an earlier \n** call to fts5StructureRead() or fts5StructureDecode().\n*/\nstatic void fts5StructureRelease(Fts5Structure *pStruct){\n  if( pStruct && 0>=(--pStruct->nRef) ){\n    int i;\n    assert( pStruct->nRef==0 );\n    for(i=0; i<pStruct->nLevel; i++){\n      sqlite3_free(pStruct->aLevel[i].aSeg);\n    }\n    sqlite3_free(pStruct);\n  }\n}\n\nstatic void fts5StructureRef(Fts5Structure *pStruct){\n  pStruct->nRef++;\n}\n\n/*\n** Deserialize and return the structure record currently stored in serialized\n** form within buffer pData/nData.\n**\n** The Fts5Structure.aLevel[] and each Fts5StructureLevel.aSeg[] array\n** are over-allocated by one slot. This allows the structure contents\n** to be more easily edited.\n**\n** If an error occurs, *ppOut is set to NULL and an SQLite error code\n** returned. Otherwise, *ppOut is set to point to the new object and\n** SQLITE_OK returned.\n*/\nstatic int fts5StructureDecode(\n  const u8 *pData,                /* Buffer containing serialized structure */\n  int nData,                      /* Size of buffer pData in bytes */\n  int *piCookie,                  /* Configuration cookie value */\n  Fts5Structure **ppOut           /* OUT: Deserialized object */\n){\n  int rc = SQLITE_OK;\n  int i = 0;\n  int iLvl;\n  int nLevel = 0;\n  int nSegment = 0;\n  int nByte;                      /* Bytes of space to allocate at pRet */\n  Fts5Structure *pRet = 0;        /* Structure object to return */\n\n  /* Grab the cookie value */\n  if( piCookie ) *piCookie = sqlite3Fts5Get32(pData);\n  i = 4;\n\n  /* Read the total number of levels and segments from the start of the\n  ** structure record.  */\n  i += fts5GetVarint32(&pData[i], nLevel);\n  i += fts5GetVarint32(&pData[i], nSegment);\n  nByte = (\n      sizeof(Fts5Structure) +                    /* Main structure */\n      sizeof(Fts5StructureLevel) * (nLevel-1)    /* aLevel[] array */\n  );\n  pRet = (Fts5Structure*)sqlite3Fts5MallocZero(&rc, nByte);\n\n  if( pRet ){\n    pRet->nRef = 1;\n    pRet->nLevel = nLevel;\n    pRet->nSegment = nSegment;\n    i += sqlite3Fts5GetVarint(&pData[i], &pRet->nWriteCounter);\n\n    for(iLvl=0; rc==SQLITE_OK && iLvl<nLevel; iLvl++){\n      Fts5StructureLevel *pLvl = &pRet->aLevel[iLvl];\n      int nTotal = 0;\n      int iSeg;\n\n      if( i>=nData ){\n        rc = FTS5_CORRUPT;\n      }else{\n        i += fts5GetVarint32(&pData[i], pLvl->nMerge);\n        i += fts5GetVarint32(&pData[i], nTotal);\n        assert( nTotal>=pLvl->nMerge );\n        pLvl->aSeg = (Fts5StructureSegment*)sqlite3Fts5MallocZero(&rc, \n            nTotal * sizeof(Fts5StructureSegment)\n        );\n      }\n\n      if( rc==SQLITE_OK ){\n        pLvl->nSeg = nTotal;\n        for(iSeg=0; iSeg<nTotal; iSeg++){\n          if( i>=nData ){\n            rc = FTS5_CORRUPT;\n            break;\n          }\n          i += fts5GetVarint32(&pData[i], pLvl->aSeg[iSeg].iSegid);\n          i += fts5GetVarint32(&pData[i], pLvl->aSeg[iSeg].pgnoFirst);\n          i += fts5GetVarint32(&pData[i], pLvl->aSeg[iSeg].pgnoLast);\n        }\n      }\n    }\n    if( rc!=SQLITE_OK ){\n      fts5StructureRelease(pRet);\n      pRet = 0;\n    }\n  }\n\n  *ppOut = pRet;\n  return rc;\n}\n\n/*\n**\n*/\nstatic void fts5StructureAddLevel(int *pRc, Fts5Structure **ppStruct){\n  if( *pRc==SQLITE_OK ){\n    Fts5Structure *pStruct = *ppStruct;\n    int nLevel = pStruct->nLevel;\n    int nByte = (\n        sizeof(Fts5Structure) +                  /* Main structure */\n        sizeof(Fts5StructureLevel) * (nLevel+1)  /* aLevel[] array */\n    );\n\n    pStruct = sqlite3_realloc(pStruct, nByte);\n    if( pStruct ){\n      memset(&pStruct->aLevel[nLevel], 0, sizeof(Fts5StructureLevel));\n      pStruct->nLevel++;\n      *ppStruct = pStruct;\n    }else{\n      *pRc = SQLITE_NOMEM;\n    }\n  }\n}\n\n/*\n** Extend level iLvl so that there is room for at least nExtra more\n** segments.\n*/\nstatic void fts5StructureExtendLevel(\n  int *pRc, \n  Fts5Structure *pStruct, \n  int iLvl, \n  int nExtra, \n  int bInsert\n){\n  if( *pRc==SQLITE_OK ){\n    Fts5StructureLevel *pLvl = &pStruct->aLevel[iLvl];\n    Fts5StructureSegment *aNew;\n    int nByte;\n\n    nByte = (pLvl->nSeg + nExtra) * sizeof(Fts5StructureSegment);\n    aNew = sqlite3_realloc(pLvl->aSeg, nByte);\n    if( aNew ){\n      if( bInsert==0 ){\n        memset(&aNew[pLvl->nSeg], 0, sizeof(Fts5StructureSegment) * nExtra);\n      }else{\n        int nMove = pLvl->nSeg * sizeof(Fts5StructureSegment);\n        memmove(&aNew[nExtra], aNew, nMove);\n        memset(aNew, 0, sizeof(Fts5StructureSegment) * nExtra);\n      }\n      pLvl->aSeg = aNew;\n    }else{\n      *pRc = SQLITE_NOMEM;\n    }\n  }\n}\n\nstatic Fts5Structure *fts5StructureReadUncached(Fts5Index *p){\n  Fts5Structure *pRet = 0;\n  Fts5Config *pConfig = p->pConfig;\n  int iCookie;                    /* Configuration cookie */\n  Fts5Data *pData;\n\n  pData = fts5DataRead(p, FTS5_STRUCTURE_ROWID);\n  if( p->rc==SQLITE_OK ){\n    /* TODO: Do we need this if the leaf-index is appended? Probably... */\n    memset(&pData->p[pData->nn], 0, FTS5_DATA_PADDING);\n    p->rc = fts5StructureDecode(pData->p, pData->nn, &iCookie, &pRet);\n    if( p->rc==SQLITE_OK && pConfig->iCookie!=iCookie ){\n      p->rc = sqlite3Fts5ConfigLoad(pConfig, iCookie);\n    }\n    fts5DataRelease(pData);\n    if( p->rc!=SQLITE_OK ){\n      fts5StructureRelease(pRet);\n      pRet = 0;\n    }\n  }\n\n  return pRet;\n}\n\nstatic i64 fts5IndexDataVersion(Fts5Index *p){\n  i64 iVersion = 0;\n\n  if( p->rc==SQLITE_OK ){\n    if( p->pDataVersion==0 ){\n      p->rc = fts5IndexPrepareStmt(p, &p->pDataVersion, \n          sqlite3_mprintf(\"PRAGMA %Q.data_version\", p->pConfig->zDb)\n          );\n      if( p->rc ) return 0;\n    }\n\n    if( SQLITE_ROW==sqlite3_step(p->pDataVersion) ){\n      iVersion = sqlite3_column_int64(p->pDataVersion, 0);\n    }\n    p->rc = sqlite3_reset(p->pDataVersion);\n  }\n\n  return iVersion;\n}\n\n/*\n** Read, deserialize and return the structure record.\n**\n** The Fts5Structure.aLevel[] and each Fts5StructureLevel.aSeg[] array\n** are over-allocated as described for function fts5StructureDecode() \n** above.\n**\n** If an error occurs, NULL is returned and an error code left in the\n** Fts5Index handle. If an error has already occurred when this function\n** is called, it is a no-op.\n*/\nstatic Fts5Structure *fts5StructureRead(Fts5Index *p){\n\n  if( p->pStruct==0 ){\n    p->iStructVersion = fts5IndexDataVersion(p);\n    if( p->rc==SQLITE_OK ){\n      p->pStruct = fts5StructureReadUncached(p);\n    }\n  }\n\n#if 0\n  else{\n    Fts5Structure *pTest = fts5StructureReadUncached(p);\n    if( pTest ){\n      int i, j;\n      assert_nc( p->pStruct->nSegment==pTest->nSegment );\n      assert_nc( p->pStruct->nLevel==pTest->nLevel );\n      for(i=0; i<pTest->nLevel; i++){\n        assert_nc( p->pStruct->aLevel[i].nMerge==pTest->aLevel[i].nMerge );\n        assert_nc( p->pStruct->aLevel[i].nSeg==pTest->aLevel[i].nSeg );\n        for(j=0; j<pTest->aLevel[i].nSeg; j++){\n          Fts5StructureSegment *p1 = &pTest->aLevel[i].aSeg[j];\n          Fts5StructureSegment *p2 = &p->pStruct->aLevel[i].aSeg[j];\n          assert_nc( p1->iSegid==p2->iSegid );\n          assert_nc( p1->pgnoFirst==p2->pgnoFirst );\n          assert_nc( p1->pgnoLast==p2->pgnoLast );\n        }\n      }\n      fts5StructureRelease(pTest);\n    }\n  }\n#endif\n\n  if( p->rc!=SQLITE_OK ) return 0;\n  assert( p->iStructVersion!=0 );\n  assert( p->pStruct!=0 );\n  fts5StructureRef(p->pStruct);\n  return p->pStruct;\n}\n\nstatic void fts5StructureInvalidate(Fts5Index *p){\n  if( p->pStruct ){\n    fts5StructureRelease(p->pStruct);\n    p->pStruct = 0;\n  }\n}\n\n/*\n** Return the total number of segments in index structure pStruct. This\n** function is only ever used as part of assert() conditions.\n*/\n#ifdef SQLITE_DEBUG\nstatic int fts5StructureCountSegments(Fts5Structure *pStruct){\n  int nSegment = 0;               /* Total number of segments */\n  if( pStruct ){\n    int iLvl;                     /* Used to iterate through levels */\n    for(iLvl=0; iLvl<pStruct->nLevel; iLvl++){\n      nSegment += pStruct->aLevel[iLvl].nSeg;\n    }\n  }\n\n  return nSegment;\n}\n#endif\n\n#define fts5BufferSafeAppendBlob(pBuf, pBlob, nBlob) {     \\\n  assert( (pBuf)->nSpace>=((pBuf)->n+nBlob) );             \\\n  memcpy(&(pBuf)->p[(pBuf)->n], pBlob, nBlob);             \\\n  (pBuf)->n += nBlob;                                      \\\n}\n\n#define fts5BufferSafeAppendVarint(pBuf, iVal) {                \\\n  (pBuf)->n += sqlite3Fts5PutVarint(&(pBuf)->p[(pBuf)->n], (iVal));  \\\n  assert( (pBuf)->nSpace>=(pBuf)->n );                          \\\n}\n\n\n/*\n** Serialize and store the \"structure\" record.\n**\n** If an error occurs, leave an error code in the Fts5Index object. If an\n** error has already occurred, this function is a no-op.\n*/\nstatic void fts5StructureWrite(Fts5Index *p, Fts5Structure *pStruct){\n  if( p->rc==SQLITE_OK ){\n    Fts5Buffer buf;               /* Buffer to serialize record into */\n    int iLvl;                     /* Used to iterate through levels */\n    int iCookie;                  /* Cookie value to store */\n\n    assert( pStruct->nSegment==fts5StructureCountSegments(pStruct) );\n    memset(&buf, 0, sizeof(Fts5Buffer));\n\n    /* Append the current configuration cookie */\n    iCookie = p->pConfig->iCookie;\n    if( iCookie<0 ) iCookie = 0;\n\n    if( 0==sqlite3Fts5BufferSize(&p->rc, &buf, 4+9+9+9) ){\n      sqlite3Fts5Put32(buf.p, iCookie);\n      buf.n = 4;\n      fts5BufferSafeAppendVarint(&buf, pStruct->nLevel);\n      fts5BufferSafeAppendVarint(&buf, pStruct->nSegment);\n      fts5BufferSafeAppendVarint(&buf, (i64)pStruct->nWriteCounter);\n    }\n\n    for(iLvl=0; iLvl<pStruct->nLevel; iLvl++){\n      int iSeg;                     /* Used to iterate through segments */\n      Fts5StructureLevel *pLvl = &pStruct->aLevel[iLvl];\n      fts5BufferAppendVarint(&p->rc, &buf, pLvl->nMerge);\n      fts5BufferAppendVarint(&p->rc, &buf, pLvl->nSeg);\n      assert( pLvl->nMerge<=pLvl->nSeg );\n\n      for(iSeg=0; iSeg<pLvl->nSeg; iSeg++){\n        fts5BufferAppendVarint(&p->rc, &buf, pLvl->aSeg[iSeg].iSegid);\n        fts5BufferAppendVarint(&p->rc, &buf, pLvl->aSeg[iSeg].pgnoFirst);\n        fts5BufferAppendVarint(&p->rc, &buf, pLvl->aSeg[iSeg].pgnoLast);\n      }\n    }\n\n    fts5DataWrite(p, FTS5_STRUCTURE_ROWID, buf.p, buf.n);\n    fts5BufferFree(&buf);\n  }\n}\n\n#if 0\nstatic void fts5DebugStructure(int*,Fts5Buffer*,Fts5Structure*);\nstatic void fts5PrintStructure(const char *zCaption, Fts5Structure *pStruct){\n  int rc = SQLITE_OK;\n  Fts5Buffer buf;\n  memset(&buf, 0, sizeof(buf));\n  fts5DebugStructure(&rc, &buf, pStruct);\n  fprintf(stdout, \"%s: %s\\n\", zCaption, buf.p);\n  fflush(stdout);\n  fts5BufferFree(&buf);\n}\n#else\n# define fts5PrintStructure(x,y)\n#endif\n\nstatic int fts5SegmentSize(Fts5StructureSegment *pSeg){\n  return 1 + pSeg->pgnoLast - pSeg->pgnoFirst;\n}\n\n/*\n** Return a copy of index structure pStruct. Except, promote as many \n** segments as possible to level iPromote. If an OOM occurs, NULL is \n** returned.\n*/\nstatic void fts5StructurePromoteTo(\n  Fts5Index *p,\n  int iPromote,\n  int szPromote,\n  Fts5Structure *pStruct\n){\n  int il, is;\n  Fts5StructureLevel *pOut = &pStruct->aLevel[iPromote];\n\n  if( pOut->nMerge==0 ){\n    for(il=iPromote+1; il<pStruct->nLevel; il++){\n      Fts5StructureLevel *pLvl = &pStruct->aLevel[il];\n      if( pLvl->nMerge ) return;\n      for(is=pLvl->nSeg-1; is>=0; is--){\n        int sz = fts5SegmentSize(&pLvl->aSeg[is]);\n        if( sz>szPromote ) return;\n        fts5StructureExtendLevel(&p->rc, pStruct, iPromote, 1, 1);\n        if( p->rc ) return;\n        memcpy(pOut->aSeg, &pLvl->aSeg[is], sizeof(Fts5StructureSegment));\n        pOut->nSeg++;\n        pLvl->nSeg--;\n      }\n    }\n  }\n}\n\n/*\n** A new segment has just been written to level iLvl of index structure\n** pStruct. This function determines if any segments should be promoted\n** as a result. Segments are promoted in two scenarios:\n**\n**   a) If the segment just written is smaller than one or more segments\n**      within the previous populated level, it is promoted to the previous\n**      populated level.\n**\n**   b) If the segment just written is larger than the newest segment on\n**      the next populated level, then that segment, and any other adjacent\n**      segments that are also smaller than the one just written, are \n**      promoted. \n**\n** If one or more segments are promoted, the structure object is updated\n** to reflect this.\n*/\nstatic void fts5StructurePromote(\n  Fts5Index *p,                   /* FTS5 backend object */\n  int iLvl,                       /* Index level just updated */\n  Fts5Structure *pStruct          /* Index structure */\n){\n  if( p->rc==SQLITE_OK ){\n    int iTst;\n    int iPromote = -1;\n    int szPromote = 0;            /* Promote anything this size or smaller */\n    Fts5StructureSegment *pSeg;   /* Segment just written */\n    int szSeg;                    /* Size of segment just written */\n    int nSeg = pStruct->aLevel[iLvl].nSeg;\n\n    if( nSeg==0 ) return;\n    pSeg = &pStruct->aLevel[iLvl].aSeg[pStruct->aLevel[iLvl].nSeg-1];\n    szSeg = (1 + pSeg->pgnoLast - pSeg->pgnoFirst);\n\n    /* Check for condition (a) */\n    for(iTst=iLvl-1; iTst>=0 && pStruct->aLevel[iTst].nSeg==0; iTst--);\n    if( iTst>=0 ){\n      int i;\n      int szMax = 0;\n      Fts5StructureLevel *pTst = &pStruct->aLevel[iTst];\n      assert( pTst->nMerge==0 );\n      for(i=0; i<pTst->nSeg; i++){\n        int sz = pTst->aSeg[i].pgnoLast - pTst->aSeg[i].pgnoFirst + 1;\n        if( sz>szMax ) szMax = sz;\n      }\n      if( szMax>=szSeg ){\n        /* Condition (a) is true. Promote the newest segment on level \n        ** iLvl to level iTst.  */\n        iPromote = iTst;\n        szPromote = szMax;\n      }\n    }\n\n    /* If condition (a) is not met, assume (b) is true. StructurePromoteTo()\n    ** is a no-op if it is not.  */\n    if( iPromote<0 ){\n      iPromote = iLvl;\n      szPromote = szSeg;\n    }\n    fts5StructurePromoteTo(p, iPromote, szPromote, pStruct);\n  }\n}\n\n\n/*\n** Advance the iterator passed as the only argument. If the end of the \n** doclist-index page is reached, return non-zero.\n*/\nstatic int fts5DlidxLvlNext(Fts5DlidxLvl *pLvl){\n  Fts5Data *pData = pLvl->pData;\n\n  if( pLvl->iOff==0 ){\n    assert( pLvl->bEof==0 );\n    pLvl->iOff = 1;\n    pLvl->iOff += fts5GetVarint32(&pData->p[1], pLvl->iLeafPgno);\n    pLvl->iOff += fts5GetVarint(&pData->p[pLvl->iOff], (u64*)&pLvl->iRowid);\n    pLvl->iFirstOff = pLvl->iOff;\n  }else{\n    int iOff;\n    for(iOff=pLvl->iOff; iOff<pData->nn; iOff++){\n      if( pData->p[iOff] ) break; \n    }\n\n    if( iOff<pData->nn ){\n      i64 iVal;\n      pLvl->iLeafPgno += (iOff - pLvl->iOff) + 1;\n      iOff += fts5GetVarint(&pData->p[iOff], (u64*)&iVal);\n      pLvl->iRowid += iVal;\n      pLvl->iOff = iOff;\n    }else{\n      pLvl->bEof = 1;\n    }\n  }\n\n  return pLvl->bEof;\n}\n\n/*\n** Advance the iterator passed as the only argument.\n*/\nstatic int fts5DlidxIterNextR(Fts5Index *p, Fts5DlidxIter *pIter, int iLvl){\n  Fts5DlidxLvl *pLvl = &pIter->aLvl[iLvl];\n\n  assert( iLvl<pIter->nLvl );\n  if( fts5DlidxLvlNext(pLvl) ){\n    if( (iLvl+1) < pIter->nLvl ){\n      fts5DlidxIterNextR(p, pIter, iLvl+1);\n      if( pLvl[1].bEof==0 ){\n        fts5DataRelease(pLvl->pData);\n        memset(pLvl, 0, sizeof(Fts5DlidxLvl));\n        pLvl->pData = fts5DataRead(p, \n            FTS5_DLIDX_ROWID(pIter->iSegid, iLvl, pLvl[1].iLeafPgno)\n        );\n        if( pLvl->pData ) fts5DlidxLvlNext(pLvl);\n      }\n    }\n  }\n\n  return pIter->aLvl[0].bEof;\n}\nstatic int fts5DlidxIterNext(Fts5Index *p, Fts5DlidxIter *pIter){\n  return fts5DlidxIterNextR(p, pIter, 0);\n}\n\n/*\n** The iterator passed as the first argument has the following fields set\n** as follows. This function sets up the rest of the iterator so that it\n** points to the first rowid in the doclist-index.\n**\n**   pData:\n**     pointer to doclist-index record, \n**\n** When this function is called pIter->iLeafPgno is the page number the\n** doclist is associated with (the one featuring the term).\n*/\nstatic int fts5DlidxIterFirst(Fts5DlidxIter *pIter){\n  int i;\n  for(i=0; i<pIter->nLvl; i++){\n    fts5DlidxLvlNext(&pIter->aLvl[i]);\n  }\n  return pIter->aLvl[0].bEof;\n}\n\n\nstatic int fts5DlidxIterEof(Fts5Index *p, Fts5DlidxIter *pIter){\n  return p->rc!=SQLITE_OK || pIter->aLvl[0].bEof;\n}\n\nstatic void fts5DlidxIterLast(Fts5Index *p, Fts5DlidxIter *pIter){\n  int i;\n\n  /* Advance each level to the last entry on the last page */\n  for(i=pIter->nLvl-1; p->rc==SQLITE_OK && i>=0; i--){\n    Fts5DlidxLvl *pLvl = &pIter->aLvl[i];\n    while( fts5DlidxLvlNext(pLvl)==0 );\n    pLvl->bEof = 0;\n\n    if( i>0 ){\n      Fts5DlidxLvl *pChild = &pLvl[-1];\n      fts5DataRelease(pChild->pData);\n      memset(pChild, 0, sizeof(Fts5DlidxLvl));\n      pChild->pData = fts5DataRead(p, \n          FTS5_DLIDX_ROWID(pIter->iSegid, i-1, pLvl->iLeafPgno)\n      );\n    }\n  }\n}\n\n/*\n** Move the iterator passed as the only argument to the previous entry.\n*/\nstatic int fts5DlidxLvlPrev(Fts5DlidxLvl *pLvl){\n  int iOff = pLvl->iOff;\n\n  assert( pLvl->bEof==0 );\n  if( iOff<=pLvl->iFirstOff ){\n    pLvl->bEof = 1;\n  }else{\n    u8 *a = pLvl->pData->p;\n    i64 iVal;\n    int iLimit;\n    int ii;\n    int nZero = 0;\n\n    /* Currently iOff points to the first byte of a varint. This block \n    ** decrements iOff until it points to the first byte of the previous \n    ** varint. Taking care not to read any memory locations that occur\n    ** before the buffer in memory.  */\n    iLimit = (iOff>9 ? iOff-9 : 0);\n    for(iOff--; iOff>iLimit; iOff--){\n      if( (a[iOff-1] & 0x80)==0 ) break;\n    }\n\n    fts5GetVarint(&a[iOff], (u64*)&iVal);\n    pLvl->iRowid -= iVal;\n    pLvl->iLeafPgno--;\n\n    /* Skip backwards past any 0x00 varints. */\n    for(ii=iOff-1; ii>=pLvl->iFirstOff && a[ii]==0x00; ii--){\n      nZero++;\n    }\n    if( ii>=pLvl->iFirstOff && (a[ii] & 0x80) ){\n      /* The byte immediately before the last 0x00 byte has the 0x80 bit\n      ** set. So the last 0x00 is only a varint 0 if there are 8 more 0x80\n      ** bytes before a[ii]. */\n      int bZero = 0;              /* True if last 0x00 counts */\n      if( (ii-8)>=pLvl->iFirstOff ){\n        int j;\n        for(j=1; j<=8 && (a[ii-j] & 0x80); j++);\n        bZero = (j>8);\n      }\n      if( bZero==0 ) nZero--;\n    }\n    pLvl->iLeafPgno -= nZero;\n    pLvl->iOff = iOff - nZero;\n  }\n\n  return pLvl->bEof;\n}\n\nstatic int fts5DlidxIterPrevR(Fts5Index *p, Fts5DlidxIter *pIter, int iLvl){\n  Fts5DlidxLvl *pLvl = &pIter->aLvl[iLvl];\n\n  assert( iLvl<pIter->nLvl );\n  if( fts5DlidxLvlPrev(pLvl) ){\n    if( (iLvl+1) < pIter->nLvl ){\n      fts5DlidxIterPrevR(p, pIter, iLvl+1);\n      if( pLvl[1].bEof==0 ){\n        fts5DataRelease(pLvl->pData);\n        memset(pLvl, 0, sizeof(Fts5DlidxLvl));\n        pLvl->pData = fts5DataRead(p, \n            FTS5_DLIDX_ROWID(pIter->iSegid, iLvl, pLvl[1].iLeafPgno)\n        );\n        if( pLvl->pData ){\n          while( fts5DlidxLvlNext(pLvl)==0 );\n          pLvl->bEof = 0;\n        }\n      }\n    }\n  }\n\n  return pIter->aLvl[0].bEof;\n}\nstatic int fts5DlidxIterPrev(Fts5Index *p, Fts5DlidxIter *pIter){\n  return fts5DlidxIterPrevR(p, pIter, 0);\n}\n\n/*\n** Free a doclist-index iterator object allocated by fts5DlidxIterInit().\n*/\nstatic void fts5DlidxIterFree(Fts5DlidxIter *pIter){\n  if( pIter ){\n    int i;\n    for(i=0; i<pIter->nLvl; i++){\n      fts5DataRelease(pIter->aLvl[i].pData);\n    }\n    sqlite3_free(pIter);\n  }\n}\n\nstatic Fts5DlidxIter *fts5DlidxIterInit(\n  Fts5Index *p,                   /* Fts5 Backend to iterate within */\n  int bRev,                       /* True for ORDER BY ASC */\n  int iSegid,                     /* Segment id */\n  int iLeafPg                     /* Leaf page number to load dlidx for */\n){\n  Fts5DlidxIter *pIter = 0;\n  int i;\n  int bDone = 0;\n\n  for(i=0; p->rc==SQLITE_OK && bDone==0; i++){\n    int nByte = sizeof(Fts5DlidxIter) + i * sizeof(Fts5DlidxLvl);\n    Fts5DlidxIter *pNew;\n\n    pNew = (Fts5DlidxIter*)sqlite3_realloc(pIter, nByte);\n    if( pNew==0 ){\n      p->rc = SQLITE_NOMEM;\n    }else{\n      i64 iRowid = FTS5_DLIDX_ROWID(iSegid, i, iLeafPg);\n      Fts5DlidxLvl *pLvl = &pNew->aLvl[i];\n      pIter = pNew;\n      memset(pLvl, 0, sizeof(Fts5DlidxLvl));\n      pLvl->pData = fts5DataRead(p, iRowid);\n      if( pLvl->pData && (pLvl->pData->p[0] & 0x0001)==0 ){\n        bDone = 1;\n      }\n      pIter->nLvl = i+1;\n    }\n  }\n\n  if( p->rc==SQLITE_OK ){\n    pIter->iSegid = iSegid;\n    if( bRev==0 ){\n      fts5DlidxIterFirst(pIter);\n    }else{\n      fts5DlidxIterLast(p, pIter);\n    }\n  }\n\n  if( p->rc!=SQLITE_OK ){\n    fts5DlidxIterFree(pIter);\n    pIter = 0;\n  }\n\n  return pIter;\n}\n\nstatic i64 fts5DlidxIterRowid(Fts5DlidxIter *pIter){\n  return pIter->aLvl[0].iRowid;\n}\nstatic int fts5DlidxIterPgno(Fts5DlidxIter *pIter){\n  return pIter->aLvl[0].iLeafPgno;\n}\n\n/*\n** Load the next leaf page into the segment iterator.\n*/\nstatic void fts5SegIterNextPage(\n  Fts5Index *p,                   /* FTS5 backend object */\n  Fts5SegIter *pIter              /* Iterator to advance to next page */\n){\n  Fts5Data *pLeaf;\n  Fts5StructureSegment *pSeg = pIter->pSeg;\n  fts5DataRelease(pIter->pLeaf);\n  pIter->iLeafPgno++;\n  if( pIter->pNextLeaf ){\n    pIter->pLeaf = pIter->pNextLeaf;\n    pIter->pNextLeaf = 0;\n  }else if( pIter->iLeafPgno<=pSeg->pgnoLast ){\n    pIter->pLeaf = fts5LeafRead(p, \n        FTS5_SEGMENT_ROWID(pSeg->iSegid, pIter->iLeafPgno)\n    );\n  }else{\n    pIter->pLeaf = 0;\n  }\n  pLeaf = pIter->pLeaf;\n\n  if( pLeaf ){\n    pIter->iPgidxOff = pLeaf->szLeaf;\n    if( fts5LeafIsTermless(pLeaf) ){\n      pIter->iEndofDoclist = pLeaf->nn+1;\n    }else{\n      pIter->iPgidxOff += fts5GetVarint32(&pLeaf->p[pIter->iPgidxOff],\n          pIter->iEndofDoclist\n      );\n    }\n  }\n}\n\n/*\n** Argument p points to a buffer containing a varint to be interpreted as a\n** position list size field. Read the varint and return the number of bytes\n** read. Before returning, set *pnSz to the number of bytes in the position\n** list, and *pbDel to true if the delete flag is set, or false otherwise.\n*/\nstatic int fts5GetPoslistSize(const u8 *p, int *pnSz, int *pbDel){\n  int nSz;\n  int n = 0;\n  fts5FastGetVarint32(p, n, nSz);\n  assert_nc( nSz>=0 );\n  *pnSz = nSz/2;\n  *pbDel = nSz & 0x0001;\n  return n;\n}\n\n/*\n** Fts5SegIter.iLeafOffset currently points to the first byte of a\n** position-list size field. Read the value of the field and store it\n** in the following variables:\n**\n**   Fts5SegIter.nPos\n**   Fts5SegIter.bDel\n**\n** Leave Fts5SegIter.iLeafOffset pointing to the first byte of the \n** position list content (if any).\n*/\nstatic void fts5SegIterLoadNPos(Fts5Index *p, Fts5SegIter *pIter){\n  if( p->rc==SQLITE_OK ){\n    int iOff = pIter->iLeafOffset;  /* Offset to read at */\n    ASSERT_SZLEAF_OK(pIter->pLeaf);\n    if( p->pConfig->eDetail==FTS5_DETAIL_NONE ){\n      int iEod = MIN(pIter->iEndofDoclist, pIter->pLeaf->szLeaf);\n      pIter->bDel = 0;\n      pIter->nPos = 1;\n      if( iOff<iEod && pIter->pLeaf->p[iOff]==0 ){\n        pIter->bDel = 1;\n        iOff++;\n        if( iOff<iEod && pIter->pLeaf->p[iOff]==0 ){\n          pIter->nPos = 1;\n          iOff++;\n        }else{\n          pIter->nPos = 0;\n        }\n      }\n    }else{\n      int nSz;\n      fts5FastGetVarint32(pIter->pLeaf->p, iOff, nSz);\n      pIter->bDel = (nSz & 0x0001);\n      pIter->nPos = nSz>>1;\n      assert_nc( pIter->nPos>=0 );\n    }\n    pIter->iLeafOffset = iOff;\n  }\n}\n\nstatic void fts5SegIterLoadRowid(Fts5Index *p, Fts5SegIter *pIter){\n  u8 *a = pIter->pLeaf->p;        /* Buffer to read data from */\n  int iOff = pIter->iLeafOffset;\n\n  ASSERT_SZLEAF_OK(pIter->pLeaf);\n  if( iOff>=pIter->pLeaf->szLeaf ){\n    fts5SegIterNextPage(p, pIter);\n    if( pIter->pLeaf==0 ){\n      if( p->rc==SQLITE_OK ) p->rc = FTS5_CORRUPT;\n      return;\n    }\n    iOff = 4;\n    a = pIter->pLeaf->p;\n  }\n  iOff += sqlite3Fts5GetVarint(&a[iOff], (u64*)&pIter->iRowid);\n  pIter->iLeafOffset = iOff;\n}\n\n/*\n** Fts5SegIter.iLeafOffset currently points to the first byte of the \n** \"nSuffix\" field of a term. Function parameter nKeep contains the value\n** of the \"nPrefix\" field (if there was one - it is passed 0 if this is\n** the first term in the segment).\n**\n** This function populates:\n**\n**   Fts5SegIter.term\n**   Fts5SegIter.rowid\n**\n** accordingly and leaves (Fts5SegIter.iLeafOffset) set to the content of\n** the first position list. The position list belonging to document \n** (Fts5SegIter.iRowid).\n*/\nstatic void fts5SegIterLoadTerm(Fts5Index *p, Fts5SegIter *pIter, int nKeep){\n  u8 *a = pIter->pLeaf->p;        /* Buffer to read data from */\n  int iOff = pIter->iLeafOffset;  /* Offset to read at */\n  int nNew;                       /* Bytes of new data */\n\n  iOff += fts5GetVarint32(&a[iOff], nNew);\n  if( iOff+nNew>pIter->pLeaf->nn ){\n    p->rc = FTS5_CORRUPT;\n    return;\n  }\n  pIter->term.n = nKeep;\n  fts5BufferAppendBlob(&p->rc, &pIter->term, nNew, &a[iOff]);\n  iOff += nNew;\n  pIter->iTermLeafOffset = iOff;\n  pIter->iTermLeafPgno = pIter->iLeafPgno;\n  pIter->iLeafOffset = iOff;\n\n  if( pIter->iPgidxOff>=pIter->pLeaf->nn ){\n    pIter->iEndofDoclist = pIter->pLeaf->nn+1;\n  }else{\n    int nExtra;\n    pIter->iPgidxOff += fts5GetVarint32(&a[pIter->iPgidxOff], nExtra);\n    pIter->iEndofDoclist += nExtra;\n  }\n\n  fts5SegIterLoadRowid(p, pIter);\n}\n\nstatic void fts5SegIterNext(Fts5Index*, Fts5SegIter*, int*);\nstatic void fts5SegIterNext_Reverse(Fts5Index*, Fts5SegIter*, int*);\nstatic void fts5SegIterNext_None(Fts5Index*, Fts5SegIter*, int*);\n\nstatic void fts5SegIterSetNext(Fts5Index *p, Fts5SegIter *pIter){\n  if( pIter->flags & FTS5_SEGITER_REVERSE ){\n    pIter->xNext = fts5SegIterNext_Reverse;\n  }else if( p->pConfig->eDetail==FTS5_DETAIL_NONE ){\n    pIter->xNext = fts5SegIterNext_None;\n  }else{\n    pIter->xNext = fts5SegIterNext;\n  }\n}\n\n/*\n** Initialize the iterator object pIter to iterate through the entries in\n** segment pSeg. The iterator is left pointing to the first entry when \n** this function returns.\n**\n** If an error occurs, Fts5Index.rc is set to an appropriate error code. If \n** an error has already occurred when this function is called, it is a no-op.\n*/\nstatic void fts5SegIterInit(\n  Fts5Index *p,                   /* FTS index object */\n  Fts5StructureSegment *pSeg,     /* Description of segment */\n  Fts5SegIter *pIter              /* Object to populate */\n){\n  if( pSeg->pgnoFirst==0 ){\n    /* This happens if the segment is being used as an input to an incremental\n    ** merge and all data has already been \"trimmed\". See function\n    ** fts5TrimSegments() for details. In this case leave the iterator empty.\n    ** The caller will see the (pIter->pLeaf==0) and assume the iterator is\n    ** at EOF already. */\n    assert( pIter->pLeaf==0 );\n    return;\n  }\n\n  if( p->rc==SQLITE_OK ){\n    memset(pIter, 0, sizeof(*pIter));\n    fts5SegIterSetNext(p, pIter);\n    pIter->pSeg = pSeg;\n    pIter->iLeafPgno = pSeg->pgnoFirst-1;\n    fts5SegIterNextPage(p, pIter);\n  }\n\n  if( p->rc==SQLITE_OK ){\n    pIter->iLeafOffset = 4;\n    assert_nc( pIter->pLeaf->nn>4 );\n    assert( fts5LeafFirstTermOff(pIter->pLeaf)==4 );\n    pIter->iPgidxOff = pIter->pLeaf->szLeaf+1;\n    fts5SegIterLoadTerm(p, pIter, 0);\n    fts5SegIterLoadNPos(p, pIter);\n  }\n}\n\n/*\n** This function is only ever called on iterators created by calls to\n** Fts5IndexQuery() with the FTS5INDEX_QUERY_DESC flag set.\n**\n** The iterator is in an unusual state when this function is called: the\n** Fts5SegIter.iLeafOffset variable is set to the offset of the start of\n** the position-list size field for the first relevant rowid on the page.\n** Fts5SegIter.rowid is set, but nPos and bDel are not.\n**\n** This function advances the iterator so that it points to the last \n** relevant rowid on the page and, if necessary, initializes the \n** aRowidOffset[] and iRowidOffset variables. At this point the iterator\n** is in its regular state - Fts5SegIter.iLeafOffset points to the first\n** byte of the position list content associated with said rowid.\n*/\nstatic void fts5SegIterReverseInitPage(Fts5Index *p, Fts5SegIter *pIter){\n  int eDetail = p->pConfig->eDetail;\n  int n = pIter->pLeaf->szLeaf;\n  int i = pIter->iLeafOffset;\n  u8 *a = pIter->pLeaf->p;\n  int iRowidOffset = 0;\n\n  if( n>pIter->iEndofDoclist ){\n    n = pIter->iEndofDoclist;\n  }\n\n  ASSERT_SZLEAF_OK(pIter->pLeaf);\n  while( 1 ){\n    i64 iDelta = 0;\n\n    if( eDetail==FTS5_DETAIL_NONE ){\n      /* todo */\n      if( i<n && a[i]==0 ){\n        i++;\n        if( i<n && a[i]==0 ) i++;\n      }\n    }else{\n      int nPos;\n      int bDummy;\n      i += fts5GetPoslistSize(&a[i], &nPos, &bDummy);\n      i += nPos;\n    }\n    if( i>=n ) break;\n    i += fts5GetVarint(&a[i], (u64*)&iDelta);\n    pIter->iRowid += iDelta;\n\n    /* If necessary, grow the pIter->aRowidOffset[] array. */\n    if( iRowidOffset>=pIter->nRowidOffset ){\n      int nNew = pIter->nRowidOffset + 8;\n      int *aNew = (int*)sqlite3_realloc(pIter->aRowidOffset, nNew*sizeof(int));\n      if( aNew==0 ){\n        p->rc = SQLITE_NOMEM;\n        break;\n      }\n      pIter->aRowidOffset = aNew;\n      pIter->nRowidOffset = nNew;\n    }\n\n    pIter->aRowidOffset[iRowidOffset++] = pIter->iLeafOffset;\n    pIter->iLeafOffset = i;\n  }\n  pIter->iRowidOffset = iRowidOffset;\n  fts5SegIterLoadNPos(p, pIter);\n}\n\n/*\n**\n*/\nstatic void fts5SegIterReverseNewPage(Fts5Index *p, Fts5SegIter *pIter){\n  assert( pIter->flags & FTS5_SEGITER_REVERSE );\n  assert( pIter->flags & FTS5_SEGITER_ONETERM );\n\n  fts5DataRelease(pIter->pLeaf);\n  pIter->pLeaf = 0;\n  while( p->rc==SQLITE_OK && pIter->iLeafPgno>pIter->iTermLeafPgno ){\n    Fts5Data *pNew;\n    pIter->iLeafPgno--;\n    pNew = fts5DataRead(p, FTS5_SEGMENT_ROWID(\n          pIter->pSeg->iSegid, pIter->iLeafPgno\n    ));\n    if( pNew ){\n      /* iTermLeafOffset may be equal to szLeaf if the term is the last\n      ** thing on the page - i.e. the first rowid is on the following page.\n      ** In this case leave pIter->pLeaf==0, this iterator is at EOF. */\n      if( pIter->iLeafPgno==pIter->iTermLeafPgno ){\n        assert( pIter->pLeaf==0 );\n        if( pIter->iTermLeafOffset<pNew->szLeaf ){\n          pIter->pLeaf = pNew;\n          pIter->iLeafOffset = pIter->iTermLeafOffset;\n        }\n      }else{\n        int iRowidOff;\n        iRowidOff = fts5LeafFirstRowidOff(pNew);\n        if( iRowidOff ){\n          pIter->pLeaf = pNew;\n          pIter->iLeafOffset = iRowidOff;\n        }\n      }\n\n      if( pIter->pLeaf ){\n        u8 *a = &pIter->pLeaf->p[pIter->iLeafOffset];\n        pIter->iLeafOffset += fts5GetVarint(a, (u64*)&pIter->iRowid);\n        break;\n      }else{\n        fts5DataRelease(pNew);\n      }\n    }\n  }\n\n  if( pIter->pLeaf ){\n    pIter->iEndofDoclist = pIter->pLeaf->nn+1;\n    fts5SegIterReverseInitPage(p, pIter);\n  }\n}\n\n/*\n** Return true if the iterator passed as the second argument currently\n** points to a delete marker. A delete marker is an entry with a 0 byte\n** position-list.\n*/\nstatic int fts5MultiIterIsEmpty(Fts5Index *p, Fts5Iter *pIter){\n  Fts5SegIter *pSeg = &pIter->aSeg[pIter->aFirst[1].iFirst];\n  return (p->rc==SQLITE_OK && pSeg->pLeaf && pSeg->nPos==0);\n}\n\n/*\n** Advance iterator pIter to the next entry.\n**\n** This version of fts5SegIterNext() is only used by reverse iterators.\n*/\nstatic void fts5SegIterNext_Reverse(\n  Fts5Index *p,                   /* FTS5 backend object */\n  Fts5SegIter *pIter,             /* Iterator to advance */\n  int *pbUnused                   /* Unused */\n){\n  assert( pIter->flags & FTS5_SEGITER_REVERSE );\n  assert( pIter->pNextLeaf==0 );\n  UNUSED_PARAM(pbUnused);\n\n  if( pIter->iRowidOffset>0 ){\n    u8 *a = pIter->pLeaf->p;\n    int iOff;\n    i64 iDelta;\n\n    pIter->iRowidOffset--;\n    pIter->iLeafOffset = pIter->aRowidOffset[pIter->iRowidOffset];\n    fts5SegIterLoadNPos(p, pIter);\n    iOff = pIter->iLeafOffset;\n    if( p->pConfig->eDetail!=FTS5_DETAIL_NONE ){\n      iOff += pIter->nPos;\n    }\n    fts5GetVarint(&a[iOff], (u64*)&iDelta);\n    pIter->iRowid -= iDelta;\n  }else{\n    fts5SegIterReverseNewPage(p, pIter);\n  }\n}\n\n/*\n** Advance iterator pIter to the next entry.\n**\n** This version of fts5SegIterNext() is only used if detail=none and the\n** iterator is not a reverse direction iterator.\n*/\nstatic void fts5SegIterNext_None(\n  Fts5Index *p,                   /* FTS5 backend object */\n  Fts5SegIter *pIter,             /* Iterator to advance */\n  int *pbNewTerm                  /* OUT: Set for new term */\n){\n  int iOff;\n\n  assert( p->rc==SQLITE_OK );\n  assert( (pIter->flags & FTS5_SEGITER_REVERSE)==0 );\n  assert( p->pConfig->eDetail==FTS5_DETAIL_NONE );\n\n  ASSERT_SZLEAF_OK(pIter->pLeaf);\n  iOff = pIter->iLeafOffset;\n\n  /* Next entry is on the next page */\n  if( pIter->pSeg && iOff>=pIter->pLeaf->szLeaf ){\n    fts5SegIterNextPage(p, pIter);\n    if( p->rc || pIter->pLeaf==0 ) return;\n    pIter->iRowid = 0;\n    iOff = 4;\n  }\n\n  if( iOff<pIter->iEndofDoclist ){\n    /* Next entry is on the current page */\n    i64 iDelta;\n    iOff += sqlite3Fts5GetVarint(&pIter->pLeaf->p[iOff], (u64*)&iDelta);\n    pIter->iLeafOffset = iOff;\n    pIter->iRowid += iDelta;\n  }else if( (pIter->flags & FTS5_SEGITER_ONETERM)==0 ){\n    if( pIter->pSeg ){\n      int nKeep = 0;\n      if( iOff!=fts5LeafFirstTermOff(pIter->pLeaf) ){\n        iOff += fts5GetVarint32(&pIter->pLeaf->p[iOff], nKeep);\n      }\n      pIter->iLeafOffset = iOff;\n      fts5SegIterLoadTerm(p, pIter, nKeep);\n    }else{\n      const u8 *pList = 0;\n      const char *zTerm = 0;\n      int nList;\n      sqlite3Fts5HashScanNext(p->pHash);\n      sqlite3Fts5HashScanEntry(p->pHash, &zTerm, &pList, &nList);\n      if( pList==0 ) goto next_none_eof;\n      pIter->pLeaf->p = (u8*)pList;\n      pIter->pLeaf->nn = nList;\n      pIter->pLeaf->szLeaf = nList;\n      pIter->iEndofDoclist = nList;\n      sqlite3Fts5BufferSet(&p->rc,&pIter->term, (int)strlen(zTerm), (u8*)zTerm);\n      pIter->iLeafOffset = fts5GetVarint(pList, (u64*)&pIter->iRowid);\n    }\n\n    if( pbNewTerm ) *pbNewTerm = 1;\n  }else{\n    goto next_none_eof;\n  }\n\n  fts5SegIterLoadNPos(p, pIter);\n\n  return;\n next_none_eof:\n  fts5DataRelease(pIter->pLeaf);\n  pIter->pLeaf = 0;\n}\n\n\n/*\n** Advance iterator pIter to the next entry. \n**\n** If an error occurs, Fts5Index.rc is set to an appropriate error code. It \n** is not considered an error if the iterator reaches EOF. If an error has \n** already occurred when this function is called, it is a no-op.\n*/\nstatic void fts5SegIterNext(\n  Fts5Index *p,                   /* FTS5 backend object */\n  Fts5SegIter *pIter,             /* Iterator to advance */\n  int *pbNewTerm                  /* OUT: Set for new term */\n){\n  Fts5Data *pLeaf = pIter->pLeaf;\n  int iOff;\n  int bNewTerm = 0;\n  int nKeep = 0;\n  u8 *a;\n  int n;\n\n  assert( pbNewTerm==0 || *pbNewTerm==0 );\n  assert( p->pConfig->eDetail!=FTS5_DETAIL_NONE );\n\n  /* Search for the end of the position list within the current page. */\n  a = pLeaf->p;\n  n = pLeaf->szLeaf;\n\n  ASSERT_SZLEAF_OK(pLeaf);\n  iOff = pIter->iLeafOffset + pIter->nPos;\n\n  if( iOff<n ){\n    /* The next entry is on the current page. */\n    assert_nc( iOff<=pIter->iEndofDoclist );\n    if( iOff>=pIter->iEndofDoclist ){\n      bNewTerm = 1;\n      if( iOff!=fts5LeafFirstTermOff(pLeaf) ){\n        iOff += fts5GetVarint32(&a[iOff], nKeep);\n      }\n    }else{\n      u64 iDelta;\n      iOff += sqlite3Fts5GetVarint(&a[iOff], &iDelta);\n      pIter->iRowid += iDelta;\n      assert_nc( iDelta>0 );\n    }\n    pIter->iLeafOffset = iOff;\n\n  }else if( pIter->pSeg==0 ){\n    const u8 *pList = 0;\n    const char *zTerm = 0;\n    int nList = 0;\n    assert( (pIter->flags & FTS5_SEGITER_ONETERM) || pbNewTerm );\n    if( 0==(pIter->flags & FTS5_SEGITER_ONETERM) ){\n      sqlite3Fts5HashScanNext(p->pHash);\n      sqlite3Fts5HashScanEntry(p->pHash, &zTerm, &pList, &nList);\n    }\n    if( pList==0 ){\n      fts5DataRelease(pIter->pLeaf);\n      pIter->pLeaf = 0;\n    }else{\n      pIter->pLeaf->p = (u8*)pList;\n      pIter->pLeaf->nn = nList;\n      pIter->pLeaf->szLeaf = nList;\n      pIter->iEndofDoclist = nList+1;\n      sqlite3Fts5BufferSet(&p->rc, &pIter->term, (int)strlen(zTerm),\n          (u8*)zTerm);\n      pIter->iLeafOffset = fts5GetVarint(pList, (u64*)&pIter->iRowid);\n      *pbNewTerm = 1;\n    }\n  }else{\n    iOff = 0;\n    /* Next entry is not on the current page */\n    while( iOff==0 ){\n      fts5SegIterNextPage(p, pIter);\n      pLeaf = pIter->pLeaf;\n      if( pLeaf==0 ) break;\n      ASSERT_SZLEAF_OK(pLeaf);\n      if( (iOff = fts5LeafFirstRowidOff(pLeaf)) && iOff<pLeaf->szLeaf ){\n        iOff += sqlite3Fts5GetVarint(&pLeaf->p[iOff], (u64*)&pIter->iRowid);\n        pIter->iLeafOffset = iOff;\n\n        if( pLeaf->nn>pLeaf->szLeaf ){\n          pIter->iPgidxOff = pLeaf->szLeaf + fts5GetVarint32(\n              &pLeaf->p[pLeaf->szLeaf], pIter->iEndofDoclist\n          );\n        }\n      }\n      else if( pLeaf->nn>pLeaf->szLeaf ){\n        pIter->iPgidxOff = pLeaf->szLeaf + fts5GetVarint32(\n            &pLeaf->p[pLeaf->szLeaf], iOff\n        );\n        pIter->iLeafOffset = iOff;\n        pIter->iEndofDoclist = iOff;\n        bNewTerm = 1;\n      }\n      assert_nc( iOff<pLeaf->szLeaf );\n      if( iOff>pLeaf->szLeaf ){\n        p->rc = FTS5_CORRUPT;\n        return;\n      }\n    }\n  }\n\n  /* Check if the iterator is now at EOF. If so, return early. */\n  if( pIter->pLeaf ){\n    if( bNewTerm ){\n      if( pIter->flags & FTS5_SEGITER_ONETERM ){\n        fts5DataRelease(pIter->pLeaf);\n        pIter->pLeaf = 0;\n      }else{\n        fts5SegIterLoadTerm(p, pIter, nKeep);\n        fts5SegIterLoadNPos(p, pIter);\n        if( pbNewTerm ) *pbNewTerm = 1;\n      }\n    }else{\n      /* The following could be done by calling fts5SegIterLoadNPos(). But\n      ** this block is particularly performance critical, so equivalent\n      ** code is inlined. \n      **\n      ** Later: Switched back to fts5SegIterLoadNPos() because it supports\n      ** detail=none mode. Not ideal.\n      */\n      int nSz;\n      assert( p->rc==SQLITE_OK );\n      assert( pIter->iLeafOffset<=pIter->pLeaf->nn );\n      fts5FastGetVarint32(pIter->pLeaf->p, pIter->iLeafOffset, nSz);\n      pIter->bDel = (nSz & 0x0001);\n      pIter->nPos = nSz>>1;\n      assert_nc( pIter->nPos>=0 );\n    }\n  }\n}\n\n#define SWAPVAL(T, a, b) { T tmp; tmp=a; a=b; b=tmp; }\n\n#define fts5IndexSkipVarint(a, iOff) {            \\\n  int iEnd = iOff+9;                              \\\n  while( (a[iOff++] & 0x80) && iOff<iEnd );       \\\n}\n\n/*\n** Iterator pIter currently points to the first rowid in a doclist. This\n** function sets the iterator up so that iterates in reverse order through\n** the doclist.\n*/\nstatic void fts5SegIterReverse(Fts5Index *p, Fts5SegIter *pIter){\n  Fts5DlidxIter *pDlidx = pIter->pDlidx;\n  Fts5Data *pLast = 0;\n  int pgnoLast = 0;\n\n  if( pDlidx ){\n    int iSegid = pIter->pSeg->iSegid;\n    pgnoLast = fts5DlidxIterPgno(pDlidx);\n    pLast = fts5DataRead(p, FTS5_SEGMENT_ROWID(iSegid, pgnoLast));\n  }else{\n    Fts5Data *pLeaf = pIter->pLeaf;         /* Current leaf data */\n\n    /* Currently, Fts5SegIter.iLeafOffset points to the first byte of\n    ** position-list content for the current rowid. Back it up so that it\n    ** points to the start of the position-list size field. */\n    int iPoslist;\n    if( pIter->iTermLeafPgno==pIter->iLeafPgno ){\n      iPoslist = pIter->iTermLeafOffset;\n    }else{\n      iPoslist = 4;\n    }\n    fts5IndexSkipVarint(pLeaf->p, iPoslist);\n    pIter->iLeafOffset = iPoslist;\n\n    /* If this condition is true then the largest rowid for the current\n    ** term may not be stored on the current page. So search forward to\n    ** see where said rowid really is.  */\n    if( pIter->iEndofDoclist>=pLeaf->szLeaf ){\n      int pgno;\n      Fts5StructureSegment *pSeg = pIter->pSeg;\n\n      /* The last rowid in the doclist may not be on the current page. Search\n      ** forward to find the page containing the last rowid.  */\n      for(pgno=pIter->iLeafPgno+1; !p->rc && pgno<=pSeg->pgnoLast; pgno++){\n        i64 iAbs = FTS5_SEGMENT_ROWID(pSeg->iSegid, pgno);\n        Fts5Data *pNew = fts5DataRead(p, iAbs);\n        if( pNew ){\n          int iRowid, bTermless;\n          iRowid = fts5LeafFirstRowidOff(pNew);\n          bTermless = fts5LeafIsTermless(pNew);\n          if( iRowid ){\n            SWAPVAL(Fts5Data*, pNew, pLast);\n            pgnoLast = pgno;\n          }\n          fts5DataRelease(pNew);\n          if( bTermless==0 ) break;\n        }\n      }\n    }\n  }\n\n  /* If pLast is NULL at this point, then the last rowid for this doclist\n  ** lies on the page currently indicated by the iterator. In this case \n  ** pIter->iLeafOffset is already set to point to the position-list size\n  ** field associated with the first relevant rowid on the page.\n  **\n  ** Or, if pLast is non-NULL, then it is the page that contains the last\n  ** rowid. In this case configure the iterator so that it points to the\n  ** first rowid on this page.\n  */\n  if( pLast ){\n    int iOff;\n    fts5DataRelease(pIter->pLeaf);\n    pIter->pLeaf = pLast;\n    pIter->iLeafPgno = pgnoLast;\n    iOff = fts5LeafFirstRowidOff(pLast);\n    iOff += fts5GetVarint(&pLast->p[iOff], (u64*)&pIter->iRowid);\n    pIter->iLeafOffset = iOff;\n\n    if( fts5LeafIsTermless(pLast) ){\n      pIter->iEndofDoclist = pLast->nn+1;\n    }else{\n      pIter->iEndofDoclist = fts5LeafFirstTermOff(pLast);\n    }\n\n  }\n\n  fts5SegIterReverseInitPage(p, pIter);\n}\n\n/*\n** Iterator pIter currently points to the first rowid of a doclist.\n** There is a doclist-index associated with the final term on the current \n** page. If the current term is the last term on the page, load the \n** doclist-index from disk and initialize an iterator at (pIter->pDlidx).\n*/\nstatic void fts5SegIterLoadDlidx(Fts5Index *p, Fts5SegIter *pIter){\n  int iSeg = pIter->pSeg->iSegid;\n  int bRev = (pIter->flags & FTS5_SEGITER_REVERSE);\n  Fts5Data *pLeaf = pIter->pLeaf; /* Current leaf data */\n\n  assert( pIter->flags & FTS5_SEGITER_ONETERM );\n  assert( pIter->pDlidx==0 );\n\n  /* Check if the current doclist ends on this page. If it does, return\n  ** early without loading the doclist-index (as it belongs to a different\n  ** term. */\n  if( pIter->iTermLeafPgno==pIter->iLeafPgno \n   && pIter->iEndofDoclist<pLeaf->szLeaf \n  ){\n    return;\n  }\n\n  pIter->pDlidx = fts5DlidxIterInit(p, bRev, iSeg, pIter->iTermLeafPgno);\n}\n\n/*\n** The iterator object passed as the second argument currently contains\n** no valid values except for the Fts5SegIter.pLeaf member variable. This\n** function searches the leaf page for a term matching (pTerm/nTerm).\n**\n** If the specified term is found on the page, then the iterator is left\n** pointing to it. If argument bGe is zero and the term is not found,\n** the iterator is left pointing at EOF.\n**\n** If bGe is non-zero and the specified term is not found, then the\n** iterator is left pointing to the smallest term in the segment that\n** is larger than the specified term, even if this term is not on the\n** current page.\n*/\nstatic void fts5LeafSeek(\n  Fts5Index *p,                   /* Leave any error code here */\n  int bGe,                        /* True for a >= search */\n  Fts5SegIter *pIter,             /* Iterator to seek */\n  const u8 *pTerm, int nTerm      /* Term to search for */\n){\n  int iOff;\n  const u8 *a = pIter->pLeaf->p;\n  int szLeaf = pIter->pLeaf->szLeaf;\n  int n = pIter->pLeaf->nn;\n\n  int nMatch = 0;\n  int nKeep = 0;\n  int nNew = 0;\n  int iTermOff;\n  int iPgidx;                     /* Current offset in pgidx */\n  int bEndOfPage = 0;\n\n  assert( p->rc==SQLITE_OK );\n\n  iPgidx = szLeaf;\n  iPgidx += fts5GetVarint32(&a[iPgidx], iTermOff);\n  iOff = iTermOff;\n  if( iOff>n ){\n    p->rc = FTS5_CORRUPT;\n    return;\n  }\n\n  while( 1 ){\n\n    /* Figure out how many new bytes are in this term */\n    fts5FastGetVarint32(a, iOff, nNew);\n    if( nKeep<nMatch ){\n      goto search_failed;\n    }\n\n    assert( nKeep>=nMatch );\n    if( nKeep==nMatch ){\n      int nCmp;\n      int i;\n      nCmp = MIN(nNew, nTerm-nMatch);\n      for(i=0; i<nCmp; i++){\n        if( a[iOff+i]!=pTerm[nMatch+i] ) break;\n      }\n      nMatch += i;\n\n      if( nTerm==nMatch ){\n        if( i==nNew ){\n          goto search_success;\n        }else{\n          goto search_failed;\n        }\n      }else if( i<nNew && a[iOff+i]>pTerm[nMatch] ){\n        goto search_failed;\n      }\n    }\n\n    if( iPgidx>=n ){\n      bEndOfPage = 1;\n      break;\n    }\n\n    iPgidx += fts5GetVarint32(&a[iPgidx], nKeep);\n    iTermOff += nKeep;\n    iOff = iTermOff;\n\n    if( iOff>=n ){\n      p->rc = FTS5_CORRUPT;\n      return;\n    }\n\n    /* Read the nKeep field of the next term. */\n    fts5FastGetVarint32(a, iOff, nKeep);\n  }\n\n search_failed:\n  if( bGe==0 ){\n    fts5DataRelease(pIter->pLeaf);\n    pIter->pLeaf = 0;\n    return;\n  }else if( bEndOfPage ){\n    do {\n      fts5SegIterNextPage(p, pIter);\n      if( pIter->pLeaf==0 ) return;\n      a = pIter->pLeaf->p;\n      if( fts5LeafIsTermless(pIter->pLeaf)==0 ){\n        iPgidx = pIter->pLeaf->szLeaf;\n        iPgidx += fts5GetVarint32(&pIter->pLeaf->p[iPgidx], iOff);\n        if( iOff<4 || iOff>=pIter->pLeaf->szLeaf ){\n          p->rc = FTS5_CORRUPT;\n        }else{\n          nKeep = 0;\n          iTermOff = iOff;\n          n = pIter->pLeaf->nn;\n          iOff += fts5GetVarint32(&a[iOff], nNew);\n          break;\n        }\n      }\n    }while( 1 );\n  }\n\n search_success:\n\n  pIter->iLeafOffset = iOff + nNew;\n  pIter->iTermLeafOffset = pIter->iLeafOffset;\n  pIter->iTermLeafPgno = pIter->iLeafPgno;\n\n  fts5BufferSet(&p->rc, &pIter->term, nKeep, pTerm);\n  fts5BufferAppendBlob(&p->rc, &pIter->term, nNew, &a[iOff]);\n\n  if( iPgidx>=n ){\n    pIter->iEndofDoclist = pIter->pLeaf->nn+1;\n  }else{\n    int nExtra;\n    iPgidx += fts5GetVarint32(&a[iPgidx], nExtra);\n    pIter->iEndofDoclist = iTermOff + nExtra;\n  }\n  pIter->iPgidxOff = iPgidx;\n\n  fts5SegIterLoadRowid(p, pIter);\n  fts5SegIterLoadNPos(p, pIter);\n}\n\nstatic sqlite3_stmt *fts5IdxSelectStmt(Fts5Index *p){\n  if( p->pIdxSelect==0 ){\n    Fts5Config *pConfig = p->pConfig;\n    fts5IndexPrepareStmt(p, &p->pIdxSelect, sqlite3_mprintf(\n          \"SELECT pgno FROM '%q'.'%q_idx' WHERE \"\n          \"segid=? AND term<=? ORDER BY term DESC LIMIT 1\",\n          pConfig->zDb, pConfig->zName\n    ));\n  }\n  return p->pIdxSelect;\n}\n\n/*\n** Initialize the object pIter to point to term pTerm/nTerm within segment\n** pSeg. If there is no such term in the index, the iterator is set to EOF.\n**\n** If an error occurs, Fts5Index.rc is set to an appropriate error code. If \n** an error has already occurred when this function is called, it is a no-op.\n*/\nstatic void fts5SegIterSeekInit(\n  Fts5Index *p,                   /* FTS5 backend */\n  const u8 *pTerm, int nTerm,     /* Term to seek to */\n  int flags,                      /* Mask of FTS5INDEX_XXX flags */\n  Fts5StructureSegment *pSeg,     /* Description of segment */\n  Fts5SegIter *pIter              /* Object to populate */\n){\n  int iPg = 1;\n  int bGe = (flags & FTS5INDEX_QUERY_SCAN);\n  int bDlidx = 0;                 /* True if there is a doclist-index */\n  sqlite3_stmt *pIdxSelect = 0;\n\n  assert( bGe==0 || (flags & FTS5INDEX_QUERY_DESC)==0 );\n  assert( pTerm && nTerm );\n  memset(pIter, 0, sizeof(*pIter));\n  pIter->pSeg = pSeg;\n\n  /* This block sets stack variable iPg to the leaf page number that may\n  ** contain term (pTerm/nTerm), if it is present in the segment. */\n  pIdxSelect = fts5IdxSelectStmt(p);\n  if( p->rc ) return;\n  sqlite3_bind_int(pIdxSelect, 1, pSeg->iSegid);\n  sqlite3_bind_blob(pIdxSelect, 2, pTerm, nTerm, SQLITE_STATIC);\n  if( SQLITE_ROW==sqlite3_step(pIdxSelect) ){\n    i64 val = sqlite3_column_int(pIdxSelect, 0);\n    iPg = (int)(val>>1);\n    bDlidx = (val & 0x0001);\n  }\n  p->rc = sqlite3_reset(pIdxSelect);\n  sqlite3_bind_null(pIdxSelect, 2);\n\n  if( iPg<pSeg->pgnoFirst ){\n    iPg = pSeg->pgnoFirst;\n    bDlidx = 0;\n  }\n\n  pIter->iLeafPgno = iPg - 1;\n  fts5SegIterNextPage(p, pIter);\n\n  if( pIter->pLeaf ){\n    fts5LeafSeek(p, bGe, pIter, pTerm, nTerm);\n  }\n\n  if( p->rc==SQLITE_OK && bGe==0 ){\n    pIter->flags |= FTS5_SEGITER_ONETERM;\n    if( pIter->pLeaf ){\n      if( flags & FTS5INDEX_QUERY_DESC ){\n        pIter->flags |= FTS5_SEGITER_REVERSE;\n      }\n      if( bDlidx ){\n        fts5SegIterLoadDlidx(p, pIter);\n      }\n      if( flags & FTS5INDEX_QUERY_DESC ){\n        fts5SegIterReverse(p, pIter);\n      }\n    }\n  }\n\n  fts5SegIterSetNext(p, pIter);\n\n  /* Either:\n  **\n  **   1) an error has occurred, or\n  **   2) the iterator points to EOF, or\n  **   3) the iterator points to an entry with term (pTerm/nTerm), or\n  **   4) the FTS5INDEX_QUERY_SCAN flag was set and the iterator points\n  **      to an entry with a term greater than or equal to (pTerm/nTerm).\n  */\n  assert( p->rc!=SQLITE_OK                                          /* 1 */\n   || pIter->pLeaf==0                                               /* 2 */\n   || fts5BufferCompareBlob(&pIter->term, pTerm, nTerm)==0          /* 3 */\n   || (bGe && fts5BufferCompareBlob(&pIter->term, pTerm, nTerm)>0)  /* 4 */\n  );\n}\n\n/*\n** Initialize the object pIter to point to term pTerm/nTerm within the\n** in-memory hash table. If there is no such term in the hash-table, the \n** iterator is set to EOF.\n**\n** If an error occurs, Fts5Index.rc is set to an appropriate error code. If \n** an error has already occurred when this function is called, it is a no-op.\n*/\nstatic void fts5SegIterHashInit(\n  Fts5Index *p,                   /* FTS5 backend */\n  const u8 *pTerm, int nTerm,     /* Term to seek to */\n  int flags,                      /* Mask of FTS5INDEX_XXX flags */\n  Fts5SegIter *pIter              /* Object to populate */\n){\n  const u8 *pList = 0;\n  int nList = 0;\n  const u8 *z = 0;\n  int n = 0;\n\n  assert( p->pHash );\n  assert( p->rc==SQLITE_OK );\n\n  if( pTerm==0 || (flags & FTS5INDEX_QUERY_SCAN) ){\n    p->rc = sqlite3Fts5HashScanInit(p->pHash, (const char*)pTerm, nTerm);\n    sqlite3Fts5HashScanEntry(p->pHash, (const char**)&z, &pList, &nList);\n    n = (z ? (int)strlen((const char*)z) : 0);\n  }else{\n    pIter->flags |= FTS5_SEGITER_ONETERM;\n    sqlite3Fts5HashQuery(p->pHash, (const char*)pTerm, nTerm, &pList, &nList);\n    z = pTerm;\n    n = nTerm;\n  }\n\n  if( pList ){\n    Fts5Data *pLeaf;\n    sqlite3Fts5BufferSet(&p->rc, &pIter->term, n, z);\n    pLeaf = fts5IdxMalloc(p, sizeof(Fts5Data));\n    if( pLeaf==0 ) return;\n    pLeaf->p = (u8*)pList;\n    pLeaf->nn = pLeaf->szLeaf = nList;\n    pIter->pLeaf = pLeaf;\n    pIter->iLeafOffset = fts5GetVarint(pLeaf->p, (u64*)&pIter->iRowid);\n    pIter->iEndofDoclist = pLeaf->nn;\n\n    if( flags & FTS5INDEX_QUERY_DESC ){\n      pIter->flags |= FTS5_SEGITER_REVERSE;\n      fts5SegIterReverseInitPage(p, pIter);\n    }else{\n      fts5SegIterLoadNPos(p, pIter);\n    }\n  }\n\n  fts5SegIterSetNext(p, pIter);\n}\n\n/*\n** Zero the iterator passed as the only argument.\n*/\nstatic void fts5SegIterClear(Fts5SegIter *pIter){\n  fts5BufferFree(&pIter->term);\n  fts5DataRelease(pIter->pLeaf);\n  fts5DataRelease(pIter->pNextLeaf);\n  fts5DlidxIterFree(pIter->pDlidx);\n  sqlite3_free(pIter->aRowidOffset);\n  memset(pIter, 0, sizeof(Fts5SegIter));\n}\n\n#ifdef SQLITE_DEBUG\n\n/*\n** This function is used as part of the big assert() procedure implemented by\n** fts5AssertMultiIterSetup(). It ensures that the result currently stored\n** in *pRes is the correct result of comparing the current positions of the\n** two iterators.\n*/\nstatic void fts5AssertComparisonResult(\n  Fts5Iter *pIter, \n  Fts5SegIter *p1,\n  Fts5SegIter *p2,\n  Fts5CResult *pRes\n){\n  int i1 = p1 - pIter->aSeg;\n  int i2 = p2 - pIter->aSeg;\n\n  if( p1->pLeaf || p2->pLeaf ){\n    if( p1->pLeaf==0 ){\n      assert( pRes->iFirst==i2 );\n    }else if( p2->pLeaf==0 ){\n      assert( pRes->iFirst==i1 );\n    }else{\n      int nMin = MIN(p1->term.n, p2->term.n);\n      int res = memcmp(p1->term.p, p2->term.p, nMin);\n      if( res==0 ) res = p1->term.n - p2->term.n;\n\n      if( res==0 ){\n        assert( pRes->bTermEq==1 );\n        assert( p1->iRowid!=p2->iRowid );\n        res = ((p1->iRowid > p2->iRowid)==pIter->bRev) ? -1 : 1;\n      }else{\n        assert( pRes->bTermEq==0 );\n      }\n\n      if( res<0 ){\n        assert( pRes->iFirst==i1 );\n      }else{\n        assert( pRes->iFirst==i2 );\n      }\n    }\n  }\n}\n\n/*\n** This function is a no-op unless SQLITE_DEBUG is defined when this module\n** is compiled. In that case, this function is essentially an assert() \n** statement used to verify that the contents of the pIter->aFirst[] array\n** are correct.\n*/\nstatic void fts5AssertMultiIterSetup(Fts5Index *p, Fts5Iter *pIter){\n  if( p->rc==SQLITE_OK ){\n    Fts5SegIter *pFirst = &pIter->aSeg[ pIter->aFirst[1].iFirst ];\n    int i;\n\n    assert( (pFirst->pLeaf==0)==pIter->base.bEof );\n\n    /* Check that pIter->iSwitchRowid is set correctly. */\n    for(i=0; i<pIter->nSeg; i++){\n      Fts5SegIter *p1 = &pIter->aSeg[i];\n      assert( p1==pFirst \n           || p1->pLeaf==0 \n           || fts5BufferCompare(&pFirst->term, &p1->term) \n           || p1->iRowid==pIter->iSwitchRowid\n           || (p1->iRowid<pIter->iSwitchRowid)==pIter->bRev\n      );\n    }\n\n    for(i=0; i<pIter->nSeg; i+=2){\n      Fts5SegIter *p1 = &pIter->aSeg[i];\n      Fts5SegIter *p2 = &pIter->aSeg[i+1];\n      Fts5CResult *pRes = &pIter->aFirst[(pIter->nSeg + i) / 2];\n      fts5AssertComparisonResult(pIter, p1, p2, pRes);\n    }\n\n    for(i=1; i<(pIter->nSeg / 2); i+=2){\n      Fts5SegIter *p1 = &pIter->aSeg[ pIter->aFirst[i*2].iFirst ];\n      Fts5SegIter *p2 = &pIter->aSeg[ pIter->aFirst[i*2+1].iFirst ];\n      Fts5CResult *pRes = &pIter->aFirst[i];\n      fts5AssertComparisonResult(pIter, p1, p2, pRes);\n    }\n  }\n}\n#else\n# define fts5AssertMultiIterSetup(x,y)\n#endif\n\n/*\n** Do the comparison necessary to populate pIter->aFirst[iOut].\n**\n** If the returned value is non-zero, then it is the index of an entry\n** in the pIter->aSeg[] array that is (a) not at EOF, and (b) pointing\n** to a key that is a duplicate of another, higher priority, \n** segment-iterator in the pSeg->aSeg[] array.\n*/\nstatic int fts5MultiIterDoCompare(Fts5Iter *pIter, int iOut){\n  int i1;                         /* Index of left-hand Fts5SegIter */\n  int i2;                         /* Index of right-hand Fts5SegIter */\n  int iRes;\n  Fts5SegIter *p1;                /* Left-hand Fts5SegIter */\n  Fts5SegIter *p2;                /* Right-hand Fts5SegIter */\n  Fts5CResult *pRes = &pIter->aFirst[iOut];\n\n  assert( iOut<pIter->nSeg && iOut>0 );\n  assert( pIter->bRev==0 || pIter->bRev==1 );\n\n  if( iOut>=(pIter->nSeg/2) ){\n    i1 = (iOut - pIter->nSeg/2) * 2;\n    i2 = i1 + 1;\n  }else{\n    i1 = pIter->aFirst[iOut*2].iFirst;\n    i2 = pIter->aFirst[iOut*2+1].iFirst;\n  }\n  p1 = &pIter->aSeg[i1];\n  p2 = &pIter->aSeg[i2];\n\n  pRes->bTermEq = 0;\n  if( p1->pLeaf==0 ){           /* If p1 is at EOF */\n    iRes = i2;\n  }else if( p2->pLeaf==0 ){     /* If p2 is at EOF */\n    iRes = i1;\n  }else{\n    int res = fts5BufferCompare(&p1->term, &p2->term);\n    if( res==0 ){\n      assert( i2>i1 );\n      assert( i2!=0 );\n      pRes->bTermEq = 1;\n      if( p1->iRowid==p2->iRowid ){\n        p1->bDel = p2->bDel;\n        return i2;\n      }\n      res = ((p1->iRowid > p2->iRowid)==pIter->bRev) ? -1 : +1;\n    }\n    assert( res!=0 );\n    if( res<0 ){\n      iRes = i1;\n    }else{\n      iRes = i2;\n    }\n  }\n\n  pRes->iFirst = (u16)iRes;\n  return 0;\n}\n\n/*\n** Move the seg-iter so that it points to the first rowid on page iLeafPgno.\n** It is an error if leaf iLeafPgno does not exist or contains no rowids.\n*/\nstatic void fts5SegIterGotoPage(\n  Fts5Index *p,                   /* FTS5 backend object */\n  Fts5SegIter *pIter,             /* Iterator to advance */\n  int iLeafPgno\n){\n  assert( iLeafPgno>pIter->iLeafPgno );\n\n  if( iLeafPgno>pIter->pSeg->pgnoLast ){\n    p->rc = FTS5_CORRUPT;\n  }else{\n    fts5DataRelease(pIter->pNextLeaf);\n    pIter->pNextLeaf = 0;\n    pIter->iLeafPgno = iLeafPgno-1;\n    fts5SegIterNextPage(p, pIter);\n    assert( p->rc!=SQLITE_OK || pIter->iLeafPgno==iLeafPgno );\n\n    if( p->rc==SQLITE_OK ){\n      int iOff;\n      u8 *a = pIter->pLeaf->p;\n      int n = pIter->pLeaf->szLeaf;\n\n      iOff = fts5LeafFirstRowidOff(pIter->pLeaf);\n      if( iOff<4 || iOff>=n ){\n        p->rc = FTS5_CORRUPT;\n      }else{\n        iOff += fts5GetVarint(&a[iOff], (u64*)&pIter->iRowid);\n        pIter->iLeafOffset = iOff;\n        fts5SegIterLoadNPos(p, pIter);\n      }\n    }\n  }\n}\n\n/*\n** Advance the iterator passed as the second argument until it is at or \n** past rowid iFrom. Regardless of the value of iFrom, the iterator is\n** always advanced at least once.\n*/\nstatic void fts5SegIterNextFrom(\n  Fts5Index *p,                   /* FTS5 backend object */\n  Fts5SegIter *pIter,             /* Iterator to advance */\n  i64 iMatch                      /* Advance iterator at least this far */\n){\n  int bRev = (pIter->flags & FTS5_SEGITER_REVERSE);\n  Fts5DlidxIter *pDlidx = pIter->pDlidx;\n  int iLeafPgno = pIter->iLeafPgno;\n  int bMove = 1;\n\n  assert( pIter->flags & FTS5_SEGITER_ONETERM );\n  assert( pIter->pDlidx );\n  assert( pIter->pLeaf );\n\n  if( bRev==0 ){\n    while( !fts5DlidxIterEof(p, pDlidx) && iMatch>fts5DlidxIterRowid(pDlidx) ){\n      iLeafPgno = fts5DlidxIterPgno(pDlidx);\n      fts5DlidxIterNext(p, pDlidx);\n    }\n    assert_nc( iLeafPgno>=pIter->iLeafPgno || p->rc );\n    if( iLeafPgno>pIter->iLeafPgno ){\n      fts5SegIterGotoPage(p, pIter, iLeafPgno);\n      bMove = 0;\n    }\n  }else{\n    assert( pIter->pNextLeaf==0 );\n    assert( iMatch<pIter->iRowid );\n    while( !fts5DlidxIterEof(p, pDlidx) && iMatch<fts5DlidxIterRowid(pDlidx) ){\n      fts5DlidxIterPrev(p, pDlidx);\n    }\n    iLeafPgno = fts5DlidxIterPgno(pDlidx);\n\n    assert( fts5DlidxIterEof(p, pDlidx) || iLeafPgno<=pIter->iLeafPgno );\n\n    if( iLeafPgno<pIter->iLeafPgno ){\n      pIter->iLeafPgno = iLeafPgno+1;\n      fts5SegIterReverseNewPage(p, pIter);\n      bMove = 0;\n    }\n  }\n\n  do{\n    if( bMove && p->rc==SQLITE_OK ) pIter->xNext(p, pIter, 0);\n    if( pIter->pLeaf==0 ) break;\n    if( bRev==0 && pIter->iRowid>=iMatch ) break;\n    if( bRev!=0 && pIter->iRowid<=iMatch ) break;\n    bMove = 1;\n  }while( p->rc==SQLITE_OK );\n}\n\n\n/*\n** Free the iterator object passed as the second argument.\n*/\nstatic void fts5MultiIterFree(Fts5Iter *pIter){\n  if( pIter ){\n    int i;\n    for(i=0; i<pIter->nSeg; i++){\n      fts5SegIterClear(&pIter->aSeg[i]);\n    }\n    fts5StructureRelease(pIter->pStruct);\n    fts5BufferFree(&pIter->poslist);\n    sqlite3_free(pIter);\n  }\n}\n\nstatic void fts5MultiIterAdvanced(\n  Fts5Index *p,                   /* FTS5 backend to iterate within */\n  Fts5Iter *pIter,                /* Iterator to update aFirst[] array for */\n  int iChanged,                   /* Index of sub-iterator just advanced */\n  int iMinset                     /* Minimum entry in aFirst[] to set */\n){\n  int i;\n  for(i=(pIter->nSeg+iChanged)/2; i>=iMinset && p->rc==SQLITE_OK; i=i/2){\n    int iEq;\n    if( (iEq = fts5MultiIterDoCompare(pIter, i)) ){\n      Fts5SegIter *pSeg = &pIter->aSeg[iEq];\n      assert( p->rc==SQLITE_OK );\n      pSeg->xNext(p, pSeg, 0);\n      i = pIter->nSeg + iEq;\n    }\n  }\n}\n\n/*\n** Sub-iterator iChanged of iterator pIter has just been advanced. It still\n** points to the same term though - just a different rowid. This function\n** attempts to update the contents of the pIter->aFirst[] accordingly.\n** If it does so successfully, 0 is returned. Otherwise 1.\n**\n** If non-zero is returned, the caller should call fts5MultiIterAdvanced()\n** on the iterator instead. That function does the same as this one, except\n** that it deals with more complicated cases as well.\n*/ \nstatic int fts5MultiIterAdvanceRowid(\n  Fts5Iter *pIter,                /* Iterator to update aFirst[] array for */\n  int iChanged,                   /* Index of sub-iterator just advanced */\n  Fts5SegIter **ppFirst\n){\n  Fts5SegIter *pNew = &pIter->aSeg[iChanged];\n\n  if( pNew->iRowid==pIter->iSwitchRowid\n   || (pNew->iRowid<pIter->iSwitchRowid)==pIter->bRev\n  ){\n    int i;\n    Fts5SegIter *pOther = &pIter->aSeg[iChanged ^ 0x0001];\n    pIter->iSwitchRowid = pIter->bRev ? SMALLEST_INT64 : LARGEST_INT64;\n    for(i=(pIter->nSeg+iChanged)/2; 1; i=i/2){\n      Fts5CResult *pRes = &pIter->aFirst[i];\n\n      assert( pNew->pLeaf );\n      assert( pRes->bTermEq==0 || pOther->pLeaf );\n\n      if( pRes->bTermEq ){\n        if( pNew->iRowid==pOther->iRowid ){\n          return 1;\n        }else if( (pOther->iRowid>pNew->iRowid)==pIter->bRev ){\n          pIter->iSwitchRowid = pOther->iRowid;\n          pNew = pOther;\n        }else if( (pOther->iRowid>pIter->iSwitchRowid)==pIter->bRev ){\n          pIter->iSwitchRowid = pOther->iRowid;\n        }\n      }\n      pRes->iFirst = (u16)(pNew - pIter->aSeg);\n      if( i==1 ) break;\n\n      pOther = &pIter->aSeg[ pIter->aFirst[i ^ 0x0001].iFirst ];\n    }\n  }\n\n  *ppFirst = pNew;\n  return 0;\n}\n\n/*\n** Set the pIter->bEof variable based on the state of the sub-iterators.\n*/\nstatic void fts5MultiIterSetEof(Fts5Iter *pIter){\n  Fts5SegIter *pSeg = &pIter->aSeg[ pIter->aFirst[1].iFirst ];\n  pIter->base.bEof = pSeg->pLeaf==0;\n  pIter->iSwitchRowid = pSeg->iRowid;\n}\n\n/*\n** Move the iterator to the next entry. \n**\n** If an error occurs, an error code is left in Fts5Index.rc. It is not \n** considered an error if the iterator reaches EOF, or if it is already at \n** EOF when this function is called.\n*/\nstatic void fts5MultiIterNext(\n  Fts5Index *p, \n  Fts5Iter *pIter,\n  int bFrom,                      /* True if argument iFrom is valid */\n  i64 iFrom                       /* Advance at least as far as this */\n){\n  int bUseFrom = bFrom;\n  assert( pIter->base.bEof==0 );\n  while( p->rc==SQLITE_OK ){\n    int iFirst = pIter->aFirst[1].iFirst;\n    int bNewTerm = 0;\n    Fts5SegIter *pSeg = &pIter->aSeg[iFirst];\n    assert( p->rc==SQLITE_OK );\n    if( bUseFrom && pSeg->pDlidx ){\n      fts5SegIterNextFrom(p, pSeg, iFrom);\n    }else{\n      pSeg->xNext(p, pSeg, &bNewTerm);\n    }\n\n    if( pSeg->pLeaf==0 || bNewTerm \n     || fts5MultiIterAdvanceRowid(pIter, iFirst, &pSeg)\n    ){\n      fts5MultiIterAdvanced(p, pIter, iFirst, 1);\n      fts5MultiIterSetEof(pIter);\n      pSeg = &pIter->aSeg[pIter->aFirst[1].iFirst];\n      if( pSeg->pLeaf==0 ) return;\n    }\n\n    fts5AssertMultiIterSetup(p, pIter);\n    assert( pSeg==&pIter->aSeg[pIter->aFirst[1].iFirst] && pSeg->pLeaf );\n    if( pIter->bSkipEmpty==0 || pSeg->nPos ){\n      pIter->xSetOutputs(pIter, pSeg);\n      return;\n    }\n    bUseFrom = 0;\n  }\n}\n\nstatic void fts5MultiIterNext2(\n  Fts5Index *p, \n  Fts5Iter *pIter,\n  int *pbNewTerm                  /* OUT: True if *might* be new term */\n){\n  assert( pIter->bSkipEmpty );\n  if( p->rc==SQLITE_OK ){\n    *pbNewTerm = 0;\n    do{\n      int iFirst = pIter->aFirst[1].iFirst;\n      Fts5SegIter *pSeg = &pIter->aSeg[iFirst];\n      int bNewTerm = 0;\n\n      assert( p->rc==SQLITE_OK );\n      pSeg->xNext(p, pSeg, &bNewTerm);\n      if( pSeg->pLeaf==0 || bNewTerm \n       || fts5MultiIterAdvanceRowid(pIter, iFirst, &pSeg)\n      ){\n        fts5MultiIterAdvanced(p, pIter, iFirst, 1);\n        fts5MultiIterSetEof(pIter);\n        *pbNewTerm = 1;\n      }\n      fts5AssertMultiIterSetup(p, pIter);\n\n    }while( fts5MultiIterIsEmpty(p, pIter) );\n  }\n}\n\nstatic void fts5IterSetOutputs_Noop(Fts5Iter *pUnused1, Fts5SegIter *pUnused2){\n  UNUSED_PARAM2(pUnused1, pUnused2);\n}\n\nstatic Fts5Iter *fts5MultiIterAlloc(\n  Fts5Index *p,                   /* FTS5 backend to iterate within */\n  int nSeg\n){\n  Fts5Iter *pNew;\n  int nSlot;                      /* Power of two >= nSeg */\n\n  for(nSlot=2; nSlot<nSeg; nSlot=nSlot*2);\n  pNew = fts5IdxMalloc(p, \n      sizeof(Fts5Iter) +                  /* pNew */\n      sizeof(Fts5SegIter) * (nSlot-1) +   /* pNew->aSeg[] */\n      sizeof(Fts5CResult) * nSlot         /* pNew->aFirst[] */\n  );\n  if( pNew ){\n    pNew->nSeg = nSlot;\n    pNew->aFirst = (Fts5CResult*)&pNew->aSeg[nSlot];\n    pNew->pIndex = p;\n    pNew->xSetOutputs = fts5IterSetOutputs_Noop;\n  }\n  return pNew;\n}\n\nstatic void fts5PoslistCallback(\n  Fts5Index *pUnused, \n  void *pContext, \n  const u8 *pChunk, int nChunk\n){\n  UNUSED_PARAM(pUnused);\n  assert_nc( nChunk>=0 );\n  if( nChunk>0 ){\n    fts5BufferSafeAppendBlob((Fts5Buffer*)pContext, pChunk, nChunk);\n  }\n}\n\ntypedef struct PoslistCallbackCtx PoslistCallbackCtx;\nstruct PoslistCallbackCtx {\n  Fts5Buffer *pBuf;               /* Append to this buffer */\n  Fts5Colset *pColset;            /* Restrict matches to this column */\n  int eState;                     /* See above */\n};\n\ntypedef struct PoslistOffsetsCtx PoslistOffsetsCtx;\nstruct PoslistOffsetsCtx {\n  Fts5Buffer *pBuf;               /* Append to this buffer */\n  Fts5Colset *pColset;            /* Restrict matches to this column */\n  int iRead;\n  int iWrite;\n};\n\n/*\n** TODO: Make this more efficient!\n*/\nstatic int fts5IndexColsetTest(Fts5Colset *pColset, int iCol){\n  int i;\n  for(i=0; i<pColset->nCol; i++){\n    if( pColset->aiCol[i]==iCol ) return 1;\n  }\n  return 0;\n}\n\nstatic void fts5PoslistOffsetsCallback(\n  Fts5Index *pUnused, \n  void *pContext, \n  const u8 *pChunk, int nChunk\n){\n  PoslistOffsetsCtx *pCtx = (PoslistOffsetsCtx*)pContext;\n  UNUSED_PARAM(pUnused);\n  assert_nc( nChunk>=0 );\n  if( nChunk>0 ){\n    int i = 0;\n    while( i<nChunk ){\n      int iVal;\n      i += fts5GetVarint32(&pChunk[i], iVal);\n      iVal += pCtx->iRead - 2;\n      pCtx->iRead = iVal;\n      if( fts5IndexColsetTest(pCtx->pColset, iVal) ){\n        fts5BufferSafeAppendVarint(pCtx->pBuf, iVal + 2 - pCtx->iWrite);\n        pCtx->iWrite = iVal;\n      }\n    }\n  }\n}\n\nstatic void fts5PoslistFilterCallback(\n  Fts5Index *pUnused,\n  void *pContext, \n  const u8 *pChunk, int nChunk\n){\n  PoslistCallbackCtx *pCtx = (PoslistCallbackCtx*)pContext;\n  UNUSED_PARAM(pUnused);\n  assert_nc( nChunk>=0 );\n  if( nChunk>0 ){\n    /* Search through to find the first varint with value 1. This is the\n    ** start of the next columns hits. */\n    int i = 0;\n    int iStart = 0;\n\n    if( pCtx->eState==2 ){\n      int iCol;\n      fts5FastGetVarint32(pChunk, i, iCol);\n      if( fts5IndexColsetTest(pCtx->pColset, iCol) ){\n        pCtx->eState = 1;\n        fts5BufferSafeAppendVarint(pCtx->pBuf, 1);\n      }else{\n        pCtx->eState = 0;\n      }\n    }\n\n    do {\n      while( i<nChunk && pChunk[i]!=0x01 ){\n        while( pChunk[i] & 0x80 ) i++;\n        i++;\n      }\n      if( pCtx->eState ){\n        fts5BufferSafeAppendBlob(pCtx->pBuf, &pChunk[iStart], i-iStart);\n      }\n      if( i<nChunk ){\n        int iCol;\n        iStart = i;\n        i++;\n        if( i>=nChunk ){\n          pCtx->eState = 2;\n        }else{\n          fts5FastGetVarint32(pChunk, i, iCol);\n          pCtx->eState = fts5IndexColsetTest(pCtx->pColset, iCol);\n          if( pCtx->eState ){\n            fts5BufferSafeAppendBlob(pCtx->pBuf, &pChunk[iStart], i-iStart);\n            iStart = i;\n          }\n        }\n      }\n    }while( i<nChunk );\n  }\n}\n\nstatic void fts5ChunkIterate(\n  Fts5Index *p,                   /* Index object */\n  Fts5SegIter *pSeg,              /* Poslist of this iterator */\n  void *pCtx,                     /* Context pointer for xChunk callback */\n  void (*xChunk)(Fts5Index*, void*, const u8*, int)\n){\n  int nRem = pSeg->nPos;          /* Number of bytes still to come */\n  Fts5Data *pData = 0;\n  u8 *pChunk = &pSeg->pLeaf->p[pSeg->iLeafOffset];\n  int nChunk = MIN(nRem, pSeg->pLeaf->szLeaf - pSeg->iLeafOffset);\n  int pgno = pSeg->iLeafPgno;\n  int pgnoSave = 0;\n\n  /* This function does notmwork with detail=none databases. */\n  assert( p->pConfig->eDetail!=FTS5_DETAIL_NONE );\n\n  if( (pSeg->flags & FTS5_SEGITER_REVERSE)==0 ){\n    pgnoSave = pgno+1;\n  }\n\n  while( 1 ){\n    xChunk(p, pCtx, pChunk, nChunk);\n    nRem -= nChunk;\n    fts5DataRelease(pData);\n    if( nRem<=0 ){\n      break;\n    }else{\n      pgno++;\n      pData = fts5LeafRead(p, FTS5_SEGMENT_ROWID(pSeg->pSeg->iSegid, pgno));\n      if( pData==0 ) break;\n      pChunk = &pData->p[4];\n      nChunk = MIN(nRem, pData->szLeaf - 4);\n      if( pgno==pgnoSave ){\n        assert( pSeg->pNextLeaf==0 );\n        pSeg->pNextLeaf = pData;\n        pData = 0;\n      }\n    }\n  }\n}\n\n/*\n** Iterator pIter currently points to a valid entry (not EOF). This\n** function appends the position list data for the current entry to\n** buffer pBuf. It does not make a copy of the position-list size\n** field.\n*/\nstatic void fts5SegiterPoslist(\n  Fts5Index *p,\n  Fts5SegIter *pSeg,\n  Fts5Colset *pColset,\n  Fts5Buffer *pBuf\n){\n  if( 0==fts5BufferGrow(&p->rc, pBuf, pSeg->nPos) ){\n    if( pColset==0 ){\n      fts5ChunkIterate(p, pSeg, (void*)pBuf, fts5PoslistCallback);\n    }else{\n      if( p->pConfig->eDetail==FTS5_DETAIL_FULL ){\n        PoslistCallbackCtx sCtx;\n        sCtx.pBuf = pBuf;\n        sCtx.pColset = pColset;\n        sCtx.eState = fts5IndexColsetTest(pColset, 0);\n        assert( sCtx.eState==0 || sCtx.eState==1 );\n        fts5ChunkIterate(p, pSeg, (void*)&sCtx, fts5PoslistFilterCallback);\n      }else{\n        PoslistOffsetsCtx sCtx;\n        memset(&sCtx, 0, sizeof(sCtx));\n        sCtx.pBuf = pBuf;\n        sCtx.pColset = pColset;\n        fts5ChunkIterate(p, pSeg, (void*)&sCtx, fts5PoslistOffsetsCallback);\n      }\n    }\n  }\n}\n\n/*\n** IN/OUT parameter (*pa) points to a position list n bytes in size. If\n** the position list contains entries for column iCol, then (*pa) is set\n** to point to the sub-position-list for that column and the number of\n** bytes in it returned. Or, if the argument position list does not\n** contain any entries for column iCol, return 0.\n*/\nstatic int fts5IndexExtractCol(\n  const u8 **pa,                  /* IN/OUT: Pointer to poslist */\n  int n,                          /* IN: Size of poslist in bytes */\n  int iCol                        /* Column to extract from poslist */\n){\n  int iCurrent = 0;               /* Anything before the first 0x01 is col 0 */\n  const u8 *p = *pa;\n  const u8 *pEnd = &p[n];         /* One byte past end of position list */\n\n  while( iCol>iCurrent ){\n    /* Advance pointer p until it points to pEnd or an 0x01 byte that is\n    ** not part of a varint. Note that it is not possible for a negative\n    ** or extremely large varint to occur within an uncorrupted position \n    ** list. So the last byte of each varint may be assumed to have a clear\n    ** 0x80 bit.  */\n    while( *p!=0x01 ){\n      while( *p++ & 0x80 );\n      if( p>=pEnd ) return 0;\n    }\n    *pa = p++;\n    iCurrent = *p++;\n    if( iCurrent & 0x80 ){\n      p--;\n      p += fts5GetVarint32(p, iCurrent);\n    }\n  }\n  if( iCol!=iCurrent ) return 0;\n\n  /* Advance pointer p until it points to pEnd or an 0x01 byte that is\n  ** not part of a varint */\n  while( p<pEnd && *p!=0x01 ){\n    while( *p++ & 0x80 );\n  }\n\n  return p - (*pa);\n}\n\nstatic void fts5IndexExtractColset(\n  int *pRc,\n  Fts5Colset *pColset,            /* Colset to filter on */\n  const u8 *pPos, int nPos,       /* Position list */\n  Fts5Buffer *pBuf                /* Output buffer */\n){\n  if( *pRc==SQLITE_OK ){\n    int i;\n    fts5BufferZero(pBuf);\n    for(i=0; i<pColset->nCol; i++){\n      const u8 *pSub = pPos;\n      int nSub = fts5IndexExtractCol(&pSub, nPos, pColset->aiCol[i]);\n      if( nSub ){\n        fts5BufferAppendBlob(pRc, pBuf, nSub, pSub);\n      }\n    }\n  }\n}\n\n/*\n** xSetOutputs callback used by detail=none tables.\n*/\nstatic void fts5IterSetOutputs_None(Fts5Iter *pIter, Fts5SegIter *pSeg){\n  assert( pIter->pIndex->pConfig->eDetail==FTS5_DETAIL_NONE );\n  pIter->base.iRowid = pSeg->iRowid;\n  pIter->base.nData = pSeg->nPos;\n}\n\n/*\n** xSetOutputs callback used by detail=full and detail=col tables when no\n** column filters are specified.\n*/\nstatic void fts5IterSetOutputs_Nocolset(Fts5Iter *pIter, Fts5SegIter *pSeg){\n  pIter->base.iRowid = pSeg->iRowid;\n  pIter->base.nData = pSeg->nPos;\n\n  assert( pIter->pIndex->pConfig->eDetail!=FTS5_DETAIL_NONE );\n  assert( pIter->pColset==0 );\n\n  if( pSeg->iLeafOffset+pSeg->nPos<=pSeg->pLeaf->szLeaf ){\n    /* All data is stored on the current page. Populate the output \n    ** variables to point into the body of the page object. */\n    pIter->base.pData = &pSeg->pLeaf->p[pSeg->iLeafOffset];\n  }else{\n    /* The data is distributed over two or more pages. Copy it into the\n    ** Fts5Iter.poslist buffer and then set the output pointer to point\n    ** to this buffer.  */\n    fts5BufferZero(&pIter->poslist);\n    fts5SegiterPoslist(pIter->pIndex, pSeg, 0, &pIter->poslist);\n    pIter->base.pData = pIter->poslist.p;\n  }\n}\n\n/*\n** xSetOutputs callback used when the Fts5Colset object has nCol==0 (match\n** against no columns at all).\n*/\nstatic void fts5IterSetOutputs_ZeroColset(Fts5Iter *pIter, Fts5SegIter *pSeg){\n  UNUSED_PARAM(pSeg);\n  pIter->base.nData = 0;\n}\n\n/*\n** xSetOutputs callback used by detail=col when there is a column filter\n** and there are 100 or more columns. Also called as a fallback from\n** fts5IterSetOutputs_Col100 if the column-list spans more than one page.\n*/\nstatic void fts5IterSetOutputs_Col(Fts5Iter *pIter, Fts5SegIter *pSeg){\n  fts5BufferZero(&pIter->poslist);\n  fts5SegiterPoslist(pIter->pIndex, pSeg, pIter->pColset, &pIter->poslist);\n  pIter->base.iRowid = pSeg->iRowid;\n  pIter->base.pData = pIter->poslist.p;\n  pIter->base.nData = pIter->poslist.n;\n}\n\n/*\n** xSetOutputs callback used when: \n**\n**   * detail=col,\n**   * there is a column filter, and\n**   * the table contains 100 or fewer columns. \n**\n** The last point is to ensure all column numbers are stored as \n** single-byte varints.\n*/\nstatic void fts5IterSetOutputs_Col100(Fts5Iter *pIter, Fts5SegIter *pSeg){\n\n  assert( pIter->pIndex->pConfig->eDetail==FTS5_DETAIL_COLUMNS );\n  assert( pIter->pColset );\n\n  if( pSeg->iLeafOffset+pSeg->nPos>pSeg->pLeaf->szLeaf ){\n    fts5IterSetOutputs_Col(pIter, pSeg);\n  }else{\n    u8 *a = (u8*)&pSeg->pLeaf->p[pSeg->iLeafOffset];\n    u8 *pEnd = (u8*)&a[pSeg->nPos]; \n    int iPrev = 0;\n    int *aiCol = pIter->pColset->aiCol;\n    int *aiColEnd = &aiCol[pIter->pColset->nCol];\n\n    u8 *aOut = pIter->poslist.p;\n    int iPrevOut = 0;\n\n    pIter->base.iRowid = pSeg->iRowid;\n\n    while( a<pEnd ){\n      iPrev += (int)a++[0] - 2;\n      while( *aiCol<iPrev ){\n        aiCol++;\n        if( aiCol==aiColEnd ) goto setoutputs_col_out;\n      }\n      if( *aiCol==iPrev ){\n        *aOut++ = (u8)((iPrev - iPrevOut) + 2);\n        iPrevOut = iPrev;\n      }\n    }\n\nsetoutputs_col_out:\n    pIter->base.pData = pIter->poslist.p;\n    pIter->base.nData = aOut - pIter->poslist.p;\n  }\n}\n\n/*\n** xSetOutputs callback used by detail=full when there is a column filter.\n*/\nstatic void fts5IterSetOutputs_Full(Fts5Iter *pIter, Fts5SegIter *pSeg){\n  Fts5Colset *pColset = pIter->pColset;\n  pIter->base.iRowid = pSeg->iRowid;\n\n  assert( pIter->pIndex->pConfig->eDetail==FTS5_DETAIL_FULL );\n  assert( pColset );\n\n  if( pSeg->iLeafOffset+pSeg->nPos<=pSeg->pLeaf->szLeaf ){\n    /* All data is stored on the current page. Populate the output \n    ** variables to point into the body of the page object. */\n    const u8 *a = &pSeg->pLeaf->p[pSeg->iLeafOffset];\n    if( pColset->nCol==1 ){\n      pIter->base.nData = fts5IndexExtractCol(&a, pSeg->nPos,pColset->aiCol[0]);\n      pIter->base.pData = a;\n    }else{\n      int *pRc = &pIter->pIndex->rc;\n      fts5BufferZero(&pIter->poslist);\n      fts5IndexExtractColset(pRc, pColset, a, pSeg->nPos, &pIter->poslist);\n      pIter->base.pData = pIter->poslist.p;\n      pIter->base.nData = pIter->poslist.n;\n    }\n  }else{\n    /* The data is distributed over two or more pages. Copy it into the\n    ** Fts5Iter.poslist buffer and then set the output pointer to point\n    ** to this buffer.  */\n    fts5BufferZero(&pIter->poslist);\n    fts5SegiterPoslist(pIter->pIndex, pSeg, pColset, &pIter->poslist);\n    pIter->base.pData = pIter->poslist.p;\n    pIter->base.nData = pIter->poslist.n;\n  }\n}\n\nstatic void fts5IterSetOutputCb(int *pRc, Fts5Iter *pIter){\n  if( *pRc==SQLITE_OK ){\n    Fts5Config *pConfig = pIter->pIndex->pConfig;\n    if( pConfig->eDetail==FTS5_DETAIL_NONE ){\n      pIter->xSetOutputs = fts5IterSetOutputs_None;\n    }\n\n    else if( pIter->pColset==0 ){\n      pIter->xSetOutputs = fts5IterSetOutputs_Nocolset;\n    }\n\n    else if( pIter->pColset->nCol==0 ){\n      pIter->xSetOutputs = fts5IterSetOutputs_ZeroColset;\n    }\n\n    else if( pConfig->eDetail==FTS5_DETAIL_FULL ){\n      pIter->xSetOutputs = fts5IterSetOutputs_Full;\n    }\n\n    else{\n      assert( pConfig->eDetail==FTS5_DETAIL_COLUMNS );\n      if( pConfig->nCol<=100 ){\n        pIter->xSetOutputs = fts5IterSetOutputs_Col100;\n        sqlite3Fts5BufferSize(pRc, &pIter->poslist, pConfig->nCol);\n      }else{\n        pIter->xSetOutputs = fts5IterSetOutputs_Col;\n      }\n    }\n  }\n}\n\n\n/*\n** Allocate a new Fts5Iter object.\n**\n** The new object will be used to iterate through data in structure pStruct.\n** If iLevel is -ve, then all data in all segments is merged. Or, if iLevel\n** is zero or greater, data from the first nSegment segments on level iLevel\n** is merged.\n**\n** The iterator initially points to the first term/rowid entry in the \n** iterated data.\n*/\nstatic void fts5MultiIterNew(\n  Fts5Index *p,                   /* FTS5 backend to iterate within */\n  Fts5Structure *pStruct,         /* Structure of specific index */\n  int flags,                      /* FTS5INDEX_QUERY_XXX flags */\n  Fts5Colset *pColset,            /* Colset to filter on (or NULL) */\n  const u8 *pTerm, int nTerm,     /* Term to seek to (or NULL/0) */\n  int iLevel,                     /* Level to iterate (-1 for all) */\n  int nSegment,                   /* Number of segments to merge (iLevel>=0) */\n  Fts5Iter **ppOut                /* New object */\n){\n  int nSeg = 0;                   /* Number of segment-iters in use */\n  int iIter = 0;                  /* */\n  int iSeg;                       /* Used to iterate through segments */\n  Fts5StructureLevel *pLvl;\n  Fts5Iter *pNew;\n\n  assert( (pTerm==0 && nTerm==0) || iLevel<0 );\n\n  /* Allocate space for the new multi-seg-iterator. */\n  if( p->rc==SQLITE_OK ){\n    if( iLevel<0 ){\n      assert( pStruct->nSegment==fts5StructureCountSegments(pStruct) );\n      nSeg = pStruct->nSegment;\n      nSeg += (p->pHash ? 1 : 0);\n    }else{\n      nSeg = MIN(pStruct->aLevel[iLevel].nSeg, nSegment);\n    }\n  }\n  *ppOut = pNew = fts5MultiIterAlloc(p, nSeg);\n  if( pNew==0 ) return;\n  pNew->bRev = (0!=(flags & FTS5INDEX_QUERY_DESC));\n  pNew->bSkipEmpty = (0!=(flags & FTS5INDEX_QUERY_SKIPEMPTY));\n  pNew->pStruct = pStruct;\n  pNew->pColset = pColset;\n  fts5StructureRef(pStruct);\n  if( (flags & FTS5INDEX_QUERY_NOOUTPUT)==0 ){\n    fts5IterSetOutputCb(&p->rc, pNew);\n  }\n\n  /* Initialize each of the component segment iterators. */\n  if( p->rc==SQLITE_OK ){\n    if( iLevel<0 ){\n      Fts5StructureLevel *pEnd = &pStruct->aLevel[pStruct->nLevel];\n      if( p->pHash ){\n        /* Add a segment iterator for the current contents of the hash table. */\n        Fts5SegIter *pIter = &pNew->aSeg[iIter++];\n        fts5SegIterHashInit(p, pTerm, nTerm, flags, pIter);\n      }\n      for(pLvl=&pStruct->aLevel[0]; pLvl<pEnd; pLvl++){\n        for(iSeg=pLvl->nSeg-1; iSeg>=0; iSeg--){\n          Fts5StructureSegment *pSeg = &pLvl->aSeg[iSeg];\n          Fts5SegIter *pIter = &pNew->aSeg[iIter++];\n          if( pTerm==0 ){\n            fts5SegIterInit(p, pSeg, pIter);\n          }else{\n            fts5SegIterSeekInit(p, pTerm, nTerm, flags, pSeg, pIter);\n          }\n        }\n      }\n    }else{\n      pLvl = &pStruct->aLevel[iLevel];\n      for(iSeg=nSeg-1; iSeg>=0; iSeg--){\n        fts5SegIterInit(p, &pLvl->aSeg[iSeg], &pNew->aSeg[iIter++]);\n      }\n    }\n    assert( iIter==nSeg );\n  }\n\n  /* If the above was successful, each component iterators now points \n  ** to the first entry in its segment. In this case initialize the \n  ** aFirst[] array. Or, if an error has occurred, free the iterator\n  ** object and set the output variable to NULL.  */\n  if( p->rc==SQLITE_OK ){\n    for(iIter=pNew->nSeg-1; iIter>0; iIter--){\n      int iEq;\n      if( (iEq = fts5MultiIterDoCompare(pNew, iIter)) ){\n        Fts5SegIter *pSeg = &pNew->aSeg[iEq];\n        if( p->rc==SQLITE_OK ) pSeg->xNext(p, pSeg, 0);\n        fts5MultiIterAdvanced(p, pNew, iEq, iIter);\n      }\n    }\n    fts5MultiIterSetEof(pNew);\n    fts5AssertMultiIterSetup(p, pNew);\n\n    if( pNew->bSkipEmpty && fts5MultiIterIsEmpty(p, pNew) ){\n      fts5MultiIterNext(p, pNew, 0, 0);\n    }else if( pNew->base.bEof==0 ){\n      Fts5SegIter *pSeg = &pNew->aSeg[pNew->aFirst[1].iFirst];\n      pNew->xSetOutputs(pNew, pSeg);\n    }\n\n  }else{\n    fts5MultiIterFree(pNew);\n    *ppOut = 0;\n  }\n}\n\n/*\n** Create an Fts5Iter that iterates through the doclist provided\n** as the second argument.\n*/\nstatic void fts5MultiIterNew2(\n  Fts5Index *p,                   /* FTS5 backend to iterate within */\n  Fts5Data *pData,                /* Doclist to iterate through */\n  int bDesc,                      /* True for descending rowid order */\n  Fts5Iter **ppOut                /* New object */\n){\n  Fts5Iter *pNew;\n  pNew = fts5MultiIterAlloc(p, 2);\n  if( pNew ){\n    Fts5SegIter *pIter = &pNew->aSeg[1];\n\n    pIter->flags = FTS5_SEGITER_ONETERM;\n    if( pData->szLeaf>0 ){\n      pIter->pLeaf = pData;\n      pIter->iLeafOffset = fts5GetVarint(pData->p, (u64*)&pIter->iRowid);\n      pIter->iEndofDoclist = pData->nn;\n      pNew->aFirst[1].iFirst = 1;\n      if( bDesc ){\n        pNew->bRev = 1;\n        pIter->flags |= FTS5_SEGITER_REVERSE;\n        fts5SegIterReverseInitPage(p, pIter);\n      }else{\n        fts5SegIterLoadNPos(p, pIter);\n      }\n      pData = 0;\n    }else{\n      pNew->base.bEof = 1;\n    }\n    fts5SegIterSetNext(p, pIter);\n\n    *ppOut = pNew;\n  }\n\n  fts5DataRelease(pData);\n}\n\n/*\n** Return true if the iterator is at EOF or if an error has occurred. \n** False otherwise.\n*/\nstatic int fts5MultiIterEof(Fts5Index *p, Fts5Iter *pIter){\n  assert( p->rc \n      || (pIter->aSeg[ pIter->aFirst[1].iFirst ].pLeaf==0)==pIter->base.bEof \n  );\n  return (p->rc || pIter->base.bEof);\n}\n\n/*\n** Return the rowid of the entry that the iterator currently points\n** to. If the iterator points to EOF when this function is called the\n** results are undefined.\n*/\nstatic i64 fts5MultiIterRowid(Fts5Iter *pIter){\n  assert( pIter->aSeg[ pIter->aFirst[1].iFirst ].pLeaf );\n  return pIter->aSeg[ pIter->aFirst[1].iFirst ].iRowid;\n}\n\n/*\n** Move the iterator to the next entry at or following iMatch.\n*/\nstatic void fts5MultiIterNextFrom(\n  Fts5Index *p, \n  Fts5Iter *pIter, \n  i64 iMatch\n){\n  while( 1 ){\n    i64 iRowid;\n    fts5MultiIterNext(p, pIter, 1, iMatch);\n    if( fts5MultiIterEof(p, pIter) ) break;\n    iRowid = fts5MultiIterRowid(pIter);\n    if( pIter->bRev==0 && iRowid>=iMatch ) break;\n    if( pIter->bRev!=0 && iRowid<=iMatch ) break;\n  }\n}\n\n/*\n** Return a pointer to a buffer containing the term associated with the \n** entry that the iterator currently points to.\n*/\nstatic const u8 *fts5MultiIterTerm(Fts5Iter *pIter, int *pn){\n  Fts5SegIter *p = &pIter->aSeg[ pIter->aFirst[1].iFirst ];\n  *pn = p->term.n;\n  return p->term.p;\n}\n\n/*\n** Allocate a new segment-id for the structure pStruct. The new segment\n** id must be between 1 and 65335 inclusive, and must not be used by \n** any currently existing segment. If a free segment id cannot be found,\n** SQLITE_FULL is returned.\n**\n** If an error has already occurred, this function is a no-op. 0 is \n** returned in this case.\n*/\nstatic int fts5AllocateSegid(Fts5Index *p, Fts5Structure *pStruct){\n  int iSegid = 0;\n\n  if( p->rc==SQLITE_OK ){\n    if( pStruct->nSegment>=FTS5_MAX_SEGMENT ){\n      p->rc = SQLITE_FULL;\n    }else{\n      /* FTS5_MAX_SEGMENT is currently defined as 2000. So the following\n      ** array is 63 elements, or 252 bytes, in size.  */\n      u32 aUsed[(FTS5_MAX_SEGMENT+31) / 32];\n      int iLvl, iSeg;\n      int i;\n      u32 mask;\n      memset(aUsed, 0, sizeof(aUsed));\n      for(iLvl=0; iLvl<pStruct->nLevel; iLvl++){\n        for(iSeg=0; iSeg<pStruct->aLevel[iLvl].nSeg; iSeg++){\n          int iId = pStruct->aLevel[iLvl].aSeg[iSeg].iSegid;\n          if( iId<=FTS5_MAX_SEGMENT ){\n            aUsed[(iId-1) / 32] |= 1 << ((iId-1) % 32);\n          }\n        }\n      }\n\n      for(i=0; aUsed[i]==0xFFFFFFFF; i++);\n      mask = aUsed[i];\n      for(iSegid=0; mask & (1 << iSegid); iSegid++);\n      iSegid += 1 + i*32;\n\n#ifdef SQLITE_DEBUG\n      for(iLvl=0; iLvl<pStruct->nLevel; iLvl++){\n        for(iSeg=0; iSeg<pStruct->aLevel[iLvl].nSeg; iSeg++){\n          assert( iSegid!=pStruct->aLevel[iLvl].aSeg[iSeg].iSegid );\n        }\n      }\n      assert( iSegid>0 && iSegid<=FTS5_MAX_SEGMENT );\n\n      {\n        sqlite3_stmt *pIdxSelect = fts5IdxSelectStmt(p);\n        if( p->rc==SQLITE_OK ){\n          u8 aBlob[2] = {0xff, 0xff};\n          sqlite3_bind_int(pIdxSelect, 1, iSegid);\n          sqlite3_bind_blob(pIdxSelect, 2, aBlob, 2, SQLITE_STATIC);\n          assert( sqlite3_step(pIdxSelect)!=SQLITE_ROW );\n          p->rc = sqlite3_reset(pIdxSelect);\n          sqlite3_bind_null(pIdxSelect, 2);\n        }\n      }\n#endif\n    }\n  }\n\n  return iSegid;\n}\n\n/*\n** Discard all data currently cached in the hash-tables.\n*/\nstatic void fts5IndexDiscardData(Fts5Index *p){\n  assert( p->pHash || p->nPendingData==0 );\n  if( p->pHash ){\n    sqlite3Fts5HashClear(p->pHash);\n    p->nPendingData = 0;\n  }\n}\n\n/*\n** Return the size of the prefix, in bytes, that buffer \n** (pNew/<length-unknown>) shares with buffer (pOld/nOld).\n**\n** Buffer (pNew/<length-unknown>) is guaranteed to be greater \n** than buffer (pOld/nOld).\n*/\nstatic int fts5PrefixCompress(int nOld, const u8 *pOld, const u8 *pNew){\n  int i;\n  for(i=0; i<nOld; i++){\n    if( pOld[i]!=pNew[i] ) break;\n  }\n  return i;\n}\n\nstatic void fts5WriteDlidxClear(\n  Fts5Index *p, \n  Fts5SegWriter *pWriter,\n  int bFlush                      /* If true, write dlidx to disk */\n){\n  int i;\n  assert( bFlush==0 || (pWriter->nDlidx>0 && pWriter->aDlidx[0].buf.n>0) );\n  for(i=0; i<pWriter->nDlidx; i++){\n    Fts5DlidxWriter *pDlidx = &pWriter->aDlidx[i];\n    if( pDlidx->buf.n==0 ) break;\n    if( bFlush ){\n      assert( pDlidx->pgno!=0 );\n      fts5DataWrite(p, \n          FTS5_DLIDX_ROWID(pWriter->iSegid, i, pDlidx->pgno),\n          pDlidx->buf.p, pDlidx->buf.n\n      );\n    }\n    sqlite3Fts5BufferZero(&pDlidx->buf);\n    pDlidx->bPrevValid = 0;\n  }\n}\n\n/*\n** Grow the pWriter->aDlidx[] array to at least nLvl elements in size.\n** Any new array elements are zeroed before returning.\n*/\nstatic int fts5WriteDlidxGrow(\n  Fts5Index *p,\n  Fts5SegWriter *pWriter,\n  int nLvl\n){\n  if( p->rc==SQLITE_OK && nLvl>=pWriter->nDlidx ){\n    Fts5DlidxWriter *aDlidx = (Fts5DlidxWriter*)sqlite3_realloc(\n        pWriter->aDlidx, sizeof(Fts5DlidxWriter) * nLvl\n    );\n    if( aDlidx==0 ){\n      p->rc = SQLITE_NOMEM;\n    }else{\n      int nByte = sizeof(Fts5DlidxWriter) * (nLvl - pWriter->nDlidx);\n      memset(&aDlidx[pWriter->nDlidx], 0, nByte);\n      pWriter->aDlidx = aDlidx;\n      pWriter->nDlidx = nLvl;\n    }\n  }\n  return p->rc;\n}\n\n/*\n** If the current doclist-index accumulating in pWriter->aDlidx[] is large\n** enough, flush it to disk and return 1. Otherwise discard it and return\n** zero.\n*/\nstatic int fts5WriteFlushDlidx(Fts5Index *p, Fts5SegWriter *pWriter){\n  int bFlag = 0;\n\n  /* If there were FTS5_MIN_DLIDX_SIZE or more empty leaf pages written\n  ** to the database, also write the doclist-index to disk.  */\n  if( pWriter->aDlidx[0].buf.n>0 && pWriter->nEmpty>=FTS5_MIN_DLIDX_SIZE ){\n    bFlag = 1;\n  }\n  fts5WriteDlidxClear(p, pWriter, bFlag);\n  pWriter->nEmpty = 0;\n  return bFlag;\n}\n\n/*\n** This function is called whenever processing of the doclist for the \n** last term on leaf page (pWriter->iBtPage) is completed. \n**\n** The doclist-index for that term is currently stored in-memory within the\n** Fts5SegWriter.aDlidx[] array. If it is large enough, this function\n** writes it out to disk. Or, if it is too small to bother with, discards\n** it.\n**\n** Fts5SegWriter.btterm currently contains the first term on page iBtPage.\n*/\nstatic void fts5WriteFlushBtree(Fts5Index *p, Fts5SegWriter *pWriter){\n  int bFlag;\n\n  assert( pWriter->iBtPage || pWriter->nEmpty==0 );\n  if( pWriter->iBtPage==0 ) return;\n  bFlag = fts5WriteFlushDlidx(p, pWriter);\n\n  if( p->rc==SQLITE_OK ){\n    const char *z = (pWriter->btterm.n>0?(const char*)pWriter->btterm.p:\"\");\n    /* The following was already done in fts5WriteInit(): */\n    /* sqlite3_bind_int(p->pIdxWriter, 1, pWriter->iSegid); */\n    sqlite3_bind_blob(p->pIdxWriter, 2, z, pWriter->btterm.n, SQLITE_STATIC);\n    sqlite3_bind_int64(p->pIdxWriter, 3, bFlag + ((i64)pWriter->iBtPage<<1));\n    sqlite3_step(p->pIdxWriter);\n    p->rc = sqlite3_reset(p->pIdxWriter);\n    sqlite3_bind_null(p->pIdxWriter, 2);\n  }\n  pWriter->iBtPage = 0;\n}\n\n/*\n** This is called once for each leaf page except the first that contains\n** at least one term. Argument (nTerm/pTerm) is the split-key - a term that\n** is larger than all terms written to earlier leaves, and equal to or\n** smaller than the first term on the new leaf.\n**\n** If an error occurs, an error code is left in Fts5Index.rc. If an error\n** has already occurred when this function is called, it is a no-op.\n*/\nstatic void fts5WriteBtreeTerm(\n  Fts5Index *p,                   /* FTS5 backend object */\n  Fts5SegWriter *pWriter,         /* Writer object */\n  int nTerm, const u8 *pTerm      /* First term on new page */\n){\n  fts5WriteFlushBtree(p, pWriter);\n  fts5BufferSet(&p->rc, &pWriter->btterm, nTerm, pTerm);\n  pWriter->iBtPage = pWriter->writer.pgno;\n}\n\n/*\n** This function is called when flushing a leaf page that contains no\n** terms at all to disk.\n*/\nstatic void fts5WriteBtreeNoTerm(\n  Fts5Index *p,                   /* FTS5 backend object */\n  Fts5SegWriter *pWriter          /* Writer object */\n){\n  /* If there were no rowids on the leaf page either and the doclist-index\n  ** has already been started, append an 0x00 byte to it.  */\n  if( pWriter->bFirstRowidInPage && pWriter->aDlidx[0].buf.n>0 ){\n    Fts5DlidxWriter *pDlidx = &pWriter->aDlidx[0];\n    assert( pDlidx->bPrevValid );\n    sqlite3Fts5BufferAppendVarint(&p->rc, &pDlidx->buf, 0);\n  }\n\n  /* Increment the \"number of sequential leaves without a term\" counter. */\n  pWriter->nEmpty++;\n}\n\nstatic i64 fts5DlidxExtractFirstRowid(Fts5Buffer *pBuf){\n  i64 iRowid;\n  int iOff;\n\n  iOff = 1 + fts5GetVarint(&pBuf->p[1], (u64*)&iRowid);\n  fts5GetVarint(&pBuf->p[iOff], (u64*)&iRowid);\n  return iRowid;\n}\n\n/*\n** Rowid iRowid has just been appended to the current leaf page. It is the\n** first on the page. This function appends an appropriate entry to the current\n** doclist-index.\n*/\nstatic void fts5WriteDlidxAppend(\n  Fts5Index *p, \n  Fts5SegWriter *pWriter, \n  i64 iRowid\n){\n  int i;\n  int bDone = 0;\n\n  for(i=0; p->rc==SQLITE_OK && bDone==0; i++){\n    i64 iVal;\n    Fts5DlidxWriter *pDlidx = &pWriter->aDlidx[i];\n\n    if( pDlidx->buf.n>=p->pConfig->pgsz ){\n      /* The current doclist-index page is full. Write it to disk and push\n      ** a copy of iRowid (which will become the first rowid on the next\n      ** doclist-index leaf page) up into the next level of the b-tree \n      ** hierarchy. If the node being flushed is currently the root node,\n      ** also push its first rowid upwards. */\n      pDlidx->buf.p[0] = 0x01;    /* Not the root node */\n      fts5DataWrite(p, \n          FTS5_DLIDX_ROWID(pWriter->iSegid, i, pDlidx->pgno),\n          pDlidx->buf.p, pDlidx->buf.n\n      );\n      fts5WriteDlidxGrow(p, pWriter, i+2);\n      pDlidx = &pWriter->aDlidx[i];\n      if( p->rc==SQLITE_OK && pDlidx[1].buf.n==0 ){\n        i64 iFirst = fts5DlidxExtractFirstRowid(&pDlidx->buf);\n\n        /* This was the root node. Push its first rowid up to the new root. */\n        pDlidx[1].pgno = pDlidx->pgno;\n        sqlite3Fts5BufferAppendVarint(&p->rc, &pDlidx[1].buf, 0);\n        sqlite3Fts5BufferAppendVarint(&p->rc, &pDlidx[1].buf, pDlidx->pgno);\n        sqlite3Fts5BufferAppendVarint(&p->rc, &pDlidx[1].buf, iFirst);\n        pDlidx[1].bPrevValid = 1;\n        pDlidx[1].iPrev = iFirst;\n      }\n\n      sqlite3Fts5BufferZero(&pDlidx->buf);\n      pDlidx->bPrevValid = 0;\n      pDlidx->pgno++;\n    }else{\n      bDone = 1;\n    }\n\n    if( pDlidx->bPrevValid ){\n      iVal = iRowid - pDlidx->iPrev;\n    }else{\n      i64 iPgno = (i==0 ? pWriter->writer.pgno : pDlidx[-1].pgno);\n      assert( pDlidx->buf.n==0 );\n      sqlite3Fts5BufferAppendVarint(&p->rc, &pDlidx->buf, !bDone);\n      sqlite3Fts5BufferAppendVarint(&p->rc, &pDlidx->buf, iPgno);\n      iVal = iRowid;\n    }\n\n    sqlite3Fts5BufferAppendVarint(&p->rc, &pDlidx->buf, iVal);\n    pDlidx->bPrevValid = 1;\n    pDlidx->iPrev = iRowid;\n  }\n}\n\nstatic void fts5WriteFlushLeaf(Fts5Index *p, Fts5SegWriter *pWriter){\n  static const u8 zero[] = { 0x00, 0x00, 0x00, 0x00 };\n  Fts5PageWriter *pPage = &pWriter->writer;\n  i64 iRowid;\n\n  assert( (pPage->pgidx.n==0)==(pWriter->bFirstTermInPage) );\n\n  /* Set the szLeaf header field. */\n  assert( 0==fts5GetU16(&pPage->buf.p[2]) );\n  fts5PutU16(&pPage->buf.p[2], (u16)pPage->buf.n);\n\n  if( pWriter->bFirstTermInPage ){\n    /* No term was written to this page. */\n    assert( pPage->pgidx.n==0 );\n    fts5WriteBtreeNoTerm(p, pWriter);\n  }else{\n    /* Append the pgidx to the page buffer. Set the szLeaf header field. */\n    fts5BufferAppendBlob(&p->rc, &pPage->buf, pPage->pgidx.n, pPage->pgidx.p);\n  }\n\n  /* Write the page out to disk */\n  iRowid = FTS5_SEGMENT_ROWID(pWriter->iSegid, pPage->pgno);\n  fts5DataWrite(p, iRowid, pPage->buf.p, pPage->buf.n);\n\n  /* Initialize the next page. */\n  fts5BufferZero(&pPage->buf);\n  fts5BufferZero(&pPage->pgidx);\n  fts5BufferAppendBlob(&p->rc, &pPage->buf, 4, zero);\n  pPage->iPrevPgidx = 0;\n  pPage->pgno++;\n\n  /* Increase the leaves written counter */\n  pWriter->nLeafWritten++;\n\n  /* The new leaf holds no terms or rowids */\n  pWriter->bFirstTermInPage = 1;\n  pWriter->bFirstRowidInPage = 1;\n}\n\n/*\n** Append term pTerm/nTerm to the segment being written by the writer passed\n** as the second argument.\n**\n** If an error occurs, set the Fts5Index.rc error code. If an error has \n** already occurred, this function is a no-op.\n*/\nstatic void fts5WriteAppendTerm(\n  Fts5Index *p, \n  Fts5SegWriter *pWriter,\n  int nTerm, const u8 *pTerm \n){\n  int nPrefix;                    /* Bytes of prefix compression for term */\n  Fts5PageWriter *pPage = &pWriter->writer;\n  Fts5Buffer *pPgidx = &pWriter->writer.pgidx;\n\n  assert( p->rc==SQLITE_OK );\n  assert( pPage->buf.n>=4 );\n  assert( pPage->buf.n>4 || pWriter->bFirstTermInPage );\n\n  /* If the current leaf page is full, flush it to disk. */\n  if( (pPage->buf.n + pPgidx->n + nTerm + 2)>=p->pConfig->pgsz ){\n    if( pPage->buf.n>4 ){\n      fts5WriteFlushLeaf(p, pWriter);\n    }\n    fts5BufferGrow(&p->rc, &pPage->buf, nTerm+FTS5_DATA_PADDING);\n  }\n  \n  /* TODO1: Updating pgidx here. */\n  pPgidx->n += sqlite3Fts5PutVarint(\n      &pPgidx->p[pPgidx->n], pPage->buf.n - pPage->iPrevPgidx\n  );\n  pPage->iPrevPgidx = pPage->buf.n;\n#if 0\n  fts5PutU16(&pPgidx->p[pPgidx->n], pPage->buf.n);\n  pPgidx->n += 2;\n#endif\n\n  if( pWriter->bFirstTermInPage ){\n    nPrefix = 0;\n    if( pPage->pgno!=1 ){\n      /* This is the first term on a leaf that is not the leftmost leaf in\n      ** the segment b-tree. In this case it is necessary to add a term to\n      ** the b-tree hierarchy that is (a) larger than the largest term \n      ** already written to the segment and (b) smaller than or equal to\n      ** this term. In other words, a prefix of (pTerm/nTerm) that is one\n      ** byte longer than the longest prefix (pTerm/nTerm) shares with the\n      ** previous term. \n      **\n      ** Usually, the previous term is available in pPage->term. The exception\n      ** is if this is the first term written in an incremental-merge step.\n      ** In this case the previous term is not available, so just write a\n      ** copy of (pTerm/nTerm) into the parent node. This is slightly\n      ** inefficient, but still correct.  */\n      int n = nTerm;\n      if( pPage->term.n ){\n        n = 1 + fts5PrefixCompress(pPage->term.n, pPage->term.p, pTerm);\n      }\n      fts5WriteBtreeTerm(p, pWriter, n, pTerm);\n      pPage = &pWriter->writer;\n    }\n  }else{\n    nPrefix = fts5PrefixCompress(pPage->term.n, pPage->term.p, pTerm);\n    fts5BufferAppendVarint(&p->rc, &pPage->buf, nPrefix);\n  }\n\n  /* Append the number of bytes of new data, then the term data itself\n  ** to the page. */\n  fts5BufferAppendVarint(&p->rc, &pPage->buf, nTerm - nPrefix);\n  fts5BufferAppendBlob(&p->rc, &pPage->buf, nTerm - nPrefix, &pTerm[nPrefix]);\n\n  /* Update the Fts5PageWriter.term field. */\n  fts5BufferSet(&p->rc, &pPage->term, nTerm, pTerm);\n  pWriter->bFirstTermInPage = 0;\n\n  pWriter->bFirstRowidInPage = 0;\n  pWriter->bFirstRowidInDoclist = 1;\n\n  assert( p->rc || (pWriter->nDlidx>0 && pWriter->aDlidx[0].buf.n==0) );\n  pWriter->aDlidx[0].pgno = pPage->pgno;\n}\n\n/*\n** Append a rowid and position-list size field to the writers output. \n*/\nstatic void fts5WriteAppendRowid(\n  Fts5Index *p, \n  Fts5SegWriter *pWriter,\n  i64 iRowid\n){\n  if( p->rc==SQLITE_OK ){\n    Fts5PageWriter *pPage = &pWriter->writer;\n\n    if( (pPage->buf.n + pPage->pgidx.n)>=p->pConfig->pgsz ){\n      fts5WriteFlushLeaf(p, pWriter);\n    }\n\n    /* If this is to be the first rowid written to the page, set the \n    ** rowid-pointer in the page-header. Also append a value to the dlidx\n    ** buffer, in case a doclist-index is required.  */\n    if( pWriter->bFirstRowidInPage ){\n      fts5PutU16(pPage->buf.p, (u16)pPage->buf.n);\n      fts5WriteDlidxAppend(p, pWriter, iRowid);\n    }\n\n    /* Write the rowid. */\n    if( pWriter->bFirstRowidInDoclist || pWriter->bFirstRowidInPage ){\n      fts5BufferAppendVarint(&p->rc, &pPage->buf, iRowid);\n    }else{\n      assert( p->rc || iRowid>pWriter->iPrevRowid );\n      fts5BufferAppendVarint(&p->rc, &pPage->buf, iRowid - pWriter->iPrevRowid);\n    }\n    pWriter->iPrevRowid = iRowid;\n    pWriter->bFirstRowidInDoclist = 0;\n    pWriter->bFirstRowidInPage = 0;\n  }\n}\n\nstatic void fts5WriteAppendPoslistData(\n  Fts5Index *p, \n  Fts5SegWriter *pWriter, \n  const u8 *aData, \n  int nData\n){\n  Fts5PageWriter *pPage = &pWriter->writer;\n  const u8 *a = aData;\n  int n = nData;\n  \n  assert( p->pConfig->pgsz>0 );\n  while( p->rc==SQLITE_OK \n     && (pPage->buf.n + pPage->pgidx.n + n)>=p->pConfig->pgsz \n  ){\n    int nReq = p->pConfig->pgsz - pPage->buf.n - pPage->pgidx.n;\n    int nCopy = 0;\n    while( nCopy<nReq ){\n      i64 dummy;\n      nCopy += fts5GetVarint(&a[nCopy], (u64*)&dummy);\n    }\n    fts5BufferAppendBlob(&p->rc, &pPage->buf, nCopy, a);\n    a += nCopy;\n    n -= nCopy;\n    fts5WriteFlushLeaf(p, pWriter);\n  }\n  if( n>0 ){\n    fts5BufferAppendBlob(&p->rc, &pPage->buf, n, a);\n  }\n}\n\n/*\n** Flush any data cached by the writer object to the database. Free any\n** allocations associated with the writer.\n*/\nstatic void fts5WriteFinish(\n  Fts5Index *p, \n  Fts5SegWriter *pWriter,         /* Writer object */\n  int *pnLeaf                     /* OUT: Number of leaf pages in b-tree */\n){\n  int i;\n  Fts5PageWriter *pLeaf = &pWriter->writer;\n  if( p->rc==SQLITE_OK ){\n    assert( pLeaf->pgno>=1 );\n    if( pLeaf->buf.n>4 ){\n      fts5WriteFlushLeaf(p, pWriter);\n    }\n    *pnLeaf = pLeaf->pgno-1;\n    if( pLeaf->pgno>1 ){\n      fts5WriteFlushBtree(p, pWriter);\n    }\n  }\n  fts5BufferFree(&pLeaf->term);\n  fts5BufferFree(&pLeaf->buf);\n  fts5BufferFree(&pLeaf->pgidx);\n  fts5BufferFree(&pWriter->btterm);\n\n  for(i=0; i<pWriter->nDlidx; i++){\n    sqlite3Fts5BufferFree(&pWriter->aDlidx[i].buf);\n  }\n  sqlite3_free(pWriter->aDlidx);\n}\n\nstatic void fts5WriteInit(\n  Fts5Index *p, \n  Fts5SegWriter *pWriter, \n  int iSegid\n){\n  const int nBuffer = p->pConfig->pgsz + FTS5_DATA_PADDING;\n\n  memset(pWriter, 0, sizeof(Fts5SegWriter));\n  pWriter->iSegid = iSegid;\n\n  fts5WriteDlidxGrow(p, pWriter, 1);\n  pWriter->writer.pgno = 1;\n  pWriter->bFirstTermInPage = 1;\n  pWriter->iBtPage = 1;\n\n  assert( pWriter->writer.buf.n==0 );\n  assert( pWriter->writer.pgidx.n==0 );\n\n  /* Grow the two buffers to pgsz + padding bytes in size. */\n  sqlite3Fts5BufferSize(&p->rc, &pWriter->writer.pgidx, nBuffer);\n  sqlite3Fts5BufferSize(&p->rc, &pWriter->writer.buf, nBuffer);\n\n  if( p->pIdxWriter==0 ){\n    Fts5Config *pConfig = p->pConfig;\n    fts5IndexPrepareStmt(p, &p->pIdxWriter, sqlite3_mprintf(\n          \"INSERT INTO '%q'.'%q_idx'(segid,term,pgno) VALUES(?,?,?)\", \n          pConfig->zDb, pConfig->zName\n    ));\n  }\n\n  if( p->rc==SQLITE_OK ){\n    /* Initialize the 4-byte leaf-page header to 0x00. */\n    memset(pWriter->writer.buf.p, 0, 4);\n    pWriter->writer.buf.n = 4;\n\n    /* Bind the current output segment id to the index-writer. This is an\n    ** optimization over binding the same value over and over as rows are\n    ** inserted into %_idx by the current writer.  */\n    sqlite3_bind_int(p->pIdxWriter, 1, pWriter->iSegid);\n  }\n}\n\n/*\n** Iterator pIter was used to iterate through the input segments of on an\n** incremental merge operation. This function is called if the incremental\n** merge step has finished but the input has not been completely exhausted.\n*/\nstatic void fts5TrimSegments(Fts5Index *p, Fts5Iter *pIter){\n  int i;\n  Fts5Buffer buf;\n  memset(&buf, 0, sizeof(Fts5Buffer));\n  for(i=0; i<pIter->nSeg; i++){\n    Fts5SegIter *pSeg = &pIter->aSeg[i];\n    if( pSeg->pSeg==0 ){\n      /* no-op */\n    }else if( pSeg->pLeaf==0 ){\n      /* All keys from this input segment have been transfered to the output.\n      ** Set both the first and last page-numbers to 0 to indicate that the\n      ** segment is now empty. */\n      pSeg->pSeg->pgnoLast = 0;\n      pSeg->pSeg->pgnoFirst = 0;\n    }else{\n      int iOff = pSeg->iTermLeafOffset;     /* Offset on new first leaf page */\n      i64 iLeafRowid;\n      Fts5Data *pData;\n      int iId = pSeg->pSeg->iSegid;\n      u8 aHdr[4] = {0x00, 0x00, 0x00, 0x00};\n\n      iLeafRowid = FTS5_SEGMENT_ROWID(iId, pSeg->iTermLeafPgno);\n      pData = fts5DataRead(p, iLeafRowid);\n      if( pData ){\n        fts5BufferZero(&buf);\n        fts5BufferGrow(&p->rc, &buf, pData->nn);\n        fts5BufferAppendBlob(&p->rc, &buf, sizeof(aHdr), aHdr);\n        fts5BufferAppendVarint(&p->rc, &buf, pSeg->term.n);\n        fts5BufferAppendBlob(&p->rc, &buf, pSeg->term.n, pSeg->term.p);\n        fts5BufferAppendBlob(&p->rc, &buf, pData->szLeaf-iOff, &pData->p[iOff]);\n        if( p->rc==SQLITE_OK ){\n          /* Set the szLeaf field */\n          fts5PutU16(&buf.p[2], (u16)buf.n);\n        }\n\n        /* Set up the new page-index array */\n        fts5BufferAppendVarint(&p->rc, &buf, 4);\n        if( pSeg->iLeafPgno==pSeg->iTermLeafPgno \n         && pSeg->iEndofDoclist<pData->szLeaf \n        ){\n          int nDiff = pData->szLeaf - pSeg->iEndofDoclist;\n          fts5BufferAppendVarint(&p->rc, &buf, buf.n - 1 - nDiff - 4);\n          fts5BufferAppendBlob(&p->rc, &buf, \n              pData->nn - pSeg->iPgidxOff, &pData->p[pSeg->iPgidxOff]\n          );\n        }\n\n        fts5DataRelease(pData);\n        pSeg->pSeg->pgnoFirst = pSeg->iTermLeafPgno;\n        fts5DataDelete(p, FTS5_SEGMENT_ROWID(iId, 1), iLeafRowid);\n        fts5DataWrite(p, iLeafRowid, buf.p, buf.n);\n      }\n    }\n  }\n  fts5BufferFree(&buf);\n}\n\nstatic void fts5MergeChunkCallback(\n  Fts5Index *p, \n  void *pCtx, \n  const u8 *pChunk, int nChunk\n){\n  Fts5SegWriter *pWriter = (Fts5SegWriter*)pCtx;\n  fts5WriteAppendPoslistData(p, pWriter, pChunk, nChunk);\n}\n\n/*\n**\n*/\nstatic void fts5IndexMergeLevel(\n  Fts5Index *p,                   /* FTS5 backend object */\n  Fts5Structure **ppStruct,       /* IN/OUT: Stucture of index */\n  int iLvl,                       /* Level to read input from */\n  int *pnRem                      /* Write up to this many output leaves */\n){\n  Fts5Structure *pStruct = *ppStruct;\n  Fts5StructureLevel *pLvl = &pStruct->aLevel[iLvl];\n  Fts5StructureLevel *pLvlOut;\n  Fts5Iter *pIter = 0;       /* Iterator to read input data */\n  int nRem = pnRem ? *pnRem : 0;  /* Output leaf pages left to write */\n  int nInput;                     /* Number of input segments */\n  Fts5SegWriter writer;           /* Writer object */\n  Fts5StructureSegment *pSeg;     /* Output segment */\n  Fts5Buffer term;\n  int bOldest;                    /* True if the output segment is the oldest */\n  int eDetail = p->pConfig->eDetail;\n  const int flags = FTS5INDEX_QUERY_NOOUTPUT;\n  int bTermWritten = 0;           /* True if current term already output */\n\n  assert( iLvl<pStruct->nLevel );\n  assert( pLvl->nMerge<=pLvl->nSeg );\n\n  memset(&writer, 0, sizeof(Fts5SegWriter));\n  memset(&term, 0, sizeof(Fts5Buffer));\n  if( pLvl->nMerge ){\n    pLvlOut = &pStruct->aLevel[iLvl+1];\n    assert( pLvlOut->nSeg>0 );\n    nInput = pLvl->nMerge;\n    pSeg = &pLvlOut->aSeg[pLvlOut->nSeg-1];\n\n    fts5WriteInit(p, &writer, pSeg->iSegid);\n    writer.writer.pgno = pSeg->pgnoLast+1;\n    writer.iBtPage = 0;\n  }else{\n    int iSegid = fts5AllocateSegid(p, pStruct);\n\n    /* Extend the Fts5Structure object as required to ensure the output\n    ** segment exists. */\n    if( iLvl==pStruct->nLevel-1 ){\n      fts5StructureAddLevel(&p->rc, ppStruct);\n      pStruct = *ppStruct;\n    }\n    fts5StructureExtendLevel(&p->rc, pStruct, iLvl+1, 1, 0);\n    if( p->rc ) return;\n    pLvl = &pStruct->aLevel[iLvl];\n    pLvlOut = &pStruct->aLevel[iLvl+1];\n\n    fts5WriteInit(p, &writer, iSegid);\n\n    /* Add the new segment to the output level */\n    pSeg = &pLvlOut->aSeg[pLvlOut->nSeg];\n    pLvlOut->nSeg++;\n    pSeg->pgnoFirst = 1;\n    pSeg->iSegid = iSegid;\n    pStruct->nSegment++;\n\n    /* Read input from all segments in the input level */\n    nInput = pLvl->nSeg;\n  }\n  bOldest = (pLvlOut->nSeg==1 && pStruct->nLevel==iLvl+2);\n\n  assert( iLvl>=0 );\n  for(fts5MultiIterNew(p, pStruct, flags, 0, 0, 0, iLvl, nInput, &pIter);\n      fts5MultiIterEof(p, pIter)==0;\n      fts5MultiIterNext(p, pIter, 0, 0)\n  ){\n    Fts5SegIter *pSegIter = &pIter->aSeg[ pIter->aFirst[1].iFirst ];\n    int nPos;                     /* position-list size field value */\n    int nTerm;\n    const u8 *pTerm;\n\n    pTerm = fts5MultiIterTerm(pIter, &nTerm);\n    if( nTerm!=term.n || memcmp(pTerm, term.p, nTerm) ){\n      if( pnRem && writer.nLeafWritten>nRem ){\n        break;\n      }\n      fts5BufferSet(&p->rc, &term, nTerm, pTerm);\n      bTermWritten =0;\n    }\n\n    /* Check for key annihilation. */\n    if( pSegIter->nPos==0 && (bOldest || pSegIter->bDel==0) ) continue;\n\n    if( p->rc==SQLITE_OK && bTermWritten==0 ){\n      /* This is a new term. Append a term to the output segment. */\n      fts5WriteAppendTerm(p, &writer, nTerm, pTerm);\n      bTermWritten = 1;\n    }\n\n    /* Append the rowid to the output */\n    /* WRITEPOSLISTSIZE */\n    fts5WriteAppendRowid(p, &writer, fts5MultiIterRowid(pIter));\n\n    if( eDetail==FTS5_DETAIL_NONE ){\n      if( pSegIter->bDel ){\n        fts5BufferAppendVarint(&p->rc, &writer.writer.buf, 0);\n        if( pSegIter->nPos>0 ){\n          fts5BufferAppendVarint(&p->rc, &writer.writer.buf, 0);\n        }\n      }\n    }else{\n      /* Append the position-list data to the output */\n      nPos = pSegIter->nPos*2 + pSegIter->bDel;\n      fts5BufferAppendVarint(&p->rc, &writer.writer.buf, nPos);\n      fts5ChunkIterate(p, pSegIter, (void*)&writer, fts5MergeChunkCallback);\n    }\n  }\n\n  /* Flush the last leaf page to disk. Set the output segment b-tree height\n  ** and last leaf page number at the same time.  */\n  fts5WriteFinish(p, &writer, &pSeg->pgnoLast);\n\n  if( fts5MultiIterEof(p, pIter) ){\n    int i;\n\n    /* Remove the redundant segments from the %_data table */\n    for(i=0; i<nInput; i++){\n      fts5DataRemoveSegment(p, pLvl->aSeg[i].iSegid);\n    }\n\n    /* Remove the redundant segments from the input level */\n    if( pLvl->nSeg!=nInput ){\n      int nMove = (pLvl->nSeg - nInput) * sizeof(Fts5StructureSegment);\n      memmove(pLvl->aSeg, &pLvl->aSeg[nInput], nMove);\n    }\n    pStruct->nSegment -= nInput;\n    pLvl->nSeg -= nInput;\n    pLvl->nMerge = 0;\n    if( pSeg->pgnoLast==0 ){\n      pLvlOut->nSeg--;\n      pStruct->nSegment--;\n    }\n  }else{\n    assert( pSeg->pgnoLast>0 );\n    fts5TrimSegments(p, pIter);\n    pLvl->nMerge = nInput;\n  }\n\n  fts5MultiIterFree(pIter);\n  fts5BufferFree(&term);\n  if( pnRem ) *pnRem -= writer.nLeafWritten;\n}\n\n/*\n** Do up to nPg pages of automerge work on the index.\n**\n** Return true if any changes were actually made, or false otherwise.\n*/\nstatic int fts5IndexMerge(\n  Fts5Index *p,                   /* FTS5 backend object */\n  Fts5Structure **ppStruct,       /* IN/OUT: Current structure of index */\n  int nPg,                        /* Pages of work to do */\n  int nMin                        /* Minimum number of segments to merge */\n){\n  int nRem = nPg;\n  int bRet = 0;\n  Fts5Structure *pStruct = *ppStruct;\n  while( nRem>0 && p->rc==SQLITE_OK ){\n    int iLvl;                   /* To iterate through levels */\n    int iBestLvl = 0;           /* Level offering the most input segments */\n    int nBest = 0;              /* Number of input segments on best level */\n\n    /* Set iBestLvl to the level to read input segments from. */\n    assert( pStruct->nLevel>0 );\n    for(iLvl=0; iLvl<pStruct->nLevel; iLvl++){\n      Fts5StructureLevel *pLvl = &pStruct->aLevel[iLvl];\n      if( pLvl->nMerge ){\n        if( pLvl->nMerge>nBest ){\n          iBestLvl = iLvl;\n          nBest = pLvl->nMerge;\n        }\n        break;\n      }\n      if( pLvl->nSeg>nBest ){\n        nBest = pLvl->nSeg;\n        iBestLvl = iLvl;\n      }\n    }\n\n    /* If nBest is still 0, then the index must be empty. */\n#ifdef SQLITE_DEBUG\n    for(iLvl=0; nBest==0 && iLvl<pStruct->nLevel; iLvl++){\n      assert( pStruct->aLevel[iLvl].nSeg==0 );\n    }\n#endif\n\n    if( nBest<nMin && pStruct->aLevel[iBestLvl].nMerge==0 ){\n      break;\n    }\n    bRet = 1;\n    fts5IndexMergeLevel(p, &pStruct, iBestLvl, &nRem);\n    if( p->rc==SQLITE_OK && pStruct->aLevel[iBestLvl].nMerge==0 ){\n      fts5StructurePromote(p, iBestLvl+1, pStruct);\n    }\n  }\n  *ppStruct = pStruct;\n  return bRet;\n}\n\n/*\n** A total of nLeaf leaf pages of data has just been flushed to a level-0\n** segment. This function updates the write-counter accordingly and, if\n** necessary, performs incremental merge work.\n**\n** If an error occurs, set the Fts5Index.rc error code. If an error has \n** already occurred, this function is a no-op.\n*/\nstatic void fts5IndexAutomerge(\n  Fts5Index *p,                   /* FTS5 backend object */\n  Fts5Structure **ppStruct,       /* IN/OUT: Current structure of index */\n  int nLeaf                       /* Number of output leaves just written */\n){\n  if( p->rc==SQLITE_OK && p->pConfig->nAutomerge>0 ){\n    Fts5Structure *pStruct = *ppStruct;\n    u64 nWrite;                   /* Initial value of write-counter */\n    int nWork;                    /* Number of work-quanta to perform */\n    int nRem;                     /* Number of leaf pages left to write */\n\n    /* Update the write-counter. While doing so, set nWork. */\n    nWrite = pStruct->nWriteCounter;\n    nWork = (int)(((nWrite + nLeaf) / p->nWorkUnit) - (nWrite / p->nWorkUnit));\n    pStruct->nWriteCounter += nLeaf;\n    nRem = (int)(p->nWorkUnit * nWork * pStruct->nLevel);\n\n    fts5IndexMerge(p, ppStruct, nRem, p->pConfig->nAutomerge);\n  }\n}\n\nstatic void fts5IndexCrisismerge(\n  Fts5Index *p,                   /* FTS5 backend object */\n  Fts5Structure **ppStruct        /* IN/OUT: Current structure of index */\n){\n  const int nCrisis = p->pConfig->nCrisisMerge;\n  Fts5Structure *pStruct = *ppStruct;\n  int iLvl = 0;\n\n  assert( p->rc!=SQLITE_OK || pStruct->nLevel>0 );\n  while( p->rc==SQLITE_OK && pStruct->aLevel[iLvl].nSeg>=nCrisis ){\n    fts5IndexMergeLevel(p, &pStruct, iLvl, 0);\n    assert( p->rc!=SQLITE_OK || pStruct->nLevel>(iLvl+1) );\n    fts5StructurePromote(p, iLvl+1, pStruct);\n    iLvl++;\n  }\n  *ppStruct = pStruct;\n}\n\nstatic int fts5IndexReturn(Fts5Index *p){\n  int rc = p->rc;\n  p->rc = SQLITE_OK;\n  return rc;\n}\n\ntypedef struct Fts5FlushCtx Fts5FlushCtx;\nstruct Fts5FlushCtx {\n  Fts5Index *pIdx;\n  Fts5SegWriter writer; \n};\n\n/*\n** Buffer aBuf[] contains a list of varints, all small enough to fit\n** in a 32-bit integer. Return the size of the largest prefix of this \n** list nMax bytes or less in size.\n*/\nstatic int fts5PoslistPrefix(const u8 *aBuf, int nMax){\n  int ret;\n  u32 dummy;\n  ret = fts5GetVarint32(aBuf, dummy);\n  if( ret<nMax ){\n    while( 1 ){\n      int i = fts5GetVarint32(&aBuf[ret], dummy);\n      if( (ret + i) > nMax ) break;\n      ret += i;\n    }\n  }\n  return ret;\n}\n\n/*\n** Flush the contents of in-memory hash table iHash to a new level-0 \n** segment on disk. Also update the corresponding structure record.\n**\n** If an error occurs, set the Fts5Index.rc error code. If an error has \n** already occurred, this function is a no-op.\n*/\nstatic void fts5FlushOneHash(Fts5Index *p){\n  Fts5Hash *pHash = p->pHash;\n  Fts5Structure *pStruct;\n  int iSegid;\n  int pgnoLast = 0;                 /* Last leaf page number in segment */\n\n  /* Obtain a reference to the index structure and allocate a new segment-id\n  ** for the new level-0 segment.  */\n  pStruct = fts5StructureRead(p);\n  iSegid = fts5AllocateSegid(p, pStruct);\n  fts5StructureInvalidate(p);\n\n  if( iSegid ){\n    const int pgsz = p->pConfig->pgsz;\n    int eDetail = p->pConfig->eDetail;\n    Fts5StructureSegment *pSeg;   /* New segment within pStruct */\n    Fts5Buffer *pBuf;             /* Buffer in which to assemble leaf page */\n    Fts5Buffer *pPgidx;           /* Buffer in which to assemble pgidx */\n\n    Fts5SegWriter writer;\n    fts5WriteInit(p, &writer, iSegid);\n\n    pBuf = &writer.writer.buf;\n    pPgidx = &writer.writer.pgidx;\n\n    /* fts5WriteInit() should have initialized the buffers to (most likely)\n    ** the maximum space required. */\n    assert( p->rc || pBuf->nSpace>=(pgsz + FTS5_DATA_PADDING) );\n    assert( p->rc || pPgidx->nSpace>=(pgsz + FTS5_DATA_PADDING) );\n\n    /* Begin scanning through hash table entries. This loop runs once for each\n    ** term/doclist currently stored within the hash table. */\n    if( p->rc==SQLITE_OK ){\n      p->rc = sqlite3Fts5HashScanInit(pHash, 0, 0);\n    }\n    while( p->rc==SQLITE_OK && 0==sqlite3Fts5HashScanEof(pHash) ){\n      const char *zTerm;          /* Buffer containing term */\n      const u8 *pDoclist;         /* Pointer to doclist for this term */\n      int nDoclist;               /* Size of doclist in bytes */\n\n      /* Write the term for this entry to disk. */\n      sqlite3Fts5HashScanEntry(pHash, &zTerm, &pDoclist, &nDoclist);\n      fts5WriteAppendTerm(p, &writer, (int)strlen(zTerm), (const u8*)zTerm);\n\n      assert( writer.bFirstRowidInPage==0 );\n      if( pgsz>=(pBuf->n + pPgidx->n + nDoclist + 1) ){\n        /* The entire doclist will fit on the current leaf. */\n        fts5BufferSafeAppendBlob(pBuf, pDoclist, nDoclist);\n      }else{\n        i64 iRowid = 0;\n        i64 iDelta = 0;\n        int iOff = 0;\n\n        /* The entire doclist will not fit on this leaf. The following \n        ** loop iterates through the poslists that make up the current \n        ** doclist.  */\n        while( p->rc==SQLITE_OK && iOff<nDoclist ){\n          iOff += fts5GetVarint(&pDoclist[iOff], (u64*)&iDelta);\n          iRowid += iDelta;\n          \n          if( writer.bFirstRowidInPage ){\n            fts5PutU16(&pBuf->p[0], (u16)pBuf->n);   /* first rowid on page */\n            pBuf->n += sqlite3Fts5PutVarint(&pBuf->p[pBuf->n], iRowid);\n            writer.bFirstRowidInPage = 0;\n            fts5WriteDlidxAppend(p, &writer, iRowid);\n          }else{\n            pBuf->n += sqlite3Fts5PutVarint(&pBuf->p[pBuf->n], iDelta);\n          }\n          assert( pBuf->n<=pBuf->nSpace );\n\n          if( eDetail==FTS5_DETAIL_NONE ){\n            if( iOff<nDoclist && pDoclist[iOff]==0 ){\n              pBuf->p[pBuf->n++] = 0;\n              iOff++;\n              if( iOff<nDoclist && pDoclist[iOff]==0 ){\n                pBuf->p[pBuf->n++] = 0;\n                iOff++;\n              }\n            }\n            if( (pBuf->n + pPgidx->n)>=pgsz ){\n              fts5WriteFlushLeaf(p, &writer);\n            }\n          }else{\n            int bDummy;\n            int nPos;\n            int nCopy = fts5GetPoslistSize(&pDoclist[iOff], &nPos, &bDummy);\n            nCopy += nPos;\n            if( (pBuf->n + pPgidx->n + nCopy) <= pgsz ){\n              /* The entire poslist will fit on the current leaf. So copy\n              ** it in one go. */\n              fts5BufferSafeAppendBlob(pBuf, &pDoclist[iOff], nCopy);\n            }else{\n              /* The entire poslist will not fit on this leaf. So it needs\n              ** to be broken into sections. The only qualification being\n              ** that each varint must be stored contiguously.  */\n              const u8 *pPoslist = &pDoclist[iOff];\n              int iPos = 0;\n              while( p->rc==SQLITE_OK ){\n                int nSpace = pgsz - pBuf->n - pPgidx->n;\n                int n = 0;\n                if( (nCopy - iPos)<=nSpace ){\n                  n = nCopy - iPos;\n                }else{\n                  n = fts5PoslistPrefix(&pPoslist[iPos], nSpace);\n                }\n                assert( n>0 );\n                fts5BufferSafeAppendBlob(pBuf, &pPoslist[iPos], n);\n                iPos += n;\n                if( (pBuf->n + pPgidx->n)>=pgsz ){\n                  fts5WriteFlushLeaf(p, &writer);\n                }\n                if( iPos>=nCopy ) break;\n              }\n            }\n            iOff += nCopy;\n          }\n        }\n      }\n\n      /* TODO2: Doclist terminator written here. */\n      /* pBuf->p[pBuf->n++] = '\\0'; */\n      assert( pBuf->n<=pBuf->nSpace );\n      sqlite3Fts5HashScanNext(pHash);\n    }\n    sqlite3Fts5HashClear(pHash);\n    fts5WriteFinish(p, &writer, &pgnoLast);\n\n    /* Update the Fts5Structure. It is written back to the database by the\n    ** fts5StructureRelease() call below.  */\n    if( pStruct->nLevel==0 ){\n      fts5StructureAddLevel(&p->rc, &pStruct);\n    }\n    fts5StructureExtendLevel(&p->rc, pStruct, 0, 1, 0);\n    if( p->rc==SQLITE_OK ){\n      pSeg = &pStruct->aLevel[0].aSeg[ pStruct->aLevel[0].nSeg++ ];\n      pSeg->iSegid = iSegid;\n      pSeg->pgnoFirst = 1;\n      pSeg->pgnoLast = pgnoLast;\n      pStruct->nSegment++;\n    }\n    fts5StructurePromote(p, 0, pStruct);\n  }\n\n  fts5IndexAutomerge(p, &pStruct, pgnoLast);\n  fts5IndexCrisismerge(p, &pStruct);\n  fts5StructureWrite(p, pStruct);\n  fts5StructureRelease(pStruct);\n}\n\n/*\n** Flush any data stored in the in-memory hash tables to the database.\n*/\nstatic void fts5IndexFlush(Fts5Index *p){\n  /* Unless it is empty, flush the hash table to disk */\n  if( p->nPendingData ){\n    assert( p->pHash );\n    p->nPendingData = 0;\n    fts5FlushOneHash(p);\n  }\n}\n\nstatic Fts5Structure *fts5IndexOptimizeStruct(\n  Fts5Index *p, \n  Fts5Structure *pStruct\n){\n  Fts5Structure *pNew = 0;\n  int nByte = sizeof(Fts5Structure);\n  int nSeg = pStruct->nSegment;\n  int i;\n\n  /* Figure out if this structure requires optimization. A structure does\n  ** not require optimization if either:\n  **\n  **  + it consists of fewer than two segments, or \n  **  + all segments are on the same level, or\n  **  + all segments except one are currently inputs to a merge operation.\n  **\n  ** In the first case, return NULL. In the second, increment the ref-count\n  ** on *pStruct and return a copy of the pointer to it.\n  */\n  if( nSeg<2 ) return 0;\n  for(i=0; i<pStruct->nLevel; i++){\n    int nThis = pStruct->aLevel[i].nSeg;\n    if( nThis==nSeg || (nThis==nSeg-1 && pStruct->aLevel[i].nMerge==nThis) ){\n      fts5StructureRef(pStruct);\n      return pStruct;\n    }\n    assert( pStruct->aLevel[i].nMerge<=nThis );\n  }\n\n  nByte += (pStruct->nLevel+1) * sizeof(Fts5StructureLevel);\n  pNew = (Fts5Structure*)sqlite3Fts5MallocZero(&p->rc, nByte);\n\n  if( pNew ){\n    Fts5StructureLevel *pLvl;\n    nByte = nSeg * sizeof(Fts5StructureSegment);\n    pNew->nLevel = pStruct->nLevel+1;\n    pNew->nRef = 1;\n    pNew->nWriteCounter = pStruct->nWriteCounter;\n    pLvl = &pNew->aLevel[pStruct->nLevel];\n    pLvl->aSeg = (Fts5StructureSegment*)sqlite3Fts5MallocZero(&p->rc, nByte);\n    if( pLvl->aSeg ){\n      int iLvl, iSeg;\n      int iSegOut = 0;\n      /* Iterate through all segments, from oldest to newest. Add them to\n      ** the new Fts5Level object so that pLvl->aSeg[0] is the oldest\n      ** segment in the data structure.  */\n      for(iLvl=pStruct->nLevel-1; iLvl>=0; iLvl--){\n        for(iSeg=0; iSeg<pStruct->aLevel[iLvl].nSeg; iSeg++){\n          pLvl->aSeg[iSegOut] = pStruct->aLevel[iLvl].aSeg[iSeg];\n          iSegOut++;\n        }\n      }\n      pNew->nSegment = pLvl->nSeg = nSeg;\n    }else{\n      sqlite3_free(pNew);\n      pNew = 0;\n    }\n  }\n\n  return pNew;\n}\n\nstatic int sqlite3Fts5IndexOptimize(Fts5Index *p){\n  Fts5Structure *pStruct;\n  Fts5Structure *pNew = 0;\n\n  assert( p->rc==SQLITE_OK );\n  fts5IndexFlush(p);\n  pStruct = fts5StructureRead(p);\n  fts5StructureInvalidate(p);\n\n  if( pStruct ){\n    pNew = fts5IndexOptimizeStruct(p, pStruct);\n  }\n  fts5StructureRelease(pStruct);\n\n  assert( pNew==0 || pNew->nSegment>0 );\n  if( pNew ){\n    int iLvl;\n    for(iLvl=0; pNew->aLevel[iLvl].nSeg==0; iLvl++){}\n    while( p->rc==SQLITE_OK && pNew->aLevel[iLvl].nSeg>0 ){\n      int nRem = FTS5_OPT_WORK_UNIT;\n      fts5IndexMergeLevel(p, &pNew, iLvl, &nRem);\n    }\n\n    fts5StructureWrite(p, pNew);\n    fts5StructureRelease(pNew);\n  }\n\n  return fts5IndexReturn(p); \n}\n\n/*\n** This is called to implement the special \"VALUES('merge', $nMerge)\"\n** INSERT command.\n*/\nstatic int sqlite3Fts5IndexMerge(Fts5Index *p, int nMerge){\n  Fts5Structure *pStruct = fts5StructureRead(p);\n  if( pStruct ){\n    int nMin = p->pConfig->nUsermerge;\n    fts5StructureInvalidate(p);\n    if( nMerge<0 ){\n      Fts5Structure *pNew = fts5IndexOptimizeStruct(p, pStruct);\n      fts5StructureRelease(pStruct);\n      pStruct = pNew;\n      nMin = 2;\n      nMerge = nMerge*-1;\n    }\n    if( pStruct && pStruct->nLevel ){\n      if( fts5IndexMerge(p, &pStruct, nMerge, nMin) ){\n        fts5StructureWrite(p, pStruct);\n      }\n    }\n    fts5StructureRelease(pStruct);\n  }\n  return fts5IndexReturn(p);\n}\n\nstatic void fts5AppendRowid(\n  Fts5Index *p,\n  i64 iDelta,\n  Fts5Iter *pUnused,\n  Fts5Buffer *pBuf\n){\n  UNUSED_PARAM(pUnused);\n  fts5BufferAppendVarint(&p->rc, pBuf, iDelta);\n}\n\nstatic void fts5AppendPoslist(\n  Fts5Index *p,\n  i64 iDelta,\n  Fts5Iter *pMulti,\n  Fts5Buffer *pBuf\n){\n  int nData = pMulti->base.nData;\n  assert( nData>0 );\n  if( p->rc==SQLITE_OK && 0==fts5BufferGrow(&p->rc, pBuf, nData+9+9) ){\n    fts5BufferSafeAppendVarint(pBuf, iDelta);\n    fts5BufferSafeAppendVarint(pBuf, nData*2);\n    fts5BufferSafeAppendBlob(pBuf, pMulti->base.pData, nData);\n  }\n}\n\n\nstatic void fts5DoclistIterNext(Fts5DoclistIter *pIter){\n  u8 *p = pIter->aPoslist + pIter->nSize + pIter->nPoslist;\n\n  assert( pIter->aPoslist );\n  if( p>=pIter->aEof ){\n    pIter->aPoslist = 0;\n  }else{\n    i64 iDelta;\n\n    p += fts5GetVarint(p, (u64*)&iDelta);\n    pIter->iRowid += iDelta;\n\n    /* Read position list size */\n    if( p[0] & 0x80 ){\n      int nPos;\n      pIter->nSize = fts5GetVarint32(p, nPos);\n      pIter->nPoslist = (nPos>>1);\n    }else{\n      pIter->nPoslist = ((int)(p[0])) >> 1;\n      pIter->nSize = 1;\n    }\n\n    pIter->aPoslist = p;\n  }\n}\n\nstatic void fts5DoclistIterInit(\n  Fts5Buffer *pBuf, \n  Fts5DoclistIter *pIter\n){\n  memset(pIter, 0, sizeof(*pIter));\n  pIter->aPoslist = pBuf->p;\n  pIter->aEof = &pBuf->p[pBuf->n];\n  fts5DoclistIterNext(pIter);\n}\n\n#if 0\n/*\n** Append a doclist to buffer pBuf.\n**\n** This function assumes that space within the buffer has already been\n** allocated.\n*/\nstatic void fts5MergeAppendDocid(\n  Fts5Buffer *pBuf,               /* Buffer to write to */\n  i64 *piLastRowid,               /* IN/OUT: Previous rowid written (if any) */\n  i64 iRowid                      /* Rowid to append */\n){\n  assert( pBuf->n!=0 || (*piLastRowid)==0 );\n  fts5BufferSafeAppendVarint(pBuf, iRowid - *piLastRowid);\n  *piLastRowid = iRowid;\n}\n#endif\n\n#define fts5MergeAppendDocid(pBuf, iLastRowid, iRowid) {       \\\n  assert( (pBuf)->n!=0 || (iLastRowid)==0 );                   \\\n  fts5BufferSafeAppendVarint((pBuf), (iRowid) - (iLastRowid)); \\\n  (iLastRowid) = (iRowid);                                     \\\n}\n\n/*\n** Swap the contents of buffer *p1 with that of *p2.\n*/\nstatic void fts5BufferSwap(Fts5Buffer *p1, Fts5Buffer *p2){\n  Fts5Buffer tmp = *p1;\n  *p1 = *p2;\n  *p2 = tmp;\n}\n\nstatic void fts5NextRowid(Fts5Buffer *pBuf, int *piOff, i64 *piRowid){\n  int i = *piOff;\n  if( i>=pBuf->n ){\n    *piOff = -1;\n  }else{\n    u64 iVal;\n    *piOff = i + sqlite3Fts5GetVarint(&pBuf->p[i], &iVal);\n    *piRowid += iVal;\n  }\n}\n\n/*\n** This is the equivalent of fts5MergePrefixLists() for detail=none mode.\n** In this case the buffers consist of a delta-encoded list of rowids only.\n*/\nstatic void fts5MergeRowidLists(\n  Fts5Index *p,                   /* FTS5 backend object */\n  Fts5Buffer *p1,                 /* First list to merge */\n  Fts5Buffer *p2                  /* Second list to merge */\n){\n  int i1 = 0;\n  int i2 = 0;\n  i64 iRowid1 = 0;\n  i64 iRowid2 = 0;\n  i64 iOut = 0;\n\n  Fts5Buffer out;\n  memset(&out, 0, sizeof(out));\n  sqlite3Fts5BufferSize(&p->rc, &out, p1->n + p2->n);\n  if( p->rc ) return;\n\n  fts5NextRowid(p1, &i1, &iRowid1);\n  fts5NextRowid(p2, &i2, &iRowid2);\n  while( i1>=0 || i2>=0 ){\n    if( i1>=0 && (i2<0 || iRowid1<iRowid2) ){\n      assert( iOut==0 || iRowid1>iOut );\n      fts5BufferSafeAppendVarint(&out, iRowid1 - iOut);\n      iOut = iRowid1;\n      fts5NextRowid(p1, &i1, &iRowid1);\n    }else{\n      assert( iOut==0 || iRowid2>iOut );\n      fts5BufferSafeAppendVarint(&out, iRowid2 - iOut);\n      iOut = iRowid2;\n      if( i1>=0 && iRowid1==iRowid2 ){\n        fts5NextRowid(p1, &i1, &iRowid1);\n      }\n      fts5NextRowid(p2, &i2, &iRowid2);\n    }\n  }\n\n  fts5BufferSwap(&out, p1);\n  fts5BufferFree(&out);\n}\n\n/*\n** Buffers p1 and p2 contain doclists. This function merges the content\n** of the two doclists together and sets buffer p1 to the result before\n** returning.\n**\n** If an error occurs, an error code is left in p->rc. If an error has\n** already occurred, this function is a no-op.\n*/\nstatic void fts5MergePrefixLists(\n  Fts5Index *p,                   /* FTS5 backend object */\n  Fts5Buffer *p1,                 /* First list to merge */\n  Fts5Buffer *p2                  /* Second list to merge */\n){\n  if( p2->n ){\n    i64 iLastRowid = 0;\n    Fts5DoclistIter i1;\n    Fts5DoclistIter i2;\n    Fts5Buffer out = {0, 0, 0};\n    Fts5Buffer tmp = {0, 0, 0};\n\n    /* The maximum size of the output is equal to the sum of the two \n    ** input sizes + 1 varint (9 bytes). The extra varint is because if the\n    ** first rowid in one input is a large negative number, and the first in\n    ** the other a non-negative number, the delta for the non-negative\n    ** number will be larger on disk than the literal integer value\n    ** was.  */\n    if( sqlite3Fts5BufferSize(&p->rc, &out, p1->n + p2->n + 9) ) return;\n    fts5DoclistIterInit(p1, &i1);\n    fts5DoclistIterInit(p2, &i2);\n\n    while( 1 ){\n      if( i1.iRowid<i2.iRowid ){\n        /* Copy entry from i1 */\n        fts5MergeAppendDocid(&out, iLastRowid, i1.iRowid);\n        fts5BufferSafeAppendBlob(&out, i1.aPoslist, i1.nPoslist+i1.nSize);\n        fts5DoclistIterNext(&i1);\n        if( i1.aPoslist==0 ) break;\n      }\n      else if( i2.iRowid!=i1.iRowid ){\n        /* Copy entry from i2 */\n        fts5MergeAppendDocid(&out, iLastRowid, i2.iRowid);\n        fts5BufferSafeAppendBlob(&out, i2.aPoslist, i2.nPoslist+i2.nSize);\n        fts5DoclistIterNext(&i2);\n        if( i2.aPoslist==0 ) break;\n      }\n      else{\n        /* Merge the two position lists. */ \n        i64 iPos1 = 0;\n        i64 iPos2 = 0;\n        int iOff1 = 0;\n        int iOff2 = 0;\n        u8 *a1 = &i1.aPoslist[i1.nSize];\n        u8 *a2 = &i2.aPoslist[i2.nSize];\n\n        i64 iPrev = 0;\n        Fts5PoslistWriter writer;\n        memset(&writer, 0, sizeof(writer));\n\n        fts5MergeAppendDocid(&out, iLastRowid, i2.iRowid);\n        fts5BufferZero(&tmp);\n        sqlite3Fts5BufferSize(&p->rc, &tmp, i1.nPoslist + i2.nPoslist);\n        if( p->rc ) break;\n\n        sqlite3Fts5PoslistNext64(a1, i1.nPoslist, &iOff1, &iPos1);\n        sqlite3Fts5PoslistNext64(a2, i2.nPoslist, &iOff2, &iPos2);\n        assert( iPos1>=0 && iPos2>=0 );\n\n        if( iPos1<iPos2 ){\n          sqlite3Fts5PoslistSafeAppend(&tmp, &iPrev, iPos1);\n          sqlite3Fts5PoslistNext64(a1, i1.nPoslist, &iOff1, &iPos1);\n        }else{\n          sqlite3Fts5PoslistSafeAppend(&tmp, &iPrev, iPos2);\n          sqlite3Fts5PoslistNext64(a2, i2.nPoslist, &iOff2, &iPos2);\n        }\n\n        if( iPos1>=0 && iPos2>=0 ){\n          while( 1 ){\n            if( iPos1<iPos2 ){\n              if( iPos1!=iPrev ){\n                sqlite3Fts5PoslistSafeAppend(&tmp, &iPrev, iPos1);\n              }\n              sqlite3Fts5PoslistNext64(a1, i1.nPoslist, &iOff1, &iPos1);\n              if( iPos1<0 ) break;\n            }else{\n              assert( iPos2!=iPrev );\n              sqlite3Fts5PoslistSafeAppend(&tmp, &iPrev, iPos2);\n              sqlite3Fts5PoslistNext64(a2, i2.nPoslist, &iOff2, &iPos2);\n              if( iPos2<0 ) break;\n            }\n          }\n        }\n\n        if( iPos1>=0 ){\n          if( iPos1!=iPrev ){\n            sqlite3Fts5PoslistSafeAppend(&tmp, &iPrev, iPos1);\n          }\n          fts5BufferSafeAppendBlob(&tmp, &a1[iOff1], i1.nPoslist-iOff1);\n        }else{\n          assert( iPos2>=0 && iPos2!=iPrev );\n          sqlite3Fts5PoslistSafeAppend(&tmp, &iPrev, iPos2);\n          fts5BufferSafeAppendBlob(&tmp, &a2[iOff2], i2.nPoslist-iOff2);\n        }\n\n        /* WRITEPOSLISTSIZE */\n        fts5BufferSafeAppendVarint(&out, tmp.n * 2);\n        fts5BufferSafeAppendBlob(&out, tmp.p, tmp.n);\n        fts5DoclistIterNext(&i1);\n        fts5DoclistIterNext(&i2);\n        if( i1.aPoslist==0 || i2.aPoslist==0 ) break;\n      }\n    }\n\n    if( i1.aPoslist ){\n      fts5MergeAppendDocid(&out, iLastRowid, i1.iRowid);\n      fts5BufferSafeAppendBlob(&out, i1.aPoslist, i1.aEof - i1.aPoslist);\n    }\n    else if( i2.aPoslist ){\n      fts5MergeAppendDocid(&out, iLastRowid, i2.iRowid);\n      fts5BufferSafeAppendBlob(&out, i2.aPoslist, i2.aEof - i2.aPoslist);\n    }\n    assert( out.n<=(p1->n+p2->n+9) );\n\n    fts5BufferSet(&p->rc, p1, out.n, out.p);\n    fts5BufferFree(&tmp);\n    fts5BufferFree(&out);\n  }\n}\n\nstatic void fts5SetupPrefixIter(\n  Fts5Index *p,                   /* Index to read from */\n  int bDesc,                      /* True for \"ORDER BY rowid DESC\" */\n  const u8 *pToken,               /* Buffer containing prefix to match */\n  int nToken,                     /* Size of buffer pToken in bytes */\n  Fts5Colset *pColset,            /* Restrict matches to these columns */\n  Fts5Iter **ppIter          /* OUT: New iterator */\n){\n  Fts5Structure *pStruct;\n  Fts5Buffer *aBuf;\n  const int nBuf = 32;\n\n  void (*xMerge)(Fts5Index*, Fts5Buffer*, Fts5Buffer*);\n  void (*xAppend)(Fts5Index*, i64, Fts5Iter*, Fts5Buffer*);\n  if( p->pConfig->eDetail==FTS5_DETAIL_NONE ){\n    xMerge = fts5MergeRowidLists;\n    xAppend = fts5AppendRowid;\n  }else{\n    xMerge = fts5MergePrefixLists;\n    xAppend = fts5AppendPoslist;\n  }\n\n  aBuf = (Fts5Buffer*)fts5IdxMalloc(p, sizeof(Fts5Buffer)*nBuf);\n  pStruct = fts5StructureRead(p);\n\n  if( aBuf && pStruct ){\n    const int flags = FTS5INDEX_QUERY_SCAN \n                    | FTS5INDEX_QUERY_SKIPEMPTY \n                    | FTS5INDEX_QUERY_NOOUTPUT;\n    int i;\n    i64 iLastRowid = 0;\n    Fts5Iter *p1 = 0;     /* Iterator used to gather data from index */\n    Fts5Data *pData;\n    Fts5Buffer doclist;\n    int bNewTerm = 1;\n\n    memset(&doclist, 0, sizeof(doclist));\n    fts5MultiIterNew(p, pStruct, flags, pColset, pToken, nToken, -1, 0, &p1);\n    fts5IterSetOutputCb(&p->rc, p1);\n    for( /* no-op */ ;\n        fts5MultiIterEof(p, p1)==0;\n        fts5MultiIterNext2(p, p1, &bNewTerm)\n    ){\n      Fts5SegIter *pSeg = &p1->aSeg[ p1->aFirst[1].iFirst ];\n      int nTerm = pSeg->term.n;\n      const u8 *pTerm = pSeg->term.p;\n      p1->xSetOutputs(p1, pSeg);\n\n      assert_nc( memcmp(pToken, pTerm, MIN(nToken, nTerm))<=0 );\n      if( bNewTerm ){\n        if( nTerm<nToken || memcmp(pToken, pTerm, nToken) ) break;\n      }\n\n      if( p1->base.nData==0 ) continue;\n\n      if( p1->base.iRowid<=iLastRowid && doclist.n>0 ){\n        for(i=0; p->rc==SQLITE_OK && doclist.n; i++){\n          assert( i<nBuf );\n          if( aBuf[i].n==0 ){\n            fts5BufferSwap(&doclist, &aBuf[i]);\n            fts5BufferZero(&doclist);\n          }else{\n            xMerge(p, &doclist, &aBuf[i]);\n            fts5BufferZero(&aBuf[i]);\n          }\n        }\n        iLastRowid = 0;\n      }\n\n      xAppend(p, p1->base.iRowid-iLastRowid, p1, &doclist);\n      iLastRowid = p1->base.iRowid;\n    }\n\n    for(i=0; i<nBuf; i++){\n      if( p->rc==SQLITE_OK ){\n        xMerge(p, &doclist, &aBuf[i]);\n      }\n      fts5BufferFree(&aBuf[i]);\n    }\n    fts5MultiIterFree(p1);\n\n    pData = fts5IdxMalloc(p, sizeof(Fts5Data) + doclist.n);\n    if( pData ){\n      pData->p = (u8*)&pData[1];\n      pData->nn = pData->szLeaf = doclist.n;\n      if( doclist.n ) memcpy(pData->p, doclist.p, doclist.n);\n      fts5MultiIterNew2(p, pData, bDesc, ppIter);\n    }\n    fts5BufferFree(&doclist);\n  }\n\n  fts5StructureRelease(pStruct);\n  sqlite3_free(aBuf);\n}\n\n\n/*\n** Indicate that all subsequent calls to sqlite3Fts5IndexWrite() pertain\n** to the document with rowid iRowid.\n*/\nstatic int sqlite3Fts5IndexBeginWrite(Fts5Index *p, int bDelete, i64 iRowid){\n  assert( p->rc==SQLITE_OK );\n\n  /* Allocate the hash table if it has not already been allocated */\n  if( p->pHash==0 ){\n    p->rc = sqlite3Fts5HashNew(p->pConfig, &p->pHash, &p->nPendingData);\n  }\n\n  /* Flush the hash table to disk if required */\n  if( iRowid<p->iWriteRowid \n   || (iRowid==p->iWriteRowid && p->bDelete==0)\n   || (p->nPendingData > p->pConfig->nHashSize) \n  ){\n    fts5IndexFlush(p);\n  }\n\n  p->iWriteRowid = iRowid;\n  p->bDelete = bDelete;\n  return fts5IndexReturn(p);\n}\n\n/*\n** Commit data to disk.\n*/\nstatic int sqlite3Fts5IndexSync(Fts5Index *p){\n  assert( p->rc==SQLITE_OK );\n  fts5IndexFlush(p);\n  fts5CloseReader(p);\n  return fts5IndexReturn(p);\n}\n\n/*\n** Discard any data stored in the in-memory hash tables. Do not write it\n** to the database. Additionally, assume that the contents of the %_data\n** table may have changed on disk. So any in-memory caches of %_data \n** records must be invalidated.\n*/\nstatic int sqlite3Fts5IndexRollback(Fts5Index *p){\n  fts5CloseReader(p);\n  fts5IndexDiscardData(p);\n  fts5StructureInvalidate(p);\n  /* assert( p->rc==SQLITE_OK ); */\n  return SQLITE_OK;\n}\n\n/*\n** The %_data table is completely empty when this function is called. This\n** function populates it with the initial structure objects for each index,\n** and the initial version of the \"averages\" record (a zero-byte blob).\n*/\nstatic int sqlite3Fts5IndexReinit(Fts5Index *p){\n  Fts5Structure s;\n  fts5StructureInvalidate(p);\n  memset(&s, 0, sizeof(Fts5Structure));\n  fts5DataWrite(p, FTS5_AVERAGES_ROWID, (const u8*)\"\", 0);\n  fts5StructureWrite(p, &s);\n  return fts5IndexReturn(p);\n}\n\n/*\n** Open a new Fts5Index handle. If the bCreate argument is true, create\n** and initialize the underlying %_data table.\n**\n** If successful, set *pp to point to the new object and return SQLITE_OK.\n** Otherwise, set *pp to NULL and return an SQLite error code.\n*/\nstatic int sqlite3Fts5IndexOpen(\n  Fts5Config *pConfig, \n  int bCreate, \n  Fts5Index **pp,\n  char **pzErr\n){\n  int rc = SQLITE_OK;\n  Fts5Index *p;                   /* New object */\n\n  *pp = p = (Fts5Index*)sqlite3Fts5MallocZero(&rc, sizeof(Fts5Index));\n  if( rc==SQLITE_OK ){\n    p->pConfig = pConfig;\n    p->nWorkUnit = FTS5_WORK_UNIT;\n    p->zDataTbl = sqlite3Fts5Mprintf(&rc, \"%s_data\", pConfig->zName);\n    if( p->zDataTbl && bCreate ){\n      rc = sqlite3Fts5CreateTable(\n          pConfig, \"data\", \"id INTEGER PRIMARY KEY, block BLOB\", 0, pzErr\n      );\n      if( rc==SQLITE_OK ){\n        rc = sqlite3Fts5CreateTable(pConfig, \"idx\", \n            \"segid, term, pgno, PRIMARY KEY(segid, term)\", \n            1, pzErr\n        );\n      }\n      if( rc==SQLITE_OK ){\n        rc = sqlite3Fts5IndexReinit(p);\n      }\n    }\n  }\n\n  assert( rc!=SQLITE_OK || p->rc==SQLITE_OK );\n  if( rc ){\n    sqlite3Fts5IndexClose(p);\n    *pp = 0;\n  }\n  return rc;\n}\n\n/*\n** Close a handle opened by an earlier call to sqlite3Fts5IndexOpen().\n*/\nstatic int sqlite3Fts5IndexClose(Fts5Index *p){\n  int rc = SQLITE_OK;\n  if( p ){\n    assert( p->pReader==0 );\n    fts5StructureInvalidate(p);\n    sqlite3_finalize(p->pWriter);\n    sqlite3_finalize(p->pDeleter);\n    sqlite3_finalize(p->pIdxWriter);\n    sqlite3_finalize(p->pIdxDeleter);\n    sqlite3_finalize(p->pIdxSelect);\n    sqlite3_finalize(p->pDataVersion);\n    sqlite3Fts5HashFree(p->pHash);\n    sqlite3_free(p->zDataTbl);\n    sqlite3_free(p);\n  }\n  return rc;\n}\n\n/*\n** Argument p points to a buffer containing utf-8 text that is n bytes in \n** size. Return the number of bytes in the nChar character prefix of the\n** buffer, or 0 if there are less than nChar characters in total.\n*/\nstatic int sqlite3Fts5IndexCharlenToBytelen(\n  const char *p, \n  int nByte, \n  int nChar\n){\n  int n = 0;\n  int i;\n  for(i=0; i<nChar; i++){\n    if( n>=nByte ) return 0;      /* Input contains fewer than nChar chars */\n    if( (unsigned char)p[n++]>=0xc0 ){\n      while( (p[n] & 0xc0)==0x80 ) n++;\n    }\n  }\n  return n;\n}\n\n/*\n** pIn is a UTF-8 encoded string, nIn bytes in size. Return the number of\n** unicode characters in the string.\n*/\nstatic int fts5IndexCharlen(const char *pIn, int nIn){\n  int nChar = 0;            \n  int i = 0;\n  while( i<nIn ){\n    if( (unsigned char)pIn[i++]>=0xc0 ){\n      while( i<nIn && (pIn[i] & 0xc0)==0x80 ) i++;\n    }\n    nChar++;\n  }\n  return nChar;\n}\n\n/*\n** Insert or remove data to or from the index. Each time a document is \n** added to or removed from the index, this function is called one or more\n** times.\n**\n** For an insert, it must be called once for each token in the new document.\n** If the operation is a delete, it must be called (at least) once for each\n** unique token in the document with an iCol value less than zero. The iPos\n** argument is ignored for a delete.\n*/\nstatic int sqlite3Fts5IndexWrite(\n  Fts5Index *p,                   /* Index to write to */\n  int iCol,                       /* Column token appears in (-ve -> delete) */\n  int iPos,                       /* Position of token within column */\n  const char *pToken, int nToken  /* Token to add or remove to or from index */\n){\n  int i;                          /* Used to iterate through indexes */\n  int rc = SQLITE_OK;             /* Return code */\n  Fts5Config *pConfig = p->pConfig;\n\n  assert( p->rc==SQLITE_OK );\n  assert( (iCol<0)==p->bDelete );\n\n  /* Add the entry to the main terms index. */\n  rc = sqlite3Fts5HashWrite(\n      p->pHash, p->iWriteRowid, iCol, iPos, FTS5_MAIN_PREFIX, pToken, nToken\n  );\n\n  for(i=0; i<pConfig->nPrefix && rc==SQLITE_OK; i++){\n    const int nChar = pConfig->aPrefix[i];\n    int nByte = sqlite3Fts5IndexCharlenToBytelen(pToken, nToken, nChar);\n    if( nByte ){\n      rc = sqlite3Fts5HashWrite(p->pHash, \n          p->iWriteRowid, iCol, iPos, (char)(FTS5_MAIN_PREFIX+i+1), pToken,\n          nByte\n      );\n    }\n  }\n\n  return rc;\n}\n\n/*\n** Open a new iterator to iterate though all rowid that match the \n** specified token or token prefix.\n*/\nstatic int sqlite3Fts5IndexQuery(\n  Fts5Index *p,                   /* FTS index to query */\n  const char *pToken, int nToken, /* Token (or prefix) to query for */\n  int flags,                      /* Mask of FTS5INDEX_QUERY_X flags */\n  Fts5Colset *pColset,            /* Match these columns only */\n  Fts5IndexIter **ppIter          /* OUT: New iterator object */\n){\n  Fts5Config *pConfig = p->pConfig;\n  Fts5Iter *pRet = 0;\n  Fts5Buffer buf = {0, 0, 0};\n\n  /* If the QUERY_SCAN flag is set, all other flags must be clear. */\n  assert( (flags & FTS5INDEX_QUERY_SCAN)==0 || flags==FTS5INDEX_QUERY_SCAN );\n\n  if( sqlite3Fts5BufferSize(&p->rc, &buf, nToken+1)==0 ){\n    int iIdx = 0;                 /* Index to search */\n    if( nToken ) memcpy(&buf.p[1], pToken, nToken);\n\n    /* Figure out which index to search and set iIdx accordingly. If this\n    ** is a prefix query for which there is no prefix index, set iIdx to\n    ** greater than pConfig->nPrefix to indicate that the query will be\n    ** satisfied by scanning multiple terms in the main index.\n    **\n    ** If the QUERY_TEST_NOIDX flag was specified, then this must be a\n    ** prefix-query. Instead of using a prefix-index (if one exists), \n    ** evaluate the prefix query using the main FTS index. This is used\n    ** for internal sanity checking by the integrity-check in debug \n    ** mode only.  */\n#ifdef SQLITE_DEBUG\n    if( pConfig->bPrefixIndex==0 || (flags & FTS5INDEX_QUERY_TEST_NOIDX) ){\n      assert( flags & FTS5INDEX_QUERY_PREFIX );\n      iIdx = 1+pConfig->nPrefix;\n    }else\n#endif\n    if( flags & FTS5INDEX_QUERY_PREFIX ){\n      int nChar = fts5IndexCharlen(pToken, nToken);\n      for(iIdx=1; iIdx<=pConfig->nPrefix; iIdx++){\n        if( pConfig->aPrefix[iIdx-1]==nChar ) break;\n      }\n    }\n\n    if( iIdx<=pConfig->nPrefix ){\n      /* Straight index lookup */\n      Fts5Structure *pStruct = fts5StructureRead(p);\n      buf.p[0] = (u8)(FTS5_MAIN_PREFIX + iIdx);\n      if( pStruct ){\n        fts5MultiIterNew(p, pStruct, flags | FTS5INDEX_QUERY_SKIPEMPTY, \n            pColset, buf.p, nToken+1, -1, 0, &pRet\n        );\n        fts5StructureRelease(pStruct);\n      }\n    }else{\n      /* Scan multiple terms in the main index */\n      int bDesc = (flags & FTS5INDEX_QUERY_DESC)!=0;\n      buf.p[0] = FTS5_MAIN_PREFIX;\n      fts5SetupPrefixIter(p, bDesc, buf.p, nToken+1, pColset, &pRet);\n      assert( p->rc!=SQLITE_OK || pRet->pColset==0 );\n      fts5IterSetOutputCb(&p->rc, pRet);\n      if( p->rc==SQLITE_OK ){\n        Fts5SegIter *pSeg = &pRet->aSeg[pRet->aFirst[1].iFirst];\n        if( pSeg->pLeaf ) pRet->xSetOutputs(pRet, pSeg);\n      }\n    }\n\n    if( p->rc ){\n      sqlite3Fts5IterClose((Fts5IndexIter*)pRet);\n      pRet = 0;\n      fts5CloseReader(p);\n    }\n\n    *ppIter = &pRet->base;\n    sqlite3Fts5BufferFree(&buf);\n  }\n  return fts5IndexReturn(p);\n}\n\n/*\n** Return true if the iterator passed as the only argument is at EOF.\n*/\n/*\n** Move to the next matching rowid. \n*/\nstatic int sqlite3Fts5IterNext(Fts5IndexIter *pIndexIter){\n  Fts5Iter *pIter = (Fts5Iter*)pIndexIter;\n  assert( pIter->pIndex->rc==SQLITE_OK );\n  fts5MultiIterNext(pIter->pIndex, pIter, 0, 0);\n  return fts5IndexReturn(pIter->pIndex);\n}\n\n/*\n** Move to the next matching term/rowid. Used by the fts5vocab module.\n*/\nstatic int sqlite3Fts5IterNextScan(Fts5IndexIter *pIndexIter){\n  Fts5Iter *pIter = (Fts5Iter*)pIndexIter;\n  Fts5Index *p = pIter->pIndex;\n\n  assert( pIter->pIndex->rc==SQLITE_OK );\n\n  fts5MultiIterNext(p, pIter, 0, 0);\n  if( p->rc==SQLITE_OK ){\n    Fts5SegIter *pSeg = &pIter->aSeg[ pIter->aFirst[1].iFirst ];\n    if( pSeg->pLeaf && pSeg->term.p[0]!=FTS5_MAIN_PREFIX ){\n      fts5DataRelease(pSeg->pLeaf);\n      pSeg->pLeaf = 0;\n      pIter->base.bEof = 1;\n    }\n  }\n\n  return fts5IndexReturn(pIter->pIndex);\n}\n\n/*\n** Move to the next matching rowid that occurs at or after iMatch. The\n** definition of \"at or after\" depends on whether this iterator iterates\n** in ascending or descending rowid order.\n*/\nstatic int sqlite3Fts5IterNextFrom(Fts5IndexIter *pIndexIter, i64 iMatch){\n  Fts5Iter *pIter = (Fts5Iter*)pIndexIter;\n  fts5MultiIterNextFrom(pIter->pIndex, pIter, iMatch);\n  return fts5IndexReturn(pIter->pIndex);\n}\n\n/*\n** Return the current term.\n*/\nstatic const char *sqlite3Fts5IterTerm(Fts5IndexIter *pIndexIter, int *pn){\n  int n;\n  const char *z = (const char*)fts5MultiIterTerm((Fts5Iter*)pIndexIter, &n);\n  *pn = n-1;\n  return &z[1];\n}\n\n/*\n** Close an iterator opened by an earlier call to sqlite3Fts5IndexQuery().\n*/\nstatic void sqlite3Fts5IterClose(Fts5IndexIter *pIndexIter){\n  if( pIndexIter ){\n    Fts5Iter *pIter = (Fts5Iter*)pIndexIter;\n    Fts5Index *pIndex = pIter->pIndex;\n    fts5MultiIterFree(pIter);\n    fts5CloseReader(pIndex);\n  }\n}\n\n/*\n** Read and decode the \"averages\" record from the database. \n**\n** Parameter anSize must point to an array of size nCol, where nCol is\n** the number of user defined columns in the FTS table.\n*/\nstatic int sqlite3Fts5IndexGetAverages(Fts5Index *p, i64 *pnRow, i64 *anSize){\n  int nCol = p->pConfig->nCol;\n  Fts5Data *pData;\n\n  *pnRow = 0;\n  memset(anSize, 0, sizeof(i64) * nCol);\n  pData = fts5DataRead(p, FTS5_AVERAGES_ROWID);\n  if( p->rc==SQLITE_OK && pData->nn ){\n    int i = 0;\n    int iCol;\n    i += fts5GetVarint(&pData->p[i], (u64*)pnRow);\n    for(iCol=0; i<pData->nn && iCol<nCol; iCol++){\n      i += fts5GetVarint(&pData->p[i], (u64*)&anSize[iCol]);\n    }\n  }\n\n  fts5DataRelease(pData);\n  return fts5IndexReturn(p);\n}\n\n/*\n** Replace the current \"averages\" record with the contents of the buffer \n** supplied as the second argument.\n*/\nstatic int sqlite3Fts5IndexSetAverages(Fts5Index *p, const u8 *pData, int nData){\n  assert( p->rc==SQLITE_OK );\n  fts5DataWrite(p, FTS5_AVERAGES_ROWID, pData, nData);\n  return fts5IndexReturn(p);\n}\n\n/*\n** Return the total number of blocks this module has read from the %_data\n** table since it was created.\n*/\nstatic int sqlite3Fts5IndexReads(Fts5Index *p){\n  return p->nRead;\n}\n\n/*\n** Set the 32-bit cookie value stored at the start of all structure \n** records to the value passed as the second argument.\n**\n** Return SQLITE_OK if successful, or an SQLite error code if an error\n** occurs.\n*/\nstatic int sqlite3Fts5IndexSetCookie(Fts5Index *p, int iNew){\n  int rc;                              /* Return code */\n  Fts5Config *pConfig = p->pConfig;    /* Configuration object */\n  u8 aCookie[4];                       /* Binary representation of iNew */\n  sqlite3_blob *pBlob = 0;\n\n  assert( p->rc==SQLITE_OK );\n  sqlite3Fts5Put32(aCookie, iNew);\n\n  rc = sqlite3_blob_open(pConfig->db, pConfig->zDb, p->zDataTbl, \n      \"block\", FTS5_STRUCTURE_ROWID, 1, &pBlob\n  );\n  if( rc==SQLITE_OK ){\n    sqlite3_blob_write(pBlob, aCookie, 4, 0);\n    rc = sqlite3_blob_close(pBlob);\n  }\n\n  return rc;\n}\n\nstatic int sqlite3Fts5IndexLoadConfig(Fts5Index *p){\n  Fts5Structure *pStruct;\n  pStruct = fts5StructureRead(p);\n  fts5StructureRelease(pStruct);\n  return fts5IndexReturn(p);\n}\n\n\n/*************************************************************************\n**************************************************************************\n** Below this point is the implementation of the integrity-check \n** functionality.\n*/\n\n/*\n** Return a simple checksum value based on the arguments.\n*/\nstatic u64 sqlite3Fts5IndexEntryCksum(\n  i64 iRowid, \n  int iCol, \n  int iPos, \n  int iIdx,\n  const char *pTerm,\n  int nTerm\n){\n  int i;\n  u64 ret = iRowid;\n  ret += (ret<<3) + iCol;\n  ret += (ret<<3) + iPos;\n  if( iIdx>=0 ) ret += (ret<<3) + (FTS5_MAIN_PREFIX + iIdx);\n  for(i=0; i<nTerm; i++) ret += (ret<<3) + pTerm[i];\n  return ret;\n}\n\n#ifdef SQLITE_DEBUG\n/*\n** This function is purely an internal test. It does not contribute to \n** FTS functionality, or even the integrity-check, in any way.\n**\n** Instead, it tests that the same set of pgno/rowid combinations are \n** visited regardless of whether the doclist-index identified by parameters\n** iSegid/iLeaf is iterated in forwards or reverse order.\n*/\nstatic void fts5TestDlidxReverse(\n  Fts5Index *p, \n  int iSegid,                     /* Segment id to load from */\n  int iLeaf                       /* Load doclist-index for this leaf */\n){\n  Fts5DlidxIter *pDlidx = 0;\n  u64 cksum1 = 13;\n  u64 cksum2 = 13;\n\n  for(pDlidx=fts5DlidxIterInit(p, 0, iSegid, iLeaf);\n      fts5DlidxIterEof(p, pDlidx)==0;\n      fts5DlidxIterNext(p, pDlidx)\n  ){\n    i64 iRowid = fts5DlidxIterRowid(pDlidx);\n    int pgno = fts5DlidxIterPgno(pDlidx);\n    assert( pgno>iLeaf );\n    cksum1 += iRowid + ((i64)pgno<<32);\n  }\n  fts5DlidxIterFree(pDlidx);\n  pDlidx = 0;\n\n  for(pDlidx=fts5DlidxIterInit(p, 1, iSegid, iLeaf);\n      fts5DlidxIterEof(p, pDlidx)==0;\n      fts5DlidxIterPrev(p, pDlidx)\n  ){\n    i64 iRowid = fts5DlidxIterRowid(pDlidx);\n    int pgno = fts5DlidxIterPgno(pDlidx);\n    assert( fts5DlidxIterPgno(pDlidx)>iLeaf );\n    cksum2 += iRowid + ((i64)pgno<<32);\n  }\n  fts5DlidxIterFree(pDlidx);\n  pDlidx = 0;\n\n  if( p->rc==SQLITE_OK && cksum1!=cksum2 ) p->rc = FTS5_CORRUPT;\n}\n\nstatic int fts5QueryCksum(\n  Fts5Index *p,                   /* Fts5 index object */\n  int iIdx,\n  const char *z,                  /* Index key to query for */\n  int n,                          /* Size of index key in bytes */\n  int flags,                      /* Flags for Fts5IndexQuery */\n  u64 *pCksum                     /* IN/OUT: Checksum value */\n){\n  int eDetail = p->pConfig->eDetail;\n  u64 cksum = *pCksum;\n  Fts5IndexIter *pIter = 0;\n  int rc = sqlite3Fts5IndexQuery(p, z, n, flags, 0, &pIter);\n\n  while( rc==SQLITE_OK && 0==sqlite3Fts5IterEof(pIter) ){\n    i64 rowid = pIter->iRowid;\n\n    if( eDetail==FTS5_DETAIL_NONE ){\n      cksum ^= sqlite3Fts5IndexEntryCksum(rowid, 0, 0, iIdx, z, n);\n    }else{\n      Fts5PoslistReader sReader;\n      for(sqlite3Fts5PoslistReaderInit(pIter->pData, pIter->nData, &sReader);\n          sReader.bEof==0;\n          sqlite3Fts5PoslistReaderNext(&sReader)\n      ){\n        int iCol = FTS5_POS2COLUMN(sReader.iPos);\n        int iOff = FTS5_POS2OFFSET(sReader.iPos);\n        cksum ^= sqlite3Fts5IndexEntryCksum(rowid, iCol, iOff, iIdx, z, n);\n      }\n    }\n    if( rc==SQLITE_OK ){\n      rc = sqlite3Fts5IterNext(pIter);\n    }\n  }\n  sqlite3Fts5IterClose(pIter);\n\n  *pCksum = cksum;\n  return rc;\n}\n\n\n/*\n** This function is also purely an internal test. It does not contribute to \n** FTS functionality, or even the integrity-check, in any way.\n*/\nstatic void fts5TestTerm(\n  Fts5Index *p, \n  Fts5Buffer *pPrev,              /* Previous term */\n  const char *z, int n,           /* Possibly new term to test */\n  u64 expected,\n  u64 *pCksum\n){\n  int rc = p->rc;\n  if( pPrev->n==0 ){\n    fts5BufferSet(&rc, pPrev, n, (const u8*)z);\n  }else\n  if( rc==SQLITE_OK && (pPrev->n!=n || memcmp(pPrev->p, z, n)) ){\n    u64 cksum3 = *pCksum;\n    const char *zTerm = (const char*)&pPrev->p[1];  /* term sans prefix-byte */\n    int nTerm = pPrev->n-1;            /* Size of zTerm in bytes */\n    int iIdx = (pPrev->p[0] - FTS5_MAIN_PREFIX);\n    int flags = (iIdx==0 ? 0 : FTS5INDEX_QUERY_PREFIX);\n    u64 ck1 = 0;\n    u64 ck2 = 0;\n\n    /* Check that the results returned for ASC and DESC queries are\n    ** the same. If not, call this corruption.  */\n    rc = fts5QueryCksum(p, iIdx, zTerm, nTerm, flags, &ck1);\n    if( rc==SQLITE_OK ){\n      int f = flags|FTS5INDEX_QUERY_DESC;\n      rc = fts5QueryCksum(p, iIdx, zTerm, nTerm, f, &ck2);\n    }\n    if( rc==SQLITE_OK && ck1!=ck2 ) rc = FTS5_CORRUPT;\n\n    /* If this is a prefix query, check that the results returned if the\n    ** the index is disabled are the same. In both ASC and DESC order. \n    **\n    ** This check may only be performed if the hash table is empty. This\n    ** is because the hash table only supports a single scan query at\n    ** a time, and the multi-iter loop from which this function is called\n    ** is already performing such a scan. */\n    if( p->nPendingData==0 ){\n      if( iIdx>0 && rc==SQLITE_OK ){\n        int f = flags|FTS5INDEX_QUERY_TEST_NOIDX;\n        ck2 = 0;\n        rc = fts5QueryCksum(p, iIdx, zTerm, nTerm, f, &ck2);\n        if( rc==SQLITE_OK && ck1!=ck2 ) rc = FTS5_CORRUPT;\n      }\n      if( iIdx>0 && rc==SQLITE_OK ){\n        int f = flags|FTS5INDEX_QUERY_TEST_NOIDX|FTS5INDEX_QUERY_DESC;\n        ck2 = 0;\n        rc = fts5QueryCksum(p, iIdx, zTerm, nTerm, f, &ck2);\n        if( rc==SQLITE_OK && ck1!=ck2 ) rc = FTS5_CORRUPT;\n      }\n    }\n\n    cksum3 ^= ck1;\n    fts5BufferSet(&rc, pPrev, n, (const u8*)z);\n\n    if( rc==SQLITE_OK && cksum3!=expected ){\n      rc = FTS5_CORRUPT;\n    }\n    *pCksum = cksum3;\n  }\n  p->rc = rc;\n}\n \n#else\n# define fts5TestDlidxReverse(x,y,z)\n# define fts5TestTerm(u,v,w,x,y,z)\n#endif\n\n/*\n** Check that:\n**\n**   1) All leaves of pSeg between iFirst and iLast (inclusive) exist and\n**      contain zero terms.\n**   2) All leaves of pSeg between iNoRowid and iLast (inclusive) exist and\n**      contain zero rowids.\n*/\nstatic void fts5IndexIntegrityCheckEmpty(\n  Fts5Index *p,\n  Fts5StructureSegment *pSeg,     /* Segment to check internal consistency */\n  int iFirst,\n  int iNoRowid,\n  int iLast\n){\n  int i;\n\n  /* Now check that the iter.nEmpty leaves following the current leaf\n  ** (a) exist and (b) contain no terms. */\n  for(i=iFirst; p->rc==SQLITE_OK && i<=iLast; i++){\n    Fts5Data *pLeaf = fts5DataRead(p, FTS5_SEGMENT_ROWID(pSeg->iSegid, i));\n    if( pLeaf ){\n      if( !fts5LeafIsTermless(pLeaf) ) p->rc = FTS5_CORRUPT;\n      if( i>=iNoRowid && 0!=fts5LeafFirstRowidOff(pLeaf) ) p->rc = FTS5_CORRUPT;\n    }\n    fts5DataRelease(pLeaf);\n  }\n}\n\nstatic void fts5IntegrityCheckPgidx(Fts5Index *p, Fts5Data *pLeaf){\n  int iTermOff = 0;\n  int ii;\n\n  Fts5Buffer buf1 = {0,0,0};\n  Fts5Buffer buf2 = {0,0,0};\n\n  ii = pLeaf->szLeaf;\n  while( ii<pLeaf->nn && p->rc==SQLITE_OK ){\n    int res;\n    int iOff;\n    int nIncr;\n\n    ii += fts5GetVarint32(&pLeaf->p[ii], nIncr);\n    iTermOff += nIncr;\n    iOff = iTermOff;\n\n    if( iOff>=pLeaf->szLeaf ){\n      p->rc = FTS5_CORRUPT;\n    }else if( iTermOff==nIncr ){\n      int nByte;\n      iOff += fts5GetVarint32(&pLeaf->p[iOff], nByte);\n      if( (iOff+nByte)>pLeaf->szLeaf ){\n        p->rc = FTS5_CORRUPT;\n      }else{\n        fts5BufferSet(&p->rc, &buf1, nByte, &pLeaf->p[iOff]);\n      }\n    }else{\n      int nKeep, nByte;\n      iOff += fts5GetVarint32(&pLeaf->p[iOff], nKeep);\n      iOff += fts5GetVarint32(&pLeaf->p[iOff], nByte);\n      if( nKeep>buf1.n || (iOff+nByte)>pLeaf->szLeaf ){\n        p->rc = FTS5_CORRUPT;\n      }else{\n        buf1.n = nKeep;\n        fts5BufferAppendBlob(&p->rc, &buf1, nByte, &pLeaf->p[iOff]);\n      }\n\n      if( p->rc==SQLITE_OK ){\n        res = fts5BufferCompare(&buf1, &buf2);\n        if( res<=0 ) p->rc = FTS5_CORRUPT;\n      }\n    }\n    fts5BufferSet(&p->rc, &buf2, buf1.n, buf1.p);\n  }\n\n  fts5BufferFree(&buf1);\n  fts5BufferFree(&buf2);\n}\n\nstatic void fts5IndexIntegrityCheckSegment(\n  Fts5Index *p,                   /* FTS5 backend object */\n  Fts5StructureSegment *pSeg      /* Segment to check internal consistency */\n){\n  Fts5Config *pConfig = p->pConfig;\n  sqlite3_stmt *pStmt = 0;\n  int rc2;\n  int iIdxPrevLeaf = pSeg->pgnoFirst-1;\n  int iDlidxPrevLeaf = pSeg->pgnoLast;\n\n  if( pSeg->pgnoFirst==0 ) return;\n\n  fts5IndexPrepareStmt(p, &pStmt, sqlite3_mprintf(\n      \"SELECT segid, term, (pgno>>1), (pgno&1) FROM %Q.'%q_idx' WHERE segid=%d\",\n      pConfig->zDb, pConfig->zName, pSeg->iSegid\n  ));\n\n  /* Iterate through the b-tree hierarchy.  */\n  while( p->rc==SQLITE_OK && SQLITE_ROW==sqlite3_step(pStmt) ){\n    i64 iRow;                     /* Rowid for this leaf */\n    Fts5Data *pLeaf;              /* Data for this leaf */\n\n    int nIdxTerm = sqlite3_column_bytes(pStmt, 1);\n    const char *zIdxTerm = (const char*)sqlite3_column_text(pStmt, 1);\n    int iIdxLeaf = sqlite3_column_int(pStmt, 2);\n    int bIdxDlidx = sqlite3_column_int(pStmt, 3);\n\n    /* If the leaf in question has already been trimmed from the segment, \n    ** ignore this b-tree entry. Otherwise, load it into memory. */\n    if( iIdxLeaf<pSeg->pgnoFirst ) continue;\n    iRow = FTS5_SEGMENT_ROWID(pSeg->iSegid, iIdxLeaf);\n    pLeaf = fts5LeafRead(p, iRow);\n    if( pLeaf==0 ) break;\n\n    /* Check that the leaf contains at least one term, and that it is equal\n    ** to or larger than the split-key in zIdxTerm.  Also check that if there\n    ** is also a rowid pointer within the leaf page header, it points to a\n    ** location before the term.  */\n    if( pLeaf->nn<=pLeaf->szLeaf ){\n      p->rc = FTS5_CORRUPT;\n    }else{\n      int iOff;                   /* Offset of first term on leaf */\n      int iRowidOff;              /* Offset of first rowid on leaf */\n      int nTerm;                  /* Size of term on leaf in bytes */\n      int res;                    /* Comparison of term and split-key */\n\n      iOff = fts5LeafFirstTermOff(pLeaf);\n      iRowidOff = fts5LeafFirstRowidOff(pLeaf);\n      if( iRowidOff>=iOff ){\n        p->rc = FTS5_CORRUPT;\n      }else{\n        iOff += fts5GetVarint32(&pLeaf->p[iOff], nTerm);\n        res = memcmp(&pLeaf->p[iOff], zIdxTerm, MIN(nTerm, nIdxTerm));\n        if( res==0 ) res = nTerm - nIdxTerm;\n        if( res<0 ) p->rc = FTS5_CORRUPT;\n      }\n\n      fts5IntegrityCheckPgidx(p, pLeaf);\n    }\n    fts5DataRelease(pLeaf);\n    if( p->rc ) break;\n\n    /* Now check that the iter.nEmpty leaves following the current leaf\n    ** (a) exist and (b) contain no terms. */\n    fts5IndexIntegrityCheckEmpty(\n        p, pSeg, iIdxPrevLeaf+1, iDlidxPrevLeaf+1, iIdxLeaf-1\n    );\n    if( p->rc ) break;\n\n    /* If there is a doclist-index, check that it looks right. */\n    if( bIdxDlidx ){\n      Fts5DlidxIter *pDlidx = 0;  /* For iterating through doclist index */\n      int iPrevLeaf = iIdxLeaf;\n      int iSegid = pSeg->iSegid;\n      int iPg = 0;\n      i64 iKey;\n\n      for(pDlidx=fts5DlidxIterInit(p, 0, iSegid, iIdxLeaf);\n          fts5DlidxIterEof(p, pDlidx)==0;\n          fts5DlidxIterNext(p, pDlidx)\n      ){\n\n        /* Check any rowid-less pages that occur before the current leaf. */\n        for(iPg=iPrevLeaf+1; iPg<fts5DlidxIterPgno(pDlidx); iPg++){\n          iKey = FTS5_SEGMENT_ROWID(iSegid, iPg);\n          pLeaf = fts5DataRead(p, iKey);\n          if( pLeaf ){\n            if( fts5LeafFirstRowidOff(pLeaf)!=0 ) p->rc = FTS5_CORRUPT;\n            fts5DataRelease(pLeaf);\n          }\n        }\n        iPrevLeaf = fts5DlidxIterPgno(pDlidx);\n\n        /* Check that the leaf page indicated by the iterator really does\n        ** contain the rowid suggested by the same. */\n        iKey = FTS5_SEGMENT_ROWID(iSegid, iPrevLeaf);\n        pLeaf = fts5DataRead(p, iKey);\n        if( pLeaf ){\n          i64 iRowid;\n          int iRowidOff = fts5LeafFirstRowidOff(pLeaf);\n          ASSERT_SZLEAF_OK(pLeaf);\n          if( iRowidOff>=pLeaf->szLeaf ){\n            p->rc = FTS5_CORRUPT;\n          }else{\n            fts5GetVarint(&pLeaf->p[iRowidOff], (u64*)&iRowid);\n            if( iRowid!=fts5DlidxIterRowid(pDlidx) ) p->rc = FTS5_CORRUPT;\n          }\n          fts5DataRelease(pLeaf);\n        }\n      }\n\n      iDlidxPrevLeaf = iPg;\n      fts5DlidxIterFree(pDlidx);\n      fts5TestDlidxReverse(p, iSegid, iIdxLeaf);\n    }else{\n      iDlidxPrevLeaf = pSeg->pgnoLast;\n      /* TODO: Check there is no doclist index */\n    }\n\n    iIdxPrevLeaf = iIdxLeaf;\n  }\n\n  rc2 = sqlite3_finalize(pStmt);\n  if( p->rc==SQLITE_OK ) p->rc = rc2;\n\n  /* Page iter.iLeaf must now be the rightmost leaf-page in the segment */\n#if 0\n  if( p->rc==SQLITE_OK && iter.iLeaf!=pSeg->pgnoLast ){\n    p->rc = FTS5_CORRUPT;\n  }\n#endif\n}\n\n\n/*\n** Run internal checks to ensure that the FTS index (a) is internally \n** consistent and (b) contains entries for which the XOR of the checksums\n** as calculated by sqlite3Fts5IndexEntryCksum() is cksum.\n**\n** Return SQLITE_CORRUPT if any of the internal checks fail, or if the\n** checksum does not match. Return SQLITE_OK if all checks pass without\n** error, or some other SQLite error code if another error (e.g. OOM)\n** occurs.\n*/\nstatic int sqlite3Fts5IndexIntegrityCheck(Fts5Index *p, u64 cksum){\n  int eDetail = p->pConfig->eDetail;\n  u64 cksum2 = 0;                 /* Checksum based on contents of indexes */\n  Fts5Buffer poslist = {0,0,0};   /* Buffer used to hold a poslist */\n  Fts5Iter *pIter;                /* Used to iterate through entire index */\n  Fts5Structure *pStruct;         /* Index structure */\n\n#ifdef SQLITE_DEBUG\n  /* Used by extra internal tests only run if NDEBUG is not defined */\n  u64 cksum3 = 0;                 /* Checksum based on contents of indexes */\n  Fts5Buffer term = {0,0,0};      /* Buffer used to hold most recent term */\n#endif\n  const int flags = FTS5INDEX_QUERY_NOOUTPUT;\n  \n  /* Load the FTS index structure */\n  pStruct = fts5StructureRead(p);\n\n  /* Check that the internal nodes of each segment match the leaves */\n  if( pStruct ){\n    int iLvl, iSeg;\n    for(iLvl=0; iLvl<pStruct->nLevel; iLvl++){\n      for(iSeg=0; iSeg<pStruct->aLevel[iLvl].nSeg; iSeg++){\n        Fts5StructureSegment *pSeg = &pStruct->aLevel[iLvl].aSeg[iSeg];\n        fts5IndexIntegrityCheckSegment(p, pSeg);\n      }\n    }\n  }\n\n  /* The cksum argument passed to this function is a checksum calculated\n  ** based on all expected entries in the FTS index (including prefix index\n  ** entries). This block checks that a checksum calculated based on the\n  ** actual contents of FTS index is identical.\n  **\n  ** Two versions of the same checksum are calculated. The first (stack\n  ** variable cksum2) based on entries extracted from the full-text index\n  ** while doing a linear scan of each individual index in turn. \n  **\n  ** As each term visited by the linear scans, a separate query for the\n  ** same term is performed. cksum3 is calculated based on the entries\n  ** extracted by these queries.\n  */\n  for(fts5MultiIterNew(p, pStruct, flags, 0, 0, 0, -1, 0, &pIter);\n      fts5MultiIterEof(p, pIter)==0;\n      fts5MultiIterNext(p, pIter, 0, 0)\n  ){\n    int n;                      /* Size of term in bytes */\n    i64 iPos = 0;               /* Position read from poslist */\n    int iOff = 0;               /* Offset within poslist */\n    i64 iRowid = fts5MultiIterRowid(pIter);\n    char *z = (char*)fts5MultiIterTerm(pIter, &n);\n\n    /* If this is a new term, query for it. Update cksum3 with the results. */\n    fts5TestTerm(p, &term, z, n, cksum2, &cksum3);\n\n    if( eDetail==FTS5_DETAIL_NONE ){\n      if( 0==fts5MultiIterIsEmpty(p, pIter) ){\n        cksum2 ^= sqlite3Fts5IndexEntryCksum(iRowid, 0, 0, -1, z, n);\n      }\n    }else{\n      poslist.n = 0;\n      fts5SegiterPoslist(p, &pIter->aSeg[pIter->aFirst[1].iFirst], 0, &poslist);\n      while( 0==sqlite3Fts5PoslistNext64(poslist.p, poslist.n, &iOff, &iPos) ){\n        int iCol = FTS5_POS2COLUMN(iPos);\n        int iTokOff = FTS5_POS2OFFSET(iPos);\n        cksum2 ^= sqlite3Fts5IndexEntryCksum(iRowid, iCol, iTokOff, -1, z, n);\n      }\n    }\n  }\n  fts5TestTerm(p, &term, 0, 0, cksum2, &cksum3);\n\n  fts5MultiIterFree(pIter);\n  if( p->rc==SQLITE_OK && cksum!=cksum2 ) p->rc = FTS5_CORRUPT;\n\n  fts5StructureRelease(pStruct);\n#ifdef SQLITE_DEBUG\n  fts5BufferFree(&term);\n#endif\n  fts5BufferFree(&poslist);\n  return fts5IndexReturn(p);\n}\n\n/*************************************************************************\n**************************************************************************\n** Below this point is the implementation of the fts5_decode() scalar\n** function only.\n*/\n\n/*\n** Decode a segment-data rowid from the %_data table. This function is\n** the opposite of macro FTS5_SEGMENT_ROWID().\n*/\nstatic void fts5DecodeRowid(\n  i64 iRowid,                     /* Rowid from %_data table */\n  int *piSegid,                   /* OUT: Segment id */\n  int *pbDlidx,                   /* OUT: Dlidx flag */\n  int *piHeight,                  /* OUT: Height */\n  int *piPgno                     /* OUT: Page number */\n){\n  *piPgno = (int)(iRowid & (((i64)1 << FTS5_DATA_PAGE_B) - 1));\n  iRowid >>= FTS5_DATA_PAGE_B;\n\n  *piHeight = (int)(iRowid & (((i64)1 << FTS5_DATA_HEIGHT_B) - 1));\n  iRowid >>= FTS5_DATA_HEIGHT_B;\n\n  *pbDlidx = (int)(iRowid & 0x0001);\n  iRowid >>= FTS5_DATA_DLI_B;\n\n  *piSegid = (int)(iRowid & (((i64)1 << FTS5_DATA_ID_B) - 1));\n}\n\nstatic void fts5DebugRowid(int *pRc, Fts5Buffer *pBuf, i64 iKey){\n  int iSegid, iHeight, iPgno, bDlidx;       /* Rowid compenents */\n  fts5DecodeRowid(iKey, &iSegid, &bDlidx, &iHeight, &iPgno);\n\n  if( iSegid==0 ){\n    if( iKey==FTS5_AVERAGES_ROWID ){\n      sqlite3Fts5BufferAppendPrintf(pRc, pBuf, \"{averages} \");\n    }else{\n      sqlite3Fts5BufferAppendPrintf(pRc, pBuf, \"{structure}\");\n    }\n  }\n  else{\n    sqlite3Fts5BufferAppendPrintf(pRc, pBuf, \"{%ssegid=%d h=%d pgno=%d}\",\n        bDlidx ? \"dlidx \" : \"\", iSegid, iHeight, iPgno\n    );\n  }\n}\n\nstatic void fts5DebugStructure(\n  int *pRc,                       /* IN/OUT: error code */\n  Fts5Buffer *pBuf,\n  Fts5Structure *p\n){\n  int iLvl, iSeg;                 /* Iterate through levels, segments */\n\n  for(iLvl=0; iLvl<p->nLevel; iLvl++){\n    Fts5StructureLevel *pLvl = &p->aLevel[iLvl];\n    sqlite3Fts5BufferAppendPrintf(pRc, pBuf, \n        \" {lvl=%d nMerge=%d nSeg=%d\", iLvl, pLvl->nMerge, pLvl->nSeg\n    );\n    for(iSeg=0; iSeg<pLvl->nSeg; iSeg++){\n      Fts5StructureSegment *pSeg = &pLvl->aSeg[iSeg];\n      sqlite3Fts5BufferAppendPrintf(pRc, pBuf, \" {id=%d leaves=%d..%d}\", \n          pSeg->iSegid, pSeg->pgnoFirst, pSeg->pgnoLast\n      );\n    }\n    sqlite3Fts5BufferAppendPrintf(pRc, pBuf, \"}\");\n  }\n}\n\n/*\n** This is part of the fts5_decode() debugging aid.\n**\n** Arguments pBlob/nBlob contain a serialized Fts5Structure object. This\n** function appends a human-readable representation of the same object\n** to the buffer passed as the second argument. \n*/\nstatic void fts5DecodeStructure(\n  int *pRc,                       /* IN/OUT: error code */\n  Fts5Buffer *pBuf,\n  const u8 *pBlob, int nBlob\n){\n  int rc;                         /* Return code */\n  Fts5Structure *p = 0;           /* Decoded structure object */\n\n  rc = fts5StructureDecode(pBlob, nBlob, 0, &p);\n  if( rc!=SQLITE_OK ){\n    *pRc = rc;\n    return;\n  }\n\n  fts5DebugStructure(pRc, pBuf, p);\n  fts5StructureRelease(p);\n}\n\n/*\n** This is part of the fts5_decode() debugging aid.\n**\n** Arguments pBlob/nBlob contain an \"averages\" record. This function \n** appends a human-readable representation of record to the buffer passed \n** as the second argument. \n*/\nstatic void fts5DecodeAverages(\n  int *pRc,                       /* IN/OUT: error code */\n  Fts5Buffer *pBuf,\n  const u8 *pBlob, int nBlob\n){\n  int i = 0;\n  const char *zSpace = \"\";\n\n  while( i<nBlob ){\n    u64 iVal;\n    i += sqlite3Fts5GetVarint(&pBlob[i], &iVal);\n    sqlite3Fts5BufferAppendPrintf(pRc, pBuf, \"%s%d\", zSpace, (int)iVal);\n    zSpace = \" \";\n  }\n}\n\n/*\n** Buffer (a/n) is assumed to contain a list of serialized varints. Read\n** each varint and append its string representation to buffer pBuf. Return\n** after either the input buffer is exhausted or a 0 value is read.\n**\n** The return value is the number of bytes read from the input buffer.\n*/\nstatic int fts5DecodePoslist(int *pRc, Fts5Buffer *pBuf, const u8 *a, int n){\n  int iOff = 0;\n  while( iOff<n ){\n    int iVal;\n    iOff += fts5GetVarint32(&a[iOff], iVal);\n    sqlite3Fts5BufferAppendPrintf(pRc, pBuf, \" %d\", iVal);\n  }\n  return iOff;\n}\n\n/*\n** The start of buffer (a/n) contains the start of a doclist. The doclist\n** may or may not finish within the buffer. This function appends a text\n** representation of the part of the doclist that is present to buffer\n** pBuf. \n**\n** The return value is the number of bytes read from the input buffer.\n*/\nstatic int fts5DecodeDoclist(int *pRc, Fts5Buffer *pBuf, const u8 *a, int n){\n  i64 iDocid = 0;\n  int iOff = 0;\n\n  if( n>0 ){\n    iOff = sqlite3Fts5GetVarint(a, (u64*)&iDocid);\n    sqlite3Fts5BufferAppendPrintf(pRc, pBuf, \" id=%lld\", iDocid);\n  }\n  while( iOff<n ){\n    int nPos;\n    int bDel;\n    iOff += fts5GetPoslistSize(&a[iOff], &nPos, &bDel);\n    sqlite3Fts5BufferAppendPrintf(pRc, pBuf, \" nPos=%d%s\", nPos, bDel?\"*\":\"\");\n    iOff += fts5DecodePoslist(pRc, pBuf, &a[iOff], MIN(n-iOff, nPos));\n    if( iOff<n ){\n      i64 iDelta;\n      iOff += sqlite3Fts5GetVarint(&a[iOff], (u64*)&iDelta);\n      iDocid += iDelta;\n      sqlite3Fts5BufferAppendPrintf(pRc, pBuf, \" id=%lld\", iDocid);\n    }\n  }\n\n  return iOff;\n}\n\n/*\n** This function is part of the fts5_decode() debugging function. It is \n** only ever used with detail=none tables.\n**\n** Buffer (pData/nData) contains a doclist in the format used by detail=none\n** tables. This function appends a human-readable version of that list to\n** buffer pBuf.\n**\n** If *pRc is other than SQLITE_OK when this function is called, it is a\n** no-op. If an OOM or other error occurs within this function, *pRc is\n** set to an SQLite error code before returning. The final state of buffer\n** pBuf is undefined in this case.\n*/\nstatic void fts5DecodeRowidList(\n  int *pRc,                       /* IN/OUT: Error code */\n  Fts5Buffer *pBuf,               /* Buffer to append text to */\n  const u8 *pData, int nData      /* Data to decode list-of-rowids from */\n){\n  int i = 0;\n  i64 iRowid = 0;\n\n  while( i<nData ){\n    const char *zApp = \"\";\n    u64 iVal;\n    i += sqlite3Fts5GetVarint(&pData[i], &iVal);\n    iRowid += iVal;\n\n    if( i<nData && pData[i]==0x00 ){\n      i++;\n      if( i<nData && pData[i]==0x00 ){\n        i++;\n        zApp = \"+\";\n      }else{\n        zApp = \"*\";\n      }\n    }\n\n    sqlite3Fts5BufferAppendPrintf(pRc, pBuf, \" %lld%s\", iRowid, zApp);\n  }\n}\n\n/*\n** The implementation of user-defined scalar function fts5_decode().\n*/\nstatic void fts5DecodeFunction(\n  sqlite3_context *pCtx,          /* Function call context */\n  int nArg,                       /* Number of args (always 2) */\n  sqlite3_value **apVal           /* Function arguments */\n){\n  i64 iRowid;                     /* Rowid for record being decoded */\n  int iSegid,iHeight,iPgno,bDlidx;/* Rowid components */\n  const u8 *aBlob; int n;         /* Record to decode */\n  u8 *a = 0;\n  Fts5Buffer s;                   /* Build up text to return here */\n  int rc = SQLITE_OK;             /* Return code */\n  int nSpace = 0;\n  int eDetailNone = (sqlite3_user_data(pCtx)!=0);\n\n  assert( nArg==2 );\n  UNUSED_PARAM(nArg);\n  memset(&s, 0, sizeof(Fts5Buffer));\n  iRowid = sqlite3_value_int64(apVal[0]);\n\n  /* Make a copy of the second argument (a blob) in aBlob[]. The aBlob[]\n  ** copy is followed by FTS5_DATA_ZERO_PADDING 0x00 bytes, which prevents\n  ** buffer overreads even if the record is corrupt.  */\n  n = sqlite3_value_bytes(apVal[1]);\n  aBlob = sqlite3_value_blob(apVal[1]);\n  nSpace = n + FTS5_DATA_ZERO_PADDING;\n  a = (u8*)sqlite3Fts5MallocZero(&rc, nSpace);\n  if( a==0 ) goto decode_out;\n  memcpy(a, aBlob, n);\n\n\n  fts5DecodeRowid(iRowid, &iSegid, &bDlidx, &iHeight, &iPgno);\n\n  fts5DebugRowid(&rc, &s, iRowid);\n  if( bDlidx ){\n    Fts5Data dlidx;\n    Fts5DlidxLvl lvl;\n\n    dlidx.p = a;\n    dlidx.nn = n;\n\n    memset(&lvl, 0, sizeof(Fts5DlidxLvl));\n    lvl.pData = &dlidx;\n    lvl.iLeafPgno = iPgno;\n\n    for(fts5DlidxLvlNext(&lvl); lvl.bEof==0; fts5DlidxLvlNext(&lvl)){\n      sqlite3Fts5BufferAppendPrintf(&rc, &s, \n          \" %d(%lld)\", lvl.iLeafPgno, lvl.iRowid\n      );\n    }\n  }else if( iSegid==0 ){\n    if( iRowid==FTS5_AVERAGES_ROWID ){\n      fts5DecodeAverages(&rc, &s, a, n);\n    }else{\n      fts5DecodeStructure(&rc, &s, a, n);\n    }\n  }else if( eDetailNone ){\n    Fts5Buffer term;              /* Current term read from page */\n    int szLeaf;\n    int iPgidxOff = szLeaf = fts5GetU16(&a[2]);\n    int iTermOff;\n    int nKeep = 0;\n    int iOff;\n\n    memset(&term, 0, sizeof(Fts5Buffer));\n\n    /* Decode any entries that occur before the first term. */\n    if( szLeaf<n ){\n      iPgidxOff += fts5GetVarint32(&a[iPgidxOff], iTermOff);\n    }else{\n      iTermOff = szLeaf;\n    }\n    fts5DecodeRowidList(&rc, &s, &a[4], iTermOff-4);\n\n    iOff = iTermOff;\n    while( iOff<szLeaf ){\n      int nAppend;\n\n      /* Read the term data for the next term*/\n      iOff += fts5GetVarint32(&a[iOff], nAppend);\n      term.n = nKeep;\n      fts5BufferAppendBlob(&rc, &term, nAppend, &a[iOff]);\n      sqlite3Fts5BufferAppendPrintf(\n          &rc, &s, \" term=%.*s\", term.n, (const char*)term.p\n      );\n      iOff += nAppend;\n\n      /* Figure out where the doclist for this term ends */\n      if( iPgidxOff<n ){\n        int nIncr;\n        iPgidxOff += fts5GetVarint32(&a[iPgidxOff], nIncr);\n        iTermOff += nIncr;\n      }else{\n        iTermOff = szLeaf;\n      }\n\n      fts5DecodeRowidList(&rc, &s, &a[iOff], iTermOff-iOff);\n      iOff = iTermOff;\n      if( iOff<szLeaf ){\n        iOff += fts5GetVarint32(&a[iOff], nKeep);\n      }\n    }\n\n    fts5BufferFree(&term);\n  }else{\n    Fts5Buffer term;              /* Current term read from page */\n    int szLeaf;                   /* Offset of pgidx in a[] */\n    int iPgidxOff;\n    int iPgidxPrev = 0;           /* Previous value read from pgidx */\n    int iTermOff = 0;\n    int iRowidOff = 0;\n    int iOff;\n    int nDoclist;\n\n    memset(&term, 0, sizeof(Fts5Buffer));\n\n    if( n<4 ){\n      sqlite3Fts5BufferSet(&rc, &s, 7, (const u8*)\"corrupt\");\n      goto decode_out;\n    }else{\n      iRowidOff = fts5GetU16(&a[0]);\n      iPgidxOff = szLeaf = fts5GetU16(&a[2]);\n      if( iPgidxOff<n ){\n        fts5GetVarint32(&a[iPgidxOff], iTermOff);\n      }\n    }\n\n    /* Decode the position list tail at the start of the page */\n    if( iRowidOff!=0 ){\n      iOff = iRowidOff;\n    }else if( iTermOff!=0 ){\n      iOff = iTermOff;\n    }else{\n      iOff = szLeaf;\n    }\n    fts5DecodePoslist(&rc, &s, &a[4], iOff-4);\n\n    /* Decode any more doclist data that appears on the page before the\n    ** first term. */\n    nDoclist = (iTermOff ? iTermOff : szLeaf) - iOff;\n    fts5DecodeDoclist(&rc, &s, &a[iOff], nDoclist);\n\n    while( iPgidxOff<n ){\n      int bFirst = (iPgidxOff==szLeaf);     /* True for first term on page */\n      int nByte;                            /* Bytes of data */\n      int iEnd;\n      \n      iPgidxOff += fts5GetVarint32(&a[iPgidxOff], nByte);\n      iPgidxPrev += nByte;\n      iOff = iPgidxPrev;\n\n      if( iPgidxOff<n ){\n        fts5GetVarint32(&a[iPgidxOff], nByte);\n        iEnd = iPgidxPrev + nByte;\n      }else{\n        iEnd = szLeaf;\n      }\n\n      if( bFirst==0 ){\n        iOff += fts5GetVarint32(&a[iOff], nByte);\n        term.n = nByte;\n      }\n      iOff += fts5GetVarint32(&a[iOff], nByte);\n      fts5BufferAppendBlob(&rc, &term, nByte, &a[iOff]);\n      iOff += nByte;\n\n      sqlite3Fts5BufferAppendPrintf(\n          &rc, &s, \" term=%.*s\", term.n, (const char*)term.p\n      );\n      iOff += fts5DecodeDoclist(&rc, &s, &a[iOff], iEnd-iOff);\n    }\n\n    fts5BufferFree(&term);\n  }\n  \n decode_out:\n  sqlite3_free(a);\n  if( rc==SQLITE_OK ){\n    sqlite3_result_text(pCtx, (const char*)s.p, s.n, SQLITE_TRANSIENT);\n  }else{\n    sqlite3_result_error_code(pCtx, rc);\n  }\n  fts5BufferFree(&s);\n}\n\n/*\n** The implementation of user-defined scalar function fts5_rowid().\n*/\nstatic void fts5RowidFunction(\n  sqlite3_context *pCtx,          /* Function call context */\n  int nArg,                       /* Number of args (always 2) */\n  sqlite3_value **apVal           /* Function arguments */\n){\n  const char *zArg;\n  if( nArg==0 ){\n    sqlite3_result_error(pCtx, \"should be: fts5_rowid(subject, ....)\", -1);\n  }else{\n    zArg = (const char*)sqlite3_value_text(apVal[0]);\n    if( 0==sqlite3_stricmp(zArg, \"segment\") ){\n      i64 iRowid;\n      int segid, pgno;\n      if( nArg!=3 ){\n        sqlite3_result_error(pCtx, \n            \"should be: fts5_rowid('segment', segid, pgno))\", -1\n        );\n      }else{\n        segid = sqlite3_value_int(apVal[1]);\n        pgno = sqlite3_value_int(apVal[2]);\n        iRowid = FTS5_SEGMENT_ROWID(segid, pgno);\n        sqlite3_result_int64(pCtx, iRowid);\n      }\n    }else{\n      sqlite3_result_error(pCtx, \n        \"first arg to fts5_rowid() must be 'segment'\" , -1\n      );\n    }\n  }\n}\n\n/*\n** This is called as part of registering the FTS5 module with database\n** connection db. It registers several user-defined scalar functions useful\n** with FTS5.\n**\n** If successful, SQLITE_OK is returned. If an error occurs, some other\n** SQLite error code is returned instead.\n*/\nstatic int sqlite3Fts5IndexInit(sqlite3 *db){\n  int rc = sqlite3_create_function(\n      db, \"fts5_decode\", 2, SQLITE_UTF8, 0, fts5DecodeFunction, 0, 0\n  );\n\n  if( rc==SQLITE_OK ){\n    rc = sqlite3_create_function(\n        db, \"fts5_decode_none\", 2, \n        SQLITE_UTF8, (void*)db, fts5DecodeFunction, 0, 0\n    );\n  }\n\n  if( rc==SQLITE_OK ){\n    rc = sqlite3_create_function(\n        db, \"fts5_rowid\", -1, SQLITE_UTF8, 0, fts5RowidFunction, 0, 0\n    );\n  }\n  return rc;\n}\n\n\nstatic int sqlite3Fts5IndexReset(Fts5Index *p){\n  assert( p->pStruct==0 || p->iStructVersion!=0 );\n  if( fts5IndexDataVersion(p)!=p->iStructVersion ){\n    fts5StructureInvalidate(p);\n  }\n  return fts5IndexReturn(p);\n}\n\n/*\n** 2014 Jun 09\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n******************************************************************************\n**\n** This is an SQLite module implementing full-text search.\n*/\n\n\n/* #include \"fts5Int.h\" */\n\n/*\n** This variable is set to false when running tests for which the on disk\n** structures should not be corrupt. Otherwise, true. If it is false, extra\n** assert() conditions in the fts5 code are activated - conditions that are\n** only true if it is guaranteed that the fts5 database is not corrupt.\n*/\nSQLITE_API int sqlite3_fts5_may_be_corrupt = 1;\n\n\ntypedef struct Fts5Auxdata Fts5Auxdata;\ntypedef struct Fts5Auxiliary Fts5Auxiliary;\ntypedef struct Fts5Cursor Fts5Cursor;\ntypedef struct Fts5Sorter Fts5Sorter;\ntypedef struct Fts5Table Fts5Table;\ntypedef struct Fts5TokenizerModule Fts5TokenizerModule;\n\n/*\n** NOTES ON TRANSACTIONS: \n**\n** SQLite invokes the following virtual table methods as transactions are \n** opened and closed by the user:\n**\n**     xBegin():    Start of a new transaction.\n**     xSync():     Initial part of two-phase commit.\n**     xCommit():   Final part of two-phase commit.\n**     xRollback(): Rollback the transaction.\n**\n** Anything that is required as part of a commit that may fail is performed\n** in the xSync() callback. Current versions of SQLite ignore any errors \n** returned by xCommit().\n**\n** And as sub-transactions are opened/closed:\n**\n**     xSavepoint(int S):  Open savepoint S.\n**     xRelease(int S):    Commit and close savepoint S.\n**     xRollbackTo(int S): Rollback to start of savepoint S.\n**\n** During a write-transaction the fts5_index.c module may cache some data \n** in-memory. It is flushed to disk whenever xSync(), xRelease() or\n** xSavepoint() is called. And discarded whenever xRollback() or xRollbackTo() \n** is called.\n**\n** Additionally, if SQLITE_DEBUG is defined, an instance of the following\n** structure is used to record the current transaction state. This information\n** is not required, but it is used in the assert() statements executed by\n** function fts5CheckTransactionState() (see below).\n*/\nstruct Fts5TransactionState {\n  int eState;                     /* 0==closed, 1==open, 2==synced */\n  int iSavepoint;                 /* Number of open savepoints (0 -> none) */\n};\n\n/*\n** A single object of this type is allocated when the FTS5 module is \n** registered with a database handle. It is used to store pointers to\n** all registered FTS5 extensions - tokenizers and auxiliary functions.\n*/\nstruct Fts5Global {\n  fts5_api api;                   /* User visible part of object (see fts5.h) */\n  sqlite3 *db;                    /* Associated database connection */ \n  i64 iNextId;                    /* Used to allocate unique cursor ids */\n  Fts5Auxiliary *pAux;            /* First in list of all aux. functions */\n  Fts5TokenizerModule *pTok;      /* First in list of all tokenizer modules */\n  Fts5TokenizerModule *pDfltTok;  /* Default tokenizer module */\n  Fts5Cursor *pCsr;               /* First in list of all open cursors */\n};\n\n/*\n** Each auxiliary function registered with the FTS5 module is represented\n** by an object of the following type. All such objects are stored as part\n** of the Fts5Global.pAux list.\n*/\nstruct Fts5Auxiliary {\n  Fts5Global *pGlobal;            /* Global context for this function */\n  char *zFunc;                    /* Function name (nul-terminated) */\n  void *pUserData;                /* User-data pointer */\n  fts5_extension_function xFunc;  /* Callback function */\n  void (*xDestroy)(void*);        /* Destructor function */\n  Fts5Auxiliary *pNext;           /* Next registered auxiliary function */\n};\n\n/*\n** Each tokenizer module registered with the FTS5 module is represented\n** by an object of the following type. All such objects are stored as part\n** of the Fts5Global.pTok list.\n*/\nstruct Fts5TokenizerModule {\n  char *zName;                    /* Name of tokenizer */\n  void *pUserData;                /* User pointer passed to xCreate() */\n  fts5_tokenizer x;               /* Tokenizer functions */\n  void (*xDestroy)(void*);        /* Destructor function */\n  Fts5TokenizerModule *pNext;     /* Next registered tokenizer module */\n};\n\n/*\n** Virtual-table object.\n*/\nstruct Fts5Table {\n  sqlite3_vtab base;              /* Base class used by SQLite core */\n  Fts5Config *pConfig;            /* Virtual table configuration */\n  Fts5Index *pIndex;              /* Full-text index */\n  Fts5Storage *pStorage;          /* Document store */\n  Fts5Global *pGlobal;            /* Global (connection wide) data */\n  Fts5Cursor *pSortCsr;           /* Sort data from this cursor */\n#ifdef SQLITE_DEBUG\n  struct Fts5TransactionState ts;\n#endif\n};\n\nstruct Fts5MatchPhrase {\n  Fts5Buffer *pPoslist;           /* Pointer to current poslist */\n  int nTerm;                      /* Size of phrase in terms */\n};\n\n/*\n** pStmt:\n**   SELECT rowid, <fts> FROM <fts> ORDER BY +rank;\n**\n** aIdx[]:\n**   There is one entry in the aIdx[] array for each phrase in the query,\n**   the value of which is the offset within aPoslist[] following the last \n**   byte of the position list for the corresponding phrase.\n*/\nstruct Fts5Sorter {\n  sqlite3_stmt *pStmt;\n  i64 iRowid;                     /* Current rowid */\n  const u8 *aPoslist;             /* Position lists for current row */\n  int nIdx;                       /* Number of entries in aIdx[] */\n  int aIdx[1];                    /* Offsets into aPoslist for current row */\n};\n\n\n/*\n** Virtual-table cursor object.\n**\n** iSpecial:\n**   If this is a 'special' query (refer to function fts5SpecialMatch()), \n**   then this variable contains the result of the query. \n**\n** iFirstRowid, iLastRowid:\n**   These variables are only used for FTS5_PLAN_MATCH cursors. Assuming the\n**   cursor iterates in ascending order of rowids, iFirstRowid is the lower\n**   limit of rowids to return, and iLastRowid the upper. In other words, the\n**   WHERE clause in the user's query might have been:\n**\n**       <tbl> MATCH <expr> AND rowid BETWEEN $iFirstRowid AND $iLastRowid\n**\n**   If the cursor iterates in descending order of rowid, iFirstRowid\n**   is the upper limit (i.e. the \"first\" rowid visited) and iLastRowid\n**   the lower.\n*/\nstruct Fts5Cursor {\n  sqlite3_vtab_cursor base;       /* Base class used by SQLite core */\n  Fts5Cursor *pNext;              /* Next cursor in Fts5Cursor.pCsr list */\n  int *aColumnSize;               /* Values for xColumnSize() */\n  i64 iCsrId;                     /* Cursor id */\n\n  /* Zero from this point onwards on cursor reset */\n  int ePlan;                      /* FTS5_PLAN_XXX value */\n  int bDesc;                      /* True for \"ORDER BY rowid DESC\" queries */\n  i64 iFirstRowid;                /* Return no rowids earlier than this */\n  i64 iLastRowid;                 /* Return no rowids later than this */\n  sqlite3_stmt *pStmt;            /* Statement used to read %_content */\n  Fts5Expr *pExpr;                /* Expression for MATCH queries */\n  Fts5Sorter *pSorter;            /* Sorter for \"ORDER BY rank\" queries */\n  int csrflags;                   /* Mask of cursor flags (see below) */\n  i64 iSpecial;                   /* Result of special query */\n\n  /* \"rank\" function. Populated on demand from vtab.xColumn(). */\n  char *zRank;                    /* Custom rank function */\n  char *zRankArgs;                /* Custom rank function args */\n  Fts5Auxiliary *pRank;           /* Rank callback (or NULL) */\n  int nRankArg;                   /* Number of trailing arguments for rank() */\n  sqlite3_value **apRankArg;      /* Array of trailing arguments */\n  sqlite3_stmt *pRankArgStmt;     /* Origin of objects in apRankArg[] */\n\n  /* Auxiliary data storage */\n  Fts5Auxiliary *pAux;            /* Currently executing extension function */\n  Fts5Auxdata *pAuxdata;          /* First in linked list of saved aux-data */\n\n  /* Cache used by auxiliary functions xInst() and xInstCount() */\n  Fts5PoslistReader *aInstIter;   /* One for each phrase */\n  int nInstAlloc;                 /* Size of aInst[] array (entries / 3) */\n  int nInstCount;                 /* Number of phrase instances */\n  int *aInst;                     /* 3 integers per phrase instance */\n};\n\n/*\n** Bits that make up the \"idxNum\" parameter passed indirectly by \n** xBestIndex() to xFilter().\n*/\n#define FTS5_BI_MATCH        0x0001         /* <tbl> MATCH ? */\n#define FTS5_BI_RANK         0x0002         /* rank MATCH ? */\n#define FTS5_BI_ROWID_EQ     0x0004         /* rowid == ? */\n#define FTS5_BI_ROWID_LE     0x0008         /* rowid <= ? */\n#define FTS5_BI_ROWID_GE     0x0010         /* rowid >= ? */\n\n#define FTS5_BI_ORDER_RANK   0x0020\n#define FTS5_BI_ORDER_ROWID  0x0040\n#define FTS5_BI_ORDER_DESC   0x0080\n\n/*\n** Values for Fts5Cursor.csrflags\n*/\n#define FTS5CSR_EOF               0x01\n#define FTS5CSR_REQUIRE_CONTENT   0x02\n#define FTS5CSR_REQUIRE_DOCSIZE   0x04\n#define FTS5CSR_REQUIRE_INST      0x08\n#define FTS5CSR_FREE_ZRANK        0x10\n#define FTS5CSR_REQUIRE_RESEEK    0x20\n#define FTS5CSR_REQUIRE_POSLIST   0x40\n\n#define BitFlagAllTest(x,y) (((x) & (y))==(y))\n#define BitFlagTest(x,y)    (((x) & (y))!=0)\n\n\n/*\n** Macros to Set(), Clear() and Test() cursor flags.\n*/\n#define CsrFlagSet(pCsr, flag)   ((pCsr)->csrflags |= (flag))\n#define CsrFlagClear(pCsr, flag) ((pCsr)->csrflags &= ~(flag))\n#define CsrFlagTest(pCsr, flag)  ((pCsr)->csrflags & (flag))\n\nstruct Fts5Auxdata {\n  Fts5Auxiliary *pAux;            /* Extension to which this belongs */\n  void *pPtr;                     /* Pointer value */\n  void(*xDelete)(void*);          /* Destructor */\n  Fts5Auxdata *pNext;             /* Next object in linked list */\n};\n\n#ifdef SQLITE_DEBUG\n#define FTS5_BEGIN      1\n#define FTS5_SYNC       2\n#define FTS5_COMMIT     3\n#define FTS5_ROLLBACK   4\n#define FTS5_SAVEPOINT  5\n#define FTS5_RELEASE    6\n#define FTS5_ROLLBACKTO 7\nstatic void fts5CheckTransactionState(Fts5Table *p, int op, int iSavepoint){\n  switch( op ){\n    case FTS5_BEGIN:\n      assert( p->ts.eState==0 );\n      p->ts.eState = 1;\n      p->ts.iSavepoint = -1;\n      break;\n\n    case FTS5_SYNC:\n      assert( p->ts.eState==1 );\n      p->ts.eState = 2;\n      break;\n\n    case FTS5_COMMIT:\n      assert( p->ts.eState==2 );\n      p->ts.eState = 0;\n      break;\n\n    case FTS5_ROLLBACK:\n      assert( p->ts.eState==1 || p->ts.eState==2 || p->ts.eState==0 );\n      p->ts.eState = 0;\n      break;\n\n    case FTS5_SAVEPOINT:\n      assert( p->ts.eState==1 );\n      assert( iSavepoint>=0 );\n      assert( iSavepoint>p->ts.iSavepoint );\n      p->ts.iSavepoint = iSavepoint;\n      break;\n      \n    case FTS5_RELEASE:\n      assert( p->ts.eState==1 );\n      assert( iSavepoint>=0 );\n      assert( iSavepoint<=p->ts.iSavepoint );\n      p->ts.iSavepoint = iSavepoint-1;\n      break;\n\n    case FTS5_ROLLBACKTO:\n      assert( p->ts.eState==1 );\n      assert( iSavepoint>=0 );\n      assert( iSavepoint<=p->ts.iSavepoint );\n      p->ts.iSavepoint = iSavepoint;\n      break;\n  }\n}\n#else\n# define fts5CheckTransactionState(x,y,z)\n#endif\n\n/*\n** Return true if pTab is a contentless table.\n*/\nstatic int fts5IsContentless(Fts5Table *pTab){\n  return pTab->pConfig->eContent==FTS5_CONTENT_NONE;\n}\n\n/*\n** Delete a virtual table handle allocated by fts5InitVtab(). \n*/\nstatic void fts5FreeVtab(Fts5Table *pTab){\n  if( pTab ){\n    sqlite3Fts5IndexClose(pTab->pIndex);\n    sqlite3Fts5StorageClose(pTab->pStorage);\n    sqlite3Fts5ConfigFree(pTab->pConfig);\n    sqlite3_free(pTab);\n  }\n}\n\n/*\n** The xDisconnect() virtual table method.\n*/\nstatic int fts5DisconnectMethod(sqlite3_vtab *pVtab){\n  fts5FreeVtab((Fts5Table*)pVtab);\n  return SQLITE_OK;\n}\n\n/*\n** The xDestroy() virtual table method.\n*/\nstatic int fts5DestroyMethod(sqlite3_vtab *pVtab){\n  Fts5Table *pTab = (Fts5Table*)pVtab;\n  int rc = sqlite3Fts5DropAll(pTab->pConfig);\n  if( rc==SQLITE_OK ){\n    fts5FreeVtab((Fts5Table*)pVtab);\n  }\n  return rc;\n}\n\n/*\n** This function is the implementation of both the xConnect and xCreate\n** methods of the FTS3 virtual table.\n**\n** The argv[] array contains the following:\n**\n**   argv[0]   -> module name  (\"fts5\")\n**   argv[1]   -> database name\n**   argv[2]   -> table name\n**   argv[...] -> \"column name\" and other module argument fields.\n*/\nstatic int fts5InitVtab(\n  int bCreate,                    /* True for xCreate, false for xConnect */\n  sqlite3 *db,                    /* The SQLite database connection */\n  void *pAux,                     /* Hash table containing tokenizers */\n  int argc,                       /* Number of elements in argv array */\n  const char * const *argv,       /* xCreate/xConnect argument array */\n  sqlite3_vtab **ppVTab,          /* Write the resulting vtab structure here */\n  char **pzErr                    /* Write any error message here */\n){\n  Fts5Global *pGlobal = (Fts5Global*)pAux;\n  const char **azConfig = (const char**)argv;\n  int rc = SQLITE_OK;             /* Return code */\n  Fts5Config *pConfig = 0;        /* Results of parsing argc/argv */\n  Fts5Table *pTab = 0;            /* New virtual table object */\n\n  /* Allocate the new vtab object and parse the configuration */\n  pTab = (Fts5Table*)sqlite3Fts5MallocZero(&rc, sizeof(Fts5Table));\n  if( rc==SQLITE_OK ){\n    rc = sqlite3Fts5ConfigParse(pGlobal, db, argc, azConfig, &pConfig, pzErr);\n    assert( (rc==SQLITE_OK && *pzErr==0) || pConfig==0 );\n  }\n  if( rc==SQLITE_OK ){\n    pTab->pConfig = pConfig;\n    pTab->pGlobal = pGlobal;\n  }\n\n  /* Open the index sub-system */\n  if( rc==SQLITE_OK ){\n    rc = sqlite3Fts5IndexOpen(pConfig, bCreate, &pTab->pIndex, pzErr);\n  }\n\n  /* Open the storage sub-system */\n  if( rc==SQLITE_OK ){\n    rc = sqlite3Fts5StorageOpen(\n        pConfig, pTab->pIndex, bCreate, &pTab->pStorage, pzErr\n    );\n  }\n\n  /* Call sqlite3_declare_vtab() */\n  if( rc==SQLITE_OK ){\n    rc = sqlite3Fts5ConfigDeclareVtab(pConfig);\n  }\n\n  /* Load the initial configuration */\n  if( rc==SQLITE_OK ){\n    assert( pConfig->pzErrmsg==0 );\n    pConfig->pzErrmsg = pzErr;\n    rc = sqlite3Fts5IndexLoadConfig(pTab->pIndex);\n    sqlite3Fts5IndexRollback(pTab->pIndex);\n    pConfig->pzErrmsg = 0;\n  }\n\n  if( rc!=SQLITE_OK ){\n    fts5FreeVtab(pTab);\n    pTab = 0;\n  }else if( bCreate ){\n    fts5CheckTransactionState(pTab, FTS5_BEGIN, 0);\n  }\n  *ppVTab = (sqlite3_vtab*)pTab;\n  return rc;\n}\n\n/*\n** The xConnect() and xCreate() methods for the virtual table. All the\n** work is done in function fts5InitVtab().\n*/\nstatic int fts5ConnectMethod(\n  sqlite3 *db,                    /* Database connection */\n  void *pAux,                     /* Pointer to tokenizer hash table */\n  int argc,                       /* Number of elements in argv array */\n  const char * const *argv,       /* xCreate/xConnect argument array */\n  sqlite3_vtab **ppVtab,          /* OUT: New sqlite3_vtab object */\n  char **pzErr                    /* OUT: sqlite3_malloc'd error message */\n){\n  return fts5InitVtab(0, db, pAux, argc, argv, ppVtab, pzErr);\n}\nstatic int fts5CreateMethod(\n  sqlite3 *db,                    /* Database connection */\n  void *pAux,                     /* Pointer to tokenizer hash table */\n  int argc,                       /* Number of elements in argv array */\n  const char * const *argv,       /* xCreate/xConnect argument array */\n  sqlite3_vtab **ppVtab,          /* OUT: New sqlite3_vtab object */\n  char **pzErr                    /* OUT: sqlite3_malloc'd error message */\n){\n  return fts5InitVtab(1, db, pAux, argc, argv, ppVtab, pzErr);\n}\n\n/*\n** The different query plans.\n*/\n#define FTS5_PLAN_MATCH          1       /* (<tbl> MATCH ?) */\n#define FTS5_PLAN_SOURCE         2       /* A source cursor for SORTED_MATCH */\n#define FTS5_PLAN_SPECIAL        3       /* An internal query */\n#define FTS5_PLAN_SORTED_MATCH   4       /* (<tbl> MATCH ? ORDER BY rank) */\n#define FTS5_PLAN_SCAN           5       /* No usable constraint */\n#define FTS5_PLAN_ROWID          6       /* (rowid = ?) */\n\n/*\n** Set the SQLITE_INDEX_SCAN_UNIQUE flag in pIdxInfo->flags. Unless this\n** extension is currently being used by a version of SQLite too old to\n** support index-info flags. In that case this function is a no-op.\n*/\nstatic void fts5SetUniqueFlag(sqlite3_index_info *pIdxInfo){\n#if SQLITE_VERSION_NUMBER>=3008012\n#ifndef SQLITE_CORE\n  if( sqlite3_libversion_number()>=3008012 )\n#endif\n  {\n    pIdxInfo->idxFlags |= SQLITE_INDEX_SCAN_UNIQUE;\n  }\n#endif\n}\n\n/*\n** Implementation of the xBestIndex method for FTS5 tables. Within the \n** WHERE constraint, it searches for the following:\n**\n**   1. A MATCH constraint against the special column.\n**   2. A MATCH constraint against the \"rank\" column.\n**   3. An == constraint against the rowid column.\n**   4. A < or <= constraint against the rowid column.\n**   5. A > or >= constraint against the rowid column.\n**\n** Within the ORDER BY, either:\n**\n**   5. ORDER BY rank [ASC|DESC]\n**   6. ORDER BY rowid [ASC|DESC]\n**\n** Costs are assigned as follows:\n**\n**  a) If an unusable MATCH operator is present in the WHERE clause, the\n**     cost is unconditionally set to 1e50 (a really big number).\n**\n**  a) If a MATCH operator is present, the cost depends on the other\n**     constraints also present. As follows:\n**\n**       * No other constraints:         cost=1000.0\n**       * One rowid range constraint:   cost=750.0\n**       * Both rowid range constraints: cost=500.0\n**       * An == rowid constraint:       cost=100.0\n**\n**  b) Otherwise, if there is no MATCH:\n**\n**       * No other constraints:         cost=1000000.0\n**       * One rowid range constraint:   cost=750000.0\n**       * Both rowid range constraints: cost=250000.0\n**       * An == rowid constraint:       cost=10.0\n**\n** Costs are not modified by the ORDER BY clause.\n*/\nstatic int fts5BestIndexMethod(sqlite3_vtab *pVTab, sqlite3_index_info *pInfo){\n  Fts5Table *pTab = (Fts5Table*)pVTab;\n  Fts5Config *pConfig = pTab->pConfig;\n  const int nCol = pConfig->nCol;\n  int idxFlags = 0;               /* Parameter passed through to xFilter() */\n  int bHasMatch;\n  int iNext;\n  int i;\n\n  struct Constraint {\n    int op;                       /* Mask against sqlite3_index_constraint.op */\n    int fts5op;                   /* FTS5 mask for idxFlags */\n    int iCol;                     /* 0==rowid, 1==tbl, 2==rank */\n    int omit;                     /* True to omit this if found */\n    int iConsIndex;               /* Index in pInfo->aConstraint[] */\n  } aConstraint[] = {\n    {SQLITE_INDEX_CONSTRAINT_MATCH|SQLITE_INDEX_CONSTRAINT_EQ, \n                                    FTS5_BI_MATCH,    1, 1, -1},\n    {SQLITE_INDEX_CONSTRAINT_MATCH|SQLITE_INDEX_CONSTRAINT_EQ, \n                                    FTS5_BI_RANK,     2, 1, -1},\n    {SQLITE_INDEX_CONSTRAINT_EQ,    FTS5_BI_ROWID_EQ, 0, 0, -1},\n    {SQLITE_INDEX_CONSTRAINT_LT|SQLITE_INDEX_CONSTRAINT_LE, \n                                    FTS5_BI_ROWID_LE, 0, 0, -1},\n    {SQLITE_INDEX_CONSTRAINT_GT|SQLITE_INDEX_CONSTRAINT_GE, \n                                    FTS5_BI_ROWID_GE, 0, 0, -1},\n  };\n\n  int aColMap[3];\n  aColMap[0] = -1;\n  aColMap[1] = nCol;\n  aColMap[2] = nCol+1;\n\n  /* Set idxFlags flags for all WHERE clause terms that will be used. */\n  for(i=0; i<pInfo->nConstraint; i++){\n    struct sqlite3_index_constraint *p = &pInfo->aConstraint[i];\n    int iCol = p->iColumn;\n\n    if( (p->op==SQLITE_INDEX_CONSTRAINT_MATCH && iCol>=0 && iCol<=nCol)\n     || (p->op==SQLITE_INDEX_CONSTRAINT_EQ && iCol==nCol)\n    ){\n      /* A MATCH operator or equivalent */\n      if( p->usable ){\n        idxFlags = (idxFlags & 0xFFFF) | FTS5_BI_MATCH | (iCol << 16);\n        aConstraint[0].iConsIndex = i;\n      }else{\n        /* As there exists an unusable MATCH constraint this is an \n        ** unusable plan. Set a prohibitively high cost. */\n        pInfo->estimatedCost = 1e50;\n        return SQLITE_OK;\n      }\n    }else{\n      int j;\n      for(j=1; j<ArraySize(aConstraint); j++){\n        struct Constraint *pC = &aConstraint[j];\n        if( iCol==aColMap[pC->iCol] && p->op & pC->op && p->usable ){\n          pC->iConsIndex = i;\n          idxFlags |= pC->fts5op;\n        }\n      }\n    }\n  }\n\n  /* Set idxFlags flags for the ORDER BY clause */\n  if( pInfo->nOrderBy==1 ){\n    int iSort = pInfo->aOrderBy[0].iColumn;\n    if( iSort==(pConfig->nCol+1) && BitFlagTest(idxFlags, FTS5_BI_MATCH) ){\n      idxFlags |= FTS5_BI_ORDER_RANK;\n    }else if( iSort==-1 ){\n      idxFlags |= FTS5_BI_ORDER_ROWID;\n    }\n    if( BitFlagTest(idxFlags, FTS5_BI_ORDER_RANK|FTS5_BI_ORDER_ROWID) ){\n      pInfo->orderByConsumed = 1;\n      if( pInfo->aOrderBy[0].desc ){\n        idxFlags |= FTS5_BI_ORDER_DESC;\n      }\n    }\n  }\n\n  /* Calculate the estimated cost based on the flags set in idxFlags. */\n  bHasMatch = BitFlagTest(idxFlags, FTS5_BI_MATCH);\n  if( BitFlagTest(idxFlags, FTS5_BI_ROWID_EQ) ){\n    pInfo->estimatedCost = bHasMatch ? 100.0 : 10.0;\n    if( bHasMatch==0 ) fts5SetUniqueFlag(pInfo);\n  }else if( BitFlagAllTest(idxFlags, FTS5_BI_ROWID_LE|FTS5_BI_ROWID_GE) ){\n    pInfo->estimatedCost = bHasMatch ? 500.0 : 250000.0;\n  }else if( BitFlagTest(idxFlags, FTS5_BI_ROWID_LE|FTS5_BI_ROWID_GE) ){\n    pInfo->estimatedCost = bHasMatch ? 750.0 : 750000.0;\n  }else{\n    pInfo->estimatedCost = bHasMatch ? 1000.0 : 1000000.0;\n  }\n\n  /* Assign argvIndex values to each constraint in use. */\n  iNext = 1;\n  for(i=0; i<ArraySize(aConstraint); i++){\n    struct Constraint *pC = &aConstraint[i];\n    if( pC->iConsIndex>=0 ){\n      pInfo->aConstraintUsage[pC->iConsIndex].argvIndex = iNext++;\n      pInfo->aConstraintUsage[pC->iConsIndex].omit = (unsigned char)pC->omit;\n    }\n  }\n\n  pInfo->idxNum = idxFlags;\n  return SQLITE_OK;\n}\n\nstatic int fts5NewTransaction(Fts5Table *pTab){\n  Fts5Cursor *pCsr;\n  for(pCsr=pTab->pGlobal->pCsr; pCsr; pCsr=pCsr->pNext){\n    if( pCsr->base.pVtab==(sqlite3_vtab*)pTab ) return SQLITE_OK;\n  }\n  return sqlite3Fts5StorageReset(pTab->pStorage);\n}\n\n/*\n** Implementation of xOpen method.\n*/\nstatic int fts5OpenMethod(sqlite3_vtab *pVTab, sqlite3_vtab_cursor **ppCsr){\n  Fts5Table *pTab = (Fts5Table*)pVTab;\n  Fts5Config *pConfig = pTab->pConfig;\n  Fts5Cursor *pCsr = 0;           /* New cursor object */\n  int nByte;                      /* Bytes of space to allocate */\n  int rc;                         /* Return code */\n\n  rc = fts5NewTransaction(pTab);\n  if( rc==SQLITE_OK ){\n    nByte = sizeof(Fts5Cursor) + pConfig->nCol * sizeof(int);\n    pCsr = (Fts5Cursor*)sqlite3_malloc(nByte);\n    if( pCsr ){\n      Fts5Global *pGlobal = pTab->pGlobal;\n      memset(pCsr, 0, nByte);\n      pCsr->aColumnSize = (int*)&pCsr[1];\n      pCsr->pNext = pGlobal->pCsr;\n      pGlobal->pCsr = pCsr;\n      pCsr->iCsrId = ++pGlobal->iNextId;\n    }else{\n      rc = SQLITE_NOMEM;\n    }\n  }\n  *ppCsr = (sqlite3_vtab_cursor*)pCsr;\n  return rc;\n}\n\nstatic int fts5StmtType(Fts5Cursor *pCsr){\n  if( pCsr->ePlan==FTS5_PLAN_SCAN ){\n    return (pCsr->bDesc) ? FTS5_STMT_SCAN_DESC : FTS5_STMT_SCAN_ASC;\n  }\n  return FTS5_STMT_LOOKUP;\n}\n\n/*\n** This function is called after the cursor passed as the only argument\n** is moved to point at a different row. It clears all cached data \n** specific to the previous row stored by the cursor object.\n*/\nstatic void fts5CsrNewrow(Fts5Cursor *pCsr){\n  CsrFlagSet(pCsr, \n      FTS5CSR_REQUIRE_CONTENT \n    | FTS5CSR_REQUIRE_DOCSIZE \n    | FTS5CSR_REQUIRE_INST \n    | FTS5CSR_REQUIRE_POSLIST \n  );\n}\n\nstatic void fts5FreeCursorComponents(Fts5Cursor *pCsr){\n  Fts5Table *pTab = (Fts5Table*)(pCsr->base.pVtab);\n  Fts5Auxdata *pData;\n  Fts5Auxdata *pNext;\n\n  sqlite3_free(pCsr->aInstIter);\n  sqlite3_free(pCsr->aInst);\n  if( pCsr->pStmt ){\n    int eStmt = fts5StmtType(pCsr);\n    sqlite3Fts5StorageStmtRelease(pTab->pStorage, eStmt, pCsr->pStmt);\n  }\n  if( pCsr->pSorter ){\n    Fts5Sorter *pSorter = pCsr->pSorter;\n    sqlite3_finalize(pSorter->pStmt);\n    sqlite3_free(pSorter);\n  }\n\n  if( pCsr->ePlan!=FTS5_PLAN_SOURCE ){\n    sqlite3Fts5ExprFree(pCsr->pExpr);\n  }\n\n  for(pData=pCsr->pAuxdata; pData; pData=pNext){\n    pNext = pData->pNext;\n    if( pData->xDelete ) pData->xDelete(pData->pPtr);\n    sqlite3_free(pData);\n  }\n\n  sqlite3_finalize(pCsr->pRankArgStmt);\n  sqlite3_free(pCsr->apRankArg);\n\n  if( CsrFlagTest(pCsr, FTS5CSR_FREE_ZRANK) ){\n    sqlite3_free(pCsr->zRank);\n    sqlite3_free(pCsr->zRankArgs);\n  }\n\n  memset(&pCsr->ePlan, 0, sizeof(Fts5Cursor) - ((u8*)&pCsr->ePlan - (u8*)pCsr));\n}\n\n\n/*\n** Close the cursor.  For additional information see the documentation\n** on the xClose method of the virtual table interface.\n*/\nstatic int fts5CloseMethod(sqlite3_vtab_cursor *pCursor){\n  if( pCursor ){\n    Fts5Table *pTab = (Fts5Table*)(pCursor->pVtab);\n    Fts5Cursor *pCsr = (Fts5Cursor*)pCursor;\n    Fts5Cursor **pp;\n\n    fts5FreeCursorComponents(pCsr);\n    /* Remove the cursor from the Fts5Global.pCsr list */\n    for(pp=&pTab->pGlobal->pCsr; (*pp)!=pCsr; pp=&(*pp)->pNext);\n    *pp = pCsr->pNext;\n\n    sqlite3_free(pCsr);\n  }\n  return SQLITE_OK;\n}\n\nstatic int fts5SorterNext(Fts5Cursor *pCsr){\n  Fts5Sorter *pSorter = pCsr->pSorter;\n  int rc;\n\n  rc = sqlite3_step(pSorter->pStmt);\n  if( rc==SQLITE_DONE ){\n    rc = SQLITE_OK;\n    CsrFlagSet(pCsr, FTS5CSR_EOF);\n  }else if( rc==SQLITE_ROW ){\n    const u8 *a;\n    const u8 *aBlob;\n    int nBlob;\n    int i;\n    int iOff = 0;\n    rc = SQLITE_OK;\n\n    pSorter->iRowid = sqlite3_column_int64(pSorter->pStmt, 0);\n    nBlob = sqlite3_column_bytes(pSorter->pStmt, 1);\n    aBlob = a = sqlite3_column_blob(pSorter->pStmt, 1);\n\n    /* nBlob==0 in detail=none mode. */\n    if( nBlob>0 ){\n      for(i=0; i<(pSorter->nIdx-1); i++){\n        int iVal;\n        a += fts5GetVarint32(a, iVal);\n        iOff += iVal;\n        pSorter->aIdx[i] = iOff;\n      }\n      pSorter->aIdx[i] = &aBlob[nBlob] - a;\n      pSorter->aPoslist = a;\n    }\n\n    fts5CsrNewrow(pCsr);\n  }\n\n  return rc;\n}\n\n\n/*\n** Set the FTS5CSR_REQUIRE_RESEEK flag on all FTS5_PLAN_MATCH cursors \n** open on table pTab.\n*/\nstatic void fts5TripCursors(Fts5Table *pTab){\n  Fts5Cursor *pCsr;\n  for(pCsr=pTab->pGlobal->pCsr; pCsr; pCsr=pCsr->pNext){\n    if( pCsr->ePlan==FTS5_PLAN_MATCH\n     && pCsr->base.pVtab==(sqlite3_vtab*)pTab \n    ){\n      CsrFlagSet(pCsr, FTS5CSR_REQUIRE_RESEEK);\n    }\n  }\n}\n\n/*\n** If the REQUIRE_RESEEK flag is set on the cursor passed as the first\n** argument, close and reopen all Fts5IndexIter iterators that the cursor \n** is using. Then attempt to move the cursor to a rowid equal to or laster\n** (in the cursors sort order - ASC or DESC) than the current rowid. \n**\n** If the new rowid is not equal to the old, set output parameter *pbSkip\n** to 1 before returning. Otherwise, leave it unchanged.\n**\n** Return SQLITE_OK if successful or if no reseek was required, or an \n** error code if an error occurred.\n*/\nstatic int fts5CursorReseek(Fts5Cursor *pCsr, int *pbSkip){\n  int rc = SQLITE_OK;\n  assert( *pbSkip==0 );\n  if( CsrFlagTest(pCsr, FTS5CSR_REQUIRE_RESEEK) ){\n    Fts5Table *pTab = (Fts5Table*)(pCsr->base.pVtab);\n    int bDesc = pCsr->bDesc;\n    i64 iRowid = sqlite3Fts5ExprRowid(pCsr->pExpr);\n\n    rc = sqlite3Fts5ExprFirst(pCsr->pExpr, pTab->pIndex, iRowid, bDesc);\n    if( rc==SQLITE_OK &&  iRowid!=sqlite3Fts5ExprRowid(pCsr->pExpr) ){\n      *pbSkip = 1;\n    }\n\n    CsrFlagClear(pCsr, FTS5CSR_REQUIRE_RESEEK);\n    fts5CsrNewrow(pCsr);\n    if( sqlite3Fts5ExprEof(pCsr->pExpr) ){\n      CsrFlagSet(pCsr, FTS5CSR_EOF);\n      *pbSkip = 1;\n    }\n  }\n  return rc;\n}\n\n\n/*\n** Advance the cursor to the next row in the table that matches the \n** search criteria.\n**\n** Return SQLITE_OK if nothing goes wrong.  SQLITE_OK is returned\n** even if we reach end-of-file.  The fts5EofMethod() will be called\n** subsequently to determine whether or not an EOF was hit.\n*/\nstatic int fts5NextMethod(sqlite3_vtab_cursor *pCursor){\n  Fts5Cursor *pCsr = (Fts5Cursor*)pCursor;\n  int rc;\n\n  assert( (pCsr->ePlan<3)==\n          (pCsr->ePlan==FTS5_PLAN_MATCH || pCsr->ePlan==FTS5_PLAN_SOURCE) \n  );\n  assert( !CsrFlagTest(pCsr, FTS5CSR_EOF) );\n\n  if( pCsr->ePlan<3 ){\n    int bSkip = 0;\n    if( (rc = fts5CursorReseek(pCsr, &bSkip)) || bSkip ) return rc;\n    rc = sqlite3Fts5ExprNext(pCsr->pExpr, pCsr->iLastRowid);\n    CsrFlagSet(pCsr, sqlite3Fts5ExprEof(pCsr->pExpr));\n    fts5CsrNewrow(pCsr);\n  }else{\n    switch( pCsr->ePlan ){\n      case FTS5_PLAN_SPECIAL: {\n        CsrFlagSet(pCsr, FTS5CSR_EOF);\n        rc = SQLITE_OK;\n        break;\n      }\n  \n      case FTS5_PLAN_SORTED_MATCH: {\n        rc = fts5SorterNext(pCsr);\n        break;\n      }\n  \n      default:\n        rc = sqlite3_step(pCsr->pStmt);\n        if( rc!=SQLITE_ROW ){\n          CsrFlagSet(pCsr, FTS5CSR_EOF);\n          rc = sqlite3_reset(pCsr->pStmt);\n        }else{\n          rc = SQLITE_OK;\n        }\n        break;\n    }\n  }\n  \n  return rc;\n}\n\n\nstatic int fts5PrepareStatement(\n  sqlite3_stmt **ppStmt,\n  Fts5Config *pConfig, \n  const char *zFmt,\n  ...\n){\n  sqlite3_stmt *pRet = 0;\n  int rc;\n  char *zSql;\n  va_list ap;\n\n  va_start(ap, zFmt);\n  zSql = sqlite3_vmprintf(zFmt, ap);\n  if( zSql==0 ){\n    rc = SQLITE_NOMEM; \n  }else{\n    rc = sqlite3_prepare_v3(pConfig->db, zSql, -1, \n                            SQLITE_PREPARE_PERSISTENT, &pRet, 0);\n    if( rc!=SQLITE_OK ){\n      *pConfig->pzErrmsg = sqlite3_mprintf(\"%s\", sqlite3_errmsg(pConfig->db));\n    }\n    sqlite3_free(zSql);\n  }\n\n  va_end(ap);\n  *ppStmt = pRet;\n  return rc;\n} \n\nstatic int fts5CursorFirstSorted(Fts5Table *pTab, Fts5Cursor *pCsr, int bDesc){\n  Fts5Config *pConfig = pTab->pConfig;\n  Fts5Sorter *pSorter;\n  int nPhrase;\n  int nByte;\n  int rc;\n  const char *zRank = pCsr->zRank;\n  const char *zRankArgs = pCsr->zRankArgs;\n  \n  nPhrase = sqlite3Fts5ExprPhraseCount(pCsr->pExpr);\n  nByte = sizeof(Fts5Sorter) + sizeof(int) * (nPhrase-1);\n  pSorter = (Fts5Sorter*)sqlite3_malloc(nByte);\n  if( pSorter==0 ) return SQLITE_NOMEM;\n  memset(pSorter, 0, nByte);\n  pSorter->nIdx = nPhrase;\n\n  /* TODO: It would be better to have some system for reusing statement\n  ** handles here, rather than preparing a new one for each query. But that\n  ** is not possible as SQLite reference counts the virtual table objects.\n  ** And since the statement required here reads from this very virtual \n  ** table, saving it creates a circular reference.\n  **\n  ** If SQLite a built-in statement cache, this wouldn't be a problem. */\n  rc = fts5PrepareStatement(&pSorter->pStmt, pConfig,\n      \"SELECT rowid, rank FROM %Q.%Q ORDER BY %s(%s%s%s) %s\",\n      pConfig->zDb, pConfig->zName, zRank, pConfig->zName,\n      (zRankArgs ? \", \" : \"\"),\n      (zRankArgs ? zRankArgs : \"\"),\n      bDesc ? \"DESC\" : \"ASC\"\n  );\n\n  pCsr->pSorter = pSorter;\n  if( rc==SQLITE_OK ){\n    assert( pTab->pSortCsr==0 );\n    pTab->pSortCsr = pCsr;\n    rc = fts5SorterNext(pCsr);\n    pTab->pSortCsr = 0;\n  }\n\n  if( rc!=SQLITE_OK ){\n    sqlite3_finalize(pSorter->pStmt);\n    sqlite3_free(pSorter);\n    pCsr->pSorter = 0;\n  }\n\n  return rc;\n}\n\nstatic int fts5CursorFirst(Fts5Table *pTab, Fts5Cursor *pCsr, int bDesc){\n  int rc;\n  Fts5Expr *pExpr = pCsr->pExpr;\n  rc = sqlite3Fts5ExprFirst(pExpr, pTab->pIndex, pCsr->iFirstRowid, bDesc);\n  if( sqlite3Fts5ExprEof(pExpr) ){\n    CsrFlagSet(pCsr, FTS5CSR_EOF);\n  }\n  fts5CsrNewrow(pCsr);\n  return rc;\n}\n\n/*\n** Process a \"special\" query. A special query is identified as one with a\n** MATCH expression that begins with a '*' character. The remainder of\n** the text passed to the MATCH operator are used as  the special query\n** parameters.\n*/\nstatic int fts5SpecialMatch(\n  Fts5Table *pTab, \n  Fts5Cursor *pCsr, \n  const char *zQuery\n){\n  int rc = SQLITE_OK;             /* Return code */\n  const char *z = zQuery;         /* Special query text */\n  int n;                          /* Number of bytes in text at z */\n\n  while( z[0]==' ' ) z++;\n  for(n=0; z[n] && z[n]!=' '; n++);\n\n  assert( pTab->base.zErrMsg==0 );\n  pCsr->ePlan = FTS5_PLAN_SPECIAL;\n\n  if( 0==sqlite3_strnicmp(\"reads\", z, n) ){\n    pCsr->iSpecial = sqlite3Fts5IndexReads(pTab->pIndex);\n  }\n  else if( 0==sqlite3_strnicmp(\"id\", z, n) ){\n    pCsr->iSpecial = pCsr->iCsrId;\n  }\n  else{\n    /* An unrecognized directive. Return an error message. */\n    pTab->base.zErrMsg = sqlite3_mprintf(\"unknown special query: %.*s\", n, z);\n    rc = SQLITE_ERROR;\n  }\n\n  return rc;\n}\n\n/*\n** Search for an auxiliary function named zName that can be used with table\n** pTab. If one is found, return a pointer to the corresponding Fts5Auxiliary\n** structure. Otherwise, if no such function exists, return NULL.\n*/\nstatic Fts5Auxiliary *fts5FindAuxiliary(Fts5Table *pTab, const char *zName){\n  Fts5Auxiliary *pAux;\n\n  for(pAux=pTab->pGlobal->pAux; pAux; pAux=pAux->pNext){\n    if( sqlite3_stricmp(zName, pAux->zFunc)==0 ) return pAux;\n  }\n\n  /* No function of the specified name was found. Return 0. */\n  return 0;\n}\n\n\nstatic int fts5FindRankFunction(Fts5Cursor *pCsr){\n  Fts5Table *pTab = (Fts5Table*)(pCsr->base.pVtab);\n  Fts5Config *pConfig = pTab->pConfig;\n  int rc = SQLITE_OK;\n  Fts5Auxiliary *pAux = 0;\n  const char *zRank = pCsr->zRank;\n  const char *zRankArgs = pCsr->zRankArgs;\n\n  if( zRankArgs ){\n    char *zSql = sqlite3Fts5Mprintf(&rc, \"SELECT %s\", zRankArgs);\n    if( zSql ){\n      sqlite3_stmt *pStmt = 0;\n      rc = sqlite3_prepare_v3(pConfig->db, zSql, -1,\n                              SQLITE_PREPARE_PERSISTENT, &pStmt, 0);\n      sqlite3_free(zSql);\n      assert( rc==SQLITE_OK || pCsr->pRankArgStmt==0 );\n      if( rc==SQLITE_OK ){\n        if( SQLITE_ROW==sqlite3_step(pStmt) ){\n          int nByte;\n          pCsr->nRankArg = sqlite3_column_count(pStmt);\n          nByte = sizeof(sqlite3_value*)*pCsr->nRankArg;\n          pCsr->apRankArg = (sqlite3_value**)sqlite3Fts5MallocZero(&rc, nByte);\n          if( rc==SQLITE_OK ){\n            int i;\n            for(i=0; i<pCsr->nRankArg; i++){\n              pCsr->apRankArg[i] = sqlite3_column_value(pStmt, i);\n            }\n          }\n          pCsr->pRankArgStmt = pStmt;\n        }else{\n          rc = sqlite3_finalize(pStmt);\n          assert( rc!=SQLITE_OK );\n        }\n      }\n    }\n  }\n\n  if( rc==SQLITE_OK ){\n    pAux = fts5FindAuxiliary(pTab, zRank);\n    if( pAux==0 ){\n      assert( pTab->base.zErrMsg==0 );\n      pTab->base.zErrMsg = sqlite3_mprintf(\"no such function: %s\", zRank);\n      rc = SQLITE_ERROR;\n    }\n  }\n\n  pCsr->pRank = pAux;\n  return rc;\n}\n\n\nstatic int fts5CursorParseRank(\n  Fts5Config *pConfig,\n  Fts5Cursor *pCsr, \n  sqlite3_value *pRank\n){\n  int rc = SQLITE_OK;\n  if( pRank ){\n    const char *z = (const char*)sqlite3_value_text(pRank);\n    char *zRank = 0;\n    char *zRankArgs = 0;\n\n    if( z==0 ){\n      if( sqlite3_value_type(pRank)==SQLITE_NULL ) rc = SQLITE_ERROR;\n    }else{\n      rc = sqlite3Fts5ConfigParseRank(z, &zRank, &zRankArgs);\n    }\n    if( rc==SQLITE_OK ){\n      pCsr->zRank = zRank;\n      pCsr->zRankArgs = zRankArgs;\n      CsrFlagSet(pCsr, FTS5CSR_FREE_ZRANK);\n    }else if( rc==SQLITE_ERROR ){\n      pCsr->base.pVtab->zErrMsg = sqlite3_mprintf(\n          \"parse error in rank function: %s\", z\n      );\n    }\n  }else{\n    if( pConfig->zRank ){\n      pCsr->zRank = (char*)pConfig->zRank;\n      pCsr->zRankArgs = (char*)pConfig->zRankArgs;\n    }else{\n      pCsr->zRank = (char*)FTS5_DEFAULT_RANK;\n      pCsr->zRankArgs = 0;\n    }\n  }\n  return rc;\n}\n\nstatic i64 fts5GetRowidLimit(sqlite3_value *pVal, i64 iDefault){\n  if( pVal ){\n    int eType = sqlite3_value_numeric_type(pVal);\n    if( eType==SQLITE_INTEGER ){\n      return sqlite3_value_int64(pVal);\n    }\n  }\n  return iDefault;\n}\n\n/*\n** This is the xFilter interface for the virtual table.  See\n** the virtual table xFilter method documentation for additional\n** information.\n** \n** There are three possible query strategies:\n**\n**   1. Full-text search using a MATCH operator.\n**   2. A by-rowid lookup.\n**   3. A full-table scan.\n*/\nstatic int fts5FilterMethod(\n  sqlite3_vtab_cursor *pCursor,   /* The cursor used for this query */\n  int idxNum,                     /* Strategy index */\n  const char *zUnused,            /* Unused */\n  int nVal,                       /* Number of elements in apVal */\n  sqlite3_value **apVal           /* Arguments for the indexing scheme */\n){\n  Fts5Table *pTab = (Fts5Table*)(pCursor->pVtab);\n  Fts5Config *pConfig = pTab->pConfig;\n  Fts5Cursor *pCsr = (Fts5Cursor*)pCursor;\n  int rc = SQLITE_OK;             /* Error code */\n  int iVal = 0;                   /* Counter for apVal[] */\n  int bDesc;                      /* True if ORDER BY [rank|rowid] DESC */\n  int bOrderByRank;               /* True if ORDER BY rank */\n  sqlite3_value *pMatch = 0;      /* <tbl> MATCH ? expression (or NULL) */\n  sqlite3_value *pRank = 0;       /* rank MATCH ? expression (or NULL) */\n  sqlite3_value *pRowidEq = 0;    /* rowid = ? expression (or NULL) */\n  sqlite3_value *pRowidLe = 0;    /* rowid <= ? expression (or NULL) */\n  sqlite3_value *pRowidGe = 0;    /* rowid >= ? expression (or NULL) */\n  int iCol;                       /* Column on LHS of MATCH operator */\n  char **pzErrmsg = pConfig->pzErrmsg;\n\n  UNUSED_PARAM(zUnused);\n  UNUSED_PARAM(nVal);\n\n  if( pCsr->ePlan ){\n    fts5FreeCursorComponents(pCsr);\n    memset(&pCsr->ePlan, 0, sizeof(Fts5Cursor) - ((u8*)&pCsr->ePlan-(u8*)pCsr));\n  }\n\n  assert( pCsr->pStmt==0 );\n  assert( pCsr->pExpr==0 );\n  assert( pCsr->csrflags==0 );\n  assert( pCsr->pRank==0 );\n  assert( pCsr->zRank==0 );\n  assert( pCsr->zRankArgs==0 );\n\n  assert( pzErrmsg==0 || pzErrmsg==&pTab->base.zErrMsg );\n  pConfig->pzErrmsg = &pTab->base.zErrMsg;\n\n  /* Decode the arguments passed through to this function.\n  **\n  ** Note: The following set of if(...) statements must be in the same\n  ** order as the corresponding entries in the struct at the top of\n  ** fts5BestIndexMethod().  */\n  if( BitFlagTest(idxNum, FTS5_BI_MATCH) ) pMatch = apVal[iVal++];\n  if( BitFlagTest(idxNum, FTS5_BI_RANK) ) pRank = apVal[iVal++];\n  if( BitFlagTest(idxNum, FTS5_BI_ROWID_EQ) ) pRowidEq = apVal[iVal++];\n  if( BitFlagTest(idxNum, FTS5_BI_ROWID_LE) ) pRowidLe = apVal[iVal++];\n  if( BitFlagTest(idxNum, FTS5_BI_ROWID_GE) ) pRowidGe = apVal[iVal++];\n  iCol = (idxNum>>16);\n  assert( iCol>=0 && iCol<=pConfig->nCol );\n  assert( iVal==nVal );\n  bOrderByRank = ((idxNum & FTS5_BI_ORDER_RANK) ? 1 : 0);\n  pCsr->bDesc = bDesc = ((idxNum & FTS5_BI_ORDER_DESC) ? 1 : 0);\n\n  /* Set the cursor upper and lower rowid limits. Only some strategies \n  ** actually use them. This is ok, as the xBestIndex() method leaves the\n  ** sqlite3_index_constraint.omit flag clear for range constraints\n  ** on the rowid field.  */\n  if( pRowidEq ){\n    pRowidLe = pRowidGe = pRowidEq;\n  }\n  if( bDesc ){\n    pCsr->iFirstRowid = fts5GetRowidLimit(pRowidLe, LARGEST_INT64);\n    pCsr->iLastRowid = fts5GetRowidLimit(pRowidGe, SMALLEST_INT64);\n  }else{\n    pCsr->iLastRowid = fts5GetRowidLimit(pRowidLe, LARGEST_INT64);\n    pCsr->iFirstRowid = fts5GetRowidLimit(pRowidGe, SMALLEST_INT64);\n  }\n\n  if( pTab->pSortCsr ){\n    /* If pSortCsr is non-NULL, then this call is being made as part of \n    ** processing for a \"... MATCH <expr> ORDER BY rank\" query (ePlan is\n    ** set to FTS5_PLAN_SORTED_MATCH). pSortCsr is the cursor that will\n    ** return results to the user for this query. The current cursor \n    ** (pCursor) is used to execute the query issued by function \n    ** fts5CursorFirstSorted() above.  */\n    assert( pRowidEq==0 && pRowidLe==0 && pRowidGe==0 && pRank==0 );\n    assert( nVal==0 && pMatch==0 && bOrderByRank==0 && bDesc==0 );\n    assert( pCsr->iLastRowid==LARGEST_INT64 );\n    assert( pCsr->iFirstRowid==SMALLEST_INT64 );\n    pCsr->ePlan = FTS5_PLAN_SOURCE;\n    pCsr->pExpr = pTab->pSortCsr->pExpr;\n    rc = fts5CursorFirst(pTab, pCsr, bDesc);\n  }else if( pMatch ){\n    const char *zExpr = (const char*)sqlite3_value_text(apVal[0]);\n    if( zExpr==0 ) zExpr = \"\";\n\n    rc = fts5CursorParseRank(pConfig, pCsr, pRank);\n    if( rc==SQLITE_OK ){\n      if( zExpr[0]=='*' ){\n        /* The user has issued a query of the form \"MATCH '*...'\". This\n        ** indicates that the MATCH expression is not a full text query,\n        ** but a request for an internal parameter.  */\n        rc = fts5SpecialMatch(pTab, pCsr, &zExpr[1]);\n      }else{\n        char **pzErr = &pTab->base.zErrMsg;\n        rc = sqlite3Fts5ExprNew(pConfig, iCol, zExpr, &pCsr->pExpr, pzErr);\n        if( rc==SQLITE_OK ){\n          if( bOrderByRank ){\n            pCsr->ePlan = FTS5_PLAN_SORTED_MATCH;\n            rc = fts5CursorFirstSorted(pTab, pCsr, bDesc);\n          }else{\n            pCsr->ePlan = FTS5_PLAN_MATCH;\n            rc = fts5CursorFirst(pTab, pCsr, bDesc);\n          }\n        }\n      }\n    }\n  }else if( pConfig->zContent==0 ){\n    *pConfig->pzErrmsg = sqlite3_mprintf(\n        \"%s: table does not support scanning\", pConfig->zName\n    );\n    rc = SQLITE_ERROR;\n  }else{\n    /* This is either a full-table scan (ePlan==FTS5_PLAN_SCAN) or a lookup\n    ** by rowid (ePlan==FTS5_PLAN_ROWID).  */\n    pCsr->ePlan = (pRowidEq ? FTS5_PLAN_ROWID : FTS5_PLAN_SCAN);\n    rc = sqlite3Fts5StorageStmt(\n        pTab->pStorage, fts5StmtType(pCsr), &pCsr->pStmt, &pTab->base.zErrMsg\n    );\n    if( rc==SQLITE_OK ){\n      if( pCsr->ePlan==FTS5_PLAN_ROWID ){\n        sqlite3_bind_value(pCsr->pStmt, 1, apVal[0]);\n      }else{\n        sqlite3_bind_int64(pCsr->pStmt, 1, pCsr->iFirstRowid);\n        sqlite3_bind_int64(pCsr->pStmt, 2, pCsr->iLastRowid);\n      }\n      rc = fts5NextMethod(pCursor);\n    }\n  }\n\n  pConfig->pzErrmsg = pzErrmsg;\n  return rc;\n}\n\n/* \n** This is the xEof method of the virtual table. SQLite calls this \n** routine to find out if it has reached the end of a result set.\n*/\nstatic int fts5EofMethod(sqlite3_vtab_cursor *pCursor){\n  Fts5Cursor *pCsr = (Fts5Cursor*)pCursor;\n  return (CsrFlagTest(pCsr, FTS5CSR_EOF) ? 1 : 0);\n}\n\n/*\n** Return the rowid that the cursor currently points to.\n*/\nstatic i64 fts5CursorRowid(Fts5Cursor *pCsr){\n  assert( pCsr->ePlan==FTS5_PLAN_MATCH \n       || pCsr->ePlan==FTS5_PLAN_SORTED_MATCH \n       || pCsr->ePlan==FTS5_PLAN_SOURCE \n  );\n  if( pCsr->pSorter ){\n    return pCsr->pSorter->iRowid;\n  }else{\n    return sqlite3Fts5ExprRowid(pCsr->pExpr);\n  }\n}\n\n/* \n** This is the xRowid method. The SQLite core calls this routine to\n** retrieve the rowid for the current row of the result set. fts5\n** exposes %_content.rowid as the rowid for the virtual table. The\n** rowid should be written to *pRowid.\n*/\nstatic int fts5RowidMethod(sqlite3_vtab_cursor *pCursor, sqlite_int64 *pRowid){\n  Fts5Cursor *pCsr = (Fts5Cursor*)pCursor;\n  int ePlan = pCsr->ePlan;\n  \n  assert( CsrFlagTest(pCsr, FTS5CSR_EOF)==0 );\n  switch( ePlan ){\n    case FTS5_PLAN_SPECIAL:\n      *pRowid = 0;\n      break;\n\n    case FTS5_PLAN_SOURCE:\n    case FTS5_PLAN_MATCH:\n    case FTS5_PLAN_SORTED_MATCH:\n      *pRowid = fts5CursorRowid(pCsr);\n      break;\n\n    default:\n      *pRowid = sqlite3_column_int64(pCsr->pStmt, 0);\n      break;\n  }\n\n  return SQLITE_OK;\n}\n\n/*\n** If the cursor requires seeking (bSeekRequired flag is set), seek it.\n** Return SQLITE_OK if no error occurs, or an SQLite error code otherwise.\n**\n** If argument bErrormsg is true and an error occurs, an error message may\n** be left in sqlite3_vtab.zErrMsg.\n*/\nstatic int fts5SeekCursor(Fts5Cursor *pCsr, int bErrormsg){\n  int rc = SQLITE_OK;\n\n  /* If the cursor does not yet have a statement handle, obtain one now. */ \n  if( pCsr->pStmt==0 ){\n    Fts5Table *pTab = (Fts5Table*)(pCsr->base.pVtab);\n    int eStmt = fts5StmtType(pCsr);\n    rc = sqlite3Fts5StorageStmt(\n        pTab->pStorage, eStmt, &pCsr->pStmt, (bErrormsg?&pTab->base.zErrMsg:0)\n    );\n    assert( rc!=SQLITE_OK || pTab->base.zErrMsg==0 );\n    assert( CsrFlagTest(pCsr, FTS5CSR_REQUIRE_CONTENT) );\n  }\n\n  if( rc==SQLITE_OK && CsrFlagTest(pCsr, FTS5CSR_REQUIRE_CONTENT) ){\n    assert( pCsr->pExpr );\n    sqlite3_reset(pCsr->pStmt);\n    sqlite3_bind_int64(pCsr->pStmt, 1, fts5CursorRowid(pCsr));\n    rc = sqlite3_step(pCsr->pStmt);\n    if( rc==SQLITE_ROW ){\n      rc = SQLITE_OK;\n      CsrFlagClear(pCsr, FTS5CSR_REQUIRE_CONTENT);\n    }else{\n      rc = sqlite3_reset(pCsr->pStmt);\n      if( rc==SQLITE_OK ){\n        rc = FTS5_CORRUPT;\n      }\n    }\n  }\n  return rc;\n}\n\nstatic void fts5SetVtabError(Fts5Table *p, const char *zFormat, ...){\n  va_list ap;                     /* ... printf arguments */\n  va_start(ap, zFormat);\n  assert( p->base.zErrMsg==0 );\n  p->base.zErrMsg = sqlite3_vmprintf(zFormat, ap);\n  va_end(ap);\n}\n\n/*\n** This function is called to handle an FTS INSERT command. In other words,\n** an INSERT statement of the form:\n**\n**     INSERT INTO fts(fts) VALUES($pCmd)\n**     INSERT INTO fts(fts, rank) VALUES($pCmd, $pVal)\n**\n** Argument pVal is the value assigned to column \"fts\" by the INSERT \n** statement. This function returns SQLITE_OK if successful, or an SQLite\n** error code if an error occurs.\n**\n** The commands implemented by this function are documented in the \"Special\n** INSERT Directives\" section of the documentation. It should be updated if\n** more commands are added to this function.\n*/\nstatic int fts5SpecialInsert(\n  Fts5Table *pTab,                /* Fts5 table object */\n  const char *zCmd,               /* Text inserted into table-name column */\n  sqlite3_value *pVal             /* Value inserted into rank column */\n){\n  Fts5Config *pConfig = pTab->pConfig;\n  int rc = SQLITE_OK;\n  int bError = 0;\n\n  if( 0==sqlite3_stricmp(\"delete-all\", zCmd) ){\n    if( pConfig->eContent==FTS5_CONTENT_NORMAL ){\n      fts5SetVtabError(pTab, \n          \"'delete-all' may only be used with a \"\n          \"contentless or external content fts5 table\"\n      );\n      rc = SQLITE_ERROR;\n    }else{\n      rc = sqlite3Fts5StorageDeleteAll(pTab->pStorage);\n    }\n  }else if( 0==sqlite3_stricmp(\"rebuild\", zCmd) ){\n    if( pConfig->eContent==FTS5_CONTENT_NONE ){\n      fts5SetVtabError(pTab, \n          \"'rebuild' may not be used with a contentless fts5 table\"\n      );\n      rc = SQLITE_ERROR;\n    }else{\n      rc = sqlite3Fts5StorageRebuild(pTab->pStorage);\n    }\n  }else if( 0==sqlite3_stricmp(\"optimize\", zCmd) ){\n    rc = sqlite3Fts5StorageOptimize(pTab->pStorage);\n  }else if( 0==sqlite3_stricmp(\"merge\", zCmd) ){\n    int nMerge = sqlite3_value_int(pVal);\n    rc = sqlite3Fts5StorageMerge(pTab->pStorage, nMerge);\n  }else if( 0==sqlite3_stricmp(\"integrity-check\", zCmd) ){\n    rc = sqlite3Fts5StorageIntegrity(pTab->pStorage);\n#ifdef SQLITE_DEBUG\n  }else if( 0==sqlite3_stricmp(\"prefix-index\", zCmd) ){\n    pConfig->bPrefixIndex = sqlite3_value_int(pVal);\n#endif\n  }else{\n    rc = sqlite3Fts5IndexLoadConfig(pTab->pIndex);\n    if( rc==SQLITE_OK ){\n      rc = sqlite3Fts5ConfigSetValue(pTab->pConfig, zCmd, pVal, &bError);\n    }\n    if( rc==SQLITE_OK ){\n      if( bError ){\n        rc = SQLITE_ERROR;\n      }else{\n        rc = sqlite3Fts5StorageConfigValue(pTab->pStorage, zCmd, pVal, 0);\n      }\n    }\n  }\n  return rc;\n}\n\nstatic int fts5SpecialDelete(\n  Fts5Table *pTab, \n  sqlite3_value **apVal\n){\n  int rc = SQLITE_OK;\n  int eType1 = sqlite3_value_type(apVal[1]);\n  if( eType1==SQLITE_INTEGER ){\n    sqlite3_int64 iDel = sqlite3_value_int64(apVal[1]);\n    rc = sqlite3Fts5StorageDelete(pTab->pStorage, iDel, &apVal[2]);\n  }\n  return rc;\n}\n\nstatic void fts5StorageInsert(\n  int *pRc, \n  Fts5Table *pTab, \n  sqlite3_value **apVal, \n  i64 *piRowid\n){\n  int rc = *pRc;\n  if( rc==SQLITE_OK ){\n    rc = sqlite3Fts5StorageContentInsert(pTab->pStorage, apVal, piRowid);\n  }\n  if( rc==SQLITE_OK ){\n    rc = sqlite3Fts5StorageIndexInsert(pTab->pStorage, apVal, *piRowid);\n  }\n  *pRc = rc;\n}\n\n/* \n** This function is the implementation of the xUpdate callback used by \n** FTS3 virtual tables. It is invoked by SQLite each time a row is to be\n** inserted, updated or deleted.\n**\n** A delete specifies a single argument - the rowid of the row to remove.\n** \n** Update and insert operations pass:\n**\n**   1. The \"old\" rowid, or NULL.\n**   2. The \"new\" rowid.\n**   3. Values for each of the nCol matchable columns.\n**   4. Values for the two hidden columns (<tablename> and \"rank\").\n*/\nstatic int fts5UpdateMethod(\n  sqlite3_vtab *pVtab,            /* Virtual table handle */\n  int nArg,                       /* Size of argument array */\n  sqlite3_value **apVal,          /* Array of arguments */\n  sqlite_int64 *pRowid            /* OUT: The affected (or effected) rowid */\n){\n  Fts5Table *pTab = (Fts5Table*)pVtab;\n  Fts5Config *pConfig = pTab->pConfig;\n  int eType0;                     /* value_type() of apVal[0] */\n  int rc = SQLITE_OK;             /* Return code */\n\n  /* A transaction must be open when this is called. */\n  assert( pTab->ts.eState==1 );\n\n  assert( pVtab->zErrMsg==0 );\n  assert( nArg==1 || nArg==(2+pConfig->nCol+2) );\n  assert( nArg==1 \n      || sqlite3_value_type(apVal[1])==SQLITE_INTEGER \n      || sqlite3_value_type(apVal[1])==SQLITE_NULL \n  );\n  assert( pTab->pConfig->pzErrmsg==0 );\n  pTab->pConfig->pzErrmsg = &pTab->base.zErrMsg;\n\n  /* Put any active cursors into REQUIRE_SEEK state. */\n  fts5TripCursors(pTab);\n\n  eType0 = sqlite3_value_type(apVal[0]);\n  if( eType0==SQLITE_NULL \n   && sqlite3_value_type(apVal[2+pConfig->nCol])!=SQLITE_NULL \n  ){\n    /* A \"special\" INSERT op. These are handled separately. */\n    const char *z = (const char*)sqlite3_value_text(apVal[2+pConfig->nCol]);\n    if( pConfig->eContent!=FTS5_CONTENT_NORMAL \n      && 0==sqlite3_stricmp(\"delete\", z) \n    ){\n      rc = fts5SpecialDelete(pTab, apVal);\n    }else{\n      rc = fts5SpecialInsert(pTab, z, apVal[2 + pConfig->nCol + 1]);\n    }\n  }else{\n    /* A regular INSERT, UPDATE or DELETE statement. The trick here is that\n    ** any conflict on the rowid value must be detected before any \n    ** modifications are made to the database file. There are 4 cases:\n    **\n    **   1) DELETE\n    **   2) UPDATE (rowid not modified)\n    **   3) UPDATE (rowid modified)\n    **   4) INSERT\n    **\n    ** Cases 3 and 4 may violate the rowid constraint.\n    */\n    int eConflict = SQLITE_ABORT;\n    if( pConfig->eContent==FTS5_CONTENT_NORMAL ){\n      eConflict = sqlite3_vtab_on_conflict(pConfig->db);\n    }\n\n    assert( eType0==SQLITE_INTEGER || eType0==SQLITE_NULL );\n    assert( nArg!=1 || eType0==SQLITE_INTEGER );\n\n    /* Filter out attempts to run UPDATE or DELETE on contentless tables.\n    ** This is not suported.  */\n    if( eType0==SQLITE_INTEGER && fts5IsContentless(pTab) ){\n      pTab->base.zErrMsg = sqlite3_mprintf(\n          \"cannot %s contentless fts5 table: %s\", \n          (nArg>1 ? \"UPDATE\" : \"DELETE from\"), pConfig->zName\n      );\n      rc = SQLITE_ERROR;\n    }\n\n    /* DELETE */\n    else if( nArg==1 ){\n      i64 iDel = sqlite3_value_int64(apVal[0]);  /* Rowid to delete */\n      rc = sqlite3Fts5StorageDelete(pTab->pStorage, iDel, 0);\n    }\n\n    /* INSERT */\n    else if( eType0!=SQLITE_INTEGER ){     \n      /* If this is a REPLACE, first remove the current entry (if any) */\n      if( eConflict==SQLITE_REPLACE \n       && sqlite3_value_type(apVal[1])==SQLITE_INTEGER \n      ){\n        i64 iNew = sqlite3_value_int64(apVal[1]);  /* Rowid to delete */\n        rc = sqlite3Fts5StorageDelete(pTab->pStorage, iNew, 0);\n      }\n      fts5StorageInsert(&rc, pTab, apVal, pRowid);\n    }\n\n    /* UPDATE */\n    else{\n      i64 iOld = sqlite3_value_int64(apVal[0]);  /* Old rowid */\n      i64 iNew = sqlite3_value_int64(apVal[1]);  /* New rowid */\n      if( iOld!=iNew ){\n        if( eConflict==SQLITE_REPLACE ){\n          rc = sqlite3Fts5StorageDelete(pTab->pStorage, iOld, 0);\n          if( rc==SQLITE_OK ){\n            rc = sqlite3Fts5StorageDelete(pTab->pStorage, iNew, 0);\n          }\n          fts5StorageInsert(&rc, pTab, apVal, pRowid);\n        }else{\n          rc = sqlite3Fts5StorageContentInsert(pTab->pStorage, apVal, pRowid);\n          if( rc==SQLITE_OK ){\n            rc = sqlite3Fts5StorageDelete(pTab->pStorage, iOld, 0);\n          }\n          if( rc==SQLITE_OK ){\n            rc = sqlite3Fts5StorageIndexInsert(pTab->pStorage, apVal, *pRowid);\n          }\n        }\n      }else{\n        rc = sqlite3Fts5StorageDelete(pTab->pStorage, iOld, 0);\n        fts5StorageInsert(&rc, pTab, apVal, pRowid);\n      }\n    }\n  }\n\n  pTab->pConfig->pzErrmsg = 0;\n  return rc;\n}\n\n/*\n** Implementation of xSync() method. \n*/\nstatic int fts5SyncMethod(sqlite3_vtab *pVtab){\n  int rc;\n  Fts5Table *pTab = (Fts5Table*)pVtab;\n  fts5CheckTransactionState(pTab, FTS5_SYNC, 0);\n  pTab->pConfig->pzErrmsg = &pTab->base.zErrMsg;\n  fts5TripCursors(pTab);\n  rc = sqlite3Fts5StorageSync(pTab->pStorage);\n  pTab->pConfig->pzErrmsg = 0;\n  return rc;\n}\n\n/*\n** Implementation of xBegin() method. \n*/\nstatic int fts5BeginMethod(sqlite3_vtab *pVtab){\n  fts5CheckTransactionState((Fts5Table*)pVtab, FTS5_BEGIN, 0);\n  fts5NewTransaction((Fts5Table*)pVtab);\n  return SQLITE_OK;\n}\n\n/*\n** Implementation of xCommit() method. This is a no-op. The contents of\n** the pending-terms hash-table have already been flushed into the database\n** by fts5SyncMethod().\n*/\nstatic int fts5CommitMethod(sqlite3_vtab *pVtab){\n  UNUSED_PARAM(pVtab);  /* Call below is a no-op for NDEBUG builds */\n  fts5CheckTransactionState((Fts5Table*)pVtab, FTS5_COMMIT, 0);\n  return SQLITE_OK;\n}\n\n/*\n** Implementation of xRollback(). Discard the contents of the pending-terms\n** hash-table. Any changes made to the database are reverted by SQLite.\n*/\nstatic int fts5RollbackMethod(sqlite3_vtab *pVtab){\n  int rc;\n  Fts5Table *pTab = (Fts5Table*)pVtab;\n  fts5CheckTransactionState(pTab, FTS5_ROLLBACK, 0);\n  rc = sqlite3Fts5StorageRollback(pTab->pStorage);\n  return rc;\n}\n\nstatic int fts5CsrPoslist(Fts5Cursor*, int, const u8**, int*);\n\nstatic void *fts5ApiUserData(Fts5Context *pCtx){\n  Fts5Cursor *pCsr = (Fts5Cursor*)pCtx;\n  return pCsr->pAux->pUserData;\n}\n\nstatic int fts5ApiColumnCount(Fts5Context *pCtx){\n  Fts5Cursor *pCsr = (Fts5Cursor*)pCtx;\n  return ((Fts5Table*)(pCsr->base.pVtab))->pConfig->nCol;\n}\n\nstatic int fts5ApiColumnTotalSize(\n  Fts5Context *pCtx, \n  int iCol, \n  sqlite3_int64 *pnToken\n){\n  Fts5Cursor *pCsr = (Fts5Cursor*)pCtx;\n  Fts5Table *pTab = (Fts5Table*)(pCsr->base.pVtab);\n  return sqlite3Fts5StorageSize(pTab->pStorage, iCol, pnToken);\n}\n\nstatic int fts5ApiRowCount(Fts5Context *pCtx, i64 *pnRow){\n  Fts5Cursor *pCsr = (Fts5Cursor*)pCtx;\n  Fts5Table *pTab = (Fts5Table*)(pCsr->base.pVtab);\n  return sqlite3Fts5StorageRowCount(pTab->pStorage, pnRow);\n}\n\nstatic int fts5ApiTokenize(\n  Fts5Context *pCtx, \n  const char *pText, int nText, \n  void *pUserData,\n  int (*xToken)(void*, int, const char*, int, int, int)\n){\n  Fts5Cursor *pCsr = (Fts5Cursor*)pCtx;\n  Fts5Table *pTab = (Fts5Table*)(pCsr->base.pVtab);\n  return sqlite3Fts5Tokenize(\n      pTab->pConfig, FTS5_TOKENIZE_AUX, pText, nText, pUserData, xToken\n  );\n}\n\nstatic int fts5ApiPhraseCount(Fts5Context *pCtx){\n  Fts5Cursor *pCsr = (Fts5Cursor*)pCtx;\n  return sqlite3Fts5ExprPhraseCount(pCsr->pExpr);\n}\n\nstatic int fts5ApiPhraseSize(Fts5Context *pCtx, int iPhrase){\n  Fts5Cursor *pCsr = (Fts5Cursor*)pCtx;\n  return sqlite3Fts5ExprPhraseSize(pCsr->pExpr, iPhrase);\n}\n\nstatic int fts5ApiColumnText(\n  Fts5Context *pCtx, \n  int iCol, \n  const char **pz, \n  int *pn\n){\n  int rc = SQLITE_OK;\n  Fts5Cursor *pCsr = (Fts5Cursor*)pCtx;\n  if( fts5IsContentless((Fts5Table*)(pCsr->base.pVtab)) ){\n    *pz = 0;\n    *pn = 0;\n  }else{\n    rc = fts5SeekCursor(pCsr, 0);\n    if( rc==SQLITE_OK ){\n      *pz = (const char*)sqlite3_column_text(pCsr->pStmt, iCol+1);\n      *pn = sqlite3_column_bytes(pCsr->pStmt, iCol+1);\n    }\n  }\n  return rc;\n}\n\nstatic int fts5CsrPoslist(\n  Fts5Cursor *pCsr, \n  int iPhrase, \n  const u8 **pa,\n  int *pn\n){\n  Fts5Config *pConfig = ((Fts5Table*)(pCsr->base.pVtab))->pConfig;\n  int rc = SQLITE_OK;\n  int bLive = (pCsr->pSorter==0);\n\n  if( CsrFlagTest(pCsr, FTS5CSR_REQUIRE_POSLIST) ){\n\n    if( pConfig->eDetail!=FTS5_DETAIL_FULL ){\n      Fts5PoslistPopulator *aPopulator;\n      int i;\n      aPopulator = sqlite3Fts5ExprClearPoslists(pCsr->pExpr, bLive);\n      if( aPopulator==0 ) rc = SQLITE_NOMEM;\n      for(i=0; i<pConfig->nCol && rc==SQLITE_OK; i++){\n        int n; const char *z;\n        rc = fts5ApiColumnText((Fts5Context*)pCsr, i, &z, &n);\n        if( rc==SQLITE_OK ){\n          rc = sqlite3Fts5ExprPopulatePoslists(\n              pConfig, pCsr->pExpr, aPopulator, i, z, n\n          );\n        }\n      }\n      sqlite3_free(aPopulator);\n\n      if( pCsr->pSorter ){\n        sqlite3Fts5ExprCheckPoslists(pCsr->pExpr, pCsr->pSorter->iRowid);\n      }\n    }\n    CsrFlagClear(pCsr, FTS5CSR_REQUIRE_POSLIST);\n  }\n\n  if( pCsr->pSorter && pConfig->eDetail==FTS5_DETAIL_FULL ){\n    Fts5Sorter *pSorter = pCsr->pSorter;\n    int i1 = (iPhrase==0 ? 0 : pSorter->aIdx[iPhrase-1]);\n    *pn = pSorter->aIdx[iPhrase] - i1;\n    *pa = &pSorter->aPoslist[i1];\n  }else{\n    *pn = sqlite3Fts5ExprPoslist(pCsr->pExpr, iPhrase, pa);\n  }\n\n  return rc;\n}\n\n/*\n** Ensure that the Fts5Cursor.nInstCount and aInst[] variables are populated\n** correctly for the current view. Return SQLITE_OK if successful, or an\n** SQLite error code otherwise.\n*/\nstatic int fts5CacheInstArray(Fts5Cursor *pCsr){\n  int rc = SQLITE_OK;\n  Fts5PoslistReader *aIter;       /* One iterator for each phrase */\n  int nIter;                      /* Number of iterators/phrases */\n  \n  nIter = sqlite3Fts5ExprPhraseCount(pCsr->pExpr);\n  if( pCsr->aInstIter==0 ){\n    int nByte = sizeof(Fts5PoslistReader) * nIter;\n    pCsr->aInstIter = (Fts5PoslistReader*)sqlite3Fts5MallocZero(&rc, nByte);\n  }\n  aIter = pCsr->aInstIter;\n\n  if( aIter ){\n    int nInst = 0;                /* Number instances seen so far */\n    int i;\n\n    /* Initialize all iterators */\n    for(i=0; i<nIter && rc==SQLITE_OK; i++){\n      const u8 *a;\n      int n; \n      rc = fts5CsrPoslist(pCsr, i, &a, &n);\n      if( rc==SQLITE_OK ){\n        sqlite3Fts5PoslistReaderInit(a, n, &aIter[i]);\n      }\n    }\n\n    if( rc==SQLITE_OK ){\n      while( 1 ){\n        int *aInst;\n        int iBest = -1;\n        for(i=0; i<nIter; i++){\n          if( (aIter[i].bEof==0) \n              && (iBest<0 || aIter[i].iPos<aIter[iBest].iPos) \n            ){\n            iBest = i;\n          }\n        }\n        if( iBest<0 ) break;\n\n        nInst++;\n        if( nInst>=pCsr->nInstAlloc ){\n          pCsr->nInstAlloc = pCsr->nInstAlloc ? pCsr->nInstAlloc*2 : 32;\n          aInst = (int*)sqlite3_realloc(\n              pCsr->aInst, pCsr->nInstAlloc*sizeof(int)*3\n              );\n          if( aInst ){\n            pCsr->aInst = aInst;\n          }else{\n            rc = SQLITE_NOMEM;\n            break;\n          }\n        }\n\n        aInst = &pCsr->aInst[3 * (nInst-1)];\n        aInst[0] = iBest;\n        aInst[1] = FTS5_POS2COLUMN(aIter[iBest].iPos);\n        aInst[2] = FTS5_POS2OFFSET(aIter[iBest].iPos);\n        sqlite3Fts5PoslistReaderNext(&aIter[iBest]);\n      }\n    }\n\n    pCsr->nInstCount = nInst;\n    CsrFlagClear(pCsr, FTS5CSR_REQUIRE_INST);\n  }\n  return rc;\n}\n\nstatic int fts5ApiInstCount(Fts5Context *pCtx, int *pnInst){\n  Fts5Cursor *pCsr = (Fts5Cursor*)pCtx;\n  int rc = SQLITE_OK;\n  if( CsrFlagTest(pCsr, FTS5CSR_REQUIRE_INST)==0 \n   || SQLITE_OK==(rc = fts5CacheInstArray(pCsr)) ){\n    *pnInst = pCsr->nInstCount;\n  }\n  return rc;\n}\n\nstatic int fts5ApiInst(\n  Fts5Context *pCtx, \n  int iIdx, \n  int *piPhrase, \n  int *piCol, \n  int *piOff\n){\n  Fts5Cursor *pCsr = (Fts5Cursor*)pCtx;\n  int rc = SQLITE_OK;\n  if( CsrFlagTest(pCsr, FTS5CSR_REQUIRE_INST)==0 \n   || SQLITE_OK==(rc = fts5CacheInstArray(pCsr)) \n  ){\n    if( iIdx<0 || iIdx>=pCsr->nInstCount ){\n      rc = SQLITE_RANGE;\n#if 0\n    }else if( fts5IsOffsetless((Fts5Table*)pCsr->base.pVtab) ){\n      *piPhrase = pCsr->aInst[iIdx*3];\n      *piCol = pCsr->aInst[iIdx*3 + 2];\n      *piOff = -1;\n#endif\n    }else{\n      *piPhrase = pCsr->aInst[iIdx*3];\n      *piCol = pCsr->aInst[iIdx*3 + 1];\n      *piOff = pCsr->aInst[iIdx*3 + 2];\n    }\n  }\n  return rc;\n}\n\nstatic sqlite3_int64 fts5ApiRowid(Fts5Context *pCtx){\n  return fts5CursorRowid((Fts5Cursor*)pCtx);\n}\n\nstatic int fts5ColumnSizeCb(\n  void *pContext,                 /* Pointer to int */\n  int tflags,\n  const char *pUnused,            /* Buffer containing token */\n  int nUnused,                    /* Size of token in bytes */\n  int iUnused1,                   /* Start offset of token */\n  int iUnused2                    /* End offset of token */\n){\n  int *pCnt = (int*)pContext;\n  UNUSED_PARAM2(pUnused, nUnused);\n  UNUSED_PARAM2(iUnused1, iUnused2);\n  if( (tflags & FTS5_TOKEN_COLOCATED)==0 ){\n    (*pCnt)++;\n  }\n  return SQLITE_OK;\n}\n\nstatic int fts5ApiColumnSize(Fts5Context *pCtx, int iCol, int *pnToken){\n  Fts5Cursor *pCsr = (Fts5Cursor*)pCtx;\n  Fts5Table *pTab = (Fts5Table*)(pCsr->base.pVtab);\n  Fts5Config *pConfig = pTab->pConfig;\n  int rc = SQLITE_OK;\n\n  if( CsrFlagTest(pCsr, FTS5CSR_REQUIRE_DOCSIZE) ){\n    if( pConfig->bColumnsize ){\n      i64 iRowid = fts5CursorRowid(pCsr);\n      rc = sqlite3Fts5StorageDocsize(pTab->pStorage, iRowid, pCsr->aColumnSize);\n    }else if( pConfig->zContent==0 ){\n      int i;\n      for(i=0; i<pConfig->nCol; i++){\n        if( pConfig->abUnindexed[i]==0 ){\n          pCsr->aColumnSize[i] = -1;\n        }\n      }\n    }else{\n      int i;\n      for(i=0; rc==SQLITE_OK && i<pConfig->nCol; i++){\n        if( pConfig->abUnindexed[i]==0 ){\n          const char *z; int n;\n          void *p = (void*)(&pCsr->aColumnSize[i]);\n          pCsr->aColumnSize[i] = 0;\n          rc = fts5ApiColumnText(pCtx, i, &z, &n);\n          if( rc==SQLITE_OK ){\n            rc = sqlite3Fts5Tokenize(\n                pConfig, FTS5_TOKENIZE_AUX, z, n, p, fts5ColumnSizeCb\n            );\n          }\n        }\n      }\n    }\n    CsrFlagClear(pCsr, FTS5CSR_REQUIRE_DOCSIZE);\n  }\n  if( iCol<0 ){\n    int i;\n    *pnToken = 0;\n    for(i=0; i<pConfig->nCol; i++){\n      *pnToken += pCsr->aColumnSize[i];\n    }\n  }else if( iCol<pConfig->nCol ){\n    *pnToken = pCsr->aColumnSize[iCol];\n  }else{\n    *pnToken = 0;\n    rc = SQLITE_RANGE;\n  }\n  return rc;\n}\n\n/*\n** Implementation of the xSetAuxdata() method.\n*/\nstatic int fts5ApiSetAuxdata(\n  Fts5Context *pCtx,              /* Fts5 context */\n  void *pPtr,                     /* Pointer to save as auxdata */\n  void(*xDelete)(void*)           /* Destructor for pPtr (or NULL) */\n){\n  Fts5Cursor *pCsr = (Fts5Cursor*)pCtx;\n  Fts5Auxdata *pData;\n\n  /* Search through the cursors list of Fts5Auxdata objects for one that\n  ** corresponds to the currently executing auxiliary function.  */\n  for(pData=pCsr->pAuxdata; pData; pData=pData->pNext){\n    if( pData->pAux==pCsr->pAux ) break;\n  }\n\n  if( pData ){\n    if( pData->xDelete ){\n      pData->xDelete(pData->pPtr);\n    }\n  }else{\n    int rc = SQLITE_OK;\n    pData = (Fts5Auxdata*)sqlite3Fts5MallocZero(&rc, sizeof(Fts5Auxdata));\n    if( pData==0 ){\n      if( xDelete ) xDelete(pPtr);\n      return rc;\n    }\n    pData->pAux = pCsr->pAux;\n    pData->pNext = pCsr->pAuxdata;\n    pCsr->pAuxdata = pData;\n  }\n\n  pData->xDelete = xDelete;\n  pData->pPtr = pPtr;\n  return SQLITE_OK;\n}\n\nstatic void *fts5ApiGetAuxdata(Fts5Context *pCtx, int bClear){\n  Fts5Cursor *pCsr = (Fts5Cursor*)pCtx;\n  Fts5Auxdata *pData;\n  void *pRet = 0;\n\n  for(pData=pCsr->pAuxdata; pData; pData=pData->pNext){\n    if( pData->pAux==pCsr->pAux ) break;\n  }\n\n  if( pData ){\n    pRet = pData->pPtr;\n    if( bClear ){\n      pData->pPtr = 0;\n      pData->xDelete = 0;\n    }\n  }\n\n  return pRet;\n}\n\nstatic void fts5ApiPhraseNext(\n  Fts5Context *pUnused, \n  Fts5PhraseIter *pIter, \n  int *piCol, int *piOff\n){\n  UNUSED_PARAM(pUnused);\n  if( pIter->a>=pIter->b ){\n    *piCol = -1;\n    *piOff = -1;\n  }else{\n    int iVal;\n    pIter->a += fts5GetVarint32(pIter->a, iVal);\n    if( iVal==1 ){\n      pIter->a += fts5GetVarint32(pIter->a, iVal);\n      *piCol = iVal;\n      *piOff = 0;\n      pIter->a += fts5GetVarint32(pIter->a, iVal);\n    }\n    *piOff += (iVal-2);\n  }\n}\n\nstatic int fts5ApiPhraseFirst(\n  Fts5Context *pCtx, \n  int iPhrase, \n  Fts5PhraseIter *pIter, \n  int *piCol, int *piOff\n){\n  Fts5Cursor *pCsr = (Fts5Cursor*)pCtx;\n  int n;\n  int rc = fts5CsrPoslist(pCsr, iPhrase, &pIter->a, &n);\n  if( rc==SQLITE_OK ){\n    pIter->b = &pIter->a[n];\n    *piCol = 0;\n    *piOff = 0;\n    fts5ApiPhraseNext(pCtx, pIter, piCol, piOff);\n  }\n  return rc;\n}\n\nstatic void fts5ApiPhraseNextColumn(\n  Fts5Context *pCtx, \n  Fts5PhraseIter *pIter, \n  int *piCol\n){\n  Fts5Cursor *pCsr = (Fts5Cursor*)pCtx;\n  Fts5Config *pConfig = ((Fts5Table*)(pCsr->base.pVtab))->pConfig;\n\n  if( pConfig->eDetail==FTS5_DETAIL_COLUMNS ){\n    if( pIter->a>=pIter->b ){\n      *piCol = -1;\n    }else{\n      int iIncr;\n      pIter->a += fts5GetVarint32(&pIter->a[0], iIncr);\n      *piCol += (iIncr-2);\n    }\n  }else{\n    while( 1 ){\n      int dummy;\n      if( pIter->a>=pIter->b ){\n        *piCol = -1;\n        return;\n      }\n      if( pIter->a[0]==0x01 ) break;\n      pIter->a += fts5GetVarint32(pIter->a, dummy);\n    }\n    pIter->a += 1 + fts5GetVarint32(&pIter->a[1], *piCol);\n  }\n}\n\nstatic int fts5ApiPhraseFirstColumn(\n  Fts5Context *pCtx, \n  int iPhrase, \n  Fts5PhraseIter *pIter, \n  int *piCol\n){\n  int rc = SQLITE_OK;\n  Fts5Cursor *pCsr = (Fts5Cursor*)pCtx;\n  Fts5Config *pConfig = ((Fts5Table*)(pCsr->base.pVtab))->pConfig;\n\n  if( pConfig->eDetail==FTS5_DETAIL_COLUMNS ){\n    Fts5Sorter *pSorter = pCsr->pSorter;\n    int n;\n    if( pSorter ){\n      int i1 = (iPhrase==0 ? 0 : pSorter->aIdx[iPhrase-1]);\n      n = pSorter->aIdx[iPhrase] - i1;\n      pIter->a = &pSorter->aPoslist[i1];\n    }else{\n      rc = sqlite3Fts5ExprPhraseCollist(pCsr->pExpr, iPhrase, &pIter->a, &n);\n    }\n    if( rc==SQLITE_OK ){\n      pIter->b = &pIter->a[n];\n      *piCol = 0;\n      fts5ApiPhraseNextColumn(pCtx, pIter, piCol);\n    }\n  }else{\n    int n;\n    rc = fts5CsrPoslist(pCsr, iPhrase, &pIter->a, &n);\n    if( rc==SQLITE_OK ){\n      pIter->b = &pIter->a[n];\n      if( n<=0 ){\n        *piCol = -1;\n      }else if( pIter->a[0]==0x01 ){\n        pIter->a += 1 + fts5GetVarint32(&pIter->a[1], *piCol);\n      }else{\n        *piCol = 0;\n      }\n    }\n  }\n\n  return rc;\n}\n\n\nstatic int fts5ApiQueryPhrase(Fts5Context*, int, void*, \n    int(*)(const Fts5ExtensionApi*, Fts5Context*, void*)\n);\n\nstatic const Fts5ExtensionApi sFts5Api = {\n  2,                            /* iVersion */\n  fts5ApiUserData,\n  fts5ApiColumnCount,\n  fts5ApiRowCount,\n  fts5ApiColumnTotalSize,\n  fts5ApiTokenize,\n  fts5ApiPhraseCount,\n  fts5ApiPhraseSize,\n  fts5ApiInstCount,\n  fts5ApiInst,\n  fts5ApiRowid,\n  fts5ApiColumnText,\n  fts5ApiColumnSize,\n  fts5ApiQueryPhrase,\n  fts5ApiSetAuxdata,\n  fts5ApiGetAuxdata,\n  fts5ApiPhraseFirst,\n  fts5ApiPhraseNext,\n  fts5ApiPhraseFirstColumn,\n  fts5ApiPhraseNextColumn,\n};\n\n/*\n** Implementation of API function xQueryPhrase().\n*/\nstatic int fts5ApiQueryPhrase(\n  Fts5Context *pCtx, \n  int iPhrase, \n  void *pUserData,\n  int(*xCallback)(const Fts5ExtensionApi*, Fts5Context*, void*)\n){\n  Fts5Cursor *pCsr = (Fts5Cursor*)pCtx;\n  Fts5Table *pTab = (Fts5Table*)(pCsr->base.pVtab);\n  int rc;\n  Fts5Cursor *pNew = 0;\n\n  rc = fts5OpenMethod(pCsr->base.pVtab, (sqlite3_vtab_cursor**)&pNew);\n  if( rc==SQLITE_OK ){\n    pNew->ePlan = FTS5_PLAN_MATCH;\n    pNew->iFirstRowid = SMALLEST_INT64;\n    pNew->iLastRowid = LARGEST_INT64;\n    pNew->base.pVtab = (sqlite3_vtab*)pTab;\n    rc = sqlite3Fts5ExprClonePhrase(pCsr->pExpr, iPhrase, &pNew->pExpr);\n  }\n\n  if( rc==SQLITE_OK ){\n    for(rc = fts5CursorFirst(pTab, pNew, 0);\n        rc==SQLITE_OK && CsrFlagTest(pNew, FTS5CSR_EOF)==0;\n        rc = fts5NextMethod((sqlite3_vtab_cursor*)pNew)\n    ){\n      rc = xCallback(&sFts5Api, (Fts5Context*)pNew, pUserData);\n      if( rc!=SQLITE_OK ){\n        if( rc==SQLITE_DONE ) rc = SQLITE_OK;\n        break;\n      }\n    }\n  }\n\n  fts5CloseMethod((sqlite3_vtab_cursor*)pNew);\n  return rc;\n}\n\nstatic void fts5ApiInvoke(\n  Fts5Auxiliary *pAux,\n  Fts5Cursor *pCsr,\n  sqlite3_context *context,\n  int argc,\n  sqlite3_value **argv\n){\n  assert( pCsr->pAux==0 );\n  pCsr->pAux = pAux;\n  pAux->xFunc(&sFts5Api, (Fts5Context*)pCsr, context, argc, argv);\n  pCsr->pAux = 0;\n}\n\nstatic Fts5Cursor *fts5CursorFromCsrid(Fts5Global *pGlobal, i64 iCsrId){\n  Fts5Cursor *pCsr;\n  for(pCsr=pGlobal->pCsr; pCsr; pCsr=pCsr->pNext){\n    if( pCsr->iCsrId==iCsrId ) break;\n  }\n  return pCsr;\n}\n\nstatic void fts5ApiCallback(\n  sqlite3_context *context,\n  int argc,\n  sqlite3_value **argv\n){\n\n  Fts5Auxiliary *pAux;\n  Fts5Cursor *pCsr;\n  i64 iCsrId;\n\n  assert( argc>=1 );\n  pAux = (Fts5Auxiliary*)sqlite3_user_data(context);\n  iCsrId = sqlite3_value_int64(argv[0]);\n\n  pCsr = fts5CursorFromCsrid(pAux->pGlobal, iCsrId);\n  if( pCsr==0 ){\n    char *zErr = sqlite3_mprintf(\"no such cursor: %lld\", iCsrId);\n    sqlite3_result_error(context, zErr, -1);\n    sqlite3_free(zErr);\n  }else{\n    fts5ApiInvoke(pAux, pCsr, context, argc-1, &argv[1]);\n  }\n}\n\n\n/*\n** Given cursor id iId, return a pointer to the corresponding Fts5Index \n** object. Or NULL If the cursor id does not exist.\n**\n** If successful, set *ppConfig to point to the associated config object \n** before returning.\n*/\nstatic Fts5Index *sqlite3Fts5IndexFromCsrid(\n  Fts5Global *pGlobal,            /* FTS5 global context for db handle */\n  i64 iCsrId,                     /* Id of cursor to find */\n  Fts5Config **ppConfig           /* OUT: Configuration object */\n){\n  Fts5Cursor *pCsr;\n  Fts5Table *pTab;\n\n  pCsr = fts5CursorFromCsrid(pGlobal, iCsrId);\n  pTab = (Fts5Table*)pCsr->base.pVtab;\n  *ppConfig = pTab->pConfig;\n\n  return pTab->pIndex;\n}\n\n/*\n** Return a \"position-list blob\" corresponding to the current position of\n** cursor pCsr via sqlite3_result_blob(). A position-list blob contains\n** the current position-list for each phrase in the query associated with\n** cursor pCsr.\n**\n** A position-list blob begins with (nPhrase-1) varints, where nPhrase is\n** the number of phrases in the query. Following the varints are the\n** concatenated position lists for each phrase, in order.\n**\n** The first varint (if it exists) contains the size of the position list\n** for phrase 0. The second (same disclaimer) contains the size of position\n** list 1. And so on. There is no size field for the final position list,\n** as it can be derived from the total size of the blob.\n*/\nstatic int fts5PoslistBlob(sqlite3_context *pCtx, Fts5Cursor *pCsr){\n  int i;\n  int rc = SQLITE_OK;\n  int nPhrase = sqlite3Fts5ExprPhraseCount(pCsr->pExpr);\n  Fts5Buffer val;\n\n  memset(&val, 0, sizeof(Fts5Buffer));\n  switch( ((Fts5Table*)(pCsr->base.pVtab))->pConfig->eDetail ){\n    case FTS5_DETAIL_FULL:\n\n      /* Append the varints */\n      for(i=0; i<(nPhrase-1); i++){\n        const u8 *dummy;\n        int nByte = sqlite3Fts5ExprPoslist(pCsr->pExpr, i, &dummy);\n        sqlite3Fts5BufferAppendVarint(&rc, &val, nByte);\n      }\n\n      /* Append the position lists */\n      for(i=0; i<nPhrase; i++){\n        const u8 *pPoslist;\n        int nPoslist;\n        nPoslist = sqlite3Fts5ExprPoslist(pCsr->pExpr, i, &pPoslist);\n        sqlite3Fts5BufferAppendBlob(&rc, &val, nPoslist, pPoslist);\n      }\n      break;\n\n    case FTS5_DETAIL_COLUMNS:\n\n      /* Append the varints */\n      for(i=0; rc==SQLITE_OK && i<(nPhrase-1); i++){\n        const u8 *dummy;\n        int nByte;\n        rc = sqlite3Fts5ExprPhraseCollist(pCsr->pExpr, i, &dummy, &nByte);\n        sqlite3Fts5BufferAppendVarint(&rc, &val, nByte);\n      }\n\n      /* Append the position lists */\n      for(i=0; rc==SQLITE_OK && i<nPhrase; i++){\n        const u8 *pPoslist;\n        int nPoslist;\n        rc = sqlite3Fts5ExprPhraseCollist(pCsr->pExpr, i, &pPoslist, &nPoslist);\n        sqlite3Fts5BufferAppendBlob(&rc, &val, nPoslist, pPoslist);\n      }\n      break;\n\n    default:\n      break;\n  }\n\n  sqlite3_result_blob(pCtx, val.p, val.n, sqlite3_free);\n  return rc;\n}\n\n/* \n** This is the xColumn method, called by SQLite to request a value from\n** the row that the supplied cursor currently points to.\n*/\nstatic int fts5ColumnMethod(\n  sqlite3_vtab_cursor *pCursor,   /* Cursor to retrieve value from */\n  sqlite3_context *pCtx,          /* Context for sqlite3_result_xxx() calls */\n  int iCol                        /* Index of column to read value from */\n){\n  Fts5Table *pTab = (Fts5Table*)(pCursor->pVtab);\n  Fts5Config *pConfig = pTab->pConfig;\n  Fts5Cursor *pCsr = (Fts5Cursor*)pCursor;\n  int rc = SQLITE_OK;\n  \n  assert( CsrFlagTest(pCsr, FTS5CSR_EOF)==0 );\n\n  if( pCsr->ePlan==FTS5_PLAN_SPECIAL ){\n    if( iCol==pConfig->nCol ){\n      sqlite3_result_int64(pCtx, pCsr->iSpecial);\n    }\n  }else\n\n  if( iCol==pConfig->nCol ){\n    /* User is requesting the value of the special column with the same name\n    ** as the table. Return the cursor integer id number. This value is only\n    ** useful in that it may be passed as the first argument to an FTS5\n    ** auxiliary function.  */\n    sqlite3_result_int64(pCtx, pCsr->iCsrId);\n  }else if( iCol==pConfig->nCol+1 ){\n\n    /* The value of the \"rank\" column. */\n    if( pCsr->ePlan==FTS5_PLAN_SOURCE ){\n      fts5PoslistBlob(pCtx, pCsr);\n    }else if( \n        pCsr->ePlan==FTS5_PLAN_MATCH\n     || pCsr->ePlan==FTS5_PLAN_SORTED_MATCH\n    ){\n      if( pCsr->pRank || SQLITE_OK==(rc = fts5FindRankFunction(pCsr)) ){\n        fts5ApiInvoke(pCsr->pRank, pCsr, pCtx, pCsr->nRankArg, pCsr->apRankArg);\n      }\n    }\n  }else if( !fts5IsContentless(pTab) ){\n    rc = fts5SeekCursor(pCsr, 1);\n    if( rc==SQLITE_OK ){\n      sqlite3_result_value(pCtx, sqlite3_column_value(pCsr->pStmt, iCol+1));\n    }\n  }\n  return rc;\n}\n\n\n/*\n** This routine implements the xFindFunction method for the FTS3\n** virtual table.\n*/\nstatic int fts5FindFunctionMethod(\n  sqlite3_vtab *pVtab,            /* Virtual table handle */\n  int nUnused,                    /* Number of SQL function arguments */\n  const char *zName,              /* Name of SQL function */\n  void (**pxFunc)(sqlite3_context*,int,sqlite3_value**), /* OUT: Result */\n  void **ppArg                    /* OUT: User data for *pxFunc */\n){\n  Fts5Table *pTab = (Fts5Table*)pVtab;\n  Fts5Auxiliary *pAux;\n\n  UNUSED_PARAM(nUnused);\n  pAux = fts5FindAuxiliary(pTab, zName);\n  if( pAux ){\n    *pxFunc = fts5ApiCallback;\n    *ppArg = (void*)pAux;\n    return 1;\n  }\n\n  /* No function of the specified name was found. Return 0. */\n  return 0;\n}\n\n/*\n** Implementation of FTS5 xRename method. Rename an fts5 table.\n*/\nstatic int fts5RenameMethod(\n  sqlite3_vtab *pVtab,            /* Virtual table handle */\n  const char *zName               /* New name of table */\n){\n  Fts5Table *pTab = (Fts5Table*)pVtab;\n  return sqlite3Fts5StorageRename(pTab->pStorage, zName);\n}\n\n/*\n** The xSavepoint() method.\n**\n** Flush the contents of the pending-terms table to disk.\n*/\nstatic int fts5SavepointMethod(sqlite3_vtab *pVtab, int iSavepoint){\n  Fts5Table *pTab = (Fts5Table*)pVtab;\n  UNUSED_PARAM(iSavepoint);  /* Call below is a no-op for NDEBUG builds */\n  fts5CheckTransactionState(pTab, FTS5_SAVEPOINT, iSavepoint);\n  fts5TripCursors(pTab);\n  return sqlite3Fts5StorageSync(pTab->pStorage);\n}\n\n/*\n** The xRelease() method.\n**\n** This is a no-op.\n*/\nstatic int fts5ReleaseMethod(sqlite3_vtab *pVtab, int iSavepoint){\n  Fts5Table *pTab = (Fts5Table*)pVtab;\n  UNUSED_PARAM(iSavepoint);  /* Call below is a no-op for NDEBUG builds */\n  fts5CheckTransactionState(pTab, FTS5_RELEASE, iSavepoint);\n  fts5TripCursors(pTab);\n  return sqlite3Fts5StorageSync(pTab->pStorage);\n}\n\n/*\n** The xRollbackTo() method.\n**\n** Discard the contents of the pending terms table.\n*/\nstatic int fts5RollbackToMethod(sqlite3_vtab *pVtab, int iSavepoint){\n  Fts5Table *pTab = (Fts5Table*)pVtab;\n  UNUSED_PARAM(iSavepoint);  /* Call below is a no-op for NDEBUG builds */\n  fts5CheckTransactionState(pTab, FTS5_ROLLBACKTO, iSavepoint);\n  fts5TripCursors(pTab);\n  return sqlite3Fts5StorageRollback(pTab->pStorage);\n}\n\n/*\n** Register a new auxiliary function with global context pGlobal.\n*/\nstatic int fts5CreateAux(\n  fts5_api *pApi,                 /* Global context (one per db handle) */\n  const char *zName,              /* Name of new function */\n  void *pUserData,                /* User data for aux. function */\n  fts5_extension_function xFunc,  /* Aux. function implementation */\n  void(*xDestroy)(void*)          /* Destructor for pUserData */\n){\n  Fts5Global *pGlobal = (Fts5Global*)pApi;\n  int rc = sqlite3_overload_function(pGlobal->db, zName, -1);\n  if( rc==SQLITE_OK ){\n    Fts5Auxiliary *pAux;\n    int nName;                      /* Size of zName in bytes, including \\0 */\n    int nByte;                      /* Bytes of space to allocate */\n\n    nName = (int)strlen(zName) + 1;\n    nByte = sizeof(Fts5Auxiliary) + nName;\n    pAux = (Fts5Auxiliary*)sqlite3_malloc(nByte);\n    if( pAux ){\n      memset(pAux, 0, nByte);\n      pAux->zFunc = (char*)&pAux[1];\n      memcpy(pAux->zFunc, zName, nName);\n      pAux->pGlobal = pGlobal;\n      pAux->pUserData = pUserData;\n      pAux->xFunc = xFunc;\n      pAux->xDestroy = xDestroy;\n      pAux->pNext = pGlobal->pAux;\n      pGlobal->pAux = pAux;\n    }else{\n      rc = SQLITE_NOMEM;\n    }\n  }\n\n  return rc;\n}\n\n/*\n** Register a new tokenizer. This is the implementation of the \n** fts5_api.xCreateTokenizer() method.\n*/\nstatic int fts5CreateTokenizer(\n  fts5_api *pApi,                 /* Global context (one per db handle) */\n  const char *zName,              /* Name of new function */\n  void *pUserData,                /* User data for aux. function */\n  fts5_tokenizer *pTokenizer,     /* Tokenizer implementation */\n  void(*xDestroy)(void*)          /* Destructor for pUserData */\n){\n  Fts5Global *pGlobal = (Fts5Global*)pApi;\n  Fts5TokenizerModule *pNew;\n  int nName;                      /* Size of zName and its \\0 terminator */\n  int nByte;                      /* Bytes of space to allocate */\n  int rc = SQLITE_OK;\n\n  nName = (int)strlen(zName) + 1;\n  nByte = sizeof(Fts5TokenizerModule) + nName;\n  pNew = (Fts5TokenizerModule*)sqlite3_malloc(nByte);\n  if( pNew ){\n    memset(pNew, 0, nByte);\n    pNew->zName = (char*)&pNew[1];\n    memcpy(pNew->zName, zName, nName);\n    pNew->pUserData = pUserData;\n    pNew->x = *pTokenizer;\n    pNew->xDestroy = xDestroy;\n    pNew->pNext = pGlobal->pTok;\n    pGlobal->pTok = pNew;\n    if( pNew->pNext==0 ){\n      pGlobal->pDfltTok = pNew;\n    }\n  }else{\n    rc = SQLITE_NOMEM;\n  }\n\n  return rc;\n}\n\nstatic Fts5TokenizerModule *fts5LocateTokenizer(\n  Fts5Global *pGlobal, \n  const char *zName\n){\n  Fts5TokenizerModule *pMod = 0;\n\n  if( zName==0 ){\n    pMod = pGlobal->pDfltTok;\n  }else{\n    for(pMod=pGlobal->pTok; pMod; pMod=pMod->pNext){\n      if( sqlite3_stricmp(zName, pMod->zName)==0 ) break;\n    }\n  }\n\n  return pMod;\n}\n\n/*\n** Find a tokenizer. This is the implementation of the \n** fts5_api.xFindTokenizer() method.\n*/\nstatic int fts5FindTokenizer(\n  fts5_api *pApi,                 /* Global context (one per db handle) */\n  const char *zName,              /* Name of new function */\n  void **ppUserData,\n  fts5_tokenizer *pTokenizer      /* Populate this object */\n){\n  int rc = SQLITE_OK;\n  Fts5TokenizerModule *pMod;\n\n  pMod = fts5LocateTokenizer((Fts5Global*)pApi, zName);\n  if( pMod ){\n    *pTokenizer = pMod->x;\n    *ppUserData = pMod->pUserData;\n  }else{\n    memset(pTokenizer, 0, sizeof(fts5_tokenizer));\n    rc = SQLITE_ERROR;\n  }\n\n  return rc;\n}\n\nstatic int sqlite3Fts5GetTokenizer(\n  Fts5Global *pGlobal, \n  const char **azArg,\n  int nArg,\n  Fts5Tokenizer **ppTok,\n  fts5_tokenizer **ppTokApi,\n  char **pzErr\n){\n  Fts5TokenizerModule *pMod;\n  int rc = SQLITE_OK;\n\n  pMod = fts5LocateTokenizer(pGlobal, nArg==0 ? 0 : azArg[0]);\n  if( pMod==0 ){\n    assert( nArg>0 );\n    rc = SQLITE_ERROR;\n    *pzErr = sqlite3_mprintf(\"no such tokenizer: %s\", azArg[0]);\n  }else{\n    rc = pMod->x.xCreate(pMod->pUserData, &azArg[1], (nArg?nArg-1:0), ppTok);\n    *ppTokApi = &pMod->x;\n    if( rc!=SQLITE_OK && pzErr ){\n      *pzErr = sqlite3_mprintf(\"error in tokenizer constructor\");\n    }\n  }\n\n  if( rc!=SQLITE_OK ){\n    *ppTokApi = 0;\n    *ppTok = 0;\n  }\n\n  return rc;\n}\n\nstatic void fts5ModuleDestroy(void *pCtx){\n  Fts5TokenizerModule *pTok, *pNextTok;\n  Fts5Auxiliary *pAux, *pNextAux;\n  Fts5Global *pGlobal = (Fts5Global*)pCtx;\n\n  for(pAux=pGlobal->pAux; pAux; pAux=pNextAux){\n    pNextAux = pAux->pNext;\n    if( pAux->xDestroy ) pAux->xDestroy(pAux->pUserData);\n    sqlite3_free(pAux);\n  }\n\n  for(pTok=pGlobal->pTok; pTok; pTok=pNextTok){\n    pNextTok = pTok->pNext;\n    if( pTok->xDestroy ) pTok->xDestroy(pTok->pUserData);\n    sqlite3_free(pTok);\n  }\n\n  sqlite3_free(pGlobal);\n}\n\nstatic void fts5Fts5Func(\n  sqlite3_context *pCtx,          /* Function call context */\n  int nArg,                       /* Number of args */\n  sqlite3_value **apArg           /* Function arguments */\n){\n  Fts5Global *pGlobal = (Fts5Global*)sqlite3_user_data(pCtx);\n  fts5_api **ppApi;\n  UNUSED_PARAM(nArg);\n  assert( nArg==1 );\n  ppApi = (fts5_api**)sqlite3_value_pointer(apArg[0], \"fts5_api_ptr\");\n  if( ppApi ) *ppApi = &pGlobal->api;\n}\n\n/*\n** Implementation of fts5_source_id() function.\n*/\nstatic void fts5SourceIdFunc(\n  sqlite3_context *pCtx,          /* Function call context */\n  int nArg,                       /* Number of args */\n  sqlite3_value **apUnused        /* Function arguments */\n){\n  assert( nArg==0 );\n  UNUSED_PARAM2(nArg, apUnused);\n  sqlite3_result_text(pCtx, \"fts5: 2018-02-22 18:30:53 4290faf5f7223ebe35b8ed5c4f0ba2444c1764501cabc09a79000f9c1d0890c7\", -1, SQLITE_TRANSIENT);\n}\n\nstatic int fts5Init(sqlite3 *db){\n  static const sqlite3_module fts5Mod = {\n    /* iVersion      */ 2,\n    /* xCreate       */ fts5CreateMethod,\n    /* xConnect      */ fts5ConnectMethod,\n    /* xBestIndex    */ fts5BestIndexMethod,\n    /* xDisconnect   */ fts5DisconnectMethod,\n    /* xDestroy      */ fts5DestroyMethod,\n    /* xOpen         */ fts5OpenMethod,\n    /* xClose        */ fts5CloseMethod,\n    /* xFilter       */ fts5FilterMethod,\n    /* xNext         */ fts5NextMethod,\n    /* xEof          */ fts5EofMethod,\n    /* xColumn       */ fts5ColumnMethod,\n    /* xRowid        */ fts5RowidMethod,\n    /* xUpdate       */ fts5UpdateMethod,\n    /* xBegin        */ fts5BeginMethod,\n    /* xSync         */ fts5SyncMethod,\n    /* xCommit       */ fts5CommitMethod,\n    /* xRollback     */ fts5RollbackMethod,\n    /* xFindFunction */ fts5FindFunctionMethod,\n    /* xRename       */ fts5RenameMethod,\n    /* xSavepoint    */ fts5SavepointMethod,\n    /* xRelease      */ fts5ReleaseMethod,\n    /* xRollbackTo   */ fts5RollbackToMethod,\n  };\n\n  int rc;\n  Fts5Global *pGlobal = 0;\n\n  pGlobal = (Fts5Global*)sqlite3_malloc(sizeof(Fts5Global));\n  if( pGlobal==0 ){\n    rc = SQLITE_NOMEM;\n  }else{\n    void *p = (void*)pGlobal;\n    memset(pGlobal, 0, sizeof(Fts5Global));\n    pGlobal->db = db;\n    pGlobal->api.iVersion = 2;\n    pGlobal->api.xCreateFunction = fts5CreateAux;\n    pGlobal->api.xCreateTokenizer = fts5CreateTokenizer;\n    pGlobal->api.xFindTokenizer = fts5FindTokenizer;\n    rc = sqlite3_create_module_v2(db, \"fts5\", &fts5Mod, p, fts5ModuleDestroy);\n    if( rc==SQLITE_OK ) rc = sqlite3Fts5IndexInit(db);\n    if( rc==SQLITE_OK ) rc = sqlite3Fts5ExprInit(pGlobal, db);\n    if( rc==SQLITE_OK ) rc = sqlite3Fts5AuxInit(&pGlobal->api);\n    if( rc==SQLITE_OK ) rc = sqlite3Fts5TokenizerInit(&pGlobal->api);\n    if( rc==SQLITE_OK ) rc = sqlite3Fts5VocabInit(pGlobal, db);\n    if( rc==SQLITE_OK ){\n      rc = sqlite3_create_function(\n          db, \"fts5\", 1, SQLITE_UTF8, p, fts5Fts5Func, 0, 0\n      );\n    }\n    if( rc==SQLITE_OK ){\n      rc = sqlite3_create_function(\n          db, \"fts5_source_id\", 0, SQLITE_UTF8, p, fts5SourceIdFunc, 0, 0\n      );\n    }\n  }\n\n  /* If SQLITE_FTS5_ENABLE_TEST_MI is defined, assume that the file\n  ** fts5_test_mi.c is compiled and linked into the executable. And call\n  ** its entry point to enable the matchinfo() demo.  */\n#ifdef SQLITE_FTS5_ENABLE_TEST_MI\n  if( rc==SQLITE_OK ){\n    extern int sqlite3Fts5TestRegisterMatchinfo(sqlite3*);\n    rc = sqlite3Fts5TestRegisterMatchinfo(db);\n  }\n#endif\n\n  return rc;\n}\n\n/*\n** The following functions are used to register the module with SQLite. If\n** this module is being built as part of the SQLite core (SQLITE_CORE is\n** defined), then sqlite3_open() will call sqlite3Fts5Init() directly.\n**\n** Or, if this module is being built as a loadable extension, \n** sqlite3Fts5Init() is omitted and the two standard entry points\n** sqlite3_fts_init() and sqlite3_fts5_init() defined instead.\n*/\n#ifndef SQLITE_CORE\n#ifdef _WIN32\n__declspec(dllexport)\n#endif\nSQLITE_API int sqlite3_fts_init(\n  sqlite3 *db,\n  char **pzErrMsg,\n  const sqlite3_api_routines *pApi\n){\n  SQLITE_EXTENSION_INIT2(pApi);\n  (void)pzErrMsg;  /* Unused parameter */\n  return fts5Init(db);\n}\n\n#ifdef _WIN32\n__declspec(dllexport)\n#endif\nSQLITE_API int sqlite3_fts5_init(\n  sqlite3 *db,\n  char **pzErrMsg,\n  const sqlite3_api_routines *pApi\n){\n  SQLITE_EXTENSION_INIT2(pApi);\n  (void)pzErrMsg;  /* Unused parameter */\n  return fts5Init(db);\n}\n#else\nSQLITE_PRIVATE int sqlite3Fts5Init(sqlite3 *db){\n  return fts5Init(db);\n}\n#endif\n\n/*\n** 2014 May 31\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n******************************************************************************\n**\n*/\n\n\n\n/* #include \"fts5Int.h\" */\n\nstruct Fts5Storage {\n  Fts5Config *pConfig;\n  Fts5Index *pIndex;\n  int bTotalsValid;               /* True if nTotalRow/aTotalSize[] are valid */\n  i64 nTotalRow;                  /* Total number of rows in FTS table */\n  i64 *aTotalSize;                /* Total sizes of each column */ \n  sqlite3_stmt *aStmt[11];\n};\n\n\n#if FTS5_STMT_SCAN_ASC!=0 \n# error \"FTS5_STMT_SCAN_ASC mismatch\" \n#endif\n#if FTS5_STMT_SCAN_DESC!=1 \n# error \"FTS5_STMT_SCAN_DESC mismatch\" \n#endif\n#if FTS5_STMT_LOOKUP!=2\n# error \"FTS5_STMT_LOOKUP mismatch\" \n#endif\n\n#define FTS5_STMT_INSERT_CONTENT  3\n#define FTS5_STMT_REPLACE_CONTENT 4\n#define FTS5_STMT_DELETE_CONTENT  5\n#define FTS5_STMT_REPLACE_DOCSIZE  6\n#define FTS5_STMT_DELETE_DOCSIZE  7\n#define FTS5_STMT_LOOKUP_DOCSIZE  8\n#define FTS5_STMT_REPLACE_CONFIG 9\n#define FTS5_STMT_SCAN 10\n\n/*\n** Prepare the two insert statements - Fts5Storage.pInsertContent and\n** Fts5Storage.pInsertDocsize - if they have not already been prepared.\n** Return SQLITE_OK if successful, or an SQLite error code if an error\n** occurs.\n*/\nstatic int fts5StorageGetStmt(\n  Fts5Storage *p,                 /* Storage handle */\n  int eStmt,                      /* FTS5_STMT_XXX constant */\n  sqlite3_stmt **ppStmt,          /* OUT: Prepared statement handle */\n  char **pzErrMsg                 /* OUT: Error message (if any) */\n){\n  int rc = SQLITE_OK;\n\n  /* If there is no %_docsize table, there should be no requests for \n  ** statements to operate on it.  */\n  assert( p->pConfig->bColumnsize || (\n        eStmt!=FTS5_STMT_REPLACE_DOCSIZE \n     && eStmt!=FTS5_STMT_DELETE_DOCSIZE \n     && eStmt!=FTS5_STMT_LOOKUP_DOCSIZE \n  ));\n\n  assert( eStmt>=0 && eStmt<ArraySize(p->aStmt) );\n  if( p->aStmt[eStmt]==0 ){\n    const char *azStmt[] = {\n      \"SELECT %s FROM %s T WHERE T.%Q >= ? AND T.%Q <= ? ORDER BY T.%Q ASC\",\n      \"SELECT %s FROM %s T WHERE T.%Q <= ? AND T.%Q >= ? ORDER BY T.%Q DESC\",\n      \"SELECT %s FROM %s T WHERE T.%Q=?\",               /* LOOKUP  */\n\n      \"INSERT INTO %Q.'%q_content' VALUES(%s)\",         /* INSERT_CONTENT  */\n      \"REPLACE INTO %Q.'%q_content' VALUES(%s)\",        /* REPLACE_CONTENT */\n      \"DELETE FROM %Q.'%q_content' WHERE id=?\",         /* DELETE_CONTENT  */\n      \"REPLACE INTO %Q.'%q_docsize' VALUES(?,?)\",       /* REPLACE_DOCSIZE  */\n      \"DELETE FROM %Q.'%q_docsize' WHERE id=?\",         /* DELETE_DOCSIZE  */\n\n      \"SELECT sz FROM %Q.'%q_docsize' WHERE id=?\",      /* LOOKUP_DOCSIZE  */\n\n      \"REPLACE INTO %Q.'%q_config' VALUES(?,?)\",        /* REPLACE_CONFIG */\n      \"SELECT %s FROM %s AS T\",                         /* SCAN */\n    };\n    Fts5Config *pC = p->pConfig;\n    char *zSql = 0;\n\n    switch( eStmt ){\n      case FTS5_STMT_SCAN:\n        zSql = sqlite3_mprintf(azStmt[eStmt], \n            pC->zContentExprlist, pC->zContent\n        );\n        break;\n\n      case FTS5_STMT_SCAN_ASC:\n      case FTS5_STMT_SCAN_DESC:\n        zSql = sqlite3_mprintf(azStmt[eStmt], pC->zContentExprlist, \n            pC->zContent, pC->zContentRowid, pC->zContentRowid,\n            pC->zContentRowid\n        );\n        break;\n\n      case FTS5_STMT_LOOKUP:\n        zSql = sqlite3_mprintf(azStmt[eStmt], \n            pC->zContentExprlist, pC->zContent, pC->zContentRowid\n        );\n        break;\n\n      case FTS5_STMT_INSERT_CONTENT: \n      case FTS5_STMT_REPLACE_CONTENT: {\n        int nCol = pC->nCol + 1;\n        char *zBind;\n        int i;\n\n        zBind = sqlite3_malloc(1 + nCol*2);\n        if( zBind ){\n          for(i=0; i<nCol; i++){\n            zBind[i*2] = '?';\n            zBind[i*2 + 1] = ',';\n          }\n          zBind[i*2-1] = '\\0';\n          zSql = sqlite3_mprintf(azStmt[eStmt], pC->zDb, pC->zName, zBind);\n          sqlite3_free(zBind);\n        }\n        break;\n      }\n\n      default:\n        zSql = sqlite3_mprintf(azStmt[eStmt], pC->zDb, pC->zName);\n        break;\n    }\n\n    if( zSql==0 ){\n      rc = SQLITE_NOMEM;\n    }else{\n      rc = sqlite3_prepare_v3(pC->db, zSql, -1,\n                              SQLITE_PREPARE_PERSISTENT, &p->aStmt[eStmt], 0);\n      sqlite3_free(zSql);\n      if( rc!=SQLITE_OK && pzErrMsg ){\n        *pzErrMsg = sqlite3_mprintf(\"%s\", sqlite3_errmsg(pC->db));\n      }\n    }\n  }\n\n  *ppStmt = p->aStmt[eStmt];\n  sqlite3_reset(*ppStmt);\n  return rc;\n}\n\n\nstatic int fts5ExecPrintf(\n  sqlite3 *db,\n  char **pzErr,\n  const char *zFormat,\n  ...\n){\n  int rc;\n  va_list ap;                     /* ... printf arguments */\n  char *zSql;\n\n  va_start(ap, zFormat);\n  zSql = sqlite3_vmprintf(zFormat, ap);\n\n  if( zSql==0 ){\n    rc = SQLITE_NOMEM;\n  }else{\n    rc = sqlite3_exec(db, zSql, 0, 0, pzErr);\n    sqlite3_free(zSql);\n  }\n\n  va_end(ap);\n  return rc;\n}\n\n/*\n** Drop all shadow tables. Return SQLITE_OK if successful or an SQLite error\n** code otherwise.\n*/\nstatic int sqlite3Fts5DropAll(Fts5Config *pConfig){\n  int rc = fts5ExecPrintf(pConfig->db, 0, \n      \"DROP TABLE IF EXISTS %Q.'%q_data';\"\n      \"DROP TABLE IF EXISTS %Q.'%q_idx';\"\n      \"DROP TABLE IF EXISTS %Q.'%q_config';\",\n      pConfig->zDb, pConfig->zName,\n      pConfig->zDb, pConfig->zName,\n      pConfig->zDb, pConfig->zName\n  );\n  if( rc==SQLITE_OK && pConfig->bColumnsize ){\n    rc = fts5ExecPrintf(pConfig->db, 0, \n        \"DROP TABLE IF EXISTS %Q.'%q_docsize';\",\n        pConfig->zDb, pConfig->zName\n    );\n  }\n  if( rc==SQLITE_OK && pConfig->eContent==FTS5_CONTENT_NORMAL ){\n    rc = fts5ExecPrintf(pConfig->db, 0, \n        \"DROP TABLE IF EXISTS %Q.'%q_content';\",\n        pConfig->zDb, pConfig->zName\n    );\n  }\n  return rc;\n}\n\nstatic void fts5StorageRenameOne(\n  Fts5Config *pConfig,            /* Current FTS5 configuration */\n  int *pRc,                       /* IN/OUT: Error code */\n  const char *zTail,              /* Tail of table name e.g. \"data\", \"config\" */\n  const char *zName               /* New name of FTS5 table */\n){\n  if( *pRc==SQLITE_OK ){\n    *pRc = fts5ExecPrintf(pConfig->db, 0, \n        \"ALTER TABLE %Q.'%q_%s' RENAME TO '%q_%s';\",\n        pConfig->zDb, pConfig->zName, zTail, zName, zTail\n    );\n  }\n}\n\nstatic int sqlite3Fts5StorageRename(Fts5Storage *pStorage, const char *zName){\n  Fts5Config *pConfig = pStorage->pConfig;\n  int rc = sqlite3Fts5StorageSync(pStorage);\n\n  fts5StorageRenameOne(pConfig, &rc, \"data\", zName);\n  fts5StorageRenameOne(pConfig, &rc, \"idx\", zName);\n  fts5StorageRenameOne(pConfig, &rc, \"config\", zName);\n  if( pConfig->bColumnsize ){\n    fts5StorageRenameOne(pConfig, &rc, \"docsize\", zName);\n  }\n  if( pConfig->eContent==FTS5_CONTENT_NORMAL ){\n    fts5StorageRenameOne(pConfig, &rc, \"content\", zName);\n  }\n  return rc;\n}\n\n/*\n** Create the shadow table named zPost, with definition zDefn. Return\n** SQLITE_OK if successful, or an SQLite error code otherwise.\n*/\nstatic int sqlite3Fts5CreateTable(\n  Fts5Config *pConfig,            /* FTS5 configuration */\n  const char *zPost,              /* Shadow table to create (e.g. \"content\") */\n  const char *zDefn,              /* Columns etc. for shadow table */\n  int bWithout,                   /* True for without rowid */\n  char **pzErr                    /* OUT: Error message */\n){\n  int rc;\n  char *zErr = 0;\n\n  rc = fts5ExecPrintf(pConfig->db, &zErr, \"CREATE TABLE %Q.'%q_%q'(%s)%s\",\n      pConfig->zDb, pConfig->zName, zPost, zDefn, \n#ifndef SQLITE_FTS5_NO_WITHOUT_ROWID\n      bWithout?\" WITHOUT ROWID\":\n#endif\n      \"\"\n  );\n  if( zErr ){\n    *pzErr = sqlite3_mprintf(\n        \"fts5: error creating shadow table %q_%s: %s\", \n        pConfig->zName, zPost, zErr\n    );\n    sqlite3_free(zErr);\n  }\n\n  return rc;\n}\n\n/*\n** Open a new Fts5Index handle. If the bCreate argument is true, create\n** and initialize the underlying tables \n**\n** If successful, set *pp to point to the new object and return SQLITE_OK.\n** Otherwise, set *pp to NULL and return an SQLite error code.\n*/\nstatic int sqlite3Fts5StorageOpen(\n  Fts5Config *pConfig, \n  Fts5Index *pIndex, \n  int bCreate, \n  Fts5Storage **pp,\n  char **pzErr                    /* OUT: Error message */\n){\n  int rc = SQLITE_OK;\n  Fts5Storage *p;                 /* New object */\n  int nByte;                      /* Bytes of space to allocate */\n\n  nByte = sizeof(Fts5Storage)               /* Fts5Storage object */\n        + pConfig->nCol * sizeof(i64);      /* Fts5Storage.aTotalSize[] */\n  *pp = p = (Fts5Storage*)sqlite3_malloc(nByte);\n  if( !p ) return SQLITE_NOMEM;\n\n  memset(p, 0, nByte);\n  p->aTotalSize = (i64*)&p[1];\n  p->pConfig = pConfig;\n  p->pIndex = pIndex;\n\n  if( bCreate ){\n    if( pConfig->eContent==FTS5_CONTENT_NORMAL ){\n      int nDefn = 32 + pConfig->nCol*10;\n      char *zDefn = sqlite3_malloc(32 + pConfig->nCol * 10);\n      if( zDefn==0 ){\n        rc = SQLITE_NOMEM;\n      }else{\n        int i;\n        int iOff;\n        sqlite3_snprintf(nDefn, zDefn, \"id INTEGER PRIMARY KEY\");\n        iOff = (int)strlen(zDefn);\n        for(i=0; i<pConfig->nCol; i++){\n          sqlite3_snprintf(nDefn-iOff, &zDefn[iOff], \", c%d\", i);\n          iOff += (int)strlen(&zDefn[iOff]);\n        }\n        rc = sqlite3Fts5CreateTable(pConfig, \"content\", zDefn, 0, pzErr);\n      }\n      sqlite3_free(zDefn);\n    }\n\n    if( rc==SQLITE_OK && pConfig->bColumnsize ){\n      rc = sqlite3Fts5CreateTable(\n          pConfig, \"docsize\", \"id INTEGER PRIMARY KEY, sz BLOB\", 0, pzErr\n      );\n    }\n    if( rc==SQLITE_OK ){\n      rc = sqlite3Fts5CreateTable(\n          pConfig, \"config\", \"k PRIMARY KEY, v\", 1, pzErr\n      );\n    }\n    if( rc==SQLITE_OK ){\n      rc = sqlite3Fts5StorageConfigValue(p, \"version\", 0, FTS5_CURRENT_VERSION);\n    }\n  }\n\n  if( rc ){\n    sqlite3Fts5StorageClose(p);\n    *pp = 0;\n  }\n  return rc;\n}\n\n/*\n** Close a handle opened by an earlier call to sqlite3Fts5StorageOpen().\n*/\nstatic int sqlite3Fts5StorageClose(Fts5Storage *p){\n  int rc = SQLITE_OK;\n  if( p ){\n    int i;\n\n    /* Finalize all SQL statements */\n    for(i=0; i<ArraySize(p->aStmt); i++){\n      sqlite3_finalize(p->aStmt[i]);\n    }\n\n    sqlite3_free(p);\n  }\n  return rc;\n}\n\ntypedef struct Fts5InsertCtx Fts5InsertCtx;\nstruct Fts5InsertCtx {\n  Fts5Storage *pStorage;\n  int iCol;\n  int szCol;                      /* Size of column value in tokens */\n};\n\n/*\n** Tokenization callback used when inserting tokens into the FTS index.\n*/\nstatic int fts5StorageInsertCallback(\n  void *pContext,                 /* Pointer to Fts5InsertCtx object */\n  int tflags,\n  const char *pToken,             /* Buffer containing token */\n  int nToken,                     /* Size of token in bytes */\n  int iUnused1,                   /* Start offset of token */\n  int iUnused2                    /* End offset of token */\n){\n  Fts5InsertCtx *pCtx = (Fts5InsertCtx*)pContext;\n  Fts5Index *pIdx = pCtx->pStorage->pIndex;\n  UNUSED_PARAM2(iUnused1, iUnused2);\n  if( nToken>FTS5_MAX_TOKEN_SIZE ) nToken = FTS5_MAX_TOKEN_SIZE;\n  if( (tflags & FTS5_TOKEN_COLOCATED)==0 || pCtx->szCol==0 ){\n    pCtx->szCol++;\n  }\n  return sqlite3Fts5IndexWrite(pIdx, pCtx->iCol, pCtx->szCol-1, pToken, nToken);\n}\n\n/*\n** If a row with rowid iDel is present in the %_content table, add the\n** delete-markers to the FTS index necessary to delete it. Do not actually\n** remove the %_content row at this time though.\n*/\nstatic int fts5StorageDeleteFromIndex(\n  Fts5Storage *p, \n  i64 iDel, \n  sqlite3_value **apVal\n){\n  Fts5Config *pConfig = p->pConfig;\n  sqlite3_stmt *pSeek = 0;        /* SELECT to read row iDel from %_data */\n  int rc;                         /* Return code */\n  int rc2;                        /* sqlite3_reset() return code */\n  int iCol;\n  Fts5InsertCtx ctx;\n\n  if( apVal==0 ){\n    rc = fts5StorageGetStmt(p, FTS5_STMT_LOOKUP, &pSeek, 0);\n    if( rc!=SQLITE_OK ) return rc;\n    sqlite3_bind_int64(pSeek, 1, iDel);\n    if( sqlite3_step(pSeek)!=SQLITE_ROW ){\n      return sqlite3_reset(pSeek);\n    }\n  }\n\n  ctx.pStorage = p;\n  ctx.iCol = -1;\n  rc = sqlite3Fts5IndexBeginWrite(p->pIndex, 1, iDel);\n  for(iCol=1; rc==SQLITE_OK && iCol<=pConfig->nCol; iCol++){\n    if( pConfig->abUnindexed[iCol-1]==0 ){\n      const char *zText;\n      int nText;\n      if( pSeek ){\n        zText = (const char*)sqlite3_column_text(pSeek, iCol);\n        nText = sqlite3_column_bytes(pSeek, iCol);\n      }else{\n        zText = (const char*)sqlite3_value_text(apVal[iCol-1]);\n        nText = sqlite3_value_bytes(apVal[iCol-1]);\n      }\n      ctx.szCol = 0;\n      rc = sqlite3Fts5Tokenize(pConfig, FTS5_TOKENIZE_DOCUMENT, \n          zText, nText, (void*)&ctx, fts5StorageInsertCallback\n      );\n      p->aTotalSize[iCol-1] -= (i64)ctx.szCol;\n    }\n  }\n  p->nTotalRow--;\n\n  rc2 = sqlite3_reset(pSeek);\n  if( rc==SQLITE_OK ) rc = rc2;\n  return rc;\n}\n\n\n/*\n** Insert a record into the %_docsize table. Specifically, do:\n**\n**   INSERT OR REPLACE INTO %_docsize(id, sz) VALUES(iRowid, pBuf);\n**\n** If there is no %_docsize table (as happens if the columnsize=0 option\n** is specified when the FTS5 table is created), this function is a no-op.\n*/\nstatic int fts5StorageInsertDocsize(\n  Fts5Storage *p,                 /* Storage module to write to */\n  i64 iRowid,                     /* id value */\n  Fts5Buffer *pBuf                /* sz value */\n){\n  int rc = SQLITE_OK;\n  if( p->pConfig->bColumnsize ){\n    sqlite3_stmt *pReplace = 0;\n    rc = fts5StorageGetStmt(p, FTS5_STMT_REPLACE_DOCSIZE, &pReplace, 0);\n    if( rc==SQLITE_OK ){\n      sqlite3_bind_int64(pReplace, 1, iRowid);\n      sqlite3_bind_blob(pReplace, 2, pBuf->p, pBuf->n, SQLITE_STATIC);\n      sqlite3_step(pReplace);\n      rc = sqlite3_reset(pReplace);\n      sqlite3_bind_null(pReplace, 2);\n    }\n  }\n  return rc;\n}\n\n/*\n** Load the contents of the \"averages\" record from disk into the \n** p->nTotalRow and p->aTotalSize[] variables. If successful, and if\n** argument bCache is true, set the p->bTotalsValid flag to indicate\n** that the contents of aTotalSize[] and nTotalRow are valid until\n** further notice.\n**\n** Return SQLITE_OK if successful, or an SQLite error code if an error\n** occurs.\n*/\nstatic int fts5StorageLoadTotals(Fts5Storage *p, int bCache){\n  int rc = SQLITE_OK;\n  if( p->bTotalsValid==0 ){\n    rc = sqlite3Fts5IndexGetAverages(p->pIndex, &p->nTotalRow, p->aTotalSize);\n    p->bTotalsValid = bCache;\n  }\n  return rc;\n}\n\n/*\n** Store the current contents of the p->nTotalRow and p->aTotalSize[] \n** variables in the \"averages\" record on disk.\n**\n** Return SQLITE_OK if successful, or an SQLite error code if an error\n** occurs.\n*/\nstatic int fts5StorageSaveTotals(Fts5Storage *p){\n  int nCol = p->pConfig->nCol;\n  int i;\n  Fts5Buffer buf;\n  int rc = SQLITE_OK;\n  memset(&buf, 0, sizeof(buf));\n\n  sqlite3Fts5BufferAppendVarint(&rc, &buf, p->nTotalRow);\n  for(i=0; i<nCol; i++){\n    sqlite3Fts5BufferAppendVarint(&rc, &buf, p->aTotalSize[i]);\n  }\n  if( rc==SQLITE_OK ){\n    rc = sqlite3Fts5IndexSetAverages(p->pIndex, buf.p, buf.n);\n  }\n  sqlite3_free(buf.p);\n\n  return rc;\n}\n\n/*\n** Remove a row from the FTS table.\n*/\nstatic int sqlite3Fts5StorageDelete(Fts5Storage *p, i64 iDel, sqlite3_value **apVal){\n  Fts5Config *pConfig = p->pConfig;\n  int rc;\n  sqlite3_stmt *pDel = 0;\n\n  assert( pConfig->eContent!=FTS5_CONTENT_NORMAL || apVal==0 );\n  rc = fts5StorageLoadTotals(p, 1);\n\n  /* Delete the index records */\n  if( rc==SQLITE_OK ){\n    rc = fts5StorageDeleteFromIndex(p, iDel, apVal);\n  }\n\n  /* Delete the %_docsize record */\n  if( rc==SQLITE_OK && pConfig->bColumnsize ){\n    rc = fts5StorageGetStmt(p, FTS5_STMT_DELETE_DOCSIZE, &pDel, 0);\n    if( rc==SQLITE_OK ){\n      sqlite3_bind_int64(pDel, 1, iDel);\n      sqlite3_step(pDel);\n      rc = sqlite3_reset(pDel);\n    }\n  }\n\n  /* Delete the %_content record */\n  if( pConfig->eContent==FTS5_CONTENT_NORMAL ){\n    if( rc==SQLITE_OK ){\n      rc = fts5StorageGetStmt(p, FTS5_STMT_DELETE_CONTENT, &pDel, 0);\n    }\n    if( rc==SQLITE_OK ){\n      sqlite3_bind_int64(pDel, 1, iDel);\n      sqlite3_step(pDel);\n      rc = sqlite3_reset(pDel);\n    }\n  }\n\n  return rc;\n}\n\n/*\n** Delete all entries in the FTS5 index.\n*/\nstatic int sqlite3Fts5StorageDeleteAll(Fts5Storage *p){\n  Fts5Config *pConfig = p->pConfig;\n  int rc;\n\n  /* Delete the contents of the %_data and %_docsize tables. */\n  rc = fts5ExecPrintf(pConfig->db, 0,\n      \"DELETE FROM %Q.'%q_data';\" \n      \"DELETE FROM %Q.'%q_idx';\",\n      pConfig->zDb, pConfig->zName,\n      pConfig->zDb, pConfig->zName\n  );\n  if( rc==SQLITE_OK && pConfig->bColumnsize ){\n    rc = fts5ExecPrintf(pConfig->db, 0,\n        \"DELETE FROM %Q.'%q_docsize';\",\n        pConfig->zDb, pConfig->zName\n    );\n  }\n\n  /* Reinitialize the %_data table. This call creates the initial structure\n  ** and averages records.  */\n  if( rc==SQLITE_OK ){\n    rc = sqlite3Fts5IndexReinit(p->pIndex);\n  }\n  if( rc==SQLITE_OK ){\n    rc = sqlite3Fts5StorageConfigValue(p, \"version\", 0, FTS5_CURRENT_VERSION);\n  }\n  return rc;\n}\n\nstatic int sqlite3Fts5StorageRebuild(Fts5Storage *p){\n  Fts5Buffer buf = {0,0,0};\n  Fts5Config *pConfig = p->pConfig;\n  sqlite3_stmt *pScan = 0;\n  Fts5InsertCtx ctx;\n  int rc;\n\n  memset(&ctx, 0, sizeof(Fts5InsertCtx));\n  ctx.pStorage = p;\n  rc = sqlite3Fts5StorageDeleteAll(p);\n  if( rc==SQLITE_OK ){\n    rc = fts5StorageLoadTotals(p, 1);\n  }\n\n  if( rc==SQLITE_OK ){\n    rc = fts5StorageGetStmt(p, FTS5_STMT_SCAN, &pScan, 0);\n  }\n\n  while( rc==SQLITE_OK && SQLITE_ROW==sqlite3_step(pScan) ){\n    i64 iRowid = sqlite3_column_int64(pScan, 0);\n\n    sqlite3Fts5BufferZero(&buf);\n    rc = sqlite3Fts5IndexBeginWrite(p->pIndex, 0, iRowid);\n    for(ctx.iCol=0; rc==SQLITE_OK && ctx.iCol<pConfig->nCol; ctx.iCol++){\n      ctx.szCol = 0;\n      if( pConfig->abUnindexed[ctx.iCol]==0 ){\n        rc = sqlite3Fts5Tokenize(pConfig, \n            FTS5_TOKENIZE_DOCUMENT,\n            (const char*)sqlite3_column_text(pScan, ctx.iCol+1),\n            sqlite3_column_bytes(pScan, ctx.iCol+1),\n            (void*)&ctx,\n            fts5StorageInsertCallback\n        );\n      }\n      sqlite3Fts5BufferAppendVarint(&rc, &buf, ctx.szCol);\n      p->aTotalSize[ctx.iCol] += (i64)ctx.szCol;\n    }\n    p->nTotalRow++;\n\n    if( rc==SQLITE_OK ){\n      rc = fts5StorageInsertDocsize(p, iRowid, &buf);\n    }\n  }\n  sqlite3_free(buf.p);\n\n  /* Write the averages record */\n  if( rc==SQLITE_OK ){\n    rc = fts5StorageSaveTotals(p);\n  }\n  return rc;\n}\n\nstatic int sqlite3Fts5StorageOptimize(Fts5Storage *p){\n  return sqlite3Fts5IndexOptimize(p->pIndex);\n}\n\nstatic int sqlite3Fts5StorageMerge(Fts5Storage *p, int nMerge){\n  return sqlite3Fts5IndexMerge(p->pIndex, nMerge);\n}\n\nstatic int sqlite3Fts5StorageReset(Fts5Storage *p){\n  return sqlite3Fts5IndexReset(p->pIndex);\n}\n\n/*\n** Allocate a new rowid. This is used for \"external content\" tables when\n** a NULL value is inserted into the rowid column. The new rowid is allocated\n** by inserting a dummy row into the %_docsize table. The dummy will be\n** overwritten later.\n**\n** If the %_docsize table does not exist, SQLITE_MISMATCH is returned. In\n** this case the user is required to provide a rowid explicitly.\n*/\nstatic int fts5StorageNewRowid(Fts5Storage *p, i64 *piRowid){\n  int rc = SQLITE_MISMATCH;\n  if( p->pConfig->bColumnsize ){\n    sqlite3_stmt *pReplace = 0;\n    rc = fts5StorageGetStmt(p, FTS5_STMT_REPLACE_DOCSIZE, &pReplace, 0);\n    if( rc==SQLITE_OK ){\n      sqlite3_bind_null(pReplace, 1);\n      sqlite3_bind_null(pReplace, 2);\n      sqlite3_step(pReplace);\n      rc = sqlite3_reset(pReplace);\n    }\n    if( rc==SQLITE_OK ){\n      *piRowid = sqlite3_last_insert_rowid(p->pConfig->db);\n    }\n  }\n  return rc;\n}\n\n/*\n** Insert a new row into the FTS content table.\n*/\nstatic int sqlite3Fts5StorageContentInsert(\n  Fts5Storage *p, \n  sqlite3_value **apVal, \n  i64 *piRowid\n){\n  Fts5Config *pConfig = p->pConfig;\n  int rc = SQLITE_OK;\n\n  /* Insert the new row into the %_content table. */\n  if( pConfig->eContent!=FTS5_CONTENT_NORMAL ){\n    if( sqlite3_value_type(apVal[1])==SQLITE_INTEGER ){\n      *piRowid = sqlite3_value_int64(apVal[1]);\n    }else{\n      rc = fts5StorageNewRowid(p, piRowid);\n    }\n  }else{\n    sqlite3_stmt *pInsert = 0;    /* Statement to write %_content table */\n    int i;                        /* Counter variable */\n    rc = fts5StorageGetStmt(p, FTS5_STMT_INSERT_CONTENT, &pInsert, 0);\n    for(i=1; rc==SQLITE_OK && i<=pConfig->nCol+1; i++){\n      rc = sqlite3_bind_value(pInsert, i, apVal[i]);\n    }\n    if( rc==SQLITE_OK ){\n      sqlite3_step(pInsert);\n      rc = sqlite3_reset(pInsert);\n    }\n    *piRowid = sqlite3_last_insert_rowid(pConfig->db);\n  }\n\n  return rc;\n}\n\n/*\n** Insert new entries into the FTS index and %_docsize table.\n*/\nstatic int sqlite3Fts5StorageIndexInsert(\n  Fts5Storage *p, \n  sqlite3_value **apVal, \n  i64 iRowid\n){\n  Fts5Config *pConfig = p->pConfig;\n  int rc = SQLITE_OK;             /* Return code */\n  Fts5InsertCtx ctx;              /* Tokenization callback context object */\n  Fts5Buffer buf;                 /* Buffer used to build up %_docsize blob */\n\n  memset(&buf, 0, sizeof(Fts5Buffer));\n  ctx.pStorage = p;\n  rc = fts5StorageLoadTotals(p, 1);\n\n  if( rc==SQLITE_OK ){\n    rc = sqlite3Fts5IndexBeginWrite(p->pIndex, 0, iRowid);\n  }\n  for(ctx.iCol=0; rc==SQLITE_OK && ctx.iCol<pConfig->nCol; ctx.iCol++){\n    ctx.szCol = 0;\n    if( pConfig->abUnindexed[ctx.iCol]==0 ){\n      rc = sqlite3Fts5Tokenize(pConfig, \n          FTS5_TOKENIZE_DOCUMENT,\n          (const char*)sqlite3_value_text(apVal[ctx.iCol+2]),\n          sqlite3_value_bytes(apVal[ctx.iCol+2]),\n          (void*)&ctx,\n          fts5StorageInsertCallback\n      );\n    }\n    sqlite3Fts5BufferAppendVarint(&rc, &buf, ctx.szCol);\n    p->aTotalSize[ctx.iCol] += (i64)ctx.szCol;\n  }\n  p->nTotalRow++;\n\n  /* Write the %_docsize record */\n  if( rc==SQLITE_OK ){\n    rc = fts5StorageInsertDocsize(p, iRowid, &buf);\n  }\n  sqlite3_free(buf.p);\n\n  return rc;\n}\n\nstatic int fts5StorageCount(Fts5Storage *p, const char *zSuffix, i64 *pnRow){\n  Fts5Config *pConfig = p->pConfig;\n  char *zSql;\n  int rc;\n\n  zSql = sqlite3_mprintf(\"SELECT count(*) FROM %Q.'%q_%s'\", \n      pConfig->zDb, pConfig->zName, zSuffix\n  );\n  if( zSql==0 ){\n    rc = SQLITE_NOMEM;\n  }else{\n    sqlite3_stmt *pCnt = 0;\n    rc = sqlite3_prepare_v2(pConfig->db, zSql, -1, &pCnt, 0);\n    if( rc==SQLITE_OK ){\n      if( SQLITE_ROW==sqlite3_step(pCnt) ){\n        *pnRow = sqlite3_column_int64(pCnt, 0);\n      }\n      rc = sqlite3_finalize(pCnt);\n    }\n  }\n\n  sqlite3_free(zSql);\n  return rc;\n}\n\n/*\n** Context object used by sqlite3Fts5StorageIntegrity().\n*/\ntypedef struct Fts5IntegrityCtx Fts5IntegrityCtx;\nstruct Fts5IntegrityCtx {\n  i64 iRowid;\n  int iCol;\n  int szCol;\n  u64 cksum;\n  Fts5Termset *pTermset;\n  Fts5Config *pConfig;\n};\n\n\n/*\n** Tokenization callback used by integrity check.\n*/\nstatic int fts5StorageIntegrityCallback(\n  void *pContext,                 /* Pointer to Fts5IntegrityCtx object */\n  int tflags,\n  const char *pToken,             /* Buffer containing token */\n  int nToken,                     /* Size of token in bytes */\n  int iUnused1,                   /* Start offset of token */\n  int iUnused2                    /* End offset of token */\n){\n  Fts5IntegrityCtx *pCtx = (Fts5IntegrityCtx*)pContext;\n  Fts5Termset *pTermset = pCtx->pTermset;\n  int bPresent;\n  int ii;\n  int rc = SQLITE_OK;\n  int iPos;\n  int iCol;\n\n  UNUSED_PARAM2(iUnused1, iUnused2);\n  if( nToken>FTS5_MAX_TOKEN_SIZE ) nToken = FTS5_MAX_TOKEN_SIZE;\n\n  if( (tflags & FTS5_TOKEN_COLOCATED)==0 || pCtx->szCol==0 ){\n    pCtx->szCol++;\n  }\n\n  switch( pCtx->pConfig->eDetail ){\n    case FTS5_DETAIL_FULL:\n      iPos = pCtx->szCol-1;\n      iCol = pCtx->iCol;\n      break;\n\n    case FTS5_DETAIL_COLUMNS:\n      iPos = pCtx->iCol;\n      iCol = 0;\n      break;\n\n    default:\n      assert( pCtx->pConfig->eDetail==FTS5_DETAIL_NONE );\n      iPos = 0;\n      iCol = 0;\n      break;\n  }\n\n  rc = sqlite3Fts5TermsetAdd(pTermset, 0, pToken, nToken, &bPresent);\n  if( rc==SQLITE_OK && bPresent==0 ){\n    pCtx->cksum ^= sqlite3Fts5IndexEntryCksum(\n        pCtx->iRowid, iCol, iPos, 0, pToken, nToken\n    );\n  }\n\n  for(ii=0; rc==SQLITE_OK && ii<pCtx->pConfig->nPrefix; ii++){\n    const int nChar = pCtx->pConfig->aPrefix[ii];\n    int nByte = sqlite3Fts5IndexCharlenToBytelen(pToken, nToken, nChar);\n    if( nByte ){\n      rc = sqlite3Fts5TermsetAdd(pTermset, ii+1, pToken, nByte, &bPresent);\n      if( bPresent==0 ){\n        pCtx->cksum ^= sqlite3Fts5IndexEntryCksum(\n            pCtx->iRowid, iCol, iPos, ii+1, pToken, nByte\n        );\n      }\n    }\n  }\n\n  return rc;\n}\n\n/*\n** Check that the contents of the FTS index match that of the %_content\n** table. Return SQLITE_OK if they do, or SQLITE_CORRUPT if not. Return\n** some other SQLite error code if an error occurs while attempting to\n** determine this.\n*/\nstatic int sqlite3Fts5StorageIntegrity(Fts5Storage *p){\n  Fts5Config *pConfig = p->pConfig;\n  int rc;                         /* Return code */\n  int *aColSize;                  /* Array of size pConfig->nCol */\n  i64 *aTotalSize;                /* Array of size pConfig->nCol */\n  Fts5IntegrityCtx ctx;\n  sqlite3_stmt *pScan;\n\n  memset(&ctx, 0, sizeof(Fts5IntegrityCtx));\n  ctx.pConfig = p->pConfig;\n  aTotalSize = (i64*)sqlite3_malloc(pConfig->nCol * (sizeof(int)+sizeof(i64)));\n  if( !aTotalSize ) return SQLITE_NOMEM;\n  aColSize = (int*)&aTotalSize[pConfig->nCol];\n  memset(aTotalSize, 0, sizeof(i64) * pConfig->nCol);\n\n  /* Generate the expected index checksum based on the contents of the\n  ** %_content table. This block stores the checksum in ctx.cksum. */\n  rc = fts5StorageGetStmt(p, FTS5_STMT_SCAN, &pScan, 0);\n  if( rc==SQLITE_OK ){\n    int rc2;\n    while( SQLITE_ROW==sqlite3_step(pScan) ){\n      int i;\n      ctx.iRowid = sqlite3_column_int64(pScan, 0);\n      ctx.szCol = 0;\n      if( pConfig->bColumnsize ){\n        rc = sqlite3Fts5StorageDocsize(p, ctx.iRowid, aColSize);\n      }\n      if( rc==SQLITE_OK && pConfig->eDetail==FTS5_DETAIL_NONE ){\n        rc = sqlite3Fts5TermsetNew(&ctx.pTermset);\n      }\n      for(i=0; rc==SQLITE_OK && i<pConfig->nCol; i++){\n        if( pConfig->abUnindexed[i] ) continue;\n        ctx.iCol = i;\n        ctx.szCol = 0;\n        if( pConfig->eDetail==FTS5_DETAIL_COLUMNS ){\n          rc = sqlite3Fts5TermsetNew(&ctx.pTermset);\n        }\n        if( rc==SQLITE_OK ){\n          rc = sqlite3Fts5Tokenize(pConfig, \n              FTS5_TOKENIZE_DOCUMENT,\n              (const char*)sqlite3_column_text(pScan, i+1),\n              sqlite3_column_bytes(pScan, i+1),\n              (void*)&ctx,\n              fts5StorageIntegrityCallback\n          );\n        }\n        if( rc==SQLITE_OK && pConfig->bColumnsize && ctx.szCol!=aColSize[i] ){\n          rc = FTS5_CORRUPT;\n        }\n        aTotalSize[i] += ctx.szCol;\n        if( pConfig->eDetail==FTS5_DETAIL_COLUMNS ){\n          sqlite3Fts5TermsetFree(ctx.pTermset);\n          ctx.pTermset = 0;\n        }\n      }\n      sqlite3Fts5TermsetFree(ctx.pTermset);\n      ctx.pTermset = 0;\n\n      if( rc!=SQLITE_OK ) break;\n    }\n    rc2 = sqlite3_reset(pScan);\n    if( rc==SQLITE_OK ) rc = rc2;\n  }\n\n  /* Test that the \"totals\" (sometimes called \"averages\") record looks Ok */\n  if( rc==SQLITE_OK ){\n    int i;\n    rc = fts5StorageLoadTotals(p, 0);\n    for(i=0; rc==SQLITE_OK && i<pConfig->nCol; i++){\n      if( p->aTotalSize[i]!=aTotalSize[i] ) rc = FTS5_CORRUPT;\n    }\n  }\n\n  /* Check that the %_docsize and %_content tables contain the expected\n  ** number of rows.  */\n  if( rc==SQLITE_OK && pConfig->eContent==FTS5_CONTENT_NORMAL ){\n    i64 nRow = 0;\n    rc = fts5StorageCount(p, \"content\", &nRow);\n    if( rc==SQLITE_OK && nRow!=p->nTotalRow ) rc = FTS5_CORRUPT;\n  }\n  if( rc==SQLITE_OK && pConfig->bColumnsize ){\n    i64 nRow = 0;\n    rc = fts5StorageCount(p, \"docsize\", &nRow);\n    if( rc==SQLITE_OK && nRow!=p->nTotalRow ) rc = FTS5_CORRUPT;\n  }\n\n  /* Pass the expected checksum down to the FTS index module. It will\n  ** verify, amongst other things, that it matches the checksum generated by\n  ** inspecting the index itself.  */\n  if( rc==SQLITE_OK ){\n    rc = sqlite3Fts5IndexIntegrityCheck(p->pIndex, ctx.cksum);\n  }\n\n  sqlite3_free(aTotalSize);\n  return rc;\n}\n\n/*\n** Obtain an SQLite statement handle that may be used to read data from the\n** %_content table.\n*/\nstatic int sqlite3Fts5StorageStmt(\n  Fts5Storage *p, \n  int eStmt, \n  sqlite3_stmt **pp, \n  char **pzErrMsg\n){\n  int rc;\n  assert( eStmt==FTS5_STMT_SCAN_ASC \n       || eStmt==FTS5_STMT_SCAN_DESC\n       || eStmt==FTS5_STMT_LOOKUP\n  );\n  rc = fts5StorageGetStmt(p, eStmt, pp, pzErrMsg);\n  if( rc==SQLITE_OK ){\n    assert( p->aStmt[eStmt]==*pp );\n    p->aStmt[eStmt] = 0;\n  }\n  return rc;\n}\n\n/*\n** Release an SQLite statement handle obtained via an earlier call to\n** sqlite3Fts5StorageStmt(). The eStmt parameter passed to this function\n** must match that passed to the sqlite3Fts5StorageStmt() call.\n*/\nstatic void sqlite3Fts5StorageStmtRelease(\n  Fts5Storage *p, \n  int eStmt, \n  sqlite3_stmt *pStmt\n){\n  assert( eStmt==FTS5_STMT_SCAN_ASC\n       || eStmt==FTS5_STMT_SCAN_DESC\n       || eStmt==FTS5_STMT_LOOKUP\n  );\n  if( p->aStmt[eStmt]==0 ){\n    sqlite3_reset(pStmt);\n    p->aStmt[eStmt] = pStmt;\n  }else{\n    sqlite3_finalize(pStmt);\n  }\n}\n\nstatic int fts5StorageDecodeSizeArray(\n  int *aCol, int nCol,            /* Array to populate */\n  const u8 *aBlob, int nBlob      /* Record to read varints from */\n){\n  int i;\n  int iOff = 0;\n  for(i=0; i<nCol; i++){\n    if( iOff>=nBlob ) return 1;\n    iOff += fts5GetVarint32(&aBlob[iOff], aCol[i]);\n  }\n  return (iOff!=nBlob);\n}\n\n/*\n** Argument aCol points to an array of integers containing one entry for\n** each table column. This function reads the %_docsize record for the\n** specified rowid and populates aCol[] with the results.\n**\n** An SQLite error code is returned if an error occurs, or SQLITE_OK\n** otherwise.\n*/\nstatic int sqlite3Fts5StorageDocsize(Fts5Storage *p, i64 iRowid, int *aCol){\n  int nCol = p->pConfig->nCol;    /* Number of user columns in table */\n  sqlite3_stmt *pLookup = 0;      /* Statement to query %_docsize */\n  int rc;                         /* Return Code */\n\n  assert( p->pConfig->bColumnsize );\n  rc = fts5StorageGetStmt(p, FTS5_STMT_LOOKUP_DOCSIZE, &pLookup, 0);\n  if( rc==SQLITE_OK ){\n    int bCorrupt = 1;\n    sqlite3_bind_int64(pLookup, 1, iRowid);\n    if( SQLITE_ROW==sqlite3_step(pLookup) ){\n      const u8 *aBlob = sqlite3_column_blob(pLookup, 0);\n      int nBlob = sqlite3_column_bytes(pLookup, 0);\n      if( 0==fts5StorageDecodeSizeArray(aCol, nCol, aBlob, nBlob) ){\n        bCorrupt = 0;\n      }\n    }\n    rc = sqlite3_reset(pLookup);\n    if( bCorrupt && rc==SQLITE_OK ){\n      rc = FTS5_CORRUPT;\n    }\n  }\n\n  return rc;\n}\n\nstatic int sqlite3Fts5StorageSize(Fts5Storage *p, int iCol, i64 *pnToken){\n  int rc = fts5StorageLoadTotals(p, 0);\n  if( rc==SQLITE_OK ){\n    *pnToken = 0;\n    if( iCol<0 ){\n      int i;\n      for(i=0; i<p->pConfig->nCol; i++){\n        *pnToken += p->aTotalSize[i];\n      }\n    }else if( iCol<p->pConfig->nCol ){\n      *pnToken = p->aTotalSize[iCol];\n    }else{\n      rc = SQLITE_RANGE;\n    }\n  }\n  return rc;\n}\n\nstatic int sqlite3Fts5StorageRowCount(Fts5Storage *p, i64 *pnRow){\n  int rc = fts5StorageLoadTotals(p, 0);\n  if( rc==SQLITE_OK ){\n    *pnRow = p->nTotalRow;\n  }\n  return rc;\n}\n\n/*\n** Flush any data currently held in-memory to disk.\n*/\nstatic int sqlite3Fts5StorageSync(Fts5Storage *p){\n  int rc = SQLITE_OK;\n  i64 iLastRowid = sqlite3_last_insert_rowid(p->pConfig->db);\n  if( p->bTotalsValid ){\n    rc = fts5StorageSaveTotals(p);\n    p->bTotalsValid = 0;\n  }\n  if( rc==SQLITE_OK ){\n    rc = sqlite3Fts5IndexSync(p->pIndex);\n  }\n  sqlite3_set_last_insert_rowid(p->pConfig->db, iLastRowid);\n  return rc;\n}\n\nstatic int sqlite3Fts5StorageRollback(Fts5Storage *p){\n  p->bTotalsValid = 0;\n  return sqlite3Fts5IndexRollback(p->pIndex);\n}\n\nstatic int sqlite3Fts5StorageConfigValue(\n  Fts5Storage *p, \n  const char *z,\n  sqlite3_value *pVal,\n  int iVal\n){\n  sqlite3_stmt *pReplace = 0;\n  int rc = fts5StorageGetStmt(p, FTS5_STMT_REPLACE_CONFIG, &pReplace, 0);\n  if( rc==SQLITE_OK ){\n    sqlite3_bind_text(pReplace, 1, z, -1, SQLITE_STATIC);\n    if( pVal ){\n      sqlite3_bind_value(pReplace, 2, pVal);\n    }else{\n      sqlite3_bind_int(pReplace, 2, iVal);\n    }\n    sqlite3_step(pReplace);\n    rc = sqlite3_reset(pReplace);\n    sqlite3_bind_null(pReplace, 1);\n  }\n  if( rc==SQLITE_OK && pVal ){\n    int iNew = p->pConfig->iCookie + 1;\n    rc = sqlite3Fts5IndexSetCookie(p->pIndex, iNew);\n    if( rc==SQLITE_OK ){\n      p->pConfig->iCookie = iNew;\n    }\n  }\n  return rc;\n}\n\n/*\n** 2014 May 31\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n******************************************************************************\n*/\n\n\n/* #include \"fts5Int.h\" */\n\n/**************************************************************************\n** Start of ascii tokenizer implementation.\n*/\n\n/*\n** For tokenizers with no \"unicode\" modifier, the set of token characters\n** is the same as the set of ASCII range alphanumeric characters. \n*/\nstatic unsigned char aAsciiTokenChar[128] = {\n  0, 0, 0, 0, 0, 0, 0, 0,   0, 0, 0, 0, 0, 0, 0, 0,   /* 0x00..0x0F */\n  0, 0, 0, 0, 0, 0, 0, 0,   0, 0, 0, 0, 0, 0, 0, 0,   /* 0x10..0x1F */\n  0, 0, 0, 0, 0, 0, 0, 0,   0, 0, 0, 0, 0, 0, 0, 0,   /* 0x20..0x2F */\n  1, 1, 1, 1, 1, 1, 1, 1,   1, 1, 0, 0, 0, 0, 0, 0,   /* 0x30..0x3F */\n  0, 1, 1, 1, 1, 1, 1, 1,   1, 1, 1, 1, 1, 1, 1, 1,   /* 0x40..0x4F */\n  1, 1, 1, 1, 1, 1, 1, 1,   1, 1, 1, 0, 0, 0, 0, 0,   /* 0x50..0x5F */\n  0, 1, 1, 1, 1, 1, 1, 1,   1, 1, 1, 1, 1, 1, 1, 1,   /* 0x60..0x6F */\n  1, 1, 1, 1, 1, 1, 1, 1,   1, 1, 1, 0, 0, 0, 0, 0,   /* 0x70..0x7F */\n};\n\ntypedef struct AsciiTokenizer AsciiTokenizer;\nstruct AsciiTokenizer {\n  unsigned char aTokenChar[128];\n};\n\nstatic void fts5AsciiAddExceptions(\n  AsciiTokenizer *p, \n  const char *zArg, \n  int bTokenChars\n){\n  int i;\n  for(i=0; zArg[i]; i++){\n    if( (zArg[i] & 0x80)==0 ){\n      p->aTokenChar[(int)zArg[i]] = (unsigned char)bTokenChars;\n    }\n  }\n}\n\n/*\n** Delete a \"ascii\" tokenizer.\n*/\nstatic void fts5AsciiDelete(Fts5Tokenizer *p){\n  sqlite3_free(p);\n}\n\n/*\n** Create an \"ascii\" tokenizer.\n*/\nstatic int fts5AsciiCreate(\n  void *pUnused, \n  const char **azArg, int nArg,\n  Fts5Tokenizer **ppOut\n){\n  int rc = SQLITE_OK;\n  AsciiTokenizer *p = 0;\n  UNUSED_PARAM(pUnused);\n  if( nArg%2 ){\n    rc = SQLITE_ERROR;\n  }else{\n    p = sqlite3_malloc(sizeof(AsciiTokenizer));\n    if( p==0 ){\n      rc = SQLITE_NOMEM;\n    }else{\n      int i;\n      memset(p, 0, sizeof(AsciiTokenizer));\n      memcpy(p->aTokenChar, aAsciiTokenChar, sizeof(aAsciiTokenChar));\n      for(i=0; rc==SQLITE_OK && i<nArg; i+=2){\n        const char *zArg = azArg[i+1];\n        if( 0==sqlite3_stricmp(azArg[i], \"tokenchars\") ){\n          fts5AsciiAddExceptions(p, zArg, 1);\n        }else\n        if( 0==sqlite3_stricmp(azArg[i], \"separators\") ){\n          fts5AsciiAddExceptions(p, zArg, 0);\n        }else{\n          rc = SQLITE_ERROR;\n        }\n      }\n      if( rc!=SQLITE_OK ){\n        fts5AsciiDelete((Fts5Tokenizer*)p);\n        p = 0;\n      }\n    }\n  }\n\n  *ppOut = (Fts5Tokenizer*)p;\n  return rc;\n}\n\n\nstatic void asciiFold(char *aOut, const char *aIn, int nByte){\n  int i;\n  for(i=0; i<nByte; i++){\n    char c = aIn[i];\n    if( c>='A' && c<='Z' ) c += 32;\n    aOut[i] = c;\n  }\n}\n\n/*\n** Tokenize some text using the ascii tokenizer.\n*/\nstatic int fts5AsciiTokenize(\n  Fts5Tokenizer *pTokenizer,\n  void *pCtx,\n  int iUnused,\n  const char *pText, int nText,\n  int (*xToken)(void*, int, const char*, int nToken, int iStart, int iEnd)\n){\n  AsciiTokenizer *p = (AsciiTokenizer*)pTokenizer;\n  int rc = SQLITE_OK;\n  int ie;\n  int is = 0;\n\n  char aFold[64];\n  int nFold = sizeof(aFold);\n  char *pFold = aFold;\n  unsigned char *a = p->aTokenChar;\n\n  UNUSED_PARAM(iUnused);\n\n  while( is<nText && rc==SQLITE_OK ){\n    int nByte;\n\n    /* Skip any leading divider characters. */\n    while( is<nText && ((pText[is]&0x80)==0 && a[(int)pText[is]]==0) ){\n      is++;\n    }\n    if( is==nText ) break;\n\n    /* Count the token characters */\n    ie = is+1;\n    while( ie<nText && ((pText[ie]&0x80) || a[(int)pText[ie]] ) ){\n      ie++;\n    }\n\n    /* Fold to lower case */\n    nByte = ie-is;\n    if( nByte>nFold ){\n      if( pFold!=aFold ) sqlite3_free(pFold);\n      pFold = sqlite3_malloc(nByte*2);\n      if( pFold==0 ){\n        rc = SQLITE_NOMEM;\n        break;\n      }\n      nFold = nByte*2;\n    }\n    asciiFold(pFold, &pText[is], nByte);\n\n    /* Invoke the token callback */\n    rc = xToken(pCtx, 0, pFold, nByte, is, ie);\n    is = ie+1;\n  }\n  \n  if( pFold!=aFold ) sqlite3_free(pFold);\n  if( rc==SQLITE_DONE ) rc = SQLITE_OK;\n  return rc;\n}\n\n/**************************************************************************\n** Start of unicode61 tokenizer implementation.\n*/\n\n\n/*\n** The following two macros - READ_UTF8 and WRITE_UTF8 - have been copied\n** from the sqlite3 source file utf.c. If this file is compiled as part\n** of the amalgamation, they are not required.\n*/\n#ifndef SQLITE_AMALGAMATION\n\nstatic const unsigned char sqlite3Utf8Trans1[] = {\n  0x00, 0x01, 0x02, 0x03, 0x04, 0x05, 0x06, 0x07,\n  0x08, 0x09, 0x0a, 0x0b, 0x0c, 0x0d, 0x0e, 0x0f,\n  0x10, 0x11, 0x12, 0x13, 0x14, 0x15, 0x16, 0x17,\n  0x18, 0x19, 0x1a, 0x1b, 0x1c, 0x1d, 0x1e, 0x1f,\n  0x00, 0x01, 0x02, 0x03, 0x04, 0x05, 0x06, 0x07,\n  0x08, 0x09, 0x0a, 0x0b, 0x0c, 0x0d, 0x0e, 0x0f,\n  0x00, 0x01, 0x02, 0x03, 0x04, 0x05, 0x06, 0x07,\n  0x00, 0x01, 0x02, 0x03, 0x00, 0x01, 0x00, 0x00,\n};\n\n#define READ_UTF8(zIn, zTerm, c)                           \\\n  c = *(zIn++);                                            \\\n  if( c>=0xc0 ){                                           \\\n    c = sqlite3Utf8Trans1[c-0xc0];                         \\\n    while( zIn!=zTerm && (*zIn & 0xc0)==0x80 ){            \\\n      c = (c<<6) + (0x3f & *(zIn++));                      \\\n    }                                                      \\\n    if( c<0x80                                             \\\n        || (c&0xFFFFF800)==0xD800                          \\\n        || (c&0xFFFFFFFE)==0xFFFE ){  c = 0xFFFD; }        \\\n  }\n\n\n#define WRITE_UTF8(zOut, c) {                          \\\n  if( c<0x00080 ){                                     \\\n    *zOut++ = (unsigned char)(c&0xFF);                 \\\n  }                                                    \\\n  else if( c<0x00800 ){                                \\\n    *zOut++ = 0xC0 + (unsigned char)((c>>6)&0x1F);     \\\n    *zOut++ = 0x80 + (unsigned char)(c & 0x3F);        \\\n  }                                                    \\\n  else if( c<0x10000 ){                                \\\n    *zOut++ = 0xE0 + (unsigned char)((c>>12)&0x0F);    \\\n    *zOut++ = 0x80 + (unsigned char)((c>>6) & 0x3F);   \\\n    *zOut++ = 0x80 + (unsigned char)(c & 0x3F);        \\\n  }else{                                               \\\n    *zOut++ = 0xF0 + (unsigned char)((c>>18) & 0x07);  \\\n    *zOut++ = 0x80 + (unsigned char)((c>>12) & 0x3F);  \\\n    *zOut++ = 0x80 + (unsigned char)((c>>6) & 0x3F);   \\\n    *zOut++ = 0x80 + (unsigned char)(c & 0x3F);        \\\n  }                                                    \\\n}\n\n#endif /* ifndef SQLITE_AMALGAMATION */\n\ntypedef struct Unicode61Tokenizer Unicode61Tokenizer;\nstruct Unicode61Tokenizer {\n  unsigned char aTokenChar[128];  /* ASCII range token characters */\n  char *aFold;                    /* Buffer to fold text into */\n  int nFold;                      /* Size of aFold[] in bytes */\n  int bRemoveDiacritic;           /* True if remove_diacritics=1 is set */\n  int nException;\n  int *aiException;\n};\n\nstatic int fts5UnicodeAddExceptions(\n  Unicode61Tokenizer *p,          /* Tokenizer object */\n  const char *z,                  /* Characters to treat as exceptions */\n  int bTokenChars                 /* 1 for 'tokenchars', 0 for 'separators' */\n){\n  int rc = SQLITE_OK;\n  int n = (int)strlen(z);\n  int *aNew;\n\n  if( n>0 ){\n    aNew = (int*)sqlite3_realloc(p->aiException, (n+p->nException)*sizeof(int));\n    if( aNew ){\n      int nNew = p->nException;\n      const unsigned char *zCsr = (const unsigned char*)z;\n      const unsigned char *zTerm = (const unsigned char*)&z[n];\n      while( zCsr<zTerm ){\n        int iCode;\n        int bToken;\n        READ_UTF8(zCsr, zTerm, iCode);\n        if( iCode<128 ){\n          p->aTokenChar[iCode] = (unsigned char)bTokenChars;\n        }else{\n          bToken = sqlite3Fts5UnicodeIsalnum(iCode);\n          assert( (bToken==0 || bToken==1) ); \n          assert( (bTokenChars==0 || bTokenChars==1) );\n          if( bToken!=bTokenChars && sqlite3Fts5UnicodeIsdiacritic(iCode)==0 ){\n            int i;\n            for(i=0; i<nNew; i++){\n              if( aNew[i]>iCode ) break;\n            }\n            memmove(&aNew[i+1], &aNew[i], (nNew-i)*sizeof(int));\n            aNew[i] = iCode;\n            nNew++;\n          }\n        }\n      }\n      p->aiException = aNew;\n      p->nException = nNew;\n    }else{\n      rc = SQLITE_NOMEM;\n    }\n  }\n\n  return rc;\n}\n\n/*\n** Return true if the p->aiException[] array contains the value iCode.\n*/\nstatic int fts5UnicodeIsException(Unicode61Tokenizer *p, int iCode){\n  if( p->nException>0 ){\n    int *a = p->aiException;\n    int iLo = 0;\n    int iHi = p->nException-1;\n\n    while( iHi>=iLo ){\n      int iTest = (iHi + iLo) / 2;\n      if( iCode==a[iTest] ){\n        return 1;\n      }else if( iCode>a[iTest] ){\n        iLo = iTest+1;\n      }else{\n        iHi = iTest-1;\n      }\n    }\n  }\n\n  return 0;\n}\n\n/*\n** Delete a \"unicode61\" tokenizer.\n*/\nstatic void fts5UnicodeDelete(Fts5Tokenizer *pTok){\n  if( pTok ){\n    Unicode61Tokenizer *p = (Unicode61Tokenizer*)pTok;\n    sqlite3_free(p->aiException);\n    sqlite3_free(p->aFold);\n    sqlite3_free(p);\n  }\n  return;\n}\n\n/*\n** Create a \"unicode61\" tokenizer.\n*/\nstatic int fts5UnicodeCreate(\n  void *pUnused, \n  const char **azArg, int nArg,\n  Fts5Tokenizer **ppOut\n){\n  int rc = SQLITE_OK;             /* Return code */\n  Unicode61Tokenizer *p = 0;      /* New tokenizer object */ \n\n  UNUSED_PARAM(pUnused);\n\n  if( nArg%2 ){\n    rc = SQLITE_ERROR;\n  }else{\n    p = (Unicode61Tokenizer*)sqlite3_malloc(sizeof(Unicode61Tokenizer));\n    if( p ){\n      int i;\n      memset(p, 0, sizeof(Unicode61Tokenizer));\n      memcpy(p->aTokenChar, aAsciiTokenChar, sizeof(aAsciiTokenChar));\n      p->bRemoveDiacritic = 1;\n      p->nFold = 64;\n      p->aFold = sqlite3_malloc(p->nFold * sizeof(char));\n      if( p->aFold==0 ){\n        rc = SQLITE_NOMEM;\n      }\n      for(i=0; rc==SQLITE_OK && i<nArg; i+=2){\n        const char *zArg = azArg[i+1];\n        if( 0==sqlite3_stricmp(azArg[i], \"remove_diacritics\") ){\n          if( (zArg[0]!='0' && zArg[0]!='1') || zArg[1] ){\n            rc = SQLITE_ERROR;\n          }\n          p->bRemoveDiacritic = (zArg[0]=='1');\n        }else\n        if( 0==sqlite3_stricmp(azArg[i], \"tokenchars\") ){\n          rc = fts5UnicodeAddExceptions(p, zArg, 1);\n        }else\n        if( 0==sqlite3_stricmp(azArg[i], \"separators\") ){\n          rc = fts5UnicodeAddExceptions(p, zArg, 0);\n        }else{\n          rc = SQLITE_ERROR;\n        }\n      }\n    }else{\n      rc = SQLITE_NOMEM;\n    }\n    if( rc!=SQLITE_OK ){\n      fts5UnicodeDelete((Fts5Tokenizer*)p);\n      p = 0;\n    }\n    *ppOut = (Fts5Tokenizer*)p;\n  }\n  return rc;\n}\n\n/*\n** Return true if, for the purposes of tokenizing with the tokenizer\n** passed as the first argument, codepoint iCode is considered a token \n** character (not a separator).\n*/\nstatic int fts5UnicodeIsAlnum(Unicode61Tokenizer *p, int iCode){\n  assert( (sqlite3Fts5UnicodeIsalnum(iCode) & 0xFFFFFFFE)==0 );\n  return sqlite3Fts5UnicodeIsalnum(iCode) ^ fts5UnicodeIsException(p, iCode);\n}\n\nstatic int fts5UnicodeTokenize(\n  Fts5Tokenizer *pTokenizer,\n  void *pCtx,\n  int iUnused,\n  const char *pText, int nText,\n  int (*xToken)(void*, int, const char*, int nToken, int iStart, int iEnd)\n){\n  Unicode61Tokenizer *p = (Unicode61Tokenizer*)pTokenizer;\n  int rc = SQLITE_OK;\n  unsigned char *a = p->aTokenChar;\n\n  unsigned char *zTerm = (unsigned char*)&pText[nText];\n  unsigned char *zCsr = (unsigned char *)pText;\n\n  /* Output buffer */\n  char *aFold = p->aFold;\n  int nFold = p->nFold;\n  const char *pEnd = &aFold[nFold-6];\n\n  UNUSED_PARAM(iUnused);\n\n  /* Each iteration of this loop gobbles up a contiguous run of separators,\n  ** then the next token.  */\n  while( rc==SQLITE_OK ){\n    int iCode;                    /* non-ASCII codepoint read from input */\n    char *zOut = aFold;\n    int is;\n    int ie;\n\n    /* Skip any separator characters. */\n    while( 1 ){\n      if( zCsr>=zTerm ) goto tokenize_done;\n      if( *zCsr & 0x80 ) {\n        /* A character outside of the ascii range. Skip past it if it is\n        ** a separator character. Or break out of the loop if it is not. */\n        is = zCsr - (unsigned char*)pText;\n        READ_UTF8(zCsr, zTerm, iCode);\n        if( fts5UnicodeIsAlnum(p, iCode) ){\n          goto non_ascii_tokenchar;\n        }\n      }else{\n        if( a[*zCsr] ){\n          is = zCsr - (unsigned char*)pText;\n          goto ascii_tokenchar;\n        }\n        zCsr++;\n      }\n    }\n\n    /* Run through the tokenchars. Fold them into the output buffer along\n    ** the way.  */\n    while( zCsr<zTerm ){\n\n      /* Grow the output buffer so that there is sufficient space to fit the\n      ** largest possible utf-8 character.  */\n      if( zOut>pEnd ){\n        aFold = sqlite3_malloc(nFold*2);\n        if( aFold==0 ){\n          rc = SQLITE_NOMEM;\n          goto tokenize_done;\n        }\n        zOut = &aFold[zOut - p->aFold];\n        memcpy(aFold, p->aFold, nFold);\n        sqlite3_free(p->aFold);\n        p->aFold = aFold;\n        p->nFold = nFold = nFold*2;\n        pEnd = &aFold[nFold-6];\n      }\n\n      if( *zCsr & 0x80 ){\n        /* An non-ascii-range character. Fold it into the output buffer if\n        ** it is a token character, or break out of the loop if it is not. */\n        READ_UTF8(zCsr, zTerm, iCode);\n        if( fts5UnicodeIsAlnum(p,iCode)||sqlite3Fts5UnicodeIsdiacritic(iCode) ){\n non_ascii_tokenchar:\n          iCode = sqlite3Fts5UnicodeFold(iCode, p->bRemoveDiacritic);\n          if( iCode ) WRITE_UTF8(zOut, iCode);\n        }else{\n          break;\n        }\n      }else if( a[*zCsr]==0 ){\n        /* An ascii-range separator character. End of token. */\n        break; \n      }else{\n ascii_tokenchar:\n        if( *zCsr>='A' && *zCsr<='Z' ){\n          *zOut++ = *zCsr + 32;\n        }else{\n          *zOut++ = *zCsr;\n        }\n        zCsr++;\n      }\n      ie = zCsr - (unsigned char*)pText;\n    }\n\n    /* Invoke the token callback */\n    rc = xToken(pCtx, 0, aFold, zOut-aFold, is, ie); \n  }\n  \n tokenize_done:\n  if( rc==SQLITE_DONE ) rc = SQLITE_OK;\n  return rc;\n}\n\n/**************************************************************************\n** Start of porter stemmer implementation.\n*/\n\n/* Any tokens larger than this (in bytes) are passed through without\n** stemming. */\n#define FTS5_PORTER_MAX_TOKEN 64\n\ntypedef struct PorterTokenizer PorterTokenizer;\nstruct PorterTokenizer {\n  fts5_tokenizer tokenizer;       /* Parent tokenizer module */\n  Fts5Tokenizer *pTokenizer;      /* Parent tokenizer instance */\n  char aBuf[FTS5_PORTER_MAX_TOKEN + 64];\n};\n\n/*\n** Delete a \"porter\" tokenizer.\n*/\nstatic void fts5PorterDelete(Fts5Tokenizer *pTok){\n  if( pTok ){\n    PorterTokenizer *p = (PorterTokenizer*)pTok;\n    if( p->pTokenizer ){\n      p->tokenizer.xDelete(p->pTokenizer);\n    }\n    sqlite3_free(p);\n  }\n}\n\n/*\n** Create a \"porter\" tokenizer.\n*/\nstatic int fts5PorterCreate(\n  void *pCtx, \n  const char **azArg, int nArg,\n  Fts5Tokenizer **ppOut\n){\n  fts5_api *pApi = (fts5_api*)pCtx;\n  int rc = SQLITE_OK;\n  PorterTokenizer *pRet;\n  void *pUserdata = 0;\n  const char *zBase = \"unicode61\";\n\n  if( nArg>0 ){\n    zBase = azArg[0];\n  }\n\n  pRet = (PorterTokenizer*)sqlite3_malloc(sizeof(PorterTokenizer));\n  if( pRet ){\n    memset(pRet, 0, sizeof(PorterTokenizer));\n    rc = pApi->xFindTokenizer(pApi, zBase, &pUserdata, &pRet->tokenizer);\n  }else{\n    rc = SQLITE_NOMEM;\n  }\n  if( rc==SQLITE_OK ){\n    int nArg2 = (nArg>0 ? nArg-1 : 0);\n    const char **azArg2 = (nArg2 ? &azArg[1] : 0);\n    rc = pRet->tokenizer.xCreate(pUserdata, azArg2, nArg2, &pRet->pTokenizer);\n  }\n\n  if( rc!=SQLITE_OK ){\n    fts5PorterDelete((Fts5Tokenizer*)pRet);\n    pRet = 0;\n  }\n  *ppOut = (Fts5Tokenizer*)pRet;\n  return rc;\n}\n\ntypedef struct PorterContext PorterContext;\nstruct PorterContext {\n  void *pCtx;\n  int (*xToken)(void*, int, const char*, int, int, int);\n  char *aBuf;\n};\n\ntypedef struct PorterRule PorterRule;\nstruct PorterRule {\n  const char *zSuffix;\n  int nSuffix;\n  int (*xCond)(char *zStem, int nStem);\n  const char *zOutput;\n  int nOutput;\n};\n\n#if 0\nstatic int fts5PorterApply(char *aBuf, int *pnBuf, PorterRule *aRule){\n  int ret = -1;\n  int nBuf = *pnBuf;\n  PorterRule *p;\n\n  for(p=aRule; p->zSuffix; p++){\n    assert( strlen(p->zSuffix)==p->nSuffix );\n    assert( strlen(p->zOutput)==p->nOutput );\n    if( nBuf<p->nSuffix ) continue;\n    if( 0==memcmp(&aBuf[nBuf - p->nSuffix], p->zSuffix, p->nSuffix) ) break;\n  }\n\n  if( p->zSuffix ){\n    int nStem = nBuf - p->nSuffix;\n    if( p->xCond==0 || p->xCond(aBuf, nStem) ){\n      memcpy(&aBuf[nStem], p->zOutput, p->nOutput);\n      *pnBuf = nStem + p->nOutput;\n      ret = p - aRule;\n    }\n  }\n\n  return ret;\n}\n#endif\n\nstatic int fts5PorterIsVowel(char c, int bYIsVowel){\n  return (\n      c=='a' || c=='e' || c=='i' || c=='o' || c=='u' || (bYIsVowel && c=='y')\n  );\n}\n\nstatic int fts5PorterGobbleVC(char *zStem, int nStem, int bPrevCons){\n  int i;\n  int bCons = bPrevCons;\n\n  /* Scan for a vowel */\n  for(i=0; i<nStem; i++){\n    if( 0==(bCons = !fts5PorterIsVowel(zStem[i], bCons)) ) break;\n  }\n\n  /* Scan for a consonent */\n  for(i++; i<nStem; i++){\n    if( (bCons = !fts5PorterIsVowel(zStem[i], bCons)) ) return i+1;\n  }\n  return 0;\n}\n\n/* porter rule condition: (m > 0) */\nstatic int fts5Porter_MGt0(char *zStem, int nStem){\n  return !!fts5PorterGobbleVC(zStem, nStem, 0);\n}\n\n/* porter rule condition: (m > 1) */\nstatic int fts5Porter_MGt1(char *zStem, int nStem){\n  int n;\n  n = fts5PorterGobbleVC(zStem, nStem, 0);\n  if( n && fts5PorterGobbleVC(&zStem[n], nStem-n, 1) ){\n    return 1;\n  }\n  return 0;\n}\n\n/* porter rule condition: (m = 1) */\nstatic int fts5Porter_MEq1(char *zStem, int nStem){\n  int n;\n  n = fts5PorterGobbleVC(zStem, nStem, 0);\n  if( n && 0==fts5PorterGobbleVC(&zStem[n], nStem-n, 1) ){\n    return 1;\n  }\n  return 0;\n}\n\n/* porter rule condition: (*o) */\nstatic int fts5Porter_Ostar(char *zStem, int nStem){\n  if( zStem[nStem-1]=='w' || zStem[nStem-1]=='x' || zStem[nStem-1]=='y' ){\n    return 0;\n  }else{\n    int i;\n    int mask = 0;\n    int bCons = 0;\n    for(i=0; i<nStem; i++){\n      bCons = !fts5PorterIsVowel(zStem[i], bCons);\n      assert( bCons==0 || bCons==1 );\n      mask = (mask << 1) + bCons;\n    }\n    return ((mask & 0x0007)==0x0005);\n  }\n}\n\n/* porter rule condition: (m > 1 and (*S or *T)) */\nstatic int fts5Porter_MGt1_and_S_or_T(char *zStem, int nStem){\n  assert( nStem>0 );\n  return (zStem[nStem-1]=='s' || zStem[nStem-1]=='t') \n      && fts5Porter_MGt1(zStem, nStem);\n}\n\n/* porter rule condition: (*v*) */\nstatic int fts5Porter_Vowel(char *zStem, int nStem){\n  int i;\n  for(i=0; i<nStem; i++){\n    if( fts5PorterIsVowel(zStem[i], i>0) ){\n      return 1;\n    }\n  }\n  return 0;\n}\n\n\n/**************************************************************************\n***************************************************************************\n** GENERATED CODE STARTS HERE (mkportersteps.tcl)\n*/\n\nstatic int fts5PorterStep4(char *aBuf, int *pnBuf){\n  int ret = 0;\n  int nBuf = *pnBuf;\n  switch( aBuf[nBuf-2] ){\n    \n    case 'a': \n      if( nBuf>2 && 0==memcmp(\"al\", &aBuf[nBuf-2], 2) ){\n        if( fts5Porter_MGt1(aBuf, nBuf-2) ){\n          *pnBuf = nBuf - 2;\n        }\n      }\n      break;\n  \n    case 'c': \n      if( nBuf>4 && 0==memcmp(\"ance\", &aBuf[nBuf-4], 4) ){\n        if( fts5Porter_MGt1(aBuf, nBuf-4) ){\n          *pnBuf = nBuf - 4;\n        }\n      }else if( nBuf>4 && 0==memcmp(\"ence\", &aBuf[nBuf-4], 4) ){\n        if( fts5Porter_MGt1(aBuf, nBuf-4) ){\n          *pnBuf = nBuf - 4;\n        }\n      }\n      break;\n  \n    case 'e': \n      if( nBuf>2 && 0==memcmp(\"er\", &aBuf[nBuf-2], 2) ){\n        if( fts5Porter_MGt1(aBuf, nBuf-2) ){\n          *pnBuf = nBuf - 2;\n        }\n      }\n      break;\n  \n    case 'i': \n      if( nBuf>2 && 0==memcmp(\"ic\", &aBuf[nBuf-2], 2) ){\n        if( fts5Porter_MGt1(aBuf, nBuf-2) ){\n          *pnBuf = nBuf - 2;\n        }\n      }\n      break;\n  \n    case 'l': \n      if( nBuf>4 && 0==memcmp(\"able\", &aBuf[nBuf-4], 4) ){\n        if( fts5Porter_MGt1(aBuf, nBuf-4) ){\n          *pnBuf = nBuf - 4;\n        }\n      }else if( nBuf>4 && 0==memcmp(\"ible\", &aBuf[nBuf-4], 4) ){\n        if( fts5Porter_MGt1(aBuf, nBuf-4) ){\n          *pnBuf = nBuf - 4;\n        }\n      }\n      break;\n  \n    case 'n': \n      if( nBuf>3 && 0==memcmp(\"ant\", &aBuf[nBuf-3], 3) ){\n        if( fts5Porter_MGt1(aBuf, nBuf-3) ){\n          *pnBuf = nBuf - 3;\n        }\n      }else if( nBuf>5 && 0==memcmp(\"ement\", &aBuf[nBuf-5], 5) ){\n        if( fts5Porter_MGt1(aBuf, nBuf-5) ){\n          *pnBuf = nBuf - 5;\n        }\n      }else if( nBuf>4 && 0==memcmp(\"ment\", &aBuf[nBuf-4], 4) ){\n        if( fts5Porter_MGt1(aBuf, nBuf-4) ){\n          *pnBuf = nBuf - 4;\n        }\n      }else if( nBuf>3 && 0==memcmp(\"ent\", &aBuf[nBuf-3], 3) ){\n        if( fts5Porter_MGt1(aBuf, nBuf-3) ){\n          *pnBuf = nBuf - 3;\n        }\n      }\n      break;\n  \n    case 'o': \n      if( nBuf>3 && 0==memcmp(\"ion\", &aBuf[nBuf-3], 3) ){\n        if( fts5Porter_MGt1_and_S_or_T(aBuf, nBuf-3) ){\n          *pnBuf = nBuf - 3;\n        }\n      }else if( nBuf>2 && 0==memcmp(\"ou\", &aBuf[nBuf-2], 2) ){\n        if( fts5Porter_MGt1(aBuf, nBuf-2) ){\n          *pnBuf = nBuf - 2;\n        }\n      }\n      break;\n  \n    case 's': \n      if( nBuf>3 && 0==memcmp(\"ism\", &aBuf[nBuf-3], 3) ){\n        if( fts5Porter_MGt1(aBuf, nBuf-3) ){\n          *pnBuf = nBuf - 3;\n        }\n      }\n      break;\n  \n    case 't': \n      if( nBuf>3 && 0==memcmp(\"ate\", &aBuf[nBuf-3], 3) ){\n        if( fts5Porter_MGt1(aBuf, nBuf-3) ){\n          *pnBuf = nBuf - 3;\n        }\n      }else if( nBuf>3 && 0==memcmp(\"iti\", &aBuf[nBuf-3], 3) ){\n        if( fts5Porter_MGt1(aBuf, nBuf-3) ){\n          *pnBuf = nBuf - 3;\n        }\n      }\n      break;\n  \n    case 'u': \n      if( nBuf>3 && 0==memcmp(\"ous\", &aBuf[nBuf-3], 3) ){\n        if( fts5Porter_MGt1(aBuf, nBuf-3) ){\n          *pnBuf = nBuf - 3;\n        }\n      }\n      break;\n  \n    case 'v': \n      if( nBuf>3 && 0==memcmp(\"ive\", &aBuf[nBuf-3], 3) ){\n        if( fts5Porter_MGt1(aBuf, nBuf-3) ){\n          *pnBuf = nBuf - 3;\n        }\n      }\n      break;\n  \n    case 'z': \n      if( nBuf>3 && 0==memcmp(\"ize\", &aBuf[nBuf-3], 3) ){\n        if( fts5Porter_MGt1(aBuf, nBuf-3) ){\n          *pnBuf = nBuf - 3;\n        }\n      }\n      break;\n  \n  }\n  return ret;\n}\n  \n\nstatic int fts5PorterStep1B2(char *aBuf, int *pnBuf){\n  int ret = 0;\n  int nBuf = *pnBuf;\n  switch( aBuf[nBuf-2] ){\n    \n    case 'a': \n      if( nBuf>2 && 0==memcmp(\"at\", &aBuf[nBuf-2], 2) ){\n        memcpy(&aBuf[nBuf-2], \"ate\", 3);\n        *pnBuf = nBuf - 2 + 3;\n        ret = 1;\n      }\n      break;\n  \n    case 'b': \n      if( nBuf>2 && 0==memcmp(\"bl\", &aBuf[nBuf-2], 2) ){\n        memcpy(&aBuf[nBuf-2], \"ble\", 3);\n        *pnBuf = nBuf - 2 + 3;\n        ret = 1;\n      }\n      break;\n  \n    case 'i': \n      if( nBuf>2 && 0==memcmp(\"iz\", &aBuf[nBuf-2], 2) ){\n        memcpy(&aBuf[nBuf-2], \"ize\", 3);\n        *pnBuf = nBuf - 2 + 3;\n        ret = 1;\n      }\n      break;\n  \n  }\n  return ret;\n}\n  \n\nstatic int fts5PorterStep2(char *aBuf, int *pnBuf){\n  int ret = 0;\n  int nBuf = *pnBuf;\n  switch( aBuf[nBuf-2] ){\n    \n    case 'a': \n      if( nBuf>7 && 0==memcmp(\"ational\", &aBuf[nBuf-7], 7) ){\n        if( fts5Porter_MGt0(aBuf, nBuf-7) ){\n          memcpy(&aBuf[nBuf-7], \"ate\", 3);\n          *pnBuf = nBuf - 7 + 3;\n        }\n      }else if( nBuf>6 && 0==memcmp(\"tional\", &aBuf[nBuf-6], 6) ){\n        if( fts5Porter_MGt0(aBuf, nBuf-6) ){\n          memcpy(&aBuf[nBuf-6], \"tion\", 4);\n          *pnBuf = nBuf - 6 + 4;\n        }\n      }\n      break;\n  \n    case 'c': \n      if( nBuf>4 && 0==memcmp(\"enci\", &aBuf[nBuf-4], 4) ){\n        if( fts5Porter_MGt0(aBuf, nBuf-4) ){\n          memcpy(&aBuf[nBuf-4], \"ence\", 4);\n          *pnBuf = nBuf - 4 + 4;\n        }\n      }else if( nBuf>4 && 0==memcmp(\"anci\", &aBuf[nBuf-4], 4) ){\n        if( fts5Porter_MGt0(aBuf, nBuf-4) ){\n          memcpy(&aBuf[nBuf-4], \"ance\", 4);\n          *pnBuf = nBuf - 4 + 4;\n        }\n      }\n      break;\n  \n    case 'e': \n      if( nBuf>4 && 0==memcmp(\"izer\", &aBuf[nBuf-4], 4) ){\n        if( fts5Porter_MGt0(aBuf, nBuf-4) ){\n          memcpy(&aBuf[nBuf-4], \"ize\", 3);\n          *pnBuf = nBuf - 4 + 3;\n        }\n      }\n      break;\n  \n    case 'g': \n      if( nBuf>4 && 0==memcmp(\"logi\", &aBuf[nBuf-4], 4) ){\n        if( fts5Porter_MGt0(aBuf, nBuf-4) ){\n          memcpy(&aBuf[nBuf-4], \"log\", 3);\n          *pnBuf = nBuf - 4 + 3;\n        }\n      }\n      break;\n  \n    case 'l': \n      if( nBuf>3 && 0==memcmp(\"bli\", &aBuf[nBuf-3], 3) ){\n        if( fts5Porter_MGt0(aBuf, nBuf-3) ){\n          memcpy(&aBuf[nBuf-3], \"ble\", 3);\n          *pnBuf = nBuf - 3 + 3;\n        }\n      }else if( nBuf>4 && 0==memcmp(\"alli\", &aBuf[nBuf-4], 4) ){\n        if( fts5Porter_MGt0(aBuf, nBuf-4) ){\n          memcpy(&aBuf[nBuf-4], \"al\", 2);\n          *pnBuf = nBuf - 4 + 2;\n        }\n      }else if( nBuf>5 && 0==memcmp(\"entli\", &aBuf[nBuf-5], 5) ){\n        if( fts5Porter_MGt0(aBuf, nBuf-5) ){\n          memcpy(&aBuf[nBuf-5], \"ent\", 3);\n          *pnBuf = nBuf - 5 + 3;\n        }\n      }else if( nBuf>3 && 0==memcmp(\"eli\", &aBuf[nBuf-3], 3) ){\n        if( fts5Porter_MGt0(aBuf, nBuf-3) ){\n          memcpy(&aBuf[nBuf-3], \"e\", 1);\n          *pnBuf = nBuf - 3 + 1;\n        }\n      }else if( nBuf>5 && 0==memcmp(\"ousli\", &aBuf[nBuf-5], 5) ){\n        if( fts5Porter_MGt0(aBuf, nBuf-5) ){\n          memcpy(&aBuf[nBuf-5], \"ous\", 3);\n          *pnBuf = nBuf - 5 + 3;\n        }\n      }\n      break;\n  \n    case 'o': \n      if( nBuf>7 && 0==memcmp(\"ization\", &aBuf[nBuf-7], 7) ){\n        if( fts5Porter_MGt0(aBuf, nBuf-7) ){\n          memcpy(&aBuf[nBuf-7], \"ize\", 3);\n          *pnBuf = nBuf - 7 + 3;\n        }\n      }else if( nBuf>5 && 0==memcmp(\"ation\", &aBuf[nBuf-5], 5) ){\n        if( fts5Porter_MGt0(aBuf, nBuf-5) ){\n          memcpy(&aBuf[nBuf-5], \"ate\", 3);\n          *pnBuf = nBuf - 5 + 3;\n        }\n      }else if( nBuf>4 && 0==memcmp(\"ator\", &aBuf[nBuf-4], 4) ){\n        if( fts5Porter_MGt0(aBuf, nBuf-4) ){\n          memcpy(&aBuf[nBuf-4], \"ate\", 3);\n          *pnBuf = nBuf - 4 + 3;\n        }\n      }\n      break;\n  \n    case 's': \n      if( nBuf>5 && 0==memcmp(\"alism\", &aBuf[nBuf-5], 5) ){\n        if( fts5Porter_MGt0(aBuf, nBuf-5) ){\n          memcpy(&aBuf[nBuf-5], \"al\", 2);\n          *pnBuf = nBuf - 5 + 2;\n        }\n      }else if( nBuf>7 && 0==memcmp(\"iveness\", &aBuf[nBuf-7], 7) ){\n        if( fts5Porter_MGt0(aBuf, nBuf-7) ){\n          memcpy(&aBuf[nBuf-7], \"ive\", 3);\n          *pnBuf = nBuf - 7 + 3;\n        }\n      }else if( nBuf>7 && 0==memcmp(\"fulness\", &aBuf[nBuf-7], 7) ){\n        if( fts5Porter_MGt0(aBuf, nBuf-7) ){\n          memcpy(&aBuf[nBuf-7], \"ful\", 3);\n          *pnBuf = nBuf - 7 + 3;\n        }\n      }else if( nBuf>7 && 0==memcmp(\"ousness\", &aBuf[nBuf-7], 7) ){\n        if( fts5Porter_MGt0(aBuf, nBuf-7) ){\n          memcpy(&aBuf[nBuf-7], \"ous\", 3);\n          *pnBuf = nBuf - 7 + 3;\n        }\n      }\n      break;\n  \n    case 't': \n      if( nBuf>5 && 0==memcmp(\"aliti\", &aBuf[nBuf-5], 5) ){\n        if( fts5Porter_MGt0(aBuf, nBuf-5) ){\n          memcpy(&aBuf[nBuf-5], \"al\", 2);\n          *pnBuf = nBuf - 5 + 2;\n        }\n      }else if( nBuf>5 && 0==memcmp(\"iviti\", &aBuf[nBuf-5], 5) ){\n        if( fts5Porter_MGt0(aBuf, nBuf-5) ){\n          memcpy(&aBuf[nBuf-5], \"ive\", 3);\n          *pnBuf = nBuf - 5 + 3;\n        }\n      }else if( nBuf>6 && 0==memcmp(\"biliti\", &aBuf[nBuf-6], 6) ){\n        if( fts5Porter_MGt0(aBuf, nBuf-6) ){\n          memcpy(&aBuf[nBuf-6], \"ble\", 3);\n          *pnBuf = nBuf - 6 + 3;\n        }\n      }\n      break;\n  \n  }\n  return ret;\n}\n  \n\nstatic int fts5PorterStep3(char *aBuf, int *pnBuf){\n  int ret = 0;\n  int nBuf = *pnBuf;\n  switch( aBuf[nBuf-2] ){\n    \n    case 'a': \n      if( nBuf>4 && 0==memcmp(\"ical\", &aBuf[nBuf-4], 4) ){\n        if( fts5Porter_MGt0(aBuf, nBuf-4) ){\n          memcpy(&aBuf[nBuf-4], \"ic\", 2);\n          *pnBuf = nBuf - 4 + 2;\n        }\n      }\n      break;\n  \n    case 's': \n      if( nBuf>4 && 0==memcmp(\"ness\", &aBuf[nBuf-4], 4) ){\n        if( fts5Porter_MGt0(aBuf, nBuf-4) ){\n          *pnBuf = nBuf - 4;\n        }\n      }\n      break;\n  \n    case 't': \n      if( nBuf>5 && 0==memcmp(\"icate\", &aBuf[nBuf-5], 5) ){\n        if( fts5Porter_MGt0(aBuf, nBuf-5) ){\n          memcpy(&aBuf[nBuf-5], \"ic\", 2);\n          *pnBuf = nBuf - 5 + 2;\n        }\n      }else if( nBuf>5 && 0==memcmp(\"iciti\", &aBuf[nBuf-5], 5) ){\n        if( fts5Porter_MGt0(aBuf, nBuf-5) ){\n          memcpy(&aBuf[nBuf-5], \"ic\", 2);\n          *pnBuf = nBuf - 5 + 2;\n        }\n      }\n      break;\n  \n    case 'u': \n      if( nBuf>3 && 0==memcmp(\"ful\", &aBuf[nBuf-3], 3) ){\n        if( fts5Porter_MGt0(aBuf, nBuf-3) ){\n          *pnBuf = nBuf - 3;\n        }\n      }\n      break;\n  \n    case 'v': \n      if( nBuf>5 && 0==memcmp(\"ative\", &aBuf[nBuf-5], 5) ){\n        if( fts5Porter_MGt0(aBuf, nBuf-5) ){\n          *pnBuf = nBuf - 5;\n        }\n      }\n      break;\n  \n    case 'z': \n      if( nBuf>5 && 0==memcmp(\"alize\", &aBuf[nBuf-5], 5) ){\n        if( fts5Porter_MGt0(aBuf, nBuf-5) ){\n          memcpy(&aBuf[nBuf-5], \"al\", 2);\n          *pnBuf = nBuf - 5 + 2;\n        }\n      }\n      break;\n  \n  }\n  return ret;\n}\n  \n\nstatic int fts5PorterStep1B(char *aBuf, int *pnBuf){\n  int ret = 0;\n  int nBuf = *pnBuf;\n  switch( aBuf[nBuf-2] ){\n    \n    case 'e': \n      if( nBuf>3 && 0==memcmp(\"eed\", &aBuf[nBuf-3], 3) ){\n        if( fts5Porter_MGt0(aBuf, nBuf-3) ){\n          memcpy(&aBuf[nBuf-3], \"ee\", 2);\n          *pnBuf = nBuf - 3 + 2;\n        }\n      }else if( nBuf>2 && 0==memcmp(\"ed\", &aBuf[nBuf-2], 2) ){\n        if( fts5Porter_Vowel(aBuf, nBuf-2) ){\n          *pnBuf = nBuf - 2;\n          ret = 1;\n        }\n      }\n      break;\n  \n    case 'n': \n      if( nBuf>3 && 0==memcmp(\"ing\", &aBuf[nBuf-3], 3) ){\n        if( fts5Porter_Vowel(aBuf, nBuf-3) ){\n          *pnBuf = nBuf - 3;\n          ret = 1;\n        }\n      }\n      break;\n  \n  }\n  return ret;\n}\n  \n/* \n** GENERATED CODE ENDS HERE (mkportersteps.tcl)\n***************************************************************************\n**************************************************************************/\n\nstatic void fts5PorterStep1A(char *aBuf, int *pnBuf){\n  int nBuf = *pnBuf;\n  if( aBuf[nBuf-1]=='s' ){\n    if( aBuf[nBuf-2]=='e' ){\n      if( (nBuf>4 && aBuf[nBuf-4]=='s' && aBuf[nBuf-3]=='s') \n       || (nBuf>3 && aBuf[nBuf-3]=='i' )\n      ){\n        *pnBuf = nBuf-2;\n      }else{\n        *pnBuf = nBuf-1;\n      }\n    }\n    else if( aBuf[nBuf-2]!='s' ){\n      *pnBuf = nBuf-1;\n    }\n  }\n}\n\nstatic int fts5PorterCb(\n  void *pCtx, \n  int tflags,\n  const char *pToken, \n  int nToken, \n  int iStart, \n  int iEnd\n){\n  PorterContext *p = (PorterContext*)pCtx;\n\n  char *aBuf;\n  int nBuf;\n\n  if( nToken>FTS5_PORTER_MAX_TOKEN || nToken<3 ) goto pass_through;\n  aBuf = p->aBuf;\n  nBuf = nToken;\n  memcpy(aBuf, pToken, nBuf);\n\n  /* Step 1. */\n  fts5PorterStep1A(aBuf, &nBuf);\n  if( fts5PorterStep1B(aBuf, &nBuf) ){\n    if( fts5PorterStep1B2(aBuf, &nBuf)==0 ){\n      char c = aBuf[nBuf-1];\n      if( fts5PorterIsVowel(c, 0)==0 \n       && c!='l' && c!='s' && c!='z' && c==aBuf[nBuf-2] \n      ){\n        nBuf--;\n      }else if( fts5Porter_MEq1(aBuf, nBuf) && fts5Porter_Ostar(aBuf, nBuf) ){\n        aBuf[nBuf++] = 'e';\n      }\n    }\n  }\n\n  /* Step 1C. */\n  if( aBuf[nBuf-1]=='y' && fts5Porter_Vowel(aBuf, nBuf-1) ){\n    aBuf[nBuf-1] = 'i';\n  }\n\n  /* Steps 2 through 4. */\n  fts5PorterStep2(aBuf, &nBuf);\n  fts5PorterStep3(aBuf, &nBuf);\n  fts5PorterStep4(aBuf, &nBuf);\n\n  /* Step 5a. */\n  assert( nBuf>0 );\n  if( aBuf[nBuf-1]=='e' ){\n    if( fts5Porter_MGt1(aBuf, nBuf-1) \n     || (fts5Porter_MEq1(aBuf, nBuf-1) && !fts5Porter_Ostar(aBuf, nBuf-1))\n    ){\n      nBuf--;\n    }\n  }\n\n  /* Step 5b. */\n  if( nBuf>1 && aBuf[nBuf-1]=='l' \n   && aBuf[nBuf-2]=='l' && fts5Porter_MGt1(aBuf, nBuf-1) \n  ){\n    nBuf--;\n  }\n\n  return p->xToken(p->pCtx, tflags, aBuf, nBuf, iStart, iEnd);\n\n pass_through:\n  return p->xToken(p->pCtx, tflags, pToken, nToken, iStart, iEnd);\n}\n\n/*\n** Tokenize using the porter tokenizer.\n*/\nstatic int fts5PorterTokenize(\n  Fts5Tokenizer *pTokenizer,\n  void *pCtx,\n  int flags,\n  const char *pText, int nText,\n  int (*xToken)(void*, int, const char*, int nToken, int iStart, int iEnd)\n){\n  PorterTokenizer *p = (PorterTokenizer*)pTokenizer;\n  PorterContext sCtx;\n  sCtx.xToken = xToken;\n  sCtx.pCtx = pCtx;\n  sCtx.aBuf = p->aBuf;\n  return p->tokenizer.xTokenize(\n      p->pTokenizer, (void*)&sCtx, flags, pText, nText, fts5PorterCb\n  );\n}\n\n/*\n** Register all built-in tokenizers with FTS5.\n*/\nstatic int sqlite3Fts5TokenizerInit(fts5_api *pApi){\n  struct BuiltinTokenizer {\n    const char *zName;\n    fts5_tokenizer x;\n  } aBuiltin[] = {\n    { \"unicode61\", {fts5UnicodeCreate, fts5UnicodeDelete, fts5UnicodeTokenize}},\n    { \"ascii\",     {fts5AsciiCreate, fts5AsciiDelete, fts5AsciiTokenize }},\n    { \"porter\",    {fts5PorterCreate, fts5PorterDelete, fts5PorterTokenize }},\n  };\n  \n  int rc = SQLITE_OK;             /* Return code */\n  int i;                          /* To iterate through builtin functions */\n\n  for(i=0; rc==SQLITE_OK && i<ArraySize(aBuiltin); i++){\n    rc = pApi->xCreateTokenizer(pApi,\n        aBuiltin[i].zName,\n        (void*)pApi,\n        &aBuiltin[i].x,\n        0\n    );\n  }\n\n  return rc;\n}\n\n\n\n/*\n** 2012 May 25\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n******************************************************************************\n*/\n\n/*\n** DO NOT EDIT THIS MACHINE GENERATED FILE.\n*/\n\n\n/* #include <assert.h> */\n\n/*\n** Return true if the argument corresponds to a unicode codepoint\n** classified as either a letter or a number. Otherwise false.\n**\n** The results are undefined if the value passed to this function\n** is less than zero.\n*/\nstatic int sqlite3Fts5UnicodeIsalnum(int c){\n  /* Each unsigned integer in the following array corresponds to a contiguous\n  ** range of unicode codepoints that are not either letters or numbers (i.e.\n  ** codepoints for which this function should return 0).\n  **\n  ** The most significant 22 bits in each 32-bit value contain the first \n  ** codepoint in the range. The least significant 10 bits are used to store\n  ** the size of the range (always at least 1). In other words, the value \n  ** ((C<<22) + N) represents a range of N codepoints starting with codepoint \n  ** C. It is not possible to represent a range larger than 1023 codepoints \n  ** using this format.\n  */\n  static const unsigned int aEntry[] = {\n    0x00000030, 0x0000E807, 0x00016C06, 0x0001EC2F, 0x0002AC07,\n    0x0002D001, 0x0002D803, 0x0002EC01, 0x0002FC01, 0x00035C01,\n    0x0003DC01, 0x000B0804, 0x000B480E, 0x000B9407, 0x000BB401,\n    0x000BBC81, 0x000DD401, 0x000DF801, 0x000E1002, 0x000E1C01,\n    0x000FD801, 0x00120808, 0x00156806, 0x00162402, 0x00163C01,\n    0x00164437, 0x0017CC02, 0x00180005, 0x00181816, 0x00187802,\n    0x00192C15, 0x0019A804, 0x0019C001, 0x001B5001, 0x001B580F,\n    0x001B9C07, 0x001BF402, 0x001C000E, 0x001C3C01, 0x001C4401,\n    0x001CC01B, 0x001E980B, 0x001FAC09, 0x001FD804, 0x00205804,\n    0x00206C09, 0x00209403, 0x0020A405, 0x0020C00F, 0x00216403,\n    0x00217801, 0x0023901B, 0x00240004, 0x0024E803, 0x0024F812,\n    0x00254407, 0x00258804, 0x0025C001, 0x00260403, 0x0026F001,\n    0x0026F807, 0x00271C02, 0x00272C03, 0x00275C01, 0x00278802,\n    0x0027C802, 0x0027E802, 0x00280403, 0x0028F001, 0x0028F805,\n    0x00291C02, 0x00292C03, 0x00294401, 0x0029C002, 0x0029D401,\n    0x002A0403, 0x002AF001, 0x002AF808, 0x002B1C03, 0x002B2C03,\n    0x002B8802, 0x002BC002, 0x002C0403, 0x002CF001, 0x002CF807,\n    0x002D1C02, 0x002D2C03, 0x002D5802, 0x002D8802, 0x002DC001,\n    0x002E0801, 0x002EF805, 0x002F1803, 0x002F2804, 0x002F5C01,\n    0x002FCC08, 0x00300403, 0x0030F807, 0x00311803, 0x00312804,\n    0x00315402, 0x00318802, 0x0031FC01, 0x00320802, 0x0032F001,\n    0x0032F807, 0x00331803, 0x00332804, 0x00335402, 0x00338802,\n    0x00340802, 0x0034F807, 0x00351803, 0x00352804, 0x00355C01,\n    0x00358802, 0x0035E401, 0x00360802, 0x00372801, 0x00373C06,\n    0x00375801, 0x00376008, 0x0037C803, 0x0038C401, 0x0038D007,\n    0x0038FC01, 0x00391C09, 0x00396802, 0x003AC401, 0x003AD006,\n    0x003AEC02, 0x003B2006, 0x003C041F, 0x003CD00C, 0x003DC417,\n    0x003E340B, 0x003E6424, 0x003EF80F, 0x003F380D, 0x0040AC14,\n    0x00412806, 0x00415804, 0x00417803, 0x00418803, 0x00419C07,\n    0x0041C404, 0x0042080C, 0x00423C01, 0x00426806, 0x0043EC01,\n    0x004D740C, 0x004E400A, 0x00500001, 0x0059B402, 0x005A0001,\n    0x005A6C02, 0x005BAC03, 0x005C4803, 0x005CC805, 0x005D4802,\n    0x005DC802, 0x005ED023, 0x005F6004, 0x005F7401, 0x0060000F,\n    0x0062A401, 0x0064800C, 0x0064C00C, 0x00650001, 0x00651002,\n    0x0066C011, 0x00672002, 0x00677822, 0x00685C05, 0x00687802,\n    0x0069540A, 0x0069801D, 0x0069FC01, 0x006A8007, 0x006AA006,\n    0x006C0005, 0x006CD011, 0x006D6823, 0x006E0003, 0x006E840D,\n    0x006F980E, 0x006FF004, 0x00709014, 0x0070EC05, 0x0071F802,\n    0x00730008, 0x00734019, 0x0073B401, 0x0073C803, 0x00770027,\n    0x0077F004, 0x007EF401, 0x007EFC03, 0x007F3403, 0x007F7403,\n    0x007FB403, 0x007FF402, 0x00800065, 0x0081A806, 0x0081E805,\n    0x00822805, 0x0082801A, 0x00834021, 0x00840002, 0x00840C04,\n    0x00842002, 0x00845001, 0x00845803, 0x00847806, 0x00849401,\n    0x00849C01, 0x0084A401, 0x0084B801, 0x0084E802, 0x00850005,\n    0x00852804, 0x00853C01, 0x00864264, 0x00900027, 0x0091000B,\n    0x0092704E, 0x00940200, 0x009C0475, 0x009E53B9, 0x00AD400A,\n    0x00B39406, 0x00B3BC03, 0x00B3E404, 0x00B3F802, 0x00B5C001,\n    0x00B5FC01, 0x00B7804F, 0x00B8C00C, 0x00BA001A, 0x00BA6C59,\n    0x00BC00D6, 0x00BFC00C, 0x00C00005, 0x00C02019, 0x00C0A807,\n    0x00C0D802, 0x00C0F403, 0x00C26404, 0x00C28001, 0x00C3EC01,\n    0x00C64002, 0x00C6580A, 0x00C70024, 0x00C8001F, 0x00C8A81E,\n    0x00C94001, 0x00C98020, 0x00CA2827, 0x00CB003F, 0x00CC0100,\n    0x01370040, 0x02924037, 0x0293F802, 0x02983403, 0x0299BC10,\n    0x029A7C01, 0x029BC008, 0x029C0017, 0x029C8002, 0x029E2402,\n    0x02A00801, 0x02A01801, 0x02A02C01, 0x02A08C09, 0x02A0D804,\n    0x02A1D004, 0x02A20002, 0x02A2D011, 0x02A33802, 0x02A38012,\n    0x02A3E003, 0x02A4980A, 0x02A51C0D, 0x02A57C01, 0x02A60004,\n    0x02A6CC1B, 0x02A77802, 0x02A8A40E, 0x02A90C01, 0x02A93002,\n    0x02A97004, 0x02A9DC03, 0x02A9EC01, 0x02AAC001, 0x02AAC803,\n    0x02AADC02, 0x02AAF802, 0x02AB0401, 0x02AB7802, 0x02ABAC07,\n    0x02ABD402, 0x02AF8C0B, 0x03600001, 0x036DFC02, 0x036FFC02,\n    0x037FFC01, 0x03EC7801, 0x03ECA401, 0x03EEC810, 0x03F4F802,\n    0x03F7F002, 0x03F8001A, 0x03F88007, 0x03F8C023, 0x03F95013,\n    0x03F9A004, 0x03FBFC01, 0x03FC040F, 0x03FC6807, 0x03FCEC06,\n    0x03FD6C0B, 0x03FF8007, 0x03FFA007, 0x03FFE405, 0x04040003,\n    0x0404DC09, 0x0405E411, 0x0406400C, 0x0407402E, 0x040E7C01,\n    0x040F4001, 0x04215C01, 0x04247C01, 0x0424FC01, 0x04280403,\n    0x04281402, 0x04283004, 0x0428E003, 0x0428FC01, 0x04294009,\n    0x0429FC01, 0x042CE407, 0x04400003, 0x0440E016, 0x04420003,\n    0x0442C012, 0x04440003, 0x04449C0E, 0x04450004, 0x04460003,\n    0x0446CC0E, 0x04471404, 0x045AAC0D, 0x0491C004, 0x05BD442E,\n    0x05BE3C04, 0x074000F6, 0x07440027, 0x0744A4B5, 0x07480046,\n    0x074C0057, 0x075B0401, 0x075B6C01, 0x075BEC01, 0x075C5401,\n    0x075CD401, 0x075D3C01, 0x075DBC01, 0x075E2401, 0x075EA401,\n    0x075F0C01, 0x07BBC002, 0x07C0002C, 0x07C0C064, 0x07C2800F,\n    0x07C2C40E, 0x07C3040F, 0x07C3440F, 0x07C4401F, 0x07C4C03C,\n    0x07C5C02B, 0x07C7981D, 0x07C8402B, 0x07C90009, 0x07C94002,\n    0x07CC0021, 0x07CCC006, 0x07CCDC46, 0x07CE0014, 0x07CE8025,\n    0x07CF1805, 0x07CF8011, 0x07D0003F, 0x07D10001, 0x07D108B6,\n    0x07D3E404, 0x07D4003E, 0x07D50004, 0x07D54018, 0x07D7EC46,\n    0x07D9140B, 0x07DA0046, 0x07DC0074, 0x38000401, 0x38008060,\n    0x380400F0,\n  };\n  static const unsigned int aAscii[4] = {\n    0xFFFFFFFF, 0xFC00FFFF, 0xF8000001, 0xF8000001,\n  };\n\n  if( (unsigned int)c<128 ){\n    return ( (aAscii[c >> 5] & (1 << (c & 0x001F)))==0 );\n  }else if( (unsigned int)c<(1<<22) ){\n    unsigned int key = (((unsigned int)c)<<10) | 0x000003FF;\n    int iRes = 0;\n    int iHi = sizeof(aEntry)/sizeof(aEntry[0]) - 1;\n    int iLo = 0;\n    while( iHi>=iLo ){\n      int iTest = (iHi + iLo) / 2;\n      if( key >= aEntry[iTest] ){\n        iRes = iTest;\n        iLo = iTest+1;\n      }else{\n        iHi = iTest-1;\n      }\n    }\n    assert( aEntry[0]<key );\n    assert( key>=aEntry[iRes] );\n    return (((unsigned int)c) >= ((aEntry[iRes]>>10) + (aEntry[iRes]&0x3FF)));\n  }\n  return 1;\n}\n\n\n/*\n** If the argument is a codepoint corresponding to a lowercase letter\n** in the ASCII range with a diacritic added, return the codepoint\n** of the ASCII letter only. For example, if passed 235 - \"LATIN\n** SMALL LETTER E WITH DIAERESIS\" - return 65 (\"LATIN SMALL LETTER\n** E\"). The resuls of passing a codepoint that corresponds to an\n** uppercase letter are undefined.\n*/\nstatic int fts5_remove_diacritic(int c){\n  unsigned short aDia[] = {\n        0,  1797,  1848,  1859,  1891,  1928,  1940,  1995, \n     2024,  2040,  2060,  2110,  2168,  2206,  2264,  2286, \n     2344,  2383,  2472,  2488,  2516,  2596,  2668,  2732, \n     2782,  2842,  2894,  2954,  2984,  3000,  3028,  3336, \n     3456,  3696,  3712,  3728,  3744,  3896,  3912,  3928, \n     3968,  4008,  4040,  4106,  4138,  4170,  4202,  4234, \n     4266,  4296,  4312,  4344,  4408,  4424,  4472,  4504, \n     6148,  6198,  6264,  6280,  6360,  6429,  6505,  6529, \n    61448, 61468, 61534, 61592, 61642, 61688, 61704, 61726, \n    61784, 61800, 61836, 61880, 61914, 61948, 61998, 62122, \n    62154, 62200, 62218, 62302, 62364, 62442, 62478, 62536, \n    62554, 62584, 62604, 62640, 62648, 62656, 62664, 62730, \n    62924, 63050, 63082, 63274, 63390, \n  };\n  char aChar[] = {\n    '\\0', 'a',  'c',  'e',  'i',  'n',  'o',  'u',  'y',  'y',  'a',  'c',  \n    'd',  'e',  'e',  'g',  'h',  'i',  'j',  'k',  'l',  'n',  'o',  'r',  \n    's',  't',  'u',  'u',  'w',  'y',  'z',  'o',  'u',  'a',  'i',  'o',  \n    'u',  'g',  'k',  'o',  'j',  'g',  'n',  'a',  'e',  'i',  'o',  'r',  \n    'u',  's',  't',  'h',  'a',  'e',  'o',  'y',  '\\0', '\\0', '\\0', '\\0', \n    '\\0', '\\0', '\\0', '\\0', 'a',  'b',  'd',  'd',  'e',  'f',  'g',  'h',  \n    'h',  'i',  'k',  'l',  'l',  'm',  'n',  'p',  'r',  'r',  's',  't',  \n    'u',  'v',  'w',  'w',  'x',  'y',  'z',  'h',  't',  'w',  'y',  'a',  \n    'e',  'i',  'o',  'u',  'y',  \n  };\n\n  unsigned int key = (((unsigned int)c)<<3) | 0x00000007;\n  int iRes = 0;\n  int iHi = sizeof(aDia)/sizeof(aDia[0]) - 1;\n  int iLo = 0;\n  while( iHi>=iLo ){\n    int iTest = (iHi + iLo) / 2;\n    if( key >= aDia[iTest] ){\n      iRes = iTest;\n      iLo = iTest+1;\n    }else{\n      iHi = iTest-1;\n    }\n  }\n  assert( key>=aDia[iRes] );\n  return ((c > (aDia[iRes]>>3) + (aDia[iRes]&0x07)) ? c : (int)aChar[iRes]);\n}\n\n\n/*\n** Return true if the argument interpreted as a unicode codepoint\n** is a diacritical modifier character.\n*/\nstatic int sqlite3Fts5UnicodeIsdiacritic(int c){\n  unsigned int mask0 = 0x08029FDF;\n  unsigned int mask1 = 0x000361F8;\n  if( c<768 || c>817 ) return 0;\n  return (c < 768+32) ?\n      (mask0 & (1 << (c-768))) :\n      (mask1 & (1 << (c-768-32)));\n}\n\n\n/*\n** Interpret the argument as a unicode codepoint. If the codepoint\n** is an upper case character that has a lower case equivalent,\n** return the codepoint corresponding to the lower case version.\n** Otherwise, return a copy of the argument.\n**\n** The results are undefined if the value passed to this function\n** is less than zero.\n*/\nstatic int sqlite3Fts5UnicodeFold(int c, int bRemoveDiacritic){\n  /* Each entry in the following array defines a rule for folding a range\n  ** of codepoints to lower case. The rule applies to a range of nRange\n  ** codepoints starting at codepoint iCode.\n  **\n  ** If the least significant bit in flags is clear, then the rule applies\n  ** to all nRange codepoints (i.e. all nRange codepoints are upper case and\n  ** need to be folded). Or, if it is set, then the rule only applies to\n  ** every second codepoint in the range, starting with codepoint C.\n  **\n  ** The 7 most significant bits in flags are an index into the aiOff[]\n  ** array. If a specific codepoint C does require folding, then its lower\n  ** case equivalent is ((C + aiOff[flags>>1]) & 0xFFFF).\n  **\n  ** The contents of this array are generated by parsing the CaseFolding.txt\n  ** file distributed as part of the \"Unicode Character Database\". See\n  ** http://www.unicode.org for details.\n  */\n  static const struct TableEntry {\n    unsigned short iCode;\n    unsigned char flags;\n    unsigned char nRange;\n  } aEntry[] = {\n    {65, 14, 26},          {181, 64, 1},          {192, 14, 23},\n    {216, 14, 7},          {256, 1, 48},          {306, 1, 6},\n    {313, 1, 16},          {330, 1, 46},          {376, 116, 1},\n    {377, 1, 6},           {383, 104, 1},         {385, 50, 1},\n    {386, 1, 4},           {390, 44, 1},          {391, 0, 1},\n    {393, 42, 2},          {395, 0, 1},           {398, 32, 1},\n    {399, 38, 1},          {400, 40, 1},          {401, 0, 1},\n    {403, 42, 1},          {404, 46, 1},          {406, 52, 1},\n    {407, 48, 1},          {408, 0, 1},           {412, 52, 1},\n    {413, 54, 1},          {415, 56, 1},          {416, 1, 6},\n    {422, 60, 1},          {423, 0, 1},           {425, 60, 1},\n    {428, 0, 1},           {430, 60, 1},          {431, 0, 1},\n    {433, 58, 2},          {435, 1, 4},           {439, 62, 1},\n    {440, 0, 1},           {444, 0, 1},           {452, 2, 1},\n    {453, 0, 1},           {455, 2, 1},           {456, 0, 1},\n    {458, 2, 1},           {459, 1, 18},          {478, 1, 18},\n    {497, 2, 1},           {498, 1, 4},           {502, 122, 1},\n    {503, 134, 1},         {504, 1, 40},          {544, 110, 1},\n    {546, 1, 18},          {570, 70, 1},          {571, 0, 1},\n    {573, 108, 1},         {574, 68, 1},          {577, 0, 1},\n    {579, 106, 1},         {580, 28, 1},          {581, 30, 1},\n    {582, 1, 10},          {837, 36, 1},          {880, 1, 4},\n    {886, 0, 1},           {902, 18, 1},          {904, 16, 3},\n    {908, 26, 1},          {910, 24, 2},          {913, 14, 17},\n    {931, 14, 9},          {962, 0, 1},           {975, 4, 1},\n    {976, 140, 1},         {977, 142, 1},         {981, 146, 1},\n    {982, 144, 1},         {984, 1, 24},          {1008, 136, 1},\n    {1009, 138, 1},        {1012, 130, 1},        {1013, 128, 1},\n    {1015, 0, 1},          {1017, 152, 1},        {1018, 0, 1},\n    {1021, 110, 3},        {1024, 34, 16},        {1040, 14, 32},\n    {1120, 1, 34},         {1162, 1, 54},         {1216, 6, 1},\n    {1217, 1, 14},         {1232, 1, 88},         {1329, 22, 38},\n    {4256, 66, 38},        {4295, 66, 1},         {4301, 66, 1},\n    {7680, 1, 150},        {7835, 132, 1},        {7838, 96, 1},\n    {7840, 1, 96},         {7944, 150, 8},        {7960, 150, 6},\n    {7976, 150, 8},        {7992, 150, 8},        {8008, 150, 6},\n    {8025, 151, 8},        {8040, 150, 8},        {8072, 150, 8},\n    {8088, 150, 8},        {8104, 150, 8},        {8120, 150, 2},\n    {8122, 126, 2},        {8124, 148, 1},        {8126, 100, 1},\n    {8136, 124, 4},        {8140, 148, 1},        {8152, 150, 2},\n    {8154, 120, 2},        {8168, 150, 2},        {8170, 118, 2},\n    {8172, 152, 1},        {8184, 112, 2},        {8186, 114, 2},\n    {8188, 148, 1},        {8486, 98, 1},         {8490, 92, 1},\n    {8491, 94, 1},         {8498, 12, 1},         {8544, 8, 16},\n    {8579, 0, 1},          {9398, 10, 26},        {11264, 22, 47},\n    {11360, 0, 1},         {11362, 88, 1},        {11363, 102, 1},\n    {11364, 90, 1},        {11367, 1, 6},         {11373, 84, 1},\n    {11374, 86, 1},        {11375, 80, 1},        {11376, 82, 1},\n    {11378, 0, 1},         {11381, 0, 1},         {11390, 78, 2},\n    {11392, 1, 100},       {11499, 1, 4},         {11506, 0, 1},\n    {42560, 1, 46},        {42624, 1, 24},        {42786, 1, 14},\n    {42802, 1, 62},        {42873, 1, 4},         {42877, 76, 1},\n    {42878, 1, 10},        {42891, 0, 1},         {42893, 74, 1},\n    {42896, 1, 4},         {42912, 1, 10},        {42922, 72, 1},\n    {65313, 14, 26},       \n  };\n  static const unsigned short aiOff[] = {\n   1,     2,     8,     15,    16,    26,    28,    32,    \n   37,    38,    40,    48,    63,    64,    69,    71,    \n   79,    80,    116,   202,   203,   205,   206,   207,   \n   209,   210,   211,   213,   214,   217,   218,   219,   \n   775,   7264,  10792, 10795, 23228, 23256, 30204, 54721, \n   54753, 54754, 54756, 54787, 54793, 54809, 57153, 57274, \n   57921, 58019, 58363, 61722, 65268, 65341, 65373, 65406, \n   65408, 65410, 65415, 65424, 65436, 65439, 65450, 65462, \n   65472, 65476, 65478, 65480, 65482, 65488, 65506, 65511, \n   65514, 65521, 65527, 65528, 65529, \n  };\n\n  int ret = c;\n\n  assert( sizeof(unsigned short)==2 && sizeof(unsigned char)==1 );\n\n  if( c<128 ){\n    if( c>='A' && c<='Z' ) ret = c + ('a' - 'A');\n  }else if( c<65536 ){\n    const struct TableEntry *p;\n    int iHi = sizeof(aEntry)/sizeof(aEntry[0]) - 1;\n    int iLo = 0;\n    int iRes = -1;\n\n    assert( c>aEntry[0].iCode );\n    while( iHi>=iLo ){\n      int iTest = (iHi + iLo) / 2;\n      int cmp = (c - aEntry[iTest].iCode);\n      if( cmp>=0 ){\n        iRes = iTest;\n        iLo = iTest+1;\n      }else{\n        iHi = iTest-1;\n      }\n    }\n\n    assert( iRes>=0 && c>=aEntry[iRes].iCode );\n    p = &aEntry[iRes];\n    if( c<(p->iCode + p->nRange) && 0==(0x01 & p->flags & (p->iCode ^ c)) ){\n      ret = (c + (aiOff[p->flags>>1])) & 0x0000FFFF;\n      assert( ret>0 );\n    }\n\n    if( bRemoveDiacritic ) ret = fts5_remove_diacritic(ret);\n  }\n  \n  else if( c>=66560 && c<66600 ){\n    ret = c + 40;\n  }\n\n  return ret;\n}\n\n/*\n** 2015 May 30\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n******************************************************************************\n**\n** Routines for varint serialization and deserialization.\n*/\n\n\n/* #include \"fts5Int.h\" */\n\n/*\n** This is a copy of the sqlite3GetVarint32() routine from the SQLite core.\n** Except, this version does handle the single byte case that the core\n** version depends on being handled before its function is called.\n*/\nstatic int sqlite3Fts5GetVarint32(const unsigned char *p, u32 *v){\n  u32 a,b;\n\n  /* The 1-byte case. Overwhelmingly the most common. */\n  a = *p;\n  /* a: p0 (unmasked) */\n  if (!(a&0x80))\n  {\n    /* Values between 0 and 127 */\n    *v = a;\n    return 1;\n  }\n\n  /* The 2-byte case */\n  p++;\n  b = *p;\n  /* b: p1 (unmasked) */\n  if (!(b&0x80))\n  {\n    /* Values between 128 and 16383 */\n    a &= 0x7f;\n    a = a<<7;\n    *v = a | b;\n    return 2;\n  }\n\n  /* The 3-byte case */\n  p++;\n  a = a<<14;\n  a |= *p;\n  /* a: p0<<14 | p2 (unmasked) */\n  if (!(a&0x80))\n  {\n    /* Values between 16384 and 2097151 */\n    a &= (0x7f<<14)|(0x7f);\n    b &= 0x7f;\n    b = b<<7;\n    *v = a | b;\n    return 3;\n  }\n\n  /* A 32-bit varint is used to store size information in btrees.\n  ** Objects are rarely larger than 2MiB limit of a 3-byte varint.\n  ** A 3-byte varint is sufficient, for example, to record the size\n  ** of a 1048569-byte BLOB or string.\n  **\n  ** We only unroll the first 1-, 2-, and 3- byte cases.  The very\n  ** rare larger cases can be handled by the slower 64-bit varint\n  ** routine.\n  */\n  {\n    u64 v64;\n    u8 n;\n    p -= 2;\n    n = sqlite3Fts5GetVarint(p, &v64);\n    *v = (u32)v64;\n    assert( n>3 && n<=9 );\n    return n;\n  }\n}\n\n\n/*\n** Bitmasks used by sqlite3GetVarint().  These precomputed constants\n** are defined here rather than simply putting the constant expressions\n** inline in order to work around bugs in the RVT compiler.\n**\n** SLOT_2_0     A mask for  (0x7f<<14) | 0x7f\n**\n** SLOT_4_2_0   A mask for  (0x7f<<28) | SLOT_2_0\n*/\n#define SLOT_2_0     0x001fc07f\n#define SLOT_4_2_0   0xf01fc07f\n\n/*\n** Read a 64-bit variable-length integer from memory starting at p[0].\n** Return the number of bytes read.  The value is stored in *v.\n*/\nstatic u8 sqlite3Fts5GetVarint(const unsigned char *p, u64 *v){\n  u32 a,b,s;\n\n  a = *p;\n  /* a: p0 (unmasked) */\n  if (!(a&0x80))\n  {\n    *v = a;\n    return 1;\n  }\n\n  p++;\n  b = *p;\n  /* b: p1 (unmasked) */\n  if (!(b&0x80))\n  {\n    a &= 0x7f;\n    a = a<<7;\n    a |= b;\n    *v = a;\n    return 2;\n  }\n\n  /* Verify that constants are precomputed correctly */\n  assert( SLOT_2_0 == ((0x7f<<14) | (0x7f)) );\n  assert( SLOT_4_2_0 == ((0xfU<<28) | (0x7f<<14) | (0x7f)) );\n\n  p++;\n  a = a<<14;\n  a |= *p;\n  /* a: p0<<14 | p2 (unmasked) */\n  if (!(a&0x80))\n  {\n    a &= SLOT_2_0;\n    b &= 0x7f;\n    b = b<<7;\n    a |= b;\n    *v = a;\n    return 3;\n  }\n\n  /* CSE1 from below */\n  a &= SLOT_2_0;\n  p++;\n  b = b<<14;\n  b |= *p;\n  /* b: p1<<14 | p3 (unmasked) */\n  if (!(b&0x80))\n  {\n    b &= SLOT_2_0;\n    /* moved CSE1 up */\n    /* a &= (0x7f<<14)|(0x7f); */\n    a = a<<7;\n    a |= b;\n    *v = a;\n    return 4;\n  }\n\n  /* a: p0<<14 | p2 (masked) */\n  /* b: p1<<14 | p3 (unmasked) */\n  /* 1:save off p0<<21 | p1<<14 | p2<<7 | p3 (masked) */\n  /* moved CSE1 up */\n  /* a &= (0x7f<<14)|(0x7f); */\n  b &= SLOT_2_0;\n  s = a;\n  /* s: p0<<14 | p2 (masked) */\n\n  p++;\n  a = a<<14;\n  a |= *p;\n  /* a: p0<<28 | p2<<14 | p4 (unmasked) */\n  if (!(a&0x80))\n  {\n    /* we can skip these cause they were (effectively) done above in calc'ing s */\n    /* a &= (0x7f<<28)|(0x7f<<14)|(0x7f); */\n    /* b &= (0x7f<<14)|(0x7f); */\n    b = b<<7;\n    a |= b;\n    s = s>>18;\n    *v = ((u64)s)<<32 | a;\n    return 5;\n  }\n\n  /* 2:save off p0<<21 | p1<<14 | p2<<7 | p3 (masked) */\n  s = s<<7;\n  s |= b;\n  /* s: p0<<21 | p1<<14 | p2<<7 | p3 (masked) */\n\n  p++;\n  b = b<<14;\n  b |= *p;\n  /* b: p1<<28 | p3<<14 | p5 (unmasked) */\n  if (!(b&0x80))\n  {\n    /* we can skip this cause it was (effectively) done above in calc'ing s */\n    /* b &= (0x7f<<28)|(0x7f<<14)|(0x7f); */\n    a &= SLOT_2_0;\n    a = a<<7;\n    a |= b;\n    s = s>>18;\n    *v = ((u64)s)<<32 | a;\n    return 6;\n  }\n\n  p++;\n  a = a<<14;\n  a |= *p;\n  /* a: p2<<28 | p4<<14 | p6 (unmasked) */\n  if (!(a&0x80))\n  {\n    a &= SLOT_4_2_0;\n    b &= SLOT_2_0;\n    b = b<<7;\n    a |= b;\n    s = s>>11;\n    *v = ((u64)s)<<32 | a;\n    return 7;\n  }\n\n  /* CSE2 from below */\n  a &= SLOT_2_0;\n  p++;\n  b = b<<14;\n  b |= *p;\n  /* b: p3<<28 | p5<<14 | p7 (unmasked) */\n  if (!(b&0x80))\n  {\n    b &= SLOT_4_2_0;\n    /* moved CSE2 up */\n    /* a &= (0x7f<<14)|(0x7f); */\n    a = a<<7;\n    a |= b;\n    s = s>>4;\n    *v = ((u64)s)<<32 | a;\n    return 8;\n  }\n\n  p++;\n  a = a<<15;\n  a |= *p;\n  /* a: p4<<29 | p6<<15 | p8 (unmasked) */\n\n  /* moved CSE2 up */\n  /* a &= (0x7f<<29)|(0x7f<<15)|(0xff); */\n  b &= SLOT_2_0;\n  b = b<<8;\n  a |= b;\n\n  s = s<<4;\n  b = p[-4];\n  b &= 0x7f;\n  b = b>>3;\n  s |= b;\n\n  *v = ((u64)s)<<32 | a;\n\n  return 9;\n}\n\n/*\n** The variable-length integer encoding is as follows:\n**\n** KEY:\n**         A = 0xxxxxxx    7 bits of data and one flag bit\n**         B = 1xxxxxxx    7 bits of data and one flag bit\n**         C = xxxxxxxx    8 bits of data\n**\n**  7 bits - A\n** 14 bits - BA\n** 21 bits - BBA\n** 28 bits - BBBA\n** 35 bits - BBBBA\n** 42 bits - BBBBBA\n** 49 bits - BBBBBBA\n** 56 bits - BBBBBBBA\n** 64 bits - BBBBBBBBC\n*/\n\n#ifdef SQLITE_NOINLINE\n# define FTS5_NOINLINE SQLITE_NOINLINE\n#else\n# define FTS5_NOINLINE\n#endif\n\n/*\n** Write a 64-bit variable-length integer to memory starting at p[0].\n** The length of data write will be between 1 and 9 bytes.  The number\n** of bytes written is returned.\n**\n** A variable-length integer consists of the lower 7 bits of each byte\n** for all bytes that have the 8th bit set and one byte with the 8th\n** bit clear.  Except, if we get to the 9th byte, it stores the full\n** 8 bits and is the last byte.\n*/\nstatic int FTS5_NOINLINE fts5PutVarint64(unsigned char *p, u64 v){\n  int i, j, n;\n  u8 buf[10];\n  if( v & (((u64)0xff000000)<<32) ){\n    p[8] = (u8)v;\n    v >>= 8;\n    for(i=7; i>=0; i--){\n      p[i] = (u8)((v & 0x7f) | 0x80);\n      v >>= 7;\n    }\n    return 9;\n  }    \n  n = 0;\n  do{\n    buf[n++] = (u8)((v & 0x7f) | 0x80);\n    v >>= 7;\n  }while( v!=0 );\n  buf[0] &= 0x7f;\n  assert( n<=9 );\n  for(i=0, j=n-1; j>=0; j--, i++){\n    p[i] = buf[j];\n  }\n  return n;\n}\n\nstatic int sqlite3Fts5PutVarint(unsigned char *p, u64 v){\n  if( v<=0x7f ){\n    p[0] = v&0x7f;\n    return 1;\n  }\n  if( v<=0x3fff ){\n    p[0] = ((v>>7)&0x7f)|0x80;\n    p[1] = v&0x7f;\n    return 2;\n  }\n  return fts5PutVarint64(p,v);\n}\n\n\nstatic int sqlite3Fts5GetVarintLen(u32 iVal){\n#if 0\n  if( iVal<(1 << 7 ) ) return 1;\n#endif\n  assert( iVal>=(1 << 7) );\n  if( iVal<(1 << 14) ) return 2;\n  if( iVal<(1 << 21) ) return 3;\n  if( iVal<(1 << 28) ) return 4;\n  return 5;\n}\n\n\n/*\n** 2015 May 08\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n******************************************************************************\n**\n** This is an SQLite virtual table module implementing direct access to an\n** existing FTS5 index. The module may create several different types of \n** tables:\n**\n** col:\n**     CREATE TABLE vocab(term, col, doc, cnt, PRIMARY KEY(term, col));\n**\n**   One row for each term/column combination. The value of $doc is set to\n**   the number of fts5 rows that contain at least one instance of term\n**   $term within column $col. Field $cnt is set to the total number of \n**   instances of term $term in column $col (in any row of the fts5 table). \n**\n** row:\n**     CREATE TABLE vocab(term, doc, cnt, PRIMARY KEY(term));\n**\n**   One row for each term in the database. The value of $doc is set to\n**   the number of fts5 rows that contain at least one instance of term\n**   $term. Field $cnt is set to the total number of instances of term \n**   $term in the database.\n**\n** instance:\n**     CREATE TABLE vocab(term, doc, col, offset, PRIMARY KEY(<all-fields>));\n**\n**   One row for each term instance in the database. \n*/\n\n\n/* #include \"fts5Int.h\" */\n\n\ntypedef struct Fts5VocabTable Fts5VocabTable;\ntypedef struct Fts5VocabCursor Fts5VocabCursor;\n\nstruct Fts5VocabTable {\n  sqlite3_vtab base;\n  char *zFts5Tbl;                 /* Name of fts5 table */\n  char *zFts5Db;                  /* Db containing fts5 table */\n  sqlite3 *db;                    /* Database handle */\n  Fts5Global *pGlobal;            /* FTS5 global object for this database */\n  int eType;                      /* FTS5_VOCAB_COL, ROW or INSTANCE */\n};\n\nstruct Fts5VocabCursor {\n  sqlite3_vtab_cursor base;\n  sqlite3_stmt *pStmt;            /* Statement holding lock on pIndex */\n  Fts5Index *pIndex;              /* Associated FTS5 index */\n\n  int bEof;                       /* True if this cursor is at EOF */\n  Fts5IndexIter *pIter;           /* Term/rowid iterator object */\n\n  int nLeTerm;                    /* Size of zLeTerm in bytes */\n  char *zLeTerm;                  /* (term <= $zLeTerm) paramater, or NULL */\n\n  /* These are used by 'col' tables only */\n  Fts5Config *pConfig;            /* Fts5 table configuration */\n  int iCol;\n  i64 *aCnt;\n  i64 *aDoc;\n\n  /* Output values used by all tables. */\n  i64 rowid;                      /* This table's current rowid value */\n  Fts5Buffer term;                /* Current value of 'term' column */\n\n  /* Output values Used by 'instance' tables only */\n  i64 iInstPos;\n  int iInstOff;\n};\n\n#define FTS5_VOCAB_COL      0\n#define FTS5_VOCAB_ROW      1\n#define FTS5_VOCAB_INSTANCE 2\n\n#define FTS5_VOCAB_COL_SCHEMA  \"term, col, doc, cnt\"\n#define FTS5_VOCAB_ROW_SCHEMA  \"term, doc, cnt\"\n#define FTS5_VOCAB_INST_SCHEMA \"term, doc, col, offset\"\n\n/*\n** Bits for the mask used as the idxNum value by xBestIndex/xFilter.\n*/\n#define FTS5_VOCAB_TERM_EQ 0x01\n#define FTS5_VOCAB_TERM_GE 0x02\n#define FTS5_VOCAB_TERM_LE 0x04\n\n\n/*\n** Translate a string containing an fts5vocab table type to an \n** FTS5_VOCAB_XXX constant. If successful, set *peType to the output\n** value and return SQLITE_OK. Otherwise, set *pzErr to an error message\n** and return SQLITE_ERROR.\n*/\nstatic int fts5VocabTableType(const char *zType, char **pzErr, int *peType){\n  int rc = SQLITE_OK;\n  char *zCopy = sqlite3Fts5Strndup(&rc, zType, -1);\n  if( rc==SQLITE_OK ){\n    sqlite3Fts5Dequote(zCopy);\n    if( sqlite3_stricmp(zCopy, \"col\")==0 ){\n      *peType = FTS5_VOCAB_COL;\n    }else\n\n    if( sqlite3_stricmp(zCopy, \"row\")==0 ){\n      *peType = FTS5_VOCAB_ROW;\n    }else\n    if( sqlite3_stricmp(zCopy, \"instance\")==0 ){\n      *peType = FTS5_VOCAB_INSTANCE;\n    }else\n    {\n      *pzErr = sqlite3_mprintf(\"fts5vocab: unknown table type: %Q\", zCopy);\n      rc = SQLITE_ERROR;\n    }\n    sqlite3_free(zCopy);\n  }\n\n  return rc;\n}\n\n\n/*\n** The xDisconnect() virtual table method.\n*/\nstatic int fts5VocabDisconnectMethod(sqlite3_vtab *pVtab){\n  Fts5VocabTable *pTab = (Fts5VocabTable*)pVtab;\n  sqlite3_free(pTab);\n  return SQLITE_OK;\n}\n\n/*\n** The xDestroy() virtual table method.\n*/\nstatic int fts5VocabDestroyMethod(sqlite3_vtab *pVtab){\n  Fts5VocabTable *pTab = (Fts5VocabTable*)pVtab;\n  sqlite3_free(pTab);\n  return SQLITE_OK;\n}\n\n/*\n** This function is the implementation of both the xConnect and xCreate\n** methods of the FTS3 virtual table.\n**\n** The argv[] array contains the following:\n**\n**   argv[0]   -> module name  (\"fts5vocab\")\n**   argv[1]   -> database name\n**   argv[2]   -> table name\n**\n** then:\n**\n**   argv[3]   -> name of fts5 table\n**   argv[4]   -> type of fts5vocab table\n**\n** or, for tables in the TEMP schema only.\n**\n**   argv[3]   -> name of fts5 tables database\n**   argv[4]   -> name of fts5 table\n**   argv[5]   -> type of fts5vocab table\n*/\nstatic int fts5VocabInitVtab(\n  sqlite3 *db,                    /* The SQLite database connection */\n  void *pAux,                     /* Pointer to Fts5Global object */\n  int argc,                       /* Number of elements in argv array */\n  const char * const *argv,       /* xCreate/xConnect argument array */\n  sqlite3_vtab **ppVTab,          /* Write the resulting vtab structure here */\n  char **pzErr                    /* Write any error message here */\n){\n  const char *azSchema[] = { \n    \"CREATE TABlE vocab(\" FTS5_VOCAB_COL_SCHEMA  \")\", \n    \"CREATE TABlE vocab(\" FTS5_VOCAB_ROW_SCHEMA  \")\",\n    \"CREATE TABlE vocab(\" FTS5_VOCAB_INST_SCHEMA \")\"\n  };\n\n  Fts5VocabTable *pRet = 0;\n  int rc = SQLITE_OK;             /* Return code */\n  int bDb;\n\n  bDb = (argc==6 && strlen(argv[1])==4 && memcmp(\"temp\", argv[1], 4)==0);\n\n  if( argc!=5 && bDb==0 ){\n    *pzErr = sqlite3_mprintf(\"wrong number of vtable arguments\");\n    rc = SQLITE_ERROR;\n  }else{\n    int nByte;                      /* Bytes of space to allocate */\n    const char *zDb = bDb ? argv[3] : argv[1];\n    const char *zTab = bDb ? argv[4] : argv[3];\n    const char *zType = bDb ? argv[5] : argv[4];\n    int nDb = (int)strlen(zDb)+1; \n    int nTab = (int)strlen(zTab)+1;\n    int eType = 0;\n    \n    rc = fts5VocabTableType(zType, pzErr, &eType);\n    if( rc==SQLITE_OK ){\n      assert( eType>=0 && eType<ArraySize(azSchema) );\n      rc = sqlite3_declare_vtab(db, azSchema[eType]);\n    }\n\n    nByte = sizeof(Fts5VocabTable) + nDb + nTab;\n    pRet = sqlite3Fts5MallocZero(&rc, nByte);\n    if( pRet ){\n      pRet->pGlobal = (Fts5Global*)pAux;\n      pRet->eType = eType;\n      pRet->db = db;\n      pRet->zFts5Tbl = (char*)&pRet[1];\n      pRet->zFts5Db = &pRet->zFts5Tbl[nTab];\n      memcpy(pRet->zFts5Tbl, zTab, nTab);\n      memcpy(pRet->zFts5Db, zDb, nDb);\n      sqlite3Fts5Dequote(pRet->zFts5Tbl);\n      sqlite3Fts5Dequote(pRet->zFts5Db);\n    }\n  }\n\n  *ppVTab = (sqlite3_vtab*)pRet;\n  return rc;\n}\n\n\n/*\n** The xConnect() and xCreate() methods for the virtual table. All the\n** work is done in function fts5VocabInitVtab().\n*/\nstatic int fts5VocabConnectMethod(\n  sqlite3 *db,                    /* Database connection */\n  void *pAux,                     /* Pointer to tokenizer hash table */\n  int argc,                       /* Number of elements in argv array */\n  const char * const *argv,       /* xCreate/xConnect argument array */\n  sqlite3_vtab **ppVtab,          /* OUT: New sqlite3_vtab object */\n  char **pzErr                    /* OUT: sqlite3_malloc'd error message */\n){\n  return fts5VocabInitVtab(db, pAux, argc, argv, ppVtab, pzErr);\n}\nstatic int fts5VocabCreateMethod(\n  sqlite3 *db,                    /* Database connection */\n  void *pAux,                     /* Pointer to tokenizer hash table */\n  int argc,                       /* Number of elements in argv array */\n  const char * const *argv,       /* xCreate/xConnect argument array */\n  sqlite3_vtab **ppVtab,          /* OUT: New sqlite3_vtab object */\n  char **pzErr                    /* OUT: sqlite3_malloc'd error message */\n){\n  return fts5VocabInitVtab(db, pAux, argc, argv, ppVtab, pzErr);\n}\n\n/* \n** Implementation of the xBestIndex method.\n**\n** Only constraints of the form:\n**\n**     term <= ?\n**     term == ?\n**     term >= ?\n**\n** are interpreted. Less-than and less-than-or-equal are treated \n** identically, as are greater-than and greater-than-or-equal.\n*/\nstatic int fts5VocabBestIndexMethod(\n  sqlite3_vtab *pUnused,\n  sqlite3_index_info *pInfo\n){\n  int i;\n  int iTermEq = -1;\n  int iTermGe = -1;\n  int iTermLe = -1;\n  int idxNum = 0;\n  int nArg = 0;\n\n  UNUSED_PARAM(pUnused);\n\n  for(i=0; i<pInfo->nConstraint; i++){\n    struct sqlite3_index_constraint *p = &pInfo->aConstraint[i];\n    if( p->usable==0 ) continue;\n    if( p->iColumn==0 ){          /* term column */\n      if( p->op==SQLITE_INDEX_CONSTRAINT_EQ ) iTermEq = i;\n      if( p->op==SQLITE_INDEX_CONSTRAINT_LE ) iTermLe = i;\n      if( p->op==SQLITE_INDEX_CONSTRAINT_LT ) iTermLe = i;\n      if( p->op==SQLITE_INDEX_CONSTRAINT_GE ) iTermGe = i;\n      if( p->op==SQLITE_INDEX_CONSTRAINT_GT ) iTermGe = i;\n    }\n  }\n\n  if( iTermEq>=0 ){\n    idxNum |= FTS5_VOCAB_TERM_EQ;\n    pInfo->aConstraintUsage[iTermEq].argvIndex = ++nArg;\n    pInfo->estimatedCost = 100;\n  }else{\n    pInfo->estimatedCost = 1000000;\n    if( iTermGe>=0 ){\n      idxNum |= FTS5_VOCAB_TERM_GE;\n      pInfo->aConstraintUsage[iTermGe].argvIndex = ++nArg;\n      pInfo->estimatedCost = pInfo->estimatedCost / 2;\n    }\n    if( iTermLe>=0 ){\n      idxNum |= FTS5_VOCAB_TERM_LE;\n      pInfo->aConstraintUsage[iTermLe].argvIndex = ++nArg;\n      pInfo->estimatedCost = pInfo->estimatedCost / 2;\n    }\n  }\n\n  /* This virtual table always delivers results in ascending order of\n  ** the \"term\" column (column 0). So if the user has requested this\n  ** specifically - \"ORDER BY term\" or \"ORDER BY term ASC\" - set the\n  ** sqlite3_index_info.orderByConsumed flag to tell the core the results\n  ** are already in sorted order.  */\n  if( pInfo->nOrderBy==1 \n   && pInfo->aOrderBy[0].iColumn==0 \n   && pInfo->aOrderBy[0].desc==0\n  ){\n    pInfo->orderByConsumed = 1;\n  }\n\n  pInfo->idxNum = idxNum;\n  return SQLITE_OK;\n}\n\n/*\n** Implementation of xOpen method.\n*/\nstatic int fts5VocabOpenMethod(\n  sqlite3_vtab *pVTab, \n  sqlite3_vtab_cursor **ppCsr\n){\n  Fts5VocabTable *pTab = (Fts5VocabTable*)pVTab;\n  Fts5Index *pIndex = 0;\n  Fts5Config *pConfig = 0;\n  Fts5VocabCursor *pCsr = 0;\n  int rc = SQLITE_OK;\n  sqlite3_stmt *pStmt = 0;\n  char *zSql = 0;\n\n  zSql = sqlite3Fts5Mprintf(&rc,\n      \"SELECT t.%Q FROM %Q.%Q AS t WHERE t.%Q MATCH '*id'\",\n      pTab->zFts5Tbl, pTab->zFts5Db, pTab->zFts5Tbl, pTab->zFts5Tbl\n  );\n  if( zSql ){\n    rc = sqlite3_prepare_v2(pTab->db, zSql, -1, &pStmt, 0);\n  }\n  sqlite3_free(zSql);\n  assert( rc==SQLITE_OK || pStmt==0 );\n  if( rc==SQLITE_ERROR ) rc = SQLITE_OK;\n\n  if( pStmt && sqlite3_step(pStmt)==SQLITE_ROW ){\n    i64 iId = sqlite3_column_int64(pStmt, 0);\n    pIndex = sqlite3Fts5IndexFromCsrid(pTab->pGlobal, iId, &pConfig);\n  }\n\n  if( rc==SQLITE_OK && pIndex==0 ){\n    rc = sqlite3_finalize(pStmt);\n    pStmt = 0;\n    if( rc==SQLITE_OK ){\n      pVTab->zErrMsg = sqlite3_mprintf(\n          \"no such fts5 table: %s.%s\", pTab->zFts5Db, pTab->zFts5Tbl\n      );\n      rc = SQLITE_ERROR;\n    }\n  }\n\n  if( rc==SQLITE_OK ){\n    int nByte = pConfig->nCol * sizeof(i64) * 2 + sizeof(Fts5VocabCursor);\n    pCsr = (Fts5VocabCursor*)sqlite3Fts5MallocZero(&rc, nByte);\n  }\n\n  if( pCsr ){\n    pCsr->pIndex = pIndex;\n    pCsr->pStmt = pStmt;\n    pCsr->pConfig = pConfig;\n    pCsr->aCnt = (i64*)&pCsr[1];\n    pCsr->aDoc = &pCsr->aCnt[pConfig->nCol];\n  }else{\n    sqlite3_finalize(pStmt);\n  }\n\n  *ppCsr = (sqlite3_vtab_cursor*)pCsr;\n  return rc;\n}\n\nstatic void fts5VocabResetCursor(Fts5VocabCursor *pCsr){\n  pCsr->rowid = 0;\n  sqlite3Fts5IterClose(pCsr->pIter);\n  pCsr->pIter = 0;\n  sqlite3_free(pCsr->zLeTerm);\n  pCsr->nLeTerm = -1;\n  pCsr->zLeTerm = 0;\n}\n\n/*\n** Close the cursor.  For additional information see the documentation\n** on the xClose method of the virtual table interface.\n*/\nstatic int fts5VocabCloseMethod(sqlite3_vtab_cursor *pCursor){\n  Fts5VocabCursor *pCsr = (Fts5VocabCursor*)pCursor;\n  fts5VocabResetCursor(pCsr);\n  sqlite3Fts5BufferFree(&pCsr->term);\n  sqlite3_finalize(pCsr->pStmt);\n  sqlite3_free(pCsr);\n  return SQLITE_OK;\n}\n\nstatic int fts5VocabInstanceNewTerm(Fts5VocabCursor *pCsr){\n  int rc = SQLITE_OK;\n  \n  if( sqlite3Fts5IterEof(pCsr->pIter) ){\n    pCsr->bEof = 1;\n  }else{\n    const char *zTerm;\n    int nTerm;\n    zTerm = sqlite3Fts5IterTerm(pCsr->pIter, &nTerm);\n    if( pCsr->nLeTerm>=0 ){\n      int nCmp = MIN(nTerm, pCsr->nLeTerm);\n      int bCmp = memcmp(pCsr->zLeTerm, zTerm, nCmp);\n      if( bCmp<0 || (bCmp==0 && pCsr->nLeTerm<nTerm) ){\n        pCsr->bEof = 1;\n      }\n    }\n\n    sqlite3Fts5BufferSet(&rc, &pCsr->term, nTerm, (const u8*)zTerm);\n  }\n  return rc;\n}\n\nstatic int fts5VocabInstanceNext(Fts5VocabCursor *pCsr){\n  int eDetail = pCsr->pConfig->eDetail;\n  int rc = SQLITE_OK;\n  Fts5IndexIter *pIter = pCsr->pIter;\n  i64 *pp = &pCsr->iInstPos;\n  int *po = &pCsr->iInstOff;\n  \n  while( eDetail==FTS5_DETAIL_NONE\n      || sqlite3Fts5PoslistNext64(pIter->pData, pIter->nData, po, pp) \n  ){\n    pCsr->iInstPos = 0;\n    pCsr->iInstOff = 0;\n\n    rc = sqlite3Fts5IterNextScan(pCsr->pIter);\n    if( rc==SQLITE_OK ){\n      rc = fts5VocabInstanceNewTerm(pCsr);\n      if( eDetail==FTS5_DETAIL_NONE ) break;\n    }\n    if( rc ){\n      pCsr->bEof = 1;\n      break;\n    }\n  }\n\n  return rc;\n}\n\n/*\n** Advance the cursor to the next row in the table.\n*/\nstatic int fts5VocabNextMethod(sqlite3_vtab_cursor *pCursor){\n  Fts5VocabCursor *pCsr = (Fts5VocabCursor*)pCursor;\n  Fts5VocabTable *pTab = (Fts5VocabTable*)pCursor->pVtab;\n  int rc = SQLITE_OK;\n  int nCol = pCsr->pConfig->nCol;\n\n  pCsr->rowid++;\n\n  if( pTab->eType==FTS5_VOCAB_INSTANCE ){\n    return fts5VocabInstanceNext(pCsr);\n  }\n\n  if( pTab->eType==FTS5_VOCAB_COL ){\n    for(pCsr->iCol++; pCsr->iCol<nCol; pCsr->iCol++){\n      if( pCsr->aDoc[pCsr->iCol] ) break;\n    }\n  }\n\n  if( pTab->eType!=FTS5_VOCAB_COL || pCsr->iCol>=nCol ){\n    if( sqlite3Fts5IterEof(pCsr->pIter) ){\n      pCsr->bEof = 1;\n    }else{\n      const char *zTerm;\n      int nTerm;\n\n      zTerm = sqlite3Fts5IterTerm(pCsr->pIter, &nTerm);\n      if( pCsr->nLeTerm>=0 ){\n        int nCmp = MIN(nTerm, pCsr->nLeTerm);\n        int bCmp = memcmp(pCsr->zLeTerm, zTerm, nCmp);\n        if( bCmp<0 || (bCmp==0 && pCsr->nLeTerm<nTerm) ){\n          pCsr->bEof = 1;\n          return SQLITE_OK;\n        }\n      }\n\n      sqlite3Fts5BufferSet(&rc, &pCsr->term, nTerm, (const u8*)zTerm);\n      memset(pCsr->aCnt, 0, nCol * sizeof(i64));\n      memset(pCsr->aDoc, 0, nCol * sizeof(i64));\n      pCsr->iCol = 0;\n\n      assert( pTab->eType==FTS5_VOCAB_COL || pTab->eType==FTS5_VOCAB_ROW );\n      while( rc==SQLITE_OK ){\n        int eDetail = pCsr->pConfig->eDetail;\n        const u8 *pPos; int nPos;   /* Position list */\n        i64 iPos = 0;               /* 64-bit position read from poslist */\n        int iOff = 0;               /* Current offset within position list */\n\n        pPos = pCsr->pIter->pData;\n        nPos = pCsr->pIter->nData;\n\n        switch( pTab->eType ){\n          case FTS5_VOCAB_ROW:\n            if( eDetail==FTS5_DETAIL_FULL ){\n              while( 0==sqlite3Fts5PoslistNext64(pPos, nPos, &iOff, &iPos) ){\n                pCsr->aCnt[0]++;\n              }\n            }\n            pCsr->aDoc[0]++;\n            break;\n\n          case FTS5_VOCAB_COL:\n            if( eDetail==FTS5_DETAIL_FULL ){\n              int iCol = -1;\n              while( 0==sqlite3Fts5PoslistNext64(pPos, nPos, &iOff, &iPos) ){\n                int ii = FTS5_POS2COLUMN(iPos);\n                pCsr->aCnt[ii]++;\n                if( iCol!=ii ){\n                  if( ii>=nCol ){\n                    rc = FTS5_CORRUPT;\n                    break;\n                  }\n                  pCsr->aDoc[ii]++;\n                  iCol = ii;\n                }\n              }\n            }else if( eDetail==FTS5_DETAIL_COLUMNS ){\n              while( 0==sqlite3Fts5PoslistNext64(pPos, nPos, &iOff,&iPos) ){\n                assert_nc( iPos>=0 && iPos<nCol );\n                if( iPos>=nCol ){\n                  rc = FTS5_CORRUPT;\n                  break;\n                }\n                pCsr->aDoc[iPos]++;\n              }\n            }else{\n              assert( eDetail==FTS5_DETAIL_NONE );\n              pCsr->aDoc[0]++;\n            }\n            break;\n\n          default:\n            assert( pTab->eType==FTS5_VOCAB_INSTANCE );\n            break;\n        }\n\n        if( rc==SQLITE_OK ){\n          rc = sqlite3Fts5IterNextScan(pCsr->pIter);\n        }\n        if( pTab->eType==FTS5_VOCAB_INSTANCE ) break;\n\n        if( rc==SQLITE_OK ){\n          zTerm = sqlite3Fts5IterTerm(pCsr->pIter, &nTerm);\n          if( nTerm!=pCsr->term.n || memcmp(zTerm, pCsr->term.p, nTerm) ){\n            break;\n          }\n          if( sqlite3Fts5IterEof(pCsr->pIter) ) break;\n        }\n      }\n    }\n  }\n\n  if( rc==SQLITE_OK && pCsr->bEof==0 && pTab->eType==FTS5_VOCAB_COL ){\n    while( pCsr->aDoc[pCsr->iCol]==0 ) pCsr->iCol++;\n    assert( pCsr->iCol<pCsr->pConfig->nCol );\n  }\n  return rc;\n}\n\n/*\n** This is the xFilter implementation for the virtual table.\n*/\nstatic int fts5VocabFilterMethod(\n  sqlite3_vtab_cursor *pCursor,   /* The cursor used for this query */\n  int idxNum,                     /* Strategy index */\n  const char *zUnused,            /* Unused */\n  int nUnused,                    /* Number of elements in apVal */\n  sqlite3_value **apVal           /* Arguments for the indexing scheme */\n){\n  Fts5VocabTable *pTab = (Fts5VocabTable*)pCursor->pVtab;\n  Fts5VocabCursor *pCsr = (Fts5VocabCursor*)pCursor;\n  int eType = pTab->eType;\n  int rc = SQLITE_OK;\n\n  int iVal = 0;\n  int f = FTS5INDEX_QUERY_SCAN;\n  const char *zTerm = 0;\n  int nTerm = 0;\n\n  sqlite3_value *pEq = 0;\n  sqlite3_value *pGe = 0;\n  sqlite3_value *pLe = 0;\n\n  UNUSED_PARAM2(zUnused, nUnused);\n\n  fts5VocabResetCursor(pCsr);\n  if( idxNum & FTS5_VOCAB_TERM_EQ ) pEq = apVal[iVal++];\n  if( idxNum & FTS5_VOCAB_TERM_GE ) pGe = apVal[iVal++];\n  if( idxNum & FTS5_VOCAB_TERM_LE ) pLe = apVal[iVal++];\n\n  if( pEq ){\n    zTerm = (const char *)sqlite3_value_text(pEq);\n    nTerm = sqlite3_value_bytes(pEq);\n    f = 0;\n  }else{\n    if( pGe ){\n      zTerm = (const char *)sqlite3_value_text(pGe);\n      nTerm = sqlite3_value_bytes(pGe);\n    }\n    if( pLe ){\n      const char *zCopy = (const char *)sqlite3_value_text(pLe);\n      pCsr->nLeTerm = sqlite3_value_bytes(pLe);\n      pCsr->zLeTerm = sqlite3_malloc(pCsr->nLeTerm+1);\n      if( pCsr->zLeTerm==0 ){\n        rc = SQLITE_NOMEM;\n      }else{\n        memcpy(pCsr->zLeTerm, zCopy, pCsr->nLeTerm+1);\n      }\n    }\n  }\n\n  if( rc==SQLITE_OK ){\n    rc = sqlite3Fts5IndexQuery(pCsr->pIndex, zTerm, nTerm, f, 0, &pCsr->pIter);\n  }\n  if( rc==SQLITE_OK && eType==FTS5_VOCAB_INSTANCE ){\n    rc = fts5VocabInstanceNewTerm(pCsr);\n  }\n  if( rc==SQLITE_OK \n   && !pCsr->bEof \n   && (eType!=FTS5_VOCAB_INSTANCE || pCsr->pConfig->eDetail!=FTS5_DETAIL_NONE)\n  ){\n    rc = fts5VocabNextMethod(pCursor);\n  }\n\n  return rc;\n}\n\n/* \n** This is the xEof method of the virtual table. SQLite calls this \n** routine to find out if it has reached the end of a result set.\n*/\nstatic int fts5VocabEofMethod(sqlite3_vtab_cursor *pCursor){\n  Fts5VocabCursor *pCsr = (Fts5VocabCursor*)pCursor;\n  return pCsr->bEof;\n}\n\nstatic int fts5VocabColumnMethod(\n  sqlite3_vtab_cursor *pCursor,   /* Cursor to retrieve value from */\n  sqlite3_context *pCtx,          /* Context for sqlite3_result_xxx() calls */\n  int iCol                        /* Index of column to read value from */\n){\n  Fts5VocabCursor *pCsr = (Fts5VocabCursor*)pCursor;\n  int eDetail = pCsr->pConfig->eDetail;\n  int eType = ((Fts5VocabTable*)(pCursor->pVtab))->eType;\n  i64 iVal = 0;\n\n  if( iCol==0 ){\n    sqlite3_result_text(\n        pCtx, (const char*)pCsr->term.p, pCsr->term.n, SQLITE_TRANSIENT\n    );\n  }else if( eType==FTS5_VOCAB_COL ){\n    assert( iCol==1 || iCol==2 || iCol==3 );\n    if( iCol==1 ){\n      if( eDetail!=FTS5_DETAIL_NONE ){\n        const char *z = pCsr->pConfig->azCol[pCsr->iCol];\n        sqlite3_result_text(pCtx, z, -1, SQLITE_STATIC);\n      }\n    }else if( iCol==2 ){\n      iVal = pCsr->aDoc[pCsr->iCol];\n    }else{\n      iVal = pCsr->aCnt[pCsr->iCol];\n    }\n  }else if( eType==FTS5_VOCAB_ROW ){\n    assert( iCol==1 || iCol==2 );\n    if( iCol==1 ){\n      iVal = pCsr->aDoc[0];\n    }else{\n      iVal = pCsr->aCnt[0];\n    }\n  }else{\n    assert( eType==FTS5_VOCAB_INSTANCE );\n    switch( iCol ){\n      case 1:\n        sqlite3_result_int64(pCtx, pCsr->pIter->iRowid);\n        break;\n      case 2: {\n        int ii = -1;\n        if( eDetail==FTS5_DETAIL_FULL ){\n          ii = FTS5_POS2COLUMN(pCsr->iInstPos);\n        }else if( eDetail==FTS5_DETAIL_COLUMNS ){\n          ii = (int)pCsr->iInstPos;\n        }\n        if( ii>=0 && ii<pCsr->pConfig->nCol ){\n          const char *z = pCsr->pConfig->azCol[ii];\n          sqlite3_result_text(pCtx, z, -1, SQLITE_STATIC);\n        }\n        break;\n      }\n      default: {\n        assert( iCol==3 );\n        if( eDetail==FTS5_DETAIL_FULL ){\n          int ii = FTS5_POS2OFFSET(pCsr->iInstPos);\n          sqlite3_result_int(pCtx, ii);\n        }\n        break;\n      }\n    }\n  }\n\n  if( iVal>0 ) sqlite3_result_int64(pCtx, iVal);\n  return SQLITE_OK;\n}\n\n/* \n** This is the xRowid method. The SQLite core calls this routine to\n** retrieve the rowid for the current row of the result set. The\n** rowid should be written to *pRowid.\n*/\nstatic int fts5VocabRowidMethod(\n  sqlite3_vtab_cursor *pCursor, \n  sqlite_int64 *pRowid\n){\n  Fts5VocabCursor *pCsr = (Fts5VocabCursor*)pCursor;\n  *pRowid = pCsr->rowid;\n  return SQLITE_OK;\n}\n\nstatic int sqlite3Fts5VocabInit(Fts5Global *pGlobal, sqlite3 *db){\n  static const sqlite3_module fts5Vocab = {\n    /* iVersion      */ 2,\n    /* xCreate       */ fts5VocabCreateMethod,\n    /* xConnect      */ fts5VocabConnectMethod,\n    /* xBestIndex    */ fts5VocabBestIndexMethod,\n    /* xDisconnect   */ fts5VocabDisconnectMethod,\n    /* xDestroy      */ fts5VocabDestroyMethod,\n    /* xOpen         */ fts5VocabOpenMethod,\n    /* xClose        */ fts5VocabCloseMethod,\n    /* xFilter       */ fts5VocabFilterMethod,\n    /* xNext         */ fts5VocabNextMethod,\n    /* xEof          */ fts5VocabEofMethod,\n    /* xColumn       */ fts5VocabColumnMethod,\n    /* xRowid        */ fts5VocabRowidMethod,\n    /* xUpdate       */ 0,\n    /* xBegin        */ 0,\n    /* xSync         */ 0,\n    /* xCommit       */ 0,\n    /* xRollback     */ 0,\n    /* xFindFunction */ 0,\n    /* xRename       */ 0,\n    /* xSavepoint    */ 0,\n    /* xRelease      */ 0,\n    /* xRollbackTo   */ 0,\n  };\n  void *p = (void*)pGlobal;\n\n  return sqlite3_create_module_v2(db, \"fts5vocab\", &fts5Vocab, p, 0);\n}\n\n\n\n\n    \n#endif /* !defined(SQLITE_CORE) || defined(SQLITE_ENABLE_FTS5) */\n\n/************** End of fts5.c ************************************************/\n/************** Begin file stmt.c ********************************************/\n/*\n** 2017-05-31\n**\n** The author disclaims copyright to this source code.  In place of\n** a legal notice, here is a blessing:\n**\n**    May you do good and not evil.\n**    May you find forgiveness for yourself and forgive others.\n**    May you share freely, never taking more than you give.\n**\n*************************************************************************\n**\n** This file demonstrates an eponymous virtual table that returns information\n** about all prepared statements for the database connection.\n**\n** Usage example:\n**\n**     .load ./stmt\n**     .mode line\n**     .header on\n**     SELECT * FROM stmt;\n*/\n#if !defined(SQLITE_CORE) || defined(SQLITE_ENABLE_STMTVTAB)\n#if !defined(SQLITEINT_H)\n/* #include \"sqlite3ext.h\" */\n#endif\nSQLITE_EXTENSION_INIT1\n/* #include <assert.h> */\n/* #include <string.h> */\n\n#ifndef SQLITE_OMIT_VIRTUALTABLE\n\n/* stmt_vtab is a subclass of sqlite3_vtab which will\n** serve as the underlying representation of a stmt virtual table\n*/\ntypedef struct stmt_vtab stmt_vtab;\nstruct stmt_vtab {\n  sqlite3_vtab base;  /* Base class - must be first */\n  sqlite3 *db;        /* Database connection for this stmt vtab */\n};\n\n/* stmt_cursor is a subclass of sqlite3_vtab_cursor which will\n** serve as the underlying representation of a cursor that scans\n** over rows of the result\n*/\ntypedef struct stmt_cursor stmt_cursor;\nstruct stmt_cursor {\n  sqlite3_vtab_cursor base;  /* Base class - must be first */\n  sqlite3 *db;               /* Database connection for this cursor */\n  sqlite3_stmt *pStmt;       /* Statement cursor is currently pointing at */\n  sqlite3_int64 iRowid;      /* The rowid */\n};\n\n/*\n** The stmtConnect() method is invoked to create a new\n** stmt_vtab that describes the stmt virtual table.\n**\n** Think of this routine as the constructor for stmt_vtab objects.\n**\n** All this routine needs to do is:\n**\n**    (1) Allocate the stmt_vtab object and initialize all fields.\n**\n**    (2) Tell SQLite (via the sqlite3_declare_vtab() interface) what the\n**        result set of queries against stmt will look like.\n*/\nstatic int stmtConnect(\n  sqlite3 *db,\n  void *pAux,\n  int argc, const char *const*argv,\n  sqlite3_vtab **ppVtab,\n  char **pzErr\n){\n  stmt_vtab *pNew;\n  int rc;\n\n/* Column numbers */\n#define STMT_COLUMN_SQL     0   /* SQL for the statement */\n#define STMT_COLUMN_NCOL    1   /* Number of result columns */\n#define STMT_COLUMN_RO      2   /* True if read-only */\n#define STMT_COLUMN_BUSY    3   /* True if currently busy */\n#define STMT_COLUMN_NSCAN   4   /* SQLITE_STMTSTATUS_FULLSCAN_STEP */\n#define STMT_COLUMN_NSORT   5   /* SQLITE_STMTSTATUS_SORT */\n#define STMT_COLUMN_NAIDX   6   /* SQLITE_STMTSTATUS_AUTOINDEX */\n#define STMT_COLUMN_NSTEP   7   /* SQLITE_STMTSTATUS_VM_STEP */\n#define STMT_COLUMN_REPREP  8   /* SQLITE_STMTSTATUS_REPREPARE */\n#define STMT_COLUMN_RUN     9   /* SQLITE_STMTSTATUS_RUN */\n#define STMT_COLUMN_MEM    10   /* SQLITE_STMTSTATUS_MEMUSED */\n\n\n  rc = sqlite3_declare_vtab(db,\n     \"CREATE TABLE x(sql,ncol,ro,busy,nscan,nsort,naidx,nstep,\"\n                    \"reprep,run,mem)\");\n  if( rc==SQLITE_OK ){\n    pNew = sqlite3_malloc( sizeof(*pNew) );\n    *ppVtab = (sqlite3_vtab*)pNew;\n    if( pNew==0 ) return SQLITE_NOMEM;\n    memset(pNew, 0, sizeof(*pNew));\n    pNew->db = db;\n  }\n  return rc;\n}\n\n/*\n** This method is the destructor for stmt_cursor objects.\n*/\nstatic int stmtDisconnect(sqlite3_vtab *pVtab){\n  sqlite3_free(pVtab);\n  return SQLITE_OK;\n}\n\n/*\n** Constructor for a new stmt_cursor object.\n*/\nstatic int stmtOpen(sqlite3_vtab *p, sqlite3_vtab_cursor **ppCursor){\n  stmt_cursor *pCur;\n  pCur = sqlite3_malloc( sizeof(*pCur) );\n  if( pCur==0 ) return SQLITE_NOMEM;\n  memset(pCur, 0, sizeof(*pCur));\n  pCur->db = ((stmt_vtab*)p)->db;\n  *ppCursor = &pCur->base;\n  return SQLITE_OK;\n}\n\n/*\n** Destructor for a stmt_cursor.\n*/\nstatic int stmtClose(sqlite3_vtab_cursor *cur){\n  sqlite3_free(cur);\n  return SQLITE_OK;\n}\n\n\n/*\n** Advance a stmt_cursor to its next row of output.\n*/\nstatic int stmtNext(sqlite3_vtab_cursor *cur){\n  stmt_cursor *pCur = (stmt_cursor*)cur;\n  pCur->iRowid++;\n  pCur->pStmt = sqlite3_next_stmt(pCur->db, pCur->pStmt);\n  return SQLITE_OK;\n}\n\n/*\n** Return values of columns for the row at which the stmt_cursor\n** is currently pointing.\n*/\nstatic int stmtColumn(\n  sqlite3_vtab_cursor *cur,   /* The cursor */\n  sqlite3_context *ctx,       /* First argument to sqlite3_result_...() */\n  int i                       /* Which column to return */\n){\n  stmt_cursor *pCur = (stmt_cursor*)cur;\n  switch( i ){\n    case STMT_COLUMN_SQL: {\n      sqlite3_result_text(ctx, sqlite3_sql(pCur->pStmt), -1, SQLITE_TRANSIENT);\n      break;\n    }\n    case STMT_COLUMN_NCOL: {\n      sqlite3_result_int(ctx, sqlite3_column_count(pCur->pStmt));\n      break;\n    }\n    case STMT_COLUMN_RO: {\n      sqlite3_result_int(ctx, sqlite3_stmt_readonly(pCur->pStmt));\n      break;\n    }\n    case STMT_COLUMN_BUSY: {\n      sqlite3_result_int(ctx, sqlite3_stmt_busy(pCur->pStmt));\n      break;\n    }\n    case STMT_COLUMN_MEM: {\n      i = SQLITE_STMTSTATUS_MEMUSED + \n            STMT_COLUMN_NSCAN - SQLITE_STMTSTATUS_FULLSCAN_STEP;\n      /* Fall thru */\n    }\n    case STMT_COLUMN_NSCAN:\n    case STMT_COLUMN_NSORT:\n    case STMT_COLUMN_NAIDX:\n    case STMT_COLUMN_NSTEP:\n    case STMT_COLUMN_REPREP:\n    case STMT_COLUMN_RUN: {\n      sqlite3_result_int(ctx, sqlite3_stmt_status(pCur->pStmt,\n                      i-STMT_COLUMN_NSCAN+SQLITE_STMTSTATUS_FULLSCAN_STEP, 0));\n      break;\n    }\n  }\n  return SQLITE_OK;\n}\n\n/*\n** Return the rowid for the current row.  In this implementation, the\n** rowid is the same as the output value.\n*/\nstatic int stmtRowid(sqlite3_vtab_cursor *cur, sqlite_int64 *pRowid){\n  stmt_cursor *pCur = (stmt_cursor*)cur;\n  *pRowid = pCur->iRowid;\n  return SQLITE_OK;\n}\n\n/*\n** Return TRUE if the cursor has been moved off of the last\n** row of output.\n*/\nstatic int stmtEof(sqlite3_vtab_cursor *cur){\n  stmt_cursor *pCur = (stmt_cursor*)cur;\n  return pCur->pStmt==0;\n}\n\n/*\n** This method is called to \"rewind\" the stmt_cursor object back\n** to the first row of output.  This method is always called at least\n** once prior to any call to stmtColumn() or stmtRowid() or \n** stmtEof().\n*/\nstatic int stmtFilter(\n  sqlite3_vtab_cursor *pVtabCursor, \n  int idxNum, const char *idxStr,\n  int argc, sqlite3_value **argv\n){\n  stmt_cursor *pCur = (stmt_cursor *)pVtabCursor;\n  pCur->pStmt = 0;\n  pCur->iRowid = 0;\n  return stmtNext(pVtabCursor);\n}\n\n/*\n** SQLite will invoke this method one or more times while planning a query\n** that uses the stmt virtual table.  This routine needs to create\n** a query plan for each invocation and compute an estimated cost for that\n** plan.\n*/\nstatic int stmtBestIndex(\n  sqlite3_vtab *tab,\n  sqlite3_index_info *pIdxInfo\n){\n  pIdxInfo->estimatedCost = (double)500;\n  pIdxInfo->estimatedRows = 500;\n  return SQLITE_OK;\n}\n\n/*\n** This following structure defines all the methods for the \n** stmt virtual table.\n*/\nstatic sqlite3_module stmtModule = {\n  0,                         /* iVersion */\n  0,                         /* xCreate */\n  stmtConnect,               /* xConnect */\n  stmtBestIndex,             /* xBestIndex */\n  stmtDisconnect,            /* xDisconnect */\n  0,                         /* xDestroy */\n  stmtOpen,                  /* xOpen - open a cursor */\n  stmtClose,                 /* xClose - close a cursor */\n  stmtFilter,                /* xFilter - configure scan constraints */\n  stmtNext,                  /* xNext - advance a cursor */\n  stmtEof,                   /* xEof - check for end of scan */\n  stmtColumn,                /* xColumn - read data */\n  stmtRowid,                 /* xRowid - read data */\n  0,                         /* xUpdate */\n  0,                         /* xBegin */\n  0,                         /* xSync */\n  0,                         /* xCommit */\n  0,                         /* xRollback */\n  0,                         /* xFindMethod */\n  0,                         /* xRename */\n  0,                         /* xSavepoint */\n  0,                         /* xRelease */\n  0,                         /* xRollbackTo */\n};\n\n#endif /* SQLITE_OMIT_VIRTUALTABLE */\n\nSQLITE_PRIVATE int sqlite3StmtVtabInit(sqlite3 *db){\n  int rc = SQLITE_OK;\n#ifndef SQLITE_OMIT_VIRTUALTABLE\n  rc = sqlite3_create_module(db, \"sqlite_stmt\", &stmtModule, 0);\n#endif\n  return rc;\n}\n\n#ifndef SQLITE_CORE\n#ifdef _WIN32\n__declspec(dllexport)\n#endif\nSQLITE_API int sqlite3_stmt_init(\n  sqlite3 *db, \n  char **pzErrMsg, \n  const sqlite3_api_routines *pApi\n){\n  int rc = SQLITE_OK;\n  SQLITE_EXTENSION_INIT2(pApi);\n#ifndef SQLITE_OMIT_VIRTUALTABLE\n  rc = sqlite3StmtVtabInit(db);\n#endif\n  return rc;\n}\n#endif /* SQLITE_CORE */\n#endif /* !defined(SQLITE_CORE) || defined(SQLITE_ENABLE_STMTVTAB) */\n\n/************** End of stmt.c ************************************************/\n#if __LINE__!=207986\n#undef SQLITE_SOURCE_ID\n#define SQLITE_SOURCE_ID      \"2018-02-27 15:40:59 9a7f02c50e6c8a3dc3addf4e51b7e04bd31670d6ce58d26d55273c43b5ecalt2\"\n#endif\n/* Return the source-id for this library */\nSQLITE_API const char *sqlite3_sourceid(void){ return SQLITE_SOURCE_ID; }\n/************************** End of sqlite3.c ******************************/\n"
  },
  {
    "path": "libs/tiny-process-library/LICENSE",
    "content": "The MIT License (MIT)\n\nCopyright (c) 2015-2020 Ole Christian Eidheim\n\nPermission is hereby granted, free of charge, to any person obtaining a copy\nof this software and associated documentation files (the \"Software\"), to deal\nin the Software without restriction, including without limitation the rights\nto use, copy, modify, merge, publish, distribute, sublicense, and/or sell\ncopies of the Software, and to permit persons to whom the Software is\nfurnished to do so, subject to the following conditions:\n\nThe above copyright notice and this permission notice shall be included in all\ncopies or substantial portions of the Software.\n\nTHE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\nIMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\nFITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE\nAUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\nLIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,\nOUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE\nSOFTWARE.\n\n"
  },
  {
    "path": "libs/tiny-process-library/process.cpp",
    "content": "#include \"process.hpp\"\n\nnamespace TinyProcessLib {\n\nProcess::Process(const std::vector<string_type> &arguments, const string_type &path,\n                 std::function<void(const char *bytes, size_t n)> read_stdout,\n                 std::function<void(const char *bytes, size_t n)> read_stderr,\n                 bool open_stdin, const Config &config) noexcept\n    : closed(true), read_stdout(std::move(read_stdout)), read_stderr(std::move(read_stderr)), open_stdin(open_stdin), config(config) {\n  open(arguments, path);\n  async_read();\n}\n\nProcess::Process(const string_type &command, const string_type &path,\n                 std::function<void(const char *bytes, size_t n)> read_stdout,\n                 std::function<void(const char *bytes, size_t n)> read_stderr,\n                 bool open_stdin, const Config &config) noexcept\n    : closed(true), read_stdout(std::move(read_stdout)), read_stderr(std::move(read_stderr)), open_stdin(open_stdin), config(config) {\n  open(command, path);\n  async_read();\n}\n\nProcess::Process(const std::vector<string_type> &arguments, const string_type &path,\n                 const environment_type &environment,\n                 std::function<void(const char *bytes, size_t n)> read_stdout,\n                 std::function<void(const char *bytes, size_t n)> read_stderr,\n                 bool open_stdin, const Config &config) noexcept\n    : closed(true), read_stdout(std::move(read_stdout)), read_stderr(std::move(read_stderr)), open_stdin(open_stdin), config(config) {\n  open(arguments, path, &environment);\n  async_read();\n}\n\nProcess::Process(const string_type &command, const string_type &path,\n                 const environment_type &environment,\n                 std::function<void(const char *bytes, size_t n)> read_stdout,\n                 std::function<void(const char *bytes, size_t n)> read_stderr,\n                 bool open_stdin, const Config &config) noexcept\n    : closed(true), read_stdout(std::move(read_stdout)), read_stderr(std::move(read_stderr)), open_stdin(open_stdin), config(config) {\n  open(command, path, &environment);\n  async_read();\n}\n\nProcess::~Process() noexcept {\n  close_fds();\n}\n\nProcess::id_type Process::get_id() const noexcept {\n  return data.id;\n}\n\nbool Process::write(const std::string &str) {\n  return write(str.c_str(), str.size());\n}\n\n} // namespace TinyProcessLib\n"
  },
  {
    "path": "libs/tiny-process-library/process.hpp",
    "content": "#ifndef TINY_PROCESS_LIBRARY_HPP_\n#define TINY_PROCESS_LIBRARY_HPP_\n#include <functional>\n#include <memory>\n#include <mutex>\n#include <string>\n#include <thread>\n#include <unordered_map>\n#include <vector>\n#ifndef _WIN32\n#include <sys/wait.h>\n#endif\n\nnamespace TinyProcessLib {\n/// Additional parameters to Process constructors.\nstruct Config {\n  /// Buffer size for reading stdout and stderr. Default is 131072 (128 kB).\n  std::size_t buffer_size = 131072;\n  /// Set to true to inherit file descriptors from parent process. Default is false.\n  /// On Windows: has no effect unless read_stdout==nullptr, read_stderr==nullptr and open_stdin==false.\n  bool inherit_file_descriptors = false;\n\n  /// If set, invoked when process stdout is closed.\n  /// This call goes after last call to read_stdout().\n  std::function<void()> on_stdout_close = nullptr;\n  /// If set, invoked when process stderr is closed.\n  /// This call goes after last call to read_stderr().\n  std::function<void()> on_stderr_close = nullptr;\n\n  /// On Windows only: controls how the process is started, mimics STARTUPINFO's wShowWindow.\n  /// See: https://docs.microsoft.com/en-us/windows/desktop/api/processthreadsapi/ns-processthreadsapi-startupinfoa\n  /// and https://docs.microsoft.com/en-us/windows/desktop/api/winuser/nf-winuser-showwindow\n  enum class ShowWindow {\n    hide = 0,\n    show_normal = 1,\n    show_minimized = 2,\n    maximize = 3,\n    show_maximized = 3,\n    show_no_activate = 4,\n    show = 5,\n    minimize = 6,\n    show_min_no_active = 7,\n    show_na = 8,\n    restore = 9,\n    show_default = 10,\n    force_minimize = 11\n  };\n  /// On Windows only: controls how the window is shown.\n  ShowWindow show_window{ShowWindow::show_default};\n\n  /// Set to true to break out of flatpak sandbox by prepending all commands with `/usr/bin/flatpak-spawn --host`\n  /// which will execute the command line on the host system.\n  /// Requires the flatpak `org.freedesktop.Flatpak` portal to be opened for the current sandbox.\n  /// See https://docs.flatpak.org/en/latest/flatpak-command-reference.html#flatpak-spawn.\n  bool flatpak_spawn_host = false;\n};\n\n/// Platform independent class for creating processes.\n/// Note on Windows: it seems not possible to specify which pipes to redirect.\n/// Thus, at the moment, if read_stdout==nullptr, read_stderr==nullptr and open_stdin==false,\n/// the stdout, stderr and stdin are sent to the parent process instead.\nclass Process {\npublic:\n#ifdef _WIN32\n  typedef unsigned long id_type; // Process id type\n  typedef void *fd_type;         // File descriptor type\n#ifdef UNICODE\n  typedef std::wstring string_type;\n#else\n  typedef std::string string_type;\n#endif\n#else\n  typedef pid_t id_type;\n  typedef int fd_type;\n  typedef std::string string_type;\n#endif\n  typedef std::unordered_map<string_type, string_type> environment_type;\n\nprivate:\n  class Data {\n  public:\n    Data() noexcept;\n    id_type id;\n#ifdef _WIN32\n    void *handle{nullptr};\n#endif\n    int exit_status{-1};\n  };\n\npublic:\n  /// Starts a process with the environment of the calling process.\n  Process(const std::vector<string_type> &arguments, const string_type &path = string_type(),\n          std::function<void(const char *bytes, size_t n)> read_stdout = nullptr,\n          std::function<void(const char *bytes, size_t n)> read_stderr = nullptr,\n          bool open_stdin = false,\n          const Config &config = {}) noexcept;\n  /// Starts a process with the environment of the calling process.\n  Process(const string_type &command, const string_type &path = string_type(),\n          std::function<void(const char *bytes, size_t n)> read_stdout = nullptr,\n          std::function<void(const char *bytes, size_t n)> read_stderr = nullptr,\n          bool open_stdin = false,\n          const Config &config = {}) noexcept;\n\n  /// Starts a process with specified environment.\n  Process(const std::vector<string_type> &arguments,\n          const string_type &path,\n          const environment_type &environment,\n          std::function<void(const char *bytes, size_t n)> read_stdout = nullptr,\n          std::function<void(const char *bytes, size_t n)> read_stderr = nullptr,\n          bool open_stdin = false,\n          const Config &config = {}) noexcept;\n  /// Starts a process with specified environment.\n  Process(const string_type &command,\n          const string_type &path,\n          const environment_type &environment,\n          std::function<void(const char *bytes, size_t n)> read_stdout = nullptr,\n          std::function<void(const char *bytes, size_t n)> read_stderr = nullptr,\n          bool open_stdin = false,\n          const Config &config = {}) noexcept;\n#ifndef _WIN32\n  /// Starts a process with the environment of the calling process.\n  /// Supported on Unix-like systems only.\n  /// Since the command line is not known to the Process object itself,\n  /// this overload does not support the flatpak_spawn_host configuration.\n  Process(const std::function<void()> &function,\n          std::function<void(const char *bytes, size_t n)> read_stdout = nullptr,\n          std::function<void(const char *bytes, size_t n)> read_stderr = nullptr,\n          bool open_stdin = false,\n          const Config &config = {});\n#endif\n  ~Process() noexcept;\n\n  /// Get the process id of the started process.\n  id_type get_id() const noexcept;\n  /// Wait until process is finished, and return exit status.\n  int get_exit_status() noexcept;\n  /// If process is finished, returns true and sets the exit status. Returns false otherwise.\n  bool try_get_exit_status(int &exit_status) noexcept;\n  /// Write to stdin.\n  bool write(const char *bytes, size_t n);\n  /// Write to stdin. Convenience function using write(const char *, size_t).\n  bool write(const std::string &str);\n  /// Close stdin. If the process takes parameters from stdin, use this to notify that all parameters have been sent.\n  void close_stdin() noexcept;\n\n  /// Kill the process. force=true is only supported on Unix-like systems.\n  void kill(bool force = false) noexcept;\n  /// Kill a given process id. Use kill(bool force) instead if possible. force=true is only supported on Unix-like systems.\n  static void kill(id_type id, bool force = false) noexcept;\n#ifndef _WIN32\n  /// Send the signal signum to the process.\n  void signal(int signum) noexcept;\n#endif\n\nprivate:\n  Data data;\n  bool closed;\n  std::mutex close_mutex;\n  std::function<void(const char *bytes, size_t n)> read_stdout;\n  std::function<void(const char *bytes, size_t n)> read_stderr;\n#ifndef _WIN32\n  std::thread stdout_stderr_thread;\n#else\n  std::thread stdout_thread, stderr_thread;\n#endif\n  bool open_stdin;\n  std::mutex stdin_mutex;\n\n  Config config;\n\n  std::unique_ptr<fd_type> stdout_fd, stderr_fd, stdin_fd;\n\n  id_type open(const std::vector<string_type> &arguments, const string_type &path, const environment_type *environment = nullptr) noexcept;\n  id_type open(const string_type &command, const string_type &path, const environment_type *environment = nullptr) noexcept;\n#ifndef _WIN32\n  id_type open(const std::function<void()> &function) noexcept;\n#endif\n  void async_read() noexcept;\n  void close_fds() noexcept;\n};\n\n} // namespace TinyProcessLib\n\n#endif // TINY_PROCESS_LIBRARY_HPP_\n"
  },
  {
    "path": "libs/tiny-process-library/process_unix.cpp",
    "content": "#include \"process.hpp\"\n#include <algorithm>\n#include <bitset>\n#include <cstdlib>\n#include <errno.h>\n#include <fcntl.h>\n#include <limits.h>\n#include <poll.h>\n#include <set>\n#include <signal.h>\n#include <stdexcept>\n#include <string.h>\n#include <unistd.h>\n\nnamespace TinyProcessLib {\n\nstatic int portable_execvpe(const char *file, char *const argv[], char *const envp[]) {\n#ifdef __GLIBC__\n  // Prefer native implementation.\n  return execvpe(file, argv, envp);\n#else\n  if(!file || !*file) {\n    errno = ENOENT;\n    return -1;\n  }\n\n  if(strchr(file, '/') != nullptr) {\n    // If file contains a slash, no search is needed.\n    return execve(file, argv, envp);\n  }\n\n  const char *path = getenv(\"PATH\");\n  char cspath[PATH_MAX + 1] = {};\n  if(!path) {\n    // If env variable is not set, use static path string.\n    confstr(_CS_PATH, cspath, sizeof(cspath));\n    path = cspath;\n  }\n\n  const size_t path_len = strlen(path);\n  const size_t file_len = strlen(file);\n\n  if(file_len > NAME_MAX) {\n    errno = ENAMETOOLONG;\n    return -1;\n  }\n\n  // Indicates whether we encountered EACCESS at least once.\n  bool eacces = false;\n\n  const char *curr = nullptr;\n  const char *next = nullptr;\n\n  for(curr = path; *curr; curr = *next ? next + 1 : next) {\n    next = strchr(curr, ':');\n    if(!next) {\n      next = path + path_len;\n    }\n\n    const size_t sz = (next - curr);\n    if(sz > PATH_MAX) {\n      // Path is too long. Proceed to next path in list.\n      continue;\n    }\n\n    char exe_path[PATH_MAX + 1 + NAME_MAX + 1]; // 1 byte for slash + 1 byte for \\0\n    memcpy(exe_path, curr, sz);\n    exe_path[sz] = '/';\n    memcpy(exe_path + sz + 1, file, file_len);\n    exe_path[sz + 1 + file_len] = '\\0';\n\n    execve(exe_path, argv, envp);\n\n    switch(errno) {\n    case EACCES:\n      eacces = true;\n    case ENOENT:\n    case ESTALE:\n    case ENOTDIR:\n    case ENODEV:\n    case ETIMEDOUT:\n      // The errors above indicate that the executable was not found.\n      // The list of errors replicates one from glibc.\n      // In this case we proceed to next path in list.\n      break;\n\n    default:\n      // Other errors indicate that executable was found but failed\n      // to execute. In this case we return error.\n      return -1;\n    }\n  }\n\n  if(eacces) {\n    // If search failed, and at least one iteration reported EACCESS, it means\n    // that the needed executable exists but does not have suitable permissions.\n    // In this case we report EACEESS for user.\n    errno = EACCES;\n  }\n  // Otherwise we just keep last encountered errno.\n  return -1;\n#endif\n}\n\nProcess::Data::Data() noexcept : id(-1) {\n}\n\nProcess::Process(const std::function<void()> &function,\n                 std::function<void(const char *, size_t)> read_stdout,\n                 std::function<void(const char *, size_t)> read_stderr,\n                 bool open_stdin, const Config &config)\n    : closed(true), read_stdout(std::move(read_stdout)), read_stderr(std::move(read_stderr)), open_stdin(open_stdin), config(config) {\n  if(config.flatpak_spawn_host)\n    throw std::invalid_argument(\"Cannot break out of a flatpak sandbox with this overload.\");\n  open(function);\n  async_read();\n}\n\nProcess::id_type Process::open(const std::function<void()> &function) noexcept {\n  if(open_stdin)\n    stdin_fd = std::unique_ptr<fd_type>(new fd_type);\n  if(read_stdout)\n    stdout_fd = std::unique_ptr<fd_type>(new fd_type);\n  if(read_stderr)\n    stderr_fd = std::unique_ptr<fd_type>(new fd_type);\n\n  int stdin_p[2], stdout_p[2], stderr_p[2];\n\n  if(stdin_fd && pipe(stdin_p) != 0)\n    return -1;\n  if(stdout_fd && pipe(stdout_p) != 0) {\n    if(stdin_fd) {\n      close(stdin_p[0]);\n      close(stdin_p[1]);\n    }\n    return -1;\n  }\n  if(stderr_fd && pipe(stderr_p) != 0) {\n    if(stdin_fd) {\n      close(stdin_p[0]);\n      close(stdin_p[1]);\n    }\n    if(stdout_fd) {\n      close(stdout_p[0]);\n      close(stdout_p[1]);\n    }\n    return -1;\n  }\n\n  id_type pid = fork();\n\n  if(pid < 0) {\n    if(stdin_fd) {\n      close(stdin_p[0]);\n      close(stdin_p[1]);\n    }\n    if(stdout_fd) {\n      close(stdout_p[0]);\n      close(stdout_p[1]);\n    }\n    if(stderr_fd) {\n      close(stderr_p[0]);\n      close(stderr_p[1]);\n    }\n    return pid;\n  }\n  else if(pid == 0) {\n    if(stdin_fd)\n      dup2(stdin_p[0], 0);\n    if(stdout_fd)\n      dup2(stdout_p[1], 1);\n    if(stderr_fd)\n      dup2(stderr_p[1], 2);\n    if(stdin_fd) {\n      close(stdin_p[0]);\n      close(stdin_p[1]);\n    }\n    if(stdout_fd) {\n      close(stdout_p[0]);\n      close(stdout_p[1]);\n    }\n    if(stderr_fd) {\n      close(stderr_p[0]);\n      close(stderr_p[1]);\n    }\n\n    if(!config.inherit_file_descriptors) {\n      // Optimization on some systems: using 8 * 1024 (Debian's default _SC_OPEN_MAX) as fd_max limit\n      int fd_max = std::min(8192, static_cast<int>(sysconf(_SC_OPEN_MAX))); // Truncation is safe\n      if(fd_max < 0)\n        fd_max = 8192;\n      for(int fd = 3; fd < fd_max; fd++)\n        close(fd);\n    }\n\n    setpgid(0, 0);\n    // TODO: See here on how to emulate tty for colors: http://stackoverflow.com/questions/1401002/trick-an-application-into-thinking-its-stdin-is-interactive-not-a-pipe\n    // TODO: One solution is: echo \"command;exit\"|script -q /dev/null\n\n    if(function)\n      function();\n\n    _exit(EXIT_FAILURE);\n  }\n\n  if(stdin_fd)\n    close(stdin_p[0]);\n  if(stdout_fd)\n    close(stdout_p[1]);\n  if(stderr_fd)\n    close(stderr_p[1]);\n\n  if(stdin_fd)\n    *stdin_fd = stdin_p[1];\n  if(stdout_fd)\n    *stdout_fd = stdout_p[0];\n  if(stderr_fd)\n    *stderr_fd = stderr_p[0];\n\n  closed = false;\n  data.id = pid;\n  return pid;\n}\n\nProcess::id_type Process::open(const std::vector<string_type> &arguments, const string_type &path, const environment_type *environment) noexcept {\n  return open([this, &arguments, &path, &environment] {\n    if(arguments.empty())\n      exit(127);\n\n    std::vector<const char *> argv_ptrs;\n\n    if(config.flatpak_spawn_host) {\n      // break out of sandbox, execute on host\n      argv_ptrs.reserve(arguments.size() + 3);\n      argv_ptrs.emplace_back(\"/usr/bin/flatpak-spawn\");\n      argv_ptrs.emplace_back(\"--host\");\n    }\n    else\n      argv_ptrs.reserve(arguments.size() + 1);\n\n    for(auto &argument : arguments)\n      argv_ptrs.emplace_back(argument.c_str());\n    argv_ptrs.emplace_back(nullptr);\n\n    if(!path.empty()) {\n      if(chdir(path.c_str()) != 0)\n        exit(1);\n    }\n\n    if(!environment)\n      execvp(argv_ptrs[0], const_cast<char *const *>(argv_ptrs.data()));\n    else {\n      std::vector<std::string> env_strs;\n      std::vector<const char *> env_ptrs;\n      env_strs.reserve(environment->size());\n      env_ptrs.reserve(environment->size() + 1);\n      for(const auto &e : *environment) {\n        env_strs.emplace_back(e.first + '=' + e.second);\n        env_ptrs.emplace_back(env_strs.back().c_str());\n      }\n      env_ptrs.emplace_back(nullptr);\n\n      portable_execvpe(argv_ptrs[0], const_cast<char *const *>(argv_ptrs.data()), const_cast<char *const *>(env_ptrs.data()));\n    }\n  });\n}\n\nProcess::id_type Process::open(const std::string &command, const std::string &path, const environment_type *environment) noexcept {\n  return open([this, &command, &path, &environment] {\n    auto command_c_str = command.c_str();\n    std::string cd_path_and_command;\n    if(!path.empty()) {\n      auto path_escaped = path;\n      size_t pos = 0;\n      // Based on https://www.reddit.com/r/cpp/comments/3vpjqg/a_new_platform_independent_process_library_for_c11/cxsxyb7\n      while((pos = path_escaped.find('\\'', pos)) != std::string::npos) {\n        path_escaped.replace(pos, 1, \"'\\\\''\");\n        pos += 4;\n      }\n      cd_path_and_command = \"cd '\" + path_escaped + \"' && \" + command; // To avoid resolving symbolic links\n      command_c_str = cd_path_and_command.c_str();\n    }\n\n    if(!environment) {\n      if(config.flatpak_spawn_host)\n        // break out of sandbox, execute on host\n        execl(\"/usr/bin/flatpak-spawn\", \"/usr/bin/flatpak-spawn\", \"--host\", \"/bin/sh\", \"-c\", command_c_str, nullptr);\n      else\n        execl(\"/bin/sh\", \"/bin/sh\", \"-c\", command_c_str, nullptr);\n    }\n    else {\n      std::vector<std::string> env_strs;\n      std::vector<const char *> env_ptrs;\n      env_strs.reserve(environment->size());\n      env_ptrs.reserve(environment->size() + 1);\n      for(const auto &e : *environment) {\n        env_strs.emplace_back(e.first + '=' + e.second);\n        env_ptrs.emplace_back(env_strs.back().c_str());\n      }\n      env_ptrs.emplace_back(nullptr);\n      if(config.flatpak_spawn_host)\n        // break out of sandbox, execute on host\n        execle(\"/usr/bin/flatpak-spawn\", \"/usr/bin/flatpak-spawn\", \"--host\", \"/bin/sh\", \"-c\", command_c_str, nullptr, env_ptrs.data());\n      else\n        execle(\"/bin/sh\", \"/bin/sh\", \"-c\", command_c_str, nullptr, env_ptrs.data());\n    }\n  });\n}\n\nvoid Process::async_read() noexcept {\n  if(data.id <= 0 || (!stdout_fd && !stderr_fd))\n    return;\n\n  stdout_stderr_thread = std::thread([this] {\n    std::vector<pollfd> pollfds;\n    std::bitset<2> fd_is_stdout;\n    if(stdout_fd) {\n      fd_is_stdout.set(pollfds.size());\n      pollfds.emplace_back();\n      pollfds.back().fd = fcntl(*stdout_fd, F_SETFL, fcntl(*stdout_fd, F_GETFL) | O_NONBLOCK) == 0 ? *stdout_fd : -1;\n      pollfds.back().events = POLLIN;\n    }\n    if(stderr_fd) {\n      pollfds.emplace_back();\n      pollfds.back().fd = fcntl(*stderr_fd, F_SETFL, fcntl(*stderr_fd, F_GETFL) | O_NONBLOCK) == 0 ? *stderr_fd : -1;\n      pollfds.back().events = POLLIN;\n    }\n    auto buffer = std::unique_ptr<char[]>(new char[config.buffer_size]);\n    bool any_open = !pollfds.empty();\n    while(any_open && (poll(pollfds.data(), static_cast<nfds_t>(pollfds.size()), -1) > 0 || errno == EINTR)) {\n      any_open = false;\n      for(size_t i = 0; i < pollfds.size(); ++i) {\n        if(pollfds[i].fd >= 0) {\n          if(pollfds[i].revents & POLLIN) {\n            const ssize_t n = read(pollfds[i].fd, buffer.get(), config.buffer_size);\n            if(n > 0) {\n              if(fd_is_stdout[i])\n                read_stdout(buffer.get(), static_cast<size_t>(n));\n              else\n                read_stderr(buffer.get(), static_cast<size_t>(n));\n            }\n            else if(n == 0 || (n < 0 && errno != EINTR && errno != EAGAIN && errno != EWOULDBLOCK)) {\n              if(fd_is_stdout[i]) {\n                if(config.on_stdout_close)\n                  config.on_stdout_close();\n              }\n              else {\n                if(config.on_stderr_close)\n                  config.on_stderr_close();\n              }\n              pollfds[i].fd = -1;\n              continue;\n            }\n          }\n          else if(pollfds[i].revents & (POLLERR | POLLHUP | POLLNVAL)) {\n            if(fd_is_stdout[i]) {\n              if(config.on_stdout_close)\n                config.on_stdout_close();\n            }\n            else {\n              if(config.on_stderr_close)\n                config.on_stderr_close();\n            }\n            pollfds[i].fd = -1;\n            continue;\n          }\n          any_open = true;\n        }\n      }\n    }\n  });\n}\n\nint Process::get_exit_status() noexcept {\n  if(data.id <= 0)\n    return -1;\n\n  int exit_status;\n  id_type pid;\n  do {\n    pid = waitpid(data.id, &exit_status, 0);\n  } while(pid < 0 && errno == EINTR);\n\n  if(pid < 0 && errno == ECHILD) {\n    // PID doesn't exist anymore, return previously sampled exit status (or -1)\n    return data.exit_status;\n  }\n  else {\n    // Store exit status for future calls\n    if(exit_status >= 256)\n      exit_status = exit_status >> 8;\n    data.exit_status = exit_status;\n  }\n\n  {\n    std::lock_guard<std::mutex> lock(close_mutex);\n    closed = true;\n  }\n  close_fds();\n\n  return exit_status;\n}\n\nbool Process::try_get_exit_status(int &exit_status) noexcept {\n  if(data.id <= 0) {\n    exit_status = -1;\n    return true;\n  }\n\n  const id_type pid = waitpid(data.id, &exit_status, WNOHANG);\n  if(pid < 0 && errno == ECHILD) {\n    // PID doesn't exist anymore, set previously sampled exit status (or -1)\n    exit_status = data.exit_status;\n    return true;\n  }\n  else if(pid <= 0) {\n    // Process still running (p==0) or error\n    return false;\n  }\n  else {\n    // store exit status for future calls\n    if(exit_status >= 256)\n      exit_status = exit_status >> 8;\n    data.exit_status = exit_status;\n  }\n\n  {\n    std::lock_guard<std::mutex> lock(close_mutex);\n    closed = true;\n  }\n  close_fds();\n\n  return true;\n}\n\nvoid Process::close_fds() noexcept {\n  if(stdout_stderr_thread.joinable())\n    stdout_stderr_thread.join();\n\n  if(stdin_fd)\n    close_stdin();\n  if(stdout_fd) {\n    if(data.id > 0)\n      close(*stdout_fd);\n    stdout_fd.reset();\n  }\n  if(stderr_fd) {\n    if(data.id > 0)\n      close(*stderr_fd);\n    stderr_fd.reset();\n  }\n}\n\nbool Process::write(const char *bytes, size_t n) {\n  if(!open_stdin)\n    throw std::invalid_argument(\"Can't write to an unopened stdin pipe. Please set open_stdin=true when constructing the process.\");\n\n  std::lock_guard<std::mutex> lock(stdin_mutex);\n  if(stdin_fd) {\n    while(n != 0) {\n      const ssize_t ret = ::write(*stdin_fd, bytes, n);\n      if(ret < 0) {\n        if(errno == EINTR)\n          continue;\n        else\n          return false;\n      }\n      bytes += static_cast<size_t>(ret);\n      n -= static_cast<size_t>(ret);\n    }\n    return true;\n  }\n  return false;\n}\n\nvoid Process::close_stdin() noexcept {\n  std::lock_guard<std::mutex> lock(stdin_mutex);\n  if(stdin_fd) {\n    if(data.id > 0)\n      close(*stdin_fd);\n    stdin_fd.reset();\n  }\n}\n\nvoid Process::kill(bool force) noexcept {\n  std::lock_guard<std::mutex> lock(close_mutex);\n  if(data.id > 0 && !closed) {\n    if(force) {\n      ::kill(-data.id, SIGTERM);\n      ::kill(data.id, SIGTERM); // Based on comment in https://gitlab.com/eidheim/tiny-process-library/-/merge_requests/29#note_1146144166\n    }\n    else {\n      ::kill(-data.id, SIGINT);\n      ::kill(data.id, SIGINT);\n    }\n  }\n}\n\nvoid Process::kill(id_type id, bool force) noexcept {\n  if(id <= 0)\n    return;\n\n  if(force) {\n    ::kill(-id, SIGTERM);\n    ::kill(id, SIGTERM);\n  }\n  else {\n    ::kill(-id, SIGINT);\n    ::kill(id, SIGINT);\n  }\n}\n\nvoid Process::signal(int signum) noexcept {\n  std::lock_guard<std::mutex> lock(close_mutex);\n  if(data.id > 0 && !closed) {\n    ::kill(-data.id, signum);\n    ::kill(data.id, signum);\n  }\n}\n\n} // namespace TinyProcessLib\n"
  },
  {
    "path": "libs/tiny-process-library/process_win.cpp",
    "content": "#include \"process.hpp\"\n// clang-format off\n#include <windows.h>\n// clang-format on\n#include <cstring>\n#include <stdexcept>\n#include <tlhelp32.h>\n\nnamespace TinyProcessLib {\n\nProcess::Data::Data() noexcept : id(0) {}\n\n// Simple HANDLE wrapper to close it automatically from the destructor.\nclass Handle {\npublic:\n  Handle() noexcept : handle(INVALID_HANDLE_VALUE) {}\n  ~Handle() noexcept {\n    close();\n  }\n  void close() noexcept {\n    if(handle != INVALID_HANDLE_VALUE)\n      CloseHandle(handle);\n  }\n  HANDLE detach() noexcept {\n    HANDLE old_handle = handle;\n    handle = INVALID_HANDLE_VALUE;\n    return old_handle;\n  }\n  operator HANDLE() const noexcept { return handle; }\n  HANDLE *operator&() noexcept { return &handle; }\n\nprivate:\n  HANDLE handle;\n};\n\ntemplate <class Char>\nstruct CharSet;\n\ntemplate <>\nstruct CharSet<char> {\n  static constexpr const char *whitespace = \" \\t\\n\\v\\\"\";\n  static constexpr char space = ' ';\n  static constexpr char doublequote = '\"';\n  static constexpr char backslash = '\\\\';\n};\n\ntemplate <>\nstruct CharSet<wchar_t> {\n  static constexpr const wchar_t *whitespace = L\" \\t\\n\\v\\\"\";\n  static constexpr wchar_t space = L' ';\n  static constexpr wchar_t doublequote = L'\"';\n  static constexpr wchar_t backslash = L'\\\\';\n};\n\n// Based on blog post https://learn.microsoft.com/en-us/archive/blogs/twistylittlepassagesallalike/everyone-quotes-command-line-arguments-the-wrong-way\ntemplate <class Char>\nstatic std::basic_string<Char> join_arguments(const std::vector<std::basic_string<Char>> &args) {\n  using charset = CharSet<Char>;\n\n  std::basic_string<Char> ret;\n\n  for(const auto &arg : args) {\n    if(!ret.empty())\n      ret.push_back(charset::space);\n\n    if(!arg.empty() && arg.find_first_of(charset::whitespace) == arg.npos) {\n      ret.append(arg);\n      continue;\n    }\n\n    ret.push_back(charset::doublequote);\n\n    for(auto it = arg.begin();; ++it) {\n      size_t n_backslashes = 0;\n\n      while(it != arg.end() && *it == charset::backslash) {\n        ++it;\n        ++n_backslashes;\n      }\n\n      if(it == arg.end()) {\n        // Escape all backslashes, but let the terminating double quotation mark\n        // we add below be interpreted  as a metacharacter.\n        ret.append(n_backslashes * 2, charset::backslash);\n        break;\n      }\n      else if(*it == charset::doublequote) {\n        // Escape all backslashes and the following double quotation mark.\n        ret.append(n_backslashes * 2 + 1, charset::backslash);\n        ret.push_back(*it);\n      }\n      else {\n        // Backslashes aren't special here.\n        ret.append(n_backslashes, charset::backslash);\n        ret.push_back(*it);\n      }\n    }\n\n    ret.push_back(charset::doublequote);\n  }\n\n  return ret;\n}\n\n// Based on the discussion thread: https://www.reddit.com/r/cpp/comments/3vpjqg/a_new_platform_independent_process_library_for_c11/cxq1wsj\nstd::mutex create_process_mutex;\n\nProcess::id_type Process::open(const std::vector<string_type> &arguments, const string_type &path, const environment_type *environment) noexcept {\n  return open(join_arguments(arguments), path, environment);\n}\n\n// Based on the example at https://msdn.microsoft.com/en-us/library/windows/desktop/ms682499(v=vs.85).aspx.\nProcess::id_type Process::open(const string_type &command, const string_type &path, const environment_type *environment) noexcept {\n  if(open_stdin)\n    stdin_fd = std::unique_ptr<fd_type>(new fd_type(nullptr));\n  if(read_stdout)\n    stdout_fd = std::unique_ptr<fd_type>(new fd_type(nullptr));\n  if(read_stderr)\n    stderr_fd = std::unique_ptr<fd_type>(new fd_type(nullptr));\n\n  Handle stdin_rd_p;\n  Handle stdin_wr_p;\n  Handle stdout_rd_p;\n  Handle stdout_wr_p;\n  Handle stderr_rd_p;\n  Handle stderr_wr_p;\n\n  SECURITY_ATTRIBUTES security_attributes;\n\n  security_attributes.nLength = sizeof(SECURITY_ATTRIBUTES);\n  security_attributes.bInheritHandle = TRUE;\n  security_attributes.lpSecurityDescriptor = nullptr;\n\n  std::lock_guard<std::mutex> lock(create_process_mutex);\n  if(stdin_fd) {\n    if(!CreatePipe(&stdin_rd_p, &stdin_wr_p, &security_attributes, 0) ||\n       !SetHandleInformation(stdin_wr_p, HANDLE_FLAG_INHERIT, 0))\n      return 0;\n  }\n  if(stdout_fd) {\n    if(!CreatePipe(&stdout_rd_p, &stdout_wr_p, &security_attributes, 0) ||\n       !SetHandleInformation(stdout_rd_p, HANDLE_FLAG_INHERIT, 0)) {\n      return 0;\n    }\n  }\n  if(stderr_fd) {\n    if(!CreatePipe(&stderr_rd_p, &stderr_wr_p, &security_attributes, 0) ||\n       !SetHandleInformation(stderr_rd_p, HANDLE_FLAG_INHERIT, 0)) {\n      return 0;\n    }\n  }\n\n  PROCESS_INFORMATION process_info;\n  STARTUPINFO startup_info;\n\n  ZeroMemory(&process_info, sizeof(PROCESS_INFORMATION));\n\n  ZeroMemory(&startup_info, sizeof(STARTUPINFO));\n  startup_info.cb = sizeof(STARTUPINFO);\n  startup_info.hStdInput = stdin_rd_p;\n  startup_info.hStdOutput = stdout_wr_p;\n  startup_info.hStdError = stderr_wr_p;\n  if(stdin_fd || stdout_fd || stderr_fd)\n    startup_info.dwFlags |= STARTF_USESTDHANDLES;\n\n  if(config.show_window != Config::ShowWindow::show_default) {\n    startup_info.dwFlags |= STARTF_USESHOWWINDOW;\n    startup_info.wShowWindow = static_cast<WORD>(config.show_window);\n  }\n\n  auto process_command = command;\n#ifdef MSYS_PROCESS_USE_SH\n  size_t pos = 0;\n  while((pos = process_command.find('\\\\', pos)) != string_type::npos) {\n    process_command.replace(pos, 1, \"\\\\\\\\\\\\\\\\\");\n    pos += 4;\n  }\n  pos = 0;\n  while((pos = process_command.find('\\\"', pos)) != string_type::npos) {\n    process_command.replace(pos, 1, \"\\\\\\\"\");\n    pos += 2;\n  }\n  process_command.insert(0, \"sh -c \\\"\");\n  process_command += \"\\\"\";\n#endif\n\n  DWORD creation_flags = stdin_fd || stdout_fd || stderr_fd ? CREATE_NO_WINDOW : 0; // CREATE_NO_WINDOW cannot be used when stdout or stderr is redirected to parent process\n  string_type environment_str;\n  if(environment) {\n#ifdef UNICODE\n    for(const auto &e : *environment)\n      environment_str += e.first + L'=' + e.second + L'\\0';\n    if(!environment_str.empty())\n      environment_str += L'\\0';\n    creation_flags |= CREATE_UNICODE_ENVIRONMENT;\n#else\n    for(const auto &e : *environment)\n      environment_str += e.first + '=' + e.second + '\\0';\n    if(!environment_str.empty())\n      environment_str += '\\0';\n#endif\n  }\n  BOOL bSuccess = CreateProcess(nullptr, process_command.empty() ? nullptr : &process_command[0], nullptr, nullptr,\n                                stdin_fd || stdout_fd || stderr_fd || config.inherit_file_descriptors, // Cannot be false when stdout, stderr or stdin is used\n                                creation_flags,\n                                environment_str.empty() ? nullptr : &environment_str[0],\n                                path.empty() ? nullptr : path.c_str(),\n                                &startup_info, &process_info);\n\n  if(!bSuccess)\n    return 0;\n  else\n    CloseHandle(process_info.hThread);\n\n  if(stdin_fd)\n    *stdin_fd = stdin_wr_p.detach();\n  if(stdout_fd)\n    *stdout_fd = stdout_rd_p.detach();\n  if(stderr_fd)\n    *stderr_fd = stderr_rd_p.detach();\n\n  closed = false;\n  data.id = process_info.dwProcessId;\n  data.handle = process_info.hProcess;\n  return process_info.dwProcessId;\n}\n\nvoid Process::async_read() noexcept {\n  if(data.id == 0)\n    return;\n\n  if(stdout_fd) {\n    stdout_thread = std::thread([this]() {\n      DWORD n;\n      std::unique_ptr<char[]> buffer(new char[config.buffer_size]);\n      for(;;) {\n        BOOL bSuccess = ReadFile(*stdout_fd, static_cast<CHAR *>(buffer.get()), static_cast<DWORD>(config.buffer_size), &n, nullptr);\n        if(!bSuccess || n == 0) {\n          if(config.on_stdout_close)\n            config.on_stdout_close();\n          break;\n        }\n        read_stdout(buffer.get(), static_cast<size_t>(n));\n      }\n    });\n  }\n  if(stderr_fd) {\n    stderr_thread = std::thread([this]() {\n      DWORD n;\n      std::unique_ptr<char[]> buffer(new char[config.buffer_size]);\n      for(;;) {\n        BOOL bSuccess = ReadFile(*stderr_fd, static_cast<CHAR *>(buffer.get()), static_cast<DWORD>(config.buffer_size), &n, nullptr);\n        if(!bSuccess || n == 0) {\n          if(config.on_stderr_close)\n            config.on_stderr_close();\n          break;\n        }\n        read_stderr(buffer.get(), static_cast<size_t>(n));\n      }\n    });\n  }\n}\n\nint Process::get_exit_status() noexcept {\n  if(data.id == 0)\n    return -1;\n\n  if(!data.handle)\n    return data.exit_status;\n\n  WaitForSingleObject(data.handle, INFINITE);\n\n  DWORD exit_status;\n  if(!GetExitCodeProcess(data.handle, &exit_status))\n    data.exit_status = -1; // Store exit status for future calls\n  else\n    data.exit_status = static_cast<int>(exit_status); // Store exit status for future calls\n\n  {\n    std::lock_guard<std::mutex> lock(close_mutex);\n    CloseHandle(data.handle);\n    data.handle = nullptr;\n    closed = true;\n  }\n  close_fds();\n\n  return data.exit_status;\n}\n\nbool Process::try_get_exit_status(int &exit_status) noexcept {\n  if(data.id == 0) {\n    exit_status = -1;\n    return true;\n  }\n\n  if(!data.handle) {\n    exit_status = data.exit_status;\n    return true;\n  }\n\n  DWORD wait_status = WaitForSingleObject(data.handle, 0);\n  if(wait_status == WAIT_TIMEOUT)\n    return false;\n\n  DWORD exit_status_tmp;\n  if(!GetExitCodeProcess(data.handle, &exit_status_tmp))\n    exit_status = -1;\n  else\n    exit_status = static_cast<int>(exit_status_tmp);\n  data.exit_status = exit_status; // Store exit status for future calls\n\n  {\n    std::lock_guard<std::mutex> lock(close_mutex);\n    CloseHandle(data.handle);\n    data.handle = nullptr;\n    closed = true;\n  }\n  close_fds();\n\n  return true;\n}\n\nvoid Process::close_fds() noexcept {\n  if(stdout_thread.joinable())\n    stdout_thread.join();\n  if(stderr_thread.joinable())\n    stderr_thread.join();\n\n  if(stdin_fd)\n    close_stdin();\n  if(stdout_fd) {\n    if(*stdout_fd != nullptr)\n      CloseHandle(*stdout_fd);\n    stdout_fd.reset();\n  }\n  if(stderr_fd) {\n    if(*stderr_fd != nullptr)\n      CloseHandle(*stderr_fd);\n    stderr_fd.reset();\n  }\n}\n\nbool Process::write(const char *bytes, size_t n) {\n  if(!open_stdin)\n    throw std::invalid_argument(\"Can't write to an unopened stdin pipe. Please set open_stdin=true when constructing the process.\");\n\n  std::lock_guard<std::mutex> lock(stdin_mutex);\n  if(stdin_fd) {\n    DWORD written;\n    BOOL bSuccess = WriteFile(*stdin_fd, bytes, static_cast<DWORD>(n), &written, nullptr);\n    if(!bSuccess || written == 0) {\n      return false;\n    }\n    else {\n      return true;\n    }\n  }\n  return false;\n}\n\nvoid Process::close_stdin() noexcept {\n  std::lock_guard<std::mutex> lock(stdin_mutex);\n  if(stdin_fd) {\n    if(*stdin_fd != nullptr)\n      CloseHandle(*stdin_fd);\n    stdin_fd.reset();\n  }\n}\n\n// Based on http://stackoverflow.com/a/1173396\nvoid Process::kill(bool /*force*/) noexcept {\n  std::lock_guard<std::mutex> lock(close_mutex);\n  if(data.id > 0 && !closed) {\n    HANDLE snapshot = CreateToolhelp32Snapshot(TH32CS_SNAPPROCESS, 0);\n    if(snapshot) {\n      PROCESSENTRY32 process;\n      ZeroMemory(&process, sizeof(process));\n      process.dwSize = sizeof(process);\n      if(Process32First(snapshot, &process)) {\n        do {\n          if(process.th32ParentProcessID == data.id) {\n            HANDLE process_handle = OpenProcess(PROCESS_TERMINATE, FALSE, process.th32ProcessID);\n            if(process_handle) {\n              TerminateProcess(process_handle, 2);\n              CloseHandle(process_handle);\n            }\n          }\n        } while(Process32Next(snapshot, &process));\n      }\n      CloseHandle(snapshot);\n    }\n    TerminateProcess(data.handle, 2);\n  }\n}\n\n// Based on http://stackoverflow.com/a/1173396\nvoid Process::kill(id_type id, bool /*force*/) noexcept {\n  if(id == 0)\n    return;\n\n  HANDLE snapshot = CreateToolhelp32Snapshot(TH32CS_SNAPPROCESS, 0);\n  if(snapshot) {\n    PROCESSENTRY32 process;\n    ZeroMemory(&process, sizeof(process));\n    process.dwSize = sizeof(process);\n    if(Process32First(snapshot, &process)) {\n      do {\n        if(process.th32ParentProcessID == id) {\n          HANDLE process_handle = OpenProcess(PROCESS_TERMINATE, FALSE, process.th32ProcessID);\n          if(process_handle) {\n            TerminateProcess(process_handle, 2);\n            CloseHandle(process_handle);\n          }\n        }\n      } while(Process32Next(snapshot, &process));\n    }\n    CloseHandle(snapshot);\n  }\n  HANDLE process_handle = OpenProcess(PROCESS_TERMINATE, FALSE, id);\n  if(process_handle)\n    TerminateProcess(process_handle, 2);\n}\n\n} // namespace TinyProcessLib\n"
  },
  {
    "path": "libs/tinyxml2/CMakeLists.txt",
    "content": "cmake_minimum_required(VERSION 3.15)\r\nproject(tinyxml2 VERSION 10.0.0)\r\n\r\ninclude(CTest)\r\noption(tinyxml2_BUILD_TESTING \"Build tests for tinyxml2\" \"${BUILD_TESTING}\")\r\n\r\n##\r\n## Honor tinyxml2_SHARED_LIBS to match install interface\r\n##\r\n\r\nif (DEFINED tinyxml2_SHARED_LIBS)\r\n    set(BUILD_SHARED_LIBS \"${tinyxml2_SHARED_LIBS}\")\r\nendif ()\r\n\r\n##\r\n## Main library build\r\n##\r\n\r\nset(CMAKE_CXX_VISIBILITY_PRESET hidden)\r\nset(CMAKE_VISIBILITY_INLINES_HIDDEN YES)\r\n\r\nadd_library(tinyxml2 tinyxml2.cpp tinyxml2.h)\r\nadd_library(tinyxml2::tinyxml2 ALIAS tinyxml2)\r\n\r\n# Uncomment the following line to require C++11 (or greater) to use tinyxml2\r\n# target_compile_features(tinyxml2 PUBLIC cxx_std_11)\r\ntarget_include_directories(tinyxml2 PUBLIC \"$<BUILD_INTERFACE:${CMAKE_CURRENT_SOURCE_DIR}>\")\r\n\r\ntarget_compile_definitions(\r\n    tinyxml2\r\n    PUBLIC $<$<CONFIG:Debug>:TINYXML2_DEBUG>\r\n    INTERFACE $<$<BOOL:${BUILD_SHARED_LIBS}>:TINYXML2_IMPORT>\r\n    PRIVATE $<$<CXX_COMPILER_ID:MSVC>:_CRT_SECURE_NO_WARNINGS>\r\n    PUBLIC _FILE_OFFSET_BITS=64\r\n)\r\n\r\nset_target_properties(\r\n    tinyxml2\r\n    PROPERTIES\r\n    DEFINE_SYMBOL \"TINYXML2_EXPORT\"\r\n    VERSION \"${tinyxml2_VERSION}\"\r\n    SOVERSION \"${tinyxml2_VERSION_MAJOR}\"\r\n)\r\n\r\nif (tinyxml2_BUILD_TESTING)\r\n    add_executable(xmltest xmltest.cpp)\r\n    target_link_libraries(xmltest PRIVATE tinyxml2::tinyxml2)\r\n\r\n    add_test(\r\n        NAME xmltest\r\n        COMMAND xmltest\r\n        WORKING_DIRECTORY \"${CMAKE_CURRENT_SOURCE_DIR}\"\r\n    )\r\n\r\n    set_tests_properties(xmltest PROPERTIES PASS_REGULAR_EXPRESSION \", Fail 0\")\r\nendif ()\r\n\r\n##\r\n## Installation\r\n##\r\n\r\n## Standard modules\r\ninclude(GNUInstallDirs)\r\ninclude(CMakePackageConfigHelpers)\r\n\r\n## Custom locations\r\nset(tinyxml2_INSTALL_PKGCONFIGDIR \"${CMAKE_INSTALL_LIBDIR}/pkgconfig\"\r\n    CACHE PATH \"Directory for pkgconfig files\")\r\n\r\nset(tinyxml2_INSTALL_CMAKEDIR \"${CMAKE_INSTALL_LIBDIR}/cmake/tinyxml2\"\r\n    CACHE STRING \"Path to tinyxml2 CMake files\")\r\n\r\n## CMake targets and export scripts\r\n\r\ninstall(\r\n    TARGETS tinyxml2 EXPORT tinyxml2-targets\r\n    RUNTIME COMPONENT tinyxml2_runtime\r\n    LIBRARY COMPONENT tinyxml2_runtime\r\n    NAMELINK_COMPONENT tinyxml2_development\r\n    ARCHIVE COMPONENT tinyxml2_development\r\n    INCLUDES DESTINATION \"${CMAKE_INSTALL_INCLUDEDIR}\"\r\n)\r\n\r\n# Type-specific targets\r\n\r\nif (BUILD_SHARED_LIBS)\r\n    set(type shared)\r\nelse ()\r\n    set(type static)\r\nendif ()\r\n\r\ninstall(\r\n    EXPORT tinyxml2-targets\r\n    DESTINATION \"${tinyxml2_INSTALL_CMAKEDIR}\"\r\n    NAMESPACE tinyxml2::\r\n    FILE tinyxml2-${type}-targets.cmake\r\n    COMPONENT tinyxml2_development\r\n)\r\n\r\n# Auto-generated version compatibility file\r\nwrite_basic_package_version_file(\r\n    tinyxml2-config-version.cmake\r\n    COMPATIBILITY SameMajorVersion\r\n)\r\n\r\ninstall(\r\n    FILES\r\n    \"${CMAKE_CURRENT_SOURCE_DIR}/cmake/tinyxml2-config.cmake\"\r\n    \"${CMAKE_CURRENT_BINARY_DIR}/tinyxml2-config-version.cmake\"\r\n    DESTINATION \"${tinyxml2_INSTALL_CMAKEDIR}\"\r\n    COMPONENT tinyxml2_development\r\n)\r\n\r\n## Headers\r\n\r\ninstall(\r\n    FILES tinyxml2.h\r\n    TYPE INCLUDE\r\n    COMPONENT tinyxml2_development\r\n)\r\n\r\n## pkg-config\r\n\r\nconfigure_file(cmake/tinyxml2.pc.in tinyxml2.pc.gen @ONLY)\r\nfile(GENERATE OUTPUT tinyxml2.pc INPUT \"${CMAKE_CURRENT_BINARY_DIR}/tinyxml2.pc.gen\")\r\ninstall(\r\n    FILES \"${CMAKE_CURRENT_BINARY_DIR}/tinyxml2.pc\"\r\n    DESTINATION \"${tinyxml2_INSTALL_PKGCONFIGDIR}\"\r\n    COMPONENT tinyxml2_development\r\n)\r\n"
  },
  {
    "path": "libs/tinyxml2/cmake/tinyxml2-config.cmake",
    "content": "cmake_minimum_required(VERSION 3.15)\n\nset(tinyxml2_known_comps static shared)\nset(tinyxml2_comp_static NO)\nset(tinyxml2_comp_shared NO)\nforeach (tinyxml2_comp IN LISTS ${CMAKE_FIND_PACKAGE_NAME}_FIND_COMPONENTS)\n    if (tinyxml2_comp IN_LIST tinyxml2_known_comps)\n        set(tinyxml2_comp_${tinyxml2_comp} YES)\n    else ()\n        set(${CMAKE_FIND_PACKAGE_NAME}_NOT_FOUND_MESSAGE\n            \"tinyxml2 does not recognize component `${tinyxml2_comp}`.\")\n        set(${CMAKE_FIND_PACKAGE_NAME}_FOUND FALSE)\n        return()\n    endif ()\nendforeach ()\n\nif (tinyxml2_comp_static AND tinyxml2_comp_shared)\n    set(${CMAKE_FIND_PACKAGE_NAME}_NOT_FOUND_MESSAGE\n        \"tinyxml2 `static` and `shared` components are mutually exclusive.\")\n    set(${CMAKE_FIND_PACKAGE_NAME}_FOUND FALSE)\n    return()\nendif ()\n\nset(tinyxml2_static_targets \"${CMAKE_CURRENT_LIST_DIR}/tinyxml2-static-targets.cmake\")\nset(tinyxml2_shared_targets \"${CMAKE_CURRENT_LIST_DIR}/tinyxml2-shared-targets.cmake\")\n\nmacro(tinyxml2_load_targets type)\n    if (NOT EXISTS \"${tinyxml2_${type}_targets}\")\n        set(${CMAKE_FIND_PACKAGE_NAME}_NOT_FOUND_MESSAGE\n            \"tinyxml2 `${type}` libraries were requested but not found.\")\n        set(${CMAKE_FIND_PACKAGE_NAME}_FOUND FALSE)\n        return()\n    endif ()\n    include(\"${tinyxml2_${type}_targets}\")\nendmacro()\n\nif (tinyxml2_comp_static)\n    tinyxml2_load_targets(static)\nelseif (tinyxml2_comp_shared)\n    tinyxml2_load_targets(shared)\nelseif (DEFINED tinyxml2_SHARED_LIBS AND tinyxml2_SHARED_LIBS)\n    tinyxml2_load_targets(shared)\nelseif (DEFINED tinyxml2_SHARED_LIBS AND NOT tinyxml2_SHARED_LIBS)\n    tinyxml2_load_targets(static)\nelseif (BUILD_SHARED_LIBS)\n    if (EXISTS \"${tinyxml2_shared_targets}\")\n        tinyxml2_load_targets(shared)\n    else ()\n        tinyxml2_load_targets(static)\n    endif ()\nelse ()\n    if (EXISTS \"${tinyxml2_static_targets}\")\n        tinyxml2_load_targets(static)\n    else ()\n        tinyxml2_load_targets(shared)\n    endif ()\nendif ()\n"
  },
  {
    "path": "libs/tinyxml2/cmake/tinyxml2.pc.in",
    "content": "prefix=@CMAKE_INSTALL_PREFIX@\nexec_prefix=${prefix}\nlibdir=${exec_prefix}/@CMAKE_INSTALL_LIBDIR@\nincludedir=${prefix}/@CMAKE_INSTALL_INCLUDEDIR@\n\nName: TinyXML2\nDescription: simple, small, C++ XML parser\nVersion: @tinyxml2_VERSION@\nLibs: -L${libdir} -l$<TARGET_FILE_BASE_NAME:tinyxml2::tinyxml2>\nCflags: -I${includedir}\n"
  },
  {
    "path": "libs/tinyxml2/tinyxml2.cpp",
    "content": "/*\r\nOriginal code by Lee Thomason (www.grinninglizard.com)\r\n\r\nThis software is provided 'as-is', without any express or implied\r\nwarranty. In no event will the authors be held liable for any\r\ndamages arising from the use of this software.\r\n\r\nPermission is granted to anyone to use this software for any\r\npurpose, including commercial applications, and to alter it and\r\nredistribute it freely, subject to the following restrictions:\r\n\r\n1. The origin of this software must not be misrepresented; you must\r\nnot claim that you wrote the original software. If you use this\r\nsoftware in a product, an acknowledgment in the product documentation\r\nwould be appreciated but is not required.\r\n\r\n2. Altered source versions must be plainly marked as such, and\r\nmust not be misrepresented as being the original software.\r\n\r\n3. This notice may not be removed or altered from any source\r\ndistribution.\r\n*/\r\n\r\n#include \"tinyxml2.h\"\r\n\r\n#include <new>\t\t// yes, this one new style header, is in the Android SDK.\r\n#if defined(ANDROID_NDK) || defined(__BORLANDC__) || defined(__QNXNTO__)\r\n#   include <stddef.h>\r\n#   include <stdarg.h>\r\n#else\r\n#   include <cstddef>\r\n#   include <cstdarg>\r\n#endif\r\n\r\n#if defined(_MSC_VER) && (_MSC_VER >= 1400 ) && (!defined WINCE)\r\n\t// Microsoft Visual Studio, version 2005 and higher. Not WinCE.\r\n\t/*int _snprintf_s(\r\n\t   char *buffer,\r\n\t   size_t sizeOfBuffer,\r\n\t   size_t count,\r\n\t   const char *format [,\r\n\t\t  argument] ...\r\n\t);*/\r\n\tstatic inline int TIXML_SNPRINTF( char* buffer, size_t size, const char* format, ... )\r\n\t{\r\n\t\tva_list va;\r\n\t\tva_start( va, format );\r\n\t\tconst int result = vsnprintf_s( buffer, size, _TRUNCATE, format, va );\r\n\t\tva_end( va );\r\n\t\treturn result;\r\n\t}\r\n\r\n\tstatic inline int TIXML_VSNPRINTF( char* buffer, size_t size, const char* format, va_list va )\r\n\t{\r\n\t\tconst int result = vsnprintf_s( buffer, size, _TRUNCATE, format, va );\r\n\t\treturn result;\r\n\t}\r\n\r\n\t#define TIXML_VSCPRINTF\t_vscprintf\r\n\t#define TIXML_SSCANF\tsscanf_s\r\n#elif defined _MSC_VER\r\n\t// Microsoft Visual Studio 2003 and earlier or WinCE\r\n\t#define TIXML_SNPRINTF\t_snprintf\r\n\t#define TIXML_VSNPRINTF _vsnprintf\r\n\t#define TIXML_SSCANF\tsscanf\r\n\t#if (_MSC_VER < 1400 ) && (!defined WINCE)\r\n\t\t// Microsoft Visual Studio 2003 and not WinCE.\r\n\t\t#define TIXML_VSCPRINTF   _vscprintf // VS2003's C runtime has this, but VC6 C runtime or WinCE SDK doesn't have.\r\n\t#else\r\n\t\t// Microsoft Visual Studio 2003 and earlier or WinCE.\r\n\t\tstatic inline int TIXML_VSCPRINTF( const char* format, va_list va )\r\n\t\t{\r\n\t\t\tint len = 512;\r\n\t\t\tfor (;;) {\r\n\t\t\t\tlen = len*2;\r\n\t\t\t\tchar* str = new char[len]();\r\n\t\t\t\tconst int required = _vsnprintf(str, len, format, va);\r\n\t\t\t\tdelete[] str;\r\n\t\t\t\tif ( required != -1 ) {\r\n\t\t\t\t\tTIXMLASSERT( required >= 0 );\r\n\t\t\t\t\tlen = required;\r\n\t\t\t\t\tbreak;\r\n\t\t\t\t}\r\n\t\t\t}\r\n\t\t\tTIXMLASSERT( len >= 0 );\r\n\t\t\treturn len;\r\n\t\t}\r\n\t#endif\r\n#else\r\n\t// GCC version 3 and higher\r\n\t//#warning( \"Using sn* functions.\" )\r\n\t#define TIXML_SNPRINTF\tsnprintf\r\n\t#define TIXML_VSNPRINTF\tvsnprintf\r\n\tstatic inline int TIXML_VSCPRINTF( const char* format, va_list va )\r\n\t{\r\n\t\tint len = vsnprintf( 0, 0, format, va );\r\n\t\tTIXMLASSERT( len >= 0 );\r\n\t\treturn len;\r\n\t}\r\n\t#define TIXML_SSCANF   sscanf\r\n#endif\r\n\r\n#if defined(_WIN64)\r\n\t#define TIXML_FSEEK _fseeki64\r\n\t#define TIXML_FTELL _ftelli64\r\n#elif defined(__APPLE__) || defined(__FreeBSD__) || defined(__OpenBSD__) || defined(__NetBSD__) || defined(__DragonFly__) || defined(__CYGWIN__)\r\n\t#define TIXML_FSEEK fseeko\r\n\t#define TIXML_FTELL ftello\r\n#elif defined(__ANDROID__) \r\n    #if __ANDROID_API__ > 24\r\n        #define TIXML_FSEEK fseeko64\r\n        #define TIXML_FTELL ftello64\r\n    #else\r\n        #define TIXML_FSEEK fseeko\r\n        #define TIXML_FTELL ftello\r\n    #endif\r\n#else\r\n\t#define TIXML_FSEEK fseek\r\n\t#define TIXML_FTELL ftell\r\n#endif\r\n\r\n\r\nstatic const char LINE_FEED\t\t\t\t= static_cast<char>(0x0a);\t\t\t// all line endings are normalized to LF\r\nstatic const char LF = LINE_FEED;\r\nstatic const char CARRIAGE_RETURN\t\t= static_cast<char>(0x0d);\t\t\t// CR gets filtered out\r\nstatic const char CR = CARRIAGE_RETURN;\r\nstatic const char SINGLE_QUOTE\t\t\t= '\\'';\r\nstatic const char DOUBLE_QUOTE\t\t\t= '\\\"';\r\n\r\n// Bunch of unicode info at:\r\n//\t\thttp://www.unicode.org/faq/utf_bom.html\r\n//\tef bb bf (Microsoft \"lead bytes\") - designates UTF-8\r\n\r\nstatic const unsigned char TIXML_UTF_LEAD_0 = 0xefU;\r\nstatic const unsigned char TIXML_UTF_LEAD_1 = 0xbbU;\r\nstatic const unsigned char TIXML_UTF_LEAD_2 = 0xbfU;\r\n\r\nnamespace tinyxml2\r\n{\r\n\r\nstruct Entity {\r\n    const char* pattern;\r\n    int length;\r\n    char value;\r\n};\r\n\r\nstatic const int NUM_ENTITIES = 5;\r\nstatic const Entity entities[NUM_ENTITIES] = {\r\n    { \"quot\", 4,\tDOUBLE_QUOTE },\r\n    { \"amp\", 3,\t\t'&'  },\r\n    { \"apos\", 4,\tSINGLE_QUOTE },\r\n    { \"lt\",\t2, \t\t'<'\t },\r\n    { \"gt\",\t2,\t\t'>'\t }\r\n};\r\n\r\n\r\nStrPair::~StrPair()\r\n{\r\n    Reset();\r\n}\r\n\r\n\r\nvoid StrPair::TransferTo( StrPair* other )\r\n{\r\n    if ( this == other ) {\r\n        return;\r\n    }\r\n    // This in effect implements the assignment operator by \"moving\"\r\n    // ownership (as in auto_ptr).\r\n\r\n    TIXMLASSERT( other != 0 );\r\n    TIXMLASSERT( other->_flags == 0 );\r\n    TIXMLASSERT( other->_start == 0 );\r\n    TIXMLASSERT( other->_end == 0 );\r\n\r\n    other->Reset();\r\n\r\n    other->_flags = _flags;\r\n    other->_start = _start;\r\n    other->_end = _end;\r\n\r\n    _flags = 0;\r\n    _start = 0;\r\n    _end = 0;\r\n}\r\n\r\n\r\nvoid StrPair::Reset()\r\n{\r\n    if ( _flags & NEEDS_DELETE ) {\r\n        delete [] _start;\r\n    }\r\n    _flags = 0;\r\n    _start = 0;\r\n    _end = 0;\r\n}\r\n\r\n\r\nvoid StrPair::SetStr( const char* str, int flags )\r\n{\r\n    TIXMLASSERT( str );\r\n    Reset();\r\n    size_t len = strlen( str );\r\n    TIXMLASSERT( _start == 0 );\r\n    _start = new char[ len+1 ];\r\n    memcpy( _start, str, len+1 );\r\n    _end = _start + len;\r\n    _flags = flags | NEEDS_DELETE;\r\n}\r\n\r\n\r\nchar* StrPair::ParseText( char* p, const char* endTag, int strFlags, int* curLineNumPtr )\r\n{\r\n    TIXMLASSERT( p );\r\n    TIXMLASSERT( endTag && *endTag );\r\n\tTIXMLASSERT(curLineNumPtr);\r\n\r\n    char* start = p;\r\n    const char  endChar = *endTag;\r\n    size_t length = strlen( endTag );\r\n\r\n    // Inner loop of text parsing.\r\n    while ( *p ) {\r\n        if ( *p == endChar && strncmp( p, endTag, length ) == 0 ) {\r\n            Set( start, p, strFlags );\r\n            return p + length;\r\n        } else if (*p == '\\n') {\r\n            ++(*curLineNumPtr);\r\n        }\r\n        ++p;\r\n        TIXMLASSERT( p );\r\n    }\r\n    return 0;\r\n}\r\n\r\n\r\nchar* StrPair::ParseName( char* p )\r\n{\r\n    if ( !p || !(*p) ) {\r\n        return 0;\r\n    }\r\n    if ( !XMLUtil::IsNameStartChar( (unsigned char) *p ) ) {\r\n        return 0;\r\n    }\r\n\r\n    char* const start = p;\r\n    ++p;\r\n    while ( *p && XMLUtil::IsNameChar( (unsigned char) *p ) ) {\r\n        ++p;\r\n    }\r\n\r\n    Set( start, p, 0 );\r\n    return p;\r\n}\r\n\r\n\r\nvoid StrPair::CollapseWhitespace()\r\n{\r\n    // Adjusting _start would cause undefined behavior on delete[]\r\n    TIXMLASSERT( ( _flags & NEEDS_DELETE ) == 0 );\r\n    // Trim leading space.\r\n    _start = XMLUtil::SkipWhiteSpace( _start, 0 );\r\n\r\n    if ( *_start ) {\r\n        const char* p = _start;\t// the read pointer\r\n        char* q = _start;\t// the write pointer\r\n\r\n        while( *p ) {\r\n            if ( XMLUtil::IsWhiteSpace( *p )) {\r\n                p = XMLUtil::SkipWhiteSpace( p, 0 );\r\n                if ( *p == 0 ) {\r\n                    break;    // don't write to q; this trims the trailing space.\r\n                }\r\n                *q = ' ';\r\n                ++q;\r\n            }\r\n            *q = *p;\r\n            ++q;\r\n            ++p;\r\n        }\r\n        *q = 0;\r\n    }\r\n}\r\n\r\n\r\nconst char* StrPair::GetStr()\r\n{\r\n    TIXMLASSERT( _start );\r\n    TIXMLASSERT( _end );\r\n    if ( _flags & NEEDS_FLUSH ) {\r\n        *_end = 0;\r\n        _flags ^= NEEDS_FLUSH;\r\n\r\n        if ( _flags ) {\r\n            const char* p = _start;\t// the read pointer\r\n            char* q = _start;\t// the write pointer\r\n\r\n            while( p < _end ) {\r\n                if ( (_flags & NEEDS_NEWLINE_NORMALIZATION) && *p == CR ) {\r\n                    // CR-LF pair becomes LF\r\n                    // CR alone becomes LF\r\n                    // LF-CR becomes LF\r\n                    if ( *(p+1) == LF ) {\r\n                        p += 2;\r\n                    }\r\n                    else {\r\n                        ++p;\r\n                    }\r\n                    *q = LF;\r\n                    ++q;\r\n                }\r\n                else if ( (_flags & NEEDS_NEWLINE_NORMALIZATION) && *p == LF ) {\r\n                    if ( *(p+1) == CR ) {\r\n                        p += 2;\r\n                    }\r\n                    else {\r\n                        ++p;\r\n                    }\r\n                    *q = LF;\r\n                    ++q;\r\n                }\r\n                else if ( (_flags & NEEDS_ENTITY_PROCESSING) && *p == '&' ) {\r\n                    // Entities handled by tinyXML2:\r\n                    // - special entities in the entity table [in/out]\r\n                    // - numeric character reference [in]\r\n                    //   &#20013; or &#x4e2d;\r\n\r\n                    if ( *(p+1) == '#' ) {\r\n                        const int buflen = 10;\r\n                        char buf[buflen] = { 0 };\r\n                        int len = 0;\r\n                        const char* adjusted = const_cast<char*>( XMLUtil::GetCharacterRef( p, buf, &len ) );\r\n                        if ( adjusted == 0 ) {\r\n                            *q = *p;\r\n                            ++p;\r\n                            ++q;\r\n                        }\r\n                        else {\r\n                            TIXMLASSERT( 0 <= len && len <= buflen );\r\n                            TIXMLASSERT( q + len <= adjusted );\r\n                            p = adjusted;\r\n                            memcpy( q, buf, len );\r\n                            q += len;\r\n                        }\r\n                    }\r\n                    else {\r\n                        bool entityFound = false;\r\n                        for( int i = 0; i < NUM_ENTITIES; ++i ) {\r\n                            const Entity& entity = entities[i];\r\n                            if ( strncmp( p + 1, entity.pattern, entity.length ) == 0\r\n                                    && *( p + entity.length + 1 ) == ';' ) {\r\n                                // Found an entity - convert.\r\n                                *q = entity.value;\r\n                                ++q;\r\n                                p += entity.length + 2;\r\n                                entityFound = true;\r\n                                break;\r\n                            }\r\n                        }\r\n                        if ( !entityFound ) {\r\n                            // fixme: treat as error?\r\n                            ++p;\r\n                            ++q;\r\n                        }\r\n                    }\r\n                }\r\n                else {\r\n                    *q = *p;\r\n                    ++p;\r\n                    ++q;\r\n                }\r\n            }\r\n            *q = 0;\r\n        }\r\n        // The loop below has plenty going on, and this\r\n        // is a less useful mode. Break it out.\r\n        if ( _flags & NEEDS_WHITESPACE_COLLAPSING ) {\r\n            CollapseWhitespace();\r\n        }\r\n        _flags = (_flags & NEEDS_DELETE);\r\n    }\r\n    TIXMLASSERT( _start );\r\n    return _start;\r\n}\r\n\r\n\r\n\r\n\r\n// --------- XMLUtil ----------- //\r\n\r\nconst char* XMLUtil::writeBoolTrue  = \"true\";\r\nconst char* XMLUtil::writeBoolFalse = \"false\";\r\n\r\nvoid XMLUtil::SetBoolSerialization(const char* writeTrue, const char* writeFalse)\r\n{\r\n\tstatic const char* defTrue  = \"true\";\r\n\tstatic const char* defFalse = \"false\";\r\n\r\n\twriteBoolTrue = (writeTrue) ? writeTrue : defTrue;\r\n\twriteBoolFalse = (writeFalse) ? writeFalse : defFalse;\r\n}\r\n\r\n\r\nconst char* XMLUtil::ReadBOM( const char* p, bool* bom )\r\n{\r\n    TIXMLASSERT( p );\r\n    TIXMLASSERT( bom );\r\n    *bom = false;\r\n    const unsigned char* pu = reinterpret_cast<const unsigned char*>(p);\r\n    // Check for BOM:\r\n    if (    *(pu+0) == TIXML_UTF_LEAD_0\r\n            && *(pu+1) == TIXML_UTF_LEAD_1\r\n            && *(pu+2) == TIXML_UTF_LEAD_2 ) {\r\n        *bom = true;\r\n        p += 3;\r\n    }\r\n    TIXMLASSERT( p );\r\n    return p;\r\n}\r\n\r\n\r\nvoid XMLUtil::ConvertUTF32ToUTF8( unsigned long input, char* output, int* length )\r\n{\r\n    const unsigned long BYTE_MASK = 0xBF;\r\n    const unsigned long BYTE_MARK = 0x80;\r\n    const unsigned long FIRST_BYTE_MARK[7] = { 0x00, 0x00, 0xC0, 0xE0, 0xF0, 0xF8, 0xFC };\r\n\r\n    if (input < 0x80) {\r\n        *length = 1;\r\n    }\r\n    else if ( input < 0x800 ) {\r\n        *length = 2;\r\n    }\r\n    else if ( input < 0x10000 ) {\r\n        *length = 3;\r\n    }\r\n    else if ( input < 0x200000 ) {\r\n        *length = 4;\r\n    }\r\n    else {\r\n        *length = 0;    // This code won't convert this correctly anyway.\r\n        return;\r\n    }\r\n\r\n    output += *length;\r\n\r\n    // Scary scary fall throughs are annotated with carefully designed comments\r\n    // to suppress compiler warnings such as -Wimplicit-fallthrough in gcc\r\n    switch (*length) {\r\n        case 4:\r\n            --output;\r\n            *output = static_cast<char>((input | BYTE_MARK) & BYTE_MASK);\r\n            input >>= 6;\r\n            //fall through\r\n        case 3:\r\n            --output;\r\n            *output = static_cast<char>((input | BYTE_MARK) & BYTE_MASK);\r\n            input >>= 6;\r\n            //fall through\r\n        case 2:\r\n            --output;\r\n            *output = static_cast<char>((input | BYTE_MARK) & BYTE_MASK);\r\n            input >>= 6;\r\n            //fall through\r\n        case 1:\r\n            --output;\r\n            *output = static_cast<char>(input | FIRST_BYTE_MARK[*length]);\r\n            break;\r\n        default:\r\n            TIXMLASSERT( false );\r\n    }\r\n}\r\n\r\n\r\nconst char* XMLUtil::GetCharacterRef( const char* p, char* value, int* length )\r\n{\r\n    // Presume an entity, and pull it out.\r\n    *length = 0;\r\n\r\n    if ( *(p+1) == '#' && *(p+2) ) {\r\n        unsigned long ucs = 0;\r\n        TIXMLASSERT( sizeof( ucs ) >= 4 );\r\n        ptrdiff_t delta = 0;\r\n        unsigned mult = 1;\r\n        static const char SEMICOLON = ';';\r\n\r\n        if ( *(p+2) == 'x' ) {\r\n            // Hexadecimal.\r\n            const char* q = p+3;\r\n            if ( !(*q) ) {\r\n                return 0;\r\n            }\r\n\r\n            q = strchr( q, SEMICOLON );\r\n\r\n            if ( !q ) {\r\n                return 0;\r\n            }\r\n            TIXMLASSERT( *q == SEMICOLON );\r\n\r\n            delta = q-p;\r\n            --q;\r\n\r\n            while ( *q != 'x' ) {\r\n                unsigned int digit = 0;\r\n\r\n                if ( *q >= '0' && *q <= '9' ) {\r\n                    digit = *q - '0';\r\n                }\r\n                else if ( *q >= 'a' && *q <= 'f' ) {\r\n                    digit = *q - 'a' + 10;\r\n                }\r\n                else if ( *q >= 'A' && *q <= 'F' ) {\r\n                    digit = *q - 'A' + 10;\r\n                }\r\n                else {\r\n                    return 0;\r\n                }\r\n                TIXMLASSERT( digit < 16 );\r\n                TIXMLASSERT( digit == 0 || mult <= UINT_MAX / digit );\r\n                const unsigned int digitScaled = mult * digit;\r\n                TIXMLASSERT( ucs <= ULONG_MAX - digitScaled );\r\n                ucs += digitScaled;\r\n                TIXMLASSERT( mult <= UINT_MAX / 16 );\r\n                mult *= 16;\r\n                --q;\r\n            }\r\n        }\r\n        else {\r\n            // Decimal.\r\n            const char* q = p+2;\r\n            if ( !(*q) ) {\r\n                return 0;\r\n            }\r\n\r\n            q = strchr( q, SEMICOLON );\r\n\r\n            if ( !q ) {\r\n                return 0;\r\n            }\r\n            TIXMLASSERT( *q == SEMICOLON );\r\n\r\n            delta = q-p;\r\n            --q;\r\n\r\n            while ( *q != '#' ) {\r\n                if ( *q >= '0' && *q <= '9' ) {\r\n                    const unsigned int digit = *q - '0';\r\n                    TIXMLASSERT( digit < 10 );\r\n                    TIXMLASSERT( digit == 0 || mult <= UINT_MAX / digit );\r\n                    const unsigned int digitScaled = mult * digit;\r\n                    TIXMLASSERT( ucs <= ULONG_MAX - digitScaled );\r\n                    ucs += digitScaled;\r\n                }\r\n                else {\r\n                    return 0;\r\n                }\r\n                TIXMLASSERT( mult <= UINT_MAX / 10 );\r\n                mult *= 10;\r\n                --q;\r\n            }\r\n        }\r\n        // convert the UCS to UTF-8\r\n        ConvertUTF32ToUTF8( ucs, value, length );\r\n        return p + delta + 1;\r\n    }\r\n    return p+1;\r\n}\r\n\r\n\r\nvoid XMLUtil::ToStr( int v, char* buffer, int bufferSize )\r\n{\r\n    TIXML_SNPRINTF( buffer, bufferSize, \"%d\", v );\r\n}\r\n\r\n\r\nvoid XMLUtil::ToStr( unsigned v, char* buffer, int bufferSize )\r\n{\r\n    TIXML_SNPRINTF( buffer, bufferSize, \"%u\", v );\r\n}\r\n\r\n\r\nvoid XMLUtil::ToStr( bool v, char* buffer, int bufferSize )\r\n{\r\n    TIXML_SNPRINTF( buffer, bufferSize, \"%s\", v ? writeBoolTrue : writeBoolFalse);\r\n}\r\n\r\n/*\r\n\tToStr() of a number is a very tricky topic.\r\n\thttps://github.com/leethomason/tinyxml2/issues/106\r\n*/\r\nvoid XMLUtil::ToStr( float v, char* buffer, int bufferSize )\r\n{\r\n    TIXML_SNPRINTF( buffer, bufferSize, \"%.8g\", v );\r\n}\r\n\r\n\r\nvoid XMLUtil::ToStr( double v, char* buffer, int bufferSize )\r\n{\r\n    TIXML_SNPRINTF( buffer, bufferSize, \"%.17g\", v );\r\n}\r\n\r\n\r\nvoid XMLUtil::ToStr( int64_t v, char* buffer, int bufferSize )\r\n{\r\n\t// horrible syntax trick to make the compiler happy about %lld\r\n\tTIXML_SNPRINTF(buffer, bufferSize, \"%lld\", static_cast<long long>(v));\r\n}\r\n\r\nvoid XMLUtil::ToStr( uint64_t v, char* buffer, int bufferSize )\r\n{\r\n    // horrible syntax trick to make the compiler happy about %llu\r\n    TIXML_SNPRINTF(buffer, bufferSize, \"%llu\", (long long)v);\r\n}\r\n\r\nbool XMLUtil::ToInt(const char* str, int* value)\r\n{\r\n    if (IsPrefixHex(str)) {\r\n        unsigned v;\r\n        if (TIXML_SSCANF(str, \"%x\", &v) == 1) {\r\n            *value = static_cast<int>(v);\r\n            return true;\r\n        }\r\n    }\r\n    else {\r\n        if (TIXML_SSCANF(str, \"%d\", value) == 1) {\r\n            return true;\r\n        }\r\n    }\r\n    return false;\r\n}\r\n\r\nbool XMLUtil::ToUnsigned(const char* str, unsigned* value)\r\n{\r\n    if (TIXML_SSCANF(str, IsPrefixHex(str) ? \"%x\" : \"%u\", value) == 1) {\r\n        return true;\r\n    }\r\n    return false;\r\n}\r\n\r\nbool XMLUtil::ToBool( const char* str, bool* value )\r\n{\r\n    int ival = 0;\r\n    if ( ToInt( str, &ival )) {\r\n        *value = (ival==0) ? false : true;\r\n        return true;\r\n    }\r\n    static const char* TRUE_VALS[] = { \"true\", \"True\", \"TRUE\", 0 };\r\n    static const char* FALSE_VALS[] = { \"false\", \"False\", \"FALSE\", 0 };\r\n\r\n    for (int i = 0; TRUE_VALS[i]; ++i) {\r\n        if (StringEqual(str, TRUE_VALS[i])) {\r\n            *value = true;\r\n            return true;\r\n        }\r\n    }\r\n    for (int i = 0; FALSE_VALS[i]; ++i) {\r\n        if (StringEqual(str, FALSE_VALS[i])) {\r\n            *value = false;\r\n            return true;\r\n        }\r\n    }\r\n    return false;\r\n}\r\n\r\n\r\nbool XMLUtil::ToFloat( const char* str, float* value )\r\n{\r\n    if ( TIXML_SSCANF( str, \"%f\", value ) == 1 ) {\r\n        return true;\r\n    }\r\n    return false;\r\n}\r\n\r\n\r\nbool XMLUtil::ToDouble( const char* str, double* value )\r\n{\r\n    if ( TIXML_SSCANF( str, \"%lf\", value ) == 1 ) {\r\n        return true;\r\n    }\r\n    return false;\r\n}\r\n\r\n\r\nbool XMLUtil::ToInt64(const char* str, int64_t* value)\r\n{\r\n    if (IsPrefixHex(str)) {\r\n        unsigned long long v = 0;\t// horrible syntax trick to make the compiler happy about %llx\r\n        if (TIXML_SSCANF(str, \"%llx\", &v) == 1) {\r\n            *value = static_cast<int64_t>(v);\r\n            return true;\r\n        }\r\n    }\r\n    else {\r\n        long long v = 0;\t// horrible syntax trick to make the compiler happy about %lld\r\n        if (TIXML_SSCANF(str, \"%lld\", &v) == 1) {\r\n            *value = static_cast<int64_t>(v);\r\n            return true;\r\n        }\r\n    }\r\n\treturn false;\r\n}\r\n\r\n\r\nbool XMLUtil::ToUnsigned64(const char* str, uint64_t* value) {\r\n    unsigned long long v = 0;\t// horrible syntax trick to make the compiler happy about %llu\r\n    if(TIXML_SSCANF(str, IsPrefixHex(str) ? \"%llx\" : \"%llu\", &v) == 1) {\r\n        *value = (uint64_t)v;\r\n        return true;\r\n    }\r\n    return false;\r\n}\r\n\r\n\r\nchar* XMLDocument::Identify( char* p, XMLNode** node, bool first )\r\n{\r\n    TIXMLASSERT( node );\r\n    TIXMLASSERT( p );\r\n    char* const start = p;\r\n    int const startLine = _parseCurLineNum;\r\n    p = XMLUtil::SkipWhiteSpace( p, &_parseCurLineNum );\r\n    if( !*p ) {\r\n        *node = 0;\r\n        TIXMLASSERT( p );\r\n        return p;\r\n    }\r\n\r\n    // These strings define the matching patterns:\r\n    static const char* xmlHeader\t\t= { \"<?\" };\r\n    static const char* commentHeader\t= { \"<!--\" };\r\n    static const char* cdataHeader\t\t= { \"<![CDATA[\" };\r\n    static const char* dtdHeader\t\t= { \"<!\" };\r\n    static const char* elementHeader\t= { \"<\" };\t// and a header for everything else; check last.\r\n\r\n    static const int xmlHeaderLen\t\t= 2;\r\n    static const int commentHeaderLen\t= 4;\r\n    static const int cdataHeaderLen\t\t= 9;\r\n    static const int dtdHeaderLen\t\t= 2;\r\n    static const int elementHeaderLen\t= 1;\r\n\r\n    TIXMLASSERT( sizeof( XMLComment ) == sizeof( XMLUnknown ) );\t\t// use same memory pool\r\n    TIXMLASSERT( sizeof( XMLComment ) == sizeof( XMLDeclaration ) );\t// use same memory pool\r\n    XMLNode* returnNode = 0;\r\n    if ( XMLUtil::StringEqual( p, xmlHeader, xmlHeaderLen ) ) {\r\n        returnNode = CreateUnlinkedNode<XMLDeclaration>( _commentPool );\r\n        returnNode->_parseLineNum = _parseCurLineNum;\r\n        p += xmlHeaderLen;\r\n    }\r\n    else if ( XMLUtil::StringEqual( p, commentHeader, commentHeaderLen ) ) {\r\n        returnNode = CreateUnlinkedNode<XMLComment>( _commentPool );\r\n        returnNode->_parseLineNum = _parseCurLineNum;\r\n        p += commentHeaderLen;\r\n    }\r\n    else if ( XMLUtil::StringEqual( p, cdataHeader, cdataHeaderLen ) ) {\r\n        XMLText* text = CreateUnlinkedNode<XMLText>( _textPool );\r\n        returnNode = text;\r\n        returnNode->_parseLineNum = _parseCurLineNum;\r\n        p += cdataHeaderLen;\r\n        text->SetCData( true );\r\n    }\r\n    else if ( XMLUtil::StringEqual( p, dtdHeader, dtdHeaderLen ) ) {\r\n        returnNode = CreateUnlinkedNode<XMLUnknown>( _commentPool );\r\n        returnNode->_parseLineNum = _parseCurLineNum;\r\n        p += dtdHeaderLen;\r\n    }\r\n    else if ( XMLUtil::StringEqual( p, elementHeader, elementHeaderLen ) ) {\r\n\r\n        // Preserve whitespace pedantically before closing tag, when it's immediately after opening tag\r\n        if (WhitespaceMode() == PEDANTIC_WHITESPACE && first && p != start && *(p + elementHeaderLen) == '/') {\r\n            returnNode = CreateUnlinkedNode<XMLText>(_textPool);\r\n            returnNode->_parseLineNum = startLine;\r\n            p = start;\t// Back it up, all the text counts.\r\n            _parseCurLineNum = startLine;\r\n        }\r\n        else {\r\n            returnNode = CreateUnlinkedNode<XMLElement>(_elementPool);\r\n            returnNode->_parseLineNum = _parseCurLineNum;\r\n            p += elementHeaderLen;\r\n        }\r\n    }\r\n    else {\r\n        returnNode = CreateUnlinkedNode<XMLText>( _textPool );\r\n        returnNode->_parseLineNum = _parseCurLineNum; // Report line of first non-whitespace character\r\n        p = start;\t// Back it up, all the text counts.\r\n        _parseCurLineNum = startLine;\r\n    }\r\n\r\n    TIXMLASSERT( returnNode );\r\n    TIXMLASSERT( p );\r\n    *node = returnNode;\r\n    return p;\r\n}\r\n\r\n\r\nbool XMLDocument::Accept( XMLVisitor* visitor ) const\r\n{\r\n    TIXMLASSERT( visitor );\r\n    if ( visitor->VisitEnter( *this ) ) {\r\n        for ( const XMLNode* node=FirstChild(); node; node=node->NextSibling() ) {\r\n            if ( !node->Accept( visitor ) ) {\r\n                break;\r\n            }\r\n        }\r\n    }\r\n    return visitor->VisitExit( *this );\r\n}\r\n\r\n\r\n// --------- XMLNode ----------- //\r\n\r\nXMLNode::XMLNode( XMLDocument* doc ) :\r\n    _document( doc ),\r\n    _parent( 0 ),\r\n    _value(),\r\n    _parseLineNum( 0 ),\r\n    _firstChild( 0 ), _lastChild( 0 ),\r\n    _prev( 0 ), _next( 0 ),\r\n\t_userData( 0 ),\r\n    _memPool( 0 )\r\n{\r\n}\r\n\r\n\r\nXMLNode::~XMLNode()\r\n{\r\n    DeleteChildren();\r\n    if ( _parent ) {\r\n        _parent->Unlink( this );\r\n    }\r\n}\r\n\r\n// ChildElementCount was originally suggested by msteiger on the sourceforge page for TinyXML and modified by KB1SPH for TinyXML-2.\r\n\r\nint XMLNode::ChildElementCount(const char *value) const {\r\n\tint count = 0;\r\n\r\n\tconst XMLElement *e = FirstChildElement(value);\r\n\r\n\twhile (e) {\r\n\t\te = e->NextSiblingElement(value);\r\n\t\tcount++;\r\n\t}\r\n\r\n\treturn count;\r\n}\r\n\r\nint XMLNode::ChildElementCount() const {\r\n\tint count = 0;\r\n\r\n\tconst XMLElement *e = FirstChildElement();\r\n\r\n\twhile (e) {\r\n\t\te = e->NextSiblingElement();\r\n\t\tcount++;\r\n\t}\r\n\r\n\treturn count;\r\n}\r\n\r\nconst char* XMLNode::Value() const\r\n{\r\n    // Edge case: XMLDocuments don't have a Value. Return null.\r\n    if ( this->ToDocument() )\r\n        return 0;\r\n    return _value.GetStr();\r\n}\r\n\r\nvoid XMLNode::SetValue( const char* str, bool staticMem )\r\n{\r\n    if ( staticMem ) {\r\n        _value.SetInternedStr( str );\r\n    }\r\n    else {\r\n        _value.SetStr( str );\r\n    }\r\n}\r\n\r\nXMLNode* XMLNode::DeepClone(XMLDocument* target) const\r\n{\r\n\tXMLNode* clone = this->ShallowClone(target);\r\n\tif (!clone) return 0;\r\n\r\n\tfor (const XMLNode* child = this->FirstChild(); child; child = child->NextSibling()) {\r\n\t\tXMLNode* childClone = child->DeepClone(target);\r\n\t\tTIXMLASSERT(childClone);\r\n\t\tclone->InsertEndChild(childClone);\r\n\t}\r\n\treturn clone;\r\n}\r\n\r\nvoid XMLNode::DeleteChildren()\r\n{\r\n    while( _firstChild ) {\r\n        TIXMLASSERT( _lastChild );\r\n        DeleteChild( _firstChild );\r\n    }\r\n    _firstChild = _lastChild = 0;\r\n}\r\n\r\n\r\nvoid XMLNode::Unlink( XMLNode* child )\r\n{\r\n    TIXMLASSERT( child );\r\n    TIXMLASSERT( child->_document == _document );\r\n    TIXMLASSERT( child->_parent == this );\r\n    if ( child == _firstChild ) {\r\n        _firstChild = _firstChild->_next;\r\n    }\r\n    if ( child == _lastChild ) {\r\n        _lastChild = _lastChild->_prev;\r\n    }\r\n\r\n    if ( child->_prev ) {\r\n        child->_prev->_next = child->_next;\r\n    }\r\n    if ( child->_next ) {\r\n        child->_next->_prev = child->_prev;\r\n    }\r\n\tchild->_next = 0;\r\n\tchild->_prev = 0;\r\n\tchild->_parent = 0;\r\n}\r\n\r\n\r\nvoid XMLNode::DeleteChild( XMLNode* node )\r\n{\r\n    TIXMLASSERT( node );\r\n    TIXMLASSERT( node->_document == _document );\r\n    TIXMLASSERT( node->_parent == this );\r\n    Unlink( node );\r\n\tTIXMLASSERT(node->_prev == 0);\r\n\tTIXMLASSERT(node->_next == 0);\r\n\tTIXMLASSERT(node->_parent == 0);\r\n    DeleteNode( node );\r\n}\r\n\r\n\r\nXMLNode* XMLNode::InsertEndChild( XMLNode* addThis )\r\n{\r\n    TIXMLASSERT( addThis );\r\n    if ( addThis->_document != _document ) {\r\n        TIXMLASSERT( false );\r\n        return 0;\r\n    }\r\n    InsertChildPreamble( addThis );\r\n\r\n    if ( _lastChild ) {\r\n        TIXMLASSERT( _firstChild );\r\n        TIXMLASSERT( _lastChild->_next == 0 );\r\n        _lastChild->_next = addThis;\r\n        addThis->_prev = _lastChild;\r\n        _lastChild = addThis;\r\n\r\n        addThis->_next = 0;\r\n    }\r\n    else {\r\n        TIXMLASSERT( _firstChild == 0 );\r\n        _firstChild = _lastChild = addThis;\r\n\r\n        addThis->_prev = 0;\r\n        addThis->_next = 0;\r\n    }\r\n    addThis->_parent = this;\r\n    return addThis;\r\n}\r\n\r\n\r\nXMLNode* XMLNode::InsertFirstChild( XMLNode* addThis )\r\n{\r\n    TIXMLASSERT( addThis );\r\n    if ( addThis->_document != _document ) {\r\n        TIXMLASSERT( false );\r\n        return 0;\r\n    }\r\n    InsertChildPreamble( addThis );\r\n\r\n    if ( _firstChild ) {\r\n        TIXMLASSERT( _lastChild );\r\n        TIXMLASSERT( _firstChild->_prev == 0 );\r\n\r\n        _firstChild->_prev = addThis;\r\n        addThis->_next = _firstChild;\r\n        _firstChild = addThis;\r\n\r\n        addThis->_prev = 0;\r\n    }\r\n    else {\r\n        TIXMLASSERT( _lastChild == 0 );\r\n        _firstChild = _lastChild = addThis;\r\n\r\n        addThis->_prev = 0;\r\n        addThis->_next = 0;\r\n    }\r\n    addThis->_parent = this;\r\n    return addThis;\r\n}\r\n\r\n\r\nXMLNode* XMLNode::InsertAfterChild( XMLNode* afterThis, XMLNode* addThis )\r\n{\r\n    TIXMLASSERT( addThis );\r\n    if ( addThis->_document != _document ) {\r\n        TIXMLASSERT( false );\r\n        return 0;\r\n    }\r\n\r\n    TIXMLASSERT( afterThis );\r\n\r\n    if ( afterThis->_parent != this ) {\r\n        TIXMLASSERT( false );\r\n        return 0;\r\n    }\r\n    if ( afterThis == addThis ) {\r\n        // Current state: BeforeThis -> AddThis -> OneAfterAddThis\r\n        // Now AddThis must disappear from it's location and then\r\n        // reappear between BeforeThis and OneAfterAddThis.\r\n        // So just leave it where it is.\r\n        return addThis;\r\n    }\r\n\r\n    if ( afterThis->_next == 0 ) {\r\n        // The last node or the only node.\r\n        return InsertEndChild( addThis );\r\n    }\r\n    InsertChildPreamble( addThis );\r\n    addThis->_prev = afterThis;\r\n    addThis->_next = afterThis->_next;\r\n    afterThis->_next->_prev = addThis;\r\n    afterThis->_next = addThis;\r\n    addThis->_parent = this;\r\n    return addThis;\r\n}\r\n\r\n\r\n\r\n\r\nconst XMLElement* XMLNode::FirstChildElement( const char* name ) const\r\n{\r\n    for( const XMLNode* node = _firstChild; node; node = node->_next ) {\r\n        const XMLElement* element = node->ToElementWithName( name );\r\n        if ( element ) {\r\n            return element;\r\n        }\r\n    }\r\n    return 0;\r\n}\r\n\r\n\r\nconst XMLElement* XMLNode::LastChildElement( const char* name ) const\r\n{\r\n    for( const XMLNode* node = _lastChild; node; node = node->_prev ) {\r\n        const XMLElement* element = node->ToElementWithName( name );\r\n        if ( element ) {\r\n            return element;\r\n        }\r\n    }\r\n    return 0;\r\n}\r\n\r\n\r\nconst XMLElement* XMLNode::NextSiblingElement( const char* name ) const\r\n{\r\n    for( const XMLNode* node = _next; node; node = node->_next ) {\r\n        const XMLElement* element = node->ToElementWithName( name );\r\n        if ( element ) {\r\n            return element;\r\n        }\r\n    }\r\n    return 0;\r\n}\r\n\r\n\r\nconst XMLElement* XMLNode::PreviousSiblingElement( const char* name ) const\r\n{\r\n    for( const XMLNode* node = _prev; node; node = node->_prev ) {\r\n        const XMLElement* element = node->ToElementWithName( name );\r\n        if ( element ) {\r\n            return element;\r\n        }\r\n    }\r\n    return 0;\r\n}\r\n\r\n\r\nchar* XMLNode::ParseDeep( char* p, StrPair* parentEndTag, int* curLineNumPtr )\r\n{\r\n    // This is a recursive method, but thinking about it \"at the current level\"\r\n    // it is a pretty simple flat list:\r\n    //\t\t<foo/>\r\n    //\t\t<!-- comment -->\r\n    //\r\n    // With a special case:\r\n    //\t\t<foo>\r\n    //\t\t</foo>\r\n    //\t\t<!-- comment -->\r\n    //\r\n    // Where the closing element (/foo) *must* be the next thing after the opening\r\n    // element, and the names must match. BUT the tricky bit is that the closing\r\n    // element will be read by the child.\r\n    //\r\n    // 'endTag' is the end tag for this node, it is returned by a call to a child.\r\n    // 'parentEnd' is the end tag for the parent, which is filled in and returned.\r\n\r\n\tXMLDocument::DepthTracker tracker(_document);\r\n\tif (_document->Error())\r\n\t\treturn 0;\r\n\r\n\tbool first = true;\r\n\twhile( p && *p ) {\r\n        XMLNode* node = 0;\r\n\r\n        p = _document->Identify( p, &node, first );\r\n        TIXMLASSERT( p );\r\n        if ( node == 0 ) {\r\n            break;\r\n        }\r\n        first = false;\r\n\r\n       const int initialLineNum = node->_parseLineNum;\r\n\r\n        StrPair endTag;\r\n        p = node->ParseDeep( p, &endTag, curLineNumPtr );\r\n        if ( !p ) {\r\n            _document->DeleteNode( node );\r\n            if ( !_document->Error() ) {\r\n                _document->SetError( XML_ERROR_PARSING, initialLineNum, 0);\r\n            }\r\n            break;\r\n        }\r\n\r\n        const XMLDeclaration* const decl = node->ToDeclaration();\r\n        if ( decl ) {\r\n            // Declarations are only allowed at document level\r\n            //\r\n            // Multiple declarations are allowed but all declarations\r\n            // must occur before anything else. \r\n            //\r\n            // Optimized due to a security test case. If the first node is \r\n            // a declaration, and the last node is a declaration, then only \r\n            // declarations have so far been added.\r\n            bool wellLocated = false;\r\n\r\n            if (ToDocument()) {\r\n                if (FirstChild()) {\r\n                    wellLocated =\r\n                        FirstChild() &&\r\n                        FirstChild()->ToDeclaration() &&\r\n                        LastChild() &&\r\n                        LastChild()->ToDeclaration();\r\n                }\r\n                else {\r\n                    wellLocated = true;\r\n                }\r\n            }\r\n            if ( !wellLocated ) {\r\n                _document->SetError( XML_ERROR_PARSING_DECLARATION, initialLineNum, \"XMLDeclaration value=%s\", decl->Value());\r\n                _document->DeleteNode( node );\r\n                break;\r\n            }\r\n        }\r\n\r\n        XMLElement* ele = node->ToElement();\r\n        if ( ele ) {\r\n            // We read the end tag. Return it to the parent.\r\n            if ( ele->ClosingType() == XMLElement::CLOSING ) {\r\n                if ( parentEndTag ) {\r\n                    ele->_value.TransferTo( parentEndTag );\r\n                }\r\n                node->_memPool->SetTracked();   // created and then immediately deleted.\r\n                DeleteNode( node );\r\n                return p;\r\n            }\r\n\r\n            // Handle an end tag returned to this level.\r\n            // And handle a bunch of annoying errors.\r\n            bool mismatch = false;\r\n            if ( endTag.Empty() ) {\r\n                if ( ele->ClosingType() == XMLElement::OPEN ) {\r\n                    mismatch = true;\r\n                }\r\n            }\r\n            else {\r\n                if ( ele->ClosingType() != XMLElement::OPEN ) {\r\n                    mismatch = true;\r\n                }\r\n                else if ( !XMLUtil::StringEqual( endTag.GetStr(), ele->Name() ) ) {\r\n                    mismatch = true;\r\n                }\r\n            }\r\n            if ( mismatch ) {\r\n                _document->SetError( XML_ERROR_MISMATCHED_ELEMENT, initialLineNum, \"XMLElement name=%s\", ele->Name());\r\n                _document->DeleteNode( node );\r\n                break;\r\n            }\r\n        }\r\n        InsertEndChild( node );\r\n    }\r\n    return 0;\r\n}\r\n\r\n/*static*/ void XMLNode::DeleteNode( XMLNode* node )\r\n{\r\n    if ( node == 0 ) {\r\n        return;\r\n    }\r\n\tTIXMLASSERT(node->_document);\r\n\tif (!node->ToDocument()) {\r\n\t\tnode->_document->MarkInUse(node);\r\n\t}\r\n\r\n    MemPool* pool = node->_memPool;\r\n    node->~XMLNode();\r\n    pool->Free( node );\r\n}\r\n\r\nvoid XMLNode::InsertChildPreamble( XMLNode* insertThis ) const\r\n{\r\n    TIXMLASSERT( insertThis );\r\n    TIXMLASSERT( insertThis->_document == _document );\r\n\r\n\tif (insertThis->_parent) {\r\n        insertThis->_parent->Unlink( insertThis );\r\n\t}\r\n\telse {\r\n\t\tinsertThis->_document->MarkInUse(insertThis);\r\n        insertThis->_memPool->SetTracked();\r\n\t}\r\n}\r\n\r\nconst XMLElement* XMLNode::ToElementWithName( const char* name ) const\r\n{\r\n    const XMLElement* element = this->ToElement();\r\n    if ( element == 0 ) {\r\n        return 0;\r\n    }\r\n    if ( name == 0 ) {\r\n        return element;\r\n    }\r\n    if ( XMLUtil::StringEqual( element->Name(), name ) ) {\r\n       return element;\r\n    }\r\n    return 0;\r\n}\r\n\r\n// --------- XMLText ---------- //\r\nchar* XMLText::ParseDeep( char* p, StrPair*, int* curLineNumPtr )\r\n{\r\n    if ( this->CData() ) {\r\n        p = _value.ParseText( p, \"]]>\", StrPair::NEEDS_NEWLINE_NORMALIZATION, curLineNumPtr );\r\n        if ( !p ) {\r\n            _document->SetError( XML_ERROR_PARSING_CDATA, _parseLineNum, 0 );\r\n        }\r\n        return p;\r\n    }\r\n    else {\r\n        int flags = _document->ProcessEntities() ? StrPair::TEXT_ELEMENT : StrPair::TEXT_ELEMENT_LEAVE_ENTITIES;\r\n        if ( _document->WhitespaceMode() == COLLAPSE_WHITESPACE ) {\r\n            flags |= StrPair::NEEDS_WHITESPACE_COLLAPSING;\r\n        }\r\n\r\n        p = _value.ParseText( p, \"<\", flags, curLineNumPtr );\r\n        if ( p && *p ) {\r\n            return p-1;\r\n        }\r\n        if ( !p ) {\r\n            _document->SetError( XML_ERROR_PARSING_TEXT, _parseLineNum, 0 );\r\n        }\r\n    }\r\n    return 0;\r\n}\r\n\r\n\r\nXMLNode* XMLText::ShallowClone( XMLDocument* doc ) const\r\n{\r\n    if ( !doc ) {\r\n        doc = _document;\r\n    }\r\n    XMLText* text = doc->NewText( Value() );\t// fixme: this will always allocate memory. Intern?\r\n    text->SetCData( this->CData() );\r\n    return text;\r\n}\r\n\r\n\r\nbool XMLText::ShallowEqual( const XMLNode* compare ) const\r\n{\r\n    TIXMLASSERT( compare );\r\n    const XMLText* text = compare->ToText();\r\n    return ( text && XMLUtil::StringEqual( text->Value(), Value() ) );\r\n}\r\n\r\n\r\nbool XMLText::Accept( XMLVisitor* visitor ) const\r\n{\r\n    TIXMLASSERT( visitor );\r\n    return visitor->Visit( *this );\r\n}\r\n\r\n\r\n// --------- XMLComment ---------- //\r\n\r\nXMLComment::XMLComment( XMLDocument* doc ) : XMLNode( doc )\r\n{\r\n}\r\n\r\n\r\nXMLComment::~XMLComment()\r\n{\r\n}\r\n\r\n\r\nchar* XMLComment::ParseDeep( char* p, StrPair*, int* curLineNumPtr )\r\n{\r\n    // Comment parses as text.\r\n    p = _value.ParseText( p, \"-->\", StrPair::COMMENT, curLineNumPtr );\r\n    if ( p == 0 ) {\r\n        _document->SetError( XML_ERROR_PARSING_COMMENT, _parseLineNum, 0 );\r\n    }\r\n    return p;\r\n}\r\n\r\n\r\nXMLNode* XMLComment::ShallowClone( XMLDocument* doc ) const\r\n{\r\n    if ( !doc ) {\r\n        doc = _document;\r\n    }\r\n    XMLComment* comment = doc->NewComment( Value() );\t// fixme: this will always allocate memory. Intern?\r\n    return comment;\r\n}\r\n\r\n\r\nbool XMLComment::ShallowEqual( const XMLNode* compare ) const\r\n{\r\n    TIXMLASSERT( compare );\r\n    const XMLComment* comment = compare->ToComment();\r\n    return ( comment && XMLUtil::StringEqual( comment->Value(), Value() ));\r\n}\r\n\r\n\r\nbool XMLComment::Accept( XMLVisitor* visitor ) const\r\n{\r\n    TIXMLASSERT( visitor );\r\n    return visitor->Visit( *this );\r\n}\r\n\r\n\r\n// --------- XMLDeclaration ---------- //\r\n\r\nXMLDeclaration::XMLDeclaration( XMLDocument* doc ) : XMLNode( doc )\r\n{\r\n}\r\n\r\n\r\nXMLDeclaration::~XMLDeclaration()\r\n{\r\n    //printf( \"~XMLDeclaration\\n\" );\r\n}\r\n\r\n\r\nchar* XMLDeclaration::ParseDeep( char* p, StrPair*, int* curLineNumPtr )\r\n{\r\n    // Declaration parses as text.\r\n    p = _value.ParseText( p, \"?>\", StrPair::NEEDS_NEWLINE_NORMALIZATION, curLineNumPtr );\r\n    if ( p == 0 ) {\r\n        _document->SetError( XML_ERROR_PARSING_DECLARATION, _parseLineNum, 0 );\r\n    }\r\n    return p;\r\n}\r\n\r\n\r\nXMLNode* XMLDeclaration::ShallowClone( XMLDocument* doc ) const\r\n{\r\n    if ( !doc ) {\r\n        doc = _document;\r\n    }\r\n    XMLDeclaration* dec = doc->NewDeclaration( Value() );\t// fixme: this will always allocate memory. Intern?\r\n    return dec;\r\n}\r\n\r\n\r\nbool XMLDeclaration::ShallowEqual( const XMLNode* compare ) const\r\n{\r\n    TIXMLASSERT( compare );\r\n    const XMLDeclaration* declaration = compare->ToDeclaration();\r\n    return ( declaration && XMLUtil::StringEqual( declaration->Value(), Value() ));\r\n}\r\n\r\n\r\n\r\nbool XMLDeclaration::Accept( XMLVisitor* visitor ) const\r\n{\r\n    TIXMLASSERT( visitor );\r\n    return visitor->Visit( *this );\r\n}\r\n\r\n// --------- XMLUnknown ---------- //\r\n\r\nXMLUnknown::XMLUnknown( XMLDocument* doc ) : XMLNode( doc )\r\n{\r\n}\r\n\r\n\r\nXMLUnknown::~XMLUnknown()\r\n{\r\n}\r\n\r\n\r\nchar* XMLUnknown::ParseDeep( char* p, StrPair*, int* curLineNumPtr )\r\n{\r\n    // Unknown parses as text.\r\n    p = _value.ParseText( p, \">\", StrPair::NEEDS_NEWLINE_NORMALIZATION, curLineNumPtr );\r\n    if ( !p ) {\r\n        _document->SetError( XML_ERROR_PARSING_UNKNOWN, _parseLineNum, 0 );\r\n    }\r\n    return p;\r\n}\r\n\r\n\r\nXMLNode* XMLUnknown::ShallowClone( XMLDocument* doc ) const\r\n{\r\n    if ( !doc ) {\r\n        doc = _document;\r\n    }\r\n    XMLUnknown* text = doc->NewUnknown( Value() );\t// fixme: this will always allocate memory. Intern?\r\n    return text;\r\n}\r\n\r\n\r\nbool XMLUnknown::ShallowEqual( const XMLNode* compare ) const\r\n{\r\n    TIXMLASSERT( compare );\r\n    const XMLUnknown* unknown = compare->ToUnknown();\r\n    return ( unknown && XMLUtil::StringEqual( unknown->Value(), Value() ));\r\n}\r\n\r\n\r\nbool XMLUnknown::Accept( XMLVisitor* visitor ) const\r\n{\r\n    TIXMLASSERT( visitor );\r\n    return visitor->Visit( *this );\r\n}\r\n\r\n// --------- XMLAttribute ---------- //\r\n\r\nconst char* XMLAttribute::Name() const\r\n{\r\n    return _name.GetStr();\r\n}\r\n\r\nconst char* XMLAttribute::Value() const\r\n{\r\n    return _value.GetStr();\r\n}\r\n\r\nchar* XMLAttribute::ParseDeep( char* p, bool processEntities, int* curLineNumPtr )\r\n{\r\n    // Parse using the name rules: bug fix, was using ParseText before\r\n    p = _name.ParseName( p );\r\n    if ( !p || !*p ) {\r\n        return 0;\r\n    }\r\n\r\n    // Skip white space before =\r\n    p = XMLUtil::SkipWhiteSpace( p, curLineNumPtr );\r\n    if ( *p != '=' ) {\r\n        return 0;\r\n    }\r\n\r\n    ++p;\t// move up to opening quote\r\n    p = XMLUtil::SkipWhiteSpace( p, curLineNumPtr );\r\n    if ( *p != '\\\"' && *p != '\\'' ) {\r\n        return 0;\r\n    }\r\n\r\n    const char endTag[2] = { *p, 0 };\r\n    ++p;\t// move past opening quote\r\n\r\n    p = _value.ParseText( p, endTag, processEntities ? StrPair::ATTRIBUTE_VALUE : StrPair::ATTRIBUTE_VALUE_LEAVE_ENTITIES, curLineNumPtr );\r\n    return p;\r\n}\r\n\r\n\r\nvoid XMLAttribute::SetName( const char* n )\r\n{\r\n    _name.SetStr( n );\r\n}\r\n\r\n\r\nXMLError XMLAttribute::QueryIntValue( int* value ) const\r\n{\r\n    if ( XMLUtil::ToInt( Value(), value )) {\r\n        return XML_SUCCESS;\r\n    }\r\n    return XML_WRONG_ATTRIBUTE_TYPE;\r\n}\r\n\r\n\r\nXMLError XMLAttribute::QueryUnsignedValue( unsigned int* value ) const\r\n{\r\n    if ( XMLUtil::ToUnsigned( Value(), value )) {\r\n        return XML_SUCCESS;\r\n    }\r\n    return XML_WRONG_ATTRIBUTE_TYPE;\r\n}\r\n\r\n\r\nXMLError XMLAttribute::QueryInt64Value(int64_t* value) const\r\n{\r\n\tif (XMLUtil::ToInt64(Value(), value)) {\r\n\t\treturn XML_SUCCESS;\r\n\t}\r\n\treturn XML_WRONG_ATTRIBUTE_TYPE;\r\n}\r\n\r\n\r\nXMLError XMLAttribute::QueryUnsigned64Value(uint64_t* value) const\r\n{\r\n    if(XMLUtil::ToUnsigned64(Value(), value)) {\r\n        return XML_SUCCESS;\r\n    }\r\n    return XML_WRONG_ATTRIBUTE_TYPE;\r\n}\r\n\r\n\r\nXMLError XMLAttribute::QueryBoolValue( bool* value ) const\r\n{\r\n    if ( XMLUtil::ToBool( Value(), value )) {\r\n        return XML_SUCCESS;\r\n    }\r\n    return XML_WRONG_ATTRIBUTE_TYPE;\r\n}\r\n\r\n\r\nXMLError XMLAttribute::QueryFloatValue( float* value ) const\r\n{\r\n    if ( XMLUtil::ToFloat( Value(), value )) {\r\n        return XML_SUCCESS;\r\n    }\r\n    return XML_WRONG_ATTRIBUTE_TYPE;\r\n}\r\n\r\n\r\nXMLError XMLAttribute::QueryDoubleValue( double* value ) const\r\n{\r\n    if ( XMLUtil::ToDouble( Value(), value )) {\r\n        return XML_SUCCESS;\r\n    }\r\n    return XML_WRONG_ATTRIBUTE_TYPE;\r\n}\r\n\r\n\r\nvoid XMLAttribute::SetAttribute( const char* v )\r\n{\r\n    _value.SetStr( v );\r\n}\r\n\r\n\r\nvoid XMLAttribute::SetAttribute( int v )\r\n{\r\n    char buf[BUF_SIZE];\r\n    XMLUtil::ToStr( v, buf, BUF_SIZE );\r\n    _value.SetStr( buf );\r\n}\r\n\r\n\r\nvoid XMLAttribute::SetAttribute( unsigned v )\r\n{\r\n    char buf[BUF_SIZE];\r\n    XMLUtil::ToStr( v, buf, BUF_SIZE );\r\n    _value.SetStr( buf );\r\n}\r\n\r\n\r\nvoid XMLAttribute::SetAttribute(int64_t v)\r\n{\r\n\tchar buf[BUF_SIZE];\r\n\tXMLUtil::ToStr(v, buf, BUF_SIZE);\r\n\t_value.SetStr(buf);\r\n}\r\n\r\nvoid XMLAttribute::SetAttribute(uint64_t v)\r\n{\r\n    char buf[BUF_SIZE];\r\n    XMLUtil::ToStr(v, buf, BUF_SIZE);\r\n    _value.SetStr(buf);\r\n}\r\n\r\n\r\nvoid XMLAttribute::SetAttribute( bool v )\r\n{\r\n    char buf[BUF_SIZE];\r\n    XMLUtil::ToStr( v, buf, BUF_SIZE );\r\n    _value.SetStr( buf );\r\n}\r\n\r\nvoid XMLAttribute::SetAttribute( double v )\r\n{\r\n    char buf[BUF_SIZE];\r\n    XMLUtil::ToStr( v, buf, BUF_SIZE );\r\n    _value.SetStr( buf );\r\n}\r\n\r\nvoid XMLAttribute::SetAttribute( float v )\r\n{\r\n    char buf[BUF_SIZE];\r\n    XMLUtil::ToStr( v, buf, BUF_SIZE );\r\n    _value.SetStr( buf );\r\n}\r\n\r\n\r\n// --------- XMLElement ---------- //\r\nXMLElement::XMLElement( XMLDocument* doc ) : XMLNode( doc ),\r\n    _closingType( OPEN ),\r\n    _rootAttribute( 0 )\r\n{\r\n}\r\n\r\n\r\nXMLElement::~XMLElement()\r\n{\r\n    while( _rootAttribute ) {\r\n        XMLAttribute* next = _rootAttribute->_next;\r\n        DeleteAttribute( _rootAttribute );\r\n        _rootAttribute = next;\r\n    }\r\n}\r\n\r\n\r\nconst XMLAttribute* XMLElement::FindAttribute( const char* name ) const\r\n{\r\n    for( XMLAttribute* a = _rootAttribute; a; a = a->_next ) {\r\n        if ( XMLUtil::StringEqual( a->Name(), name ) ) {\r\n            return a;\r\n        }\r\n    }\r\n    return 0;\r\n}\r\n\r\n\r\nconst char* XMLElement::Attribute( const char* name, const char* value ) const\r\n{\r\n    const XMLAttribute* a = FindAttribute( name );\r\n    if ( !a ) {\r\n        return 0;\r\n    }\r\n    if ( !value || XMLUtil::StringEqual( a->Value(), value )) {\r\n        return a->Value();\r\n    }\r\n    return 0;\r\n}\r\n\r\nint XMLElement::IntAttribute(const char* name, int defaultValue) const\r\n{\r\n\tint i = defaultValue;\r\n\tQueryIntAttribute(name, &i);\r\n\treturn i;\r\n}\r\n\r\nunsigned XMLElement::UnsignedAttribute(const char* name, unsigned defaultValue) const\r\n{\r\n\tunsigned i = defaultValue;\r\n\tQueryUnsignedAttribute(name, &i);\r\n\treturn i;\r\n}\r\n\r\nint64_t XMLElement::Int64Attribute(const char* name, int64_t defaultValue) const\r\n{\r\n\tint64_t i = defaultValue;\r\n\tQueryInt64Attribute(name, &i);\r\n\treturn i;\r\n}\r\n\r\nuint64_t XMLElement::Unsigned64Attribute(const char* name, uint64_t defaultValue) const\r\n{\r\n\tuint64_t i = defaultValue;\r\n\tQueryUnsigned64Attribute(name, &i);\r\n\treturn i;\r\n}\r\n\r\nbool XMLElement::BoolAttribute(const char* name, bool defaultValue) const\r\n{\r\n\tbool b = defaultValue;\r\n\tQueryBoolAttribute(name, &b);\r\n\treturn b;\r\n}\r\n\r\ndouble XMLElement::DoubleAttribute(const char* name, double defaultValue) const\r\n{\r\n\tdouble d = defaultValue;\r\n\tQueryDoubleAttribute(name, &d);\r\n\treturn d;\r\n}\r\n\r\nfloat XMLElement::FloatAttribute(const char* name, float defaultValue) const\r\n{\r\n\tfloat f = defaultValue;\r\n\tQueryFloatAttribute(name, &f);\r\n\treturn f;\r\n}\r\n\r\nconst char* XMLElement::GetText() const\r\n{\r\n    /* skip comment node */\r\n    const XMLNode* node = FirstChild();\r\n    while (node) {\r\n        if (node->ToComment()) {\r\n            node = node->NextSibling();\r\n            continue;\r\n        }\r\n        break;\r\n    }\r\n\r\n    if ( node && node->ToText() ) {\r\n        return node->Value();\r\n    }\r\n    return 0;\r\n}\r\n\r\n\r\nvoid\tXMLElement::SetText( const char* inText )\r\n{\r\n\tif ( FirstChild() && FirstChild()->ToText() )\r\n\t\tFirstChild()->SetValue( inText );\r\n\telse {\r\n\t\tXMLText*\ttheText = GetDocument()->NewText( inText );\r\n\t\tInsertFirstChild( theText );\r\n\t}\r\n}\r\n\r\n\r\nvoid XMLElement::SetText( int v )\r\n{\r\n    char buf[BUF_SIZE];\r\n    XMLUtil::ToStr( v, buf, BUF_SIZE );\r\n    SetText( buf );\r\n}\r\n\r\n\r\nvoid XMLElement::SetText( unsigned v )\r\n{\r\n    char buf[BUF_SIZE];\r\n    XMLUtil::ToStr( v, buf, BUF_SIZE );\r\n    SetText( buf );\r\n}\r\n\r\n\r\nvoid XMLElement::SetText(int64_t v)\r\n{\r\n\tchar buf[BUF_SIZE];\r\n\tXMLUtil::ToStr(v, buf, BUF_SIZE);\r\n\tSetText(buf);\r\n}\r\n\r\nvoid XMLElement::SetText(uint64_t v) {\r\n    char buf[BUF_SIZE];\r\n    XMLUtil::ToStr(v, buf, BUF_SIZE);\r\n    SetText(buf);\r\n}\r\n\r\n\r\nvoid XMLElement::SetText( bool v )\r\n{\r\n    char buf[BUF_SIZE];\r\n    XMLUtil::ToStr( v, buf, BUF_SIZE );\r\n    SetText( buf );\r\n}\r\n\r\n\r\nvoid XMLElement::SetText( float v )\r\n{\r\n    char buf[BUF_SIZE];\r\n    XMLUtil::ToStr( v, buf, BUF_SIZE );\r\n    SetText( buf );\r\n}\r\n\r\n\r\nvoid XMLElement::SetText( double v )\r\n{\r\n    char buf[BUF_SIZE];\r\n    XMLUtil::ToStr( v, buf, BUF_SIZE );\r\n    SetText( buf );\r\n}\r\n\r\n\r\nXMLError XMLElement::QueryIntText( int* ival ) const\r\n{\r\n    if ( FirstChild() && FirstChild()->ToText() ) {\r\n        const char* t = FirstChild()->Value();\r\n        if ( XMLUtil::ToInt( t, ival ) ) {\r\n            return XML_SUCCESS;\r\n        }\r\n        return XML_CAN_NOT_CONVERT_TEXT;\r\n    }\r\n    return XML_NO_TEXT_NODE;\r\n}\r\n\r\n\r\nXMLError XMLElement::QueryUnsignedText( unsigned* uval ) const\r\n{\r\n    if ( FirstChild() && FirstChild()->ToText() ) {\r\n        const char* t = FirstChild()->Value();\r\n        if ( XMLUtil::ToUnsigned( t, uval ) ) {\r\n            return XML_SUCCESS;\r\n        }\r\n        return XML_CAN_NOT_CONVERT_TEXT;\r\n    }\r\n    return XML_NO_TEXT_NODE;\r\n}\r\n\r\n\r\nXMLError XMLElement::QueryInt64Text(int64_t* ival) const\r\n{\r\n\tif (FirstChild() && FirstChild()->ToText()) {\r\n\t\tconst char* t = FirstChild()->Value();\r\n\t\tif (XMLUtil::ToInt64(t, ival)) {\r\n\t\t\treturn XML_SUCCESS;\r\n\t\t}\r\n\t\treturn XML_CAN_NOT_CONVERT_TEXT;\r\n\t}\r\n\treturn XML_NO_TEXT_NODE;\r\n}\r\n\r\n\r\nXMLError XMLElement::QueryUnsigned64Text(uint64_t* uval) const\r\n{\r\n    if(FirstChild() && FirstChild()->ToText()) {\r\n        const char* t = FirstChild()->Value();\r\n        if(XMLUtil::ToUnsigned64(t, uval)) {\r\n            return XML_SUCCESS;\r\n        }\r\n        return XML_CAN_NOT_CONVERT_TEXT;\r\n    }\r\n    return XML_NO_TEXT_NODE;\r\n}\r\n\r\n\r\nXMLError XMLElement::QueryBoolText( bool* bval ) const\r\n{\r\n    if ( FirstChild() && FirstChild()->ToText() ) {\r\n        const char* t = FirstChild()->Value();\r\n        if ( XMLUtil::ToBool( t, bval ) ) {\r\n            return XML_SUCCESS;\r\n        }\r\n        return XML_CAN_NOT_CONVERT_TEXT;\r\n    }\r\n    return XML_NO_TEXT_NODE;\r\n}\r\n\r\n\r\nXMLError XMLElement::QueryDoubleText( double* dval ) const\r\n{\r\n    if ( FirstChild() && FirstChild()->ToText() ) {\r\n        const char* t = FirstChild()->Value();\r\n        if ( XMLUtil::ToDouble( t, dval ) ) {\r\n            return XML_SUCCESS;\r\n        }\r\n        return XML_CAN_NOT_CONVERT_TEXT;\r\n    }\r\n    return XML_NO_TEXT_NODE;\r\n}\r\n\r\n\r\nXMLError XMLElement::QueryFloatText( float* fval ) const\r\n{\r\n    if ( FirstChild() && FirstChild()->ToText() ) {\r\n        const char* t = FirstChild()->Value();\r\n        if ( XMLUtil::ToFloat( t, fval ) ) {\r\n            return XML_SUCCESS;\r\n        }\r\n        return XML_CAN_NOT_CONVERT_TEXT;\r\n    }\r\n    return XML_NO_TEXT_NODE;\r\n}\r\n\r\nint XMLElement::IntText(int defaultValue) const\r\n{\r\n\tint i = defaultValue;\r\n\tQueryIntText(&i);\r\n\treturn i;\r\n}\r\n\r\nunsigned XMLElement::UnsignedText(unsigned defaultValue) const\r\n{\r\n\tunsigned i = defaultValue;\r\n\tQueryUnsignedText(&i);\r\n\treturn i;\r\n}\r\n\r\nint64_t XMLElement::Int64Text(int64_t defaultValue) const\r\n{\r\n\tint64_t i = defaultValue;\r\n\tQueryInt64Text(&i);\r\n\treturn i;\r\n}\r\n\r\nuint64_t XMLElement::Unsigned64Text(uint64_t defaultValue) const\r\n{\r\n\tuint64_t i = defaultValue;\r\n\tQueryUnsigned64Text(&i);\r\n\treturn i;\r\n}\r\n\r\nbool XMLElement::BoolText(bool defaultValue) const\r\n{\r\n\tbool b = defaultValue;\r\n\tQueryBoolText(&b);\r\n\treturn b;\r\n}\r\n\r\ndouble XMLElement::DoubleText(double defaultValue) const\r\n{\r\n\tdouble d = defaultValue;\r\n\tQueryDoubleText(&d);\r\n\treturn d;\r\n}\r\n\r\nfloat XMLElement::FloatText(float defaultValue) const\r\n{\r\n\tfloat f = defaultValue;\r\n\tQueryFloatText(&f);\r\n\treturn f;\r\n}\r\n\r\n\r\nXMLAttribute* XMLElement::FindOrCreateAttribute( const char* name )\r\n{\r\n    XMLAttribute* last = 0;\r\n    XMLAttribute* attrib = 0;\r\n    for( attrib = _rootAttribute;\r\n            attrib;\r\n            last = attrib, attrib = attrib->_next ) {\r\n        if ( XMLUtil::StringEqual( attrib->Name(), name ) ) {\r\n            break;\r\n        }\r\n    }\r\n    if ( !attrib ) {\r\n        attrib = CreateAttribute();\r\n        TIXMLASSERT( attrib );\r\n        if ( last ) {\r\n            TIXMLASSERT( last->_next == 0 );\r\n            last->_next = attrib;\r\n        }\r\n        else {\r\n            TIXMLASSERT( _rootAttribute == 0 );\r\n            _rootAttribute = attrib;\r\n        }\r\n        attrib->SetName( name );\r\n    }\r\n    return attrib;\r\n}\r\n\r\n\r\nvoid XMLElement::DeleteAttribute( const char* name )\r\n{\r\n    XMLAttribute* prev = 0;\r\n    for( XMLAttribute* a=_rootAttribute; a; a=a->_next ) {\r\n        if ( XMLUtil::StringEqual( name, a->Name() ) ) {\r\n            if ( prev ) {\r\n                prev->_next = a->_next;\r\n            }\r\n            else {\r\n                _rootAttribute = a->_next;\r\n            }\r\n            DeleteAttribute( a );\r\n            break;\r\n        }\r\n        prev = a;\r\n    }\r\n}\r\n\r\n\r\nchar* XMLElement::ParseAttributes( char* p, int* curLineNumPtr )\r\n{\r\n    XMLAttribute* prevAttribute = 0;\r\n\r\n    // Read the attributes.\r\n    while( p ) {\r\n        p = XMLUtil::SkipWhiteSpace( p, curLineNumPtr );\r\n        if ( !(*p) ) {\r\n            _document->SetError( XML_ERROR_PARSING_ELEMENT, _parseLineNum, \"XMLElement name=%s\", Name() );\r\n            return 0;\r\n        }\r\n\r\n        // attribute.\r\n        if (XMLUtil::IsNameStartChar( (unsigned char) *p ) ) {\r\n            XMLAttribute* attrib = CreateAttribute();\r\n            TIXMLASSERT( attrib );\r\n            attrib->_parseLineNum = _document->_parseCurLineNum;\r\n\r\n            const int attrLineNum = attrib->_parseLineNum;\r\n\r\n            p = attrib->ParseDeep( p, _document->ProcessEntities(), curLineNumPtr );\r\n            if ( !p || Attribute( attrib->Name() ) ) {\r\n                DeleteAttribute( attrib );\r\n                _document->SetError( XML_ERROR_PARSING_ATTRIBUTE, attrLineNum, \"XMLElement name=%s\", Name() );\r\n                return 0;\r\n            }\r\n            // There is a minor bug here: if the attribute in the source xml\r\n            // document is duplicated, it will not be detected and the\r\n            // attribute will be doubly added. However, tracking the 'prevAttribute'\r\n            // avoids re-scanning the attribute list. Preferring performance for\r\n            // now, may reconsider in the future.\r\n            if ( prevAttribute ) {\r\n                TIXMLASSERT( prevAttribute->_next == 0 );\r\n                prevAttribute->_next = attrib;\r\n            }\r\n            else {\r\n                TIXMLASSERT( _rootAttribute == 0 );\r\n                _rootAttribute = attrib;\r\n            }\r\n            prevAttribute = attrib;\r\n        }\r\n        // end of the tag\r\n        else if ( *p == '>' ) {\r\n            ++p;\r\n            break;\r\n        }\r\n        // end of the tag\r\n        else if ( *p == '/' && *(p+1) == '>' ) {\r\n            _closingType = CLOSED;\r\n            return p+2;\t// done; sealed element.\r\n        }\r\n        else {\r\n            _document->SetError( XML_ERROR_PARSING_ELEMENT, _parseLineNum, 0 );\r\n            return 0;\r\n        }\r\n    }\r\n    return p;\r\n}\r\n\r\nvoid XMLElement::DeleteAttribute( XMLAttribute* attribute )\r\n{\r\n    if ( attribute == 0 ) {\r\n        return;\r\n    }\r\n    MemPool* pool = attribute->_memPool;\r\n    attribute->~XMLAttribute();\r\n    pool->Free( attribute );\r\n}\r\n\r\nXMLAttribute* XMLElement::CreateAttribute()\r\n{\r\n    TIXMLASSERT( sizeof( XMLAttribute ) == _document->_attributePool.ItemSize() );\r\n    XMLAttribute* attrib = new (_document->_attributePool.Alloc() ) XMLAttribute();\r\n    TIXMLASSERT( attrib );\r\n    attrib->_memPool = &_document->_attributePool;\r\n    attrib->_memPool->SetTracked();\r\n    return attrib;\r\n}\r\n\r\n\r\nXMLElement* XMLElement::InsertNewChildElement(const char* name)\r\n{\r\n    XMLElement* node = _document->NewElement(name);\r\n    return InsertEndChild(node) ? node : 0;\r\n}\r\n\r\nXMLComment* XMLElement::InsertNewComment(const char* comment)\r\n{\r\n    XMLComment* node = _document->NewComment(comment);\r\n    return InsertEndChild(node) ? node : 0;\r\n}\r\n\r\nXMLText* XMLElement::InsertNewText(const char* text)\r\n{\r\n    XMLText* node = _document->NewText(text);\r\n    return InsertEndChild(node) ? node : 0;\r\n}\r\n\r\nXMLDeclaration* XMLElement::InsertNewDeclaration(const char* text)\r\n{\r\n    XMLDeclaration* node = _document->NewDeclaration(text);\r\n    return InsertEndChild(node) ? node : 0;\r\n}\r\n\r\nXMLUnknown* XMLElement::InsertNewUnknown(const char* text)\r\n{\r\n    XMLUnknown* node = _document->NewUnknown(text);\r\n    return InsertEndChild(node) ? node : 0;\r\n}\r\n\r\n\r\n\r\n//\r\n//\t<ele></ele>\r\n//\t<ele>foo<b>bar</b></ele>\r\n//\r\nchar* XMLElement::ParseDeep( char* p, StrPair* parentEndTag, int* curLineNumPtr )\r\n{\r\n    // Read the element name.\r\n    p = XMLUtil::SkipWhiteSpace( p, curLineNumPtr );\r\n\r\n    // The closing element is the </element> form. It is\r\n    // parsed just like a regular element then deleted from\r\n    // the DOM.\r\n    if ( *p == '/' ) {\r\n        _closingType = CLOSING;\r\n        ++p;\r\n    }\r\n\r\n    p = _value.ParseName( p );\r\n    if ( _value.Empty() ) {\r\n        return 0;\r\n    }\r\n\r\n    p = ParseAttributes( p, curLineNumPtr );\r\n    if ( !p || !*p || _closingType != OPEN ) {\r\n        return p;\r\n    }\r\n\r\n    p = XMLNode::ParseDeep( p, parentEndTag, curLineNumPtr );\r\n    return p;\r\n}\r\n\r\n\r\n\r\nXMLNode* XMLElement::ShallowClone( XMLDocument* doc ) const\r\n{\r\n    if ( !doc ) {\r\n        doc = _document;\r\n    }\r\n    XMLElement* element = doc->NewElement( Value() );\t\t\t\t\t// fixme: this will always allocate memory. Intern?\r\n    for( const XMLAttribute* a=FirstAttribute(); a; a=a->Next() ) {\r\n        element->SetAttribute( a->Name(), a->Value() );\t\t\t\t\t// fixme: this will always allocate memory. Intern?\r\n    }\r\n    return element;\r\n}\r\n\r\n\r\nbool XMLElement::ShallowEqual( const XMLNode* compare ) const\r\n{\r\n    TIXMLASSERT( compare );\r\n    const XMLElement* other = compare->ToElement();\r\n    if ( other && XMLUtil::StringEqual( other->Name(), Name() )) {\r\n\r\n        const XMLAttribute* a=FirstAttribute();\r\n        const XMLAttribute* b=other->FirstAttribute();\r\n\r\n        while ( a && b ) {\r\n            if ( !XMLUtil::StringEqual( a->Value(), b->Value() ) ) {\r\n                return false;\r\n            }\r\n            a = a->Next();\r\n            b = b->Next();\r\n        }\r\n        if ( a || b ) {\r\n            // different count\r\n            return false;\r\n        }\r\n        return true;\r\n    }\r\n    return false;\r\n}\r\n\r\n\r\nbool XMLElement::Accept( XMLVisitor* visitor ) const\r\n{\r\n    TIXMLASSERT( visitor );\r\n    if ( visitor->VisitEnter( *this, _rootAttribute ) ) {\r\n        for ( const XMLNode* node=FirstChild(); node; node=node->NextSibling() ) {\r\n            if ( !node->Accept( visitor ) ) {\r\n                break;\r\n            }\r\n        }\r\n    }\r\n    return visitor->VisitExit( *this );\r\n}\r\n\r\n\r\n// --------- XMLDocument ----------- //\r\n\r\n// Warning: List must match 'enum XMLError'\r\nconst char* XMLDocument::_errorNames[XML_ERROR_COUNT] = {\r\n    \"XML_SUCCESS\",\r\n    \"XML_NO_ATTRIBUTE\",\r\n    \"XML_WRONG_ATTRIBUTE_TYPE\",\r\n    \"XML_ERROR_FILE_NOT_FOUND\",\r\n    \"XML_ERROR_FILE_COULD_NOT_BE_OPENED\",\r\n    \"XML_ERROR_FILE_READ_ERROR\",\r\n    \"XML_ERROR_PARSING_ELEMENT\",\r\n    \"XML_ERROR_PARSING_ATTRIBUTE\",\r\n    \"XML_ERROR_PARSING_TEXT\",\r\n    \"XML_ERROR_PARSING_CDATA\",\r\n    \"XML_ERROR_PARSING_COMMENT\",\r\n    \"XML_ERROR_PARSING_DECLARATION\",\r\n    \"XML_ERROR_PARSING_UNKNOWN\",\r\n    \"XML_ERROR_EMPTY_DOCUMENT\",\r\n    \"XML_ERROR_MISMATCHED_ELEMENT\",\r\n    \"XML_ERROR_PARSING\",\r\n    \"XML_CAN_NOT_CONVERT_TEXT\",\r\n    \"XML_NO_TEXT_NODE\",\r\n\t\"XML_ELEMENT_DEPTH_EXCEEDED\"\r\n};\r\n\r\n\r\nXMLDocument::XMLDocument( bool processEntities, Whitespace whitespaceMode ) :\r\n    XMLNode( 0 ),\r\n    _writeBOM( false ),\r\n    _processEntities( processEntities ),\r\n    _errorID(XML_SUCCESS),\r\n    _whitespaceMode( whitespaceMode ),\r\n    _errorStr(),\r\n    _errorLineNum( 0 ),\r\n    _charBuffer( 0 ),\r\n    _parseCurLineNum( 0 ),\r\n\t_parsingDepth(0),\r\n    _unlinked(),\r\n    _elementPool(),\r\n    _attributePool(),\r\n    _textPool(),\r\n    _commentPool()\r\n{\r\n    // avoid VC++ C4355 warning about 'this' in initializer list (C4355 is off by default in VS2012+)\r\n    _document = this;\r\n}\r\n\r\n\r\nXMLDocument::~XMLDocument()\r\n{\r\n    Clear();\r\n}\r\n\r\n\r\nvoid XMLDocument::MarkInUse(const XMLNode* const node)\r\n{\r\n\tTIXMLASSERT(node);\r\n\tTIXMLASSERT(node->_parent == 0);\r\n\r\n\tfor (int i = 0; i < _unlinked.Size(); ++i) {\r\n\t\tif (node == _unlinked[i]) {\r\n\t\t\t_unlinked.SwapRemove(i);\r\n\t\t\tbreak;\r\n\t\t}\r\n\t}\r\n}\r\n\r\nvoid XMLDocument::Clear()\r\n{\r\n    DeleteChildren();\r\n\twhile( _unlinked.Size()) {\r\n\t\tDeleteNode(_unlinked[0]);\t// Will remove from _unlinked as part of delete.\r\n\t}\r\n\r\n#ifdef TINYXML2_DEBUG\r\n    const bool hadError = Error();\r\n#endif\r\n    ClearError();\r\n\r\n    delete [] _charBuffer;\r\n    _charBuffer = 0;\r\n\t_parsingDepth = 0;\r\n\r\n#if 0\r\n    _textPool.Trace( \"text\" );\r\n    _elementPool.Trace( \"element\" );\r\n    _commentPool.Trace( \"comment\" );\r\n    _attributePool.Trace( \"attribute\" );\r\n#endif\r\n\r\n#ifdef TINYXML2_DEBUG\r\n    if ( !hadError ) {\r\n        TIXMLASSERT( _elementPool.CurrentAllocs()   == _elementPool.Untracked() );\r\n        TIXMLASSERT( _attributePool.CurrentAllocs() == _attributePool.Untracked() );\r\n        TIXMLASSERT( _textPool.CurrentAllocs()      == _textPool.Untracked() );\r\n        TIXMLASSERT( _commentPool.CurrentAllocs()   == _commentPool.Untracked() );\r\n    }\r\n#endif\r\n}\r\n\r\n\r\nvoid XMLDocument::DeepCopy(XMLDocument* target) const\r\n{\r\n\tTIXMLASSERT(target);\r\n    if (target == this) {\r\n        return; // technically success - a no-op.\r\n    }\r\n\r\n\ttarget->Clear();\r\n\tfor (const XMLNode* node = this->FirstChild(); node; node = node->NextSibling()) {\r\n\t\ttarget->InsertEndChild(node->DeepClone(target));\r\n\t}\r\n}\r\n\r\nXMLElement* XMLDocument::NewElement( const char* name )\r\n{\r\n    XMLElement* ele = CreateUnlinkedNode<XMLElement>( _elementPool );\r\n    ele->SetName( name );\r\n    return ele;\r\n}\r\n\r\n\r\nXMLComment* XMLDocument::NewComment( const char* str )\r\n{\r\n    XMLComment* comment = CreateUnlinkedNode<XMLComment>( _commentPool );\r\n    comment->SetValue( str );\r\n    return comment;\r\n}\r\n\r\n\r\nXMLText* XMLDocument::NewText( const char* str )\r\n{\r\n    XMLText* text = CreateUnlinkedNode<XMLText>( _textPool );\r\n    text->SetValue( str );\r\n    return text;\r\n}\r\n\r\n\r\nXMLDeclaration* XMLDocument::NewDeclaration( const char* str )\r\n{\r\n    XMLDeclaration* dec = CreateUnlinkedNode<XMLDeclaration>( _commentPool );\r\n    dec->SetValue( str ? str : \"xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"\" );\r\n    return dec;\r\n}\r\n\r\n\r\nXMLUnknown* XMLDocument::NewUnknown( const char* str )\r\n{\r\n    XMLUnknown* unk = CreateUnlinkedNode<XMLUnknown>( _commentPool );\r\n    unk->SetValue( str );\r\n    return unk;\r\n}\r\n\r\nstatic FILE* callfopen( const char* filepath, const char* mode )\r\n{\r\n    TIXMLASSERT( filepath );\r\n    TIXMLASSERT( mode );\r\n#if defined(_MSC_VER) && (_MSC_VER >= 1400 ) && (!defined WINCE)\r\n    FILE* fp = 0;\r\n    const errno_t err = fopen_s( &fp, filepath, mode );\r\n    if ( err ) {\r\n        return 0;\r\n    }\r\n#else\r\n    FILE* fp = fopen( filepath, mode );\r\n#endif\r\n    return fp;\r\n}\r\n\r\nvoid XMLDocument::DeleteNode( XMLNode* node )\t{\r\n    TIXMLASSERT( node );\r\n    TIXMLASSERT(node->_document == this );\r\n    if (node->_parent) {\r\n        node->_parent->DeleteChild( node );\r\n    }\r\n    else {\r\n        // Isn't in the tree.\r\n        // Use the parent delete.\r\n        // Also, we need to mark it tracked: we 'know'\r\n        // it was never used.\r\n        node->_memPool->SetTracked();\r\n        // Call the static XMLNode version:\r\n        XMLNode::DeleteNode(node);\r\n    }\r\n}\r\n\r\n\r\nXMLError XMLDocument::LoadFile( const char* filename )\r\n{\r\n    if ( !filename ) {\r\n        TIXMLASSERT( false );\r\n        SetError( XML_ERROR_FILE_COULD_NOT_BE_OPENED, 0, \"filename=<null>\" );\r\n        return _errorID;\r\n    }\r\n\r\n    Clear();\r\n    FILE* fp = callfopen( filename, \"rb\" );\r\n    if ( !fp ) {\r\n        SetError( XML_ERROR_FILE_NOT_FOUND, 0, \"filename=%s\", filename );\r\n        return _errorID;\r\n    }\r\n    LoadFile( fp );\r\n    fclose( fp );\r\n    return _errorID;\r\n}\r\n\r\nXMLError XMLDocument::LoadFile( FILE* fp )\r\n{\r\n    Clear();\r\n\r\n    TIXML_FSEEK( fp, 0, SEEK_SET );\r\n    if ( fgetc( fp ) == EOF && ferror( fp ) != 0 ) {\r\n        SetError( XML_ERROR_FILE_READ_ERROR, 0, 0 );\r\n        return _errorID;\r\n    }\r\n\r\n    TIXML_FSEEK( fp, 0, SEEK_END );\r\n\r\n    unsigned long long filelength;\r\n    {\r\n        const long long fileLengthSigned = TIXML_FTELL( fp );\r\n        TIXML_FSEEK( fp, 0, SEEK_SET );\r\n        if ( fileLengthSigned == -1L ) {\r\n            SetError( XML_ERROR_FILE_READ_ERROR, 0, 0 );\r\n            return _errorID;\r\n        }\r\n        TIXMLASSERT( fileLengthSigned >= 0 );\r\n        filelength = static_cast<unsigned long long>(fileLengthSigned);\r\n    }\r\n\r\n    const size_t maxSizeT = static_cast<size_t>(-1);\r\n    // We'll do the comparison as an unsigned long long, because that's guaranteed to be at\r\n    // least 8 bytes, even on a 32-bit platform.\r\n    if ( filelength >= static_cast<unsigned long long>(maxSizeT) ) {\r\n        // Cannot handle files which won't fit in buffer together with null terminator\r\n        SetError( XML_ERROR_FILE_READ_ERROR, 0, 0 );\r\n        return _errorID;\r\n    }\r\n\r\n    if ( filelength == 0 ) {\r\n        SetError( XML_ERROR_EMPTY_DOCUMENT, 0, 0 );\r\n        return _errorID;\r\n    }\r\n\r\n    const size_t size = static_cast<size_t>(filelength);\r\n    TIXMLASSERT( _charBuffer == 0 );\r\n    _charBuffer = new char[size+1];\r\n    const size_t read = fread( _charBuffer, 1, size, fp );\r\n    if ( read != size ) {\r\n        SetError( XML_ERROR_FILE_READ_ERROR, 0, 0 );\r\n        return _errorID;\r\n    }\r\n\r\n    _charBuffer[size] = 0;\r\n\r\n    Parse();\r\n    return _errorID;\r\n}\r\n\r\n\r\nXMLError XMLDocument::SaveFile( const char* filename, bool compact )\r\n{\r\n    if ( !filename ) {\r\n        TIXMLASSERT( false );\r\n        SetError( XML_ERROR_FILE_COULD_NOT_BE_OPENED, 0, \"filename=<null>\" );\r\n        return _errorID;\r\n    }\r\n\r\n    FILE* fp = callfopen( filename, \"w\" );\r\n    if ( !fp ) {\r\n        SetError( XML_ERROR_FILE_COULD_NOT_BE_OPENED, 0, \"filename=%s\", filename );\r\n        return _errorID;\r\n    }\r\n    SaveFile(fp, compact);\r\n    fclose( fp );\r\n    return _errorID;\r\n}\r\n\r\n\r\nXMLError XMLDocument::SaveFile( FILE* fp, bool compact )\r\n{\r\n    // Clear any error from the last save, otherwise it will get reported\r\n    // for *this* call.\r\n    ClearError();\r\n    XMLPrinter stream( fp, compact );\r\n    Print( &stream );\r\n    return _errorID;\r\n}\r\n\r\n\r\nXMLError XMLDocument::Parse( const char* xml, size_t nBytes )\r\n{\r\n    Clear();\r\n\r\n    if ( nBytes == 0 || !xml || !*xml ) {\r\n        SetError( XML_ERROR_EMPTY_DOCUMENT, 0, 0 );\r\n        return _errorID;\r\n    }\r\n    if ( nBytes == static_cast<size_t>(-1) ) {\r\n        nBytes = strlen( xml );\r\n    }\r\n    TIXMLASSERT( _charBuffer == 0 );\r\n    _charBuffer = new char[ nBytes+1 ];\r\n    memcpy( _charBuffer, xml, nBytes );\r\n    _charBuffer[nBytes] = 0;\r\n\r\n    Parse();\r\n    if ( Error() ) {\r\n        // clean up now essentially dangling memory.\r\n        // and the parse fail can put objects in the\r\n        // pools that are dead and inaccessible.\r\n        DeleteChildren();\r\n        _elementPool.Clear();\r\n        _attributePool.Clear();\r\n        _textPool.Clear();\r\n        _commentPool.Clear();\r\n    }\r\n    return _errorID;\r\n}\r\n\r\n\r\nvoid XMLDocument::Print( XMLPrinter* streamer ) const\r\n{\r\n    if ( streamer ) {\r\n        Accept( streamer );\r\n    }\r\n    else {\r\n        XMLPrinter stdoutStreamer( stdout );\r\n        Accept( &stdoutStreamer );\r\n    }\r\n}\r\n\r\n\r\nvoid XMLDocument::ClearError() {\r\n    _errorID = XML_SUCCESS;\r\n    _errorLineNum = 0;\r\n    _errorStr.Reset();\r\n}\r\n\r\n\r\nvoid XMLDocument::SetError( XMLError error, int lineNum, const char* format, ... )\r\n{\r\n    TIXMLASSERT( error >= 0 && error < XML_ERROR_COUNT );\r\n    _errorID = error;\r\n    _errorLineNum = lineNum;\r\n\t_errorStr.Reset();\r\n\r\n    const size_t BUFFER_SIZE = 1000;\r\n    char* buffer = new char[BUFFER_SIZE];\r\n\r\n    TIXMLASSERT(sizeof(error) <= sizeof(int));\r\n    TIXML_SNPRINTF(buffer, BUFFER_SIZE, \"Error=%s ErrorID=%d (0x%x) Line number=%d\", ErrorIDToName(error), int(error), int(error), lineNum);\r\n\r\n\tif (format) {\r\n\t\tsize_t len = strlen(buffer);\r\n\t\tTIXML_SNPRINTF(buffer + len, BUFFER_SIZE - len, \": \");\r\n\t\tlen = strlen(buffer);\r\n\r\n\t\tva_list va;\r\n\t\tva_start(va, format);\r\n\t\tTIXML_VSNPRINTF(buffer + len, BUFFER_SIZE - len, format, va);\r\n\t\tva_end(va);\r\n\t}\r\n\t_errorStr.SetStr(buffer);\r\n\tdelete[] buffer;\r\n}\r\n\r\n\r\n/*static*/ const char* XMLDocument::ErrorIDToName(XMLError errorID)\r\n{\r\n\tTIXMLASSERT( errorID >= 0 && errorID < XML_ERROR_COUNT );\r\n    const char* errorName = _errorNames[errorID];\r\n    TIXMLASSERT( errorName && errorName[0] );\r\n    return errorName;\r\n}\r\n\r\nconst char* XMLDocument::ErrorStr() const\r\n{\r\n\treturn _errorStr.Empty() ? \"\" : _errorStr.GetStr();\r\n}\r\n\r\n\r\nvoid XMLDocument::PrintError() const\r\n{\r\n    printf(\"%s\\n\", ErrorStr());\r\n}\r\n\r\nconst char* XMLDocument::ErrorName() const\r\n{\r\n    return ErrorIDToName(_errorID);\r\n}\r\n\r\nvoid XMLDocument::Parse()\r\n{\r\n    TIXMLASSERT( NoChildren() ); // Clear() must have been called previously\r\n    TIXMLASSERT( _charBuffer );\r\n    _parseCurLineNum = 1;\r\n    _parseLineNum = 1;\r\n    char* p = _charBuffer;\r\n    p = XMLUtil::SkipWhiteSpace( p, &_parseCurLineNum );\r\n    p = const_cast<char*>( XMLUtil::ReadBOM( p, &_writeBOM ) );\r\n    if ( !*p ) {\r\n        SetError( XML_ERROR_EMPTY_DOCUMENT, 0, 0 );\r\n        return;\r\n    }\r\n    ParseDeep(p, 0, &_parseCurLineNum );\r\n}\r\n\r\nvoid XMLDocument::PushDepth()\r\n{\r\n\t_parsingDepth++;\r\n\tif (_parsingDepth == TINYXML2_MAX_ELEMENT_DEPTH) {\r\n\t\tSetError(XML_ELEMENT_DEPTH_EXCEEDED, _parseCurLineNum, \"Element nesting is too deep.\" );\r\n\t}\r\n}\r\n\r\nvoid XMLDocument::PopDepth()\r\n{\r\n\tTIXMLASSERT(_parsingDepth > 0);\r\n\t--_parsingDepth;\r\n}\r\n\r\nXMLPrinter::XMLPrinter( FILE* file, bool compact, int depth ) :\r\n    _elementJustOpened( false ),\r\n    _stack(),\r\n    _firstElement( true ),\r\n    _fp( file ),\r\n    _depth( depth ),\r\n    _textDepth( -1 ),\r\n    _processEntities( true ),\r\n    _compactMode( compact ),\r\n    _buffer()\r\n{\r\n    for( int i=0; i<ENTITY_RANGE; ++i ) {\r\n        _entityFlag[i] = false;\r\n        _restrictedEntityFlag[i] = false;\r\n    }\r\n    for( int i=0; i<NUM_ENTITIES; ++i ) {\r\n        const char entityValue = entities[i].value;\r\n        const unsigned char flagIndex = static_cast<unsigned char>(entityValue);\r\n        TIXMLASSERT( flagIndex < ENTITY_RANGE );\r\n        _entityFlag[flagIndex] = true;\r\n    }\r\n    _restrictedEntityFlag[static_cast<unsigned char>('&')] = true;\r\n    _restrictedEntityFlag[static_cast<unsigned char>('<')] = true;\r\n    _restrictedEntityFlag[static_cast<unsigned char>('>')] = true;\t// not required, but consistency is nice\r\n    _buffer.Push( 0 );\r\n}\r\n\r\n\r\nvoid XMLPrinter::Print( const char* format, ... )\r\n{\r\n    va_list     va;\r\n    va_start( va, format );\r\n\r\n    if ( _fp ) {\r\n        vfprintf( _fp, format, va );\r\n    }\r\n    else {\r\n        const int len = TIXML_VSCPRINTF( format, va );\r\n        // Close out and re-start the va-args\r\n        va_end( va );\r\n        TIXMLASSERT( len >= 0 );\r\n        va_start( va, format );\r\n        TIXMLASSERT( _buffer.Size() > 0 && _buffer[_buffer.Size() - 1] == 0 );\r\n        char* p = _buffer.PushArr( len ) - 1;\t// back up over the null terminator.\r\n\t\tTIXML_VSNPRINTF( p, len+1, format, va );\r\n    }\r\n    va_end( va );\r\n}\r\n\r\n\r\nvoid XMLPrinter::Write( const char* data, size_t size )\r\n{\r\n    if ( _fp ) {\r\n        fwrite ( data , sizeof(char), size, _fp);\r\n    }\r\n    else {\r\n        char* p = _buffer.PushArr( static_cast<int>(size) ) - 1;   // back up over the null terminator.\r\n        memcpy( p, data, size );\r\n        p[size] = 0;\r\n    }\r\n}\r\n\r\n\r\nvoid XMLPrinter::Putc( char ch )\r\n{\r\n    if ( _fp ) {\r\n        fputc ( ch, _fp);\r\n    }\r\n    else {\r\n        char* p = _buffer.PushArr( sizeof(char) ) - 1;   // back up over the null terminator.\r\n        p[0] = ch;\r\n        p[1] = 0;\r\n    }\r\n}\r\n\r\n\r\nvoid XMLPrinter::PrintSpace( int depth )\r\n{\r\n    for( int i=0; i<depth; ++i ) {\r\n        Write( \"    \" );\r\n    }\r\n}\r\n\r\n\r\nvoid XMLPrinter::PrintString( const char* p, bool restricted )\r\n{\r\n    // Look for runs of bytes between entities to print.\r\n    const char* q = p;\r\n\r\n    if ( _processEntities ) {\r\n        const bool* flag = restricted ? _restrictedEntityFlag : _entityFlag;\r\n        while ( *q ) {\r\n            TIXMLASSERT( p <= q );\r\n            // Remember, char is sometimes signed. (How many times has that bitten me?)\r\n            if ( *q > 0 && *q < ENTITY_RANGE ) {\r\n                // Check for entities. If one is found, flush\r\n                // the stream up until the entity, write the\r\n                // entity, and keep looking.\r\n                if ( flag[static_cast<unsigned char>(*q)] ) {\r\n                    while ( p < q ) {\r\n                        const size_t delta = q - p;\r\n                        const int toPrint = ( INT_MAX < delta ) ? INT_MAX : static_cast<int>(delta);\r\n                        Write( p, toPrint );\r\n                        p += toPrint;\r\n                    }\r\n                    bool entityPatternPrinted = false;\r\n                    for( int i=0; i<NUM_ENTITIES; ++i ) {\r\n                        if ( entities[i].value == *q ) {\r\n                            Putc( '&' );\r\n                            Write( entities[i].pattern, entities[i].length );\r\n                            Putc( ';' );\r\n                            entityPatternPrinted = true;\r\n                            break;\r\n                        }\r\n                    }\r\n                    if ( !entityPatternPrinted ) {\r\n                        // TIXMLASSERT( entityPatternPrinted ) causes gcc -Wunused-but-set-variable in release\r\n                        TIXMLASSERT( false );\r\n                    }\r\n                    ++p;\r\n                }\r\n            }\r\n            ++q;\r\n            TIXMLASSERT( p <= q );\r\n        }\r\n        // Flush the remaining string. This will be the entire\r\n        // string if an entity wasn't found.\r\n        if ( p < q ) {\r\n            const size_t delta = q - p;\r\n            const int toPrint = ( INT_MAX < delta ) ? INT_MAX : static_cast<int>(delta);\r\n            Write( p, toPrint );\r\n        }\r\n    }\r\n    else {\r\n        Write( p );\r\n    }\r\n}\r\n\r\n\r\nvoid XMLPrinter::PushHeader( bool writeBOM, bool writeDec )\r\n{\r\n    if ( writeBOM ) {\r\n        static const unsigned char bom[] = { TIXML_UTF_LEAD_0, TIXML_UTF_LEAD_1, TIXML_UTF_LEAD_2, 0 };\r\n        Write( reinterpret_cast< const char* >( bom ) );\r\n    }\r\n    if ( writeDec ) {\r\n        PushDeclaration( \"xml version=\\\"1.0\\\"\" );\r\n    }\r\n}\r\n\r\nvoid XMLPrinter::PrepareForNewNode( bool compactMode )\r\n{\r\n    SealElementIfJustOpened();\r\n\r\n    if ( compactMode ) {\r\n        return;\r\n    }\r\n\r\n    if ( _firstElement ) {\r\n        PrintSpace (_depth);\r\n    } else if ( _textDepth < 0) {\r\n        Putc( '\\n' );\r\n        PrintSpace( _depth );\r\n    }\r\n\r\n    _firstElement = false;\r\n}\r\n\r\nvoid XMLPrinter::OpenElement( const char* name, bool compactMode )\r\n{\r\n    PrepareForNewNode( compactMode );\r\n    _stack.Push( name );\r\n\r\n    Write ( \"<\" );\r\n    Write ( name );\r\n\r\n    _elementJustOpened = true;\r\n    ++_depth;\r\n}\r\n\r\n\r\nvoid XMLPrinter::PushAttribute( const char* name, const char* value )\r\n{\r\n    TIXMLASSERT( _elementJustOpened );\r\n    Putc ( ' ' );\r\n    Write( name );\r\n    Write( \"=\\\"\" );\r\n    PrintString( value, false );\r\n    Putc ( '\\\"' );\r\n}\r\n\r\n\r\nvoid XMLPrinter::PushAttribute( const char* name, int v )\r\n{\r\n    char buf[BUF_SIZE];\r\n    XMLUtil::ToStr( v, buf, BUF_SIZE );\r\n    PushAttribute( name, buf );\r\n}\r\n\r\n\r\nvoid XMLPrinter::PushAttribute( const char* name, unsigned v )\r\n{\r\n    char buf[BUF_SIZE];\r\n    XMLUtil::ToStr( v, buf, BUF_SIZE );\r\n    PushAttribute( name, buf );\r\n}\r\n\r\n\r\nvoid XMLPrinter::PushAttribute(const char* name, int64_t v)\r\n{\r\n\tchar buf[BUF_SIZE];\r\n\tXMLUtil::ToStr(v, buf, BUF_SIZE);\r\n\tPushAttribute(name, buf);\r\n}\r\n\r\n\r\nvoid XMLPrinter::PushAttribute(const char* name, uint64_t v)\r\n{\r\n\tchar buf[BUF_SIZE];\r\n\tXMLUtil::ToStr(v, buf, BUF_SIZE);\r\n\tPushAttribute(name, buf);\r\n}\r\n\r\n\r\nvoid XMLPrinter::PushAttribute( const char* name, bool v )\r\n{\r\n    char buf[BUF_SIZE];\r\n    XMLUtil::ToStr( v, buf, BUF_SIZE );\r\n    PushAttribute( name, buf );\r\n}\r\n\r\n\r\nvoid XMLPrinter::PushAttribute( const char* name, double v )\r\n{\r\n    char buf[BUF_SIZE];\r\n    XMLUtil::ToStr( v, buf, BUF_SIZE );\r\n    PushAttribute( name, buf );\r\n}\r\n\r\n\r\nvoid XMLPrinter::CloseElement( bool compactMode )\r\n{\r\n    --_depth;\r\n    const char* name = _stack.Pop();\r\n\r\n    if ( _elementJustOpened ) {\r\n        Write( \"/>\" );\r\n    }\r\n    else {\r\n        if ( _textDepth < 0 && !compactMode) {\r\n            Putc( '\\n' );\r\n            PrintSpace( _depth );\r\n        }\r\n        Write ( \"</\" );\r\n        Write ( name );\r\n        Write ( \">\" );\r\n    }\r\n\r\n    if ( _textDepth == _depth ) {\r\n        _textDepth = -1;\r\n    }\r\n    if ( _depth == 0 && !compactMode) {\r\n        Putc( '\\n' );\r\n    }\r\n    _elementJustOpened = false;\r\n}\r\n\r\n\r\nvoid XMLPrinter::SealElementIfJustOpened()\r\n{\r\n    if ( !_elementJustOpened ) {\r\n        return;\r\n    }\r\n    _elementJustOpened = false;\r\n    Putc( '>' );\r\n}\r\n\r\n\r\nvoid XMLPrinter::PushText( const char* text, bool cdata )\r\n{\r\n    _textDepth = _depth-1;\r\n\r\n    SealElementIfJustOpened();\r\n    if ( cdata ) {\r\n        Write( \"<![CDATA[\" );\r\n        Write( text );\r\n        Write( \"]]>\" );\r\n    }\r\n    else {\r\n        PrintString( text, true );\r\n    }\r\n}\r\n\r\n\r\nvoid XMLPrinter::PushText( int64_t value )\r\n{\r\n    char buf[BUF_SIZE];\r\n    XMLUtil::ToStr( value, buf, BUF_SIZE );\r\n    PushText( buf, false );\r\n}\r\n\r\n\r\nvoid XMLPrinter::PushText( uint64_t value )\r\n{\r\n\tchar buf[BUF_SIZE];\r\n\tXMLUtil::ToStr(value, buf, BUF_SIZE);\r\n\tPushText(buf, false);\r\n}\r\n\r\n\r\nvoid XMLPrinter::PushText( int value )\r\n{\r\n    char buf[BUF_SIZE];\r\n    XMLUtil::ToStr( value, buf, BUF_SIZE );\r\n    PushText( buf, false );\r\n}\r\n\r\n\r\nvoid XMLPrinter::PushText( unsigned value )\r\n{\r\n    char buf[BUF_SIZE];\r\n    XMLUtil::ToStr( value, buf, BUF_SIZE );\r\n    PushText( buf, false );\r\n}\r\n\r\n\r\nvoid XMLPrinter::PushText( bool value )\r\n{\r\n    char buf[BUF_SIZE];\r\n    XMLUtil::ToStr( value, buf, BUF_SIZE );\r\n    PushText( buf, false );\r\n}\r\n\r\n\r\nvoid XMLPrinter::PushText( float value )\r\n{\r\n    char buf[BUF_SIZE];\r\n    XMLUtil::ToStr( value, buf, BUF_SIZE );\r\n    PushText( buf, false );\r\n}\r\n\r\n\r\nvoid XMLPrinter::PushText( double value )\r\n{\r\n    char buf[BUF_SIZE];\r\n    XMLUtil::ToStr( value, buf, BUF_SIZE );\r\n    PushText( buf, false );\r\n}\r\n\r\n\r\nvoid XMLPrinter::PushComment( const char* comment )\r\n{\r\n    PrepareForNewNode( _compactMode );\r\n\r\n    Write( \"<!--\" );\r\n    Write( comment );\r\n    Write( \"-->\" );\r\n}\r\n\r\n\r\nvoid XMLPrinter::PushDeclaration( const char* value )\r\n{\r\n    PrepareForNewNode( _compactMode );\r\n\r\n    Write( \"<?\" );\r\n    Write( value );\r\n    Write( \"?>\" );\r\n}\r\n\r\n\r\nvoid XMLPrinter::PushUnknown( const char* value )\r\n{\r\n    PrepareForNewNode( _compactMode );\r\n\r\n    Write( \"<!\" );\r\n    Write( value );\r\n    Putc( '>' );\r\n}\r\n\r\n\r\nbool XMLPrinter::VisitEnter( const XMLDocument& doc )\r\n{\r\n    _processEntities = doc.ProcessEntities();\r\n    if ( doc.HasBOM() ) {\r\n        PushHeader( true, false );\r\n    }\r\n    return true;\r\n}\r\n\r\n\r\nbool XMLPrinter::VisitEnter( const XMLElement& element, const XMLAttribute* attribute )\r\n{\r\n    const XMLElement* parentElem = 0;\r\n    if ( element.Parent() ) {\r\n        parentElem = element.Parent()->ToElement();\r\n    }\r\n    const bool compactMode = parentElem ? CompactMode( *parentElem ) : _compactMode;\r\n    OpenElement( element.Name(), compactMode );\r\n    while ( attribute ) {\r\n        PushAttribute( attribute->Name(), attribute->Value() );\r\n        attribute = attribute->Next();\r\n    }\r\n    return true;\r\n}\r\n\r\n\r\nbool XMLPrinter::VisitExit( const XMLElement& element )\r\n{\r\n    CloseElement( CompactMode(element) );\r\n    return true;\r\n}\r\n\r\n\r\nbool XMLPrinter::Visit( const XMLText& text )\r\n{\r\n    PushText( text.Value(), text.CData() );\r\n    return true;\r\n}\r\n\r\n\r\nbool XMLPrinter::Visit( const XMLComment& comment )\r\n{\r\n    PushComment( comment.Value() );\r\n    return true;\r\n}\r\n\r\nbool XMLPrinter::Visit( const XMLDeclaration& declaration )\r\n{\r\n    PushDeclaration( declaration.Value() );\r\n    return true;\r\n}\r\n\r\n\r\nbool XMLPrinter::Visit( const XMLUnknown& unknown )\r\n{\r\n    PushUnknown( unknown.Value() );\r\n    return true;\r\n}\r\n\r\n}   // namespace tinyxml2\r\n"
  },
  {
    "path": "libs/tinyxml2/tinyxml2.h",
    "content": "/*\r\nOriginal code by Lee Thomason (www.grinninglizard.com)\r\n\r\nThis software is provided 'as-is', without any express or implied\r\nwarranty. In no event will the authors be held liable for any\r\ndamages arising from the use of this software.\r\n\r\nPermission is granted to anyone to use this software for any\r\npurpose, including commercial applications, and to alter it and\r\nredistribute it freely, subject to the following restrictions:\r\n\r\n1. The origin of this software must not be misrepresented; you must\r\nnot claim that you wrote the original software. If you use this\r\nsoftware in a product, an acknowledgment in the product documentation\r\nwould be appreciated but is not required.\r\n\r\n2. Altered source versions must be plainly marked as such, and\r\nmust not be misrepresented as being the original software.\r\n\r\n3. This notice may not be removed or altered from any source\r\ndistribution.\r\n*/\r\n\r\n#ifndef TINYXML2_INCLUDED\r\n#define TINYXML2_INCLUDED\r\n\r\n#if defined(ANDROID_NDK) || defined(__BORLANDC__) || defined(__QNXNTO__)\r\n#   include <ctype.h>\r\n#   include <limits.h>\r\n#   include <stdio.h>\r\n#   include <stdlib.h>\r\n#   include <string.h>\r\n#\tif defined(__PS3__)\r\n#\t\tinclude <stddef.h>\r\n#\tendif\r\n#else\r\n#   include <cctype>\r\n#   include <climits>\r\n#   include <cstdio>\r\n#   include <cstdlib>\r\n#   include <cstring>\r\n#endif\r\n#include <stdint.h>\r\n\r\n/*\r\n\tgcc:\r\n        g++ -Wall -DTINYXML2_DEBUG tinyxml2.cpp xmltest.cpp -o gccxmltest.exe\r\n\r\n    Formatting, Artistic Style:\r\n        AStyle.exe --style=1tbs --indent-switches --break-closing-brackets --indent-preprocessor tinyxml2.cpp tinyxml2.h\r\n*/\r\n\r\n#if defined( _DEBUG ) || defined (__DEBUG__)\r\n#   ifndef TINYXML2_DEBUG\r\n#       define TINYXML2_DEBUG\r\n#   endif\r\n#endif\r\n\r\n#ifdef _MSC_VER\r\n#   pragma warning(push)\r\n#   pragma warning(disable: 4251)\r\n#endif\r\n\r\n#ifdef _MSC_VER\r\n#   ifdef TINYXML2_EXPORT\r\n#       define TINYXML2_LIB __declspec(dllexport)\r\n#   elif defined(TINYXML2_IMPORT)\r\n#       define TINYXML2_LIB __declspec(dllimport)\r\n#   else\r\n#       define TINYXML2_LIB\r\n#   endif\r\n#elif __GNUC__ >= 4\r\n#   define TINYXML2_LIB __attribute__((visibility(\"default\")))\r\n#else\r\n#   define TINYXML2_LIB\r\n#endif\r\n\r\n\r\n#if !defined(TIXMLASSERT)\r\n#if defined(TINYXML2_DEBUG)\r\n#   if defined(_MSC_VER)\r\n#       // \"(void)0,\" is for suppressing C4127 warning in \"assert(false)\", \"assert(true)\" and the like\r\n#       define TIXMLASSERT( x )           do { if ( !((void)0,(x))) { __debugbreak(); } } while(false)\r\n#   elif defined (ANDROID_NDK)\r\n#       include <android/log.h>\r\n#       define TIXMLASSERT( x )           do { if ( !(x)) { __android_log_assert( \"assert\", \"grinliz\", \"ASSERT in '%s' at %d.\", __FILE__, __LINE__ ); } } while(false)\r\n#   else\r\n#       include <assert.h>\r\n#       define TIXMLASSERT                assert\r\n#   endif\r\n#else\r\n#   define TIXMLASSERT( x )               do {} while(false)\r\n#endif\r\n#endif\r\n\r\n/* Versioning, past 1.0.14:\r\n\thttp://semver.org/\r\n*/\r\nstatic const int TIXML2_MAJOR_VERSION = 10;\r\nstatic const int TIXML2_MINOR_VERSION = 0;\r\nstatic const int TIXML2_PATCH_VERSION = 0;\r\n\r\n#define TINYXML2_MAJOR_VERSION 10\r\n#define TINYXML2_MINOR_VERSION 0\r\n#define TINYXML2_PATCH_VERSION 0\r\n\r\n// A fixed element depth limit is problematic. There needs to be a\r\n// limit to avoid a stack overflow. However, that limit varies per\r\n// system, and the capacity of the stack. On the other hand, it's a trivial\r\n// attack that can result from ill, malicious, or even correctly formed XML,\r\n// so there needs to be a limit in place.\r\nstatic const int TINYXML2_MAX_ELEMENT_DEPTH = 500;\r\n\r\nnamespace tinyxml2\r\n{\r\nclass XMLDocument;\r\nclass XMLElement;\r\nclass XMLAttribute;\r\nclass XMLComment;\r\nclass XMLText;\r\nclass XMLDeclaration;\r\nclass XMLUnknown;\r\nclass XMLPrinter;\r\n\r\n/*\r\n\tA class that wraps strings. Normally stores the start and end\r\n\tpointers into the XML file itself, and will apply normalization\r\n\tand entity translation if actually read. Can also store (and memory\r\n\tmanage) a traditional char[]\r\n\r\n    Isn't clear why TINYXML2_LIB is needed; but seems to fix #719\r\n*/\r\nclass TINYXML2_LIB StrPair\r\n{\r\npublic:\r\n    enum Mode {\r\n        NEEDS_ENTITY_PROCESSING\t\t\t= 0x01,\r\n        NEEDS_NEWLINE_NORMALIZATION\t\t= 0x02,\r\n        NEEDS_WHITESPACE_COLLAPSING     = 0x04,\r\n\r\n        TEXT_ELEMENT\t\t            = NEEDS_ENTITY_PROCESSING | NEEDS_NEWLINE_NORMALIZATION,\r\n        TEXT_ELEMENT_LEAVE_ENTITIES\t\t= NEEDS_NEWLINE_NORMALIZATION,\r\n        ATTRIBUTE_NAME\t\t            = 0,\r\n        ATTRIBUTE_VALUE\t\t            = NEEDS_ENTITY_PROCESSING | NEEDS_NEWLINE_NORMALIZATION,\r\n        ATTRIBUTE_VALUE_LEAVE_ENTITIES  = NEEDS_NEWLINE_NORMALIZATION,\r\n        COMMENT\t\t\t\t\t\t\t= NEEDS_NEWLINE_NORMALIZATION\r\n    };\r\n\r\n    StrPair() : _flags( 0 ), _start( 0 ), _end( 0 ) {}\r\n    ~StrPair();\r\n\r\n    void Set( char* start, char* end, int flags ) {\r\n        TIXMLASSERT( start );\r\n        TIXMLASSERT( end );\r\n        Reset();\r\n        _start  = start;\r\n        _end    = end;\r\n        _flags  = flags | NEEDS_FLUSH;\r\n    }\r\n\r\n    const char* GetStr();\r\n\r\n    bool Empty() const {\r\n        return _start == _end;\r\n    }\r\n\r\n    void SetInternedStr( const char* str ) {\r\n        Reset();\r\n        _start = const_cast<char*>(str);\r\n    }\r\n\r\n    void SetStr( const char* str, int flags=0 );\r\n\r\n    char* ParseText( char* in, const char* endTag, int strFlags, int* curLineNumPtr );\r\n    char* ParseName( char* in );\r\n\r\n    void TransferTo( StrPair* other );\r\n\tvoid Reset();\r\n\r\nprivate:\r\n    void CollapseWhitespace();\r\n\r\n    enum {\r\n        NEEDS_FLUSH = 0x100,\r\n        NEEDS_DELETE = 0x200\r\n    };\r\n\r\n    int     _flags;\r\n    char*   _start;\r\n    char*   _end;\r\n\r\n    StrPair( const StrPair& other );\t// not supported\r\n    void operator=( const StrPair& other );\t// not supported, use TransferTo()\r\n};\r\n\r\n\r\n/*\r\n\tA dynamic array of Plain Old Data. Doesn't support constructors, etc.\r\n\tHas a small initial memory pool, so that low or no usage will not\r\n\tcause a call to new/delete\r\n*/\r\ntemplate <class T, int INITIAL_SIZE>\r\nclass DynArray\r\n{\r\npublic:\r\n    DynArray() :\r\n        _mem( _pool ),\r\n        _allocated( INITIAL_SIZE ),\r\n        _size( 0 )\r\n    {\r\n    }\r\n\r\n    ~DynArray() {\r\n        if ( _mem != _pool ) {\r\n            delete [] _mem;\r\n        }\r\n    }\r\n\r\n    void Clear() {\r\n        _size = 0;\r\n    }\r\n\r\n    void Push( T t ) {\r\n        TIXMLASSERT( _size < INT_MAX );\r\n        EnsureCapacity( _size+1 );\r\n        _mem[_size] = t;\r\n        ++_size;\r\n    }\r\n\r\n    T* PushArr( int count ) {\r\n        TIXMLASSERT( count >= 0 );\r\n        TIXMLASSERT( _size <= INT_MAX - count );\r\n        EnsureCapacity( _size+count );\r\n        T* ret = &_mem[_size];\r\n        _size += count;\r\n        return ret;\r\n    }\r\n\r\n    T Pop() {\r\n        TIXMLASSERT( _size > 0 );\r\n        --_size;\r\n        return _mem[_size];\r\n    }\r\n\r\n    void PopArr( int count ) {\r\n        TIXMLASSERT( _size >= count );\r\n        _size -= count;\r\n    }\r\n\r\n    bool Empty() const\t\t\t\t\t{\r\n        return _size == 0;\r\n    }\r\n\r\n    T& operator[](int i)\t\t\t\t{\r\n        TIXMLASSERT( i>= 0 && i < _size );\r\n        return _mem[i];\r\n    }\r\n\r\n    const T& operator[](int i) const\t{\r\n        TIXMLASSERT( i>= 0 && i < _size );\r\n        return _mem[i];\r\n    }\r\n\r\n    const T& PeekTop() const            {\r\n        TIXMLASSERT( _size > 0 );\r\n        return _mem[ _size - 1];\r\n    }\r\n\r\n    int Size() const\t\t\t\t\t{\r\n        TIXMLASSERT( _size >= 0 );\r\n        return _size;\r\n    }\r\n\r\n    int Capacity() const\t\t\t\t{\r\n        TIXMLASSERT( _allocated >= INITIAL_SIZE );\r\n        return _allocated;\r\n    }\r\n\r\n\tvoid SwapRemove(int i) {\r\n\t\tTIXMLASSERT(i >= 0 && i < _size);\r\n\t\tTIXMLASSERT(_size > 0);\r\n\t\t_mem[i] = _mem[_size - 1];\r\n\t\t--_size;\r\n\t}\r\n\r\n    const T* Mem() const\t\t\t\t{\r\n        TIXMLASSERT( _mem );\r\n        return _mem;\r\n    }\r\n\r\n    T* Mem() {\r\n        TIXMLASSERT( _mem );\r\n        return _mem;\r\n    }\r\n\r\nprivate:\r\n    DynArray( const DynArray& ); // not supported\r\n    void operator=( const DynArray& ); // not supported\r\n\r\n    void EnsureCapacity( int cap ) {\r\n        TIXMLASSERT( cap > 0 );\r\n        if ( cap > _allocated ) {\r\n            TIXMLASSERT( cap <= INT_MAX / 2 );\r\n            const int newAllocated = cap * 2;\r\n            T* newMem = new T[static_cast<unsigned int>(newAllocated)];\r\n            TIXMLASSERT( newAllocated >= _size );\r\n            memcpy( newMem, _mem, sizeof(T)*static_cast<size_t>(_size) );\t// warning: not using constructors, only works for PODs\r\n            if ( _mem != _pool ) {\r\n                delete [] _mem;\r\n            }\r\n            _mem = newMem;\r\n            _allocated = newAllocated;\r\n        }\r\n    }\r\n\r\n    T*  _mem;\r\n    T   _pool[static_cast<size_t>(INITIAL_SIZE)];\r\n    int _allocated;\t\t// objects allocated\r\n    int _size;\t\t\t// number objects in use\r\n};\r\n\r\n\r\n/*\r\n\tParent virtual class of a pool for fast allocation\r\n\tand deallocation of objects.\r\n*/\r\nclass MemPool\r\n{\r\npublic:\r\n    MemPool() {}\r\n    virtual ~MemPool() {}\r\n\r\n    virtual int ItemSize() const = 0;\r\n    virtual void* Alloc() = 0;\r\n    virtual void Free( void* ) = 0;\r\n    virtual void SetTracked() = 0;\r\n};\r\n\r\n\r\n/*\r\n\tTemplate child class to create pools of the correct type.\r\n*/\r\ntemplate< int ITEM_SIZE >\r\nclass MemPoolT : public MemPool\r\n{\r\npublic:\r\n    MemPoolT() : _blockPtrs(), _root(0), _currentAllocs(0), _nAllocs(0), _maxAllocs(0), _nUntracked(0)\t{}\r\n    ~MemPoolT() {\r\n        MemPoolT< ITEM_SIZE >::Clear();\r\n    }\r\n\r\n    void Clear() {\r\n        // Delete the blocks.\r\n        while( !_blockPtrs.Empty()) {\r\n            Block* lastBlock = _blockPtrs.Pop();\r\n            delete lastBlock;\r\n        }\r\n        _root = 0;\r\n        _currentAllocs = 0;\r\n        _nAllocs = 0;\r\n        _maxAllocs = 0;\r\n        _nUntracked = 0;\r\n    }\r\n\r\n    virtual int ItemSize() const override{\r\n        return ITEM_SIZE;\r\n    }\r\n    int CurrentAllocs() const\t\t{\r\n        return _currentAllocs;\r\n    }\r\n\r\n    virtual void* Alloc() override{\r\n        if ( !_root ) {\r\n            // Need a new block.\r\n            Block* block = new Block;\r\n            _blockPtrs.Push( block );\r\n\r\n            Item* blockItems = block->items;\r\n            for( int i = 0; i < ITEMS_PER_BLOCK - 1; ++i ) {\r\n                blockItems[i].next = &(blockItems[i + 1]);\r\n            }\r\n            blockItems[ITEMS_PER_BLOCK - 1].next = 0;\r\n            _root = blockItems;\r\n        }\r\n        Item* const result = _root;\r\n        TIXMLASSERT( result != 0 );\r\n        _root = _root->next;\r\n\r\n        ++_currentAllocs;\r\n        if ( _currentAllocs > _maxAllocs ) {\r\n            _maxAllocs = _currentAllocs;\r\n        }\r\n        ++_nAllocs;\r\n        ++_nUntracked;\r\n        return result;\r\n    }\r\n\r\n    virtual void Free( void* mem ) override {\r\n        if ( !mem ) {\r\n            return;\r\n        }\r\n        --_currentAllocs;\r\n        Item* item = static_cast<Item*>( mem );\r\n#ifdef TINYXML2_DEBUG\r\n        memset( item, 0xfe, sizeof( *item ) );\r\n#endif\r\n        item->next = _root;\r\n        _root = item;\r\n    }\r\n    void Trace( const char* name ) {\r\n        printf( \"Mempool %s watermark=%d [%dk] current=%d size=%d nAlloc=%d blocks=%d\\n\",\r\n                name, _maxAllocs, _maxAllocs * ITEM_SIZE / 1024, _currentAllocs,\r\n                ITEM_SIZE, _nAllocs, _blockPtrs.Size() );\r\n    }\r\n\r\n    void SetTracked() override {\r\n        --_nUntracked;\r\n    }\r\n\r\n    int Untracked() const {\r\n        return _nUntracked;\r\n    }\r\n\r\n\t// This number is perf sensitive. 4k seems like a good tradeoff on my machine.\r\n\t// The test file is large, 170k.\r\n\t// Release:\t\tVS2010 gcc(no opt)\r\n\t//\t\t1k:\t\t4000\r\n\t//\t\t2k:\t\t4000\r\n\t//\t\t4k:\t\t3900\t21000\r\n\t//\t\t16k:\t5200\r\n\t//\t\t32k:\t4300\r\n\t//\t\t64k:\t4000\t21000\r\n    // Declared public because some compilers do not accept to use ITEMS_PER_BLOCK\r\n    // in private part if ITEMS_PER_BLOCK is private\r\n    enum { ITEMS_PER_BLOCK = (4 * 1024) / ITEM_SIZE };\r\n\r\nprivate:\r\n    MemPoolT( const MemPoolT& ); // not supported\r\n    void operator=( const MemPoolT& ); // not supported\r\n\r\n    union Item {\r\n        Item*   next;\r\n        char    itemData[static_cast<size_t>(ITEM_SIZE)];\r\n    };\r\n    struct Block {\r\n        Item items[ITEMS_PER_BLOCK];\r\n    };\r\n    DynArray< Block*, 10 > _blockPtrs;\r\n    Item* _root;\r\n\r\n    int _currentAllocs;\r\n    int _nAllocs;\r\n    int _maxAllocs;\r\n    int _nUntracked;\r\n};\r\n\r\n\r\n\r\n/**\r\n\tImplements the interface to the \"Visitor pattern\" (see the Accept() method.)\r\n\tIf you call the Accept() method, it requires being passed a XMLVisitor\r\n\tclass to handle callbacks. For nodes that contain other nodes (Document, Element)\r\n\tyou will get called with a VisitEnter/VisitExit pair. Nodes that are always leafs\r\n\tare simply called with Visit().\r\n\r\n\tIf you return 'true' from a Visit method, recursive parsing will continue. If you return\r\n\tfalse, <b>no children of this node or its siblings</b> will be visited.\r\n\r\n\tAll flavors of Visit methods have a default implementation that returns 'true' (continue\r\n\tvisiting). You need to only override methods that are interesting to you.\r\n\r\n\tGenerally Accept() is called on the XMLDocument, although all nodes support visiting.\r\n\r\n\tYou should never change the document from a callback.\r\n\r\n\t@sa XMLNode::Accept()\r\n*/\r\nclass TINYXML2_LIB XMLVisitor\r\n{\r\npublic:\r\n    virtual ~XMLVisitor() {}\r\n\r\n    /// Visit a document.\r\n    virtual bool VisitEnter( const XMLDocument& /*doc*/ )\t\t\t{\r\n        return true;\r\n    }\r\n    /// Visit a document.\r\n    virtual bool VisitExit( const XMLDocument& /*doc*/ )\t\t\t{\r\n        return true;\r\n    }\r\n\r\n    /// Visit an element.\r\n    virtual bool VisitEnter( const XMLElement& /*element*/, const XMLAttribute* /*firstAttribute*/ )\t{\r\n        return true;\r\n    }\r\n    /// Visit an element.\r\n    virtual bool VisitExit( const XMLElement& /*element*/ )\t\t\t{\r\n        return true;\r\n    }\r\n\r\n    /// Visit a declaration.\r\n    virtual bool Visit( const XMLDeclaration& /*declaration*/ )\t\t{\r\n        return true;\r\n    }\r\n    /// Visit a text node.\r\n    virtual bool Visit( const XMLText& /*text*/ )\t\t\t\t\t{\r\n        return true;\r\n    }\r\n    /// Visit a comment node.\r\n    virtual bool Visit( const XMLComment& /*comment*/ )\t\t\t\t{\r\n        return true;\r\n    }\r\n    /// Visit an unknown node.\r\n    virtual bool Visit( const XMLUnknown& /*unknown*/ )\t\t\t\t{\r\n        return true;\r\n    }\r\n};\r\n\r\n// WARNING: must match XMLDocument::_errorNames[]\r\nenum XMLError {\r\n    XML_SUCCESS = 0,\r\n    XML_NO_ATTRIBUTE,\r\n    XML_WRONG_ATTRIBUTE_TYPE,\r\n    XML_ERROR_FILE_NOT_FOUND,\r\n    XML_ERROR_FILE_COULD_NOT_BE_OPENED,\r\n    XML_ERROR_FILE_READ_ERROR,\r\n    XML_ERROR_PARSING_ELEMENT,\r\n    XML_ERROR_PARSING_ATTRIBUTE,\r\n    XML_ERROR_PARSING_TEXT,\r\n    XML_ERROR_PARSING_CDATA,\r\n    XML_ERROR_PARSING_COMMENT,\r\n    XML_ERROR_PARSING_DECLARATION,\r\n    XML_ERROR_PARSING_UNKNOWN,\r\n    XML_ERROR_EMPTY_DOCUMENT,\r\n    XML_ERROR_MISMATCHED_ELEMENT,\r\n    XML_ERROR_PARSING,\r\n    XML_CAN_NOT_CONVERT_TEXT,\r\n    XML_NO_TEXT_NODE,\r\n\tXML_ELEMENT_DEPTH_EXCEEDED,\r\n\r\n\tXML_ERROR_COUNT\r\n};\r\n\r\n\r\n/*\r\n\tUtility functionality.\r\n*/\r\nclass TINYXML2_LIB XMLUtil\r\n{\r\npublic:\r\n    static const char* SkipWhiteSpace( const char* p, int* curLineNumPtr )\t{\r\n        TIXMLASSERT( p );\r\n\r\n        while( IsWhiteSpace(*p) ) {\r\n            if (curLineNumPtr && *p == '\\n') {\r\n                ++(*curLineNumPtr);\r\n            }\r\n            ++p;\r\n        }\r\n        TIXMLASSERT( p );\r\n        return p;\r\n    }\r\n    static char* SkipWhiteSpace( char* const p, int* curLineNumPtr ) {\r\n        return const_cast<char*>( SkipWhiteSpace( const_cast<const char*>(p), curLineNumPtr ) );\r\n    }\r\n\r\n    // Anything in the high order range of UTF-8 is assumed to not be whitespace. This isn't\r\n    // correct, but simple, and usually works.\r\n    static bool IsWhiteSpace( char p )\t\t\t\t\t{\r\n        return !IsUTF8Continuation(p) && isspace( static_cast<unsigned char>(p) );\r\n    }\r\n\r\n    inline static bool IsNameStartChar( unsigned char ch ) {\r\n        if ( ch >= 128 ) {\r\n            // This is a heuristic guess in attempt to not implement Unicode-aware isalpha()\r\n            return true;\r\n        }\r\n        if ( isalpha( ch ) ) {\r\n            return true;\r\n        }\r\n        return ch == ':' || ch == '_';\r\n    }\r\n\r\n    inline static bool IsNameChar( unsigned char ch ) {\r\n        return IsNameStartChar( ch )\r\n               || isdigit( ch )\r\n               || ch == '.'\r\n               || ch == '-';\r\n    }\r\n\r\n    inline static bool IsPrefixHex( const char* p) {\r\n        p = SkipWhiteSpace(p, 0);\r\n        return p && *p == '0' && ( *(p + 1) == 'x' || *(p + 1) == 'X');\r\n    }\r\n\r\n    inline static bool StringEqual( const char* p, const char* q, int nChar=INT_MAX )  {\r\n        if ( p == q ) {\r\n            return true;\r\n        }\r\n        TIXMLASSERT( p );\r\n        TIXMLASSERT( q );\r\n        TIXMLASSERT( nChar >= 0 );\r\n        return strncmp( p, q, static_cast<size_t>(nChar) ) == 0;\r\n    }\r\n\r\n    inline static bool IsUTF8Continuation( const char p ) {\r\n        return ( p & 0x80 ) != 0;\r\n    }\r\n\r\n    static const char* ReadBOM( const char* p, bool* hasBOM );\r\n    // p is the starting location,\r\n    // the UTF-8 value of the entity will be placed in value, and length filled in.\r\n    static const char* GetCharacterRef( const char* p, char* value, int* length );\r\n    static void ConvertUTF32ToUTF8( unsigned long input, char* output, int* length );\r\n\r\n    // converts primitive types to strings\r\n    static void ToStr( int v, char* buffer, int bufferSize );\r\n    static void ToStr( unsigned v, char* buffer, int bufferSize );\r\n    static void ToStr( bool v, char* buffer, int bufferSize );\r\n    static void ToStr( float v, char* buffer, int bufferSize );\r\n    static void ToStr( double v, char* buffer, int bufferSize );\r\n\tstatic void ToStr(int64_t v, char* buffer, int bufferSize);\r\n    static void ToStr(uint64_t v, char* buffer, int bufferSize);\r\n\r\n    // converts strings to primitive types\r\n    static bool\tToInt( const char* str, int* value );\r\n    static bool ToUnsigned( const char* str, unsigned* value );\r\n    static bool\tToBool( const char* str, bool* value );\r\n    static bool\tToFloat( const char* str, float* value );\r\n    static bool ToDouble( const char* str, double* value );\r\n\tstatic bool ToInt64(const char* str, int64_t* value);\r\n    static bool ToUnsigned64(const char* str, uint64_t* value);\r\n\t// Changes what is serialized for a boolean value.\r\n\t// Default to \"true\" and \"false\". Shouldn't be changed\r\n\t// unless you have a special testing or compatibility need.\r\n\t// Be careful: static, global, & not thread safe.\r\n\t// Be sure to set static const memory as parameters.\r\n\tstatic void SetBoolSerialization(const char* writeTrue, const char* writeFalse);\r\n\r\nprivate:\r\n\tstatic const char* writeBoolTrue;\r\n\tstatic const char* writeBoolFalse;\r\n};\r\n\r\n\r\n/** XMLNode is a base class for every object that is in the\r\n\tXML Document Object Model (DOM), except XMLAttributes.\r\n\tNodes have siblings, a parent, and children which can\r\n\tbe navigated. A node is always in a XMLDocument.\r\n\tThe type of a XMLNode can be queried, and it can\r\n\tbe cast to its more defined type.\r\n\r\n\tA XMLDocument allocates memory for all its Nodes.\r\n\tWhen the XMLDocument gets deleted, all its Nodes\r\n\twill also be deleted.\r\n\r\n\t@verbatim\r\n\tA Document can contain:\tElement\t(container or leaf)\r\n\t\t\t\t\t\t\tComment (leaf)\r\n\t\t\t\t\t\t\tUnknown (leaf)\r\n\t\t\t\t\t\t\tDeclaration( leaf )\r\n\r\n\tAn Element can contain:\tElement (container or leaf)\r\n\t\t\t\t\t\t\tText\t(leaf)\r\n\t\t\t\t\t\t\tAttributes (not on tree)\r\n\t\t\t\t\t\t\tComment (leaf)\r\n\t\t\t\t\t\t\tUnknown (leaf)\r\n\r\n\t@endverbatim\r\n*/\r\nclass TINYXML2_LIB XMLNode\r\n{\r\n    friend class XMLDocument;\r\n    friend class XMLElement;\r\npublic:\r\n\r\n    /// Get the XMLDocument that owns this XMLNode.\r\n    const XMLDocument* GetDocument() const\t{\r\n        TIXMLASSERT( _document );\r\n        return _document;\r\n    }\r\n    /// Get the XMLDocument that owns this XMLNode.\r\n    XMLDocument* GetDocument()\t\t\t\t{\r\n        TIXMLASSERT( _document );\r\n        return _document;\r\n    }\r\n\r\n    /// Safely cast to an Element, or null.\r\n    virtual XMLElement*\t\tToElement()\t\t{\r\n        return 0;\r\n    }\r\n    /// Safely cast to Text, or null.\r\n    virtual XMLText*\t\tToText()\t\t{\r\n        return 0;\r\n    }\r\n    /// Safely cast to a Comment, or null.\r\n    virtual XMLComment*\t\tToComment()\t\t{\r\n        return 0;\r\n    }\r\n    /// Safely cast to a Document, or null.\r\n    virtual XMLDocument*\tToDocument()\t{\r\n        return 0;\r\n    }\r\n    /// Safely cast to a Declaration, or null.\r\n    virtual XMLDeclaration*\tToDeclaration()\t{\r\n        return 0;\r\n    }\r\n    /// Safely cast to an Unknown, or null.\r\n    virtual XMLUnknown*\t\tToUnknown()\t\t{\r\n        return 0;\r\n    }\r\n\r\n    virtual const XMLElement*\t\tToElement() const\t\t{\r\n        return 0;\r\n    }\r\n    virtual const XMLText*\t\t\tToText() const\t\t\t{\r\n        return 0;\r\n    }\r\n    virtual const XMLComment*\t\tToComment() const\t\t{\r\n        return 0;\r\n    }\r\n    virtual const XMLDocument*\t\tToDocument() const\t\t{\r\n        return 0;\r\n    }\r\n    virtual const XMLDeclaration*\tToDeclaration() const\t{\r\n        return 0;\r\n    }\r\n    virtual const XMLUnknown*\t\tToUnknown() const\t\t{\r\n        return 0;\r\n    }\r\n\r\n    // ChildElementCount was originally suggested by msteiger on the sourceforge page for TinyXML and modified by KB1SPH for TinyXML-2.\r\n\r\n    int ChildElementCount(const char *value) const;\r\n\r\n    int ChildElementCount() const;\r\n\r\n    /** The meaning of 'value' changes for the specific type.\r\n    \t@verbatim\r\n    \tDocument:\tempty (NULL is returned, not an empty string)\r\n    \tElement:\tname of the element\r\n    \tComment:\tthe comment text\r\n    \tUnknown:\tthe tag contents\r\n    \tText:\t\tthe text string\r\n    \t@endverbatim\r\n    */\r\n    const char* Value() const;\r\n\r\n    /** Set the Value of an XML node.\r\n    \t@sa Value()\r\n    */\r\n    void SetValue( const char* val, bool staticMem=false );\r\n\r\n    /// Gets the line number the node is in, if the document was parsed from a file.\r\n    int GetLineNum() const { return _parseLineNum; }\r\n\r\n    /// Get the parent of this node on the DOM.\r\n    const XMLNode*\tParent() const\t\t\t{\r\n        return _parent;\r\n    }\r\n\r\n    XMLNode* Parent()\t\t\t\t\t\t{\r\n        return _parent;\r\n    }\r\n\r\n    /// Returns true if this node has no children.\r\n    bool NoChildren() const\t\t\t\t\t{\r\n        return !_firstChild;\r\n    }\r\n\r\n    /// Get the first child node, or null if none exists.\r\n    const XMLNode*  FirstChild() const\t\t{\r\n        return _firstChild;\r\n    }\r\n\r\n    XMLNode*\t\tFirstChild()\t\t\t{\r\n        return _firstChild;\r\n    }\r\n\r\n    /** Get the first child element, or optionally the first child\r\n        element with the specified name.\r\n    */\r\n    const XMLElement* FirstChildElement( const char* name = 0 ) const;\r\n\r\n    XMLElement* FirstChildElement( const char* name = 0 )\t{\r\n        return const_cast<XMLElement*>(const_cast<const XMLNode*>(this)->FirstChildElement( name ));\r\n    }\r\n\r\n    /// Get the last child node, or null if none exists.\r\n    const XMLNode*\tLastChild() const\t\t\t\t\t\t{\r\n        return _lastChild;\r\n    }\r\n\r\n    XMLNode*\t\tLastChild()\t\t\t\t\t\t\t\t{\r\n        return _lastChild;\r\n    }\r\n\r\n    /** Get the last child element or optionally the last child\r\n        element with the specified name.\r\n    */\r\n    const XMLElement* LastChildElement( const char* name = 0 ) const;\r\n\r\n    XMLElement* LastChildElement( const char* name = 0 )\t{\r\n        return const_cast<XMLElement*>(const_cast<const XMLNode*>(this)->LastChildElement(name) );\r\n    }\r\n\r\n    /// Get the previous (left) sibling node of this node.\r\n    const XMLNode*\tPreviousSibling() const\t\t\t\t\t{\r\n        return _prev;\r\n    }\r\n\r\n    XMLNode*\tPreviousSibling()\t\t\t\t\t\t\t{\r\n        return _prev;\r\n    }\r\n\r\n    /// Get the previous (left) sibling element of this node, with an optionally supplied name.\r\n    const XMLElement*\tPreviousSiblingElement( const char* name = 0 ) const ;\r\n\r\n    XMLElement*\tPreviousSiblingElement( const char* name = 0 ) {\r\n        return const_cast<XMLElement*>(const_cast<const XMLNode*>(this)->PreviousSiblingElement( name ) );\r\n    }\r\n\r\n    /// Get the next (right) sibling node of this node.\r\n    const XMLNode*\tNextSibling() const\t\t\t\t\t\t{\r\n        return _next;\r\n    }\r\n\r\n    XMLNode*\tNextSibling()\t\t\t\t\t\t\t\t{\r\n        return _next;\r\n    }\r\n\r\n    /// Get the next (right) sibling element of this node, with an optionally supplied name.\r\n    const XMLElement*\tNextSiblingElement( const char* name = 0 ) const;\r\n\r\n    XMLElement*\tNextSiblingElement( const char* name = 0 )\t{\r\n        return const_cast<XMLElement*>(const_cast<const XMLNode*>(this)->NextSiblingElement( name ) );\r\n    }\r\n\r\n    /**\r\n    \tAdd a child node as the last (right) child.\r\n\t\tIf the child node is already part of the document,\r\n\t\tit is moved from its old location to the new location.\r\n\t\tReturns the addThis argument or 0 if the node does not\r\n\t\tbelong to the same document.\r\n    */\r\n    XMLNode* InsertEndChild( XMLNode* addThis );\r\n\r\n    XMLNode* LinkEndChild( XMLNode* addThis )\t{\r\n        return InsertEndChild( addThis );\r\n    }\r\n    /**\r\n    \tAdd a child node as the first (left) child.\r\n\t\tIf the child node is already part of the document,\r\n\t\tit is moved from its old location to the new location.\r\n\t\tReturns the addThis argument or 0 if the node does not\r\n\t\tbelong to the same document.\r\n    */\r\n    XMLNode* InsertFirstChild( XMLNode* addThis );\r\n    /**\r\n    \tAdd a node after the specified child node.\r\n\t\tIf the child node is already part of the document,\r\n\t\tit is moved from its old location to the new location.\r\n\t\tReturns the addThis argument or 0 if the afterThis node\r\n\t\tis not a child of this node, or if the node does not\r\n\t\tbelong to the same document.\r\n    */\r\n    XMLNode* InsertAfterChild( XMLNode* afterThis, XMLNode* addThis );\r\n\r\n    /**\r\n    \tDelete all the children of this node.\r\n    */\r\n    void DeleteChildren();\r\n\r\n    /**\r\n    \tDelete a child of this node.\r\n    */\r\n    void DeleteChild( XMLNode* node );\r\n\r\n    /**\r\n    \tMake a copy of this node, but not its children.\r\n    \tYou may pass in a Document pointer that will be\r\n    \tthe owner of the new Node. If the 'document' is\r\n    \tnull, then the node returned will be allocated\r\n    \tfrom the current Document. (this->GetDocument())\r\n\r\n    \tNote: if called on a XMLDocument, this will return null.\r\n    */\r\n    virtual XMLNode* ShallowClone( XMLDocument* document ) const = 0;\r\n\r\n\t/**\r\n\t\tMake a copy of this node and all its children.\r\n\r\n\t\tIf the 'target' is null, then the nodes will\r\n\t\tbe allocated in the current document. If 'target'\r\n        is specified, the memory will be allocated is the\r\n        specified XMLDocument.\r\n\r\n\t\tNOTE: This is probably not the correct tool to\r\n\t\tcopy a document, since XMLDocuments can have multiple\r\n\t\ttop level XMLNodes. You probably want to use\r\n        XMLDocument::DeepCopy()\r\n\t*/\r\n\tXMLNode* DeepClone( XMLDocument* target ) const;\r\n\r\n    /**\r\n    \tTest if 2 nodes are the same, but don't test children.\r\n    \tThe 2 nodes do not need to be in the same Document.\r\n\r\n    \tNote: if called on a XMLDocument, this will return false.\r\n    */\r\n    virtual bool ShallowEqual( const XMLNode* compare ) const = 0;\r\n\r\n    /** Accept a hierarchical visit of the nodes in the TinyXML-2 DOM. Every node in the\r\n    \tXML tree will be conditionally visited and the host will be called back\r\n    \tvia the XMLVisitor interface.\r\n\r\n    \tThis is essentially a SAX interface for TinyXML-2. (Note however it doesn't re-parse\r\n    \tthe XML for the callbacks, so the performance of TinyXML-2 is unchanged by using this\r\n    \tinterface versus any other.)\r\n\r\n    \tThe interface has been based on ideas from:\r\n\r\n    \t- http://www.saxproject.org/\r\n    \t- http://c2.com/cgi/wiki?HierarchicalVisitorPattern\r\n\r\n    \tWhich are both good references for \"visiting\".\r\n\r\n    \tAn example of using Accept():\r\n    \t@verbatim\r\n    \tXMLPrinter printer;\r\n    \ttinyxmlDoc.Accept( &printer );\r\n    \tconst char* xmlcstr = printer.CStr();\r\n    \t@endverbatim\r\n    */\r\n    virtual bool Accept( XMLVisitor* visitor ) const = 0;\r\n\r\n\t/**\r\n\t\tSet user data into the XMLNode. TinyXML-2 in\r\n\t\tno way processes or interprets user data.\r\n\t\tIt is initially 0.\r\n\t*/\r\n\tvoid SetUserData(void* userData)\t{ _userData = userData; }\r\n\r\n\t/**\r\n\t\tGet user data set into the XMLNode. TinyXML-2 in\r\n\t\tno way processes or interprets user data.\r\n\t\tIt is initially 0.\r\n\t*/\r\n\tvoid* GetUserData() const\t\t\t{ return _userData; }\r\n\r\nprotected:\r\n    explicit XMLNode( XMLDocument* );\r\n    virtual ~XMLNode();\r\n\r\n    virtual char* ParseDeep( char* p, StrPair* parentEndTag, int* curLineNumPtr);\r\n\r\n    XMLDocument*\t_document;\r\n    XMLNode*\t\t_parent;\r\n    mutable StrPair\t_value;\r\n    int             _parseLineNum;\r\n\r\n    XMLNode*\t\t_firstChild;\r\n    XMLNode*\t\t_lastChild;\r\n\r\n    XMLNode*\t\t_prev;\r\n    XMLNode*\t\t_next;\r\n\r\n\tvoid*\t\t\t_userData;\r\n\r\nprivate:\r\n    MemPool*\t\t_memPool;\r\n    void Unlink( XMLNode* child );\r\n    static void DeleteNode( XMLNode* node );\r\n    void InsertChildPreamble( XMLNode* insertThis ) const;\r\n    const XMLElement* ToElementWithName( const char* name ) const;\r\n\r\n    XMLNode( const XMLNode& );\t// not supported\r\n    XMLNode& operator=( const XMLNode& );\t// not supported\r\n};\r\n\r\n\r\n/** XML text.\r\n\r\n\tNote that a text node can have child element nodes, for example:\r\n\t@verbatim\r\n\t<root>This is <b>bold</b></root>\r\n\t@endverbatim\r\n\r\n\tA text node can have 2 ways to output the next. \"normal\" output\r\n\tand CDATA. It will default to the mode it was parsed from the XML file and\r\n\tyou generally want to leave it alone, but you can change the output mode with\r\n\tSetCData() and query it with CData().\r\n*/\r\nclass TINYXML2_LIB XMLText : public XMLNode\r\n{\r\n    friend class XMLDocument;\r\npublic:\r\n    virtual bool Accept( XMLVisitor* visitor ) const override;\r\n\r\n    virtual XMLText* ToText() override\t\t{\r\n        return this;\r\n    }\r\n    virtual const XMLText* ToText() const override {\r\n        return this;\r\n    }\r\n\r\n    /// Declare whether this should be CDATA or standard text.\r\n    void SetCData( bool isCData )\t\t\t{\r\n        _isCData = isCData;\r\n    }\r\n    /// Returns true if this is a CDATA text element.\r\n    bool CData() const\t\t\t\t\t\t{\r\n        return _isCData;\r\n    }\r\n\r\n    virtual XMLNode* ShallowClone( XMLDocument* document ) const override;\r\n    virtual bool ShallowEqual( const XMLNode* compare ) const override;\r\n\r\nprotected:\r\n    explicit XMLText( XMLDocument* doc )\t: XMLNode( doc ), _isCData( false )\t{}\r\n    virtual ~XMLText()\t\t\t\t\t\t\t\t\t\t\t\t{}\r\n\r\n    char* ParseDeep( char* p, StrPair* parentEndTag, int* curLineNumPtr ) override;\r\n\r\nprivate:\r\n    bool _isCData;\r\n\r\n    XMLText( const XMLText& );\t// not supported\r\n    XMLText& operator=( const XMLText& );\t// not supported\r\n};\r\n\r\n\r\n/** An XML Comment. */\r\nclass TINYXML2_LIB XMLComment : public XMLNode\r\n{\r\n    friend class XMLDocument;\r\npublic:\r\n    virtual XMLComment*\tToComment() override\t\t{\r\n        return this;\r\n    }\r\n    virtual const XMLComment* ToComment() const override {\r\n        return this;\r\n    }\r\n\r\n    virtual bool Accept( XMLVisitor* visitor ) const override;\r\n\r\n    virtual XMLNode* ShallowClone( XMLDocument* document ) const override;\r\n    virtual bool ShallowEqual( const XMLNode* compare ) const override;\r\n\r\nprotected:\r\n    explicit XMLComment( XMLDocument* doc );\r\n    virtual ~XMLComment();\r\n\r\n    char* ParseDeep( char* p, StrPair* parentEndTag, int* curLineNumPtr) override;\r\n\r\nprivate:\r\n    XMLComment( const XMLComment& );\t// not supported\r\n    XMLComment& operator=( const XMLComment& );\t// not supported\r\n};\r\n\r\n\r\n/** In correct XML the declaration is the first entry in the file.\r\n\t@verbatim\r\n\t\t<?xml version=\"1.0\" standalone=\"yes\"?>\r\n\t@endverbatim\r\n\r\n\tTinyXML-2 will happily read or write files without a declaration,\r\n\thowever.\r\n\r\n\tThe text of the declaration isn't interpreted. It is parsed\r\n\tand written as a string.\r\n*/\r\nclass TINYXML2_LIB XMLDeclaration : public XMLNode\r\n{\r\n    friend class XMLDocument;\r\npublic:\r\n    virtual XMLDeclaration*\tToDeclaration() override\t\t{\r\n        return this;\r\n    }\r\n    virtual const XMLDeclaration* ToDeclaration() const override {\r\n        return this;\r\n    }\r\n\r\n    virtual bool Accept( XMLVisitor* visitor ) const override;\r\n\r\n    virtual XMLNode* ShallowClone( XMLDocument* document ) const override;\r\n    virtual bool ShallowEqual( const XMLNode* compare ) const override;\r\n\r\nprotected:\r\n    explicit XMLDeclaration( XMLDocument* doc );\r\n    virtual ~XMLDeclaration();\r\n\r\n    char* ParseDeep( char* p, StrPair* parentEndTag, int* curLineNumPtr ) override;\r\n\r\nprivate:\r\n    XMLDeclaration( const XMLDeclaration& );\t// not supported\r\n    XMLDeclaration& operator=( const XMLDeclaration& );\t// not supported\r\n};\r\n\r\n\r\n/** Any tag that TinyXML-2 doesn't recognize is saved as an\r\n\tunknown. It is a tag of text, but should not be modified.\r\n\tIt will be written back to the XML, unchanged, when the file\r\n\tis saved.\r\n\r\n\tDTD tags get thrown into XMLUnknowns.\r\n*/\r\nclass TINYXML2_LIB XMLUnknown : public XMLNode\r\n{\r\n    friend class XMLDocument;\r\npublic:\r\n    virtual XMLUnknown*\tToUnknown() override\t\t{\r\n        return this;\r\n    }\r\n    virtual const XMLUnknown* ToUnknown() const override {\r\n        return this;\r\n    }\r\n\r\n    virtual bool Accept( XMLVisitor* visitor ) const override;\r\n\r\n    virtual XMLNode* ShallowClone( XMLDocument* document ) const override;\r\n    virtual bool ShallowEqual( const XMLNode* compare ) const override;\r\n\r\nprotected:\r\n    explicit XMLUnknown( XMLDocument* doc );\r\n    virtual ~XMLUnknown();\r\n\r\n    char* ParseDeep( char* p, StrPair* parentEndTag, int* curLineNumPtr ) override;\r\n\r\nprivate:\r\n    XMLUnknown( const XMLUnknown& );\t// not supported\r\n    XMLUnknown& operator=( const XMLUnknown& );\t// not supported\r\n};\r\n\r\n\r\n\r\n/** An attribute is a name-value pair. Elements have an arbitrary\r\n\tnumber of attributes, each with a unique name.\r\n\r\n\t@note The attributes are not XMLNodes. You may only query the\r\n\tNext() attribute in a list.\r\n*/\r\nclass TINYXML2_LIB XMLAttribute\r\n{\r\n    friend class XMLElement;\r\npublic:\r\n    /// The name of the attribute.\r\n    const char* Name() const;\r\n\r\n    /// The value of the attribute.\r\n    const char* Value() const;\r\n\r\n    /// Gets the line number the attribute is in, if the document was parsed from a file.\r\n    int GetLineNum() const { return _parseLineNum; }\r\n\r\n    /// The next attribute in the list.\r\n    const XMLAttribute* Next() const {\r\n        return _next;\r\n    }\r\n\r\n    /** IntValue interprets the attribute as an integer, and returns the value.\r\n        If the value isn't an integer, 0 will be returned. There is no error checking;\r\n    \tuse QueryIntValue() if you need error checking.\r\n    */\r\n\tint\tIntValue() const {\r\n\t\tint i = 0;\r\n\t\tQueryIntValue(&i);\r\n\t\treturn i;\r\n\t}\r\n\r\n\tint64_t Int64Value() const {\r\n\t\tint64_t i = 0;\r\n\t\tQueryInt64Value(&i);\r\n\t\treturn i;\r\n\t}\r\n\r\n    uint64_t Unsigned64Value() const {\r\n        uint64_t i = 0;\r\n        QueryUnsigned64Value(&i);\r\n        return i;\r\n    }\r\n\r\n    /// Query as an unsigned integer. See IntValue()\r\n    unsigned UnsignedValue() const\t\t\t{\r\n        unsigned i=0;\r\n        QueryUnsignedValue( &i );\r\n        return i;\r\n    }\r\n    /// Query as a boolean. See IntValue()\r\n    bool\t BoolValue() const\t\t\t\t{\r\n        bool b=false;\r\n        QueryBoolValue( &b );\r\n        return b;\r\n    }\r\n    /// Query as a double. See IntValue()\r\n    double \t DoubleValue() const\t\t\t{\r\n        double d=0;\r\n        QueryDoubleValue( &d );\r\n        return d;\r\n    }\r\n    /// Query as a float. See IntValue()\r\n    float\t FloatValue() const\t\t\t\t{\r\n        float f=0;\r\n        QueryFloatValue( &f );\r\n        return f;\r\n    }\r\n\r\n    /** QueryIntValue interprets the attribute as an integer, and returns the value\r\n    \tin the provided parameter. The function will return XML_SUCCESS on success,\r\n    \tand XML_WRONG_ATTRIBUTE_TYPE if the conversion is not successful.\r\n    */\r\n    XMLError QueryIntValue( int* value ) const;\r\n    /// See QueryIntValue\r\n    XMLError QueryUnsignedValue( unsigned int* value ) const;\r\n\t/// See QueryIntValue\r\n\tXMLError QueryInt64Value(int64_t* value) const;\r\n    /// See QueryIntValue\r\n    XMLError QueryUnsigned64Value(uint64_t* value) const;\r\n\t/// See QueryIntValue\r\n    XMLError QueryBoolValue( bool* value ) const;\r\n    /// See QueryIntValue\r\n    XMLError QueryDoubleValue( double* value ) const;\r\n    /// See QueryIntValue\r\n    XMLError QueryFloatValue( float* value ) const;\r\n\r\n    /// Set the attribute to a string value.\r\n    void SetAttribute( const char* value );\r\n    /// Set the attribute to value.\r\n    void SetAttribute( int value );\r\n    /// Set the attribute to value.\r\n    void SetAttribute( unsigned value );\r\n\t/// Set the attribute to value.\r\n\tvoid SetAttribute(int64_t value);\r\n    /// Set the attribute to value.\r\n    void SetAttribute(uint64_t value);\r\n    /// Set the attribute to value.\r\n    void SetAttribute( bool value );\r\n    /// Set the attribute to value.\r\n    void SetAttribute( double value );\r\n    /// Set the attribute to value.\r\n    void SetAttribute( float value );\r\n\r\nprivate:\r\n    enum { BUF_SIZE = 200 };\r\n\r\n    XMLAttribute() : _name(), _value(),_parseLineNum( 0 ), _next( 0 ), _memPool( 0 ) {}\r\n    virtual ~XMLAttribute()\t{}\r\n\r\n    XMLAttribute( const XMLAttribute& );\t// not supported\r\n    void operator=( const XMLAttribute& );\t// not supported\r\n    void SetName( const char* name );\r\n\r\n    char* ParseDeep( char* p, bool processEntities, int* curLineNumPtr );\r\n\r\n    mutable StrPair _name;\r\n    mutable StrPair _value;\r\n    int             _parseLineNum;\r\n    XMLAttribute*   _next;\r\n    MemPool*        _memPool;\r\n};\r\n\r\n\r\n/** The element is a container class. It has a value, the element name,\r\n\tand can contain other elements, text, comments, and unknowns.\r\n\tElements also contain an arbitrary number of attributes.\r\n*/\r\nclass TINYXML2_LIB XMLElement : public XMLNode\r\n{\r\n    friend class XMLDocument;\r\npublic:\r\n    /// Get the name of an element (which is the Value() of the node.)\r\n    const char* Name() const\t\t{\r\n        return Value();\r\n    }\r\n    /// Set the name of the element.\r\n    void SetName( const char* str, bool staticMem=false )\t{\r\n        SetValue( str, staticMem );\r\n    }\r\n\r\n    virtual XMLElement* ToElement() override\t{\r\n        return this;\r\n    }\r\n    virtual const XMLElement* ToElement() const override {\r\n        return this;\r\n    }\r\n    virtual bool Accept( XMLVisitor* visitor ) const override;\r\n\r\n    /** Given an attribute name, Attribute() returns the value\r\n    \tfor the attribute of that name, or null if none\r\n    \texists. For example:\r\n\r\n    \t@verbatim\r\n    \tconst char* value = ele->Attribute( \"foo\" );\r\n    \t@endverbatim\r\n\r\n    \tThe 'value' parameter is normally null. However, if specified,\r\n    \tthe attribute will only be returned if the 'name' and 'value'\r\n    \tmatch. This allow you to write code:\r\n\r\n    \t@verbatim\r\n    \tif ( ele->Attribute( \"foo\", \"bar\" ) ) callFooIsBar();\r\n    \t@endverbatim\r\n\r\n    \trather than:\r\n    \t@verbatim\r\n    \tif ( ele->Attribute( \"foo\" ) ) {\r\n    \t\tif ( strcmp( ele->Attribute( \"foo\" ), \"bar\" ) == 0 ) callFooIsBar();\r\n    \t}\r\n    \t@endverbatim\r\n    */\r\n    const char* Attribute( const char* name, const char* value=0 ) const;\r\n\r\n    /** Given an attribute name, IntAttribute() returns the value\r\n    \tof the attribute interpreted as an integer. The default\r\n        value will be returned if the attribute isn't present,\r\n        or if there is an error. (For a method with error\r\n    \tchecking, see QueryIntAttribute()).\r\n    */\r\n\tint IntAttribute(const char* name, int defaultValue = 0) const;\r\n    /// See IntAttribute()\r\n\tunsigned UnsignedAttribute(const char* name, unsigned defaultValue = 0) const;\r\n\t/// See IntAttribute()\r\n\tint64_t Int64Attribute(const char* name, int64_t defaultValue = 0) const;\r\n    /// See IntAttribute()\r\n    uint64_t Unsigned64Attribute(const char* name, uint64_t defaultValue = 0) const;\r\n\t/// See IntAttribute()\r\n\tbool BoolAttribute(const char* name, bool defaultValue = false) const;\r\n    /// See IntAttribute()\r\n\tdouble DoubleAttribute(const char* name, double defaultValue = 0) const;\r\n    /// See IntAttribute()\r\n\tfloat FloatAttribute(const char* name, float defaultValue = 0) const;\r\n\r\n    /** Given an attribute name, QueryIntAttribute() returns\r\n    \tXML_SUCCESS, XML_WRONG_ATTRIBUTE_TYPE if the conversion\r\n    \tcan't be performed, or XML_NO_ATTRIBUTE if the attribute\r\n    \tdoesn't exist. If successful, the result of the conversion\r\n    \twill be written to 'value'. If not successful, nothing will\r\n    \tbe written to 'value'. This allows you to provide default\r\n    \tvalue:\r\n\r\n    \t@verbatim\r\n    \tint value = 10;\r\n    \tQueryIntAttribute( \"foo\", &value );\t\t// if \"foo\" isn't found, value will still be 10\r\n    \t@endverbatim\r\n    */\r\n    XMLError QueryIntAttribute( const char* name, int* value ) const\t\t\t\t{\r\n        const XMLAttribute* a = FindAttribute( name );\r\n        if ( !a ) {\r\n            return XML_NO_ATTRIBUTE;\r\n        }\r\n        return a->QueryIntValue( value );\r\n    }\r\n\r\n\t/// See QueryIntAttribute()\r\n    XMLError QueryUnsignedAttribute( const char* name, unsigned int* value ) const\t{\r\n        const XMLAttribute* a = FindAttribute( name );\r\n        if ( !a ) {\r\n            return XML_NO_ATTRIBUTE;\r\n        }\r\n        return a->QueryUnsignedValue( value );\r\n    }\r\n\r\n\t/// See QueryIntAttribute()\r\n\tXMLError QueryInt64Attribute(const char* name, int64_t* value) const {\r\n\t\tconst XMLAttribute* a = FindAttribute(name);\r\n\t\tif (!a) {\r\n\t\t\treturn XML_NO_ATTRIBUTE;\r\n\t\t}\r\n\t\treturn a->QueryInt64Value(value);\r\n\t}\r\n\r\n    /// See QueryIntAttribute()\r\n    XMLError QueryUnsigned64Attribute(const char* name, uint64_t* value) const {\r\n        const XMLAttribute* a = FindAttribute(name);\r\n        if(!a) {\r\n            return XML_NO_ATTRIBUTE;\r\n        }\r\n        return a->QueryUnsigned64Value(value);\r\n    }\r\n\r\n\t/// See QueryIntAttribute()\r\n    XMLError QueryBoolAttribute( const char* name, bool* value ) const\t\t\t\t{\r\n        const XMLAttribute* a = FindAttribute( name );\r\n        if ( !a ) {\r\n            return XML_NO_ATTRIBUTE;\r\n        }\r\n        return a->QueryBoolValue( value );\r\n    }\r\n    /// See QueryIntAttribute()\r\n    XMLError QueryDoubleAttribute( const char* name, double* value ) const\t\t\t{\r\n        const XMLAttribute* a = FindAttribute( name );\r\n        if ( !a ) {\r\n            return XML_NO_ATTRIBUTE;\r\n        }\r\n        return a->QueryDoubleValue( value );\r\n    }\r\n    /// See QueryIntAttribute()\r\n    XMLError QueryFloatAttribute( const char* name, float* value ) const\t\t\t{\r\n        const XMLAttribute* a = FindAttribute( name );\r\n        if ( !a ) {\r\n            return XML_NO_ATTRIBUTE;\r\n        }\r\n        return a->QueryFloatValue( value );\r\n    }\r\n\r\n\t/// See QueryIntAttribute()\r\n\tXMLError QueryStringAttribute(const char* name, const char** value) const {\r\n\t\tconst XMLAttribute* a = FindAttribute(name);\r\n\t\tif (!a) {\r\n\t\t\treturn XML_NO_ATTRIBUTE;\r\n\t\t}\r\n\t\t*value = a->Value();\r\n\t\treturn XML_SUCCESS;\r\n\t}\r\n\r\n\r\n\r\n    /** Given an attribute name, QueryAttribute() returns\r\n    \tXML_SUCCESS, XML_WRONG_ATTRIBUTE_TYPE if the conversion\r\n    \tcan't be performed, or XML_NO_ATTRIBUTE if the attribute\r\n    \tdoesn't exist. It is overloaded for the primitive types,\r\n\t\tand is a generally more convenient replacement of\r\n\t\tQueryIntAttribute() and related functions.\r\n\r\n\t\tIf successful, the result of the conversion\r\n    \twill be written to 'value'. If not successful, nothing will\r\n    \tbe written to 'value'. This allows you to provide default\r\n    \tvalue:\r\n\r\n    \t@verbatim\r\n    \tint value = 10;\r\n    \tQueryAttribute( \"foo\", &value );\t\t// if \"foo\" isn't found, value will still be 10\r\n    \t@endverbatim\r\n    */\r\n\tXMLError QueryAttribute( const char* name, int* value ) const {\r\n\t\treturn QueryIntAttribute( name, value );\r\n\t}\r\n\r\n\tXMLError QueryAttribute( const char* name, unsigned int* value ) const {\r\n\t\treturn QueryUnsignedAttribute( name, value );\r\n\t}\r\n\r\n\tXMLError QueryAttribute(const char* name, int64_t* value) const {\r\n\t\treturn QueryInt64Attribute(name, value);\r\n\t}\r\n\r\n    XMLError QueryAttribute(const char* name, uint64_t* value) const {\r\n        return QueryUnsigned64Attribute(name, value);\r\n    }\r\n\r\n    XMLError QueryAttribute( const char* name, bool* value ) const {\r\n\t\treturn QueryBoolAttribute( name, value );\r\n\t}\r\n\r\n\tXMLError QueryAttribute( const char* name, double* value ) const {\r\n\t\treturn QueryDoubleAttribute( name, value );\r\n\t}\r\n\r\n\tXMLError QueryAttribute( const char* name, float* value ) const {\r\n\t\treturn QueryFloatAttribute( name, value );\r\n\t}\r\n\r\n\tXMLError QueryAttribute(const char* name, const char** value) const {\r\n\t\treturn QueryStringAttribute(name, value);\r\n\t}\r\n\r\n\t/// Sets the named attribute to value.\r\n    void SetAttribute( const char* name, const char* value )\t{\r\n        XMLAttribute* a = FindOrCreateAttribute( name );\r\n        a->SetAttribute( value );\r\n    }\r\n    /// Sets the named attribute to value.\r\n    void SetAttribute( const char* name, int value )\t\t\t{\r\n        XMLAttribute* a = FindOrCreateAttribute( name );\r\n        a->SetAttribute( value );\r\n    }\r\n    /// Sets the named attribute to value.\r\n    void SetAttribute( const char* name, unsigned value )\t\t{\r\n        XMLAttribute* a = FindOrCreateAttribute( name );\r\n        a->SetAttribute( value );\r\n    }\r\n\r\n\t/// Sets the named attribute to value.\r\n\tvoid SetAttribute(const char* name, int64_t value) {\r\n\t\tXMLAttribute* a = FindOrCreateAttribute(name);\r\n\t\ta->SetAttribute(value);\r\n\t}\r\n\r\n    /// Sets the named attribute to value.\r\n    void SetAttribute(const char* name, uint64_t value) {\r\n        XMLAttribute* a = FindOrCreateAttribute(name);\r\n        a->SetAttribute(value);\r\n    }\r\n\r\n    /// Sets the named attribute to value.\r\n    void SetAttribute( const char* name, bool value )\t\t\t{\r\n        XMLAttribute* a = FindOrCreateAttribute( name );\r\n        a->SetAttribute( value );\r\n    }\r\n    /// Sets the named attribute to value.\r\n    void SetAttribute( const char* name, double value )\t\t{\r\n        XMLAttribute* a = FindOrCreateAttribute( name );\r\n        a->SetAttribute( value );\r\n    }\r\n    /// Sets the named attribute to value.\r\n    void SetAttribute( const char* name, float value )\t\t{\r\n        XMLAttribute* a = FindOrCreateAttribute( name );\r\n        a->SetAttribute( value );\r\n    }\r\n\r\n    /**\r\n    \tDelete an attribute.\r\n    */\r\n    void DeleteAttribute( const char* name );\r\n\r\n    /// Return the first attribute in the list.\r\n    const XMLAttribute* FirstAttribute() const {\r\n        return _rootAttribute;\r\n    }\r\n    /// Query a specific attribute in the list.\r\n    const XMLAttribute* FindAttribute( const char* name ) const;\r\n\r\n    /** Convenience function for easy access to the text inside an element. Although easy\r\n    \tand concise, GetText() is limited compared to getting the XMLText child\r\n    \tand accessing it directly.\r\n\r\n    \tIf the first child of 'this' is a XMLText, the GetText()\r\n    \treturns the character string of the Text node, else null is returned.\r\n\r\n    \tThis is a convenient method for getting the text of simple contained text:\r\n    \t@verbatim\r\n    \t<foo>This is text</foo>\r\n    \t\tconst char* str = fooElement->GetText();\r\n    \t@endverbatim\r\n\r\n    \t'str' will be a pointer to \"This is text\".\r\n\r\n    \tNote that this function can be misleading. If the element foo was created from\r\n    \tthis XML:\r\n    \t@verbatim\r\n    \t\t<foo><b>This is text</b></foo>\r\n    \t@endverbatim\r\n\r\n    \tthen the value of str would be null. The first child node isn't a text node, it is\r\n    \tanother element. From this XML:\r\n    \t@verbatim\r\n    \t\t<foo>This is <b>text</b></foo>\r\n    \t@endverbatim\r\n    \tGetText() will return \"This is \".\r\n    */\r\n    const char* GetText() const;\r\n\r\n    /** Convenience function for easy access to the text inside an element. Although easy\r\n    \tand concise, SetText() is limited compared to creating an XMLText child\r\n    \tand mutating it directly.\r\n\r\n    \tIf the first child of 'this' is a XMLText, SetText() sets its value to\r\n\t\tthe given string, otherwise it will create a first child that is an XMLText.\r\n\r\n    \tThis is a convenient method for setting the text of simple contained text:\r\n    \t@verbatim\r\n    \t<foo>This is text</foo>\r\n    \t\tfooElement->SetText( \"Hullaballoo!\" );\r\n     \t<foo>Hullaballoo!</foo>\r\n\t\t@endverbatim\r\n\r\n    \tNote that this function can be misleading. If the element foo was created from\r\n    \tthis XML:\r\n    \t@verbatim\r\n    \t\t<foo><b>This is text</b></foo>\r\n    \t@endverbatim\r\n\r\n    \tthen it will not change \"This is text\", but rather prefix it with a text element:\r\n    \t@verbatim\r\n    \t\t<foo>Hullaballoo!<b>This is text</b></foo>\r\n    \t@endverbatim\r\n\r\n\t\tFor this XML:\r\n    \t@verbatim\r\n    \t\t<foo />\r\n    \t@endverbatim\r\n    \tSetText() will generate\r\n    \t@verbatim\r\n    \t\t<foo>Hullaballoo!</foo>\r\n    \t@endverbatim\r\n    */\r\n\tvoid SetText( const char* inText );\r\n    /// Convenience method for setting text inside an element. See SetText() for important limitations.\r\n    void SetText( int value );\r\n    /// Convenience method for setting text inside an element. See SetText() for important limitations.\r\n    void SetText( unsigned value );\r\n\t/// Convenience method for setting text inside an element. See SetText() for important limitations.\r\n\tvoid SetText(int64_t value);\r\n    /// Convenience method for setting text inside an element. See SetText() for important limitations.\r\n    void SetText(uint64_t value);\r\n\t/// Convenience method for setting text inside an element. See SetText() for important limitations.\r\n    void SetText( bool value );\r\n    /// Convenience method for setting text inside an element. See SetText() for important limitations.\r\n    void SetText( double value );\r\n    /// Convenience method for setting text inside an element. See SetText() for important limitations.\r\n    void SetText( float value );\r\n\r\n    /**\r\n    \tConvenience method to query the value of a child text node. This is probably best\r\n    \tshown by example. Given you have a document is this form:\r\n    \t@verbatim\r\n    \t\t<point>\r\n    \t\t\t<x>1</x>\r\n    \t\t\t<y>1.4</y>\r\n    \t\t</point>\r\n    \t@endverbatim\r\n\r\n    \tThe QueryIntText() and similar functions provide a safe and easier way to get to the\r\n    \t\"value\" of x and y.\r\n\r\n    \t@verbatim\r\n    \t\tint x = 0;\r\n    \t\tfloat y = 0;\t// types of x and y are contrived for example\r\n    \t\tconst XMLElement* xElement = pointElement->FirstChildElement( \"x\" );\r\n    \t\tconst XMLElement* yElement = pointElement->FirstChildElement( \"y\" );\r\n    \t\txElement->QueryIntText( &x );\r\n    \t\tyElement->QueryFloatText( &y );\r\n    \t@endverbatim\r\n\r\n    \t@returns XML_SUCCESS (0) on success, XML_CAN_NOT_CONVERT_TEXT if the text cannot be converted\r\n    \t\t\t to the requested type, and XML_NO_TEXT_NODE if there is no child text to query.\r\n\r\n    */\r\n    XMLError QueryIntText( int* ival ) const;\r\n    /// See QueryIntText()\r\n    XMLError QueryUnsignedText( unsigned* uval ) const;\r\n\t/// See QueryIntText()\r\n\tXMLError QueryInt64Text(int64_t* uval) const;\r\n\t/// See QueryIntText()\r\n\tXMLError QueryUnsigned64Text(uint64_t* uval) const;\r\n\t/// See QueryIntText()\r\n    XMLError QueryBoolText( bool* bval ) const;\r\n    /// See QueryIntText()\r\n    XMLError QueryDoubleText( double* dval ) const;\r\n    /// See QueryIntText()\r\n    XMLError QueryFloatText( float* fval ) const;\r\n\r\n\tint IntText(int defaultValue = 0) const;\r\n\r\n\t/// See QueryIntText()\r\n\tunsigned UnsignedText(unsigned defaultValue = 0) const;\r\n\t/// See QueryIntText()\r\n\tint64_t Int64Text(int64_t defaultValue = 0) const;\r\n    /// See QueryIntText()\r\n    uint64_t Unsigned64Text(uint64_t defaultValue = 0) const;\r\n\t/// See QueryIntText()\r\n\tbool BoolText(bool defaultValue = false) const;\r\n\t/// See QueryIntText()\r\n\tdouble DoubleText(double defaultValue = 0) const;\r\n\t/// See QueryIntText()\r\n    float FloatText(float defaultValue = 0) const;\r\n\r\n    /**\r\n        Convenience method to create a new XMLElement and add it as last (right)\r\n        child of this node. Returns the created and inserted element.\r\n    */\r\n    XMLElement* InsertNewChildElement(const char* name);\r\n    /// See InsertNewChildElement()\r\n    XMLComment* InsertNewComment(const char* comment);\r\n    /// See InsertNewChildElement()\r\n    XMLText* InsertNewText(const char* text);\r\n    /// See InsertNewChildElement()\r\n    XMLDeclaration* InsertNewDeclaration(const char* text);\r\n    /// See InsertNewChildElement()\r\n    XMLUnknown* InsertNewUnknown(const char* text);\r\n\r\n\r\n    // internal:\r\n    enum ElementClosingType {\r\n        OPEN,\t\t// <foo>\r\n        CLOSED,\t\t// <foo/>\r\n        CLOSING\t\t// </foo>\r\n    };\r\n    ElementClosingType ClosingType() const {\r\n        return _closingType;\r\n    }\r\n    virtual XMLNode* ShallowClone( XMLDocument* document ) const override;\r\n    virtual bool ShallowEqual( const XMLNode* compare ) const override;\r\n\r\nprotected:\r\n    char* ParseDeep( char* p, StrPair* parentEndTag, int* curLineNumPtr ) override;\r\n\r\nprivate:\r\n    XMLElement( XMLDocument* doc );\r\n    virtual ~XMLElement();\r\n    XMLElement( const XMLElement& );\t// not supported\r\n    void operator=( const XMLElement& );\t// not supported\r\n\r\n    XMLAttribute* FindOrCreateAttribute( const char* name );\r\n    char* ParseAttributes( char* p, int* curLineNumPtr );\r\n    static void DeleteAttribute( XMLAttribute* attribute );\r\n    XMLAttribute* CreateAttribute();\r\n\r\n    enum { BUF_SIZE = 200 };\r\n    ElementClosingType _closingType;\r\n    // The attribute list is ordered; there is no 'lastAttribute'\r\n    // because the list needs to be scanned for dupes before adding\r\n    // a new attribute.\r\n    XMLAttribute* _rootAttribute;\r\n};\r\n\r\n\r\nenum Whitespace {\r\n    PRESERVE_WHITESPACE,\r\n    COLLAPSE_WHITESPACE,\r\n    PEDANTIC_WHITESPACE\r\n};\r\n\r\n\r\n/** A Document binds together all the functionality.\r\n\tIt can be saved, loaded, and printed to the screen.\r\n\tAll Nodes are connected and allocated to a Document.\r\n\tIf the Document is deleted, all its Nodes are also deleted.\r\n*/\r\nclass TINYXML2_LIB XMLDocument : public XMLNode\r\n{\r\n    friend class XMLElement;\r\n    // Gives access to SetError and Push/PopDepth, but over-access for everything else.\r\n    // Wishing C++ had \"internal\" scope.\r\n    friend class XMLNode;\r\n    friend class XMLText;\r\n    friend class XMLComment;\r\n    friend class XMLDeclaration;\r\n    friend class XMLUnknown;\r\npublic:\r\n    /// constructor\r\n    XMLDocument( bool processEntities = true, Whitespace whitespaceMode = PRESERVE_WHITESPACE );\r\n    ~XMLDocument();\r\n\r\n    virtual XMLDocument* ToDocument() override\t\t{\r\n        TIXMLASSERT( this == _document );\r\n        return this;\r\n    }\r\n    virtual const XMLDocument* ToDocument() const override {\r\n        TIXMLASSERT( this == _document );\r\n        return this;\r\n    }\r\n\r\n    /**\r\n    \tParse an XML file from a character string.\r\n    \tReturns XML_SUCCESS (0) on success, or\r\n    \tan errorID.\r\n\r\n    \tYou may optionally pass in the 'nBytes', which is\r\n    \tthe number of bytes which will be parsed. If not\r\n    \tspecified, TinyXML-2 will assume 'xml' points to a\r\n    \tnull terminated string.\r\n    */\r\n    XMLError Parse( const char* xml, size_t nBytes=static_cast<size_t>(-1) );\r\n\r\n    /**\r\n    \tLoad an XML file from disk.\r\n    \tReturns XML_SUCCESS (0) on success, or\r\n    \tan errorID.\r\n    */\r\n    XMLError LoadFile( const char* filename );\r\n\r\n    /**\r\n    \tLoad an XML file from disk. You are responsible\r\n    \tfor providing and closing the FILE*.\r\n\r\n        NOTE: The file should be opened as binary (\"rb\")\r\n        not text in order for TinyXML-2 to correctly\r\n        do newline normalization.\r\n\r\n    \tReturns XML_SUCCESS (0) on success, or\r\n    \tan errorID.\r\n    */\r\n    XMLError LoadFile( FILE* );\r\n\r\n    /**\r\n    \tSave the XML file to disk.\r\n    \tReturns XML_SUCCESS (0) on success, or\r\n    \tan errorID.\r\n    */\r\n    XMLError SaveFile( const char* filename, bool compact = false );\r\n\r\n    /**\r\n    \tSave the XML file to disk. You are responsible\r\n    \tfor providing and closing the FILE*.\r\n\r\n    \tReturns XML_SUCCESS (0) on success, or\r\n    \tan errorID.\r\n    */\r\n    XMLError SaveFile( FILE* fp, bool compact = false );\r\n\r\n    bool ProcessEntities() const\t\t{\r\n        return _processEntities;\r\n    }\r\n    Whitespace WhitespaceMode() const\t{\r\n        return _whitespaceMode;\r\n    }\r\n\r\n    /**\r\n    \tReturns true if this document has a leading Byte Order Mark of UTF8.\r\n    */\r\n    bool HasBOM() const {\r\n        return _writeBOM;\r\n    }\r\n    /** Sets whether to write the BOM when writing the file.\r\n    */\r\n    void SetBOM( bool useBOM ) {\r\n        _writeBOM = useBOM;\r\n    }\r\n\r\n    /** Return the root element of DOM. Equivalent to FirstChildElement().\r\n        To get the first node, use FirstChild().\r\n    */\r\n    XMLElement* RootElement()\t\t\t\t{\r\n        return FirstChildElement();\r\n    }\r\n    const XMLElement* RootElement() const\t{\r\n        return FirstChildElement();\r\n    }\r\n\r\n    /** Print the Document. If the Printer is not provided, it will\r\n        print to stdout. If you provide Printer, this can print to a file:\r\n    \t@verbatim\r\n    \tXMLPrinter printer( fp );\r\n    \tdoc.Print( &printer );\r\n    \t@endverbatim\r\n\r\n    \tOr you can use a printer to print to memory:\r\n    \t@verbatim\r\n    \tXMLPrinter printer;\r\n    \tdoc.Print( &printer );\r\n    \t// printer.CStr() has a const char* to the XML\r\n    \t@endverbatim\r\n    */\r\n    void Print( XMLPrinter* streamer=0 ) const;\r\n    virtual bool Accept( XMLVisitor* visitor ) const override;\r\n\r\n    /**\r\n    \tCreate a new Element associated with\r\n    \tthis Document. The memory for the Element\r\n    \tis managed by the Document.\r\n    */\r\n    XMLElement* NewElement( const char* name );\r\n    /**\r\n    \tCreate a new Comment associated with\r\n    \tthis Document. The memory for the Comment\r\n    \tis managed by the Document.\r\n    */\r\n    XMLComment* NewComment( const char* comment );\r\n    /**\r\n    \tCreate a new Text associated with\r\n    \tthis Document. The memory for the Text\r\n    \tis managed by the Document.\r\n    */\r\n    XMLText* NewText( const char* text );\r\n    /**\r\n    \tCreate a new Declaration associated with\r\n    \tthis Document. The memory for the object\r\n    \tis managed by the Document.\r\n\r\n    \tIf the 'text' param is null, the standard\r\n    \tdeclaration is used.:\r\n    \t@verbatim\r\n    \t\t<?xml version=\"1.0\" encoding=\"UTF-8\"?>\r\n    \t@endverbatim\r\n    */\r\n    XMLDeclaration* NewDeclaration( const char* text=0 );\r\n    /**\r\n    \tCreate a new Unknown associated with\r\n    \tthis Document. The memory for the object\r\n    \tis managed by the Document.\r\n    */\r\n    XMLUnknown* NewUnknown( const char* text );\r\n\r\n    /**\r\n    \tDelete a node associated with this document.\r\n    \tIt will be unlinked from the DOM.\r\n    */\r\n    void DeleteNode( XMLNode* node );\r\n\r\n    /// Clears the error flags.\r\n    void ClearError();\r\n\r\n    /// Return true if there was an error parsing the document.\r\n    bool Error() const {\r\n        return _errorID != XML_SUCCESS;\r\n    }\r\n    /// Return the errorID.\r\n    XMLError  ErrorID() const {\r\n        return _errorID;\r\n    }\r\n\tconst char* ErrorName() const;\r\n    static const char* ErrorIDToName(XMLError errorID);\r\n\r\n    /** Returns a \"long form\" error description. A hopefully helpful\r\n        diagnostic with location, line number, and/or additional info.\r\n    */\r\n\tconst char* ErrorStr() const;\r\n\r\n    /// A (trivial) utility function that prints the ErrorStr() to stdout.\r\n    void PrintError() const;\r\n\r\n    /// Return the line where the error occurred, or zero if unknown.\r\n    int ErrorLineNum() const\r\n    {\r\n        return _errorLineNum;\r\n    }\r\n\r\n    /// Clear the document, resetting it to the initial state.\r\n    void Clear();\r\n\r\n\t/**\r\n\t\tCopies this document to a target document.\r\n\t\tThe target will be completely cleared before the copy.\r\n\t\tIf you want to copy a sub-tree, see XMLNode::DeepClone().\r\n\r\n\t\tNOTE: that the 'target' must be non-null.\r\n\t*/\r\n\tvoid DeepCopy(XMLDocument* target) const;\r\n\r\n\t// internal\r\n    char* Identify( char* p, XMLNode** node, bool first );\r\n\r\n\t// internal\r\n\tvoid MarkInUse(const XMLNode* const);\r\n\r\n    virtual XMLNode* ShallowClone( XMLDocument* /*document*/ ) const override{\r\n        return 0;\r\n    }\r\n    virtual bool ShallowEqual( const XMLNode* /*compare*/ ) const override{\r\n        return false;\r\n    }\r\n\r\nprivate:\r\n    XMLDocument( const XMLDocument& );\t// not supported\r\n    void operator=( const XMLDocument& );\t// not supported\r\n\r\n    bool\t\t\t_writeBOM;\r\n    bool\t\t\t_processEntities;\r\n    XMLError\t\t_errorID;\r\n    Whitespace\t\t_whitespaceMode;\r\n    mutable StrPair\t_errorStr;\r\n    int             _errorLineNum;\r\n    char*\t\t\t_charBuffer;\r\n    int\t\t\t\t_parseCurLineNum;\r\n\tint\t\t\t\t_parsingDepth;\r\n\t// Memory tracking does add some overhead.\r\n\t// However, the code assumes that you don't\r\n\t// have a bunch of unlinked nodes around.\r\n\t// Therefore it takes less memory to track\r\n\t// in the document vs. a linked list in the XMLNode,\r\n\t// and the performance is the same.\r\n\tDynArray<XMLNode*, 10> _unlinked;\r\n\r\n    MemPoolT< sizeof(XMLElement) >\t _elementPool;\r\n    MemPoolT< sizeof(XMLAttribute) > _attributePool;\r\n    MemPoolT< sizeof(XMLText) >\t\t _textPool;\r\n    MemPoolT< sizeof(XMLComment) >\t _commentPool;\r\n\r\n\tstatic const char* _errorNames[XML_ERROR_COUNT];\r\n\r\n    void Parse();\r\n\r\n    void SetError( XMLError error, int lineNum, const char* format, ... );\r\n\r\n\t// Something of an obvious security hole, once it was discovered.\r\n\t// Either an ill-formed XML or an excessively deep one can overflow\r\n\t// the stack. Track stack depth, and error out if needed.\r\n\tclass DepthTracker {\r\n\tpublic:\r\n\t\texplicit DepthTracker(XMLDocument * document) {\r\n\t\t\tthis->_document = document;\r\n\t\t\tdocument->PushDepth();\r\n\t\t}\r\n\t\t~DepthTracker() {\r\n\t\t\t_document->PopDepth();\r\n\t\t}\r\n\tprivate:\r\n\t\tXMLDocument * _document;\r\n\t};\r\n\tvoid PushDepth();\r\n\tvoid PopDepth();\r\n\r\n    template<class NodeType, int PoolElementSize>\r\n    NodeType* CreateUnlinkedNode( MemPoolT<PoolElementSize>& pool );\r\n};\r\n\r\ntemplate<class NodeType, int PoolElementSize>\r\ninline NodeType* XMLDocument::CreateUnlinkedNode( MemPoolT<PoolElementSize>& pool )\r\n{\r\n    TIXMLASSERT( sizeof( NodeType ) == PoolElementSize );\r\n    TIXMLASSERT( sizeof( NodeType ) == pool.ItemSize() );\r\n    NodeType* returnNode = new (pool.Alloc()) NodeType( this );\r\n    TIXMLASSERT( returnNode );\r\n    returnNode->_memPool = &pool;\r\n\r\n\t_unlinked.Push(returnNode);\r\n    return returnNode;\r\n}\r\n\r\n/**\r\n\tA XMLHandle is a class that wraps a node pointer with null checks; this is\r\n\tan incredibly useful thing. Note that XMLHandle is not part of the TinyXML-2\r\n\tDOM structure. It is a separate utility class.\r\n\r\n\tTake an example:\r\n\t@verbatim\r\n\t<Document>\r\n\t\t<Element attributeA = \"valueA\">\r\n\t\t\t<Child attributeB = \"value1\" />\r\n\t\t\t<Child attributeB = \"value2\" />\r\n\t\t</Element>\r\n\t</Document>\r\n\t@endverbatim\r\n\r\n\tAssuming you want the value of \"attributeB\" in the 2nd \"Child\" element, it's very\r\n\teasy to write a *lot* of code that looks like:\r\n\r\n\t@verbatim\r\n\tXMLElement* root = document.FirstChildElement( \"Document\" );\r\n\tif ( root )\r\n\t{\r\n\t\tXMLElement* element = root->FirstChildElement( \"Element\" );\r\n\t\tif ( element )\r\n\t\t{\r\n\t\t\tXMLElement* child = element->FirstChildElement( \"Child\" );\r\n\t\t\tif ( child )\r\n\t\t\t{\r\n\t\t\t\tXMLElement* child2 = child->NextSiblingElement( \"Child\" );\r\n\t\t\t\tif ( child2 )\r\n\t\t\t\t{\r\n\t\t\t\t\t// Finally do something useful.\r\n\t@endverbatim\r\n\r\n\tAnd that doesn't even cover \"else\" cases. XMLHandle addresses the verbosity\r\n\tof such code. A XMLHandle checks for null pointers so it is perfectly safe\r\n\tand correct to use:\r\n\r\n\t@verbatim\r\n\tXMLHandle docHandle( &document );\r\n\tXMLElement* child2 = docHandle.FirstChildElement( \"Document\" ).FirstChildElement( \"Element\" ).FirstChildElement().NextSiblingElement();\r\n\tif ( child2 )\r\n\t{\r\n\t\t// do something useful\r\n\t@endverbatim\r\n\r\n\tWhich is MUCH more concise and useful.\r\n\r\n\tIt is also safe to copy handles - internally they are nothing more than node pointers.\r\n\t@verbatim\r\n\tXMLHandle handleCopy = handle;\r\n\t@endverbatim\r\n\r\n\tSee also XMLConstHandle, which is the same as XMLHandle, but operates on const objects.\r\n*/\r\nclass TINYXML2_LIB XMLHandle\r\n{\r\npublic:\r\n    /// Create a handle from any node (at any depth of the tree.) This can be a null pointer.\r\n    explicit XMLHandle( XMLNode* node ) : _node( node ) {\r\n    }\r\n    /// Create a handle from a node.\r\n    explicit XMLHandle( XMLNode& node ) : _node( &node ) {\r\n    }\r\n    /// Copy constructor\r\n    XMLHandle( const XMLHandle& ref ) : _node( ref._node ) {\r\n    }\r\n    /// Assignment\r\n    XMLHandle& operator=( const XMLHandle& ref )\t\t\t\t\t\t\t{\r\n        _node = ref._node;\r\n        return *this;\r\n    }\r\n\r\n    /// Get the first child of this handle.\r\n    XMLHandle FirstChild() \t\t\t\t\t\t\t\t\t\t\t\t\t{\r\n        return XMLHandle( _node ? _node->FirstChild() : 0 );\r\n    }\r\n    /// Get the first child element of this handle.\r\n    XMLHandle FirstChildElement( const char* name = 0 )\t\t\t\t\t\t{\r\n        return XMLHandle( _node ? _node->FirstChildElement( name ) : 0 );\r\n    }\r\n    /// Get the last child of this handle.\r\n    XMLHandle LastChild()\t\t\t\t\t\t\t\t\t\t\t\t\t{\r\n        return XMLHandle( _node ? _node->LastChild() : 0 );\r\n    }\r\n    /// Get the last child element of this handle.\r\n    XMLHandle LastChildElement( const char* name = 0 )\t\t\t\t\t\t{\r\n        return XMLHandle( _node ? _node->LastChildElement( name ) : 0 );\r\n    }\r\n    /// Get the previous sibling of this handle.\r\n    XMLHandle PreviousSibling()\t\t\t\t\t\t\t\t\t\t\t\t{\r\n        return XMLHandle( _node ? _node->PreviousSibling() : 0 );\r\n    }\r\n    /// Get the previous sibling element of this handle.\r\n    XMLHandle PreviousSiblingElement( const char* name = 0 )\t\t\t\t{\r\n        return XMLHandle( _node ? _node->PreviousSiblingElement( name ) : 0 );\r\n    }\r\n    /// Get the next sibling of this handle.\r\n    XMLHandle NextSibling()\t\t\t\t\t\t\t\t\t\t\t\t\t{\r\n        return XMLHandle( _node ? _node->NextSibling() : 0 );\r\n    }\r\n    /// Get the next sibling element of this handle.\r\n    XMLHandle NextSiblingElement( const char* name = 0 )\t\t\t\t\t{\r\n        return XMLHandle( _node ? _node->NextSiblingElement( name ) : 0 );\r\n    }\r\n\r\n    /// Safe cast to XMLNode. This can return null.\r\n    XMLNode* ToNode()\t\t\t\t\t\t\t{\r\n        return _node;\r\n    }\r\n    /// Safe cast to XMLElement. This can return null.\r\n    XMLElement* ToElement() \t\t\t\t\t{\r\n        return ( _node ? _node->ToElement() : 0 );\r\n    }\r\n    /// Safe cast to XMLText. This can return null.\r\n    XMLText* ToText() \t\t\t\t\t\t\t{\r\n        return ( _node ? _node->ToText() : 0 );\r\n    }\r\n    /// Safe cast to XMLUnknown. This can return null.\r\n    XMLUnknown* ToUnknown() \t\t\t\t\t{\r\n        return ( _node ? _node->ToUnknown() : 0 );\r\n    }\r\n    /// Safe cast to XMLDeclaration. This can return null.\r\n    XMLDeclaration* ToDeclaration() \t\t\t{\r\n        return ( _node ? _node->ToDeclaration() : 0 );\r\n    }\r\n\r\nprivate:\r\n    XMLNode* _node;\r\n};\r\n\r\n\r\n/**\r\n\tA variant of the XMLHandle class for working with const XMLNodes and Documents. It is the\r\n\tsame in all regards, except for the 'const' qualifiers. See XMLHandle for API.\r\n*/\r\nclass TINYXML2_LIB XMLConstHandle\r\n{\r\npublic:\r\n    explicit XMLConstHandle( const XMLNode* node ) : _node( node ) {\r\n    }\r\n    explicit XMLConstHandle( const XMLNode& node ) : _node( &node ) {\r\n    }\r\n    XMLConstHandle( const XMLConstHandle& ref ) : _node( ref._node ) {\r\n    }\r\n\r\n    XMLConstHandle& operator=( const XMLConstHandle& ref )\t\t\t\t\t\t\t{\r\n        _node = ref._node;\r\n        return *this;\r\n    }\r\n\r\n    const XMLConstHandle FirstChild() const\t\t\t\t\t\t\t\t\t\t\t{\r\n        return XMLConstHandle( _node ? _node->FirstChild() : 0 );\r\n    }\r\n    const XMLConstHandle FirstChildElement( const char* name = 0 ) const\t\t\t\t{\r\n        return XMLConstHandle( _node ? _node->FirstChildElement( name ) : 0 );\r\n    }\r\n    const XMLConstHandle LastChild()\tconst\t\t\t\t\t\t\t\t\t\t{\r\n        return XMLConstHandle( _node ? _node->LastChild() : 0 );\r\n    }\r\n    const XMLConstHandle LastChildElement( const char* name = 0 ) const\t\t\t\t{\r\n        return XMLConstHandle( _node ? _node->LastChildElement( name ) : 0 );\r\n    }\r\n    const XMLConstHandle PreviousSibling() const\t\t\t\t\t\t\t\t\t{\r\n        return XMLConstHandle( _node ? _node->PreviousSibling() : 0 );\r\n    }\r\n    const XMLConstHandle PreviousSiblingElement( const char* name = 0 ) const\t\t{\r\n        return XMLConstHandle( _node ? _node->PreviousSiblingElement( name ) : 0 );\r\n    }\r\n    const XMLConstHandle NextSibling() const\t\t\t\t\t\t\t\t\t\t{\r\n        return XMLConstHandle( _node ? _node->NextSibling() : 0 );\r\n    }\r\n    const XMLConstHandle NextSiblingElement( const char* name = 0 ) const\t\t\t{\r\n        return XMLConstHandle( _node ? _node->NextSiblingElement( name ) : 0 );\r\n    }\r\n\r\n\r\n    const XMLNode* ToNode() const\t\t\t\t{\r\n        return _node;\r\n    }\r\n    const XMLElement* ToElement() const\t\t\t{\r\n        return ( _node ? _node->ToElement() : 0 );\r\n    }\r\n    const XMLText* ToText() const\t\t\t\t{\r\n        return ( _node ? _node->ToText() : 0 );\r\n    }\r\n    const XMLUnknown* ToUnknown() const\t\t\t{\r\n        return ( _node ? _node->ToUnknown() : 0 );\r\n    }\r\n    const XMLDeclaration* ToDeclaration() const\t{\r\n        return ( _node ? _node->ToDeclaration() : 0 );\r\n    }\r\n\r\nprivate:\r\n    const XMLNode* _node;\r\n};\r\n\r\n\r\n/**\r\n\tPrinting functionality. The XMLPrinter gives you more\r\n\toptions than the XMLDocument::Print() method.\r\n\r\n\tIt can:\r\n\t-# Print to memory.\r\n\t-# Print to a file you provide.\r\n\t-# Print XML without a XMLDocument.\r\n\r\n\tPrint to Memory\r\n\r\n\t@verbatim\r\n\tXMLPrinter printer;\r\n\tdoc.Print( &printer );\r\n\tSomeFunction( printer.CStr() );\r\n\t@endverbatim\r\n\r\n\tPrint to a File\r\n\r\n\tYou provide the file pointer.\r\n\t@verbatim\r\n\tXMLPrinter printer( fp );\r\n\tdoc.Print( &printer );\r\n\t@endverbatim\r\n\r\n\tPrint without a XMLDocument\r\n\r\n\tWhen loading, an XML parser is very useful. However, sometimes\r\n\twhen saving, it just gets in the way. The code is often set up\r\n\tfor streaming, and constructing the DOM is just overhead.\r\n\r\n\tThe Printer supports the streaming case. The following code\r\n\tprints out a trivially simple XML file without ever creating\r\n\tan XML document.\r\n\r\n\t@verbatim\r\n\tXMLPrinter printer( fp );\r\n\tprinter.OpenElement( \"foo\" );\r\n\tprinter.PushAttribute( \"foo\", \"bar\" );\r\n\tprinter.CloseElement();\r\n\t@endverbatim\r\n*/\r\nclass TINYXML2_LIB XMLPrinter : public XMLVisitor\r\n{\r\npublic:\r\n    /** Construct the printer. If the FILE* is specified,\r\n    \tthis will print to the FILE. Else it will print\r\n    \tto memory, and the result is available in CStr().\r\n    \tIf 'compact' is set to true, then output is created\r\n    \twith only required whitespace and newlines.\r\n    */\r\n    XMLPrinter( FILE* file=0, bool compact = false, int depth = 0 );\r\n    virtual ~XMLPrinter()\t{}\r\n\r\n    /** If streaming, write the BOM and declaration. */\r\n    void PushHeader( bool writeBOM, bool writeDeclaration );\r\n    /** If streaming, start writing an element.\r\n        The element must be closed with CloseElement()\r\n    */\r\n    void OpenElement( const char* name, bool compactMode=false );\r\n    /// If streaming, add an attribute to an open element.\r\n    void PushAttribute( const char* name, const char* value );\r\n    void PushAttribute( const char* name, int value );\r\n    void PushAttribute( const char* name, unsigned value );\r\n\tvoid PushAttribute( const char* name, int64_t value );\r\n\tvoid PushAttribute( const char* name, uint64_t value );\r\n\tvoid PushAttribute( const char* name, bool value );\r\n    void PushAttribute( const char* name, double value );\r\n    /// If streaming, close the Element.\r\n    virtual void CloseElement( bool compactMode=false );\r\n\r\n    /// Add a text node.\r\n    void PushText( const char* text, bool cdata=false );\r\n    /// Add a text node from an integer.\r\n    void PushText( int value );\r\n    /// Add a text node from an unsigned.\r\n    void PushText( unsigned value );\r\n\t/// Add a text node from a signed 64bit integer.\r\n\tvoid PushText( int64_t value );\r\n\t/// Add a text node from an unsigned 64bit integer.\r\n\tvoid PushText( uint64_t value );\r\n\t/// Add a text node from a bool.\r\n    void PushText( bool value );\r\n    /// Add a text node from a float.\r\n    void PushText( float value );\r\n    /// Add a text node from a double.\r\n    void PushText( double value );\r\n\r\n    /// Add a comment\r\n    void PushComment( const char* comment );\r\n\r\n    void PushDeclaration( const char* value );\r\n    void PushUnknown( const char* value );\r\n\r\n    virtual bool VisitEnter( const XMLDocument& /*doc*/ ) override;\r\n    virtual bool VisitExit( const XMLDocument& /*doc*/ ) override\t{\r\n        return true;\r\n    }\r\n\r\n    virtual bool VisitEnter( const XMLElement& element, const XMLAttribute* attribute ) override;\r\n    virtual bool VisitExit( const XMLElement& element ) override;\r\n\r\n    virtual bool Visit( const XMLText& text ) override;\r\n    virtual bool Visit( const XMLComment& comment ) override;\r\n    virtual bool Visit( const XMLDeclaration& declaration ) override;\r\n    virtual bool Visit( const XMLUnknown& unknown ) override;\r\n\r\n    /**\r\n    \tIf in print to memory mode, return a pointer to\r\n    \tthe XML file in memory.\r\n    */\r\n    const char* CStr() const {\r\n        return _buffer.Mem();\r\n    }\r\n    /**\r\n    \tIf in print to memory mode, return the size\r\n    \tof the XML file in memory. (Note the size returned\r\n    \tincludes the terminating null.)\r\n    */\r\n    int CStrSize() const {\r\n        return _buffer.Size();\r\n    }\r\n    /**\r\n    \tIf in print to memory mode, reset the buffer to the\r\n    \tbeginning.\r\n    */\r\n    void ClearBuffer( bool resetToFirstElement = true ) {\r\n        _buffer.Clear();\r\n        _buffer.Push(0);\r\n\t\t_firstElement = resetToFirstElement;\r\n    }\r\n\r\nprotected:\r\n\tvirtual bool CompactMode( const XMLElement& )\t{ return _compactMode; }\r\n\r\n\t/** Prints out the space before an element. You may override to change\r\n\t    the space and tabs used. A PrintSpace() override should call Print().\r\n\t*/\r\n    virtual void PrintSpace( int depth );\r\n    virtual void Print( const char* format, ... );\r\n    virtual void Write( const char* data, size_t size );\r\n    virtual void Putc( char ch );\r\n\r\n    inline void Write(const char* data) { Write(data, strlen(data)); }\r\n\r\n    void SealElementIfJustOpened();\r\n    bool _elementJustOpened;\r\n    DynArray< const char*, 10 > _stack;\r\n\r\nprivate:\r\n    /**\r\n       Prepares to write a new node. This includes sealing an element that was\r\n       just opened, and writing any whitespace necessary if not in compact mode.\r\n     */\r\n    void PrepareForNewNode( bool compactMode );\r\n    void PrintString( const char*, bool restrictedEntitySet );\t// prints out, after detecting entities.\r\n\r\n    bool _firstElement;\r\n    FILE* _fp;\r\n    int _depth;\r\n    int _textDepth;\r\n    bool _processEntities;\r\n\tbool _compactMode;\r\n\r\n    enum {\r\n        ENTITY_RANGE = 64,\r\n        BUF_SIZE = 200\r\n    };\r\n    bool _entityFlag[ENTITY_RANGE];\r\n    bool _restrictedEntityFlag[ENTITY_RANGE];\r\n\r\n    DynArray< char, 20 > _buffer;\r\n\r\n    // Prohibit cloning, intentionally not implemented\r\n    XMLPrinter( const XMLPrinter& );\r\n    XMLPrinter& operator=( const XMLPrinter& );\r\n};\r\n\r\n\r\n}\t// tinyxml2\r\n\r\n#if defined(_MSC_VER)\r\n#   pragma warning(pop)\r\n#endif\r\n\r\n#endif // TINYXML2_INCLUDED\r\n"
  },
  {
    "path": "libs/whereami/LICENSE.WTFPLv2",
    "content": "--------------------------------------------------------------------------------\n        DO WHAT THE FUCK YOU WANT TO PUBLIC LICENSE\n                    Version 2, December 2004\n\n Copyright (C) 2004 Sam Hocevar <sam@hocevar.net>\n\n Everyone is permitted to copy and distribute verbatim or modified\n copies of this license document, and changing it is allowed as long\n as the name is changed.\n\n            DO WHAT THE FUCK YOU WANT TO PUBLIC LICENSE\n   TERMS AND CONDITIONS FOR COPYING, DISTRIBUTION AND MODIFICATION\n\n  0. You just DO WHAT THE FUCK YOU WANT TO.\n  1. Bla bla bla\n  2. Montesqieu et camembert, vive la France, zut alors!\n\n--------------------------------------------------------------------------------\n\nWTFPLv2 is very permissive, see http://www.wtfpl.net/faq/\n\nHowever, if this WTFPLV2 is REALLY a blocker and is the reason you can't use\nthis project, contact me and I'll dual license it.\n\n--------------------------------------------------------------------------------\n"
  },
  {
    "path": "libs/whereami/whereami.c",
    "content": "// (‑●‑●)> dual licensed under the WTFPL v2 and MIT licenses\n//   without any warranty.\n//   by Gregory Pakosz (@gpakosz)\n// https://github.com/gpakosz/whereami\n\n// in case you want to #include \"whereami.c\" in a larger compilation unit\n#if !defined(WHEREAMI_H)\n#include <whereami.h>\n#endif\n\n#ifdef __cplusplus\nextern \"C\" {\n#endif\n\n#if defined(__linux__) || defined(__CYGWIN__)\n#undef _DEFAULT_SOURCE\n#define _DEFAULT_SOURCE\n#elif defined(__APPLE__)\n#undef _DARWIN_C_SOURCE\n#define _DARWIN_C_SOURCE\n#define _DARWIN_BETTER_REALPATH\n#endif\n\n#if !defined(WAI_MALLOC) || !defined(WAI_FREE) || !defined(WAI_REALLOC)\n#include <stdlib.h>\n#endif\n\n#if !defined(WAI_MALLOC)\n#define WAI_MALLOC(size) malloc(size)\n#endif\n\n#if !defined(WAI_FREE)\n#define WAI_FREE(p) free(p)\n#endif\n\n#if !defined(WAI_REALLOC)\n#define WAI_REALLOC(p, size) realloc(p, size)\n#endif\n\n#ifndef WAI_NOINLINE\n#if defined(_MSC_VER)\n#define WAI_NOINLINE __declspec(noinline)\n#elif defined(__GNUC__)\n#define WAI_NOINLINE __attribute__((noinline))\n#else\n#error unsupported compiler\n#endif\n#endif\n\n#if defined(_MSC_VER)\n#define WAI_RETURN_ADDRESS() _ReturnAddress()\n#elif defined(__GNUC__)\n#define WAI_RETURN_ADDRESS() __builtin_extract_return_addr(__builtin_return_address(0))\n#else\n#error unsupported compiler\n#endif\n\n#if defined(_WIN32)\n\n#ifndef WIN32_LEAN_AND_MEAN\n#define WIN32_LEAN_AND_MEAN\n#endif\n#if defined(_MSC_VER)\n#pragma warning(push, 3)\n#endif\n#include <windows.h>\n#include <intrin.h>\n#if defined(_MSC_VER)\n#pragma warning(pop)\n#endif\n#if (_MSC_VER >= 1900)\n#include <stdbool.h>\n#else\n#define bool int\n#define false 0\n#define true 1\n#endif\n\nstatic int WAI_PREFIX(getModulePath_)(HMODULE module, char* out, int capacity, int* dirname_length)\n{\n  wchar_t buffer1[MAX_PATH];\n  wchar_t buffer2[MAX_PATH];\n  wchar_t* path = NULL;\n  int length = -1;\n  bool ok;\n\n  for (ok = false; !ok; ok = true)\n  {\n    DWORD size;\n    int length_, length__;\n\n    size = GetModuleFileNameW(module, buffer1, sizeof(buffer1) / sizeof(buffer1[0]));\n\n    if (size == 0)\n      break;\n    else if (size == (DWORD)(sizeof(buffer1) / sizeof(buffer1[0])))\n    {\n      DWORD size_ = size;\n      do\n      {\n        wchar_t* path_;\n\n        path_ = (wchar_t*)WAI_REALLOC(path, sizeof(wchar_t) * size_ * 2);\n        if (!path_)\n          break;\n        size_ *= 2;\n        path = path_;\n        size = GetModuleFileNameW(module, path, size_);\n      }\n      while (size == size_);\n\n      if (size == size_)\n        break;\n    }\n    else\n      path = buffer1;\n\n    if (!_wfullpath(buffer2, path, MAX_PATH))\n      break;\n    length_ = (int)wcslen(buffer2);\n    length__ = WideCharToMultiByte(CP_UTF8, 0, buffer2, length_ , out, capacity, NULL, NULL);\n\n    if (length__ == 0)\n      length__ = WideCharToMultiByte(CP_UTF8, 0, buffer2, length_, NULL, 0, NULL, NULL);\n    if (length__ == 0)\n      break;\n\n    if (length__ <= capacity && dirname_length)\n    {\n      int i;\n\n      for (i = length__ - 1; i >= 0; --i)\n      {\n        if (out[i] == '\\\\')\n        {\n          *dirname_length = i;\n          break;\n        }\n      }\n    }\n\n    length = length__;\n  }\n\n  if (path != buffer1)\n    WAI_FREE(path);\n\n  return ok ? length : -1;\n}\n\nWAI_NOINLINE WAI_FUNCSPEC\nint WAI_PREFIX(getExecutablePath)(char* out, int capacity, int* dirname_length)\n{\n  return WAI_PREFIX(getModulePath_)(NULL, out, capacity, dirname_length);\n}\n\nWAI_NOINLINE WAI_FUNCSPEC\nint WAI_PREFIX(getModulePath)(char* out, int capacity, int* dirname_length)\n{\n  HMODULE module;\n  int length = -1;\n\n#if defined(_MSC_VER)\n#pragma warning(push)\n#pragma warning(disable: 4054)\n#endif\n  if (GetModuleHandleEx(GET_MODULE_HANDLE_EX_FLAG_FROM_ADDRESS | GET_MODULE_HANDLE_EX_FLAG_UNCHANGED_REFCOUNT, (LPCTSTR)WAI_RETURN_ADDRESS(), &module))\n#if defined(_MSC_VER)\n#pragma warning(pop)\n#endif\n  {\n    length = WAI_PREFIX(getModulePath_)(module, out, capacity, dirname_length);\n  }\n\n  return length;\n}\n\n#elif defined(__linux__) || defined(__CYGWIN__) || defined(__sun) || defined(WAI_USE_PROC_SELF_EXE)\n\n#include <stdio.h>\n#include <stdlib.h>\n#include <string.h>\n#if defined(__linux__)\n#include <linux/limits.h>\n#else\n#include <limits.h>\n#endif\n#ifndef __STDC_FORMAT_MACROS\n#define __STDC_FORMAT_MACROS\n#endif\n#include <inttypes.h>\n#include <stdbool.h>\n\n#if !defined(WAI_PROC_SELF_EXE)\n#if defined(__sun)\n#define WAI_PROC_SELF_EXE \"/proc/self/path/a.out\"\n#else\n#define WAI_PROC_SELF_EXE \"/proc/self/exe\"\n#endif\n#endif\n\nWAI_FUNCSPEC\nint WAI_PREFIX(getExecutablePath)(char* out, int capacity, int* dirname_length)\n{\n  char buffer[PATH_MAX];\n  char* resolved = NULL;\n  int length = -1;\n  bool ok;\n\n  for (ok = false; !ok; ok = true)\n  {\n    resolved = realpath(WAI_PROC_SELF_EXE, buffer);\n    if (!resolved)\n      break;\n\n    length = (int)strlen(resolved);\n    if (length <= capacity)\n    {\n      memcpy(out, resolved, length);\n\n      if (dirname_length)\n      {\n        int i;\n\n        for (i = length - 1; i >= 0; --i)\n        {\n          if (out[i] == '/')\n          {\n            *dirname_length = i;\n            break;\n          }\n        }\n      }\n    }\n  }\n\n  return ok ? length : -1;\n}\n\n#if !defined(WAI_PROC_SELF_MAPS_RETRY)\n#define WAI_PROC_SELF_MAPS_RETRY 5\n#endif\n\n#if !defined(WAI_PROC_SELF_MAPS)\n#if defined(__sun)\n#define WAI_PROC_SELF_MAPS \"/proc/self/map\"\n#else\n#define WAI_PROC_SELF_MAPS \"/proc/self/maps\"\n#endif\n#endif\n\n#if !defined(WAI_STRINGIZE)\n#define WAI_STRINGIZE(s)\n#define WAI_STRINGIZE_(s) #s\n#endif\n\n#if defined(__ANDROID__) || defined(ANDROID)\n#include <fcntl.h>\n#include <sys/mman.h>\n#include <unistd.h>\n#endif\n#include <stdbool.h>\n\nWAI_NOINLINE WAI_FUNCSPEC\nint WAI_PREFIX(getModulePath)(char* out, int capacity, int* dirname_length)\n{\n  int length = -1;\n  FILE* maps = NULL;\n\n  for (int r = 0; r < WAI_PROC_SELF_MAPS_RETRY; ++r)\n  {\n    maps = fopen(WAI_PROC_SELF_MAPS, \"r\");\n    if (!maps)\n      break;\n\n    for (;;)\n    {\n      char buffer[128 + PATH_MAX];\n      uintptr_t low, high;\n      char perms[5];\n      uint64_t offset;\n      uint32_t major, minor, inode;\n      char path[PATH_MAX + 1];\n\n      if (!fgets(buffer, sizeof(buffer), maps))\n        break;\n\n      if (sscanf(buffer, \"%\" SCNxPTR \"-%\" SCNxPTR \" %s %\" SCNx64 \" %x:%x %u %\" WAI_STRINGIZE(PATH_MAX) \"[^\\n]\\n\", &low, &high, perms, &offset, &major, &minor, &inode, path) == 8)\n      {\n        void* _addr = WAI_RETURN_ADDRESS();\n        uintptr_t addr = (uintptr_t)_addr;\n        if (low <= addr && addr <= high)\n        {\n          char* resolved;\n\n          resolved = realpath(path, buffer);\n          if (!resolved)\n            break;\n\n          length = (int)strlen(resolved);\n#if defined(__ANDROID__) || defined(ANDROID)\n          if (length > 4\n              &&buffer[length - 1] == 'k'\n              &&buffer[length - 2] == 'p'\n              &&buffer[length - 3] == 'a'\n              &&buffer[length - 4] == '.')\n          {\n            int fd = open(path, O_RDONLY);\n            if (fd == -1)\n            {\n              length = -1; // retry\n              break;\n            }\n\n            char* begin = (char*)mmap(0, offset, PROT_READ, MAP_SHARED, fd, 0);\n            if (begin == MAP_FAILED)\n            {\n              close(fd);\n              length = -1; // retry\n              break;\n            }\n\n            char* p = begin + offset - 30; // minimum size of local file header\n            while (p >= begin) // scan backwards\n            {\n              if (*((uint32_t*)p) == 0x04034b50UL) // local file header signature found\n              {\n                uint16_t length_ = *((uint16_t*)(p + 26));\n\n                if (length + 2 + length_ < (int)sizeof(buffer))\n                {\n                  memcpy(&buffer[length], \"!/\", 2);\n                  memcpy(&buffer[length + 2], p + 30, length_);\n                  length += 2 + length_;\n                }\n\n                break;\n              }\n\n              --p;\n            }\n\n            munmap(begin, offset);\n            close(fd);\n          }\n#endif\n          if (length <= capacity)\n          {\n            memcpy(out, resolved, length);\n\n            if (dirname_length)\n            {\n              int i;\n\n              for (i = length - 1; i >= 0; --i)\n              {\n                if (out[i] == '/')\n                {\n                  *dirname_length = i;\n                  break;\n                }\n              }\n            }\n          }\n\n          break;\n        }\n      }\n    }\n\n    fclose(maps);\n    maps = NULL;\n\n    if (length != -1)\n      break;\n  }\n\n  return length;\n}\n\n#elif defined(__APPLE__)\n\n#include <mach-o/dyld.h>\n#include <limits.h>\n#include <stdlib.h>\n#include <string.h>\n#include <dlfcn.h>\n#include <stdbool.h>\n\nWAI_FUNCSPEC\nint WAI_PREFIX(getExecutablePath)(char* out, int capacity, int* dirname_length)\n{\n  char buffer1[PATH_MAX];\n  char buffer2[PATH_MAX];\n  char* path = buffer1;\n  char* resolved = NULL;\n  int length = -1;\n  bool ok;\n\n  for (ok = false; !ok; ok = true)\n  {\n    uint32_t size = (uint32_t)sizeof(buffer1);\n    if (_NSGetExecutablePath(path, &size) == -1)\n    {\n      path = (char*)WAI_MALLOC(size);\n      if (!_NSGetExecutablePath(path, &size))\n        break;\n    }\n\n    resolved = realpath(path, buffer2);\n    if (!resolved)\n      break;\n\n    length = (int)strlen(resolved);\n    if (length <= capacity)\n    {\n      memcpy(out, resolved, length);\n\n      if (dirname_length)\n      {\n        int i;\n\n        for (i = length - 1; i >= 0; --i)\n        {\n          if (out[i] == '/')\n          {\n            *dirname_length = i;\n            break;\n          }\n        }\n      }\n    }\n  }\n\n  if (path != buffer1)\n    WAI_FREE(path);\n\n  return ok ? length : -1;\n}\n\nWAI_NOINLINE WAI_FUNCSPEC\nint WAI_PREFIX(getModulePath)(char* out, int capacity, int* dirname_length)\n{\n  char buffer[PATH_MAX];\n  char* resolved = NULL;\n  int length = -1;\n\n  for(;;)\n  {\n    Dl_info info;\n\n    if (dladdr(WAI_RETURN_ADDRESS(), &info))\n    {\n      resolved = realpath(info.dli_fname, buffer);\n      if (!resolved)\n        break;\n\n      length = (int)strlen(resolved);\n      if (length <= capacity)\n      {\n        memcpy(out, resolved, length);\n\n        if (dirname_length)\n        {\n          int i;\n\n          for (i = length - 1; i >= 0; --i)\n          {\n            if (out[i] == '/')\n            {\n              *dirname_length = i;\n              break;\n            }\n          }\n        }\n      }\n    }\n\n    break;\n  }\n\n  return length;\n}\n\n#elif defined(__QNXNTO__)\n\n#include <limits.h>\n#include <stdio.h>\n#include <stdlib.h>\n#include <string.h>\n#include <dlfcn.h>\n#include <stdbool.h>\n\n#if !defined(WAI_PROC_SELF_EXE)\n#define WAI_PROC_SELF_EXE \"/proc/self/exefile\"\n#endif\n\nWAI_FUNCSPEC\nint WAI_PREFIX(getExecutablePath)(char* out, int capacity, int* dirname_length)\n{\n  char buffer1[PATH_MAX];\n  char buffer2[PATH_MAX];\n  char* resolved = NULL;\n  FILE* self_exe = NULL;\n  int length = -1;\n  bool ok;\n\n  for (ok = false; !ok; ok = true)\n  {\n    self_exe = fopen(WAI_PROC_SELF_EXE, \"r\");\n    if (!self_exe)\n      break;\n\n    if (!fgets(buffer1, sizeof(buffer1), self_exe))\n      break;\n\n    resolved = realpath(buffer1, buffer2);\n    if (!resolved)\n      break;\n\n    length = (int)strlen(resolved);\n    if (length <= capacity)\n    {\n      memcpy(out, resolved, length);\n\n      if (dirname_length)\n      {\n        int i;\n\n        for (i = length - 1; i >= 0; --i)\n        {\n          if (out[i] == '/')\n          {\n            *dirname_length = i;\n            break;\n          }\n        }\n      }\n    }\n  }\n\n  fclose(self_exe);\n\n  return ok ? length : -1;\n}\n\nWAI_FUNCSPEC\nint WAI_PREFIX(getModulePath)(char* out, int capacity, int* dirname_length)\n{\n  char buffer[PATH_MAX];\n  char* resolved = NULL;\n  int length = -1;\n\n  for(;;)\n  {\n    Dl_info info;\n\n    if (dladdr(WAI_RETURN_ADDRESS(), &info))\n    {\n      resolved = realpath(info.dli_fname, buffer);\n      if (!resolved)\n        break;\n\n      length = (int)strlen(resolved);\n      if (length <= capacity)\n      {\n        memcpy(out, resolved, length);\n\n        if (dirname_length)\n        {\n          int i;\n\n          for (i = length - 1; i >= 0; --i)\n          {\n            if (out[i] == '/')\n            {\n              *dirname_length = i;\n              break;\n            }\n          }\n        }\n      }\n    }\n\n    break;\n  }\n\n  return length;\n}\n\n#elif defined(__DragonFly__) || defined(__FreeBSD__) || \\\n      defined(__FreeBSD_kernel__) || defined(__NetBSD__) || defined(__OpenBSD__)\n\n#include <limits.h>\n#include <stdlib.h>\n#include <string.h>\n#include <sys/types.h>\n#include <sys/sysctl.h>\n#include <dlfcn.h>\n#include <stdbool.h>\n\n#if defined(__OpenBSD__)\n\n#include <unistd.h>\n\nWAI_FUNCSPEC\nint WAI_PREFIX(getExecutablePath)(char* out, int capacity, int* dirname_length)\n{\n  char buffer1[4096];\n  char buffer2[PATH_MAX];\n  char buffer3[PATH_MAX];\n  char** argv = (char**)buffer1;\n  char* resolved = NULL;\n  int length = -1;\n  bool ok;\n\n  for (ok = false; !ok; ok = true)\n  {\n    int mib[4] = { CTL_KERN, KERN_PROC_ARGS, getpid(), KERN_PROC_ARGV };\n    size_t size;\n\n    if (sysctl(mib, 4, NULL, &size, NULL, 0) != 0)\n        break;\n\n    if (size > sizeof(buffer1))\n    {\n      argv = (char**)WAI_MALLOC(size);\n      if (!argv)\n        break;\n    }\n\n    if (sysctl(mib, 4, argv, &size, NULL, 0) != 0)\n        break;\n\n    if (strchr(argv[0], '/'))\n    {\n      resolved = realpath(argv[0], buffer2);\n      if (!resolved)\n        break;\n    }\n    else\n    {\n      const char* PATH = getenv(\"PATH\");\n      if (!PATH)\n        break;\n\n      size_t argv0_length = strlen(argv[0]);\n\n      const char* begin = PATH;\n      while (1)\n      {\n        const char* separator = strchr(begin, ':');\n        const char* end = separator ? separator : begin + strlen(begin);\n\n        if (end - begin > 0)\n        {\n          if (*(end -1) == '/')\n            --end;\n\n          if (((end - begin) + 1 + argv0_length + 1) <= sizeof(buffer2))\n          {\n            memcpy(buffer2, begin, end - begin);\n            buffer2[end - begin] = '/';\n            memcpy(buffer2 + (end - begin) + 1, argv[0], argv0_length + 1);\n\n            resolved = realpath(buffer2, buffer3);\n            if (resolved)\n              break;\n          }\n        }\n\n        if (!separator)\n          break;\n\n        begin = ++separator;\n      }\n\n      if (!resolved)\n        break;\n    }\n\n    length = (int)strlen(resolved);\n    if (length <= capacity)\n    {\n      memcpy(out, resolved, length);\n\n      if (dirname_length)\n      {\n        int i;\n\n        for (i = length - 1; i >= 0; --i)\n        {\n          if (out[i] == '/')\n          {\n            *dirname_length = i;\n            break;\n          }\n        }\n      }\n    }\n  }\n\n  if (argv != (char**)buffer1)\n    WAI_FREE(argv);\n\n  return ok ? length : -1;\n}\n\n#else\n\nWAI_FUNCSPEC\nint WAI_PREFIX(getExecutablePath)(char* out, int capacity, int* dirname_length)\n{\n  char buffer1[PATH_MAX];\n  char buffer2[PATH_MAX];\n  char* path = buffer1;\n  char* resolved = NULL;\n  int length = -1;\n  bool ok;\n\n  for (ok = false; !ok; ok = true)\n  {\n#if defined(__NetBSD__)\n    int mib[4] = { CTL_KERN, KERN_PROC_ARGS, -1, KERN_PROC_PATHNAME };\n#else\n    int mib[4] = { CTL_KERN, KERN_PROC, KERN_PROC_PATHNAME, -1 };\n#endif\n    size_t size = sizeof(buffer1);\n\n    if (sysctl(mib, 4, path, &size, NULL, 0) != 0)\n        break;\n\n    resolved = realpath(path, buffer2);\n    if (!resolved)\n      break;\n\n    length = (int)strlen(resolved);\n    if (length <= capacity)\n    {\n      memcpy(out, resolved, length);\n\n      if (dirname_length)\n      {\n        int i;\n\n        for (i = length - 1; i >= 0; --i)\n        {\n          if (out[i] == '/')\n          {\n            *dirname_length = i;\n            break;\n          }\n        }\n      }\n    }\n  }\n\n  return ok ? length : -1;\n}\n\n#endif\n\nWAI_NOINLINE WAI_FUNCSPEC\nint WAI_PREFIX(getModulePath)(char* out, int capacity, int* dirname_length)\n{\n  char buffer[PATH_MAX];\n  char* resolved = NULL;\n  int length = -1;\n\n  for(;;)\n  {\n    Dl_info info;\n\n    if (dladdr(WAI_RETURN_ADDRESS(), &info))\n    {\n      resolved = realpath(info.dli_fname, buffer);\n      if (!resolved)\n        break;\n\n      length = (int)strlen(resolved);\n      if (length <= capacity)\n      {\n        memcpy(out, resolved, length);\n\n        if (dirname_length)\n        {\n          int i;\n\n          for (i = length - 1; i >= 0; --i)\n          {\n            if (out[i] == '/')\n            {\n              *dirname_length = i;\n              break;\n            }\n          }\n        }\n      }\n    }\n\n    break;\n  }\n\n  return length;\n}\n\n#else\n\n#error unsupported platform\n\n#endif\n\n#ifdef __cplusplus\n}\n#endif\n"
  },
  {
    "path": "libs/whereami/whereami.h",
    "content": "// (‑●‑●)> dual licensed under the WTFPL v2 and MIT licenses\n//   without any warranty.\n//   by Gregory Pakosz (@gpakosz)\n// https://github.com/gpakosz/whereami\n\n#ifndef WHEREAMI_H\n#define WHEREAMI_H\n\n#ifdef __cplusplus\nextern \"C\" {\n#endif\n\n#ifndef WAI_FUNCSPEC\n  #define WAI_FUNCSPEC\n#endif\n#ifndef WAI_PREFIX\n#define WAI_PREFIX(function) wai_##function\n#endif\n\n/**\n * Returns the path to the current executable.\n *\n * Usage:\n *  - first call `int length = wai_getExecutablePath(NULL, 0, NULL);` to\n *    retrieve the length of the path\n *  - allocate the destination buffer with `path = (char*)malloc(length + 1);`\n *  - call `wai_getExecutablePath(path, length, NULL)` again to retrieve the\n *    path\n *  - add a terminal NUL character with `path[length] = '\\0';`\n *\n * @param out destination buffer, optional\n * @param capacity destination buffer capacity\n * @param dirname_length optional recipient for the length of the dirname part\n *   of the path. Available only when `capacity` is large enough to retrieve the\n *   path.\n *\n * @return the length of the executable path on success (without a terminal NUL\n * character), otherwise `-1`\n */\nWAI_FUNCSPEC\nint WAI_PREFIX(getExecutablePath)(char* out, int capacity, int* dirname_length);\n\n/**\n * Returns the path to the current module\n *\n * Usage:\n *  - first call `int length = wai_getModulePath(NULL, 0, NULL);` to retrieve\n *    the length  of the path\n *  - allocate the destination buffer with `path = (char*)malloc(length + 1);`\n *  - call `wai_getModulePath(path, length, NULL)` again to retrieve the path\n *  - add a terminal NUL character with `path[length] = '\\0';`\n *\n * @param out destination buffer, optional\n * @param capacity destination buffer capacity\n * @param dirname_length optional recipient for the length of the dirname part\n *   of the path. Available only when `capacity` is large enough to retrieve the\n *   path.\n *\n * @return the length of the module path on success (without a terminal NUL\n * character), otherwise `-1`\n */\nWAI_FUNCSPEC\nint WAI_PREFIX(getModulePath)(char* out, int capacity, int* dirname_length);\n\n#ifdef __cplusplus\n}\n#endif\n\n#endif // #ifndef WHEREAMI_H\n"
  },
  {
    "path": "man/man1/cadabra-server.1",
    "content": ".TH CADABRA-SERVER 1 \"Jan 22, 2019\" \"\" \"\"\n.\\\"\n.\\\" Man page written by Kasper Peeters <info@cadabra.science>\n.\\\"\n.\\\"\tThis program is free software; you can redistribute it and/or modify\n.\\\"\tit under the terms of the GNU General Public License as published by\n.\\\"\tthe Free Software Foundation; either version 3 of the License, or\n.\\\"\t(at your option) any later version.\n.\\\"\n.\\\"\tThis program is distributed in the hope that it will be useful,\n.\\\"\tbut WITHOUT ANY WARRANTY; without even the implied warranty of\n.\\\"\tMERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n.\\\"\tGNU General Public License for more details.\n.\\\"\n.\\\"\tYou should have received a copy of the GNU General Public License\n.\\\"\talong with this program; if not, write to the Free Software\n.\\\"\tFoundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.\n.\\\"\n.\\\"\n.SH NAME\ncadabra-server \\- the server backend for running Cadabra2 notebooks\n.SH SYNOPSIS\n.BR \"cadabra-server\"\n.SH DESCRIPTION\n.B On starting cadabra-server, it will print a port number on stdout, where\nconnections to the cadabra kernel can be made. All interaction with\nthe server is through that port on the localhost interface.\n\n.SH SEE ALSO\n.BR cadabra2-gtk (1), cadabra2 (1)\n\nSee the web page at\n.BR \"https://cadabra.science/\"\nfor more information and up\\-to\\-date sample notebooks.\n.SH AUTHORS\nKasper Peeters <info@cadabra.science>\n\n"
  },
  {
    "path": "man/man1/cadabra2-cli.1",
    "content": ".TH CADABRA2-CLI 1 \"Oct 30, 2020\" \"\" \"\"\n.\\\"\n.\\\" Man page written by Kasper Peeters <info@cadabra.science>\n.\\\"\n.\\\"\tThis program is free software; you can redistribute it and/or modify\n.\\\"\tit under the terms of the GNU General Public License as published by\n.\\\"\tthe Free Software Foundation; either version 3 of the License, or\n.\\\"\t(at your option) any later version.\n.\\\"\n.\\\"\tThis program is distributed in the hope that it will be useful,\n.\\\"\tbut WITHOUT ANY WARRANTY; without even the implied warranty of\n.\\\"\tMERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n.\\\"\tGNU General Public License for more details.\n.\\\"\n.\\\"\tYou should have received a copy of the GNU General Public License\n.\\\"\talong with this program; if not, write to the Free Software\n.\\\"\tFoundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.\n.\\\"\n.\\\"\n.SH NAME\ncadabra2-cli \\- command\\-line interface for cadabra2\n.SH SYNOPSIS\n.BR \"cadabra2-gtk [notebook file (.cnb)]\"\n.SH DESCRIPTION\n.B Cadabra2-cli\nis a command\\-line interface for the computer algebra system \n.B cadabra2\nwhich is a single binary, in contrast to cadabra2 which is a Python\nscript. Using cadabra2\\-cli makes it easier to debug Cadabra using\na debugger.\n\n.SH SEE ALSO\n.BR cadabra2 (1).\n\nSee the web page at\n.BR \"https://cadabra.science/\"\nfor more information and up\\-to\\-date sample notebooks.\n.SH AUTHORS\nKasper Peeters <info@cadabra.science>\n\n"
  },
  {
    "path": "man/man1/cadabra2-gtk.1",
    "content": ".TH CADABRA2-GTK 1 \"Jan 22, 2019\" \"\" \"\"\n.\\\"\n.\\\" Man page written by Kasper Peeters <info@cadabra.science>\n.\\\"\n.\\\"\tThis program is free software; you can redistribute it and/or modify\n.\\\"\tit under the terms of the GNU General Public License as published by\n.\\\"\tthe Free Software Foundation; either version 3 of the License, or\n.\\\"\t(at your option) any later version.\n.\\\"\n.\\\"\tThis program is distributed in the hope that it will be useful,\n.\\\"\tbut WITHOUT ANY WARRANTY; without even the implied warranty of\n.\\\"\tMERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n.\\\"\tGNU General Public License for more details.\n.\\\"\n.\\\"\tYou should have received a copy of the GNU General Public License\n.\\\"\talong with this program; if not, write to the Free Software\n.\\\"\tFoundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.\n.\\\"\n.\\\"\n.SH NAME\ncadabra2-gtk \\- gtk notebook front\\-end for cadabra2\n.SH SYNOPSIS\n.BR \"cadabra2-gtk [notebook file (.cnb)]\"\n.SH DESCRIPTION\n.B Cadabra2-Gtk\nis a graphical notebook front\\-end for the computer algebra system \n.B cadabra2\nwhich makes use of the Gtk toolkit.\n\n.SH SEE ALSO\n.BR cadabra2 (1).\n\nSee the web page at\n.BR \"https://cadabra.science/\"\nfor more information and up\\-to\\-date sample notebooks.\n.SH AUTHORS\nKasper Peeters <info@cadabra.science>\n\n"
  },
  {
    "path": "man/man1/cadabra2.1",
    "content": ".TH CADABRA2 1 \"Jan 22, 2019\" \"\" \"\"\n.\\\"\n.\\\" Man page written by Kasper Peeters <info@cadabra.science>\n.\\\"\n.\\\"\tThis program is free software; you can redistribute it and/or modify\n.\\\"\tit under the terms of the GNU General Public License as published by\n.\\\"\tthe Free Software Foundation; either version 3 of the License, or\n.\\\"\t(at your option) any later version.\n.\\\"\n.\\\"\tThis program is distributed in the hope that it will be useful,\n.\\\"\tbut WITHOUT ANY WARRANTY; without even the implied warranty of\n.\\\"\tMERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n.\\\"\tGNU General Public License for more details.\n.\\\"\n.\\\"\tYou should have received a copy of the GNU General Public License\n.\\\"\talong with this program; if not, write to the Free Software\n.\\\"\tFoundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.\n.\\\"\n.\\\"\n.SH NAME\ncadabra2 \\- field\\-theory motivated computer algebra system, 2.x series\n.SH SYNOPSIS\n.BR \"cadabra2 [-d] [input file (.cdb)]\"\n.SH DESCRIPTION\n.B Cadabra2\nis a computer algebra system for the solution of (quantum) field\ntheory problems. \n\nThis is the command-line client for the Cadabra2 computer algebra\nsystem for field theory problems. \n\n.SH OPTIONS\n.TP\n\\fB \\-d\\fR\nRuns under control of the default debugger. \n\n.SH ENVIRONMENT VARIABLES\nThe following variables toggle various features on or off, depending\non whether the variable is set or not:\n.TP \n\\fB CADABRA_NO_UNICODE\\fR\nDo not use UTF8 characters to display greek characters and\nmathematical symbols. Instead, use their LaTeX equivalent, so\nthat the output is pure ASCII.\n.SH SEE ALSO\n.BR cadabra2-gtk (1).\n\nSee the web page at\n.BR \"https://cadabra.science/\"\nfor binaries, example calculations and the full manual.\n.SH AUTHORS\nKasper Peeters <info@cadabra.science>\n\n"
  },
  {
    "path": "man/man1/cadabra2cadabra.1",
    "content": ".TH CADABRA2CADABRA 1 \"Jan 22, 2019\" \"\" \"\"\n.\\\"\n.\\\" Man page written by Kasper Peeters <info@cadabra.science>\n.\\\"\n.\\\"\tThis program is free software; you can redistribute it and/or modify\n.\\\"\tit under the terms of the GNU General Public License as published by\n.\\\"\tthe Free Software Foundation; either version 3 of the License, or\n.\\\"\t(at your option) any later version.\n.\\\"\n.\\\"\tThis program is distributed in the hope that it will be useful,\n.\\\"\tbut WITHOUT ANY WARRANTY; without even the implied warranty of\n.\\\"\tMERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n.\\\"\tGNU General Public License for more details.\n.\\\"\n.\\\"\tYou should have received a copy of the GNU General Public License\n.\\\"\talong with this program; if not, write to the Free Software\n.\\\"\tFoundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.\n.\\\"\n.\\\"\n.SH NAME\ncadabra2cadabra \\- convert Cadabra2 notebooks to text input files\n.SH SYNOPSIS\n.BR \"cadabra2cadabra [cadabra notebook file (.cnb)] [cadabra text file (.cdb)]\"\n.SH DESCRIPTION\n.B The Cadabra2-Gtk notebook front\\-end for Cadabra2 produces\nnotebooks in a JSON format. This command converts these to standard\ntext input files which can be processed with the command-line client\ncadabra2.\n\n.SH SEE ALSO\n.BR cadabra2-gtk (1), cadabra2 (1)\n\nSee the web page at\n.BR \"https://cadabra.science/\"\nfor more information and up\\-to\\-date sample notebooks.\n.SH AUTHORS\nKasper Peeters <info@cadabra.science>\n\n"
  },
  {
    "path": "man/man1/cadabra2html.1",
    "content": ".TH CADABRA2HTML 1 \"Jan 22, 2019\" \"\" \"\"\n.\\\"\n.\\\" Man page written by Kasper Peeters <info@cadabra.science>\n.\\\"\n.\\\"\tThis program is free software; you can redistribute it and/or modify\n.\\\"\tit under the terms of the GNU General Public License as published by\n.\\\"\tthe Free Software Foundation; either version 3 of the License, or\n.\\\"\t(at your option) any later version.\n.\\\"\n.\\\"\tThis program is distributed in the hope that it will be useful,\n.\\\"\tbut WITHOUT ANY WARRANTY; without even the implied warranty of\n.\\\"\tMERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n.\\\"\tGNU General Public License for more details.\n.\\\"\n.\\\"\tYou should have received a copy of the GNU General Public License\n.\\\"\talong with this program; if not, write to the Free Software\n.\\\"\tFoundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.\n.\\\"\n.\\\"\n.SH NAME\ncadabra2html \\- convert Cadabra2 notebooks to standalone HTML files\n.SH SYNOPSIS\n.BR \"cadabra2html [cadabra notebook file (.cnb)] [html filename]\"\n.SH DESCRIPTION\n.B This command converts Cadabra2 notebooks to a standalone HTML\nfile, including all maths and graphics. It does the same thing as\nthe 'File / Export to standalone HTML' menu option in the\ncadabra2-gtk notebook interface.\n\n.SH SEE ALSO\n.BR cadabra2-gtk (1).\n\nSee the web page at\n.BR \"https://cadabra.science/\"\nfor more information and up\\-to\\-date sample notebooks.\n.SH AUTHORS\nKasper Peeters <info@cadabra.science>\n\n"
  },
  {
    "path": "man/man1/cadabra2ipynb.1",
    "content": ".TH CADABRA2IPYNB 1 \"Jan 22, 2019\" \"\" \"\"\n.\\\"\n.\\\" Man page written by Kasper Peeters <info@cadabra.science>\n.\\\"\n.\\\"\tThis program is free software; you can redistribute it and/or modify\n.\\\"\tit under the terms of the GNU General Public License as published by\n.\\\"\tthe Free Software Foundation; either version 3 of the License, or\n.\\\"\t(at your option) any later version.\n.\\\"\n.\\\"\tThis program is distributed in the hope that it will be useful,\n.\\\"\tbut WITHOUT ANY WARRANTY; without even the implied warranty of\n.\\\"\tMERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n.\\\"\tGNU General Public License for more details.\n.\\\"\n.\\\"\tYou should have received a copy of the GNU General Public License\n.\\\"\talong with this program; if not, write to the Free Software\n.\\\"\tFoundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.\n.\\\"\n.\\\"\n.SH NAME\ncadabra2ipynb \\- convert Cadabra2 notebooks to Jupyter notebooks\n.SH SYNOPSIS\n.BR \"cadabra2cadabra [cadabra notebook file (.cnb)] [Jupyter notebook file (.ipynb)]\"\n.SH DESCRIPTION\n.B The Cadabra2-Gtk notebook front\\-end for Cadabra2 produces\nnotebooks in a JSON format, but these notebooks are not compatible\nwith Jupyter notebooks. This command converts Cadabra notebooks to\nJupyter notebooks, which can be executed using the Cadabra Jupyter\nkernel.\n\n.SH SEE ALSO\n.BR cadabra2-gtk (1), cadabra2 (1)\n\nSee the web page at\n.BR \"https://cadabra.science/\"\nfor more information and up\\-to\\-date sample notebooks.\n.SH AUTHORS\nKasper Peeters <info@cadabra.science>\n\n"
  },
  {
    "path": "man/man1/cadabra2latex.1",
    "content": ".TH CADABRA2LATEX 1 \"Oct 30, 2020\" \"\" \"\"\n.\\\"\n.\\\" Man page written by Kasper Peeters <info@cadabra.science>\n.\\\"\n.\\\"\tThis program is free software; you can redistribute it and/or modify\n.\\\"\tit under the terms of the GNU General Public License as published by\n.\\\"\tthe Free Software Foundation; either version 3 of the License, or\n.\\\"\t(at your option) any later version.\n.\\\"\n.\\\"\tThis program is distributed in the hope that it will be useful,\n.\\\"\tbut WITHOUT ANY WARRANTY; without even the implied warranty of\n.\\\"\tMERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n.\\\"\tGNU General Public License for more details.\n.\\\"\n.\\\"\tYou should have received a copy of the GNU General Public License\n.\\\"\talong with this program; if not, write to the Free Software\n.\\\"\tFoundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.\n.\\\"\n.\\\"\n.SH NAME\ncadabra2latex \\- convert Cadabra2 notebooks to standalone LaTeX files\n.SH SYNOPSIS\n.BR \"cadabra2latex [cadabra notebook file (.cnb)] [LaTeX filename]\"\n.SH DESCRIPTION\n.B This command converts Cadabra2 notebooks to a standalone LaTeX\nfile, including all maths and graphics. It does the same thing as\nthe 'File / Export to standalone LaTeX' menu option in the\ncadabra2-gtk notebook interface.\n\n.SH SEE ALSO\n.BR cadabra2-gtk (1).\n\nSee the web page at\n.BR \"https://cadabra.science/\"\nfor more information and up\\-to\\-date sample notebooks.\n.SH AUTHORS\nKasper Peeters <info@cadabra.science>\n\n"
  },
  {
    "path": "man/man1/cadabra2python.1",
    "content": ".TH CADABRA2PYTHON 1 \"Jan 22, 2019\" \"\" \"\"\n.\\\"\n.\\\" Man page written by Kasper Peeters <info@cadabra.science>\n.\\\"\n.\\\"\tThis program is free software; you can redistribute it and/or modify\n.\\\"\tit under the terms of the GNU General Public License as published by\n.\\\"\tthe Free Software Foundation; either version 3 of the License, or\n.\\\"\t(at your option) any later version.\n.\\\"\n.\\\"\tThis program is distributed in the hope that it will be useful,\n.\\\"\tbut WITHOUT ANY WARRANTY; without even the implied warranty of\n.\\\"\tMERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n.\\\"\tGNU General Public License for more details.\n.\\\"\n.\\\"\tYou should have received a copy of the GNU General Public License\n.\\\"\talong with this program; if not, write to the Free Software\n.\\\"\tFoundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.\n.\\\"\n.\\\"\n.SH NAME\ncadabra2python \\- convert Cadabra2 text input files to pure Python\n.SH SYNOPSIS\n.BR \"cadabra2python [cadabra input file (.cdb)] [python filename]\"\n.SH DESCRIPTION\n.B The input format for cadabra2 is a special mixture of Cadabra2\nnotation and Python code. The cadabra2python command converts these\ninput files to pure Python files, which can be processed by\nPython directly.\n\n.SH SEE ALSO\n.BR cadabra2 (1).\n\nSee the web page at\n.BR \"https://cadabra.science/\"\nfor more information and up\\-to\\-date sample notebooks.\n.SH AUTHORS\nKasper Peeters <info@cadabra.science>\n\n"
  },
  {
    "path": "paper/paper.bib",
    "content": "@article{cadabra_hep,\n  author    = \"Peeters, Kasper\",\n  title     = \"{Introducing Cadabra: a symbolic computer algebra system for field theory problems}\",\n  year      = \"2007\",\n  eprint    = \"hep-th/0701238\"\n}\n@article{cadabra_cpc,\n  author    = \"Peeters, Kasper\",\n  title     = \"A field-theory motivated approach to symbolic computer algebra\",\n  year      = \"2006\",\n  journal   = \"Comp.Phys.Commun.\",\n  volume    = \"176\",\n  pages     = \"550-558\",\n  eprint    = \"cs.sc/0608005\",\n  doi       = \"10.1016/j.cpc.2007.01.003\"\n}\n@article{cadabra_zenodo,\n  title     = \"Cadabra: a field-theory motivated approach to computer algebra\",\n  publisher = \"Zenodo\",\n  author    = \"Kasper Peeters\",\n  year      = \"2018\",\n  doi       = \"10.5281/zenodo.2500762\"\n}\n@misc{pybind11,\n  author    = \"Wenzel Jakob and Jason Rhinelander and Dean Moldovan\",\n  year      = \"2017\",\n  note      = \"https://github.com/pybind/pybind11\",\n  title     = \"{pybind11} -- {Seamless} operability between {C++11} and {Python}\"\n}\n@article{butter,\n  title     = {The component structure of conformal supergravity invariants in six dimensions},\n  author    = {Butter, Daniel and Novak, Joseph and Tartaglino-Mazzucchelli, Gabriele},\n  journal   = {Journal of High Energy Physics},\n  volume    = {2017},\n  number    = {5},\n  pages     = {133},\n  year      = {2017},\n  publisher = {Springer},\n  eprint    = {arXiv:1701.08163},\n  doi       = {10.1007/JHEP05(2017)133}\n}\n@article{malik,\n  title     = {Cosmological perturbations},\n  author    = {Malik, Karim A and Wands, David},\n  journal   = {Physics Reports},\n  volume    = {475},\n  number    = {1-4},\n  pages     = {1--51},\n  year      = {2009},\n  publisher = {Elsevier},\n  eprint    = {arXiv:0809.4944},\n  doi       = {10.1016/j.physrep.2009.03.001}\n}\n@article{buchel,\n  title     = {Universal holographic hydrodynamics at finite coupling},\n  author    = {Buchel, Alex and Myers, Robert C and Paulos, Miguel F and Sinha, Aninda},\n  journal   = {Physics Letters B},\n  volume    = {669},\n  number    = {5},\n  pages     = {364--370},\n  year      = {2008},\n  publisher = {Elsevier},\n  eprint    = {arXiv:0808.1837},\n  doi       = {10.1016/j.physletb.2008.10.003}\n}\n@article{durkee,\n  title     = {Generalization of the {Geroch-Held-Penrose} formalism to higher dimensions},\n  author    = {Durkee, Mark and Pravda, Vojt{\\v{e}}ch and Pravdov{\\'a}, Alena and Reall, Harvey S},\n  journal   = {Classical and Quantum Gravity},\n  volume    = {27},\n  number    = {21},\n  pages     = {215010},\n  year      = {2010},\n  publisher = {IOP Publishing},\n  eprint    = {arXiv:1002.4826},\n  doi       = {10.1088/0264-9381/27/21/215010}\n}\n@article{koile,\n  title     = {Hadron structure functions at small {$x$} from string theory},\n  author    = {Koile, Ezequiel and Kovensky, Nicolas and Schvellinger, Martin},\n  journal   = {Journal of High Energy Physics},\n  volume    = {2015},\n  number    = {5},\n  pages     = {1},\n  year      = {2015},\n  publisher = {Springer},\n  eprint    = {arXiv:1412.6509},\n  doi       = {10.1007/JHEP05(2015)001}\n}\n@article{geissbuhler,\n  title     = {Double field theory and {$N=4$} gauged supergravity},\n  author    = {Geissb{\\\"u}hler, David},\n  journal   = {Journal of High Energy Physics},\n  volume    = {2011},\n  number    = {11},\n  pages     = {116},\n  year      = {2011},\n  publisher = {Springer},\n  eprint    = {arXiv:1109.4280},\n  doi       = {10.1007/JHEP11(2011)116}\n}\n@article{christensen,\n  title     = {Boundary stress-energy tensor and {Newton-Cartan} geometry in {Lifshitz} holography},\n  author    = {Christensen, Morten H and Hartong, Jelle and Obers, Niels A and Rollier, Blaise},\n  journal   = {Journal of High Energy Physics},\n  volume    = {2014},\n  number    = {1},\n  pages     = {57},\n  year      = {2014},\n  publisher = {Springer},\n  eprint    = {arXiv:1311.6471},\n  doi       = {10.1007/JHEP01(2014)057}\n}\n@article{sympy,\n  title     = {{SymPy}: symbolic computing in {Python}},\n  author    = {Meurer, Aaron et al.},\n  year      = 2017,\n  month     = jan,\n  volume    = 3,\n  pages     = {e103},\n  journal   = {PeerJ Computer Science},\n  issn      = {2376-5992},\n  doi       = {10.7717/peerj-cs.103}\n}\n@misc{mathematica,\n  author    = \"{Wolfram Research Inc.}\",\n  title     = \"Mathematica\",\n  year      = \"2018\",\n  note      = \"Champaign, IL\"\n}\n"
  },
  {
    "path": "paper/paper.md",
    "content": "---\ntitle: 'Cadabra2: computer algebra for field theory revisited'\ntags:\n  - C++\n  - Python\n  - field theory\n  - tensor algebra\n  - physics\nauthors:\n  - name: Kasper Peeters\n    orcid: 0000-0002-3077-8193\n    affiliation: \"1\"\naffiliations:\n - name: Durham University\n   index: 1\ndate: 4 December 2018\nbibliography: paper.bib\n---\n\n# Summary\n\nField theory is an area of mathematics required in a wide range of\ntheoretical physics problems, from general relativity to high-energy\nparticle physics and condensed matter theory. Symbolic computations in\nthis field tend to be difficult to do with mainstream computer algebra\nsystems, because the required algorithmic functionality is often\nsimply not available, but also because the standard notation tends to\nhide a lot of implicit mathematical structure which cannot easily be\nrepresented.  ``Cadabra2`` is an open source computer algebra system\nspecifically written for the solution of tensor field theory\nproblems. It enables manipulation of Lagrangians, computation of\nequations of motion, analysis of symmetries and so on in an\ninteractive notebook interface, using an input format which closely\nresembles standard mathematical notation, combined with a familiar\nPython environment to manipulate expressions.\n\nThe core of ``Cadabra2`` consists of a set of algorithms for tensor\nfield theory written in C++, which are in part based on functionality\nof an earlier version of the software [@cadabra_hep; @cadabra_cpc].\nThese algorithms take care of specific tensor aspects of computer\nalgebra, such as dummy indices, implicit coordinate dependence,\nimplicit index lines and commutativity properties. All standard scalar\nalgebra is handed off to a scalar backend, currently either Sympy\n[@sympy] or Mathematica [@mathematica]. The core is accessible from\nPython, using a wrapper built using pybind11 [@pybind11]. At the\nhighest level there is a custom pre-processor which enables input in a\nmixture of LaTeX for mathematical expressions and Python for\nexpression manipulation. The user interface consists of a command-line\nclient, as well as a graphical cell-based notebook built using gtkmm,\nwith TeX-driven maths typesetting.  The software builds and runs on\nLinux, macOS and Windows.\n\n``Cadabra2`` has been used to derive or verify results in a variety of\nrecent papers, in areas such as supergravity [@geissbuhler; @butter],\ncosmology [@malik], applications of the string/gauge theory\ncorrespondence [@christensen; @buchel; @koile], and general relativity\n[@durkee], to name a few. The software is supported by an on-line Q\\&A\nforum, a collection of tutorials and on-line manual pages, and has an\nactive user base. The source code for ``Cadabra2`` has been archived\nto Zenodo with the DOI listed in [@cadabra_zenodo].\n\n# Acknowledgements\n\nSpecial thanks to José M. Martín-García, James Allen and Dominic Price\nfor various contributions to the code, and the Software Sustainability\nInstitute and the Institute of Advanced Study at Durham University for\nsupport.\n\n# References\n\n"
  },
  {
    "path": "tests/.gitignore",
    "content": "module01.py\nmodule02.py\n"
  },
  {
    "path": "tests/CMakeLists.txt",
    "content": "cmake_minimum_required(VERSION ${CADABRA_CMAKE_VERSION})\nproject(Cadabra)\n\n\n#---------------------------------------------------------------------------\n# Preamble.\n#---------------------------------------------------------------------------\n\nprint_header(\"Configuring tests\")\n\nadd_custom_target(check COMMAND ${CMAKE_CTEST_COMMAND} --output-on-failure)\n\nif(WIN32)\n  set(PYTHONPATH \"$ENV{PYTHONPATH}\\\\;${CMAKE_SOURCE_DIR}/libs/appdirs\\\\;${CMAKE_SOURCE_DIR}/core/packages\\\\;${CMAKE_SOURCE_DIR}/core\\\\;${CMAKE_BINARY_DIR}/core/packages\\\\;${CMAKE_BINARY_DIR}/core;${CMAKE_BINARY_DIR}/core/${CADABRA_BUILD_TYPE}\\\\;${CMAKE_SOURCE_DIR}/tests\")\nelse()\n  set(PYTHONPATH \"$ENV{PYTHONPATH}:${CMAKE_SOURCE_DIR}/libs/appdirs:${CMAKE_BINARY_DIR}/core/packages:${CMAKE_SOURCE_DIR}/core/packages:${CMAKE_SOURCE_DIR}/core:${CMAKE_BINARY_DIR}/core/${CADABRA_BUILD_TYPE}:${CMAKE_BINARY_DIR}/core/:${CMAKE_SOURCE_DIR}/tests\")\nendif()\nmessage(\"-- Set PYTHONPATH for testing to ${PYTHONPATH}\")\n\nif (!WIN32)\n  add_test(comparison     test_comparison)\nendif()\n\n# Notebooks with built-in tests.\n#\nset(CNBIN   ${CMAKE_SOURCE_DIR}/examples)\nset(CDBOUT  ${CMAKE_BINARY_DIR}/tests)\nset(DC      ${CMAKE_SOURCE_DIR}/client_server/cadabra2html.cc ${CMAKE_SOURCE_DIR}/core/DataCell.hh ${CMAKE_SOURCE_DIR}/core/DataCell.cc)\nset(NBTESTS\n  quickstart\n  beginners\n  tensor_monomials\n  for_previous_users\n  converge\n  fierz\n  gamma_matrix_algebra\n  poincare_algebra\n  string_states\n  bianchi_identities\n  schwarzschild\n  kaluza_klein\n  scalar_manipulations\n  )\nforeach(NBTEST ${NBTESTS})\n  add_custom_command(OUTPUT  ${CDBOUT}/${NBTEST}.cdb\n\t DEPENDS ${CNBIN}/${NBTEST}.cnb ${DC}\n\t COMMAND cadabra2cadabra\n\t ARGS    ${CNBIN}/${NBTEST}.cnb ${CDBOUT}/${NBTEST}.cdb\n\t COMMENT \"Creating ${NBTEST} notebook...\")\n  add_custom_target(\"${NBTEST}_test\" ALL DEPENDS ${CDBOUT}/${NBTEST}.cdb)\n  add_test(${NBTEST} ${CMAKE_BINARY_DIR}/core/cadabra2-cli ${CDBOUT}/${NBTEST}.cdb)\n  set_tests_properties(${NBTEST} PROPERTIES\n    ENVIRONMENT \"PYTHONPATH=${PYTHONPATH};LANG=en_US.UTF-8;LC_ALL=en_US.UTF-8;PYTHONIOENCODING=utf-8\"\n    TIMEOUT     30\n    )\nendforeach()\n\n# The main test suite.\n#\nset(RTESTS\n  nevaluate\n  index_positions\n  forms\n  packages\n  manip\n  modules\n  integrals\n  display\n  dummies\n  explicit_implicit\n  trigonometric\n  noncovariant\n  algebra\n  components\n  factor\n  field_theory\n  gamma_paper\n  implicit\n  fierz\n  selecting\n  kaluza_klein\n  paper\n  programming\n  basic\n  meld\n  numerical\n  output\n  substitute\n  canonicalise\n  derivative\n  properties\n  relativity\n  spinors\n  sympy_cdb\n  symmetry\n  vary\n  young\n  serialize\n#  youngreduce\n#  yrtrace\n  )\nif(MATHEMATICA_FOUND)\n  set(RTESTS ${RTESTS} mma)\nendif()\nforeach(RTEST ${RTESTS})\n  add_test(${RTEST} ${CMAKE_BINARY_DIR}/core/cadabra2-cli ${CMAKE_SOURCE_DIR}/tests/${RTEST}.cdb)\n  # We need to set the Python path so that we pick up the correct cadabra2.so Python module\n  # even if we did not do 'make install' yet.\n  set_tests_properties(${RTEST} PROPERTIES\n    ENVIRONMENT \"PYTHONPATH=${PYTHONPATH};LANG=en_US.UTF-8;LC_ALL=en_US.UTF-8;PYTHONIOENCODING=utf-8\"\n    TIMEOUT 30\n  )    \nendforeach()\n\n# This does not work properly, and on OSX it fails because we do not\n# use any other include settings, unless we hard-code the path to\n# where we expect gmpxx to be if Homebrew installed it.\nif(APPLE)\n   add_definitions(\"-I/usr/local/include\")\nendif()\n\nif (!WIN32)\n   find_library(GMP_LIB gmp REQUIRED)\n   find_library(GMPXX_LIB gmpxx REQUIRED)\n   include_directories(${CMAKE_SOURCE_DIR}/core ${GMPXX_LIB_INCLUDE_DIRS})\n  add_executable(test_comparison test_comparison.cc)\n  target_link_libraries(test_comparison cadabra2)\nendif()\n"
  },
  {
    "path": "tests/algebra.cdb",
    "content": "# \n# Test 1:= keep_terms\n\n# obj1:= a1 + a2 + a3 + a4 + a5 + a6 + a7;\n# @keep_terms(%){2}{4};\n# tst1:= a3 + a4 + a5 - @(obj1);\n# @collect_terms!(%);\n# @assert(tst1);\n# \n# obj2:= a1 + a2 + a3 + a4 + a5 + a6 + a7;\n# @keep_terms(%){6}{6};\n# tst2:= a7 - @(obj2);\n# @collect_terms!(%);\n# @assert(tst2);\n# \n# obj3:= a1 + a2 + a3 + a4 + a5 + a6 + a7;\n# @keep_terms(%){3};\n# tst3:= a4 + a5 + a6 + a7 - @(obj3);\n# @collect_terms!(%);\n# @assert(tst3);\n\n# Test 4:= dummy index relabelling upon @ substitution:\n#\n# def test04():\n# {m1,m2,m3,m4,m5}::Indices(vector).\n# tmp1:= A_{m1 m2} + B_{m1 m2};\n# tmp2:= C_{m3 m4} + D_{m3 m4};\n# obj4:= @(tmp1) @(tmp2) g^{m1 m3} g^{m2 m4};\n\n# Test 6 - 11:= prodsort\n#\ndef test06():\n    __cdbkernel__=create_scope()\n    {X,G,Y,A,B}::SortOrder.\n    {X,A}::AntiCommuting.\n    obj6:= A B G X A X;\n    sort_product(obj6)\n    tst6:= X X G A A B + @(obj6);\n    assert(tst6==0)\n    print(\"Test 06 passed\")\n\ntest06()\n\ndef test07():\n    __cdbkernel__=create_scope()\n    {X,G,Y,A,B}::SortOrder.\n    {X,A}::NonCommuting.\n    obj7:= A*B*G*X*A*X;\n    sort_product(_)\n    tst7:= G A X A X B - @(obj7);\n    assert(tst7==0)\n    print(\"Test 07 passed\")\n    \ntest07()\n\ndef test08():\n    __cdbkernel__=create_scope()\n    { W_{m n}, W_{m} }::SortOrder.\n    { W_{m n}, W_{m} }::AntiCommuting.\n    obj8:= W_{m n} W_{p} W_{q r} W_{s} W_{t};\n    sort_product(_)\n    tst8:= - W_{m n} W_{q r} W_{p} W_{s} W_{t} - @(obj8);\n    assert(tst8==0)\n    print(\"Test 08 passed\")\n    \ntest08()\n\ndef test09():\n    __cdbkernel__=create_scope()\n    { \\theta_a, \\theta_b }::SelfAntiCommuting.\n    obj9:= \\theta_c \\theta_b \\theta_a;\n    sort_product(_)\n    tst9:= \\theta_a \\theta_b \\theta_c + @(obj9);\n    assert(tst9==0)\n    print(\"Test 09 passed\")\n\ntest09()\n\ndef test10():\n    __cdbkernel__=create_scope()\n    {a,b,c,d}::Indices.\n    { \\theta_a, \\chi_a }::SortOrder.\n    \\theta_{a}::SelfAntiCommuting.\n    \\chi_{a}::SelfAntiCommuting.\n    { \\theta_a, \\chi_a }::Commuting.\n    obj10:= \\theta_c \\theta_b \\theta_d \\chi_d \\theta_a \\chi_a;\n    sort_product(_)\n    tst10:= \\theta_a \\theta_b \\theta_c \\theta_d \\chi_a \\chi_d + @(obj10);\n    assert(tst10==0)\n    print(\"Test 10 passed\")\n    \ntest10()\n\ndef test11():\n    __cdbkernel__=create_scope()\n    \\Gamma_{#}::GammaMatrix.\n    obj11:= \\Gamma_{m n p} \\Gamma_{r s};\n    sort_product(_)\n    tst11:= \\Gamma_{m n p} \\Gamma_{r s} - @(obj11);\n    assert(tst11==0)\n    print(\"Test 11 passed\")\n\ntest11()\n\n# Test 12:= Inherited sort order\n#\ndef test12():\n    __cdbkernel__=create_scope()\n    \\bar{#}::Accent.\n    {D,K,B,A}::SortOrder.\n    obj12:= A \\bar{B} \\bar{K} D;\n    sort_product(_)\n    tst12:= D \\bar{K} \\bar{B} A - @(obj12);\n    assert(tst12==0)\n    print(\"Test 12 passed\")\n\ntest12()\n\ndef test13():\n    __cdbkernel__=create_scope()\n    {b,d,e,f}::AntiCommuting.\n    obj13:= (a+b)*(d*e*f);\n    sort_product(_)\n    tst13:= (a+b)*(d*e*f) - @(obj13);\n    assert(tst13==0)\n    print(\"Test 13 passed\")\n\ntest13()\n        \n#def test14():\n#\n# {a,b,f}::AntiCommuting.\n# {d,e,f,a,b}::SortOrder.\n# obj14:= (a+b)*(d*e*f);\n# sort_product(_);\n# tst14:= (d*e*f)*(a+b) + @(obj14);\n# assert(tst14==0)\n\ndef test15():\n    __cdbkernel__=create_scope()\n    {b,f}::AntiCommuting.\n    obj15:= (d*e*f)*(a*b);\n    sort_product(_)\n    tst15:= (a*b)*(d*e*f) + @(obj15);\n    assert(tst15==0)\n    print(\"Test 15 passed\")\n\ntest15()\n\n\ndef test16():\n    __cdbkernel__=create_scope()\n    {A_\\mu, B_\\mu}::AntiCommuting.\n    \\diff{#}::Derivative.\n    obj16:= \\diff{B_\\mu}_{\\nu} * \\diff{A_\\rho}_{\\sigma};\n    sort_product(_)\n    tst16:= \\diff{A_\\rho}_{\\sigma} * \\diff{B_\\mu}_{\\nu} + @(obj16);\n    assert(tst16==0)\n    print(\"Test 16 passed\")\n\ntest16()\n\n\ndef test17():\n    __cdbkernel__=create_scope()\n    \\Gamma{#}::GammaMatrix.\n    obj17a:= (\\Gamma_{m n} + A_{m} \\Gamma_{n})\\Gamma_{p q r};\n    sort_product(_)\n    tst17a:= (\\Gamma_{m n} + A_{m} \\Gamma_{n})\\Gamma_{p q r} - @(obj17a);\n    assert(tst17a==0)\n    obj17b:= \\Gamma_{p q r} (\\Gamma_{m n} + A_{m} \\Gamma_{n});\n    sort_product(_)\n    tst17b:= \\Gamma_{p q r} (\\Gamma_{m n} + A_{m} \\Gamma_{n}) - @(obj17b);\n    assert(tst17b==0)\n    print(\"Test 17 passed\")\n\ntest17()\n\n# def test18():\n# \n# {\\psi, \\chi}::Spinor.\n# {\\psi, \\chi, \\Gamma_{#}}::NonCommuting.\n# \\Gamma_{#}::GammaMatrix.\n# {\\chi,\\psi}::SortOrder.\n# \\bar{#}::Accent.\n# obj18:= \\bar{\\psi} \\Gamma_{m n p} \\chi;\n# @prodsort!(%);\n# tst18:= \\bar{\\psi} \\Gamma_{m n p} \\chi - @(obj18);\n# @collect_terms!(%);\n# @assert(tst18);\n# \n\n# obj20:= (A+(B+C*(G+K))*D)*(E+F)*(M+(N+P*(H+K))*P);\n# @distribute!3(%);\n# tst20:= (A + B * D + C * (G + K) * D) * (E + F) * (M + N * P + P * (H + K) * P) - @(obj20);\n# @collect_terms(%);\n# @assert(tst20);\n# \n# obj21:= { A*(B+C*(D+E)), F*(G+H*(I+J)) };\n# @distribute!2(%);\n# tst21:= { A*B + A*C*(D+E), F*G+F*H*(I+J) } - @(obj21);\n# @collect_terms!(%);\n# @assert(tst21);\n# \n\ndef test18():\n    __cdbkernel__=create_scope()\n    {\\chi, \\psi}::Weight(label=grassmann, value=1);\n    ex:= \\chi \\psi \\chi;\n    drop_weight(_, $grassmann=2$)\n    tst1:= \\chi\\psi\\chi - @(ex);\n    assert(tst1==0)\n    drop_weight(ex, $grassmann=3$)\n    assert(ex==0)\n    print(\"Test 18 passed\")\n        \ntest18()\n\ndef test19():\n    __cdbkernel__=create_scope()\n    {\\phi, B_{m}, B^{m}}::Weight(label=small, value=1).\n    ex:= H B^{m} B_{n} + B_{n} C^{m};\n    drop_weight(_, $small=2$)\n    tst:= B_{n} C^{m} - @(ex);\n    assert(tst==0)\n    print(\"Test 19 passed\")\n        \ntest19()\n\ndef test20():\n    __cdbkernel__=create_scope()\n    {\\phi, B_{m}, B^{m}}::Weight(label=small, value=1).\n    ex:= H B^{m} B_{n} + B_{n} C^{m};\n    keep_weight(_, $small=2$)\n    tst:= H B^{m} B_{n} - @(ex);\n    assert(tst==0)\n    print(\"Test 20 passed\")\n        \ntest20()\n\ndef test21():\n    __cdbkernel__=create_scope()\n    {\\chi, \\psi}::Weight(label=grassmann, value=1).\n    ex:= \\chi \\chi \\chi + 2 \\chi \\chi + \\chi;\n    drop_weight(_, $grassmann=3$)\n    tst:= 2 \\chi \\chi + \\chi - @(ex);\n    assert(tst==0)\n    print(\"Test 21 passed\")\n        \ntest21()\n\ndef test21b():\n    __cdbkernel__=create_scope()\n    {\\chi, \\psi}::Weight(label=grassmann, value=1).\n    ex:= \\chi \\chi \\chi + \\chi \\chi * (\\chi + \\psi) + \\chi + \\chi \\chi;\n    keep_weight(_, $grassmann=3$)\n    tst:= \\chi \\chi \\chi + \\chi \\chi * (\\chi + \\psi) - @(ex);\n    assert(tst==0)\n    print(\"Test 21b passed\")\n        \ntest21b()\n\ndef test22():\n    __cdbkernel__=create_scope()\n    {\\chi, \\psi}::Weight(label=grassmann, value=1).\n    \\bar{#}::Accent.\n    ex:= \\chi \\bar{\\chi \\chi};\n    keep_weight(_, $grassmann=3$)\n    tst:= \\chi \\bar{\\chi \\chi} - @(ex);\n    assert(tst==0)\n    print(\"Test 22 passed\")\n        \ntest22()\n\ndef test23():\n    __cdbkernel__=create_scope()\n    {a,b}::Weight(label=small, value=1);\n    ex:= a**2 + a b + b**2 + a**2 b + a b c;\n    keep_weight(_, $small=2$)\n    tst:= a**2 + a b + b**2 + a b c - @(ex);\n    assert(tst==0)\n    print(\"Test 23 passed\")\n        \ntest23()\n\ndef test24():\n    __cdbkernel__=create_scope()\n    \\theta::SelfAntiCommuting;\n    ex:= \\theta \\chi \\theta + \\theta \\chi \\lambda;\n    sort_product(_)\n    tst:= \\theta\\chi - @(ex);\n    assert(tst)\n    print(\"Test 24 passed\")\n        \ntest24()\n\ndef test25():\n    __cdbkernel__=create_scope()\n    {i,j,k}::Indices;\n    \\theta_i::SelfAntiCommuting;\n    ex:= \\theta_{k} \\theta_{j} \\theta_{k} \\theta_{j};\n    sort_product(_)\n    assert(ex==0)\n    print(\"Test 25 passed\")\n\ntest25()        \n\ndef test26():\n    __cdbkernel__=create_scope()\n    A = Ex(0)\n    B = Ex(0)\n    tst:= @(A) - @(B);\n    assert(tst==0)\n    A = Ex(0)\n    B = Ex(0)\n    tst:= @(A) + @(B);\n    assert(tst==0)\n    print(\"Test 26 passed\")\n\ntest26()\n\ndef test27():\n    __cdbkernel__=create_scope()\n    \\dagger::Symbol;\n    ex:= A^{\\dagger} A^{\\dagger};\n    collect_factors(_)\n    tst:= (A^{\\dagger})**2 - @(ex);\n    assert(tst==0)\n    print(\"Test 27a passed\")\n    ex:= B^{m} B^{m};\n    collect_factors(_)\n    tst:= B^{m} B^{m} - @(ex);\n    assert(tst==0)\n    print(\"Test 27b passed\")\n\ntest27()\n        \n  \n# \\bar{#}::Accent.\n# obj22e:= \\chi \\chi \\bar{\\chi};\n# @keep_weight!(%){grassmann}{3};\n# tst22e:= \\chi \\chi \\bar{\\chi} - @(obj22e);\n# @collect_terms!(%);\n# @assert(tst22e);\n# \n# @reset.\n# {a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u#}::Indices.\n# Q_{a b c}::Weight(label=myTerms,value=3).\n# g_{a b c}::Weight(label=myTerms,value=1).\n# obj22f:=Q_{f g h} Dx^{f} Dx^{g} Dx^{h};\n# @keep_weight!(%){myTerms}{3};\n# tst22f:=Q_{f g h} Dx^{f} Dx^{g} Dx^{h} - @(obj22f);\n# @collect_terms!(%);\n# @assert(tst22f);\n# \n# @reset.\n# {A,B}::Weight(label=field, value=1).\n# obj22g:= C + A + A B;\n# @keep_weight!(%){field}{2};\n# tst22g:= A B - @(obj22g);\n# @collect_terms!(%);\n# @assert(tst22g);\n# \n# @reset.\n# A::Weight(label=field, value=1).\n# B::Weight(label=field, value=-1).\n# obj22h:= C + A + A B;\n# @keep_weight!(%){field}{0};\n# tst22h:= C + A B - @(obj22h);\n# @collect_terms!(%);\n# @assert(tst22h);\n# \n# @reset.\n# A::Weight(label=field, value=3/2).\n# B::Weight(label=field, value=-1).\n# C::Weight(label=field, value=1/2).\n# obj22i:= C + A + A B;\n# @keep_weight!(%){field}{1/2};\n# tst22i:= C + A B - @(obj22i);\n# @collect_terms!(%);\n# @assert(tst22i);\n# \n# \n# # Test 23: spinor sort\n# #\n# @reset;\n# {\\chi, \\psi, \\psi_{m}}::Spinor(dimension=10, type=MajoranaWeyl).\n# {\\chi, \\psi, \\psi_{m}}::AntiCommuting.\n# \\bar{#}::DiracBar.\n# \\Gamma{#}::GammaMatrix.\n# {\\psi_{m}, \\psi, \\chi}::SortOrder.\n# obj23:= \\bar{\\chi} \\Gamma_{m n p} \\psi;\n# @spinorsort!(%);\n# tst23:= \\bar{\\psi} \\Gamma_{m n p} \\chi - @(obj23);\n# @collect_terms!(%);\n# @assert(tst23);\n# \n# obj24:= \\bar{\\chi}\\psi;\n# @spinorsort!(%);\n# tst24:= \\bar{\\psi}\\chi - @(obj24);\n# @collect_terms!(%);\n# @assert(tst24);\n# \n# obj25:= \\chi\\Gamma_{m n p}\\psi;\n# @spinorsort!(%);\n# tst25:= \\chi\\Gamma_{m n p}\\psi - @(obj25);\n# @collect_terms!(%);\n# @assert(tst25);\n# \n# obj26:= \\bar{\\chi} \\Gamma_{m n} \\psi_{m};\n# @spinorsort!(%);\n# tst26:= - \\bar{\\psi_{m}} \\Gamma_{m n} \\chi - @(obj26);\n# @collect_terms!(%);\n# @assert(tst26);\n# \n# # Test 27:= multiple implicitindex objects\n# #\n# @reset;\n# {\\chi,\\psi, \\lambda, \\rho}::Spinor.\n# \\Gamma{#}::GammaMatrix.\n# \\bar{#}::DiracBar.\n# obj27:= \\bar{\\chi}\\Gamma_{m n p}\\psi A_{m n} \\bar{\\lambda}\\Gamma_{p}\\rho;\n# @prodsort!(%);\n# @spinorsort!(%);\n# A_{m n} \\bar{\\chi} \\Gamma_{m n p} \\psi \\bar{\\lambda} \\Gamma_{p} \\rho;\n# \n# # Test 28: powers\n# @reset.\n# obj28:= 8 d**2 - d**3;\n# @collect_terms!(%);\n# @substitute!(%)( d**3 -> Q );\n# \n# tst28:= 8 d**2 - Q - @(obj28);\n# @collect_terms!(%);\n# @assert(tst28);\n# \n# # Test 28: sumsort\n# #\n# @reset.\n# {D,A,C,B}::SortOrder;\n# obj28:= A + B + C - D + B - A;\n# @sumsort!(%);\n# @rename!(%)(\"\\sum\")(\"\\comma\");\n# tst28:= {- D,  A, -A, C, B, B} - @(obj28);\n# @collect_terms!(%);\n# @assert(tst28);\n# \n# @reset.\n# obj29:= A + B + C - D + B - A;\n# @sumsort!(%);\n# @rename!(%)(\"\\sum\")(\"\\comma\");\n# tst29:= { A, -A, B, B, C, -D } - @(obj29);\n# @collect_terms!(%);\n# @assert(tst29);\n# \n# @reset.\n# obj30:= a**{-1+d}-a**{d-1};\n# @sumsort!(%);\n# @collect_terms!(%);\n# @assert(obj30);\n# \n# # Test 31: commutativity properties\n# #\n# @reset.\n# {\\sigma_{1},\\sigma_{2},\\sigma_{3}}::NonCommuting.\n# obj31:= \\sigma_{2}\\sigma_{1};\n# @prodsort!(%);\n# tst31:= \\sigma_{2}\\sigma_{1} - @(obj31);\n# @collect_terms!(%);\n# @assert(tst31);\n# \n# @reset.\n# \\sigma{#}::SelfNonCommuting.\n# obj32:= \\sigma_{2}\\sigma_{1};\n# @prodsort!(%);\n# tst32:= \\sigma_{2}\\sigma_{1} - @(obj32);\n# @collect_terms!(%);\n# @assert(tst32);\n# \n\n# Test 32: more drop & keep\ndef test32a():\n    __cdbkernel__=create_scope()\n    {\\phi,\\chi}::Weight(label=small, value=1).\n    \\partial{#}::PartialDerivative.\n    \\partial{#}::WeightInherit(label=all, type=multiplicative).\n    obj:= \\phi \\partial_{0}{\\phi} + \\partial_{0}{\\lambda};\n    drop_weight(obj, $small=1$)\n    tst:= \\phi \\partial_{0}{\\phi} + \\partial_{0}{\\lambda} - @(obj);\n    assert(tst==0)\n    print(\"Test 32a passed\")\n\ntest32a()\n\ndef test32b():\n    __cdbkernel__=create_scope()\n    {\\phi,\\chi}::Weight(label=small, value=1).\n    \\lambda::Weight(label=small, value=3).\n    obj:= \\phi \\chi + \\lambda;\n    drop_weight(obj, $small=2$)\n    tst:= \\lambda - @(obj);\n    assert(tst==0)\n    print(\"Test 32b passed\")\n\ntest32b()\n        \ndef test32c():\n    __cdbkernel__=create_scope()\n    {\\phi,\\chi}::Weight(label=small, value=2).\n    \\lambda::Weight(label=small, value=2).\n    obj:= Q ( \\phi \\chi + \\lambda ) + ( \\phi + \\chi );\n    #           4          2           2       2\n    #             undefined                2\n    drop_weight(obj, $small=2$)\n    tst:= Q ( \\phi \\chi + \\lambda ) - @(obj);\n    assert(tst==0)\n    print(\"Test 32c passed\")\n\ntest32c()\n\n# # Test34: canonicalorder\n# #\n# @reset.\n# obj34:= A_{a b c} + A_{b a c};\n# @acanonicalorder!(%)(_{a}, _{b});\n# @collect_terms!(%);\n# @assert(obj34);\n# \n# # Test 35: keep current expression pointer consistent\n# #\n# @reset.\n# obj35a:= A B + B Q;\n# obj35b:= { A -> Z };\n# vary(obj35a, $Q -> Z$)\n# substitute(_, obj35b)\n# tst35:= B Z - @(%);\n# @collect_terms!(%);\n# @assert(tst35);\n# \n\n# Test 36: two sets of anti-commuting objects\ndef test36():\n    __cdbkernel__=create_scope()\n    {a,b}::AntiCommuting.\n    {a,c}::AntiCommuting.\n    obj36:= b*a;\n    sort_product(_)\n    tst36:= - a b - @(obj36);\n    assert(tst36==0)\n    print(\"Test 36 passed\")\n\ntest36()\n\n# # Test 37: weight inheritance\n# #\n# @reset.\n# D{#}::Derivative.\n# {a,b,c}::Symbol.\n# {a,b,c}::Weight(label=grassmann, value=1).\n# D_{a}( b c ) + D_{c}( d e );\n# @keep_weight!(%){grassmann}{3};\n# \n\n# Test 38: stupid nested expression bug\n\ndef test36():\n    __cdbkernel__=create_scope()\n    obj37:= A - ( B - ( C - ( D - E ) ) );\n    tst38:= A - B + C - D + E - @(obj37);\n    assert(tst38==0)\n    print(\"Test 38 passed\")\n\ntest36()\n\ndef test28():\n    ex:=k^{a}n_{c a}+2**{1/2} k_{c} 2**{1/2};\n    collect_factors(_)\n    tst:=k^{a}n_{c a}+2**{1/2} k_{c} 2**{1/2} - @(ex);\n    assert(tst==0)\n    print(\"Test 28 passed\")\n\ntest28()\n\ndef test29():\n    __cdbkernel__=create_scope()\n    {a,ad, ket{#}}::NonCommuting;\n    ex:= ad ad ad ket(0);\n    substitute(ex, $ad ket(n??) = \\sqrt{n?? +1} ket(n??+1) $)\n    tst:= ad ad ket(1) - @(ex);\n    assert(tst==0)\n    print(\"Test 29 passed\")\n\ntest29()\n\ndef test30():\n    __cdbkernel__=create_scope()\n    t::Coordinate;\n    a::Depends(t);\n    \\partial{#}::PartialDerivative;\n    ex:= (\\partial_{t}{a})**(-1)  (\\partial_{t}{a})**3;\n    collect_factors(ex)\n    tst:= (\\partial_{t}{a})**2 - @(ex);\n    assert(tst==0)\n    print(\"Test 30 passed\")\n\ntest30()\n\ndef test31():\n    __cdbkernel__=create_scope()\n    {A,B,C}::AntiCommuting.\n    \\partial{#}::Derivative.\n    {F,G,H}::Depends(\\partial{#}).\n    ex := \\partial{(A F + G) C};\n    unwrap(ex)\n    tst:= \\partial{(A F + G) C} - @(ex);\n    assert(tst==0)\n    print(\"Test 31a passed\")\n    ex := \\partial{(A F + B G) C};\n    unwrap(ex)\n    tst:= -C \\partial{A F + B G} - @(ex);\n    assert(tst==0)\n    print(\"Test 31b passed\")\n\ntest31()\n\ndef test32():\n    # issues/106\n    __cdbkernel__=create_scope()  \n    {A, B, C}::AntiCommuting.\n    d{#}::Derivative.\n    A::Depends(d{#}).\n    B::Depends(d{#}).\n    ex:= d{A B C};\n    unwrap(ex)\n    tst:= C d{A B} - @(ex);\n    assert(tst==0)\n    print(\"Test 32a passed\")\n    ex:= d{A B A C};\n    unwrap(ex)\n    tst:= - C d{A B A} - @(ex);\n    assert(tst==0)\n    print(\"Test 32b passed\")\n\ntest32()\n        \ndef test33():\n    __cdbkernel__=create_scope()  \n    {\\phi,\\chi}::Weight(label=small, value=2).\n    ex:= \\chi\\chi + \\phi = \\phi + \\chi;\n    keep_weight(ex, $small=2$, deep=True)    \n    tst:= (\\phi = \\phi + \\chi) - @(ex);\n    assert(tst==$0=0$)\n    print(\"Test 33 passed\")\n\ntest33()\n        \n# {A, B, C}::AntiCommuting.\n# d{#}::Derivative.\n# A::Depends(d{#}).\n# B::Depends(d{#}).\n# ex:= d_{B}{A B C};\n# unwrap(ex)\n\n# {A,B,C,D,E,F}::NonCommuting;\n# ex:= A * (B + C) * D * (E + F);\n# distribute(_);\n\ndef test34():        \n    __cdbkernel__=create_scope()  \n    ex:= [1,2,3,4];\n    tst:= -3/2 @(ex);\n    assert(tst==$[-3/2, -3, -9/2, -6]$)\n    print(\"Test 34 passed\")\n\ntest34()\n\ndef test35():\n    __cdbkernel__=create_scope()  \n    ex:= 3 a**b;\n    substitute(ex, $b -> 1$)\n    assert( ex == $3 a$ )\n    print(\"Test 35a passed\")\n    ex:= 3 2**b;\n    substitute(ex, $b -> 1$)\n    assert( ex == $6$ )\n    print(\"Test 35b passed\")\n        \n\ntest35()\n\n\ndef test36():\n    __cdbkernel__=create_scope()  \n    ex:= (2 a 3 b c)**(-1);\n    expand_power(ex)\n    tst:= 1/6 a**(-1) b**(-1) c**(-1)  - @(ex);\n    assert(tst==0)\n    print(\"Test 36a passed\")\n    ex:= (2 a 3 b c)**(-2);\n    expand_power(ex)\n    tst:= 1/36 a**(-1) b**(-1) c**(-1)  a**(-1) b**(-1) c**(-1) - @(ex);\n    assert(tst==0)\n    print(\"Test 36b passed\")\n    ex:= a**(-1);\n    expand_power(_)\n    tst:= a**(-1) - @(ex);\n    assert(tst==0)        \n    print(\"Test 36c passed\")\n    ex:= a**(-2);\n    expand_power(_)\n    tst:= a**(-1) a**(-1) - @(ex);\n    assert(tst==0)        \n    print(\"Test 36d passed\")\n    ex:= a b c (a b c)**(-1);\n    expand_power(_)\n    collect_factors(_)\n    assert(ex==1)\n    print(\"Test 36e passed\")\n    ex:= a**0;\n    expand_power(_)\n    assert(ex==1)\n    print(\"Test 36f passed\")\n\ntest36()\n        \ndef test37():\n    __cdbkernel__=create_scope()  \n    {A,X,Y}::AntiCommuting.\n    ex := X A X;\n    collect_factors(ex)\n    tst:= - X**2 A - @(ex);\n    assert(tst==0)\n    print(\"Test 37a passed\")\n    ex := X A Y X;\n    collect_factors(ex);\n    tst:= X**2 A Y - @(ex);\n    assert(tst==0)\n    print(\"Test 37b passed\")\n    ex := X A Y X Y;\n    collect_factors(ex);\n    tst:= X**2 A Y**2 - @(ex);\n    assert(tst==0)\n    print(\"Test 37c passed\")\n\n# The following does *not* yet work.\n# ex:= X A**3 X;\n# collect_factors(ex);\n# tst:= - X**2 A**3 - @(ex);\n# assert(tst==0)\n# print(\"Test 37d passed\")\n\ntest37()\n"
  },
  {
    "path": "tests/basic.cdb",
    "content": "def test06():\n    __cdbkernel__=create_scope()\n    {X,G,Y,A,B}::SortOrder.\n    {X,A}::AntiCommuting.\n    obj6:= A B G X A X;\n    sort_product(obj6)\n    tst6:= X X G A A B + @(obj6);\n    collect_terms(_)\n    assert(tst6==0)\n    print('test06 passed')\n\ntest06()\n\ndef test07():\n    __cdbkernel__=create_scope()\n    {X,G,Y,A,B}::SortOrder.\n    {X,A}::NonCommuting.\n    obj7:= A*B*G*X*A*X;\n    sort_product(_)\n    tst7:= G A X A X B - @(obj7);\n    collect_terms(_)\n    assert(tst7==0)\n    print('test07 passed')\n\ntest07()\n\ndef test08():\n    __cdbkernel__=create_scope()\n    { W_{m n}, W_{m} }::SortOrder.\n    { W_{m n}, W_{m} }::AntiCommuting.\n    obj8:= W_{m n} W_{p} W_{q r} W_{s} W_{t};\n    sort_product(_)\n    tst8:= - W_{m n} W_{q r} W_{p} W_{s} W_{t} - @(obj8);\n    collect_terms(_)\n    assert(tst8==0)\n    print('test08 passed')\n\ntest08()\n\ndef test09():\n    __cdbkernel__=create_scope()\n    { \\theta_a, \\theta_b }::SelfAntiCommuting.\n    obj9:= \\theta_c \\theta_b \\theta_a;\n    sort_product(_)\n    tst9:= \\theta_a \\theta_b \\theta_c + @(obj9);\n    assert(tst9==0)\n    print('test09 passed')\n\ntest09()\n\ndef test10():\n    __cdbkernel__=create_scope()\n    {a,b,c,d}::Indices.\n    { \\theta_a, \\chi_a }::Commuting.\n    {\\theta_{a}, \\theta_{b}}::SelfAntiCommuting.\n    {\\chi_{a},\\chi_{b}}::SelfAntiCommuting.\n    { \\theta_a, \\chi_a }::SortOrder.\n    obj10:= \\theta_c \\theta_b \\theta_d \\chi_d \\theta_a \\chi_a;\n    sort_product(_)\n    tst10:= \\theta_a \\theta_b \\theta_c \\theta_d \\chi_a \\chi_d + @(obj10);\n    assert(tst10==0)\n    print('test10 passed')\n\ntest10()\n\ndef test12():\n    __cdbkernel__=create_scope()\n    \\bar{#}::Accent.\n    {D,K,B,A}::SortOrder.\n    obj12:= A \\bar{B} \\bar{K} D;\n    sort_product(_)\n    tst12:= D \\bar{K} \\bar{B} A - @(obj12);\n    collect_terms(_)\n    assert(tst12==0)\n    print('test12 passed')\n\ntest12()\n\ndef test16():\n    __cdbkernel__=create_scope()\n    {A_\\mu, B_\\mu}::AntiCommuting.\n    \\diff{#}::Derivative.\n    obj16:= \\diff{B_\\mu}_{\\nu} * \\diff{A_\\rho}_{\\sigma};\n    sort_product(_)\n    tst16:= \\diff{A_\\rho}_{\\sigma} * \\diff{B_\\mu}_{\\nu} + @(obj16);\n    collect_terms(_)\n    assert(tst16==0)\n    print('test16 passed')\n\ntest16()\n\ndef test16b():\n    __cdbkernel__=create_scope()\n    ex:= C A D B;\n    sort_product(_);\n    tst:= A B C D - @(ex);\n    assert(tst==0)\n    print(\"Test 16b passed\")\n\ndef test17():\n    __cdbkernel__=create_scope()\n    \\Gamma{#}::GammaMatrix.\n    obj17a:= (\\Gamma_{m n} + A_{m} \\Gamma_{n})\\Gamma_{p q r};\n    sort_product(_)\n    tst17a:= (\\Gamma_{m n} + A_{m} \\Gamma_{n})\\Gamma_{p q r} - @(obj17a);\n    assert(tst17a==0)\n    obj17b:= \\Gamma_{p q r} (\\Gamma_{m n} + A_{m} \\Gamma_{n});\n    sort_product(_)\n    tst17b:= \\Gamma_{p q r} (\\Gamma_{m n} + A_{m} \\Gamma_{n}) - @(obj17b);\n    assert(tst17b==0)\n    print('test17 passed')\n\ntest17()\n\ndef test18():\n    __cdbkernel__=create_scope()\n    {\\psi, \\chi}::Spinor.\n    {\\psi, \\chi, \\Gamma_{#}}::NonCommuting.\n    \\Gamma_{#}::GammaMatrix.\n    {\\chi,\\psi}::SortOrder.\n    \\bar{#}::Accent.\n    obj18:= \\bar{\\psi} \\Gamma_{m n p} \\chi;\n    sort_product(_)\n    tst18:= \\bar{\\psi} \\Gamma_{m n p} \\chi - @(obj18);\n    collect_terms(_)\n    assert(tst18==0)\n    print('test18 passed')\n\ntest18()\n\ndef test22():\n    __cdbkernel__=create_scope()\n    {\\chi, \\psi}::Weight(label=grassmann, value=1).\n    tst22a:= \\chi \\psi \\chi;\n    #drop_weight(_, grassmann=3)\n\ntest22()\n\ndef test23():\n    __cdbkernel__=create_scope()\n    \\nabla{#}::Derivative.\n    ex:=\\nabla_{i}{ C D E };\n    substitute(_, $D->0$)\n    assert(ex==0)\n    print(\"Test 23 passed\")\n    \ntest23()\n\ndef test24():\n    __cdbkernel__=create_scope()\n    {s,r,l,k,m,n}::Indices(vector).\n    {s,r,l,k,m,n}::Integer(0..d-1).\n    \\Gamma{#}::GammaMatrix(metric=\\delta).\n    \\delta_{m n}::KroneckerDelta.\n    obj:= \\Gamma_{l r} \\Gamma_{k s} q \\Gamma_{r s} + \\Gamma_{l r} d \\Gamma_{k s} \\Gamma_{r s};\n    sort_product(_)\n    tst:= \\Gamma_{l r} \\Gamma_{k s} \\Gamma_{r s} q + \\Gamma_{l r} \\Gamma_{k s} \\Gamma_{r s} d - @(obj);\n    assert(tst==0)\n    print('Test 24 passed')\n\ntest24()\n\ndef test25():\n    __cdbkernel__=create_scope()\n    ex:=(a*d+b)*c;\n    distribute(_)\n    tst:= a d c + b c - @(ex);\n    assert(tst==0)\n    print('Test 25 passed')\n\ntest25()\n\ndef test26():\n    __cdbkernel__=create_scope()\n    # This example shows that indices can match to integers\n    # provided you declare them a such. You need to declare\n    # m,n as Symbol otherwise you cannot write one term with\n    # an 'n' index and another one with a '-n' index.\n    {m,n}::Integer.\n    {m,n}::Symbol.\n    ex:= a_{1} a_{0} a_{-1};\n    rl:= a_{n} a_{m} = a_{m} a_{n} + m \\delta_{m}_{-n};\n    substitute(ex, rl)\n    tst:= a_{0} a_{1} a_{-1} - @(ex);\n    assert(tst==0)\n    print(\"Test 26 passed\")\n    \ntest26()\n\ndef test27():\n    __cdbkernel__=create_scope()\n    ex:=A;\n    ex2:= @(ex)^{\\mu\\nu};\n    tst:=A^{\\mu\\nu} - @(ex2);\n    assert(tst==0)\n    print(\"Test 27 passed\")\n\ntest27()\n\ndef test28():\n    __cdbkernel__=create_scope()\n    ex:=A+B;\n    ex2:= @(ex)^{\\mu\\nu};\n    tst:=(A+B)^{\\mu\\nu} - @(ex2);\n    assert(tst==0)\n    print(\"Test 28 passed\")\n\ntest28()\n\n# def post_process(ex):\n# \tsort_product(ex)\n# \t#canonicalise(ex)\n# \tcollect_terms(ex)\n\n{\\mu,\\nu,\\rho}::Indices(position=free).\nx::Coordinate.\n\\partial{#}::Derivative.\n\nF_{\\mu\\nu}::AntiSymmetric.\nF_{\\mu\\nu}::Depends(x).\nA_{\\mu}::Depends(x,\\partial{#}).\n\\delta{#}::Accent.\n\nS:= -1/4 \\int{ F_{\\mu\\nu} F^{\\mu\\nu} }{x};\nrl:= F_{\\mu\\nu} = \\partial_{\\mu}{A_{\\nu}} - \\partial_{\\nu}{A_{\\mu}};\nsubstitute(S, rl);\nvary(S, $A_{\\mu} -> \\delta{A_{\\mu}}$);\ndistribute(S);\n\n\ndef test30():\n    __cdbkernel__=create_scope()\n    # Matching of numerical values in expressions to indices in patterns\n    # should respect index position.\n    {m,n}::Indices(position=fixed);\n    {m,n}::Integer(0..3).\n    g_{m}^{n}::KroneckerDelta;\n    ex:= g^{0 0};\n    ex:= 1 + g_{0}^{0};\n    ex:= g^{0 0} + g_{0}^{0};\n    substitute(_, $g^{a? b?} -> h^{a? b?}$)\n    tst:= h^{0 0} + 1 - @(ex);\n    assert(tst==0)\n\ntest30()\n\n\ndef test31():\n    __cdbkernel__=create_scope()\n    {m,n}::Indices(position=fixed);\n    {m,n}::Integer(0..3).\n    g_{m}^{n}::KroneckerDelta;\n    g_{m n}::Metric;\n    ex:= g_{0 0} + g_{0}^{0};\n    substitute(_, $g_{m n} = h_{m n}$)\n    tst:= h_{0 0} + 1 - @(ex);\n    assert(tst==0)\n    print(\"Test 31 passed\")\n\ntest31()\n\ndef test32():\n    __cdbkernel__=create_scope()\n    {m,n}::Indices(position=fixed);\n    ex1:= A_{m} A^{m};\n    try:\n        ex2:= A_{m} A_{m};\n        assert(1==0)\n    except:\n        print('Test 32 passed')\n\ntest32()\n\ndef test33():\n    __cdbkernel__=create_scope()\n    {m,n}::Indices(position=fixed);\n    try:\n        ex:= A_{m n} + A_{m};\n        assert(1==0)\n    except:\n        print('Test 33 passed')\n\ntest33()\n\ndef test34():\n    __cdbkernel__=create_scope()\n    {m,n}::Indices(position=fixed);\n    try:\n        ex:= A_{m n} A^{m} B_{m};\n        assert(1==0)\n    except:\n        print('Test 34 passed')\n\ntest34()\n\ndef test35():\n    __cdbkernel__=create_scope()\n    {\\del{#}, \\delbar{#}}::PartialDerivative.\n    {\\Psi_{\\mu}, \\Psibar_{\\mu}, \\eps, \\epsbar}::AntiCommuting;\n    {\\Psi_{\\mu}, \\Psibar_{\\mu}}::SelfAntiCommuting;\n    {\\Psi_{\\mu}, \\Psibar_{\\mu}, X_{\\mu}}::Depends(\\del{#}, \\delbar{#});\n    {i, \\Psi_\\mu, \\Psibar_\\mu, \\eps, \\epsbar, X_\\mu}::SortOrder;\n    ex:= i\\epsbar\\del{\\Psi_{\\mu}} \\delbar{X_{\\mu}};\n    sort_product(_)\n    tst:= -i\\del{\\Psi_{\\mu}} \\epsbar \\delbar{X_{\\mu}} - @(ex);\n    assert(tst==0)\n    print(\"Test 35 passed\")\n    \ntest35()\n\ndef test36():\n    __cdbkernel__=create_scope()\n    {a,b,c,d,e}::Indices;\n    x^{a}::Weight(label=field);\n    ex:= x^{a} + A_{b} x^{a} x^{b} + A_{b c} x^{a} x^{b} x^{c};\n    keep_weight(_, $field=2$);\n    tst:= A_{b} x^{a} x^{b} - @(ex);\n    assert(tst==0)\n    print(\"Test 36 passed\")\n\ntest36()\n\ndef test37():\n    __cdbkernel__=create_scope()\n    {a,b,c,d,e}::Indices;\n    x1^{a}::Weight(label=field);\n    ex:= x1^{a} + A_{b} x1^{a} x1^{b} + A_{b c} x1^{a} x1^{b} x1^{c};\n    keep_weight(_, $field=2$);\n    tst:= A_{b} x1^{a} x1^{b} - @(ex);\n    assert(tst==0)\n    print(\"Test 37 passed\")\n\ntest37()\n\ndef test38():\n    __cdbkernel__=create_scope()\n    ex1:= a+b = c+e;\n    ex2:= g+h = c;\n    ex:= 3 @(ex1) - 2 @(ex2);\n    assert(lhs(ex)==$3a + 3b - 2g - 2h$)\n    assert(rhs(ex)==$c + 3e$)\n    print(\"Test 38 passed\")\n\ntest38()\n\ndef test39():\n    __cdbkernel__=create_scope()\n    A#_{a b c}::AntiSymmetric;\n    tst:=A1_{a b c} + A1_{a c b};\n    canonicalise(_)\n    assert(tst==0)\n    print(\"Test 39 passed\")\n\ntest39()\n        \ndef test40():\n    __cdbkernel__=create_scope()\n    {a,b,c,d,e,f,g,h}::Indices(position=independent);\n    T#^{a b c}_{e f}::TableauSymmetry(shape={1,1}, indices={3,4});\n    ex:=T1^{a b c}_{e f} T2^{e f g}_{h i} - T1^{a b c}_{e f} T2^{f e g}_{h i};\n    canonicalise(ex)\n    tst:=2 T1^{a b c}_{e f} T2^{e f g}_{h i} - @(ex);\n    assert(tst==0)\n    print(\"Test 40 passed\")\n\ntest40()\n\ndef test41():\n    __cdbkernel__=create_scope()\n    ex:= -a**2;\n    substitute(ex, $a -> -b$)\n    tst:= -b**2 - @(ex);\n    assert(tst==0)\n    print(\"Test 41 passed\")\n\ntest41()\n\ndef test42():\n    try:\n       ex:=\\\\bla;\n       print(\"The above should have triggered a RuntimeError\")\n       assert(1==0)\n    except RuntimeError as ex:\n       print(\"Test 42a passed\")\n\n    try:\n       ex:= A + 1\\\n                ;\n       print(\"The above should have triggered a RuntimeError\")\n       assert(1==0)\n    except RuntimeError as ex:\n       print(\"Test 42b passed\")\n\ntest42()\n\ndef test43():\n    ex:=\\partial_\\theta{A};\n    tst:= \\partial_{\\theta}{A} - @(ex);\n    assert(tst==0)\n    print(\"Test 43 passed\")\n\ntest43()\n\n    \n"
  },
  {
    "path": "tests/callbacks.cdb",
    "content": "\n# Testing of calling back on Python routines from C++.\n\ndef fun(e):\n    print(\"received:    \"+str(e))\n    distribute(e, repeat=True)\n    print(\"turned into: \"+str(e))\n\n\\prod{#}::Distributable.\na:=A*(B+C)\n\ncallback(a)\ncallback(a, fun)\ncallback(callback=fun, ex=a)\ncallback(a, callback=fun)\n\nspl = split_terms(a)\nfor t in spl:\n\t print \"term \"+str(t)\n\n"
  },
  {
    "path": "tests/canonicalise.cdb",
    "content": "# Testing the automatic canonicalisation routines.\n\n# Simple tests with symmetric/anti-symmetric tensors, all \n# expressions vanishing identically by symmetry arguments.\n\ndef test01():\n   __cdbkernel__=create_scope()\n   a_{#}::AntiSymmetric;\n   s_{#}::Symmetric;\n   tst1:= a_{m n} s_{m n};\n   canonicalise(tst1)\n   assert(tst1==0)\n   tst2:= a_{n m q} s_{m n};\n   canonicalise(tst2)\n   assert(tst2==0)\n   tst3:= a_{m m};\n   canonicalise(tst3)\n   assert(tst3==0)\n   print('Test 01 passed')\n\ntest01()\n\ndef test02():\n   __cdbkernel__=create_scope()\n   a_{#}::AntiSymmetric;\n   s_{#}::Symmetric;\n   obj4:= s_{m n m n};\n   canonicalise(obj4)\n   tst4:= s_{m m n n}-@(obj4);\n   collect_terms(tst4)\n   assert(tst4==0)\n   print('Test 02 passed')\n   \ntest02()\n\n# Tests with more complicated tableau symmetries.\n\ndef test03():\n   __cdbkernel__=create_scope()\n   s_{#}::Symmetric;\n   R_{m n p q}::RiemannTensor;\n   tst5:= R_{m n p q}*s_{p q}*t_{m n};\n   canonicalise(tst5)\n   assert(tst5==0)\n   print('Test 03 passed')\n   \ntest03()\n\ndef test04():\n   __cdbkernel__=create_scope()\n   dW_{m n p q r s}::TableauSymmetry(shape={2,2}, indices={2,3,4,5}).\n   rtopen:= dW_{a b r3 r4 r1 r2}*q;\n   canonicalise(rtopen)\n   rtopentest:= dW_{a b r1 r2 r3 r4}*q - @(rtopen);\n   collect_terms(rtopentest)\n   assert(rtopentest==0)\n   print('Test 04 passed')\n   \ntest04()\n\n# Here, the fact that the 'second' field of the index contractions involving 'a'\n# are compared _before_ the one of the 'b' leads to a sorting in which the first\n# form is preferred:\n\ndef test05():\n   __cdbkernel__=create_scope()\n   a2_{#}::AntiSymmetric;\n   R_{m n p q}::RiemannTensor;\n   obj6a:= R_{m n p q} a_{m n} a2_{p q};\n   obj6b:= R_{m n p q} a_{p q} a2_{m n};\n   canonicalise(obj6a)\n   canonicalise(obj6b)\n   tst6:= @(obj6a)-@(obj6b);\n   collect_terms(tst6)\n   assert(tst6==0)\n   print('Test 05 passed')\n   \ntest05()\n\n# The key test that inspired it all:\n\ndef test06():\n    __cdbkernel__=create_scope()\n    F_{#}::AntiSymmetric;\n    G_{#}::AntiSymmetric;\n    R_{m n p q}::RiemannTensor;\n    tst7:= R_{d1 d2 d3 d4} R_{d4 d5 d6 d7} F_{d1 d2 d6 d7} G_{d3 d5 r5 s5};\n    canonicalise(tst7)\n    assert(tst7==0)\n    print('Test 06 passed')\n\ntest06()\n\n# A more complicated preferred-form case. The algorithm should be stable,\n# that is, it should give the same result independent of which representative\n# is chosen as input. \n\ndef test07():\n   __cdbkernel__=create_scope()\n   H_{#}::Symmetric;\n   F_{#}::AntiSymmetric;\n   R_{m n p q}::RiemannTensor;\n   obj8a:=   R_{d1 d2 d3 d4} R_{d6 d7 d4 d5} F_{d1 d2 d6 d7} H_{d3 d5 r5 s5};\n   obj8b:=   R_{d1 d2 d3 d4} R_{d4 d5 d6 d7} F_{d1 d2 d6 d7} H_{d3 d5 r5 s5};\n   obj8c:= - R_{d1 d2 d3 d4} R_{d5 d4 d6 d7} F_{d1 d2 d6 d7} H_{d3 d5 r5 s5};\n   obj8d:= - R_{d3 d4 d1 d2} R_{d5 d4 d6 d7} F_{d1 d2 d6 d7} H_{d3 d5 r5 s5};\n   canonicalise(obj8a)\n   canonicalise(obj8b)\n   canonicalise(obj8c)\n   canonicalise(obj8d)\n   tst8b:= @(obj8a)-@(obj8b);\n   collect_terms(_)\n   assert(tst8b==0)\n   tst8c:= @(obj8a)-@(obj8c);\n   collect_terms(_)\n   assert(tst8c==0)\n   tst8d:= @(obj8a)-@(obj8d);\n   collect_terms(_)\n   assert(tst8d==0)\n   print('Test 07 passed')\n   \ntest07()\n\n\n# Interchange with more than two identical objects. Note that this\n# does not require sort_product.\n\ndef test08():\n   __cdbkernel__=create_scope()\n   obj9a:= A_{m n p} A_{m n p} A_{r s t} A_{r s t};\n   obj9b:= A_{m n p} A_{r s t} A_{r s t} A_{m n p};\n   tst9:= @(obj9a)-@(obj9b);\n   canonicalise(_)\n   collect_terms(_)\n   assert(tst9==0)\n   print('Test 08 passed')\n   \ntest08()\n\n# Another one along the lines of the above.\n\ndef test10():\n   __cdbkernel__=create_scope()\n   a_{#}::AntiSymmetric;\n   s_{#}::Symmetric;\n   tst1:= a_{m n} s_{m n};\n   canonicalise(tst1)\n   assert(tst1==0)\n   tst2:= a_{n m q} s_{m n};\n   canonicalise(tst2)\n   assert(tst2==0)\n   tst3:= a_{m m};\n   canonicalise(tst3)\n   assert(tst3==0)\n   print('Test 10 passed')\n   \ntest10()\n\ndef test11():\n   __cdbkernel__=create_scope()\n   a_{#}::AntiSymmetric;\n   s_{#}::Symmetric;\n   obj4:= s_{m n m n};\n   canonicalise(obj4)\n   tst4:= s_{m m n n}-@(obj4);\n   assert(tst4==0)\n   print('Test 11 passed')\n   \ntest11()\n\n\n# Portugal's non-trivial fifth-order zero:\n\ndef test12():\n   __cdbkernel__=create_scope()\n   R_{m n p q}::RiemannTensor.\n   tst11:= R_{a b c d} R_{e f k h} R_{i a j e} R_{b c d i} R_{f k h j};\n   canonicalise(_)\n   assert(tst11==0)\n   print('Test 12 passed')\n   \ntest12()\n\n# Further tests of the same.\n\ndef test13():\n   __cdbkernel__=create_scope()\n   zeta_{m n}::Symmetric;\n   tst12:= k_a k_b zeta_{a b} - k_b k_a zeta_{a b};\n   canonicalise(_)\n   collect_terms(_)\n   assert(tst12==0)\n   print('Test 13 passed')\n   \ntest13()\n\n# This one used to trigger a bug with triple indices.\n\ndef test13b():\n   __cdbkernel__=create_scope()\n   obj13:= A_{a} * A_{a} * A_{b};\n   canonicalise(_)\n   tst13:= A_{b} A_{a} A_{a} - @(obj13);\n   collect_terms(_)\n   assert(tst13==0)\n   print('Test 13b passed')\n   \ntest13b()\n\n# Another one which at one time produced triple indices.\n\ndef test14():\n   __cdbkernel__=create_scope()\n   obj14:= C1_{d5} *k3_{d6} * k3_{d6} * k3_{d5};\n   canonicalise(_)\n   tst14:= C1_{d5} *k3_{d5} * k3_{d6} * k3_{d6} - @(obj14);\n   collect_terms(_)\n   assert(tst14==0)\n   print('Test 14 passed')\n   \ntest14()\n\n# More complicated Young tableau symmetries.\n\ndef test15():\n   __cdbkernel__=create_scope()\n   A_{a b c d}::TableauSymmetry(shape={1,1}, indices={1,2});\n   obj15:= q*A_{d c b a};\n   canonicalise(_)\n   tst15:= q A_{d b c a} + @(obj15);\n   collect_terms(_)\n   assert(tst15==0)\n   print('Test 15 passed')\n   \ntest15()\n\n# DAntiSymmetric is of course just a special case of TableauSymmetry\n# but we still need tests.\n\ndef test16():\n   __cdbkernel__=create_scope()\n   dF5_{a b c d e f}::DAntiSymmetric.\n   obj16:= dF5_{m n p q r s} AA_{r n q m s p};\n   canonicalise(_)\n   tst16:= -dF5_{m n p q r s} * AA_{n p q m r s} - @(obj16);\n   collect_terms(_)\n   assert(tst16==0)\n   print('Test 16 passed')\n   \ntest16()\n\n# def test17():\n# dF5_{a b c d e f}::DAntiSymmetric.\n# obj17:= dF5_{b1 a5 a4 a3 a2 a1} * q;\n# @indexsort(_)\n# tst17:= dF5_{b1 a1 a2 a3 a4 a5} * q - @(obj17)\n# collect_terms(_)\n# assert(tst17)\n# \n\n# Multiple tableaux.\n#\ndef test18():\n   __cdbkernel__=create_scope()\n   tt_{a b c d e f}::TableauSymmetry(shape={1,1,1,1}, indices={2,3,4,5}, shape={2}, indices={0,1}).\n   obj18:= tt_{a2 a1 a7 a6 a4 a5}*a;\n   canonicalise(_)\n   tst18:= tt_{a1 a2 a4 a5 a6 a7}*a + @(obj18);\n   collect_terms(_)\n   assert(tst18==0)\n   print('Test 18 passed')\n   \ntest18()\n\n# An old bug with KroneckerDelta; this could only be fixed properly\n# when the 'canonicalise' routine was rewritten to only use\n# TableauBase input (rather than hardcoded DAntiSymmetric and so on).\n#\ndef test19():\n   __cdbkernel__=create_scope()\n   \\delta_{a b}::KroneckerDelta.\n   obj19:= a \\delta_{c b};\n   canonicalise(_)\n   tst19:= a \\delta_{b c} - @(obj19);\n   collect_terms(_)\n   assert(tst19==0)\n   print('Test 19 passed')\n   \ntest19()\n\n# Partial derivatives next.\n\ndef test20():\n   __cdbkernel__=create_scope()\n   \\diff{#}::PartialDerivative.\n   B_{m n}::Symmetric.\n   obj20:= \\diff{A_{m}}_{n} B_{n m} - \\diff{A_{m}}_{n} B_{m n};\n   canonicalise(_)\n   collect_terms(_)\n   assert(obj20==0)\n   print('Test 20 passed')\n\ntest20()\n\n# \\diff{#}::PartialDerivative.\n# {m,n,p,q,r,s,t}::Indices(vector).\n# obj21:= \\diff{A_{m n p}}_{q r} C_{r q} - \\diff{A_{m n p}}_{q r} C_{q r};\n# @indexsort(_)\n# canonicalise(_)\n# @rename_dummies(_)\n# collect_terms(_)\n# assert(obj21)\n\n# This one used to crash:\n\ndef test22():\n   __cdbkernel__=create_scope()\n   \\diff{#}::PartialDerivative.\n   {m, n, p}::Indices(position=fixed).\n   g3_{m n}::Metric.\n   obj22:= \\diff{\\phi}_{p} * \\diff{g3_{m m1}}_{n};\n   canonicalise(_)\n   tst22:= \\diff{\\phi}_{p} * \\diff{g3_{m m1}}_{n} - @(obj22);\n   collect_terms(_)\n   assert(tst22==0)\n   print('Test 22 passed')\n   \ntest22()\n\n# Including symmetries of the argument tensor:\n\ndef test23():\n   __cdbkernel__=create_scope()\n   \\diff{#}::PartialDerivative.\n   A_{\\mu\\nu}::AntiSymmetric.\n   obj23:= q*\\diff{A_{\\mu\\nu}}_{\\mu\\nu};\n   canonicalise(_)\n   assert(obj23==0)\n   print('Test 23 passed')\n   \ntest23()\n\ndef test24():\n    __cdbkernel__=create_scope()\n    {\\mu,\\nu,\\rho,\\sigma}::Indices(position=independent).\n    \\diff{#}::PartialDerivative.\n    A_{\\mu\\nu}::AntiSymmetric.\n    obj24:= \\diff{A_{\\mu\\nu}}_{\\rho\\sigma} B^{\\nu\\mu};\n    canonicalise(_)\n    tst24:= - \\diff{A_{\\mu\\nu}}_{\\rho\\sigma} B^{\\mu\\nu} - @(obj24);\n    assert(tst24==0)\n    print('Test 24 passed')\n   \ntest24()\n\n# Do not permute tensors with indices in different positions.\n# FIXME: this already gives zero at rename_dummies, is that correct?\n\ndef test25():\n    __cdbkernel__=create_scope()\n    \\diff{#}::PartialDerivative.\n    {m,n,p,q,r,s,t,u,v,w,m1,m2,m3,m4,m5,m6,m7}::Indices(vector,position=fixed).\n    g^{m n}::Symmetric;\n    obj25:= g^{p q} \\diff{g_{m n}}_{p} \\diff{g_{r s}}_{q} T^{r s m n};\n    canonicalise(_)\n    tst25:= g^{p q} \\diff{g_{m n}}_{p} \\diff{g_{r s}}_{q} * T^{m n r s} - @(obj25);\n    rename_dummies(_)\n    assert(tst25==0)\n    print('Test 25 passed')\n   \ntest25()\n\n\n# Test 27 & 28: spinors and anti-commuting objects\n#\ndef test27():\n   __cdbkernel__=create_scope()\n   {m,n,p,q,r,s,t,u}::Indices(vector).\n   psi10001_{m}::Spinor(type=Majorana, dimension=10).\n   psi10001_{m}::SelfAntiCommuting.\n   \\Gamma_{#}::GammaMatrix.\n   H_{m n p}::AntiSymmetric.\n   obj27:= psi10001_{n} \\Gamma_{s t u} psi10001_{m} H_{p q r};\n   canonicalise(_)\n   tst27:= psi10001_{m} \\Gamma_{s t u} psi10001_{n} H_{p q r} -@(obj27);\n   collect_terms(_)\n   assert(tst27==0)\n   print('Test 27 passed')\n   \ntest27()\n\ndef test28():\n   __cdbkernel__=create_scope()\n   {m,n,p,q,r,s,t,u}::Indices(vector).\n   psi10001_{m}::Spinor(type=Majorana, dimension=10).\n   psi10001_{m}::SelfAntiCommuting.\n   \\Gamma_{#}::GammaMatrix.\n   obj28:= psi10001_{n} \\Gamma_{s} psi10001_{m} H_{p q r};\n   canonicalise(_)\n   tst28:= psi10001_{m} \\Gamma_{s} psi10001_{n} H_{p q r} + @(obj28);\n   collect_terms(_)\n   assert(tst28==0)\n   print('Test 28 passed')\n   \ntest28()\n\ndef test29():\n   __cdbkernel__=create_scope()\n   {m,n,p,q,r,s,t,u}::Indices(vector).\n   \\psi_{m}::Spinor.\n   \\psi_{m}::SelfAntiCommuting.\n   \\bar{#}::DiracBar.\n   \\Gamma_{#}::GammaMatrix.\n   obj28b:= \\bar{\\psi_{r}} A B \\Gamma_{n p} C \\psi_{m};\n   canonicalise(_)\n   tst28b:=  \\bar{\\psi_{m}} A B \\Gamma_{n p} C \\psi_{r} + @(obj28b);\n   collect_terms(_)\n   assert(tst28b==0)\n   print('Test 28b passed')\n   \ntest29()\n\n# Single-term expressions.\n\ndef test29b():\n   __cdbkernel__=create_scope()\n   {m,n,p,q,r,s,t,u}::Indices(vector).\n   dR_{m n p q r s}::TableauSymmetry(shape={4,2}, indices={2,3,0,1,4,5}).\n   dR_{m n p q r s}::Traceless.\n   tst29:= dR_{m n p q r r};\n   canonicalise(_)\n   assert(tst29==0)\n   print('Test 29b passed')\n   \ntest29b()\n\n# Extreme symmetries.\n\ndef test30():\n   __cdbkernel__=create_scope()\n   {a,b,c,d,e,f,g,h,i,j,k,l,m}::Indices(vector).\n   {a,b,c,d,e,f,g,h,i,j,k,l,m}::Integer(0..9).\n   \\eps_{a b c d e f g h i j}::AntiSymmetric.\n   W_{a b c d}::WeylTensor.\n   A_{k l}::AntiSymmetric.\n   obj30:= W_{a b d c} W_{f e g h} W_{i j k l} \\eps_{a b c d e f g h i j} A_{l k};\n   canonicalise(_)\n   tst30:= W_{a b c d} * W_{e f g h} * W_{i j k l} * \\eps_{a b c d e f g h i j} * A_{k l} + @(obj30);\n   collect_terms(_)\n   assert(tst30==0)\n   print('Test 30 passed')\n   \ntest30()\n\n# Inherited properties\n\ndef test31():\n   __cdbkernel__=create_scope()\n   {m,n,p,q,r}::Indices(vector).\n   {m,n,p,q,r}::Integer(0..10)\n   \\bar{#}::DiracBar.\n   \\psi_{m}::Spinor.\n   \\psi_{m}::SelfAntiCommuting.\n   H_{m n p}::AntiSymmetric.\n   \\Gamma_{#}::GammaMatrix.\n   obj31:= \\bar{\\psi_{m}} \\Gamma_{q n p} \\psi_{m} H_{n p q};\n   canonicalise(_)\n   tst31:= \\bar{\\psi_{m}} \\Gamma_{n p q} \\psi_{m} H_{n p q} - @(obj31);\n   collect_terms(_)\n   assert(tst31==0)\n   print('Test 31 passed')\n   \ntest31()\n\n\n# Indices in different sets should not be mixed up.\n\ndef test32():\n   __cdbkernel__=create_scope()\n   {a,b,c,d,e,f,g#}::Indices(SUFive);\n   {i,j,k,l,m,n#}::Indices(flavor);\n   HppT_{j k x}::TableauSymmetry(shape={2}, indices={0,1});\n   \\tenSp_{j a b}::TableauSymmetry(shape={1,1},indices={1,2});\n   obj32:= HppT_{i j x} * \\tenSp_{i a b} * \\fiveSp_{j a} ;\n   canonicalise(_)\n   tst32:= HppT_{i j x} * \\tenSp_{i b a} * \\fiveSp_{j a} + @(obj32);\n   collect_terms(_)\n   assert(tst32==0)\n   print('Test 32 passed')\n   \ntest32()\n\n\n# # Complicated traceless property.\n# @reset;\n# {i,j,m,n,k,p,q,l,r,r#}::Indices(vector)\n# C_{m n p q}::WeylTensor\n# \\nabla{#}::Derivative\n# \\nabla_{r}{ C_{m n p q} }::SatisfiesBianchi\n# \\nabla_{r}{ C_{m n p q} }::Traceless\n# \\delta_{i j}::KroneckerDelta\n# \n# #tst33:= Q*\\nabla_{j}{\\nabla_{q}{C_{m n p q}}};\n# #canonicalise(_)\n# #assert(tst33)\n\n# Test 34: numerical indices\n\ndef test34():\n   __cdbkernel__=create_scope()\n   A_{m? n?}::AntiSymmetric.\n   tst34a:= A_{4 4};\n   canonicalise(_)\n   assert(tst34a==0)\n   print('Test 34 passed')\n   \ntest34()\n\ndef test34b():\n   __cdbkernel__=create_scope()\n   R_{m? n? p? q?}::RiemannTensor.\n   tst34b:= R_{4 4 2 3};\n   canonicalise(_)\n   rl:={ R_{m? m? n? p?} -> 0, R_{n? p? m? m?} -> 0 };\n   substitute(tst34b, rl)\n   assert(tst34b==0)\n   print('Test 34b passed')\n   \ntest34b()\n\n# Diagonal objects\n\ndef test35b():\n   __cdbkernel__=create_scope()\n   {m,n}::Integer;\n   \\delta_{m n}::Diagonal.\n   obj35:= \\delta_{1 2} * \\delta_{1 2} - \\delta_{1 1} * \\delta_{2 2};\n   canonicalise(_)\n   tst35:= - \\delta_{1 1}\\delta_{2 2} - @(obj35);\n   collect_terms(_)\n   assert(tst35==0)\n   print('Test 35 passed')\n   \ntest35b()\n\n# Canonicalisation with upper/lower indices.\n\ndef test36():\n   __cdbkernel__=create_scope()\n   \\Gamma{#}::GammaMatrix.\n   {a,b,c,d,e}::Indices(vector, position=fixed).\n   obj36:= \\Gamma_{a c}^{b d};\n   canonicalise(_)\n   tst36:= \\Gamma_{a}^{b}_{c}^{d} + @(obj36);\n   collect_terms(_)\n   assert(tst36==0)\n   print('Test 36 passed')\n   \ntest36()\n\ndef test37():\n   __cdbkernel__=create_scope()\n   {a,b,c,d,e}::Indices(vector, position=fixed).\n   obj37:= B^{b} B_{b} A_{a} A^{a};\n   canonicalise(_)\n   tst37:= B^{a} B_{a} A^{b} A_{b} - @(obj37);\n   collect_terms(_)\n   assert(tst37==0)\n   print('Test 37 passed')\n   \ntest37()\n\n# Mixed abstract & numerical indices.\n#\n# @reset.\n# {a,b,c,d,e}::Indices(group).\n# {i,j,k}::Indices(vector).\n# \\delta{#}::KroneckerDelta.\n# \\eta^{a}_{i j}::TableauSymmetry(shape={1,1}, indices={1,2}).\n# \\epsilon^{a b c}::EpsilonTensor.\n# \\partial{#}::Derivative.\n# obj38:= \\epsilon^{a b c} \\delta^{b 3} \\epsilon^{c d e} \\delta^{e 3} \\eta^{d}_{i j} x^{i};\n# canonicalise(_)\n\n# attern indices\n#\n# @reset.\n# J_{\\mu\\nu}::AntiSymmetric.\n# obj39:= \\eta_{#1? #3?} J_{#2? #4?} - \\eta_{#1? #4?} J_{#2? #3?} - \\eta_{#2? #3?} J_{#1? #4?} + \\eta_{#2? #4?} J_{#1? #3?};\n# canonicalise(_)\n# \n# # Test 40: equality signs involved (used to crash)\n# @reset.\n# Y_{i j}::AntiSymmetric.\n# obj40:= X_{i} = Y_{j i} Z_{j};\n# canonicalise(_)\n# \n# # Test 41: upper/lower indices.\n# #\n# @reset.\n# {m,n}::Indices.\n# obj41:= R^{m}_{m} - R_{m}^{m};\n# canonicalise(_)\n# tst41:= \n# \n# # Test 42: like in xAct\n# #\n# @reset.\n# {a,b}::Indices(position=fixed).\n# K^{a}_{a};\n# canonicalise(_)\n# \n# K_{a}^{a};\n# canonicalise(_)\n# \n# @reset.\n# {a,b}::Indices(position=fixed).\n# K_{a}^{a}_{b}^{b};\n# canonicalise(_)\n# \n# K^{a}_{a}_{b}^{b};\n# canonicalise(_)\n\n# More upper/lower indices\n\ndef test42():\n   __cdbkernel__=create_scope()\n   {n,r}::Indices(position=fixed).\n   \\delta{#}::KroneckerDelta.\n   \\partial{#}::PartialDerivative.\n   obj42:= \\delta_{n}^{r} \\partial_{r}{ u^{n} };\n   canonicalise(_)\n   tst42:= \\delta^{n}_{r} * \\partial_{n}{u^{r}} - @(obj42);\n   collect_terms(_)\n   assert(tst42==0)\n   print('Test 42 passed')\n   \ntest42()\n\n# Prevent raising/lowering if there is a Derivative in the way. For\n# the time being we do not even allow this if there is a full\n# covariant derivative.\n\ndef test43():\n   __cdbkernel__=create_scope()\n   {m,n,k}::Indices(position=fixed).\n   \\partial{#}::Derivative.\n   obj43:= A_{m n} \\partial_{k}{ B^{m n} };\n   canonicalise(_)\n   tst43:= A_{m n} \\partial_{k}{ B^{m n} } - @(obj43);\n   collect_terms(_)\n   assert(tst43==0)\n   print('Test 43 passed')\n   \ntest43()\n\ndef test45():\n   __cdbkernel__=create_scope()\n   {\\mu,\\nu,\\rho,\\sigma,\\kappa,\\lambda,\\eta,\\chi#}::Indices(full, position=fixed).\n   {m,n,p,q,r,s,t,u,v,m#}::Indices(subspace, position=fixed, parent=full).\n   \\partial{#}::PartialDerivative.\n   g_{\\mu? \\nu?}::Symmetric.\n   g^{\\mu? \\nu?}::Symmetric.\n   obj45a:= \\partial_{4 n}{ g_{p 4} } g_{m1 m} g^{m1 p};\n   canonicalise(_)\n   tst45a:= \\partial_{4 n}{ g_{4 p} } g_{m}^{m1} g_{m1}^{p} - @(obj45a);\n   collect_terms(_)\n   assert(tst45a==0)\n   obj45b:= \\partial_{4 n}{ g_{4 p} } g_{m1 m} g^{m1 p};\n   canonicalise(_)\n   tst45b:= \\partial_{4 n}{ g_{4 p} } g_{m}^{m1} g_{m1}^{p} - @(obj45b);\n   collect_terms(_)\n   assert(tst45b==0)\n   obj45d:= A_{p} \\partial_{n}{ g^{m1 p} } B_{m1};\n   canonicalise(_)\n   tst45d:= A_{m1} \\partial_{n}{ g^{m1 p} } B_{p} - @(obj45d);\n   collect_terms(_)\n   assert(tst45d==0)\n   print('Test 45d passed')\n   \n#test45()\n\n# Spinor indices\n\ndef test46():\n   __cdbkernel__=create_scope()\n   {a,b,c,d}::Indices.\n   {a,b,c,d}::AntiCommuting.\n   tst46:= \\chi_{a} \\psi^{a} + \\chi^{a} \\psi_{a};\n   canonicalise(_)\n   collect_terms(_)\n   assert(tst46==0)\n   print('Test 46 passed')\n   \ntest46()\n\n# Regression in 1.21\n\ndef test47():\n   __cdbkernel__=create_scope()\n   B0:=B_{\\alpha \\mu} -> \\Delta_{\\mu \\nu}*F_{\\theta \\alpha};\n   canonicalise(_)\n   print('Test 47 passed')\n   \ntest47()\n\n# Test 48: derivatives without arguments\n#\n#@reset.\n#\\nabla{#}::PartialDerivative.\n#A_{m} \\nabla_{n} B_{k};\n#canonicalise(_)\n\ndef test48():\n   __cdbkernel__=create_scope()\n   {q,r}::Indices(full).\n   {i,j}::Indices(\"subspace1\", parent=full).\n   {A,B}::Indices(\"subspace2\", parent=full).\n   obj49:= X_{q r} Y_{q r};\n   split_index(_, $ {q, i, A} $, repeat=True)\n   canonicalise(_)\n   tst49:= X_{i j} Y_{i j} + X_{i A} Y_{i A} + X_{A i} Y_{A i} + X_{A B} Y_{A B} - @(obj49);\n   assert(tst49==0)\n   print('Test 48 passed')\n   \ntest48()\n\ndef test49():\n   __cdbkernel__=create_scope()\n   A_{m? n?}::AntiSymmetric.\n   ex:=A_{4 m} + A_{m 4};\n   canonicalise(_)\n   assert(ex==0)\n   print('Test 49 passed')\n\ntest49()\n\ndef test50():\n    __cdbkernel__=create_scope()\n    {m,n,p}::Indices(position=free);\n    A_{m n}::Symmetric;\n    ex:=\\int{ A_{m n} (A^{n m} + A^{m n}) }{x};\n    canonicalise(_)\n    tst:= 2 \\int{ A_{m n} A^{m n} }{x} - @(ex);\n    assert(tst==0)\n    print('Test 50 passed')\n\ntest50()\n\ndef test51():\n    # Sorting should be such that we first sort based on\n    # argument names, and then on index positions. Only\n    # then will canonicalise be able to collect terms\n    # which differ by index raising/lowering.\n    __cdbkernel__=create_scope()\n    {a,b,c}::Indices(position=fixed);\n    ex:= A^{a}(A) A_{a}(B) + A^{a}(B) A_{a}(A);\n    sort_product(_)\n    canonicalise(_)\n    tst:= 2 A^{a}(A) A_{a}(B) - @(ex);\n    assert(tst==0)\n    print('Test 51 passed')\n   \ntest51()\n\ndef test52():\n    __cdbkernel__=create_scope()\n    {a,b,c}::Indices(position=fixed);\n    D{#}::Derivative;\n    ex:= D^{a}{A} D_{a}{B} + D^{a}{B} D_{a}{A};\n    sort_product(_)\n    canonicalise(_)\n    tst:= 2 D^{a}{A} D_{a}{B} - @(ex);\n    assert(tst==0)\n    print('Test 52 passed')\n   \ntest52()\n\n# def test53():\n# \n# {a,b,c}::Indices(position=fixed);\n# D{#}::Derivative;\n# ex:= D^{a}{A_{b}} D_{a}{B} + D^{a}{B} D_{a}{A};\n# sort_product(_);\n# canonicalise(_);\n\ndef test53():\n   __cdbkernel__=create_scope()\n   {m,n}::Integer;       \n   {m,n}::Indices(values={1,2,3});       \n   A_{m n}::Symmetric;\n   ex:= A_{1 2} - A_{2 1};\n   canonicalise(_)\n   assert(ex==0)\n   print(\"Test 53a passed\")\n   ex:= A_{m n} - A_{n m};\n   canonicalise(_)\n   assert(ex==0)\n   print(\"Test 53b passed\")\n\ntest53()   \n\ndef test54():\n   __cdbkernel__=create_scope()\n   {m,n,p,q}::Integer;       \n   {m,n,p,q}::Indices(values={0,1,2,3});       \n   R_{m n p q}::RiemannTensor;\n   ex:=R_{3 m 3 3};\n   canonicalise(_)\n   assert(ex==0)\n   print(\"Test 54a passed\")\n   ex:=R_{3 3 m 3};\n   canonicalise(_)\n   assert(ex==0)\n   print(\"Test 54b passed\")\n\ntest54()\n       \ndef test55():\n   __cdbkernel__=create_scope()\n   {m,n,p,q}::Indices(values={1,2,3,4});\n   R_{m n p q}::RiemannTensor;\n   ex:=R_{3 m 4 3};\n   canonicalise(_)\n   tst:= - R_{4 3 m 3} - @(ex);\n   assert(tst==0)\n   ex:= R_{3 4 3 m};       \n   canonicalise(_)\n   tst:= R_{4 3 m 3} - @(ex);\n   assert(tst==0)\n   print(\"Test 55 passed\")\n\ntest55()\n\ndef test56():\n   __cdbkernel__=create_scope()\n   {t,r}::Coordinate;\n   {a,b}::Indices(values={t,r},position=fixed);\n   A_{a b}::Diagonal;\n   ex:=A_{t r} + A_{r r} + A_{r t} + A_{t t};\n   assert(str(ex)=='A_{r r} + A_{t t}')\n   print(\"Test 56 passed\")\n\ntest56()\n\ndef test57():\n   __cdbkernel__=create_scope()\n   # as above, but without the coordinate property\n   A{#}::Diagonal;\n   ex:=A_{t r};\n   assert(ex != 0)\n   assert(str(ex)=='A_{t r}')\n   print(\"Test 57 passed\")\n\ntest57()\n\ndef test58():\n   # https://cadabra.science/qa/2291/sort_product-with-position-independent-identical-variables      \n   {a,b,c,d,e,f,g}::Indices(vector,position=independent).\n   ex := x_{a} x^{b} - x^{b} x_{a};\n   sort_product(_)\n   assert(ex==0)\n   print(\"Test 58 passed\")\n      \ntest58()\n      \ndef test59():\n   # Inside powers, dummies from outside can repeat.\n   __cdbkernel__=create_scope()\n   {n,k,m,p,q}::Indices;\n   ex:= 1/(A^{n} A^{k} A^{k} A^{n} );\n   canonicalise(ex)\n   tst:= 1/(A^{k} A^{k} A^{n} A^{n} ) - @(ex);\n   assert(tst==0)\n   print(\"Test 59a passed\")      \n   # Inside powers, dummies can take names of free\n   # indices used outside.\n   ex:= A^{n} / (A^{k} A^{n} A^{k} A^{n});\n   canonicalise(ex)\n   tst:= A^{n}/(A^{k} A^{k} A^{n} A^{n} ) - @(ex);\n   assert(tst==0)\n   print(\"Test 59b passed\")\n\ntest59()\n\ndef test60():\n   # Anti-commuting objects in canonicalise did not\n   # pass their info through derivatives.\n   # Issue #113.\n   __cdbkernel__=create_scope()\n\n   {a, b, c}::Indices(Vector, position=independent);\n   X_{a}::SelfAntiCommuting ;\n   \\partial{#}::Derivative;\n   X_{a}::Depends(\\partial{#});\n   \n   foo1 := \\partial{X_{b}} \\partial{X_{a}} + X_{b} X_{a};\n   canonicalise(foo1)\n   tst := -\\partial{X_{a}} \\partial{X_{b}} - X_{a} X_{b} - @(foo1);\n   assert(tst==0)\n   print(\"Test 60a passed\")\n   \n   foo2 := \\partial{X_{b}} \\partial{X_{a}} + X_{b} X_{a};\n   sort_product(foo2)\n   tst := -\\partial{X_{a}} \\partial{X_{b}} - X_{a} X_{b} - @(foo2);\n   assert(tst==0)\n   print(\"Test 60b passed\")\n\ntest60()\n\ndef test61():\n   __cdbkernel__=create_scope()\n   {a,b,c,d#}::Indices(position=independent).\n   \\bar{#}::Accent.\n   \\bar{A}_{a b}::Symmetric.\n   \\bar{A}^{a b}::Symmetric.\n   ex := \\bar{A}_{a b} \\bar{A}^{b a};\n   canonicalise (ex)\n   tst:= \\bar{A}_{a b} \\bar{A}^{a b} - @(ex);\n   assert(tst==0)\n   print(\"Test 61 passed\")\n\ntest61()\n\ndef test62():\n   __cdbkernel__=create_scope()\n   {\\bar{\\epsilon}_{\\mu \\nu \\rho}, \\bar{\\epsilon}^{\\mu \\nu \\rho}}::AntiSymmetric;\n   ex := \\bar{\\gamma}^{\\sigma \\kappa} \\bar{\\epsilon}_{\\mu \\kappa \\nu} - \\bar{\\gamma}^{\\sigma \\kappa} \\bar{\\epsilon}_{\\mu \\nu \\kappa};\n   canonicalise(ex)\n   tst:= -2\\bar{\\gamma}^{\\sigma\\kappa} \\bar{\\epsilon}_{\\mu\\nu\\kappa} - @(ex);\n   assert(tst==0)\n   print(\"Test 62 passed\")\n\ntest62()\n\ndef test63():\n   __cdbkernel__=create_scope()\n   {a, b}::Indices(position=independent).\n   \\psi^a::SelfAntiCommuting.\n   {\\psi^a, \\rho, \\chi}::Spinor(dimension=10).\n   {\\psi^a, \\rho, \\chi}::AntiCommuting.\n   \\bar{#}::DiracBar.\n   A{#}::AntiSymmetric.\n   ex := A_{a b} \\psi^b\\bar{\\psi^a};\n   canonicalise(_)\n   tst:= - A_{a b} \\psi^a\\bar{\\psi^b} - @(ex);\n   assert(tst==0)\n   print(\"Test 63a passed\")\n   ex := A_{a b} \\bar{\\rho} \\psi^b\\bar{\\psi^a} \\chi.\n   canonicalise(_)\n   tst:= -A_{a b} \\bar{\\rho} \\psi^a\\bar{\\psi^b} \\chi - @(ex).\n   assert(tst==0)\n   print(\"Test 63b passed\")\n   ex := A_{a b}  \\bar{\\psi^b} \\rho \\bar{\\psi^a} \\chi.\n   canonicalise(_)\n   tst:=-A_{a b}  \\bar{\\psi^a} \\rho \\bar{\\psi^b} \\chi - @(ex).\n   assert(tst==0)\n   print(\"Test 63c passed\")\n   \ntest63()\n"
  },
  {
    "path": "tests/components.cdb",
    "content": "# The scalar backend used for these component tests can be switched\n# using either one of\n#\n# kernel(scalar_backend=\"sympy\")\n\n# Testing a substitution rule in which an abstract index in the \n# expression is matched against a coordinate in the pattern.\n# FIXME: this is not supposed to match!\n# {m,n,p}::Indices(values={t,r}).\n# {r,t}::Coordinate.\n# ex:= A_{m n} + B_{m n};\n# rl:= A_{t r} + B_{t r} = 3;\n# substitute(ex, rl)\n\ndef test01():\n    __cdbkernel__=create_scope()\n    print(__cdbkernel__.scalar_backend)\n    {r,t}::Coordinate.\n    {m,n}::Indices(values={t,r}, position=fixed).\n    ex:= A_{m};\n    rl:= A_{t} = 3;\n    evaluate(ex, rl, simplify=True)\n    tst:= \\components_{m}( \\comma{ \\comma{t} = 3  } ) - @(ex);\n    collect_components(_)\n    assert(tst==0)\n    print(\"Test 01 passed\")\n\ntest01()\n\ndef test02():\n    __cdbkernel__=create_scope()\n    {r,t}::Coordinate.\n    {m,n,p,s}::Indices(values={t,r}, position=free).\n    C::Depends(r,t).\n    ex:= A_{n m} B_{m n p} ( C_{p s} + D_{s p} );\n    rl:= [ A_{r t} = 3, B_{t r t} = 2, B_{t r r} = 5, C_{t r} = 1, D_{r t} = r**2*t, D_{t r}=t**2 ];\n    evaluate(ex, rl)\n    tst:= \\components_{s}{\\comma{r}= 6 r**2 t + 6, \\comma{t}=15 t**2} - @(ex):\n    collect_components(_)\n    assert(tst==0)\n    print(\"Test 02 passed\")\n\ntest02()\n\n\n# Riemann curvature example.\n\ndef test03():\n    __cdbkernel__=create_scope()\n    {r,t,\\phi,\\theta}::Coordinate.\n    {\\mu,\\nu,\\rho,\\sigma,\\lambda,\\kappa,\\gamma,\\chi}::Indices(values={t,r,\\phi,\\theta}, position=fixed).\n    \\partial{#}::PartialDerivative.\n    g_{\\mu\\nu}::Metric.\n    g^{\\mu\\nu}::InverseMetric.         \n    ss:= { g_{t t} = -(1-2 M/r),  g_{r r} = 1/(1-2 M/r),\n           g_{\\theta\\theta} = r**2,  g_{\\phi\\phi}=r**2 \\sin(\\theta)**2 };\n    complete(ss, $g^{\\mu\\nu}$)\n    ch:= \\Gamma^{\\mu}_{\\nu\\rho} = 1/2 g^{\\mu\\sigma} ( \\partial_{\\rho}{g_{\\nu\\sigma}}\n                                                +\\partial_{\\nu}{g_{\\rho\\sigma}}\n                                                -\\partial_{\\sigma}{g_{\\nu\\rho}} );\n    evaluate(ch, ss, rhsonly=True)\n    chtst=rhs(ch)\n        # Check against e.g. arxiv:0904.4184.\n    tst:=\\components^{\\mu}_{\\nu\\rho}{ {t,r,t}          =  M/r**2 (1-2 M/r)**(-1),\n                                {t,t,r}            =  M/r**2 (1-2 M/r)**(-1),\n                                {r,r,r}            = -M/r**2 (1-2 M/r)**(-1),\n                                {r,t,t}            =  M/r**2 (1-2 M/r),\n                                {r,\\theta,\\theta}  = -r (1-2M/r),\n                                {r,\\phi,\\phi}      = - (r-2M) \\sin(\\theta)**2,\n                                {\\theta,\\theta,r}  = 1/r,\n                                {\\theta,r,\\theta}  = 1/r,\n                                {\\phi,\\phi,r}      = 1/r,\n                                {\\phi,r,\\phi}      = 1/r,\n                                {\\theta,\\phi,\\phi} = -\\sin(\\theta)\\cos(\\theta),\n                                {\\phi,\\theta,\\phi} = \\cos(\\theta)/\\sin(\\theta),\n                                {\\phi,\\phi,\\theta} = \\cos(\\theta)/\\sin(\\theta)\n                            } - @(chtst);\n    collect_components(_)\n    assert(tst==0)\n    print(\"Test 03a passed\")\n    \n    rm:= R^{\\rho}_{\\sigma\\mu\\nu} = \\partial_{\\mu}{\\Gamma^{\\rho}_{\\nu\\sigma}}\n                              -\\partial_{\\nu}{\\Gamma^{\\rho}_{\\mu\\sigma}}\n                              +\\Gamma^{\\rho}_{\\mu\\lambda} \\Gamma^{\\lambda}_{\\nu\\sigma}\n                              -\\Gamma^{\\rho}_{\\nu\\lambda} \\Gamma^{\\lambda}_{\\mu\\sigma};\n\n    substitute(rm, ch)\n    evaluate(rm, ss, rhsonly=True)\n    \n    # The Ricci tensor should be zero.\n    rc:= R_{\\sigma\\nu} = R^{\\rho}_{\\sigma\\rho\\nu};\n    substitute(rc, rm)\n    evaluate(rc, ss, rhsonly=True)\n    assert(rhs(rc)==0)\n    print(\"Test 03b passed\")\n    \n    # Finally, the Kretschmann scalar.\n    K:= K = R^{\\mu}_{\\nu\\rho\\sigma} R^{\\lambda}_{\\kappa\\gamma\\chi} g_{\\mu\\lambda} g^{\\nu\\kappa} g^{\\rho\\gamma} g^{\\sigma\\chi};\n    substitute(K, rm)\n    evaluate(K, ss)\n    tmp=rhs(K)\n    tst:= 48 M**2/r**6 - @(tmp);\n    simplify(tst)\n    assert(tst==0)\n    print(\"Test 03 passed\")\n    \ntest03()\n    \ndef test04():\n    __cdbkernel__=create_scope()\n    {r,t,\\theta,\\phi}::Coordinate.\n    {m,n,p,q}::Indices(position=fixed,values={t,r,\\theta,\\phi}).\n    rl:= { X^{t} -> X^{t}, g_{t t}=-1, g_{r r}=3 };\n    ex:= g_{m n} X^{n};\n    evaluate(ex, rl)\n    tst:= \\components_{m}{ \\comma{ \\comma{t} = -X^{t} } } - @(ex);\n    collect_components(_)\n    assert(tst==0)\n    print(\"Test 04 passed\")\n\ntest04()\n\n# Component computations leading to a scalar.\n\ndef test05():\n    __cdbkernel__=create_scope()\n    {r,t}::Coordinate.\n    {m,n,p}::Indices(values={r,t}).\n    ex:= A_{m n}*A_{m n};\n    ss:= { A_{r r} -> a+b, A_{r t} -> b, A_{t t} -> c, A_{r r t}->3, A_{t t t}->c };\n    evaluate(ex, ss)\n    tst:= (a+b)**2+b**2+c**2  - @(ex);\n    assert(tst==0)\n    print(\"Test 05 passed\")\n\ntest05()\n\n# The following test components of tensor outer products. The first one\n# leads to a scalar multiplying the components tensor.\n\ndef test06():\n    __cdbkernel__=create_scope()\n    {r,t}::Coordinate.\n    {m,n}::Indices(values={t,r}).\n    ex:= g_{m n} X^{n} A;\n    rl:= { X^{t} -> X^{t}, g_{t t}=1, g_{r r}=3 };\n    evaluate(ex,rl)\n    tst:= \\components_{m}{ \\comma{ \\comma{t}= A X^{t} } } - @(ex);\n    collect_components(_)\n    assert(tst==0)\n    print(\"Test 06 passed\")\n\ntest06()\n\n \n# The second one is manifestly an outer product.\n\ndef test07():\n    __cdbkernel__=create_scope()\n    {r,t}::Coordinate.\n    {m,n,p}::Indices(values={t,r}).\n    ex:= X^{n} X^{m} X^{p};\n    rl:= { X^{t} -> T, X^{r} -> R };\n    evaluate(ex,rl)\n    tst:=\\components^{n m p}{ {t,t,t}=T**3, {t,t,r}=R T**2, {t,r,t}=R T**2,\n                            {t,r,r}=T R**2, {r,t,t}=R T**2, {r,t,r}=T R**2,\n                            {r,r,t}=R**2 T, {r,r,r}=R**3 } - @(ex);\n    collect_components(tst)\n    assert(tst==0)\n    print(\"Test 07 passed\")\n\ntest07()                          \n\n# More GR stuff.\n# {\\mu,\\nu,\\rho,\\sigma}::Indices(position=fixed).\n# \\partial{#}::PartialDerivative.\n# ex:= R^{\\mu}_{\\nu\\rho\\sigma};\n# rl:= { R^{\\mu}_{\\nu\\rho\\sigma} -> \\partial_{\\rho}{\\Gamma^{\\mu}_{\\nu\\sigma}},\n#         \\Gamma^{\\mu}_{\\nu\\rho} = 1/2 g^{\\mu\\sigma} ( \\partial_{\\rho}{g_{\\nu\\sigma}}\n#                                                  +\\partial_{\\nu}{g_{\\rho\\sigma}}\n#                                                  -\\partial_{\\sigma}{g_{\\nu\\rho}} )\n#                                                   };\n# substitute(ex, rl, repeat=True);                                                  \n\n\n# -------------------------------------------\n\n# This one does not yet work, and might be better served with a split-index\n# first.\n# {r,t,\\phi,\\theta}::Coordinate.\n# {m,n}::Indices(\"full\",values={t,r,\\phi,\\theta}).\n# {i,j}::Indices(\"3d\", parent=\"full\").\n# ex:= A_{m n}+A_{n m};\n# rl:= { A_{t t} -> 3, A_{i j} -> \\delta_{i j} };\n# evaluate(ex, rl);\n\n# Self-contracted tensors.\n\ndef test08():\n    __cdbkernel__=create_scope()\n    {r,t}::Coordinate.\n    {m,n,p}::Indices(values={r,t})\n    ex:= A_{n}^{n} A_{m}^{m};\n    rl:= { A_{t}^{r} -> S, A_{t}^{t} -> 3, A_{r}^{r} -> r };\n    evaluate(ex, rl)\n    tst:= (r+3)**2 - @(ex);\n    simplify(tst)\n    assert(tst==0)\n    print(\"Test 08 passed\")\n\ntest08()\n\ndef test09():\n    __cdbkernel__=create_scope()\n    {r,t}::Coordinate.\n    {m,n,p}::Indices(values={r,t})\n    ex:= A_{m}^{m};\n    rl:= { A_{t}^{r} -> S, A_{t}^{t} -> 3, A_{r}^{r} -> r };\n    evaluate(ex, rl)\n    tst:= r+3 - @(ex);\n    assert(tst==0)\n    print(\"Test 09 passed\")\n\ntest09()\n\ndef test10():\n    __cdbkernel__=create_scope()\n    {r,t,\\phi}::Coordinate.\n    {m,n,p}::Indices(values={r,t,\\phi}).\n    ex:= A_{n}^{n p} B_{p};\n    rl:= A_{r}^{r t} -> a, A_{r}^{r r} -> b, A_{r}^{t t} -> Q1, A_{t}^{r t} -> Q2, A_{t}^{r r} -> Q3,\n         A_{t}^{t t}-> c, A_{t}^{t r} -> d, B_{r} -> Br, B_{t} -> Bt;\n    evaluate(ex, rl)\n    tst:= a Bt + c Bt + b Br + d Br - @(ex);\n    assert(sympy.simplify(tst)==0)\n    print(\"Test 10 passed\")\n\ntest10()\n\n# This does not work when 'Q' is removed.\ndef test11():\n    __cdbkernel__=create_scope()\n    {r,t,\\phi}::Coordinate;\n    {m,n,p}::Indices(values={r,t,\\phi});\n    ex:= T_{m n} = Q A_{m n};\n    rl:= A_{r r} -> r, A_{t t} -> t, A_{r t} -> t r;\n    evaluate(ex, rl, rhsonly=True)\n    ex2:= T_{m m};\n    substitute(ex2, ex)\n    evaluate(ex2, rl)\n    tst:= Q (r+t) - @(ex2);\n    assert(tst==0)\n    print(\"Test 11 passed\")\n\ntest11()\n\ndef test12():\n    __cdbkernel__=create_scope()\n    {\\mu,\\nu,\\rho,\\sigma}::Indices(values={0,1,2,3});\n    ex:=A_{\\mu} A_{\\mu};\n    rl:= A_{0} -> -\\xi_{0}, A_{1} -> \\xi_{1}, A_{2} -> -\\xi_{2}, A_{3} -> \\xi_{3};\n    evaluate(ex, rl)\n    tst:= \\xi_{0}\\xi_{0} + \\xi_{1}\\xi_{1} + \\xi_{2}\\xi_{2} + \\xi_{3}\\xi_{3} - @(ex);\n    assert(tst==0)\n    print(\"Test 12 passed\")\n\ntest12()\n\ndef test13():\n    __cdbkernel__=create_scope()\n    {i,j,k}::Indices(values={1,2,3});\n    \\epsilon^{i j k}::EpsilonTensor;\n    ex:=\\epsilon^{i j k};\n    evaluate(ex)\n    tst:= \\components^{i j k}{ {1,2,3}=1, {1,3,2}=-1, {2,1,3}=-1, {2,3,1}=1, {3,1,2}=1, {3,2,1}=-1 } - @(ex);    \n    collect_components(tst)\n    assert(tst==0)\n    print(\"Test 13 passed\")\n\ntest13()\n        \ndef test14():        \n    __cdbkernel__=create_scope()\n    {t,x,y,z}::Coordinate;        \n    {\\mu,\\nu,\\rho,\\sigma}::Indices(values={t,x,y,z});\n    f::Depends({t,x,y,z});\n    \\partial{#}::PartialDerivative;\n    ex:= F^{\\mu} \\partial_{\\mu}{ f };\n    rl:= F^{t} = A, F^{x} = B, F^{z} = C;\n    evaluate(ex, rl)\n    canonicalise(ex)\n    tst:= A \\partial_{t}{f} + B \\partial_{x}{f} + C \\partial_{z}{f} - @(ex);\n    assert(tst==0)\n    print(\"Test 14 passed\")\n\ntest14()\n\ndef test15():        \n    __cdbkernel__=create_scope()\n    {t,x,y,z}::Coordinate;        \n    {\\mu,\\nu,\\rho,\\sigma}::Indices(values={t,x,y,z});\n    f::Depends({t,x,y,z});\n    \\partial{#}::PartialDerivative;\n    ex:= F^{\\mu\\nu} \\partial_{\\mu \\nu}{ f };\n    rl:= F^{t x} = A, F^{x y} = B, F^{z x} = C;\n    evaluate(ex, rl)\n    canonicalise(ex)\n    tst:= A \\partial_{t x}{f} + B \\partial_{x y}{f} + C \\partial_{x z}{f} - @(ex);\n    assert(tst==0)\n    print(\"Test 15 passed\")\n\ntest15()\n\ndef test16():        \n    __cdbkernel__=create_scope()\n    {x,y,z}::Coordinate;\n    f::Depends({x,y,z});\n    \\partial{#}::PartialDerivative;\n    {i,j,k,l}::Indices(values={x,y,z}, position=free);\n    ex:= 2 \\partial_{i i}{3 f} + m**2 f;\n    evaluate(ex)\n    tst:= 6\\partial_{x x}{f} + 6\\partial_{y y}{f} + 6\\partial_{z z}{f} + m**2 f - @(ex);\n    assert(tst==0)\n    print(\"Test 16 passed\")\n\ntest16()\n        \ndef test17():\n    __cdbkernel__=create_scope()\n    {x,y,z}::Coordinate;\n    {i,j,k,l}::Indices(values={x,y,z}, position=free);\n    Ax::Depends(y);\n    Ay::Depends(z);\n    Az::Depends(x);        \n    \\partial{#}::PartialDerivative;\n    ex:= \\partial_{i j}{A_{i}} + m**2 A_{j};\n    evaluate(ex, $A_x=Ax, A_y=Ay, A_z=Az$)\n    tst:= \\components_{j}{ \\comma{x}=m**2 Ax, \\comma{y}=m**2 Ay, \\comma{z}=m**2 Az } - @(ex);\n    collect_components(tst)\n    assert(tst==0)\n    print(\"Test 17 passed\")\n\ntest17()\n\ndef test18():\n    __cdbkernel__=create_scope()\n    {x,y,z}::Coordinate;\n    {i,j,k,l}::Indices(values={x,y,z}, position=free);\n    A_{i}::Depends({x,y,z});\n    \\partial{#}::PartialDerivative;\n    ex:= \\partial_{i}{A_{j}};\n    evaluate(ex, $A_{z}=z$)\n    tst:= \\components_{j i}( \\comma{ {z,z}=1 } ) - @(ex);\n    collect_components(tst)\n    assert(tst==0)\n    print(\"Test 18 passed\")\n\ntest18()\n\ndef test19():\n    __cdbkernel__=create_scope()\n    {x,y,z}::Coordinate;\n    {i,j,k,l}::Indices(values={x,y,z}, position=free);\n    A_{i}::Depends({x,y,z});\n    \\partial{#}::PartialDerivative;\n    ex:= \\partial_{i}{A_{i}} + m**2 f;\n    evaluate(ex, $A_{z}=\\sin{z}$)\n    tst:= m**2 f + \\cos{z} - @(ex);\n    sort_product(_)\n    assert(tst==0)\n    print(\"Test 19 passed\")\n\ntest19()\n\ndef test20():\n    __cdbkernel__=create_scope()\n    {r,t}::Coordinate;\n    {a,b,c}::Indices(values={r,t});\n    \\partial{#}::PartialDerivative;\n    ex:= A_{a} B_{b} C_{a b};\n    rl:= [ A_{r} = 1, A_{t} = q, B_{t} = 2, B_{r} = w, C_{r t} = 3, C_{t r}=5 ];\n    evaluate(ex, rl)\n    tst:= 6 + 5 q w - @(ex);\n    assert(tst==0)\n    print(\"Test 20 passed\")\n\ntest20()\n\ndef test21():\n    __cdbkernel__=create_scope()\n    {r,t}::Coordinate;\n    {a,b,c}::Indices(values={r,t});\n    \\partial{#}::PartialDerivative;\n    {f,g}::Depends(r);    \n    ex:= A_{a} \\partial_{a}{ f / g };\n    rl:= { A_{r} = q };\n    evaluate(ex, rl)\n    tst:= q (- f \\partial_{r}{g} + g \\partial_{r}{f} )/g**2 - @(ex);\n    assert(tst==0)\n    print(\"Test 21 passed\")\n\ntest21()\n\ndef test22():\n    __cdbkernel__=create_scope()\n    {r,t}::Coordinate;\n    {a,b,c}::Indices(values={r,t});\n    \\partial{#}::PartialDerivative;\n    {f,g}::Depends(r);    \n    ex:= A_{a} \\partial_{a}{ f * g };\n    rl:= { A_{r} = q };\n    evaluate(ex, rl)\n    tst:= q ( f \\partial_{r}{g} + g\\partial_{r}{f} ) - @(ex);\n    assert(tst==0)\n    print(\"Test 22 passed\")\n\ntest22()\n\ndef test23():\n    __cdbkernel__=create_scope()\n    {r,t}::Coordinate;        \n    {a,b,c}::Indices(values={r,t}, position=fixed);\n    \\partial{#}::PartialDerivative;\n    ex:= \\partial^{a}{ A_{a} };\n    rl:= A_{r} = r;\n    try:\n        evaluate(ex, rl);\n        assert(1==0)\n    except:\n        print(\"Test 23a passed\")\n    ex:= \\partial_{a}{ A^{a} };\n    rl:= A^{r} = r;\n    evaluate(ex, rl)\n    tst:= 1 - @(ex);\n    assert(tst==0)\n    print(\"Test 23b passed\")\n        \ntest23()\n        \n\n# \n# {r,t}::Coordinate.    \n# {a,b,c}::Indices(values={r,t});\n# \\partial{#}::PartialDerivative;\n# A_{a}::Depends(r);\n# ex:= \\partial_{a}{ A_{b} };\n# rl:= \\partial_{r}{ A_{t} } = 1;\n# evaluate(ex, rl);\n\ndef test24():\n    __cdbkernel__=create_scope()\n    {\\theta, \\varphi}::Coordinate;\n    {\\alpha, \\beta, \\gamma, \\delta, \\rho, \\sigma, \\mu, \\nu, \\lambda}::Indices(values={\\varphi, \\theta}, position=fixed);\n    \\partial{#}::PartialDerivative;\n    g_{\\alpha\\beta}::Metric.\n    g^{\\alpha\\beta}::InverseMetric.\n\n    sphe:={ g_{\\theta\\theta} = r**2,\n        g_{\\varphi\\varphi} = r**2 \\sin(\\theta)**2 }.\n    complete(sphe, $g^{\\alpha\\beta}$)\n\n    ch:= \\Gamma^{\\alpha}_{\\mu\\nu} = 1/2 g^{\\alpha\\beta} ( \\partial_{\\nu}{g_{\\beta\\mu}}\n                                                        +\\partial_{\\mu}{g_{\\beta\\nu}}\n                                                        -\\partial_{\\beta}{g_{\\mu\\nu}} );\n\n    evaluate(ch, sphe, rhsonly=True)\n\n    rm:= R^{\\rho}_{\\sigma\\mu\\nu} = +\\partial_{\\mu}{\\Gamma^{\\rho}_{\\sigma\\nu}}\n           -\\partial_{\\nu}{\\Gamma^{\\rho}_{\\sigma\\mu}}\n           +\\Gamma^{\\rho}_{\\beta\\mu} \\Gamma^{\\beta}_{\\sigma\\nu}\n           -\\Gamma^{\\rho}_{\\beta\\nu} \\Gamma^{\\beta}_{\\sigma\\mu};\n\n    substitute(rm, ch)\n    evaluate(rm, sphe, rhsonly=True)\n\n    ricci:= R_{\\sigma\\nu} = R^{\\rho}_{\\sigma\\rho\\nu};\n    substitute(ricci, rm)\n    evaluate(ricci, sphe, rhsonly=True)\n\n    R:= R = R_{\\sigma\\nu} g^{\\sigma\\nu};\n    substitute(R, ricci)\n    evaluate(R, sphe, rhsonly=True)\n    val = rhs(R)\n    tst:= @(val) - 2/r**2;\n    assert(tst==0)\n    print(\"Test 24 passed\")\n        \ntest24()\n\n# Evaluating with completely unspecified tensors.\n#\ndef test25():        \n    __cdbkernel__=create_scope()\n    {a,b,c}::Indices(values={0,1,2,3});\n    ex:= X^{a} Y_{a};\n    rl:= { Y_{0} = 3, Y_{2} = -5 };\n    evaluate(ex, rl)\n    tst:= 3 X^{0} - 5 X^{2} - @(ex);\n    assert(tst==0)\n    print(\"Test 25 passed\")\n\ntest25()\n        \ndef test26():\n    __cdbkernel__=create_scope()\n    {a,b,c}::Indices(values={0,1,2});\n    ex:= X^{a b} Y_{a b};\n    evaluate(ex)\n    tst:= X^{0 0} Y_{0 0} + X^{0 1} Y_{0 1} + X^{0 2} Y_{0 2}\n        + X^{1 0} Y_{1 0} + X^{1 1} Y_{1 1} + X^{1 2} Y_{1 2}\n        + X^{2 0} Y_{2 0} + X^{2 1} Y_{2 1} + X^{2 2} Y_{2 2} - @(ex):\n    sort_product(tst)\n    assert(tst==0)\n    print(\"Test 26 passed\")\n\ntest26()\n\ndef test27():\n    __cdbkernel__=create_scope()        \n    {r,t}::Coordinate;        \n    {m,n}::Indices(position=fixed, values={r,t});\n    {\\sigma,\\tau}::Coordinate;        \n    X^{m}::Depends(\\sigma,\\tau);\n    \\partial{#}::PartialDerivative;\n    ex:=\\partial_{\\tau}{X^{m}};\n    evaluate(ex)\n    tst:=\\components^{m}{\\comma{ \\comma{t} = \\partial_{\\tau}{X^{t}} }{ \\comma{r} = \\partial_{\\tau}{X^{r}} } } - @(ex);\n    collect_components(_)\n    assert(tst==0)\n    print(\"Test 27 passed\")\n\ntest27()\n    \n        \nimport cdb.relativity as rel\n# the line below does not work on Travis, so we state the metric here explicitly.\n#import cdb.relativity.schwarzschild as ss\n\ndef test28pre():\n    g:={g_{t t} = -1+2M/r, g_{r r} = 1/(1-2M/r), g_{\\theta\\theta} = r**2, g_{\\phi\\phi} = r**2*sin(\\theta)**2};\n    complete(g,$g^{\\mu\\nu}$);\n    ch=rel.christoffel_from_metric();\n    evaluate(ch, g, rhsonly=True);\n    \\ddot{#}::Accent;\n    \\dot{#}::Accent;\n    geodesic:= \\ddot{X^{\\mu}} + \\Gamma^{\\mu}_{\\nu\\rho} \\dot{X^{\\nu}} \\dot{X^{\\rho}} = 0;\n    # Doing evaluate here messes up the components node of the \\Gamma factor,\n    # there's a weird \\components inside a \\components. Can probably be tested\n    # with a simpler example.\n    substitute(geodesic, ch);\n    evaluate(geodesic);\n\n#test28pre()\n        \n    \ndef test28():\n    __cdbkernel__=create_scope()\n    {t,x}::Coordinate:\n    {m,n}::Indices(position=fixed, values={t,x});\n    a::Depends(t,x);\n    \\partial{#}::PartialDerivative;\n    ex:= (\\partial_{t}{a})**2/a**3+a;\n    evaluate(ex)\n    tst:= (\\partial_{t}{a})**2/a**3+a - @(ex);\n    assert(tst==0)\n    print(\"Test 28 passed\")\n\ntest28()\n\n\ndef test29():\n    __cdbkernel__=create_scope()\n    {t,r}::Coordinate;\n    {\\mu,\\nu,\\rho}::Indices(values={r,t});\n    ex:= T_{\\mu\\nu} = T_{\\mu\\nu};\n    rl:= { T_{r t} = Q, T_{t t} = N M };\n    evaluate(ex, rl, rhsonly=True)\n    # Double evaluation should not introduce additional \\components wrappers\n    # around scalars.\n    evaluate(ex, rl, rhsonly=True)\n    ex2=ex[1]\n    tst:= \\components_{\\mu\\nu}{\\comma{ \\comma{r}{t} = Q }{ \\comma{t}{t} = N M } } - @(ex2);\n    collect_components(tst)        \n    assert(tst==0)\n    print(\"Test 29 passed\")\n\ntest29()\n\ndef test30():\n    __cdbkernel__=create_scope()\n    {r,t}::Coordinate;\n    A::Depends(t);        \n    \\partial{#}::PartialDerivative;\n    ex:=\\partial_{t}{A};\n    evaluate(ex)\n    tst:=\\partial_{t}{A} - @(ex);\n    assert(tst==0)\n    print(\"Test 30a passed\")\n    ex2:= \\partial_{t}{ A**2 };\n    evaluate(ex2)\n    tst2:= 2A\\partial_{t}{A} - @(ex2);\n    assert(tst2==0)\n    print(\"Test 30b passed\")\n\ntest30()\n\ndef test31():\n    __cdbkernel__=create_scope()\n    {r,t}::Coordinate;\n    A::Depends(t);\n    \\partial{#}::PartialDerivative;\n    {\\mu,\\nu,\\rho}::Indices(values={r,t});\n    ex:= T_{\\mu\\nu} = T_{\\mu\\nu};\n    rl:= { T_{r t} = Q, T_{t t} = M };\n    glrl:= { g_{r r} = N, g_{t t} = B };\n    Rrl:= R = \\partial_{t}{A};\n    evaluate(ex, rl, rhsonly=True)\n    ex2:= T_{\\mu\\nu} - g_{\\mu\\nu} R;\n    substitute(ex2, ex)\n    substitute(ex2, Rrl)\n    evaluate(ex2, glrl)\n    tst:= \\components_{\\mu\\nu}{\\comma{ \\comma{r}{t} = Q }{ \\comma{t}{t} = -B \\partial_{t}{A} + M }{ \\comma{r}{r} = - N \\partial_{t}{A} }} - @(ex2);\n    assert(tst!=0)\n    collect_components(tst)\n    assert(tst==0)\n    print(\"Test 31 passed\")\n\ntest31()\n\n        \n\n# def test20():\n# __cdbkernel__=create_scope()\n# {a,b,c,d}::Indices(values={0,1,2}, position=fixed);\n# {a,b,c,d}::Integer(0..2);\n# \\Gamma{#}::GammaMatrix(metric=\\eta);\n# C_{a b c}::AntiSymmetric;\n# ex:= C_{a b c} \\Gamma^{a b c};\n# rl:= [ C_{0 1 2} = \\alpha ];\n# evaluate(ex, rl);\n# tst:= 6 \\Gamma^{0 1 2} - @(ex);\n# assert(tst)\n\n# def test32():\n#     # https://github.com/kpeeters/cadabra2/issues/86    \n#     __cdbkernel__=create_scope()\n#     {r,t}::Coordinate.\n#     {m,n}::Indices(values={t,r}, position=fixed).\n#     ex:= A_{m} = A_{m};\n#     rl:= A_{t} = 3;\n#     evaluate(ex, rl, rhsonly=True, simplify=True)\n#     ex2:= A_{m};\n#     evaluate(ex2, ex);\n#     tst:= \\components_{m}( \\comma{ \\comma{t} = 3  } ) - @(ex2);\n#     collect_components(_)\n#     assert(tst==0)\n#     print(\"Test 32 passed\")\n\ndef test32():\n    __cdbkernel__=create_scope()\n#kernel(scalar_backend=\"mathematica\")\n    {x,y,\\xi}::Coordinate;\n    {i,j,k}::Indices(values={x,y,\\xi});\n    \\partial{#}::PartialDerivative;\n    F_{i j}::Depends(x,\\xi);\n    ex:=\\partial_{i}{F_{i k}} + m**2 A_{k};\n    evaluate(ex)\n    tst:=\\components_{k}{ \\comma{ \\comma{\\xi} = m**2 A_{\\xi} + \\partial_{x}{F_{x \\xi}} + \\partial_{\\xi}{F_{\\xi \\xi}} }{ \\comma{y}=m**2 A_{y} + \\partial_{x}{F_{x y}} + \\partial_{\\xi}{F_{\\xi y}}}{ \\comma{x} = m**2 A_{x} + \\partial_{x}{F_{x x}} + \\partial_{\\xi}{F_{\\xi x}} } - @(ex);\n    collect_components(tst)\n    assert(tst==0)\n    print(\"Test 31 passed\")\n\ntest32()\n\ndef test33():\n    __cdbkernel__=create_scope()\n    {\\sigma,\\tau}::Coordinate;                          \n    {a,b,c}::Indices(worldsheet, values={\\sigma, \\tau});\n    #{\\mu,\\nu,\\rho}::Indices(targetspace, values={0,1,2,3} );\n    #{\\mu,\\nu,\\rho}::Indices(targetspace);\n    \\partial{#}::PartialDerivative;\n    X^{a?}::Depends(\\sigma, \\tau);\n    X^{\\mu}::Depends(\\sigma, \\tau);    \n    ex:= \\eta^{a b} \\partial_{a}{ X^{\\mu} } \\partial_{b}{ X^{\\nu} } g_{\\mu\\nu};\n    mink:= { \\eta^{\\tau\\tau}=-1, \\eta^{\\sigma\\sigma}=1 };\n    evaluate(ex, mink)\n    tst:= - g_{\\mu\\nu}\\partial_{\\tau}{X^{\\mu}}\\partial_{\\tau}{X^{\\nu}} + g_{\\mu\\nu}\\partial_{\\sigma}{X^{\\mu}}\\partial_{\\sigma}{X^{\\nu}} - @(ex);\n    assert(tst==0)\n    print(\"Test 33 passed\")\n\ntest33()\n        \ndef test34():\n    __cdbkernel__=create_scope()\n    {\\sigma,\\tau}::Coordinate;                          \n    {a,b,c}::Indices(worldsheet, values={\\sigma, \\tau});\n    \\partial{#}::PartialDerivative;\n    X^{a?}::Depends(\\sigma, \\tau);\n    X^{\\mu}::Depends(\\sigma, \\tau);    \n    ex:= \\eta^{a b} \\partial_{a}{ X^{\\mu} } \\partial_{b}{ X^{\\nu} };\n    mink:= { \\eta^{\\tau\\tau}=-1, \\eta^{\\sigma\\sigma}=1 };\n    evaluate(ex, mink)\n    tst:= - \\partial_{\\tau}{X^{\\nu}}\\partial_{\\tau}{X^{\\mu}} + \\partial_{\\sigma}{X^{\\nu}}\\partial_{\\sigma}{X^{\\mu}} - @(ex);\n    assert(tst==0)\n    print(\"Test 34 passed\")\n\ntest34()\n\ndef test35():\n    __cdbkernel__=create_scope()\n    {r,t,\\phi,\\theta}::Coordinate.\n    {\\mu,\\nu,\\rho,\\sigma,\\lambda,\\kappa,\\gamma,\\chi}::Indices(values={t,r,\\phi,\\theta}, position=fixed).\n    \\partial{#}::PartialDerivative.\n    g_{\\mu\\nu}::Metric.\n    g^{\\mu\\nu}::InverseMetric.         \n    ss:= { g_{t t} = -(1-2 M/r),  g_{r r} = 1/(1-2 M/r),\n           g_{\\theta\\theta} = r**2,  g_{\\phi\\phi}=r**2 \\sin(\\theta)**2 };\n    complete(ss, $g^{\\mu\\nu}$)\n    ch:= \\Gamma^{\\mu}_{\\nu\\rho} = 1/2 g^{\\mu\\sigma} ( \\partial_{\\rho}{g_{\\nu\\sigma}}\n                                                +\\partial_{\\nu}{g_{\\rho\\sigma}}\n                                                -\\partial_{\\sigma}{g_{\\nu\\rho}} );\n    evaluate(ch, ss, rhsonly=True)\n    comp=substitute($\\Gamma^{r}_{\\phi\\phi}$, ch)\n    tst:= (2M-r) \\sin(\\theta)**2 - @(comp);\n    assert(tst==0)\n    print(\"Test 35 passed\")\n\ntest35()\n\ndef test36():\n    __cdbkernel__=create_scope()\n    {r,t}::Coordinate;\n    {i,j}::Indices(values={r,t});\n    F::Depends(r);\n    \\partial{#}::PartialDerivative;\n    ex:=\\partial_{i}{\\exp(F)};\n    evaluate(ex)\n    tst:=\\components_{i}( \\comma{ \\comma{r} = \\exp(F) \\partial_{r}{F}  } ) - @(ex);\n    collect_components(tst)\n    assert(tst==0)\n    print(\"Test 36 passed\")\n\ntest36()\n\ndef test37():\n    __cdbkernel__=create_scope()\n    {r,t,\\phi,\\theta}::Coordinate.\n    {\\mu,\\nu,\\rho,\\sigma,\\lambda,\\kappa,\\gamma,\\chi}::Indices(values={t,r,\\phi,\\theta}, position=fixed).\n    \\partial{#}::PartialDerivative.\n    g_{\\mu\\nu}::Metric.\n    g^{\\mu\\nu}::InverseMetric.\n    g::Determinant(g_{\\mu\\nu}).\n    gt::Trace(g_{\\mu\\nu}).\n    ss:= { g_{t t} = -(1-2 M/r),  g_{r r} = 1/(1-2 M/r),\n           g_{\\theta\\theta} = r**2,  g_{\\phi\\phi}=r**2 \\sin(\\theta)**2 };\n    complete(ss, $g$)\n    complete(ss, $gt$)\n    ex:= g;\n    substitute(ex, ss)\n    simplify(ex)\n    tst:= -r**4 \\sin(\\theta)**2 - @(ex);\n    assert(tst==0)\n    print(\"Test 37 passed\")\n    ex:= gt;\n    substitute(ex, ss)\n\ntest37()\n\n\ndef test38():\n    __cdbkernel__=create_scope()\n    {\\mu,\\nu}::Indices(values={1,2,3,4}, position=fixed);\n    \\partial{#}::PartialDerivative;\n    {A^{1},A^{2},A^{3},A^{4}}::Depends(\\partial{#});\n    ex:=\\partial_{\\mu}{A^{\\mu}};\n    evaluate(ex)\n    tst:= \\partial_{1}{A^{1}} + \\partial_{2}{A^{2}} + \\partial_{3}{A^{3}} + \\partial_{4}{A^{4}} - @(ex);\n    assert(tst==0)\n    print(\"Test 38 passed\")\n\n#     So this fails, because we do not check the dependence correctly.\n#     But the general logic also fails if you have a \\partial_{\\mu}{A} \\partial_{\\mu}{A} node with\n#     a generic dependence A::Depends(\\partial{#}), because neither of the two factors will then\n#         know over which values of mu to sum, and handle_derivative only sums over index values\n#         for which we have a dependence.\n# \n#         Whenever we encounter a depencence on \\partial{#}, we need to replace that with\n#             a dependence on all index values which the unique_indices->values contains.\n#             Also do that when the dep is an index itself.\n    \n\n        \ntest38()\n\ndef test39():\n    __cdbkernel__=create_scope()\n    {i,j,k,l}::Indices(vector,fourD,values={0..3},position=fixed);\n    {i,j,k,l}::Integer(0..3);\n    \\partial{#}::Derivative;\n    {\\kappa,\\lambda,\\mu,\\nu}::Indices(vector, threeD,parent=fourD,values={1..3},position=fixed);\n    {\\kappa,\\lambda,\\mu,\\nu}::Integer(1..3);\n    \\epsilon^{\\lambda \\mu \\nu }::EpsilonTensor;\n    ex:=\\epsilon^{\\lambda \\mu \\nu };\n    evaluate(ex, $$);        \n    assert( ex[3][1][1] == -1 )\n    print(\"Test 39 passed\")\n\ntest39()\n        \nprint(list(map(lambda x: str(x), server.totals())))\n\ndef test40():\n    __cdbkernel__=create_scope()\n    {k,l,m,n}::Indices(values={1..3}).\n    \\epsilon{#}::EpsilonTensor.\n    ex:= T_{m} = e_{m 1};\n    evaluate(ex, rhsonly=True)\n    ex = rhs(ex)\n    tst:= \\components_{m}{\\comma{\\comma{1}=e_{1 1}}{\\comma{2}=e_{2 1}}{\\comma{3}=e_{3 1}}} - @(ex);\n    collect_components(tst)\n    assert(tst==0)\n    print(\"Test 40 passed.\")\n\ntest40()\n\ndef test41():\n    __cdbkernel__=create_scope()\n    {k,l,m,n}::Indices(values={1..3}).\n    \\epsilon{#}::EpsilonTensor.\n    ex:= T_{m n} = \\epsilon_{1 m n};\n    evaluate(ex, rhsonly=True);\n    ex = rhs(ex)\n    tst:= \\components_{m n}{\\comma{\\comma{2}{3}=1}{\\comma{3}{2}=-1}} - @(ex);\n    collect_components(tst)\n    assert(tst==0)\n    print(\"Test 41 passed\")\n\ntest41()\n\ndef test42():\n    __cdbkernel__=create_scope()\n    {k,l,m,n}::Indices(rotation, values={1..3}).\n    \\epsilon{#}::EpsilonTensor.\n    ex := (K_{1})_{m n} e_{1}_{n} = \\epsilon_{1 m n} e_{1}_{n};\n    evaluate(ex, $e_{1}_{1} = 1, e_{1}_{2} = a, e_{1}_{3} = b$, rhsonly=True);\n    ex = rhs(ex)\n    tst:= \\components_{m}{\\comma{\\comma{2}=b}{\\comma{3}=-a}} - @(ex);\n    collect_components(tst)\n    assert(tst==0)\n    print(\"Test 42 passed\")\n\ntest42()\n\nfrom cdb.core.component import *\n\ndef test43():\n    __cdbkernel__=create_scope()\n    \\epsilon{#}::EpsilonTensor;\n    {i,j,k}::Indices;\n    {i,j,k}::Integer(1..3);\n    ex:= \\epsilon_{i j k} a_{j} v_{k} + a_{i} a_{j} v_{j};\n    rl:= { a_{1}=1, a_{2}=1, a_{3}=1 };\n    evaluate(ex, rl);\n    c = get_component(ex, $1$)\n    tst:= 2 v_{3} + v_{1} - @(c);\n    assert(tst==0)\n\ntest43()\n"
  },
  {
    "path": "tests/decompose.cdb",
    "content": "\n{m,n,p,q,r,s,t,u,v,w,a,b,c,d,e,f}::Indices(vector);\nW_{m n p q}::WeylTensor;\nW1:= W_{m n a b} W_{n p b c} W_{p s c d} W_{s m d a};\nW2:= W_{m n a b} W_{n p b c} W_{m s c d} W_{s p d a};\nW3:= W_{m n a b} W_{p s b a} W_{m n c d} W_{p s d c};\nW4:= W_{m n a b} W_{m n b a} W_{p s c d} W_{p s d c};\nW5:= W_{m n a b} W_{n p b a} W_{p s c d} W_{s m d c};\nW6:= W_{m n a b} W_{p s b a} W_{m p c d} W_{n s d c};\nW7:= W_{m n}^{m n} W_{p q}^{p q} W_{r s}^{r s} W_{t u}^{t u};\n# @asym!(%){^{m},^{n},^{p},^{q},^{r},^{s},^{t},^{u}}:\n# @substitute!(%){W_{a b}^{c d} -> W_{a b c d}}:\n\nasym(W7, $^{m},^{n},^{p},^{q},^{r},^{s},^{t},^{u}$)\nsubstitute(W7, $W_{a b}^{c d} -> W_{a b c d}$)\ncanonicalise(W7);\n\n\nbasisW4:= { @(W1), @(W2), @(W3), @(W4), @(W5), @(W6), @(W7) };\n\nex:= W_{p q r s} W_{p t r u} W_{t v q w} W_{u v s w} - W_{p q r s} W_{p q t u} W_{r v t w} W_{s v u w};\ndecompose(ex, basisW4);\n"
  },
  {
    "path": "tests/decompose.cnb",
    "content": "{\n\t\"cells\" : \n\t[\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Indices(position=free) to~}\\\\left[m,~\\\\discretionary{}{}{} n,~\\\\discretionary{}{}{} p,~\\\\discretionary{}{}{} q,~\\\\discretionary{}{}{} r,~\\\\discretionary{}{}{} s,~\\\\discretionary{}{}{} t,~\\\\discretionary{}{}{} u,~\\\\discretionary{}{}{} v,~\\\\discretionary{}{}{} w,~\\\\discretionary{}{}{} a,~\\\\discretionary{}{}{} b,~\\\\discretionary{}{}{} c,~\\\\discretionary{}{}{} d,~\\\\discretionary{}{}{} e,~\\\\discretionary{}{}{} f\\\\right].\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property TableauSymmetryWeylTensor to~}W_{m n p q}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"W_{m n a b} W_{n p b c} W_{p s c d} W_{s m d a}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}W_{m n a b} W_{n p b c} W_{p s c d} W_{s m d a}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"W_{m n a b} W_{n p b c} W_{m s c d} W_{s p d a}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}W_{m n a b} W_{n p b c} W_{m s c d} W_{s p d a}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"W_{m n a b} W_{p s b a} W_{m n c d} W_{p s d c}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}W_{m n a b} W_{p s b a} W_{m n c d} W_{p s d c}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"W_{m n a b} W_{m n b a} W_{p s c d} W_{p s d c}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}W_{m n a b} W_{m n b a} W_{p s c d} W_{p s d c}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"W_{m n a b} W_{n p b a} W_{p s c d} W_{s m d c}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}W_{m n a b} W_{n p b a} W_{p s c d} W_{s m d c}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"W_{m n a b} W_{p s b a} W_{m p c d} W_{n s d c}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}W_{m n a b} W_{p s b a} W_{m p c d} W_{n s d c}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"W_{m n}^{m n} W_{p q}^{p q} W_{r s}^{r s} W_{t u}^{t u}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}W_{m n}\\\\,^{m n} W_{p q}\\\\,^{p q} W_{r s}\\\\,^{r s} W_{t u}\\\\,^{t u}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"{m,n,p,q,r,s,t,u,v,w,a,b,c,d,e,f}::Indices(vector);\\nW_{m n p q}::WeylTensor;\\nW1:= W_{m n a b} W_{n p b c} W_{p s c d} W_{s m d a};\\nW2:= W_{m n a b} W_{n p b c} W_{m s c d} W_{s p d a};\\nW3:= W_{m n a b} W_{p s b a} W_{m n c d} W_{p s d c};\\nW4:= W_{m n a b} W_{m n b a} W_{p s c d} W_{p s d c};\\nW5:= W_{m n a b} W_{n p b a} W_{p s c d} W_{s m d c};\\nW6:= W_{m n a b} W_{p s b a} W_{m p c d} W_{n s d c};\\nW7:= W_{m n}^{m n} W_{p q}^{p q} W_{r s}^{r s} W_{t u}^{t u};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"asym(W7, $^{m},^{n},^{p},^{q},^{r},^{s},^{t},^{u}$)\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"substitute(W7, $W_{a b}^{c d} -> W_{a b c d}$)\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \" 1/840 W_{m n p q} W_{m n p q} W_{r s t u} W_{r s t u} -  2/105 W_{m n p q} W_{m n p r} W_{q s t u} W_{r s t u} +  1/420 W_{m n p q} W_{m n r s} W_{p q t u} W_{r s t u} -  4/105 W_{m n p q} W_{m n r s} W_{p t r u} W_{q u s t} +  2/105 W_{m n p q} W_{m r p s} W_{n t q u} W_{r t s u} -  4/105 W_{m n p q} W_{m r p s} W_{n t r u} W_{q t s u}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\frac{1}{840}W_{m n p q} W_{m n p q} W_{r s t u} W_{r s t u} - \\\\frac{2}{105}W_{m n p q} W_{m n p r} W_{q s t u} W_{r s t u}+\\\\frac{1}{420}W_{m n p q} W_{m n r s} W_{p q t u} W_{r s t u} - \\\\frac{4}{105}W_{m n p q} W_{m n r s} W_{p t r u} W_{q u s t}+\\\\frac{2}{105}W_{m n p q} W_{m r p s} W_{n t q u} W_{r t s u} - \\\\frac{4}{105}W_{m n p q} W_{m r p s} W_{n t r u} W_{q t s u}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"canonicalise(W7);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"{W_{m n a b} W_{n p b c} W_{p s c d} W_{s m d a}, W_{m n a b} W_{n p b c} W_{m s c d} W_{s p d a}, W_{m n a b} W_{p s b a} W_{m n c d} W_{p s d c}, W_{m n a b} W_{m n b a} W_{p s c d} W_{p s d c}, W_{m n a b} W_{n p b a} W_{p s c d} W_{s m d c}, W_{m n a b} W_{p s b a} W_{m p c d} W_{n s d c},  1/840 W_{m n p q} W_{m n p q} W_{r s t u} W_{r s t u} -  2/105 W_{m n p q} W_{m n p r} W_{q s t u} W_{r s t u} +  1/420 W_{m n p q} W_{m n r s} W_{p q t u} W_{r s t u} -  4/105 W_{m n p q} W_{m n r s} W_{p t r u} W_{q u s t} +  2/105 W_{m n p q} W_{m r p s} W_{n t q u} W_{r t s u} -  4/105 W_{m n p q} W_{m r p s} W_{n t r u} W_{q t s u}}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\left[W_{m n a b} W_{n p b c} W_{p s c d} W_{s m d a},~\\\\discretionary{}{}{} W_{m n a b} W_{n p b c} W_{m s c d} W_{s p d a},~\\\\discretionary{}{}{} W_{m n a b} W_{p s b a} W_{m n c d} W_{p s d c},~\\\\discretionary{}{}{} W_{m n a b} W_{m n b a} W_{p s c d} W_{p s d c},~\\\\discretionary{}{}{} W_{m n a b} W_{n p b a} W_{p s c d} W_{s m d c},~\\\\discretionary{}{}{} W_{m n a b} W_{p s b a} W_{m p c d} W_{n s d c},~\\\\discretionary{}{}{} \\\\frac{1}{840}W_{m n p q} W_{m n p q} W_{r s t u} W_{r s t u} - \\\\frac{2}{105}W_{m n p q} W_{m n p r} W_{q s t u} W_{r s t u}+\\\\frac{1}{420}W_{m n p q} W_{m n r s} W_{p q t u} W_{r s t u} - \\\\frac{4}{105}W_{m n p q} W_{m n r s} W_{p t r u} W_{q u s t}+\\\\frac{2}{105}W_{m n p q} W_{m r p s} W_{n t q u} W_{r t s u} - \\\\frac{4}{105}W_{m n p q} W_{m r p s} W_{n t r u} W_{q t s u}\\\\right]\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"basisW4:= { @(W1), @(W2), @(W3), @(W4), @(W5), @(W6), @(W7) };\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"W_{p q r s} W_{p t r u} W_{t v q w} W_{u v s w}-W_{p q r s} W_{p q t u} W_{r v t w} W_{s v u w}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}W_{p q r s} W_{p t r u} W_{t v q w} W_{u v s w}-W_{p q r s} W_{p q t u} W_{r v t w} W_{s v u w}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex:= W_{p q r s} W_{p t r u} W_{t v q w} W_{u v s w} - W_{p q r s} W_{p q t u} W_{r v t w} W_{s v u w};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"{ 1/4 ,  1/2 ,  1/32 ,  1/64 ,  -  1/4 ,  1/8 ,  -  105/8 } + { -  1/4 ,  1/2 ,  -  1/32 ,  -  1/64 ,  1/4 ,  -  3/8 ,  105/8 }\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\left[\\\\frac{1}{4},~\\\\discretionary{}{}{} \\\\frac{1}{2},~\\\\discretionary{}{}{} \\\\frac{1}{32},~\\\\discretionary{}{}{} \\\\frac{1}{64},~\\\\discretionary{}{}{}  - \\\\frac{1}{4},~\\\\discretionary{}{}{} \\\\frac{1}{8},~\\\\discretionary{}{}{}  - \\\\frac{105}{8}\\\\right]+\\\\left[ - \\\\frac{1}{4},~\\\\discretionary{}{}{} \\\\frac{1}{2},~\\\\discretionary{}{}{}  - \\\\frac{1}{32},~\\\\discretionary{}{}{}  - \\\\frac{1}{64},~\\\\discretionary{}{}{} \\\\frac{1}{4},~\\\\discretionary{}{}{}  - \\\\frac{3}{8},~\\\\discretionary{}{}{} \\\\frac{105}{8}\\\\right]\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"decompose(ex, basisW4, deep=True);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1\n}\n"
  },
  {
    "path": "tests/delta.cdb",
    "content": "{a,b,c,d,e}::Indices;\n\\delta{#}::KroneckerDelta;\nex:=\\delta^{a}_{b}^{c}_{d};\nexpand_delta(_);\n\n\n{a,b,c,d,e,m,n,p,q,r,s,t}::Indices;\nA_{a b c}::AntiSymmetric;\n\\delta{#}::KroneckerDelta;\nex:=\\delta^{a}_{b}^{c}_{d} A_{a c e};\nexpand_delta(_);\n\n# Lovelock 2nd order (Gauss-Bonnet)\n{a,b,c,d,e,m,n,p,q,r,s,t}::Indices;\n\\delta{#}::KroneckerDelta;\nR_{m n p q}::RiemannTensor;\nex:=\\delta_{a m b n c p d q} R_{a b m n} R_{c d p q};\nexpand_delta(_);\ndistribute(_);\neliminate_kronecker(_);\nmeld(_);\nsubstitute(_, $R_{m n m n}=R, R_{m c p c} = R_{m p}, R_{c m c p} = R_{m p}$);\n\n# Lovelock 3rd order\n{a#, m#}::Indices;\n\\delta{#}::KroneckerDelta;\nR_{m1 m2 m3 m4}::RiemannTensor;\nex:=\\delta_{a1 m1 a2 m2 a3 m3 a4 m4 a5 m5 a6 m6} R_{a1 a2 m1 m2} R_{a3 a4 m3 m4} R_{a5 a6 m5 m6};\nexpand_delta(_);\ndistribute(_);\neliminate_kronecker(_);\nsubstitute(_, $R_{m1 m2 m1 m2}=R, R_{m1 a1 m1 a2} = R_{a1 a2}, R_{a1 m1 m1 a2} = -R_{a1 a2}, R_{m1 a1 a2 m1} = -R_{a1 a2}, R_{a1 m1 a2 m1} = R_{a1 a2}$, repeat=True);\nsort_product(_)\nmeld(_);\nprint(len(ex))\n\n# Lovelock 4th order    \n{a#, m#}::Indices;\n\\delta{#}::KroneckerDelta;\nR_{m1 m2 m3 m4}::RiemannTensor;\nex:=\\delta_{a1 m1 a2 m2 a3 m3 a4 m4 a5 m5 a6 m6 a7 m7 a8 m8} R_{a1 a2 m1 m2} R_{a3 a4 m3 m4} R_{a5 a6 m5 m6} R_{a7 a8 m7 m8};\nexpand_delta(_);\ndistribute(_);\neliminate_kronecker(_);\nprint(len(ex))\n# 2520 terms\nsubstitute(_, $R_{m1 m2 m1 m2}=R, R_{m1 a1 m1 a2} = R_{a1 a2}, R_{a1 m1 m1 a2} = -R_{a1 a2}, R_{m1 a1 a2 m1} = -R_{a1 a2}, R_{a1 m1 a2 m1} = R_{a1 a2}$, repeat=True);\nsort_product(_)\nprint(len(ex))\n# 1489 terms\ncanonicalise(_);\nrename_dummies(_);\nprint(len(ex))\n# 25 terms\nmeld(_);\nprint(len(ex))  \n# 20 terms\n\n# Lovelock 5th order    \n{a#, m#}::Indices;\n\\delta{#}::KroneckerDelta;\nR_{m1 m2 m3 m4}::RiemannTensor;\nex:=\\delta_{a1 m1 a2 m2 a3 m3 a4 m4 a5 m5 a6 m6 a7 m7 a8 m8 a9 m9 a10 m10} R_{a1 a2 m1 m2} R_{a3 a4 m3 m4} R_{a5 a6 m5 m6} R_{a7 a8 m7 m8} R_{a9 a10 m9 m10};\nexpand_delta(_)\ndistribute(_) # need l_applied_no_new_dummies; slow now\neliminate_kronecker(_) # ditto; slow now\n# 113400 terms\nprint(len(ex))\ncanonicalise(_);  # takes a long time\n# 15814 terms\nprint(len(ex))\nrename_dummies(_);\n# 452 terms\nprint(len(ex))\nmeld(_);\n#  terms\nprint(len(ex))  \nsubstitute(_, $R_{m1 m2 m1 m2}=R, R_{m1 a1 m1 a2} = R_{a1 a2}, R_{a1 m1 m1 a2} = -R_{a1 a2}, R_{m1 a1 a2 m1} = -R_{a1 a2}, R_{a1 m1 a2 m1} = R_{a1 a2}$, repeat=True);\n\n\n{m,n,p,q,r,s,t,u,x,y,s,v,z,w,a,b,c,d,e,f,i,j,k,l#}::Indices(vector).\n{m,n,p,q,r,s,t,u,x,y,s,v,z,w,a,b,c,d,e,f,i,j,k,l#}::Integer(0..D-1).\ng_{i j}::Metric.\ng^{i j}::InverseMetric.\ng_{i j}::Symmetric.\nS_{i j}::Symmetric.\nW_{m n p q}::WeylTensor.\n\\delta{#}::KroneckerDelta;\nR_{m n p q}::RiemannTensor;\n\nex5:=\\delta^{i}_{a}^{j}_{b}^{k}_{c}^{l}_{d}^{m}_{e}^{n}_{r}^{t}_{p}^{x}_{q}^{y}_{z}^{s}_{w}\nR^{a b}_{i j}R^{c d}_{k l}R^{e r}_{m n}R^{p q}_{t x}R^{z w}_{y s};\nexpand_delta(_);\n"
  },
  {
    "path": "tests/derivative.cdb",
    "content": "\n# Derivatives are generic objects satisfying the product rule\n# in one or more of their arguments. Commutators are examples of\n# such objects.\n\ndef test01():\n    __cdbkernel__=create_scope()\n    D(#)::Derivative.\n    obj1:= a*b*D(c*d*e)*f*g;\n    product_rule(_)\n    tst1:= a*b*(D(c)*d*e+c*D(d)*e+c*d*D(e))*f*g-@(obj1);\n    assert(tst1==0)\n    print(\"Test 01 passed\")\n\ntest01()\n\ndef test02():\n    __cdbkernel__=create_scope()\n    D(a??)(b??)(c??)::Derivative.\n    obj2:= a*b*D(c*d*e)(h1)(h2)*f*g;\n    product_rule(_)\n    tst2:= a*b*(D(c)(h1)(h2)*d*e+c*D(d)(h1)(h2)*e+c*d*D(e)(h1)(h2))*f*g-@(obj2);\n    assert(tst2==0)\n    print(\"Test 02 passed\")\n    \ntest02()\n\n# Using the properties of \\diff.\n\ndef test03():\n    __cdbkernel__=create_scope()\n    \\diff{#}::PartialDerivative.\n    obj5:= \\diff{A*B}_\\mu;\n    product_rule(_)\n    tst5:= \\diff{A}_\\mu * B + A * \\diff{B}_\\mu - @(obj5);\n    assert(tst5==0)\n    print(\"Test 03 passed\")\n    \ntest03()\n\ndef test04():\n    __cdbkernel__=create_scope()\n    \\diff{#}::PartialDerivative;\n    obj6:= \\diff{g^{\\mu \\kappa} * \\diff{g_{\\kappa \\nu}}_{\\rho}}_{\\sigma};\n    product_rule(_)\n    tst6:= \\diff{g^{\\mu \\kappa}}_{\\sigma} * \\diff{g_{\\kappa \\nu}}_{\\rho}\n        +g^{\\mu \\kappa} * \\diff{g_{\\kappa \\nu}}_{\\rho \\sigma} - @(obj6);\n    assert(tst6==0)\n    print(\"Test 04 passed\")\n    \ntest04()\n\ndef test07():\n    __cdbkernel__=create_scope()\n    \\diff{#}::PartialDerivative;\n    {\\mu,\\nu,\\rho,\\sigma,\\kappa,\\lambda,\\eta}::Indices(spacetime);\n    obj7:= g^{\\eta \\kappa} * \\diff{\\eta_{\\nu \\sigma}}_{\\kappa} * g^{\\mu \\lambda} * \\diff{eta_{\\lambda \\eta}}_{\\rho};\n    rl:=\\diff{\\eta_{\\mu\\nu}}_{\\rho} -> 0;\n    substitute(obj7, rl)\n    assert(obj7==0)\n    print(\"Test 07 passed\")\n    \ntest07()\n\n# \\delta in combination with \\diff\n#\ndef test08():\n    __cdbkernel__=create_scope()\n    \\delta_{n q}::KroneckerDelta;\n    \\diff{#}::Derivative;\n    obj8:= \\diff{A_{m n}}_{p} \\delta_{n q} \\delta_{p t};\n    eliminate_kronecker(_)\n    tst8:= \\diff{A_{m q}}_{t} - @(obj8);\n    assert(tst8==0)\n    print(\"Test 08 passed\")\n    \ntest08()\n\n# Multiple derivatives and the product rule\n\ndef test09():\n    __cdbkernel__=create_scope()\n    \\diff{#}::PartialDerivative.\n    obj9:= 3 \\diff_{m n}{4*A*B};\n    product_rule(_)\n    distribute(_)\n    product_rule(_)\n    tst9:= 12 \\diff_{m n}{A} B + 12 \\diff_{m}{A} \\diff_{n}{B} + 12 \\diff_{n}{A} \\diff_{m}{B} + 12 A \\diff_{m n}{B} - @(obj9);\n    assert(tst9==0)\n    print(\"Test 09 passed\")\n    \ntest09()\n\n# Order of child nodes on PartialDerivative.\n\ndef test10():\n    __cdbkernel__=create_scope()\n    {a,b,c,d}::Indices(vector).\n    \\partial{#}::PartialDerivative.\n    A_{a b}::AntiSymmetric.\n    obj10:= \\partial_{b a}{ A_{d c} };\n    canonicalise(_)\n    tst10:= \\partial_{a b}{ A_{c d} } + @(obj10);\n    collect_terms(_)\n    assert(tst10==0)\n    print(\"Test 10 passed\")\n    \ntest10()\n\ndef test10b():\n    __cdbkernel__=create_scope()\n    {a,b,c,d}::Indices(vector).\n    \\partial{#}::PartialDerivative.\n    A_{a b}::AntiSymmetric.\n    obj10b:= \\partial{ A_{d c} }_{b a};\n    canonicalise(_)\n    tst10b:= \\partial{ A_{c d} }_{a b} + @(obj10b);\n    assert(tst10b==0)\n    print(\"Test 10b passed\")\n    \ntest10b()\n\n# Multiple derivatives again\n#\n\n# def test11():\n#     __cdbkernel__=create_scope()\n#     \\partial{#}::PartialDerivative.\n#     obj11a:= \\partial(A B C)_{a b};\n#     product_rule(_)\n#     tst11a:= \\partial{\\partial(A)_{a} * B * C + A * \\partial(B)_{a} * C + A * B * \\partial(C)_{a}}_{b} - @(obj11a);\n#     collect_terms(_)\n#     assert(tst11a==0)\n# \n# test11()\n\ndef test11b():\n    __cdbkernel__=create_scope()\n    \\partial{#}::PartialDerivative.\n    obj11b:= \\partial_{a b}(A B C);\n    product_rule(_)\n    tst11b:= \\partial_{a}{\\partial_{b}(A) * B * C + A * \\partial_{b}(B) * C + A * B * \\partial_{b}(C)} - @(obj11b);\n    collect_terms(_)\n    assert(tst11b==0)\n    print(\"Test 11b passed\")\n    \ntest11b()\n\n# More tricky derivatives\ndef test12():\n    __cdbkernel__=create_scope()\n    \\Omega{#}::Derivative.\n    {A,B,C,D}::Depends(\\Omega{#});\n    obj12:= \\Omega_{a}(A B)(C D);\n    product_rule(_)\n    product_rule(_)\n    distribute(_)\n    tst12:= \\Omega_{a}(A)(C) * D * B + C * \\Omega_{a}(A)(D) * B + A * \\Omega_{a}(B)(C) * D + A * C * \\Omega_{a}(B)(D)\n        -@(obj12);\n    collect_terms(_)\n    assert(tst12==0)\n    print(\"Test 12 passed\")\n    \ntest12()\n\n# Test 13: Inheritance\n#\n# reset.\n# \\nabla{#}::Derivative.\n# A_{m n}::Traceless.\n# obj13:= \\nabla_{m}{A_{p p}}*Q_{m};\n# canonicalise(_);\n\n# Product_rule on powers\n\ndef test14():\n    __cdbkernel__=create_scope()\n    \\partial{#}::PartialDerivative.\n    obj14a:= \\partial_{m n}{A**2};\n    product_rule(_)\n    tst14a:= \\partial_{m}(2*A*\\partial_{n}{A}) - @(obj14a);\n    collect_terms(_)\n    assert(tst14a==0)\n    print(\"Test 14 passed\")\n    \ntest14()\n\ndef test14b():\n    __cdbkernel__=create_scope()\n    \\partial{#}::PartialDerivative.\n    obj14b:= \\partial_{m n}{A**3};\n    product_rule(_)\n    tst14b:= \\partial_{m}(3*A**2*\\partial_{n}{A}) - @(obj14b);\n    collect_terms(_)\n    assert(tst14b==0)\n    print(\"Test 14b passed\")\n    \ntest14b()\n\n# reset.\n# \\partial{#}::PartialDerivative.\n# obj14c:= \\partial_{m n}{A**(d+1)};\n# product_rule(_);\n# # FIXME\n\ndef test14d():\n    __cdbkernel__=create_scope()\n    \\partial{#}::PartialDerivative.\n    obj14d:= \\partial_{m n}{A**d};\n    product_rule(_)\n    tst14d:= \\partial_{m}(d * A**(d - 1) * \\partial_{n}{A}) - @(obj14d);\n    collect_terms(_)\n    assert(tst14d==0)\n    print(\"Test 14d passed\")\n    \ntest14d()\n\ndef test14f():\n    __cdbkernel__=create_scope()\n    \\partial{#}::PartialDerivative.\n    obj14f:= \\partial{A*\\partial{A}};\n    product_rule(_)\n    tst14f:= \\partial{A} * \\partial{A} + A * \\partial{\\partial{A}} - @(obj14f);\n    collect_terms(_)\n    assert(tst14f==0)\n    print(\"Test 14f passed\")\n    \ntest14f()\n\ndef test15():\n    __cdbkernel__=create_scope()\n    \\partial{#}::PartialDerivative.\n    obj15:= \\partial{-a**2};\n    product_rule(_)\n    tst15:= 2 a \\partial{a} + @(obj15);\n    collect_terms(_)\n    assert(tst15==0)\n    print(\"Test 15 passed\")\n    \ntest15()\n\ndef test16():\n    __cdbkernel__=create_scope()\n    \\partial{#}::PartialDerivative.\n    obj16:= \\partial{-a**3};\n    product_rule(_)\n    tst16:= 3 a**2 \\partial{a} + @(obj16);\n    collect_terms(_)\n    assert(tst16==0)\n    print(\"Test 16 passed\")\n    \ntest16()\n\n# Flattening\n#\ndef test17():\n    __cdbkernel__=create_scope()\n    \\partial{#}::PartialDerivative.\n    obj17:= \\partial_{a}{\\partial_{b c}{F}};\n    tst17:= \\partial_{a b c}{F} - @(obj17);\n    assert(tst17==0)\n    print(\"Test 17 passed\")\n    \ntest17()\n\n# # Test 18: more flattening\n# #\n# # FIXME: Because multi-derivatives get collected, we would now need\n# # to have a notation like \\nabla_{a??.. b}{A??} -> \n# \\partial{#}::PartialDerivative.\n# \\nabla{#}::Derivative.\n# obj18:= \\nabla_{a}{\\nabla_{b}{F}};\n# substitute(_, \"\\nabla_{a}{A??} -> \\partial_{a}{A??}\" );\n# tst18:= \\partial_{a b}{F} - @(obj18);\n# collect_terms(_);\n# assert(tst18);\n# \n\n# Test 19: Grassman derivatives\n#\ndef test19():\n    __cdbkernel__=create_scope()\n    {\\alpha,\\beta,\\gamma}::Indices(spinor).\n    \\theta^{\\alpha}::Coordinate.\n    \\theta^{\\alpha}::SelfAntiCommuting.\n    D{#}::Derivative.\n    obj19a:= D_{\\theta^{\\alpha}}{\\theta^\\beta \\theta^\\gamma};\n    product_rule(_)\n    tst19a:= D_{\\theta^{\\alpha}}{\\theta^{\\beta}} \\theta^{\\gamma}  \n             - \\theta^{\\beta} D_{\\theta^{\\alpha}}{\\theta^{\\gamma}} - @(obj19a);\n    assert(tst19a==0)\n    print(\"Test 19 passed\")\n    \ntest19()\n\ndef test19b():\n    __cdbkernel__=create_scope()\n    {\\alpha,\\beta,\\gamma}::Indices(spinor).\n    {\\alpha,\\beta,\\gamma}::AntiCommuting.\n    \\theta^{\\alpha}::Coordinate.\n    D{#}::Derivative.\n    obj19b:= D_{\\alpha}{\\theta^\\beta \\theta^\\gamma};\n    product_rule(_);\n    tst19b:= D_{\\alpha}{\\theta^{\\beta}} \\theta^{\\gamma}  \n             - \\theta^{\\beta} D_{\\alpha}{\\theta^{\\gamma}} - @(obj19b);\n    assert(tst19b==0)\n    print(\"Test 19b passed\")\n    \ndef test19c():\n    __cdbkernel__=create_scope()\n    {\\alpha,\\beta,\\gamma}::Indices(spinor, position=fixed).\n    {\\alpha,\\beta,\\gamma}::AntiCommuting.\n    D{#}::Derivative.\n    obj19c:= D^{\\alpha}{ D_{\\alpha}{T^{\\beta} S^{\\gamma}}};\n    product_rule(_)\n    distribute(_)\n    product_rule(_)\n    tst19c:= D^{\\alpha}{D_{\\alpha}{T^{\\beta}}} * S^{\\gamma} \n              + D_{\\alpha}{T^{\\beta}} * D^{\\alpha}{S^{\\gamma}} \n              - D^{\\alpha}{T^{\\beta}} * D_{\\alpha}{S^{\\gamma}}\n              + T^{\\beta} * D^{\\alpha}{D_{\\alpha}{S^{\\gamma}}} - @(obj19c);\n    assert(tst19c==0)\n    print(\"Test 19c passed\")\n    \ntest19c()\n\n# In the following test, the objects 'b' and 'c' carry an implicit\n# spinor index, and the derivative 'D' carries an explicit spinor\n# index. Moving a 'D_\\alpha' through 'b' should pick up a minus sign.\n\n# def test19d():\n# {\\alpha,\\beta,\\gamma}::Indices(spinor, position=fixed).\n# {\\alpha,\\beta,\\gamma}::AntiCommuting.\n# D{#}::Derivative.\n# {b, c}::SelfAntiCommuting.\n# {b, c}::ImplicitIndex(spinor).\n# obj19d:= D^{\\alpha}{D_{\\alpha}{b*c}};\n# product_rule(_);\n# distribute(_);\n# product_rule(_);\n# distribute(_);\n# tst19d:= D^{\\alpha}{D_{\\alpha}{b}} c\n# - D_{\\alpha}{b} D^{\\alpha}{c}\n# + D^{\\alpha}{b} D_{\\alpha}{c}\n# + b D^{\\alpha}{D_{\\alpha}{c}} - @(obj19d);\n# collect_terms(_);\n# assert(tst19d==0)\n# \n# test19d()\n\n# Anti-commuting indices.\n\ndef test20():\n    __cdbkernel__=create_scope()\n    \\dot{#}::Accent.\n    {a,b,c,d}::Indices(spinor).\n    {\\dot{a},\\dot{b},\\dot{c},\\dot{d}}::Indices(dspinor).\n    {a,b,c,d,\\dot{a},\\dot{b},\\dot{c},\\dot{d}}::AntiCommuting.\n    D{#}::Derivative.\n    obj20:= D_{a}{D_{\\dot{a}}{f g}};\n    product_rule(_)\n    distribute(_)\n    product_rule(_)\n    tst20:= D_{a}{D_{\\dot{a}}{f}} * g \n        - D_{\\dot{a}}{f} * D_{a}{g} \n        + D_{a}{f} * D_{\\dot{a}}{g} \n        + f * D_{a}{D_{\\dot{a}}{g}} - @(obj20);\n    collect_terms(_)\n    assert(tst20==0)\n    print(\"Test 20 passed\")\n    \ntest20()\n\n# Two index sets, anti-commuting\n\ndef test21():\n    __cdbkernel__=create_scope()\n    {\\alpha,\\beta,\\gamma}::Indices(Spinor).\n    {\\dalpha,\\dbeta,\\dgamma}::Indices(DottedSpinor).\n    {\\alpha,\\beta,\\gamma,\\dalpha,\\dbeta,\\dgamma,b,c}::AntiCommuting.\n    {\\bD{#}, D{#}}::Derivative.\n    obj21:= D_{\\alpha}{\\bD_{\\dalpha}{b*c}};\n    product_rule(_)\n    distribute(_)\n    product_rule(_)\n    distribute(_)\n    tst21:= D_{\\alpha}{\\bD_{\\dalpha}{b}} * c \n        + \\bD_{\\dalpha}{b} * D_{\\alpha}{c} \n        - D_{\\alpha}{b} * \\bD_{\\dalpha}{c} \n        + b * D_{\\alpha}{\\bD_{\\dalpha}{c}} - @(obj21);\n    collect_terms(_)\n    assert(tst21==0)\n    print(\"Test 21 passed\")\n    \ntest21()\n\n\n# Explicit and implicit indices\n\ndef test22():\n    __cdbkernel__=create_scope()\n    {\\alpha,\\beta,\\gamma}::Indices().\n    {\\theta,\\lambda}::ImplicitIndex().\n    {\\alpha,\\beta,\\gamma,\\theta,\\lambda}::AntiCommuting.\n    D{#}::Derivative.\n    obj22:= D_{\\alpha}{\\theta \\lambda};\n    product_rule(_)\n    tst22:= D_{\\alpha}{\\theta} \\lambda - \\theta D_{\\alpha}{\\lambda} - @(obj22);\n    collect_terms(_)\n    assert(tst22==0)\n    print(\"Test 22 passed\")\n    \ntest22()\n\n# Multiple indices on tensors.\n\ndef test23():\n    __cdbkernel__=create_scope()\n    {a,b,c,d,e}::Indices.\n    {a,b,c,d,e}::AntiCommuting.\n    D{#}::Derivative.\n    obj23:= D_{a}{A^{b} T^{c d} C^{e}}; \n    product_rule(_)\n    tst23:= D_{a}{A^{b}} * T^{c d} * C^{e} - A^{b} * D_{a}{T^{c d}} * C^{e} - A^{b} * T^{c d} * D_{a}{C^{e}}\n        - @(obj23);\n    collect_terms(_)\n    assert(tst23==0)\n    print(\"Test 23 passed\")\n    \ntest23()\n\n# Unwrapping.\n\ndef test24():\n    __cdbkernel__=create_scope()\n    \\hat{#}::Accent;\n    \\hat{#}::Distributable;\n    B::Depends(\\hat{#});\n    ex:=\\hat{A+B+C};\n    distribute(_)\n    unwrap(_)\n    tst:=\\hat{B}-@(ex);\n    assert(tst==0)\n    print(\"Test 24 passed\")\n\ntest24()\n\n# Bug reported \ndef test25():\n    __cdbkernel__=create_scope()\n    \\del{#}::Derivative.\n    X::Depends(\\del{#}).\n    ex1:= \\del{X*Y*Z*\\del{X}};\n    product_rule(ex1)\n    unwrap(ex1)\n    tst:=\\del{X} Y Z \\del{X} + X Y Z \\del{\\del{X}} - @(ex1);\n    assert(tst==0)\n    print(\"Test 25a passed\")\n    ex2:= \\del{X*Y*Z*\\del{Y}};\n    product_rule(ex2)\n    unwrap(ex2)\n    assert(ex2==0)\n    print(\"Test 25b passed\")\n\ntest25()\n\ndef test26():\n    __cdbkernel__=create_scope()\n    \\partial{#}::PartialDerivative;\n    ex:=\\partial_{\\mu}{A};\n    substitute(_, $A -> 3$)\n    assert(ex==0)\n    print(\"Test 26 passed\")\n\ntest26()\n\ndef test27():\n    __cdbkernel__=create_scope()\n    \\partial{#}::Derivative;\n    ex:=\\partial_{\\mu}{A};\n    substitute(_, $A -> 3$)\n    assert(ex==0)\n    print(\"Test 27 passed\")\n\ntest27()\n\ndef test28():\n    __cdbkernel__=create_scope()\n    \\partial{#}::PartialDerivative;\n    { A, B, C, D }::Depends(\\partial{#});\n    ex := \\partial_{\\alpha}{ A (B + r C) };\n    unwrap(ex)\n    tst:= \\partial_{\\alpha}{ A (B + r C) } - @(ex);\n    assert(tst==0)\n    print(\"Test 28 passed\")\n\ntest28()\n\ndef test29():\n    __cdbkernel__=create_scope()\n    \\partial{#}::PartialDerivative;\n    { A, B, C, D }::Depends(\\partial{#});\n    ex := \\partial_{\\alpha}{ (A + r B) (C + r D) }.\n    unwrap(ex)\n    tst:= \\partial_{\\alpha}{ (A + r B) (C + r D) } - @(ex);\n    assert(tst==0)\n    print(\"Test 29 passed\")\n\ntest29()\n\ndef test30():\n    __cdbkernel__=create_scope()\n    { \\del{#}, \\delbar{#} }::PartialDerivative;\n    X_{\\mu}::Depends(\\del{#}, \\delbar{#});\n    ex:= \\del{\\delbar{X_{\\mu}}};\n    unwrap(_)\n    tst:= \\del{\\delbar{X_{\\mu}}} - @(ex);\n    assert(tst==0)\n    print(\"Test 30 passed\")\n\ntest30()\n\ndef test31():\n    __cdbkernel__=create_scope()\n    \\hat{#}::Accent;\n    \\partial{#}::PartialDerivative;\n    A::Depends(\\partial{#}, \\hat{#});\n    ex:=\\partial{A \\hat{A} B};\n    product_rule(_)\n    unwrap(_)\n    tst:= \\partial{A} \\hat{A} B + A \\partial{\\hat{A}} B - @(ex);\n    assert(tst==0)\n    print(\"Test 31 passed\")\n\ntest31()\n        \ndef test32():\n    __cdbkernel__=create_scope()\n    \\partial{#}::PartialDerivative;\n    ex:= \\partial_{\\mu}{A_{\\nu}} = B_{\\mu\\nu};\n    ex2:= 4 \\partial^{\\mu}{ @(ex) };\n    lhs2 = lhs(ex2)\n    rhs2 = rhs(ex2)\n    lhstst:= 4 \\partial^{\\mu}_{\\mu}{A_{\\nu}} - @(lhs2);\n    rhstst:= 4 \\partial^{\\mu}{ B_{\\mu\\nu} } -  @(rhs2);\n    assert(lhstst==0)\n    assert(rhstst==0)\n    print(\"Test 32 passed\")\n\ntest32()\n\ndef test33():\n    __cdbkernel__=create_scope()\n    d{#}::ExteriorDerivative;\n    A::DifferentialForm(degree=3);\n    B::DifferentialForm(degree=3);    \n    ex:= A = B;\n    ex2:= d{ @(ex) };\n    lhs2 = lhs(ex2)\n    rhs2 = rhs(ex2)\n    lhstst := d{A} - @(lhs2);\n    rhstst := d{B} - @(rhs2);\n    assert(lhstst==0)\n    assert(rhstst==0)\n    print(\"Test 33 passed\")\n\ntest33()\n\ndef test34():\n    __cdbkernel__=create_scope()\n    {\\mu,\\nu,\\rho}::Indices(position=fixed, values={0,1,2,3});\n    \\partial{#}::PartialDerivative;\n    A^{\\mu}::Depends(\\partial{#});\n    ex:= \\partial_{\\mu}{A^{2}};\n    unwrap(ex)\n    tst:= \\partial_{\\mu}{A^{2}} - @(ex);\n    assert(tst==0)\n    print(\"Test 34 passed\")        \n\ntest34()\n        \ndef test35():\n    __cdbkernel__=create_scope()        \n    \\partial{#}::PartialDerivative;\n    {\\mu,\\nu,\\rho}::Indices;    \n    ex:= \\partial_{\\mu}{ (\\partial_{\\nu}{\\phi} \\partial^{\\nu}{\\phi})**3 };\n    product_rule(ex)\n    tst:= 3 (\\partial_{\\nu}{\\phi} \\partial^{\\nu}{\\phi})**2\n        \\partial_{\\mu}{\\partial_{\\nu}{\\phi} \\partial^{\\nu}{\\phi} } - @(ex);\n    assert(tst==0)\n    print(\"Test 35 passed\")\n\ntest35()\n\ndef test36():\n    __cdbkernel__=create_scope()        \n    # When there are more types of accents and derivatives, unwrap\n    # needs to be guided about what to unwrap, or it will do all.\n    {m, n, p, q}::Indices( position=independent);\n    \\partial{#}::PartialDerivative;\n    X_{m}::Depends(\\partial{#});\n    \\Gamma{#}::GammaMatrix;\n    { \\theta, \\psi }::Spinor(dimension=10, type=MajoranaWeyl);\n    \\bar{\\theta}::Depends(\\partial{#});\n    \\bar{#}::DiracBar;\n    ex:=\\bar{Q \\Gamma^{m} \\theta}\\partial_{\\mu}{X_{m}} + \\partial_{\\mu}{\\Gamma^{m}\\bar{\\theta}} X_{m};\n    unwrap(_, $\\partial{#}$)\n    tst:=\\bar{Q \\Gamma^{m} \\theta}\\partial_{\\mu}{X_{m}} + \\Gamma^{m} \\partial_{\\mu}{\\bar{\\theta}} X_{m} - @(ex);\n    assert(tst==0)\n    print(\"Test 36a passed\")    \n    unwrap(ex)\n    tst:=Q \\bar{\\Gamma^{m} \\theta}\\partial_{\\mu}{X_{m}} + \\Gamma^{m} \\partial_{\\mu}{\\bar{\\theta}} X_{m} - @(ex);\n    assert(tst==0)\n    print(\"Test 36b passed\")\n\ntest36()\n\ndef test37():\n    __cdbkernel__=create_scope()        \n    A::DifferentialForm(degree=1).\n    B::DifferentialForm(degree=2).\n    C::DifferentialForm(degree=3).\n    d{#}::ExteriorDerivative.\n    ex:=C= d{B}+A ^ B;\n    ge:=d{C}+A ^ C;\n    substitute(ge, ex)\n    distribute(ge)\n    product_rule(ge)\n    tst:= d{A} ^ B - @(ge);\n    assert(tst==0)\n    print(\"Test 37 passed\")                \n\ntest37()\n\ndef test38():        \n    __cdbkernel__=create_scope()        \n    A::DifferentialForm(degree=1).\n    B::DifferentialForm(degree=1).\n    C::DifferentialForm(degree=2).        \n    ex:= A ^ B + B ^ A + A ^ C + C ^ A;\n    sort_product(_)\n    tst:= 2 A ^ C - @(ex);\n    assert(tst==0)\n    print(\"Test 38 passed\")        \n\ntest38()\n\ndef test39():        \n    __cdbkernel__=create_scope()\n    A0::DifferentialForm(degree=0).        \n    A1::DifferentialForm(degree=1).\n    A2::DifferentialForm(degree=2).\n    A3::DifferentialForm(degree=3).        \n    ex:= A3 ^ A1 - A1 ^ A3 + A2 ^ A2 ^ A0;\n    sort_product(_)\n    tst:= - 2 A1 ^ A3 + A0 ^ A2 ^ A2 - @(ex);\n    assert(tst==0)\n    print(\"Test 39 passed\")        \n\ntest39()\n\n# def test40():\n#     __cdbkernel__=create_scope()\n#     {m,n,p,q}::Indices();\n#     \\partial{#}::PartialDerivative;\n#     \\phi::Depends(m);\n#     ex:=\\partial_{m}{ c \\phi };\n#     unwrap(_)\n#     tst:= c \\partial_{m}{\\phi} - @(ex);\n#     assert(tst==0)\n#     print(\"Test 40 passed\")\n# \n# test40()\n\n# {dx,dp}::DifferentialForm(degree=1);\n# ex:= ( x dp ) ^ ( p dx ) + ( p dx ) ^ ( x dp );\n# sort_product(ex);\n\ndef test40a():\n    __cdbkernel__=create_scope()        \n    {x,y}::Coordinate.\n    \\partial{#}::PartialDerivative.\n    f::Depends(x);\n    g::Depends(y);\n    ex:=\\partial_{x}{A*f*g};\n    unwrap(_)\n    tst:= A g \\partial_{x}{f} - @(ex);\n    assert(tst==0)\n    print(\"Test 40a passed\")\n\ndef test40b():\n    __cdbkernel__=create_scope()        \n    {x,y}::Coordinate.\n    \\partial{#}::PartialDerivative.\n    f::Depends(x);\n    g::Depends(y);\n    ex:=\\partial_{y}{A*f*g};\n    unwrap(_)\n    tst:= A f \\partial_{y}{g} - @(ex);\n    assert(tst==0)\n    print(\"Test 40b passed\")\n\ntest40a()\ntest40b()\n\ndef test41():\n    __cdbkernel__=create_scope()        \n    {a,b}::Indices;\n    F^{a b}::AntiSymmetric;\n    \\nabla{#}::Derivative;\n    ex:=\\nabla_{b}{F^{a b}};\n    young_project_tensor(ex)\n    tst:= \\nabla_{b}{ 1/2 F^{a b} - 1/2 F^{b a} } - @(ex);\n    assert(tst==0)\n    print(\"Test 41 passed\")\n\ntest41()\n\n\n        \n# {\\mu,\\nu,\\rho,\\sigma}::Indices;        \n# \\partial{#}::Derivative;\n# \\psi_{\\mu}::SelfAntiCommuting;    \n# ex:= \\psi_{\\nu} \\psi_{\\mu} + \\psi_{\\mu} \\psi_{\\nu};\n# sort_product(_);\n# ex:= \\partial_{\\mu}{\\psi_{\\nu}} \\psi_{\\rho} + \\psi_{\\rho} \\partial_{\\mu}{\\psi_{\\nu}};\n# sort_product(_);\n# \n# ex:= \\partial{\\psi_{\\nu}} \\partial{\\psi_{\\mu}} + \\psi_{\\nu} \\psi_{\\mu};\n# canonicalise(_);\n# \n# ex:= \\partial{\\psi_{\\nu}} \\partial{\\psi_{\\mu}} + \\psi_{\\nu} \\psi_{\\mu};\n# sort_product(_);\n\ndef test42():\n    __cdbkernel__=create_scope()        \n    \\nabla{#}::Derivative;\n    A::ImplicitIndex;\n    tr{#}::Trace;\n    \\nabla{#}::ImplicitIndex;\n    ex:=tr{\\nabla{A B}};\n    product_rule(ex)\n    tst:= tr{\\nabla{A} B + A \\nabla{B}} - @(ex);\n    assert(tst==0)\n    print(\"Test 42 passed\")\n\ntest42()\n\n"
  },
  {
    "path": "tests/display.cdb",
    "content": "\ndef test01():\n    __cdbkernel__ = create_scope()\n    ex:= 3 A_{m n} B^{m n} + q(x) r s;\n    tst=Ex(repr(ex))\n    assert(tst==ex)\n    print(\"Test 01 passed\")\n\ntest01()\n\ndef test02():\n    __cdbkernel__ = create_scope()\n    \\psia::LaTeXForm(\"\\psi_{a}\").\n    \\bar{#}::DiracBar.\n    ex:= \\bar{\\psia};\n    print(ex._latex_())\n    assert(ex._latex_()==r\"\\bar{\\psi_{a}}\")\n    print(\"Test 02 passed\")\n\ntest02()\n        \n"
  },
  {
    "path": "tests/display.cnb",
    "content": "{\n\t\"cells\" : \n\t[\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Coordinate to~}r.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property PartialDerivative to~}\\\\partial{\\\\#}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Depends to~}A.\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"r::Coordinate;\\n\\\\partial{#}::PartialDerivative;\\nA::Depends(r);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}{\\\\left(\\\\partial_{r}{{\\\\left(\\\\sin{A}\\\\right)}^{2}}\\\\right)}^{2}+{\\\\left(\\\\partial_{r}{{A}^{2}}\\\\right)}^{2}+{\\\\left(\\\\partial_{r}{{r}^{2}}\\\\right)}^{2}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex:= \\\\partial_{r}{\\\\sin{A}**2}**2 +\\\\partial_{r}{A**2}**2 + \\\\partial_{r}{ r**2 }**2;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}4{r}^{2}+\\\\frac{1}{2}\\\\left(-\\\\cos{4A}+1\\\\right) {\\\\left(\\\\partial_{r}{A}\\\\right)}^{2}+4{A}^{2} {\\\\left(\\\\partial_{r}{A}\\\\right)}^{2}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"map_sympy(ex,\\\"simplify\\\");\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\partial_{r}{{r}^{2}}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex2:= \\\\partial_{r}{r**2};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}2r\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex3=map_sympy(ex2, \\\"simplify\\\");\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}4 r^{2} + \\\\left(- \\\\frac{1}{2} \\\\cos{\\\\left (4 A{\\\\left (r \\\\right )} \\\\right )} + \\\\frac{1}{2}\\\\right) \\\\frac{d}{d r} A{\\\\left (r \\\\right )}^{2} + 4 A^{2}{\\\\left (r \\\\right )} \\\\frac{d}{d r} A{\\\\left (r \\\\right )}^{2}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"output\",\n\t\t\t\t\t\"source\" : \"\\\\begin{verbatim}<class 'sympy.core.add.Add'>\\n\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"s = ex._sympy_();\\nprint(type(s))\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}4{r}^{2}+\\\\frac{1}{2}\\\\left(-\\\\cos{4A}+1\\\\right) {\\\\left(\\\\partial_{r}{A}\\\\right)}^{2}+4{A}^{2} {\\\\left(\\\\partial_{r}{A}\\\\right)}^{2}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1\n}\n"
  },
  {
    "path": "tests/dummies.cdb",
    "content": "\n# rename_dummies tests\n\ndef test01():\n   __cdbkernel__=create_scope()\n   {m,n,p,q}::Indices(\"one\").\n   {a,b,c,d}::Indices(\"two\").\n   ex:= A_{m} A^{m} + B_{m} C^{m} + A_{n} A^{n} + Q_{c d} R^{d c}.\n   rename_dummies(ex, \"one\", \"two\")\n   tst:= 2 A_{a} A^{a} + B_{a} C^{a} + Q_{c d} R^{d c} - @(ex).\n   assert tst == 0, tst\n   print(\"Test 01 passed\")\n\ntest01()\n\ndef test02a():\n   __cdbkernel__=create_scope()\n   {n,p,q}::Indices(\"one\").\n   {m,n,p,q,r,s,t}::Indices(\"two\").\n   ex:= A_{r} = A_{m r} A^{m} + A_{n r} A^{n} + A_{s r} A^{s}.\n   rename_dummies(ex, \"two\", \"one\")\n   assert ex == $A_{r} = 3A_{n r} A^{n}$, ex\n   print(\"Test 02a passed\")\n\ntest02a()\n\ndef test02b():\n   __cdbkernel__ = create_scope()\n   {a, b, c, d, e, f}::Indices(\"one\").\n   {\\alpha, \\beta, \\gamma, \\delta}::Indices(\"two\")\n   ex1 := A_{a a \\alpha \\alpha};\n   rename_dummies(ex1, \"two\", \"one\")\n   assert ex1 == $A_{a a b b}$\n   ex2 := A_{a a \\alpha \\alpha};\n   rename_dummies(ex2, \"one\", \"two\")\n   assert ex2 == $A_{\\beta \\beta \\alpha \\alpha}$\n   print(\"Test 02b passed\")\n\ntest02b()\n\n# expand_dummies tests\n\ndef test03():\n   __cdbkernel__ = create_scope()\n   {t, x}::Coordinate.\n   {\\mu, \\nu, \\rho}::Indices(vector, values={t, x}).\n   ex := A_{\\mu} A^{\\mu}.\n   expand_dummies(ex)\n   assert ex == $A_{t}A^{t} + A_{x}A^{x}$, ex\n   print(\"Test 03 passed\")\n\ntest03()\n\ndef test04():\n   __cdbkernel__ = create_scope()\n   {t, x}::Coordinate.\n   {\\mu, \\nu, \\rho}::Indices(vector, values={t, x}).\n   ex := g^{\\mu \\nu} A_{\\nu}.\n   expand_dummies(ex)\n   assert ex == $g^{\\mu t} A_{t} + g^{\\mu x} A_{x}$, ex\n   print(\"Test 04 passed\")\n\ntest04()\n\ndef test05():\n   __cdbkernel__ = create_scope()\n   {t, x, y, z}::Coordinate.\n   {\\mu, \\nu, \\rho, \\lambda}::Indices(vector, values={t, x, y, z}).\n   mink := g_{t t} = -1, g_{x x} = 1, g_{y y} = 1, g_{z z} = 1.\n   ex := g_{\\mu \\rho} g_{\\mu \\lambda} k^{\\rho} k^{\\lambda}.\n   expand_dummies(ex, mink)\n   assert ex == $k^{t}k^{t} + k^{x}k^{x} + k^{y}k^{y} + k^{z}k^{z}$, ex\n   print(\"Test 05 passed\")\n\ntest05()\n\ndef test06():\n   __cdbkernel__ = create_scope()\n   {t, x}::Coordinate.\n   {\\mu, \\nu, \\rho, \\lambda}::Indices(vector, values={t, x}).\n   components := A_{t t} = a1, A_{x x} = a2, B_{x t} = b.\n   ex := A_{\\mu \\nu}B_{\\mu \\nu}.\n   expand_dummies(ex, components, False)\n   assert ex == $a1 B_{t t} + A_{x t} b + A_{t x} B_{t x} + a2 B_{x x}$, ex\n   print(\"Test 06 passed\")\n\ntest06()\n\n# values tests\n\ndef test07():\n   __cdbkernel__ = create_scope()\n   try:\n      {r, s}::Indices(values={-1..a}).\n      sys.exit(-1)\n   except:\n      print(\"Test 07a passed\")      \n   try:\n      {r, s}::Indices(values={-1..999}).\n      sys.exit(-1)\n   except:\n      print(\"Test 07b passed\")      \n   {a, b}::Indices(values={-1..2}).\n   {c, d}::Indices(values={-1,1,2}).\n   \\delta{#}::KroneckerDelta.\n   ex1 := \\delta_{a b} \\delta_{a b}.\n   eliminate_kronecker(ex1)\n   assert ex1 == 4\n   print(\"Test 07c passed\")\n   ex2 := \\delta_{c d} \\delta_{c d}.\n   eliminate_kronecker(ex2)\n   assert ex2 == $\\delta_{d d}$\n   print(\"Test 07d passed\")\n\ntest07()\n"
  },
  {
    "path": "tests/explicit_implicit.cdb",
    "content": "\ndef test01():\n    __cdbkernel__=create_scope()\n    {m,n,p}::Indices(spacetime, position=fixed);\n    {a,b,c,d,e,f,g,h}::Indices(spinor, position=fixed);\n    \\sigma^{p}::ImplicitIndex(\\sigma^{p a}_{b});\n    \\psi::ImplicitIndex(\\psi_{a});\n    \\chi::ImplicitIndex(\\chi^{a});\n    ex:= \\psi \\sigma^{m} \\sigma^{n} \\chi \\lambda^{a} + 1/2 \\lambda_{b} \\chi^{b} T^{m n}\\chi^{a};\n    explicit_indices(_)\n    tst:= \\psi_{c} \\sigma^{m c}_{d} \\sigma^{n d}_{e} \\chi^{e} \\lambda^{a} + 1/2 \\lambda_{b} \\chi^{b} T^{m n}\\chi^{a} - @(ex);\n    assert(tst==0)\n    print(\"Test 01a passed\")\n    ex:= \\psi \\sigma^{m} \\chi;\n    explicit_indices(_)\n    tst:= \\psi_{a} \\sigma^{m a}_{b} \\chi^{b} - @(ex);\n    assert(tst==0)\n    print(\"Test 01b passed\")\n\ntest01()\n\ndef test02():\n    __cdbkernel__=create_scope()\n    {m,n,p}::Indices(spacetime, position=fixed);\n    {a,b,c,d,e,f,g,h}::Indices(spinor, position=fixed);\n    \\sigma^{p}::ImplicitIndex(\\sigma^{p a}_{b});\n    \\psi::ImplicitIndex(\\psi_{a});\n    \\chi::ImplicitIndex(\\chi^{a});\n    \\partial{#}::PartialDerivative;\n    ex:= \\psi \\sigma^{m} \\sigma^{n} \\partial_{n}{\\chi} \\lambda^{a} + \\lambda_{b} \\chi^{b} T^{m}\\chi^{a};\n    explicit_indices(_)\n    tst:= \\psi_{c} \\sigma^{m c}_{d} \\sigma^{n d}_{e} \\partial_{n}{\\chi^{e}} \\lambda^{a} + \\lambda_{b} \\chi^{b} T^{m}\\chi^{a} - @(ex);\n    assert(tst==0)\n    print(\"Test 02 passed\")\n\ntest02()\n\ndef test03():\n    __cdbkernel__=create_scope()\n    {m,n,p}::Indices(spacetime, position=fixed);\n    {a,b,c,d,e,f,g,h}::Indices(spinor, position=fixed);\n    \\sigma^{p}::ImplicitIndex(\\sigma^{p a}_{b});\n    \\psi::ImplicitIndex(\\psi_{a});\n    \\chi::ImplicitIndex(\\chi^{a});\n    ex:= 2 \\sigma^{m} \\chi \\psi \\sigma^{n} \\chi;\n    explicit_indices(_)\n    tst:= 2 \\sigma^{m a}_{b} \\chi^{b} \\psi_{c} \\sigma^{n c}_{d} \\chi^{d} - @(ex);\n    assert(tst==0)\n    print(\"Test 03 passed\")\n        \ntest03()\n\ndef test04():\n    __cdbkernel__=create_scope()\n    {m,n,p}::Indices(spacetime, position=fixed);\n    {a,b,c,d,e,f,g,h}::Indices(spinor, position=fixed);\n    \\sigma^{p}::ImplicitIndex(\\sigma^{p}_{a b});\n    \\tau^{p}::ImplicitIndex(\\tau^{p a b});        \n    Tr{#}::Trace(indices=spinor);\n    ex:= Tr( \\sigma^{m} \\tau^{n} );\n    explicit_indices(_)\n    tst:= \\sigma^{m}_{a b} \\tau^{n b a} - @(ex);\n    assert(tst==0)\n    print(\"Test 04 passed\")\n        \ntest04()\n        \ndef test05():\n    __cdbkernel__=create_scope()\n    {m,n,p}::Indices(spacetime, position=fixed);\n    {a,b,c,d,e,f,g,h}::Indices(spinor, position=fixed);\n    \\sigma^{p}::ImplicitIndex(\\sigma^{p}_{a b});\n    \\tau^{p}::ImplicitIndex(\\tau^{p a b});        \n    Tr{#}::Trace(indices=spinor);\n    ex:= 1/3 Tr( \\sigma^{m} \\tau^{n} + \\tau^{n} \\sigma^{m} );\n    explicit_indices(_)\n    tst:= 1/3 \\sigma^{m}_{a b} \\tau^{n b a} + 1/3 \\tau^{n a b} \\sigma^{m}_{b a} - @(ex);\n    assert(tst==0)\n    print(\"Test 05 passed\")\n        \ntest05()\n\n# A more complicated example for the pattern matcher,\n# matching indices to index values, both symbolically\n# and numerically.        \ndef test06():\n    __cdbkernel__=create_scope()\n    {r,t}::Coordinate;\n    {\\mu,\\nu}::Indices(spacetime, values={r,t});\n    {a,b,c,d}::Indices(group, values={0,1});\n    \\partial{#}::PartialDerivative;\n    ex:= \\partial_{\\mu}(A_{a b}) \\partial_{\\mu}(A_{b a});\n    A_{a b}::Depends(r,t);\n    {q1,q2}::Depends(r,t);\n    rl:= { A_{0 0} = q1, A_{1 1} = q2 };\n    evaluate(ex, rl, simplify=False)\n    tst:= \\partial_{t}{q1} \\partial_{t}{q1}\n         +\\partial_{r}{q1} \\partial_{r}{q1}\n         +\\partial_{t}{q2} \\partial_{t}{q2}\n         +\\partial_{r}{q2} \\partial_{r}{q2}\n         - @(ex);\n    assert(tst==0)\n    print(\"Test 06 passed\")\n        \ntest06()\n        \ndef test07():\n    __cdbkernel__=create_scope()\n    {r,t,v,w}::Coordinate;\n    {\\mu,\\nu}::Indices(spacetime, values={r,t});\n    {a,b,c,d}::Indices(group, values={v,w});\n    \\partial{#}::PartialDerivative;\n    ex:= \\partial_{\\mu}(A_{a b}) \\partial_{\\mu}(A_{b a});\n    A_{a b}::Depends(r,t);\n    evaluate(ex, simplify=False)\n    tst:=\\partial_{t}(A_{w w}) \\partial_{t}(A_{w w}) + \\partial_{r}(A_{w w}) \\partial_{r}(A_{w w}) + \\partial_{t}(A_{v w}) \\partial_{t}(A_{w v}) + \\partial_{r}(A_{v w}) \\partial_{r}(A_{w v}) + \\partial_{t}(A_{w v}) \\partial_{t}(A_{v w}) + \\partial_{r}(A_{w v}) \\partial_{r}(A_{v w}) + \\partial_{t}(A_{v v}) \\partial_{t}(A_{v v}) + \\partial_{r}(A_{v v}) \\partial_{r}(A_{v v}) - @(ex);\n    assert(tst==0)\n    print(\"Test 07 passed\")\n\ntest07()\n        \ndef test08():\n    __cdbkernel__=create_scope()\n    {a,b,c,d}::Indices(vector).\n    tr{#}::Trace(indices=vector).\n    A::ImplicitIndex(A_{a b}).\n    B::ImplicitIndex(B_{a b}).\n    C::ImplicitIndex(C_{a b}).\n    D::ImplicitIndex(D_{a b}).\n    ex:=tr(c A B) tr(C D);\n    explicit_indices(_);\n    tst:= c A_{a b} B_{b a} C_{c d} D_{d c} - @(ex);\n    print(\"Test 08 passed\")\n\ntest08()\n    \n    \n# The original question:\n    \n# Tr{#}::Trace;\n# {\\mu,\\nu}::Indices(spacetime, values={0,1,2,3});\n# #, position=fixed);\n# {r,t}::Coordinate;\n# {a,b,c,d}::Indices(group, values={r,t});\n# A::ImplicitIndex(A_{a b});\n# \\partial{#}::PartialDerivative;\n# A::Depends(\\partial{#});\n# ex:= Tr( \\partial_{\\mu}{A} \\partial^{\\mu}{A} );\n# explicit_indices(_);\n# A_{a b}::Depends(r,t);\n# #\\partial{#});\n# #{q1, q2}::Depends(\\partial{#});\n# # \\mu\n# rl:= { A_{r r} = q1, A_{t t} = q2 };\n# evaluate(ex, simplify=False);    \n# evaluate(ex, rl, simplify=False);\n# tst:= \\partial_{\\mu}{q1} \\partial^{\\mu}{q1} + \\partial_{\\mu}{q2} \\partial^{\\mu}{q2} - @(ex);\n# assert(tst==0)\n# print(\"Test 06 passed\")\n    \n\n\n\n#ex:= \\chi \\psi \\sigma^{n} \\chi;\n#explicit_indices(_);\n        \n# Normally index contraction aims for adjacent indices.\n# With 'eager=True', contractions are generated as much\n# as possible, even if that does not lead to adjacent indices.\n\n\n# \n# {m,n,p}::Indices(spacetime, position=fixed);\n# {a,b,c,d,e,f,g,h}::Indices(spinor, position=fixed);\n# \\sigma^{p}::ImplicitIndex(\\sigma^{p}_{a b});\n# \\tau^{p}::ImplicitIndex(\\tau^{p a b});\n# \\theta::ImplicitIndex(\\theta^{a});\n# \n# ex := \\sigma^{p} \\theta \\tau^{m};\n# tst:= \\sigma^{p}_{a b} \\theta^{b} \\tau^{m a c};\n#         \n\n# The `combine` algorithm puts objects in the\n# wrong order!\n{A^{a \\alpha}, B^{b}_{\\alpha}}::NonCommuting;\nA^{a}::ImplicitIndex(A^{a \\alpha});\nB^{b}::ImplicitIndex(B^{b}_{\\alpha});\nex:=(A^a)^\\alpha (B^b)_{\\alpha};\nprint(tree(ex))\ncombine(ex);\n"
  },
  {
    "path": "tests/factor.cdb",
    "content": "def test01():\n    __cdbkernel__=create_scope()\n    ex:= a*b+a*c+d;\n    factor_in(_, $b,c$)\n    tst:=(b+c)*a + d - @(ex);\n    assert(tst==0)\n    print('Test 01 passed')\n\ntest01()\n\ndef test01b():\n    __cdbkernel__=create_scope()\n    ex:= a*b*c+a*c+d;\n    factor_in(_, $b,c$)\n    tst:=(b*c+c)*a + d - @(ex);\n    assert(tst==0)\n    print('Test 01b passed')\n\ntest01b()\n\ndef test02():\n    __cdbkernel__=create_scope()\n    ex:=2*a+b*a;\n    factor_in(_, $b$)\n    tst:=(2+b)*a - @(ex);\n    assert(tst==0)\n    print('Test 02 passed')\n\ntest02()\n    \ndef test03():\n    __cdbkernel__=create_scope()\n    ex:= 3*a*b + 5*c*b;\n    factor_in(_, $a,c$)\n    tst:=(3 a + 5 c) b - @(ex);\n    assert(tst==0)\n    print('Test 03 passed')\n\ntest03()\n\ndef test04():\n    __cdbkernel__=create_scope()\n    ex:= a b + a c e - 4 q - 2 g a d + a d - 3 p s - 9/2 a;\n    factor_out(_, $a$)\n    tst4:= -4 q - 3 p s + a*(b + c e - 2 g d + d - 9/2) - @(ex);\n    assert(tst4==0)\n    print('Test 04 passed')\n\ntest04()\n\ndef test05():\n    __cdbkernel__=create_scope()\n    ex:= c - a;\n    factor_out(_, $a$)\n    tst:= c - a - @(ex);\n    assert(tst==0)\n    print('Test 05 passed')\n\ntest05()\n    \ndef test06():\n    __cdbkernel__=create_scope()\n    ex:= 3 a b + 2 a c e + 5 a c + 7 e f - 2 c e + c d - a d + a - c;\n    factor_out(ex, $a,c$)\n    tst5:=  a * c * (2 * e + 5) + c * ( - 2 * e + d - 1) + a * (3 * b - d + 1) + 7 * e * f - @(ex);\n    assert(tst5==0)\n    print('Test 06 passed')\n\ntest06()\n    \n# Non-commuting objects\n\n# Basic behaviour\ndef test07():\n    __cdbkernel__=create_scope()\n    {A, B, C, D, E}::NonCommuting;\n    ex := A B + A C + D A + E A:\n    factor_out(_, $A$, right=True)\n    factor_out(_, $A$, right=False)\n    tst := A*(B + C) + (D + E)*A - @(ex);\n    assert(tst==0)\n    print('Test 07 passed')\n\ntest07()\n\ndef test08():\n    __cdbkernel__=create_scope()\n    {A, B, C, D}::AntiCommuting.\n    obj := A B + A C + D A:\n    factor_out(_, $A$)\n    tst := A*(B + C - D) - @(obj);\n    assert(tst==0)\n    print('Test 08 passed')\n\ntest08()\n\n# Ordering of pulled out factors\ndef test09():\n    __cdbkernel__=create_scope()\n    {A, B}::AntiCommuting.\n    obj := A B c X + c B A Y:\n    factor_out(_, $A, B, c$)\n    tst := A B c * (X - Y) - @(obj);\n    assert(tst==0)\n    print('Test 09 passed')\n\ntest09()\n\ndef test10():\n    __cdbkernel__=create_scope()\n    {A, B}::AntiCommuting.\n    {A, X, Y}::NonCommuting.\n    {B, X, Y}::NonCommuting.\n    obj := A B c X + c B A Y + X A B c + Y c B A:\n    factor_out(_, $c, A, B$)\n    factor_out(_, $c, A, B$, right=True)\n    tst := (A B (X-Y) + (-X+Y) A B) c - @(obj);\n    assert(tst==0)\n    print('Test 10 passed')\n\ntest10()\n\n# Ordering past a non commuting term\ndef test11():\n    __cdbkernel__=create_scope()\n    {A, B, C, D, E}::AntiCommuting.\n    {A, X}::NonCommuting.\n    {B, X}::NonCommuting.\n    obj := X A B Y + X B A Z:\n    factor_out(_, $A, B, X$)\n    tst := X A B (Y - Z) - @(obj);\n    assert(tst==0)\n    print('Test 11 passed')\n\ntest11()\n\ndef test12():\n    __cdbkernel__=create_scope()\n    {A, B, C, D, E}::AntiCommuting.\n    {A, X}::NonCommuting.\n    {B, X}::NonCommuting.\n    obj := A B X A B Y + B A X B A Z:\n    factor_out(_, $A, B, X$)\n    tst := A B X A B (Y + Z) - @(obj);\n    assert(tst==0)\n    print('Test 12 passed')\n\ntest12()\n\ndef test13():\n    __cdbkernel__=create_scope()\n    {A, B, C, D, E}::AntiCommuting.\n    {A, X}::NonCommuting.\n    {B, X}::NonCommuting.\n    obj := A B C D Y + D A B C Z:\n    factor_out(_, $A, B, C, D$)\n    tst := A B C D (Y - Z) - @(obj);\n    assert(tst==0)\n    print('Test 13 passed')\n\ntest13()\n\n# Indices.\n\ndef test14():\n    __cdbkernel__=create_scope()\n    obj:= A_{a} B_{b} + A_{a} C_{b} + A_{b} D_{a};\n    factor_out(_, $A_{a}$)\n    tst:= A_{a} (B_{b} + C_{b}) + A_{b} D_{a} - @(obj);\n    assert(tst==0)\n    print('Test 14 passed')\n\ntest14()\n\ndef test15():\n    __cdbkernel__=create_scope()\n    ex:=  3 A G B_{m} C D + 4 E_{m}  ;\n    factor_out(_,  $  A $ )\n    tst:= 3 A G B_{m} C D + 4 E_{m}  - @(ex);\n    assert(tst==0)\n    print('Test 15 passed')\n\ntest15()\n\ndef test16():\n    __cdbkernel__=create_scope()\n    ex:=  3 A G B_{m} C D + 4 E_{m}  ;\n    factor_out(_,  $  A $, right=True )\n    tst:= 4 E_{m} + 3 G B_{m} C D A - @(ex);\n    assert(tst==0)\n    print('Test 16 passed')\n\ntest16()\n\ndef test17():\n    __cdbkernel__=create_scope()\n    ex:= x*x + x*x*x;\n    factor_in(ex, $x$)\n    tst:= x*x + x*x*x - @(ex);\n    assert(tst==0)\n    print(\"Test 17 passed\")\n\ntest17()\n    \ndef test18():\n    __cdbkernel__=create_scope()\n    {a,b,c,d,e}::Indices;\n    D{#}::Derivative;\n    ex:= D_{a}{D_{b}{F}} - D_{b}{D_{a}{F}} - S A_{a b};\n    factor_in(ex, $ S $)\n    tst:= D_{a}{D_{b}{F}} - D_{b}{D_{a}{F}} - S A_{a b} - @(ex);\n    assert(tst==0)\n    print(\"Test 18 passed\")\n\ntest18()\n\n\n# @reset.\n# {a,b,m,n,p,q}::Indices.\n# obj6:= A_{m n} C_{m n} D_{p q} + A_{p m} C_{m n} D_{n q} + A_{m n} C_{m n} E_{p q} Q;\n# @factor_out!(%){ A_{a b}, C_{m n} };\n# \n# NOTE: see the email to James Allen on Thu, 14 Oct 2010 20:58:52 +0100. \n# Should be solved by modifying @rename_dummies. The text below is obsolete but\n# kept until the bug is fixed.\n#\n# This is very subtle. Consider\n#\n#   A_{m n} C_{n p} D_{m p} + A_{q r} C_{r s} E_{q t} F_{t s}\n#\n# This can clearly factor_out A & C. Standard comparison of the two prefactors\n# would give a match, since  A_{m n} C_{n p} and A_{q r} C_{r s}  are equivalent.\n# But we would need to relabel indices along the way.\n#\n# However, @collect_terms does not do this type of collecting either: it requires\n# you to rename dummies first. If we do that, our problem goes away here too.\n\n#{m,n,p,q,r,s,t}::Indices.\n#A_{m n} C_{n p} D_{m p} + A_{q r} C_{r s} E_{q t} F_{t s};\n#@rename_dummies!(%);\n\n# So the conclusion is that we would prefer to stick to a simpler matching, in which\n# we only allow for dummy index names to differ. But what do we then do with\n\n#{m,n,p,q,r,s,t}::Indices.\n#A_{m n} D_{m p} Q_{n p} + A_{q r} E_{q t} F_{t s} Q_{r s} ;\n#@rename_dummies!(%);\n\n# -> A_{m n} * D_{m p} * Q_{n p} + A_{m n} * E_{m p} * F_{p q} * Q_{n q};\n\n# This does not lead to equal A*Q factors. So it seems that we are forced\n# to do a comparison in which we flag\n#\n#    A_{m n} Q_{m n}  and  A_{m n} Q_{n q} as un-equal \n#\n#    A_{m n} Q_{n q}  and  A_{m n} Q_{n p} as equal\n#\n#\n    \n# {m,n,p,q,r,s,t}::Indices;\n# ex:= A_{m n} D_{m p} Q_{n p} + A_{q r} E_{q t} F_{t s} Q_{r s} ;\n# factor_out(_, $A_{m n}$);\n# sort_product(_);\n# rename_dummies(_);\n"
  },
  {
    "path": "tests/field_theory.cdb",
    "content": "\ndef test01():\n    __cdbkernel__=create_scope()\n    \\delta{#}::KroneckerDelta.\n    obj1:= 2*a*\\delta^{i1 j1 i2 j2};\n    expand_delta(_)\n    distribute(_)\n    tst1:= a*\\delta^{i1 j1}\\delta^{i2 j2}-a*\\delta^{i2 j1}\\delta^{i1 j2}-@(obj1);\n    assert(tst1==0)\n    print('Test 01 passed')\n\ntest01()\n    \ndef test02():\n    __cdbkernel__=create_scope()\n    \\delta{#}::KroneckerDelta.\n    n::Integer(0..d).\n    obj2:= a*\\delta_{n n};\n    eliminate_kronecker(_)\n    tst2:= a*(d+1) - @(obj2);\n    assert(tst2==0)\n    print('Test 02 passed')\n\ntest02()\n\ndef test03():\n    __cdbkernel__=create_scope()\n    \\delta{#}::KroneckerDelta.\n    ex:= \\delta_{m?}_{-n?} \\delta^{\\mu\\nu};\n    eliminate_kronecker(_)\n    tst:= \\delta_{m?}_{-n?} \\delta^{\\mu\\nu} - @(ex);\n    assert(tst==0)\n    print('Test 03 passed')\n\ntest03()\n\ndef test04():\n    __cdbkernel__=create_scope()\n    {A,B}::Weight(label=field);\n    C::Weight(label=field, value=2);\n    ex:=A B B + A A A + A B + A C + B;\n    drop_weight(_, $field=3$)\n    tst:= A B + B - @(ex);\n    assert(tst==0)\n    print(\"Test 04 passed\")\n\ntest04()\n\ndef test05():\n    __cdbkernel__=create_scope()\n    \\delta{#}::KroneckerDelta;\n    {r,s,t}::Indices(position=fixed);\n    \\partial{#}::PartialDerivative;\n    ex:=\\partial^{r}{a} \\partial_{r}{a};\n    substitute(ex, $\\partial^{r}{a} = \\delta^{r}_{0} \\partial^{0}{a}, \\partial_{r}{a} = \\delta_{r}^{0} \\partial_{0}{a}$)\n    eliminate_kronecker(ex)\n    tst:= \\partial^{0}{a} \\partial_{0}{a} - @(ex);\n    assert(tst==0)\n    print(\"Test 05 passed\")\n\ntest05()\n\ndef test06():        \n    __cdbkernel__=create_scope()\n    {a,b,c}::Indices(name=A, position=free);\n    {m,n,p}::Indices(name=B, position=fixed);\n    ex:=A_{a b 3 m} B^{a b m};\n    lower_free_indices(_)\n    tst:=A_{a b 3 m} B_{a b}^{m} - @(ex);\n    assert(tst==0)\n    print(\"Test 06a passed\")\n    raise_free_indices(ex)\n    tst:=A^{a b}_{3 m} B^{a b m} - @(ex);\n    assert(tst==0)\n    print(\"Test 06b passed\")\n\ntest06()\n        \n# \\delta{#}::KroneckerDelta.\n# \\eps_{#}::EpsilonTensor(delta=\\delta).\n# F_{q r s a b c}::TableauSymmetry(shape={1,1}, indices={0,1}, shape={1,1,1}, indices={3,4,5}).\n# obj6:= \\eps_{m n q} \\eps_{r s t} F_{b1 b2 b3 m n q};\n# epsilon_to_delta(_);\n# expand_delta(_);\n\ndef test07():\n    __cdbkernel__=create_scope() \n    {a,b,c,d,e,f,g,h#}::Indices.\n    x::Coordinate;\n    {A^{a},B^{a}}::Weight(label=eps,value=0).\n    B{#}::Depends(x);\n    ex:=B^{a};\n    keep_weight(_, $eps=1$)\n    assert(ex==0)\n\ntest07()\n        \n\ndef test08():\n    __cdbkernel__=create_scope() \n    ex:= A_{m} A_{m};\n    einsteinify(_)\n    tst:= A^{m} A_{m} - @(ex);\n    assert(tst==0)\n    print(\"Test 08a passed\")        \n    ex:= A^{m} A^{m};\n    einsteinify(_)\n    tst:= A_{m} A^{m} - @(ex);\n    assert(tst==0)\n    print(\"Test 08b passed\")        \n    {m,n,p,q}::Indices.\n    ex:= A_{m} A_{m};\n    einsteinify(_, $\\eta$)\n    tst:= A_{m} A_{n} \\eta^{m n} - @(ex);\n    assert(tst==0)\n    print(\"Test 08c passed\")        \n    ex:= A^{m} A^{m};\n    einsteinify(_, $\\eta$)\n    tst:= A_{m} A_{n} \\eta^{m n} - @(ex);\n    assert(tst==0)\n    print(\"Test 08d passed\")        \n    ex:= A_{m n} A_{m n};\n    einsteinify(_, $\\eta$)\n    tst:= A_{m n} A_{p q} \\eta^{m p} \\eta^{n q} - @(ex);\n    assert(tst==0)\n    print(\"Test 08e passed\")        \n\ntest08()\n\ndef test09():\n    __cdbkernel__=create_scope() \n    N::Integer;\n    {i,j}::Indices(vector, position=fixed);\n    {i,j}::Integer(1..N);\n    g_{i j}::Metric;\n    g^{i j}::InverseMetric;\n    g_{i}^{j}::KroneckerDelta;\n    ex:= g_{i}^{i}:\n    eliminate_kronecker(_)\n    tst:= N - @(ex);\n    assert(tst==0)\n    print(\"Test 09a passed\")        \n    ex:= N = g_{i}^{i};\n    eliminate_kronecker(_)\n    tst:= (N = N) - @(ex);\n    assert(tst==$0=0$)\n    print(\"Test 09b passed\")\n\ntest09()\n\ndef test10():\n    __cdbkernel__=create_scope()\n    {i,j,k,l}::Indices(vector);\n    {i,j,k,l}::Integer(1..3);\n    \\delta{#}::KroneckerDelta;\n    \\epsilon_{i j k}::EpsilonTensor(delta=\\delta);\n    ex:= \\epsilon_{i j j} \\epsilon_{i k l} + \\epsilon_{i j k} \\epsilon_{i j l};\n    epsilon_to_delta(_)\n    expand_delta(_)\n    tst:= 2 \\delta_{k l} - @(ex);\n    assert(tst==0)\n    print(\"Test 10 passed\")\n\ntest10()\n\ndef test11():\n    __cdbkernel__=create_scope()\n    {a,b,c,d,e}::Indices(vector1);\n    {a,b,c,d,e}::Integer(1..3);\n    {p,q,r,s,t}::Indices(vector2);\n    {p,q,r,s,t}::Integer(1..3);\n    \\delta{#}::KroneckerDelta;\n    \\epsilon_{a b c}::EpsilonTensor(delta=\\delta);\n    E_{p q r}::EpsilonTensor(delta=\\delta);\n    ex:= \\epsilon_{a b c} E_{p q r} \\epsilon_{a d e};\n    epsilon_to_delta(_)\n    tst:= 2 E_{p q r} \\delta_{b d c e} - @(ex);\n    assert(tst==0)\n    print(\"Test 11 passed\")\n\ntest11()\n\ndef test12():\n    {a,b,c,d,e,j}::Indices;\n    {a,b,c,d,e,j}::Integer(1..3);\n    {d{#}}::KroneckerDelta;\n    {e_{a b c}}::EpsilonTensor(delta=d);\n    ex :=  e_{a j b} e_{j 3 c};\n    epsilon_to_delta(_)\n    tst:= -2 d_{a 3 b c} - @(ex);\n    assert(tst==0)\n    print(\"Test 12 passed\")\n\ntest12()\n        \ndef test13():\n    {a,b,c,i,j,k}::Indices;\n    {a,b,c,i,j,k}::Integer(1..3);\n    {d{#}}::KroneckerDelta;\n    {e_{a b c}}::EpsilonTensor(delta=d);\n    ex := e_{a j 3} e_{a k 3} n_{j} n_{k};\n    epsilon_to_delta(_)\n    tst:= 2 d_{j k 3 3} n_{j} n_{k} - @(ex);\n    assert(tst==0)\n    print(\"Test 13a passed\")\n    expand_delta(ex)\n    distribute(ex)\n    eliminate_kronecker(ex)\n    tst:= n_{k} n_{k} - n_{3} n_{3} - @(ex);\n    assert(tst==0)\n    print(\"Test 13b passed\")\n    \ntest13()\n\n        \n"
  },
  {
    "path": "tests/fierz.cdb",
    "content": "\ndef test01():\n    __cdbkernel__=create_scope()\n    {m,n,p,q,r,s}::Indices(position=fixed);\n    {m,n,p,q,r,s}::Integer(0..3);\n    \\Gamma{#}::GammaMatrix;\n    \\bar{#}::DiracBar;\n    {\\theta, \\lambda, \\psi, \\chi}::Spinor;\n    ex:=\\bar{\\theta} \\Gamma_{m} \\chi \\bar{\\psi} \\Gamma^{m} \\lambda;\n    fierz(_, $\\theta, \\lambda, \\psi, \\chi$)\n    tst:=-1/4 \\bar{\\theta} \\Gamma_{m} \\Gamma^{m} \\lambda \\bar{\\psi}\\chi - 1/4 \\bar{\\theta}\\Gamma_{m}\\Gamma^{n}\\Gamma^{m} \\lambda \\bar{\\psi}\\Gamma_{n}\\chi - 1/8 \\bar{\\theta}\\Gamma_{m}\\Gamma^{n p}\\Gamma^{m}\\lambda \\bar{\\psi}\\Gamma_{p n}\\chi - @(ex);\n    assert(tst==0)\n    print(\"Test 01 passed\")\n    \ntest01()\n"
  },
  {
    "path": "tests/fixed_point.cdb",
    "content": "\n# Test functionality that enables user-defined procedures to be applied\n# to an expression until it no longer changes (the user-defined analogue\n# of the 'repeat=True' option).\n\n\ndef fixed(fun, obj):\n    while fun(obj).state()==result_t.changed:\n        print \"ran\"\n    return obj\n\ndef runit(ex):\n    join_gamma(ex)\n    distribute(ex, keepstate=True)\n    sort_product(ex, keepstate=True)\n    print(ex)\n    return ex\n\ndef test02():\n    \\delta_{m n}::KroneckerDelta.\n    \\Gamma_{#}::GammaMatrix(metric=\\delta).\n    obj3a:= \\Gamma_{c d}\\Gamma_{m1 m2 m3}\\Gamma_{n1 n2};\n    return fixed(runit, obj3a)\n"
  },
  {
    "path": "tests/forms.cdb",
    "content": "\ndef test01():\n    __cdbkernel__=create_scope()\n    {f,g}::DifferentialForm(degree=0).\n    {V, W}::DifferentialForm(degree=1).\n    ex := f V ^ (g W + V);\n    unwrap(_);\n    tst:= f * (V ^ (g W + V) ) - @(ex);\n    assert(tst==0)\n    print(\"Test 01 passed\")\n\ntest01()\n\n\n\n\n\n\n# A::Matrix;\n# A::DifferentialForm(degree=1);\n# F::DifferentialForm(degree=2);\n# \n# ex:= A ^ A ^ A;\n# assert(ex!=0)\n# print(\"Test 01 passed\")\n# \n# ex:= A ^ F ^ A;\n# sort_product(_);\n\n"
  },
  {
    "path": "tests/gamma.cdb",
    "content": "\n# Test gamma algebra manipulations. Implicitly tests the combinatorics\n# module too.\n\ndef test01():\n    __cdbkernel__=create_scope()\n    \\Gamma_{#}::GammaMatrix(metric=\\delta).\n    obj1:= \\Gamma^{a b}\\Gamma_{c};\n    join_gamma(obj1)\n    tst1:= \\Gamma^{a b}_{c} + \\Gamma^{a} \\delta^{b}_{c} - \\Gamma^{b} \\delta^{a}_{c} - @(obj1);\n    collect_terms(tst1)\n    assert(tst1==0)\n    print(\"Test 01 passed\")\n\n#test01()\n\n# Test of the join functionality which keeps anti-symmetry in certain\n# indicated indices implicit (obj3a) versus the full thing (obj3b).\n#\n# The logic is that if you _know_ that in the final result you are\n# going to acanonicalorder in a given set of indices that appear\n# on the gamma matrices that you start with, then you may as well\n# forget about all explicit anti-symmetrisations in those indices.\n\ndef test02():\n    __cdbkernel__=create_scope()\n    \\delta_{m n}::KroneckerDelta.\n    \\Gamma_{#}::GammaMatrix(metric=\\delta).\n    obj3a:= \\Gamma_{c d}\\Gamma_{m1 m2 m3}\\Gamma_{n1 n2};\n\n#test02()\n\ndef test02b():\n    __cdbkernel__=create_scope()\n    \\bar{#}::DiracBar;\n    \\psi::Spinor(dimension=10);\n    \\Gamma{#}::GammaMatrix;\n    ex:=\\bar{\\Gamma^{m n p} \\psi};\n    expand_diracbar(ex)\n    tst:=\\bar{\\psi} \\Gamma^{m n p} - @(ex);\n    assert(tst==0)\n    print(\"Test 02b passed\")\n\n#test02b()\n\n# {m, n, p, q, r, a, b, c}::Indices(flat, position=free);\n# {m, n, p, q, r, a, b, c}::Integer(1..10);\n# \\delta_{m n}::KroneckerDelta;\n# ex:=\\delta^{q q};\n# eliminate_kronecker(ex);\n# \n# {m, n, p, q, r, a, b, c}::Indices(flat, position=fixed);\n# ex:=\\delta_{q r};\n# substitute(ex, $\\delta^{q r} -> K^{q r}$)\n# {m, n, p, q, r, a, b, c}::Indices(flat, position=free);\n# substitute(ex, $\\delta^{q r} -> K^{q r}$)\n# \n# \n# \n# \n# \\delta_{m n}::SelfCommuting;\n# \\delta_{m n}::KroneckerDelta;\n# {m, n, p, q, r, a, b, c}::Indices(flat, position=free);\n# {m, n, p, q, r, a, b, c}::Integer(1..10);\n# \n# \\GAMMA^{#}::GammaMatrix(metric=\\delta).\n# one:= \\GAMMA^{m n p q r}\\GAMMA^{a}\\GAMMA^{b}\\GAMMA^{m n p}\\GAMMA^{c}\\GAMMA^{q r};\n# join_gamma(_);\n# distribute(_);\n# eliminate_kronecker(_);\n# canonicalise(_);\n# sort_product(_);\n# \n# join_gamma(_);\n# distribute(_);\n# eliminate_kronecker(_);\n# canonicalise(_);\n# sort_product(_);\n# \n# \n# \\delta_{m n}::KroneckerDelta.\n# \\Gamma_{#}::GammaMatrix(metric=\\delta)\n# ex:=\\Gamma_{a b c}\\Gamma_{c d}\\Gamma_{e};\n# join_gamma(ex)\n# distribute(ex)\n# sort_product(ex)\n# join_gamma(ex)\n\n\n        \n# segfault\n\n# obj3b:= @(obj3a);\n# @join!(obj3a){expand}{m1,m2,m3}{n1,n2};\n# @distribute!(%);\n# @prodsort!(%);\n# @join!(%){expand}{m1,m2,m3}{n1,n2};\n# @distribute!(%);\n# @acanonicalorder!(%){_{m1},_{m2},_{m3}};\n# @acanonicalorder!(%){_{n1},_{n2}};\n# @canonicalise!(%);\n# @collect_terms!(%);\n# \n# @join!(obj3b){expand};\n# @distribute!(%);\n# @prodsort!(%);\n# @join!(%){expand};\n# @distribute!(%);\n# @acanonicalorder!(obj3b){_{m1},_{m2},_{m3}};\n# @acanonicalorder!(%){_{n1},_{n2}};\n# @collect_terms!(%);\n# \n# tst3:= @(obj3a)-@(obj3b);\n# @canonicalise!(%);\n# @collect_terms!(%);\n# @assert(tst3);\n# \n# # Another one, weird.\n# \\Gamma_{m1 m2 m3 r1 r2 r3 r4 l} * \\Gamma_{n1 n2 n3};\n# @join!(%){5}{expand}{n1,n2,n3};\n# \n# \\Gamma_{m1 m2 m3 r1 r2 r3 r4 l} * \\Gamma_{n1 n2 n3};\n# @join!(%){5}{expand};\n# \n# \n# \n# \n\n# This is one from the Abra help document. Much nicer now in\n# Cadabra 2.x.    \n\ndef test03():\n    __cdbkernel__ = create_scope()\n        \n    \\delta{#}::KroneckerDelta.\n    {m, n, p, q, r, a, b, c}::Indices(flat).\n    {m, n, p, q, r, a, b, c}::Integer(1..10).\n    \\GAMMA{#}::GammaMatrix(metric=\\delta).\n\n    def post_process(ex):\n        distribute(ex)\n        eliminate_kronecker(ex)\n        sort_product(ex)\n        canonicalise(ex)\n        collect_terms(ex)\n\n    one:= \\GAMMA^{m n p q r}\\GAMMA^{a}\\GAMMA^{b}\\GAMMA^{m n p}\\GAMMA^{c}\\GAMMA^{q r};\n    for i in range(5):\n        join_gamma(one)\n\n    tst:=- 2016 * \\GAMMA^{a b c} - 2016 * \\GAMMA^{a} * \\delta^{b c} + 2016 * \\GAMMA^{b} * \\delta^{a c} + 18144 * \\GAMMA^{c} * \\delta^{a b} - @(one);\n    assert(tst==0)\n    print(\"Test 03a passed\")\n    two:= \\GAMMA^{a}*@(one);\n    join_gamma(two)\n    assert(two==0)\n    print(\"Test 03b passed\")\n\ntest03()\n\n# \n# \n# # Test 5:= brackets\n# #\n# @reset.\n# \\Gamma_{#}::GammaMatrix(metric=\\delta).\n# obj5:= (\\Gamma_r \\Gamma_s);\n# @join!(%);\n# tst5:= (\\Gamma_{r s} + \\delta_{r s}) - @(obj5);\n# @sumflatten!(%);\n# @collect_terms!(%);\n# @assert(tst5);\n# \n# # Test 6:= taking care of dimensions\n# #\n# @reset;\n# \\Gamma_{#}::GammaMatrix(metric=\\delta).\n# {m,n,p,q,r,s,t}::Integer(0..3);\n# obj6:= \\Gamma_{m n p} \\Gamma_{q r};\n# @join!(%);\n# tst6:= 6 * \\Gamma_{m n r} * \\delta_{p q}\n#     + 6 * \\Gamma_{m} * \\delta_{p q} * \\delta_{n r} - @(obj6);\n# @collect_terms!(%);\n# @assert(tst6);\n# \n# \n# # Test 7:= back and front-split\n# #\n# @reset;\n# \\Gamma_{#}::GammaMatrix(metric=\\delta).\n# obj7:= \\Gamma_{m n p q};\n# @gammasplit(%);\n# @join!(%){expand};\n# @collect_terms!(%);\n# tst7:= \\Gamma_{m n p q} - @(obj7);\n# @collect_terms!(%);\n# @assert(tst7);\n# \n# @reset;\n# \\Gamma_{#}::GammaMatrix(metric=\\delta).\n# obj8:= \\Gamma_{m n p q};\n# @gammasplit(%){front};\n# @join!(%){expand};\n# @collect_terms!(%);\n# tst8:= \\Gamma_{m n p q} - @(obj8);\n# @collect_terms!(%);\n# @assert(tst8);\n# \n# \n# @reset;\n# \\delta_{m n}::KroneckerDelta.\n# \\Gamma_{#}::GammaMatrix(metric=\\delta).\n# \\psi_{m}::GammaTraceless.\n# \\psi_{m}::Spinor.\n# obj9:= T_{a b} * ( A_{m n} \\Gamma_{r s p t u v} \\psi_{p} B_{q r}\n#           + A_{m n} \\psi_{p} \\Gamma_{r s p t u v} B_{q r} );\n# @remove_gamma_trace!(%);\n# @distribute!(%);\n# @prodsort!(%);\n# tst9:= - A_{m n} * B_{q r} * T_{a b} * \\Gamma_{r s t u} * \\psi_{v}\n#  + A_{m n} * B_{q r} * T_{a b} * \\Gamma_{r s t v} * \\psi_{u}\n#  - A_{m n} * B_{q r} * T_{a b} * \\Gamma_{r s u v} * \\psi_{t}\n#  + A_{m n} * B_{q r} * T_{a b} * \\Gamma_{r t u v} * \\psi_{s}\n#  - A_{m n} * B_{q r} * T_{a b} * \\Gamma_{s t u v} * \\psi_{r}\n#  - A_{m n} * B_{q r} * T_{a b} * \\psi_{r} * \\Gamma_{s t u v}\n#  + A_{m n} * B_{q r} * T_{a b} * \\psi_{v} * \\Gamma_{s t u r}\n#  - A_{m n} * B_{q r} * T_{a b} * \\psi_{u} * \\Gamma_{s t v r}\n#  + A_{m n} * B_{q r} * T_{a b} * \\psi_{t} * \\Gamma_{s u v r}\n#  - A_{m n} * B_{q r} * T_{a b} * \\psi_{s} * \\Gamma_{t u v r}\n#  - @(obj9);\n# @collect_terms!(%);\n# @assert(tst9);\n# \n# # Test 10: Silly trivialities\n# @reset.\n# {m,n,p,q,r,s,t,m#}::Indices(flat).\n# {m,n,p,q,r,s,t,m#}::Integer(0..3).\n# \\Gamma_{#{m}}::GammaMatrix(metric=\\delta).\n# \\delta_{m n}::KroneckerDelta.\n# \\epsilon_{m n p q}::AntiSymmetric.\n# obj10:= \\epsilon_{m n p q} \\Gamma_{m n p q} \\Gamma_{r} \\Gamma_{s t} \\Gamma_{r};\n# @join!(%){expand};\n# @distribute!(%);\n# @eliminate_kr!(%);\n# @canonicalise!(%);\n# @rename_dummies!(%);\n# @collect_terms!(%);\n# \n# @join!(%){expand}{m,n,p,q};\n# @distribute!(%);\n# @eliminate_kr!(%);\n# @canonicalise!(%);\n# @rename_dummies!(%);\n# @collect_terms!(%);\n# \n# @join!(%){expand};\n# @distribute!(%);\n# @eliminate_kr!(%);\n# @canonicalise!(%);\n# @rename_dummies!(%);\n# @collect_terms!(%);\n# # This one is a Schouten identity, so:\n# @decompose_product!(%);\n# @collect_terms!(%):\n# @canonicalise!(%);\n# @collect_terms!(%);\n# @assert(obj10);\n# \n# \\epsilon_{m n p q}::AntiSymmetric.\n# @asym[\\epsilon_{s m n p} Q_{t}]{_{s},_{t},_{m},_{n},_{p}};\n# \n# obj10b:= \\epsilon_{m n p q} G_{m n p q} \\Gamma_{r} \\Gamma_{s t} \\Gamma_{r};\n# @join!(%){expand};\n# @distribute!(%);\n# @eliminate_kr!(%);\n# @canonicalise!(%);\n# @rename_dummies!(%);\n# @collect_terms!(%);\n# \n# @join!(%){expand}{m,n,p,q};\n# @distribute!(%);\n# @eliminate_kr!(%);\n# @canonicalise!(%);\n# @rename_dummies!(%);\n# @collect_terms!(%);\n# @assert(obj10b);\n# \n\n# Numerical indices\n\ndef test03():\n    __cdbkernel__ = create_scope()\n    \\delta{#}::KroneckerDelta.\n    \\gamma{#}::GammaMatrix(metric=\\delta).\n    obj3:= \\gamma_{1 2}\\gamma_{1 2};\n    join_gamma(_);\n    tst3:= \\gamma_{1 2 1 2} \n        + \\gamma_{1 2} * \\delta_{1 2} - \\gamma_{1 1} * \\delta_{2 2} \n        - \\gamma_{2 2} * \\delta_{1 1} + \\gamma_{2 1} * \\delta_{1 2} \n        + \\delta_{1 2} * \\delta_{1 2} - \\delta_{1 1} * \\delta_{2 2}\n        - @(obj3);\n    display(tst3)\n    assert(tst3==0)\n    print(\"Test 03 passed\")\n\ntest03()\n        \n# # Test 4: keeping upper and lower indices \n# #\n# @reset.\n# {\\mu,\\nu,\\rho,a,b,c,d}::Indices(vector, position=fixed).\n# {\\mu,\\nu,\\rho,a,b,c,d}::Integer(0..10).\n# \\Gamma{#}::GammaMatrix(metric=g).\n# obj4:= \\Gamma_{\\mu c d} \\Gamma^{\\nu \\rho a b c};\n# @join!(%){expand};\n# \n# \n\n# Indices and sub-indices (bug reported 5-Apr-2009)\n\ndef test04():\n    __cdbkernel__ = create_scope()\n    {a,b,c,d, e,f, g, h#}::Indices(group).\n    {M, N, P, Q#}::Indices(flat).\n    {M, N, P, Q#}::Integer(1..10).\n    {I,J,K,L#}::Indices(orthogonal, parent=flat).\n    {I,J,K,L#}::Integer(3..10).\n    {\\mu, \\nu, \\lambda, \\sigma#}::Indices(worldvolume, parent=flat).\n    {\\mu, \\nu, \\lambda, \\sigma#}::Integer(0..2).\n    \\delta{\\mu \\nu}::KroneckerDelta.\n    \\Gamma{#}::GammaMatrix(metric=\\delta).\n    obj1:=\\Gamma_{I J K}\\Gamma_{\\mu};\n    join_gamma(_)\n    tst1:= \\Gamma_{I J K \\mu} + \\Gamma_{I J} * \\delta_{K \\mu} - \\Gamma_{I K} * \\delta_{J \\mu} + \\Gamma_{J K} * \\delta_{I \\mu} - @(obj1);\n    assert(tst1==0)\n    print(\"Test 04a passed\")\n    obj2:=\\Gamma_{\\mu}\\Gamma_{I J K};\n    join_gamma(_)\n    tst2:= \\Gamma_{\\mu I J K} + \\Gamma_{J K} * \\delta_{I \\mu} - \\Gamma_{J I} * \\delta_{K \\mu} + \\Gamma_{K I} * \\delta_{J \\mu}\n      - @(obj2);\n    assert(tst2==0)\n    print(\"Test 04b passed\")\n\ntest04()\n        \n    # \n# # Test 5: multiple spinor lines\n# #\n# @reset.\n# \\gamma{#}::GammaMatrix(spacetime).\n# \\Gamma{#}::GammaMatrix(susy).\n# {\\psi,\\lambda}::Spinor(spacetime, susy).\n# obj5:= \\psi \\gamma \\Gamma \\lambda;\n# @prodsort!(%);\n# \n\n\ndef test05():\n    def post_process(ex):\n        sort_product(ex)\n        eliminate_kronecker(ex)\n        canonicalise(ex)\n        collect_terms(ex)\n    \n    {\\mu, \\nu, \\rho, \\sigma}::Indices(vector, position=fixed);\n    {m, n, p, q}::Indices(vector,position=fixed);\n    \\partial{#}::PartialDerivative;\n    {\\psi, \\theta}::Spinor(dimension=10, type=MajoranaWeyl);\n    {\\psi, \\theta}::AntiCommuting;\n    \\bar{#}::DiracBar;\n    \\Gamma{#}::GammaMatrix(metric=\\eta);\n    ex:=\\bar{\\Gamma^{\\mu}\\Gamma_{\\nu}\\theta} \\partial_{\\rho}{X^{\\nu}};\n    join_gamma(ex);\n    canonicalise(ex);\n\ntest05()\n\ndef test06():\n    __cdbkernel__ = create_scope()\n    {a,b,c}::Indices(flat).\n    \\gamma{#}::GammaMatrix(metric=g).\n    ex := \\gamma_{m m} \\gamma_{n};\n    join_gamma(ex);\n    tst:= assert(ex==0)\n    print(\"Test 06 passed\")\n\ntest06()\n\n#  {\\mu,\\nu}::Indices(curved).\n#  {a,b,c}::Indices(flat).\n#  \\gamma{#}::GammaMatrix(metric=g).\n#  ex := \\gamma_{\\mu} \\gamma_{a};\n#  ex2:= \\gamma_{a}\\gamma_{\\mu}\\gamma_{\\nu}\\gamma_{b};\n#  join_gamma(_);\n#  ex := \\gamma_{a} \\gamma_{b};\n#  join_gamma(_);    \n#  \n#  {\\alpha,\\beta}::Indices(position=fixed);\n#  \\gamma{#}::Matrix;\n#  \\lambda::ImplicitIndex;\n#  ex:=\\lambda^{\\alpha} (\\gamma^{m})_{\\alpha \\beta};\n#  combine(ex);\n\n\n"
  },
  {
    "path": "tests/gamma_paper.cdb",
    "content": "#!/usr/local/bin/cadabra2\n{s,r,l,k,m,n}::Indices(vector);\n{s,r,l,k,m,n}::Integer(0..d-1);\n\\Gamma_{#}::GammaMatrix(metric=\\delta);\n\\delta_{m n}::KroneckerDelta;\ndef post_process(ex):\n\tsort_product(ex)\n\teliminate_kronecker(ex)\n\tcanonicalise(ex)\n\tcollect_terms(ex)\n    \nex:=\\Gamma_{s r} \\Gamma_{r l} \\Gamma_{k m} \\Gamma_{m s};\nfor i in range(3):\n\tjoin_gamma(_)\n\tdistribute(_)\n    \nfactor_in(_, $d$);\ncollect_factors(ex);\ntst:= \\Gamma_{k l} (12 - 18 d + 8 d**2 - d**3) + \\delta_{k l} ( - 3 + 6 d - 4 d**2 + d**3) - @(ex);\ndistribute(_)\nassert(tst==0)\n"
  },
  {
    "path": "tests/implicit.cdb",
    "content": "\ndef test01():\n    __cdbkernel__=create_scope()\n    {a,b,c,d}::Indices(type1);\n    {m,n,p,q}::Indices(type2);\n    A::ImplicitIndex(A_{m n});\n    C::ImplicitIndex(C_{m n});\n    D::ImplicitIndex(D_{a b});\n    ex:= D C A D;\n    sort_product(_)\n    tst:= C A D D - @(ex);\n    assert(tst==0)\n    print(\"Test 01 passed\")\n\ntest01()\n\ndef test02():\n    __cdbkernel__=create_scope()\n    {a,b,c,d}::Indices(spinor);\n    Tr{#}::Trace(indices=spinor);\n    A::ImplicitIndex(A_{a b});\n    B::ImplicitIndex(B_{a b});    \n    ex:= Tr( A B A C B ) - Tr( C );\n    untrace(_)\n    tst:= C Tr( A B A B ) - C Tr(1) - @(ex);\n    assert(tst==0)\n    print(\"Test 02 passed\")\n\ntest02()\n\ndef test03():\n    __cdbkernel__=create_scope()\n    {a,b,c,d}::Indices(spinor);\n    \\sigma^{\\mu}::ImplicitIndex(\\sigma^{\\mu a}_{b});    \n    Tr{#}::Trace(indices=spinor);\n    ex:= Tr( \\sigma^{\\mu} q \\sigma^{\\nu} );\n    untrace(_)\n    tst:= q Tr( \\sigma^{\\mu} \\sigma^{\\nu} ) - @(ex);\n    assert(tst==0)\n    print(\"Test 03 passed\")\n    \ntest03()\n        \ndef test04():\n    __cdbkernel__=create_scope()\n    {a,b}::Indices(spinor);\n    {m,n}::Indices(vector);\n    Tr{#}::Trace(indices=spinor);\n    A::ImplicitIndex(A_{a b});\n    B::ImplicitIndex(B_{m n});\n    A::Traceless(indices=spinor);\n    B::Traceless(indices=vector);\n    ex:=Tr( A ) + Tr( B );\n    canonicalise(_)\n    tst:= Tr( B ) - @(ex);\n    assert(tst==0)\n    print(\"Test 04 passed\")\n\ntest04()\n\ndef test05():\n    __cdbkernel__=create_scope()\n    {a,b,c,d}::Indices(vector);\n    ex:=(A)_{a b} (B)_{b c} (C)_{c d};\n    combine(_)\n    tst:= (A B C)_{a d} - @(ex);\n    assert(tst==0)\n    print(\"Test 05 passed\")\n\ntest05()\n\ndef test06():\n    __cdbkernel__=create_scope()\n    {a,b}::Indices(vector);\n    ex:=(A)_{a b} (B)_{b a};\n    combine(_)\n    tst:= (B A)_{b b} - @(ex);\n    assert(tst==0)\n    print(\"Test 06 passed\")\n\ntest06()\n\ndef test07():\n    __cdbkernel__=create_scope()\n    {a,b}::Indices(vector);\n    Tr{#}::Trace(indices=vector);\n    ex:=(A)_{a b} (B)_{b a};\n    combine(_, trace_op=$Tr$)\n    tst:= Tr( B A ) - @(ex);\n    assert(tst==0)\n    print(\"Test 07 passed\")\n\ntest07()\n\ndef test08():\n    __cdbkernel__=create_scope()\n    {a,b}::Indices(vector);\n    {A,B}::AntiCommuting;\n    ex:=(A)_{a b} (B)_{b a};\n    combine(_)\n    tst:= \\indexbracket{-B A}_{b b} - @(ex);\n    assert(tst==0)\n    print(\"Test 08 passed\")\n\ntest08()\n\ndef test09():\n    __cdbkernel__=create_scope()\n    {m,n}::Indices(vector);\n    {a,b,c}::Indices(spinor, position=fixed);\n    \\Gamma^{m}::ImplicitIndex(\\Gamma^{m a}_{b});\n    \\Gamma^{m}::Matrix;\n    ex:=(\\Gamma^{m} \\Gamma^{n})^{a}_{c};\n    expand(_)\n    tst:= (\\Gamma^{m})^{a}_{b} (\\Gamma^{n})^{b}_{c} - @(ex);\n    assert(tst==0)\n    print(\"Test 09 passed\")\n\ntest09()\n\ndef test10():\n    __cdbkernel__=create_scope()\n    {a,b}::Indices(vector);\n    ex:=(u)_{a} (M)^{a b} (v)_{b};\n    combine(_)\n    tst:= \\indexbracket(u M v) - @(ex);\n    assert(tst==0)\n    print(\"Test 10 passed\")\n\nif sys.platform == \"darwin\" or sys.platform.startswith(\"freebsd\"):\n    print(\"Skipping test 10, segfault on Darwin/FreeBSD.\")\nelse:\n    test10()\n\ndef test11():\n    __cdbkernel__=create_scope()\n    {a,b,c}::Indices(vector);\n    ex:=(B)_{b c} (A)_{a b};\n    combine(_)\n    tst:= (A B)_{a c} - @(ex);\n    assert(tst==0)\n    print(\"Test 11 passed\")\n\ntest11()\n\ndef test12():\n    __cdbkernel__=create_scope()\n    {a,b}::Indices(vector);\n    Tr{#}::Trace(indices=vector);\n    A::ImplicitIndex(A_{a b});\n    B::ImplicitIndex(B_{a b});\n    {A_{a b}, B_{a b}, C, D}::AntiCommuting;\n    ex:=Tr( A C B D );\n    untrace(_)\n    sort_product(_)\n    tst:= -C D Tr( A B ) - @(ex);\n    assert(tst==0)\n    print(\"Test 12 passed\")\n\ntest12()\n\ndef test13():\n    __cdbkernel__=create_scope()\n    {a,b}::Indices(vector);\n    Tr{#}::Trace(indices=vector);\n    A::ImplicitIndex(A_{a b});\n    B::ImplicitIndex(B_{a b});\n    {A_{a b}, B_{a b}}::AntiCommuting;\n    ex:=Tr( B A );\n    sort_product(_)\n    tst:= Tr( -A B ) - @(ex);\n    assert(tst==0)\n    print(\"Test 13 passed\")\n\ntest13()\n\ndef test14():\n    __cdbkernel__=create_scope()\n    {A,B,C}::ImplicitIndex;\n    ex:=(B A C)_{a a};\n    sort_product(_)\n    tst:= (A C B)_{a a} - @(ex);\n    assert(tst==0)\n    print(\"Test 14 passed\")\n\ntest14()\n\ndef test15():\n    __cdbkernel__=create_scope()\n    {\\mu,\\nu,\\rho}::Indices(vector).\n    {a^{\\mu},b^{\\mu},c^{\\mu}}::NonCommuting.\n    tr{#}::Trace.\n    ex:=tr(a^{\\mu} b^{\\nu} c^{\\rho}  a^{\\mu} b^{\\rho} c^{\\nu}+b^{\\mu} c^{\\nu} a^{\\rho} b^{\\nu} c^{\\mu} a^{\\rho}+c^{\\mu} a^{\\nu} b^{\\mu} c^{\\rho} a^{\\nu} b^{\\rho});\n    sort_product(_)\n    rename_dummies(_)\n    tst:= 3 tr( a^{\\mu} b^{\\nu} c^{\\rho}  a^{\\mu} b^{\\rho} c^{\\nu} ) - @(ex);\n    assert(tst==0)\n    print(\"Test 15 passed\")\n    \ntest15()\n        \ndef test16():\n    __cdbkernel__=create_scope()\n    {\\mu,\\nu,\\rho}::Indices(vector).\n    {a^{\\mu},b^{\\mu},c^{\\mu}}::NonCommuting.\n    tr{#}::Trace.\n    ex:=tr( b^{\\mu} c^{\\nu} a^{\\rho} b^{\\nu} c^{\\mu} a^{\\rho} );\n    sort_product(_)\n    rename_dummies(_)\n    tst:= tr( a^{\\mu} b^{\\nu} c^{\\rho}  a^{\\mu} b^{\\rho} c^{\\nu} ) - @(ex);\n    assert(tst==0)\n    print(\"Test 16 passed\")\n    \ntest16()\n\ndef test17():\n    __cdbkernel__=create_scope()\n    {A,B}::ImplicitIndex.\n    tr{#}::Trace.\n    ex:=tr( A B B A );\n    sort_product(_)\n    tst:= tr( A A B B ) - @(ex);\n    assert(tst==0)\n    print(\"Test 17 passed\")\n\ntest17()\n\ndef test18():\n    __cdbkernel__=create_scope()\n    {\\mu,\\nu}::Indices(vector).\n    tr{#}::Trace.\n    {a^{\\mu},b^{\\mu}}::NonCommuting.\n    {a^{\\mu},b^{\\mu}}::SelfNonCommuting.\n    ex:=tr{a^{\\mu} b^{\\mu} b^{\\nu} a^{\\nu}} - tr{a^{\\mu} a^{\\nu} b^{\\nu} b^{\\mu} };\n    sort_product(_)\n    rename_dummies(_)        \n    assert(ex==0)\n    print(\"Test 18 passed\")\n\ntest18()\n\ndef test19():\n    __cdbkernel__=create_scope()\n    i::ImaginaryI;\n    A::ImplicitIndex.\n    tr{#}::Trace.\n    ex:= i tr(i A);\n    untrace(_, repeat=True)\n    tst:= -tr(A) - @(ex);\n    assert(\"Test 19 passed\")\n\ntest19()\n\ndef test20():\n    __cdbkernel__=create_scope()\n    {\\mu,\\nu}::Indices(vector).\n    tr{#}::Trace.\n    ex:=A A tr{u^{\\mu} u^{\\nu}} tr{u^{\\nu} u^{\\mu}}- B B tr{u^{\\mu} u^{\\nu}} tr{u^{\\mu} u^{\\nu}};\n    collect_factors(_)\n    tst:= A**2 tr{u^{\\mu} u^{\\nu}} tr{u^{\\nu} u^{\\mu}}- B**2 tr{u^{\\mu} u^{\\nu}} tr{u^{\\mu} u^{\\nu}} - @(ex);\n    assert(tst==0)\n    print(\"Test 20 passed\")\n\ntest20()\n\ndef test21():\n    __cdbkernel__=create_scope()\n    {\\mu,\\nu}::Indices(vector).\n    A^{\\mu\\nu}::Symmetric.\n    B^{\\mu\\nu}::AntiSymmetric.\n    tr{#}::Trace.\n    B^{\\mu\\nu}::ImplicitIndex.\n    \\epsilon^{\\mu\\nu\\rho\\sigma}::EpsilonTensor.\n    ex:=A^{\\mu\\nu} tr{B^{\\mu\\nu}};\n    canonicalise(_)\n    assert ex==0\n    print(\"Test 21a passed\")\n    ex:=\\epsilon^{\\mu\\nu\\rho\\sigma} tr{A^{\\mu\\nu} B^{\\rho\\sigma}};\n    canonicalise(_)\n    assert ex==0\n    print(\"Test 21b passed\")    \n    ex:=\\epsilon^{\\mu\\nu\\rho\\sigma} A^{\\nu\\mu} B^{\\rho\\sigma};\n    canonicalise(_)\n    assert ex==0\n    print(\"Test 21c passed\")    \n    ex:=\\epsilon^{\\mu\\nu\\rho\\sigma} tr{ A^{\\nu\\mu} B^{\\rho\\sigma} };\n    canonicalise(_)    \n    assert ex==0\n    print(\"Test 21d passed\")    \n    ex:=\\epsilon^{\\mu\\nu\\rho\\sigma} tr{ A^{\\nu\\mu} B^{\\rho\\sigma} + A^{\\mu\\nu} B^{\\rho\\sigma} };\n    # FIXME: this does not work with repeat=True?\n    canonicalise(_)\n    canonicalise(_)\n    assert ex==0\n    print(\"Test 21e passed\")\n    \ntest21()\n"
  },
  {
    "path": "tests/index_positions.cdb",
    "content": "\n# This tests whether free, fixed and independent indices\n# are treated correctly.\n\n{x,y,z}::Symbol;\n{a,b,c}::Indices(name=\"free_indices\", position=free);\n{m,n,p}::Indices(name=\"fixed_indices\", position=fixed);\nprint(properties())\n\nex:= A_{x} + A_{y};\nprint(\"Test 01 passed\")\n\nex:= A_{a} + A^{a};\nlower_free_indices(_);\ntst:= 2 A_{a} - @(ex);\nassert(tst==0)\nprint(\"Test 02 passed\")\n\ntry:\n    ex:= A_{m} + A^{m};\n    assert(1==0)\nexcept:\n    print(\"Test 03 passed\")\n\n\n\\m::LaTeXForm(\"\\mu\").\nD{#}::Derivative;\n{\\m,\\n}::Indices(s,position=fixed);\n\n{x_\\m}::Coordinate;\n\nex:= D_{x_\\m}{A^\\m};\n\nprint(tree(ex))\n    \nfor i in ex.top().free_indices(): \n   display(i);\n   \n    \n"
  },
  {
    "path": "tests/integrals.cdb",
    "content": "\ndef test01():\n    __cdbkernel__=create_scope()\n    \\partial{#}::PartialDerivative;\n    a::Depends(\\partial{#});\n    ex:= \\int{ \\partial_{0}{a} \\partial_{0}{a} }{x};\n    integrate_by_parts(_, $a$)\n    tst:= \\int{ -a \\partial_{0 0}{a} }{x} - @(ex);\n    assert(tst==0)\n    print(\"Test 01 passed\")\n\ntest01()\n        \ndef test02():\n    __cdbkernel__=create_scope()\n    \\partial{#}::PartialDerivative;\n    a::Depends(\\partial{#});\n    ex:= \\int{ a \\partial_{0}{\\partial_{0}{a}} }{x};\n    integrate_by_parts(_, $\\partial_{0}{a}$)\n    tst:= \\int{ - \\partial_{0}{a} \\partial_{0}{a} }{x} - @(ex);\n    assert(tst==0)\n    print(\"Test 02 passed\")\n\ntest02()\n\ndef test03():\n    __cdbkernel__=create_scope()\n    \\nabla{#}::Derivative;\n    a::Depends(\\nabla{#});\n    ex:= \\int{ a \\nabla_{0}{\\nabla_{0}{a}} }{x};\n    integrate_by_parts(_, $a$)\n    tst:= \\int{ a \\nabla_{0}{\\nabla_{0}{a}} }{x} - @(ex);\n    assert(tst==0)\n    print(\"Test 03 passed\")\n\ntest03()\n\ndef test04():\n    __cdbkernel__=create_scope()\n    \\partial{#}::PartialDerivative;        \n    ex:= \\int{ a \\partial_{0 0}{b} c }{x};\n    integrate_by_parts(_, $b$)\n    tst:= \\int{ a \\partial_{0 0}{b} c }{x} - @(ex);\n    assert(tst==0)\n    print(\"Test 04 passed\")\n\ntest04()\n\ndef test05():\n    __cdbkernel__=create_scope()\n    \\partial{#}::PartialDerivative;\n    ex:=  \\int{  A_{i j} }{x};\n    integrate_by_parts(_, $h$)  \n    tst:= \\int{  A_{i j} }{x} - @(ex);\n    assert(tst==0)\n    print(\"Test 05a passed\")\n    ex:= \\int{ h A_{i j} }{x};\n    integrate_by_parts(_, $h$)\n    tst:= \\int{ h A_{i j} }{x} - @(ex);\n    assert(tst==0)\n    print(\"Test 05b passed\")\n    \\partial{#}::PartialDerivative;\n    ex:=  \\int{  A_{i j} + \\partial_{i j}{h} }{x};\n    integrate_by_parts(_, $h$)\n    tst:=  \\int{  A_{i j} }{x} - @(ex);\n    assert(tst==0)\n    print(\"Test 05c passed\")\n\ntest05()\n\ndef test06():\n    __cdbkernel__=create_scope()        \n    \\partial{#}::Derivative;\n    \\tau::Coordinate;\n    {t,r}::Depends(\\partial{#});\n    \\delta{#}::Accent;\n    ex:=\\int{ \\partial{\\delta{t}} \\partial{t} r }{\\tau};\n    integrate_by_parts(ex, $\\delta{t}$)\n    tst:= - \\int{ \\delta{t} \\partial{ \\partial{t} r} }{\\tau} - @(ex);\n    assert(tst==0)\n    print(\"Test 06 passed\")\n\ntest06()\n\ndef test07():\n    __cdbkernel__=create_scope()        \n    {A,B,C,D,E,F,F#}::Indices(full);\n    {a,b,c,d,e,f,f#}::Indices(space1);\n    {m,n,o,p,q,r,r#}::Indices(space2);\n    \\partial{#}::PartialDerivative.\n    \\delta{#}::Accent.\n    F_{A B C}::AntiSymmetric.\n    F_{a b c}::AntiSymmetric.\n    F_{m n p}::AntiSymmetric.\n    F_{#}::Depends(\\partial{#}).\n    \n    ex:=\\int{ c_{0} \\partial_{a d}{ \\delta{F_{a b c}}} F_{d b c}\n          + 2 c_{1} \\partial_{a c}{ \\delta{F_{m a b}}} F_{m c b} }{x};\n    \n    integrate_by_parts(ex, $\\partial_{n?}{\\delta{F_{m? a b}}}$)\n    tst:=\\int{ -\\partial_{a}{c_{0}} \\partial_{d}{\\delta{F_{a b c}}} F_{d b c}\n               - c_{0}  \\partial_{d}{\\delta{F_{a b c}}} \\partial_{a}{ F_{d b c} }\n               - 2 \\partial_{a}{c_{1}} \\partial_{c}{\\delta{F_{m a b}}} F_{m c b}\n               - 2 c_{1} \\partial_{c}{\\delta{F_{m a b}}} \\partial_{a}{ F_{m c b} } }{x} - @(ex);\n    assert(tst==0)\n    print(\"Test 07 passed\")\n\ntest07()\n    \n"
  },
  {
    "path": "tests/ipynb_module.ipynb",
    "content": "{\n \"cells\": [\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 2,\n   \"metadata\": {},\n   \"outputs\": [\n    {\n     \"data\": {\n      \"text/markdown\": [\n       \"${}A_{m n p}$\"\n      ]\n     },\n     \"metadata\": {},\n     \"output_type\": \"display_data\"\n    }\n   ],\n   \"source\": [\n    \"ex:=A_{m n p};\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": null,\n   \"metadata\": {},\n   \"outputs\": [],\n   \"source\": []\n  }\n ],\n \"metadata\": {\n  \"kernelspec\": {\n   \"display_name\": \"Cadabra2\",\n   \"language\": \"python\",\n   \"name\": \"cadabra2\"\n  },\n  \"language_info\": {\n   \"codemirror_mode\": \"cadabra\",\n   \"file_extension\": \".ipynb\",\n   \"mimetype\": \"text/cadabra\",\n   \"name\": \"cadabra2\",\n   \"pygments_lexer\": \"cadabra\"\n  }\n },\n \"nbformat\": 4,\n \"nbformat_minor\": 4\n}\n"
  },
  {
    "path": "tests/kaluza_klein.cdb",
    "content": "#!/usr/local/bin/cadabra2\n{\\mu,\\nu,\\rho,\\sigma,\\kappa,\\lambda,\\eta,\\chi#}::Indices(full, position=independent);\n{m,n,p,q,r,s,t,u,v,w,x,y,z,m#}::Indices(subspace, position=independent, parent=full);\n\\partial{#}::PartialDerivative.\ng_{\\mu\\nu}::Metric.\ng^{\\mu\\nu}::InverseMetric.\ng_{\\mu? \\nu?}::Symmetric.\ng^{\\mu? \\nu?}::Symmetric.\nh_{m n}::Metric.\nh^{m n}::InverseMetric.\n\\delta^{\\mu?}_{\\nu?}::KroneckerDelta.\n\\delta_{\\mu?}^{\\nu?}::KroneckerDelta.\nF_{m n}::AntiSymmetric.\nRtoG:= R^{\\lambda?}_{\\mu?\\nu?\\kappa?} -> \n - \\partial_{\\kappa?}{ \\Gamma^{\\lambda?}_{\\mu?\\nu?} }\n + \\partial_{\\nu?}{ \\Gamma^{\\lambda?}_{\\mu?\\kappa?} }\n - \\Gamma^{\\eta}_{\\mu?\\nu?} \\Gamma^{\\lambda?}_{\\kappa?\\eta}\n + \\Gamma^{\\eta}_{\\mu?\\kappa?} \\Gamma^{\\lambda?}_{\\nu?\\eta};\n\nGtog:= \\Gamma^{\\lambda?}_{\\mu?\\nu?} ->\n  (1/2) * g^{\\lambda?\\kappa} ( \n        \\partial_{\\nu?}{ g_{\\kappa\\mu?} } + \\partial_{\\mu?}{ g_{\\kappa\\nu?} } - \\partial_{\\kappa}{ g_{\\mu?\\nu?} } );\ntodo:= g_{m1 m} R^{m1}_{4 n 4} + g_{4 m} R^{4}_{4 n 4};\nsubstitute(_, RtoG)\nsubstitute(_, Gtog)\ndistribute(_)\nproduct_rule(_)\ndistribute(_)\nsort_product(_);\nsubstitute(_, $\\partial_{4}{A??} -> 0$, repeat=True)\nsubstitute(_, $\\partial_{4 m?}{A??} -> 0$, repeat=True)\nsubstitute(_, $\\partial_{m? 4}{A??} -> 0$, repeat=True);\nsplit_index(_, $\\mu, m1, 4$, repeat=True)\nsubstitute(_, $\\partial_{4}{A??} -> 0$, repeat=True)\nsubstitute(_, $\\partial_{4 m?}{A??} -> 0$, repeat=True)\nsubstitute(_, $\\partial_{m? 4}{A??} -> 0$, repeat=True)\ncanonicalise(_);\nsubstitute(_, $g_{4 4} -> \\phi$ )\nsubstitute(_, $g_{m 4} -> \\phi A_{m}$ )\nsubstitute(_, $g_{4 m} -> \\phi A_{m}$ )\nsubstitute(_, $g_{m n} -> \\phi**{-1} h_{m n} + \\phi A_{m} A_{n}$ )\nsubstitute(_, $g^{4 4} -> \\phi**{-1} + \\phi A_{m} h^{m n} A_{n}$ )\nsubstitute(_, $g^{m 4} -> - \\phi h^{m n} A_{n}$ )\nsubstitute(_, $g^{4 m} -> - \\phi h^{m n} A_{n}$ )\nsubstitute(_, $g^{m n} -> \\phi h^{m n}$ );\nconverge(todo):\n    distribute(_)\n    product_rule(_)\n    canonicalise(_)\n;\nsubstitute(_, $\\partial_{p}{h^{n m}} h_{q m} -> - \\partial_{p}{h_{q m}} h^{n m}$ )\ncollect_factors(_)\nsort_product(_)\nconverge(todo):\n\tsubstitute(_, $h_{m1 m2} h^{m3 m2} -> \\delta_{m1}^{m3}$, repeat=True )\n\teliminate_kronecker(_)\n\tcanonicalise(_)\n;\nsubstitute(_, $\\partial_{n}{A_{m}} -> 1/2*\\partial_{n}{A_{m}} + 1/2*F_{n m} + 1/2*\\partial_{m}{A_{n}}$ )\ndistribute(_)\nsort_product(_)\ncanonicalise(_)\nrename_dummies(_);\n    \ntst:= - 1/4 * \\partial_{m}{\\phi} * \\partial_{n}{\\phi} * \\phi**(-1) + 1/4 * \\partial_{p}{\\phi} * \\partial_{n}{h_{m q}} * h^{p q} - 1/2 * \\partial_{m n}{\\phi} + 1/4 * F_{m p} * F_{n q} * \\phi**3 * h^{p q} + 1/4 * \\partial_{p}{\\phi} * \\partial_{q}{\\phi} * \\phi**(-1) * h_{m n} * h^{p q} - 1/4 * \\partial_{p}{\\phi} * \\partial_{q}{h_{m n}} * h^{p q} + 1/4 * \\partial_{p}{\\phi} * \\partial_{m}{h_{n q}} * h^{p q} - @(todo);\n\nassert(tst==0)\n\n"
  },
  {
    "path": "tests/kerr.cnb",
    "content": "__cdbkernel__.scalar_backend=scalar_backend_t.mathematica\"\n\n{t,r,\\theta,\\phi}::Coordinate;\n{\\mu,\\nu,\\rho,\\sigma,\\kappa,\\lambda}::Indices(values={t,r,\\phi,\\theta}, position=fixed).\nrs::LaTeXForm(\"r_s\").\ng_{\\mu\\nu}::Metric;\ng^{\\mu\\nu}::InverseMetric;\n\\partial{#}::PartialDerivative.\n\n\\Delta::Depends(r);\n\\Sigma::Depends(r);\n\nkerr:= { g_{t t}            = - (1 - rs r / \\Sigma),\n         g_{t \\phi}         = - rs a r \\sin(\\theta)**2 / \\Sigma,\n         g_{\\phi t}         = - rs a r \\sin(\\theta)**2 / \\Sigma,\n         g_{r r}            = \\Sigma / \\Delta,\n         g_{\\theta \\theta } = \\Sigma,\n         g_{\\phi \\phi}      = ( r**2 + a**2 + rs a**2 r \\sin(\\theta)**2 / \\Sigma ) \\sin(\\theta)**2 };\n\ncomplete(kerr, $g^{\\mu\\nu}$);\n\nDeltaSigma:= { \\Delta = r**2 - 2 m r + a**2, \\Sigma = r**2 + a**2 \\cos(\\theta)**2 };\n\nsubstitute(kerr, DeltaSigma)\nsimplify(kerr);\ndisplay(kerr)\n\n# import cdb.relativity as gr\n# \n# ch = gr.christoffel_from_metric()\n# evaluate(ch, kerr, rhsonly=True);\n\n"
  },
  {
    "path": "tests/latexform.cnb",
    "content": "\n{\n\t\"cells\" : \n\t[\n\t\t\n\t\t{\n\t\t\t\"cell_id\" : 3,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 1,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property LaTeXForm to~}a.\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"a::LaTeXForm(latex=\\\"\\\\alpha\\\");\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_id\" : 4,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\" : 1,\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex:=a;\"\n\t\t},\n\t\t\n\t\t{\n\t\t\t\"cell_id\" : 5,\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1.0\n}\n\n"
  },
  {
    "path": "tests/manip.cdb",
    "content": "\nimport cdb.core.manip as manip\n\ndef test01():\n    __cdbkernel__=create_scope()\n    ex:= A_{m n} B^{m n} + q = C_{m} D^{m};\n    manip.isolate(ex, $q$)\n    exrhs=rhs(ex)\n    tst:= C_{m} D^{m} - A_{m n} B^{m n} - @(exrhs);\n    assert(tst==0)\n    print(\"Test 01 passed\")\n\ntest01()\n\ndef test02():\n    __cdbkernel__=create_scope()\n    ex := a - b = c + d;\n    manip.to_rhs(ex, $b$)\n    manip.to_rhs(ex, $a$)\n    tst:= ( 0 = c + d + b - a ) - @(ex);\n    assert(tst==$0=0$)\n    print(\"Test 02 passed\")\n#to_lhs(ex0, $d + b$);\n\ntest02()\n\ndef test03():\n    __cdbkernel__=create_scope()\n    ex1 := a_{\\mu}a^{\\mu} + b = c;\n    manip.eq_to_subrule(ex1)\n    manip.get_lhs(ex1)\n    manip.get_rhs(ex1)\n    manip.multiply_through(ex1, $k_{\\alpha}$)\n    manip.swap_sides(ex1)\n    tst:= (k_{\\alpha} c = k_{\\alpha} (a_{\\mu} a^{\\mu} + b ) ) - @(ex1);\n    assert(tst==$0=0$)\n    print(\"Test 03 passed\")\n\ntest03()\n\ndef test04():\n#    __cdbkernel__=create_scope()\n    {f, i}::Symbol;\n    ex := w_{f} - w_{i} > 2 \\pi W_{a b}\\beta^{a}\\beta^{b};\n    manip.get_lhs(ex)\n    manip.get_rhs(ex)\n    manip.swap_sides(ex)\n    manip.swap_sides(ex)\n    manip.multiply_through(ex, $2n$)\n    exrhs=manip.get_rhs(ex)\n    tst:= 4n \\pi W_{a b} \\beta^{a} \\beta^{b}  - @(exrhs);\n    assert(tst==0)\n    print(\"Test 04 passed\")\n\ntest04()\n\ndef test05():\n    __cdbkernel__=create_scope()\n    ex:= a, b, c;\n    try:\n        manip.eq_to_subrule(ex)\n        assert(1==0)\n    except Exception as e:\n        print(\"Test 05a passed\")\n    try:\n        manip.get_lhs(ex)\n        assert(1==0)\n    except Exception as e:\n        print(\"Test 05b passed\")\n    try:\n        manip.get_rhs(ex)\n        assert(1==0)\n    except Exception as e:\n        print(\"Test 05c passed\")\n    try:\n        manip.swap_sides(ex)\n        assert(1==0)\n    except Exception as e:\n        print(\"Test 05d passed\")\n    try:\n        manip.to_rhs(ex, $a$)\n        assert(1==0)\n    except Exception as e:\n        print(\"Test 05e passed\")\n    try:\n        manip.to_rhs(ex, $a$)\n        assert(1==0)\n    except Exception as e:\n        print(\"Test 05f passed\")\n    try:\n        t::Coordinate.\n        {i, j}::Indices(values={t}, position=fixed).\n        ex := a_{i};\n        evaluate(ex, ${a_{t} = 1}$)\n        manip.get_component(ex, $x$)\n        manip.to_rhs(ex, $a$)\n        assert(1==0)\n    except Exception as e:\n        print(\"Test 05g passed\")\n\ntest05()\n\ndef test06():\n    __cdbkernel__=create_scope()\n    ex:= 2a+b+j*b+k*b = c+d;\n    manip.to_lhs(ex)\n    tst := (2a+b+j*b+k*b-c-d = 0) - @(ex);\n    assert(tst==$0=0$)\n    print(\"Test 06 passed\")\n\ntest06()\n\ndef test07():\n    __cdbkernel__=create_scope()\n    ex:= p V = k T;\n    ex2:= @(ex)/V;\n    collect_factors(ex2)\n    tst:= (p = k T / V) - @(ex2);\n    assert(tst==$0=0$)\n    print(\"Test 07a passed\")\n    \n    try:\n       ex1:= A = B;\n       ex2:= C = D;\n       ex3:= @(ex1) @(ex2);\n       assert(1==0)\n    except RuntimeError as e:\n        print(\"Test 07b passed\")\n    \n    ex3:= Q @(ex) R;\n    assert( ex3 == $Q p V R = Q k T R$ )\n    print(\"Test 07c passed\")\n\ntest07()\n\ndef test08():\n    __cdbkernel__=create_scope()\n    __cdbkernel__.call_embedded_python_functions=True\n    ex:= f(x) \\sin(x) \\int{ \\cos(y) }{y, 0, x}; \n    print(\"Test 08 passed\")\n\ntest08()\n"
  },
  {
    "path": "tests/meld.cdb",
    "content": "# Testing that some expressions are canonicalised\n# properly using the meld algorithm\nimport timeit\nimport sys\n\n# Flag to skip the comparison tests\nno_comp = (\"--no-comp\" in sys.argv)\n    \n\n# *_tableaux tests\n\n# Simple symmetric/antisymmetic tensors\ndef tab01():\n    __cdbkernel__ = create_scope()\n    S_{a b c}::Symmetric.\n    ex:= S_{a b c}S_{b a c} + S_{b a c}S_{c a b}:\n    meld(ex)\n    assert ex == $2S_{a b c}S_{b a c}$, ex\n    print(\"Test tab01 passed\")\n\ntab01()\n\ndef tab02():\n    __cdbkernel__ = create_scope()\n    A_{a b c}::AntiSymmetric.\n    ex = meld($A_{a b c} - A_{b a c}$)\n    assert ex == $2A_{a b c}$, ex\n    print(\"Test tab02 passed\")\n   \ntab02()\n\ndef tab03():\n    __cdbkernel__ = create_scope()\n    A_{a b c}::AntiSymmetric.\n    ex = meld($A_{a b c} + A_{a c b}$)\n    assert ex == $0$, ex\n    print(\"Test tab03 passed\")\n\ntab03()\n\ndef tab04():\n    __cdbkernel__ = create_scope()\n    A_{a b c}::AntiSymmetric.\n    ex = meld($A_{c a b}A_{b a c} + A_{b c a}A_{c b a} + 2A_{a b c}A_{a b c}$)\n    assert ex == 0, ex\n    print(\"Test tab04 passed\")\n\ntab04()\n\ndef tab05():\n    __cdbkernel__ = create_scope()\n    A_{a b}::AntiSymmetric.\n    ex = meld($k * A_{a b} + l * A_{b a}$)\n    assert ex == $(k - l) A_{a b}$, ex\n    print(\"Test tab05 passed\")\n   \ntab05()\n\n# Bianchi identities\n\ndef tab06():\n    __cdbkernel__ = create_scope()\n    R_{a b c d}::RiemannTensor.\n    ex = meld($R_{a b c d} + R_{a c d b} + R_{a d b c}$)\n    assert ex == $0$, ex\n    print(\"Test tab06 passed\")\n\ntab06()\n\ndef tab07():\n    __cdbkernel__ = create_scope()\n    R_{a b c d}::RiemannTensor.\n    ex = meld($k * R_{a b c d}R_{a b c d} + l * R_{a b c d}R_{a c b d}$)\n    assert ex == $(k + 1/2 l) R_{a b c d} R_{a b c d}$, ex\n    print(\"Test tab07 passed\")\n   \ntab07()\n\ndef tab08():\n    __cdbkernel__ = create_scope()\n    R_{a b c d}::RiemannTensor.\n    #ex = meld($R_{a b c d}R_{a b c d} + R_{a b c d}R_{a c b d}$)\n    ex = meld($R_{a b c d}R_{a b c d} + R_{a b c d}R_{a c b d}$)\n    assert ex == $3/2 R_{a b c d}R_{a b c d}$, ex\n    print(\"Test tab08 passed\")\n   \ntab08()\n\n\ndef tab09():\n    __cdbkernel__ = create_scope()\n    R_{a b c d}::RiemannTensor.\n    ex := R_{a b c d} + R_{a d b c};\n    meld(ex)\n    assert ex == $R_{a b c d} + R_{a d b c}$, ex\n    print(\"Test tab09 passed\")\n   \ntab09()\n\ndef tab10():\n    __cdbkernel__ = create_scope()\n    {a, b, c, d, e, f, g, h}::Indices.\n    A_{a b}::AntiSymmetric.\n    S_{a b}::Symmetric.\n    ex = $A_{a b}S_{c d}A_{e f}S_{g h} + A_{b a}S_{c d}A_{e f}S_{h g}$\n    meld(ex)\n    assert ex == $0$, ex\n    print(\"Test tab10 passed\")\n   \ntab10()\n\ndef tab11():\n    __cdbkernel__ = create_scope()\n    {a, b, c, d, e, f, g, h}::Indices.\n    T_{a b c}::Symmetric.\n    ex = meld($T_0 + m_1 * T_{a b c}T^{b a c} + m_2 * T_{b c a}T^{c b a}$)\n    assert ex == $T_0 + (m_1 + m_2) T_{a b c}T^{b a c}$, ex\n    print(\"Test tab11 passed\")\n   \ntab11()\n\ndef tab12a():\n    __cdbkernel__ = create_scope()\n    {m,n,p,q,r,s,t,u,v,w,a,b,c,d,e,f}::Indices(vector).\n    W_{m n p q}::WeylTensor.\n    ex:= W_{p q r s} W_{p t r u} W_{t v q w} W_{u v s w} \n        - W_{p q r s} W_{p q t u} W_{r v t w} W_{s v u w}\n        - W_{m n a b} W_{n p b c} W_{m s c d} W_{s p d a}\n        + (1/4) W_{m n a b} W_{p s b a} W_{m p c d} W_{n s d c}.\n    meld(ex)\n    assert ex == 0, ex\n\nif no_comp:\n    tab12a()\n    print(\"Test tab12 passed\")\nelse:\n    print(\"Test tab12a (using meld)         passed in\", timeit.timeit(tab12a,number=1))\n\ndef tab12b():\n    __cdbkernel__ = create_scope()\n    {m,n,p,q,r,s,t,u,v,w,a,b,c,d,e,f}::Indices(vector).\n    W_{m n p q}::WeylTensor.\n    ex:= W_{p q r s} W_{p t r u} W_{t v q w} W_{u v s w} \n        - W_{p q r s} W_{p q t u} W_{r v t w} W_{s v u w}\n        - W_{m n a b} W_{n p b c} W_{m s c d} W_{s p d a}\n        + (1/4) W_{m n a b} W_{p s b a} W_{m p c d} W_{n s d c}.\n    young_project_product(ex)\n    rename_dummies(ex)\n    assert ex == 0, ex\n  \nif not no_comp:\n    print(\"Test tab12b (using young_*)      passed in\", timeit.timeit(tab12b,number=1))\n\ndef tab13():\n    __cdbkernel__ = create_scope()\n    R_{a b c d}::RiemannTensor.\n    A^{a b c}::AntiSymmetric.\n    ex:= R_{a b c d} A^{a b c}.\n    meld(ex)\n    assert(ex == 0)\n    print(\"Test tab13a passed\")\n    ex:=R_{a b c d} A_{a b c}.\n    meld(ex)\n    assert ex == $R_{a b c d} A_{a b c}$, ex\n    print(\"Test tab13b passed\")\n\ntab13()\n\ndef tab14():\n    __cdbkernel__ = create_scope()\n    A_{a b c d e}::AntiSymmetric.\n    ex = meld($9A_{b a c e d} - 3A_{e d c b a}$)\n    assert ex == $6A_{b a c e d}$, ex\n    print(\"Test tab14 passed\")\n    \ntab14()\n\ndef tab15():\n    __cdbkernel__ = create_scope()\n    R_{a b c d}::RiemannTensor.\n    ex := k * R_{a b c d} + l * R_{a c d b} + m * R_{a d b c}:\n    meld(ex)\n    assert ex == $(k - m) R_{a b c d} + (l - m) R_{a c d b}$, ex\n    print(\"Test tab15 passed\")\n\ntab15()\n\ndef tab16():\n    __cdbkernel__ = create_scope()\n    S_{a b c}::Symmetric.\n    assert meld($a + b + c$) == $a + b + c$\n    assert meld($0$) == $0$\n    print(\"Test tab16 passed\")\n\ntab16()\n\ndef tab17():\n    __cdbkernel__ = create_scope()\n    ex := A_{m n} B_{m n} - A_{p q} B_{p q}.\n    meld(ex)\n    assert ex == 0, ex\n    print(\"Test tab17 passed\")\n\ntab17()\n\n\ndef tab18a():\n    __cdbkernel__ = create_scope()\n    {a,b,c,d}::Indices(group).\n    {\\mu,\\nu,\\rho,\\sigma}::Indices(spacetime).\n    \\epsilon^{\\mu\\nu\\rho\\sigma}::EpsilonTensor.\n    ex1:=F^{a b}_{\\mu\\sigma} A^{b c}_{\\nu} A^{c a}_{\\rho} \\epsilon^{\\mu\\sigma\\nu\\rho}; \n    ex2:=A^{a b}_{\\mu} F^{b c}_{\\nu\\sigma} A^{c a}_{\\rho} \\epsilon^{\\mu\\nu\\sigma\\rho};\n    ex:=@(ex1)+@(ex2);\n    sort_product(ex)\n    meld(ex)\n    assert ex == 0, ex\n\nif no_comp:\n    tab18a()\n    print(\"Test tab18 passed\")\nelse:\n    print(\"Test tab18a (using meld)         passed in\", timeit.timeit(tab18a,number=1000))\n\ndef test18b():\n    __cdbkernel__ = create_scope()\n    {a,b,c,d}::Indices(group).\n    {\\mu,\\nu,\\rho,\\sigma}::Indices(spacetime).\n    \\epsilon^{\\mu\\nu\\rho\\sigma}::EpsilonTensor.\n    ex1:=F^{a b}_{\\mu\\sigma} A^{b c}_{\\nu} A^{c a}_{\\rho} \\epsilon^{\\mu\\sigma\\nu\\rho}; \n    ex2:=A^{a b}_{\\mu} F^{b c}_{\\nu\\sigma} A^{c a}_{\\rho} \\epsilon^{\\mu\\nu\\sigma\\rho};\n    ex:=@(ex1)+@(ex2);\n    sort_product(ex)\n    canonicalise(ex)\n    assert ex == 0, ex\n\nif not no_comp:\n    print(\"Test tab18b (using canonicalise) passed in\", timeit.timeit(test18b,number=1000))\n\ndef tab19():\n    __cdbkernel__ = create_scope()\n    {\\mu,\\nu,\\rho,\\sigma}::Indices(spacetime).\n    \\epsilon^{\\mu\\nu\\rho\\sigma}::EpsilonTensor.\n    {a,b,c,d}::Indices(group).\n    F_{\\mu\\sigma}::ImplicitIndex(F^{b c}_{\\mu\\sigma}).\n    A_{\\mu}::ImplicitIndex(A^{a b}_{\\mu}).\n    Tr{#}::Trace(indices=group).\n    ex1:= F_{\\mu\\sigma} A_{\\nu} A_{\\rho} \\epsilon^{\\mu\\sigma\\nu\\rho}:\n    ex2:= A_{\\mu} F_{\\nu\\sigma} A_{\\rho} \\epsilon^{\\mu\\nu\\sigma\\rho}:\n    ex:= Tr {@(ex1) + @(ex2)};\n# This crashes here:\n    explicit_indices(ex)\n    sort_product(ex)\n    meld(ex)\n    assert ex == 0, ex\n    print(\"Test tab19 passed\")\n    \n#tab19()\nprint(\"Test tab19 SKIPPED\")\n\ndef tab20():\n    __cdbkernel__ = create_scope()\n    {\\mu, \\nu, \\rho}::Indices(vector)\n    A_{\\mu, \\nu}::AntiSymmetric.\n    {a^{\\mu}, b^{\\nu}}::NonCommuting.\n    ex := A_{\\mu \\nu} a^{\\mu} b^{\\rho} a^{\\nu}:\n    meld(ex)\n    assert ex == $A_{\\mu \\nu} a^{\\mu} b^{\\rho} a^{\\nu}$, ex\n    print(\"Test tab20 passed\")\n\ntab20()\n\ndef tab21():\n    __cdbkernel__ = create_scope()\n    T_{a b c}::SelfAntiCommuting.\n    ex := T_{a b c}T_{b a c} + T_{b a c}T_{a b c}:\n    meld(ex)\n    assert ex == $0$, ex\n    print(\"Test tab21 passed\")\n\ntab21()\n\ndef tab22():        \n    __cdbkernel__ = create_scope()\n    {m,n,p,q,r,s}::Indices.\n    A_{m n}::AntiSymmetric.\n    B_{m n}::Symmetric.\n    ex:= A_{m n} B_{n p} - A_{n m} B_{n p} + A_{m p} B_{q r} B_{q r} - A_{p m} B_{q s} B_{q s};\n    meld(ex, repeat=False)\n    assert ex == $2A_{m n} B_{n p} + 2A_{m p} B_{q r} B_{q r}$, ex\n    print(\"Test tab22 passed\")\n\ntab22()\n        \n# Portugal's example.\ndef tab23():\n    __cdbkernel__ = create_scope()\n    R_{a b c d}::RiemannTensor.\n    ex:= 2 R_{a b c d} R_{e f a k} R_{h c k b} R_{d h e f}\n        +4 R_{a b c d} R_{e f k a} R_{h b c e} R_{d k f h}\n        -  R_{a b c d} R_{e f k a} R_{h b f e} R_{c d k h}\n        +4 R_{a b c d} R_{h k d f} R_{e f k a} R_{h b c e}.\n    meld(ex)\n    assert ex == 0, ex\n    print(\"Test tab23 passed\")\n\ntab23()\n\n# RiemannRule13 from MathTensor\ndef tab24():\n    __cdbkernel__ = create_scope()\n    R_{a b c d}::RiemannTensor.\n    ex:= R_{a b c d} R_{e a g b} R_{c d e g}\n       -1/2 R_{p q r s} R_{t u p q} R_{r s t u}.\n    meld(ex)\n    assert ex == 0, ex\n    print(\"Test tab24 passed\")\n\ntab24()\n\ndef tab25():\n    import numpy as np\n    {n#}::Indices;\n    R_{n1 n2 n3 n4}::RiemannTensor;\n    str=\"\"\n    for n in range(4):\n       p = np.random.permutation(4*4)\n       for tensor in range(4):\n           str+=\"R_{\"\n           for index in range(4):\n               str+=ilist[p[tensor*4+index]]+' '\n           str+=\"} \"\n       if n<3:\n          str+=\"+ \"\n        \n    ex=Ex(str)\n    meld(ex);\n    print(\"Test tab25 passed\")\n\n#tab25()\nprint(\"Test tab25 SKIPPED\")\n\n# Bianchi identity with coordinates and integers\ndef tab26():\n    R_{a b c d}::RiemannTensor.\n    {t, x, y, z}::Coordinate.\n    ex = meld($R_{t a b c} + R_{t b c a} + R_{t c a b}$)\n    assert ex == 0, ex\n    print(\"Test tab26 passed\")\n\ntab26()\n\n# Raising and lowering indices\ndef tab27():\n    {\\mu, \\nu, \\rho, \\lambda}::Indices(setA, position=fixed).\n    {A, B, C, D}::Indices(setB, position=independent)\n    {t, r, \\phi, \\theta}::Coordinate.\n    # Fixed and free indices combine\n    ex = meld($a_{\\mu} b^{\\mu} - a^{\\mu} b_{\\mu}$)\n    assert ex == 0, ex\n    ex = meld($T_{\\mu\\nu} K^{\\mu} - T^{\\mu}_{\\nu} K_{\\mu}$)\n    assert ex == 0, ex\n    ex = meld($a_{i}b^{i} - a^{i}b_{i}$)\n    assert ex == 0, ex\n    # Independent indices and coordinates don't\n    ex = meld($a_{A}b^{A} + a^{A}b_{A}$)\n    assert ex == $a_{A}b^{A} + a^{A}b_{A}$, ex\n    ex = meld($a_{t}b^{t} + a^{t}b_{t}$)\n    assert ex == $a_{t}b^{t} + a^{t}b_{t}$, ex\n    print(\"Test tab27 passed\")\n\ntab27()\n\n# Raising and lowering through a derivative\ndef tab28():\n    \\partial{#}::PartialDerivative.\n    \\nabla{#}::Derivative.\n    {\\mu, \\nu, \\rho, \\lambda}::Indices(setA, position=fixed).\n    # Free indices through a derivative do combine\n    ex = meld($a_{i} \\partial_{\\nu}{b^{i}} + a^{i} \\partial_{\\nu}{b_{i}}$)\n    assert ex == $2a_{i} \\partial_{\\nu}{b^{i}}$, ex\n    # Fixed indices through a derivative don't combine\n    ex = meld($a_{\\mu} \\partial_{\\nu}{b^{\\mu}} + a^{\\mu} \\partial_{\\nu}{b_{\\mu}}$)\n    assert ex == $a_{\\mu} \\partial_{\\nu}{b^{\\mu}} + a^{\\mu} \\partial_{\\nu}{b_{\\mu}}$, ex\n    ex = meld($a_{\\mu} \\partial_{t}{b^{\\mu}} + a^{\\mu} \\partial_{t}{b_{\\mu}}$)\n    assert ex == $a_{\\mu} \\partial_{t}{b^{\\mu}} + a^{\\mu} \\partial_{t}{b_{\\mu}}$, ex\n    ex = meld($a_{\\mu} \\nabla_{\\nu}{b^{\\mu}} - a^{\\mu} \\partial_{\\nu}{b_{\\mu}}$)\n    assert ex == $a_{\\mu} \\nabla_{\\nu}{b^{\\mu}} - a^{\\mu} \\partial_{\\nu}{b_{\\mu}}$, ex\n    print(\"Test tab28 passed\")\n\ntab28()\n    \n# Multiple tableaux as product\ndef tab29():\n    T_{a b c d}::TableauSymmetry(shape={1,1}, indices={0,1}, shape={1,1}, indices={2,3}).\n    ex := T_{a b c d} + T_{b a c d} + T_{a b d c} + T_{b a d c}.\n    meld(ex)\n    assert ex == 0, ex\n    # Bianchi shouldn't hold for this\n    ex := T_{a b c d} + T_{a c d b} + T_{a d b c}.\n    meld(ex)\n    assert ex == $T_{a b c d} + T_{a c d b} + T_{a d b c}$, ex\n    print(\"Test tab29 passed\")\n\ntab29()\n\ndef tab30():\n    T_{a b c}::TableauSymmetry(shape={2}, indices={0,1}, shape={1,1}, indices={0,1}).\n    ex := T_{a b c}.\n    meld(ex)\n    assert ex == 0, ex\n    print(\"Test tab30 passed\")\n\ntab30()\n\n# Multiple tableaux as sum\ndef tab31():\n    T_{a b c}::TableauSymmetry(shape={2,1}, indices={0,2,1}, shape={1,1,1}, indices={0,1,2}).\n    ex := T_{a b c} + T_{b a c}.\n    meld(ex, project_as_sum=True)\n    assert ex == 0, ex\n    print(\"Test tab31 passed\")\n\ntab31()\n\ndef tab32():\n    R_{a b c d e}::TableauSymmetry(shape={3,2}, indices={0,2,4,1,3}, shape={2,2,1}, indices={0,2,1,3,4}).\n    ex = meld($R_{a b c d e} + R_{a c d b e} + R_{a d b c e}$, project_as_sum=True)\n    assert ex == 0, ex\n    print(\"Test tab32 passed\")\n\ntab32()\n\n# Automicatically construct tableaux for derivatives of Riemann tensors\ndef tab33():\n\tD{#}::Derivative.\n\tR_{a b c d}::RiemannTensor.\n\tex := D_{e}{D_{a}{R_{a b c d}}} D_{h}{D_{i}{R_{b e f g}}} D_{d}{D_{h}{R_{c f g i}}} - \n\t  1/8 D_{e}{D_{e}{R_{a b c d}}} D_{h}{D_{i}{R_{a b f g}}} D_{i}{D_{h}{R_{c d f g}}}.\n\tmeld(ex)\n\tassert ex == 0, ex\n\tprint(\"Test tab33 passed\")\n\t\ntab33()\n\ndef tab34():\n\t\\nabla{#}::Derivative.\n\tR_{a b c d}::RiemannTensor.\n\tex := \\nabla_{e}{R_{a b c d}} + \\nabla_{c}{R_{a b d e}} + \\nabla_{d}{R_{a b e c}}.\n\tmeld(ex)\n\tassert ex == 0, ex\n\tprint(\"Test 34 passed\")\n\t\ntab34()\n\ndef tab35():\n\t{j,k}::Indices;\n\tex := A = - x x n_{k} n_{k} - x x n_{j} n_{j};\n\tmeld(_);\n\tassert ex == $-2 x x n_{k} n_{k}$, ex\n\tprint(\"Test 35 passed\")\n\ndef tab36():\n    {a,b,c}::Indices.\n    {a,b,c}::Integer(1..3).\n    {X,Y}::Symbol.\n    {X,Y,n_{a}}::Commuting.\n    exA := 10 X n_{a} Y + 2 Y X n_{a}.\n    exB := @(exA).\n    meld(exA)\n    assert exA == $(10X Y + 2Y X) n_{a}$, exA\n    sort_product(exB)\n    meld(exB)\n    assert exB == $12X Y n_{a}$, exB\n    print(\"Test 36 passed\")\n\n\n# *_cycle_traces tests\n\ndef cyctrace01():\n    from cdb.core.trace import combine_traces\n    __cdbkernel__ = create_scope()\n    Tr{#}::Trace.\n    {A, B, C, D}::NonCommuting.\n    ex := Tr{A B C D + C D A B + B C D A} - Tr{D A B C}.\n    combine_traces(ex)\n    meld(ex)\n    assert ex == $2 * Tr{A B C D}$, ex\n    print(\"Test cyctrace01 passed\")\n\ncyctrace01()\n\ndef cyctrace02():\n    __cdbkernel__ = create_scope()\n    {\\mu,\\nu,\\rho}::Indices(vector).\n    {a^{\\mu},b^{\\mu},c^{\\mu}}::NonCommuting.\n    tr{#}::Trace.\n    ex := tr(a^{\\mu} b^{\\nu} c^{\\rho} a^{\\mu} b^{\\rho} c^{\\nu} + \n              b^{\\mu} c^{\\nu} a^{\\rho} b^{\\nu} c^{\\mu} a^{\\rho} + \n              c^{\\mu} a^{\\nu} b^{\\mu} c^{\\rho} a^{\\nu} b^{\\rho}).\n    meld(ex)\n    assert ex == $3 * tr(a^{\\mu} b^{\\nu} c^{\\rho} a^{\\mu} b^{\\rho} c^{\\nu}$, ex\n    print(\"Test cyctrace02 passed\")\n\ncyctrace02()\n\ndef cyctrace03():\n    __cdbkernel__ = create_scope()\n    {\\mu,\\nu}::Indices(vector).\n    u^{\\mu}::ImplicitIndex.\n    u^{\\mu}::SelfNonCommuting.\n    tr{#}::Trace.\n    ex := tr{u^{\\mu} u^{\\mu} u^{\\nu} u^{\\nu}} - \n        tr{u^{\\mu} u^{\\nu} u^{\\nu} u^{\\mu}}.\n    meld(ex)\n    assert ex == $0$, ex\n    print(\"Test cyctrace03 passed\")\n\n# cyctrace03()\nprint(\"Test cyctrace03 SKIPPED\")\n\ndef cyctrace04():\n    __cdbkernel__ = create_scope()\n    {\\mu,\\nu,\\rho}::Indices(vector).\n    A^{\\mu\\nu}::AntiSymmetric.\n    B^{\\mu\\nu}::Symmetric.\n    C^{\\mu\\nu}::AntiSymmetric.\n    tr{#}::Trace.\n    {A^{\\mu\\nu},B^{\\mu\\nu},C^{\\mu\\nu}}::NonCommuting.\n    {A^{\\mu\\nu},B^{\\mu\\nu},C^{\\mu\\nu}}::SelfNonCommuting.\n    {A^{\\mu\\nu},B^{\\mu\\nu},C^{\\mu\\nu}}::ImplicitIndex.\n    ex := a tr{A^{\\mu\\nu} B^{\\mu\\rho} B^{\\nu\\rho}}+b tr{C^{\\mu\\nu} A^{\\mu\\rho} B^{\\nu\\rho}}+c tr{C^{\\mu\\nu} B^{\\mu\\rho} A^{\\nu\\rho}}.\n    meld(ex)\n    assert ex == $a tr{A^{\\mu\\nu} B^{\\mu\\rho} B^{\\nu\\rho}}+b tr{C^{\\mu\\nu} A^{\\mu\\rho} B^{\\nu\\rho}}+c tr{C^{\\mu\\nu} B^{\\mu\\rho} A^{\\nu\\rho}}$, ex\n    print(\"Test cyctrace04 passed\")\n\ncyctrace04()\n\ndef cyctrace05():\n    __cdbkernel__ = create_scope()\n    {\\mu,\\nu}::Indices(vector).\n    tr{#}::Trace.\n    u^{\\mu}::SelfNonCommuting.\n    u^{\\mu}::ImplicitIndex.\n    ex:=tr{A u^{\\nu} u^{\\mu} u^{\\mu} u^{\\nu} + B u^{\\mu} u^{\\mu} u^{\\nu} u^{\\nu}}.\n    meld(ex)\n    assert ex == $tr{ (A+B) u^{\\nu} u^{\\mu} u^{\\mu} u^{\\nu} }$, ex\n    print(\"Test cyctrace05 passed\")\n\ncyctrace05()\n\ndef cyctrace06():\n    __cdbkernel__ = create_scope()\n    {\\mu,\\nu,\\rho}::Indices(vector).\n    A^{\\mu\\nu}::AntiSymmetric.\n    B^{\\mu\\nu}::Symmetric.\n    C^{\\mu\\nu}::AntiSymmetric.\n    tr{#}::Trace.\n    {A^{\\mu\\nu},B^{\\mu\\nu},C^{\\mu\\nu}}::NonCommuting.\n    {A^{\\mu\\nu},B^{\\mu\\nu},C^{\\mu\\nu}}::SelfNonCommuting.\n    {A^{\\mu\\nu},B^{\\mu\\nu},C^{\\mu\\nu}}::ImplicitIndex.\n\n    ex := tr{\n        a A^{\\mu\\nu} B^{\\mu\\rho} B^{\\nu\\rho} + \n        b C^{\\mu\\nu} A^{\\mu\\rho} B^{\\nu\\rho} +\n        c C^{\\mu\\nu} B^{\\mu\\rho} A^{\\nu\\rho}\n    }.\n    assert meld($@(ex)$) == ex\n    print(\"Test cyctrace06 passed\")\n\ncyctrace06()\n\n\n# *_diagonal tests\n\ndef diag01():\n   __cdbkernel__=create_scope()\n   {t,r}::Coordinate.\n   {a,b}::Indices(values={t,r},position=fixed).\n   A_{a b}::Diagonal.\n   ex = $A_{t r}$ + $A_{r r}$ + $A_{r t}$ + $A_{t t}$\n   meld(ex)\n   assert ex == $A_{r r} + A_{t t}$, ex\n   print(\"Test diag01 passed\")\n\ndiag01()\n\ndef diag02():\n   __cdbkernel__=create_scope()\n   {m,n}::Integer.\n   \\delta_{m n}::Diagonal.\n   ex = $-\\delta_{1 1}\\delta_{2 2}$ + $\\delta_{1 2}\\delta_{1 2}$ + $\\delta_{1 1}\\delta_{2 2}$\n   meld(ex)\n   assert ex == $0$, ex\n   print('Test diag02 passed')\n   \ndiag02()\n\n\n# *_traceless tests\n\ndef traceless01():\n   __cdbkernel__=create_scope()\n   {m,n,p,q,r,s,t,u}::Indices(vector).\n   dR_{m n p q r s}::TableauSymmetry(shape={4,2}, indices={2,3,0,1,4,5}).\n   dR_{m n p q r s}::Traceless.\n   ex := dR_{m n p q r r};\n   meld(_)\n   assert ex == $0$, ex\n   print(\"Test traceless01 passed\")\n   \ntraceless01()\n\ndef tab33b():\n   __cdbkernel__=create_scope()\n   {a,b,c,d}::Indices.\n   X_{a b c}::TableauSymmetry(shape=(2,1), indices=(0,2,1)).\n   ex:=X_{a d d};\n   meld(ex)\n   tst:= X_{a d d} - @(ex);\n   assert(tst==0)\n   print(\"Test tab33b passed\")\n\ntab33b()\n\n\n# {a,b,c,i,j,k}::Indices;\n# {a,b,c,i,j,k}::Integer(1..3);\n# {ct, st}::Symbol;\n# \\nabla{#}::Derivative;\n# {st,ct,n_{k}}::Depends(\\nabla{#})\n# \n# {d{#}}::KroneckerDelta;\n# {e_{a b c}}::EpsilonTensor(delta=d);\n# \n# rota := R_{a j} = ct d_{a j} + (1-ct) n_{a} n_{j} - st e_{a j k} n_{k};\n# FGR := \\nabla_{j}{R_{a k}} \\nabla_{j}{R_{a k}};\n# \n# substitute(FGR, rota); distribute(_, repeat=True);\n# product_rule(_); unwrap(_);\n# distribute(_, repeat=True);\n# collect_factors(_); sort_product(_);\n# \n# sort_sum(_);\n# \n# meld(_);        \n# \n# \n# \n# {a,b,c,i,j,k}::Indices;\n# {a,b,c,i,j,k}::Integer(1..3);\n# {ct, st}::Symbol;\n# \\nabla{#}::Derivative;\n# {st,ct,n_{k}}::Depends(\\nabla{#})\n# \n# {d{#}}::KroneckerDelta;\n# {e_{a b c}}::EpsilonTensor(delta=d);\n# \n# rota := R_{a j} = ct d_{a j} + (1-ct) n_{a} n_{j} - st e_{a j k} n_{k};\n# FGR := \\nabla{R_{a k}}_{j} \\nabla{R_{a k}}_{j};\n# \n# substitute(FGR, rota); distribute(_, repeat=True);\\\n# product_rule(_); unwrap(_);\\\n# distribute(_, repeat=True);\\\n# collect_factors(_); sort_product(_); sort_sum(_);\\\n# meld(_);"
  },
  {
    "path": "tests/mma.cdb",
    "content": "\n# Tests for the connection to a Mathematica kernel.\n\ndef test01():\n    ex:= \\alpha \\beta \\cos{\\gamma \\Delta}:\n    out=ex.mma_form()\n    tst=\"α*β*Cos[γ*Δ]\"\n    assert(out==tst)\n    print(\"Test 01a passed\")\n    out=ex.mma_form(unicode=False)\n    tst=\"\\[Alpha]*\\[Beta]*Cos[\\[Gamma]*\\[CapitalDelta]]\"\n    assert(out==tst)\n    print(\"Test 01b passed\")\n    out=ex.mma_form(unicode=True)\n    tst=\"α*β*Cos[γ*Δ]\"\n    assert(out==tst)\n    print(\"Test 01c passed\")\n\ntest01()\n\ndef test02():\n    ex:= \\cos{\\alpha}**2 + \\sin{2 \\alpha}**2;\n    map_mma(ex)\n    tst:= \\cos{\\alpha}**2 + \\sin{2 \\alpha}**2 - @(ex);\n    assert(tst==0)\n    print(\"Test 02a passed\")\n    ex:= \\cos{x}**2 + \\sin{x}**2;\n    map_mma(ex, \"FullSimplify\")\n    tst:=1 - @(ex);\n    assert(tst==0)\n    print(\"Test 02b passed\")\n#ex:=Integrate( \\sin{x} + x**2, {x,0,\\pi} );\n#map_mma(ex);\n\ntest02()\n\ndef test03():\n    __cdbkernel__=create_scope()\n    r::Coordinate;\n    \\partial{#}::PartialDerivative;\n    ex:= \\partial_{r}{ r**2 + \\sin{r} };\n    map_mma(ex, \"FullSimplify\")\n    tst:= 2 r + \\cos{r} - @(ex);\n    assert(tst==0)\n    print(\"Test 03 passed\")\n\ntest03()\n#ex:= (a*\\cos{\\theta})**2;\n#map_mma(ex);\n\ndef test04():\n    __cdbkernel__=create_scope()\n    __cdbkernel__.scalar_backend = scalar_backend_t.mathematica\n    ex:=\\sin(x)**2 + \\cos(x)**2;\n    simplify(_)\n    assert(ex==1)\n    print(\"Test 04 passed\")\n\ntest04()\n\ndef test05():\n    kernel(scalar_backend=\"mathematica\")\n    {r,t}::Coordinate;\n    {a,b,c,d,e}::Indices(values={r,t});\n    \\partial{#}::PartialDerivative;\n    f::Depends(r,t);\n    rl:= { g_{r r} = f r**2 };\n    ex:= \\Gamma_{a b c} = \\partial_{a}{ g_{b c} };\n    evaluate(ex, rl, rhsonly=True)\n    c1=ex[1][3][1][1]\n    tst:=@(c1) - r (r\\partial_{r}{f} + 2 f);\n    distribute(tst)\n    assert(tst==0)\n    print(\"Test 05a passed\")\n    c2=ex[1][3][0][1]\n    tst:=@(c2) - r**2 \\partial_{t}{f};\n    distribute(tst)\n    assert(tst==0)\n    print(\"Test 05b passed\")\n\ntest05()\n    \n\n    \n"
  },
  {
    "path": "tests/mma.cnb",
    "content": "{\n\t\"cells\" : \n\t[\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"We can use a Mathematica kernel to simplify all scalar expressions while\\nusing all tensor capabilities of Cadabra, by simply running mathematica on\\non expressions after every manipulation step.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"We can use a Mathematica kernel to simplify all scalar expressions while\\nusing all tensor capabilities of Cadabra, by simply running mathematica on\\non expressions after every manipulation step.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"def post_process(ex):\\n\\tmap_mma(ex, \\\"FullSimplify\\\")\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"The following shows this in action.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"The following shows this in action.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}1\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex:= \\\\cos{\\\\alpha}**2 + \\\\sin{\\\\alpha}**2;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\cos\\\\left(\\\\alpha+\\\\beta\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex:= \\\\cos{\\\\alpha}\\\\cos{\\\\beta} - \\\\sin{\\\\alpha}\\\\sin{\\\\beta};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{} - \\\\frac{1}{2}{\\\\left(\\\\cos{x}\\\\right)}^{2}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex:= \\\\int{ \\\\cos{x} \\\\sin{x}}{x};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Indices(position=free) to~}\\\\left[m,~\\\\discretionary{}{}{} n,~\\\\discretionary{}{}{} p\\\\right].\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"{m,n,p}::Indices(values={0,1,2});\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}A_{m n} A^{m n}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex:= A_{m n} A^{m n};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\left[A_{0 1} = \\\\sin{x},~\\\\discretionary{}{}{} A_{1 2} = x+\\\\cos{x}\\\\right]\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"rl:={ A_{0 1} = \\\\sin{x}, A_{1 2} = \\\\cos{x} + x };\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}1+{x}^{2}+2x \\\\cos{x}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"evaluate(ex, rl);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}2x {\\\\left(-1+{x}^{2}\\\\right)}^{-1}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex:= 1/(x+1) + 1/(x-1);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"Just to see how fast this is, let's do this in a loop.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"Just to see how fast this is, let's do this in a loop.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"for i in range(100):\\n\\tex:= 1/(x+1) + 1/(x-1).\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}2x {\\\\left(-1+{x}^{2}\\\\right)}^{-1}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"The same loop but now with the sympy backend is considerably slower:\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"The same loop but now with the sympy backend is considerably slower:\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"def post_process(ex):\\n\\tmap_sympy(ex, \\\"simplify\\\")\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\frac{2x}{{x}^{2}-1}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex:=1/(x+1) + 1/(x-1);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"for i in range(100):\\n\\tex:= 1/(x+1) + 1/(x-1).\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\frac{2x}{{x}^{2}-1}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"{}$\\\\big[$\\\\verb|cadabra::evaluate: 1 calls, 0 steps, 147 ms|,\\\\discretionary{}{}{} \\\\verb|cadabra::map_mma: 109 calls, 0 steps, 705 ms|,\\\\discretionary{}{}{} \\\\verb|cadabra::map_sympy: 101 calls, 0 steps, 1933 ms|,\\\\discretionary{}{}{} \\\\verb|sympy: 1 calls, 0 steps, 146 ms|$\\\\big]$\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"server.totals();\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"Back to the Mathematica post-processing. It is possible to use Mathematica syntax directly, as the Cadabra parser handles\\nthat notation. You can even mix Cadabra and Mathematica notation to some extent, as the following example shows.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"Back to the Mathematica post-processing. It is possible to use Mathematica syntax directly, as the Cadabra parser handles\\nthat notation. You can even mix Cadabra and Mathematica notation to some extent, as the following example shows.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"def post_process(ex):\\n\\tmap_mma(ex, \\\"FullSimplify\\\")\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}2\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex:= Integrate[ \\\\sin{x}, {x, 0, \\\\pi}];\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}2+\\\\frac{1}{3}{\\\\pi}^{3}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex:= \\\\int{ \\\\sin{x}+x**2 }{ {x,0,\\\\pi} };\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}1\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex:= Limit[ \\\\sin{x}/x, x->0 ];\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1\n}\n"
  },
  {
    "path": "tests/module01.cnb",
    "content": "{\n\t\"cell_id\": 11133545823733131797,\n\t\"cells\": [\n\t\t{\n\t\t\t\"cell_id\": 9393063997868488130,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 2958649168197266717,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\text{Property PartialDerivative attached to~}\\\\backslash\\\\texttt{partial}\\\\{\\\\#\\\\}.\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"\\\\partial{#}::PartialDerivative;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 10618251854465000699,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 7560854228305782685,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 3839881997668378415,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"\\\\partial_{m}(A_{n p})\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}\\\\partial_{m}\\\\!{A_{n p}}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"ex:=\\\\partial_{m}{A_{n p}};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 11150854340261852790,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"\"\n\t\t}\n\t],\n\t\"description\": \"Cadabra JSON notebook format\",\n\t\"flags\": {\n\t\t\"hide_input_cells\": false\n\t},\n\t\"version\": 1.0\n}\n"
  },
  {
    "path": "tests/module02.cnb",
    "content": "{\n\t\"cells\" : \n\t[\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property PartialDerivative to~}\\\\nabla{\\\\#}.\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"\\\\nabla{#}::PartialDerivative;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"cells\" : \n\t\t\t\t\t[\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\t\t\"cell_type\" : \"input_form\",\n\t\t\t\t\t\t\t\"source\" : \"\\\\nabla_{m}(B_{q})\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\nabla_{m}{B_{q}}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex2:=\\\\nabla_{m}{ B_{q} };\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1\n}\n"
  },
  {
    "path": "tests/module03.cdb",
    "content": "\nex:= Q_{m} R^{m};\n"
  },
  {
    "path": "tests/modules.cdb",
    "content": "\nfrom module01 import *\n\ndisplay(ex)\n\nex0:=\\partial_{m}{A_{n p}}:\n\ndef test01():\n    bla:= T_{m n p} + @(ex);\n    tst:= \\partial_{m}{A_{n p}} - @(ex0);\n    assert(tst==0)\n    print(\"Test 01a passed\")\n    tst:= \\partial_{m}{A_{n p}} - @(ex);\n    assert(tst==0)\n    print(\"Test 01b passed\")\n    \ntest01()\n\nfrom module01 import ex as ex3\n\ndef test02():\n    tst:= \\partial_{m}{A_{n p}} - @(ex3);\n    assert(tst==0)\n    print(\"Test 02 passed\")\n    \ntest02()\n\n\nfrom module03 import ex as ex4\n\ndef test03():\n    tst:= Q_{m} R^{m} - @(ex4);\n    assert(tst==0)\n    print(\"Test 03 passed\")\n\ntest03()\n\n\nfrom ipynb_module import ex as ex5\n\ndef test04():\n    assert(ex5==$A_{m n p}$)\n    print(\"Test 04 passed\")\n\ntest04()\n\n\n# import module02\n# \n# def test02():\n#     tst:= \\nabla_{m}{B_{q}} - @(module02.ex2);\n#     assert(tst==0)\n#     print(\"Test 02 passed\")\n# \n# test02()\n"
  },
  {
    "path": "tests/multiterm.cdb",
    "content": "# Portugal's examples involving Ricci cycling do not yet work:\n#\nR_{m n p q}::RiemannTensor.\ntst11a:= R_{a b c d} R_{e a c f} R_{f b d e} \n  +  R_{a b e f} R_{c d a b} R_{c e d f}\n  +2 R_{a b c d} R_{e a f c} R_{f d b e};\n@riemann_index_regroup!(%);\n@canonicalise!(%);\n@collect_terms!(%);\n\ntst11b:= R_{a b c d} R_{e f a k} R_{h c k b} R_{d h e f}\n +4 R_{a b c d} R_{e f k a} R_{h b c e} R_{d k f h}\n -  R_{a b c d} R_{e f k a} R_{h b f e} R_{c d k h}\n +4 R_{a b c d} R_{h k d f} R_{e f k a} R_{h b c e};\n@riemann_index_regroup!(%);\n@canonicalise!(%);\n@collect_terms!(%);\n\n\n\n# One other non-trivial one involving the cyclic identity.\n# This one is not handled because the anti-symmetrisation in the \n# brackets is not recognised, and therefore the regroup function \n# does not see that it can Ricci cycle.\n#\nW_{a b m n} W_{a b p q} - 2*(W_{a m b n} W_{a p b q} - W_{a m b n} W_{a q b p});\n#\n# Use this one to test the Young tableau idea. I think it should\n# handle this one, since it essentially boils down to the idea\n# that you write down the full Young symmetrised objects of all\n# terms, and then collect.\n"
  },
  {
    "path": "tests/nevaluate.cdb",
    "content": "\n# ex:=A + B \\cos(x);\n# nevaluate(ex, {$A$: 1, $B$: 3, $x$: np.linspace(0, 10, 10)});\n\nimport time\n# import matplotlib.pyplot as plt\nimport numpy as np\n\ndef test01():\n   start = time.time()\n   ex:= \\cos(x) \\sin(y).\n   xv = np.linspace(0, 3.14/2, 50)\n   yv = np.linspace(0, 3.14, 100)\n   z = np.array( nevaluate(ex, {$x$: xv, $y$: yv} ) )\n   end = time.time()\n   # print(\"that took\", end-start, \"seconds\")\n   xp = xv[10]\n   yp = yv[20]\n   import math\n   want=math.cos(xp)*math.sin(yp)\n   assert( z.shape == (50, 100) )\n   assert( abs( z[10, 20] - want ) < 0.001)\n   print(\"Test 01 passed\")\n   # XV, YV=np.meshgrid(xv, yv)\n   # plt.figure(figsize=(20, 10))\n   # ax = plt.axes(projection='3d')\n   # ax.plot_surface(XV, YV, z, rstride=1, cstride=1, cmap='terrain', edgecolor=None)                   \n\ntest01()\n\n\n\ndef test02():\n   res = np.array(nevaluate( $3\\cos(x)$, {$x$: [0]}))\n   assert(abs(res[0] - 3.0) < 0.001)\n   print(\"Test 02a passed\")\n   res = np.array(nevaluate( $3\\cos(3 x + \\pi/4)$, {$x$: [0]}))\n   assert(abs(res[0] - 2.1213) < 0.001)\n   print(\"Test 02b passed\")\n\ntest02()\n\ndef test03():\n   res = np.array(nevaluate( $\\pi x$, {$x$: [0,1,2]}))\n   assert(np.max(res - np.array([0, 3.14, 6.28])) < 0.01)\n   print(\"Test 03a passed\")\n   res = np.array(nevaluate( $x \\pi$, {$x$: [0,1,2]}))\n   assert(np.max(res - np.array([0, 3.14, 6.28])) < 0.01)\n   print(\"Test 03b passed\")\n   res = np.array(nevaluate( $\\pi + x$, {$x$: [0,1,2]}))\n   assert(np.max(res - np.array([3.14, 4.14, 5.14])) < 0.01)\n   print(\"Test 03c passed\")\n   res = np.array(nevaluate( $x + \\pi$, {$x$: [0,1,2]}))\n   assert(np.max(res - np.array([3.14, 4.14, 5.14])) < 0.01)\n   print(\"Test 03d passed\")\n\ntest03()\n\ndef test04():\n   res = np.array( nevaluate($3 \\cos(5 x)$, {$x$: [0.1, 0.3]}) )\n   assert(np.max(res - np.array([2.6327, 0.2112])) < 0.01)\n   print(\"Test 04a passed\")\n   xv = np.array([2.0, 5.0])\n   res = np.array( nevaluate($\\sin(3.0*x)*\\cos(-1/2 x)*\\exp(-x**(2/5))$, {$x$: xv} ))\n   assert(np.max(res - np.sin(3.0*xv)*np.cos(-1/2*xv)*np.exp(-xv**(2/5))) < 0.01)\n   print(\"Test 04b passed\")\n\ntest04()\n\ndef test05():\n   import numpy as np\n   i::ImaginaryI.\n   ex := a + b i.\n   q = np.array(nevaluate(ex, {$a$: 2, $b$: 3}))\n   assert( q[0] == 2 + 3j )\n   print(\"Test 05 passed\")\n\ntest05()\n"
  },
  {
    "path": "tests/new_paper.cdb",
    "content": "\n{\\tau}::Coordinate;\n{t,r,\\phi,\\theta}::Coordinate;\n{\\mu,\\nu,\\rho,\\lambda}::Indices(values={t,r,\\phi,\\theta});\nX^{\\mu}::Depends(\\tau);\n\\partial{#}::PartialDerivative;\nex:= \\partial_{\\tau\\tau}{X^{\\mu}} + \\Gamma^{\\mu}_{\\nu\\rho} \\partial_{\\tau}{X^{\\nu}}\\partial_{\\tau}{X^{\\rho}};\nevaluate(_, simplify=False);\n\n{\\tau}::Coordinate;\n{t,r,\\phi,\\theta}::Coordinate;\n{\\mu,\\nu,\\rho,\\sigma,\\lambda,\\kappa,\\gamma,\\chi}::Indices(values={t,r,\\phi,\\theta}, position=fixed).\nX^{\\mu}::Depends(\\tau);\n\\partial{#}::PartialDerivative;\ng_{\\mu\\nu}::Metric.\ng^{\\mu\\nu}::InverseMetric.         \nss:= { g_{t t} = -(1-2 M/r),  g_{r r} = 1/(1-2 M/r),\n       g_{\\theta\\theta} = r**2,  g_{\\phi\\phi}=r**2 \\sin(\\theta)**2 };\ncomplete(ss, $g^{\\mu\\nu}$)\nch:= \\Gamma^{\\mu}_{\\nu\\rho} = 1/2 g^{\\mu\\sigma} ( \\partial_{\\rho}{g_{\\nu\\sigma}}\n                                                +\\partial_{\\nu}{g_{\\rho\\sigma}}\n                                                -\\partial_{\\sigma}{g_{\\nu\\rho}} );\nevaluate(ch, ss, rhsonly=True)\n\nex:= \\partial_{\\tau\\tau}{X^{\\mu}} + \\Gamma^{\\mu}_{\\nu\\rho} \\partial_{\\tau}{X^{\\nu}}\\partial_{\\tau}{X^{\\rho}};\nsubstitute(ex, ch)\nevaluate(_);\n\n    \ndef fourier_transform(ex):\n    expand_power(ex);\n    for term in ex.iterator().terms():\n        num=1\n        for factor in term.factors():\n            k = Ex(\"I k\"+str(num))\n            if factor.name==\"\\\\partial\":\n                for index in factor.indices():\n                     factor.insert(k).append_child(index)\n                for arg in factor.args():\n                     arg.append_child(k)\n                     factor.insert(arg)\n                factor.erase()\n            else:\n                factor.append_child(k)\n            num+=1\n    return ex\n\ndef fourier_transform(ex):\n    expand_power(ex);\n    terms=ex[\"\\\\sum\"].__next__().children()\n    for term in terms:\n        if term.name==\"\\\\prod\":\n            num=1\n            for factor in term.children():\n                if factor.name==\"\\\\partial\":\n                    for index in factor.indices():\n                         k = Ex(\"k\"+str(num))\n                         factor.insert(k).append_child(index)\n                         factor.insert(Ex(\"I\"))\n                    for arg in factor.args():\n                         arg.append_child(Ex(\"k\"+str(num)))\n                         factor.insert(arg)\n                    factor.erase()\n                else:\n                    factor.append_child(Ex(\"k\"+str(num)))\n                num+=1\n        else:\n            term.append_child(Ex(\"k1\"))\n    return ex\n\n\\partial{#}::PartialDerivative;\nA_{\\mu}, \\phi}::Depends(\\partial{#});\nex:= \\partial_{\\mu}{A_{\\nu}} \\partial_{\\mu}{A_{\\nu}} + \\partial_{\\mu}{\\phi}\\partial_{\\mu}{\\phi} - m**2 \\phi**2;\nfourier_transform(ex);\n"
  },
  {
    "path": "tests/noncovariant.cdb",
    "content": "\ndef test01():\n   __cdbkernel__=create_scope()\n   t::Coordinate;\n   {\\mu,\\nu}::Indices(spacetime);\n   {i,j,k}::Indices(space, parent=spacetime);\n   ex:= A_{\\mu} B^{\\mu};\n   split_index(_, $\\mu, t, i$)\n   print(\"Test 01 passed\")\n\ntest01()\n\ndef test02():\n   __cdbkernel__=create_scope()\n   \\partial{#}::Derivative;\n   t::Coordinate;\n   {i,j}::Indices;\n   ex:=\\partial_{t}{ \\psi_{1} } \\partial_{i}{ v0_{i} } \n      -\\partial_{i}{ v0_{i} } \\partial_{t}{ \\psi_{1} }    ;\n   sort_product(_)\n   assert(ex==0)\n   print(\"Test 02 passed\")\n\ntest02()\n\ndef test03():\n   __cdbkernel__=create_scope()\n   {\\mu, \\nu, \\rho, \\sigma, \\alpha, \\beta, \\gamma, \\delta, \\tau}::Indices(full);\n   {t, r, \\theta, \\phi}::Coordinate;\n   {a, b, c, d, e, f, g, h, i, j, k, l, m, n, s}::Indices(space1, values={t, r});\n   {A, B, C, E, F, G, H}::Indices(space2, values={\\theta, \\phi});\n   {\\theta, \\phi}::Coordinate;\n   D{#}::Derivative;\n   \\partial{#}::PartialDerivative;\n   duRaA:=duR_{\\mu a A \\sigma} = \\frac{1}{2} e_{\\mu a}^{\\alpha \\beta} R_{\\alpha \\beta A \\sigma};\n   ex:=K_{a A} = D_{\\tau}{D_{\\sigma}{\\Theta}} duR^{\\tau}_{a A}^{\\sigma};\n   substitute(ex, duRaA)\n   split_index(_, $\\mu, a, A$)\n   tst:= (K_{a A} = 1/2 D_{\\tau}{D_{\\sigma}{\\Theta}} e^{\\tau}_{a}^{b \\beta} R_{b \\beta A}^{\\sigma}\n       + 1/2 D_{\\tau}{D_{\\sigma}{\\Theta}} e^{\\tau}_{a}^{B \\beta} R_{B \\beta A}^{\\sigma}) - @(ex);\n   assert(tst==$0=0$)\n   print(\"Test 03 passed\")\n\ntest03()\n"
  },
  {
    "path": "tests/numerical.cdb",
    "content": "\n\ndef test01():\n    __cdbkernel__=create_scope()\n    {i,j,k}::Indices;\n    {i,j,k}::Integer(1..3);\n    rl:= N_{i j} -> A_{i j};\n    ex:= N_{1 2};\n    substitute(ex, rl)\n    tst:= A_{1 2} - @(ex);\n    assert(tst==0)\n    print(\"Test 01 passed\")\n\ntest01()\n\n\n\n# A{#}::NumericalFlat.\n# ex:= A{3}{B}{D};\n# \n# \\bar{#}::DiracBar;\n# ex:= \\bar{4 \\psi};\n# \n\ndef test02():\n    __cdbkernel__=create_scope()\n    i::ImaginaryI;\n    ex:= i i A_{m n} i  B^{m} i i C i D i ;\n    tst:= - A_{m n} B^{m} C D i - @(ex);\n    assert(tst==0)\n    print(\"Test 02 passed\")\n\ntest02()\n\ndef test03():\n    __cdbkernel__=create_scope()\n    ex:= (2 r**2)**6;\n    tst:= 64 r**(12) - @(ex);\n    assert(tst==0)\n    print(\"Test 03a passed\")\n    a::Integer;    \n    ex:= (2 r**2)**a;\n    tst:= 2**a r**(2 a) - @(ex);\n    assert(tst==0)\n    print(\"Test 03b passed\")\n    ex:= (2 r**2)**b;\n    tst:= (2 r**2)**b - @(ex);\n    assert(tst==0)\n    print(\"Test 03c passed\")\n    ex:= (2 r)**6;\n    tst:= 64 r**6 - @(ex);\n    assert(tst==0)\n    print(\"Test 03d passed\")\n    ex:= (2 (3 r)**2)**6;\n    tst:= 34012224 r**(12) - @(ex);\n    assert(tst==0)\n    print(\"Test 03e passed\")\n    ex:= (2 r**2)**(-6);\n    tst:= 1/64 r**(-12) - @(ex);\n    assert(tst==0)\n    print(\"Test 03f passed\")\n    tst:= s - s**2;\n    substitute(tst, $s=1$)\n    assert(tst==0)\n    print(\"Test 03g passed\")\n    tst:= s - 3 s**2;\n    substitute(tst, $s=1$)\n    assert(tst==-2)\n    print(\"Test 03h passed\")\n    \ntest03()\n\ndef test04():\n    __cdbkernel__=create_scope()\n    \\partial{#}::PartialDerivative;\n    t::Coordinate;\n    ex:= - 2\\frac{\\partial_{t}{a**2}**3}{a**3};\n    product_rule(_)\n    tst:= -16 (a \\partial_{t}{a} )**3 a**(-3) - @(ex);\n    assert(tst==0)\n    print(\"Test 04 passed\")\n\ntest04()\n\ndef test05():\n    __cdbkernel__=create_scope()\n    ex:= 2**3;\n    expand_power(_)\n    tst:= 8 - @(ex);\n    assert(tst==0)\n    print(\"Test 05 passed\")\n\ntest05()\n\n\ndef test06():\n    __cdbkernel__=create_scope()\n    {t}::Coordinate;\n    ex := Q / (f**2 - Q**2);\n    substitute(ex, $ f = (Q**2 - \\alpha )**(1/2) $)\n    tst:= - Q / \\alpha - @(ex);\n    assert(tst==0)\n    print(\"Test 06 passed\")\n\ntest06()\n\ndef test07():\n    try:\n       ex:=1/0;\n       assert(1==0)\n    except RuntimeError as err:\n       print(\"Test 07a passed\")\n    try:\n       ex:=1/a;\n       substitute(ex, $a->0$)\n       assert(1==0)\n    except RuntimeError as err:\n       print(\"Test 07b passed\")\n    try:\n       ex:=1/(a-b);\n       substitute(ex, $a->b$)\n       assert(1==0)\n    except RuntimeError as err:\n       print(\"Test 07c passed\")\n\ntest07()\n\ndef test08():\n    import numpy as np\n    try:\n       ex:= x**2;\n       q = np.array(ex)\n       assert(1==0)\n    except RuntimeError as err:\n       print(\"Test 08a passed\")\n    v = nevaluate($x**2$, {$x$: [0,1,2,3]})\n    q = np.array(v)\n    assert(q[2]==4)\n    print(\"Test 08b passed\")\n\n# test08() # FIXME: something weird happening on linux/macos with np.array above.\n\ndef test09():\n    __cdbkernel__=create_scope()\n    import numpy as np\n    a = 0.1\n    q = np.array( nevaluate($x+@(a)$, {$x$: [0,1]}) )\n    assert(q[0]==0.1)\n    assert(q[1]==1.1)\n    print(\"Test 09 passed\")\n\ntest09()\n\n\\tau::Coordinate;\n\\dot{#}::PartialDerivative(\\tau);\n{X,Y}::Depends(\\tau);\nfuncs:= { X, Y };\nodes:= { \\dot{\\dot{X}} + X Y = - X Y, \\dot{\\dot{Y}} - X Y = 0  };\nfirst_order_form(odes, funcs);\n\n# \\tau::Coordinate;\n# \\dot{#}::PartialDerivative(\\tau);\n# funcs:= { X(\\tau), Y(\\tau) };\n# odes:= { \\dot{\\dot{X(\\tau)}} + X(\\tau) Y(\\tau) = 0, \\dot{\\dot{Y(\\tau)}} - X(\\tau) Y(\\tau) = 0 };\n# first_order_form(odes, funcs);\n"
  },
  {
    "path": "tests/output.cdb",
    "content": "def test01():\n    ex:=(2/3)**(1/5).\n    res=ex.mma_form()\n    assert(res==\"(2/3)^(1/5)\")\n    res=ex.sympy_form()\n    assert(res==\"(2/3)**(1/5)\")\n    res=ex.input_form()\n    assert(res==\"( 2/3 )**( 1/5 )\")\n    print(\"Test 01 passed\")\n\ntest01()\n\ndef test02():\n    ex:=(2/3 p q)**(2 a + b);\n    res=ex.mma_form()\n    assert(res==\"(2/3*p*q)^((2*a+b))\")\n    res=ex.sympy_form()\n    assert(res==\"(2/3*p*q)**((2*a+b))\")\n    print(\"Test 02 passed\")\n\ntest02()\n\ndef test03():\n    c::Integer;\n    ex:=(a**b)**c;\n    res=ex.input_form();\n    assert(res==\"(a)**(b c)\")\n    res=ex.mma_form();\n    assert(res==\"(a)^((b*c))\")\n    res=ex.sympy_form();\n    assert(res==\"(a)**((b*c))\")\n    print(\"Test 03 passed\")\n\ntest03()\n\ndef test04():\n    ex:=a**(-4) + a**(2 b);\n    res=ex.input_form();\n    assert(res==\"(a)**(-4) + (a)**(2b)\")\n    ex:=a**(-b) + a**( 2/3 );\n    res=ex.input_form();\n    assert(res==\"(a)**(-b) + (a)**( 2/3 )\")\n    print(\"Test 04 passed\")\n\ntest04()\n\ndef test05():\n    __cdbkernel__=create_scope()\n    ket{A??}::LaTeXForm(\"|\", A??, \"\\rangle\");\n    ex:= a ket{n};\n    res=ex._latex_();\n    assert(res==r\"a |n\\rangle\")\n    print(\"Test 05a passed\")\n    Q{A??}::LaTeXForm(\"R\");\n    ex:= b Q{n};\n    res=ex._latex_();\n    assert(res==r\"b R\\left(n\\right)\")\n    T{A??}::LaTeXForm(T_{A??});\n    ex:= b T{n_{1}};\n    res=ex._latex_();\n    assert(res==r\"b T_{n_{1}}\")\n    print(\"Test 05b passed\")\n    \ntest05()\n"
  },
  {
    "path": "tests/packages.cdb",
    "content": "\nimport cdb.relativity.abstract as rel\n\ndef test01():\n    __cdbkernel__=create_scope()\n    \\partial{#}::PartialDerivative;\n    ex = rel.riemann_from_christoffel($Q$, $\\gamma$)\n    exl = lhs(ex)\n    exr = rhs(ex)\n    tstl := Q^{\\rho}_{\\sigma\\mu\\nu} - @(exl);\n    assert(tstl==0)\n    print(\"Test 01a passed\")\n    tstr := \\partial_{\\mu}{\\gamma^{\\rho}_{\\nu\\sigma}} -\\partial_{\\nu}{\\gamma^{\\rho}_{\\mu\\sigma}} + \\gamma^{\\rho}_{\\mu\\lambda} \\gamma^{\\lambda}_{\\nu\\sigma} - \\gamma^{\\rho}_{\\nu\\lambda} \\gamma^{\\lambda}_{\\mu\\sigma} - @(exr);\n    assert(tstr==0)\n    print(\"Test 01b passed\")\n\ntest01()\n\ndef test02():\n    __cdbkernel__=create_scope()\n    import cdb.core.manip as manip\n    {I,J}::Indices(position=fixed);\n    \\delta{#}::Derivative;\n    ex:= A = B C;\n    lhs= manip.get_lhs(ex)\n    rhs= manip.get_rhs(ex)        \n    ex2:= \\delta_{I}{ @(lhs) } = \\delta_{I}{ @(rhs) };\n    tst:= (\\delta_{I}{A} = \\delta_{I}{B C}) - @(ex2);\n    assert tst == $0=0$\n    print(\"Test 02 passed\")\n\ntest02()\n\n\n"
  },
  {
    "path": "tests/packages.cnb",
    "content": "{\n\t\"cells\" : \n\t[\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"import cdb.gr as gr\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}R^{\\\\rho}\\\\,_{\\\\sigma \\\\mu \\\\nu} = \\\\partial_{\\\\mu}\\\\left(\\\\Gamma^{\\\\rho}\\\\,_{\\\\nu \\\\sigma}\\\\right)-\\\\partial_{\\\\nu}\\\\left(\\\\Gamma^{\\\\rho}\\\\,_{\\\\mu \\\\sigma}\\\\right)+\\\\Gamma^{\\\\rho}\\\\,_{\\\\mu \\\\lambda} \\\\Gamma^{\\\\lambda}\\\\,_{\\\\nu \\\\sigma}-\\\\Gamma^{\\\\rho}\\\\,_{\\\\nu \\\\lambda} \\\\Gamma^{\\\\lambda}\\\\,_{\\\\mu \\\\sigma}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex = gr.RiemannFromChristoffel($R$, $\\\\Gamma$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}Q^{\\\\rho}\\\\,_{\\\\sigma \\\\mu \\\\nu} = \\\\partial_{\\\\mu}\\\\left(\\\\gamma^{\\\\rho}\\\\,_{\\\\nu \\\\sigma}\\\\right)-\\\\partial_{\\\\nu}\\\\left(\\\\gamma^{\\\\rho}\\\\,_{\\\\mu \\\\sigma}\\\\right)+\\\\gamma^{\\\\rho}\\\\,_{\\\\mu \\\\lambda} \\\\gamma^{\\\\lambda}\\\\,_{\\\\nu \\\\sigma}-\\\\gamma^{\\\\rho}\\\\,_{\\\\nu \\\\lambda} \\\\gamma^{\\\\lambda}\\\\,_{\\\\mu \\\\sigma}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex = gr.RiemannFromChristoffel($Q$, $\\\\gamma$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}R^{\\\\mu}\\\\,_{\\\\nu \\\\rho \\\\sigma} R^{\\\\nu}\\\\,_{\\\\mu \\\\lambda \\\\kappa}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"error\",\n\t\t\t\t\t\"source\" : \"{\\\\color{red}{\\\\begin{verbatim}Traceback (most recent call last):\\n  File \\\"<string>\\\", line 2, in <module>\\nNameError: name 'ChristoffelSymbol' is not defined\\n\\\\end{verbatim}}}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex:=R^{\\\\mu}_{\\\\nu\\\\rho\\\\sigma} R^{\\\\nu}_{\\\\mu\\\\lambda\\\\kappa};\\n\\\\Gamma^{\\\\mu}_{\\\\nu\\\\rho}::ChristoffelSymbol;\\ngr.RiemannToChristoffel(ex, $\\\\Gamma^{\\\\mu}_{\\\\nu\\\\rho}$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"error\",\n\t\t\t\t\t\"source\" : \"{\\\\color{red}{\\\\begin{verbatim}Traceback (most recent call last):\\n  File \\\"<string>\\\", line 1, in <module>\\nAttributeError: 'module' object has no attribute 'RiemannToChristoffel'\\n\\\\end{verbatim}}}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"substitute(ex, gr.RiemannToChristoffel);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}S = \\\\int{}F_{\\\\mu \\\\nu} F^{\\\\mu \\\\nu}\\\\, {\\\\rm d}x\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex:=S=\\\\int{ F_{\\\\mu\\\\nu}F^{\\\\mu\\\\nu} }{x};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property PartialDerivative to~}\\\\partial{\\\\#}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}S = \\\\int{}\\\\left(\\\\partial_{\\\\mu}{A_{\\\\nu}}-\\\\partial_{\\\\nu}{A_{\\\\mu}}\\\\right) F^{\\\\mu \\\\nu}\\\\, {\\\\rm d}x\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"\\\\partial{#}::PartialDerivative;\\nsubstitute(ex, $F_{\\\\mu\\\\nu} = \\\\partial_{\\\\mu}{A_{\\\\nu}} - \\\\partial_{\\\\nu}{A_{\\\\mu}}$ );\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\\\\nabla{#}::Derivative(torsion=$T$);\\nR^{\\\\mu}_{\\\\nu\\\\rho\\\\sigma}::RiemannTensor(derivative=$\\\\nabla$, christoffel=$\\\\Gamma$, torsion=$T$);\\nR^{\\\\mu}_{\\\\nu\\\\rho\\\\sigma}::RiemannTensor(derivative=nabla, christoffel=gamma);\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1\n}\n"
  },
  {
    "path": "tests/paper.cdb",
    "content": "# All examples from the hep-th paper, converted to version 2 format.\nimport timeit\n\ndef test01():\n    __cdbkernel__=create_scope()\n    { a, b, c, d }::Indices.\n    obj:= A_{a b} B_{b c};\n    substitute(_, $B_{a b} ->  C_{a b c} D_{c}$ )\n    tst:= A_{a b}  C_{b c d} D_{d} - @(obj);\n    assert(tst==0)\n    print('Test 01 passed')\n\nprint(timeit.timeit(test01,number=1))\n\n#-------\n\ndef test02():\n    __cdbkernel__=create_scope()\n    A_{\\dot{a} \\dot{b}}::AntiSymmetric.\n    obj:= A_{\\dot{b} \\dot{a}}:\n    canonicalise(_)\n    tst:= A_{\\dot{a} \\dot{b}} + @(obj);\n    assert(tst==0)\n    print('Test 02 passed')\n\nprint(timeit.timeit(test02,number=1))\n\n#-------\n\ndef test03():\n    __cdbkernel__=create_scope()\n    { a_{1}, a_{2}, a_{3}, a_{4} }::Indices(vector).\n    obj:= V_{a_{1}} W_{a_{1}}:\n    substitute(_, $V_{a_{2}} -> M_{a_{2} a_{1}} N_{a_{1}}$ )\n    tst:= M_{a_{1} a_{2}}  N_{a_{2}}  W_{a_{1}} - @(obj);\n    collect_terms(_)\n    assert(tst==0)\n    print('Test 03 passed')\n\nprint(timeit.timeit(test03,number=1))\n\n#-------\n\ndef test04():\n    __cdbkernel__=create_scope()\n    R_{a b c d}::TableauSymmetry(shape={2,2}, indices={0,2,1,3}).\n    obj:= R_{a b c d} R_{d c a b}:\n    canonicalise(_)\n    tst:= (-1) R_{a b c d} R_{a b c d} - @(obj);\n    collect_terms(_)\n    assert(tst==0)\n    print('Test 04 passed')\n\nprint(timeit.timeit(test04,number=1))\n\n#-------\n\ndef test05():\n    __cdbkernel__=create_scope()\n    {m,n,p,q}::Indices(position=free).\n    \\nabla{#}::Derivative.\n    \\partial{#}::PartialDerivative.\n    A_{m n}::AntiSymmetric.\n    V_{m}::Depends(\\nabla{#}).\n    obj:= \\partial_{m p}( A_{q r} V_{n} ) A^{p m};\n    canonicalise(_)\n    assert(obj==0)\n    print('Test 05a passed')\n    obj:= \\nabla_{m p}( A_{q r} V_{n} ) A^{p m};\n    canonicalise(_)\n    tst:= (-1) \\nabla_{m p}( A_{q r} V_{n} ) A^{m p} - @(obj);\n    canonicalise(_)\n    assert(tst==0)\n    print('Test 05b passed')\n    unwrap(obj)\n    tst:= (-1) A_{q r} \\nabla_{m p}{ V_{n} } A^{m p} - @(obj);\n    canonicalise(_)\n    assert(tst==0)\n    print('Test 05c passed')\n\nprint(timeit.timeit(test05,number=1))\n\n#-------\n\ndef test06():\n    __cdbkernel__=create_scope()\n    {m,n,p,q,r,s,t#}::Indices(vector).\n    \\nabla{#}::Derivative.\n    R_{m n p q}::RiemannTensor.\n    \\nabla_{m}{R_{p q r s}}::SatisfiesBianchi.\n    obj:= \\nabla_{m}{R_{p q r s}} + \\nabla_{p}{R_{q m r s}} + \\nabla_{q}{R_{m p r s}}:\n    young_project_tensor(_, depth=1, modulo_monoterm=True);\n    assert(obj==0)\n    print('Test 06 passed')\n\nprint(timeit.timeit(test06,number=1))\n\n#-------\n\ndef test07():\n    __cdbkernel__=create_scope()\n    { m, n, p, q }::Indices(vector).\n    { A_{m n p}, B_{m n p} }::AntiSymmetric.\n    { m, n, p, q }::Integer(1..4).\n    obj:= A_{m n p} B_{m n q} - A_{m n q} B_{m n p};\n    decompose_product(_)\n    canonicalise(_)\n    tst:= A_{m n p} B_{m n q} - A_{m n q} B_{m n p} - @(obj);\n    canonicalise(_)\n    assert(tst==0)\n    print('Test 07 passed')\n\nprint(timeit.timeit(test07,number=1))\n\n#-------\n\ndef test08():\n    __cdbkernel__=create_scope()\n    { m, n, p, q }::Indices(vector).\n    { A_{m n p}, B_{m n p} }::AntiSymmetric.\n    { m, n, p, q }::Integer(1..3).\n    obj:= A_{m n p} B_{m n q} - A_{m n q} B_{m n p};\n    decompose_product(_)\n    canonicalise(_)\n    assert(obj==0)\n    print('Test 08 passed')\n\nprint(timeit.timeit(test08,number=1))\n\n#-------\n\ndef test08b():\n    __cdbkernel__=create_scope() \n    \\ftableau{#}::FilledTableau(dimension=10);\n    ex:=\\ftableau{0,0}{1,1} \\ftableau{a,a}{b,b};\n    lr_tensor(_);    \n\nprint(timeit.timeit(test08b, number=1))\n        \n#-------\n\ndef test09():\n    __cdbkernel__=create_scope()\n\n    {i,j,m,n,k,p,q,l,r,r#}::Indices(vector).\n    C_{m n p q}::WeylTensor.\n    \\nabla{#}::Derivative.\n    \\nabla_{r}{ C_{m n p q} }::SatisfiesBianchi.\n    \\delta_{i j}::KroneckerDelta.\n    \n    Eij:=- C_{i m k l} C_{j p k q} C_{l p m q} + 1/4 C_{i m k l} C_{j m p q} C_{k l p q}\n         - 1/2 C_{i k j l} C_{k m p q} C_{l m p q};\n    \n    E:=  C_{j m n k} C_{m p q n} C_{p j k q} + 1/2 C_{j k m n} C_{p q m n} C_{j k p q};\n    \n    exp:= \\nabla_{i}{\\nabla_{j}{ @(Eij) }} - 1/6 \\nabla_{i}{\\nabla_{i}{ @(E) }};\n    print('one')\n    \n    distribute(_)\n    product_rule(_)\n    distribute(_)\n    product_rule(_)\n    print('two')\n    \n    sort_product(_)\n    canonicalise(_)\n    rename_dummies(_)\n    print('three')\n        \n    rl:={ \\nabla_{i}{C_{k i l m}} -> 0, \\nabla_{i}{C_{k m l i}} -> 0 };\n    substitute(exp, rl)\n    print('four')\n    \n    young_project_product(exp)\n    assert(exp==0)\n    print('Test 09 passed')\n\nprint(timeit.timeit(test09,number=1))\n\n#-------\n\ndef test10():\n    __cdbkernel__=create_scope()\n    {M, N, P}::Indices(space).\n    {m, n, p}::Indices(subspace1).\n    {a, b, c}::Indices(subspace2).\n    obj:= A_{M N} B_{N P};\n    split_index(_, $M, m, a$)\n    tst:= A_{M m}  B_{m P} + A_{M a} B_{a P} - @(obj);\n    assert(tst==0)\n    print('Test 10 passed')\n\nprint(timeit.timeit(test10,number=1))\n\n#-------\n\ndef test11():\n    __cdbkernel__=create_scope()\n    {a,b,c,d#}::Indices(spinor).\n    \\Gamma_{#}::GammaMatrix(metric=\\delta).\n    obj:=(\\Gamma_{m n})_{a b} (\\Gamma_{n p})_{b c};\n    combine(_);\n    join_gamma(_);\n    canonicalise(_);\n    tst:= (\\Gamma_{m p} \\delta_{n n} - \\Gamma_{m n} \\delta_{n p} + \\Gamma_{p n} \\delta_{m n} + \\delta_{n n} \\delta_{m p} - \\delta_{m n} \\delta_{n p})_{a c} - @(obj);\n    assert(tst==0)\n    distribute(obj);\n    expand(obj);\n    tst:= (\\Gamma_{m p})_{a c} \\delta_{n n} - (\\Gamma_{m n})_{a c} \\delta_{n p} \n    + (\\Gamma_{p n})_{a c} \\delta_{m n} + (\\delta_{n n} \\delta_{m p} )_{a c} \n    - (\\delta_{m n} \\delta_{n p})_{a c} - @(obj);\n    assert(tst==0)\n    print('Test 11 passed')\n\nprint(timeit.timeit(test11,number=1))\n\n#-------\n\ndef test12():\n    __cdbkernel__=create_scope()\n    {\\mu,\\nu,\\rho}::Indices(curved, position=fixed).\n    {m,n,p,q,r,s,t}::Indices(flat, position=free).\n    {m,n,p,q,r,s,t}::Integer(0..10).\n    T^{#{\\mu}}::AntiSymmetric.\n    \\psi_{\\mu}::SelfAntiCommuting.\n    \\psi_{\\mu}::Spinor(dimension=11, type=Majorana).\n    \\theta::Spinor(dimension=11, type=Majorana).\n    \\epsilon::Spinor(dimension=11, type=Majorana).\n    {\\theta,\\epsilon,\\psi_{\\mu}}::AntiCommuting.\n    \\bar{#}::DiracBar.\n    \\delta{#}::KroneckerDelta.\n    \\Gamma^{#{m}}::GammaMatrix(metric=\\delta).\n\n    obj:= T^{\\mu\\nu\\rho} e_{\\nu}^{s}\n        \\bar{\\theta} \\Gamma^{r s} \\psi_{\\rho}\n        \\bar{\\psi_{\\mu}} \\Gamma^{r} \\epsilon;\n\n    fierz(_, $\\theta, \\epsilon, \\psi_{\\mu}, \\psi_{\\rho}$ );\n    converge(obj):\n        join_gamma(obj)\n        distribute(obj)\n        eliminate_kronecker(obj)\n        eliminate_metric(obj)\n\n    canonicalise(_)\n    rename_dummies(_)\n    tst:=1/4 T^{\\mu \\nu \\rho} e_{\\mu}^{m} \\bar{\\theta} \\Gamma^{m n}\n        \\epsilon \\bar{\\psi_{\\nu}} \\Gamma^{n} \\psi_{\\rho} \n        + 5/16 T^{\\mu \\nu \\rho} e_{\\mu}^{m} \\bar{\\theta} \\epsilon\n        \\bar{\\psi_{\\nu}} \\Gamma^{m} \\psi_{\\rho} \n        + 3/32 T^{\\mu \\nu \\rho} e_{\\mu}^{m} \\bar{\\theta} \\Gamma^{m n p} \\epsilon\n        \\bar{\\psi_{\\nu}} \\Gamma^{n p} \\psi_{\\rho} \n        + 1/4 T^{\\mu \\nu \\rho} e_{\\mu}^{m} \\bar{\\theta} \\Gamma^{n}\n        \\epsilon \\bar{\\psi_{\\nu}} \\Gamma^{m n} \\psi_{\\rho} \n        + 1/384 T^{\\mu \\nu \\rho} e_{\\mu}^{m} \\bar{\\theta}\n        \\Gamma^{n p q r} \\epsilon \\bar{\\psi_{\\nu}} \\Gamma^{m n p q r} \\psi_{\\rho}\n        - @(obj);\n    rename_dummies(tst);\n    assert(tst==0)\n    print(\"Test 12 passed\")\n\nprint(timeit.timeit(test12,number=1))\n\n#-------\n\ndef test13():\n    __cdbkernel__=create_scope()\n    \\psi_{\\mu}::SelfAntiCommuting.\n    {\\chi, \\psi_{\\mu} }::AntiCommuting.\n    ex:= \\chi A^{\\mu\\nu} \\psi_{\\mu} \\chi \\psi_{\\nu};\n    substitute(_, $\\psi_{\\mu} \\psi_{nu} -> B_{\\mu\\nu}$ );\n    tst:= - \\chi A^{\\mu\\nu} B_{\\mu\\nu} \\chi - @(ex);\n    assert(tst==0)\n    print(\"Test 13a passed\")\n    A^{\\mu\\nu}::Symmetric;\n    ex:= \\chi A^{\\mu\\nu} \\psi_{\\mu} \\chi \\psi_{\\nu};\n    canonicalise(_)\n    assert(ex==0)\n    print(\"Test 13b passed\")\n\nprint(timeit.timeit(test13,number=1))\n\n#-------\n\nD{#}::Derivative.\n\\bar{#}::DiracBar.\n\\delta{A??}::Derivative.\n{m,n,p,q,r,s,t,u,m#}::Indices(flat).\n{m,n,p,q,r,s,t,u,m#}::Integer(0..3).\n{\\mu,\\nu,\\rho,\\sigma,\\kappa,\\lambda,\\alpha,\\beta}::Indices(curved,position=fixed).\n{\\mu,\\nu,\\rho,\\sigma,\\kappa,\\lambda,\\alpha,\\beta}::Integer(0..3).\n\ne^{m \\mu}::Vielbein.\ne_{m \\mu}::InverseVielbein.\ng^{\\mu\\nu}::InverseMetric.\ng_{\\mu\\nu}::Metric.\n\n{ \\epsilon,\\psi_{\\mu},\\psi_{\\mu\\nu} }::Spinor(dimension=4, type=Majorana).\n\\Gamma_{#{m}}::GammaMatrix(metric=\\delta).\n{ \\psi_{\\mu\\nu}, \\psi_{\\mu}, \\epsilon }::AntiCommuting.\n{ \\psi_{\\mu}, \\psi_{\\mu\\nu} }::SelfAntiCommuting.\n{ \\epsilon, \\psi_{\\mu}, \\psi_{\\mu\\nu} }::SortOrder.\n\\Gamma_{#}::Depends(\\bar).\n\\psi_{\\mu\\nu}::AntiSymmetric.\n\nL:= -1/2 e e^{n \\nu} e^{m \\mu} R_{\\mu\\nu n m}\n- 1/2 e \\bar{\\psi_\\mu} \\Gamma^{\\mu\\nu\\rho} D_{\\nu}{\\psi_{\\rho}}:\nrewrite_indices(_, $\\Gamma^{m n p}$, $e^{n \\mu}$ );\n\nsusy:= { e^{n \\mu} -> -\\bar{\\epsilon} \\Gamma^m \\psi_\\nu e^{m \\mu} e^{n \\nu},\n         e         -> e \\bar{\\epsilon} \\Gamma^n \\psi_\\mu e^{n\\mu},\n         \\psi_\\mu -> D_{\\mu}{\\epsilon} };\n\nvary(L, susy);\n"
  },
  {
    "path": "tests/programming.cdb",
    "content": "\ndef test01():\n    __cdbkernel__ = create_scope()\n    \n    def post_process(ex):\n        distribute(ex)\n        eliminate_kronecker(ex)\n        sort_product(ex)\n        canonicalise(ex)\n        collect_terms(ex)\n\n    \\delta{#}::KroneckerDelta;\n    \\GAMMA{#}::GammaMatrix;\n    ex:=\\GAMMA^{m} \\GAMMA^{n p q} \\GAMMA^{n p q m r} \\delta^{a b} \\delta^{c r};\n    # display(ex)\n    tst:= \\GAMMA^{m} \\GAMMA^{n p q} \\GAMMA^{n p q m c} \\delta^{a b} - @(ex);\n    # display(tst)\n    assert(tst==0)\n    print(\"Test 01 passed\")\n\ntest01()\n\ndef test02():\n    def orderx(var, n):\n        cn=Ex(n)\n        drop_weight(var, $field=@(cn)$)\n        return var\n\n    {A,B,C}::Weight(label=field, value=1);\n    ex:=A B C + A B + A A + A C + A B C D;\n    orderx(ex, 2)\n    tst:= A B C + A B C D - @(ex);\n    assert(tst==0)\n    print(\"Test 02 passed\")\n\ntest02()\n\ndef test03():\n    __cdbkernel__ = create_scope()\n    ex:= Q Q Q Q Q Q;\n    converge(ex):\n        substitute(_, $Q->A+B, A B->3$, repeat=True)\n        distribute(_)\n    tst:= A A A A A A + 18 A A A A + 135 A A + 540 + 18 B B B B + 135 B B + B B B B B B - @(ex);\n    assert(tst==0)\n    print(\"Test 03 passed\")\n\ntest03()\n\n\n# \n# \\partial{#}::PartialDerivative;        \n# ex:=A_{m n} \\partial_{r}{ B^{m n} } \\partial^{r}{ Q } + \\partial_{m}{ A^{m} } R;  \n# num=1\n# for partial in ex[\"\\\\partial\"]:\n#     partial.name=\"k\"+str(num)\n#     num+=1\n# \n# ex;\n#     \n# # this one still not working?! Does not stop and restart at second product.\n# \\partial{#}::PartialDerivative;        \n# ex:=A_{m n} \\partial_{r}{ B^{m n} } \\partial^{r}{ Q } + \\partial_{m}{ A^{m} } R;  \n# for prod in ex[\"\\\\prod\"]:\n#     num=1\n#     for partial in prod[\"\\\\partial\"]:\n#         partial.name=\"k\"+str(num)\n#         num+=1\n# \n# ex;\n# print(tree(ex))\n#     \n# \n# \\partial{#}::PartialDerivative;        \n# ex:=A_{m n} \\partial_{r}{ 3 B^{m n} } \\partial^{r}{ 2 Q } + \\partial_{m}{ 5 A^{m} } R;  \n# for prod in ex[\"\\\\prod\"]:\n#     num=1\n#     for partial in prod[\"\\\\partial\"]:\n#         for index in partial.indices():\n#             print(index)\n#             num+=1\n# \n# ex;\n# print(tree(ex))\n#   \n\ndef test04():\n    __cdbkernel__ = create_scope()\n    \\partial{#}::PartialDerivative;\n    \\dot{#}::Accent;\n    NoMomList= [ Ex(r'A_{a? b?}'), Ex(r'T{#}'), Ex(r'S(t)'), Ex(r'a**2'), Ex(r\"V'(\\phi)\"), Ex(r\"\\partial_{0}{a}\") ]\n    ex:=Q_{m n \\dot{r} p q s_{2} k} + T_{m n \\dot{r} p q s_{2} k} + a**2 \\partial_{0}{a} A_{m n} \\partial_{\\dot{r}}{ B_{p q} } S(t) V'(\\phi) \\partial_{s_{2}}{ C } \\partial_{0}{D_{k}} ;\n    terms=ex[\"\\\\sum\"].__next__().children()\n    for term in terms:\n        if term.name==\"\\\\prod\":\n            num=1\n            for factor in term.children():\n                matches = map(lambda x: x.matches(factor), NoMomList)\n                if not True in matches:\n                    if factor.name==\"\\\\partial\":\n                        for index in factor.own_indices():\n                            k = Ex(\"k\"+str(num))\n                            factor.insert(k).append_child(index)\n                            factor.insert(Ex(\"I\"))\n                        for arg in factor.args():\n                            matches = map(lambda x: x.matches(arg), NoMomList)\n                            if not True in matches:\n                                 arg.append_child(Ex(\"k\"+str(num)))\n                                 factor.insert(arg)\n                        factor.erase()\n                        num+=1\n                    else:\n                        factor.append_child(Ex(\"k\"+str(num)))\n                        num+=1\n        else:\n            matches = map(lambda x: x.matches(term), NoMomList)\n            if not True in matches:\n                term.append_child(Ex(\"k1\"))\n\n    tst:= Q_{m n \\dot{r} p q s_{2} k}(k1) + T_{m n \\dot{r} p q s_{2} k} + a**2 \\partial_{0}{a} A_{m n} k1_{\\dot{r}} I B_{p q}(k1) S(t) V'(\\phi) k2_{s_{2}} I C(k2) k3_{0} I D_{k}(k3) - @(ex);\n    assert(tst==0)\n    print(\"Test 04 passed\")\n\ntest04()\n\ndef test05():\n    ex:= A_{m n} B^{0 m} + C_{n};\n    lst=[]\n    for n in ex:\n        lst.append(str(n))\n    \n    tst=['A_{m n} B^{0 m} + C_{n}', 'A_{m n} B^{0 m}', 'A_{m n}', 'm', 'n', 'B^{0 m}', '0', 'm', 'C_{n}', 'n']\n    assert(tst==lst)\n    print(\"Test 05 passed\")\n\ntest05()\n\n# ex:=A + B + C;\n# lst=[]\n# for sum in ex[\"\\\\sum\"]:\n#     for term in sum:\n#         lst.append(term.name)\n# \n# assert(lst==[\"A\", \"B\", \"C\"])\n# print(\"Test 05 passed\")\n        \n \n\n# ex:= Q ( A_{m n} (Q+S) + B_{m n} ) + D_{m n};\n# for term in ex.top().terms():\n#     print(\"term:\")\n#     for factor in term.factors():\n#         print(\"factor:\")\n#         print(factor)\n# \n#\n        \n# \\nabla{#}::Derivative;        \n# ex:= \\nabla_{q}{ T_{m n}^{p} };\n# for term in ex.top().terms():\n#     \n\ndef test_expand(ex):\n   tst:= (A??)^{\\dagger};\n   for node in ex:\n      if tst.matches( node ):\n         rep=$P$\n         lst=[]\n         for prod in node[\"\\\\prod\"]:\n            for factor in prod.factors():\n               lst.append($ @(factor) $)\n         for factor in list(reversed(lst)):\n            rep.top().append_child($ @(factor)^{\\dagger} $)\n         rep.top().name=r\"\\prod\"\n         node.replace(rep)\n   return ex\n\ndef test06():\n    __cdbkernel__ = create_scope()\n    \\dagger::Symbol;\n    ex:= (A B C)^{\\dagger} + Q + (D E)^{\\dagger};\n    test_expand(ex)\n    tst:= C^{\\dagger} B^{\\dagger} A^{\\dagger} + Q + E^{\\dagger} D^{\\dagger} - @(ex);\n    assert(tst==0)\n    print(\"Test 06 passed\")\n\ntest06()\n\ndef test07():\n    __cdbkernel__ = create_scope()\n    {a,b,c,d#,z}::Indices.\n    ex:= 1/2 D_{b} C^{a b c} A_{c};\n    fi=ex.top().free_indices()\n    assert(next(fi).name=='a')\n    print(\"Test 07a passed\")\n    ex:= 1/2 C^{a b c} D_{b} A_{c};\n    fi=ex.top().free_indices()\n    assert(next(fi).name=='a')\n    print(\"Test 07b passed\")\n    ex:= 1/2 D_{b} A_{c} C^{a b c};\n    fi=ex.top().free_indices()\n    assert(next(fi).name=='a')\n    print(\"Test 07c passed\")\n\ntest07()\n\ndef test08():\n    __cdbkernel__ = create_scope()\n    ex:= A C + B D + C ;\n    for term in ex.top().terms():\n        term.multiplier *= 3\n    \n    tst:= 3 A C + 3 B D + 3 C - @(ex);\n    assert(tst==0)\n    print(\"Test 08 passed\")\n\ntest08()\n\ndef test09():\n    __cdbkernel__ = create_scope()\n    ex:= A + B(C+D) + Q(E);\n    for node in ex:\n       num=2\n       # print(\"node\", node)\n       for term in node.terms():\n          # print(\"term\", term)\n          term.multiplier *= num\n          num+=1\n    \n    tst:= 2A + 3 B(2C+3D) + 4Q(2E) - @(ex);\n    assert(tst==0)\n    print(\"Test 09 passed\")\n\ntest09()\n     \ndef test10():     \n    __cdbkernel__ = create_scope()\n    A_{m n p}::TableauSymmetry(shape={1,1}, indices={1,2});\n    p = TableauSymmetry.get($A_{m n p}$)\n    p.attach($B_{m n p}$)\n    ex:= B_{m n p} - B_{m p n};\n    meld(ex)\n    tst:= 2 B_{m n p} - @(ex);\n    assert(tst==0)\n    print(\"Test 10 passed\")\n\ntest10()\n\ndef test11():\n   __cdbkernel__ = create_scope()\n   R_{m n p q}::RiemannTensor;\n   p = RiemannTensor.get($R_{m n p q}$)\n   try:\n     p.attach($A_{m n}$)\n     assert(1==0)\n   except RuntimeError:\n     print(\"Test 11 passed\")\n\ntest11()\n\ndef test12():\n   __cdbkernel__ = create_scope()\n   sub:=3 q;\n   ex:=A^{@(sub)};\n   tst:= A^{3*q} - @(ex);\n   assert(tst==0)\n   print(\"Test 12 passed\")\n\ntest12()\n     \ndef test13():\n    __cdbkernel__ = create_scope()\n    {m,n,k,l}::Indices(flat, values={a,b});\n    {\\mu,\\nu,\\rho,\\sigma}::Indices(curved, values={0,1,2,3});\n    assert( $A_{m n}$.matches($A_{a b}$) == True )\n    print(\"Test 13a passed\")\n    assert( $A_{m n}$.matches($A_{a a}$) == True )\n    print(\"Test 13b passed\")\n    assert( $A_{m n}$.matches($A_{a c}$) == False )\n    print(\"Test 13c passed\")\n    assert( $A_{m n}$.matches($A_{0 1}$) == False )\n    print(\"Test 13d passed\")\n    assert( $A_{\\mu\\nu}$.matches($A_{0 1}$) == True )\n    print(\"Test 13e passed\")\n    assert( $A_{\\mu\\nu}$.matches($A^{0 1}$) == True )     \n    print(\"Test 13f passed\")\n    assert( $A_{\\mu\\nu}$.matches($A_{0 4}$) == False )\n    print(\"Test 13g passed\")\n    assert( $A_{m n}$.matches($A_{k l}$) == True )\n    print(\"Test 13h passed\")\n    assert( $A_{m n}$.matches($A_{m n}$) == True )    \n    print(\"Test 13i passed\")\n    assert( $A_{m n}$.matches($A_{\\mu \\nu}$) == False )\n    print(\"Test 13j passed\")\n\ntest13()\n\ndef test14():\n    __cdbkernel__ = create_scope()\n    ex:={A,B} ~ {C,D};\n    assert(ex==${A,B,C,D}$)\n    print(\"Test 14a passed\")\n    ex1:= {A,B};\n    ex2:= {C,D};\n    ex3 = join(ex1, ex2)\n    assert(ex3==${A,B,C,D}$)\n    print(\"Test 14b passed\")\n    ex1:= A;\n    ex2:= {C,D};\n    ex3 = join(ex1, ex2)\n    assert(ex3==${A,C,D}$)\n    print(\"Test 14c passed\")\n    ex1:= {A,B};\n    ex2:= C;\n    ex3 = join(ex1, ex2)\n    assert(ex3==${A,B,C}$)\n    print(\"Test 14d passed\")\n    ex1:= A;\n    ex2:= C;\n    ex3 = join(ex1, ex2)\n    assert(ex3==${A,C}$)\n    print(\"Test 14e passed\")\n    ex1:= {A,B};\n    ex2:= C;\n    ex3:= {D, E};\n    ex4= join(ex1, ex2, ex3)\n    assert(ex4==${A,B,C,D,E}$)\n    print(\"Test 14f passed\")\n    ex1:= A;\n    ex2:= C;\n    ex3:= {D, E};\n    ex4= join(ex1, ex2, ex3)\n    assert(ex4==${A,C,D,E}$)\n    print(\"Test 14g passed\")\n    ex1:= A;\n    ex4 = join(ex1, Ex(\"\"))\n    assert(ex4==$A$)\n    print(\"Test 14h passed\")\n    ex1:= A;\n    ex2:= \\comma{};\n    ex4= join(ex1, ex2)\n    assert(ex4==$A$)\n    print(\"Test 14i passed\")\n\ntest14()\n\ndef test15():\n    assert(Ex('X').matches(Ex(' '))==False)\n    print(\"Test 15a passed\")\n    assert(Ex(' ').matches(Ex(' '))==True)\n    print(\"Test 15b passed\")\n    assert(Ex(' ').matches(Ex('X'))==False)\n    print(\"Test 15c passed\")\n\ntest15()\n\ndef test16():\n    # There are many ways in which a match can fail...\n    __cdbkernel__ = create_scope()\n    {a,b,c}::Indices(vector, position=independent).\n    {i,j,k}::Indices(isospin, position=independent).\n    assert($\\Lambda_{a}$.matches($\\Lambda_{i}$)==False)\n    assert($\\Lambda_{a}$.matches($\\Lambda^{i}$)==False)\n    print(\"Test 16 passed\")\n    \ntest16()\n\ndef test17():\n    x::Weight(value=42, label=field);\n    tst1 = Weight.get($x$, label=\"field\").value(\"field\")\n    assert(tst1==42)\n    print(\"Test 17a passed\")\n    ex:= 3 a;\n    ex.top().multiplier = tst1\n    tst2:= 42 a - @(ex);\n    assert(tst2==0)\n    print(\"Test 17b passed\")\n\ntest17()\n\n\n#  {i,j,k,l}::Indices(cartesian, values={x,y,z}).\n#  {\\mu,\\nu,\\rho,\\sigma}::Indices(polar, values={r,\\theta,\\phi}).\n#  ex:= x^{i} x^{i} + p_{\\mu} p^{\\mu};\n#  for node in ex:\n#       prop = Indices.get(node)\n#       if prop is not None:\n#           print(node)\n#           print(node.name, prop.values)\n#  \n#  ind = Indices.get($i$);\n\ndef test18():\n    ex:= A + B + C + D + E;\n    s1 = ex[0:2]\n    tst:= A + B - @(s1);\n    assert(tst==0)\n    print(\"Test 18a passed\")\n    s2 = ex[0:-2:2]\n    tst:= A + C - @(s2);\n    assert(tst==0)\n    print(\"Test 18b passed\")\n    ex:= A + B + C + D + E + F;     \n    s3 = ex[0:-2:2]\n    tst:= A + C - @(s3);\n    print(\"Test 18c passed\")\n    ex:= A + B + C + D + E + F;     \n    s4 = ex[1:-2:2]\n    tst:= B + D - @(s4);\n    print(\"Test 18d passed\")\n    ex:= A + B + C + D + E;\n    s5 = ex[2:3]\n    tst:= C - @(s5);\n    assert(tst==0)\n    print(\"Test 18e passed\")\n\ntest18()\n\n# \n# import numpy as np\n# a = np.array([[1,2],[3,4]])\n# a[0,1]=3\n# print(a)\n# \n# ex:=[[1,2],[3,4]];\n# ex[0][1]=3\n# ex;\n# "
  },
  {
    "path": "tests/properties.cdb",
    "content": "\ndef test01():\n    __cdbkernel__=create_scope()\n    try:\n        {c,d}::Coordinate;\n        {a,b,c,d}::Indices;\n        assert(1==0)\n    except RuntimeError as e:\n        print(\"Test 01 passed\")\n\ntest01()\n\ndef test02():\n    __cdbkernel__=create_scope()\n    try:\n        {a,b,c,d}::Indices;\n        {c,d}::Coordinate;\n        assert(1==0)\n    except RuntimeError as e:\n        print(\"Test 02 passed\")\n\ntest02()\n"
  },
  {
    "path": "tests/reduce.cdb",
    "content": "\n{a,b,c,d,e}::Indices;\nR_{a b c d}::RiemannTensor;\nex:= R_{a b c d} + R_{a c d b} + R_{a d b c};\nyoung_reduce(_);\n\nex:= R_{a b c d} + R_{a c d b};\nyoung_reduce(_);\n\nex:= 2 R_{a b c d} R_{a c b d} - R_{a b c d} R_{a b c d};\nyoung_reduce(_);\n\n"
  },
  {
    "path": "tests/relativity.cdb",
    "content": "\ndef test01():\n    __cdbkernel__=create_scope()\n    {m, n, p, q, r}::Indices(vector, position=fixed).\n    {m, n, p, q, r}::Integer(0..9).\n    g_{m n}::Metric.\n    g^{m n}::InverseMetric.\n    g_{m}^{n}::KroneckerDelta.\n    g^{m}_{n}::KroneckerDelta.\n    obj10:= g_{m p} g^{p m};\n    eliminate_metric(_)\n    eliminate_kronecker(_)\n    tst10:= 10 - @(obj10);\n    assert(tst10==0)\n    print(\"Test 01 passed\")\n\ntest01()\n\ndef test02():\n    __cdbkernel__=create_scope()\n    {m, n, p, q, r}::Indices(vector, position=fixed).\n    g_{m n}::Metric.\n    g^{m n}::InverseMetric.\n    obj11b:= 3 g_{m p} g^{m p};\n    eliminate_metric(_)\n    tst11b:= 3 g_{p}^{p} - @(obj11b);\n    assert(tst11b==0)\n    print(\"Test 02 passed\")\n\ntest02()\n\n# Eliminating metrics in presence of derivatives.\n\ndef test03():\n    __cdbkernel__=create_scope()\n    {m, n, p, q, r}::Indices(vector, position=fixed).\n    g_{m n}::Metric.\n    \\partial{#}::Derivative.\n    obj12a:= g_{m n} \\partial_{p}{ A^{n} };\n    eliminate_metric(_)\n    tst12a:= \\partial_{p}{ A_{m} } - @(obj12a);\n    assert(tst12a==0)\n    print(\"Test 03 passed\")\n    \ntest03()\n\ndef test04():\n    __cdbkernel__=create_scope()\n    {m, n, p, q, r}::Indices(vector, position=fixed).\n    g_{m n}::Metric.\n    \\partial{#}::Derivative.\n    g_{m n}::Depends(\\partial{#}).\n    obj12b:= g_{m n} \\partial_{p}{ A^{n} };\n    eliminate_metric(_)\n    tst12b:= g_{m n} \\partial_{p}{ A^{n} } - @(obj12b);\n    assert(tst12b==0)\n    print(\"Test 04 passed\")\n\ntest04()\n\n# Reported bug with eliminate_metric.\n# {a,b,c,d,e,i,j,k}::Indices(curved).\n# g^{a b}::InverseMetric.\n# \\nabla{#}::Derivative.\n# h_{a b}::Symmetric.\n# ex:=g^{a k} * \\nabla_{b}{h_{k c}} +g^{a k} * \\nabla_{c}{h_{k b}};\n# eliminate_metric(_);\n\ndef test05():\n    __cdbkernel__=create_scope()\n    { m, n, p }::Indices(flat, position=fixed).\n    { \\mu, \\nu, \\rho, \\sigma, \\kappa }::Indices(curved, position=fixed).\n    obj:= H_{m n p} ( B^{m n p} + H^{m n p} );\n    rewrite_indices(_, $H_{\\mu\\nu\\rho}$, $e_{m}^{\\mu}$)\n    tst:= H_{\\mu \\nu \\rho} * ( B^{m n p} + H^{m n p} ) * e_{m}^{\\mu} * e_{n}^{\\nu} * e_{p}^{\\rho} - @(obj);\n    assert(tst==0)\n    print(\"Test 05 passed\")\n\ntest05()\n\ndef test06():\n    __cdbkernel__=create_scope()\n    { m, n, p }::Indices(flat).\n    { \\mu, \\nu, \\rho, \\mu# }::Indices(curved, position=fixed).\n    obj:= H_{m n p} [ B^{m n p} + H^{m n p} ];\n    rewrite_indices(_, $H_{\\mu\\nu\\rho}$, $e_{m \\mu}$)\n    tst:= H_{m n p} [ B^{m n p} + H^{m n p} ] - @(obj);\n    assert(tst==0)\n    print(\"Test 06 passed\")\n\ntest06()\n\ndef test08():\n    __cdbkernel__=create_scope()\n    { m,n,p,q,r,s,t,u }::Indices(curved, position=fixed).\n    obj:= B_{m n p} B^{m n q} C_{q};\n    rewrite_indices(_, $B_{m n p}$, $g^{m n}$)\n    tst:= B_{m n p} B_{r s t} C_{q} g^{m r} g^{n s} g^{q t} - @(obj);\n    assert(tst==0)\n    print(\"Test 08 passed\")\n\ntest08()\n\ndef test09():\n    __cdbkernel__=create_scope()\n    { m,n,p,q,r,s,t,u }::Indices(curved, position=free).\n    obj:= B_{m n p} B_{m n q} C_{q};\n    rewrite_indices(_, $B_{m n p}$, $g^{m n}$)\n    tst:= B_{m n p} B_{m n q} C_{q} - @(obj);\n    assert(tst==0)\n    print(\"Test 09 passed\")\n\ntest09()\n\ndef test10():\n    __cdbkernel__=create_scope()\n    {m,n,p,q,r,s}::Indices(curved, position=fixed).\n    ex:=H_{m n p};\n    rewrite_indices(_, $H^{m n p}$, $g_{m n}$)\n    tst:=H^{q r s} g_{m q} g_{n r} g_{p s} - @(ex);\n    assert(tst==0)\n    print(\"Test 10 passed\")\n\ntest10()\n\ndef test11():\n    __cdbkernel__=create_scope()\n    {a, b, c, d, e, f}::Indices(position=fixed).\n    \\eta_{a b}::Metric.\n    ex:=F_{a}^{b} G_{b c} + F^{b d}G_{d a c b};\n    rewrite_indices(_, $F_{a b}$, $\\eta^{a b}$)\n    tst:=F_{a d} G_{b c} \\eta^{b d} + F_{e f} G_{d a c b} \\eta^{b e} \\eta^{d f} - @(ex);\n    assert(tst==0)\n    print(\"Test 11 passed\")\n\ntest11()\n\ndef test12():\n    __cdbkernel__=create_scope()  \n    x::Coordinate.\n    {a, b}::Indices(position=fixed).\n    {a, b}::Integer(0..3).\n    g_{a b}::Metric.\n    g^{a b}::InverseMetric.\n    g^{\\mu?}_{\\nu?}::KroneckerDelta.\n    g_{\\mu?}^{\\nu?}::KroneckerDelta.\n    \\hat{#}::Accent.\n    ex:=\\hat{g^{a b}} \\hat{g_{a b}};\n    eliminate_metric(_)\n    eliminate_kronecker(_)\n    tst:= 4 - @(ex);\n    assert(tst==0)\n    print(\"Test 12 passed\")\n\ntest12()\n\ndef test13():\n    __cdbkernel__=create_scope()  \n    { m, n, p }::Indices(flat).\n    { \\mu, \\nu, \\rho }::Indices(curved).\n    e^{m}_{\\mu}::Vielbein.\n    ex:= H_{m n p} e^{m}_{\\mu} e^{p}_{\\rho};\n    eliminate_vielbein(_, repeat=True)\n    tst:= H_{\\mu n \\rho} - @(ex);\n    assert(tst==0)\n    print(\"Test 13 passed\")\n\ntest13()\n\ndef test14():\n    __cdbkernel__=create_scope()\n    {a,b,c,d,e,f}::Indices(position=fixed).\n    g_{a b}::Metric().\n    g^{a b}::InverseMetric().\n    A:=X_{a} g^{a b} g_{b c} g^{c d} g_{d e} g^{e f};\n    eliminate_metric(_, repeat=True)\n    tst:= X^{f} - @(A);\n    assert(tst==0)\n    print(\"Test 14a passed\")\n    A:=X_{a} g^{a b} g_{b c} g^{c d} g_{d e} g^{e f};\n    eliminate_metric(_, repeat=True, redundant=True)\n    tst:= X_{e} g^{e f} - @(A);\n    assert(tst==0)\n    print(\"Test 14b passed\")\n\ntest14()\n        \ndef test15():\n    __cdbkernel__=create_scope()\n\n    {m, n}::Indices(vector, position=fixed).\n    \\delta^{m}_{n}::KroneckerDelta.\n    \n    {m, n, p, q, r}::Integer(0..2*D-1);\n    ex:=7 \\delta^{m}_{m};\n    eliminate_kronecker(_);\n    tst:= 14 D - @(ex);\n    assert(tst==0)\n    print(\"Test15a passed\")\n    ex:=7 \\delta^{m}_{m} A;\n    eliminate_kronecker(_);\n    tst:= 14 D A - @(ex);\n    assert(tst==0)\n    print(\"Test15b passed\")\n    \n    {m, n, p, q, r}::Integer(0..D).\n    ex:=\\delta^{m}_{m};\n    eliminate_kronecker(_);\n    tst:= D + 1 - @(ex);\n    assert(tst==0)\n    print(\"Test15c passed\")    \n    \n    {m, n, p, q, r}::Integer(0..2 D + 1).\n    ex:=\\delta^{m}_{m};\n    eliminate_kronecker(_);\n    tst:= 2 D + 2 - @(ex);\n    assert(tst==0)\n    print(\"Test15d passed\")\n            \n    {m, n, p, q, r}::Integer(0..3D-1);\n    ex:=\\delta^{m}_{m};\n    eliminate_kronecker(_);\n    tst:= 3 D - @(ex);\n    assert(tst==0)\n    print(\"Test15e passed\")\n    \n    {m, n, p, q, r}::Integer(0..2*(D-1));\n    ex:=\\delta^{m}_{m};\n    eliminate_kronecker(_);\n    tst:= 2 D - 1 - @(ex);\n    assert(tst==0)\n    print(\"Test15f passed\")\n\n\n# { m, n, p }::Indices(flat).\n# { \\mu, \\nu, \\rho }::Indices(curved).\n# e^{m}_{\\mu}::Vielbein.\n# e_{m}^{\\mu}::InverseVielbein.\n# ex:= e_{m}^{\\mu} e^{m}_{\\nu};\n# eliminate_vielbein(_);\n\n# def post_process(ex):\n#     substitute(ex, $\\delta^{0}_{\\alpha} -> 0$)\n#     return ex\n#         \n# {a,b,c,d,e}::Indices(fourD, position=independent);\n# {a,b,c,d,e}::Integer(0..4);\n# {\\alpha,\\beta,\\gamma,\\delta,\\epsilon}::Indices(threeD, position=independent, parent=fourD);\n# {\\alpha,\\beta,\\gamma,\\delta,\\epsilon}::Integer(1..3);\n# \\delta{#}::KroneckerDelta();\n# ex := \\gamma^{\\alpha \\beta} \\delta^{0}_{d} \\delta^{d}_{\\alpha};\n# eliminate_kronecker(ex, repeat=False);\n\n        \n    \n"
  },
  {
    "path": "tests/scope.cdb",
    "content": "\n# The following lets a property escape from local context without\n# being kept on the cadabra stack. This is undefined.\n\ndef fun():\n    {A,B,C}::AntiCommuting.\n    ex:= C B A\n    sort_product(_)\n    print(\"inside fun\")\n    print(_)\n    return __cdbtmp__\n\nprop=fun()\nprint(prop)\n\nex:= C B A\nsort_product(_)\n\n# Mixing properties from global and local scope.\n\n{A,B,C}::AntiCommuting.\nqg = 42\n\ndef fun3():\n    print('=== locals in fun3 scope ===')\n    # print(q) # this would not work\n    print(qg)\n    {K,L}::AntiCommuting.\n    ex:= C B A\n    sort_product(_)\n    print(_)\n    # This function does not see things declared in fun2,\n    # and it should not, because it does not see 'q' above either.\n    ex2:= F E D \n    sort_product(_)\n    print(_)\n    print(locals())\n\n# FIXME: in this problem, even though three local kernels get created,\n# only two of them show up: in fun3 & fun4 the kernel is the same. \n\ndef fun2():\n    q=3\n    {D,E,F}::AntiCommuting.\n    print(\"fun2 scope \"+str(properties()))\n    ex:= C B A\n    sort_product(_)\n    print(_)\n    ex2:= F E D\n    sort_product(_)\n    print(_)\n    fun3()\n    __cdbkernel__ = Kernel()\n    print(__cdbkernel__)\n    def fun4():\n        print('=== locals in fun4 scope ===')\n        print(\"fun4 scope \"+str(properties()))\n        print(locals());\n        print q\n        # If you drop this print below, __cdbkernel__ will not be in locals above.\n        #print __cdbkernel__\n        {Q,R}::AntiCommuting.\n        ex4:= R Q\n        sort_product(_)\n        print(_)\n        # This does not see the fun2 scope (but it does of course see\n        # the global scope). That's wrong...\n        ex5:= D E F\n        sort_product(_)\n        print(_)\n    fun4()\n    print(\"fun2 scope \"+str(properties()))\n    ex3:= R Q\n    sort_product(_)\n    print(_)\n    print('=== locals in fun2 scope ===')\n    print(locals())\n    # print('=== globals ===')\n    # print(globals())\n\nfun2()\nex3:= F E D\nsort_product(_)\nprint(_)\n\n\n"
  },
  {
    "path": "tests/selecting.cdb",
    "content": "\ndef test01():\n    __cdbkernel__=create_scope()\n    ex:= A + B D G + C D A;\n    zoom(_, $D Q??$)\n    substitute(_, $A = Q$)\n    unzoom(_)\n    tst:= A + B D G + C D Q - @(ex);\n    assert(tst==0)\n    print(\"Test 01a passed\")\n    ex:= A + B D G + C D A;\n    zoom(_, $D Q??$)\n    substitute(_, $D = 0$)\n    unzoom(_)\n    tst:= A - @(ex);\n    assert(tst==0)\n    print(\"Test 01b passed\")\n    ex:= R = \\int{A + B D G + C D A}{x};\n    zoom(_, $D Q??$)\n    substitute(_, $A = Q$)\n    unzoom(_)\n    tst:= ( R = \\int{A + B D G + C D Q}{x} ) - @(ex);\n    print(\"Test 01c passed\")\n    ex:= R = \\int{A + B D G + C D A}{x};\n    zoom(_, $D Q??$)\n    substitute(_, $A = 0$)\n    unzoom(_)\n    tst:= ( R = \\int{A + B D G}{x} ) - @(ex);\n    assert(tst== $0 = 0$)\n    print(\"Test 01d passed\")\n    ex:= R + S = \\int{A + B D G + C D A}{x};\n    zoom(_, $D Q??$)\n    substitute(_, $A = 0$)\n    unzoom(_)\n    tst:= ( R + S = \\int{A + B D G}{x} ) - @(ex);\n    assert(tst== $0 = 0$)\n    print(\"Test 01e passed\")\n\ntest01()\n\n# def test02():\n#     __cdbkernel__=create_scope()\n# a:= A,B,C;\n# b:= D,E,F;\n# c:= Q;\n# d:= R+S;\n# ex1=a+b\n# ex2=a+c\n# ex3=c+a\n# ex4=a+d\n# tst1:= {A,B,C,D,E,F};\n# tst2:= {A,B,C,Q};\n# tst3:= {Q,A,B,C};\n# tst4:= {A,B,C,R+S};\n# assert(tst1==ex1)\n# assert(tst2==ex2)\n# assert(tst3==ex3)\n# assert(tst4==ex4)\n#     print(\"Test 02 passed\")\n# \n# test02()\n\ndef test03():\n    # zoom should also work to select terms in an integral\n    # and then replace them later.\n    __cdbkernel__=create_scope()\n    ex:= 5\\int{A+3 B M + C N+D}{dx};\n    zoom(_, $B Q??$)\n    substitute(_, $B->2 P$)\n    unzoom(_)\n    tst:= 5\\int{A + 6 P M + C N + D}{dx} - @(ex);\n    assert(tst==0)\n    print(\"Test 03 passed\")\n\ntest03()\n\ndef test04():\n    # zoom should also work to select terms in an integral\n    # and then replace them later.\n    __cdbkernel__=create_scope()\n    ex:= 5\\int{A+3 B M + C N+D}{dx};\n    zoom(_, $B Q??$)\n    substitute(_, $B->0$)\n    unzoom(_)\n    tst:= 5\\int{A + C N + D}{dx} - @(ex);\n    assert(tst==0)\n    print(\"Test 04 passed\")\n\ntest04()\n\ndef test05():\n    __cdbkernel__=create_scope()\n    \\partial{#}::PartialDerivative;\n    ex:=\\int{A_{i} h_{j} + \\partial_{i}{B_{j}} D }{x};\n    zoom(_, $\\partial_{i}{B_{j}} Q??$)\n    substitute(_, $D -> E$)\n    unzoom(_)\n    tst:=\\int{A_{i} h_{j} + \\partial_{i}{B_{j}} E}{x} - @(ex);\n    assert(tst==0)\n    print(\"Test 05 passed\")\n\ntest05()\n\n\n# ex:= \\sin( 3 \\int{ A E + B_{m} C^{m} + Q D }{x} ) + \\cos( \\int{ A K + B E }{x} );\n# zoom(_, $A Q??$);\n# substitute(_, $E->1$);\n# tst:= \\sin( 3 \\int{ A + B_{m} C^{m} + Q D }{x} ) + \\cos( \\int{ A K + B E }{x} ) - @(ex);\n\ndef test06():\n    __cdbkernel__=create_scope()\n    \\partial{#}::PartialDerivative;\n    ex:=  \\int{ 3 A_{i j} + 2 \\partial_{i}{\\partial_{j}{h}}}{x};\n    zoom(_, $A_{i j}$)\n    substitute(_,$A_{i j} -> B_{i j}$)\n    unzoom(_)\n    tst:= \\int{ 3 B_{i j} + 2 \\partial_{i}{\\partial_{j}{h}}}{x} - @(ex);\n    assert(tst==0)\n    print(\"Test 06 passed\")\n\ntest06()\n\ndef test07():\n    __cdbkernel__=create_scope()\n    \\partial{#}::PartialDerivative;\n    ex:=  \\int{ 3 h A_{i j} + 2 \\partial_{i}{\\partial_{j}{h}}}{x};\n    zoom(_, $A_{i j} Q??$)\n    substitute(_,$A_{i j} -> B_{i j}$)\n    integrate_by_parts(_, $h$)  \n    unzoom(_)\n    tst:= \\int{ 3 h B_{i j} + 2 \\partial_{i}{\\partial_{j}{h}}}{x} - @(ex);\n    assert(tst==0)\n    print(\"Test 07 passed\")\n\ntest07()\n\ndef test08():\n    __cdbkernel__=create_scope()\n    ex:= A + B D + E B + C Q + D;\n    cp1:= @(ex);        \n    zoom(ex, $B Q??$)\n    cp2:= @(ex);        \n    zoom(ex, $E Q??$)\n    unzoom(ex)\n    tst:= @(cp2) - @(ex);\n    assert(tst==0)\n    print(\"Test 08a passed\")\n    unzoom(ex)\n    tst:= @(cp1) - @(ex);\n    assert(tst==0)\n    print(\"Test 08b passed\")\n    ex:= A + B D + E B + C Q + D;\n    cp1:= @(ex)        \n    zoom(ex, $B Q??$)\n    cp2:= @(ex)        \n    zoom(ex, $E Q??$)\n    unzoom(ex, repeat=True)\n    tst:= @(cp1) - @(ex);\n    assert(tst==0)\n    print(\"Test 08c passed\")\n\ntest08()        \n\ndef test09():\n   def doit(ex):\n      for nabla in ex[r'\\nabla']:\n         nabla.name = r'\\partial'\n      return ex\n   \n   ex:= \\nabla{A} + \\nabla{B};\n   zoom(ex, $\\nabla{A}$)\n   doit(_)\n   unzoom(ex)\n   tst:= \\partial{A} + \\nabla{B} - @(ex);\n   assert(tst==0)\n   print(\"Test 09 passed\")\n\ntest09()\n\ndef test10():\n    __cdbkernel__=create_scope()\n    ex := x A1 + y A2 + z A3;\n    zoom(ex, ${A?? x, A?? z}$)\n    tst:= x A1 + \\ldots{y A2} + z A3 - @(ex);\n    assert(tst==0)\n    print(\"Test 10 passed\")\n\ntest10()\n\ndef test11():\n    __cdbkernel__=create_scope()\n    ex:=A D + A B C D E;\n    zoom(_, $A D$, partial=False)\n    substitute(ex, $A->Q$)\n    unzoom(_)\n    tst:= Q D + A B C D E - @(ex);\n    assert(tst==0)\n    print(\"Test 11 passed\")\n\ntest11()\n\n#def test08():\n# \n# \\epsilon::Weight(label=field, value=1);\n# Exp:=\\epsilon**4+\\epsilon*(\\epsilon**3+5);\n# zoom(_, $\\epsilon * A??$);\n# distribute(_);\n# unzoom(_);\n# drop_weight(_, $field=4$);\n\n"
  },
  {
    "path": "tests/semicolon-is-display.cnb",
    "content": "{\n\t\"cell_id\": 13676201060787162409,\n\t\"cells\": [\n\t\t{\n\t\t\t\"cell_id\": 3365546030754312399,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 13486784106139061322,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"verbatim\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}0\\\\end{verbatim}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 13390342818350060915,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"verbatim\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}1\\\\end{verbatim}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 14181760388372354144,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"verbatim\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}2\\\\end{verbatim}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 13566449661308298725,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"verbatim\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}3\\\\end{verbatim}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 11641129919142346415,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"verbatim\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}4\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"for i in range(5):\\n   i;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 5507328018153950723,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 2763088547631021006,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 245401456593838818,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"0\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}0\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 1995969635477801872,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 5620480623049908368,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"A_{m}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}A_{m}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 1308278093665708998,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 9246712614825963706,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"2A_{m}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}2A_{m}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 10180185725480085968,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 16955994692508884179,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"3A_{m}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}3A_{m}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 14917983779495832154,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 8631749922978581387,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"4A_{m}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}4A_{m}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"for i in range(5):\\n   ex:= @(i) A_{m};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 2709367108842624886,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 991548420766733209,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"verbatim\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}hello\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"\\\"hello\\\";\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 9531952093182759138,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 14715685231577451918,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"verbatim\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}3\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"a=3;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 1003469794776916302,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 13314650427008455028,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"verbatim\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}3\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"a;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 7344323184728307736,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 5955032504006603414,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"verbatim\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}0\\\\end{verbatim}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 5551752701089688736,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"verbatim\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}1\\\\end{verbatim}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 3621255758561886641,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"verbatim\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}3\\\\end{verbatim}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 13345939733285062586,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"verbatim\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}6\\\\end{verbatim}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 10311848031432336392,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"verbatim\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}10\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"k=0\\nfor i in range(5):\\n   k = k + \\\\\\n         i;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 17000456916826804357,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 8639669874106212937,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"verbatim\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}0\\\\end{verbatim}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 409035913217772958,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"verbatim\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}1\\\\end{verbatim}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 2143506441780659444,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"verbatim\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}3\\\\end{verbatim}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 14765554027532246253,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"verbatim\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}6\\\\end{verbatim}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 17740545678693912988,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"verbatim\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}10\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"k=0\\nfor i in range(5):\\n   j = 0\\n   k = k + \\\\\\n         i;\\n   j = 3\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 12612305425360331126,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 8694258832895160516,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"verbatim\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}0\\\\end{verbatim}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 8446751972143242502,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"verbatim\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}0\\\\end{verbatim}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9542511904054497326,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 16055832822636808925,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"A_{m}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}A_{m}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 14810623720671467046,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"verbatim\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}0\\\\end{verbatim}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 8453600701020721187,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"verbatim\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}1\\\\end{verbatim}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 12653146955963079181,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 11958933549239202803,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"A_{m}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}A_{m}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 15300923306790611083,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"verbatim\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}0\\\\end{verbatim}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 7097758010575342651,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"verbatim\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}3\\\\end{verbatim}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 12110137980363554801,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 8530446612060511589,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"A_{m}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}A_{m}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 16745216850334751695,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"verbatim\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}0\\\\end{verbatim}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 5611823266073639070,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"verbatim\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}6\\\\end{verbatim}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 16409729764063395803,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 1710386025033510743,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"A_{m}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}A_{m}\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 6247403346351003199,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"verbatim\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}0\\\\end{verbatim}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 13692604609052235241,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"verbatim\",\n\t\t\t\t\t\"source\": \"\\\\begin{verbatim}10\\\\end{verbatim}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 3249881876588662702,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 14799719248347315493,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"A_{m}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}A_{m}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"k=0\\nfor i in range(5):\\n   j = 0;\\n   k = k + \\\\\\n         i;\\n   ex:= A_{m};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 8699779233906986329,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"def test():\\n   ex:= A_{m};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 7024647649488156255,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"cells\": [\n\t\t\t\t{\n\t\t\t\t\t\"cell_id\": 9642367199354074488,\n\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\"cell_type\": \"latex_view\",\n\t\t\t\t\t\"cells\": [\n\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\"cell_id\": 9234383094430850768,\n\t\t\t\t\t\t\t\"cell_origin\": \"server\",\n\t\t\t\t\t\t\t\"cell_type\": \"input_form\",\n\t\t\t\t\t\t\t\"source\": \"A_{m}\"\n\t\t\t\t\t\t}\n\t\t\t\t\t],\n\t\t\t\t\t\"source\": \"\\\\begin{dmath*}{}A_{m}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": \"test()\"\n\t\t},\n\t\t{\n\t\t\t\"cell_id\": 14333362801236857588,\n\t\t\t\"cell_origin\": \"client\",\n\t\t\t\"cell_type\": \"input\",\n\t\t\t\"source\": \"\"\n\t\t}\n\t],\n\t\"description\": \"Cadabra JSON notebook format\",\n\t\"version\": 1.0\n}\n"
  },
  {
    "path": "tests/serialize.cdb",
    "content": "import pickle\n\ndef test01():\n   ex := A_{\\mu} + B_{\\mu};\n   obj = pickle.dumps(ex)\n   assert(ex == pickle.loads(obj))\n   print(\"Test 01 passed\")\n\ntest01()\n"
  },
  {
    "path": "tests/simplify.cdb",
    "content": "\n{m,n}::Indices;\nex:= \\sin(x)**2 + \\cos(x)**2 + A_{m} A^{m};\nsimplify(ex);\n\nmap_sympy(ex, \"simplify\");\n"
  },
  {
    "path": "tests/spinors.cdb",
    "content": "\ndef test01():\n    __cdbkernel__=create_scope()\n    {\\chi, \\psi, \\psi_{m}}::Spinor(dimension=10, type=MajoranaWeyl).\n    {\\chi, \\psi, \\psi_{m}}::AntiCommuting.\n    \\bar{#}::DiracBar.\n    \\Gamma{#}::GammaMatrix.\n    {\\psi_{m}, \\psi, \\chi}::SortOrder.\n    ex:= \\bar{\\chi} \\Gamma_{m n p} \\psi;\n    sort_spinors(_)\n    tst:= \\bar{\\psi} \\Gamma_{m n p} \\chi - @(ex);\n    assert(tst==0)\n    print(\"Test 01 passed\")\n\ntest01()\n\ndef test02():\n    __cdbkernel__=create_scope()\n    {\\chi, \\psi, \\psi_{m}}::Spinor(dimension=10, type=MajoranaWeyl).\n    {\\chi, \\psi, \\psi_{m}}::AntiCommuting.\n    \\bar{#}::DiracBar.\n    \\Gamma{#}::GammaMatrix.\n    {\\psi_{m}, \\psi, \\chi}::SortOrder.\n    ex:= \\bar{\\chi}\\psi;\n    sort_spinors(_)\n    tst:= \\bar{\\psi}\\chi - @(ex);\n    assert(tst==0)\n    print(\"Test 02a passed\")\n    ex:= \\chi\\Gamma_{m n p}\\psi;\n    sort_spinors(_)\n    tst:= \\chi\\Gamma_{m n p}\\psi - @(ex);\n    assert(tst==0)\n    print(\"Test 02b passed\")\n    ex:= \\bar{\\chi} \\Gamma_{m n} \\psi_{m};\n    sort_spinors(_)\n    tst:= - \\bar{\\psi_{m}} \\Gamma_{m n} \\chi - @(ex);\n    assert(tst==0)\n    print(\"Test 02c passed\")\n\ntest02()\n\n# Multiple ImplicitIndex objects\ndef test03():\n    __cdbkernel__=create_scope()\n    {\\chi,\\psi, \\lambda, \\rho}::Spinor.\n    \\Gamma{#}::GammaMatrix.\n    \\bar{#}::DiracBar.\n    ex:= \\bar{\\chi}\\Gamma_{m n p}\\psi A_{m n} \\bar{\\lambda}\\Gamma_{p}\\rho;\n    sort_product(_)\n    sort_spinors(_)\n    tst:=A_{m n} \\bar{\\chi} \\Gamma_{m n p} \\psi \\bar{\\lambda} \\Gamma_{p} \\rho - @(ex);\n    assert(tst==0)\n    print(\"Test 03 passed\")\n\ntest03()\n\n# Spinors with partial derivatives on them should still be\n# detected as spinors.\ndef test04():\n    __cdbkernel__=create_scope()  \n    {\\chi, \\psi, \\psi_{m}}::Spinor(dimension=10, type=MajoranaWeyl).\n    {\\chi, \\psi, \\psi_{m}}::AntiCommuting.\n    \\bar{#}::DiracBar.\n    \\Gamma{#}::GammaMatrix.\n    \\partial{#}::PartialDerivative.\n    {\\psi_{m}, \\psi, \\chi}::SortOrder.\n    ex:= \\bar{\\partial_{m}{\\chi}} \\Gamma_{m n p} \\psi;\n    sort_spinors(_)\n    tst:= \\bar{\\psi} \\Gamma_{m n p} \\partial_{m}{\\chi} - @(ex);\n    assert(tst==0)\n    print(\"Test 04 passed\")\n\ntest04()\n        \n"
  },
  {
    "path": "tests/substitute.cdb",
    "content": "\n# Substituting requires many dummy index relabelling. \n#\n# Test 1: 'm' relabelling is triggered by a_{m} outside\n#         'n' relabelling in second term ditto\n#         'n' relabelling in first term because c_{pmn} -> c_{nmn} .\n\ndef test01():\n    __cdbkernel__=create_scope()\n    {d1,d2,d3,d4,m,n,p,r}::Indices(vector).\n    obj1:= a_{m}*b_{n} + c_r b_r d_{m n};\n    substitute(_, $b_{p} -> c_{p m n} A^{m n} + c_{p}$ )\n    distribute(_)\n    tst1:= a_{m} * c_{n d2 d1} * A^{d2 d1} + a_{m} * c_{n} + c_{r} * c_{r d1 d2} * A^{d1 d2} * d_{m n} + c_{r} * c_{r} * d_{m n} - @(obj1); \n    assert(tst1==0)\n    print('Test 01 passed')\n\ntest01()\n\ndef test02():\n    __cdbkernel__=create_scope()\n    {m,n,p}::Indices(position=fixed).\n    ex:= F_{m n} F^{m n};\n    rl:= F_{m n} -> G_{m n};\n    substitute(ex, rl)\n    tst:= G_{m n} F^{m n} - @(ex);\n    assert(tst==0)\n    print('Test 02 passed')    \n\ntest02()\n\ndef test02b():\n    # Product substitutions.\n    __cdbkernel__=create_scope()\n    {d1,d2,d3,d4,m,n,p,r,s,t,a,b}::Indices(vector).\n    obj2:= a_{m n} * q * e * b_{m p} * o + d_{n p};\n    substitute(obj2, $a_{r s} b_{r t} -> c_{s t}$ )\n    tst2:= c_{n p} q e o + d_{n p} - @(obj2);\n    assert(tst2==0)\n    print('Test 02b passed')    \n\ntest02b()\n\ndef test02c():\n    # Reducing to zero\n    __cdbkernel__=create_scope()\n    obj3:= A_{m n} B_{m n} k1_{a} k1_{a} k2_{b};\n    substitute(_,  $k1_a k1_a -> 0$ )\n    assert(obj3==0)\n    print('Test 02c passed')    \n\ntest02c()\n    \ndef test03():\n    # Upper and lower indices replaced automagically.\n    #\n    # Side note: the replacement\n    #    rl:= F_{m n} -> G_{m n} + H^{m n};\n    # is tricky. A rule will be generated for all objects\n    # matched on the lhs. So _m and _n to something. But on the rhs, that would\n    # not normally match. Best to disallow these rules.\n    __cdbkernel__=create_scope()\n    {m,n,p,q}::Indices(position=free).\n    ex:= F_{p q} F^{p q};\n    rl:= F_{m n} -> G_{m n};\n    substitute(ex, rl)\n    rename_dummies(ex)\n    tst2:= G_{m n} G^{m n} - @(ex);\n    assert(tst2==0)\n    print('Test 03 passed')\n    \ntest03()\n\ndef test04():\n    # Basic test of variational derivative.\n    __cdbkernel__=create_scope()\n    obj43:= A*B*A + D*E;\n    vary(obj43, $A->C$)\n    tst43:= C*B*A + A*B*C - @(obj43);\n    assert(tst43==0)\n    print('Test 04 passed')\n    \ntest04()\n\ndef test04b():\n    # Indices in the pattern.\n    __cdbkernel__=create_scope()\n    obj4:= A_m A_n + B_m C_n + D_{m n} A_p A_p;\n    substitute(_, $A_a A_a -> q$ )\n    tst4:= A_m A_n + B_m C_n + D_{m n} q - @(obj4);\n    assert(tst4==0)\n    print('Test 04b passed')\n    \n#test04b()\n\n\ndef test05():\n    # Variational derivative under Accents.\n    __cdbkernel__=create_scope()\n    \\bar{?}::Accent.\n    obj45:= \\bar{A}*B*A;\n    vary(obj45, $A -> C$)\n    tst45:= \\bar{C}*B*A + \\bar{A}*B*C - @(obj45);\n    assert(tst45==0)\n    print('Test 05 passed')\n    \ntest05()\n\ndef test06():\n    # Nested substitutes.\n    __cdbkernel__=create_scope()\n    {a,b,c,d}::Indices.\n    { \\partial{#}, \\partialp{#} }::PartialDerivative.\n    A::Depends(\\partial{#}).\n    B::Depends(\\partialp{#}).\n    \\Omega{#}::Derivative.\n    obj46:= \\Omega( \\partial_{a}{A} )( \\partialp_{b}{B} );\n    rl:= \\Omega( \\partial_{a}{A??} )( B?? ) -> \\partial_{a}{ \\Omega(A??)(B??) };\n    substitute(obj46, rl)\n    tst46:= \\partial_{a}{ \\Omega(A)(\\partialp_{b}{B}) } - @(obj46);\n    assert(tst46==0)\n    print('Test 06 passed')\n    \ntest06()\n\ndef test07():\n    # Vary multiple terms and single-factor terms.\n    __cdbkernel__=create_scope()\n    obj70:= A + B Q;\n    vary(_, $A -> Q, B -> Z$ )\n    tst70:= Q + Z Q - @(obj70);\n    assert(tst70==0)\n    print('Test 07 passed')\n    \ntest07()\n\ndef test17():\n    # Test 17: Object wildcards\n    obj17:= [ A B, C];\n    substitute(_, $[ M? N?, P? ] -> P? M? N?$ )\n    tst17:= @(obj17) - C A B;\n    assert(tst17==0)\n    print('Test 17 passed')\n    \ntest17()\n\ndef test84():\n    # Bug reported Sun, 9 Nov 2014 15:51:05 +0800\n    \\partial{#}::PartialDerivative.\n    yy:= a+ a*A;\n    vary(yy, $A->\\delta{A}$ )\n    tst84:= a \\delta{A} - @(yy);\n    assert(tst84==0)\n    print('Test 84 passed')\n\ntest84()\n\ndef test100():\n    {\\mu,\\nu,\\rho}::Indices(position=free).\n    \\partial{#}::PartialDerivative.\n    ex:= \\int{\\partial_{\\mu}{A_{\\nu}} - \\partial_{\\nu}{A_{\\mu}}}{x};\n    vary(ex, $A_{\\mu} -> \\delta{A_{\\mu}}$)\n\n\ndef test101():\n    __cdbkernel__=create_scope()\n    {m,n,p}::Integer;\n    A_{m}::SelfNonCommuting.\n    ex:= A_{3} A_{2} A_{1} A_{0} + A_{0} A_{8};\n    rl:= A_{m} A_{n} | m > n -> Q;\n    substitute(ex, rl, repeat=True)\n    tst:= Q Q + A_{0} A_{8} - @(ex);\n    assert(tst==0)\n    print('Test 101 passed')\n\ntest101()\n\ndef test102():\n    __cdbkernel__=create_scope()\n    {m,n,p}::Integer;\n    {m,n,p}::Symbol;\n    A_{m}::SelfNonCommuting;\n    ex:= A_{2} A_{3} A_{1} + A_{1} A_{0};\n    rl:= A_{m} A_{n} | m > n -> A_{n} A_{m} + Q;\n    ex.reset()\n    while ex.changed():\n        distribute(ex)\n        substitute(ex, rl)\n        sort_product(ex)\n    \n    tst:= A_{1} A_{2} A_{3} + A_{3} Q + A_{2} Q + A_{0} A_{1} + Q - @(ex);\n    assert(tst==0)\n    print('Test 102 passed')\n\ntest102()\n    \ndef test103():\n    __cdbkernel__=create_scope()\n    \\partial{#}::PartialDerivative;\n    rl:= A_{m? n?} -> \\partial_{m?}{B_{n?}};\n    ex:= A_{4 k} A_{k 4};\n    substitute(ex, rl)\n    tst:= \\partial_{4}{B_{k}} \\partial_{k}{B_{4}} - @(ex);\n    assert(tst==0)\n\ntest103()\n\ndef test104():\n    __cdbkernel__=create_scope()\n    {m,n,p}::Indices(position=independent);\n    ex:= g^{4};\n    rl:= g_{4} -> A;\n    # How is this thing supposed to know that 4 is in the {m,n,p} set?\n    substitute(ex, rl)\n    tst:= g^{4} - @(ex);\n    assert(tst==0)\n    print(\"Test 104 passed\")\n\ntest104()\n\ndef test105():\n    __cdbkernel__=create_scope()\n    ex:= A_{m n} + B_{m n};\n    rl:= C?_{m? n?} -> n? C?_{n?};\n    substitute(ex, rl)\n    tst:= n A_{n} + n B_{n} - @(ex);\n    assert(tst==0)\n    print(\"Test 105 passed\")\n\ntest105()\n\ndef test106():\n    __cdbkernel__=create_scope()\n    {m,n,p}::Indices(position=free);\n    ex:=\\int{ A_{m} A^{m} }{x};\n    rl:= A_{m} -> B_{m n} C^{n};\n    substitute(ex, rl)\n    tst:= \\int{ B_{m n} C^{n} B^{m}_{p} C^{p} }{x} - @(ex);\n    assert(tst==0)\n    print(\"Test 106 passed\")\n    \ntest106()\n    \ndef test107():\n    __cdbkernel__=create_scope()\n    ex:= A_{m n} - B_{m n};\n    substitute(ex, $_{m} -> _{2}$)\n    tst:= A_{2 n} - B_{2 n} - @(ex);\n    assert(tst==0)\n    print(\"Test 107 passed\")\n\ntest107()\n\ndef test108():\n    __cdbkernel__=create_scope()\n    \\nabla{#}::Derivative;\n    {\\mu,\\nu,\\rho,\\sigma}::Indices(position=fixed);\n    ex:= \\nabla_{\\mu}{K^{\\nu}} = B_{\\mu} D^{\\nu};\n    substitute(_, $\\nabla_{\\mu}{A?^{\\nu}} = C_{\\mu}^{\\nu}$)\n    tst:= C_{\\mu}^{\\nu} = B_{\\mu} D^{\\nu};\n    assert(ex==tst)\n    print(\"Test 108 passed\")\n\ntest108()\n\ndef test109():\n    __cdbkernel__=create_scope()\n    {\\mu,\\nu,\\rho,\\sigma}::Indices(position=fixed);\n    \\partial{#}::PartialDerivative;\n    g_{\\mu\\nu}::Metric;\n    g^{\\mu\\nu}::InverseMetric;\n    g^{\\mu}_{\\nu}::KroneckerDelta;\n    g_{\\mu}^{\\nu}::KroneckerDelta;\n    ex:= \\partial_{5}{ g^{5 5} } \\partial_{5}{ g_{5 5} }  - A_{5};\n    substitute(ex, $g_{5 5} -> B$)\n    tst:= \\partial_{5}{ g^{5 5} } \\partial_{5}{B} - A_{5} - @(ex);\n    assert(tst==0)\n    print(\"Test 109 passed\")\n\ntest109()\n\n# def test110():\n# {\\mu,\\nu,\\rho}::Integer(0..d-1).\n# {\\mu,\\nu,\\rho}::Indices.\n# {m,n}::Integer.\n# rl:= \\alpha_{m}^{\\mu} \\alpha_{n}^{\\nu} | m > n -> \\alpha_{n}^{\\nu} \\alpha_{m}^{\\mu} +  \\delta_{m}_{-n} \\delta^{\\mu\\nu};\n# ex:= \\alpha_{1}^{\\mu} \\alpha_{0}^{\\mu};\n# substitute(ex, rl);\n\ndef test110():        \n    __cdbkernel__=create_scope()\n    ex:= A + 2 B + C + 2 D;\n    substitute(_, $B + D = Q$)\n    tst:= A + C + 2 Q - @(ex);\n    assert(tst==0)\n    print(\"Test 110 passed\")\n\ntest110()\n\ndef test111():\n    __cdbkernel__=create_scope()        \n    {t,x}::Coordinate;        \n    {\\mu, \\nu, \\rho, \\sigma}::Indices(values={t,x}, position=fixed);\n    \\partial{#}::PartialDerivative;\n    ex:= \\partial_{\\mu}{ g_{\\rho\\sigma} };\n    rl:= \\partial_{t}{ g_{\\mu\\nu} } -> C_{\\mu\\nu};\n    substitute(ex, rl)\n    tst:= \\partial_{\\mu}{ g_{\\rho\\sigma} } - @(ex);\n    assert(tst==0)\n    print(\"Test 111 passed\")\n\ntest111()\n\ndef test112():\n    __cdbkernel__=create_scope()\n    {m,n,p,q}::Indices;        \n    ex:=A B_{m n} C;\n    rl:=A?_{p q} -> - 2 A?_{p q};\n    substitute(ex, rl)\n    tst:=-2 A B_{m n} C - @(ex);\n    assert(tst==0)\n    print(\"Test 112 passed\")\n\ntest112()\n\ndef test113():\n    # spotted by Leo Brewin 15-Mar-2018.\n    __cdbkernel__=create_scope()\n    {a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s}::Indices(position=fixed).\n    ex := A^{f} A^{m} B_{g f} G^{a}_{m e} G^{e}_{b d}.\n    substitute(_, $A^{e} B_{c e} G^{a}_{b d} -> A^{f} B_{f} R^{a}_{b c d}$)\n    tst:= A^{f} B_{f} R^{a}_{m g e} A^{m} G^{e}_{b d} - @(ex);\n    assert(tst==0)\n    print(\"Test 113 passed\")\n\ntest113()\n\ndef test114():\n    __cdbkernel__=create_scope()\n    {a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s}::Indices(position=fixed).       \n    ex := B^{c}_{a d} A^{d} A^{e}.\n    substitute(ex, $A^{c} A^{b} B^{a}_{d b} -> A^{b} A^{c} C^{a}_{b d}$)\n    tst:= A^{d} A^{e} C^{c}_{d a} - @(ex);\n    assert(tst==0)\n    print(\"Test 114 passed\")\n\ntest114()\n\ndef test115():\n    __cdbkernel__=create_scope()\n    {a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s}::Indices(position=fixed).\n    ex := B^{c}_{a d} A^{d} A^{e}.\n    substitute(ex, $B^{a}_{d b} A^{c} A^{b} -> A^{b} A^{c} C^{a}_{b d}$)\n    tst:= A^{d} A^{e} C^{c}_{d a} - @(ex);\n    assert(tst==0)\n    print(\"Test 115 passed\")\n\ntest115()\n\ndef test116():\n    __cdbkernel__=create_scope()\n    D{#}::Derivative;\n    {\\epsilon, \\psi_{\\mu},\\psi_{\\mu\\nu} }::Spinor(dimension=4, type=Majorana);\n    \\Gamma_{#}::GammaMatrix(metric=\\delta);\n    ex:= \\bar{D_{\\mu}{\\epsilon}} \\Gamma^{m n p} D_{\\nu}{\\psi_{\\rho}} e e_{m}^{\\mu} e_{n}^{\\nu} e_{p}^{\\rho} + Q;\n    pat:= \\bar{D_{\\mu}{\\epsilon}} A??;\n    sort_product(_)\n    take_match(ex, pat)\n    tst:= \\bar{D_{\\mu}{\\epsilon}} \\Gamma^{m n p} D_{\\nu}{\\psi_{\\rho}} e e_{m}^{\\mu} e_{n}^{\\nu} e_{p}^{\\rho} - @(ex);\n    assert(tst==0)\n    print(\"Test 116 passed\")\n\ntest116()\n\ndef test117():\n    __cdbkernel__=create_scope()\n    ex:= s A_{s};\n    substitute(ex, $s -> 1$)\n    tst:= A_{s} - @(ex);\n    assert(tst==0)\n    print(\"Test 117a passed\")\n    {p,q,r,s,t,u,v,w}::Indices.\n    ex := s**2 y^{r} y^{s} A_{r s};\n    substitute(ex, $s->1$)\n    tst:= y^{r} y^{s} A_{r s} - @(ex);\n    assert(tst==0)\n    print(\"Test 117b passed\")\n\ntest117()\n\ndef test118():\n    __cdbkernel__=create_scope()\n    ex:= s A_{s};\n    substitute(ex, $_{s} -> _{1}$)\n    tst:= s A_{1} - @(ex);\n    assert(tst==0)\n    print(\"Test 118 passed\")\n\ntest118()\n\ndef test119():\n    __cdbkernel__=create_scope()\n    {a,b,c,d,e,f}::Indices(spinor);\n    {m,n,p,q}::Indices(spacetime);\n    \\theta^{a}::SelfAntiCommuting;\n    ex:=\\theta^{a} \\sigma^{m}_{a b} \\theta^{b} \\tau^{n c d} \\sigma^{p}_{d e} \\theta^{e} \\theta^{f};\n    rl:=\\theta^{a} \\theta^{b} \\theta^{c} \\sigma^{m}_{c d} \\theta^{d} -> \\tau^{m a b};\n    substitute(ex, rl)\n    tst:= \\tau^{n c d} \\sigma^{p}_{d e} \\tau^{m e f} - @(ex);\n    assert(tst==0)\n    print(\"Test 119 passed\")\n\ntest119()\n\ndef test120():\n    __cdbkernel__=create_scope()\n    {a,b,c,d,e,f}::Indices(spinor);\n    {m,n,p,q}::Indices(spacetime);\n    \\theta^{a}::SelfAntiCommuting;\n    ex:=\\theta^{b} \\sigma^{m}_{a b} \\theta^{a} \\tau^{n c d} \\sigma^{p}_{d e} \\theta^{e} \\theta^{f};\n    rl:=\\theta^{a} \\theta^{b} \\theta^{c} \\sigma^{m}_{c d} \\theta^{d} -> \\tau^{m a b};\n    substitute(ex, rl)\n    tst:= -\\tau^{n c d} \\sigma^{p}_{d e} \\tau^{m e f} - @(ex);\n    assert(tst==0)\n    print(\"Test 120 passed\")\n\ntest120()\n\ndef test121():\n    __cdbkernel__=create_scope()\n    {\\dagger}::Symbol.\n    {a,n,\\sigma,\\tau}::Symbol;\n    {\\Gamma^{\\dagger}_{\\tau?}, N_{a? \\tau?}, G_{n? \\sigma?}}::NonCommuting.\n    {\\Gamma^{\\dagger}_{\\tau?}, N_{a? \\tau?}}::Depends(\\commutator{#});\n    rule:= N_{a? \\tau?} G_{n?? \\sigma?} -> n?? G_{(n??-1) \\sigma?}\n             \\commutator{N_{a? \\tau?}}{\\Gamma^{\\dagger}_{\\sigma?}}\n           + 1/2 n?? (n??-1)\n              \\commutator{\\commutator{N_{a? \\tau?}}{\\Gamma^{\\dagger}_{\\sigma?}}}{\\Gamma^{\\dagger}_{\\sigma?}} G_{(n??-2) \\sigma?};\n    ex:=N_{a \\tau} G_{{n-1} \\sigma};\n    substitute(_,rule)\n    tst:= (n-1) G_{{n-2} \\sigma} \\commutator{ N_{a \\tau} }{ \\Gamma^{\\dagger}_{\\sigma} } +\n          1/2 (n-1) (n-2) \\commutator{ \\commutator{ N_{a \\tau} }{ \\Gamma^{\\dagger}_{\\sigma} }}{ \\Gamma^{\\dagger}_{\\sigma} } G_{{n-3} \\sigma} - @(ex);\n    assert(tst==0)\n    print(\"Test 121 passed\")\n\ntest121()\n\ndef test122():        \n    __cdbkernel__=create_scope()\n    ex:= L_{0 1} + L_{4 5};\n    rl:= L_{a? b?} | a? > 3 -> Q_{a? b?};\n    substitute(ex, rl)\n    tst:= L_{0 1} + Q_{4 5} - @(ex);\n    assert(tst==0)\n    print(\"Test 122 passed\")\n\ntest122()\n\ndef test123():\n    __cdbkernel__=create_scope()\n    {A, B, C, D, E, F}::NonCommuting;\n    ex:= A B C D E F + B C A D E F;\n    substitute(_, $C D E -> Q$)\n    tst:= A B F + B C A D E F - @(ex);\n    assert(tst==0)\n    print(\"Test 123a passed\")        \n    ex:= A B C D E F + B C A D E F;\n    substitute(_, $C D E -> Q$, partial=False)\n    tst:= A B C D E F + B C A D E F - @(ex);\n    assert(tst==0)\n    print(\"Test 123b passed\")\n    ex:= A + B + C + D;\n    substitute(_, $A + C = Q$);\n    tst:= Q + B + D - @(ex);\n    assert(tst==0)\n    print(\"Test 123c passed\")\n    ex:= A + B + C + D;\n    substitute(_, $A + C = Q$, partial=False);\n    tst:= A + B + C + D - @(ex);\n    assert(tst==0)\n    print(\"Test 123d passed\")\n\n#test123()\n        \n# substitute(_, $A C?* F -> F A B C?* $, partial=False);        \n\ndef test124():\n    __cdbkernel__=create_scope()\n    \\dot{#}::Accent;\n    {\\dot{\\alpha}, \\dot{\\beta}, \\dot{\\gamma}, \\dot{\\delta}}::Indices(spinor, position=fixed);\n    {\\dot{\\alpha}, \\dot{\\beta}, \\dot{\\gamma}, \\dot{\\delta}}::Integer(1..2);\n    \\nabla{#}::Derivative;\n    ex:=\\nabla^{\\dot{\\gamma}}(\\theta^{\\dot{\\alpha}}) \\theta_{\\dot{\\alpha}};\n    substitute(_, $\\nabla^{\\dot{\\alpha}}{\\theta^{\\dot{\\beta}}} -> \\epsilon^{\\dot{\\beta} \\dot{\\alpha}}$)\n    tst:= \\epsilon^{\\dot{\\alpha} \\dot{\\gamma}} \\theta_{\\dot{\\alpha}} - @(ex);\n    assert(tst==0)\n    print(\"Test 124 passed\")\n\ntest124()\n\ndef test125():\n    __cdbkernel__=create_scope()\n    ex:=T_{A};\n    substitute(ex, $T{A?} = Q$)\n    try:\n        tst:= T_{A} - @(ex);\n        assert(tst==0)\n        print(\"Test 125a passed\")\n    except:\n        assert(False)\n    \n    ex:=T{A};\n    substitute(ex, $T_{A?} = Q$)\n    try:\n        tst:= T{A} - @(ex);\n        assert(tst==0)\n        print(\"Test 125b passed\")\n    except:\n        assert(False)\n\ntest125()\n\n# \\del{#}::LaTeXForm(\"\\partial\").\n# ex:=\\del_{m}{A};\n# res=ex._latex_()\n#     \n# ex:=A_{m}(x);\n# substitute(ex, $A{#}->Q$);\n#         \n# \\hat{R}_{a b c d}\n# R(x,y)\n\ndef test126():\n    # Inside powers, dummies can be repeated.\n    __cdbkernel__=create_scope()\n    {n,m,p,q}::Indices;\n    ex:= A^{n} / (A^{m} A^{m});\n    rename_dummies(ex)\n    tst:= A^{n} / (A^{n} A^{n}) - @(ex);\n    assert(tst==0)\n    print(\"Test 126 passed\")\n\ntest126()\n        \ndef test127():\n    # Expect an exception when substituting with empty rule.\n    __cdbkernel__=create_scope()\n    ex:= A + B;\n    try:\n        substitute(ex, $ $);\n        assert(False)\n    except Exception:\n        print(\"Test 127a passed\")\n    try:\n        substitute(ex, ${ }$)\n        assert(1==0)\n    except Exception:\n        print(\"Test 127b passed\")\n    \ntest127()\n\ndef test128():\n    # FIXME: adding create_scope here makes things fail, why?\n    # __cdbkernel__=create_scope()\n    a::Symbol;\n    b::Symbol;\n    \n    {a**m?, b**n?, a, b}::NonCommuting;\n    \n    r1 := {\n    a b**m?  -> (1+b a) b**{m?-1},\n    a b -> 1 + b a,\n    };\n    \n    def act(ex):\n        converge(ex):\n            substitute(ex,r1)\n            distribute(ex)\n            collect_factors(ex)\n            print(ex)\n        return ex\n    \n    ex:=a b**5;\n    act(ex);\n    tst:= 5 b**4 + b**5 a - @(ex);\n    assert(tst==0)\n    print(\"Test 128 passed\")\n\ntest128()\n\ndef test129():\n    __cdbkernel__=create_scope()\n    ex:= A_{\\mu} - B_{\\mu}^{a} B^{\\nu}_{a} A_{\\nu};\n    substitute(_, $A_{\\mu} = 0$, partial=False);\n    tst:= -B_{\\mu}^{a} B^{\\nu}_{a} A_{\\nu} - @(ex);\n    assert(tst==0)\n    print(\"Test 129 passed\")\n\ntest129()\n\ndef test130():\n    # Test the effect of the substitute rule cache.\n    __cdbkernel__=create_scope()\n\n    megasum := x+y;\n    for i in range(10000):\n       megasum.top().append_child(Ex( r'B'+str(i) ))    \n    \n    rules = $$\n    for i in range(100):\n       rules = join(rules, Ex( r'A'+str(i)+'-> @(megasum)' ))\n    \n    ex:=A0;\n    substitute(ex, rules)\n    assert(ex[10001]==$B9999$)\n    print(\"Test 130 passed\")\n\ntest130()\n\ndef test131():\n    __cdbkernel__=create_scope()\n    ex := 2 A + 3 B + 4 C.\n    substitute(ex, $A? -> 5 A?$)\n    tst:= 10 A + 15 B + 20 C - @(ex):\n    assert(tst==0)\n    print(\"Test 131a passed\")\n    ex := 2 A + 3 B + 4 C.\n    substitute(ex, $A? -> \\theta A?$)\n    tst:= 2 \\theta A + 3 \\theta B + 4 \\theta C - @(ex):\n    assert(tst==0)\n    print(\"Test 131b passed\")\n    ex := 2 A Q + 3 B R + 4 C S.\n    substitute(ex, $A? -> \\theta A?$)\n    tst:= 2 \\theta A \\theta Q + 3 \\theta B \\theta R + 4 \\theta C \\theta S - @(ex):\n    assert(tst==0)\n    print(\"Test 131c passed\")\n    {i,j,k,l}::Indices;    \n    ex:= 2 A_{i j} + 3 B_{i j};\n    substitute(ex, $A_{k l} -> C_{k l}$)\n    tst:= 2 C_{i j} + 3 B_{i j} - @(ex):\n    assert(tst==0)\n    print(\"Test 131d passed\")\n    {m,n}::Symbol;    \n    {m,n}::Integer;\n    ex:= 2 A_{0} A_{1};\n    substitute(ex, $A_{m} A_{n} -> A_{n} A_{m}$);\n\ntest131()\n\ndef test132():\n    __cdbkernel__=create_scope()\n    \\alpha_{n}::SelfNonCommuting;\n    {m,n}::Integer.\n    {m,n}::Symbol.\n    \\delta{#}::KroneckerDelta.\n    \\delta{#}::Diagonal.\n    rl:= \\alpha_{m} \\alpha_{n} -> \\delta_{m}_{-n} \\delta^{\\mu\\nu};\n    ex:= \\alpha_{1} \\alpha_{-1} \\vac;\n    substitute(ex, rl)\n    tmp:= \\delta^{\\mu\\nu}\\vac - @(ex);\n    assert(tmp==0)\n    print(\"Test 132 passed\")\n\ntest132()\n\ndef test133():\n    __cdbkernel__=create_scope()\n    ex:= A + B3 + C7.\n    substitute(_, $A + M? + N? | \\regex{M?}{\"[A-Z]7\"} -> \\sin(M? N?)/N?$)\n    tst:= \\sin(C7 B3)/B3 - @(ex);\n    assert(tst==0)\n    print(\"Test 133 passed\")\n\ntest133()\n\n    "
  },
  {
    "path": "tests/symmetry.cdb",
    "content": "# The Young tableau\n#\n#   i k\n#   j\n# \n# is defined by:\n#\ndef test01():\n    __cdbkernel__=create_scope()\n    obj1:= b*a^{i j k};\n    sym(_, $^{i},^{k} $)\n    # FIXME: if you put a space in front of the ^ operator, it turns into a wedge, and asym fails.\n    asym(_, $^{i},^{j} $)\n    tst1:= b/4*( a^{i j k} + a^{k j i} - a^{j i k} - a^{k i j} ) - @(obj1);\n    distribute(_)\n    assert(tst1==0)\n    print('Test 01 passed')\n\ntest01()\n\n# It is possible to (anti)symmetrise modulo implicit\n# (anti)symmetrisations:\n#\n# obj2:= A_{m n p} B_{q r s};\n# @asym!(%){_{m},_{n},_{q}}{0,1};\n# tst2:= 1/3 * A_{m n p} * B_{q r s}\n#     - 1/3 * A_{m q p} * B_{n r s}\n#     + 1/3 * A_{q m p} * B_{n r s} - @(obj2);\n# @collect_terms!(%);\n# @assert(tst2);\n\n# Symmetrising in sets:\n\ndef test03():\n    __cdbkernel__=create_scope()\n    obj3:= A_{i k l m}*q;\n    asym(_, $ {_{i},_{k}}, {_{l},_{m}} } $)\n    tst3:= (1/2) * A_{i k l m}*q - (1/2) * A_{l m i k}*q - @(obj3);\n    assert(tst3==0)\n    print('Test 03 passed')\n\ntest03()\n\ndef test04():\n    __cdbkernel__=create_scope()\n    R_{a b c d}::WeylTensor.\n    obj4:= R_{r1 r2 r3 r4}*q;\n    asym(_, $ _{r1}, _{r2} $)\n    asym(_, $ _{r3}, _{r4} $)\n    sym(_,  $ {_{r1},_{r2}}, {_{r3},_{r4}} $)\n    tst4:= R_{r1 r2 r3 r4}*q - @(obj4);\n    indexsort(_)\n    assert(tst4==0)\n    print('Test 04 passed')\n\ntest04()\n\ndef test05():\n    __cdbkernel__=create_scope()\n    R_{a b c d}::WeylTensor.\n    obj5:= R_{r1 r2 r4 r3}*q;\n    asym(_, $ {_{r1},_{r2}}, {_{r3},_{r4}} $)\n    tst5:= (1/2) * R_{r1 r2 r4 r3}*q - (1/2) * R_{r4 r3 r1 r2}*q - @(obj5);\n    assert(tst5==0)\n    print('Test 05 passed')\n\ntest05()\n\n# Generating subsets of permutations, in order to split up\n# very large ones (no longer possible in v2)\n#\n# obj6:= q*A_{a b c d};\n# @sym!(%){_{a},_{b},_{c},_{d}}{Start:>2}{End:>4};\n# tst6:= q/24 A_{a c b d} + q/24 A_{a c d b} - @(obj6);\n# @collect_terms!(%);\n# @assert(tst6);\n\n\n# Test 8: sym/asym on whole tensors, with different index lengths\n\ndef test08():\n    __cdbkernel__=create_scope()\n    obj8:=A_{a b} B_{c};\n    sym(_, $ A_{a b}, B_{c} $)\n    tst8:=1/2 A_{a b} B_{c} + 1/2 B_{c} A_{a b} - @(obj8);\n    assert(tst8==0)\n    print('Test 08 passed')\n\t\t\ntest08()\t \n\ndef test09():\n    __cdbkernel__=create_scope()\n    ex:= 1/2 A_{a b} B_{c d};\n    slot_asym(ex, [1,2], deep=False)\n    tst:= 1/4 A_{a b} B_{c d} - 1/4 A_{a c} B_{b d} - @(ex);\n    assert(tst==0)\n    print(\"Test 09 passed\")\n\ntest09()\n"
  },
  {
    "path": "tests/sympy_bridge.cnb",
    "content": "{\n\t\"cells\" : \n\t[\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Coordinate to~}\\\\left(r, \\\\linebreak[0] t\\\\right).\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property PartialDerivative to~}\\\\partial{\\\\#}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Depends to~}\\\\rho.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Depends to~}\\\\chi.\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"{r,t}::Coordinate;\\n\\\\partial{#}::PartialDerivative;\\n\\\\rho::Depends(r,t);\\n\\\\chi::Depends(r);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\rho+\\\\rho^{2}+\\\\partial_{t r}{\\\\rho}+\\\\partial_{r}{\\\\chi}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex:= \\\\rho+\\\\rho**2 +\\\\partial_{t r}{\\\\rho} + \\\\partial_{r}{\\\\chi};\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\rho^{2}+\\\\rho+\\\\partial_{r}{\\\\chi}+\\\\partial_{r t}{\\\\rho}\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"res=scas(ex, \\\"\\\");\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"latex\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"We need to strip off the arguments again.\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"hidden\" : true,\n\t\t\t\"source\" : \"We need to strip off the arguments again.\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"output\",\n\t\t\t\t\t\"source\" : \"\\\\begin{verbatim}{\\\\sum}  (0x7f6a280272f8)\\n  1:{\\\\pow}  (0x7f6a28021078)\\n  2:  {\\\\rho}  (0x7f6a280236c8)\\n  3:  {1}  2  (0x7f6a28020fd8)\\n  4:{\\\\rho}  (0x7f6a28023718)\\n  5:{\\\\partial}  (0x7f6a28025c38)\\n  6:  _{r}  (0x7f6a2801de28)\\n  7:  {\\\\chi}  (0x7f6a2801ddd8)\\n  8:{\\\\partial}  (0x7f6a28010c28)\\n  9:  _{r}  (0x7f6a280274d8)\\n 10:  _{t}  (0x7f6a2800a698)\\n 11:  {\\\\rho}  (0x7f6a2800a6e8)\\n\\n\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"print(tree(res))\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Coordinate to~}\\\\left(r, \\\\linebreak[0] t\\\\right).\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Indices(position=free) to~}\\\\left(m, \\\\linebreak[0] n\\\\right).\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Depends to~}\\\\Delta.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property Metric to~}g_{m n}.\\\\end{dmath*}\"\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\text{Attached property TableauSymmetry to~}g^{m n}.\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"{r,t}::Coordinate;\\n{m,n}::Indices(values={r,t});\\n\\\\Delta::Depends(r);\\n\\\\partial{#}::PartialDerivative;\\ng_{m n}::Metric;\\ng^{m n}::InverseMetric;\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\left(g_{t t} = \\\\Delta, \\\\linebreak[0] g_{r r} = \\\\sin\\\\left(t\\\\right)\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"rl:= g_{t t} = \\\\Delta, g_{r r} = \\\\sin(t);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\left(g_{t t} = \\\\Delta, \\\\linebreak[0] g_{r r} = \\\\sin\\\\left(t\\\\right), \\\\linebreak[0] g^{r r} = \\\\frac{1}{\\\\sin\\\\left(t\\\\right)}, \\\\linebreak[0] g^{t t} = \\\\frac{1}{\\\\Delta}\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"complete(rl, $g^{m n}$);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\partial_{\\\\mu}\\\\left(g_{\\\\mu \\\\nu}\\\\right)\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"ex2:=\\\\partial_{\\\\mu}{ g_{\\\\mu\\\\nu} };\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"latex_view\",\n\t\t\t\t\t\"source\" : \"\\\\begin{dmath*}{}\\\\left\\\\{\\\\begin{aligned}\\\\end{aligned}\\\\right.\\n\\\\end{dmath*}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"evaluate(ex2, rl);\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"cells\" : \n\t\t\t[\n\t\t\t\t{\n\t\t\t\t\t\"cell_origin\" : \"server\",\n\t\t\t\t\t\"cell_type\" : \"output\",\n\t\t\t\t\t\"source\" : \"\\\\begin{verbatim}{\\\\components}  (0x7fcdb0001048)\\n  1:_{\\\\mu}  (0x7fcdb00096d8)\\n  2:{\\\\comma}  (0x7fcdb0003648)\\n\\n\\\\end{verbatim}\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\" : \"print(tree(ex2))\"\n\t\t},\n\t\t{\n\t\t\t\"cell_origin\" : \"client\",\n\t\t\t\"cell_type\" : \"input\",\n\t\t\t\"source\" : \"\"\n\t\t}\n\t],\n\t\"description\" : \"Cadabra JSON notebook format\",\n\t\"version\" : 1\n}\n"
  },
  {
    "path": "tests/sympy_cdb.cdb",
    "content": "\n    \ndef test01():\n   __cdbkernel__=create_scope()    \n   ex:=3x + x**2 + a x**2 + b x;\n   q=SympyBridge(ex)\n   q.from_sympy( sympy.collect(q.to_sympy(), $x$) )\n   tst:= (a + 1) x**2 + (b + 3) x - @(ex);\n   assert(tst==0)\n   print(\"Test 01 passed\")\n    \ntest01()\n\ndef test02():\n   __cdbkernel__=create_scope()\n   {r,t}::Coordinate.\n   f::Depends(r,t).\n   ex:=f*A;\n   \\partial{#}::PartialDerivative.\n   ex:= \\partial_{r}{ f + (\\sin(r)**2)**2 };\n   map_sympy(ex)\n   tst:= \\partial_{r}{f} + 4 \\sin(r)**3 \\cos(r) - @(ex);\n   assert(tst==0)\n   print(\"Test 02 passed\")\n\ntest02()\n\ndef test03():\n   __cdbkernel__=create_scope() \n   \\tau::Coordinate.\n   \\partial{#}::Derivative(\\tau).\n   r::Depends(\\tau).\n   ex:=\\partial{r};\n   q=SympyBridge(ex)\n   q.from_sympy( q.to_sympy() )\n   ex;\n   tst:= \\partial{r} - @(ex);\n   assert(tst==0)\n   print(\"Test 03a passed\")\n\n   ex:=\\partial{\\partial{r}};\n   q=SympyBridge(ex)\n   q.from_sympy( q.to_sympy() )\n   tst:= \\partial{\\partial{r}} - @(ex);\n   assert(tst==0)\n   print(\"Test 03b passed\")\n\ntest03()\n\n\ndef test04():\n   __cdbkernel__=create_scope() \n   ex:= 1 - (-1)**2;\n   simplify(_)\n   assert(ex==0)\n   print(\"Test 04 passed\")\n\ntest04()\n\nfrom cdb.sympy.calculus import integrate\n      \ndef test05():\n   __cdbkernel__=create_scope() \n   ex:= \\exp(-x);\n   tst = integrate(ex, ($x$, 0, $\\infty$))\n   assert(tst==1)\n   print(\"Test 05 passed\")\n\ntest05()\n      \ndef test06():\n   # When acting on a super- or sub-script expression,\n   # make sure that this parent_rel is not dropped.\n   __cdbkernel__=create_scope()\n   {r,\\theta}::Coordinate.\n   \\partial{#}::PartialDerivative.\n   # Evaluate works, but that looks explicity at\n   # both sides separately and calls simplify on\n   # it without 'deep=True'.\n   ex:= \\partial_{r}{\\theta};\n   evaluate(ex, $$)\n   assert(ex==0)\n   print(\"Test 06a passed\")\n   # When using 'deep=True', simplify gets called\n   # on the sub-script, and we need to be careful\n   # not to turn this into '\\partial{r}{\\theta}',\n   # as that is meaningless in sympy.\n   ex:= \\partial_{r}{\\theta};\n   simplify(ex, deep=True)\n   assert(ex==0)\n   print(\"Test 06b passed\")\n\ntest06()\n\ndef test07():\n   __cdbkernel__=create_scope()\n   {r,\\theta}::Coordinate.\n   \\partial{#}::PartialDerivative.\n   f::Depends(r).\n   ex:= \\partial_{r}{3 f};\n   simplify(ex, deep=True)\n   tst:= 3 \\partial_{r}{f} - @(ex);\n   assert(tst==0)\n   print(\"Test 07 passed\")\n\ntest07()\n\ndef test08():\n   __cdbkernel__=create_scope()\n   {M,N}::AntiCommuting;\n   ex:= M N - N M:\n   try:\n      simplify(ex)\n      assert(1==0)\n   except RuntimeError as e:\n      print(\"Test08 passed\")\n\ntest08()\n\ndef test09():\n   __cdbkernel__=create_scope()\n   ex:= \\sin(x);\n   ex2 = integrate(ex, $x$);\n   tst:= -\\cos(x) - @(ex2);\n   assert(tst==0)\n   print(\"Test 09 passed\")\n\ntest09()\n\nfrom cdb.sympy.solvers import *\n\ndef test10():\n   __cdbkernel__=create_scope()\n   syst := {x**2 = y + z, z = x - 3};\n   sol=nonlinsolve(syst, $x, y$);\n   assert(sol == $\\comma{x -> z + 3, y->z**2 + 5z + 9}$)\n   print(\"Test 10 passed\")\n\ntest10()\n\nfrom cdb.sympy.solvers import *\n\ndef test11():\n   \\tau::Coordinate;\n   \\dot{#}::Derivative(\\tau);\n   X::Depends(\\tau);\n   ex:= \\dot{\\dot{X}} + m**2 X = 0;\n   sol = rhs(dsolve(ex, $X$))\n   tst:= \\exp( -\\tau m \\iu ) C1 + \\exp( \\tau m \\iu ) C2 - @(sol);\n   assert(tst==0)\n\ntest11()\n\n\n"
  },
  {
    "path": "tests/test_comparison.cc",
    "content": "\n#include \"Compare.hh\"\n#include \"Storage.hh\"\n\nint main()\n\t{\n\tEx a1(\"A\"), a2(\"A\");\n\n\ta1.begin()->fl.parent_rel=str_node::p_sub;\n\ta2.begin()->fl.parent_rel=str_node::p_super;\n\n\ttree_exact_less_for_indexmap_obj compare;\n\n\tstd::cerr << compare(a2, a1) << std::endl;\n\tassert(compare(a1, a2)!=compare(a2,a1));\n\t}\n"
  },
  {
    "path": "tests/tests.cdb",
    "content": "\ntst1:= (b/4)*(a^{i} + a^{j} - a^{j} );\n\n# The Redberry authors claim we cannot do the following:\n\ndef testRB():\n    ex:= K_a (A^{a b} - A^{b a});\n    rl:= K_c (A^{c d} - A^{d c}) -> F^{d};\n    substitute(ex, rl)\n    tst:= F^{b} - @(ex);\n    assert(tst==0)\n\ntestRB()\n\n\n\n\nex:= C B A D;\norder(ex, 'A, B, C, D', anticommuting=True)\n\nex:= A B C D;\nsym(ex, 'A, B, D')\n\nex:=     \n\n\ndef test04():\n    \\diff{#}::PartialDerivative.\n    obj6:= \\diff{g^{\\mu \\kappa} * \\diff{g_{\\kappa \\nu}}_{\\rho}}_{\\sigma};\n    product_rule(_)\n    tst6:= \\diff{g^{\\mu \\kappa}}_{\\sigma} * \\diff{g_{\\kappa \\nu}}_{\\rho}\n        +g^{\\mu \\kappa} * \\diff{g_{\\kappa \\nu}}_{\\rho \\sigma} - @(obj6);\n    collect_terms(_);\n\ntest04()\n\nctest([1,2,3])\nex:=a+b+c+d;\nkeep_terms(_, [1,2,3])\n"
  },
  {
    "path": "tests/trigonometric.cdb",
    "content": "\ndef test01():\n    __cdbkernel__=create_scope()\n    rl:= \\sin{A??}**2 + \\cos{A??}**2 = 1;\n    ex:= \\sin{x}**2 + 3 + \\cos{x}**2 + Q;\n    substitute(ex, rl)\n    tst:= 4 + Q - @(ex);\n    assert(tst==0)\n    print(\"Test 01 passed\")\n\ntest01()\n\ndef test02():\n    __cdbkernel__=create_scope()\n    rl:= \\sin{A??}**2 + \\cos{A??}**2 = 1;\n    ex:= \\sin{A_{m} A^{m}}**2 + \\cos{A_{n} A^{n}}**2;\n    substitute(ex, rl)\n    tst:= 1 - @(ex);\n    assert(tst==0)\n    print(\"Test 02 passed\")\n\ntest02()\n\ndef test03():\n    __cdbkernel__=create_scope()\n    rl:= \\sin{A??}**2 + \\cos{A??}**2 = 1;\n    ex:= \\sin{A_{m} A^{m} B_{n} B^{n}}**2 + \\cos{A_{m} A^{n} B_{n} B^{m}}**2;\n    substitute(ex, rl)\n    tst:= \\sin{A_{m} A^{m} B_{n} B^{n}}**2 + \\cos{A_{m} A^{n} B_{n} B^{m}}**2 - @(ex);\n    assert(tst==0)\n    print(\"Test 03 passed\")\n\ntest03()\n"
  },
  {
    "path": "tests/unicode.cdb",
    "content": "\ndef test01():\n\nA{#}::Symmetric;\nex:= A_{α β};\nex:= A_{α β} - A_{β α};\nsubstitute(ex, $A_{a? b?} -> Ω_{a? b?}$);\n\n"
  },
  {
    "path": "tests/vary.cdb",
    "content": "\ndef test01():\n    __cdbkernel__=create_scope()\n    x^{\\mu}::Coordinate;\n    x::Coordinate;\n    #x::Implicit(x^{\\mu});\n    \\phi::Depends(x);\n    \\partial{#}::PartialDerivative;\n    ex:= \\int{ \\partial_{\\mu}{ \\epsilon^{\\mu} \\phi } }{x};\n    integrate_by_parts(ex, $\\epsilon^{\\mu}$)\n    assert(ex==0)\n    print('Test 01 passed')\n\ntest01()\n\ndef test02():\n    __cdbkernel__=create_scope()\n    \\partial{#}::PartialDerivative;\n    ex:= \\int{ \\partial_{\\mu}{ \\delta{\\phi} } \\phi \\chi }{x};\n    integrate_by_parts(ex, $\\epsilon$)\n    integrate_by_parts(ex, $\\delta{\\phi}$, repeat=True)\n    tst:= \\int{ \\delta{\\phi} \\partial_{\\mu}{  \\phi \\chi } }{x} + @(ex);\n    assert(tst==0)\n    print('Test 02 passed')\n    \ntest02()\n    \ndef test03():\n    __cdbkernel__=create_scope()\n    \\partial{#}::PartialDerivative;\n    ex:= \\int{ \\phi \\chi \\partial_{\\mu}{ \\delta{\\phi} } }{x};\n    integrate_by_parts(ex, $\\delta{\\phi}$)\n    tst:= \\int{ \\partial_{\\mu}{\\phi \\chi}  \\delta{\\phi} }{x} + @(ex);\n    assert(tst==0)\n    print('Test 03 passed')\n    \ntest03()\n    \ndef test04():\n    __cdbkernel__=create_scope()\n    \\partial{#}::PartialDerivative;\n    ex:= \\int{ \\phi \\chi \\partial_{\\mu}{ \\delta{\\phi} } + \\partial_{\\mu}{ \\delta{\\phi} } \\phi \\chi }{x};\n    integrate_by_parts(ex, $\\delta{\\phi}$)\n    tst:= \\int{ -\\partial_{\\mu}{ \\phi \\chi } \\delta{\\phi} - \\delta{\\phi} \\partial_{\\mu}{ \\phi \\chi } }{x} - @(ex);\n    assert(tst==0)\n    print('Test 04 passed')\n    \ntest04()\n\ndef test05():\n    __cdbkernel__=create_scope()\n    \\partial{#}::PartialDerivative;\n    ex:= \\int{ \\phi \\chi \\partial_{\\mu}{ \\delta{\\phi} } \\Phi \\Chi }{x};\n    integrate_by_parts(ex, $\\delta{\\phi}$)\n    tst:=\\int{ -\\partial_{\\mu}{ \\phi \\chi } \\delta{\\phi} \\Phi \\Chi - \\phi \\chi \\delta{\\phi} \\partial_{\\mu}{ \\Phi \\Chi} }{x} - @(ex);\n    assert(tst==0)\n    print('Test 05 passed')\n    \ntest05()\n\ndef test06():\n    __cdbkernel__=create_scope()\n    x::Coordinate;\n    \\phi::Depends(x);\n    \\delta{\\phi}::Depends(x);\n    \\partial{#}::PartialDerivative;\n    ex:= -1/2 \\int{m**2 \\phi**2}{x};\n    vary(_, $\\phi -> \\delta{\\phi}$)\n    tst:= - \\int{m**2 \\delta{\\phi}\\phi}{x} - @(ex);\n    assert(tst)\n    print('Test 06 passed')\n    \ntest06()\n\ndef test07():\n    __cdbkernel__=create_scope()\n    ex:= \\commutator{a}{b};\n    vary(_, $a -> \\delta{a}, b->\\delta{b}$)\n    tst:= \\commutator{\\delta{a}}{b} + \\commutator{a}{\\delta{b}} - @(ex);\n    assert(tst==0)\n    print(\"Test 07 passed\")\n\ntest07()\n\n# def test08():\n#     __cdbkernel__=create_scope()\n#     ex:= \\log(a);\n#     vary(_, $a -> \\delta{a}$)\n#     tst:= \\log(\\delta{a}) - @(ex);\n#     assert(tst==0)\n#\n# test08()\n\ndef test08():\n    __cdbkernel__=create_scope()\n    \\partial{#}::PartialDerivative;\n    ex:= \\int{ Q + R +  A \\partial{B} C }{x};\n    integrate_by_parts(_, $B$)\n    tst:= \\int{ Q + R - \\partial{A} B C - A B \\partial{C} }{x} - @(ex);\n    assert(tst==0)\n    print(\"Test 08 passed\")\n\ntest08()\n \ndef test09():\n    __cdbkernel__=create_scope()\n    \\partial{#}::PartialDerivative;\n    \\delta{#}::Accent;    \n    ex:= S = \\int{ Q + R +  A \\partial{B} C }{x};\n    vary(_, $S -> \\delta{S}, B -> b$)\n    tst:= (\\delta{S} = \\int{ A \\partial{b} C }{x}) - @(ex);\n    assert(tst==$0=0$)\n    print(\"Test 09 passed\")\n\ntest09()\n\ndef test10():\n    __cdbkernel__=create_scope()\n    ex:=x_{m};\n    vary(_, $x_{m} -> b_{m}$)\n    tst:=b_{m} - @(ex);        \n    assert(tst==0)\n    print(\"Test 10 passed\")\n\ntest10()\n        \ndef test11():\n    __cdbkernel__=create_scope()\n    \\partial{#}::Derivative;\n    ex:= A \\partial{A C + B} + D A;\n    vary(ex, $A->a, B->b, C->c, D->d$)\n    tst:= a\\partial{A C + B} + A\\partial{a C + A c + b} + d A + D a - @(ex);\n    assert(tst==0)\n    print(\"Test 11 passed\")\n\ntest11()\n\ndef test12():\n    __cdbkernel__=create_scope()\n    ex:= A/B + A B;\n    vary(ex, $A->a, B->b$)\n    tst:= a/B - A/B**2 b + a B + A b - @(ex);\n    assert(tst==0)\n    print(\"Test 12 passed\")\n\ntest12()\n\n# def test13():\n#     __cdbkernel__=create_scope()\n#     \\partial{#}::PartialDerivative;\n#     \\delta{#}::Accent;\n#     x::Coordinate;\n#     {A,B}::Depends(x);\n#     ex:=\\int{ \\sqrt{A \\partial_{x}{B} + B \\partial_{x}{C} } }{x};\n#     vary(ex, $B->b$);\n#     distribute(_);\n#     integrate_by_parts(_, $b$);\n#     map_sympy(_, \"simplify\");\n\n# \\partial{#}::PartialDerivative;\n# {\\mu,\\nu,\\rho}::Indices;\n# \\delta{#}::Accent;    \n# ex:=  \\int{ -1/2 g^{\\mu\\nu}\\partial_{\\mu}{\\phi} \\partial_{\\nu}{\\phi} + V(\\phi) }{x};\n# vary(ex, $\\phi-> \\delta{\\phi}$);\n\ndef test14():\n    __cdbkernel__=create_scope()\n    {\\mu,\\nu}::Indices(vector).\n    \\delta{#}::Accent.\n    \\Vt{#}::LaTeXForm(\"{\\tilde{V}}\").\n    ex:=\\int{\\Vt_{\\mu}\\Vt^{\\mu}}{x};\n    vary(_,$\\Vt_{\\mu}->\\delta{\\Vt_{\\mu}}$)\n    tst:= \\int{\\delta{\\Vt_{\\mu}} \\Vt^{\\mu} + \\Vt_{\\mu} \\delta{\\Vt^{\\mu}}}{x} - @(ex);\n    assert(tst==0)\n    print(\"Test 14 passed\")\n\ntest14()\n\ndef test15():        \n    __cdbkernel__=create_scope()\n    ex:=A;\n    vary(_, $A -> a$)\n    assert(ex==$a$)\n    print(\"Test 15a passed\")        \n    ex:=0;        \n    vary(_, $A -> a$)\n    assert(ex==0)\n    print(\"Test 15b passed\")\n\ntest15()\n"
  },
  {
    "path": "tests/working.cdb",
    "content": "\nex1=Ex(0)\nex2=Ex('0')\nex3=Ex('1')\nprint ex1==ex2\nprint ex2==ex3\nprint ex1==0\n\ndef defaults(ex):\n    collect_terms(ex)\n\n\ndef test():\n    {m,n,p,a,b}::AntiCommuting.\n    ex1:=p m n a;\n    sort_product(ex1);\n    print(ex1)\n    tst1:= - a m n p - @(ex1)\n    collect_terms(tst1)\n    if tst1==0:\n        print 'ex1 ok'\n    else:\n        print 'ex1 not ok'\n    ex2:= A_{m n} ( B_{m p}+C_{m p} );\n    distribute(ex2);\t\n    tst2:= A_{m n} B_{m p} + A_{m n} C_{m p} - @(ex2)\n    print(tst2)\n    map(defaults, [tst2])\n    if tst2==0:\n        print 'ex2 ok'\n    else:\n        print 'ex2 not ok'\n\ntest()\n\n# This does not see the property declared in test():\nex3:=p m n a;\nsort_product(ex3);\ntst3:= a m n p - @(ex3)\ncollect_terms(tst3)\nif tst3==0:\n    print 'ex3 ok'\nelse:\n    print 'ex3 not ok'\n\n\n# Test with scope, index relabelling and python calls.\n\n{m,n,p,q,r,s,t}::Indices.\n\ndef test(inex):\n    ex:= A_{m n} ( B_{m p}+C_{m p} ) @(inex)\n    distribute(ex);\n    repl:= B_{m p} -> K_{m n} K_{n p}\n    substitute(ex, repl)\n    return ex\n\nmyex:= D^{n q}\nprint test(myex)\n\n# Automatic renaming of dummies upon using @(...).\n#\n{m,n,p,q}::Indices.\nex := A_{m n} B_{m n};\nex2 := @(ex) @(ex);\ntst2 := A_{m n} B_{m n} A_{p q} B_{p q} - @(ex2);\ncollect_terms(tst2)\nassert(tst2==0)\n"
  },
  {
    "path": "tests/young.cdb",
    "content": "# Testing the young tableau routines by determining the projection\n# of the square of a four-component tensor onto the 2x4 tableau.\n\ndef test01():\n    __cdbkernel__=create_scope()\n    W_{a b c d}::WeylTensor.\n    WWa:= W_{r1 r2 s1 s2} W_{r3 r4 s3 s4};\n    WWb:= 16/5*@(WWa):\n    # Note: the 16/5 normalisation was computed separately.\n    # The direct route:\n    young_project(WWa, shape=[2,2,2,2], indices=[0,2,1,3,4,6,5,7])\n    indexsort(WWa)\n    order(WWa, $_{r1},_{r2},_{r3},_{r4}$, anticommuting=True)\n    order(WWa, $_{s1},_{s2},_{s3},_{s4}$, anticommuting=True)\n    # Doing it by hand:\n    sym(WWb, $_{r1},_{s1}$)\n    sym(WWb, $_{r2},_{s2}$)\n    sym(WWb, $_{r3},_{s3}$)\n    sym(WWb, $_{r4},_{s4}$)\n    asym(WWb, $_{r1},_{r2},_{r3},_{r4}$)\n    asym(WWb, $_{s1},_{s2},_{s3},_{s4}$)\n    indexsort(WWb)\n    order(WWb, $_{r1},_{r2},_{r3},_{r4}$, anticommuting=True)\n    order(WWb, $_{s1},_{s2},_{s3},_{s4}$, anticommuting=True)\n    tst1:= @(WWa)-@(WWb);\n    assert(tst1==0)\n    print('Test 01 passed')\n\ntest01()\n\n# Test 27: The example from the paper with Michael and Christian:\n#\n\ndef test27():\n    __cdbkernel__=create_scope()\n    R_{m n p q}::RiemannTensor.\n    {m,n,p,q,r,s,t,u}::Indices(vector).\n    term1:= R_{m n p q} R_{m n p q};\n    young_project_tensor(_)\n    distribute(_)\n    canonicalise(_)\n    term2:= R_{m n p q} R_{m p n q};\n    young_project_tensor(_)\n    distribute(_)\n    canonicalise(_)\n    tst27:= 2*@(term2) - @(term1);\n    assert(tst27==0)\n    print('Test 27 passed')\n\ntest27()\n\n# Test 27b: The same as above, but now using young_project_product.\n\ndef test27b():\n    __cdbkernel__=create_scope()\n    R_{m n p q}::RiemannTensor.\n    {m,n,p,q,r,s,t,u}::Indices(vector).\n    term1:= R_{m n p q} R_{m n p q};\n    young_project_product(_)\n    term2:= R_{m n p q} R_{m p n q};\n    young_project_product(_)\n    tst27b:= 2*@(term2) - @(term1);\n    assert(tst27b==0)\n    print('Test 27b passed')\n\ntest27b()\n\n# Test 28: Simple Bianchi.\n\ndef test28():\n    __cdbkernel__=create_scope()\n    {m,n,p,q,r,s,t#}::Indices(vector).\n    \\nabla{#}::Derivative.\n    R_{m n p q}::RiemannTensor.\n    \\nabla_{m}{R_{p q r s}}::SatisfiesBianchi.\n    obj28:= \\nabla_{m}{R_{p q r s}} + \\nabla_{p}{R_{q m r s}} + \\nabla_{q}{R_{m p r s}}:\n    young_project_tensor(_, deep=False, depth=1)\n    assert(obj28==0)\n    print('Test 28 passed')\n\ntest28()\n\n# Test 30: SatisfiesBianchi\n#\n\n# {r,m,n,p,q,s,k,j}::Indices(vector).\n# dC_{r m n p q}::TableauSymmetry(shape={3,2}, indices={1,3,0,2,4}).\n# C_{m n p q}::WeylTensor.\n# \\nabla{#}::Derivative.\n# \\nabla_{r}{ C_{m n p q} }::SatisfiesBianchi.\n# \n# pl1:= dC_{r m n p q};\n# young_project_tensor(_)\n# pl2:= \\nabla_{s}{\\nabla_{r}{C_{m n p q}}};\n# young_project_tensor(_, depth=1)\n# \n# rl:=dC_{r m n p q} -> \\nabla_{s}{\\nabla_{r}{C_{m n p q}}};\n# substitute(pl1, rl)\n# tst:= @(pl1) - @(pl2);\n# @collect_terms!(%);\n# @assert(tst);\n# \n\ndef test29():\n    __cdbkernel__=create_scope()\n    R_{m n p q}::RiemannTensor.\n    {m,n,p,q,r,s,t,u}::Indices(vector).\n    term1:= R_{m n p q} R_{m n p q};\n    young_project_tensor(_, modulo_monoterm=True)\n    distribute(_)\n    term2:= R_{m n p q} R_{m p n q};\n    young_project_tensor(_, modulo_monoterm=True)\n    distribute(_)\n    tst:= 2*@(term2) - @(term1);\n    canonicalise(_)\n    assert(tst==0)\n    print('Test 29 passed')\n\ntest29()\n\n# The 8x8 tensor product in Young tableaux.\n#\ndef test30():\n    \\tableau{#}::Tableau(dimension=3);\n    \\ftableau{#}::FilledTableau(dimension=3);\n    ex:=\\tableau{2}{1}\\tableau{2}{1};\n    lr_tensor(_)\n    q=[int(tab_dimension(t.ex())) for t in ex.top().terms()]\n    assert(q==[27,10,10,16,1])\n    print(\"Test 30a passed\")\n    ex:=\\ftableau{c,c}{c}\\ftableau{a,a}{b};\n    lr_tensor(_)\n    q=[int(tab_dimension(t.ex())) for t in ex.top().terms()]\n    assert(q==[27,10,10,8,8,1])\n    print(\"Test 30b passed\")\n\ntest30()\n    \n# def test30():\n# \\tableau{#}::Tableau(dimension=10);\n# ex:=\\tableau{2}{2}\\tableau{2}{2} \\tableau{2};\n# converge(ex):\n#     lr_tensor(ex)\n#     distribute(ex)\n# \n# q=[]\n# p=[]\n# for t in ex.top().terms():\n#     p.append(t.ex())\n#     q.append(int(tab_dimension(t.ex())))\n# \n#     \n# assert(q==[\n\n\n\n    \n"
  },
  {
    "path": "tests/yrtrace.cdb",
    "content": "#!/usr/local/bin/cadabra2\n\nfrom cdb.utils.develop import test_algo\n\n\n@test_algo($2 * Tr{A B C D}$)\ndef test01():\n\tTr{#}::Trace.\n\t{A, B, C, D}::NonCommuting.\n\tex := Tr{A B C D + C D A B + B C D A} - Tr{D A B C}.\n\treturn young_reduce_trace(ex)\ntest01()\n\n@test_algo($3 * tr(a^{\\mu} b^{\\nu} c^{\\rho} a^{\\mu} b^{\\rho} c^{\\nu}$)\ndef test02():\n\t{\\mu,\\nu,\\rho}::Indices(vector).\n\t{a^{\\mu},b^{\\mu},c^{\\mu}}::NonCommuting.\n\ttr{#}::Trace.\n\tex := tr(a^{\\mu} b^{\\nu} c^{\\rho} a^{\\mu} b^{\\rho} c^{\\nu} + \n              b^{\\mu} c^{\\nu} a^{\\rho} b^{\\nu} c^{\\mu} a^{\\rho} + \n              c^{\\mu} a^{\\nu} b^{\\mu} c^{\\rho} a^{\\nu} b^{\\rho}).\n\treturn young_reduce_trace(ex)\ntest02()\n\n@test_algo($0$)\ndef test03():\n\t{\\mu,\\nu}::Indices(vector).\n\tu^{\\mu}::ImplicitIndex.\n\tu^{\\mu}::SelfNonCommuting.\n\ttr{#}::Trace.\n\tex := tr{u^{\\mu} u^{\\mu} u^{\\nu} u^{\\nu}} - \n\t      tr{u^{\\mu} u^{\\nu} u^{\\nu} u^{\\mu}}.\n\treturn young_reduce_trace(ex)\ntest03()\n"
  },
  {
    "path": "tutorials/01_basics.py",
    "content": "#!/usr/bin/env python3\n\nfrom cdb.remote           import *\nfrom cdb.remote.speech    import init, say, warp\nfrom cdb.remote.highlight import init_highlight, mark, subtitle\nfrom cdb.remote.record    import *\nimport sys\n\nif len(sys.argv)<2:\n    print(\"Usage: 01_basics.py [OBS password]\", file=sys.stderr)\n    sys.exit(-1)\n\npassword = sys.argv[1]    \n\ntry:\n   init()\n   \n   cdb = CadabraRemote()\n   cdb.start([\"--geometry\", \"1920x1080\", \"--title\", \"Cadabra tutorial 1\"])\n   time.sleep(1)\n   \n   setup_region_capture(\"Cadabra tutorial 1\", password)\n   start_record()\n   \n   init_highlight(\"Cadabra tutorial 1\")\n   \n   #warp(True)\n   subtitle(\"Tutorial 1: the basics of Cadabra\", large=True)\n   time.sleep(4)\n   subtitle()\n\n   cdb.insert_text(\"ex:= \\cos(x)**2 + \\sin(x)**2;\")\n   \n   say(\"In this tutorial, you will learn the basics of the Cadabra computer-algebra system.\")\n   say(\"You will get a flavour of how you can setup computations with it, and how you can manipulate maths expressions.\")\n   say(\"After you start it, you are presented with the notebook interface as you see here.\", block=True)\n   time.sleep(1)\n   say(\"The top of the screen has the menu bar and some control buttons.\", block=True)\n   time.sleep(0.5)\n   mark(\"Open\")\n   time.sleep(0.5)\n   mark()\n   mark(\"Save\")\n   time.sleep(0.5)\n   mark()\n   mark(\"Save as\")\n   time.sleep(0.5)\n   mark()\n   mark(\"Run\")\n   time.sleep(0.5)\n   mark()\n   mark(\"Stop\")\n   time.sleep(0.5)\n   mark()\n   mark(\"Restart kernel\")\n   time.sleep(0.5)\n   mark()\n   \n   subtitle()\n   time.sleep(1)\n   say(\"The bottom of the screen shows status information.\", block=True)\n   time.sleep(1)\n   subtitle()\n   time.sleep(1)\n   say(\"Finally, the blank canvas in the middle is where our computations will go. Right now, it has a single empty cell.\", block=True)\n   time.sleep(0.5)\n   subtitle()\n   time.sleep(1)\n   \n   say(\"Let's add a maths expression in this first cell.\", block=True)\n   time.sleep(1)\n   subtitle()\n   time.sleep(1)\n   cell_id = cdb.add_cell(r\"ex := x \\cos(x);\")\n   time.sleep(2)\n   \n   say(\"Mathematical expressions are entered using the colon-equals notation.\",\n       subtext=\"Mathematical expressions are entered using the ':=' notation.\")\n   say(\"The left-hand side is the 'name' of the expression.\")\n   say(\"The right-hand side is 'maths', and written using lay tech-notation.\",\n       subtext=\"The right-hand side is maths, and written using LaTeX notation.\", block=True)\n   say(\"You do not need to 'declare' variables in maths expressions; just write them.\", block=True)\n   say(\"If you end the expression with a semi-colon, like here, it will be displayed.\", block=True)\n   \n   mark(\"Run\")\n   say(\"You can run the whole notebook using the 'run' button, or run a single cell by pressing shift-enter.\", block=True)\n   time.sleep(1)\n   cdb.run_all_cells()\n   mark()\n   \n   say(\"This will show the expression properly typeset.\")\n   say(\"You can manipulate it by using a wide variety of 'algorithms'.\", block=True)\n   \n   cell_id = cdb.add_cell(r\"substitute( ex, $x -> 2 y + \\pi$ );\")\n   say(\"Here we are replacing the 'x' variable with '2 y plus pi'.\")\n   #warp(False)\n   say(\"Note how we used an 'inline' maths expression, using laytech dollar notation.\",\n       subtext=\"Note how we used an 'inline' maths expression, using LaTeX dollar notation.\", block=True)\n   cdb.run_cell(cell_id)\n   say(\"Again, the semi-colon at the end has resulted in Cadabra displaying the result.\", block=True);\n   #warp()\n   subtitle()\n\n   time.sleep(1)\n   say(\"You will notice that Cadabra has only done the substitution.\", block=True)\n   say(\"In general, Cadabra behaves as a scratch pad: it does not try to be clever about rewriting expressions, unless you tell it to.\", block=True)\n   say(\"Of course, we can for instance tell it to distribute the product.\", block=True)\n   cell_id = cdb.add_cell(\"distribute( ex );\")\n   \n#    time.sleep(2)\n#    say(\"You can plot expressions like these, by importing the plotting functionality from a package.\", block=True)\n#    time.sleep(2)\n#    cdb.add_cell(\"from cdb.graphics.plot import *\\nplot(ex, ($y$,0,10));\");\n#    time.sleep(2)\n#    subtitle()\n#    cdb.run_all_cells()\n#    time.sleep(2)\n#    say(\"Documentation for all packages is available from the web site.\", block=True)\n#    time.sleep(2)\n\n   \n\n   subtitle()\n   mark()\n   \n   stop_record()\n   cdb.wait()\n\nexcept Exception as ex:\n   print(f\"Error: {ex}\")\n   cdb.process.terminate()\n\n"
  },
  {
    "path": "vcpkg.json",
    "content": "{\n\t\"dependencies\": [\n\t\t\"mpir\",\n\t\t\"glibmm\",\n\t\t\"gtkmm\",\n\t\t\"boost-system\",\n\t\t\"boost-asio\",\n\t\t\"boost-uuid\",\n\t\t\"boost-program-options\",\n\t\t\"boost-signals2\",\n\t\t\"boost-property-tree\",\n\t\t\"boost-date-time\",\n\t\t\"boost-filesystem\",\n\t\t\"boost-ublas\"\n\t],\n\t\"overrides\":  [\n\t\t{ \"name\": \"atk\", \"version-string\": \"2.24.0-5\", \"port-version\": 2 },\n\t\t{ \"name\": \"atkmm\", \"version-string\": \"2.24.2\", \"port-version\": 5 },\n\t\t{ \"name\": \"cairo\", \"version-string\": \"1.16.0\", \"port-version\": 10 },\n\t\t{ \"name\": \"cairomm\", \"version-string\": \"1.15.3\", \"port-version\": 6 },\n\t\t{ \"name\": \"gdk-pixbuf\", \"version-string\": \"2.36.9-5\", \"port-version\": 7 },\n\t\t{ \"name\": \"glib\", \"version-string\": \"2.52.3\", \"port-version\": 27 },\n\t\t{ \"name\": \"glibmm\", \"version-string\": \"2.52.1\", \"port-version\": 14 },\n\t\t{ \"name\": \"gtk\", \"version-string\": \"3.22.19-4\", \"port-version\": 0 },\n\t\t{ \"name\": \"gtkmm\", \"version-string\": \"3.22.2\", \"port-version\": 5 },\n\t\t{ \"name\": \"harfbuzz\", \"version-string\": \"2.7.4\", \"port-version\": 1 },\n\t\t{ \"name\": \"libsigcpp\", \"version-string\": \"2.10-3\", \"port-version\": 2 },\n\t\t{ \"name\": \"pango\", \"version-string\": \"1.40.11\", \"port-version\": 9 },\n\t\t{ \"name\": \"pangomm\", \"version-string\": \"2.40.1\", \"port-version\": 4 },\n\t\t{ \"name\": \"pixman\", \"version-string\": \"0.38.4\", \"port-version\": 2 },\n\t\t{ \"name\": \"tool-meson\", \"version-string\": \"0.56.02\", \"port-version\": 0 }\n\t],\n\t\"builtin-baseline\": \"3508985146f1b1d248c67ead13f8f54be5b4f5da\"\n}\n"
  },
  {
    "path": "web2/CMakeLists.txt",
    "content": "print_header(\"Configuring documentation\")\n\nset(HTMLOUTDIR ${CMAKE_SOURCE_DIR}/web2/cadabra2/source/notebooks)\nset(BOOKOUTDIR ${CMAKE_BINARY_DIR}/book)\nset(TOCOUTDIR  ${CMAKE_SOURCE_DIR}/web2/cadabra2/source/)\nset(MANOUTDIR  ${CMAKE_SOURCE_DIR}/web2/cadabra2/source/manual)\nset(CNBDIR     ${CMAKE_SOURCE_DIR}/examples)\nset(CONTRIBDIR ${CMAKE_SOURCE_DIR}/contrib)\nset(ALGODIR    ${CMAKE_SOURCE_DIR}/core/algorithms)\nset(PROPDIR    ${CMAKE_SOURCE_DIR}/core/properties)\nset(PACKAGEDIR ${CMAKE_SOURCE_DIR}/core/packages)\nset(DC         ${CMAKE_SOURCE_DIR}/client_server/cadabra2html.cc ${CMAKE_SOURCE_DIR}/core/DataCell.hh ${CMAKE_SOURCE_DIR}/core/DataCell.cc)\n\n\n# Sample/tutorial notebooks.\n\nset(TUTORIALS\n  quickstart\n  beginners\n  tensor_monomials\n  for_previous_users\n  converge\n  fierz\n  gamma_matrix_algebra\n  poincare_algebra\n  string_states\n  bianchi_identities\n  sphere\n  schwarzschild\n  exterior\n  kaluza_klein\n  plotting\n  scalar_manipulations\n\n  input_format\n  ref_printing\n  ref_patterns\n  ref_numerical\n  ref_ndsolve\n  ref_properties\n  ref_indices\n  ref_derivatives\n  ref_default_simplification\n  ref_programming\n  ref_sympy\n  ref_kernel\n  ref_dynamical_updates\n  ref_plotting\n  ref_import\n  ref_exponents\n  ref_spacing\n  ref_implicit_versus_explicit\n  ref_indexbrackets\n  ref_accents\n  ref_ordering\n  ref_selecting\n  ref_c++_library\n  ref_flags_variables\n  )\n\n# The Book\nset(BOOK_PARTS\n   input_format\n   ref_printing\n   ref_patterns\n   ref_numerical\n   ref_ndsolve\n   ref_properties\n   ref_indices\n   ref_derivatives\n   ref_default_simplification\n   ref_programming\n   ref_sympy\n   ref_kernel\n   ref_dynamical_updates\n   ref_plotting\n   ref_import\n   ref_exponents\n   ref_spacing\n   ref_implicit_versus_explicit\n   ref_indexbrackets\n   ref_accents\n   ref_ordering\n   ref_selecting\n   ref_c++_library\n   ref_flags_variables\n)   \n\n# 3rd party contributions\n\nset(CONTRIBS\n  einstein_equations\n  structure_equations_and_bianchi\n  )\n\n# Manual pages; just add the algorithm or property name to the lists below\n# and the rest will be taken care of automatically.\n\nset(ALGOS\n  asym\n  slot_asym\n  canonicalise\n  collect_factors\n  collect_terms\n  combine\n  complete\n  decompose\n  decompose_product\n  distribute\n  drop_weight\n  einsteinify\n  eliminate_kronecker\n  eliminate_metric\n  eliminate_vielbein  \n  epsilon_to_delta\n  evaluate\n  expand\n  expand_delta\n  expand_diracbar\n  expand_power\n  explicit_indices\n  factor_in\n  factor_out\n  fierz\n  integrate_by_parts\n  join_gamma\n  keep_weight\n  lower_free_indices\n  lr_tensor\n  map_sympy\n  meld\n  ndsolve\n  nevaluate\n  nval\n  product_rule\n  raise_free_indices\n  reduce_delta\n  rename_dummies\n  replace_match\n  rewrite_indices\n  simplify\n  sort_product\n  sort_spinors\n  sort_sum\n  split_gamma\n  split_index\n  substitute\n  take_match\n  untrace\n  unwrap\n  vary\n  young_project_product\n  young_project_tensor\n  zoom\n)\nset(PROPS\n  Accent\n  AntiCommuting\n  AntiSymmetric\n  CommutingAsProduct\n  CommutingAsSum\n  Commuting\n  Coordinate\n  DAntiSymmetric\n  Depends\n  Derivative\n  Determinant\n  Diagonal\n  DiracBar\n  Distributable\n  EpsilonTensor\n  FilledTableau\n  GammaMatrix\n  ImplicitIndex\n  IndexInherit\n  Indices\n  Integer\n  InverseMetric\n  KroneckerDelta\n  LaTeXForm\n  Metric\n  NonCommuting\n  PartialDerivative\n  RiemannTensor\n  SatisfiesBianchi\n  SelfAntiCommuting\n  SelfCommuting\n  SelfNonCommuting\n  SortOrder\n  Spinor\n  Symbol\n  Symmetric\n  Tableau\n  TableauSymmetry\n  Weight\n  WeightInherit\n)\n\n# Packages\n\nset(PACKAGES\n  cdb/core/manip\n  cdb/core/component\n  cdb/core/trace\n  cdb/utils/develop\n  cdb/utils/indices\n  cdb/utils/node  \n  cdb/utils/types    \n  cdb/sympy/solvers\n  cdb/sympy/calculus\n  cdb/relativity/abstract\n  cdb/relativity/schwarzschild\n  cdb/numeric/evaluate\n#  cdb/numeric/integrate\n  cdb/graphics/plot\n  )\n\n# Table of contents\n\nset(SCAN ${CMAKE_SOURCE_DIR}/web2/scan.py)\n\nadd_custom_target(algo_toc ALL \n                  COMMAND ${SCAN} ${ALGODIR} ${ALGOS} > ${TOCOUTDIR}/algo_toc.html\n                  COMMENT \"Creating algorithms table-of-contents...\")\nadd_custom_target(prop_toc ALL \n                  COMMAND ${SCAN} ${PROPDIR} ${PROPS} > ${TOCOUTDIR}/prop_toc.html\n                  COMMENT \"Creating properties table-of-contents...\")\nadd_custom_target(package_toc ALL \n                  COMMAND ${SCAN} ${PACKAGEDIR} ${PACKAGES} > ${TOCOUTDIR}/packages_toc.html\n                  COMMENT \"Creating packages table-of-contents...\")\n\nforeach(ALGO ${ALGOS})\n   add_custom_command(OUTPUT  ${MANOUTDIR}/${ALGO}.html\n\t                   DEPENDS ${ALGODIR}/${ALGO}.cnb ${DC}\n                      COMMAND ${CMAKE_INSTALL_PREFIX}/bin/cadabra2html\n                      ARGS    --segment ${ALGODIR}/${ALGO}.cnb ${MANOUTDIR}/${ALGO}.html\n                      COMMENT \"Creating ${ALGO} manual page...\")\n   add_custom_target(\"${ALGO}_manual\" ALL echo -n DEPENDS ${MANOUTDIR}/${ALGO}.html)\nendforeach()\n\nforeach(PROP ${PROPS})\n   add_custom_command(OUTPUT  ${MANOUTDIR}/${PROP}.html\n\t                   DEPENDS ${PROPDIR}/${PROP}.cnb ${DC}\n                      COMMAND ${CMAKE_INSTALL_PREFIX}/bin/cadabra2html\n                      ARGS    --segment ${PROPDIR}/${PROP}.cnb ${MANOUTDIR}/${PROP}.html\n                      COMMENT \"Creating ${PROP} manual page...\")\n   add_custom_target(\"${PROP}_manual\" ALL echo -n DEPENDS ${MANOUTDIR}/${PROP}.html)\nendforeach()\n\nforeach(PACKAGE ${PACKAGES})\n   get_filename_component(THISDESTPATH ${MANOUTDIR}/${PACKAGE}.html DIRECTORY)\n   file(MAKE_DIRECTORY ${THISDESTPATH})\n   add_custom_command(OUTPUT  ${MANOUTDIR}/${PACKAGE}.html\n\t                   DEPENDS ${PACKAGEDIR}/${PACKAGE}.cnb ${DC}\n                      COMMAND ${CMAKE_INSTALL_PREFIX}/bin/cadabra2html\n                      ARGS    --segment --strip-code ${PACKAGEDIR}/${PACKAGE}.cnb ${MANOUTDIR}/${PACKAGE}.html\n                      COMMENT \"Creating ${PACKAGE} manual page...\")\n\tstring(REPLACE \"/\" \"_\" MANGLED ${PACKAGE})\n   add_custom_target(\"${MANGLED}_manual\" ALL echo -n DEPENDS ${MANOUTDIR}/${PACKAGE}.html)\nendforeach()\n\nforeach(TUT ${TUTORIALS})\n  add_custom_command(OUTPUT  ${HTMLOUTDIR}/${TUT}.html\n                     DEPENDS ${CNBDIR}/${TUT}.cnb ${DC}\n                     COMMAND ${CMAKE_INSTALL_PREFIX}/bin/cadabra2html \n                     ARGS    --segment ${CNBDIR}/${TUT}.cnb ${HTMLOUTDIR}/${TUT}.html \n                     COMMENT \"Creating ${TUT}.html\")\n  add_custom_target(\"${TUT}_html\" ALL echo -n DEPENDS ${HTMLOUTDIR}/${TUT}.html)\t\t\n  add_custom_command(OUTPUT  ${HTMLOUTDIR}/${TUT}.cnb\n                     DEPENDS ${CNBDIR}/${TUT}.cnb \n                     COMMAND cp\n                     ARGS    ${CNBDIR}/${TUT}.cnb ${HTMLOUTDIR}/${TUT}.cnb\n                     COMMENT \"Creating ${TUT}.cnb\")\n  add_custom_target(\"${TUT}_cnb\" ALL echo -n DEPENDS ${HTMLOUTDIR}/${TUT}.html ${HTMLOUTDIR}/${TUT}.cnb )\t\t\nendforeach()\n\nforeach(TUT ${CONTRIBS})\n  add_custom_command(OUTPUT  ${HTMLOUTDIR}/${TUT}.html\n                     DEPENDS ${CONTRIBDIR}/${TUT}.cnb ${DC}\n                     COMMAND ${CMAKE_INSTALL_PREFIX}/bin/cadabra2html \n                     ARGS    --segment ${CONTRIBDIR}/${TUT}.cnb ${HTMLOUTDIR}/${TUT}.html \n                     COMMENT \"Creating ${TUT}.html\")\n  add_custom_target(\"${TUT}_html\" ALL echo -n DEPENDS ${HTMLOUTDIR}/${TUT}.html)\t\t\n  add_custom_command(OUTPUT  ${HTMLOUTDIR}/${TUT}.cnb\n                     DEPENDS ${CONTRIBDIR}/${TUT}.cnb \n                     COMMAND cp\n                     ARGS    ${CONTRIBDIR}/${TUT}.cnb ${HTMLOUTDIR}/${TUT}.cnb\n                     COMMENT \"Creating ${TUT}.cnb\")\n  add_custom_target(\"${TUT}_cnb\" ALL echo -n DEPENDS ${HTMLOUTDIR}/${TUT}.html ${HTMLOUTDIR}/${TUT}.cnb )\t\t\nendforeach()\n\nfile(MAKE_DIRECTORY ${BOOKOUTDIR})\n\n# The Cadabra Book.\n\nforeach(BOOK_PART ${BOOK_PARTS})\n#   message(STATUS \"Found book section ${BOOK_PART}\")\n   set(ALLTEX ${ALLTEX} ${BOOKOUTDIR}/${BOOK_PART}.tex)\n   add_custom_command(\n      OUTPUT   ${BOOKOUTDIR}/${BOOK_PART}.tex\n      DEPENDS  ${CNBDIR}/${BOOK_PART}.cnb ${DC}\n      COMMAND  ${CMAKE_INSTALL_PREFIX}/bin/cadabra2latex\n      ARGS    --segment ${CNBDIR}/${BOOK_PART}.cnb ${BOOKOUTDIR}/${BOOK_PART}.tex\n      COMMENT \"Creating ${BOOK_PART}.tex\")\n   add_custom_target(\"${BOOK_PART}\" ALL echo -n DEPENDS ${BOOKOUTDIR}/${BOOK_PART}.tex)\nendforeach()\nforeach(ALGO_PART ${ALGOS})\n#   message(STATUS \"Found book algorithm section ${ALGO_PART}\")\n   set(ALLTEX ${ALLTEX} ${BOOKOUTDIR}/${ALGO_PART}.tex)\n   add_custom_command(\n      OUTPUT   ${BOOKOUTDIR}/${ALGO_PART}.tex\n      DEPENDS  ${ALGODIR}/${ALGO_PART}.cnb ${DC}\n      COMMAND  ${CMAKE_INSTALL_PREFIX}/bin/cadabra2latex\n      ARGS    --segment ${ALGODIR}/${ALGO_PART}.cnb ${BOOKOUTDIR}/${ALGO_PART}.tex\n      COMMENT \"Creating ${ALGO_PART}.tex\")\n   add_custom_target(\"${ALGO_PART}\" ALL echo -n DEPENDS ${BOOKOUTDIR}/${ALGO_PART}.tex)\nendforeach()\nmessage(STATUS \"Book will be created in ${BOOKOUTDIR}\")\nadd_custom_command(\n   OUTPUT   ${BOOKOUTDIR}/the_cadabra_book.pdf\n   DEPENDS  ${CMAKE_SOURCE_DIR}/doc/the_cadabra_book.tex\n            ${CMAKE_SOURCE_DIR}/doc/book_cover.pdf \n            ${CMAKE_SOURCE_DIR}/doc/the_cadabra_book.bib ${ALLTEX}   \n   COMMAND  cp\n   ARGS     ${CMAKE_SOURCE_DIR}/doc/the_cadabra_book.tex\n            ${CMAKE_SOURCE_DIR}/doc/the_cadabra_book.bib\n            ${BOOKOUTDIR}/\n   COMMAND  cp\n   ARGS     ${CMAKE_SOURCE_DIR}/doc/book_cover.pdf ${BOOKOUTDIR}/\n   COMMAND  pdflatex\n   ARGS     the_cadabra_book.tex\n   COMMAND  biber\n   ARGS     the_cadabra_book\n   COMMAND  pdflatex\n   ARGS     the_cadabra_book.tex\n   COMMAND  pdflatex\n   ARGS     the_cadabra_book.tex\n   COMMAND  cp\n   ARGS     the_cadabra_book.pdf ${CMAKE_SOURCE_DIR}/web2/cadabra2/source\n   WORKING_DIRECTORY ${BOOKOUTDIR}\n   COMMENT  \"Creating the_cadabra_book.pdf\")\nadd_custom_target(book ALL echo -n DEPENDS ${BOOKOUTDIR}/the_cadabra_book.pdf)\n\nadd_custom_command(\n   OUTPUT   ${BOOKOUTDIR}/writing_algorithms.pdf\n   DEPENDS  ${CMAKE_SOURCE_DIR}/doc/writing_algorithms.tex\n   COMMAND  cp\n   ARGS     ${CMAKE_SOURCE_DIR}/doc/writing_algorithms.tex\n            ${CMAKE_SOURCE_DIR}/doc/autogobble.sty\n            ${BOOKOUTDIR}/\n   COMMAND  pdflatex\n   ARGS     writing_algorithms.tex\n   COMMAND  pdflatex\n   ARGS     writing_algorithms.tex\n   COMMAND  cp\n   ARGS     writing_algorithms.pdf ${CMAKE_SOURCE_DIR}/web2/cadabra2/source\n   WORKING_DIRECTORY ${BOOKOUTDIR}\n   COMMENT  \"Creating writing_algorithms.pdf\")\nadd_custom_target(writing ALL echo -n DEPENDS ${BOOKOUTDIR}/writing_algorithms.pdf)\n\nadd_custom_command(\n   OUTPUT   ${BOOKOUTDIR}/cadabra2_hep.pdf\n   DEPENDS  ${CMAKE_SOURCE_DIR}/doc/cadabra2_hep.tex\n   COMMAND  cp\n   ARGS     ${CMAKE_SOURCE_DIR}/doc/cadabra2_hep.tex\n            ${CMAKE_SOURCE_DIR}/doc/tableaux.sty\n            ${BOOKOUTDIR}/\n   COMMAND  pdflatex\n   ARGS     cadabra2_hep.tex\n   COMMAND  pdflatex\n   ARGS     cadabra2_hep.tex\n   COMMAND  cp\n   ARGS     cadabra2_hep.pdf ${CMAKE_SOURCE_DIR}/web2/cadabra2/source\n   WORKING_DIRECTORY ${BOOKOUTDIR}\n   COMMENT  \"Creating cadabra2_hep.pdf\")\nadd_custom_target(hep_paper ALL echo -n DEPENDS ${BOOKOUTDIR}/cadabra2_hep.pdf)\n"
  },
  {
    "path": "web2/README.txt",
    "content": "The static version of the Cadabra web site is located in\nthe \n\n   cadabra2/build\n\ndirectory. This web site is built using 'Clay', available from\n\n   http://lucuma.github.io/Clay/\n\nand installable with\n\n   pip install clay\n\nYou also need\n\n   sudo apt install doxygen\n\nClay builds the static site from the template files in\ncadabra2/source. To do this, \n\n   cd cadabra2\n   clay build \n\nor use the built-in web server which does this on-the-fly,\n\n   cd cadabra2\n   clay run\n\n\n"
  },
  {
    "path": "web2/cadabra2/.gitignore",
    "content": "# See http://help.github.com/ignore-files/ for more about ignoring files.\n#\n# If you find yourself ignoring temporary files generated by your text editor\n# or operating system, you probably want to add a global ignore instead:\n#   git config --global core.excludesfile ~/.gitignore_global\n\n~*\n*.py[co]\n.DS_Store\n.webassets-cache\nalgo_toc.html\nprop_toc.html\npackages_toc.html\nsource/the_cadabra_book.pdf\nsource/writing_algorithms.pdf\n"
  },
  {
    "path": "web2/cadabra2/robots.txt",
    "content": "User-agent: *\nDisallow:\n"
  },
  {
    "path": "web2/cadabra2/source/blog.html",
    "content": "{% extends \"layout.html\" %}\n\n{% block title %}Cadabra: blog{% endblock %}\n\n{% block head %}{%- endblock %}\n\n{% block main %}\n\n<h1>Cadabra blog</h1>\n<p>A random collection of noteworthy things related to computer\n  algebra and scientific software development...</p>\n\n<h2 class=\"blog\">Why we should give credit to code creators</h2>\n<p class=\"blog\">\n  From \"Physics World\": With software development becoming ever more\n  important in physics research, Arfon Smith argues that we need to\n  adopt better ways of recognizing those who contribute to this\n  largely unrewarded\n  activity. <a href=\"http://physicsworld.com/cws/article/indepth/2017/mar/09/why-we-should-give-credit-to-code-creators\">Read\n  more</a>.\n</p>\n\n{%- endblock %}\n\n"
  },
  {
    "path": "web2/cadabra2/source/changelog.html",
    "content": "{% extends \"layout.html\" %}\n\n{% block title %}Cadabra: change log{% endblock %}\n\n{% block head %}{%- endblock %}\n\n{% block main %}\n\n<h1>Change log</h1>\n<p>\n  The list below gives a human-readable overview of the changes from\n  one version to the next. For details of precisely what is changed at\n  the code level, consult\n  the <a href=\"http://github.com/kpeeters/cadabra2\">github\n  repository</a>. Odd patch levels correspond to versions in\n  development which you can only get by building from source, while\n  even-numbered ones are released in packaged/installer form.\n</p>\n<a name=\"devel\"></a>\n<h3>github devel branch (2.5.15)</h3>\n<ul>\n  <li>New \"restart kernel and run entire notebook\" button.</li>\n</ul>\n\n<a name=\"2.5.14\"></a>\n<h3>2.5.14 (released 31-Jul-2025)</h3>\n<ul>\n  <li>TeXmacs is supported again, including plotting (put\n    the <tt>config/init-cadabra2.scm</tt> file in the appropriate\n    location).</li>\n  <li>Plotting is now supported again by the Jupyter kernel.</li>\n  <li>Support for plotting in Kitty and iTerm2 terminals.</li>\n  <li>Group equal components when displaying component values of tensors.</li>\n  <li>Internal: some operations now use multiple threads (work in progress).</li>\n  <li>Internal: use a pool allocator for tree nodes.</li>\n  <li>Internal: speedup in handling of <tt>Multiplier</tt> (test suite speedup by 1.5x).</li>\n  <li>Docs: add <tt>SympyBridge</tt> docs.</li>\n  <li>Fix bug when subtracting two <tt>component</tt> expressions.</li>\n  <li>Fix bug with <tt>NTensor</tt> broadcasting from scalar.</li>\n  <li>Fix <tt>cadabra2-cli</tt> argument handling.</li>\n  <li>Fix handling of code blocks in <tt>cadabra2-cli</tt>, making it consistent with the notebook.</li>\n  <li>Stability improvement to the SymPy bridge by walking the SymPy AST directly instead of parsing printed output.</li>\n  <li>Make Homebrew package provide a working Jupyter kernel too.</li>\n  <li>Made <tt>\\iu</tt> the imaginary unit, by default displaying as $i$.</li>\n  <li>AppImages are back, on both x86_64 and arm64.</li>\n  <li>Fix loading <tt>cadabra2_defaults.py</tt> in the Jupyter kernel.</li>\n  <li>Fix scrolling bug in notebook which would make the document jump around for no good reason.</li>\n  <li>Fix homebrew package (by avoiding svg icons on macOS, as homebrew does not package librsvg correctly).</li>\n  <li>Internal: refactor to enable cleaner insertion of related properties on property declaration.</li>\n  <li>Fix handling substitute with regex (<a href=\"https://github.com/kpeeters/cadabra2/issues/230\">#230</a>, David).</li>\n</ul>\n\n<a name=\"2.5.12\"></a>\n<h3>2.5.12 (released 07-May-2025)</h3>\n<ul>\n  <li>Make <tt>evaluate</tt> handle expressions in which indices have\n    been fixed to integers explicitly (e.g. an epsilon tensor with one\n    index fixed to a number).</li>\n  <li>New functionality to update and re-run cells based on the value\n    of a slider, to enable e.g. interactive plots.</li>\n  <li>Initial support for numerical solving of ODEs.</li>\n  <li>Bug fixes for <tt>nevaluate</tt>.</li>\n  <li>Enable <tt>evaluate</tt> to figure out index ranges\n    from <tt>Integer</tt> properties.</li>\n  <li>Avoid multiple identically-named notebook files used\n    in <tt>import</tt> mapping to the same converted <tt>.py</tt>\n    file.\n  <li>Various fixes for hDPI displays to make plots and icons sharp\n    and decorations render at the correct size.</li>\n  <li>Scrolling notebook to cell is now smooth.</li>\n  <li>(Internal) Remove all dependence on deprecated gtkmm-3.0\n  features, in preparation of making the notebook build with\n    gtkmm-4.0.</li>\n  <li>Add option to hide all input cells (for presentation purposes).</li>\n  <li>Add context menu for graphics/plot output to save as SVG.</li>\n  <li>Make semicolons more reliably print the expression they\n    terminate.</li>\n  <li>Add <tt>nintegrate</tt> for numerical integration.</li>\n  <li>Make <tt>nevaluate</tt> handle complex-valued expressions.</li>\n  <li>Better handling of floating point numbers. All multipliers are now\n    either rationals or doubles.</li>\n  <li>New <tt>nval</tt> function to act as a generic frontend for numerical\n    evaluation of (sub-)expressions (work-in-progress).</li>\n  <li>Add safeguards against passing expressions through the SymPy bridge\n    which SymPy cannot (yet) handle.</li>\n  <li>Add functionality to drive the notebook via an external script.</li>\n  <li>New, more modern Windows installer, which also adds a desktop icon.</li>\n  <li>Removed terminal window on Windows.</li>\n  <li>Fix export of notebooks to HTML.</li>\n  <li>Packages are now provided for <tt>arm64</tt> in addition\n    to <tt>x86_64</tt> for various Linux distributions (e.g. to run\n    Cadabra inside a Linux VM on your Apple Silicon MacBook) and for\n    Windows.</li>\n  <li>The command line client <tt>cadabra2-cli</tt> is now the default (with a symlink\n    <tt>cadabra2</tt> for backward compatibility) to streamline code and prepare\n    for future improvements.</li>\n</ul>\n\n<a name=\"2.5.10\"></a>\n<h3>2.5.10 (released 24-Dec-2024)</h3>\n<ul>\n  <li>Bugfix for eliminate_kronecker.</li>\n  <li>Fix for building Cadabra as a C++ library.</li>\n  <li>Various UI and typesetting bug fixes.</li>\n  <li>Get rid of websocketpp in favour of boost::beast so we can build with boost >= 1.87.0.</li>\n  <li>Fix for the homebrew package, and option to install the development branch using homebrew.</li>\n  <li>Add caching to the processing of substitution rules (Daniel).</li>\n  <li>Fixes for inline execution of Python functions in maths expressions.</li>\n  <li>Do not gobble normal output when an error occurs notebook execution.</li>\n  <li>Fix inconsistent behaviour and crashes with split-view mode.</li>\n  <li>Fix display of LaTeXForm properties.</li>\n  <li>Documentation updates.</li>\n  <li>Close LaTeX input cells on running them (configurable).</li>\n  <li>Cleanup and document kernel options.</li>\n  <li>Various additions to the plotting package <tt>cdb.graphics.plot</tt> including docs.</li>\n  <li>Add preliminary support for Plotly as plotting backend.</li>\n  <li>Word wrap LaTeX input cells to keep notebooks readable for any window width.</li>\n  <li>Internal changes for python path handling.</li>\n  <li>Bugfix for <tt>eliminate_kronecker</tt>.</li>\n  <li>Fix for building Cadabra as a C++ library.</li>\n  <li>Various UI and typesetting bug fixes.</li>\n  <li>Fix for the homebrew package, and option to install the development branch using homebrew.</li>\n  <li>Remove dependence on websocketpp to enable building with current version (1.87.0) of boost.</li>\n</ul>\n\n<a name=\"2.5.8\"></a>\n<h3>2.5.8 (released 25-Oct-2024)</h3>\n<ul>\n  <li>Fix handling of spurious backslashes\n  (<a href=\"https://github.com/kpeeters/cadabra2/issues/240\">#240</a>)\n  and double backslashes\n  (<a href=\"https://github.com/kpeeters/cadabra2/issues/155\">#155</a>).</li>\n  <li>Fix handling of backslash names (e.g. Greek characters)\n  appearing without curly brackets as sub- or superscripts\n  (<a href=\"https://github.com/kpeeters/cadabra2/issues/312\">#312</a>).</li>\n  <li>Fix the path to our python files in the Docker container\n  build.</li>\n  <li>When an expression is fed through the sympy bridge, make sure to\n  not remove outer parent relations (so that the expression remains a\n    sub/superscript if it was one before entering the bridge).</li>\n  <li>Fix several bugs with the undo system, and add redo.</li>\n  <li>Fix split-view mode.</li>\n  <li>Added optional <tt>partial=False</tt> flag to <tt>zoom</tt> to\n    enable zooming on exact matches (Daniel).</li>\n  <li>Add some more standard keybindings (ctrl-k, ctrl-a, ctrl-e) to\n  input cells.</li>\n  <li>Generate source tarball asset with microtex included.</li>\n</ul>\n\n<a name=\"2.5.6\"></a>\n<h3>2.5.6 (released 29-Sep-2024)</h3>\n<ul>\n  <li>Windows build is working again, now using MSYS2 because that's the only system that provides binary packages of our dependencies and also still carries gtkmm-3.0. An installer is now auto-generated by the CI on every release.</li>\n  <li>Updates to the AppImage build to fix issues with sympy and matplotlib.</li>\n  <li>Many other small fixes and updates to ensure that all binaries can be built by the CI.</li>\n</ul>\n\n<a name=\"2.5.2\"></a>\n<h3>2.5.2 (released 14-Jun-2024)</h3>\n<ul>\n  <li>Fix simplification of <tt>pow</tt> nodes.</li>\n  <li>Make <tt>ExNode</tt> iterators skip nodes hidden by <tt>zoom</tt>.</li>\n  <li>Fix <tt>canonicalise</tt> acting on expressions with self-anticommuting objects and derivatives (Daniel).</li>\n  <li>Fix crash when comparing with empty expressions.</li>\n  <li>Make <tt>zoom</tt> accept a list of patterns (Daniel).</li>\n  <li>Fix bugs in getting Weight values from Python, and setting multipliers in Python.</li>\n  <li>Add <tt>LaTeXString</tt> object to display LaTeX formatted strings on capable frontends.</li>\n  <li>Fix a <a href=\"https://cadabra.science/qa/2723/interaction-between-canonicalise-and-vector-spinors\">bug</a> with <tt>canonicalise</tt> acting on vector-spinor objects.</li>\n  <li>Enable the use of Unicode greek characters as input (which will get converted to LaTeX automatically) to enable cut-n-paste in the terminal (Connor).</li>\n  <li>Fix handling of multi-line expressions (newlines now count as a whitespace).</li>\n  <li>Fix <tt>canonicalise</tt> to allow for factors which are sums, as long as these do not have indices.</li>\n  <li>Ability to use builtin MicroTeX for typesetting (the default in 2.5.x),\n    which removes the requirement to have a LaTeX installation.</li>\n  <li>Experimental AppImages now available for Linux on both x86-64\n  and arm64 architectures.</li>\n  <li>Removed deprecated GTK-3 features and cleaned up the UI.</li>\n  <li>Fix bug in code to interrupt a running computation.</li>\n  <li>Added dynamical cell updates, e.g. to create animations.</li>\n</ul>\n\n<a name=\"2.4.4\"></a>\n<h3>2.4.4 (released 20-Sep-2023)</h3>\n<ul>\n  <li>Fix canonicalisation of rationals.</li>\n  <li>Make <tt>expand_power</tt> work on zero and negative\n    powers.</li>\n  <li>Prevent dummy indices from leaking out of <tt>\\pow</tt> nodes.</li>\n</ul>\n\n<a name=\"2.4.2\"></a>\n<h3>2.4.2 (released 22-Oct-2022)</h3>\n<ul>\n  <li>Add missing trig functions for display and passthrough to sympy (Oscar).</li>\n  <li>Allow for index values to be specified as an integer range.</li>\n  <li>Expanded <tt>nevaluate</tt> to numerically evaluate more expressions.</li>\n  <li>New\n  package <a href=\"/manual/cdb/sympy/calculus.html\"><tt>cdb.sympy.calculus</tt></a>\n  to make it easy to apply SymPy calculus functions on Cadabra\n    expressions.</li>\n  <li>New\n  package <a href=\"/manual/cdb/graphics/plot.html\"><tt>cdb.graphics.plot</tt></a>\n    for easy plotting of functions of one or two variables.</li>\n  <li>Fix compatibility issues with Python-3.11.</li>\n</ul>\n\n<a name=\"2.4.0\"></a>\n<h3>2.4.0 (released 25-Aug-2022)</h3>\n<ul>\n  <li>Version to accompany the publication of\n  the <a href=\"http://arxiv.org/abs/2208.11946\">paper about the meld\n  algorithm</a>.</li>\n  <li>Several fixes to <tt>meld</tt> (Dominic).</li>\n  <li>Make typesetting run in a separate thread to prevent the UI from\n\t feeling sluggish.</li>\n  <li>Some changes in the behaviour of list addition/multiplication,\n\t to match Mathematica's behaviour.</li>\n  <li>New <tt>nevaluate</tt> algorithm for fast numerical evaluation\n  of expressions (work-in-progress).</li>\n  <li>Fix for Python 3.10.x.</li>\n  <li>Fix for automatic cleanup of <tt>Diagonal</tt> objects.</li>\n  <li>Fix crash with tab-completion.</li>\n  <li>Make '+' operator add lists component-wise, and introduce the\n    tie operator '~' and <tt>join</tt> function to join lists.</li>\n  <li>Fix printing of objects with <tt>LaTeXForm</tt> which are\n  wrapped in another LaTeX operator.</li>\n</ul>\n\n<a name=\"2.3.8\"></a>\n<h3>2.3.8 (released 21-Nov-2021)</h3>\n<ul>\n  <li>Option to display negative powers as fractions (Dominic).</li>\n  <li>New algorithm <tt>slot_asym</tt> to (anti-)symmetrise objects in\n  indices by giving index positions instead of names.</li>\n  <li>New functionality to implement algorithms in Python (Dominic).</li>\n  <li>Faster re-implementation of <tt>get_component</tt> using new\n\t C++ function modules (Dominic).</li>\n  <li>New <tt>cdb.numeric.evaluate</tt>\n  and <tt>cdb.numeric.integrate</tt> modules to evaluate expressions\n  numerically or integrate differential equations numerically (Dominic).</li>\n  <li>Updates to <tt>cdb.utils.indices</tt> and <tt>cdb.core.manip</tt>.</li>\n  <li>Add warnings functionality to the kernel (Dominic).</li>\n  <li>Add infrastructure to let algorithms display progress\n  information while running (Dominic).</li>\n  <li>Add cell cursor position to status bar (Dominic).</li>\n  <li>Fix bug in <tt>expand_delta</tt> when the delta occurs at\n  top-level in an expression.</li>\n  <li>Many <tt>meld</tt> fixes and improvements (Dominic).</li>\n  <li>Fix handling of auto-declare names (names with a '#' character).</li>\n  <li>Keep LaTeX log/aux files on error to aid debugging.</li>\n  <li>Fix LaTeX code to avoid some global variable name clashes.</li>\n  <li>Fix for compilation on Apple silicon.</li>\n</ul>\n\n<a name=\"2.3.6\"></a>\n<h3>2.3.6 (released 30-Dec-2020)</h3>\n<ul>\n  <li>Once further change to the installation path of\n  the <tt>cadabra2.so</tt> module, so that it conforms with standard\n  conventions, in particular Debian packaging rules. On Debian-based\n  systems, you should now be able to use the Cadabra python module\n  without path settings, and the Jupyter kernel will work nicely with\n    the Jupyter package in Debian. </li>\n  <li>Fix display of lists containing <tt>Ex</tt> objects.</li>\n  <li>Fix import of Jupyter notebooks.</li>\n  <li>Fix bug related to automatic dummy index relabelling.</li>\n  <li>Fix tab-completion.</li>\n  <li>Fix build issues on recent versions of HomeBrew/macOS.</li>\n</ul>\n\n<a name=\"2.3.4\"></a>\n<h3>2.3.4 (released 16-Nov-2020)</h3>\n<ul>\n  <li>Fix a display bug which turned all products into tensor\n    products.</li>\n  <li>Enable attaching properties queried with <tt>Property.get</tt>\n    to new symbols.</li>\n  <li>Fix bug pulling with <tt>@(...)</tt> operator.</li>\n  <li>Add option <tt>redundant</tt> to <tt>eliminate_metric</tt> to\n    only eliminate metrics which have two dummy indices (David).</li>\n  <li>Added option to export notebooks to Jupyter, and a command-line\n    utility to do the same.</li>\n</ul>\n\n<a name=\"2.3.2\"></a>\n<h3>2.3.2 (released 31-Oct-2020)</h3>\n<ul>\n  <li>Fixed bug in pattern matching logic used\n  in <tt>integrate_by_parts</tt>;\n  see <a href=\"https://cadabra.science/qa/1755/integrate-by-parts-multiple-tensors-at-once\">this\n  Q&amp;A post</a>.</li>\n  <li>Fixed bug which would prevent assignment to node multiplier from\n  Python.</li>\n  <li>Tab-completion on command line and in the notebook.</li>\n  <li>Install the <tt>cadabra2</tt> python module in a standard\n    location (Atri). You may still need to set <tt>PYTHONPATH</tt> if\n    you are on Debian/Ubuntu.</li>\n  <li>Fixes for the Mathematica scalar backend.</li>\n  <li>Make <tt>expand_delta</tt> much faster when the Kronecker delta\n    is contracted with objects which have anti-symmetry.</li>\n  <li>Make meld work correctly with non/anti-commuting objects\n    (Dominic).</li>\n  <li>Make numbered indices like <tt>a1</tt> display with a subscript\n    automatically <tt>a<sub>1</sub></tt>.</li>\n  <li>Provide <tt>pickle</tt> functionality for expressions\n    (Dominic).</li>\n  <li>Fixes for compatibility with newer <tt>SymPy</tt> versions.</li>\n  <li>Added a 'find' function in the notebook, to search input cells.</li>\n  <li>New Jupyter kernel (enabled by default) which does not require\n  Xeus; you can now get access to Cadabra on Jupyter on all supported\n    systems, not just Conda (Fergus).</li>\n  <li>Various improvements and fixed for handling and display of Young\n    tableaux.</li>\n  <li>Added <tt>ExNode::ex()</tt> to obtain an <tt>Ex</tt> object from\n  an <tt>ExNode</tt> iterator.</li>\n</ul>\n\n<a name=\"2.3.0\"></a>\n<h3>2.3.0 (released 10-Jun-2020)</h3>\n<ul>\n  <li>Fix bug which would collect powers of objects with indices and\n  then report an error.</li>\n  <li>Functionality to read Cadabra Cloud notebooks into the desktop\n    Cadabra.</li>\n  <li>Use a better hash function for expression trees (avoiding a bug\n    in <tt>factor_in</tt>).\n  <li>Expose index symmetries through traces, so that canonicalise and\n  related algorithms work correctly. Introduced a new\n    property <tt>TableauInherit</tt>.</li>\n  <li>More flexible <tt>LaTeXForm</tt> property, to enable more\n    flexible object display in the notebook.</li>\n  <li>Various fixes for behaviour of <tt>unwrap</tt> with anti- or\n    non-commuting arguments.</li>\n  <li>New <tt>meld</tt> algorithm for canonicalisation (Dominic).</li>\n</ul>\n\n<a name=\"2.2.8\"></a>\n<h3>2.2.8 (released 10-Dec-2019)</h3>\n<ul>\n  <li>More versatile handling of <tt>Trace</tt>, including sorting\n  using cyclic symmetry (Connor).</li>\n  <li>Fixes for <tt>combine</tt> (Connor).</li>\n  <li>Save command-line history (Connor).</li>\n  <li>Make imported notebooks use the default <tt>post_process</tt> function.</li>\n  <li>Make <tt>unwrap</tt> move scalars out of exterior (wedge)\n  products, see <a href=\"https://cadabra.science/qa/1287/collecting-scalar-terms-expressions-with-differentialforms\">this\n\t\tQ&amp;A post</a>.</li>\n  <li>Fix bug with indices with accents (<a href=\"https://github.com/kpeeters/cadabra2/issues/166\">github/166</a>).</li>\n  <li>Added a <tt>cadabra2latex</tt> command to convert notebooks to\n    LaTeX.</li>\n  <li>Fixed issue building with latest Homebrew on macOS.</li>\n  <li>Fixed Windows build issues and add python path settings at runtime.</li>\n  <li>Fixed bug with multipliers not reducing to canonical form.</li>\n</ul>\n\n<a name=\"2.2.7\"></a>\n<h3>2.2.7 (released 25-Jun-2019)</h3>\n<ul>\n  <li>Added <tt>cdb.utils.develop</tt> and <tt>cdb.relativity.abstract</tt>.\n  <li>Added authentication token to all client-server communication.</li>\n  <li>Various extensions to the <tt>Trace</tt> property.</li>\n  <li>Make property info available from Python (Dominic).</li>\n  <li>Fixed integration by parts with index-less derivatives.</li>\n  <li>Added <tt>eliminate_vielbein</tt>.</li>\n  <li>Fixed display of lists of sympy expressions.</li>\n  <li>Fixed (finally) UTF8 input for non-English symbols.</li>\n</ul>\n\n<a name=\"2.2.6\"></a>\n<h3>2.2.6 (released 16-Apr-2019)</h3>\n<ul>\n  <li>Experimental notebook diff viewer (Dominic).</li>\n  <li>Warn when about to overwrite an existing notebook.</li>\n  <li>Improvements for HiDPI screens especially on macOS.</li>\n  <li>Fix crash in <tt>sym/asym</tt>.</li>\n  <li>Fix undo/redo crash in notebook when deleting cells.</li>\n  <li>Improvements to the <tt>cdb.core.manip</tt> package (Dominic).</li>\n  <li>Fix in <tt>young_project_tensor</tt>.</li>\n  <li>Fix pattern matching for anti-commuting factors.</li>\n  <li>Added <a href=\"/manual/explicit_indices.html\"><tt>explicit_indices</tt></a>\n  to convert expressions with implicit indices to their explicit\n\t form.</li>\n  <li>Add option to build a Jupyter kernel.</li>\n  <li>Fix bug in <tt>split_index</tt> (acted on wrong parts of\n\t expressions).</li>\n  <li>Fix bug with substitute not checking constraints for\n\t single-factor patterns.</li>\n  <li>Add <tt>partial</tt> option\n  to <a href=\"/manual/substitute.html\">substitute</a> to require that\n  products or sums match all terms, not just a partial sum or partial\n  product.</li>\n</ul>\n\n<a name=\"2.2.5\"></a>\n<h3>2.2.5 (released 05-Feb-2019)</h3>\n<ul>\n  <li>Fix issues with <tt>Derivative</tt> objects going through Sympy.</li>\n  <li>Fix a bug with LaTeX export.</li>\n  <li>Enable build against system-supplied JSONCPP.</li>\n</ul>\n\n<a name=\"2.2.4\"></a>\n<h3>2.2.4 (released 19-Dec-2018)</h3>\n<ul>\n  <li>Fix to make simplify see the Mathematica backend again.</li>\n  <li>Fix export of notebooks to LaTeX.</li>\n  <li>Fix display of LaTeXForm property declaration.</li>\n  <li>Added Python methods to traverse the expression tree.</li>\n  <li>Fix for power simplification bug\n\t (<a href=\"https://github.com/kpeeters/cadabra2/issues/85\">github/85</a>)</li>\n  <li>Fix to make command line version accept primes in expression\n  input\n\t (<a href=\"https://github.com/kpeeters/cadabra2/issues/85\">github/85</a>)</li>\n  <li>Fix for indices being treated as dependencies\n\t (<a href=\"https://github.com/kpeeters/cadabra2/issues/89\">github/89</a>)</li>\n  <li>Various improvements\n\t for <a href=\"/manual/replace_match.html\"><tt>replace_match</tt></a>.\n  <li>Optional syntax highlighting in input cells (Dominic).</li>\n  <li>Added <a href=\"/manual/lower_free_indices.html\"><tt>lower_free_indices</tt></a>\n\t and <a href=\"/manual/raise_free_indices.html\"><tt>raise_free_indices</tt></a>.\n  <li>Various small fixes for terminal output.</li>\n  <li>'Evaluate to cursor' in the notebook now works.</li>\n  <li>Substituting now properly distinguishes between indices and\n  non-indices,\n  see <a href=\"https://cadabra.science/qa/609/should-substitute-act-on-indices\">this\n\t\tQ&amp;A post</a>.</li>\n  <li>Added <a href=\"/manual/einsteinify.html\"><tt>einsteinify</tt></a>.</li>\n  <li>Do not attempt to write out sums over index values\n  in <a href=\"/manual/evaluate.html\"><tt>evaluate</tt></a> if the\n  range is not known, simply keep them unevaluated (instead of\n\t throwing an error).</li>\n  <li>Introducing <a href=\"/manual/zoom.html\"><tt>zoom</tt></a>/unzoom\n  as a more friendly and powerful alternative\n\t to <a href=\"/manual/take_match.html\"><tt>take_match</tt></a>/<a href=\"/manual/replace_match.html\"><tt>replace_match</tt></a>.</li>\n  <li>Fix for display of LaTeXForm'ed objects in\n\t sub/superscripts.</li>\n  <li>New build system using Ninja on Windows (Dominic).</li>\n  <li>Fix bug in unwrap with derivatives with respect to explicit coordinates\n  (see <a href=\"https://cadabra.science/qa/854/applied-expresion-partial-derivative-variable-functions\">Unwrap\n\t\tapplied...</a>).</li>\n  <li>It is now possible to import notebooks into other notebooks\n\t (Dominic).</li>\n  <li>New system package for expression manipulation\n\t (cdb.core.manip).</li>\n  <li>Export to LaTeX fixed, and now also exports figures.</li>\n  <li>Added a debugging console to the notebook interface (Dominic).</li>\n</ul>\n\n<a name=\"2.2.0\"></a>\n<h3>2.2.0 \"Easter Bunny\" (released 29-Mar-2018)</h3>\n<ul>\n  <li>Now builds on <a href=\"download.html\">Windows</a> (Dominic).</li>\n  <li>Experimental support for modifying the expression tree directly\n  from Python (see e.g. <a href=\"https://cadabra.science/qa/605/fourier-transform\">Fourier transforms</a>).</li>\n  <li>Now building on OpenBSD.\n  <li>Fix for integration by parts (<a href=\"https://github.com/kpeeters/cadabra2/issues/71\">github/71</a>)</li>\n  <li>Fix for incorrect conversion to sympy expressions.</li>\n  <li>Optionally build with support for (experimental!) Mathematica scalar\n\t backend; see <tt><a href=\"/manual/map_mma.html\">map_mma</a></tt>.</li>\n  <li>Many bugfixes for expression display and sympy conversion.</li>\n  <li>Now using pybind instead of boost.python, in preparation for\n  Windows port, and to enable building against Anaconda.</li>\n  <li>Copy/paste of output cells added.</li>\n  <li>New <tt><a href=\"/manual/simplify.html\">simplify</a></tt>\n\t command, which simplifies the scalar parts of expressions, and can\n\t be switched to use either Sympy or Mathematica.</li>\n  <li>Fix to treat derivatives with respect to explicit coordinates as\n  scalars in <a href=\"/manual/evaluate.html\"><tt>evaluate</tt></a>;\n  see <a href=\"https://cadabra.science/qa/534/curious-behaviour-of-evaluate-algorithm\">this\n  Q&amp;A post</a>.</li>\n  <li>Fix for failure to flag errors\n  for <a href=\"/manual/WeightInherit.html\">WeightInherit</a></tt> property.</li>\n  <li>Fixed: vary on single-term expressions (<a href=\"https://github.com/kpeeters/cadabra2/issues/57\">github/57</a>)</li>\n  <li>Fixed: evaluate with dense factors and no 'values' property on\n\t indices (<a href=\"https://github.com/kpeeters/cadabra2/issues/68\">github/68</a>)</li>\n</ul>\n\n<a name=\"2.1.7\"></a>\n<h3>2.1.7 (released 20-Nov-2017)</h3>\n<ul>\n  <li>Various bugfixes.</li>\n</ul>\n\n<a name=\"2.1.6\"></a>\n<h3>2.1.6 (released 1-Nov-2017)</h3>\n<ul>\n  <li>Make the wedge product distributable.</li>\n  <li>Fix printing of wedge products with sums in factors.</li>\n  <li>Fixed printing of index brackets.</li>\n  <li>Add RPATH to binaries to avoid having to run <tt>ldconfig</tt>\n  after installation.</li>\n  <li>Fix for the theming to avoid invisible text with dark\n\t themes.</li>\n</ul>\n\n<a name=\"2.1.5\"></a>\n<h3>2.1.5 (released 6-Aug-2017)</h3>\n<ul>\n  <li>Introduced <tt><a href=\"/manual/map_sympy.html\">map_sympy</a></tt>\n  which can be used to apply Sympy functions to Cadabra expressions,\n  acting in-place.</li>\n  <li>Fixed: expressions with powers often lack brackets.</li>\n</ul>\n\n<a name=\"2.1.4\"></a>\n<h3>2.1.4 (released 14-Apr-2017)</h3>\n<ul>\n  <li>Enable packages to be written using Cadabra notation, instead of\n\t only pure Python (still experimental).</li>\n  <li>Young tableaux\n\t properties <tt><a href=\"/manual/Tableau.html\">Tableau</a></tt> and\n\t <tt><a href=\"/manual/FilledTableau.html\">FilledTableau</a></tt>\n\t the related\n\t algorithm <tt><a href=\"/manual/lr_tensor.html\">lr_tensor</a></tt>\n\t are available again.\n  <li>Sorting Majorana spinors possible again using <tt><a href=\"/manual/sort_spinors.html\">sort_spinors</a></tt>.</li>\n  <li>Extended <tt><a href=\"/manual/rename_dummies.html\">rename_dummies</a></tt>\n  with capability to rename indices to different set.</li>\n  <li>Make <tt><a href=\"/manual/vary.html\">vary</a></tt> work on powers of expressions with dummy\n\t indices.</li>\n  <li>Substitution of sub-sums now available\n  (e.g.&nbsp;<a href=\"/manual/substitute.html\">substitute</a> of <tt>A+B=C</tt> in <tt>ex:=A+B+C+D</tt>).</li>\n  <li>Improved LaTeX export to make printed notebooks look much\n\t better.</li>\n  <li>Many improvements to the component engine, in particular for\n  handling of derivatives and fractions involving tensors.</li>\n  <li>Better line spacing for line-wrapped equations.</li>\n  <li>Smarter scroll-to-cell behaviour of the notebook.</li>\n  <li>Canonicalising expressions with component values for indices now\n\t works again.</li>\n  <li>The <tt><a href=\"/manual/unwrap.html\">unwrap</a></tt> algorithm\n  can now be guided about what to unwrap, and also knows about spinors\n  and Dirac bars.</li>\n  <li>Experimental support to use Cadabra directly from C++ code, as a\n  library (see\n  the <tt><a href=\"https://github.com/kpeeters/cadabra2/tree/master/c%2B%2Blib\">c++lib</a></tt>\n\t directory).</li>\n  <li>Fixes for using a custom <tt>post_process</tt> defined as a function nested inside another.</tt>\n  <li>Rudimentary timing logic, try <tt>server.totals();</tt></li>\n  <li>Fixed: pasting text in the notebook sometimes double-pastes.\n  <li>Fixed: <tt><a href=\"/manual/split_index.html\">split_index</a></tt> does not work properly on left- and\n\t right-hand side of equations.</li>\n  <li>Fixed: <tt><a href=\"/manual/sort_product.html\">sort_product</a></tt> does not always sort\n\t expressions.</li>\n  <li>Fixed: <tt><a href=\"/manual/eliminate_metric.html\">eliminate_metric</a></tt> only acts at top level of an\n  expression, should have <tt>deep=True</tt> by default.</li>\n  <li>Fixed: a bug which would lead to a segfault when using <tt>deep=True</tt>.\n</ul>\n\n<a name=\"2.1.2\"></a>\n<h3>2.1.2 (released 4-Jan-2017)</h3>\n<ul>\n  <li>Bug fix: Crash on opening of a notebook on Ubuntu 16.04 and possibly\n\t others, related to minor differences in gtk versions.</li>\n  <li>Bug fix: Installation paths of Debian/Ubuntu/Mint binary\n\t packages changed from <tt>/usr/local</tt> to <tt>/usr</tt>.</li>\n</ul>\n\n<a name=\"2.1.1\"></a>\n<h3>2.1.1 (released 3-Jan-2017)</h3>\n<ul>\n  <li>Bug fix: Compilation error on gtk versions lower than 3.10.0.</li>\n</ul>\n\n<a name=\"2.1.0\"></a>\n<h3>2.1.0 (released 3-Jan-2017)</h3>\n<ul>\n  <li>First properly versioned release after a series of 2.0.x\n\t releases which were meant for testing.</li>\n</ul>\n\n{%- endblock %}\n"
  },
  {
    "path": "web2/cadabra2/source/changes12.html",
    "content": "{% extends \"layout.html\" %}\n\n{% block title %}Cadabra: changes from version 1 to 2{% endblock %}\n\n{% block head %}{%- endblock %}\n\n{% block main %}\n\n<h1>New in version 2.x</h1>\n<p>\n  Many things changed/improved in version&nbsp;2.x with respect to\n  version&nbsp;1.x. The key change is probably that old&nbsp;1.x\n  notebooks are <em>not</em> compatible with the&nbsp;2.x\n  software. This was done intentionally in order to give maximal\n  flexibility to improve the system. It is conceivable that at some\n  point an automatic converter will be written, but for the time being\n  you will either need to convert the notebook by hand or keep\n  version&nbsp;1.x around.\n</p>\n<p>\n  The other user-visible changes include:\n</p>\n<ul>\n  <li>Cadabra manipulations can now programmed using Python. The\n  input format is a combination of Cadabra's old LaTeX-based\n  format mixed with standard Python, so you still get all the\n  benefits of LaTeX-style input.</li>\n\n  <li>You can now do both abstract tensor computations as well as\n  component computations. This means that you can manipulate tensorial\n  expressions as you did before, and then plug in values for their\n  components.</li>\n\n  <li>Various simplification algorithms are now part of the set of\n  default rules to apply at every manipulation stage (collecting equal\n  terms, for instance). This makes a lot of manipulations look shorter\n  and more natural.</li>\n  \n  <li>The notebook interface now also has facilities for displaying\n  plots and other graphical output. You can thus explore the results of\n  component computations graphically.</li>\n\n  <li>The user interface now takes into account text scaling settings\n  on high-dpi screens, so it the font size in LaTeX output cells\n  matches that of the input cells.</li>\n\n  <li>Where version 1.x used to write notebook files in a\n  LaTeX-compatible form, the notebook files for 2.x are JSON\n  files. This allows for more flexibility, and also enables easier\n  conversion to other formats, for instance to show notebooks on the\n  web.</li>\n</ul>\n\n<p>\n  There are also many changes under the hood:\n</p>\n<ul>\n  <li>All algorithms and all properties now live in their own\n  \\verb|.hh/.cc| files, making it easier to find and debug them.\n  </li>\n  \n  <li>Cadabra now relies solely on libraries which are rather common\n  (certainly more common than the old stumbling block \\verb|modglue|),\n  and is easier to build as it now uses CMake instead of GNU\n  autotools.\n  </li>\n\n  <li>The user interface code is now cleanly separated into a\n  system-independent base and a very thin layer, making\n  it <em>much</em> easier to write one for e.g.&nbsp;OS&nbsp;X or for\n  a different GUI toolkit like Qt.\n</ul>\n\n\n<h1>Algorithm name changes from version 1 to 2</h1>\n<p>\n  The main change with respect to algorithm names is that the '@'\n  prefix for algorithms is no longer necessary. Algorithms are now\n  standard Python functions. They take an expression as their first\n  argument, and (optionally) further arguments to determine what to\n  do. You can use an underscore to refer to the last entered\n  expression, so you can write <code>collect_factors(_)</code> where\n  you would previously write <code>@collect_factors(%)</code>.\n</p>\n\n<p>\n  Where you would previously use an exclamation mark to act at any\n  level, you now add the <code>deep=True</code> argument to a\n  function. This is the default for many algorithms where that makes\n  sense, so you often do not have to add it at all. \n</p>\n\n<p>\n  A number of algorithms (and a few properties) have changed name or\n  behaviour while going from version 1 to version 2. This was done\n  mostly to make naming more consistent and to avoid weird acronyms in\n  algorithm names. \n</p>\n\n<h2>Algorithms</h2>\n<p>\n  In general, all algorithms now have names of the form 'action' or\n  'action_object'. \n  <table>\n\t <tr>\n\t\t<th>old name</th>\n\t\t<th>new name</th>\n\t\t<th>notes</th>\n\t </tr>\n\t <tr>\n\t\t<td>@prodflatten</td>\n\t\t<td>flatten_product</td>\n\t\t<td>to avoid abbreviations</td>\n\t </tr>\n\t <tr>\n\t\t<td>@prodsort</td>\n\t\t<td>sort_product</td>\n\t\t<td>to avoid abbreviations</td>\n\t </tr>\n\t <tr>\n\t\t<td>@rewrite_diracbar</td>\n\t\t<td>expand_diracbar</td>\n\t\t<td>make meaning more clear</td>\n\t </tr>\n\t <tr>\n\t\t<td>@epsprod2gendelta</td>\n\t\t<td>epsilon_to_delta</td>\n\t\t<td>avoid obscure names</td>\n\t </tr>\n\t <tr>\n\t\t<td>@pintegrate</td>\n\t\t<td>integrate_by_parts</td>\n\t\t<td>completely reworked and more powerful</td>\n\t </tr>\n  </table>\n</p>\n\n<h2>Properties</h2>\n<p>\n</p>\n\n\n{%- endblock %}\n"
  },
  {
    "path": "web2/cadabra2/source/clay.yaml",
    "content": "---\n# Shell-style patterns files/folders that must not be copied.\n# Use quotes.\nexclude:\n  - \".DS_Store\"\n  - \"build/*\"\n  - \"webassets-cache/*\"\n  - \".webassets-cache\"\n  - \"layout.html\"\n  - \"*.nb.html\"\n  - \"README.txt\"\n  - \"static/*\"\n  - \"notebooks/README*\"\n  - \"notebooks/.gitignore\"\n  - \"notebooks/*~\"\n  - \"notebooks/*.cnb\"\n  - \"notebooks/*segment.html\"\n  - \"*~\"\n\n# Shell-style patterns files/folders that *must be* copied, even if\n# they are in the exclude list.\n# Use quotes.\n#include:\n#  - \"robots.txt\"\n#    - \"humans.txt\"\n\n# Jinja extensions to use\njinja_extensions:\n\n# Shell-style patterns of files outside `static/` that must be copied\n# as-is instead of trying to interpret them as Jinja templates.\n# Use quotes.\n#binaries:\n#  - \"favicon.ico\""
  },
  {
    "path": "web2/cadabra2/source/comparison.html",
    "content": "{% extends \"layout.html\" %}\n\n{% block title %}Cadabra: comparison with other systems{% endblock %}\n\n{% block head %}{%- endblock %}\n\n{% block main %}\n<h1>Comparison of Cadabra with other systems</h1>\n<p>\n  In order to understand whether Cadabra is useful for you, a\n  comparison to other system may help. Without going too much into\n  detail, here are some notable differences and similarities with\n  other systems.\n</p>\n\n<h2>Patterns versus maths</h2>\n<p>\n  Cadabra is predominantly a 'field theory aware notebook'. What this\n  means is that is is designed to be useful for the manipulations of\n  patterns which occur in the description of field theory problems. It\n  knows about patterns more than it knows about the mathematical\n  meaning of those patterns. \n</p>\n<p>\n  Other programs in this class are FORM and its predecessor\n  Schoonship, which both know relatively little about the maths of\n  physics which people do with them, but primarily provide a cleverly\n  thought-out toolbox of algorithms to manipulate expressions. Just\n  like when you compute things with pen and paper, you can do things\n  with these programs which are manifest mathematical nonsense.\n</p>\n<p>\n  Programs like Sage (with SageManifolds) and xAct tend to be much\n  more strict in how you define your problem: they know a lot about\n  the mathematical meaning of symbols, and \n</p>\n<p>\n  Neither of these approaches is best, they are just different.\n</p>\n\n<h2>Automatic versus guided</h2>\n<p>\n  Cadabra typically does not automatically evaluate, simplify or\n  canonicalise expressions. It expects that you will want to\n  gradually transform or work on an expression\n</p>\n<p>\n  To achieve this, Cadabra has the concept of 'zooming into' parts of\n  an expression, applying algorithms on those parts, and then 'zooming\n  out' again to see the full expression. \n</p>\n\n<h2>Object instances versus property attachments</h2>\n<p>\n</p>\n<p>\n  \n</p>\n\n<h2>Targetted versus comprehensive</h2>\n<p>\n  Cadabra is intentionally not designed to cover 'as much of\n  mathematics as we can implement'. It is specifically meant to help\n  solving a particular class of problems which occur in field\n  theory. This is in part because of its roots (it originally was just\n  a simple tool to help write research papers), and in part because\n  I do not believe that a 'megalomanic' approach can work. \n</p>\n<p>\n  Programs like Mathematica, Maple and Sage have a different\n  philosophy. They try to target, not always with success, a very\n  large audience, by aiming to cover 'all of maths'. \n</p>\n\n<h2></h2>\n<p>\n  nval versus sval, e.g. commutator has sval, but integral has both\n  sval and nval. \n\n\n{%- endblock %}\n\n"
  },
  {
    "path": "web2/cadabra2/source/developers.html",
    "content": "{% extends \"layout.html\" %}\n\n{% block title %}Cadabra: Developers' corner{% endblock %}\n\n{% block head %}{%- endblock %}\n\n{% block main %}\n\n<h1>How to contribute</h1>\n<p>\n  If you want to help out with Cadabra, or think you can contribute a\n  useful add-on package or perhaps just a sample notebook or a bit of\n  documentation, you are more than welcome! Even just dropping us a\n  note with some details about what computations you do with Cadabra\n  is a useful contribution, and helps to get a better idea of what\n  people expect from the software. \n</p>\n<p>\n  Below are some tips on how to get started contributing to\n  Cadabra. For any questions, please post in\n  the <a href=\"/qa\">questions&amp;answers</a> forum or get in touch\n  directly via email\n  at <a href=\"mailto:info@cadabra.science\">info@cadabra.science</a>.\n</p>\n<h2>Sharing your notebooks</h2>\n<p>\n  If you think you have a nice notebook which could be useful for\n  other people to learn from, please consider sharing it. You can\n  either email it\n  to <a href=\"mailto:info@cadabra.science\">info@cadabra.science</a>,\n  or use\n  the <a href=\"https://github.com/kpeeters/cadabra2-contrib\">cadabra2-contrib</a>\n  repository on github.\n</p>\n\n<h2>Get familiar with the software</h2>\n<p>\n  The first thing to do is to get familiar with how the software works,\n  by playing with the <a href=\"/tutorials.html\">tutorials</a>. Details\n  of the software, including some of the logic that is behind its\n  inner workings, are described in the <a href=\"/help.html\">Cadabra book</a>, and documentation is available separately for all\n  <a href=\"/man.html\">properties and algorithms</a>. If you get\n  stuck, do not hesitate to post a question on\n  the <a href=\"/qa\">questions&amp;answers</a> site. If you want to\n  contribute at the level of the C++ core, or if you are simply\n  interested in how things work behind the scenes, you will find the\n  <a href=\"/doxygen/html/\">doxygen</a> documentation useful.\n</p>\n\n<h2>Identify something to work on</h2>\n<p>\n  Most likely you will have used (or will have tried to use) Cadabra\n  for a concrete project, and found that you see room for\n  improvement. This can be as simple as reporting a bug, perhaps even\n  fixing it, or adding a tutorial or other documentation, providing\n  add-on functionality in the form of packages, or helping with the\n  core. We are also always interested to hear about issues installing\n  Cadabra on new systems. \n</p>\n\n<h2>Setup your development environment</h2>\n<p>\n  Contributions in any form are welcome, but if you want to submit\n  substantial code contributions, it is useful to get familiar with\n  the git version control system. This is used to track software\n  changes over time and to effectively manage contributions from\n  different authors. We also\n  utilise <a href=\"https://github.com/kpeeters/cadabra2\">github</a>, a\n  web interface to git, extensively and use it for communication,\n  issue tracking, merging patches (pull requests) and so on. Check out\n  the source code from there and follow the instructions on how to\n  build it.\n</p>\n\n<h1>Source code and documentation</h1>\n<p>\n  The source code is documented in quite some detail and the resulting\n  <a href=\"/doxygen/html/\">Cadabra doxygen documentation</a> is worth\n  consulting if you want to become a developer. This is automatically\n  generated from the latest status of the master branch on github\n  whenever this web site is updated.\n</p>\n<p>\n  You can also generate this doxygen tree yourself in your own working\n  copy by running <code>make doc</code> in the project root (not\n  the <code>build</code> folder). The documentation then ends up in\n  the <code>doxygen/html</code> folder.\n</p>\n<p>\n  The source code is formatted with the\n  following <a href=\"http://astyle.sourceforge.net/astyle.html\">astyle</a>\n  switches:\n</p>\n  <pre>\n      --style=k/r\n      --indent=tab=3\n      --recursive\n      --attach-classes\n      --attach-namespaces\n      --indent-classes\n      --indent-namespaces\n      --break-closing-braces\n  </pre>\n<p>\n  This is followed by indenting all curly brackets by one tab. All\n  this is automated by calling <code>make format</code> from the\n  top-level directory.\n</p>\n\n\n{%- endblock %}\n"
  },
  {
    "path": "web2/cadabra2/source/download.html",
    "content": "{% extends \"layout.html\" %}\n\n{% block title %}Cadabra: Download{% endblock %}\n\n{% block head %}{%- endblock %}\n\n{% block main %}\n\n<h1>Download and install</h1>\n\n<h2>Build from source (Linux/macOS/Windows)</h2>\n<p>\n  The source is of Cadabra is distributed via github, see the\n  <a href=\"https://github.com/kpeeters/cadabra2\">kpeeters/cadabra2</a>\n  repository for more details, including the pre-requisites.\n</p>\n<p>\n  You can build .deb and .rpm packages yourself when building from\n  source, by running <code>sudo cpack</code> after a successful\n  build. \n</p>\n\n<h2>Binary packages</h2>\n<p>\n  Packages for various Linux distributions and an installer for\n  Windows are available\n  for <a href=\"https://github.com/kpeeters/cadabra2/releases/latest\">download\n  from github</a>. These are generated automatically on every\n  release. Installation on macOS can be done through HomeBrew or\n  MacPorts; see below. There is also a Docker image if you only want\n  to use Cadabra via Jupyter.\n</p>\n<p>\n  Use these packages at your own risk. Because of time constraints\n  some of these packages receive almost no testing, so any feedback is\n  welcome.  If you want to help getting these into official\n  distribution repositories, please let me know.\n</p>\n\n<div class=\"packages\">\n  <div class=\"distrotype\">\n    <img src=\"static/images/appimage.svg\"/>\n    <div class=\"distrotxt\">\n      The AppImage version of Cadabra can be installed on any\n      reasonably modern Linux distribution and it is completely\n      self-contained (which is inefficient, so prefer a distro package\n      below if there is one for your system). Just download and make\n      the file executable with <tt>chmod u+x *.AppImage</tt>. Versions\n      are provided for\n      <tt>x86_64</tt> and <tt>aarch64</tt> architectures from\n      the <a href=\"https://github.com/kpeeters/cadabra2/releases/latest\">github\n      release page</a>.\n    </div>\n  </div>\n  \n  <div class=\"distrotype\">\n    <img src=\"static/images/ubuntulogo.png\"/>\n    <div class=\"distrotxt\">\n      Packages for Ubuntu 22.04 Jammy and 24.04 Noble are available\n      from\n      the <a href=\"https://github.com/kpeeters/cadabra2/releases/latest\">github\n      release page</a>. Cadabra is now also available from the\n      official repositories, by installing the <tt>cadabra2</tt>\n      package (though this may not always be the most recent\n      version). Thanks to Alex Myczko for making this happen.\n    </div>\n  </div>\n\n  <div class=\"distrotype\">\n    <img src=\"static/images/fedora-logo.png\"/>\n    <div class=\"distrotxt\">\n      Packages for Fedora 40, 41 and 42 are available from\n      the <a href=\"https://github.com/kpeeters/cadabra2/releases/latest\">github\n      release page</a>. \n    </div>\n  </div>\n\n<!--  <div class=\"distrotype\">\n    <img src=\"static/images/mintlogo.png\"/>\n    <div class=\"distronum\"><a href=\"https://cadabra.science/packages/mint19/\">Mint Tara 19</a></div>\n    <div class=\"distronum\"><a href=\"https://cadabra.science/packages/mint20/\">Mint Ulyana 20</a></div>\n    <div class=\"distronum\"><a href=\"https://cadabra.science/packages/mint21/\">Mint Vanessa 21</a></div>\n  </div> -->\n\n  <!--  <div class=\"distrotype\">\n\t<img src=\"static/images/centoslogo.png\"/>\n\t<div class=\"distronum\"><a href=\"https://cadabra.science/packages/centos7/\">CentOS 7</a></div>\n\t<div class=\"distrotxt\">\n\t  After installation you also need to run\n\t  <code>sudo yum install epel-release; sudo yum\n\t    install python-pip; sudo pip install sympy</code>\n\t  in order to enable component computations.\n\t</div>\n  </div>\n\n  <div class=\"distrotype\">\n    <img src=\"static/images/scientific_linux_logo.png\"/>\n    <div class=\"distronum\"><a href=\"https://cadabra.science/packages/scientific7x/\">Scientific Linux 7x</a></div>\n    <div class=\"distrotxt\">\n      After installation you also need to run\n      <code>sudo yum install epel-release; sudo yum\n\tinstall python-pip; sudo pip install sympy</code>\n      in order to enable component computations.\n    </div>\n  </div> -->\n\n  <div class=\"distrotype\">\n    <img src=\"static/images/opensuse_logo.png\"/>\n    <div class=\"distrotxt\">\n      A package for openSUSE Tumbleweed is available from\n      the <a href=\"https://github.com/kpeeters/cadabra2/releases/latest\">github\n\trelease page</a>. You can still build it on openSUSE Leap, but you will need\n      to build from source or rely on 3rd party repositories.\n    </div>\n  </div>\n\n  <div class=\"distrotype\">\n    <img src=\"static/images/debian-logo.jpg\"/>\n    <div class=\"distrotxt\">\n      Cadabra is now available in Debian 11 (Bullseye) from the\n      official repositories, by installing the <tt>cadabra2</tt>\n      package (though this may not always be the most recent\n      version). Thanks to Alex Myczko for making this happen.\n    </div>\n  </div>\n\n  <div class=\"distrotype\">\n    <img src=\"static/images/docker-logo-blue.svg\"/>\n    <div class=\"distrotxt\">\n      If you only want to use Cadabra from within Jupyter, you can use\n      the <a href=\"https://hub.docker.com/r/kpeeters/cadabra2-jupyter\">official\n      Docker image at DockerHub</a>. This container exposes the\n      Jupyter server on a local URL which you can access using your\n      browser, and stores notebooks in your home directory. Available\n      for both AMD64 and ARM64 architectures. Be aware that you will\n      miss out on some of the goodies of the Cadabra notebook\n      interface.\n    </div>\n  </div>\n\n  <div class=\"distrotype\">\n    <img src=\"static/images/apple_logo.png\"/>\n    <div class=\"distronum\">macOS</a></div>\n    <div class=\"distrotxt\">\n      Cadabra is available via the Homebrew package manager. This is\n      the \"official\" method, in the sense that this package gets\n      updated and tested automatically on every Cadabra\n      release. Simply do\n      <code>brew tap kpeeters/repo</code>\t\t\n      <code>brew install cadabra2</code>\n      Alternatively, if you want to live on the bleeding edge and\n      want to run the current development branch, install <tt>cadabra2-devel</tt>.\n      If you encounter problems, please\n      email <a href=\"mailto:info@cadabra.science\">info@cadabra.science</a>\n      so they can be fixed and other people can benefit from it.\n    </div>\n    <div class=\"distrotxt\">\n      Cadabra is\n      also <a href=\"https://ports.macports.org/port/cadabra2/\">available\n        via MacPorts</a>,\n      <code>sudo port install cadabra2</code> should do the trick. For\n      more details follow the link above. Thanks to Marius Schamschula\n      for maintaining this.\n    </div>\n    <div class=\"distrotxt\">\n      If you want to build from source,\n      see <a href=\"https://github.com/kpeeters/cadabra2#macos\">macOS\n        build instructions</a> for details.\n    </div>\n</div>\n\n<a name=\"windows\"></a>\n<div class=\"distrotype\">\n  <img src=\"static/images/windows_logo.png\"/>\n  <div class=\"distronum\">Windows 11</div>\n  <div class=\"distrotxt\">\n    A Windows installer for Cadabra is finally available again. There\n    are some rough edges that still need to be fine-tuned, but it\n    seems to be mostly functional, including plotting. Download\n    the <a href=\"https://github.com/kpeeters/cadabra2/releases/latest\">Windows\n    installer from the github release page</a> (available for x86_64\n    right now only). All batteries are included so you do not need to\n    install anything else. Many thanks to Dominic Price for doing most\n    of the work a few years ago.\n  </div>\n  <div class=\"distrotxt\">\n    Once installed, navigate to your installation folder and\n    start <tt>cadabra2-gtk</tt> (sorry, no start menu entry yet). There are\n    some sample notebooks in the <tt>Examples</tt> folder.\n  </div>\n</div>\n\n<a name=\"freebsd\"></a>\n<div class=\"distrotype\">\n  <img src=\"static/images/freebsd_logo.png\"/>\n  <div class=\"distronum\">FreeBSD</div>\n  <div class=\"distrotxt\">\n    Cadabra is available via the FreeBSD package manager. Simply run\n    <tt>pkg install cadabra2</tt>. Thanks to Yuri Victorovich for\n    maintaining this port.\n  </div>\n</div>\n\n<!--<div class=\"distrotype\">\n  <img src=\"static/images/conda.png\"/>\n  <div class=\"distrotxt\">\n    <b>The Conda packages are outdated and contain known bugs; if you\n      can, avoid it and use one of the other available packages.</b>\n  </div>\n  <div class=\"distrotxt\">\n    On Linux and macOS, you can install Cadabra, its native notebook\n    interface, and the Jupyter kernel via Conda or Anaconda, thanks\n    to the work of Isuru Fernando. Activate the <tt>conda-forge</tt>\n    channel if you have not done that already, with\n    <code>conda config --add channels conda-forge</code>\n    <code>conda config --set channel_priority strict</code>\n    and then install these packages by using one of the following\n    lines:\n    <code>conda install cadabra2</code>\n    <code>conda install cadabra2-gtk</code>\n    <code>conda install cadabra2-jupyter-kernel</code>\n  </div>\n</div>-->\n\n</div>\n\n<p>\n  Is your distribution or operating system not listed above? Either\n  build Cadabra from source (see below) or send an email\n  to <a href=\"mailto:info@cadabra.science\">info@cadabra.science</a> to\n  request a package for your system.\n</p>\n\n\n{%- endblock %}\n"
  },
  {
    "path": "web2/cadabra2/source/faq.html",
    "content": "\n{% extends \"layout.html\" %}\n\n{% block title %}Cadabra: Frequently Asked Questions{% endblock %}\n\n{% block head %}{%- endblock %}\n\n{% block main %}\n\n<h1>Frequently Asked Questions</h1>\n\n<input type=\"radio\" name=\"collapse\" id=\"dummy\" checked=\"checked\">\n\n<h2>Installation</h2>\n\n<div class='faq_item'>\n  <a name=\"q_01_01\"></a>\n  <input type=\"radio\" name=\"collapse\" id=\"q_01_01\">    \n  <h3 class=\"handle\">\n    <label for=\"q_01_01\">The Jupyter kernel does not start.</label>\n  </h3>\n  <div class=\"content\">\n    <p>\n      In order for Jupyter to start the Cadabra kernel, it has to be\n      able to find the <tt>cadabra2</tt> and <tt>cadabra2_jupyter</tt>\n      modules. If you are using a binary package, these things will be\n      installed in a path searched by the system python, but if you\n      built from source, they may not be.\n    </p>\n    <p>\n      Typically, if you configure with <tt>cmake ..</tt> with no\n      further options, the installation will be into\n      <tt>/usr/local/lib/python3.7/site-packages</tt> (possibly with a\n      different python version number). You need to add this to\n      your <tt>PYTHONPATH</tt>, e.g. using\n      <div class='verbatim'>\n        <div class=\"source donthyphenate\">\n          <pre class='output'>export PYTHONPATH=${PYTHONPATH}:/usr/local/lib/python3.7/site-packages</pre>\n        </div>\n      </div>\n      in the terminal, before starting <tt>jupyter notebook</tt> from\n      there. You can stick this into the <tt>~/.bashrc</tt> file to\n      make it automatic at every terminal start.\n    </p>\n  </div>\n</div>\n\n<div class='faq_item'>\n  <input type=\"radio\" name=\"collapse\" id=\"q_01_02\">    \n  <h3 class=\"handle\">\n    <label for=\"q_01_02\">I get a 'Generic LaTeX error' when evaluating a cell.</label>\n  </h3>\n  <div class=\"content\">\n    <p>\n      This is typically caused by a missing LaTeX package. The error\n      dialog may give you a hint, but if you want to see the full\n      LaTeX error, take note of the file name in the error dialog, and\n      try to run that file through <tt>latex</tt> by hand.\n    </p>\n    <p>\n      The most common missing package is <tt>ytableau</tt>, which you\n      can get on Debian/Ubuntu systems by installing\n      the <tt>texlive-science</tt> package (or on older versions,\n      the <tt>texlive-math-extra</tt> package) and on Fedora by\n      installing <tt>texlive-ytableau</tt>.\n    </p>\n  </div>\n</div>\n\n<h2>How to...</h2>\n\n<div class='faq_item'>\n  <input type=\"radio\" name=\"collapse\" id=\"q_02_01\">    \n  <h3 class=\"handle\">\n    <label for=\"q_02_01\">What is the difference between free, fixed\n    and independent indices?</label>\n  </h3>\n  <div class=\"content\">\n    When you declare an index set, you can give it a <tt>position</tt>\n    property, which takes one of three\n    values <tt>free</tt>, <tt>fixed</tt>\n    or <tt>independent</tt>. Indices which are <tt>free</tt> can be\n    raised or lowered at will, and pairs can be at the same position;\n    these are typically used in case there is no metric associated to\n    them. Indices which have a different meaning when they are in\n    subscript or superscript position should, instead, be\n    declared <tt>fixed</tt>; this is what you would typically do in\n    special/general relativity, where the difference between an upper\n    or lower index is a factor of the metric. Cadabra can still swap\n    the position of pairs of indices in e.g. the <tt>canonicalise</tt>\n    function. If you want Cadabra to never touch the position of\n    indices in a set, declare them <tt>independent</tt>.\n  </div>\n</div>\n\n<div class='faq_item'>\n  <input type=\"radio\" name=\"collapse\" id=\"q_02_02\">    \n  <h3 class=\"handle\">\n    <label for=\"q_02_02\">How can I select all terms which contain a particular symbol?</label>\n  </h3>\n  <div class=\"content\">\n    Consider an expression like\n    <div class='verbatim'>\n      <div class=\"source donthyphenate\">\n        <pre class='output'>ex:= A + A B + A B C + B C + D E;</pre>\n      </div>\n    </div>\n    There are two ways to use <tt>zoom</tt> to select terms which\n    contain <tt>A</tt>. One will select terms which <strong>only</strong>\n    contain the factor <tt>A</tt>,\n    <div class='verbatim'>\n      <div class=\"source donthyphenate\">\n        <pre class='output'>zoom(ex, $A$);\n\t</pre>\n      </div>\n    </div>\n    The other one selects all terms which have <tt>A</tt> <strong>as\n    well as</strong> other factors,\n    <div class='verbatim'>\n      <div class=\"source donthyphenate\">\n        <pre class='output'>zoom(ex, $A B??$);\n\t</pre>\n      </div>\n    </div>\n    You can combine these two to select all terms which contain either\n    a bare <tt>A</tt> or <tt>A</tt> multiplied with other things,\n    <div class='verbatim'>\n      <div class=\"source donthyphenate\">\n        <pre class='output'>zoom(ex, $A, A B??$);\n\t</pre>\n      </div>\n    </div>\n  </div>\n</div>\n\n<h2>Error messages</h2>\n\n<div class='faq_item'>\n  <input type=\"radio\" name=\"collapse\" id=\"q_04_01\">    \n  <h3 class=\"handle\">\n    <label for=\"q_04_01\">RuntimeError: Dependencies on derivatives\n    are not yet handled in the sympy bridge.</label>\n  </h3>\n  <div class=\"content\">\n    This error occurs when you try to use the <tt>evaluate</tt>\n    algorithm on an expression with derivatives, and the expression\n    contains objects which were declared with a\n    property <tt>::Depends(\\partial{&#35;})</tt> or something to that\n    extent.\n\n    To avoid the issue, there are two ways out. Either declare the\n    dependence of that object directly on the coordinate. So instead\n    do something like\n    <div class='verbatim'>\n      <div class=\"source donthyphenate\">\n        <pre class='output'>x::Coordinate;\nA::Depends(x);</pre></div></div>\n    The other alternative is to simply switch off automatic\n    simplification, by using the <tt>simplify=False</tt> argument to\n    the <tt>evaluate</tt> function.\n  </div>\n</div>\n  \n<h2>Design and philosophy</h2>\n\n\n<div class='faq_item'>\n  <input type=\"radio\" name=\"collapse\" id=\"q_03_01\">    \n  <h3 class=\"handle\">\n    <label for=\"q_03_01\">Why not build the tensor functionality into\n      Sympy, and wedge into Sympy's expression parser?\n    </label>\n  </h3>\n  <div class=\"content\">\n    Cadabra uses the philosophy that expressions should be represented\n    in their own language, not Python. However, one can do something\n    like that in Sympy, by only feeding expressions in string form to\n    the logic in <code>sympy.parsing.sympy_parser</code>. So in a\n    sense Sympy supports this Cadabraesque mode of working, even\n    though the tutorials and examples do not emphasise it.\n\n    The reason why Cadabra nevertheless uses its own parser, and its\n    own tree representation of expressions, is simply that an enormous\n    amount of work would have to be done to rewrite the lot so that it\n    fits into the Sympy framework. Moreover, little would be gained by\n    doing this: almost all functionality which is in Sympy and which\n    would make sense when applied to tensors (think of taking\n    derivatives, or pattern matching) would require a lot of extra\n    Sympy code to extend it beyond scalars.\n\n    The way things are now the separation is clean, localised, and\n    relatively easy to maintain. If you would ever rewrite\n    Cadabra+Sympy from scratch you might take a different approach,\n    but that's not going to happen soon.\n  </div>\n</div>\n\n<div class='faq_item'>\n  <input type=\"radio\" name=\"collapse\" id=\"q_03_02\" >    \n  <h3 class=\"handle\">\n    <label for=\"q_03_02\">Why an independent notebook interface instead of building on\n      IPython?</label>\n  </h3>\n  <div class=\"content\">\n    There are a number of reasons for this. For starters, Cadabra's\n      notebook interface predates IPython (that is, a publically\n      available version of it) by quite a few years. That by itself is\n      of course not a very good reason to keep developing the Cadabra\n      notebook interface, but it does play a certain role.\n\n    <p>A more important reason has to do with the fact that there are,\n      despite what one might think at first inspection, quite a few\n      differences between IPython/Jupyter and the Cadabra interface. The\n      most obvious one is that Cadabra is a native application, which\n      does not rely on a web browser to display its results. I still\n      think that native applications have their place, as they tend to\n      look and feel much better than web apps.</p>\n\n    <p>IPython/Jupyter tend to be focussed a lot on data-centric\n      problems, and less so on being a nice front-end for symbolic\n      mathematics. These two do differ.</p>\n\n    <p>Another reason to keep developing the Cadabra notebook\n      interface is that it allows me much more flexibility in trying new\n      features and ideas. \n  </div>\n</div>\n\n\n{%- endblock %}\n"
  },
  {
    "path": "web2/cadabra2/source/features.html",
    "content": "{% extends \"layout.html\" %}\n\n{% block title %}Cadabra: features{% endblock %}\n\n{% block head %}{%- endblock %}\n\n{% block main %}\n\n<h1>Features</h1>\n<p>\n  ... \n</p>\n\n\n<h1>Comparison of Cadabra with other systems</h1>\n<p>\n  In order to understand whether Cadabra is useful for you, a\n  comparison to other system may help. Without going too much into\n  detail, here are some notable differences and similarities with\n  other systems.\n</p>\n\n<h2>Patterns versus maths</h2>\n<p>\n  Cadabra is predominantly a 'field theory aware notebook'. What this\n  means is that is is designed to be useful for the manipulations of\n  patterns which occur in the description of field theory problems. It\n  knows about patterns more than it knows about the mathematical\n  meaning of those patterns. \n</p>\n<p>\n  Other programs in this class\n  are <a href=\"http://www.nikhef.nl/~form/\">FORM</a> and its\n  predecessor <a href=\"http://www-personal.umich.edu/~williams/archive/schoonschip/\">Schoonship</a>,\n  which both know relatively little about the maths or physics which\n  people do with them, but primarily provide a cleverly thought-out\n  toolbox of algorithms to manipulate expressions. Just like when you\n  compute things with pen and paper, you can do things with these\n  programs which are manifest mathematical nonsense.\n</p>\n<p>\n  Programs like Sage\n  (with <a href=\"http://sagemanifolds.obspm.fr/\">SageManifolds</a>)\n  and <a href=\"http://www.xact.es/\">xAct</a> tend to be much more strict in how you define your problem:\n  they know a lot about the mathematical meaning of symbols, and often\n  insist that you are very precise about defining them. Cadabra can be\n  much more relaxed, which tends to make its input easier to read.\n</p>\n<p>\n  Neither of these approaches is best, they are just different.\n</p>\n\n<h2>Targetted versus comprehensive</h2>\n<p>\n  Cadabra is intentionally not designed to cover 'as much of\n  mathematics as we can implement'. It is specifically meant to help\n  solving a particular class of problems which occur in field\n  theory. This is in part because of its roots (it originally was just\n  a simple tool to help write research papers), and in part because\n  I do not believe that a 'megalomanic' approach can work. Especially\n  not if you do not have hundreds of developers. \n</p>\n<p>\n  Programs like Mathematica, Maple and Sage have a different\n  philosophy. They try to target, not always with success, a very\n  large audience, by aiming to cover 'all of maths'. \n</p>\n\n\n\n\n{%- endblock %}\n"
  },
  {
    "path": "web2/cadabra2/source/help.html",
    "content": "{% extends \"layout.html\" %}\n\n{% block title %}Cadabra: Help{% endblock %}\n\n{% block head %}{%- endblock %}\n\n{% block main %}\n<h1>Help and book</h1>\n\n<h2>Forum</h2>\n\n<p>All questions about using Cadabra can be posted on\n  the <a href=\"/qa\">Cadabra Q&amp;A</a> forum. The forum accepts LaTeX\n  formulas and is fully searchable. If you feel your question is not\n  ready for public consumption, please email me\n  at <a href=\"mailto:info@cadabra.science\">info@cadabra.science</a>. \n</p>\n\n<h2>Frequently asked questions</h2>\n<p>\n  If you have a question, please first consult the list of\n  <a href=\"faq.html\">frequently asked questions</a>; yours may be on\n  it already.\n</p>\n\n\n<h2>The Cadabra book</h2>\n<p>\n  This book is the place to go for a detailed specification of how\n  Cadabra works. You can browse it online or download the lot as a\n  <a href=\"the_cadabra_book.pdf\">single PDF file</a> by clicking on\n  the book cover. If you prefer to learn by example, you are better\n  off with the <a href=\"tutorials.html\">tutorials</a>. Also don't\n  forget to have a look at Leo Brewin's\n  excellent <a href=\"papers.html#brewin\">introductory papers on\n    Cadabra</a>.\n</p>\n<p>\n  For detailed information on how to write Cadabra algorithms (in\n  Python or C++), please\n  consult <a href=\"writing_algorithms.pdf\">Writing Algorithms in\n  Cadabra2</a> by Dominic Price.\n</p>\n<p>\n  <div class=\"splash_image book_cover\">\n\t <a href=\"/the_cadabra_book.pdf\"><img src=\"/static/images/the_cadabra_book.png\" alt=\"[cadabra book cover]\"/></a>\n  </div>\n  <ol class=\"table_of_contents\">\n\t <li>The input format\n\t\t<ol>\n\t\t  <li><a href=\"notebooks/input_format.html\">Basics about the input format</a></li>\n\t\t  <li><a href=\"notebooks/ref_printing.html\">Printing expressions</li>\n\t\t  <li><a href=\"notebooks/ref_properties.html\">Object properties and declaration</a></li>\n\t\t  <li><a href=\"notebooks/ref_indices.html\">Indices, dummy indices and automatic index renaming</a></li>\n\t\t  <li><a href=\"notebooks/ref_exponents.html\">Exponents, indices and labels</a></li>\n\t\t  <li><a href=\"notebooks/ref_spacing.html\">Spacing and brackets</a></li>\n\t\t  <li><a href=\"notebooks/ref_implicit_versus_explicit.html\">Implicit versus explicit indices</a></li>\n\t\t  <li><a href=\"notebooks/ref_indexbrackets.html\">Index brackets</a></li>\n\t\t</ol>\n\t </li>\n\t <li>Mathematical properties\n\t\t<ol>\n\t\t  <li><a href=\"notebooks/ref_derivatives.html\">Derivatives and implicit dependence on coordinates</a></li>\n\t\t  <li><a href=\"notebooks/ref_accents.html\">Accents</a></li>\n\t\t  <li><a href=\"notebooks/ref_ordering.html\">Symbol ordering and commutation properties</a></li>\n\t\t  <li>Anti-commuting objects and derivatives</li>\n\t\t</ol>\n\t <li>Manipulating expressions\n\t\t<ol>\n\t\t  <li><a href=\"notebooks/ref_selecting.html\">Selecting parts of expressions</a></li>\n\t\t  <li>Elementary operations on expressions</li>\n\t\t  <li><a href=\"notebooks/ref_import.html\">Using multiple files and notebooks</a></li>\n\t\t  <li><a href=\"notebooks/ref_default_simplification.html\">Default simplification</a></li>\n\t\t  <li><a href=\"notebooks/ref_patterns.html\">Patterns, conditionals and regular expressions</a></li>\n\t\t  <li><a href=\"notebooks/ref_numerical.html\">Numerical evaluation of expressions</a></li>\n\t\t  <li><a href=\"notebooks/ref_dynamical_updates.html\">Dynamic cell updates and animations</a></li>\n\t\t  <li><a href=\"notebooks/ref_plotting.html\">Plotting functions and data</a></li>\n\t\t  <li><a href=\"notebooks/ref_ndsolve.html\">Numerical solution of differential equations</a></li>\n\t\t</ol>\n\t </li>\n\t <li>Writing your own packages\n\t\t<ol>\n\t\t  <li><a href=\"notebooks/ref_programming.html\">Programming in Cadabra</a></li>\n\t\t  <li><a href=\"notebooks/ref_sympy.html\">Using SymPy on Cadabra expressions</a></li>\n\t\t  <li><a href=\"notebooks/ref_kernel.html\">The kernel and other internals</li>\n\t\t  <li><a href=\"notebooks/ref_c++_library.html\">Using Cadabra directly from C++</a></li>\n\t\t  <li><a href=\"notebooks/ref_flags_variables.html\">Environment variables and startup flags</a></li>\n\t\t</ol>\n\t </li>\n  </ol>\n</p>\n\n\n<h2>Old reference guide</h2>\n\n\t<p>An extensive reference guide of version 1.x of the program, with a description\n\tof the input language, the algorithms and technical details on how\n\tto extend it by adding new C++ modules, is available as</p>\n\t<blockquote class=\"reference\">\n\t<div class=\"author\">Kasper Peeters</div>\n\t<div class=\"title\"><a href=\"/static/pdf/cadabra.pdf\">Cadabra: reference guide and tutorial</a></div>\n\t<div class=\"pubinfo\">preprint AEI-2006-038</div>\n\t<div class=\"pubinfo\">last version: November 2nd, 2012</div>\n\t</blockquote>\n    <p>\n    Go here if the new 2.x reference manual above does not yet have\n\t  the information you need.</p>\n\n{%- endblock %}\n"
  },
  {
    "path": "web2/cadabra2/source/index.html",
    "content": "{% extends \"layout.html\" %}\n\n{% block title %}Cadabra: a field-theory motivated approach to computer algebra{% endblock %}\n\n{% block head %}\n<meta name=\"description\" content=\"Cadabra is a symbolic computer\n\t\t\t\t\t\t\t\t\t\t\t algebra system designed to solve\n\t\t\t\t\t\t\t\t\t\t\t problems in classical and quantum\n\t\t\t\t\t\t\t\t\t\t\t field theory.\" />\n{%- endblock %}\n\n{% block main %}\n\n<h1>News</h1>\n<p>See the <a href=\"changelog.html\">change log</a> for latest changes\n  only available on github.</p>\n<p><div id=\"cloud\">\n    <img class=\"running_image\" src=\"/static/icons/cadabra2-cloud.png\">\n    <div>\n      Now available: Cadabra in the\n      cloud, from your\n      browser. Email <a href=\"mailto:cloud@cadabra.science?Subject=Cadabra%20Cloud%20access&Body=I%20would%20like%20to%20register%20for%20beta%20access%20to%20Cadabra%20Cloud.\">cloud@cadabra.science</a>\n      if you want to get access (please provide some details about\n      what you want to use it for).\n    </div>\n  </div>\n</p>\n<dl>\n  <dt>31 July 2025</dt>\n  <dd>Release of 2.5.14 (<a href=\"changelog.html#2.5.14\">changes</a>).\n    Various plotting improvements and fixes, improvements to the SymPy\n    bridge and component computations, fixes for a number of binary\n    packages, and speedups.\n  </dd>\n  <dt>7 May 2025</dt>\n  <dd>Release of 2.5.12 (<a href=\"changelog.html#2.5.12\">changes</a>).\n    Many new features and usability improvements.\n  </dd>\n  <dt>24 December 2024</dt>\n  <dd>Release of 2.5.10 (<a href=\"changelog.html#2.5.10\">changes</a>).\n    Various improvements to the notebook interface including dynamical\n    graphics and better typesetting. Speedups for <tt>substitute</tt> (Daniel).\n    Internal changes and improvements to the CI pipeline.\n  </dd>\n<!--  <dt>25 October 2024</dt>\n  <dd>Release of 2.5.8 (<a href=\"changelog.html#2.5.8\">changes</a>).\n    Mostly bug fixes and some improvements to the notebook interface.\n  </dd>\n  <dt>24 September 2024</dt>\n  <dd>Windows installer now available again, get it from the\n    <a href=\"https://github.com/kpeeters/cadabra2/releases/latest\">github release page</a>.\n    Please report any issues.\n  </dd>\n  <dt>15 June 2024</dt>\n  <dd>Release of 2.5.2 (<a href=\"changelog.html#2.5.2\">changes</a>).\n    Cadabra now\n    uses <a href=\"https://github.com/NanoMichael/MicroTeX\">MicroTeX</a>\n    to do the maths typesetting in the notebook interface. This is not\n    only much faster, but also means that LaTeX is no longer a\n    dependency, and we can distribute Cadabra as an AppImage. The GUI\n    has been updated and there are many new features, such as full\n    UTF-8 support, dynamical cell updates and plot animations.\n  </dd>\n  <dt>20 Sep 2023</dt>\n  <dd>Release of 2.4.4 (<a href=\"changelog.html#2.4.4\">changes</a>).\n    Many new features for numerical evaluation and plotting of expressions\n    using <tt>nevaluate</tt> (see\n    the <a href=\"https://cadabra.science/notebooks/ref_numerical.html\">numerical\n    evaluation</a> chapter in the book) and many bug fixes.\n  </dd>\n  <dt>25 Aug 2022</dt>\n  <dd>Release of 2.4.0 (<a href=\"changelog.html#2.4.0\">changes</a>).\n    Update to accompany the release of\n    the <a href=\"http://arxiv.org/abs/2208.11946\">paper about the meld\n    algorithm</a>.  Many bug fixes and various functionality\n    improvements and UI enhancements.</dd>\n    \n  <dt>21 Nov 2021</dt>\n  <dd>Release of 2.3.8 (<a href=\"changelog.html#2.3.8\">changes</a>).\n\t Update to make Cadabra build on Apple silicon, and many bugfixes\n\t and small enhancements throughout.</dd>\n\n  <dt>30 Dec 2020</dt>\n  <dd>Release of 2.3.6 (<a href=\"changelog.html#2.3.6\">changes</a>).\n\t Various bug fixes.\n  <dt>08 Dec 2020</dt>\n  <dd>New Windows installer, for version 2.3.5, now available from the\n    <a href=\"download.html#windows\">download page</a>. Please provide feedback if you want the Windows\n    version to receive regular updates.\n  </dd>\n  \n  <dt>16 Nov 2020</dt>\n  <dd>Release of 2.3.4 (<a href=\"changelog.html#2.3.4\">changes</a>).\n    Mostly a bug-fix release. Also contains functionality to save\n    Cadabra notebooks as Jupyter notebooks, to make it easier to\n    exchange them between the native app and Jupyter.\n  </dd>\n\n  <dt>31 Oct 2020</dt>\n  <dd>Release of 2.3.2 (<a href=\"changelog.html#2.3.2\">changes</a>).\n\t Various new features and fixes, and a new Jupyter kernel\n\t which is installed by default, thanks to Fergus Baker. \n  </dd>\n\n  <dt>11 June 2020</dt>\n  <dd>Release of 2.3.0 (<a href=\"changelog.html#2.3.0\">changes</a>).\n\t Various new features and fixes. Available on Linux,\n\t macOS and Windows. \n    Now also available through conda-forge, from which you can also\n\t install the <a href=\"jupyter.html\">Cadabra Jupyter kernel</a>.\n  </dd>\n\n  <dt>01 April 2020</dt>\n  <dd>No, this is not an April fools joke. There is now\n    an <a href=\"jupyter.html\">Anaconda package for the Cadabra\n    Jupyter kernel</a>. Only for Linux for now.\n  </dd> \n  <dt>10 December 2019</dt>\n  <dd>Release of 2.2.8 (<a href=\"changelog.html#2.2.8\">changes</a>).\n\t Various new features, long overdue release. Available on Linux,\n\t macOS and Windows. \n  </dd>\n  <dt>11 November 2019</dt>\n  <dd>New Windows installer. Thanks to feedback from many users, there\n  is now a new Windows installer which hopefully takes care of many of\n  the installation problems encountered with earlier versions. \n  <a href=\"/packages/windows/cadabra-2.2.7g-installer.exe\">Download the Windows installer (2.2.7)</a>.\n  </dd>\n  <dt>18 April 2019</dt>\n  <dd>Release of 2.2.6\n  (<a href=\"changelog.html#2.2.6\">changes</a>). Many features for\n  implicit indices, possibility to build as Jupyter kernel)</dd>\n  <dt>3 March 2019</dt>\n  <dd>There is now an experimental Jupyter kernel for Cadabra. For the\n  time being you will have to build this from source, but hopefully\n\t there will soon be a way to run this on a cloud service. See\n\t <a href=\"https://github.com/kpeeters/cadabra2/blob/master/JUPYTER.rst\">build\n\t instructions</a> for more details.\n  </dd>\n  <dt>20 January 2019</dt>\n  <dd>\n\t Cadabra can now be used on-line (without installing it on your\n\t own computer) through the <a href=\"https://cocalc.com\">CoCalc</a>\n\t service. CoCalc is the successor to SageMathCloud, and allows you\n\t to run a large variety of mathematics software in the cloud. To\n\t use Cadabra there, create a 'X11 desktop' session and then run\n\t <tt>cadabra2-gtk</tt>.\n  </dd>\n   <dt>19 December 2018</dt>\n  <dd>Release of 2.2.4\n\t (<a href=\"changelog.html#2.2.4\">changes</a>).\n\t Loads of new features, available on Linux, macOS and Windows.\n  </dd>\n <dt>15 February 2018</dt>\n  <dd>Preparing for 2.2.0 (<a href=\"changelog.html#master\">changes</a>).</dd>\n  <dt>6 August 2017</dt>\n  <dd>Version 2.1.5 released (<a href=\"changelog.html#2.1.5\">changes</a>).</dd>\n  <dt>14 April 2017</dt>\n  <dd>Version 2.1.4 released (<a href=\"changelog.html#2.1.4\">changes</a>).</dd>\n  <dt>4 January 2017</dt>\n  <dd>Version 2.1.2 released (<a href=\"changelog.html#2.1.2\">changes</a>).</dd>\n  <dt>3 January 2017</dt>\n  <dd>Version 2.1.0 released\n  (<a href=\"changelog.html#2.1.0\">changes</a>).</dd>\n-->\n<!--\n  <dt>3 January 2017</dt>\n  <dd>The old site has been turned off. Cadabra 1.x will still be\n\t supported with bug fixes, and it will continue to be available\n\t via Debian-based distros, but all further development will take\n\t place on the 2.x versions.</dd>\n  <dt>6 November 2016</dt>\n  <dd>We are now generating packages for all major Linux distributions\n\t automatically so they track the latest release available on\n\t github. Get them from the <a href=\"download.html\">download\n\t page</a>.</dd> -->\n</dl>\n\n<h1>What is Cadabra?</h1>\n<p  class=\"hyphenate\">\n  Cadabra is a symbolic computer algebra system (CAS) designed\n  specifically for the solution of problems encountered in field\n  theory. It has extensive functionality for tensor computer\n  algebra, <a href=\"/notebooks/tensor_monomials.html\">tensor\n  polynomial simplification</a> including multi-term symmetries,\n  fermions and anti-commuting\n  variables, <a href=\"/notebooks/gamma_matrix_algebra.html\">Clifford\n  algebras</a> and <a href=\"/notebooks/fierz.html\">Fierz\n  transformations</a>, <a href=\"/notebooks/schwarzschild.html\">component computations</a>,\n  implicit coordinate dependence, multiple index\n  types and many more. The input format is a subset of TeX.</p>\n\n<p class=\"hyphenate\">\n  Both a command-line and a graphical notebook interface are\n  available, and you can also use Cadabra from Jupyter by using the\n  <a href=\"jupyter.html\">Cadabra Jupyter kernel</a>, or\n  from <a href=\"https://www.texmacs.org\">TeXmacs</a>.\n</p>\n\n  <div class=\"splash_image\">\n\t <img src=\"/static/images/screenshot.png\" alt=\"[screenshot]\"/>\n  </div>\n  <ul class=\"hyphenate\">\n\t <li>\n\t\tDesigned for field-theory problems, with handling of\n\t\tanti-commuting and non-commuting objects without special notations\n\t\tfor their products, gamma matrix algebra, Fierz identities, Dirac\n\t\tconjugation, vielbeine, flat and curved, covariant and\n\t\tcontravariant indices, implicit dependence of tensors on\n\t\tcoordinates, partial and covariant derivatives...\n\t </li>\n\t <li>\n\t\tPowerful tensor simplification algorithms, not just for\n\t\tmono-term symmetries but also for multi-terms symmetries like\n\t\tthe Bianchi identity, or dimensionally-dependent symmetries like\n\t\tthe Schouten identity.\n\t </li>\n\t <li>\n\t\tAllows for both abstract and component computations.\n\t </li>\n\t <li>\n\t\tA standalone graphical notebook interface which can also be\n\t\tused as a front-end for SymPy.\n\t </li>\n\t <li>\n\t\tInput and output using a subset of LaTeX notation.\n\t </li>\n\t <li>\n\t\tProgrammable using Python, but also usable as\n\t\ta <a href=\"notebooks/ref_c++_library.html\">standalone library\n\t\tfrom C++</a>.\n\t </li>\n  </ul>\n<br/>\n\n<h1>Cadabra's design philosophy</h1>\n<p  class=\"hyphenate\">\n  Cadabra is built around the fact that many computations do not have\n  one single and unique path between the starting point and the end\n  result. When we do computations on paper, we often take bits of an\n  expression apart, do some manipulations on them, stick them back\n  into the main expression, and so on. Often, the manipulations that\n  we do are far from uniquely determined by the problem, and often\n  there is no way even in principle for a computer to figure out what\n  is 'the best' thing to do. \n</p>\n<p  class=\"hyphenate\">\n  What we need the computer to do, in such a case, is to be good at\n  performing simple but tedious steps, without enforcing on the user\n  how to do a particular computation. In other words, we want the\n  computer algebra system to be a scratchpad, leaving us in control of\n  which steps to take, not forcing us to return to a 'canonical'\n  expression at every stage.\n</p>\n<p  class=\"hyphenate\">\n  Most existing computer algebra systems allow for this kind of work\n  flow only by requiring to stick clumsy 'inert' or 'hold' arguments\n  onto expressions, by default always 'simplifying' every input to\n  some form they think is best. Cadabra starts from the other end of\n  the spectrum, and as a general rule keeps your expression untouched, \n  unless you explicitly ask for something to be done to it.\n</p>\n<p  class=\"hyphenate\">\n  Another key issue in the design of symbolic computer algebra systems has\n  always been whether or not there should be a distinction between the\n  'data language' (the language used to write down mathematical\n  expressions), the 'manipulation language' (the language used to write\n  down what you want to do with those expressions) and the\n  'implementation language' (the language used to implement algorithms\n  which act on mathematical expressions). Many computer algebra systems\n  take the approach in which these languages are the same (Axiom,\n  Reduce, Sympy) or mostly the same apart from a small core which uses a\n  different implementation language (Mathematica, Maple). The Cadabra\n  project is rooted in the idea that for many applications, it is better\n  to keep a clean distinction between these three languages. Cadabra\n  writes mathematics using LaTeX, is programmable in Python, and is\n  under the hood largely written in C++.\n</p>\n<br/>\n\n<h1>History</h1>\n<p class=\"hyphenate\">\n  Cadabra was originally written around 2001 to\n  solve <a href=\"https://arxiv.org/abs/hep-th/0010167\">a\n  number</a> <a href=\"https://arxiv.org/abs/hep-th/0307298\">of\n  problems</a> related to higher-derivative supergravity. It was then\n  expanded and polished, and first saw its public\n  release <a href=\"https://arxiv.org/abs/hep-th/0701238\">in 2007</a>.\n  During the years that followed, it became clear that several design\n  decisions were not ideal, such as the use of a custom programming\n  language and the lack of functionality for component computations. Over\n  the course of 2015-2016 a large rewrite took place, which resulted\n  in Cadabra 2.x.  This new version is programmable in Python and does\n  both abstract and component computations. This new web site, with\n  new tutorials and all manual pages accessible online, will also\n  hopefully help to make Cadabra easier to use.\n</p>\n<p class=\"hyphenate\">\n  Since 2018 Cadabra is available on all major platforms (Linux,\n  MacOS, Windows, BSD). Visit the <a href=\"/qa\">Q&amp;A forum</a> for\n  help using it.\n</p>\n\n<br/>\n\n{%- endblock %}\n\n"
  },
  {
    "path": "web2/cadabra2/source/jupyter.html",
    "content": "{% extends \"layout.html\" %}\n\n{% block title %}Cadabra: use with Jupyter{% endblock %}\n\n{% block head %}{%- endblock %}\n\n{% block main %}\n<h1>Cadabra in Jupyter</h1>\n\n<h2>General</h2>\n<p class=\"hyphenate\">\n  By virtue of the Cadabra kernel for Jupyter, it is possible to use\n  Cadabra from a Jupyter notebook. This allows you to use Cadabra\n  notation in a familiar environment, and make use of\n  e.g.&nbsp;Jupyter widgets for visualisation, or other things which\n  are currently not possible in the Cadabra notebook interface.\n</p>\n  <div class=\"splash_image\">\n\t <img src=\"/static/images/ss_jupyter.png\" alt=\"[screenshot]\"/>\n  </div>\n<p class=\"hyphenate\">\n  The Cadabra Cloud service makes use of Jupyter to provide you with\n  an on-line service to run Cadabra; send an email\n  to <a href=\"mailto:cloud@cadabra.science?Subject=Cadabra%20Cloud%20access&Body=I%20would%20like%20to%20register%20for%20beta%20access%20to%20Cadabra%20Cloud.\">cloud@cadabra.science</a>\n  if you want to get access.\n</p>\n<br/>\n\n<h2>Installation</h2>\n<p class=\"hyphenate\">\n  If you do a standard build from source, or if you obtained Cadabra\n  from a binary package (at least version 2.3.1.15), you will get the\n  Cadabra Jupyter kernel automatically. You should be able to start\n  the Jupyter notebook as usual with\n</p>\n<div class=\"output\">  jupyter notebook</div>\n<p class=\"hyphenate\">\n  The 'New' button in the top-right of the screen should then give you\n  the option of creating a new notebook with a 'Cadabra2' kernel. If\n  that fails, and the error messages produced by Jupyter indicate that\n  it cannot find the Cadabra kernel, you may need\n  to <a href=\"faq.html#q_01_01\">adjust your <tt>PYTHONPATH</tt></a>.\n</p>\n\n<h2>Docker version</h2>\n<p class=\"hyphenate\">\n  Alternatively, you can use\n  the <a href=\"https://hub.docker.com/r/kpeeters/cadabra2-jupyter\">official\n  Docker image for Cadabra</a>, available from DockerHub, which\n  contains a Jupyter server with the Cadabra kernel. This will not be\n  able to see existing Python package installations on your system,\n  but has the advantage of being easy to install (and easy to remove,\n  if you ever want to do that).\n</p>\n\n  <!--<h2>Old Xeus-based kernel</h2>\n<p>\n  To obtain the Cadabra kernel for Jupyter, you need to either install\n  it from Anaconda,\n  or <a href=\"https://github.com/kpeeters/cadabra2/JUPYTER.rst\">build\n  it yourself</a>. To install, ensure that the required channel is\n  active, and update/install:\n</p>\n<div class=\"output\">  conda config --add channels conda-forge\n  conda update --all\n  conda install cadabra2-jupyter-kernel</div>\n<p>\n  If the above went well, you should now be able to start the Jupyter\n  notebook as usual with\n</p>\n<div class=\"output\">  jupyter notebook</div>\n<p>\n  The 'New' button in the top-right of the screen should then give you\n  the option of creating a new notebook with a Cadabra kernel.\n</p>-->\n\n<h2>Differences with Cadabra's own notebook</h2>\n<p class=\"hyphenate\">\n  When you use Cadabra within Jupyter, most things will work as in\n  Cadabra's own notebook interface. The main thing to keep in mind is\n  that Jupyter notebooks (with extension <tt>.ipynb</tt>) and Cadabra\n  notebooks (with extension <tt>.cnb</tt>) are not the same file\n  format. You can read notebooks created in Jupyter into the Cadabra\n  <tt>cadabra2-gtk</tt> client, and you can (as of version 2.3.3)\n  export Cadabra notebooks as Jupyter notebooks (or convert them using\n  the <tt>cadabra2ipynb</tt> command-line utility), but it is good to\n  keep this in mind.\n</p>\n<p class=\"hyphenate\">\n  You <em>can</em>, however, make use of Cadabra packages inside the\n  Jupyter notebook, so you can still do <tt>import something</tt>\n  where <tt>something.cnb</tt> is a Cadabra notebook.\n</p>\n\n{%- endblock %}\n\n"
  },
  {
    "path": "web2/cadabra2/source/layout.html",
    "content": "<!DOCTYPE html>\n<html lang=en>\n  <head>\n\t <meta charset=\"utf-8\">\n\t <meta name=\"viewport\" content=\"width=device-width,initial-scale=1\">\n\t <meta name=\"robots\" content=\"index, follow\" />\n\n\t <meta keywords=\"cadabra, computer algebra, symbolic computer\n\t algebra, cas, tensors, general relativity, relativity, metric,\n\t field theory, quantum field theory, mathematica, maple, xact,\n\t grtensor, sheep\" />\n\n\t <meta name=\"copyright\" content=\"Kasper Peeters\" />\n\t <title>{% block title %}{% endblock %}</title>\n\t <link rel=\"shortcut icon\" type=\"image/png\" href=\"/static/icons/cadabra2.png\">\n\n\t <script type=\"text/javascript\" \n\t\t\t\tsrc='https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML'></script>\n\n\t </script>\n\t <link href='https://fonts.googleapis.com/css?family=Inconsolata' rel='stylesheet' type='text/css'>\n\t <link href='https://fonts.googleapis.com/css?family=Lato:300,:400' rel='stylesheet' type='text/css'>\n\t <link href=\"https://fonts.googleapis.com/css?family=Bree+Serif\" rel=\"stylesheet\" type=\"text/css\">\n\t <link rel=\"stylesheet\" href=\"/static/fonts/Bright/cmun-bright.css\">\n\t <script>\n\t\tMathJax.Hub.Config({\n\t\ttex2jax: {\n\t\tinlineMath: [['$','$'], ['\\\\(','\\\\)']],\n\t\tprocessEscapes: true,\n\t\tdisplayAlign: \"left\",\n\t\tignoreClass: \"python\",\n\t\tprocessClass: \"latex_view\",\n      linebreaks: { automatic: true }\n\t\t},\n\t\t\"HTML-CSS\": {\n\t\tscale: 105,\n\t\tpreferredFont: \"TeX\",\n\t\twebFont: \"TeX\",\n\t\tmtextFontInherit: false,\n\t\tmatchFontHeight: false,\n      linebreaks: { automatic: true }\n\t\t},\n\t\t\"SVG\": {\n      linebreaks: { automatic: true }\n\t\t}\n\t\t});\n\t </script>\n\t <link href=\"/static/styles/cadabra-web.css\" rel=\"stylesheet\" type=\"text/css\" />\n\n\t {% block head %}{% endblock %}\n  </head>\n  <body>\n    <div id=\"topflex\">\n\t <div id=\"logobar\">\n\t\t<a href=\"/\">\n\t\t  <div id=\"cadabra_logo\">\n\t\t\t <img src=\"/static/icons/cadabra2.png\" />\n\t\t  </div>\n\t\t  <div id=\"cadabra\">\n\t\t\t Cadabra\n\t\t  </div>\n\t\t</a>\n\t\t<div id=\"subtext\">\n\t\t  a field-theory motivated approach to computer algebra\n\t\t</div>\n\t\t<!--\t\t<div id=\"author\">\n\t\t\t\t\tKasper Peeters<br/>\n\t\t\t\t\tcadabra@phi-sci.com\n\t\t\t\t\t</div> -->\n\t </div>\n\t <div id=\"search\">\n<script>\n  (function() {\n    var cx = '016915739931163127408:1ha2sk1dyg0';\n    var gcse = document.createElement('script');\n    gcse.type = 'text/javascript';\n    gcse.async = true;\n    gcse.src = 'https://cse.google.com/cse.js?cx=' + cx;\n    var s = document.getElementsByTagName('script')[0];\n    s.parentNode.insertBefore(gcse, s);\n  })();\n</script>\n<gcse:search></gcse:search>\n\t </div>\n\t </div>\n<!--\t <hr id=\"below_logo\"/> -->\n\t <div id=\"menubar\">\n\t\t<a href=\"/download.html\">\n\t\t  <div class=\"icon_background\" >\n\t\t\t <img src=\"/static/icons/download.png\" alt=\"[download]\" />\n\t\t\t <div class=\"icon_text\">\n\t\t\t\tDownload\n\t\t\t </div>\n\t\t  </div>\n\t\t</a>\n\t\t<a href=\"/jupyter.html\">\n\t\t  <div class=\"icon_background\" >\n\t\t\t <img class=\"jupyter_icon\" src=\"/static/icons/jupyter.png\" alt=\"[cadabra in jupyter]\" />\n\t\t\t <div class=\"icon_text\">\n\t\t\t\tJupyter\n\t\t\t </div>\n\t\t  </div>\n\t\t</a>\n\t\t<a href=\"/notebooks/quickstart.html\">\n\t\t  <div class=\"icon_background\" >\n\t\t\t <img src=\"/static/icons/quickstart.png\" alt=\"[quick start]\" />\n\t\t\t <div class=\"icon_text\">\n\t\t\t\tQuick start\n\t\t\t </div>\n\t\t  </div>\n\t\t</a>\n<!--\t\t<a href=\"/v1x.html\">\n\t\t  <div class=\"icon_background\" >\n\t\t\t <img src=\"/static/icons/v1.png\" alt=\"[upgrade]\" />\n\t\t\t <div class=\"icon_text\">\n\t\t\t\tUpgrade\n\t\t\t </div>\n\t\t  </div>\n\t\t</a> -->\n\t\t<hr/>\n\t\t<a href=\"/help.html\">\n\t\t  <div class=\"icon_background\" >\n\t\t\t <img src=\"/static/icons/help.png\" alt=\"[help]\" />\n\t\t\t <div class=\"icon_text\">\n\t\t\t\tHelp&nbsp;&amp;&nbsp;book\n\t\t\t </div>\n\t\t  </div>\n\t\t</a>\n\t\t<a href=\"/tutorials.html\">\n\t\t  <div class=\"icon_background\" >\n\t\t\t <img src=\"/static/icons/tutorials.png\" alt=\"[tutorials]\" />\n\t\t\t <div class=\"icon_text\">\n\t\t\t\tTutorials\n\t\t\t </div>\n\t\t  </div>\n\t\t</a>\n\t\t<a href=\"/man.html\">\n\t\t  <div class=\"icon_background\" >\n\t\t\t <img src=\"/static/icons/features.png\" alt=\"[features]\" />\n\t\t\t <div class=\"icon_text\">\n\t\t\t\t<div class=\"firstline\">Reference</div><div>manual</div>\n\t\t\t </div>\n\t\t  </div>\n\t\t</a>\n\t\t<a href=\"/papers.html\">\n\t\t  <div class=\"icon_background\" >\n\t\t\t <img src=\"/static/icons/paper.png\" alt=\"[paper]\" />\n\t\t\t <div class=\"icon_text\">\n\t\t\t\tPapers\n\t\t\t </div>\n\t\t  </div>\n\t\t</a>\n\t\t<hr/>\n\t\t<a href=\"/user_notebooks.html\">\n\t\t  <div class=\"icon_background\" >\n\t\t\t <img src=\"/static/icons/contrib.png\" alt=\"[user notebooks]\" />\n\t\t\t <div class=\"icon_text\">\n\t\t\t\t<div class=\"firstline\">User</div><div>notebooks</div>\n\t\t\t </div>\n\t\t  </div>\n\t\t</a>\n\t\t<a href=\"/developers.html\">\n\t\t  <div class=\"icon_background\" >\n\t\t\t <img src=\"/static/icons/puzzle.png\" alt=\"[contribute]\" />\n\t\t\t <div class=\"icon_text\">\n\t\t\t\tContribute\n\t\t\t </div>\n\t\t  </div>\n\t\t</a>\n\t\t<hr/>\n\t\t<a href=\"/people.html\">\n\t\t  <div class=\"icon_background\" >\n\t\t\t <img src=\"/static/icons/people.png\" alt=\"[people]\" />\n\t\t\t <div class=\"icon_text\">\n\t\t\t\tPeople\n\t\t\t </div>\n\t\t  </div>\n\t\t</a>\n\t\t<a href=\"/license.html\">\n\t\t  <div class=\"icon_background\" >\n\t\t\t <img src=\"/static/icons/license.png\" alt=\"[license]\" />\n\t\t\t <div class=\"icon_text\">\n\t\t\t\tLicense\n\t\t\t </div>\n\t\t  </div>\n\t\t</a>\n\t\t<a href=\"https://github.com/kpeeters/cadabra2/\">\n\t\t  <div class=\"icon_background\" >\n\t\t    <img src=\"/static/icons/GitHub-Mark-64px-white.png\" alt=\"[github]\" />\n\t\t    <div class=\"icon_text\">\n\t\t      Source\n\t\t    </div>\n\t\t  </div>\n\t\t</a>\n\t </div>\n\t \n\t <div id=\"main\">\n\t\t{% block main %}{% endblock %}\n\t </div>\n\t \n\t <div id=\"bottombar\">\n\t\t<div id=\"bottomleft\">Copyright &copy; 2001-2025 Kasper Peeters</div>\n\t\t<div id=\"bottomright\">Questions? <a href=\"mailto:info@cadabra.science\">info@cadabra.science</a></div>\n\t </div>\n\t \n\t <script type=\"application/ld+json\">\n\t\t{\n\t\t\"@context\": \"http://schema.org\",\n\t\t\"@type\": \"Organization\",\n\t\t\"url\": \"https://cadabra.science\",\n\t\t\"logo\": \"https://cadabra.science/static/icons/cadabra2.png\"\n\t\t}\n\t </script>\n\t <script type=\"text/javascript\" src=\"/static/js/cadabra.js\"></script>\n  </body>\n</html>\n"
  },
  {
    "path": "web2/cadabra2/source/license.html",
    "content": "{% extends \"layout.html\" %}\n\n{% block title %}Cadabra: License{% endblock %}\n\n{% block head %}{%- endblock %}\n\n{% block main %}\n<h1>License</h1>\n<h2>Show your support</h2>\n<p>\n  If you use Cadabra or even just play with it, I would like to hear\n  about it. Please register using the notebook interface, or send me\n  an email so that I can get an idea of who is interested in this\n  project. And remember:</p>\n<p class=\"quote\">\n  The \"rule of 3\": It takes 1 unit of work to get something for\n  yourself. It takes 3x1 units of work to make it so your office\n  neighbor can use it. It takes 3x3x1 units of work so you can use it\n  \"in the department\" and in courses. It takes 3x3x3x1 units of work to\n  give it to the world for free without support. It takes 3x3x3x3x1\n  units of work to provide it to the world and support it.\n</p>\n<p>So if you use Cadabra in your own work,\n  please cite the papers \"<em>Introducing Cadabra: a symbolic\n\t computer algebra system for field-theory problems</em>\" and\n  \"<em>A field-theory motivated approach to symbolic computer\n\t algebra</em>\" (see <a\n\t\t\t\t\t\t\t\t  href=\"/papers.html\">papers</a> for publication details)\n  to keep the bean counters happy.\n</p>\n<h2>Legal stuff</h2>\n<p>Cadabra is available under the conditions of the \n  <a\n\t  href=\"http://www.gnu.org/copyleft/gpl.html\">GNU General\n\t Public License</a> (version 3). \n</p>\n\n{%- endblock %}\n\n"
  },
  {
    "path": "web2/cadabra2/source/man.html",
    "content": "{% extends \"layout.html\" %}\n\n{% block title %}Cadabra: Manual pages{% endblock %}\n\n{% block head %}{%- endblock %}\n\n{% block main %}\n\n<h1>Manual pages</h1>\n<p>\n  Every algorithm and every property has a manual page with examples,\n  which you can view online here, or by pressing <code>F1</code> in\n  the Cadabra notebook interface when your cursor is located on an\n  algorithm or property name. Consider this the \"dry\" version of the\n  documentation: to-the-point, but not very useful if you do not have\n  an understanding of the big picture yet.\n</p>\n<p>\n  For a more introductory description of the basics of Cadabra, you\n  may be better off first reading or skimming through\n  the <a href=\"tutorials.html\">tutorials</a> or\n  the <a href=\"help.html\">Cadabra book</a>.\n</p>\n<h2>Packages</h2>\n<p>\n  Cadabra comes with various add-on packages, which can be imported in\n  the usual Python way with <code>import</code>. Their content is\n  listed below.\n</p>\n  <table class=\"package-toc-table\">\n\t {% include \"packages_toc.html\" %}\n  </table>\n\n<h2>Core algorithms</h2>\n  <table>\n\t {% include \"algo_toc.html\" %}\n  </table>\n\n<h2>Core properties</h2>\n  <table>\n\t {% include \"prop_toc.html\" %}\n  </table>\n\n{%- endblock %}\n"
  },
  {
    "path": "web2/cadabra2/source/manual/.gitignore",
    "content": "*.html\n"
  },
  {
    "path": "web2/cadabra2/source/manual/README.txt",
    "content": "This folder will hold the manual notebooks for algorithms and\nproperties which are automatically converted by 'cadabra2html' from\nCadabra notebooks in the 'core/algorithms' and 'core/properties/ folders.\n"
  },
  {
    "path": "web2/cadabra2/source/notebook_layout.html",
    "content": "{% extends \"layout.html\" %}\n\n{% block sidebar %}\n<div class=\"tooltip\" tiptext=\"Automatically generated from a Cadabra notebook.\">\n  <img  src=\"/static/images/icon_notebook.png\" />\n</div>\n{%- endblock %}\n"
  },
  {
    "path": "web2/cadabra2/source/notebooks/.gitignore",
    "content": "*.cnb\n*.html\n\n"
  },
  {
    "path": "web2/cadabra2/source/notebooks/README.txt",
    "content": "This folder will hold the example notebooks which are automatically\nconverted by 'cadabra2html' from Cadabra notebooks in the 'examples'\ndirectory in the root.\n"
  },
  {
    "path": "web2/cadabra2/source/papers.html",
    "content": "{% extends \"layout.html\" %}\n\n{% block title %}Cadabra: Papers using Cadabra{% endblock %}\n\n{% block head %}{%- endblock %}\n\n{% block main %}\n<h1>Papers about Cadabra</h1>\n\n<p>\n  The canonical introduction to Cadabra for high-energy physicists is\n  the original paper (now updated for 2.x syntax),\n</p>\n<blockquote class=\"reference\">\n  <div class=\"author\">Kasper Peeters</div>\n  <div class=\"title\"><a href=\"https://cadabra.science/cadabra2_hep.pdf\">Introducing Cadabra:\n\t\ta symbolic computer algebra system for field theory problems</a></div>\n  <div class=\"pubinfo\"><a href=\"http://arxiv.org/abs/hep-th/0701238\">hep-th/0701238</a>\n\t (now updated for 2.x syntax)</div>\n</blockquote>\n<p>\n  The Cadabra 2.x software is published as\n</p>\n  <blockquote class=\"reference\">\n\t <div class=\"author\">Kasper Peeters</div>\n\t <div class=\"title\">Cadabra2: computer algebra for field theory\n\t\trevisited</div>\n\t <div class=\"pubinfo\"><a href=\"https://doi.org/10.21105/joss.01118\">Journal\n\t\t  of Open Source Software, 3(32), 1118</a></div>\n\t <div class=\"pubinfo\"><a href=\"https://doi.org/10.21105/joss.01118\"><img src=\"https://joss.theoj.org/papers/10.21105/joss.01118/status.svg\"/></a>\n\t </div>\n  </blockquote>\n<p>A technical explanation of the  motivation for writing this software,\n  as well as a sketch of the internal structure, can be found in\n  the paper</p>\n<blockquote class=\"reference\">\n  <div class=\"author\">Kasper Peeters</div>\n  <div class=\"title\">A field-theory\n\t\tmotivated approach to symbolic computer algebra</div>\n  <div class=\"pubinfo\"><a\n\t\t\t\t\t\t\t\t  href=\"http://arxiv.org/abs/cs.SC/0608005\">cs.SC/0608005</a>,\n\t <a href=\"http://dx.doi.org/10.1016/j.cpc.2007.01.003\">Comp.&nbsp;Phys.&nbsp;Commun.&nbsp;176 (2007) 550-558.</a></div>\n</blockquote>\n<p>\n  Please cite the three papers above when you use Cadabra in your own\n  work; those citations are the only way to convince the bean counters\n  that this software is useful!\n</p>\n<p>\n  A lot of information on the internals of Cadabra and various parts\n  written by Dominic Price has appeared in his thesis,\n</p>\n<blockquote class=\"reference\">\n  <div class=\"author\">Dominic Price</div>\n  <div class=\"title\">Routines and Applications of Symbolic Algebra Software</div>\n  <div class=\"pubinfo\"><a href=\"http://etheses.dur.ac.uk/14811/\">http://etheses.dur.ac.uk/14811/</a></div>\n</blockquote>\n<p>\n  The <tt>meld</tt> algorithm has also been documented in the paper\n</p>\n<blockquote class=\"reference\">\n  <div class=\"author\">Dominic Price, Kasper Peeters and Marija Zamaklar</div>\n  <div class=\"title\">Hiding canonicalisation in tensor computer algebra</div>\n  <div class=\"pubinfo\"><a href=\"https://arxiv.org/abs/2208.11946\">arXiv:2208.11946</a></div>\n</blockquote>\n<p>Finally, a general introduction to the old version of Cadabra for a\n  wider public can be found in</p>\n<blockquote class=\"reference\">\n  <div class=\"author\">Kasper Peeters</div>\n  <div class=\"title\">Symbolic field theory with Cadabra</div>\n  <div class=\"pubinfo\"><a href=\"https://fachgruppe-computeralgebra.de/data/CA-Rundbrief/car41.pdf\">Computeralgebra Rundbrief 41 (2007) 16.</a></div>\n</blockquote>\n<p>\n  A proper introduction to the new features of Cadabra 2 may appear at\n  some point in the future.  \n</p>\n\n\n<h1>Introductory papers to learn Cadabra</h1>\n<a name=\"brewin\"></a>\n\n<p>Leo Brewin has written a very thorough new introduction to Cadabra for people\n  who intend to use it in General Relativity, with loads of examples\n  suitable for beginners,</p>\n<blockquote class=\"reference\">\n  <div class=\"author\">Leo Brewin</div>\n  <div class=\"title\">Using Cadabra for tensor computations in General Relativity</div>\n  <div class=\"pubinfo\">available as <a href=\"http://arxiv.org/abs/1912.08839\">arxiv:1912.08839</a></div>\n</blockquote>\n<p>\nAlso from his hand is a nice paper on how to do Riemann normal\ncoordinate expansions with Cadabra, now updated to use Cadabra2 notation,\n<blockquote class=\"reference\">\n  <div class=\"author\">Leo Brewin</div>\n  <div class=\"title\">Riemann Normal Coordinate expansions using Cadabra</div>\n  <div class=\"pubinfo\">available as <a href=\"http://arxiv.org/abs/0903.2087v2\">arxiv:0903.2087v2</a></div>\n</blockquote>\n<!--<blockquote class=\"reference\">\n  <div class=\"author\">Leo Brewin</div>\n  <div class=\"title\"><a href=\"http://users.monash.edu.au/~leo/research/papers/files/lcb09-02.pdf\">A\n\t\tbrief introduction to Cadabra: a tool for tensor computations in\n\t\tGeneral Relativity</a></div>\n  <div class=\"pubinfo\">also available as <a href=\"http://arxiv.org/abs/0903.2085\">arxiv:0903.2085</a></div>\n</blockquote>-->\n</p>\n\n<h1>Research papers citing Cadabra</h1>\n\n<p>The list of papers citing cadabra is getting too long to\n  maintain by hand, but Google Scholar does an excellent job at it.\n  See the\n  <a href=\"http://scholar.google.com/scholar?oi=bibs&hl=en&cites=13084737546483891451\">list\n\t of papers citing the Comp.Phys.Comm. paper</a>, the\n  <a href=\"http://scholar.google.com/scholar?oi=bibs&hl=en&cites=6862449820033381676\">list\n    of papers citing the hep-th paper</a> and\n    the <a href=\"https://scholar.google.co.uk/scholar?cites=12816060198742513768&as_sdt=2005&sciodt=0,5&hl=en\">list\n    of papers citing the Cadabra2 paper</a>.\n</p>\n\n{%- endblock %}\n\n"
  },
  {
    "path": "web2/cadabra2/source/people.html",
    "content": "{% extends \"layout.html\" %}\n\n{% block title %}Cadabra: People{% endblock %}\n\n{% block head %}{%- endblock %}\n\n{% block main %}\n\n<h1>People and support</h1>\n<h2>Development</h2>\n<p>\n  Cadabra is designed and written\n  by <span class=\"author\"><a href=\"https://www.maths.dur.ac.uk/users/kasper.peeters/\">Kasper\n  Peeters</a></span> with help from various contributors listed below.\n</p>\n\n<h2>Contributors</h2>\n<dl>\n  <dt class=\"author\">Dominic Price</dt>\n  <dd>Many additions and improvements written during the course of his\n\t PhD, such as: the conversion to pybind, the Windows port, the logic\n\t that enables importing notebooks into other notebooks, the meld\n\t algorithm, various add-on packages, syntax highlighting and\n\t various other enhancements to the notebook interface, and many\n\t more.</dd>\n  <dt class=\"author\">Connor Behan</dt>\n  <dd>Improvements to trace operators and various other parts.</dd>\n  <dt class=\"author\">Fergus Baker</dt>\n  <dd>The new default Jupyter kernel.</dd>\n</dl>\n\n<h2>Acknowledgements</h2>\n<p>\nSpecial thanks to José M. Martín-García (for the xPerm\ncanonicalisation code), James Allen (for writing much of the original\nfactoring code), Leo Brewin (for writing beautiful\ntutorials), Mattia Scomparin (for contributing tutorial notebooks),\nOscar Felisola (for LaTeX related patches), the\nSoftware Sustainability Institute and the Durham Institute of Advanced Study\n(for financial support). Thanks to the many people who have sent me\nbug reports (keep 'm coming), and thanks to all of you who use\nCadabra, sent feedback or cited the Cadabra papers.\n</p>\n<p>\n  The name Cadabra is an implicit acknowledgement to\n  <a href=\"https://www.researchgate.net/profile/Mees_Roo\">Mees de\nRoo</a>, who introduced me to his (so far unpublished) Pascal program\n<tt>Abra</tt> in the fall of 2000. This program has an extremely\nphysicist-friendly way of dealing with fermions and tensor symmetries,\nand a formula history mechanism still not found in any other\ncomparable computer algebra system. Cadabra was originally planned to be\n\"my private C++ version of <tt>Abra</tt>\", and even though it does not\nshow much similarity anymore, the development was to a large extent\ninspired by <tt>Abra</tt>.\n</p>\n\n<h2>Financial support</h2>\n<p>\n  Cadabra has been, is, or will be supported by the following\n  organisations:<br/>\n\t <a href=\"https://www.software.ac.uk/\"><img src=\"static/images/ssi_logo_with_name-small2.png\"\n  alt=\"SSI logo\" /></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<a href=\"https://www.dur.ac.uk/ias/\"><img height=\"78\"\n  src=\"static/images/ias-logo.jpg\"\n  alt=\"IAS logo\" /></a><br/>\n</p>\n\n{%- endblock %}\n"
  },
  {
    "path": "web2/cadabra2/source/quickstart.html",
    "content": "{% extends \"layout.html\" %}\n\n{% block title %}Cadabra: quickstart{% endblock %}\n\n{% block head %}{%- endblock %}\n\n{% block main %}\n<h1>Cadabra quick start</h1>\n<p>\n  For this quick start, we will assume that you have ...\n</p>\n<p>\n  If you come from version 1, you may want to consult\n  the list of <a href=\"changes12.html\">changes from version 1 to 2</a>.\n</p>\n\n{%- endblock %}\n\n"
  },
  {
    "path": "web2/cadabra2/source/static/cadabra_in_ipython.nb",
    "content": "{\n \"cells\": [\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"Cadabra inside IPython/Jupyter\\n\",\n    \"=================\\n\",\n    \"\\n\",\n    \"This is a short and simple Jupyter notebook shows how to use Cadabra functionality from with Jupyter. The first thing to do is to import the cadabra2 module. To save typing, we will import everything into the global namespace.\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 1,\n   \"metadata\": {\n    \"collapsed\": false\n   },\n   \"outputs\": [],\n   \"source\": [\n    \"from cadabra2 import *\\n\",\n    \"from IPython.display import display, Math, Latex\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"Expressions are declared by typing them as standard LaTeX, and feeding that into the Ex object. The result is a standard Python object.\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 9,\n   \"metadata\": {\n    \"collapsed\": false\n   },\n   \"outputs\": [],\n   \"source\": [\n    \"ex=Ex(r\\\"A_{m n} B^{m n}\\\")\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"Printing is still a bit messy in IPython/Jupyter, but you can get the nicely typeset form of the expression using the following:\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 10,\n   \"metadata\": {\n    \"collapsed\": false\n   },\n   \"outputs\": [\n    {\n     \"data\": {\n      \"text/latex\": [\n       \"$$A_{m n} B^{m n}$$\"\n      ],\n      \"text/plain\": [\n       \"<IPython.core.display.Math object>\"\n      ]\n     },\n     \"metadata\": {},\n     \"output_type\": \"display_data\"\n    }\n   ],\n   \"source\": [\n    \"display(Math(str(ex)))\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"Properties get assigned to symbols or patterns by using their Cadabra name,\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 12,\n   \"metadata\": {\n    \"collapsed\": false\n   },\n   \"outputs\": [\n    {\n     \"data\": {\n      \"text/plain\": [\n       \"Property::repr: AntiSymmetric\"\n      ]\n     },\n     \"execution_count\": 12,\n     \"metadata\": {},\n     \"output_type\": \"execute_result\"\n    }\n   ],\n   \"source\": [\n    \"Symmetric(Ex(r\\\"A_{m n}\\\"))\\n\",\n    \"AntiSymmetric(Ex(r\\\"B_{m n\\\"))\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"Cadabra algorithms are ordinary python functions. They always act on the expression that you pass it, and modify it in-place. Here's an example: the contraction of an antisymmetric and a symmetric tensor is zero:\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 17,\n   \"metadata\": {\n    \"collapsed\": false\n   },\n   \"outputs\": [\n    {\n     \"data\": {\n      \"text/latex\": [\n       \"$$C_{m}\\\\,^{p} D_{p n} B^{m n}$$\"\n      ],\n      \"text/plain\": [\n       \"<IPython.core.display.Math object>\"\n      ]\n     },\n     \"metadata\": {},\n     \"output_type\": \"display_data\"\n    }\n   ],\n   \"source\": [\n    \"display(Math(str(canonicalise(ex))))\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"Let's do another example, with substitution. Note how indices get relabelled automatically.\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": 20,\n   \"metadata\": {\n    \"collapsed\": false\n   },\n   \"outputs\": [\n    {\n     \"data\": {\n      \"text/latex\": [\n       \"$$D_{m r} D^{r}\\\\,_{n} B^{m p} C_{p q}$$\"\n      ],\n      \"text/plain\": [\n       \"<IPython.core.display.Math object>\"\n      ]\n     },\n     \"metadata\": {},\n     \"output_type\": \"display_data\"\n    }\n   ],\n   \"source\": [\n    \"Indices(Ex(r\\\"{m,n,p,q,r,s,t}\\\"))\\n\",\n    \"ex=Ex(r\\\"A_{m n} B^{m p} C_{p q}\\\")\\n\",\n    \"display(Math(str(substitute(ex, Ex(r\\\"A_{m n} -> D_{m q} D^{q}_{n}\\\")))))\"\n   ]\n  },\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"If you are interested in more of this, get in touch by emailing me at info@cadabra.science !\"\n   ]\n  },\n  {\n   \"cell_type\": \"code\",\n   \"execution_count\": null,\n   \"metadata\": {\n    \"collapsed\": true\n   },\n   \"outputs\": [],\n   \"source\": []\n  }\n ],\n \"metadata\": {\n  \"kernelspec\": {\n   \"display_name\": \"Python 2\",\n   \"language\": \"python\",\n   \"name\": \"python2\"\n  },\n  \"language_info\": {\n   \"codemirror_mode\": {\n    \"name\": \"ipython\",\n    \"version\": 2\n   },\n   \"file_extension\": \".py\",\n   \"mimetype\": \"text/x-python\",\n   \"name\": \"python\",\n   \"nbconvert_exporter\": \"python\",\n   \"pygments_lexer\": \"ipython2\",\n   \"version\": \"2.7.6\"\n  }\n },\n \"nbformat\": 4,\n \"nbformat_minor\": 0\n}\n"
  },
  {
    "path": "web2/cadabra2/source/static/cadabra_in_ipython.nb.html",
    "content": "<!DOCTYPE html>\n<html>\n<head>\n\n<meta charset=\"utf-8\" />\n<title>cadabra_in_ipython.nb</title>\n\n<script src=\"https://cdnjs.cloudflare.com/ajax/libs/require.js/2.1.10/require.min.js\"></script>\n<script src=\"https://cdnjs.cloudflare.com/ajax/libs/jquery/2.0.3/jquery.min.js\"></script>\n\n<style type=\"text/css\">\n    /*!\n*\n* Twitter Bootstrap\n*\n*//*! normalize.css v3.0.2 | MIT License | git.io/normalize */html{font-family:sans-serif;-ms-text-size-adjust:100%;-webkit-text-size-adjust:100%}body{margin:0}article,aside,details,figcaption,figure,footer,header,hgroup,main,menu,nav,section,summary{display:block}audio,canvas,progress,video{display:inline-block;vertical-align:baseline}audio:not([controls]){display:none;height:0}[hidden],template{display:none}a{background-color:transparent}a:active,a:hover{outline:0}abbr[title]{border-bottom:1px dotted}b,strong{font-weight:bold}dfn{font-style:italic}h1{font-size:2em;margin:.67em 0}mark{background:#ff0;color:#000}small{font-size:80%}sub,sup{font-size:75%;line-height:0;position:relative;vertical-align:baseline}sup{top:-0.5em}sub{bottom:-0.25em}img{border:0}svg:not(:root){overflow:hidden}figure{margin:1em 40px}hr{-moz-box-sizing:content-box;box-sizing:content-box;height:0}pre{overflow:auto}code,kbd,pre,samp{font-family:monospace,monospace;font-size:1em}button,input,optgroup,select,textarea{color:inherit;font:inherit;margin:0}button{overflow:visible}button,select{text-transform:none}button,html input[type=\"button\"],input[type=\"reset\"],input[type=\"submit\"]{-webkit-appearance:button;cursor:pointer}button[disabled],html input[disabled]{cursor:default}button::-moz-focus-inner,input::-moz-focus-inner{border:0;padding:0}input{line-height:normal}input[type=\"checkbox\"],input[type=\"radio\"]{box-sizing:border-box;padding:0}input[type=\"number\"]::-webkit-inner-spin-button,input[type=\"number\"]::-webkit-outer-spin-button{height:auto}input[type=\"search\"]{-webkit-appearance:textfield;-moz-box-sizing:content-box;-webkit-box-sizing:content-box;box-sizing:content-box}input[type=\"search\"]::-webkit-search-cancel-button,input[type=\"search\"]::-webkit-search-decoration{-webkit-appearance:none}fieldset{border:1px solid #c0c0c0;margin:0 2px;padding:.35em .625em .75em}legend{border:0;padding:0}textarea{overflow:auto}optgroup{font-weight:bold}table{border-collapse:collapse;border-spacing:0}td,th{padding:0}/*! Source: https://github.com/h5bp/html5-boilerplate/blob/master/src/css/main.css */@media print{*,*:before,*:after{background:transparent !important;color:#000 !important;box-shadow:none !important;text-shadow:none !important}a,a:visited{text-decoration:underline}a[href]:after{content:\" (\" attr(href) \")\"}abbr[title]:after{content:\" (\" attr(title) \")\"}a[href^=\"#\"]:after,a[href^=\"javascript:\"]:after{content:\"\"}pre,blockquote{border:1px solid #999;page-break-inside:avoid}thead{display:table-header-group}tr,img{page-break-inside:avoid}img{max-width:100% !important}p,h2,h3{orphans:3;widows:3}h2,h3{page-break-after:avoid}select{background:#fff !important}.navbar{display:none}.btn>.caret,.dropup>.btn>.caret{border-top-color:#000 !important}.label{border:1px solid #000}.table{border-collapse:collapse !important}.table td,.table th{background-color:#fff !important}.table-bordered th,.table-bordered td{border:1px solid #ddd !important}}@font-face{font-family:'Glyphicons Halflings';src:url('../components/bootstrap/fonts/glyphicons-halflings-regular.eot');src:url('../components/bootstrap/fonts/glyphicons-halflings-regular.eot?#iefix') format('embedded-opentype'),url('../components/bootstrap/fonts/glyphicons-halflings-regular.woff') format('woff'),url('../components/bootstrap/fonts/glyphicons-halflings-regular.ttf') format('truetype'),url('../components/bootstrap/fonts/glyphicons-halflings-regular.svg#glyphicons_halflingsregular') format('svg')}.glyphicon{position:relative;top:1px;display:inline-block;font-family:'Glyphicons Halflings';font-style:normal;font-weight:normal;line-height:1;-webkit-font-smoothing:antialiased;-moz-osx-font-smoothing:grayscale}.glyphicon-asterisk:before{content:\"\\2a\"}.glyphicon-plus:before{content:\"\\2b\"}.glyphicon-euro:before,.glyphicon-eur:before{content:\"\\20ac\"}.glyphicon-minus:before{content:\"\\2212\"}.glyphicon-cloud:before{content:\"\\2601\"}.glyphicon-envelope:before{content:\"\\2709\"}.glyphicon-pencil:before{content:\"\\270f\"}.glyphicon-glass:before{content:\"\\e001\"}.glyphicon-music:before{content:\"\\e002\"}.glyphicon-search:before{content:\"\\e003\"}.glyphicon-heart:before{content:\"\\e005\"}.glyphicon-star:before{content:\"\\e006\"}.glyphicon-star-empty:before{content:\"\\e007\"}.glyphicon-user:before{content:\"\\e008\"}.glyphicon-film:before{content:\"\\e009\"}.glyphicon-th-large:before{content:\"\\e010\"}.glyphicon-th:before{content:\"\\e011\"}.glyphicon-th-list:before{content:\"\\e012\"}.glyphicon-ok:before{content:\"\\e013\"}.glyphicon-remove:before{content:\"\\e014\"}.glyphicon-zoom-in:before{content:\"\\e015\"}.glyphicon-zoom-out:before{content:\"\\e016\"}.glyphicon-off:before{content:\"\\e017\"}.glyphicon-signal:before{content:\"\\e018\"}.glyphicon-cog:before{content:\"\\e019\"}.glyphicon-trash:before{content:\"\\e020\"}.glyphicon-home:before{content:\"\\e021\"}.glyphicon-file:before{content:\"\\e022\"}.glyphicon-time:before{content:\"\\e023\"}.glyphicon-road:before{content:\"\\e024\"}.glyphicon-download-alt:before{content:\"\\e025\"}.glyphicon-download:before{content:\"\\e026\"}.glyphicon-upload:before{content:\"\\e027\"}.glyphicon-inbox:before{content:\"\\e028\"}.glyphicon-play-circle:before{content:\"\\e029\"}.glyphicon-repeat:before{content:\"\\e030\"}.glyphicon-refresh:before{content:\"\\e031\"}.glyphicon-list-alt:before{content:\"\\e032\"}.glyphicon-lock:before{content:\"\\e033\"}.glyphicon-flag:before{content:\"\\e034\"}.glyphicon-headphones:before{content:\"\\e035\"}.glyphicon-volume-off:before{content:\"\\e036\"}.glyphicon-volume-down:before{content:\"\\e037\"}.glyphicon-volume-up:before{content:\"\\e038\"}.glyphicon-qrcode:before{content:\"\\e039\"}.glyphicon-barcode:before{content:\"\\e040\"}.glyphicon-tag:before{content:\"\\e041\"}.glyphicon-tags:before{content:\"\\e042\"}.glyphicon-book:before{content:\"\\e043\"}.glyphicon-bookmark:before{content:\"\\e044\"}.glyphicon-print:before{content:\"\\e045\"}.glyphicon-camera:before{content:\"\\e046\"}.glyphicon-font:before{content:\"\\e047\"}.glyphicon-bold:before{content:\"\\e048\"}.glyphicon-italic:before{content:\"\\e049\"}.glyphicon-text-height:before{content:\"\\e050\"}.glyphicon-text-width:before{content:\"\\e051\"}.glyphicon-align-left:before{content:\"\\e052\"}.glyphicon-align-center:before{content:\"\\e053\"}.glyphicon-align-right:before{content:\"\\e054\"}.glyphicon-align-justify:before{content:\"\\e055\"}.glyphicon-list:before{content:\"\\e056\"}.glyphicon-indent-left:before{content:\"\\e057\"}.glyphicon-indent-right:before{content:\"\\e058\"}.glyphicon-facetime-video:before{content:\"\\e059\"}.glyphicon-picture:before{content:\"\\e060\"}.glyphicon-map-marker:before{content:\"\\e062\"}.glyphicon-adjust:before{content:\"\\e063\"}.glyphicon-tint:before{content:\"\\e064\"}.glyphicon-edit:before{content:\"\\e065\"}.glyphicon-share:before{content:\"\\e066\"}.glyphicon-check:before{content:\"\\e067\"}.glyphicon-move:before{content:\"\\e068\"}.glyphicon-step-backward:before{content:\"\\e069\"}.glyphicon-fast-backward:before{content:\"\\e070\"}.glyphicon-backward:before{content:\"\\e071\"}.glyphicon-play:before{content:\"\\e072\"}.glyphicon-pause:before{content:\"\\e073\"}.glyphicon-stop:before{content:\"\\e074\"}.glyphicon-forward:before{content:\"\\e075\"}.glyphicon-fast-forward:before{content:\"\\e076\"}.glyphicon-step-forward:before{content:\"\\e077\"}.glyphicon-eject:before{content:\"\\e078\"}.glyphicon-chevron-left:before{content:\"\\e079\"}.glyphicon-chevron-right:before{content:\"\\e080\"}.glyphicon-plus-sign:before{content:\"\\e081\"}.glyphicon-minus-sign:before{content:\"\\e082\"}.glyphicon-remove-sign:before{content:\"\\e083\"}.glyphicon-ok-sign:before{content:\"\\e084\"}.glyphicon-question-sign:before{content:\"\\e085\"}.glyphicon-info-sign:before{content:\"\\e086\"}.glyphicon-screenshot:before{content:\"\\e087\"}.glyphicon-remove-circle:before{content:\"\\e088\"}.glyphicon-ok-circle:before{content:\"\\e089\"}.glyphicon-ban-circle:before{content:\"\\e090\"}.glyphicon-arrow-left:before{content:\"\\e091\"}.glyphicon-arrow-right:before{content:\"\\e092\"}.glyphicon-arrow-up:before{content:\"\\e093\"}.glyphicon-arrow-down:before{content:\"\\e094\"}.glyphicon-share-alt:before{content:\"\\e095\"}.glyphicon-resize-full:before{content:\"\\e096\"}.glyphicon-resize-small:before{content:\"\\e097\"}.glyphicon-exclamation-sign:before{content:\"\\e101\"}.glyphicon-gift:before{content:\"\\e102\"}.glyphicon-leaf:before{content:\"\\e103\"}.glyphicon-fire:before{content:\"\\e104\"}.glyphicon-eye-open:before{content:\"\\e105\"}.glyphicon-eye-close:before{content:\"\\e106\"}.glyphicon-warning-sign:before{content:\"\\e107\"}.glyphicon-plane:before{content:\"\\e108\"}.glyphicon-calendar:before{content:\"\\e109\"}.glyphicon-random:before{content:\"\\e110\"}.glyphicon-comment:before{content:\"\\e111\"}.glyphicon-magnet:before{content:\"\\e112\"}.glyphicon-chevron-up:before{content:\"\\e113\"}.glyphicon-chevron-down:before{content:\"\\e114\"}.glyphicon-retweet:before{content:\"\\e115\"}.glyphicon-shopping-cart:before{content:\"\\e116\"}.glyphicon-folder-close:before{content:\"\\e117\"}.glyphicon-folder-open:before{content:\"\\e118\"}.glyphicon-resize-vertical:before{content:\"\\e119\"}.glyphicon-resize-horizontal:before{content:\"\\e120\"}.glyphicon-hdd:before{content:\"\\e121\"}.glyphicon-bullhorn:before{content:\"\\e122\"}.glyphicon-bell:before{content:\"\\e123\"}.glyphicon-certificate:before{content:\"\\e124\"}.glyphicon-thumbs-up:before{content:\"\\e125\"}.glyphicon-thumbs-down:before{content:\"\\e126\"}.glyphicon-hand-right:before{content:\"\\e127\"}.glyphicon-hand-left:before{content:\"\\e128\"}.glyphicon-hand-up:before{content:\"\\e129\"}.glyphicon-hand-down:before{content:\"\\e130\"}.glyphicon-circle-arrow-right:before{content:\"\\e131\"}.glyphicon-circle-arrow-left:before{content:\"\\e132\"}.glyphicon-circle-arrow-up:before{content:\"\\e133\"}.glyphicon-circle-arrow-down:before{content:\"\\e134\"}.glyphicon-globe:before{content:\"\\e135\"}.glyphicon-wrench:before{content:\"\\e136\"}.glyphicon-tasks:before{content:\"\\e137\"}.glyphicon-filter:before{content:\"\\e138\"}.glyphicon-briefcase:before{content:\"\\e139\"}.glyphicon-fullscreen:before{content:\"\\e140\"}.glyphicon-dashboard:before{content:\"\\e141\"}.glyphicon-paperclip:before{content:\"\\e142\"}.glyphicon-heart-empty:before{content:\"\\e143\"}.glyphicon-link:before{content:\"\\e144\"}.glyphicon-phone:before{content:\"\\e145\"}.glyphicon-pushpin:before{content:\"\\e146\"}.glyphicon-usd:before{content:\"\\e148\"}.glyphicon-gbp:before{content:\"\\e149\"}.glyphicon-sort:before{content:\"\\e150\"}.glyphicon-sort-by-alphabet:before{content:\"\\e151\"}.glyphicon-sort-by-alphabet-alt:before{content:\"\\e152\"}.glyphicon-sort-by-order:before{content:\"\\e153\"}.glyphicon-sort-by-order-alt:before{content:\"\\e154\"}.glyphicon-sort-by-attributes:before{content:\"\\e155\"}.glyphicon-sort-by-attributes-alt:before{content:\"\\e156\"}.glyphicon-unchecked:before{content:\"\\e157\"}.glyphicon-expand:before{content:\"\\e158\"}.glyphicon-collapse-down:before{content:\"\\e159\"}.glyphicon-collapse-up:before{content:\"\\e160\"}.glyphicon-log-in:before{content:\"\\e161\"}.glyphicon-flash:before{content:\"\\e162\"}.glyphicon-log-out:before{content:\"\\e163\"}.glyphicon-new-window:before{content:\"\\e164\"}.glyphicon-record:before{content:\"\\e165\"}.glyphicon-save:before{content:\"\\e166\"}.glyphicon-open:before{content:\"\\e167\"}.glyphicon-saved:before{content:\"\\e168\"}.glyphicon-import:before{content:\"\\e169\"}.glyphicon-export:before{content:\"\\e170\"}.glyphicon-send:before{content:\"\\e171\"}.glyphicon-floppy-disk:before{content:\"\\e172\"}.glyphicon-floppy-saved:before{content:\"\\e173\"}.glyphicon-floppy-remove:before{content:\"\\e174\"}.glyphicon-floppy-save:before{content:\"\\e175\"}.glyphicon-floppy-open:before{content:\"\\e176\"}.glyphicon-credit-card:before{content:\"\\e177\"}.glyphicon-transfer:before{content:\"\\e178\"}.glyphicon-cutlery:before{content:\"\\e179\"}.glyphicon-header:before{content:\"\\e180\"}.glyphicon-compressed:before{content:\"\\e181\"}.glyphicon-earphone:before{content:\"\\e182\"}.glyphicon-phone-alt:before{content:\"\\e183\"}.glyphicon-tower:before{content:\"\\e184\"}.glyphicon-stats:before{content:\"\\e185\"}.glyphicon-sd-video:before{content:\"\\e186\"}.glyphicon-hd-video:before{content:\"\\e187\"}.glyphicon-subtitles:before{content:\"\\e188\"}.glyphicon-sound-stereo:before{content:\"\\e189\"}.glyphicon-sound-dolby:before{content:\"\\e190\"}.glyphicon-sound-5-1:before{content:\"\\e191\"}.glyphicon-sound-6-1:before{content:\"\\e192\"}.glyphicon-sound-7-1:before{content:\"\\e193\"}.glyphicon-copyright-mark:before{content:\"\\e194\"}.glyphicon-registration-mark:before{content:\"\\e195\"}.glyphicon-cloud-download:before{content:\"\\e197\"}.glyphicon-cloud-upload:before{content:\"\\e198\"}.glyphicon-tree-conifer:before{content:\"\\e199\"}.glyphicon-tree-deciduous:before{content:\"\\e200\"}*{-webkit-box-sizing:border-box;-moz-box-sizing:border-box;box-sizing:border-box}*:before,*:after{-webkit-box-sizing:border-box;-moz-box-sizing:border-box;box-sizing:border-box}html{font-size:10px;-webkit-tap-highlight-color:rgba(0,0,0,0)}body{font-family:\"Helvetica Neue\",Helvetica,Arial,sans-serif;font-size:13px;line-height:1.42857143;color:#000;background-color:#fff}input,button,select,textarea{font-family:inherit;font-size:inherit;line-height:inherit}a{color:#337ab7;text-decoration:none}a:hover,a:focus{color:#23527c;text-decoration:underline}a:focus{outline:thin dotted;outline:5px auto -webkit-focus-ring-color;outline-offset:-2px}figure{margin:0}img{vertical-align:middle}.img-responsive,.thumbnail>img,.thumbnail a>img,.carousel-inner>.item>img,.carousel-inner>.item>a>img{display:block;max-width:100%;height:auto}.img-rounded{border-radius:3px}.img-thumbnail{padding:4px;line-height:1.42857143;background-color:#fff;border:1px solid #ddd;border-radius:2px;-webkit-transition:all .2s ease-in-out;-o-transition:all .2s ease-in-out;transition:all .2s ease-in-out;display:inline-block;max-width:100%;height:auto}.img-circle{border-radius:50%}hr{margin-top:18px;margin-bottom:18px;border:0;border-top:1px solid #eee}.sr-only{position:absolute;width:1px;height:1px;margin:-1px;padding:0;overflow:hidden;clip:rect(0, 0, 0, 0);border:0}.sr-only-focusable:active,.sr-only-focusable:focus{position:static;width:auto;height:auto;margin:0;overflow:visible;clip:auto}h1,h2,h3,h4,h5,h6,.h1,.h2,.h3,.h4,.h5,.h6{font-family:inherit;font-weight:500;line-height:1.1;color:inherit}h1 small,h2 small,h3 small,h4 small,h5 small,h6 small,.h1 small,.h2 small,.h3 small,.h4 small,.h5 small,.h6 small,h1 .small,h2 .small,h3 .small,h4 .small,h5 .small,h6 .small,.h1 .small,.h2 .small,.h3 .small,.h4 .small,.h5 .small,.h6 .small{font-weight:normal;line-height:1;color:#777}h1,.h1,h2,.h2,h3,.h3{margin-top:18px;margin-bottom:9px}h1 small,.h1 small,h2 small,.h2 small,h3 small,.h3 small,h1 .small,.h1 .small,h2 .small,.h2 .small,h3 .small,.h3 .small{font-size:65%}h4,.h4,h5,.h5,h6,.h6{margin-top:9px;margin-bottom:9px}h4 small,.h4 small,h5 small,.h5 small,h6 small,.h6 small,h4 .small,.h4 .small,h5 .small,.h5 .small,h6 .small,.h6 .small{font-size:75%}h1,.h1{font-size:33px}h2,.h2{font-size:27px}h3,.h3{font-size:23px}h4,.h4{font-size:17px}h5,.h5{font-size:13px}h6,.h6{font-size:12px}p{margin:0 0 9px}.lead{margin-bottom:18px;font-size:14px;font-weight:300;line-height:1.4}@media (min-width:768px){.lead{font-size:19.5px}}small,.small{font-size:92%}mark,.mark{background-color:#fcf8e3;padding:.2em}.text-left{text-align:left}.text-right{text-align:right}.text-center{text-align:center}.text-justify{text-align:justify}.text-nowrap{white-space:nowrap}.text-lowercase{text-transform:lowercase}.text-uppercase{text-transform:uppercase}.text-capitalize{text-transform:capitalize}.text-muted{color:#777}.text-primary{color:#337ab7}a.text-primary:hover{color:#286090}.text-success{color:#3c763d}a.text-success:hover{color:#2b542c}.text-info{color:#31708f}a.text-info:hover{color:#245269}.text-warning{color:#8a6d3b}a.text-warning:hover{color:#66512c}.text-danger{color:#a94442}a.text-danger:hover{color:#843534}.bg-primary{color:#fff;background-color:#337ab7}a.bg-primary:hover{background-color:#286090}.bg-success{background-color:#dff0d8}a.bg-success:hover{background-color:#c1e2b3}.bg-info{background-color:#d9edf7}a.bg-info:hover{background-color:#afd9ee}.bg-warning{background-color:#fcf8e3}a.bg-warning:hover{background-color:#f7ecb5}.bg-danger{background-color:#f2dede}a.bg-danger:hover{background-color:#e4b9b9}.page-header{padding-bottom:8px;margin:36px 0 18px;border-bottom:1px solid #eee}ul,ol{margin-top:0;margin-bottom:9px}ul ul,ol ul,ul ol,ol ol{margin-bottom:0}.list-unstyled{padding-left:0;list-style:none}.list-inline{padding-left:0;list-style:none;margin-left:-5px}.list-inline>li{display:inline-block;padding-left:5px;padding-right:5px}dl{margin-top:0;margin-bottom:18px}dt,dd{line-height:1.42857143}dt{font-weight:bold}dd{margin-left:0}@media (min-width:541px){.dl-horizontal dt{float:left;width:160px;clear:left;text-align:right;overflow:hidden;text-overflow:ellipsis;white-space:nowrap}.dl-horizontal dd{margin-left:180px}}abbr[title],abbr[data-original-title]{cursor:help;border-bottom:1px dotted #777}.initialism{font-size:90%;text-transform:uppercase}blockquote{padding:9px 18px;margin:0 0 18px;font-size:inherit;border-left:5px solid #eee}blockquote p:last-child,blockquote ul:last-child,blockquote ol:last-child{margin-bottom:0}blockquote footer,blockquote small,blockquote .small{display:block;font-size:80%;line-height:1.42857143;color:#777}blockquote footer:before,blockquote small:before,blockquote .small:before{content:'\\2014 \\00A0'}.blockquote-reverse,blockquote.pull-right{padding-right:15px;padding-left:0;border-right:5px solid #eee;border-left:0;text-align:right}.blockquote-reverse footer:before,blockquote.pull-right footer:before,.blockquote-reverse small:before,blockquote.pull-right small:before,.blockquote-reverse .small:before,blockquote.pull-right .small:before{content:''}.blockquote-reverse footer:after,blockquote.pull-right footer:after,.blockquote-reverse small:after,blockquote.pull-right small:after,.blockquote-reverse .small:after,blockquote.pull-right .small:after{content:'\\00A0 \\2014'}address{margin-bottom:18px;font-style:normal;line-height:1.42857143}code,kbd,pre,samp{font-family:monospace}code{padding:2px 4px;font-size:90%;color:#c7254e;background-color:#f9f2f4;border-radius:2px}kbd{padding:2px 4px;font-size:90%;color:#fff;background-color:#333;border-radius:1px;box-shadow:inset 0 -1px 0 rgba(0,0,0,0.25)}kbd kbd{padding:0;font-size:100%;font-weight:bold;box-shadow:none}pre{display:block;padding:8.5px;margin:0 0 9px;font-size:12px;line-height:1.42857143;word-break:break-all;word-wrap:break-word;color:#333;background-color:#f5f5f5;border:1px solid #ccc;border-radius:2px}pre code{padding:0;font-size:inherit;color:inherit;white-space:pre-wrap;background-color:transparent;border-radius:0}.pre-scrollable{max-height:340px;overflow-y:scroll}.container{margin-right:auto;margin-left:auto;padding-left:0;padding-right:0}@media (min-width:768px){.container{width:768px}}@media (min-width:992px){.container{width:940px}}@media (min-width:1200px){.container{width:1140px}}.container-fluid{margin-right:auto;margin-left:auto;padding-left:0;padding-right:0}.row{margin-left:0;margin-right:0}.col-xs-1, .col-sm-1, .col-md-1, .col-lg-1, .col-xs-2, .col-sm-2, .col-md-2, .col-lg-2, .col-xs-3, .col-sm-3, .col-md-3, .col-lg-3, .col-xs-4, .col-sm-4, .col-md-4, .col-lg-4, .col-xs-5, .col-sm-5, .col-md-5, .col-lg-5, .col-xs-6, .col-sm-6, .col-md-6, .col-lg-6, .col-xs-7, .col-sm-7, .col-md-7, .col-lg-7, .col-xs-8, .col-sm-8, .col-md-8, .col-lg-8, .col-xs-9, .col-sm-9, .col-md-9, .col-lg-9, .col-xs-10, .col-sm-10, .col-md-10, .col-lg-10, .col-xs-11, .col-sm-11, .col-md-11, .col-lg-11, .col-xs-12, .col-sm-12, .col-md-12, .col-lg-12{position:relative;min-height:1px;padding-left:0;padding-right:0}.col-xs-1, .col-xs-2, .col-xs-3, .col-xs-4, .col-xs-5, .col-xs-6, .col-xs-7, .col-xs-8, .col-xs-9, .col-xs-10, .col-xs-11, .col-xs-12{float:left}.col-xs-12{width:100%}.col-xs-11{width:91.66666667%}.col-xs-10{width:83.33333333%}.col-xs-9{width:75%}.col-xs-8{width:66.66666667%}.col-xs-7{width:58.33333333%}.col-xs-6{width:50%}.col-xs-5{width:41.66666667%}.col-xs-4{width:33.33333333%}.col-xs-3{width:25%}.col-xs-2{width:16.66666667%}.col-xs-1{width:8.33333333%}.col-xs-pull-12{right:100%}.col-xs-pull-11{right:91.66666667%}.col-xs-pull-10{right:83.33333333%}.col-xs-pull-9{right:75%}.col-xs-pull-8{right:66.66666667%}.col-xs-pull-7{right:58.33333333%}.col-xs-pull-6{right:50%}.col-xs-pull-5{right:41.66666667%}.col-xs-pull-4{right:33.33333333%}.col-xs-pull-3{right:25%}.col-xs-pull-2{right:16.66666667%}.col-xs-pull-1{right:8.33333333%}.col-xs-pull-0{right:auto}.col-xs-push-12{left:100%}.col-xs-push-11{left:91.66666667%}.col-xs-push-10{left:83.33333333%}.col-xs-push-9{left:75%}.col-xs-push-8{left:66.66666667%}.col-xs-push-7{left:58.33333333%}.col-xs-push-6{left:50%}.col-xs-push-5{left:41.66666667%}.col-xs-push-4{left:33.33333333%}.col-xs-push-3{left:25%}.col-xs-push-2{left:16.66666667%}.col-xs-push-1{left:8.33333333%}.col-xs-push-0{left:auto}.col-xs-offset-12{margin-left:100%}.col-xs-offset-11{margin-left:91.66666667%}.col-xs-offset-10{margin-left:83.33333333%}.col-xs-offset-9{margin-left:75%}.col-xs-offset-8{margin-left:66.66666667%}.col-xs-offset-7{margin-left:58.33333333%}.col-xs-offset-6{margin-left:50%}.col-xs-offset-5{margin-left:41.66666667%}.col-xs-offset-4{margin-left:33.33333333%}.col-xs-offset-3{margin-left:25%}.col-xs-offset-2{margin-left:16.66666667%}.col-xs-offset-1{margin-left:8.33333333%}.col-xs-offset-0{margin-left:0}@media (min-width:768px){.col-sm-1, .col-sm-2, .col-sm-3, .col-sm-4, .col-sm-5, .col-sm-6, .col-sm-7, .col-sm-8, .col-sm-9, .col-sm-10, .col-sm-11, .col-sm-12{float:left}.col-sm-12{width:100%}.col-sm-11{width:91.66666667%}.col-sm-10{width:83.33333333%}.col-sm-9{width:75%}.col-sm-8{width:66.66666667%}.col-sm-7{width:58.33333333%}.col-sm-6{width:50%}.col-sm-5{width:41.66666667%}.col-sm-4{width:33.33333333%}.col-sm-3{width:25%}.col-sm-2{width:16.66666667%}.col-sm-1{width:8.33333333%}.col-sm-pull-12{right:100%}.col-sm-pull-11{right:91.66666667%}.col-sm-pull-10{right:83.33333333%}.col-sm-pull-9{right:75%}.col-sm-pull-8{right:66.66666667%}.col-sm-pull-7{right:58.33333333%}.col-sm-pull-6{right:50%}.col-sm-pull-5{right:41.66666667%}.col-sm-pull-4{right:33.33333333%}.col-sm-pull-3{right:25%}.col-sm-pull-2{right:16.66666667%}.col-sm-pull-1{right:8.33333333%}.col-sm-pull-0{right:auto}.col-sm-push-12{left:100%}.col-sm-push-11{left:91.66666667%}.col-sm-push-10{left:83.33333333%}.col-sm-push-9{left:75%}.col-sm-push-8{left:66.66666667%}.col-sm-push-7{left:58.33333333%}.col-sm-push-6{left:50%}.col-sm-push-5{left:41.66666667%}.col-sm-push-4{left:33.33333333%}.col-sm-push-3{left:25%}.col-sm-push-2{left:16.66666667%}.col-sm-push-1{left:8.33333333%}.col-sm-push-0{left:auto}.col-sm-offset-12{margin-left:100%}.col-sm-offset-11{margin-left:91.66666667%}.col-sm-offset-10{margin-left:83.33333333%}.col-sm-offset-9{margin-left:75%}.col-sm-offset-8{margin-left:66.66666667%}.col-sm-offset-7{margin-left:58.33333333%}.col-sm-offset-6{margin-left:50%}.col-sm-offset-5{margin-left:41.66666667%}.col-sm-offset-4{margin-left:33.33333333%}.col-sm-offset-3{margin-left:25%}.col-sm-offset-2{margin-left:16.66666667%}.col-sm-offset-1{margin-left:8.33333333%}.col-sm-offset-0{margin-left:0}}@media (min-width:992px){.col-md-1, .col-md-2, .col-md-3, .col-md-4, .col-md-5, .col-md-6, .col-md-7, .col-md-8, .col-md-9, .col-md-10, .col-md-11, .col-md-12{float:left}.col-md-12{width:100%}.col-md-11{width:91.66666667%}.col-md-10{width:83.33333333%}.col-md-9{width:75%}.col-md-8{width:66.66666667%}.col-md-7{width:58.33333333%}.col-md-6{width:50%}.col-md-5{width:41.66666667%}.col-md-4{width:33.33333333%}.col-md-3{width:25%}.col-md-2{width:16.66666667%}.col-md-1{width:8.33333333%}.col-md-pull-12{right:100%}.col-md-pull-11{right:91.66666667%}.col-md-pull-10{right:83.33333333%}.col-md-pull-9{right:75%}.col-md-pull-8{right:66.66666667%}.col-md-pull-7{right:58.33333333%}.col-md-pull-6{right:50%}.col-md-pull-5{right:41.66666667%}.col-md-pull-4{right:33.33333333%}.col-md-pull-3{right:25%}.col-md-pull-2{right:16.66666667%}.col-md-pull-1{right:8.33333333%}.col-md-pull-0{right:auto}.col-md-push-12{left:100%}.col-md-push-11{left:91.66666667%}.col-md-push-10{left:83.33333333%}.col-md-push-9{left:75%}.col-md-push-8{left:66.66666667%}.col-md-push-7{left:58.33333333%}.col-md-push-6{left:50%}.col-md-push-5{left:41.66666667%}.col-md-push-4{left:33.33333333%}.col-md-push-3{left:25%}.col-md-push-2{left:16.66666667%}.col-md-push-1{left:8.33333333%}.col-md-push-0{left:auto}.col-md-offset-12{margin-left:100%}.col-md-offset-11{margin-left:91.66666667%}.col-md-offset-10{margin-left:83.33333333%}.col-md-offset-9{margin-left:75%}.col-md-offset-8{margin-left:66.66666667%}.col-md-offset-7{margin-left:58.33333333%}.col-md-offset-6{margin-left:50%}.col-md-offset-5{margin-left:41.66666667%}.col-md-offset-4{margin-left:33.33333333%}.col-md-offset-3{margin-left:25%}.col-md-offset-2{margin-left:16.66666667%}.col-md-offset-1{margin-left:8.33333333%}.col-md-offset-0{margin-left:0}}@media (min-width:1200px){.col-lg-1, .col-lg-2, .col-lg-3, .col-lg-4, .col-lg-5, .col-lg-6, .col-lg-7, .col-lg-8, .col-lg-9, .col-lg-10, .col-lg-11, .col-lg-12{float:left}.col-lg-12{width:100%}.col-lg-11{width:91.66666667%}.col-lg-10{width:83.33333333%}.col-lg-9{width:75%}.col-lg-8{width:66.66666667%}.col-lg-7{width:58.33333333%}.col-lg-6{width:50%}.col-lg-5{width:41.66666667%}.col-lg-4{width:33.33333333%}.col-lg-3{width:25%}.col-lg-2{width:16.66666667%}.col-lg-1{width:8.33333333%}.col-lg-pull-12{right:100%}.col-lg-pull-11{right:91.66666667%}.col-lg-pull-10{right:83.33333333%}.col-lg-pull-9{right:75%}.col-lg-pull-8{right:66.66666667%}.col-lg-pull-7{right:58.33333333%}.col-lg-pull-6{right:50%}.col-lg-pull-5{right:41.66666667%}.col-lg-pull-4{right:33.33333333%}.col-lg-pull-3{right:25%}.col-lg-pull-2{right:16.66666667%}.col-lg-pull-1{right:8.33333333%}.col-lg-pull-0{right:auto}.col-lg-push-12{left:100%}.col-lg-push-11{left:91.66666667%}.col-lg-push-10{left:83.33333333%}.col-lg-push-9{left:75%}.col-lg-push-8{left:66.66666667%}.col-lg-push-7{left:58.33333333%}.col-lg-push-6{left:50%}.col-lg-push-5{left:41.66666667%}.col-lg-push-4{left:33.33333333%}.col-lg-push-3{left:25%}.col-lg-push-2{left:16.66666667%}.col-lg-push-1{left:8.33333333%}.col-lg-push-0{left:auto}.col-lg-offset-12{margin-left:100%}.col-lg-offset-11{margin-left:91.66666667%}.col-lg-offset-10{margin-left:83.33333333%}.col-lg-offset-9{margin-left:75%}.col-lg-offset-8{margin-left:66.66666667%}.col-lg-offset-7{margin-left:58.33333333%}.col-lg-offset-6{margin-left:50%}.col-lg-offset-5{margin-left:41.66666667%}.col-lg-offset-4{margin-left:33.33333333%}.col-lg-offset-3{margin-left:25%}.col-lg-offset-2{margin-left:16.66666667%}.col-lg-offset-1{margin-left:8.33333333%}.col-lg-offset-0{margin-left:0}}table{background-color:transparent}caption{padding-top:8px;padding-bottom:8px;color:#777;text-align:left}th{text-align:left}.table{width:100%;max-width:100%;margin-bottom:18px}.table>thead>tr>th,.table>tbody>tr>th,.table>tfoot>tr>th,.table>thead>tr>td,.table>tbody>tr>td,.table>tfoot>tr>td{padding:8px;line-height:1.42857143;vertical-align:top;border-top:1px solid #ddd}.table>thead>tr>th{vertical-align:bottom;border-bottom:2px solid #ddd}.table>caption+thead>tr:first-child>th,.table>colgroup+thead>tr:first-child>th,.table>thead:first-child>tr:first-child>th,.table>caption+thead>tr:first-child>td,.table>colgroup+thead>tr:first-child>td,.table>thead:first-child>tr:first-child>td{border-top:0}.table>tbody+tbody{border-top:2px solid #ddd}.table .table{background-color:#fff}.table-condensed>thead>tr>th,.table-condensed>tbody>tr>th,.table-condensed>tfoot>tr>th,.table-condensed>thead>tr>td,.table-condensed>tbody>tr>td,.table-condensed>tfoot>tr>td{padding:5px}.table-bordered{border:1px solid #ddd}.table-bordered>thead>tr>th,.table-bordered>tbody>tr>th,.table-bordered>tfoot>tr>th,.table-bordered>thead>tr>td,.table-bordered>tbody>tr>td,.table-bordered>tfoot>tr>td{border:1px solid #ddd}.table-bordered>thead>tr>th,.table-bordered>thead>tr>td{border-bottom-width:2px}.table-striped>tbody>tr:nth-child(odd){background-color:#f9f9f9}.table-hover>tbody>tr:hover{background-color:#f5f5f5}table col[class*=\"col-\"]{position:static;float:none;display:table-column}table td[class*=\"col-\"],table th[class*=\"col-\"]{position:static;float:none;display:table-cell}.table>thead>tr>td.active,.table>tbody>tr>td.active,.table>tfoot>tr>td.active,.table>thead>tr>th.active,.table>tbody>tr>th.active,.table>tfoot>tr>th.active,.table>thead>tr.active>td,.table>tbody>tr.active>td,.table>tfoot>tr.active>td,.table>thead>tr.active>th,.table>tbody>tr.active>th,.table>tfoot>tr.active>th{background-color:#f5f5f5}.table-hover>tbody>tr>td.active:hover,.table-hover>tbody>tr>th.active:hover,.table-hover>tbody>tr.active:hover>td,.table-hover>tbody>tr:hover>.active,.table-hover>tbody>tr.active:hover>th{background-color:#e8e8e8}.table>thead>tr>td.success,.table>tbody>tr>td.success,.table>tfoot>tr>td.success,.table>thead>tr>th.success,.table>tbody>tr>th.success,.table>tfoot>tr>th.success,.table>thead>tr.success>td,.table>tbody>tr.success>td,.table>tfoot>tr.success>td,.table>thead>tr.success>th,.table>tbody>tr.success>th,.table>tfoot>tr.success>th{background-color:#dff0d8}.table-hover>tbody>tr>td.success:hover,.table-hover>tbody>tr>th.success:hover,.table-hover>tbody>tr.success:hover>td,.table-hover>tbody>tr:hover>.success,.table-hover>tbody>tr.success:hover>th{background-color:#d0e9c6}.table>thead>tr>td.info,.table>tbody>tr>td.info,.table>tfoot>tr>td.info,.table>thead>tr>th.info,.table>tbody>tr>th.info,.table>tfoot>tr>th.info,.table>thead>tr.info>td,.table>tbody>tr.info>td,.table>tfoot>tr.info>td,.table>thead>tr.info>th,.table>tbody>tr.info>th,.table>tfoot>tr.info>th{background-color:#d9edf7}.table-hover>tbody>tr>td.info:hover,.table-hover>tbody>tr>th.info:hover,.table-hover>tbody>tr.info:hover>td,.table-hover>tbody>tr:hover>.info,.table-hover>tbody>tr.info:hover>th{background-color:#c4e3f3}.table>thead>tr>td.warning,.table>tbody>tr>td.warning,.table>tfoot>tr>td.warning,.table>thead>tr>th.warning,.table>tbody>tr>th.warning,.table>tfoot>tr>th.warning,.table>thead>tr.warning>td,.table>tbody>tr.warning>td,.table>tfoot>tr.warning>td,.table>thead>tr.warning>th,.table>tbody>tr.warning>th,.table>tfoot>tr.warning>th{background-color:#fcf8e3}.table-hover>tbody>tr>td.warning:hover,.table-hover>tbody>tr>th.warning:hover,.table-hover>tbody>tr.warning:hover>td,.table-hover>tbody>tr:hover>.warning,.table-hover>tbody>tr.warning:hover>th{background-color:#faf2cc}.table>thead>tr>td.danger,.table>tbody>tr>td.danger,.table>tfoot>tr>td.danger,.table>thead>tr>th.danger,.table>tbody>tr>th.danger,.table>tfoot>tr>th.danger,.table>thead>tr.danger>td,.table>tbody>tr.danger>td,.table>tfoot>tr.danger>td,.table>thead>tr.danger>th,.table>tbody>tr.danger>th,.table>tfoot>tr.danger>th{background-color:#f2dede}.table-hover>tbody>tr>td.danger:hover,.table-hover>tbody>tr>th.danger:hover,.table-hover>tbody>tr.danger:hover>td,.table-hover>tbody>tr:hover>.danger,.table-hover>tbody>tr.danger:hover>th{background-color:#ebcccc}.table-responsive{overflow-x:auto;min-height:.01%}@media screen and (max-width:767px){.table-responsive{width:100%;margin-bottom:13.5px;overflow-y:hidden;-ms-overflow-style:-ms-autohiding-scrollbar;border:1px solid #ddd}.table-responsive>.table{margin-bottom:0}.table-responsive>.table>thead>tr>th,.table-responsive>.table>tbody>tr>th,.table-responsive>.table>tfoot>tr>th,.table-responsive>.table>thead>tr>td,.table-responsive>.table>tbody>tr>td,.table-responsive>.table>tfoot>tr>td{white-space:nowrap}.table-responsive>.table-bordered{border:0}.table-responsive>.table-bordered>thead>tr>th:first-child,.table-responsive>.table-bordered>tbody>tr>th:first-child,.table-responsive>.table-bordered>tfoot>tr>th:first-child,.table-responsive>.table-bordered>thead>tr>td:first-child,.table-responsive>.table-bordered>tbody>tr>td:first-child,.table-responsive>.table-bordered>tfoot>tr>td:first-child{border-left:0}.table-responsive>.table-bordered>thead>tr>th:last-child,.table-responsive>.table-bordered>tbody>tr>th:last-child,.table-responsive>.table-bordered>tfoot>tr>th:last-child,.table-responsive>.table-bordered>thead>tr>td:last-child,.table-responsive>.table-bordered>tbody>tr>td:last-child,.table-responsive>.table-bordered>tfoot>tr>td:last-child{border-right:0}.table-responsive>.table-bordered>tbody>tr:last-child>th,.table-responsive>.table-bordered>tfoot>tr:last-child>th,.table-responsive>.table-bordered>tbody>tr:last-child>td,.table-responsive>.table-bordered>tfoot>tr:last-child>td{border-bottom:0}}fieldset{padding:0;margin:0;border:0;min-width:0}legend{display:block;width:100%;padding:0;margin-bottom:18px;font-size:19.5px;line-height:inherit;color:#333;border:0;border-bottom:1px solid #e5e5e5}label{display:inline-block;max-width:100%;margin-bottom:5px;font-weight:bold}input[type=\"search\"]{-webkit-box-sizing:border-box;-moz-box-sizing:border-box;box-sizing:border-box}input[type=\"radio\"],input[type=\"checkbox\"]{margin:4px 0 0;margin-top:1px \\9;line-height:normal}input[type=\"file\"]{display:block}input[type=\"range\"]{display:block;width:100%}select[multiple],select[size]{height:auto}input[type=\"file\"]:focus,input[type=\"radio\"]:focus,input[type=\"checkbox\"]:focus{outline:thin dotted;outline:5px auto -webkit-focus-ring-color;outline-offset:-2px}output{display:block;padding-top:7px;font-size:13px;line-height:1.42857143;color:#555}.form-control{display:block;width:100%;height:32px;padding:6px 12px;font-size:13px;line-height:1.42857143;color:#555;background-color:#fff;background-image:none;border:1px solid #ccc;border-radius:2px;-webkit-box-shadow:inset 0 1px 1px rgba(0,0,0,0.075);box-shadow:inset 0 1px 1px rgba(0,0,0,0.075);-webkit-transition:border-color ease-in-out .15s, box-shadow ease-in-out .15s;-o-transition:border-color ease-in-out .15s, box-shadow ease-in-out .15s;transition:border-color ease-in-out .15s, box-shadow ease-in-out .15s}.form-control:focus{border-color:#66afe9;outline:0;-webkit-box-shadow:inset 0 1px 1px rgba(0,0,0,.075), 0 0 8px rgba(102, 175, 233, 0.6);box-shadow:inset 0 1px 1px rgba(0,0,0,.075), 0 0 8px rgba(102, 175, 233, 0.6)}.form-control::-moz-placeholder{color:#999;opacity:1}.form-control:-ms-input-placeholder{color:#999}.form-control::-webkit-input-placeholder{color:#999}.form-control[disabled],.form-control[readonly],fieldset[disabled] .form-control{cursor:not-allowed;background-color:#eee;opacity:1}textarea.form-control{height:auto}input[type=\"search\"]{-webkit-appearance:none}@media screen and (-webkit-min-device-pixel-ratio:0){input[type=\"date\"],input[type=\"time\"],input[type=\"datetime-local\"],input[type=\"month\"]{line-height:32px}input[type=\"date\"].input-sm,input[type=\"time\"].input-sm,input[type=\"datetime-local\"].input-sm,input[type=\"month\"].input-sm{line-height:30px}input[type=\"date\"].input-lg,input[type=\"time\"].input-lg,input[type=\"datetime-local\"].input-lg,input[type=\"month\"].input-lg{line-height:45px}}.form-group{margin-bottom:15px}.radio,.checkbox{position:relative;display:block;margin-top:10px;margin-bottom:10px}.radio label,.checkbox label{min-height:18px;padding-left:20px;margin-bottom:0;font-weight:normal;cursor:pointer}.radio input[type=\"radio\"],.radio-inline input[type=\"radio\"],.checkbox input[type=\"checkbox\"],.checkbox-inline input[type=\"checkbox\"]{position:absolute;margin-left:-20px;margin-top:4px \\9}.radio+.radio,.checkbox+.checkbox{margin-top:-5px}.radio-inline,.checkbox-inline{display:inline-block;padding-left:20px;margin-bottom:0;vertical-align:middle;font-weight:normal;cursor:pointer}.radio-inline+.radio-inline,.checkbox-inline+.checkbox-inline{margin-top:0;margin-left:10px}input[type=\"radio\"][disabled],input[type=\"checkbox\"][disabled],input[type=\"radio\"].disabled,input[type=\"checkbox\"].disabled,fieldset[disabled] input[type=\"radio\"],fieldset[disabled] input[type=\"checkbox\"]{cursor:not-allowed}.radio-inline.disabled,.checkbox-inline.disabled,fieldset[disabled] .radio-inline,fieldset[disabled] .checkbox-inline{cursor:not-allowed}.radio.disabled label,.checkbox.disabled label,fieldset[disabled] .radio label,fieldset[disabled] .checkbox label{cursor:not-allowed}.form-control-static{padding-top:7px;padding-bottom:7px;margin-bottom:0}.form-control-static.input-lg,.form-control-static.input-sm{padding-left:0;padding-right:0}.input-sm,.form-group-sm .form-control{height:30px;padding:5px 10px;font-size:12px;line-height:1.5;border-radius:1px}select.input-sm,select.form-group-sm .form-control{height:30px;line-height:30px}textarea.input-sm,textarea.form-group-sm .form-control,select[multiple].input-sm,select[multiple].form-group-sm .form-control{height:auto}.input-lg,.form-group-lg .form-control{height:45px;padding:10px 16px;font-size:17px;line-height:1.33;border-radius:3px}select.input-lg,select.form-group-lg .form-control{height:45px;line-height:45px}textarea.input-lg,textarea.form-group-lg .form-control,select[multiple].input-lg,select[multiple].form-group-lg .form-control{height:auto}.has-feedback{position:relative}.has-feedback .form-control{padding-right:40px}.form-control-feedback{position:absolute;top:0;right:0;z-index:2;display:block;width:32px;height:32px;line-height:32px;text-align:center;pointer-events:none}.input-lg+.form-control-feedback{width:45px;height:45px;line-height:45px}.input-sm+.form-control-feedback{width:30px;height:30px;line-height:30px}.has-success .help-block,.has-success .control-label,.has-success .radio,.has-success .checkbox,.has-success .radio-inline,.has-success .checkbox-inline,.has-success.radio label,.has-success.checkbox label,.has-success.radio-inline label,.has-success.checkbox-inline label{color:#3c763d}.has-success .form-control{border-color:#3c763d;-webkit-box-shadow:inset 0 1px 1px rgba(0,0,0,0.075);box-shadow:inset 0 1px 1px rgba(0,0,0,0.075)}.has-success .form-control:focus{border-color:#2b542c;-webkit-box-shadow:inset 0 1px 1px rgba(0,0,0,0.075),0 0 6px #67b168;box-shadow:inset 0 1px 1px rgba(0,0,0,0.075),0 0 6px #67b168}.has-success .input-group-addon{color:#3c763d;border-color:#3c763d;background-color:#dff0d8}.has-success .form-control-feedback{color:#3c763d}.has-warning .help-block,.has-warning .control-label,.has-warning .radio,.has-warning .checkbox,.has-warning .radio-inline,.has-warning .checkbox-inline,.has-warning.radio label,.has-warning.checkbox label,.has-warning.radio-inline label,.has-warning.checkbox-inline label{color:#8a6d3b}.has-warning .form-control{border-color:#8a6d3b;-webkit-box-shadow:inset 0 1px 1px rgba(0,0,0,0.075);box-shadow:inset 0 1px 1px rgba(0,0,0,0.075)}.has-warning .form-control:focus{border-color:#66512c;-webkit-box-shadow:inset 0 1px 1px rgba(0,0,0,0.075),0 0 6px #c0a16b;box-shadow:inset 0 1px 1px rgba(0,0,0,0.075),0 0 6px #c0a16b}.has-warning .input-group-addon{color:#8a6d3b;border-color:#8a6d3b;background-color:#fcf8e3}.has-warning .form-control-feedback{color:#8a6d3b}.has-error .help-block,.has-error .control-label,.has-error .radio,.has-error .checkbox,.has-error .radio-inline,.has-error .checkbox-inline,.has-error.radio label,.has-error.checkbox label,.has-error.radio-inline label,.has-error.checkbox-inline label{color:#a94442}.has-error .form-control{border-color:#a94442;-webkit-box-shadow:inset 0 1px 1px rgba(0,0,0,0.075);box-shadow:inset 0 1px 1px rgba(0,0,0,0.075)}.has-error .form-control:focus{border-color:#843534;-webkit-box-shadow:inset 0 1px 1px rgba(0,0,0,0.075),0 0 6px #ce8483;box-shadow:inset 0 1px 1px rgba(0,0,0,0.075),0 0 6px #ce8483}.has-error .input-group-addon{color:#a94442;border-color:#a94442;background-color:#f2dede}.has-error .form-control-feedback{color:#a94442}.has-feedback label~.form-control-feedback{top:23px}.has-feedback label.sr-only~.form-control-feedback{top:0}.help-block{display:block;margin-top:5px;margin-bottom:10px;color:#404040}@media (min-width:768px){.form-inline .form-group{display:inline-block;margin-bottom:0;vertical-align:middle}.form-inline .form-control{display:inline-block;width:auto;vertical-align:middle}.form-inline .form-control-static{display:inline-block}.form-inline .input-group{display:inline-table;vertical-align:middle}.form-inline .input-group .input-group-addon,.form-inline .input-group .input-group-btn,.form-inline .input-group .form-control{width:auto}.form-inline .input-group>.form-control{width:100%}.form-inline .control-label{margin-bottom:0;vertical-align:middle}.form-inline .radio,.form-inline .checkbox{display:inline-block;margin-top:0;margin-bottom:0;vertical-align:middle}.form-inline .radio label,.form-inline .checkbox label{padding-left:0}.form-inline .radio input[type=\"radio\"],.form-inline .checkbox input[type=\"checkbox\"]{position:relative;margin-left:0}.form-inline .has-feedback .form-control-feedback{top:0}}.form-horizontal .radio,.form-horizontal .checkbox,.form-horizontal .radio-inline,.form-horizontal .checkbox-inline{margin-top:0;margin-bottom:0;padding-top:7px}.form-horizontal .radio,.form-horizontal .checkbox{min-height:25px}.form-horizontal .form-group{margin-left:0;margin-right:0}@media (min-width:768px){.form-horizontal .control-label{text-align:right;margin-bottom:0;padding-top:7px}}.form-horizontal .has-feedback .form-control-feedback{right:0}@media (min-width:768px){.form-horizontal .form-group-lg .control-label{padding-top:14.3px}}@media (min-width:768px){.form-horizontal .form-group-sm .control-label{padding-top:6px}}.btn{display:inline-block;margin-bottom:0;font-weight:normal;text-align:center;vertical-align:middle;touch-action:manipulation;cursor:pointer;background-image:none;border:1px solid transparent;white-space:nowrap;padding:6px 12px;font-size:13px;line-height:1.42857143;border-radius:2px;-webkit-user-select:none;-moz-user-select:none;-ms-user-select:none;user-select:none}.btn:focus,.btn:active:focus,.btn.active:focus,.btn.focus,.btn:active.focus,.btn.active.focus{outline:thin dotted;outline:5px auto -webkit-focus-ring-color;outline-offset:-2px}.btn:hover,.btn:focus,.btn.focus{color:#333;text-decoration:none}.btn:active,.btn.active{outline:0;background-image:none;-webkit-box-shadow:inset 0 3px 5px rgba(0,0,0,0.125);box-shadow:inset 0 3px 5px rgba(0,0,0,0.125)}.btn.disabled,.btn[disabled],fieldset[disabled] .btn{cursor:not-allowed;pointer-events:none;opacity:.65;filter:alpha(opacity=65);-webkit-box-shadow:none;box-shadow:none}.btn-default{color:#333;background-color:#fff;border-color:#ccc}.btn-default:hover,.btn-default:focus,.btn-default.focus,.btn-default:active,.btn-default.active,.open>.dropdown-toggle.btn-default{color:#333;background-color:#e6e6e6;border-color:#adadad}.btn-default:active,.btn-default.active,.open>.dropdown-toggle.btn-default{background-image:none}.btn-default.disabled,.btn-default[disabled],fieldset[disabled] .btn-default,.btn-default.disabled:hover,.btn-default[disabled]:hover,fieldset[disabled] .btn-default:hover,.btn-default.disabled:focus,.btn-default[disabled]:focus,fieldset[disabled] .btn-default:focus,.btn-default.disabled.focus,.btn-default[disabled].focus,fieldset[disabled] .btn-default.focus,.btn-default.disabled:active,.btn-default[disabled]:active,fieldset[disabled] .btn-default:active,.btn-default.disabled.active,.btn-default[disabled].active,fieldset[disabled] .btn-default.active{background-color:#fff;border-color:#ccc}.btn-default .badge{color:#fff;background-color:#333}.btn-primary{color:#fff;background-color:#337ab7;border-color:#2e6da4}.btn-primary:hover,.btn-primary:focus,.btn-primary.focus,.btn-primary:active,.btn-primary.active,.open>.dropdown-toggle.btn-primary{color:#fff;background-color:#286090;border-color:#204d74}.btn-primary:active,.btn-primary.active,.open>.dropdown-toggle.btn-primary{background-image:none}.btn-primary.disabled,.btn-primary[disabled],fieldset[disabled] .btn-primary,.btn-primary.disabled:hover,.btn-primary[disabled]:hover,fieldset[disabled] .btn-primary:hover,.btn-primary.disabled:focus,.btn-primary[disabled]:focus,fieldset[disabled] .btn-primary:focus,.btn-primary.disabled.focus,.btn-primary[disabled].focus,fieldset[disabled] .btn-primary.focus,.btn-primary.disabled:active,.btn-primary[disabled]:active,fieldset[disabled] .btn-primary:active,.btn-primary.disabled.active,.btn-primary[disabled].active,fieldset[disabled] .btn-primary.active{background-color:#337ab7;border-color:#2e6da4}.btn-primary .badge{color:#337ab7;background-color:#fff}.btn-success{color:#fff;background-color:#5cb85c;border-color:#4cae4c}.btn-success:hover,.btn-success:focus,.btn-success.focus,.btn-success:active,.btn-success.active,.open>.dropdown-toggle.btn-success{color:#fff;background-color:#449d44;border-color:#398439}.btn-success:active,.btn-success.active,.open>.dropdown-toggle.btn-success{background-image:none}.btn-success.disabled,.btn-success[disabled],fieldset[disabled] .btn-success,.btn-success.disabled:hover,.btn-success[disabled]:hover,fieldset[disabled] .btn-success:hover,.btn-success.disabled:focus,.btn-success[disabled]:focus,fieldset[disabled] .btn-success:focus,.btn-success.disabled.focus,.btn-success[disabled].focus,fieldset[disabled] .btn-success.focus,.btn-success.disabled:active,.btn-success[disabled]:active,fieldset[disabled] .btn-success:active,.btn-success.disabled.active,.btn-success[disabled].active,fieldset[disabled] .btn-success.active{background-color:#5cb85c;border-color:#4cae4c}.btn-success .badge{color:#5cb85c;background-color:#fff}.btn-info{color:#fff;background-color:#5bc0de;border-color:#46b8da}.btn-info:hover,.btn-info:focus,.btn-info.focus,.btn-info:active,.btn-info.active,.open>.dropdown-toggle.btn-info{color:#fff;background-color:#31b0d5;border-color:#269abc}.btn-info:active,.btn-info.active,.open>.dropdown-toggle.btn-info{background-image:none}.btn-info.disabled,.btn-info[disabled],fieldset[disabled] .btn-info,.btn-info.disabled:hover,.btn-info[disabled]:hover,fieldset[disabled] .btn-info:hover,.btn-info.disabled:focus,.btn-info[disabled]:focus,fieldset[disabled] .btn-info:focus,.btn-info.disabled.focus,.btn-info[disabled].focus,fieldset[disabled] .btn-info.focus,.btn-info.disabled:active,.btn-info[disabled]:active,fieldset[disabled] .btn-info:active,.btn-info.disabled.active,.btn-info[disabled].active,fieldset[disabled] .btn-info.active{background-color:#5bc0de;border-color:#46b8da}.btn-info .badge{color:#5bc0de;background-color:#fff}.btn-warning{color:#fff;background-color:#f0ad4e;border-color:#eea236}.btn-warning:hover,.btn-warning:focus,.btn-warning.focus,.btn-warning:active,.btn-warning.active,.open>.dropdown-toggle.btn-warning{color:#fff;background-color:#ec971f;border-color:#d58512}.btn-warning:active,.btn-warning.active,.open>.dropdown-toggle.btn-warning{background-image:none}.btn-warning.disabled,.btn-warning[disabled],fieldset[disabled] .btn-warning,.btn-warning.disabled:hover,.btn-warning[disabled]:hover,fieldset[disabled] .btn-warning:hover,.btn-warning.disabled:focus,.btn-warning[disabled]:focus,fieldset[disabled] .btn-warning:focus,.btn-warning.disabled.focus,.btn-warning[disabled].focus,fieldset[disabled] .btn-warning.focus,.btn-warning.disabled:active,.btn-warning[disabled]:active,fieldset[disabled] .btn-warning:active,.btn-warning.disabled.active,.btn-warning[disabled].active,fieldset[disabled] .btn-warning.active{background-color:#f0ad4e;border-color:#eea236}.btn-warning .badge{color:#f0ad4e;background-color:#fff}.btn-danger{color:#fff;background-color:#d9534f;border-color:#d43f3a}.btn-danger:hover,.btn-danger:focus,.btn-danger.focus,.btn-danger:active,.btn-danger.active,.open>.dropdown-toggle.btn-danger{color:#fff;background-color:#c9302c;border-color:#ac2925}.btn-danger:active,.btn-danger.active,.open>.dropdown-toggle.btn-danger{background-image:none}.btn-danger.disabled,.btn-danger[disabled],fieldset[disabled] .btn-danger,.btn-danger.disabled:hover,.btn-danger[disabled]:hover,fieldset[disabled] .btn-danger:hover,.btn-danger.disabled:focus,.btn-danger[disabled]:focus,fieldset[disabled] .btn-danger:focus,.btn-danger.disabled.focus,.btn-danger[disabled].focus,fieldset[disabled] .btn-danger.focus,.btn-danger.disabled:active,.btn-danger[disabled]:active,fieldset[disabled] .btn-danger:active,.btn-danger.disabled.active,.btn-danger[disabled].active,fieldset[disabled] .btn-danger.active{background-color:#d9534f;border-color:#d43f3a}.btn-danger .badge{color:#d9534f;background-color:#fff}.btn-link{color:#337ab7;font-weight:normal;border-radius:0}.btn-link,.btn-link:active,.btn-link.active,.btn-link[disabled],fieldset[disabled] .btn-link{background-color:transparent;-webkit-box-shadow:none;box-shadow:none}.btn-link,.btn-link:hover,.btn-link:focus,.btn-link:active{border-color:transparent}.btn-link:hover,.btn-link:focus{color:#23527c;text-decoration:underline;background-color:transparent}.btn-link[disabled]:hover,fieldset[disabled] .btn-link:hover,.btn-link[disabled]:focus,fieldset[disabled] .btn-link:focus{color:#777;text-decoration:none}.btn-lg,.btn-group-lg>.btn{padding:10px 16px;font-size:17px;line-height:1.33;border-radius:3px}.btn-sm,.btn-group-sm>.btn{padding:5px 10px;font-size:12px;line-height:1.5;border-radius:1px}.btn-xs,.btn-group-xs>.btn{padding:1px 5px;font-size:12px;line-height:1.5;border-radius:1px}.btn-block{display:block;width:100%}.btn-block+.btn-block{margin-top:5px}input[type=\"submit\"].btn-block,input[type=\"reset\"].btn-block,input[type=\"button\"].btn-block{width:100%}.fade{opacity:0;-webkit-transition:opacity .15s linear;-o-transition:opacity .15s linear;transition:opacity .15s linear}.fade.in{opacity:1}.collapse{display:none;visibility:hidden}.collapse.in{display:block;visibility:visible}tr.collapse.in{display:table-row}tbody.collapse.in{display:table-row-group}.collapsing{position:relative;height:0;overflow:hidden;-webkit-transition-property:height, visibility;transition-property:height, visibility;-webkit-transition-duration:.35s;transition-duration:.35s;-webkit-transition-timing-function:ease;transition-timing-function:ease}.caret{display:inline-block;width:0;height:0;margin-left:2px;vertical-align:middle;border-top:4px solid;border-right:4px solid transparent;border-left:4px solid transparent}.dropdown{position:relative}.dropdown-toggle:focus{outline:0}.dropdown-menu{position:absolute;top:100%;left:0;z-index:1000;display:none;float:left;min-width:160px;padding:5px 0;margin:2px 0 0;list-style:none;font-size:13px;text-align:left;background-color:#fff;border:1px solid #ccc;border:1px solid rgba(0,0,0,0.15);border-radius:2px;-webkit-box-shadow:0 6px 12px rgba(0,0,0,0.175);box-shadow:0 6px 12px rgba(0,0,0,0.175);background-clip:padding-box}.dropdown-menu.pull-right{right:0;left:auto}.dropdown-menu .divider{height:1px;margin:8px 0;overflow:hidden;background-color:#e5e5e5}.dropdown-menu>li>a{display:block;padding:3px 20px;clear:both;font-weight:normal;line-height:1.42857143;color:#333;white-space:nowrap}.dropdown-menu>li>a:hover,.dropdown-menu>li>a:focus{text-decoration:none;color:#262626;background-color:#f5f5f5}.dropdown-menu>.active>a,.dropdown-menu>.active>a:hover,.dropdown-menu>.active>a:focus{color:#fff;text-decoration:none;outline:0;background-color:#337ab7}.dropdown-menu>.disabled>a,.dropdown-menu>.disabled>a:hover,.dropdown-menu>.disabled>a:focus{color:#777}.dropdown-menu>.disabled>a:hover,.dropdown-menu>.disabled>a:focus{text-decoration:none;background-color:transparent;background-image:none;filter:progid:DXImageTransform.Microsoft.gradient(enabled = false);cursor:not-allowed}.open>.dropdown-menu{display:block}.open>a{outline:0}.dropdown-menu-right{left:auto;right:0}.dropdown-menu-left{left:0;right:auto}.dropdown-header{display:block;padding:3px 20px;font-size:12px;line-height:1.42857143;color:#777;white-space:nowrap}.dropdown-backdrop{position:fixed;left:0;right:0;bottom:0;top:0;z-index:990}.pull-right>.dropdown-menu{right:0;left:auto}.dropup .caret,.navbar-fixed-bottom .dropdown .caret{border-top:0;border-bottom:4px solid;content:\"\"}.dropup .dropdown-menu,.navbar-fixed-bottom .dropdown .dropdown-menu{top:auto;bottom:100%;margin-bottom:1px}@media (min-width:541px){.navbar-right .dropdown-menu{left:auto;right:0}.navbar-right .dropdown-menu-left{left:0;right:auto}}.btn-group,.btn-group-vertical{position:relative;display:inline-block;vertical-align:middle}.btn-group>.btn,.btn-group-vertical>.btn{position:relative;float:left}.btn-group>.btn:hover,.btn-group-vertical>.btn:hover,.btn-group>.btn:focus,.btn-group-vertical>.btn:focus,.btn-group>.btn:active,.btn-group-vertical>.btn:active,.btn-group>.btn.active,.btn-group-vertical>.btn.active{z-index:2}.btn-group .btn+.btn,.btn-group .btn+.btn-group,.btn-group .btn-group+.btn,.btn-group .btn-group+.btn-group{margin-left:-1px}.btn-toolbar{margin-left:-5px}.btn-toolbar .btn-group,.btn-toolbar .input-group{float:left}.btn-toolbar>.btn,.btn-toolbar>.btn-group,.btn-toolbar>.input-group{margin-left:5px}.btn-group>.btn:not(:first-child):not(:last-child):not(.dropdown-toggle){border-radius:0}.btn-group>.btn:first-child{margin-left:0}.btn-group>.btn:first-child:not(:last-child):not(.dropdown-toggle){border-bottom-right-radius:0;border-top-right-radius:0}.btn-group>.btn:last-child:not(:first-child),.btn-group>.dropdown-toggle:not(:first-child){border-bottom-left-radius:0;border-top-left-radius:0}.btn-group>.btn-group{float:left}.btn-group>.btn-group:not(:first-child):not(:last-child)>.btn{border-radius:0}.btn-group>.btn-group:first-child>.btn:last-child,.btn-group>.btn-group:first-child>.dropdown-toggle{border-bottom-right-radius:0;border-top-right-radius:0}.btn-group>.btn-group:last-child>.btn:first-child{border-bottom-left-radius:0;border-top-left-radius:0}.btn-group .dropdown-toggle:active,.btn-group.open .dropdown-toggle{outline:0}.btn-group>.btn+.dropdown-toggle{padding-left:8px;padding-right:8px}.btn-group>.btn-lg+.dropdown-toggle{padding-left:12px;padding-right:12px}.btn-group.open .dropdown-toggle{-webkit-box-shadow:inset 0 3px 5px rgba(0,0,0,0.125);box-shadow:inset 0 3px 5px rgba(0,0,0,0.125)}.btn-group.open .dropdown-toggle.btn-link{-webkit-box-shadow:none;box-shadow:none}.btn .caret{margin-left:0}.btn-lg .caret{border-width:5px 5px 0;border-bottom-width:0}.dropup .btn-lg .caret{border-width:0 5px 5px}.btn-group-vertical>.btn,.btn-group-vertical>.btn-group,.btn-group-vertical>.btn-group>.btn{display:block;float:none;width:100%;max-width:100%}.btn-group-vertical>.btn-group>.btn{float:none}.btn-group-vertical>.btn+.btn,.btn-group-vertical>.btn+.btn-group,.btn-group-vertical>.btn-group+.btn,.btn-group-vertical>.btn-group+.btn-group{margin-top:-1px;margin-left:0}.btn-group-vertical>.btn:not(:first-child):not(:last-child){border-radius:0}.btn-group-vertical>.btn:first-child:not(:last-child){border-top-right-radius:2px;border-bottom-right-radius:0;border-bottom-left-radius:0}.btn-group-vertical>.btn:last-child:not(:first-child){border-bottom-left-radius:2px;border-top-right-radius:0;border-top-left-radius:0}.btn-group-vertical>.btn-group:not(:first-child):not(:last-child)>.btn{border-radius:0}.btn-group-vertical>.btn-group:first-child:not(:last-child)>.btn:last-child,.btn-group-vertical>.btn-group:first-child:not(:last-child)>.dropdown-toggle{border-bottom-right-radius:0;border-bottom-left-radius:0}.btn-group-vertical>.btn-group:last-child:not(:first-child)>.btn:first-child{border-top-right-radius:0;border-top-left-radius:0}.btn-group-justified{display:table;width:100%;table-layout:fixed;border-collapse:separate}.btn-group-justified>.btn,.btn-group-justified>.btn-group{float:none;display:table-cell;width:1%}.btn-group-justified>.btn-group .btn{width:100%}.btn-group-justified>.btn-group .dropdown-menu{left:auto}[data-toggle=\"buttons\"]>.btn input[type=\"radio\"],[data-toggle=\"buttons\"]>.btn-group>.btn input[type=\"radio\"],[data-toggle=\"buttons\"]>.btn input[type=\"checkbox\"],[data-toggle=\"buttons\"]>.btn-group>.btn input[type=\"checkbox\"]{position:absolute;clip:rect(0, 0, 0, 0);pointer-events:none}.input-group{position:relative;display:table;border-collapse:separate}.input-group[class*=\"col-\"]{float:none;padding-left:0;padding-right:0}.input-group .form-control{position:relative;z-index:2;float:left;width:100%;margin-bottom:0}.input-group-lg>.form-control,.input-group-lg>.input-group-addon,.input-group-lg>.input-group-btn>.btn{height:45px;padding:10px 16px;font-size:17px;line-height:1.33;border-radius:3px}select.input-group-lg>.form-control,select.input-group-lg>.input-group-addon,select.input-group-lg>.input-group-btn>.btn{height:45px;line-height:45px}textarea.input-group-lg>.form-control,textarea.input-group-lg>.input-group-addon,textarea.input-group-lg>.input-group-btn>.btn,select[multiple].input-group-lg>.form-control,select[multiple].input-group-lg>.input-group-addon,select[multiple].input-group-lg>.input-group-btn>.btn{height:auto}.input-group-sm>.form-control,.input-group-sm>.input-group-addon,.input-group-sm>.input-group-btn>.btn{height:30px;padding:5px 10px;font-size:12px;line-height:1.5;border-radius:1px}select.input-group-sm>.form-control,select.input-group-sm>.input-group-addon,select.input-group-sm>.input-group-btn>.btn{height:30px;line-height:30px}textarea.input-group-sm>.form-control,textarea.input-group-sm>.input-group-addon,textarea.input-group-sm>.input-group-btn>.btn,select[multiple].input-group-sm>.form-control,select[multiple].input-group-sm>.input-group-addon,select[multiple].input-group-sm>.input-group-btn>.btn{height:auto}.input-group-addon,.input-group-btn,.input-group .form-control{display:table-cell}.input-group-addon:not(:first-child):not(:last-child),.input-group-btn:not(:first-child):not(:last-child),.input-group .form-control:not(:first-child):not(:last-child){border-radius:0}.input-group-addon,.input-group-btn{width:1%;white-space:nowrap;vertical-align:middle}.input-group-addon{padding:6px 12px;font-size:13px;font-weight:normal;line-height:1;color:#555;text-align:center;background-color:#eee;border:1px solid #ccc;border-radius:2px}.input-group-addon.input-sm{padding:5px 10px;font-size:12px;border-radius:1px}.input-group-addon.input-lg{padding:10px 16px;font-size:17px;border-radius:3px}.input-group-addon input[type=\"radio\"],.input-group-addon input[type=\"checkbox\"]{margin-top:0}.input-group .form-control:first-child,.input-group-addon:first-child,.input-group-btn:first-child>.btn,.input-group-btn:first-child>.btn-group>.btn,.input-group-btn:first-child>.dropdown-toggle,.input-group-btn:last-child>.btn:not(:last-child):not(.dropdown-toggle),.input-group-btn:last-child>.btn-group:not(:last-child)>.btn{border-bottom-right-radius:0;border-top-right-radius:0}.input-group-addon:first-child{border-right:0}.input-group .form-control:last-child,.input-group-addon:last-child,.input-group-btn:last-child>.btn,.input-group-btn:last-child>.btn-group>.btn,.input-group-btn:last-child>.dropdown-toggle,.input-group-btn:first-child>.btn:not(:first-child),.input-group-btn:first-child>.btn-group:not(:first-child)>.btn{border-bottom-left-radius:0;border-top-left-radius:0}.input-group-addon:last-child{border-left:0}.input-group-btn{position:relative;font-size:0;white-space:nowrap}.input-group-btn>.btn{position:relative}.input-group-btn>.btn+.btn{margin-left:-1px}.input-group-btn>.btn:hover,.input-group-btn>.btn:focus,.input-group-btn>.btn:active{z-index:2}.input-group-btn:first-child>.btn,.input-group-btn:first-child>.btn-group{margin-right:-1px}.input-group-btn:last-child>.btn,.input-group-btn:last-child>.btn-group{margin-left:-1px}.nav{margin-bottom:0;padding-left:0;list-style:none}.nav>li{position:relative;display:block}.nav>li>a{position:relative;display:block;padding:10px 15px}.nav>li>a:hover,.nav>li>a:focus{text-decoration:none;background-color:#eee}.nav>li.disabled>a{color:#777}.nav>li.disabled>a:hover,.nav>li.disabled>a:focus{color:#777;text-decoration:none;background-color:transparent;cursor:not-allowed}.nav .open>a,.nav .open>a:hover,.nav .open>a:focus{background-color:#eee;border-color:#337ab7}.nav .nav-divider{height:1px;margin:8px 0;overflow:hidden;background-color:#e5e5e5}.nav>li>a>img{max-width:none}.nav-tabs{border-bottom:1px solid #ddd}.nav-tabs>li{float:left;margin-bottom:-1px}.nav-tabs>li>a{margin-right:2px;line-height:1.42857143;border:1px solid transparent;border-radius:2px 2px 0 0}.nav-tabs>li>a:hover{border-color:#eee #eee #ddd}.nav-tabs>li.active>a,.nav-tabs>li.active>a:hover,.nav-tabs>li.active>a:focus{color:#555;background-color:#fff;border:1px solid #ddd;border-bottom-color:transparent;cursor:default}.nav-tabs.nav-justified{width:100%;border-bottom:0}.nav-tabs.nav-justified>li{float:none}.nav-tabs.nav-justified>li>a{text-align:center;margin-bottom:5px}.nav-tabs.nav-justified>.dropdown .dropdown-menu{top:auto;left:auto}@media (min-width:768px){.nav-tabs.nav-justified>li{display:table-cell;width:1%}.nav-tabs.nav-justified>li>a{margin-bottom:0}}.nav-tabs.nav-justified>li>a{margin-right:0;border-radius:2px}.nav-tabs.nav-justified>.active>a,.nav-tabs.nav-justified>.active>a:hover,.nav-tabs.nav-justified>.active>a:focus{border:1px solid #ddd}@media (min-width:768px){.nav-tabs.nav-justified>li>a{border-bottom:1px solid #ddd;border-radius:2px 2px 0 0}.nav-tabs.nav-justified>.active>a,.nav-tabs.nav-justified>.active>a:hover,.nav-tabs.nav-justified>.active>a:focus{border-bottom-color:#fff}}.nav-pills>li{float:left}.nav-pills>li>a{border-radius:2px}.nav-pills>li+li{margin-left:2px}.nav-pills>li.active>a,.nav-pills>li.active>a:hover,.nav-pills>li.active>a:focus{color:#fff;background-color:#337ab7}.nav-stacked>li{float:none}.nav-stacked>li+li{margin-top:2px;margin-left:0}.nav-justified{width:100%}.nav-justified>li{float:none}.nav-justified>li>a{text-align:center;margin-bottom:5px}.nav-justified>.dropdown .dropdown-menu{top:auto;left:auto}@media (min-width:768px){.nav-justified>li{display:table-cell;width:1%}.nav-justified>li>a{margin-bottom:0}}.nav-tabs-justified{border-bottom:0}.nav-tabs-justified>li>a{margin-right:0;border-radius:2px}.nav-tabs-justified>.active>a,.nav-tabs-justified>.active>a:hover,.nav-tabs-justified>.active>a:focus{border:1px solid #ddd}@media (min-width:768px){.nav-tabs-justified>li>a{border-bottom:1px solid #ddd;border-radius:2px 2px 0 0}.nav-tabs-justified>.active>a,.nav-tabs-justified>.active>a:hover,.nav-tabs-justified>.active>a:focus{border-bottom-color:#fff}}.tab-content>.tab-pane{display:none;visibility:hidden}.tab-content>.active{display:block;visibility:visible}.nav-tabs .dropdown-menu{margin-top:-1px;border-top-right-radius:0;border-top-left-radius:0}.navbar{position:relative;min-height:30px;margin-bottom:18px;border:1px solid transparent}@media (min-width:541px){.navbar{border-radius:2px}}@media (min-width:541px){.navbar-header{float:left}}.navbar-collapse{overflow-x:visible;padding-right:0;padding-left:0;border-top:1px solid transparent;box-shadow:inset 0 1px 0 rgba(255,255,255,0.1);-webkit-overflow-scrolling:touch}.navbar-collapse.in{overflow-y:auto}@media (min-width:541px){.navbar-collapse{width:auto;border-top:0;box-shadow:none}.navbar-collapse.collapse{display:block !important;visibility:visible !important;height:auto !important;padding-bottom:0;overflow:visible !important}.navbar-collapse.in{overflow-y:visible}.navbar-fixed-top .navbar-collapse,.navbar-static-top .navbar-collapse,.navbar-fixed-bottom .navbar-collapse{padding-left:0;padding-right:0}}.navbar-fixed-top .navbar-collapse,.navbar-fixed-bottom .navbar-collapse{max-height:340px}@media (max-device-width:540px) and (orientation:landscape){.navbar-fixed-top .navbar-collapse,.navbar-fixed-bottom .navbar-collapse{max-height:200px}}.container>.navbar-header,.container-fluid>.navbar-header,.container>.navbar-collapse,.container-fluid>.navbar-collapse{margin-right:0;margin-left:0}@media (min-width:541px){.container>.navbar-header,.container-fluid>.navbar-header,.container>.navbar-collapse,.container-fluid>.navbar-collapse{margin-right:0;margin-left:0}}.navbar-static-top{z-index:1000;border-width:0 0 1px}@media (min-width:541px){.navbar-static-top{border-radius:0}}.navbar-fixed-top,.navbar-fixed-bottom{position:fixed;right:0;left:0;z-index:1030}@media (min-width:541px){.navbar-fixed-top,.navbar-fixed-bottom{border-radius:0}}.navbar-fixed-top{top:0;border-width:0 0 1px}.navbar-fixed-bottom{bottom:0;margin-bottom:0;border-width:1px 0 0}.navbar-brand{float:left;padding:6px 0;font-size:17px;line-height:18px;height:30px}.navbar-brand:hover,.navbar-brand:focus{text-decoration:none}.navbar-brand>img{display:block}@media (min-width:541px){.navbar>.container .navbar-brand,.navbar>.container-fluid .navbar-brand{margin-left:0}}.navbar-toggle{position:relative;float:right;margin-right:0;padding:9px 10px;margin-top:-2px;margin-bottom:-2px;background-color:transparent;background-image:none;border:1px solid transparent;border-radius:2px}.navbar-toggle:focus{outline:0}.navbar-toggle .icon-bar{display:block;width:22px;height:2px;border-radius:1px}.navbar-toggle .icon-bar+.icon-bar{margin-top:4px}@media (min-width:541px){.navbar-toggle{display:none}}.navbar-nav{margin:3px 0}.navbar-nav>li>a{padding-top:10px;padding-bottom:10px;line-height:18px}@media (max-width:540px){.navbar-nav .open .dropdown-menu{position:static;float:none;width:auto;margin-top:0;background-color:transparent;border:0;box-shadow:none}.navbar-nav .open .dropdown-menu>li>a,.navbar-nav .open .dropdown-menu .dropdown-header{padding:5px 15px 5px 25px}.navbar-nav .open .dropdown-menu>li>a{line-height:18px}.navbar-nav .open .dropdown-menu>li>a:hover,.navbar-nav .open .dropdown-menu>li>a:focus{background-image:none}}@media (min-width:541px){.navbar-nav{float:left;margin:0}.navbar-nav>li{float:left}.navbar-nav>li>a{padding-top:6px;padding-bottom:6px}}.navbar-form{margin-left:0;margin-right:0;padding:10px 0;border-top:1px solid transparent;border-bottom:1px solid transparent;-webkit-box-shadow:inset 0 1px 0 rgba(255,255,255,0.1),0 1px 0 rgba(255,255,255,0.1);box-shadow:inset 0 1px 0 rgba(255,255,255,0.1),0 1px 0 rgba(255,255,255,0.1);margin-top:-1px;margin-bottom:-1px}@media (min-width:768px){.navbar-form .form-group{display:inline-block;margin-bottom:0;vertical-align:middle}.navbar-form .form-control{display:inline-block;width:auto;vertical-align:middle}.navbar-form .form-control-static{display:inline-block}.navbar-form .input-group{display:inline-table;vertical-align:middle}.navbar-form .input-group .input-group-addon,.navbar-form .input-group .input-group-btn,.navbar-form .input-group .form-control{width:auto}.navbar-form .input-group>.form-control{width:100%}.navbar-form .control-label{margin-bottom:0;vertical-align:middle}.navbar-form .radio,.navbar-form .checkbox{display:inline-block;margin-top:0;margin-bottom:0;vertical-align:middle}.navbar-form .radio label,.navbar-form .checkbox label{padding-left:0}.navbar-form .radio input[type=\"radio\"],.navbar-form .checkbox input[type=\"checkbox\"]{position:relative;margin-left:0}.navbar-form .has-feedback .form-control-feedback{top:0}}@media (max-width:540px){.navbar-form .form-group{margin-bottom:5px}.navbar-form .form-group:last-child{margin-bottom:0}}@media (min-width:541px){.navbar-form{width:auto;border:0;margin-left:0;margin-right:0;padding-top:0;padding-bottom:0;-webkit-box-shadow:none;box-shadow:none}}.navbar-nav>li>.dropdown-menu{margin-top:0;border-top-right-radius:0;border-top-left-radius:0}.navbar-fixed-bottom .navbar-nav>li>.dropdown-menu{border-top-right-radius:2px;border-top-left-radius:2px;border-bottom-right-radius:0;border-bottom-left-radius:0}.navbar-btn{margin-top:-1px;margin-bottom:-1px}.navbar-btn.btn-sm{margin-top:0;margin-bottom:0}.navbar-btn.btn-xs{margin-top:4px;margin-bottom:4px}.navbar-text{margin-top:6px;margin-bottom:6px}@media (min-width:541px){.navbar-text{float:left;margin-left:0;margin-right:0}}@media (min-width:541px){.navbar-left{float:left !important;float:left}.navbar-right{float:right !important;float:right;margin-right:0}.navbar-right~.navbar-right{margin-right:0}}.navbar-default{background-color:#f8f8f8;border-color:#e7e7e7}.navbar-default .navbar-brand{color:#777}.navbar-default .navbar-brand:hover,.navbar-default .navbar-brand:focus{color:#5e5e5e;background-color:transparent}.navbar-default .navbar-text{color:#777}.navbar-default .navbar-nav>li>a{color:#777}.navbar-default .navbar-nav>li>a:hover,.navbar-default .navbar-nav>li>a:focus{color:#333;background-color:transparent}.navbar-default .navbar-nav>.active>a,.navbar-default .navbar-nav>.active>a:hover,.navbar-default .navbar-nav>.active>a:focus{color:#555;background-color:#e7e7e7}.navbar-default .navbar-nav>.disabled>a,.navbar-default .navbar-nav>.disabled>a:hover,.navbar-default .navbar-nav>.disabled>a:focus{color:#ccc;background-color:transparent}.navbar-default .navbar-toggle{border-color:#ddd}.navbar-default .navbar-toggle:hover,.navbar-default .navbar-toggle:focus{background-color:#ddd}.navbar-default .navbar-toggle .icon-bar{background-color:#888}.navbar-default .navbar-collapse,.navbar-default .navbar-form{border-color:#e7e7e7}.navbar-default .navbar-nav>.open>a,.navbar-default .navbar-nav>.open>a:hover,.navbar-default .navbar-nav>.open>a:focus{background-color:#e7e7e7;color:#555}@media (max-width:540px){.navbar-default .navbar-nav .open .dropdown-menu>li>a{color:#777}.navbar-default .navbar-nav .open .dropdown-menu>li>a:hover,.navbar-default .navbar-nav .open .dropdown-menu>li>a:focus{color:#333;background-color:transparent}.navbar-default .navbar-nav .open .dropdown-menu>.active>a,.navbar-default .navbar-nav .open .dropdown-menu>.active>a:hover,.navbar-default .navbar-nav .open .dropdown-menu>.active>a:focus{color:#555;background-color:#e7e7e7}.navbar-default .navbar-nav .open .dropdown-menu>.disabled>a,.navbar-default .navbar-nav .open .dropdown-menu>.disabled>a:hover,.navbar-default .navbar-nav .open .dropdown-menu>.disabled>a:focus{color:#ccc;background-color:transparent}}.navbar-default .navbar-link{color:#777}.navbar-default .navbar-link:hover{color:#333}.navbar-default .btn-link{color:#777}.navbar-default .btn-link:hover,.navbar-default .btn-link:focus{color:#333}.navbar-default .btn-link[disabled]:hover,fieldset[disabled] .navbar-default .btn-link:hover,.navbar-default .btn-link[disabled]:focus,fieldset[disabled] .navbar-default .btn-link:focus{color:#ccc}.navbar-inverse{background-color:#222;border-color:#080808}.navbar-inverse .navbar-brand{color:#9d9d9d}.navbar-inverse .navbar-brand:hover,.navbar-inverse .navbar-brand:focus{color:#fff;background-color:transparent}.navbar-inverse .navbar-text{color:#9d9d9d}.navbar-inverse .navbar-nav>li>a{color:#9d9d9d}.navbar-inverse .navbar-nav>li>a:hover,.navbar-inverse .navbar-nav>li>a:focus{color:#fff;background-color:transparent}.navbar-inverse .navbar-nav>.active>a,.navbar-inverse .navbar-nav>.active>a:hover,.navbar-inverse .navbar-nav>.active>a:focus{color:#fff;background-color:#080808}.navbar-inverse .navbar-nav>.disabled>a,.navbar-inverse .navbar-nav>.disabled>a:hover,.navbar-inverse .navbar-nav>.disabled>a:focus{color:#444;background-color:transparent}.navbar-inverse .navbar-toggle{border-color:#333}.navbar-inverse .navbar-toggle:hover,.navbar-inverse .navbar-toggle:focus{background-color:#333}.navbar-inverse .navbar-toggle .icon-bar{background-color:#fff}.navbar-inverse .navbar-collapse,.navbar-inverse .navbar-form{border-color:#101010}.navbar-inverse .navbar-nav>.open>a,.navbar-inverse .navbar-nav>.open>a:hover,.navbar-inverse .navbar-nav>.open>a:focus{background-color:#080808;color:#fff}@media (max-width:540px){.navbar-inverse .navbar-nav .open .dropdown-menu>.dropdown-header{border-color:#080808}.navbar-inverse .navbar-nav .open .dropdown-menu .divider{background-color:#080808}.navbar-inverse .navbar-nav .open .dropdown-menu>li>a{color:#9d9d9d}.navbar-inverse .navbar-nav .open .dropdown-menu>li>a:hover,.navbar-inverse .navbar-nav .open .dropdown-menu>li>a:focus{color:#fff;background-color:transparent}.navbar-inverse .navbar-nav .open .dropdown-menu>.active>a,.navbar-inverse .navbar-nav .open .dropdown-menu>.active>a:hover,.navbar-inverse .navbar-nav .open .dropdown-menu>.active>a:focus{color:#fff;background-color:#080808}.navbar-inverse .navbar-nav .open .dropdown-menu>.disabled>a,.navbar-inverse .navbar-nav .open .dropdown-menu>.disabled>a:hover,.navbar-inverse .navbar-nav .open .dropdown-menu>.disabled>a:focus{color:#444;background-color:transparent}}.navbar-inverse .navbar-link{color:#9d9d9d}.navbar-inverse .navbar-link:hover{color:#fff}.navbar-inverse .btn-link{color:#9d9d9d}.navbar-inverse .btn-link:hover,.navbar-inverse .btn-link:focus{color:#fff}.navbar-inverse .btn-link[disabled]:hover,fieldset[disabled] .navbar-inverse .btn-link:hover,.navbar-inverse .btn-link[disabled]:focus,fieldset[disabled] .navbar-inverse .btn-link:focus{color:#444}.breadcrumb{padding:8px 15px;margin-bottom:18px;list-style:none;background-color:#f5f5f5;border-radius:2px}.breadcrumb>li{display:inline-block}.breadcrumb>li+li:before{content:\"/\\00a0\";padding:0 5px;color:#5e5e5e}.breadcrumb>.active{color:#777}.pagination{display:inline-block;padding-left:0;margin:18px 0;border-radius:2px}.pagination>li{display:inline}.pagination>li>a,.pagination>li>span{position:relative;float:left;padding:6px 12px;line-height:1.42857143;text-decoration:none;color:#337ab7;background-color:#fff;border:1px solid #ddd;margin-left:-1px}.pagination>li:first-child>a,.pagination>li:first-child>span{margin-left:0;border-bottom-left-radius:2px;border-top-left-radius:2px}.pagination>li:last-child>a,.pagination>li:last-child>span{border-bottom-right-radius:2px;border-top-right-radius:2px}.pagination>li>a:hover,.pagination>li>span:hover,.pagination>li>a:focus,.pagination>li>span:focus{color:#23527c;background-color:#eee;border-color:#ddd}.pagination>.active>a,.pagination>.active>span,.pagination>.active>a:hover,.pagination>.active>span:hover,.pagination>.active>a:focus,.pagination>.active>span:focus{z-index:2;color:#fff;background-color:#337ab7;border-color:#337ab7;cursor:default}.pagination>.disabled>span,.pagination>.disabled>span:hover,.pagination>.disabled>span:focus,.pagination>.disabled>a,.pagination>.disabled>a:hover,.pagination>.disabled>a:focus{color:#777;background-color:#fff;border-color:#ddd;cursor:not-allowed}.pagination-lg>li>a,.pagination-lg>li>span{padding:10px 16px;font-size:17px}.pagination-lg>li:first-child>a,.pagination-lg>li:first-child>span{border-bottom-left-radius:3px;border-top-left-radius:3px}.pagination-lg>li:last-child>a,.pagination-lg>li:last-child>span{border-bottom-right-radius:3px;border-top-right-radius:3px}.pagination-sm>li>a,.pagination-sm>li>span{padding:5px 10px;font-size:12px}.pagination-sm>li:first-child>a,.pagination-sm>li:first-child>span{border-bottom-left-radius:1px;border-top-left-radius:1px}.pagination-sm>li:last-child>a,.pagination-sm>li:last-child>span{border-bottom-right-radius:1px;border-top-right-radius:1px}.pager{padding-left:0;margin:18px 0;list-style:none;text-align:center}.pager li{display:inline}.pager li>a,.pager li>span{display:inline-block;padding:5px 14px;background-color:#fff;border:1px solid #ddd;border-radius:15px}.pager li>a:hover,.pager li>a:focus{text-decoration:none;background-color:#eee}.pager .next>a,.pager .next>span{float:right}.pager .previous>a,.pager .previous>span{float:left}.pager .disabled>a,.pager .disabled>a:hover,.pager .disabled>a:focus,.pager .disabled>span{color:#777;background-color:#fff;cursor:not-allowed}.label{display:inline;padding:.2em .6em .3em;font-size:75%;font-weight:bold;line-height:1;color:#fff;text-align:center;white-space:nowrap;vertical-align:baseline;border-radius:.25em}a.label:hover,a.label:focus{color:#fff;text-decoration:none;cursor:pointer}.label:empty{display:none}.btn .label{position:relative;top:-1px}.label-default{background-color:#777}.label-default[href]:hover,.label-default[href]:focus{background-color:#5e5e5e}.label-primary{background-color:#337ab7}.label-primary[href]:hover,.label-primary[href]:focus{background-color:#286090}.label-success{background-color:#5cb85c}.label-success[href]:hover,.label-success[href]:focus{background-color:#449d44}.label-info{background-color:#5bc0de}.label-info[href]:hover,.label-info[href]:focus{background-color:#31b0d5}.label-warning{background-color:#f0ad4e}.label-warning[href]:hover,.label-warning[href]:focus{background-color:#ec971f}.label-danger{background-color:#d9534f}.label-danger[href]:hover,.label-danger[href]:focus{background-color:#c9302c}.badge{display:inline-block;min-width:10px;padding:3px 7px;font-size:12px;font-weight:bold;color:#fff;line-height:1;vertical-align:baseline;white-space:nowrap;text-align:center;background-color:#777;border-radius:10px}.badge:empty{display:none}.btn .badge{position:relative;top:-1px}.btn-xs .badge{top:0;padding:1px 5px}a.badge:hover,a.badge:focus{color:#fff;text-decoration:none;cursor:pointer}.list-group-item.active>.badge,.nav-pills>.active>a>.badge{color:#337ab7;background-color:#fff}.list-group-item>.badge{float:right}.list-group-item>.badge+.badge{margin-right:5px}.nav-pills>li>a>.badge{margin-left:3px}.jumbotron{padding:30px 15px;margin-bottom:30px;color:inherit;background-color:#eee}.jumbotron h1,.jumbotron .h1{color:inherit}.jumbotron p{margin-bottom:15px;font-size:20px;font-weight:200}.jumbotron>hr{border-top-color:#d5d5d5}.container .jumbotron,.container-fluid .jumbotron{border-radius:3px}.jumbotron .container{max-width:100%}@media screen and (min-width:768px){.jumbotron{padding:48px 0}.container .jumbotron,.container-fluid .jumbotron{padding-left:60px;padding-right:60px}.jumbotron h1,.jumbotron .h1{font-size:58.5px}}.thumbnail{display:block;padding:4px;margin-bottom:18px;line-height:1.42857143;background-color:#fff;border:1px solid #ddd;border-radius:2px;-webkit-transition:border .2s ease-in-out;-o-transition:border .2s ease-in-out;transition:border .2s ease-in-out}.thumbnail>img,.thumbnail a>img{margin-left:auto;margin-right:auto}a.thumbnail:hover,a.thumbnail:focus,a.thumbnail.active{border-color:#337ab7}.thumbnail .caption{padding:9px;color:#000}.alert{padding:15px;margin-bottom:18px;border:1px solid transparent;border-radius:2px}.alert h4{margin-top:0;color:inherit}.alert .alert-link{font-weight:bold}.alert>p,.alert>ul{margin-bottom:0}.alert>p+p{margin-top:5px}.alert-dismissable,.alert-dismissible{padding-right:35px}.alert-dismissable .close,.alert-dismissible .close{position:relative;top:-2px;right:-21px;color:inherit}.alert-success{background-color:#dff0d8;border-color:#d6e9c6;color:#3c763d}.alert-success hr{border-top-color:#c9e2b3}.alert-success .alert-link{color:#2b542c}.alert-info{background-color:#d9edf7;border-color:#bce8f1;color:#31708f}.alert-info hr{border-top-color:#a6e1ec}.alert-info .alert-link{color:#245269}.alert-warning{background-color:#fcf8e3;border-color:#faebcc;color:#8a6d3b}.alert-warning hr{border-top-color:#f7e1b5}.alert-warning .alert-link{color:#66512c}.alert-danger{background-color:#f2dede;border-color:#ebccd1;color:#a94442}.alert-danger hr{border-top-color:#e4b9c0}.alert-danger .alert-link{color:#843534}@-webkit-keyframes progress-bar-stripes{from{background-position:40px 0}to{background-position:0 0}}@keyframes progress-bar-stripes{from{background-position:40px 0}to{background-position:0 0}}.progress{overflow:hidden;height:18px;margin-bottom:18px;background-color:#f5f5f5;border-radius:2px;-webkit-box-shadow:inset 0 1px 2px rgba(0,0,0,0.1);box-shadow:inset 0 1px 2px rgba(0,0,0,0.1)}.progress-bar{float:left;width:0;height:100%;font-size:12px;line-height:18px;color:#fff;text-align:center;background-color:#337ab7;-webkit-box-shadow:inset 0 -1px 0 rgba(0,0,0,0.15);box-shadow:inset 0 -1px 0 rgba(0,0,0,0.15);-webkit-transition:width .6s ease;-o-transition:width .6s ease;transition:width .6s ease}.progress-striped .progress-bar,.progress-bar-striped{background-image:-webkit-linear-gradient(45deg, rgba(255,255,255,0.15) 25%, transparent 25%, transparent 50%, rgba(255,255,255,0.15) 50%, rgba(255,255,255,0.15) 75%, transparent 75%, transparent);background-image:-o-linear-gradient(45deg, rgba(255,255,255,0.15) 25%, transparent 25%, transparent 50%, rgba(255,255,255,0.15) 50%, rgba(255,255,255,0.15) 75%, transparent 75%, transparent);background-image:linear-gradient(45deg, rgba(255,255,255,0.15) 25%, transparent 25%, transparent 50%, rgba(255,255,255,0.15) 50%, rgba(255,255,255,0.15) 75%, transparent 75%, transparent);background-size:40px 40px}.progress.active .progress-bar,.progress-bar.active{-webkit-animation:progress-bar-stripes 2s linear infinite;-o-animation:progress-bar-stripes 2s linear infinite;animation:progress-bar-stripes 2s linear infinite}.progress-bar-success{background-color:#5cb85c}.progress-striped .progress-bar-success{background-image:-webkit-linear-gradient(45deg, rgba(255,255,255,0.15) 25%, transparent 25%, transparent 50%, rgba(255,255,255,0.15) 50%, rgba(255,255,255,0.15) 75%, transparent 75%, transparent);background-image:-o-linear-gradient(45deg, rgba(255,255,255,0.15) 25%, transparent 25%, transparent 50%, rgba(255,255,255,0.15) 50%, rgba(255,255,255,0.15) 75%, transparent 75%, transparent);background-image:linear-gradient(45deg, rgba(255,255,255,0.15) 25%, transparent 25%, transparent 50%, rgba(255,255,255,0.15) 50%, rgba(255,255,255,0.15) 75%, transparent 75%, transparent)}.progress-bar-info{background-color:#5bc0de}.progress-striped .progress-bar-info{background-image:-webkit-linear-gradient(45deg, rgba(255,255,255,0.15) 25%, transparent 25%, transparent 50%, rgba(255,255,255,0.15) 50%, rgba(255,255,255,0.15) 75%, transparent 75%, transparent);background-image:-o-linear-gradient(45deg, rgba(255,255,255,0.15) 25%, transparent 25%, transparent 50%, rgba(255,255,255,0.15) 50%, rgba(255,255,255,0.15) 75%, transparent 75%, transparent);background-image:linear-gradient(45deg, rgba(255,255,255,0.15) 25%, transparent 25%, transparent 50%, rgba(255,255,255,0.15) 50%, rgba(255,255,255,0.15) 75%, transparent 75%, transparent)}.progress-bar-warning{background-color:#f0ad4e}.progress-striped .progress-bar-warning{background-image:-webkit-linear-gradient(45deg, rgba(255,255,255,0.15) 25%, transparent 25%, transparent 50%, rgba(255,255,255,0.15) 50%, rgba(255,255,255,0.15) 75%, transparent 75%, transparent);background-image:-o-linear-gradient(45deg, rgba(255,255,255,0.15) 25%, transparent 25%, transparent 50%, rgba(255,255,255,0.15) 50%, rgba(255,255,255,0.15) 75%, transparent 75%, transparent);background-image:linear-gradient(45deg, rgba(255,255,255,0.15) 25%, transparent 25%, transparent 50%, rgba(255,255,255,0.15) 50%, rgba(255,255,255,0.15) 75%, transparent 75%, transparent)}.progress-bar-danger{background-color:#d9534f}.progress-striped .progress-bar-danger{background-image:-webkit-linear-gradient(45deg, rgba(255,255,255,0.15) 25%, transparent 25%, transparent 50%, rgba(255,255,255,0.15) 50%, rgba(255,255,255,0.15) 75%, transparent 75%, transparent);background-image:-o-linear-gradient(45deg, rgba(255,255,255,0.15) 25%, transparent 25%, transparent 50%, rgba(255,255,255,0.15) 50%, rgba(255,255,255,0.15) 75%, transparent 75%, transparent);background-image:linear-gradient(45deg, rgba(255,255,255,0.15) 25%, transparent 25%, transparent 50%, rgba(255,255,255,0.15) 50%, rgba(255,255,255,0.15) 75%, transparent 75%, transparent)}.media{margin-top:15px}.media:first-child{margin-top:0}.media-right,.media>.pull-right{padding-left:10px}.media-left,.media>.pull-left{padding-right:10px}.media-left,.media-right,.media-body{display:table-cell;vertical-align:top}.media-middle{vertical-align:middle}.media-bottom{vertical-align:bottom}.media-heading{margin-top:0;margin-bottom:5px}.media-list{padding-left:0;list-style:none}.list-group{margin-bottom:20px;padding-left:0}.list-group-item{position:relative;display:block;padding:10px 15px;margin-bottom:-1px;background-color:#fff;border:1px solid #ddd}.list-group-item:first-child{border-top-right-radius:2px;border-top-left-radius:2px}.list-group-item:last-child{margin-bottom:0;border-bottom-right-radius:2px;border-bottom-left-radius:2px}a.list-group-item{color:#555}a.list-group-item .list-group-item-heading{color:#333}a.list-group-item:hover,a.list-group-item:focus{text-decoration:none;color:#555;background-color:#f5f5f5}.list-group-item.disabled,.list-group-item.disabled:hover,.list-group-item.disabled:focus{background-color:#eee;color:#777;cursor:not-allowed}.list-group-item.disabled .list-group-item-heading,.list-group-item.disabled:hover .list-group-item-heading,.list-group-item.disabled:focus .list-group-item-heading{color:inherit}.list-group-item.disabled .list-group-item-text,.list-group-item.disabled:hover .list-group-item-text,.list-group-item.disabled:focus .list-group-item-text{color:#777}.list-group-item.active,.list-group-item.active:hover,.list-group-item.active:focus{z-index:2;color:#fff;background-color:#337ab7;border-color:#337ab7}.list-group-item.active .list-group-item-heading,.list-group-item.active:hover .list-group-item-heading,.list-group-item.active:focus .list-group-item-heading,.list-group-item.active .list-group-item-heading>small,.list-group-item.active:hover .list-group-item-heading>small,.list-group-item.active:focus .list-group-item-heading>small,.list-group-item.active .list-group-item-heading>.small,.list-group-item.active:hover .list-group-item-heading>.small,.list-group-item.active:focus .list-group-item-heading>.small{color:inherit}.list-group-item.active .list-group-item-text,.list-group-item.active:hover .list-group-item-text,.list-group-item.active:focus .list-group-item-text{color:#c7ddef}.list-group-item-success{color:#3c763d;background-color:#dff0d8}a.list-group-item-success{color:#3c763d}a.list-group-item-success .list-group-item-heading{color:inherit}a.list-group-item-success:hover,a.list-group-item-success:focus{color:#3c763d;background-color:#d0e9c6}a.list-group-item-success.active,a.list-group-item-success.active:hover,a.list-group-item-success.active:focus{color:#fff;background-color:#3c763d;border-color:#3c763d}.list-group-item-info{color:#31708f;background-color:#d9edf7}a.list-group-item-info{color:#31708f}a.list-group-item-info .list-group-item-heading{color:inherit}a.list-group-item-info:hover,a.list-group-item-info:focus{color:#31708f;background-color:#c4e3f3}a.list-group-item-info.active,a.list-group-item-info.active:hover,a.list-group-item-info.active:focus{color:#fff;background-color:#31708f;border-color:#31708f}.list-group-item-warning{color:#8a6d3b;background-color:#fcf8e3}a.list-group-item-warning{color:#8a6d3b}a.list-group-item-warning .list-group-item-heading{color:inherit}a.list-group-item-warning:hover,a.list-group-item-warning:focus{color:#8a6d3b;background-color:#faf2cc}a.list-group-item-warning.active,a.list-group-item-warning.active:hover,a.list-group-item-warning.active:focus{color:#fff;background-color:#8a6d3b;border-color:#8a6d3b}.list-group-item-danger{color:#a94442;background-color:#f2dede}a.list-group-item-danger{color:#a94442}a.list-group-item-danger .list-group-item-heading{color:inherit}a.list-group-item-danger:hover,a.list-group-item-danger:focus{color:#a94442;background-color:#ebcccc}a.list-group-item-danger.active,a.list-group-item-danger.active:hover,a.list-group-item-danger.active:focus{color:#fff;background-color:#a94442;border-color:#a94442}.list-group-item-heading{margin-top:0;margin-bottom:5px}.list-group-item-text{margin-bottom:0;line-height:1.3}.panel{margin-bottom:18px;background-color:#fff;border:1px solid transparent;border-radius:2px;-webkit-box-shadow:0 1px 1px rgba(0,0,0,0.05);box-shadow:0 1px 1px rgba(0,0,0,0.05)}.panel-body{padding:15px}.panel-heading{padding:10px 15px;border-bottom:1px solid transparent;border-top-right-radius:1px;border-top-left-radius:1px}.panel-heading>.dropdown .dropdown-toggle{color:inherit}.panel-title{margin-top:0;margin-bottom:0;font-size:15px;color:inherit}.panel-title>a{color:inherit}.panel-footer{padding:10px 15px;background-color:#f5f5f5;border-top:1px solid #ddd;border-bottom-right-radius:1px;border-bottom-left-radius:1px}.panel>.list-group,.panel>.panel-collapse>.list-group{margin-bottom:0}.panel>.list-group .list-group-item,.panel>.panel-collapse>.list-group .list-group-item{border-width:1px 0;border-radius:0}.panel>.list-group:first-child .list-group-item:first-child,.panel>.panel-collapse>.list-group:first-child .list-group-item:first-child{border-top:0;border-top-right-radius:1px;border-top-left-radius:1px}.panel>.list-group:last-child .list-group-item:last-child,.panel>.panel-collapse>.list-group:last-child .list-group-item:last-child{border-bottom:0;border-bottom-right-radius:1px;border-bottom-left-radius:1px}.panel-heading+.list-group .list-group-item:first-child{border-top-width:0}.list-group+.panel-footer{border-top-width:0}.panel>.table,.panel>.table-responsive>.table,.panel>.panel-collapse>.table{margin-bottom:0}.panel>.table caption,.panel>.table-responsive>.table caption,.panel>.panel-collapse>.table caption{padding-left:15px;padding-right:15px}.panel>.table:first-child,.panel>.table-responsive:first-child>.table:first-child{border-top-right-radius:1px;border-top-left-radius:1px}.panel>.table:first-child>thead:first-child>tr:first-child,.panel>.table-responsive:first-child>.table:first-child>thead:first-child>tr:first-child,.panel>.table:first-child>tbody:first-child>tr:first-child,.panel>.table-responsive:first-child>.table:first-child>tbody:first-child>tr:first-child{border-top-left-radius:1px;border-top-right-radius:1px}.panel>.table:first-child>thead:first-child>tr:first-child td:first-child,.panel>.table-responsive:first-child>.table:first-child>thead:first-child>tr:first-child td:first-child,.panel>.table:first-child>tbody:first-child>tr:first-child td:first-child,.panel>.table-responsive:first-child>.table:first-child>tbody:first-child>tr:first-child td:first-child,.panel>.table:first-child>thead:first-child>tr:first-child th:first-child,.panel>.table-responsive:first-child>.table:first-child>thead:first-child>tr:first-child th:first-child,.panel>.table:first-child>tbody:first-child>tr:first-child th:first-child,.panel>.table-responsive:first-child>.table:first-child>tbody:first-child>tr:first-child th:first-child{border-top-left-radius:1px}.panel>.table:first-child>thead:first-child>tr:first-child td:last-child,.panel>.table-responsive:first-child>.table:first-child>thead:first-child>tr:first-child td:last-child,.panel>.table:first-child>tbody:first-child>tr:first-child td:last-child,.panel>.table-responsive:first-child>.table:first-child>tbody:first-child>tr:first-child td:last-child,.panel>.table:first-child>thead:first-child>tr:first-child th:last-child,.panel>.table-responsive:first-child>.table:first-child>thead:first-child>tr:first-child th:last-child,.panel>.table:first-child>tbody:first-child>tr:first-child th:last-child,.panel>.table-responsive:first-child>.table:first-child>tbody:first-child>tr:first-child th:last-child{border-top-right-radius:1px}.panel>.table:last-child,.panel>.table-responsive:last-child>.table:last-child{border-bottom-right-radius:1px;border-bottom-left-radius:1px}.panel>.table:last-child>tbody:last-child>tr:last-child,.panel>.table-responsive:last-child>.table:last-child>tbody:last-child>tr:last-child,.panel>.table:last-child>tfoot:last-child>tr:last-child,.panel>.table-responsive:last-child>.table:last-child>tfoot:last-child>tr:last-child{border-bottom-left-radius:1px;border-bottom-right-radius:1px}.panel>.table:last-child>tbody:last-child>tr:last-child td:first-child,.panel>.table-responsive:last-child>.table:last-child>tbody:last-child>tr:last-child td:first-child,.panel>.table:last-child>tfoot:last-child>tr:last-child td:first-child,.panel>.table-responsive:last-child>.table:last-child>tfoot:last-child>tr:last-child td:first-child,.panel>.table:last-child>tbody:last-child>tr:last-child th:first-child,.panel>.table-responsive:last-child>.table:last-child>tbody:last-child>tr:last-child th:first-child,.panel>.table:last-child>tfoot:last-child>tr:last-child th:first-child,.panel>.table-responsive:last-child>.table:last-child>tfoot:last-child>tr:last-child th:first-child{border-bottom-left-radius:1px}.panel>.table:last-child>tbody:last-child>tr:last-child td:last-child,.panel>.table-responsive:last-child>.table:last-child>tbody:last-child>tr:last-child td:last-child,.panel>.table:last-child>tfoot:last-child>tr:last-child td:last-child,.panel>.table-responsive:last-child>.table:last-child>tfoot:last-child>tr:last-child td:last-child,.panel>.table:last-child>tbody:last-child>tr:last-child th:last-child,.panel>.table-responsive:last-child>.table:last-child>tbody:last-child>tr:last-child th:last-child,.panel>.table:last-child>tfoot:last-child>tr:last-child th:last-child,.panel>.table-responsive:last-child>.table:last-child>tfoot:last-child>tr:last-child th:last-child{border-bottom-right-radius:1px}.panel>.panel-body+.table,.panel>.panel-body+.table-responsive,.panel>.table+.panel-body,.panel>.table-responsive+.panel-body{border-top:1px solid #ddd}.panel>.table>tbody:first-child>tr:first-child th,.panel>.table>tbody:first-child>tr:first-child td{border-top:0}.panel>.table-bordered,.panel>.table-responsive>.table-bordered{border:0}.panel>.table-bordered>thead>tr>th:first-child,.panel>.table-responsive>.table-bordered>thead>tr>th:first-child,.panel>.table-bordered>tbody>tr>th:first-child,.panel>.table-responsive>.table-bordered>tbody>tr>th:first-child,.panel>.table-bordered>tfoot>tr>th:first-child,.panel>.table-responsive>.table-bordered>tfoot>tr>th:first-child,.panel>.table-bordered>thead>tr>td:first-child,.panel>.table-responsive>.table-bordered>thead>tr>td:first-child,.panel>.table-bordered>tbody>tr>td:first-child,.panel>.table-responsive>.table-bordered>tbody>tr>td:first-child,.panel>.table-bordered>tfoot>tr>td:first-child,.panel>.table-responsive>.table-bordered>tfoot>tr>td:first-child{border-left:0}.panel>.table-bordered>thead>tr>th:last-child,.panel>.table-responsive>.table-bordered>thead>tr>th:last-child,.panel>.table-bordered>tbody>tr>th:last-child,.panel>.table-responsive>.table-bordered>tbody>tr>th:last-child,.panel>.table-bordered>tfoot>tr>th:last-child,.panel>.table-responsive>.table-bordered>tfoot>tr>th:last-child,.panel>.table-bordered>thead>tr>td:last-child,.panel>.table-responsive>.table-bordered>thead>tr>td:last-child,.panel>.table-bordered>tbody>tr>td:last-child,.panel>.table-responsive>.table-bordered>tbody>tr>td:last-child,.panel>.table-bordered>tfoot>tr>td:last-child,.panel>.table-responsive>.table-bordered>tfoot>tr>td:last-child{border-right:0}.panel>.table-bordered>thead>tr:first-child>td,.panel>.table-responsive>.table-bordered>thead>tr:first-child>td,.panel>.table-bordered>tbody>tr:first-child>td,.panel>.table-responsive>.table-bordered>tbody>tr:first-child>td,.panel>.table-bordered>thead>tr:first-child>th,.panel>.table-responsive>.table-bordered>thead>tr:first-child>th,.panel>.table-bordered>tbody>tr:first-child>th,.panel>.table-responsive>.table-bordered>tbody>tr:first-child>th{border-bottom:0}.panel>.table-bordered>tbody>tr:last-child>td,.panel>.table-responsive>.table-bordered>tbody>tr:last-child>td,.panel>.table-bordered>tfoot>tr:last-child>td,.panel>.table-responsive>.table-bordered>tfoot>tr:last-child>td,.panel>.table-bordered>tbody>tr:last-child>th,.panel>.table-responsive>.table-bordered>tbody>tr:last-child>th,.panel>.table-bordered>tfoot>tr:last-child>th,.panel>.table-responsive>.table-bordered>tfoot>tr:last-child>th{border-bottom:0}.panel>.table-responsive{border:0;margin-bottom:0}.panel-group{margin-bottom:18px}.panel-group .panel{margin-bottom:0;border-radius:2px}.panel-group .panel+.panel{margin-top:5px}.panel-group .panel-heading{border-bottom:0}.panel-group .panel-heading+.panel-collapse>.panel-body,.panel-group .panel-heading+.panel-collapse>.list-group{border-top:1px solid #ddd}.panel-group .panel-footer{border-top:0}.panel-group .panel-footer+.panel-collapse .panel-body{border-bottom:1px solid #ddd}.panel-default{border-color:#ddd}.panel-default>.panel-heading{color:#333;background-color:#f5f5f5;border-color:#ddd}.panel-default>.panel-heading+.panel-collapse>.panel-body{border-top-color:#ddd}.panel-default>.panel-heading .badge{color:#f5f5f5;background-color:#333}.panel-default>.panel-footer+.panel-collapse>.panel-body{border-bottom-color:#ddd}.panel-primary{border-color:#337ab7}.panel-primary>.panel-heading{color:#fff;background-color:#337ab7;border-color:#337ab7}.panel-primary>.panel-heading+.panel-collapse>.panel-body{border-top-color:#337ab7}.panel-primary>.panel-heading .badge{color:#337ab7;background-color:#fff}.panel-primary>.panel-footer+.panel-collapse>.panel-body{border-bottom-color:#337ab7}.panel-success{border-color:#d6e9c6}.panel-success>.panel-heading{color:#3c763d;background-color:#dff0d8;border-color:#d6e9c6}.panel-success>.panel-heading+.panel-collapse>.panel-body{border-top-color:#d6e9c6}.panel-success>.panel-heading .badge{color:#dff0d8;background-color:#3c763d}.panel-success>.panel-footer+.panel-collapse>.panel-body{border-bottom-color:#d6e9c6}.panel-info{border-color:#bce8f1}.panel-info>.panel-heading{color:#31708f;background-color:#d9edf7;border-color:#bce8f1}.panel-info>.panel-heading+.panel-collapse>.panel-body{border-top-color:#bce8f1}.panel-info>.panel-heading .badge{color:#d9edf7;background-color:#31708f}.panel-info>.panel-footer+.panel-collapse>.panel-body{border-bottom-color:#bce8f1}.panel-warning{border-color:#faebcc}.panel-warning>.panel-heading{color:#8a6d3b;background-color:#fcf8e3;border-color:#faebcc}.panel-warning>.panel-heading+.panel-collapse>.panel-body{border-top-color:#faebcc}.panel-warning>.panel-heading .badge{color:#fcf8e3;background-color:#8a6d3b}.panel-warning>.panel-footer+.panel-collapse>.panel-body{border-bottom-color:#faebcc}.panel-danger{border-color:#ebccd1}.panel-danger>.panel-heading{color:#a94442;background-color:#f2dede;border-color:#ebccd1}.panel-danger>.panel-heading+.panel-collapse>.panel-body{border-top-color:#ebccd1}.panel-danger>.panel-heading .badge{color:#f2dede;background-color:#a94442}.panel-danger>.panel-footer+.panel-collapse>.panel-body{border-bottom-color:#ebccd1}.embed-responsive{position:relative;display:block;height:0;padding:0;overflow:hidden}.embed-responsive .embed-responsive-item,.embed-responsive iframe,.embed-responsive embed,.embed-responsive object,.embed-responsive video{position:absolute;top:0;left:0;bottom:0;height:100%;width:100%;border:0}.embed-responsive.embed-responsive-16by9{padding-bottom:56.25%}.embed-responsive.embed-responsive-4by3{padding-bottom:75%}.well{min-height:20px;padding:19px;margin-bottom:20px;background-color:#f5f5f5;border:1px solid #e3e3e3;border-radius:2px;-webkit-box-shadow:inset 0 1px 1px rgba(0,0,0,0.05);box-shadow:inset 0 1px 1px rgba(0,0,0,0.05)}.well blockquote{border-color:#ddd;border-color:rgba(0,0,0,0.15)}.well-lg{padding:24px;border-radius:3px}.well-sm{padding:9px;border-radius:1px}.close{float:right;font-size:19.5px;font-weight:bold;line-height:1;color:#000;text-shadow:0 1px 0 #fff;opacity:.2;filter:alpha(opacity=20)}.close:hover,.close:focus{color:#000;text-decoration:none;cursor:pointer;opacity:.5;filter:alpha(opacity=50)}button.close{padding:0;cursor:pointer;background:transparent;border:0;-webkit-appearance:none}.modal-open{overflow:hidden}.modal{display:none;overflow:hidden;position:fixed;top:0;right:0;bottom:0;left:0;z-index:1040;-webkit-overflow-scrolling:touch;outline:0}.modal.fade .modal-dialog{-webkit-transform:translate(0, -25%);-ms-transform:translate(0, -25%);-o-transform:translate(0, -25%);transform:translate(0, -25%);-webkit-transition:-webkit-transform 0.3s ease-out;-moz-transition:-moz-transform 0.3s ease-out;-o-transition:-o-transform 0.3s ease-out;transition:transform 0.3s ease-out}.modal.in .modal-dialog{-webkit-transform:translate(0, 0);-ms-transform:translate(0, 0);-o-transform:translate(0, 0);transform:translate(0, 0)}.modal-open .modal{overflow-x:hidden;overflow-y:auto}.modal-dialog{position:relative;width:auto;margin:10px}.modal-content{position:relative;background-color:#fff;border:1px solid #999;border:1px solid rgba(0,0,0,0.2);border-radius:3px;-webkit-box-shadow:0 3px 9px rgba(0,0,0,0.5);box-shadow:0 3px 9px rgba(0,0,0,0.5);background-clip:padding-box;outline:0}.modal-backdrop{position:absolute;top:0;right:0;left:0;background-color:#000}.modal-backdrop.fade{opacity:0;filter:alpha(opacity=0)}.modal-backdrop.in{opacity:.5;filter:alpha(opacity=50)}.modal-header{padding:15px;border-bottom:1px solid #e5e5e5;min-height:16.42857143px}.modal-header .close{margin-top:-2px}.modal-title{margin:0;line-height:1.42857143}.modal-body{position:relative;padding:15px}.modal-footer{padding:15px;text-align:right;border-top:1px solid #e5e5e5}.modal-footer .btn+.btn{margin-left:5px;margin-bottom:0}.modal-footer .btn-group .btn+.btn{margin-left:-1px}.modal-footer .btn-block+.btn-block{margin-left:0}.modal-scrollbar-measure{position:absolute;top:-9999px;width:50px;height:50px;overflow:scroll}@media (min-width:768px){.modal-dialog{width:600px;margin:30px auto}.modal-content{-webkit-box-shadow:0 5px 15px rgba(0,0,0,0.5);box-shadow:0 5px 15px rgba(0,0,0,0.5)}.modal-sm{width:300px}}@media (min-width:992px){.modal-lg{width:900px}}.tooltip{position:absolute;z-index:1070;display:block;visibility:visible;font-family:\"Helvetica Neue\",Helvetica,Arial,sans-serif;font-size:12px;font-weight:normal;line-height:1.4;opacity:0;filter:alpha(opacity=0)}.tooltip.in{opacity:.9;filter:alpha(opacity=90)}.tooltip.top{margin-top:-3px;padding:5px 0}.tooltip.right{margin-left:3px;padding:0 5px}.tooltip.bottom{margin-top:3px;padding:5px 0}.tooltip.left{margin-left:-3px;padding:0 5px}.tooltip-inner{max-width:200px;padding:3px 8px;color:#fff;text-align:center;text-decoration:none;background-color:#000;border-radius:2px}.tooltip-arrow{position:absolute;width:0;height:0;border-color:transparent;border-style:solid}.tooltip.top .tooltip-arrow{bottom:0;left:50%;margin-left:-5px;border-width:5px 5px 0;border-top-color:#000}.tooltip.top-left .tooltip-arrow{bottom:0;right:5px;margin-bottom:-5px;border-width:5px 5px 0;border-top-color:#000}.tooltip.top-right .tooltip-arrow{bottom:0;left:5px;margin-bottom:-5px;border-width:5px 5px 0;border-top-color:#000}.tooltip.right .tooltip-arrow{top:50%;left:0;margin-top:-5px;border-width:5px 5px 5px 0;border-right-color:#000}.tooltip.left .tooltip-arrow{top:50%;right:0;margin-top:-5px;border-width:5px 0 5px 5px;border-left-color:#000}.tooltip.bottom .tooltip-arrow{top:0;left:50%;margin-left:-5px;border-width:0 5px 5px;border-bottom-color:#000}.tooltip.bottom-left .tooltip-arrow{top:0;right:5px;margin-top:-5px;border-width:0 5px 5px;border-bottom-color:#000}.tooltip.bottom-right .tooltip-arrow{top:0;left:5px;margin-top:-5px;border-width:0 5px 5px;border-bottom-color:#000}.popover{position:absolute;top:0;left:0;z-index:1060;display:none;max-width:276px;padding:1px;font-family:\"Helvetica Neue\",Helvetica,Arial,sans-serif;font-size:13px;font-weight:normal;line-height:1.42857143;text-align:left;background-color:#fff;background-clip:padding-box;border:1px solid #ccc;border:1px solid rgba(0,0,0,0.2);border-radius:3px;-webkit-box-shadow:0 5px 10px rgba(0,0,0,0.2);box-shadow:0 5px 10px rgba(0,0,0,0.2);white-space:normal}.popover.top{margin-top:-10px}.popover.right{margin-left:10px}.popover.bottom{margin-top:10px}.popover.left{margin-left:-10px}.popover-title{margin:0;padding:8px 14px;font-size:13px;background-color:#f7f7f7;border-bottom:1px solid #ebebeb;border-radius:2px 2px 0 0}.popover-content{padding:9px 14px}.popover>.arrow,.popover>.arrow:after{position:absolute;display:block;width:0;height:0;border-color:transparent;border-style:solid}.popover>.arrow{border-width:11px}.popover>.arrow:after{border-width:10px;content:\"\"}.popover.top>.arrow{left:50%;margin-left:-11px;border-bottom-width:0;border-top-color:#999;border-top-color:rgba(0,0,0,0.25);bottom:-11px}.popover.top>.arrow:after{content:\" \";bottom:1px;margin-left:-10px;border-bottom-width:0;border-top-color:#fff}.popover.right>.arrow{top:50%;left:-11px;margin-top:-11px;border-left-width:0;border-right-color:#999;border-right-color:rgba(0,0,0,0.25)}.popover.right>.arrow:after{content:\" \";left:1px;bottom:-10px;border-left-width:0;border-right-color:#fff}.popover.bottom>.arrow{left:50%;margin-left:-11px;border-top-width:0;border-bottom-color:#999;border-bottom-color:rgba(0,0,0,0.25);top:-11px}.popover.bottom>.arrow:after{content:\" \";top:1px;margin-left:-10px;border-top-width:0;border-bottom-color:#fff}.popover.left>.arrow{top:50%;right:-11px;margin-top:-11px;border-right-width:0;border-left-color:#999;border-left-color:rgba(0,0,0,0.25)}.popover.left>.arrow:after{content:\" \";right:1px;border-right-width:0;border-left-color:#fff;bottom:-10px}.carousel{position:relative}.carousel-inner{position:relative;overflow:hidden;width:100%}.carousel-inner>.item{display:none;position:relative;-webkit-transition:.6s ease-in-out left;-o-transition:.6s ease-in-out left;transition:.6s ease-in-out left}.carousel-inner>.item>img,.carousel-inner>.item>a>img{line-height:1}@media all and (transform-3d),(-webkit-transform-3d){.carousel-inner>.item{transition:transform .6s ease-in-out;backface-visibility:hidden;perspective:1000}.carousel-inner>.item.next,.carousel-inner>.item.active.right{transform:translate3d(100%, 0, 0);left:0}.carousel-inner>.item.prev,.carousel-inner>.item.active.left{transform:translate3d(-100%, 0, 0);left:0}.carousel-inner>.item.next.left,.carousel-inner>.item.prev.right,.carousel-inner>.item.active{transform:translate3d(0, 0, 0);left:0}}.carousel-inner>.active,.carousel-inner>.next,.carousel-inner>.prev{display:block}.carousel-inner>.active{left:0}.carousel-inner>.next,.carousel-inner>.prev{position:absolute;top:0;width:100%}.carousel-inner>.next{left:100%}.carousel-inner>.prev{left:-100%}.carousel-inner>.next.left,.carousel-inner>.prev.right{left:0}.carousel-inner>.active.left{left:-100%}.carousel-inner>.active.right{left:100%}.carousel-control{position:absolute;top:0;left:0;bottom:0;width:15%;opacity:.5;filter:alpha(opacity=50);font-size:20px;color:#fff;text-align:center;text-shadow:0 1px 2px rgba(0,0,0,0.6)}.carousel-control.left{background-image:-webkit-linear-gradient(left, rgba(0,0,0,0.5) 0, rgba(0,0,0,0.0001) 100%);background-image:-o-linear-gradient(left, rgba(0,0,0,0.5) 0, rgba(0,0,0,0.0001) 100%);background-image:linear-gradient(to right, rgba(0,0,0,0.5) 0, rgba(0,0,0,0.0001) 100%);background-repeat:repeat-x;filter:progid:DXImageTransform.Microsoft.gradient(startColorstr='#80000000', endColorstr='#00000000', GradientType=1)}.carousel-control.right{left:auto;right:0;background-image:-webkit-linear-gradient(left, rgba(0,0,0,0.0001) 0, rgba(0,0,0,0.5) 100%);background-image:-o-linear-gradient(left, rgba(0,0,0,0.0001) 0, rgba(0,0,0,0.5) 100%);background-image:linear-gradient(to right, rgba(0,0,0,0.0001) 0, rgba(0,0,0,0.5) 100%);background-repeat:repeat-x;filter:progid:DXImageTransform.Microsoft.gradient(startColorstr='#00000000', endColorstr='#80000000', GradientType=1)}.carousel-control:hover,.carousel-control:focus{outline:0;color:#fff;text-decoration:none;opacity:.9;filter:alpha(opacity=90)}.carousel-control .icon-prev,.carousel-control .icon-next,.carousel-control .glyphicon-chevron-left,.carousel-control .glyphicon-chevron-right{position:absolute;top:50%;z-index:5;display:inline-block}.carousel-control .icon-prev,.carousel-control .glyphicon-chevron-left{left:50%;margin-left:-10px}.carousel-control .icon-next,.carousel-control .glyphicon-chevron-right{right:50%;margin-right:-10px}.carousel-control .icon-prev,.carousel-control .icon-next{width:20px;height:20px;margin-top:-10px;font-family:serif}.carousel-control .icon-prev:before{content:'\\2039'}.carousel-control .icon-next:before{content:'\\203a'}.carousel-indicators{position:absolute;bottom:10px;left:50%;z-index:15;width:60%;margin-left:-30%;padding-left:0;list-style:none;text-align:center}.carousel-indicators li{display:inline-block;width:10px;height:10px;margin:1px;text-indent:-999px;border:1px solid #fff;border-radius:10px;cursor:pointer;background-color:#000 \\9;background-color:rgba(0,0,0,0)}.carousel-indicators .active{margin:0;width:12px;height:12px;background-color:#fff}.carousel-caption{position:absolute;left:15%;right:15%;bottom:20px;z-index:10;padding-top:20px;padding-bottom:20px;color:#fff;text-align:center;text-shadow:0 1px 2px rgba(0,0,0,0.6)}.carousel-caption .btn{text-shadow:none}@media screen and (min-width:768px){.carousel-control .glyphicon-chevron-left,.carousel-control .glyphicon-chevron-right,.carousel-control .icon-prev,.carousel-control .icon-next{width:30px;height:30px;margin-top:-15px;font-size:30px}.carousel-control .glyphicon-chevron-left,.carousel-control .icon-prev{margin-left:-15px}.carousel-control .glyphicon-chevron-right,.carousel-control .icon-next{margin-right:-15px}.carousel-caption{left:20%;right:20%;padding-bottom:30px}.carousel-indicators{bottom:20px}}.clearfix:before,.clearfix:after,.dl-horizontal dd:before,.dl-horizontal dd:after,.container:before,.container:after,.container-fluid:before,.container-fluid:after,.row:before,.row:after,.form-horizontal .form-group:before,.form-horizontal .form-group:after,.btn-toolbar:before,.btn-toolbar:after,.btn-group-vertical>.btn-group:before,.btn-group-vertical>.btn-group:after,.nav:before,.nav:after,.navbar:before,.navbar:after,.navbar-header:before,.navbar-header:after,.navbar-collapse:before,.navbar-collapse:after,.pager:before,.pager:after,.panel-body:before,.panel-body:after,.modal-footer:before,.modal-footer:after,.item_buttons:before,.item_buttons:after{content:\" \";display:table}.clearfix:after,.dl-horizontal dd:after,.container:after,.container-fluid:after,.row:after,.form-horizontal .form-group:after,.btn-toolbar:after,.btn-group-vertical>.btn-group:after,.nav:after,.navbar:after,.navbar-header:after,.navbar-collapse:after,.pager:after,.panel-body:after,.modal-footer:after,.item_buttons:after{clear:both}.center-block{display:block;margin-left:auto;margin-right:auto}.pull-right{float:right !important}.pull-left{float:left !important}.hide{display:none !important}.show{display:block !important}.invisible{visibility:hidden}.text-hide{font:0/0 a;color:transparent;text-shadow:none;background-color:transparent;border:0}.hidden{display:none !important;visibility:hidden !important}.affix{position:fixed}@-ms-viewport{width:device-width}.visible-xs,.visible-sm,.visible-md,.visible-lg{display:none !important}.visible-xs-block,.visible-xs-inline,.visible-xs-inline-block,.visible-sm-block,.visible-sm-inline,.visible-sm-inline-block,.visible-md-block,.visible-md-inline,.visible-md-inline-block,.visible-lg-block,.visible-lg-inline,.visible-lg-inline-block{display:none !important}@media (max-width:767px){.visible-xs{display:block !important}table.visible-xs{display:table}tr.visible-xs{display:table-row !important}th.visible-xs,td.visible-xs{display:table-cell !important}}@media (max-width:767px){.visible-xs-block{display:block !important}}@media (max-width:767px){.visible-xs-inline{display:inline !important}}@media (max-width:767px){.visible-xs-inline-block{display:inline-block !important}}@media (min-width:768px) and (max-width:991px){.visible-sm{display:block !important}table.visible-sm{display:table}tr.visible-sm{display:table-row !important}th.visible-sm,td.visible-sm{display:table-cell !important}}@media (min-width:768px) and (max-width:991px){.visible-sm-block{display:block !important}}@media (min-width:768px) and (max-width:991px){.visible-sm-inline{display:inline !important}}@media (min-width:768px) and (max-width:991px){.visible-sm-inline-block{display:inline-block !important}}@media (min-width:992px) and (max-width:1199px){.visible-md{display:block !important}table.visible-md{display:table}tr.visible-md{display:table-row !important}th.visible-md,td.visible-md{display:table-cell !important}}@media (min-width:992px) and (max-width:1199px){.visible-md-block{display:block !important}}@media (min-width:992px) and (max-width:1199px){.visible-md-inline{display:inline !important}}@media (min-width:992px) and (max-width:1199px){.visible-md-inline-block{display:inline-block !important}}@media (min-width:1200px){.visible-lg{display:block !important}table.visible-lg{display:table}tr.visible-lg{display:table-row !important}th.visible-lg,td.visible-lg{display:table-cell !important}}@media (min-width:1200px){.visible-lg-block{display:block !important}}@media (min-width:1200px){.visible-lg-inline{display:inline !important}}@media (min-width:1200px){.visible-lg-inline-block{display:inline-block !important}}@media (max-width:767px){.hidden-xs{display:none !important}}@media (min-width:768px) and (max-width:991px){.hidden-sm{display:none !important}}@media (min-width:992px) and (max-width:1199px){.hidden-md{display:none !important}}@media (min-width:1200px){.hidden-lg{display:none !important}}.visible-print{display:none !important}@media print{.visible-print{display:block !important}table.visible-print{display:table}tr.visible-print{display:table-row !important}th.visible-print,td.visible-print{display:table-cell !important}}.visible-print-block{display:none !important}@media print{.visible-print-block{display:block !important}}.visible-print-inline{display:none !important}@media print{.visible-print-inline{display:inline !important}}.visible-print-inline-block{display:none !important}@media print{.visible-print-inline-block{display:inline-block !important}}@media print{.hidden-print{display:none !important}}/*!\n*\n* Font Awesome\n*\n*//*!\n *  Font Awesome 4.3.0 by @davegandy - http://fontawesome.io - @fontawesome\n *  License - http://fontawesome.io/license (Font: SIL OFL 1.1, CSS: MIT License)\n */@font-face{font-family:'FontAwesome';src:url('../components/font-awesome/fonts/fontawesome-webfont.eot?v=4.3.0');src:url('../components/font-awesome/fonts/fontawesome-webfont.eot?#iefix&v=4.3.0') format('embedded-opentype'),url('../components/font-awesome/fonts/fontawesome-webfont.woff2?v=4.3.0') format('woff2'),url('../components/font-awesome/fonts/fontawesome-webfont.woff?v=4.3.0') format('woff'),url('../components/font-awesome/fonts/fontawesome-webfont.ttf?v=4.3.0') format('truetype'),url('../components/font-awesome/fonts/fontawesome-webfont.svg?v=4.3.0#fontawesomeregular') format('svg');font-weight:normal;font-style:normal}.fa{display:inline-block;font:normal normal normal 14px/1 FontAwesome;font-size:inherit;text-rendering:auto;-webkit-font-smoothing:antialiased;-moz-osx-font-smoothing:grayscale;transform:translate(0, 0)}.fa-lg{font-size:1.33333333em;line-height:.75em;vertical-align:-15%}.fa-2x{font-size:2em}.fa-3x{font-size:3em}.fa-4x{font-size:4em}.fa-5x{font-size:5em}.fa-fw{width:1.28571429em;text-align:center}.fa-ul{padding-left:0;margin-left:2.14285714em;list-style-type:none}.fa-ul>li{position:relative}.fa-li{position:absolute;left:-2.14285714em;width:2.14285714em;top:.14285714em;text-align:center}.fa-li.fa-lg{left:-1.85714286em}.fa-border{padding:.2em .25em .15em;border:solid .08em #eee;border-radius:.1em}.pull-right{float:right}.pull-left{float:left}.fa.pull-left{margin-right:.3em}.fa.pull-right{margin-left:.3em}.fa-spin{-webkit-animation:fa-spin 2s infinite linear;animation:fa-spin 2s infinite linear}.fa-pulse{-webkit-animation:fa-spin 1s infinite steps(8);animation:fa-spin 1s infinite steps(8)}@-webkit-keyframes fa-spin{0%{-webkit-transform:rotate(0deg);transform:rotate(0deg)}100%{-webkit-transform:rotate(359deg);transform:rotate(359deg)}}@keyframes fa-spin{0%{-webkit-transform:rotate(0deg);transform:rotate(0deg)}100%{-webkit-transform:rotate(359deg);transform:rotate(359deg)}}.fa-rotate-90{filter:progid:DXImageTransform.Microsoft.BasicImage(rotation=1);-webkit-transform:rotate(90deg);-ms-transform:rotate(90deg);transform:rotate(90deg)}.fa-rotate-180{filter:progid:DXImageTransform.Microsoft.BasicImage(rotation=2);-webkit-transform:rotate(180deg);-ms-transform:rotate(180deg);transform:rotate(180deg)}.fa-rotate-270{filter:progid:DXImageTransform.Microsoft.BasicImage(rotation=3);-webkit-transform:rotate(270deg);-ms-transform:rotate(270deg);transform:rotate(270deg)}.fa-flip-horizontal{filter:progid:DXImageTransform.Microsoft.BasicImage(rotation=0, mirror=1);-webkit-transform:scale(-1, 1);-ms-transform:scale(-1, 1);transform:scale(-1, 1)}.fa-flip-vertical{filter:progid:DXImageTransform.Microsoft.BasicImage(rotation=2, mirror=1);-webkit-transform:scale(1, -1);-ms-transform:scale(1, -1);transform:scale(1, -1)}:root .fa-rotate-90,:root .fa-rotate-180,:root .fa-rotate-270,:root .fa-flip-horizontal,:root .fa-flip-vertical{filter:none}.fa-stack{position:relative;display:inline-block;width:2em;height:2em;line-height:2em;vertical-align:middle}.fa-stack-1x,.fa-stack-2x{position:absolute;left:0;width:100%;text-align:center}.fa-stack-1x{line-height:inherit}.fa-stack-2x{font-size:2em}.fa-inverse{color:#fff}.fa-glass:before{content:\"\\f000\"}.fa-music:before{content:\"\\f001\"}.fa-search:before{content:\"\\f002\"}.fa-envelope-o:before{content:\"\\f003\"}.fa-heart:before{content:\"\\f004\"}.fa-star:before{content:\"\\f005\"}.fa-star-o:before{content:\"\\f006\"}.fa-user:before{content:\"\\f007\"}.fa-film:before{content:\"\\f008\"}.fa-th-large:before{content:\"\\f009\"}.fa-th:before{content:\"\\f00a\"}.fa-th-list:before{content:\"\\f00b\"}.fa-check:before{content:\"\\f00c\"}.fa-remove:before,.fa-close:before,.fa-times:before{content:\"\\f00d\"}.fa-search-plus:before{content:\"\\f00e\"}.fa-search-minus:before{content:\"\\f010\"}.fa-power-off:before{content:\"\\f011\"}.fa-signal:before{content:\"\\f012\"}.fa-gear:before,.fa-cog:before{content:\"\\f013\"}.fa-trash-o:before{content:\"\\f014\"}.fa-home:before{content:\"\\f015\"}.fa-file-o:before{content:\"\\f016\"}.fa-clock-o:before{content:\"\\f017\"}.fa-road:before{content:\"\\f018\"}.fa-download:before{content:\"\\f019\"}.fa-arrow-circle-o-down:before{content:\"\\f01a\"}.fa-arrow-circle-o-up:before{content:\"\\f01b\"}.fa-inbox:before{content:\"\\f01c\"}.fa-play-circle-o:before{content:\"\\f01d\"}.fa-rotate-right:before,.fa-repeat:before{content:\"\\f01e\"}.fa-refresh:before{content:\"\\f021\"}.fa-list-alt:before{content:\"\\f022\"}.fa-lock:before{content:\"\\f023\"}.fa-flag:before{content:\"\\f024\"}.fa-headphones:before{content:\"\\f025\"}.fa-volume-off:before{content:\"\\f026\"}.fa-volume-down:before{content:\"\\f027\"}.fa-volume-up:before{content:\"\\f028\"}.fa-qrcode:before{content:\"\\f029\"}.fa-barcode:before{content:\"\\f02a\"}.fa-tag:before{content:\"\\f02b\"}.fa-tags:before{content:\"\\f02c\"}.fa-book:before{content:\"\\f02d\"}.fa-bookmark:before{content:\"\\f02e\"}.fa-print:before{content:\"\\f02f\"}.fa-camera:before{content:\"\\f030\"}.fa-font:before{content:\"\\f031\"}.fa-bold:before{content:\"\\f032\"}.fa-italic:before{content:\"\\f033\"}.fa-text-height:before{content:\"\\f034\"}.fa-text-width:before{content:\"\\f035\"}.fa-align-left:before{content:\"\\f036\"}.fa-align-center:before{content:\"\\f037\"}.fa-align-right:before{content:\"\\f038\"}.fa-align-justify:before{content:\"\\f039\"}.fa-list:before{content:\"\\f03a\"}.fa-dedent:before,.fa-outdent:before{content:\"\\f03b\"}.fa-indent:before{content:\"\\f03c\"}.fa-video-camera:before{content:\"\\f03d\"}.fa-photo:before,.fa-image:before,.fa-picture-o:before{content:\"\\f03e\"}.fa-pencil:before{content:\"\\f040\"}.fa-map-marker:before{content:\"\\f041\"}.fa-adjust:before{content:\"\\f042\"}.fa-tint:before{content:\"\\f043\"}.fa-edit:before,.fa-pencil-square-o:before{content:\"\\f044\"}.fa-share-square-o:before{content:\"\\f045\"}.fa-check-square-o:before{content:\"\\f046\"}.fa-arrows:before{content:\"\\f047\"}.fa-step-backward:before{content:\"\\f048\"}.fa-fast-backward:before{content:\"\\f049\"}.fa-backward:before{content:\"\\f04a\"}.fa-play:before{content:\"\\f04b\"}.fa-pause:before{content:\"\\f04c\"}.fa-stop:before{content:\"\\f04d\"}.fa-forward:before{content:\"\\f04e\"}.fa-fast-forward:before{content:\"\\f050\"}.fa-step-forward:before{content:\"\\f051\"}.fa-eject:before{content:\"\\f052\"}.fa-chevron-left:before{content:\"\\f053\"}.fa-chevron-right:before{content:\"\\f054\"}.fa-plus-circle:before{content:\"\\f055\"}.fa-minus-circle:before{content:\"\\f056\"}.fa-times-circle:before{content:\"\\f057\"}.fa-check-circle:before{content:\"\\f058\"}.fa-question-circle:before{content:\"\\f059\"}.fa-info-circle:before{content:\"\\f05a\"}.fa-crosshairs:before{content:\"\\f05b\"}.fa-times-circle-o:before{content:\"\\f05c\"}.fa-check-circle-o:before{content:\"\\f05d\"}.fa-ban:before{content:\"\\f05e\"}.fa-arrow-left:before{content:\"\\f060\"}.fa-arrow-right:before{content:\"\\f061\"}.fa-arrow-up:before{content:\"\\f062\"}.fa-arrow-down:before{content:\"\\f063\"}.fa-mail-forward:before,.fa-share:before{content:\"\\f064\"}.fa-expand:before{content:\"\\f065\"}.fa-compress:before{content:\"\\f066\"}.fa-plus:before{content:\"\\f067\"}.fa-minus:before{content:\"\\f068\"}.fa-asterisk:before{content:\"\\f069\"}.fa-exclamation-circle:before{content:\"\\f06a\"}.fa-gift:before{content:\"\\f06b\"}.fa-leaf:before{content:\"\\f06c\"}.fa-fire:before{content:\"\\f06d\"}.fa-eye:before{content:\"\\f06e\"}.fa-eye-slash:before{content:\"\\f070\"}.fa-warning:before,.fa-exclamation-triangle:before{content:\"\\f071\"}.fa-plane:before{content:\"\\f072\"}.fa-calendar:before{content:\"\\f073\"}.fa-random:before{content:\"\\f074\"}.fa-comment:before{content:\"\\f075\"}.fa-magnet:before{content:\"\\f076\"}.fa-chevron-up:before{content:\"\\f077\"}.fa-chevron-down:before{content:\"\\f078\"}.fa-retweet:before{content:\"\\f079\"}.fa-shopping-cart:before{content:\"\\f07a\"}.fa-folder:before{content:\"\\f07b\"}.fa-folder-open:before{content:\"\\f07c\"}.fa-arrows-v:before{content:\"\\f07d\"}.fa-arrows-h:before{content:\"\\f07e\"}.fa-bar-chart-o:before,.fa-bar-chart:before{content:\"\\f080\"}.fa-twitter-square:before{content:\"\\f081\"}.fa-facebook-square:before{content:\"\\f082\"}.fa-camera-retro:before{content:\"\\f083\"}.fa-key:before{content:\"\\f084\"}.fa-gears:before,.fa-cogs:before{content:\"\\f085\"}.fa-comments:before{content:\"\\f086\"}.fa-thumbs-o-up:before{content:\"\\f087\"}.fa-thumbs-o-down:before{content:\"\\f088\"}.fa-star-half:before{content:\"\\f089\"}.fa-heart-o:before{content:\"\\f08a\"}.fa-sign-out:before{content:\"\\f08b\"}.fa-linkedin-square:before{content:\"\\f08c\"}.fa-thumb-tack:before{content:\"\\f08d\"}.fa-external-link:before{content:\"\\f08e\"}.fa-sign-in:before{content:\"\\f090\"}.fa-trophy:before{content:\"\\f091\"}.fa-github-square:before{content:\"\\f092\"}.fa-upload:before{content:\"\\f093\"}.fa-lemon-o:before{content:\"\\f094\"}.fa-phone:before{content:\"\\f095\"}.fa-square-o:before{content:\"\\f096\"}.fa-bookmark-o:before{content:\"\\f097\"}.fa-phone-square:before{content:\"\\f098\"}.fa-twitter:before{content:\"\\f099\"}.fa-facebook-f:before,.fa-facebook:before{content:\"\\f09a\"}.fa-github:before{content:\"\\f09b\"}.fa-unlock:before{content:\"\\f09c\"}.fa-credit-card:before{content:\"\\f09d\"}.fa-rss:before{content:\"\\f09e\"}.fa-hdd-o:before{content:\"\\f0a0\"}.fa-bullhorn:before{content:\"\\f0a1\"}.fa-bell:before{content:\"\\f0f3\"}.fa-certificate:before{content:\"\\f0a3\"}.fa-hand-o-right:before{content:\"\\f0a4\"}.fa-hand-o-left:before{content:\"\\f0a5\"}.fa-hand-o-up:before{content:\"\\f0a6\"}.fa-hand-o-down:before{content:\"\\f0a7\"}.fa-arrow-circle-left:before{content:\"\\f0a8\"}.fa-arrow-circle-right:before{content:\"\\f0a9\"}.fa-arrow-circle-up:before{content:\"\\f0aa\"}.fa-arrow-circle-down:before{content:\"\\f0ab\"}.fa-globe:before{content:\"\\f0ac\"}.fa-wrench:before{content:\"\\f0ad\"}.fa-tasks:before{content:\"\\f0ae\"}.fa-filter:before{content:\"\\f0b0\"}.fa-briefcase:before{content:\"\\f0b1\"}.fa-arrows-alt:before{content:\"\\f0b2\"}.fa-group:before,.fa-users:before{content:\"\\f0c0\"}.fa-chain:before,.fa-link:before{content:\"\\f0c1\"}.fa-cloud:before{content:\"\\f0c2\"}.fa-flask:before{content:\"\\f0c3\"}.fa-cut:before,.fa-scissors:before{content:\"\\f0c4\"}.fa-copy:before,.fa-files-o:before{content:\"\\f0c5\"}.fa-paperclip:before{content:\"\\f0c6\"}.fa-save:before,.fa-floppy-o:before{content:\"\\f0c7\"}.fa-square:before{content:\"\\f0c8\"}.fa-navicon:before,.fa-reorder:before,.fa-bars:before{content:\"\\f0c9\"}.fa-list-ul:before{content:\"\\f0ca\"}.fa-list-ol:before{content:\"\\f0cb\"}.fa-strikethrough:before{content:\"\\f0cc\"}.fa-underline:before{content:\"\\f0cd\"}.fa-table:before{content:\"\\f0ce\"}.fa-magic:before{content:\"\\f0d0\"}.fa-truck:before{content:\"\\f0d1\"}.fa-pinterest:before{content:\"\\f0d2\"}.fa-pinterest-square:before{content:\"\\f0d3\"}.fa-google-plus-square:before{content:\"\\f0d4\"}.fa-google-plus:before{content:\"\\f0d5\"}.fa-money:before{content:\"\\f0d6\"}.fa-caret-down:before{content:\"\\f0d7\"}.fa-caret-up:before{content:\"\\f0d8\"}.fa-caret-left:before{content:\"\\f0d9\"}.fa-caret-right:before{content:\"\\f0da\"}.fa-columns:before{content:\"\\f0db\"}.fa-unsorted:before,.fa-sort:before{content:\"\\f0dc\"}.fa-sort-down:before,.fa-sort-desc:before{content:\"\\f0dd\"}.fa-sort-up:before,.fa-sort-asc:before{content:\"\\f0de\"}.fa-envelope:before{content:\"\\f0e0\"}.fa-linkedin:before{content:\"\\f0e1\"}.fa-rotate-left:before,.fa-undo:before{content:\"\\f0e2\"}.fa-legal:before,.fa-gavel:before{content:\"\\f0e3\"}.fa-dashboard:before,.fa-tachometer:before{content:\"\\f0e4\"}.fa-comment-o:before{content:\"\\f0e5\"}.fa-comments-o:before{content:\"\\f0e6\"}.fa-flash:before,.fa-bolt:before{content:\"\\f0e7\"}.fa-sitemap:before{content:\"\\f0e8\"}.fa-umbrella:before{content:\"\\f0e9\"}.fa-paste:before,.fa-clipboard:before{content:\"\\f0ea\"}.fa-lightbulb-o:before{content:\"\\f0eb\"}.fa-exchange:before{content:\"\\f0ec\"}.fa-cloud-download:before{content:\"\\f0ed\"}.fa-cloud-upload:before{content:\"\\f0ee\"}.fa-user-md:before{content:\"\\f0f0\"}.fa-stethoscope:before{content:\"\\f0f1\"}.fa-suitcase:before{content:\"\\f0f2\"}.fa-bell-o:before{content:\"\\f0a2\"}.fa-coffee:before{content:\"\\f0f4\"}.fa-cutlery:before{content:\"\\f0f5\"}.fa-file-text-o:before{content:\"\\f0f6\"}.fa-building-o:before{content:\"\\f0f7\"}.fa-hospital-o:before{content:\"\\f0f8\"}.fa-ambulance:before{content:\"\\f0f9\"}.fa-medkit:before{content:\"\\f0fa\"}.fa-fighter-jet:before{content:\"\\f0fb\"}.fa-beer:before{content:\"\\f0fc\"}.fa-h-square:before{content:\"\\f0fd\"}.fa-plus-square:before{content:\"\\f0fe\"}.fa-angle-double-left:before{content:\"\\f100\"}.fa-angle-double-right:before{content:\"\\f101\"}.fa-angle-double-up:before{content:\"\\f102\"}.fa-angle-double-down:before{content:\"\\f103\"}.fa-angle-left:before{content:\"\\f104\"}.fa-angle-right:before{content:\"\\f105\"}.fa-angle-up:before{content:\"\\f106\"}.fa-angle-down:before{content:\"\\f107\"}.fa-desktop:before{content:\"\\f108\"}.fa-laptop:before{content:\"\\f109\"}.fa-tablet:before{content:\"\\f10a\"}.fa-mobile-phone:before,.fa-mobile:before{content:\"\\f10b\"}.fa-circle-o:before{content:\"\\f10c\"}.fa-quote-left:before{content:\"\\f10d\"}.fa-quote-right:before{content:\"\\f10e\"}.fa-spinner:before{content:\"\\f110\"}.fa-circle:before{content:\"\\f111\"}.fa-mail-reply:before,.fa-reply:before{content:\"\\f112\"}.fa-github-alt:before{content:\"\\f113\"}.fa-folder-o:before{content:\"\\f114\"}.fa-folder-open-o:before{content:\"\\f115\"}.fa-smile-o:before{content:\"\\f118\"}.fa-frown-o:before{content:\"\\f119\"}.fa-meh-o:before{content:\"\\f11a\"}.fa-gamepad:before{content:\"\\f11b\"}.fa-keyboard-o:before{content:\"\\f11c\"}.fa-flag-o:before{content:\"\\f11d\"}.fa-flag-checkered:before{content:\"\\f11e\"}.fa-terminal:before{content:\"\\f120\"}.fa-code:before{content:\"\\f121\"}.fa-mail-reply-all:before,.fa-reply-all:before{content:\"\\f122\"}.fa-star-half-empty:before,.fa-star-half-full:before,.fa-star-half-o:before{content:\"\\f123\"}.fa-location-arrow:before{content:\"\\f124\"}.fa-crop:before{content:\"\\f125\"}.fa-code-fork:before{content:\"\\f126\"}.fa-unlink:before,.fa-chain-broken:before{content:\"\\f127\"}.fa-question:before{content:\"\\f128\"}.fa-info:before{content:\"\\f129\"}.fa-exclamation:before{content:\"\\f12a\"}.fa-superscript:before{content:\"\\f12b\"}.fa-subscript:before{content:\"\\f12c\"}.fa-eraser:before{content:\"\\f12d\"}.fa-puzzle-piece:before{content:\"\\f12e\"}.fa-microphone:before{content:\"\\f130\"}.fa-microphone-slash:before{content:\"\\f131\"}.fa-shield:before{content:\"\\f132\"}.fa-calendar-o:before{content:\"\\f133\"}.fa-fire-extinguisher:before{content:\"\\f134\"}.fa-rocket:before{content:\"\\f135\"}.fa-maxcdn:before{content:\"\\f136\"}.fa-chevron-circle-left:before{content:\"\\f137\"}.fa-chevron-circle-right:before{content:\"\\f138\"}.fa-chevron-circle-up:before{content:\"\\f139\"}.fa-chevron-circle-down:before{content:\"\\f13a\"}.fa-html5:before{content:\"\\f13b\"}.fa-css3:before{content:\"\\f13c\"}.fa-anchor:before{content:\"\\f13d\"}.fa-unlock-alt:before{content:\"\\f13e\"}.fa-bullseye:before{content:\"\\f140\"}.fa-ellipsis-h:before{content:\"\\f141\"}.fa-ellipsis-v:before{content:\"\\f142\"}.fa-rss-square:before{content:\"\\f143\"}.fa-play-circle:before{content:\"\\f144\"}.fa-ticket:before{content:\"\\f145\"}.fa-minus-square:before{content:\"\\f146\"}.fa-minus-square-o:before{content:\"\\f147\"}.fa-level-up:before{content:\"\\f148\"}.fa-level-down:before{content:\"\\f149\"}.fa-check-square:before{content:\"\\f14a\"}.fa-pencil-square:before{content:\"\\f14b\"}.fa-external-link-square:before{content:\"\\f14c\"}.fa-share-square:before{content:\"\\f14d\"}.fa-compass:before{content:\"\\f14e\"}.fa-toggle-down:before,.fa-caret-square-o-down:before{content:\"\\f150\"}.fa-toggle-up:before,.fa-caret-square-o-up:before{content:\"\\f151\"}.fa-toggle-right:before,.fa-caret-square-o-right:before{content:\"\\f152\"}.fa-euro:before,.fa-eur:before{content:\"\\f153\"}.fa-gbp:before{content:\"\\f154\"}.fa-dollar:before,.fa-usd:before{content:\"\\f155\"}.fa-rupee:before,.fa-inr:before{content:\"\\f156\"}.fa-cny:before,.fa-rmb:before,.fa-yen:before,.fa-jpy:before{content:\"\\f157\"}.fa-ruble:before,.fa-rouble:before,.fa-rub:before{content:\"\\f158\"}.fa-won:before,.fa-krw:before{content:\"\\f159\"}.fa-bitcoin:before,.fa-btc:before{content:\"\\f15a\"}.fa-file:before{content:\"\\f15b\"}.fa-file-text:before{content:\"\\f15c\"}.fa-sort-alpha-asc:before{content:\"\\f15d\"}.fa-sort-alpha-desc:before{content:\"\\f15e\"}.fa-sort-amount-asc:before{content:\"\\f160\"}.fa-sort-amount-desc:before{content:\"\\f161\"}.fa-sort-numeric-asc:before{content:\"\\f162\"}.fa-sort-numeric-desc:before{content:\"\\f163\"}.fa-thumbs-up:before{content:\"\\f164\"}.fa-thumbs-down:before{content:\"\\f165\"}.fa-youtube-square:before{content:\"\\f166\"}.fa-youtube:before{content:\"\\f167\"}.fa-xing:before{content:\"\\f168\"}.fa-xing-square:before{content:\"\\f169\"}.fa-youtube-play:before{content:\"\\f16a\"}.fa-dropbox:before{content:\"\\f16b\"}.fa-stack-overflow:before{content:\"\\f16c\"}.fa-instagram:before{content:\"\\f16d\"}.fa-flickr:before{content:\"\\f16e\"}.fa-adn:before{content:\"\\f170\"}.fa-bitbucket:before{content:\"\\f171\"}.fa-bitbucket-square:before{content:\"\\f172\"}.fa-tumblr:before{content:\"\\f173\"}.fa-tumblr-square:before{content:\"\\f174\"}.fa-long-arrow-down:before{content:\"\\f175\"}.fa-long-arrow-up:before{content:\"\\f176\"}.fa-long-arrow-left:before{content:\"\\f177\"}.fa-long-arrow-right:before{content:\"\\f178\"}.fa-apple:before{content:\"\\f179\"}.fa-windows:before{content:\"\\f17a\"}.fa-android:before{content:\"\\f17b\"}.fa-linux:before{content:\"\\f17c\"}.fa-dribbble:before{content:\"\\f17d\"}.fa-skype:before{content:\"\\f17e\"}.fa-foursquare:before{content:\"\\f180\"}.fa-trello:before{content:\"\\f181\"}.fa-female:before{content:\"\\f182\"}.fa-male:before{content:\"\\f183\"}.fa-gittip:before,.fa-gratipay:before{content:\"\\f184\"}.fa-sun-o:before{content:\"\\f185\"}.fa-moon-o:before{content:\"\\f186\"}.fa-archive:before{content:\"\\f187\"}.fa-bug:before{content:\"\\f188\"}.fa-vk:before{content:\"\\f189\"}.fa-weibo:before{content:\"\\f18a\"}.fa-renren:before{content:\"\\f18b\"}.fa-pagelines:before{content:\"\\f18c\"}.fa-stack-exchange:before{content:\"\\f18d\"}.fa-arrow-circle-o-right:before{content:\"\\f18e\"}.fa-arrow-circle-o-left:before{content:\"\\f190\"}.fa-toggle-left:before,.fa-caret-square-o-left:before{content:\"\\f191\"}.fa-dot-circle-o:before{content:\"\\f192\"}.fa-wheelchair:before{content:\"\\f193\"}.fa-vimeo-square:before{content:\"\\f194\"}.fa-turkish-lira:before,.fa-try:before{content:\"\\f195\"}.fa-plus-square-o:before{content:\"\\f196\"}.fa-space-shuttle:before{content:\"\\f197\"}.fa-slack:before{content:\"\\f198\"}.fa-envelope-square:before{content:\"\\f199\"}.fa-wordpress:before{content:\"\\f19a\"}.fa-openid:before{content:\"\\f19b\"}.fa-institution:before,.fa-bank:before,.fa-university:before{content:\"\\f19c\"}.fa-mortar-board:before,.fa-graduation-cap:before{content:\"\\f19d\"}.fa-yahoo:before{content:\"\\f19e\"}.fa-google:before{content:\"\\f1a0\"}.fa-reddit:before{content:\"\\f1a1\"}.fa-reddit-square:before{content:\"\\f1a2\"}.fa-stumbleupon-circle:before{content:\"\\f1a3\"}.fa-stumbleupon:before{content:\"\\f1a4\"}.fa-delicious:before{content:\"\\f1a5\"}.fa-digg:before{content:\"\\f1a6\"}.fa-pied-piper:before{content:\"\\f1a7\"}.fa-pied-piper-alt:before{content:\"\\f1a8\"}.fa-drupal:before{content:\"\\f1a9\"}.fa-joomla:before{content:\"\\f1aa\"}.fa-language:before{content:\"\\f1ab\"}.fa-fax:before{content:\"\\f1ac\"}.fa-building:before{content:\"\\f1ad\"}.fa-child:before{content:\"\\f1ae\"}.fa-paw:before{content:\"\\f1b0\"}.fa-spoon:before{content:\"\\f1b1\"}.fa-cube:before{content:\"\\f1b2\"}.fa-cubes:before{content:\"\\f1b3\"}.fa-behance:before{content:\"\\f1b4\"}.fa-behance-square:before{content:\"\\f1b5\"}.fa-steam:before{content:\"\\f1b6\"}.fa-steam-square:before{content:\"\\f1b7\"}.fa-recycle:before{content:\"\\f1b8\"}.fa-automobile:before,.fa-car:before{content:\"\\f1b9\"}.fa-cab:before,.fa-taxi:before{content:\"\\f1ba\"}.fa-tree:before{content:\"\\f1bb\"}.fa-spotify:before{content:\"\\f1bc\"}.fa-deviantart:before{content:\"\\f1bd\"}.fa-soundcloud:before{content:\"\\f1be\"}.fa-database:before{content:\"\\f1c0\"}.fa-file-pdf-o:before{content:\"\\f1c1\"}.fa-file-word-o:before{content:\"\\f1c2\"}.fa-file-excel-o:before{content:\"\\f1c3\"}.fa-file-powerpoint-o:before{content:\"\\f1c4\"}.fa-file-photo-o:before,.fa-file-picture-o:before,.fa-file-image-o:before{content:\"\\f1c5\"}.fa-file-zip-o:before,.fa-file-archive-o:before{content:\"\\f1c6\"}.fa-file-sound-o:before,.fa-file-audio-o:before{content:\"\\f1c7\"}.fa-file-movie-o:before,.fa-file-video-o:before{content:\"\\f1c8\"}.fa-file-code-o:before{content:\"\\f1c9\"}.fa-vine:before{content:\"\\f1ca\"}.fa-codepen:before{content:\"\\f1cb\"}.fa-jsfiddle:before{content:\"\\f1cc\"}.fa-life-bouy:before,.fa-life-buoy:before,.fa-life-saver:before,.fa-support:before,.fa-life-ring:before{content:\"\\f1cd\"}.fa-circle-o-notch:before{content:\"\\f1ce\"}.fa-ra:before,.fa-rebel:before{content:\"\\f1d0\"}.fa-ge:before,.fa-empire:before{content:\"\\f1d1\"}.fa-git-square:before{content:\"\\f1d2\"}.fa-git:before{content:\"\\f1d3\"}.fa-hacker-news:before{content:\"\\f1d4\"}.fa-tencent-weibo:before{content:\"\\f1d5\"}.fa-qq:before{content:\"\\f1d6\"}.fa-wechat:before,.fa-weixin:before{content:\"\\f1d7\"}.fa-send:before,.fa-paper-plane:before{content:\"\\f1d8\"}.fa-send-o:before,.fa-paper-plane-o:before{content:\"\\f1d9\"}.fa-history:before{content:\"\\f1da\"}.fa-genderless:before,.fa-circle-thin:before{content:\"\\f1db\"}.fa-header:before{content:\"\\f1dc\"}.fa-paragraph:before{content:\"\\f1dd\"}.fa-sliders:before{content:\"\\f1de\"}.fa-share-alt:before{content:\"\\f1e0\"}.fa-share-alt-square:before{content:\"\\f1e1\"}.fa-bomb:before{content:\"\\f1e2\"}.fa-soccer-ball-o:before,.fa-futbol-o:before{content:\"\\f1e3\"}.fa-tty:before{content:\"\\f1e4\"}.fa-binoculars:before{content:\"\\f1e5\"}.fa-plug:before{content:\"\\f1e6\"}.fa-slideshare:before{content:\"\\f1e7\"}.fa-twitch:before{content:\"\\f1e8\"}.fa-yelp:before{content:\"\\f1e9\"}.fa-newspaper-o:before{content:\"\\f1ea\"}.fa-wifi:before{content:\"\\f1eb\"}.fa-calculator:before{content:\"\\f1ec\"}.fa-paypal:before{content:\"\\f1ed\"}.fa-google-wallet:before{content:\"\\f1ee\"}.fa-cc-visa:before{content:\"\\f1f0\"}.fa-cc-mastercard:before{content:\"\\f1f1\"}.fa-cc-discover:before{content:\"\\f1f2\"}.fa-cc-amex:before{content:\"\\f1f3\"}.fa-cc-paypal:before{content:\"\\f1f4\"}.fa-cc-stripe:before{content:\"\\f1f5\"}.fa-bell-slash:before{content:\"\\f1f6\"}.fa-bell-slash-o:before{content:\"\\f1f7\"}.fa-trash:before{content:\"\\f1f8\"}.fa-copyright:before{content:\"\\f1f9\"}.fa-at:before{content:\"\\f1fa\"}.fa-eyedropper:before{content:\"\\f1fb\"}.fa-paint-brush:before{content:\"\\f1fc\"}.fa-birthday-cake:before{content:\"\\f1fd\"}.fa-area-chart:before{content:\"\\f1fe\"}.fa-pie-chart:before{content:\"\\f200\"}.fa-line-chart:before{content:\"\\f201\"}.fa-lastfm:before{content:\"\\f202\"}.fa-lastfm-square:before{content:\"\\f203\"}.fa-toggle-off:before{content:\"\\f204\"}.fa-toggle-on:before{content:\"\\f205\"}.fa-bicycle:before{content:\"\\f206\"}.fa-bus:before{content:\"\\f207\"}.fa-ioxhost:before{content:\"\\f208\"}.fa-angellist:before{content:\"\\f209\"}.fa-cc:before{content:\"\\f20a\"}.fa-shekel:before,.fa-sheqel:before,.fa-ils:before{content:\"\\f20b\"}.fa-meanpath:before{content:\"\\f20c\"}.fa-buysellads:before{content:\"\\f20d\"}.fa-connectdevelop:before{content:\"\\f20e\"}.fa-dashcube:before{content:\"\\f210\"}.fa-forumbee:before{content:\"\\f211\"}.fa-leanpub:before{content:\"\\f212\"}.fa-sellsy:before{content:\"\\f213\"}.fa-shirtsinbulk:before{content:\"\\f214\"}.fa-simplybuilt:before{content:\"\\f215\"}.fa-skyatlas:before{content:\"\\f216\"}.fa-cart-plus:before{content:\"\\f217\"}.fa-cart-arrow-down:before{content:\"\\f218\"}.fa-diamond:before{content:\"\\f219\"}.fa-ship:before{content:\"\\f21a\"}.fa-user-secret:before{content:\"\\f21b\"}.fa-motorcycle:before{content:\"\\f21c\"}.fa-street-view:before{content:\"\\f21d\"}.fa-heartbeat:before{content:\"\\f21e\"}.fa-venus:before{content:\"\\f221\"}.fa-mars:before{content:\"\\f222\"}.fa-mercury:before{content:\"\\f223\"}.fa-transgender:before{content:\"\\f224\"}.fa-transgender-alt:before{content:\"\\f225\"}.fa-venus-double:before{content:\"\\f226\"}.fa-mars-double:before{content:\"\\f227\"}.fa-venus-mars:before{content:\"\\f228\"}.fa-mars-stroke:before{content:\"\\f229\"}.fa-mars-stroke-v:before{content:\"\\f22a\"}.fa-mars-stroke-h:before{content:\"\\f22b\"}.fa-neuter:before{content:\"\\f22c\"}.fa-facebook-official:before{content:\"\\f230\"}.fa-pinterest-p:before{content:\"\\f231\"}.fa-whatsapp:before{content:\"\\f232\"}.fa-server:before{content:\"\\f233\"}.fa-user-plus:before{content:\"\\f234\"}.fa-user-times:before{content:\"\\f235\"}.fa-hotel:before,.fa-bed:before{content:\"\\f236\"}.fa-viacoin:before{content:\"\\f237\"}.fa-train:before{content:\"\\f238\"}.fa-subway:before{content:\"\\f239\"}.fa-medium:before{content:\"\\f23a\"}/*!\n*\n* IPython base\n*\n*/.modal.fade .modal-dialog{-webkit-transform:translate(0, 0);-ms-transform:translate(0, 0);-o-transform:translate(0, 0);transform:translate(0, 0)}code{color:#000}pre{font-size:inherit;line-height:inherit}label{font-weight:normal}.border-box-sizing{box-sizing:border-box;-moz-box-sizing:border-box;-webkit-box-sizing:border-box}.corner-all{border-radius:2px}.no-padding{padding:0}.hbox{display:-webkit-box;-webkit-box-orient:horizontal;-webkit-box-align:stretch;display:-moz-box;-moz-box-orient:horizontal;-moz-box-align:stretch;display:box;box-orient:horizontal;box-align:stretch;display:flex;flex-direction:row;align-items:stretch}.hbox>*{-webkit-box-flex:0;-moz-box-flex:0;box-flex:0;flex:none}.vbox{display:-webkit-box;-webkit-box-orient:vertical;-webkit-box-align:stretch;display:-moz-box;-moz-box-orient:vertical;-moz-box-align:stretch;display:box;box-orient:vertical;box-align:stretch;display:flex;flex-direction:column;align-items:stretch}.vbox>*{-webkit-box-flex:0;-moz-box-flex:0;box-flex:0;flex:none}.hbox.reverse,.vbox.reverse,.reverse{-webkit-box-direction:reverse;-moz-box-direction:reverse;box-direction:reverse;flex-direction:row-reverse}.hbox.box-flex0,.vbox.box-flex0,.box-flex0{-webkit-box-flex:0;-moz-box-flex:0;box-flex:0;flex:none;width:auto}.hbox.box-flex1,.vbox.box-flex1,.box-flex1{-webkit-box-flex:1;-moz-box-flex:1;box-flex:1;flex:1}.hbox.box-flex,.vbox.box-flex,.box-flex{-webkit-box-flex:1;-moz-box-flex:1;box-flex:1;flex:1}.hbox.box-flex2,.vbox.box-flex2,.box-flex2{-webkit-box-flex:2;-moz-box-flex:2;box-flex:2;flex:2}.box-group1{-webkit-box-flex-group:1;-moz-box-flex-group:1;box-flex-group:1}.box-group2{-webkit-box-flex-group:2;-moz-box-flex-group:2;box-flex-group:2}.hbox.start,.vbox.start,.start{-webkit-box-pack:start;-moz-box-pack:start;box-pack:start;justify-content:flex-start}.hbox.end,.vbox.end,.end{-webkit-box-pack:end;-moz-box-pack:end;box-pack:end;justify-content:flex-end}.hbox.center,.vbox.center,.center{-webkit-box-pack:center;-moz-box-pack:center;box-pack:center;justify-content:center}.hbox.baseline,.vbox.baseline,.baseline{-webkit-box-pack:baseline;-moz-box-pack:baseline;box-pack:baseline;justify-content:baseline}.hbox.stretch,.vbox.stretch,.stretch{-webkit-box-pack:stretch;-moz-box-pack:stretch;box-pack:stretch;justify-content:stretch}.hbox.align-start,.vbox.align-start,.align-start{-webkit-box-align:start;-moz-box-align:start;box-align:start;align-items:flex-start}.hbox.align-end,.vbox.align-end,.align-end{-webkit-box-align:end;-moz-box-align:end;box-align:end;align-items:flex-end}.hbox.align-center,.vbox.align-center,.align-center{-webkit-box-align:center;-moz-box-align:center;box-align:center;align-items:center}.hbox.align-baseline,.vbox.align-baseline,.align-baseline{-webkit-box-align:baseline;-moz-box-align:baseline;box-align:baseline;align-items:baseline}.hbox.align-stretch,.vbox.align-stretch,.align-stretch{-webkit-box-align:stretch;-moz-box-align:stretch;box-align:stretch;align-items:stretch}div.error{margin:2em;text-align:center}div.error>h1{font-size:500%;line-height:normal}div.error>p{font-size:200%;line-height:normal}div.traceback-wrapper{text-align:left;max-width:800px;margin:auto}body{background-color:#fff;position:absolute;left:0;right:0;top:0;bottom:0;overflow:visible}#header{display:none;background-color:#fff;position:relative;z-index:100}#header #header-container{padding-bottom:5px;padding-top:5px;box-sizing:border-box;-moz-box-sizing:border-box;-webkit-box-sizing:border-box}#header .header-bar{width:100%;height:1px;background:#e7e7e7;margin-bottom:-1px}@media print{#header{display:none !important}}#header-spacer{width:100%;visibility:hidden}@media print{#header-spacer{display:none}}#ipython_notebook{padding-left:0;padding-top:1px;padding-bottom:1px}@media (max-width:991px){#ipython_notebook{margin-left:10px}}#noscript{width:auto;padding-top:16px;padding-bottom:16px;text-align:center;font-size:22px;color:red;font-weight:bold}#ipython_notebook img{height:28px}#site{width:100%;display:none;box-sizing:border-box;-moz-box-sizing:border-box;-webkit-box-sizing:border-box;overflow:auto}@media print{#site{height:auto !important}}.ui-button .ui-button-text{padding:.2em .8em;font-size:77%}input.ui-button{padding:.3em .9em}span#login_widget{float:right}span#login_widget>.button,#logout{color:#333;background-color:#fff;border-color:#ccc}span#login_widget>.button:hover,#logout:hover,span#login_widget>.button:focus,#logout:focus,span#login_widget>.button.focus,#logout.focus,span#login_widget>.button:active,#logout:active,span#login_widget>.button.active,#logout.active,.open>.dropdown-togglespan#login_widget>.button,.open>.dropdown-toggle#logout{color:#333;background-color:#e6e6e6;border-color:#adadad}span#login_widget>.button:active,#logout:active,span#login_widget>.button.active,#logout.active,.open>.dropdown-togglespan#login_widget>.button,.open>.dropdown-toggle#logout{background-image:none}span#login_widget>.button.disabled,#logout.disabled,span#login_widget>.button[disabled],#logout[disabled],fieldset[disabled] span#login_widget>.button,fieldset[disabled] #logout,span#login_widget>.button.disabled:hover,#logout.disabled:hover,span#login_widget>.button[disabled]:hover,#logout[disabled]:hover,fieldset[disabled] span#login_widget>.button:hover,fieldset[disabled] #logout:hover,span#login_widget>.button.disabled:focus,#logout.disabled:focus,span#login_widget>.button[disabled]:focus,#logout[disabled]:focus,fieldset[disabled] span#login_widget>.button:focus,fieldset[disabled] #logout:focus,span#login_widget>.button.disabled.focus,#logout.disabled.focus,span#login_widget>.button[disabled].focus,#logout[disabled].focus,fieldset[disabled] span#login_widget>.button.focus,fieldset[disabled] #logout.focus,span#login_widget>.button.disabled:active,#logout.disabled:active,span#login_widget>.button[disabled]:active,#logout[disabled]:active,fieldset[disabled] span#login_widget>.button:active,fieldset[disabled] #logout:active,span#login_widget>.button.disabled.active,#logout.disabled.active,span#login_widget>.button[disabled].active,#logout[disabled].active,fieldset[disabled] span#login_widget>.button.active,fieldset[disabled] #logout.active{background-color:#fff;border-color:#ccc}span#login_widget>.button .badge,#logout .badge{color:#fff;background-color:#333}.nav-header{text-transform:none}#header>span{margin-top:10px}.modal_stretch .modal-dialog{display:-webkit-box;-webkit-box-orient:vertical;-webkit-box-align:stretch;display:-moz-box;-moz-box-orient:vertical;-moz-box-align:stretch;display:box;box-orient:vertical;box-align:stretch;display:flex;flex-direction:column;align-items:stretch;min-height:80vh}.modal_stretch .modal-dialog .modal-body{max-height:calc(100vh - 200px);overflow:auto;flex:1}@media (min-width:768px){.modal .modal-dialog{width:700px}}@media (min-width:768px){select.form-control{margin-left:12px;margin-right:12px}}/*!\n*\n* IPython auth\n*\n*/.center-nav{display:inline-block;margin-bottom:-4px}/*!\n*\n* IPython tree view\n*\n*/.alternate_upload{background-color:none;display:inline}.alternate_upload.form{padding:0;margin:0}.alternate_upload input.fileinput{display:inline;opacity:0;z-index:2;width:12ex;margin-right:-12ex}.alternate_upload .btn-upload{height:22px}ul#tabs{margin-bottom:4px}ul#tabs a{padding-top:6px;padding-bottom:4px}ul.breadcrumb a:focus,ul.breadcrumb a:hover{text-decoration:none}ul.breadcrumb i.icon-home{font-size:16px;margin-right:4px}ul.breadcrumb span{color:#5e5e5e}.list_toolbar{padding:4px 0 4px 0;vertical-align:middle}.list_toolbar .tree-buttons{padding-top:1px}.dynamic-buttons{padding-top:3px;display:inline-block}.list_toolbar [class*=\"span\"]{min-height:24px}.list_header{font-weight:bold;background-color:#eee}.list_placeholder{font-weight:bold;padding-top:4px;padding-bottom:4px;padding-left:7px;padding-right:7px}.list_container{margin-top:4px;margin-bottom:20px;border:1px solid #ddd;border-radius:2px}.list_container>div{border-bottom:1px solid #ddd}.list_container>div:hover .list-item{background-color:red}.list_container>div:last-child{border:none}.list_item:hover .list_item{background-color:#ddd}.list_item a{text-decoration:none}.list_item:hover{background-color:#fafafa}.action_col{text-align:right}.list_header>div,.list_item>div{padding-top:4px;padding-bottom:4px;padding-left:7px;padding-right:7px;line-height:22px}.list_header>div input,.list_item>div input{margin-right:7px;margin-left:14px;vertical-align:baseline;line-height:22px;position:relative;top:-1px}.list_header>div .item_link,.list_item>div .item_link{margin-left:-1px;vertical-align:baseline;line-height:22px}.new-file input[type=checkbox]{visibility:hidden}.item_name{line-height:22px;height:24px}.item_icon{font-size:14px;color:#5e5e5e;margin-right:7px;margin-left:7px;line-height:22px;vertical-align:baseline}.item_buttons{line-height:1em;margin-left:-5px}.item_buttons .btn-group,.item_buttons .input-group{float:left}.item_buttons>.btn,.item_buttons>.btn-group,.item_buttons>.input-group{margin-left:5px}.item_buttons .btn{min-width:13ex}.item_buttons .running-indicator{padding-top:4px;color:#5cb85c}.toolbar_info{height:24px;line-height:24px}input.nbname_input,input.engine_num_input{padding-top:3px;padding-bottom:3px;height:22px;line-height:14px;margin:0}input.engine_num_input{width:60px}.highlight_text{color:blue}#project_name{display:inline-block;padding-left:7px;margin-left:-2px}#project_name>.breadcrumb{padding:0;margin-bottom:0;background-color:transparent;font-weight:bold}#tree-selector{padding-right:0}#button-select-all{min-width:50px}#select-all{margin-left:7px;margin-right:2px}.menu_icon{margin-right:2px}.tab-content .row{margin-left:0;margin-right:0}.folder_icon:before{display:inline-block;font:normal normal normal 14px/1 FontAwesome;font-size:inherit;text-rendering:auto;-webkit-font-smoothing:antialiased;-moz-osx-font-smoothing:grayscale;transform:translate(0, 0);content:\"\\f114\"}.folder_icon:before.pull-left{margin-right:.3em}.folder_icon:before.pull-right{margin-left:.3em}.notebook_icon:before{display:inline-block;font:normal normal normal 14px/1 FontAwesome;font-size:inherit;text-rendering:auto;-webkit-font-smoothing:antialiased;-moz-osx-font-smoothing:grayscale;transform:translate(0, 0);content:\"\\f02d\";position:relative;top:-1px}.notebook_icon:before.pull-left{margin-right:.3em}.notebook_icon:before.pull-right{margin-left:.3em}.running_notebook_icon:before{display:inline-block;font:normal normal normal 14px/1 FontAwesome;font-size:inherit;text-rendering:auto;-webkit-font-smoothing:antialiased;-moz-osx-font-smoothing:grayscale;transform:translate(0, 0);content:\"\\f02d\";position:relative;top:-1px;color:#5cb85c}.running_notebook_icon:before.pull-left{margin-right:.3em}.running_notebook_icon:before.pull-right{margin-left:.3em}.file_icon:before{display:inline-block;font:normal normal normal 14px/1 FontAwesome;font-size:inherit;text-rendering:auto;-webkit-font-smoothing:antialiased;-moz-osx-font-smoothing:grayscale;transform:translate(0, 0);content:\"\\f016\";position:relative;top:-2px}.file_icon:before.pull-left{margin-right:.3em}.file_icon:before.pull-right{margin-left:.3em}#notebook_toolbar .pull-right{padding-top:0;margin-right:-1px}ul#new-menu{left:auto;right:0}.kernel-menu-icon{padding-right:12px;width:24px;content:\"\\f096\"}.kernel-menu-icon:before{content:\"\\f096\"}.kernel-menu-icon-current:before{content:\"\\f00c\"}#tab_content{padding-top:20px}#running .panel-group .panel{margin-top:3px;margin-bottom:1em}#running .panel-group .panel .panel-heading{background-color:#eee;padding-top:4px;padding-bottom:4px;padding-left:7px;padding-right:7px;line-height:22px}#running .panel-group .panel .panel-heading a:focus,#running .panel-group .panel .panel-heading a:hover{text-decoration:none}#running .panel-group .panel .panel-body{padding:0}#running .panel-group .panel .panel-body .list_container{margin-top:0;margin-bottom:0;border:0;border-radius:0}#running .panel-group .panel .panel-body .list_container .list_item{border-bottom:1px solid #ddd}#running .panel-group .panel .panel-body .list_container .list_item:last-child{border-bottom:0}.delete-button{display:none}.duplicate-button{display:none}.rename-button{display:none}.shutdown-button{display:none}.dynamic-instructions{display:inline-block;padding-top:4px}/*!\n*\n* IPython text editor webapp\n*\n*/.selected-keymap i.fa{padding:0 5px}.selected-keymap i.fa:before{content:\"\\f00c\"}#mode-menu{overflow:auto;max-height:20em}.edit_app #header{-webkit-box-shadow:0 0 12px 1px rgba(87,87,87,0.2);box-shadow:0 0 12px 1px rgba(87,87,87,0.2)}.edit_app #menubar .navbar{margin-bottom:-1px}.dirty-indicator{display:inline-block;font:normal normal normal 14px/1 FontAwesome;font-size:inherit;text-rendering:auto;-webkit-font-smoothing:antialiased;-moz-osx-font-smoothing:grayscale;transform:translate(0, 0);width:20px}.dirty-indicator.pull-left{margin-right:.3em}.dirty-indicator.pull-right{margin-left:.3em}.dirty-indicator-dirty{display:inline-block;font:normal normal normal 14px/1 FontAwesome;font-size:inherit;text-rendering:auto;-webkit-font-smoothing:antialiased;-moz-osx-font-smoothing:grayscale;transform:translate(0, 0);width:20px}.dirty-indicator-dirty.pull-left{margin-right:.3em}.dirty-indicator-dirty.pull-right{margin-left:.3em}.dirty-indicator-clean{display:inline-block;font:normal normal normal 14px/1 FontAwesome;font-size:inherit;text-rendering:auto;-webkit-font-smoothing:antialiased;-moz-osx-font-smoothing:grayscale;transform:translate(0, 0);width:20px}.dirty-indicator-clean.pull-left{margin-right:.3em}.dirty-indicator-clean.pull-right{margin-left:.3em}.dirty-indicator-clean:before{display:inline-block;font:normal normal normal 14px/1 FontAwesome;font-size:inherit;text-rendering:auto;-webkit-font-smoothing:antialiased;-moz-osx-font-smoothing:grayscale;transform:translate(0, 0);content:\"\\f00c\"}.dirty-indicator-clean:before.pull-left{margin-right:.3em}.dirty-indicator-clean:before.pull-right{margin-left:.3em}#filename{font-size:16pt;display:table;padding:0 5px}#current-mode{padding-left:5px;padding-right:5px}#texteditor-backdrop{padding-top:20px;padding-bottom:20px}@media not print{#texteditor-backdrop{background-color:#eee}}@media print{#texteditor-backdrop #texteditor-container .CodeMirror-gutter,#texteditor-backdrop #texteditor-container .CodeMirror-gutters{background-color:#fff}}@media not print{#texteditor-backdrop #texteditor-container .CodeMirror-gutter,#texteditor-backdrop #texteditor-container .CodeMirror-gutters{background-color:#fff}}@media not print{#texteditor-backdrop #texteditor-container{padding:0;background-color:#fff;-webkit-box-shadow:0 0 12px 1px rgba(87,87,87,0.2);box-shadow:0 0 12px 1px rgba(87,87,87,0.2)}}/*!\n*\n* IPython notebook\n*\n*/.ansibold{font-weight:bold}.ansiblack{color:black}.ansired{color:darkred}.ansigreen{color:darkgreen}.ansiyellow{color:#c4a000}.ansiblue{color:darkblue}.ansipurple{color:darkviolet}.ansicyan{color:steelblue}.ansigray{color:gray}.ansibgblack{background-color:black}.ansibgred{background-color:red}.ansibggreen{background-color:green}.ansibgyellow{background-color:yellow}.ansibgblue{background-color:blue}.ansibgpurple{background-color:magenta}.ansibgcyan{background-color:cyan}.ansibggray{background-color:gray}div.cell{border:1px solid transparent;display:-webkit-box;-webkit-box-orient:vertical;-webkit-box-align:stretch;display:-moz-box;-moz-box-orient:vertical;-moz-box-align:stretch;display:box;box-orient:vertical;box-align:stretch;display:flex;flex-direction:column;align-items:stretch;border-radius:2px;box-sizing:border-box;-moz-box-sizing:border-box;-webkit-box-sizing:border-box;border-width:thin;border-style:solid;width:100%;padding:5px;margin:0;outline:none}div.cell.selected{border-color:#ababab}@media print{div.cell.selected{border-color:transparent}}.edit_mode div.cell.selected{border-color:green}@media print{.edit_mode div.cell.selected{border-color:transparent}}.prompt{min-width:14ex;padding:.4em;margin:0;font-family:monospace;text-align:right;line-height:1.21429em}@media (max-width:540px){.prompt{text-align:left}}div.inner_cell{display:-webkit-box;-webkit-box-orient:vertical;-webkit-box-align:stretch;display:-moz-box;-moz-box-orient:vertical;-moz-box-align:stretch;display:box;box-orient:vertical;box-align:stretch;display:flex;flex-direction:column;align-items:stretch;-webkit-box-flex:1;-moz-box-flex:1;box-flex:1;flex:1}@-moz-document url-prefix(){div.inner_cell{overflow-x:hidden}}div.input_area{border:1px solid #cfcfcf;border-radius:2px;background:#f7f7f7;line-height:1.21429em}div.prompt:empty{padding-top:0;padding-bottom:0}div.unrecognized_cell{padding:5px 5px 5px 0;display:-webkit-box;-webkit-box-orient:horizontal;-webkit-box-align:stretch;display:-moz-box;-moz-box-orient:horizontal;-moz-box-align:stretch;display:box;box-orient:horizontal;box-align:stretch;display:flex;flex-direction:row;align-items:stretch}div.unrecognized_cell .inner_cell{border-radius:2px;padding:5px;font-weight:bold;color:red;border:1px solid #cfcfcf;background:#eaeaea}div.unrecognized_cell .inner_cell a{color:inherit;text-decoration:none}div.unrecognized_cell .inner_cell a:hover{color:inherit;text-decoration:none}@media (max-width:540px){div.unrecognized_cell>div.prompt{display:none}}@media print{div.code_cell{page-break-inside:avoid}}div.input{page-break-inside:avoid;display:-webkit-box;-webkit-box-orient:horizontal;-webkit-box-align:stretch;display:-moz-box;-moz-box-orient:horizontal;-moz-box-align:stretch;display:box;box-orient:horizontal;box-align:stretch;display:flex;flex-direction:row;align-items:stretch}@media (max-width:540px){div.input{display:-webkit-box;-webkit-box-orient:vertical;-webkit-box-align:stretch;display:-moz-box;-moz-box-orient:vertical;-moz-box-align:stretch;display:box;box-orient:vertical;box-align:stretch;display:flex;flex-direction:column;align-items:stretch}}div.input_prompt{color:navy;border-top:1px solid transparent}div.input_area>div.highlight{margin:.4em;border:none;padding:0;background-color:transparent}div.input_area>div.highlight>pre{margin:0;border:none;padding:0;background-color:transparent}.CodeMirror{line-height:1.21429em;font-size:14px;height:auto;background:none}.CodeMirror-scroll{overflow-y:hidden;overflow-x:auto}.CodeMirror-lines{padding:.4em}.CodeMirror-linenumber{padding:0 8px 0 4px}.CodeMirror-gutters{border-bottom-left-radius:2px;border-top-left-radius:2px}.CodeMirror pre{padding:0;border:0;border-radius:0}.highlight-base{color:#000}.highlight-variable{color:#000}.highlight-variable-2{color:#1a1a1a}.highlight-variable-3{color:#333}.highlight-string{color:#ba2121}.highlight-comment{color:#408080;font-style:italic}.highlight-number{color:#080}.highlight-atom{color:#88f}.highlight-keyword{color:#008000;font-weight:bold}.highlight-builtin{color:#008000}.highlight-error{color:#f00}.highlight-operator{color:#a2f;font-weight:bold}.highlight-meta{color:#a2f}.highlight-def{color:#00f}.highlight-string-2{color:#f50}.highlight-qualifier{color:#555}.highlight-bracket{color:#997}.highlight-tag{color:#170}.highlight-attribute{color:#00c}.highlight-header{color:blue}.highlight-quote{color:#090}.highlight-link{color:#00c}.cm-s-ipython span.cm-keyword{color:#008000;font-weight:bold}.cm-s-ipython span.cm-atom{color:#88f}.cm-s-ipython span.cm-number{color:#080}.cm-s-ipython span.cm-def{color:#00f}.cm-s-ipython span.cm-variable{color:#000}.cm-s-ipython span.cm-operator{color:#a2f;font-weight:bold}.cm-s-ipython span.cm-variable-2{color:#1a1a1a}.cm-s-ipython span.cm-variable-3{color:#333}.cm-s-ipython span.cm-comment{color:#408080;font-style:italic}.cm-s-ipython span.cm-string{color:#ba2121}.cm-s-ipython span.cm-string-2{color:#f50}.cm-s-ipython span.cm-meta{color:#a2f}.cm-s-ipython span.cm-qualifier{color:#555}.cm-s-ipython span.cm-builtin{color:#008000}.cm-s-ipython span.cm-bracket{color:#997}.cm-s-ipython span.cm-tag{color:#170}.cm-s-ipython span.cm-attribute{color:#00c}.cm-s-ipython span.cm-header{color:blue}.cm-s-ipython span.cm-quote{color:#090}.cm-s-ipython span.cm-link{color:#00c}.cm-s-ipython span.cm-error{color:#f00}.cm-s-ipython span.cm-tab{background:url(data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADAAAAAMCAYAAAAkuj5RAAAAAXNSR0IArs4c6QAAAGFJREFUSMft1LsRQFAQheHPowAKoACx3IgEKtaEHujDjORSgWTH/ZOdnZOcM/sgk/kFFWY0qV8foQwS4MKBCS3qR6ixBJvElOobYAtivseIE120FaowJPN75GMu8j/LfMwNjh4HUpwg4LUAAAAASUVORK5CYII=);background-position:right;background-repeat:no-repeat}div.output_wrapper{position:relative;display:-webkit-box;-webkit-box-orient:vertical;-webkit-box-align:stretch;display:-moz-box;-moz-box-orient:vertical;-moz-box-align:stretch;display:box;box-orient:vertical;box-align:stretch;display:flex;flex-direction:column;align-items:stretch;z-index:1}div.output_scroll{height:24em;width:100%;overflow:auto;border-radius:2px;-webkit-box-shadow:inset 0 2px 8px rgba(0,0,0,0.8);box-shadow:inset 0 2px 8px rgba(0,0,0,0.8);display:block}div.output_collapsed{margin:0;padding:0;display:-webkit-box;-webkit-box-orient:vertical;-webkit-box-align:stretch;display:-moz-box;-moz-box-orient:vertical;-moz-box-align:stretch;display:box;box-orient:vertical;box-align:stretch;display:flex;flex-direction:column;align-items:stretch}div.out_prompt_overlay{height:100%;padding:0 .4em;position:absolute;border-radius:2px}div.out_prompt_overlay:hover{-webkit-box-shadow:inset 0 0 1px #000;box-shadow:inset 0 0 1px #000;background:rgba(240,240,240,0.5)}div.output_prompt{color:darkred}div.output_area{padding:0;page-break-inside:avoid;display:-webkit-box;-webkit-box-orient:horizontal;-webkit-box-align:stretch;display:-moz-box;-moz-box-orient:horizontal;-moz-box-align:stretch;display:box;box-orient:horizontal;box-align:stretch;display:flex;flex-direction:row;align-items:stretch}div.output_area .MathJax_Display{text-align:left !important}div.output_area .rendered_html table{margin-left:0;margin-right:0}div.output_area .rendered_html img{margin-left:0;margin-right:0}div.output_area img,div.output_area svg{max-width:100%;height:auto}div.output_area img.unconfined,div.output_area svg.unconfined{max-width:none}.output{display:-webkit-box;-webkit-box-orient:vertical;-webkit-box-align:stretch;display:-moz-box;-moz-box-orient:vertical;-moz-box-align:stretch;display:box;box-orient:vertical;box-align:stretch;display:flex;flex-direction:column;align-items:stretch}@media (max-width:540px){div.output_area{display:-webkit-box;-webkit-box-orient:vertical;-webkit-box-align:stretch;display:-moz-box;-moz-box-orient:vertical;-moz-box-align:stretch;display:box;box-orient:vertical;box-align:stretch;display:flex;flex-direction:column;align-items:stretch}}div.output_area pre{margin:0;padding:0;border:0;vertical-align:baseline;color:black;background-color:transparent;border-radius:0}div.output_subarea{overflow-x:auto;padding:.4em;-webkit-box-flex:1;-moz-box-flex:1;box-flex:1;flex:1;max-width:calc(100% - 14ex)}div.output_text{text-align:left;color:#000;line-height:1.21429em}div.output_stderr{background:#fdd}div.output_latex{text-align:left}div.output_javascript:empty{padding:0}.js-error{color:darkred}div.raw_input_container{font-family:monospace;padding-top:5px}input.raw_input{font-family:inherit;font-size:inherit;color:inherit;width:auto;vertical-align:baseline;padding:0 .25em;margin:0 .25em}input.raw_input:focus{box-shadow:none}p.p-space{margin-bottom:10px}div.output_unrecognized{padding:5px;font-weight:bold;color:red}div.output_unrecognized a{color:inherit;text-decoration:none}div.output_unrecognized a:hover{color:inherit;text-decoration:none}.rendered_html{color:#000}.rendered_html em{font-style:italic}.rendered_html strong{font-weight:bold}.rendered_html u{text-decoration:underline}.rendered_html :link{text-decoration:underline}.rendered_html :visited{text-decoration:underline}.rendered_html h1{font-size:185.7%;margin:1.08em 0 0 0;font-weight:bold;line-height:1}.rendered_html h2{font-size:157.1%;margin:1.27em 0 0 0;font-weight:bold;line-height:1}.rendered_html h3{font-size:128.6%;margin:1.55em 0 0 0;font-weight:bold;line-height:1}.rendered_html h4{font-size:100%;margin:2em 0 0 0;font-weight:bold;line-height:1}.rendered_html h5{font-size:100%;margin:2em 0 0 0;font-weight:bold;line-height:1;font-style:italic}.rendered_html h6{font-size:100%;margin:2em 0 0 0;font-weight:bold;line-height:1;font-style:italic}.rendered_html h1:first-child{margin-top:.538em}.rendered_html h2:first-child{margin-top:.636em}.rendered_html h3:first-child{margin-top:.777em}.rendered_html h4:first-child{margin-top:1em}.rendered_html h5:first-child{margin-top:1em}.rendered_html h6:first-child{margin-top:1em}.rendered_html ul{list-style:disc;margin:0 2em;padding-left:0}.rendered_html ul ul{list-style:square;margin:0 2em}.rendered_html ul ul ul{list-style:circle;margin:0 2em}.rendered_html ol{list-style:decimal;margin:0 2em;padding-left:0}.rendered_html ol ol{list-style:upper-alpha;margin:0 2em}.rendered_html ol ol ol{list-style:lower-alpha;margin:0 2em}.rendered_html ol ol ol ol{list-style:lower-roman;margin:0 2em}.rendered_html ol ol ol ol ol{list-style:decimal;margin:0 2em}.rendered_html *+ul{margin-top:1em}.rendered_html *+ol{margin-top:1em}.rendered_html hr{color:black;background-color:black}.rendered_html pre{margin:1em 2em}.rendered_html pre,.rendered_html code{border:0;background-color:#fff;color:#000;font-size:100%;padding:0}.rendered_html blockquote{margin:1em 2em}.rendered_html table{margin-left:auto;margin-right:auto;border:1px solid black;border-collapse:collapse}.rendered_html tr,.rendered_html th,.rendered_html td{border:1px solid black;border-collapse:collapse;margin:1em 2em}.rendered_html td,.rendered_html th{text-align:left;vertical-align:middle;padding:4px}.rendered_html th{font-weight:bold}.rendered_html *+table{margin-top:1em}.rendered_html p{text-align:left}.rendered_html *+p{margin-top:1em}.rendered_html img{display:block;margin-left:auto;margin-right:auto}.rendered_html *+img{margin-top:1em}.rendered_html img,.rendered_html svg{max-width:100%;height:auto}.rendered_html img.unconfined,.rendered_html svg.unconfined{max-width:none}div.text_cell{display:-webkit-box;-webkit-box-orient:horizontal;-webkit-box-align:stretch;display:-moz-box;-moz-box-orient:horizontal;-moz-box-align:stretch;display:box;box-orient:horizontal;box-align:stretch;display:flex;flex-direction:row;align-items:stretch}@media (max-width:540px){div.text_cell>div.prompt{display:none}}div.text_cell_render{outline:none;resize:none;width:inherit;border-style:none;padding:.5em .5em .5em .4em;color:#000;box-sizing:border-box;-moz-box-sizing:border-box;-webkit-box-sizing:border-box}a.anchor-link:link{text-decoration:none;padding:0 20px;visibility:hidden}h1:hover .anchor-link,h2:hover .anchor-link,h3:hover .anchor-link,h4:hover .anchor-link,h5:hover .anchor-link,h6:hover .anchor-link{visibility:visible}.text_cell.rendered .input_area{display:none}.text_cell.rendered .rendered_html{overflow-x:auto}.text_cell.unrendered .text_cell_render{display:none}.cm-header-1,.cm-header-2,.cm-header-3,.cm-header-4,.cm-header-5,.cm-header-6{font-weight:bold;font-family:\"Helvetica Neue\",Helvetica,Arial,sans-serif}.cm-header-1{font-size:185.7%}.cm-header-2{font-size:157.1%}.cm-header-3{font-size:128.6%}.cm-header-4{font-size:110%}.cm-header-5{font-size:100%;font-style:italic}.cm-header-6{font-size:100%;font-style:italic}.widget-interact>div,.widget-interact>input{padding:2.5px}.widget-area{page-break-inside:avoid;display:-webkit-box;-webkit-box-orient:horizontal;-webkit-box-align:stretch;display:-moz-box;-moz-box-orient:horizontal;-moz-box-align:stretch;display:box;box-orient:horizontal;box-align:stretch;display:flex;flex-direction:row;align-items:stretch}.widget-area .widget-subarea{padding:.44em .4em .4em 1px;margin-left:6px;box-sizing:border-box;-moz-box-sizing:border-box;-webkit-box-sizing:border-box;display:-webkit-box;-webkit-box-orient:vertical;-webkit-box-align:stretch;display:-moz-box;-moz-box-orient:vertical;-moz-box-align:stretch;display:box;box-orient:vertical;box-align:stretch;display:flex;flex-direction:column;align-items:stretch;-webkit-box-flex:2;-moz-box-flex:2;box-flex:2;flex:2;-webkit-box-align:start;-moz-box-align:start;box-align:start;align-items:flex-start}.widget-area.connection-problems .prompt:after{content:\"\\f127\";font-family:'FontAwesome';color:#d9534f;font-size:14px;top:3px;padding:3px}.slide-track{border:1px solid #ccc;background:#fff;border-radius:2px}.widget-hslider{padding-left:8px;padding-right:2px;overflow:visible;width:350px;height:5px;max-height:5px;margin-top:13px;margin-bottom:10px;border:1px solid #ccc;background:#fff;border-radius:2px;display:-webkit-box;-webkit-box-orient:horizontal;-webkit-box-align:stretch;display:-moz-box;-moz-box-orient:horizontal;-moz-box-align:stretch;display:box;box-orient:horizontal;box-align:stretch;display:flex;flex-direction:row;align-items:stretch}.widget-hslider .ui-slider{border:0;background:none;display:-webkit-box;-webkit-box-orient:horizontal;-webkit-box-align:stretch;display:-moz-box;-moz-box-orient:horizontal;-moz-box-align:stretch;display:box;box-orient:horizontal;box-align:stretch;display:flex;flex-direction:row;align-items:stretch;-webkit-box-flex:1;-moz-box-flex:1;box-flex:1;flex:1}.widget-hslider .ui-slider .ui-slider-handle{width:12px;height:28px;margin-top:-8px;border-radius:2px}.widget-hslider .ui-slider .ui-slider-range{height:12px;margin-top:-4px;background:#eee}.widget-vslider{padding-bottom:5px;overflow:visible;width:5px;max-width:5px;height:250px;margin-left:12px;border:1px solid #ccc;background:#fff;border-radius:2px;display:-webkit-box;-webkit-box-orient:vertical;-webkit-box-align:stretch;display:-moz-box;-moz-box-orient:vertical;-moz-box-align:stretch;display:box;box-orient:vertical;box-align:stretch;display:flex;flex-direction:column;align-items:stretch}.widget-vslider .ui-slider{border:0;background:none;margin-left:-4px;margin-top:5px;display:-webkit-box;-webkit-box-orient:vertical;-webkit-box-align:stretch;display:-moz-box;-moz-box-orient:vertical;-moz-box-align:stretch;display:box;box-orient:vertical;box-align:stretch;display:flex;flex-direction:column;align-items:stretch;-webkit-box-flex:1;-moz-box-flex:1;box-flex:1;flex:1}.widget-vslider .ui-slider .ui-slider-handle{width:28px;height:12px;margin-left:-9px;border-radius:2px}.widget-vslider .ui-slider .ui-slider-range{width:12px;margin-left:-1px;background:#eee}.widget-text{width:350px;margin:0}.widget-listbox{width:350px;margin-bottom:0}.widget-numeric-text{width:150px;margin:0}.widget-progress{margin-top:6px;min-width:350px}.widget-progress .progress-bar{-webkit-transition:none;-moz-transition:none;-ms-transition:none;-o-transition:none;transition:none}.widget-combo-btn{min-width:125px}.widget_item .dropdown-menu li a{color:inherit}.widget-hbox{display:-webkit-box;-webkit-box-orient:horizontal;-webkit-box-align:stretch;display:-moz-box;-moz-box-orient:horizontal;-moz-box-align:stretch;display:box;box-orient:horizontal;box-align:stretch;display:flex;flex-direction:row;align-items:stretch}.widget-hbox input[type=\"checkbox\"]{margin-top:9px;margin-bottom:10px}.widget-hbox .widget-label{min-width:10ex;padding-right:8px;padding-top:5px;text-align:right;vertical-align:text-top}.widget-hbox .widget-readout{padding-left:8px;padding-top:5px;text-align:left;vertical-align:text-top}.widget-vbox{display:-webkit-box;-webkit-box-orient:vertical;-webkit-box-align:stretch;display:-moz-box;-moz-box-orient:vertical;-moz-box-align:stretch;display:box;box-orient:vertical;box-align:stretch;display:flex;flex-direction:column;align-items:stretch}.widget-vbox .widget-label{padding-bottom:5px;text-align:center;vertical-align:text-bottom}.widget-vbox .widget-readout{padding-top:5px;text-align:center;vertical-align:text-top}.widget-box{box-sizing:border-box;-moz-box-sizing:border-box;-webkit-box-sizing:border-box;-webkit-box-align:start;-moz-box-align:start;box-align:start;align-items:flex-start}.widget-radio-box{display:-webkit-box;-webkit-box-orient:vertical;-webkit-box-align:stretch;display:-moz-box;-moz-box-orient:vertical;-moz-box-align:stretch;display:box;box-orient:vertical;box-align:stretch;display:flex;flex-direction:column;align-items:stretch;box-sizing:border-box;-moz-box-sizing:border-box;-webkit-box-sizing:border-box;padding-top:4px}.widget-radio-box label{margin-top:0;margin-left:20px}/*!\n*\n* IPython notebook webapp\n*\n*/@media (max-width:767px){.notebook_app{padding-left:0;padding-right:0}}#ipython-main-app{box-sizing:border-box;-moz-box-sizing:border-box;-webkit-box-sizing:border-box;height:100%}div#notebook_panel{margin:0;padding:0;box-sizing:border-box;-moz-box-sizing:border-box;-webkit-box-sizing:border-box;height:100%}#notebook{font-size:14px;line-height:20px;overflow-y:hidden;overflow-x:auto;width:100%;padding-top:20px;margin:0;outline:none;box-sizing:border-box;-moz-box-sizing:border-box;-webkit-box-sizing:border-box;min-height:100%}@media not print{#notebook-container{padding:15px;background-color:#fff;min-height:0;-webkit-box-shadow:0 0 12px 1px rgba(87,87,87,0.2);box-shadow:0 0 12px 1px rgba(87,87,87,0.2)}}div.ui-widget-content{border:1px solid #ababab;outline:none}pre.dialog{background-color:#f7f7f7;border:1px solid #ddd;border-radius:2px;padding:.4em;padding-left:2em}p.dialog{padding:.2em}pre,code,kbd,samp{white-space:pre-wrap}#fonttest{font-family:monospace}p{margin-bottom:0}.end_space{min-height:100px;transition:height .2s ease}.notebook_app #header{-webkit-box-shadow:0 0 12px 1px rgba(87,87,87,0.2);box-shadow:0 0 12px 1px rgba(87,87,87,0.2)}@media not print{.notebook_app{background-color:#eee}}.celltoolbar{border:thin solid #cfcfcf;border-bottom:none;background:#eee;border-radius:2px 2px 0 0;width:100%;height:29px;padding-right:4px;display:-webkit-box;-webkit-box-orient:horizontal;-webkit-box-align:stretch;display:-moz-box;-moz-box-orient:horizontal;-moz-box-align:stretch;display:box;box-orient:horizontal;box-align:stretch;display:flex;flex-direction:row;align-items:stretch;-webkit-box-pack:end;-moz-box-pack:end;box-pack:end;justify-content:flex-end}@media print{.celltoolbar{display:none}}.ctb_hideshow{display:none;vertical-align:bottom}.ctb_global_show .ctb_show.ctb_hideshow{display:block}.ctb_global_show .ctb_show+.input_area,.ctb_global_show .ctb_show+div.text_cell_input,.ctb_global_show .ctb_show~div.text_cell_render{border-top-right-radius:0;border-top-left-radius:0}.ctb_global_show .ctb_show~div.text_cell_render{border:1px solid #cfcfcf}.celltoolbar{font-size:87%;padding-top:3px}.celltoolbar select{display:block;width:100%;height:32px;padding:6px 12px;font-size:13px;line-height:1.42857143;color:#555;background-color:#fff;background-image:none;border:1px solid #ccc;border-radius:2px;-webkit-box-shadow:inset 0 1px 1px rgba(0,0,0,0.075);box-shadow:inset 0 1px 1px rgba(0,0,0,0.075);-webkit-transition:border-color ease-in-out .15s, box-shadow ease-in-out .15s;-o-transition:border-color ease-in-out .15s, box-shadow ease-in-out .15s;transition:border-color ease-in-out .15s, box-shadow ease-in-out .15s;height:30px;padding:5px 10px;font-size:12px;line-height:1.5;border-radius:1px;width:inherit;font-size:inherit;height:22px;padding:0;display:inline-block}.celltoolbar select:focus{border-color:#66afe9;outline:0;-webkit-box-shadow:inset 0 1px 1px rgba(0,0,0,.075), 0 0 8px rgba(102, 175, 233, 0.6);box-shadow:inset 0 1px 1px rgba(0,0,0,.075), 0 0 8px rgba(102, 175, 233, 0.6)}.celltoolbar select::-moz-placeholder{color:#999;opacity:1}.celltoolbar select:-ms-input-placeholder{color:#999}.celltoolbar select::-webkit-input-placeholder{color:#999}.celltoolbar select[disabled],.celltoolbar select[readonly],fieldset[disabled] .celltoolbar select{cursor:not-allowed;background-color:#eee;opacity:1}textarea.celltoolbar select{height:auto}select.celltoolbar select{height:30px;line-height:30px}textarea.celltoolbar select,select[multiple].celltoolbar select{height:auto}.celltoolbar label{margin-left:5px;margin-right:5px}.completions{position:absolute;z-index:10;overflow:hidden;border:1px solid #ababab;border-radius:2px;-webkit-box-shadow:0 6px 10px -1px #adadad;box-shadow:0 6px 10px -1px #adadad}.completions select{background:white;outline:none;border:none;padding:0;margin:0;overflow:auto;font-family:monospace;font-size:110%;color:#000;width:auto}.completions select option.context{color:#286090}#kernel_logo_widget{float:right !important;float:right}#kernel_logo_widget .current_kernel_logo{display:none;margin-top:-1px;margin-bottom:-1px;width:32px;height:32px}#menubar{box-sizing:border-box;-moz-box-sizing:border-box;-webkit-box-sizing:border-box;margin-top:1px}#menubar .navbar{border-top:1px;border-radius:0 0 2px 2px;margin-bottom:0}#menubar .navbar-toggle{float:left;padding-top:7px;padding-bottom:7px;border:none}#menubar .navbar-collapse{clear:left}.nav-wrapper{border-bottom:1px solid #e7e7e7}i.menu-icon{padding-top:4px}ul#help_menu li a{overflow:hidden;padding-right:2.2em}ul#help_menu li a i{margin-right:-1.2em}.dropdown-submenu{position:relative}.dropdown-submenu>.dropdown-menu{top:0;left:100%;margin-top:-6px;margin-left:-1px}.dropdown-submenu:hover>.dropdown-menu{display:block}.dropdown-submenu>a:after{display:inline-block;font:normal normal normal 14px/1 FontAwesome;font-size:inherit;text-rendering:auto;-webkit-font-smoothing:antialiased;-moz-osx-font-smoothing:grayscale;transform:translate(0, 0);display:block;content:\"\\f0da\";float:right;color:#333;margin-top:2px;margin-right:-10px}.dropdown-submenu>a:after.pull-left{margin-right:.3em}.dropdown-submenu>a:after.pull-right{margin-left:.3em}.dropdown-submenu:hover>a:after{color:#262626}.dropdown-submenu.pull-left{float:none}.dropdown-submenu.pull-left>.dropdown-menu{left:-100%;margin-left:10px}#notification_area{float:right !important;float:right;z-index:10}.indicator_area{float:right !important;float:right;color:#777;margin-left:5px;margin-right:5px;width:11px;z-index:10;text-align:center;width:auto}#kernel_indicator{float:right !important;float:right;color:#777;margin-left:5px;margin-right:5px;width:11px;z-index:10;text-align:center;width:auto;border-left:1px solid}#kernel_indicator .kernel_indicator_name{padding-left:5px;padding-right:5px}#modal_indicator{float:right !important;float:right;color:#777;margin-left:5px;margin-right:5px;width:11px;z-index:10;text-align:center;width:auto}#readonly-indicator{float:right !important;float:right;color:#777;margin-left:5px;margin-right:5px;width:11px;z-index:10;text-align:center;width:auto;margin-top:2px;margin-bottom:0;margin-left:0;margin-right:0;display:none}.modal_indicator:before{width:1.28571429em;text-align:center}.edit_mode .modal_indicator:before{display:inline-block;font:normal normal normal 14px/1 FontAwesome;font-size:inherit;text-rendering:auto;-webkit-font-smoothing:antialiased;-moz-osx-font-smoothing:grayscale;transform:translate(0, 0);content:\"\\f040\"}.edit_mode .modal_indicator:before.pull-left{margin-right:.3em}.edit_mode .modal_indicator:before.pull-right{margin-left:.3em}.command_mode .modal_indicator:before{display:inline-block;font:normal normal normal 14px/1 FontAwesome;font-size:inherit;text-rendering:auto;-webkit-font-smoothing:antialiased;-moz-osx-font-smoothing:grayscale;transform:translate(0, 0);content:' '}.command_mode .modal_indicator:before.pull-left{margin-right:.3em}.command_mode .modal_indicator:before.pull-right{margin-left:.3em}.kernel_idle_icon:before{display:inline-block;font:normal normal normal 14px/1 FontAwesome;font-size:inherit;text-rendering:auto;-webkit-font-smoothing:antialiased;-moz-osx-font-smoothing:grayscale;transform:translate(0, 0);content:\"\\f10c\"}.kernel_idle_icon:before.pull-left{margin-right:.3em}.kernel_idle_icon:before.pull-right{margin-left:.3em}.kernel_busy_icon:before{display:inline-block;font:normal normal normal 14px/1 FontAwesome;font-size:inherit;text-rendering:auto;-webkit-font-smoothing:antialiased;-moz-osx-font-smoothing:grayscale;transform:translate(0, 0);content:\"\\f111\"}.kernel_busy_icon:before.pull-left{margin-right:.3em}.kernel_busy_icon:before.pull-right{margin-left:.3em}.kernel_dead_icon:before{display:inline-block;font:normal normal normal 14px/1 FontAwesome;font-size:inherit;text-rendering:auto;-webkit-font-smoothing:antialiased;-moz-osx-font-smoothing:grayscale;transform:translate(0, 0);content:\"\\f1e2\"}.kernel_dead_icon:before.pull-left{margin-right:.3em}.kernel_dead_icon:before.pull-right{margin-left:.3em}.kernel_disconnected_icon:before{display:inline-block;font:normal normal normal 14px/1 FontAwesome;font-size:inherit;text-rendering:auto;-webkit-font-smoothing:antialiased;-moz-osx-font-smoothing:grayscale;transform:translate(0, 0);content:\"\\f127\"}.kernel_disconnected_icon:before.pull-left{margin-right:.3em}.kernel_disconnected_icon:before.pull-right{margin-left:.3em}.notification_widget{color:#777;z-index:10;background:rgba(240,240,240,0.5);margin-right:4px;color:#333;background-color:#fff;border-color:#ccc}.notification_widget:hover,.notification_widget:focus,.notification_widget.focus,.notification_widget:active,.notification_widget.active,.open>.dropdown-toggle.notification_widget{color:#333;background-color:#e6e6e6;border-color:#adadad}.notification_widget:active,.notification_widget.active,.open>.dropdown-toggle.notification_widget{background-image:none}.notification_widget.disabled,.notification_widget[disabled],fieldset[disabled] .notification_widget,.notification_widget.disabled:hover,.notification_widget[disabled]:hover,fieldset[disabled] .notification_widget:hover,.notification_widget.disabled:focus,.notification_widget[disabled]:focus,fieldset[disabled] .notification_widget:focus,.notification_widget.disabled.focus,.notification_widget[disabled].focus,fieldset[disabled] .notification_widget.focus,.notification_widget.disabled:active,.notification_widget[disabled]:active,fieldset[disabled] .notification_widget:active,.notification_widget.disabled.active,.notification_widget[disabled].active,fieldset[disabled] .notification_widget.active{background-color:#fff;border-color:#ccc}.notification_widget .badge{color:#fff;background-color:#333}.notification_widget.warning{color:#fff;background-color:#f0ad4e;border-color:#eea236}.notification_widget.warning:hover,.notification_widget.warning:focus,.notification_widget.warning.focus,.notification_widget.warning:active,.notification_widget.warning.active,.open>.dropdown-toggle.notification_widget.warning{color:#fff;background-color:#ec971f;border-color:#d58512}.notification_widget.warning:active,.notification_widget.warning.active,.open>.dropdown-toggle.notification_widget.warning{background-image:none}.notification_widget.warning.disabled,.notification_widget.warning[disabled],fieldset[disabled] .notification_widget.warning,.notification_widget.warning.disabled:hover,.notification_widget.warning[disabled]:hover,fieldset[disabled] .notification_widget.warning:hover,.notification_widget.warning.disabled:focus,.notification_widget.warning[disabled]:focus,fieldset[disabled] .notification_widget.warning:focus,.notification_widget.warning.disabled.focus,.notification_widget.warning[disabled].focus,fieldset[disabled] .notification_widget.warning.focus,.notification_widget.warning.disabled:active,.notification_widget.warning[disabled]:active,fieldset[disabled] .notification_widget.warning:active,.notification_widget.warning.disabled.active,.notification_widget.warning[disabled].active,fieldset[disabled] .notification_widget.warning.active{background-color:#f0ad4e;border-color:#eea236}.notification_widget.warning .badge{color:#f0ad4e;background-color:#fff}.notification_widget.success{color:#fff;background-color:#5cb85c;border-color:#4cae4c}.notification_widget.success:hover,.notification_widget.success:focus,.notification_widget.success.focus,.notification_widget.success:active,.notification_widget.success.active,.open>.dropdown-toggle.notification_widget.success{color:#fff;background-color:#449d44;border-color:#398439}.notification_widget.success:active,.notification_widget.success.active,.open>.dropdown-toggle.notification_widget.success{background-image:none}.notification_widget.success.disabled,.notification_widget.success[disabled],fieldset[disabled] .notification_widget.success,.notification_widget.success.disabled:hover,.notification_widget.success[disabled]:hover,fieldset[disabled] .notification_widget.success:hover,.notification_widget.success.disabled:focus,.notification_widget.success[disabled]:focus,fieldset[disabled] .notification_widget.success:focus,.notification_widget.success.disabled.focus,.notification_widget.success[disabled].focus,fieldset[disabled] .notification_widget.success.focus,.notification_widget.success.disabled:active,.notification_widget.success[disabled]:active,fieldset[disabled] .notification_widget.success:active,.notification_widget.success.disabled.active,.notification_widget.success[disabled].active,fieldset[disabled] .notification_widget.success.active{background-color:#5cb85c;border-color:#4cae4c}.notification_widget.success .badge{color:#5cb85c;background-color:#fff}.notification_widget.info{color:#fff;background-color:#5bc0de;border-color:#46b8da}.notification_widget.info:hover,.notification_widget.info:focus,.notification_widget.info.focus,.notification_widget.info:active,.notification_widget.info.active,.open>.dropdown-toggle.notification_widget.info{color:#fff;background-color:#31b0d5;border-color:#269abc}.notification_widget.info:active,.notification_widget.info.active,.open>.dropdown-toggle.notification_widget.info{background-image:none}.notification_widget.info.disabled,.notification_widget.info[disabled],fieldset[disabled] .notification_widget.info,.notification_widget.info.disabled:hover,.notification_widget.info[disabled]:hover,fieldset[disabled] .notification_widget.info:hover,.notification_widget.info.disabled:focus,.notification_widget.info[disabled]:focus,fieldset[disabled] .notification_widget.info:focus,.notification_widget.info.disabled.focus,.notification_widget.info[disabled].focus,fieldset[disabled] .notification_widget.info.focus,.notification_widget.info.disabled:active,.notification_widget.info[disabled]:active,fieldset[disabled] .notification_widget.info:active,.notification_widget.info.disabled.active,.notification_widget.info[disabled].active,fieldset[disabled] .notification_widget.info.active{background-color:#5bc0de;border-color:#46b8da}.notification_widget.info .badge{color:#5bc0de;background-color:#fff}.notification_widget.danger{color:#fff;background-color:#d9534f;border-color:#d43f3a}.notification_widget.danger:hover,.notification_widget.danger:focus,.notification_widget.danger.focus,.notification_widget.danger:active,.notification_widget.danger.active,.open>.dropdown-toggle.notification_widget.danger{color:#fff;background-color:#c9302c;border-color:#ac2925}.notification_widget.danger:active,.notification_widget.danger.active,.open>.dropdown-toggle.notification_widget.danger{background-image:none}.notification_widget.danger.disabled,.notification_widget.danger[disabled],fieldset[disabled] .notification_widget.danger,.notification_widget.danger.disabled:hover,.notification_widget.danger[disabled]:hover,fieldset[disabled] .notification_widget.danger:hover,.notification_widget.danger.disabled:focus,.notification_widget.danger[disabled]:focus,fieldset[disabled] .notification_widget.danger:focus,.notification_widget.danger.disabled.focus,.notification_widget.danger[disabled].focus,fieldset[disabled] .notification_widget.danger.focus,.notification_widget.danger.disabled:active,.notification_widget.danger[disabled]:active,fieldset[disabled] .notification_widget.danger:active,.notification_widget.danger.disabled.active,.notification_widget.danger[disabled].active,fieldset[disabled] .notification_widget.danger.active{background-color:#d9534f;border-color:#d43f3a}.notification_widget.danger .badge{color:#d9534f;background-color:#fff}div#pager{background-color:#fff;font-size:14px;line-height:20px;overflow:hidden;display:none;position:fixed;bottom:0;width:100%;max-height:50%;padding-top:8px;-webkit-box-shadow:0 0 12px 1px rgba(87,87,87,0.2);box-shadow:0 0 12px 1px rgba(87,87,87,0.2);z-index:100;top:auto !important}div#pager pre{line-height:1.21429em;color:#000;background-color:#f7f7f7;padding:.4em}div#pager #pager-button-area{position:absolute;top:8px;right:20px}div#pager #pager-contents{position:relative;overflow:auto;width:100%;height:100%}div#pager #pager-contents #pager-container{position:relative;padding:15px 0;box-sizing:border-box;-moz-box-sizing:border-box;-webkit-box-sizing:border-box}div#pager .ui-resizable-handle{top:0;height:8px;background:#f7f7f7;border-top:1px solid #cfcfcf;border-bottom:1px solid #cfcfcf}div#pager .ui-resizable-handle::after{content:'';top:2px;left:50%;height:3px;width:30px;margin-left:-15px;position:absolute;border-top:1px solid #cfcfcf}.quickhelp{display:-webkit-box;-webkit-box-orient:horizontal;-webkit-box-align:stretch;display:-moz-box;-moz-box-orient:horizontal;-moz-box-align:stretch;display:box;box-orient:horizontal;box-align:stretch;display:flex;flex-direction:row;align-items:stretch}.shortcut_key{display:inline-block;width:20ex;text-align:right;font-family:monospace}.shortcut_descr{display:inline-block;-webkit-box-flex:1;-moz-box-flex:1;box-flex:1;flex:1}span.save_widget{margin-top:6px}span.save_widget span.filename{height:1em;line-height:1em;padding:3px;margin-left:16px;border:none;font-size:146.5%;border-radius:2px}span.save_widget span.filename:hover{background-color:#e6e6e6}span.checkpoint_status,span.autosave_status{font-size:small}@media (max-width:767px){span.save_widget{font-size:small}span.checkpoint_status,span.autosave_status{display:none}}@media (min-width:768px) and (max-width:991px){span.checkpoint_status{display:none}span.autosave_status{font-size:x-small}}.toolbar{padding:0;margin-left:-5px;margin-top:2px;margin-bottom:5px;box-sizing:border-box;-moz-box-sizing:border-box;-webkit-box-sizing:border-box}.toolbar select,.toolbar label{width:auto;vertical-align:middle;margin-right:2px;margin-bottom:0;display:inline;font-size:92%;margin-left:.3em;margin-right:.3em;padding:0;padding-top:3px}.toolbar .btn{padding:2px 8px}.toolbar .btn-group{margin-top:0;margin-left:5px}#maintoolbar{margin-bottom:-3px;margin-top:-8px;border:0;min-height:27px;margin-left:0;padding-top:11px;padding-bottom:3px}#maintoolbar .navbar-text{float:none;vertical-align:middle;text-align:right;margin-left:5px;margin-right:0;margin-top:0}.select-xs{height:24px}@-moz-keyframes fadeOut{from{opacity:1}to{opacity:0}}@-webkit-keyframes fadeOut{from{opacity:1}to{opacity:0}}@-moz-keyframes fadeIn{from{opacity:0}to{opacity:1}}@-webkit-keyframes fadeIn{from{opacity:0}to{opacity:1}}.bigtooltip{overflow:auto;height:200px;-webkit-transition-property:height;-webkit-transition-duration:500ms;-moz-transition-property:height;-moz-transition-duration:500ms;transition-property:height;transition-duration:500ms}.smalltooltip{-webkit-transition-property:height;-webkit-transition-duration:500ms;-moz-transition-property:height;-moz-transition-duration:500ms;transition-property:height;transition-duration:500ms;text-overflow:ellipsis;overflow:hidden;height:80px}.tooltipbuttons{position:absolute;padding-right:15px;top:0;right:0}.tooltiptext{padding-right:30px}.ipython_tooltip{max-width:700px;-webkit-animation:fadeOut 400ms;-moz-animation:fadeOut 400ms;animation:fadeOut 400ms;-webkit-animation:fadeIn 400ms;-moz-animation:fadeIn 400ms;animation:fadeIn 400ms;vertical-align:middle;background-color:#f7f7f7;overflow:visible;border:#ababab 1px solid;outline:none;padding:3px;margin:0;padding-left:7px;font-family:monospace;min-height:50px;-moz-box-shadow:0 6px 10px -1px #adadad;-webkit-box-shadow:0 6px 10px -1px #adadad;box-shadow:0 6px 10px -1px #adadad;border-radius:2px;position:absolute;z-index:1000}.ipython_tooltip a{float:right}.ipython_tooltip .tooltiptext pre{border:0;border-radius:0;font-size:100%;background-color:#f7f7f7}.pretooltiparrow{left:0;margin:0;top:-16px;width:40px;height:16px;overflow:hidden;position:absolute}.pretooltiparrow:before{background-color:#f7f7f7;border:1px #ababab solid;z-index:11;content:\"\";position:absolute;left:15px;top:10px;width:25px;height:25px;-webkit-transform:rotate(45deg);-moz-transform:rotate(45deg);-ms-transform:rotate(45deg);-o-transform:rotate(45deg)}.terminal-app{background:#eee}.terminal-app #header{background:#fff;-webkit-box-shadow:0 0 12px 1px rgba(87,87,87,0.2);box-shadow:0 0 12px 1px rgba(87,87,87,0.2)}.terminal-app .terminal{float:left;font-family:monospace;color:white;background:black;padding:.4em;border-radius:2px;-webkit-box-shadow:0 0 12px 1px rgba(87,87,87,0.4);box-shadow:0 0 12px 1px rgba(87,87,87,0.4)}.terminal-app .terminal,.terminal-app .terminal dummy-screen{line-height:1em;font-size:14px}.terminal-app .terminal-cursor{color:black;background:white}.terminal-app #terminado-container{margin-top:20px}/*# sourceMappingURL=style.min.css.map */\n    </style>\n<style type=\"text/css\">\n    .highlight .hll { background-color: #ffffcc }\n.highlight  { background: #f8f8f8; }\n.highlight .c { color: #408080; font-style: italic } /* Comment */\n.highlight .err { border: 1px solid #FF0000 } /* Error */\n.highlight .k { color: #008000; font-weight: bold } /* Keyword */\n.highlight .o { color: #666666 } /* Operator */\n.highlight .cm { color: #408080; font-style: italic } /* Comment.Multiline */\n.highlight .cp { color: #BC7A00 } /* Comment.Preproc */\n.highlight .c1 { color: #408080; font-style: italic } /* Comment.Single */\n.highlight .cs { color: #408080; font-style: italic } /* Comment.Special */\n.highlight .gd { color: #A00000 } /* Generic.Deleted */\n.highlight .ge { font-style: italic } /* Generic.Emph */\n.highlight .gr { color: #FF0000 } /* Generic.Error */\n.highlight .gh { color: #000080; font-weight: bold } /* Generic.Heading */\n.highlight .gi { color: #00A000 } /* Generic.Inserted */\n.highlight .go { color: #888888 } /* Generic.Output */\n.highlight .gp { color: #000080; font-weight: bold } /* Generic.Prompt */\n.highlight .gs { font-weight: bold } /* Generic.Strong */\n.highlight .gu { color: #800080; font-weight: bold } /* Generic.Subheading */\n.highlight .gt { color: #0044DD } /* Generic.Traceback */\n.highlight .kc { color: #008000; font-weight: bold } /* Keyword.Constant */\n.highlight .kd { color: #008000; font-weight: bold } /* Keyword.Declaration */\n.highlight .kn { color: #008000; font-weight: bold } /* Keyword.Namespace */\n.highlight .kp { color: #008000 } /* Keyword.Pseudo */\n.highlight .kr { color: #008000; font-weight: bold } /* Keyword.Reserved */\n.highlight .kt { color: #B00040 } /* Keyword.Type */\n.highlight .m { color: #666666 } /* Literal.Number */\n.highlight .s { color: #BA2121 } /* Literal.String */\n.highlight .na { color: #7D9029 } /* Name.Attribute */\n.highlight .nb { color: #008000 } /* Name.Builtin */\n.highlight .nc { color: #0000FF; font-weight: bold } /* Name.Class */\n.highlight .no { color: #880000 } /* Name.Constant */\n.highlight .nd { color: #AA22FF } /* Name.Decorator */\n.highlight .ni { color: #999999; font-weight: bold } /* Name.Entity */\n.highlight .ne { color: #D2413A; font-weight: bold } /* Name.Exception */\n.highlight .nf { color: #0000FF } /* Name.Function */\n.highlight .nl { color: #A0A000 } /* Name.Label */\n.highlight .nn { color: #0000FF; font-weight: bold } /* Name.Namespace */\n.highlight .nt { color: #008000; font-weight: bold } /* Name.Tag */\n.highlight .nv { color: #19177C } /* Name.Variable */\n.highlight .ow { color: #AA22FF; font-weight: bold } /* Operator.Word */\n.highlight .w { color: #bbbbbb } /* Text.Whitespace */\n.highlight .mb { color: #666666 } /* Literal.Number.Bin */\n.highlight .mf { color: #666666 } /* Literal.Number.Float */\n.highlight .mh { color: #666666 } /* Literal.Number.Hex */\n.highlight .mi { color: #666666 } /* Literal.Number.Integer */\n.highlight .mo { color: #666666 } /* Literal.Number.Oct */\n.highlight .sb { color: #BA2121 } /* Literal.String.Backtick */\n.highlight .sc { color: #BA2121 } /* Literal.String.Char */\n.highlight .sd { color: #BA2121; font-style: italic } /* Literal.String.Doc */\n.highlight .s2 { color: #BA2121 } /* Literal.String.Double */\n.highlight .se { color: #BB6622; font-weight: bold } /* Literal.String.Escape */\n.highlight .sh { color: #BA2121 } /* Literal.String.Heredoc */\n.highlight .si { color: #BB6688; font-weight: bold } /* Literal.String.Interpol */\n.highlight .sx { color: #008000 } /* Literal.String.Other */\n.highlight .sr { color: #BB6688 } /* Literal.String.Regex */\n.highlight .s1 { color: #BA2121 } /* Literal.String.Single */\n.highlight .ss { color: #19177C } /* Literal.String.Symbol */\n.highlight .bp { color: #008000 } /* Name.Builtin.Pseudo */\n.highlight .vc { color: #19177C } /* Name.Variable.Class */\n.highlight .vg { color: #19177C } /* Name.Variable.Global */\n.highlight .vi { color: #19177C } /* Name.Variable.Instance */\n.highlight .il { color: #666666 } /* Literal.Number.Integer.Long */\n    </style>\n\n\n<style type=\"text/css\">\n/* Overrides of notebook CSS for static HTML export */\nbody {\n  overflow: visible;\n  padding: 8px;\n}\n\ndiv#notebook {\n  overflow: visible;\n  border-top: none;\n}\n\n@media print {\n  div.cell {\n    display: block;\n    page-break-inside: avoid;\n  } \n  div.output_wrapper { \n    display: block;\n    page-break-inside: avoid; \n  }\n  div.output { \n    display: block;\n    page-break-inside: avoid; \n  }\n}\n</style>\n\n<!-- Custom stylesheet, it must be in the same directory as the html file -->\n<link rel=\"stylesheet\" href=\"custom.css\">\n\n<!-- Loading mathjax macro -->\n<!-- Load mathjax -->\n    <script src=\"https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS_HTML\"></script>\n    <!-- MathJax configuration -->\n    <script type=\"text/x-mathjax-config\">\n    MathJax.Hub.Config({\n        tex2jax: {\n            inlineMath: [ ['$','$'], [\"\\\\(\",\"\\\\)\"] ],\n            displayMath: [ ['$$','$$'], [\"\\\\[\",\"\\\\]\"] ],\n            processEscapes: true,\n            processEnvironments: true\n        },\n        // Center justify equations in code and markdown cells. Elsewhere\n        // we use CSS to left justify single line equations in code cells.\n        displayAlign: 'center',\n        \"HTML-CSS\": {\n            styles: {'.MathJax_Display': {\"margin\": 0}},\n            linebreaks: { automatic: true }\n        }\n    });\n    </script>\n    <!-- End of mathjax configuration -->\n\n</head>\n<body>\n  <div tabindex=\"-1\" id=\"notebook\" class=\"border-box-sizing\">\n    <div class=\"container\" id=\"notebook-container\">\n\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\">\n</div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h1 id=\"Cadabra-inside-IPython/Jupyter\">Cadabra inside IPython/Jupyter<a class=\"anchor-link\" href=\"#Cadabra-inside-IPython/Jupyter\">&#182;</a></h1><p>This is a short and simple Jupyter notebook shows how to use Cadabra functionality from with Jupyter. The first thing to do is to import the cadabra2 module. To save typing, we will import everything into the global namespace.</p>\n\n</div>\n</div>\n</div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In&nbsp;[1]:</div>\n<div class=\"inner_cell\">\n    <div class=\"input_area\">\n<div class=\" highlight hl-ipython2\"><pre><span class=\"kn\">from</span> <span class=\"nn\">cadabra2</span> <span class=\"kn\">import</span> <span class=\"o\">*</span>\n<span class=\"kn\">from</span> <span class=\"nn\">IPython.display</span> <span class=\"kn\">import</span> <span class=\"n\">display</span><span class=\"p\">,</span> <span class=\"n\">Math</span><span class=\"p\">,</span> <span class=\"n\">Latex</span>\n</pre></div>\n\n</div>\n</div>\n</div>\n\n</div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\">\n</div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>Expressions are declared by typing them as standard LaTeX, and feeding that into the Ex object. The result is a standard Python object.</p>\n\n</div>\n</div>\n</div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In&nbsp;[9]:</div>\n<div class=\"inner_cell\">\n    <div class=\"input_area\">\n<div class=\" highlight hl-ipython2\"><pre><span class=\"n\">ex</span><span class=\"o\">=</span><span class=\"n\">Ex</span><span class=\"p\">(</span><span class=\"s\">r&quot;A_{m n} B^{m n}&quot;</span><span class=\"p\">)</span>\n</pre></div>\n\n</div>\n</div>\n</div>\n\n</div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\">\n</div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>Printing is still a bit messy in IPython/Jupyter, but you can get the nicely typeset form of the expression using the following:</p>\n\n</div>\n</div>\n</div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In&nbsp;[10]:</div>\n<div class=\"inner_cell\">\n    <div class=\"input_area\">\n<div class=\" highlight hl-ipython2\"><pre><span class=\"n\">display</span><span class=\"p\">(</span><span class=\"n\">Math</span><span class=\"p\">(</span><span class=\"nb\">str</span><span class=\"p\">(</span><span class=\"n\">ex</span><span class=\"p\">)))</span>\n</pre></div>\n\n</div>\n</div>\n</div>\n\n<div class=\"output_wrapper\">\n<div class=\"output\">\n\n\n<div class=\"output_area\"><div class=\"prompt\"></div>\n\n\n<div class=\"output_latex output_subarea \">\n$$A_{m n} B^{m n}$$\n</div>\n\n</div>\n\n</div>\n</div>\n\n</div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\">\n</div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>Properties get assigned to symbols or patterns by using their Cadabra name,</p>\n\n</div>\n</div>\n</div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In&nbsp;[12]:</div>\n<div class=\"inner_cell\">\n    <div class=\"input_area\">\n<div class=\" highlight hl-ipython2\"><pre><span class=\"n\">Symmetric</span><span class=\"p\">(</span><span class=\"n\">Ex</span><span class=\"p\">(</span><span class=\"s\">r&quot;A_{m n}&quot;</span><span class=\"p\">))</span>\n<span class=\"n\">AntiSymmetric</span><span class=\"p\">(</span><span class=\"n\">Ex</span><span class=\"p\">(</span><span class=\"s\">r&quot;B_{m n&quot;</span><span class=\"p\">))</span>\n</pre></div>\n\n</div>\n</div>\n</div>\n\n<div class=\"output_wrapper\">\n<div class=\"output\">\n\n\n<div class=\"output_area\"><div class=\"prompt output_prompt\">Out[12]:</div>\n\n\n<div class=\"output_text output_subarea output_execute_result\">\n<pre>Property::repr: AntiSymmetric</pre>\n</div>\n\n</div>\n\n</div>\n</div>\n\n</div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\">\n</div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>Cadabra algorithms are ordinary python functions. They always act on the expression that you pass it, and modify it in-place. Here's an example: the contraction of an antisymmetric and a symmetric tensor is zero:</p>\n\n</div>\n</div>\n</div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In&nbsp;[17]:</div>\n<div class=\"inner_cell\">\n    <div class=\"input_area\">\n<div class=\" highlight hl-ipython2\"><pre><span class=\"n\">display</span><span class=\"p\">(</span><span class=\"n\">Math</span><span class=\"p\">(</span><span class=\"nb\">str</span><span class=\"p\">(</span><span class=\"n\">canonicalise</span><span class=\"p\">(</span><span class=\"n\">ex</span><span class=\"p\">))))</span>\n</pre></div>\n\n</div>\n</div>\n</div>\n\n<div class=\"output_wrapper\">\n<div class=\"output\">\n\n\n<div class=\"output_area\"><div class=\"prompt\"></div>\n\n\n<div class=\"output_latex output_subarea \">\n$$C_{m}\\,^{p} D_{p n} B^{m n}$$\n</div>\n\n</div>\n\n</div>\n</div>\n\n</div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\">\n</div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>Let's do another example, with substitution. Note how indices get relabelled automatically.</p>\n\n</div>\n</div>\n</div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In&nbsp;[20]:</div>\n<div class=\"inner_cell\">\n    <div class=\"input_area\">\n<div class=\" highlight hl-ipython2\"><pre><span class=\"n\">Indices</span><span class=\"p\">(</span><span class=\"n\">Ex</span><span class=\"p\">(</span><span class=\"s\">r&quot;{m,n,p,q,r,s,t}&quot;</span><span class=\"p\">))</span>\n<span class=\"n\">ex</span><span class=\"o\">=</span><span class=\"n\">Ex</span><span class=\"p\">(</span><span class=\"s\">r&quot;A_{m n} B^{m p} C_{p q}&quot;</span><span class=\"p\">)</span>\n<span class=\"n\">display</span><span class=\"p\">(</span><span class=\"n\">Math</span><span class=\"p\">(</span><span class=\"nb\">str</span><span class=\"p\">(</span><span class=\"n\">substitute</span><span class=\"p\">(</span><span class=\"n\">ex</span><span class=\"p\">,</span> <span class=\"n\">Ex</span><span class=\"p\">(</span><span class=\"s\">r&quot;A_{m n} -&gt; D_{m q} D^{q}_{n}&quot;</span><span class=\"p\">)))))</span>\n</pre></div>\n\n</div>\n</div>\n</div>\n\n<div class=\"output_wrapper\">\n<div class=\"output\">\n\n\n<div class=\"output_area\"><div class=\"prompt\"></div>\n\n\n<div class=\"output_latex output_subarea \">\n$$D_{m r} D^{r}\\,_{n} B^{m p} C_{p q}$$\n</div>\n\n</div>\n\n</div>\n</div>\n\n</div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\">\n</div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>If you are interested in more of this, get in touch by emailing me at info@cadabra.science !</p>\n\n</div>\n</div>\n</div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In&nbsp;[&nbsp;]:</div>\n<div class=\"inner_cell\">\n    <div class=\"input_area\">\n<div class=\" highlight hl-ipython2\"><pre> \n</pre></div>\n\n</div>\n</div>\n</div>\n\n</div>\n    </div>\n  </div>\n</body>\n</html>\n"
  },
  {
    "path": "web2/cadabra2/source/static/fonts/Bright/OFL-FAQ.txt",
    "content": "OFL FAQ - Frequently Asked Questions about the SIL Open Font License (OFL)\nVersion 1.1 - 26 February 2007\n(See http://scripts.sil.org/OFL for updates)\n\n\n1  ABOUT USING AND DISTRIBUTING FONTS LICENSED UNDER THE OFL\n\n1.1  Can I use the fonts in any publication, even embedded in the file?\nYes. You may use them like most other fonts, but unlike some fonts you may include an embedded subset of the fonts in your document. Such use does not require you to include this license or other files (listed in OFL condition 2), nor does it require any type of acknowledgement within the publication. Some mention of the font name within the publication information (such as in a colophon) is usually appreciated. If you wish to include the complete font as a separate file, you should distribute the full font package, including all existing acknowledgements, and comply with the OFL conditions. Of course, referencing or embedding an OFL font in any document does not change the license of the document itself. The requirement for fonts to remain under the OFL does not apply to any document created using the fonts and their derivatives. Similarly, creating any kind of graphic using a font under OFL does not make the resulting artwork subject to the OFL.\n\n1.2  Can I make web pages using these fonts?\nYes! Go ahead! Using CSS (Cascading Style Sheets) is recommended.\n\n1.3  Can I make the fonts available to others from my web site?\nYes, as long as you meet the conditions of the license (do not sell by itself, include the necessary files, rename Modified Versions, do not abuse the Author(s)' name(s) and do not sublicense).\n\n1.4  Can the fonts be included with Free/Libre and Open Source Software collections such as GNU/Linux and BSD distributions?\nYes! Fonts licensed under the OFL can be freely aggregated with software under FLOSS (Free/Libre and Open Source Software) licenses. Since fonts are much more useful aggregated to than merged with existing software, possible incompatibility with existing software licenses is not a problem. You can also repackage the fonts and the accompanying components in a .rpm or .deb package and include them in distro CD/DVDs and online repositories.\n\n1.5  I want to distribute the fonts with my program. Does this mean my program also has to be free and open source software?\nNo. Only the portions based on the font software are required to be released under the OFL. The intent of the license is to allow aggregation or bundling with software under restricted licensing as well.\n\n1.6  Can I include the fonts on a CD of freeware or commercial fonts?\nYes, as long some other font or software is also on the disk, so the OFL font is not sold by itself.\n\n1.7  Can I sell a software package that includes these fonts?\nYes, you can do this with both the Original Version and a Modified Version. Examples of bundling made possible by the OFL would include: word processors, design and publishing applications, training and educational software, edutainment software, etc.\n\n1.8  Why won't the OFL let me sell the fonts alone?\nThe intent is to keep people from making money by simply redistributing the fonts. The only people who ought to profit directly from the fonts should be the original authors, and those authors have kindly given up potential direct income to distribute their fonts under the OFL. Please honor and respect their contribution!\n\n1.9  I've come across a font released under the OFL. How can I easily get more information about the Original Version? How can I know where it stands compared to the Original Version or other Modified Versions?\nConsult the copyright statement(s) in the license for ways to contact the original authors. Consult the FONTLOG for information on how the font differs from the Original Version, and get in touch with the various contributors via the information in the acknowledgment section. Please consider using the Original Versions of the fonts whenever possible.\n\n1.10  What do you mean in condition 4? Can you provide examples of abusive promotion / endorsement / advertisement vs. normal acknowledgement?\nThe intent is that the goodwill and reputation of the author(s) should not be used in a way that makes it sound like the original author(s) endorse or approve of a specific Modified Version or software bundle. For example, it would not be right to advertise a word processor by naming the author(s) in a listing of software features, or to promote a Modified Version on a web site by saying \"designed by ...\". However, it would be appropriate to acknowledge the author(s) if your software package has a list of people who deserve thanks. We realize that this can seem to be a gray area, but the standard used to judge an acknowledgement is that if the acknowledgement benefits the author(s) it is allowed, but if it primarily benefits other parties, or could reflect poorly on the author(s), then it is not.\n\n\n2  ABOUT MODIFYING OFL LICENSED FONTS\n\n2.1  Can I change the fonts? Are there any limitations to what things I can and cannot change?\nYou are allowed to change anything, as long as such changes do not violate the terms of the license. In other words, you are not allowed to remove the copyright statement(s) from the font, but you could add additional information into it that covers your contribution.\n\n2.2  I have a font that needs a few extra glyphs - can I take them from an OFL licensed font and copy them into mine?\nYes, but if you distribute that font to others it must be under the OFL, and include the information mentioned in condition 2 of the license.\n\n2.3  Can I charge people for my additional work? In other words, if I add a bunch of special glyphs and/or OpenType/Graphite code, can I sell the enhanced font?\nNot by itself. Derivative fonts must be released under the OFL and cannot be sold by themselves. It is permitted, however, to include them in a larger software package (such as text editors, office suites or operating systems), even if the larger package is sold. In that case, you are strongly encouraged, but not required, to also make that derived font easily and freely available outside of the larger package.\n\n2.4  Can I pay someone to enhance the fonts for my use and distribution?\nYes. This is a good way to fund the further development of the fonts. Keep in mind, however, that if the font is distributed to others it must be under the OFL. You won't be able to recover your investment by exclusively selling the font, but you will be making a valuable contribution to the community. Please remember how you have benefitted from the contributions of others.\n\n2.5  I need to make substantial revisions to the font to make it work with my program. It will be a lot of work, and a big investment, and I want to be sure that it can only be distributed with my program. Can I restrict its use?\nNo. If you redistribute a Modified Version of the font it must be under the OFL. You may not restrict it in any way. This is intended to ensure that all released improvements to the fonts become available to everyone. But you will likely get an edge over competitors by being the first to distribute a bundle with the enhancements. Again, please remember how you have benefitted from the contributions of others.\n\n2.6  Do I have to make any derivative fonts (including source files, build scripts, documentation, etc.) publicly available?\nNo, but please do share your improvements with others. You may find that you receive more than what you gave in return.\n\n2.7  Why can't I use the Reserved Font Name(s) in my derivative font names? I'd like people to know where the design came from.\nThe best way to acknowledge the source of the design is to thank the original authors and any other contributors in the files that are distributed with your revised font (although no acknowledgement is required). The FONTLOG is a natural place to do this. Reserved Font Name(s) ensure that the only fonts that have the original names are the unmodified Original Versions. This allows designers to maintain artistic integrity while allowing collaboration to happen. It eliminates potential confusion and name conflicts. When choosing a name be creative and avoid names that reuse almost all the same letters in the same order or sound like the original. Keep in mind that the Copyright Holder(s) can allow a specific trusted partner to use Reserved Font Name(s) through a separate written agreement.\n\n2.8  What do you mean by \"primary name as presented to the user\"? Are you referring to the font menu name?\nYes, the requirement to change the visible name used to differentiate the font from others applies to the font menu name and other mechanisms to specify a font in a document. It would be fine, for example, to keep a text reference to the original fonts in the description field, in your modified source file or in documentation provided alongside your derivative as long as no one could be confused that your modified source is the original. But you cannot use the Reserved Font Names in any way to identify the font to the user (unless the Copyright Holder(s) allow(s) it through a separate agreement; see section 2.7). Users who install derivatives (\"Modified Versions\") on their systems should not see any of the original names (\"Reserved Font Names\") in their font menus, for example. Again, this is to ensure that users are not confused and do not mistake a font for another and so expect features only another derivative or the Original Version can actually offer. Ultimately, creating name conflicts will cause many problems for the users as well as for the designer of both the Original and Modified versions, so please think ahead and find a good name for your own derivative. Font substitution systems like fontconfig, or application-level font fallback configuration within OpenOffice.org or Scribus, will also get very confused if the name of the font they are configured to substitute to actually refers to another physical font on the user's hard drive. It will help everyone if Original Versions and Modified Versions can easily be distinguished from one another and from other derivatives. The substitution mechanism itself is outside the scope of the license. Users can always manually change a font reference in a document or set up some kind of substitution at a higher level but at the lower level the fonts themselves have to respect the Reserved Font Name(s) requirement to prevent ambiguity. If a substitution is currently active the user should be aware of it.\n\n2.9  Am I not allowed to use any part of the Reserved Font Names?\nYou may not use the words of the font names, but you would be allowed to use parts of words, as long as you do not use any word from the Reserved Font Names entirely. We do not recommend using parts of words because of potential confusion, but it is allowed. For example, if \"Foobar\" was a Reserved Font Name, you would be allowed to use \"Foo\" or \"bar\", although we would not recommend it. Such an unfortunate choice would confuse the users of your fonts as well as make it harder for other designers to contribute.\n\n2.10  So what should I, as an author, identify as Reserved Font Names?\nOriginal authors are encouraged to name their fonts using clear, distinct names, and only declare the unique parts of the name as Reserved Font Names. For example, the author of a font called \"Foobar Sans\" would declare \"Foobar\" as a Reserved Font Name, but not \"Sans\", as that is a common typographical term, and may be a useful word to use in a derivative font name. Reserved Font Names should also be single words. A font called \"Flowing River\" should have Reserved Font Names \"Flowing\" and \"River\", not \"Flowing River\".\n\n2.11  Do I, as an author, have to identify any Reserved Font Names?\nNo, but we strongly encourage you to do so. This is to avoid confusion between your work and Modified versions. You may, however, give certain trusted parties the right to use any of your Reserved Font Names through separate written agreements. For example, even if \"Foobar\" is a RFN, you could write up an agreement to give company \"XYZ\" the right to distribute a modified version with a name that includes \"Foobar\". This allows for freedom without confusion.\n\n2.12  Are any names (such as the main font name) reserved by default?\nNo. That is a change to the license as of version 1.1. If you want any names to be Reserved Font Names, they must be specified after the copyright statement(s).\n\n2.13  What is this FONTLOG thing exactly?\nIt has three purposes: 1) to provide basic information on the font to users and other developers, 2) to document changes that have been made to the font or accompanying files, either by the original authors or others, and 3) to provide a place to acknowledge the authors and other contributors. Please use it! See below for details on how changes should be noted.\n\n2.14  Am I required to update the FONTLOG?\nNo, but users, designers and other developers might get very frustrated at you if you don't! People need to know how derivative fonts differ from the original, and how to take advantage of the changes, or build on them.\n\n\n3  ABOUT THE FONTLOG\n\nThe FONTLOG can take a variety of formats, but should include these four sections:\n\n3.1  FONTLOG for <FontFamilyName>\nThis file provides detailed information on the <FontFamilyName> font software. This information should be distributed along with the <FontFamilyName> fonts and any derivative works.\n\n3.2  Basic Font Information\n(Here is where you would describe the purpose and brief specifications for the font project, and where users can find more detailed documentation. It can also include references to how changes can be contributed back to the Original Version. You may also wish to include a short guide to the design, or a reference to such a document.)\n\n3.3  ChangeLog\n(This should list both major and minor changes, most recent first. Here are some examples:)\n\n7 February 2007 (Pat Johnson) <NewFontFamilyName> Version 1.3\n- Added Greek and Cyrillic glyphs\n- Released as \"<NewFontFamilyName>\"\n\n7 March 2006 (Fred Foobar) <NewFontFamilyName> Version 1.2\n- Tweaked contextual behaviours\n- Released as \"<NewFontFamilyName>\"\n\n1 Feb 2005 (Jane Doe) <NewFontFamilyName> Version 1.1\n- Improved build script performance and verbosity\n- Extended the smart code documentation\n- Corrected minor typos in the documentation\n- Fixed position of combining inverted breve below (U+032F)\n- Added OpenType/Graphite smart code for Armenian\n- Added Armenian glyphs (U+0531 -> U+0587) \n- Released as \"<NewFontFamilyName>\"\n\n1 Jan 2005 (Joe Smith) <FontFamilyName> Version 1.0\n- Initial release of font \"<FontFamilyName>\"\n\n3.4  Acknowledgements\n(Here is where contributors can be acknowledged. \n\nIf you make modifications be sure to add your name (N), email (E), web-address (W) and description (D). This list is sorted by last name in alphabetical order.)\n\nN: Jane Doe\nE: jane@university.edu\nW: http://art.university.edu/projects/fonts\nD: Contributor - Armenian glyphs and code\n\nN: Fred Foobar\nE: fred@foobar.org\nW: http://foobar.org\nD: Contributor - misc Graphite fixes\n\nN: Pat Johnson\nE: pat@fontstudio.org\nW: http://pat.fontstudio.org\nD: Designer - Greek & Cyrillic glyphs based on Roman design\n\nN: Tom Parker\nE: tom@company.com\nW: http://www.company.com/tom/projects/fonts\nD: Engineer - original smart font code\n\nN: Joe Smith\nE: joe@fontstudio.org\nW: http://joe.fontstudio.org\nD: Designer - original Roman glyphs\n\n(Original authors can also include information here about their organization.)\n\n\n4  ABOUT MAKING CONTRIBUTIONS\n\n4.1  Why should I contribute my changes back to the original authors?\nIt would benefit many people if you contributed back to what you've received. Providing your contributions and improvements to the fonts and other components (data files, source code, build scripts, documentation, etc.) could be a tremendous help and would encourage others to contribute as well and 'give back', which means you will have an opportunity to benefit from other people's contributions as well. Sometimes maintaining your own separate version takes more effort than merging back with the original. Be aware that any contributions, however, must be either your own original creation or work that you own, and you may be asked to affirm that clearly when you contribute.\n\n4.2  I've made some very nice improvements to the font, will you consider adopting them and putting them into future Original Versions?\nMost authors would be very happy to receive such contributions. Keep in mind that it is unlikely that they would want to incorporate major changes that would require additional work on their end. Any contributions would likely need to be made for all the fonts in a family and match the overall design and style. Authors are encouraged to include a guide to the design with the fonts. It would also help to have contributions submitted as patches or clearly marked changes (the use of smart source revision control systems like subversion, svk or bzr is a good idea). Examples of useful contributions are bug fixes, additional glyphs, stylistic alternates (and the smart font code to access them) or improved hinting.\n\n4.3  How can I financially support the development of OFL fonts?\nIt is likely that most authors of OFL fonts would accept financial contributions - contact them for instructions on how to do this. Such contributions would support future development. You can also pay for others to enhance the fonts and contribute the results back to the original authors for inclusion in the Original Version.\n\n\n5  ABOUT THE LICENSE\n\n5.1  I see that this is version 1.1 of the license. Will there be later changes?\nVersion 1.1 is the first minor revision of the OFL. We are confident that version 1.1 will meet most needs, but are open to future improvements. Any revisions would be for future font releases, and previously existing licenses would remain in effect. No retroactive changes are possible, although the Copyright Holder(s) can re-release the font under a revised OFL. All versions will be available on our web site: http://scripts.sil.org/OFL.\n\n5.2  Can I use the SIL Open Font License for my own fonts?\nYes! We heartily encourage anyone to use the OFL to distribute their own original fonts. It is a carefully constructed license that allows great freedom along with enough artistic integrity protection for the work of the authors as well as clear rules for other contributors and those who redistribute the fonts. Some additional information about using the OFL is included at the end of this FAQ.\n\n5.3  Does this license restrict the rights of the Copyright Holder(s)?\nNo. The Copyright Holder(s) still retain(s) all the rights to their creation; they are only releasing a portion of it for use in a specific way. For example, the Copyright Holder(s) may choose to release a 'basic' version of their font under the OFL, but sell a restricted 'enhanced' version. Only the Copyright Holder(s) can do this.\n\n5.4 Is the OFL a contract or a license?\nThe OFL is a license and not a contract and so does not require you to sign it to have legal validity. By using, modifying and redistributing components under the OFL you indicate that you accept the license.\n\n5.5 How about translating the license and the FAQ into other languages?\nSIL certainly recognises the need for people who are not familiar with English to be able to understand the OFL and this FAQ better in their own language. Making the license very clear and readable is a key goal of the OFL.\n\nIf you are an experienced translator, you are very welcome to help by translating the OFL and its FAQ so that designers and users in your language community can understand the license better. But only the original English version of the license has legal value and has been approved by the community. Translations do not count as legal substitutes and should only serve as a way to explain the original license. SIL - as the author and steward of the license for the community at large - does not approve any translation of the OFL as legally valid because even small translation ambiguities could be abused and create problems.\n\nWe give permission to publish unofficial translations into other languages provided that they comply with the following guidelines:\n\n- put the following disclaimer in both English and the target language stating clearly that the translation is unofficial:\n\n\"This is an unofficial translation of the SIL Open Font License into $language. It was not published by SIL International, and does not legally state the distribution terms for fonts that use the OFL. A release under the OFL is only valid when using the original English text.\n\nHowever, we recognize that this unofficial translation will help users and designers not familiar with English to understand the SIL OFL better and make it easier to use and release font families under this collaborative font design model. We encourage designers who consider releasing their creation under the OFL to read the FAQ in their own language if it is available.\n \nPlease go to http://scripts.sil.org/OFL for the official version of the license and the accompanying FAQ.\"\n\n- keep your unofficial translation current and update it at our request if needed, for example if there is any ambiguity which could lead to confusion.  \n\nIf you start such a unofficial translation effort of the OFL and its accompanying FAQ please let us know, thank you.\n\n\n6  ABOUT SIL INTERNATIONAL\n\n6.1  Who is SIL International and what does it do?\nSIL International is a worldwide faith-based education and development organization (NGO) that studies, documents, and assists in developing the world's lesser-known languages through literacy, linguistics, translation, and other academic disciplines. SIL makes its services available to all without regard to religious belief, political ideology, gender, race, or ethnic background. SIL's members and volunteers share a Christian commitment.\n\n6.2  What does this have to do with font licensing?\nThe ability to read, write, type and publish in one's own language is one of the most critical needs for millions of people around the world. This requires fonts that are widely available and support lesser-known languages. SIL develops - and encourages others to develop - a complete stack of writing systems implementation components available under open licenses. This open stack includes input methods, smart fonts, smart rendering libraries and smart applications. There has been a need for a common open license that is specifically applicable to fonts and related software (a crucial component of this stack) so SIL developed the SIL Open Font License with the help of the FLOSS community.\n\n6.3  How can I contact SIL?\nOur main web site is: http://www.sil.org/\nOur site about complex scripts is: http://scripts.sil.org/\nInformation about this license (including contact email information) is at: http://scripts.sil.org/OFL\n\n\n7  ABOUT USING THE OFL FOR YOUR ORIGINAL FONTS\n\nIf you want to release your fonts under the OFL, you only need to do the following:\n\n7.1  Put your copyright and reserved font names information in the beginning of the main OFL file.\n7.2  Put your copyright and the OFL references in your various font files (such as in the copyright, license and description fields) and in your other components (build scripts, glyph databases, documentation, rendering samples, etc).\n7.3  Write an initial FONTLOG for your font and include it in the release package.\n7.4  Include the OFL in your release package.\n7.5  We also highly recommend you include the relevant practical documentation on the license by putting the OFL-FAQ in your package.\n7.6  If you wish, you can use the OFL Graphics on your web page.\n\n\n\nThat's all. If you have any more questions please get in touch with us.\n\n\n"
  },
  {
    "path": "web2/cadabra2/source/static/fonts/Bright/OFL.txt",
    "content": "Copyright (C) Authors of original metafont fonts:\nDonald Ervin Knuth (cm, concrete fonts)\n1995, 1996, 1997 J\"org Knappen, 1990, 1992 Norbert Schwarz (ec fonts)\n1992-2006 A.Khodulev, O.Lapko, A.Berdnikov, V.Volovich (lh fonts)\n1997-2005 Claudio Beccari (cb greek fonts)\n2002 FUKUI Rei (tipa fonts)\n2003-2005 Han The Thanh (Vietnamese fonts)\n1996-2005 Walter Schmidt (cmbright fonts)\n\nCopyright (C) 2003-2009, Andrey V. Panov (panov@canopus.iacp.dvo.ru),\nwith Reserved Font Family Name \"Computer Modern Unicode fonts\".\n\nThis Font Software is licensed under the SIL Open Font License, Version 1.1.\nThis license is copied below, and is also available with a FAQ at:\nhttp://scripts.sil.org/OFL\n\n\n-----------------------------------------------------------\nSIL OPEN FONT LICENSE Version 1.1 - 26 February 2007\n-----------------------------------------------------------\n\nPREAMBLE\nThe goals of the Open Font License (OFL) are to stimulate worldwide\ndevelopment of collaborative font projects, to support the font creation\nefforts of academic and linguistic communities, and to provide a free and\nopen framework in which fonts may be shared and improved in partnership\nwith others.\n\nThe OFL allows the licensed fonts to be used, studied, modified and\nredistributed freely as long as they are not sold by themselves. The\nfonts, including any derivative works, can be bundled, embedded, \nredistributed and/or sold with any software provided that any reserved\nnames are not used by derivative works. The fonts and derivatives,\nhowever, cannot be released under any other type of license. The\nrequirement for fonts to remain under this license does not apply\nto any document created using the fonts or their derivatives.\n\nDEFINITIONS\n\"Font Software\" refers to the set of files released by the Copyright\nHolder(s) under this license and clearly marked as such. This may\ninclude source files, build scripts and documentation.\n\n\"Reserved Font Name\" refers to any names specified as such after the\ncopyright statement(s).\n\n\"Original Version\" refers to the collection of Font Software components as\ndistributed by the Copyright Holder(s).\n\n\"Modified Version\" refers to any derivative made by adding to, deleting,\nor substituting -- in part or in whole -- any of the components of the\nOriginal Version, by changing formats or by porting the Font Software to a\nnew environment.\n\n\"Author\" refers to any designer, engineer, programmer, technical\nwriter or other person who contributed to the Font Software.\n\nPERMISSION & CONDITIONS\nPermission is hereby granted, free of charge, to any person obtaining\na copy of the Font Software, to use, study, copy, merge, embed, modify,\nredistribute, and sell modified and unmodified copies of the Font\nSoftware, subject to the following conditions:\n\n1) Neither the Font Software nor any of its individual components,\nin Original or Modified Versions, may be sold by itself.\n\n2) Original or Modified Versions of the Font Software may be bundled,\nredistributed and/or sold with any software, provided that each copy\ncontains the above copyright notice and this license. These can be\nincluded either as stand-alone text files, human-readable headers or\nin the appropriate machine-readable metadata fields within text or\nbinary files as long as those fields can be easily viewed by the user.\n\n3) No Modified Version of the Font Software may use the Reserved Font\nName(s) unless explicit written permission is granted by the corresponding\nCopyright Holder. This restriction only applies to the primary font name as\npresented to the users.\n\n4) The name(s) of the Copyright Holder(s) or the Author(s) of the Font\nSoftware shall not be used to promote, endorse or advertise any\nModified Version, except to acknowledge the contribution(s) of the\nCopyright Holder(s) and the Author(s) or with their explicit written\npermission.\n\n5) The Font Software, modified or unmodified, in part or in whole,\nmust be distributed entirely under this license, and must not be\ndistributed under any other license. The requirement for fonts to\nremain under this license does not apply to any document created\nusing the Font Software.\n\nTERMINATION\nThis license becomes null and void if any of the above conditions are\nnot met.\n\nDISCLAIMER\nTHE FONT SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND,\nEXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO ANY WARRANTIES OF\nMERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT\nOF COPYRIGHT, PATENT, TRADEMARK, OR OTHER RIGHT. IN NO EVENT SHALL THE\nCOPYRIGHT HOLDER BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,\nINCLUDING ANY GENERAL, SPECIAL, INDIRECT, INCIDENTAL, OR CONSEQUENTIAL\nDAMAGES, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\nFROM, OUT OF THE USE OR INABILITY TO USE THE FONT SOFTWARE OR FROM\nOTHER DEALINGS IN THE FONT SOFTWARE.\n"
  },
  {
    "path": "web2/cadabra2/source/static/fonts/Bright/README.txt",
    "content": "This package was compiled by Christian Perfect (http://checkmyworking.com) from the Computer Modern Unicode fonts created by Andrey V. Panov (http://cm-unicode.sourceforge.net/)\r\n\r\nThey're released under the SIL Open Font License. See OFL.txt and OFL-FAQ.txt for the terms.\r\n\r\nA demo page for these fonts was at http://www.checkmyworking.com/cm-web-fonts/ when I released them. I can only apologise, citizen of the future, if that address doesn't exist any more.\r\n"
  },
  {
    "path": "web2/cadabra2/source/static/fonts/Bright/cmun-bright.css",
    "content": "@font-face {\r\n\tfont-family: 'Computer Modern Bright';\r\n\tsrc: url('/static/fonts/Bright/cmunbmr.eot');\r\n\tsrc: url('/static/fonts/Bright/cmunbmr.eot?#iefix') format('embedded-opentype'),\r\n\t\t url('/static/fonts/Bright/cmunbmr.woff') format('woff'),\r\n\t\t url('/static/fonts/Bright/cmunbmr.ttf') format('truetype'),\r\n\t\t url('/static/fonts/Bright/cmunbmr.svg#cmunbmr') format('svg');\r\n\tfont-weight: normal;\r\n\tfont-style: normal;\r\n}\r\n\r\n@font-face {\r\n\tfont-family: 'Computer Modern Bright';\r\n\tsrc: url('/static/fonts/Bright/cmunbbx.eot');\r\n\tsrc: url('/static/fonts/Bright/cmunbbx.eot?#iefix') format('embedded-opentype'),\r\n\t\t url('/static/fonts/Bright/cmunbbx.woff') format('woff'),\r\n\t\t url('/static/fonts/Bright/cmunbbx.ttf') format('truetype'),\r\n\t\t url('/static/fonts/Bright/cmunbbx.svg#cmunbbx') format('svg');\r\n\tfont-weight: bold;\r\n\tfont-style: normal;\r\n}\r\n\r\n@font-face {\r\n\tfont-family: 'Computer Modern Bright';\r\n\tsrc: url('/static/fonts/Bright/cmunbmo.eot');\r\n\tsrc: url('/static/fonts/Bright/cmunbmo.eot?#iefix') format('embedded-opentype'),\r\n\t\t url('/static/fonts/Bright/cmunbmo.woff') format('woff'),\r\n\t\t url('/static/fonts/Bright/cmunbmo.ttf') format('truetype'),\r\n\t\t url('/static/fonts/Bright/cmunbmo.svg#cmunbmo') format('svg');\r\n\tfont-weight: normal;\r\n\tfont-style: italic;\r\n}\r\n\r\n@font-face {\r\n\tfont-family: 'Computer Modern Bright';\r\n\tsrc: url('/static/fonts/Bright/cmunbxo.eot');\r\n\tsrc: url('/static/fonts/Bright/cmunbxo.eot?#iefix') format('embedded-opentype'),\r\n\t\t url('/static/fonts/Bright/cmunbxo.woff') format('woff'),\r\n\t\t url('/static/fonts/Bright/cmunbxo.ttf') format('truetype'),\r\n\t\t url('/static/fonts/Bright/cmunbxo.svg#cmunbxo') format('svg');\r\n\tfont-weight: bold;\r\n\tfont-style: italic;\r\n}\r\n\r\n\r\n"
  },
  {
    "path": "web2/cadabra2/source/static/humans.txt",
    "content": ""
  },
  {
    "path": "web2/cadabra2/source/static/images/logo.tex",
    "content": "\\documentclass{article}\n\\begin{document}\n$$C_{\\delta\\beta}$$\n\\end{document}\n"
  },
  {
    "path": "web2/cadabra2/source/static/js/cadabra.js",
    "content": "var x = document.querySelectorAll(\".folding .package-name\");\nvar i;\nfor (i = 0; i < x.length; i++) {\n    console.log(x[i]);\n    x[i].onclick = function(el) {\n        if(el.currentTarget.parentElement.classList.contains('uncovered')) {\n\t    el.currentTarget.parentElement.classList.remove('uncovered');\n        } else {\n\t    el.currentTarget.parentElement.classList.add('uncovered');\n        }\n    }\n}\n\n\n"
  },
  {
    "path": "web2/cadabra2/source/static/robots.txt",
    "content": "#User-Agent: *\n#Disallow: /\n"
  },
  {
    "path": "web2/cadabra2/source/static/styles/cadabra-web.css",
    "content": "html {\n\t height: 100%;\n}\nbody {\n/* Lato is just a tad too thin to be nicely readable (at 300) or a bit too thick (at 400) */\n/* \t font-family: \"Lato\"; \n\t font-weight: 300; */\n/*\t font-family: \"Computer Modern Serif\"; */\n\t font-family: \"Computer Modern Bright\"; \n/*\t font-weight: 300; */\n\t font-size: 17px;\n\t height: 100%;\n\t line-height: 1.4;\n\t background: white;\n\t text-align: justify;\n         hyphens: auto;\n\t margin: 0px;\n}\na {\n  color: #209020;\n  background-color: transparent;\t\n  text-decoration: none;\n  }\n\na:hover {\n  color: #209020;\n  background-color: #e0e0e0;\n}\n#logobar a:hover {\n\t background-color: white !important;\n}\nhr {\n    border: 0;\n    height: 1px;\n    background: #ccc;\n\t margin-top: 20px;\n\t margin-bottom: 20px;\n}\nhr#below_logo {\n\t margin-left: 40px;\n\t margin-right: 40px;\n\t margin-top: 0px;\n\t margin-bottom: 0px;\n}\ndiv#logobar {\n\t margin-left: 40px;\n\t margin-right: 40px;\n\t padding-bottom: 20px;\n}\ndiv#logobar div#cadabra_logo {\n\t width: 42px;\n\t position: relative;\n\t top: 3px;\n\t margin-left: 0px;\n\t margin-right: 10px;\n\t vertical-align: middle;\n\t display: inline-block;\n}\ndiv#logobar div#cadabra_logo img {\n\t vertical-align: middle;\t \n\t width: 100%;\n}\ndiv#logobar #cadabra {\n\t vertical-align: middle;\t \n\t display: inline-block;\n\t color: green;\n\t font: 400 60px/1.3 \"Bree Serif\";\n\t font-size: 48px;\n}\ndiv#topflex {\n\t display: flex;\n\t justify-content: space-between;\n\t box-shadow: 0 2px 8px rgba(0,0,0,0.1);\n}\ndiv#topflex div#search {\n\t margin-top: 32px;\n\t width: 300px;\n\t margin-right: 30px;\n}\ndiv#logobar #subtext {\n\t font-family: \"Computer Modern Bright\";\n\t font-size: 14px;\n\t font-weight: 300;\n\t padding-left: 5px;\n}\ndiv#logobar #author {\n\t float: right;\n\t margin-top: 20px;\n\t font: 400 14px \"Bree Serif\";\n}\ndiv#menubar {\n\t display: inline-block;\n\t vertical-align: top;\n\t margin-left: 40px;\n\t margin-top: 30px;\n}\ndiv#menubar ul {\n\t list-style-type: none;\n}\ndiv#menubar ul li {\n\t cursor: pointer;\n\t margin-bottom: 5px;\n}\ndiv#menubar ul li:hover {\n\t background: yellow;\n}\ndiv.splash_image {\n\t width: 50%;\n\t float: right;\n\t margin-left: 50px;\n\t margin-bottom: 20px;\n}\ndiv.splash_image img {\n\t width: 100%;\n}\ndiv#main {\n\t display: inline-block;\n\t vertical-align: top;\n\t margin-top: 20px;\n\t margin-left: 40px;\n\t width: calc(100% - 280px);\n\t margin-bottom: 40px;\n}\ndiv#main > p {\n\t margin-bottom: 20px;\n\t margin-left: 40px;\n}\ndiv#main > dl {\n\t margin-bottom: 20px;\n\t margin-left: 40px;\n}\ndiv#main > dl dt {\n\t font-style: oblique;\n\t font-size: smaller;\n}\ndiv#main > dl dd {\n\t margin-bottom: 10px;\n}\n.quote {\n\t width: 80%;\n\t margin-left: auto !important;\n\t margin-right: auto !important;\n}\ndiv#main blockquote {\n\t margin-top: -5px;\n\t margin-left: 60px;\n}\ndiv#main ul {\n\t margin-top: 0px;\n\t margin-left: 40px;\n}\ndiv#main br {\n\t margin-bottom: 40px;\n}\ndiv#main h1 {\n\t text-align: left;\n\t overflow: hidden;\n\t margin-top: 4px;\n\t font: 400 60px/1.3 \"Bree Serif\";\n\t color: green;\n\t font-size: 24px;\n\t border-bottom: 1px solid #bbb;\n\t margin-bottom: 20px;\n}\ndiv.summary {\n\t font-style: italic;\n\t margin-bottom: 20px;\n\t margin-top: 0px;\n}\ndiv#main h2 {\n\t width: 100%;\n\t margin-top: 24px;\n\t font-family: \"Bree Serif\";\n\t font-weight: normal;\n\t color: green;\n\t font-size: 20px;\n\t border-bottom: 1px solid #bbb; \n}\ndiv#main h3 {\n\t margin-top: 24px;\n\t margin-left: 40px;\n\t font-family: \"Bree Serif\";\n\t font-weight: normal;\n\t color: green;\n\t font-size: 16px;\n}\ntable.package-toc-table {\n    border-spacing: 0px;\n}\n.package-toc-table .package-name {\n    height: 2em;\n    vertical-align: bottom;\n\t font-family: \"Bree Serif\";\n\t font-weight: normal;\n\t color: green;\n\t font-size: 16px;\n\t cursor: pointer;\n}\n.package-toc-table tr td:first-child {\n    min-width: 30px;\n}\n.package-toc-table .package-desc {\n    height: 2em;\n    vertical-align: top;\n}\n.package-toc-table td {\n    padding-top: 0;\n    padding-bottom: 0;\n}\n.package-toc-table tr:not(:nth-child(1)):not(:nth-child(2)) {\n    transform: scale(1, 0);\n    line-height: 0px;\n    transition: transform .5s, line-height .5s;\n    visibility: none;\n}\n.package-toc-table tr:not(:nth-child(1)):not(:nth-child(2)) {\n    padding: 0px;\n}\n.package-toc-table tbody.uncovered tr:not(:nth-child(1)):not(:nth-child(2)) {\n    transform: scale(1, 1);\n    line-height: 1.5em;\n}\n\n.latex_view h3 {\n\t margin-left: 0px !important;\n}\ndiv#main h1 span.date {\n\t margin-top: 10px;\n\t float: right;\n\t font-size: 10px;\n\t font-family: sans;\n\t font-weight: normal;\n}\n\n#cloud {\n    display: flex;\n    flex-direction: row;\n    align-items: center;\n}\n#cloud div {\n    margin-left: 20px;\n}\n.running_image {\n    margin-left: 40px;\n\t height: 40px;\n\t width: 40px;\n}\n\ndiv.icon_background {\n\t position: relative;\n\t width: 130px;\n\t height: 42px;\n/* \t background: #D56203;/* #36a750;  */\n \t background: green; \n\t cursor: pointer;\n\t margin-bottom: 10px;\n\t padding-left: 5px;\n\t padding-top: 5px;\n\t border-bottom: 4px solid green;\n\t transition: border-bottom 0.5s;\n/*\t border-radius: 4px; */\n}\ndiv.icon_background path {\n/* \t fill: #fa6; */\n\t fill: #cfc;\n\t transition-duration: 0.5s;  \n}\t \ndiv.icon_background img {\n\t transition-duration: 0.5s;  \n\t height: 70%;\n\t margin-left: 3px;\n\t margin-top: 3px;\n\t opacity: 0.6;\n\t outline: 1px solid transparent;\n}\ndiv.icon_background svg {\n\t transition-duration: 0.5s;  \n\t height: 80%;\n}\ndiv.icon_background div.icon_text {\n\t position: absolute;\n\t bottom: 5px;\n\t right: 10px;\n\t font-size: 14px;\n\t color: white;\n\t font-family: \"Bree Serif\";\n\t font-weight: 400;\n\t transition-duration: 0.5s;  \n}\ndiv.icon_background img.jupyter_icon {\n    margin-left: 5px;\n    opacity: 1.0;\n}\ndiv.firstline {\n\t position: relative;\n\t top: 6px;\n}\n/* div.icon_background:hover div.icon_text {\n\t font-size: 15px;\n\t transition-duration: 0.5s;  \n} */\ndiv.icon_background:hover {\n    border-bottom: 4px solid #ada;\n}\ndiv.icon_background:hover img {\n\t transition-duration: 0.5s;  \n\t opacity: 1.0;\n\t height: 85%;\n}\ndiv.icon_background:hover svg {\n\t transition-duration: 0.5s;  \n\t height: 100%;\n}\ndiv.icon_background:hover svg path {\n\t transition-duration: 0.5s;  \n\t fill: white;\n}\n\n/* Book */\n\ndiv.book_cover {\n    width: 33%;\n    border: 1px solid #777;\n}\n\n/* Notebooks */\n\ndiv.latex div.output { \n\t display: none; \n}\ndiv.image_png { \n\t width: 400px; \n}\ndiv.image_svg { \n\t width: 400px; \n}\ndiv.output { \n\t padding-left: 40px;\n\t font-family: monospace;\n    white-space: pre;\n\t color: black;\n}\ncode {\n\t font-size: 14px;\n}\ndiv.verbatim {\n\t padding-left: 40px;\n\t font-size: 14px;\n\t color: black;\n}\ndiv.latex { \n/* \t font-family: 'STIXGENERAL';  */\n\t padding-left: 10px; \n\t margin-bottom: 10px; \n}\ndiv.latex_view h1 { \n\t margin-left: -20px;\n}\ndiv.latex_view { \n\t color: black;\n\t font-size: 16px;\n\t padding-left: 20px; \n\t margin-bottom: 15px; \n}\ndiv.MathJax_Display {\n    text-align: left !important;\t \n\t margin-bottom: 5px !important;\n\t margin-top: 5px !important;\n\t margin-left: 30px;\n\t padding-bottom: 0px !important;\n}\n.mjx-chtml {\n\t text-align: left !important;\n}\n.MathJax_SVG_Display {\n\t text-align: left !important;\n\t font-size: 14px;\n}\ndiv.image_png img { \n\t width: 100%; \n}\ndiv.image_svg img { \n\t width: 100%; \n}\ndiv.python {\n\t margin-left: 40px;\n}\ndiv.python > div.source { \n\t font-family: \"Inconsolata\", monospace; \n\t font-size: 15.8px;\n\t padding-left: 10px; \n\t margin-bottom: 10px; \n\t padding-bottom: 0px;\n\t margin-top: 10px;\n\t white-space: pre-wrap; \n\t line-height: 20px;\n\t color: blue; \n\t margin-left: 0px;\n\t border-left: 1px solid blue;\n\t tab-size: 3;\n\t -moz-tab-size: 3;\t \n}\ndiv.input_form {\n\t display: none;\n}\n\ndiv.view_options {\n\t margin-left: 20px;\n\t margin-top: -10px;\n\t margin-bottom: 10px;\n}\ndiv.view_options span::before {\n    content: \"• \";\n}\ndiv.view_options span {\n\t display: inline-block;\n\t margin-left: 40px;\n\t font-style: italic;\n\t min-width: 300px;\n\t width: 300px;\n}\ndiv.download_options {\n\t margin-left: 50px;\n\t margin-bottom: 20px;\n}\ndiv.view_options a {\n\t margin-left: 20px;\n}\npre {\n\t margin-left: 30px;\n\t font-size: 14px;\n}\npre.output {\n\t margin-left: 0px;\n\t font-size: 14px;\n}\ndiv#main table {\n\t margin-left: 50px;\n}\n\n/* Tooltips */\n\n.tooltip {\n\t position: relative;\n}\n\n.tooltip:hover:after{\n    background: rgba(0,100,0,0.8);\n    border-radius: 5px;\n    bottom: 26px;\n    color: #fff;\n    content: attr(tiptext);\n    left: -120px;\n\t font-size: smaller;\n    padding: 5px 15px;\n    position: absolute;\n    z-index: 98;\n    width: 160px;\n}\n.tooltip:hover:before{\n    border: solid;\n    border-color: rgba(0,100,0,0.8) transparent;\n    border-width: 6px 6px 0 6px;\n    bottom: 20px;\n    content: \"\";\n    left: 14%;\n    position: absolute;\n    z-index: 99;\n}\n\ndiv#bottombar {\n\t clear: both;\n\t margin-top: 80px;\n\t padding-top: 5px;\n\t margin-left: 40px;\n\t margin-right: 40px;\n\t border-top: 1px solid #bbb;\n\t font-size: small;\n}\ndiv#bottomleft {\n\t float:left;\n\t padding-bottom: 10px;\n}\ndiv#bottomright {\n\t float:right;\n\t padding-bottom: 10px;\n}\n\ntt {\n\t font-family: \"Inconsolata\", monospace; \n\t font-size: 15.8px;\n}\n\t \ndiv.literal {\n\t font-family: \"Inconsolata\", monospace; \n\t font-size: 15.8px;\n\t color: blue; \n\t line-height: 20px;\n\t margin-left: 50px;\n}\n\ndiv.packages {\n\t margin-left: 50px;\n}\ndiv.distrotype {\n\t border-top: 1px solid #bbb;\n\t margin-top: 10px;\n\t padding-top: 15px;\n\t margin-bottom: 40px;\n}\ndiv.distrotype img {\n\t max-width: 200px;\n\t max-height: 80px;\n\t margin-bottom: 20px;\n}\ndiv.distrotxt {\n\t margin-top: 10px;\n\t margin-left: 30px;\n}\ndiv.distronum {\n\t margin-left: 20px;\n}\n\ntable.packages {\n\t border-collapse: separate;\n    border-spacing:  5px 10px;\n}\ntable.packages .system {\n\t white-space: nowrap;\n}\ntable.packages .date {\n\t white-space: nowrap;\n}\ntable.packages .instructions {\n\t font-size: smaller;\n\t padding-left: 20px;\n\t text-align: left;\n}\ntable.packages td {\n\t vertical-align: top;\n}\ntable.packages tr {\n}\ndiv.distrotxt code {\n\t display: block;\n\t font-size: 12px;\n\t margin-left: 10px;\n\t margin-top: 5px;\n\t margin-bottom:5px;\n}\ndiv#main > dl dt.author {\n    font-size: 17px;\n    font-style: oblique;\n}\nspan.author {\n    font-size: 17px;\n    font-style: oblique;\n}\n\n/* Young tableaux */\n\ndiv.young_box {\n\t display: inline-block;\n\t border: 1px solid black;\n\t width: 10px;\n\t min-width: 10px;\n\t height: 10px;\n\t min-height: 10px;\n\t margin: 0px;\n\t padding: 0px;\n}\ndiv.filled {\n\t background: red;\n}\ndiv.young_tableau {\n\t display: inline-block;\n}\ndiv.young_row {\n\t padding: 0px;\n\t margin: 0px;\n\t height: 10px;\n}\n\nol.table_of_contents {\n\t margin-left: 40px;\n}\n\n/* Blog */\n\nh2.blog {\n\t width: 60%;\n}\np.blog {\n\t width: 60%;\n}\n\n/* Search */\n\n#gsc-i-id1 {\n\t font-size: 14px;\n}\n#gs_tti50 {\n\t padding-top: 0px !important;\n}\n\n/* FAQ */\n\ndiv#main div.faq_item h3 {\n    font-style: normal;\n    color: #209020;\n    font-family: \"Computer Modern Bright\";\n    font-size: 17px;\n    text-align: left;\n    margin-top: 2px !important;\n    margin-bottom: 2px !important;    \n}\ndiv#main div.faq_item label:hover {\n    cursor: pointer;\n    background-color: #e0e0e0;\n}\ninput[name=\"collapse\"] {\n    display: none; \n}\ndiv#main div.faq_item .content {\n    margin-left: 60px;\n    margin-right: 60px;\n    max-height: 0px;\n    overflow-y: hidden;\n    transition: max-height 0.5s;\n}\ndiv#main div.faq_item input[name=\"collapse\"]:checked ~ .content {\n    max-height: 1000px;\n    transition: max-height 0.5s;\n    margin-bottom: 10px;\n}\ndiv#main div.faq_item input[name=\"collapse\"]:checked ~ h3 {\n    margin-bottom: 5px !important;\n    transition: max-height 0.5s;\n}\ndiv.github-link {\n\t width: 32px;\n\t height: 32px;\n\t margin-left: 10px;\n\t margin-top: 10px;\n}\ndiv.github-link a img {\n\t width: 100%;\n}\n\n/* Small screens */\n\n@media screen and (max-width: 800px) {\n    div#topflex {\n\tflex-direction: column;\n    }\n    div#topflex div#search {\n\tmargin-top: 0px;\n\tmargin-left: auto;\n\tmargin-right: 0px;\n    }\n    div#logobar {\n\tpadding-bottom: 0px;\n    }\n    ol.table_of_contents {\n\tmargin-left: 0px;\n\tpadding-left: 6%;\n    }\n    div.view_options span {\n\tmargin-left: 0px;\n\tdisplay: block;\n    }\n\t div#main {\n\t\t  position: relative;\n\t\t  margin-left: 2%;\n\t\t  margin-right: 2%;\n\t\t  width: 96%;\n\t }\n\t div#menubar {\n\t\t  margin-left: 2%;\n\t\t  margin-right: 2%;\n\t\t  width: auto;\n\t\t  text-align: left;\n\t }\n\t div#menubar .icon_background {\n\t\t  display: inline-block;\n\t\t  margin-bottom: 5px;\n\t\t  width: 30%;\n\t\t  height: 34px;\n\t }\n\t div#menubar hr {\n\t\t  display: none;\n\t\t  margin-top: 0px;\n\t\t  margin-bottom: 5px;\n\t }\n\t div#main > p {\n\t\t  margin-bottom: 20px;\n\t\t  margin-left: 0px;\n\t }\n\t div#main ul {\n\t\t  margin-left: 0px;\n\t }\n\t div.splash_image {\n\t\t  width: 100%;\n\t }\n\t div#logobar {\n\t\t  margin-left: 2%;\n\t\t  margin-right: 2%;\n\t }\n\t div#bottombar {\n\t\t  margin-left: 2%;\n\t\t  margin-right: 2%;\n\t }\n\t hr#below_logo {\n\t\t  margin-left: 2%;\n\t\t  margin-right: 2%;\n\t }\n\t div.latex_view h1 { \n\t\t  margin-left: 0px;\n\t }\n\t div.latex_view { \n\t\t  padding-left: 0px; \n\t }\n\t div.latex { \n\t\t  padding-left: 0px; \n\t\t  margin-bottom: 10px; \n\t }\n\t div.python { \n\t\t  margin-left: 1%;\n\t }\n\t div.python > div.source { \n\t\t  width: calc(100% - 20px);\n\t\t  overflow-x: scroll;\n\t }\n\t div#main blockquote {\n\t\t  margin-left: 15px;\n\t }\n\t div.literal {\n\t\t  white-space: nowrap;\n\t\t  overflow-x: scroll;\n\t\t  margin-left: 10px;\n\t }\n}\n"
  },
  {
    "path": "web2/cadabra2/source/static/styles/normalize.css",
    "content": "/*! normalize.css v3.0.1 | MIT License | git.io/normalize */\n\n/**\n * 1. Set default font family to sans-serif.\n * 2. Prevent iOS text size adjust after orientation change, without disabling\n *    user zoom.\n */\n\nhtml {\n  font-family: sans-serif; /* 1 */\n  -ms-text-size-adjust: 100%; /* 2 */\n  -webkit-text-size-adjust: 100%; /* 2 */\n}\n\n/**\n * Remove default margin.\n */\n\nbody {\n  margin: 0;\n}\n\n/* HTML5 display definitions\n   ========================================================================== */\n\n/**\n * Correct `block` display not defined for any HTML5 element in IE 8/9.\n * Correct `block` display not defined for `details` or `summary` in IE 10/11 and Firefox.\n * Correct `block` display not defined for `main` in IE 11.\n */\n\narticle,\naside,\ndetails,\nfigcaption,\nfigure,\nfooter,\nheader,\nhgroup,\nmain,\nnav,\nsection,\nsummary {\n  display: block;\n}\n\n/**\n * 1. Correct `inline-block` display not defined in IE 8/9.\n * 2. Normalize vertical alignment of `progress` in Chrome, Firefox, and Opera.\n */\n\naudio,\ncanvas,\nprogress,\nvideo {\n  display: inline-block; /* 1 */\n  vertical-align: baseline; /* 2 */\n}\n\n/**\n * Prevent modern browsers from displaying `audio` without controls.\n * Remove excess height in iOS 5 devices.\n */\n\naudio:not([controls]) {\n  display: none;\n  height: 0;\n}\n\n/**\n * Address `[hidden]` styling not present in IE 8/9/10.\n * Hide the `template` element in IE 8/9/11, Safari, and Firefox < 22.\n */\n\n[hidden],\ntemplate {\n  display: none;\n}\n\n/* Links\n   ========================================================================== */\n\n/**\n * Remove the gray background color from active links in IE 10.\n */\n\na {\n  background: transparent;\n}\n\n/**\n * Improve readability when focused and also mouse hovered in all browsers.\n */\n\na:active,\na:hover {\n  outline: 0;\n}\n\n/* Text-level semantics\n   ========================================================================== */\n\n/**\n * Address styling not present in IE 8/9/10/11, Safari, and Chrome.\n */\n\nabbr[title] {\n  border-bottom: 1px dotted;\n}\n\n/**\n * Address style set to `bolder` in Firefox 4+, Safari, and Chrome.\n */\n\nb,\nstrong {\n  font-weight: bold;\n}\n\n/**\n * Address styling not present in Safari and Chrome.\n */\n\ndfn {\n  font-style: italic;\n}\n\n/**\n * Address variable `h1` font-size and margin within `section` and `article`\n * contexts in Firefox 4+, Safari, and Chrome.\n */\n\nh1 {\n  font-size: 2em;\n  margin: 0.67em 0;\n}\n\n/**\n * Address styling not present in IE 8/9.\n */\n\nmark {\n  background: #ff0;\n  color: #000;\n}\n\n/**\n * Address inconsistent and variable font size in all browsers.\n */\n\nsmall {\n  font-size: 80%;\n}\n\n/**\n * Prevent `sub` and `sup` affecting `line-height` in all browsers.\n */\n\nsub,\nsup {\n  font-size: 75%;\n  line-height: 0;\n  position: relative;\n  vertical-align: baseline;\n}\n\nsup {\n  top: -0.5em;\n}\n\nsub {\n  bottom: -0.25em;\n}\n\n/* Embedded content\n   ========================================================================== */\n\n/**\n * Remove border when inside `a` element in IE 8/9/10.\n */\n\nimg {\n  border: 0;\n}\n\n/**\n * Correct overflow not hidden in IE 9/10/11.\n */\n\nsvg:not(:root) {\n  overflow: hidden;\n}\n\n/* Grouping content\n   ========================================================================== */\n\n/**\n * Address margin not present in IE 8/9 and Safari.\n */\n\nfigure {\n  margin: 1em 40px;\n}\n\n/**\n * Address differences between Firefox and other browsers.\n */\n\nhr {\n  -moz-box-sizing: content-box;\n  box-sizing: content-box;\n  height: 0;\n}\n\n/**\n * Contain overflow in all browsers.\n */\n\npre {\n  overflow: auto;\n}\n\n/**\n * Address odd `em`-unit font size rendering in all browsers.\n */\n\ncode,\nkbd,\npre,\nsamp {\n  font-family: monospace, monospace;\n  font-size: 1em;\n}\n\n/* Forms\n   ========================================================================== */\n\n/**\n * Known limitation: by default, Chrome and Safari on OS X allow very limited\n * styling of `select`, unless a `border` property is set.\n */\n\n/**\n * 1. Correct color not being inherited.\n *    Known issue: affects color of disabled elements.\n * 2. Correct font properties not being inherited.\n * 3. Address margins set differently in Firefox 4+, Safari, and Chrome.\n */\n\nbutton,\ninput,\noptgroup,\nselect,\ntextarea {\n  color: inherit; /* 1 */\n  font: inherit; /* 2 */\n  margin: 0; /* 3 */\n}\n\n/**\n * Address `overflow` set to `hidden` in IE 8/9/10/11.\n */\n\nbutton {\n  overflow: visible;\n}\n\n/**\n * Address inconsistent `text-transform` inheritance for `button` and `select`.\n * All other form control elements do not inherit `text-transform` values.\n * Correct `button` style inheritance in Firefox, IE 8/9/10/11, and Opera.\n * Correct `select` style inheritance in Firefox.\n */\n\nbutton,\nselect {\n  text-transform: none;\n}\n\n/**\n * 1. Avoid the WebKit bug in Android 4.0.* where (2) destroys native `audio`\n *    and `video` controls.\n * 2. Correct inability to style clickable `input` types in iOS.\n * 3. Improve usability and consistency of cursor style between image-type\n *    `input` and others.\n */\n\nbutton,\nhtml input[type=\"button\"], /* 1 */\ninput[type=\"reset\"],\ninput[type=\"submit\"] {\n  -webkit-appearance: button; /* 2 */\n  cursor: pointer; /* 3 */\n}\n\n/**\n * Re-set default cursor for disabled elements.\n */\n\nbutton[disabled],\nhtml input[disabled] {\n  cursor: default;\n}\n\n/**\n * Remove inner padding and border in Firefox 4+.\n */\n\nbutton::-moz-focus-inner,\ninput::-moz-focus-inner {\n  border: 0;\n  padding: 0;\n}\n\n/**\n * Address Firefox 4+ setting `line-height` on `input` using `!important` in\n * the UA stylesheet.\n */\n\ninput {\n  line-height: normal;\n}\n\n/**\n * It's recommended that you don't attempt to style these elements.\n * Firefox's implementation doesn't respect box-sizing, padding, or width.\n *\n * 1. Address box sizing set to `content-box` in IE 8/9/10.\n * 2. Remove excess padding in IE 8/9/10.\n */\n\ninput[type=\"checkbox\"],\ninput[type=\"radio\"] {\n  box-sizing: border-box; /* 1 */\n  padding: 0; /* 2 */\n}\n\n/**\n * Fix the cursor style for Chrome's increment/decrement buttons. For certain\n * `font-size` values of the `input`, it causes the cursor style of the\n * decrement button to change from `default` to `text`.\n */\n\ninput[type=\"number\"]::-webkit-inner-spin-button,\ninput[type=\"number\"]::-webkit-outer-spin-button {\n  height: auto;\n}\n\n/**\n * 1. Address `appearance` set to `searchfield` in Safari and Chrome.\n * 2. Address `box-sizing` set to `border-box` in Safari and Chrome\n *    (include `-moz` to future-proof).\n */\n\ninput[type=\"search\"] {\n  -webkit-appearance: textfield; /* 1 */\n  -moz-box-sizing: content-box;\n  -webkit-box-sizing: content-box; /* 2 */\n  box-sizing: content-box;\n}\n\n/**\n * Remove inner padding and search cancel button in Safari and Chrome on OS X.\n * Safari (but not Chrome) clips the cancel button when the search input has\n * padding (and `textfield` appearance).\n */\n\ninput[type=\"search\"]::-webkit-search-cancel-button,\ninput[type=\"search\"]::-webkit-search-decoration {\n  -webkit-appearance: none;\n}\n\n/**\n * Define consistent border, margin, and padding.\n */\n\nfieldset {\n  border: 1px solid #c0c0c0;\n  margin: 0 2px;\n  padding: 0.35em 0.625em 0.75em;\n}\n\n/**\n * 1. Correct `color` not being inherited in IE 8/9/10/11.\n * 2. Remove padding so people aren't caught out if they zero out fieldsets.\n */\n\nlegend {\n  border: 0; /* 1 */\n  padding: 0; /* 2 */\n}\n\n/**\n * Remove default vertical scrollbar in IE 8/9/10/11.\n */\n\ntextarea {\n  overflow: auto;\n}\n\n/**\n * Don't inherit the `font-weight` (applied by a rule above).\n * NOTE: the default cannot safely be changed in Chrome and Safari on OS X.\n */\n\noptgroup {\n  font-weight: bold;\n}\n\n/* Tables\n   ========================================================================== */\n\n/**\n * Remove most spacing between table cells.\n */\n\ntable {\n  border-collapse: collapse;\n  border-spacing: 0;\n}\n\ntd,\nth {\n  padding: 0;\n}"
  },
  {
    "path": "web2/cadabra2/source/tutorials.html",
    "content": "{% extends \"layout.html\" %}\n\n{% block title %}Cadabra: Tutorials{% endblock %}\n\n{% block head %}{%- endblock %}\n\n{% block main %}\n<h1>Cadabra tutorials</h1>\n<p>\n  The tutorials listed below are meant to illustrate Cadabra concepts\n  at the level of simple examples; for research-level applications of\n  Cadabra please see the <a href=\"/papers.html\">papers</a> section.\n</p>\n<p>\n  The pages linked below are produced from actual Cadabra\n  notebooks. Instead of reading them on-line, you can also download\n  the notebooks and play with them inside Cadabra. These notebooks all\n  require the new 2.x version of the software and will not work with\n  the old version 1.x. If you have a nice notebook that you think\n  would help others to learn Cadabra,\n  please <a href=\"mailto:info@cadabra.science\">get in touch</a>.\n</p>\n\n<h2>Absolute beginners</h2>\n\n<p>\n  This notebook explains how to enter expressions, how to do simple\n  substitutions on them, how to use wildcards. It also explains how the\n  new Python functionality works. If you have never used Cadabra\n  before, start here. \n</p>\n<div class=\"view_options\">\n  <span>Beginners tutorial:</span>\n  <a href=\"notebooks/beginners.html\">read online</a>\n  <a href=\"notebooks/beginners.cnb\">download notebook</a>\n</div>\n<p>\n  For a bit more advanced material, try one of the following tutorials.\n</p>\n<div class=\"view_options\">\n  <span>Tensor monomials:</span>\n  <a href=\"notebooks/tensor_monomials.html\">read online</a>\n  <a href=\"notebooks/tensor_monomials.cnb\">download notebook</a>\n</div>\n<p>\n  If you have used old versions of Cadabra but are new to series 2.x,\n  give the following notebook a shot.\n</p>\n<div class=\"view_options\">\n  <span>Tutorial for 1.x users:</span>\n  <a href=\"notebooks/for_previous_users.html\">read online</a>\n  <a href=\"notebooks/for_previous_users.cnb\">download notebook</a>\n</div>\n\n<h2>Writing packages for Cadabra</h2>\n<p>\n  One of the key reasons for the rewrite of Cadabra was to make it\n  much easier for users to contribute small bits of functionality. As\n  all of its internals are available via Python, it becomes much\n  easier to write small add-on packages, just like you can for other\n  computer algebra systems. \n</p>\n<p>\n  A more step-by-step tutorial for writing packages will follow; for\n  the time being here are some smaller tutorials describing a number of\n  Cadabra programming concepts.\n</p>\n<div class=\"view_options\">\n  <span>Convergence of operations:</span>\n  <a href=\"notebooks/converge.html\">read online</a>\n  <a href=\"notebooks/converge.cnb\">download notebook</a>\n</div>\n\n\n\n\n<h2>Actions, equations of motion, variational derivatives</h2>\n<p>\n  \n</p>\n<div class=\"view_options\">\n  <span>Fierz transformations:</span>\n  <a href=\"notebooks/fierz.html\">read online</a>\n  <a href=\"notebooks/fierz.cnb\">download notebook</a>\n</div>\n\n\n<h2>Quantum mechanics, groups and algebras</h2>\n<p>\n  Dirac gamma matrix algebra is very simple with Cadabra, and it can\n  handle them in arbitrary dimensions.\n</p>\n<div class=\"view_options\">\n  <span>Gamma matrix algebra:</span>\n  <a href=\"notebooks/gamma_matrix_algebra.html\">read online</a>\n  <a href=\"notebooks/gamma_matrix_algebra.cnb\">download notebook</a>\n</div>\n<p>\n  An frequently asked question is how to do commutator algebra with\n  Cadabra. The following notebook shows how this works by verifying\n  the invariance of the two quadratic Casimirs of the Poincaré\n  algebra. It shows how to make good use of <code>post_process</code> to\n  simplify expressions automatically.\n</p>\n<div class=\"view_options\">\n  <span>Poincaré algebra Casimirs:</span>\n  <a href=\"notebooks/poincare_algebra.html\">read online</a>\n  <a href=\"notebooks/poincare_algebra.cnb\">download notebook</a>\n</div>\n<p>\n  Because of fact that you can use natural LaTeX notation and because\n  Cadabra understand non-commuting objects, many tedious operator\n  algebra computations in quantum mechanics become relatively\n  simple. Here is an example from string theory, in which we verify\n  that certain states satisfy the quantum string constraints.\n</p>\n<div class=\"view_options\">\n  <span>String states:</span>\n  <a href=\"notebooks/string_states.html\">read online</a>\n  <a href=\"notebooks/string_states.cnb\">download notebook</a>\n</div>\n\n<h2>Abstract general relativity and differential geometry</h2>\n<p>\n  Cadabra was originally written in order to facilitate computations\n  in extensions of general relativity. The following example shows how\n  to prove a particular polynomial identity cubic in the Weyl tensor,\n  by virtue of its multi-term symmetries.\n</p>\n<div class=\"view_options\">\n  <span>Bianchi identities:</span>\n  <a href=\"notebooks/bianchi_identities.html\">read online</a>\n  <a href=\"notebooks/bianchi_identities.cnb\">download notebook</a>\n</div>\n<p>\n  You can also do computations with abstract differential forms and\n  the exterior derivative, as in the example below.\n<div class=\"view_options\">\n  <span>Differential forms:</span>\n  <a href=\"notebooks/exterior.html\">read online</a>\n  <a href=\"notebooks/exterior.cnb\">download notebook</a>\n</div>\n</p>\n\n<h2>Component computations</h2>\n<p>\n  From version 2.x you can do abstract as well as component\n  computations with Cadabra. The logic is very simple and based on a\n  few key ideas rooted in Cadabra's substitution engine. Examples of\n  varying difficulty are available below.\n</p>\n<p>\n  The first one is a trivial example of computing the curvature tensor\n  and scalar for a 2-sphere. Easy to do by hand, too, of course.\n</p>\n<div class=\"view_options\">\n  <span>Sphere curvature:</span>\n  <a href=\"notebooks/sphere.html\">read online</a>\n  <a href=\"notebooks/sphere.cnb\">download notebook</a>\n</div>\n<p>\n  The next one computes\n  Christoffel symbols and related for the Schwarzschild metric;\n  definitely a frequently requested feature...\n</p>\n<div class=\"view_options\">\n  <span>Schwarzschild spacetime:</span>\n  <a href=\"notebooks/schwarzschild.html\">read online</a>\n  <a href=\"notebooks/schwarzschild.cnb\">download notebook</a>\n</div>\n<p>\n  Somewhat related to component computations is the concept of \n  splitting a vector bundle into two parts, like you do in\n  Kaluza-Klein models. The following notebook is also discussed in the\n  original Cadabra\n  paper <a href=\"http://arxiv.org/abs/hep-th/0701238\">hep-th/0701238</a>.\n</p>\n<div class=\"view_options\">\n  <span>Kaluza-Klein:</span>\n  <a href=\"notebooks/kaluza_klein.html\">read online</a>\n  <a href=\"notebooks/kaluza_klein.cnb\">download notebook</a>\n</div>\n\n<h2>Numerics and plotting</h2>\n\n<p>\n  Cadabra's notebook now displays graphics from a variety of Python\n  sources; see the notebook below for some basic examples.\n</p>\n<div class=\"view_options\">\n  <span>Plotting tutorial:</span>\n  <a href=\"notebooks/plotting.html\">read online</a>\n  <a href=\"notebooks/plotting.cnb\">download notebook</a>\n</div>\n<p>\n  The <tt>ndsolve</tt> algorithm can be used to solve differential\n  equations numerically. You feed it (a system of) differential\n  equations and initial conditions, and get back one or more\n  anonymous (interpolating) functions.\n</p>\n<div class=\"view_options\">\n  <span>Solving differential equations numerically:</span>\n  <a href=\"notebooks/ndsolve.html\">read online</a>\n  <a href=\"notebooks/ndsolve.cnb\">download notebook</a>\n</div>\n\n\n<h2>SymPy users</h2>\n<p>\n  Cadabra relies on <a href=\"http://www.sympy.org\">SymPy</a> for a lot\n  of scalar computer algebra, that is, for algebra on expressions\n  which do not involve indices. Here is a simple notebook to\n  illustrate the basic concepts. This may also be a useful read if you\n  want to use the Cadabra notebook interface just to work with SymPy.\n</p>\n<div class=\"view_options\">\n  <span>SymPy inside Cadabra:</span>\n  <a href=\"notebooks/scalar_manipulations.html\">read online</a>\n  <a href=\"notebooks/scalar_manipulations.cnb\">download notebook</a>\n</div>\n\n\n<h2>Using Cadabra from IPython/Jupyter</h2>\n\n<p>\n  Cadabra now ships with a Jupyter kernel which is installed by\n  default; see <a href=\"jupyter.html\">Cadabra Jupyter kernel</a> for\n  more details. This is the easiest way to use Cadabra in Jupyter as\n  it allows you to use standard Cadabra notation, just like in\n  Cadabra's own notebook interface.\n</p>\n<p>\n  If you do not want to rely on the Cadabra kernel but would like to\n  use the <tt>cadabra2</tt> Python module directly in your Python\n  code, consult the following notebook for some of the absolute\n  basics. \n</p>\n<div class=\"view_options\">\n  <span>Cadabra inside Jupyter:</span>\n  <a href=\"static/cadabra_in_ipython.nb.html\">read online</a>\n  <a href=\"static/cadabra_in_ipython.nb\">download notebook</a>\n</div>\n\n{%- endblock %}\n\n"
  },
  {
    "path": "web2/cadabra2/source/user_notebooks.html",
    "content": "{% extends \"layout.html\" %}\n\n{% block title %}Cadabra: User contributed notebooks{% endblock %}\n\n{% block head %}{%- endblock %}\n\n{% block main %}\n\n<h1>User contributed notebooks</h1>\n<p>\n  This page contains a number of user-contributed notebooks. Do you\n  have a computation done with Cadabra that you think other people\n  could benefit from? Please get in touch directly via email\n  at <a href=\"mailto:info@cadabra.science\">info@cadabra.science</a>.\n</p>\n<h2>Notebooks</h2>\n<p>\n</p>\n<div class=\"view_options\">\n  <span>Einstein equations:</span>\n  <a href=\"notebooks/einstein_equations.html\">read online</a>\n  <a href=\"notebooks/einstein_equations.cnb\">download notebook</a>\n</div>\n<div class=\"view_options\">\n  <span>Structure equations and Bianchi ids:</span>\n  <a href=\"notebooks/structure_equations_and_bianchi.html\">read online</a>\n  <a href=\"notebooks/structure_equations_and_bianchi.cnb\">download notebook</a>\n</div>\n\n{%- endblock %}\n"
  },
  {
    "path": "web2/cadabra2/source/v1x.html",
    "content": "{% extends \"layout.html\" %}\n\n{% block title %}Cadabra: Version 1.x{% endblock %}\n\n{% block head %}{%- endblock %}\n\n{% block main %}\n\n<h1>The new Cadabra is here</h1>\n\n<p>\n  The old Cadabra site at <tt>cadabra.phi-sci.com</tt> has been\n  disabled, and all information about Cadabra, in particular the new 2.x\n  series, can be found here. This page lists some things about the 1.x\n  release which may still be relevant for its current users.\n</p>\n\n<p>\n  The new Cadabra 2.x series is a rewrite and extension of the old 1.x\n  series, which first saw the light in 2007. Many things have changed\n  and improved. This page tells you what you need to know about the\n  differences. Unless you have old 1.x notebooks which you need to run,\n  you are strongly encouraged to try installing 2.x. Support for 1.x\n  will not go away, but there will be no more improvements, only bug\n  fixes.\n</p>\n\n<h2>Getting the software</h2>\n\n<p>\n  Version 1.x is available in many Linux distributions and on\n  MacPorts, and has just been accepted for the new Debian release, so\n  it will continue to be available for some time to come.  Version 2.x\n  is still undergoing many rapid changes, so it is at the moment not\n  yet available in any distributions. Instead, you can get it directly\n  from this web site's <a href=\"/download.html\">download page</a>, in\n  the form of various packages for Linux distributions, a Homebrew\n  port for macOS, and a Windows installer.\n</p>\n\n<p>\n  You can install 1.x and 2.x on the same system without any clashes,\n  so you can continue to work with 1.x and at the same time get used\n  to 2.x.\n</p>\n\n<p>\n  I will no longer provide source tarballs for 1.x, but you can easily\n  get the source from\n  the <a href=\"http://github.com/kpeeters/cadabra\">Cadabra 1.x github\n  repository</a>.\n</p>\n\n<h2>Notebook (in)compatibility</h2>\n\n<p>\n  The new 2.x notebooks are not compatible with the old 1.x notebooks,\n  and you can not (yet?) read old notebooks into the new version. The\n  main reason for not providing backward compatibility is that there\n  have been many changes in the input format, and writing a converter\n  takes time. However, if you have large 1.x notebooks that you would\n  really like to auto-convert, get in touch and we'll see what we can\n  do.\n</p>\n\n\n{%- endblock %}\n"
  },
  {
    "path": "web2/scan.py",
    "content": "#!/usr/bin/env python\n\nimport json\nimport os\nimport re\nimport sys\n\n# Scan one Cadabra notebook file for an \\algorithm{...}{...}\n# or \\property{...}{...} command and use this to output HTML\n# code to produce a table-of-contents of all manual pages.\n\n# FIXME: the regex expressions below should be exchanged for\n# something that parses latex properly, in order to deal with\n# nested curly bracket situations. At the moment this will fail\n# to correctly detect things like \\algorithm{foobar}{Something {in} brackets}.\n\ndef scan_file(prevcat, dir, filename, ext):\n    with open(dir+filename+ext) as jsonfile:\n        data = json.load(jsonfile)\n        jsonfile.close()\n\n        # is this a multi-algorithm file?\n        count=0\n        package_name=\"\"\n        for cell in data[\"cells\"]:\n            if not \"cells\" in cell:\n                continue\n            src = cell[\"cells\"][0][\"source\"]\n            src = src.replace('\\n',' ')\n            m = re.search('\\\\\\\\algorithm{(.*)}.*', src)\n            if m:\n                count+=1\n            m = re.search('\\\\\\\\property{(.*)}.*', src)\n            if m:\n                count+=1\n            m = re.search('\\\\\\\\package{([^}]*)}{([^}]*)}.*', src)\n            if m:\n                package_name=m.group(1)\n                package_desc=m.group(2)\n        is_multi = (package_name!=\"\")\n\n        if is_multi:\n            print('<tbody class=\"folding\">')\n            print('<tr class=\"package-name\"><td colspan=4>'+package_name+'</td></tr>')\n            print('<tr class=\"package-desc\"><td colspan=4>'+package_desc+'</td></tr>')\n        \n        for cell in data[\"cells\"]:\n            if not \"cells\" in cell:\n                continue\n            src = cell[\"cells\"][0][\"source\"]\n            src = src.replace('\\n',' ')\n            m = re.search('\\\\\\\\algorithm{([^}]*)}{([^}]*)}.*', src)\n            if m:\n                algo=m.group(1)\n                desc=m.group(2)\n                cat=algo[0].upper()\n                if cat==prevcat:\n                    cat=''\n                else:\n                    prevcat=cat\n                if is_multi:\n                    cat=''\n                m2 = re.search('([^\\(]*)\\(.*', algo)\n                if m2:\n                    algo = m2.group(1)\n                print('<tr><td>'+cat+'<td></td><td><a href=\"manual/'+filename+'.html\">'+algo+'</a></td>')\n                print('<td>'+desc+'</td></tr>')\n            m = re.search('\\\\\\\\property{([^}]*)}{([^}]*)}', src)\n            if m:\n                algo=m.group(1)\n                desc=m.group(2)\n                cat=algo[0].upper()\n                if cat==prevcat:\n                    cat=''\n                else:\n                    prevcat=cat\n                if is_multi:\n                    cat=''\n                print('<tr><td>'+cat+'<td></td><td><a href=\"manual/'+filename+'.html\">'+algo+'</a></td>')\n                print('<td>'+desc+'</td></tr>')\n\n        if is_multi:\n            print('<tr><td colspan=4>&nbsp;</td></tr></tbody>')\n\n    return prevcat\n\n\n# Scan all manual pages for algorithms.\n\n#lst=set()\n#for file in os.listdir(dir):\n#    filename, ext = os.path.splitext(file)\n#    if ext=='.cnb':\n#        lst.add( filename )\n\nalgodir=sys.argv[1]+\"/\"\ncat=''\nfor nb in sorted(sys.argv[2:]):\n    cat=scan_file(cat, algodir, nb, '.cnb')\n\n\n"
  }
]